LMFDB - Embedded newform 650.2.o.g.549.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [650,2,Mod(399,650)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(650, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("650.399"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,4,0,0,0,0,28,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.3317760000.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 25x^{4} + 625 $ x^8 - 25*x^4 + 625
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			549.3
Root			$-2.15988 - 0.578737i$ of defining polynomial
Character	$\chi$	$=$	650.549
Dual form			650.2.o.g.399.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 0.500000i) q^{2} +(-2.73861 + 1.58114i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.58114 + 2.73861i) q^{6} +(0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(3.50000 - 6.06218i) q^{9} +(-1.08114 - 1.87259i) q^{11} +3.16228i q^{12} +(1.87259 + 3.08114i) q^{13} +1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(4.47066 + 2.58114i) q^{17} -7.00000i q^{18} +(-0.918861 + 1.59151i) q^{19} -3.16228 q^{21} +(-1.87259 - 1.08114i) q^{22} +(-5.19615 + 3.00000i) q^{23} +(1.58114 + 2.73861i) q^{24} +(3.16228 + 1.73205i) q^{26} +12.6491i q^{27} +(0.866025 - 0.500000i) q^{28} +(5.16228 + 8.94133i) q^{29} +7.16228 q^{31} +(-0.866025 - 0.500000i) q^{32} +(5.92164 + 3.41886i) q^{33} +5.16228 q^{34} +(-3.50000 - 6.06218i) q^{36} +(-0.140537 + 0.0811388i) q^{37} +1.83772i q^{38} +(-10.0000 - 5.47723i) q^{39} +(5.16228 + 8.94133i) q^{41} +(-2.73861 + 1.58114i) q^{42} +(1.73205 + 1.00000i) q^{43} -2.16228 q^{44} +(-3.00000 + 5.19615i) q^{46} -3.00000i q^{47} +(2.73861 + 1.58114i) q^{48} +(-3.00000 - 5.19615i) q^{49} -16.3246 q^{51} +(3.60464 - 0.0811388i) q^{52} +2.16228i q^{53} +(6.32456 + 10.9545i) q^{54} +(0.500000 - 0.866025i) q^{56} -5.81139i q^{57} +(8.94133 + 5.16228i) q^{58} +(-5.16228 + 8.94133i) q^{59} +(3.74342 - 6.48379i) q^{61} +(6.20271 - 3.58114i) q^{62} +(6.06218 - 3.50000i) q^{63} -1.00000 q^{64} +6.83772 q^{66} +(-2.01312 + 1.16228i) q^{67} +(4.47066 - 2.58114i) q^{68} +(9.48683 - 16.4317i) q^{69} +(2.16228 - 3.74517i) q^{71} +(-6.06218 - 3.50000i) q^{72} -2.83772i q^{73} +(-0.0811388 + 0.140537i) q^{74} +(0.918861 + 1.59151i) q^{76} -2.16228i q^{77} +(-11.3989 + 0.256584i) q^{78} +13.4868 q^{79} +(-9.50000 - 16.4545i) q^{81} +(8.94133 + 5.16228i) q^{82} -9.48683i q^{83} +(-1.58114 + 2.73861i) q^{84} +2.00000 q^{86} +(-28.2750 - 16.3246i) q^{87} +(-1.87259 + 1.08114i) q^{88} +(-3.66228 - 6.34325i) q^{89} +(0.0811388 + 3.60464i) q^{91} +6.00000i q^{92} +(-19.6147 + 11.3246i) q^{93} +(-1.50000 - 2.59808i) q^{94} +3.16228 q^{96} +(6.48379 + 3.74342i) q^{97} +(-5.19615 - 3.00000i) q^{98} -15.1359 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} + 28 q^{9} + 4 q^{11} + 8 q^{14} - 4 q^{16} - 20 q^{19} + 16 q^{29} + 32 q^{31} + 16 q^{34} - 28 q^{36} - 80 q^{39} + 16 q^{41} + 8 q^{44} - 24 q^{46} - 24 q^{49} - 80 q^{51} + 4 q^{56} - 16 q^{59}+ \cdots + 56 q^{99}+O(q^{100}) $ 8 * q + 4 * q^4 + 28 * q^9 + 4 * q^11 + 8 * q^14 - 4 * q^16 - 20 * q^19 + 16 * q^29 + 32 * q^31 + 16 * q^34 - 28 * q^36 - 80 * q^39 + 16 * q^41 + 8 * q^44 - 24 * q^46 - 24 * q^49 - 80 * q^51 + 4 * q^56 - 16 * q^59 - 8 * q^61 - 8 * q^64 + 80 * q^66 - 8 * q^71 + 12 * q^74 + 20 * q^76 + 32 * q^79 - 76 * q^81 + 16 * q^86 - 4 * q^89 - 12 * q^91 - 12 * q^94 + 56 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	−2.73861	+	1.58114i	−1.58114	+	0.912871i	−0.586445	+	0.809989i	$0.699473\pi$
$3$	−2.73861	+	1.58114i	−1.58114	+	0.912871i	−0.994694	+	0.102882i	$0.967194\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−1.58114	+	2.73861i	−0.645497	+	1.11803i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i	0.654654	−	0.755929i	$-0.272814\pi$
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i	−0.327327	+	0.944911i	$0.606148\pi$
$8$		−	1.00000i		−	0.353553i
$9$	3.50000	−	6.06218i	1.16667	−	2.02073i
$10$		0			0
$11$	−1.08114	−	1.87259i	−0.325976	−	0.564606i	0.655734	−	0.754992i	$-0.272359\pi$
$11$	−1.08114	−	1.87259i	−0.325976	−	0.564606i	−0.981709	+	0.190386i	$0.939026\pi$
$12$			3.16228i			0.912871i
$13$	1.87259	+	3.08114i	0.519362	+	0.854554i
$13$	1.87259	+	3.08114i	0.519362	+	0.854554i
$14$	1.00000			0.267261
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	4.47066	+	2.58114i	1.08430	+	0.626018i	0.932052	−	0.362325i	$-0.118017\pi$
$17$	4.47066	+	2.58114i	1.08430	+	0.626018i	0.152243	+	0.988343i	$0.451350\pi$
$18$		−	7.00000i		−	1.64992i
$19$	−0.918861	+	1.59151i	−0.210801	+	0.365118i	−0.951966	−	0.306205i	$-0.900941\pi$
$19$	−0.918861	+	1.59151i	−0.210801	+	0.365118i	0.741164	+	0.671324i	$0.234274\pi$
$20$		0			0
$21$	−3.16228			−0.690066
$22$	−1.87259	−	1.08114i	−0.399237	−	0.230500i
$23$	−5.19615	+	3.00000i	−1.08347	+	0.625543i	−0.931831	−	0.362892i	$-0.881789\pi$
$23$	−5.19615	+	3.00000i	−1.08347	+	0.625543i	−0.151642	+	0.988436i	$0.548456\pi$
$24$	1.58114	+	2.73861i	0.322749	+	0.559017i
$25$		0			0
$26$	3.16228	+	1.73205i	0.620174	+	0.339683i
$27$			12.6491i			2.43432i
$28$	0.866025	−	0.500000i	0.163663	−	0.0944911i
$29$	5.16228	+	8.94133i	0.958611	+	1.66036i	0.725880	+	0.687822i	$0.241433\pi$
$29$	5.16228	+	8.94133i	0.958611	+	1.66036i	0.232731	+	0.972541i	$0.425234\pi$
$30$		0			0
$31$	7.16228			1.28638			0.643192	−	0.765705i	$-0.277610\pi$
$31$	7.16228			1.28638			0.643192	+	0.765705i	$0.277610\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	5.92164	+	3.41886i	1.03083	+	0.595147i
$34$	5.16228			0.885323
$35$		0			0
$36$	−3.50000	−	6.06218i	−0.583333	−	1.01036i
$37$	−0.140537	+	0.0811388i	−0.0231041	+	0.0133391i	−0.511508	−	0.859279i	$-0.670913\pi$
$37$	−0.140537	+	0.0811388i	−0.0231041	+	0.0133391i	0.488403	+	0.872618i	$0.337579\pi$
$38$			1.83772i			0.298118i
$39$	−10.0000	−	5.47723i	−1.60128	−	0.877058i
$40$		0			0
$41$	5.16228	+	8.94133i	0.806212	+	1.39640i	0.915470	+	0.402387i	$0.131819\pi$
$41$	5.16228	+	8.94133i	0.806212	+	1.39640i	−0.109257	+	0.994014i	$0.534847\pi$
$42$	−2.73861	+	1.58114i	−0.422577	+	0.243975i
$43$	1.73205	+	1.00000i	0.264135	+	0.152499i	0.626219	−	0.779647i	$-0.284601\pi$
$43$	1.73205	+	1.00000i	0.264135	+	0.152499i	−0.362084	+	0.932145i	$0.617935\pi$
$44$	−2.16228			−0.325976
$45$		0			0
$46$	−3.00000	+	5.19615i	−0.442326	+	0.766131i
$47$		−	3.00000i		−	0.437595i	−0.975770	−	0.218797i	$-0.929787\pi$
$47$		−	3.00000i		−	0.437595i	0.975770	−	0.218797i	$-0.0702134\pi$
$48$	2.73861	+	1.58114i	0.395285	+	0.228218i
$49$	−3.00000	−	5.19615i	−0.428571	−	0.742307i
$50$		0			0
$51$	−16.3246			−2.28589
$52$	3.60464	−	0.0811388i	0.499873	−	0.0112519i
$53$			2.16228i			0.297012i	0.988912	+	0.148506i	$0.0474464\pi$
$53$			2.16228i			0.297012i	−0.988912	+	0.148506i	$0.952554\pi$
$54$	6.32456	+	10.9545i	0.860663	+	1.49071i
$55$		0			0
$56$	0.500000	−	0.866025i	0.0668153	−	0.115728i
$57$		−	5.81139i		−	0.769737i
$58$	8.94133	+	5.16228i	1.17405	+	0.677840i
$59$	−5.16228	+	8.94133i	−0.672071	+	1.16406i	0.305244	+	0.952274i	$0.401262\pi$
$59$	−5.16228	+	8.94133i	−0.672071	+	1.16406i	−0.977316	+	0.211788i	$0.932071\pi$
$60$		0			0
$61$	3.74342	−	6.48379i	0.479295	−	0.830164i	−0.520423	−	0.853909i	$-0.674226\pi$
$61$	3.74342	−	6.48379i	0.479295	−	0.830164i	0.999718	+	0.0237449i	$0.00755894\pi$
$62$	6.20271	−	3.58114i	0.787746	−	0.454805i
$63$	6.06218	−	3.50000i	0.763763	−	0.440959i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	6.83772			0.841665
$67$	−2.01312	+	1.16228i	−0.245942	+	0.141995i	−0.617905	−	0.786253i	$-0.712018\pi$
$67$	−2.01312	+	1.16228i	−0.245942	+	0.141995i	0.371963	+	0.928248i	$0.378685\pi$
$68$	4.47066	−	2.58114i	0.542148	−	0.313009i
$69$	9.48683	−	16.4317i	1.14208	−	1.97814i
$70$		0			0
$71$	2.16228	−	3.74517i	0.256615	−	0.444470i	−0.708718	−	0.705492i	$-0.750726\pi$
$71$	2.16228	−	3.74517i	0.256615	−	0.444470i	0.965333	+	0.261022i	$0.0840594\pi$
$72$	−6.06218	−	3.50000i	−0.714435	−	0.412479i
$73$		−	2.83772i		−	0.332130i	−0.986115	−	0.166065i	$-0.946894\pi$
$73$		−	2.83772i		−	0.332130i	0.986115	−	0.166065i	$-0.0531062\pi$
$74$	−0.0811388	+	0.140537i	−0.00943220	+	0.0163370i
$75$		0			0
$76$	0.918861	+	1.59151i	0.105401	+	0.182559i
$77$		−	2.16228i		−	0.246414i
$78$	−11.3989	+	0.256584i	−1.29067	+	0.0290524i
$79$	13.4868			1.51739			0.758694	−	0.651448i	$-0.225838\pi$
$79$	13.4868			1.51739			0.758694	+	0.651448i	$0.225838\pi$
$80$		0			0
$81$	−9.50000	−	16.4545i	−1.05556	−	1.82828i
$82$	8.94133	+	5.16228i	0.987404	+	0.570078i
$83$		−	9.48683i		−	1.04132i	−0.853766	−	0.520658i	$-0.825687\pi$
$83$		−	9.48683i		−	1.04132i	0.853766	−	0.520658i	$-0.174313\pi$
$84$	−1.58114	+	2.73861i	−0.172516	+	0.298807i
$85$		0			0
$86$	2.00000			0.215666
$87$	−28.2750	−	16.3246i	−3.03139	−	1.75018i
$88$	−1.87259	+	1.08114i	−0.199618	+	0.115250i
$89$	−3.66228	−	6.34325i	−0.388201	−	0.672383i	0.604007	−	0.796979i	$-0.293570\pi$
$89$	−3.66228	−	6.34325i	−0.388201	−	0.672383i	−0.992208	+	0.124596i	$0.960237\pi$
$90$		0			0
$91$	0.0811388	+	3.60464i	0.00850566	+	0.377869i
$92$			6.00000i			0.625543i
$93$	−19.6147	+	11.3246i	−2.03395	+	1.17430i
$94$	−1.50000	−	2.59808i	−0.154713	−	0.267971i
$95$		0			0
$96$	3.16228			0.322749
$97$	6.48379	+	3.74342i	0.658329	+	0.380086i	0.791640	−	0.610988i	$-0.209228\pi$
$97$	6.48379	+	3.74342i	0.658329	+	0.380086i	−0.133311	+	0.991074i	$0.542561\pi$
$98$	−5.19615	−	3.00000i	−0.524891	−	0.303046i
$99$	−15.1359			−1.52122
$100$		0			0
$101$	5.58114	+	9.66682i	0.555344	+	0.961884i	0.997877	+	0.0651317i	$0.0207468\pi$
$101$	5.58114	+	9.66682i	0.555344	+	0.961884i	−0.442533	+	0.896752i	$0.645920\pi$
$102$	−14.1375	+	8.16228i	−1.39982	+	0.808186i
$103$		−	0.675445i		−	0.0665535i	−0.999446	−	0.0332768i	$-0.989406\pi$
$103$		−	0.675445i		−	0.0665535i	0.999446	−	0.0332768i	$-0.0105943\pi$
$104$	3.08114	−	1.87259i	0.302131	−	0.183622i
$105$		0			0
$106$	1.08114	+	1.87259i	0.105009	+	0.181882i
$107$	−3.01969	+	1.74342i	−0.291924	+	0.168542i	−0.638809	−	0.769365i	$-0.720573\pi$
$107$	−3.01969	+	1.74342i	−0.291924	+	0.168542i	0.346885	+	0.937908i	$0.387239\pi$
$108$	10.9545	+	6.32456i	1.05409	+	0.608581i
$109$	−10.6491			−1.02000			−0.510000	−	0.860174i	$-0.670355\pi$
$109$	−10.6491			−1.02000			−0.510000	+	0.860174i	$0.670355\pi$
$110$		0			0
$111$	0.256584	−	0.444416i	0.0243538	−	0.0421821i
$112$		−	1.00000i		−	0.0944911i
$113$	−7.49035	−	4.32456i	−0.704633	−	0.406820i	0.104438	−	0.994531i	$-0.466696\pi$
$113$	−7.49035	−	4.32456i	−0.704633	−	0.406820i	−0.809071	+	0.587711i	$0.800029\pi$
$114$	−2.90569	−	5.03281i	−0.272143	−	0.471366i
$115$		0			0
$116$	10.3246			0.958611
$117$	25.2325	−	0.567972i	2.33274	−	0.0525090i
$118$			10.3246i			0.950452i
$119$	2.58114	+	4.47066i	0.236613	+	0.409825i
$120$		0			0
$121$	3.16228	−	5.47723i	0.287480	−	0.497930i
$122$		−	7.48683i		−	0.677826i
$123$	−28.2750	−	16.3246i	−2.54947	−	1.47194i
$124$	3.58114	−	6.20271i	0.321596	−	0.557020i
$125$		0			0
$126$	3.50000	−	6.06218i	0.311805	−	0.540062i
$127$	2.87915	−	1.66228i	0.255483	−	0.147503i	−0.366789	−	0.930304i	$-0.619543\pi$
$127$	2.87915	−	1.66228i	0.255483	−	0.147503i	0.622272	+	0.782801i	$0.286210\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−6.32456			−0.556846
$130$		0			0
$131$	−10.8114			−0.944595			−0.472298	−	0.881439i	$-0.656575\pi$
$131$	−10.8114			−0.944595			−0.472298	+	0.881439i	$0.656575\pi$
$132$	5.92164	−	3.41886i	0.515413	−	0.297574i
$133$	−1.59151	+	0.918861i	−0.138002	+	0.0796754i
$134$	−1.16228	+	2.01312i	−0.100405	+	0.173907i
$135$		0			0
$136$	2.58114	−	4.47066i	0.221331	−	0.383356i
$137$	−13.4120	−	7.74342i	−1.14586	−	0.661565i	−0.197988	−	0.980204i	$-0.563441\pi$
$137$	−13.4120	−	7.74342i	−1.14586	−	0.661565i	−0.947876	+	0.318640i	$0.896774\pi$
$138$		−	18.9737i		−	1.61515i
$139$	−6.08114	+	10.5328i	−0.515795	+	0.893384i	0.484036	+	0.875048i	$0.339170\pi$
$139$	−6.08114	+	10.5328i	−0.515795	+	0.893384i	−0.999832	+	0.0183361i	$0.994163\pi$
$140$		0			0
$141$	4.74342	+	8.21584i	0.399468	+	0.691898i
$142$		−	4.32456i		−	0.362909i
$143$	3.74517	−	6.83772i	0.313187	−	0.571799i
$144$	−7.00000			−0.583333
$145$		0			0
$146$	−1.41886	−	2.45754i	−0.117426	−	0.203387i
$147$	16.4317	+	9.48683i	1.35526	+	0.782461i
$148$			0.162278i			0.0133391i
$149$	8.16228	−	14.1375i	0.668680	−	1.15819i	−0.309594	−	0.950869i	$-0.600193\pi$
$149$	8.16228	−	14.1375i	0.668680	−	1.15819i	0.978273	−	0.207319i	$-0.0664736\pi$
$150$		0			0
$151$	−4.83772			−0.393688			−0.196844	−	0.980435i	$-0.563069\pi$
$151$	−4.83772			−0.393688			−0.196844	+	0.980435i	$0.563069\pi$
$152$	1.59151	+	0.918861i	0.129089	+	0.0745295i
$153$	31.2946	−	18.0680i	2.53002	−	1.46071i
$154$	−1.08114	−	1.87259i	−0.0871206	−	0.150897i
$155$		0			0
$156$	−9.74342	+	5.92164i	−0.780098	+	0.474111i
$157$		−	12.1623i		−	0.970655i	−0.874332	−	0.485328i	$-0.838700\pi$
$157$		−	12.1623i		−	0.970655i	0.874332	−	0.485328i	$-0.161300\pi$
$158$	11.6799	−	6.74342i	0.929206	−	0.536477i
$159$	−3.41886	−	5.92164i	−0.271133	−	0.469617i
$160$		0			0
$161$	−6.00000			−0.472866
$162$	−16.4545	−	9.50000i	−1.29279	−	0.746390i
$163$	15.1440	+	8.74342i	1.18617	+	0.684837i	0.957434	−	0.288651i	$-0.0932066\pi$
$163$	15.1440	+	8.74342i	1.18617	+	0.684837i	0.228738	+	0.973488i	$0.426540\pi$
$164$	10.3246			0.806212
$165$		0			0
$166$	−4.74342	−	8.21584i	−0.368161	−	0.637673i
$167$	11.5394	−	6.66228i	0.892946	−	0.515543i	0.0180409	−	0.999837i	$-0.494257\pi$
$167$	11.5394	−	6.66228i	0.892946	−	0.515543i	0.874905	+	0.484295i	$0.160924\pi$
$168$			3.16228i			0.243975i
$169$	−5.98683	+	11.5394i	−0.460526	+	0.887646i
$170$		0			0
$171$	6.43203	+	11.1406i	0.491869	+	0.851943i
$172$	1.73205	−	1.00000i	0.132068	−	0.0762493i
$173$	1.87259	+	1.08114i	0.142370	+	0.0821975i	0.569493	−	0.821996i	$-0.307140\pi$
$173$	1.87259	+	1.08114i	0.142370	+	0.0821975i	−0.427123	+	0.904194i	$0.640473\pi$
$174$	−32.6491			−2.47512
$175$		0			0
$176$	−1.08114	+	1.87259i	−0.0814939	+	0.141152i
$177$		−	32.6491i		−	2.45406i
$178$	−6.34325	−	3.66228i	−0.475447	−	0.274499i
$179$	11.1623	+	19.3336i	0.834308	+	1.44506i	0.894593	+	0.446882i	$0.147466\pi$
$179$	11.1623	+	19.3336i	0.834308	+	1.44506i	−0.0602850	+	0.998181i	$0.519201\pi$
$180$		0			0
$181$	9.81139			0.729275			0.364637	−	0.931150i	$-0.381193\pi$
$181$	9.81139			0.729275			0.364637	+	0.931150i	$0.381193\pi$
$182$	1.87259	+	3.08114i	0.138805	+	0.228389i
$183$			23.6754i			1.75014i
$184$	3.00000	+	5.19615i	0.221163	+	0.383065i
$185$		0			0
$186$	−11.3246	+	19.6147i	−0.830357	+	1.43822i
$187$		−	11.1623i		−	0.816267i
$188$	−2.59808	−	1.50000i	−0.189484	−	0.109399i
$189$	−6.32456	+	10.9545i	−0.460044	+	0.796819i
$190$		0			0
$191$	−4.74342	+	8.21584i	−0.343222	+	0.594477i	−0.985029	−	0.172389i	$-0.944852\pi$
$191$	−4.74342	+	8.21584i	−0.343222	+	0.594477i	0.641807	+	0.766866i	$0.278185\pi$
$192$	2.73861	−	1.58114i	0.197642	−	0.114109i
$193$	3.46410	−	2.00000i	0.249351	−	0.143963i	−0.370116	−	0.928986i	$-0.620682\pi$
$193$	3.46410	−	2.00000i	0.249351	−	0.143963i	0.619467	+	0.785022i	$0.287349\pi$
$194$	7.48683			0.537523
$195$		0			0
$196$	−6.00000			−0.428571
$197$	−16.0101	+	9.24342i	−1.14067	+	0.658566i	−0.946596	−	0.322421i	$-0.895503\pi$
$197$	−16.0101	+	9.24342i	−1.14067	+	0.658566i	−0.194074	+	0.980987i	$0.562170\pi$
$198$	−13.1081	+	7.56797i	−0.931553	+	0.537832i
$199$	−0.675445	+	1.16990i	−0.0478810	+	0.0829323i	−0.888973	−	0.457960i	$-0.848580\pi$
$199$	−0.675445	+	1.16990i	−0.0478810	+	0.0829323i	0.841092	+	0.540893i	$0.181913\pi$
$200$		0			0
$201$	3.67544	−	6.36606i	0.259246	−	0.449027i
$202$	9.66682	+	5.58114i	0.680155	+	0.392688i
$203$			10.3246i			0.724642i
$204$	−8.16228	+	14.1375i	−0.571474	+	0.989822i
$205$		0			0
$206$	−0.337722	−	0.584952i	−0.0235302	−	0.0407556i
$207$			42.0000i			2.91920i
$208$	1.73205	−	3.16228i	0.120096	−	0.219265i
$209$	3.97367			0.274864
$210$		0			0
$211$	−5.91886	−	10.2518i	−0.407471	−	0.705761i	0.587134	−	0.809489i	$-0.300256\pi$
$211$	−5.91886	−	10.2518i	−0.407471	−	0.705761i	−0.994606	+	0.103729i	$0.966923\pi$
$212$	1.87259	+	1.08114i	0.128610	+	0.0742529i
$213$			13.6754i			0.937026i
$214$	−1.74342	+	3.01969i	−0.119177	+	0.206421i
$215$		0			0
$216$	12.6491			0.860663
$217$	6.20271	+	3.58114i	0.421068	+	0.243104i
$218$	−9.22240	+	5.32456i	−0.624620	+	0.360624i
$219$	4.48683	+	7.77142i	0.303192	+	0.525144i
$220$		0			0
$221$	0.418861	+	18.6081i	0.0281757	+	1.25172i
$222$		−	0.513167i		−	0.0344415i
$223$	−2.87915	+	1.66228i	−0.192802	+	0.111314i	−0.593294	−	0.804986i	$-0.702173\pi$
$223$	−2.87915	+	1.66228i	−0.192802	+	0.111314i	0.400492	+	0.916300i	$0.368839\pi$
$224$	−0.500000	−	0.866025i	−0.0334077	−	0.0578638i
$225$		0			0
$226$	−8.64911			−0.575330
$227$	−8.94133	−	5.16228i	−0.593457	−	0.342632i	0.173006	−	0.984921i	$-0.444652\pi$
$227$	−8.94133	−	5.16228i	−0.593457	−	0.342632i	−0.766463	+	0.642288i	$0.777985\pi$
$228$	−5.03281	−	2.90569i	−0.333306	−	0.192434i
$229$	−2.83772			−0.187522			−0.0937610	−	0.995595i	$-0.529889\pi$
$229$	−2.83772			−0.187522			−0.0937610	+	0.995595i	$0.529889\pi$
$230$		0			0
$231$	3.41886	+	5.92164i	0.224945	+	0.389615i
$232$	8.94133	−	5.16228i	0.587027	−	0.338920i
$233$		−	9.48683i		−	0.621503i	−0.950491	−	0.310752i	$-0.899419\pi$
$233$		−	9.48683i		−	0.621503i	0.950491	−	0.310752i	$-0.100581\pi$
$234$	21.5680	−	13.1081i	1.40994	−	0.856904i
$235$		0			0
$236$	5.16228	+	8.94133i	0.336036	+	0.582031i
$237$	−36.9352	+	21.3246i	−2.39920	+	1.38518i
$238$	4.47066	+	2.58114i	0.289790	+	0.167310i
$239$	−11.1623			−0.722028			−0.361014	−	0.932560i	$-0.617569\pi$
$239$	−11.1623			−0.722028			−0.361014	+	0.932560i	$0.617569\pi$
$240$		0			0
$241$	12.9868	−	22.4939i	0.836555	−	1.44896i	−0.0562022	−	0.998419i	$-0.517899\pi$
$241$	12.9868	−	22.4939i	0.836555	−	1.44896i	0.892758	−	0.450537i	$-0.148768\pi$
$242$		−	6.32456i		−	0.406558i
$243$	19.1703	+	11.0680i	1.22977	+	0.710011i
$244$	−3.74342	−	6.48379i	−0.239648	−	0.415082i
$245$		0			0
$246$	−32.6491			−2.08163
$247$	−6.62432	+	0.149111i	−0.421496	+	0.00948768i
$248$		−	7.16228i		−	0.454805i
$249$	15.0000	+	25.9808i	0.950586	+	1.64646i
$250$		0			0
$251$	−6.24342	+	10.8139i	−0.394081	+	0.682568i	−0.992983	−	0.118254i	$-0.962270\pi$
$251$	−6.24342	+	10.8139i	−0.394081	+	0.682568i	0.598902	+	0.800822i	$0.295604\pi$
$252$		−	7.00000i		−	0.440959i
$253$	11.2355	+	6.48683i	0.706371	+	0.407824i
$254$	1.66228	−	2.87915i	0.104301	−	0.180654i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$257$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$258$	−5.47723	+	3.16228i	−0.340997	+	0.196875i
$259$	−0.162278			−0.0100834
$260$		0			0
$261$	72.2719			4.47352
$262$	−9.36294	+	5.40569i	−0.578444	+	0.333965i
$263$	10.0884	−	5.82456i	0.622079	−	0.359157i	−0.155599	−	0.987820i	$-0.549731\pi$
$263$	10.0884	−	5.82456i	0.622079	−	0.359157i	0.777678	+	0.628663i	$0.216397\pi$
$264$	3.41886	−	5.92164i	0.210416	−	0.364452i
$265$		0			0
$266$	−0.918861	+	1.59151i	−0.0563390	+	0.0975820i
$267$	20.0591	+	11.5811i	1.22760	+	0.708754i
$268$			2.32456i			0.141995i
$269$	1.25658	−	2.17647i	0.0766152	−	0.132702i	−0.825172	−	0.564881i	$-0.808922\pi$
$269$	1.25658	−	2.17647i	0.0766152	−	0.132702i	0.901788	+	0.432180i	$0.142255\pi$
$270$		0			0
$271$	−3.16228	−	5.47723i	−0.192095	−	0.332718i	0.753850	−	0.657047i	$-0.228195\pi$
$271$	−3.16228	−	5.47723i	−0.192095	−	0.332718i	−0.945944	+	0.324329i	$0.894861\pi$
$272$		−	5.16228i		−	0.313009i
$273$	−5.92164	−	9.74342i	−0.358394	−	0.589698i
$274$	−15.4868			−0.935594
$275$		0			0
$276$	−9.48683	−	16.4317i	−0.571040	−	0.989071i
$277$	−1.31044	−	0.756584i	−0.0787368	−	0.0454587i	0.460115	−	0.887859i	$-0.347808\pi$
$277$	−1.31044	−	0.756584i	−0.0787368	−	0.0454587i	−0.538851	+	0.842401i	$0.681142\pi$
$278$			12.1623i			0.729445i
$279$	25.0680	−	43.4190i	1.50078	−	2.59943i
$280$		0			0
$281$	−18.9737			−1.13187			−0.565937	−	0.824448i	$-0.691485\pi$
$281$	−18.9737			−1.13187			−0.565937	+	0.824448i	$0.691485\pi$
$282$	8.21584	+	4.74342i	0.489246	+	0.282466i
$283$	19.0526	−	11.0000i	1.13256	−	0.653882i	0.187980	−	0.982173i	$-0.439806\pi$
$283$	19.0526	−	11.0000i	1.13256	−	0.653882i	0.944577	+	0.328291i	$0.106473\pi$
$284$	−2.16228	−	3.74517i	−0.128308	−	0.222235i
$285$		0			0
$286$	−0.175445	−	7.79423i	−0.0103743	−	0.460882i
$287$			10.3246i			0.609439i
$288$	−6.06218	+	3.50000i	−0.357217	+	0.206239i
$289$	4.82456	+	8.35637i	0.283797	+	0.491551i
$290$		0			0
$291$	−23.6754			−1.38788
$292$	−2.45754	−	1.41886i	−0.143817	−	0.0830326i
$293$	−18.9120	−	10.9189i	−1.10485	−	0.637887i	−0.167361	−	0.985896i	$-0.553525\pi$
$293$	−18.9120	−	10.9189i	−1.10485	−	0.637887i	−0.937491	+	0.348009i	$0.886858\pi$
$294$	18.9737			1.10657
$295$		0			0
$296$	0.0811388	+	0.140537i	0.00471610	+	0.00816852i
$297$	23.6866	−	13.6754i	1.37443	−	0.793530i
$298$		−	16.3246i		−	0.945656i
$299$	−18.9737	−	10.3923i	−1.09728	−	0.601003i
$300$		0			0
$301$	1.00000	+	1.73205i	0.0576390	+	0.0998337i
$302$	−4.18959	+	2.41886i	−0.241084	+	0.139190i
$303$	−30.5692	−	17.6491i	−1.75615	−	1.01391i
$304$	1.83772			0.105401
$305$		0			0
$306$	18.0680	−	31.2946i	1.03288	−	1.78900i
$307$			15.6754i			0.894645i	0.894373	+	0.447322i	$0.147622\pi$
$307$			15.6754i			0.894645i	−0.894373	+	0.447322i	$0.852378\pi$
$308$	−1.87259	−	1.08114i	−0.106701	−	0.0616036i
$309$	1.06797	+	1.84978i	0.0607548	+	0.105230i
$310$		0			0
$311$	−3.48683			−0.197720			−0.0988601	−	0.995101i	$-0.531520\pi$
$311$	−3.48683			−0.197720			−0.0988601	+	0.995101i	$0.531520\pi$
$312$	−5.47723	+	10.0000i	−0.310087	+	0.566139i
$313$			8.32456i			0.470532i	0.971931	+	0.235266i	$0.0755961\pi$
$313$			8.32456i			0.470532i	−0.971931	+	0.235266i	$0.924404\pi$
$314$	−6.08114	−	10.5328i	−0.343179	−	0.594403i
$315$		0			0
$316$	6.74342	−	11.6799i	0.379347	−	0.657048i
$317$			12.4868i			0.701330i	0.936501	+	0.350665i	$0.114044\pi$
$317$			12.4868i			0.701330i	−0.936501	+	0.350665i	$0.885956\pi$
$318$	−5.92164	−	3.41886i	−0.332069	−	0.191720i
$319$	11.1623	−	19.3336i	0.624968	−	1.08248i
$320$		0			0
$321$	5.51317	−	9.54909i	0.307715	−	0.532978i
$322$	−5.19615	+	3.00000i	−0.289570	+	0.167183i
$323$	−8.21584	+	4.74342i	−0.457141	+	0.263931i
$324$	−19.0000			−1.05556
$325$		0			0
$326$	17.4868			0.968506
$327$	29.1638	−	16.8377i	1.61276	−	0.931128i
$328$	8.94133	−	5.16228i	0.493702	−	0.285039i
$329$	1.50000	−	2.59808i	0.0826977	−	0.143237i
$330$		0			0
$331$	12.3246	−	21.3468i	0.677419	−	1.17332i	−0.298337	−	0.954461i	$-0.596432\pi$
$331$	12.3246	−	21.3468i	0.677419	−	1.17332i	0.975756	−	0.218863i	$-0.0702348\pi$
$332$	−8.21584	−	4.74342i	−0.450903	−	0.260329i
$333$			1.13594i			0.0622493i
$334$	6.66228	−	11.5394i	0.364544	−	0.631408i
$335$		0			0
$336$	1.58114	+	2.73861i	0.0862582	+	0.149404i
$337$			17.4868i			0.952568i	0.879291	+	0.476284i	$0.158017\pi$
$337$			17.4868i			0.952568i	−0.879291	+	0.476284i	$0.841983\pi$
$338$	0.584952	+	12.9868i	0.0318172	+	0.706391i
$339$	27.3509			1.48550
$340$		0			0
$341$	−7.74342	−	13.4120i	−0.419330	−	0.726300i
$342$	11.1406	+	6.43203i	0.602415	+	0.347804i
$343$		−	13.0000i		−	0.701934i
$344$	1.00000	−	1.73205i	0.0539164	−	0.0933859i
$345$		0			0
$346$	2.16228			0.116245
$347$	−2.17647	−	1.25658i	−0.116839	−	0.0674569i	0.440442	−	0.897781i	$-0.354822\pi$
$347$	−2.17647	−	1.25658i	−0.116839	−	0.0674569i	−0.557281	+	0.830324i	$0.688155\pi$
$348$	−28.2750	+	16.3246i	−1.51570	+	0.875088i
$349$	8.74342	+	15.1440i	0.468024	+	0.810642i	0.999332	−	0.0365368i	$-0.0116326\pi$
$349$	8.74342	+	15.1440i	0.468024	+	0.810642i	−0.531308	+	0.847179i	$0.678299\pi$
$350$		0			0
$351$	−38.9737	+	23.6866i	−2.08026	+	1.26430i
$352$			2.16228i			0.115250i
$353$	−4.47066	+	2.58114i	−0.237949	+	0.137380i	−0.614234	−	0.789124i	$-0.710535\pi$
$353$	−4.47066	+	2.58114i	−0.237949	+	0.137380i	0.376284	+	0.926504i	$0.377202\pi$
$354$	−16.3246	−	28.2750i	−0.867640	−	1.50280i
$355$		0			0
$356$	−7.32456			−0.388201
$357$	−14.1375	−	8.16228i	−0.748235	−	0.431994i
$358$	19.3336	+	11.1623i	1.02181	+	0.589945i
$359$	6.00000			0.316668			0.158334	−	0.987386i	$-0.449388\pi$
$359$	6.00000			0.316668			0.158334	+	0.987386i	$0.449388\pi$
$360$		0			0
$361$	7.81139	+	13.5297i	0.411126	+	0.712091i
$362$	8.49691	−	4.90569i	0.446588	−	0.257838i
$363$			20.0000i			1.04973i
$364$	3.16228	+	1.73205i	0.165748	+	0.0907841i
$365$		0			0
$366$	11.8377	+	20.5035i	0.618768	+	1.07174i
$367$	4.02625	−	2.32456i	0.210168	−	0.121341i	−0.391221	−	0.920297i	$-0.627947\pi$
$367$	4.02625	−	2.32456i	0.210168	−	0.121341i	0.601390	+	0.798956i	$0.294614\pi$
$368$	5.19615	+	3.00000i	0.270868	+	0.156386i
$369$	72.2719			3.76232
$370$		0			0
$371$	−1.08114	+	1.87259i	−0.0561299	+	0.0972199i
$372$			22.6491i			1.17430i
$373$	−26.5429	−	15.3246i	−1.37434	−	0.793475i	−0.382869	−	0.923803i	$-0.625064\pi$
$373$	−26.5429	−	15.3246i	−1.37434	−	0.793475i	−0.991471	+	0.130327i	$0.958397\pi$
$374$	−5.58114	−	9.66682i	−0.288594	−	0.499859i
$375$		0			0
$376$	−3.00000			−0.154713
$377$	−17.8827	+	32.6491i	−0.921004	+	1.68151i
$378$			12.6491i			0.650600i
$379$	−19.4057	−	33.6116i	−0.996804	−	1.72651i	−0.567590	−	0.823311i	$-0.692124\pi$
$379$	−19.4057	−	33.6116i	−0.996804	−	1.72651i	−0.429214	−	0.903203i	$-0.641209\pi$
$380$		0			0
$381$	−5.25658	+	9.10467i	−0.269303	+	0.466446i
$382$			9.48683i			0.485389i
$383$	25.9808	+	15.0000i	1.32755	+	0.766464i	0.984921	−	0.173005i	$-0.0553476\pi$
$383$	25.9808	+	15.0000i	1.32755	+	0.766464i	0.342634	+	0.939469i	$0.388681\pi$
$384$	1.58114	−	2.73861i	0.0806872	−	0.139754i
$385$		0			0
$386$	2.00000	−	3.46410i	0.101797	−	0.176318i
$387$	12.1244	−	7.00000i	0.616316	−	0.355830i
$388$	6.48379	−	3.74342i	0.329164	−	0.190043i
$389$	−12.8377			−0.650898			−0.325449	−	0.945560i	$-0.605516\pi$
$389$	−12.8377			−0.650898			−0.325449	+	0.945560i	$0.605516\pi$
$390$		0			0
$391$	−30.9737			−1.56641
$392$	−5.19615	+	3.00000i	−0.262445	+	0.151523i
$393$	29.6082	−	17.0943i	1.49354	−	0.862294i
$394$	−9.24342	+	16.0101i	−0.465677	+	0.806576i
$395$		0			0
$396$	−7.56797	+	13.1081i	−0.380305	+	0.658707i
$397$	−33.3306	−	19.2434i	−1.67281	−	0.965799i	−0.966052	−	0.258348i	$-0.916822\pi$
$397$	−33.3306	−	19.2434i	−1.67281	−	0.965799i	−0.706762	−	0.707452i	$-0.749845\pi$
$398$			1.35089i			0.0677140i
$399$	2.90569	−	5.03281i	0.145467	−	0.251956i
$400$		0			0
$401$	−10.9868	−	19.0298i	−0.548656	−	0.950301i	−0.998367	−	0.0571262i	$-0.981806\pi$
$401$	−10.9868	−	19.0298i	−0.548656	−	0.950301i	0.449711	−	0.893174i	$-0.351527\pi$
$402$		−	7.35089i		−	0.366629i
$403$	13.4120	+	22.0680i	0.668099	+	1.09928i
$404$	11.1623			0.555344
$405$		0			0
$406$	5.16228	+	8.94133i	0.256200	+	0.443751i
$407$	0.303879	+	0.175445i	0.0150627	+	0.00869647i
$408$			16.3246i			0.808186i
$409$	−10.8246	+	18.7487i	−0.535240	+	0.927063i	0.463912	+	0.885881i	$0.346445\pi$
$409$	−10.8246	+	18.7487i	−0.535240	+	0.927063i	−0.999152	+	0.0411812i	$0.986888\pi$
$410$		0			0
$411$	48.9737			2.41569
$412$	−0.584952	−	0.337722i	−0.0288185	−	0.0166384i
$413$	−8.94133	+	5.16228i	−0.439974	+	0.254019i
$414$	21.0000	+	36.3731i	1.03209	+	1.78764i
$415$		0			0
$416$	−0.0811388	−	3.60464i	−0.00397816	−	0.176732i
$417$		−	38.4605i		−	1.88342i
$418$	3.44130	−	1.98683i	0.168319	−	0.0971792i
$419$	7.32456	+	12.6865i	0.357828	+	0.619776i	0.987598	−	0.157006i	$-0.0501841\pi$
$419$	7.32456	+	12.6865i	0.357828	+	0.619776i	−0.629770	+	0.776782i	$0.716851\pi$
$420$		0			0
$421$	−3.16228			−0.154120			−0.0770600	−	0.997026i	$-0.524553\pi$
$421$	−3.16228			−0.154120			−0.0770600	+	0.997026i	$0.524553\pi$
$422$	−10.2518	−	5.91886i	−0.499048	−	0.288126i
$423$	−18.1865	−	10.5000i	−0.884260	−	0.510527i
$424$	2.16228			0.105009
$425$		0			0
$426$	6.83772	+	11.8433i	0.331289	+	0.573809i
$427$	6.48379	−	3.74342i	0.313772	−	0.181157i
$428$			3.48683i			0.168542i
$429$	0.554805	+	24.6475i	0.0267862	+	1.18999i
$430$		0			0
$431$	−7.74342	−	13.4120i	−0.372987	−	0.646033i	0.617036	−	0.786935i	$-0.288333\pi$
$431$	−7.74342	−	13.4120i	−0.372987	−	0.646033i	−0.990024	+	0.140902i	$0.955000\pi$
$432$	10.9545	−	6.32456i	0.527046	−	0.304290i
$433$	5.47723	+	3.16228i	0.263219	+	0.151969i	0.625802	−	0.779982i	$-0.284772\pi$
$433$	5.47723	+	3.16228i	0.263219	+	0.151969i	−0.362583	+	0.931951i	$0.618105\pi$
$434$	7.16228			0.343800
$435$		0			0
$436$	−5.32456	+	9.22240i	−0.255000	+	0.441673i
$437$		−	11.0263i		−	0.527461i
$438$	7.77142	+	4.48683i	0.371333	+	0.214389i
$439$	1.90569	+	3.30076i	0.0909538	+	0.157537i	0.907913	−	0.419159i	$-0.137675\pi$
$439$	1.90569	+	3.30076i	0.0909538	+	0.157537i	−0.816959	+	0.576696i	$0.804342\pi$
$440$		0			0
$441$	−42.0000			−2.00000
$442$	9.66682	+	15.9057i	0.459804	+	0.756557i
$443$		−	26.6491i		−	1.26614i	−0.774096	−	0.633069i	$-0.781795\pi$
$443$		−	26.6491i		−	1.26614i	0.774096	−	0.633069i	$-0.218205\pi$
$444$	−0.256584	−	0.444416i	−0.0121769	−	0.0210910i
$445$		0			0
$446$	−1.66228	+	2.87915i	−0.0787111	+	0.136332i
$447$			51.6228i			2.44167i
$448$	−0.866025	−	0.500000i	−0.0409159	−	0.0236228i
$449$	−1.01317	+	1.75486i	−0.0478143	+	0.0828168i	−0.888942	−	0.458020i	$-0.848559\pi$
$449$	−1.01317	+	1.75486i	−0.0478143	+	0.0828168i	0.841128	+	0.540837i	$0.181892\pi$
$450$		0			0
$451$	11.1623	−	19.3336i	0.525611	−	0.910385i
$452$	−7.49035	+	4.32456i	−0.352316	+	0.203410i
$453$	13.2486	−	7.64911i	0.622476	−	0.359387i
$454$	−10.3246			−0.484555
$455$		0			0
$456$	−5.81139			−0.272143
$457$	21.1834	−	12.2302i	0.990918	−	0.572107i	0.0853696	−	0.996349i	$-0.472793\pi$
$457$	21.1834	−	12.2302i	0.990918	−	0.572107i	0.905549	+	0.424242i	$0.139460\pi$
$458$	−2.45754	+	1.41886i	−0.114833	+	0.0662990i
$459$	−32.6491	+	56.5499i	−1.52393	+	2.63952i
$460$		0			0
$461$	−10.7434	+	18.6081i	−0.500371	+	0.866668i	0.499629	+	0.866239i	$0.333470\pi$
$461$	−10.7434	+	18.6081i	−0.500371	+	0.866668i	−1.00000		0.000428205i	$0.999864\pi$
$462$	5.92164	+	3.41886i	0.275500	+	0.159060i
$463$		−	12.3246i		−	0.572771i	−0.958115	−	0.286385i	$-0.907546\pi$
$463$		−	12.3246i		−	0.572771i	0.958115	−	0.286385i	$-0.0924537\pi$
$464$	5.16228	−	8.94133i	0.239653	−	0.415091i
$465$		0			0
$466$	−4.74342	−	8.21584i	−0.219735	−	0.380591i
$467$			32.6491i			1.51082i	0.655252	+	0.755410i	$0.272562\pi$
$467$			32.6491i			1.51082i	−0.655252	+	0.755410i	$0.727438\pi$
$468$	12.1244	−	22.1359i	0.560449	−	1.02323i
$469$	−2.32456			−0.107338
$470$		0			0
$471$	19.2302	+	33.3078i	0.886083	+	1.53474i
$472$	8.94133	+	5.16228i	0.411558	+	0.237613i
$473$		−	4.32456i		−	0.198843i
$474$	−21.3246	+	36.9352i	−0.979469	+	1.69649i
$475$		0			0
$476$	5.16228			0.236613
$477$	13.1081	+	7.56797i	0.600179	+	0.346514i
$478$	−9.66682	+	5.58114i	−0.442150	+	0.255275i
$479$	−6.06797	−	10.5100i	−0.277253	−	0.480216i	0.693448	−	0.720506i	$-0.256091\pi$
$479$	−6.06797	−	10.5100i	−0.277253	−	0.480216i	−0.970701	+	0.240291i	$0.922757\pi$
$480$		0			0
$481$	−0.513167	−	0.281073i	−0.0233984	−	0.0128158i
$482$		−	25.9737i		−	1.18307i
$483$	16.4317	−	9.48683i	0.747667	−	0.431666i
$484$	−3.16228	−	5.47723i	−0.143740	−	0.248965i
$485$		0			0
$486$	22.1359			1.00411
$487$	0.866025	+	0.500000i	0.0392434	+	0.0226572i	0.519493	−	0.854475i	$-0.326121\pi$
$487$	0.866025	+	0.500000i	0.0392434	+	0.0226572i	−0.480250	+	0.877132i	$0.659454\pi$
$488$	−6.48379	−	3.74342i	−0.293507	−	0.169457i
$489$	−55.2982			−2.50067
$490$		0			0
$491$	−8.75658	−	15.1668i	−0.395179	−	0.684470i	0.597945	−	0.801537i	$-0.295984\pi$
$491$	−8.75658	−	15.1668i	−0.395179	−	0.684470i	−0.993124	+	0.117067i	$0.962651\pi$
$492$	−28.2750	+	16.3246i	−1.27473	+	0.735968i
$493$			53.2982i			2.40043i
$494$	−5.66228	+	3.44130i	−0.254758	+	0.154831i
$495$		0			0
$496$	−3.58114	−	6.20271i	−0.160798	−	0.278510i
$497$	3.74517	−	2.16228i	0.167994	−	0.0969914i
$498$	25.9808	+	15.0000i	1.16423	+	0.672166i
$499$	22.0000			0.984855			0.492428	−	0.870353i	$-0.336110\pi$
$499$	22.0000			0.984855			0.492428	+	0.870353i	$0.336110\pi$
$500$		0			0
$501$	−21.0680	+	36.4908i	−0.941248	+	1.63029i
$502$			12.4868i			0.557315i
$503$	−12.3826	−	7.14911i	−0.552114	−	0.318763i	0.197860	−	0.980230i	$-0.436601\pi$
$503$	−12.3826	−	7.14911i	−0.552114	−	0.318763i	−0.749974	+	0.661467i	$0.769934\pi$
$504$	−3.50000	−	6.06218i	−0.155902	−	0.270031i
$505$		0			0
$506$	12.9737			0.576750
$507$	−1.84978	−	41.0680i	−0.0821517	−	1.82389i
$508$		−	3.32456i		−	0.147503i
$509$	−0.486833	−	0.843219i	−0.0215785	−	0.0373750i	0.855035	−	0.518571i	$-0.173536\pi$
$509$	−0.486833	−	0.843219i	−0.0215785	−	0.0373750i	−0.876613	+	0.481196i	$0.840203\pi$
$510$		0			0
$511$	1.41886	−	2.45754i	0.0627667	−	0.108715i
$512$			1.00000i			0.0441942i
$513$	−20.1312	−	11.6228i	−0.888816	−	0.513158i
$514$		0			0
$515$		0			0
$516$	−3.16228	+	5.47723i	−0.139212	+	0.241121i
$517$	−5.61776	+	3.24342i	−0.247069	+	0.142645i
$518$	−0.140537	+	0.0811388i	−0.00617482	+	0.00356504i
$519$	−6.83772			−0.300143
$520$		0			0
$521$	22.6754			0.993429			0.496715	−	0.867914i	$-0.334540\pi$
$521$	22.6754			0.993429			0.496715	+	0.867914i	$0.334540\pi$
$522$	62.5893	−	36.1359i	2.73946	−	1.58163i
$523$	34.0333	−	19.6491i	1.48817	−	0.859196i	0.488262	−	0.872697i	$-0.337631\pi$
$523$	34.0333	−	19.6491i	1.48817	−	0.859196i	0.999909	+	0.0135017i	$0.00429785\pi$
$524$	−5.40569	+	9.36294i	−0.236149	+	0.409022i
$525$		0			0
$526$	5.82456	−	10.0884i	0.253963	−	0.439876i
$527$	32.0201	+	18.4868i	1.39482	+	0.805299i
$528$		−	6.83772i		−	0.297574i
$529$	6.50000	−	11.2583i	0.282609	−	0.489493i
$530$		0			0
$531$	36.1359	+	62.5893i	1.56817	+	2.71614i
$532$			1.83772i			0.0796754i
$533$	−17.8827	+	32.6491i	−0.774584	+	1.41419i
$534$	23.1623			1.00233
$535$		0			0
$536$	1.16228	+	2.01312i	0.0502027	+	0.0869537i
$537$	−61.1383	−	35.2982i	−2.63831	−	1.52323i
$538$		−	2.51317i		−	0.108350i
$539$	−6.48683	+	11.2355i	−0.279408	+	0.483948i
$540$		0			0
$541$	26.8377			1.15384			0.576922	−	0.816799i	$-0.304254\pi$
$541$	26.8377			1.15384			0.576922	+	0.816799i	$0.304254\pi$
$542$	−5.47723	−	3.16228i	−0.235267	−	0.135831i
$543$	−26.8696	+	15.5132i	−1.15308	+	0.665734i
$544$	−2.58114	−	4.47066i	−0.110665	−	0.191678i
$545$		0			0
$546$	−10.0000	−	5.47723i	−0.427960	−	0.234404i
$547$		−	6.64911i		−	0.284295i	−0.989845	−	0.142148i	$-0.954599\pi$
$547$		−	6.64911i		−	0.284295i	0.989845	−	0.142148i	$-0.0454008\pi$
$548$	−13.4120	+	7.74342i	−0.572932	+	0.330782i
$549$	−26.2039	−	45.3865i	−1.11836	−	1.93705i
$550$		0			0
$551$	−18.9737			−0.808305
$552$	−16.4317	−	9.48683i	−0.699379	−	0.403786i
$553$	11.6799	+	6.74342i	0.496682	+	0.286759i
$554$	−1.51317			−0.0642883
$555$		0			0
$556$	6.08114	+	10.5328i	0.257898	+	0.446692i
$557$	13.7159	−	7.91886i	0.581160	−	0.335533i	−0.180434	−	0.983587i	$-0.557750\pi$
$557$	13.7159	−	7.91886i	0.581160	−	0.335533i	0.761594	+	0.648054i	$0.224417\pi$
$558$		−	50.1359i		−	2.12242i
$559$	0.162278	+	7.20928i	0.00686361	+	0.304920i
$560$		0			0
$561$	17.6491	+	30.5692i	0.745146	+	1.29063i
$562$	−16.4317	+	9.48683i	−0.693128	+	0.400178i
$563$	−20.7846	−	12.0000i	−0.875967	−	0.505740i	−0.00664037	−	0.999978i	$-0.502114\pi$
$563$	−20.7846	−	12.0000i	−0.875967	−	0.505740i	−0.869326	+	0.494238i	$0.835447\pi$
$564$	9.48683			0.399468
$565$		0			0
$566$	11.0000	−	19.0526i	0.462364	−	0.800839i
$567$		−	19.0000i		−	0.797925i
$568$	−3.74517	−	2.16228i	−0.157144	−	0.0907272i
$569$	−16.9868	−	29.4221i	−0.712125	−	1.23344i	−0.964058	−	0.265692i	$-0.914400\pi$
$569$	−16.9868	−	29.4221i	−0.712125	−	1.23344i	0.251933	−	0.967745i	$-0.418934\pi$
$570$		0			0
$571$	−25.1359			−1.05191			−0.525953	−	0.850513i	$-0.676291\pi$
$571$	−25.1359			−1.05191			−0.525953	+	0.850513i	$0.676291\pi$
$572$	−4.04905	−	6.66228i	−0.169299	−	0.278564i
$573$		−	30.0000i		−	1.25327i
$574$	5.16228	+	8.94133i	0.215469	+	0.373204i
$575$		0			0
$576$	−3.50000	+	6.06218i	−0.145833	+	0.252591i
$577$			7.16228i			0.298170i	0.988824	+	0.149085i	$0.0476327\pi$
$577$			7.16228i			0.298170i	−0.988824	+	0.149085i	$0.952367\pi$
$578$	8.35637	+	4.82456i	0.347579	+	0.200675i
$579$	−6.32456	+	10.9545i	−0.262840	+	0.455251i
$580$		0			0
$581$	4.74342	−	8.21584i	0.196790	−	0.340850i
$582$	−20.5035	+	11.8377i	−0.849899	+	0.490689i
$583$	4.04905	−	2.33772i	0.167695	−	0.0968186i
$584$	−2.83772			−0.117426
$585$		0			0
$586$	−21.8377			−0.902108
$587$	11.2355	−	6.48683i	0.463740	−	0.267740i	−0.249876	−	0.968278i	$-0.580390\pi$
$587$	11.2355	−	6.48683i	0.463740	−	0.267740i	0.713615	+	0.700538i	$0.247056\pi$
$588$	16.4317	−	9.48683i	0.677631	−	0.391230i
$589$	−6.58114	+	11.3989i	−0.271171	+	0.469682i
$590$		0			0
$591$	29.2302	−	50.6283i	1.20237	−	2.08257i
$592$	0.140537	+	0.0811388i	0.00577602	+	0.00333479i
$593$			3.35089i			0.137605i	0.997630	+	0.0688023i	$0.0219178\pi$
$593$			3.35089i			0.137605i	−0.997630	+	0.0688023i	$0.978082\pi$
$594$	13.6754	−	23.6866i	0.561110	−	0.971872i
$595$		0			0
$596$	−8.16228	−	14.1375i	−0.334340	−	0.579094i
$597$		−	4.27189i		−	0.174837i
$598$	−21.6278	+	0.486833i	−0.884428	+	0.0199081i
$599$	−43.9473			−1.79564			−0.897820	−	0.440363i	$-0.854850\pi$
$599$	−43.9473			−1.79564			−0.897820	+	0.440363i	$0.854850\pi$
$600$		0			0
$601$	−17.1491	−	29.7031i	−0.699527	−	1.21162i	−0.968631	−	0.248505i	$-0.920061\pi$
$601$	−17.1491	−	29.7031i	−0.699527	−	1.21162i	0.269104	−	0.963111i	$-0.413273\pi$
$602$	1.73205	+	1.00000i	0.0705931	+	0.0407570i
$603$			16.2719i			0.662642i
$604$	−2.41886	+	4.18959i	−0.0984221	+	0.170472i
$605$		0			0
$606$	−35.2982			−1.43389
$607$	−4.33013	−	2.50000i	−0.175754	−	0.101472i	0.409542	−	0.912291i	$-0.365689\pi$
$607$	−4.33013	−	2.50000i	−0.175754	−	0.101472i	−0.585296	+	0.810819i	$0.699022\pi$
$608$	1.59151	−	0.918861i	0.0645444	−	0.0372647i
$609$	−16.3246	−	28.2750i	−0.661504	−	1.14576i
$610$		0			0
$611$	9.24342	−	5.61776i	0.373949	−	0.227270i
$612$		−	36.1359i		−	1.46071i
$613$	−17.7421	+	10.2434i	−0.716597	+	0.413728i	−0.813499	−	0.581566i	$-0.802440\pi$
$613$	−17.7421	+	10.2434i	−0.716597	+	0.413728i	0.0969016	+	0.995294i	$0.469107\pi$
$614$	7.83772	+	13.5753i	0.316305	+	0.547856i
$615$		0			0
$616$	−2.16228			−0.0871206
$617$	27.6672	+	15.9737i	1.11384	+	0.643076i	0.939821	−	0.341667i	$-0.110991\pi$
$617$	27.6672	+	15.9737i	1.11384	+	0.643076i	0.174018	+	0.984742i	$0.444325\pi$
$618$	1.84978	+	1.06797i	0.0744091	+	0.0429601i
$619$	29.4605			1.18412			0.592059	−	0.805895i	$-0.298315\pi$
$619$	29.4605			1.18412			0.592059	+	0.805895i	$0.298315\pi$
$620$		0			0
$621$	−37.9473	−	65.7267i	−1.52277	−	2.63752i
$622$	−3.01969	+	1.74342i	−0.121078	+	0.0699046i
$623$		−	7.32456i		−	0.293452i
$624$	0.256584	+	11.3989i	0.0102716	+	0.456320i
$625$		0			0
$626$	4.16228	+	7.20928i	0.166358	+	0.288141i
$627$	−10.8823	+	6.28292i	−0.434598	+	0.250916i
$628$	−10.5328	−	6.08114i	−0.420306	−	0.242664i
$629$	−0.837722			−0.0334022
$630$		0			0
$631$	7.16228	−	12.4054i	0.285126	−	0.493852i	−0.687514	−	0.726171i	$-0.741298\pi$
$631$	7.16228	−	12.4054i	0.285126	−	0.493852i	0.972640	+	0.232319i	$0.0746313\pi$
$632$		−	13.4868i		−	0.536477i
$633$	32.4189	+	18.7171i	1.28854	+	0.743937i
$634$	6.24342	+	10.8139i	0.247958	+	0.429475i
$635$		0			0
$636$	−6.83772			−0.271133
$637$	10.3923	−	18.9737i	0.411758	−	0.751764i
$638$		−	22.3246i		−	0.883838i
$639$	−15.1359	−	26.2162i	−0.598769	−	1.03710i
$640$		0			0
$641$	4.98683	−	8.63745i	0.196968	−	0.341159i	−0.750576	−	0.660784i	$-0.770224\pi$
$641$	4.98683	−	8.63745i	0.196968	−	0.341159i	0.947544	+	0.319626i	$0.103557\pi$
$642$		−	11.0263i		−	0.435175i
$643$	10.7911	+	6.23025i	0.425560	+	0.245697i	0.697453	−	0.716630i	$-0.254316\pi$
$643$	10.7911	+	6.23025i	0.425560	+	0.245697i	−0.271893	+	0.962327i	$0.587650\pi$
$644$	−3.00000	+	5.19615i	−0.118217	+	0.204757i
$645$		0			0
$646$	−4.74342	+	8.21584i	−0.186627	+	0.323248i
$647$	−13.8336	+	7.98683i	−0.543855	+	0.313995i	−0.746640	−	0.665229i	$-0.768334\pi$
$647$	−13.8336	+	7.98683i	−0.543855	+	0.313995i	0.202785	+	0.979223i	$0.435001\pi$
$648$	−16.4545	+	9.50000i	−0.646393	+	0.373195i
$649$	22.3246			0.876315
$650$		0			0
$651$	−22.6491			−0.887689
$652$	15.1440	−	8.74342i	0.593086	−	0.342419i
$653$	−15.1668	+	8.75658i	−0.593525	+	0.342672i	−0.766490	−	0.642256i	$-0.777998\pi$
$653$	−15.1668	+	8.75658i	−0.593525	+	0.342672i	0.172965	+	0.984928i	$0.444665\pi$
$654$	16.8377	−	29.1638i	0.658407	−	1.14039i
$655$		0			0
$656$	5.16228	−	8.94133i	0.201553	−	0.349100i
$657$	−17.2028	−	9.93203i	−0.671144	−	0.387485i
$658$		−	3.00000i		−	0.116952i
$659$	11.6491	−	20.1769i	0.453785	−	0.785979i	−0.544833	−	0.838545i	$-0.683407\pi$
$659$	11.6491	−	20.1769i	0.453785	−	0.785979i	0.998617	+	0.0525663i	$0.0167401\pi$
$660$		0			0
$661$	5.41886	+	9.38574i	0.210769	+	0.365063i	0.951956	−	0.306236i	$-0.0990698\pi$
$661$	5.41886	+	9.38574i	0.210769	+	0.365063i	−0.741186	+	0.671299i	$0.765736\pi$
$662$		−	24.6491i		−	0.958015i
$663$	−30.5692	−	50.2982i	−1.18721	−	1.95342i
$664$	−9.48683			−0.368161
$665$		0			0
$666$	0.567972	+	0.983756i	0.0220085	+	0.0381198i
$667$	−53.6480	−	30.9737i	−2.07726	−	1.19931i
$668$		−	13.3246i		−	0.515543i
$669$	5.25658	−	9.10467i	0.203231	−	0.352007i
$670$		0			0
$671$	−16.1886			−0.624954
$672$	2.73861	+	1.58114i	0.105644	+	0.0609938i
$673$	−12.9676	+	7.48683i	−0.499863	+	0.288596i	−0.728657	−	0.684879i	$-0.759855\pi$
$673$	−12.9676	+	7.48683i	−0.499863	+	0.288596i	0.228794	+	0.973475i	$0.426522\pi$
$674$	8.74342	+	15.1440i	0.336784	+	0.583327i
$675$		0			0
$676$	7.00000	+	10.9545i	0.269231	+	0.421325i
$677$		−	12.9737i		−	0.498618i	−0.968424	−	0.249309i	$-0.919796\pi$
$677$		−	12.9737i		−	0.498618i	0.968424	−	0.249309i	$-0.0802036\pi$
$678$	23.6866	−	13.6754i	0.909677	−	0.525202i
$679$	3.74342	+	6.48379i	0.143659	+	0.248825i
$680$		0			0
$681$	32.6491			1.25112
$682$	−13.4120	−	7.74342i	−0.513572	−	0.296511i
$683$	17.0394	+	9.83772i	0.651996	+	0.376430i	0.789220	−	0.614110i	$-0.210485\pi$
$683$	17.0394	+	9.83772i	0.651996	+	0.376430i	−0.137225	+	0.990540i	$0.543818\pi$
$684$	12.8641			0.491869
$685$		0			0
$686$	−6.50000	−	11.2583i	−0.248171	−	0.429845i
$687$	7.77142	−	4.48683i	0.296498	−	0.171183i
$688$		−	2.00000i		−	0.0762493i
$689$	−6.66228	+	4.04905i	−0.253813	+	0.154257i
$690$		0			0
$691$	18.5680	+	32.1607i	0.706359	+	1.22345i	0.966199	+	0.257798i	$0.0829969\pi$
$691$	18.5680	+	32.1607i	0.706359	+	1.22345i	−0.259840	+	0.965652i	$0.583670\pi$
$692$	1.87259	−	1.08114i	0.0711851	−	0.0410987i
$693$	−13.1081	−	7.56797i	−0.497936	−	0.287483i
$694$	−2.51317			−0.0953985
$695$		0			0
$696$	−16.3246	+	28.2750i	−0.618781	+	1.07176i
$697$			53.2982i			2.01881i
$698$	15.1440	+	8.74342i	0.573210	+	0.330943i
$699$	15.0000	+	25.9808i	0.567352	+	0.982683i
$700$		0			0
$701$	−23.1623			−0.874827			−0.437414	−	0.899260i	$-0.644105\pi$
$701$	−23.1623			−0.874827			−0.437414	+	0.899260i	$0.644105\pi$
$702$	−21.9089	+	40.0000i	−0.826898	+	1.50970i
$703$		−	0.298221i		−	0.0112476i
$704$	1.08114	+	1.87259i	0.0407470	+	0.0705758i
$705$		0			0
$706$	−2.58114	+	4.47066i	−0.0971424	+	0.168256i
$707$			11.1623i			0.419801i
$708$	−28.2750	−	16.3246i	−1.06264	−	0.613514i
$709$	20.7434	−	35.9287i	0.779035	−	1.34933i	−0.153463	−	0.988154i	$-0.549043\pi$
$709$	20.7434	−	35.9287i	0.779035	−	1.34933i	0.932498	−	0.361174i	$-0.117624\pi$
$710$		0			0
$711$	47.2039	−	81.7596i	1.77029	−	3.06622i
$712$	−6.34325	+	3.66228i	−0.237723	+	0.137250i
$713$	−37.2163	+	21.4868i	−1.39376	+	0.804688i
$714$	−16.3246			−0.610931
$715$		0			0
$716$	22.3246			0.834308
$717$	30.5692	−	17.6491i	1.14163	−	0.659118i
$718$	5.19615	−	3.00000i	0.193919	−	0.111959i
$719$	6.00000	−	10.3923i	0.223762	−	0.387568i	−0.732185	−	0.681106i	$-0.761499\pi$
$719$	6.00000	−	10.3923i	0.223762	−	0.387568i	0.955947	+	0.293538i	$0.0948328\pi$
$720$		0			0
$721$	0.337722	−	0.584952i	0.0125774	−	0.0217848i
$722$	13.5297	+	7.81139i	0.503524	+	0.290710i
$723$			82.1359i			3.05467i
$724$	4.90569	−	8.49691i	0.182319	−	0.315785i
$725$		0			0
$726$	10.0000	+	17.3205i	0.371135	+	0.642824i
$727$		−	20.6754i		−	0.766810i	−0.923580	−	0.383405i	$-0.874751\pi$
$727$		−	20.6754i		−	0.766810i	0.923580	−	0.383405i	$-0.125249\pi$
$728$	3.60464	−	0.0811388i	0.133597	−	0.00300721i
$729$	−13.0000			−0.481481
$730$		0			0
$731$	5.16228	+	8.94133i	0.190934	+	0.330707i
$732$	20.5035	+	11.8377i	0.757833	+	0.437535i
$733$		−	8.48683i		−	0.313468i	−0.987641	−	0.156734i	$-0.949903\pi$
$733$		−	8.48683i		−	0.313468i	0.987641	−	0.156734i	$-0.0500966\pi$
$734$	2.32456	−	4.02625i	0.0858009	−	0.148612i
$735$		0			0
$736$	6.00000			0.221163
$737$	4.35293	+	2.51317i	0.160342	+	0.0925737i
$738$	62.5893	−	36.1359i	2.30394	−	1.33018i
$739$	−22.4057	−	38.8078i	−0.824207	−	1.42757i	−0.902524	−	0.430640i	$-0.858288\pi$
$739$	−22.4057	−	38.8078i	−0.824207	−	1.42757i	0.0783172	−	0.996928i	$-0.475045\pi$
$740$		0			0
$741$	17.9057	−	10.8823i	0.657782	−	0.399772i
$742$			2.16228i			0.0793797i
$743$	15.5885	−	9.00000i	0.571885	−	0.330178i	−0.186017	−	0.982547i	$-0.559558\pi$
$743$	15.5885	−	9.00000i	0.571885	−	0.330178i	0.757902	+	0.652369i	$0.226225\pi$
$744$	11.3246	+	19.6147i	0.415178	+	0.719110i
$745$		0			0
$746$	−30.6491			−1.12214
$747$	−57.5109	−	33.2039i	−2.10421	−	1.21487i
$748$	−9.66682	−	5.58114i	−0.353454	−	0.204067i
$749$	−3.48683			−0.127406
$750$		0			0
$751$	17.4868	+	30.2881i	0.638104	+	1.10523i	0.985849	+	0.167639i	$0.0536142\pi$
$751$	17.4868	+	30.2881i	0.638104	+	1.10523i	−0.347745	+	0.937589i	$0.613052\pi$
$752$	−2.59808	+	1.50000i	−0.0947421	+	0.0546994i
$753$		−	39.4868i		−	1.43898i
$754$	0.837722	+	37.2163i	0.0305080	+	1.35534i
$755$		0			0
$756$	6.32456	+	10.9545i	0.230022	+	0.398410i
$757$	29.5854	−	17.0811i	1.07530	−	0.620825i	0.145675	−	0.989332i	$-0.453465\pi$
$757$	29.5854	−	17.0811i	1.07530	−	0.620825i	0.929625	+	0.368508i	$0.120131\pi$
$758$	−33.6116	−	19.4057i	−1.22083	−	0.704847i
$759$	−41.0263			−1.48916
$760$		0			0
$761$	4.14911	−	7.18647i	0.150405	−	0.260509i	−0.780971	−	0.624567i	$-0.785276\pi$
$761$	4.14911	−	7.18647i	0.150405	−	0.260509i	0.931376	+	0.364058i	$0.118609\pi$
$762$			10.5132i			0.380852i
$763$	−9.22240	−	5.32456i	−0.333873	−	0.192762i
$764$	4.74342	+	8.21584i	0.171611	+	0.297239i
$765$		0			0
$766$	30.0000			1.08394
$767$	−37.2163	+	0.837722i	−1.34380	+	0.0302484i
$768$		−	3.16228i		−	0.114109i
$769$	3.16228	+	5.47723i	0.114035	+	0.197514i	0.917393	−	0.397981i	$-0.130289\pi$
$769$	3.16228	+	5.47723i	0.114035	+	0.197514i	−0.803359	+	0.595495i	$0.796956\pi$
$770$		0			0
$771$		0			0
$772$		−	4.00000i		−	0.143963i
$773$	41.3831	+	23.8925i	1.48845	+	0.859354i	0.999913	−	0.0131912i	$-0.00419900\pi$
$773$	41.3831	+	23.8925i	1.48845	+	0.859354i	0.488533	+	0.872546i	$0.337532\pi$
$774$	7.00000	−	12.1244i	0.251610	−	0.435801i
$775$		0			0
$776$	3.74342	−	6.48379i	0.134381	−	0.232754i
$777$	0.444416	−	0.256584i	0.0159433	−	0.00920488i
$778$	−11.1178	+	6.41886i	−0.398592	+	0.230127i
$779$	−18.9737			−0.679802
$780$		0			0
$781$	−9.35089			−0.334601
$782$	−26.8240	+	15.4868i	−0.959224	+	0.553808i
$783$	−113.100	+	65.2982i	−4.04186	+	2.33357i
$784$	−3.00000	+	5.19615i	−0.107143	+	0.185577i
$785$		0			0
$786$	17.0943	−	29.6082i	0.609734	−	1.05609i
$787$	39.9549	+	23.0680i	1.42424	+	0.822284i	0.996658	−	0.0816928i	$-0.0260326\pi$
$787$	39.9549	+	23.0680i	1.42424	+	0.822284i	0.427581	+	0.903977i	$0.359366\pi$
$788$			18.4868i			0.658566i
$789$	−18.4189	+	31.9024i	−0.655729	+	1.13576i
$790$		0			0
$791$	−4.32456	−	7.49035i	−0.153763	−	0.266326i
$792$			15.1359i			0.537832i
$793$	26.9873	−	0.607473i	0.958348	−	0.0215720i
$794$	−38.4868			−1.36585
$795$		0			0
$796$	0.675445	+	1.16990i	0.0239405	+	0.0414662i
$797$	11.8433	+	6.83772i	0.419511	+	0.242205i	0.694868	−	0.719137i	$-0.255463\pi$
$797$	11.8433	+	6.83772i	0.419511	+	0.242205i	−0.275357	+	0.961342i	$0.588796\pi$
$798$		−	5.81139i		−	0.205721i
$799$	7.74342	−	13.4120i	0.273942	−	0.474482i
$800$		0			0
$801$	−51.2719			−1.81160
$802$	−19.0298	−	10.9868i	−0.671964	−	0.387959i
$803$	−5.31388	+	3.06797i	−0.187523	+	0.108266i
$804$	−3.67544	−	6.36606i	−0.129623	−	0.224514i
$805$		0			0
$806$	22.6491	+	12.4054i	0.797781	+	0.436963i
$807$			7.94733i			0.279759i
$808$	9.66682	−	5.58114i	0.340077	−	0.196344i
$809$	5.16228	+	8.94133i	0.181496	+	0.314360i	0.942390	−	0.334516i	$-0.108573\pi$
$809$	5.16228	+	8.94133i	0.181496	+	0.314360i	−0.760894	+	0.648876i	$0.775239\pi$
$810$		0			0
$811$	−6.16228			−0.216387			−0.108193	−	0.994130i	$-0.534507\pi$
$811$	−6.16228			−0.216387			−0.108193	+	0.994130i	$0.534507\pi$
$812$	8.94133	+	5.16228i	0.313779	+	0.181160i
$813$	17.3205	+	10.0000i	0.607457	+	0.350715i
$814$	0.350889			0.0122987
$815$		0			0
$816$	8.16228	+	14.1375i	0.285737	+	0.494911i
$817$	−3.18303	+	1.83772i	−0.111360	+	0.0642938i
$818$			21.6491i			0.756943i
$819$	22.1359	+	12.1244i	0.773492	+	0.423659i
$820$		0			0
$821$	2.58114	+	4.47066i	0.0900824	+	0.156027i	0.907546	−	0.419954i	$-0.137954\pi$
$821$	2.58114	+	4.47066i	0.0900824	+	0.156027i	−0.817463	+	0.575981i	$0.804620\pi$
$822$	42.4124	−	24.4868i	1.47930	−	0.854076i
$823$	40.7032	+	23.5000i	1.41882	+	0.819159i	0.996196	−	0.0871445i	$-0.0277742\pi$
$823$	40.7032	+	23.5000i	1.41882	+	0.819159i	0.422628	+	0.906303i	$0.361108\pi$
$824$	−0.675445			−0.0235302
$825$		0			0
$826$	−5.16228	+	8.94133i	−0.179619	+	0.311109i
$827$		−	51.4868i		−	1.79037i	−0.445692	−	0.895186i	$-0.647042\pi$
$827$		−	51.4868i		−	1.79037i	0.445692	−	0.895186i	$-0.352958\pi$
$828$	36.3731	+	21.0000i	1.26405	+	0.729800i
$829$	16.0000	+	27.7128i	0.555703	+	0.962506i	0.997848	+	0.0655624i	$0.0208842\pi$
$829$	16.0000	+	27.7128i	0.555703	+	0.962506i	−0.442145	+	0.896943i	$0.645783\pi$
$830$		0			0
$831$	4.78505			0.165992
$832$	−1.87259	−	3.08114i	−0.0649203	−	0.106819i
$833$		−	30.9737i		−	1.07317i
$834$	−19.2302	−	33.3078i	−0.665889	−	1.15335i
$835$		0			0
$836$	1.98683	−	3.44130i	0.0687161	−	0.119020i
$837$			90.5964i			3.13147i
$838$	12.6865	+	7.32456i	0.438248	+	0.253023i
$839$	−11.5811	+	20.0591i	−0.399825	+	0.692518i	−0.993704	−	0.112037i	$-0.964263\pi$
$839$	−11.5811	+	20.0591i	−0.399825	+	0.692518i	0.593879	+	0.804555i	$0.297596\pi$
$840$		0			0
$841$	−38.7982	+	67.2005i	−1.33787	+	2.31726i
$842$	−2.73861	+	1.58114i	−0.0943788	+	0.0544896i
$843$	51.9615	−	30.0000i	1.78965	−	1.03325i
$844$	−11.8377			−0.407471
$845$		0			0
$846$	−21.0000			−0.721995
$847$	5.47723	−	3.16228i	0.188200	−	0.108657i
$848$	1.87259	−	1.08114i	0.0643049	−	0.0371265i
$849$	−34.7851	+	60.2495i	−1.19382	+	2.06776i
$850$		0			0
$851$	0.486833	−	0.843219i	0.0166884	−	0.0289052i
$852$	11.8433	+	6.83772i	0.405744	+	0.234257i
$853$		−	56.2719i		−	1.92671i	−0.268225	−	0.963356i	$-0.586437\pi$
$853$		−	56.2719i		−	1.92671i	0.268225	−	0.963356i	$-0.413563\pi$
$854$	3.74342	−	6.48379i	0.128097	−	0.221871i
$855$		0			0
$856$	1.74342	+	3.01969i	0.0595887	+	0.103211i
$857$			30.1359i			1.02942i	0.857363	+	0.514712i	$0.172101\pi$
$857$			30.1359i			1.02942i	−0.857363	+	0.514712i	$0.827899\pi$
$858$	12.8042	+	21.0680i	0.437129	+	0.719249i
$859$	−47.1359			−1.60826			−0.804129	−	0.594455i	$-0.797368\pi$
$859$	−47.1359			−1.60826			−0.804129	+	0.594455i	$0.797368\pi$
$860$		0			0
$861$	−16.3246	−	28.2750i	−0.556339	−	0.963608i
$862$	−13.4120	−	7.74342i	−0.456814	−	0.263742i
$863$			18.0000i			0.612727i	0.951915	+	0.306364i	$0.0991123\pi$
$863$			18.0000i			0.612727i	−0.951915	+	0.306364i	$0.900888\pi$
$864$	6.32456	−	10.9545i	0.215166	−	0.372678i
$865$		0			0
$866$	6.32456			0.214917
$867$	−26.4252	−	15.2566i	−0.897446	−	0.518141i
$868$	6.20271	−	3.58114i	0.210534	−	0.121552i
$869$	−14.5811	−	25.2553i	−0.494631	−	0.856726i
$870$		0			0
$871$	−7.35089	−	4.02625i	−0.249075	−	0.136424i
$872$			10.6491i			0.360624i
$873$	45.3865	−	26.2039i	1.53610	−	0.886868i
$874$	−5.51317	−	9.54909i	−0.186486	−	0.323003i
$875$		0			0
$876$	8.97367			0.303192
$877$	20.5035	+	11.8377i	0.692355	+	0.399731i	0.804494	−	0.593961i	$-0.202437\pi$
$877$	20.5035	+	11.8377i	0.692355	+	0.399731i	−0.112139	+	0.993693i	$0.535770\pi$
$878$	3.30076	+	1.90569i	0.111395	+	0.0643141i
$879$	69.0569			2.32923
$880$		0			0
$881$	28.9868	+	50.2067i	0.976591	+	1.69151i	0.674581	+	0.738201i	$0.264324\pi$
$881$	28.9868	+	50.2067i	0.976591	+	1.69151i	0.302010	+	0.953305i	$0.402342\pi$
$882$	−36.3731	+	21.0000i	−1.22474	+	0.707107i
$883$		−	35.4868i		−	1.19423i	−0.802157	−	0.597114i	$-0.796314\pi$
$883$		−	35.4868i		−	1.19423i	0.802157	−	0.597114i	$-0.203686\pi$
$884$	16.3246	+	8.94133i	0.549054	+	0.300729i
$885$		0			0
$886$	−13.3246	−	23.0788i	−0.447647	−	0.775348i
$887$	31.7163	−	18.3114i	1.06493	−	0.614836i	0.138136	−	0.990413i	$-0.455889\pi$
$887$	31.7163	−	18.3114i	1.06493	−	0.614836i	0.926791	+	0.375577i	$0.122555\pi$
$888$	−0.444416	−	0.256584i	−0.0149136	−	0.00861038i
$889$	3.32456			0.111502
$890$		0			0
$891$	−20.5416	+	35.5792i	−0.688171	+	1.19195i
$892$			3.32456i			0.111314i
$893$	4.77454	+	2.75658i	0.159774	+	0.0922455i
$894$	25.8114	+	44.7066i	0.863262	+	1.49521i
$895$		0			0
$896$	−1.00000			−0.0334077
$897$	68.3932	−	1.53950i	2.28358	−	0.0514024i
$898$			2.02633i			0.0676196i
$899$	36.9737	+	64.0403i	1.23314	+	2.13586i
$900$		0			0
$901$	−5.58114	+	9.66682i	−0.185935	+	0.322048i
$902$		−	22.3246i		−	0.743326i
$903$	−5.47723	−	3.16228i	−0.182271	−	0.105234i
$904$	−4.32456	+	7.49035i	−0.143833	+	0.249125i
$905$		0			0
$906$	7.64911	−	13.2486i	0.254125	−	0.440157i
$907$	−13.9741	+	8.06797i	−0.464004	+	0.267893i	−0.713726	−	0.700425i	$-0.752994\pi$
$907$	−13.9741	+	8.06797i	−0.464004	+	0.267893i	0.249723	+	0.968317i	$0.419661\pi$
$908$	−8.94133	+	5.16228i	−0.296728	+	0.171316i
$909$	78.1359			2.59161
$910$		0			0
$911$	−17.2982			−0.573116			−0.286558	−	0.958063i	$-0.592511\pi$
$911$	−17.2982			−0.573116			−0.286558	+	0.958063i	$0.592511\pi$
$912$	−5.03281	+	2.90569i	−0.166653	+	0.0962171i
$913$	−17.7649	+	10.2566i	−0.587933	+	0.339443i
$914$	12.2302	−	21.1834i	0.404541	−	0.700685i
$915$		0			0
$916$	−1.41886	+	2.45754i	−0.0468805	+	0.0811994i
$917$	−9.36294	−	5.40569i	−0.309191	−	0.178512i
$918$			65.2982i			2.15516i
$919$	−5.83772	+	10.1112i	−0.192569	+	0.333539i	−0.946101	−	0.323872i	$-0.895015\pi$
$919$	−5.83772	+	10.1112i	−0.192569	+	0.333539i	0.753532	+	0.657411i	$0.228348\pi$
$920$		0			0
$921$	−24.7851	−	42.9290i	−0.816695	−	1.41456i
$922$			21.4868i			0.707631i
$923$	15.5885	−	0.350889i	0.513100	−	0.0115497i
$924$	6.83772			0.224945
$925$		0			0
$926$	−6.16228	−	10.6734i	−0.202505	−	0.350749i
$927$	−4.09467	−	2.36406i	−0.134486	−	0.0776458i
$928$		−	10.3246i		−	0.338920i
$929$	27.0000	−	46.7654i	0.885841	−	1.53432i	0.0410949	−	0.999155i	$-0.486915\pi$
$929$	27.0000	−	46.7654i	0.885841	−	1.53432i	0.844746	−	0.535167i	$-0.179751\pi$
$930$		0			0
$931$	11.0263			0.361374
$932$	−8.21584	−	4.74342i	−0.269119	−	0.155376i
$933$	9.54909	−	5.51317i	0.312623	−	0.180493i
$934$	16.3246	+	28.2750i	0.534156	+	0.925185i
$935$		0			0
$936$	−0.567972	−	25.2325i	−0.0185647	−	0.824749i
$937$			27.6754i			0.904117i	0.891988	+	0.452059i	$0.149310\pi$
$937$			27.6754i			0.904117i	−0.891988	+	0.452059i	$0.850690\pi$
$938$	−2.01312	+	1.16228i	−0.0657308	+	0.0379497i
$939$	−13.1623	−	22.7977i	−0.429535	−	0.743976i
$940$		0			0
$941$	22.3246			0.727760			0.363880	−	0.931446i	$-0.381452\pi$
$941$	22.3246			0.727760			0.363880	+	0.931446i	$0.381452\pi$
$942$	33.3078	+	19.2302i	1.08523	+	0.626555i
$943$	−53.6480	−	30.9737i	−1.74702	−	1.00864i
$944$	10.3246			0.336036
$945$		0			0
$946$	−2.16228	−	3.74517i	−0.0703017	−	0.121766i
$947$	−1.56871	+	0.905694i	−0.0509762	+	0.0294311i	−0.525271	−	0.850935i	$-0.676036\pi$
$947$	−1.56871	+	0.905694i	−0.0509762	+	0.0294311i	0.474295	+	0.880366i	$0.342703\pi$
$948$			42.6491i			1.38518i
$949$	8.74342	−	5.31388i	0.283823	−	0.172496i
$950$		0			0
$951$	−19.7434	−	34.1966i	−0.640224	−	1.10890i
$952$	4.47066	−	2.58114i	0.144895	−	0.0836552i
$953$	−2.17647	−	1.25658i	−0.0705027	−	0.0407047i	0.464334	−	0.885660i	$-0.346294\pi$
$953$	−2.17647	−	1.25658i	−0.0705027	−	0.0407047i	−0.534837	+	0.844955i	$0.679627\pi$
$954$	15.1359			0.490044
$955$		0			0
$956$	−5.58114	+	9.66682i	−0.180507	+	0.312647i
$957$			70.5964i			2.28206i
$958$	−10.5100	−	6.06797i	−0.339564	−	0.196047i
$959$	−7.74342	−	13.4120i	−0.250048	−	0.433096i
$960$		0			0
$961$	20.2982			0.654781
$962$	−0.584952	+	0.0131670i	−0.0188596	+	0.000424522i
$963$			24.4078i			0.786531i
$964$	−12.9868	−	22.4939i	−0.418278	−	0.724478i
$965$		0			0
$966$	9.48683	−	16.4317i	0.305234	−	0.528681i
$967$		−	16.6228i		−	0.534552i	−0.963620	−	0.267276i	$-0.913876\pi$
$967$		−	16.6228i		−	0.534552i	0.963620	−	0.267276i	$-0.0861236\pi$
$968$	−5.47723	−	3.16228i	−0.176045	−	0.101639i
$969$	15.0000	−	25.9808i	0.481869	−	0.834622i
$970$		0			0
$971$	−29.8925	+	51.7754i	−0.959297	+	1.66155i	−0.235083	+	0.971975i	$0.575536\pi$
$971$	−29.8925	+	51.7754i	−0.959297	+	1.66155i	−0.724214	+	0.689576i	$0.757797\pi$
$972$	19.1703	−	11.0680i	0.614887	−	0.355005i
$973$	−10.5328	+	6.08114i	−0.337667	+	0.194952i
$974$	1.00000			0.0320421
$975$		0			0
$976$	−7.48683			−0.239648
$977$	16.4317	−	9.48683i	0.525696	−	0.303511i	−0.213566	−	0.976929i	$-0.568508\pi$
$977$	16.4317	−	9.48683i	0.525696	−	0.303511i	0.739262	+	0.673418i	$0.235175\pi$
$978$	−47.8897	+	27.6491i	−1.53134	+	0.884121i
$979$	−7.91886	+	13.7159i	−0.253088	+	0.438361i
$980$		0			0
$981$	−37.2719	+	64.5568i	−1.19000	+	2.06114i
$982$	−15.1668	−	8.75658i	−0.483994	−	0.279434i
$983$		−	30.3509i		−	0.968043i	−0.875056	−	0.484022i	$-0.839176\pi$
$983$		−	30.3509i		−	0.968043i	0.875056	−	0.484022i	$-0.160824\pi$
$984$	−16.3246	+	28.2750i	−0.520408	+	0.901373i
$985$		0			0
$986$	26.6491	+	46.1576i	0.848681	+	1.46996i
$987$			9.48683i			0.301969i
$988$	−3.18303	+	5.81139i	−0.101266	+	0.184885i
$989$	−12.0000			−0.381578
$990$		0			0
$991$	19.6491	+	34.0333i	0.624175	+	1.08110i	0.988700	+	0.149909i	$0.0478979\pi$
$991$	19.6491	+	34.0333i	0.624175	+	1.08110i	−0.364525	+	0.931193i	$0.618769\pi$
$992$	−6.20271	−	3.58114i	−0.196936	−	0.113701i
$993$			77.9473i			2.47358i
$994$	2.16228	−	3.74517i	0.0685833	−	0.118790i
$995$		0			0
$996$	30.0000			0.950586
$997$	−10.2518	−	5.91886i	−0.324677	−	0.187452i	0.328798	−	0.944400i	$-0.393356\pi$
$997$	−10.2518	−	5.91886i	−0.324677	−	0.187452i	−0.653475	+	0.756948i	$0.726690\pi$
$998$	19.0526	−	11.0000i	0.603098	−	0.348199i
$999$	−1.02633	−	1.77766i	−0.0324718	−	0.0562428i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.o.g.549.3		8
5.2	odd	4		650.2.e.h.601.2		4
5.3	odd	4		130.2.e.c.81.1	yes	4
5.4	even	2	inner	650.2.o.g.549.2		8
13.9	even	3	inner	650.2.o.g.399.2		8
15.8	even	4		1170.2.i.q.991.2		4
20.3	even	4		1040.2.q.m.81.2		4
65.3	odd	12		1690.2.a.n.1.2		2
65.8	even	4		1690.2.l.k.361.3		8
65.9	even	6	inner	650.2.o.g.399.3		8
65.18	even	4		1690.2.l.k.361.1		8
65.22	odd	12		650.2.e.h.451.2		4
65.23	odd	12		1690.2.a.k.1.2		2
65.28	even	12		1690.2.d.g.1351.2		4
65.33	even	12		1690.2.l.k.1161.1		8
65.38	odd	4		1690.2.e.m.991.1		4
65.42	odd	12		8450.2.a.bc.1.1		2
65.43	odd	12		1690.2.e.m.191.1		4
65.48	odd	12		130.2.e.c.61.1	✓	4
65.58	even	12		1690.2.l.k.1161.3		8
65.62	odd	12		8450.2.a.bj.1.1		2
65.63	even	12		1690.2.d.g.1351.4		4
195.113	even	12		1170.2.i.q.451.2		4
260.243	even	12		1040.2.q.m.321.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.e.c.61.1	✓	4	65.48	odd	12
130.2.e.c.81.1	yes	4	5.3	odd	4
650.2.e.h.451.2		4	65.22	odd	12
650.2.e.h.601.2		4	5.2	odd	4
650.2.o.g.399.2		8	13.9	even	3	inner
650.2.o.g.399.3		8	65.9	even	6	inner
650.2.o.g.549.2		8	5.4	even	2	inner
650.2.o.g.549.3		8	1.1	even	1	trivial
1040.2.q.m.81.2		4	20.3	even	4
1040.2.q.m.321.2		4	260.243	even	12
1170.2.i.q.451.2		4	195.113	even	12
1170.2.i.q.991.2		4	15.8	even	4
1690.2.a.k.1.2		2	65.23	odd	12
1690.2.a.n.1.2		2	65.3	odd	12
1690.2.d.g.1351.2		4	65.28	even	12
1690.2.d.g.1351.4		4	65.63	even	12
1690.2.e.m.191.1		4	65.43	odd	12
1690.2.e.m.991.1		4	65.38	odd	4
1690.2.l.k.361.1		8	65.18	even	4
1690.2.l.k.361.3		8	65.8	even	4
1690.2.l.k.1161.1		8	65.33	even	12
1690.2.l.k.1161.3		8	65.58	even	12
8450.2.a.bc.1.1		2	65.42	odd	12
8450.2.a.bj.1.1		2	65.62	odd	12

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:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-2.73861 + 1.58114i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.58114 + 2.73861i) q^{6} +(0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(3.50000 - 6.06218i) q^{9} +(-1.08114 - 1.87259i) q^{11} +3.16228i q^{12} +(1.87259 + 3.08114i) q^{13} +1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(4.47066 + 2.58114i) q^{17} -7.00000i q^{18} +(-0.918861 + 1.59151i) q^{19} -3.16228 q^{21} +(-1.87259 - 1.08114i) q^{22} +(-5.19615 + 3.00000i) q^{23} +(1.58114 + 2.73861i) q^{24} +(3.16228 + 1.73205i) q^{26} +12.6491i q^{27} +(0.866025 - 0.500000i) q^{28} +(5.16228 + 8.94133i) q^{29} +7.16228 q^{31} +(-0.866025 - 0.500000i) q^{32} +(5.92164 + 3.41886i) q^{33} +5.16228 q^{34} +(-3.50000 - 6.06218i) q^{36} +(-0.140537 + 0.0811388i) q^{37} +1.83772i q^{38} +(-10.0000 - 5.47723i) q^{39} +(5.16228 + 8.94133i) q^{41} +(-2.73861 + 1.58114i) q^{42} +(1.73205 + 1.00000i) q^{43} -2.16228 q^{44} +(-3.00000 + 5.19615i) q^{46} -3.00000i q^{47} +(2.73861 + 1.58114i) q^{48} +(-3.00000 - 5.19615i) q^{49} -16.3246 q^{51} +(3.60464 - 0.0811388i) q^{52} +2.16228i q^{53} +(6.32456 + 10.9545i) q^{54} +(0.500000 - 0.866025i) q^{56} -5.81139i q^{57} +(8.94133 + 5.16228i) q^{58} +(-5.16228 + 8.94133i) q^{59} +(3.74342 - 6.48379i) q^{61} +(6.20271 - 3.58114i) q^{62} +(6.06218 - 3.50000i) q^{63} -1.00000 q^{64} +6.83772 q^{66} +(-2.01312 + 1.16228i) q^{67} +(4.47066 - 2.58114i) q^{68} +(9.48683 - 16.4317i) q^{69} +(2.16228 - 3.74517i) q^{71} +(-6.06218 - 3.50000i) q^{72} -2.83772i q^{73} +(-0.0811388 + 0.140537i) q^{74} +(0.918861 + 1.59151i) q^{76} -2.16228i q^{77} +(-11.3989 + 0.256584i) q^{78} +13.4868 q^{79} +(-9.50000 - 16.4545i) q^{81} +(8.94133 + 5.16228i) q^{82} -9.48683i q^{83} +(-1.58114 + 2.73861i) q^{84} +2.00000 q^{86} +(-28.2750 - 16.3246i) q^{87} +(-1.87259 + 1.08114i) q^{88} +(-3.66228 - 6.34325i) q^{89} +(0.0811388 + 3.60464i) q^{91} +6.00000i q^{92} +(-19.6147 + 11.3246i) q^{93} +(-1.50000 - 2.59808i) q^{94} +3.16228 q^{96} +(6.48379 + 3.74342i) q^{97} +(-5.19615 - 3.00000i) q^{98} -15.1359 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} + 28 q^{9} + 4 q^{11} + 8 q^{14} - 4 q^{16} - 20 q^{19} + 16 q^{29} + 32 q^{31} + 16 q^{34} - 28 q^{36} - 80 q^{39} + 16 q^{41} + 8 q^{44} - 24 q^{46} - 24 q^{49} - 80 q^{51} + 4 q^{56} - 16 q^{59}+ \cdots + 56 q^{99}+O(q^{100}) \) 8 * q + 4 * q^4 + 28 * q^9 + 4 * q^11 + 8 * q^14 - 4 * q^16 - 20 * q^19 + 16 * q^29 + 32 * q^31 + 16 * q^34 - 28 * q^36 - 80 * q^39 + 16 * q^41 + 8 * q^44 - 24 * q^46 - 24 * q^49 - 80 * q^51 + 4 * q^56 - 16 * q^59 - 8 * q^61 - 8 * q^64 + 80 * q^66 - 8 * q^71 + 12 * q^74 + 20 * q^76 + 32 * q^79 - 76 * q^81 + 16 * q^86 - 4 * q^89 - 12 * q^91 - 12 * q^94 + 56 * q^99

Introduction

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