LMFDB - Embedded newform 483.2.d.d.461.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(461,483)]

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, 1, 0]))

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

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

chi := DirichletCharacter("483.461");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.d (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:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			461.14
Character	$\chi$	$=$	483.461
Dual form			483.2.d.d.461.32

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.77247i q^{2} +(1.65077 + 0.524365i) q^{3} -1.14166 q^{4} +3.73040 q^{5} +(0.929423 - 2.92594i) q^{6} +(-2.02732 + 1.69999i) q^{7} -1.52139i q^{8} +(2.45008 + 1.73121i) q^{9} +O(q^{10})$	\(q-1.77247i q^{2} +(1.65077 + 0.524365i) q^{3} -1.14166 q^{4} +3.73040 q^{5} +(0.929423 - 2.92594i) q^{6} +(-2.02732 + 1.69999i) q^{7} -1.52139i q^{8} +(2.45008 + 1.73121i) q^{9} -6.61202i q^{10} +1.46465i q^{11} +(-1.88461 - 0.598646i) q^{12} -0.721305i q^{13} +(3.01319 + 3.59337i) q^{14} +(6.15803 + 1.95609i) q^{15} -4.97993 q^{16} -4.35922 q^{17} +(3.06853 - 4.34270i) q^{18} -0.368396i q^{19} -4.25884 q^{20} +(-4.23806 + 1.74324i) q^{21} +2.59604 q^{22} +1.00000i q^{23} +(0.797763 - 2.51146i) q^{24} +8.91586 q^{25} -1.27849 q^{26} +(3.13673 + 4.14257i) q^{27} +(2.31451 - 1.94081i) q^{28} +2.64952i q^{29} +(3.46712 - 10.9149i) q^{30} -9.03547i q^{31} +5.78402i q^{32} +(-0.768010 + 2.41779i) q^{33} +7.72659i q^{34} +(-7.56271 + 6.34164i) q^{35} +(-2.79716 - 1.97645i) q^{36} -4.69075 q^{37} -0.652972 q^{38} +(0.378227 - 1.19071i) q^{39} -5.67538i q^{40} -1.09158 q^{41} +(3.08984 + 7.51184i) q^{42} -9.97781 q^{43} -1.67212i q^{44} +(9.13978 + 6.45811i) q^{45} +1.77247 q^{46} +4.98810 q^{47} +(-8.22072 - 2.61130i) q^{48} +(1.22005 - 6.89286i) q^{49} -15.8031i q^{50} +(-7.19606 - 2.28582i) q^{51} +0.823484i q^{52} -10.0930i q^{53} +(7.34259 - 5.55977i) q^{54} +5.46371i q^{55} +(2.58635 + 3.08434i) q^{56} +(0.193174 - 0.608137i) q^{57} +4.69620 q^{58} -7.05443 q^{59} +(-7.03036 - 2.23319i) q^{60} +7.71575i q^{61} -16.0151 q^{62} +(-7.91015 + 0.655397i) q^{63} +0.292145 q^{64} -2.69075i q^{65} +(4.28547 + 1.36128i) q^{66} -3.88582 q^{67} +4.97673 q^{68} +(-0.524365 + 1.65077i) q^{69} +(11.2404 + 13.4047i) q^{70} +12.2778i q^{71} +(2.63385 - 3.72752i) q^{72} -14.1534i q^{73} +8.31423i q^{74} +(14.7180 + 4.67517i) q^{75} +0.420582i q^{76} +(-2.48989 - 2.96931i) q^{77} +(-2.11050 - 0.670398i) q^{78} -9.18209 q^{79} -18.5771 q^{80} +(3.00580 + 8.48323i) q^{81} +1.93480i q^{82} +1.74687 q^{83} +(4.83841 - 1.99018i) q^{84} -16.2616 q^{85} +17.6854i q^{86} +(-1.38931 + 4.37374i) q^{87} +2.22829 q^{88} +11.0784 q^{89} +(11.4468 - 16.2000i) q^{90} +(1.22621 + 1.46232i) q^{91} -1.14166i q^{92} +(4.73789 - 14.9155i) q^{93} -8.84126i q^{94} -1.37426i q^{95} +(-3.03294 + 9.54808i) q^{96} -10.2060i q^{97} +(-12.2174 - 2.16251i) q^{98} +(-2.53561 + 3.58850i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 76 q^{4} - 8 q^{7} + 20 q^{9}+O(q^{10}) $ 44 * q - 76 * q^4 - 8 * q^7 + 20 * q^9	$ 44 q - 76 q^{4} - 8 q^{7} + 20 q^{9} + 4 q^{15} + 92 q^{16} + 4 q^{18} - 22 q^{21} + 12 q^{22} + 16 q^{25} + 16 q^{28} - 32 q^{30} - 112 q^{37} + 4 q^{39} - 12 q^{42} - 68 q^{43} + 4 q^{46} + 44 q^{49} + 32 q^{51} + 16 q^{57} + 28 q^{58} - 44 q^{60} - 10 q^{63} - 16 q^{64} + 108 q^{67} - 60 q^{70} + 112 q^{72} - 48 q^{78} + 40 q^{79} - 4 q^{81} - 26 q^{84} - 108 q^{85} + 8 q^{88} + 24 q^{91} + 4 q^{93} + 4 q^{99}+O(q^{100}) $ 44 * q - 76 * q^4 - 8 * q^7 + 20 * q^9 + 4 * q^15 + 92 * q^16 + 4 * q^18 - 22 * q^21 + 12 * q^22 + 16 * q^25 + 16 * q^28 - 32 * q^30 - 112 * q^37 + 4 * q^39 - 12 * q^42 - 68 * q^43 + 4 * q^46 + 44 * q^49 + 32 * q^51 + 16 * q^57 + 28 * q^58 - 44 * q^60 - 10 * q^63 - 16 * q^64 + 108 * q^67 - 60 * q^70 + 112 * q^72 - 48 * q^78 + 40 * q^79 - 4 * q^81 - 26 * q^84 - 108 * q^85 + 8 * q^88 + 24 * q^91 + 4 * q^93 + 4 * q^99

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 $

$2$		−	1.77247i		−	1.25333i	−0.779290	−	0.626664i	$-0.784420\pi$
$2$		−	1.77247i		−	1.25333i	0.779290	−	0.626664i	$-0.215580\pi$
$3$	1.65077	+	0.524365i	0.953072	+	0.302742i
$3$	1.65077	+	0.524365i	0.953072	+	0.302742i
$4$	−1.14166			−0.570829
$5$	3.73040			1.66828			0.834142	−	0.551550i	$-0.185963\pi$
$5$	3.73040			1.66828			0.834142	+	0.551550i	$0.185963\pi$
$6$	0.929423	−	2.92594i	0.379435	−	1.19451i
$7$	−2.02732	+	1.69999i	−0.766255	+	0.642537i
$7$	−2.02732	+	1.69999i	−0.766255	+	0.642537i
$8$		−	1.52139i		−	0.537892i
$9$	2.45008	+	1.73121i	0.816694	+	0.577071i
$10$		−	6.61202i		−	2.09091i
$11$			1.46465i			0.441607i	0.975318	+	0.220804i	$0.0708680\pi$
$11$			1.46465i			0.441607i	−0.975318	+	0.220804i	$0.929132\pi$
$12$	−1.88461	−	0.598646i	−0.544041	−	0.172814i
$13$		−	0.721305i		−	0.200054i	−0.994985	−	0.100027i	$-0.968107\pi$
$13$		−	0.721305i		−	0.200054i	0.994985	−	0.100027i	$-0.0318929\pi$
$14$	3.01319	+	3.59337i	0.805309	+	0.960368i
$15$	6.15803	+	1.95609i	1.59000	+	0.505060i
$16$	−4.97993			−1.24498
$17$	−4.35922			−1.05727			−0.528633	−	0.848851i	$-0.677295\pi$
$17$	−4.35922			−1.05727			−0.528633	+	0.848851i	$0.677295\pi$
$18$	3.06853	−	4.34270i	0.723259	−	1.02358i
$19$		−	0.368396i		−	0.0845159i	−0.999107	−	0.0422579i	$-0.986545\pi$
$19$		−	0.368396i		−	0.0845159i	0.999107	−	0.0422579i	$-0.0134551\pi$
$20$	−4.25884			−0.952305
$21$	−4.23806	+	1.74324i	−0.924820	+	0.380406i
$22$	2.59604			0.553479
$23$			1.00000i			0.208514i
$23$			1.00000i			0.208514i
$24$	0.797763	−	2.51146i	0.162843	−	0.512650i
$25$	8.91586			1.78317
$26$	−1.27849			−0.250733
$27$	3.13673	+	4.14257i	0.603665	+	0.797238i
$28$	2.31451	−	1.94081i	0.437401	−	0.366778i
$29$			2.64952i			0.492003i	0.969269	+	0.246001i	$0.0791168\pi$
$29$			2.64952i			0.492003i	−0.969269	+	0.246001i	$0.920883\pi$
$30$	3.46712	−	10.9149i	0.633006	−	1.99278i
$31$		−	9.03547i		−	1.62282i	−0.584479	−	0.811409i	$-0.698701\pi$
$31$		−	9.03547i		−	1.62282i	0.584479	−	0.811409i	$-0.301299\pi$
$32$			5.78402i			1.02248i
$33$	−0.768010	+	2.41779i	−0.133693	+	0.420884i
$34$			7.72659i			1.32510i
$35$	−7.56271	+	6.34164i	−1.27833	+	1.07193i
$36$	−2.79716	−	1.97645i	−0.466193	−	0.329409i
$37$	−4.69075			−0.771155			−0.385578	−	0.922675i	$-0.625998\pi$
$37$	−4.69075			−0.771155			−0.385578	+	0.922675i	$0.625998\pi$
$38$	−0.652972			−0.105926
$39$	0.378227	−	1.19071i	0.0605649	−	0.190666i
$40$		−	5.67538i		−	0.897356i
$41$	−1.09158			−0.170476			−0.0852381	−	0.996361i	$-0.527165\pi$
$41$	−1.09158			−0.170476			−0.0852381	+	0.996361i	$0.527165\pi$
$42$	3.08984	+	7.51184i	0.476773	+	1.15910i
$43$	−9.97781			−1.52160			−0.760801	−	0.648986i	$-0.775194\pi$
$43$	−9.97781			−1.52160			−0.760801	+	0.648986i	$0.775194\pi$
$44$		−	1.67212i		−	0.252082i
$45$	9.13978	+	6.45811i	1.36248	+	0.962718i
$46$	1.77247			0.261337
$47$	4.98810			0.727589			0.363794	−	0.931479i	$-0.381481\pi$
$47$	4.98810			0.727589			0.363794	+	0.931479i	$0.381481\pi$
$48$	−8.22072	−	2.61130i	−1.18656	−	0.376909i
$49$	1.22005	−	6.89286i	0.174293	−	0.984694i
$50$		−	15.8031i		−	2.23490i
$51$	−7.19606	−	2.28582i	−1.00765	−	0.320079i
$52$			0.823484i			0.114197i
$53$		−	10.0930i		−	1.38638i	−0.720754	−	0.693190i	$-0.756204\pi$
$53$		−	10.0930i		−	1.38638i	0.720754	−	0.693190i	$-0.243796\pi$
$54$	7.34259	−	5.55977i	0.999201	−	0.756589i
$55$			5.46371i			0.736727i
$56$	2.58635	+	3.08434i	0.345615	+	0.412162i
$57$	0.193174	−	0.608137i	0.0255865	−	0.0805497i
$58$	4.69620			0.616641
$59$	−7.05443			−0.918409			−0.459204	−	0.888331i	$-0.651865\pi$
$59$	−7.05443			−0.918409			−0.459204	+	0.888331i	$0.651865\pi$
$60$	−7.03036	−	2.23319i	−0.907615	−	0.288303i
$61$			7.71575i			0.987901i	0.869490	+	0.493951i	$0.164448\pi$
$61$			7.71575i			0.987901i	−0.869490	+	0.493951i	$0.835552\pi$
$62$	−16.0151			−2.03392
$63$	−7.91015	+	0.655397i	−0.996585	+	0.0825722i
$64$	0.292145			0.0365181
$65$		−	2.69075i		−	0.333747i
$66$	4.28547	+	1.36128i	0.527505	+	0.167561i
$67$	−3.88582			−0.474728			−0.237364	−	0.971421i	$-0.576283\pi$
$67$	−3.88582			−0.474728			−0.237364	+	0.971421i	$0.576283\pi$
$68$	4.97673			0.603518
$69$	−0.524365	+	1.65077i	−0.0631262	+	0.198729i
$70$	11.2404	+	13.4047i	1.34348	+	1.60217i
$71$			12.2778i			1.45711i	0.684989	+	0.728553i	$0.259807\pi$
$71$			12.2778i			1.45711i	−0.684989	+	0.728553i	$0.740193\pi$
$72$	2.63385	−	3.72752i	0.310402	−	0.439293i
$73$		−	14.1534i		−	1.65653i	−0.560339	−	0.828263i	$-0.689329\pi$
$73$		−	14.1534i		−	1.65653i	0.560339	−	0.828263i	$-0.310671\pi$
$74$			8.31423i			0.966510i
$75$	14.7180	+	4.67517i	1.69949	+	0.539842i
$76$			0.420582i			0.0482441i
$77$	−2.48989	−	2.96931i	−0.283749	−	0.338384i
$78$	−2.11050	−	0.670398i	−0.238967	−	0.0759076i
$79$	−9.18209			−1.03307			−0.516533	−	0.856267i	$-0.672778\pi$
$79$	−9.18209			−1.03307			−0.516533	+	0.856267i	$0.672778\pi$
$80$	−18.5771			−2.07699
$81$	3.00580	+	8.48323i	0.333978	+	0.942581i
$82$			1.93480i			0.213663i
$83$	1.74687			0.191744			0.0958718	−	0.995394i	$-0.469436\pi$
$83$	1.74687			0.191744			0.0958718	+	0.995394i	$0.469436\pi$
$84$	4.83841	−	1.99018i	0.527914	−	0.217147i
$85$	−16.2616			−1.76382
$86$			17.6854i			1.90706i
$87$	−1.38931	+	4.37374i	−0.148950	+	0.468914i
$88$	2.22829			0.237537
$89$	11.0784			1.17431			0.587155	−	0.809475i	$-0.300248\pi$
$89$	11.0784			1.17431			0.587155	+	0.809475i	$0.300248\pi$
$90$	11.4468	−	16.2000i	1.20660	−	1.70763i
$91$	1.22621	+	1.46232i	0.128542	+	0.153292i
$92$		−	1.14166i		−	0.119026i
$93$	4.73789	−	14.9155i	0.491296	−	1.54666i
$94$		−	8.84126i		−	0.911907i
$95$		−	1.37426i		−	0.140996i
$96$	−3.03294	+	9.54808i	−0.309548	+	0.974497i
$97$		−	10.2060i		−	1.03626i	−0.855302	−	0.518130i	$-0.826628\pi$
$97$		−	10.2060i		−	1.03626i	0.855302	−	0.518130i	$-0.173372\pi$
$98$	−12.2174	−	2.16251i	−1.23414	−	0.218447i
$99$	−2.53561	+	3.58850i	−0.254839	+	0.360658i
$100$	−10.1789			−1.01789
$101$	12.9543			1.28901			0.644503	−	0.764602i	$-0.277064\pi$
$101$	12.9543			1.28901			0.644503	+	0.764602i	$0.277064\pi$
$102$	−4.05156	+	12.7548i	−0.401164	+	1.26292i
$103$			17.1001i			1.68493i	0.538754	+	0.842463i	$0.318895\pi$
$103$			17.1001i			1.68493i	−0.538754	+	0.842463i	$0.681105\pi$
$104$	−1.09738			−0.107607
$105$	−15.8096	+	6.50297i	−1.54286	+	0.634625i
$106$	−17.8896			−1.73759
$107$			13.6307i			1.31773i	0.752262	+	0.658864i	$0.228963\pi$
$107$			13.6307i			1.31773i	−0.752262	+	0.658864i	$0.771037\pi$
$108$	−3.58108	−	4.72940i	−0.344589	−	0.455087i
$109$	13.3298			1.27676			0.638381	−	0.769721i	$-0.279605\pi$
$109$	13.3298			1.27676			0.638381	+	0.769721i	$0.279605\pi$
$110$	9.68428			0.923359
$111$	−7.74336	−	2.45967i	−0.734967	−	0.233461i
$112$	10.0959	−	8.46585i	0.953975	−	0.799947i
$113$			7.67037i			0.721567i	0.932650	+	0.360784i	$0.117491\pi$
$113$			7.67037i			0.721567i	−0.932650	+	0.360784i	$0.882509\pi$
$114$	−1.07791	−	0.342396i	−0.100955	−	0.0320683i
$115$			3.73040i			0.347861i
$116$		−	3.02484i		−	0.280850i
$117$	1.24873	−	1.76726i	0.115445	−	0.163383i
$118$			12.5038i			1.15107i
$119$	8.83753	−	7.41063i	0.810135	−	0.679332i
$120$	2.97597	−	9.36874i	0.271668	−	0.855245i
$121$	8.85481			0.804983
$122$	13.6760			1.23816
$123$	−1.80195	−	0.572387i	−0.162476	−	0.0516104i
$124$			10.3154i			0.926352i
$125$	14.6077			1.30655
$126$	1.16167	+	14.0205i	0.103490	+	1.24905i
$127$	9.52045			0.844803			0.422402	−	0.906409i	$-0.361187\pi$
$127$	9.52045			0.844803			0.422402	+	0.906409i	$0.361187\pi$
$128$			11.0502i			0.976710i
$129$	−16.4711	−	5.23202i	−1.45020	−	0.460653i
$130$	−4.76929			−0.418294
$131$	15.1798			1.32627			0.663133	−	0.748501i	$-0.269226\pi$
$131$	15.1798			1.32627			0.663133	+	0.748501i	$0.269226\pi$
$132$	0.876804	−	2.76029i	0.0763160	−	0.240253i
$133$	0.626270	+	0.746857i	0.0543045	+	0.0647607i
$134$			6.88750i			0.594990i
$135$	11.7013	+	15.4534i	1.00708	+	1.33002i
$136$			6.63206i			0.568694i
$137$			6.78435i			0.579626i	0.957083	+	0.289813i	$0.0935931\pi$
$137$			6.78435i			0.579626i	−0.957083	+	0.289813i	$0.906407\pi$
$138$	2.92594	+	0.929423i	0.249073	+	0.0791177i
$139$			4.76223i			0.403927i	0.979393	+	0.201964i	$0.0647322\pi$
$139$			4.76223i			0.403927i	−0.979393	+	0.201964i	$0.935268\pi$
$140$	8.63403	−	7.23999i	0.729708	−	0.611891i
$141$	8.23420	+	2.61559i	0.693445	+	0.220272i
$142$	21.7621			1.82623
$143$	1.05646			0.0883454
$144$	−12.2012	−	8.62133i	−1.01677	−	0.718444i
$145$			9.88375i			0.820801i
$146$	−25.0865			−2.07617
$147$	5.62840	−	10.7388i	0.464223	−	0.885718i
$148$	5.35524			0.440198
$149$		−	13.2681i		−	1.08697i	−0.839420	−	0.543484i	$-0.817105\pi$
$149$		−	13.2681i		−	1.08697i	0.839420	−	0.543484i	$-0.182895\pi$
$150$	8.28661	−	26.0873i	0.676598	−	2.13002i
$151$	−23.7288			−1.93102			−0.965512	−	0.260360i	$-0.916159\pi$
$151$	−23.7288			−1.93102			−0.965512	+	0.260360i	$0.916159\pi$
$152$	−0.560473			−0.0454604
$153$	−10.6804	−	7.54673i	−0.863462	−	0.610117i
$154$	−5.26301	+	4.41326i	−0.424106	+	0.355630i
$155$		−	33.7059i		−	2.70732i
$156$	−0.431806	+	1.35938i	−0.0345722	+	0.108838i
$157$			1.91563i			0.152884i	0.997074	+	0.0764420i	$0.0243560\pi$
$157$			1.91563i			0.152884i	−0.997074	+	0.0764420i	$0.975644\pi$
$158$			16.2750i			1.29477i
$159$	5.29242	−	16.6612i	0.419716	−	1.32132i
$160$			21.5767i			1.70579i
$161$	−1.69999	−	2.02732i	−0.133978	−	0.159775i
$162$	15.0363	−	5.32770i	1.18136	−	0.418584i
$163$	3.55406			0.278375			0.139188	−	0.990266i	$-0.455551\pi$
$163$	3.55406			0.278375			0.139188	+	0.990266i	$0.455551\pi$
$164$	1.24621			0.0973128
$165$	−2.86498	+	9.01933i	−0.223038	+	0.702154i
$166$		−	3.09627i		−	0.240317i
$167$	2.54349			0.196821			0.0984105	−	0.995146i	$-0.468624\pi$
$167$	2.54349			0.196821			0.0984105	+	0.995146i	$0.468624\pi$
$168$	2.65214	+	6.44773i	0.204617	+	0.497453i
$169$	12.4797			0.959978
$170$			28.8232i			2.21064i
$171$	0.637772	−	0.902601i	0.0487716	−	0.0690236i
$172$	11.3912			0.868574
$173$	−7.10039			−0.539832			−0.269916	−	0.962884i	$-0.586996\pi$
$173$	−7.10039			−0.539832			−0.269916	+	0.962884i	$0.586996\pi$
$174$	7.75234	+	2.46252i	0.587703	+	0.186683i
$175$	−18.0753	+	15.1569i	−1.36636	+	1.14575i
$176$		−	7.29384i		−	0.549794i
$177$	−11.6452	−	3.69910i	−0.875310	−	0.278041i
$178$		−	19.6362i		−	1.47179i
$179$		−	3.70289i		−	0.276767i	−0.990379	−	0.138384i	$-0.955809\pi$
$179$		−	3.70289i		−	0.276767i	0.990379	−	0.138384i	$-0.0441907\pi$
$180$	−10.4345	−	7.37295i	−0.777742	−	0.549548i
$181$		−	4.00729i		−	0.297859i	−0.988848	−	0.148930i	$-0.952417\pi$
$181$		−	4.00729i		−	0.297859i	0.988848	−	0.148930i	$-0.0475828\pi$
$182$	2.59192	−	2.17343i	0.192126	−	0.161105i
$183$	−4.04587	+	12.7369i	−0.299080	+	0.941541i
$184$	1.52139			0.112158
$185$	−17.4984			−1.28651
$186$	−26.4373	−	8.39777i	−1.93847	−	0.615755i
$187$		−	6.38471i		−	0.466896i
$188$	−5.69470			−0.415329
$189$	−13.4015	−	3.06590i	−0.974816	−	0.223011i
$190$	−2.43584			−0.176715
$191$			8.12959i			0.588236i	0.955769	+	0.294118i	$0.0950259\pi$
$191$			8.12959i			0.588236i	−0.955769	+	0.294118i	$0.904974\pi$
$192$	0.482264	+	0.153191i	0.0348044	+	0.0110556i
$193$	−7.95087			−0.572316			−0.286158	−	0.958182i	$-0.592378\pi$
$193$	−7.95087			−0.572316			−0.286158	+	0.958182i	$0.592378\pi$
$194$	−18.0898			−1.29877
$195$	1.41094	−	4.44182i	0.101039	−	0.318085i
$196$	−1.39288	+	7.86928i	−0.0994917	+	0.562092i
$197$			19.8760i			1.41610i	0.706161	+	0.708051i	$0.250426\pi$
$197$			19.8760i			1.41610i	−0.706161	+	0.708051i	$0.749574\pi$
$198$	6.36052	+	4.49431i	0.452023	+	0.319396i
$199$			4.10541i			0.291025i	0.989356	+	0.145512i	$0.0464830\pi$
$199$			4.10541i			0.291025i	−0.989356	+	0.145512i	$0.953517\pi$
$200$		−	13.5645i		−	0.959153i
$201$	−6.41459	−	2.03759i	−0.452450	−	0.143720i
$202$		−	22.9612i		−	1.61555i
$203$	−4.50416	−	5.37142i	−0.316130	−	0.377000i
$204$	8.21544	+	2.60963i	0.575196	+	0.182710i
$205$	−4.07203			−0.284403
$206$	30.3095			2.11176
$207$	−1.73121	+	2.45008i	−0.120328	+	0.170292i
$208$			3.59205i			0.249064i
$209$	0.539570			0.0373228
$210$	11.5263	+	28.0221i	0.795393	+	1.93371i
$211$	−15.9972			−1.10129			−0.550647	−	0.834738i	$-0.685619\pi$
$211$	−15.9972			−1.10129			−0.550647	+	0.834738i	$0.685619\pi$
$212$			11.5228i			0.791386i
$213$	−6.43805	+	20.2678i	−0.441128	+	1.38873i
$214$	24.1600			1.65154
$215$	−37.2212			−2.53846
$216$	6.30246	−	4.77219i	0.428828	−	0.324706i
$217$	15.3602	+	18.3178i	1.04272	+	1.24349i
$218$		−	23.6267i		−	1.60020i
$219$	7.42154	−	23.3640i	0.501501	−	1.57879i
$220$		−	6.23769i		−	0.420545i
$221$			3.14433i			0.211510i
$222$	−4.35970	+	13.7249i	−0.292604	+	0.921154i
$223$			5.62191i			0.376471i	0.982124	+	0.188235i	$0.0602768\pi$
$223$			5.62191i			0.376471i	−0.982124	+	0.188235i	$0.939723\pi$
$224$	−9.83278	−	11.7261i	−0.656981	−	0.783480i
$225$	21.8446	+	15.4353i	1.45631	+	1.02902i
$226$	13.5955			0.904360
$227$	−6.13431			−0.407148			−0.203574	−	0.979060i	$-0.565256\pi$
$227$	−6.13431			−0.407148			−0.203574	+	0.979060i	$0.565256\pi$
$228$	−0.220539	+	0.694284i	−0.0146055	+	0.0459801i
$229$		−	10.1719i		−	0.672180i	−0.941830	−	0.336090i	$-0.890895\pi$
$229$		−	10.1719i		−	0.672180i	0.941830	−	0.336090i	$-0.109105\pi$
$230$	6.61202			0.435984
$231$	−2.55323	−	6.20725i	−0.167990	−	0.408407i
$232$	4.03094			0.264644
$233$		−	28.1706i		−	1.84552i	−0.385377	−	0.922759i	$-0.625928\pi$
$233$		−	28.1706i		−	1.84552i	0.385377	−	0.922759i	$-0.374072\pi$
$234$	−3.13241	−	2.21334i	−0.204772	−	0.144691i
$235$	18.6076			1.21382
$236$	8.05375			0.524254
$237$	−15.1575	−	4.81477i	−0.984587	−	0.312753i
$238$	−13.1351	−	15.6643i	−0.851425	−	1.01536i
$239$		−	22.5818i		−	1.46070i	−0.683075	−	0.730349i	$-0.739358\pi$
$239$		−	22.5818i		−	1.46070i	0.683075	−	0.730349i	$-0.260642\pi$
$240$	−30.6666	−	9.74120i	−1.97952	−	0.628792i
$241$			15.8266i			1.01948i	0.860328	+	0.509741i	$0.170259\pi$
$241$			15.8266i			1.01948i	−0.860328	+	0.509741i	$0.829741\pi$
$242$		−	15.6949i		−	1.00891i
$243$	0.513577	+	15.5800i	0.0329460	+	0.999457i
$244$		−	8.80875i		−	0.563923i
$245$	4.55128	−	25.7131i	0.290771	−	1.64275i
$246$	−1.01454	+	3.19390i	−0.0646847	+	0.203636i
$247$	−0.265726			−0.0169077
$248$	−13.7465			−0.872900
$249$	2.88367	+	0.915996i	0.182745	+	0.0580489i
$250$		−	25.8918i		−	1.63754i
$251$	26.0692			1.64547			0.822736	−	0.568424i	$-0.192447\pi$
$251$	26.0692			1.64547			0.822736	+	0.568424i	$0.192447\pi$
$252$	9.03068	−	0.748239i	0.568880	−	0.0471346i
$253$	−1.46465			−0.0920815
$254$		−	16.8747i		−	1.05881i
$255$	−26.8442	−	8.52702i	−1.68105	−	0.533983i
$256$	20.1705			1.26066
$257$	−21.0300			−1.31181			−0.655907	−	0.754842i	$-0.727714\pi$
$257$	−21.0300			−1.31181			−0.655907	+	0.754842i	$0.727714\pi$
$258$	−9.27360	+	29.1945i	−0.577349	+	1.81757i
$259$	9.50966	−	7.97425i	0.590902	−	0.495496i
$260$			3.07192i			0.190512i
$261$	−4.58688	+	6.49153i	−0.283921	+	0.401816i
$262$		−	26.9058i		−	1.66225i
$263$		−	25.0166i		−	1.54259i	−0.636479	−	0.771294i	$-0.719610\pi$
$263$		−	25.0166i		−	1.54259i	0.636479	−	0.771294i	$-0.280390\pi$
$264$	3.67840	+	1.16844i	0.226390	+	0.0719125i
$265$		−	37.6509i		−	2.31288i
$266$	1.32378	−	1.11005i	0.0811663	−	0.0680613i
$267$	18.2879	+	5.80914i	1.11920	+	0.355514i
$268$	4.43627			0.270989
$269$	3.94543			0.240557			0.120279	−	0.992740i	$-0.461621\pi$
$269$	3.94543			0.240557			0.120279	+	0.992740i	$0.461621\pi$
$270$	27.3908	−	20.7402i	1.66695	−	1.26221i
$271$			8.24716i			0.500980i	0.968119	+	0.250490i	$0.0805916\pi$
$271$			8.24716i			0.500980i	−0.968119	+	0.250490i	$0.919408\pi$
$272$	21.7086			1.31628
$273$	1.25741	+	3.05693i	0.0761018	+	0.185014i
$274$	12.0251			0.726461
$275$			13.0586i			0.787462i
$276$	0.598646	−	1.88461i	0.0360342	−	0.113440i
$277$	−12.4750			−0.749551			−0.374775	−	0.927116i	$-0.622280\pi$
$277$	−12.4750			−0.749551			−0.374775	+	0.927116i	$0.622280\pi$
$278$	8.44092			0.506253
$279$	15.6423	−	22.1376i	0.936481	−	1.32535i
$280$	9.64810	+	11.5058i	0.576584	+	0.687604i
$281$			11.7666i			0.701937i	0.936387	+	0.350968i	$0.114148\pi$
$281$			11.7666i			0.701937i	−0.936387	+	0.350968i	$0.885852\pi$
$282$	4.63605	−	14.5949i	0.276073	−	0.869113i
$283$		−	23.9527i		−	1.42384i	−0.702259	−	0.711921i	$-0.747825\pi$
$283$		−	23.9527i		−	1.42384i	0.702259	−	0.711921i	$-0.252175\pi$
$284$		−	14.0170i		−	0.831758i
$285$	0.720616	−	2.26859i	0.0426856	−	0.134380i
$286$		−	1.87254i		−	0.110726i
$287$	2.21298	−	1.85568i	0.130628	−	0.109537i
$288$	−10.0134	+	14.1713i	−0.590043	+	0.835053i
$289$	2.00276			0.117809
$290$	17.5187			1.02873
$291$	5.35166	−	16.8477i	0.313720	−	0.987631i
$292$			16.1583i			0.945593i
$293$	22.1705			1.29521			0.647607	−	0.761975i	$-0.275770\pi$
$293$	22.1705			1.29521			0.647607	+	0.761975i	$0.275770\pi$
$294$	−19.0342	−	9.97619i	−1.11009	−	0.581823i
$295$	−26.3158			−1.53217
$296$			7.13646i			0.414798i
$297$	−6.06740	+	4.59420i	−0.352066	+	0.266583i
$298$	−23.5174			−1.36233
$299$	0.721305			0.0417142
$300$	−16.8030	−	5.33744i	−0.970119	−	0.308157i
$301$	20.2282	−	16.9622i	1.16593	−	0.977685i
$302$			42.0587i			2.42020i
$303$	21.3846	+	6.79281i	1.22852	+	0.390237i
$304$			1.83459i			0.105221i
$305$			28.7828i			1.64810i
$306$	−13.3764	+	18.9308i	−0.764676	+	1.08220i
$307$		−	9.89404i		−	0.564683i	−0.959314	−	0.282341i	$-0.908889\pi$
$307$		−	9.89404i		−	0.564683i	0.959314	−	0.282341i	$-0.0911111\pi$
$308$	2.84260	+	3.38993i	0.161972	+	0.193159i
$309$	−8.96672	+	28.2284i	−0.510099	+	1.60586i
$310$	−59.7427			−3.39316
$311$	11.6649			0.661458			0.330729	−	0.943726i	$-0.392705\pi$
$311$	11.6649			0.661458			0.330729	+	0.943726i	$0.392705\pi$
$312$	−1.81153	−	0.575431i	−0.102558	−	0.0325773i
$313$			3.49850i			0.197747i	0.995100	+	0.0988733i	$0.0315239\pi$
$313$			3.49850i			0.197747i	−0.995100	+	0.0988733i	$0.968476\pi$
$314$	3.39540			0.191614
$315$	−29.5080	+	2.44489i	−1.66259	+	0.137754i
$316$	10.4828			0.589704
$317$			2.52012i			0.141544i	0.997493	+	0.0707721i	$0.0225463\pi$
$317$			2.52012i			0.141544i	−0.997493	+	0.0707721i	$0.977454\pi$
$318$	−29.5316	−	9.38067i	−1.65605	−	0.526042i
$319$	−3.88060			−0.217272
$320$	1.08982			0.0609226
$321$	−7.14746	+	22.5011i	−0.398932	+	1.25589i
$322$	−3.59337	+	3.01319i	−0.200251	+	0.167918i
$323$			1.60592i			0.0893557i
$324$	−3.43160	−	9.68494i	−0.190644	−	0.538052i
$325$		−	6.43106i		−	0.356731i
$326$		−	6.29947i		−	0.348895i
$327$	22.0044	+	6.98968i	1.21685	+	0.386530i
$328$			1.66072i			0.0916978i
$329$	−10.1125	+	8.47973i	−0.557518	+	0.467502i
$330$	15.9865	+	5.07810i	0.880028	+	0.279540i
$331$	11.0411			0.606872			0.303436	−	0.952852i	$-0.401866\pi$
$331$	11.0411			0.606872			0.303436	+	0.952852i	$0.401866\pi$
$332$	−1.99432			−0.109453
$333$	−11.4927	−	8.12070i	−0.629798	−	0.445011i
$334$		−	4.50826i		−	0.246681i
$335$	−14.4956			−0.791981
$336$	21.1052	−	8.68121i	1.15138	−	0.473599i
$337$	6.64145			0.361783			0.180891	−	0.983503i	$-0.442102\pi$
$337$	6.64145			0.361783			0.180891	+	0.983503i	$0.442102\pi$
$338$		−	22.1200i		−	1.20317i
$339$	−4.02207	+	12.6620i	−0.218449	+	0.687706i
$340$	18.5652			1.00684
$341$	13.2338			0.716649
$342$	−1.59983	−	1.13043i	−0.0865091	−	0.0611268i
$343$	9.24436	+	16.0481i	0.499149	+	0.866516i
$344$			15.1801i			0.818457i
$345$	−1.95609	+	6.15803i	−0.105312	+	0.331537i
$346$			12.5852i			0.676587i
$347$		−	17.3486i		−	0.931320i	−0.884964	−	0.465660i	$-0.845817\pi$
$347$		−	17.3486i		−	0.931320i	0.884964	−	0.465660i	$-0.154183\pi$
$348$	1.58612	−	4.99332i	0.0850251	−	0.267670i
$349$		−	26.2088i		−	1.40292i	−0.712708	−	0.701461i	$-0.752531\pi$
$349$		−	26.2088i		−	1.40292i	0.712708	−	0.701461i	$-0.247469\pi$
$350$	26.8652	+	32.0380i	1.43600	+	1.71250i
$351$	2.98806	−	2.26254i	0.159491	−	0.120766i
$352$	−8.47154			−0.451535
$353$	8.27830			0.440609			0.220305	−	0.975431i	$-0.429295\pi$
$353$	8.27830			0.440609			0.220305	+	0.975431i	$0.429295\pi$
$354$	−6.55655	+	20.6409i	−0.348477	+	1.09705i
$355$			45.8011i			2.43087i
$356$	−12.6478			−0.670330
$357$	18.4746	−	7.59916i	0.977779	−	0.402190i
$358$	−6.56327			−0.346880
$359$			33.5012i			1.76813i	0.467367	+	0.884063i	$0.345203\pi$
$359$			33.5012i			1.76813i	−0.467367	+	0.884063i	$0.654797\pi$
$360$	9.82529	−	13.9051i	0.517838	−	0.732865i
$361$	18.8643			0.992857
$362$	−7.10281			−0.373315
$363$	14.6173	+	4.64316i	0.767207	+	0.243703i
$364$	−1.39992	−	1.66947i	−0.0733755	−	0.0875038i
$365$		−	52.7977i		−	2.76356i
$366$	22.5759	+	7.17120i	1.18006	+	0.374845i
$367$			10.7489i			0.561089i	0.959841	+	0.280544i	$0.0905150\pi$
$367$			10.7489i			0.561089i	−0.959841	+	0.280544i	$0.909485\pi$
$368$		−	4.97993i		−	0.259597i
$369$	−2.67446	−	1.88976i	−0.139227	−	0.0983769i
$370$			31.0154i			1.61241i
$371$	17.1580	+	20.4618i	0.890801	+	1.06232i
$372$	−5.40905	+	17.0284i	−0.280446	+	0.882880i
$373$	−24.6762			−1.27769			−0.638843	−	0.769337i	$-0.720587\pi$
$373$	−24.6762			−1.27769			−0.638843	+	0.769337i	$0.720587\pi$
$374$	−11.3167			−0.585174
$375$	24.1140	+	7.65978i	1.24524	+	0.395549i
$376$		−	7.58883i		−	0.391364i
$377$	1.91111			0.0984272
$378$	−5.43422	+	23.7538i	−0.279506	+	1.22176i
$379$	−16.3424			−0.839452			−0.419726	−	0.907651i	$-0.637874\pi$
$379$	−16.3424			−0.839452			−0.419726	+	0.907651i	$0.637874\pi$
$380$			1.56894i			0.0804849i
$381$	15.7161	+	4.99219i	0.805159	+	0.255758i
$382$	14.4095			0.737252
$383$	18.6853			0.954775			0.477388	−	0.878693i	$-0.341584\pi$
$383$	18.6853			0.954775			0.477388	+	0.878693i	$0.341584\pi$
$384$	−5.79435	+	18.2414i	−0.295692	+	0.930876i
$385$	−9.28827	−	11.0767i	−0.473374	−	0.564520i
$386$			14.0927i			0.717299i
$387$	−24.4464	−	17.2737i	−1.24268	−	0.878072i
$388$			11.6517i			0.591528i
$389$			20.0791i			1.01805i	0.860751	+	0.509026i	$0.169994\pi$
$389$			20.0791i			1.01805i	−0.860751	+	0.509026i	$0.830006\pi$
$390$	−7.87300	−	2.50085i	−0.398665	−	0.126635i
$391$		−	4.35922i		−	0.220455i
$392$	−10.4867	−	1.85617i	−0.529659	−	0.0937510i
$393$	25.0584	+	7.95977i	1.26403	+	0.401517i
$394$	35.2296			1.77484
$395$	−34.2528			−1.72345
$396$	2.89480	−	4.09684i	0.145469	−	0.205874i
$397$		−	7.32716i		−	0.367740i	−0.982951	−	0.183870i	$-0.941138\pi$
$397$		−	7.32716i		−	0.367740i	0.982951	−	0.183870i	$-0.0588625\pi$
$398$	7.27672			0.364749
$399$	0.642202	+	1.56128i	0.0321503	+	0.0781619i
$400$	−44.4004			−2.22002
$401$		−	18.6003i		−	0.928855i	−0.885611	−	0.464428i	$-0.846260\pi$
$401$		−	18.6003i		−	0.928855i	0.885611	−	0.464428i	$-0.153740\pi$
$402$	−3.61157	+	11.3697i	−0.180129	+	0.567068i
$403$	−6.51733			−0.324651
$404$	−14.7894			−0.735801
$405$	11.2128	+	31.6458i	0.557170	+	1.57249i
$406$	−9.52069	+	7.98349i	−0.472504	+	0.396214i
$407$		−	6.87030i		−	0.340548i
$408$	−3.47762	+	10.9480i	−0.172168	+	0.542007i
$409$		−	22.6848i		−	1.12169i	−0.827921	−	0.560844i	$-0.810477\pi$
$409$		−	22.6848i		−	1.12169i	0.827921	−	0.560844i	$-0.189523\pi$
$410$			7.21756i			0.356450i
$411$	−3.55748	+	11.1994i	−0.175477	+	0.552425i
$412$		−	19.5225i		−	0.961805i
$413$	14.3016	−	11.9925i	0.703735	−	0.590111i
$414$	4.34270	+	3.06853i	0.213432	+	0.150810i
$415$	6.51651			0.319883
$416$	4.17204			0.204551
$417$	−2.49715	+	7.86134i	−0.122286	+	0.384972i
$418$		−	0.956373i		−	0.0467777i
$419$	−0.471187			−0.0230190			−0.0115095	−	0.999934i	$-0.503664\pi$
$419$	−0.471187			−0.0230190			−0.0115095	+	0.999934i	$0.503664\pi$
$420$	18.0492	−	7.42417i	0.880710	−	0.362262i
$421$	4.91173			0.239383			0.119692	−	0.992811i	$-0.461809\pi$
$421$	4.91173			0.239383			0.119692	+	0.992811i	$0.461809\pi$
$422$			28.3546i			1.38028i
$423$	12.2212	+	8.63546i	0.594217	+	0.419870i
$424$	−15.3554			−0.745723
$425$	−38.8662			−1.88529
$426$	35.9241	+	11.4113i	1.74053	+	0.552878i
$427$	−13.1167	−	15.6423i	−0.634763	−	0.756984i
$428$		−	15.5616i		−	0.752197i
$429$	1.74397	+	0.553969i	0.0841995	+	0.0267459i
$430$			65.9735i			3.18152i
$431$			20.4216i			0.983675i	0.870687	+	0.491837i	$0.163675\pi$
$431$			20.4216i			0.983675i	−0.870687	+	0.491837i	$0.836325\pi$
$432$	−15.6207	−	20.6297i	−0.751552	−	0.992548i
$433$		−	11.8655i		−	0.570219i	−0.958495	−	0.285109i	$-0.907970\pi$
$433$		−	11.8655i		−	0.570219i	0.958495	−	0.285109i	$-0.0920299\pi$
$434$	32.4678	−	27.2256i	1.55850	−	1.30687i
$435$	−5.18270	+	16.3158i	−0.248491	+	0.782282i
$436$	−15.2180			−0.728812
$437$	0.368396			0.0176228
$438$	−41.4120	−	13.1545i	−1.97874	−	0.628545i
$439$			7.26940i			0.346950i	0.984838	+	0.173475i	$0.0554995\pi$
$439$			7.26940i			0.346950i	−0.984838	+	0.173475i	$0.944500\pi$
$440$	8.31242			0.396279
$441$	14.9222	−	14.7759i	0.710583	−	0.703614i
$442$	5.57323			0.265091
$443$		−	9.87895i		−	0.469363i	−0.972072	−	0.234682i	$-0.924595\pi$
$443$		−	9.87895i		−	0.469363i	0.972072	−	0.234682i	$-0.0754047\pi$
$444$	8.84026	+	2.80810i	0.419540	+	0.133267i
$445$	41.3269			1.95908
$446$	9.96468			0.471841
$447$	6.95735	−	21.9026i	0.329071	−	1.03596i
$448$	−0.592271	+	0.496644i	−0.0279822	+	0.0234642i
$449$			1.29357i			0.0610474i	0.999534	+	0.0305237i	$0.00971751\pi$
$449$			1.29357i			0.0610474i	−0.999534	+	0.0305237i	$0.990282\pi$
$450$	27.3586	−	38.7189i	1.28969	−	1.82523i
$451$		−	1.59878i		−	0.0752836i
$452$		−	8.75693i		−	0.411891i
$453$	−39.1708	−	12.4426i	−1.84040	−	0.584603i
$454$			10.8729i			0.510290i
$455$	4.57426	+	5.45502i	0.214445	+	0.255735i
$456$	−0.925212	−	0.293893i	−0.0433270	−	0.0137628i
$457$	3.85327			0.180248			0.0901241	−	0.995931i	$-0.471274\pi$
$457$	3.85327			0.180248			0.0901241	+	0.995931i	$0.471274\pi$
$458$	−18.0295			−0.842461
$459$	−13.6737	−	18.0584i	−0.638233	−	0.842892i
$460$		−	4.25884i		−	0.198569i
$461$	−13.5913			−0.633011			−0.316505	−	0.948591i	$-0.602509\pi$
$461$	−13.5913			−0.633011			−0.316505	+	0.948591i	$0.602509\pi$
$462$	−11.0022	+	4.52553i	−0.511868	+	0.210547i
$463$	−18.7344			−0.870660			−0.435330	−	0.900271i	$-0.643368\pi$
$463$	−18.7344			−0.870660			−0.435330	+	0.900271i	$0.643368\pi$
$464$		−	13.1944i		−	0.612535i
$465$	17.6742	−	55.6407i	0.819621	−	2.58027i
$466$	−49.9316			−2.31304
$467$	18.2881			0.846271			0.423135	−	0.906067i	$-0.360929\pi$
$467$	18.2881			0.846271			0.423135	+	0.906067i	$0.360929\pi$
$468$	−1.42563	+	2.01760i	−0.0658996	+	0.0932637i
$469$	7.87779	−	6.60586i	0.363763	−	0.305030i
$470$		−	32.9814i		−	1.52132i
$471$	−1.00449	+	3.16227i	−0.0462845	+	0.145710i
$472$			10.7325i			0.494005i
$473$		−	14.6140i		−	0.671950i
$474$	−8.53405	+	26.8663i	−0.391982	+	1.23401i
$475$		−	3.28457i		−	0.150706i
$476$	−10.0894	+	8.46041i	−0.462448	+	0.387782i
$477$	17.4731	−	24.7287i	0.800040	−	1.13225i
$478$	−40.0257			−1.83073
$479$	24.6378			1.12573			0.562864	−	0.826550i	$-0.309700\pi$
$479$	24.6378			1.12573			0.562864	+	0.826550i	$0.309700\pi$
$480$	−11.3141	+	35.6181i	−0.516414	+	1.62574i
$481$			3.38347i			0.154273i
$482$	28.0522			1.27774
$483$	−1.74324	−	4.23806i	−0.0793201	−	0.192838i
$484$	−10.1092			−0.459508
$485$		−	38.0724i		−	1.72878i
$486$	27.6151	−	0.910302i	1.25265	−	0.0412921i
$487$	−41.9451			−1.90072			−0.950358	−	0.311159i	$-0.899283\pi$
$487$	−41.9451			−1.90072			−0.950358	+	0.311159i	$0.899283\pi$
$488$	11.7387			0.531384
$489$	5.86693	+	1.86363i	0.265312	+	0.0842760i
$490$	−45.5757	−	8.06703i	−2.05890	−	0.364431i
$491$		−	30.1995i		−	1.36288i	−0.731873	−	0.681442i	$-0.761353\pi$
$491$		−	30.1995i		−	1.36288i	0.731873	−	0.681442i	$-0.238647\pi$
$492$	2.05721	+	0.653470i	0.0927461	+	0.0294607i
$493$		−	11.5498i		−	0.520178i
$494$			0.470992i			0.0211909i
$495$	−9.45885	+	13.3865i	−0.425144	+	0.601680i
$496$			44.9960i			2.02038i
$497$	−20.8722	−	24.8910i	−0.936244	−	1.11652i
$498$	1.62358	−	5.11123i	0.0727543	−	0.229040i
$499$	16.7224			0.748597			0.374299	−	0.927308i	$-0.377883\pi$
$499$	16.7224			0.748597			0.374299	+	0.927308i	$0.377883\pi$
$500$	−16.6770			−0.745818
$501$	4.19871	+	1.33372i	0.187585	+	0.0595861i
$502$		−	46.2069i		−	2.06231i
$503$	11.3702			0.506970			0.253485	−	0.967339i	$-0.418423\pi$
$503$	11.3702			0.506970			0.253485	+	0.967339i	$0.418423\pi$
$504$	0.997112	+	12.0344i	0.0444149	+	0.536055i
$505$	48.3248			2.15043
$506$			2.59604i			0.115408i
$507$	20.6011	+	6.54393i	0.914929	+	0.290626i
$508$	−10.8691			−0.482238
$509$	20.0274			0.887697			0.443848	−	0.896102i	$-0.353613\pi$
$509$	20.0274			0.887697			0.443848	+	0.896102i	$0.353613\pi$
$510$	−15.1139	+	47.5805i	−0.669255	+	2.10690i
$511$	24.0606	+	28.6934i	1.06438	+	1.26932i
$512$		−	13.6512i		−	0.603304i
$513$	1.52611	−	1.15556i	0.0673793	−	0.0510192i
$514$			37.2750i			1.64413i
$515$			63.7903i			2.81094i
$516$	18.8043	+	5.97317i	0.827814	+	0.262954i
$517$			7.30580i			0.321309i
$518$	−14.1341	−	16.8556i	−0.621018	−	0.740593i
$519$	−11.7211	−	3.72320i	−0.514499	−	0.163430i
$520$	−4.09368			−0.179520
$521$	−39.5881			−1.73439			−0.867193	−	0.497972i	$-0.834078\pi$
$521$	−39.5881			−1.73439			−0.867193	+	0.497972i	$0.834078\pi$
$522$	11.5061	+	8.13011i	0.503607	+	0.355845i
$523$		−	10.8950i		−	0.476406i	−0.971215	−	0.238203i	$-0.923442\pi$
$523$		−	10.8950i		−	0.476406i	0.971215	−	0.238203i	$-0.0765584\pi$
$524$	−17.3301			−0.757071
$525$	−37.7859	+	15.5425i	−1.64911	+	0.678329i
$526$	−44.3412			−1.93337
$527$			39.3876i			1.71575i
$528$	3.82464	−	12.0404i	0.166446	−	0.523993i
$529$	−1.00000			−0.0434783
$530$	−66.7352			−2.89879
$531$	−17.2839	−	12.2127i	−0.750059	−	0.529987i
$532$	−0.714987	−	0.852655i	−0.0309986	−	0.0369673i
$533$			0.787363i			0.0341045i
$534$	10.2965	−	32.4148i	0.445575	−	1.40273i
$535$			50.8479i			2.19834i
$536$			5.91183i			0.255352i
$537$	1.94167	−	6.11262i	0.0837892	−	0.263779i
$538$		−	6.99317i		−	0.301497i
$539$	10.0956	+	1.78695i	0.434848	+	0.0769693i
$540$	−13.3588	−	17.6425i	−0.574873	−	0.759214i
$541$	−10.7046			−0.460227			−0.230114	−	0.973164i	$-0.573910\pi$
$541$	−10.7046			−0.460227			−0.230114	+	0.973164i	$0.573910\pi$
$542$	14.6179			0.627891
$543$	2.10128	−	6.61511i	0.0901747	−	0.283882i
$544$		−	25.2138i		−	1.08103i
$545$	49.7254			2.13000
$546$	5.41833	−	2.22872i	0.231883	−	0.0953804i
$547$	13.9835			0.597893			0.298947	−	0.954270i	$-0.403365\pi$
$547$	13.9835			0.597893			0.298947	+	0.954270i	$0.403365\pi$
$548$		−	7.74540i		−	0.330867i
$549$	−13.3576	+	18.9042i	−0.570089	+	0.806813i
$550$	23.1460			0.986947
$551$	0.976072			0.0415820
$552$	2.51146	+	0.797763i	0.106895	+	0.0339550i
$553$	18.6150	−	15.6095i	0.791592	−	0.663783i
$554$			22.1116i			0.939433i
$555$	−28.8858	−	9.17554i	−1.22613	−	0.389480i
$556$		−	5.43684i		−	0.230573i
$557$			16.3205i			0.691521i	0.938323	+	0.345761i	$0.112379\pi$
$557$			16.3205i			0.691521i	−0.938323	+	0.345761i	$0.887621\pi$
$558$	−39.2384	−	27.7256i	−1.66109	−	1.17372i
$559$			7.19704i			0.304403i
$560$	37.6618	−	31.5810i	1.59150	−	1.33454i
$561$	3.34792	−	10.5397i	0.141349	−	0.444986i
$562$	20.8560			0.879756
$563$	−1.34491			−0.0566813			−0.0283406	−	0.999598i	$-0.509022\pi$
$563$	−1.34491			−0.0566813			−0.0283406	+	0.999598i	$0.509022\pi$
$564$	−9.40064	−	2.98610i	−0.395838	−	0.125738i
$565$			28.6135i			1.20378i
$566$	−42.4556			−1.78454
$567$	−20.5151	−	12.0884i	−0.861555	−	0.507664i
$568$	18.6793			0.783765
$569$			14.2214i			0.596190i	0.954536	+	0.298095i	$0.0963513\pi$
$569$			14.2214i			0.596190i	−0.954536	+	0.298095i	$0.903649\pi$
$570$	−4.02102	−	1.27727i	−0.168422	−	0.0534990i
$571$	−28.1769			−1.17917			−0.589583	−	0.807707i	$-0.700708\pi$
$571$	−28.1769			−1.17917			−0.589583	+	0.807707i	$0.700708\pi$
$572$	−1.20611			−0.0504301
$573$	−4.26287	+	13.4201i	−0.178084	+	0.560632i
$574$	−3.28914	−	3.92245i	−0.137286	−	0.163720i
$575$			8.91586i			0.371817i
$576$	0.715779	+	0.505765i	0.0298241	+	0.0210736i
$577$		−	3.44148i		−	0.143271i	−0.997431	−	0.0716353i	$-0.977178\pi$
$577$		−	3.44148i		−	0.143271i	0.997431	−	0.0716353i	$-0.0228218\pi$
$578$		−	3.54984i		−	0.147654i
$579$	−13.1250	−	4.16916i	−0.545458	−	0.173264i
$580$		−	11.2839i		−	0.468537i
$581$	−3.54146	+	2.96966i	−0.146924	+	0.123202i
$582$	−29.8621	−	9.48568i	−1.23783	−	0.393194i
$583$	14.7827			0.612236
$584$	−21.5328			−0.891032
$585$	4.65827	−	6.59257i	0.192596	−	0.272569i
$586$		−	39.2966i		−	1.62333i
$587$	−24.2670			−1.00161			−0.500803	−	0.865561i	$-0.666962\pi$
$587$	−24.2670			−1.00161			−0.500803	+	0.865561i	$0.666962\pi$
$588$	−6.42571	+	12.2600i	−0.264992	+	0.505594i
$589$	−3.32863			−0.137154
$590$			46.6441i			1.92031i
$591$	−10.4223	+	32.8106i	−0.428715	+	1.34965i
$592$	23.3596			0.960075
$593$	39.4084			1.61831			0.809155	−	0.587596i	$-0.199926\pi$
$593$	39.4084			1.61831			0.809155	+	0.587596i	$0.199926\pi$
$594$	8.14310	+	10.7543i	0.334115	+	0.441254i
$595$	32.9675	−	27.6446i	1.35153	−	1.13332i
$596$			15.1477i			0.620473i
$597$	−2.15273	+	6.77708i	−0.0881055	+	0.277367i
$598$		−	1.27849i		−	0.0522815i
$599$			17.4159i			0.711594i	0.934563	+	0.355797i	$0.115791\pi$
$599$			17.4159i			0.711594i	−0.934563	+	0.355797i	$0.884209\pi$
$600$	7.11274	−	22.3918i	0.290376	−	0.914143i
$601$			8.09571i			0.330231i	0.986274	+	0.165116i	$0.0527997\pi$
$601$			8.09571i			0.330231i	−0.986274	+	0.165116i	$0.947200\pi$
$602$	−30.0650	−	35.8539i	−1.22536	−	1.46130i
$603$	−9.52057	−	6.72718i	−0.387708	−	0.273952i
$604$	27.0902			1.10228
$605$	33.0320			1.34294
$606$	12.0401	−	37.9037i	0.489094	−	1.53973i
$607$			28.9405i			1.17466i	0.809349	+	0.587329i	$0.199820\pi$
$607$			28.9405i			1.17466i	−0.809349	+	0.587329i	$0.800180\pi$
$608$	2.13081			0.0864157
$609$	−4.61874	−	11.2288i	−0.187161	−	0.455014i
$610$	51.0168			2.06561
$611$		−	3.59794i		−	0.145557i
$612$	12.1934	+	8.61578i	0.492889	+	0.348272i
$613$	−25.3921			−1.02558			−0.512788	−	0.858515i	$-0.671387\pi$
$613$	−25.3921			−1.02558			−0.512788	+	0.858515i	$0.671387\pi$
$614$	−17.5369			−0.707732
$615$	−6.72198	−	2.13523i	−0.271056	−	0.0861008i
$616$	−4.51747	+	3.78808i	−0.182014	+	0.152626i
$617$		−	34.5143i		−	1.38949i	−0.719255	−	0.694746i	$-0.755517\pi$
$617$		−	34.5143i		−	1.38949i	0.719255	−	0.694746i	$-0.244483\pi$
$618$	50.0340	+	15.8933i	2.01266	+	0.639321i
$619$		−	14.4014i		−	0.578840i	−0.957202	−	0.289420i	$-0.906538\pi$
$619$		−	14.4014i		−	0.578840i	0.957202	−	0.289420i	$-0.0934624\pi$
$620$			38.4806i			1.54542i
$621$	−4.14257	+	3.13673i	−0.166236	+	0.125873i
$622$		−	20.6758i		−	0.829024i
$623$	−22.4595	+	18.8332i	−0.899821	+	0.754537i
$624$	−1.88355	+	5.92965i	−0.0754022	+	0.237376i
$625$	9.91325			0.396530
$626$	6.20099			0.247841
$627$	0.890706	+	0.282932i	0.0355714	+	0.0112992i
$628$		−	2.18700i		−	0.0872706i
$629$	20.4480			0.815316
$630$	4.33350	+	52.3021i	0.172651	+	2.08377i
$631$	36.2849			1.44448			0.722240	−	0.691643i	$-0.243113\pi$
$631$	36.2849			1.44448			0.722240	+	0.691643i	$0.243113\pi$
$632$			13.9695i			0.555678i
$633$	−26.4077	−	8.38839i	−1.04961	−	0.333408i
$634$	4.46685			0.177401
$635$	35.5150			1.40937
$636$	−6.04214	+	19.0214i	−0.239586	+	0.754249i
$637$	−4.97185	−	0.880031i	−0.196992	−	0.0348681i
$638$			6.87826i			0.272313i
$639$	−21.2555	+	30.0816i	−0.840854	+	1.19001i
$640$			41.2217i			1.62943i
$641$		−	4.60784i		−	0.181999i	−0.995851	−	0.0909993i	$-0.970994\pi$
$641$		−	4.60784i		−	0.181999i	0.995851	−	0.0909993i	$-0.0290061\pi$
$642$	39.8826	+	12.6687i	1.57404	+	0.499993i
$643$		−	48.3819i		−	1.90800i	−0.299814	−	0.953998i	$-0.596925\pi$
$643$		−	48.3819i		−	1.90800i	0.299814	−	0.953998i	$-0.403075\pi$
$644$	1.94081	+	2.31451i	0.0764786	+	0.0912043i
$645$	−61.4436	−	19.5175i	−2.41934	−	0.768501i
$646$	2.84644			0.111992
$647$	−41.0112			−1.61232			−0.806158	−	0.591701i	$-0.798457\pi$
$647$	−41.0112			−1.61232			−0.806158	+	0.591701i	$0.798457\pi$
$648$	12.9063	−	4.57299i	0.507006	−	0.179644i
$649$		−	10.3322i		−	0.405576i
$650$	−11.3989			−0.447100
$651$	15.7510	+	38.2928i	0.617330	+	1.50081i
$652$	−4.05752			−0.158905
$653$			18.7983i			0.735635i	0.929898	+	0.367818i	$0.119895\pi$
$653$			18.7983i			0.735635i	−0.929898	+	0.367818i	$0.880105\pi$
$654$	12.3890	−	39.0022i	0.484448	−	1.52511i
$655$	56.6267			2.21259
$656$	5.43600			0.212240
$657$	24.5025	−	34.6769i	0.955934	−	1.35288i
$658$	15.0301	+	17.9241i	0.585933	+	0.698753i
$659$			0.705848i			0.0274959i	0.999905	+	0.0137480i	$0.00437625\pi$
$659$			0.705848i			0.0274959i	−0.999905	+	0.0137480i	$0.995624\pi$
$660$	3.27083	−	10.2970i	0.127317	−	0.400810i
$661$			40.1317i			1.56094i	0.625192	+	0.780471i	$0.285021\pi$
$661$			40.1317i			1.56094i	−0.625192	+	0.780471i	$0.714979\pi$
$662$		−	19.5700i		−	0.760609i
$663$	−1.64878	+	5.19056i	−0.0640331	+	0.201585i
$664$		−	2.65766i		−	0.103137i
$665$	2.33624	+	2.78607i	0.0905954	+	0.108039i
$666$	−14.3937	+	20.3706i	−0.557745	+	0.789343i
$667$	−2.64952			−0.102590
$668$	−2.90379			−0.112351
$669$	−2.94793	+	9.28048i	−0.113974	+	0.358804i
$670$			25.6931i			0.992612i
$671$	−11.3008			−0.436264
$672$	−10.0829	−	24.5130i	−0.388957	−	0.945609i
$673$	−40.4264			−1.55832			−0.779162	−	0.626823i	$-0.784355\pi$
$673$	−40.4264			−1.55832			−0.779162	+	0.626823i	$0.784355\pi$
$674$		−	11.7718i		−	0.453432i
$675$	27.9667	+	36.9346i	1.07644	+	1.42161i
$676$	−14.2476			−0.547983
$677$	−2.97373			−0.114290			−0.0571448	−	0.998366i	$-0.518200\pi$
$677$	−2.97373			−0.114290			−0.0571448	+	0.998366i	$0.518200\pi$
$678$	22.4431	+	7.12901i	0.861920	+	0.273788i
$679$	17.3501	+	20.6908i	0.665835	+	0.794040i
$680$			24.7402i			0.948743i
$681$	−10.1263	−	3.21662i	−0.388042	−	0.123261i
$682$		−	23.4565i		−	0.898195i
$683$		−	21.9342i		−	0.839289i	−0.907689	−	0.419644i	$-0.862155\pi$
$683$		−	21.9342i		−	0.839289i	0.907689	−	0.419644i	$-0.137845\pi$
$684$	−0.728117	+	1.03046i	−0.0278403	+	0.0394007i
$685$			25.3083i			0.966981i
$686$	28.4448	−	16.3854i	1.08603	−	0.625596i
$687$	5.33381	−	16.7915i	0.203497	−	0.640636i
$688$	49.6888			1.89437
$689$	−7.28014			−0.277351
$690$	10.9149	+	3.46712i	0.415524	+	0.131991i
$691$		−	30.2315i		−	1.15006i	−0.818132	−	0.575031i	$-0.804990\pi$
$691$		−	30.2315i		−	1.15006i	0.818132	−	0.575031i	$-0.195010\pi$
$692$	8.10621			0.308152
$693$	−0.959924	−	11.5856i	−0.0364645	−	0.440099i
$694$	−30.7499			−1.16725
$695$			17.7650i			0.673865i
$696$	6.65416	+	2.11369i	0.252225	+	0.0801191i
$697$	4.75844			0.180239
$698$	−46.4543			−1.75832
$699$	14.7717	−	46.5032i	0.558717	−	1.75891i
$700$	20.6358	−	17.3040i	0.779960	−	0.654029i
$701$		−	1.73134i		−	0.0653916i	−0.999465	−	0.0326958i	$-0.989591\pi$
$701$		−	1.73134i		−	0.0653916i	0.999465	−	0.0326958i	$-0.0104093\pi$
$702$	−4.01029	−	5.29625i	−0.151359	−	0.199894i
$703$			1.72806i			0.0651748i
$704$			0.427889i			0.0161267i
$705$	30.7168	+	9.75717i	1.15686	+	0.367476i
$706$		−	14.6731i		−	0.552228i
$707$	−26.2626	+	22.0223i	−0.987707	+	0.828233i
$708$	13.2949	+	4.22311i	0.499652	+	0.158714i
$709$	29.5045			1.10807			0.554033	−	0.832495i	$-0.313088\pi$
$709$	29.5045			1.10807			0.554033	+	0.832495i	$0.313088\pi$
$710$	81.1811			3.04667
$711$	−22.4969	−	15.8962i	−0.843699	−	0.596153i
$712$		−	16.8546i		−	0.631652i
$713$	9.03547			0.338381
$714$	−13.4693	−	32.7457i	−0.504076	−	1.22548i
$715$	3.94100			0.147385
$716$			4.22743i			0.157987i
$717$	11.8411	−	37.2774i	0.442215	−	1.39215i
$718$	59.3800			2.21604
$719$	−35.7217			−1.33220			−0.666098	−	0.745864i	$-0.732037\pi$
$719$	−35.7217			−1.33220			−0.666098	+	0.745864i	$0.732037\pi$
$720$	−45.5155	−	32.1610i	−1.69626	−	1.19857i
$721$	−29.0701	−	34.6674i	−1.08263	−	1.29108i
$722$		−	33.4364i		−	1.24437i
$723$	−8.29893	+	26.1261i	−0.308640	+	0.971640i
$724$			4.57495i			0.170027i
$725$			23.6227i			0.877326i
$726$	8.22987	−	25.9087i	0.305439	−	0.961561i
$727$		−	41.5182i		−	1.53983i	−0.638149	−	0.769913i	$-0.720299\pi$
$727$		−	41.5182i		−	1.53983i	0.638149	−	0.769913i	$-0.279701\pi$
$728$	2.22475	−	1.86555i	0.0824547	−	0.0691417i
$729$	−7.32181	+	25.9883i	−0.271178	+	0.962529i
$730$	−93.5824			−3.46364
$731$	43.4954			1.60874
$732$	4.61900	−	14.5412i	0.170723	−	0.537459i
$733$		−	0.944228i		−	0.0348759i	−0.999848	−	0.0174379i	$-0.994449\pi$
$733$		−	0.944228i		−	0.0348759i	0.999848	−	0.0174379i	$-0.00555095\pi$
$734$	19.0522			0.703228
$735$	20.9962	−	40.0599i	0.774456	−	1.47763i
$736$	−5.78402			−0.213202
$737$		−	5.69135i		−	0.209643i
$738$	−3.34954	+	4.74041i	−0.123298	+	0.174497i
$739$	39.9702			1.47033			0.735164	−	0.677889i	$-0.237105\pi$
$739$	39.9702			1.47033			0.735164	+	0.677889i	$0.237105\pi$
$740$	19.9772			0.734375
$741$	−0.438652	−	0.139338i	−0.0161143	−	0.00511869i
$742$	36.2679	−	30.4121i	1.33144	−	1.11646i
$743$		−	40.8692i		−	1.49935i	−0.661808	−	0.749674i	$-0.730210\pi$
$743$		−	40.8692i		−	1.49935i	0.661808	−	0.749674i	$-0.269790\pi$
$744$	−22.6922	−	7.20816i	−0.831937	−	0.264264i
$745$		−	49.4954i		−	1.81337i
$746$			43.7379i			1.60136i
$747$	4.27997	+	3.02420i	0.156596	+	0.110650i
$748$			7.28915i			0.266518i
$749$	−23.1721	−	27.6338i	−0.846689	−	1.00972i
$750$	13.5767	−	42.7413i	0.495752	−	1.56069i
$751$	−0.886061			−0.0323328			−0.0161664	−	0.999869i	$-0.505146\pi$
$751$	−0.886061			−0.0323328			−0.0161664	+	0.999869i	$0.505146\pi$
$752$	−24.8404			−0.905836
$753$	43.0342	+	13.6698i	1.56825	+	0.498154i
$754$		−	3.38739i		−	0.123361i
$755$	−88.5179			−3.22150
$756$	15.2999	+	3.50021i	0.556453	+	0.127301i
$757$	2.72950			0.0992054			0.0496027	−	0.998769i	$-0.484204\pi$
$757$	2.72950			0.0992054			0.0496027	+	0.998769i	$0.484204\pi$
$758$			28.9664i			1.05211i
$759$	−2.41779	−	0.768010i	−0.0877603	−	0.0278770i
$760$	−2.09079			−0.0758408
$761$	13.4104			0.486127			0.243063	−	0.970010i	$-0.421848\pi$
$761$	13.4104			0.486127			0.243063	+	0.970010i	$0.421848\pi$
$762$	8.84852	−	27.8563i	0.320548	−	1.00913i
$763$	−27.0237	+	22.6605i	−0.978325	+	0.820366i
$764$		−	9.28121i		−	0.335782i
$765$	−39.8423	−	28.1523i	−1.44050	−	1.01785i
$766$		−	33.1192i		−	1.19665i
$767$			5.08840i			0.183731i
$768$	33.2968	+	10.5767i	1.20150	+	0.381654i
$769$			52.6106i			1.89719i	0.316500	+	0.948593i	$0.397492\pi$
$769$			52.6106i			1.89719i	−0.316500	+	0.948593i	$0.602508\pi$
$770$	−19.6331	+	16.4632i	−0.707529	+	0.593292i
$771$	−34.7156	−	11.0274i	−1.25025	−	0.397142i
$772$	9.07717			0.326694
$773$	−4.77010			−0.171569			−0.0857843	−	0.996314i	$-0.527340\pi$
$773$	−4.77010			−0.171569			−0.0857843	+	0.996314i	$0.527340\pi$
$774$	−30.6172	+	43.3306i	−1.10051	+	1.55749i
$775$		−	80.5590i		−	2.89376i
$776$	−15.5273			−0.557396
$777$	19.8797	−	8.17711i	0.713180	−	0.293352i
$778$	35.5897			1.27595
$779$			0.402134i			0.0144079i
$780$	−1.61081	+	5.07103i	−0.0576762	+	0.181572i
$781$	−17.9826			−0.643469
$782$	−7.72659			−0.276302
$783$	−10.9758	+	8.31083i	−0.392244	+	0.297005i
$784$	−6.07579	+	34.3260i	−0.216992	+	1.22593i
$785$			7.14606i			0.255054i
$786$	14.1085	−	44.4153i	0.503232	−	1.58424i
$787$			33.1294i			1.18093i	0.807062	+	0.590467i	$0.201056\pi$
$787$			33.1294i			1.18093i	−0.807062	+	0.590467i	$0.798944\pi$
$788$		−	22.6915i		−	0.808352i
$789$	13.1178	−	41.2966i	0.467007	−	1.47020i
$790$			60.7122i			2.16004i
$791$	−13.0396	−	15.5503i	−0.463633	−	0.552905i
$792$	5.45950	+	3.85765i	0.193995	+	0.137076i
$793$	5.56541			0.197634
$794$	−12.9872			−0.460898
$795$	19.7428	−	62.1530i	0.700206	−	2.20434i
$796$		−	4.68697i		−	0.166125i
$797$	−9.85958			−0.349244			−0.174622	−	0.984636i	$-0.555870\pi$
$797$	−9.85958			−0.349244			−0.174622	+	0.984636i	$0.555870\pi$
$798$	2.76733	−	1.13829i	0.0979625	−	0.0402949i
$799$	−21.7442			−0.769254
$800$			51.5695i			1.82326i
$801$	27.1430	+	19.1791i	0.959052	+	0.677660i
$802$	−32.9685			−1.16416
$803$	20.7297			0.731535
$804$	7.32327	+	2.32623i	0.258272	+	0.0820397i
$805$	−6.34164	−	7.56271i	−0.223514	−	0.266550i
$806$			11.5518i			0.406894i
$807$	6.51300	+	2.06885i	0.229268	+	0.0728269i
$808$		−	19.7086i		−	0.693345i
$809$		−	1.51224i		−	0.0531676i	−0.999647	−	0.0265838i	$-0.991537\pi$
$809$		−	1.51224i		−	0.0531676i	0.999647	−	0.0265838i	$-0.00846288\pi$
$810$	56.0913	−	19.8744i	1.97085	−	0.698317i
$811$			55.4084i			1.94565i	0.231539	+	0.972826i	$0.425624\pi$
$811$			55.4084i			1.94565i	−0.231539	+	0.972826i	$0.574376\pi$
$812$	5.14221	+	6.13232i	0.180456	+	0.215202i
$813$	−4.32453	+	13.6142i	−0.151668	+	0.477470i
$814$	−12.1774			−0.426818
$815$	13.2580			0.464409
$816$	35.8359	+	11.3832i	1.25451	+	0.398493i
$817$			3.67578i			0.128599i
$818$	−40.2081			−1.40584
$819$	0.472741	+	5.70563i	0.0165189	+	0.199371i
$820$	4.64886			0.162345
$821$		−	19.4785i		−	0.679803i	−0.940461	−	0.339901i	$-0.889606\pi$
$821$		−	19.4785i		−	0.679803i	0.940461	−	0.339901i	$-0.110394\pi$
$822$	19.8506	+	6.30553i	0.692370	+	0.219931i
$823$	14.4889			0.505053			0.252526	−	0.967590i	$-0.418739\pi$
$823$	14.4889			0.505053			0.252526	+	0.967590i	$0.418739\pi$
$824$	26.0159			0.906308
$825$	−6.84747	+	21.5567i	−0.238398	+	0.750508i
$826$	−21.2563	−	25.3492i	−0.739603	−	0.882011i
$827$			10.3340i			0.359348i	0.983726	+	0.179674i	$0.0575042\pi$
$827$			10.3340i			0.359348i	−0.983726	+	0.179674i	$0.942496\pi$
$828$	1.97645	−	2.79716i	0.0686865	−	0.0972079i
$829$			39.9867i			1.38880i	0.719591	+	0.694399i	$0.244329\pi$
$829$			39.9867i			1.38880i	−0.719591	+	0.694399i	$0.755671\pi$
$830$		−	11.5503i		−	0.400918i
$831$	−20.5934	−	6.54147i	−0.714376	−	0.226921i
$832$		−	0.210726i		−	0.00730560i
$833$	−5.31848	+	30.0474i	−0.184274	+	1.04108i
$834$	13.9340	+	4.42613i	0.482496	+	0.153264i
$835$	9.48821			0.328353
$836$	−0.616004			−0.0213049
$837$	37.4301	−	28.3419i	1.29377	−	0.979638i
$838$			0.835166i			0.0288503i
$839$	−4.22603			−0.145899			−0.0729494	−	0.997336i	$-0.523241\pi$
$839$	−4.22603			−0.145899			−0.0729494	+	0.997336i	$0.523241\pi$
$840$	9.89354	+	24.0526i	0.341360	+	0.829893i
$841$	21.9801			0.757933
$842$		−	8.70591i		−	0.300025i
$843$	−6.17000	+	19.4239i	−0.212506	+	0.668996i
$844$	18.2633			0.628650
$845$	46.5543			1.60152
$846$	15.3061	−	21.6618i	0.526235	−	0.744749i
$847$	−17.9515	+	15.0531i	−0.616822	+	0.517231i
$848$			50.2625i			1.72602i
$849$	12.5600	−	39.5405i	0.431058	−	1.35703i
$850$			68.8892i			2.36288i
$851$		−	4.69075i		−	0.160797i
$852$	7.35005	−	23.1389i	0.251809	−	0.792726i
$853$			5.18694i			0.177597i	0.996050	+	0.0887987i	$0.0283028\pi$
$853$			5.18694i			0.177597i	−0.996050	+	0.0887987i	$0.971697\pi$
$854$	−27.7255	+	23.2490i	−0.948749	+	0.795565i
$855$	2.37914	−	3.36706i	0.0813650	−	0.115151i
$856$	20.7376			0.708795
$857$	9.97426			0.340714			0.170357	−	0.985382i	$-0.445508\pi$
$857$	9.97426			0.340714			0.170357	+	0.985382i	$0.445508\pi$
$858$	0.981895	−	3.09113i	0.0335214	−	0.105530i
$859$		−	20.4004i		−	0.696054i	−0.937485	−	0.348027i	$-0.886852\pi$
$859$		−	20.4004i		−	0.696054i	0.937485	−	0.348027i	$-0.113148\pi$
$860$	42.4939			1.44903
$861$	4.62618	−	1.90289i	0.157660	−	0.0648502i
$862$	36.1968			1.23287
$863$			26.5865i			0.905015i	0.891761	+	0.452507i	$0.149470\pi$
$863$			26.5865i			0.905015i	−0.891761	+	0.452507i	$0.850530\pi$
$864$	−23.9607	+	18.1429i	−0.815160	+	0.617235i
$865$	−26.4873			−0.900594
$866$	−21.0312			−0.714670
$867$	3.30610	+	1.05018i	0.112281	+	0.0356659i
$868$	−17.5361	−	20.9126i	−0.595215	−	0.709821i
$869$		−	13.4485i		−	0.456210i
$870$	28.9193	+	9.18618i	0.980456	+	0.311441i
$871$			2.80286i			0.0949713i
$872$		−	20.2798i		−	0.686759i
$873$	17.6687	−	25.0055i	0.597996	−	0.846308i
$874$		−	0.652972i		−	0.0220871i
$875$	−29.6145	+	24.8330i	−1.00115	+	0.839508i
$876$	−8.47286	+	26.6736i	−0.286271	+	0.901219i
$877$	−6.55898			−0.221481			−0.110741	−	0.993849i	$-0.535322\pi$
$877$	−6.55898			−0.221481			−0.110741	+	0.993849i	$0.535322\pi$
$878$	12.8848			0.434841
$879$	36.5984	+	11.6254i	1.23443	+	0.392116i
$880$		−	27.2089i		−	0.917212i
$881$	−56.1290			−1.89103			−0.945517	−	0.325572i	$-0.894443\pi$
$881$	−56.1290			−1.89103			−0.945517	+	0.325572i	$0.894443\pi$
$882$	−26.1899	−	26.4492i	−0.881858	−	0.890592i
$883$	46.6903			1.57125			0.785627	−	0.618701i	$-0.212341\pi$
$883$	46.6903			1.57125			0.785627	+	0.618701i	$0.212341\pi$
$884$		−	3.58974i		−	0.120736i
$885$	−43.4414	−	13.7991i	−1.46027	−	0.463852i
$886$	−17.5102			−0.588266
$887$	−6.55324			−0.220036			−0.110018	−	0.993930i	$-0.535091\pi$
$887$	−6.55324			−0.220036			−0.110018	+	0.993930i	$0.535091\pi$
$888$	−3.74211	+	11.7806i	−0.125577	+	0.395333i
$889$	−19.3010	+	16.1847i	−0.647335	+	0.542817i
$890$		−	73.2508i		−	2.45537i
$891$	−12.4249	+	4.40244i	−0.416251	+	0.147487i
$892$		−	6.41830i		−	0.214900i
$893$		−	1.83760i		−	0.0614928i
$894$	−38.8218	−	12.3317i	−1.29840	−	0.412434i
$895$		−	13.8133i		−	0.461726i
$896$	−18.7853	−	22.4023i	−0.627572	−	0.748409i
$897$	1.19071	+	0.378227i	0.0397566	+	0.0126286i
$898$	2.29282			0.0765124
$899$	23.9396			0.798431
$900$	−24.9390	−	17.6218i	−0.831301	−	0.587393i
$901$			43.9976i			1.46577i
$902$	−2.83379			−0.0943549
$903$	42.2865	−	17.3937i	1.40721	−	0.578826i
$904$	11.6696			0.388125
$905$		−	14.9488i		−	0.496914i
$906$	−22.0541	+	69.4292i	−0.732699	+	2.30663i
$907$	−24.1619			−0.802282			−0.401141	−	0.916016i	$-0.631386\pi$
$907$	−24.1619			−0.802282			−0.401141	+	0.916016i	$0.631386\pi$
$908$	7.00328			0.232412
$909$	31.7392	+	22.4267i	1.05272	+	0.743848i
$910$	9.66887	−	8.10775i	0.320520	−	0.268769i
$911$			40.3501i			1.33686i	0.743776	+	0.668429i	$0.233033\pi$
$911$			40.3501i			1.33686i	−0.743776	+	0.668429i	$0.766967\pi$
$912$	−0.961994	+	3.02848i	−0.0318548	+	0.100283i
$913$			2.55854i			0.0846754i
$914$		−	6.82981i		−	0.225910i
$915$	−15.0927	+	47.5138i	−0.498950	+	1.57076i
$916$			11.6129i			0.383700i
$917$	−30.7743	+	25.8056i	−1.01626	+	0.852175i
$918$	−32.0080	+	24.2362i	−1.05642	+	0.799915i
$919$	0.135381			0.00446580			0.00223290	−	0.999998i	$-0.499289\pi$
$919$	0.135381			0.00446580			0.00223290	+	0.999998i	$0.499289\pi$
$920$	5.67538			0.187112
$921$	5.18809	−	16.3328i	0.170953	−	0.538183i
$922$			24.0902i			0.793369i
$923$	8.85604			0.291500
$924$	2.91491	+	7.08656i	0.0958936	+	0.233131i
$925$	−41.8221			−1.37510
$926$			33.2061i			1.09122i
$927$	−29.6040	+	41.8967i	−0.972322	+	1.37607i
$928$	−15.3249			−0.503063
$929$	28.3554			0.930310			0.465155	−	0.885229i	$-0.345999\pi$
$929$	28.3554			0.930310			0.465155	+	0.885229i	$0.345999\pi$
$930$	−98.6215	−	31.3270i	−3.23393	−	1.02725i
$931$	−2.53930	−	0.449463i	−0.0832222	−	0.0147306i
$932$			32.1612i			1.05348i
$933$	19.2561	+	6.11669i	0.630418	+	0.200252i
$934$		−	32.4151i		−	1.06065i
$935$		−	23.8175i		−	0.778915i
$936$	−2.68868	−	1.89981i	−0.0878823	−	0.0620971i
$937$		−	5.65684i		−	0.184801i	−0.995722	−	0.0924005i	$-0.970546\pi$
$937$		−	5.65684i		−	0.184801i	0.995722	−	0.0924005i	$-0.0294540\pi$
$938$	−11.7087	−	13.9632i	−0.382303	−	0.455914i
$939$	−1.83449	+	5.77521i	−0.0598663	+	0.188467i
$940$	−21.2435			−0.692886
$941$	32.8816			1.07191			0.535954	−	0.844247i	$-0.319952\pi$
$941$	32.8816			1.07191			0.535954	+	0.844247i	$0.319952\pi$
$942$	5.60503	+	1.78043i	0.182622	+	0.0580096i
$943$		−	1.09158i		−	0.0355468i
$944$	35.1306			1.14340
$945$	−49.9929	−	11.4370i	−1.62627	−	0.372046i
$946$	−25.9028			−0.842174
$947$		−	17.5810i		−	0.571307i	−0.958333	−	0.285654i	$-0.907789\pi$
$947$		−	17.5810i		−	0.571307i	0.958333	−	0.285654i	$-0.0922106\pi$
$948$	17.3047	+	5.49682i	0.562031	+	0.178528i
$949$	−10.2089			−0.331395
$950$	−5.82180			−0.188884
$951$	−1.32146	+	4.16014i	−0.0428514	+	0.134902i
$952$	−11.2744	−	13.4453i	−0.365407	−	0.435765i
$953$		−	15.6588i		−	0.507238i	−0.967304	−	0.253619i	$-0.918379\pi$
$953$		−	15.6588i		−	0.507238i	0.967304	−	0.253619i	$-0.0816209\pi$
$954$	−43.8309	−	30.9707i	−1.41908	−	1.00271i
$955$			30.3266i			0.981345i
$956$			25.7807i			0.833808i
$957$	−6.40598	−	2.03485i	−0.207076	−	0.0657775i
$958$		−	43.6697i		−	1.41091i
$959$	−11.5333	−	13.7540i	−0.372431	−	0.444141i
$960$	1.79904	+	0.571462i	0.0580637	+	0.0184439i
$961$	−50.6397			−1.63354
$962$	5.99710			0.193354
$963$	−23.5976	+	33.3963i	−0.760423	+	1.07618i
$964$		−	18.0686i		−	0.581950i
$965$	−29.6599			−0.954785
$966$	−7.51184	+	3.08984i	−0.241689	+	0.0994141i
$967$	1.31708			0.0423544			0.0211772	−	0.999776i	$-0.493259\pi$
$967$	1.31708			0.0423544			0.0211772	+	0.999776i	$0.493259\pi$
$968$		−	13.4716i		−	0.432994i
$969$	−0.842088	+	2.65100i	−0.0270518	+	0.0851624i
$970$	−67.4822			−2.16672
$971$	−47.8936			−1.53698			−0.768489	−	0.639863i	$-0.778991\pi$
$971$	−47.8936			−1.53698			−0.768489	+	0.639863i	$0.778991\pi$
$972$	−0.586330	−	17.7870i	−0.0188065	−	0.570519i
$973$	−8.09575	−	9.65456i	−0.259538	−	0.309511i
$974$			74.3466i			2.38222i
$975$	3.37222	−	10.6162i	0.107998	−	0.339990i
$976$		−	38.4239i		−	1.22992i
$977$		−	51.4263i		−	1.64527i	−0.568568	−	0.822636i	$-0.692502\pi$
$977$		−	51.4263i		−	1.64527i	0.568568	−	0.822636i	$-0.307498\pi$
$978$	3.30322	−	10.3990i	0.105625	−	0.332523i
$979$			16.2260i			0.518584i
$980$	−5.19601	+	29.3555i	−0.165980	+	0.937729i
$981$	32.6591	+	23.0767i	1.04272	+	0.736782i
$982$	−53.5277			−1.70814
$983$	−1.32253			−0.0421820			−0.0210910	−	0.999778i	$-0.506714\pi$
$983$	−1.32253			−0.0421820			−0.0210910	+	0.999778i	$0.506714\pi$
$984$	−0.870823	+	2.74146i	−0.0277608	+	0.0873946i
$985$			74.1452i			2.36246i
$986$	−20.4717			−0.651953
$987$	−21.1398	+	8.69545i	−0.672888	+	0.276779i
$988$	0.303368			0.00965143
$989$		−	9.97781i		−	0.317276i
$990$	23.7273	+	16.7655i	0.754102	+	0.532844i
$991$	−48.5436			−1.54204			−0.771019	−	0.636812i	$-0.780253\pi$
$991$	−48.5436			−1.54204			−0.771019	+	0.636812i	$0.780253\pi$
$992$	52.2613			1.65930
$993$	18.2263	+	5.78955i	0.578393	+	0.183726i
$994$	−44.1186	+	36.9953i	−1.39936	+	1.17342i
$995$			15.3148i			0.485512i
$996$	−3.29217	−	1.04575i	−0.104316	−	0.0331360i
$997$			32.5747i			1.03165i	0.856693	+	0.515826i	$0.172515\pi$
$997$			32.5747i			1.03165i	−0.856693	+	0.515826i	$0.827485\pi$
$998$		−	29.6400i		−	0.938237i
$999$	−14.7136	−	19.4318i	−0.465519	−	0.614795i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.d.d.461.14	yes	44
3.2	odd	2	inner	483.2.d.d.461.31	yes	44
7.6	odd	2	inner	483.2.d.d.461.13	✓	44
21.20	even	2	inner	483.2.d.d.461.32	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.d.d.461.13	✓	44	7.6	odd	2	inner
483.2.d.d.461.14	yes	44	1.1	even	1	trivial
483.2.d.d.461.31	yes	44	3.2	odd	2	inner
483.2.d.d.461.32	yes	44	21.20	even	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.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.77247i q^{2} +(1.65077 + 0.524365i) q^{3} -1.14166 q^{4} +3.73040 q^{5} +(0.929423 - 2.92594i) q^{6} +(-2.02732 + 1.69999i) q^{7} -1.52139i q^{8} +(2.45008 + 1.73121i) q^{9} +O(q^{10})\)	\(q-1.77247i q^{2} +(1.65077 + 0.524365i) q^{3} -1.14166 q^{4} +3.73040 q^{5} +(0.929423 - 2.92594i) q^{6} +(-2.02732 + 1.69999i) q^{7} -1.52139i q^{8} +(2.45008 + 1.73121i) q^{9} -6.61202i q^{10} +1.46465i q^{11} +(-1.88461 - 0.598646i) q^{12} -0.721305i q^{13} +(3.01319 + 3.59337i) q^{14} +(6.15803 + 1.95609i) q^{15} -4.97993 q^{16} -4.35922 q^{17} +(3.06853 - 4.34270i) q^{18} -0.368396i q^{19} -4.25884 q^{20} +(-4.23806 + 1.74324i) q^{21} +2.59604 q^{22} +1.00000i q^{23} +(0.797763 - 2.51146i) q^{24} +8.91586 q^{25} -1.27849 q^{26} +(3.13673 + 4.14257i) q^{27} +(2.31451 - 1.94081i) q^{28} +2.64952i q^{29} +(3.46712 - 10.9149i) q^{30} -9.03547i q^{31} +5.78402i q^{32} +(-0.768010 + 2.41779i) q^{33} +7.72659i q^{34} +(-7.56271 + 6.34164i) q^{35} +(-2.79716 - 1.97645i) q^{36} -4.69075 q^{37} -0.652972 q^{38} +(0.378227 - 1.19071i) q^{39} -5.67538i q^{40} -1.09158 q^{41} +(3.08984 + 7.51184i) q^{42} -9.97781 q^{43} -1.67212i q^{44} +(9.13978 + 6.45811i) q^{45} +1.77247 q^{46} +4.98810 q^{47} +(-8.22072 - 2.61130i) q^{48} +(1.22005 - 6.89286i) q^{49} -15.8031i q^{50} +(-7.19606 - 2.28582i) q^{51} +0.823484i q^{52} -10.0930i q^{53} +(7.34259 - 5.55977i) q^{54} +5.46371i q^{55} +(2.58635 + 3.08434i) q^{56} +(0.193174 - 0.608137i) q^{57} +4.69620 q^{58} -7.05443 q^{59} +(-7.03036 - 2.23319i) q^{60} +7.71575i q^{61} -16.0151 q^{62} +(-7.91015 + 0.655397i) q^{63} +0.292145 q^{64} -2.69075i q^{65} +(4.28547 + 1.36128i) q^{66} -3.88582 q^{67} +4.97673 q^{68} +(-0.524365 + 1.65077i) q^{69} +(11.2404 + 13.4047i) q^{70} +12.2778i q^{71} +(2.63385 - 3.72752i) q^{72} -14.1534i q^{73} +8.31423i q^{74} +(14.7180 + 4.67517i) q^{75} +0.420582i q^{76} +(-2.48989 - 2.96931i) q^{77} +(-2.11050 - 0.670398i) q^{78} -9.18209 q^{79} -18.5771 q^{80} +(3.00580 + 8.48323i) q^{81} +1.93480i q^{82} +1.74687 q^{83} +(4.83841 - 1.99018i) q^{84} -16.2616 q^{85} +17.6854i q^{86} +(-1.38931 + 4.37374i) q^{87} +2.22829 q^{88} +11.0784 q^{89} +(11.4468 - 16.2000i) q^{90} +(1.22621 + 1.46232i) q^{91} -1.14166i q^{92} +(4.73789 - 14.9155i) q^{93} -8.84126i q^{94} -1.37426i q^{95} +(-3.03294 + 9.54808i) q^{96} -10.2060i q^{97} +(-12.2174 - 2.16251i) q^{98} +(-2.53561 + 3.58850i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 76 q^{4} - 8 q^{7} + 20 q^{9}+O(q^{10}) \) 44 * q - 76 * q^4 - 8 * q^7 + 20 * q^9	\( 44 q - 76 q^{4} - 8 q^{7} + 20 q^{9} + 4 q^{15} + 92 q^{16} + 4 q^{18} - 22 q^{21} + 12 q^{22} + 16 q^{25} + 16 q^{28} - 32 q^{30} - 112 q^{37} + 4 q^{39} - 12 q^{42} - 68 q^{43} + 4 q^{46} + 44 q^{49} + 32 q^{51} + 16 q^{57} + 28 q^{58} - 44 q^{60} - 10 q^{63} - 16 q^{64} + 108 q^{67} - 60 q^{70} + 112 q^{72} - 48 q^{78} + 40 q^{79} - 4 q^{81} - 26 q^{84} - 108 q^{85} + 8 q^{88} + 24 q^{91} + 4 q^{93} + 4 q^{99}+O(q^{100}) \) 44 * q - 76 * q^4 - 8 * q^7 + 20 * q^9 + 4 * q^15 + 92 * q^16 + 4 * q^18 - 22 * q^21 + 12 * q^22 + 16 * q^25 + 16 * q^28 - 32 * q^30 - 112 * q^37 + 4 * q^39 - 12 * q^42 - 68 * q^43 + 4 * q^46 + 44 * q^49 + 32 * q^51 + 16 * q^57 + 28 * q^58 - 44 * q^60 - 10 * q^63 - 16 * q^64 + 108 * q^67 - 60 * q^70 + 112 * q^72 - 48 * q^78 + 40 * q^79 - 4 * q^81 - 26 * q^84 - 108 * q^85 + 8 * q^88 + 24 * q^91 + 4 * q^93 + 4 * q^99

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