LMFDB - Embedded newform 171.2.u.c.55.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [171,2,Mod(28,171)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(171, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("171.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	171.u (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.36544187456$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			55.1
Root			$-0.173648 + 0.984808i$ of defining polynomial
Character	$\chi$	$=$	171.55
Dual form			171.2.u.c.28.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.233956 - 1.32683i) q^{2} +(0.173648 + 0.0632028i) q^{4} +(0.826352 - 0.300767i) q^{5} +(-0.173648 - 0.300767i) q^{7} +(1.47178 - 2.54920i) q^{8} +O(q^{10})$	\(q+(0.233956 - 1.32683i) q^{2} +(0.173648 + 0.0632028i) q^{4} +(0.826352 - 0.300767i) q^{5} +(-0.173648 - 0.300767i) q^{7} +(1.47178 - 2.54920i) q^{8} +(-0.205737 - 1.16679i) q^{10} +(-1.11334 + 1.92836i) q^{11} +(1.97178 - 1.65452i) q^{13} +(-0.439693 + 0.160035i) q^{14} +(-2.75490 - 2.31164i) q^{16} +(-0.0812519 + 0.460802i) q^{17} +(-4.29813 + 0.725293i) q^{19} +0.162504 q^{20} +(2.29813 + 1.92836i) q^{22} +(-2.53209 - 0.921605i) q^{23} +(-3.23783 + 2.71686i) q^{25} +(-1.73396 - 3.00330i) q^{26} +(-0.0111444 - 0.0632028i) q^{28} +(1.19459 + 6.77487i) q^{29} +(3.55303 + 6.15403i) q^{31} +(0.798133 - 0.669713i) q^{32} +(0.592396 + 0.215615i) q^{34} +(-0.233956 - 0.196312i) q^{35} +4.94356 q^{37} +(-0.0432332 + 5.87257i) q^{38} +(0.449493 - 2.54920i) q^{40} +(-1.89646 - 1.59132i) q^{41} +(-3.66637 + 1.33445i) q^{43} +(-0.315207 + 0.264490i) q^{44} +(-1.81521 + 3.14403i) q^{46} +(1.26604 + 7.18009i) q^{47} +(3.43969 - 5.95772i) q^{49} +(2.84730 + 4.93166i) q^{50} +(0.446967 - 0.162683i) q^{52} +(-2.66637 - 0.970481i) q^{53} +(-0.340022 + 1.92836i) q^{55} -1.02229 q^{56} +9.26857 q^{58} +(1.09492 - 6.20961i) q^{59} +(-8.57785 - 3.12208i) q^{61} +(8.99660 - 3.27449i) q^{62} +(-4.29813 - 7.44459i) q^{64} +(1.13176 - 1.96026i) q^{65} +(1.33275 + 7.55839i) q^{67} +(-0.0432332 + 0.0748822i) q^{68} +(-0.315207 + 0.264490i) q^{70} +(-8.74422 + 3.18264i) q^{71} +(1.06418 + 0.892951i) q^{73} +(1.15657 - 6.55926i) q^{74} +(-0.792204 - 0.145708i) q^{76} +0.773318 q^{77} +(-9.07398 - 7.61397i) q^{79} +(-2.97178 - 1.08164i) q^{80} +(-2.55509 + 2.14398i) q^{82} +(-7.41534 - 12.8438i) q^{83} +(0.0714517 + 0.405223i) q^{85} +(0.912818 + 5.17685i) q^{86} +(3.27719 + 5.67626i) q^{88} +(7.88326 - 6.61484i) q^{89} +(-0.840022 - 0.305743i) q^{91} +(-0.381445 - 0.320070i) q^{92} +9.82295 q^{94} +(-3.33363 + 1.89209i) q^{95} +(1.64156 - 9.30975i) q^{97} +(-7.10014 - 5.95772i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 6 q^{5} - 6 q^{8}+O(q^{10}) $ 6 * q + 6 * q^2 + 6 * q^5 - 6 * q^8	$ 6 q + 6 q^{2} + 6 q^{5} - 6 q^{8} + 9 q^{10} - 3 q^{13} + 3 q^{14} - 18 q^{16} - 3 q^{17} - 12 q^{19} + 6 q^{20} - 6 q^{23} - 15 q^{26} + 6 q^{28} + 3 q^{29} + 9 q^{31} - 9 q^{32} - 6 q^{35} + 15 q^{38} - 21 q^{41} - 3 q^{43} - 9 q^{44} - 18 q^{46} + 3 q^{47} + 15 q^{49} + 15 q^{50} + 15 q^{52} + 3 q^{53} + 18 q^{55} + 6 q^{56} + 36 q^{58} - 12 q^{59} - 12 q^{61} + 12 q^{62} - 12 q^{64} + 12 q^{65} - 30 q^{67} + 15 q^{68} - 9 q^{70} + 6 q^{71} - 12 q^{73} - 15 q^{74} + 36 q^{76} + 18 q^{77} - 39 q^{79} - 3 q^{80} - 54 q^{82} - 24 q^{86} + 9 q^{88} + 12 q^{89} + 15 q^{91} - 42 q^{92} + 18 q^{94} - 39 q^{95} + 18 q^{97} + 9 q^{98}+O(q^{100}) $ 6 * q + 6 * q^2 + 6 * q^5 - 6 * q^8 + 9 * q^10 - 3 * q^13 + 3 * q^14 - 18 * q^16 - 3 * q^17 - 12 * q^19 + 6 * q^20 - 6 * q^23 - 15 * q^26 + 6 * q^28 + 3 * q^29 + 9 * q^31 - 9 * q^32 - 6 * q^35 + 15 * q^38 - 21 * q^41 - 3 * q^43 - 9 * q^44 - 18 * q^46 + 3 * q^47 + 15 * q^49 + 15 * q^50 + 15 * q^52 + 3 * q^53 + 18 * q^55 + 6 * q^56 + 36 * q^58 - 12 * q^59 - 12 * q^61 + 12 * q^62 - 12 * q^64 + 12 * q^65 - 30 * q^67 + 15 * q^68 - 9 * q^70 + 6 * q^71 - 12 * q^73 - 15 * q^74 + 36 * q^76 + 18 * q^77 - 39 * q^79 - 3 * q^80 - 54 * q^82 - 24 * q^86 + 9 * q^88 + 12 * q^89 + 15 * q^91 - 42 * q^92 + 18 * q^94 - 39 * q^95 + 18 * q^97 + 9 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$1$	$e\left(\frac{5}{9}\right)$

Coefficient data

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

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

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

$2$	0.233956	−	1.32683i	0.165432	−	0.938209i	−0.783187	−	0.621786i	$-0.786407\pi$
$2$	0.233956	−	1.32683i	0.165432	−	0.938209i	0.948618	−	0.316423i	$-0.102482\pi$
$3$		0			0
$3$		0			0
$4$	0.173648	+	0.0632028i	0.0868241	+	0.0316014i
$5$	0.826352	−	0.300767i	0.369556	−	0.134507i	−0.150565	−	0.988600i	$-0.548109\pi$
$5$	0.826352	−	0.300767i	0.369556	−	0.134507i	0.520121	+	0.854093i	$0.325887\pi$
$6$		0			0
$7$	−0.173648	−	0.300767i	−0.0656328	−	0.113679i	0.831342	−	0.555762i	$-0.187573\pi$
$7$	−0.173648	−	0.300767i	−0.0656328	−	0.113679i	−0.896975	+	0.442082i	$0.854240\pi$
$8$	1.47178	−	2.54920i	0.520353	−	0.901278i
$9$		0			0
$10$	−0.205737	−	1.16679i	−0.0650598	−	0.368972i
$11$	−1.11334	+	1.92836i	−0.335685	+	0.581423i	−0.983616	−	0.180276i	$-0.942301\pi$
$11$	−1.11334	+	1.92836i	−0.335685	+	0.581423i	0.647931	+	0.761699i	$0.275634\pi$
$12$		0			0
$13$	1.97178	−	1.65452i	0.546874	−	0.458882i	−0.327007	−	0.945022i	$-0.606040\pi$
$13$	1.97178	−	1.65452i	0.546874	−	0.458882i	0.873881	+	0.486140i	$0.161596\pi$
$14$	−0.439693	+	0.160035i	−0.117513	+	0.0427712i
$15$		0			0
$16$	−2.75490	−	2.31164i	−0.688725	−	0.577909i
$17$	−0.0812519	+	0.460802i	−0.0197065	+	0.111761i	−0.993074	−	0.117488i	$-0.962516\pi$
$17$	−0.0812519	+	0.460802i	−0.0197065	+	0.111761i	0.973368	+	0.229249i	$0.0736270\pi$
$18$		0			0
$19$	−4.29813	+	0.725293i	−0.986059	+	0.166394i
$19$	−4.29813	+	0.725293i	−0.986059	+	0.166394i
$20$	0.162504			0.0363370
$21$		0			0
$22$	2.29813	+	1.92836i	0.489964	+	0.411128i
$23$	−2.53209	−	0.921605i	−0.527977	−	0.192168i	0.0642578	−	0.997933i	$-0.479532\pi$
$23$	−2.53209	−	0.921605i	−0.527977	−	0.192168i	−0.592235	+	0.805765i	$0.701754\pi$
$24$		0			0
$25$	−3.23783	+	2.71686i	−0.647565	+	0.543372i
$26$	−1.73396	−	3.00330i	−0.340057	−	0.588995i
$27$		0			0
$28$	−0.0111444	−	0.0632028i	−0.00210608	−	0.0119442i
$29$	1.19459	+	6.77487i	0.221830	+	1.25806i	0.868653	+	0.495421i	$0.164986\pi$
$29$	1.19459	+	6.77487i	0.221830	+	1.25806i	−0.646822	+	0.762641i	$0.723903\pi$
$30$		0			0
$31$	3.55303	+	6.15403i	0.638144	+	1.10530i	0.985840	+	0.167690i	$0.0536307\pi$
$31$	3.55303	+	6.15403i	0.638144	+	1.10530i	−0.347696	+	0.937607i	$0.613036\pi$
$32$	0.798133	−	0.669713i	0.141091	−	0.118390i
$33$		0			0
$34$	0.592396	+	0.215615i	0.101595	+	0.0369776i
$35$	−0.233956	−	0.196312i	−0.0395457	−	0.0331828i
$36$		0			0
$37$	4.94356			0.812717			0.406358	−	0.913714i	$-0.366798\pi$
$37$	4.94356			0.812717			0.406358	+	0.913714i	$0.366798\pi$
$38$	−0.0432332	+	5.87257i	−0.00701336	+	0.952657i
$39$		0			0
$40$	0.449493	−	2.54920i	0.0710711	−	0.403064i
$41$	−1.89646	−	1.59132i	−0.296177	−	0.248522i	0.482574	−	0.875855i	$-0.339702\pi$
$41$	−1.89646	−	1.59132i	−0.296177	−	0.248522i	−0.778751	+	0.627333i	$0.784146\pi$
$42$		0			0
$43$	−3.66637	+	1.33445i	−0.559117	+	0.203502i	−0.606093	−	0.795394i	$-0.707264\pi$
$43$	−3.66637	+	1.33445i	−0.559117	+	0.203502i	0.0469757	+	0.998896i	$0.485042\pi$
$44$	−0.315207	+	0.264490i	−0.0475193	+	0.0398734i
$45$		0			0
$46$	−1.81521	+	3.14403i	−0.267638	+	0.463562i
$47$	1.26604	+	7.18009i	0.184672	+	1.04732i	0.926377	+	0.376598i	$0.122906\pi$
$47$	1.26604	+	7.18009i	0.184672	+	1.04732i	−0.741705	+	0.670726i	$0.765983\pi$
$48$		0			0
$49$	3.43969	−	5.95772i	0.491385	−	0.851103i
$50$	2.84730	+	4.93166i	0.402669	+	0.697442i
$51$		0			0
$52$	0.446967	−	0.162683i	0.0619831	−	0.0225600i
$53$	−2.66637	−	0.970481i	−0.366255	−	0.133306i	0.152335	−	0.988329i	$-0.451321\pi$
$53$	−2.66637	−	0.970481i	−0.366255	−	0.133306i	−0.518590	+	0.855023i	$0.673543\pi$
$54$		0			0
$55$	−0.340022	+	1.92836i	−0.0458486	+	0.260020i
$56$	−1.02229			−0.136609
$57$		0			0
$58$	9.26857			1.21702
$59$	1.09492	−	6.20961i	0.142547	−	0.808423i	−0.826757	−	0.562559i	$-0.809817\pi$
$59$	1.09492	−	6.20961i	0.142547	−	0.808423i	0.969304	−	0.245864i	$-0.0790718\pi$
$60$		0			0
$61$	−8.57785	−	3.12208i	−1.09828	−	0.399742i	−0.271599	−	0.962411i	$-0.587552\pi$
$61$	−8.57785	−	3.12208i	−1.09828	−	0.399742i	−0.826682	+	0.562669i	$0.809775\pi$
$62$	8.99660	−	3.27449i	1.14257	−	0.415861i
$63$		0			0
$64$	−4.29813	−	7.44459i	−0.537267	−	0.930573i
$65$	1.13176	−	1.96026i	0.140377	−	0.243141i
$66$		0			0
$67$	1.33275	+	7.55839i	0.162821	+	0.923405i	0.951283	+	0.308320i	$0.0997669\pi$
$67$	1.33275	+	7.55839i	0.162821	+	0.923405i	−0.788461	+	0.615084i	$0.789122\pi$
$68$	−0.0432332	+	0.0748822i	−0.00524280	+	0.00908080i
$69$		0			0
$70$	−0.315207	+	0.264490i	−0.0376745	+	0.0316127i
$71$	−8.74422	+	3.18264i	−1.03775	+	0.377709i	−0.804026	−	0.594594i	$-0.797313\pi$
$71$	−8.74422	+	3.18264i	−1.03775	+	0.377709i	−0.233722	+	0.972303i	$0.575091\pi$
$72$		0			0
$73$	1.06418	+	0.892951i	0.124553	+	0.104512i	0.702936	−	0.711253i	$-0.251872\pi$
$73$	1.06418	+	0.892951i	0.124553	+	0.104512i	−0.578384	+	0.815765i	$0.696316\pi$
$74$	1.15657	−	6.55926i	0.134449	−	0.762498i
$75$		0			0
$76$	−0.792204	−	0.145708i	−0.0908720	−	0.0167139i
$77$	0.773318			0.0881278
$78$		0			0
$79$	−9.07398	−	7.61397i	−1.02090	−	0.856639i	−0.0311616	−	0.999514i	$-0.509921\pi$
$79$	−9.07398	−	7.61397i	−1.02090	−	0.856639i	−0.989741	+	0.142876i	$0.954365\pi$
$80$	−2.97178	−	1.08164i	−0.332255	−	0.120931i
$81$		0			0
$82$	−2.55509	+	2.14398i	−0.282163	+	0.236763i
$83$	−7.41534	−	12.8438i	−0.813940	−	1.40979i	−0.910087	−	0.414418i	$-0.863985\pi$
$83$	−7.41534	−	12.8438i	−0.813940	−	1.40979i	0.0961469	−	0.995367i	$-0.469348\pi$
$84$		0			0
$85$	0.0714517	+	0.405223i	0.00775003	+	0.0439526i
$86$	0.912818	+	5.17685i	0.0984317	+	0.558234i
$87$		0			0
$88$	3.27719	+	5.67626i	0.349349	+	0.605091i
$89$	7.88326	−	6.61484i	0.835623	−	0.701171i	−0.120951	−	0.992658i	$-0.538594\pi$
$89$	7.88326	−	6.61484i	0.835623	−	0.701171i	0.956575	+	0.291487i	$0.0941501\pi$
$90$		0			0
$91$	−0.840022	−	0.305743i	−0.0880583	−	0.0320506i
$92$	−0.381445	−	0.320070i	−0.0397684	−	0.0333696i
$93$		0			0
$94$	9.82295			1.01316
$95$	−3.33363	+	1.89209i	−0.342023	+	0.194124i
$96$		0			0
$97$	1.64156	−	9.30975i	0.166675	−	0.945261i	−0.780645	−	0.624974i	$-0.785109\pi$
$97$	1.64156	−	9.30975i	0.166675	−	0.945261i	0.947320	−	0.320287i	$-0.103779\pi$
$98$	−7.10014	−	5.95772i	−0.717222	−	0.601821i
$99$		0			0
$100$	−0.733956	+	0.267138i	−0.0733956	+	0.0267138i
$101$	7.08512	−	5.94512i	0.704996	−	0.591562i	−0.218194	−	0.975905i	$-0.570017\pi$
$101$	7.08512	−	5.94512i	0.704996	−	0.591562i	0.923190	+	0.384343i	$0.125572\pi$
$102$		0			0
$103$	2.75490	−	4.77163i	0.271448	−	0.470162i	−0.697785	−	0.716308i	$-0.745831\pi$
$103$	2.75490	−	4.77163i	0.271448	−	0.470162i	0.969233	+	0.246145i	$0.0791640\pi$
$104$	−1.31567	−	7.46156i	−0.129012	−	0.731666i
$105$		0			0
$106$	−1.91147	+	3.31077i	−0.185659	+	0.321570i
$107$	5.11721	+	8.86327i	0.494699	+	0.856845i	0.999981	−	0.00610974i	$-0.00194480\pi$
$107$	5.11721	+	8.86327i	0.494699	+	0.856845i	−0.505282	+	0.862954i	$0.668611\pi$
$108$		0			0
$109$	1.71301	−	0.623485i	0.164077	−	0.0597190i	−0.258676	−	0.965964i	$-0.583286\pi$
$109$	1.71301	−	0.623485i	0.164077	−	0.0597190i	0.422753	+	0.906245i	$0.361064\pi$
$110$	2.47906	+	0.902302i	0.236369	+	0.0860312i
$111$		0			0
$112$	−0.216881	+	1.23000i	−0.0204934	+	0.116224i
$113$	17.6878			1.66393			0.831963	−	0.554830i	$-0.187217\pi$
$113$	17.6878			1.66393			0.831963	+	0.554830i	$0.187217\pi$
$114$		0			0
$115$	−2.36959			−0.220965
$116$	−0.220752	+	1.25195i	−0.0204963	+	0.116240i
$117$		0			0
$118$	−7.98293	−	2.90555i	−0.734888	−	0.267477i
$119$	0.152704	−	0.0555796i	0.0139983	−	0.00509497i
$120$		0			0
$121$	3.02094	+	5.23243i	0.274631	+	0.475675i
$122$	−6.14930	+	10.6509i	−0.556731	+	0.964287i
$123$		0			0
$124$	0.228026	+	1.29320i	0.0204773	+	0.116133i
$125$	−4.05690	+	7.02676i	−0.362861	+	0.628493i
$126$		0			0
$127$	8.88919	−	7.45891i	0.788788	−	0.661871i	−0.156657	−	0.987653i	$-0.550072\pi$
$127$	8.88919	−	7.45891i	0.788788	−	0.661871i	0.945445	+	0.325782i	$0.105627\pi$
$128$	−8.92514	+	3.24849i	−0.788879	+	0.287128i
$129$		0			0
$130$	−2.33615	−	1.96026i	−0.204894	−	0.171927i
$131$	−0.320422	+	1.81720i	−0.0279954	+	0.158770i	−0.995601	−	0.0936982i	$-0.970131\pi$
$131$	−0.320422	+	1.81720i	−0.0279954	+	0.158770i	0.967605	+	0.252468i	$0.0812422\pi$
$132$		0			0
$133$	0.964508	+	1.16679i	0.0836334	+	0.101174i
$134$	10.3405			0.893282
$135$		0			0
$136$	1.05509	+	0.885328i	0.0904735	+	0.0759162i
$137$	0.240352	+	0.0874810i	0.0205347	+	0.00747401i	0.352267	−	0.935900i	$-0.385411\pi$
$137$	0.240352	+	0.0874810i	0.0205347	+	0.00747401i	−0.331732	+	0.943374i	$0.607633\pi$
$138$		0			0
$139$	3.26604	−	2.74054i	0.277022	−	0.232449i	−0.493682	−	0.869643i	$-0.664349\pi$
$139$	3.26604	−	2.74054i	0.277022	−	0.232449i	0.770704	+	0.637193i	$0.219905\pi$
$140$	−0.0282185	−	0.0488759i	−0.00238490	−	0.00413076i
$141$		0			0
$142$	2.17705	+	12.3467i	0.182694	+	1.03611i
$143$	0.995252	+	5.64436i	0.0832272	+	0.472005i
$144$		0			0
$145$	3.02481	+	5.23913i	0.251197	+	0.435086i
$146$	1.43376	−	1.20307i	0.118659	−	0.0995668i
$147$		0			0
$148$	0.858441	+	0.312447i	0.0705634	+	0.0256830i
$149$	−12.6853	−	10.6442i	−1.03922	−	0.872007i	−0.0472981	−	0.998881i	$-0.515061\pi$
$149$	−12.6853	−	10.6442i	−1.03922	−	0.872007i	−0.991919	+	0.126874i	$0.959506\pi$
$150$		0			0
$151$	−4.36184			−0.354962			−0.177481	−	0.984124i	$-0.556795\pi$
$151$	−4.36184			−0.354962			−0.177481	+	0.984124i	$0.556795\pi$
$152$	−4.47700	+	12.0243i	−0.363132	+	0.975298i
$153$		0			0
$154$	0.180922	−	1.02606i	0.0145791	−	0.0826823i
$155$	4.78699	+	4.01676i	0.384500	+	0.322634i
$156$		0			0
$157$	9.03849	−	3.28974i	0.721350	−	0.262550i	0.0448510	−	0.998994i	$-0.485719\pi$
$157$	9.03849	−	3.28974i	0.721350	−	0.262550i	0.676499	+	0.736444i	$0.263496\pi$
$158$	−12.2253	+	10.2583i	−0.972596	+	0.816105i
$159$		0			0
$160$	0.458111	−	0.793471i	0.0362168	−	0.0627294i
$161$	0.162504	+	0.921605i	0.0128071	+	0.0726326i
$162$		0			0
$163$	−4.17752	+	7.23567i	−0.327209	+	0.566742i	−0.981957	−	0.189105i	$-0.939441\pi$
$163$	−4.17752	+	7.23567i	−0.327209	+	0.566742i	0.654748	+	0.755847i	$0.272775\pi$
$164$	−0.228741	−	0.396191i	−0.0178617	−	0.0309373i
$165$		0			0
$166$	−18.7763	+	6.83402i	−1.45732	+	0.530423i
$167$	3.79174	+	1.38008i	0.293413	+	0.106794i	0.484533	−	0.874773i	$-0.338990\pi$
$167$	3.79174	+	1.38008i	0.293413	+	0.106794i	−0.191120	+	0.981567i	$0.561212\pi$
$168$		0			0
$169$	−1.10694	+	6.27779i	−0.0851496	+	0.482907i
$170$	0.554378			0.0425188
$171$		0			0
$172$	−0.721000			−0.0549758
$173$	3.49794	−	19.8378i	0.265943	−	1.50824i	−0.500391	−	0.865799i	$-0.666811\pi$
$173$	3.49794	−	19.8378i	0.265943	−	1.50824i	0.766335	−	0.642441i	$-0.222078\pi$
$174$		0			0
$175$	1.37939	+	0.502055i	0.104272	+	0.0379518i
$176$	7.52481	−	2.73881i	0.567204	−	0.206445i
$177$		0			0
$178$	−6.93242	−	12.0073i	−0.519607	−	0.899985i
$179$	−5.75624	+	9.97011i	−0.430242	+	0.745201i	−0.996894	−	0.0787564i	$-0.974905\pi$
$179$	−5.75624	+	9.97011i	−0.430242	+	0.745201i	0.566652	+	0.823957i	$0.308238\pi$
$180$		0			0
$181$	1.48246	+	8.40744i	0.110190	+	0.624920i	0.989020	+	0.147784i	$0.0472141\pi$
$181$	1.48246	+	8.40744i	0.110190	+	0.624920i	−0.878829	+	0.477136i	$0.841675\pi$
$182$	−0.602196	+	1.04303i	−0.0446378	+	0.0773149i
$183$		0			0
$184$	−6.07604	+	5.09840i	−0.447931	+	0.375859i
$185$	4.08512	−	1.48686i	0.300344	−	0.109316i
$186$		0			0
$187$	−0.798133	−	0.669713i	−0.0583653	−	0.0489743i
$188$	−0.233956	+	1.32683i	−0.0170630	+	0.0967689i
$189$		0			0
$190$	1.73055	+	4.86581i	0.125547	+	0.353003i
$191$	−18.3354			−1.32671			−0.663353	−	0.748307i	$-0.730867\pi$
$191$	−18.3354			−1.32671			−0.663353	+	0.748307i	$0.730867\pi$
$192$		0			0
$193$	0.228026	+	0.191336i	0.0164137	+	0.0137727i	0.650958	−	0.759114i	$-0.274368\pi$
$193$	0.228026	+	0.191336i	0.0164137	+	0.0137727i	−0.634544	+	0.772887i	$0.718812\pi$
$194$	−11.9684	−	4.35613i	−0.859279	−	0.312752i
$195$		0			0
$196$	0.973841	−	0.817150i	0.0695601	−	0.0583678i
$197$	6.57057	+	11.3806i	0.468134	+	0.810832i	0.999337	−	0.0364128i	$-0.0115931\pi$
$197$	6.57057	+	11.3806i	0.468134	+	0.810832i	−0.531203	+	0.847245i	$0.678260\pi$
$198$		0			0
$199$	−0.0445774	−	0.252811i	−0.00316001	−	0.0179213i	0.983187	−	0.182602i	$-0.0584519\pi$
$199$	−0.0445774	−	0.252811i	−0.00316001	−	0.0179213i	−0.986347	+	0.164680i	$0.947341\pi$
$200$	2.16044	+	12.2525i	0.152766	+	0.866382i
$201$		0			0
$202$	−6.23055	−	10.7916i	−0.438380	−	0.759297i
$203$	1.83022	−	1.53574i	0.128456	−	0.107788i
$204$		0			0
$205$	−2.04576	−	0.744596i	−0.142882	−	0.0520048i
$206$	−5.68660	−	4.77163i	−0.396204	−	0.332455i
$207$		0			0
$208$	−9.25671			−0.641837
$209$	3.38666	−	9.09586i	0.234260	−	0.629174i
$210$		0			0
$211$	0.425145	−	2.41112i	0.0292682	−	0.165988i	−0.966670	−	0.256024i	$-0.917587\pi$
$211$	0.425145	−	2.41112i	0.0292682	−	0.165988i	0.995938	+	0.0900364i	$0.0286983\pi$
$212$	−0.401674	−	0.337044i	−0.0275871	−	0.0231483i
$213$		0			0
$214$	12.9572	−	4.71605i	0.885738	−	0.322382i
$215$	−2.62836	+	2.20545i	−0.179252	+	0.150411i
$216$		0			0
$217$	1.23396	−	2.13727i	0.0837664	−	0.145088i
$218$	−0.426489	−	2.41874i	−0.0288855	−	0.163818i
$219$		0			0
$220$	−0.180922	+	0.313366i	−0.0121978	+	0.0211272i
$221$	0.602196	+	1.04303i	0.0405081	+	0.0701621i
$222$		0			0
$223$	7.99660	−	2.91052i	0.535492	−	0.194903i	−0.0600971	−	0.998193i	$-0.519141\pi$
$223$	7.99660	−	2.91052i	0.535492	−	0.194903i	0.595589	+	0.803289i	$0.296919\pi$
$224$	−0.340022	−	0.123758i	−0.0227187	−	0.00826893i
$225$		0			0
$226$	4.13816	−	23.4686i	0.275266	−	1.56111i
$227$	14.1506			0.939211			0.469606	−	0.882876i	$-0.344396\pi$
$227$	14.1506			0.939211			0.469606	+	0.882876i	$0.344396\pi$
$228$		0			0
$229$	−20.5330			−1.35686			−0.678430	−	0.734665i	$-0.737339\pi$
$229$	−20.5330			−1.35686			−0.678430	+	0.734665i	$0.737339\pi$
$230$	−0.554378	+	3.14403i	−0.0365546	+	0.207311i
$231$		0			0
$232$	19.0287	+	6.92588i	1.24929	+	0.454706i
$233$	16.5865	−	6.03698i	1.08662	−	0.395496i	0.264249	−	0.964454i	$-0.414876\pi$
$233$	16.5865	−	6.03698i	1.08662	−	0.395496i	0.822366	+	0.568959i	$0.192654\pi$
$234$		0			0
$235$	3.20574	+	5.55250i	0.209119	+	0.362205i
$236$	0.582596	−	1.00909i	0.0379238	−	0.0656859i
$237$		0			0
$238$	−0.0380187	−	0.215615i	−0.00246438	−	0.0139762i
$239$	1.17617	−	2.03719i	0.0760804	−	0.131775i	−0.825475	−	0.564438i	$-0.809093\pi$
$239$	1.17617	−	2.03719i	0.0760804	−	0.131775i	0.901556	+	0.432663i	$0.142426\pi$
$240$		0			0
$241$	10.5719	−	8.87089i	0.680997	−	0.571424i	−0.235300	−	0.971923i	$-0.575607\pi$
$241$	10.5719	−	8.87089i	0.680997	−	0.571424i	0.916298	+	0.400498i	$0.131163\pi$
$242$	7.64930	−	2.78412i	0.491716	−	0.178970i
$243$		0			0
$244$	−1.29220	−	1.08429i	−0.0827249	−	0.0694144i
$245$	1.05051	−	5.95772i	0.0671144	−	0.380625i
$246$		0			0
$247$	−7.27497	+	8.54147i	−0.462895	+	0.543481i
$248$	20.9172			1.32824
$249$		0			0
$250$	8.37417	+	7.02676i	0.529629	+	0.444412i
$251$	−3.91400	−	1.42458i	−0.247050	−	0.0899187i	0.215528	−	0.976498i	$-0.430853\pi$
$251$	−3.91400	−	1.42458i	−0.247050	−	0.0899187i	−0.462577	+	0.886579i	$0.653075\pi$
$252$		0			0
$253$	4.59627	−	3.85673i	0.288965	−	0.242470i
$254$	−7.81702	−	13.5395i	−0.490483	−	0.849542i
$255$		0			0
$256$	−0.763356	−	4.32921i	−0.0477098	−	0.270575i
$257$	−0.115867	−	0.657115i	−0.00722759	−	0.0409897i	0.980981	−	0.194105i	$-0.0621804\pi$
$257$	−0.115867	−	0.657115i	−0.00722759	−	0.0409897i	−0.988208	+	0.153116i	$0.951069\pi$
$258$		0			0
$259$	−0.858441	−	1.48686i	−0.0533409	−	0.0923892i
$260$	0.320422	−	0.268866i	0.0198717	−	0.0166744i
$261$		0			0
$262$	2.33615	+	0.850290i	0.144328	+	0.0525311i
$263$	−8.73261	−	7.32753i	−0.538476	−	0.451835i	0.332540	−	0.943089i	$-0.392094\pi$
$263$	−8.73261	−	7.32753i	−0.538476	−	0.451835i	−0.871016	+	0.491254i	$0.836539\pi$
$264$		0			0
$265$	−2.49525			−0.153282
$266$	1.77379	−	1.00676i	0.108758	−	0.0617283i
$267$		0			0
$268$	−0.246282	+	1.39673i	−0.0150441	+	0.0853191i
$269$	−14.8537	−	12.4637i	−0.905646	−	0.759927i	0.0656400	−	0.997843i	$-0.479091\pi$
$269$	−14.8537	−	12.4637i	−0.905646	−	0.759927i	−0.971286	+	0.237916i	$0.923536\pi$
$270$		0			0
$271$	12.5865	−	4.58110i	0.764573	−	0.278282i	0.0698486	−	0.997558i	$-0.477748\pi$
$271$	12.5865	−	4.58110i	0.764573	−	0.278282i	0.694725	+	0.719276i	$0.255526\pi$
$272$	1.28905	−	1.08164i	0.0781600	−	0.0655841i
$273$		0			0
$274$	0.172304	−	0.298439i	0.0104093	−	0.0180294i
$275$	−1.63429	−	9.26849i	−0.0985511	−	0.558911i
$276$		0			0
$277$	−8.87346	+	15.3693i	−0.533154	+	0.923450i	0.466096	+	0.884734i	$0.345660\pi$
$277$	−8.87346	+	15.3693i	−0.533154	+	0.923450i	−0.999250	+	0.0387161i	$0.987673\pi$
$278$	−2.87211	−	4.97464i	−0.172258	−	0.298359i
$279$		0			0
$280$	−0.844770	+	0.307471i	−0.0504847	+	0.0183749i
$281$	17.1766	+	6.25179i	1.02467	+	0.372950i	0.799050	−	0.601265i	$-0.205336\pi$
$281$	17.1766	+	6.25179i	1.02467	+	0.372950i	0.225622	+	0.974215i	$0.427558\pi$
$282$		0			0
$283$	1.33497	−	7.57099i	0.0793557	−	0.450049i	−0.919077	−	0.394079i	$-0.871064\pi$
$283$	1.33497	−	7.57099i	0.0793557	−	0.450049i	0.998432	−	0.0559700i	$-0.0178251\pi$
$284$	−1.71957			−0.102038
$285$		0			0
$286$	7.72193			0.456608
$287$	−0.149300	+	0.846723i	−0.00881290	+	0.0499805i
$288$		0			0
$289$	15.7690	+	5.73946i	0.927590	+	0.337615i
$290$	7.65910	−	2.78768i	0.449758	−	0.163698i
$291$		0			0
$292$	0.128356	+	0.222318i	0.00751144	+	0.0130102i
$293$	−5.25150	+	9.09586i	−0.306796	+	0.531386i	−0.977660	−	0.210195i	$-0.932590\pi$
$293$	−5.25150	+	9.09586i	−0.306796	+	0.531386i	0.670864	+	0.741581i	$0.265924\pi$
$294$		0			0
$295$	−0.962859	−	5.46064i	−0.0560598	−	0.317931i
$296$	7.27584	−	12.6021i	0.422900	−	0.732484i
$297$		0			0
$298$	−17.0908	+	14.3409i	−0.990044	+	0.830745i
$299$	−6.51754	+	2.37219i	−0.376919	+	0.137187i
$300$		0			0
$301$	1.03802	+	0.871001i	0.0598304	+	0.0502037i
$302$	−1.02048	+	5.78742i	−0.0587219	+	0.333028i
$303$		0			0
$304$	13.5175	+	7.93761i	0.775284	+	0.455253i
$305$	−8.02734			−0.459644
$306$		0			0
$307$	−8.95929	−	7.51774i	−0.511334	−	0.429060i	0.350264	−	0.936651i	$-0.386092\pi$
$307$	−8.95929	−	7.51774i	−0.511334	−	0.429060i	−0.861598	+	0.507591i	$0.830536\pi$
$308$	0.134285	+	0.0488759i	0.00765162	+	0.00278496i
$309$		0			0
$310$	6.44949	−	5.41177i	0.366307	−	0.307368i
$311$	7.98293	+	13.8268i	0.452670	+	0.784048i	0.998551	−	0.0538151i	$-0.0171382\pi$
$311$	7.98293	+	13.8268i	0.452670	+	0.784048i	−0.545881	+	0.837863i	$0.683805\pi$
$312$		0			0
$313$	−4.62402	−	26.2241i	−0.261365	−	1.48227i	−0.779190	−	0.626788i	$-0.784369\pi$
$313$	−4.62402	−	26.2241i	−0.261365	−	1.48227i	0.517825	−	0.855487i	$-0.326742\pi$
$314$	−2.25031	−	12.7622i	−0.126993	−	0.720211i
$315$		0			0
$316$	−1.09446	−	1.89565i	−0.0615679	−	0.106639i
$317$	−22.6229	+	18.9829i	−1.27063	+	1.06618i	−0.276164	+	0.961111i	$0.589063\pi$
$317$	−22.6229	+	18.9829i	−1.27063	+	1.06618i	−0.994465	+	0.105073i	$0.966492\pi$
$318$		0			0
$319$	−14.3944	−	5.23913i	−0.805932	−	0.293335i
$320$	−5.79086	−	4.85911i	−0.323719	−	0.271632i
$321$		0			0
$322$	1.26083			0.0702633
$323$	0.0150147	−	2.03952i	0.000835443	−	0.113482i
$324$		0			0
$325$	−1.88919	+	10.7141i	−0.104793	+	0.594311i
$326$	8.62314	+	7.23567i	0.477592	+	0.400747i
$327$		0			0
$328$	−6.84776	+	2.49238i	−0.378104	+	0.137619i
$329$	1.93969	−	1.62760i	0.106939	−	0.0897322i
$330$		0			0
$331$	−13.8327	+	23.9590i	−0.760317	+	1.31691i	0.182371	+	0.983230i	$0.441623\pi$
$331$	−13.8327	+	23.9590i	−0.760317	+	1.31691i	−0.942687	+	0.333677i	$0.891710\pi$
$332$	−0.475900	−	2.69896i	−0.0261184	−	0.148125i
$333$		0			0
$334$	2.71823	−	4.70810i	0.148735	−	0.257616i
$335$	3.37464	+	5.84504i	0.184376	+	0.319349i
$336$		0			0
$337$	−16.7827	+	6.10841i	−0.914212	+	0.332746i	−0.755934	−	0.654648i	$-0.772817\pi$
$337$	−16.7827	+	6.10841i	−0.914212	+	0.332746i	−0.158279	+	0.987394i	$0.550594\pi$
$338$	8.07057	+	2.93745i	0.438981	+	0.159776i
$339$		0			0
$340$	−0.0132037	+	0.0748822i	−0.000716074	+	0.00406106i
$341$	−15.8229			−0.856861
$342$		0			0
$343$	−4.82026			−0.260270
$344$	−1.99432	+	11.3103i	−0.107526	+	0.609813i
$345$		0			0
$346$	−25.5030	−	9.28233i	−1.37105	−	0.499021i
$347$	−5.45084	+	1.98394i	−0.292616	+	0.106504i	−0.484157	−	0.874981i	$-0.660874\pi$
$347$	−5.45084	+	1.98394i	−0.292616	+	0.106504i	0.191541	+	0.981485i	$0.438652\pi$
$348$		0			0
$349$	−2.68614	−	4.65253i	−0.143786	−	0.249044i	0.785134	−	0.619326i	$-0.212594\pi$
$349$	−2.68614	−	4.65253i	−0.143786	−	0.249044i	−0.928919	+	0.370282i	$0.879261\pi$
$350$	0.988856	−	1.71275i	0.0528566	−	0.0915502i
$351$		0			0
$352$	0.402856	+	2.28471i	0.0214723	+	0.121775i
$353$	−12.6172	+	21.8537i	−0.671546	+	1.16315i	0.305919	+	0.952057i	$0.401036\pi$
$353$	−12.6172	+	21.8537i	−0.671546	+	1.16315i	−0.977466	+	0.211095i	$0.932297\pi$
$354$		0			0
$355$	−6.26857	+	5.25996i	−0.332701	+	0.279169i
$356$	1.78699	−	0.650411i	0.0947102	−	0.0344717i
$357$		0			0
$358$	11.8819	+	9.97011i	0.627979	+	0.526937i
$359$	−1.16116	+	6.58526i	−0.0612837	+	0.347557i	0.938712	+	0.344702i	$0.112020\pi$
$359$	−1.16116	+	6.58526i	−0.0612837	+	0.347557i	−0.999996	+	0.00285518i	$0.999091\pi$
$360$		0			0
$361$	17.9479	−	6.23481i	0.944626	−	0.328148i
$362$	11.5021			0.604535
$363$		0			0
$364$	−0.126545	−	0.106183i	−0.00663274	−	0.00556553i
$365$	1.14796	+	0.417822i	0.0600868	+	0.0218698i
$366$		0			0
$367$	6.21941	−	5.21870i	0.324650	−	0.272414i	−0.465865	−	0.884856i	$-0.654257\pi$
$367$	6.21941	−	5.21870i	0.324650	−	0.272414i	0.790516	+	0.612441i	$0.209812\pi$
$368$	4.84524	+	8.39220i	0.252575	+	0.437473i
$369$		0			0
$370$	−1.01707	−	5.76811i	−0.0528752	−	0.299870i
$371$	0.171122	+	0.970481i	0.00888421	+	0.0503849i
$372$		0			0
$373$	−17.4488	−	30.2222i	−0.903463	−	1.56484i	−0.822967	−	0.568090i	$-0.807683\pi$
$373$	−17.4488	−	30.2222i	−0.903463	−	1.56484i	−0.0804968	−	0.996755i	$-0.525651\pi$
$374$	−1.07532	+	0.902302i	−0.0556036	+	0.0466569i
$375$		0			0
$376$	20.1668	+	7.34013i	1.04003	+	0.378538i
$377$	13.5646	+	11.3821i	0.698615	+	0.586207i
$378$		0			0
$379$	1.70140			0.0873950			0.0436975	−	0.999045i	$-0.486086\pi$
$379$	1.70140			0.0873950			0.0436975	+	0.999045i	$0.486086\pi$
$380$	−0.698463	+	0.117863i	−0.0358304	+	0.00604624i
$381$		0			0
$382$	−4.28968	+	24.3280i	−0.219479	+	1.24473i
$383$	−2.24969	−	1.88771i	−0.114954	−	0.0964575i	0.583499	−	0.812114i	$-0.301683\pi$
$383$	−2.24969	−	1.88771i	−0.114954	−	0.0964575i	−0.698453	+	0.715656i	$0.746128\pi$
$384$		0			0
$385$	0.639033	−	0.232589i	0.0325681	−	0.0118538i
$386$	0.307218	−	0.257787i	0.0156370	−	0.0131210i
$387$		0			0
$388$	0.873455	−	1.51287i	0.0443430	−	0.0768043i
$389$	4.26604	+	24.1939i	0.216297	+	1.22668i	0.878642	+	0.477482i	$0.158450\pi$
$389$	4.26604	+	24.1939i	0.216297	+	1.22668i	−0.662344	+	0.749199i	$0.730438\pi$
$390$		0			0
$391$	0.630415	−	1.09191i	0.0318815	−	0.0552203i
$392$	−10.1250	−	17.5369i	−0.511387	−	0.885749i
$393$		0			0
$394$	16.6373	−	6.05547i	0.838174	−	0.305070i
$395$	−9.78833	−	3.56266i	−0.492504	−	0.179257i
$396$		0			0
$397$	−5.52822	+	31.3521i	−0.277453	+	1.57352i	0.453606	+	0.891202i	$0.350137\pi$
$397$	−5.52822	+	31.3521i	−0.277453	+	1.57352i	−0.731059	+	0.682314i	$0.760974\pi$
$398$	−0.345866			−0.0173367
$399$		0			0
$400$	15.2003			0.760014
$401$	0.0150147	−	0.0851529i	0.000749801	−	0.00425233i	−0.984431	−	0.175774i	$-0.943757\pi$
$401$	0.0150147	−	0.0851529i	0.000749801	−	0.00425233i	0.985180	+	0.171522i	$0.0548683\pi$
$402$		0			0
$403$	17.1878	+	6.25584i	0.856185	+	0.311626i
$404$	1.60607	−	0.584561i	0.0799048	−	0.0290830i
$405$		0			0
$406$	−1.60947	−	2.78768i	−0.0798767	−	0.138350i
$407$	−5.50387	+	9.53298i	−0.272817	+	0.472532i
$408$		0			0
$409$	3.47400	+	19.7021i	0.171778	+	0.974204i	0.941797	+	0.336182i	$0.109136\pi$
$409$	3.47400	+	19.7021i	0.171778	+	0.974204i	−0.770019	+	0.638021i	$0.779753\pi$
$410$	−1.46657	+	2.54017i	−0.0724286	+	0.125450i
$411$		0			0
$412$	0.779963	−	0.654467i	0.0384260	−	0.0322433i
$413$	−2.05778	+	0.748971i	−0.101257	+	0.0368545i
$414$		0			0
$415$	−9.99067	−	8.38316i	−0.490423	−	0.411513i
$416$	0.465690	−	2.64106i	0.0228323	−	0.129488i
$417$		0			0
$418$	−11.2763	−	6.62154i	−0.551542	−	0.323870i
$419$	−25.4097			−1.24135			−0.620673	−	0.784070i	$-0.713141\pi$
$419$	−25.4097			−1.24135			−0.620673	+	0.784070i	$0.713141\pi$
$420$		0			0
$421$	3.34730	+	2.80872i	0.163137	+	0.136888i	0.720702	−	0.693245i	$-0.243820\pi$
$421$	3.34730	+	2.80872i	0.163137	+	0.136888i	−0.557565	+	0.830134i	$0.688264\pi$
$422$	−3.09967	−	1.12819i	−0.150890	−	0.0549193i
$423$		0			0
$424$	−6.39827	+	5.36879i	−0.310727	+	0.260731i
$425$	−0.988856	−	1.71275i	−0.0479665	−	0.0830805i
$426$		0			0
$427$	0.550507	+	3.12208i	0.0266409	+	0.151088i
$428$	0.328411	+	1.86251i	0.0158744	+	0.0900279i
$429$		0			0
$430$	2.31134	+	4.00335i	0.111463	+	0.193059i
$431$	29.3444	−	24.6228i	1.41347	−	1.18604i	0.458736	−	0.888572i	$-0.348302\pi$
$431$	29.3444	−	24.6228i	1.41347	−	1.18604i	0.954732	−	0.297468i	$-0.0961422\pi$
$432$		0			0
$433$	17.0376	+	6.20118i	0.818775	+	0.298010i	0.717244	−	0.696823i	$-0.245403\pi$
$433$	17.0376	+	6.20118i	0.818775	+	0.298010i	0.101532	+	0.994832i	$0.467626\pi$
$434$	−2.54710	−	2.13727i	−0.122265	−	0.102592i
$435$		0			0
$436$	0.336867			0.0161330
$437$	11.5517	+	2.12467i	0.552592	+	0.101637i
$438$		0			0
$439$	−1.05762	+	5.99806i	−0.0504774	+	0.286272i	−0.999589	−	0.0286685i	$-0.990873\pi$
$439$	−1.05762	+	5.99806i	−0.0504774	+	0.286272i	0.949112	+	0.314940i	$0.101984\pi$
$440$	4.41534	+	3.70491i	0.210493	+	0.176625i
$441$		0			0
$442$	1.52481	−	0.554987i	0.0725280	−	0.0263981i
$443$	22.8995	−	19.2149i	1.08799	−	0.912928i	0.0914266	−	0.995812i	$-0.470857\pi$
$443$	22.8995	−	19.2149i	1.08799	−	0.912928i	0.996559	+	0.0828833i	$0.0264129\pi$
$444$		0			0
$445$	4.52481	−	7.83721i	0.214497	−	0.371519i
$446$	−1.99092	−	11.2910i	−0.0942726	−	0.534646i
$447$		0			0
$448$	−1.49273	+	2.58548i	−0.0705247	+	0.122152i
$449$	−5.62495	−	9.74270i	−0.265458	−	0.459787i	0.702226	−	0.711955i	$-0.252190\pi$
$449$	−5.62495	−	9.74270i	−0.265458	−	0.459787i	−0.967683	+	0.252168i	$0.918856\pi$
$450$		0			0
$451$	5.18004	−	1.88538i	0.243919	−	0.0887792i
$452$	3.07145	+	1.11792i	0.144469	+	0.0525824i
$453$		0			0
$454$	3.31062	−	18.7755i	0.155375	−	0.881176i
$455$	−0.786112			−0.0368535
$456$		0			0
$457$	−23.3901			−1.09414			−0.547072	−	0.837086i	$-0.684258\pi$
$457$	−23.3901			−1.09414			−0.547072	+	0.837086i	$0.684258\pi$
$458$	−4.80381	+	27.2438i	−0.224468	+	1.27302i
$459$		0			0
$460$	−0.411474	−	0.149764i	−0.0191851	−	0.00698280i
$461$	−34.4149	+	12.5260i	−1.60286	+	0.583395i	−0.980011	−	0.198945i	$-0.936249\pi$
$461$	−34.4149	+	12.5260i	−1.60286	+	0.583395i	−0.622853	+	0.782339i	$0.714026\pi$
$462$		0			0
$463$	21.4932	+	37.2273i	0.998873	+	1.73010i	0.540534	+	0.841322i	$0.318222\pi$
$463$	21.4932	+	37.2273i	0.998873	+	1.73010i	0.458340	+	0.888777i	$0.348444\pi$
$464$	12.3701	−	21.4256i	0.574265	−	0.994657i
$465$		0			0
$466$	−4.12954	−	23.4198i	−0.191297	−	1.08490i
$467$	12.7981	−	22.1670i	0.592227	−	1.02577i	−0.401705	−	0.915769i	$-0.631582\pi$
$467$	12.7981	−	22.1670i	0.592227	−	1.02577i	0.993932	−	0.109998i	$-0.0350845\pi$
$468$		0			0
$469$	2.04189	−	1.71335i	0.0942857	−	0.0791151i
$470$	8.11721	−	2.95442i	0.374419	−	0.136277i
$471$		0			0
$472$	−14.2181	−	11.9304i	−0.654439	−	0.549140i
$473$	1.50862	−	8.55580i	0.0693663	−	0.393396i
$474$		0			0
$475$	11.9461	−	14.0258i	0.548124	−	0.643548i
$476$	0.0300295			0.00137640
$477$		0			0
$478$	−2.42783	−	2.03719i	−0.111046	−	0.0931791i
$479$	35.8739	+	13.0570i	1.63912	+	0.596591i	0.986885	−	0.161424i	$-0.0516088\pi$
$479$	35.8739	+	13.0570i	1.63912	+	0.596591i	0.652236	+	0.758016i	$0.273831\pi$
$480$		0			0
$481$	9.74763	−	8.17923i	0.444453	−	0.372941i
$482$	−9.29679	−	16.1025i	−0.423457	−	0.733449i
$483$		0			0
$484$	0.193877	+	1.09953i	0.00881261	+	0.0499788i
$485$	−1.44356	−	8.18685i	−0.0655488	−	0.371746i
$486$		0			0
$487$	−3.88191	−	6.72367i	−0.175906	−	0.304678i	0.764568	−	0.644543i	$-0.222952\pi$
$487$	−3.88191	−	6.72367i	−0.175906	−	0.304678i	−0.940475	+	0.339864i	$0.889619\pi$
$488$	−20.5835	+	17.2716i	−0.931773	+	0.781850i
$489$		0			0
$490$	−7.65910	−	2.78768i	−0.346003	−	0.125935i
$491$	28.1313	+	23.6050i	1.26955	+	1.06528i	0.994596	+	0.103822i	$0.0331071\pi$
$491$	28.1313	+	23.6050i	1.26955	+	1.06528i	0.274954	+	0.961457i	$0.411337\pi$
$492$		0			0
$493$	−3.21894			−0.144974
$494$	9.63104	+	11.6510i	0.433321	+	0.524201i
$495$		0			0
$496$	4.43763	−	25.1671i	0.199256	−	1.13003i
$497$	2.47565	+	2.07732i	0.111048	+	0.0931805i
$498$		0			0
$499$	−4.62923	+	1.68490i	−0.207233	+	0.0754266i	−0.443551	−	0.896249i	$-0.646281\pi$
$499$	−4.62923	+	1.68490i	−0.207233	+	0.0754266i	0.236318	+	0.971676i	$0.424059\pi$
$500$	−1.14858	+	0.963777i	−0.0513663	+	0.0431014i
$501$		0			0
$502$	−2.80587	+	4.85992i	−0.125232	+	0.216909i
$503$	−5.72163	−	32.4490i	−0.255115	−	1.44683i	−0.795778	−	0.605589i	$-0.792938\pi$
$503$	−5.72163	−	32.4490i	−0.255115	−	1.44683i	0.540663	−	0.841239i	$-0.318173\pi$
$504$		0			0
$505$	4.06670	−	7.04374i	0.180966	−	0.313442i
$506$	−4.04189	−	7.00076i	−0.179684	−	0.311222i
$507$		0			0
$508$	2.01501	−	0.733405i	0.0894018	−	0.0325396i
$509$	−34.7075	−	12.6325i	−1.53839	−	0.559926i	−0.572728	−	0.819746i	$-0.694115\pi$
$509$	−34.7075	−	12.6325i	−1.53839	−	0.559926i	−0.965657	+	0.259819i	$0.916337\pi$
$510$		0			0
$511$	0.0837781	−	0.475129i	0.00370613	−	0.0210185i
$512$	−24.9186			−1.10126
$513$		0			0
$514$	−0.898986			−0.0396526
$515$	0.841367	−	4.77163i	0.0370750	−	0.210263i
$516$		0			0
$517$	−15.2554	−	5.55250i	−0.670930	−	0.244199i
$518$	−2.17365	+	0.791143i	−0.0955046	+	0.0347608i
$519$		0			0
$520$	−3.33140	−	5.77016i	−0.146092	−	0.253038i
$521$	4.64590	−	8.04693i	0.203540	−	0.352542i	−0.746126	−	0.665804i	$-0.768088\pi$
$521$	4.64590	−	8.04693i	0.203540	−	0.352542i	0.949667	+	0.313262i	$0.101422\pi$
$522$		0			0
$523$	−4.93423	−	27.9834i	−0.215759	−	1.22363i	−0.879585	−	0.475742i	$-0.842180\pi$
$523$	−4.93423	−	27.9834i	−0.215759	−	1.22363i	0.663826	−	0.747887i	$-0.268932\pi$
$524$	−0.170493	+	0.295303i	−0.00744802	+	0.0129004i
$525$		0			0
$526$	−11.7654	+	9.87236i	−0.512996	+	0.430455i
$527$	−3.12449	+	1.13722i	−0.136105	+	0.0495381i
$528$		0			0
$529$	−12.0569	−	10.1169i	−0.524213	−	0.439867i
$530$	−0.583778	+	3.31077i	−0.0253577	+	0.143811i
$531$		0			0
$532$	0.0937404	+	0.263571i	0.00406416	+	0.0114273i
$533$	−6.37227			−0.276014
$534$		0			0
$535$	6.89440	+	5.78509i	0.298071	+	0.250111i
$536$	21.2294	+	7.72686i	0.916969	+	0.333749i
$537$		0			0
$538$	−20.0123	+	16.7923i	−0.862793	+	0.723969i
$539$	7.65910	+	13.2660i	0.329901	+	0.571405i
$540$		0			0
$541$	2.60220	+	14.7578i	0.111877	+	0.634487i	0.988249	+	0.152852i	$0.0488458\pi$
$541$	2.60220	+	14.7578i	0.111877	+	0.634487i	−0.876372	+	0.481635i	$0.840043\pi$
$542$	−3.13366	−	17.7718i	−0.134602	−	0.763366i
$543$		0			0
$544$	0.243756	+	0.422197i	0.0104509	+	0.0181016i
$545$	1.22803	−	1.03044i	0.0526028	−	0.0441390i
$546$		0			0
$547$	3.65270	+	1.32948i	0.156178	+	0.0568443i	0.418926	−	0.908020i	$-0.362407\pi$
$547$	3.65270	+	1.32948i	0.156178	+	0.0568443i	−0.262748	+	0.964864i	$0.584629\pi$
$548$	0.0362077	+	0.0303818i	0.00154672	+	0.00129785i
$549$		0			0
$550$	−12.6800			−0.540679
$551$	−10.0483	−	28.2529i	−0.428071	−	1.20361i
$552$		0			0
$553$	−0.714355	+	4.05131i	−0.0303775	+	0.172279i
$554$	18.3164	+	15.3693i	0.778189	+	0.652978i
$555$		0			0
$556$	0.740352	−	0.269466i	0.0313979	−	0.0114279i
$557$	−10.1152	+	8.48762i	−0.428593	+	0.359632i	−0.831420	−	0.555644i	$-0.812472\pi$
$557$	−10.1152	+	8.48762i	−0.428593	+	0.359632i	0.402828	+	0.915276i	$0.368027\pi$
$558$		0			0
$559$	−5.02141	+	8.69734i	−0.212383	+	0.367858i
$560$	0.190722	+	1.08164i	0.00805949	+	0.0457076i
$561$		0			0
$562$	12.3136	−	21.3278i	0.519418	−	0.899659i
$563$	5.35638	+	9.27752i	0.225745	+	0.391001i	0.956543	−	0.291593i	$-0.0941852\pi$
$563$	5.35638	+	9.27752i	0.225745	+	0.391001i	−0.730798	+	0.682594i	$0.760852\pi$
$564$		0			0
$565$	14.6163	−	5.31991i	0.614914	−	0.223810i
$566$	−9.73308	−	3.54255i	−0.409112	−	0.148905i
$567$		0			0
$568$	−4.75641	+	26.9749i	−0.199574	+	1.13184i
$569$	13.4706			0.564717			0.282358	−	0.959309i	$-0.408883\pi$
$569$	13.4706			0.564717			0.282358	+	0.959309i	$0.408883\pi$
$570$		0			0
$571$	12.6655			0.530035			0.265017	−	0.964244i	$-0.414622\pi$
$571$	12.6655			0.530035			0.265017	+	0.964244i	$0.414622\pi$
$572$	−0.183915	+	1.04303i	−0.00768988	+	0.0436115i
$573$		0			0
$574$	1.08853	+	0.396191i	0.0454342	+	0.0165367i
$575$	10.7023	−	3.89533i	0.446318	−	0.162447i
$576$		0			0
$577$	5.27719	+	9.14036i	0.219692	+	0.380518i	0.954714	−	0.297526i	$-0.0961613\pi$
$577$	5.27719	+	9.14036i	0.219692	+	0.380518i	−0.735022	+	0.678044i	$0.762828\pi$
$578$	11.3045	−	19.5800i	0.470206	−	0.814421i
$579$		0			0
$580$	0.194126	+	1.10094i	0.00806064	+	0.0457142i
$581$	−2.57532	+	4.46059i	−0.106842	+	0.185056i
$582$		0			0
$583$	4.84002	−	4.06126i	0.200453	−	0.168200i
$584$	3.84255	−	1.39857i	0.159006	−	0.0578734i
$585$		0			0
$586$	10.8400	+	9.09586i	0.447797	+	0.375746i
$587$	3.32619	−	18.8638i	0.137287	−	0.778591i	−0.835954	−	0.548800i	$-0.815085\pi$
$587$	3.32619	−	18.8638i	0.137287	−	0.778591i	0.973240	−	0.229791i	$-0.0738041\pi$
$588$		0			0
$589$	−19.7349	−	23.8739i	−0.813162	−	0.983706i
$590$	−7.47060			−0.307560
$591$		0			0
$592$	−13.6190	−	11.4277i	−0.559738	−	0.469676i
$593$	−8.17024	−	2.97373i	−0.335512	−	0.122116i	0.168770	−	0.985655i	$-0.446020\pi$
$593$	−8.17024	−	2.97373i	−0.335512	−	0.122116i	−0.504282	+	0.863539i	$0.668243\pi$
$594$		0			0
$595$	0.109470	−	0.0918566i	0.00448785	−	0.00376575i
$596$	−1.53003	−	2.65009i	−0.0626724	−	0.108552i
$597$		0			0
$598$	1.62267	+	9.20264i	0.0663561	+	0.376324i
$599$	−3.44373	−	19.5303i	−0.140707	−	0.797988i	−0.970715	−	0.240236i	$-0.922775\pi$
$599$	−3.44373	−	19.5303i	−0.140707	−	0.797988i	0.830008	−	0.557752i	$-0.188336\pi$
$600$		0			0
$601$	16.8807	+	29.2383i	0.688579	+	1.19265i	0.972298	+	0.233747i	$0.0750986\pi$
$601$	16.8807	+	29.2383i	0.688579	+	1.19265i	−0.283718	+	0.958908i	$0.591568\pi$
$602$	1.39852	−	1.17350i	0.0569994	−	0.0478282i
$603$		0			0
$604$	−0.757426	−	0.275681i	−0.0308192	−	0.0112173i
$605$	4.07011	+	3.41523i	0.165473	+	0.138849i
$606$		0			0
$607$	35.2850			1.43217			0.716087	−	0.698011i	$-0.245932\pi$
$607$	35.2850			1.43217			0.716087	+	0.698011i	$0.245932\pi$
$608$	−2.94475	+	3.45740i	−0.119425	+	0.140216i
$609$		0			0
$610$	−1.87804	+	10.6509i	−0.0760397	+	0.431242i
$611$	14.3760	+	12.0629i	0.581590	+	0.488012i
$612$		0			0
$613$	−17.3405	+	6.31142i	−0.700376	+	0.254916i	−0.667571	−	0.744546i	$-0.732666\pi$
$613$	−17.3405	+	6.31142i	−0.700376	+	0.254916i	−0.0328044	+	0.999462i	$0.510444\pi$
$614$	−12.0708	+	10.1286i	−0.487139	+	0.408758i
$615$		0			0
$616$	1.13816	−	1.97134i	0.0458576	−	0.0794277i
$617$	6.19671	+	35.1433i	0.249470	+	1.41482i	0.809878	+	0.586598i	$0.199533\pi$
$617$	6.19671	+	35.1433i	0.249470	+	1.41482i	−0.560408	+	0.828217i	$0.689356\pi$
$618$		0			0
$619$	−1.82976	+	3.16923i	−0.0735441	+	0.127382i	−0.900452	−	0.434955i	$-0.856764\pi$
$619$	−1.82976	+	3.16923i	−0.0735441	+	0.127382i	0.826908	+	0.562337i	$0.190098\pi$
$620$	0.577382	+	1.00005i	0.0231882	+	0.0401631i
$621$		0			0
$622$	20.2135	−	7.35710i	0.810487	−	0.294993i
$623$	−3.35844	−	1.22237i	−0.134553	−	0.0489733i
$624$		0			0
$625$	2.43077	−	13.7856i	0.0972308	−	0.551423i
$626$	−35.8767			−1.43392
$627$		0			0
$628$	1.77744			0.0709275
$629$	−0.401674	+	2.27801i	−0.0160158	+	0.0908301i
$630$		0			0
$631$	0.745977	+	0.271514i	0.0296969	+	0.0108088i	0.356826	−	0.934171i	$-0.383859\pi$
$631$	0.745977	+	0.271514i	0.0296969	+	0.0108088i	−0.327129	+	0.944980i	$0.606081\pi$
$632$	−32.7645	+	11.9253i	−1.30330	+	0.474362i
$633$		0			0
$634$	19.8942	+	34.4578i	0.790101	+	1.36850i
$635$	5.10220	−	8.83726i	0.202474	−	0.350696i
$636$		0			0
$637$	−3.07486	−	17.4384i	−0.121830	−	0.690933i
$638$	−10.3191	+	17.8732i	−0.408536	+	0.707605i
$639$		0			0
$640$	−6.39827	+	5.36879i	−0.252914	+	0.212220i
$641$	27.6104	−	10.0494i	1.09055	−	0.396926i	0.266723	−	0.963773i	$-0.414059\pi$
$641$	27.6104	−	10.0494i	1.09055	−	0.396926i	0.823823	+	0.566847i	$0.191837\pi$
$642$		0			0
$643$	17.0168	+	14.2788i	0.671078	+	0.563101i	0.913384	−	0.407098i	$-0.133459\pi$
$643$	17.0168	+	14.2788i	0.671078	+	0.563101i	−0.242306	+	0.970200i	$0.577904\pi$
$644$	−0.0300295	+	0.170306i	−0.00118333	+	0.00671099i
$645$		0			0
$646$	−2.70258	−	0.497079i	−0.106332	−	0.0195573i
$647$	−11.2591			−0.442640			−0.221320	−	0.975201i	$-0.571037\pi$
$647$	−11.2591			−0.442640			−0.221320	+	0.975201i	$0.571037\pi$
$648$		0			0
$649$	10.7554	+	9.02482i	0.422185	+	0.354255i
$650$	13.7738	+	5.01325i	0.540252	+	0.196636i
$651$		0			0
$652$	−1.18273	+	0.992431i	−0.0463194	+	0.0388666i
$653$	13.5000	+	23.3827i	0.528296	+	0.915035i	0.999456	+	0.0329874i	$0.0105021\pi$
$653$	13.5000	+	23.3827i	0.528296	+	0.915035i	−0.471160	+	0.882048i	$0.656165\pi$
$654$		0			0
$655$	0.281774	+	1.59802i	0.0110098	+	0.0624399i
$656$	1.54601	+	8.76785i	0.0603615	+	0.342327i
$657$		0			0
$658$	−1.70574	−	2.95442i	−0.0664966	−	0.115175i
$659$	−21.4691	+	18.0147i	−0.836317	+	0.701753i	−0.956732	−	0.290970i	$-0.906022\pi$
$659$	−21.4691	+	18.0147i	−0.836317	+	0.701753i	0.120415	+	0.992724i	$0.461577\pi$
$660$		0			0
$661$	−10.6823	−	3.88803i	−0.415492	−	0.151227i	0.125811	−	0.992054i	$-0.459847\pi$
$661$	−10.6823	−	3.88803i	−0.415492	−	0.151227i	−0.541303	+	0.840827i	$0.682069\pi$
$662$	28.5533	+	23.9590i	1.10975	+	0.931194i
$663$		0			0
$664$	−43.6551			−1.69415
$665$	1.14796	+	0.674089i	0.0445158	+	0.0261400i
$666$		0			0
$667$	3.21894	−	18.2555i	0.124638	−	0.706857i
$668$	0.571203	+	0.479297i	0.0221005	+	0.0185445i
$669$		0			0
$670$	8.54488	−	3.11008i	0.330118	−	0.120153i
$671$	15.5706	−	13.0653i	0.601095	−	0.504379i
$672$		0			0
$673$	8.28359	−	14.3476i	0.319309	−	0.553059i	−0.661035	−	0.750355i	$-0.729883\pi$
$673$	8.28359	−	14.3476i	0.319309	−	0.553059i	0.980344	+	0.197296i	$0.0632160\pi$
$674$	4.17840	+	23.6969i	0.160946	+	0.912769i
$675$		0			0
$676$	−0.588993	+	1.02017i	−0.0226536	+	0.0392371i
$677$	−4.52481	−	7.83721i	−0.173903	−	0.301208i	0.765878	−	0.642986i	$-0.222305\pi$
$677$	−4.52481	−	7.83721i	−0.173903	−	0.301208i	−0.939781	+	0.341777i	$0.888971\pi$
$678$		0			0
$679$	−3.08512	+	1.12289i	−0.118396	+	0.0430927i
$680$	1.13816	+	0.414255i	0.0436463	+	0.0158859i
$681$		0			0
$682$	−3.70187	+	20.9943i	−0.141752	+	0.803914i
$683$	−8.73143			−0.334099			−0.167049	−	0.985949i	$-0.553424\pi$
$683$	−8.73143			−0.334099			−0.167049	+	0.985949i	$0.553424\pi$
$684$		0			0
$685$	0.224927			0.00859402
$686$	−1.12773	+	6.39566i	−0.0430568	+	0.244187i
$687$		0			0
$688$	13.1853	+	4.79904i	0.502683	+	0.182962i
$689$	−6.86319	+	2.49800i	−0.261467	+	0.0951661i
$690$		0			0
$691$	−17.3601	−	30.0686i	−0.660409	−	1.14386i	−0.980508	−	0.196478i	$-0.937050\pi$
$691$	−17.3601	−	30.0686i	−0.660409	−	1.14386i	0.320099	−	0.947384i	$-0.396284\pi$
$692$	1.86122	−	3.22372i	0.0707528	−	0.122547i
$693$		0			0
$694$	1.35710	+	7.69648i	0.0515147	+	0.292154i
$695$	1.87464	−	3.24697i	0.0711091	−	0.123164i
$696$		0			0
$697$	0.887374	−	0.744596i	0.0336117	−	0.0282036i
$698$	−6.80154	+	2.47556i	−0.257442	+	0.0937012i
$699$		0			0
$700$	0.207796	+	0.174362i	0.00785397	+	0.00659026i
$701$	−6.84436	+	38.8163i	−0.258508	+	1.46607i	0.528397	+	0.848997i	$0.322793\pi$
$701$	−6.84436	+	38.8163i	−0.258508	+	1.46607i	−0.786905	+	0.617074i	$0.788318\pi$
$702$		0			0
$703$	−21.2481	+	3.58553i	−0.801387	+	0.135231i
$704$	19.1411			0.721409
$705$		0			0
$706$	26.0442	+	21.8537i	0.980185	+	0.822473i
$707$	−3.01842	−	1.09861i	−0.113519	−	0.0413176i
$708$		0			0
$709$	−31.5009	+	26.4324i	−1.18304	+	0.992690i	−0.183088	+	0.983096i	$0.558609\pi$
$709$	−31.5009	+	26.4324i	−1.18304	+	0.992690i	−0.999954	+	0.00959399i	$0.996946\pi$
$710$	5.51249	+	9.54791i	0.206880	+	0.358327i
$711$		0			0
$712$	−5.26011	−	29.8316i	−0.197131	−	1.11799i
$713$	−3.32501	−	18.8571i	−0.124523	−	0.706202i
$714$		0			0
$715$	2.52007	+	4.36488i	0.0942452	+	0.163237i
$716$	−1.62970	+	1.36748i	−0.0609047	+	0.0511051i
$717$		0			0
$718$	8.46585	+	3.08132i	0.315943	+	0.114994i
$719$	32.4768	+	27.2513i	1.21118	+	1.01630i	0.999238	+	0.0390200i	$0.0124236\pi$
$719$	32.4768	+	27.2513i	1.21118	+	1.01630i	0.211943	+	0.977282i	$0.432021\pi$
$720$		0			0
$721$	−1.91353			−0.0712637
$722$	−4.07351	−	25.2724i	−0.151600	−	0.940543i
$723$		0			0
$724$	−0.273947	+	1.55363i	−0.0101812	+	0.0577403i
$725$	−22.2743	−	18.6903i	−0.827245	−	0.694141i
$726$		0			0
$727$	−48.5411	+	17.6675i	−1.80029	+	0.655251i	−0.801965	+	0.597371i	$0.796212\pi$
$727$	−48.5411	+	17.6675i	−1.80029	+	0.655251i	−0.998324	+	0.0578805i	$0.981566\pi$
$728$	−2.01573	+	1.69140i	−0.0747079	+	0.0626874i
$729$		0			0
$730$	0.822948	−	1.42539i	0.0304587	−	0.0527560i
$731$	−0.317018	−	1.79790i	−0.0117254	−	0.0664978i
$732$		0			0
$733$	11.4581	−	19.8460i	0.423215	−	0.733030i	−0.573037	−	0.819530i	$-0.694235\pi$
$733$	11.4581	−	19.8460i	0.423215	−	0.733030i	0.996252	+	0.0864997i	$0.0275682\pi$
$734$	−5.46926	−	9.47303i	−0.201874	−	0.349656i
$735$		0			0
$736$	−2.63816	+	0.960210i	−0.0972437	+	0.0353938i
$737$	−16.0591	−	5.84504i	−0.591545	−	0.215305i
$738$		0			0
$739$	4.88413	−	27.6993i	0.179666	−	1.01894i	−0.752954	−	0.658074i	$-0.771372\pi$
$739$	4.88413	−	27.6993i	0.179666	−	1.01894i	0.932619	−	0.360862i	$-0.117517\pi$
$740$	0.803348			0.0295317
$741$		0			0
$742$	1.32770			0.0487413
$743$	−1.06489	+	6.03931i	−0.0390671	+	0.221561i	−0.998091	−	0.0617657i	$-0.980327\pi$
$743$	−1.06489	+	6.03931i	−0.0390671	+	0.221561i	0.959024	+	0.283326i	$0.0914380\pi$
$744$		0			0
$745$	−13.6839	−	4.98054i	−0.501340	−	0.182473i
$746$	−44.1819	+	16.0809i	−1.61761	+	0.588763i
$747$		0			0
$748$	−0.0962667	−	0.166739i	−0.00351986	−	0.00609657i
$749$	1.77719	−	3.07818i	0.0649371	−	0.112474i
$750$		0			0
$751$	0.979522	+	5.55515i	0.0357433	+	0.202710i	0.997450	−	0.0713710i	$-0.0227374\pi$
$751$	0.979522	+	5.55515i	0.0357433	+	0.202710i	−0.961707	+	0.274081i	$0.911626\pi$
$752$	13.1099	−	22.7071i	0.478070	−	0.828042i
$753$		0			0
$754$	18.2756	−	15.3350i	0.665558	−	0.558469i
$755$	−3.60442	+	1.31190i	−0.131178	+	0.0477450i
$756$		0			0
$757$	12.0207	+	10.0866i	0.436900	+	0.366602i	0.834548	−	0.550936i	$-0.185729\pi$
$757$	12.0207	+	10.0866i	0.436900	+	0.366602i	−0.397648	+	0.917538i	$0.630173\pi$
$758$	0.398052	−	2.25746i	0.0144579	−	0.0819948i
$759$		0			0
$760$	−0.0830629	+	11.2828i	−0.00301301	+	0.409271i
$761$	−4.86484			−0.176350			−0.0881751	−	0.996105i	$-0.528104\pi$
$761$	−4.86484			−0.176350			−0.0881751	+	0.996105i	$0.528104\pi$
$762$		0			0
$763$	−0.484985	−	0.406951i	−0.0175576	−	0.0147326i
$764$	−3.18392	−	1.15885i	−0.115190	−	0.0419257i
$765$		0			0
$766$	−3.03099	+	2.54331i	−0.109514	+	0.0918934i
$767$	−8.11499	−	14.0556i	−0.293015	−	0.507517i
$768$		0			0
$769$	3.91266	+	22.1898i	0.141094	+	0.800184i	0.970421	+	0.241420i	$0.0776131\pi$
$769$	3.91266	+	22.1898i	0.141094	+	0.800184i	−0.829327	+	0.558764i	$0.811276\pi$
$770$	−0.159100	−	0.902302i	−0.00573358	−	0.0325167i
$771$		0			0
$772$	0.0275033	+	0.0476371i	0.000989864	+	0.00171450i
$773$	20.2481	−	16.9902i	0.728273	−	0.611094i	−0.201387	−	0.979512i	$-0.564545\pi$
$773$	20.2481	−	16.9902i	0.728273	−	0.611094i	0.929660	+	0.368418i	$0.120100\pi$
$774$		0			0
$775$	−28.2237	−	10.2726i	−1.01383	−	0.369003i
$776$	−21.3164	−	17.8866i	−0.765214	−	0.642091i
$777$		0			0
$778$	33.0993			1.18667
$779$	9.30541	+	5.46421i	0.333401	+	0.195776i
$780$		0			0
$781$	3.59802	−	20.4054i	0.128747	−	0.730162i
$782$	−1.30129	−	1.09191i	−0.0465340	−	0.0390466i
$783$		0			0
$784$	−23.2481	+	8.46161i	−0.830289	+	0.302200i
$785$	6.47952	−	5.43696i	0.231264	−	0.194054i
$786$		0			0
$787$	7.77884	−	13.4733i	0.277286	−	0.480273i	−0.693424	−	0.720530i	$-0.743899\pi$
$787$	7.77884	−	13.4733i	0.277286	−	0.480273i	0.970709	+	0.240257i	$0.0772318\pi$
$788$	0.421685	+	2.39149i	0.0150219	+	0.0851934i
$789$		0			0
$790$	−7.01707	+	12.1539i	−0.249656	+	0.432417i
$791$	−3.07145	−	5.31991i	−0.109208	−	0.189154i
$792$		0			0
$793$	−22.0792	+	8.03617i	−0.784055	+	0.285373i
$794$	40.3055	+	14.6700i	1.43039	+	0.520618i
$795$		0			0
$796$	0.00823757	−	0.0467176i	0.000291973	−	0.00165586i
$797$	−33.4935			−1.18640			−0.593200	−	0.805055i	$-0.702136\pi$
$797$	−33.4935			−1.18640			−0.593200	+	0.805055i	$0.702136\pi$
$798$		0			0
$799$	−3.41147			−0.120689
$800$	−0.764700	+	4.33683i	−0.0270362	+	0.153330i
$801$		0			0
$802$	−0.109470	−	0.0398440i	−0.00386553	−	0.00140694i
$803$	−2.90673	+	1.05796i	−0.102576	+	0.0373347i
$804$		0			0
$805$	0.411474	+	0.712694i	0.0145026	+	0.0251192i
$806$	12.3216	−	21.3416i	0.434010	−	0.751727i
$807$		0			0
$808$	−4.72756	−	26.8113i	−0.166315	−	0.943219i
$809$	20.5581	−	35.6076i	0.722784	−	1.25190i	−0.237096	−	0.971486i	$-0.576196\pi$
$809$	20.5581	−	35.6076i	0.722784	−	1.25190i	0.959880	−	0.280412i	$-0.0904711\pi$
$810$		0			0
$811$	12.7836	−	10.7267i	0.448892	−	0.376665i	−0.390132	−	0.920759i	$-0.627571\pi$
$811$	12.7836	−	10.7267i	0.448892	−	0.376665i	0.839025	+	0.544093i	$0.183126\pi$
$812$	0.414878	−	0.151003i	0.0145594	−	0.00529917i
$813$		0			0
$814$	11.3610	+	9.53298i	0.398202	+	0.334131i
$815$	−1.27584	+	7.23567i	−0.0446909	+	0.253455i
$816$		0			0
$817$	14.7907	−	8.39484i	0.517461	−	0.293698i
$818$	26.9540			0.942424
$819$		0			0
$820$	−0.308182	−	0.258595i	−0.0107622	−	0.00903054i
$821$	−29.4971	−	10.7361i	−1.02945	−	0.374691i	−0.228581	−	0.973525i	$-0.573409\pi$
$821$	−29.4971	−	10.7361i	−1.02945	−	0.374691i	−0.800873	+	0.598834i	$0.795631\pi$
$822$		0			0
$823$	35.4877	−	29.7777i	1.23702	−	1.03799i	0.239274	−	0.970952i	$-0.423091\pi$
$823$	35.4877	−	29.7777i	1.23702	−	1.03799i	0.997751	−	0.0670347i	$-0.0213538\pi$
$824$	−8.10922	−	14.0456i	−0.282498	−	0.489301i
$825$		0			0
$826$	0.512326	+	2.90555i	0.0178261	+	0.101097i
$827$	−7.07769	−	40.1396i	−0.246115	−	1.39579i	−0.817888	−	0.575377i	$-0.804855\pi$
$827$	−7.07769	−	40.1396i	−0.246115	−	1.39579i	0.571773	−	0.820412i	$-0.306256\pi$
$828$		0			0
$829$	17.7417	+	30.7295i	0.616195	+	1.06728i	0.990174	+	0.139843i	$0.0446598\pi$
$829$	17.7417	+	30.7295i	0.616195	+	1.06728i	−0.373979	+	0.927437i	$0.622007\pi$
$830$	−13.4604	+	11.2946i	−0.467217	+	0.392042i
$831$		0			0
$832$	−20.7922	−	7.56774i	−0.720840	−	0.262364i
$833$	2.46585	+	2.06910i	0.0854367	+	0.0716899i
$834$		0			0
$835$	3.54839			0.122797
$836$	1.16297	−	1.36543i	0.0402222	−	0.0472245i
$837$		0			0
$838$	−5.94475	+	33.7143i	−0.205358	+	1.16464i
$839$	29.2649	+	24.5562i	1.01034	+	0.847774i	0.988383	−	0.151985i	$-0.0485667\pi$
$839$	29.2649	+	24.5562i	1.01034	+	0.847774i	0.0219545	+	0.999759i	$0.493011\pi$
$840$		0			0
$841$	−17.2208	+	6.26784i	−0.593819	+	0.216132i
$842$	4.50980	−	3.78417i	0.155418	−	0.130411i
$843$		0			0
$844$	0.226215	−	0.391815i	0.00778663	−	0.0134868i
$845$	0.973430	+	5.52060i	0.0334870	+	0.189914i
$846$		0			0
$847$	1.04916	−	1.81720i	0.0360497	−	0.0624399i
$848$	5.10220	+	8.83726i	0.175210	+	0.303473i
$849$		0			0
$850$	−2.50387	+	0.911334i	−0.0858820	+	0.0312585i
$851$	−12.5175	−	4.55601i	−0.429096	−	0.156178i
$852$		0			0
$853$	−4.44568	+	25.2127i	−0.152217	+	0.863266i	0.809069	+	0.587714i	$0.199972\pi$
$853$	−4.44568	+	25.2127i	−0.152217	+	0.863266i	−0.961286	+	0.275552i	$0.911139\pi$
$854$	4.27126			0.146159
$855$		0			0
$856$	30.1257			1.02967
$857$	3.66163	−	20.7661i	0.125079	−	0.709357i	−0.856182	−	0.516674i	$-0.827170\pi$
$857$	3.66163	−	20.7661i	0.125079	−	0.709357i	0.981261	−	0.192683i	$-0.0617189\pi$
$858$		0			0
$859$	18.3871	+	6.69237i	0.627361	+	0.228341i	0.636082	−	0.771621i	$-0.280554\pi$
$859$	18.3871	+	6.69237i	0.627361	+	0.228341i	−0.00872148	+	0.999962i	$0.502776\pi$
$860$	−0.595800	+	0.216853i	−0.0203166	+	0.00739464i
$861$		0			0
$862$	−25.8050	−	44.6956i	−0.878922	−	1.52234i
$863$	2.47447	−	4.28591i	0.0842319	−	0.145894i	−0.820832	−	0.571170i	$-0.806490\pi$
$863$	2.47447	−	4.28591i	0.0842319	−	0.145894i	0.905064	+	0.425276i	$0.139823\pi$
$864$		0			0
$865$	−3.07604	−	17.4451i	−0.104588	−	0.593150i
$866$	12.2139	−	21.1552i	0.415047	−	0.718882i
$867$		0			0
$868$	0.349356	−	0.293144i	0.0118579	−	0.00994997i
$869$	24.7849	−	9.02098i	0.840771	−	0.306016i
$870$		0			0
$871$	15.1334	+	12.6984i	0.512776	+	0.430270i
$872$	0.931790	−	5.28444i	0.0315544	−	0.178954i
$873$		0			0
$874$	5.52166	−	14.8300i	0.186773	−	0.501633i
$875$	2.81790			0.0952623
$876$		0			0
$877$	0.934478	+	0.784120i	0.0315551	+	0.0264779i	0.658429	−	0.752643i	$-0.271221\pi$
$877$	0.934478	+	0.784120i	0.0315551	+	0.0264779i	−0.626874	+	0.779121i	$0.715666\pi$
$878$	7.71095	+	2.80656i	0.260232	+	0.0947167i
$879$		0			0
$880$	5.39440	−	4.52644i	0.181845	−	0.152586i
$881$	23.2515	+	40.2728i	0.783363	+	1.35682i	0.929972	+	0.367630i	$0.119831\pi$
$881$	23.2515	+	40.2728i	0.783363	+	1.35682i	−0.146609	+	0.989194i	$0.546836\pi$
$882$		0			0
$883$	2.24438	+	12.7285i	0.0755296	+	0.428349i	0.999001	+	0.0446828i	$0.0142277\pi$
$883$	2.24438	+	12.7285i	0.0755296	+	0.428349i	−0.923472	+	0.383667i	$0.874661\pi$
$884$	0.0386476	+	0.219182i	0.00129986	+	0.00737187i
$885$		0			0
$886$	−20.1374	−	34.8791i	−0.676531	−	1.17179i
$887$	17.7909	−	14.9283i	0.597359	−	0.501243i	−0.293237	−	0.956040i	$-0.594732\pi$
$887$	17.7909	−	14.9283i	0.597359	−	0.501243i	0.890595	+	0.454796i	$0.150288\pi$
$888$		0			0
$889$	−3.78699	−	1.37835i	−0.127012	−	0.0462284i
$890$	−9.34002	−	7.83721i	−0.313078	−	0.262704i
$891$		0			0
$892$	1.57255			0.0526528
$893$	−10.6493	−	29.9428i	−0.356365	−	1.00200i
$894$		0			0
$895$	−1.75800	+	9.97011i	−0.0587634	+	0.333264i
$896$	2.52687	+	2.12030i	0.0844169	+	0.0708342i
$897$		0			0
$898$	−14.2429	+	5.18398i	−0.475291	+	0.172992i
$899$	−37.4484	+	31.4229i	−1.24897	+	1.04801i
$900$		0			0
$901$	0.663848	−	1.14982i	0.0221160	−	0.0383060i
$902$	−1.28968	−	7.31412i	−0.0429416	−	0.243534i
$903$		0			0
$904$	26.0326	−	45.0897i	0.865830	−	1.49966i
$905$	3.75372	+	6.50163i	0.124778	+	0.216122i
$906$		0			0
$907$	37.5847	−	13.6797i	1.24798	−	0.454228i	0.368261	−	0.929722i	$-0.379953\pi$
$907$	37.5847	−	13.6797i	1.24798	−	0.454228i	0.879719	+	0.475495i	$0.157731\pi$
$908$	2.45723	+	0.894360i	0.0815462	+	0.0296804i
$909$		0			0
$910$	−0.183915	+	1.04303i	−0.00609673	+	0.0345763i
$911$	18.7997			0.622863			0.311431	−	0.950269i	$-0.399192\pi$
$911$	18.7997			0.622863			0.311431	+	0.950269i	$0.399192\pi$
$912$		0			0
$913$	33.0232			1.09291
$914$	−5.47225	+	31.0347i	−0.181006	+	1.02654i
$915$		0			0
$916$	−3.56552	−	1.29774i	−0.117808	−	0.0428787i
$917$	0.602196	−	0.219182i	0.0198863	−	0.00723801i
$918$		0			0
$919$	−19.9158	−	34.4952i	−0.656962	−	1.13789i	−0.981398	−	0.191984i	$-0.938508\pi$
$919$	−19.9158	−	34.4952i	−0.656962	−	1.13789i	0.324436	−	0.945908i	$-0.394825\pi$
$920$	−3.48751	+	6.04055i	−0.114980	+	0.199151i
$921$		0			0
$922$	8.56830	+	48.5932i	0.282182	+	1.60033i
$923$	−11.9760	+	20.7430i	−0.394193	+	0.682763i
$924$		0			0
$925$	−16.0064	+	13.4310i	−0.526287	+	0.441607i
$926$	54.4227	−	19.8082i	1.78844	−	0.650939i
$927$		0			0
$928$	5.49067	+	4.60722i	0.180240	+	0.151239i
$929$	−4.68051	+	26.5445i	−0.153563	+	0.870897i	0.806526	+	0.591199i	$0.201345\pi$
$929$	−4.68051	+	26.5445i	−0.153563	+	0.870897i	−0.960088	+	0.279698i	$0.909766\pi$
$930$		0			0
$931$	−10.4632	+	28.1019i	−0.342916	+	0.921002i
$932$	3.26176			0.106843
$933$		0			0
$934$	−26.4176	−	22.1670i	−0.864411	−	0.725327i
$935$	−0.860967	−	0.313366i	−0.0281566	−	0.0102482i
$936$		0			0
$937$	2.00980	−	1.68642i	0.0656573	−	0.0550930i	−0.609368	−	0.792887i	$-0.708577\pi$
$937$	2.00980	−	1.68642i	0.0656573	−	0.0550930i	0.675026	+	0.737794i	$0.264133\pi$
$938$	−1.79561	−	3.11008i	−0.0586287	−	0.101548i
$939$		0			0
$940$	0.205737	+	1.16679i	0.00671040	+	0.0380566i
$941$	3.24194	+	18.3860i	0.105684	+	0.599366i	0.990945	+	0.134270i	$0.0428690\pi$
$941$	3.24194	+	18.3860i	0.105684	+	0.599366i	−0.885260	+	0.465096i	$0.846020\pi$
$942$		0			0
$943$	3.33544	+	5.77715i	0.108617	+	0.188130i
$944$	−17.3708	+	14.5758i	−0.565370	+	0.474402i
$945$		0			0
$946$	−10.9991	−	4.00335i	−0.357612	−	0.130160i
$947$	−6.43448	−	5.39917i	−0.209092	−	0.175449i	0.532227	−	0.846602i	$-0.321355\pi$
$947$	−6.43448	−	5.39917i	−0.209092	−	0.175449i	−0.741320	+	0.671152i	$0.765800\pi$
$948$		0			0
$949$	3.57573			0.116073
$950$	−15.8150	−	19.1318i	−0.513105	−	0.620718i
$951$		0			0
$952$	0.0830629	−	0.471073i	0.00269208	−	0.0152676i
$953$	−25.8102	−	21.6573i	−0.836075	−	0.701550i	0.120602	−	0.992701i	$-0.461517\pi$
$953$	−25.8102	−	21.6573i	−0.836075	−	0.701550i	−0.956677	+	0.291151i	$0.905962\pi$
$954$		0			0
$955$	−15.1515	+	5.51470i	−0.490292	+	0.178452i
$956$	0.332997	−	0.279418i	0.0107699	−	0.00903701i
$957$		0			0
$958$	25.7173	−	44.5438i	0.830890	−	1.43914i
$959$	−0.0154253	−	0.0874810i	−0.000498108	−	0.00282491i
$960$		0			0
$961$	−9.74809	+	16.8842i	−0.314455	+	0.544651i
$962$	−8.57192	−	14.8470i	−0.276370	−	0.478686i
$963$		0			0
$964$	2.39646	−	0.872240i	0.0771848	−	0.0280930i
$965$	0.245977	+	0.0895284i	0.00791829	+	0.00288202i
$966$		0			0
$967$	2.03920	−	11.5649i	0.0655763	−	0.371902i	−0.934305	−	0.356475i	$-0.883978\pi$
$967$	2.03920	−	11.5649i	0.0655763	−	0.371902i	0.999881	−	0.0154262i	$-0.00491051\pi$
$968$	17.7847			0.571621
$969$		0			0
$970$	−11.2003			−0.359619
$971$	−2.22432	+	12.6147i	−0.0713817	+	0.404826i	0.928091	+	0.372354i	$0.121449\pi$
$971$	−2.22432	+	12.6147i	−0.0713817	+	0.404826i	−0.999473	+	0.0324723i	$0.989662\pi$
$972$		0			0
$973$	−1.39141	−	0.506431i	−0.0446065	−	0.0162354i
$974$	−9.82934	+	3.57759i	−0.314953	+	0.114633i
$975$		0			0
$976$	16.4140	+	28.4299i	0.525399	+	0.910018i
$977$	7.26382	−	12.5813i	0.232390	−	0.402512i	−0.726121	−	0.687567i	$-0.758679\pi$
$977$	7.26382	−	12.5813i	0.232390	−	0.402512i	0.958511	+	0.285055i	$0.0920120\pi$
$978$		0			0
$979$	3.97906	+	22.5663i	0.127171	+	0.721224i
$980$	0.558963	−	0.968153i	0.0178554	−	0.0309265i
$981$		0			0
$982$	37.9013	−	31.8029i	1.20948	−	1.01487i
$983$	−34.8158	+	12.6719i	−1.11045	+	0.404172i	−0.831159	−	0.556034i	$-0.812322\pi$
$983$	−34.8158	+	12.6719i	−1.11045	+	0.404172i	−0.279293	+	0.960206i	$0.590100\pi$
$984$		0			0
$985$	8.85251	+	7.42814i	0.282064	+	0.236680i
$986$	−0.753089	+	4.27098i	−0.0239832	+	0.136016i
$987$		0			0
$988$	−1.80313	+	1.02341i	−0.0573652	+	0.0325591i
$989$	10.5134			0.334307
$990$		0			0
$991$	2.62860	+	2.20566i	0.0835004	+	0.0700651i	0.683582	−	0.729873i	$-0.260421\pi$
$991$	2.62860	+	2.20566i	0.0835004	+	0.0700651i	−0.600082	+	0.799938i	$0.704865\pi$
$992$	6.95723	+	2.53223i	0.220892	+	0.0803983i
$993$		0			0
$994$	3.33544	−	2.79876i	0.105794	−	0.0887714i
$995$	−0.112874	−	0.195503i	−0.00357835	−	0.00619788i
$996$		0			0
$997$	2.21853	+	12.5819i	0.0702616	+	0.398473i	0.999574	+	0.0291792i	$0.00928933\pi$
$997$	2.21853	+	12.5819i	0.0702616	+	0.398473i	−0.929313	+	0.369294i	$0.879600\pi$
$998$	1.15254	+	6.53639i	0.0364831	+	0.206906i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.2.u.c.55.1		6
3.2	odd	2		19.2.e.a.17.1	yes	6
12.11	even	2		304.2.u.b.17.1		6
15.2	even	4		475.2.u.a.74.1		12
15.8	even	4		475.2.u.a.74.2		12
15.14	odd	2		475.2.l.a.226.1		6
19.3	odd	18		3249.2.a.s.1.2		3
19.9	even	9	inner	171.2.u.c.28.1		6
19.16	even	9		3249.2.a.z.1.2		3
21.2	odd	6		931.2.v.b.606.1		6
21.5	even	6		931.2.v.a.606.1		6
21.11	odd	6		931.2.x.a.226.1		6
21.17	even	6		931.2.x.b.226.1		6
21.20	even	2		931.2.w.a.834.1		6
57.2	even	18		361.2.c.h.68.2		6
57.5	odd	18		361.2.c.i.292.2		6
57.8	even	6		361.2.e.b.62.1		6
57.11	odd	6		361.2.e.f.62.1		6
57.14	even	18		361.2.c.h.292.2		6
57.17	odd	18		361.2.c.i.68.2		6
57.23	odd	18		361.2.e.g.234.1		6
57.26	odd	6		361.2.e.g.54.1		6
57.29	even	18		361.2.e.h.28.1		6
57.32	even	18		361.2.e.b.99.1		6
57.35	odd	18		361.2.a.g.1.2		3
57.41	even	18		361.2.a.h.1.2		3
57.44	odd	18		361.2.e.f.99.1		6
57.47	odd	18		19.2.e.a.9.1	✓	6
57.50	even	6		361.2.e.a.54.1		6
57.53	even	18		361.2.e.a.234.1		6
57.56	even	2		361.2.e.h.245.1		6
228.35	even	18		5776.2.a.br.1.3		3
228.47	even	18		304.2.u.b.161.1		6
228.155	odd	18		5776.2.a.bi.1.1		3
285.47	even	36		475.2.u.a.199.2		12
285.104	odd	18		475.2.l.a.351.1		6
285.149	odd	18		9025.2.a.bd.1.2		3
285.218	even	36		475.2.u.a.199.1		12
285.269	even	18		9025.2.a.x.1.2		3
399.47	even	18		931.2.x.b.655.1		6
399.104	even	18		931.2.w.a.883.1		6
399.275	odd	18		931.2.x.a.655.1		6
399.332	even	18		931.2.v.a.275.1		6
399.389	odd	18		931.2.v.b.275.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.2.e.a.9.1	✓	6	57.47	odd	18
19.2.e.a.17.1	yes	6	3.2	odd	2
171.2.u.c.28.1		6	19.9	even	9	inner
171.2.u.c.55.1		6	1.1	even	1	trivial
304.2.u.b.17.1		6	12.11	even	2
304.2.u.b.161.1		6	228.47	even	18
361.2.a.g.1.2		3	57.35	odd	18
361.2.a.h.1.2		3	57.41	even	18
361.2.c.h.68.2		6	57.2	even	18
361.2.c.h.292.2		6	57.14	even	18
361.2.c.i.68.2		6	57.17	odd	18
361.2.c.i.292.2		6	57.5	odd	18
361.2.e.a.54.1		6	57.50	even	6
361.2.e.a.234.1		6	57.53	even	18
361.2.e.b.62.1		6	57.8	even	6
361.2.e.b.99.1		6	57.32	even	18
361.2.e.f.62.1		6	57.11	odd	6
361.2.e.f.99.1		6	57.44	odd	18
361.2.e.g.54.1		6	57.26	odd	6
361.2.e.g.234.1		6	57.23	odd	18
361.2.e.h.28.1		6	57.29	even	18
361.2.e.h.245.1		6	57.56	even	2
475.2.l.a.226.1		6	15.14	odd	2
475.2.l.a.351.1		6	285.104	odd	18
475.2.u.a.74.1		12	15.2	even	4
475.2.u.a.74.2		12	15.8	even	4
475.2.u.a.199.1		12	285.218	even	36
475.2.u.a.199.2		12	285.47	even	36
931.2.v.a.275.1		6	399.332	even	18
931.2.v.a.606.1		6	21.5	even	6
931.2.v.b.275.1		6	399.389	odd	18
931.2.v.b.606.1		6	21.2	odd	6
931.2.w.a.834.1		6	21.20	even	2
931.2.w.a.883.1		6	399.104	even	18
931.2.x.a.226.1		6	21.11	odd	6
931.2.x.a.655.1		6	399.275	odd	18
931.2.x.b.226.1		6	21.17	even	6
931.2.x.b.655.1		6	399.47	even	18
3249.2.a.s.1.2		3	19.3	odd	18
3249.2.a.z.1.2		3	19.16	even	9
5776.2.a.bi.1.1		3	228.155	odd	18
5776.2.a.br.1.3		3	228.35	even	18
9025.2.a.x.1.2		3	285.269	even	18
9025.2.a.bd.1.2		3	285.149	odd	18

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:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	171.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.233956 - 1.32683i) q^{2} +(0.173648 + 0.0632028i) q^{4} +(0.826352 - 0.300767i) q^{5} +(-0.173648 - 0.300767i) q^{7} +(1.47178 - 2.54920i) q^{8} +O(q^{10})\)	\(q+(0.233956 - 1.32683i) q^{2} +(0.173648 + 0.0632028i) q^{4} +(0.826352 - 0.300767i) q^{5} +(-0.173648 - 0.300767i) q^{7} +(1.47178 - 2.54920i) q^{8} +(-0.205737 - 1.16679i) q^{10} +(-1.11334 + 1.92836i) q^{11} +(1.97178 - 1.65452i) q^{13} +(-0.439693 + 0.160035i) q^{14} +(-2.75490 - 2.31164i) q^{16} +(-0.0812519 + 0.460802i) q^{17} +(-4.29813 + 0.725293i) q^{19} +0.162504 q^{20} +(2.29813 + 1.92836i) q^{22} +(-2.53209 - 0.921605i) q^{23} +(-3.23783 + 2.71686i) q^{25} +(-1.73396 - 3.00330i) q^{26} +(-0.0111444 - 0.0632028i) q^{28} +(1.19459 + 6.77487i) q^{29} +(3.55303 + 6.15403i) q^{31} +(0.798133 - 0.669713i) q^{32} +(0.592396 + 0.215615i) q^{34} +(-0.233956 - 0.196312i) q^{35} +4.94356 q^{37} +(-0.0432332 + 5.87257i) q^{38} +(0.449493 - 2.54920i) q^{40} +(-1.89646 - 1.59132i) q^{41} +(-3.66637 + 1.33445i) q^{43} +(-0.315207 + 0.264490i) q^{44} +(-1.81521 + 3.14403i) q^{46} +(1.26604 + 7.18009i) q^{47} +(3.43969 - 5.95772i) q^{49} +(2.84730 + 4.93166i) q^{50} +(0.446967 - 0.162683i) q^{52} +(-2.66637 - 0.970481i) q^{53} +(-0.340022 + 1.92836i) q^{55} -1.02229 q^{56} +9.26857 q^{58} +(1.09492 - 6.20961i) q^{59} +(-8.57785 - 3.12208i) q^{61} +(8.99660 - 3.27449i) q^{62} +(-4.29813 - 7.44459i) q^{64} +(1.13176 - 1.96026i) q^{65} +(1.33275 + 7.55839i) q^{67} +(-0.0432332 + 0.0748822i) q^{68} +(-0.315207 + 0.264490i) q^{70} +(-8.74422 + 3.18264i) q^{71} +(1.06418 + 0.892951i) q^{73} +(1.15657 - 6.55926i) q^{74} +(-0.792204 - 0.145708i) q^{76} +0.773318 q^{77} +(-9.07398 - 7.61397i) q^{79} +(-2.97178 - 1.08164i) q^{80} +(-2.55509 + 2.14398i) q^{82} +(-7.41534 - 12.8438i) q^{83} +(0.0714517 + 0.405223i) q^{85} +(0.912818 + 5.17685i) q^{86} +(3.27719 + 5.67626i) q^{88} +(7.88326 - 6.61484i) q^{89} +(-0.840022 - 0.305743i) q^{91} +(-0.381445 - 0.320070i) q^{92} +9.82295 q^{94} +(-3.33363 + 1.89209i) q^{95} +(1.64156 - 9.30975i) q^{97} +(-7.10014 - 5.95772i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 6 q^{5} - 6 q^{8}+O(q^{10}) \) 6 * q + 6 * q^2 + 6 * q^5 - 6 * q^8	\( 6 q + 6 q^{2} + 6 q^{5} - 6 q^{8} + 9 q^{10} - 3 q^{13} + 3 q^{14} - 18 q^{16} - 3 q^{17} - 12 q^{19} + 6 q^{20} - 6 q^{23} - 15 q^{26} + 6 q^{28} + 3 q^{29} + 9 q^{31} - 9 q^{32} - 6 q^{35} + 15 q^{38} - 21 q^{41} - 3 q^{43} - 9 q^{44} - 18 q^{46} + 3 q^{47} + 15 q^{49} + 15 q^{50} + 15 q^{52} + 3 q^{53} + 18 q^{55} + 6 q^{56} + 36 q^{58} - 12 q^{59} - 12 q^{61} + 12 q^{62} - 12 q^{64} + 12 q^{65} - 30 q^{67} + 15 q^{68} - 9 q^{70} + 6 q^{71} - 12 q^{73} - 15 q^{74} + 36 q^{76} + 18 q^{77} - 39 q^{79} - 3 q^{80} - 54 q^{82} - 24 q^{86} + 9 q^{88} + 12 q^{89} + 15 q^{91} - 42 q^{92} + 18 q^{94} - 39 q^{95} + 18 q^{97} + 9 q^{98}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^5 - 6 * q^8 + 9 * q^10 - 3 * q^13 + 3 * q^14 - 18 * q^16 - 3 * q^17 - 12 * q^19 + 6 * q^20 - 6 * q^23 - 15 * q^26 + 6 * q^28 + 3 * q^29 + 9 * q^31 - 9 * q^32 - 6 * q^35 + 15 * q^38 - 21 * q^41 - 3 * q^43 - 9 * q^44 - 18 * q^46 + 3 * q^47 + 15 * q^49 + 15 * q^50 + 15 * q^52 + 3 * q^53 + 18 * q^55 + 6 * q^56 + 36 * q^58 - 12 * q^59 - 12 * q^61 + 12 * q^62 - 12 * q^64 + 12 * q^65 - 30 * q^67 + 15 * q^68 - 9 * q^70 + 6 * q^71 - 12 * q^73 - 15 * q^74 + 36 * q^76 + 18 * q^77 - 39 * q^79 - 3 * q^80 - 54 * q^82 - 24 * q^86 + 9 * q^88 + 12 * q^89 + 15 * q^91 - 42 * q^92 + 18 * q^94 - 39 * q^95 + 18 * q^97 + 9 * q^98

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