LMFDB - Embedded newform 600.2.b.e.251.2

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			251.2
Root			$1.40014 - 0.199044i$ of defining polynomial
Character	$\chi$	$=$	600.251
Dual form			600.2.b.e.251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40014 + 0.199044i) q^{2} +(0.520627 + 1.65195i) q^{3} +(1.92076 - 0.557378i) q^{4} +(-1.05776 - 2.20933i) q^{6} -1.92736i q^{7} +(-2.57839 + 1.16272i) q^{8} +(-2.45790 + 1.72010i) q^{9} +O(q^{10})$	\(q+(-1.40014 + 0.199044i) q^{2} +(0.520627 + 1.65195i) q^{3} +(1.92076 - 0.557378i) q^{4} +(-1.05776 - 2.20933i) q^{6} -1.92736i q^{7} +(-2.57839 + 1.16272i) q^{8} +(-2.45790 + 1.72010i) q^{9} -4.02057i q^{11} +(1.92076 + 2.88282i) q^{12} -4.81675i q^{13} +(0.383629 + 2.69856i) q^{14} +(3.37866 - 2.14118i) q^{16} -5.23126i q^{17} +(3.09901 - 2.89761i) q^{18} -0.684753 q^{19} +(3.18390 - 1.00343i) q^{21} +(0.800272 + 5.62935i) q^{22} +1.72601 q^{23} +(-3.26314 - 3.65403i) 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} +(-3.76229 + 4.67388i) q^{36} +9.83221i q^{37} +(0.958747 - 0.136296i) q^{38} +(7.95705 - 2.50773i) q^{39} -3.44020i q^{41} +(-4.25817 + 2.03868i) q^{42} -1.04125 q^{43} +(-2.24098 - 7.72257i) q^{44} +(-2.41664 + 0.343552i) q^{46} +7.55759 q^{47} +(5.29615 + 4.46663i) q^{48} +3.28530 q^{49} +(8.64180 - 2.72353i) q^{51} +(-2.68475 - 9.25184i) q^{52} -4.08251 q^{53} +(6.40014 + 3.61085i) 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} +(-8.88278 + 4.25280i) q^{66} +14.8728 q^{67} +(-2.91579 - 10.0480i) q^{68} +(0.898604 + 2.85128i) q^{69} +9.28360 q^{71} +(4.33741 - 7.29294i) q^{72} -11.2836 q^{73} +(-1.95705 - 13.7664i) q^{74} +(-1.31525 + 0.381666i) q^{76} -7.74908 q^{77} +(-10.6418 + 5.09497i) q^{78} -9.25184i q^{79} +(3.08251 - 8.45566i) q^{81} +(0.684753 + 4.81675i) q^{82} -7.15862i q^{83} +(5.55623 - 3.70199i) 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} +(-8.30439 - 5.19972i) 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} + q^{6} - 7 q^{8}+O(q^{10}) $ 8 * q - q^2 + q^4 + q^6 - 7 * q^8	$ 8 q - q^{2} + q^{4} + q^{6} - 7 q^{8} + q^{12} - 6 q^{14} - 7 q^{16} + 7 q^{18} - 4 q^{19} - 4 q^{21} - 14 q^{22} + 4 q^{23} - 11 q^{24} + 16 q^{26} + 12 q^{27} + 2 q^{28} - 11 q^{32} + 4 q^{33} + 13 q^{36} + 16 q^{38} + 16 q^{39} + 6 q^{42} - 30 q^{44} - 8 q^{46} - 28 q^{47} + 25 q^{48} - 16 q^{49} + 20 q^{51} - 20 q^{52} - 16 q^{53} + 41 q^{54} + 30 q^{56} + 4 q^{57} + 2 q^{58} + 34 q^{62} + 28 q^{63} + 25 q^{64} - 34 q^{66} + 32 q^{67} + 16 q^{68} + 20 q^{69} - 24 q^{71} + 9 q^{72} + 8 q^{73} + 32 q^{74} - 12 q^{76} - 36 q^{78} + 8 q^{81} + 4 q^{82} + 58 q^{84} - 8 q^{86} - 36 q^{87} - 14 q^{88} + 24 q^{91} + 28 q^{92} - 40 q^{94} - 43 q^{96} - 8 q^{97} - 47 q^{98} + 16 q^{99}+O(q^{100}) $ 8 * q - q^2 + q^4 + q^6 - 7 * q^8 + q^12 - 6 * q^14 - 7 * q^16 + 7 * q^18 - 4 * q^19 - 4 * q^21 - 14 * q^22 + 4 * q^23 - 11 * q^24 + 16 * q^26 + 12 * q^27 + 2 * q^28 - 11 * q^32 + 4 * q^33 + 13 * q^36 + 16 * q^38 + 16 * q^39 + 6 * q^42 - 30 * q^44 - 8 * q^46 - 28 * q^47 + 25 * q^48 - 16 * q^49 + 20 * q^51 - 20 * q^52 - 16 * q^53 + 41 * q^54 + 30 * q^56 + 4 * q^57 + 2 * q^58 + 34 * q^62 + 28 * q^63 + 25 * q^64 - 34 * q^66 + 32 * q^67 + 16 * q^68 + 20 * q^69 - 24 * q^71 + 9 * q^72 + 8 * q^73 + 32 * q^74 - 12 * q^76 - 36 * q^78 + 8 * q^81 + 4 * q^82 + 58 * q^84 - 8 * q^86 - 36 * q^87 - 14 * q^88 + 24 * q^91 + 28 * q^92 - 40 * q^94 - 43 * 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
$6$	−1.05776	−	2.20933i	−0.431829	−	0.901956i
$7$		−	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	$-0.792723\pi$
$11$		−	4.02057i		−	1.21225i	0.795370	−	0.606124i	$-0.207277\pi$
$12$	1.92076	+	2.88282i	0.554476	+	0.832199i
$13$		−	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	$-0.781254\pi$
$17$		−	5.23126i		−	1.26877i	0.773018	−	0.634384i	$-0.218746\pi$
$18$	3.09901	−	2.89761i	0.730444	−	0.682972i
$19$	−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	$-0.442407\pi$
$23$	1.72601			0.359897			0.179949	+	0.983676i	$0.442407\pi$
$24$	−3.26314	−	3.65403i	−0.666085	−	0.745875i
$25$		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	$-0.725137\pi$
$29$	−6.99830			−1.29955			−0.649776	+	0.760126i	$0.725137\pi$
$30$		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
$36$	−3.76229	+	4.67388i	−0.627048	+	0.778981i
$37$			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	$-0.913428\pi$
$41$		−	3.44020i		−	0.537269i	0.963242	−	0.268635i	$-0.0865724\pi$
$42$	−4.25817	+	2.03868i	−0.657050	+	0.314575i
$43$	−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	$-0.314172\pi$
$47$	7.55759			1.10239			0.551194	+	0.834377i	$0.314172\pi$
$48$	5.29615	+	4.46663i	0.764434	+	0.644702i
$49$	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	$-0.590463\pi$
$53$	−4.08251			−0.560775			−0.280388	+	0.959887i	$0.590463\pi$
$54$	6.40014	+	3.61085i	0.870948	+	0.491375i
$55$		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	$0.0206286\pi$
$59$			0.994883i			0.129523i	−0.997901	+	0.0647614i	$0.979371\pi$
$60$		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
$66$	−8.88278	+	4.25280i	−1.09339	+	0.523484i
$67$	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	$-0.314292\pi$
$71$	9.28360			1.10176			0.550880	+	0.834584i	$0.314292\pi$
$72$	4.33741	−	7.29294i	0.511168	−	0.859481i
$73$	−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
$78$	−10.6418	+	5.09497i	−1.20495	+	0.576891i
$79$		−	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	$-0.871479\pi$
$83$		−	7.15862i		−	0.785760i	0.919590	−	0.392880i	$-0.128521\pi$
$84$	5.55623	−	3.70199i	0.606234	−	0.403921i
$85$		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	$-0.986010\pi$
$89$		−	0.829022i		−	0.0878762i	0.999034	−	0.0439381i	$-0.0139904\pi$
$90$		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
$96$	−8.30439	−	5.19972i	−0.847563	−	0.530694i
$97$	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	$-0.567052\pi$
$101$	−4.20279			−0.418193			−0.209097	+	0.977895i	$0.567052\pi$
$102$	−11.5576	+	5.53342i	−1.14437	+	0.547890i
$103$			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	$-0.877562\pi$
$107$		−	7.76293i		−	0.750471i	0.926930	−	0.375235i	$-0.122438\pi$
$108$	−9.67978	−	3.78177i	−0.931437	−	0.363901i
$109$			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	$-0.996769\pi$
$113$		−	0.215805i		−	0.0203013i	0.999948	−	0.0101506i	$-0.00323110\pi$
$114$	0.724304	+	1.51285i	0.0678373	+	0.141691i
$115$		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
$126$	−5.58472	−	5.97290i	−0.497526	−	0.532108i
$127$		−	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	$0.0788543\pi$
$131$			5.61293i			0.490404i	−0.969472	+	0.245202i	$0.921146\pi$
$132$	11.5906	−	7.72257i	1.00883	−	0.672163i
$133$			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	$0.131791\pi$
$137$			9.41770i			0.804608i	−0.915506	+	0.402304i	$0.868209\pi$
$138$	−1.82570	−	3.81332i	−0.155414	−	0.324611i
$139$	−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
$144$	−4.62134	+	11.0744i	−0.385112	+	0.922870i
$145$		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	$-0.400131\pi$
$149$	7.53452			0.617252			0.308626	+	0.951184i	$0.400131\pi$
$150$		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
$156$	13.8858	−	9.25184i	1.11176	−	0.740740i
$157$			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
$162$	−2.63288	+	12.4526i	−0.206858	+	0.978371i
$163$	−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	$-0.354698\pi$
$167$	11.3926			0.881584			0.440792	+	0.897609i	$0.354698\pi$
$168$	−7.04261	+	6.28923i	−0.543350	+	0.485225i
$169$	−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	$-0.473773\pi$
$173$	2.16501			0.164603			0.0823014	+	0.996607i	$0.473773\pi$
$174$	7.40252	+	15.4616i	0.561184	+	1.17214i
$175$		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	$-0.936043\pi$
$179$		−	5.34034i		−	0.399155i	0.979882	−	0.199578i	$-0.0639570\pi$
$180$		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
$186$	−9.35956	+	4.48107i	−0.686277	+	0.328568i
$187$	−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	$-0.246656\pi$
$191$	19.7491			1.42899			0.714497	+	0.699639i	$0.246656\pi$
$192$	12.6623	+	5.62737i	0.913819	+	0.406121i
$193$	−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	$-0.798836\pi$
$197$	−22.6497			−1.61372			−0.806862	+	0.590740i	$0.798836\pi$
$198$	−11.6500	−	12.4598i	−0.827932	−	0.885480i
$199$		−	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
$204$	15.0808	−	10.0480i	1.05587	−	0.703502i
$205$		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
$216$	14.3058	+	3.36829i	0.973383	+	0.229183i
$217$	−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
$222$	21.7226	−	10.4001i	1.45793	−	0.698010i
$223$		−	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	$0.268545\pi$
$227$			22.5118i			1.49416i	−0.664735	+	0.747080i	$0.731455\pi$
$228$	−1.31525	−	1.97402i	−0.0871044	−	0.130733i
$229$		−	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	$-0.884332\pi$
$233$		−	10.8510i		−	0.710875i	0.934700	−	0.355437i	$-0.115668\pi$
$234$	−13.9570	−	14.9272i	−0.912401	−	0.975820i
$235$		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	$-0.431206\pi$
$239$	6.63049			0.428891			0.214446	+	0.976736i	$0.431206\pi$
$240$		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
$246$	−7.60054	+	3.63891i	−0.484593	+	0.232008i
$247$			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	$0.159789\pi$
$251$			15.2464i			0.962346i	−0.876626	+	0.481173i	$0.840211\pi$
$252$	9.00824	+	7.25127i	0.567466	+	0.456787i
$253$		−	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	$-0.831573\pi$
$257$		−	16.1845i		−	1.00956i	0.863247	−	0.504782i	$-0.168427\pi$
$258$	1.10140	+	2.30047i	0.0685699	+	0.143221i
$259$	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	$-0.269663\pi$
$263$	21.4751			1.32421			0.662105	+	0.749411i	$0.269663\pi$
$264$	−14.6913	+	13.1197i	−0.904186	+	0.807461i
$265$		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	$-0.252218\pi$
$269$	23.0327			1.40433			0.702163	+	0.712016i	$0.252218\pi$
$270$		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
$276$	3.31525	+	4.97577i	0.199554	+	0.299506i
$277$			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	$0.313724\pi$
$281$			27.9474i			1.66720i	−0.552368	+	0.833600i	$0.686276\pi$
$282$	−7.99412	−	16.6972i	−0.476043	−	0.994305i
$283$	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
$288$	4.26620	−	16.4256i	0.251388	−	0.967886i
$289$	−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	$-0.443923\pi$
$293$	6.00000			0.350524			0.175262	+	0.984522i	$0.443923\pi$
$294$	−3.47506	−	7.25831i	−0.202669	−	0.423313i
$295$		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
$306$	−15.1581	−	16.2117i	−0.866533	−	0.926764i
$307$	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	$-0.618973\pi$
$311$	−12.8780			−0.730245			−0.365123	+	0.930959i	$0.618973\pi$
$312$	−17.6005	+	15.7177i	−0.996435	+	0.889841i
$313$	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	$-0.452053\pi$
$317$	5.34350			0.300121			0.150060	+	0.988677i	$0.452053\pi$
$318$	4.31831	+	9.01961i	0.242159	+	0.505794i
$319$			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
$324$	1.20776	−	17.9594i	0.0670979	−	0.997746i
$325$		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
$336$	8.60878	−	10.2076i	0.469648	−	0.556869i
$337$	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
$342$	−2.12206	+	1.98414i	−0.114748	+	0.107290i
$343$		−	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	$0.0813173\pi$
$347$			9.41442i			0.505392i	−0.967546	+	0.252696i	$0.918683\pi$
$348$	−13.4421	−	20.1749i	−0.720571	−	1.08149i
$349$		−	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	$0.182927\pi$
$353$			20.4254i			1.08713i	−0.839366	+	0.543567i	$0.817073\pi$
$354$	2.19803	−	1.05235i	0.116824	−	0.0559316i
$355$		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	$-0.558037\pi$
$359$	−6.87107			−0.362641			−0.181320	+	0.983424i	$0.558037\pi$
$360$		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
$366$	6.99830	−	3.35057i	0.365807	−	0.175137i
$367$			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
$372$	12.2127	−	8.13708i	0.633201	−	0.421888i
$373$		−	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
$378$	6.95940	−	12.3353i	0.357953	−	0.634462i
$379$	−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	$-0.299172\pi$
$383$	23.0887			1.17978			0.589889	+	0.807484i	$0.299172\pi$
$384$	−18.8490	−	5.35874i	−0.961883	−	0.273462i
$385$		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	$-0.606081\pi$
$389$	−12.9040			−0.654260			−0.327130	+	0.944979i	$0.606081\pi$
$390$		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
$396$	18.7917	+	15.1266i	0.944318	+	0.760138i
$397$		−	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	$-0.681066\pi$
$401$		−	33.7433i		−	1.68506i	0.538651	−	0.842529i	$-0.318934\pi$
$402$	−15.7319	−	32.8590i	−0.784635	−	1.63886i
$403$	−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
$408$	−19.1152	+	17.0703i	−0.946342	+	0.845108i
$409$	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
$414$	5.34891	−	5.00128i	0.262885	−	0.245800i
$415$		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	$0.260593\pi$
$419$			29.8954i			1.46049i	−0.683188	+	0.730243i	$0.739407\pi$
$420$		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
$426$	−9.81981	−	20.5105i	−0.475772	−	0.993739i
$427$	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	$-0.339828\pi$
$431$	20.0226			0.964455			0.482228	+	0.876046i	$0.339828\pi$
$432$	−20.7004	−	1.86859i	−0.995951	−	0.0899026i
$433$	−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
$438$	11.9353	+	24.9292i	0.570292	+	1.19116i
$439$			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	$-0.966176\pi$
$443$		−	4.46465i		−	0.212122i	0.994360	−	0.106061i	$-0.0338239\pi$
$444$	−28.3445	+	18.8853i	−1.34517	+	0.896258i
$445$		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	$0.225265\pi$
$449$			27.5500i			1.30016i	−0.759865	+	0.650081i	$0.774735\pi$
$450$		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
$456$	2.23444	+	2.50211i	0.104637	+	0.117172i
$457$	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	$-0.438393\pi$
$461$	8.25929			0.384673			0.192337	+	0.981329i	$0.438393\pi$
$462$	8.19666	+	17.1203i	0.381343	+	0.796507i
$463$			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	$-0.869802\pi$
$467$		−	17.1895i		−	0.795437i	0.917508	−	0.397718i	$-0.130198\pi$
$468$	22.5129	+	18.1220i	1.04066	+	0.837690i
$469$		−	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
$474$	−20.4404	+	9.78622i	−0.938857	+	0.449496i
$475$		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	$-0.415093\pi$
$479$	11.5379			0.527181			0.263591	+	0.964635i	$0.415093\pi$
$480$		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
$486$	−21.9419	+	2.13378i	−0.995305	+	0.0967902i
$487$			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	$-0.839888\pi$
$491$		−	21.3635i		−	0.964121i	0.876138	−	0.482061i	$-0.160112\pi$
$492$	9.91749	−	6.60781i	0.447115	−	0.297903i
$493$			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
$498$	−15.8158	+	7.57210i	−0.708721	+	0.339314i
$499$	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	$-0.486737\pi$
$503$	1.86841			0.0833084			0.0416542	+	0.999132i	$0.486737\pi$
$504$	−14.0561	−	8.35973i	−0.626108	−	0.372372i
$505$		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	$-0.488507\pi$
$509$	1.62879			0.0721950			0.0360975	+	0.999348i	$0.488507\pi$
$510$		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
$516$	−2.00000	−	3.00175i	−0.0880451	−	0.132145i
$517$		−	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	$0.0548512\pi$
$521$			7.82768i			0.342937i	−0.985190	+	0.171469i	$0.945149\pi$
$522$	−21.6878	+	20.2783i	−0.949250	+	0.887557i
$523$	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
$528$	17.9584	−	21.2936i	0.781539	−	0.926684i
$529$	−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
$534$	−1.83158	+	0.876906i	−0.0792604	+	0.0379474i
$535$		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
$546$	9.81981	+	20.5105i	0.420249	+	0.877770i
$547$	−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
$552$	−5.63220	−	6.30687i	−0.239722	−	0.268438i
$553$	−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	$-0.556494\pi$
$557$	−8.33343			−0.353099			−0.176549	+	0.984292i	$0.556494\pi$
$558$	−12.2754	−	13.1286i	−0.519657	−	0.555778i
$559$			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	$-0.903986\pi$
$563$		−	14.0982i		−	0.594166i	0.954852	−	0.297083i	$-0.0960138\pi$
$564$	14.5163	+	21.7872i	0.611248	+	0.917406i
$565$		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	$-0.937019\pi$
$569$		−	9.37801i		−	0.393147i	0.980489	−	0.196573i	$-0.0629814\pi$
$570$		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
$576$	−2.70385	+	23.8472i	−0.112660	+	0.993634i
$577$	−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
$582$	−1.53588	−	3.20797i	−0.0636642	−	0.132975i
$583$			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	$-0.741782\pi$
$587$		−	35.1368i		−	1.45025i	0.688617	−	0.725125i	$-0.258218\pi$
$588$	6.31028	+	9.47093i	0.260231	+	0.390575i
$589$			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	$-0.923309\pi$
$593$		−	11.6209i		−	0.477214i	0.971116	−	0.238607i	$-0.0766908\pi$
$594$	14.5177	−	25.7322i	0.595668	−	1.05581i
$595$		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	$-0.563495\pi$
$599$	−9.69953			−0.396312			−0.198156	+	0.980170i	$0.563495\pi$
$600$		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
$606$	4.44554	+	9.28536i	0.180588	+	0.377192i
$607$			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
$612$	24.4503	+	19.6815i	0.988345	+	0.795578i
$613$			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	$-0.908068\pi$
$617$		−	14.1493i		−	0.569630i	0.958583	−	0.284815i	$-0.0919322\pi$
$618$	15.6903	−	7.51203i	0.631156	−	0.302178i
$619$	−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
$624$	21.5146	−	25.5102i	0.861275	−	1.02123i
$625$		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
$636$	−7.84153	−	11.7691i	−0.310937	−	0.466677i
$637$		−	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	$-0.750266\pi$
$641$		−	35.7751i		−	1.41303i	0.707698	−	0.706515i	$-0.249734\pi$
$642$	−17.1509	+	8.21132i	−0.676892	+	0.324075i
$643$	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	$-0.543314\pi$
$647$	−6.90109			−0.271310			−0.135655	+	0.990756i	$0.543314\pi$
$648$	1.88369	+	25.3861i	0.0739984	+	0.997258i
$649$	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	$-0.606736\pi$
$653$	−16.8181			−0.658144			−0.329072	+	0.944305i	$0.606736\pi$
$654$	45.3146	−	21.6952i	1.77194	−	0.848350i
$655$		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	$-0.903217\pi$
$659$		−	15.3712i		−	0.598779i	0.954131	−	0.299389i	$-0.0967830\pi$
$660$		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
$666$	28.4899	+	30.4701i	1.10396	+	1.18069i
$667$	−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
$672$	−10.0217	+	16.0055i	−0.386596	+	0.617426i
$673$	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	$-0.294272\pi$
$677$	31.3401			1.20450			0.602249	+	0.798308i	$0.294272\pi$
$678$	−0.476786	+	0.228270i	−0.0183108	+	0.00876667i
$679$		−	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	$-0.958709\pi$
$683$		−	6.76121i		−	0.258710i	0.991598	−	0.129355i	$-0.0412907\pi$
$684$	2.57624	−	3.20045i	0.0985049	−	0.122372i
$685$		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
$696$	22.8364	+	25.5720i	0.865612	+	0.969303i
$697$	−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	$-0.559465\pi$
$701$	−9.83499			−0.371462			−0.185731	+	0.982601i	$0.559465\pi$
$702$	17.3926	−	30.8279i	0.656441	−	1.16352i
$703$		−	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
$708$	−2.86807	+	1.91093i	−0.107789	+	0.0718173i
$709$			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
$714$	10.6649	+	22.2756i	0.399123	+	0.833643i
$715$		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	$-0.676485\pi$
$719$	−28.2338			−1.05294			−0.526471	+	0.850193i	$0.676485\pi$
$720$		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
$726$	5.46334	+	11.4112i	0.202764	+	0.423510i
$727$		−	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
$732$	−9.13166	+	6.08423i	−0.337516	+	0.224879i
$733$			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
$738$	−9.96835	−	10.6612i	−0.366940	−	0.392445i
$739$	−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	$-0.729336\pi$
$743$	−35.9667			−1.31949			−0.659745	+	0.751489i	$0.729336\pi$
$744$	−15.4798	+	13.8239i	−0.567519	+	0.506809i
$745$		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
$756$	−7.28883	+	18.6564i	−0.265092	+	0.678526i
$757$		−	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	$0.319394\pi$
$761$			46.5273i			1.68661i	−0.537434	+	0.843306i	$0.680606\pi$
$762$	−36.6226	+	17.5338i	−1.32670	+	0.635181i
$763$	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
$768$	27.4578	+	3.75118i	0.990797	+	0.135359i
$769$	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	$-0.231354\pi$
$773$	41.5537			1.49458			0.747292	+	0.664496i	$0.231354\pi$
$774$	−3.22686	+	3.01714i	−0.115987	+	0.108449i
$775$		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
$786$	12.4008	−	5.93713i	0.442322	−	0.211770i
$787$	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
$792$	−29.3218	−	17.4389i	−1.04190	−	0.619663i
$793$	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	$-0.692317\pi$
$797$	−32.0757			−1.13618			−0.568090	+	0.822967i	$0.692317\pi$
$798$	2.91579	−	1.39599i	0.103218	−	0.0494176i
$799$		−	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
$804$	28.5672	+	42.8758i	1.00749	+	1.51211i
$805$		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	$0.00612785\pi$
$809$			1.09505i			0.0385001i	−0.999815	+	0.0192500i	$0.993872\pi$
$810$		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
$816$	23.3661	−	27.7056i	0.817977	−	0.969889i
$817$	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	$-0.193569\pi$
$821$	47.0327			1.64145			0.820726	+	0.571322i	$0.193569\pi$
$822$	20.8068	−	9.96166i	0.725721	−	0.347453i
$823$		−	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	$0.182660\pi$
$827$			31.2229i			1.08573i	−0.839821	+	0.542864i	$0.817340\pi$
$828$	−6.49373	+	8.06715i	−0.225673	+	0.280353i
$829$		−	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
$834$	6.89272	+	14.3967i	0.238675	+	0.498519i
$835$		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	$-0.578033\pi$
$839$	−14.0599			−0.485402			−0.242701	+	0.970101i	$0.578033\pi$
$840$		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
$846$	23.4211	−	21.8989i	0.805233	−	0.752900i
$847$			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
$852$	17.8316	+	26.7630i	0.610900	+	0.916884i
$853$		−	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	$0.294297\pi$
$857$			46.7431i			1.59671i	−0.602185	+	0.798357i	$0.705703\pi$
$858$	20.4847	+	42.7861i	0.699336	+	1.46069i
$859$	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	$-0.733858\pi$
$863$	−39.3858			−1.34071			−0.670354	+	0.742042i	$0.733858\pi$
$864$	29.3554	−	1.50402i	0.998690	−	0.0511679i
$865$		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
$876$	−21.6731	−	32.5286i	−0.732267	−	1.09904i
$877$			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	$-0.731886\pi$
$881$		−	44.2957i		−	1.49236i	0.665744	−	0.746180i	$-0.268114\pi$
$882$	10.1812	−	9.51950i	0.342818	−	0.320538i
$883$	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	$-0.617405\pi$
$887$	−21.4751			−0.721063			−0.360531	+	0.932747i	$0.617405\pi$
$888$	35.9272	−	32.0839i	1.20564	−	1.07666i
$889$	−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
$894$	−7.96971	−	16.6462i	−0.266547	−	0.556734i
$895$		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
$906$	20.7917	−	9.95442i	0.690758	−	0.330714i
$907$	−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	$-0.390788\pi$
$911$	20.3074			0.672815			0.336407	+	0.941717i	$0.390788\pi$
$912$	−3.62655	−	3.05854i	−0.120087	−	0.101278i
$913$	−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
$918$	18.8893	−	33.4808i	0.623440	−	1.10503i
$919$			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
$924$	−14.8841	−	22.3392i	−0.489652	−	0.734907i
$925$		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	$-0.891461\pi$
$929$		−	20.3857i		−	0.668834i	0.942425	−	0.334417i	$-0.108539\pi$
$930$		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
$936$	−35.1283	−	20.8922i	−1.14820	−	0.682883i
$937$	−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	$-0.429698\pi$
$941$	13.4402			0.438139			0.219070	+	0.975709i	$0.429698\pi$
$942$	7.72601	−	3.69897i	0.251727	−	0.120519i
$943$		−	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	$0.0256903\pi$
$947$			4.96195i			0.161242i	−0.996745	+	0.0806208i	$0.974310\pi$
$948$	26.6714	−	17.7706i	0.866247	−	0.577162i
$949$			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	$0.313239\pi$
$953$			51.4156i			1.66551i	−0.553639	+	0.832757i	$0.686761\pi$
$954$	−12.6517	+	11.8295i	−0.409615	+	0.382994i
$955$		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
$966$	−7.34962	+	3.51877i	−0.236470	+	0.113215i
$967$		−	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	$0.133861\pi$
$971$			25.4429i			0.816502i	−0.912870	+	0.408251i	$0.866139\pi$
$972$	30.2969	−	7.35499i	0.971775	−	0.235911i
$973$			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	$0.140182\pi$
$977$			26.6495i			0.852593i	−0.904584	+	0.426296i	$0.859818\pi$
$978$	17.9347	+	37.4600i	0.573488	+	1.19784i
$979$	−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	$-0.229597\pi$
$983$	47.0887			1.50190			0.750948	+	0.660361i	$0.229597\pi$
$984$	−12.5706	+	11.2259i	−0.400736	+	0.357867i
$985$		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
$996$	20.6370	−	13.7500i	0.653909	−	0.435686i
$997$			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.e.251.2		8
3.2	odd	2		600.2.b.f.251.7		8
4.3	odd	2		2400.2.b.e.2351.3		8
5.2	odd	4		600.2.m.d.299.7		16
5.3	odd	4		600.2.m.d.299.10		16
5.4	even	2		120.2.b.b.11.7	yes	8
8.3	odd	2		600.2.b.f.251.8		8
8.5	even	2		2400.2.b.f.2351.3		8
12.11	even	2		2400.2.b.f.2351.4		8
15.2	even	4		600.2.m.c.299.10		16
15.8	even	4		600.2.m.c.299.7		16
15.14	odd	2		120.2.b.a.11.2	yes	8
20.3	even	4		2400.2.m.c.1199.15		16
20.7	even	4		2400.2.m.c.1199.2		16
20.19	odd	2		480.2.b.a.431.6		8
24.5	odd	2		2400.2.b.e.2351.4		8
24.11	even	2	inner	600.2.b.e.251.1		8
40.3	even	4		600.2.m.c.299.9		16
40.13	odd	4		2400.2.m.d.1199.15		16
40.19	odd	2		120.2.b.a.11.1	✓	8
40.27	even	4		600.2.m.c.299.8		16
40.29	even	2		480.2.b.b.431.6		8
40.37	odd	4		2400.2.m.d.1199.2		16
60.23	odd	4		2400.2.m.d.1199.1		16
60.47	odd	4		2400.2.m.d.1199.16		16
60.59	even	2		480.2.b.b.431.5		8
120.29	odd	2		480.2.b.a.431.5		8
120.53	even	4		2400.2.m.c.1199.1		16
120.59	even	2		120.2.b.b.11.8	yes	8
120.77	even	4		2400.2.m.c.1199.16		16
120.83	odd	4		600.2.m.d.299.8		16
120.107	odd	4		600.2.m.d.299.9		16

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

\(f(q)\)	\(=\)	\(q+(-1.40014 + 0.199044i) q^{2} +(0.520627 + 1.65195i) q^{3} +(1.92076 - 0.557378i) q^{4} +(-1.05776 - 2.20933i) q^{6} -1.92736i q^{7} +(-2.57839 + 1.16272i) q^{8} +(-2.45790 + 1.72010i) q^{9} +O(q^{10})\)	\(q+(-1.40014 + 0.199044i) q^{2} +(0.520627 + 1.65195i) q^{3} +(1.92076 - 0.557378i) q^{4} +(-1.05776 - 2.20933i) q^{6} -1.92736i q^{7} +(-2.57839 + 1.16272i) q^{8} +(-2.45790 + 1.72010i) q^{9} -4.02057i q^{11} +(1.92076 + 2.88282i) q^{12} -4.81675i q^{13} +(0.383629 + 2.69856i) q^{14} +(3.37866 - 2.14118i) q^{16} -5.23126i q^{17} +(3.09901 - 2.89761i) q^{18} -0.684753 q^{19} +(3.18390 - 1.00343i) q^{21} +(0.800272 + 5.62935i) q^{22} +1.72601 q^{23} +(-3.26314 - 3.65403i) 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} +(-3.76229 + 4.67388i) q^{36} +9.83221i q^{37} +(0.958747 - 0.136296i) q^{38} +(7.95705 - 2.50773i) q^{39} -3.44020i q^{41} +(-4.25817 + 2.03868i) q^{42} -1.04125 q^{43} +(-2.24098 - 7.72257i) q^{44} +(-2.41664 + 0.343552i) q^{46} +7.55759 q^{47} +(5.29615 + 4.46663i) q^{48} +3.28530 q^{49} +(8.64180 - 2.72353i) q^{51} +(-2.68475 - 9.25184i) q^{52} -4.08251 q^{53} +(6.40014 + 3.61085i) 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} +(-8.88278 + 4.25280i) q^{66} +14.8728 q^{67} +(-2.91579 - 10.0480i) q^{68} +(0.898604 + 2.85128i) q^{69} +9.28360 q^{71} +(4.33741 - 7.29294i) q^{72} -11.2836 q^{73} +(-1.95705 - 13.7664i) q^{74} +(-1.31525 + 0.381666i) q^{76} -7.74908 q^{77} +(-10.6418 + 5.09497i) q^{78} -9.25184i q^{79} +(3.08251 - 8.45566i) q^{81} +(0.684753 + 4.81675i) q^{82} -7.15862i q^{83} +(5.55623 - 3.70199i) 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} +(-8.30439 - 5.19972i) q^{96} +1.45201 q^{97} +(-4.59986 + 0.653920i) q^{98} +(6.91579 + 9.88215i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} + q^{4} + q^{6} - 7 q^{8}+O(q^{10}) \) 8 * q - q^2 + q^4 + q^6 - 7 * q^8	\( 8 q - q^{2} + q^{4} + q^{6} - 7 q^{8} + q^{12} - 6 q^{14} - 7 q^{16} + 7 q^{18} - 4 q^{19} - 4 q^{21} - 14 q^{22} + 4 q^{23} - 11 q^{24} + 16 q^{26} + 12 q^{27} + 2 q^{28} - 11 q^{32} + 4 q^{33} + 13 q^{36} + 16 q^{38} + 16 q^{39} + 6 q^{42} - 30 q^{44} - 8 q^{46} - 28 q^{47} + 25 q^{48} - 16 q^{49} + 20 q^{51} - 20 q^{52} - 16 q^{53} + 41 q^{54} + 30 q^{56} + 4 q^{57} + 2 q^{58} + 34 q^{62} + 28 q^{63} + 25 q^{64} - 34 q^{66} + 32 q^{67} + 16 q^{68} + 20 q^{69} - 24 q^{71} + 9 q^{72} + 8 q^{73} + 32 q^{74} - 12 q^{76} - 36 q^{78} + 8 q^{81} + 4 q^{82} + 58 q^{84} - 8 q^{86} - 36 q^{87} - 14 q^{88} + 24 q^{91} + 28 q^{92} - 40 q^{94} - 43 q^{96} - 8 q^{97} - 47 q^{98} + 16 q^{99}+O(q^{100}) \) 8 * q - q^2 + q^4 + q^6 - 7 * q^8 + q^12 - 6 * q^14 - 7 * q^16 + 7 * q^18 - 4 * q^19 - 4 * q^21 - 14 * q^22 + 4 * q^23 - 11 * q^24 + 16 * q^26 + 12 * q^27 + 2 * q^28 - 11 * q^32 + 4 * q^33 + 13 * q^36 + 16 * q^38 + 16 * q^39 + 6 * q^42 - 30 * q^44 - 8 * q^46 - 28 * q^47 + 25 * q^48 - 16 * q^49 + 20 * q^51 - 20 * q^52 - 16 * q^53 + 41 * q^54 + 30 * q^56 + 4 * q^57 + 2 * q^58 + 34 * q^62 + 28 * q^63 + 25 * q^64 - 34 * q^66 + 32 * q^67 + 16 * q^68 + 20 * q^69 - 24 * q^71 + 9 * q^72 + 8 * q^73 + 32 * q^74 - 12 * q^76 - 36 * q^78 + 8 * q^81 + 4 * q^82 + 58 * q^84 - 8 * q^86 - 36 * q^87 - 14 * q^88 + 24 * q^91 + 28 * q^92 - 40 * q^94 - 43 * q^96 - 8 * q^97 - 47 * q^98 + 16 * q^99

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