LMFDB - Embedded newform 1100.2.cb.d.449.8

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			449.8
Character	$\chi$	$=$	1100.449
Dual form			1100.2.cb.d.49.8

$q$-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 $\left(\mathbb{Z}/1100\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$551$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$-1$	$1$

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	0.913476	+	0.406892i	$0.133388\pi$
$3$	1.76353	+	2.42729i	1.01817	+	1.40140i	0.104698	+	0.994504i	$0.466612\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.992679	+	1.36631i	−0.375197	+	0.516415i	−0.954304	−	0.298837i	$-0.903401\pi$
$7$	−0.992679	+	1.36631i	−0.375197	+	0.516415i	0.579107	+	0.815252i	$0.303401\pi$
$8$		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	0.754336	−	0.656488i	$-0.227959\pi$
$13$	3.52887	+	1.14660i	0.978733	+	0.318010i	0.224397	+	0.974498i	$0.427959\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.68071	−	1.19594i	0.892704	−	0.290057i	0.173481	−	0.984837i	$-0.444498\pi$
$17$	3.68071	−	1.19594i	0.892704	−	0.290057i	0.719222	+	0.694780i	$0.244498\pi$
$18$		0			0
$19$	−5.21062	+	3.78574i	−1.19540	+	0.868508i	−0.993824	−	0.110965i	$-0.964606\pi$
$19$	−5.21062	+	3.78574i	−1.19540	+	0.868508i	−0.201575	+	0.979473i	$0.564606\pi$
$20$		0			0
$21$	−5.06704			−1.10572
$22$		0			0
$23$		−	7.43878i		−	1.55109i	−0.631291	−	0.775546i	$-0.717475\pi$
$23$		−	7.43878i		−	1.55109i	0.631291	−	0.775546i	$-0.282525\pi$
$24$		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	0.324201	−	0.945988i	$-0.394905\pi$
$29$	−2.55959	−	1.85965i	−0.475303	−	0.345328i	−0.799505	+	0.600660i	$0.794905\pi$
$30$		0			0
$31$	0.787699	−	2.42429i	0.141475	−	0.435415i	−0.855066	−	0.518519i	$-0.826483\pi$
$31$	0.787699	−	2.42429i	0.141475	−	0.435415i	0.996541	+	0.0831043i	$0.0264835\pi$
$32$		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	−0.998210	−	0.0598135i	$-0.980949\pi$
$37$	−3.84954	+	5.29843i	−0.632860	+	0.871057i	0.365350	+	0.930870i	$0.380949\pi$
$38$		0			0
$39$	3.44014	+	10.5877i	0.550863	+	1.69538i
$40$		0			0
$41$	−6.93840	+	5.04104i	−1.08360	+	0.787279i	−0.978306	−	0.207163i	$-0.933577\pi$
$41$	−6.93840	+	5.04104i	−1.08360	+	0.787279i	−0.105290	+	0.994442i	$0.533577\pi$
$42$		0			0
$43$		−	3.49875i		−	0.533554i	−0.963758	−	0.266777i	$-0.914041\pi$
$43$		−	3.49875i		−	0.533554i	0.963758	−	0.266777i	$-0.0859587\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.49933	−	3.44003i	−0.364565	−	0.501781i	0.586849	−	0.809697i	$-0.300368\pi$
$47$	−2.49933	−	3.44003i	−0.364565	−	0.501781i	−0.951414	+	0.307916i	$0.900368\pi$
$48$		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	0.865133	−	0.501542i	$-0.167234\pi$
$53$	9.24750	+	3.00470i	1.27024	+	0.412727i	0.405109	+	0.914269i	$0.367234\pi$
$54$		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	0.425061	−	0.905165i	$-0.360253\pi$
$59$	−2.33853	−	1.69904i	−0.304450	−	0.221196i	−0.729512	+	0.683968i	$0.760253\pi$
$60$		0			0
$61$	1.93043	+	5.94126i	0.247167	+	0.760700i	0.995273	+	0.0971212i	$0.0309634\pi$
$61$	1.93043	+	5.94126i	0.247167	+	0.760700i	−0.748106	+	0.663579i	$0.769037\pi$
$62$		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	$-0.777377\pi$
$67$		−	10.5387i		−	1.28750i	0.765235	−	0.643751i	$-0.222623\pi$
$68$		0			0
$69$	18.0561	−	13.1185i	2.17369	−	1.57928i
$70$		0			0
$71$	2.85383	+	8.78318i	0.338687	+	1.04237i	0.964877	+	0.262701i	$0.0846133\pi$
$71$	2.85383	+	8.78318i	0.338687	+	1.04237i	−0.626190	+	0.779670i	$0.715387\pi$
$72$		0			0
$73$	−2.15062	+	2.96007i	−0.251711	+	0.346450i	−0.916110	−	0.400928i	$-0.868688\pi$
$73$	−2.15062	+	2.96007i	−0.251711	+	0.346450i	0.664399	+	0.747378i	$0.268688\pi$
$74$		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	0.00842422	−	0.999965i	$-0.497318\pi$
$79$	5.23846	−	16.1223i	0.589373	−	1.81390i	0.580949	−	0.813940i	$-0.302682\pi$
$80$		0			0
$81$	−7.29404	−	5.29943i	−0.810449	−	0.588825i
$82$		0			0
$83$	−11.4422	+	3.71779i	−1.25594	+	0.408080i	−0.860047	−	0.510215i	$-0.829566\pi$
$83$	−11.4422	+	3.71779i	−1.25594	+	0.408080i	−0.395896	+	0.918296i	$0.629566\pi$
$84$		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	0.614500	−	0.788916i	$-0.289358\pi$
$97$	6.38135	+	2.07343i	0.647928	+	0.210525i	0.0334279	+	0.999441i	$0.489358\pi$
$98$		0			0
$99$	−15.5308	+	12.4510i	−1.56090	+	1.25138i
$100$		0			0
$101$	1.51211	−	4.65380i	0.150461	−	0.463071i	−0.847212	−	0.531255i	$-0.821721\pi$
$101$	1.51211	−	4.65380i	0.150461	−	0.463071i	0.997673	+	0.0681843i	$0.0217206\pi$
$102$		0			0
$103$	9.80269	−	13.4922i	0.965888	−	1.32943i	0.0217908	−	0.999763i	$-0.493063\pi$
$103$	9.80269	−	13.4922i	0.965888	−	1.32943i	0.944097	−	0.329668i	$-0.106937\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.39979	−	1.92664i	−0.135323	−	0.186256i	0.735978	−	0.677006i	$-0.236723\pi$
$107$	−1.39979	−	1.92664i	−0.135323	−	0.186256i	−0.871300	+	0.490750i	$0.836723\pi$
$108$		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	0.757819	−	0.652465i	$-0.226265\pi$
$113$	−1.02997	−	1.41763i	−0.0968910	−	0.133359i	−0.854710	+	0.519106i	$0.826265\pi$
$114$		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	0.113546	−	0.993533i	$-0.463779\pi$
$127$	8.89597	−	2.89048i	0.789390	−	0.256488i	0.675844	+	0.737045i	$0.263779\pi$
$128$		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	0.398408	−	0.917208i	$-0.369563\pi$
$137$	14.7461	−	4.79131i	1.25985	−	0.409349i	0.861440	+	0.507859i	$0.169563\pi$
$138$		0			0
$139$	−16.9807	−	12.3372i	−1.44029	−	1.04643i	−0.987982	−	0.154567i	$-0.950602\pi$
$139$	−16.9807	−	12.3372i	−1.44029	−	1.04643i	−0.452305	−	0.891863i	$-0.649398\pi$
$140$		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	0.981127	−	0.193363i	$-0.0619397\pi$
$149$	0.899897	+	2.76960i	0.0737224	+	0.226894i	−0.907405	+	0.420258i	$0.861940\pi$
$150$		0			0
$151$	3.65731	−	2.65719i	0.297628	−	0.216239i	−0.428942	−	0.903332i	$-0.641113\pi$
$151$	3.65731	−	2.65719i	0.297628	−	0.216239i	0.726570	+	0.687093i	$0.241113\pi$
$152$		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	0.969452	−	0.245279i	$-0.0788796\pi$
$157$	5.47059	+	7.52962i	0.436601	+	0.600929i	−0.532852	+	0.846209i	$0.678880\pi$
$158$		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	0.739635	−	0.673008i	$-0.234998\pi$
$163$	12.0321	+	3.90948i	0.942429	+	0.306214i	0.202794	+	0.979221i	$0.434998\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	16.1672	+	5.25303i	1.25105	+	0.406492i	0.858298	−	0.513152i	$-0.171522\pi$
$167$	16.1672	+	5.25303i	1.25105	+	0.406492i	0.392754	+	0.919643i	$0.371522\pi$
$168$		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	0.991106	−	0.133074i	$-0.0424849\pi$
$173$	7.34298	+	10.1067i	0.558276	+	0.768401i	−0.432830	+	0.901476i	$0.642485\pi$
$174$		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	−0.548609	−	0.836079i	$-0.684842\pi$
$179$	1.03046	−	0.748673i	0.0770202	−	0.0559584i	0.625629	+	0.780121i	$0.284842\pi$
$180$		0			0
$181$	−5.34282	−	16.4435i	−0.397129	−	1.22224i	−0.927291	−	0.374341i	$-0.877869\pi$
$181$	−5.34282	−	16.4435i	−0.397129	−	1.22224i	0.530162	−	0.847896i	$-0.322131\pi$
$182$		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	0.934183	−	0.356794i	$-0.116130\pi$
$191$	12.2106	+	8.87154i	0.883530	+	0.641922i	−0.0506530	+	0.998716i	$0.516130\pi$
$192$		0			0
$193$	20.8527	−	6.77546i	1.50101	−	0.487708i	0.560699	−	0.828020i	$-0.310533\pi$
$193$	20.8527	−	6.77546i	1.50101	−	0.487708i	0.940313	+	0.340312i	$0.110533\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	19.4874i		−	1.38842i	−0.719772	−	0.694210i	$-0.755754\pi$
$197$		−	19.4874i		−	1.38842i	0.719772	−	0.694210i	$-0.244246\pi$
$198$		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	0.207687	+	0.978195i	$0.433406\pi$
$211$	−7.77574	+	23.9313i	−0.535304	+	1.64750i	−0.742991	+	0.669301i	$0.766594\pi$
$212$		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	−0.912959	−	0.408051i	$-0.866208\pi$
$223$	−15.2157	−	20.9426i	−1.01892	−	1.40242i	−0.105960	−	0.994370i	$-0.533792\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−14.4444	+	19.8810i	−0.958710	+	1.31955i	−0.0111621	+	0.999938i	$0.503553\pi$
$227$	−14.4444	+	19.8810i	−0.958710	+	1.31955i	−0.947548	+	0.319614i	$0.896447\pi$
$228$		0			0
$229$	−3.90485	+	12.0179i	−0.258040	+	0.794165i	0.735175	+	0.677877i	$0.237100\pi$
$229$	−3.90485	+	12.0179i	−0.258040	+	0.794165i	−0.993215	+	0.116289i	$0.962900\pi$
$230$		0			0
$231$	−14.0492	−	9.22189i	−0.924370	−	0.606756i
$232$		0			0
$233$	−6.07238	−	1.97304i	−0.397815	−	0.129258i	0.103276	−	0.994653i	$-0.467068\pi$
$233$	−6.07238	−	1.97304i	−0.397815	−	0.129258i	−0.501090	+	0.865395i	$0.667068\pi$
$234$		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	−0.175359	−	0.984505i	$-0.556109\pi$
$239$	10.9264	−	7.93851i	0.706771	−	0.513499i	0.882130	+	0.471005i	$0.156109\pi$
$240$		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	−0.866197	−	0.499703i	$-0.833442\pi$
$251$	2.03249	−	6.25535i	0.128289	−	0.394834i	0.994486	+	0.104869i	$0.0334424\pi$
$252$		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	−0.294485	−	0.955656i	$-0.595148\pi$
$257$	11.3084	−	15.5647i	0.705399	−	0.970898i	0.999884	−	0.0152419i	$-0.00485184\pi$
$258$		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	$-0.951734\pi$
$263$		−	4.89929i		−	0.302103i	0.988526	−	0.151052i	$-0.0482660\pi$
$264$		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	0.910286	−	0.413979i	$-0.135861\pi$
$269$	−1.13958	−	3.50727i	−0.0694814	−	0.213842i	−0.979768	+	0.200137i	$0.935861\pi$
$270$		0			0
$271$	−3.28380	−	2.38582i	−0.199477	−	0.144928i	0.483563	−	0.875310i	$-0.339342\pi$
$271$	−3.28380	−	2.38582i	−0.199477	−	0.144928i	−0.683040	+	0.730381i	$0.739342\pi$
$272$		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	−0.0151373	−	0.999885i	$-0.504819\pi$
$277$	−10.2373	−	3.32631i	−0.615101	−	0.199859i	−0.599964	+	0.800027i	$0.704819\pi$
$278$		0			0
$279$	12.3770	+	8.99240i	0.740991	+	0.538361i
$280$		0			0
$281$	−4.18268	−	12.8730i	−0.249518	−	0.767936i	−0.994860	−	0.101255i	$-0.967714\pi$
$281$	−4.18268	−	12.8730i	−0.249518	−	0.767936i	0.745343	−	0.666681i	$-0.232286\pi$
$282$		0			0
$283$	−6.57386	−	9.04814i	−0.390775	−	0.537856i	0.567624	−	0.823288i	$-0.307863\pi$
$283$	−6.57386	−	9.04814i	−0.390775	−	0.537856i	−0.958399	+	0.285432i	$0.907863\pi$
$284$		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	−0.941960	−	0.335724i	$-0.891019\pi$
$293$	−5.67584	+	7.81212i	−0.331586	+	0.456389i	0.610374	+	0.792113i	$0.291019\pi$
$294$		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	$0.0474971\pi$
$307$			5.20959i			0.297327i	−0.988888	+	0.148664i	$0.952503\pi$
$308$		0			0
$309$	50.0369			2.84650
$310$		0			0
$311$	−19.5453	+	14.2005i	−1.10831	+	0.805237i	−0.982397	−	0.186803i	$-0.940187\pi$
$311$	−19.5453	+	14.2005i	−1.10831	+	0.805237i	−0.125917	+	0.992041i	$0.540187\pi$
$312$		0			0
$313$	12.4633	−	4.04956i	0.704465	−	0.228895i	0.0651903	−	0.997873i	$-0.479235\pi$
$313$	12.4633	−	4.04956i	0.704465	−	0.228895i	0.639275	+	0.768978i	$0.279235\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	6.73454	+	2.18818i	0.378249	+	0.122901i	0.491970	−	0.870612i	$-0.336277\pi$
$317$	6.73454	+	2.18818i	0.378249	+	0.122901i	−0.113721	+	0.993513i	$0.536277\pi$
$318$		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	−0.955536	−	0.294874i	$-0.904722\pi$
$337$	−6.97253	+	9.59687i	−0.379818	+	0.522775i	0.575718	+	0.817648i	$0.304722\pi$
$338$		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	−0.0935864	−	0.995611i	$-0.529833\pi$
$347$	7.74747	−	2.51731i	0.415906	−	0.135136i	0.509493	+	0.860475i	$0.329833\pi$
$348$		0			0
$349$	13.8784	−	10.0832i	0.742893	−	0.539743i	−0.150723	−	0.988576i	$-0.548160\pi$
$349$	13.8784	−	10.0832i	0.742893	−	0.539743i	0.893616	+	0.448833i	$0.148160\pi$
$350$		0			0
$351$	−33.4173			−1.78368
$352$		0			0
$353$			9.89553i			0.526686i	0.964702	+	0.263343i	$0.0848251\pi$
$353$			9.89553i			0.526686i	−0.964702	+	0.263343i	$0.915175\pi$
$354$		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	0.894561	+	0.446946i	$0.147488\pi$
$359$	30.2411	+	21.9715i	1.59607	+	1.15961i	0.701506	+	0.712664i	$0.252512\pi$
$360$		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	−0.400403	−	0.916339i	$-0.631130\pi$
$367$	11.3951	−	15.6840i	0.594819	−	0.818698i	0.995222	+	0.0976415i	$0.0311299\pi$
$368$		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	$-0.991533\pi$
$373$		−	1.02733i		−	0.0531933i	0.999646	−	0.0265967i	$-0.00846698\pi$
$374$		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	0.873357	−	0.487080i	$-0.161938\pi$
$379$	−2.32646	−	7.16010i	−0.119502	−	0.367790i	−0.992859	+	0.119290i	$0.961938\pi$
$380$		0			0
$381$	22.7043	+	16.4957i	1.16318	+	0.845098i
$382$		0			0
$383$	−14.3960	−	4.67756i	−0.735603	−	0.239012i	−0.0828281	−	0.996564i	$-0.526395\pi$
$383$	−14.3960	−	4.67756i	−0.735603	−	0.239012i	−0.652775	+	0.757552i	$0.726395\pi$
$384$		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	0.687103	−	0.726560i	$-0.258882\pi$
$389$	4.11088	+	2.98673i	0.208430	+	0.151433i	−0.478673	+	0.877993i	$0.658882\pi$
$390$		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	$0.0463345\pi$
$397$			5.78023i			0.290101i	−0.989424	+	0.145051i	$0.953665\pi$
$398$		0			0
$399$	26.4024	−	19.1825i	1.32177	−	0.960326i
$400$		0			0
$401$	7.23049	+	22.2532i	0.361074	+	1.11127i	0.952403	+	0.304841i	$0.0986032\pi$
$401$	7.23049	+	22.2532i	0.361074	+	1.11127i	−0.591330	+	0.806430i	$0.701397\pi$
$402$		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	−0.994832	−	0.101531i	$-0.967626\pi$
$409$	−2.63551	+	8.11126i	−0.130318	+	0.401076i	0.864515	+	0.502607i	$0.167626\pi$
$410$		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	−0.0335437	−	0.999437i	$-0.510679\pi$
$421$	18.6021	−	13.5152i	0.906612	−	0.658692i	0.940156	+	0.340745i	$0.110679\pi$
$422$		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	−0.934030	−	0.357193i	$-0.883734\pi$
$431$	0.655391	−	2.01708i	0.0315691	−	0.0971596i	0.965600	+	0.260034i	$0.0837337\pi$
$432$		0			0
$433$	16.0975	−	22.1563i	0.773597	−	1.06476i	−0.222363	−	0.974964i	$-0.571377\pi$
$433$	16.0975	−	22.1563i	0.773597	−	1.06476i	0.995960	−	0.0898005i	$-0.0286230\pi$
$434$		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	0.704792	−	0.709414i	$-0.251040\pi$
$443$	−3.95050	−	5.43740i	−0.187694	−	0.258339i	−0.892486	+	0.451076i	$0.851040\pi$
$444$		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	−0.999990	−	0.00450672i	$-0.998565\pi$
$449$	−3.99069	+	12.2821i	−0.188332	+	0.579627i	0.811658	+	0.584133i	$0.198565\pi$
$450$		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	−0.546448	−	0.837493i	$-0.684020\pi$
$457$	−10.6090	+	3.44706i	−0.496267	+	0.161247i	0.0501808	+	0.998740i	$0.484020\pi$
$458$		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	$-0.919377\pi$
$463$		−	10.7840i		−	0.501173i	0.968094	−	0.250586i	$-0.0806234\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−19.8907	+	6.46289i	−0.920433	+	0.299067i	−0.730644	−	0.682758i	$-0.760780\pi$
$467$	−19.8907	+	6.46289i	−0.920433	+	0.299067i	−0.189789	+	0.981825i	$0.560780\pi$
$468$		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	0.998542	−	0.0539745i	$-0.0171890\pi$
$479$	3.47943	+	10.7086i	0.158979	+	0.489288i	−0.839563	+	0.543262i	$0.817189\pi$
$480$		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	0.907131	−	0.420848i	$-0.138268\pi$
$487$	4.99978	+	6.88160i	0.226562	+	0.311835i	−0.680569	+	0.732684i	$0.738268\pi$
$488$		0			0
$489$	11.7296	+	36.0999i	0.530430	+	1.63250i
$490$		0			0
$491$	−11.2974	−	8.20808i	−0.509847	−	0.370425i	0.302919	−	0.953016i	$-0.402039\pi$
$491$	−11.2974	−	8.20808i	−0.509847	−	0.370425i	−0.812765	+	0.582591i	$0.802039\pi$
$492$		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	0.483146	−	0.875540i	$-0.339494\pi$
$499$	−4.47304	−	3.24985i	−0.200241	−	0.145483i	−0.683387	+	0.730056i	$0.739494\pi$
$500$		0			0
$501$	15.7606	+	48.5062i	0.704133	+	2.16710i
$502$		0			0
$503$	5.40452	+	7.43868i	0.240976	+	0.331674i	0.912325	−	0.409466i	$-0.134285\pi$
$503$	5.40452	+	7.43868i	0.240976	+	0.331674i	−0.671350	+	0.741141i	$0.734285\pi$
$504$		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	−0.371033	−	0.928620i	$-0.620996\pi$
$509$	8.96759	−	6.51534i	0.397482	−	0.288787i	0.768514	+	0.639832i	$0.220996\pi$
$510$		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	0.211786	−	0.977316i	$-0.432072\pi$
$521$	−14.8879	−	10.8167i	−0.652252	−	0.473889i	−0.864038	+	0.503427i	$0.832072\pi$
$522$		0			0
$523$	−23.4323	+	7.61361i	−1.02462	+	0.332920i	−0.772662	−	0.634818i	$-0.781075\pi$
$523$	−23.4323	+	7.61361i	−1.02462	+	0.332920i	−0.251960	+	0.967738i	$0.581075\pi$
$524$		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	−0.897946	−	0.440106i	$-0.854941\pi$
$541$	2.02811	−	6.24188i	0.0871953	−	0.268360i	0.985141	+	0.171746i	$0.0549409\pi$
$542$		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	0.817137	−	0.576443i	$-0.195560\pi$
$547$	0.383526	+	0.527878i	0.0163984	+	0.0225704i	−0.800739	+	0.599013i	$0.795560\pi$
$548$		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	−0.787295	−	0.616576i	$-0.788519\pi$
$557$	1.00048	−	1.37704i	0.0423915	−	0.0583469i	0.829687	+	0.558230i	$0.188519\pi$
$558$		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	0.996309	−	0.0858390i	$-0.0273571\pi$
$563$	41.5681	+	13.5063i	1.75189	+	0.569222i	0.755576	+	0.655061i	$0.227357\pi$
$564$		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	−0.974658	−	0.223700i	$-0.928187\pi$
$569$	−25.3587	+	18.4242i	−1.06309	+	0.772382i	−0.0884349	+	0.996082i	$0.528187\pi$
$570$		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	−0.771261	−	0.636519i	$-0.780374\pi$
$577$	−24.5274	+	7.96943i	−1.02109	+	0.331772i	−0.249827	+	0.968290i	$0.580374\pi$
$578$		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	−0.821726	−	0.569882i	$-0.806989\pi$
$587$	−0.625301	+	0.860653i	−0.0258089	+	0.0355229i	0.795918	+	0.605405i	$0.206989\pi$
$588$		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	$0.133199\pi$
$593$			19.7906i			0.812702i	−0.913717	+	0.406351i	$0.866801\pi$
$594$		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	0.975599	−	0.219559i	$-0.0704619\pi$
$599$	1.40163	+	4.31378i	0.0572692	+	0.176256i	−0.918330	+	0.395816i	$0.870462\pi$
$600$		0			0
$601$	−38.2474	−	27.7883i	−1.56014	−	1.13351i	−0.935892	−	0.352286i	$-0.885404\pi$
$601$	−38.2474	−	27.7883i	−1.56014	−	1.13351i	−0.624251	−	0.781224i	$-0.714596\pi$
$602$		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	0.543033	−	0.839711i	$-0.317276\pi$
$607$	12.0424	+	3.91282i	0.488787	+	0.158817i	−0.0542464	+	0.998528i	$0.517276\pi$
$608$		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	0.649835	−	0.760075i	$-0.274838\pi$
$613$	−6.78018	−	9.33212i	−0.273849	−	0.376921i	−0.923684	+	0.383154i	$0.874838\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			9.58142i			0.385733i	0.981225	+	0.192867i	$0.0617785\pi$
$617$			9.58142i			0.385733i	−0.981225	+	0.192867i	$0.938221\pi$
$618$		0			0
$619$	−0.972177	+	0.706328i	−0.0390751	+	0.0283897i	−0.607151	−	0.794586i	$-0.707688\pi$
$619$	−0.972177	+	0.706328i	−0.0390751	+	0.0283897i	0.568076	+	0.822976i	$0.307688\pi$
$620$		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	0.332882	−	0.942968i	$-0.391979\pi$
$631$	−11.5819	−	8.41474i	−0.461068	−	0.334985i	−0.793950	+	0.607983i	$0.791979\pi$
$632$		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	0.190637	−	0.981661i	$-0.438945\pi$
$641$	29.9553	−	21.7638i	1.18316	−	0.859618i	0.992525	+	0.122043i	$0.0389445\pi$
$642$		0			0
$643$	4.25667	−	1.38308i	0.167867	−	0.0545432i	−0.223878	−	0.974617i	$-0.571872\pi$
$643$	4.25667	−	1.38308i	0.167867	−	0.0545432i	0.391745	+	0.920074i	$0.371872\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−27.1713	−	8.82850i	−1.06822	−	0.347084i	−0.278423	−	0.960458i	$-0.589812\pi$
$647$	−27.1713	−	8.82850i	−1.06822	−	0.347084i	−0.789792	+	0.613374i	$0.789812\pi$
$648$		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	−0.816704	−	0.577057i	$-0.804201\pi$
$653$	−0.396454	+	0.545672i	−0.0155144	+	0.0213538i	0.801189	+	0.598411i	$0.204201\pi$
$654$		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	0.338188	−	0.941079i	$-0.390186\pi$
$673$	1.52112	+	0.494242i	0.0586349	+	0.0190516i	−0.279553	+	0.960130i	$0.590186\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	9.91287	−	3.22089i	0.380982	−	0.123789i	−0.112264	−	0.993678i	$-0.535810\pi$
$677$	9.91287	−	3.22089i	0.380982	−	0.123789i	0.493246	+	0.869890i	$0.335810\pi$
$678$		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	$-0.737209\pi$
$683$		−	38.4144i		−	1.46988i	0.678130	−	0.734942i	$-0.262791\pi$
$684$		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	−0.795199	−	0.606349i	$-0.792633\pi$
$691$	5.37655	−	16.5473i	0.204534	−	0.629490i	0.999732	−	0.0231407i	$-0.00736657\pi$
$692$		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	−0.625771	+	0.780007i	$0.715216\pi$
$701$	−41.3290	+	30.0273i	−1.56098	+	1.13412i	−0.935204	+	0.354109i	$0.884784\pi$
$702$		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	0.992332	−	0.123603i	$-0.0394448\pi$
$709$	3.11182	+	9.57719i	0.116867	+	0.359679i	−0.875465	+	0.483281i	$0.839445\pi$
$710$		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	0.201867	−	0.979413i	$-0.435299\pi$
$719$	−17.8912	−	12.9987i	−0.667230	−	0.484771i	−0.869097	+	0.494642i	$0.835299\pi$
$720$		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	$0.159276\pi$
$727$			25.8714i			0.959517i	−0.877401	+	0.479758i	$0.840724\pi$
$728$		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	−0.201274	−	0.979535i	$-0.564508\pi$
$733$	21.4566	−	29.5324i	0.792516	−	1.09080i	0.993790	−	0.111270i	$-0.0354917\pi$
$734$		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	0.797055	+	0.603907i	$0.206390\pi$
$739$	−5.51149	+	16.9626i	−0.202743	+	0.623980i	−0.999799	+	0.0200734i	$0.993610\pi$
$740$		0			0
$741$	−58.0074	−	42.1448i	−2.13096	−	1.54823i
$742$		0			0
$743$	−37.6450	+	12.2316i	−1.38106	+	0.448733i	−0.903018	−	0.429604i	$-0.858653\pi$
$743$	−37.6450	+	12.2316i	−1.38106	+	0.448733i	−0.478042	+	0.878337i	$0.658653\pi$
$744$		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	−0.478257	−	0.878220i	$-0.658731\pi$
$751$	5.73271	−	4.16506i	0.209190	−	0.151985i	0.687447	+	0.726235i	$0.258731\pi$
$752$		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	0.168774	−	0.985655i	$-0.446019\pi$
$757$	−7.53982	−	2.44983i	−0.274039	−	0.0890407i	−0.442813	+	0.896614i	$0.646019\pi$
$758$		0			0
$759$	73.9388	−	3.51161i	2.68381	−	0.127463i
$760$		0			0
$761$	9.04626	−	27.8415i	0.327927	−	1.00925i	−0.642175	−	0.766558i	$-0.721968\pi$
$761$	9.04626	−	27.8415i	0.327927	−	1.00925i	0.970102	−	0.242697i	$-0.0780321\pi$
$762$		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	0.780880	−	0.624682i	$-0.214771\pi$
$773$	−1.51617	−	2.08683i	−0.0545329	−	0.0750581i	−0.835413	+	0.549623i	$0.814771\pi$
$774$		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	−0.531811	−	0.846863i	$-0.678488\pi$
$787$	−13.0248	+	4.23200i	−0.464282	+	0.150854i	0.0675291	+	0.997717i	$0.478488\pi$
$788$		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	−0.957160	−	0.289561i	$-0.906491\pi$
$797$	−44.0779	+	14.3218i	−1.56132	+	0.507303i	−0.604159	+	0.796864i	$0.706491\pi$
$798$		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	0.901078	−	0.433658i	$-0.142777\pi$
$809$	−2.35528	−	7.24879i	−0.0828071	−	0.254854i	−0.983885	+	0.178804i	$0.942777\pi$
$810$		0			0
$811$	−23.5550	+	17.1137i	−0.827127	+	0.600943i	−0.918745	−	0.394851i	$-0.870796\pi$
$811$	−23.5550	+	17.1137i	−0.827127	+	0.600943i	0.0916180	+	0.995794i	$0.470796\pi$
$812$		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	−0.996292	−	0.0860379i	$-0.972579\pi$
$821$	−39.7129	−	28.8531i	−1.38599	−	1.00698i	−0.389698	−	0.920943i	$-0.627421\pi$
$822$		0			0
$823$	−53.1942	−	17.2838i	−1.85423	−	0.602476i	−0.996015	−	0.0891893i	$-0.971572\pi$
$823$	−53.1942	−	17.2838i	−1.85423	−	0.602476i	−0.858217	−	0.513287i	$-0.828428\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−18.3419	−	5.95965i	−0.637811	−	0.207237i	−0.0277792	−	0.999614i	$-0.508844\pi$
$827$	−18.3419	−	5.95965i	−0.637811	−	0.207237i	−0.610032	+	0.792377i	$0.708844\pi$
$828$		0			0
$829$	−13.8870	−	10.0895i	−0.482316	−	0.350423i	0.319906	−	0.947449i	$-0.396349\pi$
$829$	−13.8870	−	10.0895i	−0.482316	−	0.350423i	−0.802222	+	0.597026i	$0.796349\pi$
$830$		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	0.0820317	−	0.996630i	$-0.473859\pi$
$839$	30.5653	−	22.2070i	1.05523	−	0.766671i	0.973200	+	0.229959i	$0.0738591\pi$
$840$		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	−0.476002	−	0.879444i	$-0.657914\pi$
$853$	−10.0519	+	3.26607i	−0.344171	+	0.111828i	0.131831	+	0.991272i	$0.457914\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		−	14.6489i		−	0.500395i	−0.968195	−	0.250198i	$-0.919504\pi$
$857$		−	14.6489i		−	0.500395i	0.968195	−	0.250198i	$-0.0804956\pi$
$858$		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	−0.958323	−	0.285687i	$-0.907778\pi$
$863$	−45.9954	+	14.9448i	−1.56570	+	0.508727i	−0.607377	+	0.794414i	$0.707778\pi$
$864$		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	0.877926	−	0.478795i	$-0.158926\pi$
$877$	4.47976	+	6.16586i	0.151271	+	0.208206i	−0.726656	+	0.687002i	$0.758926\pi$
$878$		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	0.995878	−	0.0907061i	$-0.0289124\pi$
$883$	17.8847	+	24.6162i	0.601868	+	0.828400i	−0.394010	+	0.919106i	$0.628912\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	29.4474	−	40.5308i	0.988746	−	1.36089i	0.0567640	−	0.998388i	$-0.481922\pi$
$887$	29.4474	−	40.5308i	0.988746	−	1.36089i	0.931982	−	0.362504i	$-0.118078\pi$
$888$		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	0.312810	−	0.949816i	$-0.398730\pi$
$907$	33.8559	−	11.0004i	1.12417	−	0.365264i	0.811356	+	0.584552i	$0.198730\pi$
$908$		0			0
$909$	23.7596	+	17.2623i	0.788055	+	0.572556i
$910$		0			0
$911$	14.7216	−	45.3086i	0.487750	−	1.50114i	−0.340208	−	0.940350i	$-0.610498\pi$
$911$	14.7216	−	45.3086i	0.487750	−	1.50114i	0.827958	−	0.560790i	$-0.189502\pi$
$912$		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	−0.646380	−	0.763016i	$-0.723718\pi$
$919$	−17.3383	−	53.3617i	−0.571937	−	1.76024i	0.0744426	−	0.997225i	$-0.476282\pi$
$920$		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	0.989781	+	0.142596i	$0.0455450\pi$
$929$	8.31625	+	25.5948i	0.272847	+	0.839737i	−0.716934	+	0.697141i	$0.754455\pi$
$930$		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	0.197126	−	0.980378i	$-0.436839\pi$
$937$	−6.72349	−	2.18459i	−0.219647	−	0.0713676i	−0.416773	+	0.909010i	$0.636839\pi$
$938$		0			0
$939$	31.8088	+	23.1104i	1.03804	+	0.754180i
$940$		0			0
$941$	−4.39849	−	13.5372i	−0.143387	−	0.441298i	0.853413	−	0.521235i	$-0.174528\pi$
$941$	−4.39849	−	13.5372i	−0.143387	−	0.441298i	−0.996800	+	0.0799361i	$0.974528\pi$
$942$		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	$0.0739044\pi$
$947$			14.1617i			0.460194i	−0.973168	+	0.230097i	$0.926096\pi$
$948$		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	−0.812030	−	0.583615i	$-0.801638\pi$
$953$	−0.186709	+	0.256983i	−0.00604809	+	0.00832448i	0.805982	+	0.591940i	$0.201638\pi$
$954$		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	$-0.794828\pi$
$967$		−	37.3690i		−	1.20171i	0.799359	−	0.600853i	$-0.205172\pi$
$968$		0			0
$969$	−74.7862			−2.40248
$970$		0			0
$971$	−24.6036	+	17.8756i	−0.789568	+	0.573655i	−0.907835	−	0.419327i	$-0.862266\pi$
$971$	−24.6036	+	17.8756i	−0.789568	+	0.573655i	0.118267	+	0.992982i	$0.462266\pi$
$972$		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	0.618235	−	0.785994i	$-0.287848\pi$
$977$	20.5171	+	6.66642i	0.656401	+	0.213278i	0.0381668	+	0.999271i	$0.487848\pi$
$978$		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	−0.686944	−	0.726711i	$-0.741048\pi$
$983$	6.78715	−	9.34171i	0.216477	−	0.297954i	0.903420	+	0.428756i	$0.141048\pi$
$984$		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	−0.998353	−	0.0573683i	$-0.981729\pi$
$997$	−20.0593	+	27.6093i	−0.635285	+	0.874394i	0.363069	+	0.931762i	$0.381729\pi$
$998$		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.449.8		32
5.2	odd	4		1100.2.n.e.801.4	yes	16
5.3	odd	4		1100.2.n.d.801.1	yes	16
5.4	even	2	inner	1100.2.cb.d.449.1		32
11.5	even	5	inner	1100.2.cb.d.49.1		32
55.27	odd	20		1100.2.n.e.401.4	yes	16
55.38	odd	20		1100.2.n.d.401.1	✓	16
55.49	even	10	inner	1100.2.cb.d.49.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1100.2.n.d.401.1	✓	16	55.38	odd	20
1100.2.n.d.801.1	yes	16	5.3	odd	4
1100.2.n.e.401.4	yes	16	55.27	odd	20
1100.2.n.e.801.4	yes	16	5.2	odd	4
1100.2.cb.d.49.1		32	11.5	even	5	inner
1100.2.cb.d.49.8		32	55.49	even	10	inner
1100.2.cb.d.449.1		32	5.4	even	2	inner
1100.2.cb.d.449.8		32	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \)
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

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