LMFDB - Embedded newform 896.2.z.a.159.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [896,2,Mod(31,896)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(896, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("896.31"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.z (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [56,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.15459602111$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			159.13
Character	$\chi$	$=$	896.159
Dual form			896.2.z.a.479.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.29647 + 0.615336i) q^{3} +(0.223959 + 0.835825i) q^{5} +(1.25761 + 2.32775i) q^{7} +(2.29704 + 1.32620i) q^{9} +(-2.03316 - 0.544785i) q^{11} +(0.336492 + 0.336492i) q^{13} +2.05725i q^{15} +(-0.0488652 + 0.0282123i) q^{17} +(2.11632 + 7.89820i) q^{19} +(1.45571 + 6.11945i) q^{21} +(3.59814 - 6.23216i) q^{23} +(3.68168 - 2.12562i) q^{25} +(-0.584366 - 0.584366i) q^{27} +(-4.81700 + 4.81700i) q^{29} +(1.84955 + 3.20351i) q^{31} +(-4.33387 - 2.50216i) q^{33} +(-1.66394 + 1.57246i) q^{35} +(-3.27008 + 0.876214i) q^{37} +(0.565687 + 0.979798i) q^{39} -4.95983 q^{41} +(4.99825 - 4.99825i) q^{43} +(-0.594027 + 2.21694i) q^{45} +(5.50377 - 9.53281i) q^{47} +(-3.83684 + 5.85480i) q^{49} +(-0.129577 + 0.0347202i) q^{51} +(0.971464 - 3.62555i) q^{53} -1.82138i q^{55} +19.4402i q^{57} +(-2.27632 + 8.49533i) q^{59} +(-6.21929 + 1.66645i) q^{61} +(-0.198278 + 7.01478i) q^{63} +(-0.205888 + 0.356609i) q^{65} +(2.80281 - 10.4602i) q^{67} +(12.0979 - 12.0979i) q^{69} +13.1246 q^{71} +(-2.69592 - 4.66948i) q^{73} +(9.76283 - 2.61594i) q^{75} +(-1.28880 - 5.41782i) q^{77} +(-4.99619 - 2.88455i) q^{79} +(-4.96099 - 8.59269i) q^{81} +(4.52860 - 4.52860i) q^{83} +(-0.0345244 - 0.0345244i) q^{85} +(-14.0261 + 8.09800i) q^{87} +(1.28218 - 2.22080i) q^{89} +(-0.360094 + 1.20644i) q^{91} +(2.27619 + 8.49484i) q^{93} +(-6.12755 + 3.53774i) q^{95} +9.06313i q^{97} +(-3.94777 - 3.94777i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 6 q^{3} + 6 q^{5} + 8 q^{7} + 2 q^{11} - 12 q^{17} - 6 q^{19} + 10 q^{21} + 12 q^{23} + 24 q^{29} - 12 q^{33} - 2 q^{35} - 6 q^{37} + 4 q^{39} - 12 q^{45} - 8 q^{49} - 34 q^{51} - 6 q^{53} + 42 q^{59}+ \cdots - 16 q^{99}+O(q^{100}) $ 56 * q - 6 * q^3 + 6 * q^5 + 8 * q^7 + 2 * q^11 - 12 * q^17 - 6 * q^19 + 10 * q^21 + 12 * q^23 + 24 * q^29 - 12 * q^33 - 2 * q^35 - 6 * q^37 + 4 * q^39 - 12 * q^45 - 8 * q^49 - 34 * q^51 - 6 * q^53 + 42 * q^59 + 6 * q^61 - 4 * q^65 + 6 * q^67 + 80 * q^71 + 24 * q^75 - 10 * q^77 - 8 * q^81 + 28 * q^85 + 12 * q^87 + 16 * q^91 - 10 * q^93 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$645$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	2.29647	+	0.615336i	1.32587	+	0.355265i	0.851172	−	0.524887i	$-0.175892\pi$
$3$	2.29647	+	0.615336i	1.32587	+	0.355265i	0.474693	+	0.880151i	$0.342559\pi$
$4$		0			0
$5$	0.223959	+	0.835825i	0.100157	+	0.373792i	0.997751	−	0.0670318i	$-0.0213529\pi$
$5$	0.223959	+	0.835825i	0.100157	+	0.373792i	−0.897593	+	0.440824i	$0.854686\pi$
$6$		0			0
$7$	1.25761	+	2.32775i	0.475331	+	0.879807i
$7$	1.25761	+	2.32775i	0.475331	+	0.879807i
$8$		0			0
$9$	2.29704	+	1.32620i	0.765681	+	0.442066i
$10$		0			0
$11$	−2.03316	−	0.544785i	−0.613022	−	0.164259i	−0.0610684	−	0.998134i	$-0.519451\pi$
$11$	−2.03316	−	0.544785i	−0.613022	−	0.164259i	−0.551954	+	0.833875i	$0.686117\pi$
$12$		0			0
$13$	0.336492	+	0.336492i	0.0933261	+	0.0933261i	0.752228	−	0.658902i	$-0.228979\pi$
$13$	0.336492	+	0.336492i	0.0933261	+	0.0933261i	−0.658902	+	0.752228i	$0.728979\pi$
$14$		0			0
$15$			2.05725i			0.531181i
$16$		0			0
$17$	−0.0488652	+	0.0282123i	−0.0118516	+	0.00684250i	−0.505914	−	0.862584i	$-0.668845\pi$
$17$	−0.0488652	+	0.0282123i	−0.0118516	+	0.00684250i	0.494063	+	0.869426i	$0.335511\pi$
$18$		0			0
$19$	2.11632	+	7.89820i	0.485516	+	1.81197i	0.577724	+	0.816232i	$0.303941\pi$
$19$	2.11632	+	7.89820i	0.485516	+	1.81197i	−0.0922079	+	0.995740i	$0.529392\pi$
$20$		0			0
$21$	1.45571	+	6.11945i	0.317661	+	1.33537i
$22$		0			0
$23$	3.59814	−	6.23216i	0.750264	−	1.29949i	−0.197431	−	0.980317i	$-0.563260\pi$
$23$	3.59814	−	6.23216i	0.750264	−	1.29949i	0.947695	−	0.319178i	$-0.103407\pi$
$24$		0			0
$25$	3.68168	−	2.12562i	0.736336	−	0.425124i
$26$		0			0
$27$	−0.584366	−	0.584366i	−0.112461	−	0.112461i
$28$		0			0
$29$	−4.81700	+	4.81700i	−0.894494	+	0.894494i	−0.994942	−	0.100448i	$-0.967972\pi$
$29$	−4.81700	+	4.81700i	−0.894494	+	0.894494i	0.100448	+	0.994942i	$0.467972\pi$
$30$		0			0
$31$	1.84955	+	3.20351i	0.332188	+	0.575367i	0.982941	−	0.183923i	$-0.0588797\pi$
$31$	1.84955	+	3.20351i	0.332188	+	0.575367i	−0.650752	+	0.759290i	$0.725546\pi$
$32$		0			0
$33$	−4.33387	−	2.50216i	−0.754429	−	0.435570i
$34$		0			0
$35$	−1.66394	+	1.57246i	−0.281257	+	0.265794i
$36$		0			0
$37$	−3.27008	+	0.876214i	−0.537597	+	0.144049i	−0.517394	−	0.855747i	$-0.673098\pi$
$37$	−3.27008	+	0.876214i	−0.537597	+	0.144049i	−0.0202030	+	0.999796i	$0.506431\pi$
$38$		0			0
$39$	0.565687	+	0.979798i	0.0905824	+	0.156893i
$40$		0			0
$41$	−4.95983			−0.774596			−0.387298	−	0.921955i	$-0.626592\pi$
$41$	−4.95983			−0.774596			−0.387298	+	0.921955i	$0.626592\pi$
$42$		0			0
$43$	4.99825	−	4.99825i	0.762225	−	0.762225i	−0.214499	−	0.976724i	$-0.568812\pi$
$43$	4.99825	−	4.99825i	0.762225	−	0.762225i	0.976724	+	0.214499i	$0.0688118\pi$
$44$		0			0
$45$	−0.594027	+	2.21694i	−0.0885524	+	0.330482i
$46$		0			0
$47$	5.50377	−	9.53281i	0.802807	−	1.39050i	−0.114954	−	0.993371i	$-0.536672\pi$
$47$	5.50377	−	9.53281i	0.802807	−	1.39050i	0.917761	−	0.397132i	$-0.129995\pi$
$48$		0			0
$49$	−3.83684	+	5.85480i	−0.548120	+	0.836399i
$50$		0			0
$51$	−0.129577	+	0.0347202i	−0.0181445	+	0.00486179i
$52$		0			0
$53$	0.971464	−	3.62555i	0.133441	−	0.498008i	−0.866559	−	0.499075i	$-0.833673\pi$
$53$	0.971464	−	3.62555i	0.133441	−	0.498008i	0.999999	+	0.00106745i	$0.000339780\pi$
$54$		0			0
$55$		−	1.82138i		−	0.245595i
$56$		0			0
$57$			19.4402i			2.57492i
$58$		0			0
$59$	−2.27632	+	8.49533i	−0.296351	+	1.10600i	0.643787	+	0.765204i	$0.277362\pi$
$59$	−2.27632	+	8.49533i	−0.296351	+	1.10600i	−0.940138	+	0.340793i	$0.889305\pi$
$60$		0			0
$61$	−6.21929	+	1.66645i	−0.796298	+	0.213367i	−0.633958	−	0.773367i	$-0.718571\pi$
$61$	−6.21929	+	1.66645i	−0.796298	+	0.213367i	−0.162340	+	0.986735i	$0.551904\pi$
$62$		0			0
$63$	−0.198278	+	7.01478i	−0.0249807	+	0.883779i
$64$		0			0
$65$	−0.205888	+	0.356609i	−0.0255373	+	0.0442319i
$66$		0			0
$67$	2.80281	−	10.4602i	0.342417	−	1.27792i	−0.553184	−	0.833059i	$-0.686587\pi$
$67$	2.80281	−	10.4602i	0.342417	−	1.27792i	0.895601	−	0.444859i	$-0.146746\pi$
$68$		0			0
$69$	12.0979	−	12.0979i	1.45641	−	1.45641i
$70$		0			0
$71$	13.1246			1.55760			0.778800	−	0.627272i	$-0.215829\pi$
$71$	13.1246			1.55760			0.778800	+	0.627272i	$0.215829\pi$
$72$		0			0
$73$	−2.69592	−	4.66948i	−0.315534	−	0.546521i	0.664017	−	0.747718i	$-0.268850\pi$
$73$	−2.69592	−	4.66948i	−0.315534	−	0.546521i	−0.979551	+	0.201197i	$0.935517\pi$
$74$		0			0
$75$	9.76283	−	2.61594i	1.12731	−	0.302063i
$76$		0			0
$77$	−1.28880	−	5.41782i	−0.146873	−	0.617418i
$78$		0			0
$79$	−4.99619	−	2.88455i	−0.562116	−	0.324538i	0.191878	−	0.981419i	$-0.438542\pi$
$79$	−4.99619	−	2.88455i	−0.562116	−	0.324538i	−0.753994	+	0.656881i	$0.771875\pi$
$80$		0			0
$81$	−4.96099	−	8.59269i	−0.551221	−	0.954743i
$82$		0			0
$83$	4.52860	−	4.52860i	0.497079	−	0.497079i	−0.413449	−	0.910527i	$-0.635676\pi$
$83$	4.52860	−	4.52860i	0.497079	−	0.497079i	0.910527	+	0.413449i	$0.135676\pi$
$84$		0			0
$85$	−0.0345244	−	0.0345244i	−0.00374469	−	0.00374469i
$86$		0			0
$87$	−14.0261	+	8.09800i	−1.50376	+	0.868197i
$88$		0			0
$89$	1.28218	−	2.22080i	0.135911	−	0.235404i	−0.790034	−	0.613063i	$-0.789937\pi$
$89$	1.28218	−	2.22080i	0.135911	−	0.235404i	0.925945	+	0.377659i	$0.123271\pi$
$90$		0			0
$91$	−0.360094	+	1.20644i	−0.0377481	+	0.126470i
$92$		0			0
$93$	2.27619	+	8.49484i	0.236030	+	0.880874i
$94$		0			0
$95$	−6.12755	+	3.53774i	−0.628673	+	0.362965i
$96$		0			0
$97$			9.06313i			0.920222i	0.887861	+	0.460111i	$0.152190\pi$
$97$			9.06313i			0.920222i	−0.887861	+	0.460111i	$0.847810\pi$
$98$		0			0
$99$	−3.94777	−	3.94777i	−0.396766	−	0.396766i
$100$		0			0
$101$	−9.27207	−	2.48444i	−0.922605	−	0.247211i	−0.233907	−	0.972259i	$-0.575151\pi$
$101$	−9.27207	−	2.48444i	−0.922605	−	0.247211i	−0.688699	+	0.725048i	$0.741818\pi$
$102$		0			0
$103$	1.18973	+	0.686893i	0.117228	+	0.0676816i	0.557467	−	0.830199i	$-0.311773\pi$
$103$	1.18973	+	0.686893i	0.117228	+	0.0676816i	−0.440239	+	0.897880i	$0.645106\pi$
$104$		0			0
$105$	−4.78878	+	2.58722i	−0.467337	+	0.252487i
$106$		0			0
$107$	−3.62137	−	13.5151i	−0.350091	−	1.30656i	−0.886551	−	0.462632i	$-0.846905\pi$
$107$	−3.62137	−	13.5151i	−0.350091	−	1.30656i	0.536459	−	0.843926i	$-0.319761\pi$
$108$		0			0
$109$	2.68896	+	0.720506i	0.257556	+	0.0690119i	0.385287	−	0.922797i	$-0.374103\pi$
$109$	2.68896	+	0.720506i	0.257556	+	0.0690119i	−0.127731	+	0.991809i	$0.540769\pi$
$110$		0			0
$111$	−8.04879			−0.763957
$112$		0			0
$113$	6.74317			0.634344			0.317172	−	0.948368i	$-0.397267\pi$
$113$	6.74317			0.634344			0.317172	+	0.948368i	$0.397267\pi$
$114$		0			0
$115$	6.01483	+	1.61167i	0.560886	+	0.150289i
$116$		0			0
$117$	0.326681	+	1.21919i	0.0302017	+	0.112714i
$118$		0			0
$119$	−0.127125	−	0.0782659i	−0.0116535	−	0.00717463i
$120$		0			0
$121$	−5.68931	−	3.28473i	−0.517210	−	0.298612i
$122$		0			0
$123$	−11.3901	−	3.05197i	−1.02701	−	0.275187i
$124$		0			0
$125$	5.66052	+	5.66052i	0.506293	+	0.506293i
$126$		0			0
$127$			8.62463i			0.765312i	0.923891	+	0.382656i	$0.124991\pi$
$127$			8.62463i			0.765312i	−0.923891	+	0.382656i	$0.875009\pi$
$128$		0			0
$129$	14.5539	−	8.40270i	1.28140	−	0.739817i
$130$		0			0
$131$	−1.39401	−	5.20253i	−0.121796	−	0.454547i	0.877910	−	0.478826i	$-0.158938\pi$
$131$	−1.39401	−	5.20253i	−0.121796	−	0.454547i	−0.999705	+	0.0242790i	$0.992271\pi$
$132$		0			0
$133$	−15.7235	+	14.8591i	−1.36340	+	1.28845i
$134$		0			0
$135$	0.357554	−	0.619302i	0.0307734	−	0.0533010i
$136$		0			0
$137$	9.31969	−	5.38073i	0.796235	−	0.459707i	−0.0459178	−	0.998945i	$-0.514621\pi$
$137$	9.31969	−	5.38073i	0.796235	−	0.459707i	0.842153	+	0.539239i	$0.181288\pi$
$138$		0			0
$139$	13.2045	+	13.2045i	1.11999	+	1.11999i	0.991742	+	0.128251i	$0.0409362\pi$
$139$	13.2045	+	13.2045i	1.11999	+	1.11999i	0.128251	+	0.991742i	$0.459064\pi$
$140$		0			0
$141$	18.5051	−	18.5051i	1.55841	−	1.55841i
$142$		0			0
$143$	−0.500828	−	0.867459i	−0.0418813	−	0.0725406i
$144$		0			0
$145$	−5.10498	−	2.94736i	−0.423945	−	0.244765i
$146$		0			0
$147$	−12.4138	+	11.0844i	−1.02388	+	0.914225i
$148$		0			0
$149$	3.90087	−	1.04523i	0.319571	−	0.0856289i	−0.0954676	−	0.995433i	$-0.530435\pi$
$149$	3.90087	−	1.04523i	0.319571	−	0.0856289i	0.415039	+	0.909804i	$0.363768\pi$
$150$		0			0
$151$	−3.94869	−	6.83934i	−0.321340	−	0.556577i	0.659425	−	0.751771i	$-0.270800\pi$
$151$	−3.94869	−	6.83934i	−0.321340	−	0.556577i	−0.980765	+	0.195193i	$0.937467\pi$
$152$		0			0
$153$	−0.149661			−0.0120993
$154$		0			0
$155$	−2.26335	+	2.26335i	−0.181797	+	0.181797i
$156$		0			0
$157$	4.18229	−	15.6085i	0.333783	−	1.24570i	−0.571399	−	0.820672i	$-0.693599\pi$
$157$	4.18229	−	15.6085i	0.333783	−	1.24570i	0.905182	−	0.425023i	$-0.139734\pi$
$158$		0			0
$159$	4.46187	−	7.72818i	0.353849	−	0.612885i
$160$		0			0
$161$	19.0320	+	0.537953i	1.49993	+	0.0423966i
$162$		0			0
$163$	−2.99018	+	0.801215i	−0.234209	+	0.0627560i	−0.374014	−	0.927423i	$-0.622019\pi$
$163$	−2.99018	+	0.801215i	−0.234209	+	0.0627560i	0.139806	+	0.990179i	$0.455352\pi$
$164$		0			0
$165$	1.12076	−	4.18274i	0.0872511	−	0.325626i
$166$		0			0
$167$			5.62954i			0.435627i	0.975990	+	0.217813i	$0.0698924\pi$
$167$			5.62954i			0.435627i	−0.975990	+	0.217813i	$0.930108\pi$
$168$		0			0
$169$		−	12.7735i		−	0.982580i
$170$		0			0
$171$	−5.61331	+	20.9492i	−0.429261	+	1.60202i
$172$		0			0
$173$	−1.69727	+	0.454783i	−0.129041	+	0.0345765i	−0.322762	−	0.946480i	$-0.604611\pi$
$173$	−1.69727	+	0.454783i	−0.129041	+	0.0345765i	0.193720	+	0.981057i	$0.437945\pi$
$174$		0			0
$175$	9.57802	+	5.89684i	0.724030	+	0.445759i
$176$		0			0
$177$	−10.4550	+	18.1085i	−0.785843	+	1.36112i
$178$		0			0
$179$	−1.98267	+	7.39942i	−0.148192	+	0.553059i	0.851401	+	0.524515i	$0.175754\pi$
$179$	−1.98267	+	7.39942i	−0.148192	+	0.553059i	−0.999593	+	0.0285433i	$0.990913\pi$
$180$		0			0
$181$	0.00448004	−	0.00448004i	0.000332999	−	0.000332999i	−0.706940	−	0.707273i	$-0.749925\pi$
$181$	0.00448004	−	0.00448004i	0.000332999	−	0.000332999i	0.707273	+	0.706940i	$0.249925\pi$
$182$		0			0
$183$	−15.3078			−1.13159
$184$		0			0
$185$	−1.46472	−	2.53698i	−0.107689	−	0.186522i
$186$		0			0
$187$	0.114721	−	0.0307393i	0.00838920	−	0.00224788i
$188$		0			0
$189$	0.625355	−	2.09516i	0.0454879	−	0.152401i
$190$		0			0
$191$	−13.3381	−	7.70073i	−0.965108	−	0.557206i	−0.0673669	−	0.997728i	$-0.521460\pi$
$191$	−13.3381	−	7.70073i	−0.965108	−	0.557206i	−0.897741	+	0.440523i	$0.854793\pi$
$192$		0			0
$193$	0.775325	+	1.34290i	0.0558091	+	0.0966642i	0.892580	−	0.450889i	$-0.148893\pi$
$193$	0.775325	+	1.34290i	0.0558091	+	0.0966642i	−0.836771	+	0.547553i	$0.815560\pi$
$194$		0			0
$195$	−0.692250	+	0.692250i	−0.0495730	+	0.0495730i
$196$		0			0
$197$	−1.05178	−	1.05178i	−0.0749363	−	0.0749363i	0.668645	−	0.743582i	$-0.266874\pi$
$197$	−1.05178	−	1.05178i	−0.0749363	−	0.0749363i	−0.743582	+	0.668645i	$0.766874\pi$
$198$		0			0
$199$	−10.9631	+	6.32954i	−0.777152	+	0.448689i	−0.835420	−	0.549612i	$-0.814776\pi$
$199$	−10.9631	+	6.32954i	−0.777152	+	0.448689i	0.0582680	+	0.998301i	$0.481442\pi$
$200$		0			0
$201$	12.8731	−	22.2969i	0.907998	−	1.57270i
$202$		0			0
$203$	−17.2707	−	5.15487i	−1.21216	−	0.361801i
$204$		0			0
$205$	−1.11080	−	4.14556i	−0.0775815	−	0.289538i
$206$		0			0
$207$	16.5302	−	9.54369i	1.14893	−	0.663332i
$208$		0			0
$209$		−	17.2113i		−	1.19053i
$210$		0			0
$211$	0.830513	+	0.830513i	0.0571749	+	0.0571749i	0.735116	−	0.677941i	$-0.237128\pi$
$211$	0.830513	+	0.830513i	0.0571749	+	0.0571749i	−0.677941	+	0.735116i	$0.737128\pi$
$212$		0			0
$213$	30.1402	+	8.07603i	2.06517	+	0.553360i
$214$		0			0
$215$	5.29706	+	3.05826i	0.361257	+	0.208572i
$216$		0			0
$217$	−5.13096	+	8.33404i	−0.348313	+	0.565752i
$218$		0			0
$219$	−3.31780	−	12.3822i	−0.224196	−	0.836712i
$220$		0			0
$221$	−0.0259360	−	0.00694952i	−0.00174464	−	0.000467476i
$222$		0			0
$223$	4.19686			0.281043			0.140521	−	0.990078i	$-0.455122\pi$
$223$	4.19686			0.281043			0.140521	+	0.990078i	$0.455122\pi$
$224$		0			0
$225$	11.2760			0.751731
$226$		0			0
$227$	−12.4236	−	3.32889i	−0.824583	−	0.220946i	−0.178234	−	0.983988i	$-0.557038\pi$
$227$	−12.4236	−	3.32889i	−0.824583	−	0.220946i	−0.646349	+	0.763042i	$0.723705\pi$
$228$		0			0
$229$	−5.23675	−	19.5438i	−0.346054	−	1.29149i	−0.891376	−	0.453265i	$-0.850259\pi$
$229$	−5.23675	−	19.5438i	−0.346054	−	1.29149i	0.545322	−	0.838227i	$-0.316408\pi$
$230$		0			0
$231$	0.374094	−	13.2349i	0.0246136	−	0.870792i
$232$		0			0
$233$	−19.8589	−	11.4655i	−1.30100	−	0.751132i	−0.320423	−	0.947275i	$-0.603825\pi$
$233$	−19.8589	−	11.4655i	−1.30100	−	0.751132i	−0.980575	+	0.196143i	$0.937158\pi$
$234$		0			0
$235$	9.20038	+	2.46523i	0.600167	+	0.160814i
$236$		0			0
$237$	−9.69862	−	9.69862i	−0.629993	−	0.629993i
$238$		0			0
$239$			5.12967i			0.331811i	0.986142	+	0.165905i	$0.0530546\pi$
$239$			5.12967i			0.331811i	−0.986142	+	0.165905i	$0.946945\pi$
$240$		0			0
$241$	−14.6795	+	8.47521i	−0.945589	+	0.545936i	−0.891708	−	0.452611i	$-0.850492\pi$
$241$	−14.6795	+	8.47521i	−0.945589	+	0.545936i	−0.0538810	+	0.998547i	$0.517159\pi$
$242$		0			0
$243$	−5.46368	−	20.3907i	−0.350495	−	1.30807i
$244$		0			0
$245$	−5.75288	−	1.89570i	−0.367538	−	0.121112i
$246$		0			0
$247$	−1.94556	+	3.36981i	−0.123793	+	0.214416i
$248$		0			0
$249$	13.1864	−	7.61317i	0.835654	−	0.482465i
$250$		0			0
$251$	−1.63771	−	1.63771i	−0.103371	−	0.103371i	0.653530	−	0.756901i	$-0.273288\pi$
$251$	−1.63771	−	1.63771i	−0.103371	−	0.103371i	−0.756901	+	0.653530i	$0.773288\pi$
$252$		0			0
$253$	−10.7108	+	10.7108i	−0.673381	+	0.673381i
$254$		0			0
$255$	−0.0580400	−	0.100528i	−0.00363460	−	0.00629532i
$256$		0			0
$257$	−7.00954	−	4.04696i	−0.437243	−	0.252443i	0.265184	−	0.964198i	$-0.414567\pi$
$257$	−7.00954	−	4.04696i	−0.437243	−	0.252443i	−0.702428	+	0.711755i	$0.747901\pi$
$258$		0			0
$259$	−6.15208	−	6.50999i	−0.382272	−	0.404511i
$260$		0			0
$261$	−17.4531	+	4.67656i	−1.08032	+	0.289472i
$262$		0			0
$263$	−7.41829	−	12.8489i	−0.457431	−	0.792295i	0.541393	−	0.840770i	$-0.317897\pi$
$263$	−7.41829	−	12.8489i	−0.457431	−	0.792295i	−0.998824	+	0.0484751i	$0.984564\pi$
$264$		0			0
$265$	3.24790			0.199517
$266$		0			0
$267$	4.31102	−	4.31102i	0.263830	−	0.263830i
$268$		0			0
$269$	0.0627208	−	0.234077i	0.00382415	−	0.0142719i	−0.963987	−	0.265948i	$-0.914315\pi$
$269$	0.0627208	−	0.234077i	0.00382415	−	0.0142719i	0.967812	+	0.251676i	$0.0809817\pi$
$270$		0			0
$271$	11.2144	−	19.4240i	0.681229	−	1.17992i	−0.293377	−	0.955997i	$-0.594779\pi$
$271$	11.2144	−	19.4240i	0.681229	−	1.17992i	0.974606	−	0.223926i	$-0.0718875\pi$
$272$		0			0
$273$	−1.56931	+	2.54898i	−0.0949792	+	0.154271i
$274$		0			0
$275$	−8.64346	+	2.31601i	−0.521221	+	0.139661i
$276$		0			0
$277$	−5.03722	+	18.7992i	−0.302657	+	1.12953i	0.632286	+	0.774735i	$0.282117\pi$
$277$	−5.03722	+	18.7992i	−0.302657	+	1.12953i	−0.934943	+	0.354797i	$0.884550\pi$
$278$		0			0
$279$			9.81146i			0.587397i
$280$		0			0
$281$			12.3856i			0.738865i	0.929258	+	0.369432i	$0.120448\pi$
$281$			12.3856i			0.738865i	−0.929258	+	0.369432i	$0.879552\pi$
$282$		0			0
$283$	0.977993	−	3.64992i	0.0581357	−	0.216965i	−0.930747	−	0.365664i	$-0.880842\pi$
$283$	0.977993	−	3.64992i	0.0581357	−	0.216965i	0.988883	+	0.148699i	$0.0475085\pi$
$284$		0			0
$285$	−16.2486	+	4.35380i	−0.962485	+	0.257897i
$286$		0			0
$287$	−6.23753	−	11.5453i	−0.368190	−	0.681495i
$288$		0			0
$289$	−8.49841	+	14.7197i	−0.499906	+	0.865863i
$290$		0			0
$291$	−5.57687	+	20.8132i	−0.326922	+	1.22009i
$292$		0			0
$293$	−2.83797	+	2.83797i	−0.165796	+	0.165796i	−0.785129	−	0.619333i	$-0.787403\pi$
$293$	−2.83797	+	2.83797i	−0.165796	+	0.165796i	0.619333	+	0.785129i	$0.287403\pi$
$294$		0			0
$295$	−7.61041			−0.443095
$296$		0			0
$297$	0.869758	+	1.50647i	0.0504685	+	0.0874140i
$298$		0			0
$299$	3.30782	−	0.886326i	0.191296	−	0.0512576i
$300$		0			0
$301$	17.9205	+	5.34883i	1.03292	+	0.308302i
$302$		0			0
$303$	−19.7642	−	11.4109i	−1.13542	−	0.655538i
$304$		0			0
$305$	−2.78573	−	4.82502i	−0.159510	−	0.276280i
$306$		0			0
$307$	17.5282	−	17.5282i	1.00038	−	1.00038i	0.000384595	−	1.00000i	$-0.499878\pi$
$307$	17.5282	−	17.5282i	1.00038	−	1.00038i	1.00000		0.000384595i	$-0.000122420\pi$
$308$		0			0
$309$	2.30951	+	2.30951i	0.131384	+	0.131384i
$310$		0			0
$311$	19.4160	−	11.2098i	1.10098	−	0.635651i	0.164502	−	0.986377i	$-0.447398\pi$
$311$	19.4160	−	11.2098i	1.10098	−	0.635651i	0.936478	+	0.350725i	$0.114065\pi$
$312$		0			0
$313$	−3.86930	+	6.70183i	−0.218706	+	0.378810i	−0.954413	−	0.298491i	$-0.903517\pi$
$313$	−3.86930	+	6.70183i	−0.218706	+	0.378810i	0.735707	+	0.677300i	$0.236850\pi$
$314$		0			0
$315$	−5.90754	+	1.40530i	−0.332852	+	0.0791794i
$316$		0			0
$317$	0.838356	+	3.12879i	0.0470868	+	0.175730i	0.985465	−	0.169881i	$-0.0543383\pi$
$317$	0.838356	+	3.12879i	0.0470868	+	0.175730i	−0.938378	+	0.345611i	$0.887672\pi$
$318$		0			0
$319$	12.4180	−	7.16952i	0.695273	−	0.401416i
$320$		0			0
$321$		−	33.2654i		−	1.85669i
$322$		0			0
$323$	−0.326241	−	0.326241i	−0.0181525	−	0.0181525i
$324$		0			0
$325$	1.95411	+	0.523602i	0.108395	+	0.0290442i
$326$		0			0
$327$	5.73176	+	3.30923i	0.316967	+	0.183001i
$328$		0			0
$329$	29.1116	+	0.822861i	1.60497	+	0.0453658i
$330$		0			0
$331$	1.07762	+	4.02175i	0.0592316	+	0.221055i	0.989197	−	0.146591i	$-0.0468303\pi$
$331$	1.07762	+	4.02175i	0.0592316	+	0.221055i	−0.929966	+	0.367647i	$0.880164\pi$
$332$		0			0
$333$	−8.67354	−	2.32407i	−0.475307	−	0.127358i
$334$		0			0
$335$	9.37062			0.511972
$336$		0			0
$337$	−6.10926			−0.332793			−0.166396	−	0.986059i	$-0.553213\pi$
$337$	−6.10926			−0.332793			−0.166396	+	0.986059i	$0.553213\pi$
$338$		0			0
$339$	15.4855	+	4.14932i	0.841055	+	0.225360i
$340$		0			0
$341$	−2.01521	−	7.52086i	−0.109130	−	0.407278i
$342$		0			0
$343$	−18.4537	−	1.56817i	−0.996409	−	0.0846732i
$344$		0			0
$345$	12.8211	+	7.40229i	0.690267	+	0.398526i
$346$		0			0
$347$	30.0141	+	8.04225i	1.61124	+	0.431730i	0.948412	−	0.317041i	$-0.102689\pi$
$347$	30.0141	+	8.04225i	1.61124	+	0.431730i	0.662828	+	0.748772i	$0.269356\pi$
$348$		0			0
$349$	5.02028	+	5.02028i	0.268730	+	0.268730i	0.828588	−	0.559859i	$-0.189145\pi$
$349$	5.02028	+	5.02028i	0.268730	+	0.268730i	−0.559859	+	0.828588i	$0.689145\pi$
$350$		0			0
$351$		−	0.393269i		−	0.0209911i
$352$		0			0
$353$	19.5681	−	11.2977i	1.04151	−	0.601314i	0.121247	−	0.992622i	$-0.461311\pi$
$353$	19.5681	−	11.2977i	1.04151	−	0.601314i	0.920260	+	0.391308i	$0.127977\pi$
$354$		0			0
$355$	2.93936	+	10.9699i	0.156005	+	0.582219i
$356$		0			0
$357$	−0.243777	−	0.257959i	−0.0129021	−	0.0136527i
$358$		0			0
$359$	−5.80528	+	10.0550i	−0.306391	+	0.530684i	−0.977570	−	0.210611i	$-0.932455\pi$
$359$	−5.80528	+	10.0550i	−0.306391	+	0.530684i	0.671179	+	0.741295i	$0.265788\pi$
$360$		0			0
$361$	−41.4483	+	23.9302i	−2.18149	+	1.25948i
$362$		0			0
$363$	−11.0441	−	11.0441i	−0.579665	−	0.579665i
$364$		0			0
$365$	3.29909	−	3.29909i	0.172682	−	0.172682i
$366$		0			0
$367$	17.1290	+	29.6683i	0.894126	+	1.54867i	0.834883	+	0.550428i	$0.185535\pi$
$367$	17.1290	+	29.6683i	0.894126	+	1.54867i	0.0592429	+	0.998244i	$0.481131\pi$
$368$		0			0
$369$	−11.3930	−	6.57772i	−0.593093	−	0.342423i
$370$		0			0
$371$	9.66110	−	2.29820i	0.501579	−	0.119317i
$372$		0			0
$373$	−24.2089	+	6.48675i	−1.25349	+	0.335871i	−0.823683	−	0.567050i	$-0.808085\pi$
$373$	−24.2089	+	6.48675i	−1.25349	+	0.335871i	−0.429805	+	0.902922i	$0.641418\pi$
$374$		0			0
$375$	9.51608	+	16.4823i	0.491408	+	0.851144i
$376$		0			0
$377$	−3.24176			−0.166959
$378$		0			0
$379$	−19.0292	+	19.0292i	−0.977466	+	0.977466i	−0.999752	−	0.0222852i	$-0.992906\pi$
$379$	−19.0292	+	19.0292i	−0.977466	+	0.977466i	0.0222852	+	0.999752i	$0.492906\pi$
$380$		0			0
$381$	−5.30705	+	19.8062i	−0.271888	+	1.01470i
$382$		0			0
$383$	−11.3643	+	19.6836i	−0.580690	+	1.00578i	0.414708	+	0.909954i	$0.363884\pi$
$383$	−11.3643	+	19.6836i	−0.580690	+	1.00578i	−0.995398	+	0.0958295i	$0.969450\pi$
$384$		0			0
$385$	4.23972	−	2.29058i	0.216076	−	0.116739i
$386$		0			0
$387$	18.1099	−	4.85252i	0.920576	−	0.246667i
$388$		0			0
$389$	6.98465	−	26.0671i	0.354136	−	1.32165i	−0.527433	−	0.849597i	$-0.676845\pi$
$389$	6.98465	−	26.0671i	0.354136	−	1.32165i	0.881569	−	0.472056i	$-0.156488\pi$
$390$		0			0
$391$			0.406048i			0.0205347i
$392$		0			0
$393$		−	12.8052i		−	0.645938i
$394$		0			0
$395$	1.29204	−	4.82197i	0.0650097	−	0.242620i
$396$		0			0
$397$	24.4484	−	6.55093i	1.22703	−	0.328782i	0.413608	−	0.910455i	$-0.364269\pi$
$397$	24.4484	−	6.55093i	1.22703	−	0.328782i	0.813422	+	0.581673i	$0.197602\pi$
$398$		0			0
$399$	−45.2519	+	24.4482i	−2.26543	+	1.22394i
$400$		0			0
$401$	1.75827	−	3.04541i	0.0878037	−	0.152080i	−0.818779	−	0.574109i	$-0.805349\pi$
$401$	1.75827	−	3.04541i	0.0878037	−	0.152080i	0.906582	+	0.422029i	$0.138682\pi$
$402$		0			0
$403$	−0.455597	+	1.70031i	−0.0226949	+	0.0846986i
$404$		0			0
$405$	6.07093	−	6.07093i	0.301667	−	0.301667i
$406$		0			0
$407$	7.12595			0.353220
$408$		0			0
$409$	9.33621	+	16.1708i	0.461646	+	0.799594i	0.999043	−	0.0437352i	$-0.0139258\pi$
$409$	9.33621	+	16.1708i	0.461646	+	0.799594i	−0.537397	+	0.843329i	$0.680592\pi$
$410$		0			0
$411$	24.7133	−	6.62191i	1.21902	−	0.326635i
$412$		0			0
$413$	−22.6377	+	5.38510i	−1.11393	+	0.264983i
$414$		0			0
$415$	4.79934	+	2.77090i	0.235590	+	0.136018i
$416$		0			0
$417$	22.1985	+	38.4490i	1.08707	+	1.88285i
$418$		0			0
$419$	−2.28986	+	2.28986i	−0.111867	+	0.111867i	−0.760825	−	0.648958i	$-0.775205\pi$
$419$	−2.28986	+	2.28986i	−0.111867	+	0.111867i	0.648958	+	0.760825i	$0.275205\pi$
$420$		0			0
$421$	0.821840	+	0.821840i	0.0400540	+	0.0400540i	0.726850	−	0.686796i	$-0.240983\pi$
$421$	0.821840	+	0.821840i	0.0400540	+	0.0400540i	−0.686796	+	0.726850i	$0.740983\pi$
$422$		0			0
$423$	25.2848	−	14.5982i	1.22939	−	0.709788i
$424$		0			0
$425$	−0.119937	+	0.207738i	−0.00581782	+	0.0100768i
$426$		0			0
$427$	−11.7005	−	12.3812i	−0.566228	−	0.599168i
$428$		0			0
$429$	−0.616355	−	2.30027i	−0.0297579	−	0.111058i
$430$		0			0
$431$	−17.6989	+	10.2185i	−0.852528	+	0.492207i	−0.861503	−	0.507753i	$-0.830476\pi$
$431$	−17.6989	+	10.2185i	−0.852528	+	0.492207i	0.00897512	+	0.999960i	$0.497143\pi$
$432$		0			0
$433$			34.7460i			1.66979i	0.550413	+	0.834893i	$0.314470\pi$
$433$			34.7460i			1.66979i	−0.550413	+	0.834893i	$0.685530\pi$
$434$		0			0
$435$	−9.90979	−	9.90979i	−0.475138	−	0.475138i
$436$		0			0
$437$	56.8376	+	15.2296i	2.71891	+	0.728531i
$438$		0			0
$439$	28.2441	+	16.3067i	1.34802	+	0.778278i	0.987969	−	0.154655i	$-0.0494266\pi$
$439$	28.2441	+	16.3067i	1.34802	+	0.778278i	0.360049	+	0.932933i	$0.382760\pi$
$440$		0			0
$441$	−16.5780	+	8.36030i	−0.789429	+	0.398110i
$442$		0			0
$443$	−3.57386	−	13.3378i	−0.169799	−	0.633699i	−0.997379	−	0.0723511i	$-0.976950\pi$
$443$	−3.57386	−	13.3378i	−0.169799	−	0.633699i	0.827580	−	0.561347i	$-0.189717\pi$
$444$		0			0
$445$	2.14335	+	0.574310i	0.101605	+	0.0272249i
$446$		0			0
$447$	9.60138			0.454130
$448$		0			0
$449$	−17.6685			−0.833830			−0.416915	−	0.908946i	$-0.636889\pi$
$449$	−17.6685			−0.833830			−0.416915	+	0.908946i	$0.636889\pi$
$450$		0			0
$451$	10.0842	+	2.70204i	0.474844	+	0.127234i
$452$		0			0
$453$	−4.85955	−	18.1361i	−0.228321	−	0.852107i
$454$		0			0
$455$	−1.08902	−	0.0307821i	−0.0510542	−	0.00144309i
$456$		0			0
$457$	−3.51049	−	2.02678i	−0.164214	−	0.0948090i	0.415641	−	0.909529i	$-0.363557\pi$
$457$	−3.51049	−	2.02678i	−0.164214	−	0.0948090i	−0.579855	+	0.814720i	$0.696891\pi$
$458$		0			0
$459$	0.0450415	+	0.0120688i	0.00210236	+	0.000563325i
$460$		0			0
$461$	2.39386	+	2.39386i	0.111493	+	0.111493i	0.760653	−	0.649159i	$-0.224879\pi$
$461$	2.39386	+	2.39386i	0.111493	+	0.111493i	−0.649159	+	0.760653i	$0.724879\pi$
$462$		0			0
$463$			30.7630i			1.42968i	0.699289	+	0.714839i	$0.253500\pi$
$463$			30.7630i			1.42968i	−0.699289	+	0.714839i	$0.746500\pi$
$464$		0			0
$465$	−6.59043	+	3.80499i	−0.305624	+	0.176452i
$466$		0			0
$467$	1.86256	+	6.95118i	0.0861891	+	0.321662i	0.995537	−	0.0943750i	$-0.0300853\pi$
$467$	1.86256	+	6.95118i	0.0861891	+	0.321662i	−0.909348	+	0.416037i	$0.863419\pi$
$468$		0			0
$469$	27.8736	−	6.63062i	1.28708	−	0.306174i
$470$		0			0
$471$	19.2090	−	33.2709i	0.885103	−	1.53304i
$472$		0			0
$473$	−12.8852	+	7.43929i	−0.592463	+	0.342059i
$474$		0			0
$475$	24.5802	+	24.5802i	1.12782	+	1.12782i
$476$		0			0
$477$	7.03969	−	7.03969i	0.322325	−	0.322325i
$478$		0			0
$479$	1.42754	+	2.47257i	0.0652259	+	0.112975i	0.896794	−	0.442448i	$-0.145890\pi$
$479$	1.42754	+	2.47257i	0.0652259	+	0.112975i	−0.831568	+	0.555423i	$0.812557\pi$
$480$		0			0
$481$	−1.39519	−	0.805515i	−0.0636153	−	0.0367283i
$482$		0			0
$483$	43.3752	+	12.9464i	1.97364	+	0.589084i
$484$		0			0
$485$	−7.57520	+	2.02977i	−0.343972	+	0.0921670i
$486$		0			0
$487$	16.6053	+	28.7612i	0.752457	+	1.30329i	0.946629	+	0.322326i	$0.104465\pi$
$487$	16.6053	+	28.7612i	0.752457	+	1.30329i	−0.194172	+	0.980968i	$0.562202\pi$
$488$		0			0
$489$	−7.35986			−0.332824
$490$		0			0
$491$	−23.0686	+	23.0686i	−1.04107	+	1.04107i	−0.0419533	+	0.999120i	$0.513358\pi$
$491$	−23.0686	+	23.0686i	−1.04107	+	1.04107i	−0.999120	+	0.0419533i	$0.986642\pi$
$492$		0			0
$493$	0.0994848	−	0.371282i	0.00448057	−	0.0167217i
$494$		0			0
$495$	2.41551	−	4.18379i	0.108569	−	0.188047i
$496$		0			0
$497$	16.5056	+	30.5507i	0.740376	+	1.37039i
$498$		0			0
$499$	−20.0630	+	5.37586i	−0.898143	+	0.240657i	−0.678219	−	0.734860i	$-0.737248\pi$
$499$	−20.0630	+	5.37586i	−0.898143	+	0.240657i	−0.219924	+	0.975517i	$0.570581\pi$
$500$		0			0
$501$	−3.46406	+	12.9280i	−0.154763	+	0.577582i
$502$		0			0
$503$		−	0.960903i		−	0.0428445i	−0.999771	−	0.0214223i	$-0.993181\pi$
$503$		−	0.960903i		−	0.0428445i	0.999771	−	0.0214223i	$-0.00681944\pi$
$504$		0			0
$505$		−	8.30624i		−	0.369623i
$506$		0			0
$507$	7.86003	−	29.3340i	0.349076	−	1.30277i
$508$		0			0
$509$	−2.64231	+	0.708005i	−0.117118	+	0.0313818i	−0.316902	−	0.948458i	$-0.602643\pi$
$509$	−2.64231	+	0.708005i	−0.117118	+	0.0313818i	0.199784	+	0.979840i	$0.435976\pi$
$510$		0			0
$511$	7.47896	−	12.1478i	0.330850	−	0.537388i
$512$		0			0
$513$	3.37874	−	5.85215i	0.149175	−	0.258379i
$514$		0			0
$515$	−0.307672	+	1.14825i	−0.0135576	+	0.0505978i
$516$		0			0
$517$	−16.3834	+	16.3834i	−0.720541	+	0.720541i
$518$		0			0
$519$	−4.17758			−0.183375
$520$		0			0
$521$	19.6749	+	34.0779i	0.861972	+	1.49298i	0.870023	+	0.493012i	$0.164104\pi$
$521$	19.6749	+	34.0779i	0.861972	+	1.49298i	−0.00805046	+	0.999968i	$0.502563\pi$
$522$		0			0
$523$	−3.79685	+	1.01736i	−0.166025	+	0.0444861i	−0.340874	−	0.940109i	$-0.610723\pi$
$523$	−3.79685	+	1.01736i	−0.166025	+	0.0444861i	0.174849	+	0.984595i	$0.444056\pi$
$524$		0			0
$525$	18.3671	+	19.4356i	0.801605	+	0.848239i
$526$		0			0
$527$	−0.180757	−	0.104360i	−0.00787390	−	0.00454600i
$528$		0			0
$529$	−14.3932	−	24.9297i	−0.625791	−	1.08390i
$530$		0			0
$531$	−16.4953	+	16.4953i	−0.715834	+	0.715834i
$532$		0			0
$533$	−1.66894	−	1.66894i	−0.0722900	−	0.0722900i
$534$		0			0
$535$	10.4853	−	6.05367i	0.453317	−	0.261723i
$536$		0			0
$537$	−9.10627	+	15.7725i	−0.392964	+	0.680634i
$538$		0			0
$539$	10.9905	−	9.81351i	0.473396	−	0.422698i
$540$		0			0
$541$	9.89977	+	36.9465i	0.425624	+	1.58845i	0.762556	+	0.646923i	$0.223944\pi$
$541$	9.89977	+	36.9465i	0.425624	+	1.58845i	−0.336931	+	0.941529i	$0.609389\pi$
$542$		0			0
$543$	0.0130450	−	0.00753154i	0.000559815	−	0.000323209i
$544$		0			0
$545$			2.40887i			0.103185i
$546$		0			0
$547$	17.4654	+	17.4654i	0.746767	+	0.746767i	0.973871	−	0.227104i	$-0.0729256\pi$
$547$	17.4654	+	17.4654i	0.746767	+	0.746767i	−0.227104	+	0.973871i	$0.572926\pi$
$548$		0			0
$549$	−16.4960	−	4.42009i	−0.704033	−	0.188645i
$550$		0			0
$551$	−48.2399	−	27.8513i	−2.05509	−	1.18651i
$552$		0			0
$553$	0.431266	−	15.2575i	0.0183393	−	0.648816i
$554$		0			0
$555$	−1.80260	−	6.72738i	−0.0765159	−	0.285561i
$556$		0			0
$557$	−22.3434	−	5.98690i	−0.946721	−	0.253673i	−0.247751	−	0.968824i	$-0.579691\pi$
$557$	−22.3434	−	5.98690i	−0.946721	−	0.253673i	−0.698970	+	0.715151i	$0.746358\pi$
$558$		0			0
$559$	3.36374			0.142271
$560$		0			0
$561$	0.282367			0.0119215
$562$		0			0
$563$	−16.6774	−	4.46869i	−0.702868	−	0.188333i	−0.110353	−	0.993892i	$-0.535198\pi$
$563$	−16.6774	−	4.46869i	−0.702868	−	0.188333i	−0.592515	+	0.805560i	$0.701865\pi$
$564$		0			0
$565$	1.51019	+	5.63612i	0.0635343	+	0.237113i
$566$		0			0
$567$	13.7626	−	22.3542i	0.577977	−	0.938787i
$568$		0			0
$569$	18.2857	+	10.5573i	0.766577	+	0.442583i	0.831652	−	0.555297i	$-0.187395\pi$
$569$	18.2857	+	10.5573i	0.766577	+	0.442583i	−0.0650753	+	0.997880i	$0.520729\pi$
$570$		0			0
$571$	−12.7451	−	3.41504i	−0.533366	−	0.142915i	−0.0179237	−	0.999839i	$-0.505706\pi$
$571$	−12.7451	−	3.41504i	−0.533366	−	0.142915i	−0.515442	+	0.856924i	$0.672372\pi$
$572$		0			0
$573$	−25.8919	−	25.8919i	−1.08165	−	1.08165i
$574$		0			0
$575$		−	30.5931i		−	1.27582i
$576$		0			0
$577$	21.7205	−	12.5403i	0.904235	−	0.522061i	0.0256635	−	0.999671i	$-0.491830\pi$
$577$	21.7205	−	12.5403i	0.904235	−	0.522061i	0.878572	+	0.477610i	$0.158497\pi$
$578$		0			0
$579$	0.954171	+	3.56101i	0.0396540	+	0.147991i
$580$		0			0
$581$	16.2367	+	4.84625i	0.673611	+	0.201056i
$582$		0			0
$583$	−3.95029	+	6.84210i	−0.163604	+	0.283371i
$584$		0			0
$585$	−0.945868	+	0.546097i	−0.0391068	+	0.0225783i
$586$		0			0
$587$	0.705313	+	0.705313i	0.0291114	+	0.0291114i	0.721513	−	0.692401i	$-0.243447\pi$
$587$	0.705313	+	0.705313i	0.0291114	+	0.0291114i	−0.692401	+	0.721513i	$0.743447\pi$
$588$		0			0
$589$	−21.3877	+	21.3877i	−0.881266	+	0.881266i
$590$		0			0
$591$	−1.76818	−	3.06258i	−0.0727333	−	0.125978i
$592$		0			0
$593$	−37.2581	−	21.5110i	−1.53001	−	0.883350i	−0.999361	−	0.0357564i	$-0.988616\pi$
$593$	−37.2581	−	21.5110i	−1.53001	−	0.883350i	−0.530646	−	0.847593i	$-0.678051\pi$
$594$		0			0
$595$	0.0369460	−	0.123782i	0.00151464	−	0.00507458i
$596$		0			0
$597$	−29.0711	+	7.78959i	−1.18980	+	0.318807i
$598$		0			0
$599$	11.7482	+	20.3485i	0.480019	+	0.831418i	0.999737	−	0.0229200i	$-0.00729631\pi$
$599$	11.7482	+	20.3485i	0.480019	+	0.831418i	−0.519718	+	0.854338i	$0.673963\pi$
$600$		0			0
$601$	42.4771			1.73268			0.866339	−	0.499456i	$-0.166467\pi$
$601$	42.4771			1.73268			0.866339	+	0.499456i	$0.166467\pi$
$602$		0			0
$603$	20.3105	−	20.3105i	0.827107	−	0.827107i
$604$		0			0
$605$	1.47129	−	5.49092i	0.0598163	−	0.223238i
$606$		0			0
$607$	10.5533	−	18.2788i	0.428345	−	0.741915i	−0.568382	−	0.822765i	$-0.692430\pi$
$607$	10.5533	−	18.2788i	0.428345	−	0.741915i	0.996726	+	0.0808504i	$0.0257636\pi$
$608$		0			0
$609$	−36.4895	−	22.4653i	−1.47863	−	0.910338i
$610$		0			0
$611$	5.05969	−	1.35574i	0.204693	−	0.0548473i
$612$		0			0
$613$	2.89016	−	10.7862i	0.116733	−	0.435652i	−0.882678	−	0.469978i	$-0.844262\pi$
$613$	2.89016	−	10.7862i	0.116733	−	0.435652i	0.999411	+	0.0343262i	$0.0109285\pi$
$614$		0			0
$615$		−	10.2036i		−	0.411451i
$616$		0			0
$617$		−	18.9275i		−	0.761992i	−0.924577	−	0.380996i	$-0.875581\pi$
$617$		−	18.9275i		−	0.761992i	0.924577	−	0.380996i	$-0.124419\pi$
$618$		0			0
$619$	−2.19722	+	8.20013i	−0.0883137	+	0.329591i	−0.995921	−	0.0902289i	$-0.971240\pi$
$619$	−2.19722	+	8.20013i	−0.0883137	+	0.329591i	0.907607	+	0.419820i	$0.137907\pi$
$620$		0			0
$621$	−5.74449	+	1.53923i	−0.230518	+	0.0617672i
$622$		0			0
$623$	6.78194	+	0.191697i	0.271713	+	0.00768017i
$624$		0			0
$625$	7.16461	−	12.4095i	0.286584	−	0.496379i
$626$		0			0
$627$	10.5907	−	39.5251i	0.422953	−	1.57848i
$628$		0			0
$629$	0.135073	−	0.135073i	0.00538571	−	0.00538571i
$630$		0			0
$631$	−8.88067			−0.353534			−0.176767	−	0.984253i	$-0.556564\pi$
$631$	−8.88067			−0.353534			−0.176767	+	0.984253i	$0.556564\pi$
$632$		0			0
$633$	1.39620	+	2.41829i	0.0554940	+	0.0961184i
$634$		0			0
$635$	−7.20868	+	1.93156i	−0.286068	+	0.0766516i
$636$		0			0
$637$	−3.26116	+	0.679025i	−0.129212	+	0.0269040i
$638$		0			0
$639$	30.1477	+	17.4058i	1.19263	+	0.688563i
$640$		0			0
$641$	1.02617	+	1.77738i	0.0405314	+	0.0702024i	0.885579	−	0.464488i	$-0.153762\pi$
$641$	1.02617	+	1.77738i	0.0405314	+	0.0702024i	−0.845048	+	0.534690i	$0.820428\pi$
$642$		0			0
$643$	−20.1070	+	20.1070i	−0.792942	+	0.792942i	−0.981971	−	0.189029i	$-0.939466\pi$
$643$	−20.1070	+	20.1070i	−0.792942	+	0.792942i	0.189029	+	0.981971i	$0.439466\pi$
$644$		0			0
$645$	10.2827	+	10.2827i	0.404880	+	0.404880i
$646$		0			0
$647$	−10.6872	+	6.17028i	−0.420159	+	0.242579i	−0.695145	−	0.718869i	$-0.744660\pi$
$647$	−10.6872	+	6.17028i	−0.420159	+	0.242579i	0.274987	+	0.961448i	$0.411327\pi$
$648$		0			0
$649$	9.25625	−	16.0323i	0.363339	−	0.629322i
$650$		0			0
$651$	−16.9113	+	15.9816i	−0.662807	+	0.626368i
$652$		0			0
$653$	−11.0441	−	41.2170i	−0.432187	−	1.61294i	−0.747709	−	0.664026i	$-0.768846\pi$
$653$	−11.0441	−	41.2170i	−0.432187	−	1.61294i	0.315522	−	0.948918i	$-0.397820\pi$
$654$		0			0
$655$	4.03621	−	2.33030i	0.157708	−	0.0910525i
$656$		0			0
$657$		−	14.3013i		−	0.557948i
$658$		0			0
$659$	19.4114	+	19.4114i	0.756162	+	0.756162i	0.975622	−	0.219460i	$-0.0704294\pi$
$659$	19.4114	+	19.4114i	0.756162	+	0.756162i	−0.219460	+	0.975622i	$0.570429\pi$
$660$		0			0
$661$	−31.9327	−	8.55633i	−1.24204	−	0.332803i	−0.422782	−	0.906232i	$-0.638946\pi$
$661$	−31.9327	−	8.55633i	−1.24204	−	0.332803i	−0.819255	+	0.573429i	$0.805613\pi$
$662$		0			0
$663$	−0.0552848	−	0.0319187i	−0.00214708	−	0.00123962i
$664$		0			0
$665$	−15.9410	−	9.81431i	−0.618167	−	0.380583i
$666$		0			0
$667$	12.6881	+	47.3525i	0.491284	+	1.83350i
$668$		0			0
$669$	9.63796	+	2.58248i	0.372625	+	0.0998446i
$670$		0			0
$671$	13.5527			0.523196
$672$		0			0
$673$	−2.56169			−0.0987460			−0.0493730	−	0.998780i	$-0.515722\pi$
$673$	−2.56169			−0.0987460			−0.0493730	+	0.998780i	$0.515722\pi$
$674$		0			0
$675$	−3.39359	−	0.909309i	−0.130619	−	0.0349993i
$676$		0			0
$677$	6.22338	+	23.2260i	0.239184	+	0.892646i	0.976218	+	0.216791i	$0.0695590\pi$
$677$	6.22338	+	23.2260i	0.239184	+	0.892646i	−0.737034	+	0.675855i	$0.763774\pi$
$678$		0			0
$679$	−21.0967	+	11.3979i	−0.809617	+	0.437410i
$680$		0			0
$681$	−26.4820	−	15.2894i	−1.01479	−	0.585890i
$682$		0			0
$683$	13.9020	+	3.72504i	0.531946	+	0.142535i	0.514787	−	0.857318i	$-0.327871\pi$
$683$	13.9020	+	3.72504i	0.531946	+	0.142535i	0.0171593	+	0.999853i	$0.494538\pi$
$684$		0			0
$685$	6.58458	+	6.58458i	0.251584	+	0.251584i
$686$		0			0
$687$		−	48.1041i		−	1.83529i
$688$		0			0
$689$	1.54686	−	0.893079i	0.0589306	−	0.0340236i
$690$		0			0
$691$	−11.3894	−	42.5057i	−0.433272	−	1.61699i	−0.745169	−	0.666876i	$-0.767631\pi$
$691$	−11.3894	−	42.5057i	−0.433272	−	1.61699i	0.311897	−	0.950116i	$-0.399036\pi$
$692$		0			0
$693$	4.22468	−	14.1542i	0.160482	−	0.537673i
$694$		0			0
$695$	−8.07940	+	13.9939i	−0.306469	+	0.530820i
$696$		0			0
$697$	0.242363	−	0.139929i	0.00918017	−	0.00530017i
$698$		0			0
$699$	−38.5501	−	38.5501i	−1.45810	−	1.45810i
$700$		0			0
$701$	−15.8844	+	15.8844i	−0.599946	+	0.599946i	−0.940298	−	0.340352i	$-0.889454\pi$
$701$	−15.8844	+	15.8844i	−0.599946	+	0.599946i	0.340352	+	0.940298i	$0.389454\pi$
$702$		0			0
$703$	−13.8410	−	23.9734i	−0.522024	−	0.904173i
$704$		0			0
$705$	19.6114	+	11.3227i	0.738609	+	0.426436i
$706$		0			0
$707$	−5.87747	−	24.7075i	−0.221045	−	0.929222i
$708$		0			0
$709$	25.3348	−	6.78844i	0.951469	−	0.254945i	0.250483	−	0.968121i	$-0.419410\pi$
$709$	25.3348	−	6.78844i	0.951469	−	0.254945i	0.700985	+	0.713176i	$0.252744\pi$
$710$		0			0
$711$	−7.65098	−	13.2519i	−0.286934	−	0.496985i
$712$		0			0
$713$	26.6197			0.996916
$714$		0			0
$715$	0.612879	−	0.612879i	0.0229204	−	0.0229204i
$716$		0			0
$717$	−3.15647	+	11.7801i	−0.117881	+	0.439936i
$718$		0			0
$719$	−7.85533	+	13.6058i	−0.292954	+	0.507412i	−0.974507	−	0.224357i	$-0.927972\pi$
$719$	−7.85533	+	13.6058i	−0.292954	+	0.507412i	0.681553	+	0.731769i	$0.261305\pi$
$720$		0			0
$721$	−0.102697	+	3.63325i	−0.00382462	+	0.135309i
$722$		0			0
$723$	−38.9260	+	10.4302i	−1.44768	+	0.387903i
$724$		0			0
$725$	−7.49554	+	27.9737i	−0.278377	+	1.03892i
$726$		0			0
$727$			24.4125i			0.905411i	0.891660	+	0.452705i	$0.149541\pi$
$727$			24.4125i			0.905411i	−0.891660	+	0.452705i	$0.850459\pi$
$728$		0			0
$729$		−	20.4227i		−	0.756395i
$730$		0			0
$731$	−0.103228	+	0.385253i	−0.00381803	+	0.0142491i
$732$		0			0
$733$	−7.87397	+	2.10982i	−0.290832	+	0.0779281i	−0.401285	−	0.915953i	$-0.631436\pi$
$733$	−7.87397	+	2.10982i	−0.290832	+	0.0779281i	0.110453	+	0.993881i	$0.464770\pi$
$734$		0			0
$735$	−12.0448	−	7.89336i	−0.444279	−	0.291151i
$736$		0			0
$737$	−11.3971	+	19.7404i	−0.419818	+	0.727147i
$738$		0			0
$739$	1.94045	−	7.24186i	0.0713807	−	0.266396i	−0.921008	−	0.389545i	$-0.872632\pi$
$739$	1.94045	−	7.24186i	0.0713807	−	0.266396i	0.992388	+	0.123148i	$0.0392991\pi$
$740$		0			0
$741$	−6.54147	+	6.54147i	−0.240307	+	0.240307i
$742$		0			0
$743$	−5.21163			−0.191196			−0.0955980	−	0.995420i	$-0.530476\pi$
$743$	−5.21163			−0.191196			−0.0955980	+	0.995420i	$0.530476\pi$
$744$		0			0
$745$	1.74727	+	3.02635i	0.0640149	+	0.110877i
$746$		0			0
$747$	16.4082	−	4.39657i	0.600346	−	0.160862i
$748$		0			0
$749$	26.9056	−	25.4264i	0.983109	−	0.929060i
$750$		0			0
$751$	3.60025	+	2.07860i	0.131375	+	0.0758493i	0.564247	−	0.825606i	$-0.309167\pi$
$751$	3.60025	+	2.07860i	0.131375	+	0.0758493i	−0.432872	+	0.901455i	$0.642500\pi$
$752$		0			0
$753$	−2.75320	−	4.76869i	−0.100332	−	0.173781i
$754$		0			0
$755$	4.83215	−	4.83215i	0.175860	−	0.175860i
$756$		0			0
$757$	−5.25365	−	5.25365i	−0.190947	−	0.190947i	0.605158	−	0.796105i	$-0.293110\pi$
$757$	−5.25365	−	5.25365i	−0.190947	−	0.190947i	−0.796105	+	0.605158i	$0.793110\pi$
$758$		0			0
$759$	−31.1877	+	18.0062i	−1.13204	+	0.653585i
$760$		0			0
$761$	−4.74872	+	8.22502i	−0.172141	+	0.298157i	−0.939168	−	0.343458i	$-0.888402\pi$
$761$	−4.74872	+	8.22502i	−0.172141	+	0.298157i	0.767027	+	0.641615i	$0.221735\pi$
$762$		0			0
$763$	1.70451	+	7.16535i	0.0617073	+	0.259403i
$764$		0			0
$765$	−0.0335178	−	0.125090i	−0.00121184	−	0.00452264i
$766$		0			0
$767$	−3.62457	+	2.09265i	−0.130876	+	0.0755611i
$768$		0			0
$769$			21.7626i			0.784779i	0.919799	+	0.392390i	$0.128352\pi$
$769$			21.7626i			0.784779i	−0.919799	+	0.392390i	$0.871648\pi$
$770$		0			0
$771$	−13.6069	−	13.6069i	−0.490042	−	0.490042i
$772$		0			0
$773$	−38.1522	−	10.2229i	−1.37224	−	0.367690i	−0.503943	−	0.863737i	$-0.668118\pi$
$773$	−38.1522	−	10.2229i	−1.37224	−	0.367690i	−0.868296	+	0.496046i	$0.834785\pi$
$774$		0			0
$775$	13.6189	+	7.86287i	0.489205	+	0.282442i
$776$		0			0
$777$	−10.1222	−	18.7356i	−0.363133	−	0.672135i
$778$		0			0
$779$	−10.4966	−	39.1738i	−0.376079	−	1.40355i
$780$		0			0
$781$	−26.6844	−	7.15007i	−0.954843	−	0.255850i
$782$		0			0
$783$	5.62978			0.201192
$784$		0			0
$785$	13.9827			0.499062
$786$		0			0
$787$	25.9373	+	6.94989i	0.924567	+	0.247737i	0.689536	−	0.724251i	$-0.257814\pi$
$787$	25.9373	+	6.94989i	0.924567	+	0.247737i	0.235030	+	0.971988i	$0.424481\pi$
$788$		0			0
$789$	−9.12949	−	34.0717i	−0.325018	−	1.21299i
$790$		0			0
$791$	8.48027	+	15.6964i	0.301524	+	0.558101i
$792$		0			0
$793$	−2.65349	−	1.53199i	−0.0942281	−	0.0544026i
$794$		0			0
$795$	7.45868	+	1.99855i	0.264532	+	0.0708812i
$796$		0			0
$797$	28.0289	+	28.0289i	0.992834	+	0.992834i	0.999975	−	0.00714087i	$-0.00227303\pi$
$797$	28.0289	+	28.0289i	0.992834	+	0.992834i	−0.00714087	+	0.999975i	$0.502273\pi$
$798$		0			0
$799$			0.621097i			0.0219728i
$800$		0			0
$801$	5.89044	−	3.40084i	0.208128	−	0.120163i
$802$		0			0
$803$	2.93740	+	10.9625i	0.103658	+	0.386859i
$804$		0			0
$805$	3.81274	+	16.0279i	0.134381	+	0.564908i
$806$		0			0
$807$	0.288072	−	0.498956i	0.0101406	−	0.0175641i
$808$		0			0
$809$	14.7231	−	8.50038i	0.517636	−	0.298857i	−0.218331	−	0.975875i	$-0.570061\pi$
$809$	14.7231	−	8.50038i	0.517636	−	0.298857i	0.735967	+	0.677017i	$0.236728\pi$
$810$		0			0
$811$	−0.379489	−	0.379489i	−0.0133256	−	0.0133256i	0.700413	−	0.713738i	$-0.252999\pi$
$811$	−0.379489	−	0.379489i	−0.0133256	−	0.0133256i	−0.713738	+	0.700413i	$0.752999\pi$
$812$		0			0
$813$	37.7059	−	37.7059i	1.32240	−	1.32240i
$814$		0			0
$815$	−1.33935	−	2.31983i	−0.0469155	−	0.0812600i
$816$		0			0
$817$	50.0550	+	28.8993i	1.75120	+	1.01106i
$818$		0			0
$819$	−2.42714	+	2.29370i	−0.0848110	+	0.0801483i
$820$		0			0
$821$	30.7660	−	8.24372i	1.07374	−	0.287708i	0.321711	−	0.946838i	$-0.395742\pi$
$821$	30.7660	−	8.24372i	1.07374	−	0.287708i	0.752029	+	0.659130i	$0.229075\pi$
$822$		0			0
$823$	−22.7033	−	39.3232i	−0.791386	−	1.37072i	−0.925109	−	0.379703i	$-0.876026\pi$
$823$	−22.7033	−	39.3232i	−0.791386	−	1.37072i	0.133722	−	0.991019i	$-0.457307\pi$
$824$		0			0
$825$	−21.2746			−0.740685
$826$		0			0
$827$	−5.61746	+	5.61746i	−0.195338	+	0.195338i	−0.797998	−	0.602660i	$-0.794108\pi$
$827$	−5.61746	+	5.61746i	−0.195338	+	0.195338i	0.602660	+	0.797998i	$0.294108\pi$
$828$		0			0
$829$	13.7815	−	51.4334i	0.478652	−	1.78636i	−0.128432	−	0.991718i	$-0.540995\pi$
$829$	13.7815	−	51.4334i	0.478652	−	1.78636i	0.607085	−	0.794637i	$-0.292339\pi$
$830$		0			0
$831$	−23.1356	+	40.0721i	−0.802565	+	1.39008i
$832$		0			0
$833$	0.0223106	−	0.394342i	0.000773016	−	0.0136631i
$834$		0			0
$835$	−4.70531	+	1.26078i	−0.162834	+	0.0436312i
$836$		0			0
$837$	0.791210	−	2.95283i	0.0273482	−	0.102065i
$838$		0			0
$839$		−	42.8593i		−	1.47967i	−0.672790	−	0.739834i	$-0.734904\pi$
$839$		−	42.8593i		−	1.47967i	0.672790	−	0.739834i	$-0.265096\pi$
$840$		0			0
$841$		−	17.4069i		−	0.600238i
$842$		0			0
$843$	−7.62133	+	28.4432i	−0.262492	+	0.979635i
$844$		0			0
$845$	10.6765	−	2.86075i	0.367281	−	0.0984127i
$846$		0			0
$847$	0.491095	−	17.3742i	0.0168742	−	0.596985i
$848$		0			0
$849$	4.49186	−	7.78012i	0.154160	−	0.267013i
$850$		0			0
$851$	−6.30548	+	23.5324i	−0.216149	+	0.806679i
$852$		0			0
$853$	−1.26515	+	1.26515i	−0.0433180	+	0.0433180i	−0.728434	−	0.685116i	$-0.759751\pi$
$853$	−1.26515	+	1.26515i	−0.0433180	+	0.0433180i	0.685116	+	0.728434i	$0.259751\pi$
$854$		0			0
$855$	−18.7670			−0.641818
$856$		0			0
$857$	−19.6774	−	34.0822i	−0.672166	−	1.16423i	−0.977289	−	0.211912i	$-0.932031\pi$
$857$	−19.6774	−	34.0822i	−0.672166	−	1.16423i	0.305123	−	0.952313i	$-0.401302\pi$
$858$		0			0
$859$	−28.9153	+	7.74782i	−0.986576	+	0.264352i	−0.715812	−	0.698293i	$-0.753943\pi$
$859$	−28.9153	+	7.74782i	−0.986576	+	0.264352i	−0.270764	+	0.962646i	$0.587276\pi$
$860$		0			0
$861$	−7.22006	−	30.3515i	−0.246059	−	1.03438i
$862$		0			0
$863$	1.42367	+	0.821957i	0.0484624	+	0.0279798i	0.524035	−	0.851696i	$-0.324426\pi$
$863$	1.42367	+	0.821957i	0.0484624	+	0.0279798i	−0.475573	+	0.879676i	$0.657759\pi$
$864$		0			0
$865$	−0.760238	−	1.31677i	−0.0258489	−	0.0447716i
$866$		0			0
$867$	−28.5739	+	28.5739i	−0.970419	+	0.970419i
$868$		0			0
$869$	8.58662	+	8.58662i	0.291281	+	0.291281i
$870$		0			0
$871$	4.46290	−	2.57666i	0.151220	−	0.0873066i
$872$		0			0
$873$	−12.0195	+	20.8184i	−0.406799	+	0.704596i
$874$		0			0
$875$	−6.05756	+	20.2950i	−0.204783	+	0.686096i
$876$		0			0
$877$	−2.19077	−	8.17605i	−0.0739769	−	0.276086i	0.919022	−	0.394205i	$-0.128980\pi$
$877$	−2.19077	−	8.17605i	−0.0739769	−	0.276086i	−0.992999	+	0.118120i	$0.962313\pi$
$878$		0			0
$879$	−8.26360	+	4.77099i	−0.278724	+	0.160922i
$880$		0			0
$881$		−	21.6012i		−	0.727763i	−0.931445	−	0.363881i	$-0.881451\pi$
$881$		−	21.6012i		−	0.727763i	0.931445	−	0.363881i	$-0.118549\pi$
$882$		0			0
$883$	13.8898	+	13.8898i	0.467428	+	0.467428i	0.901080	−	0.433652i	$-0.142775\pi$
$883$	13.8898	+	13.8898i	0.467428	+	0.467428i	−0.433652	+	0.901080i	$0.642775\pi$
$884$		0			0
$885$	−17.4770	−	4.68296i	−0.587485	−	0.157416i
$886$		0			0
$887$	−6.26306	−	3.61598i	−0.210293	−	0.121413i	0.391155	−	0.920325i	$-0.372076\pi$
$887$	−6.26306	−	3.61598i	−0.210293	−	0.121413i	−0.601448	+	0.798912i	$0.705409\pi$
$888$		0			0
$889$	−20.0760	+	10.8464i	−0.673327	+	0.363777i
$890$		0			0
$891$	5.40534	+	20.1730i	0.181086	+	0.675821i
$892$		0			0
$893$	86.9398	+	23.2954i	2.90933	+	0.779552i
$894$		0			0
$895$	−6.62866			−0.221572
$896$		0			0
$897$	8.14168			0.271843
$898$		0			0
$899$	−24.3406	−	6.52203i	−0.811803	−	0.217522i
$900$		0			0
$901$	0.0548145	+	0.204571i	0.00182614	+	0.00681524i
$902$		0			0
$903$	37.8625	+	23.3106i	1.25999	+	0.775727i
$904$		0			0
$905$	0.00474788	+	0.00274119i	0.000157825	+	9.11202e-5i
$906$		0			0
$907$	−19.9743	−	5.35210i	−0.663237	−	0.177714i	−0.0885303	−	0.996073i	$-0.528217\pi$
$907$	−19.9743	−	5.35210i	−0.663237	−	0.177714i	−0.574706	+	0.818360i	$0.694884\pi$
$908$		0			0
$909$	−18.0035	−	18.0035i	−0.597137	−	0.597137i
$910$		0			0
$911$		−	0.154520i		−	0.00511948i	−0.999997	−	0.00255974i	$-0.999185\pi$
$911$		−	0.154520i		−	0.00511948i	0.999997	−	0.00255974i	$-0.000814791\pi$
$912$		0			0
$913$	−11.6745	+	6.74028i	−0.386370	+	0.223071i
$914$		0			0
$915$	−3.42832	−	12.7947i	−0.113337	−	0.422978i
$916$		0			0
$917$	10.3571	−	9.78766i	0.342021	−	0.323217i
$918$		0			0
$919$	17.9792	−	31.1409i	0.593079	−	1.02724i	−0.400736	−	0.916194i	$-0.631246\pi$
$919$	17.9792	−	31.1409i	0.593079	−	1.02724i	0.993815	−	0.111049i	$-0.0354211\pi$
$920$		0			0
$921$	51.0385	−	29.4671i	1.68178	−	0.970974i
$922$		0			0
$923$	4.41631	+	4.41631i	0.145365	+	0.145365i
$924$		0			0
$925$	−10.1769	+	10.1769i	−0.334614	+	0.334614i
$926$		0			0
$927$	1.82191	+	3.15565i	0.0598395	+	0.103645i
$928$		0			0
$929$	13.9612	+	8.06050i	0.458052	+	0.264456i	0.711225	−	0.702965i	$-0.248141\pi$
$929$	13.9612	+	8.06050i	0.458052	+	0.264456i	−0.253173	+	0.967421i	$0.581474\pi$
$930$		0			0
$931$	−54.3623	−	17.9136i	−1.78165	−	0.587093i
$932$		0			0
$933$	51.4860	−	13.7956i	1.68558	−	0.451649i
$934$		0			0
$935$	0.0513854	+	0.0890021i	0.00168048	+	0.00291068i
$936$		0			0
$937$	−8.23172			−0.268919			−0.134459	−	0.990919i	$-0.542930\pi$
$937$	−8.23172			−0.268919			−0.134459	+	0.990919i	$0.542930\pi$
$938$		0			0
$939$	−13.0096	+	13.0096i	−0.424552	+	0.424552i
$940$		0			0
$941$	−6.14005	+	22.9150i	−0.200160	+	0.747007i	0.790710	+	0.612190i	$0.209711\pi$
$941$	−6.14005	+	22.9150i	−0.200160	+	0.747007i	−0.990870	+	0.134817i	$0.956955\pi$
$942$		0			0
$943$	−17.8462	+	30.9105i	−0.581151	+	1.00658i
$944$		0			0
$945$	1.89124	+	0.0534574i	0.0615221	+	0.00173897i
$946$		0			0
$947$	31.9395	−	8.55816i	1.03789	−	0.278103i	0.300654	−	0.953733i	$-0.402795\pi$
$947$	31.9395	−	8.55816i	1.03789	−	0.278103i	0.737240	+	0.675631i	$0.236129\pi$
$948$		0			0
$949$	0.664085	−	2.47840i	0.0215571	−	0.0804522i
$950$		0			0
$951$			7.70103i			0.249723i
$952$		0			0
$953$			21.4014i			0.693259i	0.938002	+	0.346630i	$0.112674\pi$
$953$			21.4014i			0.693259i	−0.938002	+	0.346630i	$0.887326\pi$
$954$		0			0
$955$	3.44929	−	12.8729i	0.111617	−	0.416558i
$956$		0			0
$957$	32.9291	−	8.82333i	1.06445	−	0.285218i
$958$		0			0
$959$	24.2455	+	14.9271i	0.782929	+	0.482020i
$960$		0			0
$961$	8.65835	−	14.9967i	0.279302	−	0.483765i
$962$		0			0
$963$	9.60531	−	35.8475i	0.309527	−	1.15517i
$964$		0			0
$965$	−0.948791	+	0.948791i	−0.0305426	+	0.0305426i
$966$		0			0
$967$	4.85592			0.156156			0.0780779	−	0.996947i	$-0.475122\pi$
$967$	4.85592			0.156156			0.0780779	+	0.996947i	$0.475122\pi$
$968$		0			0
$969$	−0.548454	−	0.949950i	−0.0176189	−	0.0305168i
$970$		0			0
$971$	59.5122	−	15.9462i	1.90984	−	0.511739i	0.915956	−	0.401280i	$-0.131434\pi$
$971$	59.5122	−	15.9462i	1.90984	−	0.511739i	0.993881	−	0.110459i	$-0.0352322\pi$
$972$		0			0
$973$	−14.1307	+	47.3429i	−0.453010	+	1.51774i
$974$		0			0
$975$	4.16536	+	2.40487i	0.133398	+	0.0770175i
$976$		0			0
$977$	−6.98255	−	12.0941i	−0.223392	−	0.386926i	0.732444	−	0.680827i	$-0.238380\pi$
$977$	−6.98255	−	12.0941i	−0.223392	−	0.386926i	−0.955836	+	0.293902i	$0.905046\pi$
$978$		0			0
$979$	−3.81673	+	3.81673i	−0.121983	+	0.121983i
$980$		0			0
$981$	5.22113	+	5.22113i	0.166698	+	0.166698i
$982$		0			0
$983$	−48.8774	+	28.2194i	−1.55895	+	0.900058i	−0.561588	+	0.827417i	$0.689810\pi$
$983$	−48.8774	+	28.2194i	−1.55895	+	0.900058i	−0.997358	+	0.0726413i	$0.976857\pi$
$984$		0			0
$985$	0.643550	−	1.11466i	0.0205052	−	0.0355161i
$986$		0			0
$987$	66.3474	+	19.8031i	2.11186	+	0.630339i
$988$		0			0
$989$	−13.1655	−	49.1342i	−0.418638	−	1.56238i
$990$		0			0
$991$	−39.5634	+	22.8419i	−1.25677	+	0.725598i	−0.972446	−	0.233129i	$-0.925104\pi$
$991$	−39.5634	+	22.8419i	−1.25677	+	0.725598i	−0.284327	+	0.958727i	$0.591770\pi$
$992$		0			0
$993$			9.89891i			0.314132i
$994$		0			0
$995$	−7.74566	−	7.74566i	−0.245554	−	0.245554i
$996$		0			0
$997$	−13.2530	−	3.55112i	−0.419726	−	0.112465i	0.0427736	−	0.999085i	$-0.486381\pi$
$997$	−13.2530	−	3.55112i	−0.419726	−	0.112465i	−0.462499	+	0.886620i	$0.653047\pi$
$998$		0			0
$999$	2.42295	+	1.39889i	0.0766588	+	0.0442590i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.z.a.159.13		56
4.3	odd	2		896.2.z.b.159.2		56
7.3	odd	6	inner	896.2.z.a.31.13		56
8.3	odd	2		112.2.v.a.75.10	yes	56
8.5	even	2		448.2.z.a.271.2		56
16.3	odd	4	inner	896.2.z.a.607.13		56
16.5	even	4		112.2.v.a.19.1	yes	56
16.11	odd	4		448.2.z.a.47.2		56
16.13	even	4		896.2.z.b.607.2		56
28.3	even	6		896.2.z.b.31.2		56
56.3	even	6		112.2.v.a.59.1	yes	56
56.11	odd	6		784.2.w.f.619.1		56
56.19	even	6		784.2.j.a.587.20		56
56.27	even	2		784.2.w.f.411.10		56
56.45	odd	6		448.2.z.a.143.2		56
56.51	odd	6		784.2.j.a.587.19		56
112.3	even	12	inner	896.2.z.a.479.13		56
112.5	odd	12		784.2.j.a.195.19		56
112.37	even	12		784.2.j.a.195.20		56
112.45	odd	12		896.2.z.b.479.2		56
112.53	even	12		784.2.w.f.227.10		56
112.59	even	12		448.2.z.a.367.2		56
112.69	odd	4		784.2.w.f.19.1		56
112.101	odd	12		112.2.v.a.3.10	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.v.a.3.10	✓	56	112.101	odd	12
112.2.v.a.19.1	yes	56	16.5	even	4
112.2.v.a.59.1	yes	56	56.3	even	6
112.2.v.a.75.10	yes	56	8.3	odd	2
448.2.z.a.47.2		56	16.11	odd	4
448.2.z.a.143.2		56	56.45	odd	6
448.2.z.a.271.2		56	8.5	even	2
448.2.z.a.367.2		56	112.59	even	12
784.2.j.a.195.19		56	112.5	odd	12
784.2.j.a.195.20		56	112.37	even	12
784.2.j.a.587.19		56	56.51	odd	6
784.2.j.a.587.20		56	56.19	even	6
784.2.w.f.19.1		56	112.69	odd	4
784.2.w.f.227.10		56	112.53	even	12
784.2.w.f.411.10		56	56.27	even	2
784.2.w.f.619.1		56	56.11	odd	6
896.2.z.a.31.13		56	7.3	odd	6	inner
896.2.z.a.159.13		56	1.1	even	1	trivial
896.2.z.a.479.13		56	112.3	even	12	inner
896.2.z.a.607.13		56	16.3	odd	4	inner
896.2.z.b.31.2		56	28.3	even	6
896.2.z.b.159.2		56	4.3	odd	2
896.2.z.b.479.2		56	112.45	odd	12
896.2.z.b.607.2		56	16.13	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.z (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.29647 + 0.615336i) q^{3} +(0.223959 + 0.835825i) q^{5} +(1.25761 + 2.32775i) q^{7} +(2.29704 + 1.32620i) q^{9} +(-2.03316 - 0.544785i) q^{11} +(0.336492 + 0.336492i) q^{13} +2.05725i q^{15} +(-0.0488652 + 0.0282123i) q^{17} +(2.11632 + 7.89820i) q^{19} +(1.45571 + 6.11945i) q^{21} +(3.59814 - 6.23216i) q^{23} +(3.68168 - 2.12562i) q^{25} +(-0.584366 - 0.584366i) q^{27} +(-4.81700 + 4.81700i) q^{29} +(1.84955 + 3.20351i) q^{31} +(-4.33387 - 2.50216i) q^{33} +(-1.66394 + 1.57246i) q^{35} +(-3.27008 + 0.876214i) q^{37} +(0.565687 + 0.979798i) q^{39} -4.95983 q^{41} +(4.99825 - 4.99825i) q^{43} +(-0.594027 + 2.21694i) q^{45} +(5.50377 - 9.53281i) q^{47} +(-3.83684 + 5.85480i) q^{49} +(-0.129577 + 0.0347202i) q^{51} +(0.971464 - 3.62555i) q^{53} -1.82138i q^{55} +19.4402i q^{57} +(-2.27632 + 8.49533i) q^{59} +(-6.21929 + 1.66645i) q^{61} +(-0.198278 + 7.01478i) q^{63} +(-0.205888 + 0.356609i) q^{65} +(2.80281 - 10.4602i) q^{67} +(12.0979 - 12.0979i) q^{69} +13.1246 q^{71} +(-2.69592 - 4.66948i) q^{73} +(9.76283 - 2.61594i) q^{75} +(-1.28880 - 5.41782i) q^{77} +(-4.99619 - 2.88455i) q^{79} +(-4.96099 - 8.59269i) q^{81} +(4.52860 - 4.52860i) q^{83} +(-0.0345244 - 0.0345244i) q^{85} +(-14.0261 + 8.09800i) q^{87} +(1.28218 - 2.22080i) q^{89} +(-0.360094 + 1.20644i) q^{91} +(2.27619 + 8.49484i) q^{93} +(-6.12755 + 3.53774i) q^{95} +9.06313i q^{97} +(-3.94777 - 3.94777i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 6 q^{3} + 6 q^{5} + 8 q^{7} + 2 q^{11} - 12 q^{17} - 6 q^{19} + 10 q^{21} + 12 q^{23} + 24 q^{29} - 12 q^{33} - 2 q^{35} - 6 q^{37} + 4 q^{39} - 12 q^{45} - 8 q^{49} - 34 q^{51} - 6 q^{53} + 42 q^{59}+ \cdots - 16 q^{99}+O(q^{100}) \) 56 * q - 6 * q^3 + 6 * q^5 + 8 * q^7 + 2 * q^11 - 12 * q^17 - 6 * q^19 + 10 * q^21 + 12 * q^23 + 24 * q^29 - 12 * q^33 - 2 * q^35 - 6 * q^37 + 4 * q^39 - 12 * q^45 - 8 * q^49 - 34 * q^51 - 6 * q^53 + 42 * q^59 + 6 * q^61 - 4 * q^65 + 6 * q^67 + 80 * q^71 + 24 * q^75 - 10 * q^77 - 8 * q^81 + 28 * q^85 + 12 * q^87 + 16 * q^91 - 10 * q^93 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more