LMFDB - Embedded newform 735.2.q.e.214.4

Newspace parameters

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.q (of order $6$, degree $2$, not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.89539436150784.1
Defining polynomial:	$ x^{12} - 2x^{11} + 2x^{10} - 8x^{9} + 4x^{8} + 16x^{7} - 8x^{6} + 20x^{5} + 20x^{4} - 24x^{3} + 8x^{2} - 8x + 4 $ x^12 - 2x^11 + 2x^10 - 8x^9 + 4x^8 + 16x^7 - 8x^6 + 20x^5 + 20x^4 - 24x^3 + 8x^2 - 8*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			214.4
Root			$0.550552 + 0.147520i$ of defining polynomial
Character	$\chi$	$=$	735.214
Dual form			735.2.q.e.79.4

$q$-expansion

$f(q)$	$=$	$q+(0.167954 - 0.0969683i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.981194 + 1.69948i) q^{4} +(2.19130 + 0.445186i) q^{5} -0.193937 q^{6} +0.768452i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.167954 - 0.0969683i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.981194 + 1.69948i) q^{4} +(2.19130 + 0.445186i) q^{5} -0.193937 q^{6} +0.768452i q^{8} +(0.500000 + 0.866025i) q^{9} +(0.411207 - 0.137716i) q^{10} +(-1.00000 + 1.73205i) q^{11} +(1.69948 - 0.981194i) q^{12} -1.35026i q^{13} +(-1.67513 - 1.48119i) q^{15} +(-1.88787 - 3.26989i) q^{16} +(2.90141 + 1.67513i) q^{17} +(0.167954 + 0.0969683i) q^{18} +(2.67513 + 4.63346i) q^{19} +(-2.90668 + 3.28726i) q^{20} +0.387873i q^{22} +(-4.29755 + 2.48119i) q^{23} +(0.384226 - 0.665499i) q^{24} +(4.60362 + 1.95108i) q^{25} +(-0.130933 - 0.226782i) q^{26} -1.00000i q^{27} -7.92478 q^{29} +(-0.424974 - 0.0863379i) q^{30} +(-2.28726 + 3.96165i) q^{31} +(-1.96515 - 1.13458i) q^{32} +(1.73205 - 1.00000i) q^{33} +0.649738 q^{34} -1.96239 q^{36} +(-0.671816 + 0.387873i) q^{37} +(0.898598 + 0.518806i) q^{38} +(-0.675131 + 1.16936i) q^{39} +(-0.342104 + 1.68391i) q^{40} +3.73813 q^{41} +12.6253i q^{43} +(-1.96239 - 3.39896i) q^{44} +(0.710109 + 2.12032i) q^{45} +(-0.481194 + 0.833453i) q^{46} +(8.59511 - 4.96239i) q^{47} +3.77575i q^{48} +(0.962389 - 0.118714i) q^{50} +(-1.67513 - 2.90141i) q^{51} +(2.29474 + 1.32487i) q^{52} +(7.42575 + 4.28726i) q^{53} +(-0.0969683 - 0.167954i) q^{54} +(-2.96239 + 3.35026i) q^{55} -5.35026i q^{57} +(-1.33100 + 0.768452i) q^{58} +(-4.31265 + 7.46973i) q^{59} +(4.16089 - 1.39351i) q^{60} +(4.35026 + 7.53487i) q^{61} +0.887166i q^{62} +7.11142 q^{64} +(0.601118 - 2.95883i) q^{65} +(0.193937 - 0.335908i) q^{66} +(-8.59511 - 4.96239i) q^{67} +(-5.69370 + 3.28726i) q^{68} +4.96239 q^{69} +2.00000 q^{71} +(-0.665499 + 0.384226i) q^{72} +(-8.09756 - 4.67513i) q^{73} +(-0.0752228 + 0.130290i) q^{74} +(-3.01131 - 3.99149i) q^{75} -10.4993 q^{76} +0.261865i q^{78} +(5.35026 + 9.26693i) q^{79} +(-2.68119 - 8.00578i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.627835 - 0.362481i) q^{82} -3.22425i q^{83} +(5.61213 + 4.96239i) q^{85} +(1.22425 + 2.12047i) q^{86} +(6.86306 + 3.96239i) q^{87} +(-1.33100 - 0.768452i) q^{88} +(0.518806 + 0.898598i) q^{89} +(0.324869 + 0.287258i) q^{90} -9.73813i q^{92} +(3.96165 - 2.28726i) q^{93} +(0.962389 - 1.66691i) q^{94} +(3.79927 + 11.3443i) q^{95} +(1.13458 + 1.96515i) q^{96} -18.4993i q^{97} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 10 q^{4} - 2 q^{5} - 4 q^{6} + 6 q^{9}+O(q^{10}) $ 12 * q + 10 * q^4 - 2 * q^5 - 4 * q^6 + 6 * q^9	$ 12 q + 10 q^{4} - 2 q^{5} - 4 q^{6} + 6 q^{9} + 12 q^{10} - 12 q^{11} - 26 q^{16} + 12 q^{19} - 60 q^{20} - 18 q^{24} + 2 q^{25} - 20 q^{26} - 8 q^{29} + 10 q^{30} - 4 q^{31} + 48 q^{34} + 20 q^{36} + 12 q^{39} - 4 q^{40} + 8 q^{41} + 20 q^{44} + 2 q^{45} + 16 q^{46} - 32 q^{50} - 2 q^{54} + 8 q^{55} + 32 q^{59} + 8 q^{60} + 12 q^{61} - 52 q^{64} - 32 q^{65} + 4 q^{66} + 16 q^{69} + 24 q^{71} - 88 q^{74} - 8 q^{75} + 8 q^{76} + 24 q^{79} - 46 q^{80} - 6 q^{81} + 64 q^{85} + 8 q^{86} + 28 q^{89} + 24 q^{90} - 32 q^{94} - 4 q^{95} + 58 q^{96} - 24 q^{99}+O(q^{100}) $ 12 * q + 10 * q^4 - 2 * q^5 - 4 * q^6 + 6 * q^9 + 12 * q^10 - 12 * q^11 - 26 * q^16 + 12 * q^19 - 60 * q^20 - 18 * q^24 + 2 * q^25 - 20 * q^26 - 8 * q^29 + 10 * q^30 - 4 * q^31 + 48 * q^34 + 20 * q^36 + 12 * q^39 - 4 * q^40 + 8 * q^41 + 20 * q^44 + 2 * q^45 + 16 * q^46 - 32 * q^50 - 2 * q^54 + 8 * q^55 + 32 * q^59 + 8 * q^60 + 12 * q^61 - 52 * q^64 - 32 * q^65 + 4 * q^66 + 16 * q^69 + 24 * q^71 - 88 * q^74 - 8 * q^75 + 8 * q^76 + 24 * q^79 - 46 * q^80 - 6 * q^81 + 64 * q^85 + 8 * q^86 + 28 * q^89 + 24 * q^90 - 32 * q^94 - 4 * q^95 + 58 * q^96 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.167954	−	0.0969683i	0.118761	−	0.0685669i	−0.439443	−	0.898271i	$-0.644824\pi$
$2$	0.167954	−	0.0969683i	0.118761	−	0.0685669i	0.558204	+	0.829704i	$0.311491\pi$
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	−0.981194	+	1.69948i	−0.490597	+	0.849739i
$5$	2.19130	+	0.445186i	0.979981	+	0.199093i
$5$	2.19130	+	0.445186i	0.979981	+	0.199093i
$6$	−0.193937			−0.0791743
$7$		0			0
$7$		0			0
$8$			0.768452i			0.271689i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	0.411207	−	0.137716i	0.130035	−	0.0435496i
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	−0.976478	−	0.215615i	$-0.930824\pi$
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	0.674967	+	0.737848i	$0.264158\pi$
$12$	1.69948	−	0.981194i	0.490597	−	0.283246i
$13$		−	1.35026i		−	0.374495i	−0.982313	−	0.187248i	$-0.940043\pi$
$13$		−	1.35026i		−	0.374495i	0.982313	−	0.187248i	$-0.0599567\pi$
$14$		0			0
$15$	−1.67513	−	1.48119i	−0.432517	−	0.382443i
$16$	−1.88787	−	3.26989i	−0.471968	−	0.817473i
$17$	2.90141	+	1.67513i	0.703696	+	0.406279i	0.808722	−	0.588190i	$-0.200159\pi$
$17$	2.90141	+	1.67513i	0.703696	+	0.406279i	−0.105027	+	0.994469i	$0.533493\pi$
$18$	0.167954	+	0.0969683i	0.0395871	+	0.0228556i
$19$	2.67513	+	4.63346i	0.613717	+	1.06299i	0.990608	+	0.136732i	$0.0436598\pi$
$19$	2.67513	+	4.63346i	0.613717	+	1.06299i	−0.376891	+	0.926258i	$0.623007\pi$
$20$	−2.90668	+	3.28726i	−0.649953	+	0.735053i
$21$		0			0
$22$			0.387873i			0.0826948i
$23$	−4.29755	+	2.48119i	−0.896102	+	0.517365i	−0.875934	−	0.482432i	$-0.839754\pi$
$23$	−4.29755	+	2.48119i	−0.896102	+	0.517365i	−0.0201686	+	0.999797i	$0.506420\pi$
$24$	0.384226	−	0.665499i	0.0784298	−	0.135844i
$25$	4.60362	+	1.95108i	0.920724	+	0.390215i
$26$	−0.130933	−	0.226782i	−0.0256780	−	0.0444756i
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$	−7.92478			−1.47159			−0.735797	−	0.677202i	$-0.763192\pi$
$29$	−7.92478			−1.47159			−0.735797	+	0.677202i	$0.763192\pi$
$30$	−0.424974	−	0.0863379i	−0.0775892	−	0.0157631i
$31$	−2.28726	+	3.96165i	−0.410804	+	0.711533i	−0.994978	−	0.100096i	$-0.968085\pi$
$31$	−2.28726	+	3.96165i	−0.410804	+	0.711533i	0.584174	+	0.811628i	$0.301418\pi$
$32$	−1.96515	−	1.13458i	−0.347393	−	0.200567i
$33$	1.73205	−	1.00000i	0.301511	−	0.174078i
$34$	0.649738			0.111429
$35$		0			0
$36$	−1.96239			−0.327065
$37$	−0.671816	+	0.387873i	−0.110446	+	0.0637660i	−0.554205	−	0.832380i	$-0.686978\pi$
$37$	−0.671816	+	0.387873i	−0.110446	+	0.0637660i	0.443760	+	0.896146i	$0.353644\pi$
$38$	0.898598	+	0.518806i	0.145772	+	0.0841614i
$39$	−0.675131	+	1.16936i	−0.108107	+	0.187248i
$40$	−0.342104	+	1.68391i	−0.0540915	+	0.266250i
$41$	3.73813			0.583799			0.291899	−	0.956449i	$-0.405713\pi$
$41$	3.73813			0.583799			0.291899	+	0.956449i	$0.405713\pi$
$42$		0			0
$43$			12.6253i			1.92534i	0.270677	+	0.962670i	$0.412752\pi$
$43$			12.6253i			1.92534i	−0.270677	+	0.962670i	$0.587248\pi$
$44$	−1.96239	−	3.39896i	−0.295841	−	0.512412i
$45$	0.710109	+	2.12032i	0.105857	+	0.316078i
$46$	−0.481194	+	0.833453i	−0.0709482	+	0.122886i
$47$	8.59511	−	4.96239i	1.25373	−	0.723839i	0.281878	−	0.959450i	$-0.409043\pi$
$47$	8.59511	−	4.96239i	1.25373	−	0.723839i	0.971847	+	0.235611i	$0.0757093\pi$
$48$			3.77575i			0.544982i
$49$		0			0
$50$	0.962389	−	0.118714i	0.136102	−	0.0167887i
$51$	−1.67513	−	2.90141i	−0.234565	−	0.406279i
$52$	2.29474	+	1.32487i	0.318223	+	0.183726i
$53$	7.42575	+	4.28726i	1.02000	+	0.588900i	0.914105	−	0.405477i	$-0.132894\pi$
$53$	7.42575	+	4.28726i	1.02000	+	0.588900i	0.105900	+	0.994377i	$0.466228\pi$
$54$	−0.0969683	−	0.167954i	−0.0131957	−	0.0228556i
$55$	−2.96239	+	3.35026i	−0.399448	+	0.451749i
$56$		0			0
$57$		−	5.35026i		−	0.708659i
$58$	−1.33100	+	0.768452i	−0.174769	+	0.100903i
$59$	−4.31265	+	7.46973i	−0.561459	+	0.972476i	0.435910	+	0.899990i	$0.356427\pi$
$59$	−4.31265	+	7.46973i	−0.561459	+	0.972476i	−0.997369	+	0.0724858i	$0.976907\pi$
$60$	4.16089	−	1.39351i	0.537168	−	0.179901i
$61$	4.35026	+	7.53487i	0.556994	+	0.964742i	0.997745	+	0.0671126i	$0.0213787\pi$
$61$	4.35026	+	7.53487i	0.556994	+	0.964742i	−0.440751	+	0.897629i	$0.645288\pi$
$62$			0.887166i			0.112670i
$63$		0			0
$64$	7.11142			0.888927
$65$	0.601118	−	2.95883i	0.0745595	−	0.366998i
$66$	0.193937	−	0.335908i	0.0238719	−	0.0413474i
$67$	−8.59511	−	4.96239i	−1.05006	−	0.606252i	−0.127394	−	0.991852i	$-0.540661\pi$
$67$	−8.59511	−	4.96239i	−1.05006	−	0.606252i	−0.922666	+	0.385600i	$0.873994\pi$
$68$	−5.69370	+	3.28726i	−0.690462	+	0.398639i
$69$	4.96239			0.597401
$70$		0			0
$71$	2.00000			0.237356			0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000			0.237356			0.118678	+	0.992933i	$0.462134\pi$
$72$	−0.665499	+	0.384226i	−0.0784298	+	0.0452815i
$73$	−8.09756	−	4.67513i	−0.947748	−	0.547183i	−0.0553675	−	0.998466i	$-0.517633\pi$
$73$	−8.09756	−	4.67513i	−0.947748	−	0.547183i	−0.892381	+	0.451283i	$0.850966\pi$
$74$	−0.0752228	+	0.130290i	−0.00874447	+	0.0151459i
$75$	−3.01131	−	3.99149i	−0.347716	−	0.460898i
$76$	−10.4993			−1.20435
$77$		0			0
$78$			0.261865i			0.0296504i
$79$	5.35026	+	9.26693i	0.601951	+	1.04261i	0.992525	+	0.122039i	$0.0389433\pi$
$79$	5.35026	+	9.26693i	0.601951	+	1.04261i	−0.390574	+	0.920572i	$0.627723\pi$
$80$	−2.68119	−	8.00578i	−0.299766	−	0.895073i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	0.627835	−	0.362481i	0.0693327	−	0.0400293i
$83$		−	3.22425i		−	0.353908i	−0.984219	−	0.176954i	$-0.943376\pi$
$83$		−	3.22425i		−	0.353908i	0.984219	−	0.176954i	$-0.0566244\pi$
$84$		0			0
$85$	5.61213	+	4.96239i	0.608721	+	0.538247i
$86$	1.22425	+	2.12047i	0.132015	+	0.228656i
$87$	6.86306	+	3.96239i	0.735797	+	0.424813i
$88$	−1.33100	−	0.768452i	−0.141885	−	0.0819173i
$89$	0.518806	+	0.898598i	0.0549933	+	0.0952512i	0.892212	−	0.451618i	$-0.149153\pi$
$89$	0.518806	+	0.898598i	0.0549933	+	0.0952512i	−0.837218	+	0.546869i	$0.815820\pi$
$90$	0.324869	+	0.287258i	0.0342442	+	0.0302796i
$91$		0			0
$92$		−	9.73813i		−	1.01527i
$93$	3.96165	−	2.28726i	0.410804	−	0.237178i
$94$	0.962389	−	1.66691i	0.0992628	−	0.171928i
$95$	3.79927	+	11.3443i	0.389797	+	1.16390i
$96$	1.13458	+	1.96515i	0.115798	+	0.200567i
$97$		−	18.4993i		−	1.87832i	−0.343482	−	0.939159i	$-0.611606\pi$
$97$		−	18.4993i		−	1.87832i	0.343482	−	0.939159i	$-0.388394\pi$
$98$		0			0
$99$	−2.00000			−0.201008
$100$	−7.83286	+	5.90936i	−0.783286	+	0.590936i
$101$	8.83146	−	15.2965i	0.878763	−	1.52206i	0.0260630	−	0.999660i	$-0.491703\pi$
$101$	8.83146	−	15.2965i	0.878763	−	1.52206i	0.852700	−	0.522401i	$-0.174964\pi$
$102$	−0.562690	−	0.324869i	−0.0557146	−	0.0321668i
$103$	−5.80282	+	3.35026i	−0.571769	+	0.330111i	−0.757856	−	0.652422i	$-0.773753\pi$
$103$	−5.80282	+	3.35026i	−0.571769	+	0.330111i	0.186086	+	0.982533i	$0.440420\pi$
$104$	1.03761			0.101746
$105$		0			0
$106$	1.66291			0.161516
$107$	11.8976	−	6.86907i	1.15018	−	0.664058i	0.201250	−	0.979540i	$-0.435500\pi$
$107$	11.8976	−	6.86907i	1.15018	−	0.664058i	0.948932	+	0.315482i	$0.102166\pi$
$108$	1.69948	+	0.981194i	0.163532	+	0.0944155i
$109$	−1.38787	+	2.40387i	−0.132934	+	0.230249i	−0.924806	−	0.380438i	$-0.875773\pi$
$109$	−1.38787	+	2.40387i	−0.132934	+	0.230249i	0.791872	+	0.610687i	$0.209107\pi$
$110$	−0.172676	+	0.849948i	−0.0164640	+	0.0810393i
$111$	0.775746			0.0736306
$112$		0			0
$113$		−	12.0508i		−	1.13364i	−0.823841	−	0.566821i	$-0.808173\pi$
$113$		−	12.0508i		−	1.13364i	0.823841	−	0.566821i	$-0.191827\pi$
$114$	−0.518806	−	0.898598i	−0.0485906	−	0.0841614i
$115$	−10.5218	+	3.52384i	−0.981167	+	0.328599i
$116$	7.77575	−	13.4680i	0.721960	−	1.25047i
$117$	1.16936	−	0.675131i	0.108107	−	0.0624159i
$118$			1.67276i			0.153990i
$119$		0			0
$120$	1.13823	−	1.28726i	0.103905	−	0.117510i
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	1.46129	+	0.843675i	0.132299	+	0.0763827i
$123$	−3.23732	−	1.86907i	−0.291899	−	0.168528i
$124$	−4.48849	−	7.77429i	−0.403078	−	0.698152i
$125$	9.21933	+	6.32487i	0.824602	+	0.565713i
$126$		0			0
$127$			2.70052i			0.239633i	0.992796	+	0.119816i	$0.0382306\pi$
$127$			2.70052i			0.239633i	−0.992796	+	0.119816i	$0.961769\pi$
$128$	5.12469	−	2.95874i	0.452963	−	0.261518i
$129$	6.31265	−	10.9338i	0.555798	−	0.962670i
$130$	−0.185953	−	0.555237i	−0.0163091	−	0.0486975i
$131$	−10.3127	−	17.8620i	−0.901020	−	1.56061i	−0.826172	−	0.563418i	$-0.809486\pi$
$131$	−10.3127	−	17.8620i	−0.901020	−	1.56061i	−0.0748486	−	0.997195i	$-0.523847\pi$
$132$			3.92478i			0.341608i
$133$		0			0
$134$	−1.92478			−0.166275
$135$	0.445186	−	2.19130i	0.0383155	−	0.188597i
$136$	−1.28726	+	2.22960i	−0.110381	+	0.191186i
$137$	−19.4850	−	11.2496i	−1.66471	−	0.961122i	−0.970418	−	0.241431i	$-0.922383\pi$
$137$	−19.4850	−	11.2496i	−1.66471	−	0.961122i	−0.694294	−	0.719691i	$-0.744283\pi$
$138$	0.833453	−	0.481194i	0.0709482	−	0.0409620i
$139$	3.27504			0.277785			0.138893	−	0.990307i	$-0.455646\pi$
$139$	3.27504			0.277785			0.138893	+	0.990307i	$0.455646\pi$
$140$		0			0
$141$	−9.92478			−0.835817
$142$	0.335908	−	0.193937i	0.0281888	−	0.0162748i
$143$	2.33872	+	1.35026i	0.195574	+	0.112915i
$144$	1.88787	−	3.26989i	0.157323	−	0.272491i
$145$	−17.3656	−	3.52800i	−1.44213	−	0.292985i
$146$	−1.81336			−0.150075
$147$		0			0
$148$		−	1.52232i		−	0.125134i
$149$	−2.22425	−	3.85252i	−0.182218	−	0.315611i	0.760418	−	0.649434i	$-0.224994\pi$
$149$	−2.22425	−	3.85252i	−0.182218	−	0.315611i	−0.942636	+	0.333824i	$0.891661\pi$
$150$	−0.892810	−	0.378385i	−0.0728976	−	0.0308950i
$151$	−0.649738	+	1.12538i	−0.0528749	+	0.0915821i	−0.891251	−	0.453510i	$-0.850172\pi$
$151$	−0.649738	+	1.12538i	−0.0528749	+	0.0915821i	0.838376	+	0.545092i	$0.183505\pi$
$152$	−3.56059	+	2.05571i	−0.288802	+	0.166740i
$153$			3.35026i			0.270853i
$154$		0			0
$155$	−6.77575	+	7.66291i	−0.544241	+	0.615500i
$156$	−1.32487	−	2.29474i	−0.106074	−	0.183726i
$157$	2.29474	+	1.32487i	0.183140	+	0.105736i	0.588767	−	0.808303i	$-0.299613\pi$
$157$	2.29474	+	1.32487i	0.183140	+	0.105736i	−0.405627	+	0.914039i	$0.632947\pi$
$158$	1.79720	+	1.03761i	0.142977	+	0.0825479i
$159$	−4.28726	−	7.42575i	−0.340002	−	0.588900i
$160$	−3.80114	−	3.36107i	−0.300506	−	0.265716i
$161$		0			0
$162$			0.193937i			0.0152371i
$163$	−4.58948	+	2.64974i	−0.359476	+	0.207544i	−0.668851	−	0.743397i	$-0.733214\pi$
$163$	−4.58948	+	2.64974i	−0.359476	+	0.207544i	0.309375	+	0.950940i	$0.399880\pi$
$164$	−3.66784	+	6.35288i	−0.286410	+	0.496077i
$165$	4.24063	−	1.42022i	0.330133	−	0.110564i
$166$	−0.312650	−	0.541526i	−0.0242664	−	0.0420306i
$167$		−	14.5501i		−	1.12592i	−0.826485	−	0.562959i	$-0.809663\pi$
$167$		−	14.5501i		−	1.12592i	0.826485	−	0.562959i	$-0.190337\pi$
$168$		0			0
$169$	11.1768			0.859753
$170$	1.42377	+	0.289255i	0.109198	+	0.0221848i
$171$	−2.67513	+	4.63346i	−0.204572	+	0.354330i
$172$	−21.4564	−	12.3879i	−1.63604	−	0.944566i
$173$	3.89650	−	2.24965i	0.296246	−	0.171037i	−0.344509	−	0.938783i	$-0.611955\pi$
$173$	3.89650	−	2.24965i	0.296246	−	0.171037i	0.640755	+	0.767745i	$0.278621\pi$
$174$	1.53690			0.116512
$175$		0			0
$176$	7.55149			0.569215
$177$	7.46973	−	4.31265i	0.561459	−	0.324159i
$178$	0.174271	+	0.100615i	0.0130622	+	0.00754144i
$179$	5.00000	−	8.66025i	0.373718	−	0.647298i	−0.616417	−	0.787420i	$-0.711416\pi$
$179$	5.00000	−	8.66025i	0.373718	−	0.647298i	0.990134	+	0.140122i	$0.0447496\pi$
$180$	−4.30019	−	0.873629i	−0.320517	−	0.0651164i
$181$	10.6253			0.789772			0.394886	−	0.918730i	$-0.370784\pi$
$181$	10.6253			0.789772			0.394886	+	0.918730i	$0.370784\pi$
$182$		0			0
$183$		−	8.70052i		−	0.643161i
$184$	−1.90668	−	3.30246i	−0.140562	−	0.243461i
$185$	−1.64483	+	0.550864i	−0.120930	+	0.0405003i
$186$	0.443583	−	0.768308i	0.0325251	−	0.0563351i
$187$	−5.80282	+	3.35026i	−0.424344	+	0.244995i
$188$			19.4763i			1.42045i
$189$		0			0
$190$	1.73813	+	1.53690i	0.126098	+	0.111499i
$191$	6.92478	+	11.9941i	0.501059	+	0.867860i	0.999999	+	0.00122360i	$0.000389484\pi$
$191$	6.92478	+	11.9941i	0.501059	+	0.867860i	−0.498940	+	0.866637i	$0.666277\pi$
$192$	−6.15867	−	3.55571i	−0.444464	−	0.256611i
$193$	13.2726	+	7.66291i	0.955379	+	0.551588i	0.894748	−	0.446572i	$-0.147355\pi$
$193$	13.2726	+	7.66291i	0.955379	+	0.551588i	0.0606314	+	0.998160i	$0.480689\pi$
$194$	−1.79384	−	3.10703i	−0.128791	−	0.223072i
$195$	−2.00000	+	2.26187i	−0.143223	+	0.161976i
$196$		0			0
$197$		−	0.574515i		−	0.0409325i	−0.999791	−	0.0204663i	$-0.993485\pi$
$197$		−	0.574515i		−	0.0409325i	0.999791	−	0.0204663i	$-0.00651507\pi$
$198$	−0.335908	+	0.193937i	−0.0238719	+	0.0137825i
$199$	−0.100615	+	0.174271i	−0.00713244	+	0.0123537i	−0.869570	−	0.493810i	$-0.835604\pi$
$199$	−0.100615	+	0.174271i	−0.00713244	+	0.0123537i	0.862437	+	0.506164i	$0.168937\pi$
$200$	−1.49931	+	3.53766i	−0.106017	+	0.250150i
$201$	4.96239	+	8.59511i	0.350020	+	0.606252i
$202$		−	3.42548i		−	0.241016i
$203$		0			0
$204$	6.57452			0.460308
$205$	8.19139	+	1.66417i	0.572111	+	0.116230i
$206$	−0.649738	+	1.12538i	−0.0452694	+	0.0784089i
$207$	−4.29755	−	2.48119i	−0.298701	−	0.172455i
$208$	−4.41521	+	2.54912i	−0.306140	+	0.176750i
$209$	−10.7005			−0.740171
$210$		0			0
$211$	6.44851			0.443934			0.221967	−	0.975054i	$-0.428752\pi$
$211$	6.44851			0.443934			0.221967	+	0.975054i	$0.428752\pi$
$212$	−14.5722	+	8.41327i	−1.00082	+	0.577825i
$213$	−1.73205	−	1.00000i	−0.118678	−	0.0685189i
$214$	1.33216	−	2.30737i	0.0910648	−	0.157729i
$215$	−5.62061	+	27.6659i	−0.383323	+	1.88680i
$216$	0.768452			0.0522865
$217$		0			0
$218$			0.538319i			0.0364595i
$219$	4.67513	+	8.09756i	0.315916	+	0.547183i
$220$	−2.78702	−	8.32177i	−0.187901	−	0.561054i
$221$	2.26187	−	3.91767i	0.152150	−	0.263531i
$222$	0.130290	−	0.0752228i	0.00874447	−	0.00504862i
$223$		−	1.55149i		−	0.103896i	−0.998650	−	0.0519478i	$-0.983457\pi$
$223$		−	1.55149i		−	0.103896i	0.998650	−	0.0519478i	$-0.0165429\pi$
$224$		0			0
$225$	0.612127	+	4.96239i	0.0408085	+	0.330826i
$226$	−1.16854	−	2.02398i	−0.0777304	−	0.134633i
$227$	11.3874	+	6.57452i	0.755808	+	0.436366i	0.827789	−	0.561040i	$-0.189599\pi$
$227$	11.3874	+	6.57452i	0.755808	+	0.436366i	−0.0719807	+	0.997406i	$0.522932\pi$
$228$	9.09265	+	5.24965i	0.602176	+	0.347666i
$229$	1.38787	+	2.40387i	0.0917132	+	0.158852i	0.908232	−	0.418467i	$-0.137432\pi$
$229$	1.38787	+	2.40387i	0.0917132	+	0.158852i	−0.816519	+	0.577319i	$0.804099\pi$
$230$	−1.42548	+	1.61213i	−0.0939937	+	0.106300i
$231$		0			0
$232$		−	6.08981i		−	0.399816i
$233$	0.0439813	−	0.0253926i	0.00288131	−	0.00166353i	−0.498559	−	0.866856i	$-0.666137\pi$
$233$	0.0439813	−	0.0253926i	0.00288131	−	0.00166353i	0.501440	+	0.865192i	$0.332804\pi$
$234$	0.130933	−	0.226782i	0.00855933	−	0.0148252i
$235$	21.0437	−	7.04767i	1.37274	−	0.459739i
$236$	−8.46310	−	14.6585i	−0.550901	−	0.954188i
$237$		−	10.7005i		−	0.695074i
$238$		0			0
$239$	−5.84955			−0.378376			−0.189188	−	0.981941i	$-0.560586\pi$
$239$	−5.84955			−0.378376			−0.189188	+	0.981941i	$0.560586\pi$
$240$	−1.68091	+	8.27380i	−0.108502	+	0.534072i
$241$	0.0376114	−	0.0651448i	0.00242276	−	0.00419635i	−0.864811	−	0.502097i	$-0.832562\pi$
$241$	0.0376114	−	0.0651448i	0.00242276	−	0.00419635i	0.867234	+	0.497900i	$0.165895\pi$
$242$	1.17568	+	0.678778i	0.0755754	+	0.0436335i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	−17.0738			−1.09304
$245$		0			0
$246$	−0.724961			−0.0462218
$247$	6.25639	−	3.61213i	0.398084	−	0.229834i
$248$	−3.04434	−	1.75765i	−0.193315	−	0.111611i
$249$	−1.61213	+	2.79229i	−0.102164	+	0.176954i
$250$	2.16173	+	0.168305i	0.136720	+	0.0106445i
$251$	19.2243			1.21342			0.606712	−	0.794922i	$-0.292488\pi$
$251$	19.2243			1.21342			0.606712	+	0.794922i	$0.292488\pi$
$252$		0			0
$253$		−	9.92478i		−	0.623965i
$254$	0.261865	+	0.453564i	0.0164309	+	0.0284591i
$255$	−2.37905	−	7.10362i	−0.148982	−	0.444846i
$256$	−6.53761	+	11.3235i	−0.408601	+	0.707717i
$257$	6.36551	−	3.67513i	0.397070	−	0.229248i	−0.288149	−	0.957586i	$-0.593040\pi$
$257$	6.36551	−	3.67513i	0.397070	−	0.229248i	0.685219	+	0.728337i	$0.259707\pi$
$258$		−	2.44851i		−	0.152437i
$259$		0			0
$260$	4.43866	+	3.92478i	0.275274	+	0.243404i
$261$	−3.96239	−	6.86306i	−0.245266	−	0.424813i
$262$	−3.46410	−	2.00000i	−0.214013	−	0.123560i
$263$	−11.2258	−	6.48119i	−0.692210	−	0.399648i	0.112229	−	0.993682i	$-0.464201\pi$
$263$	−11.2258	−	6.48119i	−0.692210	−	0.399648i	−0.804439	+	0.594035i	$0.797534\pi$
$264$	0.768452	+	1.33100i	0.0472950	+	0.0819173i
$265$	14.3634	+	12.7005i	0.882339	+	0.780187i
$266$		0			0
$267$		−	1.03761i		−	0.0635008i
$268$	16.8669	−	9.73813i	1.03031	−	0.594851i
$269$	2.05571	−	3.56059i	0.125339	−	0.217093i	−0.796527	−	0.604604i	$-0.793332\pi$
$269$	2.05571	−	3.56059i	0.125339	−	0.217093i	0.921865	+	0.387510i	$0.126665\pi$
$270$	−0.137716	−	0.411207i	−0.00838113	−	0.0250253i
$271$	8.21203	+	14.2237i	0.498846	+	0.864026i	0.999999	−	0.00133248i	$-0.000424141\pi$
$271$	8.21203	+	14.2237i	0.498846	+	0.864026i	−0.501154	+	0.865358i	$0.667091\pi$
$272$		−	12.6497i		−	0.767003i
$273$		0			0
$274$	−4.36344			−0.263605
$275$	−7.98298	+	6.02262i	−0.481392	+	0.363178i
$276$	−4.86907	+	8.43347i	−0.293083	+	0.507635i
$277$	9.59020	+	5.53690i	0.576219	+	0.332680i	0.759629	−	0.650356i	$-0.225380\pi$
$277$	9.59020	+	5.53690i	0.576219	+	0.332680i	−0.183410	+	0.983036i	$0.558714\pi$
$278$	0.550056	−	0.317575i	0.0329902	−	0.0190469i
$279$	−4.57452			−0.273869
$280$		0			0
$281$	14.3733			0.857438			0.428719	−	0.903438i	$-0.358965\pi$
$281$	14.3733			0.857438			0.428719	+	0.903438i	$0.358965\pi$
$282$	−1.66691	+	0.962389i	−0.0992628	+	0.0573094i
$283$	0.995090	+	0.574515i	0.0591520	+	0.0341514i	0.529284	−	0.848445i	$-0.322460\pi$
$283$	0.995090	+	0.574515i	0.0591520	+	0.0341514i	−0.470132	+	0.882596i	$0.655794\pi$
$284$	−1.96239	+	3.39896i	−0.116446	+	0.201691i
$285$	2.38186	−	11.7240i	0.141089	−	0.694472i
$286$	0.523730			0.0309688
$287$		0			0
$288$		−	2.26916i		−	0.133711i
$289$	−2.88787	−	5.00194i	−0.169875	−	0.294232i
$290$	−3.25872	+	1.09137i	−0.191359	+	0.0640874i
$291$	−9.24965	+	16.0209i	−0.542224	+	0.939159i
$292$	15.8906	−	9.17442i	0.929925	−	0.536893i
$293$		−	0.649738i		−	0.0379581i	−0.999820	−	0.0189791i	$-0.993958\pi$
$293$		−	0.649738i		−	0.0379581i	0.999820	−	0.0189791i	$-0.00604158\pi$
$294$		0			0
$295$	−12.7757	+	14.4485i	−0.743833	+	0.841225i
$296$	−0.298062	−	0.516258i	−0.0173245	−	0.0300069i
$297$	1.73205	+	1.00000i	0.100504	+	0.0580259i
$298$	−0.747145	−	0.431364i	−0.0432809	−	0.0249883i
$299$	3.35026	+	5.80282i	0.193751	+	0.335586i
$300$	9.73813	−	1.20123i	0.562231	−	0.0693531i
$301$		0			0
$302$			0.252016i			0.0145019i
$303$	−15.2965	+	8.83146i	−0.878763	+	0.507354i
$304$	10.1006	−	17.4948i	0.579310	−	1.00339i
$305$	6.17832	+	18.4479i	0.353769	+	1.05632i
$306$	0.324869	+	0.562690i	0.0185715	+	0.0321668i
$307$			24.1016i			1.37555i	0.725924	+	0.687775i	$0.241412\pi$
$307$			24.1016i			1.37555i	−0.725924	+	0.687775i	$0.758588\pi$
$308$		0			0
$309$	6.70052			0.381179
$310$	−0.394954	+	1.94405i	−0.0224319	+	0.110415i
$311$	−4.12601	+	7.14646i	−0.233964	+	0.405238i	−0.958971	−	0.283503i	$-0.908503\pi$
$311$	−4.12601	+	7.14646i	−0.233964	+	0.405238i	0.725007	+	0.688742i	$0.241837\pi$
$312$	−0.898598	−	0.518806i	−0.0508731	−	0.0293716i
$313$	12.9053	−	7.45088i	0.729451	−	0.421148i	−0.0887706	−	0.996052i	$-0.528294\pi$
$313$	12.9053	−	7.45088i	0.729451	−	0.421148i	0.818221	+	0.574904i	$0.194960\pi$
$314$	0.513881			0.0290000
$315$		0			0
$316$	−20.9986			−1.18126
$317$	8.76938	−	5.06300i	0.492537	−	0.284367i	−0.233089	−	0.972455i	$-0.574883\pi$
$317$	8.76938	−	5.06300i	0.492537	−	0.284367i	0.725627	+	0.688089i	$0.241550\pi$
$318$	−1.44012	−	0.831456i	−0.0807582	−	0.0466257i
$319$	7.92478	−	13.7261i	0.443702	−	0.768515i
$320$	15.5833	+	3.16591i	0.871132	+	0.176980i
$321$	−13.7381			−0.766788
$322$		0			0
$323$			17.9248i			0.997361i
$324$	−0.981194	−	1.69948i	−0.0545108	−	0.0944155i
$325$	2.63446	−	6.21609i	0.146134	−	0.344807i
$326$	−0.513881	+	0.890068i	−0.0284612	+	0.0492963i
$327$	2.40387	−	1.38787i	0.132934	−	0.0767496i
$328$			2.87258i			0.158612i
$329$		0			0
$330$	0.574515	−	0.649738i	0.0316260	−	0.0357669i
$331$	−13.9248	−	24.1184i	−0.765375	−	1.32567i	−0.940048	−	0.341042i	$-0.889220\pi$
$331$	−13.9248	−	24.1184i	−0.765375	−	1.32567i	0.174673	−	0.984626i	$-0.444113\pi$
$332$	5.47955	+	3.16362i	0.300729	+	0.173626i
$333$	−0.671816	−	0.387873i	−0.0368153	−	0.0212553i
$334$	−1.41090	−	2.44374i	−0.0772008	−	0.133716i
$335$	−16.6253	−	14.7005i	−0.908337	−	0.803175i
$336$		0			0
$337$		−	3.84955i		−	0.209699i	−0.994488	−	0.104849i	$-0.966564\pi$
$337$		−	3.84955i		−	0.209699i	0.994488	−	0.104849i	$-0.0334360\pi$
$338$	1.87719	−	1.08379i	0.102106	−	0.0589506i
$339$	−6.02539	+	10.4363i	−0.327254	+	0.566821i
$340$	−13.9401	+	4.66862i	−0.756006	+	0.253192i
$341$	−4.57452	−	7.92329i	−0.247724	−	0.429070i
$342$			1.03761i			0.0561076i
$343$		0			0
$344$	−9.70194			−0.523093
$345$	10.8741	+	2.20919i	0.585442	+	0.118939i
$346$	0.436289	−	0.755674i	0.0234550	−	0.0406253i
$347$	−8.30318	−	4.79384i	−0.445738	−	0.257347i	0.260290	−	0.965530i	$-0.416182\pi$
$347$	−8.30318	−	4.79384i	−0.445738	−	0.257347i	−0.706029	+	0.708183i	$0.749515\pi$
$348$	−13.4680	+	7.77575i	−0.721960	+	0.416824i
$349$	15.1490			0.810909			0.405455	−	0.914115i	$-0.367113\pi$
$349$	15.1490			0.810909			0.405455	+	0.914115i	$0.367113\pi$
$350$		0			0
$351$	−1.35026			−0.0720716
$352$	3.93030	−	2.26916i	0.209486	−	0.120947i
$353$	−17.6226	−	10.1744i	−0.937957	−	0.541530i	−0.0486379	−	0.998816i	$-0.515488\pi$
$353$	−17.6226	−	10.1744i	−0.937957	−	0.541530i	−0.889319	+	0.457287i	$0.848821\pi$
$354$	0.836381	−	1.44865i	0.0444531	−	0.0769951i
$355$	4.38261	+	0.890373i	0.232605	+	0.0472561i
$356$	−2.03620			−0.107918
$357$		0			0
$358$		−	1.93937i		−	0.102499i
$359$	−15.7005	−	27.1941i	−0.828642	−	1.43525i	−0.899104	−	0.437735i	$-0.855781\pi$
$359$	−15.7005	−	27.1941i	−0.828642	−	1.43525i	0.0704619	−	0.997514i	$-0.477553\pi$
$360$	−1.62936	+	0.545685i	−0.0858749	+	0.0287601i
$361$	−4.81265	+	8.33575i	−0.253297	+	0.438724i
$362$	1.78456	−	1.03032i	0.0937945	−	0.0541523i
$363$		−	7.00000i		−	0.367405i
$364$		0			0
$365$	−15.6629	−	13.8496i	−0.819834	−	0.724919i
$366$	−0.843675	−	1.46129i	−0.0440996	−	0.0763827i
$367$	25.4621	+	14.7005i	1.32911	+	0.767361i	0.985162	−	0.171628i	$-0.0549028\pi$
$367$	25.4621	+	14.7005i	1.32911	+	0.767361i	0.343947	+	0.938989i	$0.388236\pi$
$368$	16.2265	+	9.36836i	0.845864	+	0.488360i
$369$	1.86907	+	3.23732i	0.0972998	+	0.168528i
$370$	−0.222839	+	0.252016i	−0.0115849	+	0.0131017i
$371$		0			0
$372$			8.97698i			0.465435i
$373$	−13.8564	+	8.00000i	−0.717458	+	0.414224i	−0.813816	−	0.581122i	$-0.802614\pi$
$373$	−13.8564	+	8.00000i	−0.717458	+	0.414224i	0.0963587	+	0.995347i	$0.469280\pi$
$374$	−0.649738	+	1.12538i	−0.0335972	+	0.0581920i
$375$	−4.82174	−	10.0872i	−0.248994	−	0.520899i
$376$	3.81336	+	6.60493i	0.196659	+	0.340623i
$377$			10.7005i			0.551105i
$378$		0			0
$379$	−10.7005			−0.549649			−0.274824	−	0.961494i	$-0.588620\pi$
$379$	−10.7005			−0.549649			−0.274824	+	0.961494i	$0.588620\pi$
$380$	−23.0071	−	4.67414i	−1.18024	−	0.239778i
$381$	1.35026	−	2.33872i	0.0691760	−	0.119816i
$382$	2.32609	+	1.34297i	0.119013	+	0.0687122i
$383$	14.5282	−	8.38787i	0.742357	−	0.428600i	−0.0805684	−	0.996749i	$-0.525674\pi$
$383$	14.5282	−	8.38787i	0.742357	−	0.428600i	0.822926	+	0.568149i	$0.192340\pi$
$384$	−5.91748			−0.301975
$385$		0			0
$386$	2.97224			0.151283
$387$	−10.9338	+	6.31265i	−0.555798	+	0.320890i
$388$	31.4391	+	18.1514i	1.59608	+	0.921498i
$389$	−14.6629	+	25.3969i	−0.743439	+	1.28767i	0.207481	+	0.978239i	$0.433473\pi$
$389$	−14.6629	+	25.3969i	−0.743439	+	1.28767i	−0.950920	+	0.309435i	$0.899860\pi$
$390$	−0.116579	+	0.573826i	−0.00590320	+	0.0290568i
$391$	−16.6253			−0.840778
$392$		0			0
$393$			20.6253i			1.04041i
$394$	−0.0557098	−	0.0964922i	−0.00280662	−	0.00486121i
$395$	7.59854	+	22.6885i	0.382324	+	1.14158i
$396$	1.96239	−	3.39896i	0.0986137	−	0.170804i
$397$	15.8906	−	9.17442i	0.797525	−	0.460451i	−0.0450802	−	0.998983i	$-0.514354\pi$
$397$	15.8906	−	9.17442i	0.797525	−	0.460451i	0.842605	+	0.538532i	$0.181021\pi$
$398$			0.0390260i			0.00195620i
$399$		0			0
$400$	−2.31124	−	18.7367i	−0.115562	−	0.936836i
$401$	18.6629	+	32.3251i	0.931981	+	1.61424i	0.779930	+	0.625866i	$0.215254\pi$
$401$	18.6629	+	32.3251i	0.931981	+	1.61424i	0.152051	+	0.988373i	$0.451412\pi$
$402$	1.66691	+	0.962389i	0.0831377	+	0.0479996i
$403$	5.34926	+	3.08840i	0.266466	+	0.153844i
$404$	17.3307	+	30.0177i	0.862237	+	1.49344i
$405$	−1.48119	+	1.67513i	−0.0736011	+	0.0832379i
$406$		0			0
$407$		−	1.55149i		−	0.0769046i
$408$	2.22960	−	1.28726i	0.110381	−	0.0637288i
$409$	−11.1866	+	19.3758i	−0.553144	+	0.958073i	0.444901	+	0.895580i	$0.353239\pi$
$409$	−11.1866	+	19.3758i	−0.553144	+	0.958073i	−0.998045	+	0.0624938i	$0.980095\pi$
$410$	1.53715	−	0.514801i	0.0759143	−	0.0254242i
$411$	11.2496	+	19.4850i	0.554904	+	0.961122i
$412$		−	13.1490i		−	0.647806i
$413$		0			0
$414$	−0.962389			−0.0472988
$415$	1.43539	−	7.06532i	0.0704607	−	0.346823i
$416$	−1.53198	+	2.65347i	−0.0751115	+	0.130097i
$417$	−2.83627	−	1.63752i	−0.138893	−	0.0801897i
$418$	−1.79720	+	1.03761i	−0.0879037	+	0.0507512i
$419$	−23.4763			−1.14689			−0.573445	−	0.819244i	$-0.694394\pi$
$419$	−23.4763			−1.14689			−0.573445	+	0.819244i	$0.694394\pi$
$420$		0			0
$421$	−25.2243			−1.22935			−0.614677	−	0.788779i	$-0.710714\pi$
$421$	−25.2243			−1.22935			−0.614677	+	0.788779i	$0.710714\pi$
$422$	1.08305	−	0.625301i	0.0527222	−	0.0304392i
$423$	8.59511	+	4.96239i	0.417909	+	0.241280i
$424$	−3.29455	+	5.70633i	−0.159998	+	0.277124i
$425$	10.0887	+	13.3725i	0.489373	+	0.648663i
$426$	−0.387873			−0.0187925
$427$		0			0
$428$			26.9596i			1.30314i
$429$	−1.35026	−	2.33872i	−0.0651913	−	0.112915i
$430$	1.73871	+	5.19161i	0.0838479	+	0.250362i
$431$	9.70052	−	16.8018i	0.467258	−	0.809314i	−0.532042	−	0.846718i	$-0.678575\pi$
$431$	9.70052	−	16.8018i	0.467258	−	0.809314i	0.999300	+	0.0374035i	$0.0119087\pi$
$432$	−3.26989	+	1.88787i	−0.157323	+	0.0908303i
$433$		−	6.49929i		−	0.312336i	−0.987731	−	0.156168i	$-0.950086\pi$
$433$		−	6.49929i		−	0.312336i	0.987731	−	0.156168i	$-0.0499141\pi$
$434$		0			0
$435$	13.2750	+	11.7381i	0.636489	+	0.562800i
$436$	−2.72355	−	4.71732i	−0.130434	−	0.225919i
$437$	−22.9930	−	13.2750i	−1.09991	−	0.635031i
$438$	1.57041	+	0.906679i	0.0750373	+	0.0433228i
$439$	−7.32487	−	12.6870i	−0.349597	−	0.605520i	0.636581	−	0.771210i	$-0.280348\pi$
$439$	−7.32487	−	12.6870i	−0.349597	−	0.605520i	−0.986178	+	0.165690i	$0.947015\pi$
$440$	−2.57452	−	2.27645i	−0.122735	−	0.108526i
$441$		0			0
$442$		−	0.877317i		−	0.0417297i
$443$	−16.5750	+	9.56959i	−0.787503	+	0.454665i	−0.839083	−	0.544004i	$-0.816908\pi$
$443$	−16.5750	+	9.56959i	−0.787503	+	0.454665i	0.0515798	+	0.998669i	$0.483574\pi$
$444$	−0.761158	+	1.31836i	−0.0361230	+	0.0625668i
$445$	0.736817	+	2.20007i	0.0349285	+	0.104293i
$446$	−0.150446	−	0.260579i	−0.00712380	−	0.0123388i
$447$			4.44851i			0.210407i
$448$		0			0
$449$	32.8021			1.54803			0.774013	−	0.633169i	$-0.218246\pi$
$449$	32.8021			1.54803			0.774013	+	0.633169i	$0.218246\pi$
$450$	0.584003	+	0.774096i	0.0275302	+	0.0364912i
$451$	−3.73813	+	6.47464i	−0.176022	+	0.304879i
$452$	20.4800	+	11.8242i	0.963300	+	0.556162i
$453$	1.12538	−	0.649738i	0.0528749	−	0.0305274i
$454$	2.55008			0.119681
$455$		0			0
$456$	4.11142			0.192535
$457$	−16.1951	+	9.35026i	−0.757576	+	0.437387i	−0.828425	−	0.560100i	$-0.810763\pi$
$457$	−16.1951	+	9.35026i	−0.757576	+	0.437387i	0.0708487	+	0.997487i	$0.477429\pi$
$458$	0.466198	+	0.269159i	0.0217840	+	0.0125770i
$459$	1.67513	−	2.90141i	0.0781884	−	0.135426i
$460$	4.33529	−	21.3392i	0.202134	−	0.994946i
$461$	−6.96239			−0.324271			−0.162135	−	0.986769i	$-0.551838\pi$
$461$	−6.96239			−0.324271			−0.162135	+	0.986769i	$0.551838\pi$
$462$		0			0
$463$		−	5.29948i		−	0.246288i	−0.992389	−	0.123144i	$-0.960702\pi$
$463$		−	5.29948i		−	0.246288i	0.992389	−	0.123144i	$-0.0392976\pi$
$464$	14.9610	+	25.9132i	0.694546	+	1.20299i
$465$	9.69942	−	3.24840i	0.449800	−	0.150641i
$466$	0.00492456	−	0.00852958i	0.000228126	−	0.000395125i
$467$	−11.3874	+	6.57452i	−0.526946	+	0.304232i	−0.739772	−	0.672858i	$-0.765067\pi$
$467$	−11.3874	+	6.57452i	−0.526946	+	0.304232i	0.212826	+	0.977090i	$0.431733\pi$
$468$			2.64974i			0.122484i
$469$		0			0
$470$	2.85097	−	3.22425i	0.131505	−	0.148724i
$471$	−1.32487	−	2.29474i	−0.0610467	−	0.105736i
$472$	−5.74013	−	3.31406i	−0.264211	−	0.152542i
$473$	−21.8677	−	12.6253i	−1.00548	−	0.580512i
$474$	−1.03761	−	1.79720i	−0.0476591	−	0.0825479i
$475$	3.27504	+	26.5501i	0.150269	+	1.21820i
$476$		0			0
$477$			8.57452i			0.392600i
$478$	−0.982456	+	0.567221i	−0.0449365	+	0.0259441i
$479$	2.57452	−	4.45919i	0.117633	−	0.203746i	−0.801196	−	0.598401i	$-0.795803\pi$
$479$	2.57452	−	4.45919i	0.117633	−	0.203746i	0.918829	+	0.394656i	$0.129136\pi$
$480$	1.61135	+	4.81134i	0.0735477	+	0.219607i
$481$	0.523730	+	0.907127i	0.0238800	+	0.0413614i
$482$		−	0.0145884i		−	0.000664486i
$483$		0			0
$484$	−13.7367			−0.624396
$485$	8.23563	−	40.5376i	0.373961	−	1.84072i
$486$	0.0969683	−	0.167954i	0.00439857	−	0.00761855i
$487$	19.2057	+	11.0884i	0.870292	+	0.502463i	0.867445	−	0.497533i	$-0.165761\pi$
$487$	19.2057	+	11.0884i	0.870292	+	0.502463i	0.00284661	+	0.999996i	$0.499094\pi$
$488$	−5.79019	+	3.34297i	−0.262110	+	0.151329i
$489$	5.29948			0.239651
$490$		0			0
$491$	2.00000			0.0902587			0.0451294	−	0.998981i	$-0.485630\pi$
$491$	2.00000			0.0902587			0.0451294	+	0.998981i	$0.485630\pi$
$492$	6.35288	−	3.66784i	0.286410	−	0.165359i
$493$	−22.9930	−	13.2750i	−1.03555	−	0.597878i
$494$	0.700523	−	1.21334i	0.0315180	−	0.0545908i
$495$	−4.38261	−	0.890373i	−0.196983	−	0.0400193i
$496$	17.2722			0.775545
$497$		0			0
$498$			0.625301i			0.0280204i
$499$	−3.27504	−	5.67253i	−0.146611	−	0.253937i	0.783362	−	0.621566i	$-0.213503\pi$
$499$	−3.27504	−	5.67253i	−0.146611	−	0.253937i	−0.929973	+	0.367628i	$0.880170\pi$
$500$	−19.7949	+	9.46213i	−0.885256	+	0.423159i
$501$	−7.27504	+	12.6007i	−0.325025	+	0.562959i
$502$	3.22879	−	1.86414i	0.144108	−	0.0832008i
$503$		−	8.77575i		−	0.391291i	−0.980675	−	0.195646i	$-0.937320\pi$
$503$		−	8.77575i		−	0.391291i	0.980675	−	0.195646i	$-0.0626802\pi$
$504$		0			0
$505$	26.1622	−	29.5877i	1.16420	−	1.31663i
$506$	−0.962389	−	1.66691i	−0.0427834	−	0.0741030i
$507$	−9.67939	−	5.58840i	−0.429877	−	0.248189i
$508$	−4.58948	−	2.64974i	−0.203625	−	0.117563i
$509$	6.56959	+	11.3789i	0.291192	+	0.504359i	0.974092	−	0.226153i	$-0.0726148\pi$
$509$	6.56959	+	11.3789i	0.291192	+	0.504359i	−0.682900	+	0.730512i	$0.739281\pi$
$510$	−1.08840	−	0.962389i	−0.0481950	−	0.0426153i
$511$		0			0
$512$			14.3707i			0.635103i
$513$	4.63346	−	2.67513i	0.204572	−	0.118110i
$514$	0.712742	−	1.23451i	0.0314377	−	0.0544517i
$515$	−14.2072	+	4.75810i	−0.626046	+	0.209667i
$516$	12.3879	+	21.4564i	0.545346	+	0.944566i
$517$			19.8496i			0.872982i
$518$		0			0
$519$	−4.49929			−0.197497
$520$	2.27372	+	0.461931i	0.0997093	+	0.0202570i
$521$	18.8315	−	32.6170i	0.825021	−	1.42898i	−0.0768821	−	0.997040i	$-0.524497\pi$
$521$	18.8315	−	32.6170i	0.825021	−	1.42898i	0.901903	−	0.431938i	$-0.142170\pi$
$522$	−1.33100	−	0.768452i	−0.0582562	−	0.0336342i
$523$	3.46410	−	2.00000i	0.151475	−	0.0874539i	−0.422347	−	0.906434i	$-0.638794\pi$
$523$	3.46410	−	2.00000i	0.151475	−	0.0874539i	0.573822	+	0.818980i	$0.305460\pi$
$524$	40.4749			1.76815
$525$		0			0
$526$	−2.51388			−0.109610
$527$	−13.2726	+	7.66291i	−0.578161	+	0.333802i
$528$	−6.53978	−	3.77575i	−0.284608	−	0.164318i
$529$	0.812650	−	1.40755i	0.0353326	−	0.0611979i
$530$	3.64394	+	0.740306i	0.158283	+	0.0321568i
$531$	−8.62530			−0.374306
$532$		0			0
$533$		−	5.04746i		−	0.218630i
$534$	−0.100615	−	0.174271i	−0.00435405	−	0.00754144i
$535$	29.1292	−	9.75557i	1.25937	−	0.421770i
$536$	3.81336	−	6.60493i	0.164712	−	0.285289i
$537$	−8.66025	+	5.00000i	−0.373718	+	0.215766i
$538$		−	0.797355i		−	0.0343764i
$539$		0			0
$540$	3.28726	+	2.90668i	0.141461	+	0.125084i
$541$	11.2374	+	19.4638i	0.483135	+	0.836814i	0.999812	−	0.0193660i	$-0.00616479\pi$
$541$	11.2374	+	19.4638i	0.483135	+	0.836814i	−0.516678	+	0.856180i	$0.672831\pi$
$542$	2.75849	+	1.59261i	0.118487	+	0.0684086i
$543$	−9.20178	−	5.31265i	−0.394886	−	0.227988i
$544$	−3.80114	−	6.58377i	−0.162972	−	0.282277i
$545$	−4.11142	+	4.64974i	−0.176114	+	0.199173i
$546$		0			0
$547$		−	25.9248i		−	1.10846i	−0.832362	−	0.554232i	$-0.813012\pi$
$547$		−	25.9248i		−	1.10846i	0.832362	−	0.554232i	$-0.186988\pi$
$548$	38.2371	−	22.0762i	1.63341	−	0.943048i
$549$	−4.35026	+	7.53487i	−0.185665	+	0.321581i
$550$	−0.756770	+	1.78562i	−0.0322688	+	0.0761391i
$551$	−21.1998	−	36.7192i	−0.903143	−	1.56429i
$552$			3.81336i			0.162307i
$553$		0			0
$554$	2.14762			0.0912435
$555$	1.69990	+	0.345352i	0.0721565	+	0.0146594i
$556$	−3.21345	+	5.56586i	−0.136281	+	0.236045i
$557$	24.7039	+	14.2628i	1.04674	+	0.604335i	0.921735	−	0.387821i	$-0.126772\pi$
$557$	24.7039	+	14.2628i	1.04674	+	0.604335i	0.125004	+	0.992156i	$0.460105\pi$
$558$	−0.768308	+	0.443583i	−0.0325251	+	0.0187784i
$559$	17.0475			0.721031
$560$		0			0
$561$	6.70052			0.282896
$562$	2.41405	−	1.39375i	0.101831	−	0.0587919i
$563$	−10.0690	−	5.81336i	−0.424359	−	0.245004i	0.272582	−	0.962133i	$-0.412123\pi$
$563$	−10.0690	−	5.81336i	−0.424359	−	0.245004i	−0.696941	+	0.717129i	$0.745456\pi$
$564$	9.73813	−	16.8669i	0.410049	−	0.710226i
$565$	5.36485	−	26.4069i	0.225701	−	1.11095i
$566$	0.222839			0.00936663
$567$		0			0
$568$			1.53690i			0.0644871i
$569$	4.66291	+	8.07640i	0.195479	+	0.338580i	0.947058	−	0.321064i	$-0.104040\pi$
$569$	4.66291	+	8.07640i	0.195479	+	0.338580i	−0.751578	+	0.659644i	$0.770707\pi$
$570$	−0.736817	−	2.20007i	−0.0308619	−	0.0921506i
$571$	9.84955	−	17.0599i	0.412191	−	0.713936i	−0.582938	−	0.812517i	$-0.698097\pi$
$571$	9.84955	−	17.0599i	0.412191	−	0.713936i	0.995129	+	0.0985808i	$0.0314303\pi$
$572$	−4.58948	+	2.64974i	−0.191896	+	0.110791i
$573$		−	13.8496i		−	0.578573i
$574$		0			0
$575$	−24.6253	+	3.03761i	−1.02695	+	0.126677i
$576$	3.55571	+	6.15867i	0.148155	+	0.256611i
$577$	−28.4033	−	16.3987i	−1.18245	−	0.682686i	−0.225867	−	0.974158i	$-0.572522\pi$
$577$	−28.4033	−	16.3987i	−1.18245	−	0.682686i	−0.956579	+	0.291472i	$0.905855\pi$
$578$	−0.970060	−	0.560064i	−0.0403492	−	0.0232956i
$579$	−7.66291	−	13.2726i	−0.318460	−	0.551588i
$580$	23.0348	−	26.0508i	0.956467	−	1.08170i
$581$		0			0
$582$			3.58769i			0.148715i
$583$	−14.8515	+	8.57452i	−0.615086	+	0.355120i
$584$	3.59261	−	6.22259i	0.148663	−	0.257493i
$585$	2.86298	−	0.958833i	0.118370	−	0.0396429i
$586$	−0.0630040	−	0.109126i	−0.00260267	−	0.00450796i
$587$			18.8218i			0.776859i	0.921479	+	0.388429i	$0.126982\pi$
$587$			18.8218i			0.776859i	−0.921479	+	0.388429i	$0.873018\pi$
$588$		0			0
$589$	−24.4749			−1.00847
$590$	−0.744691	+	3.66553i	−0.0306584	+	0.150907i
$591$	−0.287258	+	0.497545i	−0.0118162	+	0.0204663i
$592$	2.53661	+	1.46451i	0.104254	+	0.0601910i
$593$	−29.2283	+	16.8749i	−1.20026	+	0.692971i	−0.960613	−	0.277889i	$-0.910365\pi$
$593$	−29.2283	+	16.8749i	−1.20026	+	0.692971i	−0.239648	+	0.970860i	$0.577032\pi$
$594$	0.387873			0.0159146
$595$		0			0
$596$	8.72970			0.357582
$597$	0.174271	−	0.100615i	0.00713244	−	0.00411791i
$598$	1.12538	+	0.649738i	0.0460202	+	0.0265698i
$599$	−10.1490	+	17.5786i	−0.414678	+	0.718244i	−0.995395	−	0.0958622i	$-0.969439\pi$
$599$	−10.1490	+	17.5786i	−0.414678	+	0.718244i	0.580716	+	0.814106i	$0.302773\pi$
$600$	3.06727	−	2.31405i	0.125221	−	0.0944706i
$601$	−13.8496			−0.564935			−0.282468	−	0.959277i	$-0.591153\pi$
$601$	−13.8496			−0.564935			−0.282468	+	0.959277i	$0.591153\pi$
$602$		0			0
$603$		−	9.92478i		−	0.404168i
$604$	−1.27504	−	2.20843i	−0.0518806	−	0.0898598i
$605$	4.97076	+	14.8422i	0.202090	+	0.603422i
$606$	−1.71274	+	2.96656i	−0.0695754	+	0.120508i
$607$	−21.8677	+	12.6253i	−0.887581	+	0.512445i	−0.873150	−	0.487451i	$-0.837927\pi$
$607$	−21.8677	+	12.6253i	−0.887581	+	0.512445i	−0.0144305	+	0.999896i	$0.504594\pi$
$608$		−	12.1406i		−	0.492366i
$609$		0			0
$610$	2.82653	+	2.49929i	0.114443	+	0.101193i
$611$	−6.70052	−	11.6056i	−0.271074	−	0.469514i
$612$	−5.69370	−	3.28726i	−0.230154	−	0.132880i
$613$	−7.92329	−	4.57452i	−0.320019	−	0.184763i	0.331382	−	0.943497i	$-0.392485\pi$
$613$	−7.92329	−	4.57452i	−0.320019	−	0.184763i	−0.651401	+	0.758734i	$0.725818\pi$
$614$	2.33709	+	4.04796i	0.0943172	+	0.163362i
$615$	−6.26187	−	5.53690i	−0.252503	−	0.223270i
$616$		0			0
$617$			15.9492i			0.642091i	0.947064	+	0.321046i	$0.104034\pi$
$617$			15.9492i			0.642091i	−0.947064	+	0.321046i	$0.895966\pi$
$618$	1.12538	−	0.649738i	0.0452694	−	0.0261363i
$619$	5.58673	−	9.67651i	0.224550	−	0.388932i	−0.731634	−	0.681697i	$-0.761242\pi$
$619$	5.58673	−	9.67651i	0.224550	−	0.388932i	0.956184	+	0.292765i	$0.0945755\pi$
$620$	−6.37463	−	19.0340i	−0.256011	−	0.764425i
$621$	2.48119	+	4.29755i	0.0995669	+	0.172455i
$622$			1.60037i			0.0641689i
$623$		0			0
$624$	5.09825			0.204093
$625$	17.3866	+	17.9640i	0.695464	+	0.718561i
$626$	1.44500	−	2.50281i	0.0577537	−	0.100032i
$627$	9.26693	+	5.35026i	0.370085	+	0.213669i
$628$	−4.50317	+	2.59991i	−0.179696	+	0.103748i
$629$	−2.59895			−0.103627
$630$		0			0
$631$	−14.5501			−0.579229			−0.289615	−	0.957143i	$-0.593527\pi$
$631$	−14.5501			−0.579229			−0.289615	+	0.957143i	$0.593527\pi$
$632$	−7.12119	+	4.11142i	−0.283266	+	0.163543i
$633$	−5.58457	−	3.22425i	−0.221967	−	0.128153i
$634$	0.981902	−	1.70070i	0.0389963	−	0.0675436i
$635$	−1.20224	+	5.91767i	−0.0477093	+	0.234835i
$636$	16.8265			0.667215
$637$		0			0
$638$		−	3.07381i		−	0.121693i
$639$	1.00000	+	1.73205i	0.0395594	+	0.0685189i
$640$	12.5469	−	4.20206i	0.495961	−	0.166101i
$641$	19.3634	−	33.5385i	0.764810	−	1.32469i	−0.175537	−	0.984473i	$-0.556166\pi$
$641$	19.3634	−	33.5385i	0.764810	−	1.32469i	0.940347	−	0.340217i	$-0.110500\pi$
$642$	−2.30737	+	1.33216i	−0.0910648	+	0.0525763i
$643$			11.9511i			0.471306i	0.971837	+	0.235653i	$0.0757229\pi$
$643$			11.9511i			0.471306i	−0.971837	+	0.235653i	$0.924277\pi$
$644$		0			0
$645$	18.7005	−	21.1490i	0.736332	−	0.832742i
$646$	1.73813	+	3.01054i	0.0683860	+	0.118448i
$647$	12.6007	+	7.27504i	0.495386	+	0.286011i	0.726806	−	0.686843i	$-0.241004\pi$
$647$	12.6007	+	7.27504i	0.495386	+	0.286011i	−0.231420	+	0.972854i	$0.574337\pi$
$648$	−0.665499	−	0.384226i	−0.0261433	−	0.0150938i
$649$	−8.62530	−	14.9395i	−0.338573	−	0.586425i
$650$	−0.160295	−	1.29948i	−0.00628727	−	0.0509697i
$651$		0			0
$652$		−	10.3996i		−	0.407281i
$653$	−43.2801	+	24.9878i	−1.69368	+	0.977847i	−0.742181	+	0.670199i	$0.766209\pi$
$653$	−43.2801	+	24.9878i	−1.69368	+	0.977847i	−0.951500	+	0.307648i	$0.900458\pi$
$654$	0.269159	−	0.466198i	0.0105250	−	0.0182298i
$655$	−14.6462	−	43.7322i	−0.572275	−	1.70876i
$656$	−7.05712	−	12.2233i	−0.275534	−	0.477240i
$657$		−	9.35026i		−	0.364788i
$658$		0			0
$659$	16.9525			0.660377			0.330189	−	0.943915i	$-0.392888\pi$
$659$	16.9525			0.660377			0.330189	+	0.943915i	$0.392888\pi$
$660$	−1.74726	+	8.60038i	−0.0680119	+	0.334769i
$661$	7.82653	−	13.5560i	0.304417	−	0.527265i	−0.672715	−	0.739902i	$-0.734872\pi$
$661$	7.82653	−	13.5560i	0.304417	−	0.527265i	0.977131	+	0.212637i	$0.0682051\pi$
$662$	−4.67744	−	2.70052i	−0.181794	−	0.104959i
$663$	−3.91767	+	2.26187i	−0.152150	+	0.0878436i
$664$	2.47768			0.0961528
$665$		0			0
$666$	−0.150446			−0.00582965
$667$	34.0572	−	19.6629i	1.31870	−	0.761351i
$668$	24.7275	+	14.2765i	0.956737	+	0.552373i
$669$	−0.775746	+	1.34363i	−0.0299921	+	0.0519478i
$670$	−4.21777	−	0.856885i	−0.162947	−	0.0331043i
$671$	−17.4010			−0.671760
$672$		0			0
$673$		−	26.0263i		−	1.00324i	−0.865088	−	0.501621i	$-0.832737\pi$
$673$		−	26.0263i		−	1.00324i	0.865088	−	0.501621i	$-0.167263\pi$
$674$	−0.373285	−	0.646548i	−0.0143784	−	0.0249041i
$675$	1.95108	−	4.60362i	0.0750970	−	0.177193i
$676$	−10.9666	+	18.9947i	−0.421793	+	0.730566i
$677$	−30.7022	+	17.7259i	−1.17998	+	0.681262i	−0.956010	−	0.293334i	$-0.905235\pi$
$677$	−30.7022	+	17.7259i	−1.17998	+	0.681262i	−0.223971	+	0.974596i	$0.571902\pi$
$678$			2.33709i			0.0897553i
$679$		0			0
$680$	−3.81336	+	4.31265i	−0.146236	+	0.165383i
$681$	−6.57452	−	11.3874i	−0.251936	−	0.436366i
$682$	−1.53662	−	0.887166i	−0.0588401	−	0.0339713i
$683$	−20.4927	−	11.8315i	−0.784131	−	0.452718i	0.0537615	−	0.998554i	$-0.482879\pi$
$683$	−20.4927	−	11.8315i	−0.784131	−	0.452718i	−0.837892	+	0.545836i	$0.816212\pi$
$684$	−5.24965	−	9.09265i	−0.200725	−	0.347666i
$685$	−37.6893	−	33.3258i	−1.44003	−	1.27331i
$686$		0			0
$687$		−	2.77575i		−	0.105901i
$688$	41.2834	−	23.8350i	1.57391	−	0.908700i
$689$	5.78892	−	10.0267i	0.220540	−	0.381987i
$690$	2.04057	−	0.683401i	0.0776831	−	0.0260166i
$691$	0.287258	+	0.497545i	0.0109278	+	0.0189275i	0.871438	−	0.490506i	$-0.163188\pi$
$691$	0.287258	+	0.497545i	0.0109278	+	0.0189275i	−0.860510	+	0.509434i	$0.829855\pi$
$692$			8.82936i			0.335642i
$693$		0			0
$694$	−1.85940			−0.0705820
$695$	7.17660	+	1.45800i	0.272224	+	0.0553052i
$696$	−3.04491	+	5.27393i	−0.115417	+	0.199908i
$697$	10.8459	+	6.26187i	0.410817	+	0.237185i
$698$	2.54434	−	1.46898i	0.0963047	−	0.0556015i
$699$	−0.0507852			−0.00192087
$700$		0			0
$701$	42.7269			1.61377			0.806886	−	0.590707i	$-0.201151\pi$
$701$	42.7269			1.61377			0.806886	+	0.590707i	$0.201151\pi$
$702$	−0.226782	+	0.130933i	−0.00855933	+	0.00494173i
$703$	−3.59439	−	2.07522i	−0.135565	−	0.0782685i
$704$	−7.11142	+	12.3173i	−0.268022	+	0.464227i
$705$	−21.7482	−	4.41838i	−0.819084	−	0.166406i
$706$	−3.94639			−0.148524
$707$		0			0
$708$			16.9262i			0.636125i
$709$	13.6253	+	23.5997i	0.511709	+	0.886306i	0.999908	+	0.0135735i	$0.00432070\pi$
$709$	13.6253	+	23.5997i	0.511709	+	0.886306i	−0.488199	+	0.872732i	$0.662346\pi$
$710$	0.822414	−	0.275432i	0.0308647	−	0.0103368i
$711$	−5.35026	+	9.26693i	−0.200650	+	0.347537i
$712$	−0.690529	+	0.398677i	−0.0258787	+	0.0149411i
$713$		−	22.7005i		−	0.850141i
$714$		0			0
$715$	4.52373	+	4.00000i	0.169178	+	0.149592i
$716$	9.81194	+	16.9948i	0.366690	+	0.635125i
$717$	5.06586	+	2.92478i	0.189188	+	0.109228i
$718$	−5.27393	−	3.04491i	−0.196821	−	0.113635i
$719$	−5.35026	−	9.26693i	−0.199531	−	0.345598i	0.748845	−	0.662745i	$-0.230609\pi$
$719$	−5.35026	−	9.26693i	−0.199531	−	0.345598i	−0.948376	+	0.317147i	$0.897275\pi$
$720$	5.59261	−	6.32487i	0.208424	−	0.235714i
$721$		0			0
$722$			1.86670i			0.0694713i
$723$	−0.0651448	+	0.0376114i	−0.00242276	+	0.00139878i
$724$	−10.4255	+	18.0575i	−0.387460	+	0.671101i
$725$	−36.4826	−	15.4618i	−1.35493	−	0.574239i
$726$	−0.678778	−	1.17568i	−0.0251918	−	0.0436335i
$727$			39.9511i			1.48171i	0.671668	+	0.740853i	$0.265578\pi$
$727$			39.9511i			1.48171i	−0.671668	+	0.740853i	$0.734422\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	−3.97362	−	0.807282i	−0.147070	−	0.0298789i
$731$	−21.1490	+	36.6312i	−0.782225	+	1.35485i
$732$	14.7864	+	8.53690i	0.546519	+	0.315533i
$733$	26.2829	−	15.1744i	0.970780	−	0.560480i	0.0713061	−	0.997454i	$-0.477283\pi$
$733$	26.2829	−	15.1744i	0.970780	−	0.560480i	0.899474	+	0.436974i	$0.143950\pi$
$734$	5.70194			0.210462
$735$		0			0
$736$	11.2605			0.415066
$737$	17.1902	−	9.92478i	0.633210	−	0.365584i
$738$	0.627835	+	0.362481i	0.0231109	+	0.0133431i
$739$	18.6253	−	32.2600i	0.685143	−	1.18670i	−0.288249	−	0.957555i	$-0.593073\pi$
$739$	18.6253	−	32.2600i	0.685143	−	1.18670i	0.973392	−	0.229147i	$-0.0735935\pi$
$740$	0.677714	−	3.33585i	0.0249133	−	0.122628i
$741$	−7.22425			−0.265390
$742$		0			0
$743$		−	26.3634i		−	0.967181i	−0.875294	−	0.483590i	$-0.839332\pi$
$743$		−	26.3634i		−	0.967181i	0.875294	−	0.483590i	$-0.160668\pi$
$744$	1.75765	+	3.04434i	0.0644385	+	0.111611i
$745$	−3.15892	−	9.43225i	−0.115734	−	0.345571i
$746$	−1.55149	+	2.68726i	−0.0568042	+	0.0983877i
$747$	2.79229	−	1.61213i	0.102164	−	0.0589846i
$748$		−	13.1490i		−	0.480776i
$749$		0			0
$750$	−1.78797	−	1.22662i	−0.0652873	−	0.0447900i
$751$	−25.3258	−	43.8656i	−0.924152	−	1.60068i	−0.792919	−	0.609328i	$-0.791439\pi$
$751$	−25.3258	−	43.8656i	−0.924152	−	1.60068i	−0.131234	−	0.991351i	$-0.541894\pi$
$752$	−32.4530	−	18.7367i	−1.18344	−	0.683258i
$753$	−16.6487	−	9.61213i	−0.606712	−	0.350285i
$754$	1.03761	+	1.79720i	0.0377876	+	0.0654500i
$755$	−1.92478	+	2.17679i	−0.0700498	+	0.0792216i
$756$		0			0
$757$			38.9525i			1.41575i	0.706336	+	0.707877i	$0.250347\pi$
$757$			38.9525i			1.41575i	−0.706336	+	0.707877i	$0.749653\pi$
$758$	−1.79720	+	1.03761i	−0.0652771	+	0.0376877i
$759$	−4.96239	+	8.59511i	−0.180123	+	0.311983i
$760$	−8.71751	+	2.91955i	−0.316217	+	0.105903i
$761$	−24.1065	−	41.7537i	−0.873860	−	1.51357i	−0.857972	−	0.513696i	$-0.828276\pi$
$761$	−24.1065	−	41.7537i	−0.873860	−	1.51357i	−0.0158873	−	0.999874i	$-0.505057\pi$
$762$		−	0.523730i		−	0.0189727i
$763$		0			0
$764$	−27.1782			−0.983273
$765$	−1.49149	+	7.34144i	−0.0539250	+	0.265430i
$766$	1.62672	−	2.81755i	0.0587756	−	0.101802i
$767$	10.0861	+	5.82321i	0.364188	+	0.210264i
$768$	11.3235	−	6.53761i	0.408601	−	0.235906i
$769$	−4.44851			−0.160417			−0.0802086	−	0.996778i	$-0.525559\pi$
$769$	−4.44851			−0.160417			−0.0802086	+	0.996778i	$0.525559\pi$
$770$		0			0
$771$	−7.35026			−0.264713
$772$	−26.0459	+	15.0376i	−0.937413	+	0.541215i
$773$	34.0360	+	19.6507i	1.22419	+	0.706786i	0.965808	−	0.259257i	$-0.0834776\pi$
$773$	34.0360	+	19.6507i	1.22419	+	0.706786i	0.258381	+	0.966043i	$0.416811\pi$
$774$	−1.22425	+	2.12047i	−0.0440049	+	0.0762187i
$775$	−18.2591	+	13.7753i	−0.655888	+	0.494823i
$776$	14.2158			0.510318
$777$		0			0
$778$

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:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.167954 - 0.0969683i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.981194 + 1.69948i) q^{4} +(2.19130 + 0.445186i) q^{5} -0.193937 q^{6} +0.768452i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.167954 - 0.0969683i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.981194 + 1.69948i) q^{4} +(2.19130 + 0.445186i) q^{5} -0.193937 q^{6} +0.768452i q^{8} +(0.500000 + 0.866025i) q^{9} +(0.411207 - 0.137716i) q^{10} +(-1.00000 + 1.73205i) q^{11} +(1.69948 - 0.981194i) q^{12} -1.35026i q^{13} +(-1.67513 - 1.48119i) q^{15} +(-1.88787 - 3.26989i) q^{16} +(2.90141 + 1.67513i) q^{17} +(0.167954 + 0.0969683i) q^{18} +(2.67513 + 4.63346i) q^{19} +(-2.90668 + 3.28726i) q^{20} +0.387873i q^{22} +(-4.29755 + 2.48119i) q^{23} +(0.384226 - 0.665499i) q^{24} +(4.60362 + 1.95108i) q^{25} +(-0.130933 - 0.226782i) q^{26} -1.00000i q^{27} -7.92478 q^{29} +(-0.424974 - 0.0863379i) q^{30} +(-2.28726 + 3.96165i) q^{31} +(-1.96515 - 1.13458i) q^{32} +(1.73205 - 1.00000i) q^{33} +0.649738 q^{34} -1.96239 q^{36} +(-0.671816 + 0.387873i) q^{37} +(0.898598 + 0.518806i) q^{38} +(-0.675131 + 1.16936i) q^{39} +(-0.342104 + 1.68391i) q^{40} +3.73813 q^{41} +12.6253i q^{43} +(-1.96239 - 3.39896i) q^{44} +(0.710109 + 2.12032i) q^{45} +(-0.481194 + 0.833453i) q^{46} +(8.59511 - 4.96239i) q^{47} +3.77575i q^{48} +(0.962389 - 0.118714i) q^{50} +(-1.67513 - 2.90141i) q^{51} +(2.29474 + 1.32487i) q^{52} +(7.42575 + 4.28726i) q^{53} +(-0.0969683 - 0.167954i) q^{54} +(-2.96239 + 3.35026i) q^{55} -5.35026i q^{57} +(-1.33100 + 0.768452i) q^{58} +(-4.31265 + 7.46973i) q^{59} +(4.16089 - 1.39351i) q^{60} +(4.35026 + 7.53487i) q^{61} +0.887166i q^{62} +7.11142 q^{64} +(0.601118 - 2.95883i) q^{65} +(0.193937 - 0.335908i) q^{66} +(-8.59511 - 4.96239i) q^{67} +(-5.69370 + 3.28726i) q^{68} +4.96239 q^{69} +2.00000 q^{71} +(-0.665499 + 0.384226i) q^{72} +(-8.09756 - 4.67513i) q^{73} +(-0.0752228 + 0.130290i) q^{74} +(-3.01131 - 3.99149i) q^{75} -10.4993 q^{76} +0.261865i q^{78} +(5.35026 + 9.26693i) q^{79} +(-2.68119 - 8.00578i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.627835 - 0.362481i) q^{82} -3.22425i q^{83} +(5.61213 + 4.96239i) q^{85} +(1.22425 + 2.12047i) q^{86} +(6.86306 + 3.96239i) q^{87} +(-1.33100 - 0.768452i) q^{88} +(0.518806 + 0.898598i) q^{89} +(0.324869 + 0.287258i) q^{90} -9.73813i q^{92} +(3.96165 - 2.28726i) q^{93} +(0.962389 - 1.66691i) q^{94} +(3.79927 + 11.3443i) q^{95} +(1.13458 + 1.96515i) q^{96} -18.4993i q^{97} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 10 q^{4} - 2 q^{5} - 4 q^{6} + 6 q^{9}+O(q^{10}) \) 12 * q + 10 * q^4 - 2 * q^5 - 4 * q^6 + 6 * q^9	\( 12 q + 10 q^{4} - 2 q^{5} - 4 q^{6} + 6 q^{9} + 12 q^{10} - 12 q^{11} - 26 q^{16} + 12 q^{19} - 60 q^{20} - 18 q^{24} + 2 q^{25} - 20 q^{26} - 8 q^{29} + 10 q^{30} - 4 q^{31} + 48 q^{34} + 20 q^{36} + 12 q^{39} - 4 q^{40} + 8 q^{41} + 20 q^{44} + 2 q^{45} + 16 q^{46} - 32 q^{50} - 2 q^{54} + 8 q^{55} + 32 q^{59} + 8 q^{60} + 12 q^{61} - 52 q^{64} - 32 q^{65} + 4 q^{66} + 16 q^{69} + 24 q^{71} - 88 q^{74} - 8 q^{75} + 8 q^{76} + 24 q^{79} - 46 q^{80} - 6 q^{81} + 64 q^{85} + 8 q^{86} + 28 q^{89} + 24 q^{90} - 32 q^{94} - 4 q^{95} + 58 q^{96} - 24 q^{99}+O(q^{100}) \) 12 * q + 10 * q^4 - 2 * q^5 - 4 * q^6 + 6 * q^9 + 12 * q^10 - 12 * q^11 - 26 * q^16 + 12 * q^19 - 60 * q^20 - 18 * q^24 + 2 * q^25 - 20 * q^26 - 8 * q^29 + 10 * q^30 - 4 * q^31 + 48 * q^34 + 20 * q^36 + 12 * q^39 - 4 * q^40 + 8 * q^41 + 20 * q^44 + 2 * q^45 + 16 * q^46 - 32 * q^50 - 2 * q^54 + 8 * q^55 + 32 * q^59 + 8 * q^60 + 12 * q^61 - 52 * q^64 - 32 * q^65 + 4 * q^66 + 16 * q^69 + 24 * q^71 - 88 * q^74 - 8 * q^75 + 8 * q^76 + 24 * q^79 - 46 * q^80 - 6 * q^81 + 64 * q^85 + 8 * q^86 + 28 * q^89 + 24 * q^90 - 32 * q^94 - 4 * q^95 + 58 * q^96 - 24 * q^99

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