LMFDB - Embedded newform 567.2.v.b.442.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(64,567)]

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([2, 0]))

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

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

chi := DirichletCharacter("567.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.v (of order $9$, 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:	$54$
Relative dimension:	$9$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			442.8
Character	$\chi$	$=$	567.442
Dual form			567.2.v.b.127.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.17963 - 0.989828i) q^{2} +(0.0644735 - 0.365648i) q^{4} +(1.99174 - 0.724932i) q^{5} +(0.173648 + 0.984808i) q^{7} +(1.25403 + 2.17204i) q^{8} +O(q^{10})$	\(q+(1.17963 - 0.989828i) q^{2} +(0.0644735 - 0.365648i) q^{4} +(1.99174 - 0.724932i) q^{5} +(0.173648 + 0.984808i) q^{7} +(1.25403 + 2.17204i) q^{8} +(1.63195 - 2.82663i) q^{10} +(0.848433 + 0.308804i) q^{11} +(1.15251 + 0.967070i) q^{13} +(1.17963 + 0.989828i) q^{14} +(4.32702 + 1.57491i) q^{16} +(-0.841276 + 1.45713i) q^{17} +(-1.00997 - 1.74932i) q^{19} +(-0.136656 - 0.775012i) q^{20} +(1.30650 - 0.475528i) q^{22} +(1.35659 - 7.69360i) q^{23} +(-0.388738 + 0.326190i) q^{25} +2.31677 q^{26} +0.371288 q^{28} +(-0.185749 + 0.155862i) q^{29} +(0.233808 - 1.32599i) q^{31} +(1.94958 - 0.709590i) q^{32} +(0.449915 + 2.55160i) q^{34} +(1.05978 + 1.83559i) q^{35} +(-1.42718 + 2.47195i) q^{37} +(-2.92292 - 1.06386i) q^{38} +(4.07227 + 3.41704i) q^{40} +(-7.73512 - 6.49053i) q^{41} +(9.52529 + 3.46692i) q^{43} +(0.167615 - 0.290318i) q^{44} +(-6.01507 - 10.4184i) q^{46} +(-1.00540 - 5.70189i) q^{47} +(-0.939693 + 0.342020i) q^{49} +(-0.135696 + 0.769568i) q^{50} +(0.427913 - 0.359062i) q^{52} -12.2478 q^{53} +1.91372 q^{55} +(-1.92128 + 1.61214i) q^{56} +(-0.0648388 + 0.367719i) q^{58} +(6.69703 - 2.43752i) q^{59} +(-0.860819 - 4.88195i) q^{61} +(-1.03670 - 1.79561i) q^{62} +(-3.00731 + 5.20881i) q^{64} +(2.99655 + 1.09066i) q^{65} +(6.80399 + 5.70922i) q^{67} +(0.478557 + 0.401557i) q^{68} +(3.06707 + 1.11632i) q^{70} +(-5.10249 + 8.83777i) q^{71} +(-6.65153 - 11.5208i) q^{73} +(0.763260 + 4.32866i) q^{74} +(-0.704751 + 0.256509i) q^{76} +(-0.156784 + 0.889167i) q^{77} +(-13.3476 + 11.2000i) q^{79} +9.75999 q^{80} -15.5491 q^{82} +(-5.41210 + 4.54129i) q^{83} +(-0.619276 + 3.51209i) q^{85} +(14.6680 - 5.33871i) q^{86} +(0.393223 + 2.23008i) q^{88} +(4.97553 + 8.61787i) q^{89} +(-0.752247 + 1.30293i) q^{91} +(-2.72568 - 0.992068i) q^{92} +(-6.82989 - 5.73096i) q^{94} +(-3.27973 - 2.75202i) q^{95} +(-8.75800 - 3.18765i) q^{97} +(-0.769949 + 1.33359i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + 3 q^{5} + 27 q^{8}+O(q^{10}) $ 54 * q + 3 * q^5 + 27 * q^8	$ 54 q + 3 q^{5} + 27 q^{8} + 6 q^{11} - 9 q^{13} + 30 q^{17} + 12 q^{20} - 9 q^{22} + 12 q^{23} + 27 q^{25} - 18 q^{26} + 54 q^{28} - 6 q^{29} - 9 q^{31} + 9 q^{32} - 9 q^{34} + 12 q^{35} - 54 q^{38} - 45 q^{40} + 15 q^{41} - 9 q^{43} + 42 q^{44} + 45 q^{47} - 18 q^{50} - 63 q^{52} - 132 q^{53} + 9 q^{56} - 27 q^{58} + 36 q^{62} - 27 q^{64} - 66 q^{65} + 45 q^{67} - 87 q^{68} + 72 q^{71} + 72 q^{74} + 54 q^{76} - 3 q^{77} - 36 q^{79} - 42 q^{80} - 24 q^{83} + 18 q^{85} + 90 q^{86} + 54 q^{88} + 42 q^{89} - 87 q^{92} - 90 q^{94} - 12 q^{95} - 18 q^{97} + 9 q^{98}+O(q^{100}) $ 54 * q + 3 * q^5 + 27 * q^8 + 6 * q^11 - 9 * q^13 + 30 * q^17 + 12 * q^20 - 9 * q^22 + 12 * q^23 + 27 * q^25 - 18 * q^26 + 54 * q^28 - 6 * q^29 - 9 * q^31 + 9 * q^32 - 9 * q^34 + 12 * q^35 - 54 * q^38 - 45 * q^40 + 15 * q^41 - 9 * q^43 + 42 * q^44 + 45 * q^47 - 18 * q^50 - 63 * q^52 - 132 * q^53 + 9 * q^56 - 27 * q^58 + 36 * q^62 - 27 * q^64 - 66 * q^65 + 45 * q^67 - 87 * q^68 + 72 * q^71 + 72 * q^74 + 54 * q^76 - 3 * q^77 - 36 * q^79 - 42 * q^80 - 24 * q^83 + 18 * q^85 + 90 * q^86 + 54 * q^88 + 42 * q^89 - 87 * q^92 - 90 * q^94 - 12 * q^95 - 18 * q^97 + 9 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$407$
$\chi(n)$	$1$	$e\left(\frac{7}{9}\right)$

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 $

$2$	1.17963	−	0.989828i	0.834125	−	0.699914i	−0.122109	−	0.992517i	$-0.538966\pi$
$2$	1.17963	−	0.989828i	0.834125	−	0.699914i	0.956234	+	0.292603i	$0.0945213\pi$
$3$		0			0
$3$		0			0
$4$	0.0644735	−	0.365648i	0.0322368	−	0.182824i
$5$	1.99174	−	0.724932i	0.890731	−	0.324200i	0.144199	−	0.989549i	$-0.453940\pi$
$5$	1.99174	−	0.724932i	0.890731	−	0.324200i	0.746532	+	0.665349i	$0.231717\pi$
$6$		0			0
$7$	0.173648	+	0.984808i	0.0656328	+	0.372222i
$7$	0.173648	+	0.984808i	0.0656328	+	0.372222i
$8$	1.25403	+	2.17204i	0.443365	+	0.767931i
$9$		0			0
$10$	1.63195	−	2.82663i	0.516069	−	0.893858i
$11$	0.848433	+	0.308804i	0.255812	+	0.0931081i	0.466743	−	0.884393i	$-0.345427\pi$
$11$	0.848433	+	0.308804i	0.255812	+	0.0931081i	−0.210931	+	0.977501i	$0.567649\pi$
$12$		0			0
$13$	1.15251	+	0.967070i	0.319648	+	0.268217i	0.788466	−	0.615078i	$-0.210875\pi$
$13$	1.15251	+	0.967070i	0.319648	+	0.268217i	−0.468818	+	0.883295i	$0.655320\pi$
$14$	1.17963	+	0.989828i	0.315270	+	0.264543i
$15$		0			0
$16$	4.32702	+	1.57491i	1.08176	+	0.393727i
$17$	−0.841276	+	1.45713i	−0.204039	+	0.353406i	−0.949826	−	0.312778i	$-0.898740\pi$
$17$	−0.841276	+	1.45713i	−0.204039	+	0.353406i	0.745787	+	0.666185i	$0.232074\pi$
$18$		0			0
$19$	−1.00997	−	1.74932i	−0.231703	−	0.401322i	0.726606	−	0.687054i	$-0.241096\pi$
$19$	−1.00997	−	1.74932i	−0.231703	−	0.401322i	−0.958309	+	0.285732i	$0.907763\pi$
$20$	−0.136656	−	0.775012i	−0.0305571	−	0.173298i
$21$		0			0
$22$	1.30650	−	0.475528i	0.278547	−	0.101383i
$23$	1.35659	−	7.69360i	0.282868	−	1.60423i	−0.429933	−	0.902861i	$-0.641463\pi$
$23$	1.35659	−	7.69360i	0.282868	−	1.60423i	0.712801	−	0.701366i	$-0.247426\pi$
$24$		0			0
$25$	−0.388738	+	0.326190i	−0.0777477	+	0.0652381i
$26$	2.31677			0.454356
$27$		0			0
$28$	0.371288			0.0701669
$29$	−0.185749	+	0.155862i	−0.0344927	+	0.0289429i	−0.659871	−	0.751379i	$-0.729389\pi$
$29$	−0.185749	+	0.155862i	−0.0344927	+	0.0289429i	0.625378	+	0.780322i	$0.284945\pi$
$30$		0			0
$31$	0.233808	−	1.32599i	0.0419932	−	0.238155i	−0.956586	−	0.291452i	$-0.905862\pi$
$31$	0.233808	−	1.32599i	0.0419932	−	0.238155i	0.998579	+	0.0532964i	$0.0169728\pi$
$32$	1.94958	−	0.709590i	0.344641	−	0.125439i
$33$		0			0
$34$	0.449915	+	2.55160i	0.0771598	+	0.437595i
$35$	1.05978	+	1.83559i	0.179136	+	0.310272i
$36$		0			0
$37$	−1.42718	+	2.47195i	−0.234628	+	0.406387i	−0.959164	−	0.282849i	$-0.908720\pi$
$37$	−1.42718	+	2.47195i	−0.234628	+	0.406387i	0.724537	+	0.689236i	$0.242054\pi$
$38$	−2.92292	−	1.06386i	−0.474160	−	0.172580i
$39$		0			0
$40$	4.07227	+	3.41704i	0.643882	+	0.540281i
$41$	−7.73512	−	6.49053i	−1.20802	−	1.01365i	−0.999364	−	0.0356626i	$-0.988646\pi$
$41$	−7.73512	−	6.49053i	−1.20802	−	1.01365i	−0.208659	−	0.977989i	$-0.566910\pi$
$42$		0			0
$43$	9.52529	+	3.46692i	1.45259	+	0.528701i	0.943314	−	0.331900i	$-0.107690\pi$
$43$	9.52529	+	3.46692i	1.45259	+	0.528701i	0.509279	+	0.860601i	$0.329912\pi$
$44$	0.167615	−	0.290318i	0.0252689	−	0.0437671i
$45$		0			0
$46$	−6.01507	−	10.4184i	−0.886873	−	1.53611i
$47$	−1.00540	−	5.70189i	−0.146652	−	0.831707i	−0.966026	−	0.258446i	$-0.916790\pi$
$47$	−1.00540	−	5.70189i	−0.146652	−	0.831707i	0.819373	−	0.573260i	$-0.194322\pi$
$48$		0			0
$49$	−0.939693	+	0.342020i	−0.134242	+	0.0488600i
$50$	−0.135696	+	0.769568i	−0.0191903	+	0.108833i
$51$		0			0
$52$	0.427913	−	0.359062i	0.0593409	−	0.0497929i
$53$	−12.2478			−1.68236			−0.841181	−	0.540754i	$-0.818139\pi$
$53$	−12.2478			−1.68236			−0.841181	+	0.540754i	$0.818139\pi$
$54$		0			0
$55$	1.91372			0.258046
$56$	−1.92128	+	1.61214i	−0.256742	+	0.215432i
$57$		0			0
$58$	−0.0648388	+	0.367719i	−0.00851376	+	0.0482839i
$59$	6.69703	−	2.43752i	0.871879	−	0.317338i	0.132951	−	0.991123i	$-0.457555\pi$
$59$	6.69703	−	2.43752i	0.871879	−	0.317338i	0.738928	+	0.673785i	$0.235332\pi$
$60$		0			0
$61$	−0.860819	−	4.88195i	−0.110217	−	0.625069i	−0.989008	−	0.147863i	$-0.952761\pi$
$61$	−0.860819	−	4.88195i	−0.110217	−	0.625069i	0.878791	−	0.477206i	$-0.158351\pi$
$62$	−1.03670	−	1.79561i	−0.131661	−	0.228043i
$63$		0			0
$64$	−3.00731	+	5.20881i	−0.375913	+	0.651101i
$65$	2.99655	+	1.09066i	0.371677	+	0.135279i
$66$		0			0
$67$	6.80399	+	5.70922i	0.831239	+	0.697493i	0.955575	−	0.294748i	$-0.0952356\pi$
$67$	6.80399	+	5.70922i	0.831239	+	0.697493i	−0.124336	+	0.992240i	$0.539680\pi$
$68$	0.478557	+	0.401557i	0.0580336	+	0.0486959i
$69$		0			0
$70$	3.06707	+	1.11632i	0.366585	+	0.133426i
$71$	−5.10249	+	8.83777i	−0.605554	+	1.04885i	0.386410	+	0.922327i	$0.373715\pi$
$71$	−5.10249	+	8.83777i	−0.605554	+	1.04885i	−0.991964	+	0.126523i	$0.959618\pi$
$72$		0			0
$73$	−6.65153	−	11.5208i	−0.778503	−	1.34841i	−0.932805	−	0.360382i	$-0.882646\pi$
$73$	−6.65153	−	11.5208i	−0.778503	−	1.34841i	0.154302	−	0.988024i	$-0.450687\pi$
$74$	0.763260	+	4.32866i	0.0887271	+	0.503196i
$75$		0			0
$76$	−0.704751	+	0.256509i	−0.0808405	+	0.0294236i
$77$	−0.156784	+	0.889167i	−0.0178672	+	0.101330i
$78$		0			0
$79$	−13.3476	+	11.2000i	−1.50173	+	1.26010i	−0.623532	+	0.781798i	$0.714303\pi$
$79$	−13.3476	+	11.2000i	−1.50173	+	1.26010i	−0.878196	+	0.478301i	$0.841253\pi$
$80$	9.75999			1.09120
$81$		0			0
$82$	−15.5491			−1.71711
$83$	−5.41210	+	4.54129i	−0.594056	+	0.498472i	−0.889529	−	0.456879i	$-0.848967\pi$
$83$	−5.41210	+	4.54129i	−0.594056	+	0.498472i	0.295473	+	0.955351i	$0.404523\pi$
$84$		0			0
$85$	−0.619276	+	3.51209i	−0.0671699	+	0.380940i
$86$	14.6680	−	5.33871i	1.58169	−	0.575688i
$87$		0			0
$88$	0.393223	+	2.23008i	0.0419177	+	0.237727i
$89$	4.97553	+	8.61787i	0.527405	+	0.913492i	0.999490	+	0.0319390i	$0.0101682\pi$
$89$	4.97553	+	8.61787i	0.527405	+	0.913492i	−0.472085	+	0.881553i	$0.656498\pi$
$90$		0			0
$91$	−0.752247	+	1.30293i	−0.0788569	+	0.136584i
$92$	−2.72568	−	0.992068i	−0.284172	−	0.103430i
$93$		0			0
$94$	−6.82989	−	5.73096i	−0.704449	−	0.591103i
$95$	−3.27973	−	2.75202i	−0.336494	−	0.282352i
$96$		0			0
$97$	−8.75800	−	3.18765i	−0.889240	−	0.323657i	−0.143307	−	0.989678i	$-0.545774\pi$
$97$	−8.75800	−	3.18765i	−0.889240	−	0.323657i	−0.745933	+	0.666021i	$0.767996\pi$
$98$	−0.769949	+	1.33359i	−0.0777766	+	0.134713i
$99$		0			0
$100$	0.0942074	+	0.163172i	0.00942074	+	0.0163172i
$101$	−1.43623	−	8.14528i	−0.142911	−	0.810486i	−0.969021	−	0.246978i	$-0.920562\pi$
$101$	−1.43623	−	8.14528i	−0.142911	−	0.810486i	0.826111	−	0.563508i	$-0.190549\pi$
$102$		0			0
$103$	12.9804	−	4.72449i	1.27900	−	0.465518i	0.388899	−	0.921280i	$-0.372856\pi$
$103$	12.9804	−	4.72449i	1.27900	−	0.465518i	0.890102	+	0.455762i	$0.150633\pi$
$104$	−0.655235	+	3.71602i	−0.0642511	+	0.364386i
$105$		0			0
$106$	−14.4479	+	12.1232i	−1.40330	+	1.17751i
$107$	−13.2462			−1.28056			−0.640281	−	0.768141i	$-0.721182\pi$
$107$	−13.2462			−1.28056			−0.640281	+	0.768141i	$0.721182\pi$
$108$		0			0
$109$	−2.27619			−0.218020			−0.109010	−	0.994041i	$-0.534768\pi$
$109$	−2.27619			−0.218020			−0.109010	+	0.994041i	$0.534768\pi$
$110$	2.25748	−	1.89425i	0.215242	−	0.180610i
$111$		0			0
$112$	−0.799602	+	4.53477i	−0.0755552	+	0.428495i
$113$	4.87263	−	1.77349i	0.458378	−	0.166836i	−0.102502	−	0.994733i	$-0.532685\pi$
$113$	4.87263	−	1.77349i	0.458378	−	0.166836i	0.560881	+	0.827897i	$0.310463\pi$
$114$		0			0
$115$	−2.87537	−	16.3071i	−0.268130	−	1.52064i
$116$	0.0450147	+	0.0779677i	0.00417951	+	0.00723912i
$117$		0			0
$118$	5.48730	−	9.50428i	0.505147	−	0.874940i
$119$	−1.58108	−	0.575466i	−0.144937	−	0.0527529i
$120$		0			0
$121$	−7.80201	−	6.54666i	−0.709274	−	0.595151i
$122$	−5.84773	−	4.90683i	−0.529429	−	0.444244i
$123$		0			0
$124$	−0.469772	−	0.170983i	−0.0421868	−	0.0153547i
$125$	−5.83670	+	10.1095i	−0.522050	+	0.904218i
$126$		0			0
$127$	9.54713	+	16.5361i	0.847171	+	1.46734i	0.883723	+	0.468011i	$0.155029\pi$
$127$	9.54713	+	16.5361i	0.847171	+	1.46734i	−0.0365516	+	0.999332i	$0.511637\pi$
$128$	2.32885	+	13.2076i	0.205843	+	1.16739i
$129$		0			0
$130$	4.61439	−	1.67950i	0.404709	−	0.147302i
$131$	−2.87073	+	16.2807i	−0.250817	+	1.42245i	0.555770	+	0.831336i	$0.312424\pi$
$131$	−2.87073	+	16.2807i	−0.250817	+	1.42245i	−0.806586	+	0.591116i	$0.798687\pi$
$132$		0			0
$133$	1.54737	−	1.29839i	0.134174	−	0.112585i
$134$	13.6773			1.18154
$135$		0			0
$136$	−4.21992			−0.361856
$137$	−3.40229	+	2.85486i	−0.290677	+	0.243907i	−0.776451	−	0.630177i	$-0.782982\pi$
$137$	−3.40229	+	2.85486i	−0.290677	+	0.243907i	0.485774	+	0.874084i	$0.338538\pi$
$138$		0			0
$139$	3.91490	−	22.2025i	0.332057	−	1.88319i	−0.122495	−	0.992469i	$-0.539090\pi$
$139$	3.91490	−	22.2025i	0.332057	−	1.88319i	0.454552	−	0.890720i	$-0.349799\pi$
$140$	0.739508	−	0.269159i	0.0624999	−	0.0227481i
$141$		0			0
$142$	2.72882	+	15.4759i	0.228997	+	1.29871i
$143$	0.679191	+	1.17639i	0.0567968	+	0.0983750i
$144$		0			0
$145$	−0.256974	+	0.445092i	−0.0213405	+	0.0369628i
$146$	−19.2499	−	7.00641i	−1.59314	−	0.579854i
$147$		0			0
$148$	0.811849	+	0.681222i	0.0667336	+	0.0559961i
$149$	−0.0860211	−	0.0721803i	−0.00704713	−	0.00591324i	0.639257	−	0.768993i	$-0.279242\pi$
$149$	−0.0860211	−	0.0721803i	−0.00704713	−	0.00591324i	−0.646304	+	0.763080i	$0.723686\pi$
$150$		0			0
$151$	8.43705	+	3.07084i	0.686598	+	0.249901i	0.661678	−	0.749788i	$-0.269845\pi$
$151$	8.43705	+	3.07084i	0.686598	+	0.249901i	0.0249200	+	0.999689i	$0.492067\pi$
$152$	2.53306	−	4.38739i	0.205458	−	0.355864i
$153$		0			0
$154$	0.695175	+	1.20408i	0.0560188	+	0.0970274i
$155$	−0.495571	−	2.81052i	−0.0398052	−	0.225747i
$156$		0			0
$157$	−9.93592	+	3.61638i	−0.792972	+	0.288618i	−0.706571	−	0.707642i	$-0.749759\pi$
$157$	−9.93592	+	3.61638i	−0.792972	+	0.288618i	−0.0864013	+	0.996260i	$0.527537\pi$
$158$	−4.65922	+	26.4237i	−0.370668	+	2.10216i
$159$		0			0
$160$	3.36865	−	2.82663i	0.266315	−	0.223465i
$161$	7.81229			0.615695
$162$		0			0
$163$	19.6000			1.53519			0.767596	−	0.640933i	$-0.221453\pi$
$163$	19.6000			1.53519			0.767596	+	0.640933i	$0.221453\pi$
$164$	−2.87196	+	2.40986i	−0.224262	+	0.188178i
$165$		0			0
$166$	−1.88919	+	10.7141i	−0.146629	+	0.831576i
$167$	11.7814	−	4.28809i	0.911674	−	0.331822i	0.156753	−	0.987638i	$-0.449897\pi$
$167$	11.7814	−	4.28809i	0.911674	−	0.331822i	0.754921	+	0.655815i	$0.227675\pi$
$168$		0			0
$169$	−1.86437	−	10.5734i	−0.143413	−	0.813338i
$170$	2.74585	+	4.75595i	0.210597	+	0.364764i
$171$		0			0
$172$	1.88180	−	3.25938i	0.143486	−	0.248525i
$173$	−2.90638	−	1.05783i	−0.220968	−	0.0804257i	0.229164	−	0.973388i	$-0.426401\pi$
$173$	−2.90638	−	1.05783i	−0.220968	−	0.0804257i	−0.450132	+	0.892962i	$0.648623\pi$
$174$		0			0
$175$	−0.388738	−	0.326190i	−0.0293859	−	0.0246577i
$176$	3.18485	+	2.67241i	0.240067	+	0.201440i
$177$		0			0
$178$	14.3995	+	5.24099i	1.07929	+	0.392829i
$179$	6.82084	−	11.8140i	0.509814	−	0.883023i	−0.490122	−	0.871654i	$-0.663048\pi$
$179$	6.82084	−	11.8140i	0.509814	−	0.883023i	0.999935	−	0.0113694i	$-0.00361906\pi$
$180$		0			0
$181$	3.74731	+	6.49053i	0.278535	+	0.482438i	0.971021	−	0.238994i	$-0.0768177\pi$
$181$	3.74731	+	6.49053i	0.278535	+	0.482438i	−0.692486	+	0.721432i	$0.743484\pi$
$182$	0.402302	+	2.28157i	0.0298206	+	0.169121i
$183$		0			0
$184$	18.4120	−	6.70141i	1.35735	−	0.494035i
$185$	−1.05057	+	5.95809i	−0.0772396	+	0.438048i
$186$		0			0
$187$	−1.16374	+	0.976490i	−0.0851008	+	0.0714080i
$188$	−2.14971			−0.156783
$189$		0			0
$190$	−6.59291			−0.478300
$191$	9.28748	−	7.79312i	0.672018	−	0.563890i	−0.241644	−	0.970365i	$-0.577686\pi$
$191$	9.28748	−	7.79312i	0.672018	−	0.563890i	0.913662	+	0.406475i	$0.133242\pi$
$192$		0			0
$193$	0.841645	−	4.77321i	0.0605830	−	0.343583i	−0.939417	−	0.342777i	$-0.888632\pi$
$193$	0.841645	−	4.77321i	0.0605830	−	0.343583i	1.00000		0.000805806i	$-0.000256496\pi$
$194$	−13.4864	+	4.90866i	−0.968269	+	0.352421i
$195$		0			0
$196$	0.0644735	+	0.365648i	0.00460525	+	0.0261177i
$197$	−0.769346	−	1.33255i	−0.0548136	−	0.0949400i	0.837317	−	0.546718i	$-0.184123\pi$
$197$	−0.769346	−	1.33255i	−0.0548136	−	0.0949400i	−0.892130	+	0.451778i	$0.850790\pi$
$198$		0			0
$199$	−5.70067	+	9.87385i	−0.404110	+	0.699939i	−0.994217	−	0.107386i	$-0.965752\pi$
$199$	−5.70067	+	9.87385i	−0.404110	+	0.699939i	0.590108	+	0.807325i	$0.299085\pi$
$200$	−1.19599	−	0.435303i	−0.0845689	−	0.0307806i
$201$		0			0
$202$	−9.75665	−	8.18681i	−0.686476	−	0.576022i
$203$	−0.185749	−	0.155862i	−0.0130370	−	0.0109394i
$204$		0			0
$205$	−20.1115	−	7.31999i	−1.40465	−	0.511250i
$206$	10.6357	−	18.4216i	0.741024	−	1.28349i
$207$		0			0
$208$	3.46389	+	5.99963i	0.240177	+	0.415999i
$209$	−0.316695	−	1.79607i	−0.0219062	−	0.124236i
$210$		0			0
$211$	0.714324	−	0.259993i	0.0491761	−	0.0178986i	−0.317315	−	0.948320i	$-0.602781\pi$
$211$	0.714324	−	0.259993i	0.0491761	−	0.0178986i	0.366491	+	0.930422i	$0.380559\pi$
$212$	−0.789657	+	4.47837i	−0.0542339	+	0.307576i
$213$		0			0
$214$	−15.6257	+	13.1115i	−1.06815	+	0.896283i
$215$	21.4852			1.46528
$216$		0			0
$217$	1.34645			0.0914029
$218$	−2.68506	+	2.25304i	−0.181856	+	0.152595i
$219$		0			0
$220$	0.123384	−	0.699746i	0.00831856	−	0.0471769i
$221$	−2.37873	+	0.865785i	−0.160010	+	0.0582390i
$222$		0			0
$223$	−3.74696	−	21.2501i	−0.250915	−	1.42301i	−0.806344	−	0.591446i	$-0.798557\pi$
$223$	−3.74696	−	21.2501i	−0.250915	−	1.42301i	0.555429	−	0.831564i	$-0.312554\pi$
$224$	1.03735	+	1.79675i	0.0693110	+	0.120050i
$225$		0			0
$226$	3.99245	−	6.91513i	0.265574	−	0.459988i
$227$	−21.0535	−	7.66286i	−1.39737	−	0.508602i	−0.469975	−	0.882680i	$-0.655737\pi$
$227$	−21.0535	−	7.66286i	−1.39737	−	0.508602i	−0.927397	+	0.374078i	$0.877959\pi$
$228$		0			0
$229$	6.92937	+	5.81443i	0.457905	+	0.384228i	0.842360	−	0.538916i	$-0.181166\pi$
$229$	6.92937	+	5.81443i	0.457905	+	0.384228i	−0.384454	+	0.923144i	$0.625610\pi$
$230$	−19.5331	−	16.3902i	−1.28797	−	1.08074i
$231$		0			0
$232$	−0.571472	−	0.207999i	−0.0375190	−	0.0136558i
$233$	−1.65434	+	2.86540i	−0.108380	+	0.187719i	−0.915114	−	0.403195i	$-0.867900\pi$
$233$	−1.65434	+	2.86540i	−0.108380	+	0.187719i	0.806734	+	0.590914i	$0.201233\pi$
$234$		0			0
$235$	−6.13597	−	10.6278i	−0.400267	−	0.693282i
$236$	−0.459492	−	2.60591i	−0.0299104	−	0.169630i
$237$		0			0
$238$	−2.43470	+	0.886160i	−0.157818	+	0.0574412i
$239$	−0.0219287	+	0.124364i	−0.00141845	+	0.00804442i	−0.985509	−	0.169625i	$-0.945745\pi$
$239$	−0.0219287	+	0.124364i	−0.00141845	+	0.00804442i	0.984090	+	0.177669i	$0.0568556\pi$
$240$		0			0
$241$	7.02297	−	5.89297i	0.452389	−	0.379600i	−0.387932	−	0.921688i	$-0.626811\pi$
$241$	7.02297	−	5.89297i	0.452389	−	0.379600i	0.840322	+	0.542088i	$0.182366\pi$
$242$	−15.6836			−1.00818
$243$		0			0
$244$	−1.84057			−0.117831
$245$	−1.62368	+	1.36243i	−0.103733	+	0.0870423i
$246$		0			0
$247$	0.527715	−	2.99282i	0.0335777	−	0.190429i
$248$	3.17331	−	1.15499i	0.201505	−	0.0733419i
$249$		0			0
$250$	3.12147	+	17.7028i	0.197419	+	1.11962i
$251$	−2.67545	−	4.63401i	−0.168873	−	0.292496i	0.769151	−	0.639067i	$-0.220679\pi$
$251$	−2.67545	−	4.63401i	−0.168873	−	0.292496i	−0.938024	+	0.346571i	$0.887346\pi$
$252$		0			0
$253$	3.52679	−	6.10859i	0.221728	−	0.384044i
$254$	27.6300	+	10.0565i	1.73366	+	0.631001i
$255$		0			0
$256$	6.60546	+	5.54264i	0.412842	+	0.346415i
$257$	8.24543	+	6.91874i	0.514336	+	0.431579i	0.862652	−	0.505798i	$-0.168802\pi$
$257$	8.24543	+	6.91874i	0.514336	+	0.431579i	−0.348316	+	0.937377i	$0.613246\pi$
$258$		0			0
$259$	−2.68223	−	0.976251i	−0.166666	−	0.0606613i
$260$	0.591994	−	1.02536i	0.0367139	−	0.0635904i
$261$		0			0
$262$	12.7287	+	22.0468i	0.786382	+	1.36205i
$263$	−5.22940	−	29.6574i	−0.322459	−	1.82875i	−0.526964	−	0.849888i	$-0.676670\pi$
$263$	−5.22940	−	29.6574i	−0.322459	−	1.82875i	0.204505	−	0.978865i	$-0.434441\pi$
$264$		0			0
$265$	−24.3943	+	8.87881i	−1.49853	+	0.545421i
$266$	0.540134	−	3.06325i	0.0331177	−	0.187820i
$267$		0			0
$268$	2.52624	−	2.11977i	0.154315	−	0.129485i
$269$	−3.20280			−0.195278			−0.0976390	−	0.995222i	$-0.531129\pi$
$269$	−3.20280			−0.195278			−0.0976390	+	0.995222i	$0.531129\pi$
$270$		0			0
$271$	−1.50570			−0.0914650			−0.0457325	−	0.998954i	$-0.514562\pi$
$271$	−1.50570			−0.0914650			−0.0457325	+	0.998954i	$0.514562\pi$
$272$	−5.93507	+	4.98011i	−0.359866	+	0.301964i
$273$		0			0
$274$	−1.18762	+	6.73535i	−0.0717470	+	0.406898i
$275$	−0.430548	+	0.156707i	−0.0259630	+	0.00944976i
$276$		0			0
$277$	−0.695989	−	3.94715i	−0.0418179	−	0.237161i	0.956734	−	0.290965i	$-0.0939765\pi$
$277$	−0.695989	−	3.94715i	−0.0418179	−	0.237161i	−0.998552	+	0.0538041i	$0.982865\pi$
$278$	−17.3585	−	30.0658i	−1.04109	−	1.80323i
$279$		0			0
$280$	−2.65798	+	4.60376i	−0.158845	+	0.275127i
$281$	20.7974	+	7.56964i	1.24067	+	0.451567i	0.877239	−	0.480054i	$-0.159383\pi$
$281$	20.7974	+	7.56964i	1.24067	+	0.451567i	0.363431	+	0.931621i	$0.381605\pi$
$282$		0			0
$283$	10.5194	+	8.82683i	0.625313	+	0.524700i	0.899469	−	0.436985i	$-0.143954\pi$
$283$	10.5194	+	8.82683i	0.625313	+	0.524700i	−0.274155	+	0.961685i	$0.588398\pi$
$284$	2.90253	+	2.43551i	0.172234	+	0.144521i
$285$		0			0
$286$	1.96562	+	0.715428i	0.116230	+	0.0423042i
$287$	5.04874	−	8.74467i	0.298018	−	0.516182i
$288$		0			0
$289$	7.08451	+	12.2707i	0.416736	+	0.721808i
$290$	0.137430	+	0.779403i	0.00807016	+	0.0457681i
$291$		0			0
$292$	−4.64140	+	1.68933i	−0.271617	+	0.0988606i
$293$	4.56992	−	25.9173i	0.266978	−	1.51411i	−0.496366	−	0.868113i	$-0.665333\pi$
$293$	4.56992	−	25.9173i	0.266978	−	1.51411i	0.763344	−	0.645993i	$-0.223556\pi$
$294$		0			0
$295$	11.5717	−	9.70979i	0.673729	−	0.565326i
$296$	−7.15890			−0.416103
$297$		0			0
$298$	−0.172919			−0.0100169
$299$	9.00373	−	7.55503i	0.520699	−	0.436918i
$300$		0			0
$301$	−1.76020	+	9.98261i	−0.101456	+	0.575388i
$302$	12.9922	−	4.72878i	0.747618	−	0.272111i
$303$		0			0
$304$	−1.61515	−	9.15996i	−0.0926351	−	0.525360i
$305$	−5.25360	−	9.09951i	−0.300821	−	0.521036i
$306$		0			0
$307$	−9.18538	+	15.9096i	−0.524238	+	0.908006i	0.475364	+	0.879789i	$0.342316\pi$
$307$	−9.18538	+	15.9096i	−0.524238	+	0.908006i	−0.999602	+	0.0282171i	$0.991017\pi$
$308$	0.315013	+	0.114656i	0.0179496	+	0.00653310i
$309$		0			0
$310$	−3.36653	−	2.82485i	−0.191206	−	0.160441i
$311$	−3.42058	−	2.87021i	−0.193963	−	0.162755i	0.540634	−	0.841258i	$-0.318184\pi$
$311$	−3.42058	−	2.87021i	−0.193963	−	0.162755i	−0.734597	+	0.678503i	$0.762629\pi$
$312$		0			0
$313$	−5.92706	−	2.15727i	−0.335017	−	0.121936i	0.169034	−	0.985610i	$-0.445935\pi$
$313$	−5.92706	−	2.15727i	−0.335017	−	0.121936i	−0.504051	+	0.863674i	$0.668158\pi$
$314$	−8.14112	+	14.1008i	−0.459430	+	0.795756i
$315$		0			0
$316$	3.23469	+	5.60264i	0.181965	+	0.315173i
$317$	3.68869	+	20.9196i	0.207178	+	1.17496i	0.893976	+	0.448115i	$0.147904\pi$
$317$	3.68869	+	20.9196i	0.207178	+	1.17496i	−0.686799	+	0.726848i	$0.740985\pi$
$318$		0			0
$319$	−0.205727	+	0.0748784i	−0.0115185	+	0.00419238i
$320$	−2.21372	+	12.5547i	−0.123751	+	0.701827i
$321$		0			0
$322$	9.21562	−	7.73282i	0.513566	−	0.430933i
$323$	3.39866			0.189106
$324$		0			0
$325$	−0.763473			−0.0423499
$326$	23.1208	−	19.4007i	1.28054	−	1.07450i
$327$		0			0
$328$	4.39764	−	24.9403i	0.242819	−	1.37709i
$329$	5.44068	−	1.98025i	0.299955	−	0.109175i
$330$		0			0
$331$	1.73937	+	9.86443i	0.0956042	+	0.542198i	0.994561	+	0.104160i	$0.0332154\pi$
$331$	1.73937	+	9.86443i	0.0956042	+	0.542198i	−0.898956	+	0.438038i	$0.855673\pi$
$332$	1.31158	+	2.27172i	0.0719821	+	0.124677i
$333$		0			0
$334$	9.65327	−	16.7200i	0.528203	−	0.914875i
$335$	17.6905	+	6.43883i	0.966538	+	0.351791i
$336$		0			0
$337$	−14.8835	−	12.4887i	−0.810756	−	0.680305i	0.140032	−	0.990147i	$-0.455279\pi$
$337$	−14.8835	−	12.4887i	−0.810756	−	0.680305i	−0.950788	+	0.309842i	$0.899724\pi$
$338$	−12.6651	−	10.6273i	−0.688891	−	0.578048i
$339$		0			0
$340$	1.24426	+	0.452874i	0.0674795	+	0.0245605i
$341$	0.607844	−	1.05282i	0.0329166	−	0.0570132i
$342$		0			0
$343$	−0.500000	−	0.866025i	−0.0269975	−	0.0467610i
$344$	4.41468	+	25.0369i	0.238024	+	1.34990i
$345$		0			0
$346$	−4.47553	+	1.62896i	−0.240606	+	0.0875734i
$347$	−2.12214	+	12.0352i	−0.113922	+	0.646085i	0.873356	+	0.487082i	$0.161939\pi$
$347$	−2.12214	+	12.0352i	−0.113922	+	0.646085i	−0.987278	+	0.159002i	$0.949172\pi$
$348$		0			0
$349$	19.7729	−	16.5914i	1.05842	−	0.888120i	0.0644661	−	0.997920i	$-0.479466\pi$
$349$	19.7729	−	16.5914i	1.05842	−	0.888120i	0.993954	+	0.109800i	$0.0350211\pi$
$350$	−0.781440			−0.0417697
$351$		0			0
$352$	1.87322			0.0998428
$353$	−9.92008	+	8.32394i	−0.527993	+	0.443038i	−0.867408	−	0.497598i	$-0.834215\pi$
$353$	−9.92008	+	8.32394i	−0.527993	+	0.443038i	0.339415	+	0.940637i	$0.389771\pi$
$354$		0			0
$355$	−3.75602	+	21.3015i	−0.199349	+	1.13056i
$356$	3.47189	−	1.26367i	0.184010	−	0.0669741i
$357$		0			0
$358$	−3.64780	−	20.6877i	−0.192792	−	1.09338i
$359$	−0.878299	−	1.52126i	−0.0463549	−	0.0802890i	0.841917	−	0.539607i	$-0.181427\pi$
$359$	−0.878299	−	1.52126i	−0.0463549	−	0.0802890i	−0.888272	+	0.459318i	$0.848094\pi$
$360$		0			0
$361$	7.45992	−	12.9210i	0.392627	−	0.680050i
$362$	10.8450	+	3.94724i	0.569998	+	0.207462i
$363$		0			0
$364$	0.427913	+	0.359062i	0.0224287	+	0.0188199i
$365$	−21.5999	−	18.1244i	−1.13059	−	0.948677i
$366$		0			0
$367$	8.87975	+	3.23196i	0.463519	+	0.168707i	0.563214	−	0.826311i	$-0.309565\pi$
$367$	8.87975	+	3.23196i	0.463519	+	0.168707i	−0.0996952	+	0.995018i	$0.531787\pi$
$368$	17.9867	−	31.1539i	0.937622	−	1.62401i
$369$		0			0
$370$	4.65820	+	8.06823i	0.242168	+	0.419448i
$371$	−2.12680	−	12.0617i	−0.110418	−	0.626212i
$372$		0			0
$373$	−9.26976	+	3.37392i	−0.479970	+	0.174695i	−0.570663	−	0.821184i	$-0.693314\pi$
$373$	−9.26976	+	3.37392i	−0.479970	+	0.174695i	0.0906935	+	0.995879i	$0.471092\pi$
$374$	−0.406221	+	2.30380i	−0.0210052	+	0.119126i
$375$		0			0
$376$	11.1239	−	9.33408i	0.573672	−	0.481368i
$377$	−0.364807			−0.0187885
$378$		0			0
$379$	26.4901			1.36070			0.680352	−	0.732886i	$-0.261827\pi$
$379$	26.4901			1.36070			0.680352	+	0.732886i	$0.261827\pi$
$380$	−1.21773	+	1.02179i	−0.0624681	+	0.0524170i
$381$		0			0
$382$	3.24195	−	18.3860i	0.165873	−	0.940710i
$383$	18.4370	−	6.71052i	0.942086	−	0.342891i	0.175097	−	0.984551i	$-0.443976\pi$
$383$	18.4370	−	6.71052i	0.942086	−	0.342891i	0.766989	+	0.641660i	$0.221754\pi$
$384$		0			0
$385$	0.332314	+	1.88464i	0.0169363	+	0.0960503i
$386$	−3.73182	−	6.46371i	−0.189945	−	0.328994i
$387$		0			0
$388$	−1.73022	+	2.99682i	−0.0878384	+	0.152141i
$389$	16.4697	+	5.99449i	0.835049	+	0.303933i	0.723929	−	0.689874i	$-0.242334\pi$
$389$	16.4697	+	5.99449i	0.835049	+	0.303933i	0.111119	+	0.993807i	$0.464556\pi$
$390$		0			0
$391$	10.0693	+	8.44917i	0.509228	+	0.427293i
$392$	−1.92128	−	1.61214i	−0.0970392	−	0.0814256i
$393$		0			0
$394$	−2.22653	−	0.810392i	−0.112171	−	0.0408270i
$395$	−18.4657	+	31.9836i	−0.929112	+	1.60927i
$396$		0			0
$397$	−3.37381	−	5.84361i	−0.169327	−	0.293283i	0.768857	−	0.639421i	$-0.220826\pi$
$397$	−3.37381	−	5.84361i	−0.169327	−	0.293283i	−0.938183	+	0.346139i	$0.887493\pi$
$398$	3.04873	+	17.2902i	0.152819	+	0.866679i
$399$		0			0
$400$	−2.19580	+	0.799206i	−0.109790	+	0.0399603i
$401$	−3.68355	+	20.8905i	−0.183948	+	1.04322i	0.743352	+	0.668901i	$0.233235\pi$
$401$	−3.68355	+	20.8905i	−0.183948	+	1.04322i	−0.927300	+	0.374320i	$0.877876\pi$
$402$		0			0
$403$	1.55179	−	1.30211i	0.0773004	−	0.0648627i
$404$	−3.07090			−0.152783
$405$		0			0
$406$	−0.373392			−0.0185311
$407$	−1.97422	+	1.65657i	−0.0978585	+	0.0821130i
$408$		0			0
$409$	−6.46776	+	36.6805i	−0.319810	+	1.81373i	0.224071	+	0.974573i	$0.428065\pi$
$409$	−6.46776	+	36.6805i	−0.319810	+	1.81373i	−0.543882	+	0.839162i	$0.683046\pi$
$410$	−30.9697	+	11.2720i	−1.52948	+	0.556687i
$411$		0			0
$412$	−0.890605	−	5.05087i	−0.0438770	−	0.248839i
$413$	3.56341	+	6.17201i	0.175344	+	0.303705i
$414$		0			0
$415$	−7.48735	+	12.9685i	−0.367539	+	0.636597i
$416$	2.93314	+	1.06757i	0.143809	+	0.0523421i
$417$		0			0
$418$	−2.15138	−	1.80522i	−0.105227	−	0.0882963i
$419$	12.5130	+	10.4997i	0.611302	+	0.512944i	0.895056	−	0.445954i	$-0.147135\pi$
$419$	12.5130	+	10.4997i	0.611302	+	0.512944i	−0.283754	+	0.958897i	$0.591580\pi$
$420$		0			0
$421$	14.4065	+	5.24355i	0.702132	+	0.255555i	0.668321	−	0.743873i	$-0.267013\pi$
$421$	14.4065	+	5.24355i	0.702132	+	0.255555i	0.0338111	+	0.999428i	$0.489236\pi$
$422$	0.585291	−	1.01375i	0.0284915	−	0.0493487i
$423$		0			0
$424$	−15.3590	−	26.6026i	−0.745900	−	1.29194i
$425$	−0.148266	−	0.840859i	−0.00719197	−	0.0407877i
$426$		0			0
$427$	4.65830	−	1.69548i	0.225431	−	0.0820501i
$428$	−0.854032	+	4.84346i	−0.0412812	+	0.234117i
$429$		0			0
$430$	25.3446	−	21.2666i	1.22222	−	1.02557i
$431$	−9.38184			−0.451908			−0.225954	−	0.974138i	$-0.572550\pi$
$431$	−9.38184			−0.451908			−0.225954	+	0.974138i	$0.572550\pi$
$432$		0			0
$433$	28.5661			1.37280			0.686400	−	0.727224i	$-0.259190\pi$
$433$	28.5661			1.37280			0.686400	+	0.727224i	$0.259190\pi$
$434$	1.58831	−	1.33275i	0.0762415	−	0.0639742i
$435$		0			0
$436$	−0.146754	+	0.832284i	−0.00702825	+	0.0398592i
$437$	−14.8287	+	5.39720i	−0.709353	+	0.258183i
$438$		0			0
$439$	4.86947	+	27.6161i	0.232407	+	1.31805i	0.848006	+	0.529986i	$0.177803\pi$
$439$	4.86947	+	27.6161i	0.232407	+	1.31805i	−0.615600	+	0.788059i	$0.711086\pi$
$440$	2.39985	+	4.15666i	0.114408	+	0.198161i
$441$		0			0
$442$	−1.94904	+	3.37584i	−0.0927064	+	0.160572i
$443$	15.0919	+	5.49299i	0.717037	+	0.260980i	0.674667	−	0.738122i	$-0.264287\pi$
$443$	15.0919	+	5.49299i	0.717037	+	0.260980i	0.0423693	+	0.999102i	$0.486509\pi$
$444$		0			0
$445$	16.1573	+	13.5576i	0.765930	+	0.642691i
$446$	−25.4539	−	21.3584i	−1.20528	−	1.01135i
$447$		0			0
$448$	−5.65188	−	2.05712i	−0.267026	−	0.0971897i
$449$	−1.56835	+	2.71646i	−0.0740150	+	0.128198i	−0.900658	−	0.434530i	$-0.856915\pi$
$449$	−1.56835	+	2.71646i	−0.0740150	+	0.128198i	0.826642	+	0.562727i	$0.190248\pi$
$450$		0			0
$451$	−4.55843	−	7.89543i	−0.214648	−	0.371781i
$452$	−0.334318	−	1.89601i	−0.0157250	−	0.0891808i
$453$		0			0
$454$	−32.4203	+	11.8000i	−1.52156	+	0.553803i
$455$	−0.553741	+	3.14042i	−0.0259598	+	0.147225i
$456$		0			0
$457$	−5.23113	+	4.38944i	−0.244702	+	0.205329i	−0.756887	−	0.653546i	$-0.773281\pi$
$457$	−5.23113	+	4.38944i	−0.244702	+	0.205329i	0.512185	+	0.858875i	$0.328836\pi$
$458$	13.9294			0.650877
$459$		0			0
$460$	−6.14802			−0.286653
$461$	−7.20211	+	6.04329i	−0.335436	+	0.281464i	−0.794910	−	0.606727i	$-0.792482\pi$
$461$	−7.20211	+	6.04329i	−0.335436	+	0.281464i	0.459475	+	0.888191i	$0.348038\pi$
$462$		0			0
$463$	−2.16463	+	12.2762i	−0.100599	+	0.570525i	0.892288	+	0.451466i	$0.149099\pi$
$463$	−2.16463	+	12.2762i	−0.100599	+	0.570525i	−0.992887	+	0.119059i	$0.962012\pi$
$464$	−1.04921	+	0.381881i	−0.0487083	+	0.0177284i
$465$		0			0
$466$	0.884744	+	5.01763i	0.0409850	+	0.232437i
$467$	−9.70778	−	16.8144i	−0.449222	−	0.778076i	0.549113	−	0.835748i	$-0.314966\pi$
$467$	−9.70778	−	16.8144i	−0.449222	−	0.778076i	−0.998336	+	0.0576719i	$0.981632\pi$
$468$		0			0
$469$	−4.44099	+	7.69201i	−0.205066	+	0.355184i
$470$	−17.7579	−	6.46334i	−0.819111	−	0.298132i
$471$		0			0
$472$	13.6926	+	11.4895i	0.630254	+	0.528846i
$473$	7.01098	+	5.88291i	0.322365	+	0.270496i
$474$		0			0
$475$	0.963226	+	0.350586i	0.0441958	+	0.0160860i
$476$	−0.312356	+	0.541016i	−0.0143168	+	0.0247974i
$477$		0			0
$478$	0.0972309	+	0.168409i	0.00444724	+	0.00770284i
$479$	3.37078	+	19.1166i	0.154015	+	0.873461i	0.959681	+	0.281091i	$0.0906964\pi$
$479$	3.37078	+	19.1166i	0.154015	+	0.873461i	−0.805666	+	0.592370i	$0.798193\pi$
$480$		0			0
$481$	−4.03539	+	1.46876i	−0.183998	+	0.0669698i
$482$	2.45148	−	13.9031i	0.111662	−	0.633267i
$483$		0			0
$484$	−2.89680	+	2.43070i	−0.131673	+	0.110486i
$485$	−19.7544			−0.897003
$486$		0			0
$487$	−30.3132			−1.37362			−0.686811	−	0.726836i	$-0.740990\pi$
$487$	−30.3132			−1.37362			−0.686811	+	0.726836i	$0.740990\pi$
$488$	9.52427	−	7.99181i	0.431144	−	0.361772i
$489$		0			0
$490$	−0.566772	+	3.21432i	−0.0256041	+	0.145208i
$491$	17.8731	−	6.50529i	0.806603	−	0.293579i	0.0943831	−	0.995536i	$-0.469912\pi$
$491$	17.8731	−	6.50529i	0.806603	−	0.293579i	0.712220	+	0.701956i	$0.247690\pi$
$492$		0			0
$493$	−0.0708454	−	0.401784i	−0.00319071	−	0.0180954i
$494$	−2.33987	−	4.05277i	−0.105276	−	0.182343i
$495$		0			0
$496$	3.10001	−	5.36938i	0.139195	−	0.241092i
$497$	−9.58954	−	3.49031i	−0.430150	−	0.156562i
$498$		0			0
$499$	−26.3639	−	22.1220i	−1.18021	−	0.990315i	−0.999978	−	0.00669080i	$-0.997870\pi$
$499$	−26.3639	−	22.1220i	−1.18021	−	0.990315i	−0.180233	−	0.983624i	$-0.557685\pi$
$500$	3.32019	+	2.78597i	0.148483	+	0.124592i
$501$		0			0
$502$	−7.74291	−	2.81819i	−0.345583	−	0.125782i
$503$	6.76988	−	11.7258i	0.301854	−	0.522826i	−0.674702	−	0.738090i	$-0.735728\pi$
$503$	6.76988	−	11.7258i	0.301854	−	0.522826i	0.976556	+	0.215264i	$0.0690612\pi$
$504$		0			0
$505$	−8.76538	−	15.1821i	−0.390054	−	0.675594i
$506$	−1.88613	−	10.6968i	−0.0838489	−	0.475531i
$507$		0			0
$508$	6.66193	−	2.42474i	0.295575	−	0.107581i
$509$	−5.94951	+	33.7414i	−0.263708	+	1.49556i	0.508983	+	0.860777i	$0.330022\pi$
$509$	−5.94951	+	33.7414i	−0.263708	+	1.49556i	−0.772690	+	0.634783i	$0.781089\pi$
$510$		0			0
$511$	10.1907	−	8.55104i	0.450811	−	0.378276i
$512$	−13.5443			−0.598580
$513$		0			0
$514$	16.5749			0.731089
$515$	22.4287	−	18.8199i	0.988325	−	0.829303i
$516$		0			0
$517$	0.907757	−	5.14815i	0.0399231	−	0.226415i
$518$	−4.13036	+	1.50333i	−0.181478	+	0.0660524i
$519$		0			0
$520$	1.38881	+	7.87633i	0.0609033	+	0.345400i
$521$	21.9994	+	38.1040i	0.963810	+	1.66937i	0.712780	+	0.701388i	$0.247436\pi$
$521$	21.9994	+	38.1040i	0.963810	+	1.66937i	0.251030	+	0.967979i	$0.419231\pi$
$522$		0			0
$523$	4.73424	−	8.19994i	0.207014	−	0.358558i	−0.743759	−	0.668448i	$-0.766959\pi$
$523$	4.73424	−	8.19994i	0.207014	−	0.358558i	0.950772	+	0.309890i	$0.100292\pi$
$524$	5.76792	+	2.09935i	0.251973	+	0.0917106i
$525$		0			0
$526$	−35.5245	−	29.8086i	−1.54894	−	1.29972i
$527$	1.73545	+	1.45622i	0.0755974	+	0.0634338i
$528$		0			0
$529$	−35.7382	−	13.0077i	−1.55384	−	0.565550i
$530$	−19.9878	+	34.6199i	−0.868215	+	1.50379i
$531$		0			0
$532$	−0.374990	−	0.649502i	−0.0162579	−	0.0281595i
$533$	−2.63799	−	14.9608i	−0.114264	−	0.648024i
$534$		0			0
$535$	−26.3830	+	9.60263i	−1.14064	+	0.415158i
$536$	−3.86826	+	21.9380i	−0.167084	+	0.947578i
$537$		0			0
$538$	−3.77812	+	3.17022i	−0.162886	+	0.136678i
$539$	−0.902884			−0.0388900
$540$		0			0
$541$	14.5697			0.626400			0.313200	−	0.949687i	$-0.398599\pi$
$541$	14.5697			0.626400			0.313200	+	0.949687i	$0.398599\pi$
$542$	−1.77618	+	1.49039i	−0.0762933	+	0.0640177i
$543$		0			0
$544$	−0.606170	+	3.43776i	−0.0259893	+	0.147393i
$545$	−4.53357	+	1.65008i	−0.194197	+	0.0706819i
$546$		0			0
$547$	3.36369	+	19.0765i	0.143821	+	0.815650i	0.968306	+	0.249766i	$0.0803539\pi$
$547$	3.36369	+	19.0765i	0.143821	+	0.815650i	−0.824485	+	0.565884i	$0.808535\pi$
$548$	0.824514	+	1.42810i	0.0352215	+	0.0610054i
$549$		0			0
$550$	−0.352775	+	0.611024i	−0.0150424	+	0.0260542i
$551$	0.460254	+	0.167519i	0.0196075	+	0.00713654i
$552$		0			0
$553$	−13.3476	−	11.2000i	−0.567600	−	0.476273i
$554$	−4.72801	−	3.96727i	−0.200874	−	0.168553i
$555$		0			0
$556$	−7.86588	−	2.86294i	−0.333587	−	0.121416i
$557$	−1.80761	+	3.13087i	−0.0765908	+	0.132659i	−0.901777	−	0.432202i	$-0.857737\pi$
$557$	−1.80761	+	3.13087i	−0.0765908	+	0.132659i	0.825186	+	0.564861i	$0.191070\pi$
$558$		0			0
$559$	7.62523	+	13.2073i	0.322513	+	0.558609i
$560$	1.69480	+	9.61171i	0.0716185	+	0.406169i
$561$		0			0
$562$	32.0259	−	11.6565i	1.35093	−	0.491699i
$563$	−1.27140	+	7.21049i	−0.0535833	+	0.303886i	−0.999807	−	0.0196259i	$-0.993752\pi$
$563$	−1.27140	+	7.21049i	−0.0535833	+	0.303886i	0.946224	+	0.323512i	$0.104864\pi$
$564$		0			0
$565$	8.41933	−	7.06466i	0.354204	−	0.297212i
$566$	21.1460			0.888835
$567$		0			0
$568$	−25.5946			−1.07393
$569$	−12.5440	+	10.5256i	−0.525871	+	0.441258i	−0.866673	−	0.498877i	$-0.833746\pi$
$569$	−12.5440	+	10.5256i	−0.525871	+	0.441258i	0.340802	+	0.940135i	$0.389301\pi$
$570$		0			0
$571$	−1.73532	+	9.84146i	−0.0726207	+	0.411852i	0.926727	+	0.375736i	$0.122610\pi$
$571$	−1.73532	+	9.84146i	−0.0726207	+	0.411852i	−0.999348	+	0.0361168i	$0.988501\pi$
$572$	0.473936	−	0.172498i	0.0198162	−	0.00721252i
$573$		0			0
$574$	−2.70007	−	15.3129i	−0.112699	−	0.639147i
$575$	1.98222	+	3.43331i	0.0826643	+	0.143179i
$576$		0			0
$577$	−17.1251	+	29.6615i	−0.712925	+	1.23482i	0.250829	+	0.968031i	$0.419297\pi$
$577$	−17.1251	+	29.6615i	−0.712925	+	1.23482i	−0.963754	+	0.266791i	$0.914037\pi$
$578$	20.5030	+	7.46249i	0.852813	+	0.310399i
$579$		0			0
$580$	0.146179	+	0.122658i	0.00606974	+	0.00509312i
$581$	−5.41210	−	4.54129i	−0.224532	−	0.188405i
$582$		0			0
$583$	−10.3914	−	3.78217i	−0.430369	−	0.156641i
$584$	16.6824	−	28.8947i	0.690322	−	1.19567i
$585$		0			0
$586$	−20.2629	−	35.0963i	−0.837051	−	1.44982i
$587$	0.377989	+	2.14368i	0.0156013	+	0.0884792i	0.991614	−	0.129233i	$-0.0412516\pi$
$587$	0.377989	+	2.14368i	0.0156013	+	0.0884792i	−0.976013	+	0.217712i	$0.930140\pi$
$588$		0			0
$589$	−2.55573	+	0.930209i	−0.105307	+	0.0383286i
$590$	4.03929	−	22.9079i	0.166295	−	0.943104i
$591$		0			0
$592$	−10.0686	+	8.44852i	−0.413815	+	0.347232i
$593$	−1.26274			−0.0518544			−0.0259272	−	0.999664i	$-0.508254\pi$
$593$	−1.26274			−0.0518544			−0.0259272	+	0.999664i	$0.508254\pi$
$594$		0			0
$595$	−3.56627			−0.146203
$596$	−0.0319386	+	0.0267997i	−0.00130826	+	0.00109776i
$597$		0			0
$598$	3.14290	−	17.8243i	0.128523	−	0.728889i
$599$	−1.39053	+	0.506111i	−0.0568155	+	0.0206792i	−0.370272	−	0.928924i	$-0.620735\pi$
$599$	−1.39053	+	0.506111i	−0.0568155	+	0.0206792i	0.313456	+	0.949603i	$0.398513\pi$
$600$		0			0
$601$	2.91327	+	16.5220i	0.118835	+	0.673945i	0.984780	+	0.173806i	$0.0556065\pi$
$601$	2.91327	+	16.5220i	0.118835	+	0.673945i	−0.865945	+	0.500139i	$0.833282\pi$
$602$	7.80467	+	13.5181i	0.318095	+	0.550956i
$603$		0			0
$604$	1.66681	−	2.88700i	0.0678216	−	0.117470i
$605$	−20.2854	−	7.38329i	−0.824720	−	0.300174i
$606$		0			0
$607$	−20.2725	−	17.0107i	−0.822837	−	0.690442i	0.130798	−	0.991409i	$-0.458246\pi$
$607$	−20.2725	−	17.0107i	−0.822837	−	0.690442i	−0.953635	+	0.300967i	$0.902691\pi$
$608$	−3.21032	−	2.69378i	−0.130196	−	0.109247i
$609$		0			0
$610$	−15.2043	−	5.53390i	−0.615603	−	0.224061i
$611$	4.35540	−	7.54377i	0.176201	−	0.305188i
$612$		0			0
$613$	−4.06687	−	7.04403i	−0.164259	−	0.284506i	0.772133	−	0.635461i	$-0.219190\pi$
$613$	−4.06687	−	7.04403i	−0.164259	−	0.284506i	−0.936392	+	0.350956i	$0.885857\pi$
$614$	4.91236	+	27.8594i	0.198247	+	1.12431i
$615$		0			0
$616$	−2.12791	+	0.774497i	−0.0857361	+	0.0312054i
$617$	8.04849	−	45.6452i	0.324020	−	1.83761i	−0.192455	−	0.981306i	$-0.561645\pi$
$617$	8.04849	−	45.6452i	0.324020	−	1.83761i	0.516475	−	0.856302i	$-0.327244\pi$
$618$		0			0
$619$	−20.6854	+	17.3571i	−0.831415	+	0.697640i	−0.955615	−	0.294617i	$-0.904808\pi$
$619$	−20.6854	+	17.3571i	−0.831415	+	0.697640i	0.124201	+	0.992257i	$0.460363\pi$
$620$	−1.05961			−0.0425551
$621$		0			0
$622$	−6.87604			−0.275704
$623$	−7.62295	+	6.39642i	−0.305407	+	0.256267i
$624$		0			0
$625$	−3.85589	+	21.8678i	−0.154236	+	0.874713i
$626$	−9.12707	+	3.32198i	−0.364791	+	0.132773i
$627$		0			0
$628$	0.681716	+	3.86620i	0.0272034	+	0.154278i
$629$	−2.40131	−	4.15919i	−0.0957465	−	0.165838i
$630$		0			0
$631$	−0.0693419	+	0.120104i	−0.00276046	+	0.00478125i	−0.867402	−	0.497607i	$-0.834212\pi$
$631$	−0.0693419	+	0.120104i	−0.00276046	+	0.00478125i	0.864642	+	0.502389i	$0.167545\pi$
$632$	−41.0651	−	14.9465i	−1.63348	−	0.594539i
$633$		0			0
$634$	25.0581	+	21.0263i	0.995185	+	0.835059i
$635$	31.0029	+	26.0145i	1.23031	+	1.03236i
$636$		0			0
$637$	−1.41376	−	0.514567i	−0.0560153	−	0.0203879i
$638$	−0.168565	+	0.291963i	−0.00667354	+	0.0115589i
$639$		0			0
$640$	14.2130	+	24.6177i	0.561819	+	0.973100i
$641$	3.42005	+	19.3961i	0.135084	+	0.766099i	0.974801	+	0.223075i	$0.0716096\pi$
$641$	3.42005	+	19.3961i	0.135084	+	0.766099i	−0.839717	+	0.543024i	$0.817279\pi$
$642$		0			0
$643$	−24.7040	+	8.99151i	−0.974229	+	0.354590i	−0.779594	−	0.626285i	$-0.784575\pi$
$643$	−24.7040	+	8.99151i	−0.974229	+	0.354590i	−0.194635	+	0.980876i	$0.562352\pi$
$644$	0.503686	−	2.85654i	0.0198480	−	0.112564i
$645$		0			0
$646$	4.00916	−	3.36408i	0.157738	−	0.132358i
$647$	−17.1708			−0.675053			−0.337527	−	0.941316i	$-0.609590\pi$
$647$	−17.1708			−0.675053			−0.337527	+	0.941316i	$0.609590\pi$
$648$		0			0
$649$	6.43470			0.252584
$650$	−0.900617	+	0.755707i	−0.0353251	+	0.0296413i
$651$		0			0
$652$	1.26368	−	7.16671i	0.0494897	−	0.280670i
$653$	−17.1546	+	6.24378i	−0.671313	+	0.244338i	−0.655113	−	0.755531i	$-0.727379\pi$
$653$	−17.1546	+	6.24378i	−0.671313	+	0.244338i	−0.0161999	+	0.999869i	$0.505157\pi$
$654$		0			0
$655$	6.08468	+	34.5080i	0.237748	+	1.34834i
$656$	−23.2480	−	40.2668i	−0.907683	−	1.57215i
$657$		0			0
$658$	4.45789	−	7.72130i	0.173787	−	0.301008i
$659$	7.04455	+	2.56401i	0.274417	+	0.0998795i	0.475563	−	0.879682i	$-0.342244\pi$
$659$	7.04455	+	2.56401i	0.274417	+	0.0998795i	−0.201146	+	0.979561i	$0.564467\pi$
$660$		0			0
$661$	−15.0804	−	12.6540i	−0.586560	−	0.492182i	0.300534	−	0.953771i	$-0.402835\pi$
$661$	−15.0804	−	12.6540i	−0.586560	−	0.492182i	−0.887094	+	0.461589i	$0.847279\pi$
$662$	11.8159	+	9.91472i	0.459238	+	0.385346i
$663$		0			0
$664$	−16.6508	−	6.06038i	−0.646175	−	0.235189i
$665$	2.14069	−	3.70779i	0.0830126	−	0.143782i
$666$		0			0
$667$	0.947155	+	1.64052i	0.0366740	+	0.0635212i
$668$	−0.808339	−	4.58432i	−0.0312756	−	0.177373i
$669$		0			0
$670$	27.2416	−	9.91515i	1.05244	−	0.383056i
$671$	0.777219	−	4.40783i	0.0300042	−	0.170162i
$672$		0			0
$673$	6.06001	−	5.08495i	0.233596	−	0.196010i	−0.518474	−	0.855093i	$-0.673500\pi$
$673$	6.06001	−	5.08495i	0.233596	−	0.196010i	0.752070	+	0.659083i	$0.229055\pi$
$674$	−29.9187			−1.15243
$675$		0			0
$676$	−3.98634			−0.153321
$677$	−29.7137	+	24.9328i	−1.14199	+	0.958245i	−0.999502	−	0.0315516i	$-0.989955\pi$
$677$	−29.7137	+	24.9328i	−1.14199	+	0.958245i	−0.142489	+	0.989796i	$0.545511\pi$
$678$		0			0
$679$	1.61841	−	9.17847i	0.0621090	−	0.352237i
$680$	−8.40497	+	3.05916i	−0.322316	+	0.117313i
$681$		0			0
$682$	−0.325076	−	1.84359i	−0.0124478	−	0.0705949i
$683$	−4.92463	−	8.52970i	−0.188436	−	0.326380i	0.756293	−	0.654233i	$-0.227008\pi$
$683$	−4.92463	−	8.52970i	−0.188436	−	0.326380i	−0.944729	+	0.327853i	$0.893675\pi$
$684$		0			0
$685$	−4.70687	+	8.15255i	−0.179840	+	0.311493i
$686$	−1.44703	−	0.526676i	−0.0552479	−	0.0201086i
$687$		0			0
$688$	35.7561	+	30.0029i	1.36319	+	1.14385i
$689$	−14.1157	−	11.8445i	−0.537764	−	0.451238i
$690$		0			0
$691$	6.68513	+	2.43319i	0.254314	+	0.0925628i	0.466031	−	0.884768i	$-0.345683\pi$
$691$	6.68513	+	2.43319i	0.254314	+	0.0925628i	−0.211717	+	0.977331i	$0.567906\pi$
$692$	−0.574179	+	0.994508i	−0.0218270	+	0.0378055i
$693$		0			0
$694$	9.40947	+	16.2977i	0.357179	+	0.618651i
$695$	−8.29786	−	47.0595i	−0.314756	−	1.78507i
$696$		0			0
$697$	15.9649	−	5.81076i	0.604715	−	0.220098i
$698$	6.90207	−	39.1436i	0.261247	−	1.48161i
$699$		0			0
$700$	−0.144334	+	0.121111i	−0.00545532	+	0.00457755i
$701$	25.3495			0.957437			0.478719	−	0.877968i	$-0.341101\pi$
$701$	25.3495			0.957437			0.478719	+	0.877968i	$0.341101\pi$
$702$		0			0
$703$	5.76566			0.217456
$704$	−4.16000	+	3.49065i	−0.156786	+	0.131559i
$705$		0			0
$706$	−3.46277	+	19.6383i	−0.130323	+	0.739099i
$707$	7.77214	−	2.82883i	0.292301	−	0.106389i
$708$		0			0
$709$	−2.01926	−	11.4518i	−0.0758351	−	0.430082i	−0.998961	−	0.0455832i	$-0.985485\pi$
$709$	−2.01926	−	11.4518i	−0.0758351	−	0.430082i	0.923125	−	0.384499i	$-0.125626\pi$
$710$	16.6541	+	28.8457i	0.625016	+	1.08256i
$711$		0			0
$712$	−12.4789	+	21.6141i	−0.467666	+	0.810021i
$713$	−9.88448	−	3.59766i	−0.370177	−	0.134733i
$714$		0			0
$715$	2.20558	+	1.85070i	0.0824839	+	0.0692122i
$716$	−3.88002	−	3.25572i	−0.145003	−	0.121672i
$717$		0			0
$718$	−2.54185	−	0.925159i	−0.0948611	−	0.0345266i
$719$	−17.6258	+	30.5288i	−0.657332	+	1.13853i	0.323972	+	0.946067i	$0.394982\pi$
$719$	−17.6258	+	30.5288i	−0.657332	+	1.13853i	−0.981304	+	0.192466i	$0.938352\pi$
$720$		0			0
$721$	6.90675	+	11.9628i	0.257221	+	0.445519i
$722$	−3.98957	−	22.6260i	−0.148477	−	0.842052i
$723$		0			0
$724$	2.61485	−	0.951728i	0.0971802	−	0.0353707i
$725$	0.0213671	−	0.121179i	0.000793556	−	0.00450048i
$726$		0			0
$727$	11.7990	−	9.90056i	0.437602	−	0.367192i	−0.397209	−	0.917728i	$-0.630021\pi$
$727$	11.7990	−	9.90056i	0.437602	−	0.367192i	0.834811	+	0.550537i	$0.185577\pi$
$728$	−3.77335			−0.139850
$729$		0			0
$730$	−43.4200			−1.60705
$731$	−13.0652	+	10.9630i	−0.483233	+	0.405480i
$732$		0			0
$733$	6.14604	−	34.8559i	0.227009	−	1.28743i	−0.631798	−	0.775133i	$-0.717683\pi$
$733$	6.14604	−	34.8559i	0.227009	−	1.28743i	0.858807	−	0.512299i	$-0.171206\pi$
$734$	13.6739	−	4.97690i	0.504713	−	0.183701i
$735$		0			0
$736$	−2.81452	−	15.9619i	−0.103745	−	0.588365i
$737$	4.00970	+	6.94500i	0.147699	+	0.255822i
$738$		0			0
$739$	3.43312	−	5.94634i	0.126289	−	0.218740i	−0.795947	−	0.605367i	$-0.793027\pi$
$739$	3.43312	−	5.94634i	0.126289	−	0.218740i	0.922236	+	0.386627i	$0.126360\pi$
$740$	2.11083	+	0.768279i	0.0775956	+	0.0282425i
$741$		0			0
$742$	−14.4479	−	12.1232i	−0.530397	−	0.445056i
$743$	15.5184	+	13.0215i	0.569315	+	0.477712i	0.881419	−	0.472336i	$-0.156589\pi$
$743$	15.5184	+	13.0215i	0.569315	+	0.477712i	−0.312104	+	0.950048i	$0.601034\pi$
$744$		0			0
$745$	−0.223657	−	0.0814046i	−0.00819417	−	0.00298243i
$746$	−7.59530	+	13.1554i	−0.278084	+	0.481655i
$747$		0			0
$748$	0.282021	+	0.488475i	0.0103117	+	0.0178604i
$749$	−2.30018	−	13.0450i	−0.0840469	−	0.476654i
$750$		0			0
$751$	34.6106	−	12.5972i	1.26296	−	0.459680i	0.378198	−	0.925725i	$-0.376544\pi$
$751$	34.6106	−	12.5972i	1.26296	−	0.459680i	0.884761	+	0.466045i	$0.154322\pi$
$752$	4.62958	−	26.2556i	0.168823	−	0.957444i
$753$		0			0
$754$	−0.430338	+	0.361096i	−0.0156720	+	0.0131503i
$755$	19.0305			0.692592
$756$		0			0
$757$	29.3524			1.06683			0.533416	−	0.845853i	$-0.320908\pi$
$757$	29.3524			1.06683			0.533416	+	0.845853i	$0.320908\pi$
$758$	31.2485	−	26.2206i	1.13500	−	0.952375i
$759$		0			0
$760$	1.86462	−	10.5748i	0.0676370	−	0.383589i
$761$	−24.7638	+	9.01328i	−0.897686	+	0.326731i	−0.749325	−	0.662202i	$-0.769622\pi$
$761$	−24.7638	+	9.01328i	−0.897686	+	0.326731i	−0.148361	+	0.988933i	$0.547400\pi$
$762$		0			0
$763$	−0.395256	−	2.24161i	−0.0143092	−	0.0811517i
$764$	−2.25074	−	3.89840i	−0.0814289	−	0.141039i
$765$		0			0
$766$	15.1066	−	26.1654i	0.545823	−	0.945394i
$767$	10.0756	+	3.66723i	0.363810	+	0.132416i
$768$		0			0
$769$	39.5315	+	33.1709i	1.42554	+	1.19617i	0.948289	+	0.317408i	$0.102812\pi$
$769$	39.5315	+	33.1709i	1.42554	+	1.19617i	0.477255	+	0.878765i	$0.341632\pi$
$770$	2.25748	+	1.89425i	0.0813539	+	0.0682641i
$771$		0			0
$772$	−1.69105	−	0.615491i	−0.0608622	−	0.0221520i
$773$	20.8083	−	36.0411i	0.748423	−	1.29631i	−0.200155	−	0.979764i	$-0.564145\pi$
$773$	20.8083	−	36.0411i	0.748423	−	1.29631i	0.948578	−	0.316542i	$-0.102522\pi$
$774$		0			0
$775$	0.341636	+	0.591731i	0.0122719	+	0.0212556i
$776$	−4.05906	−	23.0201i	−0.145712	−	0.826373i
$777$		0			0
$778$	25.3617	−	9.23091i	0.909262	−	0.330944i
$779$	−3.54178	+	20.0865i	−0.126898	+	0.719672i
$780$		0			0
$781$	−7.05826	+	5.92259i	−0.252565	+	0.211927i
$782$	20.2413			0.723828
$783$		0			0
$784$	−4.60472			−0.164454
$785$	−17.1681	+	14.4057i	−0.612755	+	0.514163i
$786$		0			0
$787$	9.05787	−	51.3697i	0.322878	−	1.83113i	−0.201307	−	0.979528i	$-0.564519\pi$
$787$	9.05787	−	51.3697i	0.322878	−	1.83113i	0.524185	−	0.851604i	$-0.324370\pi$
$788$	−0.536845	+	0.195395i	−0.0191243	+	0.00696068i
$789$		0			0
$790$	9.87550	+	56.0067i	0.351354	+	1.99263i
$791$	2.59267	+	4.49064i	0.0921848	+	0.159669i
$792$		0			0
$793$	3.72908	−	6.45896i	0.132424	−	0.229364i
$794$	−9.76403	−	3.55381i	−0.346512	−	0.126120i
$795$		0			0
$796$	3.24281	+	2.72104i	0.114938	+	0.0964447i
$797$	34.1618	+	28.6652i	1.21007	+	1.01537i	0.999284	+	0.0378418i	$0.0120483\pi$
$797$	34.1618	+	28.6652i	1.21007	+	1.01537i	0.210791	+	0.977531i	$0.432396\pi$
$798$		0			0
$799$	9.15423	+	3.33187i	0.323853	+	0.117873i
$800$	−0.526417	+	0.911780i	−0.0186116	+	0.0322363i
$801$		0			0
$802$	16.3327	+	28.2891i	0.576729	+	0.998924i
$803$	−2.08571	−	11.8286i	−0.0736031	−	0.417424i
$804$		0			0
$805$	15.5600	−	5.66338i	0.548418	−	0.199608i
$806$	0.541680	−	3.07202i	0.0190799	−	0.108207i
$807$		0			0
$808$	15.8908	−	13.3339i	0.559036	−	0.469087i
$809$	1.74549			0.0613680			0.0306840	−	0.999529i	$-0.490231\pi$
$809$	1.74549			0.0613680			0.0306840	+	0.999529i	$0.490231\pi$
$810$		0			0
$811$	16.5975			0.582818			0.291409	−	0.956599i	$-0.405876\pi$
$811$	16.5975			0.582818			0.291409	+	0.956599i	$0.405876\pi$
$812$	−0.0689665	+	0.0578698i	−0.00242025	+	0.00203083i
$813$		0			0
$814$	−0.689135	+	3.90828i	−0.0241542	+	0.136985i
$815$	39.0381	−	14.2087i	1.36744	−	0.497709i
$816$		0			0
$817$	−3.55551	−	20.1643i	−0.124391	−	0.705459i
$818$	28.6778	+	49.6714i	1.00270	+	1.73672i
$819$		0			0
$820$	−3.97320	+	6.88178i	−0.138750	+	0.240322i
$821$	−3.72522	−	1.35587i	−0.130011	−	0.0473201i	0.276195	−	0.961102i	$-0.410926\pi$
$821$	−3.72522	−	1.35587i	−0.130011	−	0.0473201i	−0.406206	+	0.913781i	$0.633149\pi$
$822$		0			0
$823$	33.9202	+	28.4624i	1.18238	+	0.992137i	0.999960	+	0.00891637i	$0.00283821\pi$
$823$	33.9202	+	28.4624i	1.18238	+	0.992137i	0.182422	+	0.983220i	$0.441606\pi$
$824$	26.5396	+	22.2693i	0.924550	+	0.775789i
$825$		0			0
$826$	10.3127	+	3.75353i	0.358826	+	0.130602i
$827$	−10.1785	+	17.6297i	−0.353941	+	0.613043i	−0.986936	−	0.161112i	$-0.948492\pi$
$827$	−10.1785	+	17.6297i	−0.353941	+	0.613043i	0.632995	+	0.774156i	$0.281825\pi$
$828$		0			0
$829$	−12.0044	−	20.7922i	−0.416929	−	0.722142i	0.578700	−	0.815541i	$-0.303560\pi$
$829$	−12.0044	−	20.7922i	−0.416929	−	0.722142i	−0.995629	+	0.0933984i	$0.970227\pi$
$830$	4.00424	+	22.7092i	0.138989	+	0.788248i
$831$		0			0
$832$	−8.50322	+	3.09492i	−0.294796	+	0.107297i
$833$	0.292172	−	1.65699i	0.0101232	−	0.0574113i
$834$		0			0
$835$	20.3569	−	17.0815i	0.704480	−	0.591129i
$836$	−0.677146			−0.0234196
$837$		0			0
$838$	25.1537			0.868919
$839$	−1.11354	+	0.934370i	−0.0384436	+	0.0322581i	−0.661807	−	0.749674i	$-0.730210\pi$
$839$	−1.11354	+	0.934370i	−0.0384436	+	0.0322581i	0.623363	+	0.781932i	$0.285766\pi$
$840$		0			0
$841$	−5.02559	+	28.5015i	−0.173296	+	0.982811i
$842$	22.1846	−	8.07454i	0.764532	−	0.278267i
$843$		0			0
$844$	−0.0490107	−	0.277954i	−0.00168702	−	0.00956756i
$845$	−11.3783	−	19.7078i	−0.391427	−	0.677971i
$846$		0			0
$847$	5.09240	−	8.82030i	0.174977	−	0.303069i
$848$	−52.9964	−	19.2891i	−1.81990	−	0.662391i
$849$		0			0
$850$	−1.00721	−	0.845146i	−0.0345469	−	0.0289883i
$851$	17.0821	+	14.3336i	0.585568	+	0.491350i
$852$		0			0
$853$	−20.9348	−	7.61963i	−0.716792	−	0.260891i	−0.0422289	−	0.999108i	$-0.513446\pi$
$853$	−20.9348	−	7.61963i	−0.716792	−	0.260891i	−0.674563	+	0.738217i	$0.735668\pi$
$854$	3.81684	−	6.61096i	0.130609	−	0.226222i
$855$		0			0
$856$	−16.6111	−	28.7713i	−0.567756	−	0.983383i
$857$	0.898555	+	5.09596i	0.0306940	+	0.174075i	0.996301	−	0.0859314i	$-0.0273866\pi$
$857$	0.898555	+	5.09596i	0.0306940	+	0.174075i	−0.965607	+	0.260006i	$0.916275\pi$
$858$		0			0
$859$	44.1442	−	16.0672i	1.50618	−	0.548205i	0.548529	−	0.836132i	$-0.315188\pi$
$859$	44.1442	−	16.0672i	1.50618	−	0.548205i	0.957653	+	0.287926i	$0.0929659\pi$
$860$	1.38522	−	7.85600i	0.0472358	−	0.267887i
$861$		0			0
$862$	−11.0671	+	9.28641i	−0.376947	+	0.316296i
$863$	17.6075			0.599366			0.299683	−	0.954039i	$-0.403119\pi$
$863$	17.6075			0.599366			0.299683	+	0.954039i	$0.403119\pi$
$864$		0			0
$865$	−6.55559			−0.222897
$866$	33.6975	−	28.2755i	1.14509	−	0.960842i
$867$		0			0
$868$	0.0868103	−	0.492326i	0.00294654	−	0.0167106i
$869$	−14.7832	+	5.38065i	−0.501486	+	0.182526i
$870$		0			0
$871$	2.32044	+	13.1599i	0.0786251	+	0.445905i
$872$	−2.85440	−	4.94397i	−0.0966622	−	0.167424i
$873$		0			0
$874$	−12.1501	+	21.0446i	−0.410983	+	0.711843i
$875$	−10.9694	−	3.99254i	−0.370834	−	0.134972i
$876$		0			0
$877$	−23.8329	−	19.9982i	−0.804780	−	0.675290i	0.144576	−	0.989494i	$-0.453818\pi$
$877$	−23.8329	−	19.9982i	−0.804780	−	0.675290i	−0.949356	+	0.314203i	$0.898263\pi$
$878$	33.0794	+	27.7569i	1.11637	+	0.936750i
$879$		0			0
$880$	8.28070	+	3.01393i	0.279142	+	0.101599i
$881$	14.4765	−	25.0741i	0.487726	−	0.844767i	−0.512174	−	0.858882i	$-0.671160\pi$
$881$	14.4765	−	25.0741i	0.487726	−	0.844767i	0.999900	+	0.0141150i	$0.00449309\pi$
$882$		0			0
$883$	−27.1065	−	46.9499i	−0.912208	−	1.57999i	−0.810939	−	0.585131i	$-0.801043\pi$
$883$	−27.1065	−	46.9499i	−0.912208	−	1.57999i	−0.101269	−	0.994859i	$-0.532290\pi$
$884$	0.163208	+	0.925596i	0.00548926	+	0.0311312i
$885$		0			0
$886$	23.2400	−	8.45865i	0.780762	−	0.284174i
$887$	4.25337	−	24.1221i	0.142814	−	0.809939i	−0.826282	−	0.563256i	$-0.809548\pi$
$887$	4.25337	−	24.1221i	0.142814	−	0.809939i	0.969096	−	0.246683i	$-0.0793406\pi$
$888$		0			0
$889$	−14.6271	+	12.2736i	−0.490576	+	0.411642i
$890$	32.4793			1.08871
$891$		0			0
$892$	−8.01162			−0.268249
$893$	−8.95902	+	7.51751i	−0.299802	+	0.251564i
$894$		0			0
$895$	5.02093	−	28.4751i	0.167831	−	0.951818i
$896$	−12.6025	+	4.58693i	−0.421020	+	0.153239i
$897$		0			0
$898$	0.838756	+	4.75682i	0.0279896	+	0.158737i
$899$	0.163242	+	0.282744i	0.00544444	+	0.00943004i
$900$		0			0
$901$	10.3038	−	17.8466i	0.343268	−	0.594557i
$902$	−13.1924	−	4.80163i	−0.439258	−	0.159877i
$903$		0			0
$904$	9.96249	+	8.35952i	0.331348	+	0.278034i
$905$	12.1689	+	10.2109i	0.404506	+	0.339421i
$906$		0			0
$907$	28.2122	+	10.2684i	0.936771	+	0.340957i	0.764890	−	0.644161i	$-0.222793\pi$
$907$	28.2122	+	10.2684i	0.936771	+	0.340957i	0.171881	+	0.985118i	$0.445015\pi$
$908$	−4.15930	+	7.20413i	−0.138031	+	0.239077i
$909$		0			0
$910$	2.45526	+	4.25264i	0.0813912	+	0.140974i
$911$	−0.894807	−	5.07470i	−0.0296463	−	0.168132i	0.966390	−	0.257081i	$-0.0827606\pi$
$911$	−0.894807	−	5.07470i	−0.0296463	−	0.168132i	−0.996036	+	0.0889482i	$0.971649\pi$
$912$		0			0
$913$	−5.99418	+	2.18170i	−0.198378	+	0.0722039i
$914$	−1.82601	+	10.3558i	−0.0603992	+	0.342541i
$915$		0			0
$916$	2.57279	−	2.15883i	0.0850075	−	0.0713297i
$917$	−16.5319			−0.545930
$918$		0			0
$919$	−33.6253			−1.10920			−0.554598	−	0.832119i	$-0.687128\pi$
$919$	−33.6253			−1.10920			−0.554598	+	0.832119i	$0.687128\pi$
$920$	31.8137	−	26.6949i	1.04887	−	0.880104i
$921$		0			0
$922$	−2.51402	+	14.2577i	−0.0827947	+	0.469552i
$923$	−14.4274	+	5.25114i	−0.474884	+	0.172844i
$924$		0			0
$925$	−0.251526	−	1.42648i	−0.00827014	−	0.0469023i
$926$	9.59790	+	16.6240i	0.315406	+	0.546300i
$927$		0			0
$928$	−0.251535	+	0.435672i	−0.00825705	+	0.0143016i
$929$	−13.3506	−	4.85922i	−0.438019	−	0.159426i	0.113592	−	0.993528i	$-0.463764\pi$
$929$	−13.3506	−	4.85922i	−0.438019	−	0.159426i	−0.551611	+	0.834102i	$0.685987\pi$
$930$		0			0
$931$	1.54737	+	1.29839i	0.0507128	+	0.0425531i
$932$	0.941067	+	0.789649i	0.0308257	+	0.0258658i
$933$		0			0
$934$	−28.0949	−	10.2257i	−0.919294	−	0.334596i
$935$	−1.60996	+	2.78854i	−0.0526514	+	0.0911950i
$936$		0			0
$937$	19.9939	+	34.6304i	0.653171	+	1.13133i	0.982349	+	0.187057i	$0.0598950\pi$
$937$	19.9939	+	34.6304i	0.653171	+	1.13133i	−0.329178	+	0.944268i	$0.606772\pi$
$938$	2.37505	+	13.4696i	0.0775480	+	0.439796i
$939$		0			0
$940$	−4.28164	+	1.55839i	−0.139652	+	0.0508291i
$941$	7.06981	−	40.0949i	0.230469	−	1.30706i	−0.621480	−	0.783430i	$-0.713468\pi$
$941$	7.06981	−	40.0949i	0.230469	−	1.30706i	0.851949	−	0.523625i	$-0.175421\pi$
$942$		0			0
$943$	−60.4290	+	50.7059i	−1.96784	+	1.65121i
$944$	32.8171			1.06810
$945$		0			0
$946$	14.0934			0.458217
$947$	−9.80184	+	8.22472i	−0.318517	+	0.267267i	−0.788002	−	0.615673i	$-0.788884\pi$
$947$	−9.80184	+	8.22472i	−0.318517	+	0.267267i	0.469485	+	0.882941i	$0.344440\pi$
$948$		0			0
$949$	3.47546	−	19.7103i	0.112818	−	0.639823i
$950$	1.48327	−	0.539866i	0.0481237	−	0.0175156i
$951$		0			0
$952$	−0.732782	−	4.15581i	−0.0237496	−	0.134691i
$953$	−10.6572	−	18.4588i	−0.345220	−	0.597938i	0.640174	−	0.768230i	$-0.278862\pi$
$953$	−10.6572	−	18.4588i	−0.345220	−	0.597938i	−0.985394	+	0.170292i	$0.945529\pi$
$954$		0			0
$955$	12.8487	−	22.2546i	0.415775	−	0.720143i
$956$	0.0440595	+	0.0160363i	0.00142498	+	0.000518652i
$957$		0			0
$958$	22.8984	+	19.2141i	0.739815	+	0.620779i
$959$	−3.40229	−	2.85486i	−0.109866	−	0.0921881i
$960$		0			0
$961$	27.4269	+	9.98257i	0.884738	+	0.322018i
$962$	−3.30645	+	5.72694i	−0.106604	+	0.184644i
$963$		0			0
$964$	−1.70196	−	2.94787i	−0.0548163	−	0.0949446i
$965$	−1.78392	−	10.1171i	−0.0574264	−	0.325681i
$966$		0			0
$967$	21.4027	−	7.78996i	0.688266	−	0.250508i	0.0258732	−	0.999665i	$-0.491763\pi$
$967$	21.4027	−	7.78996i	0.688266	−	0.250508i	0.662392	+	0.749157i	$0.269541\pi$
$968$	4.43567	−	25.1559i	0.142568	−	0.808542i
$969$		0			0
$970$	−23.3030	+	19.5535i	−0.748213	+	0.627825i
$971$	37.7866			1.21263			0.606315	−	0.795225i	$-0.292647\pi$
$971$	37.7866			1.21263			0.606315	+	0.795225i	$0.292647\pi$
$972$		0			0
$973$	22.5450			0.722759
$974$	−35.7584	+	30.0048i	−1.14577	+	0.961417i
$975$		0			0
$976$	3.96383	−	22.4800i	0.126879	−	0.719567i
$977$	26.3651	−	9.59611i	0.843494	−	0.307007i	0.116109	−	0.993236i	$-0.462958\pi$
$977$	26.3651	−	9.59611i	0.843494	−	0.307007i	0.727385	+	0.686230i	$0.240736\pi$
$978$		0			0
$979$	1.56017	+	8.84815i	0.0498632	+	0.282788i
$980$	0.393484	+	0.681535i	0.0125694	+	0.0217708i
$981$		0			0
$982$	14.6446	−	25.3652i	0.467327	−	0.809435i
$983$	34.9393	+	12.7169i	1.11439	+	0.405605i	0.832602	−	0.553872i	$-0.186850\pi$
$983$	34.9393	+	12.7169i	1.11439	+	0.405605i	0.281788	+	0.959477i	$0.409072\pi$
$984$		0			0
$985$	−2.49834	−	2.09636i	−0.0796037	−	0.0667954i
$986$	−0.481268	−	0.403832i	−0.0153267	−	0.0128606i
$987$		0			0
$988$	−1.06029	−	0.385915i	−0.0337324	−	0.0122776i
$989$	39.5950	−	68.5806i	1.25905	−	2.18074i
$990$		0			0
$991$	−6.66753	−	11.5485i	−0.211801	−	0.366850i	0.740477	−	0.672081i	$-0.234600\pi$
$991$	−6.66753	−	11.5485i	−0.211801	−	0.366850i	−0.952278	+	0.305231i	$0.901266\pi$
$992$	−0.485083	−	2.75104i	−0.0154014	−	0.0873457i
$993$		0			0
$994$	−14.7669	+	5.37472i	−0.468378	+	0.170476i
$995$	−4.19635	+	23.7987i	−0.133033	+	0.754470i
$996$		0			0
$997$	−18.4370	+	15.4705i	−0.583905	+	0.489954i	−0.886227	−	0.463252i	$-0.846683\pi$
$997$	−18.4370	+	15.4705i	−0.583905	+	0.489954i	0.302322	+	0.953206i	$0.402238\pi$
$998$	−52.9966			−1.67758
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.v.b.442.8		54
3.2	odd	2		189.2.v.a.22.2	✓	54
27.4	even	9		5103.2.a.f.1.22		27
27.11	odd	18		189.2.v.a.43.2	yes	54
27.16	even	9	inner	567.2.v.b.127.8		54
27.23	odd	18		5103.2.a.i.1.6		27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.v.a.22.2	✓	54	3.2	odd	2
189.2.v.a.43.2	yes	54	27.11	odd	18
567.2.v.b.127.8		54	27.16	even	9	inner
567.2.v.b.442.8		54	1.1	even	1	trivial
5103.2.a.f.1.22		27	27.4	even	9
5103.2.a.i.1.6		27	27.23	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.v (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.17963 - 0.989828i) q^{2} +(0.0644735 - 0.365648i) q^{4} +(1.99174 - 0.724932i) q^{5} +(0.173648 + 0.984808i) q^{7} +(1.25403 + 2.17204i) q^{8} +O(q^{10})\)	\(q+(1.17963 - 0.989828i) q^{2} +(0.0644735 - 0.365648i) q^{4} +(1.99174 - 0.724932i) q^{5} +(0.173648 + 0.984808i) q^{7} +(1.25403 + 2.17204i) q^{8} +(1.63195 - 2.82663i) q^{10} +(0.848433 + 0.308804i) q^{11} +(1.15251 + 0.967070i) q^{13} +(1.17963 + 0.989828i) q^{14} +(4.32702 + 1.57491i) q^{16} +(-0.841276 + 1.45713i) q^{17} +(-1.00997 - 1.74932i) q^{19} +(-0.136656 - 0.775012i) q^{20} +(1.30650 - 0.475528i) q^{22} +(1.35659 - 7.69360i) q^{23} +(-0.388738 + 0.326190i) q^{25} +2.31677 q^{26} +0.371288 q^{28} +(-0.185749 + 0.155862i) q^{29} +(0.233808 - 1.32599i) q^{31} +(1.94958 - 0.709590i) q^{32} +(0.449915 + 2.55160i) q^{34} +(1.05978 + 1.83559i) q^{35} +(-1.42718 + 2.47195i) q^{37} +(-2.92292 - 1.06386i) q^{38} +(4.07227 + 3.41704i) q^{40} +(-7.73512 - 6.49053i) q^{41} +(9.52529 + 3.46692i) q^{43} +(0.167615 - 0.290318i) q^{44} +(-6.01507 - 10.4184i) q^{46} +(-1.00540 - 5.70189i) q^{47} +(-0.939693 + 0.342020i) q^{49} +(-0.135696 + 0.769568i) q^{50} +(0.427913 - 0.359062i) q^{52} -12.2478 q^{53} +1.91372 q^{55} +(-1.92128 + 1.61214i) q^{56} +(-0.0648388 + 0.367719i) q^{58} +(6.69703 - 2.43752i) q^{59} +(-0.860819 - 4.88195i) q^{61} +(-1.03670 - 1.79561i) q^{62} +(-3.00731 + 5.20881i) q^{64} +(2.99655 + 1.09066i) q^{65} +(6.80399 + 5.70922i) q^{67} +(0.478557 + 0.401557i) q^{68} +(3.06707 + 1.11632i) q^{70} +(-5.10249 + 8.83777i) q^{71} +(-6.65153 - 11.5208i) q^{73} +(0.763260 + 4.32866i) q^{74} +(-0.704751 + 0.256509i) q^{76} +(-0.156784 + 0.889167i) q^{77} +(-13.3476 + 11.2000i) q^{79} +9.75999 q^{80} -15.5491 q^{82} +(-5.41210 + 4.54129i) q^{83} +(-0.619276 + 3.51209i) q^{85} +(14.6680 - 5.33871i) q^{86} +(0.393223 + 2.23008i) q^{88} +(4.97553 + 8.61787i) q^{89} +(-0.752247 + 1.30293i) q^{91} +(-2.72568 - 0.992068i) q^{92} +(-6.82989 - 5.73096i) q^{94} +(-3.27973 - 2.75202i) q^{95} +(-8.75800 - 3.18765i) q^{97} +(-0.769949 + 1.33359i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 3 q^{5} + 27 q^{8}+O(q^{10}) \) 54 * q + 3 * q^5 + 27 * q^8	\( 54 q + 3 q^{5} + 27 q^{8} + 6 q^{11} - 9 q^{13} + 30 q^{17} + 12 q^{20} - 9 q^{22} + 12 q^{23} + 27 q^{25} - 18 q^{26} + 54 q^{28} - 6 q^{29} - 9 q^{31} + 9 q^{32} - 9 q^{34} + 12 q^{35} - 54 q^{38} - 45 q^{40} + 15 q^{41} - 9 q^{43} + 42 q^{44} + 45 q^{47} - 18 q^{50} - 63 q^{52} - 132 q^{53} + 9 q^{56} - 27 q^{58} + 36 q^{62} - 27 q^{64} - 66 q^{65} + 45 q^{67} - 87 q^{68} + 72 q^{71} + 72 q^{74} + 54 q^{76} - 3 q^{77} - 36 q^{79} - 42 q^{80} - 24 q^{83} + 18 q^{85} + 90 q^{86} + 54 q^{88} + 42 q^{89} - 87 q^{92} - 90 q^{94} - 12 q^{95} - 18 q^{97} + 9 q^{98}+O(q^{100}) \) 54 * q + 3 * q^5 + 27 * q^8 + 6 * q^11 - 9 * q^13 + 30 * q^17 + 12 * q^20 - 9 * q^22 + 12 * q^23 + 27 * q^25 - 18 * q^26 + 54 * q^28 - 6 * q^29 - 9 * q^31 + 9 * q^32 - 9 * q^34 + 12 * q^35 - 54 * q^38 - 45 * q^40 + 15 * q^41 - 9 * q^43 + 42 * q^44 + 45 * q^47 - 18 * q^50 - 63 * q^52 - 132 * q^53 + 9 * q^56 - 27 * q^58 + 36 * q^62 - 27 * q^64 - 66 * q^65 + 45 * q^67 - 87 * q^68 + 72 * q^71 + 72 * q^74 + 54 * q^76 - 3 * q^77 - 36 * q^79 - 42 * q^80 - 24 * q^83 + 18 * q^85 + 90 * q^86 + 54 * q^88 + 42 * q^89 - 87 * q^92 - 90 * q^94 - 12 * q^95 - 18 * q^97 + 9 * q^98

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