LMFDB - Embedded newform 198.2.f.e.181.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [198,2,Mod(37,198)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(198, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("198.37"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 198 = 2 \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	198.f (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,1,0,-1,6,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$1.58103796002$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 22)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			181.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	198.181
Dual form			198.2.f.e.163.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.309017 - 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{4} +(0.381966 - 1.17557i) q^{5} +(1.61803 - 1.17557i) q^{7} +(0.809017 + 0.587785i) q^{8} -1.23607 q^{10} +(0.809017 - 3.21644i) q^{11} +(-1.00000 - 3.07768i) q^{13} +(-1.61803 - 1.17557i) q^{14} +(0.309017 - 0.951057i) q^{16} +(-0.500000 + 1.53884i) q^{17} +(-0.690983 - 0.502029i) q^{19} +(0.381966 + 1.17557i) q^{20} +(-3.30902 + 0.224514i) q^{22} +3.23607 q^{23} +(2.80902 + 2.04087i) q^{25} +(-2.61803 + 1.90211i) q^{26} +(-0.618034 + 1.90211i) q^{28} +(-3.61803 + 2.62866i) q^{29} +(0.618034 + 1.90211i) q^{31} -1.00000 q^{32} +1.61803 q^{34} +(-0.763932 - 2.35114i) q^{35} +(-7.85410 + 5.70634i) q^{37} +(-0.263932 + 0.812299i) q^{38} +(1.00000 - 0.726543i) q^{40} +(2.73607 + 1.98787i) q^{41} +11.5623 q^{43} +(1.23607 + 3.07768i) q^{44} +(-1.00000 - 3.07768i) q^{46} +(2.00000 + 1.45309i) q^{47} +(-0.927051 + 2.85317i) q^{49} +(1.07295 - 3.30220i) q^{50} +(2.61803 + 1.90211i) q^{52} +(3.23607 + 9.95959i) q^{53} +(-3.47214 - 2.17963i) q^{55} +2.00000 q^{56} +(3.61803 + 2.62866i) q^{58} +(-5.16312 + 3.75123i) q^{59} +(2.00000 - 6.15537i) q^{61} +(1.61803 - 1.17557i) q^{62} +(0.309017 + 0.951057i) q^{64} -4.00000 q^{65} -0.0901699 q^{67} +(-0.500000 - 1.53884i) q^{68} +(-2.00000 + 1.45309i) q^{70} +(0.236068 - 0.726543i) q^{71} +(-10.2082 + 7.41669i) q^{73} +(7.85410 + 5.70634i) q^{74} +0.854102 q^{76} +(-2.47214 - 6.15537i) q^{77} +(-4.14590 - 12.7598i) q^{79} +(-1.00000 - 0.726543i) q^{80} +(1.04508 - 3.21644i) q^{82} +(1.95492 - 6.01661i) q^{83} +(1.61803 + 1.17557i) q^{85} +(-3.57295 - 10.9964i) q^{86} +(2.54508 - 2.12663i) q^{88} -3.09017 q^{89} +(-5.23607 - 3.80423i) q^{91} +(-2.61803 + 1.90211i) q^{92} +(0.763932 - 2.35114i) q^{94} +(-0.854102 + 0.620541i) q^{95} +(4.28115 + 13.1760i) q^{97} +3.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - q^{4} + 6 q^{5} + 2 q^{7} + q^{8} + 4 q^{10} + q^{11} - 4 q^{13} - 2 q^{14} - q^{16} - 2 q^{17} - 5 q^{19} + 6 q^{20} - 11 q^{22} + 4 q^{23} + 9 q^{25} - 6 q^{26} + 2 q^{28} - 10 q^{29}+ \cdots + 12 q^{98}+O(q^{100}) $ 4 * q + q^2 - q^4 + 6 * q^5 + 2 * q^7 + q^8 + 4 * q^10 + q^11 - 4 * q^13 - 2 * q^14 - q^16 - 2 * q^17 - 5 * q^19 + 6 * q^20 - 11 * q^22 + 4 * q^23 + 9 * q^25 - 6 * q^26 + 2 * q^28 - 10 * q^29 - 2 * q^31 - 4 * q^32 + 2 * q^34 - 12 * q^35 - 18 * q^37 - 10 * q^38 + 4 * q^40 + 2 * q^41 + 6 * q^43 - 4 * q^44 - 4 * q^46 + 8 * q^47 + 3 * q^49 + 11 * q^50 + 6 * q^52 + 4 * q^53 + 4 * q^55 + 8 * q^56 + 10 * q^58 - 5 * q^59 + 8 * q^61 + 2 * q^62 - q^64 - 16 * q^65 + 22 * q^67 - 2 * q^68 - 8 * q^70 - 8 * q^71 - 14 * q^73 + 18 * q^74 - 10 * q^76 + 8 * q^77 - 30 * q^79 - 4 * q^80 - 7 * q^82 + 19 * q^83 + 2 * q^85 - 21 * q^86 - q^88 + 10 * q^89 - 12 * q^91 - 6 * q^92 + 12 * q^94 + 10 * q^95 - 3 * q^97 + 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/198\mathbb{Z}\right)^\times$.

$n$	$145$	$155$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

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 $

$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$3$		0			0
$3$		0			0
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	0.381966	−	1.17557i	0.170820	−	0.525731i	−0.828598	−	0.559845i	$-0.810861\pi$
$5$	0.381966	−	1.17557i	0.170820	−	0.525731i	0.999418	+	0.0341136i	$0.0108608\pi$
$6$		0			0
$7$	1.61803	−	1.17557i	0.611559	−	0.444324i	−0.238404	−	0.971166i	$-0.576624\pi$
$7$	1.61803	−	1.17557i	0.611559	−	0.444324i	0.849963	+	0.526842i	$0.176624\pi$
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$		0			0
$10$	−1.23607			−0.390879
$11$	0.809017	−	3.21644i	0.243928	−	0.969793i
$11$	0.809017	−	3.21644i	0.243928	−	0.969793i
$12$		0			0
$13$	−1.00000	−	3.07768i	−0.277350	−	0.853596i	−0.988588	−	0.150644i	$-0.951865\pi$
$13$	−1.00000	−	3.07768i	−0.277350	−	0.853596i	0.711238	−	0.702951i	$-0.248135\pi$
$14$	−1.61803	−	1.17557i	−0.432438	−	0.314184i
$15$		0			0
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−0.500000	+	1.53884i	−0.121268	+	0.373224i	−0.993203	−	0.116398i	$-0.962865\pi$
$17$	−0.500000	+	1.53884i	−0.121268	+	0.373224i	0.871935	+	0.489622i	$0.162865\pi$
$18$		0			0
$19$	−0.690983	−	0.502029i	−0.158522	−	0.115173i	0.505696	−	0.862712i	$-0.331236\pi$
$19$	−0.690983	−	0.502029i	−0.158522	−	0.115173i	−0.664219	+	0.747538i	$0.731236\pi$
$20$	0.381966	+	1.17557i	0.0854102	+	0.262866i
$21$		0			0
$22$	−3.30902	+	0.224514i	−0.705485	+	0.0478665i
$23$	3.23607			0.674767			0.337383	−	0.941367i	$-0.390458\pi$
$23$	3.23607			0.674767			0.337383	+	0.941367i	$0.390458\pi$
$24$		0			0
$25$	2.80902	+	2.04087i	0.561803	+	0.408174i
$26$	−2.61803	+	1.90211i	−0.513439	+	0.373035i
$27$		0			0
$28$	−0.618034	+	1.90211i	−0.116797	+	0.359466i
$29$	−3.61803	+	2.62866i	−0.671852	+	0.488129i	−0.870645	−	0.491912i	$-0.836298\pi$
$29$	−3.61803	+	2.62866i	−0.671852	+	0.488129i	0.198793	+	0.980042i	$0.436298\pi$
$30$		0			0
$31$	0.618034	+	1.90211i	0.111002	+	0.341630i	0.991092	−	0.133177i	$-0.0425179\pi$
$31$	0.618034	+	1.90211i	0.111002	+	0.341630i	−0.880090	+	0.474807i	$0.842518\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	1.61803			0.277491
$35$	−0.763932	−	2.35114i	−0.129128	−	0.397415i
$36$		0			0
$37$	−7.85410	+	5.70634i	−1.29121	+	0.938116i	−0.999829	−	0.0184918i	$-0.994114\pi$
$37$	−7.85410	+	5.70634i	−1.29121	+	0.938116i	−0.291377	+	0.956608i	$0.594114\pi$
$38$	−0.263932	+	0.812299i	−0.0428154	+	0.131772i
$39$		0			0
$40$	1.00000	−	0.726543i	0.158114	−	0.114876i
$41$	2.73607	+	1.98787i	0.427302	+	0.310453i	0.780569	−	0.625069i	$-0.214929\pi$
$41$	2.73607	+	1.98787i	0.427302	+	0.310453i	−0.353267	+	0.935522i	$0.614929\pi$
$42$		0			0
$43$	11.5623			1.76324			0.881618	−	0.471964i	$-0.156455\pi$
$43$	11.5623			1.76324			0.881618	+	0.471964i	$0.156455\pi$
$44$	1.23607	+	3.07768i	0.186344	+	0.463978i
$45$		0			0
$46$	−1.00000	−	3.07768i	−0.147442	−	0.453780i
$47$	2.00000	+	1.45309i	0.291730	+	0.211954i	0.724018	−	0.689782i	$-0.242293\pi$
$47$	2.00000	+	1.45309i	0.291730	+	0.211954i	−0.432288	+	0.901736i	$0.642293\pi$
$48$		0			0
$49$	−0.927051	+	2.85317i	−0.132436	+	0.407596i
$50$	1.07295	−	3.30220i	0.151738	−	0.467001i
$51$		0			0
$52$	2.61803	+	1.90211i	0.363056	+	0.263776i
$53$	3.23607	+	9.95959i	0.444508	+	1.36806i	0.883022	+	0.469331i	$0.155505\pi$
$53$	3.23607	+	9.95959i	0.444508	+	1.36806i	−0.438514	+	0.898724i	$0.644495\pi$
$54$		0			0
$55$	−3.47214	−	2.17963i	−0.468183	−	0.293901i
$56$	2.00000			0.267261
$57$		0			0
$58$	3.61803	+	2.62866i	0.475071	+	0.345159i
$59$	−5.16312	+	3.75123i	−0.672181	+	0.488368i	−0.870755	−	0.491718i	$-0.836369\pi$
$59$	−5.16312	+	3.75123i	−0.672181	+	0.488368i	0.198574	+	0.980086i	$0.436369\pi$
$60$		0			0
$61$	2.00000	−	6.15537i	0.256074	−	0.788114i	−0.737542	−	0.675301i	$-0.764014\pi$
$61$	2.00000	−	6.15537i	0.256074	−	0.788114i	0.993616	−	0.112813i	$-0.0359862\pi$
$62$	1.61803	−	1.17557i	0.205491	−	0.149298i
$63$		0			0
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−4.00000			−0.496139
$66$		0			0
$67$	−0.0901699			−0.0110160			−0.00550801	−	0.999985i	$-0.501753\pi$
$67$	−0.0901699			−0.0110160			−0.00550801	+	0.999985i	$0.501753\pi$
$68$	−0.500000	−	1.53884i	−0.0606339	−	0.186612i
$69$		0			0
$70$	−2.00000	+	1.45309i	−0.239046	+	0.173677i
$71$	0.236068	−	0.726543i	0.0280161	−	0.0862247i	−0.936071	−	0.351812i	$-0.885566\pi$
$71$	0.236068	−	0.726543i	0.0280161	−	0.0862247i	0.964087	+	0.265587i	$0.0855657\pi$
$72$		0			0
$73$	−10.2082	+	7.41669i	−1.19478	+	0.868058i	−0.993761	−	0.111529i	$-0.964425\pi$
$73$	−10.2082	+	7.41669i	−1.19478	+	0.868058i	−0.201019	+	0.979587i	$0.564425\pi$
$74$	7.85410	+	5.70634i	0.913021	+	0.663348i
$75$		0			0
$76$	0.854102			0.0979722
$77$	−2.47214	−	6.15537i	−0.281726	−	0.701469i
$78$		0			0
$79$	−4.14590	−	12.7598i	−0.466450	−	1.43559i	−0.857150	−	0.515067i	$-0.827767\pi$
$79$	−4.14590	−	12.7598i	−0.466450	−	1.43559i	0.390700	−	0.920518i	$-0.372233\pi$
$80$	−1.00000	−	0.726543i	−0.111803	−	0.0812299i
$81$		0			0
$82$	1.04508	−	3.21644i	0.115410	−	0.355196i
$83$	1.95492	−	6.01661i	0.214580	−	0.660409i	−0.784603	−	0.619998i	$-0.787133\pi$
$83$	1.95492	−	6.01661i	0.214580	−	0.660409i	0.999183	−	0.0404107i	$-0.0128666\pi$
$84$		0			0
$85$	1.61803	+	1.17557i	0.175500	+	0.127509i
$86$	−3.57295	−	10.9964i	−0.385281	−	1.18577i
$87$		0			0
$88$	2.54508	−	2.12663i	0.271307	−	0.226699i
$89$	−3.09017			−0.327557			−0.163779	−	0.986497i	$-0.552368\pi$
$89$	−3.09017			−0.327557			−0.163779	+	0.986497i	$0.552368\pi$
$90$		0			0
$91$	−5.23607	−	3.80423i	−0.548889	−	0.398791i
$92$	−2.61803	+	1.90211i	−0.272949	+	0.198309i
$93$		0			0
$94$	0.763932	−	2.35114i	0.0787936	−	0.242502i
$95$	−0.854102	+	0.620541i	−0.0876290	+	0.0636662i
$96$		0			0
$97$	4.28115	+	13.1760i	0.434685	+	1.33782i	0.893409	+	0.449245i	$0.148307\pi$
$97$	4.28115	+	13.1760i	0.434685	+	1.33782i	−0.458724	+	0.888579i	$0.651693\pi$
$98$	3.00000			0.303046
$99$		0			0
$100$	−3.47214			−0.347214
$101$	−5.61803	−	17.2905i	−0.559015	−	1.72047i	−0.685097	−	0.728452i	$-0.740240\pi$
$101$	−5.61803	−	17.2905i	−0.559015	−	1.72047i	0.126081	−	0.992020i	$-0.459760\pi$
$102$		0			0
$103$	−1.85410	+	1.34708i	−0.182690	+	0.132732i	−0.675372	−	0.737478i	$-0.736017\pi$
$103$	−1.85410	+	1.34708i	−0.182690	+	0.132732i	0.492682	+	0.870210i	$0.336017\pi$
$104$	1.00000	−	3.07768i	0.0980581	−	0.301792i
$105$		0			0
$106$	8.47214	−	6.15537i	0.822887	−	0.597862i
$107$	−6.35410	−	4.61653i	−0.614274	−	0.446296i	0.236643	−	0.971597i	$-0.423953\pi$
$107$	−6.35410	−	4.61653i	−0.614274	−	0.446296i	−0.850917	+	0.525300i	$0.823953\pi$
$108$		0			0
$109$	1.05573			0.101120			0.0505602	−	0.998721i	$-0.483899\pi$
$109$	1.05573			0.101120			0.0505602	+	0.998721i	$0.483899\pi$
$110$	−1.00000	+	3.97574i	−0.0953463	+	0.379072i
$111$		0			0
$112$	−0.618034	−	1.90211i	−0.0583987	−	0.179733i
$113$	3.92705	+	2.85317i	0.369426	+	0.268404i	0.756973	−	0.653446i	$-0.226677\pi$
$113$	3.92705	+	2.85317i	0.369426	+	0.268404i	−0.387547	+	0.921850i	$0.626677\pi$
$114$		0			0
$115$	1.23607	−	3.80423i	0.115264	−	0.354746i
$116$	1.38197	−	4.25325i	0.128312	−	0.394905i
$117$		0			0
$118$	5.16312	+	3.75123i	0.475304	+	0.345328i
$119$	1.00000	+	3.07768i	0.0916698	+	0.282131i
$120$		0			0
$121$	−9.69098	−	5.20431i	−0.880998	−	0.473119i
$122$	−6.47214			−0.585960
$123$		0			0
$124$	−1.61803	−	1.17557i	−0.145304	−	0.105569i
$125$	8.47214	−	6.15537i	0.757771	−	0.550553i
$126$		0			0
$127$	2.14590	−	6.60440i	0.190418	−	0.586045i	−0.809582	−	0.587007i	$-0.800306\pi$
$127$	2.14590	−	6.60440i	0.190418	−	0.586045i	1.00000		0.000961675i	$0.000306111\pi$
$128$	0.809017	−	0.587785i	0.0715077	−	0.0519534i
$129$		0			0
$130$	1.23607	+	3.80423i	0.108410	+	0.333653i
$131$	17.7984			1.55505			0.777526	−	0.628851i	$-0.216475\pi$
$131$	17.7984			1.55505			0.777526	+	0.628851i	$0.216475\pi$
$132$		0			0
$133$	−1.70820			−0.148120
$134$	0.0278640	+	0.0857567i	0.00240709	+	0.00740825i
$135$		0			0
$136$	−1.30902	+	0.951057i	−0.112247	+	0.0815524i
$137$	−1.51722	+	4.66953i	−0.129625	+	0.398945i	−0.994715	−	0.102671i	$-0.967261\pi$
$137$	−1.51722	+	4.66953i	−0.129625	+	0.398945i	0.865090	+	0.501616i	$0.167261\pi$
$138$		0			0
$139$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$139$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$140$	2.00000	+	1.45309i	0.169031	+	0.122808i
$141$		0			0
$142$	−0.763932			−0.0641078
$143$	−10.7082	+	0.726543i	−0.895465	+	0.0607565i
$144$		0			0
$145$	1.70820	+	5.25731i	0.141859	+	0.436596i
$146$	10.2082	+	7.41669i	0.844837	+	0.613810i
$147$		0			0
$148$	3.00000	−	9.23305i	0.246598	−	0.758952i
$149$	−5.00000	+	15.3884i	−0.409616	+	1.26067i	0.507363	+	0.861732i	$0.330620\pi$
$149$	−5.00000	+	15.3884i	−0.409616	+	1.26067i	−0.916979	+	0.398936i	$0.869380\pi$
$150$		0			0
$151$	6.47214	+	4.70228i	0.526695	+	0.382666i	0.819120	−	0.573622i	$-0.194462\pi$
$151$	6.47214	+	4.70228i	0.526695	+	0.382666i	−0.292425	+	0.956288i	$0.594462\pi$
$152$	−0.263932	−	0.812299i	−0.0214077	−	0.0658862i
$153$		0			0
$154$	−5.09017	+	4.25325i	−0.410178	+	0.342737i
$155$	2.47214			0.198567
$156$		0			0
$157$	3.00000	+	2.17963i	0.239426	+	0.173953i	0.701028	−	0.713134i	$-0.252725\pi$
$157$	3.00000	+	2.17963i	0.239426	+	0.173953i	−0.461601	+	0.887087i	$0.652725\pi$
$158$	−10.8541	+	7.88597i	−0.863506	+	0.627374i
$159$		0			0
$160$	−0.381966	+	1.17557i	−0.0301971	+	0.0929370i
$161$	5.23607	−	3.80423i	0.412660	−	0.299815i
$162$		0			0
$163$	3.73607	+	11.4984i	0.292631	+	0.900627i	0.984007	+	0.178131i	$0.0570051\pi$
$163$	3.73607	+	11.4984i	0.292631	+	0.900627i	−0.691375	+	0.722496i	$0.742995\pi$
$164$	−3.38197			−0.264087
$165$		0			0
$166$	−6.32624			−0.491011
$167$	5.94427	+	18.2946i	0.459982	+	1.41568i	0.865186	+	0.501451i	$0.167200\pi$
$167$	5.94427	+	18.2946i	0.459982	+	1.41568i	−0.405204	+	0.914226i	$0.632800\pi$
$168$		0			0
$169$	2.04508	−	1.48584i	0.157314	−	0.114295i
$170$	0.618034	−	1.90211i	0.0474010	−	0.145885i
$171$		0			0
$172$	−9.35410	+	6.79615i	−0.713244	+	0.518202i
$173$	−11.2361	−	8.16348i	−0.854262	−	0.620658i	0.0720555	−	0.997401i	$-0.477044\pi$
$173$	−11.2361	−	8.16348i	−0.854262	−	0.620658i	−0.926318	+	0.376743i	$0.877044\pi$
$174$		0			0
$175$	6.94427			0.524938
$176$	−2.80902	−	1.76336i	−0.211738	−	0.132918i
$177$		0			0
$178$	0.954915	+	2.93893i	0.0715739	+	0.220282i
$179$	−5.16312	−	3.75123i	−0.385910	−	0.280380i	0.377868	−	0.925860i	$-0.376657\pi$
$179$	−5.16312	−	3.75123i	−0.385910	−	0.280380i	−0.763777	+	0.645480i	$0.776657\pi$
$180$		0			0
$181$	5.61803	−	17.2905i	0.417585	−	1.28520i	−0.492333	−	0.870407i	$-0.663856\pi$
$181$	5.61803	−	17.2905i	0.417585	−	1.28520i	0.909918	−	0.414788i	$-0.136144\pi$
$182$	−2.00000	+	6.15537i	−0.148250	+	0.456266i
$183$		0			0
$184$	2.61803	+	1.90211i	0.193004	+	0.140226i
$185$	3.70820	+	11.4127i	0.272633	+	0.839077i
$186$		0			0
$187$	4.54508	+	2.85317i	0.332370	+	0.208644i
$188$	−2.47214			−0.180299
$189$		0			0
$190$	0.854102	+	0.620541i	0.0619631	+	0.0450188i
$191$	7.47214	−	5.42882i	0.540665	−	0.392816i	−0.283667	−	0.958923i	$-0.591551\pi$
$191$	7.47214	−	5.42882i	0.540665	−	0.392816i	0.824332	+	0.566107i	$0.191551\pi$
$192$		0			0
$193$	−2.90983	+	8.95554i	−0.209454	+	0.644634i	0.790047	+	0.613046i	$0.210056\pi$
$193$	−2.90983	+	8.95554i	−0.209454	+	0.644634i	−0.999501	+	0.0315871i	$0.989944\pi$
$194$	11.2082	−	8.14324i	0.804702	−	0.584650i
$195$		0			0
$196$	−0.927051	−	2.85317i	−0.0662179	−	0.203798i
$197$	3.05573			0.217712			0.108856	−	0.994058i	$-0.465281\pi$
$197$	3.05573			0.217712			0.108856	+	0.994058i	$0.465281\pi$
$198$		0			0
$199$	−1.05573			−0.0748386			−0.0374193	−	0.999300i	$-0.511914\pi$
$199$	−1.05573			−0.0748386			−0.0374193	+	0.999300i	$0.511914\pi$
$200$	1.07295	+	3.30220i	0.0758690	+	0.233501i
$201$		0			0
$202$	−14.7082	+	10.6861i	−1.03487	+	0.751874i
$203$	−2.76393	+	8.50651i	−0.193990	+	0.597040i
$204$		0			0
$205$	3.38197	−	2.45714i	0.236207	−	0.171614i
$206$	1.85410	+	1.34708i	0.129181	+	0.0938558i
$207$		0			0
$208$	−3.23607			−0.224381
$209$	−2.17376	+	1.81636i	−0.150362	+	0.125640i
$210$		0			0
$211$	1.57295	+	4.84104i	0.108286	+	0.333271i	0.990488	−	0.137601i	$-0.0439393\pi$
$211$	1.57295	+	4.84104i	0.108286	+	0.333271i	−0.882201	+	0.470872i	$0.843939\pi$
$212$	−8.47214	−	6.15537i	−0.581869	−	0.422752i
$213$		0			0
$214$	−2.42705	+	7.46969i	−0.165910	+	0.510618i
$215$	4.41641	−	13.5923i	0.301197	−	0.926988i
$216$		0			0
$217$	3.23607	+	2.35114i	0.219679	+	0.159606i
$218$	−0.326238	−	1.00406i	−0.0220956	−	0.0680033i
$219$		0			0
$220$	4.09017	−	0.277515i	0.275759	−	0.0187100i
$221$	5.23607			0.352216
$222$		0			0
$223$	−9.94427	−	7.22494i	−0.665918	−	0.483818i	0.202739	−	0.979233i	$-0.435016\pi$
$223$	−9.94427	−	7.22494i	−0.665918	−	0.483818i	−0.868656	+	0.495415i	$0.835016\pi$
$224$	−1.61803	+	1.17557i	−0.108109	+	0.0785461i
$225$		0			0
$226$	1.50000	−	4.61653i	0.0997785	−	0.307087i
$227$	−19.0172	+	13.8168i	−1.26222	+	0.917055i	−0.998864	−	0.0476450i	$-0.984828\pi$
$227$	−19.0172	+	13.8168i	−1.26222	+	0.917055i	−0.263353	+	0.964700i	$0.584828\pi$
$228$		0			0
$229$	−3.61803	−	11.1352i	−0.239086	−	0.735832i	−0.996553	−	0.0829584i	$-0.973563\pi$
$229$	−3.61803	−	11.1352i	−0.239086	−	0.735832i	0.757467	−	0.652874i	$-0.226437\pi$
$230$	−4.00000			−0.263752
$231$		0			0
$232$	−4.47214			−0.293610
$233$	2.28115	+	7.02067i	0.149443	+	0.459939i	0.997556	−	0.0698773i	$-0.0222608\pi$
$233$	2.28115	+	7.02067i	0.149443	+	0.459939i	−0.848112	+	0.529817i	$0.822261\pi$
$234$		0			0
$235$	2.47214	−	1.79611i	0.161264	−	0.117165i
$236$	1.97214	−	6.06961i	0.128375	−	0.395098i
$237$		0			0
$238$	2.61803	−	1.90211i	0.169702	−	0.123296i
$239$	−6.70820	−	4.87380i	−0.433918	−	0.315260i	0.349296	−	0.937012i	$-0.386421\pi$
$239$	−6.70820	−	4.87380i	−0.433918	−	0.315260i	−0.783213	+	0.621753i	$0.786421\pi$
$240$		0			0
$241$	0.0901699			0.00580836			0.00290418	−	0.999996i	$-0.499076\pi$
$241$	0.0901699			0.00580836			0.00290418	+	0.999996i	$0.499076\pi$
$242$	−1.95492	+	10.8249i	−0.125667	+	0.695850i
$243$		0			0
$244$	2.00000	+	6.15537i	0.128037	+	0.394057i
$245$	3.00000	+	2.17963i	0.191663	+	0.139251i
$246$		0			0
$247$	−0.854102	+	2.62866i	−0.0543452	+	0.167257i
$248$	−0.618034	+	1.90211i	−0.0392452	+	0.120784i
$249$		0			0
$250$	−8.47214	−	6.15537i	−0.535825	−	0.389300i
$251$	−0.944272	−	2.90617i	−0.0596019	−	0.183436i	0.916823	−	0.399295i	$-0.130745\pi$
$251$	−0.944272	−	2.90617i	−0.0596019	−	0.183436i	−0.976425	+	0.215859i	$0.930745\pi$
$252$		0			0
$253$	2.61803	−	10.4086i	0.164594	−	0.654384i
$254$	−6.94427			−0.435722
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−2.73607	+	1.98787i	−0.170671	+	0.124000i	−0.669842	−	0.742504i	$-0.733638\pi$
$257$	−2.73607	+	1.98787i	−0.170671	+	0.124000i	0.499171	+	0.866504i	$0.333638\pi$
$258$		0			0
$259$	−6.00000	+	18.4661i	−0.372822	+	1.14743i
$260$	3.23607	−	2.35114i	0.200692	−	0.145812i
$261$		0			0
$262$	−5.50000	−	16.9273i	−0.339791	−	1.04577i
$263$	18.7639			1.15703			0.578517	−	0.815670i	$-0.303632\pi$
$263$	18.7639			1.15703			0.578517	+	0.815670i	$0.303632\pi$
$264$		0			0
$265$	12.9443			0.795160
$266$	0.527864	+	1.62460i	0.0323654	+	0.0996105i
$267$		0			0
$268$	0.0729490	−	0.0530006i	0.00445607	−	0.00323752i
$269$	5.00000	−	15.3884i	0.304855	−	0.938248i	−0.674876	−	0.737931i	$-0.735803\pi$
$269$	5.00000	−	15.3884i	0.304855	−	0.938248i	0.979731	−	0.200317i	$-0.0641972\pi$
$270$		0			0
$271$	−1.61803	+	1.17557i	−0.0982886	+	0.0714108i	−0.635844	−	0.771818i	$-0.719348\pi$
$271$	−1.61803	+	1.17557i	−0.0982886	+	0.0714108i	0.537555	+	0.843228i	$0.319348\pi$
$272$	1.30902	+	0.951057i	0.0793708	+	0.0576663i
$273$		0			0
$274$	4.90983			0.296614
$275$	8.83688	−	7.38394i	0.532884	−	0.445268i
$276$		0			0
$277$	−3.18034	−	9.78808i	−0.191088	−	0.588109i	−1.00000		0.000178809i	$-0.999943\pi$
$277$	−3.18034	−	9.78808i	−0.191088	−	0.588109i	0.808912	−	0.587930i	$-0.200057\pi$
$278$		0			0
$279$		0			0
$280$	0.763932	−	2.35114i	0.0456537	−	0.140508i
$281$	1.51722	−	4.66953i	0.0905098	−	0.278561i	−0.895548	−	0.444966i	$-0.853216\pi$
$281$	1.51722	−	4.66953i	0.0905098	−	0.278561i	0.986057	+	0.166405i	$0.0532159\pi$
$282$		0			0
$283$	−19.4164	−	14.1068i	−1.15419	−	0.838565i	−0.165154	−	0.986268i	$-0.552812\pi$
$283$	−19.4164	−	14.1068i	−1.15419	−	0.838565i	−0.989032	+	0.147703i	$0.952812\pi$
$284$	0.236068	+	0.726543i	0.0140081	+	0.0431124i
$285$		0			0
$286$	4.00000	+	9.95959i	0.236525	+	0.588923i
$287$	6.76393			0.399262
$288$		0			0
$289$	11.6353	+	8.45351i	0.684427	+	0.497265i
$290$	4.47214	−	3.24920i	0.262613	−	0.190799i
$291$		0			0
$292$	3.89919	−	12.0005i	0.228183	−	0.702274i
$293$	13.2361	−	9.61657i	0.773259	−	0.561806i	−0.129689	−	0.991555i	$-0.541398\pi$
$293$	13.2361	−	9.61657i	0.773259	−	0.561806i	0.902948	+	0.429749i	$0.141398\pi$
$294$		0			0
$295$	2.43769	+	7.50245i	0.141928	+	0.436810i
$296$	−9.70820			−0.564278
$297$		0			0
$298$	16.1803			0.937302
$299$	−3.23607	−	9.95959i	−0.187147	−	0.575978i
$300$		0			0
$301$	18.7082	−	13.5923i	1.07832	−	0.783447i
$302$	2.47214	−	7.60845i	0.142255	−	0.437817i
$303$		0			0
$304$	−0.690983	+	0.502029i	−0.0396306	+	0.0287933i
$305$	−6.47214	−	4.70228i	−0.370593	−	0.269252i
$306$		0			0
$307$	3.20163			0.182726			0.0913632	−	0.995818i	$-0.470878\pi$
$307$	3.20163			0.182726			0.0913632	+	0.995818i	$0.470878\pi$
$308$	5.61803	+	3.52671i	0.320117	+	0.200953i
$309$		0			0
$310$	−0.763932	−	2.35114i	−0.0433884	−	0.133536i
$311$	−25.9443	−	18.8496i	−1.47116	−	1.06886i	−0.980274	−	0.197642i	$-0.936672\pi$
$311$	−25.9443	−	18.8496i	−1.47116	−	1.06886i	−0.490891	−	0.871221i	$-0.663328\pi$
$312$		0			0
$313$	−3.50000	+	10.7719i	−0.197832	+	0.608863i	0.802100	+	0.597190i	$0.203716\pi$
$313$	−3.50000	+	10.7719i	−0.197832	+	0.608863i	−0.999932	+	0.0116738i	$0.996284\pi$
$314$	1.14590	−	3.52671i	0.0646668	−	0.199024i
$315$		0			0
$316$	10.8541	+	7.88597i	0.610591	+	0.443620i
$317$	−3.00000	−	9.23305i	−0.168497	−	0.518580i	0.830780	−	0.556601i	$-0.187895\pi$
$317$	−3.00000	−	9.23305i	−0.168497	−	0.518580i	−0.999277	+	0.0380209i	$0.987895\pi$
$318$		0			0
$319$	5.52786	+	13.7638i	0.309501	+	0.770626i
$320$	1.23607			0.0690983
$321$		0			0
$322$	−5.23607	−	3.80423i	−0.291795	−	0.212001i
$323$	1.11803	−	0.812299i	0.0622091	−	0.0451975i
$324$		0			0
$325$	3.47214	−	10.6861i	0.192599	−	0.592760i
$326$	9.78115	−	7.10642i	0.541728	−	0.393588i
$327$		0			0
$328$	1.04508	+	3.21644i	0.0577052	+	0.177598i
$329$	4.94427			0.272587
$330$		0			0
$331$	−27.2705			−1.49892			−0.749461	−	0.662048i	$-0.769687\pi$
$331$	−27.2705			−1.49892			−0.749461	+	0.662048i	$0.769687\pi$
$332$	1.95492	+	6.01661i	0.107290	+	0.330204i
$333$		0			0
$334$	15.5623	−	11.3067i	0.851531	−	0.618674i
$335$	−0.0344419	+	0.106001i	−0.00188176	+	0.00579146i
$336$		0			0
$337$	1.78115	−	1.29408i	0.0970256	−	0.0704932i	−0.538215	−	0.842808i	$-0.680901\pi$
$337$	1.78115	−	1.29408i	0.0970256	−	0.0704932i	0.635240	+	0.772315i	$0.280901\pi$
$338$	−2.04508	−	1.48584i	−0.111238	−	0.0808191i
$339$		0			0
$340$	−2.00000			−0.108465
$341$	6.61803	−	0.449028i	0.358387	−	0.0243162i
$342$		0			0
$343$	6.18034	+	19.0211i	0.333707	+	1.02704i
$344$	9.35410	+	6.79615i	0.504339	+	0.366424i
$345$		0			0
$346$	−4.29180	+	13.2088i	−0.230728	+	0.710109i
$347$	−4.44427	+	13.6781i	−0.238581	+	0.734277i	0.758045	+	0.652202i	$0.226155\pi$
$347$	−4.44427	+	13.6781i	−0.238581	+	0.734277i	−0.996626	+	0.0820748i	$0.973845\pi$
$348$		0			0
$349$	−23.9443	−	17.3965i	−1.28171	−	0.931215i	−0.282104	−	0.959384i	$-0.591032\pi$
$349$	−23.9443	−	17.3965i	−1.28171	−	0.931215i	−0.999603	+	0.0281687i	$0.991032\pi$
$350$	−2.14590	−	6.60440i	−0.114703	−	0.353020i
$351$		0			0
$352$	−0.809017	+	3.21644i	−0.0431208	+	0.171437i
$353$	−30.3820			−1.61707			−0.808534	−	0.588449i	$-0.799739\pi$
$353$	−30.3820			−1.61707			−0.808534	+	0.588449i	$0.799739\pi$
$354$		0			0
$355$	−0.763932	−	0.555029i	−0.0405453	−	0.0294579i
$356$	2.50000	−	1.81636i	0.132500	−	0.0962667i
$357$		0			0
$358$	−1.97214	+	6.06961i	−0.104231	+	0.320789i
$359$	−28.4164	+	20.6457i	−1.49976	+	1.08964i	−0.529284	+	0.848445i	$0.677539\pi$
$359$	−28.4164	+	20.6457i	−1.49976	+	1.08964i	−0.970477	+	0.241195i	$0.922461\pi$
$360$		0			0
$361$	−5.64590	−	17.3763i	−0.297153	−	0.914541i
$362$	−18.1803			−0.955537
$363$		0			0
$364$	6.47214			0.339232
$365$	4.81966	+	14.8334i	0.252273	+	0.776415i
$366$		0			0
$367$	−5.09017	+	3.69822i	−0.265705	+	0.193046i	−0.712658	−	0.701511i	$-0.752509\pi$
$367$	−5.09017	+	3.69822i	−0.265705	+	0.193046i	0.446954	+	0.894557i	$0.352509\pi$
$368$	1.00000	−	3.07768i	0.0521286	−	0.160435i
$369$		0			0
$370$	9.70820	−	7.05342i	0.504705	−	0.366690i
$371$	16.9443	+	12.3107i	0.879703	+	0.639141i
$372$		0			0
$373$	−17.7082			−0.916896			−0.458448	−	0.888721i	$-0.651594\pi$
$373$	−17.7082			−0.916896			−0.458448	+	0.888721i	$0.651594\pi$
$374$	1.30902	−	5.20431i	0.0676877	−	0.269108i
$375$		0			0
$376$	0.763932	+	2.35114i	0.0393968	+	0.121251i
$377$	11.7082	+	8.50651i	0.603003	+	0.438107i
$378$		0			0
$379$	−5.95492	+	18.3273i	−0.305883	+	0.941412i	0.673463	+	0.739221i	$0.264806\pi$
$379$	−5.95492	+	18.3273i	−0.305883	+	0.941412i	−0.979346	+	0.202191i	$0.935194\pi$
$380$	0.326238	−	1.00406i	0.0167357	−	0.0515070i
$381$		0			0
$382$	−7.47214	−	5.42882i	−0.382308	−	0.277763i
$383$	−5.05573	−	15.5599i	−0.258336	−	0.795075i	−0.993154	−	0.116812i	$-0.962733\pi$
$383$	−5.05573	−	15.5599i	−0.258336	−	0.795075i	0.734818	−	0.678264i	$-0.237267\pi$
$384$		0			0
$385$	−8.18034	+	0.555029i	−0.416909	+	0.0282869i
$386$	9.41641			0.479283
$387$		0			0
$388$	−11.2082	−	8.14324i	−0.569010	−	0.413410i
$389$	16.7082	−	12.1392i	0.847140	−	0.615483i	−0.0772163	−	0.997014i	$-0.524603\pi$
$389$	16.7082	−	12.1392i	0.847140	−	0.615483i	0.924356	+	0.381531i	$0.124603\pi$
$390$		0			0
$391$	−1.61803	+	4.97980i	−0.0818275	+	0.251839i
$392$	−2.42705	+	1.76336i	−0.122585	+	0.0890629i
$393$		0			0
$394$	−0.944272	−	2.90617i	−0.0475717	−	0.146411i
$395$	−16.5836			−0.834411
$396$		0			0
$397$	23.1246			1.16059			0.580295	−	0.814406i	$-0.302937\pi$
$397$	23.1246			1.16059			0.580295	+	0.814406i	$0.302937\pi$
$398$	0.326238	+	1.00406i	0.0163528	+	0.0503288i
$399$		0			0
$400$	2.80902	−	2.04087i	0.140451	−	0.102044i
$401$	−2.10081	+	6.46564i	−0.104910	+	0.322879i	−0.989709	−	0.143093i	$-0.954295\pi$
$401$	−2.10081	+	6.46564i	−0.104910	+	0.322879i	0.884800	+	0.465972i	$0.154295\pi$
$402$		0			0
$403$	5.23607	−	3.80423i	0.260827	−	0.189502i
$404$	14.7082	+	10.6861i	0.731760	+	0.531655i
$405$		0			0
$406$	8.94427			0.443897
$407$	12.0000	+	29.8788i	0.594818	+	1.48104i
$408$		0			0
$409$	4.14590	+	12.7598i	0.205001	+	0.630930i	0.999713	+	0.0239428i	$0.00762195\pi$
$409$	4.14590	+	12.7598i	0.205001	+	0.630930i	−0.794712	+	0.606987i	$0.792378\pi$
$410$	−3.38197	−	2.45714i	−0.167023	−	0.121350i
$411$		0			0
$412$	0.708204	−	2.17963i	0.0348907	−	0.107383i
$413$	−3.94427	+	12.1392i	−0.194085	+	0.597332i
$414$		0			0
$415$	−6.32624	−	4.59628i	−0.310543	−	0.225623i
$416$	1.00000	+	3.07768i	0.0490290	+	0.150896i
$417$		0			0
$418$	2.39919	+	1.50609i	0.117348	+	0.0736651i
$419$	4.14590			0.202540			0.101270	−	0.994859i	$-0.467709\pi$
$419$	4.14590			0.202540			0.101270	+	0.994859i	$0.467709\pi$
$420$		0			0
$421$	3.70820	+	2.69417i	0.180727	+	0.131306i	0.674471	−	0.738302i	$-0.264372\pi$
$421$	3.70820	+	2.69417i	0.180727	+	0.131306i	−0.493744	+	0.869607i	$0.664372\pi$
$422$	4.11803	−	2.99193i	0.200463	−	0.145645i
$423$		0			0
$424$	−3.23607	+	9.95959i	−0.157157	+	0.483681i
$425$	−4.54508	+	3.30220i	−0.220469	+	0.160180i
$426$		0			0
$427$	−4.00000	−	12.3107i	−0.193574	−	0.595758i
$428$	7.85410			0.379642
$429$		0			0
$430$	−14.2918			−0.689212
$431$	−0.291796	−	0.898056i	−0.0140553	−	0.0432578i	0.943783	−	0.330566i	$-0.107240\pi$
$431$	−0.291796	−	0.898056i	−0.0140553	−	0.0432578i	−0.957838	+	0.287308i	$0.907240\pi$
$432$		0			0
$433$	11.9271	−	8.66551i	0.573177	−	0.416438i	−0.263081	−	0.964774i	$-0.584739\pi$
$433$	11.9271	−	8.66551i	0.573177	−	0.416438i	0.836258	+	0.548336i	$0.184739\pi$
$434$	1.23607	−	3.80423i	0.0593332	−	0.182609i
$435$		0			0
$436$	−0.854102	+	0.620541i	−0.0409041	+	0.0297185i
$437$	−2.23607	−	1.62460i	−0.106966	−	0.0777151i
$438$		0			0
$439$	−33.4164			−1.59488			−0.797439	−	0.603399i	$-0.793812\pi$
$439$	−33.4164			−1.59488			−0.797439	+	0.603399i	$0.793812\pi$
$440$	−1.52786	−	3.80423i	−0.0728381	−	0.181359i
$441$		0			0
$442$	−1.61803	−	4.97980i	−0.0769620	−	0.236865i
$443$	9.35410	+	6.79615i	0.444427	+	0.322895i	0.787391	−	0.616453i	$-0.211431\pi$
$443$	9.35410	+	6.79615i	0.444427	+	0.322895i	−0.342965	+	0.939348i	$0.611431\pi$
$444$		0			0
$445$	−1.18034	+	3.63271i	−0.0559535	+	0.172207i
$446$	−3.79837	+	11.6902i	−0.179858	+	0.553547i
$447$		0			0
$448$	1.61803	+	1.17557i	0.0764449	+	0.0555405i
$449$	7.50000	+	23.0826i	0.353947	+	1.08934i	0.956618	+	0.291347i	$0.0941033\pi$
$449$	7.50000	+	23.0826i	0.353947	+	1.08934i	−0.602671	+	0.797990i	$0.705897\pi$
$450$		0			0
$451$	8.60739	−	7.19218i	0.405306	−	0.338667i
$452$	−4.85410			−0.228318
$453$		0			0
$454$	19.0172	+	13.8168i	0.892522	+	0.648455i
$455$	−6.47214	+	4.70228i	−0.303418	+	0.220446i
$456$		0			0
$457$	−9.13525	+	28.1154i	−0.427329	+	1.31518i	0.473417	+	0.880838i	$0.343020\pi$
$457$	−9.13525	+	28.1154i	−0.427329	+	1.31518i	−0.900746	+	0.434346i	$0.856980\pi$
$458$	−9.47214	+	6.88191i	−0.442604	+	0.321571i
$459$		0			0
$460$	1.23607	+	3.80423i	0.0576320	+	0.177373i
$461$	−32.6525			−1.52078			−0.760389	−	0.649468i	$-0.774992\pi$
$461$	−32.6525			−1.52078			−0.760389	+	0.649468i	$0.774992\pi$
$462$		0			0
$463$	7.41641			0.344670			0.172335	−	0.985038i	$-0.444869\pi$
$463$	7.41641			0.344670			0.172335	+	0.985038i	$0.444869\pi$
$464$	1.38197	+	4.25325i	0.0641562	+	0.197452i
$465$		0			0
$466$	5.97214	−	4.33901i	0.276654	−	0.201001i
$467$	−9.05573	+	27.8707i	−0.419049	+	1.28970i	0.489530	+	0.871987i	$0.337169\pi$
$467$	−9.05573	+	27.8707i	−0.419049	+	1.28970i	−0.908579	+	0.417714i	$0.862831\pi$
$468$		0			0
$469$	−0.145898	+	0.106001i	−0.00673695	+	0.00489468i
$470$	−2.47214	−	1.79611i	−0.114031	−	0.0828485i
$471$		0			0
$472$	−6.38197			−0.293754
$473$	9.35410	−	37.1895i	0.430102	−	1.70997i
$474$		0			0
$475$	−0.916408	−	2.82041i	−0.0420477	−	0.129409i
$476$	−2.61803	−	1.90211i	−0.119997	−	0.0871832i
$477$		0			0
$478$	−2.56231	+	7.88597i	−0.117197	+	0.360696i
$479$	7.88854	−	24.2784i	0.360437	−	1.10931i	−0.592353	−	0.805679i	$-0.701801\pi$
$479$	7.88854	−	24.2784i	0.360437	−	1.10931i	0.952790	−	0.303632i	$-0.0981992\pi$
$480$		0			0
$481$	25.4164	+	18.4661i	1.15889	+	0.841982i
$482$	−0.0278640	−	0.0857567i	−0.00126917	−	0.00390611i
$483$		0			0
$484$	10.8992	−	1.48584i	0.495418	−	0.0675382i
$485$	17.1246			0.777589
$486$		0			0
$487$	26.4164	+	19.1926i	1.19704	+	0.869702i	0.993990	−	0.109466i	$-0.0349142\pi$
$487$	26.4164	+	19.1926i	1.19704	+	0.869702i	0.203051	+	0.979168i	$0.434914\pi$
$488$	5.23607	−	3.80423i	0.237026	−	0.172209i
$489$		0			0
$490$	1.14590	−	3.52671i	0.0517664	−	0.159321i
$491$	13.0623	−	9.49032i	0.589494	−	0.428292i	−0.252641	−	0.967560i	$-0.581299\pi$
$491$	13.0623	−	9.49032i	0.589494	−	0.428292i	0.842134	+	0.539268i	$0.181299\pi$
$492$		0			0
$493$	−2.23607	−	6.88191i	−0.100707	−	0.309946i
$494$	2.76393			0.124355
$495$		0			0
$496$	2.00000			0.0898027
$497$	−0.472136	−	1.45309i	−0.0211782	−	0.0651798i
$498$		0			0
$499$	19.5344	−	14.1926i	0.874482	−	0.635348i	−0.0573041	−	0.998357i	$-0.518250\pi$
$499$	19.5344	−	14.1926i	0.874482	−	0.635348i	0.931786	+	0.363009i	$0.118250\pi$
$500$	−3.23607	+	9.95959i	−0.144721	+	0.445407i
$501$		0			0
$502$	−2.47214	+	1.79611i	−0.110337	+	0.0801644i
$503$	1.00000	+	0.726543i	0.0445878	+	0.0323949i	0.609856	−	0.792512i	$-0.291227\pi$
$503$	1.00000	+	0.726543i	0.0445878	+	0.0323949i	−0.565268	+	0.824907i	$0.691227\pi$
$504$		0			0
$505$	−22.4721			−0.999997
$506$	−10.7082	+	0.726543i	−0.476038	+	0.0322988i
$507$		0			0
$508$	2.14590	+	6.60440i	0.0952088	+	0.293023i
$509$	−17.5623	−	12.7598i	−0.778436	−	0.565567i	0.126074	−	0.992021i	$-0.459762\pi$
$509$	−17.5623	−	12.7598i	−0.778436	−	0.565567i	−0.904509	+	0.426454i	$0.859762\pi$
$510$		0			0
$511$	−7.79837	+	24.0009i	−0.344980	+	1.06174i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$		0			0
$514$	2.73607	+	1.98787i	0.120683	+	0.0876812i
$515$	0.875388	+	2.69417i	0.0385742	+	0.118719i
$516$		0			0
$517$	6.29180	−	5.25731i	0.276713	−	0.231216i
$518$	19.4164			0.853108
$519$		0			0
$520$	−3.23607	−	2.35114i	−0.141911	−	0.103104i
$521$	7.30902	−	5.31031i	0.320214	−	0.232649i	−0.416053	−	0.909340i	$-0.636587\pi$
$521$	7.30902	−	5.31031i	0.320214	−	0.232649i	0.736267	+	0.676691i	$0.236587\pi$
$522$		0			0
$523$	10.4443	−	32.1442i	0.456696	−	1.40557i	−0.412436	−	0.910986i	$-0.635322\pi$
$523$	10.4443	−	32.1442i	0.456696	−	1.40557i	0.869132	−	0.494580i	$-0.164678\pi$
$524$	−14.3992	+	10.4616i	−0.629031	+	0.457018i
$525$		0			0
$526$	−5.79837	−	17.8456i	−0.252821	−	0.778103i
$527$	−3.23607			−0.140965
$528$		0			0
$529$	−12.5279			−0.544690
$530$	−4.00000	−	12.3107i	−0.173749	−	0.534744i
$531$		0			0
$532$	1.38197	−	1.00406i	0.0599158	−	0.0435314i
$533$	3.38197	−	10.4086i	0.146489	−	0.450847i
$534$		0			0
$535$	−7.85410	+	5.70634i	−0.339562	+	0.246707i
$536$	−0.0729490	−	0.0530006i	−0.00315092	−	0.00228928i
$537$		0			0
$538$	−16.1803			−0.697584
$539$	8.42705	+	5.29007i	0.362979	+	0.227859i
$540$		0			0
$541$	11.4721	+	35.3076i	0.493226	+	1.51799i	0.819704	+	0.572788i	$0.194138\pi$
$541$	11.4721	+	35.3076i	0.493226	+	1.51799i	−0.326478	+	0.945205i	$0.605862\pi$
$542$	1.61803	+	1.17557i	0.0695005	+	0.0504951i
$543$		0			0
$544$	0.500000	−	1.53884i	0.0214373	−	0.0659773i
$545$	0.403252	−	1.24108i	0.0172734	−	0.0531621i
$546$		0			0
$547$	5.92705	+	4.30625i	0.253422	+	0.184122i	0.707242	−	0.706971i	$-0.249939\pi$
$547$	5.92705	+	4.30625i	0.253422	+	0.184122i	−0.453820	+	0.891093i	$0.649939\pi$
$548$	−1.51722	−	4.66953i	−0.0648125	−	0.199472i
$549$		0			0
$550$	−9.75329	−	6.12261i	−0.415882	−	0.261069i
$551$	3.81966			0.162723
$552$		0			0
$553$	−21.7082	−	15.7719i	−0.923127	−	0.670691i
$554$	−8.32624	+	6.04937i	−0.353748	+	0.257013i
$555$		0			0
$556$		0			0
$557$	24.8885	−	18.0826i	1.05456	−	0.766184i	0.0814869	−	0.996674i	$-0.474033\pi$
$557$	24.8885	−	18.0826i	1.05456	−	0.766184i	0.973075	+	0.230491i	$0.0740331\pi$
$558$		0			0
$559$	−11.5623	−	35.5851i	−0.489033	−	1.50509i
$560$	−2.47214			−0.104467
$561$		0			0
$562$	−4.90983			−0.207109
$563$	−0.809017	−	2.48990i	−0.0340960	−	0.104937i	0.932560	−	0.361015i	$-0.117570\pi$
$563$	−0.809017	−	2.48990i	−0.0340960	−	0.104937i	−0.966656	+	0.256078i	$0.917570\pi$
$564$		0			0
$565$	4.85410	−	3.52671i	0.204214	−	0.148370i
$566$	−7.41641	+	22.8254i	−0.311735	+	0.959421i
$567$		0			0
$568$	0.618034	−	0.449028i	0.0259321	−	0.0188408i
$569$	−10.6910	−	7.76745i	−0.448189	−	0.325629i	0.340691	−	0.940175i	$-0.389339\pi$
$569$	−10.6910	−	7.76745i	−0.448189	−	0.325629i	−0.788880	+	0.614547i	$0.789339\pi$
$570$		0			0
$571$	6.47214			0.270850			0.135425	−	0.990788i	$-0.456760\pi$
$571$	6.47214			0.270850			0.135425	+	0.990788i	$0.456760\pi$
$572$	8.23607	−	6.88191i	0.344367	−	0.287747i
$573$		0			0
$574$	−2.09017	−	6.43288i	−0.0872420	−	0.268503i
$575$	9.09017	+	6.60440i	0.379086	+	0.275422i
$576$		0			0
$577$	5.50000	−	16.9273i	0.228968	−	0.704691i	−0.768897	−	0.639373i	$-0.779194\pi$
$577$	5.50000	−	16.9273i	0.228968	−	0.704691i	0.997865	−	0.0653178i	$-0.0208061\pi$
$578$	4.44427	−	13.6781i	0.184857	−	0.568932i
$579$		0			0
$580$	−4.47214	−	3.24920i	−0.185695	−	0.134916i
$581$	−3.90983	−	12.0332i	−0.162207	−	0.499222i
$582$		0			0
$583$	34.6525	−	2.35114i	1.43516	−	0.0973743i
$584$	−12.6180			−0.522138
$585$		0			0
$586$	−13.2361	−	9.61657i	−0.546777	−	0.397257i
$587$	23.3435	−	16.9600i	0.963488	−	0.700015i	0.00952954	−	0.999955i	$-0.496967\pi$
$587$	23.3435	−	16.9600i	0.963488	−	0.700015i	0.953958	+	0.299940i	$0.0969666\pi$
$588$		0			0
$589$	0.527864	−	1.62460i	0.0217503	−	0.0669404i
$590$	6.38197	−	4.63677i	0.262741	−	0.190893i
$591$		0			0
$592$	3.00000	+	9.23305i	0.123299	+	0.379476i
$593$	−31.6869			−1.30123			−0.650613	−	0.759410i	$-0.725488\pi$
$593$	−31.6869			−1.30123			−0.650613	+	0.759410i	$0.725488\pi$
$594$		0			0
$595$	4.00000			0.163984
$596$	−5.00000	−	15.3884i	−0.204808	−	0.630334i
$597$		0			0
$598$	−8.47214	+	6.15537i	−0.346451	+	0.251712i
$599$	−4.14590	+	12.7598i	−0.169397	+	0.521350i	−0.999333	−	0.0365080i	$-0.988377\pi$
$599$	−4.14590	+	12.7598i	−0.169397	+	0.521350i	0.829937	+	0.557858i	$0.188377\pi$
$600$		0			0
$601$	27.3885	−	19.8989i	1.11720	−	0.811695i	0.133419	−	0.991060i	$-0.457404\pi$
$601$	27.3885	−	19.8989i	1.11720	−	0.811695i	0.983783	+	0.179365i	$0.0574043\pi$
$602$	−18.7082	−	13.5923i	−0.762489	−	0.553981i
$603$		0			0
$604$	−8.00000			−0.325515
$605$	−9.81966	+	9.40456i	−0.399226	+	0.382350i
$606$		0			0
$607$	−5.29180	−	16.2865i	−0.214787	−	0.661048i	−0.999169	−	0.0407685i	$-0.987019\pi$
$607$	−5.29180	−	16.2865i	−0.214787	−	0.661048i	0.784381	−	0.620279i	$-0.212981\pi$
$608$	0.690983	+	0.502029i	0.0280231	+	0.0203599i
$609$		0			0
$610$	−2.47214	+	7.60845i	−0.100094	+	0.308057i
$611$	2.47214	−	7.60845i	0.100012	−	0.307805i
$612$		0			0
$613$	−18.0344	−	13.1028i	−0.728404	−	0.529217i	0.160654	−	0.987011i	$-0.448640\pi$
$613$	−18.0344	−	13.1028i	−0.728404	−	0.529217i	−0.889058	+	0.457794i	$0.848640\pi$
$614$	−0.989357	−	3.04493i	−0.0399272	−	0.122883i
$615$		0			0
$616$	1.61803	−	6.43288i	0.0651924	−	0.259188i
$617$	32.4508			1.30642			0.653211	−	0.757176i	$-0.273421\pi$
$617$	32.4508			1.30642			0.653211	+	0.757176i	$0.273421\pi$
$618$		0			0
$619$	−24.1074	−	17.5150i	−0.968958	−	0.703989i	−0.0137440	−	0.999906i	$-0.504375\pi$
$619$	−24.1074	−	17.5150i	−0.968958	−	0.703989i	−0.955214	+	0.295916i	$0.904375\pi$
$620$	−2.00000	+	1.45309i	−0.0803219	+	0.0583573i
$621$		0			0
$622$	−9.90983	+	30.4993i	−0.397348	+	1.22291i
$623$	−5.00000	+	3.63271i	−0.200321	+	0.145542i
$624$		0			0
$625$	1.36475	+	4.20025i	0.0545898	+	0.168010i
$626$	11.3262			0.452688
$627$		0			0
$628$	−3.70820			−0.147973
$629$	−4.85410	−	14.9394i	−0.193546	−	0.595672i
$630$		0			0
$631$	−8.32624	+	6.04937i	−0.331462	+	0.240821i	−0.741051	−	0.671449i	$-0.765672\pi$
$631$	−8.32624	+	6.04937i	−0.331462	+	0.240821i	0.409589	+	0.912270i	$0.365672\pi$
$632$	4.14590	−	12.7598i	0.164915	−	0.507556i
$633$		0			0
$634$	−7.85410	+	5.70634i	−0.311926	+	0.226628i
$635$	−6.94427	−	5.04531i	−0.275575	−	0.200217i
$636$		0			0
$637$	9.70820			0.384653
$638$	11.3820	−	9.51057i	0.450616	−	0.376527i
$639$		0			0
$640$	−0.381966	−	1.17557i	−0.0150985	−	0.0464685i
$641$	26.1525	+	19.0009i	1.03296	+	0.750490i	0.968899	−	0.247456i	$-0.0795946\pi$
$641$	26.1525	+	19.0009i	1.03296	+	0.750490i	0.0640616	+	0.997946i	$0.479595\pi$
$642$		0			0
$643$	−2.15654	+	6.63715i	−0.0850457	+	0.261744i	−0.984532	−	0.175205i	$-0.943941\pi$
$643$	−2.15654	+	6.63715i	−0.0850457	+	0.261744i	0.899486	+	0.436949i	$0.143941\pi$
$644$	−2.00000	+	6.15537i	−0.0788110	+	0.242555i
$645$		0			0
$646$	−1.11803	−	0.812299i	−0.0439885	−	0.0319595i
$647$	−14.5066	−	44.6467i	−0.570312	−	1.75524i	−0.651613	−	0.758552i	$-0.725907\pi$
$647$	−14.5066	−	44.6467i	−0.570312	−	1.75524i	0.0813006	−	0.996690i	$-0.474093\pi$
$648$		0			0
$649$	7.88854	+	19.6417i	0.309652	+	0.771003i
$650$	−11.2361			−0.440715
$651$		0			0
$652$	−9.78115	−	7.10642i	−0.383060	−	0.278309i
$653$	−37.7426	+	27.4216i	−1.47698	+	1.07309i	−0.498471	+	0.866906i	$0.666105\pi$
$653$	−37.7426	+	27.4216i	−1.47698	+	1.07309i	−0.978513	+	0.206185i	$0.933895\pi$
$654$		0			0
$655$	6.79837	−	20.9232i	0.265634	−	0.817539i
$656$	2.73607	−	1.98787i	0.106826	−	0.0776133i
$657$		0			0
$658$	−1.52786	−	4.70228i	−0.0595623	−	0.183314i
$659$	28.0902			1.09424			0.547119	−	0.837055i	$-0.315725\pi$
$659$	28.0902			1.09424			0.547119	+	0.837055i	$0.315725\pi$
$660$		0			0
$661$	−12.4721			−0.485110			−0.242555	−	0.970138i	$-0.577985\pi$
$661$	−12.4721			−0.485110			−0.242555	+	0.970138i	$0.577985\pi$
$662$	8.42705	+	25.9358i	0.327527	+	1.00802i
$663$		0			0
$664$	5.11803	−	3.71847i	0.198618	−	0.144305i
$665$	−0.652476	+	2.00811i	−0.0253019	+	0.0778713i
$666$		0			0
$667$	−11.7082	+	8.50651i	−0.453343	+	0.329373i
$668$	−15.5623	−	11.3067i	−0.602124	−	0.437468i
$669$		0			0
$670$	0.111456			0.00430593
$671$	−18.1803	−	11.4127i	−0.701844	−	0.440582i
$672$		0			0
$673$	0.972136	+	2.99193i	0.0374731	+	0.115330i	0.968043	−	0.250783i	$-0.0806882\pi$
$673$	0.972136	+	2.99193i	0.0374731	+	0.115330i	−0.930570	+	0.366114i	$0.880688\pi$
$674$	−1.78115	−	1.29408i	−0.0686074	−	0.0498462i
$675$		0			0
$676$	−0.781153	+	2.40414i	−0.0300443	+	0.0924670i
$677$	−9.38197	+	28.8747i	−0.360578	+	1.10975i	0.592126	+	0.805846i	$0.298289\pi$
$677$	−9.38197	+	28.8747i	−0.360578	+	1.10975i	−0.952704	+	0.303900i	$0.901711\pi$
$678$		0			0
$679$	22.4164	+	16.2865i	0.860263	+	0.625017i
$680$	0.618034	+	1.90211i	0.0237005	+	0.0729427i
$681$		0			0
$682$	−2.47214	−	6.15537i	−0.0946630	−	0.235701i
$683$	−9.52786			−0.364574			−0.182287	−	0.983245i	$-0.558350\pi$
$683$	−9.52786			−0.364574			−0.182287	+	0.983245i	$0.558350\pi$
$684$		0			0
$685$	4.90983	+	3.56720i	0.187595	+	0.136296i
$686$	16.1803	−	11.7557i	0.617768	−	0.448835i
$687$		0			0
$688$	3.57295	−	10.9964i	0.136217	−	0.419234i
$689$	27.4164	−	19.9192i	1.04448	−	0.758861i
$690$		0			0
$691$	7.79180	+	23.9807i	0.296414	+	0.912268i	0.982743	+	0.184977i	$0.0592210\pi$
$691$	7.79180	+	23.9807i	0.296414	+	0.912268i	−0.686329	+	0.727291i	$0.740779\pi$
$692$	13.8885			0.527963
$693$		0			0
$694$	14.3820			0.545932
$695$		0			0
$696$		0			0
$697$	−4.42705	+	3.21644i	−0.167687	+	0.121831i
$698$	−9.14590	+	28.1482i	−0.346177	+	1.06542i
$699$		0			0
$700$	−5.61803	+	4.08174i	−0.212342	+	0.154275i
$701$	31.4164	+	22.8254i	1.18658	+	0.862102i	0.992899	−	0.118962i	$-0.0379568\pi$
$701$	31.4164	+	22.8254i	1.18658	+	0.862102i	0.193683	+	0.981064i	$0.437957\pi$
$702$		0			0
$703$	8.29180			0.312731
$704$	3.30902	−	0.224514i	0.124713	−	0.00846169i
$705$		0			0
$706$	9.38854	+	28.8950i	0.353343	+	1.08748i
$707$	−29.4164	−	21.3723i	−1.10632	−	0.803787i
$708$		0			0
$709$	4.79837	−	14.7679i	0.180207	−	0.554619i	−0.819626	−	0.572899i	$-0.805819\pi$
$709$	4.79837	−	14.7679i	0.180207	−	0.554619i	0.999833	+	0.0182794i	$0.00581885\pi$
$710$	−0.291796	+	0.898056i	−0.0109509	+	0.0337034i
$711$		0			0
$712$	−2.50000	−	1.81636i	−0.0936915	−	0.0680708i
$713$	2.00000	+	6.15537i	0.0749006	+	0.230520i
$714$		0			0
$715$	−3.23607	+	12.8658i	−0.121022	+	0.481152i
$716$	6.38197			0.238505
$717$		0			0
$718$	28.4164	+	20.6457i	1.06049	+	0.770492i
$719$	−21.7082	+	15.7719i	−0.809579	+	0.588194i	−0.913709	−	0.406370i	$-0.866794\pi$
$719$	−21.7082	+	15.7719i	−0.809579	+	0.588194i	0.104129	+	0.994564i	$0.466794\pi$
$720$		0			0
$721$	−1.41641	+	4.35926i	−0.0527498	+	0.162347i
$722$	−14.7812	+	10.7391i	−0.550098	+	0.399669i
$723$		0			0
$724$	5.61803	+	17.2905i	0.208793	+	0.642598i
$725$	−15.5279			−0.576690
$726$		0			0
$727$	43.1246			1.59940			0.799702	−	0.600398i	$-0.204991\pi$
$727$	43.1246			1.59940			0.799702	+	0.600398i	$0.204991\pi$
$728$	−2.00000	−	6.15537i	−0.0741249	−	0.228133i
$729$		0			0
$730$	12.6180	−	9.16754i	0.467014	−	0.339306i
$731$	−5.78115	+	17.7926i	−0.213824	+	0.658082i
$732$		0			0
$733$	−14.0902	+	10.2371i	−0.520432	+	0.378116i	−0.816767	−	0.576968i	$-0.804236\pi$
$733$	−14.0902	+	10.2371i	−0.520432	+	0.378116i	0.296334	+	0.955084i	$0.404236\pi$
$734$	5.09017	+	3.69822i	0.187882	+	0.136504i
$735$		0			0
$736$	−3.23607			−0.119283
$737$	−0.0729490	+	0.290026i	−0.00268711	+	0.0106833i
$738$		0			0
$739$	−5.38854	−	16.5842i	−0.198221	−	0.610061i	−0.999924	−	0.0123384i	$-0.996072\pi$
$739$	−5.38854	−	16.5842i	−0.198221	−	0.610061i	0.801703	−	0.597722i	$-0.203928\pi$
$740$	−9.70820	−	7.05342i	−0.356881	−	0.259289i
$741$		0			0
$742$	6.47214	−	19.9192i	0.237600	−	0.731256i
$743$	4.09017	−	12.5882i	0.150054	−	0.461818i	−0.847572	−	0.530680i	$-0.821937\pi$
$743$	4.09017	−	12.5882i	0.150054	−	0.461818i	0.997626	+	0.0688617i	$0.0219367\pi$
$744$		0			0
$745$	16.1803	+	11.7557i	0.592802	+	0.430696i
$746$	5.47214	+	16.8415i	0.200349	+	0.616611i
$747$		0			0
$748$	−5.35410	+	0.363271i	−0.195765	+	0.0132825i
$749$	−15.7082			−0.573965
$750$		0			0
$751$	−30.5623	−	22.2048i	−1.11523	−	0.810265i	−0.131754	−	0.991282i	$-0.542061\pi$
$751$	−30.5623	−	22.2048i	−1.11523	−	0.810265i	−0.983480	+	0.181017i	$0.942061\pi$
$752$	2.00000	−	1.45309i	0.0729325	−	0.0529886i
$753$		0			0
$754$	4.47214	−	13.7638i	0.162866	−	0.501249i
$755$	8.00000	−	5.81234i	0.291150	−	0.211533i
$756$		0			0
$757$	8.85410	+	27.2501i	0.321808	+	0.990423i	0.972861	+	0.231390i	$0.0743275\pi$
$757$	8.85410	+	27.2501i	0.321808	+	0.990423i	−0.651053	+	0.759032i	$0.725673\pi$
$758$	19.2705			0.699936
$759$		0			0
$760$	−1.05573			−0.0382953
$761$	14.4443	+	44.4549i	0.523604	+	1.61149i	0.767059	+	0.641576i	$0.221719\pi$
$761$	14.4443	+	44.4549i	0.523604	+	1.61149i	−0.243455	+	0.969912i	$0.578281\pi$
$762$		0			0
$763$	1.70820	−	1.24108i	0.0618411	−	0.0449302i
$764$	−2.85410	+	8.78402i	−0.103258	+	0.317795i
$765$		0			0
$766$	−13.2361	+	9.61657i	−0.478239	+	0.347461i
$767$	16.7082	+	12.1392i	0.603298	+	0.438322i
$768$		0			0
$769$	−13.4164			−0.483808			−0.241904	−	0.970300i	$-0.577772\pi$
$769$	−13.4164			−0.483808			−0.241904	+	0.970300i	$0.577772\pi$
$770$	3.05573	+	7.60845i	0.110121	+	0.274190i
$771$		0			0
$772$	−2.90983	−	8.95554i	−0.104727	−	0.322317i
$773$	25.7984	+	18.7436i	0.927903	+	0.674161i	0.945478	−	0.325685i	$-0.105595\pi$
$773$	25.7984	+	18.7436i	0.927903	+	0.674161i	−0.0175755	+	0.999846i	$0.505595\pi$
$774$		0			0
$775$	−2.14590	+	6.60440i	−0.0770829	+	0.237237i
$776$	−4.28115	+	13.1760i	−0.153684	+	0.472992i
$777$		0			0
$778$	−16.7082	−	12.1392i	−0.599018	−	0.435212i
$779$	−0.892609	−	2.74717i	−0.0319810	−	0.0984275i
$780$		0			0
$781$	−2.14590	−	1.34708i	−0.0767863	−	0.0482025i
$782$	5.23607			0.187241
$783$		0			0
$784$	2.42705	+	1.76336i	0.0866804	+	0.0629770i
$785$	3.70820	−	2.69417i	0.132351	−	0.0961590i
$786$		0			0
$787$	−7.79180	+	23.9807i	−0.277748	+	0.854819i	0.710732	+	0.703463i	$0.248364\pi$
$787$	−7.79180	+	23.9807i	−0.277748	+	0.854819i	−0.988479	+	0.151356i	$0.951636\pi$
$788$	−2.47214	+	1.79611i	−0.0880662	+	0.0639838i
$789$		0			0
$790$	5.12461	+	15.7719i	0.182326	+	0.561140i
$791$	9.70820			0.345184
$792$		0			0
$793$	−20.9443			−0.743753
$794$	−7.14590	−	21.9928i	−0.253598	−	0.780496i
$795$		0			0
$796$	0.854102	−	0.620541i	0.0302728	−	0.0219945i
$797$	9.03444	−	27.8052i	0.320016	−	0.984909i	−0.653624	−	0.756820i	$-0.726752\pi$
$797$	9.03444	−	27.8052i	0.320016	−	0.984909i	0.973640	−	0.228089i	$-0.0732479\pi$
$798$		0			0
$799$	−3.23607	+	2.35114i	−0.114484	+	0.0831774i
$800$	−2.80902	−	2.04087i	−0.0993137	−	0.0721557i
$801$		0			0
$802$	6.79837			0.240059
$803$	15.5967	+	38.8343i	0.550397	+	1.37043i
$804$		0			0
$805$	−2.47214	−	7.60845i	−0.0871313	−	0.268163i
$806$	−5.23607	−	3.80423i	−0.184433	−	0.133998i
$807$		0			0
$808$	5.61803	−	17.2905i	0.197642	−	0.608279i
$809$	−8.68034	+	26.7153i	−0.305184	+	0.939261i	0.674424	+	0.738344i	$0.264392\pi$
$809$	−8.68034	+	26.7153i	−0.305184	+	0.939261i	−0.979608	+	0.200917i	$0.935608\pi$
$810$		0			0
$811$	−8.59017	−	6.24112i	−0.301642	−	0.219155i	0.426660	−	0.904412i	$-0.359690\pi$
$811$	−8.59017	−	6.24112i	−0.301642	−	0.219155i	−0.728302	+	0.685257i	$0.759690\pi$
$812$	−2.76393	−	8.50651i	−0.0969950	−	0.298520i
$813$		0			0
$814$	24.7082	−	20.6457i	0.866022	−	0.723632i
$815$	14.9443			0.523475
$816$		0			0
$817$	−7.98936	−	5.80461i	−0.279512	−	0.203078i
$818$	10.8541	−	7.88597i	0.379505	−	0.275726i
$819$		0			0
$820$	−1.29180	+	3.97574i	−0.0451115	+	0.138839i
$821$	−29.5623	+	21.4783i	−1.03173	+	0.749597i	−0.968655	−	0.248412i	$-0.920091\pi$
$821$	−29.5623	+	21.4783i	−1.03173	+	0.749597i	−0.0630771	+	0.998009i	$0.520091\pi$
$822$		0			0
$823$	−7.90983	−	24.3440i	−0.275719	−	0.848577i	−0.989028	−	0.147727i	$-0.952804\pi$
$823$	−7.90983	−	24.3440i	−0.275719	−	0.848577i	0.713309	−	0.700850i	$-0.247196\pi$
$824$	−2.29180			−0.0798385
$825$		0			0
$826$	12.7639			0.444114
$827$	−12.8607	−	39.5811i	−0.447210	−	1.37637i	−0.880042	−	0.474895i	$-0.842486\pi$
$827$	−12.8607	−	39.5811i	−0.447210	−	1.37637i	0.432833	−	0.901474i	$-0.357514\pi$
$828$		0			0
$829$	−39.5967	+	28.7687i	−1.37525	+	0.999179i	−0.377946	+	0.925828i	$0.623369\pi$
$829$	−39.5967	+	28.7687i	−1.37525	+	0.999179i	−0.997306	+	0.0733512i	$0.976631\pi$
$830$	−2.41641	+	7.43694i	−0.0838747	+	0.258140i
$831$		0			0
$832$	2.61803	−	1.90211i	0.0907640	−	0.0659439i
$833$	−3.92705	−	2.85317i	−0.136064	−	0.0988565i
$834$		0			0
$835$	23.7771			0.822840
$836$	0.690983	−	2.74717i	0.0238981	−	0.0950128i
$837$		0			0
$838$	−1.28115	−	3.94298i	−0.0442567	−	0.136208i
$839$	38.7426	+	28.1482i	1.33754	+	0.971783i	0.999530	+	0.0306421i	$0.00975521\pi$
$839$	38.7426	+	28.1482i	1.33754	+	0.971783i	0.338014	+	0.941141i	$0.390245\pi$
$840$		0			0
$841$	−2.78115	+	8.55951i	−0.0959018	+	0.295155i
$842$	1.41641	−	4.35926i	0.0488126	−	0.150230i
$843$		0			0
$844$	−4.11803	−	2.99193i	−0.141749	−	0.102986i
$845$	−0.965558	−	2.97168i	−0.0332162	−	0.102229i
$846$		0			0
$847$	−21.7984	+	2.97168i	−0.749001	+	0.102108i
$848$	10.4721			0.359615
$849$		0			0
$850$	4.54508	+	3.30220i	0.155895	+	0.113264i
$851$	−25.4164	+	18.4661i	−0.871263	+	0.633010i
$852$		0			0
$853$	−6.65248	+	20.4742i	−0.227776	+	0.701024i	0.770221	+	0.637777i	$0.220146\pi$
$853$	−6.65248	+	20.4742i	−0.227776	+	0.701024i	−0.997998	+	0.0632472i	$0.979854\pi$
$854$	−10.4721	+	7.60845i	−0.358349	+	0.260356i
$855$		0			0
$856$	−2.42705	−	7.46969i	−0.0829549	−	0.255309i
$857$	−31.7426			−1.08431			−0.542154	−	0.840279i	$-0.682391\pi$
$857$	−31.7426			−1.08431			−0.542154	+	0.840279i	$0.682391\pi$
$858$		0			0
$859$	8.49342			0.289792			0.144896	−	0.989447i	$-0.453715\pi$
$859$	8.49342			0.289792			0.144896	+	0.989447i	$0.453715\pi$
$860$	4.41641	+	13.5923i	0.150598	+	0.463494i
$861$		0			0
$862$	−0.763932	+	0.555029i	−0.0260196	+	0.0189044i
$863$	8.88854	−	27.3561i	0.302570	−	0.931213i	−0.678003	−	0.735059i	$-0.737155\pi$
$863$	8.88854	−	27.3561i	0.302570	−	0.931213i	0.980573	−	0.196155i	$-0.0628454\pi$
$864$		0			0
$865$	−13.8885	+	10.0906i	−0.472225	+	0.343091i
$866$	−11.9271	−	8.66551i	−0.405298	−	0.294466i
$867$		0			0
$868$	−4.00000			−0.135769
$869$	−44.3951	+	3.01217i	−1.50600	+	0.102181i
$870$		0			0
$871$	0.0901699	+	0.277515i	0.00305529	+	0.00940322i
$872$	0.854102	+	0.620541i	0.0289235	+	0.0210142i
$873$		0			0
$874$	−0.854102	+	2.62866i	−0.0288904	+	0.0889156i
$875$	6.47214	−	19.9192i	0.218798	−	0.673391i
$876$		0			0
$877$	4.70820	+	3.42071i	0.158985	+	0.115509i	0.664433	−	0.747348i	$-0.268673\pi$
$877$	4.70820	+	3.42071i	0.158985	+	0.115509i	−0.505449	+	0.862857i	$0.668673\pi$
$878$	10.3262	+	31.7809i	0.348494	+	1.07255i
$879$		0			0
$880$	−3.14590	+	2.62866i	−0.106048	+	0.0886120i
$881$	−45.3394			−1.52752			−0.763761	−	0.645499i	$-0.776650\pi$
$881$	−45.3394			−1.52752			−0.763761	+	0.645499i	$0.776650\pi$
$882$		0			0
$883$	19.0623	+	13.8496i	0.641498	+	0.466075i	0.860364	−	0.509679i	$-0.170236\pi$
$883$	19.0623	+	13.8496i	0.641498	+	0.466075i	−0.218867	+	0.975755i	$0.570236\pi$
$884$	−4.23607	+	3.07768i	−0.142474	+	0.103514i
$885$		0			0
$886$	3.57295	−	10.9964i	0.120036	−	0.369431i
$887$	27.3262	−	19.8537i	0.917525	−	0.666621i	−0.0253815	−	0.999678i	$-0.508080\pi$
$887$	27.3262	−	19.8537i	0.917525	−	0.666621i	0.942907	+	0.333057i	$0.108080\pi$
$888$		0			0
$889$	−4.29180	−	13.2088i	−0.143942	−	0.443009i
$890$	3.81966			0.128035
$891$		0			0
$892$	12.2918			0.411560
$893$	−0.652476	−	2.00811i	−0.0218343	−	0.0671990i
$894$		0			0
$895$	−6.38197	+	4.63677i	−0.213326	+	0.154990i
$896$	0.618034	−	1.90211i	0.0206471	−	0.0635451i
$897$		0			0
$898$	19.6353	−	14.2658i	0.655237	−	0.476058i
$899$	−7.23607	−	5.25731i	−0.241336	−	0.175341i
$900$		0			0
$901$	−16.9443			−0.564496
$902$	−9.50000	−	5.96361i	−0.316315	−	0.198566i
$903$		0			0
$904$	1.50000	+	4.61653i	0.0498893	+	0.153543i
$905$	−18.1803	−	13.2088i	−0.604335	−	0.439075i
$906$		0			0
$907$	9.44427	−	29.0665i	0.313592	−	0.965137i	−0.662738	−	0.748851i	$-0.730606\pi$
$907$	9.44427	−	29.0665i	0.313592	−	0.965137i	0.976330	−	0.216286i	$-0.0693942\pi$
$908$	7.26393	−	22.3561i	0.241062	−	0.741913i
$909$		0			0
$910$	6.47214	+	4.70228i	0.214549	+	0.155879i
$911$	1.29180	+	3.97574i	0.0427991	+	0.131722i	0.970173	−	0.242414i	$-0.0779393\pi$
$911$	1.29180	+	3.97574i	0.0427991	+	0.131722i	−0.927374	+	0.374136i	$0.877939\pi$
$912$		0			0
$913$	−17.7705	−	11.1554i	−0.588118	−	0.369190i
$914$	29.5623			0.977834
$915$		0			0
$916$	9.47214	+	6.88191i	0.312968	+	0.227385i
$917$	28.7984	−	20.9232i	0.951006	−	0.690946i
$918$		0			0
$919$	5.12461	−	15.7719i	0.169045	−	0.520268i	−0.830266	−	0.557367i	$-0.811812\pi$
$919$	5.12461	−	15.7719i	0.169045	−	0.520268i	0.999312	+	0.0370989i	$0.0118117\pi$
$920$	3.23607	−	2.35114i	0.106690	−	0.0775148i
$921$		0			0
$922$	10.0902	+	31.0543i	0.332302	+	1.02272i
$923$	−2.47214			−0.0813713
$924$		0			0
$925$	−33.7082			−1.10832
$926$	−2.29180	−	7.05342i	−0.0753131	−	0.231790i
$927$		0			0
$928$	3.61803	−	2.62866i	0.118768	−	0.0862898i
$929$	18.1525	−	55.8676i	0.595563	−	1.83296i	0.0436620	−	0.999046i	$-0.486098\pi$
$929$	18.1525	−	55.8676i	0.595563	−	1.83296i	0.551901	−	0.833909i	$-0.313902\pi$
$930$		0			0
$931$	2.07295	−	1.50609i	0.0679382	−	0.0493600i
$932$	−5.97214	−	4.33901i	−0.195624	−	0.142129i
$933$		0			0
$934$	29.3050			0.958887
$935$	5.09017	−	4.25325i	0.166466	−	0.139096i
$936$		0			0
$937$	−9.62461	−	29.6215i	−0.314422	−	0.967693i	−0.975992	−	0.217808i	$-0.930109\pi$
$937$	−9.62461	−	29.6215i	−0.314422	−	0.967693i	0.661569	−	0.749884i	$-0.269891\pi$
$938$	0.145898	+	0.106001i	0.00476374	+	0.00346106i
$939$		0			0
$940$	−0.944272	+	2.90617i	−0.0307988	+	0.0947888i
$941$	−7.97871	+	24.5560i	−0.260099	+	0.800501i	0.732684	+	0.680570i	$0.238268\pi$
$941$	−7.97871	+	24.5560i	−0.260099	+	0.800501i	−0.992782	+	0.119932i	$0.961732\pi$
$942$		0			0
$943$	8.85410	+	6.43288i	0.288329	+	0.209483i
$944$	1.97214	+	6.06961i	0.0641876	+	0.197549i
$945$		0			0
$946$	−38.2599	+	2.59590i	−1.24394	+	0.0844000i
$947$	−21.2148			−0.689388			−0.344694	−	0.938715i	$-0.612017\pi$
$947$	−21.2148			−0.689388			−0.344694	+	0.938715i	$0.612017\pi$
$948$		0			0
$949$	33.0344	+	24.0009i	1.07234	+	0.779103i
$950$	−2.39919	+	1.74311i	−0.0778399	+	0.0565540i
$951$		0			0
$952$	−1.00000	+	3.07768i	−0.0324102	+	0.0997483i
$953$	3.50000	−	2.54290i	0.113376	−	0.0823726i	−0.529652	−	0.848215i	$-0.677678\pi$
$953$	3.50000	−	2.54290i	0.113376	−	0.0823726i	0.643029	+	0.765842i	$0.277678\pi$
$954$		0			0
$955$	−3.52786	−	10.8576i	−0.114159	−	0.351345i
$956$	8.29180			0.268176
$957$		0			0
$958$	−25.5279			−0.824768
$959$	3.03444	+	9.33905i	0.0979872	+	0.301574i
$960$		0			0
$961$	21.8435	−	15.8702i	0.704628	−	0.511942i
$962$	9.70820	−	29.8788i	0.313005	−	0.963331i
$963$		0			0
$964$	−0.0729490	+	0.0530006i	−0.00234953	+	0.00170703i
$965$	9.41641	+	6.84142i	0.303125	+	0.220233i
$966$		0			0
$967$	38.0000			1.22200			0.610999	−	0.791632i	$-0.290768\pi$
$967$	38.0000			1.22200			0.610999	+	0.791632i	$0.290768\pi$
$968$	−4.78115	−	9.90659i	−0.153672	−	0.318410i
$969$		0			0
$970$	−5.29180	−	16.2865i	−0.169909	−	0.522927i
$971$	−37.1246	−	26.9726i	−1.19139	−	0.865592i	−0.197975	−	0.980207i	$-0.563437\pi$
$971$	−37.1246	−	26.9726i	−1.19139	−	0.865592i	−0.993410	+	0.114615i	$0.963437\pi$
$972$		0			0
$973$		0			0
$974$	10.0902	−	31.0543i	0.323310	−	0.995046i
$975$		0			0
$976$	−5.23607	−	3.80423i	−0.167602	−	0.121770i
$977$	−5.96556	−	18.3601i	−0.190855	−	0.587392i	0.809145	−	0.587609i	$-0.199931\pi$
$977$	−5.96556	−	18.3601i	−0.190855	−	0.587392i	−1.00000		0.000217575i	$0.999931\pi$
$978$		0			0
$979$	−2.50000	+	9.93935i	−0.0799003	+	0.317663i
$980$	−3.70820			−0.118454
$981$		0			0
$982$	−13.0623	−	9.49032i	−0.416835	−	0.302848i
$983$	−4.85410	+	3.52671i	−0.154822	+	0.112485i	−0.662499	−	0.749063i	$-0.730504\pi$
$983$	−4.85410	+	3.52671i	−0.154822	+	0.112485i	0.507677	+	0.861547i	$0.330504\pi$
$984$		0			0
$985$	1.16718	−	3.59222i	0.0371896	−	0.114458i
$986$	−5.85410	+	4.25325i	−0.186433	+	0.135451i
$987$		0			0
$988$	−0.854102	−	2.62866i	−0.0271726	−	0.0836287i
$989$	37.4164			1.18977
$990$		0			0
$991$	−36.5410			−1.16076			−0.580382	−	0.814344i	$-0.697097\pi$
$991$	−36.5410			−1.16076			−0.580382	+	0.814344i	$0.697097\pi$
$992$	−0.618034	−	1.90211i	−0.0196226	−	0.0603921i
$993$		0			0
$994$	−1.23607	+	0.898056i	−0.0392057	+	0.0284846i
$995$	−0.403252	+	1.24108i	−0.0127840	+	0.0393450i
$996$		0			0
$997$	18.3262	−	13.3148i	0.580398	−	0.421684i	−0.258470	−	0.966019i	$-0.583218\pi$
$997$	18.3262	−	13.3148i	0.580398	−	0.421684i	0.838867	+	0.544336i	$0.183218\pi$
$998$	−19.5344	−	14.1926i	−0.618352	−	0.449259i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	198.2.f.e.181.1		4
3.2	odd	2		22.2.c.a.5.1	✓	4
11.3	even	5		2178.2.a.p.1.2		2
11.8	odd	10		2178.2.a.x.1.2		2
11.9	even	5	inner	198.2.f.e.163.1		4
12.11	even	2		176.2.m.c.49.1		4
15.2	even	4		550.2.ba.c.49.1		8
15.8	even	4		550.2.ba.c.49.2		8
15.14	odd	2		550.2.h.h.401.1		4
24.5	odd	2		704.2.m.h.577.1		4
24.11	even	2		704.2.m.a.577.1		4
33.2	even	10		242.2.c.c.9.1		4
33.5	odd	10		242.2.c.a.81.1		4
33.8	even	10		242.2.a.d.1.2		2
33.14	odd	10		242.2.a.f.1.2		2
33.17	even	10		242.2.c.d.81.1		4
33.20	odd	10		22.2.c.a.9.1	yes	4
33.26	odd	10		242.2.c.a.3.1		4
33.29	even	10		242.2.c.d.3.1		4
33.32	even	2		242.2.c.c.27.1		4
132.47	even	10		1936.2.a.o.1.1		2
132.107	odd	10		1936.2.a.n.1.1		2
132.119	even	10		176.2.m.c.97.1		4
165.14	odd	10		6050.2.a.bs.1.1		2
165.53	even	20		550.2.ba.c.449.1		8
165.74	even	10		6050.2.a.ci.1.1		2
165.119	odd	10		550.2.h.h.251.1		4
165.152	even	20		550.2.ba.c.449.2		8
264.53	odd	10		704.2.m.h.449.1		4
264.107	odd	10		7744.2.a.cy.1.2		2
264.173	even	10		7744.2.a.bn.1.1		2
264.179	even	10		7744.2.a.cz.1.2		2
264.245	odd	10		7744.2.a.bm.1.1		2
264.251	even	10		704.2.m.a.449.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.2.c.a.5.1	✓	4	3.2	odd	2
22.2.c.a.9.1	yes	4	33.20	odd	10
176.2.m.c.49.1		4	12.11	even	2
176.2.m.c.97.1		4	132.119	even	10
198.2.f.e.163.1		4	11.9	even	5	inner
198.2.f.e.181.1		4	1.1	even	1	trivial
242.2.a.d.1.2		2	33.8	even	10
242.2.a.f.1.2		2	33.14	odd	10
242.2.c.a.3.1		4	33.26	odd	10
242.2.c.a.81.1		4	33.5	odd	10
242.2.c.c.9.1		4	33.2	even	10
242.2.c.c.27.1		4	33.32	even	2
242.2.c.d.3.1		4	33.29	even	10
242.2.c.d.81.1		4	33.17	even	10
550.2.h.h.251.1		4	165.119	odd	10
550.2.h.h.401.1		4	15.14	odd	2
550.2.ba.c.49.1		8	15.2	even	4
550.2.ba.c.49.2		8	15.8	even	4
550.2.ba.c.449.1		8	165.53	even	20
550.2.ba.c.449.2		8	165.152	even	20
704.2.m.a.449.1		4	264.251	even	10
704.2.m.a.577.1		4	24.11	even	2
704.2.m.h.449.1		4	264.53	odd	10
704.2.m.h.577.1		4	24.5	odd	2
1936.2.a.n.1.1		2	132.107	odd	10
1936.2.a.o.1.1		2	132.47	even	10
2178.2.a.p.1.2		2	11.3	even	5
2178.2.a.x.1.2		2	11.8	odd	10
6050.2.a.bs.1.1		2	165.14	odd	10
6050.2.a.ci.1.1		2	165.74	even	10
7744.2.a.bm.1.1		2	264.245	odd	10
7744.2.a.bn.1.1		2	264.173	even	10
7744.2.a.cy.1.2		2	264.107	odd	10
7744.2.a.cz.1.2		2	264.179	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 198 = 2 \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	198.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{4} +(0.381966 - 1.17557i) q^{5} +(1.61803 - 1.17557i) q^{7} +(0.809017 + 0.587785i) q^{8} -1.23607 q^{10} +(0.809017 - 3.21644i) q^{11} +(-1.00000 - 3.07768i) q^{13} +(-1.61803 - 1.17557i) q^{14} +(0.309017 - 0.951057i) q^{16} +(-0.500000 + 1.53884i) q^{17} +(-0.690983 - 0.502029i) q^{19} +(0.381966 + 1.17557i) q^{20} +(-3.30902 + 0.224514i) q^{22} +3.23607 q^{23} +(2.80902 + 2.04087i) q^{25} +(-2.61803 + 1.90211i) q^{26} +(-0.618034 + 1.90211i) q^{28} +(-3.61803 + 2.62866i) q^{29} +(0.618034 + 1.90211i) q^{31} -1.00000 q^{32} +1.61803 q^{34} +(-0.763932 - 2.35114i) q^{35} +(-7.85410 + 5.70634i) q^{37} +(-0.263932 + 0.812299i) q^{38} +(1.00000 - 0.726543i) q^{40} +(2.73607 + 1.98787i) q^{41} +11.5623 q^{43} +(1.23607 + 3.07768i) q^{44} +(-1.00000 - 3.07768i) q^{46} +(2.00000 + 1.45309i) q^{47} +(-0.927051 + 2.85317i) q^{49} +(1.07295 - 3.30220i) q^{50} +(2.61803 + 1.90211i) q^{52} +(3.23607 + 9.95959i) q^{53} +(-3.47214 - 2.17963i) q^{55} +2.00000 q^{56} +(3.61803 + 2.62866i) q^{58} +(-5.16312 + 3.75123i) q^{59} +(2.00000 - 6.15537i) q^{61} +(1.61803 - 1.17557i) q^{62} +(0.309017 + 0.951057i) q^{64} -4.00000 q^{65} -0.0901699 q^{67} +(-0.500000 - 1.53884i) q^{68} +(-2.00000 + 1.45309i) q^{70} +(0.236068 - 0.726543i) q^{71} +(-10.2082 + 7.41669i) q^{73} +(7.85410 + 5.70634i) q^{74} +0.854102 q^{76} +(-2.47214 - 6.15537i) q^{77} +(-4.14590 - 12.7598i) q^{79} +(-1.00000 - 0.726543i) q^{80} +(1.04508 - 3.21644i) q^{82} +(1.95492 - 6.01661i) q^{83} +(1.61803 + 1.17557i) q^{85} +(-3.57295 - 10.9964i) q^{86} +(2.54508 - 2.12663i) q^{88} -3.09017 q^{89} +(-5.23607 - 3.80423i) q^{91} +(-2.61803 + 1.90211i) q^{92} +(0.763932 - 2.35114i) q^{94} +(-0.854102 + 0.620541i) q^{95} +(4.28115 + 13.1760i) q^{97} +3.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - q^{4} + 6 q^{5} + 2 q^{7} + q^{8} + 4 q^{10} + q^{11} - 4 q^{13} - 2 q^{14} - q^{16} - 2 q^{17} - 5 q^{19} + 6 q^{20} - 11 q^{22} + 4 q^{23} + 9 q^{25} - 6 q^{26} + 2 q^{28} - 10 q^{29}+ \cdots + 12 q^{98}+O(q^{100}) \) 4 * q + q^2 - q^4 + 6 * q^5 + 2 * q^7 + q^8 + 4 * q^10 + q^11 - 4 * q^13 - 2 * q^14 - q^16 - 2 * q^17 - 5 * q^19 + 6 * q^20 - 11 * q^22 + 4 * q^23 + 9 * q^25 - 6 * q^26 + 2 * q^28 - 10 * q^29 - 2 * q^31 - 4 * q^32 + 2 * q^34 - 12 * q^35 - 18 * q^37 - 10 * q^38 + 4 * q^40 + 2 * q^41 + 6 * q^43 - 4 * q^44 - 4 * q^46 + 8 * q^47 + 3 * q^49 + 11 * q^50 + 6 * q^52 + 4 * q^53 + 4 * q^55 + 8 * q^56 + 10 * q^58 - 5 * q^59 + 8 * q^61 + 2 * q^62 - q^64 - 16 * q^65 + 22 * q^67 - 2 * q^68 - 8 * q^70 - 8 * q^71 - 14 * q^73 + 18 * q^74 - 10 * q^76 + 8 * q^77 - 30 * q^79 - 4 * q^80 - 7 * q^82 + 19 * q^83 + 2 * q^85 - 21 * q^86 - q^88 + 10 * q^89 - 12 * q^91 - 6 * q^92 + 12 * q^94 + 10 * q^95 - 3 * q^97 + 12 * q^98

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