LMFDB - Embedded newform 441.2.w.a.188.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(62,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 11]))

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

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

chi := DirichletCharacter("441.62");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.w (of order $14$, degree $6$, 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:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			188.14
Character	$\chi$	$=$	441.188
Dual form			441.2.w.a.251.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.947442 - 0.755560i) q^{2} +(-0.118266 + 0.518156i) q^{4} +(3.15639 - 1.52004i) q^{5} +(1.53392 + 2.15571i) q^{7} +(1.33103 + 2.76391i) q^{8} +O(q^{10})$	\(q+(0.947442 - 0.755560i) q^{2} +(-0.118266 + 0.518156i) q^{4} +(3.15639 - 1.52004i) q^{5} +(1.53392 + 2.15571i) q^{7} +(1.33103 + 2.76391i) q^{8} +(1.84202 - 3.82499i) q^{10} +(-0.959544 + 0.765211i) q^{11} +(-4.81566 + 3.84036i) q^{13} +(3.08207 + 0.883437i) q^{14} +(2.39168 + 1.15177i) q^{16} +(-0.101589 - 0.445092i) q^{17} -8.04235i q^{19} +(0.414324 + 1.81527i) q^{20} +(-0.330950 + 1.44999i) q^{22} +(-1.94273 - 0.443416i) q^{23} +(4.53483 - 5.68650i) q^{25} +(-1.66094 + 7.27704i) q^{26} +(-1.29840 + 0.539866i) q^{28} +(6.85693 - 1.56505i) q^{29} -6.87818i q^{31} +(-2.84538 + 0.649440i) q^{32} +(-0.432544 - 0.344943i) q^{34} +(8.11842 + 4.47263i) q^{35} +(0.226997 + 0.994537i) q^{37} +(-6.07648 - 7.61967i) q^{38} +(8.40250 + 6.70077i) q^{40} +(5.35226 - 2.57751i) q^{41} +(-8.06594 - 3.88435i) q^{43} +(-0.283018 - 0.587692i) q^{44} +(-2.17566 + 1.04774i) q^{46} +(-0.922167 - 1.15636i) q^{47} +(-2.29415 + 6.61339i) q^{49} -8.81397i q^{50} +(-1.42038 - 2.94945i) q^{52} +(-7.14540 - 1.63089i) q^{53} +(-1.86555 + 3.87385i) q^{55} +(-3.91649 + 7.10894i) q^{56} +(5.31406 - 6.66362i) q^{58} +(6.83339 + 3.29079i) q^{59} +(-6.28213 + 1.43385i) q^{61} +(-5.19688 - 6.51668i) q^{62} +(-5.51533 + 6.91601i) q^{64} +(-9.36261 + 19.4417i) q^{65} +1.41606 q^{67} +0.242642 q^{68} +(11.0711 - 1.89639i) q^{70} +(-14.0112 - 3.19797i) q^{71} +(-1.23210 - 0.982563i) q^{73} +(0.966498 + 0.770757i) q^{74} +(4.16720 + 0.951136i) q^{76} +(-3.12144 - 0.894721i) q^{77} -6.59140 q^{79} +9.29981 q^{80} +(3.12349 - 6.48600i) q^{82} +(3.24033 - 4.06324i) q^{83} +(-0.997213 - 1.25047i) q^{85} +(-10.5769 + 2.41410i) q^{86} +(-3.39216 - 1.63358i) q^{88} +(8.27979 - 10.3825i) q^{89} +(-15.6656 - 4.49033i) q^{91} +(0.459518 - 0.954199i) q^{92} +(-1.74740 - 0.398833i) q^{94} +(-12.2247 - 25.3848i) q^{95} +11.9798i q^{97} +(2.82323 + 7.99917i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 24 q^{4}+O(q^{10}) $ 120 * q + 24 * q^4	$ 120 q + 24 q^{4} - 32 q^{16} - 44 q^{22} - 4 q^{25} - 56 q^{28} + 112 q^{34} - 76 q^{37} + 28 q^{40} + 8 q^{43} - 40 q^{46} - 84 q^{49} - 140 q^{52} + 12 q^{58} - 84 q^{61} + 24 q^{64} + 16 q^{67} + 112 q^{70} - 84 q^{76} - 24 q^{79} + 140 q^{82} - 96 q^{85} - 24 q^{88} - 112 q^{91} - 112 q^{94}+O(q^{100}) $ 120 * q + 24 * q^4 - 32 * q^16 - 44 * q^22 - 4 * q^25 - 56 * q^28 + 112 * q^34 - 76 * q^37 + 28 * q^40 + 8 * q^43 - 40 * q^46 - 84 * q^49 - 140 * q^52 + 12 * q^58 - 84 * q^61 + 24 * q^64 + 16 * q^67 + 112 * q^70 - 84 * q^76 - 24 * q^79 + 140 * q^82 - 96 * q^85 - 24 * q^88 - 112 * q^91 - 112 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{5}{14}\right)$	$-1$

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 $

$2$	0.947442	−	0.755560i	0.669943	−	0.534262i	−0.228394	−	0.973569i	$-0.573347\pi$
$2$	0.947442	−	0.755560i	0.669943	−	0.534262i	0.898337	+	0.439307i	$0.144776\pi$
$3$		0			0
$3$		0			0
$4$	−0.118266	+	0.518156i	−0.0591329	+	0.259078i
$5$	3.15639	−	1.52004i	1.41158	−	0.679781i	0.436106	−	0.899895i	$-0.356357\pi$
$5$	3.15639	−	1.52004i	1.41158	−	0.679781i	0.975474	+	0.220114i	$0.0706429\pi$
$6$		0			0
$7$	1.53392	+	2.15571i	0.579769	+	0.814781i
$7$	1.53392	+	2.15571i	0.579769	+	0.814781i
$8$	1.33103	+	2.76391i	0.470590	+	0.977191i
$9$		0			0
$10$	1.84202	−	3.82499i	0.582497	−	1.20957i
$11$	−0.959544	+	0.765211i	−0.289313	+	0.230720i	−0.757381	−	0.652973i	$-0.773522\pi$
$11$	−0.959544	+	0.765211i	−0.289313	+	0.230720i	0.468068	+	0.883692i	$0.344950\pi$
$12$		0			0
$13$	−4.81566	+	3.84036i	−1.33562	+	1.06512i	−0.343595	+	0.939118i	$0.611645\pi$
$13$	−4.81566	+	3.84036i	−1.33562	+	1.06512i	−0.992029	+	0.126006i	$0.959784\pi$
$14$	3.08207	+	0.883437i	0.823718	+	0.236108i
$15$		0			0
$16$	2.39168	+	1.15177i	0.597920	+	0.287943i
$17$	−0.101589	−	0.445092i	−0.0246391	−	0.107951i	0.961113	−	0.276155i	$-0.0890603\pi$
$17$	−0.101589	−	0.445092i	−0.0246391	−	0.107951i	−0.985752	+	0.168204i	$0.946203\pi$
$18$		0			0
$19$		−	8.04235i		−	1.84504i	−0.385946	−	0.922521i	$-0.626125\pi$
$19$		−	8.04235i		−	1.84504i	0.385946	−	0.922521i	$-0.373875\pi$
$20$	0.414324	+	1.81527i	0.0926457	+	0.405907i
$21$		0			0
$22$	−0.330950	+	1.44999i	−0.0705588	+	0.309138i
$23$	−1.94273	−	0.443416i	−0.405088	−	0.0924587i	0.0151218	−	0.999886i	$-0.495186\pi$
$23$	−1.94273	−	0.443416i	−0.405088	−	0.0924587i	−0.420210	+	0.907427i	$0.638044\pi$
$24$		0			0
$25$	4.53483	−	5.68650i	0.906967	−	1.13730i
$26$	−1.66094	+	7.27704i	−0.325737	+	1.42715i
$27$		0			0
$28$	−1.29840	+	0.539866i	−0.245375	+	0.102025i
$29$	6.85693	−	1.56505i	1.27330	−	0.290623i	0.468127	−	0.883661i	$-0.344929\pi$
$29$	6.85693	−	1.56505i	1.27330	−	0.290623i	0.805174	+	0.593039i	$0.202072\pi$
$30$		0			0
$31$		−	6.87818i		−	1.23536i	−0.786430	−	0.617679i	$-0.788073\pi$
$31$		−	6.87818i		−	1.23536i	0.786430	−	0.617679i	$-0.211927\pi$
$32$	−2.84538	+	0.649440i	−0.502998	+	0.114806i
$33$		0			0
$34$	−0.432544	−	0.344943i	−0.0741807	−	0.0591572i
$35$	8.11842	+	4.47263i	1.37226	+	0.756013i
$36$		0			0
$37$	0.226997	+	0.994537i	0.0373180	+	0.163501i	0.990153	−	0.139987i	$-0.0447060\pi$
$37$	0.226997	+	0.994537i	0.0373180	+	0.163501i	−0.952835	+	0.303488i	$0.901849\pi$
$38$	−6.07648	−	7.61967i	−0.985736	−	1.23607i
$39$		0			0
$40$	8.40250	+	6.70077i	1.32855	+	1.05948i
$41$	5.35226	−	2.57751i	0.835882	−	0.402540i	0.0335644	−	0.999437i	$-0.489314\pi$
$41$	5.35226	−	2.57751i	0.835882	−	0.402540i	0.802318	+	0.596897i	$0.203600\pi$
$42$		0			0
$43$	−8.06594	−	3.88435i	−1.23004	−	0.592358i	−0.297953	−	0.954581i	$-0.596304\pi$
$43$	−8.06594	−	3.88435i	−1.23004	−	0.592358i	−0.932092	+	0.362223i	$0.882018\pi$
$44$	−0.283018	−	0.587692i	−0.0426665	−	0.0885979i
$45$		0			0
$46$	−2.17566	+	1.04774i	−0.320783	+	0.154481i
$47$	−0.922167	−	1.15636i	−0.134512	−	0.168672i	0.710014	−	0.704188i	$-0.248689\pi$
$47$	−0.922167	−	1.15636i	−0.134512	−	0.168672i	−0.844525	+	0.535515i	$0.820117\pi$
$48$		0			0
$49$	−2.29415	+	6.61339i	−0.327736	+	0.944769i
$50$		−	8.81397i		−	1.24648i
$51$		0			0
$52$	−1.42038	−	2.94945i	−0.196971	−	0.409015i
$53$	−7.14540	−	1.63089i	−0.981496	−	0.224020i	−0.298474	−	0.954418i	$-0.596478\pi$
$53$	−7.14540	−	1.63089i	−0.981496	−	0.224020i	−0.683022	+	0.730398i	$0.739335\pi$
$54$		0			0
$55$	−1.86555	+	3.87385i	−0.251550	+	0.522349i
$56$	−3.91649	+	7.10894i	−0.523363	+	0.949973i
$57$		0			0
$58$	5.31406	−	6.66362i	0.697770	−	0.874976i
$59$	6.83339	+	3.29079i	0.889631	+	0.428424i	0.822133	−	0.569296i	$-0.192784\pi$
$59$	6.83339	+	3.29079i	0.889631	+	0.428424i	0.0674982	+	0.997719i	$0.478498\pi$
$60$		0			0
$61$	−6.28213	+	1.43385i	−0.804344	+	0.183586i	−0.604878	−	0.796318i	$-0.706778\pi$
$61$	−6.28213	+	1.43385i	−0.804344	+	0.183586i	−0.199466	+	0.979905i	$0.563921\pi$
$62$	−5.19688	−	6.51668i	−0.660004	−	0.827619i
$63$		0			0
$64$	−5.51533	+	6.91601i	−0.689417	+	0.864501i
$65$	−9.36261	+	19.4417i	−1.16129	+	2.41144i
$66$		0			0
$67$	1.41606			0.172999			0.0864996	−	0.996252i	$-0.472432\pi$
$67$	1.41606			0.172999			0.0864996	+	0.996252i	$0.472432\pi$
$68$	0.242642			0.0294247
$69$		0			0
$70$	11.0711	−	1.89639i	1.32325	−	0.226662i
$71$	−14.0112	−	3.19797i	−1.66283	−	0.379529i	−0.715202	−	0.698918i	$-0.753665\pi$
$71$	−14.0112	−	3.19797i	−1.66283	−	0.379529i	−0.947624	+	0.319388i	$0.896523\pi$
$72$		0			0
$73$	−1.23210	−	0.982563i	−0.144206	−	0.115000i	0.548730	−	0.836000i	$-0.315112\pi$
$73$	−1.23210	−	0.982563i	−0.144206	−	0.115000i	−0.692936	+	0.720999i	$0.743683\pi$
$74$	0.966498	+	0.770757i	0.112353	+	0.0895987i
$75$		0			0
$76$	4.16720	+	0.951136i	0.478010	+	0.109103i
$77$	−3.12144	−	0.894721i	−0.355721	−	0.101963i
$78$		0			0
$79$	−6.59140			−0.741591			−0.370795	−	0.928715i	$-0.620915\pi$
$79$	−6.59140			−0.741591			−0.370795	+	0.928715i	$0.620915\pi$
$80$	9.29981			1.03975
$81$		0			0
$82$	3.12349	−	6.48600i	0.344932	−	0.716259i
$83$	3.24033	−	4.06324i	0.355672	−	0.445999i	−0.571518	−	0.820589i	$-0.693645\pi$
$83$	3.24033	−	4.06324i	0.355672	−	0.445999i	0.927190	+	0.374591i	$0.122217\pi$
$84$		0			0
$85$	−0.997213	−	1.25047i	−0.108163	−	0.135632i
$86$	−10.5769	+	2.41410i	−1.14053	+	0.260319i
$87$		0			0
$88$	−3.39216	−	1.63358i	−0.361605	−	0.174140i
$89$	8.27979	−	10.3825i	0.877656	−	1.10055i	−0.116564	−	0.993183i	$-0.537188\pi$
$89$	8.27979	−	10.3825i	0.877656	−	1.10055i	0.994220	−	0.107362i	$-0.0342405\pi$
$90$		0			0
$91$	−15.6656	−	4.49033i	−1.64220	−	0.470715i
$92$	0.459518	−	0.954199i	0.0479081	−	0.0994821i
$93$		0			0
$94$	−1.74740	−	0.398833i	−0.180230	−	0.0411364i
$95$	−12.2247	−	25.3848i	−1.25423	−	2.60443i
$96$		0			0
$97$			11.9798i			1.21636i	0.793798	+	0.608182i	$0.208101\pi$
$97$			11.9798i			1.21636i	−0.793798	+	0.608182i	$0.791899\pi$
$98$	2.82323	+	7.99917i	0.285190	+	0.808038i
$99$		0			0
$100$	2.41018	+	3.02227i	0.241018	+	0.302227i
$101$	6.88920	−	3.31766i	0.685501	−	0.330120i	−0.0585104	−	0.998287i	$-0.518635\pi$
$101$	6.88920	−	3.31766i	0.685501	−	0.330120i	0.744011	+	0.668167i	$0.232921\pi$
$102$		0			0
$103$	5.15066	+	10.6955i	0.507509	+	1.05385i	0.984571	+	0.174984i	$0.0559875\pi$
$103$	5.15066	+	10.6955i	0.507509	+	1.05385i	−0.477062	+	0.878870i	$0.658298\pi$
$104$	−17.0242	−	8.19843i	−1.66936	−	0.803922i
$105$		0			0
$106$	−8.00209	+	3.85360i	−0.777232	+	0.374295i
$107$	−5.08805	−	4.05759i	−0.491881	−	0.392262i	0.345898	−	0.938272i	$-0.387574\pi$
$107$	−5.08805	−	4.05759i	−0.491881	−	0.392262i	−0.837778	+	0.546010i	$0.816146\pi$
$108$		0			0
$109$	6.58122	+	8.25259i	0.630366	+	0.790454i	0.989762	−	0.142731i	$-0.0455884\pi$
$109$	6.58122	+	8.25259i	0.630366	+	0.790454i	−0.359395	+	0.933185i	$0.617017\pi$
$110$	1.15943	+	5.07978i	0.110547	+	0.484338i
$111$		0			0
$112$	1.18577	+	6.92249i	0.112045	+	0.654114i
$113$	15.7697	+	12.5759i	1.48348	+	1.18304i	0.938831	+	0.344379i	$0.111911\pi$
$113$	15.7697	+	12.5759i	1.48348	+	1.18304i	0.544654	+	0.838661i	$0.316661\pi$
$114$		0			0
$115$	−6.80603	+	1.55343i	−0.634666	+	0.144858i
$116$			3.73806i			0.347070i
$117$		0			0
$118$	8.96063	−	2.04520i	0.824892	−	0.188276i
$119$	0.803659	−	0.901735i	0.0736713	−	0.0826619i
$120$		0			0
$121$	−2.11255	+	9.25570i	−0.192050	+	0.841427i
$122$	−4.86859	+	6.10502i	−0.440781	+	0.552722i
$123$		0			0
$124$	3.56397	+	0.813454i	0.320054	+	0.0730503i
$125$	1.77219	−	7.76447i	0.158510	−	0.694476i
$126$		0			0
$127$	−1.06065	−	4.64701i	−0.0941174	−	0.412355i	0.905819	−	0.423666i	$-0.139257\pi$
$127$	−1.06065	−	4.64701i	−0.0941174	−	0.412355i	−0.999936	+	0.0113103i	$0.996400\pi$
$128$			4.88257i			0.431562i
$129$		0			0
$130$	5.81881	+	25.4939i	0.510343	+	2.23596i
$131$	10.8445	+	5.22244i	0.947489	+	0.456287i	0.842805	−	0.538219i	$-0.180903\pi$
$131$	10.8445	+	5.22244i	0.947489	+	0.456287i	0.104684	+	0.994506i	$0.466617\pi$
$132$		0			0
$133$	17.3370	−	12.3364i	1.50331	−	1.06970i
$134$	1.34163	−	1.06992i	0.115900	−	0.0924268i
$135$		0			0
$136$	1.09498	−	0.873216i	0.0938936	−	0.0748776i
$137$	−5.84780	+	12.1431i	−0.499611	+	1.03745i	0.486854	+	0.873483i	$0.338144\pi$
$137$	−5.84780	+	12.1431i	−0.499611	+	1.03745i	−0.986465	+	0.163970i	$0.947570\pi$
$138$		0			0
$139$	1.37251	+	2.85004i	0.116415	+	0.241737i	0.951032	−	0.309093i	$-0.100025\pi$
$139$	1.37251	+	2.85004i	0.116415	+	0.241737i	−0.834617	+	0.550830i	$0.814311\pi$
$140$	−3.27765	+	3.67765i	−0.277012	+	0.310818i
$141$		0			0
$142$	−15.6911	+	7.55643i	−1.31677	+	0.634121i
$143$	1.68215	−	7.36999i	0.140669	−	0.616310i
$144$		0			0
$145$	19.2642	−	15.3627i	1.59981	−	1.27580i
$146$	−1.90973			−0.158050
$147$		0			0
$148$	−0.542172			−0.0445662
$149$	4.48031	−	3.57293i	0.367041	−	0.292706i	−0.422549	−	0.906340i	$-0.638865\pi$
$149$	4.48031	−	3.57293i	0.367041	−	0.292706i	0.789590	+	0.613634i	$0.210293\pi$
$150$		0			0
$151$	−1.58064	+	6.92523i	−0.128631	+	0.563567i	0.869003	+	0.494807i	$0.164761\pi$
$151$	−1.58064	+	6.92523i	−0.128631	+	0.563567i	−0.997633	+	0.0687598i	$0.978096\pi$
$152$	22.2284	−	10.7046i	1.80296	−	0.868259i
$153$		0			0
$154$	−3.63340	+	1.51074i	−0.292788	+	0.121739i
$155$	−10.4551	−	21.7102i	−0.839773	−	1.74381i
$156$		0			0
$157$	−4.34877	+	9.03031i	−0.347069	+	0.720697i	−0.999303	−	0.0373208i	$-0.988118\pi$
$157$	−4.34877	+	9.03031i	−0.347069	+	0.720697i	0.652234	+	0.758018i	$0.273832\pi$
$158$	−6.24497	+	4.98020i	−0.496823	+	0.396203i
$159$		0			0
$160$	−7.99397	+	6.37498i	−0.631979	+	0.503986i
$161$	−2.02413	−	4.86813i	−0.159524	−	0.383663i
$162$		0			0
$163$	−7.55622	−	3.63888i	−0.591849	−	0.285019i	0.113888	−	0.993494i	$-0.463670\pi$
$163$	−7.55622	−	3.63888i	−0.591849	−	0.285019i	−0.705737	+	0.708474i	$0.749384\pi$
$164$	0.702565	+	3.07814i	0.0548611	+	0.240362i
$165$		0			0
$166$		−	6.29795i		−	0.488816i
$167$	−2.03637	−	8.92191i	−0.157579	−	0.690398i	−0.990558	−	0.137094i	$-0.956224\pi$
$167$	−2.03637	−	8.92191i	−0.157579	−	0.690398i	0.832979	−	0.553304i	$-0.186633\pi$
$168$		0			0
$169$	5.54944	−	24.3137i	0.426880	−	1.87028i
$170$	−1.88960	−	0.431290i	−0.144926	−	0.0330784i
$171$		0			0
$172$	2.96663	−	3.72003i	0.226203	−	0.283650i
$173$	0.0716983	−	0.314131i	0.00545112	−	0.0238829i	−0.972129	−	0.234446i	$-0.924672\pi$
$173$	0.0716983	−	0.314131i	0.00545112	−	0.0238829i	0.977580	+	0.210563i	$0.0675296\pi$
$174$		0			0
$175$	19.2145	+	1.05311i	1.45248	+	0.0796078i
$176$	−3.17627	+	0.724963i	−0.239420	+	0.0546461i
$177$		0			0
$178$		−	16.0927i		−	1.20620i
$179$	−7.72502	+	1.76319i	−0.577395	+	0.131787i	−0.501238	−	0.865309i	$-0.667122\pi$
$179$	−7.72502	+	1.76319i	−0.577395	+	0.131787i	−0.0761567	+	0.997096i	$0.524265\pi$
$180$		0			0
$181$	−17.3051	−	13.8004i	−1.28628	−	1.02577i	−0.997663	−	0.0683268i	$-0.978234\pi$
$181$	−17.3051	−	13.8004i	−1.28628	−	1.02577i	−0.288615	−	0.957445i	$-0.593195\pi$
$182$	−18.2349	+	7.58194i	−1.35166	+	0.562011i
$183$		0			0
$184$	−1.36027	−	5.95975i	−0.100281	−	0.439358i
$185$	2.22822	+	2.79410i	0.163822	+	0.205427i
$186$		0			0
$187$	0.438069	+	0.349348i	0.0320348	+	0.0255469i
$188$	0.708236	−	0.341069i	0.0516534	−	0.0248750i
$189$		0			0
$190$	−30.7619	−	14.8142i	−2.23170	−	1.07473i
$191$	10.0965	+	20.9655i	0.730555	+	1.51701i	0.851500	+	0.524354i	$0.175693\pi$
$191$	10.0965	+	20.9655i	0.730555	+	1.51701i	−0.120945	+	0.992659i	$0.538593\pi$
$192$		0			0
$193$	−3.10991	+	1.49765i	−0.223856	+	0.107803i	−0.542451	−	0.840088i	$-0.682503\pi$
$193$	−3.10991	+	1.49765i	−0.223856	+	0.107803i	0.318595	+	0.947891i	$0.396789\pi$
$194$	9.05146	+	11.3502i	0.649857	+	0.814894i
$195$		0			0
$196$	−3.15545	−	1.97087i	−0.225389	−	0.140776i
$197$		−	2.77362i		−	0.197612i	−0.995107	−	0.0988062i	$-0.968498\pi$
$197$		−	2.77362i		−	0.197612i	0.995107	−	0.0988062i	$-0.0315024\pi$
$198$		0			0
$199$	−1.14907	−	2.38608i	−0.0814557	−	0.169145i	0.856263	−	0.516540i	$-0.172780\pi$
$199$	−1.14907	−	2.38608i	−0.0814557	−	0.169145i	−0.937719	+	0.347396i	$0.887066\pi$
$200$	21.7530	+	4.96498i	1.53817	+	0.351077i
$201$		0			0
$202$	4.02043	−	8.34850i	0.282876	−	0.587398i
$203$	13.8918	+	12.3809i	0.975014	+	0.868967i
$204$		0			0
$205$	12.9759	−	16.2713i	0.906276	−	1.13643i
$206$	12.9610	+	6.24169i	0.903036	+	0.434879i
$207$		0			0
$208$	−15.9407	+	3.63837i	−1.10529	+	0.252275i
$209$	6.15410	+	7.71699i	0.425688	+	0.533796i
$210$		0			0
$211$	−2.79124	+	3.50010i	−0.192157	+	0.240957i	−0.868571	−	0.495564i	$-0.834961\pi$
$211$	−2.79124	+	3.50010i	−0.192157	+	0.240957i	0.676415	+	0.736521i	$0.263533\pi$
$212$	1.69011	−	3.50956i	0.116077	−	0.241037i
$213$		0			0
$214$	−7.88639			−0.539102
$215$	−31.3636			−2.13898
$216$		0			0
$217$	14.8273	−	10.5506i	1.00655	−	0.716222i
$218$	12.4707	+	2.84634i	0.844619	+	0.192779i
$219$		0			0
$220$	−1.78663	−	1.42479i	−0.120454	−	0.0960592i
$221$	2.19854	+	1.75327i	0.147890	+	0.117938i
$222$		0			0
$223$	3.45202	+	0.787902i	0.231165	+	0.0527618i	0.336534	−	0.941671i	$-0.390745\pi$
$223$	3.45202	+	0.787902i	0.231165	+	0.0527618i	−0.105369	+	0.994433i	$0.533602\pi$
$224$	−5.76461	−	5.13762i	−0.385164	−	0.343272i
$225$		0			0
$226$	24.4427			1.62590
$227$	−14.9921			−0.995061			−0.497530	−	0.867447i	$-0.665760\pi$
$227$	−14.9921			−0.995061			−0.497530	+	0.867447i	$0.665760\pi$
$228$		0			0
$229$	4.82346	−	10.0160i	0.318743	−	0.661877i	−0.678617	−	0.734492i	$-0.737420\pi$
$229$	4.82346	−	10.0160i	0.318743	−	0.661877i	0.997360	+	0.0726156i	$0.0231346\pi$
$230$	−5.27461	+	6.61416i	−0.347798	+	0.436125i
$231$		0			0
$232$	13.4524	+	16.8688i	0.883196	+	1.10749i
$233$	7.35458	−	1.67864i	0.481815	−	0.109971i	0.0252870	−	0.999680i	$-0.491950\pi$
$233$	7.35458	−	1.67864i	0.481815	−	0.109971i	0.456528	+	0.889709i	$0.349093\pi$
$234$		0			0
$235$	−4.66843	−	2.24820i	−0.304535	−	0.146656i
$236$	−2.51330	+	3.15158i	−0.163602	+	0.205150i
$237$		0			0
$238$	0.0801051	−	1.46155i	0.00519244	−	0.0947385i
$239$	1.14542	−	2.37849i	0.0740912	−	0.153852i	−0.860633	−	0.509225i	$-0.829932\pi$
$239$	1.14542	−	2.37849i	0.0740912	−	0.153852i	0.934724	+	0.355373i	$0.115646\pi$
$240$		0			0
$241$	−4.91058	−	1.12081i	−0.316318	−	0.0721976i	0.0614142	−	0.998112i	$-0.480439\pi$
$241$	−4.91058	−	1.12081i	−0.316318	−	0.0721976i	−0.377732	+	0.925915i	$0.623296\pi$
$242$	4.99172	+	10.3654i	0.320880	+	0.666313i
$243$		0			0
$244$		−	3.42470i		−	0.219244i
$245$	2.81136	+	24.3616i	0.179611	+	1.55641i
$246$		0			0
$247$	30.8855	+	38.7292i	1.96520	+	2.46428i
$248$	19.0107	−	9.15506i	1.20718	−	0.581347i
$249$		0			0
$250$	−4.18748	−	8.69539i	−0.264839	−	0.549945i
$251$	−2.02229	−	0.973881i	−0.127646	−	0.0614708i	0.368971	−	0.929441i	$-0.379710\pi$
$251$	−2.02229	−	0.973881i	−0.127646	−	0.0614708i	−0.496617	+	0.867970i	$0.665424\pi$
$252$		0			0
$253$	2.20345	−	1.06112i	0.138529	−	0.0667123i
$254$	−4.51600	−	3.60139i	−0.283359	−	0.225971i
$255$		0			0
$256$	−7.34159	−	9.20606i	−0.458849	−	0.575379i
$257$	1.76621	+	7.73825i	0.110173	+	0.482699i	0.999668	+	0.0257548i	$0.00819892\pi$
$257$	1.76621	+	7.73825i	0.110173	+	0.482699i	−0.889495	+	0.456944i	$0.848944\pi$
$258$		0			0
$259$	−1.79574	+	2.01488i	−0.111582	+	0.125199i
$260$	−8.96655	−	7.15058i	−0.556082	−	0.443460i
$261$		0			0
$262$	14.2204	−	3.24572i	0.878540	−	0.200521i
$263$		−	20.6681i		−	1.27445i	−0.770678	−	0.637225i	$-0.780082\pi$
$263$		−	20.6681i		−	1.27445i	0.770678	−	0.637225i	$-0.219918\pi$
$264$		0			0
$265$	−25.0327	+	5.71355i	−1.53775	+	0.350980i
$266$	7.10491	−	24.7871i	0.435630	−	1.51980i
$267$		0			0
$268$	−0.167471	+	0.733740i	−0.0102299	+	0.0448203i
$269$	5.27129	−	6.60999i	0.321396	−	0.403018i	−0.594719	−	0.803934i	$-0.702737\pi$
$269$	5.27129	−	6.60999i	0.321396	−	0.403018i	0.916115	+	0.400916i	$0.131308\pi$
$270$		0			0
$271$	−8.94561	−	2.04178i	−0.543407	−	0.124029i	−0.0579988	−	0.998317i	$-0.518472\pi$
$271$	−8.94561	−	2.04178i	−0.543407	−	0.124029i	−0.485408	+	0.874287i	$0.661329\pi$
$272$	0.269676	−	1.18153i	0.0163515	−	0.0716405i
$273$		0			0
$274$	3.63438	+	15.9232i	0.219561	+	0.961958i
$275$			8.92655i			0.538291i
$276$		0			0
$277$	−1.96408	−	8.60518i	−0.118010	−	0.517035i	−0.999033	−	0.0439623i	$-0.986002\pi$
$277$	−1.96408	−	8.60518i	−0.118010	−	0.517035i	0.881023	−	0.473073i	$-0.156855\pi$
$278$	3.45375	+	1.66324i	0.207142	+	0.0997544i
$279$		0			0
$280$	−1.55610	+	28.3918i	−0.0929949	+	1.69673i
$281$	14.4181	−	11.4980i	0.860110	−	0.685915i	−0.0906366	−	0.995884i	$-0.528890\pi$
$281$	14.4181	−	11.4980i	0.860110	−	0.685915i	0.950747	+	0.309969i	$0.100319\pi$
$282$		0			0
$283$	3.08371	−	2.45917i	0.183307	−	0.146183i	−0.527537	−	0.849532i	$-0.676884\pi$
$283$	3.08371	−	2.45917i	0.183307	−	0.146183i	0.710844	+	0.703349i	$0.248313\pi$
$284$	3.31410	−	6.88180i	0.196656	−	0.408359i
$285$		0			0
$286$	−3.97473	−	8.25361i	−0.235031	−	0.488046i
$287$	13.7663	+	7.58420i	0.812600	+	0.447681i
$288$		0			0
$289$	15.1287	−	7.28559i	0.889923	−	0.428564i
$290$	6.64429	−	29.1106i	0.390166	−	1.70943i
$291$		0			0
$292$	0.654836	−	0.522215i	0.0383214	−	0.0305603i
$293$	0.602753			0.0352132			0.0176066	−	0.999845i	$-0.494395\pi$
$293$	0.602753			0.0352132			0.0176066	+	0.999845i	$0.494395\pi$
$294$		0			0
$295$	26.5709			1.54702
$296$	−2.44667	+	1.95116i	−0.142210	+	0.113409i
$297$		0			0
$298$	1.54527	−	6.77029i	0.0895153	−	0.392192i
$299$	11.0584	−	5.32546i	0.639525	−	0.307979i
$300$		0			0
$301$	−3.99901	−	23.3461i	−0.230499	−	1.34565i
$302$	3.73486	+	7.75552i	0.214917	+	0.446280i
$303$		0			0
$304$	9.26296	−	19.2347i	0.531267	−	1.10319i
$305$	−17.6493	+	14.0749i	−1.01060	+	0.805925i
$306$		0			0
$307$	−2.84674	+	2.27020i	−0.162472	+	0.129567i	−0.701351	−	0.712816i	$-0.747419\pi$
$307$	−2.84674	+	2.27020i	−0.162472	+	0.129567i	0.538879	+	0.842383i	$0.318848\pi$
$308$	0.832765	−	1.51158i	0.0474512	−	0.0861302i
$309$		0			0
$310$	−26.3090	−	12.6697i	−1.49425	−	0.719592i
$311$	7.31324	+	32.0414i	0.414696	+	1.81690i	0.561186	+	0.827689i	$0.310345\pi$
$311$	7.31324	+	32.0414i	0.414696	+	1.81690i	−0.146491	+	0.989212i	$0.546798\pi$
$312$		0			0
$313$			4.97171i			0.281018i	0.990079	+	0.140509i	$0.0448739\pi$
$313$			4.97171i			0.281018i	−0.990079	+	0.140509i	$0.955126\pi$
$314$	2.70273	+	11.8414i	0.152524	+	0.668252i
$315$		0			0
$316$	0.779538	−	3.41538i	0.0438524	−	0.192130i
$317$	−5.13426	−	1.17186i	−0.288369	−	0.0658183i	0.0758895	−	0.997116i	$-0.475820\pi$
$317$	−5.13426	−	1.17186i	−0.288369	−	0.0658183i	−0.364258	+	0.931298i	$0.618678\pi$
$318$		0			0
$319$	−5.38194	+	6.74873i	−0.301331	+	0.377857i
$320$	−6.89595	+	30.2131i	−0.385495	+	1.68897i
$321$		0			0
$322$	−5.59591	−	3.08292i	−0.311848	−	0.171805i
$323$	−3.57959	+	0.817018i	−0.199174	+	0.0454601i
$324$		0			0
$325$			44.7997i			2.48504i
$326$	−9.90848	+	2.26155i	−0.548780	+	0.125255i
$327$		0			0
$328$	14.2480	+	11.3624i	0.786716	+	0.627385i
$329$	1.07824	−	3.76169i	0.0594454	−	0.207389i
$330$		0			0
$331$	6.80413	+	29.8108i	0.373989	+	1.63855i	0.715456	+	0.698658i	$0.246219\pi$
$331$	6.80413	+	29.8108i	0.373989	+	1.63855i	−0.341467	+	0.939894i	$0.610924\pi$
$332$	1.72217	+	2.15954i	0.0945166	+	0.118520i
$333$		0			0
$334$	−8.67038	−	6.91440i	−0.474422	−	0.378339i
$335$	4.46963	−	2.15246i	0.244202	−	0.117602i
$336$		0			0
$337$	24.4093	+	11.7549i	1.32966	+	0.640330i	0.957660	−	0.287903i	$-0.0929581\pi$
$337$	24.4093	+	11.7549i	1.32966	+	0.640330i	0.371999	+	0.928233i	$0.378672\pi$
$338$	−13.1127	−	27.2288i	−0.713236	−	1.48105i
$339$		0			0
$340$	0.765873	−	0.368825i	0.0415353	−	0.0200023i
$341$	5.26326	+	6.59992i	0.285021	+	0.357406i
$342$		0			0
$343$	−17.7756	+	5.19891i	−0.959791	+	0.280715i
$344$		−	27.4637i		−	1.48075i
$345$		0			0
$346$	−0.169415	−	0.351793i	−0.00910779	−	0.0189125i
$347$	−11.7839	−	2.68961i	−0.632596	−	0.144386i	−0.105813	−	0.994386i	$-0.533745\pi$
$347$	−11.7839	−	2.68961i	−0.632596	−	0.144386i	−0.526782	+	0.850000i	$0.676602\pi$
$348$		0			0
$349$	10.3760	−	21.5459i	0.555413	−	1.15333i	−0.414539	−	0.910032i	$-0.636057\pi$
$349$	10.3760	−	21.5459i	0.555413	−	1.15333i	0.969952	−	0.243296i	$-0.0782285\pi$
$350$	19.0004	−	13.5200i	1.01561	−	0.722673i
$351$		0			0
$352$	2.23331	−	2.80048i	0.119036	−	0.149266i
$353$	−11.6343	−	5.60277i	−0.619230	−	0.298205i	0.0978448	−	0.995202i	$-0.468805\pi$
$353$	−11.6343	−	5.60277i	−0.619230	−	0.298205i	−0.717075	+	0.696996i	$0.754519\pi$
$354$		0			0
$355$	−49.0859	+	11.2035i	−2.60521	+	0.594622i
$356$	4.40056	+	5.51812i	0.233229	+	0.292460i
$357$		0			0
$358$	−5.98682	+	7.50723i	−0.316413	+	0.396770i
$359$	11.4734	−	23.8248i	0.605544	−	1.25742i	−0.342569	−	0.939493i	$-0.611297\pi$
$359$	11.4734	−	23.8248i	0.605544	−	1.25742i	0.948113	−	0.317932i	$-0.102989\pi$
$360$		0			0
$361$	−45.6795			−2.40418
$362$	−26.8226			−1.40976
$363$		0			0
$364$	4.17940	−	7.58616i	0.219060	−	0.397623i
$365$	−5.38251	−	1.22852i	−0.281733	−	0.0643038i
$366$		0			0
$367$	1.33611	+	1.06551i	0.0697442	+	0.0556191i	0.657741	−	0.753244i	$-0.271512\pi$
$367$	1.33611	+	1.06551i	0.0697442	+	0.0556191i	−0.587997	+	0.808863i	$0.700083\pi$
$368$	−4.13568	−	3.29810i	−0.215587	−	0.171925i
$369$		0			0
$370$	4.22222	+	0.963695i	0.219503	+	0.0501001i
$371$	−7.44478	−	17.9051i	−0.386514	−	0.929584i
$372$		0			0
$373$	−11.0506			−0.572178			−0.286089	−	0.958203i	$-0.592355\pi$
$373$	−11.0506			−0.572178			−0.286089	+	0.958203i	$0.592355\pi$
$374$	0.678999			0.0351102
$375$		0			0
$376$	1.96865	−	4.08794i	0.101525	−	0.210819i
$377$	−27.0103	+	33.8699i	−1.39110	+	1.74439i
$378$		0			0
$379$	−5.73260	−	7.18846i	−0.294464	−	0.369246i	0.612488	−	0.790480i	$-0.290169\pi$
$379$	−5.73260	−	7.18846i	−0.294464	−	0.369246i	−0.906952	+	0.421234i	$0.861597\pi$
$380$	14.5991	−	3.33214i	0.748916	−	0.170935i
$381$		0			0
$382$	25.4066	+	12.2352i	1.29991	+	0.626005i
$383$	1.52822	−	1.91633i	0.0780883	−	0.0979196i	−0.741253	−	0.671226i	$-0.765768\pi$
$383$	1.52822	−	1.91633i	0.0780883	−	0.0979196i	0.819341	+	0.573306i	$0.194339\pi$
$384$		0			0
$385$	−11.2125	+	1.92062i	−0.571441	+	0.0978836i
$386$	−1.81489	+	3.76866i	−0.0923755	+	0.191820i
$387$		0			0
$388$	−6.20741	−	1.41680i	−0.315133	−	0.0719272i
$389$	11.6682	+	24.2293i	0.591603	+	1.22848i	0.954935	+	0.296816i	$0.0959248\pi$
$389$	11.6682	+	24.2293i	0.591603	+	1.22848i	−0.363332	+	0.931660i	$0.618361\pi$
$390$		0			0
$391$			0.909742i			0.0460077i
$392$	−21.3324	+	2.46178i	−1.07745	+	0.124339i
$393$		0			0
$394$	−2.09564	−	2.62785i	−0.105577	−	0.132389i
$395$	−20.8050	+	10.0192i	−1.04681	+	0.504119i
$396$		0			0
$397$	5.53457	+	11.4927i	0.277772	+	0.576800i	0.992449	−	0.122654i	$-0.0391407\pi$
$397$	5.53457	+	11.4927i	0.277772	+	0.576800i	−0.714677	+	0.699454i	$0.753426\pi$
$398$	−2.89151	−	1.39248i	−0.144938	−	0.0697985i
$399$		0			0
$400$	17.3954	−	8.37719i	0.869771	−	0.418860i
$401$	−28.1965	−	22.4860i	−1.40807	−	1.12290i	−0.975171	−	0.221451i	$-0.928921\pi$
$401$	−28.1965	−	22.4860i	−1.40807	−	1.12290i	−0.432895	−	0.901444i	$-0.642508\pi$
$402$		0			0
$403$	26.4147	+	33.1230i	1.31581	+	1.64997i
$404$	0.904312	+	3.96205i	0.0449912	+	0.197119i
$405$		0			0
$406$	22.5162	+	1.23407i	1.11746	+	0.0612459i
$407$	−0.978843	−	0.780602i	−0.0485195	−	0.0386930i
$408$		0			0
$409$	25.5082	−	5.82209i	1.26130	−	0.287884i	0.460956	−	0.887423i	$-0.347507\pi$
$409$	25.5082	−	5.82209i	1.26130	−	0.287884i	0.800345	+	0.599539i	$0.204649\pi$
$410$		−	25.2202i		−	1.24553i
$411$		0			0
$412$	−6.15106	+	1.40394i	−0.303041	+	0.0691672i
$413$	3.38793	+	19.7786i	0.166709	+	0.973241i
$414$		0			0
$415$	4.05146	−	17.7506i	0.198878	−	0.871342i
$416$	11.2083	−	14.0548i	0.549533	−	0.689093i
$417$		0			0
$418$	11.6613	+	2.66162i	0.570373	+	0.130184i
$419$	5.59073	−	24.4946i	0.273125	−	1.19664i	−0.633176	−	0.774008i	$-0.718249\pi$
$419$	5.59073	−	24.4946i	0.273125	−	1.19664i	0.906301	−	0.422632i	$-0.138894\pi$
$420$		0			0
$421$	8.50256	+	37.2521i	0.414389	+	1.81556i	0.562753	+	0.826625i	$0.309742\pi$
$421$	8.50256	+	37.2521i	0.414389	+	1.81556i	−0.148364	+	0.988933i	$0.547401\pi$
$422$			5.42509i			0.264089i
$423$		0			0
$424$	−5.00310	−	21.9200i	−0.242972	−	1.06453i
$425$	−2.99171	−	1.44073i	−0.145119	−	0.0698858i
$426$		0			0
$427$	−12.7273	−	11.3430i	−0.615916	−	0.548926i
$428$	2.70421	−	2.15653i	0.130713	−	0.104240i
$429$		0			0
$430$	−29.7152	+	23.6971i	−1.43299	+	1.14278i
$431$	−4.00001	+	8.30611i	−0.192674	+	0.400091i	−0.974817	−	0.223008i	$-0.928412\pi$
$431$	−4.00001	+	8.30611i	−0.192674	+	0.400091i	0.782143	+	0.623099i	$0.214127\pi$
$432$		0			0
$433$	11.6174	+	24.1238i	0.558298	+	1.15932i	0.968888	+	0.247498i	$0.0796083\pi$
$433$	11.6174	+	24.1238i	0.558298	+	1.15932i	−0.410590	+	0.911820i	$0.634677\pi$
$434$	6.07644	−	21.1990i	0.291678	−	1.01759i
$435$		0			0
$436$	−5.05446	+	2.43410i	−0.242065	+	0.116572i
$437$	−3.56611	+	15.6242i	−0.170590	+	0.747405i
$438$		0			0
$439$	−10.4707	+	8.35012i	−0.499740	+	0.398530i	−0.840660	−	0.541563i	$-0.817833\pi$
$439$	−10.4707	+	8.35012i	−0.499740	+	0.398530i	0.340920	+	0.940092i	$0.389261\pi$
$440$	−13.1901			−0.628812
$441$		0			0
$442$	3.40769			0.162087
$443$	10.3485	−	8.25263i	0.491671	−	0.392094i	−0.346030	−	0.938223i	$-0.612471\pi$
$443$	10.3485	−	8.25263i	0.491671	−	0.392094i	0.837701	+	0.546129i	$0.183899\pi$
$444$		0			0
$445$	10.3524	−	45.3569i	0.490751	−	2.15012i
$446$	3.86590	−	1.86172i	0.183056	−	0.0881550i
$447$		0			0
$448$	−23.3690	−	1.28081i	−1.10408	−	0.0605126i
$449$	14.2954	+	29.6847i	0.674642	+	1.40091i	0.903986	+	0.427562i	$0.140628\pi$
$449$	14.2954	+	29.6847i	0.674642	+	1.40091i	−0.229344	+	0.973345i	$0.573658\pi$
$450$		0			0
$451$	−3.16339	+	6.56884i	−0.148958	+	0.309315i
$452$	−8.38129	+	6.68385i	−0.394223	+	0.314382i
$453$		0			0
$454$	−14.2042	+	11.3274i	−0.666634	+	0.531623i
$455$	−56.2721	+	9.63899i	−2.63808	+	0.451883i
$456$		0			0
$457$	18.7239	+	9.01697i	0.875869	+	0.421796i	0.817114	−	0.576476i	$-0.195573\pi$
$457$	18.7239	+	9.01697i	0.875869	+	0.421796i	0.0587548	+	0.998272i	$0.481287\pi$
$458$	−2.99775	−	13.1340i	−0.140076	−	0.613712i
$459$		0			0
$460$		−	3.71031i		−	0.172994i
$461$	−6.40585	−	28.0659i	−0.298350	−	1.30716i	−0.872583	−	0.488465i	$-0.837557\pi$
$461$	−6.40585	−	28.0659i	−0.298350	−	1.30716i	0.574233	−	0.818692i	$-0.305300\pi$
$462$		0			0
$463$	1.43641	−	6.29331i	0.0667554	−	0.292475i	−0.930520	−	0.366241i	$-0.880645\pi$
$463$	1.43641	−	6.29331i	0.0667554	−	0.292475i	0.997276	+	0.0737660i	$0.0235018\pi$
$464$	18.2022	+	4.15453i	0.845014	+	0.192869i
$465$		0			0
$466$	5.69973	−	7.14724i	0.264035	−	0.331090i
$467$	4.54647	−	19.9194i	0.210385	−	0.921759i	−0.753920	−	0.656966i	$-0.771839\pi$
$467$	4.54647	−	19.9194i	0.210385	−	0.921759i	0.964305	−	0.264793i	$-0.0853035\pi$
$468$		0			0
$469$	2.17213	+	3.05261i	0.100300	+	0.140956i
$470$	−6.12171	+	1.39724i	−0.282374	+	0.0644499i
$471$		0			0
$472$			23.2670i			1.07095i
$473$	10.7120	−	2.44494i	0.492537	−	0.112418i
$474$		0			0
$475$	−45.7329	−	36.4707i	−2.09837	−	1.67339i
$476$	0.372195	+	0.523065i	0.0170595	+	0.0239747i
$477$		0			0
$478$	−0.711873	−	3.11892i	−0.0325603	−	0.142656i
$479$	−10.7585	−	13.4908i	−0.491570	−	0.616409i	0.472735	−	0.881205i	$-0.343267\pi$
$479$	−10.7585	−	13.4908i	−0.491570	−	0.616409i	−0.964305	+	0.264796i	$0.914696\pi$
$480$		0			0
$481$	−4.91252	−	3.91760i	−0.223992	−	0.178627i
$482$	−5.49933	+	2.64834i	−0.250488	+	0.120628i
$483$		0			0
$484$	−4.54606	−	2.18927i	−0.206639	−	0.0995121i
$485$	18.2097	+	37.8129i	0.826862	+	1.71700i
$486$		0			0
$487$	−11.7080	+	5.63827i	−0.530540	+	0.255495i	−0.679921	−	0.733285i	$-0.737986\pi$
$487$	−11.7080	+	5.63827i	−0.530540	+	0.255495i	0.149381	+	0.988780i	$0.452272\pi$
$488$	−12.3247	−	15.4547i	−0.557915	−	0.699603i
$489$		0			0
$490$	21.0703	+	20.9571i	0.951858	+	0.946744i
$491$			23.6167i			1.06581i	0.846176	+	0.532903i	$0.178899\pi$
$491$			23.6167i			1.06581i	−0.846176	+	0.532903i	$0.821101\pi$
$492$		0			0
$493$	−1.39318	−	2.89298i	−0.0627459	−	0.130293i
$494$	58.5245	+	13.3578i	2.63314	+	0.600998i
$495$		0			0
$496$	7.92209	−	16.4504i	0.355713	−	0.738645i
$497$	−14.5983	−	35.1095i	−0.654822	−	1.57488i
$498$		0			0
$499$	−0.765079	+	0.959378i	−0.0342496	+	0.0429477i	−0.798661	−	0.601781i	$-0.794458\pi$
$499$	−0.765079	+	0.959378i	−0.0342496	+	0.0429477i	0.764412	+	0.644728i	$0.223030\pi$
$500$	3.81362	+	1.83654i	0.170550	+	0.0821327i
$501$		0			0
$502$	−2.65182	+	0.605262i	−0.118357	+	0.0270142i
$503$	−0.0680914	−	0.0853839i	−0.00303605	−	0.00380708i	0.780311	−	0.625391i	$-0.215061\pi$
$503$	−0.0680914	−	0.0853839i	−0.00303605	−	0.00380708i	−0.783347	+	0.621584i	$0.786489\pi$
$504$		0			0
$505$	16.7020	−	20.9437i	0.743230	−	0.931982i
$506$	1.28590	−	2.67019i	0.0571650	−	0.118704i
$507$		0			0
$508$	2.53332			0.112398
$509$	−19.6325			−0.870194			−0.435097	−	0.900384i	$-0.643286\pi$
$509$	−19.6325			−0.870194			−0.435097	+	0.900384i	$0.643286\pi$
$510$		0			0
$511$	0.228178	−	4.16322i	0.0100940	−	0.184170i
$512$	−23.4318	−	5.34815i	−1.03555	−	0.236357i
$513$		0			0
$514$	7.52009	+	5.99707i	0.331697	+	0.264520i
$515$	32.5150	+	25.9298i	1.43278	+	1.14260i
$516$		0			0
$517$	1.76972	+	0.403927i	0.0778321	+	0.0177647i
$518$	−0.178991	+	3.26577i	−0.00786440	+	0.143490i
$519$		0			0
$520$	−66.1970			−2.90293
$521$	−34.5444			−1.51342			−0.756709	−	0.653752i	$-0.773194\pi$
$521$	−34.5444			−1.51342			−0.756709	+	0.653752i	$0.773194\pi$
$522$		0			0
$523$	−1.36808	+	2.84085i	−0.0598219	+	0.124222i	−0.928736	−	0.370741i	$-0.879104\pi$
$523$	−1.36808	+	2.84085i	−0.0598219	+	0.124222i	0.868914	+	0.494962i	$0.164818\pi$
$524$	−3.98858	+	5.00152i	−0.174242	+	0.218492i
$525$		0			0
$526$	−15.6160	−	19.5818i	−0.680889	−	0.853808i
$527$	−3.06143	+	0.698751i	−0.133358	+	0.0304381i
$528$		0			0
$529$	−17.1447	−	8.25645i	−0.745421	−	0.358976i
$530$	−19.4001	+	24.3270i	−0.842687	+	1.05670i
$531$		0			0
$532$	4.34180	+	10.4422i	0.188241	+	0.452728i
$533$	−15.8761	+	32.9670i	−0.687670	+	1.42796i
$534$		0			0
$535$	−22.2276	−	5.07330i	−0.960981	−	0.219338i
$536$	1.88482	+	3.91386i	0.0814117	+	0.169053i
$537$		0			0
$538$		−	10.2454i		−	0.441709i
$539$	−2.85929	−	8.10134i	−0.123159	−	0.348950i
$540$		0			0
$541$	−5.55764	−	6.96905i	−0.238941	−	0.299623i	0.647873	−	0.761748i	$-0.275659\pi$
$541$	−5.55764	−	6.96905i	−0.238941	−	0.299623i	−0.886815	+	0.462125i	$0.847087\pi$
$542$	−10.0181	+	4.82448i	−0.430316	+	0.207229i
$543$		0			0
$544$	0.578122	+	1.20048i	0.0247868	+	0.0514703i
$545$	33.3171	+	16.0447i	1.42715	+	0.687279i
$546$		0			0
$547$	7.85815	−	3.78428i	0.335990	−	0.161804i	−0.258279	−	0.966070i	$-0.583156\pi$
$547$	7.85815	−	3.78428i	0.335990	−	0.161804i	0.594270	+	0.804266i	$0.297441\pi$
$548$	−5.60042	−	4.46619i	−0.239238	−	0.190786i
$549$		0			0
$550$	6.74455	+	8.45740i	0.287588	+	0.360625i
$551$	−12.5867	−	55.1459i	−0.536211	−	2.34929i
$552$		0			0
$553$	−10.1107	−	14.2091i	−0.429951	−	0.604234i
$554$	−8.36258	−	6.66894i	−0.355292	−	0.283336i
$555$		0			0
$556$	−1.63909	+	0.374111i	−0.0695129	+	0.0158659i
$557$		−	37.9448i		−	1.60777i	−0.594783	−	0.803886i	$-0.702762\pi$
$557$		−	37.9448i		−	1.60777i	0.594783	−	0.803886i	$-0.297238\pi$
$558$		0			0
$559$	53.7601	−	12.2704i	2.27381	−	0.518983i
$560$	14.2652	+	20.0477i	0.602815	+	0.847169i
$561$		0			0
$562$	4.97284	−	21.7874i	0.209767	−	0.919048i
$563$	−19.0788	+	23.9240i	−0.804075	+	1.00828i	0.195544	+	0.980695i	$0.437353\pi$
$563$	−19.0788	+	23.9240i	−0.804075	+	1.00828i	−0.999620	+	0.0275835i	$0.991219\pi$
$564$		0			0
$565$	68.8910	+	15.7239i	2.89827	+	0.661510i
$566$	1.06358	−	4.65985i	0.0447056	−	0.195868i
$567$		0			0
$568$	−9.81045	−	42.9824i	−0.411637	−	1.80350i
$569$			6.76360i			0.283545i	0.989899	+	0.141772i	$0.0452801\pi$
$569$			6.76360i			0.283545i	−0.989899	+	0.141772i	$0.954720\pi$
$570$		0			0
$571$	3.05357	+	13.3785i	0.127788	+	0.559875i	0.997767	+	0.0667868i	$0.0212747\pi$
$571$	3.05357	+	13.3785i	0.127788	+	0.559875i	−0.869980	+	0.493088i	$0.835868\pi$
$572$	3.61987	+	1.74324i	0.151354	+	0.0728884i
$573$		0			0
$574$	18.7731	−	3.21569i	0.783575	−	0.134221i
$575$	−11.3315	+	9.03654i	−0.472555	+	0.376850i
$576$		0			0
$577$	−7.51312	+	5.99151i	−0.312775	+	0.249430i	−0.767277	−	0.641316i	$-0.778389\pi$
$577$	−7.51312	+	5.99151i	−0.312775	+	0.249430i	0.454502	+	0.890746i	$0.349817\pi$
$578$	8.82886	−	18.3333i	0.367232	−	0.762565i
$579$		0			0
$580$	5.68199	+	11.7988i	0.235932	+	0.489917i
$581$	13.7296	+	0.752492i	0.569599	+	0.0312186i
$582$		0			0
$583$	8.10430	−	3.90283i	0.335646	−	0.161639i
$584$	1.07576	−	4.71323i	0.0445154	−	0.195035i
$585$		0			0
$586$	0.571074	−	0.455416i	0.0235909	−	0.0188131i
$587$	40.3617			1.66591			0.832953	−	0.553343i	$-0.186648\pi$
$587$	40.3617			1.66591			0.832953	+	0.553343i	$0.186648\pi$
$588$		0			0
$589$	−55.3168			−2.27929
$590$	25.1744	−	20.0759i	1.03642	−	0.826514i
$591$		0			0
$592$	−0.602577	+	2.64006i	−0.0247657	+	0.108506i
$593$	24.5780	−	11.8361i	1.00930	−	0.486052i	0.145214	−	0.989400i	$-0.453613\pi$
$593$	24.5780	−	11.8361i	1.00930	−	0.486052i	0.864083	+	0.503349i	$0.167899\pi$
$594$		0			0
$595$	1.16599	−	4.06782i	0.0478009	−	0.166764i
$596$	1.32147	+	2.74406i	0.0541294	+	0.112401i
$597$		0			0
$598$	6.45352	−	13.4009i	0.263904	−	0.548002i
$599$	−19.4803	+	15.5350i	−0.795945	+	0.634745i	−0.934642	−	0.355590i	$-0.884280\pi$
$599$	−19.4803	+	15.5350i	−0.795945	+	0.634745i	0.138697	+	0.990335i	$0.455709\pi$
$600$		0			0
$601$	21.3996	−	17.0656i	0.872908	−	0.696121i	−0.0808401	−	0.996727i	$-0.525760\pi$
$601$	21.3996	−	17.0656i	0.872908	−	0.696121i	0.953748	+	0.300606i	$0.0971889\pi$
$602$	−21.4282	−	19.0976i	−0.873349	−	0.778360i
$603$		0			0
$604$	−3.40142	−	1.63804i	−0.138402	−	0.0666507i
$605$	7.40097	+	32.4258i	0.300892	+	1.31829i
$606$		0			0
$607$			45.4228i			1.84365i	0.387601	+	0.921827i	$0.373304\pi$
$607$			45.4228i			1.84365i	−0.387601	+	0.921827i	$0.626696\pi$
$608$	5.22303	+	22.8836i	0.211822	+	0.928052i
$609$		0			0
$610$	−6.08731	+	26.6703i	−0.246468	+	1.07985i
$611$	8.88168	+	2.02719i	0.359314	+	0.0820112i
$612$		0			0
$613$	−25.1836	+	31.5792i	−1.01716	+	1.27547i	−0.0563031	+	0.998414i	$0.517931\pi$
$613$	−25.1836	+	31.5792i	−1.01716	+	1.27547i	−0.960853	+	0.277059i	$0.910640\pi$
$614$	−0.981849	+	4.30176i	−0.0396242	+	0.173605i
$615$		0			0
$616$	−1.68180	−	9.81828i	−0.0677616	−	0.395590i
$617$	7.28753	−	1.66333i	0.293385	−	0.0669632i	−0.0732951	−	0.997310i	$-0.523351\pi$
$617$	7.28753	−	1.66333i	0.293385	−	0.0669632i	0.366680	+	0.930347i	$0.380494\pi$
$618$		0			0
$619$		−	7.04484i		−	0.283156i	−0.989927	−	0.141578i	$-0.954782\pi$
$619$		−	7.04484i		−	0.283156i	0.989927	−	0.141578i	$-0.0452176\pi$
$620$	12.4858	−	2.84980i	0.501441	−	0.114451i
$621$		0			0
$622$	31.1381	+	24.8318i	1.24852	+	0.995664i
$623$	35.0823	+	1.92279i	1.40554	+	0.0770351i
$624$		0			0
$625$	1.88375	+	8.25327i	0.0753502	+	0.330131i
$626$	3.75643	+	4.71041i	0.150137	+	0.188266i
$627$		0			0
$628$	−4.16480	−	3.32132i	−0.166194	−	0.132535i
$629$	0.419600	−	0.202069i	0.0167306	−	0.00805701i
$630$		0			0
$631$	29.1127	+	14.0199i	1.15896	+	0.558125i	0.911713	−	0.410828i	$-0.134760\pi$
$631$	29.1127	+	14.0199i	1.15896	+	0.558125i	0.247245	+	0.968953i	$0.420475\pi$
$632$	−8.77335	−	18.2181i	−0.348985	−	0.724675i
$633$		0			0
$634$	−5.74983	+	2.76897i	−0.228355	+	0.109970i
$635$	−10.4115	−	13.0555i	−0.413166	−	0.518094i
$636$		0			0
$637$	−14.3499	−	40.6582i	−0.568565	−	1.61094i
$638$			10.4604i			0.414132i
$639$		0			0
$640$	7.42169	+	15.4113i	0.293368	+	0.609185i
$641$	18.0881	+	4.12849i	0.714437	+	0.163066i	0.564264	−	0.825594i	$-0.309160\pi$
$641$	18.0881	+	4.12849i	0.714437	+	0.163066i	0.150173	+	0.988660i	$0.452017\pi$
$642$		0			0
$643$	20.8180	−	43.2289i	0.820980	−	1.70478i	0.118644	−	0.992937i	$-0.462145\pi$
$643$	20.8180	−	43.2289i	0.820980	−	1.70478i	0.702336	−	0.711845i	$-0.252140\pi$
$644$	2.76184	−	0.473083i	0.108832	−	0.0186421i
$645$		0			0
$646$	−2.77415	+	3.47867i	−0.109147	+	0.136867i
$647$	11.5543	+	5.56424i	0.454245	+	0.218753i	0.646994	−	0.762495i	$-0.276026\pi$
$647$	11.5543	+	5.56424i	0.454245	+	0.218753i	−0.192749	+	0.981248i	$0.561740\pi$
$648$		0			0
$649$	−9.07508	+	2.07133i	−0.356228	+	0.0813067i
$650$	33.8488	+	42.4451i	1.32766	+	1.66483i
$651$		0			0
$652$	2.77915	−	3.48495i	0.108840	−	0.136481i
$653$	−12.3764	+	25.6998i	−0.484326	+	1.00571i	0.505420	+	0.862873i	$0.331337\pi$
$653$	−12.3764	+	25.6998i	−0.484326	+	1.00571i	−0.989746	+	0.142839i	$0.954377\pi$
$654$		0			0
$655$	42.1678			1.64763
$656$	15.7696			0.615699
$657$		0			0
$658$	−1.82061	−	4.37866i	−0.0709749	−	0.170698i
$659$	9.05005	+	2.06562i	0.352540	+	0.0804650i	0.395124	−	0.918628i	$-0.370702\pi$
$659$	9.05005	+	2.06562i	0.352540	+	0.0804650i	−0.0425836	+	0.999093i	$0.513559\pi$
$660$		0			0
$661$	19.7343	+	15.7376i	0.767574	+	0.612120i	0.926988	−	0.375092i	$-0.122389\pi$
$661$	19.7343	+	15.7376i	0.767574	+	0.612120i	−0.159413	+	0.987212i	$0.550960\pi$
$662$	28.9704	+	23.1031i	1.12597	+	0.897928i
$663$		0			0
$664$	15.5434	+	3.54768i	0.603201	+	0.137677i
$665$	35.9705	−	65.2912i	1.39488	−	2.53188i
$666$		0			0
$667$	−14.0152			−0.542669
$668$	4.86378			0.188185
$669$		0			0
$670$	2.60841	−	5.41641i	0.100772	−	0.209254i
$671$	4.93078	−	6.18300i	0.190350	−	0.238692i
$672$		0			0
$673$	16.1270	+	20.2226i	0.621650	+	0.779525i	0.988576	−	0.150726i	$-0.0481610\pi$
$673$	16.1270	+	20.2226i	0.621650	+	0.779525i	−0.366926	+	0.930250i	$0.619590\pi$
$674$	32.0079	−	7.30560i	1.23290	−	0.281401i
$675$		0			0
$676$	11.9420	+	5.75096i	0.459307	+	0.221191i
$677$	−4.15405	+	5.20902i	−0.159653	+	0.200199i	−0.855224	−	0.518259i	$-0.826580\pi$
$677$	−4.15405	+	5.20902i	−0.159653	+	0.200199i	0.695570	+	0.718458i	$0.255152\pi$
$678$		0			0
$679$	−25.8249	+	18.3761i	−0.991070	+	0.705210i
$680$	2.12886	−	4.42062i	0.0816379	−	0.169523i
$681$		0			0
$682$	9.97327	+	2.27633i	0.381896	+	0.0871653i
$683$	−10.2335	−	21.2501i	−0.391574	−	0.813111i	−0.999813	−	0.0193570i	$-0.993838\pi$
$683$	−10.2335	−	21.2501i	−0.391574	−	0.813111i	0.608239	−	0.793754i	$-0.291876\pi$
$684$		0			0
$685$			47.2172i			1.80408i
$686$	−12.9132	+	18.3562i	−0.493030	+	0.700843i
$687$		0			0
$688$	−14.8172	−	18.5802i	−0.564902	−	0.708365i
$689$	40.6730	−	19.5871i	1.54952	−	0.746209i
$690$		0			0
$691$	−14.9765	−	31.0991i	−0.569735	−	1.18307i	−0.964451	−	0.264263i	$-0.914871\pi$
$691$	−14.9765	−	31.0991i	−0.569735	−	1.18307i	0.394716	−	0.918803i	$-0.370843\pi$
$692$	0.154289	+	0.0743019i	0.00586520	+	0.00282453i
$693$		0			0
$694$	−13.1968	+	6.35523i	−0.500943	+	0.241241i
$695$	8.66434	+	6.90958i	0.328657	+	0.262095i
$696$		0			0
$697$	−1.69096	−	2.12040i	−0.0640498	−	0.0803160i
$698$	−6.44861	−	28.2532i	−0.244083	−	1.06940i
$699$		0			0
$700$	−2.81810	+	9.83159i	−0.106514	+	0.371599i
$701$	11.8358	+	9.43876i	0.447033	+	0.356497i	0.820984	−	0.570952i	$-0.193426\pi$
$701$	11.8358	+	9.43876i	0.447033	+	0.356497i	−0.373951	+	0.927449i	$0.621997\pi$
$702$		0			0
$703$	7.99842	−	1.82559i	0.301666	−	0.0688533i
$704$		−	10.8566i		−	0.409174i
$705$		0			0
$706$	−15.2560	+	3.48209i	−0.574168	+	0.131050i
$707$	17.7194	+	9.76206i	0.666408	+	0.367140i
$708$		0			0
$709$	1.11533	−	4.88659i	0.0418872	−	0.183520i	−0.949656	−	0.313293i	$-0.898568\pi$
$709$	1.11533	−	4.88659i	0.0418872	−	0.183520i	0.991544	+	0.129773i	$0.0414249\pi$
$710$	−38.0411	+	47.7021i	−1.42766	+	1.79023i
$711$		0			0
$712$	39.7170	+	9.06515i	1.48846	+	0.339731i
$713$	−3.04990	+	13.3625i	−0.114220	+	0.500429i
$714$		0			0
$715$	−5.89313	−	25.8195i	−0.220391	−	0.965595i
$716$		−	4.21129i		−	0.157383i
$717$		0			0
$718$	−7.13067	−	31.2415i	−0.266114	−	1.16592i
$719$	−0.983816	−	0.473781i	−0.0366902	−	0.0176690i	0.415449	−	0.909617i	$-0.363625\pi$
$719$	−0.983816	−	0.473781i	−0.0366902	−	0.0176690i	−0.452139	+	0.891948i	$0.649339\pi$
$720$		0			0
$721$	−15.1555	+	27.5093i	−0.564422	+	1.02450i
$722$	−43.2787	+	34.5136i	−1.61066	+	1.28446i
$723$		0			0
$724$	9.19734	−	7.33464i	0.341817	−	0.272590i
$725$	22.1954	−	46.0892i	0.824316	−	1.71171i
$726$		0			0
$727$	0.203786	+	0.423166i	0.00755800	+	0.0156943i	0.904714	−	0.426020i	$-0.140085\pi$
$727$	0.203786	+	0.423166i	0.00755800	+	0.0156943i	−0.897156	+	0.441714i	$0.854370\pi$
$728$	−8.44044	−	49.2750i	−0.312823	−	1.82625i
$729$		0			0
$730$	−6.02784	+	2.90285i	−0.223100	+	0.107439i
$731$	−0.909481	+	3.98470i	−0.0336384	+	0.147379i
$732$		0			0
$733$	18.9851	−	15.1401i	0.701231	−	0.559213i	−0.206663	−	0.978412i	$-0.566261\pi$
$733$	18.9851	−	15.1401i	0.701231	−	0.559213i	0.907894	+	0.419199i	$0.137689\pi$
$734$	2.07094			0.0764398
$735$		0			0
$736$	5.81580			0.214373
$737$	−1.35877	+	1.08358i	−0.0500510	+	0.0399143i
$738$		0			0
$739$	3.50584	−	15.3601i	0.128964	−	0.565030i	−0.868615	−	0.495488i	$-0.834989\pi$
$739$	3.50584	−	15.3601i	0.128964	−	0.565030i	0.997579	−	0.0695415i	$-0.0221536\pi$
$740$	−1.71130	+	0.824121i	−0.0629088	+	0.0302953i
$741$		0			0
$742$	−20.5819	−	11.3390i	−0.755584	−	0.416269i
$743$	12.0733	+	25.0705i	0.442928	+	0.919749i	0.996229	+	0.0867673i	$0.0276537\pi$
$743$	12.0733	+	25.0705i	0.442928	+	0.919749i	−0.553301	+	0.832981i	$0.686632\pi$
$744$		0			0
$745$	8.71062	−	18.0878i	0.319132	−	0.662685i
$746$	−10.4698	+	8.34939i	−0.383327	+	0.305693i
$747$		0			0
$748$	−0.232826	+	0.185672i	−0.00851295	+	0.00678885i
$749$	0.942283	−	17.1924i	0.0344303	−	0.628196i
$750$		0			0
$751$	−30.9414	−	14.9006i	−1.12907	−	0.543730i	−0.226384	−	0.974038i	$-0.572691\pi$
$751$	−30.9414	−	14.9006i	−1.12907	−	0.543730i	−0.902682	+	0.430308i	$0.858405\pi$
$752$	−0.873663	−	3.82777i	−0.0318592	−	0.139584i
$753$		0			0
$754$			52.4976i			1.91185i
$755$	5.53750	+	24.2614i	0.201530	+	0.882961i
$756$		0			0
$757$	−3.15791	+	13.8357i	−0.114776	+	0.502867i	0.884560	+	0.466427i	$0.154459\pi$
$757$	−3.15791	+	13.8357i	−0.114776	+	0.502867i	−0.999336	+	0.0364402i	$0.988398\pi$
$758$	−10.8626	−	2.47932i	−0.394548	−	0.0900531i
$759$		0			0
$760$	53.8900	−	67.5759i	1.95479	−	2.45123i
$761$	−4.34948	+	19.0563i	−0.157669	+	0.690792i	0.832860	+	0.553484i	$0.186702\pi$
$761$	−4.34948	+	19.0563i	−0.157669	+	0.690792i	−0.990528	+	0.137308i	$0.956155\pi$
$762$		0			0
$763$	−7.69507	+	26.8460i	−0.278580	+	0.971891i
$764$	−12.0575	+	2.75205i	−0.436225	+	0.0995655i
$765$		0			0
$766$		−	2.97027i		−	0.107320i
$767$	−45.5451	+	10.3954i	−1.64454	+	0.375355i
$768$		0			0
$769$	−14.6692	−	11.6983i	−0.528984	−	0.421851i	0.322236	−	0.946659i	$-0.395565\pi$
$769$	−14.6692	−	11.6983i	−0.528984	−	0.421851i	−0.851220	+	0.524809i	$0.824137\pi$
$770$	−9.17204	+	10.2914i	−0.330538	+	0.370876i
$771$		0			0
$772$	−0.408222	−	1.78854i	−0.0146922	−	0.0643709i
$773$	−29.4407	−	36.9175i	−1.05891	−	1.32783i	−0.942344	−	0.334645i	$-0.891383\pi$
$773$	−29.4407	−	36.9175i	−1.05891	−	1.32783i	−0.116564	−	0.993183i	$-0.537188\pi$
$774$		0			0
$775$	−39.1128	−	31.1914i	−1.40497	−	1.12043i
$776$	−33.1111	+	15.9455i	−1.18862	+	0.572409i
$777$		0			0
$778$	29.3617	+	14.1398i	1.05267	+	0.506938i
$779$	−20.7293	−	43.0448i	−0.742703	−	1.54224i
$780$		0			0
$781$	15.8915	−	7.65295i	0.568643	−	0.273844i
$782$	0.687365	+	0.861929i	0.0245801	+	0.0308225i
$783$		0			0
$784$	−13.1040	+	13.1748i	−0.467999	+	0.470527i
$785$			35.1135i			1.25325i
$786$		0			0
$787$	−20.5290	−	42.6290i	−0.731781	−	1.51956i	−0.850122	−	0.526585i	$-0.823472\pi$
$787$	−20.5290	−	42.6290i	−0.731781	−	1.51956i	0.118342	−	0.992973i	$-0.462242\pi$
$788$	1.43717	+	0.328025i	0.0511971	+	0.0116854i
$789$		0			0
$790$	−12.1415	+	25.2120i	−0.431975	+	0.897004i
$791$	−2.92046	+	53.2852i	−0.103840	+	1.89460i
$792$		0			0
$793$	24.7461	−	31.0306i	0.878759	−	1.10193i
$794$	13.9271	+	6.70693i	0.494254	+	0.238020i
$795$		0			0
$796$	1.37226	−	0.313209i	0.0486384	−	0.0111014i
$797$	−3.45337	−	4.33039i	−0.122325	−	0.153390i	0.716898	−	0.697178i	$-0.245561\pi$
$797$	−3.45337	−	4.33039i	−0.122325	−	0.153390i	−0.839223	+	0.543787i	$0.816990\pi$
$798$		0			0
$799$	−0.421005	+	0.527923i	−0.0148941	+	0.0186766i
$800$	−9.21030	+	19.1254i	−0.325633	+	0.676185i
$801$		0			0
$802$	−43.7041			−1.54324
$803$	1.93412			0.0682535
$804$		0			0
$805$	−13.7887	−	12.2890i	−0.485987	−	0.433129i
$806$	50.0528	+	11.4242i	1.76303	+	0.402401i
$807$		0			0
$808$	18.3395	+	14.6252i	0.645180	+	0.514514i
$809$	10.1043	+	8.05787i	0.355247	+	0.283300i	0.784809	−	0.619737i	$-0.212761\pi$
$809$	10.1043	+	8.05787i	0.355247	+	0.283300i	−0.429563	+	0.903037i	$0.641332\pi$
$810$		0			0
$811$	48.0052	+	10.9569i	1.68569	+	0.384748i	0.954684	−	0.297623i	$-0.0961937\pi$
$811$	48.0052	+	10.9569i	1.68569	+	0.384748i	0.731007	+	0.682370i	$0.239051\pi$
$812$	−8.05816	+	5.73390i	−0.282786	+	0.201220i
$813$		0			0
$814$	−1.51719			−0.0531775
$815$	−29.3816			−1.02919
$816$		0			0
$817$	−31.2393	+	64.8691i	−1.09293	+	2.26948i
$818$	19.7686	−	24.7891i	0.691195	−	0.866731i
$819$		0			0
$820$	6.89646	+	8.64788i	0.240835	+	0.301997i
$821$	28.7907	−	6.57129i	1.00480	−	0.229340i	0.311701	−	0.950180i	$-0.399101\pi$
$821$	28.7907	−	6.57129i	1.00480	−	0.229340i	0.693101	+	0.720841i	$0.256244\pi$
$822$		0			0
$823$	−24.8559	−	11.9700i	−0.866422	−	0.417247i	−0.0527754	−	0.998606i	$-0.516807\pi$
$823$	−24.8559	−	11.9700i	−0.866422	−	0.417247i	−0.813647	+	0.581359i	$0.802521\pi$
$824$	−22.7056	+	28.4719i	−0.790987	+	0.991867i
$825$		0			0
$826$	18.1538	+	16.1793i	0.631651	+	0.562950i
$827$	14.5476	−	30.2085i	0.505871	−	1.05045i	−0.479105	−	0.877758i	$-0.659039\pi$
$827$	14.5476	−	30.2085i	0.505871	−	1.05045i	0.984976	−	0.172694i	$-0.0552472\pi$
$828$		0			0
$829$	−3.86996	−	0.883292i	−0.134409	−	0.0306780i	0.154787	−	0.987948i	$-0.450531\pi$
$829$	−3.86996	−	0.883292i	−0.134409	−	0.0306780i	−0.289196	+	0.957270i	$0.593388\pi$
$830$	−9.57312	−	19.8788i	−0.332288	−	0.690003i
$831$		0			0
$832$		−	54.4860i		−	1.88896i
$833$	3.17663	+	0.349259i	0.110064	+	0.0121011i
$834$		0			0
$835$	−19.9892	−	25.0657i	−0.691755	−	0.867434i
$836$	−4.72643	+	2.27613i	−0.163467	+	0.0787215i
$837$		0			0
$838$	−13.2102	−	27.4314i	−0.456340	−	0.947601i
$839$	−31.3761	−	15.1099i	−1.08322	−	0.521653i	−0.194878	−	0.980827i	$-0.562431\pi$
$839$	−31.3761	−	15.1099i	−1.08322	−	0.521653i	−0.888346	+	0.459174i	$0.848145\pi$
$840$		0			0
$841$	18.4401	−	8.88026i	0.635864	−	0.306216i
$842$	36.2019	+	28.8701i	1.24760	+	0.994928i
$843$		0			0
$844$	−1.48349	−	1.86024i	−0.0510639	−	0.0640321i
$845$	−19.4415	−	85.1788i	−0.668808	−	2.93024i
$846$		0			0
$847$	−23.1931	+	9.64350i	−0.796924	+	0.331354i
$848$	−15.2111	−	12.1304i	−0.522351	−	0.416561i
$849$		0			0
$850$	−3.92303	+	0.895407i	−0.134559	+	0.0307122i
$851$		−	2.03277i		−	0.0696826i
$852$		0			0
$853$	−26.7011	+	6.09436i	−0.914230	+	0.208667i	−0.653660	−	0.756788i	$-0.726767\pi$
$853$	−26.7011	+	6.09436i	−0.914230	+	0.208667i	−0.260570	+	0.965455i	$0.583910\pi$
$854$	−20.6287	−	1.13062i	−0.705899	−	0.0386890i
$855$		0			0
$856$	4.44246	−	19.4637i	0.151840	−	0.665256i
$857$	−21.1265	+	26.4918i	−0.721667	+	0.904941i	−0.998431	−	0.0559966i	$-0.982166\pi$
$857$	−21.1265	+	26.4918i	−0.721667	+	0.904941i	0.276764	+	0.960938i	$0.410738\pi$
$858$		0			0
$859$	16.9809	+	3.87577i	0.579379	+	0.132240i	0.502160	−	0.864775i	$-0.332539\pi$
$859$	16.9809	+	3.87577i	0.579379	+	0.132240i	0.0772191	+	0.997014i	$0.475396\pi$
$860$	3.70924	−	16.2513i	0.126484	−	0.554163i
$861$		0			0
$862$	2.48598	+	10.8918i	0.0846730	+	0.370977i
$863$			7.83227i			0.266614i	0.991075	+	0.133307i	$0.0425596\pi$
$863$			7.83227i			0.266614i	−0.991075	+	0.133307i	$0.957440\pi$
$864$		0			0
$865$	−0.251183	−	1.10050i	−0.00854047	−	0.0374182i
$866$	29.2339	+	14.0783i	0.993407	+	0.478399i
$867$		0			0
$868$	3.71330	+	8.93066i	0.126038	+	0.303126i
$869$	6.32474	−	5.04381i	0.214552	−	0.171100i
$870$		0			0
$871$	−6.81926	+	5.43818i	−0.231062	+	0.184266i
$872$	−14.0496	+	29.1744i	−0.475780	+	0.987968i
$873$		0			0
$874$	8.42630	+	17.4974i	0.285024	+	0.591858i
$875$	19.4563	−	8.08979i	0.657744	−	0.273485i
$876$		0			0
$877$	−15.3566	+	7.39537i	−0.518557	+	0.249724i	−0.674808	−	0.737994i	$-0.735773\pi$
$877$	−15.3566	+	7.39537i	−0.518557	+	0.249724i	0.156251	+	0.987717i	$0.450059\pi$
$878$	−3.61139	+	15.8225i	−0.121878	+	0.533984i
$879$		0			0
$880$	−8.92357	+	7.11631i	−0.300814	+	0.239891i
$881$	19.0578			0.642072			0.321036	−	0.947067i	$-0.395969\pi$
$881$	19.0578			0.642072			0.321036	+	0.947067i	$0.395969\pi$
$882$		0			0
$883$	−29.0746			−0.978438			−0.489219	−	0.872161i	$-0.662718\pi$
$883$	−29.0746			−0.978438			−0.489219	+	0.872161i	$0.662718\pi$
$884$	−1.16848	+	0.931833i	−0.0393003	+	0.0313409i
$885$		0			0
$886$	3.56922	−	15.6378i	0.119910	−	0.525361i
$887$	3.47402	−	1.67300i	0.116646	−	0.0561739i	−0.374651	−	0.927166i	$-0.622237\pi$
$887$	3.47402	−	1.67300i	0.116646	−	0.0561739i	0.491297	+	0.870992i	$0.336523\pi$
$888$		0			0
$889$	8.39064	−	9.41461i	0.281413	−	0.315756i
$890$	−24.4615	−	50.7949i	−0.819952	−	1.70265i
$891$		0			0
$892$	−0.816513	+	1.69551i	−0.0273389	+	0.0567697i
$893$	−9.29986	+	7.41639i	−0.311208	+	0.248180i
$894$		0			0
$895$	−21.7031	+	17.3076i	−0.725454	+	0.578530i
$896$	−10.5254	+	7.48949i	−0.351629	+	0.250206i
$897$		0			0
$898$	35.9726	+	17.3235i	1.20042	+	0.578093i
$899$	−10.7647	−	47.1632i	−0.359023	−	1.57298i
$900$		0			0
$901$			3.34605i			0.111473i
$902$	1.96603	+	8.61373i	0.0654616	+	0.286806i
$903$		0			0
$904$	−13.7688	+	60.3248i	−0.457942	+	2.00637i
$905$	−75.5987	−	17.2549i	−2.51298	−	0.573572i
$906$		0			0
$907$	33.4297	−	41.9196i	1.11002	−	1.39192i	0.198774	−	0.980045i	$-0.436304\pi$
$907$	33.4297	−	41.9196i	1.11002	−	1.39192i	0.911242	−	0.411871i	$-0.135124\pi$
$908$	1.77305	−	7.76826i	0.0588409	−	0.257799i
$909$		0			0
$910$	−46.0317	+	51.6493i	−1.52594	+	1.71216i
$911$	−7.59821	+	1.73424i	−0.251740	+	0.0574580i	−0.346529	−	0.938039i	$-0.612640\pi$
$911$	−7.59821	+	1.73424i	−0.251740	+	0.0574580i	0.0947886	+	0.995497i	$0.469782\pi$
$912$		0			0
$913$			6.37839i			0.211094i
$914$	24.5527	−	5.60400i	0.812132	−	0.185364i
$915$		0			0
$916$	4.61941	+	3.68386i	0.152630	+	0.121718i
$917$	5.37660	+	31.3884i	0.177551	+	1.03654i
$918$		0			0
$919$	−6.02750	−	26.4082i	−0.198829	−	0.871127i	−0.971635	−	0.236485i	$-0.924005\pi$
$919$	−6.02750	−	26.4082i	−0.198829	−	0.871127i	0.772806	−	0.634642i	$-0.218852\pi$
$920$	−13.3526	−	16.7436i	−0.440222	−	0.552021i
$921$		0			0
$922$	−27.2746	−	21.7508i	−0.898241	−	0.716324i
$923$	79.7547	−	38.4078i	2.62516	−	1.26421i
$924$		0			0
$925$	6.68483	+	3.21924i	0.219796	+	0.105848i
$926$	−3.39406	−	7.04784i	−0.111536	−	0.231606i
$927$		0			0
$928$	−18.4942	+	8.90634i	−0.607102	+	0.292365i
$929$	16.2963	+	20.4349i	0.534664	+	0.670447i	0.973650	−	0.228047i	$-0.0732338\pi$
$929$	16.2963	+	20.4349i	0.534664	+	0.670447i	−0.438987	+	0.898494i	$0.644662\pi$
$930$		0			0
$931$	53.1872	+	18.4504i	1.74314	+	0.604687i
$932$			4.00935i			0.131331i
$933$		0			0
$934$	−10.7428	−	22.3076i	−0.351514	−	0.729927i
$935$	1.91374	+	0.436799i	0.0625860	+	0.0142848i
$936$		0			0
$937$	−11.4705	+	23.8187i	−0.374725	+	0.778124i	−0.999997	−	0.00228220i	$-0.999274\pi$
$937$	−11.4705	+	23.8187i	−0.374725	+	0.778124i	0.625272	+	0.780407i	$0.284988\pi$
$938$	4.36439	+	1.25100i	0.142503	+	0.0408465i
$939$		0			0
$940$	1.71703	−	2.15309i	0.0560034	−	0.0702261i
$941$	−44.8904	−	21.6181i	−1.46338	−	0.704729i	−0.478523	−	0.878075i	$-0.658828\pi$
$941$	−44.8904	−	21.6181i	−1.46338	−	0.704729i	−0.984861	+	0.173346i	$0.944542\pi$
$942$		0			0
$943$	−11.5409	+	2.63414i	−0.375824	+	0.0857794i
$944$	12.5530	+	15.7410i	0.408566	+	0.512326i
$945$		0			0
$946$	8.30168	−	10.4100i	0.269911	−	0.338457i
$947$	18.8535	−	39.1498i	0.612657	−	1.27220i	−0.331734	−	0.943373i	$-0.607634\pi$
$947$	18.8535	−	39.1498i	0.612657	−	1.27220i	0.944392	−	0.328823i	$-0.106652\pi$
$948$		0			0
$949$	9.70675			0.315095
$950$	−70.8851			−2.29982
$951$		0			0
$952$	3.56201	+	1.02101i	0.115445	+	0.0330910i
$953$	44.2539	+	10.1007i	1.43353	+	0.327193i	0.867600	−	0.497263i	$-0.165662\pi$
$953$	44.2539	+	10.1007i	1.43353	+	0.327193i	0.565926	+	0.824456i	$0.308519\pi$
$954$		0			0
$955$	63.7368	+	50.8284i	2.06247	+	1.64477i
$956$	1.09697	+	0.874803i	0.0354785	+	0.0282931i
$957$		0			0
$958$	−20.3862	−	4.65301i	−0.658648	−	0.150332i
$959$	−35.1470	+	6.02042i	−1.13496	+	0.194410i
$960$		0			0
$961$	−16.3094			−0.526109
$962$	−7.61431			−0.245495
$963$		0			0
$964$	1.16151	−	2.41190i	0.0374097	−	0.0776819i
$965$	−7.53959	+	9.45435i	−0.242708	+	0.304346i
$966$		0			0
$967$	−0.340770	−	0.427312i	−0.0109584	−	0.0137414i	0.776322	−	0.630336i	$-0.217083\pi$
$967$	−0.340770	−	0.427312i	−0.0109584	−	0.0137414i	−0.787280	+	0.616595i	$0.788512\pi$
$968$	−28.3938	+	6.48070i	−0.912612	+	0.208298i
$969$		0			0
$970$	45.8226	+	22.0670i	1.47128	+	0.708529i
$971$	−10.2002	+	12.7907i	−0.327341	+	0.410472i	−0.918083	−	0.396388i	$-0.870264\pi$
$971$	−10.2002	+	12.7907i	−0.327341	+	0.410472i	0.590742	+	0.806860i	$0.298835\pi$
$972$		0			0
$973$	−4.03854	+	7.33048i	−0.129469	+	0.235004i
$974$	−6.83260	+	14.1880i	−0.218930	+	0.454614i
$975$		0			0
$976$	−16.6763	−	3.80626i	−0.533795	−	0.121835i
$977$	−24.1115	−	50.0681i	−0.771396	−	1.60182i	−0.798357	−	0.602184i	$-0.794297\pi$
$977$	−24.1115	−	50.0681i	−0.771396	−	1.60182i	0.0269607	−	0.999636i	$-0.491417\pi$
$978$		0			0
$979$			16.2983i			0.520895i
$980$	−12.9556	−	1.42443i	−0.413852	−	0.0455016i
$981$		0			0
$982$	17.8438	+	22.3755i	0.569419	+	0.714029i
$983$	−49.2295	+	23.7077i	−1.57018	+	0.756157i	−0.997954	−	0.0639412i	$-0.979633\pi$
$983$	−49.2295	+	23.7077i	−1.57018	+	0.756157i	−0.572223	+	0.820098i	$0.693919\pi$
$984$		0			0
$985$	−4.21601	−	8.75463i	−0.134333	−	0.278946i
$986$	−3.50578	−	1.68829i	−0.111647	−	0.0537662i
$987$		0			0
$988$	−23.7205	+	11.4232i	−0.754650	+	0.363420i
$989$	13.9476	+	11.1228i	0.443507	+	0.353685i
$990$		0			0
$991$	16.9954	+	21.3116i	0.539877	+	0.676984i	0.974696	−	0.223534i	$-0.0717592\pi$
$991$	16.9954	+	21.3116i	0.539877	+	0.676984i	−0.434819	+	0.900518i	$0.643188\pi$
$992$	4.46697	+	19.5711i	0.141826	+	0.621382i
$993$		0			0
$994$	−40.3584	−	22.2344i	−1.28009	−	0.705232i
$995$	−7.25386	−	5.78476i	−0.229963	−	0.183389i
$996$		0			0
$997$	−10.0827	+	2.30130i	−0.319321	+	0.0728830i	−0.379177	−	0.925324i	$-0.623793\pi$
$997$	−10.0827	+	2.30130i	−0.319321	+	0.0728830i	0.0598560	+	0.998207i	$0.480936\pi$
$998$			1.48702i			0.0470707i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.w.a.188.14	yes	120
3.2	odd	2	inner	441.2.w.a.188.7	✓	120
49.6	odd	14	inner	441.2.w.a.251.7	yes	120
147.104	even	14	inner	441.2.w.a.251.14	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.w.a.188.7	✓	120	3.2	odd	2	inner
441.2.w.a.188.14	yes	120	1.1	even	1	trivial
441.2.w.a.251.7	yes	120	49.6	odd	14	inner
441.2.w.a.251.14	yes	120	147.104	even	14	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.w (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.947442 - 0.755560i) q^{2} +(-0.118266 + 0.518156i) q^{4} +(3.15639 - 1.52004i) q^{5} +(1.53392 + 2.15571i) q^{7} +(1.33103 + 2.76391i) q^{8} +O(q^{10})\)	\(q+(0.947442 - 0.755560i) q^{2} +(-0.118266 + 0.518156i) q^{4} +(3.15639 - 1.52004i) q^{5} +(1.53392 + 2.15571i) q^{7} +(1.33103 + 2.76391i) q^{8} +(1.84202 - 3.82499i) q^{10} +(-0.959544 + 0.765211i) q^{11} +(-4.81566 + 3.84036i) q^{13} +(3.08207 + 0.883437i) q^{14} +(2.39168 + 1.15177i) q^{16} +(-0.101589 - 0.445092i) q^{17} -8.04235i q^{19} +(0.414324 + 1.81527i) q^{20} +(-0.330950 + 1.44999i) q^{22} +(-1.94273 - 0.443416i) q^{23} +(4.53483 - 5.68650i) q^{25} +(-1.66094 + 7.27704i) q^{26} +(-1.29840 + 0.539866i) q^{28} +(6.85693 - 1.56505i) q^{29} -6.87818i q^{31} +(-2.84538 + 0.649440i) q^{32} +(-0.432544 - 0.344943i) q^{34} +(8.11842 + 4.47263i) q^{35} +(0.226997 + 0.994537i) q^{37} +(-6.07648 - 7.61967i) q^{38} +(8.40250 + 6.70077i) q^{40} +(5.35226 - 2.57751i) q^{41} +(-8.06594 - 3.88435i) q^{43} +(-0.283018 - 0.587692i) q^{44} +(-2.17566 + 1.04774i) q^{46} +(-0.922167 - 1.15636i) q^{47} +(-2.29415 + 6.61339i) q^{49} -8.81397i q^{50} +(-1.42038 - 2.94945i) q^{52} +(-7.14540 - 1.63089i) q^{53} +(-1.86555 + 3.87385i) q^{55} +(-3.91649 + 7.10894i) q^{56} +(5.31406 - 6.66362i) q^{58} +(6.83339 + 3.29079i) q^{59} +(-6.28213 + 1.43385i) q^{61} +(-5.19688 - 6.51668i) q^{62} +(-5.51533 + 6.91601i) q^{64} +(-9.36261 + 19.4417i) q^{65} +1.41606 q^{67} +0.242642 q^{68} +(11.0711 - 1.89639i) q^{70} +(-14.0112 - 3.19797i) q^{71} +(-1.23210 - 0.982563i) q^{73} +(0.966498 + 0.770757i) q^{74} +(4.16720 + 0.951136i) q^{76} +(-3.12144 - 0.894721i) q^{77} -6.59140 q^{79} +9.29981 q^{80} +(3.12349 - 6.48600i) q^{82} +(3.24033 - 4.06324i) q^{83} +(-0.997213 - 1.25047i) q^{85} +(-10.5769 + 2.41410i) q^{86} +(-3.39216 - 1.63358i) q^{88} +(8.27979 - 10.3825i) q^{89} +(-15.6656 - 4.49033i) q^{91} +(0.459518 - 0.954199i) q^{92} +(-1.74740 - 0.398833i) q^{94} +(-12.2247 - 25.3848i) q^{95} +11.9798i q^{97} +(2.82323 + 7.99917i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 24 q^{4}+O(q^{10}) \) 120 * q + 24 * q^4	\( 120 q + 24 q^{4} - 32 q^{16} - 44 q^{22} - 4 q^{25} - 56 q^{28} + 112 q^{34} - 76 q^{37} + 28 q^{40} + 8 q^{43} - 40 q^{46} - 84 q^{49} - 140 q^{52} + 12 q^{58} - 84 q^{61} + 24 q^{64} + 16 q^{67} + 112 q^{70} - 84 q^{76} - 24 q^{79} + 140 q^{82} - 96 q^{85} - 24 q^{88} - 112 q^{91} - 112 q^{94}+O(q^{100}) \) 120 * q + 24 * q^4 - 32 * q^16 - 44 * q^22 - 4 * q^25 - 56 * q^28 + 112 * q^34 - 76 * q^37 + 28 * q^40 + 8 * q^43 - 40 * q^46 - 84 * q^49 - 140 * q^52 + 12 * q^58 - 84 * q^61 + 24 * q^64 + 16 * q^67 + 112 * q^70 - 84 * q^76 - 24 * q^79 + 140 * q^82 - 96 * q^85 - 24 * q^88 - 112 * q^91 - 112 * q^94

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