LMFDB - Embedded newform 300.2.j.a.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(7,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 1]))

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

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

chi := DirichletCharacter("300.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.j (of order $4$, degree $2$, 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:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			7.1
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	300.7
Dual form			300.2.j.a.43.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 1.22474i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-0.366025 + 1.36603i) q^{6} +(3.15660 - 3.15660i) q^{7} +2.82843 q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 - 1.22474i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-0.366025 + 1.36603i) q^{6} +(3.15660 - 3.15660i) q^{7} +2.82843 q^{8} +1.00000i q^{9} -2.00000i q^{11} +(1.93185 - 0.517638i) q^{12} +(-1.60368 + 1.60368i) q^{13} +(-6.09808 - 1.63397i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-4.24264 - 4.24264i) q^{17} +(1.22474 - 0.707107i) q^{18} +3.19615 q^{19} -4.46410 q^{21} +(-2.44949 + 1.41421i) q^{22} +(-5.27792 - 5.27792i) q^{23} +(-2.00000 - 2.00000i) q^{24} +(3.09808 + 0.830127i) q^{26} +(0.707107 - 0.707107i) q^{27} +(2.31079 + 8.62398i) q^{28} +0.535898i q^{29} -3.73205i q^{31} +(-2.82843 + 4.89898i) q^{32} +(-1.41421 + 1.41421i) q^{33} +(-2.19615 + 8.19615i) q^{34} +(-1.73205 - 1.00000i) q^{36} +(7.72741 + 7.72741i) q^{37} +(-2.26002 - 3.91447i) q^{38} +2.26795 q^{39} +1.46410 q^{41} +(3.15660 + 5.46739i) q^{42} +(-3.15660 - 3.15660i) q^{43} +(3.46410 + 2.00000i) q^{44} +(-2.73205 + 10.1962i) q^{46} +(-0.656339 + 0.656339i) q^{47} +(-1.03528 + 3.86370i) q^{48} -12.9282i q^{49} +6.00000i q^{51} +(-1.17398 - 4.38134i) q^{52} +(3.86370 - 3.86370i) q^{53} +(-1.36603 - 0.366025i) q^{54} +(8.92820 - 8.92820i) q^{56} +(-2.26002 - 2.26002i) q^{57} +(0.656339 - 0.378937i) q^{58} +11.4641 q^{59} +3.00000 q^{61} +(-4.57081 + 2.63896i) q^{62} +(3.15660 + 3.15660i) q^{63} +8.00000 q^{64} +(2.73205 + 0.732051i) q^{66} +(-3.91447 + 3.91447i) q^{67} +(11.5911 - 3.10583i) q^{68} +7.46410i q^{69} +2.53590i q^{71} +2.82843i q^{72} +(2.82843 - 2.82843i) q^{73} +(4.00000 - 14.9282i) q^{74} +(-3.19615 + 5.53590i) q^{76} +(-6.31319 - 6.31319i) q^{77} +(-1.60368 - 2.77766i) q^{78} -7.46410 q^{79} -1.00000 q^{81} +(-1.03528 - 1.79315i) q^{82} +(9.14162 + 9.14162i) q^{83} +(4.46410 - 7.73205i) q^{84} +(-1.63397 + 6.09808i) q^{86} +(0.378937 - 0.378937i) q^{87} -5.65685i q^{88} +6.92820i q^{89} +10.1244i q^{91} +(14.4195 - 3.86370i) q^{92} +(-2.63896 + 2.63896i) q^{93} +(1.26795 + 0.339746i) q^{94} +(5.46410 - 1.46410i) q^{96} +(6.88160 + 6.88160i) q^{97} +(-15.8338 + 9.14162i) q^{98} +2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} + 4 q^{6}+O(q^{10}) $ 8 * q - 8 * q^4 + 4 * q^6	$ 8 q - 8 q^{4} + 4 q^{6} - 28 q^{14} - 16 q^{16} - 16 q^{19} - 8 q^{21} - 16 q^{24} + 4 q^{26} + 24 q^{34} + 32 q^{39} - 16 q^{41} - 8 q^{46} - 4 q^{54} + 16 q^{56} + 64 q^{59} + 24 q^{61} + 64 q^{64} + 8 q^{66} + 32 q^{74} + 16 q^{76} - 32 q^{79} - 8 q^{81} + 8 q^{84} - 20 q^{86} + 24 q^{94} + 16 q^{96} + 16 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 + 4 * q^6 - 28 * q^14 - 16 * q^16 - 16 * q^19 - 8 * q^21 - 16 * q^24 + 4 * q^26 + 24 * q^34 + 32 * q^39 - 16 * q^41 - 8 * q^46 - 4 * q^54 + 16 * q^56 + 64 * q^59 + 24 * q^61 + 64 * q^64 + 8 * q^66 + 32 * q^74 + 16 * q^76 - 32 * q^79 - 8 * q^81 + 8 * q^84 - 20 * q^86 + 24 * q^94 + 16 * q^96 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.707107	−	1.22474i	−0.500000	−	0.866025i
$2$	−0.707107	−	1.22474i	−0.500000	−	0.866025i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$	−1.00000	+	1.73205i	−0.500000	+	0.866025i
$5$		0			0
$5$		0			0
$6$	−0.366025	+	1.36603i	−0.149429	+	0.557678i
$7$	3.15660	−	3.15660i	1.19308	−	1.19308i	0.216884	−	0.976197i	$-0.430411\pi$
$7$	3.15660	−	3.15660i	1.19308	−	1.19308i	0.976197	−	0.216884i	$-0.0695893\pi$
$8$	2.82843			1.00000
$9$			1.00000i			0.333333i
$10$		0			0
$11$		−	2.00000i		−	0.603023i	−0.953463	−	0.301511i	$-0.902509\pi$
$11$		−	2.00000i		−	0.603023i	0.953463	−	0.301511i	$-0.0974911\pi$
$12$	1.93185	−	0.517638i	0.557678	−	0.149429i
$13$	−1.60368	+	1.60368i	−0.444781	+	0.444781i	−0.893615	−	0.448834i	$-0.851840\pi$
$13$	−1.60368	+	1.60368i	−0.444781	+	0.444781i	0.448834	+	0.893615i	$0.351840\pi$
$14$	−6.09808	−	1.63397i	−1.62978	−	0.436698i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.500000	−	0.866025i
$17$	−4.24264	−	4.24264i	−1.02899	−	1.02899i	−0.999567	−	0.0294245i	$-0.990633\pi$
$17$	−4.24264	−	4.24264i	−1.02899	−	1.02899i	−0.0294245	−	0.999567i	$-0.509367\pi$
$18$	1.22474	−	0.707107i	0.288675	−	0.166667i
$19$	3.19615			0.733248			0.366624	−	0.930369i	$-0.380514\pi$
$19$	3.19615			0.733248			0.366624	+	0.930369i	$0.380514\pi$
$20$		0			0
$21$	−4.46410			−0.974147
$22$	−2.44949	+	1.41421i	−0.522233	+	0.301511i
$23$	−5.27792	−	5.27792i	−1.10052	−	1.10052i	−0.994348	−	0.106174i	$-0.966140\pi$
$23$	−5.27792	−	5.27792i	−1.10052	−	1.10052i	−0.106174	−	0.994348i	$-0.533860\pi$
$24$	−2.00000	−	2.00000i	−0.408248	−	0.408248i
$25$		0			0
$26$	3.09808	+	0.830127i	0.607583	+	0.162801i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	2.31079	+	8.62398i	0.436698	+	1.62978i
$29$			0.535898i			0.0995138i	0.998761	+	0.0497569i	$0.0158447\pi$
$29$			0.535898i			0.0995138i	−0.998761	+	0.0497569i	$0.984155\pi$
$30$		0			0
$31$		−	3.73205i		−	0.670296i	−0.942165	−	0.335148i	$-0.891214\pi$
$31$		−	3.73205i		−	0.670296i	0.942165	−	0.335148i	$-0.108786\pi$
$32$	−2.82843	+	4.89898i	−0.500000	+	0.866025i
$33$	−1.41421	+	1.41421i	−0.246183	+	0.246183i
$34$	−2.19615	+	8.19615i	−0.376637	+	1.40563i
$35$		0			0
$36$	−1.73205	−	1.00000i	−0.288675	−	0.166667i
$37$	7.72741	+	7.72741i	1.27038	+	1.27038i	0.945890	+	0.324488i	$0.105192\pi$
$37$	7.72741	+	7.72741i	1.27038	+	1.27038i	0.324488	+	0.945890i	$0.394808\pi$
$38$	−2.26002	−	3.91447i	−0.366624	−	0.635011i
$39$	2.26795			0.363163
$40$		0			0
$41$	1.46410			0.228654			0.114327	−	0.993443i	$-0.463529\pi$
$41$	1.46410			0.228654			0.114327	+	0.993443i	$0.463529\pi$
$42$	3.15660	+	5.46739i	0.487073	+	0.843636i
$43$	−3.15660	−	3.15660i	−0.481376	−	0.481376i	0.424195	−	0.905571i	$-0.360557\pi$
$43$	−3.15660	−	3.15660i	−0.481376	−	0.481376i	−0.905571	+	0.424195i	$0.860557\pi$
$44$	3.46410	+	2.00000i	0.522233	+	0.301511i
$45$		0			0
$46$	−2.73205	+	10.1962i	−0.402819	+	1.50334i
$47$	−0.656339	+	0.656339i	−0.0957369	+	0.0957369i	−0.753353	−	0.657616i	$-0.771565\pi$
$47$	−0.656339	+	0.656339i	−0.0957369	+	0.0957369i	0.657616	+	0.753353i	$0.271565\pi$
$48$	−1.03528	+	3.86370i	−0.149429	+	0.557678i
$49$		−	12.9282i		−	1.84689i
$50$		0			0
$51$			6.00000i			0.840168i
$52$	−1.17398	−	4.38134i	−0.162801	−	0.607583i
$53$	3.86370	−	3.86370i	0.530720	−	0.530720i	−0.390066	−	0.920787i	$-0.627548\pi$
$53$	3.86370	−	3.86370i	0.530720	−	0.530720i	0.920787	+	0.390066i	$0.127548\pi$
$54$	−1.36603	−	0.366025i	−0.185893	−	0.0498097i
$55$		0			0
$56$	8.92820	−	8.92820i	1.19308	−	1.19308i
$57$	−2.26002	−	2.26002i	−0.299347	−	0.299347i
$58$	0.656339	−	0.378937i	0.0861815	−	0.0497569i
$59$	11.4641			1.49250			0.746249	−	0.665666i	$-0.231853\pi$
$59$	11.4641			1.49250			0.746249	+	0.665666i	$0.231853\pi$
$60$		0			0
$61$	3.00000			0.384111			0.192055	−	0.981384i	$-0.438485\pi$
$61$	3.00000			0.384111			0.192055	+	0.981384i	$0.438485\pi$
$62$	−4.57081	+	2.63896i	−0.580493	+	0.335148i
$63$	3.15660	+	3.15660i	0.397694	+	0.397694i
$64$	8.00000			1.00000
$65$		0			0
$66$	2.73205	+	0.732051i	0.336292	+	0.0901092i
$67$	−3.91447	+	3.91447i	−0.478229	+	0.478229i	−0.904565	−	0.426336i	$-0.859804\pi$
$67$	−3.91447	+	3.91447i	−0.478229	+	0.478229i	0.426336	+	0.904565i	$0.359804\pi$
$68$	11.5911	−	3.10583i	1.40563	−	0.376637i
$69$			7.46410i			0.898572i
$70$		0			0
$71$			2.53590i			0.300956i	0.988613	+	0.150478i	$0.0480812\pi$
$71$			2.53590i			0.300956i	−0.988613	+	0.150478i	$0.951919\pi$
$72$			2.82843i			0.333333i
$73$	2.82843	−	2.82843i	0.331042	−	0.331042i	−0.521940	−	0.852982i	$-0.674791\pi$
$73$	2.82843	−	2.82843i	0.331042	−	0.331042i	0.852982	+	0.521940i	$0.174791\pi$
$74$	4.00000	−	14.9282i	0.464991	−	1.73537i
$75$		0			0
$76$	−3.19615	+	5.53590i	−0.366624	+	0.635011i
$77$	−6.31319	−	6.31319i	−0.719455	−	0.719455i
$78$	−1.60368	−	2.77766i	−0.181581	−	0.314508i
$79$	−7.46410			−0.839777			−0.419889	−	0.907576i	$-0.637931\pi$
$79$	−7.46410			−0.839777			−0.419889	+	0.907576i	$0.637931\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$	−1.03528	−	1.79315i	−0.114327	−	0.198020i
$83$	9.14162	+	9.14162i	1.00342	+	1.00342i	0.999994	+	0.00342905i	$0.00109150\pi$
$83$	9.14162	+	9.14162i	1.00342	+	1.00342i	0.00342905	+	0.999994i	$0.498908\pi$
$84$	4.46410	−	7.73205i	0.487073	−	0.843636i
$85$		0			0
$86$	−1.63397	+	6.09808i	−0.176196	+	0.657572i
$87$	0.378937	−	0.378937i	0.0406264	−	0.0406264i
$88$		−	5.65685i		−	0.603023i
$89$			6.92820i			0.734388i	0.930144	+	0.367194i	$0.119682\pi$
$89$			6.92820i			0.734388i	−0.930144	+	0.367194i	$0.880318\pi$
$90$		0			0
$91$			10.1244i			1.06132i
$92$	14.4195	−	3.86370i	1.50334	−	0.402819i
$93$	−2.63896	+	2.63896i	−0.273647	+	0.273647i
$94$	1.26795	+	0.339746i	0.130779	+	0.0350421i
$95$		0			0
$96$	5.46410	−	1.46410i	0.557678	−	0.149429i
$97$	6.88160	+	6.88160i	0.698721	+	0.698721i	0.964135	−	0.265414i	$-0.0855086\pi$
$97$	6.88160	+	6.88160i	0.698721	+	0.698721i	−0.265414	+	0.964135i	$0.585509\pi$
$98$	−15.8338	+	9.14162i	−1.59945	+	0.923443i
$99$	2.00000			0.201008
$100$		0			0
$101$	5.46410			0.543698			0.271849	−	0.962340i	$-0.412365\pi$
$101$	5.46410			0.543698			0.271849	+	0.962340i	$0.412365\pi$
$102$	7.34847	−	4.24264i	0.727607	−	0.420084i
$103$	4.89898	+	4.89898i	0.482711	+	0.482711i	0.905996	−	0.423286i	$-0.139123\pi$
$103$	4.89898	+	4.89898i	0.482711	+	0.482711i	−0.423286	+	0.905996i	$0.639123\pi$
$104$	−4.53590	+	4.53590i	−0.444781	+	0.444781i
$105$		0			0
$106$	−7.46410	−	2.00000i	−0.724978	−	0.194257i
$107$	−9.52056	+	9.52056i	−0.920387	+	0.920387i	−0.997057	−	0.0766695i	$-0.975571\pi$
$107$	−9.52056	+	9.52056i	−0.920387	+	0.920387i	0.0766695	+	0.997057i	$0.475571\pi$
$108$	0.517638	+	1.93185i	0.0498097	+	0.185893i
$109$		−	7.00000i		−	0.670478i	−0.942133	−	0.335239i	$-0.891183\pi$
$109$		−	7.00000i		−	0.670478i	0.942133	−	0.335239i	$-0.108817\pi$
$110$		0			0
$111$		−	10.9282i		−	1.03726i
$112$	−17.2480	−	4.62158i	−1.62978	−	0.436698i
$113$	−9.79796	+	9.79796i	−0.921714	+	0.921714i	−0.997151	−	0.0754362i	$-0.975965\pi$
$113$	−9.79796	+	9.79796i	−0.921714	+	0.921714i	0.0754362	+	0.997151i	$0.475965\pi$
$114$	−1.16987	+	4.36603i	−0.109569	+	0.408916i
$115$		0			0
$116$	−0.928203	−	0.535898i	−0.0861815	−	0.0497569i
$117$	−1.60368	−	1.60368i	−0.148260	−	0.148260i
$118$	−8.10634	−	14.0406i	−0.746249	−	1.29254i
$119$	−26.7846			−2.45534
$120$		0			0
$121$	7.00000			0.636364
$122$	−2.12132	−	3.67423i	−0.192055	−	0.332650i
$123$	−1.03528	−	1.03528i	−0.0933477	−	0.0933477i
$124$	6.46410	+	3.73205i	0.580493	+	0.335148i
$125$		0			0
$126$	1.63397	−	6.09808i	0.145566	−	0.543260i
$127$	7.72741	−	7.72741i	0.685696	−	0.685696i	−0.275581	−	0.961278i	$-0.588870\pi$
$127$	7.72741	−	7.72741i	0.685696	−	0.685696i	0.961278	+	0.275581i	$0.0888703\pi$
$128$	−5.65685	−	9.79796i	−0.500000	−	0.866025i
$129$			4.46410i			0.393042i
$130$		0			0
$131$		−	2.53590i		−	0.221562i	−0.993845	−	0.110781i	$-0.964665\pi$
$131$		−	2.53590i		−	0.221562i	0.993845	−	0.110781i	$-0.0353353\pi$
$132$	−1.03528	−	3.86370i	−0.0901092	−	0.336292i
$133$	10.0890	−	10.0890i	0.874824	−	0.874824i
$134$	7.56218	+	2.02628i	0.653273	+	0.175044i
$135$		0			0
$136$	−12.0000	−	12.0000i	−1.02899	−	1.02899i
$137$	10.9348	+	10.9348i	0.934221	+	0.934221i	0.997966	−	0.0637456i	$-0.0203046\pi$
$137$	10.9348	+	10.9348i	0.934221	+	0.934221i	−0.0637456	+	0.997966i	$0.520305\pi$
$138$	9.14162	−	5.27792i	0.778186	−	0.449286i
$139$	−12.5359			−1.06328			−0.531641	−	0.846970i	$-0.678424\pi$
$139$	−12.5359			−1.06328			−0.531641	+	0.846970i	$0.678424\pi$
$140$		0			0
$141$	0.928203			0.0781688
$142$	3.10583	−	1.79315i	0.260635	−	0.150478i
$143$	3.20736	+	3.20736i	0.268213	+	0.268213i
$144$	3.46410	−	2.00000i	0.288675	−	0.166667i
$145$		0			0
$146$	−5.46410	−	1.46410i	−0.452212	−	0.121170i
$147$	−9.14162	+	9.14162i	−0.753988	+	0.753988i
$148$	−21.1117	+	5.65685i	−1.73537	+	0.464991i
$149$			11.8564i			0.971315i	0.874149	+	0.485657i	$0.161420\pi$
$149$			11.8564i			0.971315i	−0.874149	+	0.485657i	$0.838580\pi$
$150$		0			0
$151$		−	7.73205i		−	0.629225i	−0.949220	−	0.314613i	$-0.898125\pi$
$151$		−	7.73205i		−	0.629225i	0.949220	−	0.314613i	$-0.101875\pi$
$152$	9.04008			0.733248
$153$	4.24264	−	4.24264i	0.342997	−	0.342997i
$154$	−3.26795	+	12.1962i	−0.263339	+	0.982794i
$155$		0			0
$156$	−2.26795	+	3.92820i	−0.181581	+	0.314508i
$157$	−4.43211	−	4.43211i	−0.353721	−	0.353721i	0.507771	−	0.861492i	$-0.330470\pi$
$157$	−4.43211	−	4.43211i	−0.353721	−	0.353721i	−0.861492	+	0.507771i	$0.830470\pi$
$158$	5.27792	+	9.14162i	0.419889	+	0.727268i
$159$	−5.46410			−0.433331
$160$		0			0
$161$	−33.3205			−2.62602
$162$	0.707107	+	1.22474i	0.0555556	+	0.0962250i
$163$	5.32868	+	5.32868i	0.417375	+	0.417375i	0.884298	−	0.466923i	$-0.154638\pi$
$163$	5.32868	+	5.32868i	0.417375	+	0.417375i	−0.466923	+	0.884298i	$0.654638\pi$
$164$	−1.46410	+	2.53590i	−0.114327	+	0.198020i
$165$		0			0
$166$	4.73205	−	17.6603i	0.367278	−	1.37070i
$167$	11.5911	−	11.5911i	0.896947	−	0.896947i	−0.0982179	−	0.995165i	$-0.531314\pi$
$167$	11.5911	−	11.5911i	0.896947	−	0.896947i	0.995165	+	0.0982179i	$0.0313142\pi$
$168$	−12.6264			−0.974147
$169$			7.85641i			0.604339i
$170$		0			0
$171$			3.19615i			0.244416i
$172$	8.62398	−	2.31079i	0.657572	−	0.176196i
$173$	3.48477	−	3.48477i	0.264942	−	0.264942i	−0.562116	−	0.827058i	$-0.690013\pi$
$173$	3.48477	−	3.48477i	0.264942	−	0.264942i	0.827058	+	0.562116i	$0.190013\pi$
$174$	−0.732051	−	0.196152i	−0.0554966	−	0.0148703i
$175$		0			0
$176$	−6.92820	+	4.00000i	−0.522233	+	0.301511i
$177$	−8.10634	−	8.10634i	−0.609310	−	0.609310i
$178$	8.48528	−	4.89898i	0.635999	−	0.367194i
$179$	9.32051			0.696647			0.348324	−	0.937374i	$-0.386751\pi$
$179$	9.32051			0.696647			0.348324	+	0.937374i	$0.386751\pi$
$180$		0			0
$181$	−0.0717968			−0.00533661			−0.00266831	−	0.999996i	$-0.500849\pi$
$181$	−0.0717968			−0.00533661			−0.00266831	+	0.999996i	$0.500849\pi$
$182$	12.3998	−	7.15900i	0.919131	−	0.530660i
$183$	−2.12132	−	2.12132i	−0.156813	−	0.156813i
$184$	−14.9282	−	14.9282i	−1.10052	−	1.10052i
$185$		0			0
$186$	5.09808	+	1.36603i	0.373809	+	0.100162i
$187$	−8.48528	+	8.48528i	−0.620505	+	0.620505i
$188$	−0.480473	−	1.79315i	−0.0350421	−	0.130779i
$189$		−	4.46410i		−	0.324716i
$190$		0			0
$191$			3.07180i			0.222267i	0.993805	+	0.111134i	$0.0354482\pi$
$191$			3.07180i			0.222267i	−0.993805	+	0.111134i	$0.964552\pi$
$192$	−5.65685	−	5.65685i	−0.408248	−	0.408248i
$193$	−7.26054	+	7.26054i	−0.522625	+	0.522625i	−0.918363	−	0.395738i	$-0.870489\pi$
$193$	−7.26054	+	7.26054i	−0.522625	+	0.522625i	0.395738	+	0.918363i	$0.370489\pi$
$194$	3.56218	−	13.2942i	0.255749	−	0.954470i
$195$		0			0
$196$	22.3923	+	12.9282i	1.59945	+	0.923443i
$197$	−4.52004	−	4.52004i	−0.322040	−	0.322040i	0.527509	−	0.849549i	$-0.323126\pi$
$197$	−4.52004	−	4.52004i	−0.322040	−	0.322040i	−0.849549	+	0.527509i	$0.823126\pi$
$198$	−1.41421	−	2.44949i	−0.100504	−	0.174078i
$199$	−10.1244			−0.717697			−0.358848	−	0.933396i	$-0.616830\pi$
$199$	−10.1244			−0.717697			−0.358848	+	0.933396i	$0.616830\pi$
$200$		0			0
$201$	5.53590			0.390472
$202$	−3.86370	−	6.69213i	−0.271849	−	0.470857i
$203$	1.69161	+	1.69161i	0.118728	+	0.118728i
$204$	−10.3923	−	6.00000i	−0.727607	−	0.420084i
$205$		0			0
$206$	2.53590	−	9.46410i	0.176684	−	0.659395i
$207$	5.27792	−	5.27792i	0.366841	−	0.366841i
$208$	8.76268	+	2.34795i	0.607583	+	0.162801i
$209$		−	6.39230i		−	0.442165i
$210$		0			0
$211$		−	3.19615i		−	0.220032i	−0.993930	−	0.110016i	$-0.964910\pi$
$211$		−	3.19615i		−	0.220032i	0.993930	−	0.110016i	$-0.0350902\pi$
$212$	2.82843	+	10.5558i	0.194257	+	0.724978i
$213$	1.79315	−	1.79315i	0.122865	−	0.122865i
$214$	18.3923	+	4.92820i	1.25727	+	0.336885i
$215$		0			0
$216$	2.00000	−	2.00000i	0.136083	−	0.136083i
$217$	−11.7806	−	11.7806i	−0.799718	−	0.799718i
$218$	−8.57321	+	4.94975i	−0.580651	+	0.335239i
$219$	−4.00000			−0.270295
$220$		0			0
$221$	13.6077			0.915353
$222$	−13.3843	+	7.72741i	−0.898293	+	0.518630i
$223$	−6.64136	−	6.64136i	−0.444739	−	0.444739i	0.448862	−	0.893601i	$-0.351829\pi$
$223$	−6.64136	−	6.64136i	−0.444739	−	0.444739i	−0.893601	+	0.448862i	$0.851829\pi$
$224$	6.53590	+	24.3923i	0.436698	+	1.62978i
$225$		0			0
$226$	18.9282	+	5.07180i	1.25909	+	0.337371i
$227$	5.93426	−	5.93426i	0.393870	−	0.393870i	−0.482194	−	0.876064i	$-0.660160\pi$
$227$	5.93426	−	5.93426i	0.393870	−	0.393870i	0.876064	+	0.482194i	$0.160160\pi$
$228$	6.17449	−	1.65445i	0.408916	−	0.109569i
$229$		−	2.85641i		−	0.188757i	−0.995536	−	0.0943783i	$-0.969914\pi$
$229$		−	2.85641i		−	0.188757i	0.995536	−	0.0943783i	$-0.0300863\pi$
$230$		0			0
$231$			8.92820i			0.587433i
$232$			1.51575i			0.0995138i
$233$	5.93426	−	5.93426i	0.388766	−	0.388766i	−0.485481	−	0.874247i	$-0.661356\pi$
$233$	5.93426	−	5.93426i	0.388766	−	0.388766i	0.874247	+	0.485481i	$0.161356\pi$
$234$	−0.830127	+	3.09808i	−0.0542671	+	0.202528i
$235$		0			0
$236$	−11.4641	+	19.8564i	−0.746249	+	1.29254i
$237$	5.27792	+	5.27792i	0.342838	+	0.342838i
$238$	18.9396	+	32.8043i	1.22767	+	2.12639i
$239$	10.5359			0.681511			0.340755	−	0.940152i	$-0.389317\pi$
$239$	10.5359			0.681511			0.340755	+	0.940152i	$0.389317\pi$
$240$		0			0
$241$	12.8564			0.828154			0.414077	−	0.910242i	$-0.364104\pi$
$241$	12.8564			0.828154			0.414077	+	0.910242i	$0.364104\pi$
$242$	−4.94975	−	8.57321i	−0.318182	−	0.551107i
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	−3.00000	+	5.19615i	−0.192055	+	0.332650i
$245$		0			0
$246$	−0.535898	+	2.00000i	−0.0341676	+	0.127515i
$247$	−5.12561	+	5.12561i	−0.326135	+	0.326135i
$248$		−	10.5558i		−	0.670296i
$249$		−	12.9282i		−	0.819292i
$250$		0			0
$251$			29.8564i			1.88452i	0.334883	+	0.942260i	$0.391303\pi$
$251$			29.8564i			1.88452i	−0.334883	+	0.942260i	$0.608697\pi$
$252$	−8.62398	+	2.31079i	−0.543260	+	0.145566i
$253$	−10.5558	+	10.5558i	−0.663640	+	0.663640i
$254$	−14.9282	−	4.00000i	−0.936679	−	0.250982i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	20.3538	+	20.3538i	1.26963	+	1.26963i	0.946277	+	0.323358i	$0.104812\pi$
$257$	20.3538	+	20.3538i	1.26963	+	1.26963i	0.323358	+	0.946277i	$0.395188\pi$
$258$	5.46739	−	3.15660i	0.340385	−	0.196521i
$259$	48.7846			3.03133
$260$		0			0
$261$	−0.535898			−0.0331713
$262$	−3.10583	+	1.79315i	−0.191879	+	0.110781i
$263$	−10.2784	−	10.2784i	−0.633795	−	0.633795i	0.315223	−	0.949018i	$-0.397921\pi$
$263$	−10.2784	−	10.2784i	−0.633795	−	0.633795i	−0.949018	+	0.315223i	$0.897921\pi$
$264$	−4.00000	+	4.00000i	−0.246183	+	0.246183i
$265$		0			0
$266$	−19.4904	−	5.22243i	−1.19503	−	0.320208i
$267$	4.89898	−	4.89898i	0.299813	−	0.299813i
$268$	−2.86559	−	10.6945i	−0.175044	−	0.653273i
$269$		−	22.3923i		−	1.36528i	−0.730753	−	0.682641i	$-0.760831\pi$
$269$		−	22.3923i		−	1.36528i	0.730753	−	0.682641i	$-0.239169\pi$
$270$		0			0
$271$		−	24.2487i		−	1.47300i	−0.676435	−	0.736502i	$-0.736476\pi$
$271$		−	24.2487i		−	1.47300i	0.676435	−	0.736502i	$-0.263524\pi$
$272$	−6.21166	+	23.1822i	−0.376637	+	1.40563i
$273$	7.15900	−	7.15900i	0.433282	−	0.433282i
$274$	5.66025	−	21.1244i	0.341948	−	1.27617i
$275$		0			0
$276$	−12.9282	−	7.46410i	−0.778186	−	0.449286i
$277$	6.50266	+	6.50266i	0.390707	+	0.390707i	0.874939	−	0.484232i	$-0.160901\pi$
$277$	6.50266	+	6.50266i	0.390707	+	0.390707i	−0.484232	+	0.874939i	$0.660901\pi$
$278$	8.86422	+	15.3533i	0.531641	+	0.920828i
$279$	3.73205			0.223432
$280$		0			0
$281$	6.39230			0.381333			0.190666	−	0.981655i	$-0.438935\pi$
$281$	6.39230			0.381333			0.190666	+	0.981655i	$0.438935\pi$
$282$	−0.656339	−	1.13681i	−0.0390844	−	0.0676962i
$283$	−0.429705	−	0.429705i	−0.0255433	−	0.0255433i	0.694220	−	0.719763i	$-0.255750\pi$
$283$	−0.429705	−	0.429705i	−0.0255433	−	0.0255433i	−0.719763	+	0.694220i	$0.755750\pi$
$284$	−4.39230	−	2.53590i	−0.260635	−	0.150478i
$285$		0			0
$286$	1.66025	−	6.19615i	0.0981729	−	0.366386i
$287$	4.62158	−	4.62158i	0.272803	−	0.272803i
$288$	−4.89898	−	2.82843i	−0.288675	−	0.166667i
$289$			19.0000i			1.11765i
$290$		0			0
$291$		−	9.73205i		−	0.570503i
$292$	2.07055	+	7.72741i	0.121170	+	0.452212i
$293$	−13.7632	+	13.7632i	−0.804055	+	0.804055i	−0.983727	−	0.179672i	$-0.942496\pi$
$293$	−13.7632	+	13.7632i	−0.804055	+	0.804055i	0.179672	+	0.983727i	$0.442496\pi$
$294$	17.6603	+	4.73205i	1.02997	+	0.275979i
$295$		0			0
$296$	21.8564	+	21.8564i	1.27038	+	1.27038i
$297$	−1.41421	−	1.41421i	−0.0820610	−	0.0820610i
$298$	14.5211	−	8.38375i	0.841183	−	0.485657i
$299$	16.9282			0.978983
$300$		0			0
$301$	−19.9282			−1.14864
$302$	−9.46979	+	5.46739i	−0.544925	+	0.314613i
$303$	−3.86370	−	3.86370i	−0.221964	−	0.221964i
$304$	−6.39230	−	11.0718i	−0.366624	−	0.635011i
$305$		0			0
$306$	−8.19615	−	2.19615i	−0.468543	−	0.125546i
$307$	−5.22715	+	5.22715i	−0.298329	+	0.298329i	−0.840359	−	0.542030i	$-0.817656\pi$
$307$	−5.22715	+	5.22715i	−0.298329	+	0.298329i	0.542030	+	0.840359i	$0.317656\pi$
$308$	17.2480	−	4.62158i	0.982794	−	0.263339i
$309$		−	6.92820i		−	0.394132i
$310$		0			0
$311$		−	20.5359i		−	1.16448i	−0.813016	−	0.582242i	$-0.802176\pi$
$311$		−	20.5359i		−	1.16448i	0.813016	−	0.582242i	$-0.197824\pi$
$312$	6.41473			0.363163
$313$	11.4016	−	11.4016i	0.644459	−	0.644459i	−0.307190	−	0.951648i	$-0.599389\pi$
$313$	11.4016	−	11.4016i	0.644459	−	0.644459i	0.951648	+	0.307190i	$0.0993885\pi$
$314$	−2.29423	+	8.56218i	−0.129471	+	0.483192i
$315$		0			0
$316$	7.46410	−	12.9282i	0.419889	−	0.727268i
$317$	−4.89898	−	4.89898i	−0.275154	−	0.275154i	0.556017	−	0.831171i	$-0.312329\pi$
$317$	−4.89898	−	4.89898i	−0.275154	−	0.275154i	−0.831171	+	0.556017i	$0.812329\pi$
$318$	3.86370	+	6.69213i	0.216666	+	0.375276i
$319$	1.07180			0.0600091
$320$		0			0
$321$	13.4641			0.751493
$322$	23.5612	+	40.8091i	1.31301	+	2.27420i
$323$	−13.5601	−	13.5601i	−0.754506	−	0.754506i
$324$	1.00000	−	1.73205i	0.0555556	−	0.0962250i
$325$		0			0
$326$	2.75833	−	10.2942i	0.152770	−	0.570145i
$327$	−4.94975	+	4.94975i	−0.273722	+	0.273722i
$328$	4.14110			0.228654
$329$			4.14359i			0.228444i
$330$		0			0
$331$			18.3923i			1.01093i	0.862846	+	0.505466i	$0.168679\pi$
$331$			18.3923i			1.01093i	−0.862846	+	0.505466i	$0.831321\pi$
$332$	−24.9754	+	6.69213i	−1.37070	+	0.367278i
$333$	−7.72741	+	7.72741i	−0.423459	+	0.423459i
$334$	−22.3923	−	6.00000i	−1.22525	−	0.328305i
$335$		0			0
$336$	8.92820	+	15.4641i	0.487073	+	0.843636i
$337$	−20.2659	−	20.2659i	−1.10395	−	1.10395i	−0.993929	−	0.110023i	$-0.964908\pi$
$337$	−20.2659	−	20.2659i	−1.10395	−	1.10395i	−0.110023	−	0.993929i	$-0.535092\pi$
$338$	9.62209	−	5.55532i	0.523373	−	0.302169i
$339$	13.8564			0.752577
$340$		0			0
$341$	−7.46410			−0.404204
$342$	3.91447	−	2.26002i	0.211670	−	0.122208i
$343$	−18.7129	−	18.7129i	−1.01040	−	1.01040i
$344$	−8.92820	−	8.92820i	−0.481376	−	0.481376i
$345$		0			0
$346$	−6.73205	−	1.80385i	−0.361917	−	0.0969754i
$347$	−17.6269	+	17.6269i	−0.946262	+	0.946262i	−0.998628	−	0.0523663i	$-0.983324\pi$
$347$	−17.6269	+	17.6269i	−0.946262	+	0.946262i	0.0523663	+	0.998628i	$0.483324\pi$
$348$	0.277401	+	1.03528i	0.0148703	+	0.0554966i
$349$			23.8564i			1.27700i	0.769620	+	0.638502i	$0.220446\pi$
$349$			23.8564i			1.27700i	−0.769620	+	0.638502i	$0.779554\pi$
$350$		0			0
$351$			2.26795i			0.121054i
$352$	9.79796	+	5.65685i	0.522233	+	0.301511i
$353$	−8.38375	+	8.38375i	−0.446222	+	0.446222i	−0.894096	−	0.447875i	$-0.852181\pi$
$353$	−8.38375	+	8.38375i	−0.446222	+	0.446222i	0.447875	+	0.894096i	$0.352181\pi$
$354$	−4.19615	+	15.6603i	−0.223023	+	0.832333i
$355$		0			0
$356$	−12.0000	−	6.92820i	−0.635999	−	0.367194i
$357$	18.9396	+	18.9396i	1.00239	+	1.00239i
$358$	−6.59059	−	11.4152i	−0.348324	−	0.603314i
$359$	−3.60770			−0.190407			−0.0952034	−	0.995458i	$-0.530350\pi$
$359$	−3.60770			−0.190407			−0.0952034	+	0.995458i	$0.530350\pi$
$360$		0			0
$361$	−8.78461			−0.462348
$362$	0.0507680	+	0.0879327i	0.00266831	+	0.00462164i
$363$	−4.94975	−	4.94975i	−0.259794	−	0.259794i
$364$	−17.5359	−	10.1244i	−0.919131	−	0.530660i
$365$		0			0
$366$	−1.09808	+	4.09808i	−0.0573974	+	0.214210i
$367$	22.1977	−	22.1977i	1.15871	−	1.15871i	0.173958	−	0.984753i	$-0.444344\pi$
$367$	22.1977	−	22.1977i	1.15871	−	1.15871i	0.984753	−	0.173958i	$-0.0556557\pi$
$368$	−7.72741	+	28.8391i	−0.402819	+	1.50334i
$369$			1.46410i			0.0762181i
$370$		0			0
$371$		−	24.3923i		−	1.26639i
$372$	−1.93185	−	7.20977i	−0.100162	−	0.373809i
$373$	−25.9227	+	25.9227i	−1.34223	+	1.34223i	−0.448388	+	0.893839i	$0.648002\pi$
$373$	−25.9227	+	25.9227i	−1.34223	+	1.34223i	−0.893839	+	0.448388i	$0.851998\pi$
$374$	16.3923	+	4.39230i	0.847626	+	0.227121i
$375$		0			0
$376$	−1.85641	+	1.85641i	−0.0957369	+	0.0957369i
$377$	−0.859411	−	0.859411i	−0.0442619	−	0.0442619i
$378$	−5.46739	+	3.15660i	−0.281212	+	0.162358i
$379$	12.2679			0.630162			0.315081	−	0.949065i	$-0.397968\pi$
$379$	12.2679			0.630162			0.315081	+	0.949065i	$0.397968\pi$
$380$		0			0
$381$	−10.9282			−0.559869
$382$	3.76217	−	2.17209i	0.192489	−	0.111134i
$383$	17.5254	+	17.5254i	0.895504	+	0.895504i	0.995035	−	0.0995302i	$-0.0317340\pi$
$383$	17.5254	+	17.5254i	0.895504	+	0.895504i	−0.0995302	+	0.995035i	$0.531734\pi$
$384$	−2.92820	+	10.9282i	−0.149429	+	0.557678i
$385$		0			0
$386$	14.0263	+	3.75833i	0.713919	+	0.191294i
$387$	3.15660	−	3.15660i	0.160459	−	0.160459i
$388$	−18.8009	+	5.03768i	−0.954470	+	0.255749i
$389$		−	21.4641i		−	1.08827i	−0.838997	−	0.544137i	$-0.816857\pi$
$389$		−	21.4641i		−	1.08827i	0.838997	−	0.544137i	$-0.183143\pi$
$390$		0			0
$391$			44.7846i			2.26486i
$392$		−	36.5665i		−	1.84689i
$393$	−1.79315	+	1.79315i	−0.0904525	+	0.0904525i
$394$	−2.33975	+	8.73205i	−0.117875	+	0.439914i
$395$		0			0
$396$	−2.00000	+	3.46410i	−0.100504	+	0.174078i
$397$	−8.19428	−	8.19428i	−0.411259	−	0.411259i	0.470918	−	0.882177i	$-0.343923\pi$
$397$	−8.19428	−	8.19428i	−0.411259	−	0.411259i	−0.882177	+	0.470918i	$0.843923\pi$
$398$	7.15900	+	12.3998i	0.358848	+	0.621543i
$399$	−14.2679			−0.714291
$400$		0			0
$401$	29.1769			1.45703			0.728513	−	0.685032i	$-0.240212\pi$
$401$	29.1769			1.45703			0.728513	+	0.685032i	$0.240212\pi$
$402$	−3.91447	−	6.78006i	−0.195236	−	0.338159i
$403$	5.98502	+	5.98502i	0.298135	+	0.298135i
$404$	−5.46410	+	9.46410i	−0.271849	+	0.470857i
$405$		0			0
$406$	0.875644	−	3.26795i	0.0434575	−	0.162186i
$407$	15.4548	−	15.4548i	0.766067	−	0.766067i
$408$			16.9706i			0.840168i
$409$		−	13.7846i		−	0.681605i	−0.940135	−	0.340803i	$-0.889301\pi$
$409$		−	13.7846i		−	0.681605i	0.940135	−	0.340803i	$-0.110699\pi$
$410$		0			0
$411$		−	15.4641i		−	0.762788i
$412$	−13.3843	+	3.58630i	−0.659395	+	0.176684i
$413$	36.1875	−	36.1875i	1.78067	−	1.78067i
$414$	−10.1962	−	2.73205i	−0.501114	−	0.134273i
$415$		0			0
$416$	−3.32051	−	12.3923i	−0.162801	−	0.607583i
$417$	8.86422	+	8.86422i	0.434083	+	0.434083i
$418$	−7.82894	+	4.52004i	−0.382926	+	0.221082i
$419$	−33.4641			−1.63483			−0.817414	−	0.576050i	$-0.804593\pi$
$419$	−33.4641			−1.63483			−0.817414	+	0.576050i	$0.804593\pi$
$420$		0			0
$421$	−34.7846			−1.69530			−0.847649	−	0.530557i	$-0.821983\pi$
$421$	−34.7846			−1.69530			−0.847649	+	0.530557i	$0.821983\pi$
$422$	−3.91447	+	2.26002i	−0.190553	+	0.110016i
$423$	−0.656339	−	0.656339i	−0.0319123	−	0.0319123i
$424$	10.9282	−	10.9282i	0.530720	−	0.530720i
$425$		0			0
$426$	−3.46410	−	0.928203i	−0.167836	−	0.0449716i
$427$	9.46979	−	9.46979i	0.458275	−	0.458275i
$428$	−6.96953	−	26.0106i	−0.336885	−	1.25727i
$429$		−	4.53590i		−	0.218995i
$430$		0			0
$431$		−	29.7128i		−	1.43122i	−0.698502	−	0.715608i	$-0.746150\pi$
$431$		−	29.7128i		−	1.43122i	0.698502	−	0.715608i	$-0.253850\pi$
$432$	−3.86370	−	1.03528i	−0.185893	−	0.0498097i
$433$	25.1648	−	25.1648i	1.20935	−	1.20935i	0.238106	−	0.971239i	$-0.423474\pi$
$433$	25.1648	−	25.1648i	1.20935	−	1.20935i	0.971239	−	0.238106i	$-0.0765265\pi$
$434$	−6.09808	+	22.7583i	−0.292717	+	1.09243i
$435$		0			0
$436$	12.1244	+	7.00000i	0.580651	+	0.335239i
$437$	−16.8690	−	16.8690i	−0.806955	−	0.806955i
$438$	2.82843	+	4.89898i	0.135147	+	0.234082i
$439$	−23.9808			−1.14454			−0.572270	−	0.820066i	$-0.693937\pi$
$439$	−23.9808			−1.14454			−0.572270	+	0.820066i	$0.693937\pi$
$440$		0			0
$441$	12.9282			0.615629
$442$	−9.62209	−	16.6660i	−0.457676	−	0.792719i
$443$	−20.3538	−	20.3538i	−0.967038	−	0.967038i	0.0324359	−	0.999474i	$-0.489674\pi$
$443$	−20.3538	−	20.3538i	−0.967038	−	0.967038i	−0.999474	+	0.0324359i	$0.989674\pi$
$444$	18.9282	+	10.9282i	0.898293	+	0.518630i
$445$		0			0
$446$	−3.43782	+	12.8301i	−0.162786	+	0.607524i
$447$	8.38375	−	8.38375i	0.396538	−	0.396538i
$448$	25.2528	−	25.2528i	1.19308	−	1.19308i
$449$		−	6.14359i		−	0.289934i	−0.989436	−	0.144967i	$-0.953692\pi$
$449$		−	6.14359i		−	0.289934i	0.989436	−	0.144967i	$-0.0463076\pi$
$450$		0			0
$451$		−	2.92820i		−	0.137884i
$452$	−7.17260	−	26.7685i	−0.337371	−	1.25909i
$453$	−5.46739	+	5.46739i	−0.256880	+	0.256880i
$454$	−11.4641	−	3.07180i	−0.538037	−	0.144167i
$455$		0			0
$456$	−6.39230	−	6.39230i	−0.299347	−	0.299347i
$457$	−13.9391	−	13.9391i	−0.652042	−	0.652042i	0.301442	−	0.953484i	$-0.402532\pi$
$457$	−13.9391	−	13.9391i	−0.652042	−	0.652042i	−0.953484	+	0.301442i	$0.902532\pi$
$458$	−3.49837	+	2.01978i	−0.163468	+	0.0943783i
$459$	−6.00000			−0.280056
$460$		0			0
$461$	36.3923			1.69496			0.847479	−	0.530828i	$-0.178119\pi$
$461$	36.3923			1.69496			0.847479	+	0.530828i	$0.178119\pi$
$462$	10.9348	−	6.31319i	0.508732	−	0.293716i
$463$	19.0411	+	19.0411i	0.884916	+	0.884916i	0.994029	−	0.109114i	$-0.0348012\pi$
$463$	19.0411	+	19.0411i	0.884916	+	0.884916i	−0.109114	+	0.994029i	$0.534801\pi$
$464$	1.85641	−	1.07180i	0.0861815	−	0.0497569i
$465$		0			0
$466$	−11.4641	−	3.07180i	−0.531064	−	0.142298i
$467$	2.44949	−	2.44949i	0.113349	−	0.113349i	−0.648157	−	0.761506i	$-0.724460\pi$
$467$	2.44949	−	2.44949i	0.113349	−	0.113349i	0.761506	+	0.648157i	$0.224460\pi$
$468$	4.38134	−	1.17398i	0.202528	−	0.0542671i
$469$			24.7128i			1.14113i
$470$		0			0
$471$			6.26795i			0.288812i
$472$	32.4254			1.49250
$473$	−6.31319	+	6.31319i	−0.290281	+	0.290281i
$474$	2.73205	−	10.1962i	0.125487	−	0.468325i
$475$		0			0
$476$	26.7846	−	46.3923i	1.22767	−	2.12639i
$477$	3.86370	+	3.86370i	0.176907	+	0.176907i
$478$	−7.45001	−	12.9038i	−0.340755	−	0.590206i
$479$	21.3205			0.974159			0.487079	−	0.873358i	$-0.338062\pi$
$479$	21.3205			0.974159			0.487079	+	0.873358i	$0.338062\pi$
$480$		0			0
$481$	−24.7846			−1.13008
$482$	−9.09085	−	15.7458i	−0.414077	−	0.717202i
$483$	23.5612	+	23.5612i	1.07207	+	1.07207i
$484$	−7.00000	+	12.1244i	−0.318182	+	0.551107i
$485$		0			0
$486$	0.366025	−	1.36603i	0.0166032	−	0.0619642i
$487$	−20.1272	+	20.1272i	−0.912049	+	0.912049i	−0.996433	−	0.0843846i	$-0.973108\pi$
$487$	−20.1272	+	20.1272i	−0.912049	+	0.912049i	0.0843846	+	0.996433i	$0.473108\pi$
$488$	8.48528			0.384111
$489$		−	7.53590i		−	0.340785i
$490$		0			0
$491$			34.6410i			1.56333i	0.623700	+	0.781664i	$0.285629\pi$
$491$			34.6410i			1.56333i	−0.623700	+	0.781664i	$0.714371\pi$
$492$	2.82843	−	0.757875i	0.127515	−	0.0341676i
$493$	2.27362	−	2.27362i	0.102399	−	0.102399i
$494$	9.90192	+	2.65321i	0.445509	+	0.119374i
$495$		0			0
$496$	−12.9282	+	7.46410i	−0.580493	+	0.335148i
$497$	8.00481	+	8.00481i	0.359065	+	0.359065i
$498$	−15.8338	+	9.14162i	−0.709527	+	0.409646i
$499$	−30.1244			−1.34855			−0.674276	−	0.738480i	$-0.735544\pi$
$499$	−30.1244			−1.34855			−0.674276	+	0.738480i	$0.735544\pi$
$500$		0			0
$501$	−16.3923			−0.732354
$502$	36.5665	−	21.1117i	1.63204	−	0.942260i
$503$	−0.277401	−	0.277401i	−0.0123687	−	0.0123687i	0.700895	−	0.713264i	$-0.252784\pi$
$503$	−0.277401	−	0.277401i	−0.0123687	−	0.0123687i	−0.713264	+	0.700895i	$0.752784\pi$
$504$	8.92820	+	8.92820i	0.397694	+	0.397694i
$505$		0			0
$506$	20.3923	+	5.46410i	0.906549	+	0.242909i
$507$	5.55532	−	5.55532i	0.246720	−	0.246720i
$508$	5.65685	+	21.1117i	0.250982	+	0.936679i
$509$			24.9282i			1.10492i	0.833538	+	0.552462i	$0.186311\pi$
$509$			24.9282i			1.10492i	−0.833538	+	0.552462i	$0.813689\pi$
$510$		0			0
$511$		−	17.8564i		−	0.789921i
$512$	22.6274			1.00000
$513$	2.26002	−	2.26002i	0.0997824	−	0.0997824i
$514$	10.5359	−	39.3205i	0.464719	−	1.73435i
$515$		0			0
$516$	−7.73205	−	4.46410i	−0.340385	−	0.196521i
$517$	1.31268	+	1.31268i	0.0577315	+	0.0577315i
$518$	−34.4959	−	59.7487i	−1.51566	−	2.62521i
$519$	−4.92820			−0.216324
$520$		0			0
$521$	−38.3923			−1.68200			−0.840999	−	0.541037i	$-0.818032\pi$
$521$	−38.3923			−1.68200			−0.840999	+	0.541037i	$0.818032\pi$
$522$	0.378937	+	0.656339i	0.0165856	+	0.0287272i
$523$	0.984508	+	0.984508i	0.0430495	+	0.0430495i	0.728304	−	0.685254i	$-0.240309\pi$
$523$	0.984508	+	0.984508i	0.0430495	+	0.0430495i	−0.685254	+	0.728304i	$0.740309\pi$
$524$	4.39230	+	2.53590i	0.191879	+	0.110781i
$525$		0			0
$526$	−5.32051	+	19.8564i	−0.231985	+	0.865780i
$527$	−15.8338	+	15.8338i	−0.689729	+	0.689729i
$528$	7.72741	+	2.07055i	0.336292	+	0.0901092i
$529$			32.7128i			1.42230i
$530$		0			0
$531$			11.4641i			0.497500i
$532$	7.38563	+	27.5636i	0.320208	+	1.19503i
$533$	−2.34795	+	2.34795i	−0.101701	+	0.101701i
$534$	−9.46410	−	2.53590i	−0.409552	−	0.109739i
$535$		0			0
$536$	−11.0718	+	11.0718i	−0.478229	+	0.478229i
$537$	−6.59059	−	6.59059i	−0.284405	−	0.284405i
$538$	−27.4249	+	15.8338i	−1.18237	+	0.682641i
$539$	−25.8564			−1.11371
$540$		0			0
$541$	7.78461			0.334687			0.167343	−	0.985899i	$-0.446481\pi$
$541$	7.78461			0.334687			0.167343	+	0.985899i	$0.446481\pi$
$542$	−29.6985	+	17.1464i	−1.27566	+	0.736502i
$543$	0.0507680	+	0.0507680i	0.00217866	+	0.00217866i
$544$	32.7846	−	8.78461i	1.40563	−	0.376637i
$545$		0			0
$546$	−13.8301	−	3.70577i	−0.591875	−	0.158592i
$547$	−11.8685	+	11.8685i	−0.507461	+	0.507461i	−0.913746	−	0.406285i	$-0.866824\pi$
$547$	−11.8685	+	11.8685i	−0.507461	+	0.507461i	0.406285	+	0.913746i	$0.366824\pi$
$548$	−29.8744	+	8.00481i	−1.27617	+	0.341948i
$549$			3.00000i			0.128037i
$550$		0			0
$551$			1.71281i			0.0729683i
$552$			21.1117i			0.898572i
$553$	−23.5612	+	23.5612i	−1.00192	+	1.00192i
$554$	3.36603	−	12.5622i	0.143009	−	0.533716i
$555$		0			0
$556$	12.5359	−	21.7128i	0.531641	−	0.920828i
$557$	−8.66115	−	8.66115i	−0.366985	−	0.366985i	0.499392	−	0.866376i	$-0.333557\pi$
$557$	−8.66115	−	8.66115i	−0.366985	−	0.366985i	−0.866376	+	0.499392i	$0.833557\pi$
$558$	−2.63896	−	4.57081i	−0.111716	−	0.193498i
$559$	10.1244			0.428215
$560$		0			0
$561$	12.0000			0.506640
$562$	−4.52004	−	7.82894i	−0.190666	−	0.330244i
$563$	27.7023	+	27.7023i	1.16751	+	1.16751i	0.982791	+	0.184720i	$0.0591378\pi$
$563$	27.7023	+	27.7023i	1.16751	+	1.16751i	0.184720	+	0.982791i	$0.440862\pi$
$564$	−0.928203	+	1.60770i	−0.0390844	+	0.0676962i
$565$		0			0
$566$	−0.222432	+	0.830127i	−0.00934951	+	0.0348928i
$567$	−3.15660	+	3.15660i	−0.132565	+	0.132565i
$568$			7.17260i			0.300956i
$569$			17.3205i			0.726113i	0.931767	+	0.363057i	$0.118267\pi$
$569$			17.3205i			0.726113i	−0.931767	+	0.363057i	$0.881733\pi$
$570$		0			0
$571$		−	27.1962i		−	1.13812i	−0.822295	−	0.569062i	$-0.807307\pi$
$571$		−	27.1962i		−	1.13812i	0.822295	−	0.569062i	$-0.192693\pi$
$572$	−8.76268	+	2.34795i	−0.366386	+	0.0981729i
$573$	2.17209	−	2.17209i	0.0907403	−	0.0907403i
$574$	−8.92820	−	2.39230i	−0.372656	−	0.0998529i
$575$		0			0
$576$			8.00000i			0.333333i
$577$	23.0943	+	23.0943i	0.961428	+	0.961428i	0.999283	−	0.0378555i	$-0.0120527\pi$
$577$	23.0943	+	23.0943i	0.961428	+	0.961428i	−0.0378555	+	0.999283i	$0.512053\pi$
$578$	23.2702	−	13.4350i	0.967911	−	0.558824i
$579$	10.2679			0.426721
$580$		0			0
$581$	57.7128			2.39433
$582$	−11.9193	+	6.88160i	−0.494070	+	0.285251i
$583$	−7.72741	−	7.72741i	−0.320036	−	0.320036i
$584$	8.00000	−	8.00000i	0.331042	−	0.331042i
$585$		0			0
$586$	26.5885	+	7.12436i	1.09836	+	0.294304i
$587$	−10.8332	+	10.8332i	−0.447135	+	0.447135i	−0.894401	−	0.447266i	$-0.852398\pi$
$587$	−10.8332	+	10.8332i	−0.447135	+	0.447135i	0.447266	+	0.894401i	$0.352398\pi$
$588$	−6.69213	−	24.9754i	−0.275979	−	1.02997i
$589$		−	11.9282i		−	0.491493i
$590$		0			0
$591$			6.39230i			0.262944i
$592$	11.3137	−	42.2233i	0.464991	−	1.73537i
$593$	8.20788	−	8.20788i	0.337057	−	0.337057i	−0.518201	−	0.855259i	$-0.673398\pi$
$593$	8.20788	−	8.20788i	0.337057	−	0.337057i	0.855259	+	0.518201i	$0.173398\pi$
$594$	−0.732051	+	2.73205i	−0.0300364	+	0.112097i
$595$		0			0
$596$	−20.5359	−	11.8564i	−0.841183	−	0.485657i
$597$	7.15900	+	7.15900i	0.292998	+	0.292998i
$598$	−11.9700	−	20.7327i	−0.489492	−	0.847824i
$599$	−22.6410			−0.925087			−0.462543	−	0.886597i	$-0.653063\pi$
$599$	−22.6410			−0.925087			−0.462543	+	0.886597i	$0.653063\pi$
$600$		0			0
$601$	21.7846			0.888613			0.444306	−	0.895875i	$-0.353450\pi$
$601$	21.7846			0.888613			0.444306	+	0.895875i	$0.353450\pi$
$602$	14.0914	+	24.4070i	0.574321	+	0.994754i
$603$	−3.91447	−	3.91447i	−0.159410	−	0.159410i
$604$	13.3923	+	7.73205i	0.544925	+	0.314613i
$605$		0			0
$606$	−2.00000	+	7.46410i	−0.0812444	+	0.303208i
$607$	−25.2528	+	25.2528i	−1.02498	+	1.02498i	−0.0252985	+	0.999680i	$0.508054\pi$
$607$	−25.2528	+	25.2528i	−1.02498	+	1.02498i	−0.999680	+	0.0252985i	$0.991946\pi$
$608$	−9.04008	+	15.6579i	−0.366624	+	0.635011i
$609$		−	2.39230i		−	0.0969411i
$610$		0			0
$611$		−	2.10512i		−	0.0851639i
$612$	3.10583	+	11.5911i	0.125546	+	0.468543i
$613$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$613$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$614$	10.0981	+	2.70577i	0.407525	+	0.109196i
$615$		0			0
$616$	−17.8564	−	17.8564i	−0.719455	−	0.719455i
$617$	24.2175	+	24.2175i	0.974960	+	0.974960i	0.999694	−	0.0247344i	$-0.00787400\pi$
$617$	24.2175	+	24.2175i	0.974960	+	0.974960i	−0.0247344	+	0.999694i	$0.507874\pi$
$618$	−8.48528	+	4.89898i	−0.341328	+	0.197066i
$619$	−15.9808			−0.642321			−0.321161	−	0.947025i	$-0.604073\pi$
$619$	−15.9808			−0.642321			−0.321161	+	0.947025i	$0.604073\pi$
$620$		0			0
$621$	−7.46410			−0.299524
$622$	−25.1512	+	14.5211i	−1.00847	+	0.582242i
$623$	21.8695	+	21.8695i	0.876185	+	0.876185i
$624$	−4.53590	−	7.85641i	−0.181581	−	0.314508i
$625$		0			0
$626$	−22.0263	−	5.90192i	−0.880347	−	0.235888i
$627$	−4.52004	+	4.52004i	−0.180513	+	0.180513i
$628$	12.1087	−	3.24453i	0.483192	−	0.129471i
$629$		−	65.5692i		−	2.61442i
$630$		0			0
$631$			29.5885i			1.17790i	0.808170	+	0.588949i	$0.200458\pi$
$631$			29.5885i			1.17790i	−0.808170	+	0.588949i	$0.799542\pi$
$632$	−21.1117			−0.839777
$633$	−2.26002	+	2.26002i	−0.0898278	+	0.0898278i
$634$	−2.53590	+	9.46410i	−0.100713	+	0.375867i
$635$		0			0
$636$	5.46410	−	9.46410i	0.216666	−	0.375276i
$637$	20.7327	+	20.7327i	0.821461	+	0.821461i
$638$	−0.757875	−	1.31268i	−0.0300045	−	0.0519694i
$639$	−2.53590			−0.100319
$640$		0			0
$641$	−44.7846			−1.76889			−0.884443	−	0.466648i	$-0.845461\pi$
$641$	−44.7846			−1.76889			−0.884443	+	0.466648i	$0.845461\pi$
$642$	−9.52056	−	16.4901i	−0.375746	−	0.650812i
$643$	21.8695	+	21.8695i	0.862451	+	0.862451i	0.991622	−	0.129172i	$-0.0412318\pi$
$643$	21.8695	+	21.8695i	0.862451	+	0.862451i	−0.129172	+	0.991622i	$0.541232\pi$
$644$	33.3205	−	57.7128i	1.31301	−	2.27420i
$645$		0			0
$646$	−7.01924	+	26.1962i	−0.276168	+	1.03067i
$647$	−13.3843	+	13.3843i	−0.526190	+	0.526190i	−0.919434	−	0.393244i	$-0.871353\pi$
$647$	−13.3843	+	13.3843i	−0.526190	+	0.526190i	0.393244	+	0.919434i	$0.371353\pi$
$648$	−2.82843			−0.111111
$649$		−	22.9282i		−	0.900011i
$650$		0			0
$651$			16.6603i			0.652967i
$652$	−14.5582	+	3.90087i	−0.570145	+	0.152770i
$653$	7.34847	−	7.34847i	0.287568	−	0.287568i	−0.548550	−	0.836118i	$-0.684820\pi$
$653$	7.34847	−	7.34847i	0.287568	−	0.287568i	0.836118	+	0.548550i	$0.184820\pi$
$654$	9.56218	+	2.56218i	0.373911	+	0.100189i
$655$		0			0
$656$	−2.92820	−	5.07180i	−0.114327	−	0.198020i
$657$	2.82843	+	2.82843i	0.110347	+	0.110347i
$658$	5.07484	−	2.92996i	0.197838	−	0.114222i
$659$	21.4641			0.836123			0.418061	−	0.908419i	$-0.362710\pi$
$659$	21.4641			0.836123			0.418061	+	0.908419i	$0.362710\pi$
$660$		0			0
$661$	19.8564			0.772325			0.386162	−	0.922431i	$-0.373800\pi$
$661$	19.8564			0.772325			0.386162	+	0.922431i	$0.373800\pi$
$662$	22.5259	−	13.0053i	0.875493	−	0.505466i
$663$	−9.62209	−	9.62209i	−0.373691	−	0.373691i
$664$	25.8564	+	25.8564i	1.00342	+	1.00342i
$665$		0			0
$666$	14.9282	+	4.00000i	0.578456	+	0.154997i
$667$	2.82843	−	2.82843i	0.109517	−	0.109517i
$668$	8.48528	+	31.6675i	0.328305	+	1.22525i
$669$			9.39230i			0.363127i
$670$		0			0
$671$		−	6.00000i		−	0.231627i
$672$	12.6264	−	21.8695i	0.487073	−	0.843636i
$673$	−2.82843	+	2.82843i	−0.109028	+	0.109028i	−0.759516	−	0.650488i	$-0.774564\pi$
$673$	−2.82843	+	2.82843i	−0.109028	+	0.109028i	0.650488	+	0.759516i	$0.274564\pi$
$674$	−10.4904	+	39.1506i	−0.404074	+	1.50803i
$675$		0			0
$676$	−13.6077	−	7.85641i	−0.523373	−	0.302169i
$677$	−23.0807	−	23.0807i	−0.887063	−	0.887063i	0.107177	−	0.994240i	$-0.465819\pi$
$677$	−23.0807	−	23.0807i	−0.887063	−	0.887063i	−0.994240	+	0.107177i	$0.965819\pi$
$678$	−9.79796	−	16.9706i	−0.376288	−	0.651751i
$679$	43.4449			1.66726
$680$		0			0
$681$	−8.39230			−0.321594
$682$	5.27792	+	9.14162i	0.202102	+	0.350051i
$683$	−13.3843	−	13.3843i	−0.512135	−	0.512135i	0.403045	−	0.915180i	$-0.367952\pi$
$683$	−13.3843	−	13.3843i	−0.512135	−	0.512135i	−0.915180	+	0.403045i	$0.867952\pi$
$684$	−5.53590	−	3.19615i	−0.211670	−	0.122208i
$685$		0			0
$686$	−9.68653	+	36.1506i	−0.369834	+	1.38024i
$687$	−2.01978	+	2.01978i	−0.0770596	+	0.0770596i
$688$	−4.62158	+	17.2480i	−0.176196	+	0.657572i
$689$			12.3923i			0.472109i
$690$		0			0
$691$		−	9.32051i		−	0.354569i	−0.984160	−	0.177284i	$-0.943269\pi$
$691$		−	9.32051i		−	0.354569i	0.984160	−	0.177284i	$-0.0567312\pi$
$692$	2.55103	+	9.52056i	0.0969754	+	0.361917i
$693$	6.31319	−	6.31319i	0.239818	−	0.239818i
$694$	34.0526	+	9.12436i	1.29262	+	0.346356i
$695$		0			0
$696$	1.07180	−	1.07180i	0.0406264	−	0.0406264i
$697$	−6.21166	−	6.21166i	−0.235283	−	0.235283i
$698$	29.2180	−	16.8690i	1.10592	−	0.638502i
$699$	−8.39230			−0.317426
$700$		0			0
$701$	−8.53590			−0.322396			−0.161198	−	0.986922i	$-0.551536\pi$
$701$	−8.53590			−0.322396			−0.161198	+	0.986922i	$0.551536\pi$
$702$	2.77766	−	1.60368i	0.104836	−	0.0605271i
$703$	24.6980	+	24.6980i	0.931502	+	0.931502i
$704$		−	16.0000i		−	0.603023i
$705$		0			0
$706$	16.1962	+	4.33975i	0.609550	+	0.163328i
$707$	17.2480	−	17.2480i	0.648676	−	0.648676i
$708$	22.1469	−	5.93426i	0.832333	−	0.223023i
$709$		−	2.85641i		−	0.107275i	−0.998560	−	0.0536373i	$-0.982919\pi$
$709$		−	2.85641i		−	0.107275i	0.998560	−	0.0536373i	$-0.0170815\pi$
$710$		0			0
$711$		−	7.46410i		−	0.279926i
$712$			19.5959i			0.734388i
$713$	−19.6975	+	19.6975i	−0.737675	+	0.737675i
$714$	9.80385	−	36.5885i	0.366900	−	1.36929i
$715$		0			0
$716$	−9.32051	+	16.1436i	−0.348324	+	0.603314i
$717$	−7.45001	−	7.45001i	−0.278226	−	0.278226i
$718$	2.55103	+	4.41851i	0.0952034	+	0.164897i
$719$	0.928203			0.0346161			0.0173081	−	0.999850i	$-0.494490\pi$
$719$	0.928203			0.0346161			0.0173081	+	0.999850i	$0.494490\pi$
$720$		0			0
$721$	30.9282			1.15183
$722$	6.21166	+	10.7589i	0.231174	+	0.400405i
$723$	−9.09085	−	9.09085i	−0.338092	−	0.338092i
$724$	0.0717968	−	0.124356i	0.00266831	−	0.00462164i
$725$		0			0
$726$	−2.56218	+	9.56218i	−0.0950913	+	0.354886i
$727$	20.5804	−	20.5804i	0.763286	−	0.763286i	−0.213629	−	0.976915i	$-0.568528\pi$
$727$	20.5804	−	20.5804i	0.763286	−	0.763286i	0.976915	+	0.213629i	$0.0685284\pi$
$728$			28.6360i			1.06132i
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$			26.7846i			0.990665i
$732$	5.79555	−	1.55291i	0.214210	−	0.0573974i
$733$	25.2528	−	25.2528i	0.932732	−	0.932732i	−0.0651435	−	0.997876i	$-0.520751\pi$
$733$	25.2528	−	25.2528i	0.932732	−	0.932732i	0.997876	+	0.0651435i	$0.0207505\pi$
$734$	−42.8827	−	11.4904i	−1.58283	−	0.424118i
$735$		0			0
$736$	40.7846	−	10.9282i	1.50334	−	0.402819i
$737$	7.82894	+	7.82894i	0.288383	+	0.288383i
$738$	1.79315	−	1.03528i	0.0660068	−	0.0381090i
$739$	6.39230			0.235145			0.117572	−	0.993064i	$-0.462489\pi$
$739$	6.39230			0.235145			0.117572	+	0.993064i	$0.462489\pi$
$740$		0			0
$741$	7.24871			0.266288
$742$	−29.8744	+	17.2480i	−1.09672	+	0.633193i
$743$	−12.0716	−	12.0716i	−0.442863	−	0.442863i	0.450110	−	0.892973i	$-0.351385\pi$
$743$	−12.0716	−	12.0716i	−0.442863	−	0.442863i	−0.892973	+	0.450110i	$0.851385\pi$
$744$	−7.46410	+	7.46410i	−0.273647	+	0.273647i
$745$		0			0
$746$	50.0788	+	13.4186i	1.83352	+	0.491289i
$747$	−9.14162	+	9.14162i	−0.334474	+	0.334474i
$748$	−6.21166	−	23.1822i	−0.227121	−	0.847626i
$749$			60.1051i			2.19619i
$750$		0			0
$751$			4.53590i			0.165517i	0.996570	+	0.0827586i	$0.0263731\pi$
$751$			4.53590i			0.165517i	−0.996570	+	0.0827586i	$0.973627\pi$
$752$	3.58630	+	0.960947i	0.130779	+	0.0350421i
$753$	21.1117	−	21.1117i	0.769352	−	0.769352i
$754$	−0.444864	+	1.66025i	−0.0162010	+	0.0604629i
$755$		0			0
$756$	7.73205	+	4.46410i	0.281212	+	0.162358i
$757$	−13.2963	−	13.2963i	−0.483263	−	0.483263i	0.422909	−	0.906172i	$-0.361009\pi$
$757$	−13.2963	−	13.2963i	−0.483263	−	0.483263i	−0.906172	+	0.422909i	$0.861009\pi$
$758$	−8.67475	−	15.0251i	−0.315081	−	0.545736i
$759$	14.9282			0.541859
$760$		0			0
$761$	−22.6410			−0.820736			−0.410368	−	0.911920i	$-0.634600\pi$
$761$	−22.6410			−0.820736			−0.410368	+	0.911920i	$0.634600\pi$
$762$	7.72741	+	13.3843i	0.279934	+	0.484861i
$763$	−22.0962	−	22.0962i	−0.799935	−	0.799935i
$764$	−5.32051	−	3.07180i	−0.192489	−	0.111134i
$765$		0			0
$766$	9.07180	−	33.8564i	0.327777	−	1.22328i
$767$	−18.3848	+	18.3848i	−0.663836	+	0.663836i
$768$	15.4548	−	4.14110i	0.557678	−	0.149429i
$769$		−	16.0718i		−	0.579564i	−0.957093	−	0.289782i	$-0.906417\pi$
$769$		−	16.0718i		−	0.579564i	0.957093	−	0.289782i	$-0.0935828\pi$
$770$		0			0
$771$		−	28.7846i		−	1.03665i
$772$	−5.31508	−	19.8362i	−0.191294	−	0.713919i
$773$	20.6312	−	20.6312i	0.742052	−	0.742052i	−0.230920	−	0.972973i	$-0.574174\pi$
$773$	20.6312	−	20.6312i	0.742052	−	0.742052i	0.972973	+	0.230920i	$0.0741736\pi$
$774$	−6.09808	−	1.63397i	−0.219191	−	0.0587320i
$775$		0			0
$776$	19.4641	+	19.4641i	0.698721	+	0.698721i
$777$	−34.4959	−	34.4959i	−1.23753	−	1.23753i
$778$	−26.2880	+	15.1774i	−0.942472	+	0.544137i
$779$	4.67949			0.167660
$780$		0			0
$781$	5.07180			0.181483
$782$	54.8497	−	31.6675i	1.96142	−	1.13243i
$783$	0.378937	+	0.378937i	0.0135421	+	0.0135421i
$784$	−44.7846	+	25.8564i	−1.59945	+	0.923443i
$785$		0			0
$786$	3.46410	+	0.928203i	0.123560	+	0.0331079i
$787$	34.0662	−	34.0662i	1.21433	−	1.21433i	0.244741	−	0.969588i	$-0.421297\pi$
$787$	34.0662	−	34.0662i	1.21433	−	1.21433i	0.969588	−	0.244741i	$-0.0787030\pi$
$788$	12.3490	−	3.30890i	0.439914	−	0.117875i
$789$			14.5359i			0.517492i
$790$		0			0
$791$			61.8564i			2.19936i
$792$	5.65685			0.201008
$793$	−4.81105	+	4.81105i	−0.170845	+	0.170845i
$794$	−4.24167	+	15.8301i	−0.150531	+	0.561790i
$795$		0			0
$796$	10.1244	−	17.5359i	0.358848	−	0.621543i
$797$	9.79796	+	9.79796i	0.347062	+	0.347062i	0.859014	−	0.511952i	$-0.171078\pi$
$797$	9.79796	+	9.79796i	0.347062	+	0.347062i	−0.511952	+	0.859014i	$0.671078\pi$
$798$	10.0890	+	17.4746i	0.357145	+	0.618594i
$799$	5.56922			0.197025
$800$		0			0
$801$	−6.92820			−0.244796
$802$	−20.6312	−	35.7343i	−0.728513	−	1.26182i
$803$	−5.65685	−	5.65685i	−0.199626	−	0.199626i
$804$	−5.53590	+	9.58846i	−0.195236	+	0.338159i
$805$		0			0
$806$	3.09808	−	11.5622i	0.109125	−	0.407260i
$807$	−15.8338	+	15.8338i	−0.557374	+	0.557374i
$808$	15.4548			0.543698
$809$		−	13.1769i		−	0.463276i	−0.972802	−	0.231638i	$-0.925592\pi$
$809$		−	13.1769i		−	0.463276i	0.972802	−	0.231638i	$-0.0744084\pi$
$810$		0			0
$811$		−	1.87564i		−	0.0658628i	−0.999458	−	0.0329314i	$-0.989516\pi$
$811$		−	1.87564i		−	0.0658628i	0.999458	−	0.0329314i	$-0.0104843\pi$
$812$	−4.62158	+	1.23835i	−0.162186	+	0.0434575i
$813$	−17.1464	+	17.1464i	−0.601351	+	0.601351i
$814$	−29.8564	−	8.00000i	−1.04647	−	0.280400i
$815$		0			0
$816$	20.7846	−	12.0000i	0.727607	−	0.420084i
$817$	−10.0890	−	10.0890i	−0.352968	−	0.352968i
$818$	−16.8826	+	9.74719i	−0.590287	+	0.340803i
$819$	−10.1244			−0.353774
$820$		0			0
$821$	−27.5692			−0.962172			−0.481086	−	0.876673i	$-0.659758\pi$
$821$	−27.5692			−0.962172			−0.481086	+	0.876673i	$0.659758\pi$
$822$	−18.9396	+	10.9348i	−0.660594	+	0.381394i
$823$	−18.8145	−	18.8145i	−0.655832	−	0.655832i	0.298559	−	0.954391i	$-0.403494\pi$
$823$	−18.8145	−	18.8145i	−0.655832	−	0.655832i	−0.954391	+	0.298559i	$0.903494\pi$
$824$	13.8564	+	13.8564i	0.482711	+	0.482711i
$825$		0			0
$826$	−69.9090	−	18.7321i	−2.43244	−	0.651771i
$827$	34.9764	−	34.9764i	1.21625	−	1.21625i	0.247313	−	0.968936i	$-0.420452\pi$
$827$	34.9764	−	34.9764i	1.21625	−	1.21625i	0.968936	−	0.247313i	$-0.0795476\pi$
$828$	3.86370	+	14.4195i	0.134273	+	0.501114i
$829$		−	37.7128i		−	1.30982i	−0.755707	−	0.654910i	$-0.772706\pi$
$829$		−	37.7128i		−	1.30982i	0.755707	−	0.654910i	$-0.227294\pi$
$830$		0			0
$831$		−	9.19615i		−	0.319011i
$832$	−12.8295	+	12.8295i	−0.444781	+	0.444781i
$833$	−54.8497	+	54.8497i	−1.90043	+	1.90043i
$834$	4.58846	−	17.1244i	0.158885	−	0.592968i
$835$		0			0
$836$	11.0718	+	6.39230i	0.382926	+	0.221082i
$837$	−2.63896	−	2.63896i	−0.0912157	−	0.0912157i
$838$	23.6627	+	40.9850i	0.817414	+	1.41580i
$839$	28.6410			0.988798			0.494399	−	0.869235i	$-0.335388\pi$
$839$	28.6410			0.988798			0.494399	+	0.869235i	$0.335388\pi$
$840$		0			0
$841$	28.7128			0.990097
$842$	24.5964	+	42.6023i	0.847649	+	1.46817i
$843$	−4.52004	−	4.52004i	−0.155679	−	0.155679i
$844$	5.53590	+	3.19615i	0.190553	+	0.110016i
$845$		0			0
$846$	−0.339746	+	1.26795i	−0.0116807	+	0.0435930i
$847$	22.0962	−	22.0962i	0.759234	−	0.759234i
$848$	−21.1117	−	5.65685i	−0.724978	−	0.194257i
$849$			0.607695i			0.0208560i
$850$		0			0
$851$		−	81.5692i		−	2.79616i
$852$	1.31268	+	4.89898i	0.0449716	+	0.167836i
$853$	11.0227	−	11.0227i	0.377410	−	0.377410i	−0.492757	−	0.870167i	$-0.664011\pi$
$853$	11.0227	−	11.0227i	0.377410	−	0.377410i	0.870167	+	0.492757i	$0.164011\pi$
$854$	−18.2942	−	4.90192i	−0.626016	−	0.167740i
$855$		0			0
$856$	−26.9282	+	26.9282i	−0.920387	+	0.920387i
$857$	5.45378	+	5.45378i	0.186298	+	0.186298i	0.794093	−	0.607796i	$-0.207946\pi$
$857$	5.45378	+	5.45378i	0.186298	+	0.186298i	−0.607796	+	0.794093i	$0.707946\pi$
$858$	−5.55532	+	3.20736i	−0.189655	+	0.109498i
$859$	−42.3923			−1.44641			−0.723203	−	0.690635i	$-0.757331\pi$
$859$	−42.3923			−1.44641			−0.723203	+	0.690635i	$0.757331\pi$
$860$		0			0
$861$	−6.53590			−0.222743
$862$	−36.3906	+	21.0101i	−1.23947	+	0.715608i
$863$	−21.6665	−	21.6665i	−0.737535	−	0.737535i	0.234565	−	0.972100i	$-0.424633\pi$
$863$	−21.6665	−	21.6665i	−0.737535	−	0.737535i	−0.972100	+	0.234565i	$0.924633\pi$
$864$	1.46410	+	5.46410i	0.0498097	+	0.185893i
$865$		0			0
$866$	−48.6147	−	13.0263i	−1.65200	−	0.442651i
$867$	13.4350	−	13.4350i	0.456278	−	0.456278i
$868$	32.1851	−	8.62398i	1.09243	−	0.292717i
$869$			14.9282i			0.506405i
$870$		0			0
$871$		−	12.5551i		−	0.425415i
$872$		−	19.7990i		−	0.670478i
$873$	−6.88160	+	6.88160i	−0.232907	+	0.232907i
$874$	−8.73205	+	32.5885i	−0.295366	+	1.10232i
$875$		0			0
$876$	4.00000	−	6.92820i	0.135147	−	0.234082i
$877$	33.8260	+	33.8260i	1.14222	+	1.14222i	0.988043	+	0.154180i	$0.0492734\pi$
$877$	33.8260	+	33.8260i	1.14222	+	1.14222i	0.154180	+	0.988043i	$0.450727\pi$
$878$	16.9570	+	29.3703i	0.572270	+	0.991200i
$879$	19.4641			0.656508
$880$		0			0
$881$	−37.0718			−1.24898			−0.624490	−	0.781033i	$-0.714693\pi$
$881$	−37.0718			−1.24898			−0.624490	+	0.781033i	$0.714693\pi$
$882$	−9.14162	−	15.8338i	−0.307814	−	0.533150i
$883$	−22.7525	−	22.7525i	−0.765683	−	0.765683i	0.211660	−	0.977343i	$-0.432113\pi$
$883$	−22.7525	−	22.7525i	−0.765683	−	0.765683i	−0.977343	+	0.211660i	$0.932113\pi$
$884$	−13.6077	+	23.5692i	−0.457676	+	0.792719i
$885$		0			0
$886$	−10.5359	+	39.3205i	−0.353960	+	1.32100i
$887$	14.0406	−	14.0406i	0.471437	−	0.471437i	−0.430942	−	0.902379i	$-0.641819\pi$
$887$	14.0406	−	14.0406i	0.471437	−	0.471437i	0.902379	+	0.430942i	$0.141819\pi$
$888$		−	30.9096i		−	1.03726i
$889$		−	48.7846i		−	1.63618i
$890$		0			0
$891$			2.00000i			0.0670025i
$892$	18.1445	−	4.86181i	0.607524	−	0.162786i
$893$	−2.09776	+	2.09776i	−0.0701988	+	0.0701988i
$894$	−16.1962	−	4.33975i	−0.541680	−	0.145143i
$895$		0			0
$896$	−48.7846	−	13.0718i	−1.62978	−	0.436698i
$897$	−11.9700	−	11.9700i	−0.399668	−	0.399668i
$898$	−7.52433	+	4.34418i	−0.251090	+	0.144967i
$899$	2.00000			0.0667037
$900$		0			0
$901$	−32.7846			−1.09221
$902$	−3.58630	+	2.07055i	−0.119411	+	0.0689419i
$903$	14.0914	+	14.0914i	0.468931	+	0.468931i
$904$	−27.7128	+	27.7128i	−0.921714	+	0.921714i
$905$		0			0
$906$	10.5622	+	2.83013i	0.350905	+	0.0940247i
$907$	−12.6264	+	12.6264i	−0.419252	+	0.419252i	−0.884946	−	0.465694i	$-0.845805\pi$
$907$	−12.6264	+	12.6264i	−0.419252	+	0.419252i	0.465694	+	0.884946i	$0.345805\pi$
$908$	4.34418	+	16.2127i	0.144167	+	0.538037i
$909$			5.46410i			0.181233i
$910$		0			0
$911$			5.60770i			0.185791i	0.995676	+	0.0928956i	$0.0296123\pi$
$911$			5.60770i			0.185791i	−0.995676	+	0.0928956i	$0.970388\pi$
$912$	−3.30890	+	12.3490i	−0.109569	+	0.408916i
$913$	18.2832	−	18.2832i	0.605087	−	0.605087i
$914$	−7.21539	+	26.9282i	−0.238664	+	0.890706i
$915$		0			0
$916$	4.94744	+	2.85641i	0.163468	+	0.0943783i
$917$	−8.00481	−	8.00481i	−0.264342	−	0.264342i
$918$	4.24264	+	7.34847i	0.140028	+	0.242536i
$919$	−26.6603			−0.879441			−0.439720	−	0.898135i	$-0.644922\pi$
$919$	−26.6603			−0.879441			−0.439720	+	0.898135i	$0.644922\pi$
$920$		0			0
$921$	7.39230			0.243585
$922$	−25.7332	−	44.5713i	−0.847479	−	1.46788i
$923$	−4.06678	−	4.06678i	−0.133860	−	0.133860i
$924$	−15.4641	−	8.92820i	−0.508732	−	0.293716i
$925$		0			0
$926$	9.85641	−	36.7846i	0.323902	−	1.20882i
$927$	−4.89898	+	4.89898i	−0.160904	+	0.160904i
$928$	−2.62536	−	1.51575i	−0.0861815	−	0.0497569i
$929$			0.535898i			0.0175823i	0.999961	+	0.00879113i	$0.00279834\pi$
$929$			0.535898i			0.0175823i	−0.999961	+	0.00879113i	$0.997202\pi$
$930$		0			0
$931$		−	41.3205i		−	1.35422i
$932$	4.34418	+	16.2127i	0.142298	+	0.531064i
$933$	−14.5211	+	14.5211i	−0.475399	+	0.475399i
$934$	−4.73205	−	1.26795i	−0.154837	−	0.0414886i
$935$		0			0
$936$	−4.53590	−	4.53590i	−0.148260	−	0.148260i
$937$	9.12802	+	9.12802i	0.298199	+	0.298199i	0.840308	−	0.542109i	$-0.182374\pi$
$937$	9.12802	+	9.12802i	0.298199	+	0.298199i	−0.542109	+	0.840308i	$0.682374\pi$
$938$	30.2669	−	17.4746i	0.988249	−	0.570566i
$939$	−16.1244			−0.526198
$940$		0			0
$941$	11.0718			0.360930			0.180465	−	0.983581i	$-0.442240\pi$
$941$	11.0718			0.360930			0.180465	+	0.983581i	$0.442240\pi$
$942$	7.67664	−	4.43211i	0.250118	−	0.144406i
$943$	−7.72741	−	7.72741i	−0.251639	−	0.251639i
$944$	−22.9282	−	39.7128i	−0.746249	−	1.29254i
$945$		0			0
$946$	12.1962	+	3.26795i	0.396531	+	0.106250i
$947$	22.8033	−	22.8033i	0.741007	−	0.741007i	−0.231765	−	0.972772i	$-0.574450\pi$
$947$	22.8033	−	22.8033i	0.741007	−	0.741007i	0.972772	+	0.231765i	$0.0744500\pi$
$948$	−14.4195	+	3.86370i	−0.468325	+	0.125487i
$949$			9.07180i			0.294483i
$950$		0			0
$951$			6.92820i			0.224662i
$952$	−75.7583			−2.45534
$953$	28.0812	−	28.0812i	0.909639	−	0.909639i	−0.0866036	−	0.996243i	$-0.527601\pi$
$953$	28.0812	−	28.0812i	0.909639	−	0.909639i	0.996243	+	0.0866036i	$0.0276014\pi$
$954$	2.00000	−	7.46410i	0.0647524	−	0.241659i
$955$		0			0
$956$	−10.5359	+	18.2487i	−0.340755	+	0.590206i
$957$	−0.757875	−	0.757875i	−0.0244986	−	0.0244986i
$958$	−15.0759	−	26.1122i	−0.487079	−	0.843646i
$959$	69.0333			2.22920
$960$		0			0
$961$	17.0718			0.550703
$962$	17.5254	+	30.3548i	0.565040	+	0.978679i
$963$	−9.52056	−	9.52056i	−0.306796	−	0.306796i
$964$	−12.8564	+	22.2679i	−0.414077	+	0.717202i
$965$		0			0
$966$	12.1962	−	45.5167i	0.392405	−	1.46447i
$967$	−33.9411	+	33.9411i	−1.09147	+	1.09147i	−0.0961015	+	0.995372i	$0.530637\pi$
$967$	−33.9411	+	33.9411i	−1.09147	+	1.09147i	−0.995372	+	0.0961015i	$0.969363\pi$
$968$	19.7990			0.636364
$969$			19.1769i			0.616051i
$970$		0			0
$971$		−	43.1769i		−	1.38561i	−0.721123	−	0.692807i	$-0.756374\pi$
$971$		−	43.1769i		−	1.38561i	0.721123	−	0.692807i	$-0.243626\pi$
$972$	−1.93185	+	0.517638i	−0.0619642	+	0.0166032i
$973$	−39.5708	+	39.5708i	−1.26858	+	1.26858i
$974$	38.8827	+	10.4186i	1.24588	+	0.333833i
$975$		0			0
$976$	−6.00000	−	10.3923i	−0.192055	−	0.332650i
$977$	−16.3886	−	16.3886i	−0.524316	−	0.524316i	0.394556	−	0.918872i	$-0.370899\pi$
$977$	−16.3886	−	16.3886i	−0.524316	−	0.524316i	−0.918872	+	0.394556i	$0.870899\pi$
$978$	−9.22955	+	5.32868i	−0.295129	+	0.170393i
$979$	13.8564			0.442853
$980$		0			0
$981$	7.00000			0.223493
$982$	42.4264	−	24.4949i	1.35388	−	0.781664i
$983$	1.31268	+	1.31268i	0.0418679	+	0.0418679i	0.727731	−	0.685863i	$-0.240575\pi$
$983$	1.31268	+	1.31268i	0.0418679	+	0.0418679i	−0.685863	+	0.727731i	$0.740575\pi$
$984$	−2.92820	−	2.92820i	−0.0933477	−	0.0933477i
$985$		0			0
$986$	−4.39230	−	1.17691i	−0.139879	−	0.0374806i
$987$	2.92996	−	2.92996i	0.0932618	−	0.0932618i
$988$	−3.75221	−	14.0034i	−0.119374	−	0.445509i
$989$			33.3205i			1.05953i
$990$		0			0
$991$		−	26.4115i		−	0.838990i	−0.907758	−	0.419495i	$-0.862207\pi$
$991$		−	26.4115i		−	0.838990i	0.907758	−	0.419495i	$-0.137793\pi$
$992$	18.2832	+	10.5558i	0.580493	+	0.335148i
$993$	13.0053	−	13.0053i	0.412711	−	0.412711i
$994$	4.14359	−	15.4641i	0.131427	−	0.490492i
$995$		0			0
$996$	22.3923	+	12.9282i	0.709527	+	0.409646i
$997$	19.5959	+	19.5959i	0.620609	+	0.620609i	0.945687	−	0.325078i	$-0.105391\pi$
$997$	19.5959	+	19.5959i	0.620609	+	0.620609i	−0.325078	+	0.945687i	$0.605391\pi$
$998$	21.3011	+	36.8947i	0.674276	+	1.16788i
$999$	10.9282			0.345753

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.j.a.7.1	✓	8
3.2	odd	2		900.2.k.g.307.4		8
4.3	odd	2		300.2.j.c.7.1	yes	8
5.2	odd	4		300.2.j.c.43.3	yes	8
5.3	odd	4		300.2.j.c.43.2	yes	8
5.4	even	2	inner	300.2.j.a.7.4	yes	8
12.11	even	2		900.2.k.l.307.4		8
15.2	even	4		900.2.k.l.343.2		8
15.8	even	4		900.2.k.l.343.3		8
15.14	odd	2		900.2.k.g.307.1		8
20.3	even	4	inner	300.2.j.a.43.2	yes	8
20.7	even	4	inner	300.2.j.a.43.3	yes	8
20.19	odd	2		300.2.j.c.7.4	yes	8
60.23	odd	4		900.2.k.g.343.3		8
60.47	odd	4		900.2.k.g.343.2		8
60.59	even	2		900.2.k.l.307.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.j.a.7.1	✓	8	1.1	even	1	trivial
300.2.j.a.7.4	yes	8	5.4	even	2	inner
300.2.j.a.43.2	yes	8	20.3	even	4	inner
300.2.j.a.43.3	yes	8	20.7	even	4	inner
300.2.j.c.7.1	yes	8	4.3	odd	2
300.2.j.c.7.4	yes	8	20.19	odd	2
300.2.j.c.43.2	yes	8	5.3	odd	4
300.2.j.c.43.3	yes	8	5.2	odd	4
900.2.k.g.307.1		8	15.14	odd	2
900.2.k.g.307.4		8	3.2	odd	2
900.2.k.g.343.2		8	60.47	odd	4
900.2.k.g.343.3		8	60.23	odd	4
900.2.k.l.307.1		8	60.59	even	2
900.2.k.l.307.4		8	12.11	even	2
900.2.k.l.343.2		8	15.2	even	4
900.2.k.l.343.3		8	15.8	even	4

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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-0.366025 + 1.36603i) q^{6} +(3.15660 - 3.15660i) q^{7} +2.82843 q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-0.366025 + 1.36603i) q^{6} +(3.15660 - 3.15660i) q^{7} +2.82843 q^{8} +1.00000i q^{9} -2.00000i q^{11} +(1.93185 - 0.517638i) q^{12} +(-1.60368 + 1.60368i) q^{13} +(-6.09808 - 1.63397i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-4.24264 - 4.24264i) q^{17} +(1.22474 - 0.707107i) q^{18} +3.19615 q^{19} -4.46410 q^{21} +(-2.44949 + 1.41421i) q^{22} +(-5.27792 - 5.27792i) q^{23} +(-2.00000 - 2.00000i) q^{24} +(3.09808 + 0.830127i) q^{26} +(0.707107 - 0.707107i) q^{27} +(2.31079 + 8.62398i) q^{28} +0.535898i q^{29} -3.73205i q^{31} +(-2.82843 + 4.89898i) q^{32} +(-1.41421 + 1.41421i) q^{33} +(-2.19615 + 8.19615i) q^{34} +(-1.73205 - 1.00000i) q^{36} +(7.72741 + 7.72741i) q^{37} +(-2.26002 - 3.91447i) q^{38} +2.26795 q^{39} +1.46410 q^{41} +(3.15660 + 5.46739i) q^{42} +(-3.15660 - 3.15660i) q^{43} +(3.46410 + 2.00000i) q^{44} +(-2.73205 + 10.1962i) q^{46} +(-0.656339 + 0.656339i) q^{47} +(-1.03528 + 3.86370i) q^{48} -12.9282i q^{49} +6.00000i q^{51} +(-1.17398 - 4.38134i) q^{52} +(3.86370 - 3.86370i) q^{53} +(-1.36603 - 0.366025i) q^{54} +(8.92820 - 8.92820i) q^{56} +(-2.26002 - 2.26002i) q^{57} +(0.656339 - 0.378937i) q^{58} +11.4641 q^{59} +3.00000 q^{61} +(-4.57081 + 2.63896i) q^{62} +(3.15660 + 3.15660i) q^{63} +8.00000 q^{64} +(2.73205 + 0.732051i) q^{66} +(-3.91447 + 3.91447i) q^{67} +(11.5911 - 3.10583i) q^{68} +7.46410i q^{69} +2.53590i q^{71} +2.82843i q^{72} +(2.82843 - 2.82843i) q^{73} +(4.00000 - 14.9282i) q^{74} +(-3.19615 + 5.53590i) q^{76} +(-6.31319 - 6.31319i) q^{77} +(-1.60368 - 2.77766i) q^{78} -7.46410 q^{79} -1.00000 q^{81} +(-1.03528 - 1.79315i) q^{82} +(9.14162 + 9.14162i) q^{83} +(4.46410 - 7.73205i) q^{84} +(-1.63397 + 6.09808i) q^{86} +(0.378937 - 0.378937i) q^{87} -5.65685i q^{88} +6.92820i q^{89} +10.1244i q^{91} +(14.4195 - 3.86370i) q^{92} +(-2.63896 + 2.63896i) q^{93} +(1.26795 + 0.339746i) q^{94} +(5.46410 - 1.46410i) q^{96} +(6.88160 + 6.88160i) q^{97} +(-15.8338 + 9.14162i) q^{98} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} + 4 q^{6}+O(q^{10}) \) 8 * q - 8 * q^4 + 4 * q^6	\( 8 q - 8 q^{4} + 4 q^{6} - 28 q^{14} - 16 q^{16} - 16 q^{19} - 8 q^{21} - 16 q^{24} + 4 q^{26} + 24 q^{34} + 32 q^{39} - 16 q^{41} - 8 q^{46} - 4 q^{54} + 16 q^{56} + 64 q^{59} + 24 q^{61} + 64 q^{64} + 8 q^{66} + 32 q^{74} + 16 q^{76} - 32 q^{79} - 8 q^{81} + 8 q^{84} - 20 q^{86} + 24 q^{94} + 16 q^{96} + 16 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 + 4 * q^6 - 28 * q^14 - 16 * q^16 - 16 * q^19 - 8 * q^21 - 16 * q^24 + 4 * q^26 + 24 * q^34 + 32 * q^39 - 16 * q^41 - 8 * q^46 - 4 * q^54 + 16 * q^56 + 64 * q^59 + 24 * q^61 + 64 * q^64 + 8 * q^66 + 32 * q^74 + 16 * q^76 - 32 * q^79 - 8 * q^81 + 8 * q^84 - 20 * q^86 + 24 * q^94 + 16 * q^96 + 16 * q^99

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