LMFDB - Embedded newform 1148.2.k.b.729.5

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			729.5
Character	$\chi$	$=$	1148.729
Dual form			1148.2.k.b.337.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38781 + 1.38781i) q^{3} -2.11167i q^{5} +(0.707107 - 0.707107i) q^{7} -0.852014i q^{9} +O(q^{10})$	\(q+(-1.38781 + 1.38781i) q^{3} -2.11167i q^{5} +(0.707107 - 0.707107i) q^{7} -0.852014i q^{9} +(-0.520395 + 0.520395i) q^{11} +(0.612447 - 0.612447i) q^{13} +(2.93059 + 2.93059i) q^{15} +(1.16252 + 1.16252i) q^{17} +(-2.68768 - 2.68768i) q^{19} +1.96265i q^{21} -3.65691 q^{23} +0.540846 q^{25} +(-2.98099 - 2.98099i) q^{27} +(3.93269 - 3.93269i) q^{29} -4.96601 q^{31} -1.44442i q^{33} +(-1.49318 - 1.49318i) q^{35} -1.57189 q^{37} +1.69992i q^{39} +(1.38487 - 6.25157i) q^{41} -8.44151i q^{43} -1.79917 q^{45} +(-1.57218 - 1.57218i) q^{47} -1.00000i q^{49} -3.22672 q^{51} +(2.25691 - 2.25691i) q^{53} +(1.09890 + 1.09890i) q^{55} +7.45997 q^{57} +6.36540 q^{59} -8.42809i q^{61} +(-0.602465 - 0.602465i) q^{63} +(-1.29329 - 1.29329i) q^{65} +(-0.439215 - 0.439215i) q^{67} +(5.07508 - 5.07508i) q^{69} +(-1.13798 + 1.13798i) q^{71} -0.278184i q^{73} +(-0.750589 + 0.750589i) q^{75} +0.735950i q^{77} +(-3.94424 + 3.94424i) q^{79} +10.8301 q^{81} +8.17699 q^{83} +(2.45487 - 2.45487i) q^{85} +10.9156i q^{87} +(11.2391 - 11.2391i) q^{89} -0.866131i q^{91} +(6.89187 - 6.89187i) q^{93} +(-5.67550 + 5.67550i) q^{95} +(-9.32999 - 9.32999i) q^{97} +(0.443384 + 0.443384i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.38781	+	1.38781i	−0.801250	+	0.801250i	−0.983291	−	0.182041i	$-0.941730\pi$
$3$	−1.38781	+	1.38781i	−0.801250	+	0.801250i	0.182041	+	0.983291i	$0.441730\pi$
$4$		0			0
$5$		−	2.11167i		−	0.944368i	−0.881500	−	0.472184i	$-0.843466\pi$
$5$		−	2.11167i		−	0.944368i	0.881500	−	0.472184i	$-0.156534\pi$
$6$		0			0
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$8$		0			0
$9$		−	0.852014i		−	0.284005i
$10$		0			0
$11$	−0.520395	+	0.520395i	−0.156905	+	0.156905i	−0.781194	−	0.624289i	$-0.785389\pi$
$11$	−0.520395	+	0.520395i	−0.156905	+	0.156905i	0.624289	+	0.781194i	$0.285389\pi$
$12$		0			0
$13$	0.612447	−	0.612447i	0.169862	−	0.169862i	−0.617057	−	0.786919i	$-0.711675\pi$
$13$	0.612447	−	0.612447i	0.169862	−	0.169862i	0.786919	+	0.617057i	$0.211675\pi$
$14$		0			0
$15$	2.93059	+	2.93059i	0.756675	+	0.756675i
$16$		0			0
$17$	1.16252	+	1.16252i	0.281954	+	0.281954i	0.833888	−	0.551934i	$-0.186110\pi$
$17$	1.16252	+	1.16252i	0.281954	+	0.281954i	−0.551934	+	0.833888i	$0.686110\pi$
$18$		0			0
$19$	−2.68768	−	2.68768i	−0.616597	−	0.616597i	0.328060	−	0.944657i	$-0.393605\pi$
$19$	−2.68768	−	2.68768i	−0.616597	−	0.616597i	−0.944657	+	0.328060i	$0.893605\pi$
$20$		0			0
$21$			1.96265i			0.428286i
$22$		0			0
$23$	−3.65691			−0.762518			−0.381259	−	0.924468i	$-0.624509\pi$
$23$	−3.65691			−0.762518			−0.381259	+	0.924468i	$0.624509\pi$
$24$		0			0
$25$	0.540846			0.108169
$26$		0			0
$27$	−2.98099	−	2.98099i	−0.573692	−	0.573692i
$28$		0			0
$29$	3.93269	−	3.93269i	0.730282	−	0.730282i	−0.240393	−	0.970676i	$-0.577276\pi$
$29$	3.93269	−	3.93269i	0.730282	−	0.730282i	0.970676	+	0.240393i	$0.0772764\pi$
$30$		0			0
$31$	−4.96601			−0.891922			−0.445961	−	0.895052i	$-0.647138\pi$
$31$	−4.96601			−0.891922			−0.445961	+	0.895052i	$0.647138\pi$
$32$		0			0
$33$		−	1.44442i		−	0.251441i
$34$		0			0
$35$	−1.49318	−	1.49318i	−0.252393	−	0.252393i
$36$		0			0
$37$	−1.57189			−0.258417			−0.129208	−	0.991617i	$-0.541244\pi$
$37$	−1.57189			−0.258417			−0.129208	+	0.991617i	$0.541244\pi$
$38$		0			0
$39$			1.69992i			0.272204i
$40$		0			0
$41$	1.38487	−	6.25157i	0.216281	−	0.976331i
$41$	1.38487	−	6.25157i	0.216281	−	0.976331i
$42$		0			0
$43$		−	8.44151i		−	1.28732i	−0.765313	−	0.643659i	$-0.777416\pi$
$43$		−	8.44151i		−	1.28732i	0.765313	−	0.643659i	$-0.222584\pi$
$44$		0			0
$45$	−1.79917			−0.268205
$46$		0			0
$47$	−1.57218	−	1.57218i	−0.229326	−	0.229326i	0.583085	−	0.812411i	$-0.301845\pi$
$47$	−1.57218	−	1.57218i	−0.229326	−	0.229326i	−0.812411	+	0.583085i	$0.801845\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$		0			0
$51$	−3.22672			−0.451831
$52$		0			0
$53$	2.25691	−	2.25691i	0.310011	−	0.310011i	−0.534903	−	0.844914i	$-0.679652\pi$
$53$	2.25691	−	2.25691i	0.310011	−	0.310011i	0.844914	+	0.534903i	$0.179652\pi$
$54$		0			0
$55$	1.09890	+	1.09890i	0.148176	+	0.148176i
$56$		0			0
$57$	7.45997			0.988097
$58$		0			0
$59$	6.36540			0.828704			0.414352	−	0.910117i	$-0.364008\pi$
$59$	6.36540			0.828704			0.414352	+	0.910117i	$0.364008\pi$
$60$		0			0
$61$		−	8.42809i		−	1.07911i	−0.841952	−	0.539553i	$-0.818593\pi$
$61$		−	8.42809i		−	1.07911i	0.841952	−	0.539553i	$-0.181407\pi$
$62$		0			0
$63$	−0.602465	−	0.602465i	−0.0759034	−	0.0759034i
$64$		0			0
$65$	−1.29329	−	1.29329i	−0.160413	−	0.160413i
$66$		0			0
$67$	−0.439215	−	0.439215i	−0.0536586	−	0.0536586i	0.679768	−	0.733427i	$-0.262080\pi$
$67$	−0.439215	−	0.439215i	−0.0536586	−	0.0536586i	−0.733427	+	0.679768i	$0.762080\pi$
$68$		0			0
$69$	5.07508	−	5.07508i	0.610968	−	0.610968i
$70$		0			0
$71$	−1.13798	+	1.13798i	−0.135054	+	0.135054i	−0.771402	−	0.636348i	$-0.780444\pi$
$71$	−1.13798	+	1.13798i	−0.135054	+	0.135054i	0.636348	+	0.771402i	$0.280444\pi$
$72$		0			0
$73$		−	0.278184i		−	0.0325590i	−0.999867	−	0.0162795i	$-0.994818\pi$
$73$		−	0.278184i		−	0.0325590i	0.999867	−	0.0162795i	$-0.00518215\pi$
$74$		0			0
$75$	−0.750589	+	0.750589i	−0.0866706	+	0.0866706i
$76$		0			0
$77$			0.735950i			0.0838693i
$78$		0			0
$79$	−3.94424	+	3.94424i	−0.443762	+	0.443762i	−0.893274	−	0.449512i	$-0.851598\pi$
$79$	−3.94424	+	3.94424i	−0.443762	+	0.443762i	0.449512	+	0.893274i	$0.351598\pi$
$80$		0			0
$81$	10.8301			1.20335
$82$		0			0
$83$	8.17699			0.897541			0.448771	−	0.893647i	$-0.351862\pi$
$83$	8.17699			0.897541			0.448771	+	0.893647i	$0.351862\pi$
$84$		0			0
$85$	2.45487	−	2.45487i	0.266268	−	0.266268i
$86$		0			0
$87$			10.9156i			1.17028i
$88$		0			0
$89$	11.2391	−	11.2391i	1.19134	−	1.19134i	0.214652	−	0.976691i	$-0.431138\pi$
$89$	11.2391	−	11.2391i	1.19134	−	1.19134i	0.976691	−	0.214652i	$-0.0688617\pi$
$90$		0			0
$91$		−	0.866131i		−	0.0907952i
$92$		0			0
$93$	6.89187	−	6.89187i	0.714653	−	0.714653i
$94$		0			0
$95$	−5.67550	+	5.67550i	−0.582294	+	0.582294i
$96$		0			0
$97$	−9.32999	−	9.32999i	−0.947317	−	0.947317i	0.0513627	−	0.998680i	$-0.483644\pi$
$97$	−9.32999	−	9.32999i	−0.947317	−	0.947317i	−0.998680	+	0.0513627i	$0.983644\pi$
$98$		0			0
$99$	0.443384	+	0.443384i	0.0445618	+	0.0445618i
$100$		0			0
$101$	−8.06655	−	8.06655i	−0.802652	−	0.802652i	0.180857	−	0.983509i	$-0.442113\pi$
$101$	−8.06655	−	8.06655i	−0.802652	−	0.802652i	−0.983509	+	0.180857i	$0.942113\pi$
$102$		0			0
$103$		−	8.71515i		−	0.858729i	−0.903131	−	0.429364i	$-0.858738\pi$
$103$		−	8.71515i		−	0.858729i	0.903131	−	0.429364i	$-0.141262\pi$
$104$		0			0
$105$	4.14448			0.404460
$106$		0			0
$107$	12.4476			1.20336			0.601678	−	0.798738i	$-0.294499\pi$
$107$	12.4476			1.20336			0.601678	+	0.798738i	$0.294499\pi$
$108$		0			0
$109$	−0.538916	−	0.538916i	−0.0516188	−	0.0516188i	0.680826	−	0.732445i	$-0.261621\pi$
$109$	−0.538916	−	0.538916i	−0.0516188	−	0.0516188i	−0.732445	+	0.680826i	$0.761621\pi$
$110$		0			0
$111$	2.18148	−	2.18148i	0.207057	−	0.207057i
$112$		0			0
$113$	−3.47377			−0.326785			−0.163393	−	0.986561i	$-0.552244\pi$
$113$	−3.47377			−0.326785			−0.163393	+	0.986561i	$0.552244\pi$
$114$		0			0
$115$			7.72218i			0.720097i
$116$		0			0
$117$	−0.521814	−	0.521814i	−0.0482417	−	0.0482417i
$118$		0			0
$119$	1.64406			0.150711
$120$		0			0
$121$			10.4584i			0.950762i
$122$		0			0
$123$	6.75403	+	10.5979i	0.608991	+	0.955581i
$124$		0			0
$125$		−	11.7004i		−	1.04652i
$126$		0			0
$127$	−0.723418			−0.0641930			−0.0320965	−	0.999485i	$-0.510218\pi$
$127$	−0.723418			−0.0641930			−0.0320965	+	0.999485i	$0.510218\pi$
$128$		0			0
$129$	11.7152	+	11.7152i	1.03146	+	1.03146i
$130$		0			0
$131$		−	13.8945i		−	1.21397i	−0.794715	−	0.606983i	$-0.792380\pi$
$131$		−	13.8945i		−	1.21397i	0.794715	−	0.606983i	$-0.207620\pi$
$132$		0			0
$133$	−3.80096			−0.329585
$134$		0			0
$135$	−6.29487	+	6.29487i	−0.541776	+	0.541776i
$136$		0			0
$137$	−1.45697	−	1.45697i	−0.124477	−	0.124477i	0.642124	−	0.766601i	$-0.278053\pi$
$137$	−1.45697	−	1.45697i	−0.124477	−	0.124477i	−0.766601	+	0.642124i	$0.778053\pi$
$138$		0			0
$139$	−0.798436			−0.0677225			−0.0338612	−	0.999427i	$-0.510780\pi$
$139$	−0.798436			−0.0677225			−0.0338612	+	0.999427i	$0.510780\pi$
$140$		0			0
$141$	4.36375			0.367494
$142$		0			0
$143$			0.637429i			0.0533045i
$144$		0			0
$145$	−8.30455	−	8.30455i	−0.689655	−	0.689655i
$146$		0			0
$147$	1.38781	+	1.38781i	0.114464	+	0.114464i
$148$		0			0
$149$	2.04524	+	2.04524i	0.167553	+	0.167553i	0.785903	−	0.618350i	$-0.212199\pi$
$149$	2.04524	+	2.04524i	0.167553	+	0.167553i	−0.618350	+	0.785903i	$0.712199\pi$
$150$		0			0
$151$	−7.07106	+	7.07106i	−0.575435	+	0.575435i	−0.933642	−	0.358207i	$-0.883388\pi$
$151$	−7.07106	+	7.07106i	−0.575435	+	0.575435i	0.358207	+	0.933642i	$0.383388\pi$
$152$		0			0
$153$	0.990487	−	0.990487i	0.0800762	−	0.0800762i
$154$		0			0
$155$			10.4866i			0.842303i
$156$		0			0
$157$	−11.5420	+	11.5420i	−0.921148	+	0.921148i	−0.997111	−	0.0759626i	$-0.975797\pi$
$157$	−11.5420	+	11.5420i	−0.921148	+	0.921148i	0.0759626	+	0.997111i	$0.475797\pi$
$158$		0			0
$159$			6.26432i			0.496793i
$160$		0			0
$161$	−2.58582	+	2.58582i	−0.203791	+	0.203791i
$162$		0			0
$163$	−5.12099			−0.401107			−0.200553	−	0.979683i	$-0.564274\pi$
$163$	−5.12099			−0.401107			−0.200553	+	0.979683i	$0.564274\pi$
$164$		0			0
$165$	−3.05013			−0.237452
$166$		0			0
$167$	−14.9884	+	14.9884i	−1.15984	+	1.15984i	−0.175325	+	0.984511i	$0.556098\pi$
$167$	−14.9884	+	14.9884i	−1.15984	+	1.15984i	−0.984511	+	0.175325i	$0.943902\pi$
$168$		0			0
$169$			12.2498i			0.942294i
$170$		0			0
$171$	−2.28994	+	2.28994i	−0.175116	+	0.175116i
$172$		0			0
$173$		−	7.58618i		−	0.576767i	−0.957515	−	0.288383i	$-0.906882\pi$
$173$		−	7.58618i		−	0.576767i	0.957515	−	0.288383i	$-0.0931177\pi$
$174$		0			0
$175$	0.382436	−	0.382436i	0.0289094	−	0.0289094i
$176$		0			0
$177$	−8.83394	+	8.83394i	−0.664000	+	0.664000i
$178$		0			0
$179$	1.75522	+	1.75522i	0.131191	+	0.131191i	0.769653	−	0.638462i	$-0.220429\pi$
$179$	1.75522	+	1.75522i	0.131191	+	0.131191i	−0.638462	+	0.769653i	$0.720429\pi$
$180$		0			0
$181$	0.764776	+	0.764776i	0.0568454	+	0.0568454i	0.734958	−	0.678113i	$-0.237202\pi$
$181$	0.764776	+	0.764776i	0.0568454	+	0.0568454i	−0.678113	+	0.734958i	$0.737202\pi$
$182$		0			0
$183$	11.6966	+	11.6966i	0.864634	+	0.864634i
$184$		0			0
$185$			3.31931i			0.244041i
$186$		0			0
$187$	−1.20995			−0.0884800
$188$		0			0
$189$	−4.21576			−0.306651
$190$		0			0
$191$	−6.87828	−	6.87828i	−0.497695	−	0.497695i	0.413025	−	0.910720i	$-0.364472\pi$
$191$	−6.87828	−	6.87828i	−0.497695	−	0.497695i	−0.910720	+	0.413025i	$0.864472\pi$
$192$		0			0
$193$	0.863929	−	0.863929i	0.0621870	−	0.0621870i	−0.675329	−	0.737516i	$-0.735999\pi$
$193$	0.863929	−	0.863929i	0.0621870	−	0.0621870i	0.737516	+	0.675329i	$0.235999\pi$
$194$		0			0
$195$	3.58966			0.257061
$196$		0			0
$197$			8.98320i			0.640026i	0.947413	+	0.320013i	$0.103687\pi$
$197$			8.98320i			0.640026i	−0.947413	+	0.320013i	$0.896313\pi$
$198$		0			0
$199$	−1.06602	−	1.06602i	−0.0755679	−	0.0755679i	0.668313	−	0.743881i	$-0.267017\pi$
$199$	−1.06602	−	1.06602i	−0.0755679	−	0.0755679i	−0.743881	+	0.668313i	$0.767017\pi$
$200$		0			0
$201$	1.21909			0.0859880
$202$		0			0
$203$		−	5.56166i		−	0.390352i
$204$		0			0
$205$	−13.2013	−	2.92440i	−0.922016	−	0.204249i
$206$		0			0
$207$			3.11574i			0.216559i
$208$		0			0
$209$	2.79732			0.193494
$210$		0			0
$211$	9.61928	+	9.61928i	0.662218	+	0.662218i	0.955903	−	0.293684i	$-0.0948814\pi$
$211$	9.61928	+	9.61928i	0.662218	+	0.662218i	−0.293684	+	0.955903i	$0.594881\pi$
$212$		0			0
$213$		−	3.15860i		−	0.216424i
$214$		0			0
$215$	−17.8257			−1.21570
$216$		0			0
$217$	−3.51150	+	3.51150i	−0.238376	+	0.238376i
$218$		0			0
$219$	0.386065	+	0.386065i	0.0260879	+	0.0260879i
$220$		0			0
$221$	1.42397			0.0957866
$222$		0			0
$223$	−27.4521			−1.83833			−0.919165	−	0.393873i	$-0.871135\pi$
$223$	−27.4521			−1.83833			−0.919165	+	0.393873i	$0.871135\pi$
$224$		0			0
$225$		−	0.460808i		−	0.0307205i
$226$		0			0
$227$	4.14726	+	4.14726i	0.275263	+	0.275263i	0.831215	−	0.555952i	$-0.187646\pi$
$227$	4.14726	+	4.14726i	0.275263	+	0.275263i	−0.555952	+	0.831215i	$0.687646\pi$
$228$		0			0
$229$	−2.45124	−	2.45124i	−0.161983	−	0.161983i	0.621462	−	0.783444i	$-0.286539\pi$
$229$	−2.45124	−	2.45124i	−0.161983	−	0.161983i	−0.783444	+	0.621462i	$0.786539\pi$
$230$		0			0
$231$	−1.02136	−	1.02136i	−0.0672003	−	0.0672003i
$232$		0			0
$233$	−4.11812	+	4.11812i	−0.269787	+	0.269787i	−0.829014	−	0.559227i	$-0.811098\pi$
$233$	−4.11812	+	4.11812i	−0.269787	+	0.269787i	0.559227	+	0.829014i	$0.311098\pi$
$234$		0			0
$235$	−3.31992	+	3.31992i	−0.216568	+	0.216568i
$236$		0			0
$237$		−	10.9477i		−	0.711129i
$238$		0			0
$239$	−1.41383	+	1.41383i	−0.0914532	+	0.0914532i	−0.751353	−	0.659900i	$-0.770599\pi$
$239$	−1.41383	+	1.41383i	−0.0914532	+	0.0914532i	0.659900	+	0.751353i	$0.270599\pi$
$240$		0			0
$241$			3.30462i			0.212870i	0.994320	+	0.106435i	$0.0339435\pi$
$241$			3.30462i			0.212870i	−0.994320	+	0.106435i	$0.966056\pi$
$242$		0			0
$243$	−6.08714	+	6.08714i	−0.390490	+	0.390490i
$244$		0			0
$245$	−2.11167			−0.134910
$246$		0			0
$247$	−3.29213			−0.209473
$248$		0			0
$249$	−11.3481	+	11.3481i	−0.719155	+	0.719155i
$250$		0			0
$251$		−	2.78594i		−	0.175847i	−0.996127	−	0.0879236i	$-0.971977\pi$
$251$		−	2.78594i		−	0.175847i	0.996127	−	0.0879236i	$-0.0280231\pi$
$252$		0			0
$253$	1.90304	−	1.90304i	0.119643	−	0.119643i
$254$		0			0
$255$			6.81377i			0.426695i
$256$		0			0
$257$	1.00595	−	1.00595i	0.0627496	−	0.0627496i	−0.675036	−	0.737785i	$-0.735872\pi$
$257$	1.00595	−	1.00595i	0.0627496	−	0.0627496i	0.737785	+	0.675036i	$0.235872\pi$
$258$		0			0
$259$	−1.11149	+	1.11149i	−0.0690648	+	0.0690648i
$260$		0			0
$261$	−3.35071	−	3.35071i	−0.207404	−	0.207404i
$262$		0			0
$263$	15.3098	+	15.3098i	0.944044	+	0.944044i	0.998515	−	0.0544715i	$-0.0173474\pi$
$263$	15.3098	+	15.3098i	0.944044	+	0.944044i	−0.0544715	+	0.998515i	$0.517347\pi$
$264$		0			0
$265$	−4.76586	−	4.76586i	−0.292764	−	0.292764i
$266$		0			0
$267$			31.1954i			1.90913i
$268$		0			0
$269$	6.79639			0.414383			0.207192	−	0.978300i	$-0.433568\pi$
$269$	6.79639			0.414383			0.207192	+	0.978300i	$0.433568\pi$
$270$		0			0
$271$	8.93799			0.542944			0.271472	−	0.962446i	$-0.412490\pi$
$271$	8.93799			0.542944			0.271472	+	0.962446i	$0.412490\pi$
$272$		0			0
$273$	1.20202	+	1.20202i	0.0727497	+	0.0727497i
$274$		0			0
$275$	−0.281454	+	0.281454i	−0.0169723	+	0.0169723i
$276$		0			0
$277$	−16.7403			−1.00583			−0.502914	−	0.864337i	$-0.667739\pi$
$277$	−16.7403			−1.00583			−0.502914	+	0.864337i	$0.667739\pi$
$278$		0			0
$279$			4.23111i			0.253310i
$280$		0			0
$281$	7.83300	+	7.83300i	0.467278	+	0.467278i	0.901032	−	0.433754i	$-0.142811\pi$
$281$	7.83300	+	7.83300i	0.467278	+	0.467278i	−0.433754	+	0.901032i	$0.642811\pi$
$282$		0			0
$283$	7.10090			0.422105			0.211052	−	0.977475i	$-0.432311\pi$
$283$	7.10090			0.422105			0.211052	+	0.977475i	$0.432311\pi$
$284$		0			0
$285$		−	15.7530i		−	0.933127i
$286$		0			0
$287$	−3.44127	−	5.39978i	−0.203132	−	0.318739i
$288$		0			0
$289$		−	14.2971i		−	0.841004i
$290$		0			0
$291$	25.8965			1.51808
$292$		0			0
$293$	17.2745	+	17.2745i	1.00919	+	1.00919i	0.999957	+	0.00922862i	$0.00293760\pi$
$293$	17.2745	+	17.2745i	1.00919	+	1.00919i	0.00922862	+	0.999957i	$0.497062\pi$
$294$		0			0
$295$		−	13.4416i		−	0.782602i
$296$		0			0
$297$	3.10259			0.180030
$298$		0			0
$299$	−2.23966	+	2.23966i	−0.129523	+	0.129523i
$300$		0			0
$301$	−5.96905	−	5.96905i	−0.344050	−	0.344050i
$302$		0			0
$303$	22.3896			1.28625
$304$		0			0
$305$	−17.7974			−1.01907
$306$		0			0
$307$			6.19217i			0.353406i	0.984264	+	0.176703i	$0.0565432\pi$
$307$			6.19217i			0.353406i	−0.984264	+	0.176703i	$0.943457\pi$
$308$		0			0
$309$	12.0949	+	12.0949i	0.688057	+	0.688057i
$310$		0			0
$311$	12.6559	+	12.6559i	0.717649	+	0.717649i	0.968123	−	0.250474i	$-0.0805866\pi$
$311$	12.6559	+	12.6559i	0.717649	+	0.717649i	−0.250474	+	0.968123i	$0.580587\pi$
$312$		0			0
$313$	0.840639	+	0.840639i	0.0475157	+	0.0475157i	0.730465	−	0.682950i	$-0.239303\pi$
$313$	0.840639	+	0.840639i	0.0475157	+	0.0475157i	−0.682950	+	0.730465i	$0.739303\pi$
$314$		0			0
$315$	−1.27221	+	1.27221i	−0.0716808	+	0.0716808i
$316$		0			0
$317$	−8.19168	+	8.19168i	−0.460090	+	0.460090i	−0.898685	−	0.438595i	$-0.855476\pi$
$317$	−8.19168	+	8.19168i	−0.460090	+	0.460090i	0.438595	+	0.898685i	$0.355476\pi$
$318$		0			0
$319$			4.09311i			0.229170i
$320$		0			0
$321$	−17.2749	+	17.2749i	−0.964190	+	0.964190i
$322$		0			0
$323$		−	6.24900i		−	0.347703i
$324$		0			0
$325$	0.331239	−	0.331239i	0.0183739	−	0.0183739i
$326$		0			0
$327$	1.49582			0.0827192
$328$		0			0
$329$	−2.22339			−0.122580
$330$		0			0
$331$	19.0714	−	19.0714i	1.04826	−	1.04826i	0.0494840	−	0.998775i	$-0.484242\pi$
$331$	19.0714	−	19.0714i	1.04826	−	1.04826i	0.998775	−	0.0494840i	$-0.0157577\pi$
$332$		0			0
$333$			1.33927i			0.0733916i
$334$		0			0
$335$	−0.927477	+	0.927477i	−0.0506735	+	0.0506735i
$336$		0			0
$337$			24.1450i			1.31526i	0.753341	+	0.657630i	$0.228441\pi$
$337$			24.1450i			1.31526i	−0.753341	+	0.657630i	$0.771559\pi$
$338$		0			0
$339$	4.82093	−	4.82093i	0.261837	−	0.261837i
$340$		0			0
$341$	2.58429	−	2.58429i	0.139947	−	0.139947i
$342$		0			0
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$		0			0
$345$	−10.7169	−	10.7169i	−0.576978	−	0.576978i
$346$		0			0
$347$	8.46341	+	8.46341i	0.454340	+	0.454340i	0.896792	−	0.442452i	$-0.145891\pi$
$347$	8.46341	+	8.46341i	0.454340	+	0.454340i	−0.442452	+	0.896792i	$0.645891\pi$
$348$		0			0
$349$		−	26.1570i		−	1.40015i	−0.714069	−	0.700075i	$-0.753150\pi$
$349$		−	26.1570i		−	1.40015i	0.714069	−	0.700075i	$-0.246850\pi$
$350$		0			0
$351$	−3.65140			−0.194897
$352$		0			0
$353$	30.1016			1.60215			0.801074	−	0.598565i	$-0.204262\pi$
$353$	30.1016			1.60215			0.801074	+	0.598565i	$0.204262\pi$
$354$		0			0
$355$	2.40305	+	2.40305i	0.127541	+	0.127541i
$356$		0			0
$357$	−2.28164	+	2.28164i	−0.120757	+	0.120757i
$358$		0			0
$359$	6.71114			0.354200			0.177100	−	0.984193i	$-0.443328\pi$
$359$	6.71114			0.354200			0.177100	+	0.984193i	$0.443328\pi$
$360$		0			0
$361$		−	4.55272i		−	0.239617i
$362$		0			0
$363$	−14.5142	−	14.5142i	−0.761798	−	0.761798i
$364$		0			0
$365$	−0.587433			−0.0307476
$366$		0			0
$367$		−	18.0624i		−	0.942847i	−0.881907	−	0.471424i	$-0.843740\pi$
$367$		−	18.0624i		−	0.942847i	0.881907	−	0.471424i	$-0.156260\pi$
$368$		0			0
$369$	−5.32642	−	1.17993i	−0.277283	−	0.0614248i
$370$		0			0
$371$		−	3.19176i		−	0.165708i
$372$		0			0
$373$	15.3347			0.794000			0.397000	−	0.917819i	$-0.370051\pi$
$373$	15.3347			0.794000			0.397000	+	0.917819i	$0.370051\pi$
$374$		0			0
$375$	16.2380	+	16.2380i	0.838524	+	0.838524i
$376$		0			0
$377$		−	4.81713i		−	0.248095i
$378$		0			0
$379$	−7.86104			−0.403794			−0.201897	−	0.979407i	$-0.564711\pi$
$379$	−7.86104			−0.403794			−0.201897	+	0.979407i	$0.564711\pi$
$380$		0			0
$381$	1.00396	−	1.00396i	0.0514346	−	0.0514346i
$382$		0			0
$383$	−7.82055	−	7.82055i	−0.399612	−	0.399612i	0.478484	−	0.878096i	$-0.341186\pi$
$383$	−7.82055	−	7.82055i	−0.399612	−	0.399612i	−0.878096	+	0.478484i	$0.841186\pi$
$384$		0			0
$385$	1.55408			0.0792035
$386$		0			0
$387$	−7.19228			−0.365604
$388$		0			0
$389$		−	5.90513i		−	0.299402i	−0.988731	−	0.149701i	$-0.952169\pi$
$389$		−	5.90513i		−	0.299402i	0.988731	−	0.149701i	$-0.0478311\pi$
$390$		0			0
$391$	−4.25124	−	4.25124i	−0.214995	−	0.214995i
$392$		0			0
$393$	19.2828	+	19.2828i	0.972691	+	0.972691i
$394$		0			0
$395$	8.32894	+	8.32894i	0.419075	+	0.419075i
$396$		0			0
$397$	−20.3757	+	20.3757i	−1.02263	+	1.02263i	−0.0228914	+	0.999738i	$0.507287\pi$
$397$	−20.3757	+	20.3757i	−1.02263	+	1.02263i	−0.999738	+	0.0228914i	$0.992713\pi$
$398$		0			0
$399$	5.27499	−	5.27499i	0.264080	−	0.264080i
$400$		0			0
$401$		−	10.3889i		−	0.518798i	−0.965770	−	0.259399i	$-0.916476\pi$
$401$		−	10.3889i		−	0.518798i	0.965770	−	0.259399i	$-0.0835245\pi$
$402$		0			0
$403$	−3.04142	+	3.04142i	−0.151504	+	0.151504i
$404$		0			0
$405$		−	22.8696i		−	1.13640i
$406$		0			0
$407$	0.818004	−	0.818004i	0.0405469	−	0.0405469i
$408$		0			0
$409$	22.8922			1.13195			0.565974	−	0.824423i	$-0.308500\pi$
$409$	22.8922			1.13195			0.565974	+	0.824423i	$0.308500\pi$
$410$		0			0
$411$	4.04397			0.199474
$412$		0			0
$413$	4.50102	−	4.50102i	0.221481	−	0.221481i
$414$		0			0
$415$		−	17.2671i		−	0.847609i
$416$		0			0
$417$	1.10808	−	1.10808i	0.0542627	−	0.0542627i
$418$		0			0
$419$		−	5.91881i		−	0.289153i	−0.989494	−	0.144576i	$-0.953818\pi$
$419$		−	5.91881i		−	0.289153i	0.989494	−	0.144576i	$-0.0461819\pi$
$420$		0			0
$421$	−4.46517	+	4.46517i	−0.217619	+	0.217619i	−0.807494	−	0.589875i	$-0.799177\pi$
$421$	−4.46517	+	4.46517i	−0.217619	+	0.217619i	0.589875	+	0.807494i	$0.299177\pi$
$422$		0			0
$423$	−1.33952	+	1.33952i	−0.0651295	+	0.0651295i
$424$		0			0
$425$	0.628746	+	0.628746i	0.0304987	+	0.0304987i
$426$		0			0
$427$	−5.95956	−	5.95956i	−0.288403	−	0.288403i
$428$		0			0
$429$	−0.884629	−	0.884629i	−0.0427103	−	0.0427103i
$430$		0			0
$431$		−	9.00868i		−	0.433933i	−0.976179	−	0.216966i	$-0.930384\pi$
$431$		−	9.00868i		−	0.433933i	0.976179	−	0.216966i	$-0.0696162\pi$
$432$		0			0
$433$	−8.47139			−0.407109			−0.203555	−	0.979064i	$-0.565249\pi$
$433$	−8.47139			−0.407109			−0.203555	+	0.979064i	$0.565249\pi$
$434$		0			0
$435$	23.0502			1.10517
$436$		0			0
$437$	9.82861	+	9.82861i	0.470166	+	0.470166i
$438$		0			0
$439$	−2.29786	+	2.29786i	−0.109671	+	0.109671i	−0.759813	−	0.650142i	$-0.774709\pi$
$439$	−2.29786	+	2.29786i	−0.109671	+	0.109671i	0.650142	+	0.759813i	$0.274709\pi$
$440$		0			0
$441$	−0.852014			−0.0405721
$442$		0			0
$443$			1.31899i			0.0626673i	0.999509	+	0.0313336i	$0.00997544\pi$
$443$			1.31899i			0.0626673i	−0.999509	+	0.0313336i	$0.990025\pi$
$444$		0			0
$445$	−23.7333	−	23.7333i	−1.12507	−	1.12507i
$446$		0			0
$447$	−5.67680			−0.268504
$448$		0			0
$449$			20.9279i			0.987649i	0.869561	+	0.493825i	$0.164402\pi$
$449$			20.9279i			0.987649i	−0.869561	+	0.493825i	$0.835598\pi$
$450$		0			0
$451$	2.53261	+	3.97397i	0.119256	+	0.187127i
$452$		0			0
$453$		−	19.6265i		−	0.922135i
$454$		0			0
$455$	−1.82898			−0.0857441
$456$		0			0
$457$	13.6067	+	13.6067i	0.636493	+	0.636493i	0.949689	−	0.313196i	$-0.101400\pi$
$457$	13.6067	+	13.6067i	0.636493	+	0.636493i	−0.313196	+	0.949689i	$0.601400\pi$
$458$		0			0
$459$		−	6.93095i		−	0.323509i
$460$		0			0
$461$	29.5007			1.37398			0.686992	−	0.726665i	$-0.258931\pi$
$461$	29.5007			1.37398			0.686992	+	0.726665i	$0.258931\pi$
$462$		0			0
$463$	−20.4091	+	20.4091i	−0.948490	+	0.948490i	−0.998737	−	0.0502464i	$-0.983999\pi$
$463$	−20.4091	+	20.4091i	−0.948490	+	0.948490i	0.0502464	+	0.998737i	$0.483999\pi$
$464$		0			0
$465$	−14.5534	−	14.5534i	−0.674896	−	0.674896i
$466$		0			0
$467$	15.6883			0.725969			0.362984	−	0.931795i	$-0.381758\pi$
$467$	15.6883			0.725969			0.362984	+	0.931795i	$0.381758\pi$
$468$		0			0
$469$	−0.621143			−0.0286817
$470$		0			0
$471$		−	32.0360i		−	1.47614i
$472$		0			0
$473$	4.39292	+	4.39292i	0.201987	+	0.201987i
$474$		0			0
$475$	−1.45362	−	1.45362i	−0.0666967	−	0.0666967i
$476$		0			0
$477$	−1.92292	−	1.92292i	−0.0880446	−	0.0880446i
$478$		0			0
$479$	−7.85693	+	7.85693i	−0.358992	+	0.358992i	−0.863441	−	0.504449i	$-0.831696\pi$
$479$	−7.85693	+	7.85693i	−0.358992	+	0.358992i	0.504449	+	0.863441i	$0.331696\pi$
$480$		0			0
$481$	−0.962699	+	0.962699i	−0.0438953	+	0.0438953i
$482$		0			0
$483$		−	7.17725i		−	0.326576i
$484$		0			0
$485$	−19.7019	+	19.7019i	−0.894616	+	0.894616i
$486$		0			0
$487$			6.60885i			0.299476i	0.988726	+	0.149738i	$0.0478430\pi$
$487$			6.60885i			0.299476i	−0.988726	+	0.149738i	$0.952157\pi$
$488$		0			0
$489$	7.10694	−	7.10694i	0.321387	−	0.321387i
$490$		0			0
$491$	−13.0898			−0.590733			−0.295367	−	0.955384i	$-0.595442\pi$
$491$	−13.0898			−0.590733			−0.295367	+	0.955384i	$0.595442\pi$
$492$		0			0
$493$	9.14370			0.411812
$494$		0			0
$495$	0.936282	−	0.936282i	0.0420827	−	0.0420827i
$496$		0			0
$497$			1.60935i			0.0721893i
$498$		0			0
$499$	18.6689	−	18.6689i	0.835734	−	0.835734i	−0.152560	−	0.988294i	$-0.548752\pi$
$499$	18.6689	−	18.6689i	0.835734	−	0.835734i	0.988294	+	0.152560i	$0.0487518\pi$
$500$		0			0
$501$		−	41.6019i		−	1.85864i
$502$		0			0
$503$	−28.7586	+	28.7586i	−1.28228	+	1.28228i	−0.342914	+	0.939367i	$0.611414\pi$
$503$	−28.7586	+	28.7586i	−1.28228	+	1.28228i	−0.939367	+	0.342914i	$0.888586\pi$
$504$		0			0
$505$	−17.0339	+	17.0339i	−0.757999	+	0.757999i
$506$		0			0
$507$	−17.0004	−	17.0004i	−0.755013	−	0.755013i
$508$		0			0
$509$	1.29529	+	1.29529i	0.0574128	+	0.0574128i	0.735230	−	0.677817i	$-0.237074\pi$
$509$	1.29529	+	1.29529i	0.0574128	+	0.0574128i	−0.677817	+	0.735230i	$0.737074\pi$
$510$		0			0
$511$	−0.196706	−	0.196706i	−0.00870175	−	0.00870175i
$512$		0			0
$513$			16.0239i			0.707473i
$514$		0			0
$515$	−18.4035			−0.810956
$516$		0			0
$517$	1.63631			0.0719647
$518$		0			0
$519$	10.5282	+	10.5282i	0.462135	+	0.462135i
$520$		0			0
$521$	10.6591	−	10.6591i	0.466983	−	0.466983i	−0.433953	−	0.900936i	$-0.642882\pi$
$521$	10.6591	−	10.6591i	0.466983	−	0.466983i	0.900936	+	0.433953i	$0.142882\pi$
$522$		0			0
$523$	−20.5879			−0.900245			−0.450123	−	0.892967i	$-0.648620\pi$
$523$	−20.5879			−0.900245			−0.450123	+	0.892967i	$0.648620\pi$
$524$		0			0
$525$			1.06149i			0.0463274i
$526$		0			0
$527$	−5.77311	−	5.77311i	−0.251481	−	0.251481i
$528$		0			0
$529$	−9.62703			−0.418567
$530$		0			0
$531$		−	5.42341i		−	0.235356i
$532$		0			0
$533$	−2.98059	−	4.67692i	−0.129104	−	0.202580i
$534$		0			0
$535$		−	26.2853i		−	1.13641i
$536$		0			0
$537$	−4.87180			−0.210234
$538$		0			0
$539$	0.520395	+	0.520395i	0.0224150	+	0.0224150i
$540$		0			0
$541$		−	22.2711i		−	0.957508i	−0.877949	−	0.478754i	$-0.841089\pi$
$541$		−	22.2711i		−	0.957508i	0.877949	−	0.478754i	$-0.158911\pi$
$542$		0			0
$543$	−2.12272			−0.0910948
$544$		0			0
$545$	−1.13801	+	1.13801i	−0.0487472	+	0.0487472i
$546$		0			0
$547$	−28.8837	−	28.8837i	−1.23498	−	1.23498i	−0.962028	−	0.272951i	$-0.912000\pi$
$547$	−28.8837	−	28.8837i	−1.23498	−	1.23498i	−0.272951	−	0.962028i	$-0.588000\pi$
$548$		0			0
$549$	−7.18085			−0.306471
$550$		0			0
$551$	−21.1397			−0.900580
$552$		0			0
$553$			5.57800i			0.237201i
$554$		0			0
$555$	−4.60656	−	4.60656i	−0.195538	−	0.195538i
$556$		0			0
$557$	5.69310	+	5.69310i	0.241224	+	0.241224i	0.817357	−	0.576132i	$-0.195439\pi$
$557$	5.69310	+	5.69310i	0.241224	+	0.241224i	−0.576132	+	0.817357i	$0.695439\pi$
$558$		0			0
$559$	−5.16998	−	5.16998i	−0.218667	−	0.218667i
$560$		0			0
$561$	1.67917	−	1.67917i	0.0708946	−	0.0708946i
$562$		0			0
$563$	17.2253	−	17.2253i	0.725960	−	0.725960i	−0.243852	−	0.969812i	$-0.578411\pi$
$563$	17.2253	−	17.2253i	0.725960	−	0.725960i	0.969812	+	0.243852i	$0.0784111\pi$
$564$		0			0
$565$			7.33547i			0.308605i
$566$		0			0
$567$	7.65805	−	7.65805i	0.321608	−	0.321608i
$568$		0			0
$569$		−	42.3445i		−	1.77517i	−0.460640	−	0.887587i	$-0.652380\pi$
$569$		−	42.3445i		−	1.77517i	0.460640	−	0.887587i	$-0.347620\pi$
$570$		0			0
$571$	−5.34409	+	5.34409i	−0.223643	+	0.223643i	−0.810031	−	0.586388i	$-0.800550\pi$
$571$	−5.34409	+	5.34409i	−0.223643	+	0.223643i	0.586388	+	0.810031i	$0.300550\pi$
$572$		0			0
$573$	19.0914			0.797557
$574$		0			0
$575$	−1.97782			−0.0824809
$576$		0			0
$577$	−32.9190	+	32.9190i	−1.37044	+	1.37044i	−0.510648	+	0.859790i	$0.670594\pi$
$577$	−32.9190	+	32.9190i	−1.37044	+	1.37044i	−0.859790	+	0.510648i	$0.829406\pi$
$578$		0			0
$579$			2.39793i			0.0996547i
$580$		0			0
$581$	5.78201	−	5.78201i	0.239878	−	0.239878i
$582$		0			0
$583$			2.34898i			0.0972846i
$584$		0			0
$585$	−1.10190	+	1.10190i	−0.0455579	+	0.0455579i
$586$		0			0
$587$	−20.6815	+	20.6815i	−0.853616	+	0.853616i	−0.990577	−	0.136960i	$-0.956267\pi$
$587$	−20.6815	+	20.6815i	−0.853616	+	0.853616i	0.136960	+	0.990577i	$0.456267\pi$
$588$		0			0
$589$	13.3471	+	13.3471i	0.549957	+	0.549957i
$590$		0			0
$591$	−12.4669	−	12.4669i	−0.512822	−	0.512822i
$592$		0			0
$593$	4.00333	+	4.00333i	0.164397	+	0.164397i	0.784511	−	0.620114i	$-0.212914\pi$
$593$	4.00333	+	4.00333i	0.164397	+	0.164397i	−0.620114	+	0.784511i	$0.712914\pi$
$594$		0			0
$595$		−	3.47171i		−	0.142326i
$596$		0			0
$597$	2.95885			0.121098
$598$		0			0
$599$	47.6272			1.94600			0.972998	−	0.230812i	$-0.0741383\pi$
$599$	47.6272			1.94600			0.972998	+	0.230812i	$0.0741383\pi$
$600$		0			0
$601$	−8.81011	−	8.81011i	−0.359372	−	0.359372i	0.504210	−	0.863581i	$-0.331784\pi$
$601$	−8.81011	−	8.81011i	−0.359372	−	0.359372i	−0.863581	+	0.504210i	$0.831784\pi$
$602$		0			0
$603$	−0.374217	+	0.374217i	−0.0152393	+	0.0152393i
$604$		0			0
$605$	22.0847			0.897869
$606$		0			0
$607$			36.5165i			1.48216i	0.671418	+	0.741078i	$0.265685\pi$
$607$			36.5165i			1.48216i	−0.671418	+	0.741078i	$0.734315\pi$
$608$		0			0
$609$	7.71851	+	7.71851i	0.312770	+	0.312770i
$610$		0			0
$611$	−1.92575			−0.0779075
$612$		0			0
$613$		−	32.2352i		−	1.30197i	−0.759092	−	0.650984i	$-0.774357\pi$
$613$		−	32.2352i		−	1.30197i	0.759092	−	0.650984i	$-0.225643\pi$
$614$		0			0
$615$	22.3793	−	14.2623i	0.902420	−	0.575111i
$616$		0			0
$617$			18.8966i			0.760749i	0.924833	+	0.380374i	$0.124205\pi$
$617$			18.8966i			0.760749i	−0.924833	+	0.380374i	$0.875795\pi$
$618$		0			0
$619$	−7.32834			−0.294551			−0.147275	−	0.989096i	$-0.547050\pi$
$619$	−7.32834			−0.294551			−0.147275	+	0.989096i	$0.547050\pi$
$620$		0			0
$621$	10.9012	+	10.9012i	0.437450	+	0.437450i
$622$		0			0
$623$		−	15.8945i		−	0.636799i
$624$		0			0
$625$	−22.0033			−0.880130
$626$		0			0
$627$	−3.88213	+	3.88213i	−0.155037	+	0.155037i
$628$		0			0
$629$	−1.82736	−	1.82736i	−0.0728616	−	0.0728616i
$630$		0			0
$631$	39.8793			1.58757			0.793785	−	0.608198i	$-0.208107\pi$
$631$	39.8793			1.58757			0.793785	+	0.608198i	$0.208107\pi$
$632$		0			0
$633$	−26.6994			−1.06121
$634$		0			0
$635$			1.52762i			0.0606218i
$636$		0			0
$637$	−0.612447	−	0.612447i	−0.0242660	−	0.0242660i
$638$		0			0
$639$	0.969578	+	0.969578i	0.0383559	+	0.0383559i
$640$		0			0
$641$	−9.47633	−	9.47633i	−0.374292	−	0.374292i	0.494745	−	0.869038i	$-0.335261\pi$
$641$	−9.47633	−	9.47633i	−0.374292	−	0.374292i	−0.869038	+	0.494745i	$0.835261\pi$
$642$		0			0
$643$	14.2664	−	14.2664i	0.562614	−	0.562614i	−0.367435	−	0.930049i	$-0.619764\pi$
$643$	14.2664	−	14.2664i	0.562614	−	0.562614i	0.930049	+	0.367435i	$0.119764\pi$
$644$		0			0
$645$	24.7386	−	24.7386i	0.974081	−	0.974081i
$646$		0			0
$647$			17.0892i			0.671846i	0.941889	+	0.335923i	$0.109048\pi$
$647$			17.0892i			0.671846i	−0.941889	+	0.335923i	$0.890952\pi$
$648$		0			0
$649$	−3.31252	+	3.31252i	−0.130028	+	0.130028i
$650$		0			0
$651$		−	9.74657i		−	0.381998i
$652$		0			0
$653$	11.1468	−	11.1468i	0.436207	−	0.436207i	−0.454526	−	0.890733i	$-0.650191\pi$
$653$	11.1468	−	11.1468i	0.436207	−	0.436207i	0.890733	+	0.454526i	$0.150191\pi$
$654$		0			0
$655$	−29.3406			−1.14643
$656$		0			0
$657$	−0.237017			−0.00924690
$658$		0			0
$659$	0.418356	−	0.418356i	0.0162968	−	0.0162968i	−0.698911	−	0.715208i	$-0.746332\pi$
$659$	0.418356	−	0.418356i	0.0162968	−	0.0162968i	0.715208	+	0.698911i	$0.246332\pi$
$660$		0			0
$661$			5.10196i			0.198443i	0.995065	+	0.0992216i	$0.0316353\pi$
$661$			5.10196i			0.198443i	−0.995065	+	0.0992216i	$0.968365\pi$
$662$		0			0
$663$	−1.97620	+	1.97620i	−0.0767491	+	0.0767491i
$664$		0			0
$665$			8.02637i			0.311249i
$666$		0			0
$667$	−14.3815	+	14.3815i	−0.556853	+	0.556853i
$668$		0			0
$669$	38.0982	−	38.0982i	1.47296	−	1.47296i
$670$		0			0
$671$	4.38594	+	4.38594i	0.169317	+	0.169317i
$672$		0			0
$673$	18.9106	+	18.9106i	0.728952	+	0.728952i	0.970411	−	0.241459i	$-0.0776261\pi$
$673$	18.9106	+	18.9106i	0.728952	+	0.728952i	−0.241459	+	0.970411i	$0.577626\pi$
$674$		0			0
$675$	−1.61225	−	1.61225i	−0.0620557	−	0.0620557i
$676$		0			0
$677$			22.4278i			0.861969i	0.902359	+	0.430984i	$0.141834\pi$
$677$			22.4278i			0.861969i	−0.902359	+	0.430984i	$0.858166\pi$
$678$		0			0
$679$	−13.1946			−0.506362
$680$		0			0
$681$	−11.5112			−0.441109
$682$		0			0
$683$	16.6486	+	16.6486i	0.637040	+	0.637040i	0.949824	−	0.312784i	$-0.101262\pi$
$683$	16.6486	+	16.6486i	0.637040	+	0.637040i	−0.312784	+	0.949824i	$0.601262\pi$
$684$		0			0
$685$	−3.07663	+	3.07663i	−0.117552	+	0.117552i
$686$		0			0
$687$	6.80370			0.259577
$688$		0			0
$689$		−	2.76448i		−	0.105318i
$690$		0			0
$691$	−19.3720	−	19.3720i	−0.736945	−	0.736945i	0.235040	−	0.971986i	$-0.424478\pi$
$691$	−19.3720	−	19.3720i	−0.736945	−	0.736945i	−0.971986	+	0.235040i	$0.924478\pi$
$692$		0			0
$693$	0.627040			0.0238193
$694$		0			0
$695$			1.68603i			0.0639549i
$696$		0			0
$697$	8.87756	−	5.65765i	0.336261	−	0.214299i
$698$		0			0
$699$		−	11.4303i		−	0.432334i
$700$		0			0
$701$	7.05364			0.266412			0.133206	−	0.991088i	$-0.457473\pi$
$701$	7.05364			0.266412			0.133206	+	0.991088i	$0.457473\pi$
$702$		0			0
$703$	4.22474	+	4.22474i	0.159339	+	0.159339i
$704$		0			0
$705$		−	9.21481i		−	0.347050i
$706$		0			0
$707$	−11.4078			−0.429036
$708$		0			0
$709$	−13.3339	+	13.3339i	−0.500767	+	0.500767i	−0.911676	−	0.410909i	$-0.865211\pi$
$709$	−13.3339	+	13.3339i	−0.500767	+	0.500767i	0.410909	+	0.911676i	$0.365211\pi$
$710$		0			0
$711$	3.36055	+	3.36055i	0.126030	+	0.126030i
$712$		0			0
$713$	18.1603			0.680107
$714$		0			0
$715$	1.34604			0.0503391
$716$		0			0
$717$		−	3.92425i		−	0.146554i
$718$		0			0
$719$	21.6670	+	21.6670i	0.808044	+	0.808044i	0.984338	−	0.176294i	$-0.0564109\pi$
$719$	21.6670	+	21.6670i	0.808044	+	0.808044i	−0.176294	+	0.984338i	$0.556411\pi$
$720$		0			0
$721$	−6.16254	−	6.16254i	−0.229505	−	0.229505i
$722$		0			0
$723$	−4.58618	−	4.58618i	−0.170562	−	0.170562i
$724$		0			0
$725$	2.12698	−	2.12698i	0.0789940	−	0.0789940i
$726$		0			0
$727$	4.23623	−	4.23623i	0.157113	−	0.157113i	−0.624173	−	0.781286i	$-0.714564\pi$
$727$	4.23623	−	4.23623i	0.157113	−	0.157113i	0.781286	+	0.624173i	$0.214564\pi$
$728$		0			0
$729$			15.5948i			0.577585i
$730$		0			0
$731$	9.81346	−	9.81346i	0.362964	−	0.362964i
$732$		0			0
$733$		−	48.0360i		−	1.77425i	−0.461531	−	0.887124i	$-0.652700\pi$
$733$		−	48.0360i		−	1.77425i	0.461531	−	0.887124i	$-0.347300\pi$
$734$		0			0
$735$	2.93059	−	2.93059i	0.108096	−	0.108096i
$736$		0			0
$737$	0.457131			0.0168386
$738$		0			0
$739$	25.0807			0.922608			0.461304	−	0.887242i	$-0.347382\pi$
$739$	25.0807			0.922608			0.461304	+	0.887242i	$0.347382\pi$
$740$		0			0
$741$	4.56884	−	4.56884i	0.167840	−	0.167840i
$742$		0			0
$743$		−	23.1665i		−	0.849897i	−0.905218	−	0.424948i	$-0.860292\pi$
$743$		−	23.1665i		−	0.849897i	0.905218	−	0.424948i	$-0.139708\pi$
$744$		0			0
$745$	4.31888	−	4.31888i	0.158232	−	0.158232i
$746$		0			0
$747$		−	6.96691i		−	0.254906i
$748$		0			0
$749$	8.80180	−	8.80180i	0.321611	−	0.321611i
$750$		0			0
$751$	22.4974	−	22.4974i	0.820942	−	0.820942i	−0.165301	−	0.986243i	$-0.552860\pi$
$751$	22.4974	−	22.4974i	0.820942	−	0.820942i	0.986243	+	0.165301i	$0.0528595\pi$
$752$		0			0
$753$	3.86635	+	3.86635i	0.140898	+	0.140898i
$754$		0			0
$755$	14.9318	+	14.9318i	0.543422	+	0.543422i
$756$		0			0
$757$	−8.62170	−	8.62170i	−0.313361	−	0.313361i	0.532849	−	0.846210i	$-0.321121\pi$
$757$	−8.62170	−	8.62170i	−0.313361	−	0.313361i	−0.846210	+	0.532849i	$0.821121\pi$
$758$		0			0
$759$			5.28210i			0.191728i
$760$		0			0
$761$	−4.67890			−0.169610			−0.0848049	−	0.996398i	$-0.527027\pi$
$761$	−4.67890			−0.169610			−0.0848049	+	0.996398i	$0.527027\pi$
$762$		0			0
$763$	−0.762143			−0.0275914
$764$		0			0
$765$	−2.09158	−	2.09158i	−0.0756214	−	0.0756214i
$766$		0			0
$767$	3.89847	−	3.89847i	0.140766	−	0.140766i
$768$		0			0
$769$	7.68935			0.277285			0.138643	−	0.990342i	$-0.455726\pi$
$769$	7.68935			0.277285			0.138643	+	0.990342i	$0.455726\pi$
$770$		0			0
$771$			2.79214i			0.100556i
$772$		0			0
$773$	6.51065	+	6.51065i	0.234172	+	0.234172i	0.814432	−	0.580260i	$-0.197049\pi$
$773$	6.51065	+	6.51065i	0.234172	+	0.234172i	−0.580260	+	0.814432i	$0.697049\pi$
$774$		0			0
$775$	−2.68585			−0.0964785
$776$		0			0
$777$		−	3.08507i		−	0.110676i
$778$		0			0
$779$	−20.5243	+	13.0801i	−0.735361	+	0.468644i
$780$		0			0
$781$		−	1.18440i		−	0.0423813i
$782$		0			0
$783$	−23.4466			−0.837914
$784$		0			0
$785$	24.3728	+	24.3728i	0.869903	+	0.869903i
$786$		0			0
$787$		−	38.8016i		−	1.38313i	−0.722314	−	0.691565i	$-0.756922\pi$
$787$		−	38.8016i		−	1.38313i	0.722314	−	0.691565i	$-0.243078\pi$
$788$		0			0
$789$	−42.4941			−1.51283
$790$		0			0
$791$	−2.45633	+	2.45633i	−0.0873370	+	0.0873370i
$792$		0			0
$793$	−5.16176	−	5.16176i	−0.183299	−	0.183299i
$794$		0			0
$795$	13.2282			0.469155
$796$		0			0
$797$	−39.6615			−1.40488			−0.702441	−	0.711742i	$-0.747907\pi$
$797$	−39.6615			−1.40488			−0.702441	+	0.711742i	$0.747907\pi$
$798$		0			0
$799$		−	3.65539i		−	0.129318i
$800$		0			0
$801$	−9.57587	−	9.57587i	−0.338347	−	0.338347i
$802$		0			0
$803$	0.144766	+	0.144766i	0.00510867	+	0.00510867i
$804$		0			0
$805$	5.46041	+	5.46041i	0.192454	+	0.192454i
$806$		0			0
$807$	−9.43208	+	9.43208i	−0.332025	+	0.332025i
$808$		0			0
$809$	30.2934	−	30.2934i	1.06506	−	1.06506i	0.0673269	−	0.997731i	$-0.478553\pi$
$809$	30.2934	−	30.2934i	1.06506	−	1.06506i	0.997731	−	0.0673269i	$-0.0214470\pi$
$810$		0			0
$811$		−	24.5648i		−	0.862587i	−0.902212	−	0.431294i	$-0.858057\pi$
$811$		−	24.5648i		−	0.862587i	0.902212	−	0.431294i	$-0.141943\pi$
$812$		0			0
$813$	−12.4042	+	12.4042i	−0.435034	+	0.435034i
$814$		0			0
$815$			10.8138i			0.378792i
$816$		0			0
$817$	−22.6881	+	22.6881i	−0.793756	+	0.793756i
$818$		0			0
$819$	−0.737956			−0.0257863
$820$		0			0
$821$	1.37822			0.0481001			0.0240500	−	0.999711i	$-0.492344\pi$
$821$	1.37822			0.0481001			0.0240500	+	0.999711i	$0.492344\pi$
$822$		0			0
$823$	−3.51453	+	3.51453i	−0.122509	+	0.122509i	−0.765703	−	0.643194i	$-0.777609\pi$
$823$	−3.51453	+	3.51453i	−0.122509	+	0.122509i	0.643194	+	0.765703i	$0.277609\pi$
$824$		0			0
$825$		−	0.781206i		−	0.0271981i
$826$		0			0
$827$	8.56446	−	8.56446i	0.297815	−	0.297815i	−0.542342	−	0.840158i	$-0.682462\pi$
$827$	8.56446	−	8.56446i	0.297815	−	0.297815i	0.840158	+	0.542342i	$0.182462\pi$
$828$		0			0
$829$			29.0041i			1.00735i	0.863892	+	0.503677i	$0.168020\pi$
$829$			29.0041i			1.00735i	−0.863892	+	0.503677i	$0.831980\pi$
$830$		0			0
$831$	23.2323	−	23.2323i	0.805920	−	0.805920i
$832$		0			0
$833$	1.16252	−	1.16252i	0.0402791	−	0.0402791i
$834$		0			0
$835$	31.6505	+	31.6505i	1.09531	+	1.09531i
$836$		0			0
$837$	14.8036	+	14.8036i	0.511688	+	0.511688i
$838$		0			0
$839$	−26.7499	−	26.7499i	−0.923510	−	0.923510i	0.0737653	−	0.997276i	$-0.476498\pi$
$839$	−26.7499	−	26.7499i	−0.923510	−	0.923510i	−0.997276	+	0.0737653i	$0.976498\pi$
$840$		0			0
$841$		−	1.93211i		−	0.0666246i
$842$		0			0
$843$	−21.7414			−0.748813
$844$		0			0
$845$	25.8676			0.889872
$846$		0			0
$847$	7.39519	+	7.39519i	0.254102	+	0.254102i
$848$		0			0
$849$	−9.85468	+	9.85468i	−0.338212	+	0.338212i
$850$		0			0
$851$	5.74825			0.197047
$852$		0			0
$853$		−	21.9534i		−	0.751670i	−0.926687	−	0.375835i	$-0.877356\pi$
$853$		−	21.9534i		−	0.751670i	0.926687	−	0.375835i	$-0.122644\pi$
$854$		0			0
$855$	4.83561	+	4.83561i	0.165374	+	0.165374i
$856$		0			0
$857$	13.9767			0.477434			0.238717	−	0.971089i	$-0.423273\pi$
$857$	13.9767			0.477434			0.238717	+	0.971089i	$0.423273\pi$
$858$		0			0
$859$			15.6320i			0.533357i	0.963786	+	0.266679i	$0.0859262\pi$
$859$			15.6320i			0.533357i	−0.963786	+	0.266679i	$0.914074\pi$
$860$		0			0
$861$	12.2697	+	2.71803i	0.418149	+	0.0926302i
$862$		0			0
$863$		−	55.7402i		−	1.89742i	−0.316151	−	0.948709i	$-0.602390\pi$
$863$		−	55.7402i		−	1.89742i	0.316151	−	0.948709i	$-0.397610\pi$
$864$		0			0
$865$	−16.0195			−0.544680
$866$		0			0
$867$	19.8416	+	19.8416i	0.673855	+	0.673855i
$868$		0			0
$869$		−	4.10513i		−	0.139257i
$870$		0			0
$871$	−0.537991			−0.0182291
$872$		0			0
$873$	−7.94929	+	7.94929i	−0.269043	+	0.269043i
$874$		0			0
$875$	−8.27346	−	8.27346i	−0.279694	−	0.279694i
$876$		0			0
$877$	57.2454			1.93304			0.966519	−	0.256594i	$-0.0826004\pi$
$877$	57.2454			1.93304			0.966519	+	0.256594i	$0.0826004\pi$
$878$		0			0
$879$	−47.9473			−1.61722
$880$		0			0
$881$			39.8961i			1.34413i	0.740491	+	0.672066i	$0.234593\pi$
$881$			39.8961i			1.34413i	−0.740491	+	0.672066i	$0.765407\pi$
$882$		0			0
$883$	0.151721	+	0.151721i	0.00510581	+	0.00510581i	0.709655	−	0.704549i	$-0.248851\pi$
$883$	0.151721	+	0.151721i	0.00510581	+	0.00510581i	−0.704549	+	0.709655i	$0.748851\pi$
$884$		0			0
$885$	18.6544	+	18.6544i	0.627060	+	0.627060i
$886$		0			0
$887$	6.81787	+	6.81787i	0.228922	+	0.228922i	0.812242	−	0.583320i	$-0.198247\pi$
$887$	6.81787	+	6.81787i	0.228922	+	0.228922i	−0.583320	+	0.812242i	$0.698247\pi$
$888$		0			0
$889$	−0.511534	+	0.511534i	−0.0171563	+	0.0171563i
$890$		0			0
$891$	−5.63594	+	5.63594i	−0.188811	+	0.188811i
$892$		0			0
$893$			8.45103i			0.282803i
$894$		0			0
$895$	3.70644	−	3.70644i	0.123893	−	0.123893i
$896$		0			0
$897$		−	6.21644i		−	0.207561i
$898$		0			0
$899$	−19.5298	+	19.5298i	−0.651355	+	0.651355i
$900$		0			0
$901$	5.24744			0.174817
$902$		0			0
$903$	16.5678			0.551341
$904$		0			0
$905$	1.61496	−	1.61496i	0.0536830	−	0.0536830i
$906$		0			0
$907$			31.0676i			1.03158i	0.856714	+	0.515791i	$0.172502\pi$
$907$			31.0676i			1.03158i	−0.856714	+	0.515791i	$0.827498\pi$
$908$		0			0
$909$	−6.87282	+	6.87282i	−0.227957	+	0.227957i
$910$		0			0
$911$		−	54.9756i		−	1.82142i	−0.413042	−	0.910712i	$-0.635534\pi$
$911$		−	54.9756i		−	1.82142i	0.413042	−	0.910712i	$-0.364466\pi$
$912$		0			0
$913$	−4.25527	+	4.25527i	−0.140829	+	0.140829i
$914$		0			0
$915$	24.6993	−	24.6993i	0.816533	−	0.816533i
$916$		0			0
$917$	−9.82488	−	9.82488i	−0.324446	−	0.324446i
$918$		0			0
$919$	14.2472	+	14.2472i	0.469972	+	0.469972i	0.901905	−	0.431934i	$-0.142169\pi$
$919$	14.2472	+	14.2472i	0.469972	+	0.469972i	−0.431934	+	0.901905i	$0.642169\pi$
$920$		0			0
$921$	−8.59354	−	8.59354i	−0.283167	−	0.283167i
$922$		0			0
$923$			1.39391i			0.0458811i
$924$		0			0
$925$	−0.850149			−0.0279527
$926$		0			0
$927$	−7.42543			−0.243883
$928$		0			0
$929$	6.08578	+	6.08578i	0.199668	+	0.199668i	0.799858	−	0.600190i	$-0.204908\pi$
$929$	6.08578	+	6.08578i	0.199668	+	0.199668i	−0.600190	+	0.799858i	$0.704908\pi$
$930$		0			0
$931$	−2.68768	+	2.68768i	−0.0880853	+	0.0880853i
$932$		0			0
$933$	−35.1278			−1.15003
$934$		0			0
$935$			2.55501i			0.0835576i
$936$		0			0
$937$	−1.41689	−	1.41689i	−0.0462878	−	0.0462878i	0.683584	−	0.729872i	$-0.260420\pi$
$937$	−1.41689	−	1.41689i	−0.0462878	−	0.0462878i	−0.729872	+	0.683584i	$0.760420\pi$
$938$		0			0
$939$	−2.33329			−0.0761440
$940$		0			0
$941$			14.4776i			0.471956i	0.971758	+	0.235978i	$0.0758294\pi$
$941$			14.4776i			0.471956i	−0.971758	+	0.235978i	$0.924171\pi$
$942$		0			0
$943$	−5.06436	+	22.8614i	−0.164918	+	0.744470i
$944$		0			0
$945$			8.90229i			0.289591i
$946$		0			0
$947$	−1.27765			−0.0415182			−0.0207591	−	0.999785i	$-0.506608\pi$
$947$	−1.27765			−0.0415182			−0.0207591	+	0.999785i	$0.506608\pi$
$948$		0			0
$949$	−0.170373	−	0.170373i	−0.00553054	−	0.00553054i
$950$		0			0
$951$		−	22.7369i		−	0.737295i
$952$		0			0
$953$	−15.6253			−0.506154			−0.253077	−	0.967446i	$-0.581443\pi$
$953$	−15.6253			−0.506154			−0.253077	+	0.967446i	$0.581443\pi$
$954$		0			0
$955$	−14.5247	+	14.5247i	−0.470007	+	0.470007i
$956$		0			0
$957$	−5.68044	−	5.68044i	−0.183623	−	0.183623i
$958$		0			0
$959$	−2.06046			−0.0665357
$960$		0			0
$961$	−6.33870			−0.204474
$962$		0			0
$963$		−	10.6055i		−	0.341759i
$964$		0			0
$965$	−1.82433	−	1.82433i	−0.0587274	−	0.0587274i
$966$		0			0
$967$	16.9846	+	16.9846i	0.546187	+	0.546187i	0.925336	−	0.379149i	$-0.123783\pi$
$967$	16.9846	+	16.9846i	0.546187	+	0.546187i	−0.379149	+	0.925336i	$0.623783\pi$
$968$		0			0
$969$	8.67240	+	8.67240i	0.278598	+	0.278598i
$970$		0			0
$971$	−0.218722	+	0.218722i	−0.00701914	+	0.00701914i	−0.710608	−	0.703589i	$-0.751580\pi$
$971$	−0.218722	+	0.218722i	−0.00701914	+	0.00701914i	0.703589	+	0.710608i	$0.251580\pi$
$972$		0			0
$973$	−0.564580	+	0.564580i	−0.0180996	+	0.0180996i
$974$		0			0
$975$			0.919392i			0.0294441i
$976$		0			0
$977$	−33.9439	+	33.9439i	−1.08596	+	1.08596i	−0.0900206	+	0.995940i	$0.528693\pi$
$977$	−33.9439	+	33.9439i	−1.08596	+	1.08596i	−0.995940	+	0.0900206i	$0.971307\pi$
$978$		0			0
$979$			11.6976i			0.373855i
$980$		0			0
$981$	−0.459164	+	0.459164i	−0.0146600	+	0.0146600i
$982$		0			0
$983$	−11.5678			−0.368957			−0.184478	−	0.982837i	$-0.559060\pi$
$983$	−11.5678			−0.368957			−0.184478	+	0.982837i	$0.559060\pi$
$984$		0			0
$985$	18.9696			0.604421
$986$		0			0
$987$	3.08564	−	3.08564i	0.0982170	−	0.0982170i
$988$		0			0
$989$			30.8698i			0.981602i
$990$		0			0
$991$	22.7912	−	22.7912i	0.723988	−	0.723988i	−0.245427	−	0.969415i	$-0.578928\pi$
$991$	22.7912	−	22.7912i	0.723988	−	0.723988i	0.969415	+	0.245427i	$0.0789283\pi$
$992$		0			0
$993$			52.9348i			1.67984i
$994$		0			0
$995$	−2.25107	+	2.25107i	−0.0713639	+	0.0713639i
$996$		0			0
$997$	−27.1411	+	27.1411i	−0.859569	+	0.859569i	−0.991287	−	0.131719i	$-0.957950\pi$
$997$	−27.1411	+	27.1411i	−0.859569	+	0.859569i	0.131719	+	0.991287i	$0.457950\pi$
$998$		0			0
$999$	4.68578	+	4.68578i	0.148252	+	0.148252i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.k.b.729.5	yes	36
41.9	even	4	inner	1148.2.k.b.337.5	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.k.b.337.5	✓	36	41.9	even	4	inner
1148.2.k.b.729.5	yes	36	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-1.38781 + 1.38781i) q^{3} -2.11167i q^{5} +(0.707107 - 0.707107i) q^{7} -0.852014i q^{9} +O(q^{10})\)	\(q+(-1.38781 + 1.38781i) q^{3} -2.11167i q^{5} +(0.707107 - 0.707107i) q^{7} -0.852014i q^{9} +(-0.520395 + 0.520395i) q^{11} +(0.612447 - 0.612447i) q^{13} +(2.93059 + 2.93059i) q^{15} +(1.16252 + 1.16252i) q^{17} +(-2.68768 - 2.68768i) q^{19} +1.96265i q^{21} -3.65691 q^{23} +0.540846 q^{25} +(-2.98099 - 2.98099i) q^{27} +(3.93269 - 3.93269i) q^{29} -4.96601 q^{31} -1.44442i q^{33} +(-1.49318 - 1.49318i) q^{35} -1.57189 q^{37} +1.69992i q^{39} +(1.38487 - 6.25157i) q^{41} -8.44151i q^{43} -1.79917 q^{45} +(-1.57218 - 1.57218i) q^{47} -1.00000i q^{49} -3.22672 q^{51} +(2.25691 - 2.25691i) q^{53} +(1.09890 + 1.09890i) q^{55} +7.45997 q^{57} +6.36540 q^{59} -8.42809i q^{61} +(-0.602465 - 0.602465i) q^{63} +(-1.29329 - 1.29329i) q^{65} +(-0.439215 - 0.439215i) q^{67} +(5.07508 - 5.07508i) q^{69} +(-1.13798 + 1.13798i) q^{71} -0.278184i q^{73} +(-0.750589 + 0.750589i) q^{75} +0.735950i q^{77} +(-3.94424 + 3.94424i) q^{79} +10.8301 q^{81} +8.17699 q^{83} +(2.45487 - 2.45487i) q^{85} +10.9156i q^{87} +(11.2391 - 11.2391i) q^{89} -0.866131i q^{91} +(6.89187 - 6.89187i) q^{93} +(-5.67550 + 5.67550i) q^{95} +(-9.32999 - 9.32999i) q^{97} +(0.443384 + 0.443384i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q+O(q^{10}) \) 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

Varieties

Fields

Representations

Groups

Database

Properties

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