LMFDB - Embedded newform 441.2.bb.c.100.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [441,2,Mod(37,441)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(441, base_ring=CyclotomicField(42)) chi = DirichletCharacter(H, H._module([0, 32])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("441.37"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bb (of order $21$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 147)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			100.1
Character	$\chi$	$=$	441.100
Dual form			441.2.bb.c.172.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.24916 - 0.693774i) q^{2} +(2.92492 + 1.99418i) q^{4} +(0.982858 - 0.148142i) q^{5} +(-2.07146 - 1.64592i) q^{7} +(-2.26005 - 2.83402i) q^{8} +(-2.31338 - 0.348686i) q^{10} +(-3.21592 + 2.98394i) q^{11} +(-0.00383811 - 0.0168159i) q^{13} +(3.51714 + 5.13907i) q^{14} +(0.530409 + 1.35146i) q^{16} +(-0.149951 - 2.00095i) q^{17} +(-0.178003 + 0.308310i) q^{19} +(3.17020 + 1.52669i) q^{20} +(9.30331 - 4.48024i) q^{22} +(0.512321 - 6.83645i) q^{23} +(-3.83380 + 1.18257i) q^{25} +(-0.00303388 + 0.0404844i) q^{26} +(-2.77659 - 8.94505i) q^{28} +(-2.89389 - 1.39362i) q^{29} +(-2.52299 - 4.36995i) q^{31} +(0.286403 + 3.82178i) q^{32} +(-1.05095 + 4.60450i) q^{34} +(-2.27978 - 1.31084i) q^{35} +(-9.67885 + 6.59893i) q^{37} +(0.614254 - 0.569944i) q^{38} +(-2.64115 - 2.45063i) q^{40} +(6.39800 + 8.02284i) q^{41} +(2.58159 - 3.23721i) q^{43} +(-15.3568 + 2.31467i) q^{44} +(-5.89525 + 15.0208i) q^{46} +(-9.52767 - 2.93890i) q^{47} +(1.58188 + 6.81892i) q^{49} +9.44327 q^{50} +(0.0223077 - 0.0568390i) q^{52} +(-4.57690 - 3.12048i) q^{53} +(-2.71875 + 3.40920i) q^{55} +(0.0170352 + 9.59042i) q^{56} +(5.54195 + 5.14218i) q^{58} +(-10.9381 - 1.64865i) q^{59} +(-11.3038 + 7.70678i) q^{61} +(2.64286 + 11.5791i) q^{62} +(2.65341 - 11.6253i) q^{64} +(-0.00626346 - 0.0159590i) q^{65} +(-3.48108 - 6.02941i) q^{67} +(3.55166 - 6.15166i) q^{68} +(4.21816 + 4.52993i) q^{70} +(-3.82385 + 1.84147i) q^{71} +(11.2807 - 3.47963i) q^{73} +(26.3475 - 8.12711i) q^{74} +(-1.13547 + 0.546813i) q^{76} +(11.5730 - 0.887951i) q^{77} +(0.240066 - 0.415807i) q^{79} +(0.721524 + 1.24972i) q^{80} +(-8.82410 - 22.4834i) q^{82} +(0.429851 - 1.88330i) q^{83} +(-0.443806 - 1.94444i) q^{85} +(-8.05230 + 5.48997i) q^{86} +(15.7247 + 2.37012i) q^{88} +(-6.29680 - 5.84258i) q^{89} +(-0.0197271 + 0.0411506i) q^{91} +(15.1316 - 18.9744i) q^{92} +(19.3903 + 13.2201i) q^{94} +(-0.129278 + 0.329394i) q^{95} +12.4244 q^{97} +(1.17289 - 16.4343i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + q^{2} + 3 q^{4} - 6 q^{8} + 30 q^{10} + 9 q^{11} + 42 q^{14} + 29 q^{16} + 5 q^{17} - 26 q^{19} + 5 q^{20} + q^{22} + 4 q^{23} - 56 q^{25} + 62 q^{26} + 7 q^{28} - 12 q^{29} - 36 q^{31} + 14 q^{32}+ \cdots - 119 q^{98}+O(q^{100}) $ 48 * q + q^2 + 3 * q^4 - 6 * q^8 + 30 * q^10 + 9 * q^11 + 42 * q^14 + 29 * q^16 + 5 * q^17 - 26 * q^19 + 5 * q^20 + q^22 + 4 * q^23 - 56 * q^25 + 62 * q^26 + 7 * q^28 - 12 * q^29 - 36 * q^31 + 14 * q^32 - 76 * q^34 - 7 * q^35 - 20 * q^37 + 60 * q^38 + 28 * q^40 - 41 * q^41 + 12 * q^43 - 44 * q^44 + 16 * q^46 - 13 * q^47 - 84 * q^49 + 12 * q^50 + 92 * q^52 - 14 * q^53 - 38 * q^55 - 105 * q^56 + 3 * q^58 - 57 * q^59 + 11 * q^61 + 16 * q^62 - 110 * q^64 - 21 * q^65 + 34 * q^67 - 22 * q^68 - 6 * q^71 - 69 * q^73 + 90 * q^74 - 49 * q^76 + 34 * q^79 - 55 * q^80 + 91 * q^82 - 28 * q^83 - 44 * q^85 + 26 * q^86 + 45 * q^88 - 11 * q^89 - 84 * q^92 + 90 * q^94 - 150 * q^95 + 124 * q^97 - 119 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{13}{21}\right)$	$1$

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 $

$2$	−2.24916	−	0.693774i	−1.59040	−	0.490572i	−0.631750	−	0.775172i	$-0.717663\pi$
$2$	−2.24916	−	0.693774i	−1.59040	−	0.490572i	−0.958646	+	0.284600i	$0.908139\pi$
$3$		0			0
$3$		0			0
$4$	2.92492	+	1.99418i	1.46246	+	0.997089i
$5$	0.982858	−	0.148142i	0.439547	−	0.0662511i	0.0744592	−	0.997224i	$-0.476277\pi$
$5$	0.982858	−	0.148142i	0.439547	−	0.0662511i	0.365088	+	0.930973i	$0.381039\pi$
$6$		0			0
$7$	−2.07146	−	1.64592i	−0.782938	−	0.622100i
$7$	−2.07146	−	1.64592i	−0.782938	−	0.622100i
$8$	−2.26005	−	2.83402i	−0.799050	−	1.00198i
$9$		0			0
$10$	−2.31338	−	0.348686i	−0.731555	−	0.110264i
$11$	−3.21592	+	2.98394i	−0.969638	+	0.899692i	−0.994989	−	0.0999863i	$-0.968120\pi$
$11$	−3.21592	+	2.98394i	−0.969638	+	0.899692i	0.0253511	+	0.999679i	$0.491930\pi$
$12$		0			0
$13$	−0.00383811	−	0.0168159i	−0.00106450	−	0.00466388i	0.974393	−	0.224852i	$-0.0721899\pi$
$13$	−0.00383811	−	0.0168159i	−0.00106450	−	0.00466388i	−0.975457	+	0.220188i	$0.929333\pi$
$14$	3.51714	+	5.13907i	0.939996	+	1.37347i
$15$		0			0
$16$	0.530409	+	1.35146i	0.132602	+	0.337865i
$17$	−0.149951	−	2.00095i	−0.0363684	−	0.485303i	−0.985415	−	0.170167i	$-0.945569\pi$
$17$	−0.149951	−	2.00095i	−0.0363684	−	0.485303i	0.949047	−	0.315135i	$-0.102050\pi$
$18$		0			0
$19$	−0.178003	+	0.308310i	−0.0408366	+	0.0707311i	−0.885721	−	0.464217i	$-0.846336\pi$
$19$	−0.178003	+	0.308310i	−0.0408366	+	0.0707311i	0.844885	+	0.534948i	$0.179669\pi$
$20$	3.17020	+	1.52669i	0.708879	+	0.341378i
$21$		0			0
$22$	9.30331	−	4.48024i	1.98347	−	0.955190i
$23$	0.512321	−	6.83645i	0.106826	−	1.42550i	−0.644013	−	0.765014i	$-0.722732\pi$
$23$	0.512321	−	6.83645i	0.106826	−	1.42550i	0.750840	−	0.660485i	$-0.229649\pi$
$24$		0			0
$25$	−3.83380	+	1.18257i	−0.766760	+	0.236514i
$26$	−0.00303388	+	0.0404844i	−0.000594994	+	0.00793964i
$27$		0			0
$28$	−2.77659	−	8.94505i	−0.524727	−	1.69046i
$29$	−2.89389	−	1.39362i	−0.537381	−	0.258789i	0.145450	−	0.989366i	$-0.453537\pi$
$29$	−2.89389	−	1.39362i	−0.537381	−	0.258789i	−0.682831	+	0.730577i	$0.739251\pi$
$30$		0			0
$31$	−2.52299	−	4.36995i	−0.453143	−	0.784867i	0.545436	−	0.838152i	$-0.316364\pi$
$31$	−2.52299	−	4.36995i	−0.453143	−	0.784867i	−0.998579	+	0.0532856i	$0.983031\pi$
$32$	0.286403	+	3.82178i	0.0506294	+	0.675602i
$33$		0			0
$34$	−1.05095	+	4.60450i	−0.180236	+	0.789665i
$35$	−2.27978	−	1.31084i	−0.385353	−	0.221572i
$36$		0			0
$37$	−9.67885	+	6.59893i	−1.59119	+	1.08486i	−0.643608	+	0.765356i	$0.722563\pi$
$37$	−9.67885	+	6.59893i	−1.59119	+	1.08486i	−0.947586	+	0.319502i	$0.896484\pi$
$38$	0.614254	−	0.569944i	0.0996451	−	0.0924572i
$39$		0			0
$40$	−2.64115	−	2.45063i	−0.417602	−	0.387478i
$41$	6.39800	+	8.02284i	0.999200	+	1.25296i	0.967345	+	0.253465i	$0.0815703\pi$
$41$	6.39800	+	8.02284i	0.999200	+	1.25296i	0.0318559	+	0.999492i	$0.489858\pi$
$42$		0			0
$43$	2.58159	−	3.23721i	0.393689	−	0.493670i	−0.545000	−	0.838436i	$-0.683470\pi$
$43$	2.58159	−	3.23721i	0.393689	−	0.493670i	0.938689	+	0.344766i	$0.112042\pi$
$44$	−15.3568	+	2.31467i	−2.31513	+	0.348950i
$45$		0			0
$46$	−5.89525	+	15.0208i	−0.869207	+	2.21470i
$47$	−9.52767	−	2.93890i	−1.38975	−	0.428682i	−0.492544	−	0.870287i	$-0.663933\pi$
$47$	−9.52767	−	2.93890i	−1.38975	−	0.428682i	−0.897209	+	0.441605i	$0.854409\pi$
$48$		0			0
$49$	1.58188	+	6.81892i	0.225983	+	0.974131i
$50$	9.44327			1.33548
$51$		0			0
$52$	0.0223077	−	0.0568390i	0.00309352	−	0.00788215i
$53$	−4.57690	−	3.12048i	−0.628685	−	0.428630i	0.206616	−	0.978422i	$-0.433755\pi$
$53$	−4.57690	−	3.12048i	−0.628685	−	0.428630i	−0.835302	+	0.549792i	$0.814707\pi$
$54$		0			0
$55$	−2.71875	+	3.40920i	−0.366596	+	0.459697i
$56$	0.0170352	+	9.59042i	0.00227642	+	1.28157i
$57$		0			0
$58$	5.54195	+	5.14218i	0.727694	+	0.675202i
$59$	−10.9381	−	1.64865i	−1.42402	−	0.214636i	−0.608585	−	0.793489i	$-0.708263\pi$
$59$	−10.9381	−	1.64865i	−1.42402	−	0.214636i	−0.815432	+	0.578853i	$0.803501\pi$
$60$		0			0
$61$	−11.3038	+	7.70678i	−1.44730	+	0.986752i	−0.451786	+	0.892126i	$0.649213\pi$
$61$	−11.3038	+	7.70678i	−1.44730	+	0.986752i	−0.995513	+	0.0946251i	$0.969835\pi$
$62$	2.64286	+	11.5791i	0.335643	+	1.47055i
$63$		0			0
$64$	2.65341	−	11.6253i	0.331676	−	1.45317i
$65$	−0.00626346	−	0.0159590i	−0.000776886	−	0.00197947i
$66$		0			0
$67$	−3.48108	−	6.02941i	−0.425282	−	0.736610i	0.571165	−	0.820835i	$-0.306492\pi$
$67$	−3.48108	−	6.02941i	−0.425282	−	0.736610i	−0.996447	+	0.0842256i	$0.973158\pi$
$68$	3.55166	−	6.15166i	0.430703	−	0.745999i
$69$		0			0
$70$	4.21816	+	4.52993i	0.504167	+	0.541431i
$71$	−3.82385	+	1.84147i	−0.453808	+	0.218542i	−0.646802	−	0.762658i	$-0.723894\pi$
$71$	−3.82385	+	1.84147i	−0.453808	+	0.218542i	0.192995	+	0.981200i	$0.438180\pi$
$72$		0			0
$73$	11.2807	−	3.47963i	1.32030	−	0.407260i	0.447044	−	0.894512i	$-0.352477\pi$
$73$	11.2807	−	3.47963i	1.32030	−	0.407260i	0.873261	+	0.487252i	$0.162001\pi$
$74$	26.3475	−	8.12711i	3.06283	−	0.944758i
$75$		0			0
$76$	−1.13547	+	0.546813i	−0.130247	+	0.0627237i
$77$	11.5730	−	0.887951i	1.31886	−	0.101191i
$78$		0			0
$79$	0.240066	−	0.415807i	0.0270096	−	0.0467820i	−0.852205	−	0.523209i	$-0.824735\pi$
$79$	0.240066	−	0.415807i	0.0270096	−	0.0467820i	0.879214	+	0.476427i	$0.158068\pi$
$80$	0.721524	+	1.24972i	0.0806689	+	0.139723i
$81$		0			0
$82$	−8.82410	−	22.4834i	−0.974458	−	2.48288i
$83$	0.429851	−	1.88330i	0.0471823	−	0.206719i	−0.945842	−	0.324626i	$-0.894761\pi$
$83$	0.429851	−	1.88330i	0.0471823	−	0.206719i	0.993025	+	0.117907i	$0.0376186\pi$
$84$		0			0
$85$	−0.443806	−	1.94444i	−0.0481375	−	0.210904i
$86$	−8.05230	+	5.48997i	−0.868302	+	0.591998i
$87$		0			0
$88$	15.7247	+	2.37012i	1.67626	+	0.252655i
$89$	−6.29680	−	5.84258i	−0.667460	−	0.619312i	0.271867	−	0.962335i	$-0.412359\pi$
$89$	−6.29680	−	5.84258i	−0.667460	−	0.619312i	−0.939327	+	0.343023i	$0.888549\pi$
$90$		0			0
$91$	−0.0197271	+	0.0411506i	−0.00206796	+	0.00431376i
$92$	15.1316	−	18.9744i	1.57758	−	1.97822i
$93$		0			0
$94$	19.3903	+	13.2201i	1.99996	+	1.36355i
$95$	−0.129278	+	0.329394i	−0.0132636	+	0.0337951i
$96$		0			0
$97$	12.4244			1.26151			0.630754	−	0.775983i	$-0.282746\pi$
$97$	12.4244			1.26151			0.630754	+	0.775983i	$0.282746\pi$
$98$	1.17289	−	16.4343i	0.118479	−	1.66012i
$99$		0			0
$100$	−13.5718	−	4.18635i	−1.35718	−	0.418635i
$101$	−0.455493	+	1.16058i	−0.0453233	+	0.115482i	−0.951743	−	0.306897i	$-0.900709\pi$
$101$	−0.455493	+	1.16058i	−0.0453233	+	0.115482i	0.906420	+	0.422378i	$0.138805\pi$
$102$		0			0
$103$	2.99443	−	0.451338i	0.295050	−	0.0444717i	0.000150958	−	1.00000i	$-0.499952\pi$
$103$	2.99443	−	0.451338i	0.295050	−	0.0444717i	0.294899	+	0.955528i	$0.404714\pi$
$104$	−0.0389821	+	0.0488821i	−0.00382251	+	0.00479328i
$105$		0			0
$106$	8.12927	+	10.1938i	0.789585	+	0.990108i
$107$	2.73582	+	2.53847i	0.264482	+	0.245403i	0.801255	−	0.598324i	$-0.204166\pi$
$107$	2.73582	+	2.53847i	0.264482	+	0.245403i	−0.536773	+	0.843727i	$0.680357\pi$
$108$		0			0
$109$	1.83300	−	1.70078i	0.175570	−	0.162905i	−0.587493	−	0.809229i	$-0.699885\pi$
$109$	1.83300	−	1.70078i	0.175570	−	0.162905i	0.763063	+	0.646324i	$0.223695\pi$
$110$	8.48012	−	5.78165i	0.808548	−	0.551258i
$111$		0			0
$112$	1.12568	−	3.67251i	0.106367	−	0.347019i
$113$	1.50750	−	6.60481i	0.141814	−	0.621328i	−0.853199	−	0.521585i	$-0.825341\pi$
$113$	1.50750	−	6.60481i	0.141814	−	0.621328i	0.995013	−	0.0997429i	$-0.0318020\pi$
$114$		0			0
$115$	−0.509227	−	6.79516i	−0.0474856	−	0.633652i
$116$	−5.68526	−	9.84716i	−0.527863	−	0.914286i
$117$		0			0
$118$	23.4577	+	11.2966i	2.15946	+	1.03994i
$119$	−2.98280	+	4.39170i	−0.273433	+	0.402587i
$120$		0			0
$121$	0.616230	−	8.22302i	0.0560209	−	0.747547i
$122$	30.7707	−	9.49151i	2.78585	−	0.859321i
$123$		0			0
$124$	1.33490	−	17.8131i	0.119878	−	1.59966i
$125$	−8.07053	+	3.88656i	−0.721850	+	0.347625i
$126$		0			0
$127$	7.34145	+	3.53546i	0.651449	+	0.313721i	0.730261	−	0.683168i	$-0.239398\pi$
$127$	7.34145	+	3.53546i	0.651449	+	0.313721i	−0.0788122	+	0.996889i	$0.525113\pi$
$128$	−10.2008	+	17.6683i	−0.901632	+	1.56167i
$129$		0			0
$130$	0.00301556	+	0.0402398i	0.000264482	+	0.00352927i
$131$	5.44096	+	13.8633i	0.475379	+	1.21125i	0.944617	+	0.328174i	$0.106433\pi$
$131$	5.44096	+	13.8633i	0.475379	+	1.21125i	−0.469239	+	0.883071i	$0.655472\pi$
$132$		0			0
$133$	0.876179	−	0.345672i	0.0759744	−	0.0299736i
$134$	3.64646	+	15.9762i	0.315006	+	1.38013i
$135$		0			0
$136$	−5.33184	+	4.94723i	−0.457202	+	0.424221i
$137$	17.4682	+	2.63291i	1.49241	+	0.224945i	0.844000	−	0.536344i	$-0.180195\pi$
$137$	17.4682	+	2.63291i	1.49241	+	0.224945i	0.648413	+	0.761289i	$0.275433\pi$
$138$		0			0
$139$	−12.4178	−	15.5715i	−1.05327	−	1.32075i	−0.945158	−	0.326614i	$-0.894092\pi$
$139$	−12.4178	−	15.5715i	−1.05327	−	1.32075i	−0.108108	−	0.994139i	$-0.534479\pi$
$140$	−4.05413	−	8.38038i	−0.342637	−	0.708271i
$141$		0			0
$142$	9.87802	−	1.48887i	0.828945	−	0.124943i
$143$	0.0625207	+	0.0426259i	0.00522824	+	0.00356455i
$144$		0			0
$145$	−3.05073	−	0.941026i	−0.253350	−	0.0781480i
$146$	−27.7862			−2.29960
$147$		0			0
$148$	−41.4693			−3.40876
$149$	18.2025	+	5.61472i	1.49121	+	0.459976i	0.929956	−	0.367671i	$-0.119845\pi$
$149$	18.2025	+	5.61472i	1.49121	+	0.459976i	0.561249	+	0.827647i	$0.310321\pi$
$150$		0			0
$151$	5.43875	+	3.70808i	0.442600	+	0.301759i	0.764038	−	0.645171i	$-0.223214\pi$
$151$	5.43875	+	3.70808i	0.442600	+	0.301759i	−0.321438	+	0.946930i	$0.604166\pi$
$152$	1.27605	−	0.192334i	0.103501	−	0.0156003i
$153$		0			0
$154$	−26.6455	−	6.03190i	−2.14716	−	0.486064i
$155$	−3.12712	−	3.92128i	−0.251176	−	0.314965i
$156$		0			0
$157$	−17.9382	−	2.70374i	−1.43162	−	0.215782i	−0.612985	−	0.790094i	$-0.710032\pi$
$157$	−17.9382	−	2.70374i	−1.43162	−	0.215782i	−0.818636	+	0.574312i	$0.805270\pi$
$158$	−0.828424	+	0.768665i	−0.0659059	+	0.0611517i
$159$		0			0
$160$	0.847660	+	3.71384i	0.0670134	+	0.293605i
$161$	−12.3135	+	13.3182i	−0.970441	+	1.04962i
$162$		0			0
$163$	−3.41833	−	8.70977i	−0.267744	−	0.682202i	−0.999999	−	0.00117098i	$-0.999627\pi$
$163$	−3.41833	−	8.70977i	−0.267744	−	0.682202i	0.732255	−	0.681031i	$-0.238468\pi$
$164$	2.71468	+	36.2249i	0.211981	+	2.82869i
$165$		0			0
$166$	−2.27339	+	3.93762i	−0.176449	+	0.305619i
$167$	4.77897	+	2.30143i	0.369808	+	0.178090i	0.609552	−	0.792746i	$-0.291349\pi$
$167$	4.77897	+	2.30143i	0.369808	+	0.178090i	−0.239744	+	0.970836i	$0.577064\pi$
$168$		0			0
$169$	11.7123	−	5.64036i	0.900948	−	0.433874i
$170$	−0.350812	+	4.68126i	−0.0269060	+	0.359036i
$171$		0			0
$172$	14.0065	−	4.32044i	1.06799	−	0.329430i
$173$	1.34974	−	18.0110i	0.102619	−	1.36935i	−0.673697	−	0.739008i	$-0.735295\pi$
$173$	1.34974	−	18.0110i	0.102619	−	1.36935i	0.776315	−	0.630345i	$-0.217086\pi$
$174$		0			0
$175$	9.88798	+	3.86049i	0.747461	+	0.291826i
$176$	−5.73843	−	2.76348i	−0.432551	−	0.208305i
$177$		0			0
$178$	10.1091	+	17.5095i	0.757708	+	1.31239i
$179$	−0.485682	−	6.48097i	−0.0363016	−	0.484411i	−0.985494	−	0.169713i	$-0.945716\pi$
$179$	−0.485682	−	6.48097i	−0.0363016	−	0.484411i	0.949192	−	0.314698i	$-0.101903\pi$
$180$		0			0
$181$	−0.428051	+	1.87541i	−0.0318168	+	0.139398i	−0.988342	−	0.152252i	$-0.951347\pi$
$181$	−0.428051	+	1.87541i	−0.0318168	+	0.139398i	0.956525	+	0.291651i	$0.0942045\pi$
$182$	0.0729187	−	0.0788682i	0.00540509	−	0.00584610i
$183$		0			0
$184$	−20.5325	+	13.9988i	−1.51368	+	1.03201i
$185$	−8.53536	+	7.91965i	−0.627532	+	0.582264i
$186$		0			0
$187$	6.45296	+	5.98747i	0.471887	+	0.437848i
$188$	−22.0070	−	27.5959i	−1.60503	−	2.01264i
$189$		0			0
$190$	0.519292	−	0.651171i	0.0376734	−	0.0472409i
$191$	−4.61872	+	0.696160i	−0.334199	+	0.0503724i	−0.313998	−	0.949424i	$-0.601669\pi$
$191$	−4.61872	+	0.696160i	−0.334199	+	0.0503724i	−0.0202006	+	0.999796i	$0.506430\pi$
$192$		0			0
$193$	−0.0593246	+	0.151157i	−0.00427028	+	0.0108805i	−0.932993	−	0.359895i	$-0.882813\pi$
$193$	−0.0593246	+	0.151157i	−0.00427028	+	0.0108805i	0.928723	+	0.370775i	$0.120908\pi$
$194$	−27.9445	−	8.61974i	−2.00630	−	0.618861i
$195$		0			0
$196$	−8.97126	+	23.0993i	−0.640804	+	1.64995i
$197$	−5.26305			−0.374977			−0.187488	−	0.982267i	$-0.560035\pi$
$197$	−5.26305			−0.374977			−0.187488	+	0.982267i	$0.560035\pi$
$198$		0			0
$199$	5.45072	−	13.8882i	0.386391	−	0.984509i	−0.596875	−	0.802334i	$-0.703591\pi$
$199$	5.45072	−	13.8882i	0.386391	−	0.984509i	0.983266	−	0.182175i	$-0.0583137\pi$
$200$	12.0160	+	8.19239i	0.849661	+	0.579289i
$201$		0			0
$202$	1.82966	−	2.29432i	0.128734	−	0.161428i
$203$	3.70077	+	7.64994i	0.259743	+	0.536921i
$204$		0			0
$205$	7.47685	+	6.93750i	0.522206	+	0.484536i
$206$	−7.04809	−	1.06233i	−0.491064	−	0.0740159i
$207$		0			0
$208$	0.0206902	−	0.0141063i	0.00143461	−	0.000978099i
$209$	−0.347535	−	1.52265i	−0.0240395	−	0.105324i
$210$		0			0
$211$	−0.734828	+	3.21949i	−0.0505876	+	0.221639i	−0.993903	−	0.110259i	$-0.964832\pi$
$211$	−0.734828	+	3.21949i	−0.0505876	+	0.221639i	0.943315	+	0.331898i	$0.107689\pi$
$212$	−7.16428	−	18.2543i	−0.492045	−	1.25371i
$213$		0			0
$214$	−4.39217	−	7.60747i	−0.300243	−	0.520036i
$215$	2.05777	−	3.56416i	0.140339	−	0.243074i
$216$		0			0
$217$	−1.96633	+	13.2048i	−0.133483	+	0.896402i
$218$	−5.30267	+	2.55363i	−0.359142	+	0.172954i
$219$		0			0
$220$	−14.7507	+	4.54998i	−0.994491	+	0.306760i
$221$	−0.0330723	+	0.0102014i	−0.00222468	+	0.000686224i
$222$		0			0
$223$	−12.4405	+	5.99104i	−0.833079	+	0.401190i	−0.801269	−	0.598304i	$-0.795842\pi$
$223$	−12.4405	+	5.99104i	−0.833079	+	0.401190i	−0.0318102	+	0.999494i	$0.510127\pi$
$224$	5.69709	−	8.38807i	0.380653	−	0.560451i
$225$		0			0
$226$	−7.97286	+	13.8094i	−0.530347	+	0.918588i
$227$	4.95599	+	8.58403i	0.328941	+	0.569742i	0.982302	−	0.187304i	$-0.0599750\pi$
$227$	4.95599	+	8.58403i	0.328941	+	0.569742i	−0.653361	+	0.757046i	$0.726642\pi$
$228$		0			0
$229$	7.46424	+	19.0186i	0.493251	+	1.25678i	0.933394	+	0.358854i	$0.116833\pi$
$229$	7.46424	+	19.0186i	0.493251	+	1.25678i	−0.440143	+	0.897928i	$0.645072\pi$
$230$	−3.56897	+	15.6367i	−0.235331	+	1.03105i
$231$		0			0
$232$	2.59079	+	11.3510i	0.170094	+	0.745229i
$233$	11.8038	−	8.04770i	0.773294	−	0.527223i	−0.111187	−	0.993799i	$-0.535465\pi$
$233$	11.8038	−	8.04770i	0.773294	−	0.527223i	0.884481	+	0.466577i	$0.154513\pi$
$234$		0			0
$235$	−9.79972	−	1.47707i	−0.639263	−	0.0963534i
$236$	−28.7053	−	26.6346i	−1.86856	−	1.73377i
$237$		0			0
$238$	9.75564	−	7.80825i	0.632364	−	0.506134i
$239$	−1.15092	+	1.44321i	−0.0744469	+	0.0933535i	−0.817660	−	0.575701i	$-0.804729\pi$
$239$	−1.15092	+	1.44321i	−0.0744469	+	0.0933535i	0.743213	+	0.669054i	$0.233301\pi$
$240$		0			0
$241$	−3.11018	−	2.12049i	−0.200345	−	0.136593i	0.458992	−	0.888440i	$-0.348211\pi$
$241$	−3.11018	−	2.12049i	−0.200345	−	0.136593i	−0.659337	+	0.751848i	$0.729163\pi$
$242$	−7.09092	+	18.0674i	−0.455822	+	1.16141i
$243$		0			0
$244$	−48.4313			−3.10050
$245$	2.56493	+	6.46768i	0.163867	+	0.413205i
$246$		0			0
$247$	0.00586769	+	0.00180994i	0.000373352	+	0.000115164i
$248$	−6.68242	+	17.0265i	−0.424334	+	1.08119i
$249$		0			0
$250$	20.8483	−	3.14238i	1.31856	−	0.198741i
$251$	7.35006	−	9.21668i	0.463932	−	0.581752i	−0.493742	−	0.869608i	$-0.664371\pi$
$251$	7.35006	−	9.21668i	0.463932	−	0.581752i	0.957673	+	0.287857i	$0.0929427\pi$
$252$		0			0
$253$	18.7520	+	23.5143i	1.17893	+	1.47833i
$254$	−14.0593	−	13.0451i	−0.882159	−	0.818524i
$255$		0			0
$256$	17.7188	−	16.4406i	1.10742	−	1.02754i
$257$	−16.4532	+	11.2176i	−1.02632	+	0.699735i	−0.954661	−	0.297694i	$-0.903782\pi$
$257$	−16.4532	+	11.2176i	−1.02632	+	0.699735i	−0.0716610	+	0.997429i	$0.522830\pi$
$258$		0			0
$259$	30.9107	+	2.26123i	1.92070	+	0.140506i
$260$	0.0135050	−	0.0591693i	0.000837545	−	0.00366953i
$261$		0			0
$262$	−2.61956	−	34.9557i	−0.161837	−	2.15957i
$263$	−12.5442	−	21.7272i	−0.773509	−	1.33976i	−0.935629	−	0.352986i	$-0.885166\pi$
$263$	−12.5442	−	21.7272i	−0.773509	−	1.33976i	0.162120	−	0.986771i	$-0.448167\pi$
$264$		0			0
$265$	−4.96071	−	2.38895i	−0.304734	−	0.146752i
$266$	−2.21049	+	0.169602i	−0.135534	+	0.0103990i
$267$		0			0
$268$	1.84182	−	24.5774i	0.112507	−	1.50131i
$269$	15.7600	−	4.86132i	0.960905	−	0.296400i	0.225663	−	0.974205i	$-0.427545\pi$
$269$	15.7600	−	4.86132i	0.960905	−	0.296400i	0.735241	+	0.677805i	$0.237069\pi$
$270$		0			0
$271$	0.457879	−	6.10998i	0.0278142	−	0.371155i	−0.965877	−	0.259002i	$-0.916606\pi$
$271$	0.457879	−	6.10998i	0.0278142	−	0.371155i	0.993691	−	0.112153i	$-0.0357746\pi$
$272$	2.62467	−	1.26398i	0.159144	−	0.0766399i
$273$		0			0
$274$	−37.4622	−	18.0409i	−2.26318	−	1.08989i
$275$	8.80049	−	15.2429i	0.530690	−	0.919181i
$276$		0			0
$277$	−2.08589	−	27.8342i	−0.125329	−	1.67240i	−0.605977	−	0.795482i	$-0.707218\pi$
$277$	−2.08589	−	27.8342i	−0.125329	−	1.67240i	0.480648	−	0.876913i	$-0.340401\pi$
$278$	17.1266	+	43.6378i	1.02718	+	2.61722i
$279$		0			0
$280$	1.43749	+	9.42350i	0.0859063	+	0.563162i
$281$	1.28818	+	5.64389i	0.0768464	+	0.336686i	0.998707	−	0.0508354i	$-0.0161884\pi$
$281$	1.28818	+	5.64389i	0.0768464	+	0.336686i	−0.921861	+	0.387522i	$0.873331\pi$
$282$		0			0
$283$	−18.6556	+	17.3098i	−1.10896	+	1.02896i	−0.109570	+	0.993979i	$0.534947\pi$
$283$	−18.6556	+	17.3098i	−1.10896	+	1.02896i	−0.999388	+	0.0349835i	$0.988862\pi$
$284$	−14.8567	−	2.23928i	−0.881582	−	0.132877i
$285$		0			0
$286$	−0.111046	−	0.139248i	−0.00656630	−	0.00823389i
$287$	−0.0482251	−	27.1496i	−0.00284664	−	1.60259i
$288$		0			0
$289$	12.8288	−	1.93363i	0.754635	−	0.113743i
$290$	6.20873	+	4.23304i	0.364589	+	0.248573i
$291$		0			0
$292$	39.9341	+	12.3180i	2.33697	+	0.720859i
$293$	−5.59675			−0.326966			−0.163483	−	0.986546i	$-0.552273\pi$
$293$	−5.59675			−0.326966			−0.163483	+	0.986546i	$0.552273\pi$
$294$		0			0
$295$	−10.9948			−0.640143
$296$	40.5762	+	12.5161i	2.35844	+	0.727484i
$297$		0			0
$298$	−37.0449	−	25.2568i	−2.14596	−	1.46309i
$299$	−0.116927	+	0.0176240i	−0.00676208	+	0.00101922i
$300$		0			0
$301$	−10.6759	+	2.45665i	−0.615346	+	0.141599i
$302$	−9.66006	−	12.1133i	−0.555874	−	0.697044i
$303$		0			0
$304$	−0.511083	−	0.0770333i	−0.0293126	−	0.00441816i
$305$	−9.96830	+	9.24923i	−0.570783	+	0.529609i
$306$		0			0
$307$	7.00991	+	30.7124i	0.400077	+	1.75285i	0.627078	+	0.778957i	$0.284251\pi$
$307$	7.00991	+	30.7124i	0.400077	+	1.75285i	−0.227001	+	0.973895i	$0.572892\pi$
$308$	35.6208	+	20.4814i	2.02968	+	1.16704i
$309$		0			0
$310$	4.31290	+	10.9891i	0.244956	+	0.624139i
$311$	0.216425	+	2.88799i	0.0122724	+	0.163763i	0.999973	+	0.00740384i	$0.00235674\pi$
$311$	0.216425	+	2.88799i	0.0122724	+	0.163763i	−0.987700	+	0.156359i	$0.950024\pi$
$312$		0			0
$313$	−11.1490	+	19.3106i	−0.630178	+	1.09150i	0.357337	+	0.933975i	$0.383685\pi$
$313$	−11.1490	+	19.3106i	−0.630178	+	1.09150i	−0.987515	+	0.157524i	$0.949649\pi$
$314$	38.4700	+	18.5262i	2.17099	+	1.04549i
$315$		0			0
$316$	1.53137	−	0.737468i	0.0861462	−	0.0414858i
$317$	0.267380	−	3.56794i	0.0150176	−	0.200396i	−0.984648	−	0.174550i	$-0.944153\pi$
$317$	0.267380	−	3.56794i	0.0150176	−	0.200396i	0.999666	−	0.0258459i	$-0.00822792\pi$
$318$		0			0
$319$	13.4650	−	4.15340i	0.753896	−	0.232546i
$320$	0.885722	−	11.8191i	0.0495134	−	0.660710i
$321$		0			0
$322$	36.9349	−	21.4119i	2.05830	−	1.19324i
$323$	0.643606	+	0.309944i	0.0358112	+	0.0172458i
$324$		0			0
$325$	0.0346005	+	0.0599299i	0.00191929	+	0.00332431i
$326$	1.64577	+	21.9612i	0.0911505	+	1.21632i
$327$		0			0
$328$	8.27705	−	36.2641i	0.457024	−	2.00235i
$329$	14.8990	+	21.7696i	0.821407	+	1.20020i
$330$		0			0
$331$	4.78132	−	3.25985i	0.262805	−	0.179178i	−0.424748	−	0.905312i	$-0.639637\pi$
$331$	4.78132	−	3.25985i	0.262805	−	0.179178i	0.687553	+	0.726134i	$0.258685\pi$
$332$	5.01292	−	4.65131i	0.275119	−	0.255274i
$333$		0			0
$334$	−9.15199	−	8.49181i	−0.500775	−	0.464651i
$335$	−4.31462	−	5.41036i	−0.235733	−	0.295599i
$336$		0			0
$337$	13.0314	−	16.3408i	0.709863	−	0.890141i	−0.287854	−	0.957674i	$-0.592942\pi$
$337$	13.0314	−	16.3408i	0.709863	−	0.890141i	0.997717	+	0.0675339i	$0.0215131\pi$
$338$	−30.2560	+	4.56036i	−1.64571	+	0.248051i
$339$		0			0
$340$	2.57946	−	6.57236i	0.139891	−	0.356436i
$341$	21.1534	+	6.52497i	1.14552	+	0.353347i
$342$		0			0
$343$	7.94661	−	16.7288i	0.429077	−	0.903268i
$344$	−15.0089			−0.809223
$345$		0			0
$346$	−15.5314	+	39.5733i	−0.834971	+	2.12747i
$347$	−8.95112	−	6.10277i	−0.480521	−	0.327614i	0.298717	−	0.954342i	$-0.403441\pi$
$347$	−8.95112	−	6.10277i	−0.480521	−	0.327614i	−0.779238	+	0.626728i	$0.784394\pi$
$348$		0			0
$349$	−8.36176	+	10.4853i	−0.447595	+	0.561266i	−0.953527	−	0.301307i	$-0.902577\pi$
$349$	−8.36176	+	10.4853i	−0.447595	+	0.561266i	0.505932	+	0.862573i	$0.331149\pi$
$350$	−19.5613	−	15.5429i	−1.04560	−	0.830802i
$351$		0			0
$352$	−12.3250	−	11.4360i	−0.656927	−	0.609539i
$353$	−20.6354	−	3.11028i	−1.09831	−	0.165544i	−0.425210	−	0.905095i	$-0.639800\pi$
$353$	−20.6354	−	3.11028i	−1.09831	−	0.165544i	−0.673100	+	0.739551i	$0.735038\pi$
$354$		0			0
$355$	−3.48550	+	2.37638i	−0.184991	+	0.126125i
$356$	−6.76651	−	29.6460i	−0.358624	−	1.57124i
$357$		0			0
$358$	−3.40395	+	14.9137i	−0.179905	+	0.788214i
$359$	0.908275	+	2.31425i	0.0479369	+	0.122141i	0.952837	−	0.303483i	$-0.0981497\pi$
$359$	0.908275	+	2.31425i	0.0479369	+	0.122141i	−0.904900	+	0.425625i	$0.860054\pi$
$360$		0			0
$361$	9.43663	+	16.3447i	0.496665	+	0.860249i
$362$	2.26387	−	3.92114i	0.118986	−	0.206090i
$363$		0			0
$364$	−0.139762	+	0.0810229i	−0.00732552	+	0.00424676i
$365$	10.5718	−	5.09113i	0.553355	−	0.266482i
$366$		0			0
$367$	6.39029	−	1.97114i	0.333570	−	0.102893i	−0.123446	−	0.992351i	$-0.539394\pi$
$367$	6.39029	−	1.97114i	0.333570	−	0.102893i	0.457016	+	0.889458i	$0.348918\pi$
$368$	9.51093	−	2.93373i	0.495792	−	0.152931i
$369$		0			0
$370$	24.6918	−	11.8910i	1.28367	−	0.618182i
$371$	4.34479	+	13.9972i	0.225570	+	0.726696i
$372$		0			0
$373$	18.6519	−	32.3061i	0.965761	−	1.67275i	0.258204	−	0.966090i	$-0.416869\pi$
$373$	18.6519	−	32.3061i	0.965761	−	1.67275i	0.707557	−	0.706656i	$-0.249797\pi$
$374$	−10.3598	−	17.9437i	−0.535692	−	0.927846i
$375$		0			0
$376$	13.2042	+	33.6437i	0.680953	+	1.73504i
$377$	−0.0123279	+	0.0540121i	−0.000634920	+	0.00278177i
$378$		0			0
$379$	−1.75528	−	7.69038i	−0.0901626	−	0.395028i	0.909629	−	0.415421i	$-0.136366\pi$
$379$	−1.75528	−	7.69038i	−0.0901626	−	0.395028i	−0.999792	+	0.0203923i	$0.993508\pi$
$380$	−1.03500	+	0.705650i	−0.0530943	+	0.0361991i
$381$		0			0
$382$	10.8712	+	1.63857i	0.556220	+	0.0838367i
$383$	12.7244	+	11.8065i	0.650185	+	0.603284i	0.934721	−	0.355382i	$-0.115649\pi$
$383$	12.7244	+	11.8065i	0.650185	+	0.603284i	−0.284536	+	0.958665i	$0.591840\pi$
$384$		0			0
$385$	11.2431	−	2.58717i	0.572999	−	0.131855i
$386$	0.238299	−	0.298818i	0.0121291	−	0.0152094i
$387$		0			0
$388$	36.3404	+	24.7765i	1.84491	+	1.25784i
$389$	3.27199	−	8.33689i	0.165896	−	0.422697i	−0.823616	−	0.567148i	$-0.808047\pi$
$389$	3.27199	−	8.33689i	0.165896	−	0.422697i	0.989512	+	0.144452i	$0.0461418\pi$
$390$		0			0
$391$	−13.7563			−0.695684
$392$	15.7498	−	19.8942i	0.795485	−	1.00481i
$393$		0			0
$394$	11.8374	+	3.65136i	0.596361	+	0.183953i
$395$	0.174353	−	0.444243i	0.00877264	−	0.0223523i
$396$		0			0
$397$	−20.0460	+	3.02144i	−1.00608	+	0.151642i	−0.631354	−	0.775495i	$-0.717501\pi$
$397$	−20.0460	+	3.02144i	−1.00608	+	0.151642i	−0.374724	+	0.927136i	$0.622262\pi$
$398$	−21.8948	+	27.4552i	−1.09749	+	1.37621i
$399$		0			0
$400$	−3.63168	−	4.55398i	−0.181584	−	0.227699i
$401$	11.7873	+	10.9371i	0.588632	+	0.546170i	0.917260	−	0.398289i	$-0.130396\pi$
$401$	11.7873	+	10.9371i	0.588632	+	0.546170i	−0.328628	+	0.944459i	$0.606586\pi$
$402$		0			0
$403$	−0.0638010	+	0.0591987i	−0.00317816	+	0.00294890i
$404$	−3.64668	+	2.48626i	−0.181429	+	0.123696i
$405$		0			0
$406$	−3.01630	−	19.7734i	−0.149696	−	0.981340i
$407$	11.4356	−	50.1028i	0.566843	−	2.48350i
$408$		0			0
$409$	−0.573863	−	7.65766i	−0.0283757	−	0.378647i	−0.993255	−	0.115953i	$-0.963008\pi$
$409$	−0.573863	−	7.65766i	−0.0283757	−	0.378647i	0.964879	−	0.262694i	$-0.0846111\pi$
$410$	−12.0036	−	20.7908i	−0.592814	−	1.02678i
$411$		0			0
$412$	9.65853	+	4.65130i	0.475842	+	0.229153i
$413$	19.9442	+	21.4183i	0.981392	+	1.05393i
$414$		0			0
$415$	0.143487	−	1.91470i	0.00704348	−	0.0939887i
$416$	0.0631674	−	0.0194846i	0.00309704	−	0.000955309i
$417$		0			0
$418$	−0.274713	+	3.66580i	−0.0134367	+	0.179300i
$419$	14.6563	−	7.05810i	0.716007	−	0.344811i	−0.0401568	−	0.999193i	$-0.512786\pi$
$419$	14.6563	−	7.05810i	0.716007	−	0.344811i	0.756164	+	0.654383i	$0.227071\pi$
$420$		0			0
$421$	−21.8730	−	10.5335i	−1.06602	−	0.513370i	−0.183200	−	0.983076i	$-0.558646\pi$
$421$	−21.8730	−	10.5335i	−1.06602	−	0.513370i	−0.882823	+	0.469706i	$0.844360\pi$
$422$	3.88635	−	6.73135i	0.189184	−	0.327677i
$423$		0			0
$424$	1.50055	+	20.0235i	0.0728732	+	0.972425i
$425$	2.94115	+	7.49393i	0.142667	+	0.363509i
$426$		0			0
$427$	36.1000	+	2.64085i	1.74700	+	0.127800i
$428$	2.93990	+	12.8805i	0.142105	+	0.622604i
$429$		0			0
$430$	−7.10098	+	6.58874i	−0.342439	+	0.317737i
$431$	0.458634	+	0.0691279i	0.0220916	+	0.00332977i	0.160079	−	0.987104i	$-0.448825\pi$
$431$	0.458634	+	0.0691279i	0.0220916	+	0.00332977i	−0.137987	+	0.990434i	$0.544063\pi$
$432$		0			0
$433$	3.73958	+	4.68928i	0.179713	+	0.225352i	0.863526	−	0.504305i	$-0.168251\pi$
$433$	3.73958	+	4.68928i	0.179713	+	0.225352i	−0.683813	+	0.729657i	$0.739680\pi$
$434$	13.5837	−	28.3356i	0.652041	−	1.36015i
$435$		0			0
$436$	8.75304	−	1.31931i	0.419195	−	0.0631834i
$437$	2.01655	+	1.37486i	0.0964647	+	0.0657685i
$438$		0			0
$439$	−26.2140	−	8.08594i	−1.25112	−	0.385921i	−0.402746	−	0.915312i	$-0.631944\pi$
$439$	−26.2140	−	8.08594i	−1.25112	−	0.385921i	−0.848378	+	0.529391i	$0.822421\pi$
$440$	15.8063			0.753534
$441$		0			0
$442$	0.0814623			0.00387477
$443$	−21.2713	−	6.56133i	−1.01063	−	0.311738i	−0.255144	−	0.966903i	$-0.582123\pi$
$443$	−21.2713	−	6.56133i	−1.01063	−	0.311738i	−0.755486	+	0.655165i	$0.772599\pi$
$444$		0			0
$445$	−7.05439	−	4.80960i	−0.334410	−	0.227997i
$446$	32.1372	−	4.84390i	1.52174	−	0.229365i
$447$		0			0
$448$	−24.6308	+	19.7141i	−1.16370	+	0.931404i
$449$	7.67300	+	9.62163i	0.362111	+	0.454073i	0.929197	−	0.369586i	$-0.120500\pi$
$449$	7.67300	+	9.62163i	0.362111	+	0.454073i	−0.567085	+	0.823659i	$0.691929\pi$
$450$		0			0
$451$	−44.5152	−	6.70959i	−2.09614	−	0.315942i
$452$	17.5805	−	16.3123i	0.826917	−	0.767267i
$453$		0			0
$454$	−5.19145	−	22.7452i	−0.243647	−	1.06749i
$455$	−0.0132928	+	0.0433676i	−0.000623177	+	0.00203311i
$456$		0			0
$457$	−1.02222	−	2.60456i	−0.0478172	−	0.121836i	0.904970	−	0.425476i	$-0.139893\pi$
$457$	−1.02222	−	2.60456i	−0.0478172	−	0.121836i	−0.952787	+	0.303640i	$0.901798\pi$
$458$	−3.59368	−	47.9543i	−0.167921	−	2.24076i
$459$		0			0
$460$	12.0613	−	20.8908i	0.562361	−	0.974038i
$461$	−7.93737	−	3.82243i	−0.369680	−	0.178029i	0.239815	−	0.970819i	$-0.422913\pi$
$461$	−7.93737	−	3.82243i	−0.369680	−	0.178029i	−0.609495	+	0.792790i	$0.708628\pi$
$462$		0			0
$463$	−30.1465	+	14.5178i	−1.40103	+	0.674700i	−0.973370	−	0.229241i	$-0.926376\pi$
$463$	−30.1465	+	14.5178i	−1.40103	+	0.674700i	−0.427658	+	0.903940i	$0.640661\pi$
$464$	0.348481	−	4.65016i	0.0161778	−	0.215878i
$465$		0			0
$466$	−32.1320	+	9.91140i	−1.48848	+	0.459137i
$467$	−3.05427	+	40.7564i	−0.141335	+	1.88598i	0.253651	+	0.967296i	$0.418369\pi$
$467$	−3.05427	+	40.7564i	−0.141335	+	1.88598i	−0.394986	+	0.918687i	$0.629251\pi$
$468$		0			0
$469$	−2.71302	+	18.2193i	−0.125276	+	0.841287i
$470$	21.0164	+	10.1210i	0.969413	+	0.466845i
$471$		0			0
$472$	20.0483	+	34.7248i	0.922800	+	1.59834i
$473$	1.35745	+	18.1139i	0.0624157	+	0.832880i
$474$		0			0
$475$	0.317829	−	1.39250i	0.0145830	−	0.0638922i
$476$	−17.4823	+	6.89715i	−0.801299	+	0.316130i
$477$		0			0
$478$	3.58987	−	2.44753i	0.164197	−	0.111947i
$479$	−18.9653	+	17.5973i	−0.866548	+	0.804039i	−0.981923	−	0.189283i	$-0.939384\pi$
$479$	−18.9653	+	17.5973i	−0.866548	+	0.804039i	0.115374	+	0.993322i	$0.463193\pi$
$480$		0			0
$481$	0.148115	+	0.137431i	0.00675348	+	0.00626631i
$482$	5.52416	+	6.92708i	0.251619	+	0.315520i
$483$		0			0
$484$	18.2006	−	22.8228i	0.827299	−	1.03740i
$485$	12.2114	−	1.84058i	0.554493	−	0.0835763i
$486$		0			0
$487$	−7.49639	+	19.1005i	−0.339694	+	0.865526i	0.654314	+	0.756223i	$0.272957\pi$
$487$	−7.49639	+	19.1005i	−0.339694	+	0.865526i	−0.994008	+	0.109304i	$0.965138\pi$
$488$	47.3883	+	14.6173i	2.14517	+	0.661696i
$489$		0			0
$490$	−1.28183	−	16.3263i	−0.0579072	−	0.737549i
$491$	−25.4140			−1.14692			−0.573459	−	0.819234i	$-0.694399\pi$
$491$	−25.4140			−1.14692			−0.573459	+	0.819234i	$0.694399\pi$
$492$		0			0
$493$	−2.35463	+	5.99951i	−0.106047	+	0.270204i
$494$	−0.0119417	−	0.00814171i	−0.000537282	−	0.000366313i
$495$		0			0
$496$	4.56760	−	5.72759i	0.205091	−	0.257176i
$497$	10.9519	+	2.47923i	0.491258	+	0.111209i
$498$		0			0
$499$	5.29357	+	4.91172i	0.236973	+	0.219879i	0.789715	−	0.613473i	$-0.210228\pi$
$499$	5.29357	+	4.91172i	0.236973	+	0.219879i	−0.552743	+	0.833352i	$0.686419\pi$
$500$	−31.3561	−	4.72618i	−1.40229	−	0.211361i
$501$		0			0
$502$	−22.9257	+	15.6305i	−1.02323	+	0.697624i
$503$	−2.69104	−	11.7902i	−0.119988	−	0.525700i	−0.998820	−	0.0485691i	$-0.984534\pi$
$503$	−2.69104	−	11.7902i	−0.119988	−	0.525700i	0.878832	−	0.477131i	$-0.158323\pi$
$504$		0			0
$505$	−0.275755	+	1.20816i	−0.0122709	+	0.0537624i
$506$	−25.8626	−	65.8970i	−1.14974	−	2.92948i
$507$		0			0
$508$	14.4228	+	24.9811i	0.639910	+	1.10836i
$509$	−18.3510	+	31.7848i	−0.813392	+	1.40884i	0.0970849	+	0.995276i	$0.469048\pi$
$509$	−18.3510	+	31.7848i	−0.813392	+	1.40884i	−0.910477	+	0.413560i	$0.864285\pi$
$510$		0			0
$511$	−29.0947	−	11.3592i	−1.28707	−	0.502502i
$512$	−14.4960	+	6.98090i	−0.640638	+	0.308515i
$513$		0			0
$514$	44.7884	−	13.8154i	1.97553	−	0.609370i
$515$	2.87624	−	0.887203i	0.126742	−	0.0390948i
$516$		0			0
$517$	39.4098	−	18.9787i	1.73324	−	0.834684i
$518$	−67.9542	−	26.5309i	−2.98574	−	1.16570i
$519$		0			0
$520$	−0.0310724	+	0.0538190i	−0.00136262	+	0.00236012i
$521$	−7.40909	−	12.8329i	−0.324598	−	0.562221i	0.656833	−	0.754036i	$-0.271896\pi$
$521$	−7.40909	−	12.8329i	−0.324598	−	0.562221i	−0.981431	+	0.191816i	$0.938562\pi$
$522$		0			0
$523$	4.04898	+	10.3166i	0.177050	+	0.451115i	0.991658	−	0.128896i	$-0.0411434\pi$
$523$	4.04898	+	10.3166i	0.177050	+	0.451115i	−0.814608	+	0.580011i	$0.803048\pi$
$524$	−11.7316	+	51.3994i	−0.512496	+	2.24539i
$525$		0			0
$526$	13.1402	+	57.5708i	0.572938	+	2.51021i
$527$	−8.36575	+	5.70367i	−0.364418	+	0.248456i
$528$		0			0
$529$	−23.7315	−	3.57695i	−1.03180	−	0.155519i
$530$	9.50005	+	8.81475i	0.412656	+	0.382888i
$531$		0			0
$532$	3.25209	+	0.736192i	0.140996	+	0.0319180i
$533$	0.110355	−	0.138381i	0.00478000	−	0.00599393i
$534$		0			0
$535$	3.06498	+	2.08967i	0.132511	+	0.0903441i
$536$	−9.22002	+	23.4922i	−0.398244	+	1.01471i
$537$		0			0
$538$	−38.8194			−1.67363
$539$	−25.4345	−	17.2089i	−1.09554	−	0.741239i
$540$		0			0
$541$	3.05469	+	0.942248i	0.131331	+	0.0405104i	0.359724	−	0.933059i	$-0.382871\pi$
$541$	3.05469	+	0.942248i	0.131331	+	0.0405104i	−0.228393	+	0.973569i	$0.573347\pi$
$542$	−5.26879	+	13.4246i	−0.226314	+	0.576638i
$543$		0			0
$544$	7.60427	−	1.14616i	0.326030	−	0.0491412i
$545$	1.54962	−	1.94317i	0.0663786	−	0.0832362i
$546$		0			0
$547$	−10.2680	−	12.8756i	−0.439027	−	0.550522i	0.512260	−	0.858831i	$-0.328808\pi$
$547$	−10.2680	−	12.8756i	−0.439027	−	0.550522i	−0.951286	+	0.308309i	$0.900237\pi$
$548$	45.8427	+	42.5358i	1.95830	+	1.81704i
$549$		0			0
$550$	−30.3688	+	28.1782i	−1.29493	+	1.20152i
$551$	0.944787	−	0.644145i	0.0402493	−	0.0274415i
$552$		0			0
$553$	−1.18167	+	0.466197i	−0.0502499	+	0.0198247i
$554$	−14.6192	+	64.0507i	−0.621109	+	2.72125i
$555$		0			0
$556$	−5.26890	−	70.3086i	−0.223451	−	2.98175i
$557$	−8.30543	−	14.3854i	−0.351912	−	0.609530i	0.634672	−	0.772782i	$-0.281135\pi$
$557$	−8.30543	−	14.3854i	−0.351912	−	0.609530i	−0.986585	+	0.163251i	$0.947802\pi$
$558$		0			0
$559$	−0.0643450	−	0.0309869i	−0.00272150	−	0.00131061i
$560$	0.562329	−	3.77631i	0.0237627	−	0.159578i
$561$		0			0
$562$	1.01826	−	13.5877i	0.0429527	−	0.573163i
$563$	4.43221	−	1.36716i	0.186795	−	0.0576187i	−0.199946	−	0.979807i	$-0.564077\pi$
$563$	4.43221	−	1.36716i	0.186795	−	0.0576187i	0.386742	+	0.922188i	$0.373601\pi$
$564$		0			0
$565$	0.503213	−	6.71491i	0.0211703	−	0.282499i
$566$	53.9684	−	25.9898i	2.26846	−	1.09243i
$567$		0			0
$568$	13.8609	+	6.67504i	0.581589	+	0.280078i
$569$	0.117839	−	0.204103i	0.00494007	−	0.00855645i	−0.863545	−	0.504272i	$-0.831761\pi$
$569$	0.117839	−	0.204103i	0.00494007	−	0.00855645i	0.868485	+	0.495716i	$0.165094\pi$
$570$		0			0
$571$	−0.387445	−	5.17010i	−0.0162141	−	0.216362i	−0.999426	−	0.0338919i	$-0.989210\pi$
$571$	−0.387445	−	5.17010i	−0.0162141	−	0.216362i	0.983211	−	0.182470i	$-0.0584092\pi$
$572$	0.0978645	+	0.249355i	0.00409192	+	0.0104260i
$573$		0			0
$574$	−18.7272	+	61.0973i	−0.781659	+	2.55015i
$575$	6.12045	+	26.8155i	0.255240	+	1.11828i
$576$		0			0
$577$	2.16795	−	2.01156i	0.0902529	−	0.0837425i	−0.633756	−	0.773533i	$-0.718488\pi$
$577$	2.16795	−	2.01156i	0.0902529	−	0.0837425i	0.724009	+	0.689790i	$0.242297\pi$
$578$	−30.1955	−	4.55124i	−1.25597	−	0.189307i
$579$		0			0
$580$	−7.04658	−	8.83613i	−0.292593	−	0.366900i
$581$	−3.99018	+	3.19368i	−0.165541	+	0.132496i
$582$		0			0
$583$	24.0303	−	3.62198i	0.995233	−	0.150007i
$584$	−35.3563	−	24.1055i	−1.46305	−	0.997494i
$585$		0			0
$586$	12.5880	+	3.88288i	0.520005	+	0.160400i
$587$	−18.3860			−0.758871			−0.379435	−	0.925218i	$-0.623882\pi$
$587$	−18.3860			−0.758871			−0.379435	+	0.925218i	$0.623882\pi$
$588$		0			0
$589$	1.79640			0.0740193
$590$	24.7291	+	7.62792i	1.01808	+	0.314036i
$591$		0			0
$592$	−14.0519	−	9.58045i	−0.577531	−	0.393754i
$593$	−12.6432	+	1.90566i	−0.519194	+	0.0782559i	−0.403411	−	0.915019i	$-0.632176\pi$
$593$	−12.6432	+	1.90566i	−0.519194	+	0.0782559i	−0.115782	+	0.993275i	$0.536938\pi$
$594$		0			0
$595$	−2.28107	+	4.75830i	−0.0935148	+	0.195071i
$596$	42.0441	+	52.7216i	1.72219	+	2.15956i
$597$		0			0
$598$	0.275215	+	0.0414820i	0.0112544	+	0.00169633i
$599$	23.2147	−	21.5401i	0.948526	−	0.880103i	−0.0443793	−	0.999015i	$-0.514131\pi$
$599$	23.2147	−	21.5401i	0.948526	−	0.880103i	0.992905	+	0.118912i	$0.0379405\pi$
$600$		0			0
$601$	−5.75775	−	25.2263i	−0.234864	−	1.02900i	−0.945545	−	0.325491i	$-0.894471\pi$
$601$	−5.75775	−	25.2263i	−0.234864	−	1.02900i	0.710682	−	0.703514i	$-0.248387\pi$
$602$	25.7161	+	1.88122i	1.04811	+	0.0766730i
$603$		0			0
$604$	8.51336	+	21.6917i	0.346404	+	0.882622i
$605$	−0.612508	−	8.17335i	−0.0249020	−	0.332294i
$606$		0			0
$607$	−2.18386	+	3.78256i	−0.0886402	+	0.153529i	−0.906937	−	0.421267i	$-0.861585\pi$
$607$	−2.18386	+	3.78256i	−0.0886402	+	0.153529i	0.818296	+	0.574796i	$0.194919\pi$
$608$	−1.22927	−	0.591987i	−0.0498537	−	0.0240083i
$609$		0			0
$610$	28.8372	−	13.8872i	1.16758	−	0.562278i
$611$	−0.0128518	+	0.171496i	−0.000519930	+	0.00693798i
$612$		0			0
$613$	−6.50100	+	2.00529i	−0.262573	+	0.0809930i	−0.423246	−	0.906015i	$-0.639110\pi$
$613$	−6.50100	+	2.00529i	−0.262573	+	0.0809930i	0.160674	+	0.987008i	$0.448633\pi$
$614$	5.54107	−	73.9405i	0.223620	−	2.98400i
$615$		0			0
$616$	−28.6720	−	30.7912i	−1.15523	−	1.24061i
$617$	−34.1847	−	16.4625i	−1.37623	−	0.662755i	−0.408034	−	0.912967i	$-0.633786\pi$
$617$	−34.1847	−	16.4625i	−1.37623	−	0.662755i	−0.968191	+	0.250211i	$0.919500\pi$
$618$		0			0
$619$	5.00528	+	8.66939i	0.201179	+	0.348452i	0.948909	−	0.315551i	$-0.102189\pi$
$619$	5.00528	+	8.66939i	0.201179	+	0.348452i	−0.747730	+	0.664003i	$0.768856\pi$
$620$	−1.32684	−	17.7055i	−0.0532872	−	0.711068i
$621$		0			0
$622$	1.51684	−	6.64571i	0.0608198	−	0.266469i
$623$	3.42714	+	22.4667i	0.137305	+	0.900109i
$624$		0			0
$625$	9.21812	−	6.28481i	0.368725	−	0.251392i
$626$	38.4730	−	35.6978i	1.53769	−	1.42677i
$627$		0			0
$628$	−47.0760	−	43.6801i	−1.87854	−	1.74303i
$629$	14.6555	+	18.3774i	0.584354	+	0.732756i
$630$		0			0
$631$	27.9507	−	35.0491i	1.11270	−	1.39528i	0.203424	−	0.979091i	$-0.434793\pi$
$631$	27.9507	−	35.0491i	1.11270	−	1.39528i	0.909277	−	0.416192i	$-0.136636\pi$
$632$	−1.72097	+	0.259394i	−0.0684565	+	0.0103182i
$633$		0			0
$634$	−3.07673	+	7.83937i	−0.122192	+	0.311341i
$635$	7.73935	+	2.38727i	0.307127	+	0.0947361i
$636$		0			0
$637$	0.108595	−	0.0527725i	0.00430268	−	0.00209092i
$638$	−33.1665			−1.31307
$639$		0			0
$640$	−7.40852	+	18.8766i	−0.292847	+	0.746163i
$641$	6.48813	+	4.42353i	0.256266	+	0.174719i	0.684638	−	0.728883i	$-0.259960\pi$
$641$	6.48813	+	4.42353i	0.256266	+	0.174719i	−0.428372	+	0.903602i	$0.640913\pi$
$642$		0			0
$643$	−10.7356	+	13.4620i	−0.423371	+	0.530891i	−0.947076	−	0.321009i	$-0.895978\pi$
$643$	−10.7356	+	13.4620i	−0.423371	+	0.530891i	0.523705	+	0.851900i	$0.324549\pi$
$644$	−62.5749	+	14.3993i	−2.46580	+	0.567412i
$645$		0			0
$646$	−1.23254	−	1.14363i	−0.0484937	−	0.0449955i
$647$	22.6750	+	3.41771i	0.891446	+	0.134364i	0.578765	−	0.815494i	$-0.303535\pi$
$647$	22.6750	+	3.41771i	0.891446	+	0.134364i	0.312681	+	0.949858i	$0.398773\pi$
$648$		0			0
$649$	40.0955	−	27.3367i	1.57389	−	1.07306i
$650$	−0.0362443	−	0.158797i	−0.00142162	−	0.00622852i
$651$		0			0
$652$	7.37047	−	32.2921i	0.288650	−	1.26466i
$653$	11.0092	+	28.0509i	0.430822	+	1.09772i	0.967262	+	0.253779i	$0.0816736\pi$
$653$	11.0092	+	28.0509i	0.430822	+	1.09772i	−0.536440	+	0.843939i	$0.680231\pi$
$654$		0			0
$655$	7.40143	+	12.8197i	0.289198	+	0.500905i
$656$	−7.44899	+	12.9020i	−0.290834	+	0.503740i
$657$		0			0
$658$	−18.4070	−	59.2999i	−0.717580	−	2.31175i
$659$	31.5242	−	15.1812i	1.22801	−	0.591377i	0.296477	−	0.955040i	$-0.404188\pi$
$659$	31.5242	−	15.1812i	1.22801	−	0.591377i	0.931531	+	0.363663i	$0.118474\pi$
$660$		0			0
$661$	11.2852	−	3.48101i	0.438942	−	0.135396i	−0.0674047	−	0.997726i	$-0.521472\pi$
$661$	11.2852	−	3.48101i	0.438942	−	0.135396i	0.506347	+	0.862330i	$0.330996\pi$
$662$	−13.0156	+	4.01477i	−0.505864	+	0.156038i
$663$		0			0
$664$	−6.30879	+	3.03816i	−0.244829	+	0.117903i
$665$	0.809951	−	0.469546i	0.0314086	−	0.0182082i
$666$		0			0
$667$	−11.0100	+	19.0699i	−0.426310	+	0.738391i
$668$	9.38865	+	16.2616i	0.363258	+	0.629181i
$669$		0			0
$670$	5.95070	+	15.1621i	0.229896	+	0.585764i
$671$	13.3555	−	58.5142i	0.515583	−	2.25892i
$672$		0			0
$673$	11.1693	+	48.9358i	0.430544	+	1.88634i	0.462089	+	0.886834i	$0.347100\pi$
$673$	11.1693	+	48.9358i	0.430544	+	1.88634i	−0.0315450	+	0.999502i	$0.510043\pi$
$674$	−40.6464	+	27.7123i	−1.56564	+	1.06744i
$675$		0			0
$676$	45.5055	+	6.85885i	1.75021	+	0.263802i
$677$	−11.5899	−	10.7538i	−0.445435	−	0.413303i	0.425303	−	0.905051i	$-0.360168\pi$
$677$	−11.5899	−	10.7538i	−0.445435	−	0.413303i	−0.870738	+	0.491748i	$0.836358\pi$
$678$		0			0
$679$	−25.7367	−	20.4496i	−0.987682	−	0.784784i
$680$	−4.50755	+	5.65229i	−0.172857	+	0.216756i
$681$		0			0
$682$	−43.0506	−	29.3514i	−1.64849	−	1.12392i
$683$	9.36098	−	23.8514i	0.358188	−	0.912648i	−0.632260	−	0.774757i	$-0.717872\pi$
$683$	9.36098	−	23.8514i	0.358188	−	0.912648i	0.990447	−	0.137891i	$-0.0440324\pi$
$684$		0			0
$685$	17.5588			0.670889
$686$	−29.4792	+	32.1125i	−1.12552	+	1.22606i
$687$		0			0
$688$	5.74426	+	1.77187i	0.218998	+	0.0675519i
$689$	−0.0349069	+	0.0889413i	−0.00132985	+	0.00338839i
$690$		0			0
$691$	−9.05624	+	1.36501i	−0.344516	+	0.0519274i	−0.319021	−	0.947748i	$-0.603354\pi$
$691$	−9.05624	+	1.36501i	−0.344516	+	0.0519274i	−0.0254945	+	0.999675i	$0.508116\pi$
$692$	39.8651	−	49.9892i	1.51544	−	1.90030i
$693$		0			0
$694$	15.8986	+	19.9362i	0.603501	+	0.756767i
$695$	−14.5117	−	13.4649i	−0.550461	−	0.510754i
$696$		0			0
$697$	15.0940	−	14.0051i	0.571725	−	0.530483i
$698$	26.0814	−	17.7820i	0.987195	−	0.673058i
$699$		0			0
$700$	21.2231	+	31.0100i	0.802156	+	1.17207i
$701$	−4.72038	+	20.6813i	−0.178286	+	0.781123i	0.804135	+	0.594446i	$0.202629\pi$
$701$	−4.72038	+	20.6813i	−0.178286	+	0.781123i	−0.982421	+	0.186677i	$0.940228\pi$
$702$		0			0
$703$	−0.311652	−	4.15871i	−0.0117542	−	0.156849i
$704$	26.1562	+	45.3038i	0.985798	+	1.70745i
$705$		0			0
$706$	44.2544	+	21.3118i	1.66554	+	0.802080i
$707$	2.85376	−	1.65438i	0.107327	−	0.0622195i
$708$		0			0
$709$	−1.05733	+	14.1090i	−0.0397087	+	0.529876i	0.941511	+	0.336982i	$0.109406\pi$
$709$	−1.05733	+	14.1090i	−0.0397087	+	0.529876i	−0.981220	+	0.192893i	$0.938213\pi$
$710$	9.48812	−	2.92670i	0.356083	−	0.109837i
$711$		0			0
$712$	−2.32686	+	31.0498i	−0.0872028	+	1.16364i
$713$	−31.1676	+	15.0095i	−1.16723	+	0.562110i
$714$		0			0
$715$	0.0677636	+	0.0326332i	0.00253422	+	0.00122041i
$716$	11.5036	−	19.9249i	0.429911	−	0.744627i
$717$		0			0
$718$	−0.437291	−	5.83525i	−0.0163196	−	0.217769i
$719$	−18.1884	−	46.3434i	−0.678315	−	1.72832i	−0.685214	−	0.728341i	$-0.740291\pi$
$719$	−18.1884	−	46.3434i	−0.678315	−	1.72832i	0.00689962	−	0.999976i	$-0.497804\pi$
$720$		0			0
$721$	−6.94571	−	3.99368i	−0.258672	−	0.148732i
$722$	−9.88495	−	43.3088i	−0.367880	−	1.61179i
$723$		0			0
$724$	−4.99192	+	4.63183i	−0.185523	+	0.172141i
$725$	12.7426	+	1.92064i	0.473250	+	0.0713309i
$726$		0			0
$727$	−3.31554	−	4.15755i	−0.122966	−	0.154195i	0.716538	−	0.697548i	$-0.245726\pi$
$727$	−3.31554	−	4.15755i	−0.122966	−	0.154195i	−0.839504	+	0.543353i	$0.817154\pi$
$728$	0.161206	−	0.0370956i	0.00597469	−	0.00137485i
$729$		0			0
$730$	−27.3098	+	4.11630i	−1.01078	+	0.152351i
$731$	−6.86463	−	4.68022i	−0.253897	−	0.173104i
$732$		0			0
$733$	−36.1916	−	11.1636i	−1.33677	−	0.412338i	−0.457729	−	0.889092i	$-0.651337\pi$
$733$	−36.1916	−	11.1636i	−1.33677	−	0.412338i	−0.879037	+	0.476754i	$0.841813\pi$
$734$	−15.7403			−0.580986
$735$		0			0
$736$	26.2742			0.968479
$737$	29.1863	+	9.00278i	1.07509	+	0.331622i
$738$		0			0
$739$	34.5927	+	23.5849i	1.27251	+	0.867584i	0.995636	−	0.0933223i	$-0.0297487\pi$
$739$	34.5927	+	23.5849i	1.27251	+	0.867584i	0.276875	+	0.960906i	$0.410701\pi$
$740$	−40.7584	+	6.14335i	−1.49831	+	0.225834i
$741$		0			0
$742$	−0.0612745	−	34.4962i	−0.00224946	−	1.26639i
$743$	10.9103	+	13.6810i	0.400259	+	0.501909i	0.940590	−	0.339543i	$-0.110273\pi$
$743$	10.9103	+	13.6810i	0.400259	+	0.501909i	−0.540331	+	0.841452i	$0.681701\pi$
$744$		0			0
$745$	18.7222	+	2.82192i	0.685929	+	0.103387i
$746$	−64.3643	+	59.7214i	−2.35655	+	2.18655i
$747$		0			0
$748$	6.93432	+	30.3812i	0.253544	+	1.11085i
$749$	−1.48901	−	9.76128i	−0.0544074	−	0.356670i
$750$		0			0
$751$	8.47774	+	21.6009i	0.309357	+	0.788229i	0.998005	+	0.0631331i	$0.0201093\pi$
$751$	8.47774	+	21.6009i	0.309357	+	0.788229i	−0.688648	+	0.725096i	$0.741796\pi$
$752$	−1.08176	−	14.4351i	−0.0394477	−	0.526393i
$753$		0			0
$754$	0.0651996	−	0.112929i	0.00237443	−	0.00411264i
$755$	5.89484	+	2.83881i	0.214535	+	0.103315i
$756$		0			0
$757$	−17.7338	+	8.54016i	−0.644547	+	0.310397i	−0.727450	−	0.686160i	$-0.759295\pi$
$757$	−17.7338	+	8.54016i	−0.644547	+	0.310397i	0.0829038	+	0.996558i	$0.473581\pi$
$758$	−1.38748	+	18.5147i	−0.0503956	+	0.672483i
$759$		0			0
$760$	1.22568	−	0.378073i	0.0444602	−	0.0137142i
$761$	2.59517	−	34.6301i	0.0940748	−	1.25534i	−0.727847	−	0.685740i	$-0.759479\pi$
$761$	2.59517	−	34.6301i	0.0940748	−	1.25534i	0.821922	−	0.569601i	$-0.192902\pi$
$762$		0			0
$763$	−6.59634	+	0.506112i	−0.238804	+	0.0183225i
$764$	−14.8977	−	7.17433i	−0.538978	−	0.259558i
$765$		0			0
$766$	−20.4281	−	35.3825i	−0.738098	−	1.27842i
$767$	0.0142581	+	0.190261i	0.000514830	+	0.00686993i
$768$		0			0
$769$	−4.56216	+	19.9881i	−0.164516	+	0.720791i	0.823612	+	0.567154i	$0.191956\pi$
$769$	−4.56216	+	19.9881i	−0.164516	+	0.720791i	−0.988127	+	0.153636i	$0.950902\pi$
$770$	−27.0824	−	1.98117i	−0.975980	−	0.0713965i
$771$		0			0
$772$	−0.474953	+	0.323817i	−0.0170939	+	0.0116544i
$773$	34.5058	−	32.0167i	1.24109	−	1.15156i	0.258449	−	0.966025i	$-0.416789\pi$
$773$	34.5058	−	32.0167i	1.24109	−	1.15156i	0.982638	−	0.185535i	$-0.0594019\pi$
$774$		0			0
$775$	14.8404	+	13.7699i	0.533084	+	0.494630i
$776$	−28.0798	−	35.2110i	−1.00801	−	1.26400i
$777$		0			0
$778$	−13.1431	+	16.4810i	−0.471204	+	0.590871i
$779$	−3.61238	+	0.544479i	−0.129427	+	0.0195080i
$780$		0			0
$781$	6.80238	−	17.3322i	0.243408	−	0.620194i
$782$	30.9400	+	9.54373i	1.10641	+	0.341283i
$783$		0			0
$784$	−8.37645	+	5.75466i	−0.299159	+	0.205524i
$785$	−18.0312			−0.643561
$786$		0			0
$787$	7.59737	−	19.3578i	0.270817	−	0.690030i	−0.729167	−	0.684336i	$-0.760092\pi$
$787$	7.59737	−	19.3578i	0.270817	−	0.690030i	0.999984	−	0.00569425i	$-0.00181255\pi$
$788$	−15.3940	−	10.4954i	−0.548388	−	0.373885i
$789$		0			0
$790$	−0.700352	+	0.878213i	−0.0249174	+	0.0312454i
$791$	−13.9937	+	11.2004i	−0.497560	+	0.398239i
$792$		0			0
$793$	0.172981	+	0.160503i	0.00614275	+	0.00569964i
$794$	47.1828	+	7.11166i	1.67445	+	0.252383i
$795$		0			0
$796$	43.6385	−	29.7522i	1.54673	−	1.05454i
$797$	2.53045	+	11.0866i	0.0896330	+	0.392708i	0.999767	−	0.0216072i	$-0.00687831\pi$
$797$	2.53045	+	11.0866i	0.0896330	+	0.392708i	−0.910134	+	0.414315i	$0.864021\pi$
$798$		0			0
$799$	−4.45192	+	19.5051i	−0.157498	+	0.690042i
$800$	−5.61754	−	14.3133i	−0.198610	−	0.506050i
$801$		0			0
$802$	−18.9238	−	32.7769i	−0.668222	−	1.15739i
$803$	−25.8948	+	44.8512i	−0.913809	+	1.58276i
$804$		0			0
$805$	−10.1295	+	14.9140i	−0.357016	+	0.525651i
$806$	0.184569	−	0.0888839i	0.00650118	−	0.00313080i
$807$		0			0
$808$	4.31854	−	1.33209i	0.151926	−	0.0468629i
$809$	−43.2131	+	13.3295i	−1.51929	+	0.468639i	−0.938461	−	0.345386i	$-0.887748\pi$
$809$	−43.2131	+	13.3295i	−1.51929	+	0.468639i	−0.580830	+	0.814025i	$0.697272\pi$
$810$		0			0
$811$	19.9771	−	9.62047i	0.701492	−	0.337821i	−0.0489096	−	0.998803i	$-0.515575\pi$
$811$	19.9771	−	9.62047i	0.701492	−	0.337821i	0.750401	+	0.660983i	$0.229860\pi$
$812$	−4.43088	+	29.7555i	−0.155493	+	1.04421i
$813$		0			0
$814$	−60.4806	+	104.755i	−2.11984	+	3.67168i
$815$	−4.65002	−	8.05406i	−0.162883	−	0.282122i
$816$		0			0
$817$	0.538534	+	1.37216i	0.0188409	+	0.0480059i
$818$	−4.02198	+	17.6214i	−0.140625	+	0.616119i
$819$		0			0
$820$	8.03458	+	35.2018i	0.280580	+	1.22930i
$821$	−0.318345	+	0.217044i	−0.0111103	+	0.00757488i	−0.568862	−	0.822433i	$-0.692616\pi$
$821$	−0.318345	+	0.217044i	−0.0111103	+	0.00757488i	0.557752	+	0.830008i	$0.311664\pi$
$822$		0			0
$823$	−4.31815	−	0.650856i	−0.150521	−	0.0226874i	0.0733494	−	0.997306i	$-0.476631\pi$
$823$	−4.31815	−	0.650856i	−0.150521	−	0.0226874i	−0.223870	+	0.974619i	$0.571869\pi$
$824$	−8.04668	−	7.46623i	−0.280320	−	0.260098i
$825$		0			0
$826$	−29.9983	−	62.0101i	−1.04377	−	2.15761i
$827$	−15.2781	+	19.1582i	−0.531273	+	0.666196i	−0.972960	−	0.230974i	$-0.925809\pi$
$827$	−15.2781	+	19.1582i	−0.531273	+	0.666196i	0.441687	+	0.897169i	$0.354380\pi$
$828$		0			0
$829$	45.6653	+	31.1341i	1.58602	+	1.08133i	0.951156	+	0.308710i	$0.0998972\pi$
$829$	45.6653	+	31.1341i	1.58602	+	1.08133i	0.634866	+	0.772622i	$0.281055\pi$
$830$	−1.65109	+	4.20691i	−0.0573102	+	0.146024i
$831$		0			0
$832$	−0.205674			−0.00713048
$833$	13.4071	−	4.18777i	0.464530	−	0.145098i
$834$		0			0
$835$	5.03798	+	1.55401i	0.174347	+	0.0537788i
$836$	2.01992	−	5.14668i	0.0698605	−	0.178002i
$837$		0			0
$838$	−37.8611	+	5.70664i	−1.30789	+	0.197133i
$839$	21.7576	−	27.2832i	0.751157	−	0.941921i	−0.248486	−	0.968636i	$-0.579933\pi$
$839$	21.7576	−	27.2832i	0.751157	−	0.941921i	0.999643	+	0.0267142i	$0.00850440\pi$
$840$		0			0
$841$	−11.6488	−	14.6071i	−0.401683	−	0.503695i
$842$	41.8880	+	38.8664i	1.44355	+	1.33942i
$843$		0			0
$844$	−8.56955	+	7.95138i	−0.294976	+	0.273698i
$845$	10.6760	−	7.27876i	0.367265	−	0.250397i
$846$		0			0
$847$	−14.8109	+	16.0194i	−0.508910	+	0.550432i
$848$	1.78957	−	7.84062i	0.0614541	−	0.269248i
$849$		0			0
$850$	−1.41603	−	18.8956i	−0.0485693	−	0.648112i
$851$	40.1546	+	69.5498i	1.37648	+	2.38414i
$852$		0			0
$853$	−7.73120	−	3.72315i	−0.264711	−	0.127478i	0.296821	−	0.954933i	$-0.404074\pi$
$853$	−7.73120	−	3.72315i	−0.264711	−	0.127478i	−0.561532	+	0.827455i	$0.689788\pi$
$854$	−79.3626	−	30.9850i	−2.71573	−	1.06028i
$855$		0			0
$856$	1.01097	−	13.4904i	0.0345542	−	0.461094i
$857$	−9.92447	+	3.06129i	−0.339013	+	0.104572i	−0.459587	−	0.888133i	$-0.652003\pi$
$857$	−9.92447	+	3.06129i	−0.339013	+	0.104572i	0.120574	+	0.992704i	$0.461526\pi$
$858$		0			0
$859$	2.23764	−	29.8593i	0.0763474	−	1.01879i	−0.819110	−	0.573637i	$-0.805532\pi$
$859$	2.23764	−	29.8593i	0.0763474	−	1.01879i	0.895457	−	0.445148i	$-0.146849\pi$
$860$	13.1264	−	6.32133i	0.447606	−	0.215556i
$861$		0			0
$862$	−0.983581	−	0.473668i	−0.0335009	−	0.0161332i
$863$	−14.6824	+	25.4307i	−0.499795	+	0.865670i	−1.00000		0.000236754i	$-0.999925\pi$
$863$	−14.6824	+	25.4307i	−0.499795	+	0.865670i	0.500205	+	0.865907i	$0.333258\pi$
$864$		0			0
$865$	−1.34159	−	17.9022i	−0.0456153	−	0.608694i
$866$	−5.15760	−	13.1414i	−0.175263	−	0.446562i
$867$		0			0
$868$	−32.0841	+	34.7019i	−1.08901	+	1.17786i
$869$	0.468709	+	2.05355i	0.0158999	+	0.0696619i
$870$		0			0
$871$	−0.0880290	+	0.0816790i	−0.00298275	+	0.00276759i
$872$	−8.96272	−	1.35091i	−0.303516	−	0.0457477i
$873$		0			0
$874$	−3.58170	−	4.49131i	−0.121153	−	0.151921i
$875$	23.1147	+	5.23261i	0.781421	+	0.176894i
$876$		0			0
$877$	−34.5025	+	5.20042i	−1.16507	+	0.175606i	−0.702967	−	0.711222i	$-0.748142\pi$
$877$	−34.5025	+	5.20042i	−1.16507	+	0.175606i	−0.462100	+	0.886828i	$0.652904\pi$
$878$	53.3496	+	36.3731i	1.80046	+	1.22753i
$879$		0			0
$880$	−6.04945	−	1.86601i	−0.203927	−	0.0629031i
$881$	−39.1959			−1.32054			−0.660272	−	0.751027i	$-0.729559\pi$
$881$	−39.1959			−1.32054			−0.660272	+	0.751027i	$0.729559\pi$
$882$		0			0
$883$	−27.6657			−0.931024			−0.465512	−	0.885042i	$-0.654130\pi$
$883$	−27.6657			−0.931024			−0.465512	+	0.885042i	$0.654130\pi$
$884$	−0.117077	−	0.0361136i	−0.00393774	−	0.00121463i
$885$		0			0
$886$	43.2905	+	29.5149i	1.45437	+	0.991574i
$887$	−2.46598	+	0.371686i	−0.0827994	+	0.0124800i	−0.190311	−	0.981724i	$-0.560950\pi$
$887$	−2.46598	+	0.371686i	−0.0827994	+	0.0124800i	0.107512	+	0.994204i	$0.465712\pi$
$888$		0			0
$889$	−9.38843	−	19.4070i	−0.314878	−	0.650890i
$890$	12.5297	+	15.7117i	0.419996	+	0.526658i
$891$		0			0
$892$	−48.3348	−	7.28529i	−1.61837	−	0.243930i
$893$	2.60204	−	2.41434i	0.0870740	−	0.0807929i
$894$		0			0
$895$	−1.43746	−	6.29793i	−0.0480490	−	0.210516i
$896$	50.2112	−	19.8094i	1.67744	−	0.661787i
$897$		0			0
$898$	−10.5826	−	26.9639i	−0.353145	−	0.899798i
$899$	1.21119	+	16.1622i	0.0403955	+	0.539041i
$900$		0			0
$901$	−5.55762	+	9.62609i	−0.185151	+	0.320691i
$902$	95.4669	+	45.9744i	3.17870	+	1.53078i
$903$		0			0
$904$	−22.1252	+	10.6549i	−0.735873	+	0.354378i
$905$	−0.142886	+	1.90668i	−0.00474968	+	0.0633801i
$906$		0			0
$907$	−36.2296	+	11.1753i	−1.20298	+	0.371071i	−0.830527	−	0.556978i	$-0.811961\pi$
$907$	−36.2296	+	11.1753i	−1.20298	+	0.371071i	−0.372456	+	0.928050i	$0.621484\pi$
$908$	−2.62219	+	34.9908i	−0.0870206	+	1.16121i
$909$		0			0
$910$	0.0599850	−	0.0883185i	0.00198848	−	0.00292773i
$911$	−15.3453	−	7.38993i	−0.508414	−	0.244839i	0.162048	−	0.986783i	$-0.448190\pi$
$911$	−15.3453	−	7.38993i	−0.508414	−	0.244839i	−0.670462	+	0.741944i	$0.733904\pi$
$912$		0			0
$913$	4.23729	+	7.33920i	0.140234	+	0.242892i
$914$	0.492148	+	6.56726i	0.0162788	+	0.217226i
$915$		0			0
$916$	−16.0941	+	70.5128i	−0.531764	+	2.32981i
$917$	11.5473	−	37.6727i	0.381324	−	1.24406i
$918$		0			0
$919$	−6.03762	+	4.11638i	−0.199163	+	0.135787i	−0.658795	−	0.752322i	$-0.728934\pi$
$919$	−6.03762	+	4.11638i	−0.199163	+	0.135787i	0.459632	+	0.888109i	$0.347981\pi$
$920$	−18.1067	+	16.8006i	−0.596961	+	0.553899i
$921$		0			0
$922$	15.2005	+	14.1040i	0.500602	+	0.464491i
$923$	0.0456423	+	0.0572336i	0.00150233	+	0.00188387i
$924$		0			0
$925$	29.3031	−	36.7449i	0.963480	−	1.20817i
$926$	77.8764	−	11.7380i	2.55918	−	0.385734i
$927$		0			0
$928$	4.49731	−	11.4589i	0.147631	−	0.376158i
$929$	10.1458	+	3.12955i	0.332871	+	0.102677i	0.456685	−	0.889628i	$-0.349036\pi$
$929$	10.1458	+	3.12955i	0.332871	+	0.102677i	−0.123814	+	0.992305i	$0.539513\pi$
$930$		0			0
$931$	−2.38392	−	0.726077i	−0.0781298	−	0.0237962i
$932$	50.5738			1.65660
$933$		0			0
$934$	35.1453	−	89.5488i	1.14999	−	2.93013i
$935$	7.22934	+	4.92888i	0.236425	+	0.161192i
$936$		0			0
$937$	−16.2061	+	20.3218i	−0.529431	+	0.663886i	−0.972582	−	0.232561i	$-0.925289\pi$
$937$	−16.2061	+	20.3218i	−0.529431	+	0.663886i	0.443150	+	0.896447i	$0.353861\pi$
$938$	18.7421	−	39.0958i	0.611950	−	1.27652i
$939$		0			0
$940$	−25.7179	−	23.8627i	−0.838824	−	0.778315i
$941$	−38.2277	−	5.76190i	−1.24619	−	0.187832i	−0.507364	−	0.861732i	$-0.669380\pi$
$941$	−38.2277	−	5.76190i	−1.24619	−	0.187832i	−0.738823	+	0.673900i	$0.764618\pi$
$942$		0			0
$943$	58.1256	−	39.6294i	1.89283	−	1.29051i
$944$	−3.57357	−	15.6568i	−0.116310	−	0.509587i
$945$		0			0
$946$	9.51386	−	41.6829i	0.309322	−	1.35523i
$947$	−7.35886	−	18.7501i	−0.239131	−	0.609295i	0.760046	−	0.649870i	$-0.225177\pi$
$947$	−7.35886	−	18.7501i	−0.239131	−	0.609295i	−0.999177	+	0.0405742i	$0.987081\pi$
$948$		0			0
$949$	−0.101810	−	0.176339i	−0.00330488	−	0.00572422i
$950$	−1.68093	+	2.91145i	−0.0545365	+	0.0944600i
$951$		0			0
$952$	19.1874	−	1.47218i	0.621869	−	0.0477136i
$953$	−0.463686	+	0.223300i	−0.0150203	+	0.00723338i	−0.441379	−	0.897321i	$-0.645510\pi$
$953$	−0.463686	+	0.223300i	−0.0150203	+	0.00723338i	0.426359	+	0.904554i	$0.359796\pi$
$954$		0			0
$955$	−4.43641	+	1.36845i	−0.143559	+	0.0442821i
$956$	−6.24437	+	1.92613i	−0.201957	+	0.0622956i
$957$		0			0
$958$	54.8646	−	26.4214i	1.77259	−	0.853637i
$959$	−31.8512	−	34.2053i	−1.02853	−	1.10455i
$960$		0			0
$961$	2.76901	−	4.79606i	0.0893229	−	0.154712i
$962$	−0.237789	−	0.411863i	−0.00766663	−	0.0132790i
$963$		0			0
$964$	−4.86841	−	12.4045i	−0.156801	−	0.399523i
$965$	−0.0359150	+	0.157354i	−0.00115615	+	0.00506540i
$966$		0			0
$967$	−11.2256	−	49.1824i	−0.360990	−	1.58160i	−0.750687	−	0.660658i	$-0.770278\pi$
$967$	−11.2256	−	49.1824i	−0.360990	−	1.58160i	0.389697	−	0.920943i	$-0.372580\pi$
$968$	−24.6969	+	16.8381i	−0.793789	+	0.541196i
$969$		0			0
$970$	−28.7424	−	4.33222i	−0.922863	−	0.139099i
$971$	25.4043	+	23.5717i	0.815261	+	0.756452i	0.972945	−	0.231038i	$-0.0742121\pi$
$971$	25.4043	+	23.5717i	0.815261	+	0.756452i	−0.157683	+	0.987490i	$0.550403\pi$
$972$		0			0
$973$	0.0935995	+	52.6944i	0.00300066	+	1.68930i
$974$	30.1120	−	37.7593i	0.964851	−	1.20989i
$975$		0			0
$976$	−16.4110	−	11.1888i	−0.525304	−	0.358146i
$977$	21.6039	−	55.0460i	0.691172	−	1.76108i	0.0436280	−	0.999048i	$-0.486108\pi$
$977$	21.6039	−	55.0460i	0.691172	−	1.76108i	0.647544	−	0.762028i	$-0.275796\pi$
$978$		0			0
$979$	37.6840			1.20438
$980$	−5.39549	+	24.0324i	−0.172352	+	0.767687i
$981$		0			0
$982$	57.1602	+	17.6316i	1.82406	+	0.562646i
$983$	−0.654461	+	1.66754i	−0.0208741	+	0.0531863i	−0.940931	−	0.338599i	$-0.890047\pi$
$983$	−0.654461	+	1.66754i	−0.0208741	+	0.0531863i	0.920057	+	0.391785i	$0.128142\pi$
$984$		0			0
$985$	−5.17283	+	0.779678i	−0.164820	+	0.0248426i
$986$	9.45825	−	11.8603i	0.301212	−	0.377708i
$987$		0			0
$988$	0.0135532	+	0.0169952i	0.000431184	+	0.000540688i
$989$	−20.8084	−	19.3074i	−0.661670	−	0.613940i
$990$		0			0
$991$	13.3751	−	12.4102i	0.424873	−	0.394224i	−0.438549	−	0.898707i	$-0.644507\pi$
$991$	13.3751	−	12.4102i	0.424873	−	0.394224i	0.863422	+	0.504483i	$0.168317\pi$
$992$	15.9784	−	10.8939i	0.507315	−	0.345882i
$993$		0			0
$994$	−22.9125	−	13.1743i	−0.726739	−	0.417864i
$995$	3.29986	−	14.4576i	0.104612	−	0.458337i
$996$		0			0
$997$	1.77504	+	23.6862i	0.0562160	+	0.750150i	0.952085	+	0.305833i	$0.0989348\pi$
$997$	1.77504	+	23.6862i	0.0562160	+	0.750150i	−0.895869	+	0.444318i	$0.853446\pi$
$998$	−8.49847	−	14.7198i	−0.269014	−	0.465946i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bb.c.100.1		48
3.2	odd	2		147.2.m.a.100.4	yes	48
49.25	even	21	inner	441.2.bb.c.172.1		48
147.5	even	42		7203.2.a.k.1.24		24
147.44	odd	42		7203.2.a.i.1.24		24
147.74	odd	42		147.2.m.a.25.4	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.m.a.25.4	✓	48	147.74	odd	42
147.2.m.a.100.4	yes	48	3.2	odd	2
441.2.bb.c.100.1		48	1.1	even	1	trivial
441.2.bb.c.172.1		48	49.25	even	21	inner
7203.2.a.i.1.24		24	147.44	odd	42
7203.2.a.k.1.24		24	147.5	even	42

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.bb (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.24916 - 0.693774i) q^{2} +(2.92492 + 1.99418i) q^{4} +(0.982858 - 0.148142i) q^{5} +(-2.07146 - 1.64592i) q^{7} +(-2.26005 - 2.83402i) q^{8} +(-2.31338 - 0.348686i) q^{10} +(-3.21592 + 2.98394i) q^{11} +(-0.00383811 - 0.0168159i) q^{13} +(3.51714 + 5.13907i) q^{14} +(0.530409 + 1.35146i) q^{16} +(-0.149951 - 2.00095i) q^{17} +(-0.178003 + 0.308310i) q^{19} +(3.17020 + 1.52669i) q^{20} +(9.30331 - 4.48024i) q^{22} +(0.512321 - 6.83645i) q^{23} +(-3.83380 + 1.18257i) q^{25} +(-0.00303388 + 0.0404844i) q^{26} +(-2.77659 - 8.94505i) q^{28} +(-2.89389 - 1.39362i) q^{29} +(-2.52299 - 4.36995i) q^{31} +(0.286403 + 3.82178i) q^{32} +(-1.05095 + 4.60450i) q^{34} +(-2.27978 - 1.31084i) q^{35} +(-9.67885 + 6.59893i) q^{37} +(0.614254 - 0.569944i) q^{38} +(-2.64115 - 2.45063i) q^{40} +(6.39800 + 8.02284i) q^{41} +(2.58159 - 3.23721i) q^{43} +(-15.3568 + 2.31467i) q^{44} +(-5.89525 + 15.0208i) q^{46} +(-9.52767 - 2.93890i) q^{47} +(1.58188 + 6.81892i) q^{49} +9.44327 q^{50} +(0.0223077 - 0.0568390i) q^{52} +(-4.57690 - 3.12048i) q^{53} +(-2.71875 + 3.40920i) q^{55} +(0.0170352 + 9.59042i) q^{56} +(5.54195 + 5.14218i) q^{58} +(-10.9381 - 1.64865i) q^{59} +(-11.3038 + 7.70678i) q^{61} +(2.64286 + 11.5791i) q^{62} +(2.65341 - 11.6253i) q^{64} +(-0.00626346 - 0.0159590i) q^{65} +(-3.48108 - 6.02941i) q^{67} +(3.55166 - 6.15166i) q^{68} +(4.21816 + 4.52993i) q^{70} +(-3.82385 + 1.84147i) q^{71} +(11.2807 - 3.47963i) q^{73} +(26.3475 - 8.12711i) q^{74} +(-1.13547 + 0.546813i) q^{76} +(11.5730 - 0.887951i) q^{77} +(0.240066 - 0.415807i) q^{79} +(0.721524 + 1.24972i) q^{80} +(-8.82410 - 22.4834i) q^{82} +(0.429851 - 1.88330i) q^{83} +(-0.443806 - 1.94444i) q^{85} +(-8.05230 + 5.48997i) q^{86} +(15.7247 + 2.37012i) q^{88} +(-6.29680 - 5.84258i) q^{89} +(-0.0197271 + 0.0411506i) q^{91} +(15.1316 - 18.9744i) q^{92} +(19.3903 + 13.2201i) q^{94} +(-0.129278 + 0.329394i) q^{95} +12.4244 q^{97} +(1.17289 - 16.4343i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + q^{2} + 3 q^{4} - 6 q^{8} + 30 q^{10} + 9 q^{11} + 42 q^{14} + 29 q^{16} + 5 q^{17} - 26 q^{19} + 5 q^{20} + q^{22} + 4 q^{23} - 56 q^{25} + 62 q^{26} + 7 q^{28} - 12 q^{29} - 36 q^{31} + 14 q^{32}+ \cdots - 119 q^{98}+O(q^{100}) \) 48 * q + q^2 + 3 * q^4 - 6 * q^8 + 30 * q^10 + 9 * q^11 + 42 * q^14 + 29 * q^16 + 5 * q^17 - 26 * q^19 + 5 * q^20 + q^22 + 4 * q^23 - 56 * q^25 + 62 * q^26 + 7 * q^28 - 12 * q^29 - 36 * q^31 + 14 * q^32 - 76 * q^34 - 7 * q^35 - 20 * q^37 + 60 * q^38 + 28 * q^40 - 41 * q^41 + 12 * q^43 - 44 * q^44 + 16 * q^46 - 13 * q^47 - 84 * q^49 + 12 * q^50 + 92 * q^52 - 14 * q^53 - 38 * q^55 - 105 * q^56 + 3 * q^58 - 57 * q^59 + 11 * q^61 + 16 * q^62 - 110 * q^64 - 21 * q^65 + 34 * q^67 - 22 * q^68 - 6 * q^71 - 69 * q^73 + 90 * q^74 - 49 * q^76 + 34 * q^79 - 55 * q^80 + 91 * q^82 - 28 * q^83 - 44 * q^85 + 26 * q^86 + 45 * q^88 - 11 * q^89 - 84 * q^92 + 90 * q^94 - 150 * q^95 + 124 * q^97 - 119 * q^98

Introduction

L-functions

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