LMFDB - Embedded newform 1024.2.g.e.897.3

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			897.3
Root			$-1.50947 - 0.849413i$ of defining polynomial
Character	$\chi$	$=$	1024.897
Dual form			1024.2.g.e.129.3

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

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

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	0.991757	+	0.128134i	$0.0408988\pi$
$3$	0.660056	+	1.59352i	0.381083	+	0.920017i	−0.610673	+	0.791883i	$0.709101\pi$
$4$		0			0
$5$	−0.512517	−	0.212292i	−0.229205	−	0.0949397i	0.265125	−	0.964214i	$-0.414587\pi$
$5$	−0.512517	−	0.212292i	−0.229205	−	0.0949397i	−0.494330	+	0.869274i	$0.664587\pi$
$6$		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
$11$	1.42542	−	3.44127i	0.429781	−	1.03758i	−0.549576	−	0.835444i	$-0.685211\pi$
$11$	1.42542	−	3.44127i	0.429781	−	1.03758i	0.979357	−	0.202139i	$-0.0647894\pi$
$12$		0			0
$13$	−5.65154	+	2.34094i	−1.56746	+	0.649261i	−0.986364	−	0.164577i	$-0.947374\pi$
$13$	−5.65154	+	2.34094i	−1.56746	+	0.649261i	−0.581091	+	0.813839i	$0.697374\pi$
$14$		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
$19$	3.80083	−	1.57436i	0.871970	−	0.361182i	0.0985928	−	0.995128i	$-0.468566\pi$
$19$	3.80083	−	1.57436i	0.871970	−	0.361182i	0.773377	+	0.633946i	$0.218566\pi$
$20$		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	$-0.530686\pi$
$23$	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
$27$	4.82044	+	1.99669i	0.927694	+	0.384263i
$28$		0			0
$29$	−0.512517	−	1.23733i	−0.0951721	−	0.229766i	0.869123	−	0.494596i	$-0.164684\pi$
$29$	−0.512517	−	1.23733i	−0.0951721	−	0.229766i	−0.964295	+	0.264830i	$0.914684\pi$
$30$		0			0
$31$	−1.53073			−0.274928			−0.137464	−	0.990507i	$-0.543895\pi$
$31$	−1.53073			−0.274928			−0.137464	+	0.990507i	$0.543895\pi$
$32$		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	0.659581	−	0.751634i	$-0.270734\pi$
$37$	3.61614	+	1.49785i	0.594489	+	0.246245i	−0.0650915	+	0.997879i	$0.520734\pi$
$38$		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	$0.659551\pi$
$41$	−8.69226	+	8.69226i	−1.35750	+	1.35750i	−0.876985	+	0.480518i	$0.840449\pi$
$42$		0			0
$43$	−0.211714	+	0.511123i	−0.0322861	+	0.0779456i	−0.939200	−	0.343370i	$-0.888432\pi$
$43$	−0.211714	+	0.511123i	−0.0322861	+	0.0779456i	0.906914	+	0.421316i	$0.138432\pi$
$44$		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	−0.608477	−	0.793572i	$-0.708219\pi$
$53$	2.78771	−	6.73012i	0.382921	−	0.924454i	0.991398	−	0.130882i	$-0.0417809\pi$
$54$		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	$-0.312596\pi$
$59$	2.76469	+	1.14517i	0.359933	+	0.149089i	−0.195387	+	0.980726i	$0.562596\pi$
$60$		0			0
$61$	3.06575	+	7.40138i	0.392529	+	0.947650i	0.989387	+	0.145303i	$0.0464157\pi$
$61$	3.06575	+	7.40138i	0.392529	+	0.947650i	−0.596858	+	0.802347i	$0.703584\pi$
$62$		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	$-0.239756\pi$
$67$	−2.20995	−	5.33529i	−0.269988	−	0.651810i	−0.999482	+	0.0321778i	$0.989756\pi$
$68$		0			0
$69$	9.71729	+	4.02503i	1.16982	+	0.484557i
$70$		0			0
$71$	9.45315	+	9.45315i	1.12188	+	1.12188i	0.991458	+	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	−0.799547	−	0.600603i	$-0.794927\pi$
$73$	−1.69977	+	1.69977i	−0.198944	+	0.198944i	0.600603	+	0.799547i	$0.294927\pi$
$74$		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	$-0.641471\pi$
$83$	−0.870678	+	0.360647i	−0.0955693	+	0.0395861i	0.334387	+	0.942436i	$0.391471\pi$
$84$		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	0.643560	−	0.765396i	$-0.277457\pi$
$89$	−1.14939	−	1.14939i	−0.121835	−	0.121835i	−0.765396	+	0.643560i	$0.777457\pi$
$90$		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	0.293259	−	0.956033i	$-0.405260\pi$
$101$	−1.76267	−	0.730123i	−0.175393	−	0.0726500i	−0.468652	+	0.883383i	$0.655260\pi$
$102$		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
$107$	−7.19848	+	17.3787i	−0.695904	+	1.68006i	0.0366299	+	0.999329i	$0.488338\pi$
$107$	−7.19848	+	17.3787i	−0.695904	+	1.68006i	−0.732534	+	0.680731i	$0.761662\pi$
$108$		0			0
$109$	6.31591	−	2.61614i	0.604954	−	0.250580i	−0.0591151	−	0.998251i	$-0.518828\pi$
$109$	6.31591	−	2.61614i	0.604954	−	0.250580i	0.664070	+	0.747671i	$0.268828\pi$
$110$		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
$115$	−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	$-0.562079\pi$
$127$	−4.36789			−0.387588			−0.193794	+	0.981042i	$0.562079\pi$
$128$		0			0
$129$	−0.954226			−0.0840149
$130$		0			0
$131$	2.60628	+	6.29212i	0.227712	+	0.549745i	0.995898	−	0.0904813i	$-0.0288405\pi$
$131$	2.60628	+	6.29212i	0.227712	+	0.549745i	−0.768186	+	0.640226i	$0.778841\pi$
$132$		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	−0.433448	−	0.901179i	$-0.642703\pi$
$137$	5.47465	−	5.47465i	0.467731	−	0.467731i	0.901179	+	0.433448i	$0.142703\pi$
$138$		0			0
$139$	4.44282	−	10.7259i	0.376835	−	0.909760i	−0.615721	−	0.787965i	$-0.711135\pi$
$139$	4.44282	−	10.7259i	0.376835	−	0.909760i	0.992555	−	0.121795i	$-0.0388650\pi$
$140$		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	−0.822240	−	0.569141i	$-0.807276\pi$
$149$	1.97276	−	4.76267i	0.161615	−	0.390173i	0.983855	+	0.178968i	$0.0572758\pi$
$150$		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
$155$	0.784527	+	0.324962i	0.0630148	+	0.0261016i
$156$		0			0
$157$	−6.64117	−	16.0332i	−0.530023	−	1.27959i	−0.931507	−	0.363723i	$-0.881506\pi$
$157$	−6.64117	−	16.0332i	−0.530023	−	1.27959i	0.401484	−	0.915866i	$-0.368494\pi$
$158$		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	$-0.189053\pi$
$163$	−1.95307	−	4.71513i	−0.152976	−	0.369317i	−0.981725	+	0.190303i	$0.939053\pi$
$164$		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	$-0.188174\pi$
$167$	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
$171$	0.0394132	−	0.0951518i	0.00301400	−	0.00727644i
$172$		0			0
$173$	−15.1973	+	6.29491i	−1.15543	+	0.478593i	−0.876350	−	0.481676i	$-0.840028\pi$
$173$	−15.1973	+	6.29491i	−1.15543	+	0.478593i	−0.279077	+	0.960269i	$0.590028\pi$
$174$		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	$-0.945799\pi$
$179$	−20.9061	+	8.65959i	−1.56260	+	0.647248i	−0.577057	+	0.816704i	$0.695799\pi$
$180$		0			0
$181$	−8.60862	+	20.7830i	−0.639874	+	1.54479i	0.186974	+	0.982365i	$0.440132\pi$
$181$	−8.60862	+	20.7830i	−0.639874	+	1.54479i	−0.826847	+	0.562427i	$0.809868\pi$
$182$		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	$-0.376755\pi$
$191$	10.4366			0.755168			0.377584	+	0.925975i	$0.376755\pi$
$192$		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	−0.207452	−	0.978245i	$-0.566517\pi$
$197$	−14.6794	−	6.08042i	−1.04587	−	0.433212i	−0.838414	+	0.545033i	$0.816517\pi$
$198$		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
$203$	−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	$-0.789787\pi$
$211$	−13.2826	+	5.50184i	−0.914413	+	0.378762i	−0.124669	+	0.992198i	$0.539787\pi$
$212$		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	$-0.684614\pi$
$223$	−16.3670			−1.09602			−0.548008	+	0.836473i	$0.684614\pi$
$224$		0			0
$225$	−0.117468			−0.00783122
$226$		0			0
$227$	2.15247	+	5.19652i	0.142864	+	0.344905i	0.979074	−	0.203505i	$-0.0652333\pi$
$227$	2.15247	+	5.19652i	0.142864	+	0.344905i	−0.836210	+	0.548410i	$0.815233\pi$
$228$		0			0
$229$	−12.1694	−	5.04072i	−0.804175	−	0.333100i	−0.0575475	−	0.998343i	$-0.518328\pi$
$229$	−12.1694	−	5.04072i	−0.804175	−	0.333100i	−0.746627	+	0.665243i	$0.768328\pi$
$230$		0			0
$231$	−10.9143	−	10.9143i	−0.718105	−	0.718105i
$232$		0			0
$233$	1.74984	−	1.74984i	0.114636	−	0.114636i	−0.647462	−	0.762098i	$-0.724169\pi$
$233$	1.74984	−	1.74984i	0.114636	−	0.114636i	0.762098	+	0.647462i	$0.224169\pi$
$234$		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	$0.209174\pi$
$241$			18.9660i			1.22171i	−0.791743	+	0.610854i	$0.790826\pi$
$242$		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	$-0.475689\pi$
$251$	−9.10639	−	3.77199i	−0.574790	−	0.238086i	−0.651092	+	0.758999i	$0.725689\pi$
$252$		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	0.994246	+	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
$267$	1.07291	−	2.59024i	0.0656611	−	0.158520i
$268$		0			0
$269$	13.6544	−	5.65583i	0.832523	−	0.344842i	0.0746220	−	0.997212i	$-0.476225\pi$
$269$	13.6544	−	5.65583i	0.832523	−	0.344842i	0.757901	+	0.652370i	$0.226225\pi$
$270$		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	−0.766206	−	0.642595i	$-0.777858\pi$
$277$	3.82741	−	9.24018i	0.229967	−	0.555189i	0.996173	+	0.0874063i	$0.0278578\pi$
$278$		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	$0.0662900\pi$
$281$	19.8667	+	19.8667i	1.18515	+	1.18515i	0.206754	+	0.978393i	$0.433710\pi$
$282$		0			0
$283$	4.76511	+	1.97378i	0.283257	+	0.117329i	0.519788	−	0.854295i	$-0.326011\pi$
$283$	4.76511	+	1.97378i	0.283257	+	0.117329i	−0.236532	+	0.971624i	$0.576011\pi$
$284$		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	0.885568	−	0.464510i	$-0.153770\pi$
$293$	20.2548	+	8.38983i	1.18330	+	0.490139i	0.297733	+	0.954649i	$0.403770\pi$
$294$		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	$-0.413850\pi$
$307$	19.9354	−	8.25751i	1.13777	−	0.471281i	0.870416	+	0.492317i	$0.163850\pi$
$308$		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	$-0.536855\pi$
$311$	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	0.186028	−	0.982544i	$-0.440438\pi$
$313$	−14.0918	−	14.0918i	−0.796516	−	0.796516i	−0.982544	+	0.186028i	$0.940438\pi$
$314$		0			0
$315$	0.0308256	+	0.0127684i	0.00173682	+	0.000719416i
$316$		0			0
$317$	3.05683	+	7.37983i	0.171688	+	0.414492i	0.986179	−	0.165685i	$-0.0529834\pi$
$317$	3.05683	+	7.37983i	0.171688	+	0.414492i	−0.814490	+	0.580177i	$0.802983\pi$
$318$		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	$-0.813298\pi$
$331$	2.68230	−	6.47564i	0.147433	−	0.355934i	0.980293	+	0.197550i	$0.0632983\pi$
$332$		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	$0.0245460\pi$
$337$			2.82843i			0.154074i	−0.997028	+	0.0770371i	$0.975454\pi$
$338$		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	$-0.275314\pi$
$347$	10.6041	+	4.39235i	0.569256	+	0.235794i	−0.0794417	+	0.996840i	$0.525314\pi$
$348$		0			0
$349$	8.18404	+	19.7580i	0.438081	+	1.05762i	0.976611	+	0.215015i	$0.0689801\pi$
$349$	8.18404	+	19.7580i	0.438081	+	1.05762i	−0.538529	+	0.842607i	$0.681020\pi$
$350$		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	$-0.168640\pi$
$359$	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
$363$	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	−0.979961	−	0.199190i	$-0.936169\pi$
$373$	−2.82311	+	6.81560i	−0.146175	+	0.352898i	0.833786	+	0.552088i	$0.186169\pi$
$374$		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	$-0.259130\pi$
$379$	12.8072	+	5.30491i	0.657861	+	0.272495i	−0.0286774	+	0.999589i	$0.509130\pi$
$380$		0			0
$381$	−2.88305	−	6.96030i	−0.147703	−	0.356587i
$382$		0			0
$383$	3.78803			0.193559			0.0967797	−	0.995306i	$-0.469146\pi$
$383$	3.78803			0.193559			0.0967797	+	0.995306i	$0.469146\pi$
$384$		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	−0.159791	−	0.987151i	$-0.551082\pi$
$389$	−19.1472	−	7.93103i	−0.970801	−	0.402119i	−0.811010	+	0.585032i	$0.801082\pi$
$390$		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	−0.215930	−	0.976409i	$-0.569278\pi$
$397$	6.41201	−	2.65594i	0.321810	−	0.133298i	0.537740	+	0.843111i	$0.319278\pi$
$398$		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
$403$	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	0.704460	−	0.709743i	$-0.251189\pi$
$409$	−0.106839	−	0.106839i	−0.00528285	−	0.00528285i	−0.709743	+	0.704460i	$0.751189\pi$
$410$		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	0.992144	+	0.125099i	$0.0399250\pi$
$419$	7.75898	+	18.7318i	0.379051	+	0.915110i	−0.613093	+	0.790011i	$0.710075\pi$
$420$		0			0
$421$	12.2756	+	5.08471i	0.598275	+	0.247814i	0.661206	−	0.750204i	$-0.270045\pi$
$421$	12.2756	+	5.08471i	0.598275	+	0.247814i	−0.0629310	+	0.998018i	$0.520045\pi$
$422$		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	$0.0240913\pi$
$433$			3.14680i			0.151225i	−0.997137	+	0.0756127i	$0.975909\pi$
$434$		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	$-0.692145\pi$
$439$	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
$443$	−17.2372	−	7.13988i	−0.818964	−	0.339226i	−0.0664397	−	0.997790i	$-0.521164\pi$
$443$	−17.2372	−	7.13988i	−0.818964	−	0.339226i	−0.752524	+	0.658564i	$0.771164\pi$
$444$		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	−0.444207	−	0.895924i	$-0.646515\pi$
$457$	9.65659	−	9.65659i	0.451716	−	0.451716i	0.895924	+	0.444207i	$0.146515\pi$
$458$		0			0
$459$	10.5179	−	25.3925i	0.490935	−	1.18522i
$460$		0			0
$461$	−23.2966	+	9.64976i	−1.08503	+	0.449434i	−0.852271	−	0.523100i	$-0.824775\pi$
$461$	−23.2966	+	9.64976i	−1.08503	+	0.449434i	−0.232759	+	0.972534i	$0.574775\pi$
$462$		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	$-0.423306\pi$
$467$	23.6421	−	9.79289i	1.09403	−	0.453161i	0.855409	+	0.517953i	$0.173306\pi$
$468$		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	$-0.304760\pi$
$479$	25.1963			1.15125			0.575623	+	0.817715i	$0.304760\pi$
$480$		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	$-0.414564\pi$
$487$	−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
$491$	11.9376	−	28.8199i	0.538736	−	1.30062i	−0.386870	−	0.922134i	$-0.626444\pi$
$491$	11.9376	−	28.8199i	0.538736	−	1.30062i	0.925606	−	0.378489i	$-0.123556\pi$
$492$		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	$-0.298834\pi$
$499$	35.2722	−	14.6102i	1.57900	−	0.654043i	0.988255	+	0.152814i	$0.0488337\pi$
$500$		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	$-0.771919\pi$
$503$	−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
$507$	38.9135	+	16.1185i	1.72821	+	0.715848i
$508$		0			0
$509$	3.08482	+	7.44742i	0.136732	+	0.330101i	0.977383	−	0.211477i	$-0.0678272\pi$
$509$	3.08482	+	7.44742i	0.136732	+	0.330101i	−0.840651	+	0.541578i	$0.817827\pi$
$510$		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	−0.842689	−	0.538400i	$-0.819029\pi$
$521$	−6.94553	+	6.94553i	−0.304289	+	0.304289i	0.538400	+	0.842689i	$0.319029\pi$
$522$		0			0
$523$	0.930625	−	2.24673i	0.0406934	−	0.0982425i	−0.902226	−	0.431263i	$-0.858068\pi$
$523$	0.930625	−	2.24673i	0.0406934	−	0.0982425i	0.942919	+	0.333021i	$0.108068\pi$
$524$		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	−0.971350	−	0.237653i	$-0.923622\pi$
$541$	−10.5260	−	25.4120i	−0.452548	−	1.09255i	0.518802	−	0.854894i	$-0.326378\pi$
$542$		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	$-0.143616\pi$
$547$	−1.04627	−	2.52591i	−0.0447351	−	0.108000i	−0.944668	+	0.328029i	$0.893616\pi$
$548$		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	−0.776983	−	0.629522i	$-0.783251\pi$
$557$	−20.7983	+	8.61495i	−0.881254	+	0.365027i	−0.104271	+	0.994549i	$0.533251\pi$
$558$		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	$-0.783333\pi$
$563$	−20.9200	+	8.66534i	−0.881672	+	0.365201i	−0.104527	+	0.994522i	$0.533333\pi$
$564$		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	0.701284	−	0.712882i	$-0.252610\pi$
$569$	−0.276633	−	0.276633i	−0.0115970	−	0.0115970i	−0.712882	+	0.701284i	$0.752610\pi$
$570$		0			0
$571$	31.9788	+	13.2460i	1.33827	+	0.554329i	0.933003	−	0.359869i	$-0.117179\pi$
$571$	31.9788	+	13.2460i	1.33827	+	0.554329i	0.405267	+	0.914198i	$0.367179\pi$
$572$		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	0.348575	+	0.937281i	$0.386665\pi$
$587$	−13.5838	+	32.7941i	−0.560662	+	1.35356i	−0.909238	+	0.416277i	$0.863335\pi$
$588$		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	$-0.982570\pi$
$593$		−	2.66555i		−	0.109461i	0.998501	−	0.0547306i	$-0.0174300\pi$
$594$		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	$-0.861793\pi$
$599$	−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	0.668045	−	0.744121i	$-0.267131\pi$
$601$	−1.86501	−	1.86501i	−0.0760755	−	0.0760755i	−0.744121	+	0.668045i	$0.767131\pi$
$602$		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	$-0.444994\pi$
$607$	8.47275			0.343898			0.171949	+	0.985106i	$0.444994\pi$
$608$		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	0.800805	−	0.598926i	$-0.204405\pi$
$613$	23.3613	+	9.67657i	0.943555	+	0.390833i	0.142750	+	0.989759i	$0.454405\pi$
$614$		0			0
$615$	8.31700	+	8.31700i	0.335374	+	0.335374i
$616$		0			0
$617$	−8.91738	+	8.91738i	−0.359000	+	0.359000i	−0.863444	−	0.504444i	$-0.831697\pi$
$617$	−8.91738	+	8.91738i	−0.359000	+	0.359000i	0.504444	+	0.863444i	$0.331697\pi$
$618$		0			0
$619$	2.30623	−	5.56774i	0.0926953	−	0.223786i	−0.870731	−	0.491760i	$-0.836354\pi$
$619$	2.30623	−	5.56774i	0.0926953	−	0.223786i	0.963426	+	0.267973i	$0.0863539\pi$
$620$		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	0.430981	−	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
$635$	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	−0.941534	−	0.336918i	$-0.890616\pi$
$643$	−13.0339	−	31.4666i	−0.514006	−	1.24092i	0.427528	−	0.904002i	$-0.359384\pi$
$644$		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	$-0.192795\pi$
$647$	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
$651$	−2.42742	+	5.86030i	−0.0951380	+	0.229683i
$652$		0			0
$653$	−12.6294	+	5.23125i	−0.494225	+	0.204715i	−0.615853	−	0.787861i	$-0.711188\pi$
$653$	−12.6294	+	5.23125i	−0.494225	+	0.204715i	0.121628	+	0.992576i	$0.461188\pi$
$654$		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	$-0.527180\pi$
$659$	14.3485	−	5.94335i	0.558939	−	0.231520i	0.644224	+	0.764837i	$0.277180\pi$
$660$		0			0
$661$	8.79664	−	21.2370i	0.342150	−	0.826022i	−0.655348	−	0.755327i	$-0.727478\pi$
$661$	8.79664	−	21.2370i	0.342150	−	0.826022i	0.997498	−	0.0706953i	$-0.0225218\pi$
$662$		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	0.727992	−	0.685586i	$-0.240454\pi$
$677$	19.7220	+	8.16911i	0.757977	+	0.313964i	0.0299855	+	0.999550i	$0.490454\pi$
$678$		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	−0.635941	−	0.771738i	$-0.719388\pi$
$683$	9.39365	−	22.6783i	0.359438	−	0.867760i	0.995379	−	0.0960227i	$-0.0306121\pi$
$684$		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	$-0.534574\pi$
$691$	13.6135	−	5.63891i	0.517883	−	0.214514i	0.626287	+	0.779593i	$0.284574\pi$
$692$		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	0.787917	+	0.615781i	$0.211160\pi$
$701$	17.6385	+	42.5832i	0.666199	+	1.60835i	−0.121718	+	0.992565i	$0.538840\pi$
$702$		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	0.825118	−	0.564960i	$-0.191108\pi$
$709$	26.8688	+	11.1294i	1.00908	+	0.417974i	0.183960	+	0.982934i	$0.441108\pi$
$710$		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	$-0.927512\pi$
$727$	−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
$731$	2.69243	+	1.11524i	0.0995832	+	0.0412487i
$732$		0			0
$733$	4.66073	+	11.2520i	0.172148	+	0.415602i	0.986281	−	0.165077i	$-0.0527873\pi$
$733$	4.66073	+	11.2520i	0.172148	+	0.415602i	−0.814133	+	0.580679i	$0.802787\pi$
$734$		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	−0.997167	−	0.0752197i	$-0.976034\pi$
$739$	−9.38552	−	22.6586i	−0.345252	−	0.833512i	0.651915	−	0.758292i	$-0.273966\pi$
$740$		0			0
$741$	−40.1024	−	16.6110i	−1.47320	−	0.610219i
$742$		0			0
$743$	30.4077	+	30.4077i	1.11555	+	1.11555i	0.992386	+	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
$747$	−0.00902860	+	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	−0.902629	−	0.430420i	$-0.858365\pi$
$757$	1.09998	−	2.65558i	0.0399793	−	0.0965185i	0.942608	+	0.333902i	$0.108365\pi$
$758$		0			0
$759$	27.7025	−	27.7025i	1.00554	−	1.00554i
$760$		0			0
$761$	17.9432	+	17.9432i	0.650442	+	0.650442i	0.953099	−	0.302658i	$-0.0978739\pi$
$761$	17.9432	+	17.9432i	0.650442	+	0.650442i	−0.302658	+	0.953099i	$0.597874\pi$
$762$		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	0.673056	−	0.739591i	$-0.264981\pi$
$773$	17.4049	+	7.20933i	0.626009	+	0.259302i	−0.0470471	+	0.998893i	$0.514981\pi$
$774$		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	$-0.837751\pi$
$787$	−32.1235	+	13.3060i	−1.14508	+	0.474307i	−0.272198	+	0.962241i	$0.587751\pi$
$788$		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	0.755101	−	0.655609i	$-0.227588\pi$
$797$	−6.84385	−	16.5225i	−0.242422	−	0.585258i	−0.997522	+	0.0703512i	$0.977588\pi$
$798$		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	−0.867886	−	0.496763i	$-0.834522\pi$
$809$	−10.5558	+	10.5558i	−0.371123	+	0.371123i	0.496763	+	0.867886i	$0.334522\pi$
$810$		0			0
$811$	−1.78652	+	4.31304i	−0.0627333	+	0.151451i	−0.952138	−	0.305670i	$-0.901120\pi$
$811$	−1.78652	+	4.31304i	−0.0627333	+	0.151451i	0.889404	+	0.457122i	$0.151120\pi$
$812$		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	0.626658	+	0.779295i	$0.284422\pi$
$821$	−10.5300	+	25.4218i	−0.367501	+	0.887225i	−0.994158	+	0.107931i	$0.965578\pi$
$822$		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
$827$	14.6219	+	6.05658i	0.508453	+	0.210608i	0.622136	−	0.782909i	$-0.286265\pi$
$827$	14.6219	+	6.05658i	0.508453	+	0.210608i	−0.113683	+	0.993517i	$0.536265\pi$
$828$		0			0
$829$	−11.7436	−	28.3516i	−0.407872	−	0.984691i	−0.985697	−	0.168530i	$-0.946098\pi$
$829$	−11.7436	−	28.3516i	−0.407872	−	0.984691i	0.577824	−	0.816161i	$-0.303902\pi$
$830$		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	$-0.405878\pi$
$839$	−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
$843$	−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	−0.989864	−	0.142016i	$-0.954642\pi$
$853$	−5.53470	+	13.3619i	−0.189504	+	0.457504i	0.800360	+	0.599520i	$0.204642\pi$
$854$		0			0
$855$	−0.0403999	+	0.0403999i	−0.00138165	+	0.00138165i
$856$		0			0
$857$	−16.2115	−	16.2115i	−0.553775	−	0.553775i	0.373753	−	0.927528i	$-0.378071\pi$
$857$	−16.2115	−	16.2115i	−0.553775	−	0.553775i	−0.927528	+	0.373753i	$0.878071\pi$
$858$		0			0
$859$	−25.6351	−	10.6184i	−0.874658	−	0.362295i	−0.100235	−	0.994964i	$-0.531960\pi$
$859$	−25.6351	−	10.6184i	−0.874658	−	0.362295i	−0.774423	+	0.632669i	$0.781960\pi$
$860$		0			0
$861$	19.4936	+	47.0617i	0.664341	+	1.60386i
$862$		0			0
$863$	40.8195			1.38951			0.694755	−	0.719246i	$-0.255513\pi$
$863$	40.8195			1.38951			0.694755	+	0.719246i	$0.255513\pi$
$864$		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	0.512407	−	0.858743i	$-0.328754\pi$
$877$	43.8869	−	18.1786i	1.48196	−	0.613846i	0.969549	+	0.244896i	$0.0787540\pi$
$878$		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
$883$	−49.9223	+	20.6785i	−1.68002	+	0.695886i	−0.999327	−	0.0366838i	$-0.988321\pi$
$883$	−49.9223	+	20.6785i	−1.68002	+	0.695886i	−0.680692	+	0.732570i	$0.738321\pi$
$884$		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	$-0.610671\pi$
$887$	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
$891$	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	$-0.933983\pi$
$907$	−4.24679	+	10.2527i	−0.141012	+	0.340434i	0.837558	+	0.546349i	$0.183983\pi$
$908$		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	$-0.711518\pi$
$919$	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
$923$	−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	0.0577344	−	0.998332i	$-0.481612\pi$
$937$	32.3267	−	32.3267i	1.05607	−	1.05607i	0.998332	−	0.0577344i	$-0.0183876\pi$
$938$		0			0
$939$	13.1541	−	31.7569i	0.429269	−	1.03635i
$940$		0			0
$941$	23.9077	−	9.90288i	0.779368	−	0.322825i	0.0427073	−	0.999088i	$-0.486402\pi$
$941$	23.9077	−	9.90288i	0.779368	−	0.322825i	0.736660	+	0.676263i	$0.236402\pi$
$942$		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	$-0.749495\pi$
$947$	−21.6767	+	8.97880i	−0.704399	+	0.291772i	0.00158544	+	0.999999i	$0.499495\pi$
$948$		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	0.754092	−	0.656769i	$-0.228077\pi$
$953$	3.00440	+	3.00440i	0.0973222	+	0.0973222i	−0.656769	+	0.754092i	$0.728077\pi$
$954$		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	$-0.480251\pi$
$967$	−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
$971$	−0.258452	+	0.623957i	−0.00829411	+	0.0200237i	−0.927972	−	0.372649i	$-0.878450\pi$
$971$	−0.258452	+	0.623957i	−0.00829411	+	0.0200237i	0.919678	+	0.392673i	$0.128450\pi$
$972$		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	$-0.822362\pi$
$977$		−	33.1041i		−	1.05909i	0.848281	−	0.529546i	$-0.177638\pi$
$978$		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	$-0.760762\pi$
$983$	−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
$987$	−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	$-0.364836\pi$
$991$	25.9387			0.823970			0.411985	+	0.911191i	$0.364836\pi$
$992$		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	0.286074	−	0.958208i	$-0.407650\pi$
$997$	−5.97395	−	2.47449i	−0.189197	−	0.0783679i	−0.475270	+	0.879840i	$0.657650\pi$
$998$		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.897.3	yes	16
4.3	odd	2	inner	1024.2.g.e.897.2	yes	16
8.3	odd	2		1024.2.g.b.897.3	yes	16
8.5	even	2		1024.2.g.b.897.2	yes	16
16.3	odd	4		1024.2.g.h.385.3	yes	16
16.5	even	4		1024.2.g.c.385.3	yes	16
16.11	odd	4		1024.2.g.c.385.2	yes	16
16.13	even	4		1024.2.g.h.385.2	yes	16
32.3	odd	8		1024.2.g.b.129.3	yes	16
32.5	even	8		1024.2.g.h.641.2	yes	16
32.11	odd	8		1024.2.g.c.641.2	yes	16
32.13	even	8	inner	1024.2.g.e.129.3	yes	16
32.19	odd	8	inner	1024.2.g.e.129.2	yes	16
32.21	even	8		1024.2.g.c.641.3	yes	16
32.27	odd	8		1024.2.g.h.641.3	yes	16
32.29	even	8		1024.2.g.b.129.2	✓	16
64.13	even	16		4096.2.a.n.1.5		8
64.19	odd	16		4096.2.a.n.1.6		8
64.45	even	16		4096.2.a.o.1.4		8
64.51	odd	16		4096.2.a.o.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1024.2.g.b.129.2	✓	16	32.29	even	8
1024.2.g.b.129.3	yes	16	32.3	odd	8
1024.2.g.b.897.2	yes	16	8.5	even	2
1024.2.g.b.897.3	yes	16	8.3	odd	2
1024.2.g.c.385.2	yes	16	16.11	odd	4
1024.2.g.c.385.3	yes	16	16.5	even	4
1024.2.g.c.641.2	yes	16	32.11	odd	8
1024.2.g.c.641.3	yes	16	32.21	even	8
1024.2.g.e.129.2	yes	16	32.19	odd	8	inner
1024.2.g.e.129.3	yes	16	32.13	even	8	inner
1024.2.g.e.897.2	yes	16	4.3	odd	2	inner
1024.2.g.e.897.3	yes	16	1.1	even	1	trivial
1024.2.g.h.385.2	yes	16	16.13	even	4
1024.2.g.h.385.3	yes	16	16.3	odd	4
1024.2.g.h.641.2	yes	16	32.5	even	8
1024.2.g.h.641.3	yes	16	32.27	odd	8
4096.2.a.n.1.5		8	64.13	even	16
4096.2.a.n.1.6		8	64.19	odd	16
4096.2.a.o.1.3		8	64.51	odd	16
4096.2.a.o.1.4		8	64.45	even	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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Varieties

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Groups

Database

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