LMFDB - Embedded newform 441.2.bg.a.26.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(17,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 25]))

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

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

chi := DirichletCharacter("441.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bg (of order $42$, degree $12$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$18$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			26.2
Character	$\chi$	$=$	441.26
Dual form			441.2.bg.a.17.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.47614 - 0.185561i) q^{2} +(4.11916 + 0.620863i) q^{4} +(1.08753 + 1.00908i) q^{5} +(0.513890 + 2.59536i) q^{7} +(-5.24274 - 1.19662i) q^{8} +O(q^{10})$	\(q+(-2.47614 - 0.185561i) q^{2} +(4.11916 + 0.620863i) q^{4} +(1.08753 + 1.00908i) q^{5} +(0.513890 + 2.59536i) q^{7} +(-5.24274 - 1.19662i) q^{8} +(-2.50562 - 2.70041i) q^{10} +(-2.86056 + 4.19566i) q^{11} +(1.61021 + 3.34363i) q^{13} +(-0.790865 - 6.52183i) q^{14} +(4.79846 + 1.48013i) q^{16} +(0.776596 - 1.97873i) q^{17} +(-6.02269 - 3.47720i) q^{19} +(3.85319 + 4.83175i) q^{20} +(7.86168 - 9.85823i) q^{22} +(-2.05621 + 0.807003i) q^{23} +(-0.209174 - 2.79123i) q^{25} +(-3.36665 - 8.57809i) q^{26} +(0.505430 + 11.0098i) q^{28} +(4.95700 - 3.95308i) q^{29} +(-4.78772 + 2.76419i) q^{31} +(-1.59532 - 0.626117i) q^{32} +(-2.29013 + 4.75551i) q^{34} +(-2.06005 + 3.34108i) q^{35} +(-5.79147 + 0.872923i) q^{37} +(14.2678 + 9.72760i) q^{38} +(-4.49413 - 6.59168i) q^{40} +(-2.11729 + 9.27644i) q^{41} +(0.698939 + 3.06225i) q^{43} +(-14.3880 + 15.5066i) q^{44} +(5.24120 - 1.61670i) q^{46} +(0.0268270 - 0.357982i) q^{47} +(-6.47183 + 2.66747i) q^{49} +6.95027i q^{50} +(4.55677 + 14.7727i) q^{52} +(-0.164957 + 1.09442i) q^{53} +(-7.34467 + 1.67637i) q^{55} +(0.411474 - 14.2217i) q^{56} +(-13.0077 + 8.86853i) q^{58} +(0.357938 - 0.332118i) q^{59} +(0.0559846 + 0.371434i) q^{61} +(12.3680 - 5.95610i) q^{62} +(-5.21448 - 2.51116i) q^{64} +(-1.62284 + 5.26111i) q^{65} +(7.11502 + 12.3236i) q^{67} +(4.42744 - 7.66855i) q^{68} +(5.72094 - 7.89070i) q^{70} +(-5.83320 - 4.65182i) q^{71} +(14.8390 - 1.11203i) q^{73} +(14.5024 - 1.08681i) q^{74} +(-22.6495 - 18.0624i) q^{76} +(-12.3593 - 5.26807i) q^{77} +(0.176652 - 0.305970i) q^{79} +(3.72489 + 6.45169i) q^{80} +(6.96404 - 22.5769i) q^{82} +(6.78359 + 3.26680i) q^{83} +(2.84126 - 1.36828i) q^{85} +(-1.16243 - 7.71224i) q^{86} +(20.0178 - 18.5738i) q^{88} +(-13.1119 + 8.93952i) q^{89} +(-7.85048 + 5.89734i) q^{91} +(-8.97089 + 2.04755i) q^{92} +(-0.132855 + 0.881434i) q^{94} +(-3.04107 - 9.85890i) q^{95} +3.33101i q^{97} +(16.5201 - 5.40409i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 16 q^{4} + 2 q^{7}+O(q^{10}) $ 216 * q - 16 * q^4 + 2 * q^7	$ 216 q - 16 q^{4} + 2 q^{7} + 12 q^{10} + 12 q^{16} - 6 q^{19} + 44 q^{22} + 26 q^{25} + 84 q^{28} - 6 q^{31} - 112 q^{34} + 60 q^{37} - 304 q^{40} + 20 q^{43} - 20 q^{46} - 86 q^{49} - 168 q^{52} - 84 q^{55} - 120 q^{58} - 2 q^{61} + 32 q^{64} + 22 q^{67} - 136 q^{70} - 6 q^{73} + 84 q^{76} + 2 q^{79} - 104 q^{82} + 96 q^{85} - 12 q^{88} + 58 q^{91} + 52 q^{94}+O(q^{100}) $ 216 * q - 16 * q^4 + 2 * q^7 + 12 * q^10 + 12 * q^16 - 6 * q^19 + 44 * q^22 + 26 * q^25 + 84 * q^28 - 6 * q^31 - 112 * q^34 + 60 * q^37 - 304 * q^40 + 20 * q^43 - 20 * q^46 - 86 * q^49 - 168 * q^52 - 84 * q^55 - 120 * q^58 - 2 * q^61 + 32 * q^64 + 22 * q^67 - 136 * q^70 - 6 * q^73 + 84 * q^76 + 2 * q^79 - 104 * q^82 + 96 * q^85 - 12 * q^88 + 58 * q^91 + 52 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{17}{42}\right)$	$-1$

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 $

$2$	−2.47614	−	0.185561i	−1.75089	−	0.131211i	−0.839662	−	0.543109i	$-0.817247\pi$
$2$	−2.47614	−	0.185561i	−1.75089	−	0.131211i	−0.911230	+	0.411897i	$0.864866\pi$
$3$		0			0
$3$		0			0
$4$	4.11916	+	0.620863i	2.05958	+	0.310431i
$5$	1.08753	+	1.00908i	0.486356	+	0.451273i	0.884835	−	0.465905i	$-0.154271\pi$
$5$	1.08753	+	1.00908i	0.486356	+	0.451273i	−0.398479	+	0.917178i	$0.630462\pi$
$6$		0			0
$7$	0.513890	+	2.59536i	0.194232	+	0.980956i
$7$	0.513890	+	2.59536i	0.194232	+	0.980956i
$8$	−5.24274	−	1.19662i	−1.85359	−	0.423069i
$9$		0			0
$10$	−2.50562	−	2.70041i	−0.792346	−	0.853945i
$11$	−2.86056	+	4.19566i	−0.862490	+	1.26504i	0.100346	+	0.994953i	$0.468005\pi$
$11$	−2.86056	+	4.19566i	−0.862490	+	1.26504i	−0.962836	+	0.270088i	$0.912947\pi$
$12$		0			0
$13$	1.61021	+	3.34363i	0.446592	+	0.927357i	0.995790	+	0.0916652i	$0.0292190\pi$
$13$	1.61021	+	3.34363i	0.446592	+	0.927357i	−0.549198	+	0.835692i	$0.685067\pi$
$14$	−0.790865	−	6.52183i	−0.211368	−	1.74303i
$15$		0			0
$16$	4.79846	+	1.48013i	1.19962	+	0.370032i
$17$	0.776596	−	1.97873i	0.188352	−	0.479913i	−0.805239	−	0.592951i	$-0.797963\pi$
$17$	0.776596	−	1.97873i	0.188352	−	0.479913i	0.993591	+	0.113038i	$0.0360581\pi$
$18$		0			0
$19$	−6.02269	−	3.47720i	−1.38170	−	0.797725i	−0.389339	−	0.921094i	$-0.627297\pi$
$19$	−6.02269	−	3.47720i	−1.38170	−	0.797725i	−0.992361	+	0.123369i	$0.960630\pi$
$20$	3.85319	+	4.83175i	0.861599	+	1.08041i
$21$		0			0
$22$	7.86168	−	9.85823i	1.67611	−	2.10178i
$23$	−2.05621	+	0.807003i	−0.428749	+	0.168272i	−0.569896	−	0.821717i	$-0.693016\pi$
$23$	−2.05621	+	0.807003i	−0.428749	+	0.168272i	0.141146	+	0.989989i	$0.454921\pi$
$24$		0			0
$25$	−0.209174	−	2.79123i	−0.0418347	−	0.558245i
$26$	−3.36665	−	8.57809i	−0.660255	−	1.68230i
$27$		0			0
$28$	0.505430	+	11.0098i	0.0955172	+	2.08065i
$29$	4.95700	−	3.95308i	0.920492	−	0.734068i	−0.0437638	−	0.999042i	$-0.513935\pi$
$29$	4.95700	−	3.95308i	0.920492	−	0.734068i	0.964255	+	0.264974i	$0.0853635\pi$
$30$		0			0
$31$	−4.78772	+	2.76419i	−0.859900	+	0.496463i	−0.863979	−	0.503528i	$-0.832035\pi$
$31$	−4.78772	+	2.76419i	−0.859900	+	0.496463i	0.00407904	+	0.999992i	$0.498702\pi$
$32$	−1.59532	−	0.626117i	−0.282015	−	0.110683i
$33$		0			0
$34$	−2.29013	+	4.75551i	−0.392754	+	0.815563i
$35$	−2.06005	+	3.34108i	−0.348212	+	0.564746i
$36$		0			0
$37$	−5.79147	+	0.872923i	−0.952111	+	0.143508i	−0.606689	−	0.794940i	$-0.707503\pi$
$37$	−5.79147	+	0.872923i	−0.952111	+	0.143508i	−0.345423	+	0.938447i	$0.612264\pi$
$38$	14.2678	+	9.72760i	2.31454	+	1.57803i
$39$		0			0
$40$	−4.49413	−	6.59168i	−0.710584	−	1.04224i
$41$	−2.11729	+	9.27644i	−0.330665	+	1.44874i	0.487182	+	0.873301i	$0.338025\pi$
$41$	−2.11729	+	9.27644i	−0.330665	+	1.44874i	−0.817846	+	0.575436i	$0.804832\pi$
$42$		0			0
$43$	0.698939	+	3.06225i	0.106587	+	0.466989i	0.999848	+	0.0174495i	$0.00555464\pi$
$43$	0.698939	+	3.06225i	0.106587	+	0.466989i	−0.893261	+	0.449539i	$0.851588\pi$
$44$	−14.3880	+	15.5066i	−2.16907	+	2.33771i
$45$		0			0
$46$	5.24120	−	1.61670i	0.772773	−	0.238369i
$47$	0.0268270	−	0.357982i	0.00391312	−	0.0522170i	−0.994905	−	0.100813i	$-0.967856\pi$
$47$	0.0268270	−	0.357982i	0.00391312	−	0.0522170i	0.998819	+	0.0485960i	$0.0154747\pi$
$48$		0			0
$49$	−6.47183	+	2.66747i	−0.924548	+	0.381067i
$50$			6.95027i			0.982917i
$51$		0			0
$52$	4.55677	+	14.7727i	0.631910	+	2.04860i
$53$	−0.164957	+	1.09442i	−0.0226585	+	0.150330i	−0.997299	−	0.0734463i	$-0.976600\pi$
$53$	−0.164957	+	1.09442i	−0.0226585	+	0.150330i	0.974641	+	0.223776i	$0.0718383\pi$
$54$		0			0
$55$	−7.34467	+	1.67637i	−0.990355	+	0.226042i
$56$	0.411474	−	14.2217i	0.0549855	−	1.90046i
$57$		0			0
$58$	−13.0077	+	8.86853i	−1.70800	+	1.16449i
$59$	0.357938	−	0.332118i	0.0465995	−	0.0432380i	−0.656529	−	0.754301i	$-0.727976\pi$
$59$	0.357938	−	0.332118i	0.0465995	−	0.0432380i	0.703129	+	0.711062i	$0.251786\pi$
$60$		0			0
$61$	0.0559846	+	0.371434i	0.00716810	+	0.0475572i	0.992129	−	0.125221i	$-0.0399639\pi$
$61$	0.0559846	+	0.371434i	0.00716810	+	0.0475572i	−0.984961	+	0.172778i	$0.944726\pi$
$62$	12.3680	−	5.95610i	1.57073	−	0.756425i
$63$		0			0
$64$	−5.21448	−	2.51116i	−0.651810	−	0.313895i
$65$	−1.62284	+	5.26111i	−0.201288	+	0.652561i
$66$		0			0
$67$	7.11502	+	12.3236i	0.869238	+	1.50556i	0.862777	+	0.505585i	$0.168723\pi$
$67$	7.11502	+	12.3236i	0.869238	+	1.50556i	0.00646154	+	0.999979i	$0.497943\pi$
$68$	4.42744	−	7.66855i	0.536906	−	0.929949i
$69$		0			0
$70$	5.72094	−	7.89070i	0.683783	−	0.943120i
$71$	−5.83320	−	4.65182i	−0.692274	−	0.552070i	0.212920	−	0.977070i	$-0.431703\pi$
$71$	−5.83320	−	4.65182i	−0.692274	−	0.552070i	−0.905193	+	0.425000i	$0.860274\pi$
$72$		0			0
$73$	14.8390	−	1.11203i	1.73677	−	0.130153i	0.831646	−	0.555306i	$-0.187399\pi$
$73$	14.8390	−	1.11203i	1.73677	−	0.130153i	0.905122	+	0.425153i	$0.139780\pi$
$74$	14.5024	−	1.08681i	1.68587	−	0.126339i
$75$		0			0
$76$	−22.6495	−	18.0624i	−2.59808	−	2.07190i
$77$	−12.3593	−	5.26807i	−1.40847	−	0.600353i
$78$		0			0
$79$	0.176652	−	0.305970i	0.0198749	−	0.0344243i	−0.855917	−	0.517113i	$-0.827007\pi$
$79$	0.176652	−	0.305970i	0.0198749	−	0.0344243i	0.875792	+	0.482689i	$0.160340\pi$
$80$	3.72489	+	6.45169i	0.416455	+	0.721321i
$81$		0			0
$82$	6.96404	−	22.5769i	0.769049	−	2.49320i
$83$	6.78359	+	3.26680i	0.744596	+	0.358578i	0.767406	−	0.641162i	$-0.221547\pi$
$83$	6.78359	+	3.26680i	0.744596	+	0.358578i	−0.0228105	+	0.999740i	$0.507261\pi$
$84$		0			0
$85$	2.84126	−	1.36828i	0.308178	−	0.148411i
$86$	−1.16243	−	7.71224i	−0.125348	−	0.831633i
$87$		0			0
$88$	20.0178	−	18.5738i	2.13390	−	1.97997i
$89$	−13.1119	+	8.93952i	−1.38985	+	0.947587i	−0.390215	+	0.920724i	$0.627599\pi$
$89$	−13.1119	+	8.93952i	−1.38985	+	0.947587i	−0.999639	+	0.0268632i	$0.991448\pi$
$90$		0			0
$91$	−7.85048	+	5.89734i	−0.822954	+	0.618209i
$92$	−8.97089	+	2.04755i	−0.935280	+	0.213471i
$93$		0			0
$94$	−0.132855	+	0.881434i	−0.0137029	+	0.0909129i
$95$	−3.04107	−	9.85890i	−0.312007	−	1.01150i
$96$		0			0
$97$			3.33101i			0.338213i	0.985598	+	0.169107i	$0.0540882\pi$
$97$			3.33101i			0.338213i	−0.985598	+	0.169107i	$0.945912\pi$
$98$	16.5201	−	5.40409i	1.66878	−	0.545896i
$99$		0			0
$100$	0.871351	−	11.6274i	0.0871351	−	1.16274i
$101$	16.1690	−	4.98749i	1.60888	−	0.496274i	0.645352	−	0.763885i	$-0.276711\pi$
$101$	16.1690	−	4.98749i	1.60888	−	0.496274i	0.963527	+	0.267611i	$0.0862344\pi$
$102$		0			0
$103$	11.4357	−	12.3247i	1.12679	−	1.21439i	0.152691	−	0.988274i	$-0.451206\pi$
$103$	11.4357	−	12.3247i	1.12679	−	1.21439i	0.974100	−	0.226118i	$-0.0726035\pi$
$104$	−4.44084	−	19.4566i	−0.435461	−	1.90788i
$105$		0			0
$106$	0.611536	−	2.67931i	0.0593976	−	0.260238i
$107$	3.05482	+	4.48060i	0.295321	+	0.433156i	0.945009	−	0.327045i	$-0.106053\pi$
$107$	3.05482	+	4.48060i	0.295321	+	0.433156i	−0.649688	+	0.760201i	$0.725100\pi$
$108$		0			0
$109$	0.474570	+	0.323557i	0.0454556	+	0.0309911i	0.585835	−	0.810431i	$-0.300767\pi$
$109$	0.474570	+	0.323557i	0.0454556	+	0.0309911i	−0.540379	+	0.841422i	$0.681719\pi$
$110$	18.4975	−	2.78805i	1.76367	−	0.265830i
$111$		0			0
$112$	−1.37559	+	13.2144i	−0.129981	+	1.24864i
$113$	−4.33396	+	8.99957i	−0.407705	+	0.846608i	0.591483	+	0.806317i	$0.298543\pi$
$113$	−4.33396	+	8.99957i	−0.407705	+	0.846608i	−0.999188	+	0.0402907i	$0.987172\pi$
$114$		0			0
$115$	−3.05051	−	1.19724i	−0.284461	−	0.111643i
$116$	22.8730	−	13.2057i	2.12370	−	1.22612i
$117$		0			0
$118$	−0.947931	+	0.755950i	−0.0872641	+	0.0695908i
$119$	5.53462	+	0.998696i	0.507358	+	0.0915504i
$120$		0			0
$121$	−5.40207	−	13.7642i	−0.491097	−	1.25130i
$122$	−0.0697020	−	0.930109i	−0.00631052	−	0.0842081i
$123$		0			0
$124$	−21.4375	+	8.41362i	−1.92515	+	0.755565i
$125$	7.21400	−	9.04607i	0.645240	−	0.809105i
$126$		0			0
$127$	12.6589	+	15.8738i	1.12330	+	1.40857i	0.901122	+	0.433565i	$0.142745\pi$
$127$	12.6589	+	15.8738i	1.12330	+	1.40857i	0.222176	+	0.975006i	$0.428684\pi$
$128$	15.4142	+	8.89937i	1.36243	+	0.786601i
$129$		0			0
$130$	4.99462	−	12.7261i	0.438058	−	1.11615i
$131$	−15.7234	−	4.85003i	−1.37376	−	0.423749i	−0.481967	−	0.876190i	$-0.660077\pi$
$131$	−15.7234	−	4.85003i	−1.37376	−	0.423749i	−0.891795	+	0.452440i	$0.850554\pi$
$132$		0			0
$133$	5.92960	−	17.4180i	0.514162	−	1.51033i
$134$	−15.3310	−	31.8351i	−1.32440	−	2.75014i
$135$		0			0
$136$	−6.43928	+	9.44469i	−0.552164	+	0.809875i
$137$	−2.28239	−	2.45983i	−0.194998	−	0.210157i	0.627983	−	0.778227i	$-0.283881\pi$
$137$	−2.28239	−	2.45983i	−0.194998	−	0.210157i	−0.822980	+	0.568070i	$0.807690\pi$
$138$		0			0
$139$	9.00168	+	2.05457i	0.763512	+	0.174267i	0.586508	−	0.809943i	$-0.300502\pi$
$139$	9.00168	+	2.05457i	0.763512	+	0.174267i	0.177004	+	0.984210i	$0.443359\pi$
$140$	−10.5600	+	12.4834i	−0.892485	+	1.05504i
$141$		0			0
$142$	13.5806	+	12.6010i	1.13966	+	1.05745i
$143$	−18.6349	−	2.80875i	−1.55833	−	0.234880i
$144$		0			0
$145$	9.37982	+	0.702920i	0.778951	+	0.0583743i
$146$	−36.9496			−3.05797
$147$		0			0
$148$	−24.3979			−2.00550
$149$	11.6944	+	0.876373i	0.958041	+	0.0717953i	0.544564	−	0.838719i	$-0.316695\pi$
$149$	11.6944	+	0.876373i	0.958041	+	0.0717953i	0.413477	+	0.910514i	$0.364314\pi$
$150$		0			0
$151$	−19.9269	−	3.00350i	−1.62163	−	0.244422i	−0.725504	−	0.688218i	$-0.758393\pi$
$151$	−19.9269	−	3.00350i	−1.62163	−	0.244422i	−0.896128	+	0.443796i	$0.853631\pi$
$152$	27.4145	+	25.4369i	2.22361	+	2.06321i
$153$		0			0
$154$	29.6257	+	15.3379i	2.38731	+	1.23596i
$155$	−7.99605	−	1.82505i	−0.642258	−	0.146591i
$156$		0			0
$157$	−0.637147	−	0.686681i	−0.0508498	−	0.0548031i	0.707115	−	0.707099i	$-0.249996\pi$
$157$	−0.637147	−	0.686681i	−0.0508498	−	0.0548031i	−0.757964	+	0.652296i	$0.773806\pi$
$158$	−0.494190	+	0.724844i	−0.0393156	+	0.0576655i
$159$		0			0
$160$	−1.10315	−	2.29072i	−0.0872118	−	0.181097i
$161$	−3.15113	−	4.92190i	−0.248344	−	0.387900i
$162$		0			0
$163$	0.425820	+	0.131348i	0.0333528	+	0.0102880i	0.311387	−	0.950283i	$-0.399207\pi$
$163$	0.425820	+	0.131348i	0.0333528	+	0.0102880i	−0.278034	+	0.960571i	$0.589683\pi$
$164$	−14.4808	+	36.8966i	−1.13076	+	2.88114i
$165$		0			0
$166$	−16.1909	−	9.34782i	−1.25666	−	0.725531i
$167$	−4.97380	−	6.23695i	−0.384884	−	0.482630i	0.551216	−	0.834363i	$-0.314164\pi$
$167$	−4.97380	−	6.23695i	−0.384884	−	0.482630i	−0.936100	+	0.351733i	$0.885593\pi$
$168$		0			0
$169$	−0.481750	+	0.604096i	−0.0370577	+	0.0464689i
$170$	−7.28925	+	2.86082i	−0.559060	+	0.219415i
$171$		0			0
$172$	0.977800	+	13.0478i	0.0745565	+	0.994888i
$173$	4.68337	+	11.9330i	0.356070	+	0.907252i	0.990900	+	0.134600i	$0.0429750\pi$
$173$	4.68337	+	11.9330i	0.356070	+	0.907252i	−0.634830	+	0.772652i	$0.718930\pi$
$174$		0			0
$175$	7.13676	−	1.97727i	0.539488	−	0.149467i
$176$	−19.9364	+	15.8987i	−1.50276	+	1.19841i
$177$		0			0
$178$	34.1256	−	19.7024i	2.55782	−	1.47676i
$179$	10.2255	+	4.01321i	0.764288	+	0.299961i	0.715281	−	0.698837i	$-0.246299\pi$
$179$	10.2255	+	4.01321i	0.764288	+	0.299961i	0.0490077	+	0.998798i	$0.484394\pi$
$180$		0			0
$181$	−1.65300	+	3.43249i	−0.122867	+	0.255135i	−0.953325	−	0.301945i	$-0.902364\pi$
$181$	−1.65300	+	3.43249i	−0.122867	+	0.255135i	0.830459	+	0.557080i	$0.188078\pi$
$182$	20.5332	−	13.1459i	1.52202	−	0.974438i
$183$		0			0
$184$	11.7458	−	1.77040i	0.865915	−	0.130516i
$185$	−7.17921	−	4.89471i	−0.527826	−	0.359866i
$186$		0			0
$187$	6.08061	+	8.91861i	0.444658	+	0.652193i
$188$	0.332762	−	1.45793i	0.0242692	−	0.106330i
$189$		0			0
$190$	5.70067	+	24.9763i	0.413570	+	1.81197i
$191$	−15.1504	+	16.3282i	−1.09624	+	1.18147i	−0.114074	+	0.993472i	$0.536390\pi$
$191$	−15.1504	+	16.3282i	−1.09624	+	1.18147i	−0.982170	+	0.187997i	$0.939800\pi$
$192$		0			0
$193$	−8.18635	+	2.52516i	−0.589267	+	0.181765i	−0.575028	−	0.818134i	$-0.695009\pi$
$193$	−8.18635	+	2.52516i	−0.589267	+	0.181765i	−0.0142390	+	0.999899i	$0.504533\pi$
$194$	0.618105	−	8.24804i	0.0443774	−	0.592175i
$195$		0			0
$196$	−28.3146	+	6.96959i	−2.02247	+	0.497828i
$197$		−	14.9250i		−	1.06336i	−0.846945	−	0.531681i	$-0.821561\pi$
$197$		−	14.9250i		−	1.06336i	0.846945	−	0.531681i	$-0.178439\pi$
$198$		0			0
$199$	4.57873	+	14.8439i	0.324578	+	1.05226i	0.959979	+	0.280073i	$0.0903587\pi$
$199$	4.57873	+	14.8439i	0.324578	+	1.05226i	−0.635401	+	0.772182i	$0.719165\pi$
$200$	−2.24340	+	14.8840i	−0.158632	+	1.05246i
$201$		0			0
$202$	−40.9622	+	9.34936i	−2.88209	+	0.657819i
$203$	12.8070	+	10.8338i	0.898877	+	0.760382i
$204$		0			0
$205$	−11.6632	+	7.95186i	−0.814596	+	0.555382i
$206$	−30.6033	+	28.3957i	−2.13223	+	1.97842i
$207$		0			0
$208$	2.77752	+	18.4276i	0.192586	+	1.27773i
$209$	31.8174	−	15.3225i	2.20086	−	1.05988i
$210$		0			0
$211$	20.9748	+	10.1009i	1.44396	+	0.695376i	0.981535	−	0.191282i	$-0.0612644\pi$
$211$	20.9748	+	10.1009i	1.44396	+	0.695376i	0.462427	+	0.886657i	$0.346979\pi$
$212$	−1.35896	+	4.40565i	−0.0933340	+	0.302581i
$213$		0			0
$214$	−6.73274	−	11.6614i	−0.460240	−	0.797160i
$215$	−2.32993	+	4.03556i	−0.158900	+	0.275223i
$216$		0			0
$217$	−9.63444	−	11.0054i	−0.654029	−	0.747094i
$218$	−1.11506	−	0.889232i	−0.0755215	−	0.0602264i
$219$		0			0
$220$	−31.2947	+	2.34521i	−2.10989	+	0.158114i
$221$	7.86664	−	0.589523i	0.529168	−	0.0396556i
$222$		0			0
$223$	9.83354	+	7.84199i	0.658503	+	0.525138i	0.894757	−	0.446553i	$-0.147348\pi$
$223$	9.83354	+	7.84199i	0.658503	+	0.525138i	−0.236255	+	0.971691i	$0.575920\pi$
$224$	0.805182	−	4.46219i	0.0537985	−	0.298143i
$225$		0			0
$226$	12.4015	−	21.4799i	0.824932	−	1.42882i
$227$	−2.25029	−	3.89761i	−0.149357	−	0.258694i	0.781633	−	0.623739i	$-0.214387\pi$
$227$	−2.25029	−	3.89761i	−0.149357	−	0.258694i	−0.930990	+	0.365045i	$0.881054\pi$
$228$		0			0
$229$	−1.26070	+	4.08710i	−0.0833097	+	0.270083i	−0.987637	−	0.156755i	$-0.949897\pi$
$229$	−1.26070	+	4.08710i	−0.0833097	+	0.270083i	0.904328	+	0.426839i	$0.140373\pi$
$230$	7.33131	+	3.53057i	0.483413	+	0.232799i
$231$		0			0
$232$	−30.7186	+	14.7933i	−2.01677	+	0.971227i
$233$	−1.51805	−	10.0716i	−0.0994505	−	0.659811i	−0.981899	−	0.189403i	$-0.939345\pi$
$233$	−1.51805	−	10.0716i	−0.0994505	−	0.659811i	0.882449	−	0.470408i	$-0.155893\pi$
$234$		0			0
$235$	0.390406	−	0.362244i	0.0254673	−	0.0236302i
$236$	1.68060	−	1.14581i	0.109398	−	0.0745862i
$237$		0			0
$238$	−13.5192	−	3.49992i	−0.876316	−	0.226866i
$239$	8.27135	−	1.88788i	0.535029	−	0.122117i	0.0535345	−	0.998566i	$-0.482951\pi$
$239$	8.27135	−	1.88788i	0.535029	−	0.122117i	0.481494	+	0.876449i	$0.340094\pi$
$240$		0			0
$241$	3.73650	−	24.7901i	0.240689	−	1.59687i	−0.462998	−	0.886360i	$-0.653226\pi$
$241$	3.73650	−	24.7901i	0.240689	−	1.59687i	0.703687	−	0.710510i	$-0.251536\pi$
$242$	10.8222	+	35.0846i	0.695675	+	2.25532i
$243$		0			0
$244$			1.56475i			0.100173i
$245$	−9.72996	−	3.62964i	−0.621624	−	0.231889i
$246$		0			0
$247$	1.92870	−	25.7367i	0.122720	−	1.63759i
$248$	28.4084	−	8.76284i	1.80394	−	0.556441i
$249$		0			0
$250$	−19.5414	+	21.0607i	−1.23591	+	1.33199i
$251$	−5.26725	−	23.0773i	−0.332466	−	1.45663i	−0.814341	−	0.580387i	$-0.802901\pi$
$251$	−5.26725	−	23.0773i	−0.332466	−	1.45663i	0.481875	−	0.876240i	$-0.339956\pi$
$252$		0			0
$253$	2.49599	−	10.9356i	0.156921	−	0.687518i
$254$	−28.3997	−	41.6547i	−1.78195	−	2.61365i
$255$		0			0
$256$	−26.9522	−	18.3757i	−1.68452	−	1.14848i
$257$	28.0371	−	4.22591i	1.74890	−	0.263605i	0.804870	−	0.593451i	$-0.202235\pi$
$257$	28.0371	−	4.22591i	1.74890	−	0.263605i	0.944035	+	0.329846i	$0.106997\pi$
$258$		0			0
$259$	−5.24173	−	14.5824i	−0.325705	−	0.906105i
$260$	−9.95115	+	20.6638i	−0.617144	+	1.28151i
$261$		0			0
$262$	38.0333	+	14.9270i	2.34971	+	0.922192i
$263$	−15.5327	+	8.96781i	−0.957787	+	0.552979i	−0.895491	−	0.445079i	$-0.853176\pi$
$263$	−15.5327	+	8.96781i	−0.957787	+	0.552979i	−0.0622959	+	0.998058i	$0.519842\pi$
$264$		0			0
$265$	−1.28374	+	1.02375i	−0.0788597	+	0.0628885i
$266$	−17.9146	+	42.0290i	−1.09841	+	2.57696i
$267$		0			0
$268$	21.6566	+	55.1802i	1.32289	+	3.37067i
$269$	−0.912196	−	12.1724i	−0.0556176	−	0.742165i	−0.953397	−	0.301719i	$-0.902439\pi$
$269$	−0.912196	−	12.1724i	−0.0556176	−	0.742165i	0.897779	−	0.440446i	$-0.145180\pi$
$270$		0			0
$271$	14.7295	−	5.78089i	0.894751	−	0.351164i	0.126993	−	0.991904i	$-0.459467\pi$
$271$	14.7295	−	5.78089i	0.894751	−	0.351164i	0.767758	+	0.640740i	$0.221372\pi$
$272$	6.65524	−	8.34541i	0.403533	−	0.506015i
$273$		0			0
$274$	5.19506	+	6.51440i	0.313845	+	0.393549i
$275$	12.3094	+	7.10684i	0.742285	+	0.428558i
$276$		0			0
$277$	−2.19782	+	5.59995i	−0.132054	+	0.336468i	−0.981572	−	0.191091i	$-0.938797\pi$
$277$	−2.19782	+	5.59995i	−0.132054	+	0.336468i	0.849518	+	0.527559i	$0.176893\pi$
$278$	−21.9081	−	6.75777i	−1.31396	−	0.405304i
$279$		0			0
$280$	14.7983	−	15.0513i	0.884369	−	0.899488i
$281$	8.88830	+	18.4568i	0.530232	+	1.10104i	0.978330	+	0.207053i	$0.0663873\pi$
$281$	8.88830	+	18.4568i	0.530232	+	1.10104i	−0.448098	+	0.893985i	$0.647898\pi$
$282$		0			0
$283$	−0.909671	+	1.33424i	−0.0540743	+	0.0793125i	−0.852324	−	0.523015i	$-0.824807\pi$
$283$	−0.909671	+	1.33424i	−0.0540743	+	0.0793125i	0.798249	+	0.602327i	$0.205760\pi$
$284$	−21.1397	−	22.7832i	−1.25441	−	1.35193i
$285$		0			0
$286$	45.6213	+	10.4128i	2.69764	+	0.615719i
$287$	−25.1638	−	0.728058i	−1.48537	−	0.0429759i
$288$		0			0
$289$	9.14960	+	8.48959i	0.538212	+	0.499387i
$290$	−23.0953	−	3.48105i	−1.35620	−	0.204414i
$291$		0			0
$292$	61.8144	+	4.63235i	3.61741	+	0.271088i
$293$	−4.92766			−0.287877			−0.143939	−	0.989587i	$-0.545977\pi$
$293$	−4.92766			−0.287877			−0.143939	+	0.989587i	$0.545977\pi$
$294$		0			0
$295$	0.724399			0.0421761
$296$	31.4077	+	2.35368i	1.82554	+	0.136805i
$297$		0			0
$298$	−28.7943	−	4.34004i	−1.66801	−	0.251412i
$299$	−6.00925	−	5.57577i	−0.347524	−	0.322455i
$300$		0			0
$301$	−7.58848	+	3.38766i	−0.437392	+	0.195262i
$302$	48.7845	+	11.1347i	2.80723	+	0.640732i
$303$		0			0
$304$	−23.7529	−	25.5996i	−1.36232	−	1.46824i
$305$	−0.313920	+	0.460436i	−0.0179750	+	0.0263645i
$306$		0			0
$307$	−10.0777	−	20.9265i	−0.575163	−	1.19434i	−0.962218	−	0.272281i	$-0.912222\pi$
$307$	−10.0777	−	20.9265i	−0.575163	−	1.19434i	0.387055	−	0.922057i	$-0.373492\pi$
$308$	−47.6391	−	29.3734i	−2.71449	−	1.67371i
$309$		0			0
$310$	19.4606	+	6.00281i	1.10529	+	0.340937i
$311$	5.98567	−	15.2512i	0.339416	−	0.864818i	−0.654639	−	0.755942i	$-0.727179\pi$
$311$	5.98567	−	15.2512i	0.339416	−	0.864818i	0.994055	−	0.108877i	$-0.0347253\pi$
$312$		0			0
$313$	−19.9338	−	11.5088i	−1.12673	−	0.650516i	−0.183617	−	0.982998i	$-0.558781\pi$
$313$	−19.9338	−	11.5088i	−1.12673	−	0.650516i	−0.943110	+	0.332482i	$0.892114\pi$
$314$	1.45024	+	1.81854i	0.0818418	+	0.102626i
$315$		0			0
$316$	0.917622	−	1.15066i	0.0516203	−	0.0647298i
$317$	−1.27121	+	0.498913i	−0.0713982	+	0.0280217i	−0.400771	−	0.916178i	$-0.631258\pi$
$317$	−1.27121	+	0.498913i	−0.0713982	+	0.0280217i	0.329373	+	0.944200i	$0.393163\pi$
$318$		0			0
$319$	2.40600	+	32.1059i	0.134710	+	1.79759i
$320$	−3.13693	−	7.99276i	−0.175360	−	0.446809i
$321$		0			0
$322$	6.88932	+	12.7720i	0.383927	+	0.711757i
$323$	−11.5577	+	9.21692i	−0.643085	+	0.512843i
$324$		0			0
$325$	8.99603	−	5.19386i	0.499010	−	0.288103i
$326$	−1.03002	−	0.404251i	−0.0570473	−	0.0223894i
$327$		0			0
$328$	22.2008	−	46.1004i	1.22583	−	2.54547i
$329$	0.942879	−	0.114338i	0.0519826	−	0.00630363i
$330$		0			0
$331$	−16.6271	+	2.50613i	−0.913907	+	0.137749i	−0.589127	−	0.808040i	$-0.700528\pi$
$331$	−16.6271	+	2.50613i	−0.913907	+	0.137749i	−0.324780	+	0.945790i	$0.605290\pi$
$332$	25.9144	+	17.6682i	1.42224	+	0.969666i
$333$		0			0
$334$	11.1585	+	16.3665i	0.610565	+	0.895534i
$335$	−4.69766	+	20.5818i	−0.256661	+	1.12450i
$336$		0			0
$337$	1.13351	+	4.96624i	0.0617463	+	0.270528i	0.996372	−	0.0851047i	$-0.0271225\pi$
$337$	1.13351	+	4.96624i	0.0617463	+	0.270528i	−0.934626	+	0.355633i	$0.884265\pi$
$338$	1.30498	−	1.40643i	0.0709813	−	0.0764997i
$339$		0			0
$340$	12.5531	−	3.87212i	0.680788	−	0.209995i
$341$	2.09792	−	27.9948i	0.113609	−	1.51600i
$342$		0			0
$343$	−10.2489	−	15.4260i	−0.553386	−	0.832925i
$344$		−	16.8909i		−	0.910698i
$345$		0			0
$346$	−9.38236	−	30.4169i	−0.504399	−	1.63522i
$347$	−2.15705	+	14.3111i	−0.115797	+	0.768260i	0.853272	+	0.521467i	$0.174615\pi$
$347$	−2.15705	+	14.3111i	−0.115797	+	0.768260i	−0.969068	+	0.246793i	$0.920623\pi$
$348$		0			0
$349$	22.4779	−	5.13043i	1.20321	−	0.274626i	0.426505	−	0.904485i	$-0.359745\pi$
$349$	22.4779	−	5.13043i	1.20321	−	0.274626i	0.776709	+	0.629859i	$0.216888\pi$
$350$	−18.0385	+	3.57168i	−0.964198	+	0.190914i
$351$		0			0
$352$	7.19048	−	4.90239i	0.383254	−	0.261298i
$353$	10.2757	−	9.53448i	0.546922	−	0.507469i	−0.357612	−	0.933870i	$-0.616409\pi$
$353$	10.2757	−	9.53448i	0.546922	−	0.507469i	0.904534	+	0.426401i	$0.140219\pi$
$354$		0			0
$355$	−1.64971	−	10.9451i	−0.0875576	−	0.580907i
$356$	−59.5600	+	28.6826i	−3.15668	+	1.52017i
$357$		0			0
$358$	−24.5750	−	11.8347i	−1.29883	−	0.625483i
$359$	−1.56884	+	5.08606i	−0.0828003	+	0.268432i	−0.987500	−	0.157617i	$-0.949619\pi$
$359$	−1.56884	+	5.08606i	−0.0828003	+	0.268432i	0.904700	+	0.426049i	$0.140095\pi$
$360$		0			0
$361$	14.6819	+	25.4297i	0.772730	+	1.33841i
$362$	4.73000	−	8.19259i	0.248603	−	0.430593i
$363$		0			0
$364$	−35.9988	+	19.4180i	−1.88685	+	1.01778i
$365$	17.2599	+	13.7643i	0.903422	+	0.720455i
$366$		0			0
$367$	−1.18287	+	0.0886436i	−0.0617451	+	0.00462716i	−0.105567	−	0.994412i	$-0.533666\pi$
$367$	−1.18287	+	0.0886436i	−0.0617451	+	0.00462716i	0.0438217	+	0.999039i	$0.486047\pi$
$368$	−11.0611	+	0.828916i	−0.576600	+	0.0432102i
$369$		0			0
$370$	16.8684	+	13.4521i	0.876949	+	0.699343i
$371$	−2.92518	+	0.134287i	−0.151868	+	0.00697184i
$372$		0			0
$373$	−3.82288	+	6.62142i	−0.197941	+	0.342844i	−0.947861	−	0.318685i	$-0.896759\pi$
$373$	−3.82288	+	6.62142i	−0.197941	+	0.342844i	0.749920	+	0.661529i	$0.230092\pi$
$374$	−13.4015	−	23.2120i	−0.692973	−	1.20026i
$375$		0			0
$376$	−0.569016	+	1.84470i	−0.0293447	+	0.0951333i
$377$	21.1994	+	10.2091i	1.09183	+	0.525796i
$378$		0			0
$379$	−1.92569	+	0.927362i	−0.0989159	+	0.0476354i	−0.482687	−	0.875793i	$-0.660339\pi$
$379$	−1.92569	+	0.927362i	−0.0989159	+	0.0476354i	0.383772	+	0.923428i	$0.374625\pi$
$380$	−6.40561	−	42.4984i	−0.328601	−	2.18012i
$381$		0			0
$382$	40.5443	−	37.6196i	2.07443	−	1.92479i
$383$	−1.72595	+	1.17673i	−0.0881917	+	0.0601281i	−0.606613	−	0.794997i	$-0.707472\pi$
$383$	−1.72595	+	1.17673i	−0.0881917	+	0.0601281i	0.518421	+	0.855125i	$0.326520\pi$
$384$		0			0
$385$	−8.12516	−	18.2006i	−0.414096	−	0.927590i
$386$	20.7391	−	4.73356i	1.05559	−	0.240932i
$387$		0			0
$388$	−2.06810	+	13.7210i	−0.104992	+	0.696576i
$389$	6.34796	+	20.5796i	0.321855	+	1.04343i	0.961511	+	0.274766i	$0.0886004\pi$
$389$	6.34796	+	20.5796i	0.321855	+	1.04343i	−0.639657	+	0.768661i	$0.720923\pi$
$390$		0			0
$391$			4.69541i			0.237457i
$392$	37.1221	−	6.24050i	1.87495	−	0.315193i
$393$		0			0
$394$	−2.76949	+	36.9563i	−0.139525	+	1.86183i
$395$	0.500860	−	0.154495i	0.0252010	−	0.00777349i
$396$		0			0
$397$	8.48011	−	9.13939i	0.425605	−	0.458693i	−0.483449	−	0.875373i	$-0.660616\pi$
$397$	8.48011	−	9.13939i	0.425605	−	0.458693i	0.909053	+	0.416680i	$0.136806\pi$
$398$	−8.58312	−	37.6051i	−0.430233	−	1.88497i
$399$		0			0
$400$	3.12766	−	13.7032i	0.156383	−	0.685160i
$401$	13.6040	+	19.9534i	0.679351	+	0.996425i	0.998807	+	0.0488238i	$0.0155473\pi$
$401$	13.6040	+	19.9534i	0.679351	+	0.996425i	−0.319457	+	0.947601i	$0.603500\pi$
$402$		0			0
$403$	−16.9517	−	11.5575i	−0.844423	−	0.575718i
$404$	69.6993	−	10.5055i	3.46767	−	0.522667i
$405$		0			0
$406$	−29.7016	−	29.2024i	−1.47407	−	1.44929i
$407$	12.9043	−	26.7961i	0.639643	−	1.32823i
$408$		0			0
$409$	6.30198	+	2.47334i	0.311613	+	0.122299i	0.515994	−	0.856592i	$-0.327423\pi$
$409$	6.30198	+	2.47334i	0.311613	+	0.122299i	−0.204381	+	0.978891i	$0.565518\pi$
$410$	30.3553	−	17.5257i	1.49914	−	0.865531i
$411$		0			0
$412$	54.7573	−	43.6675i	2.69770	−	2.15134i
$413$	1.04591	+	0.758307i	0.0514657	+	0.0373138i
$414$		0			0
$415$	4.08087	+	10.3979i	0.200322	+	0.510412i
$416$	−0.475293	−	6.34235i	−0.0233032	−	0.310959i
$417$		0			0
$418$	−81.6275	+	32.0364i	−3.99253	+	1.56695i
$419$	8.95596	−	11.2304i	0.437527	−	0.548642i	−0.513362	−	0.858172i	$-0.671600\pi$
$419$	8.95596	−	11.2304i	0.437527	−	0.548642i	0.950890	+	0.309530i	$0.100172\pi$
$420$		0			0
$421$	−11.8843	−	14.9024i	−0.579205	−	0.726301i	0.402772	−	0.915300i	$-0.368047\pi$
$421$	−11.8843	−	14.9024i	−0.579205	−	0.726301i	−0.981977	+	0.189000i	$0.939475\pi$
$422$	−50.0620	−	28.9033i	−2.43698	−	1.40699i
$423$		0			0
$424$	2.17442	−	5.54034i	0.105599	−	0.269063i
$425$	−5.68554	−	1.75376i	−0.275789	−	0.0850696i
$426$		0			0
$427$	−0.935236	+	0.336177i	−0.0452592	+	0.0162687i
$428$	9.80146	+	20.3529i	0.473771	+	0.983796i
$429$		0			0
$430$	6.51807	−	9.56025i	0.314329	−	0.461036i
$431$	−5.40042	−	5.82027i	−0.260129	−	0.280352i	0.589460	−	0.807797i	$-0.299341\pi$
$431$	−5.40042	−	5.82027i	−0.260129	−	0.280352i	−0.849589	+	0.527445i	$0.823150\pi$
$432$		0			0
$433$	−19.9380	−	4.55072i	−0.958159	−	0.218694i	−0.285279	−	0.958445i	$-0.592086\pi$
$433$	−19.9380	−	4.55072i	−0.958159	−	0.218694i	−0.672881	+	0.739751i	$0.734943\pi$
$434$	21.8140	+	29.0386i	1.04711	+	1.39390i
$435$		0			0
$436$	1.75394	+	1.62742i	0.0839987	+	0.0779394i
$437$	15.1900	+	2.28953i	0.726638	+	0.109523i
$438$		0			0
$439$	27.5969	+	2.06810i	1.31713	+	0.0987052i	0.714680	−	0.699452i	$-0.246572\pi$
$439$	27.5969	+	2.06810i	1.31713	+	0.0987052i	0.602450	+	0.798157i	$0.294191\pi$
$440$	40.5122			1.93134
$441$		0			0
$442$	−19.5883			−0.931719
$443$	26.0648	+	1.95329i	1.23838	+	0.0928035i	0.677767	−	0.735277i	$-0.262948\pi$
$443$	26.0648	+	1.95329i	1.23838	+	0.0928035i	0.560610	+	0.828080i	$0.310567\pi$
$444$		0			0
$445$	−23.2801	−	3.50892i	−1.10358	−	0.166339i
$446$	−22.8940	−	21.2426i	−1.08406	−	1.00586i
$447$		0			0
$448$	3.83771	−	14.8239i	0.181315	−	0.700365i
$449$	5.92314	+	1.35192i	0.279530	+	0.0638010i	0.359988	−	0.932957i	$-0.382781\pi$
$449$	5.92314	+	1.35192i	0.279530	+	0.0638010i	−0.0804573	+	0.996758i	$0.525638\pi$
$450$		0			0
$451$	−32.8642	−	35.4192i	−1.54752	−	1.66783i
$452$	−23.4398	+	34.3798i	−1.10251	+	1.61709i
$453$		0			0
$454$	4.84878	+	10.0686i	0.227564	+	0.472542i
$455$	−14.4885	−	1.50822i	−0.679230	−	0.0707065i
$456$		0			0
$457$	19.9681	+	6.15934i	0.934068	+	0.288122i	0.724186	−	0.689605i	$-0.242216\pi$
$457$	19.9681	+	6.15934i	0.934068	+	0.288122i	0.209882	+	0.977727i	$0.432692\pi$
$458$	3.88008	−	9.88628i	0.181304	−	0.461956i
$459$		0			0
$460$	−11.8222	−	6.82555i	−0.551213	−	0.318243i
$461$	21.9413	+	27.5135i	1.02191	+	1.28143i	0.958999	+	0.283411i	$0.0914660\pi$
$461$	21.9413	+	27.5135i	1.02191	+	1.28143i	0.0629077	+	0.998019i	$0.479963\pi$
$462$		0			0
$463$	−21.3590	+	26.7834i	−0.992638	+	1.24473i	−0.0231134	+	0.999733i	$0.507358\pi$
$463$	−21.3590	+	26.7834i	−0.992638	+	1.24473i	−0.969524	+	0.244995i	$0.921214\pi$
$464$	29.6370	−	11.6317i	1.37586	−	0.539987i
$465$		0			0
$466$	1.89000	+	25.2203i	0.0875525	+	1.16831i
$467$	5.93434	+	15.1204i	0.274608	+	0.699691i	0.999936	+	0.0112872i	$0.00359290\pi$
$467$	5.93434	+	15.1204i	0.274608	+	0.699691i	−0.725328	+	0.688403i	$0.758312\pi$
$468$		0			0
$469$	−28.3278	+	24.7990i	−1.30806	+	1.14511i
$470$	−1.03392	+	0.824521i	−0.0476910	+	0.0380323i
$471$		0			0
$472$	−2.27399	+	1.31289i	−0.104669	+	0.0604307i
$473$	−14.8475	−	5.82722i	−0.682690	−	0.267936i
$474$		0			0
$475$	−8.44587	+	17.5380i	−0.387523	+	0.804700i
$476$	22.1779	+	7.55003i	1.01652	+	0.346055i
$477$		0			0
$478$	−20.8313	+	3.13981i	−0.952801	+	0.143612i
$479$	−3.01433	−	2.05513i	−0.137728	−	0.0939014i	0.492496	−	0.870315i	$-0.336085\pi$
$479$	−3.01433	−	2.05513i	−0.137728	−	0.0939014i	−0.630224	+	0.776413i	$0.717037\pi$
$480$		0			0
$481$	−12.2442	−	17.9590i	−0.558288	−	0.818858i
$482$	−13.8522	+	60.6903i	−0.630949	+	2.76437i
$483$		0			0
$484$	−13.7063	−	60.0510i	−0.623012	−	2.72959i
$485$	−3.36125	+	3.62256i	−0.152626	+	0.164492i
$486$		0			0
$487$	−21.6516	+	6.67864i	−0.981128	+	0.302638i	−0.743513	−	0.668721i	$-0.766842\pi$
$487$	−21.6516	+	6.67864i	−0.981128	+	0.302638i	−0.237615	+	0.971359i	$0.576366\pi$
$488$	0.150953	−	2.01432i	0.00683330	−	0.0911841i
$489$		0			0
$490$	23.4192	+	10.7930i	1.05797	+	0.487577i
$491$			3.09931i			0.139870i	0.997552	+	0.0699349i	$0.0222791\pi$
$491$			3.09931i			0.139870i	−0.997552	+	0.0699349i	$0.977721\pi$
$492$		0			0
$493$	−3.97250	−	12.8785i	−0.178912	−	0.580019i
$494$	−9.55144	+	63.3697i	−0.429740	+	2.85114i
$495$		0			0
$496$	−27.0650	+	6.17742i	−1.21526	+	0.277374i
$497$	9.07555	−	17.5298i	0.407094	−	0.786320i
$498$		0			0
$499$	0.317926	−	0.216758i	0.0142323	−	0.00970343i	−0.556183	−	0.831060i	$-0.687735\pi$
$499$	0.317926	−	0.216758i	0.0142323	−	0.00970343i	0.570415	+	0.821356i	$0.306782\pi$
$500$	35.3320	−	32.7833i	1.58009	−	1.46611i
$501$		0			0
$502$	8.76018	+	58.1200i	0.390986	+	2.59402i
$503$	−2.47384	+	1.19134i	−0.110303	+	0.0531192i	−0.488222	−	0.872720i	$-0.662354\pi$
$503$	−2.47384	+	1.19134i	−0.110303	+	0.0531192i	0.377919	+	0.925839i	$0.376640\pi$
$504$		0			0
$505$	22.6170	+	10.8918i	1.00644	+	0.484677i
$506$	−8.20964	+	26.6150i	−0.364963	+	1.18318i
$507$		0			0
$508$	42.2887	+	73.2461i	1.87626	+	3.24977i
$509$	−8.64500	+	14.9736i	−0.383183	+	0.663693i	−0.991515	−	0.129990i	$-0.958505\pi$
$509$	−8.64500	+	14.9736i	−0.383183	+	0.663693i	0.608332	+	0.793682i	$0.291839\pi$
$510$		0			0
$511$	10.5117	+	37.9410i	0.465011	+	1.67841i
$512$	35.4964	+	28.3074i	1.56873	+	1.25102i
$513$		0			0
$514$	−70.2078	+	5.26135i	−3.09673	+	0.232068i
$515$	24.8732	−	1.86399i	1.09604	−	0.0821371i
$516$		0			0
$517$	1.42523	+	1.13658i	0.0626816	+	0.0499869i
$518$	10.2733	+	37.0806i	0.451384	+	1.62923i
$519$		0			0
$520$	14.8037	−	25.6407i	0.649184	−	1.12442i
$521$	−5.47476	−	9.48256i	−0.239854	−	0.415439i	0.720819	−	0.693124i	$-0.243766\pi$
$521$	−5.47476	−	9.48256i	−0.239854	−	0.415439i	−0.960672	+	0.277685i	$0.910433\pi$
$522$		0			0
$523$	0.504756	−	1.63638i	0.0220714	−	0.0715539i	−0.943867	−	0.330325i	$-0.892841\pi$
$523$	0.504756	−	1.63638i	0.0220714	−	0.0715539i	0.965939	+	0.258772i	$0.0833177\pi$
$524$	−61.7560	−	29.7401i	−2.69782	−	1.29920i
$525$		0			0
$526$	40.1251	−	19.3233i	1.74954	−	0.842534i
$527$	1.75147	+	11.6203i	0.0762954	+	0.506187i
$528$		0			0
$529$	−13.2834	+	12.3252i	−0.577541	+	0.535880i
$530$	3.36869	−	2.29673i	0.146327	−	0.0997638i
$531$		0			0
$532$	35.2391	−	68.0659i	1.52781	−	2.95103i
$533$	−34.4263	+	7.85758i	−1.49117	+	0.340350i
$534$		0			0
$535$	−1.19907	+	7.95532i	−0.0518404	+	0.343939i
$536$	−22.5555	−	73.1233i	−0.974251	−	3.15844i
$537$		0			0
$538$			30.3098i			1.30675i
$539$	7.32125	−	34.7841i	0.315348	−	1.49826i
$540$		0			0
$541$	2.41502	−	32.2262i	0.103830	−	1.38551i	−0.665374	−	0.746510i	$-0.731728\pi$
$541$	2.41502	−	32.2262i	0.103830	−	1.38551i	0.769204	−	0.639004i	$-0.220653\pi$
$542$	−37.5449	+	11.5811i	−1.61269	+	0.497449i
$543$		0			0
$544$	−2.47784	+	2.67047i	−0.106236	+	0.114496i
$545$	0.189614	+	0.830754i	0.00812217	+	0.0355856i
$546$		0			0
$547$	−4.98810	+	21.8543i	−0.213276	+	0.934423i	0.749048	+	0.662516i	$0.230511\pi$
$547$	−4.98810	+	21.8543i	−0.213276	+	0.934423i	−0.962324	+	0.271907i	$0.912346\pi$
$548$	−7.87430	−	11.5495i	−0.336373	−	0.493369i
$549$		0			0
$550$	−29.1610	−	19.8816i	−1.24343	−	0.847756i
$551$	−43.6001	+	6.57166i	−1.85743	+	0.279962i
$552$		0			0
$553$	0.884883	+	0.301241i	0.0376291	+	0.0128101i
$554$	6.48123	−	13.4584i	0.275361	−	0.571793i
$555$		0			0
$556$	35.8037	+	14.0519i	1.51842	+	0.595934i
$557$	−19.7361	+	11.3946i	−0.836244	+	0.482806i	−0.855986	−	0.516999i	$-0.827049\pi$
$557$	−19.7361	+	11.3946i	−0.836244	+	0.482806i	0.0197418	+	0.999805i	$0.493716\pi$
$558$		0			0
$559$	−9.11361	+	7.26786i	−0.385464	+	0.307398i
$560$	−14.8303	+	12.9829i	−0.626695	+	0.548628i
$561$		0			0
$562$	−18.5838	−	47.3508i	−0.783910	−	1.99737i
$563$	−0.0611578	−	0.816094i	−0.00257750	−	0.0343943i	0.995767	−	0.0919161i	$-0.0292992\pi$
$563$	−0.0611578	−	0.816094i	−0.00257750	−	0.0343943i	−0.998344	+	0.0575218i	$0.981680\pi$
$564$		0			0
$565$	−13.7945	+	5.41396i	−0.580341	+	0.227767i
$566$	2.50005	−	3.13497i	0.105085	−	0.131773i
$567$		0			0
$568$	25.0155	+	31.3684i	1.04963	+	1.31619i
$569$	9.61535	+	5.55143i	0.403097	+	0.232728i	0.687819	−	0.725882i	$-0.258568\pi$
$569$	9.61535	+	5.55143i	0.403097	+	0.232728i	−0.284723	+	0.958610i	$0.591902\pi$
$570$		0			0
$571$	3.77958	−	9.63021i	0.158170	−	0.403012i	−0.829717	−	0.558184i	$-0.811498\pi$
$571$	3.77958	−	9.63021i	0.158170	−	0.403012i	0.987887	+	0.155173i	$0.0495934\pi$
$572$	−75.0161	−	23.1394i	−3.13658	−	0.967507i
$573$		0			0
$574$	62.1739	+	6.47218i	2.59509	+	0.270144i
$575$	2.68263	+	5.57054i	0.111874	+	0.232308i
$576$		0			0
$577$	3.61648	−	5.30441i	0.150556	−	0.220825i	−0.743550	−	0.668680i	$-0.766860\pi$
$577$	3.61648	−	5.30441i	0.150556	−	0.220825i	0.894106	+	0.447855i	$0.147812\pi$
$578$	−21.0803	−	22.7192i	−0.876826	−	0.944993i
$579$		0			0
$580$	38.2005	+	8.71902i	1.58619	+	0.362038i
$581$	−4.99253	+	19.2847i	−0.207125	+	0.800063i
$582$		0			0
$583$	−4.11993	−	3.82274i	−0.170630	−	0.158322i
$584$	−79.1274	−	11.9265i	−3.27432	−	0.493524i
$585$		0			0
$586$	12.2016	+	0.914381i	0.504042	+	0.0377727i
$587$	39.2508			1.62005			0.810027	−	0.586393i	$-0.199453\pi$
$587$	39.2508			1.62005			0.810027	+	0.586393i	$0.199453\pi$
$588$		0			0
$589$	38.4466			1.58416
$590$	−1.79371	−	0.134420i	−0.0738459	−	0.00553398i
$591$		0			0
$592$	−29.0822	−	4.38343i	−1.19527	−	0.180158i
$593$	30.9329	+	28.7015i	1.27026	+	1.17863i	0.974752	+	0.223291i	$0.0716799\pi$
$593$	30.9329	+	28.7015i	1.27026	+	1.17863i	0.295510	+	0.955340i	$0.404511\pi$
$594$		0			0
$595$	5.01128	+	6.67096i	0.205442	+	0.273483i
$596$	47.6269	+	10.8705i	1.95087	+	0.445274i
$597$		0			0
$598$	13.8451	+	14.9214i	0.566167	+	0.610183i
$599$	2.35453	−	3.45346i	0.0962035	−	0.141105i	−0.775119	−	0.631815i	$-0.782310\pi$
$599$	2.35453	−	3.45346i	0.0962035	−	0.141105i	0.871323	+	0.490710i	$0.163263\pi$
$600$		0			0
$601$	−6.38869	−	13.2662i	−0.260600	−	0.541142i	0.729081	−	0.684427i	$-0.239948\pi$
$601$	−6.38869	−	13.2662i	−0.260600	−	0.541142i	−0.989681	+	0.143285i	$0.954233\pi$
$602$	19.4187	−	6.98019i	0.791448	−	0.284491i
$603$		0			0
$604$	−80.2174	−	24.7438i	−3.26400	−	1.00681i
$605$	8.01429	−	20.4201i	0.325827	−	0.830194i
$606$		0			0
$607$	12.6579	+	7.30804i	0.513768	+	0.296624i	0.734381	−	0.678737i	$-0.237473\pi$
$607$	12.6579	+	7.30804i	0.513768	+	0.296624i	−0.220613	+	0.975361i	$0.570806\pi$
$608$	7.43098	+	9.31816i	0.301366	+	0.377901i
$609$		0			0
$610$	0.862748	−	1.08185i	0.0349316	−	0.0438029i
$611$	1.24016	−	0.486726i	0.0501714	−	0.0196908i
$612$		0			0
$613$	−0.710467	−	9.48052i	−0.0286955	−	0.382914i	−0.993000	−	0.118117i	$-0.962314\pi$
$613$	−0.710467	−	9.48052i	−0.0286955	−	0.382914i	0.964304	−	0.264797i	$-0.0853050\pi$
$614$	21.0705	+	53.6868i	0.850338	+	2.16662i
$615$		0			0
$616$	58.4926	+	42.4085i	2.35674	+	1.70869i
$617$	−3.32360	+	2.65048i	−0.133803	+	0.106704i	−0.688104	−	0.725612i	$-0.741557\pi$
$617$	−3.32360	+	2.65048i	−0.133803	+	0.106704i	0.554301	+	0.832316i	$0.312985\pi$
$618$		0			0
$619$	31.6920	−	18.2974i	1.27381	−	0.735435i	0.298107	−	0.954532i	$-0.403645\pi$
$619$	31.6920	−	18.2974i	1.27381	−	0.735435i	0.975703	+	0.219098i	$0.0703113\pi$
$620$	−31.8039	−	12.4821i	−1.27727	−	0.501293i
$621$		0			0
$622$	−17.6514	+	36.6534i	−0.707755	+	1.46967i
$623$	−29.9394	−	29.4361i	−1.19950	−	1.17933i
$624$		0			0
$625$	3.13463	−	0.472469i	0.125385	−	0.0188988i
$626$	47.2233	+	32.1963i	1.88742	+	1.28682i
$627$		0			0
$628$	−2.19817	−	3.22413i	−0.0877166	−	0.128657i
$629$	−2.77035	+	12.1377i	−0.110461	+	0.483961i
$630$		0			0
$631$	0.216545	+	0.948747i	0.00862054	+	0.0377690i	0.979055	−	0.203595i	$-0.0652625\pi$
$631$	0.216545	+	0.948747i	0.00862054	+	0.0377690i	−0.970435	+	0.241364i	$0.922405\pi$
$632$	−1.29227	+	1.39274i	−0.0514037	+	0.0554000i
$633$		0			0
$634$	3.24026	−	0.999489i	0.128687	−	0.0396948i
$635$	−2.25096	+	30.0370i	−0.0893267	+	1.19198i
$636$		0			0
$637$	−19.3400	−	17.3443i	−0.766280	−	0.687205i
$638$		−	79.9450i		−	3.16505i
$639$		0			0
$640$	7.78315	+	25.2324i	0.307656	+	0.997396i
$641$	3.03766	−	20.1536i	0.119981	−	0.796019i	−0.845203	−	0.534445i	$-0.820521\pi$
$641$	3.03766	−	20.1536i	0.119981	−	0.796019i	0.965184	−	0.261573i	$-0.0842414\pi$
$642$		0			0
$643$	22.4745	−	5.12967i	0.886310	−	0.202294i	0.244951	−	0.969535i	$-0.421228\pi$
$643$	22.4745	−	5.12967i	0.886310	−	0.202294i	0.641359	+	0.767241i	$0.278371\pi$
$644$	−9.92418	−	22.2305i	−0.391068	−	0.876005i
$645$		0			0
$646$	30.3286	−	20.6777i	1.19326	−	0.813553i
$647$	−14.3695	+	13.3330i	−0.564925	+	0.524174i	−0.910113	−	0.414359i	$-0.864006\pi$
$647$	−14.3695	+	13.3330i	−0.564925	+	0.524174i	0.345188	+	0.938534i	$0.387815\pi$
$648$		0			0
$649$	0.369554	+	2.45183i	0.0145062	+	0.0962427i
$650$	−23.2392	+	11.1914i	−0.911515	+	0.438963i
$651$		0			0
$652$	1.67247	+	0.805419i	0.0654990	+	0.0315426i
$653$	13.5875	−	44.0497i	0.531722	−	1.72380i	−0.146751	−	0.989173i	$-0.546882\pi$
$653$	13.5875	−	44.0497i	0.531722	−	1.72380i	0.678472	−	0.734626i	$-0.262642\pi$
$654$		0			0
$655$	−12.2056	−	21.1407i	−0.476911	−	0.826034i
$656$	−23.8901	+	41.3788i	−0.932750	+	1.61557i
$657$		0			0
$658$	−2.35591	+	0.108154i	−0.0918431	+	0.00421628i
$659$	−27.1757	−	21.6719i	−1.05861	−	0.844217i	−0.0704346	−	0.997516i	$-0.522439\pi$
$659$	−27.1757	−	21.6719i	−1.05861	−	0.844217i	−0.988180	+	0.153300i	$0.951010\pi$
$660$		0			0
$661$	−30.4024	+	2.27835i	−1.18252	+	0.0886174i	−0.651436	−	0.758704i	$-0.725833\pi$
$661$	−30.4024	+	2.27835i	−1.18252	+	0.0886174i	−0.531081	+	0.847321i	$0.678214\pi$
$662$	41.6359	−	3.12018i	1.61823	−	0.121269i
$663$		0			0
$664$	−31.6555	−	25.2444i	−1.22847	−	0.979672i
$665$	24.0247	−	12.9591i	0.931637	−	0.502531i
$666$		0			0
$667$	−7.00249	+	12.1287i	−0.271137	+	0.469624i
$668$	−16.6156	−	28.7790i	−0.642876	−	1.11349i
$669$		0			0
$670$	15.4512	−	50.0916i	0.596933	−	1.93521i
$671$	−1.71856	−	0.827614i	−0.0663442	−	0.0319497i
$672$		0			0
$673$	−7.74136	+	3.72804i	−0.298408	+	0.143706i	−0.577097	−	0.816676i	$-0.695814\pi$
$673$	−7.74136	+	3.72804i	−0.298408	+	0.143706i	0.278689	+	0.960381i	$0.410100\pi$
$674$	−1.88519	−	12.5074i	−0.0726148	−	0.481768i
$675$		0			0
$676$	−2.35947	+	2.18926i	−0.0907487	+	0.0842024i
$677$	10.4403	−	7.11811i	0.401255	−	0.273571i	−0.345833	−	0.938296i	$-0.612404\pi$
$677$	10.4403	−	7.11811i	0.401255	−	0.273571i	0.747088	+	0.664725i	$0.231451\pi$
$678$		0			0
$679$	−8.64519	+	1.71178i	−0.331772	+	0.0656919i
$680$	−16.5333	+	3.77362i	−0.634023	+	0.144712i
$681$		0			0
$682$	−10.3895	+	68.9296i	−0.397833	+	2.63945i
$683$	−8.07426	−	26.1761i	−0.308953	−	1.00160i	−0.968306	−	0.249767i	$-0.919646\pi$
$683$	−8.07426	−	26.1761i	−0.308953	−	1.00160i	0.659353	−	0.751833i	$-0.270830\pi$
$684$		0			0
$685$		−	4.97823i		−	0.190208i
$686$	22.5151	+	40.0986i	0.859631	+	1.53097i
$687$		0			0
$688$	−1.17870	+	15.7286i	−0.0449374	+	0.599647i
$689$	−3.92494	+	1.21068i	−0.149528	+	0.0461234i
$690$		0			0
$691$	−5.70636	+	6.15000i	−0.217080	+	0.233957i	−0.832198	−	0.554478i	$-0.812918\pi$
$691$	−5.70636	+	6.15000i	−0.217080	+	0.233957i	0.615118	+	0.788435i	$0.289108\pi$
$692$	11.8828	+	52.0618i	0.451715	+	1.97909i
$693$		0			0
$694$	7.99673	−	35.0360i	0.303552	−	1.32995i
$695$	7.71633	+	11.3178i	0.292697	+	0.429308i
$696$		0			0
$697$	16.7113	+	11.3936i	0.632987	+	0.431563i
$698$	−56.6103	+	8.53264i	−2.14273	+	0.322965i
$699$		0			0
$700$	30.6250	−	3.71372i	1.15752	−	0.140365i
$701$	−3.12850	+	6.49640i	−0.118162	+	0.245366i	−0.951658	−	0.307160i	$-0.900621\pi$
$701$	−3.12850	+	6.49640i	−0.118162	+	0.245366i	0.833496	+	0.552525i	$0.186336\pi$
$702$		0			0
$703$	37.9155	+	14.8808i	1.43001	+	0.561238i
$704$	25.4523	−	14.6949i	0.959270	−	0.553835i
$705$		0			0
$706$	−27.2133	+	21.7019i	−1.02419	+	0.816762i
$707$	21.2535	+	39.4015i	0.799319	+	1.48185i
$708$		0			0
$709$	−9.84995	−	25.0973i	−0.369923	−	0.942548i	−0.987723	−	0.156213i	$-0.950071\pi$
$709$	−9.84995	−	25.0973i	−0.369923	−	0.942548i	0.617801	−	0.786335i	$-0.288024\pi$
$710$	2.05393	+	27.4077i	0.0770825	+	1.02859i
$711$		0			0
$712$	79.4393	−	31.1776i	2.97711	−	1.16843i
$713$	7.61384	−	9.54746i	0.285141	−	0.357555i
$714$		0			0
$715$	−17.4316	−	21.8586i	−0.651906	−	0.817465i
$716$	39.6287	+	22.8796i	1.48099	+	0.855052i
$717$		0			0
$718$	4.82844	−	12.3027i	0.180196	−	0.459131i
$719$	17.2294	+	5.31457i	0.642548	+	0.198200i	0.598871	−	0.800846i	$-0.295616\pi$
$719$	17.2294	+	5.31457i	0.642548	+	0.198200i	0.0436777	+	0.999046i	$0.486093\pi$
$720$		0			0
$721$	37.8639	+	23.3462i	1.41012	+	0.869458i
$722$	−31.6356	−	65.6919i	−1.17735	−	2.44480i
$723$		0			0
$724$	−8.94008	+	13.1127i	−0.332256	+	0.487329i
$725$	−12.0708	−	13.0092i	−0.448298	−	0.483151i
$726$		0			0
$727$	−50.0302	−	11.4191i	−1.85552	−	0.423510i	−0.859382	−	0.511335i	$-0.829151\pi$
$727$	−50.0302	−	11.4191i	−1.85552	−	0.423510i	−0.996136	+	0.0878248i	$0.972008\pi$
$728$	48.2149	−	21.5242i	1.78696	−	0.797739i
$729$		0			0
$730$	−40.1837	−	37.2850i	−1.48726	−	1.37998i
$731$	6.60217	+	0.995117i	0.244190	+	0.0368057i
$732$		0			0
$733$	47.5796	+	3.56560i	1.75739	+	0.131698i	0.914031	−	0.405645i	$-0.132953\pi$
$733$	47.5796	+	3.56560i	1.75739	+	0.131698i	0.843363	+	0.537344i	$0.180572\pi$
$734$	2.94539			0.108716
$735$		0			0
$736$	3.78559			0.139539
$737$	−72.0585	−	5.40004i	−2.65431	−	0.198913i
$738$		0			0
$739$	35.0737	+	5.28651i	1.29021	+	0.194467i	0.758060	−	0.652185i	$-0.226147\pi$
$739$	35.0737	+	5.28651i	1.29021	+	0.194467i	0.532147	+	0.846652i	$0.321385\pi$
$740$	−26.5334	−	24.6194i	−0.975386	−	0.905026i
$741$		0			0
$742$	7.26805	+	0.210285i	0.266819	+	0.00771979i
$743$	−16.2874	−	3.71749i	−0.597527	−	0.136382i	−0.0869483	−	0.996213i	$-0.527712\pi$
$743$	−16.2874	−	3.71749i	−0.597527	−	0.136382i	−0.510578	+	0.859831i	$0.670569\pi$
$744$		0			0
$745$	11.8336	+	12.7536i	0.433550	+	0.467256i
$746$	10.6946	−	15.6862i	0.391559	−	0.574311i
$747$		0			0
$748$	19.5097	+	40.5124i	0.713346	+	1.48128i
$749$	−10.0590	+	10.2309i	−0.367546	+	0.373830i
$750$		0			0
$751$	4.80396	+	1.48183i	0.175299	+	0.0540726i	0.381162	−	0.924508i	$-0.375524\pi$
$751$	4.80396	+	1.48183i	0.175299	+	0.0540726i	−0.205863	+	0.978581i	$0.566000\pi$
$752$	0.658588	−	1.67805i	0.0240162	−	0.0611923i
$753$		0			0
$754$	−50.5983	−	29.2129i	−1.84268	−	1.06387i
$755$	−18.6403	−	23.3742i	−0.678390	−	0.850674i
$756$		0			0
$757$	11.0411	−	13.8452i	0.401297	−	0.503211i	−0.539591	−	0.841927i	$-0.681421\pi$
$757$	11.0411	−	13.8452i	0.401297	−	0.503211i	0.940889	+	0.338716i	$0.109993\pi$
$758$	4.94035	−	1.93894i	0.179441	−	0.0704256i
$759$		0			0
$760$	4.14616	+	55.3266i	0.150397	+	2.00691i
$761$	−14.6478	−	37.3219i	−0.530981	−	1.35292i	−0.904967	−	0.425482i	$-0.860104\pi$
$761$	−14.6478	−	37.3219i	−0.530981	−	1.35292i	0.373986	−	0.927434i	$-0.377991\pi$
$762$		0			0
$763$	−0.595870	+	1.39796i	−0.0215719	+	0.0506094i
$764$	−72.5444	+	57.8522i	−2.62456	+	2.09302i
$765$		0			0
$766$	4.49203	−	2.59348i	0.162304	−	0.0937061i
$767$	1.68684	+	0.662034i	0.0609081	+	0.0239047i
$768$		0			0
$769$	−2.57015	+	5.33697i	−0.0926820	+	0.192456i	−0.942156	−	0.335174i	$-0.891205\pi$
$769$	−2.57015	+	5.33697i	−0.0926820	+	0.192456i	0.849474	+	0.527630i	$0.176919\pi$
$770$	16.7417	+	46.5749i	0.603328	+	1.67844i
$771$		0			0
$772$	−35.2887	+	5.31891i	−1.27007	+	0.191432i
$773$	−0.738041	−	0.503188i	−0.0265455	−	0.0180984i	0.549975	−	0.835181i	$-0.314637\pi$
$773$	−0.738041	−	0.503188i	−0.0265455	−	0.0180984i	−0.576520	+	0.817083i	$0.695590\pi$
$774$		0			0
$775$	8.71695	+	12.7854i	0.313122	+	0.459266i
$776$	3.98596	−	17.4636i	0.143088	−	0.626908i
$777$		0			0
$778$	−11.8997	−	52.1358i	−0.426623	−	1.86916i
$779$	45.0078	−	48.5069i	1.61257	−	1.73794i
$780$		0			0
$781$	36.2037	−	11.1674i	1.29547	−	0.399600i
$782$	0.871283	−	11.6265i	0.0311570	−	0.415761i
$783$		0			0
$784$	−35.0030	+	3.22058i	−1.25011	+	0.115021i
$785$		−	1.38971i		−	0.0496010i
$786$		0			0
$787$	5.15825	+	16.7226i	0.183872	+	0.596098i	0.999838	+	0.0179981i	$0.00572928\pi$
$787$	5.15825	+	16.7226i	0.183872	+	0.596098i	−0.815966	+	0.578100i	$0.803795\pi$
$788$	9.26638	−	61.4784i	0.330101	−	2.19008i
$789$		0			0
$790$	−1.26887	+	0.289611i	−0.0451443	+	0.0103039i
$791$	−25.5843	−	6.62342i	−0.909675	−	0.235502i
$792$		0			0
$793$	−1.15179	+	0.785278i	−0.0409013	+	0.0278860i
$794$	−22.6938	+	21.0568i	−0.805374	+	0.747278i
$795$		0			0
$796$	9.64450	+	63.9871i	0.341840	+	2.26796i
$797$	−28.6478	+	13.7961i	−1.01476	+	0.488681i	−0.865921	−	0.500180i	$-0.833267\pi$
$797$	−28.6478	+	13.7961i	−1.01476	+	0.488681i	−0.148836	+	0.988862i	$0.547553\pi$
$798$		0			0
$799$	−0.687517	−	0.331091i	−0.0243226	−	0.0117131i
$800$	−1.41394	+	4.58387i	−0.0499902	+	0.162064i
$801$		0			0
$802$	−29.9828	−	51.9317i	−1.05873	−	1.83377i
$803$	−37.7820	+	65.4403i	−1.33330	+	2.30934i
$804$		0			0
$805$	1.53964	−	8.53243i	0.0542651	−	0.300729i
$806$	39.8300	+	31.7634i	1.40295	+	1.11882i
$807$		0			0
$808$	−90.7382	+	6.79989i	−3.19216	+	0.239219i
$809$	−19.8835	+	1.49006i	−0.699067	+	0.0523878i	−0.419523	−	0.907745i	$-0.637802\pi$
$809$	−19.8835	+	1.49006i	−0.699067	+	0.0523878i	−0.279545	+	0.960133i	$0.590183\pi$
$810$		0			0
$811$	10.4867	+	8.36286i	0.368237	+	0.293660i	0.790073	−	0.613013i	$-0.210043\pi$
$811$	10.4867	+	8.36286i	0.368237	+	0.293660i	−0.421836	+	0.906672i	$0.638614\pi$
$812$	46.0279	+	52.5774i	1.61526	+	1.84511i
$813$		0			0
$814$	−36.9252	+	63.9563i	−1.29423	+	2.24167i
$815$	0.330550	+	0.572529i	0.0115787	+	0.0200548i
$816$		0			0
$817$	6.43857	−	20.8733i	0.225257	−	0.730266i
$818$	−15.1456	−	7.29374i	−0.529553	−	0.255019i
$819$		0			0
$820$	−52.9797	+	25.5137i	−1.85013	+	0.890977i
$821$	7.34693	+	48.7437i	0.256410	+	1.70117i	0.632481	+	0.774576i	$0.282037\pi$
$821$	7.34693	+	48.7437i	0.256410	+	1.70117i	−0.376072	+	0.926591i	$0.622725\pi$
$822$		0			0
$823$	36.8550	−	34.1964i	1.28468	−	1.19201i	0.314605	−	0.949223i	$-0.398128\pi$
$823$	36.8550	−	34.1964i	1.28468	−	1.19201i	0.970079	−	0.242790i	$-0.0780626\pi$
$824$	−74.7023	+	50.9312i	−2.60238	+	1.77427i
$825$		0			0
$826$	−2.44910	−	2.07175i	−0.0852150	−	0.0720854i
$827$	−2.64435	+	0.603555i	−0.0919530	+	0.0209877i	−0.268250	−	0.963349i	$-0.586445\pi$
$827$	−2.64435	+	0.603555i	−0.0919530	+	0.0209877i	0.176297	+	0.984337i	$0.443588\pi$
$828$		0			0
$829$	−0.645418	+	4.28207i	−0.0224163	+	0.148722i	−0.997239	−	0.0742590i	$-0.976341\pi$
$829$	−0.645418	+	4.28207i	−0.0224163	+	0.148722i	0.974823	+	0.222981i	$0.0715789\pi$
$830$	−8.17535	−	26.5038i	−0.283771	−	0.919962i
$831$		0			0
$832$		−	21.4788i		−	0.744644i
$833$	0.252207	+	14.8776i	0.00873844	+	0.515477i
$834$		0			0
$835$	0.884422	−	11.8018i	0.0306067	−	0.408418i
$836$	140.574	−	43.3614i	4.86186	−	1.49968i
$837$		0			0
$838$	−24.2601	+	26.1462i	−0.838051	+	0.903204i
$839$	−3.08789	−	13.5289i	−0.106606	−	0.467071i	−0.999847	−	0.0174929i	$-0.994432\pi$
$839$	−3.08789	−	13.5289i	−0.106606	−	0.467071i	0.893241	−	0.449578i	$-0.148426\pi$
$840$		0			0
$841$	2.49193	−	10.9179i	0.0859287	−	0.376478i
$842$	26.6618	+	39.1057i	0.918828	+	1.34767i
$843$		0			0
$844$	80.1270	+	54.6297i	2.75809	+	1.88043i
$845$	−1.13349	+	0.170847i	−0.0389934	+	0.00587731i
$846$		0			0
$847$	32.9472	−	21.0937i	1.13208	−	0.724787i
$848$	−2.41141	+	5.00735i	−0.0828083	+	0.171953i
$849$		0			0
$850$	13.7527	+	5.39755i	0.471715	+	0.185134i
$851$	11.2040	−	6.46864i	0.384069	−	0.221742i
$852$		0			0
$853$	−9.48236	+	7.56193i	−0.324670	+	0.258915i	−0.772237	−	0.635335i	$-0.780862\pi$
$853$	−9.48236	+	7.56193i	−0.324670	+	0.258915i	0.447567	+	0.894250i	$0.352291\pi$
$854$	2.37815	−	0.658876i	0.0813787	−	0.0225463i
$855$		0			0
$856$	−10.6541	−	27.1461i	−0.364148	−	0.927835i
$857$	−0.750495	−	10.0147i	−0.0256364	−	0.342094i	−0.995243	−	0.0974245i	$-0.968940\pi$
$857$	−0.750495	−	10.0147i	−0.0256364	−	0.342094i	0.969607	−	0.244670i	$-0.0786795\pi$
$858$		0			0
$859$	−17.3506	+	6.80961i	−0.591995	+	0.232341i	−0.642376	−	0.766389i	$-0.722051\pi$
$859$	−17.3506	+	6.80961i	−0.591995	+	0.232341i	0.0503818	+	0.998730i	$0.483956\pi$
$860$	−12.1029	+	15.1765i	−0.412705	+	0.517515i
$861$		0			0
$862$	12.2922	+	15.4139i	0.418673	+	0.524999i
$863$	34.5597	+	19.9531i	1.17643	+	0.679210i	0.955185	−	0.296009i	$-0.0956560\pi$
$863$	34.5597	+	19.9531i	1.17643	+	0.679210i	0.221241	+	0.975219i	$0.428989\pi$
$864$		0			0
$865$	−6.94806	+	17.7034i	−0.236241	+	0.601932i
$866$	48.5248	+	14.9679i	1.64894	+	0.508630i
$867$		0			0
$868$	−32.8530	−	51.3146i	−1.11510	−	1.74173i
$869$	0.778425	+	1.61642i	0.0264063	+	0.0548331i
$870$		0			0
$871$	−29.7489	+	43.6336i	−1.00800	+	1.47847i
$872$	−2.10087	−	2.26420i	−0.0711445	−	0.0766756i
$873$		0			0
$874$	−37.1877	−	8.48786i	−1.25789	−	0.287106i
$875$	27.1850	+	14.0743i	0.919022	+	0.475797i
$876$		0			0
$877$	5.82353	+	5.40345i	0.196647	+	0.182462i	0.772350	−	0.635197i	$-0.219081\pi$
$877$	5.82353	+	5.40345i	0.196647	+	0.182462i	−0.575703	+	0.817659i	$0.695272\pi$
$878$	−67.9500	−	10.2418i	−2.29320	−	0.345645i
$879$		0			0
$880$	−37.7244	−	2.82705i	−1.27169	−	0.0952999i
$881$	−49.3990			−1.66430			−0.832148	−	0.554554i	$-0.812889\pi$
$881$	−49.3990			−1.66430			−0.832148	+	0.554554i	$0.812889\pi$
$882$		0			0
$883$	5.45893			0.183708			0.0918538	−	0.995773i	$-0.470721\pi$
$883$	5.45893			0.183708			0.0918538	+	0.995773i	$0.470721\pi$
$884$	32.7699	+	2.45577i	1.10217	+	0.0825964i
$885$		0			0
$886$	−64.1776	−	9.67322i	−2.15609	−	0.324978i
$887$	−8.07695	−	7.49432i	−0.271197	−	0.251634i	0.532836	−	0.846219i	$-0.321126\pi$
$887$	−8.07695	−	7.49432i	−0.271197	−	0.251634i	−0.804033	+	0.594584i	$0.797317\pi$
$888$		0			0
$889$	−34.6930	+	41.0119i	−1.16357	+	1.37550i
$890$	56.9937	+	13.0084i	1.91043	+	0.436044i
$891$		0			0
$892$	35.6371	+	38.4077i	1.19322	+	1.28598i
$893$	−1.40635	+	2.06273i	−0.0470616	+	0.0690267i
$894$		0			0
$895$	7.07084	+	14.6828i	0.236352	+	0.490790i
$896$	−15.1759	+	44.5787i	−0.506992	+	1.48927i
$897$		0			0
$898$	−14.4156	−	4.44664i	−0.481056	−	0.148386i
$899$	−12.8057	+	32.6283i	−0.427093	+	1.08821i
$900$		0			0
$901$	2.03745	+	1.17632i	0.0678774	+	0.0391890i
$902$	74.8039	+	93.8011i	2.49070	+	3.12324i
$903$		0			0
$904$	33.4909	−	41.9963i	1.11389	−	1.39678i
$905$	−5.26133	+	2.06492i	−0.174893	+	0.0686403i
$906$		0			0
$907$	1.02131	+	13.6284i	0.0339119	+	0.452523i	0.988152	+	0.153480i	$0.0490482\pi$
$907$	1.02131	+	13.6284i	0.0339119	+	0.452523i	−0.954240	+	0.299043i	$0.903333\pi$
$908$	−6.84941	−	17.4520i	−0.227306	−	0.579165i
$909$		0			0
$910$	35.5955	+	6.42305i	1.17998	+	0.212922i
$911$	−32.4342	+	25.8654i	−1.07459	+	0.856959i	−0.990226	−	0.139475i	$-0.955458\pi$
$911$	−32.4342	+	25.8654i	−1.07459	+	0.856959i	−0.0843675	+	0.996435i	$0.526887\pi$
$912$		0			0
$913$	−33.1112	+	19.1168i	−1.09582	+	0.632673i
$914$	−48.3008	−	18.9567i	−1.59765	−	0.627031i
$915$		0			0
$916$	−7.73057	+	16.0527i	−0.255425	+	0.530396i
$917$	4.50749	−	43.3004i	0.148850	−	1.42990i
$918$		0			0
$919$	13.8295	−	2.08446i	0.456193	−	0.0687600i	0.0830735	−	0.996543i	$-0.473526\pi$
$919$	13.8295	−	2.08446i	0.456193	−	0.0687600i	0.373119	+	0.927783i	$0.378288\pi$
$920$	14.5604	+	9.92710i	0.480041	+	0.327287i
$921$		0			0
$922$	−49.2241	−	72.1985i	−1.62111	−	2.37773i
$923$	6.16132	−	26.9945i	0.202802	−	0.888535i
$924$		0			0
$925$	3.64795	+	15.9827i	0.119944	+	0.525508i
$926$	57.8578	−	62.3559i	1.90132	−	2.04914i
$927$		0			0
$928$	−10.3831	+	3.20276i	−0.340842	+	0.105136i
$929$	3.76169	−	50.1962i	0.123417	−	1.64689i	−0.500748	−	0.865593i	$-0.666942\pi$
$929$	3.76169	−	50.1962i	0.123417	−	1.64689i	0.624165	−	0.781292i	$-0.285439\pi$
$930$		0			0
$931$	48.2532	+	6.43855i	1.58143	+	0.211015i
$932$		−	42.4289i		−	1.38981i
$933$		0			0
$934$	−11.8885	−	38.5415i	−0.389002	−	1.26112i
$935$	−2.38674	+	15.8350i	−0.0780549	+	0.517860i
$936$		0			0
$937$	16.1863	−	3.69443i	0.528785	−	0.120692i	0.0502103	−	0.998739i	$-0.484011\pi$
$937$	16.1863	−	3.69443i	0.528785	−	0.120692i	0.478574	+	0.878047i	$0.341154\pi$
$938$	74.7453	−	56.1493i	2.44052	−	1.83334i
$939$		0			0
$940$	1.83305	−	1.24975i	0.0597874	−	0.0407624i
$941$	29.4715	−	27.3455i	0.960742	−	0.891438i	−0.0334084	−	0.999442i	$-0.510636\pi$
$941$	29.4715	−	27.3455i	0.960742	−	0.891438i	0.994151	+	0.108003i	$0.0344457\pi$
$942$		0			0
$943$	−3.13253	−	20.7830i	−0.102009	−	0.676787i
$944$	2.20913	−	1.06386i	0.0719010	−	0.0346257i
$945$		0			0
$946$	35.6832	+	17.1841i	1.16016	+	0.558704i
$947$	2.55803	−	8.29294i	0.0831249	−	0.269484i	−0.904463	−	0.426552i	$-0.859728\pi$
$947$	2.55803	−	8.29294i	0.0831249	−	0.269484i	0.987588	+	0.157068i	$0.0502042\pi$
$948$		0			0
$949$	27.6120	+	47.8254i	0.896324	+	1.55248i
$950$	24.1675	−	41.8593i	0.784097	−	1.35810i
$951$		0			0
$952$	−27.8215	−	11.8587i	−0.901700	−	0.384344i
$953$	−1.20617	−	0.961888i	−0.0390716	−	0.0311586i	0.603759	−	0.797167i	$-0.293669\pi$
$953$	−1.20617	−	0.961888i	−0.0390716	−	0.0311586i	−0.642831	+	0.766008i	$0.722240\pi$
$954$		0			0
$955$	−32.9529	+	2.46948i	−1.06633	+	0.0799103i
$956$	35.2431	−	2.64110i	1.13984	−	0.0854194i
$957$		0			0
$958$	7.08253	+	5.64813i	0.228826	+	0.182483i
$959$	5.21126	−	7.18771i	0.168280	−	0.232103i
$960$		0			0
$961$	−0.218501	+	0.378454i	−0.00704841	+	0.0122082i
$962$	26.9859	+	46.7409i	0.870059	+	1.50699i
$963$		0			0
$964$	30.7825	−	99.7944i	0.991437	−	3.21416i
$965$	−11.4509	−	5.51448i	−0.368619	−	0.177518i
$966$		0			0
$967$	−33.0780	+	15.9295i	−1.06372	+	0.512259i	−0.882077	−	0.471106i	$-0.843855\pi$
$967$	−33.0780	+	15.9295i	−1.06372	+	0.512259i	−0.181640	+	0.983365i	$0.558141\pi$
$968$	11.8511	+	78.6266i	0.380907	+	2.52715i
$969$		0			0
$970$	8.99511	−	8.34624i	0.288815	−	0.267982i
$971$	31.7008	−	21.6132i	1.01733	−	0.693601i	0.0647499	−	0.997902i	$-0.479375\pi$
$971$	31.7008	−	21.6132i	1.01733	−	0.693601i	0.952576	+	0.304300i	$0.0984227\pi$
$972$		0			0
$973$	−0.706493	+	24.4185i	−0.0226491	+	0.782820i
$974$	54.8517	−	12.5195i	1.75756	−	0.401152i
$975$		0			0
$976$	−0.281130	+	1.86517i	−0.00899874	+	0.0597028i
$977$	9.49643	+	30.7867i	0.303818	+	0.984952i	0.970802	+	0.239881i	$0.0771084\pi$
$977$	9.49643	+	30.7867i	0.303818	+	0.984952i	−0.666985	+	0.745071i	$0.732415\pi$
$978$		0			0
$979$		−	80.5850i		−	2.57551i
$980$	−37.8257	−	20.9920i	−1.20830	−	0.670565i
$981$		0			0
$982$	0.575110	−	7.67430i	0.0183525	−	0.244897i
$983$	−8.30023	+	2.56028i	−0.264736	+	0.0816603i	−0.424282	−	0.905530i	$-0.639473\pi$
$983$	−8.30023	+	2.56028i	−0.264736	+	0.0816603i	0.159545	+	0.987191i	$0.448997\pi$
$984$		0			0
$985$	15.0605	−	16.2313i	0.479866	−	0.517173i
$986$	7.44670	+	32.6261i	0.237151	+	1.03903i
$987$		0			0
$988$	23.9236	−	104.816i	0.761110	−	3.33464i
$989$	−3.90841	−	5.73258i	−0.124280	−	0.182286i
$990$		0			0
$991$	−30.3367	−	20.6832i	−0.963676	−	0.657023i	−0.0242253	−	0.999707i	$-0.507712\pi$
$991$	−30.3367	−	20.6832i	−0.963676	−	0.657023i	−0.939451	+	0.342683i	$0.888664\pi$
$992$	9.36865	−	1.41210i	0.297455	−	0.0448341i
$993$		0			0
$994$	−25.7252	+	41.7221i	−0.815952	+	1.32335i
$995$	−9.99913	+	20.7634i	−0.316994	+	0.658244i
$996$		0			0
$997$	−43.6607	−	17.1356i	−1.38275	−	0.542689i	−0.446739	−	0.894664i	$-0.647415\pi$
$997$	−43.6607	−	17.1356i	−1.38275	−	0.542689i	−0.936009	+	0.351975i	$0.885510\pi$
$998$	−0.827450	+	0.477728i	−0.0261925	+	0.0151222i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bg.a.26.2	yes	216
3.2	odd	2	inner	441.2.bg.a.26.17	yes	216
49.17	odd	42	inner	441.2.bg.a.17.17	yes	216
147.17	even	42	inner	441.2.bg.a.17.2	✓	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.bg.a.17.2	✓	216	147.17	even	42	inner
441.2.bg.a.17.17	yes	216	49.17	odd	42	inner
441.2.bg.a.26.2	yes	216	1.1	even	1	trivial
441.2.bg.a.26.17	yes	216	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.bg (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.47614 - 0.185561i) q^{2} +(4.11916 + 0.620863i) q^{4} +(1.08753 + 1.00908i) q^{5} +(0.513890 + 2.59536i) q^{7} +(-5.24274 - 1.19662i) q^{8} +O(q^{10})\)	\(q+(-2.47614 - 0.185561i) q^{2} +(4.11916 + 0.620863i) q^{4} +(1.08753 + 1.00908i) q^{5} +(0.513890 + 2.59536i) q^{7} +(-5.24274 - 1.19662i) q^{8} +(-2.50562 - 2.70041i) q^{10} +(-2.86056 + 4.19566i) q^{11} +(1.61021 + 3.34363i) q^{13} +(-0.790865 - 6.52183i) q^{14} +(4.79846 + 1.48013i) q^{16} +(0.776596 - 1.97873i) q^{17} +(-6.02269 - 3.47720i) q^{19} +(3.85319 + 4.83175i) q^{20} +(7.86168 - 9.85823i) q^{22} +(-2.05621 + 0.807003i) q^{23} +(-0.209174 - 2.79123i) q^{25} +(-3.36665 - 8.57809i) q^{26} +(0.505430 + 11.0098i) q^{28} +(4.95700 - 3.95308i) q^{29} +(-4.78772 + 2.76419i) q^{31} +(-1.59532 - 0.626117i) q^{32} +(-2.29013 + 4.75551i) q^{34} +(-2.06005 + 3.34108i) q^{35} +(-5.79147 + 0.872923i) q^{37} +(14.2678 + 9.72760i) q^{38} +(-4.49413 - 6.59168i) q^{40} +(-2.11729 + 9.27644i) q^{41} +(0.698939 + 3.06225i) q^{43} +(-14.3880 + 15.5066i) q^{44} +(5.24120 - 1.61670i) q^{46} +(0.0268270 - 0.357982i) q^{47} +(-6.47183 + 2.66747i) q^{49} +6.95027i q^{50} +(4.55677 + 14.7727i) q^{52} +(-0.164957 + 1.09442i) q^{53} +(-7.34467 + 1.67637i) q^{55} +(0.411474 - 14.2217i) q^{56} +(-13.0077 + 8.86853i) q^{58} +(0.357938 - 0.332118i) q^{59} +(0.0559846 + 0.371434i) q^{61} +(12.3680 - 5.95610i) q^{62} +(-5.21448 - 2.51116i) q^{64} +(-1.62284 + 5.26111i) q^{65} +(7.11502 + 12.3236i) q^{67} +(4.42744 - 7.66855i) q^{68} +(5.72094 - 7.89070i) q^{70} +(-5.83320 - 4.65182i) q^{71} +(14.8390 - 1.11203i) q^{73} +(14.5024 - 1.08681i) q^{74} +(-22.6495 - 18.0624i) q^{76} +(-12.3593 - 5.26807i) q^{77} +(0.176652 - 0.305970i) q^{79} +(3.72489 + 6.45169i) q^{80} +(6.96404 - 22.5769i) q^{82} +(6.78359 + 3.26680i) q^{83} +(2.84126 - 1.36828i) q^{85} +(-1.16243 - 7.71224i) q^{86} +(20.0178 - 18.5738i) q^{88} +(-13.1119 + 8.93952i) q^{89} +(-7.85048 + 5.89734i) q^{91} +(-8.97089 + 2.04755i) q^{92} +(-0.132855 + 0.881434i) q^{94} +(-3.04107 - 9.85890i) q^{95} +3.33101i q^{97} +(16.5201 - 5.40409i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 16 q^{4} + 2 q^{7}+O(q^{10}) \) 216 * q - 16 * q^4 + 2 * q^7	\( 216 q - 16 q^{4} + 2 q^{7} + 12 q^{10} + 12 q^{16} - 6 q^{19} + 44 q^{22} + 26 q^{25} + 84 q^{28} - 6 q^{31} - 112 q^{34} + 60 q^{37} - 304 q^{40} + 20 q^{43} - 20 q^{46} - 86 q^{49} - 168 q^{52} - 84 q^{55} - 120 q^{58} - 2 q^{61} + 32 q^{64} + 22 q^{67} - 136 q^{70} - 6 q^{73} + 84 q^{76} + 2 q^{79} - 104 q^{82} + 96 q^{85} - 12 q^{88} + 58 q^{91} + 52 q^{94}+O(q^{100}) \) 216 * q - 16 * q^4 + 2 * q^7 + 12 * q^10 + 12 * q^16 - 6 * q^19 + 44 * q^22 + 26 * q^25 + 84 * q^28 - 6 * q^31 - 112 * q^34 + 60 * q^37 - 304 * q^40 + 20 * q^43 - 20 * q^46 - 86 * q^49 - 168 * q^52 - 84 * q^55 - 120 * q^58 - 2 * q^61 + 32 * q^64 + 22 * q^67 - 136 * q^70 - 6 * q^73 + 84 * q^76 + 2 * q^79 - 104 * q^82 + 96 * q^85 - 12 * q^88 + 58 * q^91 + 52 * q^94

Introduction

L-functions

Modular forms

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