LMFDB - Embedded newform 735.2.i.h.226.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [735,2,Mod(226,735)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("735.226"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(735, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [4,-2,2,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			226.1
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	735.226
Dual form			735.2.i.h.361.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.20711 + 2.09077i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.91421 - 3.31552i) q^{4} +(0.500000 - 0.866025i) q^{5} -2.41421 q^{6} +4.41421 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.20711 + 2.09077i) q^{10} +(-1.41421 - 2.44949i) q^{11} +(1.91421 - 3.31552i) q^{12} +4.82843 q^{13} +1.00000 q^{15} +(-1.50000 + 2.59808i) q^{16} +(-3.82843 - 6.63103i) q^{17} +(-1.20711 - 2.09077i) q^{18} +(-0.414214 + 0.717439i) q^{19} -3.82843 q^{20} +6.82843 q^{22} +(3.82843 - 6.63103i) q^{23} +(2.20711 + 3.82282i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-5.82843 + 10.0951i) q^{26} -1.00000 q^{27} +6.00000 q^{29} +(-1.20711 + 2.09077i) q^{30} +(3.24264 + 5.61642i) q^{31} +(0.792893 + 1.37333i) q^{32} +(1.41421 - 2.44949i) q^{33} +18.4853 q^{34} +3.82843 q^{36} +(1.82843 - 3.16693i) q^{37} +(-1.00000 - 1.73205i) q^{38} +(2.41421 + 4.18154i) q^{39} +(2.20711 - 3.82282i) q^{40} -11.6569 q^{41} +8.00000 q^{43} +(-5.41421 + 9.37769i) q^{44} +(0.500000 + 0.866025i) q^{45} +(9.24264 + 16.0087i) q^{46} +(2.82843 - 4.89898i) q^{47} -3.00000 q^{48} +2.41421 q^{50} +(3.82843 - 6.63103i) q^{51} +(-9.24264 - 16.0087i) q^{52} +(4.24264 + 7.34847i) q^{53} +(1.20711 - 2.09077i) q^{54} -2.82843 q^{55} -0.828427 q^{57} +(-7.24264 + 12.5446i) q^{58} +(1.17157 + 2.02922i) q^{59} +(-1.91421 - 3.31552i) q^{60} -15.6569 q^{62} -9.82843 q^{64} +(2.41421 - 4.18154i) q^{65} +(3.41421 + 5.91359i) q^{66} +(-14.6569 + 25.3864i) q^{68} +7.65685 q^{69} -2.82843 q^{71} +(-2.20711 + 3.82282i) q^{72} +(-5.58579 - 9.67487i) q^{73} +(4.41421 + 7.64564i) q^{74} +(0.500000 - 0.866025i) q^{75} +3.17157 q^{76} -11.6569 q^{78} +(4.00000 - 6.92820i) q^{79} +(1.50000 + 2.59808i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(14.0711 - 24.3718i) q^{82} +1.65685 q^{83} -7.65685 q^{85} +(-9.65685 + 16.7262i) q^{86} +(3.00000 + 5.19615i) q^{87} +(-6.24264 - 10.8126i) q^{88} +(-2.65685 + 4.60181i) q^{89} -2.41421 q^{90} -29.3137 q^{92} +(-3.24264 + 5.61642i) q^{93} +(6.82843 + 11.8272i) q^{94} +(0.414214 + 0.717439i) q^{95} +(-0.792893 + 1.37333i) q^{96} -6.48528 q^{97} +2.82843 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} - 4 q^{6} + 12 q^{8} - 2 q^{9} + 2 q^{10} + 2 q^{12} + 8 q^{13} + 4 q^{15} - 6 q^{16} - 4 q^{17} - 2 q^{18} + 4 q^{19} - 4 q^{20} + 16 q^{22} + 4 q^{23} + 6 q^{24}+ \cdots + 8 q^{97}+O(q^{100}) $ 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 - 4 * q^6 + 12 * q^8 - 2 * q^9 + 2 * q^10 + 2 * q^12 + 8 * q^13 + 4 * q^15 - 6 * q^16 - 4 * q^17 - 2 * q^18 + 4 * q^19 - 4 * q^20 + 16 * q^22 + 4 * q^23 + 6 * q^24 - 2 * q^25 - 12 * q^26 - 4 * q^27 + 24 * q^29 - 2 * q^30 - 4 * q^31 + 6 * q^32 + 40 * q^34 + 4 * q^36 - 4 * q^37 - 4 * q^38 + 4 * q^39 + 6 * q^40 - 24 * q^41 + 32 * q^43 - 16 * q^44 + 2 * q^45 + 20 * q^46 - 12 * q^48 + 4 * q^50 + 4 * q^51 - 20 * q^52 + 2 * q^54 + 8 * q^57 - 12 * q^58 + 16 * q^59 - 2 * q^60 - 40 * q^62 - 28 * q^64 + 4 * q^65 + 8 * q^66 - 36 * q^68 + 8 * q^69 - 6 * q^72 - 28 * q^73 + 12 * q^74 + 2 * q^75 + 24 * q^76 - 24 * q^78 + 16 * q^79 + 6 * q^80 - 2 * q^81 + 28 * q^82 - 16 * q^83 - 8 * q^85 - 16 * q^86 + 12 * q^87 - 8 * q^88 + 12 * q^89 - 4 * q^90 - 72 * q^92 + 4 * q^93 + 16 * q^94 - 4 * q^95 - 6 * q^96 + 8 * q^97

Character values

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

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

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 $

$2$	−1.20711	+	2.09077i	−0.853553	+	1.47840i	0.0244272	+	0.999702i	$0.492224\pi$
$2$	−1.20711	+	2.09077i	−0.853553	+	1.47840i	−0.877981	+	0.478696i	$0.841110\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−1.91421	−	3.31552i	−0.957107	−	1.65776i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	−2.41421			−0.985599
$7$		0			0
$7$		0			0
$8$	4.41421			1.56066
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.20711	+	2.09077i	0.381721	+	0.661160i
$11$	−1.41421	−	2.44949i	−0.426401	−	0.738549i	0.570149	−	0.821541i	$-0.306886\pi$
$11$	−1.41421	−	2.44949i	−0.426401	−	0.738549i	−0.996550	+	0.0829925i	$0.973552\pi$
$12$	1.91421	−	3.31552i	0.552586	−	0.957107i
$13$	4.82843			1.33916			0.669582	−	0.742738i	$-0.266473\pi$
$13$	4.82843			1.33916			0.669582	+	0.742738i	$0.266473\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$	−1.50000	+	2.59808i	−0.375000	+	0.649519i
$17$	−3.82843	−	6.63103i	−0.928530	−	1.60826i	−0.785783	−	0.618502i	$-0.787740\pi$
$17$	−3.82843	−	6.63103i	−0.928530	−	1.60826i	−0.142747	−	0.989759i	$-0.545593\pi$
$18$	−1.20711	−	2.09077i	−0.284518	−	0.492799i
$19$	−0.414214	+	0.717439i	−0.0950271	+	0.164592i	−0.909620	−	0.415441i	$-0.863627\pi$
$19$	−0.414214	+	0.717439i	−0.0950271	+	0.164592i	0.814593	+	0.580033i	$0.196960\pi$
$20$	−3.82843			−0.856062
$21$		0			0
$22$	6.82843			1.45583
$23$	3.82843	−	6.63103i	0.798282	−	1.38267i	−0.122452	−	0.992474i	$-0.539076\pi$
$23$	3.82843	−	6.63103i	0.798282	−	1.38267i	0.920734	−	0.390191i	$-0.127591\pi$
$24$	2.20711	+	3.82282i	0.450524	+	0.780330i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−5.82843	+	10.0951i	−1.14305	+	1.97982i
$27$	−1.00000			−0.192450
$28$		0			0
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$	−1.20711	+	2.09077i	−0.220387	+	0.381721i
$31$	3.24264	+	5.61642i	0.582395	+	1.00874i	0.995195	+	0.0979165i	$0.0312178\pi$
$31$	3.24264	+	5.61642i	0.582395	+	1.00874i	−0.412799	+	0.910822i	$0.635449\pi$
$32$	0.792893	+	1.37333i	0.140165	+	0.242773i
$33$	1.41421	−	2.44949i	0.246183	−	0.426401i
$34$	18.4853			3.17020
$35$		0			0
$36$	3.82843			0.638071
$37$	1.82843	−	3.16693i	0.300592	−	0.520640i	−0.675679	−	0.737196i	$-0.736149\pi$
$37$	1.82843	−	3.16693i	0.300592	−	0.520640i	0.976270	+	0.216557i	$0.0694826\pi$
$38$	−1.00000	−	1.73205i	−0.162221	−	0.280976i
$39$	2.41421	+	4.18154i	0.386584	+	0.669582i
$40$	2.20711	−	3.82282i	0.348974	−	0.604441i
$41$	−11.6569			−1.82049			−0.910247	−	0.414065i	$-0.864109\pi$
$41$	−11.6569			−1.82049			−0.910247	+	0.414065i	$0.864109\pi$
$42$		0			0
$43$	8.00000			1.21999			0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000			1.21999			0.609994	+	0.792406i	$0.291172\pi$
$44$	−5.41421	+	9.37769i	−0.816223	+	1.41374i
$45$	0.500000	+	0.866025i	0.0745356	+	0.129099i
$46$	9.24264	+	16.0087i	1.36275	+	2.36036i
$47$	2.82843	−	4.89898i	0.412568	−	0.714590i	−0.582601	−	0.812758i	$-0.697965\pi$
$47$	2.82843	−	4.89898i	0.412568	−	0.714590i	0.995170	+	0.0981685i	$0.0312984\pi$
$48$	−3.00000			−0.433013
$49$		0			0
$50$	2.41421			0.341421
$51$	3.82843	−	6.63103i	0.536087	−	0.928530i
$52$	−9.24264	−	16.0087i	−1.28172	−	2.22001i
$53$	4.24264	+	7.34847i	0.582772	+	1.00939i	0.995149	+	0.0983769i	$0.0313651\pi$
$53$	4.24264	+	7.34847i	0.582772	+	1.00939i	−0.412378	+	0.911013i	$0.635302\pi$
$54$	1.20711	−	2.09077i	0.164266	−	0.284518i
$55$	−2.82843			−0.381385
$56$		0			0
$57$	−0.828427			−0.109728
$58$	−7.24264	+	12.5446i	−0.951005	+	1.64719i
$59$	1.17157	+	2.02922i	0.152526	+	0.264182i	0.932155	−	0.362059i	$-0.117926\pi$
$59$	1.17157	+	2.02922i	0.152526	+	0.264182i	−0.779630	+	0.626241i	$0.784593\pi$
$60$	−1.91421	−	3.31552i	−0.247124	−	0.428031i
$61$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$61$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$62$	−15.6569			−1.98842
$63$		0			0
$64$	−9.82843			−1.22855
$65$	2.41421	−	4.18154i	0.299446	−	0.518656i
$66$	3.41421	+	5.91359i	0.420261	+	0.727913i
$67$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$67$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$68$	−14.6569	+	25.3864i	−1.77740	+	3.07856i
$69$	7.65685			0.921777
$70$		0			0
$71$	−2.82843			−0.335673			−0.167836	−	0.985815i	$-0.553678\pi$
$71$	−2.82843			−0.335673			−0.167836	+	0.985815i	$0.553678\pi$
$72$	−2.20711	+	3.82282i	−0.260110	+	0.450524i
$73$	−5.58579	−	9.67487i	−0.653767	−	1.13236i	−0.982201	−	0.187831i	$-0.939854\pi$
$73$	−5.58579	−	9.67487i	−0.653767	−	1.13236i	0.328435	−	0.944527i	$-0.393479\pi$
$74$	4.41421	+	7.64564i	0.513142	+	0.888788i
$75$	0.500000	−	0.866025i	0.0577350	−	0.100000i
$76$	3.17157			0.363804
$77$		0			0
$78$	−11.6569			−1.31988
$79$	4.00000	−	6.92820i	0.450035	−	0.779484i	−0.548352	−	0.836247i	$-0.684745\pi$
$79$	4.00000	−	6.92820i	0.450035	−	0.779484i	0.998388	+	0.0567635i	$0.0180781\pi$
$80$	1.50000	+	2.59808i	0.167705	+	0.290474i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	14.0711	−	24.3718i	1.55389	−	2.69142i
$83$	1.65685			0.181863			0.0909317	−	0.995857i	$-0.471016\pi$
$83$	1.65685			0.181863			0.0909317	+	0.995857i	$0.471016\pi$
$84$		0			0
$85$	−7.65685			−0.830502
$86$	−9.65685	+	16.7262i	−1.04133	+	1.80363i
$87$	3.00000	+	5.19615i	0.321634	+	0.557086i
$88$	−6.24264	−	10.8126i	−0.665468	−	1.15262i
$89$	−2.65685	+	4.60181i	−0.281626	+	0.487791i	−0.971785	−	0.235867i	$-0.924207\pi$
$89$	−2.65685	+	4.60181i	−0.281626	+	0.487791i	0.690159	+	0.723657i	$0.257540\pi$
$90$	−2.41421			−0.254480
$91$		0			0
$92$	−29.3137			−3.05617
$93$	−3.24264	+	5.61642i	−0.336246	+	0.582395i
$94$	6.82843	+	11.8272i	0.704298	+	1.21988i
$95$	0.414214	+	0.717439i	0.0424974	+	0.0736077i
$96$	−0.792893	+	1.37333i	−0.0809243	+	0.140165i
$97$	−6.48528			−0.658481			−0.329240	−	0.944246i	$-0.606793\pi$
$97$	−6.48528			−0.658481			−0.329240	+	0.944246i	$0.606793\pi$
$98$		0			0
$99$	2.82843			0.284268
$100$	−1.91421	+	3.31552i	−0.191421	+	0.331552i
$101$	3.82843	+	6.63103i	0.380943	+	0.659812i	0.991197	−	0.132393i	$-0.0422662\pi$
$101$	3.82843	+	6.63103i	0.380943	+	0.659812i	−0.610255	+	0.792205i	$0.708933\pi$
$102$	9.24264	+	16.0087i	0.915158	+	1.58510i
$103$	−6.00000	+	10.3923i	−0.591198	+	1.02398i	0.402874	+	0.915255i	$0.368011\pi$
$103$	−6.00000	+	10.3923i	−0.591198	+	1.02398i	−0.994071	+	0.108729i	$0.965322\pi$
$104$	21.3137			2.08998
$105$		0			0
$106$	−20.4853			−1.98971
$107$	−2.65685	+	4.60181i	−0.256848	+	0.444873i	−0.965396	−	0.260789i	$-0.916017\pi$
$107$	−2.65685	+	4.60181i	−0.256848	+	0.444873i	0.708548	+	0.705663i	$0.249351\pi$
$108$	1.91421	+	3.31552i	0.184195	+	0.319036i
$109$	−3.00000	−	5.19615i	−0.287348	−	0.497701i	0.685828	−	0.727764i	$-0.259440\pi$
$109$	−3.00000	−	5.19615i	−0.287348	−	0.497701i	−0.973176	+	0.230063i	$0.926107\pi$
$110$	3.41421	−	5.91359i	0.325532	−	0.563839i
$111$	3.65685			0.347093
$112$		0			0
$113$	2.82843			0.266076			0.133038	−	0.991111i	$-0.457527\pi$
$113$	2.82843			0.266076			0.133038	+	0.991111i	$0.457527\pi$
$114$	1.00000	−	1.73205i	0.0936586	−	0.162221i
$115$	−3.82843	−	6.63103i	−0.357003	−	0.618347i
$116$	−11.4853	−	19.8931i	−1.06638	−	1.84703i
$117$	−2.41421	+	4.18154i	−0.223194	+	0.386584i
$118$	−5.65685			−0.520756
$119$		0			0
$120$	4.41421			0.402961
$121$	1.50000	−	2.59808i	0.136364	−	0.236189i
$122$		0			0
$123$	−5.82843	−	10.0951i	−0.525532	−	0.910247i
$124$	12.4142	−	21.5020i	1.11483	−	1.93094i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	19.3137			1.71381			0.856907	−	0.515471i	$-0.172383\pi$
$127$	19.3137			1.71381			0.856907	+	0.515471i	$0.172383\pi$
$128$	10.2782	−	17.8023i	0.908471	−	1.57352i
$129$	4.00000	+	6.92820i	0.352180	+	0.609994i
$130$	5.82843	+	10.0951i	0.511187	+	0.885402i
$131$	2.82843	−	4.89898i	0.247121	−	0.428026i	−0.715605	−	0.698505i	$-0.753849\pi$
$131$	2.82843	−	4.89898i	0.247121	−	0.428026i	0.962726	+	0.270479i	$0.0871822\pi$
$132$	−10.8284			−0.942494
$133$		0			0
$134$		0			0
$135$	−0.500000	+	0.866025i	−0.0430331	+	0.0745356i
$136$	−16.8995	−	29.2708i	−1.44912	−	2.50995i
$137$	−6.58579	−	11.4069i	−0.562662	−	0.974559i	−0.997263	−	0.0739357i	$-0.976444\pi$
$137$	−6.58579	−	11.4069i	−0.562662	−	0.974559i	0.434601	−	0.900623i	$-0.356889\pi$
$138$	−9.24264	+	16.0087i	−0.786786	+	1.36275i
$139$	1.51472			0.128477			0.0642384	−	0.997935i	$-0.479538\pi$
$139$	1.51472			0.128477			0.0642384	+	0.997935i	$0.479538\pi$
$140$		0			0
$141$	5.65685			0.476393
$142$	3.41421	−	5.91359i	0.286514	−	0.496258i
$143$	−6.82843	−	11.8272i	−0.571022	−	0.989039i
$144$	−1.50000	−	2.59808i	−0.125000	−	0.216506i
$145$	3.00000	−	5.19615i	0.249136	−	0.431517i
$146$	26.9706			2.23210
$147$		0			0
$148$	−14.0000			−1.15079
$149$	3.82843	−	6.63103i	0.313637	−	0.543235i	−0.665510	−	0.746389i	$-0.731786\pi$
$149$	3.82843	−	6.63103i	0.313637	−	0.543235i	0.979147	+	0.203154i	$0.0651192\pi$
$150$	1.20711	+	2.09077i	0.0985599	+	0.170711i
$151$	8.48528	+	14.6969i	0.690522	+	1.19602i	0.971667	+	0.236354i	$0.0759526\pi$
$151$	8.48528	+	14.6969i	0.690522	+	1.19602i	−0.281145	+	0.959665i	$0.590714\pi$
$152$	−1.82843	+	3.16693i	−0.148305	+	0.256872i
$153$	7.65685			0.619020
$154$		0			0
$155$	6.48528			0.520910
$156$	9.24264	−	16.0087i	0.740003	−	1.28172i
$157$	6.07107	+	10.5154i	0.484524	+	0.839220i	0.999842	−	0.0177789i	$-0.00565951\pi$
$157$	6.07107	+	10.5154i	0.484524	+	0.839220i	−0.515318	+	0.856999i	$0.672326\pi$
$158$	9.65685	+	16.7262i	0.768258	+	1.33066i
$159$	−4.24264	+	7.34847i	−0.336463	+	0.582772i
$160$	1.58579			0.125367
$161$		0			0
$162$	2.41421			0.189679
$163$	6.00000	−	10.3923i	0.469956	−	0.813988i	−0.529454	−	0.848339i	$-0.677603\pi$
$163$	6.00000	−	10.3923i	0.469956	−	0.813988i	0.999410	+	0.0343508i	$0.0109363\pi$
$164$	22.3137	+	38.6485i	1.74241	+	3.01794i
$165$	−1.41421	−	2.44949i	−0.110096	−	0.190693i
$166$	−2.00000	+	3.46410i	−0.155230	+	0.268866i
$167$	−11.3137			−0.875481			−0.437741	−	0.899101i	$-0.644221\pi$
$167$	−11.3137			−0.875481			−0.437741	+	0.899101i	$0.644221\pi$
$168$		0			0
$169$	10.3137			0.793362
$170$	9.24264	−	16.0087i	0.708878	−	1.22781i
$171$	−0.414214	−	0.717439i	−0.0316757	−	0.0548639i
$172$	−15.3137	−	26.5241i	−1.16766	−	2.02245i
$173$	12.3137	−	21.3280i	0.936194	−	1.62154i	0.163703	−	0.986510i	$-0.447656\pi$
$173$	12.3137	−	21.3280i	0.936194	−	1.62154i	0.772491	−	0.635026i	$-0.219011\pi$
$174$	−14.4853			−1.09813
$175$		0			0
$176$	8.48528			0.639602
$177$	−1.17157	+	2.02922i	−0.0880608	+	0.152526i
$178$	−6.41421	−	11.1097i	−0.480766	−	0.832711i
$179$	0.585786	+	1.01461i	0.0437837	+	0.0758357i	0.887087	−	0.461603i	$-0.152725\pi$
$179$	0.585786	+	1.01461i	0.0437837	+	0.0758357i	−0.843303	+	0.537438i	$0.819392\pi$
$180$	1.91421	−	3.31552i	0.142677	−	0.247124i
$181$	−2.34315			−0.174165			−0.0870823	−	0.996201i	$-0.527754\pi$
$181$	−2.34315			−0.174165			−0.0870823	+	0.996201i	$0.527754\pi$
$182$		0			0
$183$		0			0
$184$	16.8995	−	29.2708i	1.24585	−	2.15787i
$185$	−1.82843	−	3.16693i	−0.134429	−	0.232837i
$186$	−7.82843	−	13.5592i	−0.574008	−	0.994211i
$187$	−10.8284	+	18.7554i	−0.791853	+	1.37153i
$188$	−21.6569			−1.57949
$189$		0			0
$190$	−2.00000			−0.145095
$191$	4.58579	−	7.94282i	0.331816	−	0.574722i	−0.651052	−	0.759033i	$-0.725672\pi$
$191$	4.58579	−	7.94282i	0.331816	−	0.574722i	0.982868	+	0.184311i	$0.0590054\pi$
$192$	−4.91421	−	8.51167i	−0.354653	−	0.614277i
$193$	−7.82843	−	13.5592i	−0.563503	−	0.976015i	−0.997187	−	0.0749503i	$-0.976120\pi$
$193$	−7.82843	−	13.5592i	−0.563503	−	0.976015i	0.433685	−	0.901065i	$-0.357213\pi$
$194$	7.82843	−	13.5592i	0.562048	−	0.973496i
$195$	4.82843			0.345771
$196$		0			0
$197$	−3.51472			−0.250413			−0.125207	−	0.992131i	$-0.539959\pi$
$197$	−3.51472			−0.250413			−0.125207	+	0.992131i	$0.539959\pi$
$198$	−3.41421	+	5.91359i	−0.242638	+	0.420261i
$199$	−0.414214	−	0.717439i	−0.0293628	−	0.0508579i	0.850971	−	0.525213i	$-0.176014\pi$
$199$	−0.414214	−	0.717439i	−0.0293628	−	0.0508579i	−0.880333	+	0.474355i	$0.842681\pi$
$200$	−2.20711	−	3.82282i	−0.156066	−	0.270314i
$201$		0			0
$202$	−18.4853			−1.30062
$203$		0			0
$204$	−29.3137			−2.05237
$205$	−5.82843	+	10.0951i	−0.407075	+	0.705075i
$206$	−14.4853	−	25.0892i	−1.00924	−	1.74805i
$207$	3.82843	+	6.63103i	0.266094	+	0.460888i
$208$	−7.24264	+	12.5446i	−0.502187	+	0.869813i
$209$	2.34315			0.162079
$210$		0			0
$211$	−9.65685			−0.664805			−0.332403	−	0.943138i	$-0.607859\pi$
$211$	−9.65685			−0.664805			−0.332403	+	0.943138i	$0.607859\pi$
$212$	16.2426	−	28.1331i	1.11555	−	1.93219i
$213$	−1.41421	−	2.44949i	−0.0969003	−	0.167836i
$214$	−6.41421	−	11.1097i	−0.438467	−	0.759446i
$215$	4.00000	−	6.92820i	0.272798	−	0.472500i
$216$	−4.41421			−0.300349
$217$		0			0
$218$	14.4853			0.981067
$219$	5.58579	−	9.67487i	0.377452	−	0.653767i
$220$	5.41421	+	9.37769i	0.365026	+	0.632244i
$221$	−18.4853	−	32.0174i	−1.24345	−	2.15373i
$222$	−4.41421	+	7.64564i	−0.296263	+	0.513142i
$223$	20.9706			1.40429			0.702146	−	0.712033i	$-0.252225\pi$
$223$	20.9706			1.40429			0.702146	+	0.712033i	$0.252225\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$	−3.41421	+	5.91359i	−0.227110	+	0.393366i
$227$	14.4853	+	25.0892i	0.961422	+	1.66523i	0.718936	+	0.695077i	$0.244630\pi$
$227$	14.4853	+	25.0892i	0.961422	+	1.66523i	0.242486	+	0.970155i	$0.422037\pi$
$228$	1.58579	+	2.74666i	0.105021	+	0.181902i
$229$	−7.65685	+	13.2621i	−0.505979	+	0.876382i	0.493997	+	0.869464i	$0.335535\pi$
$229$	−7.65685	+	13.2621i	−0.505979	+	0.876382i	−0.999976	+	0.00691797i	$0.997798\pi$
$230$	18.4853			1.21888
$231$		0			0
$232$	26.4853			1.73884
$233$	−7.41421	+	12.8418i	−0.485721	+	0.841294i	−0.999865	−	0.0164099i	$-0.994776\pi$
$233$	−7.41421	+	12.8418i	−0.485721	+	0.841294i	0.514144	+	0.857704i	$0.328110\pi$
$234$	−5.82843	−	10.0951i	−0.381016	−	0.659939i
$235$	−2.82843	−	4.89898i	−0.184506	−	0.319574i
$236$	4.48528	−	7.76874i	0.291967	−	0.505702i
$237$	8.00000			0.519656
$238$		0			0
$239$	−2.14214			−0.138563			−0.0692816	−	0.997597i	$-0.522071\pi$
$239$	−2.14214			−0.138563			−0.0692816	+	0.997597i	$0.522071\pi$
$240$	−1.50000	+	2.59808i	−0.0968246	+	0.167705i
$241$	−10.8284	−	18.7554i	−0.697520	−	1.20814i	−0.969324	−	0.245788i	$-0.920953\pi$
$241$	−10.8284	−	18.7554i	−0.697520	−	1.20814i	0.271803	−	0.962353i	$-0.412380\pi$
$242$	3.62132	+	6.27231i	0.232787	+	0.403199i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$		0			0
$245$		0			0
$246$	28.1421			1.79428
$247$	−2.00000	+	3.46410i	−0.127257	+	0.220416i
$248$	14.3137	+	24.7921i	0.908921	+	1.57430i
$249$	0.828427	+	1.43488i	0.0524994	+	0.0909317i
$250$	1.20711	−	2.09077i	0.0763441	−	0.132232i
$251$	−29.6569			−1.87192			−0.935962	−	0.352101i	$-0.885467\pi$
$251$	−29.6569			−1.87192			−0.935962	+	0.352101i	$0.885467\pi$
$252$		0			0
$253$	−21.6569			−1.36155
$254$	−23.3137	+	40.3805i	−1.46283	+	2.53370i
$255$	−3.82843	−	6.63103i	−0.239745	−	0.415251i
$256$	14.9853	+	25.9553i	0.936580	+	1.62220i
$257$	−0.171573	+	0.297173i	−0.0107024	+	0.0185371i	−0.871327	−	0.490703i	$-0.836740\pi$
$257$	−0.171573	+	0.297173i	−0.0107024	+	0.0185371i	0.860625	+	0.509240i	$0.170073\pi$
$258$	−19.3137			−1.20242
$259$		0			0
$260$	−18.4853			−1.14641
$261$	−3.00000	+	5.19615i	−0.185695	+	0.321634i
$262$	6.82843	+	11.8272i	0.421862	+	0.730686i
$263$	1.34315	+	2.32640i	0.0828219	+	0.143452i	0.904461	−	0.426556i	$-0.140273\pi$
$263$	1.34315	+	2.32640i	0.0828219	+	0.143452i	−0.821639	+	0.570008i	$0.806940\pi$
$264$	6.24264	−	10.8126i	0.384208	−	0.665468i
$265$	8.48528			0.521247
$266$		0			0
$267$	−5.31371			−0.325194
$268$		0			0
$269$	0.171573	+	0.297173i	0.0104610	+	0.0181190i	0.871209	−	0.490913i	$-0.163337\pi$
$269$	0.171573	+	0.297173i	0.0104610	+	0.0181190i	−0.860748	+	0.509032i	$0.830003\pi$
$270$	−1.20711	−	2.09077i	−0.0734622	−	0.127240i
$271$	−11.2426	+	19.4728i	−0.682942	+	1.18289i	0.291137	+	0.956681i	$0.405966\pi$
$271$	−11.2426	+	19.4728i	−0.682942	+	1.18289i	−0.974079	+	0.226209i	$0.927367\pi$
$272$	22.9706			1.39279
$273$		0			0
$274$	31.7990			1.92105
$275$	−1.41421	+	2.44949i	−0.0852803	+	0.147710i
$276$	−14.6569	−	25.3864i	−0.882239	−	1.52808i
$277$	−10.6569	−	18.4582i	−0.640308	−	1.10905i	−0.985364	−	0.170464i	$-0.945473\pi$
$277$	−10.6569	−	18.4582i	−0.640308	−	1.10905i	0.345056	−	0.938582i	$-0.387860\pi$
$278$	−1.82843	+	3.16693i	−0.109662	+	0.189940i
$279$	−6.48528			−0.388264
$280$		0			0
$281$	12.3431			0.736330			0.368165	−	0.929760i	$-0.379986\pi$
$281$	12.3431			0.736330			0.368165	+	0.929760i	$0.379986\pi$
$282$	−6.82843	+	11.8272i	−0.406627	+	0.704298i
$283$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$283$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$284$	5.41421	+	9.37769i	0.321274	+	0.556464i
$285$	−0.414214	+	0.717439i	−0.0245359	+	0.0424974i
$286$	32.9706			1.94959
$287$		0			0
$288$	−1.58579			−0.0934434
$289$	−20.8137	+	36.0504i	−1.22434	+	2.12061i
$290$	7.24264	+	12.5446i	0.425303	+	0.736646i
$291$	−3.24264	−	5.61642i	−0.190087	−	0.329240i
$292$	−21.3848	+	37.0395i	−1.25145	+	2.16757i
$293$	12.3431			0.721094			0.360547	−	0.932741i	$-0.382590\pi$
$293$	12.3431			0.721094			0.360547	+	0.932741i	$0.382590\pi$
$294$		0			0
$295$	2.34315			0.136423
$296$	8.07107	−	13.9795i	0.469121	−	0.812542i
$297$	1.41421	+	2.44949i	0.0820610	+	0.142134i
$298$	9.24264	+	16.0087i	0.535412	+	0.927360i
$299$	18.4853	−	32.0174i	1.06903	−	1.85162i
$300$	−3.82843			−0.221034
$301$		0			0
$302$	−40.9706			−2.35759
$303$	−3.82843	+	6.63103i	−0.219937	+	0.380943i
$304$	−1.24264	−	2.15232i	−0.0712703	−	0.123444i
$305$		0			0
$306$	−9.24264	+	16.0087i	−0.528367	+	0.915158i
$307$	28.9706			1.65344			0.826719	−	0.562616i	$-0.190205\pi$
$307$	28.9706			1.65344			0.826719	+	0.562616i	$0.190205\pi$
$308$		0			0
$309$	−12.0000			−0.682656
$310$	−7.82843	+	13.5592i	−0.444625	+	0.770113i
$311$	4.82843	+	8.36308i	0.273795	+	0.474227i	0.969830	−	0.243781i	$-0.0783877\pi$
$311$	4.82843	+	8.36308i	0.273795	+	0.474227i	−0.696035	+	0.718007i	$0.745054\pi$
$312$	10.6569	+	18.4582i	0.603326	+	1.04499i
$313$	1.24264	−	2.15232i	0.0702382	−	0.121656i	−0.828767	−	0.559593i	$-0.810957\pi$
$313$	1.24264	−	2.15232i	0.0702382	−	0.121656i	0.899006	+	0.437937i	$0.144291\pi$
$314$	−29.3137			−1.65427
$315$		0			0
$316$	−30.6274			−1.72293
$317$	−11.0711	+	19.1757i	−0.621813	+	1.07701i	0.367335	+	0.930089i	$0.380270\pi$
$317$	−11.0711	+	19.1757i	−0.621813	+	1.07701i	−0.989148	+	0.146923i	$0.953063\pi$
$318$	−10.2426	−	17.7408i	−0.574379	−	0.994853i
$319$	−8.48528	−	14.6969i	−0.475085	−	0.822871i
$320$	−4.91421	+	8.51167i	−0.274713	+	0.475817i
$321$	−5.31371			−0.296582
$322$		0			0
$323$	6.34315			0.352942
$324$	−1.91421	+	3.31552i	−0.106345	+	0.184195i
$325$	−2.41421	−	4.18154i	−0.133916	−	0.231950i
$326$	14.4853	+	25.0892i	0.802266	+	1.38956i
$327$	3.00000	−	5.19615i	0.165900	−	0.287348i
$328$	−51.4558			−2.84117
$329$		0			0
$330$	6.82843			0.375893
$331$	−0.828427	+	1.43488i	−0.0455345	+	0.0788680i	−0.887894	−	0.460047i	$-0.847832\pi$
$331$	−0.828427	+	1.43488i	−0.0455345	+	0.0788680i	0.842360	+	0.538915i	$0.181166\pi$
$332$	−3.17157	−	5.49333i	−0.174063	−	0.301485i
$333$	1.82843	+	3.16693i	0.100197	+	0.173547i
$334$	13.6569	−	23.6544i	0.747270	−	1.29431i
$335$		0			0
$336$		0			0
$337$	−6.97056			−0.379711			−0.189855	−	0.981812i	$-0.560802\pi$
$337$	−6.97056			−0.379711			−0.189855	+	0.981812i	$0.560802\pi$
$338$	−12.4497	+	21.5636i	−0.677177	+	1.17290i
$339$	1.41421	+	2.44949i	0.0768095	+	0.133038i
$340$	14.6569	+	25.3864i	0.794880	+	1.37677i
$341$	9.17157	−	15.8856i	0.496669	−	0.860255i
$342$	2.00000			0.108148
$343$		0			0
$344$	35.3137			1.90399
$345$	3.82843	−	6.63103i	0.206116	−	0.357003i
$346$	29.7279	+	51.4903i	1.59818	+	2.76813i
$347$	11.4853	+	19.8931i	0.616562	+	1.06792i	0.990108	+	0.140305i	$0.0448085\pi$
$347$	11.4853	+	19.8931i	0.616562	+	1.06792i	−0.373546	+	0.927612i	$0.621858\pi$
$348$	11.4853	−	19.8931i	0.615676	−	1.06638i
$349$	−16.0000			−0.856460			−0.428230	−	0.903670i	$-0.640863\pi$
$349$	−16.0000			−0.856460			−0.428230	+	0.903670i	$0.640863\pi$
$350$		0			0
$351$	−4.82843			−0.257722
$352$	2.24264	−	3.88437i	0.119533	−	0.207037i
$353$	−12.6569	−	21.9223i	−0.673656	−	1.16681i	−0.976860	−	0.213881i	$-0.931389\pi$
$353$	−12.6569	−	21.9223i	−0.673656	−	1.16681i	0.303203	−	0.952926i	$-0.401944\pi$
$354$	−2.82843	−	4.89898i	−0.150329	−	0.260378i
$355$	−1.41421	+	2.44949i	−0.0750587	+	0.130005i
$356$	20.3431			1.07818
$357$		0			0
$358$	−2.82843			−0.149487
$359$	7.89949	−	13.6823i	0.416919	−	0.722126i	−0.578708	−	0.815535i	$-0.696443\pi$
$359$	7.89949	−	13.6823i	0.416919	−	0.722126i	0.995628	+	0.0934089i	$0.0297764\pi$
$360$	2.20711	+	3.82282i	0.116325	+	0.201480i
$361$	9.15685	+	15.8601i	0.481940	+	0.834744i
$362$	2.82843	−	4.89898i	0.148659	−	0.257485i
$363$	3.00000			0.157459
$364$		0			0
$365$	−11.1716			−0.584747
$366$		0			0
$367$	−6.48528	−	11.2328i	−0.338529	−	0.586349i	0.645627	−	0.763653i	$-0.276596\pi$
$367$	−6.48528	−	11.2328i	−0.338529	−	0.586349i	−0.984156	+	0.177303i	$0.943263\pi$
$368$	11.4853	+	19.8931i	0.598712	+	1.03700i
$369$	5.82843	−	10.0951i	0.303416	−	0.525532i
$370$	8.82843			0.458968
$371$		0			0
$372$	24.8284			1.28729
$373$	12.3137	−	21.3280i	0.637580	−	1.10432i	−0.348383	−	0.937352i	$-0.613269\pi$
$373$	12.3137	−	21.3280i	0.637580	−	1.10432i	0.985962	−	0.166968i	$-0.0533976\pi$
$374$	−26.1421	−	45.2795i	−1.35178	−	2.34135i
$375$	−0.500000	−	0.866025i	−0.0258199	−	0.0447214i
$376$	12.4853	−	21.6251i	0.643879	−	1.11523i
$377$	28.9706			1.49206
$378$		0			0
$379$	−20.9706			−1.07719			−0.538593	−	0.842566i	$-0.681044\pi$
$379$	−20.9706			−1.07719			−0.538593	+	0.842566i	$0.681044\pi$
$380$	1.58579	−	2.74666i	0.0813491	−	0.140901i
$381$	9.65685	+	16.7262i	0.494736	+	0.856907i
$382$	11.0711	+	19.1757i	0.566445	+	0.981112i
$383$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$383$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$384$	20.5563			1.04901
$385$		0			0
$386$	37.7990			1.92392
$387$	−4.00000	+	6.92820i	−0.203331	+	0.352180i
$388$	12.4142	+	21.5020i	0.630236	+	1.09160i
$389$	5.82843	+	10.0951i	0.295513	+	0.511844i	0.975104	−	0.221748i	$-0.0711761\pi$
$389$	5.82843	+	10.0951i	0.295513	+	0.511844i	−0.679591	+	0.733591i	$0.737843\pi$
$390$	−5.82843	+	10.0951i	−0.295134	+	0.511187i
$391$	−58.6274			−2.96492
$392$		0			0
$393$	5.65685			0.285351
$394$	4.24264	−	7.34847i	0.213741	−	0.370211i
$395$	−4.00000	−	6.92820i	−0.201262	−	0.348596i
$396$	−5.41421	−	9.37769i	−0.272074	−	0.471247i
$397$	−12.4142	+	21.5020i	−0.623052	+	1.07916i	0.365863	+	0.930669i	$0.380774\pi$
$397$	−12.4142	+	21.5020i	−0.623052	+	1.07916i	−0.988914	+	0.148488i	$0.952559\pi$
$398$	2.00000			0.100251
$399$		0			0
$400$	3.00000			0.150000
$401$	−15.0000	+	25.9808i	−0.749064	+	1.29742i	0.199207	+	0.979957i	$0.436163\pi$
$401$	−15.0000	+	25.9808i	−0.749064	+	1.29742i	−0.948272	+	0.317460i	$0.897170\pi$
$402$		0			0
$403$	15.6569	+	27.1185i	0.779923	+	1.35087i
$404$	14.6569	−	25.3864i	0.729206	−	1.26302i
$405$	−1.00000			−0.0496904
$406$		0			0
$407$	−10.3431			−0.512691
$408$	16.8995	−	29.2708i	0.836650	−	1.44912i
$409$	6.00000	+	10.3923i	0.296681	+	0.513866i	0.975375	−	0.220555i	$-0.0707869\pi$
$409$	6.00000	+	10.3923i	0.296681	+	0.513866i	−0.678694	+	0.734422i	$0.737454\pi$
$410$	−14.0711	−	24.3718i	−0.694921	−	1.20364i
$411$	6.58579	−	11.4069i	0.324853	−	0.562662i
$412$	45.9411			2.26336
$413$		0			0
$414$	−18.4853			−0.908502
$415$	0.828427	−	1.43488i	0.0406659	−	0.0704354i
$416$	3.82843	+	6.63103i	0.187704	+	0.325113i
$417$	0.757359	+	1.31178i	0.0370880	+	0.0642384i
$418$	−2.82843	+	4.89898i	−0.138343	+	0.239617i
$419$	0.686292			0.0335275			0.0167638	−	0.999859i	$-0.494664\pi$
$419$	0.686292			0.0335275			0.0167638	+	0.999859i	$0.494664\pi$
$420$		0			0
$421$	−6.00000			−0.292422			−0.146211	−	0.989253i	$-0.546708\pi$
$421$	−6.00000			−0.292422			−0.146211	+	0.989253i	$0.546708\pi$
$422$	11.6569	−	20.1903i	0.567447	−	0.982847i
$423$	2.82843	+	4.89898i	0.137523	+	0.238197i
$424$	18.7279	+	32.4377i	0.909508	+	1.57531i
$425$	−3.82843	+	6.63103i	−0.185706	+	0.321652i
$426$	6.82843			0.330838
$427$		0			0
$428$	20.3431			0.983323
$429$	6.82843	−	11.8272i	0.329680	−	0.571022i
$430$	9.65685	+	16.7262i	0.465695	+	0.806607i
$431$	5.41421	+	9.37769i	0.260793	+	0.451708i	0.966453	−	0.256844i	$-0.0826825\pi$
$431$	5.41421	+	9.37769i	0.260793	+	0.451708i	−0.705660	+	0.708551i	$0.749349\pi$
$432$	1.50000	−	2.59808i	0.0721688	−	0.125000i
$433$	−7.17157			−0.344644			−0.172322	−	0.985041i	$-0.555127\pi$
$433$	−7.17157			−0.344644			−0.172322	+	0.985041i	$0.555127\pi$
$434$		0			0
$435$	6.00000			0.287678
$436$	−11.4853	+	19.8931i	−0.550045	+	0.952706i
$437$	3.17157	+	5.49333i	0.151717	+	0.262781i
$438$	13.4853	+	23.3572i	0.644352	+	1.11605i
$439$	−6.75736	+	11.7041i	−0.322511	+	0.558606i	−0.981005	−	0.193980i	$-0.937860\pi$
$439$	−6.75736	+	11.7041i	−0.322511	+	0.558606i	0.658494	+	0.752586i	$0.271194\pi$
$440$	−12.4853			−0.595212
$441$		0			0
$442$	89.2548			4.24542
$443$	−11.8284	+	20.4874i	−0.561986	+	0.973387i	0.435338	+	0.900267i	$0.356629\pi$
$443$	−11.8284	+	20.4874i	−0.561986	+	0.973387i	−0.997323	+	0.0731202i	$0.976704\pi$
$444$	−7.00000	−	12.1244i	−0.332205	−	0.575396i
$445$	2.65685	+	4.60181i	0.125947	+	0.218147i
$446$	−25.3137	+	43.8446i	−1.19864	+	2.07610i
$447$	7.65685			0.362157
$448$		0			0
$449$	−12.6274			−0.595925			−0.297962	−	0.954578i	$-0.596307\pi$
$449$	−12.6274			−0.595925			−0.297962	+	0.954578i	$0.596307\pi$
$450$	−1.20711	+	2.09077i	−0.0569036	+	0.0985599i
$451$	16.4853	+	28.5533i	0.776262	+	1.34452i
$452$	−5.41421	−	9.37769i	−0.254663	−	0.441090i
$453$	−8.48528	+	14.6969i	−0.398673	+	0.690522i
$454$	−69.9411			−3.28250
$455$		0			0
$456$	−3.65685			−0.171248
$457$	−8.17157	+	14.1536i	−0.382250	+	0.662077i	−0.991384	−	0.130991i	$-0.958184\pi$
$457$	−8.17157	+	14.1536i	−0.382250	+	0.662077i	0.609133	+	0.793068i	$0.291517\pi$
$458$	−18.4853	−	32.0174i	−0.863760	−	1.49608i
$459$	3.82843	+	6.63103i	0.178696	+	0.309510i
$460$	−14.6569	+	25.3864i	−0.683379	+	1.18365i
$461$	−13.3137			−0.620081			−0.310041	−	0.950723i	$-0.600343\pi$
$461$	−13.3137			−0.620081			−0.310041	+	0.950723i	$0.600343\pi$
$462$		0			0
$463$	38.6274			1.79517			0.897584	−	0.440843i	$-0.145321\pi$
$463$	38.6274			1.79517			0.897584	+	0.440843i	$0.145321\pi$
$464$	−9.00000	+	15.5885i	−0.417815	+	0.723676i
$465$	3.24264	+	5.61642i	0.150374	+	0.260455i
$466$	−17.8995	−	31.0028i	−0.829178	−	1.43618i
$467$	−12.1421	+	21.0308i	−0.561871	+	0.973189i	0.435462	+	0.900207i	$0.356585\pi$
$467$	−12.1421	+	21.0308i	−0.561871	+	0.973189i	−0.997333	+	0.0729822i	$0.976748\pi$
$468$	18.4853			0.854482
$469$		0			0
$470$	13.6569			0.629944
$471$	−6.07107	+	10.5154i	−0.279740	+	0.484524i
$472$	5.17157	+	8.95743i	0.238041	+	0.412299i
$473$	−11.3137	−	19.5959i	−0.520205	−	0.901021i
$474$	−9.65685	+	16.7262i	−0.443554	+	0.768258i
$475$	0.828427			0.0380108
$476$		0			0
$477$	−8.48528			−0.388514
$478$	2.58579	−	4.47871i	0.118271	−	0.204852i
$479$	−7.17157	−	12.4215i	−0.327678	−	0.567554i	0.654373	−	0.756172i	$-0.272933\pi$
$479$	−7.17157	−	12.4215i	−0.327678	−	0.567554i	−0.982051	+	0.188618i	$0.939599\pi$
$480$	0.792893	+	1.37333i	0.0361905	+	0.0626837i
$481$	8.82843	−	15.2913i	0.402542	−	0.697223i
$482$	52.2843			2.38148
$483$		0			0
$484$	−11.4853			−0.522058
$485$	−3.24264	+	5.61642i	−0.147241	+	0.255028i
$486$	1.20711	+	2.09077i	0.0547555	+	0.0948393i
$487$	−14.9706	−	25.9298i	−0.678381	−	1.17499i	−0.975468	−	0.220140i	$-0.929349\pi$
$487$	−14.9706	−	25.9298i	−0.678381	−	1.17499i	0.297087	−	0.954850i	$-0.403985\pi$
$488$		0			0
$489$	12.0000			0.542659
$490$		0			0
$491$	18.1421			0.818743			0.409372	−	0.912368i	$-0.365748\pi$
$491$	18.1421			0.818743			0.409372	+	0.912368i	$0.365748\pi$
$492$	−22.3137	+	38.6485i	−1.00598	+	1.74241i
$493$	−22.9706	−	39.7862i	−1.03454	−	1.79188i
$494$	−4.82843	−	8.36308i	−0.217241	−	0.376273i
$495$	1.41421	−	2.44949i	0.0635642	−	0.110096i
$496$	−19.4558			−0.873593
$497$		0			0
$498$	−4.00000			−0.179244
$499$	−2.48528	+	4.30463i	−0.111256	+	0.192702i	−0.916277	−	0.400545i	$-0.868821\pi$
$499$	−2.48528	+	4.30463i	−0.111256	+	0.192702i	0.805021	+	0.593247i	$0.202154\pi$
$500$	1.91421	+	3.31552i	0.0856062	+	0.148274i
$501$	−5.65685	−	9.79796i	−0.252730	−	0.437741i
$502$	35.7990	−	62.0057i	1.59779	−	2.76745i
$503$	−4.68629			−0.208951			−0.104476	−	0.994527i	$-0.533316\pi$
$503$	−4.68629			−0.208951			−0.104476	+	0.994527i	$0.533316\pi$
$504$		0			0
$505$	7.65685			0.340726
$506$	26.1421	−	45.2795i	1.16216	−	2.01292i
$507$	5.15685	+	8.93193i	0.229024	+	0.396681i
$508$	−36.9706	−	64.0349i	−1.64030	−	2.84109i
$509$	−14.1716	+	24.5459i	−0.628144	+	1.08798i	0.359780	+	0.933037i	$0.382852\pi$
$509$	−14.1716	+	24.5459i	−0.628144	+	1.08798i	−0.987924	+	0.154940i	$0.950482\pi$
$510$	18.4853			0.818542
$511$		0			0
$512$	−31.2426			−1.38074
$513$	0.414214	−	0.717439i	0.0182880	−	0.0316757i
$514$	−0.414214	−	0.717439i	−0.0182702	−	0.0316449i
$515$	6.00000	+	10.3923i	0.264392	+	0.457940i
$516$	15.3137	−	26.5241i	0.674148	−	1.16766i
$517$	−16.0000			−0.703679
$518$		0			0
$519$	24.6274			1.08102
$520$	10.6569	−	18.4582i	0.467334	−	0.809446i
$521$	11.1421	+	19.2987i	0.488146	+	0.845493i	0.999907	−	0.0136344i	$-0.00434009\pi$
$521$	11.1421	+	19.2987i	0.488146	+	0.845493i	−0.511761	+	0.859128i	$0.671007\pi$
$522$	−7.24264	−	12.5446i	−0.317002	−	0.549063i
$523$	18.1421	−	31.4231i	0.793300	−	1.37404i	−0.130613	−	0.991433i	$-0.541694\pi$
$523$	18.1421	−	31.4231i	0.793300	−	1.37404i	0.923913	−	0.382603i	$-0.124972\pi$
$524$	−21.6569			−0.946084
$525$		0			0
$526$	−6.48528			−0.282772
$527$	24.8284	−	43.0041i	1.08154	−	1.87329i
$528$	4.24264	+	7.34847i	0.184637	+	0.319801i
$529$	−17.8137	−	30.8542i	−0.774509	−	1.34149i
$530$	−10.2426	+	17.7408i	−0.444912	+	0.770610i
$531$	−2.34315			−0.101684
$532$		0			0
$533$	−56.2843			−2.43794
$534$	6.41421	−	11.1097i	0.277570	−	0.480766i
$535$	2.65685	+	4.60181i	0.114866	+	0.198953i
$536$		0			0
$537$	−0.585786	+	1.01461i	−0.0252786	+	0.0437837i
$538$	−0.828427			−0.0357160
$539$		0			0
$540$	3.82843			0.164749
$541$	−9.00000	+	15.5885i	−0.386940	+	0.670200i	−0.992036	−	0.125952i	$-0.959801\pi$
$541$	−9.00000	+	15.5885i	−0.386940	+	0.670200i	0.605096	+	0.796152i	$0.293135\pi$
$542$	−27.1421	−	47.0116i	−1.16585	−	2.01932i
$543$	−1.17157	−	2.02922i	−0.0502770	−	0.0870823i
$544$	6.07107	−	10.5154i	0.260295	−	0.450844i
$545$	−6.00000			−0.257012
$546$		0			0
$547$	−27.3137			−1.16785			−0.583925	−	0.811808i	$-0.698484\pi$
$547$	−27.3137			−1.16785			−0.583925	+	0.811808i	$0.698484\pi$
$548$	−25.2132	+	43.6705i	−1.07705	+	1.86551i
$549$		0			0
$550$	−3.41421	−	5.91359i	−0.145583	−	0.252156i
$551$	−2.48528	+	4.30463i	−0.105877	+	0.183384i
$552$	33.7990			1.43858
$553$		0			0
$554$	51.4558			2.18615
$555$	1.82843	−	3.16693i	0.0776124	−	0.134429i
$556$	−2.89949	−	5.02207i	−0.122966	−	0.212983i
$557$	−13.4142	−	23.2341i	−0.568378	−	0.984460i	−0.996727	−	0.0808466i	$-0.974238\pi$
$557$	−13.4142	−	23.2341i	−0.568378	−	0.984460i	0.428348	−	0.903614i	$-0.359096\pi$
$558$	7.82843	−	13.5592i	0.331404	−	0.574008i
$559$	38.6274			1.63377
$560$		0			0
$561$	−21.6569			−0.914353
$562$	−14.8995	+	25.8067i	−0.628497	+	1.08859i
$563$	4.34315	+	7.52255i	0.183042	+	0.317038i	0.942915	−	0.333034i	$-0.108072\pi$
$563$	4.34315	+	7.52255i	0.183042	+	0.317038i	−0.759873	+	0.650071i	$0.774739\pi$
$564$	−10.8284	−	18.7554i	−0.455959	−	0.789744i
$565$	1.41421	−	2.44949i	0.0594964	−	0.103051i
$566$		0			0
$567$		0			0
$568$	−12.4853			−0.523871
$569$	−5.34315	+	9.25460i	−0.223996	+	0.387973i	−0.956018	−	0.293308i	$-0.905244\pi$
$569$	−5.34315	+	9.25460i	−0.223996	+	0.387973i	0.732022	+	0.681282i	$0.238577\pi$
$570$	−1.00000	−	1.73205i	−0.0418854	−	0.0725476i
$571$	8.34315	+	14.4508i	0.349150	+	0.604745i	0.986099	−	0.166161i	$-0.0531371\pi$
$571$	8.34315	+	14.4508i	0.349150	+	0.604745i	−0.636949	+	0.770906i	$0.719804\pi$
$572$	−26.1421	+	45.2795i	−1.09306	+	1.89323i
$573$	9.17157			0.383148
$574$		0			0
$575$	−7.65685			−0.319313
$576$	4.91421	−	8.51167i	0.204759	−	0.354653i
$577$	9.24264	+	16.0087i	0.384776	+	0.666452i	0.991738	−	0.128279i	$-0.0409453\pi$
$577$	9.24264	+	16.0087i	0.384776	+	0.666452i	−0.606962	+	0.794731i	$0.707612\pi$
$578$	−50.2487	−	87.0334i	−2.09007	−	3.62011i
$579$	7.82843	−	13.5592i	0.325338	−	0.563503i
$580$	−22.9706			−0.953801
$581$		0			0
$582$	15.6569			0.648997
$583$	12.0000	−	20.7846i	0.496989	−	0.860811i
$584$	−24.6569	−	42.7069i	−1.02031	−	1.76723i
$585$	2.41421	+	4.18154i	0.0998154	+	0.172885i
$586$	−14.8995	+	25.8067i	−0.615492	+	1.06606i
$587$	8.68629			0.358522			0.179261	−	0.983802i	$-0.442629\pi$
$587$	8.68629			0.358522			0.179261	+	0.983802i	$0.442629\pi$
$588$		0			0
$589$	−5.37258			−0.221373
$590$	−2.82843	+	4.89898i	−0.116445	+	0.201688i
$591$	−1.75736	−	3.04384i	−0.0722881	−	0.125207i
$592$	5.48528	+	9.50079i	0.225444	+	0.390480i
$593$	−2.31371	+	4.00746i	−0.0950126	+	0.164567i	−0.909614	−	0.415455i	$-0.863622\pi$
$593$	−2.31371	+	4.00746i	−0.0950126	+	0.164567i	0.814601	+	0.580021i	$0.196956\pi$
$594$	−6.82843			−0.280174
$595$		0			0
$596$	−29.3137			−1.20074
$597$	0.414214	−	0.717439i	0.0169526	−	0.0293628i
$598$	44.6274	+	77.2970i	1.82495	+	3.16091i
$599$	22.2426	+	38.5254i	0.908810	+	1.57410i	0.815720	+	0.578447i	$0.196341\pi$
$599$	22.2426	+	38.5254i	0.908810	+	1.57410i	0.0930895	+	0.995658i	$0.470326\pi$
$600$	2.20711	−	3.82282i	0.0901048	−	0.156066i
$601$	−33.6569			−1.37289			−0.686446	−	0.727181i	$-0.740830\pi$
$601$	−33.6569			−1.37289			−0.686446	+	0.727181i	$0.740830\pi$
$602$		0			0
$603$		0			0
$604$	32.4853	−	56.2662i	1.32181	−	2.28944i
$605$	−1.50000	−	2.59808i	−0.0609837	−	0.105627i
$606$	−9.24264	−	16.0087i	−0.375457	−	0.650310i
$607$	−1.51472	+	2.62357i	−0.0614805	+	0.106487i	−0.895127	−	0.445810i	$-0.852916\pi$
$607$	−1.51472	+	2.62357i	−0.0614805	+	0.106487i	0.833647	+	0.552298i	$0.186249\pi$
$608$	−1.31371			−0.0532779
$609$		0			0
$610$		0			0
$611$	13.6569	−	23.6544i	0.552497	−	0.956953i
$612$	−14.6569	−	25.3864i	−0.592468	−	1.02619i
$613$	11.9706	+	20.7336i	0.483486	+	0.837423i	0.999820	−	0.0189643i	$-0.00603690\pi$
$613$	11.9706	+	20.7336i	0.483486	+	0.837423i	−0.516334	+	0.856387i	$0.672704\pi$
$614$	−34.9706	+	60.5708i	−1.41130	+	2.44444i
$615$	−11.6569			−0.470050
$616$		0			0
$617$	13.4558			0.541712			0.270856	−	0.962620i	$-0.412693\pi$
$617$	13.4558			0.541712			0.270856	+	0.962620i	$0.412693\pi$
$618$	14.4853	−	25.0892i	0.582683	−	1.00924i
$619$	−24.0711	−	41.6923i	−0.967498	−	1.67576i	−0.702749	−	0.711438i	$-0.748044\pi$
$619$	−24.0711	−	41.6923i	−0.967498	−	1.67576i	−0.264749	−	0.964317i	$-0.585289\pi$
$620$	−12.4142	−	21.5020i	−0.498567	−	0.863543i
$621$	−3.82843	+	6.63103i	−0.153629	+	0.266094i
$622$	−23.3137			−0.934795
$623$		0			0
$624$	−14.4853			−0.579875
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	3.00000	+	5.19615i	0.119904	+	0.207680i
$627$	1.17157	+	2.02922i	0.0467881	+	0.0810394i
$628$	23.2426	−	40.2574i	0.927482	−	1.60645i
$629$	−28.0000			−1.11643
$630$		0			0
$631$	3.31371			0.131917			0.0659583	−	0.997822i	$-0.478990\pi$
$631$	3.31371			0.131917			0.0659583	+	0.997822i	$0.478990\pi$
$632$	17.6569	−	30.5826i	0.702352	−	1.21651i
$633$	−4.82843	−	8.36308i	−0.191913	−	0.332403i
$634$	−26.7279	−	46.2941i	−1.06150	−	1.83857i
$635$	9.65685	−	16.7262i	0.383221	−	0.663758i
$636$	32.4853			1.28813
$637$		0			0
$638$	40.9706			1.62204
$639$	1.41421	−	2.44949i	0.0559454	−	0.0969003i
$640$	−10.2782	−	17.8023i	−0.406281	−	0.703699i
$641$	17.1421	+	29.6910i	0.677074	+	1.17273i	0.975858	+	0.218405i	$0.0700855\pi$
$641$	17.1421	+	29.6910i	0.677074	+	1.17273i	−0.298784	+	0.954321i	$0.596581\pi$
$642$	6.41421	−	11.1097i	0.253149	−	0.438467i
$643$	−4.97056			−0.196020			−0.0980099	−	0.995185i	$-0.531248\pi$
$643$	−4.97056			−0.196020			−0.0980099	+	0.995185i	$0.531248\pi$
$644$		0			0
$645$	8.00000			0.315000
$646$	−7.65685	+	13.2621i	−0.301255	+	0.521789i
$647$	−9.65685	−	16.7262i	−0.379650	−	0.657573i	0.611361	−	0.791352i	$-0.290622\pi$
$647$	−9.65685	−	16.7262i	−0.379650	−	0.657573i	−0.991011	+	0.133778i	$0.957289\pi$
$648$	−2.20711	−	3.82282i	−0.0867033	−	0.150175i
$649$	3.31371	−	5.73951i	0.130074	−	0.225296i
$650$	11.6569			0.457219
$651$		0			0
$652$	−45.9411			−1.79919
$653$	−9.89949	+	17.1464i	−0.387397	+	0.670992i	−0.992099	−	0.125461i	$-0.959959\pi$
$653$	−9.89949	+	17.1464i	−0.387397	+	0.670992i	0.604701	+	0.796452i	$0.293292\pi$
$654$	7.24264	+	12.5446i	0.283210	+	0.490534i
$655$	−2.82843	−	4.89898i	−0.110516	−	0.191419i
$656$	17.4853	−	30.2854i	0.682686	−	1.18245i
$657$	11.1716			0.435845
$658$		0			0
$659$	43.1127			1.67943			0.839716	−	0.543026i	$-0.182721\pi$
$659$	43.1127			1.67943			0.839716	+	0.543026i	$0.182721\pi$
$660$	−5.41421	+	9.37769i	−0.210748	+	0.365026i
$661$	−9.65685	−	16.7262i	−0.375608	−	0.650572i	0.614810	−	0.788675i	$-0.289233\pi$
$661$	−9.65685	−	16.7262i	−0.375608	−	0.650572i	−0.990418	+	0.138103i	$0.955899\pi$
$662$	−2.00000	−	3.46410i	−0.0777322	−	0.134636i
$663$	18.4853	−	32.0174i	0.717909	−	1.24345i
$664$	7.31371			0.283827
$665$		0			0
$666$	−8.82843			−0.342095
$667$	22.9706	−	39.7862i	0.889424	−	1.54053i
$668$	21.6569	+	37.5108i	0.837929	+	1.45134i
$669$	10.4853	+	18.1610i	0.405384	+	0.702146i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	22.9706			0.885450			0.442725	−	0.896657i	$-0.354012\pi$
$673$	22.9706			0.885450			0.442725	+	0.896657i	$0.354012\pi$
$674$	8.41421	−	14.5738i	0.324103	−	0.561364i
$675$	0.500000	+	0.866025i	0.0192450	+	0.0333333i
$676$	−19.7426	−	34.1953i	−0.759332	−	1.31520i
$677$	−7.82843	+	13.5592i	−0.300871	+	0.521124i	−0.976333	−	0.216271i	$-0.930611\pi$
$677$	−7.82843	+	13.5592i	−0.300871	+	0.521124i	0.675463	+	0.737394i	$0.263944\pi$
$678$	−6.82843			−0.262244
$679$		0			0
$680$	−33.7990			−1.29613
$681$	−14.4853	+	25.0892i	−0.555077	+	0.961422i
$682$	22.1421	+	38.3513i	0.847866	+	1.46855i
$683$	8.17157	+	14.1536i	0.312677	+	0.541572i	0.978941	−	0.204144i	$-0.0654411\pi$
$683$	8.17157	+	14.1536i	0.312677	+	0.541572i	−0.666264	+	0.745716i	$0.732108\pi$
$684$	−1.58579	+	2.74666i	−0.0606341	+	0.105021i
$685$	−13.1716			−0.503260
$686$		0			0
$687$	−15.3137			−0.584254
$688$	−12.0000	+	20.7846i	−0.457496	+	0.792406i
$689$	20.4853	+	35.4815i	0.780427	+	1.35174i
$690$	9.24264	+	16.0087i	0.351861	+	0.609442i
$691$	−3.24264	+	5.61642i	−0.123356	+	0.213659i	−0.921089	−	0.389352i	$-0.872699\pi$
$691$	−3.24264	+	5.61642i	−0.123356	+	0.213659i	0.797733	+	0.603011i	$0.206032\pi$
$692$	−94.2843			−3.58415
$693$		0			0
$694$	−55.4558			−2.10508
$695$	0.757359	−	1.31178i	0.0287283	−	0.0497588i
$696$	13.2426	+	22.9369i	0.501961	+	0.869422i
$697$	44.6274	+	77.2970i	1.69038	+	2.92783i
$698$	19.3137	−	33.4523i	0.731035	−	1.26619i
$699$	−14.8284			−0.560863
$700$		0			0
$701$	12.6274			0.476931			0.238465	−	0.971151i	$-0.423356\pi$
$701$	12.6274			0.476931			0.238465	+	0.971151i	$0.423356\pi$
$702$	5.82843	−	10.0951i	0.219980	−	0.381016i
$703$	1.51472	+	2.62357i	0.0571287	+	0.0989498i
$704$	13.8995	+	24.0746i	0.523857	+	0.907347i
$705$	2.82843	−	4.89898i	0.106525	−	0.184506i
$706$	61.1127			2.30001
$707$		0			0
$708$	8.97056			0.337134
$709$	−1.00000	+	1.73205i	−0.0375558	+	0.0650485i	−0.884192	−	0.467123i	$-0.845291\pi$
$709$	−1.00000	+	1.73205i	−0.0375558	+	0.0650485i	0.846637	+	0.532172i	$0.178624\pi$
$710$	−3.41421	−	5.91359i	−0.128133	−	0.221933i
$711$	4.00000	+	6.92820i	0.150012	+	0.259828i
$712$	−11.7279	+	20.3134i	−0.439522	+	0.761275i
$713$	49.6569			1.85966
$714$		0			0
$715$	−13.6569			−0.510737
$716$	2.24264	−	3.88437i	0.0838114	−	0.145166i
$717$	−1.07107	−	1.85514i	−0.0399998	−	0.0692816i
$718$	19.0711	+	33.0321i	0.711726	+	1.23275i
$719$	−4.82843	+	8.36308i	−0.180070	+	0.311890i	−0.941904	−	0.335882i	$-0.890966\pi$
$719$	−4.82843	+	8.36308i	−0.180070	+	0.311890i	0.761834	+	0.647772i	$0.224299\pi$
$720$	−3.00000			−0.111803
$721$		0			0
$722$	−44.2132			−1.64545
$723$	10.8284	−	18.7554i	0.402714	−	0.697520i
$724$	4.48528	+	7.76874i	0.166694	+	0.288723i
$725$	−3.00000	−	5.19615i	−0.111417	−	0.192980i
$726$	−3.62132	+	6.27231i	−0.134400	+	0.232787i
$727$	10.3431			0.383606			0.191803	−	0.981433i	$-0.438567\pi$
$727$	10.3431			0.383606			0.191803	+	0.981433i	$0.438567\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	13.4853	−	23.3572i	0.499113	−	0.864488i
$731$	−30.6274	−	53.0482i	−1.13280	−	1.96206i
$732$		0			0
$733$	−1.72792	+	2.99285i	−0.0638223	+	0.110543i	−0.896171	−	0.443709i	$-0.853662\pi$
$733$	−1.72792	+	2.99285i	−0.0638223	+	0.110543i	0.832349	+	0.554252i	$0.186996\pi$
$734$	31.3137			1.15581
$735$		0			0
$736$	12.1421			0.447565
$737$		0			0
$738$	14.0711	+	24.3718i	0.517963	+	0.897139i
$739$	14.9706	+	25.9298i	0.550701	+	0.953842i	0.998224	+	0.0595698i	$0.0189729\pi$
$739$	14.9706	+	25.9298i	0.550701	+	0.953842i	−0.447523	+	0.894272i	$0.647694\pi$
$740$	−7.00000	+	12.1244i	−0.257325	+	0.445700i
$741$	−4.00000			−0.146944
$742$		0			0
$743$	−29.3137			−1.07542			−0.537708	−	0.843131i	$-0.680710\pi$
$743$	−29.3137			−1.07542			−0.537708	+	0.843131i	$0.680710\pi$
$744$	−14.3137	+	24.7921i	−0.524766	+	0.908921i
$745$	−3.82843	−	6.63103i	−0.140263	−	0.242942i
$746$	29.7279	+	51.4903i	1.08842	+	1.88519i
$747$	−0.828427	+	1.43488i	−0.0303106	+	0.0524994i
$748$	82.9117			3.03155
$749$		0			0
$750$	2.41421			0.0881546
$751$	18.8284	−	32.6118i	0.687059	−	1.19002i	−0.285726	−	0.958311i	$-0.592235\pi$
$751$	18.8284	−	32.6118i	0.687059	−	1.19002i	0.972785	−	0.231710i	$-0.0744320\pi$
$752$	8.48528	+	14.6969i	0.309426	+	0.535942i
$753$	−14.8284	−	25.6836i	−0.540378	−	0.935962i
$754$	−34.9706	+	60.5708i	−1.27355	+	2.20586i
$755$	16.9706			0.617622
$756$		0			0
$757$	−4.34315			−0.157854			−0.0789272	−	0.996880i	$-0.525149\pi$
$757$	−4.34315			−0.157854			−0.0789272	+	0.996880i	$0.525149\pi$
$758$	25.3137	−	43.8446i	0.919435	−	1.59251i
$759$	−10.8284	−	18.7554i	−0.393047	−	0.680777i
$760$	1.82843	+	3.16693i	0.0663240	+	0.114877i
$761$	4.65685	−	8.06591i	0.168811	−	0.292389i	−0.769191	−	0.639019i	$-0.779341\pi$
$761$	4.65685	−	8.06591i	0.168811	−	0.292389i	0.938002	+	0.346630i	$0.112674\pi$
$762$	−46.6274			−1.68913
$763$		0			0
$764$	−35.1127			−1.27033
$765$	3.82843	−	6.63103i	0.138417	−	0.239745i
$766$		0			0
$767$	5.65685	+	9.79796i	0.204257	+	0.353784i
$768$	−14.9853	+	25.9553i	−0.540735	+	0.936580i
$769$	−3.02944			−0.109244			−0.0546222	−	0.998507i	$-0.517395\pi$
$769$	−3.02944			−0.109244			−0.0546222	+	0.998507i	$0.517395\pi$
$770$		0			0
$771$	−0.343146			−0.0123581
$772$	−29.9706	+	51.9105i	−1.07866	+	1.86830i
$773$	16.3137	+	28.2562i	0.586763	+	1.01630i	0.994653	+	0.103273i	$0.0329314\pi$
$773$	16.3137	+	28.2562i	0.586763	+	1.01630i	−0.407890	+	0.913031i	$0.633735\pi$
$774$	−9.65685	−	16.7262i	−0.347108	−	0.601209i
$775$	3.24264	−	5.61642i	0.116479	−	0.201748i
$776$	−28.6274			−1.02766
$777$		0			0
$778$	−28.1421			−1.00894
$779$	4.82843	−	8.36308i	0.172996	−	0.299638i
$780$	−9.24264	−	16.0087i	−0.330940	−	0.573204i
$781$	4.00000	+	6.92820i	0.143131	+	0.247911i
$782$	70.7696	−	122.576i	2.53071	−	4.38333i
$783$	−6.00000			−0.214423
$784$		0			0
$785$	12.1421			0.433371
$786$	−6.82843	+	11.8272i	−0.243562	+	0.421862i
$787$	6.82843	+	11.8272i	0.243407	+	0.421594i	0.961683	−	0.274165i	$-0.0884016\pi$
$787$	6.82843	+	11.8272i	0.243407	+	0.421594i	−0.718275	+	0.695759i	$0.755068\pi$
$788$	6.72792	+	11.6531i	0.239672	+	0.415125i
$789$	−1.34315	+	2.32640i	−0.0478173	+	0.0828219i
$790$	19.3137			0.687151
$791$		0			0
$792$	12.4853			0.443645
$793$		0			0
$794$	−29.9706	−	51.9105i	−1.06362	−	1.84224i
$795$	4.24264	+	7.34847i	0.150471	+	0.260623i
$796$	−1.58579	+	2.74666i	−0.0562067	+	0.0973529i
$797$	7.37258			0.261150			0.130575	−	0.991438i	$-0.458318\pi$
$797$	7.37258			0.261150			0.130575	+	0.991438i	$0.458318\pi$
$798$		0			0
$799$	−43.3137			−1.53233
$800$	0.792893	−	1.37333i	0.0280330	−	0.0485546i
$801$	−2.65685	−	4.60181i	−0.0938753	−	0.162597i
$802$	−36.2132	−	62.7231i	−1.27873	−	2.21483i
$803$	−15.7990	+	27.3647i	−0.557534	+	0.965678i
$804$		0			0
$805$		0			0
$806$	−75.5980			−2.66283
$807$	−0.171573	+	0.297173i	−0.00603965	+	0.0104610i
$808$	16.8995	+	29.2708i	0.594522	+	1.02974i
$809$	−1.82843	−	3.16693i	−0.0642841	−	0.111343i	0.832092	−	0.554637i	$-0.187143\pi$
$809$	−1.82843	−	3.16693i	−0.0642841	−	0.111343i	−0.896376	+	0.443294i	$0.853810\pi$
$810$	1.20711	−	2.09077i	0.0424134	−	0.0734622i
$811$	43.4558			1.52594			0.762971	−	0.646433i	$-0.223740\pi$
$811$	43.4558			1.52594			0.762971	+	0.646433i	$0.223740\pi$
$812$		0			0
$813$	−22.4853			−0.788593
$814$	12.4853	−	21.6251i	0.437609	−	0.757961i
$815$	−6.00000	−	10.3923i	−0.210171	−	0.364027i
$816$	11.4853	+	19.8931i	0.402065	+	0.696397i
$817$	−3.31371	+	5.73951i	−0.115932	+	0.200800i
$818$	−28.9706			−1.01293
$819$		0			0
$820$	44.6274			1.55846
$821$	22.3137	−	38.6485i	0.778754	−	1.34884i	−0.153907	−	0.988085i	$-0.549185\pi$
$821$	22.3137	−	38.6485i	0.778754	−	1.34884i	0.932660	−	0.360756i	$-0.117481\pi$
$822$	15.8995	+	27.5387i	0.554559	+	0.960524i
$823$	20.9706	+	36.3221i	0.730988	+	1.26611i	0.956461	+	0.291859i	$0.0942737\pi$
$823$	20.9706	+	36.3221i	0.730988	+	1.26611i	−0.225474	+	0.974249i	$0.572393\pi$
$824$	−26.4853	+	45.8739i	−0.922658	+	1.59809i
$825$	−2.82843			−0.0984732
$826$		0			0
$827$	5.31371			0.184776			0.0923879	−	0.995723i	$-0.470550\pi$
$827$	5.31371			0.184776			0.0923879	+	0.995723i	$0.470550\pi$
$828$	14.6569	−	25.3864i	0.509361	−	0.882239i
$829$	23.7990	+	41.2211i	0.826573	+	1.43167i	0.900711	+	0.434419i	$0.143046\pi$
$829$	23.7990	+	41.2211i	0.826573	+	1.43167i	−0.0741380	+	0.997248i	$0.523621\pi$
$830$	2.00000	+	3.46410i	0.0694210	+	0.120241i
$831$	10.6569	−	18.4582i	0.369682	−	0.640308i
$832$	−47.4558			−1.64524
$833$		0			0
$834$	−3.65685			−0.126627
$835$	−5.65685	+	9.79796i	−0.195764	+	0.339072i
$836$	−4.48528	−	7.76874i	−0.155127	−	0.268687i
$837$	−3.24264	−	5.61642i	−0.112082	−	0.194132i
$838$	−0.828427	+	1.43488i	−0.0286175	+	0.0495670i
$839$	46.6274			1.60976			0.804879	−	0.593439i	$-0.202230\pi$
$839$	46.6274			1.60976			0.804879	+	0.593439i	$0.202230\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$	7.24264	−	12.5446i	0.249598	−	0.432316i
$843$	6.17157	+	10.6895i	0.212560	+	0.368165i
$844$	18.4853	+	32.0174i	0.636290	+	1.10209i
$845$	5.15685	−	8.93193i	0.177401	−	0.307268i
$846$	−13.6569			−0.469532
$847$		0			0
$848$	−25.4558			−0.874157
$849$		0			0
$850$	−9.24264	−	16.0087i	−0.317020	−	0.549095i
$851$	−14.0000	−	24.2487i	−0.479914	−	0.831235i
$852$	−5.41421	+	9.37769i	−0.185488	+	0.321274i
$853$	−10.4853			−0.359009			−0.179505	−	0.983757i	$-0.557449\pi$
$853$	−10.4853			−0.359009			−0.179505	+	0.983757i	$0.557449\pi$
$854$		0			0
$855$	−0.828427			−0.0283316
$856$	−11.7279	+	20.3134i	−0.400852	+	0.694296i
$857$	22.3137	+	38.6485i	0.762222	+	1.32021i	0.941703	+	0.336445i	$0.109225\pi$
$857$	22.3137	+	38.6485i	0.762222	+	1.32021i	−0.179481	+	0.983761i	$0.557442\pi$
$858$	16.4853	+	28.5533i	0.562798	+	0.974795i
$859$	−22.8995	+	39.6631i	−0.781321	+	1.35329i	0.149852	+	0.988708i	$0.452120\pi$
$859$	−22.8995	+	39.6631i	−0.781321	+	1.35329i	−0.931173	+	0.364579i	$0.881213\pi$
$860$	−30.6274			−1.04439
$861$		0			0
$862$	−26.1421			−0.890405
$863$	−23.4853	+	40.6777i	−0.799448	+	1.38469i	0.120528	+	0.992710i	$0.461541\pi$
$863$	−23.4853	+	40.6777i	−0.799448	+	1.38469i	−0.919976	+	0.391975i	$0.871792\pi$
$864$	−0.792893	−	1.37333i	−0.0269748	−	0.0467217i
$865$	−12.3137	−	21.3280i	−0.418679	−	0.725173i
$866$	8.65685	−	14.9941i	0.294172	−	0.509521i
$867$	−41.6274			−1.41374
$868$		0			0
$869$	−22.6274			−0.767583
$870$	−7.24264	+	12.5446i	−0.245549	+	0.425303i
$871$		0			0
$872$	−13.2426	−	22.9369i	−0.448452	−	0.776742i
$873$	3.24264	−	5.61642i	0.109747	−	0.190087i
$874$	−15.3137			−0.517994
$875$		0			0
$876$	−42.7696			−1.44505
$877$	−13.9706	+	24.1977i	−0.471752	+	0.817099i	−0.999478	−	0.0323160i	$-0.989712\pi$
$877$	−13.9706	+	24.1977i	−0.471752	+	0.817099i	0.527725	+	0.849415i	$0.323045\pi$
$878$	−16.3137	−	28.2562i	−0.550561	−	0.953600i
$879$	6.17157	+	10.6895i	0.208162	+	0.360547i
$880$	4.24264	−	7.34847i	0.143019	−	0.247717i
$881$	43.2548			1.45729			0.728646	−	0.684890i	$-0.240150\pi$
$881$	43.2548			1.45729			0.728646	+	0.684890i	$0.240150\pi$
$882$		0			0
$883$	28.0000			0.942275			0.471138	−	0.882060i	$-0.343844\pi$
$883$	28.0000			0.942275			0.471138	+	0.882060i	$0.343844\pi$
$884$	−70.7696	+	122.576i	−2.38024	+	4.12269i
$885$	1.17157	+	2.02922i	0.0393820	+	0.0682116i
$886$	−28.5563	−	49.4610i	−0.959369	−	1.66168i
$887$	−3.51472	+	6.08767i	−0.118013	+	0.204404i	−0.918980	−	0.394304i	$-0.870986\pi$
$887$	−3.51472	+	6.08767i	−0.118013	+	0.204404i	0.800967	+	0.598708i	$0.204319\pi$
$888$	16.1421			0.541695
$889$		0			0
$890$	−12.8284			−0.430010
$891$	−1.41421	+	2.44949i	−0.0473779	+	0.0820610i
$892$	−40.1421	−	69.5282i	−1.34406	−	2.32798i
$893$	2.34315	+	4.05845i	0.0784104	+	0.135811i
$894$	−9.24264	+	16.0087i	−0.309120	+	0.535412i
$895$	1.17157			0.0391614
$896$		0			0
$897$	36.9706			1.23441
$898$	15.2426	−	26.4010i	0.508654	−	0.881014i
$899$	19.4558	+	33.6985i	0.648889	+	1.12391i
$900$	−1.91421	−	3.31552i	−0.0638071	−	0.110517i
$901$	32.4853	−	56.2662i	1.08224	−	1.87450i
$902$	−79.5980			−2.65032
$903$		0			0
$904$	12.4853			0.415254
$905$	−1.17157	+	2.02922i	−0.0389444	+	0.0674537i
$906$	−20.4853	−	35.4815i	−0.680578	−	1.17880i
$907$	19.6569	+	34.0467i	0.652695	+	1.13050i	0.982466	+	0.186440i	$0.0596951\pi$
$907$	19.6569	+	34.0467i	0.652695	+	1.13050i	−0.329771	+	0.944061i	$0.606972\pi$
$908$	55.4558	−	96.0523i	1.84037	−	3.18761i
$909$	−7.65685			−0.253962
$910$		0			0
$911$	−7.79899			−0.258392			−0.129196	−	0.991619i	$-0.541240\pi$
$911$	−7.79899			−0.258392			−0.129196	+	0.991619i	$0.541240\pi$
$912$	1.24264	−	2.15232i	0.0411479	−	0.0712703i
$913$	−2.34315	−	4.05845i	−0.0775468	−	0.134315i
$914$	−19.7279	−	34.1698i	−0.652542	−	1.13024i
$915$		0			0
$916$	58.6274			1.93710
$917$		0			0
$918$	−18.4853			−0.610105
$919$	−22.1421	+	38.3513i	−0.730402	+	1.26509i	0.226310	+	0.974055i	$0.427334\pi$
$919$	−22.1421	+	38.3513i	−0.730402	+	1.26509i	−0.956712	+	0.291037i	$0.906000\pi$
$920$	−16.8995	−	29.2708i	−0.557160	−	0.965029i
$921$	14.4853	+	25.0892i	0.477306	+	0.826719i
$922$	16.0711	−	27.8359i	0.529272	−	0.916727i
$923$	−13.6569			−0.449521
$924$		0			0
$925$	−3.65685			−0.120237
$926$	−46.6274	+	80.7611i	−1.53227	+	2.65397i
$927$	−6.00000	−	10.3923i	−0.197066	−	0.341328i
$928$	4.75736	+	8.23999i	0.156168	+	0.270491i
$929$	−21.0000	+	36.3731i	−0.688988	+	1.19336i	0.283178	+	0.959067i	$0.408611\pi$
$929$	−21.0000	+	36.3731i	−0.688988	+	1.19336i	−0.972166	+	0.234294i	$0.924722\pi$
$930$	−15.6569			−0.513408
$931$		0			0
$932$	56.7696			1.85955
$933$	−4.82843	+	8.36308i	−0.158076	+	0.273795i
$934$	−29.3137	−	50.7728i	−0.959174	−	1.66134i
$935$	10.8284	+	18.7554i	0.354127	+	0.613367i
$936$	−10.6569	+	18.4582i	−0.348330	+	0.603326i
$937$	−15.4558			−0.504920			−0.252460	−	0.967607i	$-0.581240\pi$
$937$	−15.4558			−0.504920			−0.252460	+	0.967607i	$0.581240\pi$
$938$		0			0
$939$	2.48528			0.0811041
$940$	−10.8284	+	18.7554i	−0.353184	+	0.611733i
$941$	−0.313708	−	0.543359i	−0.0102266	−	0.0177130i	0.860867	−	0.508830i	$-0.169922\pi$
$941$	−0.313708	−	0.543359i	−0.0102266	−	0.0177130i	−0.871093	+	0.491117i	$0.836589\pi$
$942$	−14.6569	−	25.3864i	−0.477546	−	0.827134i
$943$	−44.6274	+	77.2970i	−1.45327	+	2.51714i
$944$	−7.02944			−0.228789
$945$		0			0
$946$	54.6274			1.77609
$947$	6.17157	−	10.6895i	0.200549	−	0.347361i	−0.748156	−	0.663522i	$-0.769061\pi$
$947$	6.17157	−	10.6895i	0.200549	−	0.347361i	0.948706	+	0.316161i	$0.102394\pi$
$948$	−15.3137	−	26.5241i	−0.497366	−	0.861463i
$949$	−26.9706	−	46.7144i	−0.875502	−	1.51641i
$950$	−1.00000	+	1.73205i	−0.0324443	+	0.0561951i
$951$	−22.1421			−0.718008
$952$		0			0
$953$	6.14214			0.198963			0.0994816	−	0.995039i	$-0.468282\pi$
$953$	6.14214			0.198963			0.0994816	+	0.995039i	$0.468282\pi$
$954$	10.2426	−	17.7408i	0.331618	−	0.574379i
$955$	−4.58579	−	7.94282i	−0.148393	−	0.257023i
$956$	4.10051	+	7.10228i	0.132620	+	0.229704i
$957$	8.48528	−	14.6969i	0.274290	−	0.475085i
$958$	34.6274			1.11876
$959$		0			0
$960$	−9.82843			−0.317211
$961$	−5.52944	+	9.57727i	−0.178369	+	0.308944i
$962$	21.3137	+	36.9164i	0.687182	+	1.19023i
$963$	−2.65685	−	4.60181i	−0.0856159	−	0.148291i
$964$	−41.4558	+	71.8036i	−1.33520	+	2.31264i
$965$	−15.6569			−0.504012
$966$		0			0
$967$	5.37258			0.172771			0.0863853	−	0.996262i	$-0.472468\pi$
$967$	5.37258			0.172771			0.0863853	+	0.996262i	$0.472468\pi$
$968$	6.62132	−	11.4685i	0.212817	−	0.368610i
$969$	3.17157	+	5.49333i	0.101886	+	0.176471i
$970$	−7.82843	−	13.5592i	−0.251356	−	0.435361i
$971$	19.6569	−	34.0467i	0.630818	−	1.09261i	−0.356566	−	0.934270i	$-0.616053\pi$
$971$	19.6569	−	34.0467i	0.630818	−	1.09261i	0.987385	−	0.158340i	$-0.0506141\pi$
$972$	−3.82843			−0.122797
$973$		0			0
$974$	72.2843			2.31614
$975$	2.41421	−	4.18154i	0.0773167	−	0.133916i
$976$		0			0
$977$	10.2426	+	17.7408i	0.327691	+	0.567578i	0.982053	−	0.188604i	$-0.0603961\pi$
$977$	10.2426	+	17.7408i	0.327691	+	0.567578i	−0.654362	+	0.756181i	$0.727063\pi$
$978$	−14.4853	+	25.0892i	−0.463188	+	0.802266i
$979$	15.0294			0.480343
$980$		0			0
$981$	6.00000			0.191565
$982$	−21.8995	+	37.9310i	−0.698841	+	1.21043i
$983$	10.8284	+	18.7554i	0.345373	+	0.598204i	0.985421	−	0.170131i	$-0.0544190\pi$
$983$	10.8284	+	18.7554i	0.345373	+	0.598204i	−0.640048	+	0.768335i	$0.721086\pi$
$984$	−25.7279	−	44.5621i	−0.820176	−	1.42059i
$985$	−1.75736	+	3.04384i	−0.0559941	+	0.0969847i
$986$	110.912			3.53215
$987$		0			0
$988$	15.3137			0.487194
$989$	30.6274	−	53.0482i	0.973895	−	1.68684i
$990$	3.41421	+	5.91359i	0.108511	+	0.187946i
$991$	−8.48528	−	14.6969i	−0.269544	−	0.466864i	0.699200	−	0.714926i	$-0.253540\pi$
$991$	−8.48528	−	14.6969i	−0.269544	−	0.466864i	−0.968744	+	0.248062i	$0.920206\pi$
$992$	−5.14214	+	8.90644i	−0.163263	+	0.282780i
$993$	−1.65685			−0.0525787
$994$		0			0
$995$	−0.828427			−0.0262629
$996$	3.17157	−	5.49333i	0.100495	−	0.174063i
$997$	−27.7279	−	48.0262i	−0.878152	−	1.52100i	−0.853367	−	0.521311i	$-0.825443\pi$
$997$	−27.7279	−	48.0262i	−0.878152	−	1.52100i	−0.0247855	−	0.999693i	$-0.507890\pi$
$998$	−6.00000	−	10.3923i	−0.189927	−	0.328963i
$999$	−1.82843	+	3.16693i	−0.0578489	+	0.100197i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.i.h.226.1		4
7.2	even	3		735.2.a.l.1.2	✓	2
7.3	odd	6		735.2.i.g.361.1		4
7.4	even	3	inner	735.2.i.h.361.1		4
7.5	odd	6		735.2.a.m.1.2	yes	2
7.6	odd	2		735.2.i.g.226.1		4
21.2	odd	6		2205.2.a.r.1.1		2
21.5	even	6		2205.2.a.o.1.1		2
35.9	even	6		3675.2.a.t.1.1		2
35.19	odd	6		3675.2.a.s.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
735.2.a.l.1.2	✓	2	7.2	even	3
735.2.a.m.1.2	yes	2	7.5	odd	6
735.2.i.g.226.1		4	7.6	odd	2
735.2.i.g.361.1		4	7.3	odd	6
735.2.i.h.226.1		4	1.1	even	1	trivial
735.2.i.h.361.1		4	7.4	even	3	inner
2205.2.a.o.1.1		2	21.5	even	6
2205.2.a.r.1.1		2	21.2	odd	6
3675.2.a.s.1.1		2	35.19	odd	6
3675.2.a.t.1.1		2	35.9	even	6

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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-1.20711 + 2.09077i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.91421 - 3.31552i) q^{4} +(0.500000 - 0.866025i) q^{5} -2.41421 q^{6} +4.41421 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.20711 + 2.09077i) q^{10} +(-1.41421 - 2.44949i) q^{11} +(1.91421 - 3.31552i) q^{12} +4.82843 q^{13} +1.00000 q^{15} +(-1.50000 + 2.59808i) q^{16} +(-3.82843 - 6.63103i) q^{17} +(-1.20711 - 2.09077i) q^{18} +(-0.414214 + 0.717439i) q^{19} -3.82843 q^{20} +6.82843 q^{22} +(3.82843 - 6.63103i) q^{23} +(2.20711 + 3.82282i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-5.82843 + 10.0951i) q^{26} -1.00000 q^{27} +6.00000 q^{29} +(-1.20711 + 2.09077i) q^{30} +(3.24264 + 5.61642i) q^{31} +(0.792893 + 1.37333i) q^{32} +(1.41421 - 2.44949i) q^{33} +18.4853 q^{34} +3.82843 q^{36} +(1.82843 - 3.16693i) q^{37} +(-1.00000 - 1.73205i) q^{38} +(2.41421 + 4.18154i) q^{39} +(2.20711 - 3.82282i) q^{40} -11.6569 q^{41} +8.00000 q^{43} +(-5.41421 + 9.37769i) q^{44} +(0.500000 + 0.866025i) q^{45} +(9.24264 + 16.0087i) q^{46} +(2.82843 - 4.89898i) q^{47} -3.00000 q^{48} +2.41421 q^{50} +(3.82843 - 6.63103i) q^{51} +(-9.24264 - 16.0087i) q^{52} +(4.24264 + 7.34847i) q^{53} +(1.20711 - 2.09077i) q^{54} -2.82843 q^{55} -0.828427 q^{57} +(-7.24264 + 12.5446i) q^{58} +(1.17157 + 2.02922i) q^{59} +(-1.91421 - 3.31552i) q^{60} -15.6569 q^{62} -9.82843 q^{64} +(2.41421 - 4.18154i) q^{65} +(3.41421 + 5.91359i) q^{66} +(-14.6569 + 25.3864i) q^{68} +7.65685 q^{69} -2.82843 q^{71} +(-2.20711 + 3.82282i) q^{72} +(-5.58579 - 9.67487i) q^{73} +(4.41421 + 7.64564i) q^{74} +(0.500000 - 0.866025i) q^{75} +3.17157 q^{76} -11.6569 q^{78} +(4.00000 - 6.92820i) q^{79} +(1.50000 + 2.59808i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(14.0711 - 24.3718i) q^{82} +1.65685 q^{83} -7.65685 q^{85} +(-9.65685 + 16.7262i) q^{86} +(3.00000 + 5.19615i) q^{87} +(-6.24264 - 10.8126i) q^{88} +(-2.65685 + 4.60181i) q^{89} -2.41421 q^{90} -29.3137 q^{92} +(-3.24264 + 5.61642i) q^{93} +(6.82843 + 11.8272i) q^{94} +(0.414214 + 0.717439i) q^{95} +(-0.792893 + 1.37333i) q^{96} -6.48528 q^{97} +2.82843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} - 4 q^{6} + 12 q^{8} - 2 q^{9} + 2 q^{10} + 2 q^{12} + 8 q^{13} + 4 q^{15} - 6 q^{16} - 4 q^{17} - 2 q^{18} + 4 q^{19} - 4 q^{20} + 16 q^{22} + 4 q^{23} + 6 q^{24}+ \cdots + 8 q^{97}+O(q^{100}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 - 4 * q^6 + 12 * q^8 - 2 * q^9 + 2 * q^10 + 2 * q^12 + 8 * q^13 + 4 * q^15 - 6 * q^16 - 4 * q^17 - 2 * q^18 + 4 * q^19 - 4 * q^20 + 16 * q^22 + 4 * q^23 + 6 * q^24 - 2 * q^25 - 12 * q^26 - 4 * q^27 + 24 * q^29 - 2 * q^30 - 4 * q^31 + 6 * q^32 + 40 * q^34 + 4 * q^36 - 4 * q^37 - 4 * q^38 + 4 * q^39 + 6 * q^40 - 24 * q^41 + 32 * q^43 - 16 * q^44 + 2 * q^45 + 20 * q^46 - 12 * q^48 + 4 * q^50 + 4 * q^51 - 20 * q^52 + 2 * q^54 + 8 * q^57 - 12 * q^58 + 16 * q^59 - 2 * q^60 - 40 * q^62 - 28 * q^64 + 4 * q^65 + 8 * q^66 - 36 * q^68 + 8 * q^69 - 6 * q^72 - 28 * q^73 + 12 * q^74 + 2 * q^75 + 24 * q^76 - 24 * q^78 + 16 * q^79 + 6 * q^80 - 2 * q^81 + 28 * q^82 - 16 * q^83 - 8 * q^85 - 16 * q^86 + 12 * q^87 - 8 * q^88 + 12 * q^89 - 4 * q^90 - 72 * q^92 + 4 * q^93 + 16 * q^94 - 4 * q^95 - 6 * q^96 + 8 * q^97

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