LMFDB - Embedded newform 171.2.u.c.28.1

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			28.1
Root			$-0.173648 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	171.28
Dual form			171.2.u.c.55.1

$q$-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 $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$1$	$e\left(\frac{4}{9}\right)$

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	0.948618	+	0.316423i	$0.102482\pi$
$2$	0.233956	+	1.32683i	0.165432	+	0.938209i	−0.783187	+	0.621786i	$0.786407\pi$
$3$		0			0
$3$		0			0
$4$	0.173648	−	0.0632028i	0.0868241	−	0.0316014i
$5$	0.826352	+	0.300767i	0.369556	+	0.134507i	0.520121	−	0.854093i	$-0.325887\pi$
$5$	0.826352	+	0.300767i	0.369556	+	0.134507i	−0.150565	+	0.988600i	$0.548109\pi$
$6$		0			0
$7$	−0.173648	+	0.300767i	−0.0656328	+	0.113679i	−0.896975	−	0.442082i	$-0.854240\pi$
$7$	−0.173648	+	0.300767i	−0.0656328	+	0.113679i	0.831342	+	0.555762i	$0.187573\pi$
$8$	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	0.647931	−	0.761699i	$-0.275634\pi$
$11$	−1.11334	−	1.92836i	−0.335685	−	0.581423i	−0.983616	+	0.180276i	$0.942301\pi$
$12$		0			0
$13$	1.97178	+	1.65452i	0.546874	+	0.458882i	0.873881	−	0.486140i	$-0.161596\pi$
$13$	1.97178	+	1.65452i	0.546874	+	0.458882i	−0.327007	+	0.945022i	$0.606040\pi$
$14$	−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	0.973368	−	0.229249i	$-0.0736270\pi$
$17$	−0.0812519	−	0.460802i	−0.0197065	−	0.111761i	−0.993074	+	0.117488i	$0.962516\pi$
$18$		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	−0.592235	−	0.805765i	$-0.701754\pi$
$23$	−2.53209	+	0.921605i	−0.527977	+	0.192168i	0.0642578	+	0.997933i	$0.479532\pi$
$24$		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	−0.646822	−	0.762641i	$-0.723903\pi$
$29$	1.19459	−	6.77487i	0.221830	−	1.25806i	0.868653	−	0.495421i	$-0.164986\pi$
$30$		0			0
$31$	3.55303	−	6.15403i	0.638144	−	1.10530i	−0.347696	−	0.937607i	$-0.613036\pi$
$31$	3.55303	−	6.15403i	0.638144	−	1.10530i	0.985840	−	0.167690i	$-0.0536307\pi$
$32$	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	−0.778751	−	0.627333i	$-0.784146\pi$
$41$	−1.89646	+	1.59132i	−0.296177	+	0.248522i	0.482574	+	0.875855i	$0.339702\pi$
$42$		0			0
$43$	−3.66637	−	1.33445i	−0.559117	−	0.203502i	0.0469757	−	0.998896i	$-0.485042\pi$
$43$	−3.66637	−	1.33445i	−0.559117	−	0.203502i	−0.606093	+	0.795394i	$0.707264\pi$
$44$	−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	−0.741705	−	0.670726i	$-0.765983\pi$
$47$	1.26604	−	7.18009i	0.184672	−	1.04732i	0.926377	−	0.376598i	$-0.122906\pi$
$48$		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	−0.518590	−	0.855023i	$-0.673543\pi$
$53$	−2.66637	+	0.970481i	−0.366255	+	0.133306i	0.152335	+	0.988329i	$0.451321\pi$
$54$		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	0.969304	+	0.245864i	$0.0790718\pi$
$59$	1.09492	+	6.20961i	0.142547	+	0.808423i	−0.826757	+	0.562559i	$0.809817\pi$
$60$		0			0
$61$	−8.57785	+	3.12208i	−1.09828	+	0.399742i	−0.826682	−	0.562669i	$-0.809775\pi$
$61$	−8.57785	+	3.12208i	−1.09828	+	0.399742i	−0.271599	+	0.962411i	$0.587552\pi$
$62$	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	−0.788461	−	0.615084i	$-0.789122\pi$
$67$	1.33275	−	7.55839i	0.162821	−	0.923405i	0.951283	−	0.308320i	$-0.0997669\pi$
$68$	−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	−0.233722	−	0.972303i	$-0.575091\pi$
$71$	−8.74422	−	3.18264i	−1.03775	−	0.377709i	−0.804026	+	0.594594i	$0.797313\pi$
$72$		0			0
$73$	1.06418	−	0.892951i	0.124553	−	0.104512i	−0.578384	−	0.815765i	$-0.696316\pi$
$73$	1.06418	−	0.892951i	0.124553	−	0.104512i	0.702936	+	0.711253i	$0.251872\pi$
$74$	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	−0.989741	−	0.142876i	$-0.954365\pi$
$79$	−9.07398	+	7.61397i	−1.02090	+	0.856639i	−0.0311616	+	0.999514i	$0.509921\pi$
$80$	−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	0.0961469	+	0.995367i	$0.469348\pi$
$83$	−7.41534	+	12.8438i	−0.813940	+	1.40979i	−0.910087	+	0.414418i	$0.863985\pi$
$84$		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	0.956575	−	0.291487i	$-0.0941501\pi$
$89$	7.88326	+	6.61484i	0.835623	+	0.701171i	−0.120951	+	0.992658i	$0.538594\pi$
$90$		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	0.947320	+	0.320287i	$0.103779\pi$
$97$	1.64156	+	9.30975i	0.166675	+	0.945261i	−0.780645	+	0.624974i	$0.785109\pi$
$98$	−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	0.923190	−	0.384343i	$-0.125572\pi$
$101$	7.08512	+	5.94512i	0.704996	+	0.591562i	−0.218194	+	0.975905i	$0.570017\pi$
$102$		0			0
$103$	2.75490	+	4.77163i	0.271448	+	0.470162i	0.969233	−	0.246145i	$-0.0791640\pi$
$103$	2.75490	+	4.77163i	0.271448	+	0.470162i	−0.697785	+	0.716308i	$0.745831\pi$
$104$	−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	−0.505282	−	0.862954i	$-0.668611\pi$
$107$	5.11721	−	8.86327i	0.494699	−	0.856845i	0.999981	+	0.00610974i	$0.00194480\pi$
$108$		0			0
$109$	1.71301	+	0.623485i	0.164077	+	0.0597190i	0.422753	−	0.906245i	$-0.361064\pi$
$109$	1.71301	+	0.623485i	0.164077	+	0.0597190i	−0.258676	+	0.965964i	$0.583286\pi$
$110$	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	0.945445	−	0.325782i	$-0.105627\pi$
$127$	8.88919	+	7.45891i	0.788788	+	0.661871i	−0.156657	+	0.987653i	$0.550072\pi$
$128$	−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	0.967605	−	0.252468i	$-0.0812422\pi$
$131$	−0.320422	−	1.81720i	−0.0279954	−	0.158770i	−0.995601	+	0.0936982i	$0.970131\pi$
$132$		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	−0.331732	−	0.943374i	$-0.607633\pi$
$137$	0.240352	−	0.0874810i	0.0205347	−	0.00747401i	0.352267	+	0.935900i	$0.385411\pi$
$138$		0			0
$139$	3.26604	+	2.74054i	0.277022	+	0.232449i	0.770704	−	0.637193i	$-0.219905\pi$
$139$	3.26604	+	2.74054i	0.277022	+	0.232449i	−0.493682	+	0.869643i	$0.664349\pi$
$140$	−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	−0.991919	−	0.126874i	$-0.959506\pi$
$149$	−12.6853	+	10.6442i	−1.03922	+	0.872007i	−0.0472981	+	0.998881i	$0.515061\pi$
$150$		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	0.676499	−	0.736444i	$-0.263496\pi$
$157$	9.03849	+	3.28974i	0.721350	+	0.262550i	0.0448510	+	0.998994i	$0.485719\pi$
$158$	−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	0.654748	−	0.755847i	$-0.272775\pi$
$163$	−4.17752	−	7.23567i	−0.327209	−	0.566742i	−0.981957	+	0.189105i	$0.939441\pi$
$164$	−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	−0.191120	−	0.981567i	$-0.561212\pi$
$167$	3.79174	−	1.38008i	0.293413	−	0.106794i	0.484533	+	0.874773i	$0.338990\pi$
$168$		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	0.766335	+	0.642441i	$0.222078\pi$
$173$	3.49794	+	19.8378i	0.265943	+	1.50824i	−0.500391	+	0.865799i	$0.666811\pi$
$174$		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	0.566652	−	0.823957i	$-0.308238\pi$
$179$	−5.75624	−	9.97011i	−0.430242	−	0.745201i	−0.996894	+	0.0787564i	$0.974905\pi$
$180$		0			0
$181$	1.48246	−	8.40744i	0.110190	−	0.624920i	−0.878829	−	0.477136i	$-0.841675\pi$
$181$	1.48246	−	8.40744i	0.110190	−	0.624920i	0.989020	−	0.147784i	$-0.0472141\pi$
$182$	−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	−0.634544	−	0.772887i	$-0.718812\pi$
$193$	0.228026	−	0.191336i	0.0164137	−	0.0137727i	0.650958	+	0.759114i	$0.274368\pi$
$194$	−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	−0.531203	−	0.847245i	$-0.678260\pi$
$197$	6.57057	−	11.3806i	0.468134	−	0.810832i	0.999337	+	0.0364128i	$0.0115931\pi$
$198$		0			0
$199$	−0.0445774	+	0.252811i	−0.00316001	+	0.0179213i	−0.986347	−	0.164680i	$-0.947341\pi$
$199$	−0.0445774	+	0.252811i	−0.00316001	+	0.0179213i	0.983187	+	0.182602i	$0.0584519\pi$
$200$	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	0.995938	−	0.0900364i	$-0.0286983\pi$
$211$	0.425145	+	2.41112i	0.0292682	+	0.165988i	−0.966670	+	0.256024i	$0.917587\pi$
$212$	−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	0.595589	−	0.803289i	$-0.296919\pi$
$223$	7.99660	+	2.91052i	0.535492	+	0.194903i	−0.0600971	+	0.998193i	$0.519141\pi$
$224$	−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	0.822366	−	0.568959i	$-0.192654\pi$
$233$	16.5865	+	6.03698i	1.08662	+	0.395496i	0.264249	+	0.964454i	$0.414876\pi$
$234$		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	0.901556	−	0.432663i	$-0.142426\pi$
$239$	1.17617	+	2.03719i	0.0760804	+	0.131775i	−0.825475	+	0.564438i	$0.809093\pi$
$240$		0			0
$241$	10.5719	+	8.87089i	0.680997	+	0.571424i	0.916298	−	0.400498i	$-0.131163\pi$
$241$	10.5719	+	8.87089i	0.680997	+	0.571424i	−0.235300	+	0.971923i	$0.575607\pi$
$242$	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	−0.462577	−	0.886579i	$-0.653075\pi$
$251$	−3.91400	+	1.42458i	−0.247050	+	0.0899187i	0.215528	+	0.976498i	$0.430853\pi$
$252$		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	−0.988208	−	0.153116i	$-0.951069\pi$
$257$	−0.115867	+	0.657115i	−0.00722759	+	0.0409897i	0.980981	+	0.194105i	$0.0621804\pi$
$258$		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	−0.871016	−	0.491254i	$-0.836539\pi$
$263$	−8.73261	+	7.32753i	−0.538476	+	0.451835i	0.332540	+	0.943089i	$0.392094\pi$
$264$		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	−0.971286	−	0.237916i	$-0.923536\pi$
$269$	−14.8537	+	12.4637i	−0.905646	+	0.759927i	0.0656400	+	0.997843i	$0.479091\pi$
$270$		0			0
$271$	12.5865	+	4.58110i	0.764573	+	0.278282i	0.694725	−	0.719276i	$-0.255526\pi$
$271$	12.5865	+	4.58110i	0.764573	+	0.278282i	0.0698486	+	0.997558i	$0.477748\pi$
$272$	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	−0.999250	−	0.0387161i	$-0.987673\pi$
$277$	−8.87346	−	15.3693i	−0.533154	−	0.923450i	0.466096	−	0.884734i	$-0.345660\pi$
$278$	−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	0.225622	−	0.974215i	$-0.427558\pi$
$281$	17.1766	−	6.25179i	1.02467	−	0.372950i	0.799050	+	0.601265i	$0.205336\pi$
$282$		0			0
$283$	1.33497	+	7.57099i	0.0793557	+	0.450049i	0.998432	+	0.0559700i	$0.0178251\pi$
$283$	1.33497	+	7.57099i	0.0793557	+	0.450049i	−0.919077	+	0.394079i	$0.871064\pi$
$284$	−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	0.670864	−	0.741581i	$-0.265924\pi$
$293$	−5.25150	−	9.09586i	−0.306796	−	0.531386i	−0.977660	+	0.210195i	$0.932590\pi$
$294$		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	−0.861598	−	0.507591i	$-0.830536\pi$
$307$	−8.95929	+	7.51774i	−0.511334	+	0.429060i	0.350264	+	0.936651i	$0.386092\pi$
$308$	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	−0.545881	−	0.837863i	$-0.683805\pi$
$311$	7.98293	−	13.8268i	0.452670	−	0.784048i	0.998551	+	0.0538151i	$0.0171382\pi$
$312$		0			0
$313$	−4.62402	+	26.2241i	−0.261365	+	1.48227i	0.517825	+	0.855487i	$0.326742\pi$
$313$	−4.62402	+	26.2241i	−0.261365	+	1.48227i	−0.779190	+	0.626788i	$0.784369\pi$
$314$	−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	−0.994465	−	0.105073i	$-0.966492\pi$
$317$	−22.6229	−	18.9829i	−1.27063	−	1.06618i	−0.276164	−	0.961111i	$-0.589063\pi$
$318$		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	−0.942687	−	0.333677i	$-0.891710\pi$
$331$	−13.8327	−	23.9590i	−0.760317	−	1.31691i	0.182371	−	0.983230i	$-0.441623\pi$
$332$	−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	−0.158279	−	0.987394i	$-0.550594\pi$
$337$	−16.7827	−	6.10841i	−0.914212	−	0.332746i	−0.755934	+	0.654648i	$0.772817\pi$
$338$	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	0.191541	−	0.981485i	$-0.438652\pi$
$347$	−5.45084	−	1.98394i	−0.292616	−	0.106504i	−0.484157	+	0.874981i	$0.660874\pi$
$348$		0			0
$349$	−2.68614	+	4.65253i	−0.143786	+	0.249044i	−0.928919	−	0.370282i	$-0.879261\pi$
$349$	−2.68614	+	4.65253i	−0.143786	+	0.249044i	0.785134	+	0.619326i	$0.212594\pi$
$350$	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	−0.977466	−	0.211095i	$-0.932297\pi$
$353$	−12.6172	−	21.8537i	−0.671546	−	1.16315i	0.305919	−	0.952057i	$-0.401036\pi$
$354$		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	−0.999996	−	0.00285518i	$-0.999091\pi$
$359$	−1.16116	−	6.58526i	−0.0612837	−	0.347557i	0.938712	−	0.344702i	$-0.112020\pi$
$360$		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	0.790516	−	0.612441i	$-0.209812\pi$
$367$	6.21941	+	5.21870i	0.324650	+	0.272414i	−0.465865	+	0.884856i	$0.654257\pi$
$368$	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	−0.0804968	+	0.996755i	$0.525651\pi$
$373$	−17.4488	+	30.2222i	−0.903463	+	1.56484i	−0.822967	+	0.568090i	$0.807683\pi$
$374$	−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	−0.698453	−	0.715656i	$-0.746128\pi$
$383$	−2.24969	+	1.88771i	−0.114954	+	0.0964575i	0.583499	+	0.812114i	$0.301683\pi$
$384$		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	−0.662344	−	0.749199i	$-0.730438\pi$
$389$	4.26604	−	24.1939i	0.216297	−	1.22668i	0.878642	−	0.477482i	$-0.158450\pi$
$390$		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	−0.731059	−	0.682314i	$-0.760974\pi$
$397$	−5.52822	−	31.3521i	−0.277453	−	1.57352i	0.453606	−	0.891202i	$-0.350137\pi$
$398$	−0.345866			−0.0173367
$399$		0			0
$400$	15.2003			0.760014
$401$	0.0150147	+	0.0851529i	0.000749801	+	0.00425233i	0.985180	−	0.171522i	$-0.0548683\pi$
$401$	0.0150147	+	0.0851529i	0.000749801	+	0.00425233i	−0.984431	+	0.175774i	$0.943757\pi$
$402$		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	−0.770019	−	0.638021i	$-0.779753\pi$
$409$	3.47400	−	19.7021i	0.171778	−	0.974204i	0.941797	−	0.336182i	$-0.109136\pi$
$410$	−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	−0.557565	−	0.830134i	$-0.688264\pi$
$421$	3.34730	−	2.80872i	0.163137	−	0.136888i	0.720702	+	0.693245i	$0.243820\pi$
$422$	−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	0.954732	+	0.297468i	$0.0961422\pi$
$431$	29.3444	+	24.6228i	1.41347	+	1.18604i	0.458736	+	0.888572i	$0.348302\pi$
$432$		0			0
$433$	17.0376	−	6.20118i	0.818775	−	0.298010i	0.101532	−	0.994832i	$-0.467626\pi$
$433$	17.0376	−	6.20118i	0.818775	−	0.298010i	0.717244	+	0.696823i	$0.245403\pi$
$434$	−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	0.949112	−	0.314940i	$-0.101984\pi$
$439$	−1.05762	−	5.99806i	−0.0504774	−	0.286272i	−0.999589	+	0.0286685i	$0.990873\pi$
$440$	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	0.996559	−	0.0828833i	$-0.0264129\pi$
$443$	22.8995	+	19.2149i	1.08799	+	0.912928i	0.0914266	+	0.995812i	$0.470857\pi$
$444$		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	−0.967683	−	0.252168i	$-0.918856\pi$
$449$	−5.62495	+	9.74270i	−0.265458	+	0.459787i	0.702226	+	0.711955i	$0.252190\pi$
$450$		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	−0.622853	−	0.782339i	$-0.714026\pi$
$461$	−34.4149	−	12.5260i	−1.60286	−	0.583395i	−0.980011	+	0.198945i	$0.936249\pi$
$462$		0			0
$463$	21.4932	−	37.2273i	0.998873	−	1.73010i	0.458340	−	0.888777i	$-0.348444\pi$
$463$	21.4932	−	37.2273i	0.998873	−	1.73010i	0.540534	−	0.841322i	$-0.318222\pi$
$464$	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	0.993932	+	0.109998i	$0.0350845\pi$
$467$	12.7981	+	22.1670i	0.592227	+	1.02577i	−0.401705	+	0.915769i	$0.631582\pi$
$468$		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	0.652236	−	0.758016i	$-0.273831\pi$
$479$	35.8739	−	13.0570i	1.63912	−	0.596591i	0.986885	+	0.161424i	$0.0516088\pi$
$480$		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	−0.940475	−	0.339864i	$-0.889619\pi$
$487$	−3.88191	+	6.72367i	−0.175906	+	0.304678i	0.764568	+	0.644543i	$0.222952\pi$
$488$	−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	0.274954	−	0.961457i	$-0.411337\pi$
$491$	28.1313	−	23.6050i	1.26955	−	1.06528i	0.994596	−	0.103822i	$-0.0331071\pi$
$492$		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	0.236318	−	0.971676i	$-0.424059\pi$
$499$	−4.62923	−	1.68490i	−0.207233	−	0.0754266i	−0.443551	+	0.896249i	$0.646281\pi$
$500$	−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	0.540663	+	0.841239i	$0.318173\pi$
$503$	−5.72163	+	32.4490i	−0.255115	+	1.44683i	−0.795778	+	0.605589i	$0.792938\pi$
$504$		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	−0.965657	−	0.259819i	$-0.916337\pi$
$509$	−34.7075	+	12.6325i	−1.53839	+	0.559926i	−0.572728	+	0.819746i	$0.694115\pi$
$510$		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	0.949667	−	0.313262i	$-0.101422\pi$
$521$	4.64590	+	8.04693i	0.203540	+	0.352542i	−0.746126	+	0.665804i	$0.768088\pi$
$522$		0			0
$523$	−4.93423	+	27.9834i	−0.215759	+	1.22363i	0.663826	+	0.747887i	$0.268932\pi$
$523$	−4.93423	+	27.9834i	−0.215759	+	1.22363i	−0.879585	+	0.475742i	$0.842180\pi$
$524$	−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	−0.876372	−	0.481635i	$-0.840043\pi$
$541$	2.60220	−	14.7578i	0.111877	−	0.634487i	0.988249	−	0.152852i	$-0.0488458\pi$
$542$	−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	−0.262748	−	0.964864i	$-0.584629\pi$
$547$	3.65270	−	1.32948i	0.156178	−	0.0568443i	0.418926	+	0.908020i	$0.362407\pi$
$548$	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	0.402828	−	0.915276i	$-0.368027\pi$
$557$	−10.1152	−	8.48762i	−0.428593	−	0.359632i	−0.831420	+	0.555644i	$0.812472\pi$
$558$		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	−0.730798	−	0.682594i	$-0.760852\pi$
$563$	5.35638	−	9.27752i	0.225745	−	0.391001i	0.956543	+	0.291593i	$0.0941852\pi$
$564$		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	−0.735022	−	0.678044i	$-0.762828\pi$
$577$	5.27719	−	9.14036i	0.219692	−	0.380518i	0.954714	+	0.297526i	$0.0961613\pi$
$578$	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	0.973240	+	0.229791i	$0.0738041\pi$
$587$	3.32619	+	18.8638i	0.137287	+	0.778591i	−0.835954	+	0.548800i	$0.815085\pi$
$588$		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	−0.504282	−	0.863539i	$-0.668243\pi$
$593$	−8.17024	+	2.97373i	−0.335512	+	0.122116i	0.168770	+	0.985655i	$0.446020\pi$
$594$		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	0.830008	+	0.557752i	$0.188336\pi$
$599$	−3.44373	+	19.5303i	−0.140707	+	0.797988i	−0.970715	+	0.240236i	$0.922775\pi$
$600$		0			0
$601$	16.8807	−	29.2383i	0.688579	−	1.19265i	−0.283718	−	0.958908i	$-0.591568\pi$
$601$	16.8807	−	29.2383i	0.688579	−	1.19265i	0.972298	−	0.233747i	$-0.0750986\pi$
$602$	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	−0.0328044	−	0.999462i	$-0.510444\pi$
$613$	−17.3405	−	6.31142i	−0.700376	−	0.254916i	−0.667571	+	0.744546i	$0.732666\pi$
$614$	−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	−0.560408	−	0.828217i	$-0.689356\pi$
$617$	6.19671	−	35.1433i	0.249470	−	1.41482i	0.809878	−	0.586598i	$-0.199533\pi$
$618$		0			0
$619$	−1.82976	−	3.16923i	−0.0735441	−	0.127382i	0.826908	−	0.562337i	$-0.190098\pi$
$619$	−1.82976	−	3.16923i	−0.0735441	−	0.127382i	−0.900452	+	0.434955i	$0.856764\pi$
$620$	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	−0.327129	−	0.944980i	$-0.606081\pi$
$631$	0.745977	−	0.271514i	0.0296969	−	0.0108088i	0.356826	+	0.934171i	$0.383859\pi$
$632$	−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	0.823823	−	0.566847i	$-0.191837\pi$
$641$	27.6104	+	10.0494i	1.09055	+	0.396926i	0.266723	+	0.963773i	$0.414059\pi$
$642$		0			0
$643$	17.0168	−	14.2788i	0.671078	−	0.563101i	−0.242306	−	0.970200i	$-0.577904\pi$
$643$	17.0168	−	14.2788i	0.671078	−	0.563101i	0.913384	+	0.407098i	$0.133459\pi$
$644$	−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	−0.471160	−	0.882048i	$-0.656165\pi$
$653$	13.5000	−	23.3827i	0.528296	−	0.915035i	0.999456	−	0.0329874i	$-0.0105021\pi$
$654$		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	0.120415	−	0.992724i	$-0.461577\pi$
$659$	−21.4691	−	18.0147i	−0.836317	−	0.701753i	−0.956732	+	0.290970i	$0.906022\pi$
$660$		0			0
$661$	−10.6823	+	3.88803i	−0.415492	+	0.151227i	−0.541303	−	0.840827i	$-0.682069\pi$
$661$	−10.6823	+	3.88803i	−0.415492	+	0.151227i	0.125811	+	0.992054i	$0.459847\pi$
$662$	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	0.980344	−	0.197296i	$-0.0632160\pi$
$673$	8.28359	+	14.3476i	0.319309	+	0.553059i	−0.661035	+	0.750355i	$0.729883\pi$
$674$	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	−0.939781	−	0.341777i	$-0.888971\pi$
$677$	−4.52481	+	7.83721i	−0.173903	+	0.301208i	0.765878	+	0.642986i	$0.222305\pi$
$678$		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	0.320099	+	0.947384i	$0.396284\pi$
$691$	−17.3601	+	30.0686i	−0.660409	+	1.14386i	−0.980508	+	0.196478i	$0.937050\pi$
$692$	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	−0.786905	−	0.617074i	$-0.788318\pi$
$701$	−6.84436	−	38.8163i	−0.258508	−	1.46607i	0.528397	−	0.848997i	$-0.322793\pi$
$702$		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	−0.999954	−	0.00959399i	$-0.996946\pi$
$709$	−31.5009	−	26.4324i	−1.18304	−	0.992690i	−0.183088	−	0.983096i	$-0.558609\pi$
$710$	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	0.211943	−	0.977282i	$-0.432021\pi$
$719$	32.4768	−	27.2513i	1.21118	−	1.01630i	0.999238	−	0.0390200i	$-0.0124236\pi$
$720$		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	−0.998324	−	0.0578805i	$-0.981566\pi$
$727$	−48.5411	−	17.6675i	−1.80029	−	0.655251i	−0.801965	−	0.597371i	$-0.796212\pi$
$728$	−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	0.996252	−	0.0864997i	$-0.0275682\pi$
$733$	11.4581	+	19.8460i	0.423215	+	0.733030i	−0.573037	+	0.819530i	$0.694235\pi$
$734$	−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	0.932619	+	0.360862i	$0.117517\pi$
$739$	4.88413	+	27.6993i	0.179666	+	1.01894i	−0.752954	+	0.658074i	$0.771372\pi$
$740$	0.803348			0.0295317
$741$		0			0
$742$	1.32770			0.0487413
$743$	−1.06489	−	6.03931i	−0.0390671	−	0.221561i	0.959024	−	0.283326i	$-0.0914380\pi$
$743$	−1.06489	−	6.03931i	−0.0390671	−	0.221561i	−0.998091	+	0.0617657i	$0.980327\pi$
$744$		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	−0.961707	−	0.274081i	$-0.911626\pi$
$751$	0.979522	−	5.55515i	0.0357433	−	0.202710i	0.997450	+	0.0713710i	$0.0227374\pi$
$752$	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	−0.397648	−	0.917538i	$-0.630173\pi$
$757$	12.0207	−	10.0866i	0.436900	−	0.366602i	0.834548	+	0.550936i	$0.185729\pi$
$758$	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	−0.829327	−	0.558764i	$-0.811276\pi$
$769$	3.91266	−	22.1898i	0.141094	−	0.800184i	0.970421	−	0.241420i	$-0.0776131\pi$
$770$	−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	0.929660	−	0.368418i	$-0.120100\pi$
$773$	20.2481	+	16.9902i	0.728273	+	0.611094i	−0.201387	+	0.979512i	$0.564545\pi$
$774$		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	0.970709	−	0.240257i	$-0.0772318\pi$
$787$	7.77884	+	13.4733i	0.277286	+	0.480273i	−0.693424	+	0.720530i	$0.743899\pi$
$788$	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	0.959880	+	0.280412i	$0.0904711\pi$
$809$	20.5581	+	35.6076i	0.722784	+	1.25190i	−0.237096	+	0.971486i	$0.576196\pi$
$810$		0			0
$811$	12.7836	+	10.7267i	0.448892	+	0.376665i	0.839025	−	0.544093i	$-0.183126\pi$
$811$	12.7836	+	10.7267i	0.448892	+	0.376665i	−0.390132	+	0.920759i	$0.627571\pi$
$812$	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	−0.800873	−	0.598834i	$-0.795631\pi$
$821$	−29.4971	+	10.7361i	−1.02945	+	0.374691i	−0.228581	+	0.973525i	$0.573409\pi$
$822$		0			0
$823$	35.4877	+	29.7777i	1.23702	+	1.03799i	0.997751	+	0.0670347i	$0.0213538\pi$
$823$	35.4877	+	29.7777i	1.23702	+	1.03799i	0.239274	+	0.970952i	$0.423091\pi$
$824$	−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	0.571773	+	0.820412i	$0.306256\pi$
$827$	−7.07769	+	40.1396i	−0.246115	+	1.39579i	−0.817888	+	0.575377i	$0.804855\pi$
$828$		0			0
$829$	17.7417	−	30.7295i	0.616195	−	1.06728i	−0.373979	−	0.927437i	$-0.622007\pi$
$829$	17.7417	−	30.7295i	0.616195	−	1.06728i	0.990174	−	0.139843i	$-0.0446598\pi$
$830$	−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	0.0219545	−	0.999759i	$-0.493011\pi$
$839$	29.2649	−	24.5562i	1.01034	−	0.847774i	0.988383	+	0.151985i	$0.0485667\pi$
$840$		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	−0.961286	−	0.275552i	$-0.911139\pi$
$853$	−4.44568	−	25.2127i	−0.152217	−	0.863266i	0.809069	−	0.587714i	$-0.199972\pi$
$854$	4.27126			0.146159
$855$		0			0
$856$	30.1257			1.02967
$857$	3.66163	+	20.7661i	0.125079	+	0.709357i	0.981261	+	0.192683i	$0.0617189\pi$
$857$	3.66163	+	20.7661i	0.125079	+	0.709357i	−0.856182	+	0.516674i	$0.827170\pi$
$858$		0			0
$859$	18.3871	−	6.69237i	0.627361	−	0.228341i	−0.00872148	−	0.999962i	$-0.502776\pi$
$859$	18.3871	−	6.69237i	0.627361	−	0.228341i	0.636082	+	0.771621i	$0.280554\pi$
$860$	−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	0.905064	−	0.425276i	$-0.139823\pi$
$863$	2.47447	+	4.28591i	0.0842319	+	0.145894i	−0.820832	+	0.571170i	$0.806490\pi$
$864$		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	−0.626874	−	0.779121i	$-0.715666\pi$
$877$	0.934478	−	0.784120i	0.0315551	−	0.0264779i	0.658429	+	0.752643i	$0.271221\pi$
$878$	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	−0.146609	−	0.989194i	$-0.546836\pi$
$881$	23.2515	−	40.2728i	0.783363	−	1.35682i	0.929972	−	0.367630i	$-0.119831\pi$
$882$		0			0
$883$	2.24438	−	12.7285i	0.0755296	−	0.428349i	−0.923472	−	0.383667i	$-0.874661\pi$
$883$	2.24438	−	12.7285i	0.0755296	−	0.428349i	0.999001	−	0.0446828i	$-0.0142277\pi$
$884$	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	0.890595	−	0.454796i	$-0.150288\pi$
$887$	17.7909	+	14.9283i	0.597359	+	0.501243i	−0.293237	+	0.956040i	$0.594732\pi$
$888$		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	0.879719	−	0.475495i	$-0.157731\pi$
$907$	37.5847	+	13.6797i	1.24798	+	0.454228i	0.368261	+	0.929722i	$0.379953\pi$
$908$	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	0.324436	+	0.945908i	$0.394825\pi$
$919$	−19.9158	+	34.4952i	−0.656962	+	1.13789i	−0.981398	+	0.191984i	$0.938508\pi$
$920$	−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	−0.960088	−	0.279698i	$-0.909766\pi$
$929$	−4.68051	−	26.5445i	−0.153563	−	0.870897i	0.806526	−	0.591199i	$-0.201345\pi$
$930$		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	0.675026	−	0.737794i	$-0.264133\pi$
$937$	2.00980	+	1.68642i	0.0656573	+	0.0550930i	−0.609368	+	0.792887i	$0.708577\pi$
$938$	−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	−0.885260	−	0.465096i	$-0.846020\pi$
$941$	3.24194	−	18.3860i	0.105684	−	0.599366i	0.990945	−	0.134270i	$-0.0428690\pi$
$942$		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	−0.741320	−	0.671152i	$-0.765800\pi$
$947$	−6.43448	+	5.39917i	−0.209092	+	0.175449i	0.532227	+	0.846602i	$0.321355\pi$
$948$		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	−0.956677	−	0.291151i	$-0.905962\pi$
$953$	−25.8102	+	21.6573i	−0.836075	+	0.701550i	0.120602	+	0.992701i	$0.461517\pi$
$954$		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	0.999881	+	0.0154262i	$0.00491051\pi$
$967$	2.03920	+	11.5649i	0.0655763	+	0.371902i	−0.934305	+	0.356475i	$0.883978\pi$
$968$	17.7847			0.571621
$969$		0			0
$970$	−11.2003			−0.359619
$971$	−2.22432	−	12.6147i	−0.0713817	−	0.404826i	−0.999473	−	0.0324723i	$-0.989662\pi$
$971$	−2.22432	−	12.6147i	−0.0713817	−	0.404826i	0.928091	−	0.372354i	$-0.121449\pi$
$972$		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	0.958511	−	0.285055i	$-0.0920120\pi$
$977$	7.26382	+	12.5813i	0.232390	+	0.402512i	−0.726121	+	0.687567i	$0.758679\pi$
$978$		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	−0.279293	−	0.960206i	$-0.590100\pi$
$983$	−34.8158	−	12.6719i	−1.11045	−	0.404172i	−0.831159	+	0.556034i	$0.812322\pi$
$984$		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	−0.600082	−	0.799938i	$-0.704865\pi$
$991$	2.62860	−	2.20566i	0.0835004	−	0.0700651i	0.683582	+	0.729873i	$0.260421\pi$
$992$	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	−0.929313	−	0.369294i	$-0.879600\pi$
$997$	2.21853	−	12.5819i	0.0702616	−	0.398473i	0.999574	−	0.0291792i	$-0.00928933\pi$
$998$	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.28.1		6
3.2	odd	2		19.2.e.a.9.1	✓	6
12.11	even	2		304.2.u.b.161.1		6
15.2	even	4		475.2.u.a.199.2		12
15.8	even	4		475.2.u.a.199.1		12
15.14	odd	2		475.2.l.a.351.1		6
19.6	even	9		3249.2.a.z.1.2		3
19.13	odd	18		3249.2.a.s.1.2		3
19.17	even	9	inner	171.2.u.c.55.1		6
21.2	odd	6		931.2.x.a.655.1		6
21.5	even	6		931.2.x.b.655.1		6
21.11	odd	6		931.2.v.b.275.1		6
21.17	even	6		931.2.v.a.275.1		6
21.20	even	2		931.2.w.a.883.1		6
57.2	even	18		361.2.e.h.245.1		6
57.5	odd	18		361.2.e.g.54.1		6
57.8	even	6		361.2.e.a.234.1		6
57.11	odd	6		361.2.e.g.234.1		6
57.14	even	18		361.2.e.a.54.1		6
57.17	odd	18		19.2.e.a.17.1	yes	6
57.23	odd	18		361.2.c.i.68.2		6
57.26	odd	6		361.2.e.f.99.1		6
57.29	even	18		361.2.c.h.292.2		6
57.32	even	18		361.2.a.h.1.2		3
57.35	odd	18		361.2.e.f.62.1		6
57.41	even	18		361.2.e.b.62.1		6
57.44	odd	18		361.2.a.g.1.2		3
57.47	odd	18		361.2.c.i.292.2		6
57.50	even	6		361.2.e.b.99.1		6
57.53	even	18		361.2.c.h.68.2		6
57.56	even	2		361.2.e.h.28.1		6
228.131	even	18		304.2.u.b.17.1		6
228.203	odd	18		5776.2.a.bi.1.1		3
228.215	even	18		5776.2.a.br.1.3		3
285.17	even	36		475.2.u.a.74.1		12
285.44	odd	18		9025.2.a.bd.1.2		3
285.74	odd	18		475.2.l.a.226.1		6
285.89	even	18		9025.2.a.x.1.2		3
285.188	even	36		475.2.u.a.74.2		12
399.17	even	18		931.2.x.b.226.1		6
399.74	odd	18		931.2.x.a.226.1		6
399.131	even	18		931.2.v.a.606.1		6
399.188	even	18		931.2.w.a.834.1		6
399.359	odd	18		931.2.v.b.606.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.2.e.a.9.1	✓	6	3.2	odd	2
19.2.e.a.17.1	yes	6	57.17	odd	18
171.2.u.c.28.1		6	1.1	even	1	trivial
171.2.u.c.55.1		6	19.17	even	9	inner
304.2.u.b.17.1		6	228.131	even	18
304.2.u.b.161.1		6	12.11	even	2
361.2.a.g.1.2		3	57.44	odd	18
361.2.a.h.1.2		3	57.32	even	18
361.2.c.h.68.2		6	57.53	even	18
361.2.c.h.292.2		6	57.29	even	18
361.2.c.i.68.2		6	57.23	odd	18
361.2.c.i.292.2		6	57.47	odd	18
361.2.e.a.54.1		6	57.14	even	18
361.2.e.a.234.1		6	57.8	even	6
361.2.e.b.62.1		6	57.41	even	18
361.2.e.b.99.1		6	57.50	even	6
361.2.e.f.62.1		6	57.35	odd	18
361.2.e.f.99.1		6	57.26	odd	6
361.2.e.g.54.1		6	57.5	odd	18
361.2.e.g.234.1		6	57.11	odd	6
361.2.e.h.28.1		6	57.56	even	2
361.2.e.h.245.1		6	57.2	even	18
475.2.l.a.226.1		6	285.74	odd	18
475.2.l.a.351.1		6	15.14	odd	2
475.2.u.a.74.1		12	285.17	even	36
475.2.u.a.74.2		12	285.188	even	36
475.2.u.a.199.1		12	15.8	even	4
475.2.u.a.199.2		12	15.2	even	4
931.2.v.a.275.1		6	21.17	even	6
931.2.v.a.606.1		6	399.131	even	18
931.2.v.b.275.1		6	21.11	odd	6
931.2.v.b.606.1		6	399.359	odd	18
931.2.w.a.834.1		6	399.188	even	18
931.2.w.a.883.1		6	21.20	even	2
931.2.x.a.226.1		6	399.74	odd	18
931.2.x.a.655.1		6	21.2	odd	6
931.2.x.b.226.1		6	399.17	even	18
931.2.x.b.655.1		6	21.5	even	6
3249.2.a.s.1.2		3	19.13	odd	18
3249.2.a.z.1.2		3	19.6	even	9
5776.2.a.bi.1.1		3	228.203	odd	18
5776.2.a.br.1.3		3	228.215	even	18
9025.2.a.x.1.2		3	285.89	even	18
9025.2.a.bd.1.2		3	285.44	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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