LMFDB - Embedded newform 1024.2.g.e.129.2

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			129.2
Root			$1.50947 - 0.849413i$ of defining polynomial
Character	$\chi$	$=$	1024.129
Dual form			1024.2.g.e.897.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.660056 + 1.59352i) q^{3} +(-0.512517 + 0.212292i) q^{5} +(1.69883 - 1.69883i) q^{7} +(0.0177021 + 0.0177021i) q^{9} +O(q^{10})$	\(q+(-0.660056 + 1.59352i) q^{3} +(-0.512517 + 0.212292i) q^{5} +(1.69883 - 1.69883i) q^{7} +(0.0177021 + 0.0177021i) q^{9} +(-1.42542 - 3.44127i) q^{11} +(-5.65154 - 2.34094i) q^{13} -0.956828i q^{15} +5.26768i q^{17} +(-3.80083 - 1.57436i) q^{19} +(1.58579 + 3.82843i) q^{21} +(-4.31195 - 4.31195i) q^{23} +(-3.31793 + 3.31793i) q^{25} +(-4.82044 + 1.99669i) q^{27} +(-0.512517 + 1.23733i) q^{29} +1.53073 q^{31} +6.42458 q^{33} +(-0.510031 + 1.23132i) q^{35} +(3.61614 - 1.49785i) q^{37} +(7.46066 - 7.46066i) q^{39} +(-8.69226 - 8.69226i) q^{41} +(0.211714 + 0.511123i) q^{43} +(-0.0128306 - 0.00531461i) q^{45} -9.73339i q^{47} +1.22798i q^{49} +(-8.39412 - 3.47696i) q^{51} +(2.78771 + 6.73012i) q^{53} +(1.46111 + 1.46111i) q^{55} +(5.01752 - 5.01752i) q^{57} +(-2.76469 + 1.14517i) q^{59} +(3.06575 - 7.40138i) q^{61} +0.0601454 q^{63} +3.39347 q^{65} +(2.20995 - 5.33529i) q^{67} +(9.71729 - 4.02503i) q^{69} +(-9.45315 + 9.45315i) q^{71} +(-1.69977 - 1.69977i) q^{73} +(-3.09715 - 7.47719i) q^{75} +(-8.26768 - 3.42458i) q^{77} -12.8332i q^{79} -8.92427i q^{81} +(0.870678 + 0.360647i) q^{83} +(-1.11828 - 2.69977i) q^{85} +(-1.63341 - 1.63341i) q^{87} +(-1.14939 + 1.14939i) q^{89} +(-13.5778 + 5.62413i) q^{91} +(-1.01037 + 2.43925i) q^{93} +2.28221 q^{95} -1.83880 q^{97} +(0.0356847 - 0.0861505i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 48 q^{21} - 32 q^{25} + 8 q^{29} + 80 q^{33} + 24 q^{37} - 16 q^{41} - 104 q^{45} + 56 q^{53} - 80 q^{57} - 40 q^{61} + 32 q^{65} - 32 q^{73} - 32 q^{77} + 32 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 + 48 * q^21 - 32 * q^25 + 8 * q^29 + 80 * q^33 + 24 * q^37 - 16 * q^41 - 104 * q^45 + 56 * q^53 - 80 * q^57 - 40 * q^61 + 32 * q^65 - 32 * q^73 - 32 * q^77 + 32 * 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 $\left(\mathbb{Z}/1024\mathbb{Z}\right)^\times$.

$n$	$5$	$1023$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$

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
$3$	−0.660056	+	1.59352i	−0.381083	+	0.920017i	0.610673	+	0.791883i	$0.290899\pi$
$3$	−0.660056	+	1.59352i	−0.381083	+	0.920017i	−0.991757	+	0.128134i	$0.959101\pi$
$4$		0			0
$5$	−0.512517	+	0.212292i	−0.229205	+	0.0949397i	−0.494330	−	0.869274i	$-0.664587\pi$
$5$	−0.512517	+	0.212292i	−0.229205	+	0.0949397i	0.265125	+	0.964214i	$0.414587\pi$
$6$		0			0
$7$	1.69883	−	1.69883i	0.642096	−	0.642096i	−0.308974	−	0.951070i	$-0.599986\pi$
$7$	1.69883	−	1.69883i	0.642096	−	0.642096i	0.951070	+	0.308974i	$0.0999857\pi$
$8$		0			0
$9$	0.0177021	+	0.0177021i	0.00590068	+	0.00590068i
$10$		0			0
$11$	−1.42542	−	3.44127i	−0.429781	−	1.03758i	−0.979357	−	0.202139i	$-0.935211\pi$
$11$	−1.42542	−	3.44127i	−0.429781	−	1.03758i	0.549576	−	0.835444i	$-0.314789\pi$
$12$		0			0
$13$	−5.65154	−	2.34094i	−1.56746	−	0.649261i	−0.581091	−	0.813839i	$-0.697374\pi$
$13$	−5.65154	−	2.34094i	−1.56746	−	0.649261i	−0.986364	+	0.164577i	$0.947374\pi$
$14$		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
$19$	−3.80083	−	1.57436i	−0.871970	−	0.361182i	−0.0985928	−	0.995128i	$-0.531434\pi$
$19$	−3.80083	−	1.57436i	−0.871970	−	0.361182i	−0.773377	+	0.633946i	$0.781434\pi$
$20$		0			0
$21$	1.58579	+	3.82843i	0.346047	+	0.835431i
$22$		0			0
$23$	−4.31195	−	4.31195i	−0.899104	−	0.899104i	0.0962527	−	0.995357i	$-0.469314\pi$
$23$	−4.31195	−	4.31195i	−0.899104	−	0.899104i	−0.995357	+	0.0962527i	$0.969314\pi$
$24$		0			0
$25$	−3.31793	+	3.31793i	−0.663586	+	0.663586i
$26$		0			0
$27$	−4.82044	+	1.99669i	−0.927694	+	0.384263i
$28$		0			0
$29$	−0.512517	+	1.23733i	−0.0951721	+	0.229766i	−0.964295	−	0.264830i	$-0.914684\pi$
$29$	−0.512517	+	1.23733i	−0.0951721	+	0.229766i	0.869123	+	0.494596i	$0.164684\pi$
$30$		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
$35$	−0.510031	+	1.23132i	−0.0862110	+	0.208132i
$36$		0			0
$37$	3.61614	−	1.49785i	0.594489	−	0.246245i	−0.0650915	−	0.997879i	$-0.520734\pi$
$37$	3.61614	−	1.49785i	0.594489	−	0.246245i	0.659581	+	0.751634i	$0.270734\pi$
$38$		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	$-0.840449\pi$
$41$	−8.69226	−	8.69226i	−1.35750	−	1.35750i	−0.480518	−	0.876985i	$-0.659551\pi$
$42$		0			0
$43$	0.211714	+	0.511123i	0.0322861	+	0.0779456i	0.939200	−	0.343370i	$-0.111568\pi$
$43$	0.211714	+	0.511123i	0.0322861	+	0.0779456i	−0.906914	+	0.421316i	$0.861568\pi$
$44$		0			0
$45$	−0.0128306	−	0.00531461i	−0.00191267	−	0.000792255i
$46$		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
$51$	−8.39412	−	3.47696i	−1.17541	−	0.486872i
$52$		0			0
$53$	2.78771	+	6.73012i	0.382921	+	0.924454i	0.991398	+	0.130882i	$0.0417809\pi$
$53$	2.78771	+	6.73012i	0.382921	+	0.924454i	−0.608477	+	0.793572i	$0.708219\pi$
$54$		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
$59$	−2.76469	+	1.14517i	−0.359933	+	0.149089i	−0.555319	−	0.831637i	$-0.687404\pi$
$59$	−2.76469	+	1.14517i	−0.359933	+	0.149089i	0.195387	+	0.980726i	$0.437404\pi$
$60$		0			0
$61$	3.06575	−	7.40138i	0.392529	−	0.947650i	−0.596858	−	0.802347i	$-0.703584\pi$
$61$	3.06575	−	7.40138i	0.392529	−	0.947650i	0.989387	−	0.145303i	$-0.0464157\pi$
$62$		0			0
$63$	0.0601454			0.00757761
$64$		0			0
$65$	3.39347			0.420909
$66$		0			0
$67$	2.20995	−	5.33529i	0.269988	−	0.651810i	−0.729494	−	0.683987i	$-0.760244\pi$
$67$	2.20995	−	5.33529i	0.269988	−	0.651810i	0.999482	+	0.0321778i	$0.0102443\pi$
$68$		0			0
$69$	9.71729	−	4.02503i	1.16982	−	0.484557i
$70$		0			0
$71$	−9.45315	+	9.45315i	−1.12188	+	1.12188i	−0.130424	+	0.991458i	$0.541634\pi$
$71$	−9.45315	+	9.45315i	−1.12188	+	1.12188i	−0.991458	+	0.130424i	$0.958366\pi$
$72$		0			0
$73$	−1.69977	−	1.69977i	−0.198944	−	0.198944i	0.600603	−	0.799547i	$-0.294927\pi$
$73$	−1.69977	−	1.69977i	−0.198944	−	0.198944i	−0.799547	+	0.600603i	$0.794927\pi$
$74$		0			0
$75$	−3.09715	−	7.47719i	−0.357628	−	0.863391i
$76$		0			0
$77$	−8.26768	−	3.42458i	−0.942189	−	0.390267i
$78$		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
$83$	0.870678	+	0.360647i	0.0955693	+	0.0395861i	0.429956	−	0.902850i	$-0.358529\pi$
$83$	0.870678	+	0.360647i	0.0955693	+	0.0395861i	−0.334387	+	0.942436i	$0.608529\pi$
$84$		0			0
$85$	−1.11828	−	2.69977i	−0.121295	−	0.292832i
$86$		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	$-0.777457\pi$
$89$	−1.14939	+	1.14939i	−0.121835	+	0.121835i	0.643560	+	0.765396i	$0.277457\pi$
$90$		0			0
$91$	−13.5778	+	5.62413i	−1.42334	+	0.589569i
$92$		0			0
$93$	−1.01037	+	2.43925i	−0.104770	+	0.252938i
$94$		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
$99$	0.0356847	−	0.0861505i	0.00358645	−	0.00865845i
$100$		0			0
$101$	−1.76267	+	0.730123i	−0.175393	+	0.0726500i	−0.468652	−	0.883383i	$-0.655260\pi$
$101$	−1.76267	+	0.730123i	−0.175393	+	0.0726500i	0.293259	+	0.956033i	$0.405260\pi$
$102$		0			0
$103$	5.36725	−	5.36725i	0.528851	−	0.528851i	−0.391379	−	0.920230i	$-0.628002\pi$
$103$	5.36725	−	5.36725i	0.528851	−	0.528851i	0.920230	+	0.391379i	$0.128002\pi$
$104$		0			0
$105$	−1.62549	−	1.62549i	−0.158631	−	0.158631i
$106$		0			0
$107$	7.19848	+	17.3787i	0.695904	+	1.68006i	0.732534	+	0.680731i	$0.238338\pi$
$107$	7.19848	+	17.3787i	0.695904	+	1.68006i	−0.0366299	+	0.999329i	$0.511662\pi$
$108$		0			0
$109$	6.31591	+	2.61614i	0.604954	+	0.250580i	0.664070	−	0.747671i	$-0.268828\pi$
$109$	6.31591	+	2.61614i	0.604954	+	0.250580i	−0.0591151	+	0.998251i	$0.518828\pi$
$110$		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
$115$	3.12534	+	1.29456i	0.291440	+	0.120718i
$116$		0			0
$117$	−0.0586043	−	0.141483i	−0.00541797	−	0.0130801i
$118$		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
$123$	19.5886	−	8.11387i	1.76625	−	0.731603i
$124$		0			0
$125$	2.05758	−	4.96745i	0.184036	−	0.444302i
$126$		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
$131$	−2.60628	+	6.29212i	−0.227712	+	0.549745i	−0.995898	−	0.0904813i	$-0.971159\pi$
$131$	−2.60628	+	6.29212i	−0.227712	+	0.549745i	0.768186	+	0.640226i	$0.221159\pi$
$132$		0			0
$133$	−9.13151	+	3.78239i	−0.791802	+	0.327975i
$134$		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	$-0.142703\pi$
$137$	5.47465	+	5.47465i	0.467731	+	0.467731i	−0.433448	+	0.901179i	$0.642703\pi$
$138$		0			0
$139$	−4.44282	−	10.7259i	−0.376835	−	0.909760i	−0.992555	−	0.121795i	$-0.961135\pi$
$139$	−4.44282	−	10.7259i	−0.376835	−	0.909760i	0.615721	−	0.787965i	$-0.288865\pi$
$140$		0			0
$141$	15.5103	+	6.42458i	1.30620	+	0.541048i
$142$		0			0
$143$			22.7853i			1.90541i
$144$		0			0
$145$		−	0.742954i		−	0.0616990i
$146$		0			0
$147$	−1.95680	−	0.810533i	−0.161394	−	0.0668516i
$148$		0			0
$149$	1.97276	+	4.76267i	0.161615	+	0.390173i	0.983855	−	0.178968i	$-0.0572758\pi$
$149$	1.97276	+	4.76267i	0.161615	+	0.390173i	−0.822240	+	0.569141i	$0.807276\pi$
$150$		0			0
$151$	−13.9603	−	13.9603i	−1.13607	−	1.13607i	−0.989148	−	0.146924i	$-0.953063\pi$
$151$	−13.9603	−	13.9603i	−1.13607	−	1.13607i	−0.146924	−	0.989148i	$-0.546937\pi$
$152$		0			0
$153$	−0.0932487	+	0.0932487i	−0.00753871	+	0.00753871i
$154$		0			0
$155$	−0.784527	+	0.324962i	−0.0630148	+	0.0261016i
$156$		0			0
$157$	−6.64117	+	16.0332i	−0.530023	+	1.27959i	0.401484	+	0.915866i	$0.368494\pi$
$157$	−6.64117	+	16.0332i	−0.530023	+	1.27959i	−0.931507	+	0.363723i	$0.881506\pi$
$158$		0			0
$159$	−12.5646			−0.996438
$160$		0			0
$161$	−14.6505			−1.15462
$162$		0			0
$163$	1.95307	−	4.71513i	0.152976	−	0.369317i	−0.828749	−	0.559620i	$-0.810947\pi$
$163$	1.95307	−	4.71513i	0.152976	−	0.369317i	0.981725	+	0.190303i	$0.0609470\pi$
$164$		0			0
$165$	−3.29271	+	1.36388i	−0.256337	+	0.106178i
$166$		0			0
$167$	−3.52743	+	3.52743i	−0.272960	+	0.272960i	−0.830291	−	0.557330i	$-0.811826\pi$
$167$	−3.52743	+	3.52743i	−0.272960	+	0.272960i	0.557330	+	0.830291i	$0.311826\pi$
$168$		0			0
$169$	17.2675	+	17.2675i	1.32827	+	1.32827i
$170$		0			0
$171$	−0.0394132	−	0.0951518i	−0.00301400	−	0.00727644i
$172$		0			0
$173$	−15.1973	−	6.29491i	−1.15543	−	0.478593i	−0.279077	−	0.960269i	$-0.590028\pi$
$173$	−15.1973	−	6.29491i	−1.15543	−	0.478593i	−0.876350	+	0.481676i	$0.840028\pi$
$174$		0			0
$175$			11.2732i			0.852171i
$176$		0			0
$177$		−	5.16146i		−	0.387959i
$178$		0			0
$179$	20.9061	+	8.65959i	1.56260	+	0.647248i	0.985538	−	0.169455i	$-0.0542009\pi$
$179$	20.9061	+	8.65959i	1.56260	+	0.647248i	0.577057	+	0.816704i	$0.304201\pi$
$180$		0			0
$181$	−8.60862	−	20.7830i	−0.639874	−	1.54479i	−0.826847	−	0.562427i	$-0.809868\pi$
$181$	−8.60862	−	20.7830i	−0.639874	−	1.54479i	0.186974	−	0.982365i	$-0.440132\pi$
$182$		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
$187$	18.1275	−	7.50866i	1.32562	−	0.549088i
$188$		0			0
$189$	−4.79706	+	11.5811i	−0.348935	+	0.842403i
$190$		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
$195$	−2.23988	+	5.40755i	−0.160401	+	0.387243i
$196$		0			0
$197$	−14.6794	+	6.08042i	−1.04587	+	0.433212i	−0.838414	−	0.545033i	$-0.816517\pi$
$197$	−14.6794	+	6.08042i	−1.04587	+	0.433212i	−0.207452	+	0.978245i	$0.566517\pi$
$198$		0			0
$199$	−16.0244	+	16.0244i	−1.13594	+	1.13594i	−0.146771	+	0.989171i	$0.546888\pi$
$199$	−16.0244	+	16.0244i	−1.13594	+	1.13594i	−0.989171	+	0.146771i	$0.953112\pi$
$200$		0			0
$201$	7.04318	+	7.04318i	0.496788	+	0.496788i
$202$		0			0
$203$	1.23132	+	2.97268i	0.0864220	+	0.208641i
$204$		0			0
$205$	6.30023	+	2.60964i	0.440027	+	0.182265i
$206$		0			0
$207$		−	0.152661i		−	0.0106107i
$208$		0			0
$209$			15.3238i			1.05997i
$210$		0			0
$211$	13.2826	+	5.50184i	0.914413	+	0.378762i	0.789744	−	0.613436i	$-0.210213\pi$
$211$	13.2826	+	5.50184i	0.914413	+	0.378762i	0.124669	+	0.992198i	$0.460213\pi$
$212$		0			0
$213$	−8.82413	−	21.3033i	−0.604620	−	1.45968i
$214$		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
$219$	3.83056	−	1.58667i	0.258845	−	0.107217i
$220$		0			0
$221$	12.3313	−	29.7705i	0.829495	−	2.00258i
$222$		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
$227$	−2.15247	+	5.19652i	−0.142864	+	0.344905i	−0.979074	−	0.203505i	$-0.934767\pi$
$227$	−2.15247	+	5.19652i	−0.142864	+	0.344905i	0.836210	+	0.548410i	$0.184767\pi$
$228$		0			0
$229$	−12.1694	+	5.04072i	−0.804175	+	0.333100i	−0.746627	−	0.665243i	$-0.768328\pi$
$229$	−12.1694	+	5.04072i	−0.804175	+	0.333100i	−0.0575475	+	0.998343i	$0.518328\pi$
$230$		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	$-0.224169\pi$
$233$	1.74984	+	1.74984i	0.114636	+	0.114636i	−0.647462	+	0.762098i	$0.724169\pi$
$234$		0			0
$235$	2.06632	+	4.98853i	0.134792	+	0.325416i
$236$		0			0
$237$	20.4499	+	8.47062i	1.32836	+	0.550226i
$238$		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
$243$	−0.240356	−	0.0995586i	−0.0154188	−	0.00638669i
$244$		0			0
$245$	−0.260689	−	0.629359i	−0.0166548	−	0.0402083i
$246$		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
$251$	9.10639	−	3.77199i	0.574790	−	0.238086i	−0.0763018	−	0.997085i	$-0.524311\pi$
$251$	9.10639	−	3.77199i	0.574790	−	0.238086i	0.651092	+	0.758999i	$0.274311\pi$
$252$		0			0
$253$	−8.69226	+	20.9850i	−0.546478	+	1.31931i
$254$		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
$259$	3.59860	−	8.68778i	0.223606	−	0.539832i
$260$		0			0
$261$	−0.0309758	+	0.0128306i	−0.00191736	+	0.000794194i
$262$		0			0
$263$	−17.8612	+	17.8612i	−1.10137	+	1.10137i	−0.107120	+	0.994246i	$0.534163\pi$
$263$	−17.8612	+	17.8612i	−1.10137	+	1.10137i	−0.994246	+	0.107120i	$0.965837\pi$
$264$		0			0
$265$	−2.85750	−	2.85750i	−0.175535	−	0.175535i
$266$		0			0
$267$	−1.07291	−	2.59024i	−0.0656611	−	0.158520i
$268$		0			0
$269$	13.6544	+	5.65583i	0.832523	+	0.344842i	0.757901	−	0.652370i	$-0.226225\pi$
$269$	13.6544	+	5.65583i	0.832523	+	0.344842i	0.0746220	+	0.997212i	$0.476225\pi$
$270$		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
$275$	16.1473	+	6.68845i	0.973722	+	0.403329i
$276$		0			0
$277$	3.82741	+	9.24018i	0.229967	+	0.555189i	0.996173	−	0.0874063i	$-0.0278578\pi$
$277$	3.82741	+	9.24018i	0.229967	+	0.555189i	−0.766206	+	0.642595i	$0.777858\pi$
$278$		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	$-0.433710\pi$
$281$	19.8667	−	19.8667i	1.18515	−	1.18515i	0.978393	−	0.206754i	$-0.0662900\pi$
$282$		0			0
$283$	−4.76511	+	1.97378i	−0.283257	+	0.117329i	−0.519788	−	0.854295i	$-0.673989\pi$
$283$	−4.76511	+	1.97378i	−0.283257	+	0.117329i	0.236532	+	0.971624i	$0.423989\pi$
$284$		0			0
$285$	−1.50639	+	3.63674i	−0.0892307	+	0.215422i
$286$		0			0
$287$	−29.5333			−1.74329
$288$		0			0
$289$	−10.7484			−0.632259
$290$		0			0
$291$	1.21371	−	2.93015i	0.0711488	−	0.171769i
$292$		0			0
$293$	20.2548	−	8.38983i	1.18330	−	0.490139i	0.297733	−	0.954649i	$-0.403770\pi$
$293$	20.2548	−	8.38983i	1.18330	−	0.490139i	0.885568	+	0.464510i	$0.153770\pi$
$294$		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
$299$	14.2751	+	34.4632i	0.825552	+	1.99306i
$300$		0			0
$301$	1.22798	+	0.508644i	0.0707793	+	0.0293178i
$302$		0			0
$303$		−	3.29077i		−	0.189050i
$304$		0			0
$305$			4.44417i			0.254472i
$306$		0			0
$307$	−19.9354	−	8.25751i	−1.13777	−	0.471281i	−0.267356	−	0.963598i	$-0.586150\pi$
$307$	−19.9354	−	8.25751i	−1.13777	−	0.471281i	−0.870416	+	0.492317i	$0.836150\pi$
$308$		0			0
$309$	5.01011	+	12.0955i	0.285015	+	0.688088i
$310$		0			0
$311$	−15.4798	−	15.4798i	−0.877779	−	0.877779i	0.115526	−	0.993304i	$-0.463145\pi$
$311$	−15.4798	−	15.4798i	−0.877779	−	0.877779i	−0.993304	+	0.115526i	$0.963145\pi$
$312$		0			0
$313$	−14.0918	+	14.0918i	−0.796516	+	0.796516i	−0.982544	−	0.186028i	$-0.940438\pi$
$313$	−14.0918	+	14.0918i	−0.796516	+	0.796516i	0.186028	+	0.982544i	$0.440438\pi$
$314$		0			0
$315$	−0.0308256	+	0.0127684i	−0.00173682	+	0.000719416i
$316$		0			0
$317$	3.05683	−	7.37983i	0.171688	−	0.414492i	−0.814490	−	0.580177i	$-0.802983\pi$
$317$	3.05683	−	7.37983i	0.171688	−	0.414492i	0.986179	+	0.165685i	$0.0529834\pi$
$318$		0			0
$319$	4.98853			0.279304
$320$		0			0
$321$	−32.4446			−1.81088
$322$		0			0
$323$	8.29319	−	20.0215i	0.461445	−	1.11403i
$324$		0			0
$325$	26.5185	−	10.9843i	1.47098	−	0.609300i
$326$		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
$331$	−2.68230	−	6.47564i	−0.147433	−	0.355934i	0.832860	−	0.553483i	$-0.186702\pi$
$331$	−2.68230	−	6.47564i	−0.147433	−	0.355934i	−0.980293	+	0.197550i	$0.936702\pi$
$332$		0			0
$333$	0.0905281	+	0.0374980i	0.00496091	+	0.00205488i
$334$		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
$339$	−10.5179	−	4.35667i	−0.571255	−	0.236622i
$340$		0			0
$341$	−2.18194	−	5.26768i	−0.118159	−	0.285261i
$342$		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
$347$	−10.6041	+	4.39235i	−0.569256	+	0.235794i	−0.648698	−	0.761046i	$-0.724686\pi$
$347$	−10.6041	+	4.39235i	−0.569256	+	0.235794i	0.0794417	+	0.996840i	$0.474686\pi$
$348$		0			0
$349$	8.18404	−	19.7580i	0.438081	−	1.05762i	−0.538529	−	0.842607i	$-0.681020\pi$
$349$	8.18404	−	19.7580i	0.438081	−	1.05762i	0.976611	−	0.215015i	$-0.0689801\pi$
$350$		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
$355$	2.83808	−	6.85172i	0.150629	−	0.363652i
$356$		0			0
$357$	−20.1669	+	8.35341i	−1.06735	+	0.442109i
$358$		0			0
$359$	−6.77460	+	6.77460i	−0.357550	+	0.357550i	−0.862909	−	0.505359i	$-0.831360\pi$
$359$	−6.77460	+	6.77460i	−0.357550	+	0.357550i	0.505359	+	0.862909i	$0.331360\pi$
$360$		0			0
$361$	−1.46732	−	1.46732i	−0.0772274	−	0.0772274i
$362$		0			0
$363$	−1.89713	−	4.58008i	−0.0995737	−	0.240392i
$364$		0			0
$365$	1.23201	+	0.510316i	0.0644864	+	0.0267112i
$366$		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
$371$	16.1691	+	6.69748i	0.839460	+	0.347716i
$372$		0			0
$373$	−2.82311	−	6.81560i	−0.146175	−	0.352898i	0.833786	−	0.552088i	$-0.186169\pi$
$373$	−2.82311	−	6.81560i	−0.146175	−	0.352898i	−0.979961	+	0.199190i	$0.936169\pi$
$374$		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
$379$	−12.8072	+	5.30491i	−0.657861	+	0.272495i	−0.686538	−	0.727094i	$-0.740870\pi$
$379$	−12.8072	+	5.30491i	−0.657861	+	0.272495i	0.0286774	+	0.999589i	$0.490870\pi$
$380$		0			0
$381$	−2.88305	+	6.96030i	−0.147703	+	0.356587i
$382$		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
$387$	−0.00530016	+	0.0127957i	−0.000269422	+	0.000650442i
$388$		0			0
$389$	−19.1472	+	7.93103i	−0.970801	+	0.402119i	−0.811010	−	0.585032i	$-0.801082\pi$
$389$	−19.1472	+	7.93103i	−0.970801	+	0.402119i	−0.159791	+	0.987151i	$0.551082\pi$
$390$		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
$395$	2.72438	+	6.57723i	0.137078	+	0.330936i
$396$		0			0
$397$	6.41201	+	2.65594i	0.321810	+	0.133298i	0.537740	−	0.843111i	$-0.319278\pi$
$397$	6.41201	+	2.65594i	0.321810	+	0.133298i	−0.215930	+	0.976409i	$0.569278\pi$
$398$		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
$403$	−8.65100	−	3.58336i	−0.430937	−	0.178500i
$404$		0			0
$405$	1.89455	+	4.57384i	0.0941408	+	0.227276i
$406$		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	$-0.751189\pi$
$409$	−0.106839	+	0.106839i	−0.00528285	+	0.00528285i	0.704460	+	0.709743i	$0.251189\pi$
$410$		0			0
$411$	−12.3375	+	5.11037i	−0.608565	+	0.252076i
$412$		0			0
$413$	−2.75128	+	6.64219i	−0.135382	+	0.326841i
$414$		0			0
$415$	−0.522800			−0.0256632
$416$		0			0
$417$	20.0244			0.980599
$418$		0			0
$419$	−7.75898	+	18.7318i	−0.379051	+	0.915110i	0.613093	+	0.790011i	$0.289925\pi$
$419$	−7.75898	+	18.7318i	−0.379051	+	0.915110i	−0.992144	+	0.125099i	$0.960075\pi$
$420$		0			0
$421$	12.2756	−	5.08471i	0.598275	−	0.247814i	−0.0629310	−	0.998018i	$-0.520045\pi$
$421$	12.2756	−	5.08471i	0.598275	−	0.247814i	0.661206	+	0.750204i	$0.270045\pi$
$422$		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
$427$	−7.36548	−	17.7819i	−0.356441	−	0.860524i
$428$		0			0
$429$	−36.3088	−	15.0396i	−1.75300	−	0.726118i
$430$		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
$435$	1.18391	+	0.490391i	0.0567641	+	0.0235125i
$436$		0			0
$437$	9.60045	+	23.1775i	0.459252	+	1.10873i
$438$		0			0
$439$	−5.35602	−	5.35602i	−0.255629	−	0.255629i	0.567645	−	0.823274i	$-0.307855\pi$
$439$	−5.35602	−	5.35602i	−0.255629	−	0.255629i	−0.823274	+	0.567645i	$0.807855\pi$
$440$		0			0
$441$	−0.0217377	+	0.0217377i	−0.00103513	+	0.00103513i
$442$		0			0
$443$	17.2372	−	7.13988i	0.818964	−	0.339226i	0.0664397	−	0.997790i	$-0.478836\pi$
$443$	17.2372	−	7.13988i	0.818964	−	0.339226i	0.752524	+	0.658564i	$0.228836\pi$
$444$		0			0
$445$	0.345077	−	0.833089i	0.0163582	−	0.0394922i
$446$		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
$451$	−17.5223	+	42.3026i	−0.825093	+	1.99195i
$452$		0			0
$453$	31.4605	−	13.0314i	1.47814	−	0.612267i
$454$		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	$-0.146515\pi$
$457$	9.65659	+	9.65659i	0.451716	+	0.451716i	−0.444207	+	0.895924i	$0.646515\pi$
$458$		0			0
$459$	−10.5179	−	25.3925i	−0.490935	−	1.18522i
$460$		0			0
$461$	−23.2966	−	9.64976i	−1.08503	−	0.449434i	−0.232759	−	0.972534i	$-0.574775\pi$
$461$	−23.2966	−	9.64976i	−1.08503	−	0.449434i	−0.852271	+	0.523100i	$0.824775\pi$
$462$		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
$467$	−23.6421	−	9.79289i	−1.09403	−	0.453161i	−0.238618	−	0.971114i	$-0.576694\pi$
$467$	−23.6421	−	9.79289i	−1.09403	−	0.453161i	−0.855409	+	0.517953i	$0.826694\pi$
$468$		0			0
$469$	−5.30941	−	12.8181i	−0.245166	−	0.591883i
$470$		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
$475$	17.8345	−	7.38728i	0.818302	−	0.338952i
$476$		0			0
$477$	−0.0697888	+	0.168485i	−0.00319541	+	0.00771441i
$478$		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
$483$	9.67016	−	23.3458i	0.440008	−	1.06227i
$484$		0			0
$485$	0.942415	−	0.390361i	0.0427929	−	0.0177254i
$486$		0			0
$487$	15.4256	−	15.4256i	0.699001	−	0.699001i	−0.265194	−	0.964195i	$-0.585436\pi$
$487$	15.4256	−	15.4256i	0.699001	−	0.699001i	0.964195	+	0.265194i	$0.0854361\pi$
$488$		0			0
$489$	6.22450	+	6.22450i	0.281481	+	0.281481i
$490$		0			0
$491$	−11.9376	−	28.8199i	−0.538736	−	1.30062i	−0.925606	−	0.378489i	$-0.876444\pi$
$491$	−11.9376	−	28.8199i	−0.538736	−	1.30062i	0.386870	−	0.922134i	$-0.373556\pi$
$492$		0			0
$493$	−6.51783	−	2.69977i	−0.293548	−	0.121592i
$494$		0			0
$495$			0.0517292i			0.00232505i
$496$		0			0
$497$			32.1185i			1.44071i
$498$		0			0
$499$	−35.2722	−	14.6102i	−1.57900	−	0.654043i	−0.590746	−	0.806858i	$-0.701166\pi$
$499$	−35.2722	−	14.6102i	−1.57900	−	0.654043i	−0.988255	+	0.152814i	$0.951166\pi$
$500$		0			0
$501$	−3.29271	−	7.94930i	−0.147107	−	0.355149i
$502$		0			0
$503$	2.18240	+	2.18240i	0.0973084	+	0.0973084i	0.754085	−	0.656777i	$-0.228081\pi$
$503$	2.18240	+	2.18240i	0.0973084	+	0.0973084i	−0.656777	+	0.754085i	$0.728081\pi$
$504$		0			0
$505$	0.748402	−	0.748402i	0.0333034	−	0.0333034i
$506$		0			0
$507$	−38.9135	+	16.1185i	−1.72821	+	0.715848i
$508$		0			0
$509$	3.08482	−	7.44742i	0.136732	−	0.330101i	−0.840651	−	0.541578i	$-0.817827\pi$
$509$	3.08482	−	7.44742i	0.136732	−	0.330101i	0.977383	+	0.211477i	$0.0678272\pi$
$510$		0			0
$511$	−5.77524			−0.255482
$512$		0			0
$513$	21.4652			0.947710
$514$		0			0
$515$	−1.61139	+	3.89023i	−0.0710061	+	0.171424i
$516$		0			0
$517$	−33.4953	+	13.8742i	−1.47312	+	0.610187i
$518$		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	$-0.319029\pi$
$521$	−6.94553	−	6.94553i	−0.304289	−	0.304289i	−0.842689	+	0.538400i	$0.819029\pi$
$522$		0			0
$523$	−0.930625	−	2.24673i	−0.0406934	−	0.0982425i	0.902226	−	0.431263i	$-0.141932\pi$
$523$	−0.930625	−	2.24673i	−0.0406934	−	0.0982425i	−0.942919	+	0.333021i	$0.891932\pi$
$524$		0			0
$525$	−17.9640	−	7.44092i	−0.784012	−	0.324748i
$526$		0			0
$527$			8.06341i			0.351248i
$528$		0			0
$529$			14.1859i			0.616777i
$530$		0			0
$531$	−0.0692127	−	0.0286688i	−0.00300358	−	0.00124412i
$532$		0			0
$533$	28.7765	+	69.4727i	1.24645	+	3.00920i
$534$		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
$539$	4.22580	−	1.75038i	0.182018	−	0.0753944i
$540$		0			0
$541$	−10.5260	+	25.4120i	−0.452548	+	1.09255i	0.518802	+	0.854894i	$0.326378\pi$
$541$	−10.5260	+	25.4120i	−0.452548	+	1.09255i	−0.971350	+	0.237653i	$0.923622\pi$
$542$		0			0
$543$	38.8003			1.66508
$544$		0			0
$545$	−3.79240			−0.162448
$546$		0			0
$547$	1.04627	−	2.52591i	0.0447351	−	0.108000i	−0.899932	−	0.436029i	$-0.856384\pi$
$547$	1.04627	−	2.52591i	0.0447351	−	0.108000i	0.944668	+	0.328029i	$0.106384\pi$
$548$		0			0
$549$	0.185290	−	0.0767495i	0.00790798	−	0.00327559i
$550$		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
$555$	−1.43319	−	3.46002i	−0.0608354	−	0.146870i
$556$		0			0
$557$	−20.7983	−	8.61495i	−0.881254	−	0.365027i	−0.104271	−	0.994549i	$-0.533251\pi$
$557$	−20.7983	−	8.61495i	−0.881254	−	0.365027i	−0.776983	+	0.629522i	$0.783251\pi$
$558$		0			0
$559$		−	3.38425i		−	0.143138i
$560$		0			0
$561$			33.8426i			1.42884i
$562$		0			0
$563$	20.9200	+	8.66534i	0.881672	+	0.365201i	0.777145	−	0.629321i	$-0.216667\pi$
$563$	20.9200	+	8.66534i	0.881672	+	0.365201i	0.104527	+	0.994522i	$0.466667\pi$
$564$		0			0
$565$	−1.40122	−	3.38285i	−0.0589498	−	0.142317i
$566$		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	$-0.752610\pi$
$569$	−0.276633	+	0.276633i	−0.0115970	+	0.0115970i	0.701284	+	0.712882i	$0.252610\pi$
$570$		0			0
$571$	−31.9788	+	13.2460i	−1.33827	+	0.554329i	−0.933003	−	0.359869i	$-0.882821\pi$
$571$	−31.9788	+	13.2460i	−1.33827	+	0.554329i	−0.405267	+	0.914198i	$0.632821\pi$
$572$		0			0
$573$	6.88876	−	16.6309i	0.287782	−	0.694767i
$574$		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
$579$	2.52013	−	6.08413i	0.104733	−	0.252848i
$580$		0			0
$581$	2.09181	−	0.866455i	0.0867828	−	0.0359466i
$582$		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
$587$	13.5838	+	32.7941i	0.560662	+	1.35356i	0.909238	+	0.416277i	$0.136665\pi$
$587$	13.5838	+	32.7941i	0.560662	+	1.35356i	−0.348575	+	0.937281i	$0.613335\pi$
$588$		0			0
$589$	−5.81806	−	2.40992i	−0.239729	−	0.0992990i
$590$		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
$595$	−6.48622	−	2.68668i	−0.265909	−	0.110143i
$596$		0			0
$597$	−14.9582	−	36.1122i	−0.612197	−	1.47797i
$598$		0			0
$599$	11.9077	+	11.9077i	0.486534	+	0.486534i	0.907211	−	0.420677i	$-0.138207\pi$
$599$	11.9077	+	11.9077i	0.486534	+	0.486534i	−0.420677	+	0.907211i	$0.638207\pi$
$600$		0			0
$601$	−1.86501	+	1.86501i	−0.0760755	+	0.0760755i	−0.744121	−	0.668045i	$-0.767131\pi$
$601$	−1.86501	+	1.86501i	−0.0760755	+	0.0760755i	0.668045	+	0.744121i	$0.267131\pi$
$602$		0			0
$603$	0.133566	−	0.0553250i	0.00543924	−	0.00225301i
$604$		0			0
$605$	0.610169	−	1.47308i	0.0248069	−	0.0598891i
$606$		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
$611$	−22.7853	+	55.0087i	−0.921796	+	2.22541i
$612$		0			0
$613$	23.3613	−	9.67657i	0.943555	−	0.390833i	0.142750	−	0.989759i	$-0.454405\pi$
$613$	23.3613	−	9.67657i	0.943555	−	0.390833i	0.800805	+	0.598926i	$0.204405\pi$
$614$		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	$-0.331697\pi$
$617$	−8.91738	−	8.91738i	−0.359000	−	0.359000i	−0.863444	+	0.504444i	$0.831697\pi$
$618$		0			0
$619$	−2.30623	−	5.56774i	−0.0926953	−	0.223786i	0.870731	−	0.491760i	$-0.163646\pi$
$619$	−2.30623	−	5.56774i	−0.0926953	−	0.223786i	−0.963426	+	0.267973i	$0.913646\pi$
$620$		0			0
$621$	29.3951	+	12.1759i	1.17959	+	0.488601i
$622$		0			0
$623$			3.90524i			0.156460i
$624$		0			0
$625$		−	20.4786i		−	0.819143i
$626$		0			0
$627$	−24.4187	−	10.1146i	−0.975191	−	0.403937i
$628$		0			0
$629$	7.89020	+	19.0486i	0.314603	+	0.759519i
$630$		0			0
$631$	−33.4932	−	33.4932i	−1.33334	−	1.33334i	−0.902361	−	0.430981i	$-0.858167\pi$
$631$	−33.4932	−	33.4932i	−1.33334	−	1.33334i	−0.430981	−	0.902361i	$-0.641833\pi$
$632$		0			0
$633$	−17.5345	+	17.5345i	−0.696935	+	0.696935i
$634$		0			0
$635$	−2.23862	+	0.927266i	−0.0888369	+	0.0367974i
$636$		0			0
$637$	2.87462	−	6.93995i	0.113897	−	0.274971i
$638$		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
$643$	13.0339	−	31.4666i	0.514006	−	1.24092i	−0.427528	−	0.904002i	$-0.640616\pi$
$643$	13.0339	−	31.4666i	0.514006	−	1.24092i	0.941534	−	0.336918i	$-0.109384\pi$
$644$		0			0
$645$	0.489057	−	0.202574i	0.0192566	−	0.00797635i
$646$		0			0
$647$	−6.43000	+	6.43000i	−0.252789	+	0.252789i	−0.822113	−	0.569324i	$-0.807205\pi$
$647$	−6.43000	+	6.43000i	−0.252789	+	0.252789i	0.569324	+	0.822113i	$0.307205\pi$
$648$		0			0
$649$	7.88172	+	7.88172i	0.309384	+	0.309384i
$650$		0			0
$651$	2.42742	+	5.86030i	0.0951380	+	0.229683i
$652$		0			0
$653$	−12.6294	−	5.23125i	−0.494225	−	0.204715i	0.121628	−	0.992576i	$-0.461188\pi$
$653$	−12.6294	−	5.23125i	−0.494225	−	0.204715i	−0.615853	+	0.787861i	$0.711188\pi$
$654$		0			0
$655$		−	3.77811i		−	0.147623i
$656$		0			0
$657$		−	0.0601790i		−	0.00234781i
$658$		0			0
$659$	−14.3485	−	5.94335i	−0.558939	−	0.231520i	0.0852857	−	0.996357i	$-0.472820\pi$
$659$	−14.3485	−	5.94335i	−0.558939	−	0.231520i	−0.644224	+	0.764837i	$0.722820\pi$
$660$		0			0
$661$	8.79664	+	21.2370i	0.342150	+	0.826022i	0.997498	+	0.0706953i	$0.0225218\pi$
$661$	8.79664	+	21.2370i	0.342150	+	0.826022i	−0.655348	+	0.755327i	$0.727478\pi$
$662$		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
$667$	7.54524	−	3.12534i	0.292153	−	0.121014i
$668$		0			0
$669$	−10.8031	+	26.0811i	−0.417673	+	1.00835i
$670$		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
$675$	9.36899	−	22.6187i	0.360613	−	0.870596i
$676$		0			0
$677$	19.7220	−	8.16911i	0.757977	−	0.313964i	0.0299855	−	0.999550i	$-0.490454\pi$
$677$	19.7220	−	8.16911i	0.757977	−	0.313964i	0.727992	+	0.685586i	$0.240454\pi$
$678$		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
$683$	−9.39365	−	22.6783i	−0.359438	−	0.867760i	−0.995379	−	0.0960227i	$-0.969388\pi$
$683$	−9.39365	−	22.6783i	−0.359438	−	0.867760i	0.635941	−	0.771738i	$-0.280612\pi$
$684$		0			0
$685$	−3.96808	−	1.64363i	−0.151612	−	0.0627999i
$686$		0			0
$687$		−	22.7192i		−	0.866793i
$688$		0			0
$689$		−	44.5614i		−	1.69766i
$690$		0			0
$691$	−13.6135	−	5.63891i	−0.517883	−	0.214514i	0.108404	−	0.994107i	$-0.465426\pi$
$691$	−13.6135	−	5.63891i	−0.517883	−	0.214514i	−0.626287	+	0.779593i	$0.715426\pi$
$692$		0			0
$693$	−0.0857327	−	0.206977i	−0.00325671	−	0.00786241i
$694$		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
$699$	−3.94340	+	1.63341i	−0.149153	+	0.0617812i
$700$		0			0
$701$	17.6385	−	42.5832i	0.666199	−	1.60835i	−0.121718	−	0.992565i	$-0.538840\pi$
$701$	17.6385	−	42.5832i	0.666199	−	1.60835i	0.787917	−	0.615781i	$-0.211160\pi$
$702$		0			0
$703$	−16.1025			−0.607316
$704$		0			0
$705$	−9.31319			−0.350755
$706$		0			0
$707$	−1.75412	+	4.23483i	−0.0659706	+	0.159267i
$708$		0			0
$709$	26.8688	−	11.1294i	1.00908	−	0.417974i	0.183960	−	0.982934i	$-0.441108\pi$
$709$	26.8688	−	11.1294i	1.00908	−	0.417974i	0.825118	+	0.564960i	$0.191108\pi$
$710$		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
$715$	−4.83714	−	11.6779i	−0.180899	−	0.436728i
$716$		0			0
$717$	−20.3277	−	8.42003i	−0.759154	−	0.314452i
$718$		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
$723$	30.2226	+	12.5186i	1.12399	+	0.465573i
$724$		0			0
$725$	−2.40486	−	5.80585i	−0.0893144	−	0.215624i
$726$		0			0
$727$	20.1795	+	20.1795i	0.748416	+	0.748416i	0.974182	−	0.225765i	$-0.0724882\pi$
$727$	20.1795	+	20.1795i	0.748416	+	0.748416i	−0.225765	+	0.974182i	$0.572488\pi$
$728$		0			0
$729$	19.2485	−	19.2485i	0.712909	−	0.712909i
$730$		0			0
$731$	−2.69243	+	1.11524i	−0.0995832	+	0.0412487i
$732$		0			0
$733$	4.66073	−	11.2520i	0.172148	−	0.415602i	−0.814133	−	0.580679i	$-0.802787\pi$
$733$	4.66073	−	11.2520i	0.172148	−	0.415602i	0.986281	+	0.165077i	$0.0527873\pi$
$734$		0			0
$735$	1.17496			0.0433391
$736$		0			0
$737$	−21.5103			−0.792343
$738$		0			0
$739$	9.38552	−	22.6586i	0.345252	−	0.833512i	−0.651915	−	0.758292i	$-0.726034\pi$
$739$	9.38552	−	22.6586i	0.345252	−	0.833512i	0.997167	−	0.0752197i	$-0.0239658\pi$
$740$		0			0
$741$	−40.1024	+	16.6110i	−1.47320	+	0.610219i
$742$		0			0
$743$	−30.4077	+	30.4077i	−1.11555	+	1.11555i	−0.123164	+	0.992386i	$0.539304\pi$
$743$	−30.4077	+	30.4077i	−1.11555	+	1.11555i	−0.992386	+	0.123164i	$0.960696\pi$
$744$		0			0
$745$	−2.02215	−	2.02215i	−0.0740859	−	0.0740859i
$746$		0			0
$747$	0.00902860	+	0.0217970i	0.000330339	+	0.000797510i
$748$		0			0
$749$	41.7523	+	17.2944i	1.52560	+	0.631923i
$750$		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
$755$	10.1185	+	4.19124i	0.368251	+	0.152535i
$756$		0			0
$757$	1.09998	+	2.65558i	0.0399793	+	0.0965185i	0.942608	−	0.333902i	$-0.108365\pi$
$757$	1.09998	+	2.65558i	0.0399793	+	0.0965185i	−0.902629	+	0.430420i	$0.858365\pi$
$758$		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	$-0.597874\pi$
$761$	17.9432	−	17.9432i	0.650442	−	0.650442i	0.953099	+	0.302658i	$0.0978739\pi$
$762$		0			0
$763$	15.1740	−	6.28528i	0.549336	−	0.227542i
$764$		0			0
$765$	0.0279956	−	0.0675875i	0.00101218	−	0.00244363i
$766$		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
$771$	1.36308	−	3.29077i	0.0490902	−	0.118514i
$772$		0			0
$773$	17.4049	−	7.20933i	0.626009	−	0.259302i	−0.0470471	−	0.998893i	$-0.514981\pi$
$773$	17.4049	−	7.20933i	0.626009	−	0.259302i	0.673056	+	0.739591i	$0.264981\pi$
$774$		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
$779$	19.3531	+	46.7225i	0.693396	+	1.67401i
$780$		0			0
$781$	46.0056	+	19.0561i	1.64621	+	0.681882i
$782$		0			0
$783$		−	6.98779i		−	0.249723i
$784$		0			0
$785$		−	9.62716i		−	0.343608i
$786$		0			0
$787$	32.1235	+	13.3060i	1.14508	+	0.474307i	0.872881	−	0.487934i	$-0.162249\pi$
$787$	32.1235	+	13.3060i	1.14508	+	0.474307i	0.272198	+	0.962241i	$0.412249\pi$
$788$		0			0
$789$	−16.6727	−	40.2514i	−0.593563	−	1.43299i
$790$		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
$795$	6.43957	−	2.66736i	0.228388	−	0.0946015i
$796$		0			0
$797$	−6.84385	+	16.5225i	−0.242422	+	0.585258i	−0.997522	−	0.0703512i	$-0.977588\pi$
$797$	−6.84385	+	16.5225i	−0.242422	+	0.585258i	0.755101	+	0.655609i	$0.227588\pi$
$798$		0			0
$799$	51.2724			1.81389
$800$		0			0
$801$	−0.0406932			−0.00143782
$802$		0			0
$803$	−3.42649	+	8.27229i	−0.120918	+	0.291923i
$804$		0			0
$805$	7.50864	−	3.11018i	0.264645	−	0.109620i
$806$		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	$-0.334522\pi$
$809$	−10.5558	−	10.5558i	−0.371123	−	0.371123i	−0.867886	+	0.496763i	$0.834522\pi$
$810$		0			0
$811$	1.78652	+	4.31304i	0.0627333	+	0.151451i	0.952138	−	0.305670i	$-0.0988804\pi$
$811$	1.78652	+	4.31304i	0.0627333	+	0.151451i	−0.889404	+	0.457122i	$0.848880\pi$
$812$		0			0
$813$	−3.81894	−	1.58186i	−0.133936	−	0.0554782i
$814$		0			0
$815$			2.83121i			0.0991728i
$816$		0			0
$817$		−	2.27601i		−	0.0796274i
$818$		0			0
$819$	−0.339914	−	0.140797i	−0.0118776	−	0.00491985i
$820$		0			0
$821$	−10.5300	−	25.4218i	−0.367501	−	0.887225i	−0.994158	−	0.107931i	$-0.965578\pi$
$821$	−10.5300	−	25.4218i	−0.367501	−	0.887225i	0.626658	−	0.779295i	$-0.284422\pi$
$822$		0			0
$823$	28.1280	+	28.1280i	0.980479	+	0.980479i	0.999813	−	0.0193343i	$-0.00615470\pi$
$823$	28.1280	+	28.1280i	0.980479	+	0.980479i	−0.0193343	+	0.999813i	$0.506155\pi$
$824$		0			0
$825$	−21.3163	+	21.3163i	−0.742138	+	0.742138i
$826$		0			0
$827$	−14.6219	+	6.05658i	−0.508453	+	0.210608i	−0.622136	−	0.782909i	$-0.713735\pi$
$827$	−14.6219	+	6.05658i	−0.508453	+	0.210608i	0.113683	+	0.993517i	$0.463735\pi$
$828$		0			0
$829$	−11.7436	+	28.3516i	−0.407872	+	0.984691i	0.577824	+	0.816161i	$0.303902\pi$
$829$	−11.7436	+	28.3516i	−0.407872	+	0.984691i	−0.985697	+	0.168530i	$0.946098\pi$
$830$		0			0
$831$	−17.2507			−0.598419
$832$		0			0
$833$	−6.46858			−0.224123
$834$		0			0
$835$	1.05902	−	2.55671i	0.0366490	−	0.0884786i
$836$		0			0
$837$	−7.37881	+	3.05640i	−0.255049	+	0.105645i
$838$		0			0
$839$	19.2678	−	19.2678i	0.665199	−	0.665199i	−0.291401	−	0.956601i	$-0.594122\pi$
$839$	19.2678	−	19.2678i	0.665199	−	0.665199i	0.956601	+	0.291401i	$0.0941215\pi$
$840$		0			0
$841$	19.2378	+	19.2378i	0.663372	+	0.663372i
$842$		0			0
$843$	18.5448	+	44.7710i	0.638715	+	1.54199i
$844$		0			0
$845$	−12.5156	−	5.18414i	−0.430551	−	0.178340i
$846$		0			0
$847$			6.90528i			0.237268i
$848$		0			0
$849$		−	8.89609i		−	0.305313i
$850$		0			0
$851$	−22.0513	−	9.13394i	−0.755908	−	0.313107i
$852$		0			0
$853$	−5.53470	−	13.3619i	−0.189504	−	0.457504i	0.800360	−	0.599520i	$-0.204642\pi$
$853$	−5.53470	−	13.3619i	−0.189504	−	0.457504i	−0.989864	+	0.142016i	$0.954642\pi$
$854$		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	$-0.878071\pi$
$857$	−16.2115	+	16.2115i	−0.553775	+	0.553775i	0.373753	+	0.927528i	$0.378071\pi$
$858$		0			0
$859$	25.6351	−	10.6184i	0.874658	−	0.362295i	0.100235	−	0.994964i	$-0.468040\pi$
$859$	25.6351	−	10.6184i	0.874658	−	0.362295i	0.774423	+	0.632669i	$0.218040\pi$
$860$		0			0
$861$	19.4936	−	47.0617i	0.664341	−	1.60386i
$862$		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
$867$	7.09454	−	17.1277i	0.240943	−	0.581689i
$868$		0			0
$869$	−44.1625	+	18.2927i	−1.49811	+	0.620538i
$870$		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
$875$	−4.94336	−	11.9343i	−0.167116	−	0.403454i
$876$		0			0
$877$	43.8869	+	18.1786i	1.48196	+	0.613846i	0.969549	−	0.244896i	$-0.0787540\pi$
$877$	43.8869	+	18.1786i	1.48196	+	0.613846i	0.512407	+	0.858743i	$0.328754\pi$
$878$		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
$883$	49.9223	+	20.6785i	1.68002	+	0.695886i	0.999327	−	0.0366838i	$-0.0116794\pi$
$883$	49.9223	+	20.6785i	1.68002	+	0.695886i	0.680692	+	0.732570i	$0.261679\pi$
$884$		0			0
$885$	1.09574	+	2.64534i	0.0368327	+	0.0889221i
$886$		0			0
$887$	−17.8530	−	17.8530i	−0.599446	−	0.599446i	0.340719	−	0.940165i	$-0.389329\pi$
$887$	−17.8530	−	17.8530i	−0.599446	−	0.599446i	−0.940165	+	0.340719i	$0.889329\pi$
$888$		0			0
$889$	7.42029	−	7.42029i	0.248868	−	0.248868i
$890$		0			0
$891$	−30.7109	+	12.7209i	−1.02885	+	0.426165i
$892$		0			0
$893$	−15.3238	+	36.9950i	−0.512792	+	1.23799i
$894$		0			0
$895$	−12.5531			−0.419604
$896$		0			0
$897$	−64.3400			−2.14825
$898$		0			0
$899$	−0.784527	+	1.89402i	−0.0261655	+	0.0631690i
$900$		0			0
$901$	−35.4521	+	14.6847i	−1.18108	+	0.489220i
$902$		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
$907$	4.24679	+	10.2527i	0.141012	+	0.340434i	0.978570	−	0.205915i	$-0.0660172\pi$
$907$	4.24679	+	10.2527i	0.141012	+	0.340434i	−0.837558	+	0.546349i	$0.816017\pi$
$908$		0			0
$909$	−0.0441276	−	0.0182783i	−0.00146362	−	0.000606252i
$910$		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
$915$	−7.08185	−	2.93340i	−0.234119	−	0.0969752i
$916$		0			0
$917$	6.26160	+	15.1168i	0.206776	+	0.499202i
$918$		0			0
$919$	−5.17031	−	5.17031i	−0.170553	−	0.170553i	0.616669	−	0.787222i	$-0.288482\pi$
$919$	−5.17031	−	5.17031i	−0.170553	−	0.170553i	−0.787222	+	0.616669i	$0.788482\pi$
$920$		0			0
$921$	26.3169	−	26.3169i	0.867172	−	0.867172i
$922$		0			0
$923$	75.5541	−	31.2955i	2.48689	−	1.03011i
$924$		0			0
$925$	−7.02831	+	16.9678i	−0.231089	+	0.557899i
$926$		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
$931$	1.93327	−	4.66733i	0.0633604	−	0.152965i
$932$		0			0
$933$	34.8848	−	14.4498i	1.14208	−	0.473064i
$934$		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	$0.0183876\pi$
$937$	32.3267	+	32.3267i	1.05607	+	1.05607i	0.0577344	+	0.998332i	$0.481612\pi$
$938$		0			0
$939$	−13.1541	−	31.7569i	−0.429269	−	1.03635i
$940$		0			0
$941$	23.9077	+	9.90288i	0.779368	+	0.322825i	0.736660	−	0.676263i	$-0.236402\pi$
$941$	23.9077	+	9.90288i	0.779368	+	0.322825i	0.0427073	+	0.999088i	$0.486402\pi$
$942$		0			0
$943$			74.9612i			2.44107i
$944$		0			0
$945$		−	6.95390i		−	0.226210i
$946$		0			0
$947$	21.6767	+	8.97880i	0.704399	+	0.291772i	0.705985	−	0.708227i	$-0.250505\pi$
$947$	21.6767	+	8.97880i	0.704399	+	0.291772i	−0.00158544	+	0.999999i	$0.500505\pi$
$948$		0			0
$949$	5.62726	+	13.5854i	0.182669	+	0.441001i
$950$		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	$-0.728077\pi$
$953$	3.00440	−	3.00440i	0.0973222	−	0.0973222i	0.754092	+	0.656769i	$0.228077\pi$
$954$		0			0
$955$	5.34895	−	2.21561i	0.173088	−	0.0716954i
$956$		0			0
$957$	−3.29271	+	7.94930i	−0.106438	+	0.256965i
$958$		0			0
$959$	18.6010			0.600657
$960$		0			0
$961$	−28.6569			−0.924415
$962$		0			0
$963$	−0.180210	+	0.435066i	−0.00580720	+	0.0140198i
$964$		0			0
$965$	1.95682	−	0.810542i	0.0629923	−	0.0260923i
$966$		0			0
$967$	29.1087	−	29.1087i	0.936074	−	0.936074i	−0.0620023	−	0.998076i	$-0.519749\pi$
$967$	29.1087	−	29.1087i	0.936074	−	0.936074i	0.998076	+	0.0620023i	$0.0197486\pi$
$968$		0			0
$969$	26.4307	+	26.4307i	0.849075	+	0.849075i
$970$		0			0
$971$	0.258452	+	0.623957i	0.00829411	+	0.0200237i	0.927972	−	0.372649i	$-0.121550\pi$
$971$	0.258452	+	0.623957i	0.00829411	+	0.0200237i	−0.919678	+	0.392673i	$0.871550\pi$
$972$		0			0
$973$	−25.7690	−	10.6739i	−0.826117	−	0.342189i
$974$		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
$979$	5.59374	+	2.31700i	0.178777	+	0.0740518i
$980$		0			0
$981$	0.0654936	+	0.158116i	0.00209105	+	0.00504824i
$982$		0			0
$983$	1.49880	+	1.49880i	0.0478044	+	0.0478044i	0.730605	−	0.682800i	$-0.239238\pi$
$983$	1.49880	+	1.49880i	0.0478044	+	0.0478044i	−0.682800	+	0.730605i	$0.739238\pi$
$984$		0			0
$985$	6.23264	−	6.23264i	0.198588	−	0.198588i
$986$		0			0
$987$	37.2636	−	15.4351i	1.18611	−	0.491304i
$988$		0			0
$989$	1.29104	−	3.11684i	0.0410526	−	0.0991098i
$990$		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
$995$	4.81094	−	11.6146i	0.152517	−	0.368209i
$996$		0			0
$997$	−5.97395	+	2.47449i	−0.189197	+	0.0783679i	−0.475270	−	0.879840i	$-0.657650\pi$
$997$	−5.97395	+	2.47449i	−0.189197	+	0.0783679i	0.286074	+	0.958208i	$0.407650\pi$
$998$		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.e.129.2	yes	16
4.3	odd	2	inner	1024.2.g.e.129.3	yes	16
8.3	odd	2		1024.2.g.b.129.2	✓	16
8.5	even	2		1024.2.g.b.129.3	yes	16
16.3	odd	4		1024.2.g.c.641.3	yes	16
16.5	even	4		1024.2.g.h.641.3	yes	16
16.11	odd	4		1024.2.g.h.641.2	yes	16
16.13	even	4		1024.2.g.c.641.2	yes	16
32.3	odd	8		1024.2.g.c.385.3	yes	16
32.5	even	8	inner	1024.2.g.e.897.2	yes	16
32.11	odd	8		1024.2.g.b.897.2	yes	16
32.13	even	8		1024.2.g.h.385.3	yes	16
32.19	odd	8		1024.2.g.h.385.2	yes	16
32.21	even	8		1024.2.g.b.897.3	yes	16
32.27	odd	8	inner	1024.2.g.e.897.3	yes	16
32.29	even	8		1024.2.g.c.385.2	yes	16
64.5	even	16		4096.2.a.o.1.3		8
64.27	odd	16		4096.2.a.o.1.4		8
64.37	even	16		4096.2.a.n.1.6		8
64.59	odd	16		4096.2.a.n.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1024.2.g.b.129.2	✓	16	8.3	odd	2
1024.2.g.b.129.3	yes	16	8.5	even	2
1024.2.g.b.897.2	yes	16	32.11	odd	8
1024.2.g.b.897.3	yes	16	32.21	even	8
1024.2.g.c.385.2	yes	16	32.29	even	8
1024.2.g.c.385.3	yes	16	32.3	odd	8
1024.2.g.c.641.2	yes	16	16.13	even	4
1024.2.g.c.641.3	yes	16	16.3	odd	4
1024.2.g.e.129.2	yes	16	1.1	even	1	trivial
1024.2.g.e.129.3	yes	16	4.3	odd	2	inner
1024.2.g.e.897.2	yes	16	32.5	even	8	inner
1024.2.g.e.897.3	yes	16	32.27	odd	8	inner
1024.2.g.h.385.2	yes	16	32.19	odd	8
1024.2.g.h.385.3	yes	16	32.13	even	8
1024.2.g.h.641.2	yes	16	16.11	odd	4
1024.2.g.h.641.3	yes	16	16.5	even	4
4096.2.a.n.1.5		8	64.59	odd	16
4096.2.a.n.1.6		8	64.37	even	16
4096.2.a.o.1.3		8	64.5	even	16
4096.2.a.o.1.4		8	64.27	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)

\(f(q)\)	\(=\)	\(q+(-0.660056 + 1.59352i) q^{3} +(-0.512517 + 0.212292i) q^{5} +(1.69883 - 1.69883i) q^{7} +(0.0177021 + 0.0177021i) q^{9} +O(q^{10})\)	\(q+(-0.660056 + 1.59352i) q^{3} +(-0.512517 + 0.212292i) q^{5} +(1.69883 - 1.69883i) q^{7} +(0.0177021 + 0.0177021i) q^{9} +(-1.42542 - 3.44127i) q^{11} +(-5.65154 - 2.34094i) q^{13} -0.956828i q^{15} +5.26768i q^{17} +(-3.80083 - 1.57436i) q^{19} +(1.58579 + 3.82843i) q^{21} +(-4.31195 - 4.31195i) q^{23} +(-3.31793 + 3.31793i) q^{25} +(-4.82044 + 1.99669i) q^{27} +(-0.512517 + 1.23733i) q^{29} +1.53073 q^{31} +6.42458 q^{33} +(-0.510031 + 1.23132i) q^{35} +(3.61614 - 1.49785i) q^{37} +(7.46066 - 7.46066i) q^{39} +(-8.69226 - 8.69226i) q^{41} +(0.211714 + 0.511123i) q^{43} +(-0.0128306 - 0.00531461i) q^{45} -9.73339i q^{47} +1.22798i q^{49} +(-8.39412 - 3.47696i) q^{51} +(2.78771 + 6.73012i) q^{53} +(1.46111 + 1.46111i) q^{55} +(5.01752 - 5.01752i) q^{57} +(-2.76469 + 1.14517i) q^{59} +(3.06575 - 7.40138i) q^{61} +0.0601454 q^{63} +3.39347 q^{65} +(2.20995 - 5.33529i) q^{67} +(9.71729 - 4.02503i) q^{69} +(-9.45315 + 9.45315i) q^{71} +(-1.69977 - 1.69977i) q^{73} +(-3.09715 - 7.47719i) q^{75} +(-8.26768 - 3.42458i) q^{77} -12.8332i q^{79} -8.92427i q^{81} +(0.870678 + 0.360647i) q^{83} +(-1.11828 - 2.69977i) q^{85} +(-1.63341 - 1.63341i) q^{87} +(-1.14939 + 1.14939i) q^{89} +(-13.5778 + 5.62413i) q^{91} +(-1.01037 + 2.43925i) q^{93} +2.28221 q^{95} -1.83880 q^{97} +(0.0356847 - 0.0861505i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{5} - 16 q^{9}+O(q^{10}) \) 16 * q + 8 * q^5 - 16 * q^9	\( 16 q + 8 q^{5} - 16 q^{9} - 24 q^{13} + 48 q^{21} - 32 q^{25} + 8 q^{29} + 80 q^{33} + 24 q^{37} - 16 q^{41} - 104 q^{45} + 56 q^{53} - 80 q^{57} - 40 q^{61} + 32 q^{65} - 32 q^{73} - 32 q^{77} + 32 q^{85} + 32 q^{89} - 16 q^{93} + 16 q^{97}+O(q^{100}) \) 16 * q + 8 * q^5 - 16 * q^9 - 24 * q^13 + 48 * q^21 - 32 * q^25 + 8 * q^29 + 80 * q^33 + 24 * q^37 - 16 * q^41 - 104 * q^45 + 56 * q^53 - 80 * q^57 - 40 * q^61 + 32 * q^65 - 32 * q^73 - 32 * q^77 + 32 * q^85 + 32 * q^89 - 16 * q^93 + 16 * q^97

Introduction

L-functions

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Representations

Groups

Database

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