LMFDB - Embedded newform 486.2.e.f.109.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [486,2,Mod(55,486)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("486.55"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(486, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([16])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 486 = 2 \cdot 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	486.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$3.88072953823$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 33 x^{10} - 110 x^{9} + 318 x^{8} - 678 x^{7} + 1225 x^{6} - 1698 x^{5} + 1905 x^{4} + \cdots + 57 $ x^12 - 6x^11 + 33x^10 - 110x^9 + 318x^8 - 678x^7 + 1225x^6 - 1698x^5 + 1905x^4 - 1584x^3 + 936x^2 - 342*x + 57
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			109.1
Root			$0.500000 + 0.677980i$ of defining polynomial
Character	$\chi$	$=$	486.109
Dual form			486.2.e.f.379.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.766044 - 0.642788i) q^{2} +(0.173648 - 0.984808i) q^{4} +(-3.33937 + 1.21543i) q^{5} +(-0.0554807 - 0.314647i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-1.77684 + 3.07758i) q^{10} +(-4.18356 - 1.52269i) q^{11} +(-3.58412 - 3.00743i) q^{13} +(-0.244752 - 0.205371i) q^{14} +(-0.939693 - 0.342020i) q^{16} +(-0.567354 + 0.982686i) q^{17} +(-0.928896 - 1.60890i) q^{19} +(0.617090 + 3.49969i) q^{20} +(-4.18356 + 1.52269i) q^{22} +(0.0250421 - 0.142021i) q^{23} +(5.84389 - 4.90360i) q^{25} -4.67874 q^{26} -0.319501 q^{28} +(-3.33937 + 2.80206i) q^{29} +(0.116638 - 0.661487i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(0.197040 + 1.11747i) q^{34} +(0.567702 + 0.983289i) q^{35} +(-3.79438 + 6.57207i) q^{37} +(-1.74575 - 0.635402i) q^{38} +(2.72228 + 2.28426i) q^{40} +(1.66790 + 1.39954i) q^{41} +(6.66967 + 2.42756i) q^{43} +(-2.22603 + 3.85559i) q^{44} +(-0.0721058 - 0.124891i) q^{46} +(-1.79319 - 10.1697i) q^{47} +(6.48192 - 2.35923i) q^{49} +(1.32470 - 7.51276i) q^{50} +(-3.58412 + 3.00743i) q^{52} +0.805554 q^{53} +15.8212 q^{55} +(-0.244752 + 0.205371i) q^{56} +(-0.756973 + 4.29301i) q^{58} +(-2.80296 + 1.02019i) q^{59} +(-0.606838 - 3.44155i) q^{61} +(-0.335846 - 0.581702i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(15.6240 + 5.68668i) q^{65} +(5.70186 + 4.78443i) q^{67} +(0.869237 + 0.729376i) q^{68} +(1.06693 + 0.388331i) q^{70} +(4.04928 - 7.01356i) q^{71} +(-7.30065 - 12.6451i) q^{73} +(1.31778 + 7.47348i) q^{74} +(-1.74575 + 0.635402i) q^{76} +(-0.247003 + 1.40083i) q^{77} +(-9.64221 + 8.09077i) q^{79} +3.55368 q^{80} +2.17729 q^{82} +(-4.14708 + 3.47981i) q^{83} +(0.700218 - 3.97113i) q^{85} +(6.66967 - 2.42756i) q^{86} +(0.773091 + 4.38442i) q^{88} +(-2.52624 - 4.37558i) q^{89} +(-0.747430 + 1.29459i) q^{91} +(-0.135515 - 0.0493233i) q^{92} +(-7.91059 - 6.63778i) q^{94} +(5.05743 + 4.24369i) q^{95} +(-17.5479 - 6.38693i) q^{97} +(3.44896 - 5.97377i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{5} + 6 q^{7} - 6 q^{8} - 3 q^{10} + 6 q^{11} - 6 q^{13} - 3 q^{14} - 6 q^{17} - 9 q^{19} - 3 q^{20} + 6 q^{22} - 6 q^{23} - 27 q^{25} + 18 q^{26} + 12 q^{28} - 3 q^{29} - 27 q^{31} + 12 q^{34}+ \cdots - 12 q^{98}+O(q^{100}) $ 12 * q - 3 * q^5 + 6 * q^7 - 6 * q^8 - 3 * q^10 + 6 * q^11 - 6 * q^13 - 3 * q^14 - 6 * q^17 - 9 * q^19 - 3 * q^20 + 6 * q^22 - 6 * q^23 - 27 * q^25 + 18 * q^26 + 12 * q^28 - 3 * q^29 - 27 * q^31 + 12 * q^34 + 3 * q^35 - 15 * q^37 - 15 * q^38 + 6 * q^40 + 15 * q^41 + 18 * q^43 - 3 * q^44 + 3 * q^46 - 27 * q^47 + 42 * q^49 + 36 * q^50 - 6 * q^52 - 12 * q^53 + 18 * q^55 - 3 * q^56 - 12 * q^58 - 24 * q^59 + 27 * q^61 - 12 * q^62 - 6 * q^64 + 57 * q^65 + 9 * q^67 - 15 * q^68 - 6 * q^70 + 12 * q^71 - 21 * q^73 - 3 * q^74 - 15 * q^76 - 51 * q^77 - 42 * q^79 + 6 * q^80 + 6 * q^82 - 45 * q^85 + 18 * q^86 - 12 * q^88 + 12 * q^89 - 6 * q^91 - 24 * q^92 - 9 * q^94 + 48 * q^95 - 24 * q^97 - 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/486\mathbb{Z}\right)^\times$.

$n$	$245$
$\chi(n)$	$e\left(\frac{7}{9}\right)$

Coefficient data

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

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

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

$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$3$		0			0
$3$		0			0
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	−3.33937	+	1.21543i	−1.49341	+	0.543557i	−0.954345	−	0.298706i	$-0.903445\pi$
$5$	−3.33937	+	1.21543i	−1.49341	+	0.543557i	−0.539066	+	0.842264i	$0.681223\pi$
$6$		0			0
$7$	−0.0554807	−	0.314647i	−0.0209698	−	0.118925i	0.972526	−	0.232794i	$-0.0747868\pi$
$7$	−0.0554807	−	0.314647i	−0.0209698	−	0.118925i	−0.993496	+	0.113869i	$0.963676\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$		0			0
$10$	−1.77684	+	3.07758i	−0.561886	+	0.973216i
$11$	−4.18356	−	1.52269i	−1.26139	−	0.459109i	−0.377156	−	0.926150i	$-0.623098\pi$
$11$	−4.18356	−	1.52269i	−1.26139	−	0.459109i	−0.884236	+	0.467041i	$0.845320\pi$
$12$		0			0
$13$	−3.58412	−	3.00743i	−0.994056	−	0.834112i	−0.00790622	−	0.999969i	$-0.502517\pi$
$13$	−3.58412	−	3.00743i	−0.994056	−	0.834112i	−0.986150	+	0.165857i	$0.946961\pi$
$14$	−0.244752	−	0.205371i	−0.0654127	−	0.0548878i
$15$		0			0
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	−0.567354	+	0.982686i	−0.137604	+	0.238336i	−0.926589	−	0.376075i	$-0.877273\pi$
$17$	−0.567354	+	0.982686i	−0.137604	+	0.238336i	0.788985	+	0.614412i	$0.210607\pi$
$18$		0			0
$19$	−0.928896	−	1.60890i	−0.213103	−	0.369106i	0.739581	−	0.673068i	$-0.235024\pi$
$19$	−0.928896	−	1.60890i	−0.213103	−	0.369106i	−0.952684	+	0.303962i	$0.901690\pi$
$20$	0.617090	+	3.49969i	0.137986	+	0.782555i
$21$		0			0
$22$	−4.18356	+	1.52269i	−0.891939	+	0.324639i
$23$	0.0250421	−	0.142021i	0.00522164	−	0.0296134i	−0.982086	−	0.188435i	$-0.939658\pi$
$23$	0.0250421	−	0.142021i	0.00522164	−	0.0296134i	0.987307	+	0.158822i	$0.0507696\pi$
$24$		0			0
$25$	5.84389	−	4.90360i	1.16878	−	0.980721i
$26$	−4.67874			−0.917576
$27$		0			0
$28$	−0.319501			−0.0603800
$29$	−3.33937	+	2.80206i	−0.620105	+	0.520330i	−0.897837	−	0.440329i	$-0.854862\pi$
$29$	−3.33937	+	2.80206i	−0.620105	+	0.520330i	0.277731	+	0.960659i	$0.410417\pi$
$30$		0			0
$31$	0.116638	−	0.661487i	0.0209488	−	0.118807i	−0.972540	−	0.232735i	$-0.925232\pi$
$31$	0.116638	−	0.661487i	0.0209488	−	0.118807i	0.993489	+	0.113929i	$0.0363435\pi$
$32$	−0.939693	+	0.342020i	−0.166116	+	0.0604612i
$33$		0			0
$34$	0.197040	+	1.11747i	0.0337921	+	0.191644i
$35$	0.567702	+	0.983289i	0.0959592	+	0.166206i
$36$		0			0
$37$	−3.79438	+	6.57207i	−0.623793	+	1.08044i	0.364980	+	0.931015i	$0.381076\pi$
$37$	−3.79438	+	6.57207i	−0.623793	+	1.08044i	−0.988773	+	0.149426i	$0.952258\pi$
$38$	−1.74575	−	0.635402i	−0.283199	−	0.103076i
$39$		0			0
$40$	2.72228	+	2.28426i	0.430430	+	0.361174i
$41$	1.66790	+	1.39954i	0.260483	+	0.218571i	0.763671	−	0.645606i	$-0.223395\pi$
$41$	1.66790	+	1.39954i	0.260483	+	0.218571i	−0.503188	+	0.864177i	$0.667840\pi$
$42$		0			0
$43$	6.66967	+	2.42756i	1.01711	+	0.370199i	0.796161	−	0.605085i	$-0.206861\pi$
$43$	6.66967	+	2.42756i	1.01711	+	0.370199i	0.220954	+	0.975284i	$0.429083\pi$
$44$	−2.22603	+	3.85559i	−0.335586	+	0.581252i
$45$		0			0
$46$	−0.0721058	−	0.124891i	−0.0106314	−	0.0184142i
$47$	−1.79319	−	10.1697i	−0.261563	−	1.48340i	−0.778647	−	0.627463i	$-0.784093\pi$
$47$	−1.79319	−	10.1697i	−0.261563	−	1.48340i	0.517084	−	0.855935i	$-0.327018\pi$
$48$		0			0
$49$	6.48192	−	2.35923i	0.925989	−	0.337032i
$50$	1.32470	−	7.51276i	0.187341	−	1.06246i
$51$		0			0
$52$	−3.58412	+	3.00743i	−0.497028	+	0.417056i
$53$	0.805554			0.110651			0.0553257	−	0.998468i	$-0.482380\pi$
$53$	0.805554			0.110651			0.0553257	+	0.998468i	$0.482380\pi$
$54$		0			0
$55$	15.8212			2.13333
$56$	−0.244752	+	0.205371i	−0.0327063	+	0.0274439i
$57$		0			0
$58$	−0.756973	+	4.29301i	−0.0993955	+	0.563700i
$59$	−2.80296	+	1.02019i	−0.364914	+	0.132818i	−0.517968	−	0.855400i	$-0.673311\pi$
$59$	−2.80296	+	1.02019i	−0.364914	+	0.132818i	0.153054	+	0.988218i	$0.451089\pi$
$60$		0			0
$61$	−0.606838	−	3.44155i	−0.0776976	−	0.440645i	−0.998695	−	0.0510758i	$-0.983735\pi$
$61$	−0.606838	−	3.44155i	−0.0776976	−	0.440645i	0.920997	−	0.389569i	$-0.127376\pi$
$62$	−0.335846	−	0.581702i	−0.0426525	−	0.0738763i
$63$		0			0
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	15.6240	+	5.68668i	1.93792	+	0.705346i
$66$		0			0
$67$	5.70186	+	4.78443i	0.696593	+	0.584511i	0.920802	−	0.390030i	$-0.127535\pi$
$67$	5.70186	+	4.78443i	0.696593	+	0.584511i	−0.224209	+	0.974541i	$0.571980\pi$
$68$	0.869237	+	0.729376i	0.105410	+	0.0884499i
$69$		0			0
$70$	1.06693	+	0.388331i	0.127523	+	0.0464145i
$71$	4.04928	−	7.01356i	0.480561	−	0.832356i	−0.519190	−	0.854659i	$-0.673766\pi$
$71$	4.04928	−	7.01356i	0.480561	−	0.832356i	0.999751	+	0.0223028i	$0.00709978\pi$
$72$		0			0
$73$	−7.30065	−	12.6451i	−0.854477	−	1.48000i	−0.877129	−	0.480254i	$-0.840545\pi$
$73$	−7.30065	−	12.6451i	−0.854477	−	1.48000i	0.0226526	−	0.999743i	$-0.492789\pi$
$74$	1.31778	+	7.47348i	0.153188	+	0.868774i
$75$		0			0
$76$	−1.74575	+	0.635402i	−0.200252	+	0.0728857i
$77$	−0.247003	+	1.40083i	−0.0281486	+	0.159639i
$78$		0			0
$79$	−9.64221	+	8.09077i	−1.08483	+	0.910283i	−0.996313	−	0.0857916i	$-0.972658\pi$
$79$	−9.64221	+	8.09077i	−1.08483	+	0.910283i	−0.0885197	+	0.996074i	$0.528214\pi$
$80$	3.55368			0.397314
$81$		0			0
$82$	2.17729			0.240442
$83$	−4.14708	+	3.47981i	−0.455201	+	0.381959i	−0.841362	−	0.540472i	$-0.818246\pi$
$83$	−4.14708	+	3.47981i	−0.455201	+	0.381959i	0.386161	+	0.922432i	$0.373801\pi$
$84$		0			0
$85$	0.700218	−	3.97113i	0.0759493	−	0.430730i
$86$	6.66967	−	2.42756i	0.719209	−	0.261770i
$87$		0			0
$88$	0.773091	+	4.38442i	0.0824118	+	0.467381i
$89$	−2.52624	−	4.37558i	−0.267781	−	0.463810i	0.700508	−	0.713645i	$-0.252957\pi$
$89$	−2.52624	−	4.37558i	−0.267781	−	0.463810i	−0.968288	+	0.249835i	$0.919624\pi$
$90$		0			0
$91$	−0.747430	+	1.29459i	−0.0783520	+	0.135710i
$92$	−0.135515	−	0.0493233i	−0.0141284	−	0.00514231i
$93$		0			0
$94$	−7.91059	−	6.63778i	−0.815915	−	0.684634i
$95$	5.05743	+	4.24369i	0.518881	+	0.435393i
$96$		0			0
$97$	−17.5479	−	6.38693i	−1.78172	−	0.648494i	−0.999681	−	0.0252688i	$-0.991956\pi$
$97$	−17.5479	−	6.38693i	−1.78172	−	0.648494i	−0.782042	−	0.623225i	$-0.785822\pi$
$98$	3.44896	−	5.97377i	0.348398	−	0.603442i
$99$		0			0
$100$	−3.81433	−	6.60661i	−0.381433	−	0.660661i
$101$	−0.420171	−	2.38291i	−0.0418086	−	0.237108i	0.956741	−	0.290939i	$-0.0939678\pi$
$101$	−0.420171	−	2.38291i	−0.0418086	−	0.237108i	−0.998550	+	0.0538312i	$0.982857\pi$
$102$		0			0
$103$	−1.87502	+	0.682450i	−0.184751	+	0.0672438i	−0.432739	−	0.901519i	$-0.642453\pi$
$103$	−1.87502	+	0.682450i	−0.184751	+	0.0672438i	0.247988	+	0.968763i	$0.420231\pi$
$104$	−0.812454	+	4.60766i	−0.0796677	+	0.451818i
$105$		0			0
$106$	0.617090	−	0.517800i	0.0599371	−	0.0502932i
$107$	8.87072			0.857565			0.428783	−	0.903408i	$-0.358943\pi$
$107$	8.87072			0.857565			0.428783	+	0.903408i	$0.358943\pi$
$108$		0			0
$109$	−1.97204			−0.188887			−0.0944434	−	0.995530i	$-0.530107\pi$
$109$	−1.97204			−0.188887			−0.0944434	+	0.995530i	$0.530107\pi$
$110$	12.1197	−	10.1697i	1.15557	−	0.969639i
$111$		0			0
$112$	−0.0554807	+	0.314647i	−0.00524244	+	0.0297313i
$113$	9.04797	−	3.29319i	0.851162	−	0.309798i	0.120648	−	0.992695i	$-0.461503\pi$
$113$	9.04797	−	3.29319i	0.851162	−	0.309798i	0.730514	+	0.682898i	$0.239281\pi$
$114$		0			0
$115$	0.0889916	+	0.504696i	0.00829851	+	0.0470632i
$116$	2.17962	+	3.77521i	0.202372	+	0.350519i
$117$		0			0
$118$	−1.49142	+	2.58322i	−0.137297	+	0.237805i
$119$	0.340676	+	0.123996i	0.0312298	+	0.0113667i
$120$		0			0
$121$	6.75712	+	5.66990i	0.614284	+	0.515445i
$122$	−2.67705	−	2.24631i	−0.242369	−	0.203371i
$123$		0			0
$124$	−0.631184	−	0.229732i	−0.0566820	−	0.0206306i
$125$	−4.67070	+	8.08988i	−0.417760	+	0.723581i
$126$		0			0
$127$	−0.0796049	−	0.137880i	−0.00706379	−	0.0122348i	0.862472	−	0.506105i	$-0.168915\pi$
$127$	−0.0796049	−	0.137880i	−0.00706379	−	0.0122348i	−0.869536	+	0.493870i	$0.835582\pi$
$128$	0.173648	+	0.984808i	0.0153485	+	0.0870455i
$129$		0			0
$130$	15.6240	−	5.68668i	1.37032	−	0.498755i
$131$	−1.64720	+	9.34172i	−0.143916	+	0.816190i	0.824315	+	0.566132i	$0.191561\pi$
$131$	−1.64720	+	9.34172i	−0.143916	+	0.816190i	−0.968231	+	0.250058i	$0.919550\pi$
$132$		0			0
$133$	−0.454698	+	0.381537i	−0.0394273	+	0.0330835i
$134$	7.44325			0.642999
$135$		0			0
$136$	1.13471			0.0973004
$137$	8.96989	−	7.52663i	0.766349	−	0.643044i	−0.173422	−	0.984848i	$-0.555482\pi$
$137$	8.96989	−	7.52663i	0.766349	−	0.643044i	0.939771	+	0.341804i	$0.111038\pi$
$138$		0			0
$139$	−0.911699	+	5.17050i	−0.0773293	+	0.438556i	0.921420	+	0.388567i	$0.127030\pi$
$139$	−0.911699	+	5.17050i	−0.0773293	+	0.438556i	−0.998750	+	0.0499893i	$0.984081\pi$
$140$	1.06693	−	0.388331i	0.0901721	−	0.0328200i
$141$		0			0
$142$	−1.40630	−	7.97552i	−0.118014	−	0.669291i
$143$	10.4150	+	18.0393i	0.870946	+	1.50852i
$144$		0			0
$145$	7.74567	−	13.4159i	0.643243	−	1.11413i
$146$	−13.7207	−	4.99394i	−1.13554	−	0.413302i
$147$		0			0
$148$	5.81333	+	4.87797i	0.477853	+	0.400966i
$149$	−12.4806	−	10.4725i	−1.02245	−	0.857937i	−0.0325157	−	0.999471i	$-0.510352\pi$
$149$	−12.4806	−	10.4725i	−1.02245	−	0.857937i	−0.989933	+	0.141535i	$0.954796\pi$
$150$		0			0
$151$	14.6761	+	5.34165i	1.19432	+	0.434697i	0.861239	−	0.508201i	$-0.169689\pi$
$151$	14.6761	+	5.34165i	1.19432	+	0.434697i	0.333082	+	0.942898i	$0.391911\pi$
$152$	−0.928896	+	1.60890i	−0.0753434	+	0.130499i
$153$		0			0
$154$	0.711218	+	1.23187i	0.0573116	+	0.0992665i
$155$	0.414495	+	2.35072i	0.0332930	+	0.188814i
$156$		0			0
$157$	−16.5682	+	6.03034i	−1.32229	+	0.481274i	−0.904191	−	0.427129i	$-0.859525\pi$
$157$	−16.5682	+	6.03034i	−1.32229	+	0.481274i	−0.418098	+	0.908402i	$0.637303\pi$
$158$	−2.18571	+	12.3958i	−0.173886	+	0.986155i
$159$		0			0
$160$	2.72228	−	2.28426i	0.215215	−	0.180587i
$161$	−0.0460757			−0.00363128
$162$		0			0
$163$	−15.8801			−1.24382			−0.621912	−	0.783087i	$-0.713644\pi$
$163$	−15.8801			−1.24382			−0.621912	+	0.783087i	$0.713644\pi$
$164$	1.66790	−	1.39954i	0.130241	−	0.109286i
$165$		0			0
$166$	−0.940067	+	5.33138i	−0.0729633	+	0.413796i
$167$	12.7595	−	4.64409i	0.987363	−	0.359371i	0.202664	−	0.979248i	$-0.435040\pi$
$167$	12.7595	−	4.64409i	0.987363	−	0.359371i	0.784699	+	0.619878i	$0.212818\pi$
$168$		0			0
$169$	1.54383	+	8.75551i	0.118756	+	0.673501i
$170$	−2.01620	−	3.49215i	−0.154635	−	0.267836i
$171$		0			0
$172$	3.54885	−	6.14680i	0.270598	−	0.468689i
$173$	−6.05576	−	2.20412i	−0.460411	−	0.167576i	0.101393	−	0.994846i	$-0.467670\pi$
$173$	−6.05576	−	2.20412i	−0.460411	−	0.167576i	−0.561804	+	0.827271i	$0.689892\pi$
$174$		0			0
$175$	−1.86713	−	1.56671i	−0.141142	−	0.118432i
$176$	3.41047	+	2.86173i	0.257074	+	0.215711i
$177$		0			0
$178$	−4.74778	−	1.72805i	−0.355861	−	0.129523i
$179$	6.25613	−	10.8359i	0.467605	−	0.809915i	−0.531710	−	0.846927i	$-0.678450\pi$
$179$	6.25613	−	10.8359i	0.467605	−	0.809915i	0.999315	+	0.0370111i	$0.0117837\pi$
$180$		0			0
$181$	−0.152251	−	0.263707i	−0.0113168	−	0.0196012i	0.860312	−	0.509769i	$-0.170269\pi$
$181$	−0.152251	−	0.263707i	−0.0113168	−	0.0196012i	−0.871628	+	0.490167i	$0.836936\pi$
$182$	0.259580	+	1.47215i	0.0192413	+	0.109123i
$183$		0			0
$184$	−0.135515	+	0.0493233i	−0.00999027	+	0.00363616i
$185$	4.68296	−	26.5584i	0.344298	−	1.95261i
$186$		0			0
$187$	3.86989	−	3.24722i	0.282994	−	0.237461i
$188$	−10.3265			−0.753141
$189$		0			0
$190$	6.60200			0.478960
$191$	−11.0255	+	9.25146i	−0.797774	+	0.669412i	−0.947656	−	0.319292i	$-0.896555\pi$
$191$	−11.0255	+	9.25146i	−0.797774	+	0.669412i	0.149882	+	0.988704i	$0.452110\pi$
$192$		0			0
$193$	0.529736	−	3.00428i	0.0381312	−	0.216253i	−0.959788	−	0.280725i	$-0.909425\pi$
$193$	0.529736	−	3.00428i	0.0381312	−	0.216253i	0.997920	+	0.0644720i	$0.0205363\pi$
$194$	−17.5479	+	6.38693i	−1.25987	+	0.458555i
$195$		0			0
$196$	−1.19781	−	6.79312i	−0.0855579	−	0.485223i
$197$	−11.1321	−	19.2814i	−0.793129	−	1.37374i	−0.924020	−	0.382343i	$-0.875117\pi$
$197$	−11.1321	−	19.2814i	−0.793129	−	1.37374i	0.130891	−	0.991397i	$-0.458216\pi$
$198$		0			0
$199$	−12.2817	+	21.2725i	−0.870626	+	1.50797i	−0.00927642	+	0.999957i	$0.502953\pi$
$199$	−12.2817	+	21.2725i	−0.870626	+	1.50797i	−0.861350	+	0.508012i	$0.830381\pi$
$200$	−7.16859	−	2.60915i	−0.506896	−	0.184495i
$201$		0			0
$202$	−1.85357	−	1.55533i	−0.130417	−	0.109433i
$203$	1.06693	+	0.895262i	0.0748839	+	0.0628350i
$204$		0			0
$205$	−7.27078	−	2.64635i	−0.507814	−	0.184829i
$206$	−0.997676	+	1.72802i	−0.0695114	+	0.120397i
$207$		0			0
$208$	2.33937	+	4.05190i	0.162206	+	0.280949i
$209$	1.43624	+	8.14534i	0.0993470	+	0.563425i
$210$		0			0
$211$	2.83722	−	1.03266i	0.195322	−	0.0710915i	−0.242507	−	0.970150i	$-0.577970\pi$
$211$	2.83722	−	1.03266i	0.195322	−	0.0710915i	0.437829	+	0.899058i	$0.355747\pi$
$212$	0.139883	−	0.793316i	0.00960721	−	0.0544852i
$213$		0			0
$214$	6.79537	−	5.70199i	0.464522	−	0.389780i
$215$	−25.2230			−1.72019
$216$		0			0
$217$	−0.214606			−0.0145684
$218$	−1.51067	+	1.26760i	−0.102315	+	0.0858527i
$219$		0			0
$220$	2.74732	−	15.5808i	0.185224	−	1.05046i
$221$	4.98883	−	1.81579i	0.335585	−	0.122143i
$222$		0			0
$223$	1.73308	+	9.82877i	0.116055	+	0.658183i	0.986222	+	0.165426i	$0.0528999\pi$
$223$	1.73308	+	9.82877i	0.116055	+	0.658183i	−0.870167	+	0.492757i	$0.835989\pi$
$224$	0.159750	+	0.276696i	0.0106738	+	0.0184875i
$225$		0			0
$226$	4.81433	−	8.33866i	0.320244	−	0.554679i
$227$	19.8485	+	7.22428i	1.31739	+	0.479492i	0.902622	−	0.430434i	$-0.141639\pi$
$227$	19.8485	+	7.22428i	1.31739	+	0.479492i	0.414771	+	0.909926i	$0.363862\pi$
$228$		0			0
$229$	−17.8341	−	14.9646i	−1.17851	−	0.988887i	−0.999988	−	0.00495069i	$-0.998424\pi$
$229$	−17.8341	−	14.9646i	−1.17851	−	0.988887i	−0.178522	−	0.983936i	$-0.557131\pi$
$230$	0.392584	+	0.329417i	0.0258862	+	0.0217211i
$231$		0			0
$232$	4.09634	+	1.49095i	0.268938	+	0.0978854i
$233$	−13.3621	+	23.1439i	−0.875383	+	1.51621i	−0.0190296	+	0.999819i	$0.506058\pi$
$233$	−13.3621	+	23.1439i	−0.875383	+	1.51621i	−0.856354	+	0.516390i	$0.827276\pi$
$234$		0			0
$235$	18.3486	+	31.7808i	1.19693	+	2.07315i
$236$	0.517966	+	2.93753i	0.0337167	+	0.191217i
$237$		0			0
$238$	0.340676	−	0.123996i	0.0220828	−	0.00803747i
$239$	−4.17795	+	23.6943i	−0.270249	+	1.53266i	0.483410	+	0.875394i	$0.339398\pi$
$239$	−4.17795	+	23.6943i	−0.270249	+	1.53266i	−0.753659	+	0.657265i	$0.771713\pi$
$240$		0			0
$241$	−1.14257	+	0.958731i	−0.0735994	+	0.0617573i	−0.678845	−	0.734281i	$-0.737519\pi$
$241$	−1.14257	+	0.958731i	−0.0735994	+	0.0617573i	0.605246	+	0.796039i	$0.293075\pi$
$242$	8.82079			0.567022
$243$		0			0
$244$	−3.49464			−0.223721
$245$	−18.7781	+	15.7567i	−1.19969	+	1.00666i
$246$		0			0
$247$	−1.50937	+	8.56007i	−0.0960390	+	0.544664i
$248$	−0.631184	+	0.229732i	−0.0400802	+	0.0145880i
$249$		0			0
$250$	1.62212	+	9.19948i	0.102592	+	0.581826i
$251$	−7.28748	−	12.6223i	−0.459982	−	0.796711i	0.538978	−	0.842320i	$-0.318811\pi$
$251$	−7.28748	−	12.6223i	−0.459982	−	0.796711i	−0.998959	+	0.0456086i	$0.985477\pi$
$252$		0			0
$253$	−0.321019	+	0.556021i	−0.0201823	+	0.0349568i
$254$	−0.149608	−	0.0544529i	−0.00938725	−	0.00341668i
$255$		0			0
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−8.44535	−	7.08649i	−0.526807	−	0.442043i	0.340190	−	0.940357i	$-0.389508\pi$
$257$	−8.44535	−	7.08649i	−0.526807	−	0.442043i	−0.866997	+	0.498313i	$0.833953\pi$
$258$		0			0
$259$	2.27840	+	0.829268i	0.141573	+	0.0515282i
$260$	8.31337	−	14.3992i	0.515573	−	0.892999i
$261$		0			0
$262$	4.74292	+	8.21497i	0.293018	+	0.507523i
$263$	−2.28175	−	12.9404i	−0.140699	−	0.797941i	−0.970721	−	0.240211i	$-0.922783\pi$
$263$	−2.28175	−	12.9404i	−0.140699	−	0.797941i	0.830022	−	0.557730i	$-0.188328\pi$
$264$		0			0
$265$	−2.69004	+	0.979095i	−0.165248	+	0.0601453i
$266$	−0.103072	+	0.584549i	−0.00631973	+	0.0358410i
$267$		0			0
$268$	5.70186	−	4.78443i	0.348296	−	0.292255i
$269$	−10.3086			−0.628528			−0.314264	−	0.949336i	$-0.601758\pi$
$269$	−10.3086			−0.628528			−0.314264	+	0.949336i	$0.601758\pi$
$270$		0			0
$271$	1.01454			0.0616288			0.0308144	−	0.999525i	$-0.490190\pi$
$271$	1.01454			0.0616288			0.0308144	+	0.999525i	$0.490190\pi$
$272$	0.869237	−	0.729376i	0.0527052	−	0.0442249i
$273$		0			0
$274$	2.03331	−	11.5315i	0.122837	−	0.696641i
$275$	−31.9150	+	11.6161i	−1.92454	+	0.700477i
$276$		0			0
$277$	−1.88090	−	10.6671i	−0.113012	−	0.640926i	−0.987715	−	0.156266i	$-0.950054\pi$
$277$	−1.88090	−	10.6671i	−0.113012	−	0.640926i	0.874703	−	0.484660i	$-0.161057\pi$
$278$	2.62513	+	4.54686i	0.157445	+	0.272703i
$279$		0			0
$280$	0.567702	−	0.983289i	0.0339267	−	0.0587628i
$281$	7.96552	+	2.89921i	0.475183	+	0.172952i	0.568499	−	0.822684i	$-0.307524\pi$
$281$	7.96552	+	2.89921i	0.475183	+	0.172952i	−0.0933158	+	0.995637i	$0.529747\pi$
$282$		0			0
$283$	4.82935	+	4.05231i	0.287075	+	0.240885i	0.774941	−	0.632034i	$-0.217780\pi$
$283$	4.82935	+	4.05231i	0.287075	+	0.240885i	−0.487865	+	0.872919i	$0.662224\pi$
$284$	−6.20385	−	5.20565i	−0.368131	−	0.308899i
$285$		0			0
$286$	19.5738	+	7.12428i	1.15742	+	0.421267i
$287$	0.347824	−	0.602448i	0.0205314	−	0.0355614i
$288$		0			0
$289$	7.85622	+	13.6074i	0.462130	+	0.800434i
$290$	−2.69004	−	15.2560i	−0.157965	−	0.895862i
$291$		0			0
$292$	−13.7207	+	4.99394i	−0.802946	+	0.292248i
$293$	−0.422496	+	2.39609i	−0.0246825	+	0.139981i	−0.994659	−	0.103219i	$-0.967086\pi$
$293$	−0.422496	+	2.39609i	−0.0246825	+	0.139981i	0.969976	+	0.243200i	$0.0781970\pi$
$294$		0			0
$295$	8.12014	−	6.81361i	0.472773	−	0.396704i
$296$	7.58877			0.441088
$297$		0			0
$298$	−16.2922			−0.943784
$299$	−0.516872	+	0.433707i	−0.0298915	+	0.0250819i
$300$		0			0
$301$	0.393786	−	2.23327i	0.0226975	−	0.128724i
$302$	14.6761	−	5.34165i	0.844512	−	0.307377i
$303$		0			0
$304$	0.322602	+	1.82957i	0.0185025	+	0.104933i
$305$	6.20942	+	10.7550i	0.355550	+	0.615831i
$306$		0			0
$307$	11.8629	−	20.5471i	0.677050	−	1.17269i	−0.298815	−	0.954311i	$-0.596591\pi$
$307$	11.8629	−	20.5471i	0.677050	−	1.17269i	0.975865	−	0.218374i	$-0.0700754\pi$
$308$	1.33665	+	0.486502i	0.0761628	+	0.0277210i
$309$		0			0
$310$	1.82853	+	1.53432i	0.103854	+	0.0871436i
$311$	−8.27375	−	6.94250i	−0.469161	−	0.393673i	0.377327	−	0.926080i	$-0.376843\pi$
$311$	−8.27375	−	6.94250i	−0.469161	−	0.393673i	−0.846488	+	0.532407i	$0.821288\pi$
$312$		0			0
$313$	14.9328	+	5.43511i	0.844054	+	0.307210i	0.727613	−	0.685987i	$-0.240629\pi$
$313$	14.9328	+	5.43511i	0.844054	+	0.307210i	0.116440	+	0.993198i	$0.462852\pi$
$314$	−8.81577	+	15.2694i	−0.497503	+	0.861700i
$315$		0			0
$316$	6.29350	+	10.9007i	0.354037	+	0.613210i
$317$	−0.561759	−	3.18589i	−0.0315515	−	0.178938i	0.964959	−	0.262399i	$-0.0845136\pi$
$317$	−0.561759	−	3.18589i	−0.0315515	−	0.178938i	−0.996511	+	0.0834613i	$0.973403\pi$
$318$		0			0
$319$	18.2371	−	6.63778i	1.02108	−	0.371644i
$320$	0.617090	−	3.49969i	0.0344964	−	0.195639i
$321$		0			0
$322$	−0.0352961	+	0.0296169i	−0.00196697	+	0.00165049i
$323$	2.10805			0.117295
$324$		0			0
$325$	−35.6925			−1.97986
$326$	−12.1648	+	10.2075i	−0.673748	+	0.565342i
$327$		0			0
$328$	0.378083	−	2.14422i	0.0208761	−	0.118394i
$329$	−3.10037	+	1.12844i	−0.170929	+	0.0622130i
$330$		0			0
$331$	−3.06726	−	17.3953i	−0.168592	−	0.956133i	−0.945283	−	0.326251i	$-0.894215\pi$
$331$	−3.06726	−	17.3953i	−0.168592	−	0.956133i	0.776691	−	0.629882i	$-0.216897\pi$
$332$	2.70681	+	4.68834i	0.148556	+	0.257306i
$333$		0			0
$334$	6.78921	−	11.7593i	0.371489	−	0.643438i
$335$	−24.8557	−	9.04675i	−1.35801	−	0.494277i
$336$		0			0
$337$	−8.07631	−	6.77683i	−0.439945	−	0.369157i	0.395744	−	0.918361i	$-0.370487\pi$
$337$	−8.07631	−	6.77683i	−0.439945	−	0.369157i	−0.835689	+	0.549203i	$0.814931\pi$
$338$	6.81058	+	5.71475i	0.370447	+	0.310842i
$339$		0			0
$340$	−3.78921	−	1.37916i	−0.205499	−	0.0747954i
$341$	−1.49520	+	2.58977i	−0.0809699	+	0.140244i
$342$		0			0
$343$	−2.22020	−	3.84550i	−0.119879	−	0.207637i
$344$	−1.23250	−	6.98988i	−0.0664522	−	0.376869i
$345$		0			0
$346$	−6.05576	+	2.20412i	−0.325560	+	0.118494i
$347$	5.64438	−	32.0108i	0.303006	−	1.71843i	−0.329739	−	0.944072i	$-0.606961\pi$
$347$	5.64438	−	32.0108i	0.303006	−	1.71843i	0.632745	−	0.774360i	$-0.281928\pi$
$348$		0			0
$349$	−15.3747	+	12.9009i	−0.822991	+	0.690571i	−0.953670	−	0.300853i	$-0.902729\pi$
$349$	−15.3747	+	12.9009i	−0.822991	+	0.690571i	0.130680	+	0.991425i	$0.458284\pi$
$350$	−2.43736			−0.130282
$351$		0			0
$352$	4.45206			0.237295
$353$	8.45411	−	7.09384i	0.449967	−	0.377567i	−0.389457	−	0.921045i	$-0.627337\pi$
$353$	8.45411	−	7.09384i	0.449967	−	0.377567i	0.839424	+	0.543478i	$0.182893\pi$
$354$		0			0
$355$	−4.99754	+	28.3425i	−0.265242	+	1.50426i
$356$	−4.74778	+	1.72805i	−0.251632	+	0.0915865i
$357$		0			0
$358$	−2.17273	−	12.3222i	−0.114832	−	0.651247i
$359$	1.96044	+	3.39557i	0.103468	+	0.179212i	0.913111	−	0.407711i	$-0.133673\pi$
$359$	1.96044	+	3.39557i	0.103468	+	0.179212i	−0.809643	+	0.586922i	$0.800339\pi$
$360$		0			0
$361$	7.77430	−	13.4655i	0.409174	−	0.708710i
$362$	−0.286139	−	0.104146i	−0.0150391	−	0.00547380i
$363$		0			0
$364$	1.14513	+	0.960878i	0.0600211	+	0.0503637i
$365$	39.7488	+	33.3532i	2.08055	+	1.74579i
$366$		0			0
$367$	−27.3932	−	9.97031i	−1.42991	−	0.520446i	−0.493007	−	0.870026i	$-0.664102\pi$
$367$	−27.3932	−	9.97031i	−1.42991	−	0.520446i	−0.936907	+	0.349580i	$0.886324\pi$
$368$	−0.0721058	+	0.124891i	−0.00375878	+	0.00651039i
$369$		0			0
$370$	−13.4840	−	23.3550i	−0.701001	−	1.21417i
$371$	−0.0446927	−	0.253465i	−0.00232033	−	0.0131593i
$372$		0			0
$373$	−5.89358	+	2.14509i	−0.305158	+	0.111068i	−0.490060	−	0.871689i	$-0.663025\pi$
$373$	−5.89358	+	2.14509i	−0.305158	+	0.111068i	0.184903	+	0.982757i	$0.440803\pi$
$374$	0.877233	−	4.97504i	0.0453606	−	0.257253i
$375$		0			0
$376$	−7.91059	+	6.63778i	−0.407958	+	0.342317i
$377$	20.3957			1.05043
$378$		0			0
$379$	−26.9562			−1.38465			−0.692324	−	0.721587i	$-0.743413\pi$
$379$	−26.9562			−1.38465			−0.692324	+	0.721587i	$0.743413\pi$
$380$	5.05743	−	4.24369i	0.259441	−	0.217696i
$381$		0			0
$382$	−2.49927	+	14.1741i	−0.127874	+	0.725208i
$383$	3.05989	−	1.11371i	0.156353	−	0.0569079i	−0.262658	−	0.964889i	$-0.584599\pi$
$383$	3.05989	−	1.11371i	0.156353	−	0.0569079i	0.419011	+	0.907981i	$0.362377\pi$
$384$		0			0
$385$	−0.877771	−	4.97809i	−0.0447354	−	0.253707i
$386$	−1.52531	−	2.64192i	−0.0776364	−	0.134470i
$387$		0			0
$388$	−9.33706	+	16.1723i	−0.474018	+	0.821022i
$389$	−1.30587	−	0.475299i	−0.0662103	−	0.0240986i	0.308703	−	0.951159i	$-0.400105\pi$
$389$	−1.30587	−	0.475299i	−0.0662103	−	0.0240986i	−0.374913	+	0.927060i	$0.622327\pi$
$390$		0			0
$391$	0.125354	+	0.105185i	0.00633943	+	0.00531941i
$392$	−5.28411	−	4.43390i	−0.266888	−	0.223946i
$393$		0			0
$394$	−20.9215	−	7.61480i	−1.05401	−	0.383628i
$395$	22.3651	−	38.7375i	1.12531	−	1.94909i
$396$		0			0
$397$	−1.07010	−	1.85347i	−0.0537069	−	0.0930230i	0.837922	−	0.545790i	$-0.183770\pi$
$397$	−1.07010	−	1.85347i	−0.0537069	−	0.0930230i	−0.891629	+	0.452767i	$0.850437\pi$
$398$	4.26539	+	24.1902i	0.213805	+	1.21255i
$399$		0			0
$400$	−7.16859	+	2.60915i	−0.358429	+	0.130458i
$401$	−1.48527	+	8.42337i	−0.0741707	+	0.420643i	0.925002	+	0.379963i	$0.124063\pi$
$401$	−1.48527	+	8.42337i	−0.0741707	+	0.420643i	−0.999172	+	0.0406796i	$0.987048\pi$
$402$		0			0
$403$	−2.40742	+	2.02007i	−0.119922	+	0.100627i
$404$	−2.41967			−0.120383
$405$		0			0
$406$	1.39278			0.0691225
$407$	25.8813	−	21.7170i	1.28289	−	1.07647i
$408$		0			0
$409$	4.73571	−	26.8575i	0.234166	−	1.32802i	−0.610198	−	0.792249i	$-0.708910\pi$
$409$	4.73571	−	26.8575i	0.234166	−	1.32802i	0.844363	−	0.535771i	$-0.179979\pi$
$410$	−7.27078	+	2.64635i	−0.359078	+	0.130694i
$411$		0			0
$412$	0.346489	+	1.96504i	0.0170703	+	0.0968104i
$413$	0.476511	+	0.825342i	0.0234476	+	0.0406124i
$414$		0			0
$415$	9.61916	−	16.6609i	0.472186	−	0.817850i
$416$	4.39657	+	1.60022i	0.215560	+	0.0784573i
$417$		0			0
$418$	6.33595	+	5.31649i	0.309901	+	0.260038i
$419$	12.2685	+	10.2945i	0.599353	+	0.502917i	0.891238	−	0.453536i	$-0.149838\pi$
$419$	12.2685	+	10.2945i	0.599353	+	0.502917i	−0.291884	+	0.956454i	$0.594282\pi$
$420$		0			0
$421$	17.0526	+	6.20665i	0.831094	+	0.302494i	0.722308	−	0.691572i	$-0.243081\pi$
$421$	17.0526	+	6.20665i	0.831094	+	0.302494i	0.108786	+	0.994065i	$0.465304\pi$
$422$	1.50965	−	2.61480i	0.0734888	−	0.127286i
$423$		0			0
$424$	−0.402777	−	0.697630i	−0.0195606	−	0.0338799i
$425$	1.50315	+	8.52479i	0.0729135	+	0.413513i
$426$		0			0
$427$	−1.04921	+	0.381879i	−0.0507746	+	0.0184804i
$428$	1.54039	−	8.73596i	0.0744573	−	0.422268i
$429$		0			0
$430$	−19.3219	+	16.2130i	−0.931787	+	0.781862i
$431$	2.13698			0.102935			0.0514673	−	0.998675i	$-0.483610\pi$
$431$	2.13698			0.102935			0.0514673	+	0.998675i	$0.483610\pi$
$432$		0			0
$433$	25.1733			1.20975			0.604876	−	0.796320i	$-0.293223\pi$
$433$	25.1733			1.20975			0.604876	+	0.796320i	$0.293223\pi$
$434$	−0.164398	+	0.137946i	−0.00789135	+	0.00662163i
$435$		0			0
$436$	−0.342441	+	1.94208i	−0.0163999	+	0.0930086i
$437$	−0.251758	+	0.0916324i	−0.0120432	+	0.00438337i
$438$		0			0
$439$	4.48913	+	25.4591i	0.214255	+	1.21510i	0.882195	+	0.470884i	$0.156065\pi$
$439$	4.48913	+	25.4591i	0.214255	+	1.21510i	−0.667941	+	0.744215i	$0.732824\pi$
$440$	−7.91059	−	13.7015i	−0.377123	−	0.653196i
$441$		0			0
$442$	2.65450	−	4.59773i	0.126262	−	0.218692i
$443$	−13.0980	−	4.76727i	−0.622304	−	0.226500i	0.0115743	−	0.999933i	$-0.496316\pi$
$443$	−13.0980	−	4.76727i	−0.622304	−	0.226500i	−0.633878	+	0.773433i	$0.718538\pi$
$444$		0			0
$445$	13.7543	+	11.5412i	0.652014	+	0.547105i
$446$	7.64543	+	6.41527i	0.362021	+	0.303772i
$447$		0			0
$448$	0.300233	+	0.109276i	0.0141847	+	0.00516279i
$449$	−14.5769	+	25.2479i	−0.687927	+	1.19152i	0.284581	+	0.958652i	$0.408146\pi$
$449$	−14.5769	+	25.2479i	−0.687927	+	1.19152i	−0.972507	+	0.232872i	$0.925188\pi$
$450$		0			0
$451$	−4.84672	−	8.39476i	−0.228223	−	0.395294i
$452$	−1.67200	−	9.48237i	−0.0786442	−	0.446013i
$453$		0			0
$454$	19.8485	−	7.22428i	0.931538	−	0.339052i
$455$	0.922464	−	5.23155i	0.0432458	−	0.245259i
$456$		0			0
$457$	18.2304	−	15.2972i	0.852784	−	0.715571i	−0.107617	−	0.994192i	$-0.534322\pi$
$457$	18.2304	−	15.2972i	0.852784	−	0.715571i	0.960401	+	0.278622i	$0.0898775\pi$
$458$	−23.2807			−1.08784
$459$		0			0
$460$	0.512482			0.0238946
$461$	23.6044	−	19.8064i	1.09936	−	0.922476i	0.101982	−	0.994786i	$-0.467481\pi$
$461$	23.6044	−	19.8064i	1.09936	−	0.922476i	0.997382	+	0.0723098i	$0.0230370\pi$
$462$		0			0
$463$	6.27567	−	35.5911i	0.291655	−	1.65406i	−0.388841	−	0.921305i	$-0.627124\pi$
$463$	6.27567	−	35.5911i	0.291655	−	1.65406i	0.680495	−	0.732752i	$-0.261765\pi$
$464$	4.09634	−	1.49095i	0.190168	−	0.0692155i
$465$		0			0
$466$	4.64063	+	26.3183i	0.214973	+	1.21917i
$467$	18.4877	+	32.0217i	0.855509	+	1.48179i	0.876172	+	0.481999i	$0.160089\pi$
$467$	18.4877	+	32.0217i	0.855509	+	1.48179i	−0.0206626	+	0.999787i	$0.506578\pi$
$468$		0			0
$469$	1.18906	−	2.05952i	0.0549058	−	0.0950996i
$470$	34.4841	+	12.5512i	1.59063	+	0.578944i
$471$		0			0
$472$	2.28499	+	1.91734i	0.105175	+	0.0882526i
$473$	−24.2065	−	20.3117i	−1.11302	−	0.933933i
$474$		0			0
$475$	−13.3178	−	4.84726i	−0.611060	−	0.222408i
$476$	0.181270	−	0.313969i	0.00830850	−	0.0143908i
$477$		0			0
$478$	12.0299	+	20.8365i	0.550236	+	0.953037i
$479$	6.66478	+	37.7978i	0.304522	+	1.72703i	0.625748	+	0.780025i	$0.284794\pi$
$479$	6.66478	+	37.7978i	0.304522	+	1.72703i	−0.321227	+	0.947002i	$0.604095\pi$
$480$		0			0
$481$	33.3646	−	12.1437i	1.52129	−	0.553706i
$482$	−0.259000	+	1.46886i	−0.0117971	+	0.0669048i
$483$		0			0
$484$	6.75712	−	5.66990i	0.307142	−	0.257723i
$485$	66.3619			3.01334
$486$		0			0
$487$	34.3088			1.55468			0.777339	−	0.629082i	$-0.216569\pi$
$487$	34.3088			1.55468			0.777339	+	0.629082i	$0.216569\pi$
$488$	−2.67705	+	2.24631i	−0.121184	+	0.101686i
$489$		0			0
$490$	−4.25664	+	24.1406i	−0.192295	+	1.09056i
$491$	16.3578	−	5.95377i	0.738219	−	0.268690i	0.0545792	−	0.998509i	$-0.482618\pi$
$491$	16.3578	−	5.95377i	0.738219	−	0.268690i	0.683640	+	0.729820i	$0.260396\pi$
$492$		0			0
$493$	−0.858944	−	4.87131i	−0.0386849	−	0.219393i
$494$	4.34606	+	7.52760i	0.195539	+	0.338683i
$495$		0			0
$496$	−0.335846	+	0.581702i	−0.0150799	+	0.0261192i
$497$	−2.43145	−	0.884976i	−0.109065	−	0.0396966i
$498$		0			0
$499$	20.1341	+	16.8945i	0.901327	+	0.756303i	0.970449	−	0.241305i	$-0.0775754\pi$
$499$	20.1341	+	16.8945i	0.901327	+	0.756303i	−0.0691223	+	0.997608i	$0.522020\pi$
$500$	7.15592	+	6.00453i	0.320023	+	0.268531i
$501$		0			0
$502$	−13.6960	−	4.98493i	−0.611281	−	0.222488i
$503$	9.08930	−	15.7431i	0.405272	−	0.701952i	−0.589081	−	0.808074i	$-0.700510\pi$
$503$	9.08930	−	15.7431i	0.405272	−	0.701952i	0.994353	+	0.106122i	$0.0338435\pi$
$504$		0			0
$505$	4.29937	+	7.44672i	0.191319	+	0.331375i
$506$	0.111489	+	0.632284i	0.00495628	+	0.0281085i
$507$		0			0
$508$	−0.149608	+	0.0544529i	−0.00663779	+	0.00241596i
$509$	−4.27852	+	24.2647i	−0.189642	+	1.07551i	0.730203	+	0.683230i	$0.239426\pi$
$509$	−4.27852	+	24.2647i	−0.189642	+	1.07551i	−0.919845	+	0.392282i	$0.871686\pi$
$510$		0			0
$511$	−3.57370	+	2.99869i	−0.158091	+	0.132654i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−11.0246			−0.486275
$515$	5.43190	−	4.55791i	0.239358	−	0.200845i
$516$		0			0
$517$	−7.98336	+	45.2759i	−0.351108	+	1.99123i
$518$	2.27840	−	0.829268i	0.100107	−	0.0364360i
$519$		0			0
$520$	−2.88720	−	16.3741i	−0.126612	−	0.718054i
$521$	−15.0065	−	25.9921i	−0.657449	−	1.13873i	−0.981274	−	0.192618i	$-0.938302\pi$
$521$	−15.0065	−	25.9921i	−0.657449	−	1.13873i	0.323825	−	0.946117i	$-0.395031\pi$
$522$		0			0
$523$	13.6719	−	23.6804i	0.597829	−	1.03547i	−0.395312	−	0.918547i	$-0.629363\pi$
$523$	13.6719	−	23.6804i	0.597829	−	1.03547i	0.993141	−	0.116924i	$-0.0373033\pi$
$524$	8.91377	+	3.24435i	0.389400	+	0.141730i
$525$		0			0
$526$	−10.0659	−	8.44626i	−0.438893	−	0.368275i
$527$	0.583859	+	0.489916i	0.0254333	+	0.0213411i
$528$		0			0
$529$	21.5934	+	7.85935i	0.938843	+	0.341711i
$530$	−1.43134	+	2.47916i	−0.0621735	+	0.107688i
$531$		0			0
$532$	0.296783	+	0.514044i	0.0128672	+	0.0222866i
$533$	−1.76895	−	10.0322i	−0.0766218	−	0.434544i
$534$		0			0
$535$	−29.6226	+	10.7817i	−1.28070	+	0.466136i
$536$	1.29251	−	7.33017i	0.0558278	−	0.316615i
$537$		0			0
$538$	−7.89687	+	6.62626i	−0.340458	+	0.285678i
$539$	−30.7099			−1.32277
$540$		0			0
$541$	8.65632			0.372164			0.186082	−	0.982534i	$-0.440421\pi$
$541$	8.65632			0.372164			0.186082	+	0.982534i	$0.440421\pi$
$542$	0.777181	−	0.652132i	0.0333828	−	0.0280115i
$543$		0			0
$544$	0.197040	−	1.11747i	0.00844802	−	0.0479111i
$545$	6.58536	−	2.39687i	0.282086	−	0.102671i
$546$		0			0
$547$	4.78311	+	27.1263i	0.204511	+	1.15984i	0.898208	+	0.439571i	$0.144870\pi$
$547$	4.78311	+	27.1263i	0.204511	+	1.15984i	−0.693697	+	0.720267i	$0.744019\pi$
$548$	−5.85468	−	10.1406i	−0.250100	−	0.433185i
$549$		0			0
$550$	−16.9816	+	29.4130i	−0.724097	+	1.25417i
$551$	7.61015	+	2.76987i	0.324203	+	0.118000i
$552$		0			0
$553$	3.08069	+	2.58501i	0.131004	+	0.109926i
$554$	−8.29755	−	6.96247i	−0.352529	−	0.295807i
$555$		0			0
$556$	4.93364	+	1.79570i	0.209233	+	0.0761545i
$557$	13.0903	−	22.6730i	0.554653	−	0.960687i	−0.443278	−	0.896384i	$-0.646184\pi$
$557$	13.0903	−	22.6730i	0.554653	−	0.960687i	0.997930	−	0.0643022i	$-0.0204822\pi$
$558$		0			0
$559$	−16.6042	−	28.7592i	−0.702281	−	1.21639i
$560$	−0.197161	−	1.11816i	−0.00833157	−	0.0472507i
$561$		0			0
$562$	7.96552	−	2.89921i	0.336005	−	0.122296i
$563$	−0.689776	+	3.91192i	−0.0290706	+	0.164868i	−0.995887	−	0.0906050i	$-0.971120\pi$
$563$	−0.689776	+	3.91192i	−0.0290706	+	0.164868i	0.966816	+	0.255473i	$0.0822310\pi$
$564$		0			0
$565$	−26.2119	+	21.9944i	−1.10274	+	0.925310i
$566$	6.30428			0.264988
$567$		0			0
$568$	−8.09856			−0.339808
$569$	−31.0180	+	26.0272i	−1.30034	+	1.09112i	−0.310257	+	0.950653i	$0.600415\pi$
$569$	−31.0180	+	26.0272i	−1.30034	+	1.09112i	−0.990086	+	0.140464i	$0.955140\pi$
$570$		0			0
$571$	6.65098	−	37.7196i	0.278335	−	1.57852i	−0.449830	−	0.893114i	$-0.648515\pi$
$571$	6.65098	−	37.7196i	0.278335	−	1.57852i	0.728165	−	0.685402i	$-0.240374\pi$
$572$	19.5738	−	7.12428i	0.818421	−	0.297881i
$573$		0			0
$574$	−0.120798	−	0.685079i	−0.00504201	−	0.0285946i
$575$	−0.550070	−	0.952749i	−0.0229395	−	0.0397324i
$576$		0			0
$577$	−4.13928	+	7.16944i	−0.172320	+	0.298468i	−0.939231	−	0.343287i	$-0.888460\pi$
$577$	−4.13928	+	7.16944i	−0.172320	+	0.298468i	0.766910	+	0.641754i	$0.221793\pi$
$578$	14.7649	+	5.37397i	0.614137	+	0.223528i
$579$		0			0
$580$	−11.8671	−	9.95764i	−0.492752	−	0.413468i
$581$	1.32500	+	1.11180i	0.0549701	+	0.0461254i
$582$		0			0
$583$	−3.37009	−	1.22661i	−0.139575	−	0.0508011i
$584$	−7.30065	+	12.6451i	−0.302103	+	0.523258i
$585$		0			0
$586$	1.21653	+	2.10709i	0.0502543	+	0.0870430i
$587$	−2.42115	−	13.7310i	−0.0999314	−	0.566739i	−0.993124	−	0.117065i	$-0.962651\pi$
$587$	−2.42115	−	13.7310i	−0.0999314	−	0.566739i	0.893193	−	0.449674i	$-0.148460\pi$
$588$		0			0
$589$	−1.17261	+	0.426795i	−0.0483165	+	0.0175858i
$590$	1.84069	−	10.4391i	0.0757799	−	0.429769i
$591$		0			0
$592$	5.81333	−	4.87797i	0.238927	−	0.200483i
$593$	−41.2342			−1.69329			−0.846644	−	0.532160i	$-0.821380\pi$
$593$	−41.2342			−1.69329			−0.846644	+	0.532160i	$0.821380\pi$
$594$		0			0
$595$	−1.28835			−0.0528173
$596$	−12.4806	+	10.4725i	−0.511225	+	0.428968i
$597$		0			0
$598$	−0.117165	+	0.664478i	−0.00479125	+	0.0271725i
$599$	2.94710	−	1.07266i	0.120415	−	0.0438275i	−0.281110	−	0.959676i	$-0.590703\pi$
$599$	2.94710	−	1.07266i	0.120415	−	0.0438275i	0.401525	+	0.915848i	$0.368480\pi$
$600$		0			0
$601$	−6.04912	−	34.3063i	−0.246749	−	1.39938i	−0.816396	−	0.577493i	$-0.804031\pi$
$601$	−6.04912	−	34.3063i	−0.246749	−	1.39938i	0.569647	−	0.821890i	$-0.307080\pi$
$602$	−1.13386	−	1.96391i	−0.0462128	−	0.0800429i
$603$		0			0
$604$	7.80897	−	13.5255i	0.317742	−	0.550346i
$605$	−29.4559	−	10.7211i	−1.19755	−	0.435873i
$606$		0			0
$607$	−0.592309	−	0.497006i	−0.0240411	−	0.0201729i	0.630688	−	0.776037i	$-0.282773\pi$
$607$	−0.592309	−	0.497006i	−0.0240411	−	0.0201729i	−0.654729	+	0.755864i	$0.727217\pi$
$608$	1.42315	+	1.19417i	0.0577164	+	0.0484298i
$609$		0			0
$610$	11.6699	+	4.24749i	0.472500	+	0.171976i
$611$	−24.1576	+	41.8422i	−0.977312	+	1.69275i
$612$		0			0
$613$	−6.99919	−	12.1230i	−0.282695	−	0.489642i	0.689353	−	0.724426i	$-0.257895\pi$
$613$	−6.99919	−	12.1230i	−0.282695	−	0.489642i	−0.972048	+	0.234784i	$0.924562\pi$
$614$	−4.11993	−	23.3653i	−0.166267	−	0.942947i
$615$		0			0
$616$	1.33665	−	0.486502i	0.0538553	−	0.0196017i
$617$	2.03402	−	11.5355i	0.0818865	−	0.464402i	−0.916099	−	0.400953i	$-0.868679\pi$
$617$	2.03402	−	11.5355i	0.0818865	−	0.464402i	0.997985	−	0.0634485i	$-0.0202098\pi$
$618$		0			0
$619$	36.8005	−	30.8793i	1.47914	−	1.24114i	0.572037	−	0.820228i	$-0.306153\pi$
$619$	36.8005	−	30.8793i	1.47914	−	1.24114i	0.907100	−	0.420915i	$-0.138291\pi$
$620$	2.38698			0.0958634
$621$		0			0
$622$	−10.8006			−0.433065
$623$	−1.23660	+	1.03763i	−0.0495435	+	0.0415719i
$624$		0			0
$625$	−0.859024	+	4.87177i	−0.0343610	+	0.194871i
$626$	14.9328	−	5.43511i	0.596836	−	0.217231i
$627$		0			0
$628$	3.06168	+	17.3637i	0.122175	+	0.692886i
$629$	−4.30552	−	7.45738i	−0.171672	−	0.297345i
$630$		0			0
$631$	−19.7725	+	34.2469i	−0.787130	+	1.36335i	0.140589	+	0.990068i	$0.455100\pi$
$631$	−19.7725	+	34.2469i	−0.787130	+	1.36335i	−0.927719	+	0.373280i	$0.878233\pi$
$632$	11.8279	+	4.30501i	0.470489	+	0.171244i
$633$		0			0
$634$	−2.47819	−	2.07944i	−0.0984213	−	0.0825853i
$635$	0.433413	+	0.363677i	0.0171995	+	0.0144321i
$636$		0			0
$637$	−30.3272	−	11.0382i	−1.20161	−	0.437350i
$638$	9.70378	−	16.8074i	0.384176	−	0.665413i
$639$		0			0
$640$	−1.77684	−	3.07758i	−0.0702358	−	0.121652i
$641$	0.114836	+	0.651267i	0.00453575	+	0.0257235i	0.986992	−	0.160772i	$-0.0513983\pi$
$641$	0.114836	+	0.651267i	0.00453575	+	0.0257235i	−0.982456	+	0.186495i	$0.940287\pi$
$642$		0			0
$643$	−1.70408	+	0.620234i	−0.0672023	+	0.0244597i	−0.375403	−	0.926862i	$-0.622496\pi$
$643$	−1.70408	+	0.620234i	−0.0672023	+	0.0244597i	0.308200	+	0.951322i	$0.400273\pi$
$644$	−0.00800097	+	0.0453757i	−0.000315282	+	0.00178805i
$645$		0			0
$646$	1.61486	−	1.35503i	0.0635359	−	0.0533130i
$647$	4.13765			0.162668			0.0813339	−	0.996687i	$-0.474082\pi$
$647$	4.13765			0.162668			0.0813339	+	0.996687i	$0.474082\pi$
$648$		0			0
$649$	13.2798			0.521278
$650$	−27.3420	+	22.9427i	−1.07244	+	0.899885i
$651$		0			0
$652$	−2.75755	+	15.6388i	−0.107994	+	0.612464i
$653$	−25.2533	+	9.19145i	−0.988239	+	0.359689i	−0.785038	−	0.619448i	$-0.787357\pi$
$653$	−25.2533	+	9.19145i	−0.988239	+	0.359689i	−0.203201	+	0.979137i	$0.565134\pi$
$654$		0			0
$655$	−5.85362	−	33.1975i	−0.228720	−	1.29713i
$656$	−1.08865	−	1.88559i	−0.0425045	−	0.0736200i
$657$		0			0
$658$	−1.64967	+	2.85731i	−0.0643108	+	0.111390i
$659$	−13.5857	−	4.94480i	−0.529225	−	0.192622i	0.0635672	−	0.997978i	$-0.479752\pi$
$659$	−13.5857	−	4.94480i	−0.529225	−	0.192622i	−0.592792	+	0.805355i	$0.701975\pi$
$660$		0			0
$661$	17.0687	+	14.3223i	0.663894	+	0.557073i	0.911251	−	0.411851i	$-0.135118\pi$
$661$	17.0687	+	14.3223i	0.663894	+	0.557073i	−0.247357	+	0.968924i	$0.579562\pi$
$662$	−13.5311	−	11.3540i	−0.525903	−	0.441285i
$663$		0			0
$664$	5.08715	+	1.85157i	0.197420	+	0.0718548i
$665$	1.05467	−	1.82675i	0.0408985	−	0.0708382i
$666$		0			0
$667$	0.314326	+	0.544429i	0.0121708	+	0.0210804i
$668$	−2.35787	−	13.3721i	−0.0912286	−	0.517383i
$669$		0			0
$670$	−24.8557	+	9.04675i	−0.960261	+	0.349507i
$671$	−2.70168	+	15.3220i	−0.104297	+	0.591498i
$672$		0			0
$673$	19.0760	−	16.0067i	0.735327	−	0.617013i	−0.196251	−	0.980554i	$-0.562877\pi$
$673$	19.0760	−	16.0067i	0.735327	−	0.617013i	0.931578	+	0.363541i	$0.118432\pi$
$674$	−10.5429			−0.406096
$675$		0			0
$676$	8.89058			0.341945
$677$	6.11601	−	5.13194i	0.235057	−	0.197236i	−0.517649	−	0.855593i	$-0.673193\pi$
$677$	6.11601	−	5.13194i	0.235057	−	0.197236i	0.752706	+	0.658357i	$0.228748\pi$
$678$		0			0
$679$	−1.03605	+	5.87576i	−0.0397601	+	0.225491i
$680$	−3.78921	+	1.37916i	−0.145310	+	0.0528883i
$681$		0			0
$682$	0.519279	+	2.94498i	0.0198842	+	0.112769i
$683$	17.5306	+	30.3639i	0.670789	+	1.16184i	0.977681	+	0.210097i	$0.0673779\pi$
$683$	17.5306	+	30.3639i	0.670789	+	1.16184i	−0.306891	+	0.951745i	$0.599289\pi$
$684$		0			0
$685$	−20.8057	+	36.0365i	−0.794944	+	1.37688i
$686$	−4.17261	−	1.51871i	−0.159311	−	0.0579844i
$687$		0			0
$688$	−5.43716	−	4.56232i	−0.207290	−	0.173937i
$689$	−2.88720	−	2.42265i	−0.109994	−	0.0922957i
$690$		0			0
$691$	1.86251	+	0.677897i	0.0708531	+	0.0257884i	0.377204	−	0.926130i	$-0.376886\pi$
$691$	1.86251	+	0.677897i	0.0708531	+	0.0257884i	−0.306350	+	0.951919i	$0.599108\pi$
$692$	−3.22220	+	5.58102i	−0.122490	+	0.212159i
$693$		0			0
$694$	−16.2523	−	28.1499i	−0.616930	−	1.06855i
$695$	−3.23989	−	18.3743i	−0.122896	−	0.696978i
$696$		0			0
$697$	−2.32160	+	0.844993i	−0.0879368	+	0.0320064i
$698$	−3.48517	+	19.7654i	−0.131916	+	0.748131i
$699$		0			0
$700$	−1.86713	+	1.56671i	−0.0705708	+	0.0592159i
$701$	42.8694			1.61916			0.809578	−	0.587013i	$-0.199696\pi$
$701$	42.8694			1.61916			0.809578	+	0.587013i	$0.199696\pi$
$702$		0			0
$703$	14.0984			0.531730
$704$	3.41047	−	2.86173i	0.128537	−	0.107855i
$705$		0			0
$706$	1.91639	−	10.8684i	0.0721243	−	0.409037i
$707$	−0.726464	+	0.264411i	−0.0273215	+	0.00994420i
$708$		0			0
$709$	6.09810	+	34.5840i	0.229019	+	1.29883i	0.854851	+	0.518873i	$0.173648\pi$
$709$	6.09810	+	34.5840i	0.229019	+	1.29883i	−0.625832	+	0.779958i	$0.715240\pi$
$710$	14.3898	+	24.9239i	0.540041	+	0.935379i
$711$		0			0
$712$	−2.52624	+	4.37558i	−0.0946748	+	0.163982i
$713$	−0.0910241	−	0.0331300i	−0.00340888	−	0.00124073i
$714$		0			0
$715$	−56.7050	−	47.5812i	−2.12065	−	1.77943i
$716$	−9.58494	−	8.04272i	−0.358206	−	0.300571i
$717$		0			0
$718$	3.68441	+	1.34102i	0.137501	+	0.0500463i
$719$	−7.52422	+	13.0323i	−0.280606	+	0.486024i	−0.971534	−	0.236899i	$-0.923869\pi$
$719$	−7.52422	+	13.0323i	−0.280606	+	0.486024i	0.690928	+	0.722924i	$0.257202\pi$
$720$		0			0
$721$	0.318758	+	0.552105i	0.0118712	+	0.0205615i
$722$	−2.69999	−	15.3124i	−0.100483	−	0.569868i
$723$		0			0
$724$	−0.286139	+	0.104146i	−0.0106343	+	0.00387056i
$725$	−5.77469	+	32.7499i	−0.214466	+	1.21630i
$726$		0			0
$727$	11.2039	−	9.40117i	0.415529	−	0.348670i	−0.410930	−	0.911667i	$-0.634796\pi$
$727$	11.2039	−	9.40117i	0.415529	−	0.348670i	0.826459	+	0.562997i	$0.190352\pi$
$728$	1.49486			0.0554032
$729$		0			0
$730$	51.8884			1.92048
$731$	−6.16959	+	5.17690i	−0.228191	+	0.191475i
$732$		0			0
$733$	2.61774	−	14.8459i	0.0966885	−	0.548348i	−0.897528	−	0.440957i	$-0.854639\pi$
$733$	2.61774	−	14.8459i	0.0966885	−	0.548348i	0.994217	−	0.107391i	$-0.0342496\pi$
$734$	−27.3932	+	9.97031i	−1.01110	+	0.368011i
$735$		0			0
$736$	0.0250421	+	0.142021i	0.000923064	+	0.00523495i
$737$	−16.5689	−	28.6981i	−0.610322	−	1.05711i
$738$		0			0
$739$	−23.9031	+	41.4014i	−0.879290	+	1.52297i	−0.0271676	+	0.999631i	$0.508649\pi$
$739$	−23.9031	+	41.4014i	−0.879290	+	1.52297i	−0.852122	+	0.523343i	$0.824685\pi$
$740$	−25.3417	−	9.22362i	−0.931579	−	0.339067i
$741$		0			0
$742$	−0.197161	−	0.165438i	−0.00723800	−	0.00607341i
$743$	−35.6348	−	29.9011i	−1.30731	−	1.09697i	−0.988832	−	0.149036i	$-0.952383\pi$
$743$	−35.6348	−	29.9011i	−1.30731	−	1.09697i	−0.318481	−	0.947929i	$-0.603173\pi$
$744$		0			0
$745$	54.4058	+	19.8021i	1.99327	+	0.725492i
$746$	−3.13591	+	5.43155i	−0.114814	+	0.198863i
$747$		0			0
$748$	−2.52589	−	4.37497i	−0.0923558	−	0.159965i
$749$	−0.492154	−	2.79115i	−0.0179829	−	0.101986i
$750$		0			0
$751$	−1.65930	+	0.603936i	−0.0605488	+	0.0220379i	−0.372117	−	0.928186i	$-0.621368\pi$
$751$	−1.65930	+	0.603936i	−0.0605488	+	0.0220379i	0.311568	+	0.950224i	$0.399146\pi$
$752$	−1.79319	+	10.1697i	−0.0653908	+	0.370849i
$753$		0			0
$754$	15.6240	−	13.1101i	0.568993	−	0.477442i
$755$	−55.5012			−2.01989
$756$		0			0
$757$	3.34143			0.121446			0.0607232	−	0.998155i	$-0.480659\pi$
$757$	3.34143			0.121446			0.0607232	+	0.998155i	$0.480659\pi$
$758$	−20.6497	+	17.3271i	−0.750030	+	0.629350i
$759$		0			0
$760$	1.14643	−	6.50170i	0.0415852	−	0.235842i
$761$	−44.8723	+	16.3322i	−1.62662	+	0.592042i	−0.984627	−	0.174669i	$-0.944115\pi$
$761$	−44.8723	+	16.3322i	−1.62662	+	0.592042i	−0.641993	+	0.766710i	$0.721892\pi$
$762$		0			0
$763$	0.109410	+	0.620495i	0.00396091	+	0.0224634i
$764$	7.19635	+	12.4645i	0.260355	+	0.450948i
$765$		0			0
$766$	1.62814	−	2.82001i	0.0588269	−	0.101891i
$767$	13.1143	+	4.77322i	0.473530	+	0.172351i
$768$		0			0
$769$	−5.19772	−	4.36141i	−0.187435	−	0.157276i	0.544242	−	0.838928i	$-0.316817\pi$
$769$	−5.19772	−	4.36141i	−0.187435	−	0.157276i	−0.731677	+	0.681652i	$0.761262\pi$
$770$	−3.87226	−	3.24922i	−0.139547	−	0.117094i
$771$		0			0
$772$	−2.86665	−	1.04338i	−0.103173	−	0.0375519i
$773$	15.0683	−	26.0991i	0.541970	−	0.938720i	−0.456820	−	0.889559i	$-0.651012\pi$
$773$	15.0683	−	26.0991i	0.541970	−	0.938720i	0.998791	−	0.0491615i	$-0.0156549\pi$
$774$		0			0
$775$	−2.56205	−	4.43760i	−0.0920316	−	0.159403i
$776$	3.24273	+	18.3904i	0.116407	+	0.660178i
$777$		0			0
$778$	−1.30587	+	0.475299i	−0.0468178	+	0.0170403i
$779$	0.702400	−	3.98351i	0.0251661	−	0.142724i
$780$		0			0
$781$	−27.6199	+	23.1758i	−0.988318	+	0.829297i
$782$	0.163638			0.00585169
$783$		0			0
$784$	−6.89792			−0.246354
$785$	47.9979	−	40.2751i	1.71312	−	1.43748i
$786$		0			0
$787$	2.80522	−	15.9092i	0.0999954	−	0.567102i	−0.893106	−	0.449846i	$-0.851479\pi$
$787$	2.80522	−	15.9092i	0.0999954	−	0.567102i	0.993102	−	0.117256i	$-0.0374099\pi$
$788$	−20.9215	+	7.61480i	−0.745298	+	0.271266i
$789$		0			0
$790$	−7.76732	−	44.0507i	−0.276349	−	1.56725i
$791$	−1.53818	−	2.66421i	−0.0546914	−	0.0947284i
$792$		0			0
$793$	−8.17525	+	14.1599i	−0.290312	+	0.502835i
$794$	−2.01113	−	0.731993i	−0.0713724	−	0.0259774i
$795$		0			0
$796$	18.8167	+	15.7890i	0.666938	+	0.559628i
$797$	−0.422304	−	0.354355i	−0.0149588	−	0.0125519i	0.635278	−	0.772284i	$-0.280886\pi$
$797$	−0.422304	−	0.354355i	−0.0149588	−	0.0125519i	−0.650236	+	0.759732i	$0.725330\pi$
$798$		0			0
$799$	11.0110	+	4.00766i	0.389540	+	0.141781i
$800$	−3.81433	+	6.60661i	−0.134857	+	0.233579i
$801$		0			0
$802$	4.27666	+	7.40739i	0.151014	+	0.261564i
$803$	11.2881	+	64.0182i	0.398350	+	2.25915i
$804$		0			0
$805$	0.153864	−	0.0560019i	0.00542299	−	0.00197381i
$806$	−0.545719	+	3.09493i	−0.0192221	+	0.109014i
$807$		0			0
$808$	−1.85357	+	1.55533i	−0.0652085	+	0.0547164i
$809$	−3.04561			−0.107078			−0.0535389	−	0.998566i	$-0.517050\pi$
$809$	−3.04561			−0.107078			−0.0535389	+	0.998566i	$0.517050\pi$
$810$		0			0
$811$	−7.71732			−0.270992			−0.135496	−	0.990778i	$-0.543263\pi$
$811$	−7.71732			−0.270992			−0.135496	+	0.990778i	$0.543263\pi$
$812$	1.06693	−	0.895262i	0.0374419	−	0.0314175i
$813$		0			0
$814$	5.86681	−	33.2723i	0.205632	−	1.16619i
$815$	53.0294	−	19.3011i	1.85754	−	0.676089i
$816$		0			0
$817$	−2.28974	−	12.9857i	−0.0801078	−	0.454314i
$818$	−13.6359	−	23.6181i	−0.476769	−	0.825789i
$819$		0			0
$820$	−3.86870	+	6.70079i	−0.135101	+	0.234002i
$821$	−22.0399	−	8.02188i	−0.769199	−	0.279966i	−0.0725378	−	0.997366i	$-0.523110\pi$
$821$	−22.0399	−	8.02188i	−0.769199	−	0.279966i	−0.696661	+	0.717400i	$0.745332\pi$
$822$		0			0
$823$	−22.8881	−	19.2054i	−0.797830	−	0.669459i	0.149840	−	0.988710i	$-0.452124\pi$
$823$	−22.8881	−	19.2054i	−0.797830	−	0.669459i	−0.947670	+	0.319252i	$0.896568\pi$
$824$	1.52853	+	1.28259i	0.0532488	+	0.0446810i
$825$		0			0
$826$	0.895548	+	0.325953i	0.0311601	+	0.0113414i
$827$	9.72093	−	16.8371i	0.338030	−	0.585485i	−0.646032	−	0.763310i	$-0.723573\pi$
$827$	9.72093	−	16.8371i	0.338030	−	0.585485i	0.984062	+	0.177825i	$0.0569062\pi$
$828$		0			0
$829$	5.13594	+	8.89571i	0.178379	+	0.308961i	0.941325	−	0.337501i	$-0.109581\pi$
$829$	5.13594	+	8.89571i	0.178379	+	0.308961i	−0.762947	+	0.646461i	$0.776248\pi$
$830$	−3.34070	−	18.9460i	−0.115957	−	0.657627i
$831$		0			0
$832$	4.39657	−	1.60022i	0.152424	−	0.0554777i
$833$	−1.35917	+	7.70821i	−0.0470923	+	0.267074i
$834$		0			0
$835$	−36.9642	+	31.0167i	−1.27920	+	1.07338i
$836$	8.27099			0.286058
$837$		0			0
$838$	16.0153			0.553241
$839$	−10.3229	+	8.66197i	−0.356387	+	0.299044i	−0.803349	−	0.595509i	$-0.796951\pi$
$839$	−10.3229	+	8.66197i	−0.356387	+	0.299044i	0.446962	+	0.894553i	$0.352506\pi$
$840$		0			0
$841$	−1.73597	+	9.84519i	−0.0598611	+	0.339489i
$842$	17.0526	−	6.20665i	0.587672	−	0.213895i
$843$		0			0
$844$	−0.524297	−	2.97344i	−0.0180470	−	0.102350i
$845$	−15.7971	−	27.3614i	−0.543438	−	0.941262i
$846$		0			0
$847$	1.40913	−	2.44068i	0.0484181	−	0.0838627i
$848$	−0.756973	−	0.275516i	−0.0259946	−	0.00946125i
$849$		0			0
$850$	6.63111	+	5.56416i	0.227445	+	0.190849i
$851$	0.838350	+	0.703459i	0.0287383	+	0.0241143i
$852$		0			0
$853$	−44.6471	−	16.2502i	−1.52869	−	0.556397i	−0.565388	−	0.824825i	$-0.691274\pi$
$853$	−44.6471	−	16.2502i	−1.52869	−	0.556397i	−0.963300	+	0.268428i	$0.913496\pi$
$854$	−0.558270	+	0.966953i	−0.0191036	+	0.0330884i
$855$		0			0
$856$	−4.43536	−	7.68227i	−0.151598	−	0.262575i
$857$	4.03148	+	22.8636i	0.137713	+	0.781007i	0.972932	+	0.231091i	$0.0742293\pi$
$857$	4.03148	+	22.8636i	0.137713	+	0.781007i	−0.835220	+	0.549916i	$0.814660\pi$
$858$		0			0
$859$	−17.3565	+	6.31727i	−0.592198	+	0.215542i	−0.620696	−	0.784052i	$-0.713150\pi$
$859$	−17.3565	+	6.31727i	−0.592198	+	0.215542i	0.0284980	+	0.999594i	$0.490928\pi$
$860$	−4.37993	+	24.8398i	−0.149354	+	0.847030i
$861$		0			0
$862$	1.63702	−	1.37362i	0.0557571	−	0.0467857i
$863$	−21.1288			−0.719233			−0.359616	−	0.933100i	$-0.617092\pi$
$863$	−21.1288			−0.719233			−0.359616	+	0.933100i	$0.617092\pi$
$864$		0			0
$865$	22.9014			0.778670
$866$	19.2839	−	16.1811i	0.655293	−	0.549856i
$867$		0			0
$868$	−0.0372660	+	0.211346i	−0.00126489	+	0.00717354i
$869$	52.6585	−	19.1661i	1.78632	−	0.650167i
$870$		0			0
$871$	−6.04730	−	34.2959i	−0.204905	−	1.16207i
$872$	0.986018	+	1.70783i	0.0333908	+	0.0578345i
$873$		0			0
$874$	−0.133958	+	0.232021i	−0.00453118	+	0.00784824i
$875$	2.80459	+	1.02079i	0.0948125	+	0.0345089i
$876$		0			0
$877$	12.4202	+	10.4218i	0.419400	+	0.351919i	0.827935	−	0.560824i	$-0.189516\pi$
$877$	12.4202	+	10.4218i	0.419400	+	0.351919i	−0.408535	+	0.912743i	$0.633960\pi$
$878$	19.8037	+	16.6173i	0.668342	+	0.560806i
$879$		0			0
$880$	−14.8671	−	5.41116i	−0.501168	−	0.182410i
$881$	−22.2510	+	38.5398i	−0.749655	+	1.29844i	0.198333	+	0.980135i	$0.436447\pi$
$881$	−22.2510	+	38.5398i	−0.749655	+	1.29844i	−0.947988	+	0.318306i	$0.896886\pi$
$882$		0			0
$883$	−8.13325	−	14.0872i	−0.273706	−	0.474072i	0.696102	−	0.717943i	$-0.254916\pi$
$883$	−8.13325	−	14.0872i	−0.273706	−	0.474072i	−0.969808	+	0.243871i	$0.921583\pi$
$884$	−0.921898	−	5.22835i	−0.0310068	−	0.175848i
$885$		0			0
$886$	−13.0980	+	4.76727i	−0.440035	+	0.160160i
$887$	3.57171	−	20.2562i	0.119926	−	0.680136i	−0.864266	−	0.503035i	$-0.832217\pi$
$887$	3.57171	−	20.2562i	0.119926	−	0.680136i	0.984193	−	0.177102i	$-0.0566721\pi$
$888$		0			0
$889$	−0.0389669	+	0.0326971i	−0.00130691	+	0.00109663i
$890$	17.9549			0.601850
$891$		0			0
$892$	9.98040			0.334168
$893$	−14.6962	+	12.3316i	−0.491791	+	0.412662i
$894$		0			0
$895$	−7.72119	+	43.7891i	−0.258091	+	1.46371i
$896$	0.300233	−	0.109276i	0.0100301	−	0.00365065i
$897$		0			0
$898$	5.06251	+	28.7109i	0.168938	+	0.958095i
$899$	1.46403	+	2.53578i	0.0488282	+	0.0845729i
$900$		0			0
$901$	−0.457035	+	0.791607i	−0.0152260	+	0.0263723i
$902$	−9.10885	−	3.31535i	−0.303291	−	0.110389i
$903$		0			0
$904$	−7.37598	−	6.18918i	−0.245321	−	0.205849i
$905$	0.828941	+	0.695564i	0.0275549	+	0.0231213i
$906$		0			0
$907$	−15.5496	−	5.65959i	−0.516316	−	0.187924i	0.0707023	−	0.997497i	$-0.477476\pi$
$907$	−15.5496	−	5.65959i	−0.516316	−	0.187924i	−0.587018	+	0.809574i	$0.699698\pi$
$908$	10.5612	−	18.2925i	0.350485	−	0.607058i
$909$		0			0
$910$	−2.65613	−	4.60055i	−0.0880498	−	0.152507i
$911$	4.65954	+	26.4256i	0.154378	+	0.875519i	0.959353	+	0.282210i	$0.0910676\pi$
$911$	4.65954	+	26.4256i	0.154378	+	0.875519i	−0.804975	+	0.593309i	$0.797821\pi$
$912$		0			0
$913$	22.6483	−	8.24329i	0.749548	−	0.272813i
$914$	4.13251	−	23.4366i	0.136691	−	0.775214i
$915$		0			0
$916$	−17.8341	+	14.9646i	−0.589255	+	0.494443i
$917$	3.03073			0.100084
$918$		0			0
$919$	−26.3725			−0.869947			−0.434974	−	0.900443i	$-0.643242\pi$
$919$	−26.3725			−0.869947			−0.434974	+	0.900443i	$0.643242\pi$
$920$	0.392584	−	0.329417i	0.0129431	−	0.0108606i
$921$		0			0
$922$	5.35067	−	30.3452i	0.176215	−	0.999365i
$923$	−35.6059	+	12.9595i	−1.17198	+	0.426567i
$924$		0			0
$925$	10.0529	+	57.0126i	0.330536	+	1.87456i
$926$	−18.0701	−	31.2983i	−0.593819	−	1.02852i
$927$		0			0
$928$	2.17962	−	3.77521i	0.0715495	−	0.123927i
$929$	−40.2295	−	14.6423i	−1.31989	−	0.480400i	−0.416465	−	0.909152i	$-0.636731\pi$
$929$	−40.2295	−	14.6423i	−1.31989	−	0.480400i	−0.903422	+	0.428752i	$0.858953\pi$
$930$		0			0
$931$	−9.81679	−	8.23726i	−0.321732	−	0.269965i
$932$	20.4720	+	17.1780i	0.670583	+	0.562686i
$933$		0			0
$934$	34.7455	+	12.6463i	1.13691	+	0.413801i
$935$	−8.97622	+	15.5473i	−0.293554	+	0.508450i
$936$		0			0
$937$	7.07409	+	12.2527i	0.231100	+	0.400278i	0.958132	−	0.286326i	$-0.0924341\pi$
$937$	7.07409	+	12.2527i	0.231100	+	0.400278i	−0.727032	+	0.686604i	$0.759101\pi$
$938$	−0.412957	−	2.34200i	−0.0134835	−	0.0764689i
$939$		0			0
$940$	34.4841	−	12.5512i	1.12475	−	0.409375i
$941$	4.50073	−	25.5249i	0.146719	−	0.832087i	−0.819251	−	0.573435i	$-0.805610\pi$
$941$	4.50073	−	25.5249i	0.146719	−	0.832087i	0.965970	−	0.258652i	$-0.0832784\pi$
$942$		0			0
$943$	0.240531	−	0.201830i	0.00783277	−	0.00657247i
$944$	2.98285			0.0970834
$945$		0			0
$946$	−31.5994			−1.02738
$947$	12.5815	−	10.5572i	0.408845	−	0.343062i	−0.415055	−	0.909796i	$-0.636238\pi$
$947$	12.5815	−	10.5572i	0.408845	−	0.343062i	0.823901	+	0.566734i	$0.191793\pi$
$948$		0			0
$949$	−11.8629	+	67.2778i	−0.385086	+	2.18393i
$950$	−13.3178	+	4.84726i	−0.432085	+	0.157266i
$951$		0			0
$952$	−0.0629545	−	0.357033i	−0.00204037	−	0.0115715i
$953$	18.6267	+	32.2624i	0.603379	+	1.04508i	0.992305	+	0.123814i	$0.0395126\pi$
$953$	18.6267	+	32.2624i	0.603379	+	1.04508i	−0.388927	+	0.921269i	$0.627154\pi$
$954$		0			0
$955$	25.5736	−	44.2947i	0.827541	−	1.43334i
$956$	22.6089	+	8.22896i	0.731223	+	0.266144i
$957$		0			0
$958$	29.4015	+	24.6708i	0.949919	+	0.797077i
$959$	−2.86589	−	2.40477i	−0.0925443	−	0.0776539i
$960$		0			0
$961$	28.7065	+	10.4483i	0.926016	+	0.337042i
$962$	17.7529	−	30.7490i	0.572377	−	0.991386i
$963$		0			0
$964$	0.745760	+	1.29169i	0.0240193	+	0.0416027i
$965$	1.88251	+	10.6763i	0.0606002	+	0.343681i
$966$		0			0
$967$	9.35666	−	3.40554i	0.300890	−	0.109515i	−0.187163	−	0.982329i	$-0.559929\pi$
$967$	9.35666	−	3.40554i	0.300890	−	0.109515i	0.488053	+	0.872814i	$0.337707\pi$
$968$	1.53171	−	8.68679i	0.0492312	−	0.279204i
$969$		0			0
$970$	50.8362	−	42.6566i	1.63225	−	1.36962i
$971$	2.62332			0.0841864			0.0420932	−	0.999114i	$-0.486597\pi$
$971$	2.62332			0.0841864			0.0420932	+	0.999114i	$0.486597\pi$
$972$		0			0
$973$	1.67746			0.0537771
$974$	26.2820	−	22.0532i	0.842131	−	0.706631i
$975$		0			0
$976$	−0.606838	+	3.44155i	−0.0194244	+	0.110161i
$977$	6.23772	−	2.27034i	0.199562	−	0.0726348i	−0.240305	−	0.970697i	$-0.577248\pi$
$977$	6.23772	−	2.27034i	0.199562	−	0.0726348i	0.439868	+	0.898063i	$0.355025\pi$
$978$		0			0
$979$	3.90603	+	22.1522i	0.124837	+	0.707987i
$980$	12.2565	+	21.2289i	0.391520	+	0.678132i
$981$		0			0
$982$	8.70382	−	15.0755i	0.277750	−	0.481077i
$983$	44.5378	+	16.2104i	1.42054	+	0.517033i	0.934203	−	0.356741i	$-0.116112\pi$
$983$	44.5378	+	16.2104i	1.42054	+	0.517033i	0.486333	+	0.873774i	$0.338334\pi$
$984$		0			0
$985$	60.6093	+	50.8573i	1.93117	+	1.62045i
$986$	−3.78921	−	3.17952i	−0.120673	−	0.101257i
$987$		0			0
$988$	8.16792	+	2.97288i	0.259856	+	0.0945799i
$989$	0.511786	−	0.886440i	0.0162739	−	0.0281871i
$990$		0			0
$991$	−22.0574	−	38.2046i	−0.700678	−	1.21361i	−0.968229	−	0.250066i	$-0.919548\pi$
$991$	−22.0574	−	38.2046i	−0.700678	−	1.21361i	0.267551	−	0.963544i	$-0.413786\pi$
$992$	0.116638	+	0.661487i	0.00370326	+	0.0210022i
$993$		0			0
$994$	−2.43145	+	0.884976i	−0.0771209	+	0.0280697i
$995$	15.1578	−	85.9643i	0.480536	−	2.72525i
$996$		0			0
$997$	38.1602	−	32.0202i	1.20855	−	1.01409i	0.209203	−	0.977872i	$-0.432913\pi$
$997$	38.1602	−	32.0202i	1.20855	−	1.01409i	0.999344	−	0.0362193i	$-0.0115315\pi$
$998$	26.2832			0.831981
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	486.2.e.f.109.1		12
3.2	odd	2		486.2.e.g.109.2		12
9.2	odd	6		162.2.e.b.145.1		12
9.4	even	3		486.2.e.h.271.2		12
9.5	odd	6		486.2.e.e.271.1		12
9.7	even	3		54.2.e.b.31.1	yes	12
27.2	odd	18		162.2.e.b.19.1		12
27.4	even	9		1458.2.a.g.1.6		6
27.5	odd	18		1458.2.c.g.973.6		12
27.7	even	9		486.2.e.h.217.2		12
27.11	odd	18		486.2.e.g.379.2		12
27.13	even	9		1458.2.c.f.487.1		12
27.14	odd	18		1458.2.c.g.487.6		12
27.16	even	9	inner	486.2.e.f.379.1		12
27.20	odd	18		486.2.e.e.217.1		12
27.22	even	9		1458.2.c.f.973.1		12
27.23	odd	18		1458.2.a.f.1.1		6
27.25	even	9		54.2.e.b.7.1	✓	12
36.7	odd	6		432.2.u.b.193.2		12
108.79	odd	18		432.2.u.b.385.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.2.e.b.7.1	✓	12	27.25	even	9
54.2.e.b.31.1	yes	12	9.7	even	3
162.2.e.b.19.1		12	27.2	odd	18
162.2.e.b.145.1		12	9.2	odd	6
432.2.u.b.193.2		12	36.7	odd	6
432.2.u.b.385.2		12	108.79	odd	18
486.2.e.e.217.1		12	27.20	odd	18
486.2.e.e.271.1		12	9.5	odd	6
486.2.e.f.109.1		12	1.1	even	1	trivial
486.2.e.f.379.1		12	27.16	even	9	inner
486.2.e.g.109.2		12	3.2	odd	2
486.2.e.g.379.2		12	27.11	odd	18
486.2.e.h.217.2		12	27.7	even	9
486.2.e.h.271.2		12	9.4	even	3
1458.2.a.f.1.1		6	27.23	odd	18
1458.2.a.g.1.6		6	27.4	even	9
1458.2.c.f.487.1		12	27.13	even	9
1458.2.c.f.973.1		12	27.22	even	9
1458.2.c.g.487.6		12	27.14	odd	18
1458.2.c.g.973.6		12	27.5	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 486 = 2 \cdot 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	486.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 - 0.642788i) q^{2} +(0.173648 - 0.984808i) q^{4} +(-3.33937 + 1.21543i) q^{5} +(-0.0554807 - 0.314647i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-1.77684 + 3.07758i) q^{10} +(-4.18356 - 1.52269i) q^{11} +(-3.58412 - 3.00743i) q^{13} +(-0.244752 - 0.205371i) q^{14} +(-0.939693 - 0.342020i) q^{16} +(-0.567354 + 0.982686i) q^{17} +(-0.928896 - 1.60890i) q^{19} +(0.617090 + 3.49969i) q^{20} +(-4.18356 + 1.52269i) q^{22} +(0.0250421 - 0.142021i) q^{23} +(5.84389 - 4.90360i) q^{25} -4.67874 q^{26} -0.319501 q^{28} +(-3.33937 + 2.80206i) q^{29} +(0.116638 - 0.661487i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(0.197040 + 1.11747i) q^{34} +(0.567702 + 0.983289i) q^{35} +(-3.79438 + 6.57207i) q^{37} +(-1.74575 - 0.635402i) q^{38} +(2.72228 + 2.28426i) q^{40} +(1.66790 + 1.39954i) q^{41} +(6.66967 + 2.42756i) q^{43} +(-2.22603 + 3.85559i) q^{44} +(-0.0721058 - 0.124891i) q^{46} +(-1.79319 - 10.1697i) q^{47} +(6.48192 - 2.35923i) q^{49} +(1.32470 - 7.51276i) q^{50} +(-3.58412 + 3.00743i) q^{52} +0.805554 q^{53} +15.8212 q^{55} +(-0.244752 + 0.205371i) q^{56} +(-0.756973 + 4.29301i) q^{58} +(-2.80296 + 1.02019i) q^{59} +(-0.606838 - 3.44155i) q^{61} +(-0.335846 - 0.581702i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(15.6240 + 5.68668i) q^{65} +(5.70186 + 4.78443i) q^{67} +(0.869237 + 0.729376i) q^{68} +(1.06693 + 0.388331i) q^{70} +(4.04928 - 7.01356i) q^{71} +(-7.30065 - 12.6451i) q^{73} +(1.31778 + 7.47348i) q^{74} +(-1.74575 + 0.635402i) q^{76} +(-0.247003 + 1.40083i) q^{77} +(-9.64221 + 8.09077i) q^{79} +3.55368 q^{80} +2.17729 q^{82} +(-4.14708 + 3.47981i) q^{83} +(0.700218 - 3.97113i) q^{85} +(6.66967 - 2.42756i) q^{86} +(0.773091 + 4.38442i) q^{88} +(-2.52624 - 4.37558i) q^{89} +(-0.747430 + 1.29459i) q^{91} +(-0.135515 - 0.0493233i) q^{92} +(-7.91059 - 6.63778i) q^{94} +(5.05743 + 4.24369i) q^{95} +(-17.5479 - 6.38693i) q^{97} +(3.44896 - 5.97377i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{5} + 6 q^{7} - 6 q^{8} - 3 q^{10} + 6 q^{11} - 6 q^{13} - 3 q^{14} - 6 q^{17} - 9 q^{19} - 3 q^{20} + 6 q^{22} - 6 q^{23} - 27 q^{25} + 18 q^{26} + 12 q^{28} - 3 q^{29} - 27 q^{31} + 12 q^{34}+ \cdots - 12 q^{98}+O(q^{100}) \) 12 * q - 3 * q^5 + 6 * q^7 - 6 * q^8 - 3 * q^10 + 6 * q^11 - 6 * q^13 - 3 * q^14 - 6 * q^17 - 9 * q^19 - 3 * q^20 + 6 * q^22 - 6 * q^23 - 27 * q^25 + 18 * q^26 + 12 * q^28 - 3 * q^29 - 27 * q^31 + 12 * q^34 + 3 * q^35 - 15 * q^37 - 15 * q^38 + 6 * q^40 + 15 * q^41 + 18 * q^43 - 3 * q^44 + 3 * q^46 - 27 * q^47 + 42 * q^49 + 36 * q^50 - 6 * q^52 - 12 * q^53 + 18 * q^55 - 3 * q^56 - 12 * q^58 - 24 * q^59 + 27 * q^61 - 12 * q^62 - 6 * q^64 + 57 * q^65 + 9 * q^67 - 15 * q^68 - 6 * q^70 + 12 * q^71 - 21 * q^73 - 3 * q^74 - 15 * q^76 - 51 * q^77 - 42 * q^79 + 6 * q^80 + 6 * q^82 - 45 * q^85 + 18 * q^86 - 12 * q^88 + 12 * q^89 - 6 * q^91 - 24 * q^92 - 9 * q^94 + 48 * q^95 - 24 * q^97 - 12 * q^98

Introduction

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