LMFDB - Embedded newform 1148.2.k.b.337.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(337,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 3]))

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

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

chi := DirichletCharacter("1148.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.k (of order $4$, 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:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			337.4
Character	$\chi$	$=$	1148.337
Dual form			1148.2.k.b.729.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.64273 - 1.64273i) q^{3} -1.39147i q^{5} +(-0.707107 - 0.707107i) q^{7} +2.39713i q^{9} +O(q^{10})$	\(q+(-1.64273 - 1.64273i) q^{3} -1.39147i q^{5} +(-0.707107 - 0.707107i) q^{7} +2.39713i q^{9} +(3.79701 + 3.79701i) q^{11} +(3.40984 + 3.40984i) q^{13} +(-2.28582 + 2.28582i) q^{15} +(-2.83732 + 2.83732i) q^{17} +(-5.63692 + 5.63692i) q^{19} +2.32317i q^{21} +2.68666 q^{23} +3.06380 q^{25} +(-0.990346 + 0.990346i) q^{27} +(-2.77861 - 2.77861i) q^{29} +2.87366 q^{31} -12.4749i q^{33} +(-0.983920 + 0.983920i) q^{35} +6.03663 q^{37} -11.2029i q^{39} +(5.64675 - 3.01897i) q^{41} +1.35884i q^{43} +3.33555 q^{45} +(-9.35772 + 9.35772i) q^{47} +1.00000i q^{49} +9.32190 q^{51} +(5.67130 + 5.67130i) q^{53} +(5.28344 - 5.28344i) q^{55} +18.5199 q^{57} +6.26308 q^{59} -8.87031i q^{61} +(1.69503 - 1.69503i) q^{63} +(4.74470 - 4.74470i) q^{65} +(3.51370 - 3.51370i) q^{67} +(-4.41346 - 4.41346i) q^{69} +(-1.21557 - 1.21557i) q^{71} +12.7207i q^{73} +(-5.03301 - 5.03301i) q^{75} -5.36978i q^{77} +(-6.61093 - 6.61093i) q^{79} +10.4451 q^{81} -3.94145 q^{83} +(3.94805 + 3.94805i) q^{85} +9.12901i q^{87} +(-0.812315 - 0.812315i) q^{89} -4.82225i q^{91} +(-4.72065 - 4.72065i) q^{93} +(7.84363 + 7.84363i) q^{95} +(-13.3552 + 13.3552i) q^{97} +(-9.10195 + 9.10195i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q+O(q^{10}) $ 36 * q	$ 36 q - 12 q^{11} - 16 q^{17} - 4 q^{19} - 36 q^{23} - 64 q^{25} + 12 q^{27} + 16 q^{29} - 28 q^{31} + 12 q^{35} + 48 q^{37} + 4 q^{41} + 36 q^{45} + 12 q^{47} - 12 q^{51} - 12 q^{53} + 12 q^{55} + 76 q^{57} + 20 q^{59} - 4 q^{65} - 44 q^{67} + 72 q^{69} - 20 q^{71} + 72 q^{75} - 8 q^{79} - 100 q^{81} - 40 q^{83} - 8 q^{85} - 16 q^{89} + 20 q^{93} + 76 q^{95} - 16 q^{97} + 56 q^{99}+O(q^{100}) $ 36 * q - 12 * q^11 - 16 * q^17 - 4 * q^19 - 36 * q^23 - 64 * q^25 + 12 * q^27 + 16 * q^29 - 28 * q^31 + 12 * q^35 + 48 * q^37 + 4 * q^41 + 36 * q^45 + 12 * q^47 - 12 * q^51 - 12 * q^53 + 12 * q^55 + 76 * q^57 + 20 * q^59 - 4 * q^65 - 44 * q^67 + 72 * q^69 - 20 * q^71 + 72 * q^75 - 8 * q^79 - 100 * q^81 - 40 * q^83 - 8 * q^85 - 16 * q^89 + 20 * q^93 + 76 * q^95 - 16 * q^97 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.64273	−	1.64273i	−0.948432	−	0.948432i	0.0503025	−	0.998734i	$-0.483981\pi$
$3$	−1.64273	−	1.64273i	−0.948432	−	0.948432i	−0.998734	+	0.0503025i	$0.983981\pi$
$4$		0			0
$5$		−	1.39147i		−	0.622286i	−0.950363	−	0.311143i	$-0.899288\pi$
$5$		−	1.39147i		−	0.622286i	0.950363	−	0.311143i	$-0.100712\pi$
$6$		0			0
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$		0			0
$9$			2.39713i			0.799045i
$10$		0			0
$11$	3.79701	+	3.79701i	1.14484	+	1.14484i	0.987553	+	0.157289i	$0.0502756\pi$
$11$	3.79701	+	3.79701i	1.14484	+	1.14484i	0.157289	+	0.987553i	$0.449724\pi$
$12$		0			0
$13$	3.40984	+	3.40984i	0.945720	+	0.945720i	0.998601	−	0.0528807i	$-0.0168403\pi$
$13$	3.40984	+	3.40984i	0.945720	+	0.945720i	−0.0528807	+	0.998601i	$0.516840\pi$
$14$		0			0
$15$	−2.28582	+	2.28582i	−0.590195	+	0.590195i
$16$		0			0
$17$	−2.83732	+	2.83732i	−0.688150	+	0.688150i	−0.961823	−	0.273673i	$-0.911762\pi$
$17$	−2.83732	+	2.83732i	−0.688150	+	0.688150i	0.273673	+	0.961823i	$0.411762\pi$
$18$		0			0
$19$	−5.63692	+	5.63692i	−1.29320	+	1.29320i	−0.360401	+	0.932797i	$0.617360\pi$
$19$	−5.63692	+	5.63692i	−1.29320	+	1.29320i	−0.932797	+	0.360401i	$0.882640\pi$
$20$		0			0
$21$			2.32317i			0.506958i
$22$		0			0
$23$	2.68666			0.560208			0.280104	−	0.959970i	$-0.409631\pi$
$23$	2.68666			0.560208			0.280104	+	0.959970i	$0.409631\pi$
$24$		0			0
$25$	3.06380			0.612761
$26$		0			0
$27$	−0.990346	+	0.990346i	−0.190592	+	0.190592i
$28$		0			0
$29$	−2.77861	−	2.77861i	−0.515974	−	0.515974i	0.400377	−	0.916351i	$-0.368879\pi$
$29$	−2.77861	−	2.77861i	−0.515974	−	0.515974i	−0.916351	+	0.400377i	$0.868879\pi$
$30$		0			0
$31$	2.87366			0.516124			0.258062	−	0.966128i	$-0.416916\pi$
$31$	2.87366			0.516124			0.258062	+	0.966128i	$0.416916\pi$
$32$		0			0
$33$		−	12.4749i		−	2.17161i
$34$		0			0
$35$	−0.983920	+	0.983920i	−0.166313	+	0.166313i
$36$		0			0
$37$	6.03663			0.992416			0.496208	−	0.868204i	$-0.334725\pi$
$37$	6.03663			0.992416			0.496208	+	0.868204i	$0.334725\pi$
$38$		0			0
$39$		−	11.2029i		−	1.79390i
$40$		0			0
$41$	5.64675	−	3.01897i	0.881875	−	0.471484i
$41$	5.64675	−	3.01897i	0.881875	−	0.471484i
$42$		0			0
$43$			1.35884i			0.207221i	0.994618	+	0.103610i	$0.0330395\pi$
$43$			1.35884i			0.207221i	−0.994618	+	0.103610i	$0.966961\pi$
$44$		0			0
$45$	3.33555			0.497234
$46$		0			0
$47$	−9.35772	+	9.35772i	−1.36496	+	1.36496i	−0.497498	+	0.867465i	$0.665748\pi$
$47$	−9.35772	+	9.35772i	−1.36496	+	1.36496i	−0.867465	+	0.497498i	$0.834252\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$		0			0
$51$	9.32190			1.30533
$52$		0			0
$53$	5.67130	+	5.67130i	0.779012	+	0.779012i	0.979663	−	0.200651i	$-0.0643056\pi$
$53$	5.67130	+	5.67130i	0.779012	+	0.779012i	−0.200651	+	0.979663i	$0.564306\pi$
$54$		0			0
$55$	5.28344	−	5.28344i	0.712419	−	0.712419i
$56$		0			0
$57$	18.5199			2.45302
$58$		0			0
$59$	6.26308			0.815384			0.407692	−	0.913119i	$-0.366334\pi$
$59$	6.26308			0.815384			0.407692	+	0.913119i	$0.366334\pi$
$60$		0			0
$61$		−	8.87031i		−	1.13573i	−0.823123	−	0.567863i	$-0.807770\pi$
$61$		−	8.87031i		−	1.13573i	0.823123	−	0.567863i	$-0.192230\pi$
$62$		0			0
$63$	1.69503	−	1.69503i	0.213554	−	0.213554i
$64$		0			0
$65$	4.74470	−	4.74470i	0.588508	−	0.588508i
$66$		0			0
$67$	3.51370	−	3.51370i	0.429267	−	0.429267i	−0.459112	−	0.888379i	$-0.651832\pi$
$67$	3.51370	−	3.51370i	0.429267	−	0.429267i	0.888379	+	0.459112i	$0.151832\pi$
$68$		0			0
$69$	−4.41346	−	4.41346i	−0.531318	−	0.531318i
$70$		0			0
$71$	−1.21557	−	1.21557i	−0.144262	−	0.144262i	0.631287	−	0.775549i	$-0.282527\pi$
$71$	−1.21557	−	1.21557i	−0.144262	−	0.144262i	−0.775549	+	0.631287i	$0.782527\pi$
$72$		0			0
$73$			12.7207i			1.48884i	0.667710	+	0.744421i	$0.267275\pi$
$73$			12.7207i			1.48884i	−0.667710	+	0.744421i	$0.732725\pi$
$74$		0			0
$75$	−5.03301	−	5.03301i	−0.581161	−	0.581161i
$76$		0			0
$77$		−	5.36978i		−	0.611944i
$78$		0			0
$79$	−6.61093	−	6.61093i	−0.743788	−	0.743788i	0.229517	−	0.973305i	$-0.426285\pi$
$79$	−6.61093	−	6.61093i	−0.743788	−	0.743788i	−0.973305	+	0.229517i	$0.926285\pi$
$80$		0			0
$81$	10.4451			1.16057
$82$		0			0
$83$	−3.94145			−0.432631			−0.216315	−	0.976324i	$-0.569404\pi$
$83$	−3.94145			−0.432631			−0.216315	+	0.976324i	$0.569404\pi$
$84$		0			0
$85$	3.94805	+	3.94805i	0.428226	+	0.428226i
$86$		0			0
$87$			9.12901i			0.978732i
$88$		0			0
$89$	−0.812315	−	0.812315i	−0.0861052	−	0.0861052i	0.662742	−	0.748848i	$-0.269392\pi$
$89$	−0.812315	−	0.812315i	−0.0861052	−	0.0861052i	−0.748848	+	0.662742i	$0.769392\pi$
$90$		0			0
$91$		−	4.82225i		−	0.505509i
$92$		0			0
$93$	−4.72065	−	4.72065i	−0.489508	−	0.489508i
$94$		0			0
$95$	7.84363	+	7.84363i	0.804739	+	0.804739i
$96$		0			0
$97$	−13.3552	+	13.3552i	−1.35601	+	1.35601i	−0.477240	+	0.878773i	$0.658363\pi$
$97$	−13.3552	+	13.3552i	−1.35601	+	1.35601i	−0.878773	+	0.477240i	$0.841637\pi$
$98$		0			0
$99$	−9.10195	+	9.10195i	−0.914780	+	0.914780i
$100$		0			0
$101$	7.66669	−	7.66669i	0.762864	−	0.762864i	−0.213975	−	0.976839i	$-0.568641\pi$
$101$	7.66669	−	7.66669i	0.762864	−	0.762864i	0.976839	+	0.213975i	$0.0686410\pi$
$102$		0			0
$103$			7.71218i			0.759904i	0.925006	+	0.379952i	$0.124059\pi$
$103$			7.71218i			0.759904i	−0.925006	+	0.379952i	$0.875941\pi$
$104$		0			0
$105$	3.23263			0.315473
$106$		0			0
$107$	2.84612			0.275145			0.137572	−	0.990492i	$-0.456070\pi$
$107$	2.84612			0.275145			0.137572	+	0.990492i	$0.456070\pi$
$108$		0			0
$109$	11.1648	−	11.1648i	1.06940	−	1.06940i	0.0719931	−	0.997405i	$-0.477064\pi$
$109$	11.1648	−	11.1648i	1.06940	−	1.06940i	0.997405	−	0.0719931i	$-0.0229359\pi$
$110$		0			0
$111$	−9.91657	−	9.91657i	−0.941239	−	0.941239i
$112$		0			0
$113$	0.0526448			0.00495241			0.00247620	−	0.999997i	$-0.499212\pi$
$113$	0.0526448			0.00495241			0.00247620	+	0.999997i	$0.499212\pi$
$114$		0			0
$115$		−	3.73842i		−	0.348609i
$116$		0			0
$117$	−8.17385	+	8.17385i	−0.755673	+	0.755673i
$118$		0			0
$119$	4.01257			0.367832
$120$		0			0
$121$			17.8346i			1.62133i
$122$		0			0
$123$	−14.2355	−	4.31674i	−1.28357	−	0.389227i
$124$		0			0
$125$		−	11.2206i		−	1.00360i
$126$		0			0
$127$	−12.1760			−1.08045			−0.540223	−	0.841522i	$-0.681660\pi$
$127$	−12.1760			−1.08045			−0.540223	+	0.841522i	$0.681660\pi$
$128$		0			0
$129$	2.23220	−	2.23220i	0.196535	−	0.196535i
$130$		0			0
$131$			1.19620i			0.104512i	0.998634	+	0.0522561i	$0.0166412\pi$
$131$			1.19620i			0.104512i	−0.998634	+	0.0522561i	$0.983359\pi$
$132$		0			0
$133$	7.97181			0.691244
$134$		0			0
$135$	1.37804	+	1.37804i	0.118603	+	0.118603i
$136$		0			0
$137$	6.88192	−	6.88192i	0.587962	−	0.587962i	−0.349117	−	0.937079i	$-0.613518\pi$
$137$	6.88192	−	6.88192i	0.587962	−	0.587962i	0.937079	+	0.349117i	$0.113518\pi$
$138$		0			0
$139$	13.0070			1.10324			0.551620	−	0.834096i	$-0.314010\pi$
$139$	13.0070			1.10324			0.551620	+	0.834096i	$0.314010\pi$
$140$		0			0
$141$	30.7444			2.58915
$142$		0			0
$143$			25.8944i			2.16540i
$144$		0			0
$145$	−3.86635	+	3.86635i	−0.321083	+	0.321083i
$146$		0			0
$147$	1.64273	−	1.64273i	0.135490	−	0.135490i
$148$		0			0
$149$	−2.07975	+	2.07975i	−0.170380	+	0.170380i	−0.787146	−	0.616767i	$-0.788442\pi$
$149$	−2.07975	+	2.07975i	−0.170380	+	0.170380i	0.616767	+	0.787146i	$0.288442\pi$
$150$		0			0
$151$	10.6935	+	10.6935i	0.870224	+	0.870224i	0.992497	−	0.122272i	$-0.0390181\pi$
$151$	10.6935	+	10.6935i	0.870224	+	0.870224i	−0.122272	+	0.992497i	$0.539018\pi$
$152$		0			0
$153$	−6.80143	−	6.80143i	−0.549863	−	0.549863i
$154$		0			0
$155$		−	3.99861i		−	0.321176i
$156$		0			0
$157$	11.8460	+	11.8460i	0.945413	+	0.945413i	0.998585	−	0.0531721i	$-0.0169332\pi$
$157$	11.8460	+	11.8460i	0.945413	+	0.945413i	−0.0531721	+	0.998585i	$0.516933\pi$
$158$		0			0
$159$		−	18.6328i		−	1.47768i
$160$		0			0
$161$	−1.89976	−	1.89976i	−0.149722	−	0.149722i
$162$		0			0
$163$	−8.57541			−0.671678			−0.335839	−	0.941919i	$-0.609020\pi$
$163$	−8.57541			−0.671678			−0.335839	+	0.941919i	$0.609020\pi$
$164$		0			0
$165$	−17.3585			−1.35136
$166$		0			0
$167$	−11.6900	−	11.6900i	−0.904603	−	0.904603i	0.0912274	−	0.995830i	$-0.470921\pi$
$167$	−11.6900	−	11.6900i	−0.904603	−	0.904603i	−0.995830	+	0.0912274i	$0.970921\pi$
$168$		0			0
$169$			10.2540i			0.788773i
$170$		0			0
$171$	−13.5125	−	13.5125i	−1.03332	−	1.03332i
$172$		0			0
$173$		−	13.1738i		−	1.00158i	−0.865568	−	0.500791i	$-0.833042\pi$
$173$		−	13.1738i		−	1.00158i	0.865568	−	0.500791i	$-0.166958\pi$
$174$		0			0
$175$	−2.16644	−	2.16644i	−0.163767	−	0.163767i
$176$		0			0
$177$	−10.2886	−	10.2886i	−0.773336	−	0.773336i
$178$		0			0
$179$	−12.9575	+	12.9575i	−0.968487	+	0.968487i	−0.999518	−	0.0310315i	$-0.990121\pi$
$179$	−12.9575	+	12.9575i	−0.968487	+	0.968487i	0.0310315	+	0.999518i	$0.490121\pi$
$180$		0			0
$181$	−1.88580	+	1.88580i	−0.140170	+	0.140170i	−0.773710	−	0.633540i	$-0.781601\pi$
$181$	−1.88580	+	1.88580i	−0.140170	+	0.140170i	0.633540	+	0.773710i	$0.281601\pi$
$182$		0			0
$183$	−14.5715	+	14.5715i	−1.07716	+	1.07716i
$184$		0			0
$185$		−	8.39981i		−	0.617566i
$186$		0			0
$187$	−21.5466			−1.57565
$188$		0			0
$189$	1.40056			0.101876
$190$		0			0
$191$	−4.02417	+	4.02417i	−0.291178	+	0.291178i	−0.837546	−	0.546367i	$-0.816010\pi$
$191$	−4.02417	+	4.02417i	−0.291178	+	0.291178i	0.546367	+	0.837546i	$0.316010\pi$
$192$		0			0
$193$	12.5676	+	12.5676i	0.904637	+	0.904637i	0.995833	−	0.0911963i	$-0.0290691\pi$
$193$	12.5676	+	12.5676i	0.904637	+	0.904637i	−0.0911963	+	0.995833i	$0.529069\pi$
$194$		0			0
$195$	−15.5886			−1.11632
$196$		0			0
$197$			0.835521i			0.0595284i	0.999557	+	0.0297642i	$0.00947565\pi$
$197$			0.835521i			0.0595284i	−0.999557	+	0.0297642i	$0.990524\pi$
$198$		0			0
$199$	5.34776	−	5.34776i	0.379093	−	0.379093i	−0.491682	−	0.870775i	$-0.663618\pi$
$199$	5.34776	−	5.34776i	0.379093	−	0.379093i	0.870775	+	0.491682i	$0.163618\pi$
$200$		0			0
$201$	−11.5441			−0.814260
$202$		0			0
$203$			3.92954i			0.275800i
$204$		0			0
$205$	−4.20082	−	7.85730i	−0.293398	−	0.548778i
$206$		0			0
$207$			6.44029i			0.447631i
$208$		0			0
$209$	−42.8069			−2.96102
$210$		0			0
$211$	−9.90360	+	9.90360i	−0.681792	+	0.681792i	−0.960404	−	0.278612i	$-0.910126\pi$
$211$	−9.90360	+	9.90360i	−0.681792	+	0.681792i	0.278612	+	0.960404i	$0.410126\pi$
$212$		0			0
$213$			3.99372i			0.273645i
$214$		0			0
$215$	1.89078			0.128950
$216$		0			0
$217$	−2.03198	−	2.03198i	−0.137940	−	0.137940i
$218$		0			0
$219$	20.8967	−	20.8967i	1.41207	−	1.41207i
$220$		0			0
$221$	−19.3496			−1.30160
$222$		0			0
$223$	18.8022			1.25909			0.629543	−	0.776965i	$-0.283242\pi$
$223$	18.8022			1.25909			0.629543	+	0.776965i	$0.283242\pi$
$224$		0			0
$225$			7.34435i			0.489623i
$226$		0			0
$227$	15.7584	−	15.7584i	1.04592	−	1.04592i	0.0470287	−	0.998894i	$-0.485025\pi$
$227$	15.7584	−	15.7584i	1.04592	−	1.04592i	0.998894	−	0.0470287i	$-0.0149752\pi$
$228$		0			0
$229$	−19.5153	+	19.5153i	−1.28961	+	1.28961i	−0.354583	+	0.935024i	$0.615377\pi$
$229$	−19.5153	+	19.5153i	−1.28961	+	1.28961i	−0.935024	+	0.354583i	$0.884623\pi$
$230$		0			0
$231$	−8.82112	+	8.82112i	−0.580387	+	0.580387i
$232$		0			0
$233$	3.06475	+	3.06475i	0.200779	+	0.200779i	0.800334	−	0.599555i	$-0.204656\pi$
$233$	3.06475	+	3.06475i	0.200779	+	0.200779i	−0.599555	+	0.800334i	$0.704656\pi$
$234$		0			0
$235$	13.0210	+	13.0210i	0.849397	+	0.849397i
$236$		0			0
$237$			21.7200i			1.41086i
$238$		0			0
$239$	4.89582	+	4.89582i	0.316684	+	0.316684i	0.847492	−	0.530808i	$-0.178111\pi$
$239$	4.89582	+	4.89582i	0.316684	+	0.316684i	−0.530808	+	0.847492i	$0.678111\pi$
$240$		0			0
$241$		−	4.74927i		−	0.305928i	−0.988232	−	0.152964i	$-0.951118\pi$
$241$		−	4.74927i		−	0.305928i	0.988232	−	0.152964i	$-0.0488818\pi$
$242$		0			0
$243$	−14.1875	−	14.1875i	−0.910131	−	0.910131i
$244$		0			0
$245$	1.39147			0.0888980
$246$		0			0
$247$	−38.4420			−2.44601
$248$		0			0
$249$	6.47475	+	6.47475i	0.410321	+	0.410321i
$250$		0			0
$251$		−	9.44955i		−	0.596450i	−0.954496	−	0.298225i	$-0.903605\pi$
$251$		−	9.44955i		−	0.596450i	0.954496	−	0.298225i	$-0.0963947\pi$
$252$		0			0
$253$	10.2013	+	10.2013i	0.641349	+	0.641349i
$254$		0			0
$255$		−	12.9712i		−	0.812286i
$256$		0			0
$257$	−15.6853	−	15.6853i	−0.978419	−	0.978419i	0.0213529	−	0.999772i	$-0.493203\pi$
$257$	−15.6853	−	15.6853i	−0.978419	−	0.978419i	−0.999772	+	0.0213529i	$0.993203\pi$
$258$		0			0
$259$	−4.26854	−	4.26854i	−0.265234	−	0.265234i
$260$		0			0
$261$	6.66069	−	6.66069i	0.412286	−	0.412286i
$262$		0			0
$263$	−18.3551	+	18.3551i	−1.13183	+	1.13183i	−0.141953	+	0.989873i	$0.545338\pi$
$263$	−18.3551	+	18.3551i	−1.13183	+	1.13183i	−0.989873	+	0.141953i	$0.954662\pi$
$264$		0			0
$265$	7.89145	−	7.89145i	0.484768	−	0.484768i
$266$		0			0
$267$			2.66883i			0.163330i
$268$		0			0
$269$	29.5365			1.80087			0.900435	−	0.434991i	$-0.143248\pi$
$269$	29.5365			1.80087			0.900435	+	0.434991i	$0.143248\pi$
$270$		0			0
$271$	12.9241			0.785082			0.392541	−	0.919735i	$-0.371596\pi$
$271$	12.9241			0.785082			0.392541	+	0.919735i	$0.371596\pi$
$272$		0			0
$273$	−7.92165	+	7.92165i	−0.479440	+	0.479440i
$274$		0			0
$275$	11.6333	+	11.6333i	0.701514	+	0.701514i
$276$		0			0
$277$	−28.1335			−1.69038			−0.845189	−	0.534468i	$-0.820512\pi$
$277$	−28.1335			−1.69038			−0.845189	+	0.534468i	$0.820512\pi$
$278$		0			0
$279$			6.88854i			0.412406i
$280$		0			0
$281$	−9.16870	+	9.16870i	−0.546959	+	0.546959i	−0.925560	−	0.378601i	$-0.876405\pi$
$281$	−9.16870	+	9.16870i	−0.546959	+	0.546959i	0.378601	+	0.925560i	$0.376405\pi$
$282$		0			0
$283$	−5.44352			−0.323584			−0.161792	−	0.986825i	$-0.551727\pi$
$283$	−5.44352			−0.323584			−0.161792	+	0.986825i	$0.551727\pi$
$284$		0			0
$285$		−	25.7699i		−	1.52648i
$286$		0			0
$287$	−6.12759	−	1.85812i	−0.361700	−	0.109681i
$288$		0			0
$289$			0.899270i			0.0528982i
$290$		0			0
$291$	43.8779			2.57217
$292$		0			0
$293$	12.7779	−	12.7779i	0.746493	−	0.746493i	−0.227326	−	0.973819i	$-0.572998\pi$
$293$	12.7779	−	12.7779i	0.746493	−	0.746493i	0.973819	+	0.227326i	$0.0729982\pi$
$294$		0			0
$295$		−	8.71491i		−	0.507402i
$296$		0			0
$297$	−7.52071			−0.436396
$298$		0			0
$299$	9.16109	+	9.16109i	0.529800	+	0.529800i
$300$		0			0
$301$	0.960843	−	0.960843i	0.0553820	−	0.0553820i
$302$		0			0
$303$	−25.1886			−1.44705
$304$		0			0
$305$	−12.3428			−0.706746
$306$		0			0
$307$			26.0196i			1.48502i	0.669836	+	0.742509i	$0.266365\pi$
$307$			26.0196i			1.48502i	−0.669836	+	0.742509i	$0.733635\pi$
$308$		0			0
$309$	12.6690	−	12.6690i	0.720717	−	0.720717i
$310$		0			0
$311$	−3.91468	+	3.91468i	−0.221981	+	0.221981i	−0.809332	−	0.587351i	$-0.800171\pi$
$311$	−3.91468	+	3.91468i	−0.221981	+	0.221981i	0.587351	+	0.809332i	$0.300171\pi$
$312$		0			0
$313$	18.4030	−	18.4030i	1.04020	−	1.04020i	0.0410391	−	0.999158i	$-0.486933\pi$
$313$	18.4030	−	18.4030i	1.04020	−	1.04020i	0.999158	−	0.0410391i	$-0.0130668\pi$
$314$		0			0
$315$	−2.35859	−	2.35859i	−0.132891	−	0.132891i
$316$		0			0
$317$	−7.37950	−	7.37950i	−0.414474	−	0.414474i	0.468820	−	0.883294i	$-0.344679\pi$
$317$	−7.37950	−	7.37950i	−0.414474	−	0.414474i	−0.883294	+	0.468820i	$0.844679\pi$
$318$		0			0
$319$		−	21.1008i		−	1.18142i
$320$		0			0
$321$	−4.67541	−	4.67541i	−0.260956	−	0.260956i
$322$		0			0
$323$		−	31.9875i		−	1.77983i
$324$		0			0
$325$	10.4471	+	10.4471i	0.579500	+	0.579500i
$326$		0			0
$327$	−36.6817			−2.02850
$328$		0			0
$329$	13.2338			0.729603
$330$		0			0
$331$	−3.98460	−	3.98460i	−0.219014	−	0.219014i	0.589069	−	0.808083i	$-0.299495\pi$
$331$	−3.98460	−	3.98460i	−0.219014	−	0.219014i	−0.808083	+	0.589069i	$0.799495\pi$
$332$		0			0
$333$			14.4706i			0.792985i
$334$		0			0
$335$	−4.88922	−	4.88922i	−0.267127	−	0.267127i
$336$		0			0
$337$			29.4260i			1.60294i	0.598037	+	0.801469i	$0.295948\pi$
$337$			29.4260i			1.60294i	−0.598037	+	0.801469i	$0.704052\pi$
$338$		0			0
$339$	−0.0864813	−	0.0864813i	−0.00469702	−	0.00469702i
$340$		0			0
$341$	10.9113	+	10.9113i	0.590880	+	0.590880i
$342$		0			0
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$		0			0
$345$	−6.14121	+	6.14121i	−0.330632	+	0.330632i
$346$		0			0
$347$	23.3854	−	23.3854i	1.25540	−	1.25540i	0.302128	−	0.953267i	$-0.402303\pi$
$347$	23.3854	−	23.3854i	1.25540	−	1.25540i	0.953267	−	0.302128i	$-0.0976970\pi$
$348$		0			0
$349$			12.8398i			0.687298i	0.939098	+	0.343649i	$0.111663\pi$
$349$			12.8398i			0.687298i	−0.939098	+	0.343649i	$0.888337\pi$
$350$		0			0
$351$	−6.75385			−0.360494
$352$		0			0
$353$	−26.4153			−1.40594			−0.702971	−	0.711218i	$-0.748144\pi$
$353$	−26.4153			−1.40594			−0.702971	+	0.711218i	$0.748144\pi$
$354$		0			0
$355$	−1.69144	+	1.69144i	−0.0897722	+	0.0897722i
$356$		0			0
$357$	−6.59158	−	6.59158i	−0.348863	−	0.348863i
$358$		0			0
$359$	21.3610			1.12739			0.563695	−	0.825983i	$-0.309379\pi$
$359$	21.3610			1.12739			0.563695	+	0.825983i	$0.309379\pi$
$360$		0			0
$361$		−	44.5498i		−	2.34473i
$362$		0			0
$363$	29.2974	−	29.2974i	1.53772	−	1.53772i
$364$		0			0
$365$	17.7005			0.926485
$366$		0			0
$367$			35.7700i			1.86718i	0.358348	+	0.933588i	$0.383340\pi$
$367$			35.7700i			1.86718i	−0.358348	+	0.933588i	$0.616660\pi$
$368$		0			0
$369$	7.23688	+	13.5360i	0.376737	+	0.704657i
$370$		0			0
$371$		−	8.02042i		−	0.416400i
$372$		0			0
$373$	2.33828			0.121072			0.0605358	−	0.998166i	$-0.480719\pi$
$373$	2.33828			0.121072			0.0605358	+	0.998166i	$0.480719\pi$
$374$		0			0
$375$	−18.4324	+	18.4324i	−0.951844	+	0.951844i
$376$		0			0
$377$		−	18.9492i		−	0.975934i
$378$		0			0
$379$	16.1375			0.828930			0.414465	−	0.910065i	$-0.363969\pi$
$379$	16.1375			0.828930			0.414465	+	0.910065i	$0.363969\pi$
$380$		0			0
$381$	20.0019	+	20.0019i	1.02473	+	1.02473i
$382$		0			0
$383$	14.2602	−	14.2602i	0.728663	−	0.728663i	−0.241691	−	0.970353i	$-0.577702\pi$
$383$	14.2602	−	14.2602i	0.728663	−	0.728663i	0.970353	+	0.241691i	$0.0777019\pi$
$384$		0			0
$385$	−7.47191			−0.380804
$386$		0			0
$387$	−3.25731			−0.165579
$388$		0			0
$389$			0.673571i			0.0341514i	0.999854	+	0.0170757i	$0.00543563\pi$
$389$			0.673571i			0.0341514i	−0.999854	+	0.0170757i	$0.994564\pi$
$390$		0			0
$391$	−7.62291	+	7.62291i	−0.385507	+	0.385507i
$392$		0			0
$393$	1.96503	−	1.96503i	0.0991226	−	0.0991226i
$394$		0			0
$395$	−9.19893	+	9.19893i	−0.462849	+	0.462849i
$396$		0			0
$397$	20.1287	+	20.1287i	1.01023	+	1.01023i	0.999947	+	0.0102814i	$0.00327272\pi$
$397$	20.1287	+	20.1287i	1.01023	+	1.01023i	0.0102814	+	0.999947i	$0.496727\pi$
$398$		0			0
$399$	−13.0955	−	13.0955i	−0.655597	−	0.655597i
$400$		0			0
$401$			26.1701i			1.30687i	0.756982	+	0.653436i	$0.226673\pi$
$401$			26.1701i			1.30687i	−0.756982	+	0.653436i	$0.773327\pi$
$402$		0			0
$403$	9.79871	+	9.79871i	0.488109	+	0.488109i
$404$		0			0
$405$		−	14.5341i		−	0.722207i
$406$		0			0
$407$	22.9212	+	22.9212i	1.13616	+	1.13616i
$408$		0			0
$409$	−15.2193			−0.752545			−0.376273	−	0.926509i	$-0.622794\pi$
$409$	−15.2193			−0.752545			−0.376273	+	0.926509i	$0.622794\pi$
$410$		0			0
$411$	−22.6103			−1.11528
$412$		0			0
$413$	−4.42867	−	4.42867i	−0.217921	−	0.217921i
$414$		0			0
$415$			5.48443i			0.269220i
$416$		0			0
$417$	−21.3670	−	21.3670i	−1.04635	−	1.04635i
$418$		0			0
$419$		−	27.8634i		−	1.36121i	−0.732649	−	0.680607i	$-0.761716\pi$
$419$		−	27.8634i		−	1.36121i	0.732649	−	0.680607i	$-0.238284\pi$
$420$		0			0
$421$	10.2472	+	10.2472i	0.499420	+	0.499420i	0.911257	−	0.411838i	$-0.135113\pi$
$421$	10.2472	+	10.2472i	0.499420	+	0.499420i	−0.411838	+	0.911257i	$0.635113\pi$
$422$		0			0
$423$	−22.4317	−	22.4317i	−1.09067	−	1.09067i
$424$		0			0
$425$	−8.69298	+	8.69298i	−0.421671	+	0.421671i
$426$		0			0
$427$	−6.27225	+	6.27225i	−0.303536	+	0.303536i
$428$		0			0
$429$	42.5376	−	42.5376i	2.05373	−	2.05373i
$430$		0			0
$431$		−	16.0920i		−	0.775123i	−0.921844	−	0.387562i	$-0.873317\pi$
$431$		−	16.0920i		−	0.775123i	0.921844	−	0.387562i	$-0.126683\pi$
$432$		0			0
$433$	19.8042			0.951728			0.475864	−	0.879519i	$-0.342135\pi$
$433$	19.8042			0.951728			0.475864	+	0.879519i	$0.342135\pi$
$434$		0			0
$435$	12.7028			0.609051
$436$		0			0
$437$	−15.1445	+	15.1445i	−0.724460	+	0.724460i
$438$		0			0
$439$	−13.3291	−	13.3291i	−0.636161	−	0.636161i	0.313445	−	0.949606i	$-0.398517\pi$
$439$	−13.3291	−	13.3291i	−0.636161	−	0.636161i	−0.949606	+	0.313445i	$0.898517\pi$
$440$		0			0
$441$	−2.39713			−0.114149
$442$		0			0
$443$		−	31.6454i		−	1.50352i	−0.659439	−	0.751758i	$-0.729206\pi$
$443$		−	31.6454i		−	1.50352i	0.659439	−	0.751758i	$-0.270794\pi$
$444$		0			0
$445$	−1.13031	+	1.13031i	−0.0535820	+	0.0535820i
$446$		0			0
$447$	6.83294			0.323187
$448$		0			0
$449$			25.1004i			1.18456i	0.805732	+	0.592280i	$0.201772\pi$
$449$			25.1004i			1.18456i	−0.805732	+	0.592280i	$0.798228\pi$
$450$		0			0
$451$	32.9039	+	9.97771i	1.54938	+	0.469832i
$452$		0			0
$453$		−	35.1331i		−	1.65070i
$454$		0			0
$455$	−6.71002			−0.314571
$456$		0			0
$457$	−14.2221	+	14.2221i	−0.665281	+	0.665281i	−0.956620	−	0.291339i	$-0.905899\pi$
$457$	−14.2221	+	14.2221i	−0.665281	+	0.665281i	0.291339	+	0.956620i	$0.405899\pi$
$458$		0			0
$459$		−	5.61985i		−	0.262312i
$460$		0			0
$461$	4.50977			0.210041			0.105020	−	0.994470i	$-0.466509\pi$
$461$	4.50977			0.210041			0.105020	+	0.994470i	$0.466509\pi$
$462$		0			0
$463$	10.3359	+	10.3359i	0.480349	+	0.480349i	0.905243	−	0.424894i	$-0.139689\pi$
$463$	10.3359	+	10.3359i	0.480349	+	0.480349i	−0.424894	+	0.905243i	$0.639689\pi$
$464$		0			0
$465$	−6.56865	+	6.56865i	−0.304614	+	0.304614i
$466$		0			0
$467$	4.22742			0.195622			0.0978109	−	0.995205i	$-0.468816\pi$
$467$	4.22742			0.195622			0.0978109	+	0.995205i	$0.468816\pi$
$468$		0			0
$469$	−4.96912			−0.229453
$470$		0			0
$471$		−	38.9196i		−	1.79332i
$472$		0			0
$473$	−5.15952	+	5.15952i	−0.237235	+	0.237235i
$474$		0			0
$475$	−17.2704	+	17.2704i	−0.792421	+	0.792421i
$476$		0			0
$477$	−13.5949	+	13.5949i	−0.622466	+	0.622466i
$478$		0			0
$479$	−0.0501173	−	0.0501173i	−0.00228992	−	0.00228992i	0.705961	−	0.708251i	$-0.250515\pi$
$479$	−0.0501173	−	0.0501173i	−0.00228992	−	0.00228992i	−0.708251	+	0.705961i	$0.750515\pi$
$480$		0			0
$481$	20.5840	+	20.5840i	0.938548	+	0.938548i
$482$		0			0
$483$			6.24158i			0.284002i
$484$		0			0
$485$	18.5834	+	18.5834i	0.843827	+	0.843827i
$486$		0			0
$487$			9.41980i			0.426852i	0.976959	+	0.213426i	$0.0684622\pi$
$487$			9.41980i			0.426852i	−0.976959	+	0.213426i	$0.931538\pi$
$488$		0			0
$489$	14.0871	+	14.0871i	0.637041	+	0.637041i
$490$		0			0
$491$	26.6650			1.20338			0.601688	−	0.798731i	$-0.294495\pi$
$491$	26.6650			1.20338			0.601688	+	0.798731i	$0.294495\pi$
$492$		0			0
$493$	15.7676			0.710135
$494$		0			0
$495$	12.6651	+	12.6651i	0.569255	+	0.569255i
$496$		0			0
$497$			1.71908i			0.0771113i
$498$		0			0
$499$	8.25372	+	8.25372i	0.369487	+	0.369487i	0.867290	−	0.497803i	$-0.165860\pi$
$499$	8.25372	+	8.25372i	0.369487	+	0.369487i	−0.497803	+	0.867290i	$0.665860\pi$
$500$		0			0
$501$			38.4072i			1.71591i
$502$		0			0
$503$	9.14704	+	9.14704i	0.407847	+	0.407847i	0.880987	−	0.473140i	$-0.156880\pi$
$503$	9.14704	+	9.14704i	0.407847	+	0.407847i	−0.473140	+	0.880987i	$0.656880\pi$
$504$		0			0
$505$	−10.6680	−	10.6680i	−0.474720	−	0.474720i
$506$		0			0
$507$	16.8447	−	16.8447i	0.748097	−	0.748097i
$508$		0			0
$509$	28.9559	−	28.9559i	1.28345	−	1.28345i	0.344758	−	0.938691i	$-0.387961\pi$
$509$	28.9559	−	28.9559i	1.28345	−	1.28345i	0.938691	−	0.344758i	$-0.112039\pi$
$510$		0			0
$511$	8.99488	−	8.99488i	0.397910	−	0.397910i
$512$		0			0
$513$		−	11.1650i		−	0.492947i
$514$		0			0
$515$	10.7313			0.472877
$516$		0			0
$517$	−71.0627			−3.12533
$518$		0			0
$519$	−21.6410	+	21.6410i	−0.949933	+	0.949933i
$520$		0			0
$521$	−30.0372	−	30.0372i	−1.31595	−	1.31595i	−0.916948	−	0.399006i	$-0.869355\pi$
$521$	−30.0372	−	30.0372i	−1.31595	−	1.31595i	−0.399006	−	0.916948i	$-0.630645\pi$
$522$		0			0
$523$	−6.87633			−0.300681			−0.150340	−	0.988634i	$-0.548037\pi$
$523$	−6.87633			−0.300681			−0.150340	+	0.988634i	$0.548037\pi$
$524$		0			0
$525$			7.11774i			0.310644i
$526$		0			0
$527$	−8.15347	+	8.15347i	−0.355171	+	0.355171i
$528$		0			0
$529$	−15.7819			−0.686168
$530$		0			0
$531$			15.0135i			0.651528i
$532$		0			0
$533$	29.5488	+	8.96032i	1.27990	+	0.388114i
$534$		0			0
$535$		−	3.96030i		−	0.171219i
$536$		0			0
$537$	42.5713			1.83709
$538$		0			0
$539$	−3.79701	+	3.79701i	−0.163549	+	0.163549i
$540$		0			0
$541$		−	13.3066i		−	0.572096i	−0.958215	−	0.286048i	$-0.907658\pi$
$541$		−	13.3066i		−	0.572096i	0.958215	−	0.286048i	$-0.0923416\pi$
$542$		0			0
$543$	6.19572			0.265884
$544$		0			0
$545$	−15.5356	−	15.5356i	−0.665471	−	0.665471i
$546$		0			0
$547$	−5.31007	+	5.31007i	−0.227042	+	0.227042i	−0.811456	−	0.584414i	$-0.801325\pi$
$547$	−5.31007	+	5.31007i	−0.227042	+	0.227042i	0.584414	+	0.811456i	$0.301325\pi$
$548$		0			0
$549$	21.2633			0.907496
$550$		0			0
$551$	31.3256			1.33451
$552$		0			0
$553$			9.34927i			0.397571i
$554$		0			0
$555$	−13.7986	+	13.7986i	−0.585719	+	0.585719i
$556$		0			0
$557$	−26.0301	+	26.0301i	−1.10293	+	1.10293i	−0.108876	+	0.994055i	$0.534725\pi$
$557$	−26.0301	+	26.0301i	−1.10293	+	1.10293i	−0.994055	+	0.108876i	$0.965275\pi$
$558$		0			0
$559$	−4.63342	+	4.63342i	−0.195973	+	0.195973i
$560$		0			0
$561$	35.3954	+	35.3954i	1.49439	+	1.49439i
$562$		0			0
$563$	1.57386	+	1.57386i	0.0663304	+	0.0663304i	0.739494	−	0.673163i	$-0.235065\pi$
$563$	1.57386	+	1.57386i	0.0663304	+	0.0663304i	−0.673163	+	0.739494i	$0.735065\pi$
$564$		0			0
$565$		−	0.0732538i		−	0.00308181i
$566$		0			0
$567$	−7.38584	−	7.38584i	−0.310176	−	0.310176i
$568$		0			0
$569$		−	20.3768i		−	0.854240i	−0.904195	−	0.427120i	$-0.859528\pi$
$569$		−	20.3768i		−	0.854240i	0.904195	−	0.427120i	$-0.140472\pi$
$570$		0			0
$571$	−28.2426	−	28.2426i	−1.18191	−	1.18191i	−0.979248	−	0.202666i	$-0.935039\pi$
$571$	−28.2426	−	28.2426i	−1.18191	−	1.18191i	−0.202666	−	0.979248i	$-0.564961\pi$
$572$		0			0
$573$	13.2212			0.552326
$574$		0			0
$575$	8.23140			0.343273
$576$		0			0
$577$	−21.8765	−	21.8765i	−0.910731	−	0.910731i	0.0855985	−	0.996330i	$-0.472720\pi$
$577$	−21.8765	−	21.8765i	−0.910731	−	0.910731i	−0.996330	+	0.0855985i	$0.972720\pi$
$578$		0			0
$579$		−	41.2904i		−	1.71597i
$580$		0			0
$581$	2.78703	+	2.78703i	0.115625	+	0.115625i
$582$		0			0
$583$			43.0679i			1.78369i
$584$		0			0
$585$	11.3737	+	11.3737i	0.470244	+	0.470244i
$586$		0			0
$587$	3.07961	+	3.07961i	0.127109	+	0.127109i	0.767799	−	0.640690i	$-0.221352\pi$
$587$	3.07961	+	3.07961i	0.127109	+	0.127109i	−0.640690	+	0.767799i	$0.721352\pi$
$588$		0			0
$589$	−16.1986	+	16.1986i	−0.667451	+	0.667451i
$590$		0			0
$591$	1.37254	−	1.37254i	0.0564587	−	0.0564587i
$592$		0			0
$593$	−5.45050	+	5.45050i	−0.223825	+	0.223825i	−0.810107	−	0.586282i	$-0.800591\pi$
$593$	−5.45050	+	5.45050i	−0.223825	+	0.223825i	0.586282	+	0.810107i	$0.300591\pi$
$594$		0			0
$595$		−	5.58339i		−	0.228896i
$596$		0			0
$597$	−17.5699			−0.719087
$598$		0			0
$599$	−6.92947			−0.283131			−0.141565	−	0.989929i	$-0.545214\pi$
$599$	−6.92947			−0.283131			−0.141565	+	0.989929i	$0.545214\pi$
$600$		0			0
$601$	9.89809	−	9.89809i	0.403752	−	0.403752i	−0.475801	−	0.879553i	$-0.657842\pi$
$601$	9.89809	−	9.89809i	0.403752	−	0.403752i	0.879553	+	0.475801i	$0.157842\pi$
$602$		0			0
$603$	8.42281	+	8.42281i	0.343003	+	0.343003i
$604$		0			0
$605$	24.8164			1.00893
$606$		0			0
$607$		−	14.3632i		−	0.582983i	−0.956573	−	0.291492i	$-0.905848\pi$
$607$		−	14.3632i		−	0.582983i	0.956573	−	0.291492i	$-0.0941516\pi$
$608$		0			0
$609$	6.45518	−	6.45518i	0.261577	−	0.261577i
$610$		0			0
$611$	−63.8167			−2.58175
$612$		0			0
$613$		−	21.5867i		−	0.871877i	−0.899976	−	0.435938i	$-0.856417\pi$
$613$		−	21.5867i		−	0.871877i	0.899976	−	0.435938i	$-0.143583\pi$
$614$		0			0
$615$	−6.00663	+	19.8083i	−0.242210	+	0.798746i
$616$		0			0
$617$		−	44.0803i		−	1.77461i	−0.461188	−	0.887303i	$-0.652577\pi$
$617$		−	44.0803i		−	1.77461i	0.461188	−	0.887303i	$-0.347423\pi$
$618$		0			0
$619$	2.56103			0.102936			0.0514682	−	0.998675i	$-0.483610\pi$
$619$	2.56103			0.102936			0.0514682	+	0.998675i	$0.483610\pi$
$620$		0			0
$621$	−2.66072	+	2.66072i	−0.106771	+	0.106771i
$622$		0			0
$623$			1.14879i			0.0460252i
$624$		0			0
$625$	−0.294100			−0.0117640
$626$		0			0
$627$	70.3203	+	70.3203i	2.80832	+	2.80832i
$628$		0			0
$629$	−17.1278	+	17.1278i	−0.682932	+	0.682932i
$630$		0			0
$631$	1.71634			0.0683262			0.0341631	−	0.999416i	$-0.489123\pi$
$631$	1.71634			0.0683262			0.0341631	+	0.999416i	$0.489123\pi$
$632$		0			0
$633$	32.5379			1.29327
$634$		0			0
$635$			16.9426i			0.672346i
$636$		0			0
$637$	−3.40984	+	3.40984i	−0.135103	+	0.135103i
$638$		0			0
$639$	2.91389	−	2.91389i	0.115272	−	0.115272i
$640$		0			0
$641$	7.78184	−	7.78184i	0.307364	−	0.307364i	−0.536522	−	0.843886i	$-0.680262\pi$
$641$	7.78184	−	7.78184i	0.307364	−	0.307364i	0.843886	+	0.536522i	$0.180262\pi$
$642$		0			0
$643$	−15.1384	−	15.1384i	−0.597001	−	0.597001i	0.342512	−	0.939513i	$-0.388722\pi$
$643$	−15.1384	−	15.1384i	−0.597001	−	0.597001i	−0.939513	+	0.342512i	$0.888722\pi$
$644$		0			0
$645$	−3.10605	−	3.10605i	−0.122301	−	0.122301i
$646$		0			0
$647$			2.71048i			0.106560i	0.998580	+	0.0532799i	$0.0169676\pi$
$647$			2.71048i			0.106560i	−0.998580	+	0.0532799i	$0.983032\pi$
$648$		0			0
$649$	23.7810	+	23.7810i	0.933486	+	0.933486i
$650$		0			0
$651$			6.67600i			0.261653i
$652$		0			0
$653$	−0.968876	−	0.968876i	−0.0379150	−	0.0379150i	0.687895	−	0.725810i	$-0.258535\pi$
$653$	−0.968876	−	0.968876i	−0.0379150	−	0.0379150i	−0.725810	+	0.687895i	$0.758535\pi$
$654$		0			0
$655$	1.66447			0.0650364
$656$		0			0
$657$	−30.4932			−1.18965
$658$		0			0
$659$	1.80935	+	1.80935i	0.0704822	+	0.0704822i	0.741469	−	0.670987i	$-0.234129\pi$
$659$	1.80935	+	1.80935i	0.0704822	+	0.0704822i	−0.670987	+	0.741469i	$0.734129\pi$
$660$		0			0
$661$			42.6971i			1.66072i	0.557224	+	0.830362i	$0.311867\pi$
$661$			42.6971i			1.66072i	−0.557224	+	0.830362i	$0.688133\pi$
$662$		0			0
$663$	31.7862	+	31.7862i	1.23447	+	1.23447i
$664$		0			0
$665$		−	11.0926i		−	0.430151i
$666$		0			0
$667$	−7.46517	−	7.46517i	−0.289053	−	0.289053i
$668$		0			0
$669$	−30.8869	−	30.8869i	−1.19416	−	1.19416i
$670$		0			0
$671$	33.6807	−	33.6807i	1.30023	−	1.30023i
$672$		0			0
$673$	21.5076	−	21.5076i	0.829058	−	0.829058i	−0.158329	−	0.987386i	$-0.550611\pi$
$673$	21.5076	−	21.5076i	0.829058	−	0.829058i	0.987386	+	0.158329i	$0.0506106\pi$
$674$		0			0
$675$	−3.03422	+	3.03422i	−0.116787	+	0.116787i
$676$		0			0
$677$			17.1202i			0.657981i	0.944333	+	0.328991i	$0.106708\pi$
$677$			17.1202i			0.657981i	−0.944333	+	0.328991i	$0.893292\pi$
$678$		0			0
$679$	18.8871			0.724819
$680$		0			0
$681$	−51.7737			−1.98397
$682$		0			0
$683$	6.88317	−	6.88317i	0.263377	−	0.263377i	−0.563048	−	0.826425i	$-0.690371\pi$
$683$	6.88317	−	6.88317i	0.263377	−	0.263377i	0.826425	+	0.563048i	$0.190371\pi$
$684$		0			0
$685$	−9.57601	−	9.57601i	−0.365880	−	0.365880i
$686$		0			0
$687$	64.1168			2.44621
$688$		0			0
$689$			38.6764i			1.47346i
$690$		0			0
$691$	25.9965	−	25.9965i	0.988954	−	0.988954i	−0.0109857	−	0.999940i	$-0.503497\pi$
$691$	25.9965	−	25.9965i	0.988954	−	0.988954i	0.999940	+	0.0109857i	$0.00349692\pi$
$692$		0			0
$693$	12.8721			0.488971
$694$		0			0
$695$		−	18.0989i		−	0.686531i
$696$		0			0
$697$	−7.45584	+	24.5874i	−0.282410	+	0.931314i
$698$		0			0
$699$		−	10.0691i		−	0.380850i
$700$		0			0
$701$	−16.4487			−0.621260			−0.310630	−	0.950531i	$-0.600540\pi$
$701$	−16.4487			−0.621260			−0.310630	+	0.950531i	$0.600540\pi$
$702$		0			0
$703$	−34.0280	+	34.0280i	−1.28339	+	1.28339i
$704$		0			0
$705$		−	42.7801i		−	1.61119i
$706$		0			0
$707$	−10.8423			−0.407768
$708$		0			0
$709$	4.86608	+	4.86608i	0.182750	+	0.182750i	0.792553	−	0.609803i	$-0.208752\pi$
$709$	4.86608	+	4.86608i	0.182750	+	0.182750i	−0.609803	+	0.792553i	$0.708752\pi$
$710$		0			0
$711$	15.8473	−	15.8473i	0.594320	−	0.594320i
$712$		0			0
$713$	7.72054			0.289136
$714$		0			0
$715$	36.0314			1.34750
$716$		0			0
$717$		−	16.0850i		−	0.600707i
$718$		0			0
$719$	−2.94403	+	2.94403i	−0.109794	+	0.109794i	−0.759869	−	0.650076i	$-0.774737\pi$
$719$	−2.94403	+	2.94403i	−0.109794	+	0.109794i	0.650076	+	0.759869i	$0.274737\pi$
$720$		0			0
$721$	5.45333	−	5.45333i	0.203093	−	0.203093i
$722$		0			0
$723$	−7.80178	+	7.80178i	−0.290151	+	0.290151i
$724$		0			0
$725$	−8.51310	−	8.51310i	−0.316169	−	0.316169i
$726$		0			0
$727$	−24.1263	−	24.1263i	−0.894794	−	0.894794i	0.100176	−	0.994970i	$-0.468059\pi$
$727$	−24.1263	−	24.1263i	−0.894794	−	0.894794i	−0.994970	+	0.100176i	$0.968059\pi$
$728$		0			0
$729$			15.2772i			0.565822i
$730$		0			0
$731$	−3.85545	−	3.85545i	−0.142599	−	0.142599i
$732$		0			0
$733$		−	21.2740i		−	0.785772i	−0.919587	−	0.392886i	$-0.871477\pi$
$733$		−	21.2740i		−	0.785772i	0.919587	−	0.392886i	$-0.128523\pi$
$734$		0			0
$735$	−2.28582	−	2.28582i	−0.0843136	−	0.0843136i
$736$		0			0
$737$	26.6831			0.982885
$738$		0			0
$739$	10.9835			0.404036			0.202018	−	0.979382i	$-0.435250\pi$
$739$	10.9835			0.404036			0.202018	+	0.979382i	$0.435250\pi$
$740$		0			0
$741$	63.1499	+	63.1499i	2.31987	+	2.31987i
$742$		0			0
$743$		−	15.4013i		−	0.565020i	−0.959264	−	0.282510i	$-0.908833\pi$
$743$		−	15.4013i		−	0.565020i	0.959264	−	0.282510i	$-0.0911671\pi$
$744$		0			0
$745$	2.89391	+	2.89391i	0.106025	+	0.106025i
$746$		0			0
$747$		−	9.44819i		−	0.345691i
$748$		0			0
$749$	−2.01251	−	2.01251i	−0.0735355	−	0.0735355i
$750$		0			0
$751$	10.8862	+	10.8862i	0.397244	+	0.397244i	0.877260	−	0.480016i	$-0.159369\pi$
$751$	10.8862	+	10.8862i	0.397244	+	0.397244i	−0.480016	+	0.877260i	$0.659369\pi$
$752$		0			0
$753$	−15.5231	+	15.5231i	−0.565692	+	0.565692i
$754$		0			0
$755$	14.8797	−	14.8797i	0.541528	−	0.541528i
$756$		0			0
$757$	1.36164	−	1.36164i	0.0494898	−	0.0494898i	−0.681929	−	0.731419i	$-0.738859\pi$
$757$	1.36164	−	1.36164i	0.0494898	−	0.0494898i	0.731419	+	0.681929i	$0.238859\pi$
$758$		0			0
$759$		−	33.5159i		−	1.21655i
$760$		0			0
$761$	−47.1115			−1.70779			−0.853895	−	0.520445i	$-0.825766\pi$
$761$	−47.1115			−1.70779			−0.853895	+	0.520445i	$0.825766\pi$
$762$		0			0
$763$	−15.7895			−0.571617
$764$		0			0
$765$	−9.46401	+	9.46401i	−0.342172	+	0.342172i
$766$		0			0
$767$	21.3561	+	21.3561i	0.771125	+	0.771125i
$768$		0			0
$769$	−14.8813			−0.536634			−0.268317	−	0.963331i	$-0.586467\pi$
$769$	−14.8813			−0.536634			−0.268317	+	0.963331i	$0.586467\pi$
$770$		0			0
$771$			51.5333i			1.85593i
$772$		0			0
$773$	−15.7968	+	15.7968i	−0.568172	+	0.568172i	−0.931616	−	0.363444i	$-0.881601\pi$
$773$	−15.7968	+	15.7968i	−0.568172	+	0.568172i	0.363444	+	0.931616i	$0.381601\pi$
$774$		0			0
$775$	8.80431			0.316260
$776$		0			0
$777$			14.0241i			0.503113i
$778$		0			0
$779$	−14.8126	+	48.8480i	−0.530716	+	1.75016i
$780$		0			0
$781$		−	9.23110i		−	0.330315i
$782$		0			0
$783$	5.50356			0.196681
$784$		0			0
$785$	16.4834	−	16.4834i	0.588317	−	0.588317i
$786$		0			0
$787$		−	11.3031i		−	0.402913i	−0.979497	−	0.201457i	$-0.935433\pi$
$787$		−	11.3031i		−	0.402913i	0.979497	−	0.201457i	$-0.0645675\pi$
$788$		0			0
$789$	60.3052			2.14692
$790$		0			0
$791$	−0.0372255	−	0.0372255i	−0.00132359	−	0.00132359i
$792$		0			0
$793$	30.2463	−	30.2463i	1.07408	−	1.07408i
$794$		0			0
$795$	−25.9271			−0.919539
$796$		0			0
$797$	52.5765			1.86235			0.931177	−	0.364568i	$-0.118783\pi$
$797$	52.5765			1.86235			0.931177	+	0.364568i	$0.118783\pi$
$798$		0			0
$799$		−	53.1016i		−	1.87860i
$800$		0			0
$801$	1.94723	−	1.94723i	0.0688019	−	0.0688019i
$802$		0			0
$803$	−48.3006	+	48.3006i	−1.70449	+	1.70449i
$804$		0			0
$805$	−2.64346	+	2.64346i	−0.0931697	+	0.0931697i
$806$		0			0
$807$	−48.5205	−	48.5205i	−1.70800	−	1.70800i
$808$		0			0
$809$	−35.3815	−	35.3815i	−1.24395	−	1.24395i	−0.958350	−	0.285598i	$-0.907808\pi$
$809$	−35.3815	−	35.3815i	−1.24395	−	1.24395i	−0.285598	−	0.958350i	$-0.592192\pi$
$810$		0			0
$811$		−	5.17720i		−	0.181796i	−0.995860	−	0.0908980i	$-0.971026\pi$
$811$		−	5.17720i		−	0.181796i	0.995860	−	0.0908980i	$-0.0289737\pi$
$812$		0			0
$813$	−21.2308	−	21.2308i	−0.744596	−	0.744596i
$814$		0			0
$815$			11.9325i			0.417976i
$816$		0			0
$817$	−7.65966	−	7.65966i	−0.267977	−	0.267977i
$818$		0			0
$819$	11.5596			0.403924
$820$		0			0
$821$	6.25135			0.218174			0.109087	−	0.994032i	$-0.465207\pi$
$821$	6.25135			0.218174			0.109087	+	0.994032i	$0.465207\pi$
$822$		0			0
$823$	32.5612	+	32.5612i	1.13501	+	1.13501i	0.989332	+	0.145679i	$0.0465366\pi$
$823$	32.5612	+	32.5612i	1.13501	+	1.13501i	0.145679	+	0.989332i	$0.453463\pi$
$824$		0			0
$825$		−	38.2208i		−	1.33068i
$826$		0			0
$827$	−28.5453	−	28.5453i	−0.992618	−	0.992618i	0.00735496	−	0.999973i	$-0.497659\pi$
$827$	−28.5453	−	28.5453i	−0.992618	−	0.992618i	−0.999973	+	0.00735496i	$0.997659\pi$
$828$		0			0
$829$		−	36.3485i		−	1.26243i	−0.775606	−	0.631217i	$-0.782556\pi$
$829$		−	36.3485i		−	1.26243i	0.775606	−	0.631217i	$-0.217444\pi$
$830$		0			0
$831$	46.2158	+	46.2158i	1.60321	+	1.60321i
$832$		0			0
$833$	−2.83732	−	2.83732i	−0.0983072	−	0.0983072i
$834$		0			0
$835$	−16.2664	+	16.2664i	−0.562921	+	0.562921i
$836$		0			0
$837$	−2.84591	+	2.84591i	−0.0983692	+	0.0983692i
$838$		0			0
$839$	12.6251	−	12.6251i	0.435866	−	0.435866i	−0.454752	−	0.890618i	$-0.650272\pi$
$839$	12.6251	−	12.6251i	0.435866	−	0.435866i	0.890618	+	0.454752i	$0.150272\pi$
$840$		0			0
$841$		−	13.5587i		−	0.467542i
$842$		0			0
$843$	30.1234			1.03751
$844$		0			0
$845$	14.2682			0.490842
$846$		0			0
$847$	12.6110	−	12.6110i	0.433318	−	0.433318i
$848$		0			0
$849$	8.94224	+	8.94224i	0.306897	+	0.306897i
$850$		0			0
$851$	16.2184			0.555959
$852$		0			0
$853$		−	8.89692i		−	0.304625i	−0.988332	−	0.152312i	$-0.951328\pi$
$853$		−	8.89692i		−	0.304625i	0.988332	−	0.152312i	$-0.0486720\pi$
$854$		0			0
$855$	−18.8022	+	18.8022i	−0.643023	+	0.643023i
$856$		0			0
$857$	−10.2961			−0.351707			−0.175853	−	0.984416i	$-0.556268\pi$
$857$	−10.2961			−0.351707			−0.175853	+	0.984416i	$0.556268\pi$
$858$		0			0
$859$			9.57653i			0.326747i	0.986564	+	0.163374i	$0.0522376\pi$
$859$			9.57653i			0.326747i	−0.986564	+	0.163374i	$0.947762\pi$
$860$		0			0
$861$	7.01359	+	13.1184i	0.239023	+	0.447073i
$862$		0			0
$863$		−	13.3534i		−	0.454554i	−0.973830	−	0.227277i	$-0.927018\pi$
$863$		−	13.3534i		−	0.454554i	0.973830	−	0.227277i	$-0.0729823\pi$
$864$		0			0
$865$	−18.3309			−0.623271
$866$		0			0
$867$	1.47726	−	1.47726i	0.0501704	−	0.0501704i
$868$		0			0
$869$		−	50.2036i		−	1.70304i
$870$		0			0
$871$	23.9623			0.811933
$872$		0			0
$873$	−32.0142	−	32.0142i	−1.08352	−	1.08352i
$874$		0			0
$875$	−7.93414	+	7.93414i	−0.268223	+	0.268223i
$876$		0			0
$877$	−0.823138			−0.0277954			−0.0138977	−	0.999903i	$-0.504424\pi$
$877$	−0.823138			−0.0277954			−0.0138977	+	0.999903i	$0.504424\pi$
$878$		0			0
$879$	−41.9813			−1.41599
$880$		0			0
$881$			2.46047i			0.0828954i	0.999141	+	0.0414477i	$0.0131970\pi$
$881$			2.46047i			0.0828954i	−0.999141	+	0.0414477i	$0.986803\pi$
$882$		0			0
$883$	−24.7412	+	24.7412i	−0.832607	+	0.832607i	−0.987873	−	0.155266i	$-0.950377\pi$
$883$	−24.7412	+	24.7412i	−0.832607	+	0.832607i	0.155266	+	0.987873i	$0.450377\pi$
$884$		0			0
$885$	−14.3163	+	14.3163i	−0.481236	+	0.481236i
$886$		0			0
$887$	−11.9048	+	11.9048i	−0.399725	+	0.399725i	−0.878136	−	0.478411i	$-0.841213\pi$
$887$	−11.9048	+	11.9048i	−0.399725	+	0.399725i	0.478411	+	0.878136i	$0.341213\pi$
$888$		0			0
$889$	8.60974	+	8.60974i	0.288761	+	0.288761i
$890$		0			0
$891$	39.6604	+	39.6604i	1.32867	+	1.32867i
$892$		0			0
$893$		−	105.497i		−	3.53034i
$894$		0			0
$895$	18.0300	+	18.0300i	0.602676	+	0.602676i
$896$		0			0
$897$		−	30.0984i		−	1.00496i
$898$		0			0
$899$	−7.98476	−	7.98476i	−0.266307	−	0.266307i
$900$		0			0
$901$	−32.1825			−1.07216
$902$		0			0
$903$	−3.15681			−0.105052
$904$		0			0
$905$	2.62404	+	2.62404i	0.0872259	+	0.0872259i
$906$		0			0
$907$		−	10.8172i		−	0.359181i	−0.983741	−	0.179590i	$-0.942523\pi$
$907$		−	10.8172i		−	0.359181i	0.983741	−	0.179590i	$-0.0574772\pi$
$908$		0			0
$909$	18.3781	+	18.3781i	0.609563	+	0.609563i
$910$		0			0
$911$			11.9004i			0.394278i	0.980376	+	0.197139i	$0.0631650\pi$
$911$			11.9004i			0.394278i	−0.980376	+	0.197139i	$0.936835\pi$
$912$		0			0
$913$	−14.9657	−	14.9657i	−0.495294	−	0.495294i
$914$		0			0
$915$	20.2759	+	20.2759i	0.670300	+	0.670300i
$916$		0			0
$917$	0.845838	−	0.845838i	0.0279320	−	0.0279320i
$918$		0			0
$919$	6.14736	−	6.14736i	0.202783	−	0.202783i	−0.598408	−	0.801191i	$-0.704200\pi$
$919$	6.14736	−	6.14736i	0.202783	−	0.202783i	0.801191	+	0.598408i	$0.204200\pi$
$920$		0			0
$921$	42.7433	−	42.7433i	1.40844	−	1.40844i
$922$		0			0
$923$		−	8.28983i		−	0.272863i
$924$		0			0
$925$	18.4951			0.608114
$926$		0			0
$927$	−18.4871			−0.607197
$928$		0			0
$929$	6.26762	−	6.26762i	0.205634	−	0.205634i	−0.596775	−	0.802409i	$-0.703551\pi$
$929$	6.26762	−	6.26762i	0.205634	−	0.205634i	0.802409	+	0.596775i	$0.203551\pi$
$930$		0			0
$931$	−5.63692	−	5.63692i	−0.184743	−	0.184743i
$932$		0			0
$933$	12.8615			0.421068
$934$		0			0
$935$			29.9816i			0.980502i
$936$		0			0
$937$	0.272334	−	0.272334i	0.00889677	−	0.00889677i	−0.702644	−	0.711541i	$-0.747998\pi$
$937$	0.272334	−	0.272334i	0.00889677	−	0.00889677i	0.711541	+	0.702644i	$0.247998\pi$
$938$		0			0
$939$	−60.4622			−1.97311
$940$		0			0
$941$		−	35.1129i		−	1.14465i	−0.820028	−	0.572323i	$-0.806042\pi$
$941$		−	35.1129i		−	1.14465i	0.820028	−	0.572323i	$-0.193958\pi$
$942$		0			0
$943$	15.1709	−	8.11095i	0.494033	−	0.264129i
$944$		0			0
$945$		−	1.94884i		−	0.0633959i
$946$		0			0
$947$	−32.9638			−1.07118			−0.535589	−	0.844479i	$-0.679910\pi$
$947$	−32.9638			−1.07118			−0.535589	+	0.844479i	$0.679910\pi$
$948$		0			0
$949$	−43.3755	+	43.3755i	−1.40803	+	1.40803i
$950$		0			0
$951$			24.2451i			0.786200i
$952$		0			0
$953$	−0.980510			−0.0317618			−0.0158809	−	0.999874i	$-0.505055\pi$
$953$	−0.980510			−0.0317618			−0.0158809	+	0.999874i	$0.505055\pi$
$954$		0			0
$955$	5.59952	+	5.59952i	0.181196	+	0.181196i
$956$		0			0
$957$	−34.6629	+	34.6629i	−1.12049	+	1.12049i
$958$		0			0
$959$	−9.73251			−0.314279
$960$		0			0
$961$	−22.7421			−0.733616
$962$		0			0
$963$			6.82253i			0.219853i
$964$		0			0
$965$	17.4875	−	17.4875i	0.562942	−	0.562942i
$966$		0			0
$967$	2.11075	−	2.11075i	0.0678773	−	0.0678773i	−0.672353	−	0.740230i	$-0.734716\pi$
$967$	2.11075	−	2.11075i	0.0678773	−	0.0678773i	0.740230	+	0.672353i	$0.234716\pi$
$968$		0			0
$969$	−52.5468	+	52.5468i	−1.68805	+	1.68805i
$970$		0			0
$971$	−8.95371	−	8.95371i	−0.287338	−	0.287338i	0.548689	−	0.836027i	$-0.315127\pi$
$971$	−8.95371	−	8.95371i	−0.287338	−	0.287338i	−0.836027	+	0.548689i	$0.815127\pi$
$972$		0			0
$973$	−9.19734	−	9.19734i	−0.294853	−	0.294853i
$974$		0			0
$975$		−	34.3235i		−	1.09923i
$976$		0			0
$977$	25.7128	+	25.7128i	0.822625	+	0.822625i	0.986484	−	0.163858i	$-0.0523940\pi$
$977$	25.7128	+	25.7128i	0.822625	+	0.822625i	−0.163858	+	0.986484i	$0.552394\pi$
$978$		0			0
$979$		−	6.16874i		−	0.197154i
$980$		0			0
$981$	26.7636	+	26.7636i	0.854497	+	0.854497i
$982$		0			0
$983$	30.4305			0.970582			0.485291	−	0.874353i	$-0.338714\pi$
$983$	30.4305			0.970582			0.485291	+	0.874353i	$0.338714\pi$
$984$		0			0
$985$	1.16261			0.0370437
$986$		0			0
$987$	−21.7396	−	21.7396i	−0.691979	−	0.691979i
$988$		0			0
$989$			3.65073i			0.116087i
$990$		0			0
$991$	2.50573	+	2.50573i	0.0795971	+	0.0795971i	0.745784	−	0.666187i	$-0.232075\pi$
$991$	2.50573	+	2.50573i	0.0795971	+	0.0795971i	−0.666187	+	0.745784i	$0.732075\pi$
$992$		0			0
$993$			13.0913i			0.415439i
$994$		0			0
$995$	−7.44127	−	7.44127i	−0.235904	−	0.235904i
$996$		0			0
$997$	28.1122	+	28.1122i	0.890324	+	0.890324i	0.994553	−	0.104230i	$-0.0332377\pi$
$997$	28.1122	+	28.1122i	0.890324	+	0.890324i	−0.104230	+	0.994553i	$0.533238\pi$
$998$		0			0
$999$	−5.97836	+	5.97836i	−0.189147	+	0.189147i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.k.b.337.4	✓	36
41.32	even	4	inner	1148.2.k.b.729.4	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.k.b.337.4	✓	36	1.1	even	1	trivial
1148.2.k.b.729.4	yes	36	41.32	even	4	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.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.64273 - 1.64273i) q^{3} -1.39147i q^{5} +(-0.707107 - 0.707107i) q^{7} +2.39713i q^{9} +O(q^{10})\)	\(q+(-1.64273 - 1.64273i) q^{3} -1.39147i q^{5} +(-0.707107 - 0.707107i) q^{7} +2.39713i q^{9} +(3.79701 + 3.79701i) q^{11} +(3.40984 + 3.40984i) q^{13} +(-2.28582 + 2.28582i) q^{15} +(-2.83732 + 2.83732i) q^{17} +(-5.63692 + 5.63692i) q^{19} +2.32317i q^{21} +2.68666 q^{23} +3.06380 q^{25} +(-0.990346 + 0.990346i) q^{27} +(-2.77861 - 2.77861i) q^{29} +2.87366 q^{31} -12.4749i q^{33} +(-0.983920 + 0.983920i) q^{35} +6.03663 q^{37} -11.2029i q^{39} +(5.64675 - 3.01897i) q^{41} +1.35884i q^{43} +3.33555 q^{45} +(-9.35772 + 9.35772i) q^{47} +1.00000i q^{49} +9.32190 q^{51} +(5.67130 + 5.67130i) q^{53} +(5.28344 - 5.28344i) q^{55} +18.5199 q^{57} +6.26308 q^{59} -8.87031i q^{61} +(1.69503 - 1.69503i) q^{63} +(4.74470 - 4.74470i) q^{65} +(3.51370 - 3.51370i) q^{67} +(-4.41346 - 4.41346i) q^{69} +(-1.21557 - 1.21557i) q^{71} +12.7207i q^{73} +(-5.03301 - 5.03301i) q^{75} -5.36978i q^{77} +(-6.61093 - 6.61093i) q^{79} +10.4451 q^{81} -3.94145 q^{83} +(3.94805 + 3.94805i) q^{85} +9.12901i q^{87} +(-0.812315 - 0.812315i) q^{89} -4.82225i q^{91} +(-4.72065 - 4.72065i) q^{93} +(7.84363 + 7.84363i) q^{95} +(-13.3552 + 13.3552i) q^{97} +(-9.10195 + 9.10195i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q+O(q^{10}) \) 36 * q	\( 36 q - 12 q^{11} - 16 q^{17} - 4 q^{19} - 36 q^{23} - 64 q^{25} + 12 q^{27} + 16 q^{29} - 28 q^{31} + 12 q^{35} + 48 q^{37} + 4 q^{41} + 36 q^{45} + 12 q^{47} - 12 q^{51} - 12 q^{53} + 12 q^{55} + 76 q^{57} + 20 q^{59} - 4 q^{65} - 44 q^{67} + 72 q^{69} - 20 q^{71} + 72 q^{75} - 8 q^{79} - 100 q^{81} - 40 q^{83} - 8 q^{85} - 16 q^{89} + 20 q^{93} + 76 q^{95} - 16 q^{97} + 56 q^{99}+O(q^{100}) \) 36 * q - 12 * q^11 - 16 * q^17 - 4 * q^19 - 36 * q^23 - 64 * q^25 + 12 * q^27 + 16 * q^29 - 28 * q^31 + 12 * q^35 + 48 * q^37 + 4 * q^41 + 36 * q^45 + 12 * q^47 - 12 * q^51 - 12 * q^53 + 12 * q^55 + 76 * q^57 + 20 * q^59 - 4 * q^65 - 44 * q^67 + 72 * q^69 - 20 * q^71 + 72 * q^75 - 8 * q^79 - 100 * q^81 - 40 * q^83 - 8 * q^85 - 16 * q^89 + 20 * q^93 + 76 * q^95 - 16 * q^97 + 56 * q^99

Introduction

L-functions

Modular forms

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