LMFDB - Embedded newform 735.2.i.g.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.g.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	$-0.733527\pi$
$13$	−4.82843			−1.33916			−0.669582	+	0.742738i	$0.733527\pi$
$14$		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	$0.212260\pi$
$17$	3.82843	+	6.63103i	0.928530	+	1.60826i	0.142747	+	0.989759i	$0.454407\pi$
$18$	−1.20711	−	2.09077i	−0.284518	−	0.492799i
$19$	0.414214	−	0.717439i	0.0950271	−	0.164592i	−0.814593	−	0.580033i	$-0.803040\pi$
$19$	0.414214	−	0.717439i	0.0950271	−	0.164592i	0.909620	+	0.415441i	$0.136373\pi$
$20$	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	$-0.968782\pi$
$31$	−3.24264	−	5.61642i	−0.582395	−	1.00874i	0.412799	−	0.910822i	$-0.364551\pi$
$32$	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	$-0.135891\pi$
$41$	11.6569			1.82049			0.910247	+	0.414065i	$0.135891\pi$
$42$		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	−0.995170	−	0.0981685i	$-0.968702\pi$
$47$	−2.82843	+	4.89898i	−0.412568	+	0.714590i	0.582601	+	0.812758i	$0.302035\pi$
$48$	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	0.779630	−	0.626241i	$-0.215407\pi$
$59$	−1.17157	−	2.02922i	−0.152526	−	0.264182i	−0.932155	+	0.362059i	$0.882074\pi$
$60$	−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	$0.0601456\pi$
$73$	5.58579	+	9.67487i	0.653767	+	1.13236i	−0.328435	+	0.944527i	$0.606521\pi$
$74$	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	$-0.528984\pi$
$83$	−1.65685			−0.181863			−0.0909317	+	0.995857i	$0.528984\pi$
$84$		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	−0.690159	−	0.723657i	$-0.742460\pi$
$89$	2.65685	−	4.60181i	0.281626	−	0.487791i	0.971785	+	0.235867i	$0.0757929\pi$
$90$	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	$-0.393207\pi$
$97$	6.48528			0.658481			0.329240	+	0.944246i	$0.393207\pi$
$98$		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	0.610255	−	0.792205i	$-0.291067\pi$
$101$	−3.82843	−	6.63103i	−0.380943	−	0.659812i	−0.991197	+	0.132393i	$0.957734\pi$
$102$	9.24264	+	16.0087i	0.915158	+	1.58510i
$103$	6.00000	−	10.3923i	0.591198	−	1.02398i	−0.402874	−	0.915255i	$-0.631989\pi$
$103$	6.00000	−	10.3923i	0.591198	−	1.02398i	0.994071	−	0.108729i	$-0.0346780\pi$
$104$	−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	−0.962726	−	0.270479i	$-0.912818\pi$
$131$	−2.82843	+	4.89898i	−0.247121	+	0.428026i	0.715605	+	0.698505i	$0.246151\pi$
$132$	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	$-0.520462\pi$
$139$	−1.51472			−0.128477			−0.0642384	+	0.997935i	$0.520462\pi$
$140$		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	0.515318	−	0.856999i	$-0.327674\pi$
$157$	−6.07107	−	10.5154i	−0.484524	−	0.839220i	−0.999842	+	0.0177789i	$0.994340\pi$
$158$	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	$-0.355779\pi$
$167$	11.3137			0.875481			0.437741	+	0.899101i	$0.355779\pi$
$168$		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	$0.552344\pi$
$173$	−12.3137	+	21.3280i	−0.936194	+	1.62154i	−0.772491	+	0.635026i	$0.780989\pi$
$174$	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	$-0.472246\pi$
$181$	2.34315			0.174165			0.0870823	+	0.996201i	$0.472246\pi$
$182$		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	0.880333	−	0.474355i	$-0.157319\pi$
$199$	0.414214	+	0.717439i	0.0293628	+	0.0508579i	−0.850971	+	0.525213i	$0.823986\pi$
$200$	−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	$-0.747775\pi$
$223$	−20.9706			−1.40429			−0.702146	+	0.712033i	$0.747775\pi$
$224$		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	$-0.755370\pi$
$227$	−14.4853	−	25.0892i	−0.961422	−	1.66523i	−0.242486	−	0.970155i	$-0.577963\pi$
$228$	1.58579	+	2.74666i	0.105021	+	0.181902i
$229$	7.65685	−	13.2621i	0.505979	−	0.876382i	−0.493997	−	0.869464i	$-0.664465\pi$
$229$	7.65685	−	13.2621i	0.505979	−	0.876382i	0.999976	−	0.00691797i	$-0.00220208\pi$
$230$	−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	$0.0790466\pi$
$241$	10.8284	+	18.7554i	0.697520	+	1.20814i	−0.271803	+	0.962353i	$0.587620\pi$
$242$	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	$-0.114533\pi$
$251$	29.6569			1.87192			0.935962	+	0.352101i	$0.114533\pi$
$252$		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	−0.860625	−	0.509240i	$-0.829927\pi$
$257$	0.171573	−	0.297173i	0.0107024	−	0.0185371i	0.871327	+	0.490703i	$0.163260\pi$
$258$	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	0.860748	−	0.509032i	$-0.169997\pi$
$269$	−0.171573	−	0.297173i	−0.0104610	−	0.0181190i	−0.871209	+	0.490913i	$0.836663\pi$
$270$	−1.20711	−	2.09077i	−0.0734622	−	0.127240i
$271$	11.2426	−	19.4728i	0.682942	−	1.18289i	−0.291137	−	0.956681i	$-0.594034\pi$
$271$	11.2426	−	19.4728i	0.682942	−	1.18289i	0.974079	−	0.226209i	$-0.0726331\pi$
$272$	−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	$-0.617410\pi$
$293$	−12.3431			−0.721094			−0.360547	+	0.932741i	$0.617410\pi$
$294$		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	$-0.809795\pi$
$307$	−28.9706			−1.65344			−0.826719	+	0.562616i	$0.809795\pi$
$308$		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	0.696035	−	0.718007i	$-0.254946\pi$
$311$	−4.82843	−	8.36308i	−0.273795	−	0.474227i	−0.969830	+	0.243781i	$0.921612\pi$
$312$	10.6569	+	18.4582i	0.603326	+	1.04499i
$313$	−1.24264	+	2.15232i	−0.0702382	+	0.121656i	−0.899006	−	0.437937i	$-0.855709\pi$
$313$	−1.24264	+	2.15232i	−0.0702382	+	0.121656i	0.828767	+	0.559593i	$0.189043\pi$
$314$	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	$-0.359137\pi$
$349$	16.0000			0.856460			0.428230	+	0.903670i	$0.359137\pi$
$350$		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	$0.0686105\pi$
$353$	12.6569	+	21.9223i	0.673656	+	1.16681i	−0.303203	+	0.952926i	$0.598056\pi$
$354$	−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	0.984156	−	0.177303i	$-0.0567374\pi$
$367$	6.48528	+	11.2328i	0.338529	+	0.586349i	−0.645627	+	0.763653i	$0.723404\pi$
$368$	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	$-0.619226\pi$
$397$	12.4142	−	21.5020i	0.623052	−	1.07916i	0.988914	−	0.148488i	$-0.0474406\pi$
$398$	−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	0.678694	−	0.734422i	$-0.262546\pi$
$409$	−6.00000	−	10.3923i	−0.296681	−	0.513866i	−0.975375	+	0.220555i	$0.929213\pi$
$410$	−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	$-0.505336\pi$
$419$	−0.686292			−0.0335275			−0.0167638	+	0.999859i	$0.505336\pi$
$420$		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	$-0.444873\pi$
$433$	7.17157			0.344644			0.172322	+	0.985041i	$0.444873\pi$
$434$		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	−0.658494	−	0.752586i	$-0.728806\pi$
$439$	6.75736	−	11.7041i	0.322511	−	0.558606i	0.981005	+	0.193980i	$0.0621397\pi$
$440$	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	$-0.399657\pi$
$461$	13.3137			0.620081			0.310041	+	0.950723i	$0.399657\pi$
$462$		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	$-0.643415\pi$
$467$	12.1421	−	21.0308i	0.561871	−	0.973189i	0.997333	−	0.0729822i	$-0.0232516\pi$
$468$	−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	0.982051	−	0.188618i	$-0.0604007\pi$
$479$	7.17157	+	12.4215i	0.327678	+	0.567554i	−0.654373	+	0.756172i	$0.727067\pi$
$480$	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	$-0.466684\pi$
$503$	4.68629			0.208951			0.104476	+	0.994527i	$0.466684\pi$
$504$		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	$-0.617148\pi$
$509$	14.1716	−	24.5459i	0.628144	−	1.08798i	0.987924	−	0.154940i	$-0.0495184\pi$
$510$	−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	0.511761	−	0.859128i	$-0.328993\pi$
$521$	−11.1421	−	19.2987i	−0.488146	−	0.845493i	−0.999907	+	0.0136344i	$0.995660\pi$
$522$	−7.24264	−	12.5446i	−0.317002	−	0.549063i
$523$	−18.1421	+	31.4231i	−0.793300	+	1.37404i	0.130613	+	0.991433i	$0.458306\pi$
$523$	−18.1421	+	31.4231i	−0.793300	+	1.37404i	−0.923913	+	0.382603i	$0.875028\pi$
$524$	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	0.759873	−	0.650071i	$-0.225261\pi$
$563$	−4.34315	−	7.52255i	−0.183042	−	0.317038i	−0.942915	+	0.333034i	$0.891928\pi$
$564$	−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	0.606962	−	0.794731i	$-0.292388\pi$
$577$	−9.24264	−	16.0087i	−0.384776	−	0.666452i	−0.991738	+	0.128279i	$0.959055\pi$
$578$	−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	$-0.557371\pi$
$587$	−8.68629			−0.358522			−0.179261	+	0.983802i	$0.557371\pi$
$588$		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	−0.814601	−	0.580021i	$-0.803044\pi$
$593$	2.31371	−	4.00746i	0.0950126	−	0.164567i	0.909614	+	0.415455i	$0.136378\pi$
$594$	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	$-0.259170\pi$
$601$	33.6569			1.37289			0.686446	+	0.727181i	$0.259170\pi$
$602$		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	−0.833647	−	0.552298i	$-0.813751\pi$
$607$	1.51472	−	2.62357i	0.0614805	−	0.106487i	0.895127	+	0.445810i	$0.147084\pi$
$608$	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	$0.251956\pi$
$619$	24.0711	+	41.6923i	0.967498	+	1.67576i	0.264749	+	0.964317i	$0.414711\pi$
$620$	−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	$-0.468752\pi$
$643$	4.97056			0.196020			0.0980099	+	0.995185i	$0.468752\pi$
$644$		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	0.991011	−	0.133778i	$-0.0427110\pi$
$647$	9.65685	+	16.7262i	0.379650	+	0.657573i	−0.611361	+	0.791352i	$0.709378\pi$
$648$	−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	0.990418	−	0.138103i	$-0.0441005\pi$
$661$	9.65685	+	16.7262i	0.375608	+	0.650572i	−0.614810	+	0.788675i	$0.710767\pi$
$662$	−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	−0.675463	−	0.737394i	$-0.736056\pi$
$677$	7.82843	−	13.5592i	0.300871	−	0.521124i	0.976333	+	0.216271i	$0.0693893\pi$
$678$	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	−0.797733	−	0.603011i	$-0.793968\pi$
$691$	3.24264	−	5.61642i	0.123356	−	0.213659i	0.921089	+	0.389352i	$0.127301\pi$
$692$	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	−0.761834	−	0.647772i	$-0.775701\pi$
$719$	4.82843	−	8.36308i	0.180070	−	0.311890i	0.941904	+	0.335882i	$0.109034\pi$
$720$	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	$-0.561433\pi$
$727$	−10.3431			−0.383606			−0.191803	+	0.981433i	$0.561433\pi$
$728$		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	−0.832349	−	0.554252i	$-0.813004\pi$
$733$	1.72792	−	2.99285i	0.0638223	−	0.110543i	0.896171	+	0.443709i	$0.146338\pi$
$734$	−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	−0.938002	−	0.346630i	$-0.887326\pi$
$761$	−4.65685	+	8.06591i	−0.168811	+	0.292389i	0.769191	+	0.639019i	$0.220659\pi$
$762$	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	$-0.482605\pi$
$769$	3.02944			0.109244			0.0546222	+	0.998507i	$0.482605\pi$
$770$		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	$-0.967069\pi$
$773$	−16.3137	−	28.2562i	−0.586763	−	1.01630i	0.407890	−	0.913031i	$-0.366265\pi$
$774$	−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	0.718275	−	0.695759i	$-0.244932\pi$
$787$	−6.82843	−	11.8272i	−0.243407	−	0.421594i	−0.961683	+	0.274165i	$0.911598\pi$
$788$	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	$-0.541682\pi$
$797$	−7.37258			−0.261150			−0.130575	+	0.991438i	$0.541682\pi$
$798$		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	$-0.776260\pi$
$811$	−43.4558			−1.52594			−0.762971	+	0.646433i	$0.776260\pi$
$812$		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	$-0.856954\pi$
$829$	−23.7990	−	41.2211i	−0.826573	−	1.43167i	0.0741380	−	0.997248i	$-0.476379\pi$
$830$	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	$-0.797770\pi$
$839$	−46.6274			−1.60976			−0.804879	+	0.593439i	$0.797770\pi$
$840$		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	$-0.442551\pi$
$853$	10.4853			0.359009			0.179505	+	0.983757i	$0.442551\pi$
$854$		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	$-0.890775\pi$
$857$	−22.3137	−	38.6485i	−0.762222	−	1.32021i	0.179481	−	0.983761i	$-0.442558\pi$
$858$	16.4853	+	28.5533i	0.562798	+	0.974795i
$859$	22.8995	−	39.6631i	0.781321	−	1.35329i	−0.149852	−	0.988708i	$-0.547880\pi$
$859$	22.8995	−	39.6631i	0.781321	−	1.35329i	0.931173	−	0.364579i	$-0.118787\pi$
$860$	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	$-0.759850\pi$
$881$	−43.2548			−1.45729			−0.728646	+	0.684890i	$0.759850\pi$
$882$		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	−0.800967	−	0.598708i	$-0.795681\pi$
$887$	3.51472	−	6.08767i	0.118013	−	0.204404i	0.918980	+	0.394304i	$0.129014\pi$
$888$	−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	$-0.591389\pi$
$929$	21.0000	−	36.3731i	0.688988	−	1.19336i	0.972166	−	0.234294i	$-0.0752779\pi$
$930$	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	$-0.418760\pi$
$937$	15.4558			0.504920			0.252460	+	0.967607i	$0.418760\pi$
$938$		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	0.871093	−	0.491117i	$-0.163411\pi$
$941$	0.313708	+	0.543359i	0.0102266	+	0.0177130i	−0.860867	+	0.508830i	$0.830078\pi$
$942$	−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	$0.383947\pi$
$971$	−19.6569	+	34.0467i	−0.630818	+	1.09261i	−0.987385	+	0.158340i	$0.949386\pi$
$972$	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	0.640048	−	0.768335i	$-0.278914\pi$
$983$	−10.8284	−	18.7554i	−0.345373	−	0.598204i	−0.985421	+	0.170131i	$0.945581\pi$
$984$	−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	$0.174557\pi$
$997$	27.7279	+	48.0262i	0.878152	+	1.52100i	0.0247855	+	0.999693i	$0.492110\pi$
$998$	−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.g.226.1		4
7.2	even	3		735.2.a.m.1.2	yes	2
7.3	odd	6		735.2.i.h.361.1		4
7.4	even	3	inner	735.2.i.g.361.1		4
7.5	odd	6		735.2.a.l.1.2	✓	2
7.6	odd	2		735.2.i.h.226.1		4
21.2	odd	6		2205.2.a.o.1.1		2
21.5	even	6		2205.2.a.r.1.1		2
35.9	even	6		3675.2.a.s.1.1		2
35.19	odd	6		3675.2.a.t.1.1		2

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