LMFDB - Embedded newform 483.2.e.a.344.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(344,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("483.344");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.e (of order $2$, degree $1$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			344.15
Character	$\chi$	$=$	483.344
Dual form			483.2.e.a.344.33

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.06181i q^{2} +(-1.10086 + 1.33720i) q^{3} +0.872554 q^{4} -4.21218 q^{5} +(1.41986 + 1.16891i) q^{6} +1.00000i q^{7} -3.05011i q^{8} +(-0.576205 - 2.94414i) q^{9} +O(q^{10})$	\(q-1.06181i q^{2} +(-1.10086 + 1.33720i) q^{3} +0.872554 q^{4} -4.21218 q^{5} +(1.41986 + 1.16891i) q^{6} +1.00000i q^{7} -3.05011i q^{8} +(-0.576205 - 2.94414i) q^{9} +4.47255i q^{10} +2.41135 q^{11} +(-0.960562 + 1.16678i) q^{12} +4.65741 q^{13} +1.06181 q^{14} +(4.63703 - 5.63253i) q^{15} -1.49354 q^{16} +3.38580 q^{17} +(-3.12613 + 0.611821i) q^{18} -0.938674i q^{19} -3.67536 q^{20} +(-1.33720 - 1.10086i) q^{21} -2.56041i q^{22} +(4.79394 - 0.134572i) q^{23} +(4.07861 + 3.35776i) q^{24} +12.7425 q^{25} -4.94530i q^{26} +(4.57123 + 2.47060i) q^{27} +0.872554i q^{28} +2.21989i q^{29} +(-5.98069 - 4.92366i) q^{30} -0.993529 q^{31} -4.51437i q^{32} +(-2.65457 + 3.22446i) q^{33} -3.59509i q^{34} -4.21218i q^{35} +(-0.502770 - 2.56893i) q^{36} +0.131565i q^{37} -0.996696 q^{38} +(-5.12717 + 6.22788i) q^{39} +12.8476i q^{40} +7.16999i q^{41} +(-1.16891 + 1.41986i) q^{42} -4.89667i q^{43} +2.10404 q^{44} +(2.42708 + 12.4013i) q^{45} +(-0.142890 - 5.09027i) q^{46} -7.21495i q^{47} +(1.64418 - 1.99716i) q^{48} -1.00000 q^{49} -13.5301i q^{50} +(-3.72730 + 4.52749i) q^{51} +4.06384 q^{52} -2.35810 q^{53} +(2.62331 - 4.85379i) q^{54} -10.1571 q^{55} +3.05011 q^{56} +(1.25519 + 1.03335i) q^{57} +2.35711 q^{58} -12.6303i q^{59} +(4.04606 - 4.91468i) q^{60} -4.95737i q^{61} +1.05494i q^{62} +(2.94414 - 0.576205i) q^{63} -7.78049 q^{64} -19.6178 q^{65} +(3.42377 + 2.81865i) q^{66} -4.58116i q^{67} +2.95430 q^{68} +(-5.09752 + 6.55860i) q^{69} -4.47255 q^{70} +16.5455i q^{71} +(-8.97998 + 1.75749i) q^{72} +3.32124 q^{73} +0.139697 q^{74} +(-14.0277 + 17.0392i) q^{75} -0.819044i q^{76} +2.41135i q^{77} +(6.61285 + 5.44409i) q^{78} -8.91608i q^{79} +6.29106 q^{80} +(-8.33598 + 3.39286i) q^{81} +7.61318 q^{82} -3.38077 q^{83} +(-1.16678 - 0.960562i) q^{84} -14.2616 q^{85} -5.19934 q^{86} +(-2.96844 - 2.44380i) q^{87} -7.35491i q^{88} +15.6083 q^{89} +(13.1678 - 2.57710i) q^{90} +4.65741i q^{91} +(4.18298 - 0.117421i) q^{92} +(1.09374 - 1.32855i) q^{93} -7.66093 q^{94} +3.95386i q^{95} +(6.03661 + 4.96970i) q^{96} -15.8631i q^{97} +1.06181i q^{98} +(-1.38943 - 7.09938i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{3} - 40 q^{4} + 6 q^{6} + 4 q^{9}+O(q^{10}) $ 48 * q - 4 * q^3 - 40 * q^4 + 6 * q^6 + 4 * q^9	$ 48 q - 4 q^{3} - 40 q^{4} + 6 q^{6} + 4 q^{9} + 22 q^{12} - 8 q^{13} + 24 q^{16} - 14 q^{18} - 12 q^{24} + 88 q^{25} - 16 q^{27} - 8 q^{31} - 10 q^{36} + 8 q^{46} - 98 q^{48} - 48 q^{49} + 28 q^{52} - 28 q^{54} - 92 q^{58} + 92 q^{64} + 8 q^{69} + 8 q^{70} + 60 q^{72} + 40 q^{73} - 80 q^{75} + 114 q^{78} - 28 q^{81} - 20 q^{82} - 40 q^{85} - 28 q^{87} - 76 q^{93} - 12 q^{94} - 6 q^{96}+O(q^{100}) $ 48 * q - 4 * q^3 - 40 * q^4 + 6 * q^6 + 4 * q^9 + 22 * q^12 - 8 * q^13 + 24 * q^16 - 14 * q^18 - 12 * q^24 + 88 * q^25 - 16 * q^27 - 8 * q^31 - 10 * q^36 + 8 * q^46 - 98 * q^48 - 48 * q^49 + 28 * q^52 - 28 * q^54 - 92 * q^58 + 92 * q^64 + 8 * q^69 + 8 * q^70 + 60 * q^72 + 40 * q^73 - 80 * q^75 + 114 * q^78 - 28 * q^81 - 20 * q^82 - 40 * q^85 - 28 * q^87 - 76 * q^93 - 12 * q^94 - 6 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$		−	1.06181i		−	0.750815i	−0.926860	−	0.375407i	$-0.877503\pi$
$2$		−	1.06181i		−	0.750815i	0.926860	−	0.375407i	$-0.122497\pi$
$3$	−1.10086	+	1.33720i	−0.635583	+	0.772032i
$3$	−1.10086	+	1.33720i	−0.635583	+	0.772032i
$4$	0.872554			0.436277
$5$	−4.21218			−1.88374			−0.941872	−	0.335972i	$-0.890935\pi$
$5$	−4.21218			−1.88374			−0.941872	+	0.335972i	$0.890935\pi$
$6$	1.41986	+	1.16891i	0.579653	+	0.477205i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$		−	3.05011i		−	1.07838i
$9$	−0.576205	−	2.94414i	−0.192068	−	0.981382i
$10$			4.47255i			1.41434i
$11$	2.41135			0.727051			0.363525	−	0.931584i	$-0.381573\pi$
$11$	2.41135			0.727051			0.363525	+	0.931584i	$0.381573\pi$
$12$	−0.960562	+	1.16678i	−0.277290	+	0.336820i
$13$	4.65741			1.29173			0.645866	−	0.763450i	$-0.276496\pi$
$13$	4.65741			1.29173			0.645866	+	0.763450i	$0.276496\pi$
$14$	1.06181			0.283781
$15$	4.63703	−	5.63253i	1.19728	−	1.45431i
$16$	−1.49354			−0.373385
$17$	3.38580			0.821177			0.410589	−	0.911821i	$-0.365323\pi$
$17$	3.38580			0.821177			0.410589	+	0.911821i	$0.365323\pi$
$18$	−3.12613	+	0.611821i	−0.736836	+	0.144208i
$19$		−	0.938674i		−	0.215347i	−0.994186	−	0.107673i	$-0.965660\pi$
$19$		−	0.938674i		−	0.215347i	0.994186	−	0.107673i	$-0.0343401\pi$
$20$	−3.67536			−0.821834
$21$	−1.33720	−	1.10086i	−0.291801	−	0.240228i
$22$		−	2.56041i		−	0.545880i
$23$	4.79394	−	0.134572i	0.999606	−	0.0280601i
$23$	4.79394	−	0.134572i	0.999606	−	0.0280601i
$24$	4.07861	+	3.35776i	0.832543	+	0.685399i
$25$	12.7425			2.54849
$26$		−	4.94530i		−	0.969852i
$27$	4.57123	+	2.47060i	0.879734	+	0.475467i
$28$			0.872554i			0.164897i
$29$			2.21989i			0.412224i	0.978528	+	0.206112i	$0.0660811\pi$
$29$			2.21989i			0.412224i	−0.978528	+	0.206112i	$0.933919\pi$
$30$	−5.98069	−	4.92366i	−1.09192	−	0.898933i
$31$	−0.993529			−0.178443			−0.0892216	−	0.996012i	$-0.528438\pi$
$31$	−0.993529			−0.178443			−0.0892216	+	0.996012i	$0.528438\pi$
$32$		−	4.51437i		−	0.798035i
$33$	−2.65457	+	3.22446i	−0.462101	+	0.561307i
$34$		−	3.59509i		−	0.616552i
$35$		−	4.21218i		−	0.711988i
$36$	−0.502770	−	2.56893i	−0.0837950	−	0.428154i
$37$			0.131565i			0.0216291i	0.999942	+	0.0108146i	$0.00344245\pi$
$37$			0.131565i			0.0216291i	−0.999942	+	0.0108146i	$0.996558\pi$
$38$	−0.996696			−0.161685
$39$	−5.12717	+	6.22788i	−0.821004	+	0.997260i
$40$			12.8476i			2.03139i
$41$			7.16999i			1.11976i	0.828572	+	0.559882i	$0.189153\pi$
$41$			7.16999i			1.11976i	−0.828572	+	0.559882i	$0.810847\pi$
$42$	−1.16891	+	1.41986i	−0.180367	+	0.219088i
$43$		−	4.89667i		−	0.746735i	−0.927684	−	0.373367i	$-0.878203\pi$
$43$		−	4.89667i		−	0.746735i	0.927684	−	0.373367i	$-0.121797\pi$
$44$	2.10404			0.317196
$45$	2.42708	+	12.4013i	0.361807	+	1.84867i
$46$	−0.142890	−	5.09027i	−0.0210679	−	0.750519i
$47$		−	7.21495i		−	1.05241i	−0.850358	−	0.526204i	$-0.823615\pi$
$47$		−	7.21495i		−	1.05241i	0.850358	−	0.526204i	$-0.176385\pi$
$48$	1.64418	−	1.99716i	0.237317	−	0.288265i
$49$	−1.00000			−0.142857
$50$		−	13.5301i		−	1.91345i
$51$	−3.72730	+	4.52749i	−0.521927	+	0.633976i
$52$	4.06384			0.563553
$53$	−2.35810			−0.323910			−0.161955	−	0.986798i	$-0.551780\pi$
$53$	−2.35810			−0.323910			−0.161955	+	0.986798i	$0.551780\pi$
$54$	2.62331	−	4.85379i	0.356987	−	0.660517i
$55$	−10.1571			−1.36958
$56$	3.05011			0.407589
$57$	1.25519	+	1.03335i	0.166255	+	0.136871i
$58$	2.35711			0.309504
$59$		−	12.6303i		−	1.64432i	−0.569255	−	0.822161i	$-0.692768\pi$
$59$		−	12.6303i		−	1.64432i	0.569255	−	0.822161i	$-0.307232\pi$
$60$	4.04606	−	4.91468i	0.522344	−	0.634483i
$61$		−	4.95737i		−	0.634726i	−0.948304	−	0.317363i	$-0.897203\pi$
$61$		−	4.95737i		−	0.634726i	0.948304	−	0.317363i	$-0.102797\pi$
$62$			1.05494i			0.133978i
$63$	2.94414	−	0.576205i	0.370927	−	0.0725950i
$64$	−7.78049			−0.972562
$65$	−19.6178			−2.43329
$66$	3.42377	+	2.81865i	0.421437	+	0.346952i
$67$		−	4.58116i		−	0.559678i	−0.960047	−	0.279839i	$-0.909719\pi$
$67$		−	4.58116i		−	0.559678i	0.960047	−	0.279839i	$-0.0902810\pi$
$68$	2.95430			0.358261
$69$	−5.09752	+	6.55860i	−0.613670	+	0.789563i
$70$	−4.47255			−0.534571
$71$			16.5455i			1.96359i	0.189937	+	0.981796i	$0.439172\pi$
$71$			16.5455i			1.96359i	−0.189937	+	0.981796i	$0.560828\pi$
$72$	−8.97998	+	1.75749i	−1.05830	+	0.207122i
$73$	3.32124			0.388722			0.194361	−	0.980930i	$-0.437737\pi$
$73$	3.32124			0.388722			0.194361	+	0.980930i	$0.437737\pi$
$74$	0.139697			0.0162395
$75$	−14.0277	+	17.0392i	−1.61978	+	1.96752i
$76$		−	0.819044i		−	0.0939508i
$77$			2.41135i			0.274799i
$78$	6.61285	+	5.44409i	0.748757	+	0.616422i
$79$		−	8.91608i		−	1.00314i	−0.865118	−	0.501569i	$-0.832756\pi$
$79$		−	8.91608i		−	1.00314i	0.865118	−	0.501569i	$-0.167244\pi$
$80$	6.29106			0.703362
$81$	−8.33598	+	3.39286i	−0.926220	+	0.376984i
$82$	7.61318			0.840735
$83$	−3.38077			−0.371087			−0.185544	−	0.982636i	$-0.559405\pi$
$83$	−3.38077			−0.371087			−0.185544	+	0.982636i	$0.559405\pi$
$84$	−1.16678	−	0.960562i	−0.127306	−	0.104806i
$85$	−14.2616			−1.54689
$86$	−5.19934			−0.560660
$87$	−2.96844	−	2.44380i	−0.318250	−	0.262003i
$88$		−	7.35491i		−	0.784036i
$89$	15.6083			1.65447			0.827237	−	0.561853i	$-0.189912\pi$
$89$	15.6083			1.65447			0.827237	+	0.561853i	$0.189912\pi$
$90$	13.1678	−	2.57710i	1.38801	−	0.271650i
$91$			4.65741i			0.488229i
$92$	4.18298	−	0.117421i	0.436105	−	0.0122420i
$93$	1.09374	−	1.32855i	0.113415	−	0.137764i
$94$	−7.66093			−0.790164
$95$			3.95386i			0.405658i
$96$	6.03661	+	4.96970i	0.616109	+	0.507218i
$97$		−	15.8631i		−	1.61066i	−0.592829	−	0.805328i	$-0.701989\pi$
$97$		−	15.8631i		−	1.61066i	0.592829	−	0.805328i	$-0.298011\pi$
$98$			1.06181i			0.107259i
$99$	−1.38943	−	7.09938i	−0.139643	−	0.713514i
$100$	11.1185			1.11185
$101$			8.33097i			0.828963i	0.910058	+	0.414481i	$0.136037\pi$
$101$			8.33097i			0.828963i	−0.910058	+	0.414481i	$0.863963\pi$
$102$	4.80735	+	3.95769i	0.475998	+	0.391870i
$103$			14.6087i			1.43943i	0.694268	+	0.719717i	$0.255728\pi$
$103$			14.6087i			1.43943i	−0.694268	+	0.719717i	$0.744272\pi$
$104$		−	14.2056i		−	1.39298i
$105$	5.63253	+	4.63703i	0.549678	+	0.452528i
$106$			2.50386i			0.243196i
$107$	−0.889038			−0.0859465			−0.0429733	−	0.999076i	$-0.513683\pi$
$107$	−0.889038			−0.0859465			−0.0429733	+	0.999076i	$0.513683\pi$
$108$	3.98865	+	2.15573i	0.383808	+	0.207435i
$109$			17.3834i			1.66503i	0.554005	+	0.832514i	$0.313099\pi$
$109$			17.3834i			1.66503i	−0.554005	+	0.832514i	$0.686901\pi$
$110$			10.7849i			1.02830i
$111$	−0.175928	−	0.144835i	−0.0166984	−	0.0137471i
$112$		−	1.49354i		−	0.141126i
$113$	14.4537			1.35969			0.679844	−	0.733357i	$-0.262048\pi$
$113$	14.4537			1.35969			0.679844	+	0.733357i	$0.262048\pi$
$114$	1.09722	−	1.33278i	0.102765	−	0.124826i
$115$	−20.1930	+	0.566840i	−1.88300	+	0.0528581i
$116$			1.93698i			0.179844i
$117$	−2.68362	−	13.7121i	−0.248101	−	1.26768i
$118$	−13.4110			−1.23458
$119$			3.38580i			0.310376i
$120$	−17.1798	−	14.1435i	−1.56830	−	1.29112i
$121$	−5.18537			−0.471397
$122$	−5.26380			−0.476562
$123$	−9.58770	−	7.89317i	−0.864494	−	0.711703i
$124$	−0.866908			−0.0778507
$125$	−32.6126			−2.91696
$126$	−0.611821	−	3.12613i	−0.0545054	−	0.278498i
$127$	16.2403			1.44109			0.720546	−	0.693407i	$-0.243891\pi$
$127$	16.2403			1.44109			0.720546	+	0.693407i	$0.243891\pi$
$128$		−	0.767310i		−	0.0678212i
$129$	6.54782	+	5.39056i	0.576503	+	0.474612i
$130$			20.8305i			1.82695i
$131$			14.7593i			1.28953i	0.764383	+	0.644763i	$0.223044\pi$
$131$			14.7593i			1.28953i	−0.764383	+	0.644763i	$0.776956\pi$
$132$	−2.31626	+	2.81352i	−0.201604	+	0.244885i
$133$	0.938674			0.0813934
$134$	−4.86433			−0.420214
$135$	−19.2548	−	10.4066i	−1.65719	−	0.895658i
$136$		−	10.3271i		−	0.885540i
$137$	14.7165			1.25732			0.628658	−	0.777682i	$-0.283605\pi$
$137$	14.7165			1.25732			0.628658	+	0.777682i	$0.283605\pi$
$138$	6.96401	+	5.41261i	0.592816	+	0.460752i
$139$	−5.91018			−0.501295			−0.250648	−	0.968078i	$-0.580644\pi$
$139$	−5.91018			−0.501295			−0.250648	+	0.968078i	$0.580644\pi$
$140$		−	3.67536i		−	0.310624i
$141$	9.64783	+	7.94267i	0.812494	+	0.668893i
$142$	17.5682			1.47429
$143$	11.2307			0.939155
$144$	0.860585	+	4.39720i	0.0717154	+	0.366433i
$145$		−	9.35059i		−	0.776524i
$146$		−	3.52654i		−	0.291858i
$147$	1.10086	−	1.33720i	0.0907976	−	0.110290i
$148$			0.114797i			0.00943629i
$149$	2.19516			0.179835			0.0899174	−	0.995949i	$-0.471340\pi$
$149$	2.19516			0.179835			0.0899174	+	0.995949i	$0.471340\pi$
$150$	18.0924	+	14.8948i	1.47724	+	1.21615i
$151$	−3.43616			−0.279631			−0.139815	−	0.990178i	$-0.544651\pi$
$151$	−3.43616			−0.279631			−0.139815	+	0.990178i	$0.544651\pi$
$152$	−2.86306			−0.232225
$153$	−1.95091	−	9.96829i	−0.157722	−	0.805888i
$154$	2.56041			0.206323
$155$	4.18493			0.336141
$156$	−4.47373	+	5.43417i	−0.358185	+	0.435082i
$157$			16.9344i			1.35151i	0.737126	+	0.675755i	$0.236182\pi$
$157$			16.9344i			1.35151i	−0.737126	+	0.675755i	$0.763818\pi$
$158$	−9.46721			−0.753171
$159$	2.59594	−	3.15325i	0.205872	−	0.250069i
$160$			19.0153i			1.50329i
$161$	0.134572	+	4.79394i	0.0106057	+	0.377816i
$162$	3.60258	+	8.85124i	0.283045	+	0.695419i
$163$	−17.7382			−1.38936			−0.694682	−	0.719317i	$-0.744455\pi$
$163$	−17.7382			−1.38936			−0.694682	+	0.719317i	$0.744455\pi$
$164$			6.25620i			0.488527i
$165$	11.1815	−	13.5820i	0.870480	−	1.05736i
$166$			3.58974i			0.278618i
$167$		−	14.0212i		−	1.08499i	−0.840058	−	0.542496i	$-0.817479\pi$
$167$		−	14.0212i		−	1.08499i	0.840058	−	0.542496i	$-0.182521\pi$
$168$	−3.35776	+	4.07861i	−0.259056	+	0.314672i
$169$	8.69146			0.668574
$170$			15.1432i			1.16143i
$171$	−2.76359	+	0.540868i	−0.211337	+	0.0413612i
$172$		−	4.27261i		−	0.325783i
$173$		−	18.2431i		−	1.38699i	−0.720460	−	0.693497i	$-0.756069\pi$
$173$		−	18.2431i		−	1.38699i	0.720460	−	0.693497i	$-0.243931\pi$
$174$	−2.59485	+	3.15193i	−0.196715	+	0.238947i
$175$			12.7425i			0.963240i
$176$	−3.60146			−0.271470
$177$	16.8892	+	13.9042i	1.26947	+	1.04510i
$178$		−	16.5731i		−	1.24220i
$179$			8.75891i			0.654672i	0.944908	+	0.327336i	$0.106151\pi$
$179$			8.75891i			0.654672i	−0.944908	+	0.327336i	$0.893849\pi$
$180$	2.11776	+	10.8208i	0.157848	+	0.806533i
$181$			10.1122i			0.751631i	0.926694	+	0.375816i	$0.122637\pi$
$181$			10.1122i			0.751631i	−0.926694	+	0.375816i	$0.877363\pi$
$182$	4.94530			0.366570
$183$	6.62899	+	5.45738i	0.490029	+	0.403421i
$184$	−0.410459	−	14.6221i	−0.0302594	−	1.07795i
$185$		−	0.554175i		−	0.0407438i
$186$	−1.41067	−	1.16135i	−0.103435	−	0.0851540i
$187$	8.16437			0.597038
$188$		−	6.29544i		−	0.459142i
$189$	−2.47060	+	4.57123i	−0.179710	+	0.332508i
$190$	4.19826			0.304574
$191$	6.13674			0.444039			0.222020	−	0.975042i	$-0.428735\pi$
$191$	6.13674			0.444039			0.222020	+	0.975042i	$0.428735\pi$
$192$	8.56525	−	10.4041i	0.618144	−	0.750849i
$193$	1.72899			0.124455			0.0622276	−	0.998062i	$-0.480180\pi$
$193$	1.72899			0.124455			0.0622276	+	0.998062i	$0.480180\pi$
$194$	−16.8437			−1.20930
$195$	21.5965	−	26.2330i	1.54656	−	1.87858i
$196$	−0.872554			−0.0623253
$197$		−	4.83401i		−	0.344409i	−0.985061	−	0.172205i	$-0.944911\pi$
$197$		−	4.83401i		−	0.344409i	0.985061	−	0.172205i	$-0.0550890\pi$
$198$	−7.53821	+	1.47532i	−0.535717	+	0.104846i
$199$			6.15345i			0.436207i	0.975926	+	0.218103i	$0.0699870\pi$
$199$			6.15345i			0.436207i	−0.975926	+	0.218103i	$0.930013\pi$
$200$		−	38.8660i		−	2.74824i
$201$	6.12592	+	5.04322i	0.432089	+	0.355722i
$202$	8.84593			0.622398
$203$	−2.21989			−0.155806
$204$	−3.25227	+	3.95048i	−0.227705	+	0.276589i
$205$		−	30.2013i		−	2.10935i
$206$	15.5117			1.08075
$207$	−3.15849	−	14.0365i	−0.219530	−	0.975606i
$208$	−6.95603			−0.482314
$209$		−	2.26348i		−	0.156568i
$210$	4.92366	−	5.98069i	0.339765	−	0.412707i
$211$	−19.1885			−1.32099			−0.660494	−	0.750831i	$-0.729653\pi$
$211$	−19.1885			−1.32099			−0.660494	+	0.750831i	$0.729653\pi$
$212$	−2.05757			−0.141314
$213$	−22.1247	−	18.2143i	−1.51596	−	1.24803i
$214$			0.943991i			0.0645299i
$215$			20.6256i			1.40666i
$216$	7.53560	−	13.9428i	0.512733	−	0.948686i
$217$		−	0.993529i		−	0.0674452i
$218$	18.4579			1.25013
$219$	−3.65623	+	4.44116i	−0.247065	+	0.300106i
$220$	−8.86258			−0.597515
$221$	15.7691			1.06074
$222$	−0.153787	+	0.186803i	−0.0103215	+	0.0125374i
$223$	−10.7951			−0.722891			−0.361446	−	0.932393i	$-0.617717\pi$
$223$	−10.7951			−0.722891			−0.361446	+	0.932393i	$0.617717\pi$
$224$	4.51437			0.301629
$225$	−7.34227	−	37.5157i	−0.489484	−	2.50104i
$226$		−	15.3471i		−	1.02087i
$227$	−10.1196			−0.671663			−0.335832	−	0.941922i	$-0.609017\pi$
$227$	−10.1196			−0.671663			−0.335832	+	0.941922i	$0.609017\pi$
$228$	1.09523	+	0.901655i	0.0725331	+	0.0597135i
$229$		−	21.2890i		−	1.40682i	−0.710785	−	0.703410i	$-0.751660\pi$
$229$		−	21.2890i		−	1.40682i	0.710785	−	0.703410i	$-0.248340\pi$
$230$	0.601877	+	21.4411i	0.0396866	+	1.41379i
$231$	−3.22446	−	2.65457i	−0.212154	−	0.174658i
$232$	6.77093			0.444533
$233$		−	10.8140i		−	0.708450i	−0.935160	−	0.354225i	$-0.884745\pi$
$233$		−	10.8140i		−	0.708450i	0.935160	−	0.354225i	$-0.115255\pi$
$234$	−14.5597	+	2.84950i	−0.951795	+	0.186278i
$235$			30.3907i			1.98247i
$236$		−	11.0206i		−	0.717380i
$237$	11.9226	+	9.81538i	0.774455	+	0.637577i
$238$	3.59509			0.233035
$239$			4.92171i			0.318359i	0.987250	+	0.159180i	$0.0508849\pi$
$239$			4.92171i			0.318359i	−0.987250	+	0.159180i	$0.949115\pi$
$240$	−6.92559	+	8.41241i	−0.447045	+	0.543018i
$241$		−	22.9338i		−	1.47730i	−0.674091	−	0.738649i	$-0.735464\pi$
$241$		−	22.9338i		−	1.47730i	0.674091	−	0.738649i	$-0.264536\pi$
$242$			5.50589i			0.353932i
$243$	4.63983	−	14.8819i	0.297645	−	0.954677i
$244$		−	4.32558i		−	0.276917i
$245$	4.21218			0.269106
$246$	−8.38106	+	10.1803i	−0.534357	+	0.649075i
$247$		−	4.37179i		−	0.278170i
$248$			3.03038i			0.192429i
$249$	3.72176	−	4.52076i	0.235857	−	0.286491i
$250$			34.6285i			2.19010i
$251$	−26.6602			−1.68278			−0.841388	−	0.540432i	$-0.818261\pi$
$251$	−26.6602			−1.68278			−0.841388	+	0.540432i	$0.818261\pi$
$252$	2.56893	−	0.502770i	0.161827	−	0.0316715i
$253$	11.5599	−	0.324500i	0.726764	−	0.0204011i
$254$		−	17.2441i		−	1.08199i
$255$	15.7001	−	19.0706i	0.983176	−	1.19425i
$256$	−16.3757			−1.02348
$257$		−	3.13381i		−	0.195482i	−0.995212	−	0.0977409i	$-0.968838\pi$
$257$		−	3.13381i		−	0.195482i	0.995212	−	0.0977409i	$-0.0311616\pi$
$258$	5.72376	−	6.95256i	0.356346	−	0.432847i
$259$	−0.131565			−0.00817504
$260$	−17.1176			−1.06159
$261$	6.53569	−	1.27911i	0.404549	−	0.0791751i
$262$	15.6716			0.968195
$263$	−21.4582			−1.32317			−0.661583	−	0.749872i	$-0.730115\pi$
$263$	−21.4582			−1.32317			−0.661583	+	0.749872i	$0.730115\pi$
$264$	9.83498	+	8.09674i	0.605301	+	0.498320i
$265$	9.93273			0.610163
$266$		−	0.996696i		−	0.0611113i
$267$	−17.1826	+	20.8714i	−1.05156	+	1.27731i
$268$		−	3.99731i		−	0.244174i
$269$			0.978057i			0.0596332i	0.999555	+	0.0298166i	$0.00949233\pi$
$269$			0.978057i			0.0596332i	−0.999555	+	0.0298166i	$0.990508\pi$
$270$	−11.0499	+	20.4450i	−0.672473	+	1.24425i
$271$	13.3107			0.808566			0.404283	−	0.914634i	$-0.367521\pi$
$271$	13.3107			0.808566			0.404283	+	0.914634i	$0.367521\pi$
$272$	−5.05683			−0.306615
$273$	−6.22788	−	5.12717i	−0.376929	−	0.310310i
$274$		−	15.6262i		−	0.944011i
$275$	30.7266			1.85288
$276$	−4.44786	+	5.72274i	−0.267730	+	0.344468i
$277$	18.1224			1.08887			0.544434	−	0.838804i	$-0.316745\pi$
$277$	18.1224			1.08887			0.544434	+	0.838804i	$0.316745\pi$
$278$			6.27551i			0.376380i
$279$	0.572476	+	2.92509i	0.0342733	+	0.175121i
$280$	−12.8476			−0.767793
$281$	−7.33327			−0.437466			−0.218733	−	0.975785i	$-0.570192\pi$
$281$	−7.33327			−0.437466			−0.218733	+	0.975785i	$0.570192\pi$
$282$	8.43362	−	10.2442i	0.502215	−	0.610032i
$283$		−	15.8573i		−	0.942616i	−0.881969	−	0.471308i	$-0.843782\pi$
$283$		−	15.8573i		−	0.942616i	0.881969	−	0.471308i	$-0.156218\pi$
$284$			14.4369i			0.856670i
$285$	−5.28711	−	4.35266i	−0.313181	−	0.257829i
$286$		−	11.9249i		−	0.705132i
$287$	−7.16999			−0.423231
$288$	−13.2910	+	2.60120i	−0.783177	+	0.153277i
$289$	−5.53635			−0.325668
$290$	−9.92857			−0.583026
$291$	21.2122	+	17.4631i	1.24348	+	1.02371i
$292$	2.89796			0.169590
$293$	−24.2198			−1.41494			−0.707468	−	0.706745i	$-0.750163\pi$
$293$	−24.2198			−1.41494			−0.707468	+	0.706745i	$0.750163\pi$
$294$	−1.41986	−	1.16891i	−0.0828076	−	0.0681722i
$295$			53.2010i			3.09748i
$296$	0.401288			0.0233244
$297$	11.0229	+	5.95749i	0.639611	+	0.345688i
$298$		−	2.33085i		−	0.135023i
$299$	22.3274	−	0.626755i	1.29122	−	0.0362462i
$300$	−12.2399	+	14.8676i	−0.706672	+	0.858383i
$301$	4.89667			0.282239
$302$			3.64856i			0.209951i
$303$	−11.1402	−	9.17125i	−0.639986	−	0.526875i
$304$			1.40195i			0.0804072i
$305$			20.8813i			1.19566i
$306$	−10.5845	+	2.07151i	−0.605073	+	0.118420i
$307$	22.3941			1.27810			0.639050	−	0.769166i	$-0.279328\pi$
$307$	22.3941			1.27810			0.639050	+	0.769166i	$0.279328\pi$
$308$			2.10404i			0.119889i
$309$	−19.5347	−	16.0821i	−1.11129	−	0.914880i
$310$		−	4.44361i		−	0.252380i
$311$		−	1.33968i		−	0.0759665i	−0.999278	−	0.0379833i	$-0.987907\pi$
$311$		−	1.33968i		−	0.0759665i	0.999278	−	0.0379833i	$-0.0120934\pi$
$312$	18.9958	+	15.6384i	1.07542	+	0.885352i
$313$			0.847678i			0.0479136i	0.999713	+	0.0239568i	$0.00762642\pi$
$313$			0.847678i			0.0479136i	−0.999713	+	0.0239568i	$0.992374\pi$
$314$	17.9811			1.01473
$315$	−12.4013	+	2.42708i	−0.698732	+	0.136750i
$316$		−	7.77977i		−	0.437646i
$317$		−	3.76142i		−	0.211262i	−0.994405	−	0.105631i	$-0.966314\pi$
$317$		−	3.76142i		−	0.211262i	0.994405	−	0.105631i	$-0.0336863\pi$
$318$	−3.34816	−	2.75640i	−0.187755	−	0.154571i
$319$			5.35295i			0.299708i
$320$	32.7728			1.83206
$321$	0.978708	−	1.18882i	0.0546262	−	0.0663535i
$322$	5.09027	−	0.142890i	0.283670	−	0.00796293i
$323$		−	3.17816i		−	0.176838i
$324$	−7.27359	+	2.96045i	−0.404088	+	0.164470i
$325$	59.3469			3.29197
$326$			18.8347i			1.04316i
$327$	−23.2451	−	19.1367i	−1.28545	−	1.05826i
$328$	21.8693			1.20753
$329$	7.21495			0.397773
$330$	−14.4216	−	11.8727i	−0.793880	−	0.653570i
$331$	−13.6441			−0.749949			−0.374974	−	0.927035i	$-0.622349\pi$
$331$	−13.6441			−0.749949			−0.374974	+	0.927035i	$0.622349\pi$
$332$	−2.94990			−0.161897
$333$	0.387346	−	0.0758083i	0.0212264	−	0.00415427i
$334$	−14.8879			−0.814628
$335$			19.2967i			1.05429i
$336$	1.99716	+	1.64418i	0.108954	+	0.0896975i
$337$			4.52592i			0.246543i	0.992373	+	0.123271i	$0.0393385\pi$
$337$			4.52592i			0.246543i	−0.992373	+	0.123271i	$0.960661\pi$
$338$		−	9.22870i		−	0.501975i
$339$	−15.9115	+	19.3274i	−0.864194	+	1.04972i
$340$	−12.4440			−0.674872
$341$	−2.39575			−0.129737
$342$	0.574301	+	2.93442i	0.0310546	+	0.158675i
$343$		−	1.00000i		−	0.0539949i
$344$	−14.9354			−0.805262
$345$	21.4717	−	27.6260i	1.15600	−	1.48733i
$346$	−19.3707			−1.04138
$347$			13.6187i			0.731088i	0.930794	+	0.365544i	$0.119117\pi$
$347$			13.6187i			0.731088i	−0.930794	+	0.365544i	$0.880883\pi$
$348$	−2.59012	−	2.13235i	−0.138845	−	0.114306i
$349$	−6.10419			−0.326750			−0.163375	−	0.986564i	$-0.552238\pi$
$349$	−6.10419			−0.326750			−0.163375	+	0.986564i	$0.552238\pi$
$350$	13.5301			0.723215
$351$	21.2901	+	11.5066i	1.13638	+	0.614176i
$352$		−	10.8857i		−	0.580212i
$353$			13.1948i			0.702287i	0.936322	+	0.351143i	$0.114207\pi$
$353$			13.1948i			0.702287i	−0.936322	+	0.351143i	$0.885793\pi$
$354$	14.7637	−	17.9332i	0.784679	−	0.953137i
$355$		−	69.6927i		−	3.69891i
$356$	13.6191			0.721809
$357$	−4.52749	−	3.72730i	−0.239620	−	0.197270i
$358$	9.30032			0.491537
$359$	−9.60824			−0.507103			−0.253552	−	0.967322i	$-0.581599\pi$
$359$	−9.60824			−0.507103			−0.253552	+	0.967322i	$0.581599\pi$
$360$	37.8253	−	7.40286i	1.99357	−	0.390165i
$361$	18.1189			0.953626
$362$	10.7372			0.564336
$363$	5.70838	−	6.93387i	0.299612	−	0.363934i
$364$			4.06384i			0.213003i
$365$	−13.9897			−0.732253
$366$	5.79472	−	7.03875i	0.302895	−	0.367921i
$367$			26.7281i			1.39519i	0.716491	+	0.697597i	$0.245747\pi$
$367$			26.7281i			1.39519i	−0.716491	+	0.697597i	$0.754253\pi$
$368$	−7.15995	+	0.200988i	−0.373238	+	0.0104772i
$369$	21.1095	−	4.13138i	1.09892	−	0.215071i
$370$	−0.588430			−0.0305910
$371$		−	2.35810i		−	0.122426i
$372$	0.954347	−	1.15923i	0.0494806	−	0.0601032i
$373$			32.3336i			1.67417i	0.547072	+	0.837086i	$0.315743\pi$
$373$			32.3336i			1.67417i	−0.547072	+	0.837086i	$0.684257\pi$
$374$		−	8.66903i		−	0.448265i
$375$	35.9020	−	43.6096i	1.85397	−	2.25199i
$376$	−22.0064			−1.13489
$377$			10.3390i			0.532483i
$378$	4.85379	+	2.62331i	0.249652	+	0.134929i
$379$			21.8282i			1.12124i	0.828073	+	0.560620i	$0.189437\pi$
$379$			21.8282i			1.12124i	−0.828073	+	0.560620i	$0.810563\pi$
$380$			3.44996i			0.176979i
$381$	−17.8783	+	21.7165i	−0.915934	+	1.11257i
$382$		−	6.51607i		−	0.333391i
$383$	−20.2620			−1.03534			−0.517669	−	0.855581i	$-0.673200\pi$
$383$	−20.2620			−1.03534			−0.517669	+	0.855581i	$0.673200\pi$
$384$	1.02605	+	0.844702i	0.0523602	+	0.0431060i
$385$		−	10.1571i		−	0.517652i
$386$		−	1.83586i		−	0.0934428i
$387$	−14.4165	+	2.82148i	−0.732832	+	0.143424i
$388$		−	13.8414i		−	0.702692i
$389$	−9.72100			−0.492874			−0.246437	−	0.969159i	$-0.579260\pi$
$389$	−9.72100			−0.492874			−0.246437	+	0.969159i	$0.579260\pi$
$390$	−27.8545	−	22.9315i	−1.41047	−	1.16118i
$391$	16.2313	−	0.455632i	0.820854	−	0.0230423i
$392$			3.05011i			0.154054i
$393$	−19.7361	−	16.2480i	−0.995556	−	0.819601i
$394$	−5.13282			−0.258587
$395$			37.5562i			1.88966i
$396$	−1.21236	−	6.19459i	−0.0609232	−	0.311290i
$397$	−5.52190			−0.277136			−0.138568	−	0.990353i	$-0.544250\pi$
$397$	−5.52190			−0.277136			−0.138568	+	0.990353i	$0.544250\pi$
$398$	6.53381			0.327510
$399$	−1.03335	+	1.25519i	−0.0517323	+	0.0628383i
$400$	−19.0314			−0.951569
$401$	22.1739			1.10731			0.553657	−	0.832745i	$-0.313232\pi$
$401$	22.1739			1.10731			0.553657	+	0.832745i	$0.313232\pi$
$402$	5.35496	−	6.50458i	0.267081	−	0.324419i
$403$	−4.62727			−0.230501
$404$			7.26923i			0.361658i
$405$	35.1126	−	14.2913i	1.74476	−	0.710142i
$406$			2.35711i			0.116981i
$407$			0.317250i			0.0157255i
$408$	13.8094	+	11.3687i	0.683665	+	0.562834i
$409$	12.7628			0.631080			0.315540	−	0.948912i	$-0.397814\pi$
$409$	12.7628			0.631080			0.315540	+	0.948912i	$0.397814\pi$
$410$	−32.0681			−1.58373
$411$	−16.2008	+	19.6789i	−0.799128	+	0.970688i
$412$			12.7468i			0.627992i
$413$	12.6303			0.621495
$414$	−14.9042	+	3.35372i	−0.732499	+	0.164827i
$415$	14.2404			0.699034
$416$		−	21.0253i		−	1.03085i
$417$	6.50630	−	7.90310i	0.318615	−	0.387016i
$418$	−2.40339			−0.117554
$419$	1.14113			0.0557481			0.0278740	−	0.999611i	$-0.491126\pi$
$419$	1.14113			0.0557481			0.0278740	+	0.999611i	$0.491126\pi$
$420$	4.91468	+	4.04606i	0.239812	+	0.197428i
$421$			6.27537i			0.305843i	0.988238	+	0.152921i	$0.0488681\pi$
$421$			6.27537i			0.305843i	−0.988238	+	0.152921i	$0.951132\pi$
$422$			20.3746i			0.991818i
$423$	−21.2419	+	4.15729i	−1.03281	+	0.202134i
$424$			7.19247i			0.349297i
$425$	43.1434			2.09276
$426$	−19.3402	+	23.4922i	−0.937037	+	1.13820i
$427$	4.95737			0.239904
$428$	−0.775734			−0.0374965
$429$	−12.3634	+	15.0176i	−0.596911	+	0.725058i
$430$	21.9006			1.05614
$431$	−29.7920			−1.43503			−0.717515	−	0.696543i	$-0.754721\pi$
$431$	−29.7920			−1.43503			−0.717515	+	0.696543i	$0.754721\pi$
$432$	−6.82732	−	3.68994i	−0.328480	−	0.177532i
$433$			35.5534i			1.70859i	0.519789	+	0.854294i	$0.326010\pi$
$433$			35.5534i			1.70859i	−0.519789	+	0.854294i	$0.673990\pi$
$434$	−1.05494			−0.0506388
$435$	12.5036	+	10.2937i	0.599502	+	0.493546i
$436$			15.1680i			0.726413i
$437$	−0.126319	−	4.49995i	−0.00604265	−	0.215262i
$438$	4.71568	+	3.88223i	0.225324	+	0.185500i
$439$	13.7037			0.654041			0.327021	−	0.945017i	$-0.393955\pi$
$439$	13.7037			0.654041			0.327021	+	0.945017i	$0.393955\pi$
$440$			30.9802i			1.47692i
$441$	0.576205	+	2.94414i	0.0274383	+	0.140197i
$442$		−	16.7438i		−	0.796421i
$443$		−	3.38733i		−	0.160937i	−0.996757	−	0.0804684i	$-0.974358\pi$
$443$		−	3.38733i		−	0.160937i	0.996757	−	0.0804684i	$-0.0256416\pi$
$444$	−0.153507	−	0.126376i	−0.00728513	−	0.00599755i
$445$	−65.7449			−3.11660
$446$			11.4623i			0.542757i
$447$	−2.41657	+	2.93537i	−0.114300	+	0.138838i
$448$		−	7.78049i		−	0.367594i
$449$		−	12.2829i		−	0.579666i	−0.957077	−	0.289833i	$-0.906400\pi$
$449$		−	12.2829i		−	0.579666i	0.957077	−	0.289833i	$-0.0935997\pi$
$450$	−39.8346	+	7.79611i	−1.87782	+	0.367512i
$451$			17.2894i			0.814125i
$452$	12.6116			0.593201
$453$	3.78274	−	4.59483i	0.177729	−	0.215884i
$454$			10.7451i			0.504295i
$455$		−	19.6178i		−	0.919699i
$456$	3.15184	−	3.82849i	0.147598	−	0.179285i
$457$		−	18.7385i		−	0.876552i	−0.898840	−	0.438276i	$-0.855589\pi$
$457$		−	18.7385i		−	0.876552i	0.898840	−	0.438276i	$-0.144411\pi$
$458$	−22.6050			−1.05626
$459$	15.4773	+	8.36495i	0.722417	+	0.390442i
$460$	−17.6194	+	0.494598i	−0.821511	+	0.0230608i
$461$			19.2845i			0.898167i	0.893490	+	0.449084i	$0.148249\pi$
$461$			19.2845i			0.898167i	−0.893490	+	0.449084i	$0.851751\pi$
$462$	−2.81865	+	3.42377i	−0.131136	+	0.159288i
$463$	−32.2652			−1.49949			−0.749745	−	0.661727i	$-0.769824\pi$
$463$	−32.2652			−1.49949			−0.749745	+	0.661727i	$0.769824\pi$
$464$		−	3.31550i		−	0.153918i
$465$	−4.60703	+	5.59608i	−0.213646	+	0.259512i
$466$	−11.4825			−0.531915
$467$	18.0593			0.835687			0.417843	−	0.908519i	$-0.362786\pi$
$467$	18.0593			0.835687			0.417843	+	0.908519i	$0.362786\pi$
$468$	−2.34160	−	11.9645i	−0.108241	−	0.553061i
$469$	4.58116			0.211538
$470$	32.2692			1.48847
$471$	−22.6446	−	18.6424i	−1.04341	−	0.858997i
$472$	−38.5238			−1.77320
$473$		−	11.8076i		−	0.542914i
$474$	10.4221	−	12.6595i	0.478703	−	0.581472i
$475$		−	11.9610i		−	0.548809i
$476$			2.95430i			0.135410i
$477$	1.35875	+	6.94258i	0.0622127	+	0.317879i
$478$	5.22594			0.239029
$479$	−21.7842			−0.995345			−0.497673	−	0.867365i	$-0.665812\pi$
$479$	−21.7842			−0.995345			−0.497673	+	0.867365i	$0.665812\pi$
$480$	−25.4273	−	20.9333i	−1.16059	−	0.955468i
$481$			0.612751i			0.0279391i
$482$	−24.3514			−1.10918
$483$	−6.55860	−	5.09752i	−0.298427	−	0.231945i
$484$	−4.52452			−0.205660
$485$			66.8183i			3.03406i
$486$	−15.8018	−	4.92663i	−0.716785	−	0.223477i
$487$	−23.2316			−1.05272			−0.526362	−	0.850261i	$-0.676444\pi$
$487$	−23.2316			−1.05272			−0.526362	+	0.850261i	$0.676444\pi$
$488$	−15.1205			−0.684475
$489$	19.5273	−	23.7195i	0.883056	−	1.07263i
$490$		−	4.47255i		−	0.202049i
$491$		−	5.19357i		−	0.234382i	−0.993109	−	0.117191i	$-0.962611\pi$
$491$		−	5.19357i		−	0.234382i	0.993109	−	0.117191i	$-0.0373890\pi$
$492$	−8.36579	−	6.88722i	−0.377159	−	0.310500i
$493$			7.51612i			0.338509i
$494$	−4.64202			−0.208854
$495$	5.85254	+	29.9039i	0.263052	+	1.34408i
$496$	1.48388			0.0666280
$497$	−16.5455			−0.742168
$498$	−4.80020	−	3.95181i	−0.215102	−	0.177085i
$499$	−18.6403			−0.834453			−0.417226	−	0.908803i	$-0.636998\pi$
$499$	−18.6403			−0.834453			−0.417226	+	0.908803i	$0.636998\pi$
$500$	−28.4563			−1.27260
$501$	18.7491	+	15.4354i	0.837649	+	0.689603i
$502$			28.3081i			1.26345i
$503$	9.41798			0.419927			0.209964	−	0.977709i	$-0.432665\pi$
$503$	9.41798			0.419927			0.209964	+	0.977709i	$0.432665\pi$
$504$	−1.75749	−	8.97998i	−0.0782848	−	0.400000i
$505$		−	35.0916i		−	1.56155i
$506$	−0.344558	−	12.2744i	−0.0153175	−	0.545665i
$507$	−9.56810	+	11.6222i	−0.424934	+	0.516161i
$508$	14.1705			0.628715
$509$		−	28.5808i		−	1.26682i	−0.773815	−	0.633411i	$-0.781654\pi$
$509$		−	28.5808i		−	1.26682i	0.773815	−	0.633411i	$-0.218346\pi$
$510$	−20.2494	−	16.6705i	−0.896659	−	0.738183i
$511$			3.32124i			0.146923i
$512$			15.8533i			0.700625i
$513$	2.31909	−	4.29090i	0.102390	−	0.189448i
$514$	−3.32752			−0.146771
$515$		−	61.5343i		−	2.71153i
$516$	5.71333	+	4.70355i	0.251515	+	0.207062i
$517$		−	17.3978i		−	0.765155i
$518$			0.139697i			0.00613794i
$519$	24.3946	+	20.0831i	1.07080	+	0.881550i
$520$			59.8367i			2.62401i
$521$	−9.15694			−0.401173			−0.200586	−	0.979676i	$-0.564285\pi$
$521$	−9.15694			−0.401173			−0.200586	+	0.979676i	$0.564285\pi$
$522$	−1.35818	−	6.93967i	−0.0594458	−	0.303741i
$523$			8.30163i			0.363005i	0.983390	+	0.181502i	$0.0580960\pi$
$523$			8.30163i			0.363005i	−0.983390	+	0.181502i	$0.941904\pi$
$524$			12.8783i			0.562591i
$525$	−17.0392	−	14.0277i	−0.743652	−	0.612219i
$526$			22.7845i			0.993453i
$527$	−3.36389			−0.146533
$528$	3.96471	−	4.81587i	0.172542	−	0.209584i
$529$	22.9638	−	1.29026i	0.998425	−	0.0560981i
$530$		−	10.5467i		−	0.458119i
$531$	−37.1854	+	7.27763i	−1.61371	+	0.315822i
$532$	0.819044			0.0355101
$533$			33.3936i			1.44644i
$534$	22.1615	+	18.2447i	0.959021	+	0.789523i
$535$	3.74479			0.161901
$536$	−13.9731			−0.603544
$537$	−11.7124	−	9.64236i	−0.505428	−	0.416098i
$538$	1.03851			0.0447735
$539$	−2.41135			−0.103864
$540$	−16.8009	−	9.08032i	−0.722996	−	0.390755i
$541$	−19.4892			−0.837906			−0.418953	−	0.908008i	$-0.637603\pi$
$541$	−19.4892			−0.837906			−0.418953	+	0.908008i	$0.637603\pi$
$542$		−	14.1334i		−	0.607084i
$543$	−13.5220	−	11.1321i	−0.580284	−	0.477724i
$544$		−	15.2848i		−	0.655328i
$545$		−	73.2220i		−	3.13649i
$546$	−5.44409	+	6.61285i	−0.232985	+	0.283004i
$547$	27.8924			1.19259			0.596296	−	0.802765i	$-0.296638\pi$
$547$	27.8924			1.19259			0.596296	+	0.802765i	$0.296638\pi$
$548$	12.8409			0.548538
$549$	−14.5952	+	2.85646i	−0.622909	+	0.121911i
$550$		−	32.6259i		−	1.39117i
$551$	2.08376			0.0887710
$552$	20.0045	+	15.5480i	0.851447	+	0.661768i
$553$	8.91608			0.379150
$554$		−	19.2426i		−	0.817538i
$555$	0.741042	+	0.610070i	0.0314555	+	0.0258960i
$556$	−5.15696			−0.218704
$557$	36.4619			1.54494			0.772470	−	0.635052i	$-0.219021\pi$
$557$	36.4619			1.54494			0.772470	+	0.635052i	$0.219021\pi$
$558$	3.10590	−	0.607862i	0.131483	−	0.0257329i
$559$		−	22.8058i		−	0.964582i
$560$			6.29106i			0.265846i
$561$	−8.98784	+	10.9174i	−0.379467	+	0.460932i
$562$			7.78656i			0.328456i
$563$	22.8497			0.962999			0.481500	−	0.876446i	$-0.340092\pi$
$563$	22.8497			0.962999			0.481500	+	0.876446i	$0.340092\pi$
$564$	8.41825	+	6.93041i	0.354472	+	0.291823i
$565$	−60.8815			−2.56130
$566$	−16.8374			−0.707730
$567$	−3.39286	−	8.33598i	−0.142487	−	0.350078i
$568$	50.4657			2.11750
$569$	7.91851			0.331961			0.165981	−	0.986129i	$-0.446921\pi$
$569$	7.91851			0.331961			0.165981	+	0.986129i	$0.446921\pi$
$570$	−4.62171	+	5.61391i	−0.193582	+	0.235141i
$571$		−	24.3118i		−	1.01742i	−0.860938	−	0.508709i	$-0.830123\pi$
$571$		−	24.3118i		−	1.01742i	0.860938	−	0.508709i	$-0.169877\pi$
$572$	9.79936			0.409732
$573$	−6.75571	+	8.20605i	−0.282224	+	0.342813i
$574$			7.61318i			0.317768i
$575$	61.0866	−	1.71477i	2.54749	−	0.0715110i
$576$	4.48316	+	22.9069i	0.186798	+	0.954454i
$577$	−10.8299			−0.450856			−0.225428	−	0.974260i	$-0.572378\pi$
$577$	−10.8299			−0.450856			−0.225428	+	0.974260i	$0.572378\pi$
$578$			5.87857i			0.244516i
$579$	−1.90338	+	2.31200i	−0.0791016	+	0.0960835i
$580$		−	8.15890i		−	0.338780i
$581$		−	3.38077i		−	0.140258i
$582$	18.5426	−	22.5233i	0.768614	−	0.933622i
$583$	−5.68621			−0.235499
$584$		−	10.1302i		−	0.419189i
$585$	11.3039	+	57.7578i	0.467359	+	2.38799i
$586$			25.7169i			1.06236i
$587$			9.60537i			0.396456i	0.980156	+	0.198228i	$0.0635187\pi$
$587$			9.60537i			0.396456i	−0.980156	+	0.198228i	$0.936481\pi$
$588$	0.960562	−	1.16678i	0.0396129	−	0.0481172i
$589$			0.932600i			0.0384271i
$590$	56.4895			2.32564
$591$	6.46404	+	5.32158i	0.265895	+	0.218901i
$592$		−	0.196497i		−	0.00807600i
$593$			18.9856i			0.779644i	0.920890	+	0.389822i	$0.127463\pi$
$593$			18.9856i			0.779644i	−0.920890	+	0.389822i	$0.872537\pi$
$594$	6.32573	−	11.7042i	0.259548	−	0.480229i
$595$		−	14.2616i		−	0.584669i
$596$	1.91540			0.0784578
$597$	−8.22839	−	6.77410i	−0.336766	−	0.277246i
$598$	−0.665496	−	23.7075i	−0.0272142	−	0.969470i
$599$		−	22.0145i		−	0.899486i	−0.893158	−	0.449743i	$-0.851516\pi$
$599$		−	22.0145i		−	0.899486i	0.893158	−	0.449743i	$-0.148484\pi$
$600$	51.9715	+	42.7861i	2.12173	+	1.74673i
$601$	−7.30645			−0.298036			−0.149018	−	0.988834i	$-0.547611\pi$
$601$	−7.30645			−0.298036			−0.149018	+	0.988834i	$0.547611\pi$
$602$		−	5.19934i		−	0.211909i
$603$	−13.4876	+	2.63968i	−0.549257	+	0.107496i
$604$	−2.99824			−0.121997
$605$	21.8417			0.887992
$606$	−9.73815	+	11.8288i	−0.395585	+	0.480511i
$607$	40.9502			1.66212			0.831058	−	0.556186i	$-0.187736\pi$
$607$	40.9502			1.66212			0.831058	+	0.556186i	$0.187736\pi$
$608$	−4.23752			−0.171854
$609$	2.44380	−	2.96844i	0.0990276	−	0.120287i
$610$	22.1721			0.897721
$611$		−	33.6030i		−	1.35943i
$612$	−1.70228	−	8.69787i	−0.0688105	−	0.351591i
$613$		−	32.0724i		−	1.29539i	−0.761898	−	0.647697i	$-0.775732\pi$
$613$		−	32.0724i		−	1.29539i	0.761898	−	0.647697i	$-0.224268\pi$
$614$		−	23.7783i		−	0.959616i
$615$	40.3851	+	33.2474i	1.62849	+	1.34067i
$616$	7.35491			0.296338
$617$	5.42145			0.218259			0.109130	−	0.994028i	$-0.465194\pi$
$617$	5.42145			0.218259			0.109130	+	0.994028i	$0.465194\pi$
$618$	−17.0762	+	20.7422i	−0.686905	+	0.834373i
$619$		−	4.61996i		−	0.185692i	−0.995680	−	0.0928460i	$-0.970404\pi$
$619$		−	4.61996i		−	0.185692i	0.995680	−	0.0928460i	$-0.0295964\pi$
$620$	3.65157			0.146651
$621$	22.2467	+	11.2287i	0.892729	+	0.450594i
$622$	−1.42249			−0.0570368
$623$			15.6083i			0.625332i
$624$	7.65763	−	9.30160i	0.306551	−	0.372362i
$625$	73.6580			2.94632
$626$	0.900075			0.0359742
$627$	3.02672	+	2.49178i	0.120876	+	0.0995119i
$628$			14.7762i			0.589633i
$629$			0.445452i			0.0177614i
$630$	2.57710	+	13.1678i	0.102674	+	0.524619i
$631$		−	5.85698i		−	0.233163i	−0.993181	−	0.116581i	$-0.962806\pi$
$631$		−	5.85698i		−	0.233163i	0.993181	−	0.116581i	$-0.0371936\pi$
$632$	−27.1951			−1.08176
$633$	21.1239	−	25.6588i	0.839598	−	1.01985i
$634$	−3.99392			−0.158619
$635$	−68.4070			−2.71465
$636$	2.26510	−	2.75138i	0.0898170	−	0.109099i
$637$	−4.65741			−0.184533
$638$	5.68383			0.225025
$639$	48.7124	−	9.53361i	1.92703	−	0.377144i
$640$			3.23205i			0.127758i
$641$	−42.2757			−1.66979			−0.834894	−	0.550411i	$-0.814471\pi$
$641$	−42.2757			−1.66979			−0.834894	+	0.550411i	$0.814471\pi$
$642$	−1.26230	−	1.03920i	−0.0498192	−	0.0410141i
$643$		−	33.5648i		−	1.32367i	−0.749650	−	0.661834i	$-0.769778\pi$
$643$		−	33.5648i		−	1.32367i	0.749650	−	0.661834i	$-0.230222\pi$
$644$	0.117421	+	4.18298i	0.00462703	+	0.164832i
$645$	−27.5806	−	22.7060i	−1.08599	−	0.894048i
$646$	−3.37461			−0.132772
$647$		−	22.2496i		−	0.874721i	−0.899286	−	0.437361i	$-0.855913\pi$
$647$		−	22.2496i		−	0.874721i	0.899286	−	0.437361i	$-0.144087\pi$
$648$	10.3486	+	25.4257i	0.406532	+	0.998815i
$649$		−	30.4561i		−	1.19551i
$650$		−	63.0152i		−	2.47166i
$651$	1.32855	+	1.09374i	0.0520699	+	0.0428670i
$652$	−15.4776			−0.606148
$653$			29.9305i			1.17127i	0.810575	+	0.585635i	$0.199155\pi$
$653$			29.9305i			1.17127i	−0.810575	+	0.585635i	$0.800845\pi$
$654$	−20.3196	+	24.6819i	−0.794560	+	0.965139i
$655$		−	62.1688i		−	2.42914i
$656$		−	10.7087i		−	0.418103i
$657$	−1.91371	−	9.77822i	−0.0746611	−	0.381485i
$658$		−	7.66093i		−	0.298654i
$659$	−6.24826			−0.243397			−0.121699	−	0.992567i	$-0.538834\pi$
$659$	−6.24826			−0.243397			−0.121699	+	0.992567i	$0.538834\pi$
$660$	9.75648	−	11.8510i	0.379771	−	0.461301i
$661$			8.33622i			0.324241i	0.986771	+	0.162121i	$0.0518334\pi$
$661$			8.33622i			0.324241i	−0.986771	+	0.162121i	$0.948167\pi$
$662$			14.4875i			0.563073i
$663$	−17.3596	+	21.0864i	−0.674190	+	0.818927i
$664$			10.3117i			0.400172i
$665$	−3.95386			−0.153324
$666$	−0.0804942	−	0.411289i	−0.00311909	−	0.0159371i
$667$	0.298734	+	10.6420i	0.0115670	+	0.412062i
$668$		−	12.2342i		−	0.473357i
$669$	11.8839	−	14.4352i	0.459457	−	0.558095i
$670$	20.4894			0.791576
$671$		−	11.9540i		−	0.461478i
$672$	−4.96970	+	6.03661i	−0.191710	+	0.232867i
$673$	−1.81419			−0.0699319			−0.0349659	−	0.999389i	$-0.511132\pi$
$673$	−1.81419			−0.0699319			−0.0349659	+	0.999389i	$0.511132\pi$
$674$	4.80568			0.185108
$675$	58.2487	+	31.4815i	2.24199	+	1.21172i
$676$	7.58377			0.291683
$677$	−37.5962			−1.44494			−0.722469	−	0.691403i	$-0.756993\pi$
$677$	−37.5962			−1.44494			−0.722469	+	0.691403i	$0.756993\pi$
$678$	20.5221	+	16.8950i	0.788148	+	0.648850i
$679$	15.8631			0.608771
$680$			43.4995i			1.66813i
$681$	11.1403	−	13.5320i	0.426898	−	0.518546i
$682$			2.54384i			0.0974086i
$683$			28.8533i			1.10404i	0.833830	+	0.552021i	$0.186143\pi$
$683$			28.8533i			1.10404i	−0.833830	+	0.552021i	$0.813857\pi$
$684$	−2.41138	+	0.471937i	−0.0922016	+	0.0180450i
$685$	−61.9885			−2.36846
$686$	−1.06181			−0.0405402
$687$	28.4677	+	23.4363i	1.08611	+	0.894151i
$688$			7.31337i			0.278820i
$689$	−10.9826			−0.418405
$690$	−29.3337	−	22.7989i	−1.11671	−	0.867939i
$691$	18.7518			0.713352			0.356676	−	0.934228i	$-0.383910\pi$
$691$	18.7518			0.713352			0.356676	+	0.934228i	$0.383910\pi$
$692$		−	15.9181i		−	0.605114i
$693$	7.09938	−	1.38943i	0.269683	−	0.0527802i
$694$	14.4605			0.548912
$695$	24.8948			0.944312
$696$	−7.45386	+	9.05408i	−0.282538	+	0.343194i
$697$			24.2761i			0.919525i
$698$			6.48151i			0.245329i
$699$	14.4605	+	11.9048i	0.546947	+	0.450279i
$700$			11.1185i			0.420239i
$701$	36.8310			1.39109			0.695543	−	0.718484i	$-0.255164\pi$
$701$	36.8310			1.39109			0.695543	+	0.718484i	$0.255164\pi$
$702$	12.2178	−	22.6061i	0.461132	−	0.853212i
$703$	0.123497			0.00465776
$704$	−18.7615			−0.707102
$705$	−40.6384	−	33.4560i	−1.53053	−	1.26002i
$706$	14.0104			0.527287
$707$	−8.33097			−0.313319
$708$	14.7367	+	12.1322i	0.553841	+	0.455955i
$709$			37.9751i			1.42618i	0.701070	+	0.713092i	$0.252706\pi$
$709$			37.9751i			1.42618i	−0.701070	+	0.713092i	$0.747294\pi$
$710$	−74.0006			−2.77719
$711$	−26.2502	+	5.13749i	−0.984461	+	0.192671i
$712$		−	47.6070i		−	1.78415i
$713$	−4.76292	+	0.133701i	−0.178373	+	0.00500713i
$714$	−3.95769	+	4.80735i	−0.148113	+	0.179910i
$715$	−47.3056			−1.76913
$716$			7.64262i			0.285618i
$717$	−6.58131	−	5.41813i	−0.245784	−	0.202344i
$718$			10.2021i			0.380741i
$719$			51.9119i			1.93599i	0.250976	+	0.967993i	$0.419249\pi$
$719$			51.9119i			1.93599i	−0.250976	+	0.967993i	$0.580751\pi$
$720$	−3.62494	−	18.5218i	−0.135094	−	0.690267i
$721$	−14.6087			−0.544055
$722$		−	19.2389i		−	0.715996i
$723$	30.6671	+	25.2470i	1.14052	+	0.938945i
$724$			8.82341i			0.327920i
$725$			28.2869i			1.05055i
$726$	−7.36247	−	6.06123i	−0.273247	−	0.224953i
$727$			16.9039i			0.626932i	0.949599	+	0.313466i	$0.101490\pi$
$727$			16.9039i			0.626932i	−0.949599	+	0.313466i	$0.898510\pi$
$728$	14.2056			0.526496
$729$	14.7923	+	22.5873i	0.547863	+	0.836568i
$730$			14.8544i			0.549786i
$731$		−	16.5791i		−	0.613202i
$732$	5.78416	+	4.76186i	0.213789	+	0.176004i
$733$			30.1264i			1.11274i	0.830934	+	0.556371i	$0.187807\pi$
$733$			30.1264i			1.11274i	−0.830934	+	0.556371i	$0.812193\pi$
$734$	28.3802			1.04753
$735$	−4.63703	+	5.63253i	−0.171039	+	0.207759i
$736$	−0.607505	−	21.6416i	−0.0223929	−	0.797721i
$737$		−	11.0468i		−	0.406914i
$738$	−4.38675	−	22.4143i	−0.161478	−	0.825082i
$739$	−18.8049			−0.691748			−0.345874	−	0.938281i	$-0.612417\pi$
$739$	−18.8049			−0.691748			−0.345874	+	0.938281i	$0.612417\pi$
$740$		−	0.483548i		−	0.0177756i
$741$	5.84595	+	4.81274i	0.214756	+	0.176800i
$742$	−2.50386			−0.0919195
$743$	−9.28186			−0.340518			−0.170259	−	0.985399i	$-0.554460\pi$
$743$	−9.28186			−0.340518			−0.170259	+	0.985399i	$0.554460\pi$
$744$	−4.05222	−	3.33603i	−0.148562	−	0.122305i
$745$	−9.24642			−0.338763
$746$	34.3322			1.25699
$747$	1.94801	+	9.95346i	0.0712741	+	0.364178i
$748$	7.12385			0.260474
$749$		−	0.889038i		−	0.0324847i
$750$	−46.3052	−	38.1212i	−1.69083	−	1.39199i
$751$			18.4408i			0.672913i	0.941699	+	0.336456i	$0.109228\pi$
$751$			18.4408i			0.672913i	−0.941699	+	0.336456i	$0.890772\pi$
$752$			10.7758i			0.392954i
$753$	29.3492	−	35.6500i	1.06954	−	1.29916i
$754$	10.9780			0.399796
$755$	14.4737			0.526753
$756$	−2.15573	+	3.98865i	−0.0784031	+	0.145066i
$757$			20.7852i			0.755451i	0.925918	+	0.377725i	$0.123294\pi$
$757$			20.7852i			0.755451i	−0.925918	+	0.377725i	$0.876706\pi$
$758$	23.1775			0.841844
$759$	−12.2919	+	15.8151i	−0.446169	+	0.574052i
$760$	12.0597			0.437453
$761$		−	7.64000i		−	0.276950i	−0.990366	−	0.138475i	$-0.955780\pi$
$761$		−	7.64000i		−	0.276950i	0.990366	−	0.138475i	$-0.0442200\pi$
$762$	23.0588	+	18.9834i	0.835334	+	0.687697i
$763$	−17.3834			−0.629321
$764$	5.35464			0.193724
$765$	8.21760	+	41.9882i	0.297108	+	1.51809i
$766$			21.5144i			0.777347i
$767$		−	58.8244i		−	2.12403i
$768$	18.0274	−	21.8976i	0.650508	−	0.790162i
$769$			30.8061i			1.11090i	0.831551	+	0.555448i	$0.187453\pi$
$769$			30.8061i			1.11090i	−0.831551	+	0.555448i	$0.812547\pi$
$770$	−10.7849			−0.388661
$771$	4.19053	+	3.44989i	0.150918	+	0.124245i
$772$	1.50864			0.0542970
$773$	−14.7430			−0.530269			−0.265135	−	0.964211i	$-0.585416\pi$
$773$	−14.7430			−0.530269			−0.265135	+	0.964211i	$0.585416\pi$
$774$	2.99589	+	15.3076i	0.107685	+	0.550221i
$775$	−12.6600			−0.454761
$776$	−48.3843			−1.73690
$777$	0.144835	−	0.175928i	0.00519592	−	0.00631140i
$778$			10.3219i			0.370057i
$779$	6.73028			0.241137
$780$	18.8442	−	22.8897i	0.674729	−	0.819582i
$781$			39.8971i			1.42763i
$782$	−0.483796	−	17.2346i	−0.0173005	−	0.616309i
$783$	−5.48446	+	10.1476i	−0.195999	+	0.362647i
$784$	1.49354			0.0533407
$785$		−	71.3307i		−	2.54590i
$786$	−17.2523	+	20.9561i	−0.615369	+	0.747478i
$787$		−	9.37041i		−	0.334019i	−0.985955	−	0.167009i	$-0.946589\pi$
$787$		−	9.37041i		−	0.334019i	0.985955	−	0.167009i	$-0.0534110\pi$
$788$		−	4.21794i		−	0.150258i
$789$	23.6225	−	28.6938i	0.840982	−	1.02153i
$790$	39.8776			1.41878
$791$			14.4537i			0.513914i
$792$	−21.6539	+	4.23793i	−0.769438	+	0.150588i
$793$		−	23.0885i		−	0.819897i
$794$			5.86322i			0.208078i
$795$	−10.9346	+	13.2820i	−0.387809	+	0.471066i
$796$			5.36922i			0.190307i
$797$	−34.1176			−1.20851			−0.604253	−	0.796792i	$-0.706528\pi$
$797$	−34.1176			−1.20851			−0.604253	+	0.796792i	$0.706528\pi$
$798$	1.33278	+	1.09722i	0.0471799	+	0.0388413i
$799$		−	24.4284i		−	0.864214i
$800$		−	57.5242i		−	2.03379i
$801$	−8.99356	−	45.9530i	−0.317772	−	1.62367i
$802$		−	23.5446i		−	0.831388i
$803$	8.00869			0.282621
$804$	5.34520	+	4.40049i	0.188511	+	0.155193i
$805$	−0.566840	−	20.1930i	−0.0199785	−	0.711708i
$806$			4.91330i			0.173063i
$807$	−1.30786	−	1.07671i	−0.0460388	−	0.0379019i
$808$	25.4104			0.893935
$809$			3.23034i			0.113573i	0.998386	+	0.0567863i	$0.0180854\pi$
$809$			3.23034i			0.113573i	−0.998386	+	0.0567863i	$0.981915\pi$
$810$	−15.1747	−	37.2830i	−0.533185	−	1.30999i
$811$	−22.3696			−0.785504			−0.392752	−	0.919644i	$-0.628477\pi$
$811$	−22.3696			−0.785504			−0.392752	+	0.919644i	$0.628477\pi$
$812$	−1.93698			−0.0679746
$813$	−14.6532	+	17.7990i	−0.513911	+	0.624239i
$814$	0.336859			0.0118069
$815$	74.7166			2.61721
$816$	5.56688	−	6.76199i	0.194880	−	0.236717i
$817$	−4.59638			−0.160807
$818$		−	13.5517i		−	0.473824i
$819$	13.7121	−	2.68362i	0.479139	−	0.0937733i
$820$		−	26.3522i		−	0.920260i
$821$			18.5454i			0.647238i	0.946187	+	0.323619i	$0.104900\pi$
$821$			18.5454i			0.647238i	−0.946187	+	0.323619i	$0.895100\pi$
$822$	20.8953	+	17.2022i	0.728807	+	0.599997i
$823$	25.2642			0.880655			0.440327	−	0.897837i	$-0.354862\pi$
$823$	25.2642			0.880655			0.440327	+	0.897837i	$0.354862\pi$
$824$	44.5581			1.55225
$825$	−33.8257	+	41.0876i	−1.17766	+	1.43049i
$826$		−	13.4110i		−	0.466628i
$827$	−7.96299			−0.276900			−0.138450	−	0.990369i	$-0.544212\pi$
$827$	−7.96299			−0.276900			−0.138450	+	0.990369i	$0.544212\pi$
$828$	−2.75595	−	12.2476i	−0.0957760	−	0.425634i
$829$	31.5051			1.09422			0.547108	−	0.837062i	$-0.315729\pi$
$829$	31.5051			1.09422			0.547108	+	0.837062i	$0.315729\pi$
$830$		−	15.1206i		−	0.524845i
$831$	−19.9502	+	24.2332i	−0.692066	+	0.840641i
$832$	−36.2369			−1.25629
$833$	−3.38580			−0.117311
$834$	−8.39161	−	6.90847i	−0.290578	−	0.239221i
$835$			59.0598i			2.04385i
$836$		−	1.97501i		−	0.0683070i
$837$	−4.54165	−	2.45461i	−0.156982	−	0.0848438i
$838$		−	1.21167i		−	0.0418565i
$839$	−23.2007			−0.800975			−0.400488	−	0.916302i	$-0.631159\pi$
$839$	−23.2007			−0.800975			−0.400488	+	0.916302i	$0.631159\pi$
$840$	14.1435	−	17.1798i	0.487996	−	0.592761i
$841$	24.0721			0.830072
$842$	6.66326			0.229631
$843$	8.07292	−	9.80605i	0.278046	−	0.337738i
$844$	−16.7430			−0.576317
$845$	−36.6100			−1.25942
$846$	4.41426	+	22.5549i	0.151765	+	0.775453i
$847$		−	5.18537i		−	0.178171i
$848$	3.52192			0.120943
$849$	21.2043	+	17.4567i	0.727730	+	0.599111i
$850$		−	45.8102i		−	1.57128i
$851$	0.0177049	+	0.630714i	0.000606916	+	0.0216206i
$852$	−19.3050	−	15.8930i	−0.661377	−	0.544485i
$853$	−4.83860			−0.165670			−0.0828352	−	0.996563i	$-0.526398\pi$
$853$	−4.83860			−0.165670			−0.0828352	+	0.996563i	$0.526398\pi$
$854$		−	5.26380i		−	0.180124i
$855$	11.6407	−	2.27824i	0.398105	−	0.0779140i
$856$			2.71167i			0.0926828i
$857$		−	25.9350i		−	0.885924i	−0.896540	−	0.442962i	$-0.853928\pi$
$857$		−	25.9350i		−	0.885924i	0.896540	−	0.442962i	$-0.146072\pi$
$858$	15.9459	+	13.1276i	0.544385	+	0.448170i
$859$	14.9022			0.508456			0.254228	−	0.967144i	$-0.418179\pi$
$859$	14.9022			0.508456			0.254228	+	0.967144i	$0.418179\pi$
$860$			17.9970i			0.613692i
$861$	7.89317	−	9.58770i	0.268998	−	0.326748i
$862$			31.6335i			1.07744i
$863$			9.23792i			0.314463i	0.987562	+	0.157231i	$0.0502568\pi$
$863$			9.23792i			0.314463i	−0.987562	+	0.157231i	$0.949743\pi$
$864$	11.1532	−	20.6362i	0.379439	−	0.702058i
$865$			76.8430i			2.61274i
$866$	37.7511			1.28283
$867$	6.09476	−	7.40320i	0.206989	−	0.251426i
$868$		−	0.866908i		−	0.0294248i
$869$		−	21.4998i		−	0.729332i
$870$	10.9300	−	13.2765i	0.370561	−	0.450115i
$871$		−	21.3363i		−	0.722954i
$872$	53.0213			1.79553
$873$	−46.7033	+	9.14041i	−1.58067	+	0.309356i
$874$	−4.77810	+	0.134127i	−0.161622	+	0.00453691i
$875$		−	32.6126i		−	1.10251i
$876$	−3.19026	+	3.87516i	−0.107789	+	0.130929i
$877$	−36.9613			−1.24809			−0.624046	−	0.781387i	$-0.714512\pi$
$877$	−36.9613			−1.24809			−0.624046	+	0.781387i	$0.714512\pi$
$878$		−	14.5507i		−	0.491064i
$879$	26.6627	−	32.3867i	0.899310	−	1.09238i
$880$	15.1700			0.511380
$881$	21.1474			0.712474			0.356237	−	0.934396i	$-0.384060\pi$
$881$	21.1474			0.712474			0.356237	+	0.934396i	$0.384060\pi$
$882$	3.12613	−	0.611821i	0.105262	−	0.0206011i
$883$	5.23120			0.176044			0.0880219	−	0.996119i	$-0.471945\pi$
$883$	5.23120			0.176044			0.0880219	+	0.996119i	$0.471945\pi$
$884$	13.7594			0.462777
$885$	−71.1404	−	58.5670i	−2.39136	−	1.96871i
$886$	−3.59671			−0.120834
$887$		−	39.1077i		−	1.31311i	−0.754279	−	0.656554i	$-0.772014\pi$
$887$		−	39.1077i		−	1.31311i	0.754279	−	0.656554i	$-0.227986\pi$
$888$	−0.441763	+	0.536602i	−0.0148246	+	0.0180072i
$889$			16.2403i			0.544682i
$890$			69.8087i			2.33999i
$891$	−20.1010	+	8.18139i	−0.673409	+	0.274087i
$892$	−9.41928			−0.315381
$893$	−6.77249			−0.226633
$894$	3.11681	+	2.56595i	0.104242	+	0.0858181i
$895$		−	36.8941i		−	1.23323i
$896$	0.767310			0.0256340
$897$	−23.7412	+	30.5461i	−0.792697	+	1.01990i
$898$	−13.0421			−0.435222
$899$		−	2.20553i		−	0.0735585i
$900$	−6.40652	−	32.7344i	−0.213551	−	1.09115i
$901$	−7.98405			−0.265987
$902$	18.3581			0.611257
$903$	−5.39056	+	6.54782i	−0.179386	+	0.217898i
$904$		−	44.0854i		−	1.46626i
$905$		−	42.5943i		−	1.41588i
$906$	−4.87885	−	4.01656i	−0.162089	−	0.133441i
$907$		−	30.3583i		−	1.00803i	−0.863695	−	0.504016i	$-0.831855\pi$
$907$		−	30.3583i		−	1.00803i	0.863695	−	0.504016i	$-0.168145\pi$
$908$	−8.82992			−0.293031
$909$	24.5276	−	4.80035i	0.813529	−	0.159217i
$910$	−20.8305			−0.690524
$911$	31.1334			1.03149			0.515747	−	0.856741i	$-0.327514\pi$
$911$	31.1334			1.03149			0.515747	+	0.856741i	$0.327514\pi$
$912$	−1.87468	−	1.54335i	−0.0620770	−	0.0511055i
$913$	−8.15223			−0.269799
$914$	−19.8968			−0.658128
$915$	−27.9225	−	22.9875i	−0.923090	−	0.759943i
$916$		−	18.5758i		−	0.613763i
$917$	−14.7593			−0.487395
$918$	8.88201	−	16.4340i	0.293150	−	0.542402i
$919$			30.1426i			0.994313i	0.867661	+	0.497157i	$0.165623\pi$
$919$			30.1426i			0.994313i	−0.867661	+	0.497157i	$0.834377\pi$
$920$	1.72893	+	61.5908i	0.0570010	+	2.03059i
$921$	−24.6528	+	29.9454i	−0.812338	+	0.986734i
$922$	20.4765			0.674357
$923$			77.0593i			2.53644i
$924$	−2.81352	−	2.31626i	−0.0925579	−	0.0761992i
$925$			1.67646i			0.0551217i
$926$			34.2596i			1.12584i
$927$	43.0100	−	8.41758i	1.41263	−	0.276470i
$928$	10.0214			0.328969
$929$		−	24.6754i		−	0.809574i	−0.914411	−	0.404787i	$-0.867346\pi$
$929$		−	24.6754i		−	0.809574i	0.914411	−	0.404787i	$-0.132654\pi$
$930$	5.94199	+	4.89180i	0.194845	+	0.160408i
$931$			0.938674i			0.0307638i
$932$		−	9.43582i		−	0.309081i
$933$	1.79143	+	1.47481i	0.0586486	+	0.0482831i
$934$		−	19.1756i		−	0.627446i
$935$	−34.3898			−1.12467
$936$	−41.8234	+	8.18535i	−1.36704	+	0.267547i
$937$		−	4.53400i		−	0.148119i	−0.997254	−	0.0740596i	$-0.976404\pi$
$937$		−	4.53400i		−	0.148119i	0.997254	−	0.0740596i	$-0.0235955\pi$
$938$		−	4.86433i		−	0.158826i
$939$	−1.13351	−	0.933177i	−0.0369909	−	0.0304531i
$940$			26.5175i			0.864906i
$941$	7.29665			0.237864			0.118932	−	0.992902i	$-0.462053\pi$
$941$	7.29665			0.237864			0.118932	+	0.992902i	$0.462053\pi$
$942$	−19.7948	+	24.0444i	−0.644948	+	0.783408i
$943$	0.964876	+	34.3725i	0.0314207	+	1.11932i
$944$			18.8638i			0.613966i
$945$	10.4066	−	19.2548i	0.338527	−	0.626360i
$946$	−12.5375			−0.407628
$947$		−	51.3703i		−	1.66931i	−0.550772	−	0.834656i	$-0.685667\pi$
$947$		−	51.3703i		−	1.66931i	0.550772	−	0.834656i	$-0.314333\pi$
$948$	10.4031	+	8.56445i	0.337877	+	0.278160i
$949$	15.4684			0.502125
$950$	−12.7004			−0.412054
$951$	5.02977	+	4.14081i	0.163101	+	0.134275i
$952$	10.3271			0.334703
$953$	9.14281			0.296165			0.148082	−	0.988975i	$-0.452690\pi$
$953$	9.14281			0.296165			0.148082	+	0.988975i	$0.452690\pi$
$954$	7.37172	−	1.44273i	0.238668	−	0.0467103i
$955$	−25.8491			−0.836456
$956$			4.29446i			0.138893i
$957$	−7.15796	−	5.89286i	−0.231384	−	0.190489i
$958$			23.1307i			0.747320i
$959$			14.7165i			0.475220i
$960$	−36.0784	+	43.8238i	−1.16442	+	1.41441i
$961$	−30.0129			−0.968158
$962$	0.650627			0.0209771
$963$	0.512268	+	2.61746i	0.0165076	+	0.0843463i
$964$		−	20.0110i		−	0.644511i
$965$	−7.28281			−0.234442
$966$	−5.41261	+	6.96401i	−0.174148	+	0.224063i
$967$	−18.0409			−0.580156			−0.290078	−	0.957003i	$-0.593681\pi$
$967$	−18.0409			−0.580156			−0.290078	+	0.957003i	$0.593681\pi$
$968$			15.8160i			0.508345i
$969$	4.24984	+	3.49872i	0.136525	+	0.112395i
$970$	70.9485			2.27802
$971$	−46.9483			−1.50664			−0.753321	−	0.657653i	$-0.771549\pi$
$971$	−46.9483			−1.50664			−0.753321	+	0.657653i	$0.771549\pi$
$972$	4.04850	−	12.9853i	0.129856	−	0.416503i
$973$		−	5.91018i		−	0.189472i
$974$			24.6676i			0.790400i
$975$	−65.3327	+	79.3586i	−2.09232	+	2.54151i
$976$			7.40404i			0.236997i
$977$	2.04303			0.0653623			0.0326811	−	0.999466i	$-0.489595\pi$
$977$	2.04303			0.0653623			0.0326811	+	0.999466i	$0.489595\pi$
$978$	−25.1857	−	20.7344i	−0.805350	−	0.663012i
$979$	37.6371			1.20289
$980$	3.67536			0.117405
$981$	51.1792	−	10.0164i	1.63403	−	0.319799i
$982$	−5.51459			−0.175978
$983$	9.12267			0.290968			0.145484	−	0.989361i	$-0.453526\pi$
$983$	9.12267			0.290968			0.145484	+	0.989361i	$0.453526\pi$
$984$	−24.0751	+	29.2436i	−0.767485	+	0.932251i
$985$			20.3617i			0.648779i
$986$	7.98071			0.254158
$987$	−7.94267	+	9.64783i	−0.252818	+	0.307094i
$988$		−	3.81462i		−	0.121359i
$989$	−0.658952	−	23.4743i	−0.0209535	−	0.746441i
$990$	31.7523	−	6.21431i	1.00915	−	0.197504i
$991$	30.6737			0.974382			0.487191	−	0.873295i	$-0.338022\pi$
$991$	30.6737			0.974382			0.487191	+	0.873295i	$0.338022\pi$
$992$			4.48516i			0.142404i
$993$	15.0203	−	18.2449i	0.476655	−	0.578985i
$994$			17.5682i			0.557231i
$995$		−	25.9194i		−	0.821702i
$996$	3.24744	−	3.94461i	0.102899	−	0.124990i
$997$	6.95658			0.220317			0.110158	−	0.993914i	$-0.464864\pi$
$997$	6.95658			0.220317			0.110158	+	0.993914i	$0.464864\pi$
$998$			19.7925i			0.626519i
$999$	−0.325044	+	0.601413i	−0.0102839	+	0.0190279i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.e.a.344.15	✓	48
3.2	odd	2	inner	483.2.e.a.344.34	yes	48
23.22	odd	2	inner	483.2.e.a.344.16	yes	48
69.68	even	2	inner	483.2.e.a.344.33	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.e.a.344.15	✓	48	1.1	even	1	trivial
483.2.e.a.344.16	yes	48	23.22	odd	2	inner
483.2.e.a.344.33	yes	48	69.68	even	2	inner
483.2.e.a.344.34	yes	48	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.06181i q^{2} +(-1.10086 + 1.33720i) q^{3} +0.872554 q^{4} -4.21218 q^{5} +(1.41986 + 1.16891i) q^{6} +1.00000i q^{7} -3.05011i q^{8} +(-0.576205 - 2.94414i) q^{9} +O(q^{10})\)	\(q-1.06181i q^{2} +(-1.10086 + 1.33720i) q^{3} +0.872554 q^{4} -4.21218 q^{5} +(1.41986 + 1.16891i) q^{6} +1.00000i q^{7} -3.05011i q^{8} +(-0.576205 - 2.94414i) q^{9} +4.47255i q^{10} +2.41135 q^{11} +(-0.960562 + 1.16678i) q^{12} +4.65741 q^{13} +1.06181 q^{14} +(4.63703 - 5.63253i) q^{15} -1.49354 q^{16} +3.38580 q^{17} +(-3.12613 + 0.611821i) q^{18} -0.938674i q^{19} -3.67536 q^{20} +(-1.33720 - 1.10086i) q^{21} -2.56041i q^{22} +(4.79394 - 0.134572i) q^{23} +(4.07861 + 3.35776i) q^{24} +12.7425 q^{25} -4.94530i q^{26} +(4.57123 + 2.47060i) q^{27} +0.872554i q^{28} +2.21989i q^{29} +(-5.98069 - 4.92366i) q^{30} -0.993529 q^{31} -4.51437i q^{32} +(-2.65457 + 3.22446i) q^{33} -3.59509i q^{34} -4.21218i q^{35} +(-0.502770 - 2.56893i) q^{36} +0.131565i q^{37} -0.996696 q^{38} +(-5.12717 + 6.22788i) q^{39} +12.8476i q^{40} +7.16999i q^{41} +(-1.16891 + 1.41986i) q^{42} -4.89667i q^{43} +2.10404 q^{44} +(2.42708 + 12.4013i) q^{45} +(-0.142890 - 5.09027i) q^{46} -7.21495i q^{47} +(1.64418 - 1.99716i) q^{48} -1.00000 q^{49} -13.5301i q^{50} +(-3.72730 + 4.52749i) q^{51} +4.06384 q^{52} -2.35810 q^{53} +(2.62331 - 4.85379i) q^{54} -10.1571 q^{55} +3.05011 q^{56} +(1.25519 + 1.03335i) q^{57} +2.35711 q^{58} -12.6303i q^{59} +(4.04606 - 4.91468i) q^{60} -4.95737i q^{61} +1.05494i q^{62} +(2.94414 - 0.576205i) q^{63} -7.78049 q^{64} -19.6178 q^{65} +(3.42377 + 2.81865i) q^{66} -4.58116i q^{67} +2.95430 q^{68} +(-5.09752 + 6.55860i) q^{69} -4.47255 q^{70} +16.5455i q^{71} +(-8.97998 + 1.75749i) q^{72} +3.32124 q^{73} +0.139697 q^{74} +(-14.0277 + 17.0392i) q^{75} -0.819044i q^{76} +2.41135i q^{77} +(6.61285 + 5.44409i) q^{78} -8.91608i q^{79} +6.29106 q^{80} +(-8.33598 + 3.39286i) q^{81} +7.61318 q^{82} -3.38077 q^{83} +(-1.16678 - 0.960562i) q^{84} -14.2616 q^{85} -5.19934 q^{86} +(-2.96844 - 2.44380i) q^{87} -7.35491i q^{88} +15.6083 q^{89} +(13.1678 - 2.57710i) q^{90} +4.65741i q^{91} +(4.18298 - 0.117421i) q^{92} +(1.09374 - 1.32855i) q^{93} -7.66093 q^{94} +3.95386i q^{95} +(6.03661 + 4.96970i) q^{96} -15.8631i q^{97} +1.06181i q^{98} +(-1.38943 - 7.09938i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{3} - 40 q^{4} + 6 q^{6} + 4 q^{9}+O(q^{10}) \) 48 * q - 4 * q^3 - 40 * q^4 + 6 * q^6 + 4 * q^9	\( 48 q - 4 q^{3} - 40 q^{4} + 6 q^{6} + 4 q^{9} + 22 q^{12} - 8 q^{13} + 24 q^{16} - 14 q^{18} - 12 q^{24} + 88 q^{25} - 16 q^{27} - 8 q^{31} - 10 q^{36} + 8 q^{46} - 98 q^{48} - 48 q^{49} + 28 q^{52} - 28 q^{54} - 92 q^{58} + 92 q^{64} + 8 q^{69} + 8 q^{70} + 60 q^{72} + 40 q^{73} - 80 q^{75} + 114 q^{78} - 28 q^{81} - 20 q^{82} - 40 q^{85} - 28 q^{87} - 76 q^{93} - 12 q^{94} - 6 q^{96}+O(q^{100}) \) 48 * q - 4 * q^3 - 40 * q^4 + 6 * q^6 + 4 * q^9 + 22 * q^12 - 8 * q^13 + 24 * q^16 - 14 * q^18 - 12 * q^24 + 88 * q^25 - 16 * q^27 - 8 * q^31 - 10 * q^36 + 8 * q^46 - 98 * q^48 - 48 * q^49 + 28 * q^52 - 28 * q^54 - 92 * q^58 + 92 * q^64 + 8 * q^69 + 8 * q^70 + 60 * q^72 + 40 * q^73 - 80 * q^75 + 114 * q^78 - 28 * q^81 - 20 * q^82 - 40 * q^85 - 28 * q^87 - 76 * q^93 - 12 * q^94 - 6 * q^96

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