LMFDB - Embedded newform 640.2.s.c.287.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,2,Mod(223,640)]

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, 3, 3]))

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

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

chi := DirichletCharacter("640.223");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.s (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			287.1
Root			$0.235136 + 1.39453i$ of defining polynomial
Character	$\chi$	$=$	640.287
Dual form			640.2.s.c.223.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.96561 q^{3} +(0.177336 + 2.22902i) q^{5} +(0.115101 + 0.115101i) q^{7} +5.79486 q^{9} +O(q^{10})$	\(q-2.96561 q^{3} +(0.177336 + 2.22902i) q^{5} +(0.115101 + 0.115101i) q^{7} +5.79486 q^{9} +(2.95966 - 2.95966i) q^{11} +1.55822i q^{13} +(-0.525911 - 6.61042i) q^{15} +(0.299668 + 0.299668i) q^{17} +(-2.26261 + 2.26261i) q^{19} +(-0.341344 - 0.341344i) q^{21} +(-4.14573 + 4.14573i) q^{23} +(-4.93710 + 0.790575i) q^{25} -8.28846 q^{27} +(-0.289656 - 0.289656i) q^{29} +4.18508i q^{31} +(-8.77721 + 8.77721i) q^{33} +(-0.236151 + 0.276974i) q^{35} -1.63643i q^{37} -4.62107i q^{39} +7.61648i q^{41} +6.72651i q^{43} +(1.02764 + 12.9169i) q^{45} +(-4.38366 + 4.38366i) q^{47} -6.97350i q^{49} +(-0.888698 - 0.888698i) q^{51} -11.4324 q^{53} +(7.12202 + 6.07231i) q^{55} +(6.71003 - 6.71003i) q^{57} +(1.63497 + 1.63497i) q^{59} +(1.23034 - 1.23034i) q^{61} +(0.666993 + 0.666993i) q^{63} +(-3.47331 + 0.276329i) q^{65} +2.49337i q^{67} +(12.2946 - 12.2946i) q^{69} -8.00096 q^{71} +(-1.12102 - 1.12102i) q^{73} +(14.6415 - 2.34454i) q^{75} +0.681319 q^{77} -3.62218 q^{79} +7.19579 q^{81} +1.62629 q^{83} +(-0.614825 + 0.721109i) q^{85} +(0.859007 + 0.859007i) q^{87} -15.7149 q^{89} +(-0.179352 + 0.179352i) q^{91} -12.4113i q^{93} +(-5.44467 - 4.64218i) q^{95} +(9.69217 + 9.69217i) q^{97} +(17.1508 - 17.1508i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 2 q^{5} - 2 q^{7} + 10 q^{9}+O(q^{10}) $ 18 * q - 2 * q^5 - 2 * q^7 + 10 * q^9	$ 18 q - 2 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} - 24 q^{27} - 14 q^{29} - 8 q^{33} + 2 q^{35} + 14 q^{45} - 38 q^{47} + 8 q^{51} - 12 q^{53} + 6 q^{55} - 24 q^{57} + 10 q^{59} - 14 q^{61} + 6 q^{63} + 32 q^{69} - 24 q^{71} - 14 q^{73} + 16 q^{75} + 44 q^{77} + 16 q^{79} + 2 q^{81} + 40 q^{83} - 14 q^{85} - 24 q^{87} + 12 q^{89} - 34 q^{95} + 18 q^{97} + 22 q^{99}+O(q^{100}) $ 18 * q - 2 * 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 - 24 * q^27 - 14 * q^29 - 8 * q^33 + 2 * q^35 + 14 * q^45 - 38 * q^47 + 8 * q^51 - 12 * q^53 + 6 * q^55 - 24 * q^57 + 10 * q^59 - 14 * q^61 + 6 * q^63 + 32 * q^69 - 24 * q^71 - 14 * q^73 + 16 * q^75 + 44 * q^77 + 16 * q^79 + 2 * q^81 + 40 * q^83 - 14 * q^85 - 24 * q^87 + 12 * q^89 - 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 $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

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

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
$3$	−2.96561			−1.71220			−0.856099	−	0.516813i	$-0.827118\pi$
$3$	−2.96561			−1.71220			−0.856099	+	0.516813i	$0.827118\pi$
$4$		0			0
$5$	0.177336	+	2.22902i	0.0793073	+	0.996850i
$5$	0.177336	+	2.22902i	0.0793073	+	0.996850i
$6$		0			0
$7$	0.115101	+	0.115101i	0.0435040	+	0.0435040i	0.728524	−	0.685020i	$-0.240207\pi$
$7$	0.115101	+	0.115101i	0.0435040	+	0.0435040i	−0.685020	+	0.728524i	$0.740207\pi$
$8$		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
$13$			1.55822i			0.432172i	0.976374	+	0.216086i	$0.0693292\pi$
$13$			1.55822i			0.432172i	−0.976374	+	0.216086i	$0.930671\pi$
$14$		0			0
$15$	−0.525911	−	6.61042i	−0.135790	−	1.70680i
$16$		0			0
$17$	0.299668	+	0.299668i	0.0726801	+	0.0726801i	0.742512	−	0.669832i	$-0.233634\pi$
$17$	0.299668	+	0.299668i	0.0726801	+	0.0726801i	−0.669832	+	0.742512i	$0.733634\pi$
$18$		0			0
$19$	−2.26261	+	2.26261i	−0.519079	+	0.519079i	−0.917293	−	0.398214i	$-0.869630\pi$
$19$	−2.26261	+	2.26261i	−0.519079	+	0.519079i	0.398214	+	0.917293i	$0.369630\pi$
$20$		0			0
$21$	−0.341344	−	0.341344i	−0.0744874	−	0.0744874i
$22$		0			0
$23$	−4.14573	+	4.14573i	−0.864444	+	0.864444i	−0.991851	−	0.127406i	$-0.959335\pi$
$23$	−4.14573	+	4.14573i	−0.864444	+	0.864444i	0.127406	+	0.991851i	$0.459335\pi$
$24$		0			0
$25$	−4.93710	+	0.790575i	−0.987421	+	0.158115i
$26$		0			0
$27$	−8.28846			−1.59511
$28$		0			0
$29$	−0.289656	−	0.289656i	−0.0537878	−	0.0537878i	0.679701	−	0.733489i	$-0.262109\pi$
$29$	−0.289656	−	0.289656i	−0.0537878	−	0.0537878i	−0.733489	+	0.679701i	$0.762109\pi$
$30$		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
$35$	−0.236151	+	0.276974i	−0.0399168	+	0.0468172i
$36$		0			0
$37$		−	1.63643i		−	0.269027i	−0.990912	−	0.134514i	$-0.957053\pi$
$37$		−	1.63643i		−	0.269027i	0.990912	−	0.134514i	$-0.0429472\pi$
$38$		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
$43$			6.72651i			1.02578i	0.858453	+	0.512892i	$0.171426\pi$
$43$			6.72651i			1.02578i	−0.858453	+	0.512892i	$0.828574\pi$
$44$		0			0
$45$	1.02764	+	12.9169i	0.153191	+	1.92553i
$46$		0			0
$47$	−4.38366	+	4.38366i	−0.639423	+	0.639423i	−0.950413	−	0.310990i	$-0.899339\pi$
$47$	−4.38366	+	4.38366i	−0.639423	+	0.639423i	0.310990	+	0.950413i	$0.399339\pi$
$48$		0			0
$49$		−	6.97350i		−	0.996215i
$50$		0			0
$51$	−0.888698	−	0.888698i	−0.124443	−	0.124443i
$52$		0			0
$53$	−11.4324			−1.57036			−0.785182	−	0.619265i	$-0.787431\pi$
$53$	−11.4324			−1.57036			−0.785182	+	0.619265i	$0.787431\pi$
$54$		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	0.805479	−	0.592624i	$-0.201908\pi$
$59$	1.63497	+	1.63497i	0.212855	+	0.212855i	−0.592624	+	0.805479i	$0.701908\pi$
$60$		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
$67$			2.49337i			0.304614i	0.988333	+	0.152307i	$0.0486702\pi$
$67$			2.49337i			0.304614i	−0.988333	+	0.152307i	$0.951330\pi$
$68$		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	$-0.279574\pi$
$73$	−1.12102	−	1.12102i	−0.131205	−	0.131205i	−0.769660	+	0.638454i	$0.779574\pi$
$74$		0			0
$75$	14.6415	−	2.34454i	1.69066	−	0.270724i
$76$		0			0
$77$	0.681319			0.0776435
$78$		0			0
$79$	−3.62218			−0.407527			−0.203763	−	0.979020i	$-0.565317\pi$
$79$	−3.62218			−0.407527			−0.203763	+	0.979020i	$0.565317\pi$
$80$		0			0
$81$	7.19579			0.799532
$82$		0			0
$83$	1.62629			0.178509			0.0892545	−	0.996009i	$-0.471552\pi$
$83$	1.62629			0.178509			0.0892545	+	0.996009i	$0.471552\pi$
$84$		0			0
$85$	−0.614825	+	0.721109i	−0.0666871	+	0.0782152i
$86$		0			0
$87$	0.859007	+	0.859007i	0.0920953	+	0.0920953i
$88$		0			0
$89$	−15.7149			−1.66577			−0.832887	−	0.553443i	$-0.813314\pi$
$89$	−15.7149			−1.66577			−0.832887	+	0.553443i	$0.813314\pi$
$90$		0			0
$91$	−0.179352	+	0.179352i	−0.0188012	+	0.0188012i
$92$		0			0
$93$		−	12.4113i		−	1.28700i
$94$		0			0
$95$	−5.44467	−	4.64218i	−0.558611	−	0.476277i
$96$		0			0
$97$	9.69217	+	9.69217i	0.984091	+	0.984091i	0.999875	−	0.0157848i	$-0.00502467\pi$
$97$	9.69217	+	9.69217i	0.984091	+	0.984091i	−0.0157848	+	0.999875i	$0.505025\pi$
$98$		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	−0.460358	−	0.887733i	$-0.652279\pi$
$103$	4.33738	−	4.33738i	0.427375	−	0.427375i	0.887733	+	0.460358i	$0.152279\pi$
$104$		0			0
$105$	0.700332	−	0.821398i	0.0683454	−	0.0801602i
$106$		0			0
$107$	−11.9807			−1.15822			−0.579108	−	0.815251i	$-0.696599\pi$
$107$	−11.9807			−1.15822			−0.579108	+	0.815251i	$0.696599\pi$
$108$		0			0
$109$	−4.01503	−	4.01503i	−0.384570	−	0.384570i	0.488175	−	0.872746i	$-0.337663\pi$
$109$	−4.01503	−	4.01503i	−0.384570	−	0.384570i	−0.872746	+	0.488175i	$0.837663\pi$
$110$		0			0
$111$			4.85301i			0.460628i
$112$		0			0
$113$	6.47754	−	6.47754i	0.609356	−	0.609356i	−0.333422	−	0.942778i	$-0.608203\pi$
$113$	6.47754	−	6.47754i	0.609356	−	0.609356i	0.942778	+	0.333422i	$0.108203\pi$
$114$		0			0
$115$	−9.97612	−	8.50575i	−0.930278	−	0.793165i
$116$		0			0
$117$			9.02966i			0.834792i
$118$		0			0
$119$			0.0689840i			0.00632375i
$120$		0			0
$121$		−	6.51921i		−	0.592655i
$122$		0			0
$123$		−	22.5875i		−	2.03665i
$124$		0			0
$125$	−2.63774	−	10.8647i	−0.235927	−	0.971771i
$126$		0			0
$127$	12.2756	−	12.2756i	1.08928	−	1.08928i	0.0936781	−	0.995603i	$-0.470138\pi$
$127$	12.2756	−	12.2756i	1.08928	−	1.08928i	0.995603	−	0.0936781i	$-0.0298625\pi$
$128$		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
$133$	−0.520857			−0.0451641
$134$		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	$-0.809683\pi$
$137$	−3.08551	+	3.08551i	−0.263613	+	0.263613i	0.562907	+	0.826520i	$0.309683\pi$
$138$		0			0
$139$	12.2206	+	12.2206i	1.03654	+	1.03654i	0.999307	+	0.0372284i	$0.0118529\pi$
$139$	12.2206	+	12.2206i	1.03654	+	1.03654i	0.0372284	+	0.999307i	$0.488147\pi$
$140$		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
$147$			20.6807i			1.70572i
$148$		0			0
$149$	−2.59172	+	2.59172i	−0.212322	+	0.212322i	−0.805253	−	0.592931i	$-0.797971\pi$
$149$	−2.59172	+	2.59172i	−0.212322	+	0.212322i	0.592931	+	0.805253i	$0.297971\pi$
$150$		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
$155$	−9.32865	+	0.742168i	−0.749296	+	0.0596124i
$156$		0			0
$157$	−8.55235			−0.682552			−0.341276	−	0.939963i	$-0.610859\pi$
$157$	−8.55235			−0.682552			−0.341276	+	0.939963i	$0.610859\pi$
$158$		0			0
$159$	33.9041			2.68877
$160$		0			0
$161$	−0.954354			−0.0752136
$162$		0			0
$163$	−3.57797			−0.280248			−0.140124	−	0.990134i	$-0.544750\pi$
$163$	−3.57797			−0.280248			−0.140124	+	0.990134i	$0.544750\pi$
$164$		0			0
$165$	−21.1211	−	18.0081i	−1.64428	−	1.40193i
$166$		0			0
$167$	−0.482874	−	0.482874i	−0.0373659	−	0.0373659i	0.688177	−	0.725543i	$-0.258411\pi$
$167$	−0.482874	−	0.482874i	−0.0373659	−	0.0373659i	−0.725543	+	0.688177i	$0.758411\pi$
$168$		0			0
$169$	10.5720			0.813227
$170$		0			0
$171$	−13.1115	+	13.1115i	−1.00266	+	1.00266i
$172$		0			0
$173$			11.8189i			0.898576i	0.893387	+	0.449288i	$0.148322\pi$
$173$			11.8189i			0.898576i	−0.893387	+	0.449288i	$0.851678\pi$
$174$		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	−0.861014	−	0.508581i	$-0.830170\pi$
$179$	−4.71524	+	4.71524i	−0.352433	+	0.352433i	0.508581	+	0.861014i	$0.330170\pi$
$180$		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
$187$	1.77383			0.129715
$188$		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	−0.553158	−	0.833076i	$-0.686577\pi$
$193$	3.88875	−	3.88875i	0.279919	−	0.279919i	0.833076	+	0.553158i	$0.186577\pi$
$194$		0			0
$195$	10.3005	−	0.819485i	0.737633	−	0.0586845i
$196$		0			0
$197$			22.3277i			1.59078i	0.606097	+	0.795391i	$0.292734\pi$
$197$			22.3277i			1.59078i	−0.606097	+	0.795391i	$0.707266\pi$
$198$		0			0
$199$			9.83847i			0.697431i	0.937229	+	0.348715i	$0.113382\pi$
$199$			9.83847i			0.697431i	−0.937229	+	0.348715i	$0.886618\pi$
$200$		0			0
$201$		−	7.39437i		−	0.521559i
$202$		0			0
$203$		−	0.0666793i		−	0.00467997i
$204$		0			0
$205$	−16.9773	+	1.35068i	−1.18575	+	0.0943355i
$206$		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
$213$	23.7278			1.62580
$214$		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	$-0.340751\pi$
$223$	−5.93975	−	5.93975i	−0.397755	−	0.397755i	−0.877440	+	0.479686i	$0.840751\pi$
$224$		0			0
$225$	−28.6098	+	4.58127i	−1.90732	+	0.305418i
$226$		0			0
$227$		−	23.2105i		−	1.54054i	−0.637720	−	0.770269i	$-0.720122\pi$
$227$		−	23.2105i		−	1.54054i	0.637720	−	0.770269i	$-0.279878\pi$
$228$		0			0
$229$	−5.59944	+	5.59944i	−0.370021	+	0.370021i	−0.867485	−	0.497464i	$-0.834265\pi$
$229$	−5.59944	+	5.59944i	−0.370021	+	0.370021i	0.497464	+	0.867485i	$0.334265\pi$
$230$		0			0
$231$	−2.02053			−0.132941
$232$		0			0
$233$	3.01998	+	3.01998i	0.197845	+	0.197845i	0.799076	−	0.601230i	$-0.205323\pi$
$233$	3.01998	+	3.01998i	0.197845	+	0.197845i	−0.601230	+	0.799076i	$0.705323\pi$
$234$		0			0
$235$	−10.5487	−	8.99391i	−0.688120	−	0.586698i
$236$		0			0
$237$	10.7420			0.697766
$238$		0			0
$239$	0.00138865			8.98241e−5			4.49120e−5	−	1.00000i	$-0.499986\pi$
$239$	0.00138865			8.98241e−5			4.49120e−5		1.00000i	$0.499986\pi$
$240$		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
$243$	3.52546			0.226158
$244$		0			0
$245$	15.5441	−	1.23666i	0.993077	−	0.0790071i
$246$		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
$253$			24.5399i			1.54281i
$254$		0			0
$255$	1.82333	−	2.13853i	0.114181	−	0.133920i
$256$		0			0
$257$	21.2733	+	21.2733i	1.32699	+	1.32699i	0.907980	+	0.419013i	$0.137624\pi$
$257$	21.2733	+	21.2733i	1.32699	+	1.32699i	0.419013	+	0.907980i	$0.362376\pi$
$258$		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	0.0315818	−	0.999501i	$-0.489946\pi$
$263$	16.7214	−	16.7214i	1.03108	−	1.03108i	0.999501	−	0.0315818i	$-0.0100545\pi$
$264$		0			0
$265$	−2.02739	−	25.4832i	−0.124541	−	1.56542i
$266$		0			0
$267$	46.6043			2.85213
$268$		0			0
$269$	−15.9096	−	15.9096i	−0.970026	−	0.970026i	0.0295378	−	0.999564i	$-0.490596\pi$
$269$	−15.9096	−	15.9096i	−0.970026	−	0.970026i	−0.999564	+	0.0295378i	$0.990596\pi$
$270$		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
$275$	−12.2723	+	16.9520i	−0.740049	+	1.02224i
$276$		0			0
$277$		−	21.0270i		−	1.26339i	−0.775217	−	0.631695i	$-0.782359\pi$
$277$		−	21.0270i		−	1.26339i	0.775217	−	0.631695i	$-0.217641\pi$
$278$		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
$283$		−	12.5946i		−	0.748673i	−0.927293	−	0.374336i	$-0.877871\pi$
$283$		−	12.5946i		−	0.748673i	0.927293	−	0.374336i	$-0.122129\pi$
$284$		0			0
$285$	16.1468	+	13.7669i	0.956452	+	0.815481i
$286$		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
$293$	−3.43132			−0.200460			−0.100230	−	0.994964i	$-0.531958\pi$
$293$	−3.43132			−0.200460			−0.100230	+	0.994964i	$0.531958\pi$
$294$		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
$307$		−	11.8104i		−	0.674053i	−0.941495	−	0.337027i	$-0.890579\pi$
$307$		−	11.8104i		−	0.674053i	0.941495	−	0.337027i	$-0.109421\pi$
$308$		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	$-0.158554\pi$
$313$	7.08945	+	7.08945i	0.400719	+	0.400719i	−0.477767	+	0.878486i	$0.658554\pi$
$314$		0			0
$315$	−1.36846	+	1.60503i	−0.0771040	+	0.0904329i
$316$		0			0
$317$	25.1265			1.41124			0.705621	−	0.708589i	$-0.250668\pi$
$317$	25.1265			1.41124			0.705621	+	0.708589i	$0.250668\pi$
$318$		0			0
$319$	−1.71457			−0.0959974
$320$		0			0
$321$	35.5300			1.98309
$322$		0			0
$323$	−1.35606			−0.0754535
$324$		0			0
$325$	−1.23189	−	7.69309i	−0.0683329	−	0.426736i
$326$		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
$333$		−	9.48287i		−	0.519658i
$334$		0			0
$335$	−5.55778	+	0.442166i	−0.303654	+	0.0241581i
$336$		0			0
$337$	−7.41679	−	7.41679i	−0.404019	−	0.404019i	0.475628	−	0.879647i	$-0.342221\pi$
$337$	−7.41679	−	7.41679i	−0.404019	−	0.404019i	−0.879647	+	0.475628i	$0.842221\pi$
$338$		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
$347$	−18.2493			−0.979673			−0.489837	−	0.871814i	$-0.662944\pi$
$347$	−18.2493			−0.979673			−0.489837	+	0.871814i	$0.662944\pi$
$348$		0			0
$349$	19.4413	+	19.4413i	1.04067	+	1.04067i	0.999137	+	0.0415330i	$0.0132242\pi$
$349$	19.4413	+	19.4413i	1.04067	+	1.04067i	0.0415330	+	0.999137i	$0.486776\pi$
$350$		0			0
$351$		−	12.9152i		−	0.689364i
$352$		0			0
$353$	−1.13598	+	1.13598i	−0.0604622	+	0.0604622i	−0.736691	−	0.676229i	$-0.763613\pi$
$353$	−1.13598	+	1.13598i	−0.0604622	+	0.0604622i	0.676229	+	0.736691i	$0.263613\pi$
$354$		0			0
$355$	−1.41886	−	17.8343i	−0.0753054	−	0.946549i
$356$		0			0
$357$		−	0.204580i		−	0.0108275i
$358$		0			0
$359$		−	28.4140i		−	1.49963i	−0.661645	−	0.749817i	$-0.730141\pi$
$359$		−	28.4140i		−	1.49963i	0.661645	−	0.749817i	$-0.269859\pi$
$360$		0			0
$361$			8.76116i			0.461114i
$362$		0			0
$363$			19.3334i			1.01474i
$364$		0			0
$365$	2.29998	−	2.69758i	0.120387	−	0.141198i
$366$		0			0
$367$	2.29692	−	2.29692i	0.119898	−	0.119898i	−0.644612	−	0.764510i	$-0.722981\pi$
$367$	2.29692	−	2.29692i	0.119898	−	0.119898i	0.764510	+	0.644612i	$0.222981\pi$
$368$		0			0
$369$			44.1364i			2.29765i
$370$		0			0
$371$	−1.31588	−	1.31588i	−0.0683172	−	0.0683172i
$372$		0			0
$373$	18.0787			0.936081			0.468040	−	0.883707i	$-0.344960\pi$
$373$	18.0787			0.936081			0.468040	+	0.883707i	$0.344960\pi$
$374$		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	0.631802	−	0.775130i	$-0.282316\pi$
$379$	−2.79031	−	2.79031i	−0.143328	−	0.143328i	−0.775130	+	0.631802i	$0.782316\pi$
$380$		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	$-0.155193\pi$
$383$	8.12206	+	8.12206i	0.415018	+	0.415018i	−0.468464	+	0.883482i	$0.655193\pi$
$384$		0			0
$385$	0.120823	+	1.51868i	0.00615770	+	0.0773990i
$386$		0			0
$387$			38.9792i			1.98142i
$388$		0			0
$389$	14.4341	−	14.4341i	0.731839	−	0.731839i	−0.239145	−	0.970984i	$-0.576867\pi$
$389$	14.4341	−	14.4341i	0.731839	−	0.731839i	0.970984	+	0.239145i	$0.0768670\pi$
$390$		0			0
$391$	−2.48468			−0.125656
$392$		0			0
$393$	−23.7119	−	23.7119i	−1.19611	−	1.19611i
$394$		0			0
$395$	−0.642344	−	8.07392i	−0.0323198	−	0.406243i
$396$		0			0
$397$	35.1624			1.76475			0.882374	−	0.470549i	$-0.155944\pi$
$397$	35.1624			1.76475			0.882374	+	0.470549i	$0.155944\pi$
$398$		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
$403$	−6.52128			−0.324848
$404$		0			0
$405$	1.27608	+	16.0396i	0.0634087	+	0.797014i
$406$		0			0
$407$	−4.84328	−	4.84328i	−0.240072	−	0.240072i
$408$		0			0
$409$	23.2595			1.15011			0.575054	−	0.818115i	$-0.304981\pi$
$409$	23.2595			1.15011			0.575054	+	0.818115i	$0.304981\pi$
$410$		0			0
$411$	9.15043	−	9.15043i	0.451357	−	0.451357i
$412$		0			0
$413$			0.376374i			0.0185201i
$414$		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	−0.526069	−	0.850442i	$-0.676335\pi$
$419$	6.63975	−	6.63975i	0.324373	−	0.324373i	0.850442	+	0.526069i	$0.176335\pi$
$420$		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
$427$	0.283225			0.0137062
$428$		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	−0.00356603	+	0.999994i	$0.501135\pi$
$433$	−20.8827	+	20.8827i	−1.00356	+	1.00356i	−0.999994	+	0.00356603i	$0.998865\pi$
$434$		0			0
$435$	−1.76242	+	2.06708i	−0.0845014	+	0.0991090i
$436$		0			0
$437$		−	18.7604i		−	0.897430i
$438$		0			0
$439$			7.53661i			0.359703i	0.983694	+	0.179851i	$0.0575617\pi$
$439$			7.53661i			0.359703i	−0.983694	+	0.179851i	$0.942438\pi$
$440$		0			0
$441$		−	40.4105i		−	1.92431i
$442$		0			0
$443$			25.7280i			1.22237i	0.791486	+	0.611187i	$0.209308\pi$
$443$			25.7280i			1.22237i	−0.791486	+	0.611187i	$0.790692\pi$
$444$		0			0
$445$	−2.78682	−	35.0289i	−0.132108	−	1.66053i
$446$		0			0
$447$	7.68604	−	7.68604i	0.363537	−	0.363537i
$448$		0			0
$449$			2.33824i			0.110348i	0.998477	+	0.0551741i	$0.0175714\pi$
$449$			2.33824i			0.110348i	−0.998477	+	0.0551741i	$0.982429\pi$
$450$		0			0
$451$	22.5422	+	22.5422i	1.06147	+	1.06147i
$452$		0			0
$453$	−50.2950			−2.36306
$454$		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	$-0.637588\pi$
$457$	10.4561	−	10.4561i	0.489115	−	0.489115i	0.908027	+	0.418912i	$0.137588\pi$
$458$		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	$-0.0267791\pi$
$463$	19.6332	+	19.6332i	0.912434	+	0.912434i	−0.0840297	+	0.996463i	$0.526779\pi$
$464$		0			0
$465$	27.6652	−	2.20098i	1.28294	−	0.102068i
$466$		0			0
$467$		−	24.4862i		−	1.13309i	−0.824032	−	0.566543i	$-0.808281\pi$
$467$		−	24.4862i		−	1.13309i	0.824032	−	0.566543i	$-0.191719\pi$
$468$		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
$475$	9.38199	−	12.9595i	0.430475	−	0.594624i
$476$		0			0
$477$	−66.2493			−3.03335
$478$		0			0
$479$	−37.0609			−1.69335			−0.846677	−	0.532108i	$-0.821400\pi$
$479$	−37.0609			−1.69335			−0.846677	+	0.532108i	$0.821400\pi$
$480$		0			0
$481$	2.54991			0.116266
$482$		0			0
$483$	2.83024			0.128781
$484$		0			0
$485$	−19.8853	+	23.3229i	−0.902945	+	1.05904i
$486$		0			0
$487$	−20.1912	−	20.1912i	−0.914950	−	0.914950i	0.0817061	−	0.996656i	$-0.473963\pi$
$487$	−20.1912	−	20.1912i	−0.914950	−	0.914950i	−0.996656	+	0.0817061i	$0.973963\pi$
$488$		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
$493$		−	0.173601i		−	0.00781860i
$494$		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	−0.500062	−	0.865990i	$-0.666689\pi$
$499$	8.17420	−	8.17420i	0.365927	−	0.365927i	0.865990	+	0.500062i	$0.166689\pi$
$500$		0			0
$501$	1.43202	+	1.43202i	0.0639778	+	0.0639778i
$502$		0			0
$503$	29.2327	−	29.2327i	1.30342	−	1.30342i	0.377348	−	0.926072i	$-0.376836\pi$
$503$	29.2327	−	29.2327i	1.30342	−	1.30342i	0.926072	−	0.377348i	$-0.123164\pi$
$504$		0			0
$505$	−26.2754	+	30.8176i	−1.16924	+	1.37136i
$506$		0			0
$507$	−31.3523			−1.39241
$508$		0			0
$509$	20.0340	+	20.0340i	0.887992	+	0.887992i	0.994330	−	0.106338i	$-0.0339125\pi$
$509$	20.0340	+	20.0340i	0.887992	+	0.887992i	−0.106338	+	0.994330i	$0.533912\pi$
$510$		0			0
$511$		−	0.258061i		−	0.0114159i
$512$		0			0
$513$	18.7536	−	18.7536i	0.827991	−	0.827991i
$514$		0			0
$515$	10.4373	+	8.89895i	0.459922	+	0.392135i
$516$		0			0
$517$			25.9483i			1.14121i
$518$		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
$523$			24.6537i			1.07803i	0.842296	+	0.539015i	$0.181203\pi$
$523$			24.6537i			1.07803i	−0.842296	+	0.539015i	$0.818797\pi$
$524$		0			0
$525$	1.95511	+	1.41539i	0.0853280	+	0.0617729i
$526$		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
$533$	−11.8681			−0.514066
$534$		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
$547$			3.69225i			0.157869i	0.996880	+	0.0789347i	$0.0251519\pi$
$547$			3.69225i			0.157869i	−0.996880	+	0.0789347i	$0.974848\pi$
$548$		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
$555$	−10.8175	+	0.860616i	−0.459177	+	0.0365311i
$556$		0			0
$557$	−12.2117			−0.517426			−0.258713	−	0.965954i	$-0.583298\pi$
$557$	−12.2117			−0.517426			−0.258713	+	0.965954i	$0.583298\pi$
$558$		0			0
$559$	−10.4814			−0.443315
$560$		0			0
$561$	−5.26049			−0.222098
$562$		0			0
$563$	−12.2211			−0.515057			−0.257528	−	0.966271i	$-0.582908\pi$
$563$	−12.2211			−0.515057			−0.257528	+	0.966271i	$0.582908\pi$
$564$		0			0
$565$	15.5873	+	13.2899i	0.655763	+	0.559110i
$566$		0			0
$567$	0.828241	+	0.828241i	0.0347829	+	0.0347829i
$568$		0			0
$569$	−30.9592			−1.29788			−0.648938	−	0.760841i	$-0.724787\pi$
$569$	−30.9592			−1.29788			−0.648938	+	0.760841i	$0.724787\pi$
$570$		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
$573$		−	41.4806i		−	1.73288i
$574$		0			0
$575$	17.1904	−	23.7454i	0.716889	−	0.990252i
$576$		0			0
$577$	1.98215	+	1.98215i	0.0825181	+	0.0825181i	0.747161	−	0.664643i	$-0.231416\pi$
$577$	1.98215	+	1.98215i	0.0825181	+	0.0825181i	−0.664643	+	0.747161i	$0.731416\pi$
$578$		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
$587$	26.9680			1.11309			0.556544	−	0.830818i	$-0.312127\pi$
$587$	26.9680			1.11309			0.556544	+	0.830818i	$0.312127\pi$
$588$		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	−0.276464	−	0.961024i	$-0.589163\pi$
$593$	16.6701	−	16.6701i	0.684560	−	0.684560i	0.961024	+	0.276464i	$0.0891626\pi$
$594$		0			0
$595$	−0.153767	+	0.0122334i	−0.00630383	+	0.000501520i
$596$		0			0
$597$		−	29.1771i		−	1.19414i
$598$		0			0
$599$			28.8376i			1.17827i	0.808033	+	0.589137i	$0.200532\pi$
$599$			28.8376i			1.17827i	−0.808033	+	0.589137i	$0.799468\pi$
$600$		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
$603$			14.4487i			0.588397i
$604$		0			0
$605$	14.5315	−	1.15609i	0.590789	−	0.0470019i
$606$		0			0
$607$	7.89049	−	7.89049i	0.320265	−	0.320265i	−0.528604	−	0.848869i	$-0.677284\pi$
$607$	7.89049	−	7.89049i	0.320265	−	0.320265i	0.848869	+	0.528604i	$0.177284\pi$
$608$		0			0
$609$			0.197745i			0.00801303i
$610$		0			0
$611$	−6.83071	−	6.83071i	−0.276341	−	0.276341i
$612$		0			0
$613$	40.1035			1.61976			0.809882	−	0.586592i	$-0.199531\pi$
$613$	40.1035			1.61976			0.809882	+	0.586592i	$0.199531\pi$
$614$		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	$-0.613744\pi$
$617$	14.5821	−	14.5821i	0.587052	−	0.587052i	0.936832	+	0.349780i	$0.113744\pi$
$618$		0			0
$619$	−4.01752	−	4.01752i	−0.161478	−	0.161478i	0.621743	−	0.783221i	$-0.286425\pi$
$619$	−4.01752	−	4.01752i	−0.161478	−	0.161478i	−0.783221	+	0.621743i	$0.786425\pi$
$620$		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
$627$		−	39.7189i		−	1.58622i
$628$		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
$635$	29.5395	+	25.1856i	1.17224	+	0.999462i
$636$		0			0
$637$	10.8662			0.430536
$638$		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
$643$	29.6249			1.16829			0.584146	−	0.811648i	$-0.301429\pi$
$643$	29.6249			1.16829			0.584146	+	0.811648i	$0.301429\pi$
$644$		0			0
$645$	44.4651	−	3.53755i	1.75081	−	0.139291i
$646$		0			0
$647$	5.04426	+	5.04426i	0.198310	+	0.198310i	0.799275	−	0.600965i	$-0.205217\pi$
$647$	5.04426	+	5.04426i	0.198310	+	0.198310i	−0.600965	+	0.799275i	$0.705217\pi$
$648$		0			0
$649$	9.67794			0.379893
$650$		0			0
$651$	1.42855	−	1.42855i	0.0559895	−	0.0559895i
$652$		0			0
$653$			3.04934i			0.119330i	0.998218	+	0.0596649i	$0.0190032\pi$
$653$			3.04934i			0.119330i	−0.998218	+	0.0596649i	$0.980997\pi$
$654$		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	−0.132469	−	0.991187i	$-0.542291\pi$
$659$	22.0441	−	22.0441i	0.858718	−	0.858718i	0.991187	+	0.132469i	$0.0422906\pi$
$660$		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
$667$	2.40167			0.0929931
$668$		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	−0.0487786	+	0.998810i	$0.515533\pi$
$673$	−27.1768	+	27.1768i	−1.04759	+	1.04759i	−0.998810	+	0.0487786i	$0.984467\pi$
$674$		0			0
$675$	40.9210	−	6.55265i	1.57505	−	0.252212i
$676$		0			0
$677$		−	28.6501i		−	1.10111i	−0.834798	−	0.550557i	$-0.814415\pi$
$677$		−	28.6501i		−	1.10111i	0.834798	−	0.550557i	$-0.185585\pi$
$678$		0			0
$679$			2.23115i			0.0856238i
$680$		0			0
$681$			68.8334i			2.63770i
$682$		0			0
$683$		−	30.8472i		−	1.18034i	−0.807281	−	0.590168i	$-0.799062\pi$
$683$		−	30.8472i		−	1.18034i	0.807281	−	0.590168i	$-0.200938\pi$
$684$		0			0
$685$	−7.42485	−	6.33051i	−0.283689	−	0.241876i
$686$		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
$693$	3.94815			0.149978
$694$		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
$707$			2.94813i			0.110876i
$708$		0			0
$709$	−1.58968	+	1.58968i	−0.0597015	+	0.0597015i	−0.736327	−	0.676626i	$-0.763442\pi$
$709$	−1.58968	+	1.58968i	−0.0597015	+	0.0597015i	0.676626	+	0.736327i	$0.263442\pi$
$710$		0			0
$711$	−20.9900			−0.787186
$712$		0			0
$713$	−17.3502	−	17.3502i	−0.649771	−	0.649771i
$714$		0			0
$715$	−9.46198	+	11.0977i	−0.353858	+	0.415029i
$716$		0			0
$717$	−0.00411819			−0.000153797
$718$		0			0
$719$	22.8919			0.853722			0.426861	−	0.904317i	$-0.359619\pi$
$719$	22.8919			0.853722			0.426861	+	0.904317i	$0.359619\pi$
$720$		0			0
$721$	0.998472			0.0371850
$722$		0			0
$723$	38.1313			1.41812
$724$		0			0
$725$	1.65906	+	1.20107i	0.0616158	+	0.0446065i
$726$		0			0
$727$	−20.1893	−	20.1893i	−0.748780	−	0.748780i	0.225470	−	0.974250i	$-0.427608\pi$
$727$	−20.1893	−	20.1893i	−0.748780	−	0.748780i	−0.974250	+	0.225470i	$0.927608\pi$
$728$		0			0
$729$	−32.0425			−1.18676
$730$		0			0
$731$	−2.01572	+	2.01572i	−0.0745540	+	0.0745540i
$732$		0			0
$733$		−	14.3253i		−	0.529118i	−0.964370	−	0.264559i	$-0.914774\pi$
$733$		−	14.3253i		−	0.529118i	0.964370	−	0.264559i	$-0.0852263\pi$
$734$		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	$0.568156\pi$
$739$	−32.3401	+	32.3401i	−1.18965	+	1.18965i	−0.977164	+	0.212487i	$0.931844\pi$
$740$		0			0
$741$	10.4557	+	10.4557i	0.384100	+	0.384100i
$742$		0			0
$743$	6.06842	−	6.06842i	0.222629	−	0.222629i	−0.586976	−	0.809605i	$-0.699682\pi$
$743$	6.06842	−	6.06842i	0.222629	−	0.222629i	0.809605	+	0.586976i	$0.199682\pi$
$744$		0			0
$745$	−6.23662	−	5.31741i	−0.228492	−	0.194815i
$746$		0			0
$747$	9.42414			0.344811
$748$		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
$755$	3.00752	+	37.8029i	0.109455	+	1.37579i
$756$		0			0
$757$			9.18443i			0.333814i	0.985973	+	0.166907i	$0.0533779\pi$
$757$			9.18443i			0.333814i	−0.985973	+	0.166907i	$0.946622\pi$
$758$		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
$763$		−	0.924267i		−	0.0334607i
$764$		0			0
$765$	−3.56282	+	4.17872i	−0.128814	+	0.151082i
$766$		0			0
$767$	−2.54765	+	2.54765i	−0.0919902	+	0.0919902i
$768$		0			0
$769$			19.4153i			0.700135i	0.936724	+	0.350067i	$0.113841\pi$
$769$			19.4153i			0.700135i	−0.936724	+	0.350067i	$0.886159\pi$
$770$		0			0
$771$	−63.0884	−	63.0884i	−2.27207	−	2.27207i
$772$		0			0
$773$	−26.0890			−0.938356			−0.469178	−	0.883104i	$-0.655450\pi$
$773$	−26.0890			−0.938356			−0.469178	+	0.883104i	$0.655450\pi$
$774$		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
$787$		−	14.2339i		−	0.507384i	−0.967285	−	0.253692i	$-0.918355\pi$
$787$		−	14.2339i		−	0.507384i	0.967285	−	0.253692i	$-0.0816449\pi$
$788$		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
$795$	6.01244	+	75.5732i	0.213239	+	2.68030i
$796$		0			0
$797$	−19.8283			−0.702353			−0.351176	−	0.936309i	$-0.614218\pi$
$797$	−19.8283			−0.702353			−0.351176	+	0.936309i	$0.614218\pi$
$798$		0			0
$799$	−2.62729			−0.0929467
$800$		0			0
$801$	−91.0655			−3.21764
$802$		0			0
$803$	−6.63568			−0.234168
$804$		0			0
$805$	−0.169242	−	2.12728i	−0.00596499	−	0.0749767i
$806$		0			0
$807$	47.1817	+	47.1817i	1.66088	+	1.66088i
$808$		0			0
$809$	21.3864			0.751907			0.375954	−	0.926639i	$-0.377315\pi$
$809$	21.3864			0.751907			0.375954	+	0.926639i	$0.377315\pi$
$810$		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
$813$			36.6553i			1.28556i
$814$		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	−0.787316	−	0.616550i	$-0.788530\pi$
$823$	−4.89892	+	4.89892i	−0.170766	+	0.170766i	0.616550	+	0.787316i	$0.288530\pi$
$824$		0			0
$825$	36.3950	−	50.2731i	1.26711	−	1.75028i
$826$		0			0
$827$	1.05434			0.0366630			0.0183315	−	0.999832i	$-0.494165\pi$
$827$	1.05434			0.0366630			0.0183315	+	0.999832i	$0.494165\pi$
$828$		0			0
$829$	−11.7754	−	11.7754i	−0.408978	−	0.408978i	0.472404	−	0.881382i	$-0.343386\pi$
$829$	−11.7754	−	11.7754i	−0.408978	−	0.408978i	−0.881382	+	0.472404i	$0.843386\pi$
$830$		0			0
$831$			62.3580i			2.16317i
$832$		0			0
$833$	2.08973	−	2.08973i	0.0724050	−	0.0724050i
$834$		0			0
$835$	0.990707	−	1.16197i	0.0342848	−	0.0402116i
$836$		0			0
$837$		−	34.6879i		−	1.19899i
$838$		0			0
$839$			41.1678i			1.42127i	0.703560	+	0.710636i	$0.251593\pi$
$839$			41.1678i			1.42127i	−0.703560	+	0.710636i	$0.748407\pi$
$840$		0			0
$841$		−	28.8322i		−	0.994214i
$842$		0			0
$843$		−	31.6749i		−	1.09094i
$844$		0			0
$845$	1.87479	+	23.5651i	0.0644948	+	0.810666i
$846$		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
$853$	−11.7179			−0.401212			−0.200606	−	0.979672i	$-0.564291\pi$
$853$	−11.7179			−0.401212			−0.200606	+	0.979672i	$0.564291\pi$
$854$		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	$-0.845338\pi$
$857$	−12.2154	+	12.2154i	−0.417270	+	0.417270i	0.466992	+	0.884262i	$0.345338\pi$
$858$		0			0
$859$	17.2170	+	17.2170i	0.587436	+	0.587436i	0.936936	−	0.349500i	$-0.113649\pi$
$859$	17.2170	+	17.2170i	0.587436	+	0.587436i	−0.349500	+	0.936936i	$0.613649\pi$
$860$		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	$-0.163169\pi$
$863$	11.1929	+	11.1929i	0.381011	+	0.381011i	−0.490455	+	0.871466i	$0.663169\pi$
$864$		0			0
$865$	−26.3447	+	2.09593i	−0.895746	+	0.0712637i
$866$		0			0
$867$			49.8828i			1.69411i
$868$		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
$875$	0.946933	−	1.55415i	0.0320122	−	0.0525397i
$876$		0			0
$877$	−43.1739			−1.45788			−0.728940	−	0.684578i	$-0.759987\pi$
$877$	−43.1739			−1.45788			−0.728940	+	0.684578i	$0.759987\pi$
$878$		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
$883$	2.00362			0.0674270			0.0337135	−	0.999432i	$-0.489267\pi$
$883$	2.00362			0.0674270			0.0337135	+	0.999432i	$0.489267\pi$
$884$		0			0
$885$	9.94802	−	11.6677i	0.334399	−	0.392206i
$886$		0			0
$887$	16.1765	+	16.1765i	0.543154	+	0.543154i	0.924452	−	0.381298i	$-0.124523\pi$
$887$	16.1765	+	16.1765i	0.543154	+	0.543154i	−0.381298	+	0.924452i	$0.624523\pi$
$888$		0			0
$889$	2.82586			0.0947762
$890$		0			0
$891$	21.2971	−	21.2971i	0.713480	−	0.713480i
$892$		0			0
$893$		−	19.8371i		−	0.663822i
$894$		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
$907$	−29.7116			−0.986559			−0.493279	−	0.869871i	$-0.664202\pi$
$907$	−29.7116			−0.986559			−0.493279	+	0.869871i	$0.664202\pi$
$908$		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
$915$	−8.78009	−	7.48599i	−0.290261	−	0.247479i
$916$		0			0
$917$			1.84061i			0.0607821i
$918$		0			0
$919$			40.1278i			1.32369i	0.749639	+	0.661847i	$0.230227\pi$
$919$			40.1278i			1.32369i	−0.749639	+	0.661847i	$0.769773\pi$
$920$		0			0
$921$			35.0250i			1.15411i
$922$		0			0
$923$		−	12.4673i		−	0.410365i
$924$		0			0
$925$	1.29372	+	8.07922i	0.0425372	+	0.265643i
$926$		0			0
$927$	25.1345	−	25.1345i	0.825525	−	0.825525i
$928$		0			0
$929$			27.7519i			0.910512i	0.890361	+	0.455256i	$0.150452\pi$
$929$			27.7519i			0.910512i	−0.890361	+	0.455256i	$0.849548\pi$
$930$		0			0
$931$	15.7783	+	15.7783i	0.517114	+	0.517114i
$932$		0			0
$933$	67.1004			2.19677
$934$		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	$-0.880706\pi$
$937$	−17.2805	+	17.2805i	−0.564531	+	0.564531i	0.366060	+	0.930591i	$0.380706\pi$
$938$		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
$947$			3.37347i			0.109623i	0.998497	+	0.0548115i	$0.0174558\pi$
$947$			3.37347i			0.109623i	−0.998497	+	0.0548115i	$0.982544\pi$
$948$		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	$-0.143266\pi$
$953$	14.3663	+	14.3663i	0.465369	+	0.465369i	−0.435041	+	0.900410i	$0.643266\pi$
$954$		0			0
$955$	−31.1778	+	2.48044i	−1.00889	+	0.0802652i
$956$		0			0
$957$	5.08475			0.164366
$958$		0			0
$959$	−0.710289			−0.0229364
$960$		0			0
$961$	13.4851			0.435003
$962$		0			0
$963$	−69.4263			−2.23723
$964$		0			0
$965$	9.35775	+	7.97851i	0.301236	+	0.256837i
$966$		0			0
$967$	11.8576	+	11.8576i	0.381315	+	0.381315i	0.871576	−	0.490260i	$-0.163098\pi$
$967$	11.8576	+	11.8576i	0.381315	+	0.381315i	−0.490260	+	0.871576i	$0.663098\pi$
$968$		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
$973$			2.81319i			0.0901869i
$974$		0			0
$975$	3.65330	+	22.8147i	0.116999	+	0.730656i
$976$		0			0
$977$	12.9249	+	12.9249i	0.413504	+	0.413504i	0.882957	−	0.469454i	$-0.155549\pi$
$977$	12.9249	+	12.9249i	0.413504	+	0.413504i	−0.469454	+	0.882957i	$0.655549\pi$
$978$		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	−0.704977	−	0.709230i	$-0.749043\pi$
$983$	0.133323	−	0.133323i	0.00425235	−	0.00425235i	0.709230	+	0.704977i	$0.249043\pi$
$984$		0			0
$985$	−49.7690	+	3.95951i	−1.58577	+	0.126161i
$986$		0			0
$987$	2.99268			0.0952580
$988$		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
$995$	−21.9302	+	1.74472i	−0.695234	+	0.0553114i
$996$		0			0
$997$			54.9379i			1.73990i	0.493138	+	0.869951i	$0.335850\pi$
$997$			54.9379i			1.73990i	−0.493138	+	0.869951i	$0.664150\pi$
$998$		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.s.c.287.1		18
4.3	odd	2		640.2.s.d.287.9		18
5.3	odd	4		640.2.j.c.543.1		18
8.3	odd	2		80.2.s.b.27.5	yes	18
8.5	even	2		320.2.s.b.207.9		18
16.3	odd	4		640.2.j.c.607.9		18
16.5	even	4		80.2.j.b.67.1	yes	18
16.11	odd	4		320.2.j.b.47.1		18
16.13	even	4		640.2.j.d.607.1		18
20.3	even	4		640.2.j.d.543.9		18
24.11	even	2		720.2.z.g.667.5		18
40.3	even	4		80.2.j.b.43.1	✓	18
40.13	odd	4		320.2.j.b.143.9		18
40.19	odd	2		400.2.s.d.107.5		18
40.27	even	4		400.2.j.d.43.9		18
40.29	even	2		1600.2.s.d.207.1		18
40.37	odd	4		1600.2.j.d.143.1		18
48.5	odd	4		720.2.bd.g.307.9		18
80.3	even	4	inner	640.2.s.c.223.1		18
80.13	odd	4		640.2.s.d.223.9		18
80.27	even	4		1600.2.s.d.943.1		18
80.37	odd	4		400.2.s.d.243.5		18
80.43	even	4		320.2.s.b.303.9		18
80.53	odd	4		80.2.s.b.3.5	yes	18
80.59	odd	4		1600.2.j.d.1007.9		18
80.69	even	4		400.2.j.d.307.9		18
120.83	odd	4		720.2.bd.g.523.9		18
240.53	even	4		720.2.z.g.163.5		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.1	✓	18	40.3	even	4
80.2.j.b.67.1	yes	18	16.5	even	4
80.2.s.b.3.5	yes	18	80.53	odd	4
80.2.s.b.27.5	yes	18	8.3	odd	2
320.2.j.b.47.1		18	16.11	odd	4
320.2.j.b.143.9		18	40.13	odd	4
320.2.s.b.207.9		18	8.5	even	2
320.2.s.b.303.9		18	80.43	even	4
400.2.j.d.43.9		18	40.27	even	4
400.2.j.d.307.9		18	80.69	even	4
400.2.s.d.107.5		18	40.19	odd	2
400.2.s.d.243.5		18	80.37	odd	4
640.2.j.c.543.1		18	5.3	odd	4
640.2.j.c.607.9		18	16.3	odd	4
640.2.j.d.543.9		18	20.3	even	4
640.2.j.d.607.1		18	16.13	even	4
640.2.s.c.223.1		18	80.3	even	4	inner
640.2.s.c.287.1		18	1.1	even	1	trivial
640.2.s.d.223.9		18	80.13	odd	4
640.2.s.d.287.9		18	4.3	odd	2
720.2.z.g.163.5		18	240.53	even	4
720.2.z.g.667.5		18	24.11	even	2
720.2.bd.g.307.9		18	48.5	odd	4
720.2.bd.g.523.9		18	120.83	odd	4
1600.2.j.d.143.1		18	40.37	odd	4
1600.2.j.d.1007.9		18	80.59	odd	4
1600.2.s.d.207.1		18	40.29	even	2
1600.2.s.d.943.1		18	80.27	even	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.s (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.96561 q^{3} +(0.177336 + 2.22902i) q^{5} +(0.115101 + 0.115101i) q^{7} +5.79486 q^{9} +O(q^{10})\)	\(q-2.96561 q^{3} +(0.177336 + 2.22902i) q^{5} +(0.115101 + 0.115101i) q^{7} +5.79486 q^{9} +(2.95966 - 2.95966i) q^{11} +1.55822i q^{13} +(-0.525911 - 6.61042i) q^{15} +(0.299668 + 0.299668i) q^{17} +(-2.26261 + 2.26261i) q^{19} +(-0.341344 - 0.341344i) q^{21} +(-4.14573 + 4.14573i) q^{23} +(-4.93710 + 0.790575i) q^{25} -8.28846 q^{27} +(-0.289656 - 0.289656i) q^{29} +4.18508i q^{31} +(-8.77721 + 8.77721i) q^{33} +(-0.236151 + 0.276974i) q^{35} -1.63643i q^{37} -4.62107i q^{39} +7.61648i q^{41} +6.72651i q^{43} +(1.02764 + 12.9169i) q^{45} +(-4.38366 + 4.38366i) q^{47} -6.97350i q^{49} +(-0.888698 - 0.888698i) q^{51} -11.4324 q^{53} +(7.12202 + 6.07231i) q^{55} +(6.71003 - 6.71003i) q^{57} +(1.63497 + 1.63497i) q^{59} +(1.23034 - 1.23034i) q^{61} +(0.666993 + 0.666993i) q^{63} +(-3.47331 + 0.276329i) q^{65} +2.49337i q^{67} +(12.2946 - 12.2946i) q^{69} -8.00096 q^{71} +(-1.12102 - 1.12102i) q^{73} +(14.6415 - 2.34454i) q^{75} +0.681319 q^{77} -3.62218 q^{79} +7.19579 q^{81} +1.62629 q^{83} +(-0.614825 + 0.721109i) q^{85} +(0.859007 + 0.859007i) q^{87} -15.7149 q^{89} +(-0.179352 + 0.179352i) q^{91} -12.4113i q^{93} +(-5.44467 - 4.64218i) q^{95} +(9.69217 + 9.69217i) q^{97} +(17.1508 - 17.1508i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{5} - 2 q^{7} + 10 q^{9}+O(q^{10}) \) 18 * q - 2 * q^5 - 2 * q^7 + 10 * q^9	\( 18 q - 2 q^{5} - 2 q^{7} + 10 q^{9} - 2 q^{11} + 20 q^{15} - 6 q^{17} - 2 q^{19} + 16 q^{21} + 2 q^{23} - 6 q^{25} - 24 q^{27} - 14 q^{29} - 8 q^{33} + 2 q^{35} + 14 q^{45} - 38 q^{47} + 8 q^{51} - 12 q^{53} + 6 q^{55} - 24 q^{57} + 10 q^{59} - 14 q^{61} + 6 q^{63} + 32 q^{69} - 24 q^{71} - 14 q^{73} + 16 q^{75} + 44 q^{77} + 16 q^{79} + 2 q^{81} + 40 q^{83} - 14 q^{85} - 24 q^{87} + 12 q^{89} - 34 q^{95} + 18 q^{97} + 22 q^{99}+O(q^{100}) \) 18 * q - 2 * 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 - 24 * q^27 - 14 * q^29 - 8 * q^33 + 2 * q^35 + 14 * q^45 - 38 * q^47 + 8 * q^51 - 12 * q^53 + 6 * q^55 - 24 * q^57 + 10 * q^59 - 14 * q^61 + 6 * q^63 + 32 * q^69 - 24 * q^71 - 14 * q^73 + 16 * q^75 + 44 * q^77 + 16 * q^79 + 2 * q^81 + 40 * q^83 - 14 * q^85 - 24 * q^87 + 12 * q^89 - 34 * q^95 + 18 * q^97 + 22 * q^99

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