LMFDB - Embedded newform 513.2.y.c.244.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [513,2,Mod(28,513)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(513, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("513.28"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 513 = 3^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	513.y (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,3,0,9,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$4.09632562369$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			244.1
Root			$-0.766044 - 0.642788i$ of defining polynomial
Character	$\chi$	$=$	513.244
Dual form			513.2.y.c.82.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.03209 - 0.866025i) q^{2} +(-0.0320889 - 0.181985i) q^{4} +(0.152704 - 0.866025i) q^{5} +(0.733956 + 1.27125i) q^{7} +(-1.47178 + 2.54920i) q^{8} +(-0.907604 + 0.761570i) q^{10} +(2.61334 - 4.52644i) q^{11} +(4.58512 + 1.66885i) q^{13} +(0.343426 - 1.94767i) q^{14} +(3.37939 - 1.23000i) q^{16} +(-5.46064 - 4.58202i) q^{17} +(0.819078 - 4.28125i) q^{19} -0.162504 q^{20} +(-6.61721 + 2.40847i) q^{22} +(0.233956 + 1.32683i) q^{23} +(3.97178 + 1.44561i) q^{25} +(-3.28699 - 5.69323i) q^{26} +(0.207796 - 0.174362i) q^{28} +(-2.17365 + 1.82391i) q^{29} +(-4.17752 - 7.23567i) q^{31} +(0.979055 + 0.356347i) q^{32} +(1.66772 + 9.45810i) q^{34} +(1.21301 - 0.441500i) q^{35} -12.0642 q^{37} +(-4.55303 + 3.70929i) q^{38} +(1.98293 + 1.66387i) q^{40} +(4.81180 - 1.75135i) q^{41} +(-0.594922 + 3.37397i) q^{43} +(-0.907604 - 0.330341i) q^{44} +(0.907604 - 1.57202i) q^{46} +(3.05303 - 2.56180i) q^{47} +(2.42262 - 4.19610i) q^{49} +(-2.84730 - 4.93166i) q^{50} +(0.156574 - 0.887975i) q^{52} +(-1.47178 - 8.34689i) q^{53} +(-3.52094 - 2.95442i) q^{55} -4.32089 q^{56} +3.82295 q^{58} +(3.28699 + 2.75811i) q^{59} +(-1.64543 - 9.33170i) q^{61} +(-1.95471 + 11.0857i) q^{62} +(-4.29813 - 7.44459i) q^{64} +(2.14543 - 3.71599i) q^{65} +(-2.03209 + 1.70513i) q^{67} +(-0.658633 + 1.14079i) q^{68} +(-1.63429 - 0.594831i) q^{70} +(-2.19207 + 12.4318i) q^{71} +(-1.09967 + 0.400247i) q^{73} +(12.4513 + 10.4479i) q^{74} +(-0.805407 - 0.0116794i) q^{76} +7.67230 q^{77} +(5.81655 - 2.11705i) q^{79} +(-0.549163 - 3.11446i) q^{80} +(-6.48293 - 2.35959i) q^{82} +(-0.520945 - 0.902302i) q^{83} +(-4.80200 + 4.02936i) q^{85} +(3.53596 - 2.96702i) q^{86} +(7.69253 + 13.3239i) q^{88} +(11.9684 + 4.35613i) q^{89} +(1.24376 + 7.05369i) q^{91} +(0.233956 - 0.0851529i) q^{92} -5.36959 q^{94} +(-3.58260 - 1.36310i) q^{95} +(8.88919 + 7.45891i) q^{97} +(-6.13429 + 2.23270i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} + 9 q^{4} + 3 q^{5} + 9 q^{7} + 6 q^{8} - 9 q^{10} + 9 q^{11} + 6 q^{13} + 24 q^{14} + 9 q^{16} - 24 q^{17} - 12 q^{19} - 6 q^{20} - 9 q^{22} + 6 q^{23} + 9 q^{25} - 12 q^{26} + 42 q^{28}+ \cdots - 27 q^{98}+O(q^{100}) $ 6 * q + 3 * q^2 + 9 * q^4 + 3 * q^5 + 9 * q^7 + 6 * q^8 - 9 * q^10 + 9 * q^11 + 6 * q^13 + 24 * q^14 + 9 * q^16 - 24 * q^17 - 12 * q^19 - 6 * q^20 - 9 * q^22 + 6 * q^23 + 9 * q^25 - 12 * q^26 + 42 * q^28 - 12 * q^29 + 9 * q^32 - 18 * q^34 + 15 * q^35 - 54 * q^37 - 15 * q^38 - 9 * q^40 - 6 * q^41 + 15 * q^43 - 9 * q^44 + 9 * q^46 + 6 * q^47 - 12 * q^49 - 15 * q^50 - 21 * q^52 + 6 * q^53 - 18 * q^55 + 66 * q^56 - 18 * q^58 + 12 * q^59 + 6 * q^61 + 24 * q^62 - 12 * q^64 - 3 * q^65 - 3 * q^67 - 33 * q^68 - 24 * q^71 - 21 * q^73 - 3 * q^74 - 9 * q^76 + 54 * q^77 + 33 * q^79 - 15 * q^80 - 18 * q^82 + 9 * q^85 - 12 * q^86 - 9 * q^88 + 15 * q^89 + 15 * q^91 + 6 * q^92 - 18 * q^94 - 15 * q^95 + 45 * q^97 - 27 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/513\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$1$	$e\left(\frac{2}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.03209	−	0.866025i	−0.729797	−	0.612372i	0.200279	−	0.979739i	$-0.435815\pi$
$2$	−1.03209	−	0.866025i	−0.729797	−	0.612372i	−0.930076	+	0.367366i	$0.880260\pi$
$3$		0			0
$3$		0			0
$4$	−0.0320889	−	0.181985i	−0.0160444	−	0.0909926i
$5$	0.152704	−	0.866025i	0.0682911	−	0.387298i	−0.931435	−	0.363907i	$-0.881443\pi$
$5$	0.152704	−	0.866025i	0.0682911	−	0.387298i	0.999726	−	0.0233912i	$-0.00744633\pi$
$6$		0			0
$7$	0.733956	+	1.27125i	0.277409	+	0.480487i	0.970740	−	0.240133i	$-0.0771909\pi$
$7$	0.733956	+	1.27125i	0.277409	+	0.480487i	−0.693331	+	0.720619i	$0.743858\pi$
$8$	−1.47178	+	2.54920i	−0.520353	+	0.901278i
$9$		0			0
$10$	−0.907604	+	0.761570i	−0.287010	+	0.240830i
$11$	2.61334	−	4.52644i	0.787952	−	1.36477i	−0.139268	−	0.990255i	$-0.544475\pi$
$11$	2.61334	−	4.52644i	0.787952	−	1.36477i	0.927220	−	0.374518i	$-0.122192\pi$
$12$		0			0
$13$	4.58512	+	1.66885i	1.27168	+	0.462855i	0.887673	−	0.460473i	$-0.152320\pi$
$13$	4.58512	+	1.66885i	1.27168	+	0.462855i	0.384011	+	0.923329i	$0.374543\pi$
$14$	0.343426	−	1.94767i	0.0917844	−	0.520535i
$15$		0			0
$16$	3.37939	−	1.23000i	0.844846	−	0.307499i
$17$	−5.46064	−	4.58202i	−1.32440	−	1.11130i	−0.985352	−	0.170533i	$-0.945451\pi$
$17$	−5.46064	−	4.58202i	−1.32440	−	1.11130i	−0.339047	−	0.940769i	$-0.610105\pi$
$18$		0			0
$19$	0.819078	−	4.28125i	0.187909	−	0.982186i
$19$	0.819078	−	4.28125i	0.187909	−	0.982186i
$20$	−0.162504			−0.0363370
$21$		0			0
$22$	−6.61721	+	2.40847i	−1.41079	+	0.513487i
$23$	0.233956	+	1.32683i	0.0487831	+	0.276663i	0.999436	−	0.0335952i	$-0.0106957\pi$
$23$	0.233956	+	1.32683i	0.0487831	+	0.276663i	−0.950652	+	0.310258i	$0.899585\pi$
$24$		0			0
$25$	3.97178	+	1.44561i	0.794356	+	0.289122i
$26$	−3.28699	−	5.69323i	−0.644632	−	1.11653i
$27$		0			0
$28$	0.207796	−	0.174362i	0.0392698	−	0.0329513i
$29$	−2.17365	+	1.82391i	−0.403636	+	0.338691i	−0.821897	−	0.569636i	$-0.807084\pi$
$29$	−2.17365	+	1.82391i	−0.403636	+	0.338691i	0.418261	+	0.908327i	$0.362640\pi$
$30$		0			0
$31$	−4.17752	−	7.23567i	−0.750304	−	1.29957i	−0.947675	−	0.319237i	$-0.896574\pi$
$31$	−4.17752	−	7.23567i	−0.750304	−	1.29957i	0.197371	−	0.980329i	$-0.436760\pi$
$32$	0.979055	+	0.356347i	0.173074	+	0.0629939i
$33$		0			0
$34$	1.66772	+	9.45810i	0.286011	+	1.62205i
$35$	1.21301	−	0.441500i	0.205036	−	0.0746271i
$36$		0			0
$37$	−12.0642			−1.98334			−0.991669	−	0.128810i	$-0.958884\pi$
$37$	−12.0642			−1.98334			−0.991669	+	0.128810i	$0.958884\pi$
$38$	−4.55303	+	3.70929i	−0.738600	+	0.601726i
$39$		0			0
$40$	1.98293	+	1.66387i	0.313528	+	0.263081i
$41$	4.81180	−	1.75135i	0.751478	−	0.273515i	0.0622502	−	0.998061i	$-0.480172\pi$
$41$	4.81180	−	1.75135i	0.751478	−	0.273515i	0.689227	+	0.724545i	$0.257950\pi$
$42$		0			0
$43$	−0.594922	+	3.37397i	−0.0907248	+	0.514526i	0.905249	+	0.424881i	$0.139684\pi$
$43$	−0.594922	+	3.37397i	−0.0907248	+	0.514526i	−0.995974	+	0.0896446i	$0.971427\pi$
$44$	−0.907604	−	0.330341i	−0.136826	−	0.0498007i
$45$		0			0
$46$	0.907604	−	1.57202i	0.133819	−	0.231781i
$47$	3.05303	−	2.56180i	0.445331	−	0.373677i	−0.392369	−	0.919808i	$-0.628344\pi$
$47$	3.05303	−	2.56180i	0.445331	−	0.373677i	0.837700	+	0.546131i	$0.183900\pi$
$48$		0			0
$49$	2.42262	−	4.19610i	0.346088	−	0.599443i
$50$	−2.84730	−	4.93166i	−0.402669	−	0.697442i
$51$		0			0
$52$	0.156574	−	0.887975i	0.0217129	−	0.123140i
$53$	−1.47178	−	8.34689i	−0.202165	−	1.14653i	−0.901839	−	0.432072i	$-0.857783\pi$
$53$	−1.47178	−	8.34689i	−0.202165	−	1.14653i	0.699675	−	0.714462i	$-0.253328\pi$
$54$		0			0
$55$	−3.52094	−	2.95442i	−0.474764	−	0.398374i
$56$	−4.32089			−0.577403
$57$		0			0
$58$	3.82295			0.501978
$59$	3.28699	+	2.75811i	0.427930	+	0.359075i	0.831170	−	0.556019i	$-0.187672\pi$
$59$	3.28699	+	2.75811i	0.427930	+	0.359075i	−0.403240	+	0.915094i	$0.632116\pi$
$60$		0			0
$61$	−1.64543	−	9.33170i	−0.210676	−	1.19480i	−0.888255	−	0.459351i	$-0.848082\pi$
$61$	−1.64543	−	9.33170i	−0.210676	−	1.19480i	0.677579	−	0.735450i	$-0.263029\pi$
$62$	−1.95471	+	11.0857i	−0.248248	+	1.40788i
$63$		0			0
$64$	−4.29813	−	7.44459i	−0.537267	−	0.930573i
$65$	2.14543	−	3.71599i	0.266108	−	0.460912i
$66$		0			0
$67$	−2.03209	+	1.70513i	−0.248259	+	0.208314i	−0.758422	−	0.651763i	$-0.774029\pi$
$67$	−2.03209	+	1.70513i	−0.248259	+	0.208314i	0.510163	+	0.860078i	$0.329585\pi$
$68$	−0.658633	+	1.14079i	−0.0798710	+	0.138341i
$69$		0			0
$70$	−1.63429	−	0.594831i	−0.195334	−	0.0710959i
$71$	−2.19207	+	12.4318i	−0.260150	+	1.47539i	0.522347	+	0.852733i	$0.325056\pi$
$71$	−2.19207	+	12.4318i	−0.260150	+	1.47539i	−0.782498	+	0.622654i	$0.786055\pi$
$72$		0			0
$73$	−1.09967	+	0.400247i	−0.128707	+	0.0468454i	−0.405571	−	0.914064i	$-0.632927\pi$
$73$	−1.09967	+	0.400247i	−0.128707	+	0.0468454i	0.276864	+	0.960909i	$0.410705\pi$
$74$	12.4513	+	10.4479i	1.44743	+	1.21454i
$75$		0			0
$76$	−0.805407	−	0.0116794i	−0.0923866	−	0.00133972i
$77$	7.67230			0.874340
$78$		0			0
$79$	5.81655	−	2.11705i	0.654413	−	0.238187i	0.00659074	−	0.999978i	$-0.497902\pi$
$79$	5.81655	−	2.11705i	0.654413	−	0.238187i	0.647822	+	0.761791i	$0.275680\pi$
$80$	−0.549163	−	3.11446i	−0.0613983	−	0.348207i
$81$		0			0
$82$	−6.48293	−	2.35959i	−0.715919	−	0.260573i
$83$	−0.520945	−	0.902302i	−0.0571811	−	0.0990406i	0.836018	−	0.548702i	$-0.184878\pi$
$83$	−0.520945	−	0.902302i	−0.0571811	−	0.0990406i	−0.893199	+	0.449662i	$0.851545\pi$
$84$		0			0
$85$	−4.80200	+	4.02936i	−0.520850	+	0.437045i
$86$	3.53596	−	2.96702i	0.381292	−	0.319942i
$87$		0			0
$88$	7.69253	+	13.3239i	0.820027	+	1.42033i
$89$	11.9684	+	4.35613i	1.26865	+	0.461749i	0.886661	−	0.462420i	$-0.153019\pi$
$89$	11.9684	+	4.35613i	1.26865	+	0.461749i	0.381984	+	0.924169i	$0.375241\pi$
$90$		0			0
$91$	1.24376	+	7.05369i	0.130381	+	0.739428i
$92$	0.233956	−	0.0851529i	0.0243916	−	0.00887780i
$93$		0			0
$94$	−5.36959			−0.553830
$95$	−3.58260	−	1.36310i	−0.367567	−	0.139852i
$96$		0			0
$97$	8.88919	+	7.45891i	0.902560	+	0.757338i	0.970689	−	0.240339i	$-0.0772585\pi$
$97$	8.88919	+	7.45891i	0.902560	+	0.757338i	−0.0681291	+	0.997677i	$0.521703\pi$
$98$	−6.13429	+	2.23270i	−0.619656	+	0.225536i
$99$		0			0
$100$	0.135630	−	0.769193i	0.0135630	−	0.0769193i
$101$	−5.24510	−	1.90906i	−0.521907	−	0.189959i	0.0676142	−	0.997712i	$-0.478461\pi$
$101$	−5.24510	−	1.90906i	−0.521907	−	0.189959i	−0.589521	+	0.807753i	$0.700684\pi$
$102$		0			0
$103$	1.46064	−	2.52990i	0.143921	−	0.249278i	−0.785049	−	0.619434i	$-0.787362\pi$
$103$	1.46064	−	2.52990i	0.143921	−	0.249278i	0.928970	+	0.370155i	$0.120696\pi$
$104$	−11.0025	+	9.23222i	−1.07889	+	0.905293i
$105$		0			0
$106$	−5.70961	+	9.88933i	−0.554566	+	0.960537i
$107$	5.36097	+	9.28547i	0.518264	+	0.897660i	0.999775	+	0.0212197i	$0.00675495\pi$
$107$	5.36097	+	9.28547i	0.518264	+	0.897660i	−0.481511	+	0.876440i	$0.659912\pi$
$108$		0			0
$109$	0.355914	−	2.01849i	0.0340904	−	0.193336i	−0.963007	−	0.269478i	$-0.913149\pi$
$109$	0.355914	−	2.01849i	0.0340904	−	0.193336i	0.997097	+	0.0761414i	$0.0242600\pi$
$110$	1.07532	+	6.09845i	0.102528	+	0.581465i
$111$		0			0
$112$	4.04395	+	3.39328i	0.382117	+	0.320634i
$113$	4.86484			0.457645			0.228823	−	0.973468i	$-0.426512\pi$
$113$	4.86484			0.457645			0.228823	+	0.973468i	$0.426512\pi$
$114$		0			0
$115$	1.18479			0.110482
$116$	0.401674	+	0.337044i	0.0372945	+	0.0312938i
$117$		0			0
$118$	−1.00387	−	5.69323i	−0.0924138	−	0.524104i
$119$	1.81702	−	10.3048i	0.166566	−	0.944642i
$120$		0			0
$121$	−8.15910	−	14.1320i	−0.741736	−	1.28473i
$122$	−6.38326	+	11.0561i	−0.577913	+	1.00097i
$123$		0			0
$124$	−1.18273	+	0.992431i	−0.106213	+	0.0891229i
$125$	4.05690	−	7.02676i	0.362861	−	0.628493i
$126$		0			0
$127$	7.17024	+	2.60976i	0.636256	+	0.231578i	0.639952	−	0.768415i	$-0.278954\pi$
$127$	7.17024	+	2.60976i	0.636256	+	0.231578i	−0.00369577	+	0.999993i	$0.501176\pi$
$128$	−1.64930	+	9.35365i	−0.145779	+	0.826753i
$129$		0			0
$130$	−5.43242	+	1.97724i	−0.476455	+	0.173415i
$131$	9.20233	+	7.72167i	0.804012	+	0.674646i	0.949170	−	0.314763i	$-0.101925\pi$
$131$	9.20233	+	7.72167i	0.804012	+	0.674646i	−0.145159	+	0.989408i	$0.546369\pi$
$132$		0			0
$133$	6.04370	−	2.10100i	0.524055	−	0.182180i
$134$	3.57398			0.308745
$135$		0			0
$136$	19.7173	−	7.17653i	1.69075	−	0.615382i
$137$	0.695060	+	3.94188i	0.0593829	+	0.336777i	0.999996	−	0.00270222i	$-0.000860146\pi$
$137$	0.695060	+	3.94188i	0.0593829	+	0.336777i	−0.940613	+	0.339480i	$0.889749\pi$
$138$		0			0
$139$	21.4119	+	7.79331i	1.81614	+	0.661020i	0.996051	+	0.0887793i	$0.0282966\pi$
$139$	21.4119	+	7.79331i	1.81614	+	0.661020i	0.820086	+	0.572241i	$0.193926\pi$
$140$	−0.119271	−	0.206583i	−0.0100802	−	0.0174594i
$141$		0			0
$142$	13.0287	−	10.9324i	1.09334	−	0.917424i
$143$	19.5364	−	16.3930i	1.63372	−	1.37085i
$144$		0			0
$145$	1.24763	+	2.16095i	0.103610	+	0.179457i
$146$	1.48158	+	0.539252i	0.122617	+	0.0446288i
$147$		0			0
$148$	0.387126	+	2.19550i	0.0318216	+	0.180469i
$149$	−16.4217	+	5.97702i	−1.34532	+	0.489657i	−0.911484	−	0.411334i	$-0.865063\pi$
$149$	−16.4217	+	5.97702i	−1.34532	+	0.489657i	−0.433837	+	0.900991i	$0.642841\pi$
$150$		0			0
$151$	−0.638156			−0.0519324			−0.0259662	−	0.999663i	$-0.508266\pi$
$151$	−0.638156			−0.0519324			−0.0259662	+	0.999663i	$0.508266\pi$
$152$	9.70826	+	8.38906i	0.787444	+	0.680443i
$153$		0			0
$154$	−7.91850	−	6.64441i	−0.638091	−	0.535422i
$155$	−6.90420	+	2.51292i	−0.554559	+	0.201843i
$156$		0			0
$157$	0.216415	−	1.22735i	0.0172718	−	0.0979530i	−0.974953	−	0.222410i	$-0.928608\pi$
$157$	0.216415	−	1.22735i	0.0172718	−	0.0979530i	0.992225	+	0.124457i	$0.0397188\pi$
$158$	−7.83662	−	2.85230i	−0.623448	−	0.226916i
$159$		0			0
$160$	0.458111	−	0.793471i	0.0362168	−	0.0627294i
$161$	−1.51501	+	1.27125i	−0.119400	+	0.100188i
$162$		0			0
$163$	−3.63176	+	6.29039i	−0.284461	+	0.492701i	−0.972478	−	0.232993i	$-0.925148\pi$
$163$	−3.63176	+	6.29039i	−0.284461	+	0.492701i	0.688017	+	0.725694i	$0.258481\pi$
$164$	−0.473126	−	0.819478i	−0.0369449	−	0.0639905i
$165$		0			0
$166$	−0.243756	+	1.38241i	−0.0189191	+	0.107296i
$167$	1.92350	+	10.9087i	0.148845	+	0.844140i	0.964199	+	0.265178i	$0.0854307\pi$
$167$	1.92350	+	10.9087i	0.148845	+	0.844140i	−0.815355	+	0.578961i	$0.803458\pi$
$168$		0			0
$169$	8.27972	+	6.94751i	0.636901	+	0.534424i
$170$	8.44562			0.647750
$171$		0			0
$172$	0.633103			0.0482737
$173$	6.11927	+	5.13468i	0.465240	+	0.390382i	0.845055	−	0.534680i	$-0.179568\pi$
$173$	6.11927	+	5.13468i	0.465240	+	0.390382i	−0.379815	+	0.925062i	$0.624012\pi$
$174$		0			0
$175$	1.07738	+	6.11013i	0.0814424	+	0.461883i
$176$	3.26399	−	18.5110i	0.246032	−	1.39532i
$177$		0			0
$178$	−8.57991	−	14.8608i	−0.643091	−	1.11387i
$179$	−3.61721	+	6.26519i	−0.270363	+	0.468283i	−0.968955	−	0.247238i	$-0.920477\pi$
$179$	−3.61721	+	6.26519i	−0.270363	+	0.468283i	0.698592	+	0.715520i	$0.253810\pi$
$180$		0			0
$181$	−15.7062	+	13.1791i	−1.16743	+	0.979593i	−0.999980	−	0.00628756i	$-0.997999\pi$
$181$	−15.7062	+	13.1791i	−1.16743	+	0.979593i	−0.167453	+	0.985880i	$0.553554\pi$
$182$	4.82501	−	8.35716i	0.357653	−	0.619474i
$183$		0			0
$184$	−3.72668	−	1.35640i	−0.274735	−	0.0999952i
$185$	−1.84224	+	10.4479i	−0.135444	+	0.768144i
$186$		0			0
$187$	−35.0107	+	12.7429i	−2.56024	+	0.931851i
$188$	−0.564178	−	0.473401i	−0.0411469	−	0.0345263i
$189$		0			0
$190$	2.51707	+	4.50946i	0.182608	+	0.327151i
$191$	5.78106			0.418303			0.209151	−	0.977883i	$-0.432930\pi$
$191$	5.78106			0.418303			0.209151	+	0.977883i	$0.432930\pi$
$192$		0			0
$193$	14.7233	−	5.35883i	1.05980	−	0.385737i	0.247450	−	0.968901i	$-0.420407\pi$
$193$	14.7233	−	5.35883i	1.05980	−	0.385737i	0.812355	+	0.583163i	$0.198185\pi$
$194$	−2.71482	−	15.3965i	−0.194913	−	1.10541i
$195$		0			0
$196$	−0.841367	−	0.306232i	−0.0600976	−	0.0218737i
$197$	−11.8905	−	20.5950i	−0.847165	−	1.46733i	−0.883728	−	0.468002i	$-0.844974\pi$
$197$	−11.8905	−	20.5950i	−0.847165	−	1.46733i	0.0365624	−	0.999331i	$-0.488359\pi$
$198$		0			0
$199$	−11.4816	+	9.63419i	−0.813908	+	0.682950i	−0.951537	−	0.307534i	$-0.900496\pi$
$199$	−11.4816	+	9.63419i	−0.813908	+	0.682950i	0.137629	+	0.990484i	$0.456052\pi$
$200$	−9.53074	+	7.99724i	−0.673925	+	0.565491i
$201$		0			0
$202$	3.76011	+	6.51271i	0.264561	+	0.458233i
$203$	−3.91400	−	1.42458i	−0.274709	−	0.0999859i
$204$		0			0
$205$	−0.781937	−	4.43458i	−0.0546128	−	0.309725i
$206$	−3.69846	+	1.34613i	−0.257684	+	0.0937894i
$207$		0			0
$208$	17.5476			1.21671
$209$	−17.2383	−	14.8959i	−1.19240	−	1.03037i
$210$		0			0
$211$	−6.93036	−	5.81526i	−0.477106	−	0.400339i	0.372273	−	0.928123i	$-0.378579\pi$
$211$	−6.93036	−	5.81526i	−0.477106	−	0.400339i	−0.849379	+	0.527784i	$0.823023\pi$
$212$	−1.47178	+	0.535685i	−0.101082	+	0.0367910i
$213$		0			0
$214$	2.50846	−	14.2262i	0.171475	−	0.972480i
$215$	2.83110	+	1.03044i	0.193079	+	0.0702751i
$216$		0			0
$217$	6.13223	−	10.6213i	0.416283	−	0.721023i
$218$	−2.11540	+	1.77503i	−0.143273	+	0.120220i
$219$		0			0
$220$	−0.424678	+	0.735564i	−0.0286318	+	0.0495917i
$221$	−17.3910	−	30.1221i	−1.16985	−	2.02623i
$222$		0			0
$223$	−0.721629	+	4.09256i	−0.0483239	+	0.274058i	−0.999390	−	0.0349299i	$-0.988879\pi$
$223$	−0.721629	+	4.09256i	−0.0483239	+	0.274058i	0.951066	+	0.308988i	$0.0999903\pi$
$224$	0.265578	+	1.50617i	0.0177447	+	0.100635i
$225$		0			0
$226$	−5.02094	−	4.21307i	−0.333988	−	0.280249i
$227$	23.7050			1.57336			0.786679	−	0.617363i	$-0.211799\pi$
$227$	23.7050			1.57336			0.786679	+	0.617363i	$0.211799\pi$
$228$		0			0
$229$	−19.5175			−1.28976			−0.644878	−	0.764286i	$-0.723092\pi$
$229$	−19.5175			−1.28976			−0.644878	+	0.764286i	$0.723092\pi$
$230$	−1.22281	−	1.02606i	−0.0806298	−	0.0676564i
$231$		0			0
$232$	−1.45037	−	8.22546i	−0.0952215	−	0.540028i
$233$	−0.662666	+	3.75817i	−0.0434127	+	0.246206i	−0.998790	−	0.0491834i	$-0.984338\pi$
$233$	−0.662666	+	3.75817i	−0.0434127	+	0.246206i	0.955377	+	0.295389i	$0.0954492\pi$
$234$		0			0
$235$	−1.75237	−	3.03520i	−0.114312	−	0.197995i
$236$	0.396459	−	0.686688i	0.0258073	−	0.0446996i
$237$		0			0
$238$	−10.7996	+	9.06191i	−0.700032	+	0.587396i
$239$	−0.411474	+	0.712694i	−0.0266160	+	0.0461003i	−0.879027	−	0.476773i	$-0.841806\pi$
$239$	−0.411474	+	0.712694i	−0.0266160	+	0.0461003i	0.852411	+	0.522873i	$0.175140\pi$
$240$		0			0
$241$	8.13088	+	2.95940i	0.523756	+	0.190632i	0.590348	−	0.807149i	$-0.298990\pi$
$241$	8.13088	+	2.95940i	0.523756	+	0.190632i	−0.0665921	+	0.997780i	$0.521213\pi$
$242$	−3.81773	+	21.6514i	−0.245413	+	1.39181i
$243$		0			0
$244$	−1.64543	+	0.598887i	−0.105338	+	0.0383398i
$245$	−3.26399	−	2.73881i	−0.208528	−	0.174976i
$246$		0			0
$247$	10.9003	−	18.2631i	0.693571	−	1.16206i
$248$	24.5936			1.56169
$249$		0			0
$250$	−10.2724	+	3.73886i	−0.649686	+	0.236466i
$251$	−1.23261	−	6.99049i	−0.0778017	−	0.441236i	−0.998679	−	0.0513830i	$-0.983637\pi$
$251$	−1.23261	−	6.99049i	−0.0778017	−	0.441236i	0.920877	−	0.389853i	$-0.127474\pi$
$252$		0			0
$253$	6.61721	+	2.40847i	0.416021	+	0.151419i
$254$	−5.14022	−	8.90311i	−0.322526	−	0.558631i
$255$		0			0
$256$	−3.36753	+	2.82569i	−0.210470	+	0.176606i
$257$	−13.9795	+	11.7302i	−0.872019	+	0.731711i	−0.964522	−	0.264002i	$-0.914957\pi$
$257$	−13.9795	+	11.7302i	−0.872019	+	0.731711i	0.0925035	+	0.995712i	$0.470513\pi$
$258$		0			0
$259$	−8.85457	−	15.3366i	−0.550196	−	0.952968i
$260$	−0.745100	−	0.271194i	−0.0462091	−	0.0168187i
$261$		0			0
$262$	−2.81046	−	15.9389i	−0.173631	−	0.984709i
$263$	−12.0312	+	4.37900i	−0.741876	+	0.270021i	−0.685183	−	0.728371i	$-0.740278\pi$
$263$	−12.0312	+	4.37900i	−0.741876	+	0.270021i	−0.0566931	+	0.998392i	$0.518056\pi$
$264$		0			0
$265$	−7.45336			−0.457856
$266$	−8.05715	−	3.06558i	−0.494016	−	0.187963i
$267$		0			0
$268$	0.375515	+	0.315094i	0.0229382	+	0.0192475i
$269$	9.42989	−	3.43220i	0.574951	−	0.209265i	−0.0381469	−	0.999272i	$-0.512145\pi$
$269$	9.42989	−	3.43220i	0.574951	−	0.209265i	0.613098	+	0.790007i	$0.289923\pi$
$270$		0			0
$271$	−2.40033	+	13.6129i	−0.145810	+	0.826928i	0.820904	+	0.571066i	$0.193470\pi$
$271$	−2.40033	+	13.6129i	−0.145810	+	0.826928i	−0.966714	+	0.255861i	$0.917641\pi$
$272$	−24.0895	−	8.76785i	−1.46064	−	0.531629i
$273$		0			0
$274$	2.69640	−	4.67031i	0.162896	−	0.282144i
$275$	16.9231	−	14.2002i	1.02050	−	0.856302i
$276$		0			0
$277$	9.04189	−	15.6610i	0.543274	−	0.940979i	−0.455439	−	0.890267i	$-0.650518\pi$
$277$	9.04189	−	15.6610i	0.543274	−	0.940979i	0.998713	−	0.0507119i	$-0.0161490\pi$
$278$	−15.3498	−	26.5867i	−0.920621	−	1.59456i
$279$		0			0
$280$	−0.659815	+	3.74200i	−0.0394315	+	0.223627i
$281$	−3.21853	−	18.2532i	−0.192001	−	1.08889i	−0.916625	−	0.399749i	$-0.869097\pi$
$281$	−3.21853	−	18.2532i	−0.192001	−	1.08889i	0.724623	−	0.689145i	$-0.242014\pi$
$282$		0			0
$283$	3.86824	+	3.24584i	0.229943	+	0.192945i	0.750478	−	0.660895i	$-0.229823\pi$
$283$	3.86824	+	3.24584i	0.229943	+	0.192945i	−0.520535	+	0.853840i	$0.674268\pi$
$284$	2.33275			0.138423
$285$		0			0
$286$	−34.3601			−2.03175
$287$	5.75806	+	4.83158i	0.339887	+	0.285199i
$288$		0			0
$289$	5.87164	+	33.2998i	0.345391	+	1.95881i
$290$	0.583778	−	3.31077i	0.0342806	−	0.194415i
$291$		0			0
$292$	0.108126	+	0.187280i	0.00632761	+	0.0109597i
$293$	−5.92855	+	10.2685i	−0.346349	+	0.599895i	−0.985598	−	0.169105i	$-0.945912\pi$
$293$	−5.92855	+	10.2685i	−0.346349	+	0.599895i	0.639248	+	0.769000i	$0.279246\pi$
$294$		0			0
$295$	2.89053	−	2.42544i	0.168293	−	0.141215i
$296$	17.7558	−	30.7540i	1.03204	−	1.78754i
$297$		0			0
$298$	22.1250	+	8.05282i	1.28166	+	0.466488i
$299$	−1.14156	+	6.47410i	−0.0660181	+	0.374407i
$300$		0			0
$301$	−4.72580	+	1.72005i	−0.272391	+	0.0991422i
$302$	0.658633	+	0.552659i	0.0379001	+	0.0318020i
$303$		0			0
$304$	−2.49794	−	15.4755i	−0.143267	−	0.887578i
$305$	−8.33275			−0.477132
$306$		0			0
$307$	4.87211	−	1.77330i	0.278066	−	0.101208i	−0.199223	−	0.979954i	$-0.563842\pi$
$307$	4.87211	−	1.77330i	0.278066	−	0.101208i	0.477289	+	0.878746i	$0.341620\pi$
$308$	−0.246196	−	1.39625i	−0.0140283	−	0.0795585i
$309$		0			0
$310$	9.30200	+	3.38565i	0.528318	+	0.192292i
$311$	4.11334	+	7.12452i	0.233246	+	0.403994i	0.958762	−	0.284212i	$-0.0917319\pi$
$311$	4.11334	+	7.12452i	0.233246	+	0.403994i	−0.725515	+	0.688206i	$0.758399\pi$
$312$		0			0
$313$	−25.6006	+	21.4815i	−1.44703	+	1.21420i	−0.512321	+	0.858794i	$0.671214\pi$
$313$	−25.6006	+	21.4815i	−1.44703	+	1.21420i	−0.934711	+	0.355410i	$0.884341\pi$
$314$	−1.28627	+	1.07931i	−0.0725886	+	0.0609091i
$315$		0			0
$316$	−0.571919	−	0.990592i	−0.0321729	−	0.0557252i
$317$	19.1532	+	6.97118i	1.07575	+	0.391541i	0.818324	−	0.574757i	$-0.194904\pi$
$317$	19.1532	+	6.97118i	1.07575	+	0.391541i	0.257425	+	0.966298i	$0.417126\pi$
$318$		0			0
$319$	2.57532	+	14.6054i	0.144190	+	0.817744i
$320$	−7.10354	+	2.58548i	−0.397100	+	0.144533i
$321$		0			0
$322$	2.66456			0.148490
$323$	−24.0895	+	19.6253i	−1.34037	+	1.09198i
$324$		0			0
$325$	15.7986	+	13.2566i	0.876349	+	0.735344i
$326$	9.19594	−	3.34705i	0.509316	−	0.185376i
$327$		0			0
$328$	−2.61737	+	14.8439i	−0.144520	+	0.819615i
$329$	5.49747	+	2.00092i	0.303086	+	0.110314i
$330$		0			0
$331$	8.48932	−	14.7039i	0.466615	−	0.808202i	−0.532657	−	0.846331i	$-0.678807\pi$
$331$	8.48932	−	14.7039i	0.466615	−	0.808202i	0.999273	+	0.0381294i	$0.0121399\pi$
$332$	−0.147489	+	0.123758i	−0.00809451	+	0.00679210i
$333$		0			0
$334$	7.46198	−	12.9245i	0.408301	−	0.707199i
$335$	1.16637	+	2.02022i	0.0637258	+	0.110376i
$336$		0			0
$337$	4.23349	−	24.0093i	0.230613	−	1.30787i	−0.621046	−	0.783774i	$-0.713292\pi$
$337$	4.23349	−	24.0093i	0.230613	−	1.30787i	0.851659	−	0.524096i	$-0.175597\pi$
$338$	−2.52869	−	14.3409i	−0.137542	−	0.780041i
$339$		0			0
$340$	0.887374	+	0.744596i	0.0481246	+	0.0403814i
$341$	−43.6691			−2.36482
$342$		0			0
$343$	17.3878			0.938851
$344$	−7.72534	−	6.48233i	−0.416522	−	0.349504i
$345$		0			0
$346$	−1.86887	−	10.5989i	−0.100471	−	0.569800i
$347$	1.39734	−	7.92469i	0.0750130	−	0.425420i	−0.924055	−	0.382259i	$-0.875146\pi$
$347$	1.39734	−	7.92469i	0.0750130	−	0.425420i	0.999068	−	0.0431606i	$-0.0137427\pi$
$348$		0			0
$349$	−3.12701	−	5.41614i	−0.167385	−	0.289919i	0.770115	−	0.637906i	$-0.220199\pi$
$349$	−3.12701	−	5.41614i	−0.167385	−	0.289919i	−0.937500	+	0.347986i	$0.886866\pi$
$350$	4.17958	−	7.23924i	0.223408	−	0.386954i
$351$		0			0
$352$	4.17159	−	3.50038i	0.222346	−	0.186571i
$353$	−1.76558	+	3.05807i	−0.0939722	+	0.162765i	−0.909179	−	0.416405i	$-0.863290\pi$
$353$	−1.76558	+	3.05807i	−0.0939722	+	0.162765i	0.815207	+	0.579170i	$0.196623\pi$
$354$		0			0
$355$	10.4315	+	3.79677i	0.553649	+	0.201512i
$356$	0.408700	−	2.31785i	0.0216610	−	0.122846i
$357$		0			0
$358$	9.15910	−	3.33364i	0.484073	−	0.176188i
$359$	15.5043	+	13.0097i	0.818288	+	0.686625i	0.952570	−	0.304318i	$-0.0984286\pi$
$359$	15.5043	+	13.0097i	0.818288	+	0.686625i	−0.134283	+	0.990943i	$0.542873\pi$
$360$		0			0
$361$	−17.6582	−	7.01336i	−0.929380	−	0.369124i
$362$	27.6236			1.45186
$363$		0			0
$364$	1.24376	−	0.452690i	0.0651905	−	0.0237274i
$365$	0.178701	+	1.01346i	0.00935362	+	0.0530470i
$366$		0			0
$367$	−1.52734	−	0.555907i	−0.0797266	−	0.0290181i	0.301849	−	0.953356i	$-0.402396\pi$
$367$	−1.52734	−	0.555907i	−0.0797266	−	0.0290181i	−0.381576	+	0.924338i	$0.624618\pi$
$368$	2.42262	+	4.19610i	0.126288	+	0.218737i
$369$		0			0
$370$	10.9495	−	9.18772i	0.569237	−	0.477647i
$371$	9.53074	−	7.99724i	0.494812	−	0.415196i
$372$		0			0
$373$	16.9782	+	29.4071i	0.879097	+	1.52264i	0.852334	+	0.522998i	$0.175187\pi$
$373$	16.9782	+	29.4071i	0.879097	+	1.52264i	0.0267631	+	0.999642i	$0.491480\pi$
$374$	47.1698	+	17.1684i	2.43909	+	0.887758i
$375$		0			0
$376$	2.03714	+	11.5532i	0.105058	+	0.595811i
$377$	−13.0103	+	4.73535i	−0.670063	+	0.243883i
$378$		0			0
$379$	−16.0300			−0.823407			−0.411704	−	0.911318i	$-0.635066\pi$
$379$	−16.0300			−0.823407			−0.411704	+	0.911318i	$0.635066\pi$
$380$	−0.133103	+	0.695720i	−0.00682805	+	0.0356897i
$381$		0			0
$382$	−5.96657	−	5.00654i	−0.305276	−	0.256157i
$383$	−9.01501	+	3.28120i	−0.460646	+	0.167661i	−0.561910	−	0.827198i	$-0.689933\pi$
$383$	−9.01501	+	3.28120i	−0.460646	+	0.167661i	0.101265	+	0.994860i	$0.467711\pi$
$384$		0			0
$385$	1.17159	−	6.64441i	0.0597097	−	0.338630i
$386$	−19.8366	−	7.21994i	−1.00966	−	0.367485i
$387$		0			0
$388$	1.07217	−	1.85705i	0.0544310	−	0.0942773i
$389$	−8.48886	+	7.12300i	−0.430402	+	0.361150i	−0.832103	−	0.554621i	$-0.812863\pi$
$389$	−8.48886	+	7.12300i	−0.430402	+	0.361150i	0.401701	+	0.915771i	$0.368419\pi$
$390$		0			0
$391$	4.80200	−	8.31731i	0.242848	−	0.420625i
$392$	7.13113	+	12.3515i	0.360176	+	0.623844i
$393$		0			0
$394$	−5.56371	+	31.5534i	−0.280296	+	1.58964i
$395$	−0.945212	−	5.36056i	−0.0475588	−	0.269719i
$396$		0			0
$397$	13.2233	+	11.0956i	0.663657	+	0.556875i	0.911181	−	0.412007i	$-0.135172\pi$
$397$	13.2233	+	11.0956i	0.663657	+	0.556875i	−0.247523	+	0.968882i	$0.579617\pi$
$398$	20.1935			1.01221
$399$		0			0
$400$	15.2003			0.760014
$401$	−29.1104	−	24.4265i	−1.45370	−	1.21980i	−0.929821	−	0.368013i	$-0.880038\pi$
$401$	−29.1104	−	24.4265i	−1.45370	−	1.21980i	−0.523883	−	0.851790i	$-0.675517\pi$
$402$		0			0
$403$	−7.07919	−	40.1481i	−0.352640	−	1.99992i
$404$	−0.179111	+	1.01579i	−0.00891111	+	0.0505374i
$405$		0			0
$406$	2.80587	+	4.85992i	0.139253	+	0.241194i
$407$	−31.5278	+	54.6078i	−1.56278	+	2.70681i
$408$		0			0
$409$	0.103541	−	0.0868809i	0.00511975	−	0.00429598i	−0.640224	−	0.768188i	$-0.721159\pi$
$409$	0.103541	−	0.0868809i	0.00511975	−	0.00429598i	0.645344	+	0.763892i	$0.276714\pi$
$410$	−3.03343	+	5.25406i	−0.149811	+	0.259480i
$411$		0			0
$412$	−0.507274	−	0.184633i	−0.0249916	−	0.00909620i
$413$	−1.09374	+	6.20291i	−0.0538194	+	0.305225i
$414$		0			0
$415$	−0.860967	+	0.313366i	−0.0422632	+	0.0153825i
$416$	3.89440	+	3.26779i	0.190939	+	0.160217i
$417$		0			0
$418$	4.89124	+	30.3027i	0.239239	+	1.48215i
$419$	39.7965			1.94419			0.972094	−	0.234591i	$-0.0753751\pi$
$419$	39.7965			1.94419			0.972094	+	0.234591i	$0.0753751\pi$
$420$		0			0
$421$	−21.1604	+	7.70177i	−1.03130	+	0.375361i	−0.801575	−	0.597895i	$-0.796004\pi$
$421$	−21.1604	+	7.70177i	−1.03130	+	0.375361i	−0.229722	+	0.973256i	$0.573782\pi$
$422$	2.11658	+	12.0037i	0.103034	+	0.584333i
$423$		0			0
$424$	23.4440	+	8.53293i	1.13854	+	0.414396i
$425$	−15.0646	−	26.0927i	−0.730743	−	1.26568i
$426$		0			0
$427$	10.6552	−	8.94080i	0.515643	−	0.432676i
$428$	1.51779	−	1.27358i	0.0733651	−	0.0615606i
$429$		0			0
$430$	−2.02956	−	3.51531i	−0.0978742	−	0.169523i
$431$	3.68644	+	1.34175i	0.177570	+	0.0646301i	0.429275	−	0.903174i	$-0.358769\pi$
$431$	3.68644	+	1.34175i	0.177570	+	0.0646301i	−0.251705	+	0.967804i	$0.580991\pi$
$432$		0			0
$433$	2.76991	+	15.7090i	0.133114	+	0.754925i	0.976155	+	0.217076i	$0.0696519\pi$
$433$	2.76991	+	15.7090i	0.133114	+	0.754925i	−0.843041	+	0.537849i	$0.819237\pi$
$434$	−15.5273	+	5.65149i	−0.745336	+	0.271280i
$435$		0			0
$436$	−0.378756			−0.0181391
$437$	5.87211	+	0.0851529i	0.280901	+	0.00407341i
$438$		0			0
$439$	3.60607	+	3.02585i	0.172108	+	0.144416i	0.724773	−	0.688988i	$-0.241945\pi$
$439$	3.60607	+	3.02585i	0.172108	+	0.144416i	−0.552665	+	0.833404i	$0.686389\pi$
$440$	12.7135	−	4.62733i	0.606091	−	0.220599i
$441$		0			0
$442$	−8.13744	+	46.1497i	−0.387059	+	2.19512i
$443$	27.4513	+	9.99146i	1.30425	+	0.474708i	0.898379	−	0.439221i	$-0.144746\pi$
$443$	27.4513	+	9.99146i	1.30425	+	0.474708i	0.405872	+	0.913930i	$0.366968\pi$
$444$		0			0
$445$	5.60014	−	9.69972i	0.265472	−	0.459811i
$446$	4.28905	−	3.59894i	0.203092	−	0.170415i
$447$		0			0
$448$	6.30928	−	10.9280i	0.298085	−	0.516299i
$449$	7.39053	+	12.8008i	0.348781	+	0.604106i	0.986033	−	0.166549i	$-0.0532625\pi$
$449$	7.39053	+	12.8008i	0.348781	+	0.604106i	−0.637252	+	0.770655i	$0.719929\pi$
$450$		0			0
$451$	4.64749	−	26.3572i	0.218842	−	1.24111i
$452$	−0.156107	−	0.885328i	−0.00734267	−	0.0416423i
$453$		0			0
$454$	−24.4657	−	20.5292i	−1.14823	−	0.963481i
$455$	6.29860			0.295283
$456$		0			0
$457$	−9.71782			−0.454580			−0.227290	−	0.973827i	$-0.572987\pi$
$457$	−9.71782			−0.454580			−0.227290	+	0.973827i	$0.572987\pi$
$458$	20.1438	+	16.9027i	0.941260	+	0.789811i
$459$		0			0
$460$	−0.0380187	−	0.215615i	−0.00177263	−	0.0100531i
$461$	2.44521	−	13.8675i	0.113885	−	0.645873i	−0.873411	−	0.486983i	$-0.838097\pi$
$461$	2.44521	−	13.8675i	0.113885	−	0.645873i	0.987296	−	0.158890i	$-0.0507916\pi$
$462$		0			0
$463$	13.8255	+	23.9464i	0.642524	+	1.11288i	0.984867	+	0.173310i	$0.0554462\pi$
$463$	13.8255	+	23.9464i	0.642524	+	1.11288i	−0.342343	+	0.939575i	$0.611221\pi$
$464$	−5.10220	+	8.83726i	−0.236864	+	0.410260i
$465$		0			0
$466$	3.93860	−	3.30488i	0.182452	−	0.153095i
$467$	6.92380	−	11.9924i	0.320395	−	0.554941i	−0.660174	−	0.751112i	$-0.729518\pi$
$467$	6.92380	−	11.9924i	0.320395	−	0.554941i	0.980570	+	0.196172i	$0.0628509\pi$
$468$		0			0
$469$	−3.65910	−	1.33180i	−0.168962	−	0.0614970i
$470$	−0.819955	+	4.65020i	−0.0378217	+	0.214498i
$471$		0			0
$472$	−11.8687	+	4.31986i	−0.546302	+	0.198838i
$473$	13.7173	+	11.5102i	0.630724	+	0.529241i
$474$		0			0
$475$	9.44222	−	15.8201i	0.433239	−	0.725877i
$476$	−1.93363			−0.0886278
$477$		0			0
$478$	1.04189	−	0.379217i	0.0476549	−	0.0173450i
$479$	3.33022	+	18.8866i	0.152162	+	0.862952i	0.961335	+	0.275382i	$0.0888043\pi$
$479$	3.33022	+	18.8866i	0.152162	+	0.862952i	−0.809173	+	0.587570i	$0.800085\pi$
$480$		0			0
$481$	−55.3157	−	20.1333i	−2.52218	−	0.917999i
$482$	−5.82888	−	10.0959i	−0.265498	−	0.459856i
$483$		0			0
$484$	−2.30999	+	1.93831i	−0.105000	+	0.0881052i
$485$	7.81702	−	6.55926i	0.354953	−	0.297841i
$486$		0			0
$487$	−2.80659	−	4.86116i	−0.127179	−	0.220280i	0.795404	−	0.606080i	$-0.207259\pi$
$487$	−2.80659	−	4.86116i	−0.127179	−	0.220280i	−0.922582	+	0.385800i	$0.873926\pi$
$488$	26.2101	+	9.53969i	1.18647	+	0.431841i
$489$		0			0
$490$	0.996845	+	5.65339i	0.0450329	+	0.255394i
$491$	16.3709	−	5.95853i	0.738810	−	0.268905i	0.0549206	−	0.998491i	$-0.482509\pi$
$491$	16.3709	−	5.95853i	0.738810	−	0.268905i	0.683889	+	0.729586i	$0.260287\pi$
$492$		0			0
$493$	20.2267			0.910964
$494$	−27.0665	+	9.40923i	−1.21778	+	0.423341i
$495$		0			0
$496$	−23.0173	−	19.3138i	−1.03351	−	0.867215i
$497$	−17.4128	+	6.33775i	−0.781072	+	0.284287i
$498$		0			0
$499$	3.06434	−	17.3787i	0.137179	−	0.777979i	−0.836139	−	0.548518i	$-0.815192\pi$
$499$	3.06434	−	17.3787i	0.137179	−	0.777979i	0.973318	−	0.229461i	$-0.0736965\pi$
$500$	−1.40895	−	0.512815i	−0.0630101	−	0.0229338i
$501$		0			0
$502$	−4.78177	+	8.28228i	−0.213421	+	0.369656i
$503$	−28.9709	+	24.3095i	−1.29175	+	1.08391i	−0.300240	+	0.953864i	$0.597067\pi$
$503$	−28.9709	+	24.3095i	−1.29175	+	1.08391i	−0.991508	+	0.130042i	$0.958489\pi$
$504$		0			0
$505$	−2.45424	+	4.25087i	−0.109212	+	0.189161i
$506$	−4.74376	−	8.21643i	−0.210886	−	0.365265i
$507$		0			0
$508$	0.244852	−	1.38862i	0.0108635	−	0.0616101i
$509$	4.43036	+	25.1258i	0.196372	+	1.11368i	0.910451	+	0.413617i	$0.135735\pi$
$509$	4.43036	+	25.1258i	0.196372	+	1.11368i	−0.714079	+	0.700065i	$0.753154\pi$
$510$		0			0
$511$	−1.31592	−	1.10419i	−0.0582130	−	0.0488465i
$512$	24.9186			1.10126
$513$		0			0
$514$	24.5868			1.08448
$515$	−1.96791	−	1.65127i	−0.0867165	−	0.0727638i
$516$		0			0
$517$	−3.61721	−	20.5142i	−0.159085	−	0.902215i
$518$	−4.14315	+	23.4970i	−0.182040	+	1.03240i
$519$		0			0
$520$	6.31521	+	10.9383i	0.276940	+	0.479674i
$521$	2.74763	−	4.75903i	0.120376	−	0.208497i	−0.799540	−	0.600613i	$-0.794923\pi$
$521$	2.74763	−	4.75903i	0.120376	−	0.208497i	0.919916	+	0.392116i	$0.128257\pi$
$522$		0			0
$523$	−21.6400	+	18.1581i	−0.946250	+	0.793998i	−0.978662	−	0.205477i	$-0.934125\pi$
$523$	−21.6400	+	18.1581i	−0.946250	+	0.793998i	0.0324123	+	0.999475i	$0.489681\pi$
$524$	1.10994	−	1.92247i	0.0484878	−	0.0839834i
$525$		0			0
$526$	16.2096	+	5.89981i	0.706772	+	0.257244i
$527$	−10.3421	+	58.6529i	−0.450508	+	2.55496i
$528$		0			0
$529$	19.9072	−	7.24563i	0.865530	−	0.315027i
$530$	7.69253	+	6.45480i	0.334142	+	0.280379i
$531$		0			0
$532$	−0.576286	−	1.03244i	−0.0249852	−	0.0447622i
$533$	24.9855			1.08224
$534$		0			0
$535$	8.86009	−	3.22481i	0.383055	−	0.139421i
$536$	−1.35591	−	7.68977i	−0.0585666	−	0.332148i
$537$		0			0
$538$	−12.7049	−	4.62419i	−0.547745	−	0.199363i
$539$	−12.6623	−	21.9317i	−0.545402	−	0.944664i
$540$		0			0
$541$	11.5556	−	9.69627i	0.496812	−	0.416875i	−0.359648	−	0.933088i	$-0.617103\pi$
$541$	11.5556	−	9.69627i	0.496812	−	0.416875i	0.856460	+	0.516213i	$0.172659\pi$
$542$	14.2665	−	11.9710i	0.612799	−	0.514200i
$543$		0			0
$544$	−3.71348	−	6.43193i	−0.159214	−	0.275767i
$545$	−1.69372	−	0.616462i	−0.0725508	−	0.0264063i
$546$		0			0
$547$	3.21482	+	18.2322i	0.137456	+	0.779551i	0.973118	+	0.230307i	$0.0739731\pi$
$547$	3.21482	+	18.2322i	0.137456	+	0.779551i	−0.835662	+	0.549244i	$0.814916\pi$
$548$	0.695060	−	0.252981i	0.0296915	−	0.0108068i
$549$		0			0
$550$	−29.7638			−1.26913
$551$	6.02822	+	10.7999i	0.256811	+	0.460089i
$552$		0			0
$553$	6.96039	+	5.84046i	0.295986	+	0.248362i
$554$	−22.8949	+	8.33305i	−0.972710	+	0.354037i
$555$		0			0
$556$	0.731181	−	4.14673i	0.0310090	−	0.175861i
$557$	−20.2263	−	7.36176i	−0.857015	−	0.311928i	−0.124118	−	0.992268i	$-0.539610\pi$
$557$	−20.2263	−	7.36176i	−0.857015	−	0.311928i	−0.732897	+	0.680340i	$0.761832\pi$
$558$		0			0
$559$	−8.35844	+	14.4772i	−0.353524	+	0.612322i
$560$	3.55619	−	2.98400i	0.150276	−	0.126097i
$561$		0			0
$562$	−12.4859	+	21.6262i	−0.526687	+	0.912248i
$563$	−16.8648	−	29.2108i	−0.710768	−	1.23109i	−0.964569	−	0.263830i	$-0.915014\pi$
$563$	−16.8648	−	29.2108i	−0.710768	−	1.23109i	0.253801	−	0.967256i	$-0.418319\pi$
$564$		0			0
$565$	0.742878	−	4.21307i	0.0312531	−	0.177245i
$566$	−1.18139	−	6.69999i	−0.0496575	−	0.281622i
$567$		0			0
$568$	−28.4650	−	23.8849i	−1.19436	−	1.00219i
$569$	−15.7469			−0.660145			−0.330072	−	0.943956i	$-0.607073\pi$
$569$	−15.7469			−0.660145			−0.330072	+	0.943956i	$0.607073\pi$
$570$		0			0
$571$	42.6391			1.78439			0.892195	−	0.451650i	$-0.149164\pi$
$571$	42.6391			1.78439			0.892195	+	0.451650i	$0.149164\pi$
$572$	−3.61019	−	3.02931i	−0.150949	−	0.126662i
$573$		0			0
$574$	−1.75855	−	9.97324i	−0.0734005	−	0.416275i
$575$	−0.988856	+	5.60808i	−0.0412381	+	0.233873i
$576$		0			0
$577$	−9.75624	−	16.8983i	−0.406158	−	0.703486i	0.588298	−	0.808644i	$-0.299798\pi$
$577$	−9.75624	−	16.8983i	−0.406158	−	0.703486i	−0.994455	+	0.105159i	$0.966465\pi$
$578$	22.7784	−	39.4533i	0.947455	−	1.64104i
$579$		0			0
$580$	0.353226	−	0.296392i	0.0146669	−	0.0123070i
$581$	0.764700	−	1.32450i	0.0317251	−	0.0549495i
$582$		0			0
$583$	−41.6279	−	15.1513i	−1.72405	−	0.627504i
$584$	0.598164	−	3.39236i	0.0247522	−	0.140377i
$585$		0			0
$586$	15.0116	−	5.46378i	0.620124	−	0.225707i
$587$	−9.09808	−	7.63419i	−0.375518	−	0.315097i	0.435422	−	0.900226i	$-0.356599\pi$
$587$	−9.09808	−	7.63419i	−0.375518	−	0.315097i	−0.810940	+	0.585130i	$0.801044\pi$
$588$		0			0
$589$	−34.3995	+	11.9584i	−1.41740	+	0.492738i
$590$	−5.08378			−0.209296
$591$		0			0
$592$	−40.7695	+	14.8389i	−1.67562	+	0.609874i
$593$	0.245567	+	1.39268i	0.0100842	+	0.0571904i	0.989435	−	0.144980i	$-0.0463117\pi$
$593$	0.245567	+	1.39268i	0.0100842	+	0.0571904i	−0.979350	+	0.202170i	$0.935201\pi$
$594$		0			0
$595$	−8.64677	−	3.14717i	−0.354483	−	0.129021i
$596$	1.61468	+	2.79672i	0.0661401	+	0.114558i
$597$		0			0
$598$	6.78493	−	5.69323i	0.277456	−	0.232814i
$599$	−19.1682	+	16.0840i	−0.783191	+	0.657175i	−0.944050	−	0.329802i	$-0.893018\pi$
$599$	−19.1682	+	16.0840i	−0.783191	+	0.657175i	0.160859	+	0.986977i	$0.448573\pi$
$600$		0			0
$601$	6.92649	+	11.9970i	0.282537	+	0.489369i	0.972009	−	0.234944i	$-0.0754905\pi$
$601$	6.92649	+	11.9970i	0.282537	+	0.489369i	−0.689472	+	0.724313i	$0.742157\pi$
$602$	6.36706	+	2.31742i	0.259502	+	0.0944510i
$603$		0			0
$604$	0.0204777	+	0.116135i	0.000833226	+	0.00472546i
$605$	−13.4846	+	4.90798i	−0.548226	+	0.199538i
$606$		0			0
$607$	1.59089			0.0645722			0.0322861	−	0.999479i	$-0.489721\pi$
$607$	1.59089			0.0645722			0.0322861	+	0.999479i	$0.489721\pi$
$608$	2.32753	−	3.89971i	0.0943940	−	0.158154i
$609$		0			0
$610$	8.60014	+	7.21637i	0.348209	+	0.292182i
$611$	18.2738	−	6.65111i	0.739278	−	0.269075i
$612$		0			0
$613$	4.65317	−	26.3894i	0.187940	−	1.06586i	−0.734180	−	0.678955i	$-0.762433\pi$
$613$	4.65317	−	26.3894i	0.187940	−	1.06586i	0.922120	−	0.386905i	$-0.126456\pi$
$614$	−6.56418	−	2.38917i	−0.264909	−	0.0964189i
$615$		0			0
$616$	−11.2920	+	19.5582i	−0.454966	+	0.788024i
$617$	27.1523	−	22.7835i	1.09311	−	0.917228i	0.0961675	−	0.995365i	$-0.469342\pi$
$617$	27.1523	−	22.7835i	1.09311	−	0.917228i	0.996943	+	0.0781368i	$0.0248971\pi$
$618$		0			0
$619$	−19.9538	+	34.5610i	−0.802012	+	1.38913i	0.116278	+	0.993217i	$0.462904\pi$
$619$	−19.9538	+	34.5610i	−0.802012	+	1.38913i	−0.918290	+	0.395909i	$0.870430\pi$
$620$	0.678863	+	1.17582i	0.0272638	+	0.0472223i
$621$		0			0
$622$	1.92468	−	10.9154i	0.0771726	−	0.437667i
$623$	3.24653	+	18.4120i	0.130069	+	0.737661i
$624$		0			0
$625$	10.7233	+	8.99790i	0.428931	+	0.359916i
$626$	45.0256			1.79958
$627$		0			0
$628$	−0.230304			−0.00919011
$629$	65.8781	+	55.2783i	2.62673	+	2.20409i
$630$		0			0
$631$	−2.28905	−	12.9818i	−0.0911256	−	0.516799i	−0.995866	−	0.0908353i	$-0.971046\pi$
$631$	−2.28905	−	12.9818i	−0.0911256	−	0.516799i	0.904740	−	0.425963i	$-0.140065\pi$
$632$	−3.16390	+	17.9434i	−0.125853	+	0.713750i
$633$		0			0
$634$	−13.7306	−	23.7820i	−0.545310	−	0.944504i
$635$	3.35504	−	5.81109i	0.133141	−	0.230606i
$636$		0			0
$637$	18.1107	−	15.1966i	0.717570	−	0.602113i
$638$	9.99067	−	17.3043i	0.395534	−	0.685085i
$639$		0			0
$640$	7.84864	+	2.85667i	0.310245	+	0.112920i
$641$	−7.66250	+	43.4562i	−0.302651	+	1.71642i	0.331711	+	0.943381i	$0.392374\pi$
$641$	−7.66250	+	43.4562i	−0.302651	+	1.71642i	−0.634362	+	0.773036i	$0.718737\pi$
$642$		0			0
$643$	−10.2674	+	3.73702i	−0.404906	+	0.147374i	−0.536441	−	0.843938i	$-0.680232\pi$
$643$	−10.2674	+	3.73702i	−0.404906	+	0.147374i	0.131535	+	0.991312i	$0.458009\pi$
$644$	0.279963	+	0.234917i	0.0110321	+	0.00925703i
$645$		0			0
$646$	41.8585	+	0.607000i	1.64690	+	0.0238821i
$647$	−3.20170			−0.125872			−0.0629360	−	0.998018i	$-0.520046\pi$
$647$	−3.20170			−0.125872			−0.0629360	+	0.998018i	$0.520046\pi$
$648$		0			0
$649$	21.0744	−	7.67047i	0.827244	−	0.301092i
$650$	−4.82501	−	27.3640i	−0.189252	−	1.07330i
$651$		0			0
$652$	1.26130	+	0.459074i	0.0493962	+	0.0179787i
$653$	−12.5620	−	21.7579i	−0.491587	−	0.851454i	0.508366	−	0.861141i	$-0.330250\pi$
$653$	−12.5620	−	21.7579i	−0.491587	−	0.851454i	−0.999953	+	0.00968702i	$0.996916\pi$
$654$		0			0
$655$	8.09240	−	6.79033i	0.316196	−	0.265320i
$656$	14.1068	−	11.8370i	0.550777	−	0.462157i
$657$		0			0
$658$	−3.94104	−	6.82608i	−0.153638	−	0.266108i
$659$	−28.9111	−	10.5228i	−1.12622	−	0.409909i	−0.289298	−	0.957239i	$-0.593422\pi$
$659$	−28.9111	−	10.5228i	−1.12622	−	0.409909i	−0.836917	+	0.547330i	$0.815644\pi$
$660$		0			0
$661$	−1.60978	−	9.12949i	−0.0626130	−	0.355096i	−0.999977	−	0.00674518i	$-0.997853\pi$
$661$	−1.60978	−	9.12949i	−0.0626130	−	0.355096i	0.937364	−	0.348351i	$-0.113258\pi$
$662$	−21.4957	+	7.82380i	−0.835455	+	0.304081i
$663$		0			0
$664$	3.06687			0.119017
$665$	−0.896622	−	5.55483i	−0.0347695	−	0.215407i
$666$		0			0
$667$	−2.92855	−	2.45734i	−0.113394	−	0.0951487i
$668$	1.92350	−	0.700095i	0.0744223	−	0.0270875i
$669$		0			0
$670$	0.545759	−	3.09516i	0.0210845	−	0.119576i
$671$	−46.5394	−	16.9390i	−1.79663	−	0.653921i
$672$		0			0
$673$	4.74644	−	8.22108i	0.182962	−	0.316899i	−0.759926	−	0.650010i	$-0.774765\pi$
$673$	4.74644	−	8.22108i	0.182962	−	0.316899i	0.942888	+	0.333110i	$0.108098\pi$
$674$	−25.1620	+	21.1134i	−0.969204	+	0.813259i
$675$		0			0
$676$	0.998656	−	1.72972i	0.0384098	−	0.0665278i
$677$	−9.50774	−	16.4679i	−0.365412	−	0.632912i	0.623430	−	0.781879i	$-0.285739\pi$
$677$	−9.50774	−	16.4679i	−0.365412	−	0.632912i	−0.988842	+	0.148967i	$0.952405\pi$
$678$		0			0
$679$	−2.95786	+	16.7749i	−0.113512	+	0.643761i
$680$	−3.20414	−	18.1716i	−0.122873	−	0.696849i
$681$		0			0
$682$	45.0704	+	37.8186i	1.72584	+	1.44815i
$683$	−6.58677			−0.252036			−0.126018	−	0.992028i	$-0.540220\pi$
$683$	−6.58677			−0.252036			−0.126018	+	0.992028i	$0.540220\pi$
$684$		0			0
$685$	3.51991			0.134489
$686$	−17.9457	−	15.0582i	−0.685170	−	0.574926i
$687$		0			0
$688$	2.13950	+	12.1337i	0.0815677	+	0.462593i
$689$	7.18139	−	40.7277i	0.273589	−	1.55160i
$690$		0			0
$691$	21.3525	+	36.9836i	0.812288	+	1.40692i	0.911259	+	0.411833i	$0.135111\pi$
$691$	21.3525	+	36.9836i	0.812288	+	1.40692i	−0.0989713	+	0.995090i	$0.531555\pi$
$692$	0.738074	−	1.27838i	0.0280574	−	0.0485968i
$693$		0			0
$694$	−8.30516	+	6.96886i	−0.315260	+	0.264534i
$695$	10.0189	−	17.3532i	0.380038	−	0.658245i
$696$		0			0
$697$	−34.3002	−	12.4843i	−1.29921	−	0.472875i
$698$	−1.46316	+	8.29801i	−0.0553816	+	0.314084i
$699$		0			0
$700$	1.07738	−	0.392135i	0.0407212	−	0.0148213i
$701$	−4.64227	−	3.89533i	−0.175336	−	0.147125i	0.550896	−	0.834574i	$-0.314286\pi$
$701$	−4.64227	−	3.89533i	−0.175336	−	0.147125i	−0.726233	+	0.687449i	$0.758730\pi$
$702$		0			0
$703$	−9.88150	+	51.6498i	−0.372688	+	1.94801i
$704$	−44.9299			−1.69336
$705$		0			0
$706$	4.47060	−	1.62717i	0.168253	−	0.0612392i
$707$	−1.42278	−	8.06899i	−0.0535092	−	0.303466i
$708$		0			0
$709$	19.5937	+	7.13154i	0.735858	+	0.267831i	0.682643	−	0.730752i	$-0.260831\pi$
$709$	19.5937	+	7.13154i	0.735858	+	0.267831i	0.0532159	+	0.998583i	$0.483053\pi$
$710$	−7.47818	−	12.9526i	−0.280651	−	0.486102i
$711$		0			0
$712$	−28.7195	+	24.0985i	−1.07631	+	0.903130i
$713$	8.62314	−	7.23567i	0.322939	−	0.270978i
$714$		0			0
$715$	−11.2135	−	19.4223i	−0.419360	−	0.726353i
$716$	1.25624	+	0.457236i	0.0469481	+	0.0170877i
$717$		0			0
$718$	−4.73514	−	26.8543i	−0.176714	−	1.00219i
$719$	38.0540	−	13.8505i	1.41917	−	0.516537i	0.485365	−	0.874311i	$-0.338687\pi$
$719$	38.0540	−	13.8505i	1.41917	−	0.516537i	0.933808	+	0.357774i	$0.116464\pi$
$720$		0			0
$721$	4.28817			0.159700
$722$	12.1511	+	22.5309i	0.452218	+	0.838512i
$723$		0			0
$724$	2.90239	+	2.43539i	0.107866	+	0.0905107i
$725$	−11.2699	+	4.10191i	−0.418554	+	0.152341i
$726$		0			0
$727$	2.18913	−	12.4152i	0.0811903	−	0.460453i	−0.916924	−	0.399063i	$-0.869335\pi$
$727$	2.18913	−	12.4152i	0.0811903	−	0.460453i	0.998114	−	0.0613902i	$-0.0195534\pi$
$728$	−19.8118	−	7.21091i	−0.734274	−	0.267254i
$729$		0			0
$730$	0.693249	−	1.20074i	0.0256583	−	0.0444414i
$731$	18.7083	−	15.6981i	0.691950	−	0.580615i
$732$		0			0
$733$	9.05350	−	15.6811i	0.334399	−	0.579195i	−0.648970	−	0.760814i	$-0.724800\pi$
$733$	9.05350	−	15.6811i	0.334399	−	0.579195i	0.983369	+	0.181618i	$0.0581335\pi$
$734$	1.09492	+	1.89646i	0.0404143	+	0.0699997i
$735$		0			0
$736$	−0.243756	+	1.38241i	−0.00898496	+	0.0509562i
$737$	2.40760	+	13.6542i	0.0886852	+	0.502959i
$738$		0			0
$739$	−16.8425	−	14.1326i	−0.619563	−	0.519875i	0.278103	−	0.960551i	$-0.410294\pi$
$739$	−16.8425	−	14.1326i	−0.619563	−	0.519875i	−0.897666	+	0.440676i	$0.854739\pi$
$740$	1.96048			0.0720685
$741$		0			0
$742$	−16.7624			−0.615367
$743$	−22.9939	−	19.2942i	−0.843565	−	0.707835i	0.114798	−	0.993389i	$-0.463378\pi$
$743$	−22.9939	−	19.2942i	−0.843565	−	0.707835i	−0.958363	+	0.285554i	$0.907822\pi$
$744$		0			0
$745$	2.66860	+	15.1344i	0.0977698	+	0.554480i
$746$	7.94428	−	45.0542i	0.290861	−	1.64955i
$747$		0			0
$748$	3.44247	+	5.96253i	0.125869	+	0.218012i
$749$	−7.86942	+	13.6302i	−0.287542	+	0.498038i
$750$		0			0
$751$	23.8241	−	19.9908i	0.869355	−	0.729475i	−0.0946073	−	0.995515i	$-0.530160\pi$
$751$	23.8241	−	19.9908i	0.869355	−	0.729475i	0.963962	+	0.266039i	$0.0857151\pi$
$752$	7.16637	−	12.4125i	0.261331	−	0.452638i
$753$		0			0
$754$	17.5287	+	6.37992i	0.638357	+	0.232343i
$755$	−0.0974487	+	0.552659i	−0.00354652	+	0.0201133i
$756$		0			0
$757$	17.7481	−	6.45978i	0.645065	−	0.234785i	0.00129008	−	0.999999i	$-0.499589\pi$
$757$	17.7481	−	6.45978i	0.645065	−	0.234785i	0.643775	+	0.765215i	$0.277367\pi$
$758$	16.5444	+	13.8824i	0.600920	+	0.504232i
$759$		0			0
$760$	8.74763	−	7.12656i	0.317310	−	0.258508i
$761$	5.65539			0.205008			0.102504	−	0.994733i	$-0.467315\pi$
$761$	5.65539			0.205008			0.102504	+	0.994733i	$0.467315\pi$
$762$		0			0
$763$	2.82723	−	1.02903i	0.102353	−	0.0372533i
$764$	−0.185508	−	1.05207i	−0.00671143	−	0.0380624i
$765$		0			0
$766$	12.1459	+	4.42074i	0.438849	+	0.159728i
$767$	10.4684	+	18.1318i	0.377991	+	0.654700i
$768$		0			0
$769$	−6.03596	+	5.06477i	−0.217662	+	0.182640i	−0.745099	−	0.666954i	$-0.767598\pi$
$769$	−6.03596	+	5.06477i	−0.217662	+	0.182640i	0.527437	+	0.849594i	$0.323153\pi$
$770$	−6.96341	+	5.84300i	−0.250944	+	0.210567i
$771$		0			0
$772$	−1.44768	−	2.50746i	−0.0521032	−	0.0902454i
$773$	−21.5043	−	7.82694i	−0.773457	−	0.281515i	−0.0750155	−	0.997182i	$-0.523901\pi$
$773$	−21.5043	−	7.82694i	−0.773457	−	0.281515i	−0.698442	+	0.715667i	$0.746123\pi$
$774$		0			0
$775$	−6.13223	−	34.7776i	−0.220276	−	1.24925i
$776$	−32.0972	+	11.6824i	−1.15222	+	0.419375i
$777$		0			0
$778$	14.9299			0.535265
$779$	−3.55674	−	22.0350i	−0.127433	−	0.789487i
$780$		0			0
$781$	50.5433	+	42.4109i	1.80858	+	1.51758i
$782$	−12.1591	+	4.42555i	−0.434809	+	0.158257i
$783$		0			0
$784$	3.02578	−	17.1600i	0.108064	−	0.612859i
$785$	−1.02987	−	0.374841i	−0.0367575	−	0.0133787i
$786$		0			0
$787$	−18.6844	+	32.3623i	−0.666026	+	1.15359i	0.312980	+	0.949760i	$0.398673\pi$
$787$	−18.6844	+	32.3623i	−0.666026	+	1.15359i	−0.979006	+	0.203832i	$0.934661\pi$
$788$	−3.36643	+	2.82477i	−0.119924	+	0.100628i
$789$		0			0
$790$	−3.66684	+	6.35115i	−0.130460	+	0.225964i
$791$	3.57057	+	6.18442i	0.126955	+	0.219893i
$792$		0			0
$793$	8.02869	−	45.5329i	0.285107	−	1.61692i
$794$	−4.03849	−	22.9034i	−0.143320	−	0.812811i
$795$		0			0
$796$	2.12171	+	1.78033i	0.0752020	+	0.0631020i
$797$	−39.0324			−1.38260			−0.691299	−	0.722569i	$-0.742961\pi$
$797$	−39.0324			−1.38260			−0.691299	+	0.722569i	$0.742961\pi$
$798$		0			0
$799$	−28.4097			−1.00506
$800$	3.37346	+	2.83067i	0.119270	+	0.100079i
$801$		0			0
$802$	8.89053	+	50.4207i	0.313936	+	1.78042i
$803$	−1.06212	+	6.02357i	−0.0374813	+	0.212567i
$804$		0			0
$805$	0.869585	+	1.50617i	0.0306488	+	0.0530854i
$806$	−27.4629	+	47.5672i	−0.967340	+	1.67548i
$807$		0			0
$808$	12.5862	−	10.5611i	0.442782	−	0.371538i
$809$	19.9829	−	34.6114i	0.702562	−	1.21687i	−0.265002	−	0.964248i	$-0.585373\pi$
$809$	19.9829	−	34.6114i	0.702562	−	1.21687i	0.967564	−	0.252626i	$-0.0812941\pi$
$810$		0			0
$811$	8.21213	+	2.98897i	0.288367	+	0.104957i	0.482154	−	0.876087i	$-0.339855\pi$
$811$	8.21213	+	2.98897i	0.288367	+	0.104957i	−0.193787	+	0.981044i	$0.562077\pi$
$812$	−0.133656	+	0.758003i	−0.00469042	+	0.0266007i
$813$		0			0
$814$	79.8312	−	29.0562i	2.79808	−	1.01842i
$815$	4.89306	+	4.10576i	0.171396	+	0.143819i
$816$		0			0
$817$	13.9575	+	5.31056i	0.488312	+	0.185793i
$818$	−0.182104			−0.00636712
$819$		0			0
$820$	−0.781937	+	0.284602i	−0.0273064	+	0.00993872i
$821$	−6.66607	−	37.8052i	−0.232647	−	1.31941i	−0.847512	−	0.530776i	$-0.821900\pi$
$821$	−6.66607	−	37.8052i	−0.232647	−	1.31941i	0.614864	−	0.788633i	$-0.289211\pi$
$822$		0			0
$823$	11.3084	+	4.11592i	0.394186	+	0.143472i	0.531506	−	0.847055i	$-0.321626\pi$
$823$	11.3084	+	4.11592i	0.394186	+	0.143472i	−0.137319	+	0.990527i	$0.543849\pi$
$824$	4.29948	+	7.44691i	0.149779	+	0.259426i
$825$		0			0
$826$	6.50072	−	5.45475i	0.226189	−	0.189795i
$827$	29.6111	−	24.8467i	1.02968	−	0.864004i	0.0388667	−	0.999244i	$-0.487625\pi$
$827$	29.6111	−	24.8467i	1.02968	−	0.864004i	0.990813	+	0.135241i	$0.0431808\pi$
$828$		0			0
$829$	−16.6680	−	28.8699i	−0.578904	−	1.00269i	−0.995605	−	0.0936482i	$-0.970147\pi$
$829$	−16.6680	−	28.8699i	−0.578904	−	1.00269i	0.416701	−	0.909044i	$-0.363186\pi$
$830$	1.15998	+	0.422197i	0.0402634	+	0.0146547i
$831$		0			0
$832$	−7.28359	−	41.3073i	−0.252513	−	1.43207i
$833$	−32.4556	+	11.8129i	−1.12452	+	0.409292i
$834$		0			0
$835$	9.74092			0.337099
$836$	−2.15767	+	3.61510i	−0.0746246	+	0.125031i
$837$		0			0
$838$	−41.0736	−	34.4648i	−1.41886	−	1.19057i
$839$	27.8854	−	10.1494i	0.962710	−	0.350398i	0.187615	−	0.982243i	$-0.439924\pi$
$839$	27.8854	−	10.1494i	0.962710	−	0.350398i	0.775095	+	0.631845i	$0.217702\pi$
$840$		0			0
$841$	−3.63769	+	20.6304i	−0.125438	+	0.711392i
$842$	28.5094	+	10.3766i	0.982498	+	0.357600i
$843$		0			0
$844$	−0.835904	+	1.44783i	−0.0287730	+	0.0498363i
$845$	7.28106	−	6.10953i	0.250476	−	0.210174i
$846$		0			0
$847$	11.9768	−	20.7445i	0.411529	−	0.712789i
$848$	−15.2404	−	26.3971i	−0.523356	−	0.906479i
$849$		0			0
$850$	−7.04891	+	39.9764i	−0.241776	+	1.37118i
$851$	−2.82248	−	16.0071i	−0.0967534	−	0.548716i
$852$		0			0
$853$	15.0541	+	12.6319i	0.515444	+	0.432509i	0.863040	−	0.505136i	$-0.168558\pi$
$853$	15.0541	+	12.6319i	0.515444	+	0.432509i	−0.347596	+	0.937644i	$0.613002\pi$
$854$	−18.7401			−0.641273
$855$		0			0
$856$	−31.5607			−1.07872
$857$	15.3544	+	12.8839i	0.524497	+	0.440105i	0.866196	−	0.499704i	$-0.166558\pi$
$857$	15.3544	+	12.8839i	0.524497	+	0.440105i	−0.341699	+	0.939809i	$0.611002\pi$
$858$		0			0
$859$	8.28699	+	46.9978i	0.282748	+	1.60355i	0.713219	+	0.700941i	$0.247237\pi$
$859$	8.28699	+	46.9978i	0.282748	+	1.60355i	−0.430471	+	0.902605i	$0.641652\pi$
$860$	0.0966772	−	0.548284i	0.00329666	−	0.0186963i
$861$		0			0
$862$	−2.64274	−	4.57736i	−0.0900121	−	0.155906i
$863$	−0.260992	+	0.452051i	−0.00888427	+	0.0153880i	−0.870433	−	0.492286i	$-0.836161\pi$
$863$	−0.260992	+	0.452051i	−0.00888427	+	0.0153880i	0.861549	+	0.507674i	$0.169495\pi$
$864$		0			0
$865$	5.38120	−	4.51536i	0.182966	−	0.153527i
$866$	10.7456	−	18.6119i	0.365149	−	0.632457i
$867$		0			0
$868$	−2.12970	−	0.775147i	−0.0722867	−	0.0263102i
$869$	5.61793	−	31.8608i	0.190575	−	1.08081i
$870$		0			0
$871$	−12.1630	+	4.42696i	−0.412127	+	0.150002i
$872$	4.62171	+	3.87808i	0.156511	+	0.131328i
$873$		0			0
$874$	−5.98680	−	5.17328i	−0.202506	−	0.174989i
$875$	11.9103			0.402643
$876$		0			0
$877$	9.37851	−	3.41350i	0.316690	−	0.115266i	−0.178785	−	0.983888i	$-0.557217\pi$
$877$	9.37851	−	3.41350i	0.316690	−	0.115266i	0.495474	+	0.868623i	$0.334994\pi$
$878$	−1.10132	−	6.24589i	−0.0371677	−	0.210789i
$879$		0			0
$880$	−15.5326	−	5.65339i	−0.523602	−	0.190576i
$881$	−21.7515	−	37.6747i	−0.732827	−	1.26929i	−0.955670	−	0.294439i	$-0.904867\pi$
$881$	−21.7515	−	37.6747i	−0.732827	−	1.26929i	0.222844	−	0.974854i	$-0.428466\pi$
$882$		0			0
$883$	−18.4008	+	15.4401i	−0.619236	+	0.519601i	−0.897563	−	0.440886i	$-0.854664\pi$
$883$	−18.4008	+	15.4401i	−0.619236	+	0.519601i	0.278327	+	0.960486i	$0.410220\pi$
$884$	−4.92371	+	4.13149i	−0.165602	+	0.138957i
$885$		0			0
$886$	−19.6793	−	34.0856i	−0.661140	−	1.14513i
$887$	27.0398	+	9.84169i	0.907909	+	0.330452i	0.753417	−	0.657542i	$-0.228404\pi$
$887$	27.0398	+	9.84169i	0.907909	+	0.330452i	0.154491	+	0.987994i	$0.450626\pi$
$888$		0			0
$889$	1.94499	+	11.0306i	0.0652330	+	0.369955i
$890$	−14.1800	+	5.16111i	−0.475316	+	0.173001i
$891$		0			0
$892$	0.767942			0.0257126
$893$	−8.46703	−	15.1691i	−0.283338	−	0.507615i
$894$		0			0
$895$	4.87346	+	4.08931i	0.162902	+	0.136691i
$896$	−13.1013	+	4.76849i	−0.437684	+	0.159304i
$897$		0			0
$898$	3.45811	−	19.6119i	0.115399	−	0.654458i
$899$	22.2777	+	8.10840i	0.743001	+	0.270430i
$900$		0			0
$901$	−30.2087	+	52.3231i	−1.00640	+	1.74313i
$902$	−27.6226	+	23.1782i	−0.919733	+	0.771748i
$903$		0			0
$904$	−7.15998	+	12.4014i	−0.238137	+	0.412466i
$905$	9.01501	+	15.6145i	0.299669	+	0.519042i
$906$		0			0
$907$	−7.94625	+	45.0654i	−0.263851	+	1.49637i	0.508436	+	0.861100i	$0.330224\pi$
$907$	−7.94625	+	45.0654i	−0.263851	+	1.49637i	−0.772287	+	0.635273i	$0.780887\pi$
$908$	−0.760668	−	4.31396i	−0.0252436	−	0.143164i
$909$		0			0
$910$	−6.50072	−	5.45475i	−0.215497	−	0.180823i
$911$	−26.9067			−0.891460			−0.445730	−	0.895168i	$-0.647056\pi$
$911$	−26.9067			−0.891460			−0.445730	+	0.895168i	$0.647056\pi$
$912$		0			0
$913$	−5.44562			−0.180224
$914$	10.0296	+	8.41587i	0.331751	+	0.278372i
$915$		0			0
$916$	0.626296	+	3.55190i	0.0206934	+	0.117358i
$917$	−3.06206	+	17.3658i	−0.101118	+	0.573470i
$918$		0			0
$919$	8.96064	+	15.5203i	0.295584	+	0.511967i	0.975121	−	0.221675i	$-0.0711524\pi$
$919$	8.96064	+	15.5203i	0.295584	+	0.511967i	−0.679536	+	0.733642i	$0.737819\pi$
$920$	−1.74376	+	3.02027i	−0.0574899	+	0.0995755i
$921$		0			0
$922$	−14.5333	+	12.1949i	−0.478628	+	0.401616i
$923$	−30.7977	+	53.3432i	−1.01372	+	1.75581i
$924$		0			0
$925$	−47.9163	−	17.4401i	−1.57548	−	0.573427i
$926$	6.46909	−	36.6881i	0.212588	−	1.20564i
$927$		0			0
$928$	−2.77807	+	1.01113i	−0.0911945	+	0.0331921i
$929$	3.93763	+	3.30407i	0.129190	+	0.108403i	0.705093	−	0.709115i	$-0.250905\pi$
$929$	3.93763	+	3.30407i	0.129190	+	0.108403i	−0.575904	+	0.817518i	$0.695350\pi$
$930$		0			0
$931$	−15.9802	−	13.8088i	−0.523731	−	0.452564i
$932$	0.705194			0.0230994
$933$		0			0
$934$	−17.5317	+	6.38101i	−0.573654	+	0.208793i
$935$	5.68938	+	32.2661i	0.186063	+	1.05521i
$936$		0			0
$937$	−26.4522	−	9.62781i	−0.864155	−	0.314527i	−0.128357	−	0.991728i	$-0.540970\pi$
$937$	−26.4522	−	9.62781i	−0.864155	−	0.314527i	−0.735798	+	0.677201i	$0.763193\pi$
$938$	2.62314	+	4.54341i	0.0856486	+	0.148348i
$939$		0			0
$940$	−0.496130	+	0.416302i	−0.0161820	+	0.0135783i
$941$	25.9893	−	21.8076i	0.847228	−	0.710908i	−0.111950	−	0.993714i	$-0.535710\pi$
$941$	25.9893	−	21.8076i	0.847228	−	0.710908i	0.959177	+	0.282805i	$0.0912651\pi$
$942$		0			0
$943$	3.44949	+	5.97470i	0.112331	+	0.194563i
$944$	14.5005	+	5.27774i	0.471950	+	0.171776i
$945$		0			0
$946$	−4.18938	−	23.7591i	−0.136208	−	0.772476i
$947$	37.9577	−	13.8155i	1.23346	−	0.448943i	0.358679	−	0.933461i	$-0.383227\pi$
$947$	37.9577	−	13.8155i	1.23346	−	0.448943i	0.874781	+	0.484519i	$0.161005\pi$
$948$		0			0
$949$	−5.71007			−0.185357
$950$	−23.4458	+	8.15058i	−0.760684	+	0.264440i
$951$		0			0
$952$	23.5948	+	19.7984i	0.764712	+	0.641670i
$953$	−34.2028	+	12.4488i	−1.10794	+	0.403256i	−0.830236	−	0.557411i	$-0.811795\pi$
$953$	−34.2028	+	12.4488i	−1.10794	+	0.403256i	−0.277701	+	0.960668i	$0.589572\pi$
$954$		0			0
$955$	0.882789	−	5.00654i	0.0285664	−	0.162008i
$956$	0.142903	+	0.0520126i	0.00462183	+	0.00168221i
$957$		0			0
$958$	12.9192	−	22.3767i	0.417401	−	0.722960i
$959$	−4.50096	+	3.77676i	−0.145344	+	0.121958i
$960$		0			0
$961$	−19.4033	+	33.6075i	−0.625914	+	1.08411i
$962$	39.6548	+	68.6842i	1.27852	+	2.21447i
$963$		0			0
$964$	0.277656	−	1.57466i	0.00894269	−	0.0507165i
$965$	−2.39259	−	13.5690i	−0.0770202	−	0.436803i
$966$		0			0
$967$	−9.60195	−	8.05699i	−0.308778	−	0.259095i	0.475209	−	0.879873i	$-0.342373\pi$
$967$	−9.60195	−	8.05699i	−0.308778	−	0.259095i	−0.783987	+	0.620778i	$0.786817\pi$
$968$	48.0337			1.54386
$969$		0			0
$970$	−13.7483			−0.441433
$971$	9.94222	+	8.34251i	0.319061	+	0.267724i	0.788225	−	0.615387i	$-0.211000\pi$
$971$	9.94222	+	8.34251i	0.319061	+	0.267724i	−0.469164	+	0.883111i	$0.655445\pi$
$972$		0			0
$973$	5.80818	+	32.9398i	0.186202	+	1.05600i
$974$	−1.31323	+	7.44772i	−0.0420787	+	0.238640i
$975$		0			0
$976$	−17.0385	−	29.5115i	−0.545389	−	0.944641i
$977$	18.8610	−	32.6682i	0.603416	−	1.04515i	−0.388884	−	0.921287i	$-0.627139\pi$
$977$	18.8610	−	32.6682i	0.603416	−	1.04515i	0.992300	−	0.123860i	$-0.0395274\pi$
$978$		0			0
$979$	50.9952	−	42.7901i	1.62981	−	1.36758i
$980$	−0.393685	+	0.681882i	−0.0125758	+	0.0217819i
$981$		0			0
$982$	−22.0565	−	8.02791i	−0.703851	−	0.256181i
$983$	−1.21002	+	6.86235i	−0.0385936	+	0.218875i	−0.998005	−	0.0631351i	$-0.979890\pi$
$983$	−1.21002	+	6.86235i	−0.0385936	+	0.218875i	0.959411	+	0.282010i	$0.0910012\pi$
$984$		0			0
$985$	−19.6515	+	7.15257i	−0.626150	+	0.227900i
$986$	−20.8757	−	17.5168i	−0.664819	−	0.557849i
$987$		0			0
$988$	−3.67340	−	1.39765i	−0.116866	−	0.0444653i
$989$	−4.61587			−0.146776
$990$		0			0
$991$	19.0205	−	6.92291i	0.604207	−	0.219913i	−0.0217595	−	0.999763i	$-0.506927\pi$
$991$	19.0205	−	6.92291i	0.604207	−	0.219913i	0.625967	+	0.779850i	$0.284705\pi$
$992$	−1.51161	−	8.57277i	−0.0479937	−	0.272186i
$993$		0			0
$994$	23.4602	+	8.53882i	0.744113	+	0.270835i
$995$	6.59017	+	11.4145i	0.208923	+	0.361865i
$996$		0			0
$997$	26.3350	−	22.0977i	0.834039	−	0.699842i	−0.122176	−	0.992508i	$-0.538987\pi$
$997$	26.3350	−	22.0977i	0.834039	−	0.699842i	0.956214	+	0.292667i	$0.0945427\pi$
$998$	−18.2131	+	15.2826i	−0.576526	+	0.483762i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	513.2.y.c.244.1	yes	6
3.2	odd	2		513.2.y.a.244.1	yes	6
19.5	even	9		9747.2.a.u.1.2		3
19.6	even	9	inner	513.2.y.c.82.1	yes	6
19.14	odd	18		9747.2.a.bb.1.2		3
57.5	odd	18		9747.2.a.bd.1.2		3
57.14	even	18		9747.2.a.v.1.2		3
57.44	odd	18		513.2.y.a.82.1	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
513.2.y.a.82.1	✓	6	57.44	odd	18
513.2.y.a.244.1	yes	6	3.2	odd	2
513.2.y.c.82.1	yes	6	19.6	even	9	inner
513.2.y.c.244.1	yes	6	1.1	even	1	trivial
9747.2.a.u.1.2		3	19.5	even	9
9747.2.a.v.1.2		3	57.14	even	18
9747.2.a.bb.1.2		3	19.14	odd	18
9747.2.a.bd.1.2		3	57.5	odd	18

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:	\( N \)	\(=\)	\( 513 = 3^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	513.y (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.03209 - 0.866025i) q^{2} +(-0.0320889 - 0.181985i) q^{4} +(0.152704 - 0.866025i) q^{5} +(0.733956 + 1.27125i) q^{7} +(-1.47178 + 2.54920i) q^{8} +(-0.907604 + 0.761570i) q^{10} +(2.61334 - 4.52644i) q^{11} +(4.58512 + 1.66885i) q^{13} +(0.343426 - 1.94767i) q^{14} +(3.37939 - 1.23000i) q^{16} +(-5.46064 - 4.58202i) q^{17} +(0.819078 - 4.28125i) q^{19} -0.162504 q^{20} +(-6.61721 + 2.40847i) q^{22} +(0.233956 + 1.32683i) q^{23} +(3.97178 + 1.44561i) q^{25} +(-3.28699 - 5.69323i) q^{26} +(0.207796 - 0.174362i) q^{28} +(-2.17365 + 1.82391i) q^{29} +(-4.17752 - 7.23567i) q^{31} +(0.979055 + 0.356347i) q^{32} +(1.66772 + 9.45810i) q^{34} +(1.21301 - 0.441500i) q^{35} -12.0642 q^{37} +(-4.55303 + 3.70929i) q^{38} +(1.98293 + 1.66387i) q^{40} +(4.81180 - 1.75135i) q^{41} +(-0.594922 + 3.37397i) q^{43} +(-0.907604 - 0.330341i) q^{44} +(0.907604 - 1.57202i) q^{46} +(3.05303 - 2.56180i) q^{47} +(2.42262 - 4.19610i) q^{49} +(-2.84730 - 4.93166i) q^{50} +(0.156574 - 0.887975i) q^{52} +(-1.47178 - 8.34689i) q^{53} +(-3.52094 - 2.95442i) q^{55} -4.32089 q^{56} +3.82295 q^{58} +(3.28699 + 2.75811i) q^{59} +(-1.64543 - 9.33170i) q^{61} +(-1.95471 + 11.0857i) q^{62} +(-4.29813 - 7.44459i) q^{64} +(2.14543 - 3.71599i) q^{65} +(-2.03209 + 1.70513i) q^{67} +(-0.658633 + 1.14079i) q^{68} +(-1.63429 - 0.594831i) q^{70} +(-2.19207 + 12.4318i) q^{71} +(-1.09967 + 0.400247i) q^{73} +(12.4513 + 10.4479i) q^{74} +(-0.805407 - 0.0116794i) q^{76} +7.67230 q^{77} +(5.81655 - 2.11705i) q^{79} +(-0.549163 - 3.11446i) q^{80} +(-6.48293 - 2.35959i) q^{82} +(-0.520945 - 0.902302i) q^{83} +(-4.80200 + 4.02936i) q^{85} +(3.53596 - 2.96702i) q^{86} +(7.69253 + 13.3239i) q^{88} +(11.9684 + 4.35613i) q^{89} +(1.24376 + 7.05369i) q^{91} +(0.233956 - 0.0851529i) q^{92} -5.36959 q^{94} +(-3.58260 - 1.36310i) q^{95} +(8.88919 + 7.45891i) q^{97} +(-6.13429 + 2.23270i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} + 9 q^{4} + 3 q^{5} + 9 q^{7} + 6 q^{8} - 9 q^{10} + 9 q^{11} + 6 q^{13} + 24 q^{14} + 9 q^{16} - 24 q^{17} - 12 q^{19} - 6 q^{20} - 9 q^{22} + 6 q^{23} + 9 q^{25} - 12 q^{26} + 42 q^{28}+ \cdots - 27 q^{98}+O(q^{100}) \) 6 * q + 3 * q^2 + 9 * q^4 + 3 * q^5 + 9 * q^7 + 6 * q^8 - 9 * q^10 + 9 * q^11 + 6 * q^13 + 24 * q^14 + 9 * q^16 - 24 * q^17 - 12 * q^19 - 6 * q^20 - 9 * q^22 + 6 * q^23 + 9 * q^25 - 12 * q^26 + 42 * q^28 - 12 * q^29 + 9 * q^32 - 18 * q^34 + 15 * q^35 - 54 * q^37 - 15 * q^38 - 9 * q^40 - 6 * q^41 + 15 * q^43 - 9 * q^44 + 9 * q^46 + 6 * q^47 - 12 * q^49 - 15 * q^50 - 21 * q^52 + 6 * q^53 - 18 * q^55 + 66 * q^56 - 18 * q^58 + 12 * q^59 + 6 * q^61 + 24 * q^62 - 12 * q^64 - 3 * q^65 - 3 * q^67 - 33 * q^68 - 24 * q^71 - 21 * q^73 - 3 * q^74 - 9 * q^76 + 54 * q^77 + 33 * q^79 - 15 * q^80 - 18 * q^82 + 9 * q^85 - 12 * q^86 - 9 * q^88 + 15 * q^89 + 15 * q^91 + 6 * q^92 - 18 * q^94 - 15 * q^95 + 45 * q^97 - 27 * q^98

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