LMFDB - Embedded newform 1024.2.g.c.641.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1024,2,Mod(129,1024)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1024, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("1024.129");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1024 = 2^{10} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1024.g (of order $8$, degree $4$, 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:	$8.17668116698$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{8})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8x^{14} + 32x^{12} - 64x^{10} + 127x^{8} - 576x^{6} + 2592x^{4} - 5832x^{2} + 6561 $ x^16 - 8x^14 + 32x^12 - 64x^10 + 127x^8 - 576x^6 + 2592x^4 - 5832*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			641.2
Root			$-1.50947 + 0.849413i$ of defining polynomial
Character	$\chi$	$=$	1024.641
Dual form			1024.2.g.c.385.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.59352 - 0.660056i) q^{3} +(0.212292 + 0.512517i) q^{5} +(-1.69883 + 1.69883i) q^{7} +(-0.0177021 - 0.0177021i) q^{9} +O(q^{10})$	\(q+(-1.59352 - 0.660056i) q^{3} +(0.212292 + 0.512517i) q^{5} +(-1.69883 + 1.69883i) q^{7} +(-0.0177021 - 0.0177021i) q^{9} +(-3.44127 + 1.42542i) q^{11} +(2.34094 - 5.65154i) q^{13} -0.956828i q^{15} +5.26768i q^{17} +(1.57436 - 3.80083i) q^{19} +(3.82843 - 1.58579i) q^{21} +(4.31195 + 4.31195i) q^{23} +(3.31793 - 3.31793i) q^{25} +(1.99669 + 4.82044i) q^{27} +(-1.23733 - 0.512517i) q^{29} +1.53073 q^{31} +6.42458 q^{33} +(-1.23132 - 0.510031i) q^{35} +(-1.49785 - 3.61614i) q^{37} +(-7.46066 + 7.46066i) q^{39} +(8.69226 + 8.69226i) q^{41} +(0.511123 - 0.211714i) q^{43} +(0.00531461 - 0.0128306i) q^{45} -9.73339i q^{47} +1.22798i q^{49} +(3.47696 - 8.39412i) q^{51} +(6.73012 - 2.78771i) q^{53} +(-1.46111 - 1.46111i) q^{55} +(-5.01752 + 5.01752i) q^{57} +(1.14517 + 2.76469i) q^{59} +(7.40138 + 3.06575i) q^{61} +0.0601454 q^{63} +3.39347 q^{65} +(5.33529 + 2.20995i) q^{67} +(-4.02503 - 9.71729i) q^{69} +(9.45315 - 9.45315i) q^{71} +(1.69977 + 1.69977i) q^{73} +(-7.47719 + 3.09715i) q^{75} +(3.42458 - 8.26768i) q^{77} -12.8332i q^{79} -8.92427i q^{81} +(-0.360647 + 0.870678i) q^{83} +(-2.69977 + 1.11828i) q^{85} +(1.63341 + 1.63341i) q^{87} +(1.14939 - 1.14939i) q^{89} +(5.62413 + 13.5778i) q^{91} +(-2.43925 - 1.01037i) q^{93} +2.28221 q^{95} -1.83880 q^{97} +(0.0861505 + 0.0356847i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{5} + 16 q^{9}+O(q^{10}) $ 16 * q - 8 * q^5 + 16 * q^9	$ 16 q - 8 q^{5} + 16 q^{9} - 24 q^{13} + 16 q^{21} + 32 q^{25} + 24 q^{29} + 80 q^{33} - 40 q^{37} + 16 q^{41} - 24 q^{45} + 56 q^{53} + 80 q^{57} - 8 q^{61} + 32 q^{65} - 32 q^{69} + 32 q^{73} + 32 q^{77} - 48 q^{85} - 32 q^{89} + 16 q^{93} + 16 q^{97}+O(q^{100}) $ 16 * q - 8 * q^5 + 16 * q^9 - 24 * q^13 + 16 * q^21 + 32 * q^25 + 24 * q^29 + 80 * q^33 - 40 * q^37 + 16 * q^41 - 24 * q^45 + 56 * q^53 + 80 * q^57 - 8 * q^61 + 32 * q^65 - 32 * q^69 + 32 * q^73 + 32 * q^77 - 48 * q^85 - 32 * q^89 + 16 * q^93 + 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1024\mathbb{Z}\right)^\times$.

$n$	$5$	$1023$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$1$

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
$3$	−1.59352	−	0.660056i	−0.920017	−	0.381083i	−0.128134	−	0.991757i	$-0.540899\pi$
$3$	−1.59352	−	0.660056i	−0.920017	−	0.381083i	−0.791883	+	0.610673i	$0.790899\pi$
$4$		0			0
$5$	0.212292	+	0.512517i	0.0949397	+	0.229205i	0.964214	−	0.265125i	$-0.0854134\pi$
$5$	0.212292	+	0.512517i	0.0949397	+	0.229205i	−0.869274	+	0.494330i	$0.835413\pi$
$6$		0			0
$7$	−1.69883	+	1.69883i	−0.642096	+	0.642096i	−0.951070	−	0.308974i	$-0.900014\pi$
$7$	−1.69883	+	1.69883i	−0.642096	+	0.642096i	0.308974	+	0.951070i	$0.400014\pi$
$8$		0			0
$9$	−0.0177021	−	0.0177021i	−0.00590068	−	0.00590068i
$10$		0			0
$11$	−3.44127	+	1.42542i	−1.03758	+	0.429781i	−0.835444	−	0.549576i	$-0.814789\pi$
$11$	−3.44127	+	1.42542i	−1.03758	+	0.429781i	−0.202139	+	0.979357i	$0.564789\pi$
$12$		0			0
$13$	2.34094	−	5.65154i	0.649261	−	1.56746i	−0.164577	−	0.986364i	$-0.552626\pi$
$13$	2.34094	−	5.65154i	0.649261	−	1.56746i	0.813839	−	0.581091i	$-0.197374\pi$
$14$		0			0
$15$		−	0.956828i		−	0.247052i
$16$		0			0
$17$			5.26768i			1.27760i	0.769373	+	0.638799i	$0.220569\pi$
$17$			5.26768i			1.27760i	−0.769373	+	0.638799i	$0.779431\pi$
$18$		0			0
$19$	1.57436	−	3.80083i	0.361182	−	0.871970i	−0.633946	−	0.773377i	$-0.718566\pi$
$19$	1.57436	−	3.80083i	0.361182	−	0.871970i	0.995128	−	0.0985928i	$-0.0314341\pi$
$20$		0			0
$21$	3.82843	−	1.58579i	0.835431	−	0.346047i
$22$		0			0
$23$	4.31195	+	4.31195i	0.899104	+	0.899104i	0.995357	−	0.0962527i	$-0.0306857\pi$
$23$	4.31195	+	4.31195i	0.899104	+	0.899104i	−0.0962527	+	0.995357i	$0.530686\pi$
$24$		0			0
$25$	3.31793	−	3.31793i	0.663586	−	0.663586i
$26$		0			0
$27$	1.99669	+	4.82044i	0.384263	+	0.927694i
$28$		0			0
$29$	−1.23733	−	0.512517i	−0.229766	−	0.0951721i	0.264830	−	0.964295i	$-0.414684\pi$
$29$	−1.23733	−	0.512517i	−0.229766	−	0.0951721i	−0.494596	+	0.869123i	$0.664684\pi$
$30$		0			0
$31$	1.53073			0.274928			0.137464	−	0.990507i	$-0.456105\pi$
$31$	1.53073			0.274928			0.137464	+	0.990507i	$0.456105\pi$
$32$		0			0
$33$	6.42458			1.11838
$34$		0			0
$35$	−1.23132	−	0.510031i	−0.208132	−	0.0862110i
$36$		0			0
$37$	−1.49785	−	3.61614i	−0.246245	−	0.594489i	0.751634	−	0.659581i	$-0.229266\pi$
$37$	−1.49785	−	3.61614i	−0.246245	−	0.594489i	−0.997879	+	0.0650915i	$0.979266\pi$
$38$		0			0
$39$	−7.46066	+	7.46066i	−1.19466	+	1.19466i
$40$		0			0
$41$	8.69226	+	8.69226i	1.35750	+	1.35750i	0.876985	+	0.480518i	$0.159551\pi$
$41$	8.69226	+	8.69226i	1.35750	+	1.35750i	0.480518	+	0.876985i	$0.340449\pi$
$42$		0			0
$43$	0.511123	−	0.211714i	0.0779456	−	0.0322861i	−0.343370	−	0.939200i	$-0.611568\pi$
$43$	0.511123	−	0.211714i	0.0779456	−	0.0322861i	0.421316	+	0.906914i	$0.361568\pi$
$44$		0			0
$45$	0.00531461	−	0.0128306i	0.000792255	−	0.00191267i
$46$		0			0
$47$		−	9.73339i		−	1.41976i	−0.704322	−	0.709881i	$-0.748749\pi$
$47$		−	9.73339i		−	1.41976i	0.704322	−	0.709881i	$-0.251251\pi$
$48$		0			0
$49$			1.22798i			0.175425i
$50$		0			0
$51$	3.47696	−	8.39412i	0.486872	−	1.17541i
$52$		0			0
$53$	6.73012	−	2.78771i	0.924454	−	0.382921i	0.130882	−	0.991398i	$-0.458219\pi$
$53$	6.73012	−	2.78771i	0.924454	−	0.382921i	0.793572	+	0.608477i	$0.208219\pi$
$54$		0			0
$55$	−1.46111	−	1.46111i	−0.197016	−	0.197016i
$56$		0			0
$57$	−5.01752	+	5.01752i	−0.664587	+	0.664587i
$58$		0			0
$59$	1.14517	+	2.76469i	0.149089	+	0.359933i	0.980726	−	0.195387i	$-0.0625961\pi$
$59$	1.14517	+	2.76469i	0.149089	+	0.359933i	−0.831637	+	0.555319i	$0.812596\pi$
$60$		0			0
$61$	7.40138	+	3.06575i	0.947650	+	0.392529i	0.802347	−	0.596858i	$-0.203584\pi$
$61$	7.40138	+	3.06575i	0.947650	+	0.392529i	0.145303	+	0.989387i	$0.453584\pi$
$62$		0			0
$63$	0.0601454			0.00757761
$64$		0			0
$65$	3.39347			0.420909
$66$		0			0
$67$	5.33529	+	2.20995i	0.651810	+	0.269988i	0.683987	−	0.729494i	$-0.260244\pi$
$67$	5.33529	+	2.20995i	0.651810	+	0.269988i	−0.0321778	+	0.999482i	$0.510244\pi$
$68$		0			0
$69$	−4.02503	−	9.71729i	−0.484557	−	1.16982i
$70$		0			0
$71$	9.45315	−	9.45315i	1.12188	−	1.12188i	0.130424	−	0.991458i	$-0.458366\pi$
$71$	9.45315	−	9.45315i	1.12188	−	1.12188i	0.991458	−	0.130424i	$-0.0416338\pi$
$72$		0			0
$73$	1.69977	+	1.69977i	0.198944	+	0.198944i	0.799547	−	0.600603i	$-0.205073\pi$
$73$	1.69977	+	1.69977i	0.198944	+	0.198944i	−0.600603	+	0.799547i	$0.705073\pi$
$74$		0			0
$75$	−7.47719	+	3.09715i	−0.863391	+	0.357628i
$76$		0			0
$77$	3.42458	−	8.26768i	0.390267	−	0.942189i
$78$		0			0
$79$		−	12.8332i		−	1.44385i	−0.691973	−	0.721923i	$-0.743258\pi$
$79$		−	12.8332i		−	1.44385i	0.691973	−	0.721923i	$-0.256742\pi$
$80$		0			0
$81$		−	8.92427i		−	0.991586i
$82$		0			0
$83$	−0.360647	+	0.870678i	−0.0395861	+	0.0955693i	−0.942436	−	0.334387i	$-0.891471\pi$
$83$	−0.360647	+	0.870678i	−0.0395861	+	0.0955693i	0.902850	+	0.429956i	$0.141471\pi$
$84$		0			0
$85$	−2.69977	+	1.11828i	−0.292832	+	0.121295i
$86$		0			0
$87$	1.63341	+	1.63341i	0.175120	+	0.175120i
$88$		0			0
$89$	1.14939	−	1.14939i	0.121835	−	0.121835i	−0.643560	−	0.765396i	$-0.722543\pi$
$89$	1.14939	−	1.14939i	0.121835	−	0.121835i	0.765396	+	0.643560i	$0.222543\pi$
$90$		0			0
$91$	5.62413	+	13.5778i	0.589569	+	1.42334i
$92$		0			0
$93$	−2.43925	−	1.01037i	−0.252938	−	0.104770i
$94$		0			0
$95$	2.28221			0.234150
$96$		0			0
$97$	−1.83880			−0.186702			−0.0933508	−	0.995633i	$-0.529758\pi$
$97$	−1.83880			−0.186702			−0.0933508	+	0.995633i	$0.529758\pi$
$98$		0			0
$99$	0.0861505	+	0.0356847i	0.00865845	+	0.00358645i
$100$		0			0
$101$	0.730123	+	1.76267i	0.0726500	+	0.175393i	0.956033	−	0.293259i	$-0.0947399\pi$
$101$	0.730123	+	1.76267i	0.0726500	+	0.175393i	−0.883383	+	0.468652i	$0.844740\pi$
$102$		0			0
$103$	−5.36725	+	5.36725i	−0.528851	+	0.528851i	−0.920230	−	0.391379i	$-0.871998\pi$
$103$	−5.36725	+	5.36725i	−0.528851	+	0.528851i	0.391379	+	0.920230i	$0.371998\pi$
$104$		0			0
$105$	1.62549	+	1.62549i	0.158631	+	0.158631i
$106$		0			0
$107$	17.3787	−	7.19848i	1.68006	−	0.695904i	0.680731	−	0.732534i	$-0.261662\pi$
$107$	17.3787	−	7.19848i	1.68006	−	0.695904i	0.999329	+	0.0366299i	$0.0116623\pi$
$108$		0			0
$109$	−2.61614	+	6.31591i	−0.250580	+	0.604954i	−0.998251	−	0.0591151i	$-0.981172\pi$
$109$	−2.61614	+	6.31591i	−0.250580	+	0.604954i	0.747671	+	0.664070i	$0.231172\pi$
$110$		0			0
$111$			6.75103i			0.640780i
$112$		0			0
$113$			6.60045i			0.620918i	0.950587	+	0.310459i	$0.100483\pi$
$113$			6.60045i			0.620918i	−0.950587	+	0.310459i	$0.899517\pi$
$114$		0			0
$115$	−1.29456	+	3.12534i	−0.120718	+	0.291440i
$116$		0			0
$117$	−0.141483	+	0.0586043i	−0.0130801	+	0.00541797i
$118$		0			0
$119$	−8.94887	−	8.94887i	−0.820341	−	0.820341i
$120$		0			0
$121$	2.03237	−	2.03237i	0.184761	−	0.184761i
$122$		0			0
$123$	−8.11387	−	19.5886i	−0.731603	−	1.76625i
$124$		0			0
$125$	4.96745	+	2.05758i	0.444302	+	0.184036i
$126$		0			0
$127$	4.36789			0.387588			0.193794	−	0.981042i	$-0.437921\pi$
$127$	4.36789			0.387588			0.193794	+	0.981042i	$0.437921\pi$
$128$		0			0
$129$	−0.954226			−0.0840149
$130$		0			0
$131$	−6.29212	−	2.60628i	−0.549745	−	0.227712i	0.0904813	−	0.995898i	$-0.471159\pi$
$131$	−6.29212	−	2.60628i	−0.549745	−	0.227712i	−0.640226	+	0.768186i	$0.721159\pi$
$132$		0			0
$133$	3.78239	+	9.13151i	0.327975	+	0.791802i
$134$		0			0
$135$	−2.04668	+	2.04668i	−0.176150	+	0.176150i
$136$		0			0
$137$	−5.47465	−	5.47465i	−0.467731	−	0.467731i	0.433448	−	0.901179i	$-0.357297\pi$
$137$	−5.47465	−	5.47465i	−0.467731	−	0.467731i	−0.901179	+	0.433448i	$0.857297\pi$
$138$		0			0
$139$	−10.7259	+	4.44282i	−0.909760	+	0.376835i	−0.787965	−	0.615721i	$-0.788865\pi$
$139$	−10.7259	+	4.44282i	−0.909760	+	0.376835i	−0.121795	+	0.992555i	$0.538865\pi$
$140$		0			0
$141$	−6.42458	+	15.5103i	−0.541048	+	1.30620i
$142$		0			0
$143$			22.7853i			1.90541i
$144$		0			0
$145$		−	0.742954i		−	0.0616990i
$146$		0			0
$147$	0.810533	−	1.95680i	0.0668516	−	0.161394i
$148$		0			0
$149$	4.76267	−	1.97276i	0.390173	−	0.161615i	−0.178968	−	0.983855i	$-0.557276\pi$
$149$	4.76267	−	1.97276i	0.390173	−	0.161615i	0.569141	+	0.822240i	$0.307276\pi$
$150$		0			0
$151$	13.9603	+	13.9603i	1.13607	+	1.13607i	0.989148	+	0.146924i	$0.0469374\pi$
$151$	13.9603	+	13.9603i	1.13607	+	1.13607i	0.146924	+	0.989148i	$0.453063\pi$
$152$		0			0
$153$	0.0932487	−	0.0932487i	0.00753871	−	0.00753871i
$154$		0			0
$155$	0.324962	+	0.784527i	0.0261016	+	0.0630148i
$156$		0			0
$157$	−16.0332	−	6.64117i	−1.27959	−	0.530023i	−0.363723	−	0.931507i	$-0.618494\pi$
$157$	−16.0332	−	6.64117i	−1.27959	−	0.530023i	−0.915866	+	0.401484i	$0.868494\pi$
$158$		0			0
$159$	−12.5646			−0.996438
$160$		0			0
$161$	−14.6505			−1.15462
$162$		0			0
$163$	4.71513	+	1.95307i	0.369317	+	0.152976i	0.559620	−	0.828749i	$-0.310947\pi$
$163$	4.71513	+	1.95307i	0.369317	+	0.152976i	−0.190303	+	0.981725i	$0.560947\pi$
$164$		0			0
$165$	1.36388	+	3.29271i	0.106178	+	0.256337i
$166$		0			0
$167$	3.52743	−	3.52743i	0.272960	−	0.272960i	−0.557330	−	0.830291i	$-0.688174\pi$
$167$	3.52743	−	3.52743i	0.272960	−	0.272960i	0.830291	+	0.557330i	$0.188174\pi$
$168$		0			0
$169$	−17.2675	−	17.2675i	−1.32827	−	1.32827i
$170$		0			0
$171$	−0.0951518	+	0.0394132i	−0.00727644	+	0.00301400i
$172$		0			0
$173$	6.29491	−	15.1973i	0.478593	−	1.15543i	−0.481676	−	0.876350i	$-0.659972\pi$
$173$	6.29491	−	15.1973i	0.478593	−	1.15543i	0.960269	−	0.279077i	$-0.0900284\pi$
$174$		0			0
$175$			11.2732i			0.852171i
$176$		0			0
$177$		−	5.16146i		−	0.387959i
$178$		0			0
$179$	−8.65959	+	20.9061i	−0.647248	+	1.56260i	0.169455	+	0.985538i	$0.445799\pi$
$179$	−8.65959	+	20.9061i	−0.647248	+	1.56260i	−0.816704	+	0.577057i	$0.804201\pi$
$180$		0			0
$181$	−20.7830	+	8.60862i	−1.54479	+	0.639874i	−0.982365	−	0.186974i	$-0.940132\pi$
$181$	−20.7830	+	8.60862i	−1.54479	+	0.639874i	−0.562427	+	0.826847i	$0.690132\pi$
$182$		0			0
$183$	−9.77065	−	9.77065i	−0.722267	−	0.722267i
$184$		0			0
$185$	1.53535	−	1.53535i	0.112881	−	0.112881i
$186$		0			0
$187$	−7.50866	−	18.1275i	−0.549088	−	1.32562i
$188$		0			0
$189$	−11.5811	−	4.79706i	−0.842403	−	0.348935i
$190$		0			0
$191$	−10.4366			−0.755168			−0.377584	−	0.925975i	$-0.623245\pi$
$191$	−10.4366			−0.755168			−0.377584	+	0.925975i	$0.623245\pi$
$192$		0			0
$193$	−3.81806			−0.274830			−0.137415	−	0.990514i	$-0.543879\pi$
$193$	−3.81806			−0.274830			−0.137415	+	0.990514i	$0.543879\pi$
$194$		0			0
$195$	−5.40755	−	2.23988i	−0.387243	−	0.160401i
$196$		0			0
$197$	6.08042	+	14.6794i	0.433212	+	1.04587i	0.978245	+	0.207452i	$0.0665170\pi$
$197$	6.08042	+	14.6794i	0.433212	+	1.04587i	−0.545033	+	0.838414i	$0.683483\pi$
$198$		0			0
$199$	16.0244	−	16.0244i	1.13594	−	1.13594i	0.146771	−	0.989171i	$-0.453112\pi$
$199$	16.0244	−	16.0244i	1.13594	−	1.13594i	0.989171	−	0.146771i	$-0.0468879\pi$
$200$		0			0
$201$	−7.04318	−	7.04318i	−0.496788	−	0.496788i
$202$		0			0
$203$	2.97268	−	1.23132i	0.208641	−	0.0864220i
$204$		0			0
$205$	−2.60964	+	6.30023i	−0.182265	+	0.440027i
$206$		0			0
$207$		−	0.152661i		−	0.0106107i
$208$		0			0
$209$			15.3238i			1.05997i
$210$		0			0
$211$	−5.50184	+	13.2826i	−0.378762	+	0.914413i	0.613436	+	0.789744i	$0.289787\pi$
$211$	−5.50184	+	13.2826i	−0.378762	+	0.914413i	−0.992198	+	0.124669i	$0.960213\pi$
$212$		0			0
$213$	−21.3033	+	8.82413i	−1.45968	+	0.604620i
$214$		0			0
$215$	0.217014	+	0.217014i	0.0148003	+	0.0148003i
$216$		0			0
$217$	−2.60045	+	2.60045i	−0.176530	+	0.176530i
$218$		0			0
$219$	−1.58667	−	3.83056i	−0.107217	−	0.258845i
$220$		0			0
$221$	29.7705	+	12.3313i	2.00258	+	0.829495i
$222$		0			0
$223$	16.3670			1.09602			0.548008	−	0.836473i	$-0.315386\pi$
$223$	16.3670			1.09602			0.548008	+	0.836473i	$0.315386\pi$
$224$		0			0
$225$	−0.117468			−0.00783122
$226$		0			0
$227$	−5.19652	−	2.15247i	−0.344905	−	0.142864i	0.203505	−	0.979074i	$-0.434767\pi$
$227$	−5.19652	−	2.15247i	−0.344905	−	0.142864i	−0.548410	+	0.836210i	$0.684767\pi$
$228$		0			0
$229$	5.04072	+	12.1694i	0.333100	+	0.804175i	0.998343	+	0.0575475i	$0.0183281\pi$
$229$	5.04072	+	12.1694i	0.333100	+	0.804175i	−0.665243	+	0.746627i	$0.731672\pi$
$230$		0			0
$231$	−10.9143	+	10.9143i	−0.718105	+	0.718105i
$232$		0			0
$233$	−1.74984	−	1.74984i	−0.114636	−	0.114636i	0.647462	−	0.762098i	$-0.275831\pi$
$233$	−1.74984	−	1.74984i	−0.114636	−	0.114636i	−0.762098	+	0.647462i	$0.775831\pi$
$234$		0			0
$235$	4.98853	−	2.06632i	0.325416	−	0.134792i
$236$		0			0
$237$	−8.47062	+	20.4499i	−0.550226	+	1.32836i
$238$		0			0
$239$			12.7565i			0.825152i	0.910923	+	0.412576i	$0.135371\pi$
$239$			12.7565i			0.825152i	−0.910923	+	0.412576i	$0.864629\pi$
$240$		0			0
$241$		−	18.9660i		−	1.22171i	−0.791743	−	0.610854i	$-0.790826\pi$
$241$		−	18.9660i		−	1.22171i	0.791743	−	0.610854i	$-0.209174\pi$
$242$		0			0
$243$	0.0995586	−	0.240356i	0.00638669	−	0.0154188i
$244$		0			0
$245$	−0.629359	+	0.260689i	−0.0402083	+	0.0166548i
$246$		0			0
$247$	−17.7951	−	17.7951i	−1.13227	−	1.13227i
$248$		0			0
$249$	1.14939	−	1.14939i	0.0728398	−	0.0728398i
$250$		0			0
$251$	−3.77199	−	9.10639i	−0.238086	−	0.574790i	0.758999	−	0.651092i	$-0.225689\pi$
$251$	−3.77199	−	9.10639i	−0.238086	−	0.574790i	−0.997085	+	0.0763018i	$0.975689\pi$
$252$		0			0
$253$	−20.9850	−	8.69226i	−1.31931	−	0.546478i
$254$		0			0
$255$	5.04026			0.315633
$256$		0			0
$257$	−2.06510			−0.128817			−0.0644087	−	0.997924i	$-0.520516\pi$
$257$	−2.06510			−0.128817			−0.0644087	+	0.997924i	$0.520516\pi$
$258$		0			0
$259$	8.68778	+	3.59860i	0.539832	+	0.223606i
$260$		0			0
$261$	0.0128306	+	0.0309758i	0.000794194	+	0.00191736i
$262$		0			0
$263$	17.8612	−	17.8612i	1.10137	−	1.10137i	0.107120	−	0.994246i	$-0.465837\pi$
$263$	17.8612	−	17.8612i	1.10137	−	1.10137i	0.994246	−	0.107120i	$-0.0341629\pi$
$264$		0			0
$265$	2.85750	+	2.85750i	0.175535	+	0.175535i
$266$		0			0
$267$	−2.59024	+	1.07291i	−0.158520	+	0.0656611i
$268$		0			0
$269$	−5.65583	+	13.6544i	−0.344842	+	0.832523i	0.652370	+	0.757901i	$0.273775\pi$
$269$	−5.65583	+	13.6544i	−0.344842	+	0.832523i	−0.997212	+	0.0746220i	$0.976225\pi$
$270$		0			0
$271$			2.39655i			0.145580i	0.997347	+	0.0727901i	$0.0231903\pi$
$271$			2.39655i			0.145580i	−0.997347	+	0.0727901i	$0.976810\pi$
$272$		0			0
$273$		−	25.3487i		−	1.53418i
$274$		0			0
$275$	−6.68845	+	16.1473i	−0.403329	+	0.973722i
$276$		0			0
$277$	9.24018	−	3.82741i	0.555189	−	0.229967i	−0.0874063	−	0.996173i	$-0.527858\pi$
$277$	9.24018	−	3.82741i	0.555189	−	0.229967i	0.642595	+	0.766206i	$0.277858\pi$
$278$		0			0
$279$	−0.0270971	−	0.0270971i	−0.00162226	−	0.00162226i
$280$		0			0
$281$	−19.8667	+	19.8667i	−1.18515	+	1.18515i	−0.206754	+	0.978393i	$0.566290\pi$
$281$	−19.8667	+	19.8667i	−1.18515	+	1.18515i	−0.978393	+	0.206754i	$0.933710\pi$
$282$		0			0
$283$	1.97378	+	4.76511i	0.117329	+	0.283257i	0.971624	−	0.236532i	$-0.0760108\pi$
$283$	1.97378	+	4.76511i	0.117329	+	0.283257i	−0.854295	+	0.519788i	$0.826011\pi$
$284$		0			0
$285$	−3.63674	−	1.50639i	−0.215422	−	0.0892307i
$286$		0			0
$287$	−29.5333			−1.74329
$288$		0			0
$289$	−10.7484			−0.632259
$290$		0			0
$291$	2.93015	+	1.21371i	0.171769	+	0.0711488i
$292$		0			0
$293$	−8.38983	−	20.2548i	−0.490139	−	1.18330i	−0.954649	−	0.297733i	$-0.903770\pi$
$293$	−8.38983	−	20.2548i	−0.490139	−	1.18330i	0.464510	−	0.885568i	$-0.346230\pi$
$294$		0			0
$295$	−1.17384	+	1.17384i	−0.0683438	+	0.0683438i
$296$		0			0
$297$	−13.7423	−	13.7423i	−0.797411	−	0.797411i
$298$		0			0
$299$	34.4632	−	14.2751i	1.99306	−	0.825552i
$300$		0			0
$301$	−0.508644	+	1.22798i	−0.0293178	+	0.0707793i
$302$		0			0
$303$		−	3.29077i		−	0.189050i
$304$		0			0
$305$			4.44417i			0.254472i
$306$		0			0
$307$	8.25751	−	19.9354i	0.471281	−	1.13777i	−0.492317	−	0.870416i	$-0.663850\pi$
$307$	8.25751	−	19.9354i	0.471281	−	1.13777i	0.963598	−	0.267356i	$-0.0861501\pi$
$308$		0			0
$309$	12.0955	−	5.01011i	0.688088	−	0.285015i
$310$		0			0
$311$	15.4798	+	15.4798i	0.877779	+	0.877779i	0.993304	−	0.115526i	$-0.0368553\pi$
$311$	15.4798	+	15.4798i	0.877779	+	0.877779i	−0.115526	+	0.993304i	$0.536855\pi$
$312$		0			0
$313$	14.0918	−	14.0918i	0.796516	−	0.796516i	−0.186028	−	0.982544i	$-0.559562\pi$
$313$	14.0918	−	14.0918i	0.796516	−	0.796516i	0.982544	+	0.186028i	$0.0595616\pi$
$314$		0			0
$315$	0.0127684	+	0.0308256i	0.000719416	+	0.00173682i
$316$		0			0
$317$	7.37983	+	3.05683i	0.414492	+	0.171688i	0.580177	−	0.814490i	$-0.302983\pi$
$317$	7.37983	+	3.05683i	0.414492	+	0.171688i	−0.165685	+	0.986179i	$0.552983\pi$
$318$		0			0
$319$	4.98853			0.279304
$320$		0			0
$321$	−32.4446			−1.81088
$322$		0			0
$323$	20.0215	+	8.29319i	1.11403	+	0.461445i
$324$		0			0
$325$	−10.9843	−	26.5185i	−0.609300	−	1.47098i
$326$		0			0
$327$	8.33771	−	8.33771i	0.461076	−	0.461076i
$328$		0			0
$329$	16.5354	+	16.5354i	0.911623	+	0.911623i
$330$		0			0
$331$	−6.47564	+	2.68230i	−0.355934	+	0.147433i	−0.553483	−	0.832860i	$-0.686702\pi$
$331$	−6.47564	+	2.68230i	−0.355934	+	0.147433i	0.197550	+	0.980293i	$0.436702\pi$
$332$		0			0
$333$	−0.0374980	+	0.0905281i	−0.00205488	+	0.00496091i
$334$		0			0
$335$			3.20358i			0.175030i
$336$		0			0
$337$		−	2.82843i		−	0.154074i	−0.997028	−	0.0770371i	$-0.975454\pi$
$337$		−	2.82843i		−	0.154074i	0.997028	−	0.0770371i	$-0.0245460\pi$
$338$		0			0
$339$	4.35667	−	10.5179i	0.236622	−	0.571255i
$340$		0			0
$341$	−5.26768	+	2.18194i	−0.285261	+	0.118159i
$342$		0			0
$343$	−13.9779	−	13.9779i	−0.754736	−	0.754736i
$344$		0			0
$345$	4.12580	−	4.12580i	0.222126	−	0.222126i
$346$		0			0
$347$	4.39235	+	10.6041i	0.235794	+	0.569256i	0.996840	−	0.0794417i	$-0.0253138\pi$
$347$	4.39235	+	10.6041i	0.235794	+	0.569256i	−0.761046	+	0.648698i	$0.775314\pi$
$348$		0			0
$349$	19.7580	+	8.18404i	1.05762	+	0.438081i	0.842607	−	0.538529i	$-0.181020\pi$
$349$	19.7580	+	8.18404i	1.05762	+	0.438081i	0.215015	+	0.976611i	$0.431020\pi$
$350$		0			0
$351$	31.9170			1.70361
$352$		0			0
$353$	26.0563			1.38684			0.693418	−	0.720535i	$-0.256104\pi$
$353$	26.0563			1.38684			0.693418	+	0.720535i	$0.256104\pi$
$354$		0			0
$355$	6.85172	+	2.83808i	0.363652	+	0.150629i
$356$		0			0
$357$	8.35341	+	20.1669i	0.442109	+	1.06735i
$358$		0			0
$359$	6.77460	−	6.77460i	0.357550	−	0.357550i	−0.505359	−	0.862909i	$-0.668640\pi$
$359$	6.77460	−	6.77460i	0.357550	−	0.357550i	0.862909	+	0.505359i	$0.168640\pi$
$360$		0			0
$361$	1.46732	+	1.46732i	0.0772274	+	0.0772274i
$362$		0			0
$363$	−4.58008	+	1.89713i	−0.240392	+	0.0995737i
$364$		0			0
$365$	−0.510316	+	1.23201i	−0.0267112	+	0.0644864i
$366$		0			0
$367$		−	19.2892i		−	1.00689i	−0.864028	−	0.503444i	$-0.832066\pi$
$367$		−	19.2892i		−	1.00689i	0.864028	−	0.503444i	$-0.167934\pi$
$368$		0			0
$369$		−	0.307742i		−	0.0160204i
$370$		0			0
$371$	−6.69748	+	16.1691i	−0.347716	+	0.839460i
$372$		0			0
$373$	−6.81560	+	2.82311i	−0.352898	+	0.146175i	−0.552088	−	0.833786i	$-0.686169\pi$
$373$	−6.81560	+	2.82311i	−0.352898	+	0.146175i	0.199190	+	0.979961i	$0.436169\pi$
$374$		0			0
$375$	−6.55759	−	6.55759i	−0.338632	−	0.338632i
$376$		0			0
$377$	−5.79302	+	5.79302i	−0.298356	+	0.298356i
$378$		0			0
$379$	5.30491	+	12.8072i	0.272495	+	0.657861i	0.999589	−	0.0286774i	$-0.00912956\pi$
$379$	5.30491	+	12.8072i	0.272495	+	0.657861i	−0.727094	+	0.686538i	$0.759130\pi$
$380$		0			0
$381$	−6.96030	−	2.88305i	−0.356587	−	0.147703i
$382$		0			0
$383$	−3.78803			−0.193559			−0.0967797	−	0.995306i	$-0.530854\pi$
$383$	−3.78803			−0.193559			−0.0967797	+	0.995306i	$0.530854\pi$
$384$		0			0
$385$	4.96434			0.253006
$386$		0			0
$387$	−0.0127957	−	0.00530016i	−0.000650442	−	0.000269422i
$388$		0			0
$389$	7.93103	+	19.1472i	0.402119	+	0.970801i	0.987151	+	0.159791i	$0.0510820\pi$
$389$	7.93103	+	19.1472i	0.402119	+	0.970801i	−0.585032	+	0.811010i	$0.698918\pi$
$390$		0			0
$391$	−22.7140	+	22.7140i	−1.14869	+	1.14869i
$392$		0			0
$393$	8.30630	+	8.30630i	0.418997	+	0.418997i
$394$		0			0
$395$	6.57723	−	2.72438i	0.330936	−	0.137078i
$396$		0			0
$397$	−2.65594	+	6.41201i	−0.133298	+	0.321810i	−0.976409	−	0.215930i	$-0.930722\pi$
$397$	−2.65594	+	6.41201i	−0.133298	+	0.321810i	0.843111	+	0.537740i	$0.180722\pi$
$398$		0			0
$399$		−	17.0478i		−	0.853457i
$400$		0			0
$401$			21.0373i			1.05055i	0.850931	+	0.525277i	$0.176038\pi$
$401$			21.0373i			1.05055i	−0.850931	+	0.525277i	$0.823962\pi$
$402$		0			0
$403$	3.58336	−	8.65100i	0.178500	−	0.430937i
$404$		0			0
$405$	4.57384	−	1.89455i	0.227276	−	0.0941408i
$406$		0			0
$407$	10.3090	+	10.3090i	0.511000	+	0.511000i
$408$		0			0
$409$	0.106839	−	0.106839i	0.00528285	−	0.00528285i	−0.704460	−	0.709743i	$-0.748811\pi$
$409$	0.106839	−	0.106839i	0.00528285	−	0.00528285i	0.709743	+	0.704460i	$0.248811\pi$
$410$		0			0
$411$	5.11037	+	12.3375i	0.252076	+	0.608565i
$412$		0			0
$413$	−6.64219	−	2.75128i	−0.326841	−	0.135382i
$414$		0			0
$415$	−0.522800			−0.0256632
$416$		0			0
$417$	20.0244			0.980599
$418$		0			0
$419$	−18.7318	−	7.75898i	−0.915110	−	0.379051i	−0.125099	−	0.992144i	$-0.539925\pi$
$419$	−18.7318	−	7.75898i	−0.915110	−	0.379051i	−0.790011	+	0.613093i	$0.789925\pi$
$420$		0			0
$421$	−5.08471	−	12.2756i	−0.247814	−	0.598275i	0.750204	−	0.661206i	$-0.229955\pi$
$421$	−5.08471	−	12.2756i	−0.247814	−	0.598275i	−0.998018	+	0.0629310i	$0.979955\pi$
$422$		0			0
$423$	−0.172301	+	0.172301i	−0.00837756	+	0.00837756i
$424$		0			0
$425$	17.4778	+	17.4778i	0.847796	+	0.847796i
$426$		0			0
$427$	−17.7819	+	7.36548i	−0.860524	+	0.356441i
$428$		0			0
$429$	15.0396	−	36.3088i	0.726118	−	1.75300i
$430$		0			0
$431$		−	8.96851i		−	0.431998i	−0.976394	−	0.215999i	$-0.930699\pi$
$431$		−	8.96851i		−	0.431998i	0.976394	−	0.215999i	$-0.0693008\pi$
$432$		0			0
$433$		−	3.14680i		−	0.151225i	−0.997137	−	0.0756127i	$-0.975909\pi$
$433$		−	3.14680i		−	0.151225i	0.997137	−	0.0756127i	$-0.0240913\pi$
$434$		0			0
$435$	−0.490391	+	1.18391i	−0.0235125	+	0.0567641i
$436$		0			0
$437$	23.1775	−	9.60045i	1.10873	−	0.459252i
$438$		0			0
$439$	5.35602	+	5.35602i	0.255629	+	0.255629i	0.823274	−	0.567645i	$-0.192145\pi$
$439$	5.35602	+	5.35602i	0.255629	+	0.255629i	−0.567645	+	0.823274i	$0.692145\pi$
$440$		0			0
$441$	0.0217377	−	0.0217377i	0.00103513	−	0.00103513i
$442$		0			0
$443$	−7.13988	−	17.2372i	−0.339226	−	0.818964i	−0.997790	−	0.0664397i	$-0.978836\pi$
$443$	−7.13988	−	17.2372i	−0.339226	−	0.818964i	0.658564	−	0.752524i	$-0.271164\pi$
$444$		0			0
$445$	0.833089	+	0.345077i	0.0394922	+	0.0163582i
$446$		0			0
$447$	−8.89153			−0.420555
$448$		0			0
$449$	35.0511			1.65416			0.827082	−	0.562081i	$-0.189999\pi$
$449$	35.0511			1.65416			0.827082	+	0.562081i	$0.189999\pi$
$450$		0			0
$451$	−42.3026	−	17.5223i	−1.99195	−	0.825093i
$452$		0			0
$453$	−13.0314	−	31.4605i	−0.612267	−	1.47814i
$454$		0			0
$455$	−5.76492	+	5.76492i	−0.270264	+	0.270264i
$456$		0			0
$457$	−9.65659	−	9.65659i	−0.451716	−	0.451716i	0.444207	−	0.895924i	$-0.353485\pi$
$457$	−9.65659	−	9.65659i	−0.451716	−	0.451716i	−0.895924	+	0.444207i	$0.853485\pi$
$458$		0			0
$459$	−25.3925	+	10.5179i	−1.18522	+	0.490935i
$460$		0			0
$461$	9.64976	−	23.2966i	0.449434	−	1.08503i	−0.523100	−	0.852271i	$-0.675225\pi$
$461$	9.64976	−	23.2966i	0.449434	−	1.08503i	0.972534	−	0.232759i	$-0.0747753\pi$
$462$		0			0
$463$		−	1.57747i		−	0.0733113i	−0.999328	−	0.0366556i	$-0.988330\pi$
$463$		−	1.57747i		−	0.0733113i	0.999328	−	0.0366556i	$-0.0116705\pi$
$464$		0			0
$465$		−	1.46465i		−	0.0679215i
$466$		0			0
$467$	9.79289	−	23.6421i	0.453161	−	1.09403i	−0.517953	−	0.855409i	$-0.673306\pi$
$467$	9.79289	−	23.6421i	0.453161	−	1.09403i	0.971114	−	0.238618i	$-0.0766943\pi$
$468$		0			0
$469$	−12.8181	+	5.30941i	−0.591883	+	0.245166i
$470$		0			0
$471$	21.1656	+	21.1656i	0.975260	+	0.975260i
$472$		0			0
$473$	−1.45713	+	1.45713i	−0.0669991	+	0.0669991i
$474$		0			0
$475$	−7.38728	−	17.8345i	−0.338952	−	0.818302i
$476$		0			0
$477$	−0.168485	−	0.0697888i	−0.00771441	−	0.00319541i
$478$		0			0
$479$	−25.1963			−1.15125			−0.575623	−	0.817715i	$-0.695240\pi$
$479$	−25.1963			−1.15125			−0.575623	+	0.817715i	$0.695240\pi$
$480$		0			0
$481$	−23.9431			−1.09171
$482$		0			0
$483$	23.3458	+	9.67016i	1.06227	+	0.440008i
$484$		0			0
$485$	−0.390361	−	0.942415i	−0.0177254	−	0.0427929i
$486$		0			0
$487$	−15.4256	+	15.4256i	−0.699001	+	0.699001i	−0.964195	−	0.265194i	$-0.914564\pi$
$487$	−15.4256	+	15.4256i	−0.699001	+	0.699001i	0.265194	+	0.964195i	$0.414564\pi$
$488$		0			0
$489$	−6.22450	−	6.22450i	−0.281481	−	0.281481i
$490$		0			0
$491$	−28.8199	+	11.9376i	−1.30062	+	0.538736i	−0.922134	−	0.386870i	$-0.873556\pi$
$491$	−28.8199	+	11.9376i	−1.30062	+	0.538736i	−0.378489	+	0.925606i	$0.623556\pi$
$492$		0			0
$493$	2.69977	−	6.51783i	0.121592	−	0.293548i
$494$		0			0
$495$			0.0517292i			0.00232505i
$496$		0			0
$497$			32.1185i			1.44071i
$498$		0			0
$499$	14.6102	−	35.2722i	0.654043	−	1.57900i	−0.152814	−	0.988255i	$-0.548834\pi$
$499$	14.6102	−	35.2722i	0.654043	−	1.57900i	0.806858	−	0.590746i	$-0.201166\pi$
$500$		0			0
$501$	−7.94930	+	3.29271i	−0.355149	+	0.147107i
$502$		0			0
$503$	−2.18240	−	2.18240i	−0.0973084	−	0.0973084i	0.656777	−	0.754085i	$-0.271919\pi$
$503$	−2.18240	−	2.18240i	−0.0973084	−	0.0973084i	−0.754085	+	0.656777i	$0.771919\pi$
$504$		0			0
$505$	−0.748402	+	0.748402i	−0.0333034	+	0.0333034i
$506$		0			0
$507$	16.1185	+	38.9135i	0.715848	+	1.72821i
$508$		0			0
$509$	7.44742	+	3.08482i	0.330101	+	0.136732i	0.541578	−	0.840651i	$-0.317827\pi$
$509$	7.44742	+	3.08482i	0.330101	+	0.136732i	−0.211477	+	0.977383i	$0.567827\pi$
$510$		0			0
$511$	−5.77524			−0.255482
$512$		0			0
$513$	21.4652			0.947710
$514$		0			0
$515$	−3.89023	−	1.61139i	−0.171424	−	0.0710061i
$516$		0			0
$517$	13.8742	+	33.4953i	0.610187	+	1.47312i
$518$		0			0
$519$	−20.0621	+	20.0621i	−0.880627	+	0.880627i
$520$		0			0
$521$	6.94553	+	6.94553i	0.304289	+	0.304289i	0.842689	−	0.538400i	$-0.180971\pi$
$521$	6.94553	+	6.94553i	0.304289	+	0.304289i	−0.538400	+	0.842689i	$0.680971\pi$
$522$		0			0
$523$	−2.24673	+	0.930625i	−0.0982425	+	0.0406934i	−0.431263	−	0.902226i	$-0.641932\pi$
$523$	−2.24673	+	0.930625i	−0.0982425	+	0.0406934i	0.333021	+	0.942919i	$0.391932\pi$
$524$		0			0
$525$	7.44092	−	17.9640i	0.324748	−	0.784012i
$526$		0			0
$527$			8.06341i			0.351248i
$528$		0			0
$529$			14.1859i			0.616777i
$530$		0			0
$531$	0.0286688	−	0.0692127i	0.00124412	−	0.00300358i
$532$		0			0
$533$	69.4727	−	28.7765i	3.00920	−	1.24645i
$534$		0			0
$535$	7.37869	+	7.37869i	0.319009	+	0.319009i
$536$		0			0
$537$	27.5984	−	27.5984i	1.19096	−	1.19096i
$538$		0			0
$539$	−1.75038	−	4.22580i	−0.0753944	−	0.182018i
$540$		0			0
$541$	−25.4120	−	10.5260i	−1.09255	−	0.452548i	−0.237653	−	0.971350i	$-0.576378\pi$
$541$	−25.4120	−	10.5260i	−1.09255	−	0.452548i	−0.854894	+	0.518802i	$0.826378\pi$
$542$		0			0
$543$	38.8003			1.66508
$544$		0			0
$545$	−3.79240			−0.162448
$546$		0			0
$547$	2.52591	+	1.04627i	0.108000	+	0.0447351i	0.436029	−	0.899932i	$-0.356384\pi$
$547$	2.52591	+	1.04627i	0.108000	+	0.0447351i	−0.328029	+	0.944668i	$0.606384\pi$
$548$		0			0
$549$	−0.0767495	−	0.185290i	−0.00327559	−	0.00790798i
$550$		0			0
$551$	−3.89598	+	3.89598i	−0.165974	+	0.165974i
$552$		0			0
$553$	21.8014	+	21.8014i	0.927088	+	0.927088i
$554$		0			0
$555$	−3.46002	+	1.43319i	−0.146870	+	0.0608354i
$556$		0			0
$557$	8.61495	−	20.7983i	0.365027	−	0.881254i	−0.629522	−	0.776983i	$-0.716749\pi$
$557$	8.61495	−	20.7983i	0.365027	−	0.881254i	0.994549	−	0.104271i	$-0.0332509\pi$
$558$		0			0
$559$		−	3.38425i		−	0.143138i
$560$		0			0
$561$			33.8426i			1.42884i
$562$		0			0
$563$	−8.66534	+	20.9200i	−0.365201	+	0.881672i	0.629321	+	0.777145i	$0.283333\pi$
$563$	−8.66534	+	20.9200i	−0.365201	+	0.881672i	−0.994522	+	0.104527i	$0.966667\pi$
$564$		0			0
$565$	−3.38285	+	1.40122i	−0.142317	+	0.0589498i
$566$		0			0
$567$	15.1608	+	15.1608i	0.636693	+	0.636693i
$568$		0			0
$569$	0.276633	−	0.276633i	0.0115970	−	0.0115970i	−0.701284	−	0.712882i	$-0.747390\pi$
$569$	0.276633	−	0.276633i	0.0115970	−	0.0115970i	0.712882	+	0.701284i	$0.247390\pi$
$570$		0			0
$571$	13.2460	+	31.9788i	0.554329	+	1.33827i	0.914198	+	0.405267i	$0.132821\pi$
$571$	13.2460	+	31.9788i	0.554329	+	1.33827i	−0.359869	+	0.933003i	$0.617179\pi$
$572$		0			0
$573$	16.6309	+	6.88876i	0.694767	+	0.287782i
$574$		0			0
$575$	28.6135			1.19327
$576$		0			0
$577$	30.0407			1.25061			0.625306	−	0.780379i	$-0.284974\pi$
$577$	30.0407			1.25061			0.625306	+	0.780379i	$0.284974\pi$
$578$		0			0
$579$	6.08413	+	2.52013i	0.252848	+	0.104733i
$580$		0			0
$581$	−0.866455	−	2.09181i	−0.0359466	−	0.0867828i
$582$		0			0
$583$	−19.1865	+	19.1865i	−0.794625	+	0.794625i
$584$		0			0
$585$	−0.0600715	−	0.0600715i	−0.00248365	−	0.00248365i
$586$		0			0
$587$	32.7941	−	13.5838i	1.35356	−	0.560662i	0.416277	−	0.909238i	$-0.363335\pi$
$587$	32.7941	−	13.5838i	1.35356	−	0.560662i	0.937281	+	0.348575i	$0.113335\pi$
$588$		0			0
$589$	2.40992	−	5.81806i	0.0992990	−	0.239729i
$590$		0			0
$591$		−	27.4053i		−	1.12730i
$592$		0			0
$593$			2.66555i			0.109461i	0.998501	+	0.0547306i	$0.0174300\pi$
$593$			2.66555i			0.109461i	−0.998501	+	0.0547306i	$0.982570\pi$
$594$		0			0
$595$	2.68668	−	6.48622i	0.110143	−	0.265909i
$596$		0			0
$597$	−36.1122	+	14.9582i	−1.47797	+	0.612197i
$598$		0			0
$599$	−11.9077	−	11.9077i	−0.486534	−	0.486534i	0.420677	−	0.907211i	$-0.361793\pi$
$599$	−11.9077	−	11.9077i	−0.486534	−	0.486534i	−0.907211	+	0.420677i	$0.861793\pi$
$600$		0			0
$601$	1.86501	−	1.86501i	0.0760755	−	0.0760755i	−0.668045	−	0.744121i	$-0.732869\pi$
$601$	1.86501	−	1.86501i	0.0760755	−	0.0760755i	0.744121	+	0.668045i	$0.232869\pi$
$602$		0			0
$603$	−0.0553250	−	0.133566i	−0.00225301	−	0.00543924i
$604$		0			0
$605$	1.47308	+	0.610169i	0.0598891	+	0.0248069i
$606$		0			0
$607$	−8.47275			−0.343898			−0.171949	−	0.985106i	$-0.555006\pi$
$607$	−8.47275			−0.343898			−0.171949	+	0.985106i	$0.555006\pi$
$608$		0			0
$609$	−5.54976			−0.224887
$610$		0			0
$611$	−55.0087	−	22.7853i	−2.22541	−	0.921796i
$612$		0			0
$613$	−9.67657	−	23.3613i	−0.390833	−	0.943555i	−0.989759	−	0.142750i	$-0.954405\pi$
$613$	−9.67657	−	23.3613i	−0.390833	−	0.943555i	0.598926	−	0.800805i	$-0.295595\pi$
$614$		0			0
$615$	8.31700	−	8.31700i	0.335374	−	0.335374i
$616$		0			0
$617$	8.91738	+	8.91738i	0.359000	+	0.359000i	0.863444	−	0.504444i	$-0.168303\pi$
$617$	8.91738	+	8.91738i	0.359000	+	0.359000i	−0.504444	+	0.863444i	$0.668303\pi$
$618$		0			0
$619$	−5.56774	+	2.30623i	−0.223786	+	0.0926953i	−0.491760	−	0.870731i	$-0.663646\pi$
$619$	−5.56774	+	2.30623i	−0.223786	+	0.0926953i	0.267973	+	0.963426i	$0.413646\pi$
$620$		0			0
$621$	−12.1759	+	29.3951i	−0.488601	+	1.17959i
$622$		0			0
$623$			3.90524i			0.156460i
$624$		0			0
$625$		−	20.4786i		−	0.819143i
$626$		0			0
$627$	10.1146	−	24.4187i	0.403937	−	0.975191i
$628$		0			0
$629$	19.0486	−	7.89020i	0.759519	−	0.314603i
$630$		0			0
$631$	33.4932	+	33.4932i	1.33334	+	1.33334i	0.902361	+	0.430981i	$0.141833\pi$
$631$	33.4932	+	33.4932i	1.33334	+	1.33334i	0.430981	+	0.902361i	$0.358167\pi$
$632$		0			0
$633$	17.5345	−	17.5345i	0.696935	−	0.696935i
$634$		0			0
$635$	0.927266	+	2.23862i	0.0367974	+	0.0888369i
$636$		0			0
$637$	6.93995	+	2.87462i	0.274971	+	0.113897i
$638$		0			0
$639$	−0.334680			−0.0132397
$640$		0			0
$641$	−26.8508			−1.06054			−0.530272	−	0.847827i	$-0.677910\pi$
$641$	−26.8508			−1.06054			−0.530272	+	0.847827i	$0.677910\pi$
$642$		0			0
$643$	31.4666	+	13.0339i	1.24092	+	0.514006i	0.904002	−	0.427528i	$-0.140616\pi$
$643$	31.4666	+	13.0339i	1.24092	+	0.514006i	0.336918	+	0.941534i	$0.390616\pi$
$644$		0			0
$645$	−0.202574	−	0.489057i	−0.00797635	−	0.0192566i
$646$		0			0
$647$	6.43000	−	6.43000i	0.252789	−	0.252789i	−0.569324	−	0.822113i	$-0.692795\pi$
$647$	6.43000	−	6.43000i	0.252789	−	0.252789i	0.822113	+	0.569324i	$0.192795\pi$
$648$		0			0
$649$	−7.88172	−	7.88172i	−0.309384	−	0.309384i
$650$		0			0
$651$	5.86030	−	2.42742i	0.229683	−	0.0951380i
$652$		0			0
$653$	5.23125	−	12.6294i	0.204715	−	0.494225i	−0.787861	−	0.615853i	$-0.788812\pi$
$653$	5.23125	−	12.6294i	0.204715	−	0.494225i	0.992576	+	0.121628i	$0.0388115\pi$
$654$		0			0
$655$		−	3.77811i		−	0.147623i
$656$		0			0
$657$		−	0.0601790i		−	0.00234781i
$658$		0			0
$659$	5.94335	−	14.3485i	0.231520	−	0.558939i	−0.764837	−	0.644224i	$-0.777180\pi$
$659$	5.94335	−	14.3485i	0.231520	−	0.558939i	0.996357	+	0.0852857i	$0.0271803\pi$
$660$		0			0
$661$	21.2370	−	8.79664i	0.826022	−	0.342150i	0.0706953	−	0.997498i	$-0.477478\pi$
$661$	21.2370	−	8.79664i	0.826022	−	0.342150i	0.755327	+	0.655348i	$0.227478\pi$
$662$		0			0
$663$	−39.3003	−	39.3003i	−1.52630	−	1.52630i
$664$		0			0
$665$	−3.87708	+	3.87708i	−0.150347	+	0.150347i
$666$		0			0
$667$	−3.12534	−	7.54524i	−0.121014	−	0.292153i
$668$		0			0
$669$	−26.0811	−	10.8031i	−1.00835	−	0.417673i
$670$		0			0
$671$	−29.8402			−1.15197
$672$		0			0
$673$	39.6959			1.53017			0.765083	−	0.643932i	$-0.222698\pi$
$673$	39.6959			1.53017			0.765083	+	0.643932i	$0.222698\pi$
$674$		0			0
$675$	22.6187	+	9.36899i	0.870596	+	0.360613i
$676$		0			0
$677$	−8.16911	−	19.7220i	−0.313964	−	0.757977i	−0.999550	−	0.0299855i	$-0.990454\pi$
$677$	−8.16911	−	19.7220i	−0.313964	−	0.757977i	0.685586	−	0.727992i	$-0.259546\pi$
$678$		0			0
$679$	3.12380	−	3.12380i	0.119880	−	0.119880i
$680$		0			0
$681$	6.85998	+	6.85998i	0.262875	+	0.262875i
$682$		0			0
$683$	−22.6783	+	9.39365i	−0.867760	+	0.359438i	−0.771738	−	0.635941i	$-0.780612\pi$
$683$	−22.6783	+	9.39365i	−0.867760	+	0.359438i	−0.0960227	+	0.995379i	$0.530612\pi$
$684$		0			0
$685$	1.64363	−	3.96808i	0.0627999	−	0.151612i
$686$		0			0
$687$		−	22.7192i		−	0.866793i
$688$		0			0
$689$		−	44.5614i		−	1.69766i
$690$		0			0
$691$	5.63891	−	13.6135i	0.214514	−	0.517883i	−0.779593	−	0.626287i	$-0.784574\pi$
$691$	5.63891	−	13.6135i	0.214514	−	0.517883i	0.994107	+	0.108404i	$0.0345739\pi$
$692$		0			0
$693$	−0.206977	+	0.0857327i	−0.00786241	+	0.00325671i
$694$		0			0
$695$	−4.55404	−	4.55404i	−0.172745	−	0.172745i
$696$		0			0
$697$	−45.7880	+	45.7880i	−1.73434	+	1.73434i
$698$		0			0
$699$	1.63341	+	3.94340i	0.0617812	+	0.149153i
$700$		0			0
$701$	42.5832	+	17.6385i	1.60835	+	0.666199i	0.992565	−	0.121718i	$-0.0388405\pi$
$701$	42.5832	+	17.6385i	1.60835	+	0.666199i	0.615781	+	0.787917i	$0.288840\pi$
$702$		0			0
$703$	−16.1025			−0.607316
$704$		0			0
$705$	−9.31319			−0.350755
$706$		0			0
$707$	−4.23483	−	1.75412i	−0.159267	−	0.0659706i
$708$		0			0
$709$	−11.1294	−	26.8688i	−0.417974	−	1.00908i	−0.982934	−	0.183960i	$-0.941108\pi$
$709$	−11.1294	−	26.8688i	−0.417974	−	1.00908i	0.564960	−	0.825118i	$-0.308892\pi$
$710$		0			0
$711$	−0.227174	+	0.227174i	−0.00851968	+	0.00851968i
$712$		0			0
$713$	6.60045	+	6.60045i	0.247189	+	0.247189i
$714$		0			0
$715$	−11.6779	+	4.83714i	−0.436728	+	0.180899i
$716$		0			0
$717$	8.42003	−	20.3277i	0.314452	−	0.759154i
$718$		0			0
$719$			1.82423i			0.0680323i	0.999421	+	0.0340162i	$0.0108298\pi$
$719$			1.82423i			0.0680323i	−0.999421	+	0.0340162i	$0.989170\pi$
$720$		0			0
$721$		−	18.2360i		−	0.679146i
$722$		0			0
$723$	−12.5186	+	30.2226i	−0.465573	+	1.12399i
$724$		0			0
$725$	−5.80585	+	2.40486i	−0.215624	+	0.0893144i
$726$		0			0
$727$	−20.1795	−	20.1795i	−0.748416	−	0.748416i	0.225765	−	0.974182i	$-0.427512\pi$
$727$	−20.1795	−	20.1795i	−0.748416	−	0.748416i	−0.974182	+	0.225765i	$0.927512\pi$
$728$		0			0
$729$	−19.2485	+	19.2485i	−0.712909	+	0.712909i
$730$		0			0
$731$	1.11524	+	2.69243i	0.0412487	+	0.0995832i
$732$		0			0
$733$	11.2520	+	4.66073i	0.415602	+	0.172148i	0.580679	−	0.814133i	$-0.302787\pi$
$733$	11.2520	+	4.66073i	0.415602	+	0.172148i	−0.165077	+	0.986281i	$0.552787\pi$
$734$		0			0
$735$	1.17496			0.0433391
$736$		0			0
$737$	−21.5103			−0.792343
$738$		0			0
$739$	22.6586	+	9.38552i	0.833512	+	0.345252i	0.758292	−	0.651915i	$-0.226034\pi$
$739$	22.6586	+	9.38552i	0.833512	+	0.345252i	0.0752197	+	0.997167i	$0.476034\pi$
$740$		0			0
$741$	16.6110	+	40.1024i	0.610219	+	1.47320i
$742$		0			0
$743$	30.4077	−	30.4077i	1.11555	−	1.11555i	0.123164	−	0.992386i	$-0.460696\pi$
$743$	30.4077	−	30.4077i	1.11555	−	1.11555i	0.992386	−	0.123164i	$-0.0393041\pi$
$744$		0			0
$745$	2.02215	+	2.02215i	0.0740859	+	0.0740859i
$746$		0			0
$747$	0.0217970	−	0.00902860i	0.000797510	−	0.000330339i
$748$		0			0
$749$	−17.2944	+	41.7523i	−0.631923	+	1.52560i
$750$		0			0
$751$		−	5.81357i		−	0.212140i	−0.994359	−	0.106070i	$-0.966173\pi$
$751$		−	5.81357i		−	0.212140i	0.994359	−	0.106070i	$-0.0338268\pi$
$752$		0			0
$753$			17.0009i			0.619547i
$754$		0			0
$755$	−4.19124	+	10.1185i	−0.152535	+	0.368251i
$756$		0			0
$757$	2.65558	−	1.09998i	0.0965185	−	0.0399793i	−0.333902	−	0.942608i	$-0.608365\pi$
$757$	2.65558	−	1.09998i	0.0965185	−	0.0399793i	0.430420	+	0.902629i	$0.358365\pi$
$758$		0			0
$759$	27.7025	+	27.7025i	1.00554	+	1.00554i
$760$		0			0
$761$	−17.9432	+	17.9432i	−0.650442	+	0.650442i	−0.953099	−	0.302658i	$-0.902126\pi$
$761$	−17.9432	+	17.9432i	−0.650442	+	0.650442i	0.302658	+	0.953099i	$0.402126\pi$
$762$		0			0
$763$	−6.28528	−	15.1740i	−0.227542	−	0.549336i
$764$		0			0
$765$	0.0675875	+	0.0279956i	0.00244363	+	0.00101218i
$766$		0			0
$767$	18.3056			0.660976
$768$		0			0
$769$	−2.98104			−0.107499			−0.0537495	−	0.998554i	$-0.517117\pi$
$769$	−2.98104			−0.107499			−0.0537495	+	0.998554i	$0.517117\pi$
$770$		0			0
$771$	3.29077	+	1.36308i	0.118514	+	0.0490902i
$772$		0			0
$773$	−7.20933	−	17.4049i	−0.259302	−	0.626009i	0.739591	−	0.673056i	$-0.235019\pi$
$773$	−7.20933	−	17.4049i	−0.259302	−	0.626009i	−0.998893	+	0.0470471i	$0.985019\pi$
$774$		0			0
$775$	5.07886	−	5.07886i	0.182438	−	0.182438i
$776$		0			0
$777$	−11.4688	−	11.4688i	−0.411442	−	0.411442i
$778$		0			0
$779$	46.7225	−	19.3531i	1.67401	−	0.693396i
$780$		0			0
$781$	−19.0561	+	46.0056i	−0.681882	+	1.64621i
$782$		0			0
$783$		−	6.98779i		−	0.249723i
$784$		0			0
$785$		−	9.62716i		−	0.343608i
$786$		0			0
$787$	−13.3060	+	32.1235i	−0.474307	+	1.14508i	0.487934	+	0.872881i	$0.337751\pi$
$787$	−13.3060	+	32.1235i	−0.474307	+	1.14508i	−0.962241	+	0.272198i	$0.912249\pi$
$788$		0			0
$789$	−40.2514	+	16.6727i	−1.43299	+	0.593563i
$790$		0			0
$791$	−11.2130	−	11.2130i	−0.398689	−	0.398689i
$792$		0			0
$793$	34.6525	−	34.6525i	1.23054	−	1.23054i
$794$		0			0
$795$	−2.66736	−	6.43957i	−0.0946015	−	0.228388i
$796$		0			0
$797$	−16.5225	−	6.84385i	−0.585258	−	0.242422i	0.0703512	−	0.997522i	$-0.477588\pi$
$797$	−16.5225	−	6.84385i	−0.585258	−	0.242422i	−0.655609	+	0.755101i	$0.727588\pi$
$798$		0			0
$799$	51.2724			1.81389
$800$		0			0
$801$	−0.0406932			−0.00143782
$802$		0			0
$803$	−8.27229	−	3.42649i	−0.291923	−	0.120918i
$804$		0			0
$805$	−3.11018	−	7.50864i	−0.109620	−	0.264645i
$806$		0			0
$807$	18.0253	−	18.0253i	0.634521	−	0.634521i
$808$		0			0
$809$	10.5558	+	10.5558i	0.371123	+	0.371123i	0.867886	−	0.496763i	$-0.165478\pi$
$809$	10.5558	+	10.5558i	0.371123	+	0.371123i	−0.496763	+	0.867886i	$0.665478\pi$
$810$		0			0
$811$	4.31304	−	1.78652i	0.151451	−	0.0627333i	−0.305670	−	0.952138i	$-0.598880\pi$
$811$	4.31304	−	1.78652i	0.151451	−	0.0627333i	0.457122	+	0.889404i	$0.348880\pi$
$812$		0			0
$813$	1.58186	−	3.81894i	0.0554782	−	0.133936i
$814$		0			0
$815$			2.83121i			0.0991728i
$816$		0			0
$817$		−	2.27601i		−	0.0796274i
$818$		0			0
$819$	0.140797	−	0.339914i	0.00491985	−	0.0118776i
$820$		0			0
$821$	−25.4218	+	10.5300i	−0.887225	+	0.367501i	−0.779295	−	0.626658i	$-0.784422\pi$
$821$	−25.4218	+	10.5300i	−0.887225	+	0.367501i	−0.107931	+	0.994158i	$0.534422\pi$
$822$		0			0
$823$	−28.1280	−	28.1280i	−0.980479	−	0.980479i	0.0193343	−	0.999813i	$-0.493845\pi$
$823$	−28.1280	−	28.1280i	−0.980479	−	0.980479i	−0.999813	+	0.0193343i	$0.993845\pi$
$824$		0			0
$825$	21.3163	−	21.3163i	0.742138	−	0.742138i
$826$		0			0
$827$	6.05658	+	14.6219i	0.210608	+	0.508453i	0.993517	−	0.113683i	$-0.0362650\pi$
$827$	6.05658	+	14.6219i	0.210608	+	0.508453i	−0.782909	+	0.622136i	$0.786265\pi$
$828$		0			0
$829$	−28.3516	−	11.7436i	−0.984691	−	0.407872i	−0.168530	−	0.985697i	$-0.553902\pi$
$829$	−28.3516	−	11.7436i	−0.984691	−	0.407872i	−0.816161	+	0.577824i	$0.803902\pi$
$830$		0			0
$831$	−17.2507			−0.598419
$832$		0			0
$833$	−6.46858			−0.224123
$834$		0			0
$835$	2.55671	+	1.05902i	0.0884786	+	0.0366490i
$836$		0			0
$837$	3.05640	+	7.37881i	0.105645	+	0.255049i
$838$		0			0
$839$	−19.2678	+	19.2678i	−0.665199	+	0.665199i	−0.956601	−	0.291401i	$-0.905878\pi$
$839$	−19.2678	+	19.2678i	−0.665199	+	0.665199i	0.291401	+	0.956601i	$0.405878\pi$
$840$		0			0
$841$	−19.2378	−	19.2378i	−0.663372	−	0.663372i
$842$		0			0
$843$	44.7710	−	18.5448i	1.54199	−	0.638715i
$844$		0			0
$845$	5.18414	−	12.5156i	0.178340	−	0.430551i
$846$		0			0
$847$			6.90528i			0.237268i
$848$		0			0
$849$		−	8.89609i		−	0.305313i
$850$		0			0
$851$	9.13394	−	22.0513i	0.313107	−	0.755908i
$852$		0			0
$853$	−13.3619	+	5.53470i	−0.457504	+	0.189504i	−0.599520	−	0.800360i	$-0.704642\pi$
$853$	−13.3619	+	5.53470i	−0.457504	+	0.189504i	0.142016	+	0.989864i	$0.454642\pi$
$854$		0			0
$855$	−0.0403999	−	0.0403999i	−0.00138165	−	0.00138165i
$856$		0			0
$857$	16.2115	−	16.2115i	0.553775	−	0.553775i	−0.373753	−	0.927528i	$-0.621929\pi$
$857$	16.2115	−	16.2115i	0.553775	−	0.553775i	0.927528	+	0.373753i	$0.121929\pi$
$858$		0			0
$859$	−10.6184	−	25.6351i	−0.362295	−	0.874658i	−0.994964	−	0.100235i	$-0.968040\pi$
$859$	−10.6184	−	25.6351i	−0.362295	−	0.874658i	0.632669	−	0.774423i	$-0.281960\pi$
$860$		0			0
$861$	47.0617	+	19.4936i	1.60386	+	0.664341i
$862$		0			0
$863$	−40.8195			−1.38951			−0.694755	−	0.719246i	$-0.744487\pi$
$863$	−40.8195			−1.38951			−0.694755	+	0.719246i	$0.744487\pi$
$864$		0			0
$865$	9.12521			0.310267
$866$		0			0
$867$	17.1277	+	7.09454i	0.581689	+	0.240943i
$868$		0			0
$869$	18.2927	+	44.1625i	0.620538	+	1.49811i
$870$		0			0
$871$	24.9792	−	24.9792i	0.846389	−	0.846389i
$872$		0			0
$873$	0.0325505	+	0.0325505i	0.00110167	+	0.00110167i
$874$		0			0
$875$	−11.9343	+	4.94336i	−0.403454	+	0.167116i
$876$		0			0
$877$	−18.1786	+	43.8869i	−0.613846	+	1.48196i	0.244896	+	0.969549i	$0.421246\pi$
$877$	−18.1786	+	43.8869i	−0.613846	+	1.48196i	−0.858743	+	0.512407i	$0.828754\pi$
$878$		0			0
$879$			37.8142i			1.27544i
$880$		0			0
$881$			0.849166i			0.0286091i	0.999898	+	0.0143046i	$0.00455344\pi$
$881$			0.849166i			0.0286091i	−0.999898	+	0.0143046i	$0.995447\pi$
$882$		0			0
$883$	−20.6785	+	49.9223i	−0.695886	+	1.68002i	0.0366838	+	0.999327i	$0.488321\pi$
$883$	−20.6785	+	49.9223i	−0.695886	+	1.68002i	−0.732570	+	0.680692i	$0.761679\pi$
$884$		0			0
$885$	2.64534	−	1.09574i	0.0889221	−	0.0368327i
$886$		0			0
$887$	17.8530	+	17.8530i	0.599446	+	0.599446i	0.940165	−	0.340719i	$-0.110671\pi$
$887$	17.8530	+	17.8530i	0.599446	+	0.599446i	−0.340719	+	0.940165i	$0.610671\pi$
$888$		0			0
$889$	−7.42029	+	7.42029i	−0.248868	+	0.248868i
$890$		0			0
$891$	12.7209	+	30.7109i	0.426165	+	1.02885i
$892$		0			0
$893$	−36.9950	−	15.3238i	−1.23799	−	0.512792i
$894$		0			0
$895$	−12.5531			−0.419604
$896$		0			0
$897$	−64.3400			−2.14825
$898$		0			0
$899$	−1.89402	−	0.784527i	−0.0631690	−	0.0261655i
$900$		0			0
$901$	14.6847	+	35.4521i	0.489220	+	1.18108i
$902$		0			0
$903$	1.62107	−	1.62107i	0.0539457	−	0.0539457i
$904$		0			0
$905$	−8.82413	−	8.82413i	−0.293324	−	0.293324i
$906$		0			0
$907$	10.2527	−	4.24679i	0.340434	−	0.141012i	−0.205915	−	0.978570i	$-0.566017\pi$
$907$	10.2527	−	4.24679i	0.340434	−	0.141012i	0.546349	+	0.837558i	$0.316017\pi$
$908$		0			0
$909$	0.0182783	−	0.0441276i	0.000606252	−	0.00146362i
$910$		0			0
$911$			28.1022i			0.931067i	0.885030	+	0.465534i	$0.154138\pi$
$911$			28.1022i			0.931067i	−0.885030	+	0.465534i	$0.845862\pi$
$912$		0			0
$913$		−	3.51032i		−	0.116174i
$914$		0			0
$915$	2.93340	−	7.08185i	0.0969752	−	0.234119i
$916$		0			0
$917$	15.1168	−	6.26160i	0.499202	−	0.206776i
$918$		0			0
$919$	5.17031	+	5.17031i	0.170553	+	0.170553i	0.787222	−	0.616669i	$-0.211518\pi$
$919$	5.17031	+	5.17031i	0.170553	+	0.170553i	−0.616669	+	0.787222i	$0.711518\pi$
$920$		0			0
$921$	−26.3169	+	26.3169i	−0.867172	+	0.867172i
$922$		0			0
$923$	−31.2955	−	75.5541i	−1.03011	−	2.48689i
$924$		0			0
$925$	−16.9678	−	7.02831i	−0.557899	−	0.231089i
$926$		0			0
$927$	0.190023			0.00624116
$928$		0			0
$929$	−21.6165			−0.709215			−0.354608	−	0.935015i	$-0.615386\pi$
$929$	−21.6165			−0.709215			−0.354608	+	0.935015i	$0.615386\pi$
$930$		0			0
$931$	4.66733	+	1.93327i	0.152965	+	0.0633604i
$932$		0			0
$933$	−14.4498	−	34.8848i	−0.473064	−	1.14208i
$934$		0			0
$935$	7.69664	−	7.69664i	0.251707	−	0.251707i
$936$		0			0
$937$	−32.3267	−	32.3267i	−1.05607	−	1.05607i	−0.998332	−	0.0577344i	$-0.981612\pi$
$937$	−32.3267	−	32.3267i	−1.05607	−	1.05607i	−0.0577344	−	0.998332i	$-0.518388\pi$
$938$		0			0
$939$	−31.7569	+	13.1541i	−1.03635	+	0.429269i
$940$		0			0
$941$	−9.90288	+	23.9077i	−0.322825	+	0.779368i	0.676263	+	0.736660i	$0.263598\pi$
$941$	−9.90288	+	23.9077i	−0.322825	+	0.779368i	−0.999088	+	0.0427073i	$0.986402\pi$
$942$		0			0
$943$			74.9612i			2.44107i
$944$		0			0
$945$		−	6.95390i		−	0.226210i
$946$		0			0
$947$	−8.97880	+	21.6767i	−0.291772	+	0.704399i	−0.999999	−	0.00158544i	$-0.999495\pi$
$947$	−8.97880	+	21.6767i	−0.291772	+	0.704399i	0.708227	+	0.705985i	$0.249495\pi$
$948$		0			0
$949$	13.5854	−	5.62726i	0.441001	−	0.182669i
$950$		0			0
$951$	−9.74220	−	9.74220i	−0.315912	−	0.315912i
$952$		0			0
$953$	−3.00440	+	3.00440i	−0.0973222	+	0.0973222i	−0.754092	−	0.656769i	$-0.771923\pi$
$953$	−3.00440	+	3.00440i	−0.0973222	+	0.0973222i	0.656769	+	0.754092i	$0.271923\pi$
$954$		0			0
$955$	−2.21561	−	5.34895i	−0.0716954	−	0.173088i
$956$		0			0
$957$	−7.94930	−	3.29271i	−0.256965	−	0.106438i
$958$		0			0
$959$	18.6010			0.600657
$960$		0			0
$961$	−28.6569			−0.924415
$962$		0			0
$963$	−0.435066	−	0.180210i	−0.0140198	−	0.00580720i
$964$		0			0
$965$	−0.810542	−	1.95682i	−0.0260923	−	0.0629923i
$966$		0			0
$967$	−29.1087	+	29.1087i	−0.936074	+	0.936074i	−0.998076	−	0.0620023i	$-0.980251\pi$
$967$	−29.1087	+	29.1087i	−0.936074	+	0.936074i	0.0620023	+	0.998076i	$0.480251\pi$
$968$		0			0
$969$	−26.4307	−	26.4307i	−0.849075	−	0.849075i
$970$		0			0
$971$	0.623957	−	0.258452i	0.0200237	−	0.00829411i	−0.372649	−	0.927972i	$-0.621550\pi$
$971$	0.623957	−	0.258452i	0.0200237	−	0.00829411i	0.392673	+	0.919678i	$0.371550\pi$
$972$		0			0
$973$	10.6739	−	25.7690i	0.342189	−	0.826117i
$974$		0			0
$975$			49.5079i			1.58552i
$976$		0			0
$977$			33.1041i			1.05909i	0.848281	+	0.529546i	$0.177638\pi$
$977$			33.1041i			1.05909i	−0.848281	+	0.529546i	$0.822362\pi$
$978$		0			0
$979$	−2.31700	+	5.59374i	−0.0740518	+	0.178777i
$980$		0			0
$981$	0.158116	−	0.0654936i	0.00504824	−	0.00209105i
$982$		0			0
$983$	−1.49880	−	1.49880i	−0.0478044	−	0.0478044i	0.682800	−	0.730605i	$-0.260762\pi$
$983$	−1.49880	−	1.49880i	−0.0478044	−	0.0478044i	−0.730605	+	0.682800i	$0.760762\pi$
$984$		0			0
$985$	−6.23264	+	6.23264i	−0.198588	+	0.198588i
$986$		0			0
$987$	−15.4351	−	37.2636i	−0.491304	−	1.18611i
$988$		0			0
$989$	3.11684	+	1.29104i	0.0991098	+	0.0410526i
$990$		0			0
$991$	−25.9387			−0.823970			−0.411985	−	0.911191i	$-0.635164\pi$
$991$	−25.9387			−0.823970			−0.411985	+	0.911191i	$0.635164\pi$
$992$		0			0
$993$	12.0895			0.383649
$994$		0			0
$995$	11.6146	+	4.81094i	0.368209	+	0.152517i
$996$		0			0
$997$	2.47449	+	5.97395i	0.0783679	+	0.189197i	0.958208	−	0.286074i	$-0.0923502\pi$
$997$	2.47449	+	5.97395i	0.0783679	+	0.189197i	−0.879840	+	0.475270i	$0.842350\pi$
$998$		0			0
$999$	14.4406	−	14.4406i	0.456881	−	0.456881i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1024.2.g.c.641.2	yes	16
4.3	odd	2	inner	1024.2.g.c.641.3	yes	16
8.3	odd	2		1024.2.g.h.641.2	yes	16
8.5	even	2		1024.2.g.h.641.3	yes	16
16.3	odd	4		1024.2.g.b.129.2	✓	16
16.5	even	4		1024.2.g.e.129.2	yes	16
16.11	odd	4		1024.2.g.e.129.3	yes	16
16.13	even	4		1024.2.g.b.129.3	yes	16
32.3	odd	8		1024.2.g.e.897.3	yes	16
32.5	even	8		1024.2.g.h.385.3	yes	16
32.11	odd	8	inner	1024.2.g.c.385.3	yes	16
32.13	even	8		1024.2.g.b.897.3	yes	16
32.19	odd	8		1024.2.g.b.897.2	yes	16
32.21	even	8	inner	1024.2.g.c.385.2	yes	16
32.27	odd	8		1024.2.g.h.385.2	yes	16
32.29	even	8		1024.2.g.e.897.2	yes	16
64.11	odd	16		4096.2.a.n.1.5		8
64.21	even	16		4096.2.a.n.1.6		8
64.43	odd	16		4096.2.a.o.1.4		8
64.53	even	16		4096.2.a.o.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1024.2.g.b.129.2	✓	16	16.3	odd	4
1024.2.g.b.129.3	yes	16	16.13	even	4
1024.2.g.b.897.2	yes	16	32.19	odd	8
1024.2.g.b.897.3	yes	16	32.13	even	8
1024.2.g.c.385.2	yes	16	32.21	even	8	inner
1024.2.g.c.385.3	yes	16	32.11	odd	8	inner
1024.2.g.c.641.2	yes	16	1.1	even	1	trivial
1024.2.g.c.641.3	yes	16	4.3	odd	2	inner
1024.2.g.e.129.2	yes	16	16.5	even	4
1024.2.g.e.129.3	yes	16	16.11	odd	4
1024.2.g.e.897.2	yes	16	32.29	even	8
1024.2.g.e.897.3	yes	16	32.3	odd	8
1024.2.g.h.385.2	yes	16	32.27	odd	8
1024.2.g.h.385.3	yes	16	32.5	even	8
1024.2.g.h.641.2	yes	16	8.3	odd	2
1024.2.g.h.641.3	yes	16	8.5	even	2
4096.2.a.n.1.5		8	64.11	odd	16
4096.2.a.n.1.6		8	64.21	even	16
4096.2.a.o.1.3		8	64.53	even	16
4096.2.a.o.1.4		8	64.43	odd	16

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:	\( N \)	\(=\)	\( 1024 = 2^{10} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1024.g (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.59352 - 0.660056i) q^{3} +(0.212292 + 0.512517i) q^{5} +(-1.69883 + 1.69883i) q^{7} +(-0.0177021 - 0.0177021i) q^{9} +O(q^{10})\)	\(q+(-1.59352 - 0.660056i) q^{3} +(0.212292 + 0.512517i) q^{5} +(-1.69883 + 1.69883i) q^{7} +(-0.0177021 - 0.0177021i) q^{9} +(-3.44127 + 1.42542i) q^{11} +(2.34094 - 5.65154i) q^{13} -0.956828i q^{15} +5.26768i q^{17} +(1.57436 - 3.80083i) q^{19} +(3.82843 - 1.58579i) q^{21} +(4.31195 + 4.31195i) q^{23} +(3.31793 - 3.31793i) q^{25} +(1.99669 + 4.82044i) q^{27} +(-1.23733 - 0.512517i) q^{29} +1.53073 q^{31} +6.42458 q^{33} +(-1.23132 - 0.510031i) q^{35} +(-1.49785 - 3.61614i) q^{37} +(-7.46066 + 7.46066i) q^{39} +(8.69226 + 8.69226i) q^{41} +(0.511123 - 0.211714i) q^{43} +(0.00531461 - 0.0128306i) q^{45} -9.73339i q^{47} +1.22798i q^{49} +(3.47696 - 8.39412i) q^{51} +(6.73012 - 2.78771i) q^{53} +(-1.46111 - 1.46111i) q^{55} +(-5.01752 + 5.01752i) q^{57} +(1.14517 + 2.76469i) q^{59} +(7.40138 + 3.06575i) q^{61} +0.0601454 q^{63} +3.39347 q^{65} +(5.33529 + 2.20995i) q^{67} +(-4.02503 - 9.71729i) q^{69} +(9.45315 - 9.45315i) q^{71} +(1.69977 + 1.69977i) q^{73} +(-7.47719 + 3.09715i) q^{75} +(3.42458 - 8.26768i) q^{77} -12.8332i q^{79} -8.92427i q^{81} +(-0.360647 + 0.870678i) q^{83} +(-2.69977 + 1.11828i) q^{85} +(1.63341 + 1.63341i) q^{87} +(1.14939 - 1.14939i) q^{89} +(5.62413 + 13.5778i) q^{91} +(-2.43925 - 1.01037i) q^{93} +2.28221 q^{95} -1.83880 q^{97} +(0.0861505 + 0.0356847i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{5} + 16 q^{9}+O(q^{10}) \) 16 * q - 8 * q^5 + 16 * q^9	\( 16 q - 8 q^{5} + 16 q^{9} - 24 q^{13} + 16 q^{21} + 32 q^{25} + 24 q^{29} + 80 q^{33} - 40 q^{37} + 16 q^{41} - 24 q^{45} + 56 q^{53} + 80 q^{57} - 8 q^{61} + 32 q^{65} - 32 q^{69} + 32 q^{73} + 32 q^{77} - 48 q^{85} - 32 q^{89} + 16 q^{93} + 16 q^{97}+O(q^{100}) \) 16 * q - 8 * q^5 + 16 * q^9 - 24 * q^13 + 16 * q^21 + 32 * q^25 + 24 * q^29 + 80 * q^33 - 40 * q^37 + 16 * q^41 - 24 * q^45 + 56 * q^53 + 80 * q^57 - 8 * q^61 + 32 * q^65 - 32 * q^69 + 32 * q^73 + 32 * q^77 - 48 * q^85 - 32 * q^89 + 16 * q^93 + 16 * q^97

Introduction

L-functions

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Varieties

Fields

Representations

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Database

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