LMFDB - Embedded newform 600.2.b.f.251.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,2,Mod(251,600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(600, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))

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

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

chi := DirichletCharacter("600.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.1649659456.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{5} + 4x^{4} - 4x^{3} - 8x + 16 $ x^8 - x^7 - 2x^5 + 4x^4 - 4x^3 - 8x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			251.7
Root			$1.40014 - 0.199044i$ of defining polynomial
Character	$\chi$	$=$	600.251
Dual form			600.2.b.f.251.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40014 - 0.199044i) q^{2} +(0.520627 - 1.65195i) q^{3} +(1.92076 - 0.557378i) q^{4} +(0.400136 - 2.41659i) q^{6} -1.92736i q^{7} +(2.57839 - 1.16272i) q^{8} +(-2.45790 - 1.72010i) q^{9} +O(q^{10})$	\(q+(1.40014 - 0.199044i) q^{2} +(0.520627 - 1.65195i) q^{3} +(1.92076 - 0.557378i) q^{4} +(0.400136 - 2.41659i) q^{6} -1.92736i q^{7} +(2.57839 - 1.16272i) q^{8} +(-2.45790 - 1.72010i) q^{9} +4.02057i q^{11} +(0.0792373 - 3.46320i) q^{12} -4.81675i q^{13} +(-0.383629 - 2.69856i) q^{14} +(3.37866 - 2.14118i) q^{16} +5.23126i q^{17} +(-3.78377 - 1.91915i) q^{18} -0.684753 q^{19} +(-3.18390 - 1.00343i) q^{21} +(0.800272 + 5.62935i) q^{22} -1.72601 q^{23} +(-0.578386 - 4.86472i) q^{24} +(-0.958747 - 6.74411i) q^{26} +(-4.12117 + 3.16480i) q^{27} +(-1.07427 - 3.70199i) q^{28} +6.99830 q^{29} -4.23638i q^{31} +(4.30439 - 3.67045i) q^{32} +(6.64180 + 2.09322i) q^{33} +(1.04125 + 7.32448i) q^{34} +(-5.67978 - 1.93393i) q^{36} +9.83221i q^{37} +(-0.958747 + 0.136296i) q^{38} +(-7.95705 - 2.50773i) q^{39} +3.44020i q^{41} +(-4.65762 - 0.771205i) q^{42} -1.04125 q^{43} +(2.24098 + 7.72257i) q^{44} +(-2.41664 + 0.343552i) q^{46} -7.55759 q^{47} +(-1.77811 - 6.69614i) q^{48} +3.28530 q^{49} +(8.64180 + 2.72353i) q^{51} +(-2.68475 - 9.25184i) q^{52} +4.08251 q^{53} +(-5.14027 + 5.25144i) q^{54} +(-2.24098 - 4.96947i) q^{56} +(-0.356500 + 1.13118i) q^{57} +(9.79857 - 1.39297i) q^{58} -0.994883i q^{59} +3.16761i q^{61} +(-0.843227 - 5.93151i) q^{62} +(-3.31525 + 4.73724i) q^{63} +(5.29615 - 5.99590i) q^{64} +(9.71606 + 1.60878i) q^{66} +14.8728 q^{67} +(2.91579 + 10.0480i) q^{68} +(-0.898604 + 2.85128i) q^{69} -9.28360 q^{71} +(-8.33741 - 1.57723i) q^{72} -11.2836 q^{73} +(1.95705 + 13.7664i) q^{74} +(-1.31525 + 0.381666i) q^{76} +7.74908 q^{77} +(-11.6401 - 1.92736i) q^{78} -9.25184i q^{79} +(3.08251 + 8.45566i) q^{81} +(0.684753 + 4.81675i) q^{82} +7.15862i q^{83} +(-6.67481 - 0.152718i) q^{84} +(-1.45790 + 0.207256i) q^{86} +(3.64350 - 11.5609i) q^{87} +(4.67481 + 10.3666i) q^{88} +0.829022i q^{89} -9.28360 q^{91} +(-3.31525 + 0.962038i) q^{92} +(-6.99830 - 2.20557i) q^{93} +(-10.5817 + 1.50430i) q^{94} +(-3.82243 - 9.02159i) q^{96} +1.45201 q^{97} +(4.59986 - 0.653920i) q^{98} +(6.91579 - 9.88215i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + q^{4} - 7 q^{6} + 7 q^{8}+O(q^{10}) $ 8 * q + q^2 + q^4 - 7 * q^6 + 7 * q^8	$ 8 q + q^{2} + q^{4} - 7 q^{6} + 7 q^{8} + 15 q^{12} + 6 q^{14} - 7 q^{16} - 11 q^{18} - 4 q^{19} + 4 q^{21} - 14 q^{22} - 4 q^{23} + 9 q^{24} - 16 q^{26} + 12 q^{27} + 2 q^{28} + 11 q^{32} + 4 q^{33} - 19 q^{36} - 16 q^{38} - 16 q^{39} - 38 q^{42} + 30 q^{44} - 8 q^{46} + 28 q^{47} - 21 q^{48} - 16 q^{49} + 20 q^{51} - 20 q^{52} + 16 q^{53} - 15 q^{54} - 30 q^{56} + 4 q^{57} + 2 q^{58} - 34 q^{62} - 28 q^{63} + 25 q^{64} + 18 q^{66} + 32 q^{67} - 16 q^{68} - 20 q^{69} + 24 q^{71} - 41 q^{72} + 8 q^{73} - 32 q^{74} - 12 q^{76} + 12 q^{78} + 8 q^{81} + 4 q^{82} - 2 q^{84} + 8 q^{86} + 36 q^{87} - 14 q^{88} + 24 q^{91} - 28 q^{92} - 40 q^{94} + 17 q^{96} - 8 q^{97} + 47 q^{98} + 16 q^{99}+O(q^{100}) $ 8 * q + q^2 + q^4 - 7 * q^6 + 7 * q^8 + 15 * q^12 + 6 * q^14 - 7 * q^16 - 11 * q^18 - 4 * q^19 + 4 * q^21 - 14 * q^22 - 4 * q^23 + 9 * q^24 - 16 * q^26 + 12 * q^27 + 2 * q^28 + 11 * q^32 + 4 * q^33 - 19 * q^36 - 16 * q^38 - 16 * q^39 - 38 * q^42 + 30 * q^44 - 8 * q^46 + 28 * q^47 - 21 * q^48 - 16 * q^49 + 20 * q^51 - 20 * q^52 + 16 * q^53 - 15 * q^54 - 30 * q^56 + 4 * q^57 + 2 * q^58 - 34 * q^62 - 28 * q^63 + 25 * q^64 + 18 * q^66 + 32 * q^67 - 16 * q^68 - 20 * q^69 + 24 * q^71 - 41 * q^72 + 8 * q^73 - 32 * q^74 - 12 * q^76 + 12 * q^78 + 8 * q^81 + 4 * q^82 - 2 * q^84 + 8 * q^86 + 36 * q^87 - 14 * q^88 + 24 * q^91 - 28 * q^92 - 40 * q^94 + 17 * q^96 - 8 * q^97 + 47 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

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 $

$2$	1.40014	−	0.199044i	0.990046	−	0.140746i
$2$	1.40014	−	0.199044i	0.990046	−	0.140746i
$3$	0.520627	−	1.65195i	0.300584	−	0.953755i
$3$	0.520627	−	1.65195i	0.300584	−	0.953755i
$4$	1.92076	−	0.557378i	0.960381	−	0.278689i
$5$		0			0
$5$		0			0
$6$	0.400136	−	2.41659i	0.163355	−	0.986567i
$7$		−	1.92736i		−	0.728472i	−0.931307	−	0.364236i	$-0.881330\pi$
$7$		−	1.92736i		−	0.728472i	0.931307	−	0.364236i	$-0.118670\pi$
$8$	2.57839	−	1.16272i	0.911597	−	0.411084i
$9$	−2.45790	−	1.72010i	−0.819299	−	0.573367i
$10$		0			0
$11$			4.02057i			1.21225i	0.795370	+	0.606124i	$0.207277\pi$
$11$			4.02057i			1.21225i	−0.795370	+	0.606124i	$0.792723\pi$
$12$	0.0792373	−	3.46320i	0.0228738	−	0.999738i
$13$		−	4.81675i		−	1.33593i	−0.744194	−	0.667963i	$-0.767166\pi$
$13$		−	4.81675i		−	1.33593i	0.744194	−	0.667963i	$-0.232834\pi$
$14$	−0.383629	−	2.69856i	−0.102529	−	0.721221i
$15$		0			0
$16$	3.37866	−	2.14118i	0.844665	−	0.535296i
$17$			5.23126i			1.26877i	0.773018	+	0.634384i	$0.218746\pi$
$17$			5.23126i			1.26877i	−0.773018	+	0.634384i	$0.781254\pi$
$18$	−3.78377	−	1.91915i	−0.891842	−	0.452347i
$19$	−0.684753			−0.157093			−0.0785465	−	0.996910i	$-0.525028\pi$
$19$	−0.684753			−0.157093			−0.0785465	+	0.996910i	$0.525028\pi$
$20$		0			0
$21$	−3.18390	−	1.00343i	−0.694784	−	0.218967i
$22$	0.800272	+	5.62935i	0.170619	+	1.20018i
$23$	−1.72601			−0.359897			−0.179949	−	0.983676i	$-0.557593\pi$
$23$	−1.72601			−0.359897			−0.179949	+	0.983676i	$0.557593\pi$
$24$	−0.578386	−	4.86472i	−0.118063	−	0.993006i
$25$		0			0
$26$	−0.958747	−	6.74411i	−0.188026	−	1.32263i
$27$	−4.12117	+	3.16480i	−0.793120	+	0.609066i
$28$	−1.07427	−	3.70199i	−0.203017	−	0.699611i
$29$	6.99830			1.29955			0.649776	−	0.760126i	$-0.274863\pi$
$29$	6.99830			1.29955			0.649776	+	0.760126i	$0.274863\pi$
$30$		0			0
$31$		−	4.23638i		−	0.760876i	−0.924806	−	0.380438i	$-0.875773\pi$
$31$		−	4.23638i		−	0.760876i	0.924806	−	0.380438i	$-0.124227\pi$
$32$	4.30439	−	3.67045i	0.760916	−	0.648850i
$33$	6.64180	+	2.09322i	1.15619	+	0.364382i
$34$	1.04125	+	7.32448i	0.178573	+	1.25614i
$35$		0			0
$36$	−5.67978	−	1.93393i	−0.946630	−	0.322321i
$37$			9.83221i			1.61640i	0.588905	+	0.808202i	$0.299559\pi$
$37$			9.83221i			1.61640i	−0.588905	+	0.808202i	$0.700441\pi$
$38$	−0.958747	+	0.136296i	−0.155529	+	0.0221102i
$39$	−7.95705	−	2.50773i	−1.27415	−	0.401558i
$40$		0			0
$41$			3.44020i			0.537269i	0.963242	+	0.268635i	$0.0865724\pi$
$41$			3.44020i			0.537269i	−0.963242	+	0.268635i	$0.913428\pi$
$42$	−4.65762	−	0.771205i	−0.718687	−	0.119000i
$43$	−1.04125			−0.158790			−0.0793948	−	0.996843i	$-0.525299\pi$
$43$	−1.04125			−0.158790			−0.0793948	+	0.996843i	$0.525299\pi$
$44$	2.24098	+	7.72257i	0.337841	+	1.16422i
$45$		0			0
$46$	−2.41664	+	0.343552i	−0.356315	+	0.0506539i
$47$	−7.55759			−1.10239			−0.551194	−	0.834377i	$-0.685828\pi$
$47$	−7.55759			−1.10239			−0.551194	+	0.834377i	$0.685828\pi$
$48$	−1.77811	−	6.69614i	−0.256649	−	0.966505i
$49$	3.28530			0.469328
$50$		0			0
$51$	8.64180	+	2.72353i	1.21009	+	0.381371i
$52$	−2.68475	−	9.25184i	−0.372308	−	1.28300i
$53$	4.08251			0.560775			0.280388	−	0.959887i	$-0.409537\pi$
$53$	4.08251			0.560775			0.280388	+	0.959887i	$0.409537\pi$
$54$	−5.14027	+	5.25144i	−0.699502	+	0.714631i
$55$		0			0
$56$	−2.24098	−	4.96947i	−0.299464	−	0.664073i
$57$	−0.356500	+	1.13118i	−0.0472196	+	0.149828i
$58$	9.79857	−	1.39297i	1.28662	−	0.182906i
$59$		−	0.994883i		−	0.129523i	−0.997901	−	0.0647614i	$-0.979371\pi$
$59$		−	0.994883i		−	0.129523i	0.997901	−	0.0647614i	$-0.0206286\pi$
$60$		0			0
$61$			3.16761i			0.405571i	0.979223	+	0.202785i	$0.0649994\pi$
$61$			3.16761i			0.405571i	−0.979223	+	0.202785i	$0.935001\pi$
$62$	−0.843227	−	5.93151i	−0.107090	−	0.753302i
$63$	−3.31525	+	4.73724i	−0.417682	+	0.596836i
$64$	5.29615	−	5.99590i	0.662019	−	0.749487i
$65$		0			0
$66$	9.71606	+	1.60878i	1.19596	+	0.198027i
$67$	14.8728			1.81701			0.908503	−	0.417878i	$-0.137226\pi$
$67$	14.8728			1.81701			0.908503	+	0.417878i	$0.137226\pi$
$68$	2.91579	+	10.0480i	0.353592	+	1.21850i
$69$	−0.898604	+	2.85128i	−0.108179	+	0.343254i
$70$		0			0
$71$	−9.28360			−1.10176			−0.550880	−	0.834584i	$-0.685708\pi$
$71$	−9.28360			−1.10176			−0.550880	+	0.834584i	$0.685708\pi$
$72$	−8.33741	−	1.57723i	−0.982573	−	0.185879i
$73$	−11.2836			−1.32064			−0.660322	−	0.750982i	$-0.729580\pi$
$73$	−11.2836			−1.32064			−0.660322	+	0.750982i	$0.729580\pi$
$74$	1.95705	+	13.7664i	0.227502	+	1.60031i
$75$		0			0
$76$	−1.31525	+	0.381666i	−0.150869	+	0.0437801i
$77$	7.74908			0.883089
$78$	−11.6401	−	1.92736i	−1.31798	−	0.218230i
$79$		−	9.25184i		−	1.04091i	−0.853888	−	0.520456i	$-0.825762\pi$
$79$		−	9.25184i		−	1.04091i	0.853888	−	0.520456i	$-0.174238\pi$
$80$		0			0
$81$	3.08251	+	8.45566i	0.342501	+	0.939518i
$82$	0.684753	+	4.81675i	0.0756183	+	0.531921i
$83$			7.15862i			0.785760i	0.919590	+	0.392880i	$0.128521\pi$
$83$			7.15862i			0.785760i	−0.919590	+	0.392880i	$0.871479\pi$
$84$	−6.67481	−	0.152718i	−0.728282	−	0.0166630i
$85$		0			0
$86$	−1.45790	+	0.207256i	−0.157209	+	0.0223489i
$87$	3.64350	−	11.5609i	0.390624	−	1.23945i
$88$	4.67481	+	10.3666i	0.498337	+	1.10508i
$89$			0.829022i			0.0878762i	0.999034	+	0.0439381i	$0.0139904\pi$
$89$			0.829022i			0.0878762i	−0.999034	+	0.0439381i	$0.986010\pi$
$90$		0			0
$91$	−9.28360			−0.973185
$92$	−3.31525	+	0.962038i	−0.345638	+	0.100299i
$93$	−6.99830	−	2.20557i	−0.725690	−	0.228707i
$94$	−10.5817	+	1.50430i	−1.09141	+	0.155156i
$95$		0			0
$96$	−3.82243	−	9.02159i	−0.390125	−	0.920762i
$97$	1.45201			0.147429			0.0737147	−	0.997279i	$-0.476515\pi$
$97$	1.45201			0.147429			0.0737147	+	0.997279i	$0.476515\pi$
$98$	4.59986	−	0.653920i	0.464656	−	0.0660559i
$99$	6.91579	−	9.88215i	0.695063	−	0.993194i
$100$		0			0
$101$	4.20279			0.418193			0.209097	−	0.977895i	$-0.432948\pi$
$101$	4.20279			0.418193			0.209097	+	0.977895i	$0.432948\pi$
$102$	12.6418	+	2.09322i	1.25172	+	0.207259i
$103$			7.10183i			0.699764i	0.936794	+	0.349882i	$0.113778\pi$
$103$			7.10183i			0.699764i	−0.936794	+	0.349882i	$0.886222\pi$
$104$	−5.60054	−	12.4194i	−0.549179	−	1.21783i
$105$		0			0
$106$	5.71606	−	0.812600i	0.555193	−	0.0789267i
$107$			7.76293i			0.750471i	0.926930	+	0.375235i	$0.122438\pi$
$107$			7.76293i			0.750471i	−0.926930	+	0.375235i	$0.877562\pi$
$108$	−6.15180	+	8.37588i	−0.591957	+	0.805969i
$109$			20.5105i			1.96455i	0.187437	+	0.982277i	$0.439982\pi$
$109$			20.5105i			1.96455i	−0.187437	+	0.982277i	$0.560018\pi$
$110$		0			0
$111$	16.2423	+	5.11891i	1.54165	+	0.485865i
$112$	−4.12682	−	6.51188i	−0.389948	−	0.615315i
$113$			0.215805i			0.0203013i	0.999948	+	0.0101506i	$0.00323110\pi$
$113$			0.215805i			0.0203013i	−0.999948	+	0.0101506i	$0.996769\pi$
$114$	−0.273994	+	1.65476i	−0.0256619	+	0.154983i
$115$		0			0
$116$	13.4421	−	3.90070i	1.24806	−	0.362171i
$117$	−8.28530	+	11.8391i	−0.765976	+	1.09452i
$118$	−0.198026	−	1.39297i	−0.0182298	−	0.128233i
$119$	10.0825			0.924262
$120$		0			0
$121$	−5.16501			−0.469547
$122$	0.630495	+	4.43508i	0.0570823	+	0.401534i
$123$	5.68305	+	1.79106i	0.512423	+	0.161494i
$124$	−2.36127	−	8.13708i	−0.212048	−	0.730731i
$125$		0			0
$126$	−3.69888	+	7.29266i	−0.329522	+	0.649682i
$127$		−	16.5763i		−	1.47091i	−0.677574	−	0.735455i	$-0.736968\pi$
$127$		−	16.5763i		−	1.47091i	0.677574	−	0.735455i	$-0.263032\pi$
$128$	6.22189	−	9.44924i	0.549942	−	0.835203i
$129$	−0.542104	+	1.72010i	−0.0477296	+	0.151446i
$130$		0			0
$131$		−	5.61293i		−	0.490404i	−0.969472	−	0.245202i	$-0.921146\pi$
$131$		−	5.61293i		−	0.490404i	0.969472	−	0.245202i	$-0.0788543\pi$
$132$	13.9240	+	0.318579i	1.21193	+	0.0277288i
$133$			1.31976i			0.114438i
$134$	20.8240	−	2.96035i	1.79892	−	0.255736i
$135$		0			0
$136$	6.08251	+	13.4882i	0.521571	+	1.15660i
$137$		−	9.41770i		−	0.804608i	−0.915506	−	0.402304i	$-0.868209\pi$
$137$		−	9.41770i		−	0.804608i	0.915506	−	0.402304i	$-0.131791\pi$
$138$	−0.690637	+	4.17104i	−0.0587910	+	0.355063i
$139$	−6.51634			−0.552708			−0.276354	−	0.961056i	$-0.589126\pi$
$139$	−6.51634			−0.552708			−0.276354	+	0.961056i	$0.589126\pi$
$140$		0			0
$141$	−3.93468	+	12.4848i	−0.331360	+	1.05141i
$142$	−12.9983	+	1.84785i	−1.09079	+	0.155068i
$143$	19.3661			1.61947
$144$	−11.9874	−	0.548828i	−0.998954	−	0.0457357i
$145$		0			0
$146$	−15.7986	+	2.24594i	−1.30750	+	0.185875i
$147$	1.71041	−	5.42716i	0.141072	−	0.447624i
$148$	5.48026	+	18.8853i	0.450475	+	1.55237i
$149$	−7.53452			−0.617252			−0.308626	−	0.951184i	$-0.599869\pi$
$149$	−7.53452			−0.617252			−0.308626	+	0.951184i	$0.599869\pi$
$150$		0			0
$151$			9.41085i			0.765844i	0.923781	+	0.382922i	$0.125082\pi$
$151$			9.41085i			0.765844i	−0.923781	+	0.382922i	$0.874918\pi$
$152$	−1.76556	+	0.796177i	−0.143206	+	0.0645785i
$153$	8.99830	−	12.8579i	0.727469	−	1.03950i
$154$	10.8498	−	1.54241i	0.874299	−	0.124291i
$155$		0			0
$156$	−16.6813	−	0.381666i	−1.33558	−	0.0305578i
$157$			3.49699i			0.279090i	0.990216	+	0.139545i	$0.0445640\pi$
$157$			3.49699i			0.279090i	−0.990216	+	0.139545i	$0.955436\pi$
$158$	−1.84153	−	12.9538i	−0.146504	−	1.03055i
$159$	2.12546	−	6.74411i	0.168560	−	0.534842i
$160$		0			0
$161$			3.32663i			0.262175i
$162$	5.99898	+	11.2255i	0.471324	+	0.881960i
$163$	−16.9553			−1.32804			−0.664022	−	0.747713i	$-0.731152\pi$
$163$	−16.9553			−1.32804			−0.664022	+	0.747713i	$0.731152\pi$
$164$	1.91749	+	6.60781i	0.149731	+	0.515983i
$165$		0			0
$166$	1.42488	+	10.0230i	0.110592	+	0.777939i
$167$	−11.3926			−0.881584			−0.440792	−	0.897609i	$-0.645302\pi$
$167$	−11.3926			−0.881584			−0.440792	+	0.897609i	$0.645302\pi$
$168$	−9.37604	+	1.11476i	−0.723377	+	0.0860053i
$169$	−10.2011			−0.784699
$170$		0			0
$171$	1.68305	+	1.17784i	0.128706	+	0.0900720i
$172$	−2.00000	+	0.580372i	−0.152499	+	0.0442529i
$173$	−2.16501			−0.164603			−0.0823014	−	0.996607i	$-0.526227\pi$
$173$	−2.16501			−0.164603			−0.0823014	+	0.996607i	$0.526227\pi$
$174$	2.80027	−	16.9120i	0.212288	−	1.28209i
$175$		0			0
$176$	8.60878	+	13.5841i	0.648912	+	1.02394i
$177$	−1.64350	−	0.517962i	−0.123533	−	0.0389324i
$178$	0.165012	+	1.16074i	0.0123682	+	0.0870014i
$179$			5.34034i			0.399155i	0.979882	+	0.199578i	$0.0639570\pi$
$179$			5.34034i			0.399155i	−0.979882	+	0.199578i	$0.936043\pi$
$180$		0			0
$181$		−	10.7942i		−	0.802330i	−0.916006	−	0.401165i	$-0.868605\pi$
$181$		−	10.7942i		−	0.802330i	0.916006	−	0.401165i	$-0.131395\pi$
$182$	−12.9983	+	1.84785i	−0.963498	+	0.136972i
$183$	5.23274	+	1.64914i	0.386815	+	0.121908i
$184$	−4.45031	+	2.00687i	−0.328081	+	0.147948i
$185$		0			0
$186$	−10.2376	−	1.69513i	−0.750656	−	0.124293i
$187$	−21.0327			−1.53806
$188$	−14.5163	+	4.21244i	−1.05871	+	0.307224i
$189$	6.09969	+	7.94297i	0.443687	+	0.577766i
$190$		0			0
$191$	−19.7491			−1.42899			−0.714497	−	0.699639i	$-0.753344\pi$
$191$	−19.7491			−1.42899			−0.714497	+	0.699639i	$0.753344\pi$
$192$	−7.14762	−	11.8706i	−0.515835	−	0.856688i
$193$	−5.45201			−0.392444			−0.196222	−	0.980559i	$-0.562867\pi$
$193$	−5.45201			−0.392444			−0.196222	+	0.980559i	$0.562867\pi$
$194$	2.03301	−	0.289015i	0.145962	−	0.0207500i
$195$		0			0
$196$	6.31028	−	1.83115i	0.450734	−	0.130797i
$197$	22.6497			1.61372			0.806862	−	0.590740i	$-0.201164\pi$
$197$	22.6497			1.61372			0.806862	+	0.590740i	$0.201164\pi$
$198$	7.71606	−	15.2129i	0.548357	−	1.08113i
$199$		−	18.8853i		−	1.33875i	−0.742926	−	0.669373i	$-0.766563\pi$
$199$		−	18.8853i		−	1.33875i	0.742926	−	0.669373i	$-0.233437\pi$
$200$		0			0
$201$	7.74319	−	24.5692i	0.546163	−	1.73298i
$202$	5.88448	−	0.836542i	0.414031	−	0.0588589i
$203$		−	13.4882i		−	0.946687i
$204$	18.1169	+	0.414511i	1.26844	+	0.0290216i
$205$		0			0
$206$	1.41358	+	9.94353i	0.0984887	+	0.692799i
$207$	4.24234	+	2.96890i	0.294863	+	0.206353i
$208$	−10.3135	−	16.2742i	−0.715116	−	1.12841i
$209$		−	2.75310i		−	0.190436i
$210$		0			0
$211$	−10.7673			−0.741249			−0.370624	−	0.928783i	$-0.620856\pi$
$211$	−10.7673			−0.741249			−0.370624	+	0.928783i	$0.620856\pi$
$212$	7.84153	−	2.27550i	0.538558	−	0.156282i
$213$	−4.83329	+	15.3361i	−0.331171	+	1.05081i
$214$	1.54517	+	10.8692i	0.105625	+	0.743001i
$215$		0			0
$216$	−6.94619	+	12.9519i	−0.472628	+	0.881262i
$217$	−8.16501			−0.554277
$218$	4.08251	+	28.7175i	0.276502	+	1.94500i
$219$	−5.87454	+	18.6400i	−0.396965	+	1.25957i
$220$		0			0
$221$	25.1977			1.69498
$222$	23.7604	+	3.93422i	1.59469	+	0.264048i
$223$		−	6.54540i		−	0.438313i	−0.975690	−	0.219156i	$-0.929670\pi$
$223$		−	6.54540i		−	0.438313i	0.975690	−	0.219156i	$-0.0703304\pi$
$224$	−7.07427	−	8.29610i	−0.472669	−	0.554306i
$225$		0			0
$226$	0.0429548	+	0.302157i	0.00285731	+	0.0200992i
$227$		−	22.5118i		−	1.49416i	−0.664735	−	0.747080i	$-0.731455\pi$
$227$		−	22.5118i		−	1.49416i	0.664735	−	0.747080i	$-0.268545\pi$
$228$	−0.0542579	+	2.37143i	−0.00359332	+	0.157052i
$229$		−	12.8839i		−	0.851392i	−0.904866	−	0.425696i	$-0.860029\pi$
$229$		−	12.8839i		−	0.851392i	0.904866	−	0.425696i	$-0.139971\pi$
$230$		0			0
$231$	4.03438	−	12.8011i	0.265442	−	0.842251i
$232$	18.0443	−	8.13708i	1.18467	−	0.534225i
$233$			10.8510i			0.710875i	0.934700	+	0.355437i	$0.115668\pi$
$233$			10.8510i			0.710875i	−0.934700	+	0.355437i	$0.884332\pi$
$234$	−9.24404	+	18.2255i	−0.604302	+	1.19144i
$235$		0			0
$236$	−0.554526	−	1.91093i	−0.0360966	−	0.124391i
$237$	−15.2836	−	4.81675i	−0.992776	−	0.312882i
$238$	14.1169	−	2.00687i	0.915062	−	0.130086i
$239$	−6.63049			−0.428891			−0.214446	−	0.976736i	$-0.568794\pi$
$239$	−6.63049			−0.428891			−0.214446	+	0.976736i	$0.568794\pi$
$240$		0			0
$241$	−15.9519			−1.02755			−0.513775	−	0.857925i	$-0.671753\pi$
$241$	−15.9519			−1.02755			−0.513775	+	0.857925i	$0.671753\pi$
$242$	−7.23172	+	1.02807i	−0.464873	+	0.0660866i
$243$	15.5732	−	0.689915i	0.999020	−	0.0442580i
$244$	1.76556	+	6.08423i	0.113028	+	0.389503i
$245$		0			0
$246$	8.31355	+	1.37655i	0.530052	+	0.0877656i
$247$			3.29828i			0.209865i
$248$	−4.92573	−	10.9230i	−0.312784	−	0.693613i
$249$	11.8257	+	3.72697i	0.749423	+	0.236187i
$250$		0			0
$251$		−	15.2464i		−	0.962346i	−0.876626	−	0.481173i	$-0.840211\pi$
$251$		−	15.2464i		−	0.962346i	0.876626	−	0.481173i	$-0.159789\pi$
$252$	−3.72737	+	10.9470i	−0.234802	+	0.689594i
$253$		−	6.93953i		−	0.436285i
$254$	−3.29942	−	23.2091i	−0.207024	−	1.45627i
$255$		0			0
$256$	6.83067	−	14.4687i	0.426917	−	0.904291i
$257$			16.1845i			1.00956i	0.863247	+	0.504782i	$0.168427\pi$
$257$			16.1845i			1.00956i	−0.863247	+	0.504782i	$0.831573\pi$
$258$	−0.416643	+	2.51628i	−0.0259391	+	0.156657i
$259$	18.9502			1.17751
$260$		0			0
$261$	−17.2011	−	12.0378i	−1.06472	−	0.745120i
$262$	−1.11722	−	7.85886i	−0.0690222	−	0.485522i
$263$	−21.4751			−1.32421			−0.662105	−	0.749411i	$-0.730337\pi$
$263$	−21.4751			−1.32421			−0.662105	+	0.749411i	$0.730337\pi$
$264$	19.5590	−	2.32545i	1.20377	−	0.143121i
$265$		0			0
$266$	0.262691	+	1.84785i	0.0161066	+	0.113299i
$267$	1.36951	+	0.431611i	0.0838124	+	0.0264142i
$268$	28.5672	−	8.28980i	1.74502	−	0.506380i
$269$	−23.0327			−1.40433			−0.702163	−	0.712016i	$-0.747782\pi$
$269$	−23.0327			−1.40433			−0.702163	+	0.712016i	$0.747782\pi$
$270$		0			0
$271$		−	16.1914i		−	0.983556i	−0.870721	−	0.491778i	$-0.836347\pi$
$271$		−	16.1914i		−	0.983556i	0.870721	−	0.491778i	$-0.163653\pi$
$272$	11.2011	+	17.6746i	0.679166	+	1.07168i
$273$	−4.83329	+	15.3361i	−0.292524	+	0.928181i
$274$	−1.87454	−	13.1861i	−0.113245	−	0.796599i
$275$		0			0
$276$	−0.136764	+	5.97749i	−0.00823223	+	0.359803i
$277$			3.81503i			0.229223i	0.993410	+	0.114611i	$0.0365623\pi$
$277$			3.81503i			0.229223i	−0.993410	+	0.114611i	$0.963438\pi$
$278$	−9.12376	+	1.29704i	−0.547207	+	0.0777913i
$279$	−7.28700	+	10.4126i	−0.436261	+	0.623385i
$280$		0			0
$281$		−	27.9474i		−	1.66720i	−0.552368	−	0.833600i	$-0.686276\pi$
$281$		−	27.9474i		−	1.66720i	0.552368	−	0.833600i	$-0.313724\pi$
$282$	−3.02407	+	18.2636i	−0.180080	+	1.08758i
$283$	5.58924			0.332246			0.166123	−	0.986105i	$-0.446875\pi$
$283$	5.58924			0.332246			0.166123	+	0.986105i	$0.446875\pi$
$284$	−17.8316	+	5.17448i	−1.05811	+	0.307049i
$285$		0			0
$286$	27.1152	−	3.85471i	1.60335	−	0.227934i
$287$	6.63049			0.391386
$288$	−16.8933	+	1.61760i	−0.995447	+	0.0953179i
$289$	−10.3661			−0.609771
$290$		0			0
$291$	0.755956	−	2.39865i	0.0443149	−	0.140612i
$292$	−21.6731	+	6.28923i	−1.26832	+	0.368049i
$293$	−6.00000			−0.350524			−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000			−0.350524			−0.175262	+	0.984522i	$0.556077\pi$
$294$	1.31457	−	7.93921i	0.0766671	−	0.463024i
$295$		0			0
$296$	11.4321	+	25.3512i	0.664479	+	1.47351i
$297$	−12.7243	−	16.5695i	−0.738339	−	0.961458i
$298$	−10.5494	+	1.49970i	−0.611107	+	0.0868755i
$299$			8.31374i			0.480796i
$300$		0			0
$301$			2.00687i			0.115674i
$302$	1.87318	+	13.1765i	0.107789	+	0.758221i
$303$	2.18808	−	6.94281i	0.125702	−	0.398854i
$304$	−2.31355	+	1.46618i	−0.132691	+	0.0840912i
$305$		0			0
$306$	10.0396	−	19.7939i	0.573923	−	1.13154i
$307$	4.79033			0.273399			0.136699	−	0.990613i	$-0.456351\pi$
$307$	4.79033			0.273399			0.136699	+	0.990613i	$0.456351\pi$
$308$	14.8841	−	4.31917i	0.848103	−	0.246107i
$309$	11.7319	+	3.69740i	0.667404	+	0.210338i
$310$		0			0
$311$	12.8780			0.730245			0.365123	−	0.930959i	$-0.381027\pi$
$311$	12.8780			0.730245			0.365123	+	0.930959i	$0.381027\pi$
$312$	−23.4321	+	2.78594i	−1.32658	+	0.157723i
$313$	20.4022			1.15320			0.576600	−	0.817027i	$-0.304379\pi$
$313$	20.4022			1.15320			0.576600	+	0.817027i	$0.304379\pi$
$314$	0.696056	+	4.89626i	0.0392807	+	0.276312i
$315$		0			0
$316$	−5.15677	−	17.7706i	−0.290091	−	0.999673i
$317$	−5.34350			−0.300121			−0.150060	−	0.988677i	$-0.547947\pi$
$317$	−5.34350			−0.300121			−0.150060	+	0.988677i	$0.547947\pi$
$318$	1.63356	−	9.86573i	0.0916054	−	0.553243i
$319$			28.1372i			1.57538i
$320$		0			0
$321$	12.8240	+	4.04159i	0.715766	+	0.225579i
$322$	0.662146	+	4.65773i	0.0369000	+	0.259565i
$323$		−	3.58212i		−	0.199315i
$324$	10.6338	+	14.5232i	0.590765	+	0.806844i
$325$		0			0
$326$	−23.7398	+	3.37486i	−1.31483	+	0.186916i
$327$	33.8824	+	10.6783i	1.87370	+	0.590513i
$328$	4.00000	+	8.87017i	0.220863	+	0.489773i
$329$			14.5662i			0.803059i
$330$		0			0
$331$	25.1694			1.38344			0.691719	−	0.722167i	$-0.256854\pi$
$331$	25.1694			1.38344			0.691719	+	0.722167i	$0.256854\pi$
$332$	3.99006	+	13.7500i	0.218983	+	0.754630i
$333$	16.9124	−	24.1665i	0.926793	−	1.32432i
$334$	−15.9512	+	2.26763i	−0.872809	+	0.124079i
$335$		0			0
$336$	−12.9059	+	3.42706i	−0.704072	+	0.186961i
$337$	20.1616			1.09827			0.549136	−	0.835733i	$-0.314957\pi$
$337$	20.1616			1.09827			0.549136	+	0.835733i	$0.314957\pi$
$338$	−14.2829	+	2.03047i	−0.776888	+	0.110443i
$339$	0.356500	+	0.112354i	0.0193624	+	0.00610223i
$340$		0			0
$341$	17.0327			0.922371
$342$	2.59094	+	1.31414i	0.140102	+	0.0710605i
$343$		−	19.8234i		−	1.07036i
$344$	−2.68475	+	1.21069i	−0.144752	+	0.0652759i
$345$		0			0
$346$	−3.03131	+	0.430933i	−0.162964	+	0.0231671i
$347$		−	9.41442i		−	0.505392i	−0.967546	−	0.252696i	$-0.918683\pi$
$347$		−	9.41442i		−	0.505392i	0.967546	−	0.252696i	$-0.0813173\pi$
$348$	0.554526	−	24.2365i	0.0297257	−	1.29921i
$349$		−	10.3968i		−	0.556530i	−0.960504	−	0.278265i	$-0.910241\pi$
$349$		−	10.3968i		−	0.556530i	0.960504	−	0.278265i	$-0.0897593\pi$
$350$		0			0
$351$	15.2440	+	19.8507i	0.813667	+	1.05955i
$352$	14.7573	+	17.3061i	0.786568	+	0.922420i
$353$		−	20.4254i		−	1.08713i	−0.839366	−	0.543567i	$-0.817073\pi$
$353$		−	20.4254i		−	1.08713i	0.839366	−	0.543567i	$-0.182927\pi$
$354$	−2.40422	−	0.398089i	−0.127783	−	0.0211582i
$355$		0			0
$356$	0.462079	+	1.59235i	0.0244901	+	0.0843946i
$357$	5.24922	−	16.6558i	0.277818	−	0.881520i
$358$	1.06296	+	7.47720i	0.0561794	+	0.395182i
$359$	6.87107			0.362641			0.181320	−	0.983424i	$-0.441963\pi$
$359$	6.87107			0.362641			0.181320	+	0.983424i	$0.441963\pi$
$360$		0			0
$361$	−18.5311			−0.975322
$362$	−2.14853	−	15.1134i	−0.112924	−	0.794343i
$363$	−2.68904	+	8.53236i	−0.141138	+	0.447833i
$364$	−17.8316	+	5.17448i	−0.934629	+	0.271216i
$365$		0			0
$366$	7.65480	+	1.26748i	0.400123	+	0.0662520i
$367$			15.8130i			0.825431i	0.910860	+	0.412715i	$0.135420\pi$
$367$			15.8130i			0.825431i	−0.910860	+	0.412715i	$0.864580\pi$
$368$	−5.83158	+	3.69569i	−0.303992	+	0.192651i
$369$	5.91749	−	8.45566i	0.308052	−	0.440184i
$370$		0			0
$371$		−	7.86844i		−	0.408509i
$372$	−14.6714	−	0.335679i	−0.760677	−	0.0174042i
$373$		−	7.51072i		−	0.388890i	−0.980913	−	0.194445i	$-0.937709\pi$
$373$		−	7.51072i		−	0.388890i	0.980913	−	0.194445i	$-0.0622906\pi$
$374$	−29.4486	+	4.18643i	−1.52275	+	0.216475i
$375$		0			0
$376$	−19.4864	+	8.78738i	−1.00493	+	0.453175i
$377$		−	33.7091i		−	1.73610i
$378$	10.1214	+	9.90712i	0.520589	+	0.509567i
$379$	−13.1468			−0.675307			−0.337654	−	0.941270i	$-0.609633\pi$
$379$	−13.1468			−0.675307			−0.337654	+	0.941270i	$0.609633\pi$
$380$		0			0
$381$	−27.3833	−	8.63007i	−1.40289	−	0.442132i
$382$	−27.6514	+	3.93094i	−1.41477	+	0.201124i
$383$	−23.0887			−1.17978			−0.589889	−	0.807484i	$-0.700828\pi$
$383$	−23.0887			−1.17978			−0.589889	+	0.807484i	$0.700828\pi$
$384$	−12.3704	−	15.1978i	−0.631275	−	0.775559i
$385$		0			0
$386$	−7.63356	+	1.08519i	−0.388538	+	0.0552348i
$387$	2.55929	+	1.79106i	0.130096	+	0.0910447i
$388$	2.78897	−	0.809320i	0.141588	−	0.0410870i
$389$	12.9040			0.654260			0.327130	−	0.944979i	$-0.393919\pi$
$389$	12.9040			0.654260			0.327130	+	0.944979i	$0.393919\pi$
$390$		0			0
$391$		−	9.02919i		−	0.456626i
$392$	8.47077	−	3.81989i	0.427838	−	0.192934i
$393$	−9.27229	−	2.92224i	−0.467725	−	0.147407i
$394$	31.7127	−	4.50829i	1.59766	−	0.227125i
$395$		0			0
$396$	7.77550	−	22.8360i	0.390733	−	1.14755i
$397$		−	18.1459i		−	0.910719i	−0.890308	−	0.455359i	$-0.849511\pi$
$397$		−	18.1459i		−	0.910719i	0.890308	−	0.455359i	$-0.150489\pi$
$398$	−3.75902	−	26.4420i	−0.188423	−	1.32542i
$399$	2.18019	+	0.687103i	0.109146	+	0.0343982i
$400$		0			0
$401$			33.7433i			1.68506i	0.538651	+	0.842529i	$0.318934\pi$
$401$			33.7433i			1.68506i	−0.538651	+	0.842529i	$0.681066\pi$
$402$	5.95116	−	35.9415i	0.296817	−	1.79260i
$403$	−20.4056			−1.01647
$404$	8.07256	−	2.34254i	0.401625	−	0.116546i
$405$		0			0
$406$	−2.68475	−	18.8853i	−0.133242	−	0.937264i
$407$	−39.5311			−1.95948
$408$	25.4486	−	3.02569i	1.25989	−	0.149794i
$409$	31.6480			1.56489			0.782446	−	0.622718i	$-0.213972\pi$
$409$	31.6480			1.56489			0.782446	+	0.622718i	$0.213972\pi$
$410$		0			0
$411$	−15.5576	−	4.90310i	−0.767399	−	0.241852i
$412$	3.95841	+	13.6409i	0.195017	+	0.672041i
$413$	−1.91749			−0.0943537
$414$	6.53080	+	3.31246i	0.320971	+	0.162798i
$415$		0			0
$416$	−17.6796	−	20.7332i	−0.866816	−	1.01653i
$417$	−3.39258	+	10.7647i	−0.166135	+	0.527149i
$418$	−0.547989	−	3.85471i	−0.0268030	−	0.188540i
$419$		−	29.8954i		−	1.46049i	−0.683188	−	0.730243i	$-0.739407\pi$
$419$		−	29.8954i		−	1.46049i	0.683188	−	0.730243i	$-0.260593\pi$
$420$		0			0
$421$			6.86330i			0.334497i	0.985915	+	0.167248i	$0.0534882\pi$
$421$			6.86330i			0.334497i	−0.985915	+	0.167248i	$0.946512\pi$
$422$	−15.0756	+	2.14316i	−0.733870	+	0.104327i
$423$	18.5758	+	12.9998i	0.903185	+	0.632073i
$424$	10.5263	−	4.74682i	0.511201	−	0.230526i
$425$		0			0
$426$	−3.71470	+	22.4346i	−0.179978	+	1.08696i
$427$	6.10511			0.295447
$428$	4.32689	+	14.9108i	0.209148	+	0.720738i
$429$	10.0825	−	31.9919i	0.486788	−	1.54458i
$430$		0			0
$431$	−20.0226			−0.964455			−0.482228	−	0.876046i	$-0.660172\pi$
$431$	−20.0226			−0.964455			−0.482228	+	0.876046i	$0.660172\pi$
$432$	−7.14762	+	19.5170i	−0.343890	+	0.939010i
$433$	−10.2112			−0.490717			−0.245358	−	0.969432i	$-0.578906\pi$
$433$	−10.2112			−0.490717			−0.245358	+	0.969432i	$0.578906\pi$
$434$	−11.4321	+	1.62520i	−0.548760	+	0.0780121i
$435$		0			0
$436$	11.4321	+	39.3959i	0.547500	+	1.88672i
$437$	1.18189			0.0565373
$438$	−4.51497	+	27.2678i	−0.215734	+	1.30291i
$439$			33.6933i			1.60809i	0.594566	+	0.804047i	$0.297324\pi$
$439$			33.6933i			1.60809i	−0.594566	+	0.804047i	$0.702676\pi$
$440$		0			0
$441$	−8.07492	−	5.65104i	−0.384520	−	0.269097i
$442$	35.2802	−	5.01546i	1.67811	−	0.238561i
$443$			4.46465i			0.212122i	0.994360	+	0.106061i	$0.0338239\pi$
$443$			4.46465i			0.212122i	−0.994360	+	0.106061i	$0.966176\pi$
$444$	34.0509	+	0.779077i	1.61598	+	0.0369734i
$445$		0			0
$446$	−1.30283	−	9.16445i	−0.0616906	−	0.433949i
$447$	−3.92267	+	12.4467i	−0.185536	+	0.588707i
$448$	−11.5562	−	10.2076i	−0.545980	−	0.482263i
$449$		−	27.5500i		−	1.30016i	−0.759865	−	0.650081i	$-0.774735\pi$
$449$		−	27.5500i		−	1.30016i	0.759865	−	0.650081i	$-0.225265\pi$
$450$		0			0
$451$	−13.8316			−0.651304
$452$	0.120285	+	0.414511i	0.00565774	+	0.0194970i
$453$	15.5463	+	4.89954i	0.730428	+	0.230200i
$454$	−4.48084	−	31.5196i	−0.210296	−	1.47929i
$455$		0			0
$456$	0.396052	+	3.33113i	0.0185468	+	0.155994i
$457$	11.5016			0.538020			0.269010	−	0.963137i	$-0.413303\pi$
$457$	11.5016			0.538020			0.269010	+	0.963137i	$0.413303\pi$
$458$	−2.56447	−	18.0392i	−0.119830	−	0.842917i
$459$	−16.5559	−	21.5589i	−0.772763	−	1.00628i
$460$		0			0
$461$	−8.25929			−0.384673			−0.192337	−	0.981329i	$-0.561607\pi$
$461$	−8.25929			−0.384673			−0.192337	+	0.981329i	$0.561607\pi$
$462$	3.10069	−	18.7263i	0.144257	−	0.871227i
$463$			11.7199i			0.544669i	0.962203	+	0.272334i	$0.0877957\pi$
$463$			11.7199i			0.544669i	−0.962203	+	0.272334i	$0.912204\pi$
$464$	23.6449	−	14.9846i	1.09769	−	0.695644i
$465$		0			0
$466$	2.15984	+	15.1929i	0.100052	+	0.703799i
$467$			17.1895i			0.795437i	0.917508	+	0.397718i	$0.130198\pi$
$467$			17.1895i			0.795437i	−0.917508	+	0.397718i	$0.869802\pi$
$468$	−9.31525	+	27.3581i	−0.430597	+	1.26463i
$469$		−	28.6653i		−	1.32364i
$470$		0			0
$471$	5.77686	+	1.82062i	0.266184	+	0.0838900i
$472$	−1.15677	−	2.56519i	−0.0532448	−	0.118073i
$473$		−	4.18643i		−	0.192492i
$474$	−22.3579	−	3.70199i	−1.02693	−	0.170038i
$475$		0			0
$476$	19.3661	−	5.61977i	0.887644	−	0.257582i
$477$	−10.0344	−	7.02232i	−0.459442	−	0.321530i
$478$	−9.28360	+	1.31976i	−0.424622	+	0.0603645i
$479$	−11.5379			−0.527181			−0.263591	−	0.964635i	$-0.584907\pi$
$479$	−11.5379			−0.527181			−0.263591	+	0.964635i	$0.584907\pi$
$480$		0			0
$481$	47.3593			2.15940
$482$	−22.3348	+	3.17513i	−1.01732	+	0.144623i
$483$	5.49543	+	1.73193i	0.250051	+	0.0788056i
$484$	−9.92076	+	2.87887i	−0.450944	+	0.130858i
$485$		0			0
$486$	21.6673	−	4.06573i	0.982847	−	0.184425i
$487$			33.1015i			1.49997i	0.661455	+	0.749985i	$0.269939\pi$
$487$			33.1015i			1.49997i	−0.661455	+	0.749985i	$0.730061\pi$
$488$	3.68305	+	8.16732i	0.166724	+	0.369717i
$489$	−8.82740	+	28.0094i	−0.399189	+	1.26663i
$490$		0			0
$491$			21.3635i			0.964121i	0.876138	+	0.482061i	$0.160112\pi$
$491$			21.3635i			0.964121i	−0.876138	+	0.482061i	$0.839888\pi$
$492$	11.9141	+	0.272592i	0.537129	+	0.0122894i
$493$			36.6099i			1.64883i
$494$	0.656505	+	4.61805i	0.0295375	+	0.207776i
$495$		0			0
$496$	−9.07086	−	14.3133i	−0.407294	−	0.642685i
$497$			17.8928i			0.802602i
$498$	17.2994	+	2.86442i	0.775206	+	0.128358i
$499$	14.8464			0.664614			0.332307	−	0.943171i	$-0.392173\pi$
$499$	14.8464			0.664614			0.332307	+	0.943171i	$0.392173\pi$
$500$		0			0
$501$	−5.93128	+	18.8200i	−0.264990	+	0.840816i
$502$	−3.03472	−	21.3471i	−0.135446	−	0.952767i
$503$	−1.86841			−0.0833084			−0.0416542	−	0.999132i	$-0.513263\pi$
$503$	−1.86841			−0.0833084			−0.0416542	+	0.999132i	$0.513263\pi$
$504$	−3.03989	+	16.0692i	−0.135408	+	0.715777i
$505$		0			0
$506$	−1.38127	−	9.71629i	−0.0614051	−	0.431942i
$507$	−5.31096	+	16.8517i	−0.235868	+	0.748411i
$508$	−9.23928	−	31.8392i	−0.409927	−	1.41263i
$509$	−1.62879			−0.0721950			−0.0360975	−	0.999348i	$-0.511493\pi$
$509$	−1.62879			−0.0721950			−0.0360975	+	0.999348i	$0.511493\pi$
$510$		0			0
$511$			21.7475i			0.962053i
$512$	6.68396	−	21.6177i	0.295392	−	0.955376i
$513$	2.82198	−	2.16710i	0.124594	−	0.0956800i
$514$	3.22144	+	22.6605i	0.142092	+	0.999514i
$515$		0			0
$516$	−0.0825061	+	3.60606i	−0.00363213	+	0.158748i
$517$		−	30.3858i		−	1.33637i
$518$	26.5328	−	3.77192i	1.16578	−	0.165729i
$519$	−1.12716	+	3.57650i	−0.0494770	+	0.156991i
$520$		0			0
$521$		−	7.82768i		−	0.342937i	−0.985190	−	0.171469i	$-0.945149\pi$
$521$		−	7.82768i		−	0.342937i	0.985190	−	0.171469i	$-0.0548512\pi$
$522$	−26.4799	−	13.4308i	−1.15899	−	0.587848i
$523$	32.2423			1.40986			0.704930	−	0.709277i	$-0.250979\pi$
$523$	32.2423			1.40986			0.704930	+	0.709277i	$0.250979\pi$
$524$	−3.12852	−	10.7811i	−0.136670	−	0.470975i
$525$		0			0
$526$	−30.0680	+	4.27449i	−1.31103	+	0.186377i
$527$	22.1616			0.965375
$528$	26.9223	−	7.14904i	1.17164	−	0.311122i
$529$	−20.0209			−0.870474
$530$		0			0
$531$	−1.71130	+	2.44532i	−0.0742640	+	0.106118i
$532$	0.735607	+	2.53495i	0.0318926	+	0.109904i
$533$	16.5706			0.717752
$534$	2.00340	+	0.331722i	0.0866958	+	0.0143550i
$535$		0			0
$536$	38.3479	−	17.2930i	1.65638	−	0.746943i
$537$	8.82198	+	2.78032i	0.380697	+	0.119980i
$538$	−32.2489	+	4.58452i	−1.39035	+	0.197653i
$539$			13.2088i			0.568942i
$540$		0			0
$541$		−	3.25040i		−	0.139746i	−0.997556	−	0.0698728i	$-0.977741\pi$
$541$		−	3.25040i		−	0.139746i	0.997556	−	0.0698728i	$-0.0222593\pi$
$542$	−3.22280	−	22.6701i	−0.138431	−	0.973765i
$543$	−17.8316	−	5.61977i	−0.765227	−	0.241167i
$544$	19.2011	+	22.5174i	0.823240	+	0.965426i
$545$		0			0
$546$	−3.71470	+	22.4346i	−0.158975	+	0.960113i
$547$	−10.3248			−0.441459			−0.220729	−	0.975335i	$-0.570844\pi$
$547$	−10.3248			−0.441459			−0.220729	+	0.975335i	$0.570844\pi$
$548$	−5.24922	−	18.0892i	−0.224236	−	0.772731i
$549$	5.44861	−	7.78565i	0.232541	−	0.332284i
$550$		0			0
$551$	−4.79210			−0.204150
$552$	0.998298	+	8.39653i	0.0424904	+	0.357380i
$553$	−17.8316			−0.758276
$554$	0.759359	+	5.34156i	0.0322621	+	0.226941i
$555$		0			0
$556$	−12.5163	+	3.63207i	−0.530811	+	0.154034i
$557$	8.33343			0.353099			0.176549	−	0.984292i	$-0.443506\pi$
$557$	8.33343			0.353099			0.176549	+	0.984292i	$0.443506\pi$
$558$	−8.13023	+	16.0295i	−0.344180	+	0.678581i
$559$			5.01546i			0.212131i
$560$		0			0
$561$	−10.9502	+	34.7450i	−0.462316	+	1.46693i
$562$	−5.56277	−	39.1301i	−0.234651	−	1.65060i
$563$			14.0982i			0.594166i	0.954852	+	0.297083i	$0.0960138\pi$
$563$			14.0982i			0.594166i	−0.954852	+	0.297083i	$0.903986\pi$
$564$	−0.598843	+	26.1734i	−0.0252158	+	1.10210i
$565$		0			0
$566$	7.82570	−	1.11251i	0.328939	−	0.0467622i
$567$	16.2971	−	5.94109i	0.684412	−	0.249502i
$568$	−23.9367	+	10.7942i	−1.00436	+	0.452916i
$569$			9.37801i			0.393147i	0.980489	+	0.196573i	$0.0629814\pi$
$569$			9.37801i			0.393147i	−0.980489	+	0.196573i	$0.937019\pi$
$570$		0			0
$571$	10.1967			0.426717			0.213359	−	0.976974i	$-0.431560\pi$
$571$	10.1967			0.426717			0.213359	+	0.976974i	$0.431560\pi$
$572$	37.1977	−	10.7942i	1.55531	−	0.451330i
$573$	−10.2819	+	32.6245i	−0.429532	+	1.36291i
$574$	9.28360	−	1.31976i	0.387490	−	0.0550858i
$575$		0			0
$576$	−23.3309	+	5.62737i	−0.972122	+	0.234474i
$577$	−14.9762			−0.623466			−0.311733	−	0.950170i	$-0.600910\pi$
$577$	−14.9762			−0.623466			−0.311733	+	0.950170i	$0.600910\pi$
$578$	−14.5140	+	2.06331i	−0.603701	+	0.0858225i
$579$	−2.83846	+	9.00647i	−0.117962	+	0.374296i
$580$		0			0
$581$	13.7972			0.572405
$582$	0.581002	−	3.50891i	0.0240833	−	0.145449i
$583$			16.4140i			0.679799i
$584$	−29.0935	+	13.1197i	−1.20390	+	0.542897i
$585$		0			0
$586$	−8.40082	+	1.19427i	−0.347035	+	0.0493347i
$587$			35.1368i			1.45025i	0.688617	+	0.725125i	$0.258218\pi$
$587$			35.1368i			1.45025i	−0.688617	+	0.725125i	$0.741782\pi$
$588$	0.260318	−	11.3776i	0.0107353	−	0.469205i
$589$			2.90087i			0.119528i
$590$		0			0
$591$	11.7920	−	37.4162i	0.485059	−	1.53910i
$592$	21.0526	+	33.2197i	0.865255	+	1.36532i
$593$			11.6209i			0.477214i	0.971116	+	0.238607i	$0.0766908\pi$
$593$			11.6209i			0.477214i	−0.971116	+	0.238607i	$0.923309\pi$
$594$	−21.1138	−	20.6668i	−0.866310	−	0.847970i
$595$		0			0
$596$	−14.4720	+	4.19958i	−0.592797	+	0.172021i
$597$	−31.1977	−	9.83221i	−1.27684	−	0.402405i
$598$	1.65480	+	11.6404i	0.0676699	+	0.476010i
$599$	9.69953			0.396312			0.198156	−	0.980170i	$-0.436505\pi$
$599$	9.69953			0.396312			0.198156	+	0.980170i	$0.436505\pi$
$600$		0			0
$601$	0.585768			0.0238940			0.0119470	−	0.999929i	$-0.496197\pi$
$601$	0.585768			0.0238940			0.0119470	+	0.999929i	$0.496197\pi$
$602$	0.399455	+	2.80989i	0.0162806	+	0.114522i
$603$	−36.5559	−	25.5828i	−1.48867	−	1.04181i
$604$	5.24541	+	18.0760i	0.213433	+	0.735503i
$605$		0			0
$606$	1.68169	−	10.1564i	0.0683139	−	0.412576i
$607$			22.9594i			0.931894i	0.884813	+	0.465947i	$0.154286\pi$
$607$			22.9594i			0.931894i	−0.884813	+	0.465947i	$0.845714\pi$
$608$	−2.94744	+	2.51335i	−0.119535	+	0.101930i
$609$	−22.2819	−	7.02232i	−0.902908	−	0.284559i
$610$		0			0
$611$			36.4030i			1.47271i
$612$	10.1169	−	29.7124i	0.408951	−	1.20105i
$613$			4.10130i			0.165650i	0.996564	+	0.0828250i	$0.0263943\pi$
$613$			4.10130i			0.165650i	−0.996564	+	0.0828250i	$0.973606\pi$
$614$	6.70712	−	0.953488i	0.270677	−	0.0384797i
$615$		0			0
$616$	19.9801	−	9.01003i	0.805022	−	0.363024i
$617$			14.1493i			0.569630i	0.958583	+	0.284815i	$0.0919322\pi$
$617$			14.1493i			0.569630i	−0.958583	+	0.284815i	$0.908068\pi$
$618$	17.1622	+	2.84170i	0.690365	+	0.114310i
$619$	−10.1108			−0.406386			−0.203193	−	0.979139i	$-0.565132\pi$
$619$	−10.1108			−0.406386			−0.203193	+	0.979139i	$0.565132\pi$
$620$		0			0
$621$	7.11317	−	5.46246i	0.285441	−	0.219201i
$622$	18.0310	−	2.56330i	0.722976	−	0.102779i
$623$	1.59782			0.0640153
$624$	−32.2536	+	8.56473i	−1.29118	+	0.342864i
$625$		0			0
$626$	28.5658	−	4.06094i	1.14172	−	0.162308i
$627$	−4.54799	−	1.43334i	−0.181629	−	0.0572419i
$628$	1.94915	+	6.71689i	0.0777794	+	0.268033i
$629$	−51.4349			−2.05084
$630$		0			0
$631$			28.7572i			1.14481i	0.819972	+	0.572404i	$0.193989\pi$
$631$			28.7572i			1.14481i	−0.819972	+	0.572404i	$0.806011\pi$
$632$	−10.7573	−	23.8548i	−0.427903	−	0.948893i
$633$	−5.60572	+	17.7870i	−0.222807	+	0.706970i
$634$	−7.48162	+	1.06359i	−0.297133	+	0.0422407i
$635$		0			0
$636$	0.323487	−	14.1385i	0.0128271	−	0.560629i
$637$		−	15.8245i		−	0.626988i
$638$	5.60054	+	39.3959i	0.221728	+	1.55970i
$639$	22.8181	+	15.9687i	0.902671	+	0.631713i
$640$		0			0
$641$			35.7751i			1.41303i	0.707698	+	0.706515i	$0.249734\pi$
$641$			35.7751i			1.41303i	−0.707698	+	0.706515i	$0.750266\pi$
$642$	18.7598	+	3.10623i	0.740390	+	0.122593i
$643$	4.64793			0.183296			0.0916481	−	0.995791i	$-0.470786\pi$
$643$	4.64793			0.183296			0.0916481	+	0.995791i	$0.470786\pi$
$644$	1.85419	+	6.38966i	0.0730653	+	0.251788i
$645$		0			0
$646$	−0.713001	−	5.01546i	−0.0280526	−	0.197330i
$647$	6.90109			0.271310			0.135655	−	0.990756i	$-0.456686\pi$
$647$	6.90109			0.271310			0.135655	+	0.990756i	$0.456686\pi$
$648$	17.7795	+	18.2179i	0.698444	+	0.715665i
$649$	4.00000			0.157014
$650$		0			0
$651$	−4.25092	+	13.4882i	−0.166607	+	0.528645i
$652$	−32.5672	+	9.45054i	−1.27543	+	0.370112i
$653$	16.8181			0.658144			0.329072	−	0.944305i	$-0.393264\pi$
$653$	16.8181			0.658144			0.329072	+	0.944305i	$0.393264\pi$
$654$	49.5655	+	8.20701i	1.93816	+	0.320919i
$655$		0			0
$656$	7.36610	+	11.6233i	0.287598	+	0.453812i
$657$	27.7339	+	19.4089i	1.08200	+	0.757214i
$658$	2.89931	+	20.3946i	0.113027	+	0.795065i
$659$			15.3712i			0.598779i	0.954131	+	0.299389i	$0.0967830\pi$
$659$			15.3712i			0.598779i	−0.954131	+	0.299389i	$0.903217\pi$
$660$		0			0
$661$			14.7252i			0.572743i	0.958119	+	0.286372i	$0.0924492\pi$
$661$			14.7252i			0.572743i	−0.958119	+	0.286372i	$0.907551\pi$
$662$	35.2406	−	5.00983i	1.36967	−	0.194713i
$663$	13.1186	−	41.6254i	0.509484	−	1.61660i
$664$	8.32349	+	18.4577i	0.323014	+	0.716297i
$665$		0			0
$666$	18.8694	−	37.2028i	0.731176	−	1.44158i
$667$	−12.0791			−0.467705
$668$	−21.8824	+	6.34998i	−0.846657	+	0.245688i
$669$	−10.8127	−	3.40771i	−0.418043	−	0.131750i
$670$		0			0
$671$	−12.7356			−0.491653
$672$	−17.3878	+	7.36719i	−0.670749	+	0.284195i
$673$	44.9434			1.73244			0.866220	−	0.499663i	$-0.166543\pi$
$673$	44.9434			1.73244			0.866220	+	0.499663i	$0.166543\pi$
$674$	28.2290	−	4.01305i	1.08734	−	0.154577i
$675$		0			0
$676$	−19.5939	+	5.68587i	−0.753610	+	0.218687i
$677$	−31.3401			−1.20450			−0.602249	−	0.798308i	$-0.705728\pi$
$677$	−31.3401			−1.20450			−0.602249	+	0.798308i	$0.705728\pi$
$678$	0.521513	+	0.0863516i	0.0200286	+	0.00331631i
$679$		−	2.79854i		−	0.107398i
$680$		0			0
$681$	−37.1884	−	11.7202i	−1.42506	−	0.449120i
$682$	23.8481	−	3.39026i	0.913190	−	0.129820i
$683$			6.76121i			0.258710i	0.991598	+	0.129355i	$0.0412907\pi$
$683$			6.76121i			0.258710i	−0.991598	+	0.129355i	$0.958709\pi$
$684$	3.88925	+	1.32426i	0.148709	+	0.0506344i
$685$		0			0
$686$	−3.94574	−	27.7555i	−0.150649	−	1.05971i
$687$	−21.2836	−	6.70770i	−0.812020	−	0.255915i
$688$	−3.51804	+	2.22951i	−0.134124	+	0.0849994i
$689$		−	19.6644i		−	0.749155i
$690$		0			0
$691$	14.4304			0.548959			0.274480	−	0.961593i	$-0.411494\pi$
$691$	14.4304			0.548959			0.274480	+	0.961593i	$0.411494\pi$
$692$	−4.15847	+	1.20673i	−0.158081	+	0.0458730i
$693$	−19.0464	−	13.3292i	−0.723514	−	0.506334i
$694$	−1.87389	−	13.1815i	−0.0711317	−	0.500362i
$695$		0			0
$696$	−4.04772	−	34.0447i	−0.153428	−	1.29046i
$697$	−17.9966			−0.681670
$698$	−2.06943	−	14.5570i	−0.0783291	−	0.550990i
$699$	17.9254	+	5.64934i	0.678001	+	0.213677i
$700$		0			0
$701$	9.83499			0.371462			0.185731	−	0.982601i	$-0.440535\pi$
$701$	9.83499			0.371462			0.185731	+	0.982601i	$0.440535\pi$
$702$	25.2949	+	24.7594i	0.954694	+	0.934483i
$703$		−	6.73263i		−	0.253926i
$704$	24.1069	+	21.2936i	0.908565	+	0.802532i
$705$		0			0
$706$	−4.06556	−	28.5983i	−0.153009	−	1.07631i
$707$		−	8.10028i		−	0.304642i
$708$	−3.44547	−	0.0788318i	−0.129489	−	0.00296268i
$709$			20.4277i			0.767180i	0.923503	+	0.383590i	$0.125312\pi$
$709$			20.4277i			0.767180i	−0.923503	+	0.383590i	$0.874688\pi$
$710$		0			0
$711$	−15.9141	+	22.7401i	−0.596825	+	0.852819i
$712$	0.963923	+	2.13754i	0.0361245	+	0.0801077i
$713$			7.31201i			0.273837i
$714$	4.03438	−	24.3652i	0.150983	−	0.911847i
$715$		0			0
$716$	2.97659	+	10.2575i	0.111240	+	0.383341i
$717$	−3.45201	+	10.9533i	−0.128918	+	0.409057i
$718$	9.62043	−	1.36765i	0.359031	−	0.0510401i
$719$	28.2338			1.05294			0.526471	−	0.850193i	$-0.323515\pi$
$719$	28.2338			1.05294			0.526471	+	0.850193i	$0.323515\pi$
$720$		0			0
$721$	13.6878			0.509759
$722$	−25.9461	+	3.68851i	−0.965613	+	0.137272i
$723$	−8.30497	+	26.3517i	−0.308865	+	0.980032i
$724$	−6.01648	−	20.7332i	−0.223601	−	0.770543i
$725$		0			0
$726$	−2.06671	+	12.4817i	−0.0767027	+	0.463239i
$727$		−	28.1339i		−	1.04343i	−0.853120	−	0.521714i	$-0.825293\pi$
$727$		−	28.1339i		−	1.04343i	0.853120	−	0.521714i	$-0.174707\pi$
$728$	−23.9367	+	10.7942i	−0.887153	+	0.400061i
$729$	6.96811	−	26.0854i	0.258078	−	0.966124i
$730$		0			0
$731$		−	5.44707i		−	0.201467i
$732$	10.9701	+	0.250993i	0.405465	+	0.00927696i
$733$			10.2296i			0.377840i	0.981993	+	0.188920i	$0.0604986\pi$
$733$			10.2296i			0.377840i	−0.981993	+	0.188920i	$0.939501\pi$
$734$	3.14748	+	22.1403i	0.116176	+	0.817214i
$735$		0			0
$736$	−7.42941	+	6.33522i	−0.273852	+	0.233519i
$737$			59.7973i			2.20266i
$738$	6.60225	−	13.0169i	0.243032	−	0.479159i
$739$	−48.0440			−1.76733			−0.883664	−	0.468121i	$-0.844931\pi$
$739$	−48.0440			−1.76733			−0.883664	+	0.468121i	$0.844931\pi$
$740$		0			0
$741$	5.44861	+	1.71717i	0.200160	+	0.0630819i
$742$	−1.56617	−	11.0169i	−0.0574959	−	0.404443i
$743$	35.9667			1.31949			0.659745	−	0.751489i	$-0.270664\pi$
$743$	35.9667			1.31949			0.659745	+	0.751489i	$0.270664\pi$
$744$	−20.6088	+	2.45026i	−0.755555	+	0.0898310i
$745$		0			0
$746$	−1.49497	−	10.5160i	−0.0547346	−	0.385019i
$747$	12.3135	−	17.5951i	0.450529	−	0.643772i
$748$	−40.3988	+	11.7232i	−1.47713	+	0.428641i
$749$	14.9619			0.546697
$750$		0			0
$751$			26.4357i			0.964654i	0.875991	+	0.482327i	$0.160208\pi$
$751$			26.4357i			0.964654i	−0.875991	+	0.482327i	$0.839792\pi$
$752$	−25.5345	+	16.1822i	−0.931148	+	0.590104i
$753$	−25.1864	−	7.93770i	−0.917843	−	0.289266i
$754$	−6.70960	−	47.1973i	−0.244349	−	1.71882i
$755$		0			0
$756$	16.1433	+	11.8567i	0.587126	+	0.431225i
$757$		−	24.6881i		−	0.897303i	−0.893707	−	0.448652i	$-0.851904\pi$
$757$		−	24.6881i		−	0.897303i	0.893707	−	0.448652i	$-0.148096\pi$
$758$	−18.4074	+	2.61680i	−0.668585	+	0.0950465i
$759$	−11.4638	−	3.61290i	−0.416109	−	0.131140i
$760$		0			0
$761$		−	46.5273i		−	1.68661i	−0.537434	−	0.843306i	$-0.680606\pi$
$761$		−	46.5273i		−	1.68661i	0.537434	−	0.843306i	$-0.319394\pi$
$762$	−40.0581	−	6.63278i	−1.45115	−	0.240280i
$763$	39.5311			1.43112
$764$	−37.9333	+	11.0077i	−1.37238	+	0.398245i
$765$		0			0
$766$	−32.3273	+	4.59568i	−1.16803	+	0.166049i
$767$	−4.79210			−0.173033
$768$	−20.3453	−	18.8167i	−0.734148	−	0.678990i
$769$	36.8643			1.32936			0.664680	−	0.747129i	$-0.268568\pi$
$769$	36.8643			1.32936			0.664680	+	0.747129i	$0.268568\pi$
$770$		0			0
$771$	26.7361	+	8.42609i	0.962876	+	0.303458i
$772$	−10.4720	+	3.03883i	−0.376896	+	0.109370i
$773$	−41.5537			−1.49458			−0.747292	−	0.664496i	$-0.768646\pi$
$773$	−41.5537			−1.49458			−0.747292	+	0.664496i	$0.768646\pi$
$774$	3.93986	+	1.99832i	0.141615	+	0.0718280i
$775$		0			0
$776$	3.74385	−	1.68829i	0.134396	−	0.0606059i
$777$	9.86596	−	31.3048i	0.353939	−	1.12305i
$778$	18.0674	−	2.56847i	0.647747	−	0.0920842i
$779$		−	2.35569i		−	0.0844013i
$780$		0			0
$781$		−	37.3254i		−	1.33561i
$782$	−1.79721	−	12.6421i	−0.0642681	−	0.452080i
$783$	−28.8412	+	22.1482i	−1.03070	+	0.791512i
$784$	11.0999	−	7.03442i	0.396425	−	0.251229i
$785$		0			0
$786$	−13.5641	−	2.24594i	−0.483816	−	0.0801099i
$787$	48.4300			1.72634			0.863171	−	0.504912i	$-0.168475\pi$
$787$	48.4300			1.72634			0.863171	+	0.504912i	$0.168475\pi$
$788$	43.5047	−	12.6245i	1.54979	−	0.449727i
$789$	−11.1805	+	35.4758i	−0.398036	+	1.26297i
$790$		0			0
$791$	0.415934			0.0147889
$792$	6.34138	−	33.5212i	0.225331	−	1.19112i
$793$	15.2576			0.541813
$794$	−3.61185	−	25.4068i	−0.128180	−	0.901653i
$795$		0			0
$796$	−10.5263	−	36.2743i	−0.373094	−	1.28571i
$797$	32.0757			1.13618			0.568090	−	0.822967i	$-0.307683\pi$
$797$	32.0757			1.13618			0.568090	+	0.822967i	$0.307683\pi$
$798$	3.18932	+	0.528085i	0.112901	+	0.0186940i
$799$		−	39.5357i		−	1.39867i
$800$		0			0
$801$	1.42600	−	2.03765i	0.0503853	−	0.0719968i
$802$	6.71640	+	47.2452i	0.237164	+	1.66828i
$803$		−	45.3665i		−	1.60095i
$804$	1.17848	−	51.5075i	0.0415619	−	1.81653i
$805$		0			0
$806$	−28.5706	+	4.06162i	−1.00636	+	0.143064i
$807$	−11.9914	+	38.0489i	−0.422118	+	1.33938i
$808$	10.8364	−	4.88668i	0.381224	−	0.171913i
$809$		−	1.09505i		−	0.0385001i	−0.999815	−	0.0192500i	$-0.993872\pi$
$809$		−	1.09505i		−	0.0385001i	0.999815	−	0.0192500i	$-0.00612785\pi$
$810$		0			0
$811$	3.56617			0.125225			0.0626126	−	0.998038i	$-0.480057\pi$
$811$	3.56617			0.125225			0.0626126	+	0.998038i	$0.480057\pi$
$812$	−7.51804	−	25.9077i	−0.263831	−	0.909181i
$813$	−26.7474	−	8.42966i	−0.938071	−	0.295641i
$814$	−55.3489	+	7.86844i	−1.93998	+	0.275789i
$815$		0			0
$816$	35.0293	−	9.30178i	1.22627	−	0.325627i
$817$	0.713001			0.0249447
$818$	44.3115	−	6.29935i	1.54932	−	0.220252i
$819$	22.8181	+	15.9687i	0.797329	+	0.557992i
$820$		0			0
$821$	−47.0327			−1.64145			−0.820726	−	0.571322i	$-0.806431\pi$
$821$	−47.0327			−1.64145			−0.820726	+	0.571322i	$0.806431\pi$
$822$	−22.7587	−	3.76836i	−0.793800	−	0.131437i
$823$		−	30.2235i		−	1.05353i	−0.850012	−	0.526763i	$-0.823405\pi$
$823$		−	30.2235i		−	1.05353i	0.850012	−	0.526763i	$-0.176595\pi$
$824$	8.25746	+	18.3113i	0.287662	+	0.637903i
$825$		0			0
$826$	−2.68475	+	0.381666i	−0.0934145	+	0.0132799i
$827$		−	31.2229i		−	1.08573i	−0.839821	−	0.542864i	$-0.817340\pi$
$827$		−	31.2229i		−	1.08573i	0.839821	−	0.542864i	$-0.182660\pi$
$828$	9.80334	+	3.33797i	0.340689	+	0.116002i
$829$		−	42.0990i		−	1.46216i	−0.682292	−	0.731080i	$-0.739017\pi$
$829$		−	42.0990i		−	1.46216i	0.682292	−	0.731080i	$-0.260983\pi$
$830$		0			0
$831$	6.30224	+	1.98620i	0.218622	+	0.0689006i
$832$	−28.8807	−	25.5102i	−1.00126	−	0.884409i
$833$			17.1863i			0.595468i
$834$	−2.60742	+	15.7473i	−0.0902876	+	0.545284i
$835$		0			0
$836$	−1.53452	−	5.28805i	−0.0530724	−	0.182891i
$837$	13.4073	+	17.4588i	0.463424	+	0.603466i
$838$	−5.95051	−	41.8576i	−0.205557	−	1.44595i
$839$	14.0599			0.485402			0.242701	−	0.970101i	$-0.421967\pi$
$839$	14.0599			0.485402			0.242701	+	0.970101i	$0.421967\pi$
$840$		0			0
$841$	19.9762			0.688834
$842$	1.36610	+	9.60956i	0.0470790	+	0.331167i
$843$	−46.1677	−	14.5501i	−1.59010	−	0.501134i
$844$	−20.6813	+	6.00144i	−0.711881	+	0.206578i
$845$		0			0
$846$	28.5961	+	14.5041i	0.983156	+	0.498662i
$847$			9.95482i			0.342052i
$848$	13.7934	−	8.74139i	0.473667	−	0.300181i
$849$	2.90991	−	9.23316i	0.0998678	−	0.316881i
$850$		0			0
$851$		−	16.9704i		−	0.581739i
$852$	−0.735607	+	32.1509i	−0.0252015	+	1.10147i
$853$		−	25.1966i		−	0.862716i	−0.902181	−	0.431358i	$-0.858035\pi$
$853$		−	25.1966i		−	0.862716i	0.902181	−	0.431358i	$-0.141965\pi$
$854$	8.54799	−	1.21519i	0.292506	−	0.0415829i
$855$		0			0
$856$	9.02614	+	20.0158i	0.308507	+	0.684127i
$857$		−	46.7431i		−	1.59671i	−0.602185	−	0.798357i	$-0.705703\pi$
$857$		−	46.7431i		−	1.59671i	0.602185	−	0.798357i	$-0.294297\pi$
$858$	7.74908	−	46.7999i	0.264549	−	1.59772i
$859$	40.8430			1.39354			0.696772	−	0.717293i	$-0.254619\pi$
$859$	40.8430			1.39354			0.696772	+	0.717293i	$0.254619\pi$
$860$		0			0
$861$	3.45201	−	10.9533i	0.117644	−	0.373286i
$862$	−28.0344	+	3.98539i	−0.954855	+	0.135743i
$863$	39.3858			1.34071			0.670354	−	0.742042i	$-0.266142\pi$
$863$	39.3858			1.34071			0.670354	+	0.742042i	$0.266142\pi$
$864$	−6.12290	+	28.7491i	−0.208305	+	0.978064i
$865$		0			0
$866$	−14.2970	+	2.03247i	−0.485832	+	0.0690662i
$867$	−5.39687	+	17.1243i	−0.183287	+	0.581572i
$868$	−15.6831	+	4.55100i	−0.532317	+	0.154471i
$869$	37.1977			1.26185
$870$		0			0
$871$		−	71.6388i		−	2.42739i
$872$	23.8481	+	52.8841i	0.807597	+	1.79088i
$873$	−3.56889	−	2.49761i	−0.120789	−	0.0845312i
$874$	1.65480	−	0.235248i	0.0559745	−	0.00795738i
$875$		0			0
$876$	−0.894082	+	39.0773i	−0.0302082	+	1.32030i
$877$			57.4498i			1.93994i	0.243218	+	0.969972i	$0.421797\pi$
$877$			57.4498i			1.93994i	−0.243218	+	0.969972i	$0.578203\pi$
$878$	6.70646	+	47.1752i	0.226332	+	1.59209i
$879$	−3.12376	+	9.91172i	−0.105362	+	0.334314i
$880$		0			0
$881$			44.2957i			1.49236i	0.665744	+	0.746180i	$0.268114\pi$
$881$			44.2957i			1.49236i	−0.665744	+	0.746180i	$0.731886\pi$
$882$	−12.4308	−	6.30496i	−0.418567	−	0.212299i
$883$	25.7701			0.867231			0.433616	−	0.901098i	$-0.357238\pi$
$883$	25.7701			0.867231			0.433616	+	0.901098i	$0.357238\pi$
$884$	48.3988	−	14.0446i	1.62783	−	0.472373i
$885$		0			0
$886$	0.888663	+	6.25112i	0.0298552	+	0.210010i
$887$	21.4751			0.721063			0.360531	−	0.932747i	$-0.382595\pi$
$887$	21.4751			0.721063			0.360531	+	0.932747i	$0.382595\pi$
$888$	47.8309	−	5.68681i	1.60510	−	0.190837i
$889$	−31.9485			−1.07152
$890$		0			0
$891$	−33.9966	+	12.3934i	−1.13893	+	0.415196i
$892$	−3.64827	−	12.5722i	−0.122153	−	0.420947i
$893$	5.17508			0.173177
$894$	−3.01483	+	18.2078i	−0.100831	+	0.608960i
$895$		0			0
$896$	−18.2121	−	11.9918i	−0.608422	−	0.400618i
$897$	13.7339	+	4.32835i	0.458562	+	0.144520i
$898$	−5.48366	−	38.5737i	−0.182992	−	1.28722i
$899$		−	29.6474i		−	0.988798i
$900$		0			0
$901$			21.3567i			0.711493i
$902$	−19.3661	+	2.75310i	−0.644821	+	0.0916682i
$903$	3.31525	+	1.04483i	0.110325	+	0.0347697i
$904$	0.250922	+	0.556430i	0.00834554	+	0.0185066i
$905$		0			0
$906$	22.7421	+	3.76562i	0.755557	+	0.125104i
$907$	−34.5984			−1.14882			−0.574410	−	0.818568i	$-0.694769\pi$
$907$	−34.5984			−1.14882			−0.574410	+	0.818568i	$0.694769\pi$
$908$	−12.5476	−	43.2398i	−0.416406	−	1.43496i
$909$	−10.3300	−	7.22923i	−0.342625	−	0.239778i
$910$		0			0
$911$	−20.3074			−0.672815			−0.336407	−	0.941717i	$-0.609212\pi$
$911$	−20.3074			−0.672815			−0.336407	+	0.941717i	$0.609212\pi$
$912$	1.21757	+	4.58520i	0.0403177	+	0.151831i
$913$	−28.7818			−0.952537
$914$	16.1038	−	2.28932i	0.532665	−	0.0757240i
$915$		0			0
$916$	−7.18121	−	24.7469i	−0.237274	−	0.817661i
$917$	−10.8181			−0.357246
$918$	−27.4717	−	26.8901i	−0.906701	−	0.887505i
$919$			11.1280i			0.367080i	0.983012	+	0.183540i	$0.0587556\pi$
$919$			11.1280i			0.367080i	−0.983012	+	0.183540i	$0.941244\pi$
$920$		0			0
$921$	2.49397	−	7.91340i	0.0821792	−	0.260755i
$922$	−11.5641	+	1.64396i	−0.380844	+	0.0541411i
$923$			44.7168i			1.47187i
$924$	0.614016	−	26.8366i	0.0201996	−	0.882858i
$925$		0			0
$926$	2.33278	+	16.4094i	0.0766597	+	0.539247i
$927$	12.2159	−	17.4556i	0.401222	−	0.573316i
$928$	30.1234	−	25.6869i	0.988850	−	0.843214i
$929$			20.3857i			0.668834i	0.942425	+	0.334417i	$0.108539\pi$
$929$			20.3857i			0.668834i	−0.942425	+	0.334417i	$0.891461\pi$
$930$		0			0
$931$	−2.24962			−0.0737282
$932$	6.04813	+	20.8423i	0.198113	+	0.682711i
$933$	6.70464	−	21.2739i	0.219500	−	0.696475i
$934$	3.42148	+	24.0677i	0.111954	+	0.787519i
$935$		0			0
$936$	−7.59714	+	40.1592i	−0.248320	+	1.31264i
$937$	−35.4418			−1.15783			−0.578917	−	0.815387i	$-0.696524\pi$
$937$	−35.4418			−1.15783			−0.578917	+	0.815387i	$0.696524\pi$
$938$	−5.70566	−	40.1353i	−0.186296	−	1.31046i
$939$	10.6219	−	33.7034i	0.346633	−	1.09987i
$940$		0			0
$941$	−13.4402			−0.438139			−0.219070	−	0.975709i	$-0.570302\pi$
$941$	−13.4402			−0.438139			−0.219070	+	0.975709i	$0.570302\pi$
$942$	8.45078	+	1.39927i	0.275341	+	0.0455907i
$943$		−	5.93781i		−	0.193362i
$944$	−2.13023	−	3.36137i	−0.0693330	−	0.109403i
$945$		0			0
$946$	−0.833286	−	5.86158i	−0.0270925	−	0.190576i
$947$		−	4.96195i		−	0.161242i	−0.996745	−	0.0806208i	$-0.974310\pi$
$947$		−	4.96195i		−	0.161242i	0.996745	−	0.0806208i	$-0.0256903\pi$
$948$	−32.0409	−	0.733090i	−1.04064	−	0.0238097i
$949$			54.3503i			1.76428i
$950$		0			0
$951$	−2.78197	+	8.82720i	−0.0902114	+	0.286242i
$952$	25.9966	−	11.7232i	0.842555	−	0.379950i
$953$		−	51.4156i		−	1.66551i	−0.553639	−	0.832757i	$-0.686761\pi$
$953$		−	51.4156i		−	1.66551i	0.553639	−	0.832757i	$-0.313239\pi$
$954$	−15.4472	−	7.83492i	−0.500123	−	0.253665i
$955$		0			0
$956$	−12.7356	+	3.69569i	−0.411899	+	0.119527i
$957$	46.4813	+	14.6490i	1.50253	+	0.473534i
$958$	−16.1547	+	2.29656i	−0.521933	+	0.0741984i
$959$	−18.1513			−0.586135
$960$		0			0
$961$	13.0531			0.421068
$962$	66.3095	−	9.42660i	2.13790	−	0.303926i
$963$	13.3530	−	19.0805i	0.430295	−	0.614860i
$964$	−30.6398	+	8.89123i	−0.986840	+	0.286367i
$965$		0			0
$966$	8.03908	+	1.33110i	0.258653	+	0.0428276i
$967$		−	20.9875i		−	0.674911i	−0.941341	−	0.337456i	$-0.890434\pi$
$967$		−	20.9875i		−	0.674911i	0.941341	−	0.337456i	$-0.109566\pi$
$968$	−13.3174	+	6.00548i	−0.428037	+	0.193023i
$969$	−5.91749	−	1.86495i	−0.190097	−	0.0599107i
$970$		0			0
$971$		−	25.4429i		−	0.816502i	−0.912870	−	0.408251i	$-0.866139\pi$
$971$		−	25.4429i		−	0.816502i	0.912870	−	0.408251i	$-0.133861\pi$
$972$	29.5278	−	10.0053i	0.947106	−	0.320921i
$973$			12.5593i			0.402633i
$974$	6.58866	+	46.3466i	0.211114	+	1.48504i
$975$		0			0
$976$	6.78243	+	10.7023i	0.217100	+	0.342571i
$977$		−	26.6495i		−	0.852593i	−0.904584	−	0.426296i	$-0.859818\pi$
$977$		−	26.6495i		−	0.852593i	0.904584	−	0.426296i	$-0.140182\pi$
$978$	−6.78445	+	40.9741i	−0.216943	+	1.31021i
$979$	−3.33314			−0.106528
$980$		0			0
$981$	35.2802	−	50.4128i	1.12641	−	1.60956i
$982$	4.25228	+	29.9118i	0.135696	+	0.954524i
$983$	−47.0887			−1.50190			−0.750948	−	0.660361i	$-0.770403\pi$
$983$	−47.0887			−1.50190			−0.750948	+	0.660361i	$0.770403\pi$
$984$	16.7356	−	1.98977i	0.533512	−	0.0634314i
$985$		0			0
$986$	7.28700	+	51.2589i	0.232065	+	1.63242i
$987$	24.0626	+	7.58353i	0.765922	+	0.241387i
$988$	1.83839	+	6.33522i	0.0584870	+	0.201550i
$989$	1.79721			0.0571479
$990$		0			0
$991$		−	26.3879i		−	0.838238i	−0.907931	−	0.419119i	$-0.862339\pi$
$991$		−	26.3879i		−	0.838238i	0.907931	−	0.419119i	$-0.137661\pi$
$992$	−15.5494	−	18.2350i	−0.493695	−	0.578963i
$993$	13.1039	−	41.5787i	0.415839	−	1.31946i
$994$	3.56146	+	25.0524i	0.112963	+	0.794612i
$995$		0			0
$996$	24.7917	+	0.567230i	0.785555	+	0.0179734i
$997$			10.2047i			0.323186i	0.986858	+	0.161593i	$0.0516631\pi$
$997$			10.2047i			0.323186i	−0.986858	+	0.161593i	$0.948337\pi$
$998$	20.7869	−	2.95508i	0.657999	−	0.0935416i
$999$	−31.1170	−	40.5202i	−0.984497	−	1.28200i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.b.f.251.7		8
3.2	odd	2		600.2.b.e.251.2		8
4.3	odd	2		2400.2.b.f.2351.4		8
5.2	odd	4		600.2.m.c.299.10		16
5.3	odd	4		600.2.m.c.299.7		16
5.4	even	2		120.2.b.a.11.2	yes	8
8.3	odd	2		600.2.b.e.251.1		8
8.5	even	2		2400.2.b.e.2351.4		8
12.11	even	2		2400.2.b.e.2351.3		8
15.2	even	4		600.2.m.d.299.7		16
15.8	even	4		600.2.m.d.299.10		16
15.14	odd	2		120.2.b.b.11.7	yes	8
20.3	even	4		2400.2.m.d.1199.1		16
20.7	even	4		2400.2.m.d.1199.16		16
20.19	odd	2		480.2.b.b.431.5		8
24.5	odd	2		2400.2.b.f.2351.3		8
24.11	even	2	inner	600.2.b.f.251.8		8
40.3	even	4		600.2.m.d.299.8		16
40.13	odd	4		2400.2.m.c.1199.1		16
40.19	odd	2		120.2.b.b.11.8	yes	8
40.27	even	4		600.2.m.d.299.9		16
40.29	even	2		480.2.b.a.431.5		8
40.37	odd	4		2400.2.m.c.1199.16		16
60.23	odd	4		2400.2.m.c.1199.15		16
60.47	odd	4		2400.2.m.c.1199.2		16
60.59	even	2		480.2.b.a.431.6		8
120.29	odd	2		480.2.b.b.431.6		8
120.53	even	4		2400.2.m.d.1199.15		16
120.59	even	2		120.2.b.a.11.1	✓	8
120.77	even	4		2400.2.m.d.1199.2		16
120.83	odd	4		600.2.m.c.299.9		16
120.107	odd	4		600.2.m.c.299.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.b.a.11.1	✓	8	120.59	even	2
120.2.b.a.11.2	yes	8	5.4	even	2
120.2.b.b.11.7	yes	8	15.14	odd	2
120.2.b.b.11.8	yes	8	40.19	odd	2
480.2.b.a.431.5		8	40.29	even	2
480.2.b.a.431.6		8	60.59	even	2
480.2.b.b.431.5		8	20.19	odd	2
480.2.b.b.431.6		8	120.29	odd	2
600.2.b.e.251.1		8	8.3	odd	2
600.2.b.e.251.2		8	3.2	odd	2
600.2.b.f.251.7		8	1.1	even	1	trivial
600.2.b.f.251.8		8	24.11	even	2	inner
600.2.m.c.299.7		16	5.3	odd	4
600.2.m.c.299.8		16	120.107	odd	4
600.2.m.c.299.9		16	120.83	odd	4
600.2.m.c.299.10		16	5.2	odd	4
600.2.m.d.299.7		16	15.2	even	4
600.2.m.d.299.8		16	40.3	even	4
600.2.m.d.299.9		16	40.27	even	4
600.2.m.d.299.10		16	15.8	even	4
2400.2.b.e.2351.3		8	12.11	even	2
2400.2.b.e.2351.4		8	8.5	even	2
2400.2.b.f.2351.3		8	24.5	odd	2
2400.2.b.f.2351.4		8	4.3	odd	2
2400.2.m.c.1199.1		16	40.13	odd	4
2400.2.m.c.1199.2		16	60.47	odd	4
2400.2.m.c.1199.15		16	60.23	odd	4
2400.2.m.c.1199.16		16	40.37	odd	4
2400.2.m.d.1199.1		16	20.3	even	4
2400.2.m.d.1199.2		16	120.77	even	4
2400.2.m.d.1199.15		16	120.53	even	4
2400.2.m.d.1199.16		16	20.7	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.40014 - 0.199044i) q^{2} +(0.520627 - 1.65195i) q^{3} +(1.92076 - 0.557378i) q^{4} +(0.400136 - 2.41659i) q^{6} -1.92736i q^{7} +(2.57839 - 1.16272i) q^{8} +(-2.45790 - 1.72010i) q^{9} +O(q^{10})\)	\(q+(1.40014 - 0.199044i) q^{2} +(0.520627 - 1.65195i) q^{3} +(1.92076 - 0.557378i) q^{4} +(0.400136 - 2.41659i) q^{6} -1.92736i q^{7} +(2.57839 - 1.16272i) q^{8} +(-2.45790 - 1.72010i) q^{9} +4.02057i q^{11} +(0.0792373 - 3.46320i) q^{12} -4.81675i q^{13} +(-0.383629 - 2.69856i) q^{14} +(3.37866 - 2.14118i) q^{16} +5.23126i q^{17} +(-3.78377 - 1.91915i) q^{18} -0.684753 q^{19} +(-3.18390 - 1.00343i) q^{21} +(0.800272 + 5.62935i) q^{22} -1.72601 q^{23} +(-0.578386 - 4.86472i) q^{24} +(-0.958747 - 6.74411i) q^{26} +(-4.12117 + 3.16480i) q^{27} +(-1.07427 - 3.70199i) q^{28} +6.99830 q^{29} -4.23638i q^{31} +(4.30439 - 3.67045i) q^{32} +(6.64180 + 2.09322i) q^{33} +(1.04125 + 7.32448i) q^{34} +(-5.67978 - 1.93393i) q^{36} +9.83221i q^{37} +(-0.958747 + 0.136296i) q^{38} +(-7.95705 - 2.50773i) q^{39} +3.44020i q^{41} +(-4.65762 - 0.771205i) q^{42} -1.04125 q^{43} +(2.24098 + 7.72257i) q^{44} +(-2.41664 + 0.343552i) q^{46} -7.55759 q^{47} +(-1.77811 - 6.69614i) q^{48} +3.28530 q^{49} +(8.64180 + 2.72353i) q^{51} +(-2.68475 - 9.25184i) q^{52} +4.08251 q^{53} +(-5.14027 + 5.25144i) q^{54} +(-2.24098 - 4.96947i) q^{56} +(-0.356500 + 1.13118i) q^{57} +(9.79857 - 1.39297i) q^{58} -0.994883i q^{59} +3.16761i q^{61} +(-0.843227 - 5.93151i) q^{62} +(-3.31525 + 4.73724i) q^{63} +(5.29615 - 5.99590i) q^{64} +(9.71606 + 1.60878i) q^{66} +14.8728 q^{67} +(2.91579 + 10.0480i) q^{68} +(-0.898604 + 2.85128i) q^{69} -9.28360 q^{71} +(-8.33741 - 1.57723i) q^{72} -11.2836 q^{73} +(1.95705 + 13.7664i) q^{74} +(-1.31525 + 0.381666i) q^{76} +7.74908 q^{77} +(-11.6401 - 1.92736i) q^{78} -9.25184i q^{79} +(3.08251 + 8.45566i) q^{81} +(0.684753 + 4.81675i) q^{82} +7.15862i q^{83} +(-6.67481 - 0.152718i) q^{84} +(-1.45790 + 0.207256i) q^{86} +(3.64350 - 11.5609i) q^{87} +(4.67481 + 10.3666i) q^{88} +0.829022i q^{89} -9.28360 q^{91} +(-3.31525 + 0.962038i) q^{92} +(-6.99830 - 2.20557i) q^{93} +(-10.5817 + 1.50430i) q^{94} +(-3.82243 - 9.02159i) q^{96} +1.45201 q^{97} +(4.59986 - 0.653920i) q^{98} +(6.91579 - 9.88215i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + q^{4} - 7 q^{6} + 7 q^{8}+O(q^{10}) \) 8 * q + q^2 + q^4 - 7 * q^6 + 7 * q^8	\( 8 q + q^{2} + q^{4} - 7 q^{6} + 7 q^{8} + 15 q^{12} + 6 q^{14} - 7 q^{16} - 11 q^{18} - 4 q^{19} + 4 q^{21} - 14 q^{22} - 4 q^{23} + 9 q^{24} - 16 q^{26} + 12 q^{27} + 2 q^{28} + 11 q^{32} + 4 q^{33} - 19 q^{36} - 16 q^{38} - 16 q^{39} - 38 q^{42} + 30 q^{44} - 8 q^{46} + 28 q^{47} - 21 q^{48} - 16 q^{49} + 20 q^{51} - 20 q^{52} + 16 q^{53} - 15 q^{54} - 30 q^{56} + 4 q^{57} + 2 q^{58} - 34 q^{62} - 28 q^{63} + 25 q^{64} + 18 q^{66} + 32 q^{67} - 16 q^{68} - 20 q^{69} + 24 q^{71} - 41 q^{72} + 8 q^{73} - 32 q^{74} - 12 q^{76} + 12 q^{78} + 8 q^{81} + 4 q^{82} - 2 q^{84} + 8 q^{86} + 36 q^{87} - 14 q^{88} + 24 q^{91} - 28 q^{92} - 40 q^{94} + 17 q^{96} - 8 q^{97} + 47 q^{98} + 16 q^{99}+O(q^{100}) \) 8 * q + q^2 + q^4 - 7 * q^6 + 7 * q^8 + 15 * q^12 + 6 * q^14 - 7 * q^16 - 11 * q^18 - 4 * q^19 + 4 * q^21 - 14 * q^22 - 4 * q^23 + 9 * q^24 - 16 * q^26 + 12 * q^27 + 2 * q^28 + 11 * q^32 + 4 * q^33 - 19 * q^36 - 16 * q^38 - 16 * q^39 - 38 * q^42 + 30 * q^44 - 8 * q^46 + 28 * q^47 - 21 * q^48 - 16 * q^49 + 20 * q^51 - 20 * q^52 + 16 * q^53 - 15 * q^54 - 30 * q^56 + 4 * q^57 + 2 * q^58 - 34 * q^62 - 28 * q^63 + 25 * q^64 + 18 * q^66 + 32 * q^67 - 16 * q^68 - 20 * q^69 + 24 * q^71 - 41 * q^72 + 8 * q^73 - 32 * q^74 - 12 * q^76 + 12 * q^78 + 8 * q^81 + 4 * q^82 - 2 * q^84 + 8 * q^86 + 36 * q^87 - 14 * q^88 + 24 * q^91 - 28 * q^92 - 40 * q^94 + 17 * q^96 - 8 * q^97 + 47 * q^98 + 16 * q^99

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