LMFDB - Embedded newform 1078.2.e.s.177.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1078,2,Mod(67,1078)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1078, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("1078.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1078 = 2 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1078.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$8.60787333789$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			177.2
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1078.177
Dual form			1078.2.e.s.67.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.707107 + 1.22474i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.707107 + 1.22474i) q^{5} +1.41421 q^{6} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(0.707107 + 1.22474i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.707107 + 1.22474i) q^{5} +1.41421 q^{6} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(0.707107 + 1.22474i) q^{10} +(0.500000 + 0.866025i) q^{11} +(0.707107 - 1.22474i) q^{12} +2.82843 q^{13} -2.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.82843 + 4.89898i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-1.41421 + 2.44949i) q^{19} +1.41421 q^{20} +1.00000 q^{22} +(1.00000 - 1.73205i) q^{23} +(-0.707107 - 1.22474i) q^{24} +(1.50000 + 2.59808i) q^{25} +(1.41421 - 2.44949i) q^{26} +5.65685 q^{27} -6.00000 q^{29} +(-1.00000 + 1.73205i) q^{30} +(0.707107 + 1.22474i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.707107 + 1.22474i) q^{33} +5.65685 q^{34} -1.00000 q^{36} +(1.00000 - 1.73205i) q^{37} +(1.41421 + 2.44949i) q^{38} +(2.00000 + 3.46410i) q^{39} +(0.707107 - 1.22474i) q^{40} +5.65685 q^{41} +4.00000 q^{43} +(0.500000 - 0.866025i) q^{44} +(0.707107 + 1.22474i) q^{45} +(-1.00000 - 1.73205i) q^{46} +(-2.12132 + 3.67423i) q^{47} -1.41421 q^{48} +3.00000 q^{50} +(-4.00000 + 6.92820i) q^{51} +(-1.41421 - 2.44949i) q^{52} +(6.00000 + 10.3923i) q^{53} +(2.82843 - 4.89898i) q^{54} -1.41421 q^{55} -4.00000 q^{57} +(-3.00000 + 5.19615i) q^{58} +(-2.12132 - 3.67423i) q^{59} +(1.00000 + 1.73205i) q^{60} +(2.82843 - 4.89898i) q^{61} +1.41421 q^{62} +1.00000 q^{64} +(-2.00000 + 3.46410i) q^{65} +(0.707107 + 1.22474i) q^{66} +(1.00000 + 1.73205i) q^{67} +(2.82843 - 4.89898i) q^{68} +2.82843 q^{69} -10.0000 q^{71} +(-0.500000 + 0.866025i) q^{72} +(7.07107 + 12.2474i) q^{73} +(-1.00000 - 1.73205i) q^{74} +(-2.12132 + 3.67423i) q^{75} +2.82843 q^{76} +4.00000 q^{78} +(4.00000 - 6.92820i) q^{79} +(-0.707107 - 1.22474i) q^{80} +(2.50000 + 4.33013i) q^{81} +(2.82843 - 4.89898i) q^{82} -2.82843 q^{83} -8.00000 q^{85} +(2.00000 - 3.46410i) q^{86} +(-4.24264 - 7.34847i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(3.53553 - 6.12372i) q^{89} +1.41421 q^{90} -2.00000 q^{92} +(-1.00000 + 1.73205i) q^{93} +(2.12132 + 3.67423i) q^{94} +(-2.00000 - 3.46410i) q^{95} +(-0.707107 + 1.22474i) q^{96} -15.5563 q^{97} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} - 4 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 + 2 * q^9	$ 4 q + 2 q^{2} - 2 q^{4} - 4 q^{8} + 2 q^{9} + 2 q^{11} - 8 q^{15} - 2 q^{16} - 2 q^{18} + 4 q^{22} + 4 q^{23} + 6 q^{25} - 24 q^{29} - 4 q^{30} + 2 q^{32} - 4 q^{36} + 4 q^{37} + 8 q^{39} + 16 q^{43} + 2 q^{44} - 4 q^{46} + 12 q^{50} - 16 q^{51} + 24 q^{53} - 16 q^{57} - 12 q^{58} + 4 q^{60} + 4 q^{64} - 8 q^{65} + 4 q^{67} - 40 q^{71} - 2 q^{72} - 4 q^{74} + 16 q^{78} + 16 q^{79} + 10 q^{81} - 32 q^{85} + 8 q^{86} - 2 q^{88} - 8 q^{92} - 4 q^{93} - 8 q^{95} + 4 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 + 2 * q^9 + 2 * q^11 - 8 * q^15 - 2 * q^16 - 2 * q^18 + 4 * q^22 + 4 * q^23 + 6 * q^25 - 24 * q^29 - 4 * q^30 + 2 * q^32 - 4 * q^36 + 4 * q^37 + 8 * q^39 + 16 * q^43 + 2 * q^44 - 4 * q^46 + 12 * q^50 - 16 * q^51 + 24 * q^53 - 16 * q^57 - 12 * q^58 + 4 * q^60 + 4 * q^64 - 8 * q^65 + 4 * q^67 - 40 * q^71 - 2 * q^72 - 4 * q^74 + 16 * q^78 + 16 * q^79 + 10 * q^81 - 32 * q^85 + 8 * q^86 - 2 * q^88 - 8 * q^92 - 4 * q^93 - 8 * q^95 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times$.

$n$	$199$	$981$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	0.707107	+	1.22474i	0.408248	+	0.707107i	0.994694	−	0.102882i	$-0.0328064\pi$
$3$	0.707107	+	1.22474i	0.408248	+	0.707107i	−0.586445	+	0.809989i	$0.699473\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.707107	+	1.22474i	−0.316228	+	0.547723i	−0.979698	−	0.200480i	$-0.935750\pi$
$5$	−0.707107	+	1.22474i	−0.316228	+	0.547723i	0.663470	+	0.748203i	$0.269083\pi$
$6$	1.41421			0.577350
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	0.707107	+	1.22474i	0.223607	+	0.387298i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	0.707107	−	1.22474i	0.204124	−	0.353553i
$13$	2.82843			0.784465			0.392232	−	0.919866i	$-0.371703\pi$
$13$	2.82843			0.784465			0.392232	+	0.919866i	$0.371703\pi$
$14$		0			0
$15$	−2.00000			−0.516398
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.82843	+	4.89898i	0.685994	+	1.18818i	0.973123	+	0.230285i	$0.0739659\pi$
$17$	2.82843	+	4.89898i	0.685994	+	1.18818i	−0.287129	+	0.957892i	$0.592701\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	−1.41421	+	2.44949i	−0.324443	+	0.561951i	−0.981399	−	0.191977i	$-0.938510\pi$
$19$	−1.41421	+	2.44949i	−0.324443	+	0.561951i	0.656957	+	0.753928i	$0.271843\pi$
$20$	1.41421			0.316228
$21$		0			0
$22$	1.00000			0.213201
$23$	1.00000	−	1.73205i	0.208514	−	0.361158i	−0.742732	−	0.669588i	$-0.766471\pi$
$23$	1.00000	−	1.73205i	0.208514	−	0.361158i	0.951247	+	0.308431i	$0.0998038\pi$
$24$	−0.707107	−	1.22474i	−0.144338	−	0.250000i
$25$	1.50000	+	2.59808i	0.300000	+	0.519615i
$26$	1.41421	−	2.44949i	0.277350	−	0.480384i
$27$	5.65685			1.08866
$28$		0			0
$29$	−6.00000			−1.11417			−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000			−1.11417			−0.557086	+	0.830455i	$0.688081\pi$
$30$	−1.00000	+	1.73205i	−0.182574	+	0.316228i
$31$	0.707107	+	1.22474i	0.127000	+	0.219971i	0.922513	−	0.385966i	$-0.126132\pi$
$31$	0.707107	+	1.22474i	0.127000	+	0.219971i	−0.795513	+	0.605937i	$0.792798\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−0.707107	+	1.22474i	−0.123091	+	0.213201i
$34$	5.65685			0.970143
$35$		0			0
$36$	−1.00000			−0.166667
$37$	1.00000	−	1.73205i	0.164399	−	0.284747i	−0.772043	−	0.635571i	$-0.780765\pi$
$37$	1.00000	−	1.73205i	0.164399	−	0.284747i	0.936442	+	0.350823i	$0.114098\pi$
$38$	1.41421	+	2.44949i	0.229416	+	0.397360i
$39$	2.00000	+	3.46410i	0.320256	+	0.554700i
$40$	0.707107	−	1.22474i	0.111803	−	0.193649i
$41$	5.65685			0.883452			0.441726	−	0.897150i	$-0.354366\pi$
$41$	5.65685			0.883452			0.441726	+	0.897150i	$0.354366\pi$
$42$		0			0
$43$	4.00000			0.609994			0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000			0.609994			0.304997	+	0.952353i	$0.401344\pi$
$44$	0.500000	−	0.866025i	0.0753778	−	0.130558i
$45$	0.707107	+	1.22474i	0.105409	+	0.182574i
$46$	−1.00000	−	1.73205i	−0.147442	−	0.255377i
$47$	−2.12132	+	3.67423i	−0.309426	+	0.535942i	−0.978237	−	0.207491i	$-0.933470\pi$
$47$	−2.12132	+	3.67423i	−0.309426	+	0.535942i	0.668811	+	0.743433i	$0.266804\pi$
$48$	−1.41421			−0.204124
$49$		0			0
$50$	3.00000			0.424264
$51$	−4.00000	+	6.92820i	−0.560112	+	0.970143i
$52$	−1.41421	−	2.44949i	−0.196116	−	0.339683i
$53$	6.00000	+	10.3923i	0.824163	+	1.42749i	0.902557	+	0.430570i	$0.141688\pi$
$53$	6.00000	+	10.3923i	0.824163	+	1.42749i	−0.0783936	+	0.996922i	$0.524979\pi$
$54$	2.82843	−	4.89898i	0.384900	−	0.666667i
$55$	−1.41421			−0.190693
$56$		0			0
$57$	−4.00000			−0.529813
$58$	−3.00000	+	5.19615i	−0.393919	+	0.682288i
$59$	−2.12132	−	3.67423i	−0.276172	−	0.478345i	0.694258	−	0.719726i	$-0.255733\pi$
$59$	−2.12132	−	3.67423i	−0.276172	−	0.478345i	−0.970430	+	0.241382i	$0.922399\pi$
$60$	1.00000	+	1.73205i	0.129099	+	0.223607i
$61$	2.82843	−	4.89898i	0.362143	−	0.627250i	−0.626170	−	0.779686i	$-0.715379\pi$
$61$	2.82843	−	4.89898i	0.362143	−	0.627250i	0.988313	+	0.152436i	$0.0487119\pi$
$62$	1.41421			0.179605
$63$		0			0
$64$	1.00000			0.125000
$65$	−2.00000	+	3.46410i	−0.248069	+	0.429669i
$66$	0.707107	+	1.22474i	0.0870388	+	0.150756i
$67$	1.00000	+	1.73205i	0.122169	+	0.211604i	0.920623	−	0.390453i	$-0.127682\pi$
$67$	1.00000	+	1.73205i	0.122169	+	0.211604i	−0.798454	+	0.602056i	$0.794348\pi$
$68$	2.82843	−	4.89898i	0.342997	−	0.594089i
$69$	2.82843			0.340503
$70$		0			0
$71$	−10.0000			−1.18678			−0.593391	−	0.804914i	$-0.702211\pi$
$71$	−10.0000			−1.18678			−0.593391	+	0.804914i	$0.702211\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	7.07107	+	12.2474i	0.827606	+	1.43346i	0.899911	+	0.436073i	$0.143631\pi$
$73$	7.07107	+	12.2474i	0.827606	+	1.43346i	−0.0723054	+	0.997383i	$0.523036\pi$
$74$	−1.00000	−	1.73205i	−0.116248	−	0.201347i
$75$	−2.12132	+	3.67423i	−0.244949	+	0.424264i
$76$	2.82843			0.324443
$77$		0			0
$78$	4.00000			0.452911
$79$	4.00000	−	6.92820i	0.450035	−	0.779484i	−0.548352	−	0.836247i	$-0.684745\pi$
$79$	4.00000	−	6.92820i	0.450035	−	0.779484i	0.998388	+	0.0567635i	$0.0180781\pi$
$80$	−0.707107	−	1.22474i	−0.0790569	−	0.136931i
$81$	2.50000	+	4.33013i	0.277778	+	0.481125i
$82$	2.82843	−	4.89898i	0.312348	−	0.541002i
$83$	−2.82843			−0.310460			−0.155230	−	0.987878i	$-0.549612\pi$
$83$	−2.82843			−0.310460			−0.155230	+	0.987878i	$0.549612\pi$
$84$		0			0
$85$	−8.00000			−0.867722
$86$	2.00000	−	3.46410i	0.215666	−	0.373544i
$87$	−4.24264	−	7.34847i	−0.454859	−	0.787839i
$88$	−0.500000	−	0.866025i	−0.0533002	−	0.0923186i
$89$	3.53553	−	6.12372i	0.374766	−	0.649113i	−0.615526	−	0.788116i	$-0.711056\pi$
$89$	3.53553	−	6.12372i	0.374766	−	0.649113i	0.990292	+	0.139003i	$0.0443898\pi$
$90$	1.41421			0.149071
$91$		0			0
$92$	−2.00000			−0.208514
$93$	−1.00000	+	1.73205i	−0.103695	+	0.179605i
$94$	2.12132	+	3.67423i	0.218797	+	0.378968i
$95$	−2.00000	−	3.46410i	−0.205196	−	0.355409i
$96$	−0.707107	+	1.22474i	−0.0721688	+	0.125000i
$97$	−15.5563			−1.57951			−0.789754	−	0.613424i	$-0.789792\pi$
$97$	−15.5563			−1.57951			−0.789754	+	0.613424i	$0.789792\pi$
$98$		0			0
$99$	1.00000			0.100504
$100$	1.50000	−	2.59808i	0.150000	−	0.259808i
$101$	−1.41421	−	2.44949i	−0.140720	−	0.243733i	0.787048	−	0.616891i	$-0.211608\pi$
$101$	−1.41421	−	2.44949i	−0.140720	−	0.243733i	−0.927768	+	0.373158i	$0.878275\pi$
$102$	4.00000	+	6.92820i	0.396059	+	0.685994i
$103$	2.12132	−	3.67423i	0.209020	−	0.362033i	−0.742386	−	0.669972i	$-0.766306\pi$
$103$	2.12132	−	3.67423i	0.209020	−	0.362033i	0.951406	+	0.307939i	$0.0996393\pi$
$104$	−2.82843			−0.277350
$105$		0			0
$106$	12.0000			1.16554
$107$	10.0000	−	17.3205i	0.966736	−	1.67444i	0.261861	−	0.965106i	$-0.415664\pi$
$107$	10.0000	−	17.3205i	0.966736	−	1.67444i	0.704875	−	0.709331i	$-0.251003\pi$
$108$	−2.82843	−	4.89898i	−0.272166	−	0.471405i
$109$	−5.00000	−	8.66025i	−0.478913	−	0.829502i	0.520794	−	0.853682i	$-0.325636\pi$
$109$	−5.00000	−	8.66025i	−0.478913	−	0.829502i	−0.999708	+	0.0241802i	$0.992302\pi$
$110$	−0.707107	+	1.22474i	−0.0674200	+	0.116775i
$111$	2.82843			0.268462
$112$		0			0
$113$	−18.0000			−1.69330			−0.846649	−	0.532152i	$-0.821383\pi$
$113$	−18.0000			−1.69330			−0.846649	+	0.532152i	$0.821383\pi$
$114$	−2.00000	+	3.46410i	−0.187317	+	0.324443i
$115$	1.41421	+	2.44949i	0.131876	+	0.228416i
$116$	3.00000	+	5.19615i	0.278543	+	0.482451i
$117$	1.41421	−	2.44949i	0.130744	−	0.226455i
$118$	−4.24264			−0.390567
$119$		0			0
$120$	2.00000			0.182574
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−2.82843	−	4.89898i	−0.256074	−	0.443533i
$123$	4.00000	+	6.92820i	0.360668	+	0.624695i
$124$	0.707107	−	1.22474i	0.0635001	−	0.109985i
$125$	−11.3137			−1.01193
$126$		0			0
$127$	12.0000			1.06483			0.532414	−	0.846484i	$-0.321285\pi$
$127$	12.0000			1.06483			0.532414	+	0.846484i	$0.321285\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	2.82843	+	4.89898i	0.249029	+	0.431331i
$130$	2.00000	+	3.46410i	0.175412	+	0.303822i
$131$	−5.65685	+	9.79796i	−0.494242	+	0.856052i	−0.999978	−	0.00663646i	$-0.997888\pi$
$131$	−5.65685	+	9.79796i	−0.494242	+	0.856052i	0.505736	+	0.862688i	$0.331221\pi$
$132$	1.41421			0.123091
$133$		0			0
$134$	2.00000			0.172774
$135$	−4.00000	+	6.92820i	−0.344265	+	0.596285i
$136$	−2.82843	−	4.89898i	−0.242536	−	0.420084i
$137$	1.00000	+	1.73205i	0.0854358	+	0.147979i	0.905577	−	0.424182i	$-0.139438\pi$
$137$	1.00000	+	1.73205i	0.0854358	+	0.147979i	−0.820141	+	0.572161i	$0.806105\pi$
$138$	1.41421	−	2.44949i	0.120386	−	0.208514i
$139$	−2.82843			−0.239904			−0.119952	−	0.992780i	$-0.538274\pi$
$139$	−2.82843			−0.239904			−0.119952	+	0.992780i	$0.538274\pi$
$140$		0			0
$141$	−6.00000			−0.505291
$142$	−5.00000	+	8.66025i	−0.419591	+	0.726752i
$143$	1.41421	+	2.44949i	0.118262	+	0.204837i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	4.24264	−	7.34847i	0.352332	−	0.610257i
$146$	14.1421			1.17041
$147$		0			0
$148$	−2.00000			−0.164399
$149$	5.00000	−	8.66025i	0.409616	−	0.709476i	−0.585231	−	0.810867i	$-0.698996\pi$
$149$	5.00000	−	8.66025i	0.409616	−	0.709476i	0.994847	+	0.101391i	$0.0323294\pi$
$150$	2.12132	+	3.67423i	0.173205	+	0.300000i
$151$	−8.00000	−	13.8564i	−0.651031	−	1.12762i	−0.982873	−	0.184284i	$-0.941004\pi$
$151$	−8.00000	−	13.8564i	−0.651031	−	1.12762i	0.331842	−	0.943335i	$-0.392330\pi$
$152$	1.41421	−	2.44949i	0.114708	−	0.198680i
$153$	5.65685			0.457330
$154$		0			0
$155$	−2.00000			−0.160644
$156$	2.00000	−	3.46410i	0.160128	−	0.277350i
$157$	−9.19239	−	15.9217i	−0.733632	−	1.27069i	−0.955321	−	0.295571i	$-0.904490\pi$
$157$	−9.19239	−	15.9217i	−0.733632	−	1.27069i	0.221688	−	0.975118i	$-0.428843\pi$
$158$	−4.00000	−	6.92820i	−0.318223	−	0.551178i
$159$	−8.48528	+	14.6969i	−0.672927	+	1.16554i
$160$	−1.41421			−0.111803
$161$		0			0
$162$	5.00000			0.392837
$163$	11.0000	−	19.0526i	0.861586	−	1.49231i	−0.00881059	−	0.999961i	$-0.502805\pi$
$163$	11.0000	−	19.0526i	0.861586	−	1.49231i	0.870397	−	0.492350i	$-0.163862\pi$
$164$	−2.82843	−	4.89898i	−0.220863	−	0.382546i
$165$	−1.00000	−	1.73205i	−0.0778499	−	0.134840i
$166$	−1.41421	+	2.44949i	−0.109764	+	0.190117i
$167$	−11.3137			−0.875481			−0.437741	−	0.899101i	$-0.644221\pi$
$167$	−11.3137			−0.875481			−0.437741	+	0.899101i	$0.644221\pi$
$168$		0			0
$169$	−5.00000			−0.384615
$170$	−4.00000	+	6.92820i	−0.306786	+	0.531369i
$171$	1.41421	+	2.44949i	0.108148	+	0.187317i
$172$	−2.00000	−	3.46410i	−0.152499	−	0.264135i
$173$	−7.07107	+	12.2474i	−0.537603	+	0.931156i	0.461429	+	0.887177i	$0.347337\pi$
$173$	−7.07107	+	12.2474i	−0.537603	+	0.931156i	−0.999032	+	0.0439792i	$0.985996\pi$
$174$	−8.48528			−0.643268
$175$		0			0
$176$	−1.00000			−0.0753778
$177$	3.00000	−	5.19615i	0.225494	−	0.390567i
$178$	−3.53553	−	6.12372i	−0.264999	−	0.458993i
$179$	−10.0000	−	17.3205i	−0.747435	−	1.29460i	−0.949048	−	0.315130i	$-0.897952\pi$
$179$	−10.0000	−	17.3205i	−0.747435	−	1.29460i	0.201613	−	0.979465i	$-0.435382\pi$
$180$	0.707107	−	1.22474i	0.0527046	−	0.0912871i
$181$	12.7279			0.946059			0.473029	−	0.881047i	$-0.343160\pi$
$181$	12.7279			0.946059			0.473029	+	0.881047i	$0.343160\pi$
$182$		0			0
$183$	8.00000			0.591377
$184$	−1.00000	+	1.73205i	−0.0737210	+	0.127688i
$185$	1.41421	+	2.44949i	0.103975	+	0.180090i
$186$	1.00000	+	1.73205i	0.0733236	+	0.127000i
$187$	−2.82843	+	4.89898i	−0.206835	+	0.358249i
$188$	4.24264			0.309426
$189$		0			0
$190$	−4.00000			−0.290191
$191$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$191$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$192$	0.707107	+	1.22474i	0.0510310	+	0.0883883i
$193$	−3.00000	−	5.19615i	−0.215945	−	0.374027i	0.737620	−	0.675216i	$-0.235950\pi$
$193$	−3.00000	−	5.19615i	−0.215945	−	0.374027i	−0.953564	+	0.301189i	$0.902616\pi$
$194$	−7.77817	+	13.4722i	−0.558440	+	0.967247i
$195$	−5.65685			−0.405096
$196$		0			0
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$	0.500000	−	0.866025i	0.0355335	−	0.0615457i
$199$	−10.6066	−	18.3712i	−0.751882	−	1.30230i	−0.946910	−	0.321500i	$-0.895813\pi$
$199$	−10.6066	−	18.3712i	−0.751882	−	1.30230i	0.195027	−	0.980798i	$-0.437520\pi$
$200$	−1.50000	−	2.59808i	−0.106066	−	0.183712i
$201$	−1.41421	+	2.44949i	−0.0997509	+	0.172774i
$202$	−2.82843			−0.199007
$203$		0			0
$204$	8.00000			0.560112
$205$	−4.00000	+	6.92820i	−0.279372	+	0.483887i
$206$	−2.12132	−	3.67423i	−0.147799	−	0.255996i
$207$	−1.00000	−	1.73205i	−0.0695048	−	0.120386i
$208$	−1.41421	+	2.44949i	−0.0980581	+	0.169842i
$209$	−2.82843			−0.195646
$210$		0			0
$211$	28.0000			1.92760			0.963800	−	0.266627i	$-0.0859092\pi$
$211$	28.0000			1.92760			0.963800	+	0.266627i	$0.0859092\pi$
$212$	6.00000	−	10.3923i	0.412082	−	0.713746i
$213$	−7.07107	−	12.2474i	−0.484502	−	0.839181i
$214$	−10.0000	−	17.3205i	−0.683586	−	1.18401i
$215$	−2.82843	+	4.89898i	−0.192897	+	0.334108i
$216$	−5.65685			−0.384900
$217$		0			0
$218$	−10.0000			−0.677285
$219$	−10.0000	+	17.3205i	−0.675737	+	1.17041i
$220$	0.707107	+	1.22474i	0.0476731	+	0.0825723i
$221$	8.00000	+	13.8564i	0.538138	+	0.932083i
$222$	1.41421	−	2.44949i	0.0949158	−	0.164399i
$223$	−15.5563			−1.04173			−0.520865	−	0.853639i	$-0.674391\pi$
$223$	−15.5563			−1.04173			−0.520865	+	0.853639i	$0.674391\pi$
$224$		0			0
$225$	3.00000			0.200000
$226$	−9.00000	+	15.5885i	−0.598671	+	1.03693i
$227$	14.1421	+	24.4949i	0.938647	+	1.62578i	0.767999	+	0.640451i	$0.221253\pi$
$227$	14.1421	+	24.4949i	0.938647	+	1.62578i	0.170648	+	0.985332i	$0.445414\pi$
$228$	2.00000	+	3.46410i	0.132453	+	0.229416i
$229$	2.12132	−	3.67423i	0.140181	−	0.242800i	−0.787384	−	0.616463i	$-0.788565\pi$
$229$	2.12132	−	3.67423i	0.140181	−	0.242800i	0.927565	+	0.373663i	$0.121898\pi$
$230$	2.82843			0.186501
$231$		0			0
$232$	6.00000			0.393919
$233$	−3.00000	+	5.19615i	−0.196537	+	0.340411i	−0.947403	−	0.320043i	$-0.896303\pi$
$233$	−3.00000	+	5.19615i	−0.196537	+	0.340411i	0.750867	+	0.660454i	$0.229636\pi$
$234$	−1.41421	−	2.44949i	−0.0924500	−	0.160128i
$235$	−3.00000	−	5.19615i	−0.195698	−	0.338960i
$236$	−2.12132	+	3.67423i	−0.138086	+	0.239172i
$237$	11.3137			0.734904
$238$		0			0
$239$	−16.0000			−1.03495			−0.517477	−	0.855697i	$-0.673129\pi$
$239$	−16.0000			−1.03495			−0.517477	+	0.855697i	$0.673129\pi$
$240$	1.00000	−	1.73205i	0.0645497	−	0.111803i
$241$	2.82843	+	4.89898i	0.182195	+	0.315571i	0.942628	−	0.333846i	$-0.108346\pi$
$241$	2.82843	+	4.89898i	0.182195	+	0.315571i	−0.760433	+	0.649417i	$0.775013\pi$
$242$	0.500000	+	0.866025i	0.0321412	+	0.0556702i
$243$	4.94975	−	8.57321i	0.317526	−	0.549972i
$244$	−5.65685			−0.362143
$245$		0			0
$246$	8.00000			0.510061
$247$	−4.00000	+	6.92820i	−0.254514	+	0.440831i
$248$	−0.707107	−	1.22474i	−0.0449013	−	0.0777714i
$249$	−2.00000	−	3.46410i	−0.126745	−	0.219529i
$250$	−5.65685	+	9.79796i	−0.357771	+	0.619677i
$251$	−24.0416			−1.51749			−0.758747	−	0.651385i	$-0.774188\pi$
$251$	−24.0416			−1.51749			−0.758747	+	0.651385i	$0.774188\pi$
$252$		0			0
$253$	2.00000			0.125739
$254$	6.00000	−	10.3923i	0.376473	−	0.652071i
$255$	−5.65685	−	9.79796i	−0.354246	−	0.613572i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	4.94975	−	8.57321i	0.308757	−	0.534782i	−0.669334	−	0.742962i	$-0.733420\pi$
$257$	4.94975	−	8.57321i	0.308757	−	0.534782i	0.978091	+	0.208179i	$0.0667538\pi$
$258$	5.65685			0.352180
$259$		0			0
$260$	4.00000			0.248069
$261$	−3.00000	+	5.19615i	−0.185695	+	0.321634i
$262$	5.65685	+	9.79796i	0.349482	+	0.605320i
$263$	−12.0000	−	20.7846i	−0.739952	−	1.28163i	−0.952517	−	0.304487i	$-0.901515\pi$
$263$	−12.0000	−	20.7846i	−0.739952	−	1.28163i	0.212565	−	0.977147i	$-0.431818\pi$
$264$	0.707107	−	1.22474i	0.0435194	−	0.0753778i
$265$	−16.9706			−1.04249
$266$		0			0
$267$	10.0000			0.611990
$268$	1.00000	−	1.73205i	0.0610847	−	0.105802i
$269$	12.0208	+	20.8207i	0.732922	+	1.26946i	0.955629	+	0.294573i	$0.0951773\pi$
$269$	12.0208	+	20.8207i	0.732922	+	1.26946i	−0.222707	+	0.974885i	$0.571489\pi$
$270$	4.00000	+	6.92820i	0.243432	+	0.421637i
$271$	−4.24264	+	7.34847i	−0.257722	+	0.446388i	−0.965631	−	0.259916i	$-0.916305\pi$
$271$	−4.24264	+	7.34847i	−0.257722	+	0.446388i	0.707909	+	0.706303i	$0.249639\pi$
$272$	−5.65685			−0.342997
$273$		0			0
$274$	2.00000			0.120824
$275$	−1.50000	+	2.59808i	−0.0904534	+	0.156670i
$276$	−1.41421	−	2.44949i	−0.0851257	−	0.147442i
$277$	5.00000	+	8.66025i	0.300421	+	0.520344i	0.976231	−	0.216731i	$-0.0695395\pi$
$277$	5.00000	+	8.66025i	0.300421	+	0.520344i	−0.675810	+	0.737075i	$0.736206\pi$
$278$	−1.41421	+	2.44949i	−0.0848189	+	0.146911i
$279$	1.41421			0.0846668
$280$		0			0
$281$	18.0000			1.07379			0.536895	−	0.843649i	$-0.319597\pi$
$281$	18.0000			1.07379			0.536895	+	0.843649i	$0.319597\pi$
$282$	−3.00000	+	5.19615i	−0.178647	+	0.309426i
$283$	−8.48528	−	14.6969i	−0.504398	−	0.873642i	−0.999987	−	0.00508540i	$-0.998381\pi$
$283$	−8.48528	−	14.6969i	−0.504398	−	0.873642i	0.495589	−	0.868557i	$-0.334952\pi$
$284$	5.00000	+	8.66025i	0.296695	+	0.513892i
$285$	2.82843	−	4.89898i	0.167542	−	0.290191i
$286$	2.82843			0.167248
$287$		0			0
$288$	1.00000			0.0589256
$289$	−7.50000	+	12.9904i	−0.441176	+	0.764140i
$290$	−4.24264	−	7.34847i	−0.249136	−	0.431517i
$291$	−11.0000	−	19.0526i	−0.644831	−	1.11688i
$292$	7.07107	−	12.2474i	0.413803	−	0.716728i
$293$	16.9706			0.991431			0.495715	−	0.868485i	$-0.334906\pi$
$293$	16.9706			0.991431			0.495715	+	0.868485i	$0.334906\pi$
$294$		0			0
$295$	6.00000			0.349334
$296$	−1.00000	+	1.73205i	−0.0581238	+	0.100673i
$297$	2.82843	+	4.89898i	0.164122	+	0.284268i
$298$	−5.00000	−	8.66025i	−0.289642	−	0.501675i
$299$	2.82843	−	4.89898i	0.163572	−	0.283315i
$300$	4.24264			0.244949
$301$		0			0
$302$	−16.0000			−0.920697
$303$	2.00000	−	3.46410i	0.114897	−	0.199007i
$304$	−1.41421	−	2.44949i	−0.0811107	−	0.140488i
$305$	4.00000	+	6.92820i	0.229039	+	0.396708i
$306$	2.82843	−	4.89898i	0.161690	−	0.280056i
$307$	−11.3137			−0.645707			−0.322854	−	0.946449i	$-0.604642\pi$
$307$	−11.3137			−0.645707			−0.322854	+	0.946449i	$0.604642\pi$
$308$		0			0
$309$	6.00000			0.341328
$310$	−1.00000	+	1.73205i	−0.0567962	+	0.0983739i
$311$	4.94975	+	8.57321i	0.280674	+	0.486142i	0.971551	−	0.236830i	$-0.0761086\pi$
$311$	4.94975	+	8.57321i	0.280674	+	0.486142i	−0.690877	+	0.722973i	$0.742775\pi$
$312$	−2.00000	−	3.46410i	−0.113228	−	0.196116i
$313$	−13.4350	+	23.2702i	−0.759393	+	1.31531i	0.183768	+	0.982970i	$0.441171\pi$
$313$	−13.4350	+	23.2702i	−0.759393	+	1.31531i	−0.943161	+	0.332337i	$0.892163\pi$
$314$	−18.3848			−1.03751
$315$		0			0
$316$	−8.00000			−0.450035
$317$	13.0000	−	22.5167i	0.730153	−	1.26466i	−0.226665	−	0.973973i	$-0.572782\pi$
$317$	13.0000	−	22.5167i	0.730153	−	1.26466i	0.956818	−	0.290689i	$-0.0938844\pi$
$318$	8.48528	+	14.6969i	0.475831	+	0.824163i
$319$	−3.00000	−	5.19615i	−0.167968	−	0.290929i
$320$	−0.707107	+	1.22474i	−0.0395285	+	0.0684653i
$321$	28.2843			1.57867
$322$		0			0
$323$	−16.0000			−0.890264
$324$	2.50000	−	4.33013i	0.138889	−	0.240563i
$325$	4.24264	+	7.34847i	0.235339	+	0.407620i
$326$	−11.0000	−	19.0526i	−0.609234	−	1.05522i
$327$	7.07107	−	12.2474i	0.391031	−	0.677285i
$328$	−5.65685			−0.312348
$329$		0			0
$330$	−2.00000			−0.110096
$331$	−14.0000	+	24.2487i	−0.769510	+	1.33283i	0.168320	+	0.985732i	$0.446166\pi$
$331$	−14.0000	+	24.2487i	−0.769510	+	1.33283i	−0.937829	+	0.347097i	$0.887167\pi$
$332$	1.41421	+	2.44949i	0.0776151	+	0.134433i
$333$	−1.00000	−	1.73205i	−0.0547997	−	0.0949158i
$334$	−5.65685	+	9.79796i	−0.309529	+	0.536120i
$335$	−2.82843			−0.154533
$336$		0			0
$337$	−2.00000			−0.108947			−0.0544735	−	0.998515i	$-0.517348\pi$
$337$	−2.00000			−0.108947			−0.0544735	+	0.998515i	$0.517348\pi$
$338$	−2.50000	+	4.33013i	−0.135982	+	0.235528i
$339$	−12.7279	−	22.0454i	−0.691286	−	1.19734i
$340$	4.00000	+	6.92820i	0.216930	+	0.375735i
$341$	−0.707107	+	1.22474i	−0.0382920	+	0.0663237i
$342$	2.82843			0.152944
$343$		0			0
$344$	−4.00000			−0.215666
$345$	−2.00000	+	3.46410i	−0.107676	+	0.186501i
$346$	7.07107	+	12.2474i	0.380143	+	0.658427i
$347$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$347$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$348$	−4.24264	+	7.34847i	−0.227429	+	0.393919i
$349$	−5.65685			−0.302804			−0.151402	−	0.988472i	$-0.548379\pi$
$349$	−5.65685			−0.302804			−0.151402	+	0.988472i	$0.548379\pi$
$350$		0			0
$351$	16.0000			0.854017
$352$	−0.500000	+	0.866025i	−0.0266501	+	0.0461593i
$353$	−0.707107	−	1.22474i	−0.0376355	−	0.0651866i	0.846594	−	0.532239i	$-0.178649\pi$
$353$	−0.707107	−	1.22474i	−0.0376355	−	0.0651866i	−0.884230	+	0.467052i	$0.845316\pi$
$354$	−3.00000	−	5.19615i	−0.159448	−	0.276172i
$355$	7.07107	−	12.2474i	0.375293	−	0.650027i
$356$	−7.07107			−0.374766
$357$		0			0
$358$	−20.0000			−1.05703
$359$	−16.0000	+	27.7128i	−0.844448	+	1.46263i	0.0416523	+	0.999132i	$0.486738\pi$
$359$	−16.0000	+	27.7128i	−0.844448	+	1.46263i	−0.886100	+	0.463494i	$0.846596\pi$
$360$	−0.707107	−	1.22474i	−0.0372678	−	0.0645497i
$361$	5.50000	+	9.52628i	0.289474	+	0.501383i
$362$	6.36396	−	11.0227i	0.334482	−	0.579340i
$363$	−1.41421			−0.0742270
$364$		0			0
$365$	−20.0000			−1.04685
$366$	4.00000	−	6.92820i	0.209083	−	0.362143i
$367$	−14.8492	−	25.7196i	−0.775124	−	1.34255i	−0.934725	−	0.355373i	$-0.884354\pi$
$367$	−14.8492	−	25.7196i	−0.775124	−	1.34255i	0.159601	−	0.987182i	$-0.448979\pi$
$368$	1.00000	+	1.73205i	0.0521286	+	0.0902894i
$369$	2.82843	−	4.89898i	0.147242	−	0.255031i
$370$	2.82843			0.147043
$371$		0			0
$372$	2.00000			0.103695
$373$	7.00000	−	12.1244i	0.362446	−	0.627775i	−0.625917	−	0.779890i	$-0.715275\pi$
$373$	7.00000	−	12.1244i	0.362446	−	0.627775i	0.988363	+	0.152115i	$0.0486083\pi$
$374$	2.82843	+	4.89898i	0.146254	+	0.253320i
$375$	−8.00000	−	13.8564i	−0.413118	−	0.715542i
$376$	2.12132	−	3.67423i	0.109399	−	0.189484i
$377$	−16.9706			−0.874028
$378$		0			0
$379$	6.00000			0.308199			0.154100	−	0.988055i	$-0.450752\pi$
$379$	6.00000			0.308199			0.154100	+	0.988055i	$0.450752\pi$
$380$	−2.00000	+	3.46410i	−0.102598	+	0.177705i
$381$	8.48528	+	14.6969i	0.434714	+	0.752947i
$382$		0			0
$383$	−13.4350	+	23.2702i	−0.686498	+	1.18905i	0.286466	+	0.958091i	$0.407520\pi$
$383$	−13.4350	+	23.2702i	−0.686498	+	1.18905i	−0.972964	+	0.230959i	$0.925814\pi$
$384$	1.41421			0.0721688
$385$		0			0
$386$	−6.00000			−0.305392
$387$	2.00000	−	3.46410i	0.101666	−	0.176090i
$388$	7.77817	+	13.4722i	0.394877	+	0.683947i
$389$	14.0000	+	24.2487i	0.709828	+	1.22946i	0.964921	+	0.262542i	$0.0845608\pi$
$389$	14.0000	+	24.2487i	0.709828	+	1.22946i	−0.255092	+	0.966917i	$0.582106\pi$
$390$	−2.82843	+	4.89898i	−0.143223	+	0.248069i
$391$	11.3137			0.572159
$392$		0			0
$393$	−16.0000			−0.807093
$394$	9.00000	−	15.5885i	0.453413	−	0.785335i
$395$	5.65685	+	9.79796i	0.284627	+	0.492989i
$396$	−0.500000	−	0.866025i	−0.0251259	−	0.0435194i
$397$	12.0208	−	20.8207i	0.603307	−	1.04496i	−0.389009	−	0.921234i	$-0.627183\pi$
$397$	12.0208	−	20.8207i	0.603307	−	1.04496i	0.992317	−	0.123725i	$-0.0394841\pi$
$398$	−21.2132			−1.06332
$399$		0			0
$400$	−3.00000			−0.150000
$401$	−18.0000	+	31.1769i	−0.898877	+	1.55690i	−0.0699455	+	0.997551i	$0.522283\pi$
$401$	−18.0000	+	31.1769i	−0.898877	+	1.55690i	−0.828932	+	0.559350i	$0.811051\pi$
$402$	1.41421	+	2.44949i	0.0705346	+	0.122169i
$403$	2.00000	+	3.46410i	0.0996271	+	0.172559i
$404$	−1.41421	+	2.44949i	−0.0703598	+	0.121867i
$405$	−7.07107			−0.351364
$406$		0			0
$407$	2.00000			0.0991363
$408$	4.00000	−	6.92820i	0.198030	−	0.342997i
$409$	−15.5563	−	26.9444i	−0.769212	−	1.33231i	−0.937991	−	0.346660i	$-0.887316\pi$
$409$	−15.5563	−	26.9444i	−0.769212	−	1.33231i	0.168779	−	0.985654i	$-0.446018\pi$
$410$	4.00000	+	6.92820i	0.197546	+	0.342160i
$411$	−1.41421	+	2.44949i	−0.0697580	+	0.120824i
$412$	−4.24264			−0.209020
$413$		0			0
$414$	−2.00000			−0.0982946
$415$	2.00000	−	3.46410i	0.0981761	−	0.170046i
$416$	1.41421	+	2.44949i	0.0693375	+	0.120096i
$417$	−2.00000	−	3.46410i	−0.0979404	−	0.169638i
$418$	−1.41421	+	2.44949i	−0.0691714	+	0.119808i
$419$	−12.7279			−0.621800			−0.310900	−	0.950443i	$-0.600630\pi$
$419$	−12.7279			−0.621800			−0.310900	+	0.950443i	$0.600630\pi$
$420$		0			0
$421$	8.00000			0.389896			0.194948	−	0.980814i	$-0.437546\pi$
$421$	8.00000			0.389896			0.194948	+	0.980814i	$0.437546\pi$
$422$	14.0000	−	24.2487i	0.681509	−	1.18041i
$423$	2.12132	+	3.67423i	0.103142	+	0.178647i
$424$	−6.00000	−	10.3923i	−0.291386	−	0.504695i
$425$	−8.48528	+	14.6969i	−0.411597	+	0.712906i
$426$	−14.1421			−0.685189
$427$		0			0
$428$	−20.0000			−0.966736
$429$	−2.00000	+	3.46410i	−0.0965609	+	0.167248i
$430$	2.82843	+	4.89898i	0.136399	+	0.236250i
$431$	10.0000	+	17.3205i	0.481683	+	0.834300i	0.999779	−	0.0210230i	$-0.00669232\pi$
$431$	10.0000	+	17.3205i	0.481683	+	0.834300i	−0.518096	+	0.855323i	$0.673359\pi$
$432$	−2.82843	+	4.89898i	−0.136083	+	0.235702i
$433$	38.1838			1.83499			0.917497	−	0.397742i	$-0.130206\pi$
$433$	38.1838			1.83499			0.917497	+	0.397742i	$0.130206\pi$
$434$		0			0
$435$	12.0000			0.575356
$436$	−5.00000	+	8.66025i	−0.239457	+	0.414751i
$437$	2.82843	+	4.89898i	0.135302	+	0.234350i
$438$	10.0000	+	17.3205i	0.477818	+	0.827606i
$439$	12.7279	−	22.0454i	0.607471	−	1.05217i	−0.384185	−	0.923256i	$-0.625518\pi$
$439$	12.7279	−	22.0454i	0.607471	−	1.05217i	0.991656	−	0.128914i	$-0.0411491\pi$
$440$	1.41421			0.0674200
$441$		0			0
$442$	16.0000			0.761042
$443$	6.00000	−	10.3923i	0.285069	−	0.493753i	−0.687557	−	0.726130i	$-0.741317\pi$
$443$	6.00000	−	10.3923i	0.285069	−	0.493753i	0.972626	+	0.232377i	$0.0746503\pi$
$444$	−1.41421	−	2.44949i	−0.0671156	−	0.116248i
$445$	5.00000	+	8.66025i	0.237023	+	0.410535i
$446$	−7.77817	+	13.4722i	−0.368307	+	0.637927i
$447$	14.1421			0.668900
$448$		0			0
$449$	−12.0000			−0.566315			−0.283158	−	0.959073i	$-0.591382\pi$
$449$	−12.0000			−0.566315			−0.283158	+	0.959073i	$0.591382\pi$
$450$	1.50000	−	2.59808i	0.0707107	−	0.122474i
$451$	2.82843	+	4.89898i	0.133185	+	0.230684i
$452$	9.00000	+	15.5885i	0.423324	+	0.733219i
$453$	11.3137	−	19.5959i	0.531564	−	0.920697i
$454$	28.2843			1.32745
$455$		0			0
$456$	4.00000			0.187317
$457$	−1.00000	+	1.73205i	−0.0467780	+	0.0810219i	−0.888466	−	0.458942i	$-0.848229\pi$
$457$	−1.00000	+	1.73205i	−0.0467780	+	0.0810219i	0.841688	+	0.539964i	$0.181562\pi$
$458$	−2.12132	−	3.67423i	−0.0991228	−	0.171686i
$459$	16.0000	+	27.7128i	0.746816	+	1.29352i
$460$	1.41421	−	2.44949i	0.0659380	−	0.114208i
$461$	28.2843			1.31733			0.658665	−	0.752436i	$-0.271121\pi$
$461$	28.2843			1.31733			0.658665	+	0.752436i	$0.271121\pi$
$462$		0			0
$463$	−14.0000			−0.650635			−0.325318	−	0.945605i	$-0.605471\pi$
$463$	−14.0000			−0.650635			−0.325318	+	0.945605i	$0.605471\pi$
$464$	3.00000	−	5.19615i	0.139272	−	0.241225i
$465$	−1.41421	−	2.44949i	−0.0655826	−	0.113592i
$466$	3.00000	+	5.19615i	0.138972	+	0.240707i
$467$	−2.12132	+	3.67423i	−0.0981630	+	0.170023i	−0.910924	−	0.412574i	$-0.864630\pi$
$467$	−2.12132	+	3.67423i	−0.0981630	+	0.170023i	0.812761	+	0.582597i	$0.197963\pi$
$468$	−2.82843			−0.130744
$469$		0			0
$470$	−6.00000			−0.276759
$471$	13.0000	−	22.5167i	0.599008	−	1.03751i
$472$	2.12132	+	3.67423i	0.0976417	+	0.169120i
$473$	2.00000	+	3.46410i	0.0919601	+	0.159280i
$474$	5.65685	−	9.79796i	0.259828	−	0.450035i
$475$	−8.48528			−0.389331
$476$		0			0
$477$	12.0000			0.549442
$478$	−8.00000	+	13.8564i	−0.365911	+	0.633777i
$479$	−12.7279	−	22.0454i	−0.581554	−	1.00728i	−0.995295	−	0.0968862i	$-0.969112\pi$
$479$	−12.7279	−	22.0454i	−0.581554	−	1.00728i	0.413742	−	0.910394i	$-0.364222\pi$
$480$	−1.00000	−	1.73205i	−0.0456435	−	0.0790569i
$481$	2.82843	−	4.89898i	0.128965	−	0.223374i
$482$	5.65685			0.257663
$483$		0			0
$484$	1.00000			0.0454545
$485$	11.0000	−	19.0526i	0.499484	−	0.865132i
$486$	−4.94975	−	8.57321i	−0.224525	−	0.388889i
$487$	−5.00000	−	8.66025i	−0.226572	−	0.392434i	0.730218	−	0.683214i	$-0.239418\pi$
$487$	−5.00000	−	8.66025i	−0.226572	−	0.392434i	−0.956790	+	0.290780i	$0.906085\pi$
$488$	−2.82843	+	4.89898i	−0.128037	+	0.221766i
$489$	31.1127			1.40696
$490$		0			0
$491$	4.00000			0.180517			0.0902587	−	0.995918i	$-0.471231\pi$
$491$	4.00000			0.180517			0.0902587	+	0.995918i	$0.471231\pi$
$492$	4.00000	−	6.92820i	0.180334	−	0.312348i
$493$	−16.9706	−	29.3939i	−0.764316	−	1.32383i
$494$	4.00000	+	6.92820i	0.179969	+	0.311715i
$495$	−0.707107	+	1.22474i	−0.0317821	+	0.0550482i
$496$	−1.41421			−0.0635001
$497$		0			0
$498$	−4.00000			−0.179244
$499$	15.0000	−	25.9808i	0.671492	−	1.16306i	−0.305989	−	0.952035i	$-0.598987\pi$
$499$	15.0000	−	25.9808i	0.671492	−	1.16306i	0.977481	−	0.211024i	$-0.0676797\pi$
$500$	5.65685	+	9.79796i	0.252982	+	0.438178i
$501$	−8.00000	−	13.8564i	−0.357414	−	0.619059i
$502$	−12.0208	+	20.8207i	−0.536515	+	0.929272i
$503$	19.7990			0.882793			0.441397	−	0.897312i	$-0.354483\pi$
$503$	19.7990			0.882793			0.441397	+	0.897312i	$0.354483\pi$
$504$		0			0
$505$	4.00000			0.177998
$506$	1.00000	−	1.73205i	0.0444554	−	0.0769991i
$507$	−3.53553	−	6.12372i	−0.157019	−	0.271964i
$508$	−6.00000	−	10.3923i	−0.266207	−	0.461084i
$509$	−2.12132	+	3.67423i	−0.0940259	+	0.162858i	−0.909202	−	0.416356i	$-0.863307\pi$
$509$	−2.12132	+	3.67423i	−0.0940259	+	0.162858i	0.815176	+	0.579214i	$0.196640\pi$
$510$	−11.3137			−0.500979
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	−8.00000	+	13.8564i	−0.353209	+	0.611775i
$514$	−4.94975	−	8.57321i	−0.218324	−	0.378148i
$515$	3.00000	+	5.19615i	0.132196	+	0.228970i
$516$	2.82843	−	4.89898i	0.124515	−	0.215666i
$517$	−4.24264			−0.186591
$518$		0			0
$519$	−20.0000			−0.877903
$520$	2.00000	−	3.46410i	0.0877058	−	0.151911i
$521$	7.77817	+	13.4722i	0.340768	+	0.590228i	0.984576	−	0.174960i	$-0.0559796\pi$
$521$	7.77817	+	13.4722i	0.340768	+	0.590228i	−0.643808	+	0.765187i	$0.722646\pi$
$522$	3.00000	+	5.19615i	0.131306	+	0.227429i
$523$	8.48528	−	14.6969i	0.371035	−	0.642652i	−0.618690	−	0.785635i	$-0.712336\pi$
$523$	8.48528	−	14.6969i	0.371035	−	0.642652i	0.989725	+	0.142983i	$0.0456695\pi$
$524$	11.3137			0.494242
$525$		0			0
$526$	−24.0000			−1.04645
$527$	−4.00000	+	6.92820i	−0.174243	+	0.301797i
$528$	−0.707107	−	1.22474i	−0.0307729	−	0.0533002i
$529$	9.50000	+	16.4545i	0.413043	+	0.715412i
$530$	−8.48528	+	14.6969i	−0.368577	+	0.638394i
$531$	−4.24264			−0.184115
$532$		0			0
$533$	16.0000			0.693037
$534$	5.00000	−	8.66025i	0.216371	−	0.374766i
$535$	14.1421	+	24.4949i	0.611418	+	1.05901i
$536$	−1.00000	−	1.73205i	−0.0431934	−	0.0748132i
$537$	14.1421	−	24.4949i	0.610278	−	1.05703i
$538$	24.0416			1.03651
$539$		0			0
$540$	8.00000			0.344265
$541$	9.00000	−	15.5885i	0.386940	−	0.670200i	−0.605096	−	0.796152i	$-0.706865\pi$
$541$	9.00000	−	15.5885i	0.386940	−	0.670200i	0.992036	+	0.125952i	$0.0401986\pi$
$542$	4.24264	+	7.34847i	0.182237	+	0.315644i
$543$	9.00000	+	15.5885i	0.386227	+	0.668965i
$544$	−2.82843	+	4.89898i	−0.121268	+	0.210042i
$545$	14.1421			0.605783
$546$		0			0
$547$	28.0000			1.19719			0.598597	−	0.801050i	$-0.295725\pi$
$547$	28.0000			1.19719			0.598597	+	0.801050i	$0.295725\pi$
$548$	1.00000	−	1.73205i	0.0427179	−	0.0739895i
$549$	−2.82843	−	4.89898i	−0.120714	−	0.209083i
$550$	1.50000	+	2.59808i	0.0639602	+	0.110782i
$551$	8.48528	−	14.6969i	0.361485	−	0.626111i
$552$	−2.82843			−0.120386
$553$		0			0
$554$	10.0000			0.424859
$555$	−2.00000	+	3.46410i	−0.0848953	+	0.147043i
$556$	1.41421	+	2.44949i	0.0599760	+	0.103882i
$557$	9.00000	+	15.5885i	0.381342	+	0.660504i	0.991254	−	0.131965i	$-0.0421286\pi$
$557$	9.00000	+	15.5885i	0.381342	+	0.660504i	−0.609912	+	0.792469i	$0.708795\pi$
$558$	0.707107	−	1.22474i	0.0299342	−	0.0518476i
$559$	11.3137			0.478519
$560$		0			0
$561$	−8.00000			−0.337760
$562$	9.00000	−	15.5885i	0.379642	−	0.657559i
$563$	7.07107	+	12.2474i	0.298010	+	0.516168i	0.975681	−	0.219197i	$-0.0703438\pi$
$563$	7.07107	+	12.2474i	0.298010	+	0.516168i	−0.677671	+	0.735366i	$0.737010\pi$
$564$	3.00000	+	5.19615i	0.126323	+	0.218797i
$565$	12.7279	−	22.0454i	0.535468	−	0.927457i
$566$	−16.9706			−0.713326
$567$		0			0
$568$	10.0000			0.419591
$569$	3.00000	−	5.19615i	0.125767	−	0.217834i	−0.796266	−	0.604947i	$-0.793194\pi$
$569$	3.00000	−	5.19615i	0.125767	−	0.217834i	0.922032	+	0.387113i	$0.126528\pi$
$570$	−2.82843	−	4.89898i	−0.118470	−	0.205196i
$571$	−4.00000	−	6.92820i	−0.167395	−	0.289936i	0.770108	−	0.637913i	$-0.220202\pi$
$571$	−4.00000	−	6.92820i	−0.167395	−	0.289936i	−0.937503	+	0.347977i	$0.886869\pi$
$572$	1.41421	−	2.44949i	0.0591312	−	0.102418i
$573$		0			0
$574$		0			0
$575$	6.00000			0.250217
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	14.8492	+	25.7196i	0.618182	+	1.07072i	0.989817	+	0.142344i	$0.0454639\pi$
$577$	14.8492	+	25.7196i	0.618182	+	1.07072i	−0.371635	+	0.928379i	$0.621203\pi$
$578$	7.50000	+	12.9904i	0.311959	+	0.540329i
$579$	4.24264	−	7.34847i	0.176318	−	0.305392i
$580$	−8.48528			−0.352332
$581$		0			0
$582$	−22.0000			−0.911929
$583$	−6.00000	+	10.3923i	−0.248495	+	0.430405i
$584$	−7.07107	−	12.2474i	−0.292603	−	0.506803i
$585$	2.00000	+	3.46410i	0.0826898	+	0.143223i
$586$	8.48528	−	14.6969i	0.350524	−	0.607125i
$587$	−1.41421			−0.0583708			−0.0291854	−	0.999574i	$-0.509291\pi$
$587$	−1.41421			−0.0583708			−0.0291854	+	0.999574i	$0.509291\pi$
$588$		0			0
$589$	−4.00000			−0.164817
$590$	3.00000	−	5.19615i	0.123508	−	0.213922i
$591$	12.7279	+	22.0454i	0.523557	+	0.906827i
$592$	1.00000	+	1.73205i	0.0410997	+	0.0711868i
$593$	−9.89949	+	17.1464i	−0.406524	+	0.704119i	−0.994497	−	0.104760i	$-0.966592\pi$
$593$	−9.89949	+	17.1464i	−0.406524	+	0.704119i	0.587974	+	0.808880i	$0.299926\pi$
$594$	5.65685			0.232104
$595$		0			0
$596$	−10.0000			−0.409616
$597$	15.0000	−	25.9808i	0.613909	−	1.06332i
$598$	−2.82843	−	4.89898i	−0.115663	−	0.200334i
$599$	−9.00000	−	15.5885i	−0.367730	−	0.636927i	0.621480	−	0.783430i	$-0.286532\pi$
$599$	−9.00000	−	15.5885i	−0.367730	−	0.636927i	−0.989210	+	0.146503i	$0.953198\pi$
$600$	2.12132	−	3.67423i	0.0866025	−	0.150000i
$601$	45.2548			1.84598			0.922992	−	0.384820i	$-0.125737\pi$
$601$	45.2548			1.84598			0.922992	+	0.384820i	$0.125737\pi$
$602$		0			0
$603$	2.00000			0.0814463
$604$	−8.00000	+	13.8564i	−0.325515	+	0.563809i
$605$	−0.707107	−	1.22474i	−0.0287480	−	0.0497930i
$606$	−2.00000	−	3.46410i	−0.0812444	−	0.140720i
$607$	16.9706	−	29.3939i	0.688814	−	1.19306i	−0.283408	−	0.958999i	$-0.591465\pi$
$607$	16.9706	−	29.3939i	0.688814	−	1.19306i	0.972222	−	0.234061i	$-0.0752016\pi$
$608$	−2.82843			−0.114708
$609$		0			0
$610$	8.00000			0.323911
$611$	−6.00000	+	10.3923i	−0.242734	+	0.420428i
$612$	−2.82843	−	4.89898i	−0.114332	−	0.198030i
$613$	17.0000	+	29.4449i	0.686624	+	1.18927i	0.972924	+	0.231127i	$0.0742412\pi$
$613$	17.0000	+	29.4449i	0.686624	+	1.18927i	−0.286300	+	0.958140i	$0.592425\pi$
$614$	−5.65685	+	9.79796i	−0.228292	+	0.395413i
$615$	−11.3137			−0.456213
$616$		0			0
$617$	−6.00000			−0.241551			−0.120775	−	0.992680i	$-0.538538\pi$
$617$	−6.00000			−0.241551			−0.120775	+	0.992680i	$0.538538\pi$
$618$	3.00000	−	5.19615i	0.120678	−	0.209020i
$619$	−6.36396	−	11.0227i	−0.255789	−	0.443040i	0.709320	−	0.704886i	$-0.249002\pi$
$619$	−6.36396	−	11.0227i	−0.255789	−	0.443040i	−0.965110	+	0.261846i	$0.915669\pi$
$620$	1.00000	+	1.73205i	0.0401610	+	0.0695608i
$621$	5.65685	−	9.79796i	0.227002	−	0.393179i
$622$	9.89949			0.396934
$623$		0			0
$624$	−4.00000			−0.160128
$625$	0.500000	−	0.866025i	0.0200000	−	0.0346410i
$626$	13.4350	+	23.2702i	0.536972	+	0.930062i
$627$	−2.00000	−	3.46410i	−0.0798723	−	0.138343i
$628$	−9.19239	+	15.9217i	−0.366816	+	0.635344i
$629$	11.3137			0.451107
$630$		0			0
$631$		0			0			−	1.00000i	$-0.5\pi$
$631$		0			0				1.00000i	$0.5\pi$
$632$	−4.00000	+	6.92820i	−0.159111	+	0.275589i
$633$	19.7990	+	34.2929i	0.786939	+	1.36302i
$634$	−13.0000	−	22.5167i	−0.516296	−	0.894251i
$635$	−8.48528	+	14.6969i	−0.336728	+	0.583230i
$636$	16.9706			0.672927
$637$		0			0
$638$	−6.00000			−0.237542
$639$	−5.00000	+	8.66025i	−0.197797	+	0.342594i
$640$	0.707107	+	1.22474i	0.0279508	+	0.0484123i
$641$	−15.0000	−	25.9808i	−0.592464	−	1.02618i	−0.993899	−	0.110291i	$-0.964822\pi$
$641$	−15.0000	−	25.9808i	−0.592464	−	1.02618i	0.401435	−	0.915888i	$-0.368512\pi$
$642$	14.1421	−	24.4949i	0.558146	−	0.966736i
$643$	−12.7279			−0.501940			−0.250970	−	0.967995i	$-0.580750\pi$
$643$	−12.7279			−0.501940			−0.250970	+	0.967995i	$0.580750\pi$
$644$		0			0
$645$	−8.00000			−0.315000
$646$	−8.00000	+	13.8564i	−0.314756	+	0.545173i
$647$	−20.5061	−	35.5176i	−0.806178	−	1.39634i	−0.915493	−	0.402334i	$-0.868199\pi$
$647$	−20.5061	−	35.5176i	−0.806178	−	1.39634i	0.109315	−	0.994007i	$-0.465134\pi$
$648$	−2.50000	−	4.33013i	−0.0982093	−	0.170103i
$649$	2.12132	−	3.67423i	0.0832691	−	0.144226i
$650$	8.48528			0.332820
$651$		0			0
$652$	−22.0000			−0.861586
$653$	24.0000	−	41.5692i	0.939193	−	1.62673i	0.172211	−	0.985060i	$-0.444909\pi$
$653$	24.0000	−	41.5692i	0.939193	−	1.62673i	0.766982	−	0.641669i	$-0.221758\pi$
$654$	−7.07107	−	12.2474i	−0.276501	−	0.478913i
$655$	−8.00000	−	13.8564i	−0.312586	−	0.541415i
$656$	−2.82843	+	4.89898i	−0.110432	+	0.191273i
$657$	14.1421			0.551737
$658$		0			0
$659$	−4.00000			−0.155818			−0.0779089	−	0.996960i	$-0.524824\pi$
$659$	−4.00000			−0.155818			−0.0779089	+	0.996960i	$0.524824\pi$
$660$	−1.00000	+	1.73205i	−0.0389249	+	0.0674200i
$661$	−19.0919	−	33.0681i	−0.742588	−	1.28620i	−0.951313	−	0.308226i	$-0.900265\pi$
$661$	−19.0919	−	33.0681i	−0.742588	−	1.28620i	0.208725	−	0.977974i	$-0.433069\pi$
$662$	14.0000	+	24.2487i	0.544125	+	0.942453i
$663$	−11.3137	+	19.5959i	−0.439388	+	0.761042i
$664$	2.82843			0.109764
$665$		0			0
$666$	−2.00000			−0.0774984
$667$	−6.00000	+	10.3923i	−0.232321	+	0.402392i
$668$	5.65685	+	9.79796i	0.218870	+	0.379094i
$669$	−11.0000	−	19.0526i	−0.425285	−	0.736614i
$670$	−1.41421	+	2.44949i	−0.0546358	+	0.0946320i
$671$	5.65685			0.218380
$672$		0			0
$673$	2.00000			0.0770943			0.0385472	−	0.999257i	$-0.487727\pi$
$673$	2.00000			0.0770943			0.0385472	+	0.999257i	$0.487727\pi$
$674$	−1.00000	+	1.73205i	−0.0385186	+	0.0667161i
$675$	8.48528	+	14.6969i	0.326599	+	0.565685i
$676$	2.50000	+	4.33013i	0.0961538	+	0.166543i
$677$	−15.5563	+	26.9444i	−0.597879	+	1.03556i	0.395255	+	0.918572i	$0.370656\pi$
$677$	−15.5563	+	26.9444i	−0.597879	+	1.03556i	−0.993134	+	0.116985i	$0.962677\pi$
$678$	−25.4558			−0.977626
$679$		0			0
$680$	8.00000			0.306786
$681$	−20.0000	+	34.6410i	−0.766402	+	1.32745i
$682$	0.707107	+	1.22474i	0.0270765	+	0.0468979i
$683$	6.00000	+	10.3923i	0.229584	+	0.397650i	0.957685	−	0.287819i	$-0.0929302\pi$
$683$	6.00000	+	10.3923i	0.229584	+	0.397650i	−0.728101	+	0.685470i	$0.759597\pi$
$684$	1.41421	−	2.44949i	0.0540738	−	0.0936586i
$685$	−2.82843			−0.108069
$686$		0			0
$687$	6.00000			0.228914
$688$	−2.00000	+	3.46410i	−0.0762493	+	0.132068i
$689$	16.9706	+	29.3939i	0.646527	+	1.11982i
$690$	2.00000	+	3.46410i	0.0761387	+	0.131876i
$691$	16.2635	−	28.1691i	0.618691	−	1.07160i	−0.371034	−	0.928619i	$-0.620997\pi$
$691$	16.2635	−	28.1691i	0.618691	−	1.07160i	0.989725	−	0.142985i	$-0.0456700\pi$
$692$	14.1421			0.537603
$693$		0			0
$694$		0			0
$695$	2.00000	−	3.46410i	0.0758643	−	0.131401i
$696$	4.24264	+	7.34847i	0.160817	+	0.278543i
$697$	16.0000	+	27.7128i	0.606043	+	1.04970i
$698$	−2.82843	+	4.89898i	−0.107058	+	0.185429i
$699$	−8.48528			−0.320943
$700$		0			0
$701$	−10.0000			−0.377695			−0.188847	−	0.982006i	$-0.560475\pi$
$701$	−10.0000			−0.377695			−0.188847	+	0.982006i	$0.560475\pi$
$702$	8.00000	−	13.8564i	0.301941	−	0.522976i
$703$	2.82843	+	4.89898i	0.106676	+	0.184769i
$704$	0.500000	+	0.866025i	0.0188445	+	0.0326396i
$705$	4.24264	−	7.34847i	0.159787	−	0.276759i
$706$	−1.41421			−0.0532246
$707$		0			0
$708$	−6.00000			−0.225494
$709$	4.00000	−	6.92820i	0.150223	−	0.260194i	−0.781086	−	0.624423i	$-0.785334\pi$
$709$	4.00000	−	6.92820i	0.150223	−	0.260194i	0.931309	+	0.364229i	$0.118667\pi$
$710$	−7.07107	−	12.2474i	−0.265372	−	0.459639i
$711$	−4.00000	−	6.92820i	−0.150012	−	0.259828i
$712$	−3.53553	+	6.12372i	−0.132500	+	0.229496i
$713$	2.82843			0.105925
$714$		0			0
$715$	−4.00000			−0.149592
$716$	−10.0000	+	17.3205i	−0.373718	+	0.647298i
$717$	−11.3137	−	19.5959i	−0.422518	−	0.731823i
$718$	16.0000	+	27.7128i	0.597115	+	1.03423i
$719$	7.77817	−	13.4722i	0.290077	−	0.502428i	−0.683751	−	0.729716i	$-0.739652\pi$
$719$	7.77817	−	13.4722i	0.290077	−	0.502428i	0.973828	+	0.227288i	$0.0729858\pi$
$720$	−1.41421			−0.0527046
$721$		0			0
$722$	11.0000			0.409378
$723$	−4.00000	+	6.92820i	−0.148762	+	0.257663i
$724$	−6.36396	−	11.0227i	−0.236515	−	0.409656i
$725$	−9.00000	−	15.5885i	−0.334252	−	0.578941i
$726$	−0.707107	+	1.22474i	−0.0262432	+	0.0454545i
$727$	−32.5269			−1.20636			−0.603178	−	0.797606i	$-0.706099\pi$
$727$	−32.5269			−1.20636			−0.603178	+	0.797606i	$0.706099\pi$
$728$		0			0
$729$	29.0000			1.07407
$730$	−10.0000	+	17.3205i	−0.370117	+	0.641061i
$731$	11.3137	+	19.5959i	0.418453	+	0.724781i
$732$	−4.00000	−	6.92820i	−0.147844	−	0.256074i
$733$	8.48528	−	14.6969i	0.313411	−	0.542844i	−0.665687	−	0.746231i	$-0.731862\pi$
$733$	8.48528	−	14.6969i	0.313411	−	0.542844i	0.979098	+	0.203387i	$0.0651949\pi$
$734$	−29.6985			−1.09619
$735$		0			0
$736$	2.00000			0.0737210
$737$	−1.00000	+	1.73205i	−0.0368355	+	0.0638009i
$738$	−2.82843	−	4.89898i	−0.104116	−	0.180334i
$739$	12.0000	+	20.7846i	0.441427	+	0.764574i	0.997796	−	0.0663614i	$-0.0211390\pi$
$739$	12.0000	+	20.7846i	0.441427	+	0.764574i	−0.556369	+	0.830936i	$0.687806\pi$
$740$	1.41421	−	2.44949i	0.0519875	−	0.0900450i
$741$	−11.3137			−0.415619
$742$		0			0
$743$	−48.0000			−1.76095			−0.880475	−	0.474093i	$-0.842776\pi$
$743$	−48.0000			−1.76095			−0.880475	+	0.474093i	$0.842776\pi$
$744$	1.00000	−	1.73205i	0.0366618	−	0.0635001i
$745$	7.07107	+	12.2474i	0.259064	+	0.448712i
$746$	−7.00000	−	12.1244i	−0.256288	−	0.443904i
$747$	−1.41421	+	2.44949i	−0.0517434	+	0.0896221i
$748$	5.65685			0.206835
$749$		0			0
$750$	−16.0000			−0.584237
$751$	−13.0000	+	22.5167i	−0.474377	+	0.821645i	−0.999570	−	0.0293387i	$-0.990660\pi$
$751$	−13.0000	+	22.5167i	−0.474377	+	0.821645i	0.525193	+	0.850983i	$0.323993\pi$
$752$	−2.12132	−	3.67423i	−0.0773566	−	0.133986i
$753$	−17.0000	−	29.4449i	−0.619514	−	1.07303i
$754$	−8.48528	+	14.6969i	−0.309016	+	0.535231i
$755$	22.6274			0.823496
$756$		0			0
$757$	−44.0000			−1.59921			−0.799604	−	0.600528i	$-0.794957\pi$
$757$	−44.0000			−1.59921			−0.799604	+	0.600528i	$0.794957\pi$
$758$	3.00000	−	5.19615i	0.108965	−	0.188733i
$759$	1.41421	+	2.44949i	0.0513327	+	0.0889108i
$760$	2.00000	+	3.46410i	0.0725476	+	0.125656i
$761$	−12.7279	+	22.0454i	−0.461387	+	0.799145i	−0.999030	−	0.0440268i	$-0.985981\pi$
$761$	−12.7279	+	22.0454i	−0.461387	+	0.799145i	0.537644	+	0.843172i	$0.319315\pi$
$762$	16.9706			0.614779
$763$		0			0
$764$		0			0
$765$	−4.00000	+	6.92820i	−0.144620	+	0.250490i
$766$	13.4350	+	23.2702i	0.485427	+	0.840785i
$767$	−6.00000	−	10.3923i	−0.216647	−	0.375244i
$768$	0.707107	−	1.22474i	0.0255155	−	0.0441942i
$769$	8.48528			0.305987			0.152994	−	0.988227i	$-0.451109\pi$
$769$	8.48528			0.305987			0.152994	+	0.988227i	$0.451109\pi$
$770$		0			0
$771$	14.0000			0.504198
$772$	−3.00000	+	5.19615i	−0.107972	+	0.187014i
$773$	0.707107	+	1.22474i	0.0254329	+	0.0440510i	0.878462	−	0.477813i	$-0.158570\pi$
$773$	0.707107	+	1.22474i	0.0254329	+	0.0440510i	−0.853029	+	0.521864i	$0.825237\pi$
$774$	−2.00000	−	3.46410i	−0.0718885	−	0.124515i
$775$	−2.12132	+	3.67423i	−0.0762001	+	0.131982i
$776$	15.5563			0.558440
$777$		0			0
$778$	28.0000			1.00385
$779$	−8.00000	+	13.8564i	−0.286630	+	0.496457i
$780$	2.82843	+	4.89898i	0.101274	+	0.175412i
$781$	−5.00000	−	8.66025i	−0.178914	−	0.309888i
$782$	5.65685	−	9.79796i	0.202289	−	0.350374i
$783$	−33.9411			−1.21296
$784$		0			0
$785$	26.0000			0.927980
$786$	−8.00000	+	13.8564i	−0.285351	+	0.494242i
$787$	−21.2132	−	36.7423i	−0.756169	−	1.30972i	−0.944791	−	0.327673i	$-0.893735\pi$
$787$	−21.2132	−	36.7423i	−0.756169	−	1.30972i	0.188622	−	0.982050i	$-0.439598\pi$
$788$	−9.00000	−	15.5885i	−0.320612	−	0.555316i
$789$	16.9706	−	29.3939i	0.604168	−	1.04645i
$790$	11.3137			0.402524
$791$		0			0
$792$	−1.00000			−0.0355335
$793$	8.00000	−	13.8564i	0.284088	−	0.492055i
$794$	−12.0208	−	20.8207i	−0.426603	−	0.738898i
$795$	−12.0000	−	20.7846i	−0.425596	−	0.737154i
$796$	−10.6066	+	18.3712i	−0.375941	+	0.651149i
$797$	−18.3848			−0.651222			−0.325611	−	0.945504i	$-0.605570\pi$
$797$	−18.3848			−0.651222			−0.325611	+	0.945504i	$0.605570\pi$
$798$		0			0
$799$	−24.0000			−0.849059
$800$	−1.50000	+	2.59808i	−0.0530330	+	0.0918559i
$801$	−3.53553	−	6.12372i	−0.124922	−	0.216371i
$802$	18.0000	+	31.1769i	0.635602	+	1.10090i
$803$	−7.07107	+	12.2474i	−0.249533	+	0.432203i
$804$	2.82843			0.0997509
$805$		0			0
$806$	4.00000			0.140894
$807$	−17.0000	+	29.4449i	−0.598428	+	1.03651i
$808$	1.41421	+	2.44949i	0.0497519	+	0.0861727i
$809$	3.00000	+	5.19615i	0.105474	+	0.182687i	0.913932	−	0.405868i	$-0.133031\pi$
$809$	3.00000	+	5.19615i	0.105474	+	0.182687i	−0.808458	+	0.588555i	$0.799697\pi$
$810$	−3.53553	+	6.12372i	−0.124226	+	0.215166i
$811$		0			0			−	1.00000i	$-0.5\pi$
$811$		0			0				1.00000i	$0.5\pi$
$812$		0			0
$813$	−12.0000			−0.420858
$814$	1.00000	−	1.73205i	0.0350500	−	0.0607083i
$815$	15.5563	+	26.9444i	0.544915	+	0.943821i
$816$	−4.00000	−	6.92820i	−0.140028	−	0.242536i
$817$	−5.65685	+	9.79796i	−0.197908	+	0.342787i
$818$	−31.1127			−1.08783
$819$		0			0
$820$	8.00000			0.279372
$821$	−17.0000	+	29.4449i	−0.593304	+	1.02763i	0.400480	+	0.916306i	$0.368843\pi$
$821$	−17.0000	+	29.4449i	−0.593304	+	1.02763i	−0.993784	+	0.111327i	$0.964490\pi$
$822$	1.41421	+	2.44949i	0.0493264	+	0.0854358i
$823$	16.0000	+	27.7128i	0.557725	+	0.966008i	0.997686	+	0.0679910i	$0.0216589\pi$
$823$	16.0000	+	27.7128i	0.557725	+	0.966008i	−0.439961	+	0.898017i	$0.645008\pi$
$824$	−2.12132	+	3.67423i	−0.0738997	+	0.127998i
$825$	−4.24264			−0.147710
$826$		0			0
$827$	−8.00000			−0.278187			−0.139094	−	0.990279i	$-0.544419\pi$
$827$	−8.00000			−0.278187			−0.139094	+	0.990279i	$0.544419\pi$
$828$	−1.00000	+	1.73205i	−0.0347524	+	0.0601929i
$829$	17.6777	+	30.6186i	0.613971	+	1.06343i	0.990564	+	0.137050i	$0.0437621\pi$
$829$	17.6777	+	30.6186i	0.613971	+	1.06343i	−0.376593	+	0.926379i	$0.622905\pi$
$830$	−2.00000	−	3.46410i	−0.0694210	−	0.120241i
$831$	−7.07107	+	12.2474i	−0.245293	+	0.424859i
$832$	2.82843			0.0980581
$833$		0			0
$834$	−4.00000			−0.138509
$835$	8.00000	−	13.8564i	0.276851	−	0.479521i
$836$	1.41421	+	2.44949i	0.0489116	+	0.0847174i
$837$	4.00000	+	6.92820i	0.138260	+	0.239474i
$838$	−6.36396	+	11.0227i	−0.219839	+	0.380773i
$839$	−43.8406			−1.51355			−0.756773	−	0.653678i	$-0.773225\pi$
$839$	−43.8406			−1.51355			−0.756773	+	0.653678i	$0.773225\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$	4.00000	−	6.92820i	0.137849	−	0.238762i
$843$	12.7279	+	22.0454i	0.438373	+	0.759284i
$844$	−14.0000	−	24.2487i	−0.481900	−	0.834675i
$845$	3.53553	−	6.12372i	0.121626	−	0.210663i
$846$	4.24264			0.145865
$847$		0			0
$848$	−12.0000			−0.412082
$849$	12.0000	−	20.7846i	0.411839	−	0.713326i
$850$	8.48528	+	14.6969i	0.291043	+	0.504101i
$851$	−2.00000	−	3.46410i	−0.0685591	−	0.118748i
$852$	−7.07107	+	12.2474i	−0.242251	+	0.419591i
$853$	−2.82843			−0.0968435			−0.0484218	−	0.998827i	$-0.515419\pi$
$853$	−2.82843			−0.0968435			−0.0484218	+	0.998827i	$0.515419\pi$
$854$		0			0
$855$	−4.00000			−0.136797
$856$	−10.0000	+	17.3205i	−0.341793	+	0.592003i
$857$	4.24264	+	7.34847i	0.144926	+	0.251019i	0.929345	−	0.369212i	$-0.120372\pi$
$857$	4.24264	+	7.34847i	0.144926	+	0.251019i	−0.784419	+	0.620231i	$0.787039\pi$
$858$	2.00000	+	3.46410i	0.0682789	+	0.118262i
$859$	−19.0919	+	33.0681i	−0.651407	+	1.12827i	0.331375	+	0.943499i	$0.392487\pi$
$859$	−19.0919	+	33.0681i	−0.651407	+	1.12827i	−0.982782	+	0.184770i	$0.940846\pi$
$860$	5.65685			0.192897
$861$		0			0
$862$	20.0000			0.681203
$863$	16.0000	−	27.7128i	0.544646	−	0.943355i	−0.453983	−	0.891010i	$-0.649997\pi$
$863$	16.0000	−	27.7128i	0.544646	−	0.943355i	0.998629	−	0.0523446i	$-0.0166694\pi$
$864$	2.82843	+	4.89898i	0.0962250	+	0.166667i
$865$	−10.0000	−	17.3205i	−0.340010	−	0.588915i
$866$	19.0919	−	33.0681i	0.648769	−	1.12370i
$867$	−21.2132			−0.720438
$868$		0			0
$869$	8.00000			0.271381
$870$	6.00000	−	10.3923i	0.203419	−	0.352332i
$871$	2.82843	+	4.89898i	0.0958376	+	0.165996i
$872$	5.00000	+	8.66025i	0.169321	+	0.293273i
$873$	−7.77817	+	13.4722i	−0.263251	+	0.455965i
$874$	5.65685			0.191346
$875$		0			0
$876$	20.0000			0.675737
$877$	5.00000	−	8.66025i	0.168838	−	0.292436i	−0.769174	−	0.639040i	$-0.779332\pi$
$877$	5.00000	−	8.66025i	0.168838	−	0.292436i	0.938012	+	0.346604i	$0.112665\pi$
$878$	−12.7279	−	22.0454i	−0.429547	−	0.743996i
$879$	12.0000	+	20.7846i	0.404750	+	0.701047i
$880$	0.707107	−	1.22474i	0.0238366	−	0.0412861i
$881$	4.24264			0.142938			0.0714691	−	0.997443i	$-0.477231\pi$
$881$	4.24264			0.142938			0.0714691	+	0.997443i	$0.477231\pi$
$882$		0			0
$883$	36.0000			1.21150			0.605748	−	0.795656i	$-0.292874\pi$
$883$	36.0000			1.21150			0.605748	+	0.795656i	$0.292874\pi$
$884$	8.00000	−	13.8564i	0.269069	−	0.466041i
$885$	4.24264	+	7.34847i	0.142615	+	0.247016i
$886$	−6.00000	−	10.3923i	−0.201574	−	0.349136i
$887$	−24.0416	+	41.6413i	−0.807239	+	1.39818i	0.107530	+	0.994202i	$0.465706\pi$
$887$	−24.0416	+	41.6413i	−0.807239	+	1.39818i	−0.914769	+	0.403977i	$0.867628\pi$
$888$	−2.82843			−0.0949158
$889$		0			0
$890$	10.0000			0.335201
$891$	−2.50000	+	4.33013i	−0.0837532	+	0.145065i
$892$	7.77817	+	13.4722i	0.260433	+	0.451082i
$893$	−6.00000	−	10.3923i	−0.200782	−	0.347765i
$894$	7.07107	−	12.2474i	0.236492	−	0.409616i
$895$	28.2843			0.945439
$896$		0			0
$897$	8.00000			0.267112
$898$	−6.00000	+	10.3923i	−0.200223	+	0.346796i
$899$	−4.24264	−	7.34847i	−0.141500	−	0.245085i
$900$	−1.50000	−	2.59808i	−0.0500000	−	0.0866025i
$901$	−33.9411	+	58.7878i	−1.13074	+	1.95850i
$902$	5.65685			0.188353
$903$		0			0
$904$	18.0000			0.598671
$905$	−9.00000	+	15.5885i	−0.299170	+	0.518178i
$906$	−11.3137	−	19.5959i	−0.375873	−	0.651031i
$907$	13.0000	+	22.5167i	0.431658	+	0.747653i	0.997016	−	0.0771920i	$-0.0245954\pi$
$907$	13.0000	+	22.5167i	0.431658	+	0.747653i	−0.565358	+	0.824845i	$0.691262\pi$
$908$	14.1421	−	24.4949i	0.469323	−	0.812892i
$909$	−2.82843			−0.0938130
$910$		0			0
$911$	30.0000			0.993944			0.496972	−	0.867766i	$-0.334445\pi$
$911$	30.0000			0.993944			0.496972	+	0.867766i	$0.334445\pi$
$912$	2.00000	−	3.46410i	0.0662266	−	0.114708i
$913$	−1.41421	−	2.44949i	−0.0468036	−	0.0810663i
$914$	1.00000	+	1.73205i	0.0330771	+	0.0572911i
$915$	−5.65685	+	9.79796i	−0.187010	+	0.323911i
$916$	−4.24264			−0.140181
$917$		0			0
$918$	32.0000			1.05616
$919$	−16.0000	+	27.7128i	−0.527791	+	0.914161i	0.471684	+	0.881768i	$0.343646\pi$
$919$	−16.0000	+	27.7128i	−0.527791	+	0.914161i	−0.999475	+	0.0323936i	$0.989687\pi$
$920$	−1.41421	−	2.44949i	−0.0466252	−	0.0807573i
$921$	−8.00000	−	13.8564i	−0.263609	−	0.456584i
$922$	14.1421	−	24.4949i	0.465746	−	0.806696i
$923$	−28.2843			−0.930988
$924$		0			0
$925$	6.00000			0.197279
$926$	−7.00000	+	12.1244i	−0.230034	+	0.398431i
$927$	−2.12132	−	3.67423i	−0.0696733	−	0.120678i
$928$	−3.00000	−	5.19615i	−0.0984798	−	0.170572i
$929$	7.77817	−	13.4722i	0.255194	−	0.442008i	−0.709754	−	0.704449i	$-0.751194\pi$
$929$	7.77817	−	13.4722i	0.255194	−	0.442008i	0.964948	+	0.262441i	$0.0845275\pi$
$930$	−2.82843			−0.0927478
$931$		0			0
$932$	6.00000			0.196537
$933$	−7.00000	+	12.1244i	−0.229170	+	0.396934i
$934$	2.12132	+	3.67423i	0.0694117	+	0.120225i
$935$	−4.00000	−	6.92820i	−0.130814	−	0.226576i
$936$	−1.41421	+	2.44949i	−0.0462250	+	0.0800641i
$937$	−25.4558			−0.831606			−0.415803	−	0.909455i	$-0.636499\pi$
$937$	−25.4558			−0.831606			−0.415803	+	0.909455i	$0.636499\pi$
$938$		0			0
$939$	−38.0000			−1.24008
$940$	−3.00000	+	5.19615i	−0.0978492	+	0.169480i
$941$	−11.3137	−	19.5959i	−0.368816	−	0.638809i	0.620564	−	0.784155i	$-0.286904\pi$
$941$	−11.3137	−	19.5959i	−0.368816	−	0.638809i	−0.989381	+	0.145347i	$0.953570\pi$
$942$	−13.0000	−	22.5167i	−0.423563	−	0.733632i
$943$	5.65685	−	9.79796i	0.184213	−	0.319065i
$944$	4.24264			0.138086
$945$		0			0
$946$	4.00000			0.130051
$947$	−6.00000	+	10.3923i	−0.194974	+	0.337705i	−0.946892	−	0.321552i	$-0.895796\pi$
$947$	−6.00000	+	10.3923i	−0.194974	+	0.337705i	0.751918	+	0.659256i	$0.229129\pi$
$948$	−5.65685	−	9.79796i	−0.183726	−	0.318223i
$949$	20.0000	+	34.6410i	0.649227	+	1.12449i
$950$	−4.24264	+	7.34847i	−0.137649	+	0.238416i
$951$	36.7696			1.19233
$952$		0			0
$953$	−42.0000			−1.36051			−0.680257	−	0.732974i	$-0.738132\pi$
$953$	−42.0000			−1.36051			−0.680257	+	0.732974i	$0.738132\pi$
$954$	6.00000	−	10.3923i	0.194257	−	0.336463i
$955$		0			0
$956$	8.00000	+	13.8564i	0.258738	+	0.448148i
$957$	4.24264	−	7.34847i	0.137145	−	0.237542i
$958$	−25.4558			−0.822441
$959$		0			0
$960$	−2.00000			−0.0645497
$961$	14.5000	−	25.1147i	0.467742	−	0.810153i
$962$	−2.82843	−	4.89898i	−0.0911922	−	0.157949i
$963$	−10.0000	−	17.3205i	−0.322245	−	0.558146i
$964$	2.82843	−	4.89898i	0.0910975	−	0.157786i
$965$	8.48528			0.273151
$966$		0			0
$967$	28.0000			0.900419			0.450210	−	0.892923i	$-0.351349\pi$
$967$	28.0000			0.900419			0.450210	+	0.892923i	$0.351349\pi$
$968$	0.500000	−	0.866025i	0.0160706	−	0.0278351i
$969$	−11.3137	−	19.5959i	−0.363449	−	0.629512i
$970$	−11.0000	−	19.0526i	−0.353189	−	0.611741i
$971$	−13.4350	+	23.2702i	−0.431151	+	0.746775i	−0.996973	−	0.0777526i	$-0.975226\pi$
$971$	−13.4350	+	23.2702i	−0.431151	+	0.746775i	0.565822	+	0.824527i	$0.308559\pi$
$972$	−9.89949			−0.317526
$973$		0			0
$974$	−10.0000			−0.320421
$975$	−6.00000	+	10.3923i	−0.192154	+	0.332820i
$976$	2.82843	+	4.89898i	0.0905357	+	0.156813i
$977$	−14.0000	−	24.2487i	−0.447900	−	0.775785i	0.550349	−	0.834934i	$-0.314494\pi$
$977$	−14.0000	−	24.2487i	−0.447900	−	0.775785i	−0.998249	+	0.0591494i	$0.981161\pi$
$978$	15.5563	−	26.9444i	0.497437	−	0.861586i
$979$	7.07107			0.225992
$980$		0			0
$981$	−10.0000			−0.319275
$982$	2.00000	−	3.46410i	0.0638226	−	0.110544i
$983$	−28.9914	−	50.2145i	−0.924681	−	1.60160i	−0.792073	−	0.610427i	$-0.790998\pi$
$983$	−28.9914	−	50.2145i	−0.924681	−	1.60160i	−0.132609	−	0.991168i	$-0.542335\pi$
$984$	−4.00000	−	6.92820i	−0.127515	−	0.220863i
$985$	−12.7279	+	22.0454i	−0.405545	+	0.702425i
$986$	−33.9411			−1.08091
$987$		0			0
$988$	8.00000			0.254514
$989$	4.00000	−	6.92820i	0.127193	−	0.220304i
$990$	0.707107	+	1.22474i	0.0224733	+	0.0389249i
$991$	−25.0000	−	43.3013i	−0.794151	−	1.37551i	−0.923377	−	0.383895i	$-0.874582\pi$
$991$	−25.0000	−	43.3013i	−0.794151	−	1.37551i	0.129226	−	0.991615i	$-0.458751\pi$
$992$	−0.707107	+	1.22474i	−0.0224507	+	0.0388857i
$993$	−39.5980			−1.25660
$994$		0			0
$995$	30.0000			0.951064
$996$	−2.00000	+	3.46410i	−0.0633724	+	0.109764i
$997$	−29.6985	−	51.4393i	−0.940560	−	1.62910i	−0.764405	−	0.644736i	$-0.776967\pi$
$997$	−29.6985	−	51.4393i	−0.940560	−	1.62910i	−0.176155	−	0.984362i	$-0.556366\pi$
$998$	−15.0000	−	25.9808i	−0.474817	−	0.822407i
$999$	5.65685	−	9.79796i	0.178975	−	0.309994i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1078.2.e.s.177.2		4
7.2	even	3		1078.2.a.q.1.1	✓	2
7.3	odd	6	inner	1078.2.e.s.67.1		4
7.4	even	3	inner	1078.2.e.s.67.2		4
7.5	odd	6		1078.2.a.q.1.2	yes	2
7.6	odd	2	inner	1078.2.e.s.177.1		4
21.2	odd	6		9702.2.a.dq.1.1		2
21.5	even	6		9702.2.a.dq.1.2		2
28.19	even	6		8624.2.a.bw.1.1		2
28.23	odd	6		8624.2.a.bw.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1078.2.a.q.1.1	✓	2	7.2	even	3
1078.2.a.q.1.2	yes	2	7.5	odd	6
1078.2.e.s.67.1		4	7.3	odd	6	inner
1078.2.e.s.67.2		4	7.4	even	3	inner
1078.2.e.s.177.1		4	7.6	odd	2	inner
1078.2.e.s.177.2		4	1.1	even	1	trivial
8624.2.a.bw.1.1		2	28.19	even	6
8624.2.a.bw.1.2		2	28.23	odd	6
9702.2.a.dq.1.1		2	21.2	odd	6
9702.2.a.dq.1.2		2	21.5	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1078.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.707107 + 1.22474i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.707107 + 1.22474i) q^{5} +1.41421 q^{6} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.707107 + 1.22474i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.707107 + 1.22474i) q^{5} +1.41421 q^{6} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(0.707107 + 1.22474i) q^{10} +(0.500000 + 0.866025i) q^{11} +(0.707107 - 1.22474i) q^{12} +2.82843 q^{13} -2.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.82843 + 4.89898i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-1.41421 + 2.44949i) q^{19} +1.41421 q^{20} +1.00000 q^{22} +(1.00000 - 1.73205i) q^{23} +(-0.707107 - 1.22474i) q^{24} +(1.50000 + 2.59808i) q^{25} +(1.41421 - 2.44949i) q^{26} +5.65685 q^{27} -6.00000 q^{29} +(-1.00000 + 1.73205i) q^{30} +(0.707107 + 1.22474i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.707107 + 1.22474i) q^{33} +5.65685 q^{34} -1.00000 q^{36} +(1.00000 - 1.73205i) q^{37} +(1.41421 + 2.44949i) q^{38} +(2.00000 + 3.46410i) q^{39} +(0.707107 - 1.22474i) q^{40} +5.65685 q^{41} +4.00000 q^{43} +(0.500000 - 0.866025i) q^{44} +(0.707107 + 1.22474i) q^{45} +(-1.00000 - 1.73205i) q^{46} +(-2.12132 + 3.67423i) q^{47} -1.41421 q^{48} +3.00000 q^{50} +(-4.00000 + 6.92820i) q^{51} +(-1.41421 - 2.44949i) q^{52} +(6.00000 + 10.3923i) q^{53} +(2.82843 - 4.89898i) q^{54} -1.41421 q^{55} -4.00000 q^{57} +(-3.00000 + 5.19615i) q^{58} +(-2.12132 - 3.67423i) q^{59} +(1.00000 + 1.73205i) q^{60} +(2.82843 - 4.89898i) q^{61} +1.41421 q^{62} +1.00000 q^{64} +(-2.00000 + 3.46410i) q^{65} +(0.707107 + 1.22474i) q^{66} +(1.00000 + 1.73205i) q^{67} +(2.82843 - 4.89898i) q^{68} +2.82843 q^{69} -10.0000 q^{71} +(-0.500000 + 0.866025i) q^{72} +(7.07107 + 12.2474i) q^{73} +(-1.00000 - 1.73205i) q^{74} +(-2.12132 + 3.67423i) q^{75} +2.82843 q^{76} +4.00000 q^{78} +(4.00000 - 6.92820i) q^{79} +(-0.707107 - 1.22474i) q^{80} +(2.50000 + 4.33013i) q^{81} +(2.82843 - 4.89898i) q^{82} -2.82843 q^{83} -8.00000 q^{85} +(2.00000 - 3.46410i) q^{86} +(-4.24264 - 7.34847i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(3.53553 - 6.12372i) q^{89} +1.41421 q^{90} -2.00000 q^{92} +(-1.00000 + 1.73205i) q^{93} +(2.12132 + 3.67423i) q^{94} +(-2.00000 - 3.46410i) q^{95} +(-0.707107 + 1.22474i) q^{96} -15.5563 q^{97} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} - 4 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 + 2 * q^9	\( 4 q + 2 q^{2} - 2 q^{4} - 4 q^{8} + 2 q^{9} + 2 q^{11} - 8 q^{15} - 2 q^{16} - 2 q^{18} + 4 q^{22} + 4 q^{23} + 6 q^{25} - 24 q^{29} - 4 q^{30} + 2 q^{32} - 4 q^{36} + 4 q^{37} + 8 q^{39} + 16 q^{43} + 2 q^{44} - 4 q^{46} + 12 q^{50} - 16 q^{51} + 24 q^{53} - 16 q^{57} - 12 q^{58} + 4 q^{60} + 4 q^{64} - 8 q^{65} + 4 q^{67} - 40 q^{71} - 2 q^{72} - 4 q^{74} + 16 q^{78} + 16 q^{79} + 10 q^{81} - 32 q^{85} + 8 q^{86} - 2 q^{88} - 8 q^{92} - 4 q^{93} - 8 q^{95} + 4 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 + 2 * q^9 + 2 * q^11 - 8 * q^15 - 2 * q^16 - 2 * q^18 + 4 * q^22 + 4 * q^23 + 6 * q^25 - 24 * q^29 - 4 * q^30 + 2 * q^32 - 4 * q^36 + 4 * q^37 + 8 * q^39 + 16 * q^43 + 2 * q^44 - 4 * q^46 + 12 * q^50 - 16 * q^51 + 24 * q^53 - 16 * q^57 - 12 * q^58 + 4 * q^60 + 4 * q^64 - 8 * q^65 + 4 * q^67 - 40 * q^71 - 2 * q^72 - 4 * q^74 + 16 * q^78 + 16 * q^79 + 10 * q^81 - 32 * q^85 + 8 * q^86 - 2 * q^88 - 8 * q^92 - 4 * q^93 - 8 * q^95 + 4 * q^99

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