LMFDB - Embedded newform 567.2.ba.a.143.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(143,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([7, 3]))

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

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

chi := DirichletCharacter("567.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.ba (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			143.8
Character	$\chi$	$=$	567.143
Dual form			567.2.ba.a.341.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.594351 + 0.708320i) q^{2} +(0.198832 + 1.12763i) q^{4} +(0.386349 - 0.324185i) q^{5} +(0.529787 - 2.59217i) q^{7} +(-2.51844 - 1.45402i) q^{8} +0.466338i q^{10} +(-3.12271 + 3.72150i) q^{11} +(-1.60911 + 4.42100i) q^{13} +(1.52120 + 1.91591i) q^{14} +(0.374792 - 0.136413i) q^{16} +4.77392 q^{17} +6.37115i q^{19} +(0.442381 + 0.371202i) q^{20} +(-0.780028 - 4.42376i) q^{22} +(-1.22699 + 3.37113i) q^{23} +(-0.824071 + 4.67354i) q^{25} +(-2.17510 - 3.76739i) q^{26} +(3.02836 + 0.0819996i) q^{28} +(-0.997075 - 2.73944i) q^{29} +(-0.773023 + 0.136305i) q^{31} +(1.86308 - 5.11878i) q^{32} +(-2.83739 + 3.38147i) q^{34} +(-0.635660 - 1.17323i) q^{35} +(2.73726 - 4.74107i) q^{37} +(-4.51281 - 3.78670i) q^{38} +(-1.44437 + 0.254681i) q^{40} +(-5.44849 - 1.98309i) q^{41} +(-1.36729 + 7.75429i) q^{43} +(-4.81739 - 2.78132i) q^{44} +(-1.65857 - 2.87274i) q^{46} +(-1.33467 + 7.56931i) q^{47} +(-6.43865 - 2.74659i) q^{49} +(-2.82057 - 3.36143i) q^{50} +(-5.30521 - 0.935452i) q^{52} +(4.26125 + 2.46023i) q^{53} +2.45014i q^{55} +(-5.10329 + 5.75788i) q^{56} +(2.53301 + 0.921941i) q^{58} +(5.01169 + 1.82411i) q^{59} +(-7.07246 - 1.24706i) q^{61} +(0.362900 - 0.628561i) q^{62} +(2.91725 + 5.05283i) q^{64} +(0.811544 + 2.22970i) q^{65} +(6.70384 - 5.62519i) q^{67} +(0.949211 + 5.38324i) q^{68} +(1.20883 + 0.247060i) q^{70} +(11.3110 - 6.53043i) q^{71} +(8.42907 - 4.86653i) q^{73} +(1.73130 + 4.75671i) q^{74} +(-7.18433 + 1.26679i) q^{76} +(7.99238 + 10.0662i) q^{77} +(-3.63977 - 3.05413i) q^{79} +(0.100577 - 0.174205i) q^{80} +(4.64298 - 2.68063i) q^{82} +(-2.75845 + 1.00400i) q^{83} +(1.84440 - 1.54764i) q^{85} +(-4.67987 - 5.57725i) q^{86} +(13.2755 - 4.83188i) q^{88} -11.2094 q^{89} +(10.6075 + 6.51327i) q^{91} +(-4.04537 - 0.713308i) q^{92} +(-4.56823 - 5.44420i) q^{94} +(2.06543 + 2.46149i) q^{95} +(-2.41733 - 0.426241i) q^{97} +(5.77228 - 2.92818i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} + 9 q^{11} - 3 q^{14} + 3 q^{16} + 18 q^{17} - 18 q^{20} - 12 q^{22} + 6 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} - 3 q^{32} - 18 q^{34}+ \cdots - 27 q^{98}+O(q^{100}) $ 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 + 9 * q^11 - 3 * q^14 + 3 * q^16 + 18 * q^17 - 18 * q^20 - 12 * q^22 + 6 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 - 3 * q^32 - 18 * q^34 - 18 * q^35 + 3 * q^37 + 99 * q^38 - 54 * q^40 - 12 * q^43 + 9 * q^44 + 3 * q^46 - 45 * q^47 - 24 * q^49 + 9 * q^50 - 9 * q^52 + 45 * q^53 - 3 * q^56 - 3 * q^58 - 36 * q^59 - 9 * q^61 + 99 * q^62 + 18 * q^64 - 69 * q^65 - 3 * q^67 - 36 * q^68 + 66 * q^70 - 18 * q^71 - 9 * q^73 - 75 * q^74 + 36 * q^76 - 15 * q^77 - 21 * q^79 - 72 * q^80 - 18 * q^82 + 90 * q^83 + 9 * q^85 + 105 * q^86 - 63 * q^88 + 18 * q^89 + 6 * q^91 - 150 * q^92 - 9 * q^94 - 45 * q^95 - 27 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{18}\right)$

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 $

$2$	−0.594351	+	0.708320i	−0.420270	+	0.500858i	−0.934089	−	0.357041i	$-0.883786\pi$
$2$	−0.594351	+	0.708320i	−0.420270	+	0.500858i	0.513819	+	0.857898i	$0.328230\pi$
$3$		0			0
$3$		0			0
$4$	0.198832	+	1.12763i	0.0994162	+	0.563817i
$5$	0.386349	−	0.324185i	0.172781	−	0.144980i	−0.552297	−	0.833648i	$-0.686248\pi$
$5$	0.386349	−	0.324185i	0.172781	−	0.144980i	0.725077	+	0.688667i	$0.241804\pi$
$6$		0			0
$7$	0.529787	−	2.59217i	0.200241	−	0.979747i
$7$	0.529787	−	2.59217i	0.200241	−	0.979747i
$8$	−2.51844	−	1.45402i	−0.890401	−	0.514073i
$9$		0			0
$10$			0.466338i			0.147469i
$11$	−3.12271	+	3.72150i	−0.941533	+	1.12208i	0.0508281	+	0.998707i	$0.483814\pi$
$11$	−3.12271	+	3.72150i	−0.941533	+	1.12208i	−0.992361	+	0.123368i	$0.960631\pi$
$12$		0			0
$13$	−1.60911	+	4.42100i	−0.446287	+	1.22616i	0.489003	+	0.872282i	$0.337361\pi$
$13$	−1.60911	+	4.42100i	−0.446287	+	1.22616i	−0.935290	+	0.353882i	$0.884862\pi$
$14$	1.52120	+	1.91591i	0.406559	+	0.512050i
$15$		0			0
$16$	0.374792	−	0.136413i	0.0936980	−	0.0341033i
$17$	4.77392			1.15785			0.578923	−	0.815382i	$-0.303473\pi$
$17$	4.77392			1.15785			0.578923	+	0.815382i	$0.303473\pi$
$18$		0			0
$19$			6.37115i			1.46164i	0.682569	+	0.730821i	$0.260863\pi$
$19$			6.37115i			1.46164i	−0.682569	+	0.730821i	$0.739137\pi$
$20$	0.442381	+	0.371202i	0.0989195	+	0.0830033i
$21$		0			0
$22$	−0.780028	−	4.42376i	−0.166302	−	0.943148i
$23$	−1.22699	+	3.37113i	−0.255845	+	0.702929i	0.743567	+	0.668661i	$0.233132\pi$
$23$	−1.22699	+	3.37113i	−0.255845	+	0.702929i	−0.999413	+	0.0342682i	$0.989090\pi$
$24$		0			0
$25$	−0.824071	+	4.67354i	−0.164814	+	0.934708i
$26$	−2.17510	−	3.76739i	−0.426573	−	0.738846i
$27$		0			0
$28$	3.02836	+	0.0819996i	0.572305	+	0.0154965i
$29$	−0.997075	−	2.73944i	−0.185152	−	0.508701i	0.812039	−	0.583604i	$-0.198358\pi$
$29$	−0.997075	−	2.73944i	−0.185152	−	0.508701i	−0.997191	+	0.0749022i	$0.976136\pi$
$30$		0			0
$31$	−0.773023	+	0.136305i	−0.138839	+	0.0244811i	−0.242636	−	0.970117i	$-0.578012\pi$
$31$	−0.773023	+	0.136305i	−0.138839	+	0.0244811i	0.103797	+	0.994599i	$0.466901\pi$
$32$	1.86308	−	5.11878i	0.329349	−	0.904880i
$33$		0			0
$34$	−2.83739	+	3.38147i	−0.486608	+	0.579916i
$35$	−0.635660	−	1.17323i	−0.107446	−	0.198312i
$36$		0			0
$37$	2.73726	−	4.74107i	0.450002	−	0.779426i	−0.548383	−	0.836227i	$-0.684757\pi$
$37$	2.73726	−	4.74107i	0.450002	−	0.779426i	0.998386	+	0.0568005i	$0.0180899\pi$
$38$	−4.51281	−	3.78670i	−0.732075	−	0.614284i
$39$		0			0
$40$	−1.44437	+	0.254681i	−0.228374	+	0.0402686i
$41$	−5.44849	−	1.98309i	−0.850912	−	0.309707i	−0.120500	−	0.992713i	$-0.538450\pi$
$41$	−5.44849	−	1.98309i	−0.850912	−	0.309707i	−0.730412	+	0.683007i	$0.760672\pi$
$42$		0			0
$43$	−1.36729	+	7.75429i	−0.208510	+	1.18252i	0.683310	+	0.730128i	$0.260540\pi$
$43$	−1.36729	+	7.75429i	−0.208510	+	1.18252i	−0.891820	+	0.452390i	$0.850571\pi$
$44$	−4.81739	−	2.78132i	−0.726249	−	0.419300i
$45$		0			0
$46$	−1.65857	−	2.87274i	−0.244544	−	0.423562i
$47$	−1.33467	+	7.56931i	−0.194682	+	1.10410i	0.718188	+	0.695849i	$0.244972\pi$
$47$	−1.33467	+	7.56931i	−0.194682	+	1.10410i	−0.912871	+	0.408249i	$0.866139\pi$
$48$		0			0
$49$	−6.43865	−	2.74659i	−0.919807	−	0.392370i
$50$	−2.82057	−	3.36143i	−0.398889	−	0.475378i
$51$		0			0
$52$	−5.30521	−	0.935452i	−0.735700	−	0.129724i
$53$	4.26125	+	2.46023i	0.585328	+	0.337939i	0.763248	−	0.646106i	$-0.223604\pi$
$53$	4.26125	+	2.46023i	0.585328	+	0.337939i	−0.177920	+	0.984045i	$0.556937\pi$
$54$		0			0
$55$			2.45014i			0.330376i
$56$	−5.10329	+	5.75788i	−0.681956	+	0.769429i
$57$		0			0
$58$	2.53301	+	0.921941i	0.332601	+	0.121057i
$59$	5.01169	+	1.82411i	0.652467	+	0.237478i	0.646981	−	0.762507i	$-0.276031\pi$
$59$	5.01169	+	1.82411i	0.652467	+	0.237478i	0.00548607	+	0.999985i	$0.498254\pi$
$60$		0			0
$61$	−7.07246	−	1.24706i	−0.905535	−	0.159670i	−0.298560	−	0.954391i	$-0.596506\pi$
$61$	−7.07246	−	1.24706i	−0.905535	−	0.159670i	−0.606975	+	0.794721i	$0.707617\pi$
$62$	0.362900	−	0.628561i	0.0460883	−	0.0798273i
$63$		0			0
$64$	2.91725	+	5.05283i	0.364656	+	0.631603i
$65$	0.811544	+	2.22970i	0.100660	+	0.276560i
$66$		0			0
$67$	6.70384	−	5.62519i	0.819005	−	0.687227i	−0.133734	−	0.991017i	$-0.542697\pi$
$67$	6.70384	−	5.62519i	0.819005	−	0.687227i	0.952739	+	0.303790i	$0.0982523\pi$
$68$	0.949211	+	5.38324i	0.115109	+	0.652814i
$69$		0			0
$70$	1.20883	+	0.247060i	0.144482	+	0.0295293i
$71$	11.3110	−	6.53043i	1.34237	−	0.775019i	0.355217	−	0.934784i	$-0.384407\pi$
$71$	11.3110	−	6.53043i	1.34237	−	0.775019i	0.987155	+	0.159764i	$0.0510735\pi$
$72$		0			0
$73$	8.42907	−	4.86653i	0.986548	−	0.569584i	0.0823076	−	0.996607i	$-0.473771\pi$
$73$	8.42907	−	4.86653i	0.986548	−	0.569584i	0.904241	+	0.427023i	$0.140438\pi$
$74$	1.73130	+	4.75671i	0.201260	+	0.552956i
$75$		0			0
$76$	−7.18433	+	1.26679i	−0.824099	+	0.145311i
$77$	7.99238	+	10.0662i	0.910816	+	1.14715i
$78$		0			0
$79$	−3.63977	−	3.05413i	−0.409506	−	0.343617i	0.414648	−	0.909982i	$-0.363905\pi$
$79$	−3.63977	−	3.05413i	−0.409506	−	0.343617i	−0.824154	+	0.566365i	$0.808349\pi$
$80$	0.100577	−	0.174205i	0.0112449	−	0.0194767i
$81$		0			0
$82$	4.64298	−	2.68063i	0.512731	−	0.296026i
$83$	−2.75845	+	1.00400i	−0.302780	+	0.110203i	−0.488942	−	0.872316i	$-0.662617\pi$
$83$	−2.75845	+	1.00400i	−0.302780	+	0.110203i	0.186163	+	0.982519i	$0.440395\pi$
$84$		0			0
$85$	1.84440	−	1.54764i	0.200053	−	0.167865i
$86$	−4.67987	−	5.57725i	−0.504643	−	0.601410i
$87$		0			0
$88$	13.2755	−	4.83188i	1.41517	−	0.515080i
$89$	−11.2094			−1.18819			−0.594097	−	0.804394i	$-0.702490\pi$
$89$	−11.2094			−1.18819			−0.594097	+	0.804394i	$0.702490\pi$
$90$		0			0
$91$	10.6075	+	6.51327i	1.11197	+	0.682776i
$92$	−4.04537	−	0.713308i	−0.421759	−	0.0743675i
$93$		0			0
$94$	−4.56823	−	5.44420i	−0.471177	−	0.561527i
$95$	2.06543	+	2.46149i	0.211909	+	0.252543i
$96$		0			0
$97$	−2.41733	−	0.426241i	−0.245443	−	0.0432783i	0.0495730	−	0.998771i	$-0.484214\pi$
$97$	−2.41733	−	0.426241i	−0.245443	−	0.0432783i	−0.295016	+	0.955492i	$0.595325\pi$
$98$	5.77228	−	2.92818i	0.583089	−	0.295791i
$99$		0			0
$100$	−5.43390			−0.543390
$101$	5.68215	−	2.06813i	0.565395	−	0.205787i	−0.0434782	−	0.999054i	$-0.513844\pi$
$101$	5.68215	−	2.06813i	0.565395	−	0.205787i	0.608874	+	0.793267i	$0.291622\pi$
$102$		0			0
$103$	−6.28671	−	7.49221i	−0.619448	−	0.738229i	0.361528	−	0.932361i	$-0.382255\pi$
$103$	−6.28671	−	7.49221i	−0.619448	−	0.738229i	−0.980975	+	0.194132i	$0.937811\pi$
$104$	10.4807	−	8.79431i	1.02771	−	0.862354i
$105$		0			0
$106$	−4.27531	+	1.55609i	−0.415255	+	0.151140i
$107$	−13.9175	+	8.03528i	−1.34546	+	0.776800i	−0.987602	−	0.156977i	$-0.949825\pi$
$107$	−13.9175	+	8.03528i	−1.34546	+	0.776800i	−0.357855	+	0.933777i	$0.616492\pi$
$108$		0			0
$109$	7.22285	−	12.5103i	0.691823	−	1.19827i	−0.279417	−	0.960170i	$-0.590141\pi$
$109$	7.22285	−	12.5103i	0.691823	−	1.19827i	0.971240	−	0.238103i	$-0.0765256\pi$
$110$	−1.73548	−	1.45624i	−0.165472	−	0.138847i
$111$		0			0
$112$	−0.155046	−	1.04379i	−0.0146504	−	0.0986292i
$113$	1.50934	−	0.266138i	0.141987	−	0.0250361i	−0.102203	−	0.994764i	$-0.532589\pi$
$113$	1.50934	−	0.266138i	0.141987	−	0.0250361i	0.244190	+	0.969727i	$0.421478\pi$
$114$		0			0
$115$	0.618824	+	1.70021i	0.0577056	+	0.158545i
$116$	2.89084	−	1.66903i	0.268407	−	0.154965i
$117$		0			0
$118$	−4.27075	+	2.46572i	−0.393155	+	0.226988i
$119$	2.52916	−	12.3748i	0.231848	−	1.13440i
$120$		0			0
$121$	−2.18812	−	12.4095i	−0.198920	−	1.12813i
$122$	5.08684	−	4.26837i	0.460541	−	0.386440i
$123$		0			0
$124$	−0.307404	−	0.844586i	−0.0276057	−	0.0758461i
$125$	2.45757	+	4.25664i	0.219812	+	0.380725i
$126$		0			0
$127$	5.33708	−	9.24410i	0.473590	−	0.820281i	−0.525953	−	0.850513i	$-0.676291\pi$
$127$	5.33708	−	9.24410i	0.473590	−	0.820281i	0.999543	+	0.0302322i	$0.00962466\pi$
$128$	5.41617	+	0.955018i	0.478727	+	0.0844124i
$129$		0			0
$130$	−2.06168	−	0.750390i	−0.180821	−	0.0658136i
$131$	8.65448	+	3.14997i	0.756146	+	0.275215i	0.691189	−	0.722674i	$-0.257087\pi$
$131$	8.65448	+	3.14997i	0.756146	+	0.275215i	0.0649563	+	0.997888i	$0.479309\pi$
$132$		0			0
$133$	16.5151	+	3.37535i	1.43204	+	0.292680i
$134$			8.09180i			0.699025i
$135$		0			0
$136$	−12.0228	−	6.94138i	−1.03095	−	0.595218i
$137$	14.6628	+	2.58546i	1.25273	+	0.220890i	0.760364	−	0.649497i	$-0.225020\pi$
$137$	14.6628	+	2.58546i	1.25273	+	0.220890i	0.492368	+	0.870387i	$0.336132\pi$
$138$		0			0
$139$	6.89067	+	8.21198i	0.584459	+	0.696531i	0.974531	−	0.224254i	$-0.0719944\pi$
$139$	6.89067	+	8.21198i	0.584459	+	0.696531i	−0.390072	+	0.920784i	$0.627550\pi$
$140$	1.19659	−	0.950068i	0.101130	−	0.0802954i
$141$		0			0
$142$	−2.09709	+	11.8932i	−0.175984	+	0.998055i
$143$	−11.4280	−	19.7938i	−0.955654	−	1.65524i
$144$		0			0
$145$	−1.27331	−	0.735143i	−0.105742	−	0.0610503i
$146$	−1.56277	+	8.86290i	−0.129336	+	0.733499i
$147$		0			0
$148$	5.89045	+	2.14395i	0.484192	+	0.176231i
$149$	2.09925	−	0.370154i	0.171977	−	0.0303242i	−0.0869964	−	0.996209i	$-0.527727\pi$
$149$	2.09925	−	0.370154i	0.171977	−	0.0303242i	0.258974	+	0.965884i	$0.416616\pi$
$150$		0			0
$151$	5.09411	+	4.27446i	0.414552	+	0.347851i	0.826086	−	0.563544i	$-0.190562\pi$
$151$	5.09411	+	4.27446i	0.414552	+	0.347851i	−0.411534	+	0.911394i	$0.635007\pi$
$152$	9.26378	−	16.0453i	0.751391	−	1.30145i
$153$		0			0
$154$	−11.8804	−	0.321688i	−0.957347	−	0.0259223i
$155$	−0.254469	+	0.303264i	−0.0204394	+	0.0243588i
$156$		0			0
$157$	0.202620	−	0.556695i	0.0161709	−	0.0444291i	−0.931345	−	0.364139i	$-0.881363\pi$
$157$	0.202620	−	0.556695i	0.0161709	−	0.0444291i	0.947515	+	0.319710i	$0.103585\pi$
$158$	4.32660	−	0.762897i	0.344206	−	0.0606928i
$159$		0			0
$160$	−0.939632	−	2.58162i	−0.0742844	−	0.204095i
$161$	8.08848	+	4.96655i	0.637462	+	0.391419i
$162$		0			0
$163$	9.38783	+	16.2602i	0.735311	+	1.27360i	0.954587	+	0.297934i	$0.0962975\pi$
$163$	9.38783	+	16.2602i	0.735311	+	1.27360i	−0.219275	+	0.975663i	$0.570369\pi$
$164$	1.15286	−	6.53821i	0.0900235	−	0.510549i
$165$		0			0
$166$	0.928340	−	2.55059i	0.0720531	−	0.197964i
$167$	2.39928	+	13.6070i	0.185662	+	1.05294i	0.925102	+	0.379718i	$0.123979\pi$
$167$	2.39928	+	13.6070i	0.185662	+	1.05294i	−0.739441	+	0.673221i	$0.764910\pi$
$168$		0			0
$169$	−6.99739	−	5.87151i	−0.538261	−	0.451654i
$170$			2.22626i			0.170747i
$171$		0			0
$172$	−9.01587			−0.687454
$173$	−4.13775	+	1.50602i	−0.314588	+	0.114501i	−0.494488	−	0.869184i	$-0.664645\pi$
$173$	−4.13775	+	1.50602i	−0.314588	+	0.114501i	0.179901	+	0.983685i	$0.442422\pi$
$174$		0			0
$175$	11.6780	+	4.61211i	0.882775	+	0.348643i
$176$	−0.662705	+	1.82077i	−0.0499533	+	0.137246i
$177$		0			0
$178$	6.66231	−	7.93983i	0.499361	−	0.595116i
$179$		−	3.01335i		−	0.225228i	−0.993639	−	0.112614i	$-0.964078\pi$
$179$		−	3.01335i		−	0.225228i	0.993639	−	0.112614i	$-0.0359224\pi$
$180$		0			0
$181$	1.98157	+	1.14406i	0.147289	+	0.0850373i	0.571833	−	0.820370i	$-0.306232\pi$
$181$	1.98157	+	1.14406i	0.147289	+	0.0850373i	−0.424544	+	0.905407i	$0.639566\pi$
$182$	−10.9180	+	3.64231i	−0.809299	+	0.269986i
$183$		0			0
$184$	7.99179	−	6.70590i	0.589162	−	0.494366i
$185$	−0.479448	−	2.71908i	−0.0352497	−	0.199911i
$186$		0			0
$187$	−14.9076	+	17.7662i	−1.09015	+	1.29919i
$188$	−8.80080			−0.641864
$189$		0			0
$190$	−2.97111			−0.215547
$191$	8.45281	−	10.0737i	0.611624	−	0.728905i	−0.367982	−	0.929833i	$-0.619951\pi$
$191$	8.45281	−	10.0737i	0.611624	−	0.728905i	0.979606	+	0.200928i	$0.0643956\pi$
$192$		0			0
$193$	−0.00650905	−	0.0369147i	−0.000468532	−	0.00265717i	0.984573	−	0.174977i	$-0.0559850\pi$
$193$	−0.00650905	−	0.0369147i	−0.000468532	−	0.00265717i	−0.985041	+	0.172319i	$0.944874\pi$
$194$	1.73866	−	1.45891i	0.124829	−	0.104744i
$195$		0			0
$196$	1.81694	−	7.80656i	0.129781	−	0.557611i
$197$	4.43094	+	2.55821i	0.315692	+	0.182265i	0.649471	−	0.760387i	$-0.274991\pi$
$197$	4.43094	+	2.55821i	0.315692	+	0.182265i	−0.333779	+	0.942651i	$0.608324\pi$
$198$		0			0
$199$			6.17488i			0.437726i	0.975756	+	0.218863i	$0.0702348\pi$
$199$			6.17488i			0.437726i	−0.975756	+	0.218863i	$0.929765\pi$
$200$	8.87079	−	10.5718i	0.627260	−	0.747539i
$201$		0			0
$202$	−1.91229	+	5.25398i	−0.134548	+	0.369669i
$203$	−7.62932	+	1.13326i	−0.535473	+	0.0795395i
$204$		0			0
$205$	−2.74791	+	1.00016i	−0.191922	+	0.0698540i
$206$	9.04339			0.630083
$207$		0			0
$208$			1.87646i			0.130109i
$209$	−23.7103	−	19.8953i	−1.64007	−	1.37618i
$210$		0			0
$211$	0.583521	+	3.30931i	0.0401712	+	0.227822i	0.998283	−	0.0585715i	$-0.0186546\pi$
$211$	0.583521	+	3.30931i	0.0401712	+	0.227822i	−0.958112	+	0.286394i	$0.907543\pi$
$212$	−1.92697	+	5.29431i	−0.132345	+	0.363615i
$213$		0			0
$214$	2.58034	−	14.6338i	0.176388	−	1.00035i
$215$	1.98558	+	3.43912i	0.135415	+	0.234546i
$216$		0			0
$217$	−0.0562129	+	2.07602i	−0.00381598	+	0.140929i
$218$	4.56841	+	12.5516i	0.309412	+	0.850103i
$219$		0			0
$220$	−2.76286	+	0.487167i	−0.186272	+	0.0328448i
$221$	−7.68177	+	21.1055i	−0.516732	+	1.41971i
$222$		0			0
$223$	−4.25268	+	5.06814i	−0.284780	+	0.339388i	−0.889403	−	0.457124i	$-0.848880\pi$
$223$	−4.25268	+	5.06814i	−0.284780	+	0.339388i	0.604623	+	0.796512i	$0.293324\pi$
$224$	−12.2817	−	7.54128i	−0.820604	−	0.503873i
$225$		0			0
$226$	−0.708568	+	1.22728i	−0.0471333	+	0.0816372i
$227$	8.02989	+	6.73788i	0.532962	+	0.447209i	0.869123	−	0.494596i	$-0.164684\pi$
$227$	8.02989	+	6.73788i	0.532962	+	0.447209i	−0.336160	+	0.941805i	$0.609128\pi$
$228$		0			0
$229$	17.2043	−	3.03357i	1.13689	−	0.200464i	0.426645	−	0.904419i	$-0.359695\pi$
$229$	17.2043	−	3.03357i	1.13689	−	0.200464i	0.710245	+	0.703955i	$0.248584\pi$
$230$	−1.57209	−	0.572193i	−0.103660	−	0.0377293i
$231$		0			0
$232$	−1.47213	+	8.34887i	−0.0966501	+	0.548130i
$233$	8.89526	+	5.13568i	0.582748	+	0.336450i	0.762225	−	0.647312i	$-0.224107\pi$
$233$	8.89526	+	5.13568i	0.582748	+	0.336450i	−0.179477	+	0.983762i	$0.557440\pi$
$234$		0			0
$235$	1.93821	+	3.35708i	0.126435	+	0.218992i
$236$	−1.06044	+	6.01405i	−0.0690287	+	0.391481i
$237$		0			0
$238$	7.26211	+	9.14643i	0.470733	+	0.592875i
$239$	−14.4600	−	17.2328i	−0.935342	−	1.11470i	−0.993206	−	0.116372i	$-0.962873\pi$
$239$	−14.4600	−	17.2328i	−0.935342	−	1.11470i	0.0578640	−	0.998324i	$-0.481571\pi$
$240$		0			0
$241$	8.43248	+	1.48687i	0.543184	+	0.0957780i	0.438506	−	0.898728i	$-0.355508\pi$
$241$	8.43248	+	1.48687i	0.543184	+	0.0957780i	0.104678	+	0.994506i	$0.466619\pi$
$242$	10.0904	+	5.82569i	0.648635	+	0.374489i
$243$		0			0
$244$		−	8.22310i		−	0.526430i
$245$	−3.37797	+	1.02617i	−0.215811	+	0.0655598i
$246$		0			0
$247$	−28.1668	−	10.2519i	−1.79221	−	0.652312i
$248$	2.14500	+	0.780716i	0.136208	+	0.0495755i
$249$		0			0
$250$	−4.47572	−	0.789190i	−0.283069	−	0.0499128i
$251$	−8.90861	+	15.4302i	−0.562307	+	0.973943i	0.434988	+	0.900436i	$0.356753\pi$
$251$	−8.90861	+	15.4302i	−0.562307	+	0.973943i	−0.997295	+	0.0735073i	$0.976581\pi$
$252$		0			0
$253$	−8.71413	−	15.0933i	−0.547853	−	0.948909i
$254$	3.37568	+	9.27460i	0.211809	+	0.581940i
$255$		0			0
$256$	−12.8345	+	10.7695i	−0.802159	+	0.673091i
$257$	−4.15085	−	23.5406i	−0.258923	−	1.46842i	−0.785799	−	0.618482i	$-0.787748\pi$
$257$	−4.15085	−	23.5406i	−0.258923	−	1.46842i	0.526877	−	0.849942i	$-0.323363\pi$
$258$		0			0
$259$	−10.8395	−	9.60718i	−0.673532	−	0.596961i
$260$	−2.35292	+	1.35846i	−0.145922	+	0.0842482i
$261$		0			0
$262$	−7.37499	+	4.25795i	−0.455628	+	0.263057i
$263$	−3.04119	−	8.35561i	−0.187528	−	0.515229i	0.809927	−	0.586531i	$-0.199507\pi$
$263$	−3.04119	−	8.35561i	−0.187528	−	0.515229i	−0.997455	+	0.0713021i	$0.977285\pi$
$264$		0			0
$265$	2.44390	−	0.430926i	0.150128	−	0.0264716i
$266$	−12.2066	+	9.69181i	−0.748433	+	0.594243i
$267$		0			0
$268$	7.67611	+	6.44102i	0.468893	+	0.393448i
$269$	−0.579284	+	1.00335i	−0.0353195	+	0.0611752i	−0.883145	−	0.469100i	$-0.844578\pi$
$269$	−0.579284	+	1.00335i	−0.0353195	+	0.0611752i	0.847825	+	0.530276i	$0.177912\pi$
$270$		0			0
$271$	−22.8894	+	13.2152i	−1.39043	+	0.802766i	−0.993363	−	0.115023i	$-0.963306\pi$
$271$	−22.8894	+	13.2152i	−1.39043	+	0.802766i	−0.397069	+	0.917789i	$0.629973\pi$
$272$	1.78923	−	0.651226i	0.108488	−	0.0394864i
$273$		0			0
$274$	−10.5462	+	8.84932i	−0.637120	+	0.534607i
$275$	−14.8193	−	17.6609i	−0.893635	−	1.06499i
$276$		0			0
$277$	10.3151	−	3.75438i	0.619773	−	0.225579i	−0.0130009	−	0.999915i	$-0.504138\pi$
$277$	10.3151	−	3.75438i	0.619773	−	0.225579i	0.632774	+	0.774336i	$0.281916\pi$
$278$	−9.91218			−0.594493
$279$		0			0
$280$	−0.105032	+	3.87897i	−0.00627685	+	0.231813i
$281$	−0.726106	−	0.128032i	−0.0433159	−	0.00763776i	0.151948	−	0.988388i	$-0.451445\pi$
$281$	−0.726106	−	0.128032i	−0.0433159	−	0.00763776i	−0.195264	+	0.980751i	$0.562556\pi$
$282$		0			0
$283$	−5.91960	−	7.05471i	−0.351884	−	0.419359i	0.560847	−	0.827919i	$-0.310475\pi$
$283$	−5.91960	−	7.05471i	−0.351884	−	0.419359i	−0.912731	+	0.408560i	$0.866031\pi$
$284$	9.61294	+	11.4563i	0.570423	+	0.679803i
$285$		0			0
$286$	20.8126	+	3.66982i	1.23067	+	0.217001i
$287$	−8.02704	+	13.0728i	−0.473821	+	0.771662i
$288$		0			0
$289$	5.79036			0.340609
$290$	1.27751	−	0.464974i	0.0750178	−	0.0273042i
$291$		0			0
$292$	7.16364	+	8.53729i	0.419220	+	0.499607i
$293$	−17.3436	+	14.5530i	−1.01322	+	0.850196i	−0.988761	−	0.149505i	$-0.952232\pi$
$293$	−17.3436	+	14.5530i	−1.01322	+	0.850196i	−0.0244632	+	0.999701i	$0.507788\pi$
$294$		0			0
$295$	2.52761	−	0.919975i	0.147163	−	0.0535630i
$296$	−13.7872	+	7.96005i	−0.801365	+	0.462668i
$297$		0			0
$298$	−0.985503	+	1.70694i	−0.0570887	+	0.0988805i
$299$	−12.9294	−	10.8490i	−0.747726	−	0.627416i
$300$		0			0
$301$	19.3760	+	7.65237i	1.11682	+	0.441075i
$302$	−6.05537	+	1.06773i	−0.348448	+	0.0614407i
$303$		0			0
$304$	0.869108	+	2.38786i	0.0498468	+	0.136953i
$305$	−3.13672	+	1.81098i	−0.179608	+	0.103697i
$306$		0			0
$307$	18.3264	−	10.5807i	1.04594	−	0.603875i	0.124432	−	0.992228i	$-0.460289\pi$
$307$	18.3264	−	10.5807i	1.04594	−	0.603875i	0.921511	+	0.388353i	$0.126956\pi$
$308$	−9.76184	+	11.0140i	−0.556233	+	0.627579i
$309$		0			0
$310$	−0.0635642	−	0.360491i	−0.00361020	−	0.0204745i
$311$	−6.35195	+	5.32992i	−0.360186	+	0.302232i	−0.804865	−	0.593458i	$-0.797762\pi$
$311$	−6.35195	+	5.32992i	−0.360186	+	0.302232i	0.444679	+	0.895690i	$0.353318\pi$
$312$		0			0
$313$	−9.78199	−	26.8758i	−0.552911	−	1.51911i	−0.829717	−	0.558184i	$-0.811498\pi$
$313$	−9.78199	−	26.8758i	−0.552911	−	1.51911i	0.276807	−	0.960926i	$-0.410724\pi$
$314$	0.273890	+	0.474392i	0.0154565	+	0.0267715i
$315$		0			0
$316$	2.72024	−	4.71159i	0.153025	−	0.265048i
$317$	19.8974	+	3.50845i	1.11755	+	0.197054i	0.701765	−	0.712409i	$-0.252396\pi$
$317$	19.8974	+	3.50845i	1.11755	+	0.197054i	0.415785	+	0.909463i	$0.363507\pi$
$318$		0			0
$319$	13.3084	+	4.84387i	0.745128	+	0.271204i
$320$	2.76513	+	1.00642i	0.154575	+	0.0562609i
$321$		0			0
$322$	−8.32530	+	2.77736i	−0.463951	+	0.154776i
$323$			30.4154i			1.69236i
$324$		0			0
$325$	−19.3357	−	11.1635i	−1.07255	−	0.619238i
$326$	−17.0971	−	3.01468i	−0.946920	−	0.166968i
$327$		0			0
$328$	10.8382	+	12.9165i	0.598441	+	0.713194i
$329$	18.9138	+	7.46982i	1.04275	+	0.411825i
$330$		0			0
$331$	−2.59475	+	14.7155i	−0.142620	+	0.808840i	0.826627	+	0.562750i	$0.190257\pi$
$331$	−2.59475	+	14.7155i	−0.142620	+	0.808840i	−0.969247	+	0.246089i	$0.920854\pi$
$332$	−1.68061	−	2.91090i	−0.0922354	−	0.159756i
$333$		0			0
$334$	−11.0641	−	6.38786i	−0.605400	−	0.349528i
$335$	0.766419	−	4.34658i	0.0418739	−	0.237479i
$336$		0			0
$337$	−10.4942	−	3.81956i	−0.571653	−	0.208065i	0.0399880	−	0.999200i	$-0.487268\pi$
$337$	−10.4942	−	3.81956i	−0.571653	−	0.208065i	−0.611641	+	0.791136i	$0.709490\pi$
$338$	8.31781	−	1.46665i	0.452429	−	0.0797755i
$339$		0			0
$340$	2.11190	+	1.77209i	0.114534	+	0.0961051i
$341$	1.90667	−	3.30245i	0.103252	−	0.178838i
$342$		0			0
$343$	−10.5307	+	15.2349i	−0.568606	+	0.822610i
$344$	14.7183	−	17.5406i	0.793559	−	0.945727i
$345$		0			0
$346$	1.39253	−	3.82596i	0.0748631	−	0.205685i
$347$	−17.9205	+	3.15986i	−0.962022	+	0.169630i	−0.632537	−	0.774530i	$-0.717986\pi$
$347$	−17.9205	+	3.15986i	−0.962022	+	0.169630i	−0.329485	+	0.944161i	$0.606875\pi$
$348$		0			0
$349$	−8.74024	−	24.0136i	−0.467854	−	1.28542i	−0.919454	−	0.393198i	$-0.871369\pi$
$349$	−8.74024	−	24.0136i	−0.467854	−	1.28542i	0.451599	−	0.892221i	$-0.350854\pi$
$350$	−10.2077	+	5.53055i	−0.545624	+	0.295621i
$351$		0			0
$352$	13.2317	+	22.9179i	0.705250	+	1.22153i
$353$	2.22706	−	12.6303i	0.118535	−	0.672243i	−0.866405	−	0.499343i	$-0.833575\pi$
$353$	2.22706	−	12.6303i	0.118535	−	0.672243i	0.984939	−	0.172901i	$-0.0553140\pi$
$354$		0			0
$355$	2.25294	−	6.18990i	0.119574	−	0.328526i
$356$	−2.22879	−	12.6401i	−0.118126	−	0.669924i
$357$		0			0
$358$	2.13441	+	1.79099i	0.112807	+	0.0946565i
$359$		−	21.4389i		−	1.13150i	−0.824577	−	0.565750i	$-0.808587\pi$
$359$		−	21.4389i		−	1.13150i	0.824577	−	0.565750i	$-0.191413\pi$
$360$		0			0
$361$	−21.5916			−1.13640
$362$	−1.98811	+	0.723612i	−0.104493	+	0.0380322i
$363$		0			0
$364$	−5.23548	+	13.2564i	−0.274414	+	0.694824i
$365$	1.67891	−	4.61276i	0.0878780	−	0.241443i
$366$		0			0
$367$	−4.47982	+	5.33884i	−0.233844	+	0.278685i	−0.870187	−	0.492722i	$-0.836002\pi$
$367$	−4.47982	+	5.33884i	−0.233844	+	0.278685i	0.636343	+	0.771407i	$0.280447\pi$
$368$			1.43085i			0.0745882i
$369$		0			0
$370$	2.21094	+	1.27649i	0.114941	+	0.0663614i
$371$	8.63489	−	9.74247i	0.448301	−	0.505804i
$372$		0			0
$373$	−8.84883	+	7.42505i	−0.458175	+	0.384454i	−0.842459	−	0.538760i	$-0.818893\pi$
$373$	−8.84883	+	7.42505i	−0.458175	+	0.384454i	0.384284	+	0.923215i	$0.374448\pi$
$374$	−3.72379	−	21.1187i	−0.192553	−	1.09202i
$375$		0			0
$376$	14.3672	−	17.1222i	0.740933	−	0.883009i
$377$	13.7155			0.706382
$378$		0			0
$379$	6.46443			0.332055			0.166028	−	0.986121i	$-0.446906\pi$
$379$	6.46443			0.332055			0.166028	+	0.986121i	$0.446906\pi$
$380$	−2.36498	+	2.81848i	−0.121321	+	0.144585i
$381$		0			0
$382$	2.11144	+	11.9746i	0.108031	+	0.612673i
$383$	1.78265	−	1.49582i	0.0910889	−	0.0764327i	−0.596106	−	0.802906i	$-0.703286\pi$
$383$	1.78265	−	1.49582i	0.0910889	−	0.0764327i	0.687195	+	0.726473i	$0.258842\pi$
$384$		0			0
$385$	6.35116	+	1.29805i	0.323685	+	0.0661548i
$386$	0.0300160	+	0.0173298i	0.00152778	+	0.000882062i
$387$		0			0
$388$		−	2.81062i		−	0.142688i
$389$	21.1876	−	25.2503i	1.07425	−	1.28024i	0.116331	−	0.993211i	$-0.462887\pi$
$389$	21.1876	−	25.2503i	1.07425	−	1.28024i	0.957921	−	0.287032i	$-0.0926688\pi$
$390$		0			0
$391$	−5.85756	+	16.0935i	−0.296230	+	0.813884i
$392$	12.2217	+	16.2790i	0.617291	+	0.822216i
$393$		0			0
$394$	−4.44556	+	1.61805i	−0.223964	+	0.0815163i
$395$	−2.39633			−0.120572
$396$		0			0
$397$			25.4001i			1.27479i	0.770535	+	0.637397i	$0.219989\pi$
$397$			25.4001i			1.27479i	−0.770535	+	0.637397i	$0.780011\pi$
$398$	−4.37379	−	3.67005i	−0.219238	−	0.183963i
$399$		0			0
$400$	0.328677	+	1.86402i	0.0164339	+	0.0932010i
$401$	6.66838	−	18.3212i	0.333003	−	0.914918i	−0.654323	−	0.756215i	$-0.727046\pi$
$401$	6.66838	−	18.3212i	0.333003	−	0.914918i	0.987326	−	0.158703i	$-0.0507314\pi$
$402$		0			0
$403$	0.641277	−	3.63686i	0.0319443	−	0.181165i
$404$	3.46190	+	5.99618i	0.172236	+	0.298321i
$405$		0			0
$406$	3.73178	−	6.07756i	0.185205	−	0.301624i
$407$	9.09623	+	24.9917i	0.450883	+	1.23879i
$408$		0			0
$409$	−17.0494	+	3.00627i	−0.843038	+	0.148650i	−0.578457	−	0.815713i	$-0.696345\pi$
$409$	−17.0494	+	3.00627i	−0.843038	+	0.148650i	−0.264581	+	0.964363i	$0.585234\pi$
$410$	0.924791	−	2.54084i	0.0456722	−	0.125483i
$411$		0			0
$412$	7.19847	−	8.57880i	0.354643	−	0.422647i
$413$	7.38352	−	12.0247i	0.363319	−	0.591699i
$414$		0			0
$415$	−0.740246	+	1.28214i	−0.0363372	+	0.0629379i
$416$	19.6322	+	16.4734i	0.962547	+	0.807673i
$417$		0			0
$418$	28.1844	−	4.96967i	1.37854	−	0.243075i
$419$	−3.08710	−	1.12361i	−0.150815	−	0.0548920i	0.265510	−	0.964108i	$-0.414460\pi$
$419$	−3.08710	−	1.12361i	−0.150815	−	0.0548920i	−0.416324	+	0.909216i	$0.636682\pi$
$420$		0			0
$421$	−0.564741	+	3.20281i	−0.0275238	+	0.156095i	−0.995472	−	0.0950543i	$-0.969698\pi$
$421$	−0.564741	+	3.20281i	−0.0275238	+	0.156095i	0.967948	+	0.251150i	$0.0808086\pi$
$422$	−2.69087	−	1.55357i	−0.130989	−	0.0756267i
$423$		0			0
$424$	−7.15446	−	12.3919i	−0.347451	−	0.601803i
$425$	−3.93405	+	22.3111i	−0.190830	+	1.08225i
$426$		0			0
$427$	−6.97949	+	17.6723i	−0.337761	+	0.855223i
$428$	−11.8281	−	14.0962i	−0.571734	−	0.681366i
$429$		0			0
$430$	−3.61613	−	0.637621i	−0.174385	−	0.0307488i
$431$	29.6610	+	17.1248i	1.42872	+	0.824872i	0.997020	−	0.0771457i	$-0.0245807\pi$
$431$	29.6610	+	17.1248i	1.42872	+	0.824872i	0.431700	+	0.902017i	$0.357914\pi$
$432$		0			0
$433$			27.4243i			1.31793i	0.752174	+	0.658965i	$0.229005\pi$
$433$			27.4243i			1.31793i	−0.752174	+	0.658965i	$0.770995\pi$
$434$	−1.43707	−	1.27370i	−0.0689818	−	0.0611395i
$435$		0			0
$436$	15.5432	+	5.65727i	0.744386	+	0.270934i
$437$	−21.4780	−	7.81734i	−1.02743	−	0.373954i
$438$		0			0
$439$	3.72213	+	0.656313i	0.177648	+	0.0313241i	0.261764	−	0.965132i	$-0.415696\pi$
$439$	3.72213	+	0.656313i	0.177648	+	0.0313241i	−0.0841165	+	0.996456i	$0.526807\pi$
$440$	3.56255	−	6.17051i	0.169838	−	0.294168i
$441$		0			0
$442$	−10.3838	−	17.9852i	−0.493906	−	0.855470i
$443$	7.38522	+	20.2907i	0.350883	+	0.964042i	0.982087	+	0.188426i	$0.0603385\pi$
$443$	7.38522	+	20.2907i	0.350883	+	0.964042i	−0.631205	+	0.775616i	$0.717439\pi$
$444$		0			0
$445$	−4.33074	+	3.63392i	−0.205297	+	0.172264i
$446$	−1.06228	−	6.02451i	−0.0503006	−	0.285269i
$447$		0			0
$448$	14.6433	−	4.88508i	0.691830	−	0.230798i
$449$	15.0109	−	8.66655i	0.708408	−	0.409000i	−0.102063	−	0.994778i	$-0.532544\pi$
$449$	15.0109	−	8.66655i	0.708408	−	0.409000i	0.810471	+	0.585778i	$0.199211\pi$
$450$		0			0
$451$	24.3942	−	14.0840i	1.14868	−	0.663188i
$452$	0.600213	+	1.64907i	0.0282316	+	0.0775657i
$453$		0			0
$454$	−9.54514	+	1.68307i	−0.447976	+	0.0789902i
$455$	6.20969	−	0.922391i	0.291115	−	0.0432424i
$456$		0			0
$457$	25.1386	+	21.0938i	1.17593	+	0.986726i	0.999997	+	0.00232513i	$0.000740114\pi$
$457$	25.1386	+	21.0938i	1.17593	+	0.986726i	0.175938	+	0.984401i	$0.443704\pi$
$458$	−8.07662	+	13.9891i	−0.377396	+	0.653669i
$459$		0			0
$460$	−1.79417	+	1.03586i	−0.0836535	+	0.0482974i
$461$	0.748682	−	0.272498i	0.0348696	−	0.0126915i	−0.324526	−	0.945877i	$-0.605205\pi$
$461$	0.748682	−	0.272498i	0.0348696	−	0.0126915i	0.359396	+	0.933185i	$0.382983\pi$
$462$		0			0
$463$	8.79280	−	7.37804i	0.408636	−	0.342887i	−0.415184	−	0.909737i	$-0.636283\pi$
$463$	8.79280	−	7.37804i	0.408636	−	0.342887i	0.823820	+	0.566851i	$0.191838\pi$
$464$	−0.747391	−	0.890706i	−0.0346968	−	0.0413500i
$465$		0			0
$466$	−8.92461	+	3.24829i	−0.413425	+	0.150474i
$467$	−5.18972			−0.240151			−0.120076	−	0.992765i	$-0.538314\pi$
$467$	−5.18972			−0.240151			−0.120076	+	0.992765i	$0.538314\pi$
$468$		0			0
$469$	−11.0298	−	20.3576i	−0.509310	−	0.940028i
$470$	−3.52986	−	0.622410i	−0.162820	−	0.0287096i
$471$		0			0
$472$	−9.96933	−	11.8810i	−0.458876	−	0.546867i
$473$	−24.5880	−	29.3028i	−1.13056	−	1.34734i
$474$		0			0
$475$	−29.7758	−	5.25028i	−1.36621	−	0.240899i
$476$	14.4571	+	0.391460i	0.662642	+	0.0179425i
$477$		0			0
$478$	20.8007			0.951400
$479$	−17.4081	+	6.33602i	−0.795395	+	0.289500i	−0.707577	−	0.706637i	$-0.750212\pi$
$479$	−17.4081	+	6.33602i	−0.795395	+	0.289500i	−0.0878180	+	0.996137i	$0.527989\pi$
$480$		0			0
$481$	16.5557	+	19.7303i	0.754874	+	0.899624i
$482$	−6.06503	+	5.08917i	−0.276255	+	0.231805i
$483$		0			0
$484$	13.5583	−	4.93481i	0.616285	−	0.224310i
$485$	−1.07212	+	0.618987i	−0.0486823	+	0.0281067i
$486$		0			0
$487$	12.9714	−	22.4672i	0.587792	−	1.01809i	−0.406729	−	0.913549i	$-0.633331\pi$
$487$	12.9714	−	22.4672i	0.587792	−	1.01809i	0.994521	−	0.104537i	$-0.0333360\pi$
$488$	15.9983	+	13.4241i	0.724208	+	0.607682i
$489$		0			0
$490$	1.28084	−	3.00259i	0.0578625	−	0.135643i
$491$	−17.9073	+	3.15754i	−0.808146	+	0.142498i	−0.562431	−	0.826844i	$-0.690134\pi$
$491$	−17.9073	+	3.15754i	−0.808146	+	0.142498i	−0.245715	+	0.969342i	$0.579023\pi$
$492$		0			0
$493$	−4.75996	−	13.0779i	−0.214378	−	0.588998i
$494$	24.0026	−	13.8579i	1.07993	−	0.623497i
$495$		0			0
$496$	−0.271129	+	0.156536i	−0.0121741	+	0.00702870i
$497$	−10.9355	−	32.7798i	−0.490525	−	1.47038i
$498$		0			0
$499$	−4.24424	−	24.0703i	−0.189998	−	1.07753i	−0.919363	−	0.393410i	$-0.871295\pi$
$499$	−4.24424	−	24.0703i	−0.189998	−	1.07753i	0.729365	−	0.684125i	$-0.239816\pi$
$500$	−4.31129	+	3.61760i	−0.192807	+	0.161784i
$501$		0			0
$502$	−5.63465	−	15.4811i	−0.251487	−	0.690954i
$503$	7.81528	+	13.5365i	0.348466	+	0.603561i	0.985977	−	0.166880i	$-0.0533693\pi$
$503$	7.81528	+	13.5365i	0.348466	+	0.603561i	−0.637511	+	0.770441i	$0.720036\pi$
$504$		0			0
$505$	1.52484	−	2.64109i	0.0678543	−	0.117527i
$506$	15.8701	+	2.79833i	0.705514	+	0.124401i
$507$		0			0
$508$	11.4852	+	4.18025i	0.509571	+	0.185469i
$509$	22.9635	+	8.35802i	1.01784	+	0.370463i	0.796438	−	0.604720i	$-0.206715\pi$
$509$	22.9635	+	8.35802i	1.01784	+	0.370463i	0.221400	+	0.975183i	$0.428937\pi$
$510$		0			0
$511$	−8.14923	−	24.4278i	−0.360501	−	1.08062i
$512$		−	4.49234i		−	0.198535i
$513$		0			0
$514$	19.1413	+	11.0513i	0.844288	+	0.487450i
$515$	−4.85773	−	0.856548i	−0.214057	−	0.0377440i
$516$		0			0
$517$	−24.0014	−	28.6038i	−1.05558	−	1.25799i
$518$	13.2474	−	1.96778i	0.582057	−	0.0864591i
$519$		0			0
$520$	1.19820	−	6.79535i	0.0525447	−	0.297996i
$521$	16.5999	+	28.7519i	0.727255	+	1.25964i	0.958039	+	0.286638i	$0.0925376\pi$
$521$	16.5999	+	28.7519i	0.727255	+	1.25964i	−0.230784	+	0.973005i	$0.574129\pi$
$522$		0			0
$523$	33.9429	+	19.5969i	1.48422	+	0.856915i	0.999839	−	0.0179428i	$-0.00571167\pi$
$523$	33.9429	+	19.5969i	1.48422	+	0.856915i	0.484381	+	0.874857i	$0.339045\pi$
$524$	−1.83123	+	10.3854i	−0.0799976	+	0.453689i
$525$		0			0
$526$	7.72598	+	2.81203i	0.336869	+	0.122610i
$527$	−3.69035	+	0.650709i	−0.160754	+	0.0283453i
$528$		0			0
$529$	7.76001	+	6.51142i	0.337392	+	0.283105i
$530$	−1.14730	+	1.98719i	−0.0498356	+	0.0863178i
$531$		0			0
$532$	−0.522432	+	19.2941i	−0.0226503	+	0.836506i
$533$	17.5345	−	20.8968i	0.759502	−	0.905139i
$534$		0			0
$535$	−2.77210	+	7.61628i	−0.119848	+	0.329280i
$536$	−25.0623	+	4.41917i	−1.08253	+	0.190879i
$537$		0			0
$538$	−0.366394	−	1.00666i	−0.0157964	−	0.0434002i
$539$	30.3275	−	15.3846i	1.30630	−	0.662663i
$540$		0			0
$541$	−22.2029	−	38.4566i	−0.954578	−	1.65338i	−0.735330	−	0.677709i	$-0.762973\pi$
$541$	−22.2029	−	38.4566i	−0.954578	−	1.65338i	−0.219248	−	0.975669i	$-0.570360\pi$
$542$	4.24375	−	24.0675i	0.182284	−	1.03379i
$543$		0			0
$544$	8.89421	−	24.4366i	0.381336	−	1.04771i
$545$	−1.26513	−	7.17490i	−0.0541921	−	0.307339i
$546$		0			0
$547$	10.6883	+	8.96856i	0.456999	+	0.383468i	0.842025	−	0.539438i	$-0.181363\pi$
$547$	10.6883	+	8.96856i	0.456999	+	0.383468i	−0.385026	+	0.922906i	$0.625808\pi$
$548$			17.0484i			0.728272i
$549$		0			0
$550$	21.3174			0.908977
$551$	17.4534	−	6.35251i	0.743539	−	0.270626i
$552$		0			0
$553$	−9.84512	+	7.81685i	−0.418657	+	0.332406i
$554$	−3.47147	+	9.53780i	−0.147489	+	0.405222i
$555$		0			0
$556$	−7.89002	+	9.40296i	−0.334611	+	0.398774i
$557$			11.9840i			0.507780i	0.967233	+	0.253890i	$0.0817101\pi$
$557$			11.9840i			0.507780i	−0.967233	+	0.253890i	$0.918290\pi$
$558$		0			0
$559$	−32.0816	−	18.5223i	−1.35691	−	0.783410i
$560$	−0.398284	−	0.353005i	−0.0168306	−	0.0149172i
$561$		0			0
$562$	0.522250	−	0.438220i	0.0220298	−	0.0184852i
$563$	0.171106	+	0.970390i	0.00721125	+	0.0408970i	0.988201	−	0.153162i	$-0.0489457\pi$
$563$	0.171106	+	0.970390i	0.00721125	+	0.0408970i	−0.980990	+	0.194059i	$0.937835\pi$
$564$		0			0
$565$	0.496855	−	0.592129i	0.0209029	−	0.0249111i
$566$	8.51531			0.357925
$567$		0			0
$568$	−37.9815			−1.59367
$569$	3.55957	−	4.24213i	0.149225	−	0.177839i	−0.686254	−	0.727362i	$-0.740746\pi$
$569$	3.55957	−	4.24213i	0.149225	−	0.177839i	0.835479	+	0.549523i	$0.185190\pi$
$570$		0			0
$571$	−2.29263	−	13.0021i	−0.0959436	−	0.544123i	−0.994454	−	0.105171i	$-0.966461\pi$
$571$	−2.29263	−	13.0021i	−0.0959436	−	0.544123i	0.898511	−	0.438952i	$-0.144650\pi$
$572$	20.0479	−	16.8222i	0.838246	−	0.703372i
$573$		0			0
$574$	−4.48884	−	13.4555i	−0.187360	−	0.561623i
$575$	−14.7440	−	8.51244i	−0.614867	−	0.354993i
$576$		0			0
$577$			19.1388i			0.796760i	0.917220	+	0.398380i	$0.130427\pi$
$577$			19.1388i			0.796760i	−0.917220	+	0.398380i	$0.869573\pi$
$578$	−3.44150	+	4.10142i	−0.143148	+	0.170597i
$579$		0			0
$580$	0.575799	−	1.58199i	0.0239087	−	0.0656887i
$581$	1.14113	+	7.68228i	0.0473420	+	0.318714i
$582$		0			0
$583$	−22.4624	+	8.17565i	−0.930299	+	0.338601i
$584$	−28.3041			−1.17123
$585$		0			0
$586$		−	20.9344i		−	0.864793i
$587$	−20.7501	−	17.4114i	−0.856450	−	0.718647i	0.104750	−	0.994499i	$-0.466596\pi$
$587$	−20.7501	−	17.4114i	−0.856450	−	0.718647i	−0.961200	+	0.275852i	$0.911040\pi$
$588$		0			0
$589$	−0.868419	−	4.92505i	−0.0357826	−	0.202933i
$590$	−0.850651	+	2.33714i	−0.0350207	+	0.0962187i
$591$		0			0
$592$	0.379158	−	2.15031i	0.0155833	−	0.0883772i
$593$	−21.3668	−	37.0083i	−0.877428	−	1.51975i	−0.854154	−	0.520020i	$-0.825924\pi$
$593$	−21.3668	−	37.0083i	−0.877428	−	1.51975i	−0.0232738	−	0.999729i	$-0.507409\pi$
$594$		0			0
$595$	−3.03459	−	5.60091i	−0.124406	−	0.229615i
$596$	0.834798	+	2.29359i	0.0341946	+	0.0939490i
$597$		0			0
$598$	15.3692	−	2.71000i	0.628493	−	0.110820i
$599$	−10.7152	+	29.4398i	−0.437812	+	1.20288i	0.503100	+	0.864228i	$0.332193\pi$
$599$	−10.7152	+	29.4398i	−0.437812	+	1.20288i	−0.940912	+	0.338650i	$0.890030\pi$
$600$		0			0
$601$	3.68912	−	4.39652i	0.150482	−	0.179338i	−0.685537	−	0.728038i	$-0.740433\pi$
$601$	3.68912	−	4.39652i	0.150482	−	0.179338i	0.836019	+	0.548700i	$0.184877\pi$
$602$	−16.9365	+	9.17624i	−0.690280	+	0.373996i
$603$		0			0
$604$	−3.80716	+	6.59419i	−0.154911	+	0.268314i
$605$	−4.86835	−	4.08503i	−0.197927	−	0.166080i
$606$		0			0
$607$	−13.3273	+	2.34995i	−0.540937	+	0.0953817i	−0.437439	−	0.899248i	$-0.644114\pi$
$607$	−13.3273	+	2.34995i	−0.540937	+	0.0953817i	−0.103497	+	0.994630i	$0.533003\pi$
$608$	32.6125	+	11.8700i	1.32261	+	0.481391i
$609$		0			0
$610$	0.581554	−	3.29816i	0.0235464	−	0.133539i
$611$	−31.3163	−	18.0805i	−1.26692	−	0.731457i
$612$		0			0
$613$	−0.926764	−	1.60520i	−0.0374316	−	0.0648335i	0.846703	−	0.532066i	$-0.178584\pi$
$613$	−0.926764	−	1.60520i	−0.0374316	−	0.0648335i	−0.884134	+	0.467233i	$0.845251\pi$
$614$	−3.39775	+	19.2696i	−0.137122	+	0.777658i
$615$		0			0
$616$	−5.49186	−	36.9721i	−0.221273	−	1.48965i
$617$	30.5178	+	36.3698i	1.22860	+	1.46419i	0.839823	+	0.542860i	$0.182659\pi$
$617$	30.5178	+	36.3698i	1.22860	+	1.46419i	0.388779	+	0.921331i	$0.372897\pi$
$618$		0			0
$619$	−3.03430	−	0.535030i	−0.121959	−	0.0215047i	0.112335	−	0.993670i	$-0.464167\pi$
$619$	−3.03430	−	0.535030i	−0.121959	−	0.0215047i	−0.234294	+	0.972166i	$0.575278\pi$
$620$	−0.392568	−	0.226649i	−0.0157659	−	0.00910245i
$621$		0			0
$622$		−	7.66706i		−	0.307421i
$623$	−5.93859	+	29.0566i	−0.237925	+	1.16413i
$624$		0			0
$625$	−19.9678	−	7.26768i	−0.798711	−	0.290707i
$626$	24.8506	+	9.04487i	0.993229	+	0.361506i
$627$		0			0
$628$	0.668036	+	0.117793i	0.0266575	+	0.00470044i
$629$	13.0675	−	22.6335i	0.521033	−	0.902456i
$630$		0			0
$631$	12.7919	+	22.1562i	0.509238	+	0.882026i	0.999943	+	0.0106999i	$0.00340596\pi$
$631$	12.7919	+	22.1562i	0.509238	+	0.882026i	−0.490705	+	0.871326i	$0.663261\pi$
$632$	4.72576	+	12.9839i	0.187981	+	0.516473i
$633$		0			0
$634$	−14.3112	+	12.0085i	−0.568368	+	0.476918i
$635$	−0.934825	−	5.30165i	−0.0370974	−	0.210390i
$636$		0			0
$637$	22.5032	−	24.0457i	0.891608	−	0.952725i
$638$	−11.3409	+	6.54765i	−0.448989	+	0.259224i
$639$		0			0
$640$	2.40214	−	1.38687i	0.0949528	−	0.0548210i
$641$	−4.50967	−	12.3902i	−0.178121	−	0.489384i	0.818215	−	0.574913i	$-0.194964\pi$
$641$	−4.50967	−	12.3902i	−0.178121	−	0.489384i	−0.996336	+	0.0855292i	$0.972742\pi$
$642$		0			0
$643$	39.9985	−	7.05281i	1.57739	−	0.278136i	0.684703	−	0.728822i	$-0.259932\pi$
$643$	39.9985	−	7.05281i	1.57739	−	0.278136i	0.892682	+	0.450686i	$0.148821\pi$
$644$	−3.99220	+	10.1084i	−0.157315	+	0.398325i
$645$		0			0
$646$	−21.5438	−	18.0774i	−0.847630	−	0.711246i
$647$	−20.0184	+	34.6729i	−0.787006	+	1.36313i	0.140788	+	0.990040i	$0.455036\pi$
$647$	−20.0184	+	34.6729i	−0.787006	+	1.36313i	−0.927794	+	0.373094i	$0.878297\pi$
$648$		0			0
$649$	−22.4385	+	12.9549i	−0.880787	+	0.508523i
$650$	19.3995	−	7.06083i	0.760910	−	0.276949i
$651$		0			0
$652$	−16.4690	+	13.8191i	−0.644974	+	0.541198i
$653$	8.87922	+	10.5818i	0.347471	+	0.414100i	0.911268	−	0.411814i	$-0.135105\pi$
$653$	8.87922	+	10.5818i	0.347471	+	0.414100i	−0.563797	+	0.825913i	$0.690660\pi$
$654$		0			0
$655$	4.36483	−	1.58867i	0.170548	−	0.0620744i
$656$	−2.31257			−0.0902907
$657$		0			0
$658$	−16.5325	+	8.95734i	−0.644503	+	0.349194i
$659$	−36.6031	−	6.45411i	−1.42585	−	0.251417i	−0.593131	−	0.805106i	$-0.702108\pi$
$659$	−36.6031	−	6.45411i	−1.42585	−	0.251417i	−0.832723	+	0.553690i	$0.813219\pi$
$660$		0			0
$661$	29.0253	+	34.5910i	1.12895	+	1.34543i	0.930913	+	0.365240i	$0.119013\pi$
$661$	29.0253	+	34.5910i	1.12895	+	1.34543i	0.198040	+	0.980194i	$0.436542\pi$
$662$	−8.88112	−	10.5841i	−0.345175	−	0.411363i
$663$		0			0
$664$	8.40682	+	1.48235i	0.326248	+	0.0575263i
$665$	7.47483	−	4.04988i	0.289861	−	0.157048i
$666$		0			0
$667$	10.4584			0.404951
$668$	−14.8666	+	5.41101i	−0.575207	+	0.209358i
$669$		0			0
$670$	2.62324	+	3.12626i	0.101345	+	0.120778i
$671$	26.7262	−	22.4259i	1.03175	−	0.865744i
$672$		0			0
$673$	4.43681	−	1.61487i	0.171026	−	0.0622485i	−0.255088	−	0.966918i	$-0.582104\pi$
$673$	4.43681	−	1.61487i	0.171026	−	0.0622485i	0.426114	+	0.904669i	$0.359882\pi$
$674$	8.94268	−	5.16306i	0.344459	−	0.198874i
$675$		0			0
$676$	5.22961	−	9.05794i	0.201139	−	0.348382i
$677$	−8.09974	−	6.79649i	−0.311298	−	0.261210i	0.473730	−	0.880670i	$-0.342907\pi$
$677$	−8.09974	−	6.79649i	−0.311298	−	0.261210i	−0.785028	+	0.619460i	$0.787352\pi$
$678$		0			0
$679$	−2.38556	+	6.04032i	−0.0915494	+	0.231806i
$680$	−6.89530	+	1.21583i	−0.264423	+	0.0466248i
$681$		0			0
$682$	1.20596	+	3.31334i	0.0461786	+	0.126875i
$683$	8.04671	−	4.64577i	0.307899	−	0.177765i	−0.338087	−	0.941115i	$-0.609780\pi$
$683$	8.04671	−	4.64577i	0.307899	−	0.177765i	0.645986	+	0.763349i	$0.276447\pi$
$684$		0			0
$685$	6.50314	−	3.75459i	0.248472	−	0.143456i
$686$	−4.53226	−	16.5140i	−0.173042	−	0.630509i
$687$		0			0
$688$	0.545338	+	3.09276i	0.0207908	+	0.117911i
$689$	−17.7335	+	14.8802i	−0.675593	+	0.566890i
$690$		0			0
$691$	3.54767	+	9.74713i	0.134960	+	0.370798i	0.988701	−	0.149898i	$-0.0478945\pi$
$691$	3.54767	+	9.74713i	0.134960	+	0.370798i	−0.853742	+	0.520697i	$0.825672\pi$
$692$	−2.52096	−	4.36643i	−0.0958325	−	0.165987i
$693$		0			0
$694$	8.41286	−	14.5715i	0.319348	−	0.553126i
$695$	5.32440	+	0.938836i	0.201966	+	0.0356121i
$696$		0			0
$697$	−26.0107	−	9.46712i	−0.985226	−	0.358593i
$698$	22.2041	+	8.08163i	0.840437	+	0.305894i
$699$		0			0
$700$	−2.87881	+	14.0856i	−0.108809	+	0.532385i
$701$		−	32.6042i		−	1.23144i	−0.787964	−	0.615721i	$-0.788865\pi$
$701$		−	32.6042i		−	1.23144i	0.787964	−	0.615721i	$-0.211135\pi$
$702$		0			0
$703$	30.2060	+	17.4395i	1.13924	+	0.657742i
$704$	−27.9138	−	4.92196i	−1.05204	−	0.185503i
$705$		0			0
$706$	7.62264	+	9.08431i	0.286882	+	0.341892i
$707$	−2.35062	−	15.8248i	−0.0884040	−	0.595151i
$708$		0			0
$709$	−2.10559	+	11.9414i	−0.0790770	+	0.448468i	0.919401	+	0.393321i	$0.128674\pi$
$709$	−2.10559	+	11.9414i	−0.0790770	+	0.448468i	−0.998478	+	0.0551470i	$0.982437\pi$
$710$	3.04539	+	5.27477i	0.114291	+	0.197959i
$711$		0			0
$712$	28.2301	+	16.2987i	1.05797	+	0.610819i
$713$	0.488991	−	2.77321i	0.0183129	−	0.103857i
$714$		0			0
$715$	−10.8320	−	3.94254i	−0.405095	−	0.147443i
$716$	3.39795	−	0.599151i	0.126988	−	0.0223913i
$717$		0			0
$718$	15.1856	+	12.7422i	0.566721	+	0.475535i
$719$	5.13678	−	8.89717i	0.191570	−	0.331808i	−0.754201	−	0.656644i	$-0.771976\pi$
$719$	5.13678	−	8.89717i	0.191570	−	0.331808i	0.945771	+	0.324835i	$0.105309\pi$
$720$		0			0
$721$	−22.7517	+	12.3269i	−0.847316	+	0.459078i
$722$	12.8330	−	15.2937i	0.477593	−	0.569173i
$723$		0			0
$724$	−0.896081	+	2.46196i	−0.0333026	+	0.0914981i
$725$	13.6245	−	2.40238i	0.506003	−	0.0892220i
$726$		0			0
$727$	12.1820	+	33.4698i	0.451806	+	1.24133i	0.931452	+	0.363865i	$0.118543\pi$
$727$	12.1820	+	33.4698i	0.451806	+	1.24133i	−0.479646	+	0.877462i	$0.659235\pi$
$728$	−17.2438	−	31.8267i	−0.639098	−	1.17958i
$729$		0			0
$730$	2.26945	+	3.93080i	0.0839961	+	0.145485i
$731$	−6.52735	+	37.0184i	−0.241423	+	1.36918i
$732$		0			0
$733$	3.19323	−	8.77334i	0.117945	−	0.324051i	−0.866646	−	0.498923i	$-0.833729\pi$
$733$	3.19323	−	8.77334i	0.117945	−	0.324051i	0.984591	+	0.174872i	$0.0559513\pi$
$734$	−1.11902	−	6.34628i	−0.0413038	−	0.234246i
$735$		0			0
$736$	14.9701	+	12.5614i	0.551804	+	0.463019i
$737$			42.5142i			1.56603i
$738$		0			0
$739$	−49.8721			−1.83458			−0.917288	−	0.398226i	$-0.869626\pi$
$739$	−49.8721			−1.83458			−0.917288	+	0.398226i	$0.869626\pi$
$740$	2.97080	−	1.08128i	0.109209	−	0.0397488i
$741$		0			0
$742$	1.76863	+	11.9067i	0.0649284	+	0.437109i
$743$	13.7749	−	37.8461i	0.505350	−	1.38844i	−0.380635	−	0.924725i	$-0.624295\pi$
$743$	13.7749	−	37.8461i	0.505350	−	1.38844i	0.885985	−	0.463713i	$-0.153483\pi$
$744$		0			0
$745$	0.691044	−	0.823555i	0.0253179	−	0.0301727i
$746$		−	10.6809i		−	0.391055i
$747$		0			0
$748$	−22.9979	−	13.2778i	−0.840885	−	0.485485i
$749$	13.4555	+	40.3335i	0.491652	+	1.47375i
$750$		0			0
$751$	31.1504	−	26.1383i	1.13669	−	0.953800i	0.137369	−	0.990520i	$-0.456135\pi$
$751$	31.1504	−	26.1383i	1.13669	−	0.953800i	0.999326	+	0.0367201i	$0.0116910\pi$
$752$	0.532329	+	3.01899i	0.0194120	+	0.110091i
$753$		0			0
$754$	−8.15179	+	9.71493i	−0.296871	+	0.353797i
$755$	3.35382			0.122058
$756$		0			0
$757$	38.9341			1.41508			0.707542	−	0.706671i	$-0.249804\pi$
$757$	38.9341			1.41508			0.707542	+	0.706671i	$0.249804\pi$
$758$	−3.84214	+	4.57888i	−0.139553	+	0.166312i
$759$		0			0
$760$	−1.62261	−	9.20228i	−0.0588582	−	0.333802i
$761$	−29.3123	+	24.5960i	−1.06257	+	0.891603i	−0.994359	−	0.106067i	$-0.966174\pi$
$761$	−29.3123	+	24.5960i	−1.06257	+	0.891603i	−0.0682127	+	0.997671i	$0.521730\pi$
$762$		0			0
$763$	−28.6023	−	25.3506i	−1.03547	−	0.917755i
$764$	13.0401	+	7.52871i	0.471775	+	0.272379i
$765$		0			0
$766$			2.15172i			0.0777449i
$767$	−16.1287	+	19.2215i	−0.582375	+	0.694047i
$768$		0			0
$769$	2.38576	−	6.55481i	0.0860326	−	0.236373i	−0.889214	−	0.457491i	$-0.848748\pi$
$769$	2.38576	−	6.55481i	0.0860326	−	0.236373i	0.975247	+	0.221118i	$0.0709706\pi$
$770$	−4.69425	+	3.72715i	−0.169169	+	0.134317i
$771$		0			0
$772$	0.0403320	−	0.0146797i	0.00145158	−	0.000528333i
$773$	26.0359			0.936445			0.468222	−	0.883611i	$-0.344895\pi$
$773$	26.0359			0.936445			0.468222	+	0.883611i	$0.344895\pi$
$774$		0			0
$775$		−	3.72508i		−	0.133809i
$776$	5.46814	+	4.58831i	0.196295	+	0.164711i
$777$		0			0
$778$	5.29248	+	30.0151i	0.189744	+	1.07609i
$779$	12.6346	−	34.7132i	0.452680	−	1.24373i
$780$		0			0
$781$	−11.0181	+	62.4867i	−0.394258	+	2.23595i
$782$	−7.91791	−	13.7142i	−0.283144	−	0.490420i
$783$		0			0
$784$	−2.78783	−	0.151084i	−0.0995652	−	0.00539587i
$785$	−0.102190	−	0.280765i	−0.00364732	−	0.0100209i
$786$		0			0
$787$	27.4796	−	4.84540i	0.979543	−	0.172720i	0.339121	−	0.940743i	$-0.389871\pi$
$787$	27.4796	−	4.84540i	0.979543	−	0.172720i	0.640422	+	0.768023i	$0.278759\pi$
$788$	−2.00371	+	5.50514i	−0.0713791	+	0.196112i
$789$		0			0
$790$	1.42426	−	1.69737i	0.0506729	−	0.0603896i
$791$	0.109757	−	4.05346i	0.00390250	−	0.144125i
$792$		0			0
$793$	16.8936	−	29.2606i	0.599911	−	1.03908i
$794$	−17.9914	−	15.0966i	−0.638491	−	0.535757i
$795$		0			0
$796$	−6.96301	+	1.22777i	−0.246797	+	0.0435171i
$797$	−10.0467	−	3.65670i	−0.355873	−	0.129527i	0.157896	−	0.987456i	$-0.449529\pi$
$797$	−10.0467	−	3.65670i	−0.355873	−	0.129527i	−0.513769	+	0.857929i	$0.671751\pi$
$798$		0			0
$799$	−6.37163	+	36.1353i	−0.225412	+	1.27838i
$800$	22.3875	+	12.9254i	0.791518	+	0.456983i
$801$		0			0
$802$	9.01393	+	15.6126i	0.318293	+	0.551299i
$803$	−8.21077	+	46.5656i	−0.289752	+	1.64326i
$804$		0			0
$805$	4.73506	−	0.703348i	0.166889	−	0.0247898i
$806$	2.19492	+	2.61580i	0.0773127	+	0.0921377i
$807$		0			0
$808$	−17.3172	−	3.05350i	−0.609218	−	0.107422i
$809$	−43.9114	−	25.3522i	−1.54384	−	0.891338i	−0.998591	−	0.0530646i	$-0.983101\pi$
$809$	−43.9114	−	25.3522i	−1.54384	−	0.891338i	−0.545251	−	0.838273i	$-0.683566\pi$
$810$		0			0
$811$			4.10320i			0.144083i	0.997402	+	0.0720414i	$0.0229514\pi$
$811$			4.10320i			0.144083i	−0.997402	+	0.0720414i	$0.977049\pi$
$812$	−2.79486	−	8.37776i	−0.0980805	−	0.294002i
$813$		0			0
$814$	−23.1085	−	8.41079i	−0.809951	−	0.294798i
$815$	8.89830	+	3.23871i	0.311694	+	0.113447i
$816$		0			0
$817$	−49.4038	−	8.71122i	−1.72842	−	0.304767i
$818$	8.00392	−	13.8632i	0.279850	−	0.484715i
$819$		0			0
$820$	−1.67419	−	2.89977i	−0.0584651	−	0.101265i
$821$	−11.8782	−	32.6351i	−0.414552	−	1.13897i	−0.954744	−	0.297430i	$-0.903871\pi$
$821$	−11.8782	−	32.6351i	−0.414552	−	1.13897i	0.540192	−	0.841542i	$-0.318352\pi$
$822$		0			0
$823$	−29.5910	+	24.8298i	−1.03148	+	0.865512i	−0.991026	−	0.133669i	$-0.957324\pi$
$823$	−29.5910	+	24.8298i	−1.03148	+	0.865512i	−0.0404514	+	0.999182i	$0.512880\pi$
$824$	4.93885	+	28.0096i	0.172053	+	0.975762i
$825$		0			0
$826$	4.12897	+	12.3768i	0.143665	+	0.430644i
$827$	−28.4168	+	16.4064i	−0.988148	+	0.570508i	−0.904720	−	0.426006i	$-0.859920\pi$
$827$	−28.4168	+	16.4064i	−0.988148	+	0.570508i	−0.0834279	+	0.996514i	$0.526587\pi$
$828$		0			0
$829$	−9.16621	+	5.29211i	−0.318356	+	0.183803i	−0.650659	−	0.759370i	$-0.725507\pi$
$829$	−9.16621	+	5.29211i	−0.318356	+	0.183803i	0.332304	+	0.943172i	$0.392174\pi$
$830$	−0.468202	−	1.28637i	−0.0162515	−	0.0446507i
$831$		0			0
$832$	−27.0327	+	4.76660i	−0.937190	+	0.165252i
$833$	−30.7376	−	13.1120i	−1.06500	−	0.454305i
$834$		0			0
$835$	5.33814	+	4.47923i	0.184734	+	0.155010i
$836$	17.7202	−	30.6923i	0.612867	−	1.06152i
$837$		0			0
$838$	2.63070	−	1.51883i	0.0908759	−	0.0524672i
$839$	40.4225	−	14.7126i	1.39554	−	0.507934i	0.468687	−	0.883364i	$-0.344727\pi$
$839$	40.4225	−	14.7126i	1.39554	−	0.507934i	0.926851	+	0.375430i	$0.122505\pi$
$840$		0			0
$841$	15.7049	−	13.1780i	0.541549	−	0.454413i
$842$	−1.93296	−	2.30361i	−0.0666141	−	0.0793876i
$843$		0			0
$844$	−3.61567	+	1.31600i	−0.124456	+	0.0452985i
$845$	−4.60689			−0.158482
$846$		0			0
$847$	−33.3267	−	0.902395i	−1.14512	−	0.0310067i
$848$	1.93269	+	0.340786i	0.0663689	+	0.0117026i
$849$		0			0
$850$	−13.4652	−	16.0472i	−0.461853	−	0.550415i
$851$	12.6242	+	15.0449i	0.432751	+	0.515732i
$852$		0			0
$853$	35.0998	+	6.18904i	1.20179	+	0.211909i	0.738473	−	0.674283i	$-0.235547\pi$
$853$	35.0998	+	6.18904i	1.20179	+	0.211909i	0.463320	+	0.886191i	$0.346658\pi$
$854$	−8.36937	−	15.4473i	−0.286394	−	0.528594i
$855$		0			0
$856$	46.7338			1.59733
$857$	36.8153	−	13.3997i	1.25759	−	0.457724i	0.374628	−	0.927175i	$-0.377770\pi$
$857$	36.8153	−	13.3997i	1.25759	−	0.457724i	0.882959	+	0.469451i	$0.155548\pi$
$858$		0			0
$859$	−10.4657	−	12.4725i	−0.357083	−	0.425556i	0.557359	−	0.830272i	$-0.311815\pi$
$859$	−10.4657	−	12.4725i	−0.357083	−	0.425556i	−0.914442	+	0.404716i	$0.867370\pi$
$860$	−3.48327	+	2.92281i	−0.118779	+	0.0996671i
$861$		0			0
$862$	−29.7589	+	10.8313i	−1.01359	+	0.368917i
$863$	−30.6409	+	17.6905i	−1.04303	+	0.602193i	−0.920690	−	0.390295i	$-0.872373\pi$
$863$	−30.6409	+	17.6905i	−1.04303	+	0.602193i	−0.122339	+	0.992488i	$0.539040\pi$
$864$		0			0
$865$	−1.11039	+	1.92325i	−0.0377543	+	0.0653924i
$866$	−19.4252	−	16.2997i	−0.660095	−	0.553886i
$867$		0			0
$868$	−2.35217	+	0.349392i	−0.0798377	+	0.0118591i
$869$	22.7319	−	4.00825i	0.771127	−	0.135971i
$870$		0			0
$871$	14.0817	+	38.6892i	0.477141	+	1.31093i
$872$	−36.3806	+	21.0043i	−1.23200	+	0.711296i
$873$		0			0
$874$	18.3026	−	10.5670i	0.619096	−	0.357435i
$875$	12.3359	−	4.11532i	0.417030	−	0.139123i
$876$		0			0
$877$	−4.64641	−	26.3511i	−0.156898	−	0.889814i	−0.957030	−	0.289990i	$-0.906348\pi$
$877$	−4.64641	−	26.3511i	−0.156898	−	0.889814i	0.800131	−	0.599825i	$-0.204763\pi$
$878$	−2.67713	+	2.24638i	−0.0903489	+	0.0758117i
$879$		0			0
$880$	0.334231	+	0.918291i	0.0112669	+	0.0309556i
$881$	0.302257	+	0.523525i	0.0101833	+	0.0176380i	0.871072	−	0.491155i	$-0.163425\pi$
$881$	0.302257	+	0.523525i	0.0101833	+	0.0176380i	−0.860889	+	0.508793i	$0.830092\pi$
$882$		0			0
$883$	−10.2674	+	17.7836i	−0.345525	+	0.598466i	−0.985449	−	0.169972i	$-0.945632\pi$
$883$	−10.2674	+	17.7836i	−0.345525	+	0.598466i	0.639924	+	0.768438i	$0.278966\pi$
$884$	−25.3267	−	4.46578i	−0.851828	−	0.150200i
$885$		0			0
$886$	−18.7617	−	6.82872i	−0.630313	−	0.229415i
$887$	13.3953	+	4.87548i	0.449769	+	0.163702i	0.556966	−	0.830535i	$-0.311965\pi$
$887$	13.3953	+	4.87548i	0.449769	+	0.163702i	−0.107197	+	0.994238i	$0.534188\pi$
$888$		0			0
$889$	−21.1347	−	18.7320i	−0.708836	−	0.628252i
$890$		−	5.22737i		−	0.175222i
$891$		0			0
$892$	−6.56058	−	3.78775i	−0.219665	−	0.126823i
$893$	−48.2252	−	8.50341i	−1.61380	−	0.284556i
$894$		0			0
$895$	−0.976883	−	1.16420i	−0.0326536	−	0.0389150i
$896$	5.34498	−	13.5337i	0.178563	−	0.452128i
$897$		0			0
$898$	−2.78305	+	15.7835i	−0.0928717	+	0.526702i
$899$	1.14416	+	1.98175i	0.0381599	+	0.0660949i
$900$		0			0
$901$	20.3429	+	11.7450i	0.677720	+	0.391282i
$902$	−4.52273	+	25.6497i	−0.150590	+	0.854041i
$903$		0			0
$904$	−4.18815	−	1.52436i	−0.139296	−	0.0506995i
$905$	1.13646	−	0.200389i	0.0377774	−	0.00666117i
$906$		0			0
$907$	21.6318	+	18.1512i	0.718272	+	0.602702i	0.926907	−	0.375292i	$-0.122457\pi$
$907$	21.6318	+	18.1512i	0.718272	+	0.602702i	−0.208634	+	0.977994i	$0.566902\pi$
$908$	−6.00126	+	10.3945i	−0.199159	+	0.344953i
$909$		0			0
$910$	−3.03739	+	4.94667i	−0.100688	+	0.163981i
$911$	−20.6579	+	24.6191i	−0.684426	+	0.815667i	−0.990670	−	0.136286i	$-0.956483\pi$
$911$	−20.6579	+	24.6191i	−0.684426	+	0.815667i	0.306244	+	0.951953i	$0.400928\pi$
$912$		0			0
$913$	4.87749	−	13.4008i	0.161421	−	0.443501i
$914$	−29.8823	+	5.26906i	−0.988419	+	0.174285i
$915$		0			0
$916$	6.84153	+	18.7969i	0.226050	+	0.621068i
$917$	12.7503	−	20.7650i	0.421052	−	0.685722i
$918$		0			0
$919$	7.94398	+	13.7594i	0.262048	+	0.453880i	0.966786	−	0.255587i	$-0.0822688\pi$
$919$	7.94398	+	13.7594i	0.262048	+	0.453880i	−0.704738	+	0.709468i	$0.748936\pi$
$920$	0.913663	−	5.18164i	0.0301226	−	0.170834i
$921$		0			0
$922$	−0.251964	+	0.692265i	−0.00829799	+	0.0227985i
$923$	10.6703	+	60.5142i	0.351217	+	1.99185i
$924$		0			0
$925$	19.9019	+	16.6997i	0.654370	+	0.549081i
$926$			10.6133i			0.348773i
$927$		0			0
$928$	−15.8802			−0.521293
$929$	−30.6761	+	11.1652i	−1.00645	+	0.366318i	−0.792069	−	0.610432i	$-0.790996\pi$
$929$	−30.6761	+	11.1652i	−1.00645	+	0.366318i	−0.214382	+	0.976750i	$0.568774\pi$
$930$		0			0
$931$	17.4990	−	41.0216i	0.573505	−	1.34443i
$932$	−4.02251	+	11.0517i	−0.131762	+	0.362012i
$933$		0			0
$934$	3.08451	−	3.67598i	0.100928	−	0.120282i
$935$			11.6968i			0.382525i
$936$		0			0
$937$	3.11413	+	1.79794i	0.101734	+	0.0587362i	0.550004	−	0.835162i	$-0.314626\pi$
$937$	3.11413	+	1.79794i	0.101734	+	0.0587362i	−0.448270	+	0.893898i	$0.647960\pi$
$938$	20.9753	+	4.28693i	0.684868	+	0.139973i
$939$		0			0
$940$	−3.40018	+	2.85309i	−0.110902	+	0.0930575i
$941$	3.47924	+	19.7318i	0.113420	+	0.643237i	0.987520	+	0.157492i	$0.0503407\pi$
$941$	3.47924	+	19.7318i	0.113420	+	0.643237i	−0.874100	+	0.485745i	$0.838548\pi$
$942$		0			0
$943$	13.3705	−	15.9343i	0.435404	−	0.518894i
$944$	2.12717			0.0692336
$945$		0			0
$946$	35.3696			1.14997
$947$	31.5741	−	37.6285i	1.02602	−	1.22276i	0.0514516	−	0.998675i	$-0.483615\pi$
$947$	31.5741	−	37.6285i	1.02602	−	1.22276i	0.974569	−	0.224088i	$-0.0719403\pi$
$948$		0			0
$949$	7.95159	+	45.0957i	0.258119	+	1.46387i
$950$	21.4162	−	17.9703i	0.694832	−	0.583034i
$951$		0			0
$952$	−24.3627	+	27.4877i	−0.789601	+	0.890881i
$953$	27.6214	+	15.9472i	0.894744	+	0.516581i	0.875491	−	0.483234i	$-0.160538\pi$
$953$	27.6214	+	15.9472i	0.894744	+	0.516581i	0.0192530	+	0.999815i	$0.493871\pi$
$954$		0			0
$955$		−	6.63223i		−	0.214614i
$956$	16.5572	−	19.7321i	0.535497	−	0.638181i
$957$		0			0
$958$	5.85857	−	16.0963i	0.189282	−	0.520048i
$959$	14.4701	−	36.6388i	0.467265	−	1.18313i
$960$		0			0
$961$	−28.5515	+	10.3919i	−0.921016	+	0.335222i
$962$	−23.8152			−0.767834
$963$		0			0
$964$			9.80440i			0.315778i
$965$	−0.0144820	−	0.0121518i	−0.000466191	−	0.000391180i
$966$		0			0
$967$	−7.25864	−	41.1658i	−0.233422	−	1.32380i	−0.845911	−	0.533323i	$-0.820943\pi$
$967$	−7.25864	−	41.1658i	−0.233422	−	1.32380i	0.612489	−	0.790479i	$-0.290168\pi$
$968$	−12.5330	+	34.4340i	−0.402825	+	1.10675i
$969$		0			0
$970$	0.198773	−	1.12730i	0.00638221	−	0.0361953i
$971$	−23.9484	−	41.4799i	−0.768542	−	1.33115i	−0.938353	−	0.345677i	$-0.887649\pi$
$971$	−23.9484	−	41.4799i	−0.768542	−	1.33115i	0.169811	−	0.985477i	$-0.445684\pi$
$972$		0			0
$973$	24.9374	−	13.5112i	0.799456	−	0.433148i
$974$	8.20437	+	22.5413i	0.262885	+	0.722270i
$975$		0			0
$976$	−2.82082	+	0.497386i	−0.0902921	+	0.0159209i
$977$	8.07507	−	22.1861i	0.258344	−	0.709796i	−0.740925	−	0.671587i	$-0.765613\pi$
$977$	8.07507	−	22.1861i	0.258344	−	0.709796i	0.999270	−	0.0382082i	$-0.0121650\pi$
$978$		0			0
$979$	35.0037	−	41.7158i	1.11872	−	1.33324i
$980$	−1.82880	−	3.60508i	−0.0584188	−	0.115160i
$981$		0			0
$982$	8.40668	−	14.5608i	0.268268	−	0.464654i
$983$	47.1705	+	39.5808i	1.50451	+	1.26243i	0.873675	+	0.486510i	$0.161730\pi$
$983$	47.1705	+	39.5808i	1.50451	+	1.26243i	0.630831	+	0.775920i	$0.282714\pi$
$984$		0			0
$985$	2.54122	−	0.448086i	0.0809701	−	0.0142772i
$986$	12.0924	+	4.40128i	0.385101	+	0.140165i
$987$		0			0
$988$	5.95990	−	33.8003i	0.189610	−	1.07533i
$989$	−24.4631	−	14.1238i	−0.777881	−	0.449110i
$990$		0			0
$991$	3.19820	+	5.53945i	0.101594	+	0.175966i	0.912342	−	0.409430i	$-0.134272\pi$
$991$	3.19820	+	5.53945i	0.101594	+	0.175966i	−0.810747	+	0.585396i	$0.800939\pi$
$992$	−0.742492	+	4.21088i	−0.0235741	+	0.133696i
$993$		0			0
$994$	29.7181	+	11.7369i	0.942602	+	0.372271i
$995$	2.00181	+	2.38566i	0.0634615	+	0.0756305i
$996$		0			0
$997$	35.4811	+	6.25628i	1.12370	+	0.198138i	0.704464	−	0.709740i	$-0.251187\pi$
$997$	35.4811	+	6.25628i	1.12370	+	0.198138i	0.419234	+	0.907878i	$0.362299\pi$
$998$	19.5720	+	11.2999i	0.619542	+	0.357693i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.ba.a.143.8		132
3.2	odd	2		189.2.ba.a.101.15	✓	132
7.5	odd	6		567.2.bd.a.467.15		132
21.5	even	6		189.2.bd.a.47.8	yes	132
27.4	even	9		189.2.bd.a.185.8	yes	132
27.23	odd	18		567.2.bd.a.17.15		132
189.131	even	18	inner	567.2.ba.a.341.8		132
189.166	odd	18		189.2.ba.a.131.15	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.15	✓	132	3.2	odd	2
189.2.ba.a.131.15	yes	132	189.166	odd	18
189.2.bd.a.47.8	yes	132	21.5	even	6
189.2.bd.a.185.8	yes	132	27.4	even	9
567.2.ba.a.143.8		132	1.1	even	1	trivial
567.2.ba.a.341.8		132	189.131	even	18	inner
567.2.bd.a.17.15		132	27.23	odd	18
567.2.bd.a.467.15		132	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.ba (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.594351 + 0.708320i) q^{2} +(0.198832 + 1.12763i) q^{4} +(0.386349 - 0.324185i) q^{5} +(0.529787 - 2.59217i) q^{7} +(-2.51844 - 1.45402i) q^{8} +0.466338i q^{10} +(-3.12271 + 3.72150i) q^{11} +(-1.60911 + 4.42100i) q^{13} +(1.52120 + 1.91591i) q^{14} +(0.374792 - 0.136413i) q^{16} +4.77392 q^{17} +6.37115i q^{19} +(0.442381 + 0.371202i) q^{20} +(-0.780028 - 4.42376i) q^{22} +(-1.22699 + 3.37113i) q^{23} +(-0.824071 + 4.67354i) q^{25} +(-2.17510 - 3.76739i) q^{26} +(3.02836 + 0.0819996i) q^{28} +(-0.997075 - 2.73944i) q^{29} +(-0.773023 + 0.136305i) q^{31} +(1.86308 - 5.11878i) q^{32} +(-2.83739 + 3.38147i) q^{34} +(-0.635660 - 1.17323i) q^{35} +(2.73726 - 4.74107i) q^{37} +(-4.51281 - 3.78670i) q^{38} +(-1.44437 + 0.254681i) q^{40} +(-5.44849 - 1.98309i) q^{41} +(-1.36729 + 7.75429i) q^{43} +(-4.81739 - 2.78132i) q^{44} +(-1.65857 - 2.87274i) q^{46} +(-1.33467 + 7.56931i) q^{47} +(-6.43865 - 2.74659i) q^{49} +(-2.82057 - 3.36143i) q^{50} +(-5.30521 - 0.935452i) q^{52} +(4.26125 + 2.46023i) q^{53} +2.45014i q^{55} +(-5.10329 + 5.75788i) q^{56} +(2.53301 + 0.921941i) q^{58} +(5.01169 + 1.82411i) q^{59} +(-7.07246 - 1.24706i) q^{61} +(0.362900 - 0.628561i) q^{62} +(2.91725 + 5.05283i) q^{64} +(0.811544 + 2.22970i) q^{65} +(6.70384 - 5.62519i) q^{67} +(0.949211 + 5.38324i) q^{68} +(1.20883 + 0.247060i) q^{70} +(11.3110 - 6.53043i) q^{71} +(8.42907 - 4.86653i) q^{73} +(1.73130 + 4.75671i) q^{74} +(-7.18433 + 1.26679i) q^{76} +(7.99238 + 10.0662i) q^{77} +(-3.63977 - 3.05413i) q^{79} +(0.100577 - 0.174205i) q^{80} +(4.64298 - 2.68063i) q^{82} +(-2.75845 + 1.00400i) q^{83} +(1.84440 - 1.54764i) q^{85} +(-4.67987 - 5.57725i) q^{86} +(13.2755 - 4.83188i) q^{88} -11.2094 q^{89} +(10.6075 + 6.51327i) q^{91} +(-4.04537 - 0.713308i) q^{92} +(-4.56823 - 5.44420i) q^{94} +(2.06543 + 2.46149i) q^{95} +(-2.41733 - 0.426241i) q^{97} +(5.77228 - 2.92818i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} + 9 q^{11} - 3 q^{14} + 3 q^{16} + 18 q^{17} - 18 q^{20} - 12 q^{22} + 6 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} - 3 q^{32} - 18 q^{34}+ \cdots - 27 q^{98}+O(q^{100}) \) 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 + 9 * q^11 - 3 * q^14 + 3 * q^16 + 18 * q^17 - 18 * q^20 - 12 * q^22 + 6 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 - 3 * q^32 - 18 * q^34 - 18 * q^35 + 3 * q^37 + 99 * q^38 - 54 * q^40 - 12 * q^43 + 9 * q^44 + 3 * q^46 - 45 * q^47 - 24 * q^49 + 9 * q^50 - 9 * q^52 + 45 * q^53 - 3 * q^56 - 3 * q^58 - 36 * q^59 - 9 * q^61 + 99 * q^62 + 18 * q^64 - 69 * q^65 - 3 * q^67 - 36 * q^68 + 66 * q^70 - 18 * q^71 - 9 * q^73 - 75 * q^74 + 36 * q^76 - 15 * q^77 - 21 * q^79 - 72 * q^80 - 18 * q^82 + 90 * q^83 + 9 * q^85 + 105 * q^86 - 63 * q^88 + 18 * q^89 + 6 * q^91 - 150 * q^92 - 9 * q^94 - 45 * q^95 - 27 * q^98

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