LMFDB - Embedded newform 1024.2.g.c.385.2

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			385.2
Root			$-1.50947 - 0.849413i$ of defining polynomial
Character	$\chi$	$=$	1024.385
Dual form			1024.2.g.c.641.2

$q$-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 $\left(\mathbb{Z}/1024\mathbb{Z}\right)^\times$.

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

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	−0.791883	−	0.610673i	$-0.790899\pi$
$3$	−1.59352	+	0.660056i	−0.920017	+	0.381083i	−0.128134	+	0.991757i	$0.540899\pi$
$4$		0			0
$5$	0.212292	−	0.512517i	0.0949397	−	0.229205i	−0.869274	−	0.494330i	$-0.835413\pi$
$5$	0.212292	−	0.512517i	0.0949397	−	0.229205i	0.964214	+	0.265125i	$0.0854134\pi$
$6$		0			0
$7$	−1.69883	−	1.69883i	−0.642096	−	0.642096i	0.308974	−	0.951070i	$-0.400014\pi$
$7$	−1.69883	−	1.69883i	−0.642096	−	0.642096i	−0.951070	+	0.308974i	$0.900014\pi$
$8$		0			0
$9$	−0.0177021	+	0.0177021i	−0.00590068	+	0.00590068i
$10$		0			0
$11$	−3.44127	−	1.42542i	−1.03758	−	0.429781i	−0.202139	−	0.979357i	$-0.564789\pi$
$11$	−3.44127	−	1.42542i	−1.03758	−	0.429781i	−0.835444	+	0.549576i	$0.814789\pi$
$12$		0			0
$13$	2.34094	+	5.65154i	0.649261	+	1.56746i	0.813839	+	0.581091i	$0.197374\pi$
$13$	2.34094	+	5.65154i	0.649261	+	1.56746i	−0.164577	+	0.986364i	$0.552626\pi$
$14$		0			0
$15$			0.956828i			0.247052i
$16$		0			0
$17$		−	5.26768i		−	1.27760i	−0.769373	−	0.638799i	$-0.779431\pi$
$17$		−	5.26768i		−	1.27760i	0.769373	−	0.638799i	$-0.220569\pi$
$18$		0			0
$19$	1.57436	+	3.80083i	0.361182	+	0.871970i	0.995128	+	0.0985928i	$0.0314341\pi$
$19$	1.57436	+	3.80083i	0.361182	+	0.871970i	−0.633946	+	0.773377i	$0.718566\pi$
$20$		0			0
$21$	3.82843	+	1.58579i	0.835431	+	0.346047i
$22$		0			0
$23$	4.31195	−	4.31195i	0.899104	−	0.899104i	−0.0962527	−	0.995357i	$-0.530686\pi$
$23$	4.31195	−	4.31195i	0.899104	−	0.899104i	0.995357	+	0.0962527i	$0.0306857\pi$
$24$		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	−0.494596	−	0.869123i	$-0.664684\pi$
$29$	−1.23733	+	0.512517i	−0.229766	+	0.0951721i	0.264830	+	0.964295i	$0.414684\pi$
$30$		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	−0.997879	−	0.0650915i	$-0.979266\pi$
$37$	−1.49785	+	3.61614i	−0.246245	+	0.594489i	0.751634	+	0.659581i	$0.229266\pi$
$38$		0			0
$39$	−7.46066	−	7.46066i	−1.19466	−	1.19466i
$40$		0			0
$41$	8.69226	−	8.69226i	1.35750	−	1.35750i	0.480518	−	0.876985i	$-0.340449\pi$
$41$	8.69226	−	8.69226i	1.35750	−	1.35750i	0.876985	−	0.480518i	$-0.159551\pi$
$42$		0			0
$43$	0.511123	+	0.211714i	0.0779456	+	0.0322861i	0.421316	−	0.906914i	$-0.361568\pi$
$43$	0.511123	+	0.211714i	0.0779456	+	0.0322861i	−0.343370	+	0.939200i	$0.611568\pi$
$44$		0			0
$45$	0.00531461	+	0.0128306i	0.000792255	+	0.00191267i
$46$		0			0
$47$			9.73339i			1.41976i	0.704322	+	0.709881i	$0.251251\pi$
$47$			9.73339i			1.41976i	−0.704322	+	0.709881i	$0.748749\pi$
$48$		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	0.793572	−	0.608477i	$-0.208219\pi$
$53$	6.73012	+	2.78771i	0.924454	+	0.382921i	0.130882	+	0.991398i	$0.458219\pi$
$54$		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	−0.831637	−	0.555319i	$-0.812596\pi$
$59$	1.14517	−	2.76469i	0.149089	−	0.359933i	0.980726	+	0.195387i	$0.0625961\pi$
$60$		0			0
$61$	7.40138	−	3.06575i	0.947650	−	0.392529i	0.145303	−	0.989387i	$-0.453584\pi$
$61$	7.40138	−	3.06575i	0.947650	−	0.392529i	0.802347	+	0.596858i	$0.203584\pi$
$62$		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	−0.0321778	−	0.999482i	$-0.510244\pi$
$67$	5.33529	−	2.20995i	0.651810	−	0.269988i	0.683987	+	0.729494i	$0.260244\pi$
$68$		0			0
$69$	−4.02503	+	9.71729i	−0.484557	+	1.16982i
$70$		0			0
$71$	9.45315	+	9.45315i	1.12188	+	1.12188i	0.991458	+	0.130424i	$0.0416338\pi$
$71$	9.45315	+	9.45315i	1.12188	+	1.12188i	0.130424	+	0.991458i	$0.458366\pi$
$72$		0			0
$73$	1.69977	−	1.69977i	0.198944	−	0.198944i	−0.600603	−	0.799547i	$-0.705073\pi$
$73$	1.69977	−	1.69977i	0.198944	−	0.198944i	0.799547	+	0.600603i	$0.205073\pi$
$74$		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	$0.256742\pi$
$79$			12.8332i			1.44385i	−0.691973	+	0.721923i	$0.743258\pi$
$80$		0			0
$81$			8.92427i			0.991586i
$82$		0			0
$83$	−0.360647	−	0.870678i	−0.0395861	−	0.0955693i	0.902850	−	0.429956i	$-0.141471\pi$
$83$	−0.360647	−	0.870678i	−0.0395861	−	0.0955693i	−0.942436	+	0.334387i	$0.891471\pi$
$84$		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	0.765396	−	0.643560i	$-0.222543\pi$
$89$	1.14939	+	1.14939i	0.121835	+	0.121835i	−0.643560	+	0.765396i	$0.722543\pi$
$90$		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	−0.883383	−	0.468652i	$-0.844740\pi$
$101$	0.730123	−	1.76267i	0.0726500	−	0.175393i	0.956033	+	0.293259i	$0.0947399\pi$
$102$		0			0
$103$	−5.36725	−	5.36725i	−0.528851	−	0.528851i	0.391379	−	0.920230i	$-0.371998\pi$
$103$	−5.36725	−	5.36725i	−0.528851	−	0.528851i	−0.920230	+	0.391379i	$0.871998\pi$
$104$		0			0
$105$	1.62549	−	1.62549i	0.158631	−	0.158631i
$106$		0			0
$107$	17.3787	+	7.19848i	1.68006	+	0.695904i	0.999329	−	0.0366299i	$-0.0116623\pi$
$107$	17.3787	+	7.19848i	1.68006	+	0.695904i	0.680731	+	0.732534i	$0.261662\pi$
$108$		0			0
$109$	−2.61614	−	6.31591i	−0.250580	−	0.604954i	0.747671	−	0.664070i	$-0.231172\pi$
$109$	−2.61614	−	6.31591i	−0.250580	−	0.604954i	−0.998251	+	0.0591151i	$0.981172\pi$
$110$		0			0
$111$		−	6.75103i		−	0.640780i
$112$		0			0
$113$		−	6.60045i		−	0.620918i	−0.950587	−	0.310459i	$-0.899517\pi$
$113$		−	6.60045i		−	0.620918i	0.950587	−	0.310459i	$-0.100483\pi$
$114$		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	−0.640226	−	0.768186i	$-0.721159\pi$
$131$	−6.29212	+	2.60628i	−0.549745	+	0.227712i	0.0904813	+	0.995898i	$0.471159\pi$
$132$		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	−0.901179	−	0.433448i	$-0.857297\pi$
$137$	−5.47465	+	5.47465i	−0.467731	+	0.467731i	0.433448	+	0.901179i	$0.357297\pi$
$138$		0			0
$139$	−10.7259	−	4.44282i	−0.909760	−	0.376835i	−0.121795	−	0.992555i	$-0.538865\pi$
$139$	−10.7259	−	4.44282i	−0.909760	−	0.376835i	−0.787965	+	0.615721i	$0.788865\pi$
$140$		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	0.569141	−	0.822240i	$-0.307276\pi$
$149$	4.76267	+	1.97276i	0.390173	+	0.161615i	−0.178968	+	0.983855i	$0.557276\pi$
$150$		0			0
$151$	13.9603	−	13.9603i	1.13607	−	1.13607i	0.146924	−	0.989148i	$-0.453063\pi$
$151$	13.9603	−	13.9603i	1.13607	−	1.13607i	0.989148	−	0.146924i	$-0.0469374\pi$
$152$		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	−0.915866	−	0.401484i	$-0.868494\pi$
$157$	−16.0332	+	6.64117i	−1.27959	+	0.530023i	−0.363723	+	0.931507i	$0.618494\pi$
$158$		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	−0.190303	−	0.981725i	$-0.560947\pi$
$163$	4.71513	−	1.95307i	0.369317	−	0.152976i	0.559620	+	0.828749i	$0.310947\pi$
$164$		0			0
$165$	1.36388	−	3.29271i	0.106178	−	0.256337i
$166$		0			0
$167$	3.52743	+	3.52743i	0.272960	+	0.272960i	0.830291	−	0.557330i	$-0.188174\pi$
$167$	3.52743	+	3.52743i	0.272960	+	0.272960i	−0.557330	+	0.830291i	$0.688174\pi$
$168$		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	0.960269	+	0.279077i	$0.0900284\pi$
$173$	6.29491	+	15.1973i	0.478593	+	1.15543i	−0.481676	+	0.876350i	$0.659972\pi$
$174$		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	−0.816704	−	0.577057i	$-0.804201\pi$
$179$	−8.65959	−	20.9061i	−0.647248	−	1.56260i	0.169455	−	0.985538i	$-0.445799\pi$
$180$		0			0
$181$	−20.7830	−	8.60862i	−1.54479	−	0.639874i	−0.562427	−	0.826847i	$-0.690132\pi$
$181$	−20.7830	−	8.60862i	−1.54479	−	0.639874i	−0.982365	+	0.186974i	$0.940132\pi$
$182$		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	−0.545033	−	0.838414i	$-0.683483\pi$
$197$	6.08042	−	14.6794i	0.433212	−	1.04587i	0.978245	−	0.207452i	$-0.0665170\pi$
$198$		0			0
$199$	16.0244	+	16.0244i	1.13594	+	1.13594i	0.989171	+	0.146771i	$0.0468879\pi$
$199$	16.0244	+	16.0244i	1.13594	+	1.13594i	0.146771	+	0.989171i	$0.453112\pi$
$200$		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	−0.992198	−	0.124669i	$-0.960213\pi$
$211$	−5.50184	−	13.2826i	−0.378762	−	0.914413i	0.613436	−	0.789744i	$-0.289787\pi$
$212$		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	−0.548410	−	0.836210i	$-0.684767\pi$
$227$	−5.19652	+	2.15247i	−0.344905	+	0.142864i	0.203505	+	0.979074i	$0.434767\pi$
$228$		0			0
$229$	5.04072	−	12.1694i	0.333100	−	0.804175i	−0.665243	−	0.746627i	$-0.731672\pi$
$229$	5.04072	−	12.1694i	0.333100	−	0.804175i	0.998343	−	0.0575475i	$-0.0183281\pi$
$230$		0			0
$231$	−10.9143	−	10.9143i	−0.718105	−	0.718105i
$232$		0			0
$233$	−1.74984	+	1.74984i	−0.114636	+	0.114636i	−0.762098	−	0.647462i	$-0.775831\pi$
$233$	−1.74984	+	1.74984i	−0.114636	+	0.114636i	0.647462	+	0.762098i	$0.275831\pi$
$234$		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	$-0.864629\pi$
$239$		−	12.7565i		−	0.825152i	0.910923	−	0.412576i	$-0.135371\pi$
$240$		0			0
$241$			18.9660i			1.22171i	0.791743	+	0.610854i	$0.209174\pi$
$241$			18.9660i			1.22171i	−0.791743	+	0.610854i	$0.790826\pi$
$242$		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	−0.997085	−	0.0763018i	$-0.975689\pi$
$251$	−3.77199	+	9.10639i	−0.238086	+	0.574790i	0.758999	+	0.651092i	$0.225689\pi$
$252$		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	0.994246	+	0.107120i	$0.0341629\pi$
$263$	17.8612	+	17.8612i	1.10137	+	1.10137i	0.107120	+	0.994246i	$0.465837\pi$
$264$		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	−0.997212	−	0.0746220i	$-0.976225\pi$
$269$	−5.65583	−	13.6544i	−0.344842	−	0.832523i	0.652370	−	0.757901i	$-0.273775\pi$
$270$		0			0
$271$		−	2.39655i		−	0.145580i	−0.997347	−	0.0727901i	$-0.976810\pi$
$271$		−	2.39655i		−	0.145580i	0.997347	−	0.0727901i	$-0.0231903\pi$
$272$		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	0.642595	−	0.766206i	$-0.277858\pi$
$277$	9.24018	+	3.82741i	0.555189	+	0.229967i	−0.0874063	+	0.996173i	$0.527858\pi$
$278$		0			0
$279$	−0.0270971	+	0.0270971i	−0.00162226	+	0.00162226i
$280$		0			0
$281$	−19.8667	−	19.8667i	−1.18515	−	1.18515i	−0.978393	−	0.206754i	$-0.933710\pi$
$281$	−19.8667	−	19.8667i	−1.18515	−	1.18515i	−0.206754	−	0.978393i	$-0.566290\pi$
$282$		0			0
$283$	1.97378	−	4.76511i	0.117329	−	0.283257i	−0.854295	−	0.519788i	$-0.826011\pi$
$283$	1.97378	−	4.76511i	0.117329	−	0.283257i	0.971624	+	0.236532i	$0.0760108\pi$
$284$		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	0.464510	+	0.885568i	$0.346230\pi$
$293$	−8.38983	+	20.2548i	−0.490139	+	1.18330i	−0.954649	+	0.297733i	$0.903770\pi$
$294$		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	0.963598	+	0.267356i	$0.0861501\pi$
$307$	8.25751	+	19.9354i	0.471281	+	1.13777i	−0.492317	+	0.870416i	$0.663850\pi$
$308$		0			0
$309$	12.0955	+	5.01011i	0.688088	+	0.285015i
$310$		0			0
$311$	15.4798	−	15.4798i	0.877779	−	0.877779i	−0.115526	−	0.993304i	$-0.536855\pi$
$311$	15.4798	−	15.4798i	0.877779	−	0.877779i	0.993304	+	0.115526i	$0.0368553\pi$
$312$		0			0
$313$	14.0918	+	14.0918i	0.796516	+	0.796516i	0.982544	−	0.186028i	$-0.0595616\pi$
$313$	14.0918	+	14.0918i	0.796516	+	0.796516i	−0.186028	+	0.982544i	$0.559562\pi$
$314$		0			0
$315$	0.0127684	−	0.0308256i	0.000719416	−	0.00173682i
$316$		0			0
$317$	7.37983	−	3.05683i	0.414492	−	0.171688i	−0.165685	−	0.986179i	$-0.552983\pi$
$317$	7.37983	−	3.05683i	0.414492	−	0.171688i	0.580177	+	0.814490i	$0.302983\pi$
$318$		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	0.197550	−	0.980293i	$-0.436702\pi$
$331$	−6.47564	−	2.68230i	−0.355934	−	0.147433i	−0.553483	+	0.832860i	$0.686702\pi$
$332$		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	$0.0245460\pi$
$337$			2.82843i			0.154074i	−0.997028	+	0.0770371i	$0.975454\pi$
$338$		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	−0.761046	−	0.648698i	$-0.775314\pi$
$347$	4.39235	−	10.6041i	0.235794	−	0.569256i	0.996840	+	0.0794417i	$0.0253138\pi$
$348$		0			0
$349$	19.7580	−	8.18404i	1.05762	−	0.438081i	0.215015	−	0.976611i	$-0.431020\pi$
$349$	19.7580	−	8.18404i	1.05762	−	0.438081i	0.842607	+	0.538529i	$0.181020\pi$
$350$		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	0.862909	−	0.505359i	$-0.168640\pi$
$359$	6.77460	+	6.77460i	0.357550	+	0.357550i	−0.505359	+	0.862909i	$0.668640\pi$
$360$		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	$0.167934\pi$
$367$			19.2892i			1.00689i	−0.864028	+	0.503444i	$0.832066\pi$
$368$		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	0.199190	−	0.979961i	$-0.436169\pi$
$373$	−6.81560	−	2.82311i	−0.352898	−	0.146175i	−0.552088	+	0.833786i	$0.686169\pi$
$374$		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	−0.727094	−	0.686538i	$-0.759130\pi$
$379$	5.30491	−	12.8072i	0.272495	−	0.657861i	0.999589	+	0.0286774i	$0.00912956\pi$
$380$		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	−0.585032	−	0.811010i	$-0.698918\pi$
$389$	7.93103	−	19.1472i	0.402119	−	0.970801i	0.987151	−	0.159791i	$-0.0510820\pi$
$390$		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	0.843111	−	0.537740i	$-0.180722\pi$
$397$	−2.65594	−	6.41201i	−0.133298	−	0.321810i	−0.976409	+	0.215930i	$0.930722\pi$
$398$		0			0
$399$			17.0478i			0.853457i
$400$		0			0
$401$		−	21.0373i		−	1.05055i	−0.850931	−	0.525277i	$-0.823962\pi$
$401$		−	21.0373i		−	1.05055i	0.850931	−	0.525277i	$-0.176038\pi$
$402$		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	0.709743	−	0.704460i	$-0.248811\pi$
$409$	0.106839	+	0.106839i	0.00528285	+	0.00528285i	−0.704460	+	0.709743i	$0.748811\pi$
$410$		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	−0.790011	−	0.613093i	$-0.789925\pi$
$419$	−18.7318	+	7.75898i	−0.915110	+	0.379051i	−0.125099	+	0.992144i	$0.539925\pi$
$420$		0			0
$421$	−5.08471	+	12.2756i	−0.247814	+	0.598275i	−0.998018	−	0.0629310i	$-0.979955\pi$
$421$	−5.08471	+	12.2756i	−0.247814	+	0.598275i	0.750204	+	0.661206i	$0.229955\pi$
$422$		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	$0.0693008\pi$
$431$			8.96851i			0.431998i	−0.976394	+	0.215999i	$0.930699\pi$
$432$		0			0
$433$			3.14680i			0.151225i	0.997137	+	0.0756127i	$0.0240913\pi$
$433$			3.14680i			0.151225i	−0.997137	+	0.0756127i	$0.975909\pi$
$434$		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	−0.567645	−	0.823274i	$-0.692145\pi$
$439$	5.35602	−	5.35602i	0.255629	−	0.255629i	0.823274	+	0.567645i	$0.192145\pi$
$440$		0			0
$441$	0.0217377	+	0.0217377i	0.00103513	+	0.00103513i
$442$		0			0
$443$	−7.13988	+	17.2372i	−0.339226	+	0.818964i	0.658564	+	0.752524i	$0.271164\pi$
$443$	−7.13988	+	17.2372i	−0.339226	+	0.818964i	−0.997790	+	0.0664397i	$0.978836\pi$
$444$		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	−0.895924	−	0.444207i	$-0.853485\pi$
$457$	−9.65659	+	9.65659i	−0.451716	+	0.451716i	0.444207	+	0.895924i	$0.353485\pi$
$458$		0			0
$459$	−25.3925	−	10.5179i	−1.18522	−	0.490935i
$460$		0			0
$461$	9.64976	+	23.2966i	0.449434	+	1.08503i	0.972534	+	0.232759i	$0.0747753\pi$
$461$	9.64976	+	23.2966i	0.449434	+	1.08503i	−0.523100	+	0.852271i	$0.675225\pi$
$462$		0			0
$463$			1.57747i			0.0733113i	0.999328	+	0.0366556i	$0.0116705\pi$
$463$			1.57747i			0.0733113i	−0.999328	+	0.0366556i	$0.988330\pi$
$464$		0			0
$465$			1.46465i			0.0679215i
$466$		0			0
$467$	9.79289	+	23.6421i	0.453161	+	1.09403i	0.971114	+	0.238618i	$0.0766943\pi$
$467$	9.79289	+	23.6421i	0.453161	+	1.09403i	−0.517953	+	0.855409i	$0.673306\pi$
$468$		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	0.265194	−	0.964195i	$-0.414564\pi$
$487$	−15.4256	−	15.4256i	−0.699001	−	0.699001i	−0.964195	+	0.265194i	$0.914564\pi$
$488$		0			0
$489$	−6.22450	+	6.22450i	−0.281481	+	0.281481i
$490$		0			0
$491$	−28.8199	−	11.9376i	−1.30062	−	0.538736i	−0.378489	−	0.925606i	$-0.623556\pi$
$491$	−28.8199	−	11.9376i	−1.30062	−	0.538736i	−0.922134	+	0.386870i	$0.873556\pi$
$492$		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	0.806858	+	0.590746i	$0.201166\pi$
$499$	14.6102	+	35.2722i	0.654043	+	1.57900i	−0.152814	+	0.988255i	$0.548834\pi$
$500$		0			0
$501$	−7.94930	−	3.29271i	−0.355149	−	0.147107i
$502$		0			0
$503$	−2.18240	+	2.18240i	−0.0973084	+	0.0973084i	−0.754085	−	0.656777i	$-0.771919\pi$
$503$	−2.18240	+	2.18240i	−0.0973084	+	0.0973084i	0.656777	+	0.754085i	$0.271919\pi$
$504$		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	−0.211477	−	0.977383i	$-0.567827\pi$
$509$	7.44742	−	3.08482i	0.330101	−	0.136732i	0.541578	+	0.840651i	$0.317827\pi$
$510$		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	−0.538400	−	0.842689i	$-0.680971\pi$
$521$	6.94553	−	6.94553i	0.304289	−	0.304289i	0.842689	+	0.538400i	$0.180971\pi$
$522$		0			0
$523$	−2.24673	−	0.930625i	−0.0982425	−	0.0406934i	0.333021	−	0.942919i	$-0.391932\pi$
$523$	−2.24673	−	0.930625i	−0.0982425	−	0.0406934i	−0.431263	+	0.902226i	$0.641932\pi$
$524$		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	−0.854894	−	0.518802i	$-0.826378\pi$
$541$	−25.4120	+	10.5260i	−1.09255	+	0.452548i	−0.237653	+	0.971350i	$0.576378\pi$
$542$		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	−0.328029	−	0.944668i	$-0.606384\pi$
$547$	2.52591	−	1.04627i	0.108000	−	0.0447351i	0.436029	+	0.899932i	$0.356384\pi$
$548$		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	0.994549	+	0.104271i	$0.0332509\pi$
$557$	8.61495	+	20.7983i	0.365027	+	0.881254i	−0.629522	+	0.776983i	$0.716749\pi$
$558$		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	−0.994522	−	0.104527i	$-0.966667\pi$
$563$	−8.66534	−	20.9200i	−0.365201	−	0.881672i	0.629321	−	0.777145i	$-0.283333\pi$
$564$		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	0.712882	−	0.701284i	$-0.247390\pi$
$569$	0.276633	+	0.276633i	0.0115970	+	0.0115970i	−0.701284	+	0.712882i	$0.747390\pi$
$570$		0			0
$571$	13.2460	−	31.9788i	0.554329	−	1.33827i	−0.359869	−	0.933003i	$-0.617179\pi$
$571$	13.2460	−	31.9788i	0.554329	−	1.33827i	0.914198	−	0.405267i	$-0.132821\pi$
$572$		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	0.937281	−	0.348575i	$-0.113335\pi$
$587$	32.7941	+	13.5838i	1.35356	+	0.560662i	0.416277	+	0.909238i	$0.363335\pi$
$588$		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	$-0.982570\pi$
$593$		−	2.66555i		−	0.109461i	0.998501	−	0.0547306i	$-0.0174300\pi$
$594$		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	−0.907211	−	0.420677i	$-0.861793\pi$
$599$	−11.9077	+	11.9077i	−0.486534	+	0.486534i	0.420677	+	0.907211i	$0.361793\pi$
$600$		0			0
$601$	1.86501	+	1.86501i	0.0760755	+	0.0760755i	0.744121	−	0.668045i	$-0.232869\pi$
$601$	1.86501	+	1.86501i	0.0760755	+	0.0760755i	−0.668045	+	0.744121i	$0.732869\pi$
$602$		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	0.598926	+	0.800805i	$0.295595\pi$
$613$	−9.67657	+	23.3613i	−0.390833	+	0.943555i	−0.989759	+	0.142750i	$0.954405\pi$
$614$		0			0
$615$	8.31700	+	8.31700i	0.335374	+	0.335374i
$616$		0			0
$617$	8.91738	−	8.91738i	0.359000	−	0.359000i	−0.504444	−	0.863444i	$-0.668303\pi$
$617$	8.91738	−	8.91738i	0.359000	−	0.359000i	0.863444	+	0.504444i	$0.168303\pi$
$618$		0			0
$619$	−5.56774	−	2.30623i	−0.223786	−	0.0926953i	0.267973	−	0.963426i	$-0.413646\pi$
$619$	−5.56774	−	2.30623i	−0.223786	−	0.0926953i	−0.491760	+	0.870731i	$0.663646\pi$
$620$		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	0.430981	−	0.902361i	$-0.358167\pi$
$631$	33.4932	−	33.4932i	1.33334	−	1.33334i	0.902361	−	0.430981i	$-0.141833\pi$
$632$		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	0.336918	−	0.941534i	$-0.390616\pi$
$643$	31.4666	−	13.0339i	1.24092	−	0.514006i	0.904002	+	0.427528i	$0.140616\pi$
$644$		0			0
$645$	−0.202574	+	0.489057i	−0.00797635	+	0.0192566i
$646$		0			0
$647$	6.43000	+	6.43000i	0.252789	+	0.252789i	0.822113	−	0.569324i	$-0.192795\pi$
$647$	6.43000	+	6.43000i	0.252789	+	0.252789i	−0.569324	+	0.822113i	$0.692795\pi$
$648$		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	0.992576	−	0.121628i	$-0.0388115\pi$
$653$	5.23125	+	12.6294i	0.204715	+	0.494225i	−0.787861	+	0.615853i	$0.788812\pi$
$654$		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	0.996357	−	0.0852857i	$-0.0271803\pi$
$659$	5.94335	+	14.3485i	0.231520	+	0.558939i	−0.764837	+	0.644224i	$0.777180\pi$
$660$		0			0
$661$	21.2370	+	8.79664i	0.826022	+	0.342150i	0.755327	−	0.655348i	$-0.227478\pi$
$661$	21.2370	+	8.79664i	0.826022	+	0.342150i	0.0706953	+	0.997498i	$0.477478\pi$
$662$		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	0.685586	+	0.727992i	$0.259546\pi$
$677$	−8.16911	+	19.7220i	−0.313964	+	0.757977i	−0.999550	+	0.0299855i	$0.990454\pi$
$678$		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	−0.0960227	−	0.995379i	$-0.530612\pi$
$683$	−22.6783	−	9.39365i	−0.867760	−	0.359438i	−0.771738	+	0.635941i	$0.780612\pi$
$684$		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	0.994107	−	0.108404i	$-0.0345739\pi$
$691$	5.63891	+	13.6135i	0.214514	+	0.517883i	−0.779593	+	0.626287i	$0.784574\pi$
$692$		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	0.615781	−	0.787917i	$-0.288840\pi$
$701$	42.5832	−	17.6385i	1.60835	−	0.666199i	0.992565	+	0.121718i	$0.0388405\pi$
$702$		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	0.564960	+	0.825118i	$0.308892\pi$
$709$	−11.1294	+	26.8688i	−0.417974	+	1.00908i	−0.982934	+	0.183960i	$0.941108\pi$
$710$		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	$-0.989170\pi$
$719$		−	1.82423i		−	0.0680323i	0.999421	−	0.0340162i	$-0.0108298\pi$
$720$		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	−0.974182	−	0.225765i	$-0.927512\pi$
$727$	−20.1795	+	20.1795i	−0.748416	+	0.748416i	0.225765	+	0.974182i	$0.427512\pi$
$728$		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	−0.165077	−	0.986281i	$-0.552787\pi$
$733$	11.2520	−	4.66073i	0.415602	−	0.172148i	0.580679	+	0.814133i	$0.302787\pi$
$734$		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	0.0752197	−	0.997167i	$-0.476034\pi$
$739$	22.6586	−	9.38552i	0.833512	−	0.345252i	0.758292	+	0.651915i	$0.226034\pi$
$740$		0			0
$741$	16.6110	−	40.1024i	0.610219	−	1.47320i
$742$		0			0
$743$	30.4077	+	30.4077i	1.11555	+	1.11555i	0.992386	+	0.123164i	$0.0393041\pi$
$743$	30.4077	+	30.4077i	1.11555	+	1.11555i	0.123164	+	0.992386i	$0.460696\pi$
$744$		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	$0.0338268\pi$
$751$			5.81357i			0.212140i	−0.994359	+	0.106070i	$0.966173\pi$
$752$		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	0.430420	−	0.902629i	$-0.358365\pi$
$757$	2.65558	+	1.09998i	0.0965185	+	0.0399793i	−0.333902	+	0.942608i	$0.608365\pi$
$758$		0			0
$759$	27.7025	−	27.7025i	1.00554	−	1.00554i
$760$		0			0
$761$	−17.9432	−	17.9432i	−0.650442	−	0.650442i	0.302658	−	0.953099i	$-0.402126\pi$
$761$	−17.9432	−	17.9432i	−0.650442	−	0.650442i	−0.953099	+	0.302658i	$0.902126\pi$
$762$		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	−0.998893	−	0.0470471i	$-0.985019\pi$
$773$	−7.20933	+	17.4049i	−0.259302	+	0.626009i	0.739591	+	0.673056i	$0.235019\pi$
$774$		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	−0.962241	−	0.272198i	$-0.912249\pi$
$787$	−13.3060	−	32.1235i	−0.474307	−	1.14508i	0.487934	−	0.872881i	$-0.337751\pi$
$788$		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	−0.655609	−	0.755101i	$-0.727588\pi$
$797$	−16.5225	+	6.84385i	−0.585258	+	0.242422i	0.0703512	+	0.997522i	$0.477588\pi$
$798$		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	−0.496763	−	0.867886i	$-0.665478\pi$
$809$	10.5558	−	10.5558i	0.371123	−	0.371123i	0.867886	+	0.496763i	$0.165478\pi$
$810$		0			0
$811$	4.31304	+	1.78652i	0.151451	+	0.0627333i	0.457122	−	0.889404i	$-0.348880\pi$
$811$	4.31304	+	1.78652i	0.151451	+	0.0627333i	−0.305670	+	0.952138i	$0.598880\pi$
$812$		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	−0.107931	−	0.994158i	$-0.534422\pi$
$821$	−25.4218	−	10.5300i	−0.887225	−	0.367501i	−0.779295	+	0.626658i	$0.784422\pi$
$822$		0			0
$823$	−28.1280	+	28.1280i	−0.980479	+	0.980479i	−0.999813	−	0.0193343i	$-0.993845\pi$
$823$	−28.1280	+	28.1280i	−0.980479	+	0.980479i	0.0193343	+	0.999813i	$0.493845\pi$
$824$		0			0
$825$	21.3163	+	21.3163i	0.742138	+	0.742138i
$826$		0			0
$827$	6.05658	−	14.6219i	0.210608	−	0.508453i	−0.782909	−	0.622136i	$-0.786265\pi$
$827$	6.05658	−	14.6219i	0.210608	−	0.508453i	0.993517	+	0.113683i	$0.0362650\pi$
$828$		0			0
$829$	−28.3516	+	11.7436i	−0.984691	+	0.407872i	−0.816161	−	0.577824i	$-0.803902\pi$
$829$	−28.3516	+	11.7436i	−0.984691	+	0.407872i	−0.168530	+	0.985697i	$0.553902\pi$
$830$		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	0.291401	−	0.956601i	$-0.405878\pi$
$839$	−19.2678	−	19.2678i	−0.665199	−	0.665199i	−0.956601	+	0.291401i	$0.905878\pi$
$840$		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	0.142016	−	0.989864i	$-0.454642\pi$
$853$	−13.3619	−	5.53470i	−0.457504	−	0.189504i	−0.599520	+	0.800360i	$0.704642\pi$
$854$		0			0
$855$	−0.0403999	+	0.0403999i	−0.00138165	+	0.00138165i
$856$		0			0
$857$	16.2115	+	16.2115i	0.553775	+	0.553775i	0.927528	−	0.373753i	$-0.121929\pi$
$857$	16.2115	+	16.2115i	0.553775	+	0.553775i	−0.373753	+	0.927528i	$0.621929\pi$
$858$		0			0
$859$	−10.6184	+	25.6351i	−0.362295	+	0.874658i	0.632669	+	0.774423i	$0.281960\pi$
$859$	−10.6184	+	25.6351i	−0.362295	+	0.874658i	−0.994964	+	0.100235i	$0.968040\pi$
$860$		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	−0.858743	−	0.512407i	$-0.828754\pi$
$877$	−18.1786	−	43.8869i	−0.613846	−	1.48196i	0.244896	−	0.969549i	$-0.421246\pi$
$878$		0			0
$879$		−	37.8142i		−	1.27544i
$880$		0			0
$881$		−	0.849166i		−	0.0286091i	−0.999898	−	0.0143046i	$-0.995447\pi$
$881$		−	0.849166i		−	0.0286091i	0.999898	−	0.0143046i	$-0.00455344\pi$
$882$		0			0
$883$	−20.6785	−	49.9223i	−0.695886	−	1.68002i	−0.732570	−	0.680692i	$-0.761679\pi$
$883$	−20.6785	−	49.9223i	−0.695886	−	1.68002i	0.0366838	−	0.999327i	$-0.488321\pi$
$884$		0			0
$885$	2.64534	+	1.09574i	0.0889221	+	0.0368327i
$886$		0			0
$887$	17.8530	−	17.8530i	0.599446	−	0.599446i	−0.340719	−	0.940165i	$-0.610671\pi$
$887$	17.8530	−	17.8530i	0.599446	−	0.599446i	0.940165	+	0.340719i	$0.110671\pi$
$888$		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	0.546349	−	0.837558i	$-0.316017\pi$
$907$	10.2527	+	4.24679i	0.340434	+	0.141012i	−0.205915	+	0.978570i	$0.566017\pi$
$908$		0			0
$909$	0.0182783	+	0.0441276i	0.000606252	+	0.00146362i
$910$		0			0
$911$		−	28.1022i		−	0.931067i	−0.885030	−	0.465534i	$-0.845862\pi$
$911$		−	28.1022i		−	0.931067i	0.885030	−	0.465534i	$-0.154138\pi$
$912$		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	−0.616669	−	0.787222i	$-0.711518\pi$
$919$	5.17031	−	5.17031i	0.170553	−	0.170553i	0.787222	+	0.616669i	$0.211518\pi$
$920$		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	−0.0577344	+	0.998332i	$0.518388\pi$
$937$	−32.3267	+	32.3267i	−1.05607	+	1.05607i	−0.998332	+	0.0577344i	$0.981612\pi$
$938$		0			0
$939$	−31.7569	−	13.1541i	−1.03635	−	0.429269i
$940$		0			0
$941$	−9.90288	−	23.9077i	−0.322825	−	0.779368i	−0.999088	−	0.0427073i	$-0.986402\pi$
$941$	−9.90288	−	23.9077i	−0.322825	−	0.779368i	0.676263	−	0.736660i	$-0.263598\pi$
$942$		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	0.708227	−	0.705985i	$-0.249495\pi$
$947$	−8.97880	−	21.6767i	−0.291772	−	0.704399i	−0.999999	+	0.00158544i	$0.999495\pi$
$948$		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	0.656769	−	0.754092i	$-0.271923\pi$
$953$	−3.00440	−	3.00440i	−0.0973222	−	0.0973222i	−0.754092	+	0.656769i	$0.771923\pi$
$954$		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	0.0620023	−	0.998076i	$-0.480251\pi$
$967$	−29.1087	−	29.1087i	−0.936074	−	0.936074i	−0.998076	+	0.0620023i	$0.980251\pi$
$968$		0			0
$969$	−26.4307	+	26.4307i	−0.849075	+	0.849075i
$970$		0			0
$971$	0.623957	+	0.258452i	0.0200237	+	0.00829411i	0.392673	−	0.919678i	$-0.371550\pi$
$971$	0.623957	+	0.258452i	0.0200237	+	0.00829411i	−0.372649	+	0.927972i	$0.621550\pi$
$972$		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	$-0.822362\pi$
$977$		−	33.1041i		−	1.05909i	0.848281	−	0.529546i	$-0.177638\pi$
$978$		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	−0.730605	−	0.682800i	$-0.760762\pi$
$983$	−1.49880	+	1.49880i	−0.0478044	+	0.0478044i	0.682800	+	0.730605i	$0.260762\pi$
$984$		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	−0.879840	−	0.475270i	$-0.842350\pi$
$997$	2.47449	−	5.97395i	0.0783679	−	0.189197i	0.958208	+	0.286074i	$0.0923502\pi$
$998$		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.385.2	yes	16
4.3	odd	2	inner	1024.2.g.c.385.3	yes	16
8.3	odd	2		1024.2.g.h.385.2	yes	16
8.5	even	2		1024.2.g.h.385.3	yes	16
16.3	odd	4		1024.2.g.e.897.3	yes	16
16.5	even	4		1024.2.g.b.897.3	yes	16
16.11	odd	4		1024.2.g.b.897.2	yes	16
16.13	even	4		1024.2.g.e.897.2	yes	16
32.3	odd	8	inner	1024.2.g.c.641.3	yes	16
32.5	even	8		1024.2.g.b.129.3	yes	16
32.11	odd	8		1024.2.g.e.129.3	yes	16
32.13	even	8		1024.2.g.h.641.3	yes	16
32.19	odd	8		1024.2.g.h.641.2	yes	16
32.21	even	8		1024.2.g.e.129.2	yes	16
32.27	odd	8		1024.2.g.b.129.2	✓	16
32.29	even	8	inner	1024.2.g.c.641.2	yes	16
64.3	odd	16		4096.2.a.o.1.4		8
64.29	even	16		4096.2.a.o.1.3		8
64.35	odd	16		4096.2.a.n.1.5		8
64.61	even	16		4096.2.a.n.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1024.2.g.b.129.2	✓	16	32.27	odd	8
1024.2.g.b.129.3	yes	16	32.5	even	8
1024.2.g.b.897.2	yes	16	16.11	odd	4
1024.2.g.b.897.3	yes	16	16.5	even	4
1024.2.g.c.385.2	yes	16	1.1	even	1	trivial
1024.2.g.c.385.3	yes	16	4.3	odd	2	inner
1024.2.g.c.641.2	yes	16	32.29	even	8	inner
1024.2.g.c.641.3	yes	16	32.3	odd	8	inner
1024.2.g.e.129.2	yes	16	32.21	even	8
1024.2.g.e.129.3	yes	16	32.11	odd	8
1024.2.g.e.897.2	yes	16	16.13	even	4
1024.2.g.e.897.3	yes	16	16.3	odd	4
1024.2.g.h.385.2	yes	16	8.3	odd	2
1024.2.g.h.385.3	yes	16	8.5	even	2
1024.2.g.h.641.2	yes	16	32.19	odd	8
1024.2.g.h.641.3	yes	16	32.13	even	8
4096.2.a.n.1.5		8	64.35	odd	16
4096.2.a.n.1.6		8	64.61	even	16
4096.2.a.o.1.3		8	64.29	even	16
4096.2.a.o.1.4		8	64.3	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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