LMFDB - Embedded newform 640.2.j.c.543.1

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			543.1
Root			$0.235136 - 1.39453i$ of defining polynomial
Character	$\chi$	$=$	640.543
Dual form			640.2.j.c.607.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.96561i q^{3} +(2.22902 + 0.177336i) q^{5} +(0.115101 - 0.115101i) q^{7} -5.79486 q^{9} +O(q^{10})$	\(q-2.96561i q^{3} +(2.22902 + 0.177336i) q^{5} +(0.115101 - 0.115101i) q^{7} -5.79486 q^{9} +(2.95966 - 2.95966i) q^{11} -1.55822 q^{13} +(0.525911 - 6.61042i) q^{15} +(0.299668 - 0.299668i) q^{17} +(2.26261 - 2.26261i) q^{19} +(-0.341344 - 0.341344i) q^{21} +(-4.14573 - 4.14573i) q^{23} +(4.93710 + 0.790575i) q^{25} +8.28846i q^{27} +(0.289656 + 0.289656i) q^{29} +4.18508i q^{31} +(-8.77721 - 8.77721i) q^{33} +(0.276974 - 0.236151i) q^{35} -1.63643 q^{37} +4.62107i q^{39} +7.61648i q^{41} -6.72651 q^{43} +(-12.9169 - 1.02764i) q^{45} +(4.38366 + 4.38366i) q^{47} +6.97350i q^{49} +(-0.888698 - 0.888698i) q^{51} -11.4324i q^{53} +(7.12202 - 6.07231i) q^{55} +(-6.71003 - 6.71003i) q^{57} +(-1.63497 - 1.63497i) q^{59} +(1.23034 - 1.23034i) q^{61} +(-0.666993 + 0.666993i) q^{63} +(-3.47331 - 0.276329i) q^{65} +2.49337 q^{67} +(-12.2946 + 12.2946i) q^{69} -8.00096 q^{71} +(1.12102 - 1.12102i) q^{73} +(2.34454 - 14.6415i) q^{75} -0.681319i q^{77} +3.62218 q^{79} +7.19579 q^{81} +1.62629i q^{83} +(0.721109 - 0.614825i) q^{85} +(0.859007 - 0.859007i) q^{87} +15.7149 q^{89} +(-0.179352 + 0.179352i) q^{91} +12.4113 q^{93} +(5.44467 - 4.64218i) q^{95} +(9.69217 - 9.69217i) q^{97} +(-17.1508 + 17.1508i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

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

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
$3$		−	2.96561i		−	1.71220i	−0.516813	−	0.856099i	$-0.672882\pi$
$3$		−	2.96561i		−	1.71220i	0.516813	−	0.856099i	$-0.327118\pi$
$4$		0			0
$5$	2.22902	+	0.177336i	0.996850	+	0.0793073i
$5$	2.22902	+	0.177336i	0.996850	+	0.0793073i
$6$		0			0
$7$	0.115101	−	0.115101i	0.0435040	−	0.0435040i	−0.685020	−	0.728524i	$-0.740207\pi$
$7$	0.115101	−	0.115101i	0.0435040	−	0.0435040i	0.728524	+	0.685020i	$0.240207\pi$
$8$		0			0
$9$	−5.79486			−1.93162
$10$		0			0
$11$	2.95966	−	2.95966i	0.892372	−	0.892372i	−0.102374	−	0.994746i	$-0.532644\pi$
$11$	2.95966	−	2.95966i	0.892372	−	0.892372i	0.994746	+	0.102374i	$0.0326439\pi$
$12$		0			0
$13$	−1.55822			−0.432172			−0.216086	−	0.976374i	$-0.569329\pi$
$13$	−1.55822			−0.432172			−0.216086	+	0.976374i	$0.569329\pi$
$14$		0			0
$15$	0.525911	−	6.61042i	0.135790	−	1.70680i
$16$		0			0
$17$	0.299668	−	0.299668i	0.0726801	−	0.0726801i	−0.669832	−	0.742512i	$-0.733634\pi$
$17$	0.299668	−	0.299668i	0.0726801	−	0.0726801i	0.742512	+	0.669832i	$0.233634\pi$
$18$		0			0
$19$	2.26261	−	2.26261i	0.519079	−	0.519079i	−0.398214	−	0.917293i	$-0.630370\pi$
$19$	2.26261	−	2.26261i	0.519079	−	0.519079i	0.917293	+	0.398214i	$0.130370\pi$
$20$		0			0
$21$	−0.341344	−	0.341344i	−0.0744874	−	0.0744874i
$22$		0			0
$23$	−4.14573	−	4.14573i	−0.864444	−	0.864444i	0.127406	−	0.991851i	$-0.459335\pi$
$23$	−4.14573	−	4.14573i	−0.864444	−	0.864444i	−0.991851	+	0.127406i	$0.959335\pi$
$24$		0			0
$25$	4.93710	+	0.790575i	0.987421	+	0.158115i
$26$		0			0
$27$			8.28846i			1.59511i
$28$		0			0
$29$	0.289656	+	0.289656i	0.0537878	+	0.0537878i	0.733489	−	0.679701i	$-0.237891\pi$
$29$	0.289656	+	0.289656i	0.0537878	+	0.0537878i	−0.679701	+	0.733489i	$0.737891\pi$
$30$		0			0
$31$			4.18508i			0.751663i	0.926688	+	0.375832i	$0.122643\pi$
$31$			4.18508i			0.751663i	−0.926688	+	0.375832i	$0.877357\pi$
$32$		0			0
$33$	−8.77721	−	8.77721i	−1.52792	−	1.52792i
$34$		0			0
$35$	0.276974	−	0.236151i	0.0468172	−	0.0399168i
$36$		0			0
$37$	−1.63643			−0.269027			−0.134514	−	0.990912i	$-0.542947\pi$
$37$	−1.63643			−0.269027			−0.134514	+	0.990912i	$0.542947\pi$
$38$		0			0
$39$			4.62107i			0.739964i
$40$		0			0
$41$			7.61648i			1.18949i	0.803913	+	0.594747i	$0.202748\pi$
$41$			7.61648i			1.18949i	−0.803913	+	0.594747i	$0.797252\pi$
$42$		0			0
$43$	−6.72651			−1.02578			−0.512892	−	0.858453i	$-0.671426\pi$
$43$	−6.72651			−1.02578			−0.512892	+	0.858453i	$0.671426\pi$
$44$		0			0
$45$	−12.9169	−	1.02764i	−1.92553	−	0.153191i
$46$		0			0
$47$	4.38366	+	4.38366i	0.639423	+	0.639423i	0.950413	−	0.310990i	$-0.100661\pi$
$47$	4.38366	+	4.38366i	0.639423	+	0.639423i	−0.310990	+	0.950413i	$0.600661\pi$
$48$		0			0
$49$			6.97350i			0.996215i
$50$		0			0
$51$	−0.888698	−	0.888698i	−0.124443	−	0.124443i
$52$		0			0
$53$		−	11.4324i		−	1.57036i	−0.619265	−	0.785182i	$-0.712569\pi$
$53$		−	11.4324i		−	1.57036i	0.619265	−	0.785182i	$-0.287431\pi$
$54$		0			0
$55$	7.12202	−	6.07231i	0.960333	−	0.818790i
$56$		0			0
$57$	−6.71003	−	6.71003i	−0.888766	−	0.888766i
$58$		0			0
$59$	−1.63497	−	1.63497i	−0.212855	−	0.212855i	0.592624	−	0.805479i	$-0.298092\pi$
$59$	−1.63497	−	1.63497i	−0.212855	−	0.212855i	−0.805479	+	0.592624i	$0.798092\pi$
$60$		0			0
$61$	1.23034	−	1.23034i	0.157528	−	0.157528i	−0.623942	−	0.781471i	$-0.714470\pi$
$61$	1.23034	−	1.23034i	0.157528	−	0.157528i	0.781471	+	0.623942i	$0.214470\pi$
$62$		0			0
$63$	−0.666993	+	0.666993i	−0.0840332	+	0.0840332i
$64$		0			0
$65$	−3.47331	−	0.276329i	−0.430811	−	0.0342744i
$66$		0			0
$67$	2.49337			0.304614			0.152307	−	0.988333i	$-0.451330\pi$
$67$	2.49337			0.304614			0.152307	+	0.988333i	$0.451330\pi$
$68$		0			0
$69$	−12.2946	+	12.2946i	−1.48010	+	1.48010i
$70$		0			0
$71$	−8.00096			−0.949540			−0.474770	−	0.880110i	$-0.657469\pi$
$71$	−8.00096			−0.949540			−0.474770	+	0.880110i	$0.657469\pi$
$72$		0			0
$73$	1.12102	−	1.12102i	0.131205	−	0.131205i	−0.638454	−	0.769660i	$-0.720426\pi$
$73$	1.12102	−	1.12102i	0.131205	−	0.131205i	0.769660	+	0.638454i	$0.220426\pi$
$74$		0			0
$75$	2.34454	−	14.6415i	0.270724	−	1.69066i
$76$		0			0
$77$		−	0.681319i		−	0.0776435i
$78$		0			0
$79$	3.62218			0.407527			0.203763	−	0.979020i	$-0.434683\pi$
$79$	3.62218			0.407527			0.203763	+	0.979020i	$0.434683\pi$
$80$		0			0
$81$	7.19579			0.799532
$82$		0			0
$83$			1.62629i			0.178509i	0.996009	+	0.0892545i	$0.0284484\pi$
$83$			1.62629i			0.178509i	−0.996009	+	0.0892545i	$0.971552\pi$
$84$		0			0
$85$	0.721109	−	0.614825i	0.0782152	−	0.0666871i
$86$		0			0
$87$	0.859007	−	0.859007i	0.0920953	−	0.0920953i
$88$		0			0
$89$	15.7149			1.66577			0.832887	−	0.553443i	$-0.186686\pi$
$89$	15.7149			1.66577			0.832887	+	0.553443i	$0.186686\pi$
$90$		0			0
$91$	−0.179352	+	0.179352i	−0.0188012	+	0.0188012i
$92$		0			0
$93$	12.4113			1.28700
$94$		0			0
$95$	5.44467	−	4.64218i	0.558611	−	0.476277i
$96$		0			0
$97$	9.69217	−	9.69217i	0.984091	−	0.984091i	−0.0157848	−	0.999875i	$-0.505025\pi$
$97$	9.69217	−	9.69217i	0.984091	−	0.984091i	0.999875	+	0.0157848i	$0.00502467\pi$
$98$		0			0
$99$	−17.1508	+	17.1508i	−1.72372	+	1.72372i
$100$		0			0
$101$	12.8067	+	12.8067i	1.27432	+	1.27432i	0.943800	+	0.330516i	$0.107223\pi$
$101$	12.8067	+	12.8067i	1.27432	+	1.27432i	0.330516	+	0.943800i	$0.392777\pi$
$102$		0			0
$103$	4.33738	+	4.33738i	0.427375	+	0.427375i	0.887733	−	0.460358i	$-0.152279\pi$
$103$	4.33738	+	4.33738i	0.427375	+	0.427375i	−0.460358	+	0.887733i	$0.652279\pi$
$104$		0			0
$105$	−0.700332	−	0.821398i	−0.0683454	−	0.0801602i
$106$		0			0
$107$			11.9807i			1.15822i	0.815251	+	0.579108i	$0.196599\pi$
$107$			11.9807i			1.15822i	−0.815251	+	0.579108i	$0.803401\pi$
$108$		0			0
$109$	4.01503	+	4.01503i	0.384570	+	0.384570i	0.872746	−	0.488175i	$-0.162337\pi$
$109$	4.01503	+	4.01503i	0.384570	+	0.384570i	−0.488175	+	0.872746i	$0.662337\pi$
$110$		0			0
$111$			4.85301i			0.460628i
$112$		0			0
$113$	6.47754	+	6.47754i	0.609356	+	0.609356i	0.942778	−	0.333422i	$-0.108203\pi$
$113$	6.47754	+	6.47754i	0.609356	+	0.609356i	−0.333422	+	0.942778i	$0.608203\pi$
$114$		0			0
$115$	−8.50575	−	9.97612i	−0.793165	−	0.930278i
$116$		0			0
$117$	9.02966			0.834792
$118$		0			0
$119$		−	0.0689840i		−	0.00632375i
$120$		0			0
$121$		−	6.51921i		−	0.592655i
$122$		0			0
$123$	22.5875			2.03665
$124$		0			0
$125$	10.8647	+	2.63774i	0.971771	+	0.235927i
$126$		0			0
$127$	−12.2756	−	12.2756i	−1.08928	−	1.08928i	−0.995603	−	0.0936781i	$-0.970138\pi$
$127$	−12.2756	−	12.2756i	−1.08928	−	1.08928i	−0.0936781	−	0.995603i	$-0.529862\pi$
$128$		0			0
$129$			19.9482i			1.75634i
$130$		0			0
$131$	7.99562	+	7.99562i	0.698581	+	0.698581i	0.964104	−	0.265524i	$-0.0855448\pi$
$131$	7.99562	+	7.99562i	0.698581	+	0.698581i	−0.265524	+	0.964104i	$0.585545\pi$
$132$		0			0
$133$		−	0.520857i		−	0.0451641i
$134$		0			0
$135$	−1.46985	+	18.4752i	−0.126504	+	1.59009i
$136$		0			0
$137$	3.08551	+	3.08551i	0.263613	+	0.263613i	0.826520	−	0.562907i	$-0.190317\pi$
$137$	3.08551	+	3.08551i	0.263613	+	0.263613i	−0.562907	+	0.826520i	$0.690317\pi$
$138$		0			0
$139$	−12.2206	−	12.2206i	−1.03654	−	1.03654i	−0.999307	−	0.0372284i	$-0.988147\pi$
$139$	−12.2206	−	12.2206i	−1.03654	−	1.03654i	−0.0372284	−	0.999307i	$-0.511853\pi$
$140$		0			0
$141$	13.0002	−	13.0002i	1.09482	−	1.09482i
$142$		0			0
$143$	−4.61180	+	4.61180i	−0.385658	+	0.385658i
$144$		0			0
$145$	0.594284	+	0.697017i	0.0493526	+	0.0578841i
$146$		0			0
$147$	20.6807			1.70572
$148$		0			0
$149$	2.59172	−	2.59172i	0.212322	−	0.212322i	−0.592931	−	0.805253i	$-0.702029\pi$
$149$	2.59172	−	2.59172i	0.212322	−	0.212322i	0.805253	+	0.592931i	$0.202029\pi$
$150$		0			0
$151$	16.9594			1.38014			0.690068	−	0.723745i	$-0.257581\pi$
$151$	16.9594			1.38014			0.690068	+	0.723745i	$0.257581\pi$
$152$		0			0
$153$	−1.73653	+	1.73653i	−0.140390	+	0.140390i
$154$		0			0
$155$	−0.742168	+	9.32865i	−0.0596124	+	0.749296i
$156$		0			0
$157$			8.55235i			0.682552i	0.939963	+	0.341276i	$0.110859\pi$
$157$			8.55235i			0.682552i	−0.939963	+	0.341276i	$0.889141\pi$
$158$		0			0
$159$	−33.9041			−2.68877
$160$		0			0
$161$	−0.954354			−0.0752136
$162$		0			0
$163$		−	3.57797i		−	0.280248i	−0.990134	−	0.140124i	$-0.955250\pi$
$163$		−	3.57797i		−	0.280248i	0.990134	−	0.140124i	$-0.0447501\pi$
$164$		0			0
$165$	−18.0081	−	21.1211i	−1.40193	−	1.64428i
$166$		0			0
$167$	−0.482874	+	0.482874i	−0.0373659	+	0.0373659i	−0.725543	−	0.688177i	$-0.758411\pi$
$167$	−0.482874	+	0.482874i	−0.0373659	+	0.0373659i	0.688177	+	0.725543i	$0.258411\pi$
$168$		0			0
$169$	−10.5720			−0.813227
$170$		0			0
$171$	−13.1115	+	13.1115i	−1.00266	+	1.00266i
$172$		0			0
$173$	−11.8189			−0.898576			−0.449288	−	0.893387i	$-0.648322\pi$
$173$	−11.8189			−0.898576			−0.449288	+	0.893387i	$0.648322\pi$
$174$		0			0
$175$	0.659260	−	0.477269i	0.0498354	−	0.0360781i
$176$		0			0
$177$	−4.84870	+	4.84870i	−0.364451	+	0.364451i
$178$		0			0
$179$	4.71524	−	4.71524i	0.352433	−	0.352433i	−0.508581	−	0.861014i	$-0.669830\pi$
$179$	4.71524	−	4.71524i	0.352433	−	0.352433i	0.861014	+	0.508581i	$0.169830\pi$
$180$		0			0
$181$	−13.1843	−	13.1843i	−0.979983	−	0.979983i	0.0198205	−	0.999804i	$-0.493691\pi$
$181$	−13.1843	−	13.1843i	−0.979983	−	0.979983i	−0.999804	+	0.0198205i	$0.993691\pi$
$182$		0			0
$183$	−3.64870	−	3.64870i	−0.269720	−	0.269720i
$184$		0			0
$185$	−3.64764	−	0.290199i	−0.268180	−	0.0213358i
$186$		0			0
$187$		−	1.77383i		−	0.129715i
$188$		0			0
$189$	0.954008	+	0.954008i	0.0693939	+	0.0693939i
$190$		0			0
$191$			13.9872i			1.01208i	0.862510	+	0.506040i	$0.168891\pi$
$191$			13.9872i			1.01208i	−0.862510	+	0.506040i	$0.831109\pi$
$192$		0			0
$193$	3.88875	+	3.88875i	0.279919	+	0.279919i	0.833076	−	0.553158i	$-0.186577\pi$
$193$	3.88875	+	3.88875i	0.279919	+	0.279919i	−0.553158	+	0.833076i	$0.686577\pi$
$194$		0			0
$195$	−0.819485	+	10.3005i	−0.0586845	+	0.737633i
$196$		0			0
$197$	22.3277			1.59078			0.795391	−	0.606097i	$-0.207266\pi$
$197$	22.3277			1.59078			0.795391	+	0.606097i	$0.207266\pi$
$198$		0			0
$199$		−	9.83847i		−	0.697431i	−0.937229	−	0.348715i	$-0.886618\pi$
$199$		−	9.83847i		−	0.697431i	0.937229	−	0.348715i	$-0.113382\pi$
$200$		0			0
$201$		−	7.39437i		−	0.521559i
$202$		0			0
$203$	0.0666793			0.00467997
$204$		0			0
$205$	−1.35068	+	16.9773i	−0.0943355	+	1.18575i
$206$		0			0
$207$	24.0239	+	24.0239i	1.66978	+	1.66978i
$208$		0			0
$209$		−	13.3931i		−	0.926423i
$210$		0			0
$211$	11.0531	+	11.0531i	0.760925	+	0.760925i	0.976490	−	0.215565i	$-0.0691592\pi$
$211$	11.0531	+	11.0531i	0.760925	+	0.760925i	−0.215565	+	0.976490i	$0.569159\pi$
$212$		0			0
$213$			23.7278i			1.62580i
$214$		0			0
$215$	−14.9936	−	1.19286i	−1.02255	−	0.0813521i
$216$		0			0
$217$	0.481706	+	0.481706i	0.0327004	+	0.0327004i
$218$		0			0
$219$	−3.32451	−	3.32451i	−0.224650	−	0.224650i
$220$		0			0
$221$	−0.466948	+	0.466948i	−0.0314103	+	0.0314103i
$222$		0			0
$223$	5.93975	−	5.93975i	0.397755	−	0.397755i	−0.479686	−	0.877440i	$-0.659249\pi$
$223$	5.93975	−	5.93975i	0.397755	−	0.397755i	0.877440	+	0.479686i	$0.159249\pi$
$224$		0			0
$225$	−28.6098	−	4.58127i	−1.90732	−	0.305418i
$226$		0			0
$227$	−23.2105			−1.54054			−0.770269	−	0.637720i	$-0.779878\pi$
$227$	−23.2105			−1.54054			−0.770269	+	0.637720i	$0.779878\pi$
$228$		0			0
$229$	5.59944	−	5.59944i	0.370021	−	0.370021i	−0.497464	−	0.867485i	$-0.665735\pi$
$229$	5.59944	−	5.59944i	0.370021	−	0.370021i	0.867485	+	0.497464i	$0.165735\pi$
$230$		0			0
$231$	−2.02053			−0.132941
$232$		0			0
$233$	−3.01998	+	3.01998i	−0.197845	+	0.197845i	−0.799076	−	0.601230i	$-0.794677\pi$
$233$	−3.01998	+	3.01998i	−0.197845	+	0.197845i	0.601230	+	0.799076i	$0.294677\pi$
$234$		0			0
$235$	8.99391	+	10.5487i	0.586698	+	0.688120i
$236$		0			0
$237$		−	10.7420i		−	0.697766i
$238$		0			0
$239$	−0.00138865			−8.98241e−5			−4.49120e−5	−	1.00000i	$-0.500014\pi$
$239$	−0.00138865			−8.98241e−5			−4.49120e−5		1.00000i	$0.500014\pi$
$240$		0			0
$241$	−12.8578			−0.828245			−0.414123	−	0.910221i	$-0.635912\pi$
$241$	−12.8578			−0.828245			−0.414123	+	0.910221i	$0.635912\pi$
$242$		0			0
$243$			3.52546i			0.226158i
$244$		0			0
$245$	−1.23666	+	15.5441i	−0.0790071	+	0.993077i
$246$		0			0
$247$	−3.52565	+	3.52565i	−0.224332	+	0.224332i
$248$		0			0
$249$	4.82296			0.305643
$250$		0			0
$251$	−9.14111	+	9.14111i	−0.576982	+	0.576982i	−0.934071	−	0.357089i	$-0.883769\pi$
$251$	−9.14111	+	9.14111i	−0.576982	+	0.576982i	0.357089	+	0.934071i	$0.383769\pi$
$252$		0			0
$253$	−24.5399			−1.54281
$254$		0			0
$255$	−1.82333	−	2.13853i	−0.114181	−	0.133920i
$256$		0			0
$257$	21.2733	−	21.2733i	1.32699	−	1.32699i	0.419013	−	0.907980i	$-0.362376\pi$
$257$	21.2733	−	21.2733i	1.32699	−	1.32699i	0.907980	−	0.419013i	$-0.137624\pi$
$258$		0			0
$259$	−0.188354	+	0.188354i	−0.0117038	+	0.0117038i
$260$		0			0
$261$	−1.67851	−	1.67851i	−0.103897	−	0.103897i
$262$		0			0
$263$	16.7214	+	16.7214i	1.03108	+	1.03108i	0.999501	+	0.0315818i	$0.0100545\pi$
$263$	16.7214	+	16.7214i	1.03108	+	1.03108i	0.0315818	+	0.999501i	$0.489946\pi$
$264$		0			0
$265$	2.02739	−	25.4832i	0.124541	−	1.56542i
$266$		0			0
$267$		−	46.6043i		−	2.85213i
$268$		0			0
$269$	15.9096	+	15.9096i	0.970026	+	0.970026i	0.999564	−	0.0295378i	$-0.00940355\pi$
$269$	15.9096	+	15.9096i	0.970026	+	0.970026i	−0.0295378	+	0.999564i	$0.509404\pi$
$270$		0			0
$271$		−	12.3601i		−	0.750824i	−0.926858	−	0.375412i	$-0.877501\pi$
$271$		−	12.3601i		−	0.750824i	0.926858	−	0.375412i	$-0.122499\pi$
$272$		0			0
$273$	0.531889	+	0.531889i	0.0321914	+	0.0321914i
$274$		0			0
$275$	16.9520	−	12.2723i	1.02224	−	0.740049i
$276$		0			0
$277$	−21.0270			−1.26339			−0.631695	−	0.775217i	$-0.717641\pi$
$277$	−21.0270			−1.26339			−0.631695	+	0.775217i	$0.717641\pi$
$278$		0			0
$279$		−	24.2520i		−	1.45193i
$280$		0			0
$281$			10.6807i			0.637158i	0.947896	+	0.318579i	$0.103206\pi$
$281$			10.6807i			0.637158i	−0.947896	+	0.318579i	$0.896794\pi$
$282$		0			0
$283$	12.5946			0.748673			0.374336	−	0.927293i	$-0.377871\pi$
$283$	12.5946			0.748673			0.374336	+	0.927293i	$0.377871\pi$
$284$		0			0
$285$	−13.7669	−	16.1468i	−0.815481	−	0.956452i
$286$		0			0
$287$	0.876663	+	0.876663i	0.0517478	+	0.0517478i
$288$		0			0
$289$			16.8204i			0.989435i
$290$		0			0
$291$	−28.7432	−	28.7432i	−1.68496	−	1.68496i
$292$		0			0
$293$		−	3.43132i		−	0.200460i	−0.994964	−	0.100230i	$-0.968042\pi$
$293$		−	3.43132i		−	0.200460i	0.994964	−	0.100230i	$-0.0319579\pi$
$294$		0			0
$295$	−3.35446	−	3.93434i	−0.195304	−	0.229066i
$296$		0			0
$297$	24.5310	+	24.5310i	1.42344	+	1.42344i
$298$		0			0
$299$	6.45996	+	6.45996i	0.373589	+	0.373589i
$300$		0			0
$301$	−0.774227	+	0.774227i	−0.0446257	+	0.0446257i
$302$		0			0
$303$	37.9798	−	37.9798i	2.18188	−	2.18188i
$304$		0			0
$305$	2.96063	−	2.52427i	0.169525	−	0.144539i
$306$		0			0
$307$	−11.8104			−0.674053			−0.337027	−	0.941495i	$-0.609421\pi$
$307$	−11.8104			−0.674053			−0.337027	+	0.941495i	$0.609421\pi$
$308$		0			0
$309$	12.8630	−	12.8630i	0.731750	−	0.731750i
$310$		0			0
$311$	−22.6262			−1.28301			−0.641506	−	0.767118i	$-0.721690\pi$
$311$	−22.6262			−1.28301			−0.641506	+	0.767118i	$0.721690\pi$
$312$		0			0
$313$	−7.08945	+	7.08945i	−0.400719	+	0.400719i	−0.878486	−	0.477767i	$-0.841446\pi$
$313$	−7.08945	+	7.08945i	−0.400719	+	0.400719i	0.477767	+	0.878486i	$0.341446\pi$
$314$		0			0
$315$	−1.60503	+	1.36846i	−0.0904329	+	0.0771040i
$316$		0			0
$317$		−	25.1265i		−	1.41124i	−0.708589	−	0.705621i	$-0.750668\pi$
$317$		−	25.1265i		−	1.41124i	0.708589	−	0.705621i	$-0.249332\pi$
$318$		0			0
$319$	1.71457			0.0959974
$320$		0			0
$321$	35.5300			1.98309
$322$		0			0
$323$		−	1.35606i		−	0.0754535i
$324$		0			0
$325$	−7.69309	−	1.23189i	−0.426736	−	0.0683329i
$326$		0			0
$327$	11.9070	−	11.9070i	0.658460	−	0.658460i
$328$		0			0
$329$	1.00913			0.0556349
$330$		0			0
$331$	5.80829	−	5.80829i	0.319253	−	0.319253i	−0.529227	−	0.848480i	$-0.677518\pi$
$331$	5.80829	−	5.80829i	0.319253	−	0.319253i	0.848480	+	0.529227i	$0.177518\pi$
$332$		0			0
$333$	9.48287			0.519658
$334$		0			0
$335$	5.55778	+	0.442166i	0.303654	+	0.0241581i
$336$		0			0
$337$	−7.41679	+	7.41679i	−0.404019	+	0.404019i	−0.879647	−	0.475628i	$-0.842221\pi$
$337$	−7.41679	+	7.41679i	−0.404019	+	0.404019i	0.475628	+	0.879647i	$0.342221\pi$
$338$		0			0
$339$	19.2099	−	19.2099i	1.04334	−	1.04334i
$340$		0			0
$341$	12.3864	+	12.3864i	0.670763	+	0.670763i
$342$		0			0
$343$	1.60836	+	1.60836i	0.0868434	+	0.0868434i
$344$		0			0
$345$	−29.5853	+	25.2247i	−1.59282	+	1.35805i
$346$		0			0
$347$			18.2493i			0.979673i	0.871814	+	0.489837i	$0.162944\pi$
$347$			18.2493i			0.979673i	−0.871814	+	0.489837i	$0.837056\pi$
$348$		0			0
$349$	−19.4413	−	19.4413i	−1.04067	−	1.04067i	−0.999137	−	0.0415330i	$-0.986776\pi$
$349$	−19.4413	−	19.4413i	−1.04067	−	1.04067i	−0.0415330	−	0.999137i	$-0.513224\pi$
$350$		0			0
$351$		−	12.9152i		−	0.689364i
$352$		0			0
$353$	−1.13598	−	1.13598i	−0.0604622	−	0.0604622i	0.676229	−	0.736691i	$-0.263613\pi$
$353$	−1.13598	−	1.13598i	−0.0604622	−	0.0604622i	−0.736691	+	0.676229i	$0.763613\pi$
$354$		0			0
$355$	−17.8343	−	1.41886i	−0.946549	−	0.0753054i
$356$		0			0
$357$	−0.204580			−0.0108275
$358$		0			0
$359$			28.4140i			1.49963i	0.661645	+	0.749817i	$0.269859\pi$
$359$			28.4140i			1.49963i	−0.661645	+	0.749817i	$0.730141\pi$
$360$		0			0
$361$			8.76116i			0.461114i
$362$		0			0
$363$	−19.3334			−1.01474
$364$		0			0
$365$	2.69758	−	2.29998i	0.141198	−	0.120387i
$366$		0			0
$367$	−2.29692	−	2.29692i	−0.119898	−	0.119898i	0.644612	−	0.764510i	$-0.277019\pi$
$367$	−2.29692	−	2.29692i	−0.119898	−	0.119898i	−0.764510	+	0.644612i	$0.777019\pi$
$368$		0			0
$369$		−	44.1364i		−	2.29765i
$370$		0			0
$371$	−1.31588	−	1.31588i	−0.0683172	−	0.0683172i
$372$		0			0
$373$			18.0787i			0.936081i	0.883707	+	0.468040i	$0.155040\pi$
$373$			18.0787i			0.936081i	−0.883707	+	0.468040i	$0.844960\pi$
$374$		0			0
$375$	7.82251	−	32.2206i	0.403953	−	1.66386i
$376$		0			0
$377$	−0.451348	−	0.451348i	−0.0232456	−	0.0232456i
$378$		0			0
$379$	2.79031	+	2.79031i	0.143328	+	0.143328i	0.775130	−	0.631802i	$-0.217684\pi$
$379$	2.79031	+	2.79031i	0.143328	+	0.143328i	−0.631802	+	0.775130i	$0.717684\pi$
$380$		0			0
$381$	−36.4046	+	36.4046i	−1.86506	+	1.86506i
$382$		0			0
$383$	−8.12206	+	8.12206i	−0.415018	+	0.415018i	−0.883482	−	0.468464i	$-0.844807\pi$
$383$	−8.12206	+	8.12206i	−0.415018	+	0.415018i	0.468464	+	0.883482i	$0.344807\pi$
$384$		0			0
$385$	0.120823	−	1.51868i	0.00615770	−	0.0773990i
$386$		0			0
$387$	38.9792			1.98142
$388$		0			0
$389$	−14.4341	+	14.4341i	−0.731839	+	0.731839i	−0.970984	−	0.239145i	$-0.923133\pi$
$389$	−14.4341	+	14.4341i	−0.731839	+	0.731839i	0.239145	+	0.970984i	$0.423133\pi$
$390$		0			0
$391$	−2.48468			−0.125656
$392$		0			0
$393$	23.7119	−	23.7119i	1.19611	−	1.19611i
$394$		0			0
$395$	8.07392	+	0.642344i	0.406243	+	0.0323198i
$396$		0			0
$397$		−	35.1624i		−	1.76475i	−0.470549	−	0.882374i	$-0.655944\pi$
$397$		−	35.1624i		−	1.76475i	0.470549	−	0.882374i	$-0.344056\pi$
$398$		0			0
$399$	−1.54466			−0.0773298
$400$		0			0
$401$	−23.5164			−1.17435			−0.587176	−	0.809459i	$-0.699760\pi$
$401$	−23.5164			−1.17435			−0.587176	+	0.809459i	$0.699760\pi$
$402$		0			0
$403$		−	6.52128i		−	0.324848i
$404$		0			0
$405$	16.0396	+	1.27608i	0.797014	+	0.0634087i
$406$		0			0
$407$	−4.84328	+	4.84328i	−0.240072	+	0.240072i
$408$		0			0
$409$	−23.2595			−1.15011			−0.575054	−	0.818115i	$-0.695019\pi$
$409$	−23.2595			−1.15011			−0.575054	+	0.818115i	$0.695019\pi$
$410$		0			0
$411$	9.15043	−	9.15043i	0.451357	−	0.451357i
$412$		0			0
$413$	−0.376374			−0.0185201
$414$		0			0
$415$	−0.288401	+	3.62505i	−0.0141571	+	0.177947i
$416$		0			0
$417$	−36.2415	+	36.2415i	−1.77475	+	1.77475i
$418$		0			0
$419$	−6.63975	+	6.63975i	−0.324373	+	0.324373i	−0.850442	−	0.526069i	$-0.823665\pi$
$419$	−6.63975	+	6.63975i	−0.324373	+	0.324373i	0.526069	+	0.850442i	$0.323665\pi$
$420$		0			0
$421$	−7.28216	−	7.28216i	−0.354911	−	0.354911i	0.507022	−	0.861933i	$-0.330746\pi$
$421$	−7.28216	−	7.28216i	−0.354911	−	0.354911i	−0.861933	+	0.507022i	$0.830746\pi$
$422$		0			0
$423$	−25.4027	−	25.4027i	−1.23512	−	1.23512i
$424$		0			0
$425$	1.71640	−	1.24258i	0.0832576	−	0.0602740i
$426$		0			0
$427$		−	0.283225i		−	0.0137062i
$428$		0			0
$429$	13.6768	+	13.6768i	0.660323	+	0.660323i
$430$		0			0
$431$			11.7250i			0.564771i	0.959301	+	0.282386i	$0.0911258\pi$
$431$			11.7250i			0.564771i	−0.959301	+	0.282386i	$0.908874\pi$
$432$		0			0
$433$	−20.8827	−	20.8827i	−1.00356	−	1.00356i	−0.999994	−	0.00356603i	$-0.998865\pi$
$433$	−20.8827	−	20.8827i	−1.00356	−	1.00356i	−0.00356603	−	0.999994i	$-0.501135\pi$
$434$		0			0
$435$	2.06708	−	1.76242i	0.0991090	−	0.0845014i
$436$		0			0
$437$	−18.7604			−0.897430
$438$		0			0
$439$		−	7.53661i		−	0.359703i	−0.983694	−	0.179851i	$-0.942438\pi$
$439$		−	7.53661i		−	0.359703i	0.983694	−	0.179851i	$-0.0575617\pi$
$440$		0			0
$441$		−	40.4105i		−	1.92431i
$442$		0			0
$443$	−25.7280			−1.22237			−0.611187	−	0.791486i	$-0.709308\pi$
$443$	−25.7280			−1.22237			−0.611187	+	0.791486i	$0.709308\pi$
$444$		0			0
$445$	35.0289	+	2.78682i	1.66053	+	0.132108i
$446$		0			0
$447$	−7.68604	−	7.68604i	−0.363537	−	0.363537i
$448$		0			0
$449$		−	2.33824i		−	0.110348i	−0.998477	−	0.0551741i	$-0.982429\pi$
$449$		−	2.33824i		−	0.110348i	0.998477	−	0.0551741i	$-0.0175714\pi$
$450$		0			0
$451$	22.5422	+	22.5422i	1.06147	+	1.06147i
$452$		0			0
$453$		−	50.2950i		−	2.36306i
$454$		0			0
$455$	−0.431586	+	0.367975i	−0.0202331	+	0.0172509i
$456$		0			0
$457$	−10.4561	−	10.4561i	−0.489115	−	0.489115i	0.418912	−	0.908027i	$-0.362412\pi$
$457$	−10.4561	−	10.4561i	−0.489115	−	0.489115i	−0.908027	+	0.418912i	$0.862412\pi$
$458$		0			0
$459$	2.48378	+	2.48378i	0.115933	+	0.115933i
$460$		0			0
$461$	−15.6903	+	15.6903i	−0.730769	+	0.730769i	−0.970772	−	0.240003i	$-0.922852\pi$
$461$	−15.6903	+	15.6903i	−0.730769	+	0.730769i	0.240003	+	0.970772i	$0.422852\pi$
$462$		0			0
$463$	−19.6332	+	19.6332i	−0.912434	+	0.912434i	−0.996463	−	0.0840297i	$-0.973221\pi$
$463$	−19.6332	+	19.6332i	−0.912434	+	0.912434i	0.0840297	+	0.996463i	$0.473221\pi$
$464$		0			0
$465$	27.6652	+	2.20098i	1.28294	+	0.102068i
$466$		0			0
$467$	−24.4862			−1.13309			−0.566543	−	0.824032i	$-0.691719\pi$
$467$	−24.4862			−1.13309			−0.566543	+	0.824032i	$0.691719\pi$
$468$		0			0
$469$	0.286989	−	0.286989i	0.0132519	−	0.0132519i
$470$		0			0
$471$	25.3630			1.16866
$472$		0			0
$473$	−19.9082	+	19.9082i	−0.915380	+	0.915380i
$474$		0			0
$475$	12.9595	−	9.38199i	0.594624	−	0.430475i
$476$		0			0
$477$			66.2493i			3.03335i
$478$		0			0
$479$	37.0609			1.69335			0.846677	−	0.532108i	$-0.178600\pi$
$479$	37.0609			1.69335			0.846677	+	0.532108i	$0.178600\pi$
$480$		0			0
$481$	2.54991			0.116266
$482$		0			0
$483$			2.83024i			0.128781i
$484$		0			0
$485$	23.3229	−	19.8853i	1.05904	−	0.902945i
$486$		0			0
$487$	−20.1912	+	20.1912i	−0.914950	+	0.914950i	−0.996656	−	0.0817061i	$-0.973963\pi$
$487$	−20.1912	+	20.1912i	−0.914950	+	0.914950i	0.0817061	+	0.996656i	$0.473963\pi$
$488$		0			0
$489$	−10.6109			−0.479840
$490$		0			0
$491$	−7.45822	+	7.45822i	−0.336585	+	0.336585i	−0.855080	−	0.518496i	$-0.826492\pi$
$491$	−7.45822	+	7.45822i	−0.336585	+	0.336585i	0.518496	+	0.855080i	$0.326492\pi$
$492$		0			0
$493$	0.173601			0.00781860
$494$		0			0
$495$	−41.2711	+	35.1881i	−1.85500	+	1.58159i
$496$		0			0
$497$	−0.920917	+	0.920917i	−0.0413088	+	0.0413088i
$498$		0			0
$499$	−8.17420	+	8.17420i	−0.365927	+	0.365927i	−0.865990	−	0.500062i	$-0.833311\pi$
$499$	−8.17420	+	8.17420i	−0.365927	+	0.365927i	0.500062	+	0.865990i	$0.333311\pi$
$500$		0			0
$501$	1.43202	+	1.43202i	0.0639778	+	0.0639778i
$502$		0			0
$503$	29.2327	+	29.2327i	1.30342	+	1.30342i	0.926072	+	0.377348i	$0.123164\pi$
$503$	29.2327	+	29.2327i	1.30342	+	1.30342i	0.377348	+	0.926072i	$0.376836\pi$
$504$		0			0
$505$	26.2754	+	30.8176i	1.16924	+	1.37136i
$506$		0			0
$507$			31.3523i			1.39241i
$508$		0			0
$509$	−20.0340	−	20.0340i	−0.887992	−	0.887992i	0.106338	−	0.994330i	$-0.466088\pi$
$509$	−20.0340	−	20.0340i	−0.887992	−	0.887992i	−0.994330	+	0.106338i	$0.966088\pi$
$510$		0			0
$511$		−	0.258061i		−	0.0114159i
$512$		0			0
$513$	18.7536	+	18.7536i	0.827991	+	0.827991i
$514$		0			0
$515$	8.89895	+	10.4373i	0.392135	+	0.459922i
$516$		0			0
$517$	25.9483			1.14121
$518$		0			0
$519$			35.0504i			1.53854i
$520$		0			0
$521$		−	5.89264i		−	0.258161i	−0.991634	−	0.129081i	$-0.958797\pi$
$521$		−	5.89264i		−	0.258161i	0.991634	−	0.129081i	$-0.0412026\pi$
$522$		0			0
$523$	−24.6537			−1.07803			−0.539015	−	0.842296i	$-0.681203\pi$
$523$	−24.6537			−1.07803			−0.539015	+	0.842296i	$0.681203\pi$
$524$		0			0
$525$	−1.41539	−	1.95511i	−0.0617729	−	0.0853280i
$526$		0			0
$527$	1.25413	+	1.25413i	0.0546309	+	0.0546309i
$528$		0			0
$529$			11.3742i			0.494528i
$530$		0			0
$531$	9.47444	+	9.47444i	0.411156	+	0.411156i
$532$		0			0
$533$		−	11.8681i		−	0.514066i
$534$		0			0
$535$	−2.12461	+	26.7052i	−0.0918549	+	1.15457i
$536$		0			0
$537$	−13.9836	−	13.9836i	−0.603435	−	0.603435i
$538$		0			0
$539$	20.6392	+	20.6392i	0.888994	+	0.888994i
$540$		0			0
$541$	27.1762	−	27.1762i	1.16840	−	1.16840i	0.185812	−	0.982585i	$-0.440508\pi$
$541$	27.1762	−	27.1762i	1.16840	−	1.16840i	0.982585	−	0.185812i	$-0.0594916\pi$
$542$		0			0
$543$	−39.0996	+	39.0996i	−1.67792	+	1.67792i
$544$		0			0
$545$	8.23759	+	9.66162i	0.352860	+	0.413858i
$546$		0			0
$547$	3.69225			0.157869			0.0789347	−	0.996880i	$-0.474848\pi$
$547$	3.69225			0.157869			0.0789347	+	0.996880i	$0.474848\pi$
$548$		0			0
$549$	−7.12962	+	7.12962i	−0.304285	+	0.304285i
$550$		0			0
$551$	1.31076			0.0558402
$552$		0			0
$553$	0.416915	−	0.416915i	0.0177290	−	0.0177290i
$554$		0			0
$555$	−0.860616	+	10.8175i	−0.0365311	+	0.459177i
$556$		0			0
$557$			12.2117i			0.517426i	0.965954	+	0.258713i	$0.0832984\pi$
$557$			12.2117i			0.517426i	−0.965954	+	0.258713i	$0.916702\pi$
$558$		0			0
$559$	10.4814			0.443315
$560$		0			0
$561$	−5.26049			−0.222098
$562$		0			0
$563$		−	12.2211i		−	0.515057i	−0.966271	−	0.257528i	$-0.917092\pi$
$563$		−	12.2211i		−	0.515057i	0.966271	−	0.257528i	$-0.0829081\pi$
$564$		0			0
$565$	13.2899	+	15.5873i	0.559110	+	0.655763i
$566$		0			0
$567$	0.828241	−	0.828241i	0.0347829	−	0.0347829i
$568$		0			0
$569$	30.9592			1.29788			0.648938	−	0.760841i	$-0.275213\pi$
$569$	30.9592			1.29788			0.648938	+	0.760841i	$0.275213\pi$
$570$		0			0
$571$	30.1508	−	30.1508i	1.26177	−	1.26177i	0.311539	−	0.950233i	$-0.399156\pi$
$571$	30.1508	−	30.1508i	1.26177	−	1.26177i	0.950233	−	0.311539i	$-0.100844\pi$
$572$		0			0
$573$	41.4806			1.73288
$574$		0			0
$575$	−17.1904	−	23.7454i	−0.716889	−	0.990252i
$576$		0			0
$577$	1.98215	−	1.98215i	0.0825181	−	0.0825181i	−0.664643	−	0.747161i	$-0.731416\pi$
$577$	1.98215	−	1.98215i	0.0825181	−	0.0825181i	0.747161	+	0.664643i	$0.231416\pi$
$578$		0			0
$579$	11.5325	−	11.5325i	0.479276	−	0.479276i
$580$		0			0
$581$	0.187188	+	0.187188i	0.00776586	+	0.00776586i
$582$		0			0
$583$	−33.8361	−	33.8361i	−1.40135	−	1.40135i
$584$		0			0
$585$	20.1273	+	1.60129i	0.832163	+	0.0662051i
$586$		0			0
$587$		−	26.9680i		−	1.11309i	−0.830818	−	0.556544i	$-0.812127\pi$
$587$		−	26.9680i		−	1.11309i	0.830818	−	0.556544i	$-0.187873\pi$
$588$		0			0
$589$	9.46923	+	9.46923i	0.390173	+	0.390173i
$590$		0			0
$591$		−	66.2153i		−	2.72373i
$592$		0			0
$593$	16.6701	+	16.6701i	0.684560	+	0.684560i	0.961024	−	0.276464i	$-0.0891626\pi$
$593$	16.6701	+	16.6701i	0.684560	+	0.684560i	−0.276464	+	0.961024i	$0.589163\pi$
$594$		0			0
$595$	0.0122334	−	0.153767i	0.000501520	−	0.00630383i
$596$		0			0
$597$	−29.1771			−1.19414
$598$		0			0
$599$		−	28.8376i		−	1.17827i	−0.808033	−	0.589137i	$-0.799468\pi$
$599$		−	28.8376i		−	1.17827i	0.808033	−	0.589137i	$-0.200532\pi$
$600$		0			0
$601$		−	1.91377i		−	0.0780642i	−0.999238	−	0.0390321i	$-0.987573\pi$
$601$		−	1.91377i		−	0.0780642i	0.999238	−	0.0390321i	$-0.0124275\pi$
$602$		0			0
$603$	−14.4487			−0.588397
$604$		0			0
$605$	1.15609	−	14.5315i	0.0470019	−	0.590789i
$606$		0			0
$607$	−7.89049	−	7.89049i	−0.320265	−	0.320265i	0.528604	−	0.848869i	$-0.322716\pi$
$607$	−7.89049	−	7.89049i	−0.320265	−	0.320265i	−0.848869	+	0.528604i	$0.822716\pi$
$608$		0			0
$609$		−	0.197745i		−	0.00801303i
$610$		0			0
$611$	−6.83071	−	6.83071i	−0.276341	−	0.276341i
$612$		0			0
$613$			40.1035i			1.61976i	0.586592	+	0.809882i	$0.300469\pi$
$613$			40.1035i			1.61976i	−0.586592	+	0.809882i	$0.699531\pi$
$614$		0			0
$615$	50.3481	+	4.00559i	2.03023	+	0.161521i
$616$		0			0
$617$	−14.5821	−	14.5821i	−0.587052	−	0.587052i	0.349780	−	0.936832i	$-0.386256\pi$
$617$	−14.5821	−	14.5821i	−0.587052	−	0.587052i	−0.936832	+	0.349780i	$0.886256\pi$
$618$		0			0
$619$	4.01752	+	4.01752i	0.161478	+	0.161478i	0.783221	−	0.621743i	$-0.213575\pi$
$619$	4.01752	+	4.01752i	0.161478	+	0.161478i	−0.621743	+	0.783221i	$0.713575\pi$
$620$		0			0
$621$	34.3617	−	34.3617i	1.37889	−	1.37889i
$622$		0			0
$623$	1.80880	−	1.80880i	0.0724679	−	0.0724679i
$624$		0			0
$625$	23.7500	+	7.80630i	0.949999	+	0.312252i
$626$		0			0
$627$	−39.7189			−1.58622
$628$		0			0
$629$	−0.490385	+	0.490385i	−0.0195529	+	0.0195529i
$630$		0			0
$631$	26.9309			1.07210			0.536052	−	0.844185i	$-0.319915\pi$
$631$	26.9309			1.07210			0.536052	+	0.844185i	$0.319915\pi$
$632$		0			0
$633$	32.7791	−	32.7791i	1.30285	−	1.30285i
$634$		0			0
$635$	−25.1856	−	29.5395i	−0.999462	−	1.17224i
$636$		0			0
$637$		−	10.8662i		−	0.430536i
$638$		0			0
$639$	46.3644			1.83415
$640$		0			0
$641$	18.6880			0.738131			0.369065	−	0.929403i	$-0.379678\pi$
$641$	18.6880			0.738131			0.369065	+	0.929403i	$0.379678\pi$
$642$		0			0
$643$			29.6249i			1.16829i	0.811648	+	0.584146i	$0.198571\pi$
$643$			29.6249i			1.16829i	−0.811648	+	0.584146i	$0.801429\pi$
$644$		0			0
$645$	−3.53755	+	44.4651i	−0.139291	+	1.75081i
$646$		0			0
$647$	5.04426	−	5.04426i	0.198310	−	0.198310i	−0.600965	−	0.799275i	$-0.705217\pi$
$647$	5.04426	−	5.04426i	0.198310	−	0.198310i	0.799275	+	0.600965i	$0.205217\pi$
$648$		0			0
$649$	−9.67794			−0.379893
$650$		0			0
$651$	1.42855	−	1.42855i	0.0559895	−	0.0559895i
$652$		0			0
$653$	−3.04934			−0.119330			−0.0596649	−	0.998218i	$-0.519003\pi$
$653$	−3.04934			−0.119330			−0.0596649	+	0.998218i	$0.519003\pi$
$654$		0			0
$655$	16.4045	+	19.2404i	0.640978	+	0.751783i
$656$		0			0
$657$	−6.49615	+	6.49615i	−0.253439	+	0.253439i
$658$		0			0
$659$	−22.0441	+	22.0441i	−0.858718	+	0.858718i	−0.991187	−	0.132469i	$-0.957709\pi$
$659$	−22.0441	+	22.0441i	−0.858718	+	0.858718i	0.132469	+	0.991187i	$0.457709\pi$
$660$		0			0
$661$	−8.09788	−	8.09788i	−0.314971	−	0.314971i	0.531861	−	0.846832i	$-0.321493\pi$
$661$	−8.09788	−	8.09788i	−0.314971	−	0.314971i	−0.846832	+	0.531861i	$0.821493\pi$
$662$		0			0
$663$	1.38479	+	1.38479i	0.0537807	+	0.0537807i
$664$		0			0
$665$	0.0923670	−	1.16100i	0.00358184	−	0.0450218i
$666$		0			0
$667$		−	2.40167i		−	0.0929931i
$668$		0			0
$669$	−17.6150	−	17.6150i	−0.681035	−	0.681035i
$670$		0			0
$671$		−	7.28276i		−	0.281148i
$672$		0			0
$673$	−27.1768	−	27.1768i	−1.04759	−	1.04759i	−0.998810	−	0.0487786i	$-0.984467\pi$
$673$	−27.1768	−	27.1768i	−1.04759	−	1.04759i	−0.0487786	−	0.998810i	$-0.515533\pi$
$674$		0			0
$675$	−6.55265	+	40.9210i	−0.252212	+	1.57505i
$676$		0			0
$677$	−28.6501			−1.10111			−0.550557	−	0.834798i	$-0.685585\pi$
$677$	−28.6501			−1.10111			−0.550557	+	0.834798i	$0.685585\pi$
$678$		0			0
$679$		−	2.23115i		−	0.0856238i
$680$		0			0
$681$			68.8334i			2.63770i
$682$		0			0
$683$	30.8472			1.18034			0.590168	−	0.807281i	$-0.299062\pi$
$683$	30.8472			1.18034			0.590168	+	0.807281i	$0.299062\pi$
$684$		0			0
$685$	6.33051	+	7.42485i	0.241876	+	0.283689i
$686$		0			0
$687$	−16.6058	−	16.6058i	−0.633549	−	0.633549i
$688$		0			0
$689$			17.8142i			0.678668i
$690$		0			0
$691$	0.253186	+	0.253186i	0.00963164	+	0.00963164i	0.711906	−	0.702275i	$-0.247832\pi$
$691$	0.253186	+	0.253186i	0.00963164	+	0.00963164i	−0.702275	+	0.711906i	$0.747832\pi$
$692$		0			0
$693$			3.94815i			0.149978i
$694$		0			0
$695$	−25.0728	−	29.4071i	−0.951066	−	1.11548i
$696$		0			0
$697$	2.28241	+	2.28241i	0.0864525	+	0.0864525i
$698$		0			0
$699$	8.95608	+	8.95608i	0.338750	+	0.338750i
$700$		0			0
$701$	−10.5238	+	10.5238i	−0.397479	+	0.397479i	−0.877343	−	0.479864i	$-0.840686\pi$
$701$	−10.5238	+	10.5238i	−0.397479	+	0.397479i	0.479864	+	0.877343i	$0.340686\pi$
$702$		0			0
$703$	−3.70261	+	3.70261i	−0.139646	+	0.139646i
$704$		0			0
$705$	31.2833	−	26.6725i	1.17820	−	1.00454i
$706$		0			0
$707$	2.94813			0.110876
$708$		0			0
$709$	1.58968	−	1.58968i	0.0597015	−	0.0597015i	−0.676626	−	0.736327i	$-0.736558\pi$
$709$	1.58968	−	1.58968i	0.0597015	−	0.0597015i	0.736327	+	0.676626i	$0.236558\pi$
$710$		0			0
$711$	−20.9900			−0.787186
$712$		0			0
$713$	17.3502	−	17.3502i	0.649771	−	0.649771i
$714$		0			0
$715$	−11.0977	+	9.46198i	−0.415029	+	0.353858i
$716$		0			0
$717$			0.00411819i			0.000153797i
$718$		0			0
$719$	−22.8919			−0.853722			−0.426861	−	0.904317i	$-0.640381\pi$
$719$	−22.8919			−0.853722			−0.426861	+	0.904317i	$0.640381\pi$
$720$		0			0
$721$	0.998472			0.0371850
$722$		0			0
$723$			38.1313i			1.41812i
$724$		0			0
$725$	1.20107	+	1.65906i	0.0446065	+	0.0616158i
$726$		0			0
$727$	−20.1893	+	20.1893i	−0.748780	+	0.748780i	−0.974250	−	0.225470i	$-0.927608\pi$
$727$	−20.1893	+	20.1893i	−0.748780	+	0.748780i	0.225470	+	0.974250i	$0.427608\pi$
$728$		0			0
$729$	32.0425			1.18676
$730$		0			0
$731$	−2.01572	+	2.01572i	−0.0745540	+	0.0745540i
$732$		0			0
$733$	14.3253			0.529118			0.264559	−	0.964370i	$-0.414774\pi$
$733$	14.3253			0.529118			0.264559	+	0.964370i	$0.414774\pi$
$734$		0			0
$735$	46.0978	+	3.66744i	1.70034	+	0.135276i
$736$		0			0
$737$	7.37954	−	7.37954i	0.271829	−	0.271829i
$738$		0			0
$739$	32.3401	−	32.3401i	1.18965	−	1.18965i	0.212487	−	0.977164i	$-0.431844\pi$
$739$	32.3401	−	32.3401i	1.18965	−	1.18965i	0.977164	−	0.212487i	$-0.0681564\pi$
$740$		0			0
$741$	10.4557	+	10.4557i	0.384100	+	0.384100i
$742$		0			0
$743$	6.06842	+	6.06842i	0.222629	+	0.222629i	0.809605	−	0.586976i	$-0.199682\pi$
$743$	6.06842	+	6.06842i	0.222629	+	0.222629i	−0.586976	+	0.809605i	$0.699682\pi$
$744$		0			0
$745$	6.23662	−	5.31741i	0.228492	−	0.194815i
$746$		0			0
$747$		−	9.42414i		−	0.344811i
$748$		0			0
$749$	1.37898	+	1.37898i	0.0503870	+	0.0503870i
$750$		0			0
$751$			49.6431i			1.81150i	0.423810	+	0.905751i	$0.360692\pi$
$751$			49.6431i			1.81150i	−0.423810	+	0.905751i	$0.639308\pi$
$752$		0			0
$753$	27.1090	+	27.1090i	0.987907	+	0.987907i
$754$		0			0
$755$	37.8029	+	3.00752i	1.37579	+	0.109455i
$756$		0			0
$757$	9.18443			0.333814			0.166907	−	0.985973i	$-0.446622\pi$
$757$	9.18443			0.333814			0.166907	+	0.985973i	$0.446622\pi$
$758$		0			0
$759$			72.7759i			2.64160i
$760$		0			0
$761$			4.75310i			0.172300i	0.996282	+	0.0861499i	$0.0274564\pi$
$761$			4.75310i			0.172300i	−0.996282	+	0.0861499i	$0.972544\pi$
$762$		0			0
$763$	0.924267			0.0334607
$764$		0			0
$765$	−4.17872	+	3.56282i	−0.151082	+	0.128814i
$766$		0			0
$767$	2.54765	+	2.54765i	0.0919902	+	0.0919902i
$768$		0			0
$769$		−	19.4153i		−	0.700135i	−0.936724	−	0.350067i	$-0.886159\pi$
$769$		−	19.4153i		−	0.700135i	0.936724	−	0.350067i	$-0.113841\pi$
$770$		0			0
$771$	−63.0884	−	63.0884i	−2.27207	−	2.27207i
$772$		0			0
$773$		−	26.0890i		−	0.938356i	−0.883104	−	0.469178i	$-0.844550\pi$
$773$		−	26.0890i		−	0.938356i	0.883104	−	0.469178i	$-0.155450\pi$
$774$		0			0
$775$	−3.30862	+	20.6622i	−0.118849	+	0.742208i
$776$		0			0
$777$	0.558586	+	0.558586i	0.0200392	+	0.0200392i
$778$		0			0
$779$	17.2331	+	17.2331i	0.617442	+	0.617442i
$780$		0			0
$781$	−23.6802	+	23.6802i	−0.847343	+	0.847343i
$782$		0			0
$783$	−2.40080	+	2.40080i	−0.0857977	+	0.0857977i
$784$		0			0
$785$	−1.51664	+	19.0634i	−0.0541313	+	0.680402i
$786$		0			0
$787$	−14.2339			−0.507384			−0.253692	−	0.967285i	$-0.581645\pi$
$787$	−14.2339			−0.507384			−0.253692	+	0.967285i	$0.581645\pi$
$788$		0			0
$789$	49.5891	−	49.5891i	1.76542	−	1.76542i
$790$		0			0
$791$	1.49114			0.0530189
$792$		0			0
$793$	−1.91713	+	1.91713i	−0.0680794	+	0.0680794i
$794$		0			0
$795$	−75.5732	−	6.01244i	−2.68030	−	0.213239i
$796$		0			0
$797$			19.8283i			0.702353i	0.936309	+	0.351176i	$0.114218\pi$
$797$			19.8283i			0.702353i	−0.936309	+	0.351176i	$0.885782\pi$
$798$		0			0
$799$	2.62729			0.0929467
$800$		0			0
$801$	−91.0655			−3.21764
$802$		0			0
$803$		−	6.63568i		−	0.234168i
$804$		0			0
$805$	−2.12728	−	0.169242i	−0.0749767	−	0.00596499i
$806$		0			0
$807$	47.1817	−	47.1817i	1.66088	−	1.66088i
$808$		0			0
$809$	−21.3864			−0.751907			−0.375954	−	0.926639i	$-0.622685\pi$
$809$	−21.3864			−0.751907			−0.375954	+	0.926639i	$0.622685\pi$
$810$		0			0
$811$	−9.90624	+	9.90624i	−0.347855	+	0.347855i	−0.859310	−	0.511455i	$-0.829107\pi$
$811$	−9.90624	+	9.90624i	−0.347855	+	0.347855i	0.511455	+	0.859310i	$0.329107\pi$
$812$		0			0
$813$	−36.6553			−1.28556
$814$		0			0
$815$	0.634504	−	7.97538i	0.0222257	−	0.279365i
$816$		0			0
$817$	−15.2195	+	15.2195i	−0.532463	+	0.532463i
$818$		0			0
$819$	1.03932	−	1.03932i	0.0363168	−	0.0363168i
$820$		0			0
$821$	−22.6209	−	22.6209i	−0.789474	−	0.789474i	0.191934	−	0.981408i	$-0.438524\pi$
$821$	−22.6209	−	22.6209i	−0.789474	−	0.789474i	−0.981408	+	0.191934i	$0.938524\pi$
$822$		0			0
$823$	−4.89892	−	4.89892i	−0.170766	−	0.170766i	0.616550	−	0.787316i	$-0.288530\pi$
$823$	−4.89892	−	4.89892i	−0.170766	−	0.170766i	−0.787316	+	0.616550i	$0.788530\pi$
$824$		0			0
$825$	−36.3950	−	50.2731i	−1.26711	−	1.75028i
$826$		0			0
$827$		−	1.05434i		−	0.0366630i	−0.999832	−	0.0183315i	$-0.994165\pi$
$827$		−	1.05434i		−	0.0366630i	0.999832	−	0.0183315i	$-0.00583542\pi$
$828$		0			0
$829$	11.7754	+	11.7754i	0.408978	+	0.408978i	0.881382	−	0.472404i	$-0.156614\pi$
$829$	11.7754	+	11.7754i	0.408978	+	0.408978i	−0.472404	+	0.881382i	$0.656614\pi$
$830$		0			0
$831$			62.3580i			2.16317i
$832$		0			0
$833$	2.08973	+	2.08973i	0.0724050	+	0.0724050i
$834$		0			0
$835$	−1.16197	+	0.990707i	−0.0402116	+	0.0342848i
$836$		0			0
$837$	−34.6879			−1.19899
$838$		0			0
$839$		−	41.1678i		−	1.42127i	−0.703560	−	0.710636i	$-0.748407\pi$
$839$		−	41.1678i		−	1.42127i	0.703560	−	0.710636i	$-0.251593\pi$
$840$		0			0
$841$		−	28.8322i		−	0.994214i
$842$		0			0
$843$	31.6749			1.09094
$844$		0			0
$845$	−23.5651	−	1.87479i	−0.810666	−	0.0644948i
$846$		0			0
$847$	−0.750366	−	0.750366i	−0.0257829	−	0.0257829i
$848$		0			0
$849$		−	37.3508i		−	1.28188i
$850$		0			0
$851$	6.78419	+	6.78419i	0.232559	+	0.232559i
$852$		0			0
$853$		−	11.7179i		−	0.401212i	−0.979672	−	0.200606i	$-0.935709\pi$
$853$		−	11.7179i		−	0.401212i	0.979672	−	0.200606i	$-0.0642911\pi$
$854$		0			0
$855$	−31.5511	+	26.9008i	−1.07902	+	0.919986i
$856$		0			0
$857$	12.2154	+	12.2154i	0.417270	+	0.417270i	0.884262	−	0.466992i	$-0.154662\pi$
$857$	12.2154	+	12.2154i	0.417270	+	0.417270i	−0.466992	+	0.884262i	$0.654662\pi$
$858$		0			0
$859$	−17.2170	−	17.2170i	−0.587436	−	0.587436i	0.349500	−	0.936936i	$-0.386351\pi$
$859$	−17.2170	−	17.2170i	−0.587436	−	0.587436i	−0.936936	+	0.349500i	$0.886351\pi$
$860$		0			0
$861$	2.59984	−	2.59984i	0.0886024	−	0.0886024i
$862$		0			0
$863$	−11.1929	+	11.1929i	−0.381011	+	0.381011i	−0.871466	−	0.490455i	$-0.836831\pi$
$863$	−11.1929	+	11.1929i	−0.381011	+	0.381011i	0.490455	+	0.871466i	$0.336831\pi$
$864$		0			0
$865$	−26.3447	−	2.09593i	−0.895746	−	0.0712637i
$866$		0			0
$867$	49.8828			1.69411
$868$		0			0
$869$	10.7204	−	10.7204i	0.363665	−	0.363665i
$870$		0			0
$871$	−3.88522			−0.131646
$872$		0			0
$873$	−56.1647	+	56.1647i	−1.90089	+	1.90089i
$874$		0			0
$875$	1.55415	−	0.946933i	0.0525397	−	0.0320122i
$876$		0			0
$877$			43.1739i			1.45788i	0.684578	+	0.728940i	$0.259987\pi$
$877$			43.1739i			1.45788i	−0.684578	+	0.728940i	$0.740013\pi$
$878$		0			0
$879$	−10.1760			−0.343227
$880$		0			0
$881$	−33.4204			−1.12596			−0.562981	−	0.826470i	$-0.690346\pi$
$881$	−33.4204			−1.12596			−0.562981	+	0.826470i	$0.690346\pi$
$882$		0			0
$883$			2.00362i			0.0674270i	0.999432	+	0.0337135i	$0.0107334\pi$
$883$			2.00362i			0.0674270i	−0.999432	+	0.0337135i	$0.989267\pi$
$884$		0			0
$885$	−11.6677	+	9.94802i	−0.392206	+	0.334399i
$886$		0			0
$887$	16.1765	−	16.1765i	0.543154	−	0.543154i	−0.381298	−	0.924452i	$-0.624523\pi$
$887$	16.1765	−	16.1765i	0.543154	−	0.543154i	0.924452	+	0.381298i	$0.124523\pi$
$888$		0			0
$889$	−2.82586			−0.0947762
$890$		0			0
$891$	21.2971	−	21.2971i	0.713480	−	0.713480i
$892$		0			0
$893$	19.8371			0.663822
$894$		0			0
$895$	11.3466	−	9.67419i	0.379274	−	0.323373i
$896$		0			0
$897$	19.1577	−	19.1577i	0.639658	−	0.639658i
$898$		0			0
$899$	−1.21223	+	1.21223i	−0.0404303	+	0.0404303i
$900$		0			0
$901$	−3.42593	−	3.42593i	−0.114134	−	0.114134i
$902$		0			0
$903$	2.29606	+	2.29606i	0.0764080	+	0.0764080i
$904$		0			0
$905$	−27.0501	−	31.7262i	−0.899176	−	1.05462i
$906$		0			0
$907$			29.7116i			0.986559i	0.869871	+	0.493279i	$0.164202\pi$
$907$			29.7116i			0.986559i	−0.869871	+	0.493279i	$0.835798\pi$
$908$		0			0
$909$	−74.2131	−	74.2131i	−2.46149	−	2.46149i
$910$		0			0
$911$		−	44.6931i		−	1.48075i	−0.672195	−	0.740374i	$-0.734648\pi$
$911$		−	44.6931i		−	1.48075i	0.672195	−	0.740374i	$-0.265352\pi$
$912$		0			0
$913$	4.81328	+	4.81328i	0.159296	+	0.159296i
$914$		0			0
$915$	−7.48599	−	8.78009i	−0.247479	−	0.290261i
$916$		0			0
$917$	1.84061			0.0607821
$918$		0			0
$919$		−	40.1278i		−	1.32369i	−0.749639	−	0.661847i	$-0.769773\pi$
$919$		−	40.1278i		−	1.32369i	0.749639	−	0.661847i	$-0.230227\pi$
$920$		0			0
$921$			35.0250i			1.15411i
$922$		0			0
$923$	12.4673			0.410365
$924$		0			0
$925$	−8.07922	−	1.29372i	−0.265643	−	0.0425372i
$926$		0			0
$927$	−25.1345	−	25.1345i	−0.825525	−	0.825525i
$928$		0			0
$929$		−	27.7519i		−	0.910512i	−0.890361	−	0.455256i	$-0.849548\pi$
$929$		−	27.7519i		−	0.910512i	0.890361	−	0.455256i	$-0.150452\pi$
$930$		0			0
$931$	15.7783	+	15.7783i	0.517114	+	0.517114i
$932$		0			0
$933$			67.1004i			2.19677i
$934$		0			0
$935$	0.314565	−	3.95391i	0.0102874	−	0.129307i
$936$		0			0
$937$	17.2805	+	17.2805i	0.564531	+	0.564531i	0.930591	−	0.366060i	$-0.119294\pi$
$937$	17.2805	+	17.2805i	0.564531	+	0.564531i	−0.366060	+	0.930591i	$0.619294\pi$
$938$		0			0
$939$	21.0245	+	21.0245i	0.686110	+	0.686110i
$940$		0			0
$941$	4.81532	−	4.81532i	0.156975	−	0.156975i	−0.624250	−	0.781225i	$-0.714595\pi$
$941$	4.81532	−	4.81532i	0.156975	−	0.156975i	0.781225	+	0.624250i	$0.214595\pi$
$942$		0			0
$943$	31.5759	−	31.5759i	1.02825	−	1.02825i
$944$		0			0
$945$	1.95733	+	2.29569i	0.0636719	+	0.0746788i
$946$		0			0
$947$	3.37347			0.109623			0.0548115	−	0.998497i	$-0.482544\pi$
$947$	3.37347			0.109623			0.0548115	+	0.998497i	$0.482544\pi$
$948$		0			0
$949$	−1.74680	+	1.74680i	−0.0567034	+	0.0567034i
$950$		0			0
$951$	−74.5153			−2.41632
$952$		0			0
$953$	−14.3663	+	14.3663i	−0.465369	+	0.465369i	−0.900410	−	0.435041i	$-0.856734\pi$
$953$	−14.3663	+	14.3663i	−0.465369	+	0.465369i	0.435041	+	0.900410i	$0.356734\pi$
$954$		0			0
$955$	−2.48044	+	31.1778i	−0.0802652	+	1.00889i
$956$		0			0
$957$		−	5.08475i		−	0.164366i
$958$		0			0
$959$	0.710289			0.0229364
$960$		0			0
$961$	13.4851			0.435003
$962$		0			0
$963$		−	69.4263i		−	2.23723i
$964$		0			0
$965$	7.97851	+	9.35775i	0.256837	+	0.301236i
$966$		0			0
$967$	11.8576	−	11.8576i	0.381315	−	0.381315i	−0.490260	−	0.871576i	$-0.663098\pi$
$967$	11.8576	−	11.8576i	0.381315	−	0.381315i	0.871576	+	0.490260i	$0.163098\pi$
$968$		0			0
$969$	−4.02156			−0.129191
$970$		0			0
$971$	−14.6082	+	14.6082i	−0.468799	+	0.468799i	−0.901525	−	0.432726i	$-0.857552\pi$
$971$	−14.6082	+	14.6082i	−0.468799	+	0.468799i	0.432726	+	0.901525i	$0.357552\pi$
$972$		0			0
$973$	−2.81319			−0.0901869
$974$		0			0
$975$	−3.65330	+	22.8147i	−0.116999	+	0.730656i
$976$		0			0
$977$	12.9249	−	12.9249i	0.413504	−	0.413504i	−0.469454	−	0.882957i	$-0.655549\pi$
$977$	12.9249	−	12.9249i	0.413504	−	0.413504i	0.882957	+	0.469454i	$0.155549\pi$
$978$		0			0
$979$	46.5108	−	46.5108i	1.48649	−	1.48649i
$980$		0			0
$981$	−23.2665	−	23.2665i	−0.742843	−	0.742843i
$982$		0			0
$983$	0.133323	+	0.133323i	0.00425235	+	0.00425235i	0.709230	−	0.704977i	$-0.249043\pi$
$983$	0.133323	+	0.133323i	0.00425235	+	0.00425235i	−0.704977	+	0.709230i	$0.749043\pi$
$984$		0			0
$985$	49.7690	+	3.95951i	1.58577	+	0.126161i
$986$		0			0
$987$		−	2.99268i		−	0.0952580i
$988$		0			0
$989$	27.8863	+	27.8863i	0.886733	+	0.886733i
$990$		0			0
$991$		−	47.9032i		−	1.52170i	−0.648930	−	0.760848i	$-0.724783\pi$
$991$		−	47.9032i		−	1.52170i	0.648930	−	0.760848i	$-0.275217\pi$
$992$		0			0
$993$	−17.2251	−	17.2251i	−0.546624	−	0.546624i
$994$		0			0
$995$	1.74472	−	21.9302i	0.0553114	−	0.695234i
$996$		0			0
$997$	54.9379			1.73990			0.869951	−	0.493138i	$-0.164150\pi$
$997$	54.9379			1.73990			0.869951	+	0.493138i	$0.164150\pi$
$998$		0			0
$999$		−	13.5635i		−	0.429129i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.j.c.543.1		18
4.3	odd	2		640.2.j.d.543.9		18
5.2	odd	4		640.2.s.c.287.1		18
8.3	odd	2		80.2.j.b.43.1	✓	18
8.5	even	2		320.2.j.b.143.9		18
16.3	odd	4		640.2.s.c.223.1		18
16.5	even	4		80.2.s.b.3.5	yes	18
16.11	odd	4		320.2.s.b.303.9		18
16.13	even	4		640.2.s.d.223.9		18
20.7	even	4		640.2.s.d.287.9		18
24.11	even	2		720.2.bd.g.523.9		18
40.3	even	4		400.2.s.d.107.5		18
40.13	odd	4		1600.2.s.d.207.1		18
40.19	odd	2		400.2.j.d.43.9		18
40.27	even	4		80.2.s.b.27.5	yes	18
40.29	even	2		1600.2.j.d.143.1		18
40.37	odd	4		320.2.s.b.207.9		18
48.5	odd	4		720.2.z.g.163.5		18
80.27	even	4		320.2.j.b.47.1		18
80.37	odd	4		80.2.j.b.67.1	yes	18
80.43	even	4		1600.2.j.d.1007.9		18
80.53	odd	4		400.2.j.d.307.9		18
80.59	odd	4		1600.2.s.d.943.1		18
80.67	even	4	inner	640.2.j.c.607.9		18
80.69	even	4		400.2.s.d.243.5		18
80.77	odd	4		640.2.j.d.607.1		18
120.107	odd	4		720.2.z.g.667.5		18
240.197	even	4		720.2.bd.g.307.9		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.1	✓	18	8.3	odd	2
80.2.j.b.67.1	yes	18	80.37	odd	4
80.2.s.b.3.5	yes	18	16.5	even	4
80.2.s.b.27.5	yes	18	40.27	even	4
320.2.j.b.47.1		18	80.27	even	4
320.2.j.b.143.9		18	8.5	even	2
320.2.s.b.207.9		18	40.37	odd	4
320.2.s.b.303.9		18	16.11	odd	4
400.2.j.d.43.9		18	40.19	odd	2
400.2.j.d.307.9		18	80.53	odd	4
400.2.s.d.107.5		18	40.3	even	4
400.2.s.d.243.5		18	80.69	even	4
640.2.j.c.543.1		18	1.1	even	1	trivial
640.2.j.c.607.9		18	80.67	even	4	inner
640.2.j.d.543.9		18	4.3	odd	2
640.2.j.d.607.1		18	80.77	odd	4
640.2.s.c.223.1		18	16.3	odd	4
640.2.s.c.287.1		18	5.2	odd	4
640.2.s.d.223.9		18	16.13	even	4
640.2.s.d.287.9		18	20.7	even	4
720.2.z.g.163.5		18	48.5	odd	4
720.2.z.g.667.5		18	120.107	odd	4
720.2.bd.g.307.9		18	240.197	even	4
720.2.bd.g.523.9		18	24.11	even	2
1600.2.j.d.143.1		18	40.29	even	2
1600.2.j.d.1007.9		18	80.43	even	4
1600.2.s.d.207.1		18	40.13	odd	4
1600.2.s.d.943.1		18	80.59	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)

\(f(q)\)	\(=\)	\(q-2.96561i q^{3} +(2.22902 + 0.177336i) q^{5} +(0.115101 - 0.115101i) q^{7} -5.79486 q^{9} +O(q^{10})\)	\(q-2.96561i q^{3} +(2.22902 + 0.177336i) q^{5} +(0.115101 - 0.115101i) q^{7} -5.79486 q^{9} +(2.95966 - 2.95966i) q^{11} -1.55822 q^{13} +(0.525911 - 6.61042i) q^{15} +(0.299668 - 0.299668i) q^{17} +(2.26261 - 2.26261i) q^{19} +(-0.341344 - 0.341344i) q^{21} +(-4.14573 - 4.14573i) q^{23} +(4.93710 + 0.790575i) q^{25} +8.28846i q^{27} +(0.289656 + 0.289656i) q^{29} +4.18508i q^{31} +(-8.77721 - 8.77721i) q^{33} +(0.276974 - 0.236151i) q^{35} -1.63643 q^{37} +4.62107i q^{39} +7.61648i q^{41} -6.72651 q^{43} +(-12.9169 - 1.02764i) q^{45} +(4.38366 + 4.38366i) q^{47} +6.97350i q^{49} +(-0.888698 - 0.888698i) q^{51} -11.4324i q^{53} +(7.12202 - 6.07231i) q^{55} +(-6.71003 - 6.71003i) q^{57} +(-1.63497 - 1.63497i) q^{59} +(1.23034 - 1.23034i) q^{61} +(-0.666993 + 0.666993i) q^{63} +(-3.47331 - 0.276329i) q^{65} +2.49337 q^{67} +(-12.2946 + 12.2946i) q^{69} -8.00096 q^{71} +(1.12102 - 1.12102i) q^{73} +(2.34454 - 14.6415i) q^{75} -0.681319i q^{77} +3.62218 q^{79} +7.19579 q^{81} +1.62629i q^{83} +(0.721109 - 0.614825i) q^{85} +(0.859007 - 0.859007i) q^{87} +15.7149 q^{89} +(-0.179352 + 0.179352i) q^{91} +12.4113 q^{93} +(5.44467 - 4.64218i) q^{95} +(9.69217 - 9.69217i) q^{97} +(-17.1508 + 17.1508i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 4 q^{5} - 2 q^{7} - 10 q^{9}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more