LMFDB - Embedded newform 1148.2.n.d.57.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(57,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("1148.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.n (of order $5$, 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:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			57.5
Character	$\chi$	$=$	1148.57
Dual form			1148.2.n.d.141.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.35294 q^{3} +(2.62263 + 1.90545i) q^{5} +(0.309017 + 0.951057i) q^{7} -1.16955 q^{9} +O(q^{10})$	\(q+1.35294 q^{3} +(2.62263 + 1.90545i) q^{5} +(0.309017 + 0.951057i) q^{7} -1.16955 q^{9} +(-2.19654 + 1.59588i) q^{11} +(-1.14666 + 3.52907i) q^{13} +(3.54826 + 2.57796i) q^{15} +(-0.547062 + 0.397464i) q^{17} +(0.957037 + 2.94546i) q^{19} +(0.418082 + 1.28672i) q^{21} +(-0.591984 + 1.82194i) q^{23} +(1.70234 + 5.23927i) q^{25} -5.64116 q^{27} +(-0.00887270 - 0.00644639i) q^{29} +(6.36515 - 4.62455i) q^{31} +(-2.97179 + 2.15913i) q^{33} +(-1.00175 + 3.08308i) q^{35} +(0.699729 + 0.508383i) q^{37} +(-1.55137 + 4.77462i) q^{39} +(5.84706 + 2.60996i) q^{41} +(-0.362532 + 1.11576i) q^{43} +(-3.06729 - 2.22852i) q^{45} +(2.68243 - 8.25568i) q^{47} +(-0.809017 + 0.587785i) q^{49} +(-0.740142 + 0.537745i) q^{51} +(-0.381724 - 0.277339i) q^{53} -8.80156 q^{55} +(1.29481 + 3.98503i) q^{57} +(3.48944 - 10.7394i) q^{59} +(-1.83237 - 5.63944i) q^{61} +(-0.361411 - 1.11231i) q^{63} +(-9.73173 + 7.07051i) q^{65} +(-5.39520 - 3.91984i) q^{67} +(-0.800920 + 2.46498i) q^{69} +(5.11978 - 3.71974i) q^{71} +8.63888 q^{73} +(2.30317 + 7.08842i) q^{75} +(-2.19654 - 1.59588i) q^{77} +1.20607 q^{79} -4.12350 q^{81} +6.05430 q^{83} -2.19208 q^{85} +(-0.0120042 - 0.00872158i) q^{87} +(2.91179 + 8.96157i) q^{89} -3.71068 q^{91} +(8.61166 - 6.25674i) q^{93} +(-3.10247 + 9.54841i) q^{95} +(2.84324 + 2.06573i) q^{97} +(2.56896 - 1.86646i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 10 q^{3} + 4 q^{5} - 6 q^{7} + 38 q^{9}+O(q^{10}) $ 24 * q - 10 * q^3 + 4 * q^5 - 6 * q^7 + 38 * q^9	$ 24 q - 10 q^{3} + 4 q^{5} - 6 q^{7} + 38 q^{9} + 11 q^{11} - 4 q^{13} + 10 q^{15} + 9 q^{17} - 23 q^{19} + 5 q^{21} + 28 q^{23} - 10 q^{25} - 76 q^{27} + 28 q^{29} - 18 q^{31} - 27 q^{33} - q^{35} - 29 q^{37} - 6 q^{39} + 65 q^{41} - 15 q^{43} - 20 q^{45} - 11 q^{47} - 6 q^{49} - 18 q^{51} + 8 q^{53} - 50 q^{55} + 8 q^{57} + 55 q^{59} - 10 q^{61} - 2 q^{63} - 11 q^{65} + 65 q^{67} - 2 q^{69} - 14 q^{71} + 48 q^{73} - 77 q^{75} + 11 q^{77} + 22 q^{79} + 80 q^{81} - 22 q^{83} - 78 q^{85} - 4 q^{87} + 16 q^{89} - 4 q^{91} - 60 q^{93} + 56 q^{95} + 15 q^{97} + 80 q^{99}+O(q^{100}) $ 24 * q - 10 * q^3 + 4 * q^5 - 6 * q^7 + 38 * q^9 + 11 * q^11 - 4 * q^13 + 10 * q^15 + 9 * q^17 - 23 * q^19 + 5 * q^21 + 28 * q^23 - 10 * q^25 - 76 * q^27 + 28 * q^29 - 18 * q^31 - 27 * q^33 - q^35 - 29 * q^37 - 6 * q^39 + 65 * q^41 - 15 * q^43 - 20 * q^45 - 11 * q^47 - 6 * q^49 - 18 * q^51 + 8 * q^53 - 50 * q^55 + 8 * q^57 + 55 * q^59 - 10 * q^61 - 2 * q^63 - 11 * q^65 + 65 * q^67 - 2 * q^69 - 14 * q^71 + 48 * q^73 - 77 * q^75 + 11 * q^77 + 22 * q^79 + 80 * q^81 - 22 * q^83 - 78 * q^85 - 4 * q^87 + 16 * q^89 - 4 * q^91 - 60 * q^93 + 56 * q^95 + 15 * q^97 + 80 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

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
$3$	1.35294			0.781121			0.390560	−	0.920577i	$-0.372281\pi$
$3$	1.35294			0.781121			0.390560	+	0.920577i	$0.372281\pi$
$4$		0			0
$5$	2.62263	+	1.90545i	1.17287	+	0.852143i	0.991350	−	0.131244i	$-0.0418972\pi$
$5$	2.62263	+	1.90545i	1.17287	+	0.852143i	0.181523	+	0.983387i	$0.441897\pi$
$6$		0			0
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$8$		0			0
$9$	−1.16955			−0.389850
$10$		0			0
$11$	−2.19654	+	1.59588i	−0.662281	+	0.481175i	−0.867433	−	0.497555i	$-0.834231\pi$
$11$	−2.19654	+	1.59588i	−0.662281	+	0.481175i	0.205151	+	0.978730i	$0.434231\pi$
$12$		0			0
$13$	−1.14666	+	3.52907i	−0.318027	+	0.978787i	0.656463	+	0.754358i	$0.272052\pi$
$13$	−1.14666	+	3.52907i	−0.318027	+	0.978787i	−0.974490	+	0.224429i	$0.927948\pi$
$14$		0			0
$15$	3.54826	+	2.57796i	0.916156	+	0.665626i
$16$		0			0
$17$	−0.547062	+	0.397464i	−0.132682	+	0.0963991i	−0.652147	−	0.758093i	$-0.726131\pi$
$17$	−0.547062	+	0.397464i	−0.132682	+	0.0963991i	0.519465	+	0.854492i	$0.326131\pi$
$18$		0			0
$19$	0.957037	+	2.94546i	0.219559	+	0.675734i	0.998798	+	0.0490074i	$0.0156058\pi$
$19$	0.957037	+	2.94546i	0.219559	+	0.675734i	−0.779239	+	0.626727i	$0.784394\pi$
$20$		0			0
$21$	0.418082	+	1.28672i	0.0912329	+	0.280786i
$22$		0			0
$23$	−0.591984	+	1.82194i	−0.123437	+	0.379901i	−0.993613	−	0.112840i	$-0.964005\pi$
$23$	−0.591984	+	1.82194i	−0.123437	+	0.379901i	0.870176	+	0.492741i	$0.164005\pi$
$24$		0			0
$25$	1.70234	+	5.23927i	0.340469	+	1.04785i
$26$		0			0
$27$	−5.64116			−1.08564
$28$		0			0
$29$	−0.00887270	−	0.00644639i	−0.00164762	−	0.00119706i	0.586961	−	0.809615i	$-0.300324\pi$
$29$	−0.00887270	−	0.00644639i	−0.00164762	−	0.00119706i	−0.588609	+	0.808418i	$0.700324\pi$
$30$		0			0
$31$	6.36515	−	4.62455i	1.14321	−	0.830593i	0.155650	−	0.987812i	$-0.450253\pi$
$31$	6.36515	−	4.62455i	1.14321	−	0.830593i	0.987564	+	0.157219i	$0.0502528\pi$
$32$		0			0
$33$	−2.97179	+	2.15913i	−0.517322	+	0.375856i
$34$		0			0
$35$	−1.00175	+	3.08308i	−0.169327	+	0.521136i
$36$		0			0
$37$	0.699729	+	0.508383i	0.115035	+	0.0835776i	0.643815	−	0.765181i	$-0.277351\pi$
$37$	0.699729	+	0.508383i	0.115035	+	0.0835776i	−0.528781	+	0.848759i	$0.677351\pi$
$38$		0			0
$39$	−1.55137	+	4.77462i	−0.248418	+	0.764551i
$40$		0			0
$41$	5.84706	+	2.60996i	0.913157	+	0.407607i
$41$	5.84706	+	2.60996i	0.913157	+	0.407607i
$42$		0			0
$43$	−0.362532	+	1.11576i	−0.0552855	+	0.170151i	−0.974886	−	0.222702i	$-0.928512\pi$
$43$	−0.362532	+	1.11576i	−0.0552855	+	0.170151i	0.919601	+	0.392854i	$0.128512\pi$
$44$		0			0
$45$	−3.06729	−	2.22852i	−0.457245	−	0.332208i
$46$		0			0
$47$	2.68243	−	8.25568i	0.391273	−	1.20422i	−0.540553	−	0.841310i	$-0.681785\pi$
$47$	2.68243	−	8.25568i	0.391273	−	1.20422i	0.931826	−	0.362905i	$-0.118215\pi$
$48$		0			0
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$		0			0
$51$	−0.740142	+	0.537745i	−0.103641	+	0.0752993i
$52$		0			0
$53$	−0.381724	−	0.277339i	−0.0524338	−	0.0380954i	0.561260	−	0.827640i	$-0.310317\pi$
$53$	−0.381724	−	0.277339i	−0.0524338	−	0.0380954i	−0.613693	+	0.789544i	$0.710317\pi$
$54$		0			0
$55$	−8.80156			−1.18680
$56$		0			0
$57$	1.29481	+	3.98503i	0.171502	+	0.527830i
$58$		0			0
$59$	3.48944	−	10.7394i	0.454287	−	1.39815i	−0.417683	−	0.908593i	$-0.637158\pi$
$59$	3.48944	−	10.7394i	0.454287	−	1.39815i	0.871970	−	0.489559i	$-0.162842\pi$
$60$		0			0
$61$	−1.83237	−	5.63944i	−0.234610	−	0.722057i	−0.997173	−	0.0751420i	$-0.976059\pi$
$61$	−1.83237	−	5.63944i	−0.234610	−	0.722057i	0.762562	−	0.646915i	$-0.223941\pi$
$62$		0			0
$63$	−0.361411	−	1.11231i	−0.0455335	−	0.140138i
$64$		0			0
$65$	−9.73173	+	7.07051i	−1.20707	+	0.876989i
$66$		0			0
$67$	−5.39520	−	3.91984i	−0.659129	−	0.478885i	0.207240	−	0.978290i	$-0.433552\pi$
$67$	−5.39520	−	3.91984i	−0.659129	−	0.478885i	−0.866369	+	0.499405i	$0.833552\pi$
$68$		0			0
$69$	−0.800920	+	2.46498i	−0.0964194	+	0.296748i
$70$		0			0
$71$	5.11978	−	3.71974i	0.607606	−	0.441452i	−0.240964	−	0.970534i	$-0.577464\pi$
$71$	5.11978	−	3.71974i	0.607606	−	0.441452i	0.848571	+	0.529082i	$0.177464\pi$
$72$		0			0
$73$	8.63888			1.01110			0.505552	−	0.862796i	$-0.331289\pi$
$73$	8.63888			1.01110			0.505552	+	0.862796i	$0.331289\pi$
$74$		0			0
$75$	2.30317	+	7.08842i	0.265947	+	0.818501i
$76$		0			0
$77$	−2.19654	−	1.59588i	−0.250319	−	0.181867i
$78$		0			0
$79$	1.20607			0.135693			0.0678467	−	0.997696i	$-0.478387\pi$
$79$	1.20607			0.135693			0.0678467	+	0.997696i	$0.478387\pi$
$80$		0			0
$81$	−4.12350			−0.458166
$82$		0			0
$83$	6.05430			0.664546			0.332273	−	0.943183i	$-0.392185\pi$
$83$	6.05430			0.664546			0.332273	+	0.943183i	$0.392185\pi$
$84$		0			0
$85$	−2.19208			−0.237765
$86$		0			0
$87$	−0.0120042	−	0.00872158i	−0.00128699	−	0.000935052i
$88$		0			0
$89$	2.91179	+	8.96157i	0.308649	+	0.949925i	0.978290	+	0.207240i	$0.0664481\pi$
$89$	2.91179	+	8.96157i	0.308649	+	0.949925i	−0.669641	+	0.742685i	$0.733552\pi$
$90$		0			0
$91$	−3.71068			−0.388985
$92$		0			0
$93$	8.61166	−	6.25674i	0.892988	−	0.648794i
$94$		0			0
$95$	−3.10247	+	9.54841i	−0.318306	+	0.979647i
$96$		0			0
$97$	2.84324	+	2.06573i	0.288687	+	0.209743i	0.722698	−	0.691164i	$-0.242902\pi$
$97$	2.84324	+	2.06573i	0.288687	+	0.209743i	−0.434010	+	0.900908i	$0.642902\pi$
$98$		0			0
$99$	2.56896	−	1.86646i	0.258191	−	0.187586i
$100$		0			0
$101$	2.93383	+	9.02940i	0.291927	+	0.898459i	0.984236	+	0.176858i	$0.0565933\pi$
$101$	2.93383	+	9.02940i	0.291927	+	0.898459i	−0.692309	+	0.721601i	$0.743407\pi$
$102$		0			0
$103$	−2.07391	−	6.38284i	−0.204349	−	0.628920i	−0.999740	−	0.0228236i	$-0.992734\pi$
$103$	−2.07391	−	6.38284i	−0.204349	−	0.628920i	0.795391	−	0.606097i	$-0.207266\pi$
$104$		0			0
$105$	−1.35531	+	4.17123i	−0.132265	+	0.407070i
$106$		0			0
$107$	1.07009	+	3.29340i	0.103450	+	0.318385i	0.989363	−	0.145465i	$-0.0464677\pi$
$107$	1.07009	+	3.29340i	0.103450	+	0.318385i	−0.885914	+	0.463850i	$0.846468\pi$
$108$		0			0
$109$	5.41518			0.518681			0.259340	−	0.965786i	$-0.416495\pi$
$109$	5.41518			0.518681			0.259340	+	0.965786i	$0.416495\pi$
$110$		0			0
$111$	0.946691	+	0.687812i	0.0898560	+	0.0652842i
$112$		0			0
$113$	−6.69198	+	4.86201i	−0.629528	+	0.457379i	−0.856237	−	0.516584i	$-0.827204\pi$
$113$	−6.69198	+	4.86201i	−0.629528	+	0.457379i	0.226709	+	0.973963i	$0.427204\pi$
$114$		0			0
$115$	−5.02417	+	3.65027i	−0.468506	+	0.340390i
$116$		0			0
$117$	1.34108	−	4.12743i	0.123983	−	0.381581i
$118$		0			0
$119$	−0.547062	−	0.397464i	−0.0501491	−	0.0364354i
$120$		0			0
$121$	−1.12123	+	3.45081i	−0.101930	+	0.313710i
$122$		0			0
$123$	7.91073	+	3.53112i	0.713286	+	0.318390i
$124$		0			0
$125$	−0.509789	+	1.56897i	−0.0455969	+	0.140333i
$126$		0			0
$127$	10.3220	+	7.49938i	0.915930	+	0.665462i	0.942508	−	0.334184i	$-0.108461\pi$
$127$	10.3220	+	7.49938i	0.915930	+	0.665462i	−0.0265774	+	0.999647i	$0.508461\pi$
$128$		0			0
$129$	−0.490484	+	1.50955i	−0.0431847	+	0.132909i
$130$		0			0
$131$	13.2233	−	9.60732i	1.15533	−	0.839395i	0.166148	−	0.986101i	$-0.446867\pi$
$131$	13.2233	−	9.60732i	1.15533	−	0.839395i	0.989180	+	0.146705i	$0.0468670\pi$
$132$		0			0
$133$	−2.50556	+	1.82039i	−0.217259	+	0.157848i
$134$		0			0
$135$	−14.7946	−	10.7489i	−1.27332	−	0.925121i
$136$		0			0
$137$	10.9772			0.937845			0.468922	−	0.883239i	$-0.344642\pi$
$137$	10.9772			0.937845			0.468922	+	0.883239i	$0.344642\pi$
$138$		0			0
$139$	0.685944	+	2.11112i	0.0581810	+	0.179063i	0.975923	−	0.218113i	$-0.0699903\pi$
$139$	0.685944	+	2.11112i	0.0581810	+	0.179063i	−0.917742	+	0.397176i	$0.869990\pi$
$140$		0			0
$141$	3.62917	−	11.1695i	0.305632	−	0.940637i
$142$		0			0
$143$	−3.11327	−	9.58167i	−0.260345	−	0.801259i
$144$		0			0
$145$	−0.0109865	−	0.0338129i	−0.000912378	−	0.00280801i
$146$		0			0
$147$	−1.09455	+	0.795239i	−0.0902771	+	0.0655902i
$148$		0			0
$149$	−3.27388	−	2.37861i	−0.268206	−	0.194863i	0.445551	−	0.895257i	$-0.353008\pi$
$149$	−3.27388	−	2.37861i	−0.268206	−	0.194863i	−0.713757	+	0.700393i	$0.753008\pi$
$150$		0			0
$151$	−3.69495	+	11.3719i	−0.300691	+	0.925432i	0.680559	+	0.732693i	$0.261737\pi$
$151$	−3.69495	+	11.3719i	−0.300691	+	0.925432i	−0.981250	+	0.192739i	$0.938263\pi$
$152$		0			0
$153$	0.639817	−	0.464854i	0.0517261	−	0.0375812i
$154$		0			0
$155$	25.5052			2.04863
$156$		0			0
$157$	−3.01869	−	9.29056i	−0.240917	−	0.741468i	−0.996281	−	0.0861619i	$-0.972540\pi$
$157$	−3.01869	−	9.29056i	−0.240917	−	0.741468i	0.755364	−	0.655306i	$-0.227460\pi$
$158$		0			0
$159$	−0.516450	−	0.375223i	−0.0409572	−	0.0297571i
$160$		0			0
$161$	−1.91570			−0.150978
$162$		0			0
$163$	−1.26390			−0.0989959			−0.0494980	−	0.998774i	$-0.515762\pi$
$163$	−1.26390			−0.0989959			−0.0494980	+	0.998774i	$0.515762\pi$
$164$		0			0
$165$	−11.9080			−0.927036
$166$		0			0
$167$	10.9539			0.847641			0.423821	−	0.905746i	$-0.360689\pi$
$167$	10.9539			0.847641			0.423821	+	0.905746i	$0.360689\pi$
$168$		0			0
$169$	−0.622263	−	0.452101i	−0.0478664	−	0.0347770i
$170$		0			0
$171$	−1.11930	−	3.44486i	−0.0855953	−	0.263435i
$172$		0			0
$173$	−16.3382			−1.24217			−0.621085	−	0.783744i	$-0.713308\pi$
$173$	−16.3382			−1.24217			−0.621085	+	0.783744i	$0.713308\pi$
$174$		0			0
$175$	−4.45679	+	3.23805i	−0.336902	+	0.244773i
$176$		0			0
$177$	4.72101	−	14.5298i	0.354853	−	1.09213i
$178$		0			0
$179$	−12.1009	−	8.79185i	−0.904467	−	0.657134i	0.0351424	−	0.999382i	$-0.488812\pi$
$179$	−12.1009	−	8.79185i	−0.904467	−	0.657134i	−0.939609	+	0.342249i	$0.888812\pi$
$180$		0			0
$181$	−14.3607	+	10.4337i	−1.06742	+	0.775529i	−0.975448	−	0.220232i	$-0.929319\pi$
$181$	−14.3607	+	10.4337i	−1.06742	+	0.775529i	−0.0919770	+	0.995761i	$0.529319\pi$
$182$		0			0
$183$	−2.47908	−	7.62983i	−0.183259	−	0.564013i
$184$		0			0
$185$	0.866429	+	2.66659i	0.0637011	+	0.196052i
$186$		0			0
$187$	0.567338	−	1.74609i	0.0414879	−	0.127687i
$188$		0			0
$189$	−1.74321	−	5.36506i	−0.126800	−	0.390251i
$190$		0			0
$191$	−12.0196			−0.869709			−0.434855	−	0.900501i	$-0.643200\pi$
$191$	−12.0196			−0.869709			−0.434855	+	0.900501i	$0.643200\pi$
$192$		0			0
$193$	−12.0136	−	8.72840i	−0.864758	−	0.628284i	0.0644169	−	0.997923i	$-0.479481\pi$
$193$	−12.0136	−	8.72840i	−0.864758	−	0.628284i	−0.929175	+	0.369639i	$0.879481\pi$
$194$		0			0
$195$	−13.1665	+	9.56599i	−0.942869	+	0.685035i
$196$		0			0
$197$	15.1202	−	10.9854i	1.07727	−	0.782680i	0.100062	−	0.994981i	$-0.468096\pi$
$197$	15.1202	−	10.9854i	1.07727	−	0.782680i	0.977204	+	0.212301i	$0.0680958\pi$
$198$		0			0
$199$	−5.78480	+	17.8038i	−0.410074	+	1.26208i	0.506510	+	0.862234i	$0.330935\pi$
$199$	−5.78480	+	17.8038i	−0.410074	+	1.26208i	−0.916584	+	0.399843i	$0.869065\pi$
$200$		0			0
$201$	−7.29939	−	5.30332i	−0.514859	−	0.374067i
$202$		0			0
$203$	0.00338907	−	0.0104305i	0.000237866	−	0.000732076i
$204$		0			0
$205$	10.3615	+	17.9862i	0.723679	+	1.25621i
$206$		0			0
$207$	0.692356	−	2.13085i	0.0481221	−	0.148105i
$208$		0			0
$209$	−6.80276	−	4.94249i	−0.470557	−	0.341879i
$210$		0			0
$211$	5.55345	−	17.0918i	0.382315	−	1.17665i	−0.556094	−	0.831119i	$-0.687701\pi$
$211$	5.55345	−	17.0918i	0.382315	−	1.17665i	0.938409	−	0.345526i	$-0.112299\pi$
$212$		0			0
$213$	6.92676	−	5.03259i	0.474614	−	0.344827i
$214$		0			0
$215$	−3.07680	+	2.23543i	−0.209836	+	0.152455i
$216$		0			0
$217$	6.36515	+	4.62455i	0.432094	+	0.313935i
$218$		0			0
$219$	11.6879			0.789795
$220$		0			0
$221$	−0.775380	−	2.38638i	−0.0521577	−	0.160525i
$222$		0			0
$223$	1.75458	−	5.40003i	0.117495	−	0.361613i	−0.874964	−	0.484188i	$-0.839115\pi$
$223$	1.75458	−	5.40003i	0.117495	−	0.361613i	0.992459	+	0.122575i	$0.0391152\pi$
$224$		0			0
$225$	−1.99098	−	6.12760i	−0.132732	−	0.408506i
$226$		0			0
$227$	−5.19883	−	16.0004i	−0.345059	−	1.06198i	−0.961552	−	0.274622i	$-0.911447\pi$
$227$	−5.19883	−	16.0004i	−0.345059	−	1.06198i	0.616494	−	0.787360i	$-0.288553\pi$
$228$		0			0
$229$	−12.2532	+	8.90244i	−0.809712	+	0.588290i	−0.913747	−	0.406283i	$-0.866825\pi$
$229$	−12.2532	+	8.90244i	−0.809712	+	0.588290i	0.104035	+	0.994574i	$0.466825\pi$
$230$		0			0
$231$	−2.97179	−	2.15913i	−0.195529	−	0.142060i
$232$		0			0
$233$	−1.89330	+	5.82697i	−0.124034	+	0.381737i	−0.993724	−	0.111861i	$-0.964319\pi$
$233$	−1.89330	+	5.82697i	−0.124034	+	0.381737i	0.869690	+	0.493599i	$0.164319\pi$
$234$		0			0
$235$	22.7658	−	16.5403i	1.48508	−	1.07897i
$236$		0			0
$237$	1.63174			0.105993
$238$		0			0
$239$	−4.52134	−	13.9152i	−0.292461	−	0.900102i	−0.984063	−	0.177823i	$-0.943095\pi$
$239$	−4.52134	−	13.9152i	−0.292461	−	0.900102i	0.691602	−	0.722279i	$-0.256905\pi$
$240$		0			0
$241$	11.0979	+	8.06309i	0.714878	+	0.519389i	0.884744	−	0.466078i	$-0.154333\pi$
$241$	11.0979	+	8.06309i	0.714878	+	0.519389i	−0.169865	+	0.985467i	$0.554333\pi$
$242$		0			0
$243$	11.3446			0.727758
$244$		0			0
$245$	−3.24174			−0.207107
$246$		0			0
$247$	−11.4921			−0.731226
$248$		0			0
$249$	8.19111			0.519090
$250$		0			0
$251$	−13.6878	−	9.94474i	−0.863964	−	0.627707i	0.0649964	−	0.997885i	$-0.479296\pi$
$251$	−13.6878	−	9.94474i	−0.863964	−	0.627707i	−0.928961	+	0.370179i	$0.879296\pi$
$252$		0			0
$253$	−1.60728	−	4.94670i	−0.101049	−	0.310996i
$254$		0			0
$255$	−2.96576			−0.185723
$256$		0			0
$257$	−20.7340	+	15.0642i	−1.29335	+	0.939676i	−0.999867	−	0.0162869i	$-0.994815\pi$
$257$	−20.7340	+	15.0642i	−1.29335	+	0.939676i	−0.293486	+	0.955963i	$0.594815\pi$
$258$		0			0
$259$	−0.267273	+	0.822580i	−0.0166075	+	0.0511127i
$260$		0			0
$261$	0.0103771	+	0.00753938i	0.000642325	+	0.000466676i
$262$		0			0
$263$	17.1417	−	12.4542i	1.05700	−	0.767956i	0.0834695	−	0.996510i	$-0.473400\pi$
$263$	17.1417	−	12.4542i	1.05700	−	0.767956i	0.973531	+	0.228554i	$0.0733999\pi$
$264$		0			0
$265$	−0.472664	−	1.45471i	−0.0290355	−	0.0893622i
$266$		0			0
$267$	3.93948	+	12.1245i	0.241092	+	0.742006i
$268$		0			0
$269$	1.60639	−	4.94395i	0.0979431	−	0.301438i	−0.890066	−	0.455831i	$-0.849342\pi$
$269$	1.60639	−	4.94395i	0.0979431	−	0.301438i	0.988010	+	0.154393i	$0.0493422\pi$
$270$		0			0
$271$	−1.51883	−	4.67447i	−0.0922622	−	0.283954i	0.894268	−	0.447531i	$-0.147697\pi$
$271$	−1.51883	−	4.67447i	−0.0922622	−	0.283954i	−0.986530	+	0.163577i	$0.947697\pi$
$272$		0			0
$273$	−5.02033			−0.303844
$274$		0			0
$275$	−12.1005	−	8.79153i	−0.729688	−	0.530149i
$276$		0			0
$277$	3.36288	−	2.44328i	0.202056	−	0.146802i	−0.482156	−	0.876085i	$-0.660146\pi$
$277$	3.36288	−	2.44328i	0.202056	−	0.146802i	0.684212	+	0.729283i	$0.260146\pi$
$278$		0			0
$279$	−7.44436	+	5.40865i	−0.445682	+	0.323807i
$280$		0			0
$281$	1.78572	−	5.49589i	0.106527	−	0.327857i	−0.883559	−	0.468321i	$-0.844859\pi$
$281$	1.78572	−	5.49589i	0.106527	−	0.327857i	0.990086	+	0.140463i	$0.0448592\pi$
$282$		0			0
$283$	3.83903	+	2.78922i	0.228206	+	0.165802i	0.696013	−	0.718029i	$-0.254956\pi$
$283$	3.83903	+	2.78922i	0.228206	+	0.165802i	−0.467806	+	0.883831i	$0.654956\pi$
$284$		0			0
$285$	−4.19745	+	12.9184i	−0.248636	+	0.765222i
$286$		0			0
$287$	−0.675376	+	6.36741i	−0.0398662	+	0.375856i
$288$		0			0
$289$	−5.11199	+	15.7331i	−0.300705	+	0.925476i
$290$		0			0
$291$	3.84673	+	2.79482i	0.225500	+	0.163835i
$292$		0			0
$293$	3.77433	−	11.6162i	0.220499	−	0.678625i	−0.778219	−	0.627993i	$-0.783877\pi$
$293$	3.77433	−	11.6162i	0.220499	−	0.678625i	0.998717	−	0.0506316i	$-0.0161234\pi$
$294$		0			0
$295$	29.6149	−	21.5165i	1.72425	−	1.25274i
$296$		0			0
$297$	12.3910	−	9.00260i	0.719000	−	0.522384i
$298$		0			0
$299$	−5.75095	−	4.17831i	−0.332586	−	0.241638i
$300$		0			0
$301$	−1.17318			−0.0676208
$302$		0			0
$303$	3.96930	+	12.2162i	0.228030	+	0.701805i
$304$		0			0
$305$	5.94006	−	18.2816i	0.340127	−	1.04680i
$306$		0			0
$307$	−7.69030	−	23.6683i	−0.438908	−	1.35082i	−0.889028	−	0.457853i	$-0.848619\pi$
$307$	−7.69030	−	23.6683i	−0.438908	−	1.35082i	0.450120	−	0.892968i	$-0.351381\pi$
$308$		0			0
$309$	−2.80588	−	8.63561i	−0.159621	−	0.491263i
$310$		0			0
$311$	19.2554	−	13.9899i	1.09187	−	0.793292i	0.112159	−	0.993690i	$-0.464224\pi$
$311$	19.2554	−	13.9899i	1.09187	−	0.793292i	0.979715	+	0.200398i	$0.0642235\pi$
$312$		0			0
$313$	−15.5718	−	11.3136i	−0.880169	−	0.639480i	0.0531274	−	0.998588i	$-0.483081\pi$
$313$	−15.5718	−	11.3136i	−0.880169	−	0.639480i	−0.933296	+	0.359108i	$0.883081\pi$
$314$		0			0
$315$	1.17160	−	3.60582i	0.0660123	−	0.203165i
$316$		0			0
$317$	−19.1498	+	13.9131i	−1.07556	+	0.781440i	−0.976903	−	0.213682i	$-0.931454\pi$
$317$	−19.1498	+	13.9131i	−1.07556	+	0.781440i	−0.0986562	+	0.995122i	$0.531454\pi$
$318$		0			0
$319$	0.0297769			0.00166718
$320$		0			0
$321$	1.44777	+	4.45578i	0.0808067	+	0.248697i
$322$		0			0
$323$	−1.69427	−	1.23096i	−0.0942717	−	0.0684924i
$324$		0			0
$325$	−20.4418			−1.13390
$326$		0			0
$327$	7.32642			0.405152
$328$		0			0
$329$	8.68054			0.478574
$330$		0			0
$331$	22.0321			1.21099			0.605496	−	0.795848i	$-0.292975\pi$
$331$	22.0321			1.21099			0.605496	+	0.795848i	$0.292975\pi$
$332$		0			0
$333$	−0.818368	−	0.594579i	−0.0448463	−	0.0325828i
$334$		0			0
$335$	−6.68053	−	20.5606i	−0.364996	−	1.12334i
$336$		0			0
$337$	6.56655			0.357703			0.178851	−	0.983876i	$-0.442762\pi$
$337$	6.56655			0.357703			0.178851	+	0.983876i	$0.442762\pi$
$338$		0			0
$339$	−9.05385	+	6.57801i	−0.491737	+	0.357268i
$340$		0			0
$341$	−6.60107	+	20.3160i	−0.357468	+	1.10017i
$342$		0			0
$343$	−0.809017	−	0.587785i	−0.0436828	−	0.0317374i
$344$		0			0
$345$	−6.79740	+	4.93860i	−0.365960	+	0.265885i
$346$		0			0
$347$	−6.06370	−	18.6622i	−0.325517	−	1.00184i	−0.971207	−	0.238238i	$-0.923430\pi$
$347$	−6.06370	−	18.6622i	−0.325517	−	1.00184i	0.645690	−	0.763599i	$-0.276570\pi$
$348$		0			0
$349$	8.51102	+	26.1942i	0.455584	+	1.40214i	0.870448	+	0.492261i	$0.163829\pi$
$349$	8.51102	+	26.1942i	0.455584	+	1.40214i	−0.414863	+	0.909884i	$0.636171\pi$
$350$		0			0
$351$	6.46851	−	19.9080i	0.345263	−	1.06261i
$352$		0			0
$353$	−1.24070	−	3.81848i	−0.0660358	−	0.203237i	0.912594	−	0.408867i	$-0.134076\pi$
$353$	−1.24070	−	3.81848i	−0.0660358	−	0.203237i	−0.978630	+	0.205629i	$0.934076\pi$
$354$		0			0
$355$	20.5150			1.08883
$356$		0			0
$357$	−0.740142	−	0.537745i	−0.0391725	−	0.0284605i
$358$		0			0
$359$	−27.1103	+	19.6968i	−1.43083	+	1.03956i	−0.440964	+	0.897525i	$0.645363\pi$
$359$	−27.1103	+	19.6968i	−1.43083	+	1.03956i	−0.989862	+	0.142031i	$0.954637\pi$
$360$		0			0
$361$	7.61153	−	5.53010i	0.400607	−	0.291058i
$362$		0			0
$363$	−1.51696	+	4.66874i	−0.0796200	+	0.245045i
$364$		0			0
$365$	22.6566	+	16.4610i	1.18590	+	0.861606i
$366$		0			0
$367$	−10.0462	+	30.9190i	−0.524407	+	1.61396i	0.241079	+	0.970505i	$0.422499\pi$
$367$	−10.0462	+	30.9190i	−0.524407	+	1.61396i	−0.765486	+	0.643453i	$0.777501\pi$
$368$		0			0
$369$	−6.83844	−	3.05248i	−0.355995	−	0.158906i
$370$		0			0
$371$	0.145806	−	0.448744i	0.00756985	−	0.0232976i
$372$		0			0
$373$	−21.3955	−	15.5448i	−1.10782	−	0.804877i	−0.125500	−	0.992094i	$-0.540054\pi$
$373$	−21.3955	−	15.5448i	−1.10782	−	0.804877i	−0.982319	+	0.187216i	$0.940054\pi$
$374$		0			0
$375$	−0.689714	+	2.12272i	−0.0356167	+	0.109617i
$376$		0			0
$377$	0.0329237	−	0.0239205i	0.00169566	−	0.00123197i
$378$		0			0
$379$	21.2700	−	15.4535i	1.09257	−	0.793795i	0.112735	−	0.993625i	$-0.464039\pi$
$379$	21.2700	−	15.4535i	1.09257	−	0.793795i	0.979831	+	0.199830i	$0.0640390\pi$
$380$		0			0
$381$	13.9651	+	10.1462i	0.715452	+	0.519806i
$382$		0			0
$383$	−2.40877			−0.123082			−0.0615412	−	0.998105i	$-0.519602\pi$
$383$	−2.40877			−0.123082			−0.0615412	+	0.998105i	$0.519602\pi$
$384$		0			0
$385$	−2.71983	−	8.37078i	−0.138615	−	0.426615i
$386$		0			0
$387$	0.423999	−	1.30494i	0.0215531	−	0.0663336i
$388$		0			0
$389$	−8.43245	−	25.9524i	−0.427542	−	1.31584i	−0.900539	−	0.434776i	$-0.856828\pi$
$389$	−8.43245	−	25.9524i	−0.427542	−	1.31584i	0.472996	−	0.881064i	$-0.343172\pi$
$390$		0			0
$391$	−0.400303	−	1.23201i	−0.0202442	−	0.0623053i
$392$		0			0
$393$	17.8904	−	12.9981i	0.902451	−	0.655669i
$394$		0			0
$395$	3.16307	+	2.29810i	0.159151	+	0.115630i
$396$		0			0
$397$	−11.1602	+	34.3474i	−0.560112	+	1.72385i	0.121932	+	0.992538i	$0.461091\pi$
$397$	−11.1602	+	34.3474i	−0.560112	+	1.72385i	−0.682045	+	0.731310i	$0.738909\pi$
$398$		0			0
$399$	−3.38987	+	2.46288i	−0.169706	+	0.123298i
$400$		0			0
$401$	−4.39016			−0.219234			−0.109617	−	0.993974i	$-0.534962\pi$
$401$	−4.39016			−0.219234			−0.109617	+	0.993974i	$0.534962\pi$
$402$		0			0
$403$	9.02167	+	27.7658i	0.449401	+	1.38311i
$404$		0			0
$405$	−10.8144	−	7.85711i	−0.537371	−	0.390423i
$406$		0			0
$407$	−2.34830			−0.116401
$408$		0			0
$409$	5.36162			0.265115			0.132557	−	0.991175i	$-0.457681\pi$
$409$	5.36162			0.265115			0.132557	+	0.991175i	$0.457681\pi$
$410$		0			0
$411$	14.8515			0.732570
$412$		0			0
$413$	11.2921			0.555647
$414$		0			0
$415$	15.8782	+	11.5362i	0.779428	+	0.566288i
$416$		0			0
$417$	0.928041	+	2.85622i	0.0454464	+	0.139870i
$418$		0			0
$419$	−38.4403			−1.87793			−0.938965	−	0.344012i	$-0.888214\pi$
$419$	−38.4403			−1.87793			−0.938965	+	0.344012i	$0.888214\pi$
$420$		0			0
$421$	2.21560	−	1.60973i	0.107982	−	0.0784533i	−0.532484	−	0.846440i	$-0.678741\pi$
$421$	2.21560	−	1.60973i	0.107982	−	0.0784533i	0.640466	+	0.767987i	$0.278741\pi$
$422$		0			0
$423$	−3.13724	+	9.65544i	−0.152538	+	0.469464i
$424$		0			0
$425$	−3.01371	−	2.18959i	−0.146186	−	0.106211i
$426$		0			0
$427$	4.79720	−	3.48537i	0.232153	−	0.168669i
$428$		0			0
$429$	−4.21207	−	12.9634i	−0.203361	−	0.625880i
$430$		0			0
$431$	−7.33550	−	22.5763i	−0.353339	−	1.08746i	−0.956967	−	0.290198i	$-0.906279\pi$
$431$	−7.33550	−	22.5763i	−0.353339	−	1.08746i	0.603628	−	0.797266i	$-0.293721\pi$
$432$		0			0
$433$	−7.97229	+	24.5362i	−0.383124	+	1.17913i	0.554709	+	0.832045i	$0.312830\pi$
$433$	−7.97229	+	24.5362i	−0.383124	+	1.17913i	−0.937832	+	0.347089i	$0.887170\pi$
$434$		0			0
$435$	−0.0148641	−	0.0457469i	−0.000712677	−	0.00219340i
$436$		0			0
$437$	−5.93300			−0.283814
$438$		0			0
$439$	−2.59668	−	1.88660i	−0.123933	−	0.0900423i	0.524092	−	0.851662i	$-0.324405\pi$
$439$	−2.59668	−	1.88660i	−0.123933	−	0.0900423i	−0.648025	+	0.761619i	$0.724405\pi$
$440$		0			0
$441$	0.946187	−	0.687445i	0.0450565	−	0.0327355i
$442$		0			0
$443$	20.1118	−	14.6121i	0.955540	−	0.694241i	0.00342942	−	0.999994i	$-0.498908\pi$
$443$	20.1118	−	14.6121i	0.955540	−	0.694241i	0.952111	+	0.305754i	$0.0989084\pi$
$444$		0			0
$445$	−9.43928	+	29.0511i	−0.447465	+	1.37716i
$446$		0			0
$447$	−4.42936	−	3.21812i	−0.209502	−	0.152212i
$448$		0			0
$449$	4.63716	−	14.2717i	0.218841	−	0.673523i	−0.780018	−	0.625758i	$-0.784790\pi$
$449$	4.63716	−	14.2717i	0.218841	−	0.673523i	0.998859	−	0.0477657i	$-0.0152101\pi$
$450$		0			0
$451$	−17.0085	+	3.59833i	−0.800897	+	0.169439i
$452$		0			0
$453$	−4.99906	+	15.3855i	−0.234876	+	0.722874i
$454$		0			0
$455$	−9.73173	−	7.07051i	−0.456230	−	0.331471i
$456$		0			0
$457$	2.40139	−	7.39072i	0.112332	−	0.345723i	−0.879049	−	0.476732i	$-0.841821\pi$
$457$	2.40139	−	7.39072i	0.112332	−	0.345723i	0.991381	+	0.131008i	$0.0418214\pi$
$458$		0			0
$459$	3.08606	−	2.24215i	0.144045	−	0.104655i
$460$		0			0
$461$	34.5410	−	25.0955i	1.60873	−	1.16881i	0.741440	−	0.671019i	$-0.234143\pi$
$461$	34.5410	−	25.0955i	1.60873	−	1.16881i	0.867295	−	0.497795i	$-0.165857\pi$
$462$		0			0
$463$	−12.3921	−	9.00336i	−0.575908	−	0.418422i	0.261338	−	0.965247i	$-0.415836\pi$
$463$	−12.3921	−	9.00336i	−0.575908	−	0.418422i	−0.837247	+	0.546825i	$0.815836\pi$
$464$		0			0
$465$	34.5071			1.60023
$466$		0			0
$467$	−5.06193	−	15.5790i	−0.234238	−	0.720910i	−0.997222	−	0.0744926i	$-0.976266\pi$
$467$	−5.06193	−	15.5790i	−0.234238	−	0.720910i	0.762984	−	0.646418i	$-0.223734\pi$
$468$		0			0
$469$	2.06078	−	6.34244i	0.0951582	−	0.292867i
$470$		0			0
$471$	−4.08411	−	12.5696i	−0.188186	−	0.579176i
$472$		0			0
$473$	−0.984299	−	3.02936i	−0.0452581	−	0.139290i
$474$		0			0
$475$	−13.8028	+	10.0284i	−0.633318	+	0.460132i
$476$		0			0
$477$	0.446446	+	0.324362i	0.0204413	+	0.0148515i
$478$		0			0
$479$	0.636412	−	1.95868i	0.0290784	−	0.0894942i	−0.935464	−	0.353422i	$-0.885018\pi$
$479$	0.636412	−	1.95868i	0.0290784	−	0.0894942i	0.964542	+	0.263928i	$0.0850180\pi$
$480$		0			0
$481$	−2.59647	+	1.88645i	−0.118389	+	0.0860145i
$482$		0			0
$483$	−2.59183			−0.117932
$484$		0			0
$485$	3.52060	+	10.8353i	0.159862	+	0.492005i
$486$		0			0
$487$	9.71884	+	7.06115i	0.440403	+	0.319971i	0.785795	−	0.618487i	$-0.212254\pi$
$487$	9.71884	+	7.06115i	0.440403	+	0.319971i	−0.345392	+	0.938458i	$0.612254\pi$
$488$		0			0
$489$	−1.70998			−0.0773278
$490$		0			0
$491$	2.66930			0.120464			0.0602318	−	0.998184i	$-0.480816\pi$
$491$	2.66930			0.120464			0.0602318	+	0.998184i	$0.480816\pi$
$492$		0			0
$493$	0.00741612			0.000334005
$494$		0			0
$495$	10.2939			0.462675
$496$		0			0
$497$	5.11978	+	3.71974i	0.229654	+	0.166853i
$498$		0			0
$499$	5.37351	+	16.5380i	0.240551	+	0.740341i	0.996336	+	0.0855210i	$0.0272555\pi$
$499$	5.37351	+	16.5380i	0.240551	+	0.740341i	−0.755785	+	0.654820i	$0.772745\pi$
$500$		0			0
$501$	14.8200			0.662110
$502$		0			0
$503$	−3.87944	+	2.81858i	−0.172976	+	0.125674i	−0.670905	−	0.741544i	$-0.734094\pi$
$503$	−3.87944	+	2.81858i	−0.172976	+	0.125674i	0.497929	+	0.867218i	$0.334094\pi$
$504$		0			0
$505$	−9.51072	+	29.2710i	−0.423222	+	1.30254i
$506$		0			0
$507$	−0.841885	−	0.611666i	−0.0373894	−	0.0271650i
$508$		0			0
$509$	−35.2149	+	25.5851i	−1.56087	+	1.13404i	−0.625583	+	0.780158i	$0.715139\pi$
$509$	−35.2149	+	25.5851i	−1.56087	+	1.13404i	−0.935290	+	0.353883i	$0.884861\pi$
$510$		0			0
$511$	2.66956	+	8.21607i	0.118094	+	0.363457i
$512$		0			0
$513$	−5.39879	−	16.6158i	−0.238363	−	0.733605i
$514$		0			0
$515$	6.72309	−	20.6915i	0.296255	−	0.911778i
$516$		0			0
$517$	7.28300	+	22.4148i	0.320306	+	0.985800i
$518$		0			0
$519$	−22.1046			−0.970284
$520$		0			0
$521$	23.9137	+	17.3744i	1.04768	+	0.761184i	0.971770	−	0.235930i	$-0.0758138\pi$
$521$	23.9137	+	17.3744i	1.04768	+	0.761184i	0.0759102	+	0.997115i	$0.475814\pi$
$522$		0			0
$523$	−19.7670	+	14.3616i	−0.864352	+	0.627989i	−0.929066	−	0.369915i	$-0.879387\pi$
$523$	−19.7670	+	14.3616i	−0.864352	+	0.627989i	0.0647132	+	0.997904i	$0.479387\pi$
$524$		0			0
$525$	−6.02977	+	4.38089i	−0.263161	+	0.191198i
$526$		0			0
$527$	−1.64404	+	5.05983i	−0.0716154	+	0.220410i
$528$		0			0
$529$	15.6384	+	11.3619i	0.679929	+	0.493997i
$530$		0			0
$531$	−4.08108	+	12.5603i	−0.177104	+	0.545070i
$532$		0			0
$533$	−15.9153	+	17.6419i	−0.689370	+	0.764157i
$534$		0			0
$535$	−3.46896	+	10.6764i	−0.149976	+	0.461579i
$536$		0			0
$537$	−16.3719	−	11.8949i	−0.706498	−	0.513301i
$538$		0			0
$539$	0.839003	−	2.58219i	0.0361384	−	0.111223i
$540$		0			0
$541$	−0.443188	+	0.321995i	−0.0190541	+	0.0138436i	−0.597272	−	0.802039i	$-0.703749\pi$
$541$	−0.443188	+	0.321995i	−0.0190541	+	0.0138436i	0.578217	+	0.815883i	$0.303749\pi$
$542$		0			0
$543$	−19.4292	+	14.1162i	−0.833787	+	0.605782i
$544$		0			0
$545$	14.2020	+	10.3184i	0.608347	+	0.441990i
$546$		0			0
$547$	19.1290			0.817898			0.408949	−	0.912557i	$-0.365895\pi$
$547$	19.1290			0.817898			0.408949	+	0.912557i	$0.365895\pi$
$548$		0			0
$549$	2.14305	+	6.59562i	0.0914630	+	0.281494i
$550$		0			0
$551$	0.0104961	−	0.0323036i	0.000447148	−	0.00137618i
$552$		0			0
$553$	0.372696	+	1.14704i	0.0158487	+	0.0487771i
$554$		0			0
$555$	1.17223	+	3.60774i	0.0497583	+	0.153140i
$556$		0			0
$557$	−12.5056	+	9.08584i	−0.529879	+	0.384979i	−0.820312	−	0.571916i	$-0.806200\pi$
$557$	−12.5056	+	9.08584i	−0.529879	+	0.384979i	0.290434	+	0.956895i	$0.406200\pi$
$558$		0			0
$559$	−3.52188	−	2.55880i	−0.148960	−	0.108226i
$560$		0			0
$561$	0.767575	−	2.36235i	0.0324071	−	0.0997387i
$562$		0			0
$563$	0.443441	−	0.322179i	0.0186888	−	0.0135782i	−0.578402	−	0.815752i	$-0.696323\pi$
$563$	0.443441	−	0.322179i	0.0186888	−	0.0135782i	0.597090	+	0.802174i	$0.296323\pi$
$564$		0			0
$565$	−26.8148			−1.12811
$566$		0			0
$567$	−1.27423	−	3.92168i	−0.0535127	−	0.164695i
$568$		0			0
$569$	−9.60871	−	6.98114i	−0.402818	−	0.292665i	0.367870	−	0.929877i	$-0.380087\pi$
$569$	−9.60871	−	6.98114i	−0.402818	−	0.292665i	−0.770688	+	0.637213i	$0.780087\pi$
$570$		0			0
$571$	27.3893			1.14621			0.573103	−	0.819483i	$-0.305740\pi$
$571$	27.3893			1.14621			0.573103	+	0.819483i	$0.305740\pi$
$572$		0			0
$573$	−16.2618			−0.679348
$574$		0			0
$575$	−10.5534			−0.440107
$576$		0			0
$577$	39.7093			1.65312			0.826561	−	0.562848i	$-0.190294\pi$
$577$	39.7093			1.65312			0.826561	+	0.562848i	$0.190294\pi$
$578$		0			0
$579$	−16.2537	−	11.8090i	−0.675481	−	0.490766i
$580$		0			0
$581$	1.87088	+	5.75798i	0.0776172	+	0.238881i
$582$		0			0
$583$	1.28107			0.0530565
$584$		0			0
$585$	11.3818	−	8.26933i	0.470578	−	0.341895i
$586$		0			0
$587$	8.99057	−	27.6701i	0.371081	−	1.14207i	−0.575004	−	0.818150i	$-0.695000\pi$
$587$	8.99057	−	27.6701i	0.371081	−	1.14207i	0.946085	−	0.323918i	$-0.105000\pi$
$588$		0			0
$589$	19.7131	+	14.3224i	0.812264	+	0.590144i
$590$		0			0
$591$	20.4567	−	14.8626i	0.841475	−	0.611368i
$592$		0			0
$593$	1.16991	+	3.60060i	0.0480423	+	0.147859i	0.972200	−	0.234152i	$-0.0752315\pi$
$593$	1.16991	+	3.60060i	0.0480423	+	0.147859i	−0.924158	+	0.382012i	$0.875231\pi$
$594$		0			0
$595$	−0.677391	−	2.08480i	−0.0277703	−	0.0854683i
$596$		0			0
$597$	−7.82649	+	24.0875i	−0.320317	+	0.985835i
$598$		0			0
$599$	2.73402	+	8.41446i	0.111709	+	0.343806i	0.991246	−	0.132024i	$-0.0421478\pi$
$599$	2.73402	+	8.41446i	0.111709	+	0.343806i	−0.879537	+	0.475830i	$0.842148\pi$
$600$		0			0
$601$	34.1437			1.39275			0.696375	−	0.717678i	$-0.254795\pi$
$601$	34.1437			1.39275			0.696375	+	0.717678i	$0.254795\pi$
$602$		0			0
$603$	6.30997	+	4.58446i	0.256962	+	0.186694i
$604$		0			0
$605$	−9.51591	+	6.91371i	−0.386877	+	0.281082i
$606$		0			0
$607$	−17.6989	+	12.8590i	−0.718377	+	0.521931i	−0.885865	−	0.463943i	$-0.846434\pi$
$607$	−17.6989	+	12.8590i	−0.718377	+	0.521931i	0.167488	+	0.985874i	$0.446434\pi$
$608$		0			0
$609$	0.00458521	−	0.0141118i	0.000185802	−	0.000571840i
$610$		0			0
$611$	26.0590	+	18.9330i	1.05424	+	0.765947i
$612$		0			0
$613$	−13.3282	+	41.0199i	−0.538320	+	1.65678i	0.198043	+	0.980193i	$0.436541\pi$
$613$	−13.3282	+	41.0199i	−0.538320	+	1.65678i	−0.736363	+	0.676586i	$0.763459\pi$
$614$		0			0
$615$	14.0185	+	24.3343i	0.565281	+	0.981253i
$616$		0			0
$617$	−7.61565	+	23.4386i	−0.306595	+	0.943601i	0.672483	+	0.740113i	$0.265228\pi$
$617$	−7.61565	+	23.4386i	−0.306595	+	0.943601i	−0.979077	+	0.203489i	$0.934772\pi$
$618$		0			0
$619$	−4.43815	−	3.22451i	−0.178384	−	0.129604i	0.495010	−	0.868887i	$-0.335164\pi$
$619$	−4.43815	−	3.22451i	−0.178384	−	0.129604i	−0.673394	+	0.739283i	$0.735164\pi$
$620$		0			0
$621$	3.33948	−	10.2779i	0.134009	−	0.412436i
$622$		0			0
$623$	−7.62317	+	5.53856i	−0.305416	+	0.221898i
$624$		0			0
$625$	17.9574	−	13.0468i	0.718295	−	0.521872i
$626$		0			0
$627$	−9.20373	−	6.68690i	−0.367562	−	0.267049i
$628$		0			0
$629$	−0.584858			−0.0233198
$630$		0			0
$631$	6.60749	+	20.3358i	0.263040	+	0.809554i	0.992138	+	0.125145i	$0.0399396\pi$
$631$	6.60749	+	20.3358i	0.263040	+	0.809554i	−0.729099	+	0.684409i	$0.760060\pi$
$632$		0			0
$633$	7.51349	−	23.1241i	0.298634	−	0.919102i
$634$		0			0
$635$	12.7811	+	39.3361i	0.507202	+	1.56101i
$636$		0			0
$637$	−1.14666	−	3.52907i	−0.0454325	−	0.139827i
$638$		0			0
$639$	−5.98785	+	4.35042i	−0.236876	+	0.172100i
$640$		0			0
$641$	5.89917	+	4.28600i	0.233003	+	0.169287i	0.698160	−	0.715941i	$-0.254002\pi$
$641$	5.89917	+	4.28600i	0.233003	+	0.169287i	−0.465157	+	0.885228i	$0.654002\pi$
$642$		0			0
$643$	−11.7679	+	36.2177i	−0.464079	+	1.42829i	0.396058	+	0.918225i	$0.370378\pi$
$643$	−11.7679	+	36.2177i	−0.464079	+	1.42829i	−0.860137	+	0.510063i	$0.829622\pi$
$644$		0			0
$645$	−4.16273	+	3.02440i	−0.163907	+	0.119086i
$646$		0			0
$647$	−0.939388			−0.0369311			−0.0184656	−	0.999829i	$-0.505878\pi$
$647$	−0.939388			−0.0369311			−0.0184656	+	0.999829i	$0.505878\pi$
$648$		0			0
$649$	9.47409	+	29.1582i	0.371891	+	1.14456i
$650$		0			0
$651$	8.61166	+	6.25674i	0.337518	+	0.245221i
$652$		0			0
$653$	−9.43003			−0.369026			−0.184513	−	0.982830i	$-0.559071\pi$
$653$	−9.43003			−0.369026			−0.184513	+	0.982830i	$0.559071\pi$
$654$		0			0
$655$	52.9861			2.07034
$656$		0			0
$657$	−10.1036			−0.394180
$658$		0			0
$659$	−14.8754			−0.579463			−0.289732	−	0.957108i	$-0.593566\pi$
$659$	−14.8754			−0.579463			−0.289732	+	0.957108i	$0.593566\pi$
$660$		0			0
$661$	−11.7603	−	8.54432i	−0.457421	−	0.332336i	0.335098	−	0.942183i	$-0.391231\pi$
$661$	−11.7603	−	8.54432i	−0.457421	−	0.332336i	−0.792519	+	0.609848i	$0.791231\pi$
$662$		0			0
$663$	−1.04904	−	3.22862i	−0.0407415	−	0.125389i
$664$		0			0
$665$	−10.0398			−0.389327
$666$		0			0
$667$	0.0169974	−	0.0123494i	0.000658144	−	0.000478169i
$668$		0			0
$669$	2.37384	−	7.30592i	0.0917778	−	0.282463i
$670$		0			0
$671$	13.0247	+	9.46302i	0.502814	+	0.365316i
$672$		0			0
$673$	11.3760	−	8.26513i	0.438511	−	0.318597i	−0.346532	−	0.938038i	$-0.612641\pi$
$673$	11.3760	−	8.26513i	0.438511	−	0.318597i	0.785043	+	0.619441i	$0.212641\pi$
$674$		0			0
$675$	−9.60318	−	29.5555i	−0.369627	−	1.13759i
$676$		0			0
$677$	−12.5941	−	38.7608i	−0.484032	−	1.48970i	−0.833378	−	0.552703i	$-0.813596\pi$
$677$	−12.5941	−	38.7608i	−0.484032	−	1.48970i	0.349346	−	0.936994i	$-0.386404\pi$
$678$		0			0
$679$	−1.08602	+	3.34243i	−0.0416776	+	0.128271i
$680$		0			0
$681$	−7.03371	−	21.6475i	−0.269532	−	0.829536i
$682$		0			0
$683$	8.37685			0.320531			0.160266	−	0.987074i	$-0.448765\pi$
$683$	8.37685			0.320531			0.160266	+	0.987074i	$0.448765\pi$
$684$		0			0
$685$	28.7891	+	20.9165i	1.09997	+	0.799177i
$686$		0			0
$687$	−16.5778	+	12.0445i	−0.632483	+	0.459526i
$688$		0			0
$689$	1.41646	−	1.02912i	0.0539627	−	0.0392062i
$690$		0			0
$691$	−14.8112	+	45.5841i	−0.563443	+	1.73410i	0.109088	+	0.994032i	$0.465207\pi$
$691$	−14.8112	+	45.5841i	−0.563443	+	1.73410i	−0.672532	+	0.740068i	$0.734793\pi$
$692$		0			0
$693$	2.56896	+	1.86646i	0.0975869	+	0.0709010i
$694$		0			0
$695$	−2.22365	+	6.84370i	−0.0843479	+	0.259596i
$696$		0			0
$697$	−4.23607	+	0.896186i	−0.160452	+	0.0339455i
$698$		0			0
$699$	−2.56152	+	7.88354i	−0.0968855	+	0.298183i
$700$		0			0
$701$	0.365774	+	0.265750i	0.0138151	+	0.0100373i	0.594671	−	0.803969i	$-0.297282\pi$
$701$	0.365774	+	0.265750i	0.0138151	+	0.0100373i	−0.580856	+	0.814006i	$0.697282\pi$
$702$		0			0
$703$	−0.827753	+	2.54756i	−0.0312193	+	0.0960831i
$704$		0			0
$705$	30.8008	−	22.3781i	1.16002	−	0.842807i
$706$		0			0
$707$	−7.68087	+	5.58048i	−0.288869	+	0.209875i
$708$		0			0
$709$	9.43442	+	6.85450i	0.354317	+	0.257426i	0.750678	−	0.660668i	$-0.229727\pi$
$709$	9.43442	+	6.85450i	0.354317	+	0.257426i	−0.396361	+	0.918095i	$0.629727\pi$
$710$		0			0
$711$	−1.41056			−0.0529002
$712$		0			0
$713$	4.65759	+	14.3346i	0.174428	+	0.536834i
$714$		0			0
$715$	10.0924	−	31.0613i	0.377435	−	1.16163i
$716$		0			0
$717$	−6.11710	−	18.8265i	−0.228447	−	0.703088i
$718$		0			0
$719$	8.31505	+	25.5911i	0.310099	+	0.954387i	0.977725	+	0.209890i	$0.0673106\pi$
$719$	8.31505	+	25.5911i	0.310099	+	0.954387i	−0.667626	+	0.744497i	$0.732689\pi$
$720$		0			0
$721$	5.42957	−	3.94481i	0.202208	−	0.146913i
$722$		0			0
$723$	15.0148	+	10.9089i	0.558406	+	0.405706i
$724$		0			0
$725$	0.0186700	−	0.0574604i	0.000693387	−	0.00213403i
$726$		0			0
$727$	−25.7676	+	18.7212i	−0.955666	+	0.694332i	−0.952140	−	0.305662i	$-0.901122\pi$
$727$	−25.7676	+	18.7212i	−0.955666	+	0.694332i	−0.00352589	+	0.999994i	$0.501122\pi$
$728$		0			0
$729$	27.7191			1.02663
$730$		0			0
$731$	−0.245146	−	0.754481i	−0.00906705	−	0.0279055i
$732$		0			0
$733$	−41.8122	−	30.3783i	−1.54437	−	1.12205i	−0.947521	−	0.319694i	$-0.896420\pi$
$733$	−41.8122	−	30.3783i	−1.54437	−	1.12205i	−0.596847	−	0.802355i	$-0.703580\pi$
$734$		0			0
$735$	−4.38589			−0.161776
$736$		0			0
$737$	18.1064			0.666957
$738$		0			0
$739$	−42.4220			−1.56052			−0.780260	−	0.625456i	$-0.784913\pi$
$739$	−42.4220			−1.56052			−0.780260	+	0.625456i	$0.784913\pi$
$740$		0			0
$741$	−15.5482			−0.571176
$742$		0			0
$743$	16.7808	+	12.1919i	0.615626	+	0.447279i	0.851391	−	0.524532i	$-0.175760\pi$
$743$	16.7808	+	12.1919i	0.615626	+	0.447279i	−0.235765	+	0.971810i	$0.575760\pi$
$744$		0			0
$745$	−4.05383	−	12.4764i	−0.148521	−	0.457100i
$746$		0			0
$747$	−7.08081			−0.259073
$748$		0			0
$749$	−2.80154	+	2.03543i	−0.102366	+	0.0743732i
$750$		0			0
$751$	12.8778	−	39.6336i	0.469916	−	1.44625i	−0.382778	−	0.923840i	$-0.625032\pi$
$751$	12.8778	−	39.6336i	0.469916	−	1.44625i	0.852693	−	0.522412i	$-0.174968\pi$
$752$		0			0
$753$	−18.5187	−	13.4546i	−0.674860	−	0.490315i
$754$		0			0
$755$	−31.3591	+	22.7837i	−1.14127	+	0.829183i
$756$		0			0
$757$	7.23498	+	22.2670i	0.262960	+	0.809307i	0.992156	+	0.125003i	$0.0398940\pi$
$757$	7.23498	+	22.2670i	0.262960	+	0.809307i	−0.729197	+	0.684304i	$0.760106\pi$
$758$		0			0
$759$	−2.17455	−	6.69259i	−0.0789313	−	0.242926i
$760$		0			0
$761$	11.9445	−	36.7615i	0.432989	−	1.33260i	−0.462144	−	0.886805i	$-0.652920\pi$
$761$	11.9445	−	36.7615i	0.432989	−	1.33260i	0.895133	−	0.445798i	$-0.147080\pi$
$762$		0			0
$763$	1.67338	+	5.15015i	0.0605806	+	0.186448i
$764$		0			0
$765$	2.56376			0.0926928
$766$		0			0
$767$	33.8989	+	24.6290i	1.22402	+	0.889301i
$768$		0			0
$769$	23.3047	−	16.9318i	0.840388	−	0.610578i	−0.0820908	−	0.996625i	$-0.526160\pi$
$769$	23.3047	−	16.9318i	0.840388	−	0.610578i	0.922479	+	0.386047i	$0.126160\pi$
$770$		0			0
$771$	−28.0519	+	20.3809i	−1.01027	+	0.734001i
$772$		0			0
$773$	12.8006	−	39.3963i	0.460407	−	1.41699i	−0.404261	−	0.914644i	$-0.632471\pi$
$773$	12.8006	−	39.3963i	0.460407	−	1.41699i	0.864668	−	0.502344i	$-0.167529\pi$
$774$		0			0
$775$	35.0649	+	25.4762i	1.25957	+	0.915131i
$776$		0			0
$777$	−0.361604	+	1.11290i	−0.0129725	+	0.0399252i
$778$		0			0
$779$	−2.09166	+	19.7201i	−0.0749417	+	0.706546i
$780$		0			0
$781$	−5.30954	+	16.3411i	−0.189990	+	0.584730i
$782$		0			0
$783$	0.0500523	+	0.0363651i	0.00178872	+	0.00129958i
$784$		0			0
$785$	9.78581	−	30.1176i	0.349270	−	1.07494i
$786$		0			0
$787$	−7.97195	+	5.79196i	−0.284169	+	0.206461i	−0.720734	−	0.693212i	$-0.756195\pi$
$787$	−7.97195	+	5.79196i	−0.284169	+	0.206461i	0.436565	+	0.899673i	$0.356195\pi$
$788$		0			0
$789$	23.1917	−	16.8497i	0.825645	−	0.599866i
$790$		0			0
$791$	−6.69198	−	4.86201i	−0.237939	−	0.172873i
$792$		0			0
$793$	22.0031			0.781352
$794$		0			0
$795$	−0.639487	−	1.96814i	−0.0226803	−	0.0698027i
$796$		0			0
$797$	6.61540	−	20.3601i	0.234329	−	0.721192i	−0.762880	−	0.646540i	$-0.776215\pi$
$797$	6.61540	−	20.3601i	0.234329	−	0.721192i	0.997210	−	0.0746518i	$-0.0237845\pi$
$798$		0			0
$799$	1.81388	+	5.58254i	0.0641704	+	0.197496i
$800$		0			0
$801$	−3.40549	−	10.4810i	−0.120327	−	0.370329i
$802$		0			0
$803$	−18.9756	+	13.7866i	−0.669636	+	0.486519i
$804$		0			0
$805$	−5.02417	−	3.65027i	−0.177079	−	0.128655i
$806$		0			0
$807$	2.17335	−	6.68887i	0.0765054	−	0.235459i
$808$		0			0
$809$	22.2444	−	16.1615i	0.782070	−	0.568207i	−0.123529	−	0.992341i	$-0.539421\pi$
$809$	22.2444	−	16.1615i	0.782070	−	0.568207i	0.905600	+	0.424134i	$0.139421\pi$
$810$		0			0
$811$	−16.7049			−0.586588			−0.293294	−	0.956022i	$-0.594751\pi$
$811$	−16.7049			−0.586588			−0.293294	+	0.956022i	$0.594751\pi$
$812$		0			0
$813$	−2.05488	−	6.32428i	−0.0720679	−	0.221802i
$814$		0			0
$815$	−3.31472	−	2.40829i	−0.116110	−	0.0843586i
$816$		0			0
$817$	−3.63337			−0.127116
$818$		0			0
$819$	4.33983			0.151646
$820$		0			0
$821$	−10.9389			−0.381771			−0.190885	−	0.981612i	$-0.561136\pi$
$821$	−10.9389			−0.381771			−0.190885	+	0.981612i	$0.561136\pi$
$822$		0			0
$823$	1.87979			0.0655253			0.0327626	−	0.999463i	$-0.489569\pi$
$823$	1.87979			0.0655253			0.0327626	+	0.999463i	$0.489569\pi$
$824$		0			0
$825$	−16.3713	−	11.8944i	−0.569974	−	0.414110i
$826$		0			0
$827$	2.71008	+	8.34077i	0.0942387	+	0.290037i	0.987055	−	0.160385i	$-0.0512736\pi$
$827$	2.71008	+	8.34077i	0.0942387	+	0.290037i	−0.892816	+	0.450422i	$0.851274\pi$
$828$		0			0
$829$	−35.6266			−1.23736			−0.618681	−	0.785642i	$-0.712333\pi$
$829$	−35.6266			−1.23736			−0.618681	+	0.785642i	$0.712333\pi$
$830$		0			0
$831$	4.54978	−	3.30561i	0.157830	−	0.114670i
$832$		0			0
$833$	0.208959	−	0.643110i	0.00724000	−	0.0222824i
$834$		0			0
$835$	28.7281	+	20.8722i	0.994176	+	0.722311i
$836$		0			0
$837$	−35.9068	+	26.0878i	−1.24112	+	0.901726i
$838$		0			0
$839$	−2.14923	−	6.61465i	−0.0741997	−	0.228363i	0.907078	−	0.420963i	$-0.138308\pi$
$839$	−2.14923	−	6.61465i	−0.0741997	−	0.228363i	−0.981277	+	0.192600i	$0.938308\pi$
$840$		0			0
$841$	−8.96146	−	27.5805i	−0.309016	−	0.951053i
$842$		0			0
$843$	2.41598	−	7.43561i	0.0832106	−	0.256096i
$844$		0			0
$845$	−0.770508	−	2.37138i	−0.0265063	−	0.0815780i
$846$		0			0
$847$	−3.62839			−0.124673
$848$		0			0
$849$	5.19398	+	3.77365i	0.178257	+	0.129511i
$850$		0			0
$851$	−1.34047	+	0.973909i	−0.0459508	+	0.0333852i
$852$		0			0
$853$	−28.8063	+	20.9290i	−0.986307	+	0.716594i	−0.959109	−	0.283036i	$-0.908658\pi$
$853$	−28.8063	+	20.9290i	−0.986307	+	0.716594i	−0.0271980	+	0.999630i	$0.508658\pi$
$854$		0			0
$855$	3.62849	−	11.1674i	0.124092	−	0.381916i
$856$		0			0
$857$	41.1549	+	29.9008i	1.40583	+	1.02139i	0.993913	+	0.110169i	$0.0351391\pi$
$857$	41.1549	+	29.9008i	1.40583	+	1.02139i	0.411913	+	0.911223i	$0.364861\pi$
$858$		0			0
$859$	3.95740	−	12.1796i	0.135025	−	0.415563i	−0.860569	−	0.509333i	$-0.829892\pi$
$859$	3.95740	−	12.1796i	0.135025	−	0.415563i	0.995594	+	0.0937704i	$0.0298920\pi$
$860$		0			0
$861$	−0.913744	+	8.61472i	−0.0311403	+	0.293589i
$862$		0			0
$863$	−2.87479	+	8.84769i	−0.0978590	+	0.301179i	−0.987988	−	0.154529i	$-0.950614\pi$
$863$	−2.87479	+	8.84769i	−0.0978590	+	0.301179i	0.890129	+	0.455708i	$0.150614\pi$
$864$		0			0
$865$	−42.8489	−	31.1316i	−1.45691	−	1.05851i
$866$		0			0
$867$	−6.91622	+	21.2859i	−0.234887	+	0.722908i
$868$		0			0
$869$	−2.64918	+	1.92474i	−0.0898672	+	0.0652924i
$870$		0			0
$871$	20.0199	−	14.5453i	0.678348	−	0.492849i
$872$		0			0
$873$	−3.32531	−	2.41598i	−0.112545	−	0.0817686i
$874$		0			0
$875$	−1.64971			−0.0557704
$876$		0			0
$877$	−17.6368	−	54.2806i	−0.595553	−	1.83292i	−0.551952	−	0.833876i	$-0.686117\pi$
$877$	−17.6368	−	54.2806i	−0.595553	−	1.83292i	−0.0436015	−	0.999049i	$-0.513883\pi$
$878$		0			0
$879$	5.10644	−	15.7160i	0.172236	−	0.530088i
$880$		0			0
$881$	−10.7315	−	33.0283i	−0.361554	−	1.11275i	−0.952111	−	0.305754i	$-0.901092\pi$
$881$	−10.7315	−	33.0283i	−0.361554	−	1.11275i	0.590556	−	0.806996i	$-0.298908\pi$
$882$		0			0
$883$	−0.732465	−	2.25430i	−0.0246494	−	0.0758631i	0.937975	−	0.346703i	$-0.112699\pi$
$883$	−0.732465	−	2.25430i	−0.0246494	−	0.0758631i	−0.962625	+	0.270840i	$0.912699\pi$
$884$		0			0
$885$	40.0672	−	29.1105i	1.34684	−	0.978539i
$886$		0			0
$887$	−12.7803	−	9.28544i	−0.429121	−	0.311775i	0.352176	−	0.935934i	$-0.385442\pi$
$887$	−12.7803	−	9.28544i	−0.429121	−	0.311775i	−0.781297	+	0.624159i	$0.785442\pi$
$888$		0			0
$889$	−3.94266	+	12.1343i	−0.132232	+	0.406970i
$890$		0			0
$891$	9.05742	−	6.58060i	0.303435	−	0.220458i
$892$		0			0
$893$	26.8839			0.899637
$894$		0			0
$895$	−14.9838	−	46.1155i	−0.500854	−	1.54147i
$896$		0			0
$897$	−7.78069	−	5.65300i	−0.259790	−	0.188748i
$898$		0			0
$899$	−0.0862876			−0.00287785
$900$		0			0
$901$	0.319059			0.0106294
$902$		0			0
$903$	−1.58724			−0.0528200
$904$		0			0
$905$	−57.5436			−1.91282
$906$		0			0
$907$	−12.3122	−	8.94530i	−0.408818	−	0.297024i	0.364305	−	0.931280i	$-0.381307\pi$
$907$	−12.3122	−	8.94530i	−0.408818	−	0.297024i	−0.773123	+	0.634256i	$0.781307\pi$
$908$		0			0
$909$	−3.43126	−	10.5603i	−0.113808	−	0.350265i
$910$		0			0
$911$	−14.7435			−0.488474			−0.244237	−	0.969716i	$-0.578538\pi$
$911$	−14.7435			−0.488474			−0.244237	+	0.969716i	$0.578538\pi$
$912$		0			0
$913$	−13.2985	+	9.66193i	−0.440116	+	0.319763i
$914$		0			0
$915$	8.03655	−	24.7340i	0.265680	−	0.817679i
$916$		0			0
$917$	13.2233	+	9.60732i	0.436673	+	0.317262i
$918$		0			0
$919$	16.4984	−	11.9868i	0.544232	−	0.395408i	−0.281422	−	0.959584i	$-0.590806\pi$
$919$	16.4984	−	11.9868i	0.544232	−	0.395408i	0.825654	+	0.564176i	$0.190806\pi$
$920$		0			0
$921$	−10.4045	−	32.0218i	−0.342840	−	1.05515i
$922$		0			0
$923$	7.25654	+	22.3333i	0.238852	+	0.735111i
$924$		0			0
$925$	−1.47238	+	4.53151i	−0.0484114	+	0.148995i
$926$		0			0
$927$	2.42555	+	7.46506i	0.0796654	+	0.245185i
$928$		0			0
$929$	−13.2212			−0.433774			−0.216887	−	0.976197i	$-0.569590\pi$
$929$	−13.2212			−0.433774			−0.216887	+	0.976197i	$0.569590\pi$
$930$		0			0
$931$	−2.50556	−	1.82039i	−0.0821163	−	0.0596610i
$932$		0			0
$933$	26.0514	−	18.9275i	0.852885	−	0.619657i
$934$		0			0
$935$	4.81500	−	3.49830i	0.157467	−	0.114407i
$936$		0			0
$937$	8.93647	−	27.5036i	0.291942	−	0.898505i	−0.692290	−	0.721620i	$-0.743398\pi$
$937$	8.93647	−	27.5036i	0.291942	−	0.898505i	0.984232	−	0.176885i	$-0.0566021\pi$
$938$		0			0
$939$	−21.0677	−	15.3066i	−0.687518	−	0.499511i
$940$		0			0
$941$	16.2197	−	49.9191i	0.528747	−	1.62732i	−0.228039	−	0.973652i	$-0.573231\pi$
$941$	16.2197	−	49.9191i	0.528747	−	1.62732i	0.756785	−	0.653663i	$-0.226769\pi$
$942$		0			0
$943$	−8.21656	+	9.10794i	−0.267568	+	0.296595i
$944$		0			0
$945$	5.65105	−	17.3921i	0.183829	−	0.565766i
$946$		0			0
$947$	−4.17426	−	3.03278i	−0.135645	−	0.0985520i	0.517894	−	0.855445i	$-0.326716\pi$
$947$	−4.17426	−	3.03278i	−0.135645	−	0.0985520i	−0.653539	+	0.756893i	$0.726716\pi$
$948$		0			0
$949$	−9.90590	+	30.4872i	−0.321559	+	0.989657i
$950$		0			0
$951$	−25.9085	+	18.8237i	−0.840142	+	0.610399i
$952$		0			0
$953$	3.15537	−	2.29251i	0.102213	−	0.0742618i	−0.535505	−	0.844532i	$-0.679879\pi$
$953$	3.15537	−	2.29251i	0.102213	−	0.0742618i	0.637718	+	0.770270i	$0.279879\pi$
$954$		0			0
$955$	−31.5230	−	22.9028i	−1.02006	−	0.741116i
$956$		0			0
$957$	0.0402863			0.00130227
$958$		0			0
$959$	3.39214	+	10.4399i	0.109538	+	0.337123i
$960$		0			0
$961$	9.54910	−	29.3891i	0.308035	−	0.948035i
$962$		0			0
$963$	−1.25153	−	3.85180i	−0.0403299	−	0.124123i
$964$		0			0
$965$	−14.8757	−	45.7826i	−0.478865	−	1.47379i
$966$		0			0
$967$	−22.6945	+	16.4885i	−0.729805	+	0.530235i	−0.889502	−	0.456932i	$-0.848948\pi$
$967$	−22.6945	+	16.4885i	−0.729805	+	0.530235i	0.159696	+	0.987166i	$0.448948\pi$
$968$		0			0
$969$	−2.29225	−	1.66542i	−0.0736376	−	0.0535009i
$970$		0			0
$971$	−9.88332	+	30.4177i	−0.317171	+	0.976152i	0.657681	+	0.753297i	$0.271538\pi$
$971$	−9.88332	+	30.4177i	−0.317171	+	0.976152i	−0.974852	+	0.222855i	$0.928462\pi$
$972$		0			0
$973$	−1.79582	+	1.30474i	−0.0575715	+	0.0418281i
$974$		0			0
$975$	−27.6565			−0.885717
$976$		0			0
$977$	−15.0307	−	46.2596i	−0.480873	−	1.47998i	−0.837870	−	0.545870i	$-0.816199\pi$
$977$	−15.0307	−	46.2596i	−0.480873	−	1.47998i	0.356997	−	0.934106i	$-0.383801\pi$
$978$		0			0
$979$	−20.6974	−	15.0376i	−0.661493	−	0.480603i
$980$		0			0
$981$	−6.33334			−0.202208
$982$		0			0
$983$	0.120014			0.00382786			0.00191393	−	0.999998i	$-0.499391\pi$
$983$	0.120014			0.00382786			0.00191393	+	0.999998i	$0.499391\pi$
$984$		0			0
$985$	60.5867			1.93045
$986$		0			0
$987$	11.7443			0.373824
$988$		0			0
$989$	−1.81823	−	1.32102i	−0.0578164	−	0.0420061i
$990$		0			0
$991$	1.47107	+	4.52748i	0.0467300	+	0.143820i	0.971699	−	0.236222i	$-0.0759094\pi$
$991$	1.47107	+	4.52748i	0.0467300	+	0.143820i	−0.924969	+	0.380042i	$0.875909\pi$
$992$		0			0
$993$	29.8081			0.945931
$994$		0			0
$995$	−49.0956	+	35.6700i	−1.55643	+	1.13082i
$996$		0			0
$997$	−12.9367	+	39.8151i	−0.409709	+	1.26096i	0.507189	+	0.861835i	$0.330685\pi$
$997$	−12.9367	+	39.8151i	−0.409709	+	1.26096i	−0.916898	+	0.399121i	$0.869315\pi$
$998$		0			0
$999$	−3.94728	−	2.86787i	−0.124886	−	0.0907352i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.n.d.57.5	✓	24
41.18	even	5	inner	1148.2.n.d.141.5	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.n.d.57.5	✓	24	1.1	even	1	trivial
1148.2.n.d.141.5	yes	24	41.18	even	5	inner

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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+1.35294 q^{3} +(2.62263 + 1.90545i) q^{5} +(0.309017 + 0.951057i) q^{7} -1.16955 q^{9} +O(q^{10})\)	\(q+1.35294 q^{3} +(2.62263 + 1.90545i) q^{5} +(0.309017 + 0.951057i) q^{7} -1.16955 q^{9} +(-2.19654 + 1.59588i) q^{11} +(-1.14666 + 3.52907i) q^{13} +(3.54826 + 2.57796i) q^{15} +(-0.547062 + 0.397464i) q^{17} +(0.957037 + 2.94546i) q^{19} +(0.418082 + 1.28672i) q^{21} +(-0.591984 + 1.82194i) q^{23} +(1.70234 + 5.23927i) q^{25} -5.64116 q^{27} +(-0.00887270 - 0.00644639i) q^{29} +(6.36515 - 4.62455i) q^{31} +(-2.97179 + 2.15913i) q^{33} +(-1.00175 + 3.08308i) q^{35} +(0.699729 + 0.508383i) q^{37} +(-1.55137 + 4.77462i) q^{39} +(5.84706 + 2.60996i) q^{41} +(-0.362532 + 1.11576i) q^{43} +(-3.06729 - 2.22852i) q^{45} +(2.68243 - 8.25568i) q^{47} +(-0.809017 + 0.587785i) q^{49} +(-0.740142 + 0.537745i) q^{51} +(-0.381724 - 0.277339i) q^{53} -8.80156 q^{55} +(1.29481 + 3.98503i) q^{57} +(3.48944 - 10.7394i) q^{59} +(-1.83237 - 5.63944i) q^{61} +(-0.361411 - 1.11231i) q^{63} +(-9.73173 + 7.07051i) q^{65} +(-5.39520 - 3.91984i) q^{67} +(-0.800920 + 2.46498i) q^{69} +(5.11978 - 3.71974i) q^{71} +8.63888 q^{73} +(2.30317 + 7.08842i) q^{75} +(-2.19654 - 1.59588i) q^{77} +1.20607 q^{79} -4.12350 q^{81} +6.05430 q^{83} -2.19208 q^{85} +(-0.0120042 - 0.00872158i) q^{87} +(2.91179 + 8.96157i) q^{89} -3.71068 q^{91} +(8.61166 - 6.25674i) q^{93} +(-3.10247 + 9.54841i) q^{95} +(2.84324 + 2.06573i) q^{97} +(2.56896 - 1.86646i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 10 q^{3} + 4 q^{5} - 6 q^{7} + 38 q^{9}+O(q^{10}) \) 24 * q - 10 * q^3 + 4 * q^5 - 6 * q^7 + 38 * q^9	\( 24 q - 10 q^{3} + 4 q^{5} - 6 q^{7} + 38 q^{9} + 11 q^{11} - 4 q^{13} + 10 q^{15} + 9 q^{17} - 23 q^{19} + 5 q^{21} + 28 q^{23} - 10 q^{25} - 76 q^{27} + 28 q^{29} - 18 q^{31} - 27 q^{33} - q^{35} - 29 q^{37} - 6 q^{39} + 65 q^{41} - 15 q^{43} - 20 q^{45} - 11 q^{47} - 6 q^{49} - 18 q^{51} + 8 q^{53} - 50 q^{55} + 8 q^{57} + 55 q^{59} - 10 q^{61} - 2 q^{63} - 11 q^{65} + 65 q^{67} - 2 q^{69} - 14 q^{71} + 48 q^{73} - 77 q^{75} + 11 q^{77} + 22 q^{79} + 80 q^{81} - 22 q^{83} - 78 q^{85} - 4 q^{87} + 16 q^{89} - 4 q^{91} - 60 q^{93} + 56 q^{95} + 15 q^{97} + 80 q^{99}+O(q^{100}) \) 24 * q - 10 * q^3 + 4 * q^5 - 6 * q^7 + 38 * q^9 + 11 * q^11 - 4 * q^13 + 10 * q^15 + 9 * q^17 - 23 * q^19 + 5 * q^21 + 28 * q^23 - 10 * q^25 - 76 * q^27 + 28 * q^29 - 18 * q^31 - 27 * q^33 - q^35 - 29 * q^37 - 6 * q^39 + 65 * q^41 - 15 * q^43 - 20 * q^45 - 11 * q^47 - 6 * q^49 - 18 * q^51 + 8 * q^53 - 50 * q^55 + 8 * q^57 + 55 * q^59 - 10 * q^61 - 2 * q^63 - 11 * q^65 + 65 * q^67 - 2 * q^69 - 14 * q^71 + 48 * q^73 - 77 * q^75 + 11 * q^77 + 22 * q^79 + 80 * q^81 - 22 * q^83 - 78 * q^85 - 4 * q^87 + 16 * q^89 - 4 * q^91 - 60 * q^93 + 56 * q^95 + 15 * q^97 + 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more