LMFDB - Embedded newform 1100.2.cb.d.49.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1100,2,Mod(49,1100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1100, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 4]))

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

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

chi := DirichletCharacter("1100.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1100 = 2^{2} \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1100.cb (of order $10$, degree $4$, not 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:	$8.78354422234$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			49.8
Character	$\chi$	$=$	1100.49
Dual form			1100.2.cb.d.449.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.76353 - 2.42729i) q^{3} +(-0.992679 - 1.36631i) q^{7} +(-1.85465 - 5.70802i) q^{9} +(2.77267 - 1.81998i) q^{11} +(3.52887 - 1.14660i) q^{13} +(3.68071 + 1.19594i) q^{17} +(-5.21062 - 3.78574i) q^{19} -5.06704 q^{21} +7.43878i q^{23} +(-8.56540 - 2.78307i) q^{27} +(-2.55959 + 1.85965i) q^{29} +(0.787699 + 2.42429i) q^{31} +(0.472068 - 9.93965i) q^{33} +(-3.84954 - 5.29843i) q^{37} +(3.44014 - 10.5877i) q^{39} +(-6.93840 - 5.04104i) q^{41} +3.49875i q^{43} +(-2.49933 + 3.44003i) q^{47} +(1.28174 - 3.94479i) q^{49} +(9.39392 - 6.82509i) q^{51} +(9.24750 - 3.00470i) q^{53} +(-18.3782 + 5.97143i) q^{57} +(-2.33853 + 1.69904i) q^{59} +(1.93043 - 5.94126i) q^{61} +(-5.95783 + 8.20025i) q^{63} +10.5387i q^{67} +(18.0561 + 13.1185i) q^{69} +(2.85383 - 8.78318i) q^{71} +(-2.15062 - 2.96007i) q^{73} +(-5.23901 - 1.98166i) q^{77} +(5.23846 + 16.1223i) q^{79} +(-7.29404 + 5.29943i) q^{81} +(-11.4422 - 3.71779i) q^{83} +9.49240i q^{87} +15.5881 q^{89} +(-5.06965 - 3.68331i) q^{91} +(7.27358 + 2.36333i) q^{93} +(6.38135 - 2.07343i) q^{97} +(-15.5308 - 12.4510i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 10 q^{11} - 26 q^{19} - 12 q^{21} + 14 q^{29} + 4 q^{31} + 34 q^{39} - 30 q^{41} + 48 q^{49} + 26 q^{51} - 12 q^{59} + 48 q^{61} + 106 q^{69} + 72 q^{71} + 90 q^{79} + 34 q^{81} - 36 q^{89} + 76 q^{91}+ \cdots - 80 q^{99}+O(q^{100}) $ 32 * q - 10 * q^11 - 26 * q^19 - 12 * q^21 + 14 * q^29 + 4 * q^31 + 34 * q^39 - 30 * q^41 + 48 * q^49 + 26 * q^51 - 12 * q^59 + 48 * q^61 + 106 * q^69 + 72 * q^71 + 90 * q^79 + 34 * q^81 - 36 * q^89 + 76 * q^91 - 80 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1100\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$551$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.76353	−	2.42729i	1.01817	−	1.40140i	0.104698	−	0.994504i	$-0.466612\pi$
$3$	1.76353	−	2.42729i	1.01817	−	1.40140i	0.913476	−	0.406892i	$-0.133388\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.992679	−	1.36631i	−0.375197	−	0.516415i	0.579107	−	0.815252i	$-0.303401\pi$
$7$	−0.992679	−	1.36631i	−0.375197	−	0.516415i	−0.954304	+	0.298837i	$0.903401\pi$
$8$		0			0
$9$	−1.85465	−	5.70802i	−0.618216	−	1.90267i
$10$		0			0
$11$	2.77267	−	1.81998i	0.835991	−	0.548744i
$11$	2.77267	−	1.81998i	0.835991	−	0.548744i
$12$		0			0
$13$	3.52887	−	1.14660i	0.978733	−	0.318010i	0.224397	−	0.974498i	$-0.427959\pi$
$13$	3.52887	−	1.14660i	0.978733	−	0.318010i	0.754336	+	0.656488i	$0.227959\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.68071	+	1.19594i	0.892704	+	0.290057i	0.719222	−	0.694780i	$-0.244498\pi$
$17$	3.68071	+	1.19594i	0.892704	+	0.290057i	0.173481	+	0.984837i	$0.444498\pi$
$18$		0			0
$19$	−5.21062	−	3.78574i	−1.19540	−	0.868508i	−0.201575	−	0.979473i	$-0.564606\pi$
$19$	−5.21062	−	3.78574i	−1.19540	−	0.868508i	−0.993824	+	0.110965i	$0.964606\pi$
$20$		0			0
$21$	−5.06704			−1.10572
$22$		0			0
$23$			7.43878i			1.55109i	0.631291	+	0.775546i	$0.282525\pi$
$23$			7.43878i			1.55109i	−0.631291	+	0.775546i	$0.717475\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−8.56540	−	2.78307i	−1.64841	−	0.535601i
$28$		0			0
$29$	−2.55959	+	1.85965i	−0.475303	+	0.345328i	−0.799505	−	0.600660i	$-0.794905\pi$
$29$	−2.55959	+	1.85965i	−0.475303	+	0.345328i	0.324201	+	0.945988i	$0.394905\pi$
$30$		0			0
$31$	0.787699	+	2.42429i	0.141475	+	0.435415i	0.996541	−	0.0831043i	$-0.0264835\pi$
$31$	0.787699	+	2.42429i	0.141475	+	0.435415i	−0.855066	+	0.518519i	$0.826483\pi$
$32$		0			0
$33$	0.472068	−	9.93965i	0.0821764	−	1.73027i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−3.84954	−	5.29843i	−0.632860	−	0.871057i	0.365350	−	0.930870i	$-0.380949\pi$
$37$	−3.84954	−	5.29843i	−0.632860	−	0.871057i	−0.998210	+	0.0598135i	$0.980949\pi$
$38$		0			0
$39$	3.44014	−	10.5877i	0.550863	−	1.69538i
$40$		0			0
$41$	−6.93840	−	5.04104i	−1.08360	−	0.787279i	−0.105290	−	0.994442i	$-0.533577\pi$
$41$	−6.93840	−	5.04104i	−1.08360	−	0.787279i	−0.978306	+	0.207163i	$0.933577\pi$
$42$		0			0
$43$			3.49875i			0.533554i	0.963758	+	0.266777i	$0.0859587\pi$
$43$			3.49875i			0.533554i	−0.963758	+	0.266777i	$0.914041\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.49933	+	3.44003i	−0.364565	+	0.501781i	−0.951414	−	0.307916i	$-0.900368\pi$
$47$	−2.49933	+	3.44003i	−0.364565	+	0.501781i	0.586849	+	0.809697i	$0.300368\pi$
$48$		0			0
$49$	1.28174	−	3.94479i	0.183106	−	0.563541i
$50$		0			0
$51$	9.39392	−	6.82509i	1.31541	−	0.955703i
$52$		0			0
$53$	9.24750	−	3.00470i	1.27024	−	0.412727i	0.405109	−	0.914269i	$-0.367234\pi$
$53$	9.24750	−	3.00470i	1.27024	−	0.412727i	0.865133	+	0.501542i	$0.167234\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−18.3782	+	5.97143i	−2.43425	+	0.790935i
$58$		0			0
$59$	−2.33853	+	1.69904i	−0.304450	+	0.221196i	−0.729512	−	0.683968i	$-0.760253\pi$
$59$	−2.33853	+	1.69904i	−0.304450	+	0.221196i	0.425061	+	0.905165i	$0.360253\pi$
$60$		0			0
$61$	1.93043	−	5.94126i	0.247167	−	0.760700i	−0.748106	−	0.663579i	$-0.769037\pi$
$61$	1.93043	−	5.94126i	0.247167	−	0.760700i	0.995273	−	0.0971212i	$-0.0309634\pi$
$62$		0			0
$63$	−5.95783	+	8.20025i	−0.750616	+	1.03313i
$64$		0			0
$65$		0			0
$66$		0			0
$67$			10.5387i			1.28750i	0.765235	+	0.643751i	$0.222623\pi$
$67$			10.5387i			1.28750i	−0.765235	+	0.643751i	$0.777377\pi$
$68$		0			0
$69$	18.0561	+	13.1185i	2.17369	+	1.57928i
$70$		0			0
$71$	2.85383	−	8.78318i	0.338687	−	1.04237i	−0.626190	−	0.779670i	$-0.715387\pi$
$71$	2.85383	−	8.78318i	0.338687	−	1.04237i	0.964877	−	0.262701i	$-0.0846133\pi$
$72$		0			0
$73$	−2.15062	−	2.96007i	−0.251711	−	0.346450i	0.664399	−	0.747378i	$-0.268688\pi$
$73$	−2.15062	−	2.96007i	−0.251711	−	0.346450i	−0.916110	+	0.400928i	$0.868688\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−5.23901	−	1.98166i	−0.597041	−	0.225831i
$78$		0			0
$79$	5.23846	+	16.1223i	0.589373	+	1.81390i	0.580949	+	0.813940i	$0.302682\pi$
$79$	5.23846	+	16.1223i	0.589373	+	1.81390i	0.00842422	+	0.999965i	$0.497318\pi$
$80$		0			0
$81$	−7.29404	+	5.29943i	−0.810449	+	0.588825i
$82$		0			0
$83$	−11.4422	−	3.71779i	−1.25594	−	0.408080i	−0.395896	−	0.918296i	$-0.629566\pi$
$83$	−11.4422	−	3.71779i	−1.25594	−	0.408080i	−0.860047	+	0.510215i	$0.829566\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$			9.49240i			1.01769i
$88$		0			0
$89$	15.5881			1.65233			0.826166	−	0.563426i	$-0.190517\pi$
$89$	15.5881			1.65233			0.826166	+	0.563426i	$0.190517\pi$
$90$		0			0
$91$	−5.06965	−	3.68331i	−0.531443	−	0.386116i
$92$		0			0
$93$	7.27358	+	2.36333i	0.754235	+	0.245066i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	6.38135	−	2.07343i	0.647928	−	0.210525i	0.0334279	−	0.999441i	$-0.489358\pi$
$97$	6.38135	−	2.07343i	0.647928	−	0.210525i	0.614500	+	0.788916i	$0.289358\pi$
$98$		0			0
$99$	−15.5308	−	12.4510i	−1.56090	−	1.25138i
$100$		0			0
$101$	1.51211	+	4.65380i	0.150461	+	0.463071i	0.997673	−	0.0681843i	$-0.0217206\pi$
$101$	1.51211	+	4.65380i	0.150461	+	0.463071i	−0.847212	+	0.531255i	$0.821721\pi$
$102$		0			0
$103$	9.80269	+	13.4922i	0.965888	+	1.32943i	0.944097	+	0.329668i	$0.106937\pi$
$103$	9.80269	+	13.4922i	0.965888	+	1.32943i	0.0217908	+	0.999763i	$0.493063\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.39979	+	1.92664i	−0.135323	+	0.186256i	−0.871300	−	0.490750i	$-0.836723\pi$
$107$	−1.39979	+	1.92664i	−0.135323	+	0.186256i	0.735978	+	0.677006i	$0.236723\pi$
$108$		0			0
$109$	−15.3246			−1.46783			−0.733916	−	0.679240i	$-0.762309\pi$
$109$	−15.3246			−1.46783			−0.733916	+	0.679240i	$0.762309\pi$
$110$		0			0
$111$	−19.6496			−1.86506
$112$		0			0
$113$	−1.02997	+	1.41763i	−0.0968910	+	0.133359i	−0.854710	−	0.519106i	$-0.826265\pi$
$113$	−1.02997	+	1.41763i	−0.0968910	+	0.133359i	0.757819	+	0.652465i	$0.226265\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−13.0896	−	18.0163i	−1.21014	−	1.66561i
$118$		0			0
$119$	−2.01975	−	6.21616i	−0.185150	−	0.569834i
$120$		0			0
$121$	4.37537	−	10.0924i	0.397761	−	0.917489i
$122$		0			0
$123$	−24.4721	+	7.95148i	−2.20658	+	0.716961i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	8.89597	+	2.89048i	0.789390	+	0.256488i	0.675844	−	0.737045i	$-0.263779\pi$
$127$	8.89597	+	2.89048i	0.789390	+	0.256488i	0.113546	+	0.993533i	$0.463779\pi$
$128$		0			0
$129$	8.49247	+	6.17014i	0.747720	+	0.543251i
$130$		0			0
$131$	10.3843			0.907282			0.453641	−	0.891185i	$-0.350125\pi$
$131$	10.3843			0.907282			0.453641	+	0.891185i	$0.350125\pi$
$132$		0			0
$133$			10.8773i			0.943184i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	14.7461	+	4.79131i	1.25985	+	0.409349i	0.861440	−	0.507859i	$-0.169563\pi$
$137$	14.7461	+	4.79131i	1.25985	+	0.409349i	0.398408	+	0.917208i	$0.369563\pi$
$138$		0			0
$139$	−16.9807	+	12.3372i	−1.44029	+	1.04643i	−0.452305	+	0.891863i	$0.649398\pi$
$139$	−16.9807	+	12.3372i	−1.44029	+	1.04643i	−0.987982	+	0.154567i	$0.950602\pi$
$140$		0			0
$141$	3.94232	+	12.1332i	0.332003	+	1.02180i
$142$		0			0
$143$	7.69760	−	9.60161i	0.643706	−	0.802927i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−7.31476	−	10.0679i	−0.603311	−	0.830387i
$148$		0			0
$149$	0.899897	−	2.76960i	0.0737224	−	0.226894i	−0.907405	−	0.420258i	$-0.861940\pi$
$149$	0.899897	−	2.76960i	0.0737224	−	0.226894i	0.981127	+	0.193363i	$0.0619397\pi$
$150$		0			0
$151$	3.65731	+	2.65719i	0.297628	+	0.216239i	0.726570	−	0.687093i	$-0.241113\pi$
$151$	3.65731	+	2.65719i	0.297628	+	0.216239i	−0.428942	+	0.903332i	$0.641113\pi$
$152$		0			0
$153$		−	23.2276i		−	1.87784i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	5.47059	−	7.52962i	0.436601	−	0.600929i	−0.532852	−	0.846209i	$-0.678880\pi$
$157$	5.47059	−	7.52962i	0.436601	−	0.600929i	0.969452	+	0.245279i	$0.0788796\pi$
$158$		0			0
$159$	9.01497	−	27.7452i	0.714934	−	2.20034i
$160$		0			0
$161$	10.1636	−	7.38432i	0.801007	−	0.581966i
$162$		0			0
$163$	12.0321	−	3.90948i	0.942429	−	0.306214i	0.202794	−	0.979221i	$-0.434998\pi$
$163$	12.0321	−	3.90948i	0.942429	−	0.306214i	0.739635	+	0.673008i	$0.234998\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	16.1672	−	5.25303i	1.25105	−	0.406492i	0.392754	−	0.919643i	$-0.371522\pi$
$167$	16.1672	−	5.25303i	1.25105	−	0.406492i	0.858298	+	0.513152i	$0.171522\pi$
$168$		0			0
$169$	0.621033	−	0.451207i	0.0477718	−	0.0347082i
$170$		0			0
$171$	−11.9452	+	36.7636i	−0.913473	+	2.81138i
$172$		0			0
$173$	7.34298	−	10.1067i	0.558276	−	0.768401i	−0.432830	−	0.901476i	$-0.642485\pi$
$173$	7.34298	−	10.1067i	0.558276	−	0.768401i	0.991106	+	0.133074i	$0.0424849\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$			8.67259i			0.651872i
$178$		0			0
$179$	1.03046	+	0.748673i	0.0770202	+	0.0559584i	0.625629	−	0.780121i	$-0.284842\pi$
$179$	1.03046	+	0.748673i	0.0770202	+	0.0559584i	−0.548609	+	0.836079i	$0.684842\pi$
$180$		0			0
$181$	−5.34282	+	16.4435i	−0.397129	+	1.22224i	0.530162	+	0.847896i	$0.322131\pi$
$181$	−5.34282	+	16.4435i	−0.397129	+	1.22224i	−0.927291	+	0.374341i	$0.877869\pi$
$182$		0			0
$183$	−11.0168	−	15.1633i	−0.814384	−	1.12090i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	12.3820	−	3.38288i	0.905459	−	0.247381i
$188$		0			0
$189$	4.70017	+	14.4656i	0.341887	+	1.05222i
$190$		0			0
$191$	12.2106	−	8.87154i	0.883530	−	0.641922i	−0.0506530	−	0.998716i	$-0.516130\pi$
$191$	12.2106	−	8.87154i	0.883530	−	0.641922i	0.934183	+	0.356794i	$0.116130\pi$
$192$		0			0
$193$	20.8527	+	6.77546i	1.50101	+	0.487708i	0.940313	−	0.340312i	$-0.110533\pi$
$193$	20.8527	+	6.77546i	1.50101	+	0.487708i	0.560699	+	0.828020i	$0.310533\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			19.4874i			1.38842i	0.719772	+	0.694210i	$0.244246\pi$
$197$			19.4874i			1.38842i	−0.719772	+	0.694210i	$0.755754\pi$
$198$		0			0
$199$	4.59408			0.325666			0.162833	−	0.986654i	$-0.447937\pi$
$199$	4.59408			0.325666			0.162833	+	0.986654i	$0.447937\pi$
$200$		0			0
$201$	25.5804	+	18.5852i	1.80430	+	1.31090i
$202$		0			0
$203$	5.08170	+	1.65114i	0.356665	+	0.115888i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	42.4607	−	13.7963i	2.95122	−	0.958910i
$208$		0			0
$209$	−21.3373	−	1.01338i	−1.47593	−	0.0700970i
$210$		0			0
$211$	−7.77574	−	23.9313i	−0.535304	−	1.64750i	−0.742991	−	0.669301i	$-0.766594\pi$
$211$	−7.77574	−	23.9313i	−0.535304	−	1.64750i	0.207687	−	0.978195i	$-0.433406\pi$
$212$		0			0
$213$	−16.2865	−	22.4165i	−1.11593	−	1.53595i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	2.53039	−	3.48278i	0.171774	−	0.236426i
$218$		0			0
$219$	−10.9776			−0.741800
$220$		0			0
$221$	14.3600			0.965960
$222$		0			0
$223$	−15.2157	+	20.9426i	−1.01892	+	1.40242i	−0.105960	+	0.994370i	$0.533792\pi$
$223$	−15.2157	+	20.9426i	−1.01892	+	1.40242i	−0.912959	+	0.408051i	$0.866208\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−14.4444	−	19.8810i	−0.958710	−	1.31955i	−0.947548	−	0.319614i	$-0.896447\pi$
$227$	−14.4444	−	19.8810i	−0.958710	−	1.31955i	−0.0111621	−	0.999938i	$-0.503553\pi$
$228$		0			0
$229$	−3.90485	−	12.0179i	−0.258040	−	0.794165i	−0.993215	−	0.116289i	$-0.962900\pi$
$229$	−3.90485	−	12.0179i	−0.258040	−	0.794165i	0.735175	−	0.677877i	$-0.237100\pi$
$230$		0			0
$231$	−14.0492	+	9.22189i	−0.924370	+	0.606756i
$232$		0			0
$233$	−6.07238	+	1.97304i	−0.397815	+	0.129258i	−0.501090	−	0.865395i	$-0.667068\pi$
$233$	−6.07238	+	1.97304i	−0.397815	+	0.129258i	0.103276	+	0.994653i	$0.467068\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	48.3718	+	15.7169i	3.14208	+	1.02092i
$238$		0			0
$239$	10.9264	+	7.93851i	0.706771	+	0.513499i	0.882130	−	0.471005i	$-0.156109\pi$
$239$	10.9264	+	7.93851i	0.706771	+	0.513499i	−0.175359	+	0.984505i	$0.556109\pi$
$240$		0			0
$241$	−26.7883			−1.72559			−0.862793	−	0.505557i	$-0.831287\pi$
$241$	−26.7883			−1.72559			−0.862793	+	0.505557i	$0.831287\pi$
$242$		0			0
$243$			0.0318587i			0.00204373i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−22.7284	−	7.38489i	−1.44617	−	0.469889i
$248$		0			0
$249$	−29.2028	+	21.2171i	−1.85065	+	1.34458i
$250$		0			0
$251$	2.03249	+	6.25535i	0.128289	+	0.394834i	0.994486	−	0.104869i	$-0.0334424\pi$
$251$	2.03249	+	6.25535i	0.128289	+	0.394834i	−0.866197	+	0.499703i	$0.833442\pi$
$252$		0			0
$253$	13.5384	+	20.6253i	0.851152	+	1.29670i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	11.3084	+	15.5647i	0.705399	+	0.970898i	0.999884	+	0.0152419i	$0.00485184\pi$
$257$	11.3084	+	15.5647i	0.705399	+	0.970898i	−0.294485	+	0.955656i	$0.595148\pi$
$258$		0			0
$259$	−3.41792	+	10.5193i	−0.212379	+	0.653637i
$260$		0			0
$261$	15.3621	+	11.1612i	0.950887	+	0.690860i
$262$		0			0
$263$			4.89929i			0.302103i	0.988526	+	0.151052i	$0.0482660\pi$
$263$			4.89929i			0.302103i	−0.988526	+	0.151052i	$0.951734\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	27.4900	−	37.8368i	1.68236	−	2.31557i
$268$		0			0
$269$	−1.13958	+	3.50727i	−0.0694814	+	0.213842i	−0.979768	−	0.200137i	$-0.935861\pi$
$269$	−1.13958	+	3.50727i	−0.0694814	+	0.213842i	0.910286	+	0.413979i	$0.135861\pi$
$270$		0			0
$271$	−3.28380	+	2.38582i	−0.199477	+	0.144928i	−0.683040	−	0.730381i	$-0.739342\pi$
$271$	−3.28380	+	2.38582i	−0.199477	+	0.144928i	0.483563	+	0.875310i	$0.339342\pi$
$272$		0			0
$273$	−17.8809	+	5.80987i	−1.08220	+	0.351629i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−10.2373	+	3.32631i	−0.615101	+	0.199859i	−0.599964	−	0.800027i	$-0.704819\pi$
$277$	−10.2373	+	3.32631i	−0.615101	+	0.199859i	−0.0151373	+	0.999885i	$0.504819\pi$
$278$		0			0
$279$	12.3770	−	8.99240i	0.740991	−	0.538361i
$280$		0			0
$281$	−4.18268	+	12.8730i	−0.249518	+	0.767936i	0.745343	+	0.666681i	$0.232286\pi$
$281$	−4.18268	+	12.8730i	−0.249518	+	0.767936i	−0.994860	+	0.101255i	$0.967714\pi$
$282$		0			0
$283$	−6.57386	+	9.04814i	−0.390775	+	0.537856i	−0.958399	−	0.285432i	$-0.907863\pi$
$283$	−6.57386	+	9.04814i	−0.390775	+	0.537856i	0.567624	+	0.823288i	$0.307863\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			14.4841i			0.854970i
$288$		0			0
$289$	−1.63591	−	1.18856i	−0.0962302	−	0.0699154i
$290$		0			0
$291$	6.22089	−	19.1459i	0.364675	−	1.12236i
$292$		0			0
$293$	−5.67584	−	7.81212i	−0.331586	−	0.456389i	0.610374	−	0.792113i	$-0.291019\pi$
$293$	−5.67584	−	7.81212i	−0.331586	−	0.456389i	−0.941960	+	0.335724i	$0.891019\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−28.8141	+	7.87231i	−1.67196	+	0.456798i
$298$		0			0
$299$	8.52931	+	26.2505i	0.493262	+	1.51811i
$300$		0			0
$301$	4.78036	−	3.47313i	0.275535	−	0.200188i
$302$		0			0
$303$	13.9628	+	4.53678i	0.802141	+	0.260631i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	5.20959i		−	0.297327i	−0.988888	−	0.148664i	$-0.952503\pi$
$307$		−	5.20959i		−	0.297327i	0.988888	−	0.148664i	$-0.0474971\pi$
$308$		0			0
$309$	50.0369			2.84650
$310$		0			0
$311$	−19.5453	−	14.2005i	−1.10831	−	0.805237i	−0.125917	−	0.992041i	$-0.540187\pi$
$311$	−19.5453	−	14.2005i	−1.10831	−	0.805237i	−0.982397	+	0.186803i	$0.940187\pi$
$312$		0			0
$313$	12.4633	+	4.04956i	0.704465	+	0.228895i	0.639275	−	0.768978i	$-0.279235\pi$
$313$	12.4633	+	4.04956i	0.704465	+	0.228895i	0.0651903	+	0.997873i	$0.479235\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	6.73454	−	2.18818i	0.378249	−	0.122901i	−0.113721	−	0.993513i	$-0.536277\pi$
$317$	6.73454	−	2.18818i	0.378249	−	0.122901i	0.491970	+	0.870612i	$0.336277\pi$
$318$		0			0
$319$	−3.71236	+	9.81458i	−0.207853	+	0.549511i
$320$		0			0
$321$	2.20795	+	6.79538i	0.123236	+	0.379281i
$322$		0			0
$323$	−14.6513	−	20.1658i	−0.815220	−	1.12205i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−27.0254	+	37.1973i	−1.49451	+	2.05701i
$328$		0			0
$329$	7.18117			0.395911
$330$		0			0
$331$	−1.76299			−0.0969025			−0.0484513	−	0.998826i	$-0.515429\pi$
$331$	−1.76299			−0.0969025			−0.0484513	+	0.998826i	$0.515429\pi$
$332$		0			0
$333$	−23.1040	+	31.8000i	−1.26609	+	1.74263i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−6.97253	−	9.59687i	−0.379818	−	0.522775i	0.575718	−	0.817648i	$-0.304722\pi$
$337$	−6.97253	−	9.59687i	−0.379818	−	0.522775i	−0.955536	+	0.294874i	$0.904722\pi$
$338$		0			0
$339$	1.62461	+	5.00005i	0.0882369	+	0.271565i
$340$		0			0
$341$	6.59617	+	5.28815i	0.357203	+	0.286369i
$342$		0			0
$343$	−17.9055	+	5.81784i	−0.966804	+	0.314134i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	7.74747	+	2.51731i	0.415906	+	0.135136i	0.509493	−	0.860475i	$-0.329833\pi$
$347$	7.74747	+	2.51731i	0.415906	+	0.135136i	−0.0935864	+	0.995611i	$0.529833\pi$
$348$		0			0
$349$	13.8784	+	10.0832i	0.742893	+	0.539743i	0.893616	−	0.448833i	$-0.148160\pi$
$349$	13.8784	+	10.0832i	0.742893	+	0.539743i	−0.150723	+	0.988576i	$0.548160\pi$
$350$		0			0
$351$	−33.4173			−1.78368
$352$		0			0
$353$		−	9.89553i		−	0.526686i	−0.964702	−	0.263343i	$-0.915175\pi$
$353$		−	9.89553i		−	0.526686i	0.964702	−	0.263343i	$-0.0848251\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−18.6503	−	6.05985i	−0.987079	−	0.320721i
$358$		0			0
$359$	30.2411	−	21.9715i	1.59607	−	1.15961i	0.701506	−	0.712664i	$-0.252512\pi$
$359$	30.2411	−	21.9715i	1.59607	−	1.15961i	0.894561	−	0.446946i	$-0.147488\pi$
$360$		0			0
$361$	6.94745	+	21.3821i	0.365655	+	1.12537i
$362$		0			0
$363$	−16.7810	−	28.4185i	−0.880777	−	1.49158i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	11.3951	+	15.6840i	0.594819	+	0.818698i	0.995222	−	0.0976415i	$-0.0311299\pi$
$367$	11.3951	+	15.6840i	0.594819	+	0.818698i	−0.400403	+	0.916339i	$0.631130\pi$
$368$		0			0
$369$	−15.9061	+	48.9539i	−0.828038	+	2.54844i
$370$		0			0
$371$	−13.2851	−	9.65221i	−0.689730	−	0.501118i
$372$		0			0
$373$			1.02733i			0.0531933i	0.999646	+	0.0265967i	$0.00846698\pi$
$373$			1.02733i			0.0531933i	−0.999646	+	0.0265967i	$0.991533\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−6.90018	+	9.49729i	−0.355378	+	0.489135i
$378$		0			0
$379$	−2.32646	+	7.16010i	−0.119502	+	0.367790i	−0.992859	−	0.119290i	$-0.961938\pi$
$379$	−2.32646	+	7.16010i	−0.119502	+	0.367790i	0.873357	+	0.487080i	$0.161938\pi$
$380$		0			0
$381$	22.7043	−	16.4957i	1.16318	−	0.845098i
$382$		0			0
$383$	−14.3960	+	4.67756i	−0.735603	+	0.239012i	−0.652775	−	0.757552i	$-0.726395\pi$
$383$	−14.3960	+	4.67756i	−0.735603	+	0.239012i	−0.0828281	+	0.996564i	$0.526395\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	19.9709	−	6.48895i	1.01518	−	0.329852i
$388$		0			0
$389$	4.11088	−	2.98673i	0.208430	−	0.151433i	−0.478673	−	0.877993i	$-0.658882\pi$
$389$	4.11088	−	2.98673i	0.208430	−	0.151433i	0.687103	+	0.726560i	$0.258882\pi$
$390$		0			0
$391$	−8.89630	+	27.3800i	−0.449905	+	1.38467i
$392$		0			0
$393$	18.3130	−	25.2057i	0.923771	−	1.27146i
$394$		0			0
$395$		0			0
$396$		0			0
$397$		−	5.78023i		−	0.290101i	−0.989424	−	0.145051i	$-0.953665\pi$
$397$		−	5.78023i		−	0.290101i	0.989424	−	0.145051i	$-0.0463345\pi$
$398$		0			0
$399$	26.4024	+	19.1825i	1.32177	+	0.960326i
$400$		0			0
$401$	7.23049	−	22.2532i	0.361074	−	1.11127i	−0.591330	−	0.806430i	$-0.701397\pi$
$401$	7.23049	−	22.2532i	0.361074	−	1.11127i	0.952403	−	0.304841i	$-0.0986032\pi$
$402$		0			0
$403$	5.55938	+	7.65183i	0.276932	+	0.381165i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−20.3165	−	7.68472i	−1.00705	−	0.380917i
$408$		0			0
$409$	−2.63551	−	8.11126i	−0.130318	−	0.401076i	0.864515	−	0.502607i	$-0.167626\pi$
$409$	−2.63551	−	8.11126i	−0.130318	−	0.401076i	−0.994832	+	0.101531i	$0.967626\pi$
$410$		0			0
$411$	37.6352	−	27.3435i	1.85641	−	1.34876i
$412$		0			0
$413$	4.64282	+	1.50854i	0.228458	+	0.0742305i
$414$		0			0
$415$		0			0
$416$		0			0
$417$			62.9742i			3.08386i
$418$		0			0
$419$	−26.9789			−1.31801			−0.659003	−	0.752141i	$-0.729021\pi$
$419$	−26.9789			−1.31801			−0.659003	+	0.752141i	$0.729021\pi$
$420$		0			0
$421$	18.6021	+	13.5152i	0.906612	+	0.658692i	0.940156	−	0.340745i	$-0.110679\pi$
$421$	18.6021	+	13.5152i	0.906612	+	0.658692i	−0.0335437	+	0.999437i	$0.510679\pi$
$422$		0			0
$423$	24.2712	+	7.88618i	1.18010	+	0.383439i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−10.0339	+	3.26020i	−0.485573	+	0.157772i
$428$		0			0
$429$	−9.73094	−	35.6170i	−0.469814	−	1.71961i
$430$		0			0
$431$	0.655391	+	2.01708i	0.0315691	+	0.0971596i	0.965600	−	0.260034i	$-0.0837337\pi$
$431$	0.655391	+	2.01708i	0.0315691	+	0.0971596i	−0.934030	+	0.357193i	$0.883734\pi$
$432$		0			0
$433$	16.0975	+	22.1563i	0.773597	+	1.06476i	0.995960	+	0.0898005i	$0.0286230\pi$
$433$	16.0975	+	22.1563i	0.773597	+	1.06476i	−0.222363	+	0.974964i	$0.571377\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	28.1613	−	38.7607i	1.34714	−	1.85417i
$438$		0			0
$439$	−31.5257			−1.50464			−0.752319	−	0.658799i	$-0.771065\pi$
$439$	−31.5257			−1.50464			−0.752319	+	0.658799i	$0.771065\pi$
$440$		0			0
$441$	−24.8941			−1.18543
$442$		0			0
$443$	−3.95050	+	5.43740i	−0.187694	+	0.258339i	−0.892486	−	0.451076i	$-0.851040\pi$
$443$	−3.95050	+	5.43740i	−0.187694	+	0.258339i	0.704792	+	0.709414i	$0.251040\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−5.13562	−	7.06858i	−0.242907	−	0.334332i
$448$		0			0
$449$	−3.99069	−	12.2821i	−0.188332	−	0.579627i	0.811658	−	0.584133i	$-0.198565\pi$
$449$	−3.99069	−	12.2821i	−0.188332	−	0.579627i	−0.999990	+	0.00450672i	$0.998565\pi$
$450$		0			0
$451$	−28.4125	−	1.34940i	−1.33789	−	0.0635409i
$452$		0			0
$453$	12.8996	−	4.19132i	0.606074	−	0.196925i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−10.6090	−	3.44706i	−0.496267	−	0.161247i	0.0501808	−	0.998740i	$-0.484020\pi$
$457$	−10.6090	−	3.44706i	−0.496267	−	0.161247i	−0.546448	+	0.837493i	$0.684020\pi$
$458$		0			0
$459$	−28.1984	−	20.4873i	−1.31619	−	0.956267i
$460$		0			0
$461$	11.7060			0.545205			0.272602	−	0.962127i	$-0.412116\pi$
$461$	11.7060			0.545205			0.272602	+	0.962127i	$0.412116\pi$
$462$		0			0
$463$			10.7840i			0.501173i	0.968094	+	0.250586i	$0.0806234\pi$
$463$			10.7840i			0.501173i	−0.968094	+	0.250586i	$0.919377\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−19.8907	−	6.46289i	−0.920433	−	0.299067i	−0.189789	−	0.981825i	$-0.560780\pi$
$467$	−19.8907	−	6.46289i	−0.920433	−	0.299067i	−0.730644	+	0.682758i	$0.760780\pi$
$468$		0			0
$469$	14.3990	−	10.4615i	0.664885	−	0.483067i
$470$		0			0
$471$	−8.62903	−	26.5574i	−0.397605	−	1.22370i
$472$		0			0
$473$	6.36764	+	9.70086i	0.292784	+	0.446046i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−34.3017	−	47.2123i	−1.57057	−	2.16170i
$478$		0			0
$479$	3.47943	−	10.7086i	0.158979	−	0.489288i	−0.839563	−	0.543262i	$-0.817189\pi$
$479$	3.47943	−	10.7086i	0.158979	−	0.489288i	0.998542	+	0.0539745i	$0.0171890\pi$
$480$		0			0
$481$	−19.6597	−	14.2836i	−0.896406	−	0.651277i
$482$		0			0
$483$		−	37.6926i		−	1.71507i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	4.99978	−	6.88160i	0.226562	−	0.311835i	−0.680569	−	0.732684i	$-0.738268\pi$
$487$	4.99978	−	6.88160i	0.226562	−	0.311835i	0.907131	+	0.420848i	$0.138268\pi$
$488$		0			0
$489$	11.7296	−	36.0999i	0.530430	−	1.63250i
$490$		0			0
$491$	−11.2974	+	8.20808i	−0.509847	+	0.370425i	−0.812765	−	0.582591i	$-0.802039\pi$
$491$	−11.2974	+	8.20808i	−0.509847	+	0.370425i	0.302919	+	0.953016i	$0.402039\pi$
$492$		0			0
$493$	−11.6451	+	3.78373i	−0.524470	+	0.170411i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−14.8334	+	4.81968i	−0.665371	+	0.216192i
$498$		0			0
$499$	−4.47304	+	3.24985i	−0.200241	+	0.145483i	−0.683387	−	0.730056i	$-0.739494\pi$
$499$	−4.47304	+	3.24985i	−0.200241	+	0.145483i	0.483146	+	0.875540i	$0.339494\pi$
$500$		0			0
$501$	15.7606	−	48.5062i	0.704133	−	2.16710i
$502$		0			0
$503$	5.40452	−	7.43868i	0.240976	−	0.331674i	−0.671350	−	0.741141i	$-0.734285\pi$
$503$	5.40452	−	7.43868i	0.240976	−	0.331674i	0.912325	+	0.409466i	$0.134285\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$		−	2.30314i		−	0.102286i
$508$		0			0
$509$	8.96759	+	6.51534i	0.397482	+	0.288787i	0.768514	−	0.639832i	$-0.220996\pi$
$509$	8.96759	+	6.51534i	0.397482	+	0.288787i	−0.371033	+	0.928620i	$0.620996\pi$
$510$		0			0
$511$	−1.90949	+	5.87681i	−0.0844709	+	0.259975i
$512$		0			0
$513$	34.0951	+	46.9279i	1.50534	+	2.07192i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−0.669030	+	14.0868i	−0.0294239	+	0.619537i
$518$		0			0
$519$	−11.5824	−	35.6471i	−0.508413	−	1.56473i
$520$		0			0
$521$	−14.8879	+	10.8167i	−0.652252	+	0.473889i	−0.864038	−	0.503427i	$-0.832072\pi$
$521$	−14.8879	+	10.8167i	−0.652252	+	0.473889i	0.211786	+	0.977316i	$0.432072\pi$
$522$		0			0
$523$	−23.4323	−	7.61361i	−1.02462	−	0.332920i	−0.251960	−	0.967738i	$-0.581075\pi$
$523$	−23.4323	−	7.61361i	−1.02462	−	0.332920i	−0.772662	+	0.634818i	$0.781075\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			9.86514i			0.429732i
$528$		0			0
$529$	−32.3354			−1.40589
$530$		0			0
$531$	14.0353	+	10.1972i	0.609080	+	0.442523i
$532$		0			0
$533$	−30.2648	−	9.83363i	−1.31091	−	0.425942i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	3.63449	−	1.18092i	0.156840	−	0.0509604i
$538$		0			0
$539$	−3.62559	−	13.2703i	−0.156165	−	0.571593i
$540$		0			0
$541$	2.02811	+	6.24188i	0.0871953	+	0.268360i	0.985141	−	0.171746i	$-0.0549409\pi$
$541$	2.02811	+	6.24188i	0.0871953	+	0.268360i	−0.897946	+	0.440106i	$0.854941\pi$
$542$		0			0
$543$	30.4910	+	41.9672i	1.30849	+	1.80098i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	0.383526	−	0.527878i	0.0163984	−	0.0225704i	−0.800739	−	0.599013i	$-0.795560\pi$
$547$	0.383526	−	0.527878i	0.0163984	−	0.0225704i	0.817137	+	0.576443i	$0.195560\pi$
$548$		0			0
$549$	−37.4931			−1.60017
$550$		0			0
$551$	20.3772			0.868098
$552$		0			0
$553$	16.8279	−	23.1617i	0.715596	−	0.984934i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	1.00048	+	1.37704i	0.0423915	+	0.0583469i	0.829687	−	0.558230i	$-0.188519\pi$
$557$	1.00048	+	1.37704i	0.0423915	+	0.0583469i	−0.787295	+	0.616576i	$0.788519\pi$
$558$		0			0
$559$	4.01166	+	12.3466i	0.169675	+	0.522207i
$560$		0			0
$561$	13.6247	−	36.0204i	0.575236	−	1.52078i
$562$		0			0
$563$	41.5681	−	13.5063i	1.75189	−	0.569222i	0.755576	−	0.655061i	$-0.227357\pi$
$563$	41.5681	−	13.5063i	1.75189	−	0.569222i	0.996309	+	0.0858390i	$0.0273571\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	14.4813	+	4.70525i	0.608157	+	0.197602i
$568$		0			0
$569$	−25.3587	−	18.4242i	−1.06309	−	0.772382i	−0.0884349	−	0.996082i	$-0.528187\pi$
$569$	−25.3587	−	18.4242i	−1.06309	−	0.772382i	−0.974658	+	0.223700i	$0.928187\pi$
$570$		0			0
$571$	9.86361			0.412779			0.206390	−	0.978470i	$-0.433829\pi$
$571$	9.86361			0.412779			0.206390	+	0.978470i	$0.433829\pi$
$572$		0			0
$573$		−	45.2840i		−	1.89176i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−24.5274	−	7.96943i	−1.02109	−	0.331772i	−0.249827	−	0.968290i	$-0.580374\pi$
$577$	−24.5274	−	7.96943i	−1.02109	−	0.331772i	−0.771261	+	0.636519i	$0.780374\pi$
$578$		0			0
$579$	53.2204	−	38.6669i	2.21176	−	1.60694i
$580$		0			0
$581$	6.27878	+	19.3241i	0.260488	+	0.801698i
$582$		0			0
$583$	20.1718	−	25.1613i	0.835429	−	1.04207i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−0.625301	−	0.860653i	−0.0258089	−	0.0355229i	0.795918	−	0.605405i	$-0.206989\pi$
$587$	−0.625301	−	0.860653i	−0.0258089	−	0.0355229i	−0.821726	+	0.569882i	$0.806989\pi$
$588$		0			0
$589$	5.07332	−	15.6141i	0.209043	−	0.643367i
$590$		0			0
$591$	47.3016	+	34.3666i	1.94573	+	1.41365i
$592$		0			0
$593$		−	19.7906i		−	0.812702i	−0.913717	−	0.406351i	$-0.866801\pi$
$593$		−	19.7906i		−	0.812702i	0.913717	−	0.406351i	$-0.133199\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	8.10180	−	11.1512i	0.331585	−	0.456387i
$598$		0			0
$599$	1.40163	−	4.31378i	0.0572692	−	0.176256i	−0.918330	−	0.395816i	$-0.870462\pi$
$599$	1.40163	−	4.31378i	0.0572692	−	0.176256i	0.975599	+	0.219559i	$0.0704619\pi$
$600$		0			0
$601$	−38.2474	+	27.7883i	−1.56014	+	1.13351i	−0.624251	+	0.781224i	$0.714596\pi$
$601$	−38.2474	+	27.7883i	−1.56014	+	1.13351i	−0.935892	+	0.352286i	$0.885404\pi$
$602$		0			0
$603$	60.1549	−	19.5455i	2.44970	−	0.795954i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	12.0424	−	3.91282i	0.488787	−	0.158817i	−0.0542464	−	0.998528i	$-0.517276\pi$
$607$	12.0424	−	3.91282i	0.488787	−	0.158817i	0.543033	+	0.839711i	$0.317276\pi$
$608$		0			0
$609$	12.9695	−	9.42291i	0.525552	−	0.381836i
$610$		0			0
$611$	−4.87548	+	15.0052i	−0.197241	+	0.607045i
$612$		0			0
$613$	−6.78018	+	9.33212i	−0.273849	+	0.376921i	−0.923684	−	0.383154i	$-0.874838\pi$
$613$	−6.78018	+	9.33212i	−0.273849	+	0.376921i	0.649835	+	0.760075i	$0.274838\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	9.58142i		−	0.385733i	−0.981225	−	0.192867i	$-0.938221\pi$
$617$		−	9.58142i		−	0.385733i	0.981225	−	0.192867i	$-0.0617785\pi$
$618$		0			0
$619$	−0.972177	−	0.706328i	−0.0390751	−	0.0283897i	0.568076	−	0.822976i	$-0.307688\pi$
$619$	−0.972177	−	0.706328i	−0.0390751	−	0.0283897i	−0.607151	+	0.794586i	$0.707688\pi$
$620$		0			0
$621$	20.7026	−	63.7161i	0.830767	−	2.55684i
$622$		0			0
$623$	−15.4740	−	21.2981i	−0.619951	−	0.853289i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−40.0887	+	50.0046i	−1.60099	+	1.99699i
$628$		0			0
$629$	−7.83245	−	24.1058i	−0.312300	−	0.961161i
$630$		0			0
$631$	−11.5819	+	8.41474i	−0.461068	+	0.334985i	−0.793950	−	0.607983i	$-0.791979\pi$
$631$	−11.5819	+	8.41474i	−0.461068	+	0.334985i	0.332882	+	0.942968i	$0.391979\pi$
$632$		0			0
$633$	−71.8009	−	23.3295i	−2.85383	−	0.927265i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		−	15.3903i		−	0.609786i
$638$		0			0
$639$	−55.4274			−2.19267
$640$		0			0
$641$	29.9553	+	21.7638i	1.18316	+	0.859618i	0.992525	−	0.122043i	$-0.0389445\pi$
$641$	29.9553	+	21.7638i	1.18316	+	0.859618i	0.190637	+	0.981661i	$0.438945\pi$
$642$		0			0
$643$	4.25667	+	1.38308i	0.167867	+	0.0545432i	0.391745	−	0.920074i	$-0.371872\pi$
$643$	4.25667	+	1.38308i	0.167867	+	0.0545432i	−0.223878	+	0.974617i	$0.571872\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−27.1713	+	8.82850i	−1.06822	+	0.347084i	−0.789792	−	0.613374i	$-0.789812\pi$
$647$	−27.1713	+	8.82850i	−1.06822	+	0.347084i	−0.278423	+	0.960458i	$0.589812\pi$
$648$		0			0
$649$	−3.39175	+	8.96694i	−0.133138	+	0.351983i
$650$		0			0
$651$	−3.99130	−	12.2840i	−0.156431	−	0.481446i
$652$		0			0
$653$	−0.396454	−	0.545672i	−0.0155144	−	0.0213538i	0.801189	−	0.598411i	$-0.204201\pi$
$653$	−0.396454	−	0.545672i	−0.0155144	−	0.0213538i	−0.816704	+	0.577057i	$0.804201\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−12.9075	+	17.7657i	−0.503570	+	0.693105i
$658$		0			0
$659$	30.4518			1.18623			0.593117	−	0.805116i	$-0.297897\pi$
$659$	30.4518			1.18623			0.593117	+	0.805116i	$0.297897\pi$
$660$		0			0
$661$	−29.2772			−1.13875			−0.569375	−	0.822078i	$-0.692815\pi$
$661$	−29.2772			−1.13875			−0.569375	+	0.822078i	$0.692815\pi$
$662$		0			0
$663$	25.3243	−	34.8559i	0.983515	−	1.35369i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−13.8335	−	19.0402i	−0.535636	−	0.737239i
$668$		0			0
$669$	24.0005	+	73.8658i	0.927912	+	2.85582i
$670$		0			0
$671$	−5.46051	−	19.9865i	−0.210801	−	0.771569i
$672$		0			0
$673$	1.52112	−	0.494242i	0.0586349	−	0.0190516i	−0.279553	−	0.960130i	$-0.590186\pi$
$673$	1.52112	−	0.494242i	0.0586349	−	0.0190516i	0.338188	+	0.941079i	$0.390186\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	9.91287	+	3.22089i	0.380982	+	0.123789i	0.493246	−	0.869890i	$-0.335810\pi$
$677$	9.91287	+	3.22089i	0.380982	+	0.123789i	−0.112264	+	0.993678i	$0.535810\pi$
$678$		0			0
$679$	−9.16757	−	6.66063i	−0.351819	−	0.255612i
$680$		0			0
$681$	−73.7302			−2.82535
$682$		0			0
$683$			38.4144i			1.46988i	0.678130	+	0.734942i	$0.262791\pi$
$683$			38.4144i			1.46988i	−0.678130	+	0.734942i	$0.737209\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−36.0573	−	11.7157i	−1.37567	−	0.446982i
$688$		0			0
$689$	29.1881	−	21.2064i	1.11198	−	0.807899i
$690$		0			0
$691$	5.37655	+	16.5473i	0.204534	+	0.629490i	0.999732	+	0.0231407i	$0.00736657\pi$
$691$	5.37655	+	16.5473i	0.204534	+	0.629490i	−0.795199	+	0.606349i	$0.792633\pi$
$692$		0			0
$693$	−1.59481	+	33.5797i	−0.0605819	+	1.27559i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−19.5095	−	26.8525i	−0.738974	−	1.01711i
$698$		0			0
$699$	−5.91969	+	18.2189i	−0.223903	+	0.689103i
$700$		0			0
$701$	−41.3290	−	30.0273i	−1.56098	−	1.13412i	−0.935204	−	0.354109i	$-0.884784\pi$
$701$	−41.3290	−	30.0273i	−1.56098	−	1.13412i	−0.625771	−	0.780007i	$-0.715216\pi$
$702$		0			0
$703$			42.1815i			1.59090i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	4.85748	−	6.68574i	0.182684	−	0.251443i
$708$		0			0
$709$	3.11182	−	9.57719i	0.116867	−	0.359679i	−0.875465	−	0.483281i	$-0.839445\pi$
$709$	3.11182	−	9.57719i	0.116867	−	0.359679i	0.992332	+	0.123603i	$0.0394448\pi$
$710$		0			0
$711$	82.3111	−	59.8025i	3.08691	−	2.24277i
$712$		0			0
$713$	−18.0337	+	5.85952i	−0.675369	+	0.219441i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	38.5381	−	12.5218i	1.43923	−	0.467635i
$718$		0			0
$719$	−17.8912	+	12.9987i	−0.667230	+	0.484771i	−0.869097	−	0.494642i	$-0.835299\pi$
$719$	−17.8912	+	12.9987i	−0.667230	+	0.484771i	0.201867	+	0.979413i	$0.435299\pi$
$720$		0			0
$721$	8.70361	−	26.7869i	0.324139	−	0.997598i
$722$		0			0
$723$	−47.2420	+	65.0230i	−1.75695	+	2.41823i
$724$		0			0
$725$		0			0
$726$		0			0
$727$		−	25.8714i		−	0.959517i	−0.877401	−	0.479758i	$-0.840724\pi$
$727$		−	25.8714i		−	0.959517i	0.877401	−	0.479758i	$-0.159276\pi$
$728$		0			0
$729$	−21.8048	−	15.8421i	−0.807585	−	0.586745i
$730$		0			0
$731$	−4.18428	+	12.8779i	−0.154761	+	0.476306i
$732$		0			0
$733$	21.4566	+	29.5324i	0.792516	+	1.09080i	0.993790	+	0.111270i	$0.0354917\pi$
$733$	21.4566	+	29.5324i	0.792516	+	1.09080i	−0.201274	+	0.979535i	$0.564508\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	19.1801	+	29.2202i	0.706508	+	1.07634i
$738$		0			0
$739$	−5.51149	−	16.9626i	−0.202743	−	0.623980i	−0.999799	−	0.0200734i	$-0.993610\pi$
$739$	−5.51149	−	16.9626i	−0.202743	−	0.623980i	0.797055	−	0.603907i	$-0.206390\pi$
$740$		0			0
$741$	−58.0074	+	42.1448i	−2.13096	+	1.54823i
$742$		0			0
$743$	−37.6450	−	12.2316i	−1.38106	−	0.448733i	−0.478042	−	0.878337i	$-0.658653\pi$
$743$	−37.6450	−	12.2316i	−1.38106	−	0.448733i	−0.903018	+	0.429604i	$0.858653\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$			72.2074i			2.64193i
$748$		0			0
$749$	4.02192			0.146958
$750$		0			0
$751$	5.73271	+	4.16506i	0.209190	+	0.151985i	0.687447	−	0.726235i	$-0.258731\pi$
$751$	5.73271	+	4.16506i	0.209190	+	0.151985i	−0.478257	+	0.878220i	$0.658731\pi$
$752$		0			0
$753$	18.7679	+	6.09806i	0.683940	+	0.222226i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−7.53982	+	2.44983i	−0.274039	+	0.0890407i	−0.442813	−	0.896614i	$-0.646019\pi$
$757$	−7.53982	+	2.44983i	−0.274039	+	0.0890407i	0.168774	+	0.985655i	$0.446019\pi$
$758$		0			0
$759$	73.9388	+	3.51161i	2.68381	+	0.127463i
$760$		0			0
$761$	9.04626	+	27.8415i	0.327927	+	1.00925i	0.970102	+	0.242697i	$0.0780321\pi$
$761$	9.04626	+	27.8415i	0.327927	+	1.00925i	−0.642175	+	0.766558i	$0.721968\pi$
$762$		0			0
$763$	15.2124	+	20.9381i	0.550727	+	0.758010i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−6.30425	+	8.67705i	−0.227633	+	0.313310i
$768$		0			0
$769$	3.78340			0.136433			0.0682165	−	0.997671i	$-0.478269\pi$
$769$	3.78340			0.136433			0.0682165	+	0.997671i	$0.478269\pi$
$770$		0			0
$771$	57.7227			2.07883
$772$		0			0
$773$	−1.51617	+	2.08683i	−0.0545329	+	0.0750581i	−0.835413	−	0.549623i	$-0.814771\pi$
$773$	−1.51617	+	2.08683i	−0.0545329	+	0.0750581i	0.780880	+	0.624682i	$0.214771\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	19.5057	+	26.8474i	0.699765	+	0.963143i
$778$		0			0
$779$	17.0693	+	52.5340i	0.611572	+	1.88222i
$780$		0			0
$781$	−8.07247	−	29.5467i	−0.288856	−	1.05726i
$782$		0			0
$783$	27.0994	−	8.80513i	0.968454	−	0.314670i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−13.0248	−	4.23200i	−0.464282	−	0.150854i	0.0675291	−	0.997717i	$-0.478488\pi$
$787$	−13.0248	−	4.23200i	−0.464282	−	0.150854i	−0.531811	+	0.846863i	$0.678488\pi$
$788$		0			0
$789$	11.8920	+	8.64005i	0.423367	+	0.307594i
$790$		0			0
$791$	2.95933			0.105222
$792$		0			0
$793$		−	23.1794i		−	0.823124i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−44.0779	−	14.3218i	−1.56132	−	0.507303i	−0.604159	−	0.796864i	$-0.706491\pi$
$797$	−44.0779	−	14.3218i	−1.56132	−	0.507303i	−0.957160	+	0.289561i	$0.906491\pi$
$798$		0			0
$799$	−13.3134	+	9.67274i	−0.470993	+	0.342197i
$800$		0			0
$801$	−28.9104	−	88.9771i	−1.02150	−	3.14385i
$802$		0			0
$803$	−11.3502	−	4.29322i	−0.400541	−	0.151504i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	6.50347	+	8.95126i	0.228933	+	0.315099i
$808$		0			0
$809$	−2.35528	+	7.24879i	−0.0828071	+	0.254854i	−0.983885	−	0.178804i	$-0.942777\pi$
$809$	−2.35528	+	7.24879i	−0.0828071	+	0.254854i	0.901078	+	0.433658i	$0.142777\pi$
$810$		0			0
$811$	−23.5550	−	17.1137i	−0.827127	−	0.600943i	0.0916180	−	0.995794i	$-0.470796\pi$
$811$	−23.5550	−	17.1137i	−0.827127	−	0.600943i	−0.918745	+	0.394851i	$0.870796\pi$
$812$		0			0
$813$			12.1782i			0.427108i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	13.2453	−	18.2307i	0.463396	−	0.637810i
$818$		0			0
$819$	−11.6220	+	35.7689i	−0.406106	+	1.24987i
$820$		0			0
$821$	−39.7129	+	28.8531i	−1.38599	+	1.00698i	−0.389698	+	0.920943i	$0.627421\pi$
$821$	−39.7129	+	28.8531i	−1.38599	+	1.00698i	−0.996292	+	0.0860379i	$0.972579\pi$
$822$		0			0
$823$	−53.1942	+	17.2838i	−1.85423	+	0.602476i	−0.858217	+	0.513287i	$0.828428\pi$
$823$	−53.1942	+	17.2838i	−1.85423	+	0.602476i	−0.996015	+	0.0891893i	$0.971572\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−18.3419	+	5.95965i	−0.637811	+	0.207237i	−0.610032	−	0.792377i	$-0.708844\pi$
$827$	−18.3419	+	5.95965i	−0.637811	+	0.207237i	−0.0277792	+	0.999614i	$0.508844\pi$
$828$		0			0
$829$	−13.8870	+	10.0895i	−0.482316	+	0.350423i	−0.802222	−	0.597026i	$-0.796349\pi$
$829$	−13.8870	+	10.0895i	−0.482316	+	0.350423i	0.319906	+	0.947449i	$0.396349\pi$
$830$		0			0
$831$	−9.97991	+	30.7150i	−0.346199	+	1.06549i
$832$		0			0
$833$	9.43543	−	12.9868i	0.326918	−	0.449964i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		−	22.9572i		−	0.793517i
$838$		0			0
$839$	30.5653	+	22.2070i	1.05523	+	0.766671i	0.973200	−	0.229959i	$-0.0738591\pi$
$839$	30.5653	+	22.2070i	1.05523	+	0.766671i	0.0820317	+	0.996630i	$0.473859\pi$
$840$		0			0
$841$	−5.86830	+	18.0608i	−0.202355	+	0.622785i
$842$		0			0
$843$	23.8701	+	32.8544i	0.822131	+	1.13157i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−18.1326	+	4.04041i	−0.623044	+	0.138830i
$848$		0			0
$849$	10.3693	+	31.9133i	0.355872	+	1.09526i
$850$		0			0
$851$	39.4139	−	28.6358i	1.35109	−	0.981624i
$852$		0			0
$853$	−10.0519	−	3.26607i	−0.344171	−	0.111828i	0.131831	−	0.991272i	$-0.457914\pi$
$853$	−10.0519	−	3.26607i	−0.344171	−	0.111828i	−0.476002	+	0.879444i	$0.657914\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			14.6489i			0.500395i	0.968195	+	0.250198i	$0.0804956\pi$
$857$			14.6489i			0.500395i	−0.968195	+	0.250198i	$0.919504\pi$
$858$		0			0
$859$	1.44844			0.0494202			0.0247101	−	0.999695i	$-0.492134\pi$
$859$	1.44844			0.0494202			0.0247101	+	0.999695i	$0.492134\pi$
$860$		0			0
$861$	35.1571	+	25.5432i	1.19815	+	0.870508i
$862$		0			0
$863$	−45.9954	−	14.9448i	−1.56570	−	0.508727i	−0.607377	−	0.794414i	$-0.707778\pi$
$863$	−45.9954	−	14.9448i	−1.56570	−	0.508727i	−0.958323	+	0.285687i	$0.907778\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−5.76996	+	1.87477i	−0.195958	+	0.0636707i
$868$		0			0
$869$	43.8668	+	35.1680i	1.48808	+	1.19299i
$870$		0			0
$871$	12.0836	+	37.1896i	0.409438	+	1.26012i
$872$		0			0
$873$	−23.6703	−	32.5794i	−0.801120	−	1.10265i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	4.47976	−	6.16586i	0.151271	−	0.208206i	−0.726656	−	0.687002i	$-0.758926\pi$
$877$	4.47976	−	6.16586i	0.151271	−	0.208206i	0.877926	+	0.478795i	$0.158926\pi$
$878$		0			0
$879$	−28.9718			−0.977194
$880$		0			0
$881$	−14.1585			−0.477013			−0.238506	−	0.971141i	$-0.576658\pi$
$881$	−14.1585			−0.477013			−0.238506	+	0.971141i	$0.576658\pi$
$882$		0			0
$883$	17.8847	−	24.6162i	0.601868	−	0.828400i	−0.394010	−	0.919106i	$-0.628912\pi$
$883$	17.8847	−	24.6162i	0.601868	−	0.828400i	0.995878	+	0.0907061i	$0.0289124\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	29.4474	+	40.5308i	0.988746	+	1.36089i	0.931982	+	0.362504i	$0.118078\pi$
$887$	29.4474	+	40.5308i	0.988746	+	1.36089i	0.0567640	+	0.998388i	$0.481922\pi$
$888$		0			0
$889$	−4.88157	−	15.0239i	−0.163723	−	0.503886i
$890$		0			0
$891$	−10.5791	+	27.9685i	−0.354413	+	0.936981i
$892$		0			0
$893$	26.0462	−	8.46291i	0.871601	−	0.283200i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	78.7592	+	25.5904i	2.62969	+	0.854440i
$898$		0			0
$899$	−6.52451	−	4.74033i	−0.217605	−	0.158099i
$900$		0			0
$901$	37.6308			1.25366
$902$		0			0
$903$		−	17.7283i		−	0.589960i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	33.8559	+	11.0004i	1.12417	+	0.365264i	0.811356	−	0.584552i	$-0.198730\pi$
$907$	33.8559	+	11.0004i	1.12417	+	0.365264i	0.312810	+	0.949816i	$0.398730\pi$
$908$		0			0
$909$	23.7596	−	17.2623i	0.788055	−	0.572556i
$910$		0			0
$911$	14.7216	+	45.3086i	0.487750	+	1.50114i	0.827958	+	0.560790i	$0.189502\pi$
$911$	14.7216	+	45.3086i	0.487750	+	1.50114i	−0.340208	+	0.940350i	$0.610498\pi$
$912$		0			0
$913$	−38.4917	+	10.5163i	−1.27389	+	0.348039i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−10.3083	−	14.1881i	−0.340410	−	0.468534i
$918$		0			0
$919$	−17.3383	+	53.3617i	−0.571937	+	1.76024i	0.0744426	+	0.997225i	$0.476282\pi$
$919$	−17.3383	+	53.3617i	−0.571937	+	1.76024i	−0.646380	+	0.763016i	$0.723718\pi$
$920$		0			0
$921$	−12.6452	−	9.18726i	−0.416673	−	0.302731i
$922$		0			0
$923$		−	34.2669i		−	1.12791i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	58.8335	−	80.9773i	1.93235	−	2.65965i
$928$		0			0
$929$	8.31625	−	25.5948i	0.272847	−	0.839737i	−0.716934	−	0.697141i	$-0.754455\pi$
$929$	8.31625	−	25.5948i	0.272847	−	0.839737i	0.989781	−	0.142596i	$-0.0455450\pi$
$930$		0			0
$931$	−21.6126	+	15.7025i	−0.708325	+	0.514628i
$932$		0			0
$933$	−68.9375	+	22.3992i	−2.25691	+	0.733316i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−6.72349	+	2.18459i	−0.219647	+	0.0713676i	−0.416773	−	0.909010i	$-0.636839\pi$
$937$	−6.72349	+	2.18459i	−0.219647	+	0.0713676i	0.197126	+	0.980378i	$0.436839\pi$
$938$		0			0
$939$	31.8088	−	23.1104i	1.03804	−	0.754180i
$940$		0			0
$941$	−4.39849	+	13.5372i	−0.143387	+	0.441298i	−0.996800	−	0.0799361i	$-0.974528\pi$
$941$	−4.39849	+	13.5372i	−0.143387	+	0.441298i	0.853413	+	0.521235i	$0.174528\pi$
$942$		0			0
$943$	37.4992	−	51.6132i	1.22114	−	1.68076i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	14.1617i		−	0.460194i	−0.973168	−	0.230097i	$-0.926096\pi$
$947$		−	14.1617i		−	0.460194i	0.973168	−	0.230097i	$-0.0739044\pi$
$948$		0			0
$949$	−10.9833	−	7.97982i	−0.356533	−	0.259036i
$950$		0			0
$951$	6.56520	−	20.2056i	0.212891	−	0.655211i
$952$		0			0
$953$	−0.186709	−	0.256983i	−0.00604809	−	0.00832448i	0.805982	−	0.591940i	$-0.201638\pi$
$953$	−0.186709	−	0.256983i	−0.00604809	−	0.00832448i	−0.812030	+	0.583615i	$0.801638\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	17.2760	+	26.3193i	0.558452	+	0.850781i
$958$		0			0
$959$	−8.09179	−	24.9040i	−0.261298	−	0.804191i
$960$		0			0
$961$	19.8228	−	14.4021i	0.639446	−	0.464585i
$962$		0			0
$963$	13.5934	+	4.41678i	0.438042	+	0.142329i
$964$		0			0
$965$		0			0
$966$		0			0
$967$			37.3690i			1.20171i	0.799359	+	0.600853i	$0.205172\pi$
$967$			37.3690i			1.20171i	−0.799359	+	0.600853i	$0.794828\pi$
$968$		0			0
$969$	−74.7862			−2.40248
$970$		0			0
$971$	−24.6036	−	17.8756i	−0.789568	−	0.573655i	0.118267	−	0.992982i	$-0.462266\pi$
$971$	−24.6036	−	17.8756i	−0.789568	−	0.573655i	−0.907835	+	0.419327i	$0.862266\pi$
$972$		0			0
$973$	33.7129	+	10.9540i	1.08078	+	0.351168i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	20.5171	−	6.66642i	0.656401	−	0.213278i	0.0381668	−	0.999271i	$-0.487848\pi$
$977$	20.5171	−	6.66642i	0.656401	−	0.213278i	0.618235	+	0.785994i	$0.287848\pi$
$978$		0			0
$979$	43.2205	−	28.3699i	1.38133	−	0.906707i
$980$		0			0
$981$	28.4218	+	87.4732i	0.907437	+	2.79281i
$982$		0			0
$983$	6.78715	+	9.34171i	0.216477	+	0.297954i	0.903420	−	0.428756i	$-0.141048\pi$
$983$	6.78715	+	9.34171i	0.216477	+	0.297954i	−0.686944	+	0.726711i	$0.741048\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	12.6642	−	17.4308i	0.403106	−	0.554828i
$988$		0			0
$989$	−26.0264			−0.827591
$990$		0			0
$991$	10.6881			0.339518			0.169759	−	0.985486i	$-0.445701\pi$
$991$	10.6881			0.339518			0.169759	+	0.985486i	$0.445701\pi$
$992$		0			0
$993$	−3.10908	+	4.27928i	−0.0986636	+	0.135799i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−20.0593	−	27.6093i	−0.635285	−	0.874394i	0.363069	−	0.931762i	$-0.381729\pi$
$997$	−20.0593	−	27.6093i	−0.635285	−	0.874394i	−0.998353	+	0.0573683i	$0.981729\pi$
$998$		0			0
$999$	18.2269	+	56.0967i	0.576674	+	1.77482i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1100.2.cb.d.49.8		32
5.2	odd	4		1100.2.n.d.401.1	✓	16
5.3	odd	4		1100.2.n.e.401.4	yes	16
5.4	even	2	inner	1100.2.cb.d.49.1		32
11.9	even	5	inner	1100.2.cb.d.449.1		32
55.9	even	10	inner	1100.2.cb.d.449.8		32
55.42	odd	20		1100.2.n.d.801.1	yes	16
55.53	odd	20		1100.2.n.e.801.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1100.2.n.d.401.1	✓	16	5.2	odd	4
1100.2.n.d.801.1	yes	16	55.42	odd	20
1100.2.n.e.401.4	yes	16	5.3	odd	4
1100.2.n.e.801.4	yes	16	55.53	odd	20
1100.2.cb.d.49.1		32	5.4	even	2	inner
1100.2.cb.d.49.8		32	1.1	even	1	trivial
1100.2.cb.d.449.1		32	11.9	even	5	inner
1100.2.cb.d.449.8		32	55.9	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1100.cb (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.76353 - 2.42729i) q^{3} +(-0.992679 - 1.36631i) q^{7} +(-1.85465 - 5.70802i) q^{9} +(2.77267 - 1.81998i) q^{11} +(3.52887 - 1.14660i) q^{13} +(3.68071 + 1.19594i) q^{17} +(-5.21062 - 3.78574i) q^{19} -5.06704 q^{21} +7.43878i q^{23} +(-8.56540 - 2.78307i) q^{27} +(-2.55959 + 1.85965i) q^{29} +(0.787699 + 2.42429i) q^{31} +(0.472068 - 9.93965i) q^{33} +(-3.84954 - 5.29843i) q^{37} +(3.44014 - 10.5877i) q^{39} +(-6.93840 - 5.04104i) q^{41} +3.49875i q^{43} +(-2.49933 + 3.44003i) q^{47} +(1.28174 - 3.94479i) q^{49} +(9.39392 - 6.82509i) q^{51} +(9.24750 - 3.00470i) q^{53} +(-18.3782 + 5.97143i) q^{57} +(-2.33853 + 1.69904i) q^{59} +(1.93043 - 5.94126i) q^{61} +(-5.95783 + 8.20025i) q^{63} +10.5387i q^{67} +(18.0561 + 13.1185i) q^{69} +(2.85383 - 8.78318i) q^{71} +(-2.15062 - 2.96007i) q^{73} +(-5.23901 - 1.98166i) q^{77} +(5.23846 + 16.1223i) q^{79} +(-7.29404 + 5.29943i) q^{81} +(-11.4422 - 3.71779i) q^{83} +9.49240i q^{87} +15.5881 q^{89} +(-5.06965 - 3.68331i) q^{91} +(7.27358 + 2.36333i) q^{93} +(6.38135 - 2.07343i) q^{97} +(-15.5308 - 12.4510i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 10 q^{11} - 26 q^{19} - 12 q^{21} + 14 q^{29} + 4 q^{31} + 34 q^{39} - 30 q^{41} + 48 q^{49} + 26 q^{51} - 12 q^{59} + 48 q^{61} + 106 q^{69} + 72 q^{71} + 90 q^{79} + 34 q^{81} - 36 q^{89} + 76 q^{91}+ \cdots - 80 q^{99}+O(q^{100}) \) 32 * q - 10 * q^11 - 26 * q^19 - 12 * q^21 + 14 * q^29 + 4 * q^31 + 34 * q^39 - 30 * q^41 + 48 * q^49 + 26 * q^51 - 12 * q^59 + 48 * q^61 + 106 * q^69 + 72 * q^71 + 90 * q^79 + 34 * q^81 - 36 * q^89 + 76 * q^91 - 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more