LMFDB - Embedded newform 324.3.j.a.199.32

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,3,Mod(19,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 16]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("324.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	324.j (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:	$8.82836056527$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			199.32
Character	$\chi$	$=$	324.199
Dual form			324.3.j.a.127.32

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.96087 + 0.393671i) q^{2} +(3.69005 + 1.54388i) q^{4} +(6.55659 - 2.38640i) q^{5} +(2.70588 - 0.477119i) q^{7} +(6.62793 + 4.48001i) q^{8} +O(q^{10})$	\(q+(1.96087 + 0.393671i) q^{2} +(3.69005 + 1.54388i) q^{4} +(6.55659 - 2.38640i) q^{5} +(2.70588 - 0.477119i) q^{7} +(6.62793 + 4.48001i) q^{8} +(13.7961 - 2.09830i) q^{10} +(-2.46741 + 6.77916i) q^{11} +(-14.3149 - 12.0116i) q^{13} +(5.49371 + 0.129654i) q^{14} +(11.2329 + 11.3940i) q^{16} +(9.12428 - 15.8037i) q^{17} +(-22.9013 + 13.2221i) q^{19} +(27.8784 + 1.31662i) q^{20} +(-7.50704 + 12.3217i) q^{22} +(8.61427 + 1.51893i) q^{23} +(18.1428 - 15.2236i) q^{25} +(-23.3411 - 29.1887i) q^{26} +(10.7214 + 2.41695i) q^{28} +(-6.25669 + 5.24998i) q^{29} +(40.7671 + 7.18833i) q^{31} +(17.5408 + 26.7642i) q^{32} +(24.1130 - 27.3971i) q^{34} +(16.6027 - 9.58558i) q^{35} +(-18.4807 + 32.0094i) q^{37} +(-50.1117 + 16.9112i) q^{38} +(54.1477 + 13.5566i) q^{40} +(-31.3693 - 26.3220i) q^{41} +(-12.6968 + 34.8842i) q^{43} +(-19.5711 + 21.2060i) q^{44} +(16.2935 + 6.36961i) q^{46} +(-24.9444 + 4.39836i) q^{47} +(-38.9508 + 14.1769i) q^{49} +(41.5688 - 22.7093i) q^{50} +(-34.2782 - 66.4240i) q^{52} +90.9984 q^{53} +50.3364i q^{55} +(20.0719 + 8.96004i) q^{56} +(-14.3353 + 7.83148i) q^{58} +(-24.5239 - 67.3788i) q^{59} +(-11.9781 - 67.9315i) q^{61} +(77.1092 + 30.1442i) q^{62} +(23.8590 + 59.3864i) q^{64} +(-122.522 - 44.5942i) q^{65} +(-38.7118 + 46.1350i) q^{67} +(58.0680 - 44.2297i) q^{68} +(36.3294 - 12.2601i) q^{70} +(-51.1377 - 29.5244i) q^{71} +(35.2245 + 61.0107i) q^{73} +(-48.8394 + 55.4912i) q^{74} +(-104.920 + 13.4333i) q^{76} +(-3.44205 + 19.5208i) q^{77} +(-95.9155 - 114.308i) q^{79} +(100.840 + 47.8992i) q^{80} +(-51.1491 - 63.9633i) q^{82} +(-46.7322 - 55.6933i) q^{83} +(22.1101 - 125.393i) q^{85} +(-38.6297 + 63.4051i) q^{86} +(-46.7245 + 33.8778i) q^{88} +(7.52863 + 13.0400i) q^{89} +(-44.4654 - 25.6721i) q^{91} +(29.4420 + 18.9043i) q^{92} +(-50.6442 - 1.19523i) q^{94} +(-118.601 + 141.343i) q^{95} +(-101.970 - 37.1140i) q^{97} +(-81.9586 + 12.4654i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) $ 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8	$ 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8} - 3 q^{10} - 12 q^{13} - 39 q^{14} - 6 q^{16} + 6 q^{17} + 69 q^{20} - 6 q^{22} - 12 q^{25} + 174 q^{26} - 12 q^{28} - 60 q^{29} + 96 q^{32} + 6 q^{34} - 6 q^{37} - 72 q^{38} + 69 q^{40} + 192 q^{41} + 219 q^{44} - 3 q^{46} - 12 q^{49} + 165 q^{50} + 21 q^{52} + 24 q^{53} - 99 q^{56} - 141 q^{58} - 12 q^{61} - 294 q^{62} - 3 q^{64} + 156 q^{65} - 375 q^{68} - 165 q^{70} - 6 q^{73} - 447 q^{74} - 54 q^{76} - 132 q^{77} - 798 q^{80} - 12 q^{82} + 138 q^{85} - 606 q^{86} - 198 q^{88} + 114 q^{89} - 723 q^{92} - 357 q^{94} + 168 q^{97} - 510 q^{98}+O(q^{100}) $ 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8 - 3 * q^10 - 12 * q^13 - 39 * q^14 - 6 * q^16 + 6 * q^17 + 69 * q^20 - 6 * q^22 - 12 * q^25 + 174 * q^26 - 12 * q^28 - 60 * q^29 + 96 * q^32 + 6 * q^34 - 6 * q^37 - 72 * q^38 + 69 * q^40 + 192 * q^41 + 219 * q^44 - 3 * q^46 - 12 * q^49 + 165 * q^50 + 21 * q^52 + 24 * q^53 - 99 * q^56 - 141 * q^58 - 12 * q^61 - 294 * q^62 - 3 * q^64 + 156 * q^65 - 375 * q^68 - 165 * q^70 - 6 * q^73 - 447 * q^74 - 54 * q^76 - 132 * q^77 - 798 * q^80 - 12 * q^82 + 138 * q^85 - 606 * q^86 - 198 * q^88 + 114 * q^89 - 723 * q^92 - 357 * q^94 + 168 * q^97 - 510 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{7}{9}\right)$

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 $

$2$	1.96087	+	0.393671i	0.980437	+	0.196835i
$2$	1.96087	+	0.393671i	0.980437	+	0.196835i
$3$		0			0
$3$		0			0
$4$	3.69005	+	1.54388i	0.922512	+	0.385969i
$5$	6.55659	−	2.38640i	1.31132	−	0.477280i	0.410651	−	0.911793i	$-0.365301\pi$
$5$	6.55659	−	2.38640i	1.31132	−	0.477280i	0.900666	+	0.434512i	$0.143079\pi$
$6$		0			0
$7$	2.70588	−	0.477119i	0.386554	−	0.0681599i	0.0230059	−	0.999735i	$-0.492676\pi$
$7$	2.70588	−	0.477119i	0.386554	−	0.0681599i	0.363548	+	0.931575i	$0.381565\pi$
$8$	6.62793	+	4.48001i	0.828492	+	0.560001i
$9$		0			0
$10$	13.7961	−	2.09830i	1.37961	−	0.209830i
$11$	−2.46741	+	6.77916i	−0.224310	+	0.616287i	−0.999888	−	0.0149647i	$-0.995236\pi$
$11$	−2.46741	+	6.77916i	−0.224310	+	0.616287i	0.775578	+	0.631252i	$0.217459\pi$
$12$		0			0
$13$	−14.3149	−	12.0116i	−1.10115	−	0.923973i	−0.103646	−	0.994614i	$-0.533051\pi$
$13$	−14.3149	−	12.0116i	−1.10115	−	0.923973i	−0.997502	+	0.0706413i	$0.977495\pi$
$14$	5.49371	+	0.129654i	0.392408	+	0.00926103i
$15$		0			0
$16$	11.2329	+	11.3940i	0.702056	+	0.712122i
$17$	9.12428	−	15.8037i	0.536722	−	0.929630i	−0.462355	−	0.886695i	$-0.652996\pi$
$17$	9.12428	−	15.8037i	0.536722	−	0.929630i	0.999078	−	0.0429358i	$-0.0136711\pi$
$18$		0			0
$19$	−22.9013	+	13.2221i	−1.20533	+	0.695899i	−0.961736	−	0.273978i	$-0.911660\pi$
$19$	−22.9013	+	13.2221i	−1.20533	+	0.695899i	−0.243596	+	0.969877i	$0.578327\pi$
$20$	27.8784	+	1.31662i	1.39392	+	0.0658312i
$21$		0			0
$22$	−7.50704	+	12.3217i	−0.341229	+	0.560078i
$23$	8.61427	+	1.51893i	0.374534	+	0.0660404i	0.357747	−	0.933819i	$-0.383545\pi$
$23$	8.61427	+	1.51893i	0.374534	+	0.0660404i	0.0167870	+	0.999859i	$0.494656\pi$
$24$		0			0
$25$	18.1428	−	15.2236i	0.725711	−	0.608944i
$26$	−23.3411	−	29.1887i	−0.897735	−	1.12264i
$27$		0			0
$28$	10.7214	+	2.41695i	0.382908	+	0.0863196i
$29$	−6.25669	+	5.24998i	−0.215748	+	0.181034i	−0.744256	−	0.667894i	$-0.767196\pi$
$29$	−6.25669	+	5.24998i	−0.215748	+	0.181034i	0.528509	+	0.848928i	$0.322751\pi$
$30$		0			0
$31$	40.7671	+	7.18833i	1.31507	+	0.231882i	0.786806	−	0.617200i	$-0.211733\pi$
$31$	40.7671	+	7.18833i	1.31507	+	0.231882i	0.528261	+	0.849082i	$0.322844\pi$
$32$	17.5408	+	26.7642i	0.548150	+	0.836380i
$33$		0			0
$34$	24.1130	−	27.3971i	0.709206	−	0.805798i
$35$	16.6027	−	9.58558i	0.474363	−	0.273874i
$36$		0			0
$37$	−18.4807	+	32.0094i	−0.499477	+	0.865120i	−1.00000		0.000603501i	$-0.999808\pi$
$37$	−18.4807	+	32.0094i	−0.499477	+	0.865120i	0.500523	+	0.865723i	$0.333141\pi$
$38$	−50.1117	+	16.9112i	−1.31873	+	0.445033i
$39$		0			0
$40$	54.1477	+	13.5566i	1.35369	+	0.338916i
$41$	−31.3693	−	26.3220i	−0.765106	−	0.642000i	0.174345	−	0.984685i	$-0.444219\pi$
$41$	−31.3693	−	26.3220i	−0.765106	−	0.642000i	−0.939450	+	0.342685i	$0.888664\pi$
$42$		0			0
$43$	−12.6968	+	34.8842i	−0.295274	+	0.811260i	0.699999	+	0.714144i	$0.253184\pi$
$43$	−12.6968	+	34.8842i	−0.295274	+	0.811260i	−0.995273	+	0.0971155i	$0.969038\pi$
$44$	−19.5711	+	21.2060i	−0.444797	+	0.481955i
$45$		0			0
$46$	16.2935	+	6.36961i	0.354207	+	0.138470i
$47$	−24.9444	+	4.39836i	−0.530731	+	0.0935822i	−0.432591	−	0.901590i	$-0.642400\pi$
$47$	−24.9444	+	4.39836i	−0.530731	+	0.0935822i	−0.0981402	+	0.995173i	$0.531289\pi$
$48$		0			0
$49$	−38.9508	+	14.1769i	−0.794914	+	0.289325i
$50$	41.5688	−	22.7093i	0.831376	−	0.454186i
$51$		0			0
$52$	−34.2782	−	66.4240i	−0.659197	−	1.27739i
$53$	90.9984			1.71695			0.858475	−	0.512855i	$-0.171412\pi$
$53$	90.9984			1.71695			0.858475	+	0.512855i	$0.171412\pi$
$54$		0			0
$55$			50.3364i			0.915207i
$56$	20.0719	+	8.96004i	0.358426	+	0.160001i
$57$		0			0
$58$	−14.3353	+	7.83148i	−0.247161	+	0.135025i
$59$	−24.5239	−	67.3788i	−0.415659	−	1.14201i	−0.954136	−	0.299374i	$-0.903222\pi$
$59$	−24.5239	−	67.3788i	−0.415659	−	1.14201i	0.538477	−	0.842640i	$-0.319000\pi$
$60$		0			0
$61$	−11.9781	−	67.9315i	−0.196363	−	1.11363i	−0.910464	−	0.413588i	$-0.864275\pi$
$61$	−11.9781	−	67.9315i	−0.196363	−	1.11363i	0.714101	−	0.700043i	$-0.246836\pi$
$62$	77.1092	+	30.1442i	1.24370	+	0.486197i
$63$		0			0
$64$	23.8590	+	59.3864i	0.372797	+	0.927913i
$65$	−122.522	−	44.5942i	−1.88495	−	0.686065i
$66$		0			0
$67$	−38.7118	+	46.1350i	−0.577788	+	0.688581i	−0.973210	−	0.229918i	$-0.926154\pi$
$67$	−38.7118	+	46.1350i	−0.577788	+	0.688581i	0.395422	+	0.918500i	$0.370599\pi$
$68$	58.0680	−	44.2297i	0.853941	−	0.650437i
$69$		0			0
$70$	36.3294	−	12.2601i	0.518991	−	0.175144i
$71$	−51.1377	−	29.5244i	−0.720249	−	0.415836i	0.0945950	−	0.995516i	$-0.469844\pi$
$71$	−51.1377	−	29.5244i	−0.720249	−	0.415836i	−0.814844	+	0.579680i	$0.803178\pi$
$72$		0			0
$73$	35.2245	+	61.0107i	0.482528	+	0.835763i	0.999799	−	0.0200588i	$-0.00638534\pi$
$73$	35.2245	+	61.0107i	0.482528	+	0.835763i	−0.517271	+	0.855822i	$0.673052\pi$
$74$	−48.8394	+	55.4912i	−0.659992	+	0.749880i
$75$		0			0
$76$	−104.920	+	13.4333i	−1.38053	+	0.176754i
$77$	−3.44205	+	19.5208i	−0.0447019	+	0.253517i
$78$		0			0
$79$	−95.9155	−	114.308i	−1.21412	−	1.44693i	−0.858895	−	0.512151i	$-0.828849\pi$
$79$	−95.9155	−	114.308i	−1.21412	−	1.44693i	−0.355225	−	0.934781i	$-0.615596\pi$
$80$	100.840	+	47.8992i	1.26050	+	0.598740i
$81$		0			0
$82$	−51.1491	−	63.9633i	−0.623769	−	0.780040i
$83$	−46.7322	−	55.6933i	−0.563039	−	0.671004i	0.407148	−	0.913362i	$-0.366523\pi$
$83$	−46.7322	−	55.6933i	−0.563039	−	0.671004i	−0.970187	+	0.242358i	$0.922079\pi$
$84$		0			0
$85$	22.1101	−	125.393i	0.260119	−	1.47521i
$86$	−38.6297	+	63.4051i	−0.449182	+	0.737268i
$87$		0			0
$88$	−46.7245	+	33.8778i	−0.530961	+	0.384975i
$89$	7.52863	+	13.0400i	0.0845913	+	0.146517i	0.905217	−	0.424950i	$-0.139708\pi$
$89$	7.52863	+	13.0400i	0.0845913	+	0.146517i	−0.820626	+	0.571466i	$0.806375\pi$
$90$		0			0
$91$	−44.4654	−	25.6721i	−0.488631	−	0.282111i
$92$	29.4420	+	18.9043i	0.320022	+	0.205481i
$93$		0			0
$94$	−50.6442	−	1.19523i	−0.538768	−	0.0127152i
$95$	−118.601	+	141.343i	−1.24843	+	1.48782i
$96$		0			0
$97$	−101.970	−	37.1140i	−1.05124	−	0.382619i	−0.242107	−	0.970249i	$-0.577839\pi$
$97$	−101.970	−	37.1140i	−1.05124	−	0.382619i	−0.809129	+	0.587631i	$0.800061\pi$
$98$	−81.9586	+	12.4654i	−0.836313	+	0.127198i
$99$		0			0
$100$	90.4511	−	28.1656i	0.904511	−	0.281656i
$101$	−1.49432	−	8.47472i	−0.0147953	−	0.0839082i	0.976516	−	0.215445i	$-0.0691201\pi$
$101$	−1.49432	−	8.47472i	−0.0147953	−	0.0839082i	−0.991311	+	0.131536i	$0.958009\pi$
$102$		0			0
$103$	17.3204	+	47.5874i	0.168159	+	0.462014i	0.994935	−	0.100518i	$-0.0320499\pi$
$103$	17.3204	+	47.5874i	0.168159	+	0.462014i	−0.826776	+	0.562531i	$0.809828\pi$
$104$	−41.0661	−	143.743i	−0.394866	−	1.38215i
$105$		0			0
$106$	178.436	+	35.8234i	1.68336	+	0.337957i
$107$			151.204i			1.41312i	0.707654	+	0.706559i	$0.249754\pi$
$107$			151.204i			1.41312i	−0.707654	+	0.706559i	$0.750246\pi$
$108$		0			0
$109$	90.9385			0.834298			0.417149	−	0.908838i	$-0.363029\pi$
$109$	90.9385			0.834298			0.417149	+	0.908838i	$0.363029\pi$
$110$	−19.8160	+	98.7033i	−0.180145	+	0.897302i
$111$		0			0
$112$	35.8311	+	25.4712i	0.319921	+	0.227422i
$113$	150.223	−	54.6767i	1.32941	−	0.483865i	0.422947	−	0.906155i	$-0.360996\pi$
$113$	150.223	−	54.6767i	1.32941	−	0.483865i	0.906461	+	0.422290i	$0.138774\pi$
$114$		0			0
$115$	60.1050	−	10.5981i	0.522652	−	0.0921577i
$116$	−31.1928	+	9.71313i	−0.268903	+	0.0837339i
$117$		0			0
$118$	−21.5632	−	141.776i	−0.182739	−	1.20149i
$119$	17.1489	−	47.1163i	0.144109	−	0.395935i
$120$		0			0
$121$	52.8225	+	44.3233i	0.436550	+	0.366309i
$122$	3.25499	−	137.920i	0.0266803	−	1.13050i
$123$		0			0
$124$	139.334	+	89.4646i	1.12367	+	0.721489i
$125$	−4.59207	+	7.95369i	−0.0367365	+	0.0636296i
$126$		0			0
$127$	19.1397	−	11.0503i	0.150706	−	0.0870103i	−0.422751	−	0.906246i	$-0.638935\pi$
$127$	19.1397	−	11.0503i	0.150706	−	0.0870103i	0.573457	+	0.819236i	$0.305602\pi$
$128$	23.4059	+	125.842i	0.182858	+	0.983139i
$129$		0			0
$130$	−222.694	−	135.677i	−1.71303	−	1.04367i
$131$	−99.5842	−	17.5594i	−0.760184	−	0.134041i	−0.219899	−	0.975523i	$-0.570573\pi$
$131$	−99.5842	−	17.5594i	−0.760184	−	0.134041i	−0.540286	+	0.841482i	$0.681684\pi$
$132$		0			0
$133$	−55.6596	+	46.7040i	−0.418493	+	0.351158i
$134$	−94.0709	+	75.2251i	−0.702022	+	0.561381i
$135$		0			0
$136$	131.276	−	63.8691i	0.965264	−	0.469626i
$137$	−53.7560	+	45.1066i	−0.392380	+	0.329246i	−0.817539	−	0.575873i	$-0.804662\pi$
$137$	−53.7560	+	45.1066i	−0.392380	+	0.329246i	0.425160	+	0.905118i	$0.360218\pi$
$138$		0			0
$139$	−19.9974	−	3.52608i	−0.143866	−	0.0253675i	0.101251	−	0.994861i	$-0.467715\pi$
$139$	−19.9974	−	3.52608i	−0.143866	−	0.0253675i	−0.245117	+	0.969493i	$0.578827\pi$
$140$	76.0638	−	9.73871i	0.543313	−	0.0695622i
$141$		0			0
$142$	−88.6517	−	78.0250i	−0.624308	−	0.549472i
$143$	116.750	−	67.4055i	0.816432	−	0.471367i
$144$		0			0
$145$	−28.4939	+	49.3529i	−0.196510	+	0.340365i
$146$	45.0527	+	133.501i	0.308580	+	0.914391i
$147$		0			0
$148$	−117.613	+	89.5845i	−0.794683	+	0.605301i
$149$	79.3896	+	66.6158i	0.532816	+	0.447086i	0.869073	−	0.494685i	$-0.164716\pi$
$149$	79.3896	+	66.6158i	0.532816	+	0.447086i	−0.336256	+	0.941771i	$0.609161\pi$
$150$		0			0
$151$	55.5930	−	152.740i	0.368165	−	1.01153i	−0.607893	−	0.794019i	$-0.707985\pi$
$151$	55.5930	−	152.740i	0.368165	−	1.01153i	0.976059	−	0.217507i	$-0.0697926\pi$
$152$	−211.023	−	14.9630i	−1.38831	−	0.0984408i
$153$		0			0
$154$	−14.4342	+	36.9228i	−0.0937286	+	0.239759i
$155$	284.447	−	50.1557i	1.83514	−	0.323585i
$156$		0			0
$157$	−98.7189	+	35.9307i	−0.628783	+	0.228858i	−0.636701	−	0.771110i	$-0.719702\pi$
$157$	−98.7189	+	35.9307i	−0.628783	+	0.228858i	0.00791855	+	0.999969i	$0.497479\pi$
$158$	−143.079	−	261.902i	−0.905560	−	1.65761i
$159$		0			0
$160$	178.878	+	133.622i	1.11799	+	0.835138i
$161$	24.0339			0.149279
$162$		0			0
$163$		−	80.1029i		−	0.491429i	−0.969342	−	0.245714i	$-0.920977\pi$
$163$		−	80.1029i		−	0.491429i	0.969342	−	0.245714i	$-0.0790225\pi$
$164$	−75.1164	−	145.560i	−0.458027	−	0.887560i
$165$		0			0
$166$	−69.7112	−	127.605i	−0.419947	−	0.768703i
$167$	−22.5581	−	61.9777i	−0.135078	−	0.371124i	0.853650	−	0.520847i	$-0.174384\pi$
$167$	−22.5581	−	61.9777i	−0.135078	−	0.371124i	−0.988728	+	0.149723i	$0.952162\pi$
$168$		0			0
$169$	31.2908	+	177.459i	0.185153	+	1.05005i
$170$	92.7185	−	237.175i	0.545403	−	1.39515i
$171$		0			0
$172$	−100.709	+	109.122i	−0.585515	+	0.634430i
$173$	−58.8837	−	21.4319i	−0.340368	−	0.123884i	0.166180	−	0.986095i	$-0.446857\pi$
$173$	−58.8837	−	21.4319i	−0.340368	−	0.123884i	−0.506548	+	0.862212i	$0.669079\pi$
$174$		0			0
$175$	41.8287	−	49.8495i	0.239021	−	0.284854i
$176$	−104.958	+	48.0360i	−0.596350	+	0.272932i
$177$		0			0
$178$	9.62923	+	28.5335i	0.0540968	+	0.160301i
$179$	94.8245	+	54.7469i	0.529746	+	0.305849i	0.740913	−	0.671601i	$-0.234393\pi$
$179$	94.8245	+	54.7469i	0.529746	+	0.305849i	−0.211167	+	0.977450i	$0.567726\pi$
$180$		0			0
$181$	115.832	+	200.626i	0.639954	+	1.10843i	0.985442	+	0.170010i	$0.0543800\pi$
$181$	115.832	+	200.626i	0.639954	+	1.10843i	−0.345488	+	0.938423i	$0.612287\pi$
$182$	−77.0847	−	67.8445i	−0.423542	−	0.372772i
$183$		0			0
$184$	50.2900	+	48.6594i	0.273315	+	0.264453i
$185$	−44.7826	+	253.975i	−0.242068	+	1.37284i
$186$		0			0
$187$	84.6226	+	100.849i	0.452527	+	0.539301i
$188$	−98.8364	−	22.2808i	−0.525725	−	0.118515i
$189$		0			0
$190$	−288.205	+	230.467i	−1.51687	+	1.21298i
$191$	104.599	+	124.656i	0.547638	+	0.652650i	0.966882	−	0.255224i	$-0.0821491\pi$
$191$	104.599	+	124.656i	0.547638	+	0.652650i	−0.419244	+	0.907874i	$0.637705\pi$
$192$		0			0
$193$	41.2822	−	234.123i	0.213897	−	1.21307i	−0.668912	−	0.743342i	$-0.733240\pi$
$193$	41.2822	−	234.123i	0.213897	−	1.21307i	0.882809	−	0.469731i	$-0.155649\pi$
$194$	−185.339	−	112.918i	−0.955358	−	0.582054i
$195$		0			0
$196$	−165.618	−	7.82168i	−0.844988	−	0.0399066i
$197$	26.5893	+	46.0540i	0.134971	+	0.233777i	0.925586	−	0.378536i	$-0.123573\pi$
$197$	26.5893	+	46.0540i	0.134971	+	0.233777i	−0.790615	+	0.612313i	$0.790239\pi$
$198$		0			0
$199$	−11.7751	−	6.79836i	−0.0591714	−	0.0341626i	0.470122	−	0.882601i	$-0.344210\pi$
$199$	−11.7751	−	6.79836i	−0.0591714	−	0.0341626i	−0.529294	+	0.848439i	$0.677543\pi$
$200$	188.451	−	19.6212i	0.942255	−	0.0981061i
$201$		0			0
$202$	0.406074	−	17.2061i	0.00201027	−	0.0851789i
$203$	−14.4250	+	17.1910i	−0.0710589	+	0.0846847i
$204$		0			0
$205$	−268.491	−	97.7226i	−1.30971	−	0.476696i
$206$	15.2293	+	100.131i	0.0739288	+	0.486075i
$207$		0			0
$208$	−23.9378	−	298.029i	−0.115086	−	1.43283i
$209$	−33.1276	−	187.876i	−0.158505	−	0.898928i
$210$		0			0
$211$	6.24714	+	17.1639i	0.0296073	+	0.0813453i	0.953616	−	0.301027i	$-0.0973294\pi$
$211$	6.24714	+	17.1639i	0.0296073	+	0.0813453i	−0.924008	+	0.382372i	$0.875107\pi$
$212$	335.788	+	140.490i	1.58391	+	0.662690i
$213$		0			0
$214$	−59.5245	+	296.491i	−0.278152	+	1.38547i
$215$			259.021i			1.20475i
$216$		0			0
$217$	113.740			0.524149
$218$	178.319	+	35.7998i	0.817976	+	0.164219i
$219$		0			0
$220$	−77.7132	+	185.744i	−0.353242	+	0.844289i
$221$	−320.442	+	116.631i	−1.44996	+	0.527744i
$222$		0			0
$223$	129.135	−	22.7700i	0.579082	−	0.102108i	0.123568	−	0.992336i	$-0.460566\pi$
$223$	129.135	−	22.7700i	0.579082	−	0.102108i	0.455515	+	0.890228i	$0.349455\pi$
$224$	60.2330	+	64.0515i	0.268897	+	0.285944i
$225$		0			0
$226$	316.093	−	48.0757i	1.39864	−	0.212724i
$227$	133.527	−	366.863i	0.588225	−	1.61614i	−0.185521	−	0.982640i	$-0.559397\pi$
$227$	133.527	−	366.863i	0.588225	−	1.61614i	0.773747	−	0.633495i	$-0.218380\pi$
$228$		0			0
$229$	142.142	+	119.271i	0.620708	+	0.520836i	0.898026	−	0.439943i	$-0.145001\pi$
$229$	142.142	+	119.271i	0.620708	+	0.520836i	−0.277318	+	0.960778i	$0.589446\pi$
$230$	122.030	+	2.87998i	0.530567	+	0.0125217i
$231$		0			0
$232$	−64.9889	+	6.76653i	−0.280124	+	0.0291661i
$233$	129.370	−	224.075i	0.555235	−	0.961695i	−0.442650	−	0.896694i	$-0.645962\pi$
$233$	129.370	−	224.075i	0.555235	−	0.961695i	0.997885	−	0.0650010i	$-0.0207051\pi$
$234$		0			0
$235$	−153.054	+	88.3655i	−0.651292	+	0.376023i
$236$	13.5303	−	286.493i	0.0573318	−	1.21395i
$237$		0			0
$238$	52.1752	−	85.6380i	0.219223	−	0.359824i
$239$	179.740	+	31.6930i	0.752050	+	0.132607i	0.536517	−	0.843890i	$-0.319740\pi$
$239$	179.740	+	31.6930i	0.752050	+	0.132607i	0.215533	+	0.976496i	$0.430851\pi$
$240$		0			0
$241$	202.499	−	169.917i	0.840247	−	0.705051i	−0.117373	−	0.993088i	$-0.537447\pi$
$241$	202.499	−	169.917i	0.840247	−	0.705051i	0.957619	+	0.288037i	$0.0930027\pi$
$242$	86.1294	+	107.707i	0.355907	+	0.445071i
$243$		0			0
$244$	60.6779	−	269.163i	0.248680	−	1.10313i
$245$	−221.552	+	185.905i	−0.904296	+	0.758794i
$246$		0			0
$247$	486.649	+	85.8094i	1.97024	+	0.347407i
$248$	237.998	+	230.281i	0.959668	+	0.928551i
$249$		0			0
$250$	−12.1356	+	13.7884i	−0.0485424	+	0.0551537i
$251$	305.025	−	176.106i	1.21524	−	0.701618i	0.251343	−	0.967898i	$-0.419128\pi$
$251$	305.025	−	176.106i	1.21524	−	0.701618i	0.963896	+	0.266280i	$0.0857946\pi$
$252$		0			0
$253$	−31.5520	+	54.6497i	−0.124712	+	0.216007i
$254$	41.8807	−	14.1335i	0.164885	−	0.0556438i
$255$		0			0
$256$	−3.64433	+	255.974i	−0.0142357	+	0.999899i
$257$	25.7621	+	21.6169i	0.100241	+	0.0841126i	0.691531	−	0.722347i	$-0.256937\pi$
$257$	25.7621	+	21.6169i	0.100241	+	0.0841126i	−0.591290	+	0.806459i	$0.701381\pi$
$258$		0			0
$259$	−34.7341	+	95.4311i	−0.134108	+	0.368460i
$260$	−383.263	−	353.713i	−1.47409	−	1.36043i
$261$		0			0
$262$	−188.359	−	73.6351i	−0.718929	−	0.281050i
$263$	−418.447	+	73.7836i	−1.59106	+	0.280546i	−0.897886	−	0.440229i	$-0.854897\pi$
$263$	−418.447	+	73.7836i	−1.59106	+	0.280546i	−0.693169	+	0.720775i	$0.743786\pi$
$264$		0			0
$265$	596.639	−	217.159i	2.25147	−	0.819467i
$266$	−127.527	+	69.6690i	−0.479426	+	0.261913i
$267$		0			0
$268$	−214.075	+	110.474i	−0.798788	+	0.412216i
$269$	120.305			0.447231			0.223616	−	0.974677i	$-0.428214\pi$
$269$	120.305			0.447231			0.223616	+	0.974677i	$0.428214\pi$
$270$		0			0
$271$			73.3528i			0.270675i	0.990800	+	0.135337i	$0.0432118\pi$
$271$			73.3528i			0.270675i	−0.990800	+	0.135337i	$0.956788\pi$
$272$	282.559	−	73.5598i	1.03882	−	0.270440i
$273$		0			0
$274$	−123.166	+	67.2862i	−0.449510	+	0.245570i
$275$	58.4375	+	160.556i	0.212500	+	0.583839i
$276$		0			0
$277$	46.8683	+	265.803i	0.169200	+	0.959579i	0.944628	+	0.328143i	$0.106423\pi$
$277$	46.8683	+	265.803i	0.169200	+	0.959579i	−0.775428	+	0.631436i	$0.782466\pi$
$278$	−37.8243	−	14.7866i	−0.136059	−	0.0531892i
$279$		0			0
$280$	152.985	+	10.8477i	0.546376	+	0.0387418i
$281$	300.835	+	109.495i	1.07059	+	0.389662i	0.816396	−	0.577492i	$-0.195969\pi$
$281$	300.835	+	109.495i	1.07059	+	0.389662i	0.254191	+	0.967154i	$0.418191\pi$
$282$		0			0
$283$	35.0996	−	41.8300i	0.124027	−	0.147809i	−0.700458	−	0.713694i	$-0.747021\pi$
$283$	35.0996	−	41.8300i	0.124027	−	0.147809i	0.824484	+	0.565885i	$0.191465\pi$
$284$	−143.119	−	187.897i	−0.503939	−	0.661608i
$285$		0			0
$286$	255.467	−	86.2127i	0.893241	−	0.301443i
$287$	−97.4403	−	56.2572i	−0.339513	−	0.196018i
$288$		0			0
$289$	−22.0050	−	38.1138i	−0.0761418	−	0.131882i
$290$	−75.3018	+	85.5576i	−0.259661	+	0.295026i
$291$		0			0
$292$	35.7872	+	279.515i	0.122559	+	0.957242i
$293$	−26.7866	+	151.914i	−0.0914218	+	0.518479i	0.904363	+	0.426763i	$0.140346\pi$
$293$	−26.7866	+	151.914i	−0.0914218	+	0.518479i	−0.995785	+	0.0917158i	$0.970765\pi$
$294$		0			0
$295$	−321.586	−	383.251i	−1.09012	−	1.29916i
$296$	−265.891	+	129.363i	−0.898281	+	0.437037i
$297$		0			0
$298$	129.448	+	161.879i	0.434390	+	0.543216i
$299$	−105.068	−	125.215i	−0.351397	−	0.418779i
$300$		0			0
$301$	−17.7121	+	100.450i	−0.0588441	+	0.333721i
$302$	169.140	−	277.619i	0.560067	−	0.919269i
$303$		0			0
$304$	−407.900	−	112.414i	−1.34177	−	0.369784i
$305$	−240.648	−	416.814i	−0.789008	−	1.36660i
$306$		0			0
$307$	113.220	+	65.3674i	0.368794	+	0.212923i	0.672931	−	0.739705i	$-0.265035\pi$
$307$	113.220	+	65.3674i	0.368794	+	0.212923i	−0.304138	+	0.952628i	$0.598368\pi$
$308$	−42.8391	+	66.7187i	−0.139088	+	0.216619i
$309$		0			0
$310$	577.509	+	13.6295i	1.86293	+	0.0439662i
$311$	369.398	−	440.231i	1.18777	−	1.41553i	0.300816	−	0.953682i	$-0.402741\pi$
$311$	369.398	−	440.231i	1.18777	−	1.41553i	0.886957	−	0.461851i	$-0.152815\pi$
$312$		0			0
$313$	18.3407	+	6.67548i	0.0585966	+	0.0213274i	0.371152	−	0.928572i	$-0.378963\pi$
$313$	18.3407	+	6.67548i	0.0585966	+	0.0213274i	−0.312556	+	0.949899i	$0.601185\pi$
$314$	−207.720	+	31.5929i	−0.661529	+	0.100614i
$315$		0			0
$316$	−177.456	−	569.882i	−0.561569	−	1.80342i
$317$	32.8060	+	186.052i	0.103489	+	0.586916i	0.991813	+	0.127699i	$0.0407590\pi$
$317$	32.8060	+	186.052i	0.103489	+	0.586916i	−0.888324	+	0.459217i	$0.848130\pi$
$318$		0			0
$319$	−20.1526	−	55.3689i	−0.0631744	−	0.173570i
$320$	298.154	+	332.435i	0.931730	+	1.03886i
$321$		0			0
$322$	47.1274	+	9.46143i	0.146358	+	0.0293833i
$323$			482.568i			1.49402i
$324$		0			0
$325$	−442.573			−1.36176
$326$	31.5342	−	157.072i	0.0967306	−	0.481815i
$327$		0			0
$328$	−89.9911	−	314.995i	−0.274363	−	0.960352i
$329$	−65.3978	+	23.8029i	−0.198778	+	0.0723491i
$330$		0			0
$331$	518.701	−	91.4609i	1.56707	−	0.276317i	0.678341	−	0.734747i	$-0.262699\pi$
$331$	518.701	−	91.4609i	1.56707	−	0.276317i	0.888730	+	0.458430i	$0.151588\pi$
$332$	−86.4606	−	277.660i	−0.260423	−	0.836325i
$333$		0			0
$334$	−19.8347	−	130.411i	−0.0593852	−	0.390452i
$335$	−143.721	+	394.870i	−0.429017	+	1.17872i
$336$		0			0
$337$	−243.534	−	204.349i	−0.722651	−	0.606376i	0.205466	−	0.978664i	$-0.434129\pi$
$337$	−243.534	−	204.349i	−0.722651	−	0.606376i	−0.928117	+	0.372288i	$0.878573\pi$
$338$	−8.50311	+	360.293i	−0.0251571	+	1.06596i
$339$		0			0
$340$	275.178	−	428.569i	0.809347	−	1.26050i
$341$	−149.320	+	258.630i	−0.437889	+	0.758446i
$342$		0			0
$343$	−215.228	+	124.262i	−0.627487	+	0.362280i
$344$	−240.435	+	174.328i	−0.698939	+	0.506768i
$345$		0			0
$346$	−107.026	−	65.2060i	−0.309324	−	0.188457i
$347$	−385.479	−	67.9703i	−1.11089	−	0.195880i	−0.412052	−	0.911160i	$-0.635188\pi$
$347$	−385.479	−	67.9703i	−1.11089	−	0.195880i	−0.698838	+	0.715280i	$0.746299\pi$
$348$		0			0
$349$	−296.487	+	248.782i	−0.849532	+	0.712842i	−0.959687	−	0.281072i	$-0.909310\pi$
$349$	−296.487	+	248.782i	−0.849532	+	0.712842i	0.110154	+	0.993914i	$0.464865\pi$
$350$	101.645	−	81.2818i	0.290414	−	0.232234i
$351$		0			0
$352$	−224.719	+	52.8737i	−0.638406	+	0.150209i
$353$	412.016	−	345.722i	1.16718	−	0.979383i	0.167205	−	0.985922i	$-0.446526\pi$
$353$	412.016	−	345.722i	1.16718	−	0.979383i	0.999979	+	0.00653868i	$0.00208134\pi$
$354$		0			0
$355$	−405.746	−	71.5439i	−1.14295	−	0.201532i
$356$	7.64889	+	59.7414i	0.0214857	+	0.167813i
$357$		0			0
$358$	164.386	+	144.681i	0.459180	+	0.404138i
$359$	37.7896	−	21.8179i	0.105264	−	0.0607740i	−0.446444	−	0.894812i	$-0.647310\pi$
$359$	37.7896	−	21.8179i	0.105264	−	0.0607740i	0.551708	+	0.834038i	$0.313976\pi$
$360$		0			0
$361$	169.146	−	292.970i	0.468550	−	0.811552i
$362$	148.151	+	439.002i	0.409256	+	1.21271i
$363$		0			0
$364$	−124.445	−	163.380i	−0.341882	−	0.448847i
$365$	376.549	+	315.962i	1.03164	+	0.865649i
$366$		0			0
$367$	−226.818	+	623.177i	−0.618033	+	1.69803i	0.0937186	+	0.995599i	$0.470125\pi$
$367$	−226.818	+	623.177i	−0.618033	+	1.69803i	−0.711751	+	0.702432i	$0.752098\pi$
$368$	79.4566	+	115.213i	0.215915	+	0.313078i
$369$		0			0
$370$	−187.796	+	480.383i	−0.507555	+	1.29833i
$371$	246.231	−	43.4171i	0.663694	−	0.117027i
$372$		0			0
$373$	−352.096	+	128.152i	−0.943957	+	0.343572i	−0.767727	−	0.640777i	$-0.778612\pi$
$373$	−352.096	+	128.152i	−0.943957	+	0.343572i	−0.176230	+	0.984349i	$0.556390\pi$
$374$	126.233	+	231.066i	0.337521	+	0.617824i
$375$		0			0
$376$	−185.034	−	82.5989i	−0.492112	−	0.219678i
$377$	152.625			0.404841
$378$		0			0
$379$			65.5779i			0.173029i	0.996251	+	0.0865144i	$0.0275729\pi$
$379$			65.5779i			0.173029i	−0.996251	+	0.0865144i	$0.972427\pi$
$380$	−655.861	+	338.458i	−1.72595	+	0.890679i
$381$		0			0
$382$	156.032	+	285.612i	0.408460	+	0.747677i
$383$	99.1140	+	272.314i	0.258783	+	0.711002i	0.999243	+	0.0389008i	$0.0123856\pi$
$383$	99.1140	+	272.314i	0.258783	+	0.711002i	−0.740460	+	0.672101i	$0.765392\pi$
$384$		0			0
$385$	24.0165	+	136.204i	0.0623804	+	0.353777i
$386$	173.117	−	442.834i	0.448488	−	1.14724i
$387$		0			0
$388$	−318.974	−	294.382i	−0.822099	−	0.758715i
$389$	−172.336	−	62.7253i	−0.443024	−	0.161247i	0.110870	−	0.993835i	$-0.464636\pi$
$389$	−172.336	−	62.7253i	−0.443024	−	0.161247i	−0.553894	+	0.832587i	$0.686859\pi$
$390$		0			0
$391$	102.604	−	122.278i	0.262414	−	0.312732i
$392$	−321.676	−	80.5362i	−0.820603	−	0.205449i
$393$		0			0
$394$	34.0081	+	100.773i	0.0863150	+	0.255770i
$395$	−901.662	−	520.575i	−2.28269	−	1.31791i
$396$		0			0
$397$	−320.572	−	555.246i	−0.807485	−	1.39861i	−0.914600	−	0.404359i	$-0.867495\pi$
$397$	−320.572	−	555.246i	−0.807485	−	1.39861i	0.107115	−	0.994247i	$-0.465839\pi$
$398$	−20.4132	−	17.9662i	−0.0512894	−	0.0451413i
$399$		0			0
$400$	377.253	+	35.7130i	0.943132	+	0.0892824i
$401$	62.8864	−	356.647i	0.156824	−	0.889393i	−0.800275	−	0.599633i	$-0.795313\pi$
$401$	62.8864	−	356.647i	0.156824	−	0.889393i	0.957099	−	0.289760i	$-0.0935756\pi$
$402$		0			0
$403$	−497.234	−	592.580i	−1.23383	−	1.47042i
$404$	7.56981	−	33.5792i	0.0187371	−	0.0831168i
$405$		0			0
$406$	−35.0531	+	28.0307i	−0.0863377	+	0.0690411i
$407$	−171.398	−	204.264i	−0.421125	−	0.501877i
$408$		0			0
$409$	−108.016	+	612.590i	−0.264098	+	1.49777i	0.507493	+	0.861656i	$0.330572\pi$
$409$	−108.016	+	612.590i	−0.264098	+	1.49777i	−0.771591	+	0.636119i	$0.780539\pi$
$410$	−488.005	−	297.318i	−1.19026	−	0.725167i
$411$		0			0
$412$	−9.55599	+	202.340i	−0.0231942	+	0.491117i
$413$	−98.5064	−	170.618i	−0.238514	−	0.413119i
$414$		0			0
$415$	−439.311	−	253.636i	−1.05858	−	0.611171i
$416$	70.3863	−	593.821i	0.169198	−	1.42745i
$417$		0			0
$418$	9.00223	−	381.442i	0.0215364	−	0.912541i
$419$	−389.490	+	464.176i	−0.929570	+	1.10782i	0.0643736	+	0.997926i	$0.479495\pi$
$419$	−389.490	+	464.176i	−0.929570	+	1.10782i	−0.993943	+	0.109892i	$0.964949\pi$
$420$		0			0
$421$	−387.449	−	141.020i	−0.920306	−	0.334964i	−0.161946	−	0.986800i	$-0.551777\pi$
$421$	−387.449	−	141.020i	−0.920306	−	0.334964i	−0.758360	+	0.651836i	$0.773999\pi$
$422$	5.49293	+	36.1155i	0.0130164	+	0.0855817i
$423$		0			0
$424$	603.131	+	407.674i	1.42248	+	0.961495i
$425$	−75.0497	−	425.628i	−0.176587	−	1.00148i
$426$		0			0
$427$	−64.8228	−	178.099i	−0.151810	−	0.417094i
$428$	−233.440	+	557.949i	−0.545420	+	1.30362i
$429$		0			0
$430$	−101.969	+	507.907i	−0.237137	+	1.18118i
$431$		−	508.464i		−	1.17973i	−0.807501	−	0.589866i	$-0.799181\pi$
$431$		−	508.464i		−	1.17973i	0.807501	−	0.589866i	$-0.200819\pi$
$432$		0			0
$433$	149.074			0.344281			0.172140	−	0.985072i	$-0.444932\pi$
$433$	149.074			0.344281			0.172140	+	0.985072i	$0.444932\pi$
$434$	223.030	+	44.7763i	0.513895	+	0.103171i
$435$		0			0
$436$	335.567	+	140.398i	0.769650	+	0.322013i
$437$	−217.361	+	79.1131i	−0.497395	+	0.181037i
$438$		0			0
$439$	−43.4626	+	7.66363i	−0.0990037	+	0.0174570i	−0.222931	−	0.974834i	$-0.571562\pi$
$439$	−43.4626	+	7.66363i	−0.0990037	+	0.0174570i	0.123927	+	0.992291i	$0.460451\pi$
$440$	−225.507	+	333.626i	−0.512517	+	0.758241i
$441$		0			0
$442$	−674.261	+	102.551i	−1.52548	+	0.232015i
$443$	−89.6730	+	246.374i	−0.202422	+	0.556150i	−0.998817	−	0.0486268i	$-0.984515\pi$
$443$	−89.6730	+	246.374i	−0.202422	+	0.556150i	0.796395	+	0.604777i	$0.206738\pi$
$444$		0			0
$445$	80.4807	+	67.5313i	0.180856	+	0.151756i
$446$	262.182	+	6.18763i	0.587852	+	0.0138736i
$447$		0			0
$448$	92.8940	+	149.309i	0.207353	+	0.333278i
$449$	−20.4017	+	35.3367i	−0.0454380	+	0.0787009i	−0.887850	−	0.460133i	$-0.847802\pi$
$449$	−20.4017	+	35.3367i	−0.0454380	+	0.0787009i	0.842412	+	0.538834i	$0.181135\pi$
$450$		0			0
$451$	255.842	−	147.711i	0.567277	−	0.327518i
$452$	638.744	+	30.1662i	1.41315	+	0.0667393i
$453$		0			0
$454$	406.253	−	666.806i	0.894830	−	1.46873i
$455$	−352.805	−	62.2091i	−0.775396	−	0.136723i
$456$		0			0
$457$	393.474	−	330.164i	0.860994	−	0.722460i	−0.101188	−	0.994867i	$-0.532264\pi$
$457$	393.474	−	330.164i	0.860994	−	0.722460i	0.962182	+	0.272408i	$0.0878200\pi$
$458$	231.769	+	289.833i	0.506046	+	0.632824i
$459$		0			0
$460$	238.152	+	53.6871i	0.517723	+	0.116711i
$461$	385.698	−	323.639i	0.836654	−	0.702036i	−0.120154	−	0.992755i	$-0.538339\pi$
$461$	385.698	−	323.639i	0.836654	−	0.702036i	0.956808	+	0.290719i	$0.0938945\pi$
$462$		0			0
$463$	−372.857	−	65.7447i	−0.805306	−	0.141997i	−0.244183	−	0.969729i	$-0.578520\pi$
$463$	−372.857	−	65.7447i	−0.805306	−	0.141997i	−0.561123	+	0.827732i	$0.689631\pi$
$464$	−130.099	−	12.3159i	−0.280385	−	0.0265429i
$465$		0			0
$466$	341.890	−	388.454i	0.733668	−	0.833591i
$467$	−229.233	+	132.348i	−0.490863	+	0.283400i	−0.724932	−	0.688820i	$-0.758129\pi$
$467$	−229.233	+	132.348i	−0.490863	+	0.283400i	0.234069	+	0.972220i	$0.424796\pi$
$468$		0			0
$469$	−82.7376	+	143.306i	−0.176413	+	0.305556i
$470$	−334.905	+	113.021i	−0.712565	+	0.240470i
$471$		0			0
$472$	139.315	−	556.450i	0.295159	−	1.17892i
$473$	−205.157	−	172.147i	−0.433736	−	0.363948i
$474$		0			0
$475$	−214.206	+	588.526i	−0.450960	+	1.23900i
$476$	136.022	−	147.386i	0.285761	−	0.309633i
$477$		0			0
$478$	339.971	+	132.904i	0.711236	+	0.278043i
$479$	−120.292	+	21.2107i	−0.251131	+	0.0442812i	−0.297797	−	0.954629i	$-0.596252\pi$
$479$	−120.292	+	21.2107i	−0.251131	+	0.0442812i	0.0466653	+	0.998911i	$0.485141\pi$
$480$		0			0
$481$	649.035	−	236.230i	1.34935	−	0.491122i
$482$	463.967	−	253.468i	0.962587	−	0.525867i
$483$		0			0
$484$	126.488	+	245.107i	0.261338	+	0.506419i
$485$	−757.144			−1.56112
$486$		0			0
$487$			217.211i			0.446019i	0.974816	+	0.223010i	$0.0715881\pi$
$487$			217.211i			0.446019i	−0.974816	+	0.223010i	$0.928412\pi$
$488$	224.943	−	503.908i	0.460949	−	1.03260i
$489$		0			0
$490$	−507.621	+	277.317i	−1.03596	+	0.565952i
$491$	66.1783	+	181.823i	0.134783	+	0.370313i	0.988662	−	0.150159i	$-0.0479785\pi$
$491$	66.1783	+	181.823i	0.134783	+	0.370313i	−0.853879	+	0.520471i	$0.825756\pi$
$492$		0			0
$493$	25.8815	+	146.781i	0.0524979	+	0.297731i
$494$	920.477	+	359.841i	1.86331	+	0.728423i
$495$		0			0
$496$	376.029	+	545.244i	0.758122	+	1.09928i
$497$	−152.459	−	55.4906i	−0.306759	−	0.111651i
$498$		0			0
$499$	−295.882	+	352.618i	−0.592949	+	0.706649i	−0.976170	−	0.217008i	$-0.930370\pi$
$499$	−295.882	+	352.618i	−0.592949	+	0.706649i	0.383221	+	0.923657i	$0.374815\pi$
$500$	−29.2245	+	22.2599i	−0.0584489	+	0.0445198i
$501$		0			0
$502$	667.443	−	225.243i	1.32957	−	0.448690i
$503$	228.127	+	131.709i	0.453533	+	0.261847i	0.709321	−	0.704885i	$-0.249002\pi$
$503$	228.127	+	131.709i	0.453533	+	0.261847i	−0.255788	+	0.966733i	$0.582335\pi$
$504$		0			0
$505$	−30.0218	−	51.9992i	−0.0594490	−	0.102969i
$506$	−83.3835	+	94.7400i	−0.164790	+	0.187233i
$507$		0			0
$508$	87.6867	−	11.2268i	0.172612	−	0.0221001i
$509$	87.4113	−	495.734i	0.171731	−	0.973937i	−0.770118	−	0.637902i	$-0.779803\pi$
$509$	87.4113	−	495.734i	0.171731	−	0.973937i	0.941849	−	0.336036i	$-0.109086\pi$
$510$		0			0
$511$	124.423	+	148.281i	0.243489	+	0.290178i
$512$	−107.916	+	500.498i	−0.210773	+	0.977535i
$513$		0			0
$514$	42.0062	+	52.5298i	0.0817241	+	0.102198i
$515$	227.125	+	270.677i	0.441020	+	0.525587i
$516$		0			0
$517$	31.7308	−	179.954i	0.0613749	−	0.348074i
$518$	−105.678	+	173.454i	−0.204011	+	0.334854i
$519$		0			0
$520$	−612.283	−	844.466i	−1.17747	−	1.62397i
$521$	269.643	+	467.035i	0.517548	+	0.896420i	0.999792	+	0.0203829i	$0.00648852\pi$
$521$	269.643	+	467.035i	0.517548	+	0.896420i	−0.482244	+	0.876037i	$0.660178\pi$
$522$		0			0
$523$	524.176	+	302.633i	1.00225	+	0.578648i	0.908913	−	0.416987i	$-0.136914\pi$
$523$	524.176	+	302.633i	1.00225	+	0.578648i	0.0933352	+	0.995635i	$0.470247\pi$
$524$	−340.361	−	218.541i	−0.649543	−	0.417062i
$525$		0			0
$526$	−849.569	−	20.0503i	−1.61515	−	0.0381184i
$527$	485.573	−	578.683i	0.921390	−	1.09807i
$528$		0			0
$529$	−425.199	−	154.760i	−0.803779	−	0.292551i
$530$	1255.42	−	190.942i	2.36872	−	0.360267i
$531$		0			0
$532$	−277.492	+	86.4082i	−0.521601	+	0.162421i
$533$	132.879	+	753.595i	0.249304	+	1.41387i
$534$		0			0
$535$	360.833	+	991.380i	0.674454	+	1.85305i
$536$	−463.264	+	132.350i	−0.864299	+	0.246922i
$537$		0			0
$538$	235.903	+	47.3606i	0.438482	+	0.0880309i
$539$		−	299.034i		−	0.554794i
$540$		0			0
$541$	−135.580			−0.250609			−0.125305	−	0.992118i	$-0.539991\pi$
$541$	−135.580			−0.250609			−0.125305	+	0.992118i	$0.539991\pi$
$542$	−28.8768	+	143.836i	−0.0532783	+	0.265379i
$543$		0			0
$544$	583.020	−	33.0063i	1.07173	−	0.0606734i
$545$	596.246	−	217.016i	1.09403	−	0.398194i
$546$		0			0
$547$	850.040	−	149.885i	1.55400	−	0.274013i	0.670311	−	0.742080i	$-0.266161\pi$
$547$	850.040	−	149.885i	1.55400	−	0.274013i	0.883693	+	0.468068i	$0.155050\pi$
$548$	−268.001	+	83.4530i	−0.489053	+	0.152286i
$549$		0			0
$550$	51.3825	+	337.835i	0.0934227	+	0.614245i
$551$	73.8706	−	202.958i	0.134066	−	0.368344i
$552$		0			0
$553$	−314.074	−	263.539i	−0.567946	−	0.476563i
$554$	−12.7362	+	539.657i	−0.0229895	+	0.974111i
$555$		0			0
$556$	−68.3476	−	43.8850i	−0.122927	−	0.0789298i
$557$	−50.6707	+	87.7642i	−0.0909707	+	0.157566i	−0.907920	−	0.419144i	$-0.862330\pi$
$557$	−50.6707	+	87.7642i	−0.0909707	+	0.157566i	0.816949	+	0.576710i	$0.195664\pi$
$558$		0			0
$559$	600.770	−	346.855i	1.07472	−	0.620491i
$560$	295.714	+	81.4968i	0.528061	+	0.145530i
$561$		0			0
$562$	546.794	+	333.136i	0.972943	+	0.592768i
$563$	517.334	+	91.2200i	0.918889	+	0.162025i	0.613037	−	0.790054i	$-0.289948\pi$
$563$	517.334	+	91.2200i	0.918889	+	0.162025i	0.305852	+	0.952079i	$0.401059\pi$
$564$		0			0
$565$	854.470	−	716.985i	1.51234	−	1.26900i
$566$	85.2930	−	68.2057i	0.150694	−	0.120505i
$567$		0			0
$568$	−206.668	−	424.783i	−0.363852	−	0.747857i
$569$	−249.430	+	209.296i	−0.438365	+	0.367832i	−0.835097	−	0.550103i	$-0.814589\pi$
$569$	−249.430	+	209.296i	−0.438365	+	0.367832i	0.396732	+	0.917934i	$0.370144\pi$
$570$		0			0
$571$	−607.974	−	107.202i	−1.06475	−	0.187745i	−0.386288	−	0.922378i	$-0.626243\pi$
$571$	−607.974	−	107.202i	−1.06475	−	0.187745i	−0.678464	+	0.734634i	$0.737354\pi$
$572$	534.878	−	68.4822i	0.935101	−	0.119724i
$573$		0			0
$574$	−168.921	−	148.673i	−0.294288	−	0.259011i
$575$	179.410	−	103.583i	0.312018	−	0.180144i
$576$		0			0
$577$	249.999	−	433.011i	0.433274	−	0.750453i	−0.563879	−	0.825857i	$-0.690692\pi$
$577$	249.999	−	433.011i	0.433274	−	0.750453i	0.997153	+	0.0754047i	$0.0240249\pi$
$578$	−28.1447	−	83.3990i	−0.0486933	−	0.144289i
$579$		0			0
$580$	−181.339	+	138.123i	−0.312653	+	0.238144i
$581$	−153.024	−	128.402i	−0.263381	−	0.221003i
$582$		0			0
$583$	−224.531	+	616.893i	−0.385130	+	1.05814i
$584$	−39.8625	+	562.181i	−0.0682577	+	0.962639i
$585$		0			0
$586$	−112.329	+	287.340i	−0.191688	+	0.490341i
$587$	21.0087	−	3.70441i	0.0357900	−	0.00631075i	−0.155724	−	0.987801i	$-0.549771\pi$
$587$	21.0087	−	3.70441i	0.0357900	−	0.00631075i	0.191515	+	0.981490i	$0.438660\pi$
$588$		0			0
$589$	−1028.66	+	374.403i	−1.74646	+	0.635659i
$590$	−479.715	−	878.106i	−0.813075	−	1.48832i
$591$		0			0
$592$	−572.305	+	148.991i	−0.966732	+	0.251674i
$593$	−44.9660			−0.0758279			−0.0379140	−	0.999281i	$-0.512071\pi$
$593$	−44.9660			−0.0758279			−0.0379140	+	0.999281i	$0.512071\pi$
$594$		0			0
$595$		−	349.846i		−	0.587977i
$596$	190.105	+	368.383i	0.318968	+	0.618093i
$597$		0			0
$598$	−156.731	−	286.893i	−0.262092	−	0.479754i
$599$	−219.690	−	603.593i	−0.366761	−	1.00767i	−0.976585	−	0.215131i	$-0.930982\pi$
$599$	−219.690	−	603.593i	−0.366761	−	1.00767i	0.609824	−	0.792537i	$-0.291240\pi$
$600$		0			0
$601$	97.2120	+	551.316i	0.161750	+	0.917332i	0.952352	+	0.305001i	$0.0986568\pi$
$601$	97.2120	+	551.316i	0.161750	+	0.917332i	−0.790602	+	0.612331i	$0.790232\pi$
$602$	−74.2754	+	189.997i	−0.123381	+	0.315610i
$603$		0			0
$604$	440.953	−	477.791i	0.730055	−	0.791044i
$605$	452.108	+	164.554i	0.747287	+	0.271990i
$606$		0			0
$607$	92.3519	−	110.061i	0.152145	−	0.181319i	−0.684588	−	0.728930i	$-0.740018\pi$
$607$	92.3519	−	110.061i	0.152145	−	0.181319i	0.836733	+	0.547611i	$0.184462\pi$
$608$	−755.585	−	381.008i	−1.24274	−	0.626658i
$609$		0			0
$610$	−307.792	−	912.055i	−0.504577	−	1.49517i
$611$	409.908	+	236.661i	0.670881	+	0.387333i
$612$		0			0
$613$	76.4211	+	132.365i	0.124667	+	0.215930i	0.921603	−	0.388134i	$-0.126880\pi$
$613$	76.4211	+	132.365i	0.124667	+	0.215930i	−0.796935	+	0.604064i	$0.793547\pi$
$614$	196.276	+	172.748i	0.319668	+	0.281349i
$615$		0			0
$616$	−110.267	+	113.962i	−0.179005	+	0.185004i
$617$	148.699	−	843.316i	0.241004	−	1.36680i	−0.588589	−	0.808432i	$-0.700317\pi$
$617$	148.699	−	843.316i	0.241004	−	1.36680i	0.829593	−	0.558368i	$-0.188572\pi$
$618$		0			0
$619$	669.136	+	797.445i	1.08100	+	1.28828i	0.955115	+	0.296234i	$0.0957309\pi$
$619$	669.136	+	797.445i	1.08100	+	1.28828i	0.125880	+	0.992046i	$0.459825\pi$
$620$	1127.06	+	254.074i	1.81783	+	0.409797i
$621$		0			0
$622$	897.648	−	717.816i	1.44316	−	1.15404i
$623$	26.5932	+	31.6925i	0.0426857	+	0.0508708i
$624$		0			0
$625$	−113.943	+	646.206i	−0.182310	+	1.03393i
$626$	33.3359	+	20.3100i	0.0532522	+	0.0324441i
$627$		0			0
$628$	−419.750	−	19.8237i	−0.668392	−	0.0315664i
$629$	337.245	+	584.126i	0.536161	+	0.928659i
$630$		0			0
$631$	538.851	+	311.106i	0.853964	+	0.493037i	0.861986	−	0.506931i	$-0.169220\pi$
$631$	538.851	+	311.106i	0.853964	+	0.493037i	−0.00802217	+	0.999968i	$0.502554\pi$
$632$	−123.622	−	1187.33i	−0.195605	−	1.87868i
$633$		0			0
$634$	−8.91485	+	377.740i	−0.0140613	+	0.595804i
$635$	99.1206	−	118.127i	0.156095	−	0.186027i
$636$		0			0
$637$	727.866	+	264.922i	1.14265	+	0.415890i
$638$	−17.7197	−	116.505i	−0.0277738	−	0.182610i
$639$		0			0
$640$	453.772	+	769.237i	0.709018	+	1.20193i
$641$	43.7724	+	248.246i	0.0682876	+	0.387278i	0.999727	+	0.0233809i	$0.00744306\pi$
$641$	43.7724	+	248.246i	0.0682876	+	0.387278i	−0.931439	+	0.363898i	$0.881446\pi$
$642$		0			0
$643$	−272.895	−	749.774i	−0.424410	−	1.16606i	−0.949158	−	0.314799i	$-0.898063\pi$
$643$	−272.895	−	749.774i	−0.424410	−	1.16606i	0.524749	−	0.851257i	$-0.324159\pi$
$644$	88.6861	+	37.1053i	0.137711	+	0.0576170i
$645$		0			0
$646$	−189.973	+	946.254i	−0.294075	+	1.46479i
$647$			313.485i			0.484521i	0.970211	+	0.242261i	$0.0778889\pi$
$647$			313.485i			0.484521i	−0.970211	+	0.242261i	$0.922111\pi$
$648$		0			0
$649$	517.283			0.797045
$650$	−867.830	−	174.228i	−1.33512	−	0.268043i
$651$		0			0
$652$	123.669	−	295.583i	0.189676	−	0.453349i
$653$	49.6468	−	18.0700i	0.0760288	−	0.0276722i	−0.303726	−	0.952759i	$-0.598231\pi$
$653$	49.6468	−	18.0700i	0.0760288	−	0.0276722i	0.379755	+	0.925087i	$0.376008\pi$
$654$		0			0
$655$	−694.836	+	122.518i	−1.06082	+	0.187051i
$656$	−52.4567	−	653.093i	−0.0799645	−	0.995568i
$657$		0			0
$658$	−137.607	+	20.9292i	−0.209130	+	0.0318073i
$659$	29.3624	−	80.6725i	0.0445560	−	0.122417i	−0.915419	−	0.402502i	$-0.868141\pi$
$659$	29.3624	−	80.6725i	0.0445560	−	0.122417i	0.959975	+	0.280086i	$0.0903628\pi$
$660$		0			0
$661$	−319.237	−	267.872i	−0.482961	−	0.405253i	0.368535	−	0.929614i	$-0.379860\pi$
$661$	−319.237	−	267.872i	−0.482961	−	0.405253i	−0.851496	+	0.524362i	$0.824304\pi$
$662$	1053.11	+	24.8540i	1.59080	+	0.0375438i
$663$		0			0
$664$	−60.2317	−	578.493i	−0.0907104	−	0.871224i
$665$	−253.483	+	439.045i	−0.381177	+	0.660218i
$666$		0			0
$667$	−61.8711	+	35.7213i	−0.0927603	+	0.0535552i
$668$	12.4457	−	263.528i	0.0186313	−	0.394502i
$669$		0			0
$670$	−437.267	+	717.711i	−0.652637	+	1.07121i
$671$	490.073	+	86.4131i	0.730363	+	0.128783i
$672$		0			0
$673$	606.922	−	509.268i	0.901816	−	0.756714i	−0.0687283	−	0.997635i	$-0.521894\pi$
$673$	606.922	−	509.268i	0.901816	−	0.756714i	0.970545	+	0.240922i	$0.0774497\pi$
$674$	−397.092	−	496.574i	−0.589157	−	0.736757i
$675$		0			0
$676$	−158.510	+	703.142i	−0.234483	+	1.04015i
$677$	−393.443	+	330.138i	−0.581157	+	0.487648i	−0.885327	−	0.464969i	$-0.846065\pi$
$677$	−393.443	+	330.138i	−0.581157	+	0.487648i	0.304170	+	0.952618i	$0.401621\pi$
$678$		0			0
$679$	−293.626	−	51.7742i	−0.432439	−	0.0762507i
$680$	708.304	−	732.041i	1.04162	−	1.07653i
$681$		0			0
$682$	−394.613	+	448.358i	−0.578611	+	0.657416i
$683$	−681.718	+	393.590i	−0.998123	+	0.576267i	−0.907692	−	0.419636i	$-0.862158\pi$
$683$	−681.718	+	393.590i	−0.998123	+	0.576267i	−0.0904306	+	0.995903i	$0.528824\pi$
$684$		0			0
$685$	−244.813	+	424.029i	−0.357392	+	0.619020i
$686$	−470.953	+	158.933i	−0.686520	+	0.231681i
$687$		0			0
$688$	−540.090	+	247.183i	−0.785015	+	0.359278i
$689$	−1302.64	−	1093.04i	−1.89062	−	1.58642i
$690$		0			0
$691$	121.026	−	332.517i	0.175147	−	0.481211i	−0.820794	−	0.571224i	$-0.806469\pi$
$691$	121.026	−	332.517i	0.175147	−	0.481211i	0.995941	+	0.0900130i	$0.0286909\pi$
$692$	−184.195	−	169.994i	−0.266178	−	0.245656i
$693$		0			0
$694$	−729.117	−	285.033i	−1.05060	−	0.410710i
$695$	−139.529	+	24.6028i	−0.200762	+	0.0353997i
$696$		0			0
$697$	−702.208	+	255.583i	−1.00747	+	0.366690i
$698$	−679.311	+	371.112i	−0.973225	+	0.531679i
$699$		0			0
$700$	231.311	−	119.369i	0.330445	−	0.170527i
$701$	360.188			0.513820			0.256910	−	0.966435i	$-0.417296\pi$
$701$	360.188			0.513820			0.256910	+	0.966435i	$0.417296\pi$
$702$		0			0
$703$		−	977.410i		−	1.39034i
$704$	−461.460	+	15.2134i	−0.655483	+	0.0216100i
$705$		0			0
$706$	944.012	−	515.719i	1.33713	−	0.730480i
$707$	−8.08691	−	22.2186i	−0.0114383	−	0.0314266i
$708$		0			0
$709$	64.6362	+	366.570i	0.0911653	+	0.517024i	0.995855	+	0.0909535i	$0.0289915\pi$
$709$	64.6362	+	366.570i	0.0911653	+	0.517024i	−0.904690	+	0.426071i	$0.859897\pi$
$710$	−767.451	−	300.019i	−1.08092	−	0.422562i
$711$		0			0
$712$	−8.51991	+	120.156i	−0.0119662	+	0.168759i
$713$	340.260	+	123.845i	0.477223	+	0.173695i
$714$		0			0
$715$	604.623	−	720.562i	0.845626	−	1.00778i
$716$	265.384	+	348.416i	0.370648	+	0.486614i
$717$		0			0
$718$	82.6897	−	27.9054i	0.115167	−	0.0388654i
$719$	800.356	+	462.086i	1.11315	+	0.642678i	0.939644	−	0.342154i	$-0.111157\pi$
$719$	800.356	+	462.086i	1.11315	+	0.642678i	0.173507	+	0.984833i	$0.444490\pi$
$720$		0			0
$721$	69.5717	+	120.502i	0.0964934	+	0.167131i
$722$	447.009	−	507.889i	0.619125	−	0.703448i
$723$		0			0
$724$	117.682	+	919.151i	0.162544	+	1.26954i
$725$	−33.5900	+	190.499i	−0.0463311	+	0.262757i
$726$		0			0
$727$	−686.560	−	818.210i	−0.944374	−	1.12546i	−0.991955	−	0.126594i	$-0.959596\pi$
$727$	−686.560	−	818.210i	−0.944374	−	1.12546i	0.0475805	−	0.998867i	$-0.484849\pi$
$728$	−179.703	−	369.359i	−0.246844	−	0.507361i
$729$		0			0
$730$	613.979	+	767.797i	0.841068	+	1.05178i
$731$	435.450	+	518.949i	0.595691	+	0.709917i
$732$		0			0
$733$	−14.6569	+	83.1235i	−0.0199958	+	0.113402i	−0.993172	−	0.116659i	$-0.962781\pi$
$733$	−14.6569	+	83.1235i	−0.0199958	+	0.113402i	0.973176	+	0.230061i	$0.0738926\pi$
$734$	−690.088	+	1132.68i	−0.940174	+	1.54316i
$735$		0			0
$736$	110.448	+	257.197i	0.150066	+	0.349452i
$737$	−217.238	−	376.268i	−0.294760	−	0.510539i
$738$		0			0
$739$	−856.326	−	494.400i	−1.15876	−	0.669012i	−0.207756	−	0.978181i	$-0.566616\pi$
$739$	−856.326	−	494.400i	−1.15876	−	0.669012i	−0.951007	+	0.309168i	$0.899949\pi$
$740$	−557.356	+	868.040i	−0.753184	+	1.17303i
$741$		0			0
$742$	499.919	+	11.7983i	0.673745	+	0.0159007i
$743$	−421.175	+	501.937i	−0.566858	+	0.675555i	−0.970983	−	0.239149i	$-0.923132\pi$
$743$	−421.175	+	501.937i	−0.566858	+	0.675555i	0.404125	+	0.914704i	$0.367576\pi$
$744$		0			0
$745$	679.497	+	247.317i	0.912076	+	0.331969i
$746$	−740.865	+	112.681i	−0.993117	+	0.151047i
$747$		0			0
$748$	156.562	+	502.785i	0.209308	+	0.672173i
$749$	72.1422	+	409.139i	0.0963180	+	0.546247i
$750$		0			0
$751$	−314.538	−	864.187i	−0.418826	−	1.15071i	−0.952371	−	0.304943i	$-0.901363\pi$
$751$	−314.538	−	864.187i	−0.418826	−	1.15071i	0.533545	−	0.845772i	$-0.320860\pi$
$752$	−330.312	−	234.808i	−0.439245	−	0.312245i
$753$		0			0
$754$	299.278	+	60.0840i	0.396921	+	0.0796869i
$755$		−	1134.12i		−	1.50215i
$756$		0			0
$757$	−167.681			−0.221507			−0.110754	−	0.993848i	$-0.535326\pi$
$757$	−167.681			−0.221507			−0.110754	+	0.993848i	$0.535326\pi$
$758$	−25.8161	+	128.590i	−0.0340582	+	0.169644i
$759$		0			0
$760$	−1419.30	+	405.480i	−1.86750	+	0.533527i
$761$	223.703	−	81.4211i	0.293959	−	0.106992i	−0.190831	−	0.981623i	$-0.561118\pi$
$761$	223.703	−	81.4211i	0.293959	−	0.106992i	0.484790	+	0.874631i	$0.338896\pi$
$762$		0			0
$763$	246.068	−	43.3885i	0.322501	−	0.0568657i
$764$	193.521	+	621.475i	0.253300	+	0.813449i
$765$		0			0
$766$	87.1482	+	572.991i	0.113770	+	0.748030i
$767$	−458.273	+	1259.10i	−0.597488	+	1.64158i
$768$		0			0
$769$	−185.210	−	155.410i	−0.240846	−	0.202093i	0.514373	−	0.857567i	$-0.328025\pi$
$769$	−185.210	−	155.410i	−0.240846	−	0.202093i	−0.755218	+	0.655473i	$0.772469\pi$
$770$	−6.52633	+	276.533i	−0.00847576	+	0.359134i
$771$		0			0
$772$	513.790	−	800.190i	0.665532	−	1.03652i
$773$	−153.289	+	265.504i	−0.198303	+	0.343472i	−0.947978	−	0.318334i	$-0.896876\pi$
$773$	−153.289	+	265.504i	−0.198303	+	0.343472i	0.749675	+	0.661806i	$0.230210\pi$
$774$		0			0
$775$	849.061	−	490.205i	1.09556	−	0.632523i
$776$	−509.579	−	702.816i	−0.656674	−	0.905690i
$777$		0			0
$778$	−313.236	−	190.840i	−0.402618	−	0.245296i
$779$	1066.43	+	188.040i	1.36897	+	0.241387i
$780$		0			0
$781$	326.328	−	273.822i	0.417834	−	0.350604i
$782$	249.330	−	199.380i	0.318837	−	0.254962i
$783$		0			0
$784$	−599.061	−	284.556i	−0.764109	−	0.362954i
$785$	−561.514	+	471.166i	−0.715304	+	0.600212i
$786$		0			0
$787$	1281.44	+	225.953i	1.62826	+	0.287107i	0.911836	−	0.410555i	$-0.134665\pi$
$787$	1281.44	+	225.953i	1.62826	+	0.287107i	0.716427	+	0.697662i	$0.245776\pi$
$788$	27.0140	+	210.992i	0.0342818	+	0.267756i
$789$		0			0
$790$	−1563.11	−	1375.74i	−1.97862	−	1.74144i
$791$	380.398	−	219.623i	0.480908	−	0.277652i
$792$		0			0
$793$	−644.503	+	1116.31i	−0.812740	+	1.40771i
$794$	−410.016	−	1214.97i	−0.516393	−	1.53019i
$795$		0			0
$796$	−32.9549	−	43.2656i	−0.0414006	−	0.0543538i
$797$	−78.6983	−	66.0357i	−0.0987432	−	0.0828554i	0.592080	−	0.805879i	$-0.298307\pi$
$797$	−78.6983	−	66.0357i	−0.0987432	−	0.0828554i	−0.690823	+	0.723024i	$0.742752\pi$
$798$		0			0
$799$	−158.089	+	434.345i	−0.197858	+	0.543611i
$800$	725.686	+	218.542i	0.907108	+	0.273178i
$801$		0			0
$802$	263.714	−	674.582i	0.328820	−	0.841125i
$803$	−500.515	+	88.2543i	−0.623306	+	0.109906i
$804$		0			0
$805$	157.580	−	57.3545i	0.195752	−	0.0712478i
$806$	−741.731	−	1357.72i	−0.920262	−	1.68452i
$807$		0			0
$808$	28.0626	−	62.8645i	0.0347309	−	0.0778026i
$809$	21.6902			0.0268111			0.0134056	−	0.999910i	$-0.495733\pi$
$809$	21.6902			0.0268111			0.0134056	+	0.999910i	$0.495733\pi$
$810$		0			0
$811$			504.528i			0.622106i	0.950393	+	0.311053i	$0.100682\pi$
$811$			504.528i			0.622106i	−0.950393	+	0.311053i	$0.899318\pi$
$812$	−79.7695	+	41.1652i	−0.0982383	+	0.0506961i
$813$		0			0
$814$	−255.676	−	468.010i	−0.314099	−	0.574951i
$815$	−191.158	−	525.201i	−0.234549	−	0.644419i
$816$		0			0
$817$	−170.468	−	966.771i	−0.208651	−	1.18332i
$818$	−452.965	+	1158.69i	−0.553746	+	1.41649i
$819$		0			0
$820$	−839.871	−	775.117i	−1.02423	−	0.945265i
$821$	61.6791	+	22.4494i	0.0751268	+	0.0273439i	0.379310	−	0.925270i	$-0.376161\pi$
$821$	61.6791	+	22.4494i	0.0751268	+	0.0273439i	−0.304183	+	0.952613i	$0.598384\pi$
$822$		0			0
$823$	−889.062	+	1059.54i	−1.08027	+	1.28741i	−0.124846	+	0.992176i	$0.539844\pi$
$823$	−889.062	+	1059.54i	−1.08027	+	1.28741i	−0.955424	+	0.295239i	$0.904601\pi$
$824$	−98.3935	+	393.002i	−0.119410	+	0.476944i
$825$		0			0
$826$	−125.991	−	373.339i	−0.152532	−	0.451985i
$827$	−911.669	−	526.352i	−1.10238	−	0.636460i	−0.165536	−	0.986204i	$-0.552935\pi$
$827$	−911.669	−	526.352i	−1.10238	−	0.636460i	−0.936845	+	0.349744i	$0.886269\pi$
$828$		0			0
$829$	191.988	+	332.533i	0.231590	+	0.401126i	0.958276	−	0.285844i	$-0.0922738\pi$
$829$	191.988	+	332.533i	0.231590	+	0.401126i	−0.726686	+	0.686970i	$0.758941\pi$
$830$	−761.583	−	670.292i	−0.917570	−	0.807581i
$831$		0			0
$832$	371.788	−	1136.70i	0.446861	−	1.36622i
$833$	−131.350	+	744.922i	−0.157683	+	0.894264i
$834$		0			0
$835$	−295.808	−	352.530i	−0.354261	−	0.422191i
$836$	167.815	−	744.416i	0.200735	−	0.890450i
$837$		0			0
$838$	−946.472	+	756.859i	−1.12944	+	0.903173i
$839$	−246.231	−	293.447i	−0.293482	−	0.349758i	0.599075	−	0.800693i	$-0.295535\pi$
$839$	−246.231	−	293.447i	−0.293482	−	0.349758i	−0.892557	+	0.450935i	$0.851091\pi$
$840$		0			0
$841$	−134.454	+	762.528i	−0.159874	+	0.906692i
$842$	−704.223	−	429.049i	−0.836369	−	0.509560i
$843$		0			0
$844$	−3.44666	+	72.9803i	−0.00408372	+	0.0864695i
$845$	628.650	+	1088.85i	0.743964	+	1.28858i
$846$		0			0
$847$	164.079	+	94.7309i	0.193717	+	0.111843i
$848$	1022.18	+	1036.83i	1.20540	+	1.22268i
$849$		0			0
$850$	20.3943	−	864.147i	0.0239933	−	1.01664i
$851$	−207.817	+	247.667i	−0.244204	+	0.291031i
$852$		0			0
$853$	−1068.78	−	389.005i	−1.25297	−	0.456043i	−0.371565	−	0.928407i	$-0.621179\pi$
$853$	−1068.78	−	389.005i	−1.25297	−	0.456043i	−0.881404	+	0.472364i	$0.843401\pi$
$854$	−56.9969	−	374.749i	−0.0667411	−	0.438816i
$855$		0			0
$856$	−677.394	+	1002.17i	−0.791348	+	1.17076i
$857$	−26.3416	−	149.391i	−0.0307370	−	0.174318i	0.965575	−	0.260126i	$-0.0837640\pi$
$857$	−26.3416	−	149.391i	−0.0307370	−	0.174318i	−0.996312	+	0.0858077i	$0.972653\pi$
$858$		0			0
$859$	−295.865	−	812.883i	−0.344430	−	0.946314i	−0.984092	−	0.177658i	$-0.943148\pi$
$859$	−295.865	−	812.883i	−0.344430	−	0.946314i	0.639662	−	0.768656i	$-0.279074\pi$
$860$	−399.896	+	955.798i	−0.464995	+	1.11139i
$861$		0			0
$862$	200.167	−	997.034i	0.232213	−	1.15665i
$863$		−	797.501i		−	0.924103i	−0.886853	−	0.462051i	$-0.847114\pi$
$863$		−	797.501i		−	0.924103i	0.886853	−	0.462051i	$-0.152886\pi$
$864$		0			0
$865$	−437.221			−0.505458
$866$	292.314	+	58.6859i	0.337546	+	0.0677666i
$867$		0			0
$868$	419.707	+	175.601i	0.483534	+	0.202305i
$869$	1011.57	−	368.182i	1.16407	−	0.423685i
$870$		0			0
$871$	1108.31	−	195.426i	1.27246	−	0.224369i
$872$	602.734	+	407.405i	0.691209	+	0.467208i
$873$		0			0
$874$	−457.363	+	69.5619i	−0.523298	+	0.0795903i
$875$	−8.63071	+	23.7127i	−0.00986367	+	0.0271002i
$876$		0			0
$877$	1170.06	+	981.796i	1.33416	+	1.11949i	0.983086	+	0.183146i	$0.0586282\pi$
$877$	1170.06	+	981.796i	1.33416	+	1.11949i	0.351075	+	0.936347i	$0.385816\pi$
$878$	−88.2416	−	2.08255i	−0.100503	−	0.00237192i
$879$		0			0
$880$	−573.530	+	565.423i	−0.651739	+	0.642526i
$881$	167.754	−	290.558i	0.190413	−	0.329805i	−0.754974	−	0.655754i	$-0.772351\pi$
$881$	167.754	−	290.558i	0.190413	−	0.329805i	0.945387	+	0.325950i	$0.105684\pi$
$882$		0			0
$883$	−1342.68	+	775.199i	−1.52059	+	0.877915i	−0.520888	+	0.853625i	$0.674399\pi$
$883$	−1342.68	+	775.199i	−1.52059	+	0.877915i	−0.999705	+	0.0242893i	$0.992268\pi$
$884$	−1362.51	−	64.3477i	−1.54130	−	0.0727916i
$885$		0			0
$886$	−272.828	+	447.807i	−0.307932	+	0.505426i
$887$	312.552	+	55.1114i	0.352370	+	0.0621324i	0.347032	−	0.937853i	$-0.387190\pi$
$887$	312.552	+	55.1114i	0.352370	+	0.0621324i	0.00533848	+	0.999986i	$0.498301\pi$
$888$		0			0
$889$	46.5174	−	39.0327i	0.0523255	−	0.0439063i
$890$	131.227	+	164.103i	0.147446	+	0.184386i
$891$		0			0
$892$	511.669	+	115.346i	0.573620	+	0.129312i
$893$	513.103	−	430.544i	0.574583	−	0.482132i
$894$		0			0
$895$	752.373	+	132.664i	0.840640	+	0.148228i
$896$	123.375	+	329.345i	0.137695	+	0.367573i
$897$		0			0
$898$	−53.9161	+	61.2592i	−0.0600402	+	0.0682174i
$899$	−292.805	+	169.051i	−0.325701	+	0.188044i
$900$		0			0
$901$	830.295	−	1438.11i	0.921526	−	1.59613i
$902$	559.823	−	188.924i	0.620647	−	0.209450i
$903$		0			0
$904$	1240.62	+	310.607i	1.37237	+	0.343592i
$905$	1238.24	+	1039.00i	1.36822	+	1.14807i
$906$		0			0
$907$	35.8825	−	98.5864i	0.0395618	−	0.108695i	−0.918339	−	0.395795i	$-0.870469\pi$
$907$	35.8825	−	98.5864i	0.0395618	−	0.108695i	0.957901	+	0.287100i	$0.0926912\pi$
$908$	1059.11	−	1147.59i	1.16642	−	1.26387i
$909$		0			0
$910$	−667.317	−	260.873i	−0.733315	−	0.286674i
$911$	910.015	−	160.460i	0.998919	−	0.176136i	0.349801	−	0.936824i	$-0.386249\pi$
$911$	910.015	−	160.460i	0.998919	−	0.176136i	0.649118	+	0.760688i	$0.275138\pi$
$912$		0			0
$913$	492.862	−	179.387i	0.539827	−	0.196481i
$914$	901.529	−	492.511i	0.986355	−	0.538852i
$915$		0			0
$916$	340.371	+	659.567i	0.371584	+	0.720051i
$917$	−277.840			−0.302988
$918$		0			0
$919$		−	358.794i		−	0.390418i	−0.980762	−	0.195209i	$-0.937462\pi$
$919$		−	358.794i		−	0.390418i	0.980762	−	0.195209i	$-0.0625385\pi$
$920$	445.852	+	199.027i	0.484621	+	0.216334i
$921$		0			0
$922$	883.711	−	482.777i	0.958472	−	0.523619i
$923$	377.396	+	1036.89i	0.408880	+	1.12339i
$924$		0			0
$925$	152.008	+	862.083i	0.164333	+	0.931981i
$926$	−705.243	−	275.700i	−0.761601	−	0.297732i
$927$		0			0
$928$	−250.259	−	75.3660i	−0.269675	−	0.0812133i
$929$	189.128	+	68.8368i	0.203582	+	0.0740978i	0.441799	−	0.897114i	$-0.354341\pi$
$929$	189.128	+	68.8368i	0.203582	+	0.0740978i	−0.238217	+	0.971212i	$0.576563\pi$
$930$		0			0
$931$	704.576	−	839.681i	0.756795	−	0.901913i
$932$	823.325	−	627.116i	0.883396	−	0.672872i
$933$		0			0
$934$	−501.598	+	169.275i	−0.537043	+	0.181236i
$935$	795.502	+	459.283i	0.850804	+	0.491212i
$936$		0			0
$937$	−135.628	−	234.915i	−0.144747	−	0.250709i	0.784531	−	0.620089i	$-0.212904\pi$
$937$	−135.628	−	234.915i	−0.144747	−	0.250709i	−0.929279	+	0.369380i	$0.879570\pi$
$938$	−218.653	+	248.433i	−0.233106	+	0.264854i
$939$		0			0
$940$	−701.200	+	89.7771i	−0.745957	+	0.0955075i
$941$	−237.105	+	1344.69i	−0.251971	+	1.42900i	0.551757	+	0.834005i	$0.313958\pi$
$941$	−237.105	+	1344.69i	−0.251971	+	1.42900i	−0.803728	+	0.594996i	$0.797154\pi$
$942$		0			0
$943$	−230.243	−	274.393i	−0.244160	−	0.290978i
$944$	492.237	−	1036.28i	0.521438	−	1.09776i
$945$		0			0
$946$	−334.518	−	418.323i	−0.353613	−	0.442202i
$947$	224.688	+	267.773i	0.237263	+	0.282759i	0.871517	−	0.490366i	$-0.163137\pi$
$947$	224.688	+	267.773i	0.237263	+	0.282759i	−0.634253	+	0.773125i	$0.718692\pi$
$948$		0			0
$949$	228.602	−	1296.47i	0.240888	−	1.36614i
$950$	−651.716	+	1069.70i	−0.686017	+	1.12600i
$951$		0			0
$952$	324.743	−	235.456i	0.341117	−	0.247328i
$953$	−169.784	−	294.074i	−0.178157	−	0.308577i	0.763092	−	0.646290i	$-0.223680\pi$
$953$	−169.784	−	294.074i	−0.178157	−	0.308577i	−0.941249	+	0.337713i	$0.890347\pi$
$954$		0			0
$955$	983.291	+	567.704i	1.02962	+	0.594454i
$956$	614.319	+	394.445i	0.642593	+	0.412599i
$957$		0			0
$958$	−244.227	−	5.76389i	−0.254934	−	0.00601658i
$959$	−123.936	+	147.701i	−0.129235	+	0.154016i
$960$		0			0
$961$	707.237	+	257.413i	0.735939	+	0.267860i
$962$	1365.67	−	207.710i	1.41962	−	0.215915i
$963$		0			0
$964$	1009.56	−	314.368i	1.04727	−	0.326108i
$965$	−288.041	−	1633.56i	−0.298488	−	1.69281i
$966$		0			0
$967$	407.776	+	1120.35i	0.421692	+	1.15859i	0.950738	+	0.309995i	$0.100327\pi$
$967$	407.776	+	1120.35i	0.421692	+	1.15859i	−0.529046	+	0.848593i	$0.677450\pi$
$968$	151.535	+	530.417i	0.156545	+	0.547952i
$969$		0			0
$970$	−1484.66	−	298.065i	−1.53058	−	0.307284i
$971$		−	1336.97i		−	1.37690i	−0.725286	−	0.688448i	$-0.758292\pi$
$971$		−	1336.97i		−	1.37690i	0.725286	−	0.688448i	$-0.241708\pi$
$972$		0			0
$973$	−55.7929			−0.0573411
$974$	−85.5098	+	425.924i	−0.0877924	+	0.437294i
$975$		0			0
$976$	639.459	−	899.545i	0.655183	−	0.921665i
$977$	−1532.38	+	557.739i	−1.56845	+	0.570869i	−0.972653	−	0.232265i	$-0.925386\pi$
$977$	−1532.38	+	557.739i	−1.56845	+	0.570869i	−0.595798	+	0.803134i	$0.703164\pi$
$978$		0			0
$979$	−106.976	+	18.8628i	−0.109271	+	0.0192674i
$980$	−1104.55	+	343.947i	−1.12709	+	0.350966i
$981$		0			0
$982$	58.1887	+	382.585i	0.0592553	+	0.389598i
$983$	245.311	−	673.986i	0.249553	−	0.685641i	−0.750150	−	0.661268i	$-0.770019\pi$
$983$	245.311	−	673.986i	0.249553	−	0.685641i	0.999703	−	0.0243736i	$-0.00775912\pi$
$984$		0			0
$985$	284.238	+	238.504i	0.288567	+	0.242136i
$986$	−7.03314	+	298.008i	−0.00713301	+	0.302239i
$987$		0			0
$988$	1663.28	+	1067.97i	1.68348	+	1.08094i
$989$	−162.360	+	281.216i	−0.164166	+	0.284344i
$990$		0			0
$991$	809.706	−	467.484i	0.817059	−	0.471729i	−0.0323420	−	0.999477i	$-0.510297\pi$
$991$	809.706	−	467.484i	0.817059	−	0.471729i	0.849401	+	0.527747i	$0.176963\pi$
$992$	522.698	+	1217.19i	0.526913	+	1.22700i
$993$		0			0
$994$	−277.108	−	168.829i	−0.278781	−	0.169848i
$995$	−93.4282	−	16.4739i	−0.0938976	−	0.0165567i
$996$		0			0
$997$	−307.519	+	258.039i	−0.308444	+	0.258815i	−0.783849	−	0.620952i	$-0.786746\pi$
$997$	−307.519	+	258.039i	−0.308444	+	0.258815i	0.475404	+	0.879767i	$0.342302\pi$
$998$	−719.002	+	574.959i	−0.720442	+	0.576111i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.j.a.199.32		204
3.2	odd	2		108.3.j.a.103.3	yes	204
4.3	odd	2	inner	324.3.j.a.199.16		204
12.11	even	2		108.3.j.a.103.19	yes	204
27.11	odd	18		108.3.j.a.43.19	yes	204
27.16	even	9	inner	324.3.j.a.127.16		204
108.11	even	18		108.3.j.a.43.3	✓	204
108.43	odd	18	inner	324.3.j.a.127.32		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.j.a.43.3	✓	204	108.11	even	18
108.3.j.a.43.19	yes	204	27.11	odd	18
108.3.j.a.103.3	yes	204	3.2	odd	2
108.3.j.a.103.19	yes	204	12.11	even	2
324.3.j.a.127.16		204	27.16	even	9	inner
324.3.j.a.127.32		204	108.43	odd	18	inner
324.3.j.a.199.16		204	4.3	odd	2	inner
324.3.j.a.199.32		204	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	324.j (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.96087 + 0.393671i) q^{2} +(3.69005 + 1.54388i) q^{4} +(6.55659 - 2.38640i) q^{5} +(2.70588 - 0.477119i) q^{7} +(6.62793 + 4.48001i) q^{8} +O(q^{10})\)	\(q+(1.96087 + 0.393671i) q^{2} +(3.69005 + 1.54388i) q^{4} +(6.55659 - 2.38640i) q^{5} +(2.70588 - 0.477119i) q^{7} +(6.62793 + 4.48001i) q^{8} +(13.7961 - 2.09830i) q^{10} +(-2.46741 + 6.77916i) q^{11} +(-14.3149 - 12.0116i) q^{13} +(5.49371 + 0.129654i) q^{14} +(11.2329 + 11.3940i) q^{16} +(9.12428 - 15.8037i) q^{17} +(-22.9013 + 13.2221i) q^{19} +(27.8784 + 1.31662i) q^{20} +(-7.50704 + 12.3217i) q^{22} +(8.61427 + 1.51893i) q^{23} +(18.1428 - 15.2236i) q^{25} +(-23.3411 - 29.1887i) q^{26} +(10.7214 + 2.41695i) q^{28} +(-6.25669 + 5.24998i) q^{29} +(40.7671 + 7.18833i) q^{31} +(17.5408 + 26.7642i) q^{32} +(24.1130 - 27.3971i) q^{34} +(16.6027 - 9.58558i) q^{35} +(-18.4807 + 32.0094i) q^{37} +(-50.1117 + 16.9112i) q^{38} +(54.1477 + 13.5566i) q^{40} +(-31.3693 - 26.3220i) q^{41} +(-12.6968 + 34.8842i) q^{43} +(-19.5711 + 21.2060i) q^{44} +(16.2935 + 6.36961i) q^{46} +(-24.9444 + 4.39836i) q^{47} +(-38.9508 + 14.1769i) q^{49} +(41.5688 - 22.7093i) q^{50} +(-34.2782 - 66.4240i) q^{52} +90.9984 q^{53} +50.3364i q^{55} +(20.0719 + 8.96004i) q^{56} +(-14.3353 + 7.83148i) q^{58} +(-24.5239 - 67.3788i) q^{59} +(-11.9781 - 67.9315i) q^{61} +(77.1092 + 30.1442i) q^{62} +(23.8590 + 59.3864i) q^{64} +(-122.522 - 44.5942i) q^{65} +(-38.7118 + 46.1350i) q^{67} +(58.0680 - 44.2297i) q^{68} +(36.3294 - 12.2601i) q^{70} +(-51.1377 - 29.5244i) q^{71} +(35.2245 + 61.0107i) q^{73} +(-48.8394 + 55.4912i) q^{74} +(-104.920 + 13.4333i) q^{76} +(-3.44205 + 19.5208i) q^{77} +(-95.9155 - 114.308i) q^{79} +(100.840 + 47.8992i) q^{80} +(-51.1491 - 63.9633i) q^{82} +(-46.7322 - 55.6933i) q^{83} +(22.1101 - 125.393i) q^{85} +(-38.6297 + 63.4051i) q^{86} +(-46.7245 + 33.8778i) q^{88} +(7.52863 + 13.0400i) q^{89} +(-44.4654 - 25.6721i) q^{91} +(29.4420 + 18.9043i) q^{92} +(-50.6442 - 1.19523i) q^{94} +(-118.601 + 141.343i) q^{95} +(-101.970 - 37.1140i) q^{97} +(-81.9586 + 12.4654i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) \) 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8	\( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8} - 3 q^{10} - 12 q^{13} - 39 q^{14} - 6 q^{16} + 6 q^{17} + 69 q^{20} - 6 q^{22} - 12 q^{25} + 174 q^{26} - 12 q^{28} - 60 q^{29} + 96 q^{32} + 6 q^{34} - 6 q^{37} - 72 q^{38} + 69 q^{40} + 192 q^{41} + 219 q^{44} - 3 q^{46} - 12 q^{49} + 165 q^{50} + 21 q^{52} + 24 q^{53} - 99 q^{56} - 141 q^{58} - 12 q^{61} - 294 q^{62} - 3 q^{64} + 156 q^{65} - 375 q^{68} - 165 q^{70} - 6 q^{73} - 447 q^{74} - 54 q^{76} - 132 q^{77} - 798 q^{80} - 12 q^{82} + 138 q^{85} - 606 q^{86} - 198 q^{88} + 114 q^{89} - 723 q^{92} - 357 q^{94} + 168 q^{97} - 510 q^{98}+O(q^{100}) \) 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8 - 3 * q^10 - 12 * q^13 - 39 * q^14 - 6 * q^16 + 6 * q^17 + 69 * q^20 - 6 * q^22 - 12 * q^25 + 174 * q^26 - 12 * q^28 - 60 * q^29 + 96 * q^32 + 6 * q^34 - 6 * q^37 - 72 * q^38 + 69 * q^40 + 192 * q^41 + 219 * q^44 - 3 * q^46 - 12 * q^49 + 165 * q^50 + 21 * q^52 + 24 * q^53 - 99 * q^56 - 141 * q^58 - 12 * q^61 - 294 * q^62 - 3 * q^64 + 156 * q^65 - 375 * q^68 - 165 * q^70 - 6 * q^73 - 447 * q^74 - 54 * q^76 - 132 * q^77 - 798 * q^80 - 12 * q^82 + 138 * q^85 - 606 * q^86 - 198 * q^88 + 114 * q^89 - 723 * q^92 - 357 * q^94 + 168 * q^97 - 510 * q^98

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