LMFDB - Embedded newform 2548.2.u.f.1765.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2548,2,Mod(589,2548)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2548.589"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2548, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2548 = 2^{2} \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2548.u (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,0,0,0,0,0,-8,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$20.3458824350$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1765.7
Character	$\chi$	$=$	2548.1765
Dual form			2548.2.u.f.589.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.307410 + 0.532450i) q^{3} -2.84979i q^{5} +(1.31100 - 2.27072i) q^{9} +(-1.56065 + 0.901040i) q^{11} +(-3.01398 + 1.97887i) q^{13} +(1.51737 - 0.876054i) q^{15} +(-0.806891 + 1.39758i) q^{17} +(-4.64909 - 2.68415i) q^{19} +(-0.575859 - 0.997417i) q^{23} -3.12129 q^{25} +3.45652 q^{27} +(-1.88686 - 3.26813i) q^{29} +0.375670i q^{31} +(-0.959517 - 0.553978i) q^{33} +(1.96662 - 1.13543i) q^{37} +(-1.98018 - 0.996468i) q^{39} +(-5.59731 + 3.23161i) q^{41} +(-0.235139 + 0.407272i) q^{43} +(-6.47106 - 3.73607i) q^{45} -1.43923i q^{47} -0.992186 q^{51} -12.1308 q^{53} +(2.56777 + 4.44751i) q^{55} -3.30054i q^{57} +(-6.17352 - 3.56428i) q^{59} +(-2.80721 + 4.86224i) q^{61} +(5.63937 + 8.58920i) q^{65} +(-1.40482 + 0.811071i) q^{67} +(0.354050 - 0.613233i) q^{69} +(8.79759 + 5.07929i) q^{71} +5.62031i q^{73} +(-0.959517 - 1.66193i) q^{75} +14.3724 q^{79} +(-2.87043 - 4.97172i) q^{81} -2.93485i q^{83} +(3.98279 + 2.29947i) q^{85} +(1.16008 - 2.00931i) q^{87} +(-11.1754 + 6.45210i) q^{89} +(-0.200026 + 0.115485i) q^{93} +(-7.64927 + 13.2489i) q^{95} +(-10.4934 - 6.05837i) q^{97} +4.72505i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{9} - 12 q^{15} + 16 q^{23} + 24 q^{29} + 8 q^{39} + 4 q^{43} + 80 q^{51} - 48 q^{53} + 8 q^{65} - 24 q^{71} - 48 q^{79} + 4 q^{81} + 12 q^{85} + 48 q^{93} - 20 q^{95}+O(q^{100}) $ 24 * q - 8 * q^9 - 12 * q^15 + 16 * q^23 + 24 * q^29 + 8 * q^39 + 4 * q^43 + 80 * q^51 - 48 * q^53 + 8 * q^65 - 24 * q^71 - 48 * q^79 + 4 * q^81 + 12 * q^85 + 48 * q^93 - 20 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2548\mathbb{Z}\right)^\times$.

$n$	$197$	$885$	$1275$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.307410	+	0.532450i	0.177483	+	0.307410i	0.941018	−	0.338357i	$-0.109871\pi$
$3$	0.307410	+	0.532450i	0.177483	+	0.307410i	−0.763535	+	0.645767i	$0.776538\pi$
$4$		0			0
$5$		−	2.84979i		−	1.27446i	−0.770672	−	0.637232i	$-0.780079\pi$
$5$		−	2.84979i		−	1.27446i	0.770672	−	0.637232i	$-0.219921\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	1.31100	−	2.27072i	0.436999	−	0.756905i
$10$		0			0
$11$	−1.56065	+	0.901040i	−0.470553	+	0.271674i	−0.716471	−	0.697617i	$-0.754244\pi$
$11$	−1.56065	+	0.901040i	−0.470553	+	0.271674i	0.245918	+	0.969291i	$0.420910\pi$
$12$		0			0
$13$	−3.01398	+	1.97887i	−0.835927	+	0.548840i
$13$	−3.01398	+	1.97887i	−0.835927	+	0.548840i
$14$		0			0
$15$	1.51737	−	0.876054i	0.391783	−	0.226196i
$16$		0			0
$17$	−0.806891	+	1.39758i	−0.195700	+	0.338962i	−0.947130	−	0.320851i	$-0.896031\pi$
$17$	−0.806891	+	1.39758i	−0.195700	+	0.338962i	0.751430	+	0.659813i	$0.229364\pi$
$18$		0			0
$19$	−4.64909	−	2.68415i	−1.06657	−	0.615787i	−0.139331	−	0.990246i	$-0.544495\pi$
$19$	−4.64909	−	2.68415i	−1.06657	−	0.615787i	−0.927243	+	0.374459i	$0.877828\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.575859	−	0.997417i	−0.120075	−	0.207976i	0.799722	−	0.600370i	$-0.204980\pi$
$23$	−0.575859	−	0.997417i	−0.120075	−	0.207976i	−0.919797	+	0.392394i	$0.871647\pi$
$24$		0			0
$25$	−3.12129			−0.624259
$26$		0			0
$27$	3.45652			0.665207
$28$		0			0
$29$	−1.88686	−	3.26813i	−0.350381	−	0.606877i	0.635936	−	0.771742i	$-0.280614\pi$
$29$	−1.88686	−	3.26813i	−0.350381	−	0.606877i	−0.986316	+	0.164865i	$0.947281\pi$
$30$		0			0
$31$			0.375670i			0.0674724i	0.999431	+	0.0337362i	$0.0107406\pi$
$31$			0.375670i			0.0674724i	−0.999431	+	0.0337362i	$0.989259\pi$
$32$		0			0
$33$	−0.959517	−	0.553978i	−0.167031	−	0.0964351i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	1.96662	−	1.13543i	0.323311	−	0.186664i	−0.329556	−	0.944136i	$-0.606899\pi$
$37$	1.96662	−	1.13543i	0.323311	−	0.186664i	0.652867	+	0.757472i	$0.273566\pi$
$38$		0			0
$39$	−1.98018	−	0.996468i	−0.317082	−	0.159563i
$40$		0			0
$41$	−5.59731	+	3.23161i	−0.874153	+	0.504692i	−0.868726	−	0.495293i	$-0.835061\pi$
$41$	−5.59731	+	3.23161i	−0.874153	+	0.504692i	−0.00542662	+	0.999985i	$0.501727\pi$
$42$		0			0
$43$	−0.235139	+	0.407272i	−0.0358583	+	0.0621084i	−0.883398	−	0.468624i	$-0.844750\pi$
$43$	−0.235139	+	0.407272i	−0.0358583	+	0.0621084i	0.847539	+	0.530733i	$0.178083\pi$
$44$		0			0
$45$	−6.47106	−	3.73607i	−0.964648	−	0.556940i
$46$		0			0
$47$		−	1.43923i		−	0.209933i	−0.994476	−	0.104966i	$-0.966526\pi$
$47$		−	1.43923i		−	0.209933i	0.994476	−	0.104966i	$-0.0334735\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−0.992186			−0.138934
$52$		0			0
$53$	−12.1308			−1.66630			−0.833150	−	0.553048i	$-0.813465\pi$
$53$	−12.1308			−1.66630			−0.833150	+	0.553048i	$0.813465\pi$
$54$		0			0
$55$	2.56777	+	4.44751i	0.346238	+	0.599703i
$56$		0			0
$57$		−	3.30054i		−	0.437168i
$58$		0			0
$59$	−6.17352	−	3.56428i	−0.803724	−	0.464030i	0.0410479	−	0.999157i	$-0.486930\pi$
$59$	−6.17352	−	3.56428i	−0.803724	−	0.464030i	−0.844772	+	0.535127i	$0.820264\pi$
$60$		0			0
$61$	−2.80721	+	4.86224i	−0.359427	+	0.622546i	−0.987865	−	0.155314i	$-0.950361\pi$
$61$	−2.80721	+	4.86224i	−0.359427	+	0.622546i	0.628438	+	0.777860i	$0.283694\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	5.63937	+	8.58920i	0.699477	+	1.06536i
$66$		0			0
$67$	−1.40482	+	0.811071i	−0.171626	+	0.0990881i	−0.583352	−	0.812219i	$-0.698259\pi$
$67$	−1.40482	+	0.811071i	−0.171626	+	0.0990881i	0.411727	+	0.911307i	$0.364926\pi$
$68$		0			0
$69$	0.354050	−	0.613233i	0.0426226	−	0.0738245i
$70$		0			0
$71$	8.79759	+	5.07929i	1.04408	+	0.602801i	0.920987	−	0.389594i	$-0.127385\pi$
$71$	8.79759	+	5.07929i	1.04408	+	0.602801i	0.123095	+	0.992395i	$0.460718\pi$
$72$		0			0
$73$			5.62031i			0.657808i	0.944363	+	0.328904i	$0.106679\pi$
$73$			5.62031i			0.657808i	−0.944363	+	0.328904i	$0.893321\pi$
$74$		0			0
$75$	−0.959517	−	1.66193i	−0.110796	−	0.191903i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	14.3724			1.61702			0.808510	−	0.588482i	$-0.200274\pi$
$79$	14.3724			1.61702			0.808510	+	0.588482i	$0.200274\pi$
$80$		0			0
$81$	−2.87043	−	4.97172i	−0.318936	−	0.552414i
$82$		0			0
$83$		−	2.93485i		−	0.322141i	−0.986943	−	0.161071i	$-0.948505\pi$
$83$		−	2.93485i		−	0.322141i	0.986943	−	0.161071i	$-0.0514947\pi$
$84$		0			0
$85$	3.98279	+	2.29947i	0.431995	+	0.249412i
$86$		0			0
$87$	1.16008	−	2.00931i	0.124373	−	0.215421i
$88$		0			0
$89$	−11.1754	+	6.45210i	−1.18459	+	0.683921i	−0.957071	−	0.289854i	$-0.906393\pi$
$89$	−11.1754	+	6.45210i	−1.18459	+	0.683921i	−0.227515	+	0.973775i	$0.573060\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−0.200026	+	0.115485i	−0.0207417	+	0.0119752i
$94$		0			0
$95$	−7.64927	+	13.2489i	−0.784798	+	1.35931i
$96$		0			0
$97$	−10.4934	−	6.05837i	−1.06544	−	0.615135i	−0.138511	−	0.990361i	$-0.544232\pi$
$97$	−10.4934	−	6.05837i	−1.06544	−	0.615135i	−0.926933	+	0.375226i	$0.877565\pi$
$98$		0			0
$99$			4.72505i			0.474885i
$100$		0			0
$101$	−2.03122	−	3.51818i	−0.202114	−	0.350072i	0.747095	−	0.664717i	$-0.231448\pi$
$101$	−2.03122	−	3.51818i	−0.202114	−	0.350072i	−0.949209	+	0.314645i	$0.898115\pi$
$102$		0			0
$103$	−19.1795			−1.88981			−0.944904	−	0.327348i	$-0.893845\pi$
$103$	−19.1795			−1.88981			−0.944904	+	0.327348i	$0.893845\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.59081	+	7.95152i	0.443810	+	0.768702i	0.997968	−	0.0637093i	$-0.0202930\pi$
$107$	4.59081	+	7.95152i	0.443810	+	0.768702i	−0.554158	+	0.832411i	$0.686960\pi$
$108$		0			0
$109$		−	5.05828i		−	0.484496i	−0.970214	−	0.242248i	$-0.922115\pi$
$109$		−	5.05828i		−	0.484496i	0.970214	−	0.242248i	$-0.0778847\pi$
$110$		0			0
$111$	1.20912	+	0.698086i	0.114765	+	0.0662594i
$112$		0			0
$113$	−2.21934	+	3.84401i	−0.208778	+	0.361614i	−0.951330	−	0.308175i	$-0.900282\pi$
$113$	−2.21934	+	3.84401i	−0.208778	+	0.361614i	0.742552	+	0.669788i	$0.233615\pi$
$114$		0			0
$115$	−2.84243	+	1.64108i	−0.265058	+	0.153031i
$116$		0			0
$117$	0.542134	+	9.43818i	0.0501203	+	0.872560i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−3.87625	+	6.71387i	−0.352387	+	0.610352i
$122$		0			0
$123$	−3.44134	−	1.98686i	−0.310295	−	0.179149i
$124$		0			0
$125$		−	5.35392i		−	0.478869i
$126$		0			0
$127$	8.68065	+	15.0353i	0.770283	+	1.33417i	0.937408	+	0.348234i	$0.113218\pi$
$127$	8.68065	+	15.0353i	0.770283	+	1.33417i	−0.167125	+	0.985936i	$0.553448\pi$
$128$		0			0
$129$	−0.289136			−0.0254570
$130$		0			0
$131$	5.25994			0.459563			0.229781	−	0.973242i	$-0.426199\pi$
$131$	5.25994			0.459563			0.229781	+	0.973242i	$0.426199\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		−	9.85034i		−	0.847783i
$136$		0			0
$137$	−15.7804	−	9.11081i	−1.34821	−	0.778389i	−0.360213	−	0.932870i	$-0.617296\pi$
$137$	−15.7804	−	9.11081i	−1.34821	−	0.778389i	−0.987996	+	0.154481i	$0.950629\pi$
$138$		0			0
$139$	10.0434	−	17.3956i	0.851868	−	1.47548i	−0.0276525	−	0.999618i	$-0.508803\pi$
$139$	10.0434	−	17.3956i	0.851868	−	1.47548i	0.879520	−	0.475861i	$-0.157863\pi$
$140$		0			0
$141$	0.766317	−	0.442433i	0.0645355	−	0.0372596i
$142$		0			0
$143$	2.92071	−	5.80403i	0.244242	−	0.485358i
$144$		0			0
$145$	−9.31349	+	5.37714i	−0.773443	+	0.446547i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−12.9068	−	7.45173i	−1.05736	−	0.610469i	−0.132662	−	0.991161i	$-0.542352\pi$
$149$	−12.9068	−	7.45173i	−1.05736	−	0.610469i	−0.924702	+	0.380692i	$0.875686\pi$
$150$		0			0
$151$			6.95740i			0.566185i	0.959093	+	0.283093i	$0.0913604\pi$
$151$			6.95740i			0.566185i	−0.959093	+	0.283093i	$0.908640\pi$
$152$		0			0
$153$	2.11566	+	3.66444i	0.171041	+	0.296252i
$154$		0			0
$155$	1.07058			0.0859911
$156$		0			0
$157$	−6.21365			−0.495903			−0.247952	−	0.968772i	$-0.579757\pi$
$157$	−6.21365			−0.495903			−0.247952	+	0.968772i	$0.579757\pi$
$158$		0			0
$159$	−3.72914	−	6.45907i	−0.295740	−	0.512237i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	7.94888	+	4.58929i	0.622605	+	0.359461i	0.777882	−	0.628410i	$-0.216294\pi$
$163$	7.94888	+	4.58929i	0.622605	+	0.359461i	−0.155278	+	0.987871i	$0.549627\pi$
$164$		0			0
$165$	−1.57872	+	2.73442i	−0.122903	+	0.212874i
$166$		0			0
$167$	0.810372	−	0.467869i	0.0627085	−	0.0362048i	−0.468318	−	0.883560i	$-0.655140\pi$
$167$	0.810372	−	0.467869i	0.0627085	−	0.0362048i	0.531026	+	0.847355i	$0.321806\pi$
$168$		0			0
$169$	5.16813	−	11.9286i	0.397549	−	0.917581i
$170$		0			0
$171$	−12.1899	+	7.03784i	−0.932184	+	0.538197i
$172$		0			0
$173$	−1.73303	+	3.00170i	−0.131760	+	0.228215i	−0.924355	−	0.381533i	$-0.875396\pi$
$173$	−1.73303	+	3.00170i	−0.131760	+	0.228215i	0.792595	+	0.609748i	$0.208730\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		−	4.38279i		−	0.329430i
$178$		0			0
$179$	−1.28051	−	2.21792i	−0.0957102	−	0.165775i	0.814195	−	0.580592i	$-0.197179\pi$
$179$	−1.28051	−	2.21792i	−0.0957102	−	0.165775i	−0.909905	+	0.414817i	$0.863846\pi$
$180$		0			0
$181$	−12.9745			−0.964389			−0.482194	−	0.876064i	$-0.660160\pi$
$181$	−12.9745			−0.964389			−0.482194	+	0.876064i	$0.660160\pi$
$182$		0			0
$183$	−3.45187			−0.255169
$184$		0			0
$185$	−3.23574	−	5.60446i	−0.237896	−	0.412048i
$186$		0			0
$187$		−	2.90816i		−	0.212666i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	12.9853	−	22.4912i	0.939583	−	1.62741i	0.173334	−	0.984863i	$-0.444546\pi$
$191$	12.9853	−	22.4912i	0.939583	−	1.62741i	0.766250	−	0.642543i	$-0.222121\pi$
$192$		0			0
$193$	5.94916	−	3.43475i	0.428230	−	0.247239i	−0.270362	−	0.962759i	$-0.587143\pi$
$193$	5.94916	−	3.43475i	0.428230	−	0.247239i	0.698592	+	0.715520i	$0.253810\pi$
$194$		0			0
$195$	−2.83972	+	5.64309i	−0.203357	+	0.404110i
$196$		0			0
$197$	12.9358	−	7.46849i	0.921638	−	0.532108i	0.0374808	−	0.999297i	$-0.488067\pi$
$197$	12.9358	−	7.46849i	0.921638	−	0.532108i	0.884157	+	0.467189i	$0.154733\pi$
$198$		0			0
$199$	−2.69895	+	4.67473i	−0.191324	+	0.331383i	−0.945689	−	0.325072i	$-0.894611\pi$
$199$	−2.69895	+	4.67473i	−0.191324	+	0.331383i	0.754365	+	0.656455i	$0.227945\pi$
$200$		0			0
$201$	−0.863709	−	0.498663i	−0.0609214	−	0.0351730i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	9.20940	+	15.9511i	0.643212	+	1.11408i
$206$		0			0
$207$	−3.01980			−0.209891
$208$		0			0
$209$	9.67411			0.669172
$210$		0			0
$211$	−4.46899	−	7.74051i	−0.307658	−	0.532879i	0.670192	−	0.742188i	$-0.266212\pi$
$211$	−4.46899	−	7.74051i	−0.307658	−	0.532879i	−0.977850	+	0.209309i	$0.932879\pi$
$212$		0			0
$213$			6.24570i			0.427949i
$214$		0			0
$215$	1.16064	+	0.670096i	0.0791550	+	0.0457001i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−2.99253	+	1.72774i	−0.202217	+	0.116750i
$220$		0			0
$221$	−0.333672	−	5.80900i	−0.0224452	−	0.390755i
$222$		0			0
$223$	−12.8537	+	7.42106i	−0.860744	+	0.496951i	−0.864262	−	0.503043i	$-0.832214\pi$
$223$	−12.8537	+	7.42106i	−0.860744	+	0.496951i	0.00351707	+	0.999994i	$0.498880\pi$
$224$		0			0
$225$	−4.09201	+	7.08757i	−0.272801	+	0.472505i
$226$		0			0
$227$	−19.6000	−	11.3160i	−1.30089	−	0.751072i	−0.320337	−	0.947304i	$-0.603796\pi$
$227$	−19.6000	−	11.3160i	−1.30089	−	0.751072i	−0.980558	+	0.196232i	$0.937129\pi$
$228$		0			0
$229$		−	16.4717i		−	1.08848i	−0.838930	−	0.544240i	$-0.816818\pi$
$229$		−	16.4717i		−	1.08848i	0.838930	−	0.544240i	$-0.183182\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−14.2544			−0.933838			−0.466919	−	0.884300i	$-0.654636\pi$
$233$	−14.2544			−0.933838			−0.466919	+	0.884300i	$0.654636\pi$
$234$		0			0
$235$	−4.10149			−0.267552
$236$		0			0
$237$	4.41822	+	7.65258i	0.286994	+	0.497089i
$238$		0			0
$239$		−	25.1730i		−	1.62831i	−0.580650	−	0.814154i	$-0.697201\pi$
$239$		−	25.1730i		−	1.62831i	0.580650	−	0.814154i	$-0.302799\pi$
$240$		0			0
$241$	12.0781	+	6.97331i	0.778021	+	0.449191i	0.835728	−	0.549143i	$-0.185046\pi$
$241$	12.0781	+	6.97331i	0.778021	+	0.449191i	−0.0577074	+	0.998334i	$0.518379\pi$
$242$		0			0
$243$	6.94957	−	12.0370i	0.445815	−	0.772175i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	19.3238	−	1.10997i	1.22955	−	0.0706258i
$248$		0			0
$249$	1.56266	−	0.902202i	0.0990296	−	0.0571748i
$250$		0			0
$251$	9.08534	−	15.7363i	0.573462	−	0.993265i	−0.422745	−	0.906248i	$-0.638934\pi$
$251$	9.08534	−	15.7363i	0.573462	−	0.993265i	0.996207	−	0.0870160i	$-0.0277331\pi$
$252$		0			0
$253$	1.79743	+	1.03774i	0.113003	+	0.0652424i
$254$		0			0
$255$			2.82752i			0.177066i
$256$		0			0
$257$	−2.52851	−	4.37952i	−0.157724	−	0.273187i	0.776323	−	0.630335i	$-0.217082\pi$
$257$	−2.52851	−	4.37952i	−0.157724	−	0.273187i	−0.934048	+	0.357148i	$0.883749\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−9.89466			−0.612464
$262$		0			0
$263$	−2.60888	−	4.51872i	−0.160871	−	0.278636i	0.774311	−	0.632806i	$-0.218097\pi$
$263$	−2.60888	−	4.51872i	−0.160871	−	0.278636i	−0.935181	+	0.354170i	$0.884764\pi$
$264$		0			0
$265$			34.5703i			2.12364i
$266$		0			0
$267$	−6.87084	−	3.96688i	−0.420488	−	0.242769i
$268$		0			0
$269$	2.10274	−	3.64206i	0.128206	−	0.222060i	−0.794775	−	0.606904i	$-0.792411\pi$
$269$	2.10274	−	3.64206i	0.128206	−	0.222060i	0.922982	+	0.384844i	$0.125745\pi$
$270$		0			0
$271$	−8.34869	+	4.82012i	−0.507147	+	0.292801i	−0.731660	−	0.681670i	$-0.761254\pi$
$271$	−8.34869	+	4.82012i	−0.507147	+	0.292801i	0.224513	+	0.974471i	$0.427921\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	4.87124	−	2.81241i	0.293747	−	0.169595i
$276$		0			0
$277$	2.47816	−	4.29231i	0.148898	−	0.257900i	−0.781922	−	0.623376i	$-0.785761\pi$
$277$	2.47816	−	4.29231i	0.148898	−	0.257900i	0.930821	+	0.365476i	$0.119094\pi$
$278$		0			0
$279$	0.853040	+	0.492503i	0.0510702	+	0.0294854i
$280$		0			0
$281$		−	9.93319i		−	0.592564i	−0.955100	−	0.296282i	$-0.904253\pi$
$281$		−	9.93319i		−	0.592564i	0.955100	−	0.296282i	$-0.0957469\pi$
$282$		0			0
$283$	12.8921	+	22.3298i	0.766356	+	1.32737i	0.939527	+	0.342476i	$0.111266\pi$
$283$	12.8921	+	22.3298i	0.766356	+	1.32737i	−0.173170	+	0.984892i	$0.555401\pi$
$284$		0			0
$285$	−9.40585			−0.557154
$286$		0			0
$287$		0			0
$288$		0			0
$289$	7.19786	+	12.4671i	0.423403	+	0.733356i
$290$		0			0
$291$		−	7.44962i		−	0.436705i
$292$		0			0
$293$	8.82379	+	5.09442i	0.515492	+	0.297619i	0.735088	−	0.677972i	$-0.237141\pi$
$293$	8.82379	+	5.09442i	0.515492	+	0.297619i	−0.219597	+	0.975591i	$0.570474\pi$
$294$		0			0
$295$	−10.1575	+	17.5932i	−0.591390	+	1.02432i
$296$		0			0
$297$	−5.39440	+	3.11446i	−0.313015	+	0.180719i
$298$		0			0
$299$	3.70939	+	1.86664i	0.214519	+	0.107951i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	1.24884	−	2.16305i	0.0717438	−	0.124264i
$304$		0			0
$305$	13.8563	+	7.99997i	0.793412	+	0.458077i
$306$		0			0
$307$		−	30.2516i		−	1.72655i	−0.504734	−	0.863275i	$-0.668409\pi$
$307$		−	30.2516i		−	1.72655i	0.504734	−	0.863275i	$-0.331591\pi$
$308$		0			0
$309$	−5.89596	−	10.2121i	−0.335409	−	0.580946i
$310$		0			0
$311$	20.7199			1.17492			0.587459	−	0.809254i	$-0.300128\pi$
$311$	20.7199			1.17492			0.587459	+	0.809254i	$0.300128\pi$
$312$		0			0
$313$	11.3628			0.642266			0.321133	−	0.947034i	$-0.395936\pi$
$313$	11.3628			0.642266			0.321133	+	0.947034i	$0.395936\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$			15.7291i			0.883433i	0.897155	+	0.441717i	$0.145630\pi$
$317$			15.7291i			0.883433i	−0.897155	+	0.441717i	$0.854370\pi$
$318$		0			0
$319$	5.88944	+	3.40027i	0.329745	+	0.190378i
$320$		0			0
$321$	−2.82252	+	4.88875i	−0.157538	+	0.272864i
$322$		0			0
$323$	7.50261	−	4.33163i	0.417456	−	0.241019i
$324$		0			0
$325$	9.40751	−	6.17664i	0.521835	−	0.342618i
$326$		0			0
$327$	2.69328	−	1.55497i	0.148939	−	0.0859899i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−30.1029	−	17.3799i	−1.65461	−	0.955288i	−0.975142	−	0.221579i	$-0.928879\pi$
$331$	−30.1029	−	17.3799i	−1.65461	−	0.955288i	−0.679464	−	0.733709i	$-0.737788\pi$
$332$		0			0
$333$		−	5.95419i		−	0.326288i
$334$		0			0
$335$	2.31138	+	4.00343i	0.126284	+	0.218731i
$336$		0			0
$337$	15.4211			0.840042			0.420021	−	0.907514i	$-0.362023\pi$
$337$	15.4211			0.840042			0.420021	+	0.907514i	$0.362023\pi$
$338$		0			0
$339$	−2.72899			−0.148218
$340$		0			0
$341$	−0.338494	−	0.586289i	−0.0183305	−	0.0317493i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−1.74758	−	1.00897i	−0.0940867	−	0.0543210i
$346$		0			0
$347$	−9.17454	+	15.8908i	−0.492515	+	0.853061i	−0.999963	−	0.00862142i	$-0.997256\pi$
$347$	−9.17454	+	15.8908i	−0.492515	+	0.853061i	0.507448	+	0.861683i	$0.330589\pi$
$348$		0			0
$349$	−10.9773	+	6.33774i	−0.587600	+	0.339251i	−0.764148	−	0.645041i	$-0.776840\pi$
$349$	−10.9773	+	6.33774i	−0.587600	+	0.339251i	0.176548	+	0.984292i	$0.443507\pi$
$350$		0			0
$351$	−10.4179	+	6.84001i	−0.556065	+	0.365092i
$352$		0			0
$353$	10.2825	−	5.93658i	0.547280	−	0.315972i	−0.200744	−	0.979644i	$-0.564336\pi$
$353$	10.2825	−	5.93658i	0.547280	−	0.315972i	0.748024	+	0.663671i	$0.231003\pi$
$354$		0			0
$355$	14.4749	−	25.0713i	0.768248	−	1.33064i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	7.06966i		−	0.373122i	−0.982443	−	0.186561i	$-0.940266\pi$
$359$		−	7.06966i		−	0.373122i	0.982443	−	0.186561i	$-0.0597342\pi$
$360$		0			0
$361$	4.90935	+	8.50324i	0.258387	+	0.447539i
$362$		0			0
$363$	−4.76640			−0.250171
$364$		0			0
$365$	16.0167			0.838352
$366$		0			0
$367$	13.8085	+	23.9169i	0.720795	+	1.24845i	0.960681	+	0.277653i	$0.0895566\pi$
$367$	13.8085	+	23.9169i	0.720795	+	1.24845i	−0.239886	+	0.970801i	$0.577110\pi$
$368$		0			0
$369$			16.9465i			0.882201i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	14.3110	−	24.7874i	0.740996	−	1.28344i	−0.211046	−	0.977476i	$-0.567687\pi$
$373$	14.3110	−	24.7874i	0.740996	−	1.28344i	0.952042	−	0.305967i	$-0.0989797\pi$
$374$		0			0
$375$	2.85069	−	1.64585i	0.147209	−	0.0849912i
$376$		0			0
$377$	12.1542	+	6.11623i	0.625971	+	0.315002i
$378$		0			0
$379$	−27.8128	+	16.0577i	−1.42865	+	0.824830i	−0.997014	−	0.0772189i	$-0.975396\pi$
$379$	−27.8128	+	16.0577i	−1.42865	+	0.824830i	−0.431634	+	0.902049i	$0.642063\pi$
$380$		0			0
$381$	−5.33704	+	9.24402i	−0.273425	+	0.473586i
$382$		0			0
$383$	19.1914	+	11.0801i	0.980633	+	0.566169i	0.902461	−	0.430771i	$-0.141758\pi$
$383$	19.1914	+	11.0801i	0.980633	+	0.566169i	0.0781720	+	0.996940i	$0.475092\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	0.616533	+	1.06787i	0.0313401	+	0.0542827i
$388$		0			0
$389$	15.9099			0.806666			0.403333	−	0.915053i	$-0.367852\pi$
$389$	15.9099			0.806666			0.403333	+	0.915053i	$0.367852\pi$
$390$		0			0
$391$	1.85862			0.0939945
$392$		0			0
$393$	1.61696	+	2.80065i	0.0815648	+	0.141274i
$394$		0			0
$395$		−	40.9583i		−	2.06083i
$396$		0			0
$397$	26.1161	+	15.0781i	1.31073	+	0.756750i	0.982217	−	0.187750i	$-0.0601195\pi$
$397$	26.1161	+	15.0781i	1.31073	+	0.756750i	0.328512	+	0.944500i	$0.393453\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−29.9226	+	17.2758i	−1.49426	+	0.862712i	−0.999978	−	0.00658877i	$-0.997903\pi$
$401$	−29.9226	+	17.2758i	−1.49426	+	0.862712i	−0.494283	+	0.869301i	$0.664569\pi$
$402$		0			0
$403$	−0.743403	−	1.13226i	−0.0370316	−	0.0564020i
$404$		0			0
$405$	−14.1684	+	8.18010i	−0.704031	+	0.406473i
$406$		0			0
$407$	−2.04614	+	3.54401i	−0.101423	+	0.175670i
$408$		0			0
$409$	−24.5091	−	14.1504i	−1.21190	−	0.699690i	−0.248726	−	0.968574i	$-0.580012\pi$
$409$	−24.5091	−	14.1504i	−1.21190	−	0.699690i	−0.963173	+	0.268884i	$0.913345\pi$
$410$		0			0
$411$		−	11.2030i		−	0.552604i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−8.36370			−0.410558
$416$		0			0
$417$	12.3497			0.604770
$418$		0			0
$419$	−6.75416	−	11.6985i	−0.329962	−	0.571511i	0.652542	−	0.757753i	$-0.273703\pi$
$419$	−6.75416	−	11.6985i	−0.329962	−	0.571511i	−0.982504	+	0.186241i	$0.940369\pi$
$420$		0			0
$421$			1.45597i			0.0709594i	0.999370	+	0.0354797i	$0.0112959\pi$
$421$			1.45597i			0.0709594i	−0.999370	+	0.0354797i	$0.988704\pi$
$422$		0			0
$423$	−3.26807	−	1.88682i	−0.158899	−	0.0917405i
$424$		0			0
$425$	2.51854	−	4.36224i	0.122167	−	0.211600i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	3.98822	−	0.229085i	0.192553	−	0.0110603i
$430$		0			0
$431$	31.8357	−	18.3804i	1.53347	−	0.885352i	0.534276	−	0.845310i	$-0.320584\pi$
$431$	31.8357	−	18.3804i	1.53347	−	0.885352i	0.999198	−	0.0400414i	$-0.0127490\pi$
$432$		0			0
$433$	7.33480	−	12.7043i	0.352488	−	0.610527i	−0.634197	−	0.773172i	$-0.718669\pi$
$433$	7.33480	−	12.7043i	0.352488	−	0.610527i	0.986685	+	0.162644i	$0.0520024\pi$
$434$		0			0
$435$	−5.72612	−	3.30598i	−0.274546	−	0.158509i
$436$		0			0
$437$			6.18278i			0.295762i
$438$		0			0
$439$	8.23925	+	14.2708i	0.393238	+	0.681108i	0.992875	−	0.119164i	$-0.0380215\pi$
$439$	8.23925	+	14.2708i	0.393238	+	0.681108i	−0.599637	+	0.800272i	$0.704688\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−18.0424			−0.857221			−0.428610	−	0.903489i	$-0.640997\pi$
$443$	−18.0424			−0.857221			−0.428610	+	0.903489i	$0.640997\pi$
$444$		0			0
$445$	18.3871	+	31.8474i	0.871633	+	1.50971i
$446$		0			0
$447$		−	9.16294i		−	0.433392i
$448$		0			0
$449$	−5.28375	−	3.05058i	−0.249356	−	0.143966i	0.370113	−	0.928987i	$-0.379319\pi$
$449$	−5.28375	−	3.05058i	−0.249356	−	0.143966i	−0.619469	+	0.785021i	$0.712652\pi$
$450$		0			0
$451$	5.82361	−	10.0868i	0.274223	−	0.474969i
$452$		0			0
$453$	−3.70447	+	2.13878i	−0.174051	+	0.100488i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	1.23542	−	0.713269i	0.0577904	−	0.0333653i	−0.470826	−	0.882226i	$-0.656044\pi$
$457$	1.23542	−	0.713269i	0.0577904	−	0.0333653i	0.528617	+	0.848861i	$0.322711\pi$
$458$		0			0
$459$	−2.78903	+	4.83074i	−0.130181	+	0.225480i
$460$		0			0
$461$	−3.67565	−	2.12213i	−0.171192	−	0.0988377i	0.411956	−	0.911204i	$-0.364846\pi$
$461$	−3.67565	−	2.12213i	−0.171192	−	0.0988377i	−0.583148	+	0.812366i	$0.698179\pi$
$462$		0			0
$463$			31.0675i			1.44383i	0.691982	+	0.721915i	$0.256738\pi$
$463$			31.0675i			1.44383i	−0.691982	+	0.721915i	$0.743262\pi$
$464$		0			0
$465$	0.329107	+	0.570031i	0.0152620	+	0.0264345i
$466$		0			0
$467$	15.8029			0.731272			0.365636	−	0.930758i	$-0.380851\pi$
$467$	15.8029			0.731272			0.365636	+	0.930758i	$0.380851\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−1.91014	−	3.30846i	−0.0880146	−	0.152446i
$472$		0			0
$473$		−	0.847477i		−	0.0389671i
$474$		0			0
$475$	14.5112	+	8.37803i	0.665818	+	0.384410i
$476$		0			0
$477$	−15.9035	+	27.5457i	−0.728172	+	1.26123i
$478$		0			0
$479$	31.4478	−	18.1564i	1.43689	−	0.829586i	0.439253	−	0.898363i	$-0.355243\pi$
$479$	31.4478	−	18.1564i	1.43689	−	0.829586i	0.997632	+	0.0687771i	$0.0219097\pi$
$480$		0			0
$481$	−3.68049	+	7.31386i	−0.167816	+	0.333483i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−17.2651	+	29.9040i	−0.783967	+	1.35787i
$486$		0			0
$487$	−19.5839	−	11.3068i	−0.887432	−	0.512359i	−0.0143304	−	0.999897i	$-0.504562\pi$
$487$	−19.5839	−	11.3068i	−0.887432	−	0.512359i	−0.873102	+	0.487538i	$0.837895\pi$
$488$		0			0
$489$			5.64318i			0.255193i
$490$		0			0
$491$	0.687916	+	1.19151i	0.0310452	+	0.0537719i	0.881131	−	0.472873i	$-0.156783\pi$
$491$	0.687916	+	1.19151i	0.0310452	+	0.0537719i	−0.850085	+	0.526645i	$0.823450\pi$
$492$		0			0
$493$	6.08995			0.274278
$494$		0			0
$495$	13.4654			0.605224
$496$		0			0
$497$		0			0
$498$		0			0
$499$			0.717661i			0.0321269i	0.999871	+	0.0160635i	$0.00511338\pi$
$499$			0.717661i			0.0321269i	−0.999871	+	0.0160635i	$0.994887\pi$
$500$		0			0
$501$	0.498233	+	0.287655i	0.0222594	+	0.0128515i
$502$		0			0
$503$	16.5915	−	28.7373i	0.739777	−	1.28133i	−0.212819	−	0.977092i	$-0.568264\pi$
$503$	16.5915	−	28.7373i	0.739777	−	1.28133i	0.952596	−	0.304239i	$-0.0984023\pi$
$504$		0			0
$505$	−10.0261	+	5.78855i	−0.446154	+	0.257587i
$506$		0			0
$507$	7.94010	−	0.915187i	0.352632	−	0.0406449i
$508$		0			0
$509$	−10.8310	+	6.25329i	−0.480077	+	0.277172i	−0.720448	−	0.693509i	$-0.756064\pi$
$509$	−10.8310	+	6.25329i	−0.480077	+	0.277172i	0.240372	+	0.970681i	$0.422731\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−16.0697	−	9.27782i	−0.709493	−	0.409626i
$514$		0			0
$515$			54.6574i			2.40849i
$516$		0			0
$517$	1.29680	+	2.24613i	0.0570332	+	0.0987845i
$518$		0			0
$519$	−2.13101			−0.0935410
$520$		0			0
$521$	−9.75115			−0.427206			−0.213603	−	0.976921i	$-0.568520\pi$
$521$	−9.75115			−0.427206			−0.213603	+	0.976921i	$0.568520\pi$
$522$		0			0
$523$	8.78204	+	15.2109i	0.384012	+	0.665128i	0.991632	−	0.129100i	$-0.0412089\pi$
$523$	8.78204	+	15.2109i	0.384012	+	0.665128i	−0.607620	+	0.794228i	$0.707876\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−0.525027	−	0.303125i	−0.0228706	−	0.0132043i
$528$		0			0
$529$	10.8368	−	18.7698i	0.471164	−	0.816080i
$530$		0			0
$531$	−16.1869	+	9.34553i	−0.702453	+	0.405562i
$532$		0			0
$533$	10.4752	−	20.8163i	0.453733	−	0.901656i
$534$		0			0
$535$	22.6601	−	13.0828i	0.979683	−	0.565620i
$536$		0			0
$537$	0.787286	−	1.36362i	0.0339739	−	0.0588446i
$538$		0			0
$539$		0			0
$540$		0			0
$541$			23.0805i			0.992306i	0.868235	+	0.496153i	$0.165255\pi$
$541$			23.0805i			0.992306i	−0.868235	+	0.496153i	$0.834745\pi$
$542$		0			0
$543$	−3.98850	−	6.90829i	−0.171163	−	0.296463i
$544$		0			0
$545$	−14.4150			−0.617472
$546$		0			0
$547$	−40.2760			−1.72208			−0.861039	−	0.508538i	$-0.830186\pi$
$547$	−40.2760			−1.72208			−0.861039	+	0.508538i	$0.830186\pi$
$548$		0			0
$549$	7.36050	+	12.7488i	0.314139	+	0.544104i
$550$		0			0
$551$			20.2584i			0.863039i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	1.98940	−	3.44574i	0.0844452	−	0.146263i
$556$		0			0
$557$	21.2364	−	12.2609i	0.899817	−	0.519510i	0.0226763	−	0.999743i	$-0.492781\pi$
$557$	21.2364	−	12.2609i	0.899817	−	0.519510i	0.877141	+	0.480233i	$0.159448\pi$
$558$		0			0
$559$	−0.0972365	−	1.69282i	−0.00411266	−	0.0715986i
$560$		0			0
$561$	1.54845	−	0.893999i	0.0653757	−	0.0377447i
$562$		0			0
$563$	−6.01842	+	10.4242i	−0.253646	+	0.439328i	−0.964527	−	0.263985i	$-0.914963\pi$
$563$	−6.01842	+	10.4242i	−0.253646	+	0.439328i	0.710881	+	0.703312i	$0.248296\pi$
$564$		0			0
$565$	10.9546	+	6.32464i	0.460864	+	0.266080i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	9.72129	+	16.8378i	0.407538	+	0.705876i	0.994613	−	0.103656i	$-0.0330542\pi$
$569$	9.72129	+	16.8378i	0.407538	+	0.705876i	−0.587076	+	0.809532i	$0.699721\pi$
$570$		0			0
$571$	35.4836			1.48494			0.742470	−	0.669879i	$-0.233654\pi$
$571$	35.4836			1.48494			0.742470	+	0.669879i	$0.233654\pi$
$572$		0			0
$573$	15.9673			0.667042
$574$		0			0
$575$	1.79743	+	3.11323i	0.0749578	+	0.129831i
$576$		0			0
$577$		−	5.57375i		−	0.232038i	−0.993247	−	0.116019i	$-0.962987\pi$
$577$		−	5.57375i		−	0.232038i	0.993247	−	0.116019i	$-0.0370134\pi$
$578$		0			0
$579$	3.65767	+	2.11176i	0.152007	+	0.0877616i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	18.9320	−	10.9304i	0.784082	−	0.452690i
$584$		0			0
$585$	26.8968	−	1.54497i	1.11205	−	0.0638766i
$586$		0			0
$587$	8.01798	−	4.62918i	0.330938	−	0.191067i	−0.325320	−	0.945604i	$-0.605472\pi$
$587$	8.01798	−	4.62918i	0.330938	−	0.191067i	0.656257	+	0.754537i	$0.272139\pi$
$588$		0			0
$589$	1.00836	−	1.74652i	0.0415486	−	0.0719643i
$590$		0			0
$591$	7.95320	+	4.59178i	0.327151	+	0.188881i
$592$		0			0
$593$		−	5.14329i		−	0.211209i	−0.994408	−	0.105605i	$-0.966322\pi$
$593$		−	5.14329i		−	0.211209i	0.994408	−	0.105605i	$-0.0336778\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−3.31874			−0.135827
$598$		0			0
$599$	−16.0525			−0.655886			−0.327943	−	0.944697i	$-0.606355\pi$
$599$	−16.0525			−0.655886			−0.327943	+	0.944697i	$0.606355\pi$
$600$		0			0
$601$	−2.32115	−	4.02035i	−0.0946816	−	0.163993i	0.814794	−	0.579750i	$-0.196850\pi$
$601$	−2.32115	−	4.02035i	−0.0946816	−	0.163993i	−0.909476	+	0.415757i	$0.863517\pi$
$602$		0			0
$603$			4.25325i			0.173206i
$604$		0			0
$605$	19.1331	+	11.0465i	0.777871	+	0.449104i
$606$		0			0
$607$	4.37417	−	7.57629i	0.177542	−	0.307512i	−0.763496	−	0.645813i	$-0.776519\pi$
$607$	4.37417	−	7.57629i	0.177542	−	0.307512i	0.941038	+	0.338301i	$0.109852\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	2.84805	+	4.33780i	0.115220	+	0.175489i
$612$		0			0
$613$	40.2324	−	23.2282i	1.62497	−	0.938179i	0.639411	−	0.768865i	$-0.279178\pi$
$613$	40.2324	−	23.2282i	1.62497	−	0.938179i	0.985562	−	0.169313i	$-0.0541549\pi$
$614$		0			0
$615$	−5.66212	+	9.80709i	−0.228319	+	0.395460i
$616$		0			0
$617$	−29.0761	−	16.7871i	−1.17056	−	0.675822i	−0.216747	−	0.976228i	$-0.569545\pi$
$617$	−29.0761	−	16.7871i	−1.17056	−	0.675822i	−0.953812	+	0.300406i	$0.902878\pi$
$618$		0			0
$619$			2.42868i			0.0976169i	0.998808	+	0.0488085i	$0.0155424\pi$
$619$			2.42868i			0.0976169i	−0.998808	+	0.0488085i	$0.984458\pi$
$620$		0			0
$621$	−1.99047	−	3.44759i	−0.0798747	−	0.138347i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−30.8640			−1.23456
$626$		0			0
$627$	2.97392	+	5.15098i	0.118767	+	0.205710i
$628$		0			0
$629$			3.66467i			0.146120i
$630$		0			0
$631$	13.2815	+	7.66809i	0.528729	+	0.305262i	0.740499	−	0.672058i	$-0.234589\pi$
$631$	13.2815	+	7.66809i	0.528729	+	0.305262i	−0.211770	+	0.977320i	$0.567923\pi$
$632$		0			0
$633$	2.74762	−	4.75902i	0.109208	−	0.189154i
$634$		0			0
$635$	42.8475	−	24.7380i	1.70035	−	0.981698i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	23.0672	−	13.3179i	0.912526	−	0.526847i
$640$		0			0
$641$	−16.5124	+	28.6003i	−0.652199	+	1.12964i	0.330389	+	0.943845i	$0.392820\pi$
$641$	−16.5124	+	28.6003i	−0.652199	+	1.12964i	−0.982588	+	0.185797i	$0.940513\pi$
$642$		0			0
$643$	14.5972	+	8.42772i	0.575659	+	0.332357i	0.759406	−	0.650617i	$-0.225490\pi$
$643$	14.5972	+	8.42772i	0.575659	+	0.332357i	−0.183747	+	0.982973i	$0.558823\pi$
$644$		0			0
$645$			0.823977i			0.0324441i
$646$		0			0
$647$	22.7037	+	39.3240i	0.892576	+	1.54599i	0.836776	+	0.547545i	$0.184438\pi$
$647$	22.7037	+	39.3240i	0.892576	+	1.54599i	0.0557999	+	0.998442i	$0.482229\pi$
$648$		0			0
$649$	12.8462			0.504259
$650$		0			0
$651$		0			0
$652$		0			0
$653$	20.1975	+	34.9831i	0.790389	+	1.36899i	0.925726	+	0.378194i	$0.123455\pi$
$653$	20.1975	+	34.9831i	0.790389	+	1.36899i	−0.135338	+	0.990800i	$0.543212\pi$
$654$		0			0
$655$		−	14.9897i		−	0.585696i
$656$		0			0
$657$	12.7621	+	7.36822i	0.497898	+	0.287461i
$658$		0			0
$659$	18.2656	−	31.6369i	0.711526	−	1.23240i	−0.252758	−	0.967530i	$-0.581338\pi$
$659$	18.2656	−	31.6369i	0.711526	−	1.23240i	0.964284	−	0.264870i	$-0.0853292\pi$
$660$		0			0
$661$	−17.4301	+	10.0633i	−0.677951	+	0.391415i	−0.799083	−	0.601221i	$-0.794681\pi$
$661$	−17.4301	+	10.0633i	−0.677951	+	0.391415i	0.121131	+	0.992636i	$0.461348\pi$
$662$		0			0
$663$	2.99043	−	1.96341i	0.116139	−	0.0762524i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−2.17313	+	3.76397i	−0.0841439	+	0.145741i
$668$		0			0
$669$	−7.90269	−	4.56262i	−0.305536	−	0.176401i
$670$		0			0
$671$		−	10.1176i		−	0.390587i
$672$		0			0
$673$	−7.89716	−	13.6783i	−0.304413	−	0.527259i	0.672717	−	0.739900i	$-0.265127\pi$
$673$	−7.89716	−	13.6783i	−0.304413	−	0.527259i	−0.977131	+	0.212641i	$0.931794\pi$
$674$		0			0
$675$	−10.7888			−0.415261
$676$		0			0
$677$	25.7439			0.989419			0.494710	−	0.869058i	$-0.335274\pi$
$677$	25.7439			0.989419			0.494710	+	0.869058i	$0.335274\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		−	13.9147i		−	0.533211i
$682$		0			0
$683$	5.63910	+	3.25573i	0.215774	+	0.124577i	0.603992	−	0.796990i	$-0.293576\pi$
$683$	5.63910	+	3.25573i	0.215774	+	0.124577i	−0.388218	+	0.921568i	$0.626909\pi$
$684$		0			0
$685$	−25.9639	+	44.9708i	−0.992029	+	1.71824i
$686$		0			0
$687$	8.77035	−	5.06357i	0.334610	−	0.193187i
$688$		0			0
$689$	36.5621	−	24.0054i	1.39290	−	0.914532i
$690$		0			0
$691$	−0.965340	+	0.557340i	−0.0367233	+	0.0212022i	−0.518249	−	0.855230i	$-0.673416\pi$
$691$	−0.965340	+	0.557340i	−0.0367233	+	0.0212022i	0.481526	+	0.876432i	$0.340083\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−49.5739	−	28.6215i	−1.88044	−	1.08568i
$696$		0			0
$697$		−	10.4302i		−	0.395072i
$698$		0			0
$699$	−4.38195	−	7.58977i	−0.165741	−	0.287071i
$700$		0			0
$701$	29.3444			1.10832			0.554161	−	0.832410i	$-0.313039\pi$
$701$	29.3444			1.10832			0.554161	+	0.832410i	$0.313039\pi$
$702$		0			0
$703$	−12.1907			−0.459780
$704$		0			0
$705$	−1.26084	−	2.18384i	−0.0474860	−	0.0822482i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−34.9489	−	20.1778i	−1.31253	−	0.757792i	−0.330018	−	0.943975i	$-0.607055\pi$
$709$	−34.9489	−	20.1778i	−1.31253	−	0.757792i	−0.982515	+	0.186183i	$0.940388\pi$
$710$		0			0
$711$	18.8422	−	32.6356i	0.706637	−	1.22393i
$712$		0			0
$713$	0.374700	−	0.216333i	0.0140326	−	0.00810174i
$714$		0			0
$715$	−16.5403	−	8.32342i	−0.618571	−	0.311278i
$716$		0			0
$717$	13.4034	−	7.73844i	0.500558	−	0.288997i
$718$		0			0
$719$	15.0163	−	26.0090i	0.560013	−	0.969972i	−0.437481	−	0.899228i	$-0.644129\pi$
$719$	15.0163	−	26.0090i	0.560013	−	0.969972i	0.997494	−	0.0707441i	$-0.0225374\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$			8.57467i			0.318895i
$724$		0			0
$725$	5.88944	+	10.2008i	0.218728	+	0.378848i
$726$		0			0
$727$	30.7097			1.13896			0.569479	−	0.822006i	$-0.307145\pi$
$727$	30.7097			1.13896			0.569479	+	0.822006i	$0.307145\pi$
$728$		0			0
$729$	−8.67707			−0.321373
$730$		0			0
$731$	−0.379462	−	0.657248i	−0.0140349	−	0.0243092i
$732$		0			0
$733$			11.6482i			0.430238i	0.976588	+	0.215119i	$0.0690139\pi$
$733$			11.6482i			0.430238i	−0.976588	+	0.215119i	$0.930986\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.46161	−	2.53159i	0.0538393	−	0.0932523i
$738$		0			0
$739$	−11.8399	+	6.83578i	−0.435539	+	0.251458i	−0.701703	−	0.712469i	$-0.747577\pi$
$739$	−11.8399	+	6.83578i	−0.435539	+	0.251458i	0.266165	+	0.963928i	$0.414243\pi$
$740$		0			0
$741$	6.53135	+	9.94777i	0.239935	+	0.365440i
$742$		0			0
$743$	3.73344	−	2.15550i	0.136966	−	0.0790776i	−0.429951	−	0.902852i	$-0.641469\pi$
$743$	3.73344	−	2.15550i	0.136966	−	0.0790776i	0.566917	+	0.823775i	$0.308136\pi$
$744$		0			0
$745$	−21.2358	+	36.7816i	−0.778021	+	1.34757i
$746$		0			0
$747$	−6.66421	−	3.84758i	−0.243831	−	0.140776i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−21.3882	−	37.0454i	−0.780466	−	1.35181i	−0.931670	−	0.363305i	$-0.881648\pi$
$751$	−21.3882	−	37.0454i	−0.780466	−	1.35181i	0.151204	−	0.988503i	$-0.451685\pi$
$752$		0			0
$753$	11.1717			0.407119
$754$		0			0
$755$	19.8271			0.721583
$756$		0			0
$757$	−8.90718	−	15.4277i	−0.323737	−	0.560729i	0.657519	−	0.753438i	$-0.271606\pi$
$757$	−8.90718	−	15.4277i	−0.323737	−	0.560729i	−0.981256	+	0.192709i	$0.938273\pi$
$758$		0			0
$759$			1.27605i			0.0463178i
$760$		0			0
$761$	−18.5610	−	10.7162i	−0.672837	−	0.388463i	0.124314	−	0.992243i	$-0.460327\pi$
$761$	−18.5610	−	10.7162i	−0.672837	−	0.388463i	−0.797151	+	0.603780i	$0.793660\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	10.4429	−	6.02919i	0.377563	−	0.217986i
$766$		0			0
$767$	25.6601	−	1.47393i	0.926533	−	0.0532206i
$768$		0			0
$769$	−9.01602	+	5.20540i	−0.325126	+	0.187712i	−0.653675	−	0.756775i	$-0.726774\pi$
$769$	−9.01602	+	5.20540i	−0.325126	+	0.187712i	0.328549	+	0.944487i	$0.393440\pi$
$770$		0			0
$771$	1.55458	−	2.69262i	0.0559869	−	0.0969722i
$772$		0			0
$773$	−30.4896	−	17.6032i	−1.09663	−	0.633142i	−0.161300	−	0.986905i	$-0.551569\pi$
$773$	−30.4896	−	17.6032i	−1.09663	−	0.633142i	−0.935335	+	0.353763i	$0.884902\pi$
$774$		0			0
$775$		−	1.17258i		−	0.0421202i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	34.6965			1.24313
$780$		0			0
$781$	−18.3066			−0.655061
$782$		0			0
$783$	−6.52196	−	11.2964i	−0.233076	−	0.403699i
$784$		0			0
$785$			17.7076i			0.632011i
$786$		0			0
$787$	−35.5200	−	20.5075i	−1.26615	−	0.731014i	−0.291895	−	0.956450i	$-0.594286\pi$
$787$	−35.5200	−	20.5075i	−1.26615	−	0.731014i	−0.974258	+	0.225437i	$0.927619\pi$
$788$		0			0
$789$	1.60399	−	2.77820i	0.0571037	−	0.0989065i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−1.16086	−	20.2098i	−0.0412234	−	0.717671i
$794$		0			0
$795$	−18.4070	+	10.6273i	−0.652828	+	0.376910i
$796$		0			0
$797$	12.1708	−	21.0805i	0.431113	−	0.746710i	−0.565856	−	0.824504i	$-0.691454\pi$
$797$	12.1708	−	21.0805i	0.431113	−	0.746710i	0.996969	+	0.0777940i	$0.0247876\pi$
$798$		0			0
$799$	2.01143	+	1.16130i	0.0711592	+	0.0410838i
$800$		0			0
$801$			33.8347i			1.19549i
$802$		0			0
$803$	−5.06412	−	8.77132i	−0.178709	−	0.309533i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	2.58562			0.0910180
$808$		0			0
$809$	−6.50727	−	11.2709i	−0.228784	−	0.396265i	0.728664	−	0.684871i	$-0.240141\pi$
$809$	−6.50727	−	11.2709i	−0.228784	−	0.396265i	−0.957448	+	0.288606i	$0.906808\pi$
$810$		0			0
$811$		−	14.5520i		−	0.510988i	−0.966811	−	0.255494i	$-0.917762\pi$
$811$		−	14.5520i		−	0.510988i	0.966811	−	0.255494i	$-0.0822382\pi$
$812$		0			0
$813$	−5.13294	−	2.96351i	−0.180020	−	0.103935i
$814$		0			0
$815$	13.0785	−	22.6526i	0.458120	−	0.793487i
$816$		0			0
$817$	2.18636	−	1.26230i	0.0764911	−	0.0441622i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−8.27293	+	4.77638i	−0.288727	+	0.166697i	−0.637368	−	0.770560i	$-0.719977\pi$
$821$	−8.27293	+	4.77638i	−0.288727	+	0.166697i	0.348641	+	0.937257i	$0.386643\pi$
$822$		0			0
$823$	5.31638	−	9.20824i	0.185317	−	0.320979i	−0.758366	−	0.651829i	$-0.774002\pi$
$823$	5.31638	−	9.20824i	0.185317	−	0.320979i	0.943683	+	0.330850i	$0.107335\pi$
$824$		0			0
$825$	2.99494	+	1.72913i	0.104270	+	0.0602005i
$826$		0			0
$827$		−	44.7329i		−	1.55552i	−0.628564	−	0.777758i	$-0.716357\pi$
$827$		−	44.7329i		−	1.55552i	0.628564	−	0.777758i	$-0.283643\pi$
$828$		0			0
$829$	11.1854	+	19.3737i	0.388484	+	0.672875i	0.992246	−	0.124290i	$-0.0396654\pi$
$829$	11.1854	+	19.3737i	0.388484	+	0.672875i	−0.603761	+	0.797165i	$0.706332\pi$
$830$		0			0
$831$	3.04725			0.105708
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−1.33333	−	2.30939i	−0.0461417	−	0.0799197i
$836$		0			0
$837$			1.29851i			0.0448831i
$838$		0			0
$839$	4.05352	+	2.34030i	0.139943	+	0.0807961i	0.568337	−	0.822796i	$-0.307587\pi$
$839$	4.05352	+	2.34030i	0.139943	+	0.0807961i	−0.428394	+	0.903592i	$0.640920\pi$
$840$		0			0
$841$	7.37954	−	12.7817i	0.254467	−	0.440750i
$842$		0			0
$843$	5.28893	−	3.05356i	0.182160	−	0.105170i
$844$		0			0
$845$	−33.9939	−	14.7281i	−1.16942	−	0.506661i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−7.92633	+	13.7288i	−0.272031	+	0.471171i
$850$		0			0
$851$	−2.26500	−	1.30770i	−0.0776431	−	0.0448273i
$852$		0			0
$853$			10.1857i			0.348753i	0.984679	+	0.174376i	$0.0557910\pi$
$853$			10.1857i			0.348753i	−0.984679	+	0.174376i	$0.944209\pi$
$854$		0			0
$855$	20.0563	+	34.7386i	0.685913	+	1.18804i
$856$		0			0
$857$	48.8600			1.66903			0.834513	−	0.550988i	$-0.185749\pi$
$857$	48.8600			1.66903			0.834513	+	0.550988i	$0.185749\pi$
$858$		0			0
$859$	−4.96639			−0.169451			−0.0847256	−	0.996404i	$-0.527001\pi$
$859$	−4.96639			−0.169451			−0.0847256	+	0.996404i	$0.527001\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	29.6673i		−	1.00989i	−0.863153	−	0.504943i	$-0.831514\pi$
$863$		−	29.6673i		−	1.00989i	0.863153	−	0.504943i	$-0.168486\pi$
$864$		0			0
$865$	8.55422	+	4.93878i	0.290852	+	0.167924i
$866$		0			0
$867$	−4.42539	+	7.66500i	−0.150294	+	0.260317i
$868$		0			0
$869$	−22.4302	+	12.9501i	−0.760893	+	0.439302i
$870$		0			0
$871$	2.62908	−	5.22450i	0.0890830	−	0.177025i
$872$		0			0
$873$	−27.5137	+	15.8850i	−0.931197	+	0.537627i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−6.70755	−	3.87261i	−0.226498	−	0.130769i	0.382458	−	0.923973i	$-0.375078\pi$
$877$	−6.70755	−	3.87261i	−0.226498	−	0.130769i	−0.608955	+	0.793204i	$0.708411\pi$
$878$		0			0
$879$			6.26431i			0.211290i
$880$		0			0
$881$	−26.5762	−	46.0313i	−0.895375	−	1.55083i	−0.833340	−	0.552761i	$-0.813574\pi$
$881$	−26.5762	−	46.0313i	−0.895375	−	1.55083i	−0.0620348	−	0.998074i	$-0.519759\pi$
$882$		0			0
$883$	−19.7373			−0.664214			−0.332107	−	0.943242i	$-0.607760\pi$
$883$	−19.7373			−0.664214			−0.332107	+	0.943242i	$0.607760\pi$
$884$		0			0
$885$	−12.4900			−0.419847
$886$		0			0
$887$	−20.4840	−	35.4793i	−0.687785	−	1.19128i	−0.972553	−	0.232682i	$-0.925250\pi$
$887$	−20.4840	−	35.4793i	−0.687785	−	1.19128i	0.284768	−	0.958596i	$-0.408083\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	8.95944	+	5.17274i	0.300153	+	0.173293i
$892$		0			0
$893$	−3.86310	+	6.69109i	−0.129274	+	0.223909i
$894$		0			0
$895$	−6.32059	+	3.64920i	−0.211274	+	0.121979i
$896$		0			0
$897$	0.146410	+	2.54889i	0.00488847	+	0.0851049i
$898$		0			0
$899$	1.22774	−	0.708836i	0.0409474	−	0.0236410i
$900$		0			0
$901$	9.78826	−	16.9538i	0.326094	−	0.564812i
$902$		0			0
$903$		0			0
$904$		0			0
$905$			36.9747i			1.22908i
$906$		0			0
$907$	−2.35224	−	4.07421i	−0.0781050	−	0.135282i	0.824327	−	0.566113i	$-0.191554\pi$
$907$	−2.35224	−	4.07421i	−0.0781050	−	0.135282i	−0.902432	+	0.430832i	$0.858220\pi$
$908$		0			0
$909$	−10.6517			−0.353295
$910$		0			0
$911$	7.33499			0.243019			0.121509	−	0.992590i	$-0.461227\pi$
$911$	7.33499			0.243019			0.121509	+	0.992590i	$0.461227\pi$
$912$		0			0
$913$	2.64442	+	4.58026i	0.0875174	+	0.151585i
$914$		0			0
$915$			9.83709i			0.325204i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−3.13488	+	5.42976i	−0.103410	+	0.179111i	−0.913087	−	0.407764i	$-0.866309\pi$
$919$	−3.13488	+	5.42976i	−0.103410	+	0.179111i	0.809677	+	0.586875i	$0.199642\pi$
$920$		0			0
$921$	16.1075	−	9.29965i	0.530759	−	0.306434i
$922$		0			0
$923$	−36.5670	+	2.10043i	−1.20362	+	0.0691365i
$924$		0			0
$925$	−6.13841	+	3.54401i	−0.201830	+	0.116526i
$926$		0			0
$927$	−25.1442	+	43.5511i	−0.825845	+	1.43040i
$928$		0			0
$929$	39.7459	+	22.9473i	1.30402	+	0.752877i	0.981091	−	0.193546i	$-0.0619988\pi$
$929$	39.7459	+	22.9473i	1.30402	+	0.752877i	0.322930	+	0.946423i	$0.395332\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	6.36951	+	11.0323i	0.208528	+	0.361182i
$934$		0			0
$935$	−8.28765			−0.271035
$936$		0			0
$937$	19.9322			0.651155			0.325578	−	0.945515i	$-0.394441\pi$
$937$	19.9322			0.651155			0.325578	+	0.945515i	$0.394441\pi$
$938$		0			0
$939$	3.49305	+	6.05014i	0.113991	+	0.197439i
$940$		0			0
$941$		−	49.0230i		−	1.59810i	−0.601262	−	0.799052i	$-0.705335\pi$
$941$		−	49.0230i		−	1.59810i	0.601262	−	0.799052i	$-0.294665\pi$
$942$		0			0
$943$	6.44652	+	3.72190i	0.209928	+	0.121202i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	31.4093	−	18.1342i	1.02067	−	0.589282i	0.106369	−	0.994327i	$-0.466078\pi$
$947$	31.4093	−	18.1342i	1.02067	−	0.589282i	0.914297	+	0.405045i	$0.132744\pi$
$948$		0			0
$949$	−11.1219	−	16.9395i	−0.361031	−	0.549879i
$950$		0			0
$951$	−8.37495	+	4.83528i	−0.271576	+	0.156795i
$952$		0			0
$953$	26.4115	−	45.7461i	0.855554	−	1.48186i	−0.0205766	−	0.999788i	$-0.506550\pi$
$953$	26.4115	−	45.7461i	0.855554	−	1.48186i	0.876130	−	0.482074i	$-0.160116\pi$
$954$		0			0
$955$	−64.0952	−	37.0054i	−2.07407	−	1.19747i
$956$		0			0
$957$			4.18111i			0.135156i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	30.8589			0.995447
$962$		0			0
$963$	24.0742			0.775779
$964$		0			0
$965$	−9.78832	−	16.9539i	−0.315097	−	0.545764i
$966$		0			0
$967$			21.0424i			0.676679i	0.941024	+	0.338340i	$0.109865\pi$
$967$			21.0424i			0.676679i	−0.941024	+	0.338340i	$0.890135\pi$
$968$		0			0
$969$	4.61276	+	2.66318i	0.148183	+	0.0855536i
$970$		0			0
$971$	−22.3678	+	38.7421i	−0.717816	+	1.24329i	0.244048	+	0.969763i	$0.421525\pi$
$971$	−22.3678	+	38.7421i	−0.717816	+	1.24329i	−0.961864	+	0.273530i	$0.911809\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	6.18072	+	3.11027i	0.197941	+	0.0996083i
$976$		0			0
$977$	−28.6223	+	16.5251i	−0.915709	+	0.528685i	−0.882264	−	0.470756i	$-0.843981\pi$
$977$	−28.6223	+	16.5251i	−0.915709	+	0.528685i	−0.0334455	+	0.999441i	$0.510648\pi$
$978$		0			0
$979$	11.6272	−	20.1389i	0.371607	−	0.643642i
$980$		0			0
$981$	−11.4859	−	6.63140i	−0.366717	−	0.211724i
$982$		0			0
$983$			24.8221i			0.791703i	0.918315	+	0.395852i	$0.129551\pi$
$983$			24.8221i			0.791703i	−0.918315	+	0.395852i	$0.870449\pi$
$984$		0			0
$985$	−21.2836	−	36.8643i	−0.678153	−	1.17459i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	0.541627			0.0172227
$990$		0			0
$991$	3.37733	+	5.84970i	0.107284	+	0.185822i	0.914669	−	0.404203i	$-0.132451\pi$
$991$	3.37733	+	5.84970i	0.107284	+	0.185822i	−0.807385	+	0.590025i	$0.799118\pi$
$992$		0			0
$993$		−	21.3711i		−	0.678191i
$994$		0			0
$995$	13.3220	+	7.69145i	0.422335	+	0.243835i
$996$		0			0
$997$	−11.5038	+	19.9252i	−0.364330	+	0.631037i	−0.988668	−	0.150116i	$-0.952035\pi$
$997$	−11.5038	+	19.9252i	−0.364330	+	0.631037i	0.624339	+	0.781154i	$0.285368\pi$
$998$		0			0
$999$	6.79767	−	3.92464i	0.215069	−	0.124170i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2548.2.u.f.1765.7	yes	24
7.2	even	3		2548.2.bq.g.361.6		24
7.3	odd	6		2548.2.bb.g.569.6		24
7.4	even	3		2548.2.bb.g.569.7		24
7.5	odd	6		2548.2.bq.g.361.7		24
7.6	odd	2	inner	2548.2.u.f.1765.6	yes	24
13.4	even	6	inner	2548.2.u.f.589.7	yes	24
91.4	even	6		2548.2.bq.g.1941.6		24
91.17	odd	6		2548.2.bq.g.1941.7		24
91.30	even	6		2548.2.bb.g.1733.7		24
91.69	odd	6	inner	2548.2.u.f.589.6	✓	24
91.82	odd	6		2548.2.bb.g.1733.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2548.2.u.f.589.6	✓	24	91.69	odd	6	inner
2548.2.u.f.589.7	yes	24	13.4	even	6	inner
2548.2.u.f.1765.6	yes	24	7.6	odd	2	inner
2548.2.u.f.1765.7	yes	24	1.1	even	1	trivial
2548.2.bb.g.569.6		24	7.3	odd	6
2548.2.bb.g.569.7		24	7.4	even	3
2548.2.bb.g.1733.6		24	91.82	odd	6
2548.2.bb.g.1733.7		24	91.30	even	6
2548.2.bq.g.361.6		24	7.2	even	3
2548.2.bq.g.361.7		24	7.5	odd	6
2548.2.bq.g.1941.6		24	91.4	even	6
2548.2.bq.g.1941.7		24	91.17	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2548 = 2^{2} \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2548.u (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.307410 + 0.532450i) q^{3} -2.84979i q^{5} +(1.31100 - 2.27072i) q^{9} +(-1.56065 + 0.901040i) q^{11} +(-3.01398 + 1.97887i) q^{13} +(1.51737 - 0.876054i) q^{15} +(-0.806891 + 1.39758i) q^{17} +(-4.64909 - 2.68415i) q^{19} +(-0.575859 - 0.997417i) q^{23} -3.12129 q^{25} +3.45652 q^{27} +(-1.88686 - 3.26813i) q^{29} +0.375670i q^{31} +(-0.959517 - 0.553978i) q^{33} +(1.96662 - 1.13543i) q^{37} +(-1.98018 - 0.996468i) q^{39} +(-5.59731 + 3.23161i) q^{41} +(-0.235139 + 0.407272i) q^{43} +(-6.47106 - 3.73607i) q^{45} -1.43923i q^{47} -0.992186 q^{51} -12.1308 q^{53} +(2.56777 + 4.44751i) q^{55} -3.30054i q^{57} +(-6.17352 - 3.56428i) q^{59} +(-2.80721 + 4.86224i) q^{61} +(5.63937 + 8.58920i) q^{65} +(-1.40482 + 0.811071i) q^{67} +(0.354050 - 0.613233i) q^{69} +(8.79759 + 5.07929i) q^{71} +5.62031i q^{73} +(-0.959517 - 1.66193i) q^{75} +14.3724 q^{79} +(-2.87043 - 4.97172i) q^{81} -2.93485i q^{83} +(3.98279 + 2.29947i) q^{85} +(1.16008 - 2.00931i) q^{87} +(-11.1754 + 6.45210i) q^{89} +(-0.200026 + 0.115485i) q^{93} +(-7.64927 + 13.2489i) q^{95} +(-10.4934 - 6.05837i) q^{97} +4.72505i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{9} - 12 q^{15} + 16 q^{23} + 24 q^{29} + 8 q^{39} + 4 q^{43} + 80 q^{51} - 48 q^{53} + 8 q^{65} - 24 q^{71} - 48 q^{79} + 4 q^{81} + 12 q^{85} + 48 q^{93} - 20 q^{95}+O(q^{100}) \) 24 * q - 8 * q^9 - 12 * q^15 + 16 * q^23 + 24 * q^29 + 8 * q^39 + 4 * q^43 + 80 * q^51 - 48 * q^53 + 8 * q^65 - 24 * q^71 - 48 * q^79 + 4 * q^81 + 12 * q^85 + 48 * q^93 - 20 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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