LMFDB - Embedded newform 600.2.m.d.299.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,2,Mod(299,600)]

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, 1]))

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

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

chi := DirichletCharacter("600.299");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.m (of order $2$, degree $1$, not 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:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + x^{14} + 4x^{12} + 12x^{10} + 16x^{8} + 48x^{6} + 64x^{4} + 64x^{2} + 256 $ x^16 + x^14 + 4x^12 + 12x^10 + 16x^8 + 48x^6 + 64x^4 + 64x^2 + 256
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{11} $
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			299.9
Root			$0.199044 - 1.40014i$ of defining polynomial
Character	$\chi$	$=$	600.299
Dual form			600.2.m.d.299.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.199044 - 1.40014i) q^{2} +(-1.65195 - 0.520627i) q^{3} +(-1.92076 - 0.557378i) q^{4} +(-1.05776 + 2.20933i) q^{6} -1.92736 q^{7} +(-1.16272 + 2.57839i) q^{8} +(2.45790 + 1.72010i) q^{9} +O(q^{10})$	\(q+(0.199044 - 1.40014i) q^{2} +(-1.65195 - 0.520627i) q^{3} +(-1.92076 - 0.557378i) q^{4} +(-1.05776 + 2.20933i) q^{6} -1.92736 q^{7} +(-1.16272 + 2.57839i) q^{8} +(2.45790 + 1.72010i) q^{9} +4.02057i q^{11} +(2.88282 + 1.92076i) q^{12} +4.81675 q^{13} +(-0.383629 + 2.69856i) q^{14} +(3.37866 + 2.14118i) q^{16} -5.23126 q^{17} +(2.89761 - 3.09901i) q^{18} +0.684753 q^{19} +(3.18390 + 1.00343i) q^{21} +(5.62935 + 0.800272i) q^{22} -1.72601i q^{23} +(3.26314 - 3.65403i) q^{24} +(0.958747 - 6.74411i) q^{26} +(-3.16480 - 4.12117i) q^{27} +(3.70199 + 1.07427i) q^{28} +6.99830 q^{29} +4.23638i q^{31} +(3.67045 - 4.30439i) q^{32} +(2.09322 - 6.64180i) q^{33} +(-1.04125 + 7.32448i) q^{34} +(-3.76229 - 4.67388i) q^{36} +9.83221 q^{37} +(0.136296 - 0.958747i) q^{38} +(-7.95705 - 2.50773i) q^{39} +3.44020i q^{41} +(2.03868 - 4.25817i) q^{42} +1.04125i q^{43} +(2.24098 - 7.72257i) q^{44} +(-2.41664 - 0.343552i) q^{46} +7.55759i q^{47} +(-4.46663 - 5.29615i) q^{48} -3.28530 q^{49} +(8.64180 + 2.72353i) q^{51} +(-9.25184 - 2.68475i) q^{52} +4.08251i q^{53} +(-6.40014 + 3.61085i) q^{54} +(2.24098 - 4.96947i) q^{56} +(-1.13118 - 0.356500i) q^{57} +(1.39297 - 9.79857i) q^{58} +0.994883i q^{59} -3.16761i q^{61} +(5.93151 + 0.843227i) q^{62} +(-4.73724 - 3.31525i) q^{63} +(-5.29615 - 5.99590i) q^{64} +(-8.88278 - 4.25280i) q^{66} +14.8728i q^{67} +(10.0480 + 2.91579i) q^{68} +(-0.898604 + 2.85128i) q^{69} +9.28360 q^{71} +(-7.29294 + 4.33741i) q^{72} +11.2836i q^{73} +(1.95705 - 13.7664i) q^{74} +(-1.31525 - 0.381666i) q^{76} -7.74908i q^{77} +(-5.09497 + 10.6418i) q^{78} -9.25184i q^{79} +(3.08251 + 8.45566i) q^{81} +(4.81675 + 0.684753i) q^{82} +7.15862 q^{83} +(-5.55623 - 3.70199i) q^{84} +(1.45790 + 0.207256i) q^{86} +(-11.5609 - 3.64350i) q^{87} +(-10.3666 - 4.67481i) q^{88} -0.829022i q^{89} -9.28360 q^{91} +(-0.962038 + 3.31525i) q^{92} +(2.20557 - 6.99830i) q^{93} +(10.5817 + 1.50430i) q^{94} +(-8.30439 + 5.19972i) q^{96} +1.45201i q^{97} +(-0.653920 + 4.59986i) q^{98} +(-6.91579 + 9.88215i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{4} + 2 q^{6}+O(q^{10}) $ 16 * q - 2 * q^4 + 2 * q^6	$ 16 q - 2 q^{4} + 2 q^{6} + 12 q^{14} - 14 q^{16} + 8 q^{19} - 8 q^{21} + 22 q^{24} + 32 q^{26} + 26 q^{36} - 32 q^{39} + 60 q^{44} - 16 q^{46} + 32 q^{49} + 40 q^{51} - 82 q^{54} + 60 q^{56} - 50 q^{64} - 68 q^{66} - 40 q^{69} - 48 q^{71} - 64 q^{74} - 24 q^{76} + 16 q^{81} - 116 q^{84} - 16 q^{86} + 48 q^{91} + 80 q^{94} - 86 q^{96} - 32 q^{99}+O(q^{100}) $ 16 * q - 2 * q^4 + 2 * q^6 + 12 * q^14 - 14 * q^16 + 8 * q^19 - 8 * q^21 + 22 * q^24 + 32 * q^26 + 26 * q^36 - 32 * q^39 + 60 * q^44 - 16 * q^46 + 32 * q^49 + 40 * q^51 - 82 * q^54 + 60 * q^56 - 50 * q^64 - 68 * q^66 - 40 * q^69 - 48 * q^71 - 64 * q^74 - 24 * q^76 + 16 * q^81 - 116 * q^84 - 16 * q^86 + 48 * q^91 + 80 * q^94 - 86 * q^96 - 32 * 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 $

$2$	0.199044	−	1.40014i	0.140746	−	0.990046i
$2$	0.199044	−	1.40014i	0.140746	−	0.990046i
$3$	−1.65195	−	0.520627i	−0.953755	−	0.300584i
$3$	−1.65195	−	0.520627i	−0.953755	−	0.300584i
$4$	−1.92076	−	0.557378i	−0.960381	−	0.278689i
$5$		0			0
$5$		0			0
$6$	−1.05776	+	2.20933i	−0.431829	+	0.901956i
$7$	−1.92736			−0.728472			−0.364236	−	0.931307i	$-0.618670\pi$
$7$	−1.92736			−0.728472			−0.364236	+	0.931307i	$0.618670\pi$
$8$	−1.16272	+	2.57839i	−0.411084	+	0.911597i
$9$	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	$0.792723\pi$
$12$	2.88282	+	1.92076i	0.832199	+	0.554476i
$13$	4.81675			1.33593			0.667963	−	0.744194i	$-0.267166\pi$
$13$	4.81675			1.33593			0.667963	+	0.744194i	$0.267166\pi$
$14$	−0.383629	+	2.69856i	−0.102529	+	0.721221i
$15$		0			0
$16$	3.37866	+	2.14118i	0.844665	+	0.535296i
$17$	−5.23126			−1.26877			−0.634384	−	0.773018i	$-0.718746\pi$
$17$	−5.23126			−1.26877			−0.634384	+	0.773018i	$0.718746\pi$
$18$	2.89761	−	3.09901i	0.682972	−	0.730444i
$19$	0.684753			0.157093			0.0785465	−	0.996910i	$-0.474972\pi$
$19$	0.684753			0.157093			0.0785465	+	0.996910i	$0.474972\pi$
$20$		0			0
$21$	3.18390	+	1.00343i	0.694784	+	0.218967i
$22$	5.62935	+	0.800272i	1.20018	+	0.170619i
$23$		−	1.72601i		−	0.359897i	−0.983676	−	0.179949i	$-0.942407\pi$
$23$		−	1.72601i		−	0.359897i	0.983676	−	0.179949i	$-0.0575931\pi$
$24$	3.26314	−	3.65403i	0.666085	−	0.745875i
$25$		0			0
$26$	0.958747	−	6.74411i	0.188026	−	1.32263i
$27$	−3.16480	−	4.12117i	−0.609066	−	0.793120i
$28$	3.70199	+	1.07427i	0.699611	+	0.203017i
$29$	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	$0.124227\pi$
$31$			4.23638i			0.760876i	−0.924806	+	0.380438i	$0.875773\pi$
$32$	3.67045	−	4.30439i	0.648850	−	0.760916i
$33$	2.09322	−	6.64180i	0.364382	−	1.15619i
$34$	−1.04125	+	7.32448i	−0.178573	+	1.25614i
$35$		0			0
$36$	−3.76229	−	4.67388i	−0.627048	−	0.778981i
$37$	9.83221			1.61640			0.808202	−	0.588905i	$-0.200441\pi$
$37$	9.83221			1.61640			0.808202	+	0.588905i	$0.200441\pi$
$38$	0.136296	−	0.958747i	0.0221102	−	0.155529i
$39$	−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	$0.913428\pi$
$42$	2.03868	−	4.25817i	0.314575	−	0.657050i
$43$			1.04125i			0.158790i	0.996843	+	0.0793948i	$0.0252988\pi$
$43$			1.04125i			0.158790i	−0.996843	+	0.0793948i	$0.974701\pi$
$44$	2.24098	−	7.72257i	0.337841	−	1.16422i
$45$		0			0
$46$	−2.41664	−	0.343552i	−0.356315	−	0.0506539i
$47$			7.55759i			1.10239i	0.834377	+	0.551194i	$0.185828\pi$
$47$			7.55759i			1.10239i	−0.834377	+	0.551194i	$0.814172\pi$
$48$	−4.46663	−	5.29615i	−0.644702	−	0.764434i
$49$	−3.28530			−0.469328
$50$		0			0
$51$	8.64180	+	2.72353i	1.21009	+	0.381371i
$52$	−9.25184	−	2.68475i	−1.28300	−	0.372308i
$53$			4.08251i			0.560775i	0.959887	+	0.280388i	$0.0904630\pi$
$53$			4.08251i			0.560775i	−0.959887	+	0.280388i	$0.909537\pi$
$54$	−6.40014	+	3.61085i	−0.870948	+	0.491375i
$55$		0			0
$56$	2.24098	−	4.96947i	0.299464	−	0.664073i
$57$	−1.13118	−	0.356500i	−0.149828	−	0.0472196i
$58$	1.39297	−	9.79857i	0.182906	−	1.28662i
$59$			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	$-0.935001\pi$
$61$		−	3.16761i		−	0.405571i	0.979223	−	0.202785i	$-0.0649994\pi$
$62$	5.93151	+	0.843227i	0.753302	+	0.107090i
$63$	−4.73724	−	3.31525i	−0.596836	−	0.417682i
$64$	−5.29615	−	5.99590i	−0.662019	−	0.749487i
$65$		0			0
$66$	−8.88278	−	4.25280i	−1.09339	−	0.523484i
$67$			14.8728i			1.81701i	0.417878	+	0.908503i	$0.362774\pi$
$67$			14.8728i			1.81701i	−0.417878	+	0.908503i	$0.637226\pi$
$68$	10.0480	+	2.91579i	1.21850	+	0.353592i
$69$	−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	$0.314292\pi$
$72$	−7.29294	+	4.33741i	−0.859481	+	0.511168i
$73$			11.2836i			1.32064i	0.750982	+	0.660322i	$0.229580\pi$
$73$			11.2836i			1.32064i	−0.750982	+	0.660322i	$0.770420\pi$
$74$	1.95705	−	13.7664i	0.227502	−	1.60031i
$75$		0			0
$76$	−1.31525	−	0.381666i	−0.150869	−	0.0437801i
$77$		−	7.74908i		−	0.883089i
$78$	−5.09497	+	10.6418i	−0.576891	+	1.20495i
$79$		−	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
$82$	4.81675	+	0.684753i	0.531921	+	0.0756183i
$83$	7.15862			0.785760			0.392880	−	0.919590i	$-0.371479\pi$
$83$	7.15862			0.785760			0.392880	+	0.919590i	$0.371479\pi$
$84$	−5.55623	−	3.70199i	−0.606234	−	0.403921i
$85$		0			0
$86$	1.45790	+	0.207256i	0.157209	+	0.0223489i
$87$	−11.5609	−	3.64350i	−1.23945	−	0.390624i
$88$	−10.3666	−	4.67481i	−1.10508	−	0.498337i
$89$		−	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
$92$	−0.962038	+	3.31525i	−0.100299	+	0.345638i
$93$	2.20557	−	6.99830i	0.228707	−	0.725690i
$94$	10.5817	+	1.50430i	1.09141	+	0.155156i
$95$		0			0
$96$	−8.30439	+	5.19972i	−0.847563	+	0.530694i
$97$			1.45201i			0.147429i	0.997279	+	0.0737147i	$0.0234854\pi$
$97$			1.45201i			0.147429i	−0.997279	+	0.0737147i	$0.976515\pi$
$98$	−0.653920	+	4.59986i	−0.0660559	+	0.464656i
$99$	−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	$0.567052\pi$
$102$	5.53342	−	11.5576i	0.547890	−	1.14437i
$103$	−7.10183			−0.699764			−0.349882	−	0.936794i	$-0.613778\pi$
$103$	−7.10183			−0.699764			−0.349882	+	0.936794i	$0.613778\pi$
$104$	−5.60054	+	12.4194i	−0.549179	+	1.21783i
$105$		0			0
$106$	5.71606	+	0.812600i	0.555193	+	0.0789267i
$107$	−7.76293			−0.750471			−0.375235	−	0.926930i	$-0.622438\pi$
$107$	−7.76293			−0.750471			−0.375235	+	0.926930i	$0.622438\pi$
$108$	3.78177	+	9.67978i	0.363901	+	0.931437i
$109$			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
$112$	−6.51188	−	4.12682i	−0.615315	−	0.389948i
$113$	0.215805			0.0203013			0.0101506	−	0.999948i	$-0.496769\pi$
$113$	0.215805			0.0203013			0.0101506	+	0.999948i	$0.496769\pi$
$114$	−0.724304	+	1.51285i	−0.0678373	+	0.141691i
$115$		0			0
$116$	−13.4421	−	3.90070i	−1.24806	−	0.362171i
$117$	11.8391	+	8.28530i	1.09452	+	0.765976i
$118$	1.39297	+	0.198026i	0.128233	+	0.0182298i
$119$	10.0825			0.924262
$120$		0			0
$121$	−5.16501			−0.469547
$122$	−4.43508	−	0.630495i	−0.401534	−	0.0570823i
$123$	1.79106	−	5.68305i	0.161494	−	0.512423i
$124$	2.36127	−	8.13708i	0.212048	−	0.730731i
$125$		0			0
$126$	−5.58472	+	5.97290i	−0.497526	+	0.532108i
$127$	−16.5763			−1.47091			−0.735455	−	0.677574i	$-0.763032\pi$
$127$	−16.5763			−1.47091			−0.735455	+	0.677574i	$0.763032\pi$
$128$	−9.44924	+	6.22189i	−0.835203	+	0.549942i
$129$	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	$-0.0788543\pi$
$132$	−7.72257	+	11.5906i	−0.672163	+	1.00883i
$133$	−1.31976			−0.114438
$134$	20.8240	+	2.96035i	1.79892	+	0.255736i
$135$		0			0
$136$	6.08251	−	13.4882i	0.521571	−	1.15660i
$137$	9.41770			0.804608			0.402304	−	0.915506i	$-0.368209\pi$
$137$	9.41770			0.804608			0.402304	+	0.915506i	$0.368209\pi$
$138$	3.81332	+	1.82570i	0.324611	+	0.155414i
$139$	6.51634			0.552708			0.276354	−	0.961056i	$-0.410874\pi$
$139$	6.51634			0.552708			0.276354	+	0.961056i	$0.410874\pi$
$140$		0			0
$141$	3.93468	−	12.4848i	0.331360	−	1.05141i
$142$	1.84785	−	12.9983i	0.155068	−	1.09079i
$143$			19.3661i			1.61947i
$144$	4.62134	+	11.0744i	0.385112	+	0.922870i
$145$		0			0
$146$	15.7986	+	2.24594i	1.30750	+	0.185875i
$147$	5.42716	+	1.71041i	0.447624	+	0.141072i
$148$	−18.8853	−	5.48026i	−1.55237	−	0.450475i
$149$	−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	$-0.874918\pi$
$151$		−	9.41085i		−	0.765844i	0.923781	−	0.382922i	$-0.125082\pi$
$152$	−0.796177	+	1.76556i	−0.0645785	+	0.143206i
$153$	−12.8579	−	8.99830i	−1.03950	−	0.727469i
$154$	−10.8498	−	1.54241i	−0.874299	−	0.124291i
$155$		0			0
$156$	13.8858	+	9.25184i	1.11176	+	0.740740i
$157$	3.49699			0.279090			0.139545	−	0.990216i	$-0.455436\pi$
$157$	3.49699			0.279090			0.139545	+	0.990216i	$0.455436\pi$
$158$	−12.9538	−	1.84153i	−1.03055	−	0.146504i
$159$	2.12546	−	6.74411i	0.168560	−	0.534842i
$160$		0			0
$161$			3.32663i			0.262175i
$162$	12.4526	−	2.63288i	0.978371	−	0.206858i
$163$			16.9553i			1.32804i	0.747713	+	0.664022i	$0.231152\pi$
$163$			16.9553i			1.32804i	−0.747713	+	0.664022i	$0.768848\pi$
$164$	1.91749	−	6.60781i	0.149731	−	0.515983i
$165$		0			0
$166$	1.42488	−	10.0230i	0.110592	−	0.777939i
$167$			11.3926i			0.881584i	0.897609	+	0.440792i	$0.145302\pi$
$167$			11.3926i			0.881584i	−0.897609	+	0.440792i	$0.854698\pi$
$168$	−6.28923	+	7.04261i	−0.485225	+	0.543350i
$169$	10.2011			0.784699
$170$		0			0
$171$	1.68305	+	1.17784i	0.128706	+	0.0900720i
$172$	0.580372	−	2.00000i	0.0442529	−	0.152499i
$173$		−	2.16501i		−	0.164603i	−0.996607	−	0.0823014i	$-0.973773\pi$
$173$		−	2.16501i		−	0.164603i	0.996607	−	0.0823014i	$-0.0262270\pi$
$174$	−7.40252	+	15.4616i	−0.561184	+	1.17214i
$175$		0			0
$176$	−8.60878	+	13.5841i	−0.648912	+	1.02394i
$177$	0.517962	−	1.64350i	0.0389324	−	0.123533i
$178$	−1.16074	−	0.165012i	−0.0870014	−	0.0123682i
$179$		−	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	$0.131395\pi$
$181$			10.7942i			0.802330i	−0.916006	+	0.401165i	$0.868605\pi$
$182$	−1.84785	+	12.9983i	−0.136972	+	0.963498i
$183$	−1.64914	+	5.23274i	−0.121908	+	0.386815i
$184$	4.45031	+	2.00687i	0.328081	+	0.147948i
$185$		0			0
$186$	−9.35956	−	4.48107i	−0.686277	−	0.328568i
$187$		−	21.0327i		−	1.53806i
$188$	4.21244	−	14.5163i	0.307224	−	1.05871i
$189$	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	$0.246656\pi$
$192$	5.62737	+	12.6623i	0.406121	+	0.913819i
$193$			5.45201i			0.392444i	0.980559	+	0.196222i	$0.0628674\pi$
$193$			5.45201i			0.392444i	−0.980559	+	0.196222i	$0.937133\pi$
$194$	2.03301	+	0.289015i	0.145962	+	0.0207500i
$195$		0			0
$196$	6.31028	+	1.83115i	0.450734	+	0.130797i
$197$		−	22.6497i		−	1.61372i	−0.590740	−	0.806862i	$-0.701164\pi$
$197$		−	22.6497i		−	1.61372i	0.590740	−	0.806862i	$-0.298836\pi$
$198$	12.4598	+	11.6500i	0.885480	+	0.827932i
$199$		−	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
$202$	−0.836542	+	5.88448i	−0.0588589	+	0.414031i
$203$	−13.4882			−0.946687
$204$	−15.0808	−	10.0480i	−1.05587	−	0.703502i
$205$		0			0
$206$	−1.41358	+	9.94353i	−0.0984887	+	0.692799i
$207$	2.96890	−	4.24234i	0.206353	−	0.294863i
$208$	16.2742	+	10.3135i	1.12841	+	0.715116i
$209$			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	$0.620856\pi$
$212$	2.27550	−	7.84153i	0.156282	−	0.538558i
$213$	−15.3361	−	4.83329i	−1.05081	−	0.331171i
$214$	−1.54517	+	10.8692i	−0.105625	+	0.743001i
$215$		0			0
$216$	14.3058	−	3.36829i	0.973383	−	0.229183i
$217$		−	8.16501i		−	0.554277i
$218$	28.7175	+	4.08251i	1.94500	+	0.276502i
$219$	5.87454	−	18.6400i	0.396965	−	1.25957i
$220$		0			0
$221$	−25.1977			−1.69498
$222$	−10.4001	+	21.7226i	−0.698010	+	1.45793i
$223$	6.54540			0.438313			0.219156	−	0.975690i	$-0.429670\pi$
$223$	6.54540			0.438313			0.219156	+	0.975690i	$0.429670\pi$
$224$	−7.07427	+	8.29610i	−0.472669	+	0.554306i
$225$		0			0
$226$	0.0429548	−	0.302157i	0.00285731	−	0.0200992i
$227$	22.5118			1.49416			0.747080	−	0.664735i	$-0.231455\pi$
$227$	22.5118			1.49416			0.747080	+	0.664735i	$0.231455\pi$
$228$	1.97402	+	1.31525i	0.130733	+	0.0871044i
$229$		−	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
$232$	−8.13708	+	18.0443i	−0.534225	+	1.18467i
$233$	10.8510			0.710875			0.355437	−	0.934700i	$-0.384332\pi$
$233$	10.8510			0.710875			0.355437	+	0.934700i	$0.384332\pi$
$234$	13.9570	−	14.9272i	0.912401	−	0.975820i
$235$		0			0
$236$	0.554526	−	1.91093i	0.0360966	−	0.124391i
$237$	−4.81675	+	15.2836i	−0.312882	+	0.992776i
$238$	2.00687	−	14.1169i	0.130086	−	0.915062i
$239$	−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	$0.671753\pi$
$242$	−1.02807	+	7.23172i	−0.0660866	+	0.464873i
$243$	−0.689915	−	15.5732i	−0.0442580	−	0.999020i
$244$	−1.76556	+	6.08423i	−0.113028	+	0.389503i
$245$		0			0
$246$	−7.60054	−	3.63891i	−0.484593	−	0.232008i
$247$	3.29828			0.209865
$248$	−10.9230	−	4.92573i	−0.693613	−	0.312784i
$249$	−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	$-0.159789\pi$
$252$	7.25127	+	9.00824i	0.456787	+	0.567466i
$253$	6.93953			0.436285
$254$	−3.29942	+	23.2091i	−0.207024	+	1.45627i
$255$		0			0
$256$	6.83067	+	14.4687i	0.426917	+	0.904291i
$257$	−16.1845			−1.00956			−0.504782	−	0.863247i	$-0.668427\pi$
$257$	−16.1845			−1.00956			−0.504782	+	0.863247i	$0.668427\pi$
$258$	−2.30047	−	1.10140i	−0.143221	−	0.0685699i
$259$	−18.9502			−1.17751
$260$		0			0
$261$	17.2011	+	12.0378i	1.06472	+	0.745120i
$262$	−7.85886	−	1.11722i	−0.485522	−	0.0690222i
$263$		−	21.4751i		−	1.32421i	−0.749411	−	0.662105i	$-0.769663\pi$
$263$		−	21.4751i		−	1.32421i	0.749411	−	0.662105i	$-0.230337\pi$
$264$	14.6913	+	13.1197i	0.904186	+	0.807461i
$265$		0			0
$266$	−0.262691	+	1.84785i	−0.0161066	+	0.113299i
$267$	−0.431611	+	1.36951i	−0.0264142	+	0.0838124i
$268$	8.28980	−	28.5672i	0.506380	−	1.74502i
$269$	−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	$0.163653\pi$
$271$			16.1914i			0.983556i	−0.870721	+	0.491778i	$0.836347\pi$
$272$	−17.6746	−	11.2011i	−1.07168	−	0.679166i
$273$	15.3361	+	4.83329i	0.928181	+	0.292524i
$274$	1.87454	−	13.1861i	0.113245	−	0.796599i
$275$		0			0
$276$	3.31525	−	4.97577i	0.199554	−	0.299506i
$277$	3.81503			0.229223			0.114611	−	0.993410i	$-0.463438\pi$
$277$	3.81503			0.229223			0.114611	+	0.993410i	$0.463438\pi$
$278$	1.29704	−	9.12376i	0.0777913	−	0.547207i
$279$	−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	$-0.313724\pi$
$282$	−16.6972	−	7.99412i	−0.994305	−	0.476043i
$283$		−	5.58924i		−	0.332246i	−0.986105	−	0.166123i	$-0.946875\pi$
$283$		−	5.58924i		−	0.332246i	0.986105	−	0.166123i	$-0.0531249\pi$
$284$	−17.8316	−	5.17448i	−1.05811	−	0.307049i
$285$		0			0
$286$	27.1152	+	3.85471i	1.60335	+	0.227934i
$287$		−	6.63049i		−	0.391386i
$288$	16.4256	−	4.26620i	0.967886	−	0.251388i
$289$	10.3661			0.609771
$290$		0			0
$291$	0.755956	−	2.39865i	0.0443149	−	0.140612i
$292$	6.28923	−	21.6731i	0.368049	−	1.26832i
$293$		−	6.00000i		−	0.350524i	−0.984522	−	0.175262i	$-0.943923\pi$
$293$		−	6.00000i		−	0.350524i	0.984522	−	0.175262i	$-0.0560772\pi$
$294$	3.47506	−	7.25831i	0.202669	−	0.423313i
$295$		0			0
$296$	−11.4321	+	25.3512i	−0.664479	+	1.47351i
$297$	16.5695	−	12.7243i	0.961458	−	0.738339i
$298$	−1.49970	+	10.5494i	−0.0868755	+	0.611107i
$299$		−	8.31374i		−	0.480796i
$300$		0			0
$301$		−	2.00687i		−	0.115674i
$302$	−13.1765	−	1.87318i	−0.758221	−	0.107789i
$303$	6.94281	+	2.18808i	0.398854	+	0.125702i
$304$	2.31355	+	1.46618i	0.132691	+	0.0840912i
$305$		0			0
$306$	−15.1581	+	16.2117i	−0.866533	+	0.926764i
$307$			4.79033i			0.273399i	0.990613	+	0.136699i	$0.0436494\pi$
$307$			4.79033i			0.273399i	−0.990613	+	0.136699i	$0.956351\pi$
$308$	−4.31917	+	14.8841i	−0.246107	+	0.848103i
$309$	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	$0.618973\pi$
$312$	15.7177	−	17.6005i	0.889841	−	0.996435i
$313$		−	20.4022i		−	1.15320i	−0.817027	−	0.576600i	$-0.804379\pi$
$313$		−	20.4022i		−	1.15320i	0.817027	−	0.576600i	$-0.195621\pi$
$314$	0.696056	−	4.89626i	0.0392807	−	0.276312i
$315$		0			0
$316$	−5.15677	+	17.7706i	−0.290091	+	0.999673i
$317$			5.34350i			0.300121i	0.988677	+	0.150060i	$0.0479468\pi$
$317$			5.34350i			0.300121i	−0.988677	+	0.150060i	$0.952053\pi$
$318$	−9.01961	−	4.31831i	−0.505794	−	0.242159i
$319$			28.1372i			1.57538i
$320$		0			0
$321$	12.8240	+	4.04159i	0.715766	+	0.225579i
$322$	4.65773	+	0.662146i	0.259565	+	0.0369000i
$323$	−3.58212			−0.199315
$324$	−1.20776	−	17.9594i	−0.0670979	−	0.997746i
$325$		0			0
$326$	23.7398	+	3.37486i	1.31483	+	0.186916i
$327$	10.6783	−	33.8824i	0.590513	−	1.87370i
$328$	−8.87017	−	4.00000i	−0.489773	−	0.220863i
$329$		−	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	$0.256854\pi$
$332$	−13.7500	−	3.99006i	−0.754630	−	0.218983i
$333$	24.1665	+	16.9124i	1.32432	+	0.926793i
$334$	15.9512	+	2.26763i	0.872809	+	0.124079i
$335$		0			0
$336$	8.60878	+	10.2076i	0.469648	+	0.556869i
$337$			20.1616i			1.09827i	0.835733	+	0.549136i	$0.185043\pi$
$337$			20.1616i			1.09827i	−0.835733	+	0.549136i	$0.814957\pi$
$338$	2.03047	−	14.2829i	0.110443	−	0.776888i
$339$	−0.356500	−	0.112354i	−0.0193624	−	0.00610223i
$340$		0			0
$341$	−17.0327			−0.922371
$342$	1.98414	−	2.12206i	0.107290	−	0.114748i
$343$	19.8234			1.07036
$344$	−2.68475	−	1.21069i	−0.144752	−	0.0652759i
$345$		0			0
$346$	−3.03131	−	0.430933i	−0.162964	−	0.0231671i
$347$	9.41442			0.505392			0.252696	−	0.967546i	$-0.418683\pi$
$347$	9.41442			0.505392			0.252696	+	0.967546i	$0.418683\pi$
$348$	20.1749	+	13.4421i	1.08149	+	0.720571i
$349$		−	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
$352$	17.3061	+	14.7573i	0.922420	+	0.786568i
$353$	−20.4254			−1.08713			−0.543567	−	0.839366i	$-0.682927\pi$
$353$	−20.4254			−1.08713			−0.543567	+	0.839366i	$0.682927\pi$
$354$	−2.19803	−	1.05235i	−0.116824	−	0.0559316i
$355$		0			0
$356$	−0.462079	+	1.59235i	−0.0244901	+	0.0843946i
$357$	−16.6558	−	5.24922i	−0.881520	−	0.277818i
$358$	−7.47720	−	1.06296i	−0.395182	−	0.0561794i
$359$	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
$362$	15.1134	+	2.14853i	0.794343	+	0.112924i
$363$	8.53236	+	2.68904i	0.447833	+	0.141138i
$364$	17.8316	+	5.17448i	0.934629	+	0.271216i
$365$		0			0
$366$	6.99830	+	3.35057i	0.365807	+	0.175137i
$367$	15.8130			0.825431			0.412715	−	0.910860i	$-0.364580\pi$
$367$	15.8130			0.825431			0.412715	+	0.910860i	$0.364580\pi$
$368$	3.69569	−	5.83158i	0.192651	−	0.303992i
$369$	−5.91749	+	8.45566i	−0.308052	+	0.440184i
$370$		0			0
$371$		−	7.86844i		−	0.408509i
$372$	−8.13708	+	12.2127i	−0.421888	+	0.633201i
$373$	7.51072			0.388890			0.194445	−	0.980913i	$-0.437709\pi$
$373$	7.51072			0.388890			0.194445	+	0.980913i	$0.437709\pi$
$374$	−29.4486	−	4.18643i	−1.52275	−	0.216475i
$375$		0			0
$376$	−19.4864	−	8.78738i	−1.00493	−	0.453175i
$377$	33.7091			1.73610
$378$	12.3353	−	6.95940i	0.634462	−	0.357953i
$379$	13.1468			0.675307			0.337654	−	0.941270i	$-0.390367\pi$
$379$	13.1468			0.675307			0.337654	+	0.941270i	$0.390367\pi$
$380$		0			0
$381$	27.3833	+	8.63007i	1.40289	+	0.442132i
$382$	3.93094	−	27.6514i	0.201124	−	1.41477i
$383$		−	23.0887i		−	1.17978i	−0.807484	−	0.589889i	$-0.799172\pi$
$383$		−	23.0887i		−	1.17978i	0.807484	−	0.589889i	$-0.200828\pi$
$384$	18.8490	−	5.35874i	0.961883	−	0.273462i
$385$		0			0
$386$	7.63356	+	1.08519i	0.388538	+	0.0552348i
$387$	−1.79106	+	2.55929i	−0.0910447	+	0.130096i
$388$	0.809320	−	2.78897i	0.0410870	−	0.141588i
$389$	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
$392$	3.81989	−	8.47077i	0.192934	−	0.427838i
$393$	−2.92224	+	9.27229i	−0.147407	+	0.467725i
$394$	−31.7127	−	4.50829i	−1.59766	−	0.227125i
$395$		0			0
$396$	18.7917	−	15.1266i	0.944318	−	0.760138i
$397$	−18.1459			−0.910719			−0.455359	−	0.890308i	$-0.650489\pi$
$397$	−18.1459			−0.910719			−0.455359	+	0.890308i	$0.650489\pi$
$398$	−26.4420	−	3.75902i	−1.32542	−	0.188423i
$399$	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	$0.681066\pi$
$402$	−32.8590	−	15.7319i	−1.63886	−	0.784635i
$403$			20.4056i			1.01647i
$404$	8.07256	+	2.34254i	0.401625	+	0.116546i
$405$		0			0
$406$	−2.68475	+	18.8853i	−0.133242	+	0.937264i
$407$			39.5311i			1.95948i
$408$	−17.0703	+	19.1152i	−0.845108	+	0.946342i
$409$	−31.6480			−1.56489			−0.782446	−	0.622718i	$-0.786028\pi$
$409$	−31.6480			−1.56489			−0.782446	+	0.622718i	$0.786028\pi$
$410$		0			0
$411$	−15.5576	−	4.90310i	−0.767399	−	0.241852i
$412$	13.6409	+	3.95841i	0.672041	+	0.195017i
$413$		−	1.91749i		−	0.0943537i
$414$	−5.34891	−	5.00128i	−0.262885	−	0.245800i
$415$		0			0
$416$	17.6796	−	20.7332i	0.866816	−	1.01653i
$417$	−10.7647	−	3.39258i	−0.527149	−	0.166135i
$418$	3.85471	+	0.547989i	0.188540	+	0.0268030i
$419$			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	$-0.946512\pi$
$421$		−	6.86330i		−	0.334497i	0.985915	−	0.167248i	$-0.0534882\pi$
$422$	−2.14316	+	15.0756i	−0.104327	+	0.733870i
$423$	−12.9998	+	18.5758i	−0.632073	+	0.903185i
$424$	−10.5263	−	4.74682i	−0.511201	−	0.230526i
$425$		0			0
$426$	−9.81981	+	20.5105i	−0.475772	+	0.993739i
$427$			6.10511i			0.295447i
$428$	14.9108	+	4.32689i	0.720738	+	0.209148i
$429$	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	$0.339828\pi$
$432$	−1.86859	−	20.7004i	−0.0899026	−	0.995951i
$433$			10.2112i			0.490717i	0.969432	+	0.245358i	$0.0789057\pi$
$433$			10.2112i			0.490717i	−0.969432	+	0.245358i	$0.921094\pi$
$434$	−11.4321	−	1.62520i	−0.548760	−	0.0780121i
$435$		0			0
$436$	11.4321	−	39.3959i	0.547500	−	1.88672i
$437$		−	1.18189i		−	0.0565373i
$438$	−24.9292	−	11.9353i	−1.19116	−	0.570292i
$439$			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
$442$	−5.01546	+	35.2802i	−0.238561	+	1.67811i
$443$	4.46465			0.212122			0.106061	−	0.994360i	$-0.466176\pi$
$443$	4.46465			0.212122			0.106061	+	0.994360i	$0.466176\pi$
$444$	28.3445	+	18.8853i	1.34517	+	0.896258i
$445$		0			0
$446$	1.30283	−	9.16445i	0.0616906	−	0.433949i
$447$	12.4467	+	3.92267i	0.588707	+	0.185536i
$448$	10.2076	+	11.5562i	0.482263	+	0.545980i
$449$			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
$452$	−0.414511	−	0.120285i	−0.0194970	−	0.00565774i
$453$	−4.89954	+	15.5463i	−0.230200	+	0.730428i
$454$	4.48084	−	31.5196i	0.210296	−	1.47929i
$455$		0			0
$456$	2.23444	−	2.50211i	0.104637	−	0.117172i
$457$			11.5016i			0.538020i	0.963137	+	0.269010i	$0.0866965\pi$
$457$			11.5016i			0.538020i	−0.963137	+	0.269010i	$0.913303\pi$
$458$	−18.0392	−	2.56447i	−0.842917	−	0.119830i
$459$	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	$0.438393\pi$
$462$	17.1203	+	8.19666i	0.796507	+	0.381343i
$463$	−11.7199			−0.544669			−0.272334	−	0.962203i	$-0.587796\pi$
$463$	−11.7199			−0.544669			−0.272334	+	0.962203i	$0.587796\pi$
$464$	23.6449	+	14.9846i	1.09769	+	0.695644i
$465$		0			0
$466$	2.15984	−	15.1929i	0.100052	−	0.703799i
$467$	−17.1895			−0.795437			−0.397718	−	0.917508i	$-0.630198\pi$
$467$	−17.1895			−0.795437			−0.397718	+	0.917508i	$0.630198\pi$
$468$	−18.1220	−	22.5129i	−0.837690	−	1.04066i
$469$		−	28.6653i		−	1.32364i
$470$		0			0
$471$	−5.77686	−	1.82062i	−0.266184	−	0.0838900i
$472$	−2.56519	−	1.15677i	−0.118073	−	0.0532448i
$473$	−4.18643			−0.192492
$474$	20.4404	+	9.78622i	0.938857	+	0.449496i
$475$		0			0
$476$	−19.3661	−	5.61977i	−0.887644	−	0.257582i
$477$	−7.02232	+	10.0344i	−0.321530	+	0.459442i
$478$	−1.31976	+	9.28360i	−0.0603645	+	0.424622i
$479$	−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
$482$	−3.17513	+	22.3348i	−0.144623	+	1.01732i
$483$	1.73193	−	5.49543i	0.0788056	−	0.250051i
$484$	9.92076	+	2.87887i	0.450944	+	0.130858i
$485$		0			0
$486$	−21.9419	−	2.13378i	−0.995305	−	0.0967902i
$487$	33.1015			1.49997			0.749985	−	0.661455i	$-0.230061\pi$
$487$	33.1015			1.49997			0.749985	+	0.661455i	$0.230061\pi$
$488$	8.16732	+	3.68305i	0.369717	+	0.166724i
$489$	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	$0.839888\pi$
$492$	−6.60781	+	9.91749i	−0.297903	+	0.447115i
$493$	−36.6099			−1.64883
$494$	0.656505	−	4.61805i	0.0295375	−	0.207776i
$495$		0			0
$496$	−9.07086	+	14.3133i	−0.407294	+	0.642685i
$497$	−17.8928			−0.802602
$498$	−7.57210	+	15.8158i	−0.339314	+	0.708721i
$499$	−14.8464			−0.664614			−0.332307	−	0.943171i	$-0.607827\pi$
$499$	−14.8464			−0.664614			−0.332307	+	0.943171i	$0.607827\pi$
$500$		0			0
$501$	5.93128	−	18.8200i	0.264990	−	0.840816i
$502$	−21.3471	−	3.03472i	−0.952767	−	0.135446i
$503$		−	1.86841i		−	0.0833084i	−0.999132	−	0.0416542i	$-0.986737\pi$
$503$		−	1.86841i		−	0.0833084i	0.999132	−	0.0416542i	$-0.0132628\pi$
$504$	14.0561	−	8.35973i	0.626108	−	0.372372i
$505$		0			0
$506$	1.38127	−	9.71629i	0.0614051	−	0.431942i
$507$	−16.8517	−	5.31096i	−0.748411	−	0.235868i
$508$	31.8392	+	9.23928i	1.41263	+	0.409927i
$509$	−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
$512$	21.6177	−	6.68396i	0.955376	−	0.295392i
$513$	−2.16710	−	2.82198i	−0.0956800	−	0.124594i
$514$	−3.22144	+	22.6605i	−0.142092	+	0.999514i
$515$		0			0
$516$	−2.00000	+	3.00175i	−0.0880451	+	0.132145i
$517$	−30.3858			−1.33637
$518$	−3.77192	+	26.5328i	−0.165729	+	1.16578i
$519$	−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	$-0.0548512\pi$
$522$	20.2783	−	21.6878i	0.887557	−	0.949250i
$523$		−	32.2423i		−	1.40986i	−0.709277	−	0.704930i	$-0.750979\pi$
$523$		−	32.2423i		−	1.40986i	0.709277	−	0.704930i	$-0.249021\pi$
$524$	−3.12852	+	10.7811i	−0.136670	+	0.470975i
$525$		0			0
$526$	−30.0680	−	4.27449i	−1.31103	−	0.186377i
$527$		−	22.1616i		−	0.965375i
$528$	21.2936	−	17.9584i	0.926684	−	0.781539i
$529$	20.0209			0.870474
$530$		0			0
$531$	−1.71130	+	2.44532i	−0.0742640	+	0.106118i
$532$	2.53495	+	0.735607i	0.109904	+	0.0318926i
$533$			16.5706i			0.717752i
$534$	1.83158	+	0.876906i	0.0792604	+	0.0379474i
$535$		0			0
$536$	−38.3479	−	17.2930i	−1.65638	−	0.746943i
$537$	−2.78032	+	8.82198i	−0.119980	+	0.380697i
$538$	−4.58452	+	32.2489i	−0.197653	+	1.39035i
$539$		−	13.2088i		−	0.568942i
$540$		0			0
$541$			3.25040i			0.139746i	0.997556	+	0.0698728i	$0.0222593\pi$
$541$			3.25040i			0.139746i	−0.997556	+	0.0698728i	$0.977741\pi$
$542$	22.6701	+	3.22280i	0.973765	+	0.138431i
$543$	5.61977	−	17.8316i	0.241167	−	0.765227i
$544$	−19.2011	+	22.5174i	−0.823240	+	0.965426i
$545$		0			0
$546$	9.81981	−	20.5105i	0.420249	−	0.877770i
$547$		−	10.3248i		−	0.441459i	−0.975335	−	0.220729i	$-0.929156\pi$
$547$		−	10.3248i		−	0.441459i	0.975335	−	0.220729i	$-0.0708437\pi$
$548$	−18.0892	−	5.24922i	−0.772731	−	0.224236i
$549$	5.44861	−	7.78565i	0.232541	−	0.332284i
$550$		0			0
$551$	4.79210			0.204150
$552$	−6.30687	−	5.63220i	−0.268438	−	0.239722i
$553$			17.8316i			0.758276i
$554$	0.759359	−	5.34156i	0.0322621	−	0.226941i
$555$		0			0
$556$	−12.5163	−	3.63207i	−0.530811	−	0.154034i
$557$		−	8.33343i		−	0.353099i	−0.984292	−	0.176549i	$-0.943506\pi$
$557$		−	8.33343i		−	0.353099i	0.984292	−	0.176549i	$-0.0564935\pi$
$558$	13.1286	+	12.2754i	0.555778	+	0.519657i
$559$			5.01546i			0.212131i
$560$		0			0
$561$	−10.9502	+	34.7450i	−0.462316	+	1.46693i
$562$	−39.1301	−	5.56277i	−1.65060	−	0.234651i
$563$	14.0982			0.594166			0.297083	−	0.954852i	$-0.403986\pi$
$563$	14.0982			0.594166			0.297083	+	0.954852i	$0.403986\pi$
$564$	−14.5163	+	21.7872i	−0.611248	+	0.917406i
$565$		0			0
$566$	−7.82570	−	1.11251i	−0.328939	−	0.0467622i
$567$	−5.94109	−	16.2971i	−0.249502	−	0.684412i
$568$	−10.7942	+	23.9367i	−0.452916	+	1.00436i
$569$		−	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	$0.431560\pi$
$572$	10.7942	−	37.1977i	0.451330	−	1.55531i
$573$	−32.6245	−	10.2819i	−1.36291	−	0.429532i
$574$	−9.28360	−	1.31976i	−0.387490	−	0.0550858i
$575$		0			0
$576$	−2.70385	−	23.8472i	−0.112660	−	0.993634i
$577$		−	14.9762i		−	0.623466i	−0.950170	−	0.311733i	$-0.899090\pi$
$577$		−	14.9762i		−	0.623466i	0.950170	−	0.311733i	$-0.100910\pi$
$578$	2.06331	−	14.5140i	0.0858225	−	0.603701i
$579$	2.83846	−	9.00647i	0.117962	−	0.374296i
$580$		0			0
$581$	−13.7972			−0.572405
$582$	−3.20797	−	1.53588i	−0.132975	−	0.0636642i
$583$	−16.4140			−0.679799
$584$	−29.0935	−	13.1197i	−1.20390	−	0.542897i
$585$		0			0
$586$	−8.40082	−	1.19427i	−0.347035	−	0.0493347i
$587$	−35.1368			−1.45025			−0.725125	−	0.688617i	$-0.758218\pi$
$587$	−35.1368			−1.45025			−0.725125	+	0.688617i	$0.758218\pi$
$588$	−9.47093	−	6.31028i	−0.390575	−	0.260231i
$589$			2.90087i			0.119528i
$590$		0			0
$591$	−11.7920	+	37.4162i	−0.485059	+	1.53910i
$592$	33.2197	+	21.0526i	1.36532	+	0.865255i
$593$	11.6209			0.477214			0.238607	−	0.971116i	$-0.423309\pi$
$593$	11.6209			0.477214			0.238607	+	0.971116i	$0.423309\pi$
$594$	−14.5177	−	25.7322i	−0.595668	−	1.05581i
$595$		0			0
$596$	14.4720	+	4.19958i	0.592797	+	0.172021i
$597$	−9.83221	+	31.1977i	−0.402405	+	1.27684i
$598$	−11.6404	−	1.65480i	−0.476010	−	0.0676699i
$599$	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	$0.496197\pi$
$602$	−2.80989	−	0.399455i	−0.114522	−	0.0162806i
$603$	−25.5828	+	36.5559i	−1.04181	+	1.48867i
$604$	−5.24541	+	18.0760i	−0.213433	+	0.735503i
$605$		0			0
$606$	4.44554	−	9.28536i	0.180588	−	0.377192i
$607$	22.9594			0.931894			0.465947	−	0.884813i	$-0.345714\pi$
$607$	22.9594			0.931894			0.465947	+	0.884813i	$0.345714\pi$
$608$	2.51335	−	2.94744i	0.101930	−	0.119535i
$609$	22.2819	+	7.02232i	0.902908	+	0.284559i
$610$		0			0
$611$			36.4030i			1.47271i
$612$	19.6815	+	24.4503i	0.795578	+	0.988345i
$613$	−4.10130			−0.165650			−0.0828250	−	0.996564i	$-0.526394\pi$
$613$	−4.10130			−0.165650			−0.0828250	+	0.996564i	$0.526394\pi$
$614$	6.70712	+	0.953488i	0.270677	+	0.0384797i
$615$		0			0
$616$	19.9801	+	9.01003i	0.805022	+	0.363024i
$617$	−14.1493			−0.569630			−0.284815	−	0.958583i	$-0.591932\pi$
$617$	−14.1493			−0.569630			−0.284815	+	0.958583i	$0.591932\pi$
$618$	7.51203	−	15.6903i	0.302178	−	0.631156i
$619$	10.1108			0.406386			0.203193	−	0.979139i	$-0.434868\pi$
$619$	10.1108			0.406386			0.203193	+	0.979139i	$0.434868\pi$
$620$		0			0
$621$	−7.11317	+	5.46246i	−0.285441	+	0.219201i
$622$	−2.56330	+	18.0310i	−0.102779	+	0.722976i
$623$			1.59782i			0.0640153i
$624$	−21.5146	−	25.5102i	−0.861275	−	1.02123i
$625$		0			0
$626$	−28.5658	−	4.06094i	−1.14172	−	0.162308i
$627$	1.43334	−	4.54799i	0.0572419	−	0.181629i
$628$	−6.71689	−	1.94915i	−0.268033	−	0.0777794i
$629$	−51.4349			−2.05084
$630$		0			0
$631$		−	28.7572i		−	1.14481i	−0.819972	−	0.572404i	$-0.806011\pi$
$631$		−	28.7572i		−	1.14481i	0.819972	−	0.572404i	$-0.193989\pi$
$632$	23.8548	+	10.7573i	0.948893	+	0.427903i
$633$	17.7870	+	5.60572i	0.706970	+	0.222807i
$634$	7.48162	+	1.06359i	0.297133	+	0.0422407i
$635$		0			0
$636$	−7.84153	+	11.7691i	−0.310937	+	0.466677i
$637$	−15.8245			−0.626988
$638$	39.3959	+	5.60054i	1.55970	+	0.221728i
$639$	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	$0.750266\pi$
$642$	8.21132	−	17.1509i	0.324075	−	0.676892i
$643$		−	4.64793i		−	0.183296i	−0.995791	−	0.0916481i	$-0.970786\pi$
$643$		−	4.64793i		−	0.183296i	0.995791	−	0.0916481i	$-0.0292135\pi$
$644$	1.85419	−	6.38966i	0.0730653	−	0.251788i
$645$		0			0
$646$	−0.713001	+	5.01546i	−0.0280526	+	0.197330i
$647$		−	6.90109i		−	0.271310i	−0.990756	−	0.135655i	$-0.956686\pi$
$647$		−	6.90109i		−	0.271310i	0.990756	−	0.135655i	$-0.0433138\pi$
$648$	−25.3861	−	1.88369i	−0.997258	−	0.0739984i
$649$	−4.00000			−0.157014
$650$		0			0
$651$	−4.25092	+	13.4882i	−0.166607	+	0.528645i
$652$	9.45054	−	32.5672i	0.370112	−	1.27543i
$653$			16.8181i			0.658144i	0.944305	+	0.329072i	$0.106736\pi$
$653$			16.8181i			0.658144i	−0.944305	+	0.329072i	$0.893264\pi$
$654$	−45.3146	−	21.6952i	−1.77194	−	0.848350i
$655$		0			0
$656$	−7.36610	+	11.6233i	−0.287598	+	0.453812i
$657$	−19.4089	+	27.7339i	−0.757214	+	1.08200i
$658$	−20.3946	−	2.89931i	−0.795065	−	0.113027i
$659$		−	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	$-0.907551\pi$
$661$		−	14.7252i		−	0.572743i	0.958119	−	0.286372i	$-0.0924492\pi$
$662$	5.00983	−	35.2406i	0.194713	−	1.36967i
$663$	41.6254	+	13.1186i	1.61660	+	0.509484i
$664$	−8.32349	+	18.4577i	−0.323014	+	0.716297i
$665$		0			0
$666$	28.4899	−	30.4701i	1.10396	−	1.18069i
$667$		−	12.0791i		−	0.467705i
$668$	6.34998	−	21.8824i	0.245688	−	0.846657i
$669$	−10.8127	−	3.40771i	−0.418043	−	0.131750i
$670$		0			0
$671$	12.7356			0.491653
$672$	16.0055	−	10.0217i	0.617426	−	0.386596i
$673$		−	44.9434i		−	1.73244i	−0.499663	−	0.866220i	$-0.666543\pi$
$673$		−	44.9434i		−	1.73244i	0.499663	−	0.866220i	$-0.333457\pi$
$674$	28.2290	+	4.01305i	1.08734	+	0.154577i
$675$		0			0
$676$	−19.5939	−	5.68587i	−0.753610	−	0.218687i
$677$			31.3401i			1.20450i	0.798308	+	0.602249i	$0.205728\pi$
$677$			31.3401i			1.20450i	−0.798308	+	0.602249i	$0.794272\pi$
$678$	−0.228270	+	0.476786i	−0.00876667	+	0.0183108i
$679$		−	2.79854i		−	0.107398i
$680$		0			0
$681$	−37.1884	−	11.7202i	−1.42506	−	0.449120i
$682$	−3.39026	+	23.8481i	−0.129820	+	0.913190i
$683$	6.76121			0.258710			0.129355	−	0.991598i	$-0.458709\pi$
$683$	6.76121			0.258710			0.129355	+	0.991598i	$0.458709\pi$
$684$	−2.57624	−	3.20045i	−0.0985049	−	0.122372i
$685$		0			0
$686$	3.94574	−	27.7555i	0.150649	−	1.05971i
$687$	−6.70770	+	21.2836i	−0.255915	+	0.812020i
$688$	−2.22951	+	3.51804i	−0.0849994	+	0.134124i
$689$			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	$0.411494\pi$
$692$	−1.20673	+	4.15847i	−0.0458730	+	0.158081i
$693$	13.3292	−	19.0464i	0.506334	−	0.723514i
$694$	1.87389	−	13.1815i	0.0711317	−	0.500362i
$695$		0			0
$696$	22.8364	−	25.5720i	0.865612	−	0.969303i
$697$		−	17.9966i		−	0.681670i
$698$	−14.5570	−	2.06943i	−0.550990	−	0.0783291i
$699$	−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	$0.559465\pi$
$702$	−30.8279	+	17.3926i	−1.16352	+	0.656441i
$703$	6.73263			0.253926
$704$	24.1069	−	21.2936i	0.908565	−	0.802532i
$705$		0			0
$706$	−4.06556	+	28.5983i	−0.153009	+	1.07631i
$707$	8.10028			0.304642
$708$	−1.91093	+	2.86807i	−0.0718173	+	0.107789i
$709$			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
$712$	2.13754	+	0.963923i	0.0801077	+	0.0361245i
$713$	7.31201			0.273837
$714$	−10.6649	+	22.2756i	−0.399123	+	0.833643i
$715$		0			0
$716$	−2.97659	+	10.2575i	−0.111240	+	0.383341i
$717$	10.9533	+	3.45201i	0.409057	+	0.128918i
$718$	1.36765	−	9.62043i	0.0510401	−	0.359031i
$719$	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
$722$	−3.68851	+	25.9461i	−0.137272	+	0.965613i
$723$	26.3517	+	8.30497i	0.980032	+	0.308865i
$724$	6.01648	−	20.7332i	0.223601	−	0.770543i
$725$		0			0
$726$	5.46334	−	11.4112i	0.202764	−	0.423510i
$727$	−28.1339			−1.04343			−0.521714	−	0.853120i	$-0.674707\pi$
$727$	−28.1339			−1.04343			−0.521714	+	0.853120i	$0.674707\pi$
$728$	10.7942	−	23.9367i	0.400061	−	0.887153i
$729$	−6.96811	+	26.0854i	−0.258078	+	0.966124i
$730$		0			0
$731$		−	5.44707i		−	0.201467i
$732$	6.08423	−	9.13166i	0.224879	−	0.337516i
$733$	−10.2296			−0.377840			−0.188920	−	0.981993i	$-0.560499\pi$
$733$	−10.2296			−0.377840			−0.188920	+	0.981993i	$0.560499\pi$
$734$	3.14748	−	22.1403i	0.116176	−	0.817214i
$735$		0			0
$736$	−7.42941	−	6.33522i	−0.273852	−	0.233519i
$737$	−59.7973			−2.20266
$738$	10.6612	+	9.96835i	0.392445	+	0.366940i
$739$	48.0440			1.76733			0.883664	−	0.468121i	$-0.155069\pi$
$739$	48.0440			1.76733			0.883664	+	0.468121i	$0.155069\pi$
$740$		0			0
$741$	−5.44861	−	1.71717i	−0.200160	−	0.0630819i
$742$	−11.0169	−	1.56617i	−0.404443	−	0.0574959i
$743$			35.9667i			1.31949i	0.751489	+	0.659745i	$0.229336\pi$
$743$			35.9667i			1.31949i	−0.751489	+	0.659745i	$0.770664\pi$
$744$	15.4798	+	13.8239i	0.567519	+	0.506809i
$745$		0			0
$746$	1.49497	−	10.5160i	0.0547346	−	0.385019i
$747$	17.5951	+	12.3135i	0.643772	+	0.450529i
$748$	−11.7232	+	40.3988i	−0.428641	+	1.47713i
$749$	14.9619			0.546697
$750$		0			0
$751$		−	26.4357i		−	0.964654i	−0.875991	−	0.482327i	$-0.839792\pi$
$751$		−	26.4357i		−	0.964654i	0.875991	−	0.482327i	$-0.160208\pi$
$752$	−16.1822	+	25.5345i	−0.590104	+	0.931148i
$753$	−7.93770	+	25.1864i	−0.289266	+	0.917843i
$754$	6.70960	−	47.1973i	0.244349	−	1.71882i
$755$		0			0
$756$	−7.28883	−	18.6564i	−0.265092	−	0.678526i
$757$	−24.6881			−0.897303			−0.448652	−	0.893707i	$-0.648096\pi$
$757$	−24.6881			−0.897303			−0.448652	+	0.893707i	$0.648096\pi$
$758$	2.61680	−	18.4074i	0.0950465	−	0.668585i
$759$	−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	$-0.319394\pi$
$762$	17.5338	−	36.6226i	0.635181	−	1.32670i
$763$		−	39.5311i		−	1.43112i
$764$	−37.9333	−	11.0077i	−1.37238	−	0.398245i
$765$		0			0
$766$	−32.3273	−	4.59568i	−1.16803	−	0.166049i
$767$			4.79210i			0.173033i
$768$	−3.75118	−	27.4578i	−0.135359	−	0.990797i
$769$	−36.8643			−1.32936			−0.664680	−	0.747129i	$-0.731432\pi$
$769$	−36.8643			−1.32936			−0.664680	+	0.747129i	$0.731432\pi$
$770$		0			0
$771$	26.7361	+	8.42609i	0.962876	+	0.303458i
$772$	3.03883	−	10.4720i	0.109370	−	0.376896i
$773$		−	41.5537i		−	1.49458i	−0.664496	−	0.747292i	$-0.731354\pi$
$773$		−	41.5537i		−	1.49458i	0.664496	−	0.747292i	$-0.268646\pi$
$774$	3.22686	+	3.01714i	0.115987	+	0.108449i
$775$		0			0
$776$	−3.74385	−	1.68829i	−0.134396	−	0.0606059i
$777$	31.3048	+	9.86596i	1.12305	+	0.353939i
$778$	2.56847	−	18.0674i	0.0920842	−	0.647747i
$779$			2.35569i			0.0844013i
$780$		0			0
$781$			37.3254i			1.33561i
$782$	12.6421	+	1.79721i	0.452080	+	0.0642681i
$783$	−22.1482	−	28.8412i	−0.791512	−	1.03070i
$784$	−11.0999	−	7.03442i	−0.396425	−	0.251229i
$785$		0			0
$786$	12.4008	+	5.93713i	0.442322	+	0.211770i
$787$			48.4300i			1.72634i	0.504912	+	0.863171i	$0.331525\pi$
$787$			48.4300i			1.72634i	−0.504912	+	0.863171i	$0.668475\pi$
$788$	−12.6245	+	43.5047i	−0.449727	+	1.54979i
$789$	−11.1805	+	35.4758i	−0.398036	+	1.26297i
$790$		0			0
$791$	−0.415934			−0.0147889
$792$	−17.4389	−	29.3218i	−0.619663	−	1.04190i
$793$		−	15.2576i		−	0.541813i
$794$	−3.61185	+	25.4068i	−0.128180	+	0.901653i
$795$		0			0
$796$	−10.5263	+	36.2743i	−0.373094	+	1.28571i
$797$		−	32.0757i		−	1.13618i	−0.822967	−	0.568090i	$-0.807683\pi$
$797$		−	32.0757i		−	1.13618i	0.822967	−	0.568090i	$-0.192317\pi$
$798$	1.39599	−	2.91579i	0.0494176	−	0.103218i
$799$		−	39.5357i		−	1.39867i
$800$		0			0
$801$	1.42600	−	2.03765i	0.0503853	−	0.0719968i
$802$	47.2452	+	6.71640i	1.66828	+	0.237164i
$803$	−45.3665			−1.60095
$804$	−28.5672	+	42.8758i	−1.00749	+	1.51211i
$805$		0			0
$806$	28.5706	+	4.06162i	1.00636	+	0.143064i
$807$	38.0489	+	11.9914i	1.33938	+	0.422118i
$808$	4.88668	−	10.8364i	0.171913	−	0.381224i
$809$			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	$0.480057\pi$
$812$	25.9077	+	7.51804i	0.909181	+	0.263831i
$813$	8.42966	−	26.7474i	0.295641	−	0.938071i
$814$	55.3489	+	7.86844i	1.93998	+	0.275789i
$815$		0			0
$816$	23.3661	+	27.7056i	0.817977	+	0.969889i
$817$			0.713001i			0.0249447i
$818$	−6.29935	+	44.3115i	−0.220252	+	1.54932i
$819$	−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	$0.193569\pi$
$822$	−9.96166	+	20.8068i	−0.347453	+	0.725721i
$823$	30.2235			1.05353			0.526763	−	0.850012i	$-0.323405\pi$
$823$	30.2235			1.05353			0.526763	+	0.850012i	$0.323405\pi$
$824$	8.25746	−	18.3113i	0.287662	−	0.637903i
$825$		0			0
$826$	−2.68475	−	0.381666i	−0.0934145	−	0.0132799i
$827$	31.2229			1.08573			0.542864	−	0.839821i	$-0.317340\pi$
$827$	31.2229			1.08573			0.542864	+	0.839821i	$0.317340\pi$
$828$	−8.06715	+	6.49373i	−0.280353	+	0.225673i
$829$		−	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
$832$	−25.5102	−	28.8807i	−0.884409	−	1.00126i
$833$	17.1863			0.595468
$834$	−6.89272	+	14.3967i	−0.238675	+	0.498519i
$835$		0			0
$836$	1.53452	−	5.28805i	0.0530724	−	0.182891i
$837$	17.4588	−	13.4073i	0.603466	−	0.463424i
$838$	41.8576	+	5.95051i	1.44595	+	0.205557i
$839$	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
$842$	−9.60956	−	1.36610i	−0.331167	−	0.0470790i
$843$	−14.5501	+	46.1677i	−0.501134	+	1.59010i
$844$	20.6813	+	6.00144i	0.711881	+	0.206578i
$845$		0			0
$846$	23.4211	+	21.8989i	0.805233	+	0.752900i
$847$	9.95482			0.342052
$848$	−8.74139	+	13.7934i	−0.300181	+	0.473667i
$849$	−2.90991	+	9.23316i	−0.0998678	+	0.316881i
$850$		0			0
$851$		−	16.9704i		−	0.581739i
$852$	26.7630	+	17.8316i	0.916884	+	0.610900i
$853$	25.1966			0.862716			0.431358	−	0.902181i	$-0.358035\pi$
$853$	25.1966			0.862716			0.431358	+	0.902181i	$0.358035\pi$
$854$	8.54799	+	1.21519i	0.292506	+	0.0415829i
$855$		0			0
$856$	9.02614	−	20.0158i	0.308507	−	0.684127i
$857$	46.7431			1.59671			0.798357	−	0.602185i	$-0.205703\pi$
$857$	46.7431			1.59671			0.798357	+	0.602185i	$0.205703\pi$
$858$	−42.7861	−	20.4847i	−1.46069	−	0.699336i
$859$	−40.8430			−1.39354			−0.696772	−	0.717293i	$-0.745381\pi$
$859$	−40.8430			−1.39354			−0.696772	+	0.717293i	$0.745381\pi$
$860$		0			0
$861$	−3.45201	+	10.9533i	−0.117644	+	0.373286i
$862$	3.98539	−	28.0344i	0.135743	−	0.954855i
$863$			39.3858i			1.34071i	0.742042	+	0.670354i	$0.233858\pi$
$863$			39.3858i			1.34071i	−0.742042	+	0.670354i	$0.766142\pi$
$864$	−29.3554	−	1.50402i	−0.998690	−	0.0511679i
$865$		0			0
$866$	14.2970	+	2.03247i	0.485832	+	0.0690662i
$867$	−17.1243	−	5.39687i	−0.581572	−	0.183287i
$868$	−4.55100	+	15.6831i	−0.154471	+	0.532317i
$869$	37.1977			1.26185
$870$		0			0
$871$			71.6388i			2.42739i
$872$	−52.8841	−	23.8481i	−1.79088	−	0.807597i
$873$	−2.49761	+	3.56889i	−0.0845312	+	0.120789i
$874$	−1.65480	−	0.235248i	−0.0559745	−	0.00795738i
$875$		0			0
$876$	−21.6731	+	32.5286i	−0.732267	+	1.09904i
$877$	57.4498			1.93994			0.969972	−	0.243218i	$-0.0782029\pi$
$877$	57.4498			1.93994			0.969972	+	0.243218i	$0.0782029\pi$
$878$	47.1752	+	6.70646i	1.59209	+	0.226332i
$879$	−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	$0.731886\pi$
$882$	−9.51950	+	10.1812i	−0.320538	+	0.342818i
$883$		−	25.7701i		−	0.867231i	−0.901098	−	0.433616i	$-0.857238\pi$
$883$		−	25.7701i		−	0.867231i	0.901098	−	0.433616i	$-0.142762\pi$
$884$	48.3988	+	14.0446i	1.62783	+	0.472373i
$885$		0			0
$886$	0.888663	−	6.25112i	0.0298552	−	0.210010i
$887$		−	21.4751i		−	0.721063i	−0.932747	−	0.360531i	$-0.882595\pi$
$887$		−	21.4751i		−	0.721063i	0.932747	−	0.360531i	$-0.117405\pi$
$888$	32.0839	−	35.9272i	1.07666	−	1.20564i
$889$	31.9485			1.07152
$890$		0			0
$891$	−33.9966	+	12.3934i	−1.13893	+	0.415196i
$892$	−12.5722	−	3.64827i	−0.420947	−	0.122153i
$893$			5.17508i			0.173177i
$894$	7.96971	−	16.6462i	0.266547	−	0.556734i
$895$		0			0
$896$	18.2121	−	11.9918i	0.608422	−	0.400618i
$897$	−4.32835	+	13.7339i	−0.144520	+	0.458562i
$898$	38.5737	+	5.48366i	1.28722	+	0.182992i
$899$			29.6474i			0.988798i
$900$		0			0
$901$		−	21.3567i		−	0.711493i
$902$	−2.75310	+	19.3661i	−0.0916682	+	0.644821i
$903$	−1.04483	+	3.31525i	−0.0347697	+	0.110325i
$904$	−0.250922	+	0.556430i	−0.00834554	+	0.0185066i
$905$		0			0
$906$	20.7917	+	9.95442i	0.690758	+	0.330714i
$907$		−	34.5984i		−	1.14882i	−0.818568	−	0.574410i	$-0.805231\pi$
$907$		−	34.5984i		−	1.14882i	0.818568	−	0.574410i	$-0.194769\pi$
$908$	−43.2398	−	12.5476i	−1.43496	−	0.416406i
$909$	−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	$0.390788\pi$
$912$	−3.05854	−	3.62655i	−0.101278	−	0.120087i
$913$			28.7818i			0.952537i
$914$	16.1038	+	2.28932i	0.532665	+	0.0757240i
$915$		0			0
$916$	−7.18121	+	24.7469i	−0.237274	+	0.817661i
$917$			10.8181i			0.357246i
$918$	33.4808	−	18.8893i	1.10503	−	0.623440i
$919$			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
$922$	1.64396	−	11.5641i	0.0541411	−	0.380844i
$923$	44.7168			1.47187
$924$	14.8841	−	22.3392i	0.489652	−	0.734907i
$925$		0			0
$926$	−2.33278	+	16.4094i	−0.0766597	+	0.539247i
$927$	−17.4556	−	12.2159i	−0.573316	−	0.401222i
$928$	25.6869	−	30.1234i	0.843214	−	0.988850i
$929$		−	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
$932$	−20.8423	−	6.04813i	−0.682711	−	0.198113i
$933$	21.2739	+	6.70464i	0.696475	+	0.219500i
$934$	−3.42148	+	24.0677i	−0.111954	+	0.787519i
$935$		0			0
$936$	−35.1283	+	20.8922i	−1.14820	+	0.682883i
$937$		−	35.4418i		−	1.15783i	−0.815387	−	0.578917i	$-0.803476\pi$
$937$		−	35.4418i		−	1.15783i	0.815387	−	0.578917i	$-0.196524\pi$
$938$	−40.1353	−	5.70566i	−1.31046	−	0.186296i
$939$	−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	$0.429698\pi$
$942$	−3.69897	+	7.72601i	−0.120519	+	0.251727i
$943$	5.93781			0.193362
$944$	−2.13023	+	3.36137i	−0.0693330	+	0.109403i
$945$		0			0
$946$	−0.833286	+	5.86158i	−0.0270925	+	0.190576i
$947$	4.96195			0.161242			0.0806208	−	0.996745i	$-0.474310\pi$
$947$	4.96195			0.161242			0.0806208	+	0.996745i	$0.474310\pi$
$948$	17.7706	−	26.6714i	0.577162	−	0.866247i
$949$			54.3503i			1.76428i
$950$		0			0
$951$	2.78197	−	8.82720i	0.0902114	−	0.286242i
$952$	−11.7232	+	25.9966i	−0.379950	+	0.842555i
$953$	−51.4156			−1.66551			−0.832757	−	0.553639i	$-0.813239\pi$
$953$	−51.4156			−1.66551			−0.832757	+	0.553639i	$0.813239\pi$
$954$	12.6517	+	11.8295i	0.409615	+	0.382994i
$955$		0			0
$956$	12.7356	+	3.69569i	0.411899	+	0.119527i
$957$	14.6490	−	46.4813i	0.473534	−	1.50253i
$958$	−2.29656	+	16.1547i	−0.0741984	+	0.521933i
$959$	−18.1513			−0.586135
$960$		0			0
$961$	13.0531			0.421068
$962$	9.42660	−	66.3095i	0.303926	−	2.13790i
$963$	−19.0805	−	13.3530i	−0.614860	−	0.430295i
$964$	30.6398	+	8.89123i	0.986840	+	0.286367i
$965$		0			0
$966$	−7.34962	−	3.51877i	−0.236470	−	0.113215i
$967$	−20.9875			−0.674911			−0.337456	−	0.941341i	$-0.609566\pi$
$967$	−20.9875			−0.674911			−0.337456	+	0.941341i	$0.609566\pi$
$968$	6.00548	−	13.3174i	0.193023	−	0.428037i
$969$	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	$-0.133861\pi$
$972$	−7.35499	+	30.2969i	−0.235911	+	0.971775i
$973$	−12.5593			−0.402633
$974$	6.58866	−	46.3466i	0.211114	−	1.48504i
$975$		0			0
$976$	6.78243	−	10.7023i	0.217100	−	0.342571i
$977$	26.6495			0.852593			0.426296	−	0.904584i	$-0.359818\pi$
$977$	26.6495			0.852593			0.426296	+	0.904584i	$0.359818\pi$
$978$	−37.4600	−	17.9347i	−1.19784	−	0.573488i
$979$	3.33314			0.106528
$980$		0			0
$981$	−35.2802	+	50.4128i	−1.12641	+	1.60956i
$982$	29.9118	+	4.25228i	0.954524	+	0.135696i
$983$		−	47.0887i		−	1.50190i	−0.660361	−	0.750948i	$-0.729597\pi$
$983$		−	47.0887i		−	1.50190i	0.660361	−	0.750948i	$-0.270403\pi$
$984$	12.5706	+	11.2259i	0.400736	+	0.357867i
$985$		0			0
$986$	−7.28700	+	51.2589i	−0.232065	+	1.63242i
$987$	−7.58353	+	24.0626i	−0.241387	+	0.765922i
$988$	−6.33522	−	1.83839i	−0.201550	−	0.0584870i
$989$	1.79721			0.0571479
$990$		0			0
$991$			26.3879i			0.838238i	0.907931	+	0.419119i	$0.137661\pi$
$991$			26.3879i			0.838238i	−0.907931	+	0.419119i	$0.862339\pi$
$992$	18.2350	+	15.5494i	0.578963	+	0.493695i
$993$	−41.5787	−	13.1039i	−1.31946	−	0.415839i
$994$	−3.56146	+	25.0524i	−0.112963	+	0.794612i
$995$		0			0
$996$	20.6370	+	13.7500i	0.653909	+	0.435686i
$997$	10.2047			0.323186			0.161593	−	0.986858i	$-0.448337\pi$
$997$	10.2047			0.323186			0.161593	+	0.986858i	$0.448337\pi$
$998$	−2.95508	+	20.7869i	−0.0935416	+	0.657999i
$999$	−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.m.d.299.9		16
3.2	odd	2		600.2.m.c.299.8		16
4.3	odd	2		2400.2.m.c.1199.16		16
5.2	odd	4		120.2.b.b.11.8	yes	8
5.3	odd	4		600.2.b.e.251.1		8
5.4	even	2	inner	600.2.m.d.299.8		16
8.3	odd	2		600.2.m.c.299.10		16
8.5	even	2		2400.2.m.d.1199.16		16
12.11	even	2		2400.2.m.d.1199.2		16
15.2	even	4		120.2.b.a.11.1	✓	8
15.8	even	4		600.2.b.f.251.8		8
15.14	odd	2		600.2.m.c.299.9		16
20.3	even	4		2400.2.b.e.2351.4		8
20.7	even	4		480.2.b.a.431.5		8
20.19	odd	2		2400.2.m.c.1199.1		16
24.5	odd	2		2400.2.m.c.1199.2		16
24.11	even	2	inner	600.2.m.d.299.7		16
40.3	even	4		600.2.b.f.251.7		8
40.13	odd	4		2400.2.b.f.2351.4		8
40.19	odd	2		600.2.m.c.299.7		16
40.27	even	4		120.2.b.a.11.2	yes	8
40.29	even	2		2400.2.m.d.1199.1		16
40.37	odd	4		480.2.b.b.431.5		8
60.23	odd	4		2400.2.b.f.2351.3		8
60.47	odd	4		480.2.b.b.431.6		8
60.59	even	2		2400.2.m.d.1199.15		16
120.29	odd	2		2400.2.m.c.1199.15		16
120.53	even	4		2400.2.b.e.2351.3		8
120.59	even	2	inner	600.2.m.d.299.10		16
120.77	even	4		480.2.b.a.431.6		8
120.83	odd	4		600.2.b.e.251.2		8
120.107	odd	4		120.2.b.b.11.7	yes	8

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

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.m (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.199044 - 1.40014i) q^{2} +(-1.65195 - 0.520627i) q^{3} +(-1.92076 - 0.557378i) q^{4} +(-1.05776 + 2.20933i) q^{6} -1.92736 q^{7} +(-1.16272 + 2.57839i) q^{8} +(2.45790 + 1.72010i) q^{9} +O(q^{10})\)	\(q+(0.199044 - 1.40014i) q^{2} +(-1.65195 - 0.520627i) q^{3} +(-1.92076 - 0.557378i) q^{4} +(-1.05776 + 2.20933i) q^{6} -1.92736 q^{7} +(-1.16272 + 2.57839i) q^{8} +(2.45790 + 1.72010i) q^{9} +4.02057i q^{11} +(2.88282 + 1.92076i) q^{12} +4.81675 q^{13} +(-0.383629 + 2.69856i) q^{14} +(3.37866 + 2.14118i) q^{16} -5.23126 q^{17} +(2.89761 - 3.09901i) q^{18} +0.684753 q^{19} +(3.18390 + 1.00343i) q^{21} +(5.62935 + 0.800272i) q^{22} -1.72601i q^{23} +(3.26314 - 3.65403i) q^{24} +(0.958747 - 6.74411i) q^{26} +(-3.16480 - 4.12117i) q^{27} +(3.70199 + 1.07427i) q^{28} +6.99830 q^{29} +4.23638i q^{31} +(3.67045 - 4.30439i) q^{32} +(2.09322 - 6.64180i) q^{33} +(-1.04125 + 7.32448i) q^{34} +(-3.76229 - 4.67388i) q^{36} +9.83221 q^{37} +(0.136296 - 0.958747i) q^{38} +(-7.95705 - 2.50773i) q^{39} +3.44020i q^{41} +(2.03868 - 4.25817i) q^{42} +1.04125i q^{43} +(2.24098 - 7.72257i) q^{44} +(-2.41664 - 0.343552i) q^{46} +7.55759i q^{47} +(-4.46663 - 5.29615i) q^{48} -3.28530 q^{49} +(8.64180 + 2.72353i) q^{51} +(-9.25184 - 2.68475i) q^{52} +4.08251i q^{53} +(-6.40014 + 3.61085i) q^{54} +(2.24098 - 4.96947i) q^{56} +(-1.13118 - 0.356500i) q^{57} +(1.39297 - 9.79857i) q^{58} +0.994883i q^{59} -3.16761i q^{61} +(5.93151 + 0.843227i) q^{62} +(-4.73724 - 3.31525i) q^{63} +(-5.29615 - 5.99590i) q^{64} +(-8.88278 - 4.25280i) q^{66} +14.8728i q^{67} +(10.0480 + 2.91579i) q^{68} +(-0.898604 + 2.85128i) q^{69} +9.28360 q^{71} +(-7.29294 + 4.33741i) q^{72} +11.2836i q^{73} +(1.95705 - 13.7664i) q^{74} +(-1.31525 - 0.381666i) q^{76} -7.74908i q^{77} +(-5.09497 + 10.6418i) q^{78} -9.25184i q^{79} +(3.08251 + 8.45566i) q^{81} +(4.81675 + 0.684753i) q^{82} +7.15862 q^{83} +(-5.55623 - 3.70199i) q^{84} +(1.45790 + 0.207256i) q^{86} +(-11.5609 - 3.64350i) q^{87} +(-10.3666 - 4.67481i) q^{88} -0.829022i q^{89} -9.28360 q^{91} +(-0.962038 + 3.31525i) q^{92} +(2.20557 - 6.99830i) q^{93} +(10.5817 + 1.50430i) q^{94} +(-8.30439 + 5.19972i) q^{96} +1.45201i q^{97} +(-0.653920 + 4.59986i) q^{98} +(-6.91579 + 9.88215i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{4} + 2 q^{6}+O(q^{10}) \) 16 * q - 2 * q^4 + 2 * q^6	\( 16 q - 2 q^{4} + 2 q^{6} + 12 q^{14} - 14 q^{16} + 8 q^{19} - 8 q^{21} + 22 q^{24} + 32 q^{26} + 26 q^{36} - 32 q^{39} + 60 q^{44} - 16 q^{46} + 32 q^{49} + 40 q^{51} - 82 q^{54} + 60 q^{56} - 50 q^{64} - 68 q^{66} - 40 q^{69} - 48 q^{71} - 64 q^{74} - 24 q^{76} + 16 q^{81} - 116 q^{84} - 16 q^{86} + 48 q^{91} + 80 q^{94} - 86 q^{96} - 32 q^{99}+O(q^{100}) \) 16 * q - 2 * q^4 + 2 * q^6 + 12 * q^14 - 14 * q^16 + 8 * q^19 - 8 * q^21 + 22 * q^24 + 32 * q^26 + 26 * q^36 - 32 * q^39 + 60 * q^44 - 16 * q^46 + 32 * q^49 + 40 * q^51 - 82 * q^54 + 60 * q^56 - 50 * q^64 - 68 * q^66 - 40 * q^69 - 48 * q^71 - 64 * q^74 - 24 * q^76 + 16 * q^81 - 116 * q^84 - 16 * q^86 + 48 * q^91 + 80 * q^94 - 86 * q^96 - 32 * q^99

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