LMFDB - Embedded newform 1148.2.i.d.165.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(165,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("1148.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.i (of order $3$, degree $2$, 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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 14 x^{14} - 8 x^{13} + 136 x^{12} - 87 x^{11} + 706 x^{10} - 568 x^{9} + 2685 x^{8} + \cdots + 121 $ x^16 + 14x^14 - 8x^13 + 136x^12 - 87x^11 + 706x^10 - 568x^9 + 2685x^8 - 2100x^7 + 5529x^6 - 4919x^5 + 8145x^4 - 5182x^3 + 2775x^2 - 660x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			165.1
Root			$1.14440 - 1.98216i$ of defining polynomial
Character	$\chi$	$=$	1148.165
Dual form			1148.2.i.d.821.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.14440 + 1.98216i) q^{3} +(-0.175017 - 0.303139i) q^{5} +(-0.303923 + 2.62824i) q^{7} +(-1.11932 - 1.93871i) q^{9} +O(q^{10})$	\(q+(-1.14440 + 1.98216i) q^{3} +(-0.175017 - 0.303139i) q^{5} +(-0.303923 + 2.62824i) q^{7} +(-1.11932 - 1.93871i) q^{9} +(-1.55507 + 2.69346i) q^{11} -3.97253 q^{13} +0.801161 q^{15} +(1.35057 - 2.33925i) q^{17} +(0.341367 + 0.591264i) q^{19} +(-4.86179 - 3.61019i) q^{21} +(2.05756 + 3.56379i) q^{23} +(2.43874 - 4.22402i) q^{25} -1.74262 q^{27} -6.74476 q^{29} +(-0.232633 + 0.402933i) q^{31} +(-3.55926 - 6.16482i) q^{33} +(0.849913 - 0.367856i) q^{35} +(2.16883 + 3.75653i) q^{37} +(4.54618 - 7.87421i) q^{39} +1.00000 q^{41} -2.58476 q^{43} +(-0.391800 + 0.678617i) q^{45} +(-2.98366 - 5.16785i) q^{47} +(-6.81526 - 1.59756i) q^{49} +(3.09119 + 5.35409i) q^{51} +(-1.02277 + 1.77149i) q^{53} +1.08866 q^{55} -1.56264 q^{57} +(5.19494 - 8.99790i) q^{59} +(-1.43657 - 2.48821i) q^{61} +(5.43559 - 2.35261i) q^{63} +(0.695262 + 1.20423i) q^{65} +(1.57698 - 2.73142i) q^{67} -9.41870 q^{69} -3.23326 q^{71} +(0.299666 - 0.519036i) q^{73} +(5.58180 + 9.66796i) q^{75} +(-6.60644 - 4.90570i) q^{77} +(0.428075 + 0.741447i) q^{79} +(5.35221 - 9.27030i) q^{81} -12.9143 q^{83} -0.945491 q^{85} +(7.71873 - 13.3692i) q^{87} +(-7.01464 - 12.1497i) q^{89} +(1.20734 - 10.4408i) q^{91} +(-0.532452 - 0.922235i) q^{93} +(0.119490 - 0.206963i) q^{95} -3.40759 q^{97} +6.96247 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{9}+O(q^{10}) $ 16 * q - 4 * q^9	$ 16 q - 4 q^{9} + 8 q^{11} - 14 q^{13} - 2 q^{15} + q^{17} - 4 q^{19} + 13 q^{21} + 3 q^{23} + 4 q^{25} - 24 q^{27} - 8 q^{29} - 4 q^{31} - 23 q^{33} + 12 q^{35} + 31 q^{37} - 5 q^{39} + 16 q^{41} - 16 q^{43} - q^{45} - 24 q^{47} + 16 q^{49} + 23 q^{51} + q^{53} + 4 q^{55} - 30 q^{57} - 4 q^{59} + 4 q^{61} + 23 q^{63} + 24 q^{65} - 42 q^{69} + 16 q^{71} - 11 q^{73} + 15 q^{75} + 25 q^{77} - 14 q^{79} + 28 q^{81} - 84 q^{83} - 40 q^{85} - 25 q^{87} + 11 q^{89} + 7 q^{91} + 27 q^{93} + 15 q^{95} - 32 q^{97} - 16 q^{99}+O(q^{100}) $ 16 * q - 4 * q^9 + 8 * q^11 - 14 * q^13 - 2 * q^15 + q^17 - 4 * q^19 + 13 * q^21 + 3 * q^23 + 4 * q^25 - 24 * q^27 - 8 * q^29 - 4 * q^31 - 23 * q^33 + 12 * q^35 + 31 * q^37 - 5 * q^39 + 16 * q^41 - 16 * q^43 - q^45 - 24 * q^47 + 16 * q^49 + 23 * q^51 + q^53 + 4 * q^55 - 30 * q^57 - 4 * q^59 + 4 * q^61 + 23 * q^63 + 24 * q^65 - 42 * q^69 + 16 * q^71 - 11 * q^73 + 15 * q^75 + 25 * q^77 - 14 * q^79 + 28 * q^81 - 84 * q^83 - 40 * q^85 - 25 * q^87 + 11 * q^89 + 7 * q^91 + 27 * q^93 + 15 * q^95 - 32 * q^97 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$493$	$575$	$785$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.14440	+	1.98216i	−0.660721	+	1.14440i	0.319705	+	0.947517i	$0.396416\pi$
$3$	−1.14440	+	1.98216i	−0.660721	+	1.14440i	−0.980426	+	0.196886i	$0.936917\pi$
$4$		0			0
$5$	−0.175017	−	0.303139i	−0.0782701	−	0.135568i	0.824234	−	0.566250i	$-0.191606\pi$
$5$	−0.175017	−	0.303139i	−0.0782701	−	0.135568i	−0.902504	+	0.430682i	$0.858273\pi$
$6$		0			0
$7$	−0.303923	+	2.62824i	−0.114872	+	0.993380i
$7$	−0.303923	+	2.62824i	−0.114872	+	0.993380i
$8$		0			0
$9$	−1.11932	−	1.93871i	−0.373106	−	0.646238i
$10$		0			0
$11$	−1.55507	+	2.69346i	−0.468872	+	0.812110i	−0.999367	−	0.0355783i	$-0.988673\pi$
$11$	−1.55507	+	2.69346i	−0.468872	+	0.812110i	0.530495	+	0.847688i	$0.322006\pi$
$12$		0			0
$13$	−3.97253			−1.10178			−0.550891	−	0.834577i	$-0.685712\pi$
$13$	−3.97253			−1.10178			−0.550891	+	0.834577i	$0.685712\pi$
$14$		0			0
$15$	0.801161			0.206859
$16$		0			0
$17$	1.35057	−	2.33925i	0.327561	−	0.567352i	−0.654466	−	0.756091i	$-0.727107\pi$
$17$	1.35057	−	2.33925i	0.327561	−	0.567352i	0.982027	+	0.188739i	$0.0604400\pi$
$18$		0			0
$19$	0.341367	+	0.591264i	0.0783149	+	0.135645i	0.902523	−	0.430642i	$-0.141713\pi$
$19$	0.341367	+	0.591264i	0.0783149	+	0.135645i	−0.824208	+	0.566287i	$0.808379\pi$
$20$		0			0
$21$	−4.86179	−	3.61019i	−1.06093	−	0.787808i
$22$		0			0
$23$	2.05756	+	3.56379i	0.429030	+	0.743102i	0.996787	−	0.0800941i	$-0.0255221\pi$
$23$	2.05756	+	3.56379i	0.429030	+	0.743102i	−0.567757	+	0.823196i	$0.692189\pi$
$24$		0			0
$25$	2.43874	−	4.22402i	0.487748	−	0.844804i
$26$		0			0
$27$	−1.74262			−0.335367
$28$		0			0
$29$	−6.74476			−1.25247			−0.626236	−	0.779634i	$-0.715405\pi$
$29$	−6.74476			−1.25247			−0.626236	+	0.779634i	$0.715405\pi$
$30$		0			0
$31$	−0.232633	+	0.402933i	−0.0417822	+	0.0723688i	−0.886160	−	0.463379i	$-0.846637\pi$
$31$	−0.232633	+	0.402933i	−0.0417822	+	0.0723688i	0.844378	+	0.535748i	$0.179970\pi$
$32$		0			0
$33$	−3.55926	−	6.16482i	−0.619587	−	1.07316i
$34$		0			0
$35$	0.849913	−	0.367856i	0.143661	−	0.0621790i
$36$		0			0
$37$	2.16883	+	3.75653i	0.356554	+	0.617570i	0.987383	−	0.158352i	$-0.0506182\pi$
$37$	2.16883	+	3.75653i	0.356554	+	0.617570i	−0.630829	+	0.775922i	$0.717285\pi$
$38$		0			0
$39$	4.54618	−	7.87421i	0.727971	−	1.26088i
$40$		0			0
$41$	1.00000			0.156174
$41$	1.00000			0.156174
$42$		0			0
$43$	−2.58476			−0.394172			−0.197086	−	0.980386i	$-0.563148\pi$
$43$	−2.58476			−0.394172			−0.197086	+	0.980386i	$0.563148\pi$
$44$		0			0
$45$	−0.391800	+	0.678617i	−0.0584061	+	0.101162i
$46$		0			0
$47$	−2.98366	−	5.16785i	−0.435211	−	0.753808i	0.562101	−	0.827068i	$-0.309993\pi$
$47$	−2.98366	−	5.16785i	−0.435211	−	0.753808i	−0.997313	+	0.0732599i	$0.976660\pi$
$48$		0			0
$49$	−6.81526	−	1.59756i	−0.973609	−	0.228223i
$50$		0			0
$51$	3.09119	+	5.35409i	0.432853	+	0.749723i
$52$		0			0
$53$	−1.02277	+	1.77149i	−0.140489	+	0.243333i	−0.927681	−	0.373374i	$-0.878201\pi$
$53$	−1.02277	+	1.77149i	−0.140489	+	0.243333i	0.787192	+	0.616708i	$0.211534\pi$
$54$		0			0
$55$	1.08866			0.146795
$56$		0			0
$57$	−1.56264			−0.206977
$58$		0			0
$59$	5.19494	−	8.99790i	0.676324	−	1.17143i	−0.299756	−	0.954016i	$-0.596905\pi$
$59$	5.19494	−	8.99790i	0.676324	−	1.17143i	0.976080	−	0.217411i	$-0.0697613\pi$
$60$		0			0
$61$	−1.43657	−	2.48821i	−0.183934	−	0.318583i	0.759283	−	0.650761i	$-0.225550\pi$
$61$	−1.43657	−	2.48821i	−0.183934	−	0.318583i	−0.943217	+	0.332178i	$0.892217\pi$
$62$		0			0
$63$	5.43559	−	2.35261i	0.684820	−	0.296401i
$64$		0			0
$65$	0.695262	+	1.20423i	0.0862366	+	0.149366i
$66$		0			0
$67$	1.57698	−	2.73142i	0.192659	−	0.333696i	−0.753471	−	0.657481i	$-0.771622\pi$
$67$	1.57698	−	2.73142i	0.192659	−	0.333696i	0.946131	+	0.323785i	$0.104955\pi$
$68$		0			0
$69$	−9.41870			−1.13388
$70$		0			0
$71$	−3.23326			−0.383717			−0.191859	−	0.981423i	$-0.561452\pi$
$71$	−3.23326			−0.383717			−0.191859	+	0.981423i	$0.561452\pi$
$72$		0			0
$73$	0.299666	−	0.519036i	0.0350732	−	0.0607486i	−0.847956	−	0.530067i	$-0.822167\pi$
$73$	0.299666	−	0.519036i	0.0350732	−	0.0607486i	0.883029	+	0.469318i	$0.155500\pi$
$74$		0			0
$75$	5.58180	+	9.66796i	0.644531	+	1.11636i
$76$		0			0
$77$	−6.60644	−	4.90570i	−0.752873	−	0.559057i
$78$		0			0
$79$	0.428075	+	0.741447i	0.0481622	+	0.0834194i	0.889101	−	0.457710i	$-0.151330\pi$
$79$	0.428075	+	0.741447i	0.0481622	+	0.0834194i	−0.840939	+	0.541129i	$0.817997\pi$
$80$		0			0
$81$	5.35221	−	9.27030i	0.594690	−	1.03003i
$82$		0			0
$83$	−12.9143			−1.41753			−0.708764	−	0.705445i	$-0.750747\pi$
$83$	−12.9143			−1.41753			−0.708764	+	0.705445i	$0.750747\pi$
$84$		0			0
$85$	−0.945491			−0.102553
$86$		0			0
$87$	7.71873	−	13.3692i	0.827535	−	1.43333i
$88$		0			0
$89$	−7.01464	−	12.1497i	−0.743551	−	1.28787i	−0.950869	−	0.309594i	$-0.899807\pi$
$89$	−7.01464	−	12.1497i	−0.743551	−	1.28787i	0.207318	−	0.978274i	$-0.433526\pi$
$90$		0			0
$91$	1.20734	−	10.4408i	0.126564	−	1.09449i
$92$		0			0
$93$	−0.532452	−	0.922235i	−0.0552128	−	0.0956313i
$94$		0			0
$95$	0.119490	−	0.206963i	0.0122594	−	0.0212339i
$96$		0			0
$97$	−3.40759			−0.345988			−0.172994	−	0.984923i	$-0.555344\pi$
$97$	−3.40759			−0.345988			−0.172994	+	0.984923i	$0.555344\pi$
$98$		0			0
$99$	6.96247			0.699755
$100$		0			0
$101$	4.45009	−	7.70778i	0.442801	−	0.766953i	−0.555096	−	0.831787i	$-0.687318\pi$
$101$	4.45009	−	7.70778i	0.442801	−	0.766953i	0.997896	+	0.0648336i	$0.0206517\pi$
$102$		0			0
$103$	2.32614	+	4.02899i	0.229201	+	0.396988i	0.957572	−	0.288196i	$-0.0930553\pi$
$103$	2.32614	+	4.02899i	0.229201	+	0.396988i	−0.728370	+	0.685184i	$0.759722\pi$
$104$		0			0
$105$	−0.243491	+	2.10564i	−0.0237623	+	0.205490i
$106$		0			0
$107$	2.69478	+	4.66750i	0.260514	+	0.451224i	0.966379	−	0.257123i	$-0.0827746\pi$
$107$	2.69478	+	4.66750i	0.260514	+	0.451224i	−0.705864	+	0.708347i	$0.749441\pi$
$108$		0			0
$109$	−3.60295	+	6.24048i	−0.345100	+	0.597730i	−0.985372	−	0.170418i	$-0.945488\pi$
$109$	−3.60295	+	6.24048i	−0.345100	+	0.597730i	0.640272	+	0.768148i	$0.278822\pi$
$110$		0			0
$111$	−9.92808			−0.942332
$112$		0			0
$113$	−4.45820			−0.419392			−0.209696	−	0.977767i	$-0.567247\pi$
$113$	−4.45820			−0.419392			−0.209696	+	0.977767i	$0.567247\pi$
$114$		0			0
$115$	0.720216	−	1.24745i	0.0671605	−	0.116325i
$116$		0			0
$117$	4.44652	+	7.70161i	0.411081	+	0.712014i
$118$		0			0
$119$	5.73764	+	4.26056i	0.525969	+	0.390565i
$120$		0			0
$121$	0.663505	+	1.14922i	0.0603187	+	0.104475i
$122$		0			0
$123$	−1.14440	+	1.98216i	−0.103187	+	0.178726i
$124$		0			0
$125$	−3.45746			−0.309244
$126$		0			0
$127$	14.3286			1.27146			0.635730	−	0.771912i	$-0.280699\pi$
$127$	14.3286			1.27146			0.635730	+	0.771912i	$0.280699\pi$
$128$		0			0
$129$	2.95801	−	5.12342i	0.260438	−	0.451092i
$130$		0			0
$131$	−0.273936	−	0.474472i	−0.0239339	−	0.0414548i	0.853810	−	0.520584i	$-0.174286\pi$
$131$	−0.273936	−	0.474472i	−0.0239339	−	0.0414548i	−0.877744	+	0.479129i	$0.840952\pi$
$132$		0			0
$133$	−1.65773	+	0.717493i	−0.143744	+	0.0622146i
$134$		0			0
$135$	0.304988	+	0.528255i	0.0262492	+	0.0454650i
$136$		0			0
$137$	−5.19445	+	8.99705i	−0.443792	+	0.768670i	−0.997967	−	0.0637300i	$-0.979700\pi$
$137$	−5.19445	+	8.99705i	−0.443792	+	0.768670i	0.554175	+	0.832400i	$0.313034\pi$
$138$		0			0
$139$	−16.4437			−1.39474			−0.697368	−	0.716713i	$-0.745646\pi$
$139$	−16.4437			−1.39474			−0.697368	+	0.716713i	$0.745646\pi$
$140$		0			0
$141$	13.6580			1.15021
$142$		0			0
$143$	6.17757	−	10.6999i	0.516595	−	0.894768i
$144$		0			0
$145$	1.18045	+	2.04460i	0.0980311	+	0.169795i
$146$		0			0
$147$	10.9660	−	11.6807i	0.904464	−	0.963409i
$148$		0			0
$149$	1.50883	+	2.61338i	0.123608	+	0.214096i	0.921188	−	0.389117i	$-0.127220\pi$
$149$	1.50883	+	2.61338i	0.123608	+	0.214096i	−0.797580	+	0.603214i	$0.793887\pi$
$150$		0			0
$151$	−6.36396	+	11.0227i	−0.517892	+	0.897015i	0.481892	+	0.876231i	$0.339950\pi$
$151$	−6.36396	+	11.0227i	−0.517892	+	0.897015i	−0.999784	+	0.0207845i	$0.993384\pi$
$152$		0			0
$153$	−6.04686			−0.488859
$154$		0			0
$155$	0.162859			0.0130812
$156$		0			0
$157$	−12.1466	+	21.0386i	−0.969406	+	1.67906i	−0.272126	+	0.962262i	$0.587727\pi$
$157$	−12.1466	+	21.0386i	−0.969406	+	1.67906i	−0.697280	+	0.716799i	$0.745606\pi$
$158$		0			0
$159$	−2.34093	−	4.05461i	−0.185648	−	0.321551i
$160$		0			0
$161$	−9.99183	+	4.32463i	−0.787466	+	0.340828i
$162$		0			0
$163$	8.54021	+	14.7921i	0.668921	+	1.15861i	0.978206	+	0.207636i	$0.0665769\pi$
$163$	8.54021	+	14.7921i	0.668921	+	1.15861i	−0.309285	+	0.950969i	$0.600090\pi$
$164$		0			0
$165$	−1.24586	+	2.15790i	−0.0969903	+	0.167992i
$166$		0			0
$167$	11.3763			0.880323			0.440162	−	0.897919i	$-0.354921\pi$
$167$	11.3763			0.880323			0.440162	+	0.897919i	$0.354921\pi$
$168$		0			0
$169$	2.78101			0.213924
$170$		0			0
$171$	0.764195	−	1.32362i	0.0584395	−	0.101220i
$172$		0			0
$173$	−0.884576	−	1.53213i	−0.0672531	−	0.116486i	0.830438	−	0.557111i	$-0.188090\pi$
$173$	−0.884576	−	1.53213i	−0.0672531	−	0.116486i	−0.897691	+	0.440625i	$0.854757\pi$
$174$		0			0
$175$	10.3605	+	7.69336i	0.783183	+	0.581563i
$176$		0			0
$177$	11.8902	+	20.5945i	0.893723	+	1.54797i
$178$		0			0
$179$	3.63816	−	6.30147i	0.271929	−	0.470994i	−0.697427	−	0.716656i	$-0.745672\pi$
$179$	3.63816	−	6.30147i	0.271929	−	0.470994i	0.969356	+	0.245662i	$0.0790052\pi$
$180$		0			0
$181$	3.49738			0.259958			0.129979	−	0.991517i	$-0.458509\pi$
$181$	3.49738			0.259958			0.129979	+	0.991517i	$0.458509\pi$
$182$		0			0
$183$	6.57606			0.486116
$184$		0			0
$185$	0.759167	−	1.31492i	0.0558151	−	0.0966745i
$186$		0			0
$187$	4.20046	+	7.27541i	0.307168	+	0.532031i
$188$		0			0
$189$	0.529622	−	4.58001i	0.0385243	−	0.333147i
$190$		0			0
$191$	0.447482	+	0.775061i	0.0323786	+	0.0560815i	0.881761	−	0.471697i	$-0.156358\pi$
$191$	0.447482	+	0.775061i	0.0323786	+	0.0560815i	−0.849382	+	0.527779i	$0.823025\pi$
$192$		0			0
$193$	−6.27271	+	10.8646i	−0.451519	+	0.782054i	−0.998481	−	0.0551035i	$-0.982451\pi$
$193$	−6.27271	+	10.8646i	−0.451519	+	0.782054i	0.546961	+	0.837158i	$0.315784\pi$
$194$		0			0
$195$	−3.18264			−0.227914
$196$		0			0
$197$	9.91618			0.706499			0.353249	−	0.935529i	$-0.385077\pi$
$197$	9.91618			0.706499			0.353249	+	0.935529i	$0.385077\pi$
$198$		0			0
$199$	−10.9911	+	19.0371i	−0.779137	+	1.34951i	0.153302	+	0.988179i	$0.451009\pi$
$199$	−10.9911	+	19.0371i	−0.779137	+	1.34951i	−0.932440	+	0.361326i	$0.882324\pi$
$200$		0			0
$201$	3.60941	+	6.25168i	0.254588	+	0.440960i
$202$		0			0
$203$	2.04989	−	17.7268i	0.143874	−	1.24418i
$204$		0			0
$205$	−0.175017	−	0.303139i	−0.0122237	−	0.0211721i
$206$		0			0
$207$	4.60612	−	7.97803i	0.320147	−	0.554511i
$208$		0			0
$209$	−2.12340			−0.146878
$210$		0			0
$211$	−21.4721			−1.47820			−0.739101	−	0.673595i	$-0.764749\pi$
$211$	−21.4721			−1.47820			−0.739101	+	0.673595i	$0.764749\pi$
$212$		0			0
$213$	3.70015	−	6.40885i	0.253530	−	0.439127i
$214$		0			0
$215$	0.452378	+	0.783541i	0.0308519	+	0.0534371i
$216$		0			0
$217$	−0.988300	−	0.733876i	−0.0670902	−	0.0498187i
$218$		0			0
$219$	0.685876	+	1.18797i	0.0463472	+	0.0802758i
$220$		0			0
$221$	−5.36517	+	9.29275i	−0.360901	+	0.625098i
$222$		0			0
$223$	−7.30791			−0.489374			−0.244687	−	0.969602i	$-0.578685\pi$
$223$	−7.30791			−0.489374			−0.244687	+	0.969602i	$0.578685\pi$
$224$		0			0
$225$	−10.9189			−0.727926
$226$		0			0
$227$	−9.22902	+	15.9851i	−0.612552	+	1.06097i	0.378257	+	0.925701i	$0.376524\pi$
$227$	−9.22902	+	15.9851i	−0.612552	+	1.06097i	−0.990809	+	0.135270i	$0.956810\pi$
$228$		0			0
$229$	−2.50847	−	4.34481i	−0.165765	−	0.287113i	0.771162	−	0.636639i	$-0.219676\pi$
$229$	−2.50847	−	4.34481i	−0.165765	−	0.287113i	−0.936927	+	0.349526i	$0.886343\pi$
$230$		0			0
$231$	17.2843	−	7.48094i	1.13723	−	0.492210i
$232$		0			0
$233$	13.3778	+	23.1710i	0.876407	+	1.51798i	0.855256	+	0.518206i	$0.173400\pi$
$233$	13.3778	+	23.1710i	0.876407	+	1.51798i	0.0211515	+	0.999776i	$0.493267\pi$
$234$		0			0
$235$	−1.04438	+	1.80893i	−0.0681281	+	0.118001i
$236$		0			0
$237$	−1.95956			−0.127287
$238$		0			0
$239$	18.7665			1.21390			0.606951	−	0.794739i	$-0.292392\pi$
$239$	18.7665			1.21390			0.606951	+	0.794739i	$0.292392\pi$
$240$		0			0
$241$	−11.6394	+	20.1601i	−0.749761	+	1.29862i	0.198176	+	0.980166i	$0.436498\pi$
$241$	−11.6394	+	20.1601i	−0.749761	+	1.29862i	−0.947937	+	0.318458i	$0.896835\pi$
$242$		0			0
$243$	9.63624	+	16.6905i	0.618165	+	1.07069i
$244$		0			0
$245$	0.708505	+	2.34557i	0.0452647	+	0.149853i
$246$		0			0
$247$	−1.35609	−	2.34882i	−0.0862859	−	0.149452i
$248$		0			0
$249$	14.7792	−	25.5983i	0.936592	−	1.62222i
$250$		0			0
$251$	−20.6641			−1.30430			−0.652152	−	0.758088i	$-0.726134\pi$
$251$	−20.6641			−1.30430			−0.652152	+	0.758088i	$0.726134\pi$
$252$		0			0
$253$	−12.7986			−0.804640
$254$		0			0
$255$	1.08202	−	1.87412i	0.0677589	−	0.117362i
$256$		0			0
$257$	−4.55827	−	7.89515i	−0.284337	−	0.492486i	0.688111	−	0.725605i	$-0.258440\pi$
$257$	−4.55827	−	7.89515i	−0.284337	−	0.492486i	−0.972448	+	0.233119i	$0.925107\pi$
$258$		0			0
$259$	−10.5322	+	4.55851i	−0.654440	+	0.283252i
$260$		0			0
$261$	7.54953	+	13.0762i	0.467304	+	0.809395i
$262$		0			0
$263$	−5.99284	+	10.3799i	−0.369534	+	0.640052i	−0.989493	−	0.144583i	$-0.953816\pi$
$263$	−5.99284	+	10.3799i	−0.369534	+	0.640052i	0.619959	+	0.784635i	$0.287149\pi$
$264$		0			0
$265$	0.716012			0.0439842
$266$		0			0
$267$	32.1103			1.96512
$268$		0			0
$269$	−2.68655	+	4.65325i	−0.163802	+	0.283713i	−0.936229	−	0.351390i	$-0.885709\pi$
$269$	−2.68655	+	4.65325i	−0.163802	+	0.283713i	0.772427	+	0.635103i	$0.219043\pi$
$270$		0			0
$271$	10.9640	+	18.9902i	0.666014	+	1.15357i	0.979009	+	0.203815i	$0.0653342\pi$
$271$	10.9640	+	18.9902i	0.666014	+	1.15357i	−0.312995	+	0.949755i	$0.601332\pi$
$272$		0			0
$273$	19.3136	+	14.3416i	1.16891	+	0.867993i
$274$		0			0
$275$	7.58482	+	13.1373i	0.457382	+	0.792209i
$276$		0			0
$277$	2.71277	−	4.69865i	0.162994	−	0.282315i	−0.772947	−	0.634471i	$-0.781218\pi$
$277$	2.71277	−	4.69865i	0.162994	−	0.282315i	0.935941	+	0.352156i	$0.114551\pi$
$278$		0			0
$279$	1.04156			0.0623567
$280$		0			0
$281$	−17.6364			−1.05210			−0.526049	−	0.850454i	$-0.676327\pi$
$281$	−17.6364			−1.05210			−0.526049	+	0.850454i	$0.676327\pi$
$282$		0			0
$283$	−7.33576	+	12.7059i	−0.436066	+	0.755288i	−0.997382	−	0.0723132i	$-0.976962\pi$
$283$	−7.33576	+	12.7059i	−0.436066	+	0.755288i	0.561316	+	0.827602i	$0.310295\pi$
$284$		0			0
$285$	0.273490	+	0.473698i	0.0162001	+	0.0280595i
$286$		0			0
$287$	−0.303923	+	2.62824i	−0.0179400	+	0.155140i
$288$		0			0
$289$	4.85193	+	8.40380i	0.285408	+	0.494341i
$290$		0			0
$291$	3.89965	−	6.75439i	0.228602	−	0.395950i
$292$		0			0
$293$	7.13441			0.416797			0.208398	−	0.978044i	$-0.433175\pi$
$293$	7.13441			0.416797			0.208398	+	0.978044i	$0.433175\pi$
$294$		0			0
$295$	−3.63682			−0.211744
$296$		0			0
$297$	2.70989	−	4.69368i	0.157244	−	0.272355i
$298$		0			0
$299$	−8.17371	−	14.1573i	−0.472698	−	0.818737i
$300$		0			0
$301$	0.785569	−	6.79336i	0.0452794	−	0.391563i
$302$		0			0
$303$	10.1854	+	17.6416i	0.585136	+	1.01348i
$304$		0			0
$305$	−0.502849	+	0.870960i	−0.0287930	+	0.0498710i
$306$		0			0
$307$	17.4342			0.995024			0.497512	−	0.867457i	$-0.334247\pi$
$307$	17.4342			0.995024			0.497512	+	0.867457i	$0.334247\pi$
$308$		0			0
$309$	−10.6482			−0.605752
$310$		0			0
$311$	−0.147089	+	0.254766i	−0.00834067	+	0.0144465i	−0.870166	−	0.492759i	$-0.835988\pi$
$311$	−0.147089	+	0.254766i	−0.00834067	+	0.0144465i	0.861825	+	0.507206i	$0.169322\pi$
$312$		0			0
$313$	−16.0419	−	27.7854i	−0.906742	−	1.57052i	−0.818562	−	0.574419i	$-0.805228\pi$
$313$	−16.0419	−	27.7854i	−0.906742	−	1.57052i	−0.0881805	−	0.996105i	$-0.528105\pi$
$314$		0			0
$315$	−1.66449	−	1.23599i	−0.0937834	−	0.0696402i
$316$		0			0
$317$	4.10185	+	7.10461i	0.230383	+	0.399035i	0.957921	−	0.287033i	$-0.0926688\pi$
$317$	4.10185	+	7.10461i	0.230383	+	0.399035i	−0.727538	+	0.686067i	$0.759335\pi$
$318$		0			0
$319$	10.4886	−	18.1668i	0.587248	−	1.01714i
$320$		0			0
$321$	−12.3357			−0.688509
$322$		0			0
$323$	1.84415			0.102612
$324$		0			0
$325$	−9.68797	+	16.7800i	−0.537392	+	0.930790i
$326$		0			0
$327$	−8.24644	−	14.2833i	−0.456029	−	0.789866i
$328$		0			0
$329$	14.4891	−	6.27114i	0.798812	−	0.345739i
$330$		0			0
$331$	−6.22116	−	10.7754i	−0.341946	−	0.592268i	0.642848	−	0.765994i	$-0.277753\pi$
$331$	−6.22116	−	10.7754i	−0.341946	−	0.592268i	−0.984794	+	0.173726i	$0.944419\pi$
$332$		0			0
$333$	4.85523	−	8.40950i	0.266065	−	0.460838i
$334$		0			0
$335$	−1.10400			−0.0603178
$336$		0			0
$337$	17.6330			0.960530			0.480265	−	0.877123i	$-0.340540\pi$
$337$	17.6330			0.960530			0.480265	+	0.877123i	$0.340540\pi$
$338$		0			0
$339$	5.10198	−	8.83689i	0.277101	−	0.479954i
$340$		0			0
$341$	−0.723523	−	1.25318i	−0.0391809	−	0.0678634i
$342$		0			0
$343$	6.27009	−	17.4266i	0.338553	−	0.940947i
$344$		0			0
$345$	1.64843	+	2.85517i	0.0887487	+	0.153717i
$346$		0			0
$347$	3.14857	−	5.45348i	0.169024	−	0.292758i	−0.769053	−	0.639185i	$-0.779272\pi$
$347$	3.14857	−	5.45348i	0.169024	−	0.292758i	0.938077	+	0.346427i	$0.112605\pi$
$348$		0			0
$349$	1.11133			0.0594879			0.0297440	−	0.999558i	$-0.490531\pi$
$349$	1.11133			0.0594879			0.0297440	+	0.999558i	$0.490531\pi$
$350$		0			0
$351$	6.92260			0.369501
$352$		0			0
$353$	16.8653	−	29.2116i	0.897651	−	1.55478i	0.0671614	−	0.997742i	$-0.478606\pi$
$353$	16.8653	−	29.2116i	0.897651	−	1.55478i	0.830489	−	0.557035i	$-0.188061\pi$
$354$		0			0
$355$	0.565876	+	0.980127i	0.0300336	+	0.0520197i
$356$		0			0
$357$	−15.0113	+	6.49714i	−0.794483	+	0.343865i
$358$		0			0
$359$	−12.0242	−	20.8264i	−0.634611	−	1.09918i	−0.986597	−	0.163173i	$-0.947827\pi$
$359$	−12.0242	−	20.8264i	−0.634611	−	1.09918i	0.351987	−	0.936005i	$-0.385506\pi$
$360$		0			0
$361$	9.26694	−	16.0508i	0.487734	−	0.844779i
$362$		0			0
$363$	−3.03727			−0.159415
$364$		0			0
$365$	−0.209787			−0.0109807
$366$		0			0
$367$	14.4142	−	24.9661i	0.752414	−	1.30322i	−0.194236	−	0.980955i	$-0.562223\pi$
$367$	14.4142	−	24.9661i	0.752414	−	1.30322i	0.946650	−	0.322264i	$-0.104444\pi$
$368$		0			0
$369$	−1.11932	−	1.93871i	−0.0582693	−	0.100925i
$370$		0			0
$371$	−4.34506	−	3.22649i	−0.225584	−	0.167511i
$372$		0			0
$373$	9.18345	+	15.9062i	0.475501	+	0.823592i	0.999606	−	0.0280614i	$-0.00893341\pi$
$373$	9.18345	+	15.9062i	0.475501	+	0.823592i	−0.524105	+	0.851654i	$0.675600\pi$
$374$		0			0
$375$	3.95673	−	6.85325i	0.204324	−	0.353900i
$376$		0			0
$377$	26.7938			1.37995
$378$		0			0
$379$	−20.6497			−1.06070			−0.530352	−	0.847778i	$-0.677940\pi$
$379$	−20.6497			−1.06070			−0.530352	+	0.847778i	$0.677940\pi$
$380$		0			0
$381$	−16.3977	+	28.4017i	−0.840080	+	1.45506i
$382$		0			0
$383$	5.88459	+	10.1924i	0.300688	+	0.520808i	0.976292	−	0.216457i	$-0.0694502\pi$
$383$	5.88459	+	10.1924i	0.300688	+	0.520808i	−0.675604	+	0.737265i	$0.736117\pi$
$384$		0			0
$385$	−0.330868	+	2.86125i	−0.0168626	+	0.145823i
$386$		0			0
$387$	2.89317	+	5.01111i	0.147068	+	0.254729i
$388$		0			0
$389$	12.1393	−	21.0259i	0.615489	−	1.06606i	−0.374810	−	0.927102i	$-0.622292\pi$
$389$	12.1393	−	21.0259i	0.615489	−	1.06606i	0.990299	−	0.138956i	$-0.0443747\pi$
$390$		0			0
$391$	11.1155			0.562134
$392$		0			0
$393$	1.25397			0.0632546
$394$		0			0
$395$	0.149841	−	0.259532i	0.00753932	−	0.0130585i
$396$		0			0
$397$	10.3245	+	17.8825i	0.518171	+	0.897498i	0.999777	+	0.0211107i	$0.00672024\pi$
$397$	10.3245	+	17.8825i	0.518171	+	0.897498i	−0.481606	+	0.876388i	$0.659946\pi$
$398$		0			0
$399$	0.474924	−	4.10700i	0.0237759	−	0.205607i
$400$		0			0
$401$	−16.1881	−	28.0386i	−0.808396	−	1.40018i	−0.913975	−	0.405771i	$-0.867003\pi$
$401$	−16.1881	−	28.0386i	−0.808396	−	1.40018i	0.105579	−	0.994411i	$-0.466330\pi$
$402$		0			0
$403$	0.924143	−	1.60066i	0.0460348	−	0.0797347i
$404$		0			0
$405$	−3.74692			−0.186186
$406$		0			0
$407$	−13.4908			−0.668712
$408$		0			0
$409$	−6.40322	+	11.0907i	−0.316619	+	0.548400i	−0.979780	−	0.200076i	$-0.935881\pi$
$409$	−6.40322	+	11.0907i	−0.316619	+	0.548400i	0.663161	+	0.748476i	$0.269214\pi$
$410$		0			0
$411$	−11.8891	−	20.5925i	−0.586446	−	1.01575i
$412$		0			0
$413$	22.0698	+	16.3882i	1.08598	+	0.806411i
$414$		0			0
$415$	2.26023	+	3.91483i	0.110950	+	0.192171i
$416$		0			0
$417$	18.8182	−	32.5941i	0.921532	−	1.59614i
$418$		0			0
$419$	21.8220			1.06608			0.533038	−	0.846092i	$-0.321050\pi$
$419$	21.8220			1.06608			0.533038	+	0.846092i	$0.321050\pi$
$420$		0			0
$421$	−4.59928			−0.224155			−0.112078	−	0.993699i	$-0.535751\pi$
$421$	−4.59928			−0.224155			−0.112078	+	0.993699i	$0.535751\pi$
$422$		0			0
$423$	−6.67932	+	11.5689i	−0.324760	+	0.562501i
$424$		0			0
$425$	−6.58736	−	11.4096i	−0.319534	−	0.553449i
$426$		0			0
$427$	6.97621	−	3.01942i	0.337603	−	0.146120i
$428$		0			0
$429$	14.1393	+	24.4899i	0.682650	+	1.18238i
$430$		0			0
$431$	7.49297	−	12.9782i	0.360923	−	0.625138i	−0.627190	−	0.778867i	$-0.715795\pi$
$431$	7.49297	−	12.9782i	0.360923	−	0.625138i	0.988113	+	0.153729i	$0.0491282\pi$
$432$		0			0
$433$	−30.5080			−1.46612			−0.733060	−	0.680164i	$-0.761909\pi$
$433$	−30.5080			−1.46612			−0.733060	+	0.680164i	$0.761909\pi$
$434$		0			0
$435$	−5.40364			−0.259085
$436$		0			0
$437$	−1.40476	+	2.43312i	−0.0671989	+	0.116392i
$438$		0			0
$439$	7.19387	+	12.4601i	0.343345	+	0.594690i	0.985052	−	0.172260i	$-0.0551068\pi$
$439$	7.19387	+	12.4601i	0.343345	+	0.594690i	−0.641707	+	0.766950i	$0.721773\pi$
$440$		0			0
$441$	4.53122	+	15.0010i	0.215772	+	0.714335i
$442$		0			0
$443$	5.25972	+	9.11011i	0.249897	+	0.432834i	0.963497	−	0.267719i	$-0.0862699\pi$
$443$	5.25972	+	9.11011i	0.249897	+	0.432834i	−0.713600	+	0.700553i	$0.752937\pi$
$444$		0			0
$445$	−2.45537	+	4.25282i	−0.116396	+	0.201603i
$446$		0			0
$447$	−6.90686			−0.326683
$448$		0			0
$449$	−5.21224			−0.245981			−0.122990	−	0.992408i	$-0.539248\pi$
$449$	−5.21224			−0.245981			−0.122990	+	0.992408i	$0.539248\pi$
$450$		0			0
$451$	−1.55507	+	2.69346i	−0.0732255	+	0.126830i
$452$		0			0
$453$	−14.5659	−	25.2288i	−0.684365	−	1.18535i
$454$		0			0
$455$	−3.37631	+	1.46132i	−0.158284	+	0.0685077i
$456$		0			0
$457$	5.12783	+	8.88166i	0.239870	+	0.415466i	0.960677	−	0.277669i	$-0.0895620\pi$
$457$	5.12783	+	8.88166i	0.239870	+	0.415466i	−0.720807	+	0.693136i	$0.756229\pi$
$458$		0			0
$459$	−2.35352	+	4.07642i	−0.109853	+	0.190271i
$460$		0			0
$461$	−3.59542			−0.167456			−0.0837278	−	0.996489i	$-0.526683\pi$
$461$	−3.59542			−0.167456			−0.0837278	+	0.996489i	$0.526683\pi$
$462$		0			0
$463$	−19.8730			−0.923575			−0.461788	−	0.886991i	$-0.652792\pi$
$463$	−19.8730			−0.923575			−0.461788	+	0.886991i	$0.652792\pi$
$464$		0			0
$465$	−0.186377	+	0.322814i	−0.00864302	+	0.0149701i
$466$		0			0
$467$	19.0951	+	33.0737i	0.883617	+	1.53047i	0.847291	+	0.531129i	$0.178232\pi$
$467$	19.0951	+	33.0737i	0.883617	+	1.53047i	0.0363253	+	0.999340i	$0.488435\pi$
$468$		0			0
$469$	6.69953	+	4.97483i	0.309355	+	0.229716i
$470$		0			0
$471$	−27.8013	−	48.1532i	−1.28101	−	2.21878i
$472$		0			0
$473$	4.01949	−	6.96196i	0.184816	−	0.320111i
$474$		0			0
$475$	3.33001			0.152792
$476$		0			0
$477$	4.57923			0.209668
$478$		0			0
$479$	−9.64907	+	16.7127i	−0.440877	+	0.763622i	−0.997755	−	0.0669729i	$-0.978666\pi$
$479$	−9.64907	+	16.7127i	−0.440877	+	0.763622i	0.556878	+	0.830595i	$0.311999\pi$
$480$		0			0
$481$	−8.61576	−	14.9229i	−0.392845	−	0.680427i
$482$		0			0
$483$	2.86256	−	24.7546i	0.130251	−	1.12637i
$484$		0			0
$485$	0.596386	+	1.03297i	0.0270805	+	0.0469048i
$486$		0			0
$487$	−20.8801	+	36.1653i	−0.946166	+	1.63881i	−0.192767	+	0.981245i	$0.561746\pi$
$487$	−20.8801	+	36.1653i	−0.946166	+	1.63881i	−0.753399	+	0.657563i	$0.771587\pi$
$488$		0			0
$489$	−39.0938			−1.76788
$490$		0			0
$491$	−34.1057			−1.53917			−0.769584	−	0.638546i	$-0.779536\pi$
$491$	−34.1057			−1.53917			−0.769584	+	0.638546i	$0.779536\pi$
$492$		0			0
$493$	−9.10926	+	15.7777i	−0.410260	+	0.710592i
$494$		0			0
$495$	−1.21855	−	2.11060i	−0.0547699	−	0.0948643i
$496$		0			0
$497$	0.982662	−	8.49777i	0.0440784	−	0.381177i
$498$		0			0
$499$	−11.0229	−	19.0923i	−0.493455	−	0.854689i	0.506517	−	0.862230i	$-0.330933\pi$
$499$	−11.0229	−	19.0923i	−0.493455	−	0.854689i	−0.999972	+	0.00754120i	$0.997600\pi$
$500$		0			0
$501$	−13.0191	+	22.5497i	−0.581648	+	1.00744i
$502$		0			0
$503$	−2.01342			−0.0897738			−0.0448869	−	0.998992i	$-0.514293\pi$
$503$	−2.01342			−0.0897738			−0.0448869	+	0.998992i	$0.514293\pi$
$504$		0			0
$505$	−3.11537			−0.138632
$506$		0			0
$507$	−3.18260	+	5.51243i	−0.141344	+	0.244816i
$508$		0			0
$509$	−7.13871	−	12.3646i	−0.316418	−	0.548052i	0.663320	−	0.748336i	$-0.269147\pi$
$509$	−7.13871	−	12.3646i	−0.316418	−	0.548052i	−0.979738	+	0.200284i	$0.935814\pi$
$510$		0			0
$511$	1.27307	+	0.945339i	0.0563175	+	0.0418193i
$512$		0			0
$513$	−0.594871	−	1.03035i	−0.0262642	−	0.0454909i
$514$		0			0
$515$	0.814228	−	1.41028i	0.0358792	−	0.0621446i
$516$		0			0
$517$	18.5592			0.816233
$518$		0			0
$519$	4.04925			0.177742
$520$		0			0
$521$	5.84187	−	10.1184i	0.255937	−	0.443296i	−0.709213	−	0.704995i	$-0.750949\pi$
$521$	5.84187	−	10.1184i	0.255937	−	0.443296i	0.965150	+	0.261699i	$0.0842827\pi$
$522$		0			0
$523$	−15.7139	−	27.2173i	−0.687122	−	1.19013i	−0.972765	−	0.231794i	$-0.925540\pi$
$523$	−15.7139	−	27.2173i	−0.687122	−	1.19013i	0.285643	−	0.958336i	$-0.407793\pi$
$524$		0			0
$525$	−27.1061	+	11.7320i	−1.18301	+	0.512025i
$526$		0			0
$527$	0.628374	+	1.08838i	0.0273724	+	0.0474104i
$528$		0			0
$529$	3.03293	−	5.25318i	0.131866	−	0.228399i
$530$		0			0
$531$	−23.2592			−1.00936
$532$		0			0
$533$	−3.97253			−0.172069
$534$		0			0
$535$	0.943266	−	1.63379i	0.0407810	−	0.0706347i
$536$		0			0
$537$	8.32704	+	14.4229i	0.359338	+	0.622392i
$538$		0			0
$539$	14.9012	−	15.8723i	0.641840	−	0.683670i
$540$		0			0
$541$	20.9971	+	36.3681i	0.902736	+	1.56358i	0.823928	+	0.566695i	$0.191778\pi$
$541$	20.9971	+	36.3681i	0.902736	+	1.56358i	0.0788083	+	0.996890i	$0.474889\pi$
$542$		0			0
$543$	−4.00241	+	6.93238i	−0.171760	+	0.297497i
$544$		0			0
$545$	2.52231			0.108044
$546$		0			0
$547$	−32.0258			−1.36933			−0.684663	−	0.728860i	$-0.740050\pi$
$547$	−32.0258			−1.36933			−0.684663	+	0.728860i	$0.740050\pi$
$548$		0			0
$549$	−3.21595	+	5.57019i	−0.137254	+	0.237730i
$550$		0			0
$551$	−2.30244	−	3.98794i	−0.0980871	−	0.169892i
$552$		0			0
$553$	−2.07880	+	0.899739i	−0.0883996	+	0.0382608i
$554$		0			0
$555$	1.73759	+	3.00959i	0.0737564	+	0.127750i
$556$		0			0
$557$	−17.4282	+	30.1865i	−0.738455	+	1.27904i	0.214736	+	0.976672i	$0.431111\pi$
$557$	−17.4282	+	30.1865i	−0.738455	+	1.27904i	−0.953191	+	0.302369i	$0.902223\pi$
$558$		0			0
$559$	10.2680			0.434292
$560$		0			0
$561$	−19.2281			−0.811810
$562$		0			0
$563$	−2.31680	+	4.01281i	−0.0976413	+	0.169120i	−0.910708	−	0.413051i	$-0.864463\pi$
$563$	−2.31680	+	4.01281i	−0.0976413	+	0.169120i	0.813067	+	0.582171i	$0.197796\pi$
$564$		0			0
$565$	0.780262	+	1.35145i	0.0328259	+	0.0568561i
$566$		0			0
$567$	22.7379	+	16.8843i	0.954901	+	0.709075i
$568$		0			0
$569$	5.50425	+	9.53364i	0.230750	+	0.399671i	0.958029	−	0.286671i	$-0.0925486\pi$
$569$	5.50425	+	9.53364i	0.230750	+	0.399671i	−0.727279	+	0.686342i	$0.759215\pi$
$570$		0			0
$571$	−6.85342	+	11.8705i	−0.286807	+	0.496763i	−0.973046	−	0.230613i	$-0.925927\pi$
$571$	−6.85342	+	11.8705i	−0.286807	+	0.496763i	0.686239	+	0.727376i	$0.259260\pi$
$572$		0			0
$573$	−2.04840			−0.0855731
$574$		0			0
$575$	20.0714			0.837034
$576$		0			0
$577$	−4.28400	+	7.42011i	−0.178345	+	0.308903i	−0.941314	−	0.337532i	$-0.890408\pi$
$577$	−4.28400	+	7.42011i	−0.178345	+	0.308903i	0.762969	+	0.646436i	$0.223741\pi$
$578$		0			0
$579$	−14.3570	−	24.8671i	−0.596657	−	1.03344i
$580$		0			0
$581$	3.92495	−	33.9418i	0.162835	−	1.40815i
$582$		0			0
$583$	−3.18097	−	5.50960i	−0.131742	−	0.228184i
$584$		0			0
$585$	1.55644	−	2.69583i	0.0643508	−	0.111459i
$586$		0			0
$587$	0.718126			0.0296402			0.0148201	−	0.999890i	$-0.495282\pi$
$587$	0.718126			0.0296402			0.0148201	+	0.999890i	$0.495282\pi$
$588$		0			0
$589$	−0.317653			−0.0130887
$590$		0			0
$591$	−11.3481	+	19.6555i	−0.466799	+	0.808519i
$592$		0			0
$593$	−5.75827	−	9.97362i	−0.236464	−	0.409567i	0.723233	−	0.690604i	$-0.242655\pi$
$593$	−5.75827	−	9.97362i	−0.236464	−	0.409567i	−0.959697	+	0.281036i	$0.909322\pi$
$594$		0			0
$595$	0.287357	−	2.48497i	0.0117805	−	0.101874i
$596$		0			0
$597$	−25.1565	−	43.5723i	−1.02959	−	1.78329i
$598$		0			0
$599$	22.2112	−	38.4709i	0.907525	−	1.57188i	0.0900342	−	0.995939i	$-0.471302\pi$
$599$	22.2112	−	38.4709i	0.907525	−	1.57188i	0.817491	−	0.575941i	$-0.195364\pi$
$600$		0			0
$601$	−27.2986			−1.11353			−0.556766	−	0.830669i	$-0.687958\pi$
$601$	−27.2986			−1.11353			−0.556766	+	0.830669i	$0.687958\pi$
$602$		0			0
$603$	−7.06058			−0.287529
$604$		0			0
$605$	0.232250	−	0.402268i	0.00944230	−	0.0163545i
$606$		0			0
$607$	6.34894	+	10.9967i	0.257696	+	0.446342i	0.965624	−	0.259942i	$-0.0837035\pi$
$607$	6.34894	+	10.9967i	0.257696	+	0.446342i	−0.707929	+	0.706284i	$0.750370\pi$
$608$		0			0
$609$	32.7916	+	24.3499i	1.32878	+	0.986707i
$610$		0			0
$611$	11.8527	+	20.5295i	0.479508	+	0.830533i
$612$		0			0
$613$	0.181551	−	0.314456i	0.00733278	−	0.0127007i	−0.862336	−	0.506337i	$-0.830999\pi$
$613$	0.181551	−	0.314456i	0.00733278	−	0.0127007i	0.869669	+	0.493636i	$0.164333\pi$
$614$		0			0
$615$	0.801161			0.0323059
$616$		0			0
$617$	9.82313			0.395464			0.197732	−	0.980256i	$-0.436642\pi$
$617$	9.82313			0.395464			0.197732	+	0.980256i	$0.436642\pi$
$618$		0			0
$619$	−19.4690	+	33.7212i	−0.782524	+	1.35537i	0.147944	+	0.988996i	$0.452734\pi$
$619$	−19.4690	+	33.7212i	−0.782524	+	1.35537i	−0.930467	+	0.366375i	$0.880599\pi$
$620$		0			0
$621$	−3.58553	−	6.21033i	−0.143883	−	0.249212i
$622$		0			0
$623$	34.0643	−	14.7436i	1.36476	−	0.590688i
$624$		0			0
$625$	−11.5886	−	20.0720i	−0.463543	−	0.802880i
$626$		0			0
$627$	2.43002	−	4.20892i	0.0970458	−	0.168088i
$628$		0			0
$629$	11.7166			0.467173
$630$		0			0
$631$	−21.3256			−0.848959			−0.424479	−	0.905438i	$-0.639543\pi$
$631$	−21.3256			−0.848959			−0.424479	+	0.905438i	$0.639543\pi$
$632$		0			0
$633$	24.5728	−	42.5613i	0.976679	−	1.69166i
$634$		0			0
$635$	−2.50776	−	4.34356i	−0.0995173	−	0.172369i
$636$		0			0
$637$	27.0738	+	6.34638i	1.07270	+	0.251453i
$638$		0			0
$639$	3.61904	+	6.26837i	0.143167	+	0.247973i
$640$		0			0
$641$	21.6802	−	37.5513i	0.856318	−	1.48319i	−0.0190990	−	0.999818i	$-0.506080\pi$
$641$	21.6802	−	37.5513i	0.856318	−	1.48319i	0.875417	−	0.483369i	$-0.160587\pi$
$642$		0			0
$643$	−0.783742			−0.0309078			−0.0154539	−	0.999881i	$-0.504919\pi$
$643$	−0.783742			−0.0309078			−0.0154539	+	0.999881i	$0.504919\pi$
$644$		0			0
$645$	−2.07081			−0.0815381
$646$		0			0
$647$	−14.4800	+	25.0802i	−0.569269	+	0.986003i	0.427369	+	0.904077i	$0.359440\pi$
$647$	−14.4800	+	25.0802i	−0.569269	+	0.986003i	−0.996638	+	0.0819262i	$0.973893\pi$
$648$		0			0
$649$	16.1570	+	27.9848i	0.634218	+	1.09850i
$650$		0			0
$651$	2.58568	−	1.11912i	0.101341	−	0.0438619i
$652$		0			0
$653$	−11.0168	−	19.0817i	−0.431122	−	0.746724i	0.565849	−	0.824509i	$-0.308549\pi$
$653$	−11.0168	−	19.0817i	−0.431122	−	0.746724i	−0.996970	+	0.0777847i	$0.975215\pi$
$654$		0			0
$655$	−0.0958872	+	0.166081i	−0.00374662	+	0.00648934i
$656$		0			0
$657$	−1.34168			−0.0523441
$658$		0			0
$659$	−11.7364			−0.457186			−0.228593	−	0.973522i	$-0.573413\pi$
$659$	−11.7364			−0.457186			−0.228593	+	0.973522i	$0.573413\pi$
$660$		0			0
$661$	12.6339	−	21.8826i	0.491403	−	0.851135i	−0.508548	−	0.861034i	$-0.669818\pi$
$661$	12.6339	−	21.8826i	0.491403	−	0.851135i	0.999951	+	0.00989879i	$0.00315093\pi$
$662$		0			0
$663$	−12.2798	−	21.2693i	−0.476910	−	0.826032i
$664$		0			0
$665$	0.507632	+	0.376949i	0.0196851	+	0.0146175i
$666$		0			0
$667$	−13.8777	−	24.0369i	−0.537348	−	0.930714i
$668$		0			0
$669$	8.36320	−	14.4855i	0.323340	−	0.560041i
$670$		0			0
$671$	8.93587			0.344965
$672$		0			0
$673$	9.10303			0.350896			0.175448	−	0.984489i	$-0.443863\pi$
$673$	9.10303			0.350896			0.175448	+	0.984489i	$0.443863\pi$
$674$		0			0
$675$	−4.24979	+	7.36085i	−0.163574	+	0.283319i
$676$		0			0
$677$	−18.5501	−	32.1297i	−0.712938	−	1.23484i	−0.963749	−	0.266809i	$-0.914031\pi$
$677$	−18.5501	−	32.1297i	−0.712938	−	1.23484i	0.250812	−	0.968036i	$-0.419303\pi$
$678$		0			0
$679$	1.03564	−	8.95594i	0.0397444	−	0.343698i
$680$		0			0
$681$	−21.1234	−	36.5869i	−0.809452	−	1.40201i
$682$		0			0
$683$	−7.51013	+	13.0079i	−0.287367	+	0.497735i	−0.973180	−	0.230043i	$-0.926113\pi$
$683$	−7.51013	+	13.0079i	−0.287367	+	0.497735i	0.685813	+	0.727778i	$0.259447\pi$
$684$		0			0
$685$	3.63647			0.138943
$686$		0			0
$687$	11.4828			0.438097
$688$		0			0
$689$	4.06300	−	7.03732i	0.154788	−	0.268100i
$690$		0			0
$691$	20.7364	+	35.9165i	0.788849	+	1.36633i	0.926672	+	0.375870i	$0.122656\pi$
$691$	20.7364	+	35.9165i	0.788849	+	1.36633i	−0.137823	+	0.990457i	$0.544011\pi$
$692$		0			0
$693$	−2.11606	+	18.2990i	−0.0803824	+	0.695123i
$694$		0			0
$695$	2.87793	+	4.98472i	0.109166	+	0.189081i
$696$		0			0
$697$	1.35057	−	2.33925i	0.0511564	−	0.0886055i
$698$		0			0
$699$	−61.2383			−2.31624
$700$		0			0
$701$	−15.7161			−0.593589			−0.296794	−	0.954941i	$-0.595918\pi$
$701$	−15.7161			−0.593589			−0.296794	+	0.954941i	$0.595918\pi$
$702$		0			0
$703$	−1.48073	+	2.56471i	−0.0558470	+	0.0967298i
$704$		0			0
$705$	−2.39039	−	4.14028i	−0.0900274	−	0.155932i
$706$		0			0
$707$	18.9054	+	14.0385i	0.711011	+	0.527971i
$708$		0			0
$709$	19.7957	+	34.2872i	0.743444	+	1.28768i	0.950918	+	0.309442i	$0.100142\pi$
$709$	19.7957	+	34.2872i	0.743444	+	1.28768i	−0.207475	+	0.978240i	$0.566524\pi$
$710$		0			0
$711$	0.958303	−	1.65983i	0.0359392	−	0.0622485i
$712$		0			0
$713$	−1.91462			−0.0717032
$714$		0			0
$715$	−4.32473			−0.161736
$716$		0			0
$717$	−21.4764	+	37.1982i	−0.802052	+	1.38919i
$718$		0			0
$719$	5.65262	+	9.79062i	0.210807	+	0.365129i	0.951967	−	0.306200i	$-0.0990575\pi$
$719$	5.65262	+	9.79062i	0.210807	+	0.365129i	−0.741160	+	0.671328i	$0.765724\pi$
$720$		0			0
$721$	−11.2961	+	4.88914i	−0.420689	+	0.182081i
$722$		0			0
$723$	−26.6404	−	46.1425i	−0.990767	−	1.71606i
$724$		0			0
$725$	−16.4487	+	28.4900i	−0.610890	+	1.05809i
$726$		0			0
$727$	28.9056			1.07205			0.536025	−	0.844202i	$-0.319925\pi$
$727$	28.9056			1.07205			0.536025	+	0.844202i	$0.319925\pi$
$728$		0			0
$729$	−11.9977			−0.444361
$730$		0			0
$731$	−3.49089	+	6.04641i	−0.129115	+	0.223634i
$732$		0			0
$733$	−11.5017	−	19.9216i	−0.424826	−	0.735820i	0.571578	−	0.820547i	$-0.306331\pi$
$733$	−11.5017	−	19.9216i	−0.424826	−	0.735820i	−0.996404	+	0.0847276i	$0.972998\pi$
$734$		0			0
$735$	−5.46012	−	1.27991i	−0.201400	−	0.0472101i
$736$		0			0
$737$	4.90464	+	8.49509i	0.180665	+	0.312921i
$738$		0			0
$739$	15.0399	−	26.0498i	0.553250	−	0.958258i	−0.444787	−	0.895636i	$-0.646721\pi$
$739$	15.0399	−	26.0498i	0.553250	−	0.958258i	0.998037	−	0.0626212i	$-0.0199460\pi$
$740$		0			0
$741$	6.20765			0.228044
$742$		0			0
$743$	1.24979			0.0458503			0.0229251	−	0.999737i	$-0.492702\pi$
$743$	1.24979			0.0458503			0.0229251	+	0.999737i	$0.492702\pi$
$744$		0			0
$745$	0.528144	−	0.914772i	0.0193497	−	0.0335147i
$746$		0			0
$747$	14.4552	+	25.0371i	0.528888	+	0.916061i
$748$		0			0
$749$	−13.0863	+	5.66396i	−0.478163	+	0.206957i
$750$		0			0
$751$	4.26365	+	7.38487i	0.155583	+	0.269478i	0.933271	−	0.359173i	$-0.116941\pi$
$751$	4.26365	+	7.38487i	0.155583	+	0.269478i	−0.777688	+	0.628650i	$0.783608\pi$
$752$		0			0
$753$	23.6480	−	40.9596i	0.861782	−	1.49265i
$754$		0			0
$755$	4.45521			0.162142
$756$		0			0
$757$	11.0979			0.403359			0.201679	−	0.979452i	$-0.435360\pi$
$757$	11.0979			0.403359			0.201679	+	0.979452i	$0.435360\pi$
$758$		0			0
$759$	14.6467	−	25.3689i	0.531643	−	0.920833i
$760$		0			0
$761$	−15.5149	−	26.8726i	−0.562416	−	0.974132i	−0.997285	−	0.0736388i	$-0.976539\pi$
$761$	−15.5149	−	26.8726i	−0.562416	−	0.974132i	0.434869	−	0.900494i	$-0.356795\pi$
$762$		0			0
$763$	−15.3065	−	11.3660i	−0.554131	−	0.411478i
$764$		0			0
$765$	1.05830	+	1.83304i	0.0382631	+	0.0662736i
$766$		0			0
$767$	−20.6371	+	35.7445i	−0.745162	+	1.29066i
$768$		0			0
$769$	46.3590			1.67175			0.835874	−	0.548922i	$-0.184962\pi$
$769$	46.3590			1.67175			0.835874	+	0.548922i	$0.184962\pi$
$770$		0			0
$771$	20.8660			0.751470
$772$		0			0
$773$	0.420082	−	0.727603i	0.0151093	−	0.0261701i	−0.858372	−	0.513028i	$-0.828524\pi$
$773$	0.420082	−	0.727603i	0.0151093	−	0.0261701i	0.873481	+	0.486858i	$0.161857\pi$
$774$		0			0
$775$	1.13466	+	1.96529i	0.0407583	+	0.0705954i
$776$		0			0
$777$	3.01737	−	26.0934i	0.108248	−	0.936094i
$778$		0			0
$779$	0.341367	+	0.591264i	0.0122307	+	0.0211842i
$780$		0			0
$781$	5.02795	−	8.70866i	0.179914	−	0.311621i
$782$		0			0
$783$	11.7535			0.420037
$784$		0			0
$785$	8.50348			0.303502
$786$		0			0
$787$	−5.16156	+	8.94008i	−0.183990	+	0.318680i	−0.943236	−	0.332124i	$-0.892235\pi$
$787$	−5.16156	+	8.94008i	−0.183990	+	0.318680i	0.759246	+	0.650804i	$0.225568\pi$
$788$		0			0
$789$	−13.7164	−	23.7576i	−0.488318	−	0.845792i
$790$		0			0
$791$	1.35495	−	11.7172i	0.0481765	−	0.416616i
$792$		0			0
$793$	5.70682	+	9.88450i	0.202655	+	0.351009i
$794$		0			0
$795$	−0.819406	+	1.41925i	−0.0290613	+	0.0503357i
$796$		0			0
$797$	−14.5828			−0.516550			−0.258275	−	0.966071i	$-0.583154\pi$
$797$	−14.5828			−0.516550			−0.258275	+	0.966071i	$0.583154\pi$
$798$		0			0
$799$	−16.1185			−0.570233
$800$		0			0
$801$	−15.7032	+	27.1988i	−0.554846	+	0.961022i
$802$		0			0
$803$	0.932003	+	1.61428i	0.0328897	+	0.0569666i
$804$		0			0
$805$	3.05971	+	2.27203i	0.107840	+	0.0800784i
$806$		0			0
$807$	−6.14900	−	10.6504i	−0.216455	−	0.374911i
$808$		0			0
$809$	20.8748	−	36.1562i	0.733919	−	1.27119i	−0.221277	−	0.975211i	$-0.571022\pi$
$809$	20.8748	−	36.1562i	0.733919	−	1.27119i	0.955196	−	0.295974i	$-0.0956442\pi$
$810$		0			0
$811$	−6.25270			−0.219562			−0.109781	−	0.993956i	$-0.535015\pi$
$811$	−6.25270			−0.219562			−0.109781	+	0.993956i	$0.535015\pi$
$812$		0			0
$813$	−50.1888			−1.76020
$814$		0			0
$815$	2.98937	−	5.17774i	0.104713	−	0.181368i
$816$		0			0
$817$	−0.882351	−	1.52828i	−0.0308696	−	0.0534676i
$818$		0			0
$819$	−21.5931	+	9.34583i	−0.754522	+	0.326570i
$820$		0			0
$821$	−11.0820	−	19.1946i	−0.386765	−	0.669897i	0.605247	−	0.796038i	$-0.293074\pi$
$821$	−11.0820	−	19.1946i	−0.386765	−	0.669897i	−0.992012	+	0.126141i	$0.959741\pi$
$822$		0			0
$823$	−7.91758	+	13.7137i	−0.275990	+	0.478028i	−0.970384	−	0.241566i	$-0.922339\pi$
$823$	−7.91758	+	13.7137i	−0.275990	+	0.478028i	0.694395	+	0.719594i	$0.255672\pi$
$824$		0			0
$825$	−34.7204			−1.20881
$826$		0			0
$827$	43.9832			1.52945			0.764723	−	0.644359i	$-0.222876\pi$
$827$	43.9832			1.52945			0.764723	+	0.644359i	$0.222876\pi$
$828$		0			0
$829$	−12.0040	+	20.7915i	−0.416916	+	0.722120i	−0.995627	−	0.0934126i	$-0.970222\pi$
$829$	−12.0040	+	20.7915i	−0.416916	+	0.722120i	0.578711	+	0.815532i	$0.303556\pi$
$830$		0			0
$831$	6.20900	+	10.7543i	0.215388	+	0.373063i
$832$		0			0
$833$	−12.9416	+	13.7850i	−0.448399	+	0.477622i
$834$		0			0
$835$	−1.99105	−	3.44859i	−0.0689030	−	0.119343i
$836$		0			0
$837$	0.405391	−	0.702157i	0.0140124	−	0.0242701i
$838$		0			0
$839$	−22.4393			−0.774690			−0.387345	−	0.921935i	$-0.626608\pi$
$839$	−22.4393			−0.774690			−0.387345	+	0.921935i	$0.626608\pi$
$840$		0			0
$841$	16.4918			0.568684
$842$		0			0
$843$	20.1831	−	34.9582i	0.695144	−	1.20402i
$844$		0			0
$845$	−0.486726	−	0.843034i	−0.0167439	−	0.0290012i
$846$		0			0
$847$	−3.22209	+	1.39457i	−0.110712	+	0.0479181i
$848$		0			0
$849$	−16.7901	−	29.0814i	−0.576236	−	0.998070i
$850$		0			0
$851$	−8.92500	+	15.4585i	−0.305945	+	0.529912i
$852$		0			0
$853$	55.6852			1.90663			0.953313	−	0.301984i	$-0.0976491\pi$
$853$	55.6852			1.90663			0.953313	+	0.301984i	$0.0976491\pi$
$854$		0			0
$855$	−0.534989			−0.0182963
$856$		0			0
$857$	−2.54767	+	4.41269i	−0.0870267	+	0.150735i	−0.906253	−	0.422736i	$-0.861070\pi$
$857$	−2.54767	+	4.41269i	−0.0870267	+	0.150735i	0.819226	+	0.573470i	$0.194403\pi$
$858$		0			0
$859$	−6.11660	−	10.5943i	−0.208696	−	0.361471i	0.742608	−	0.669726i	$-0.233588\pi$
$859$	−6.11660	−	10.5943i	−0.208696	−	0.361471i	−0.951304	+	0.308255i	$0.900255\pi$
$860$		0			0
$861$	−4.86179	−	3.61019i	−0.165689	−	0.123035i
$862$		0			0
$863$	−6.34977	−	10.9981i	−0.216149	−	0.374381i	0.737479	−	0.675371i	$-0.236016\pi$
$863$	−6.34977	−	10.9981i	−0.216149	−	0.374381i	−0.953627	+	0.300990i	$0.902683\pi$
$864$		0			0
$865$	−0.309632	+	0.536299i	−0.0105278	+	0.0182347i
$866$		0			0
$867$	−22.2103			−0.754300
$868$		0			0
$869$	−2.66275			−0.0903275
$870$		0			0
$871$	−6.26462	+	10.8506i	−0.212269	+	0.367660i
$872$		0			0
$873$	3.81417	+	6.60634i	0.129090	+	0.223591i
$874$		0			0
$875$	1.05080	−	9.08702i	0.0355236	−	0.307197i
$876$		0			0
$877$	17.7643	+	30.7687i	0.599859	+	1.03899i	0.992841	+	0.119441i	$0.0381101\pi$
$877$	17.7643	+	30.7687i	0.599859	+	1.03899i	−0.392982	+	0.919546i	$0.628557\pi$
$878$		0			0
$879$	−8.16464	+	14.1416i	−0.275386	+	0.476983i
$880$		0			0
$881$	10.8665			0.366102			0.183051	−	0.983103i	$-0.441403\pi$
$881$	10.8665			0.366102			0.183051	+	0.983103i	$0.441403\pi$
$882$		0			0
$883$	17.7307			0.596686			0.298343	−	0.954459i	$-0.403566\pi$
$883$	17.7307			0.596686			0.298343	+	0.954459i	$0.403566\pi$
$884$		0			0
$885$	4.16199	−	7.20877i	0.139904	−	0.242320i
$886$		0			0
$887$	7.53182	+	13.0455i	0.252894	+	0.438025i	0.964321	−	0.264735i	$-0.0852844\pi$
$887$	7.53182	+	13.0455i	0.252894	+	0.438025i	−0.711428	+	0.702759i	$0.751951\pi$
$888$		0			0
$889$	−4.35480	+	37.6590i	−0.146055	+	1.26304i
$890$		0			0
$891$	16.6461	+	28.8320i	0.557667	+	0.965907i
$892$		0			0
$893$	2.03704	−	3.52826i	0.0681671	−	0.118069i
$894$		0			0
$895$	−2.54696			−0.0851355
$896$		0			0
$897$	37.4161			1.24929
$898$		0			0
$899$	1.56906	−	2.71769i	0.0523310	−	0.0906399i
$900$		0			0
$901$	2.76265	+	4.78505i	0.0920371	+	0.159413i
$902$		0			0
$903$	12.5666	+	9.33147i	0.418189	+	0.310532i
$904$		0			0
$905$	−0.612102	−	1.06019i	−0.0203470	−	0.0352420i
$906$		0			0
$907$	16.6955	−	28.9175i	0.554366	−	0.960190i	−0.443587	−	0.896231i	$-0.646294\pi$
$907$	16.6955	−	28.9175i	0.554366	−	0.960190i	0.997953	−	0.0639582i	$-0.0203724\pi$
$908$		0			0
$909$	−19.9243			−0.660846
$910$		0			0
$911$	−46.2548			−1.53249			−0.766244	−	0.642549i	$-0.777877\pi$
$911$	−46.2548			−1.53249			−0.766244	+	0.642549i	$0.777877\pi$
$912$		0			0
$913$	20.0827	−	34.7842i	0.664639	−	1.15119i
$914$		0			0
$915$	−1.15092	−	1.99346i	−0.0380484	−	0.0659017i
$916$		0			0
$917$	1.33028	−	0.575767i	0.0439297	−	0.0190135i
$918$		0			0
$919$	11.1094	+	19.2421i	0.366466	+	0.634737i	0.989010	−	0.147847i	$-0.0472344\pi$
$919$	11.1094	+	19.2421i	0.366466	+	0.634737i	−0.622544	+	0.782584i	$0.713901\pi$
$920$		0			0
$921$	−19.9518	+	34.5575i	−0.657434	+	1.13871i
$922$		0			0
$923$	12.8442			0.422773
$924$		0			0
$925$	21.1569			0.695634
$926$		0			0
$927$	5.20737	−	9.01943i	0.171033	−	0.296237i
$928$		0			0
$929$	−18.1840	−	31.4956i	−0.596597	−	1.03334i	−0.993319	−	0.115398i	$-0.963186\pi$
$929$	−18.1840	−	31.4956i	−0.596597	−	1.03334i	0.396722	−	0.917939i	$-0.370148\pi$
$930$		0			0
$931$	−1.38192	−	4.57498i	−0.0452906	−	0.149939i
$932$		0			0
$933$	−0.336659	−	0.583111i	−0.0110217	−	0.0190902i
$934$		0			0
$935$	1.47031	−	2.54664i	0.0480841	−	0.0832842i
$936$		0			0
$937$	50.1107			1.63704			0.818522	−	0.574475i	$-0.194794\pi$
$937$	50.1107			1.63704			0.818522	+	0.574475i	$0.194794\pi$
$938$		0			0
$939$	73.4336			2.39642
$940$		0			0
$941$	15.9476	−	27.6220i	0.519876	−	0.900451i	−0.479857	−	0.877346i	$-0.659312\pi$
$941$	15.9476	−	27.6220i	0.519876	−	0.900451i	0.999733	−	0.0231045i	$-0.00735506\pi$
$942$		0			0
$943$	2.05756	+	3.56379i	0.0670032	+	0.116053i
$944$		0			0
$945$	−1.48107	+	0.641032i	−0.0481793	+	0.0208528i
$946$		0			0
$947$	10.8022	+	18.7100i	0.351026	+	0.607995i	0.986429	−	0.164186i	$-0.0524996\pi$
$947$	10.8022	+	18.7100i	0.351026	+	0.607995i	−0.635404	+	0.772180i	$0.719166\pi$
$948$		0			0
$949$	−1.19043	+	2.06189i	−0.0386430	+	0.0669317i
$950$		0			0
$951$	−18.7767			−0.608876
$952$		0			0
$953$	24.8795			0.805928			0.402964	−	0.915216i	$-0.367980\pi$
$953$	24.8795			0.805928			0.402964	+	0.915216i	$0.367980\pi$
$954$		0			0
$955$	0.156634	−	0.271298i	0.00506856	−	0.00877901i
$956$		0			0
$957$	24.0064	+	41.5802i	0.776015	+	1.34410i
$958$		0			0
$959$	−22.0677	−	16.3867i	−0.712602	−	0.529153i
$960$		0			0
$961$	15.3918	+	26.6593i	0.496509	+	0.859978i
$962$		0			0
$963$	6.03263	−	10.4488i	0.194399	−	0.336709i
$964$		0			0
$965$	4.39133			0.141362
$966$		0			0
$967$	40.4487			1.30074			0.650371	−	0.759616i	$-0.274613\pi$
$967$	40.4487			1.30074			0.650371	+	0.759616i	$0.274613\pi$
$968$		0			0
$969$	−2.11046	+	3.65542i	−0.0677976	+	0.117429i
$970$		0			0
$971$	11.6747	+	20.2212i	0.374659	+	0.648928i	0.990276	−	0.139117i	$-0.0444265\pi$
$971$	11.6747	+	20.2212i	0.374659	+	0.648928i	−0.615617	+	0.788046i	$0.711093\pi$
$972$		0			0
$973$	4.99762	−	43.2179i	0.160216	−	1.38550i
$974$		0			0
$975$	−22.1739	−	38.4063i	−0.710132	−	1.22999i
$976$		0			0
$977$	30.3675	−	52.5981i	0.971544	−	1.68276i	0.280645	−	0.959812i	$-0.409452\pi$
$977$	30.3675	−	52.5981i	0.971544	−	1.68276i	0.690899	−	0.722951i	$-0.257215\pi$
$978$		0			0
$979$	43.6331			1.39452
$980$		0			0
$981$	16.1314			0.515035
$982$		0			0
$983$	−24.2799	+	42.0541i	−0.774409	+	1.34132i	0.160717	+	0.987001i	$0.448619\pi$
$983$	−24.2799	+	42.0541i	−0.774409	+	1.34132i	−0.935126	+	0.354315i	$0.884714\pi$
$984$		0			0
$985$	−1.73550	−	3.00598i	−0.0552977	−	0.0957785i
$986$		0			0
$987$	−4.15099	+	35.8966i	−0.132128	+	1.14260i
$988$		0			0
$989$	−5.31829	−	9.21155i	−0.169112	−	0.292910i
$990$		0			0
$991$	−8.99082	+	15.5726i	−0.285603	+	0.494678i	−0.972755	−	0.231835i	$-0.925527\pi$
$991$	−8.99082	+	15.5726i	−0.285603	+	0.494678i	0.687152	+	0.726513i	$0.258860\pi$
$992$		0			0
$993$	28.4781			0.903724
$994$		0			0
$995$	7.69452			0.243933
$996$		0			0
$997$	16.1029	−	27.8910i	0.509983	−	0.883317i	−0.489950	−	0.871751i	$-0.662985\pi$
$997$	16.1029	−	27.8910i	0.509983	−	0.883317i	0.999933	−	0.0115664i	$-0.00368177\pi$
$998$		0			0
$999$	−3.77945	−	6.54620i	−0.119576	−	0.207112i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.i.d.165.1	✓	16
7.2	even	3	inner	1148.2.i.d.821.1	yes	16
7.3	odd	6		8036.2.a.n.1.1		8
7.4	even	3		8036.2.a.m.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.i.d.165.1	✓	16	1.1	even	1	trivial
1148.2.i.d.821.1	yes	16	7.2	even	3	inner
8036.2.a.m.1.8		8	7.4	even	3
8036.2.a.n.1.1		8	7.3	odd	6

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.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.14440 + 1.98216i) q^{3} +(-0.175017 - 0.303139i) q^{5} +(-0.303923 + 2.62824i) q^{7} +(-1.11932 - 1.93871i) q^{9} +O(q^{10})\)	\(q+(-1.14440 + 1.98216i) q^{3} +(-0.175017 - 0.303139i) q^{5} +(-0.303923 + 2.62824i) q^{7} +(-1.11932 - 1.93871i) q^{9} +(-1.55507 + 2.69346i) q^{11} -3.97253 q^{13} +0.801161 q^{15} +(1.35057 - 2.33925i) q^{17} +(0.341367 + 0.591264i) q^{19} +(-4.86179 - 3.61019i) q^{21} +(2.05756 + 3.56379i) q^{23} +(2.43874 - 4.22402i) q^{25} -1.74262 q^{27} -6.74476 q^{29} +(-0.232633 + 0.402933i) q^{31} +(-3.55926 - 6.16482i) q^{33} +(0.849913 - 0.367856i) q^{35} +(2.16883 + 3.75653i) q^{37} +(4.54618 - 7.87421i) q^{39} +1.00000 q^{41} -2.58476 q^{43} +(-0.391800 + 0.678617i) q^{45} +(-2.98366 - 5.16785i) q^{47} +(-6.81526 - 1.59756i) q^{49} +(3.09119 + 5.35409i) q^{51} +(-1.02277 + 1.77149i) q^{53} +1.08866 q^{55} -1.56264 q^{57} +(5.19494 - 8.99790i) q^{59} +(-1.43657 - 2.48821i) q^{61} +(5.43559 - 2.35261i) q^{63} +(0.695262 + 1.20423i) q^{65} +(1.57698 - 2.73142i) q^{67} -9.41870 q^{69} -3.23326 q^{71} +(0.299666 - 0.519036i) q^{73} +(5.58180 + 9.66796i) q^{75} +(-6.60644 - 4.90570i) q^{77} +(0.428075 + 0.741447i) q^{79} +(5.35221 - 9.27030i) q^{81} -12.9143 q^{83} -0.945491 q^{85} +(7.71873 - 13.3692i) q^{87} +(-7.01464 - 12.1497i) q^{89} +(1.20734 - 10.4408i) q^{91} +(-0.532452 - 0.922235i) q^{93} +(0.119490 - 0.206963i) q^{95} -3.40759 q^{97} +6.96247 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{9}+O(q^{10}) \) 16 * q - 4 * q^9	\( 16 q - 4 q^{9} + 8 q^{11} - 14 q^{13} - 2 q^{15} + q^{17} - 4 q^{19} + 13 q^{21} + 3 q^{23} + 4 q^{25} - 24 q^{27} - 8 q^{29} - 4 q^{31} - 23 q^{33} + 12 q^{35} + 31 q^{37} - 5 q^{39} + 16 q^{41} - 16 q^{43} - q^{45} - 24 q^{47} + 16 q^{49} + 23 q^{51} + q^{53} + 4 q^{55} - 30 q^{57} - 4 q^{59} + 4 q^{61} + 23 q^{63} + 24 q^{65} - 42 q^{69} + 16 q^{71} - 11 q^{73} + 15 q^{75} + 25 q^{77} - 14 q^{79} + 28 q^{81} - 84 q^{83} - 40 q^{85} - 25 q^{87} + 11 q^{89} + 7 q^{91} + 27 q^{93} + 15 q^{95} - 32 q^{97} - 16 q^{99}+O(q^{100}) \) 16 * q - 4 * q^9 + 8 * q^11 - 14 * q^13 - 2 * q^15 + q^17 - 4 * q^19 + 13 * q^21 + 3 * q^23 + 4 * q^25 - 24 * q^27 - 8 * q^29 - 4 * q^31 - 23 * q^33 + 12 * q^35 + 31 * q^37 - 5 * q^39 + 16 * q^41 - 16 * q^43 - q^45 - 24 * q^47 + 16 * q^49 + 23 * q^51 + q^53 + 4 * q^55 - 30 * q^57 - 4 * q^59 + 4 * q^61 + 23 * q^63 + 24 * q^65 - 42 * q^69 + 16 * q^71 - 11 * q^73 + 15 * q^75 + 25 * q^77 - 14 * q^79 + 28 * q^81 - 84 * q^83 - 40 * q^85 - 25 * q^87 + 11 * q^89 + 7 * q^91 + 27 * q^93 + 15 * q^95 - 32 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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