LMFDB - Embedded newform 324.3.j.a.199.2

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			199.2
Character	$\chi$	$=$	324.199
Dual form			324.3.j.a.127.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.97211 + 0.332841i) q^{2} +(3.77843 - 1.31280i) q^{4} +(-3.98424 + 1.45015i) q^{5} +(2.54522 - 0.448791i) q^{7} +(-7.01454 + 3.84660i) q^{8} +O(q^{10})$	\(q+(-1.97211 + 0.332841i) q^{2} +(3.77843 - 1.31280i) q^{4} +(-3.98424 + 1.45015i) q^{5} +(2.54522 - 0.448791i) q^{7} +(-7.01454 + 3.84660i) q^{8} +(7.37470 - 4.18597i) q^{10} +(-0.818869 + 2.24982i) q^{11} +(-3.62870 - 3.04484i) q^{13} +(-4.87007 + 1.73222i) q^{14} +(12.5531 - 9.92063i) q^{16} +(8.77670 - 15.2017i) q^{17} +(-13.3776 + 7.72359i) q^{19} +(-13.1505 + 10.7098i) q^{20} +(0.866067 - 4.70945i) q^{22} +(-13.3426 - 2.35266i) q^{23} +(-5.37983 + 4.51422i) q^{25} +(8.16965 + 4.79699i) q^{26} +(9.02777 - 5.03708i) q^{28} +(33.3419 - 27.9772i) q^{29} +(-46.8128 - 8.25437i) q^{31} +(-21.4542 + 23.7428i) q^{32} +(-12.2489 + 32.9007i) q^{34} +(-9.48996 + 5.47903i) q^{35} +(23.0118 - 39.8576i) q^{37} +(23.8115 - 19.6844i) q^{38} +(22.3695 - 25.4979i) q^{40} +(-59.1080 - 49.5975i) q^{41} +(11.2366 - 30.8724i) q^{43} +(-0.140482 + 9.57582i) q^{44} +(27.0962 + 0.198746i) q^{46} +(-36.6059 + 6.45461i) q^{47} +(-39.7682 + 14.4744i) q^{49} +(9.10711 - 10.6932i) q^{50} +(-17.7081 - 6.74099i) q^{52} +35.4346 q^{53} -10.1513i q^{55} +(-16.1272 + 12.9385i) q^{56} +(-56.4420 + 66.2717i) q^{58} +(-31.4856 - 86.5061i) q^{59} +(-17.4186 - 98.7856i) q^{61} +(95.0675 + 0.697304i) q^{62} +(34.4074 - 53.9642i) q^{64} +(18.8731 + 6.86925i) q^{65} +(-18.1558 + 21.6372i) q^{67} +(13.2055 - 68.9606i) q^{68} +(16.8916 - 13.9639i) q^{70} +(-40.2696 - 23.2497i) q^{71} +(-18.0611 - 31.2827i) q^{73} +(-32.1155 + 86.2627i) q^{74} +(-40.4070 + 46.7452i) q^{76} +(-1.07450 + 6.09379i) q^{77} +(58.8468 + 70.1309i) q^{79} +(-35.6284 + 57.7301i) q^{80} +(133.076 + 78.1382i) q^{82} +(50.7354 + 60.4641i) q^{83} +(-12.9238 + 73.2948i) q^{85} +(-11.8843 + 64.6238i) q^{86} +(-2.91018 - 18.9313i) q^{88} +(31.6951 + 54.8975i) q^{89} +(-10.6023 - 6.12126i) q^{91} +(-53.5028 + 8.62676i) q^{92} +(70.0426 - 24.9132i) q^{94} +(42.0995 - 50.1722i) q^{95} +(-74.9366 - 27.2747i) q^{97} +(73.6096 - 41.7817i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.97211	+	0.332841i	−0.986055	+	0.166420i
$2$	−1.97211	+	0.332841i	−0.986055	+	0.166420i
$3$		0			0
$3$		0			0
$4$	3.77843	−	1.31280i	0.944609	−	0.328199i
$5$	−3.98424	+	1.45015i	−0.796849	+	0.290029i	−0.708180	−	0.706032i	$-0.750484\pi$
$5$	−3.98424	+	1.45015i	−0.796849	+	0.290029i	−0.0886688	+	0.996061i	$0.528261\pi$
$6$		0			0
$7$	2.54522	−	0.448791i	0.363603	−	0.0641129i	0.0111376	−	0.999938i	$-0.496455\pi$
$7$	2.54522	−	0.448791i	0.363603	−	0.0641129i	0.352465	+	0.935825i	$0.385344\pi$
$8$	−7.01454	+	3.84660i	−0.876817	+	0.480824i
$9$		0			0
$10$	7.37470	−	4.18597i	0.737470	−	0.418597i
$11$	−0.818869	+	2.24982i	−0.0744426	+	0.204529i	−0.971333	−	0.237724i	$-0.923599\pi$
$11$	−0.818869	+	2.24982i	−0.0744426	+	0.204529i	0.896890	+	0.442253i	$0.145821\pi$
$12$		0			0
$13$	−3.62870	−	3.04484i	−0.279131	−	0.234219i	0.492464	−	0.870333i	$-0.336096\pi$
$13$	−3.62870	−	3.04484i	−0.279131	−	0.234219i	−0.771595	+	0.636114i	$0.780541\pi$
$14$	−4.87007	+	1.73222i	−0.347862	+	0.123730i
$15$		0			0
$16$	12.5531	−	9.92063i	0.784571	−	0.620039i
$17$	8.77670	−	15.2017i	0.516277	−	0.894218i	−0.483545	−	0.875320i	$-0.660651\pi$
$17$	8.77670	−	15.2017i	0.516277	−	0.894218i	0.999821	−	0.0188979i	$-0.00601573\pi$
$18$		0			0
$19$	−13.3776	+	7.72359i	−0.704086	+	0.406504i	−0.808868	−	0.587991i	$-0.799919\pi$
$19$	−13.3776	+	7.72359i	−0.704086	+	0.406504i	0.104781	+	0.994495i	$0.466586\pi$
$20$	−13.1505	+	10.7098i	−0.657523	+	0.535489i
$21$		0			0
$22$	0.866067	−	4.70945i	0.0393667	−	0.214066i
$23$	−13.3426	−	2.35266i	−0.580114	−	0.102290i	−0.124112	−	0.992268i	$-0.539608\pi$
$23$	−13.3426	−	2.35266i	−0.580114	−	0.102290i	−0.456002	+	0.889979i	$0.650719\pi$
$24$		0			0
$25$	−5.37983	+	4.51422i	−0.215193	+	0.180569i
$26$	8.16965	+	4.79699i	0.314217	+	0.184499i
$27$		0			0
$28$	9.02777	−	5.03708i	0.322420	−	0.179896i
$29$	33.3419	−	27.9772i	1.14972	−	0.964731i	0.150009	−	0.988685i	$-0.452070\pi$
$29$	33.3419	−	27.9772i	1.14972	−	0.964731i	0.999713	+	0.0239532i	$0.00762528\pi$
$30$		0			0
$31$	−46.8128	−	8.25437i	−1.51009	−	0.266270i	−0.643562	−	0.765394i	$-0.722544\pi$
$31$	−46.8128	−	8.25437i	−1.51009	−	0.266270i	−0.866530	+	0.499124i	$0.833655\pi$
$32$	−21.4542	+	23.7428i	−0.670443	+	0.741961i
$33$		0			0
$34$	−12.2489	+	32.9007i	−0.360261	+	0.967667i
$35$	−9.48996	+	5.47903i	−0.271142	+	0.156544i
$36$		0			0
$37$	23.0118	−	39.8576i	0.621940	−	1.07723i	−0.367184	−	0.930148i	$-0.619678\pi$
$37$	23.0118	−	39.8576i	0.621940	−	1.07723i	0.989124	−	0.147083i	$-0.0469885\pi$
$38$	23.8115	−	19.6844i	0.626617	−	0.518010i
$39$		0			0
$40$	22.3695	−	25.4979i	0.559237	−	0.637447i
$41$	−59.1080	−	49.5975i	−1.44166	−	1.20970i	−0.938396	−	0.345563i	$-0.887688\pi$
$41$	−59.1080	−	49.5975i	−1.44166	−	1.20970i	−0.503264	−	0.864133i	$-0.667868\pi$
$42$		0			0
$43$	11.2366	−	30.8724i	0.261317	−	0.717963i	−0.737762	−	0.675061i	$-0.764117\pi$
$43$	11.2366	−	30.8724i	0.261317	−	0.717963i	0.999079	−	0.0429024i	$-0.0136605\pi$
$44$	−0.140482	+	9.57582i	−0.00319276	+	0.217632i
$45$		0			0
$46$	27.0962	+	0.198746i	0.589047	+	0.00432056i
$47$	−36.6059	+	6.45461i	−0.778850	+	0.137332i	−0.548920	−	0.835875i	$-0.684961\pi$
$47$	−36.6059	+	6.45461i	−0.778850	+	0.137332i	−0.229930	+	0.973207i	$0.573850\pi$
$48$		0			0
$49$	−39.7682	+	14.4744i	−0.811596	+	0.295397i
$50$	9.10711	−	10.6932i	0.182142	−	0.213863i
$51$		0			0
$52$	−17.7081	−	6.74099i	−0.340540	−	0.129634i
$53$	35.4346			0.668578			0.334289	−	0.942471i	$-0.391504\pi$
$53$	35.4346			0.668578			0.334289	+	0.942471i	$0.391504\pi$
$54$		0			0
$55$		−	10.1513i		−	0.184570i
$56$	−16.1272	+	12.9385i	−0.287986	+	0.231044i
$57$		0			0
$58$	−56.4420	+	66.2717i	−0.973138	+	1.14262i
$59$	−31.4856	−	86.5061i	−0.533655	−	1.46620i	−0.854691	−	0.519138i	$-0.826253\pi$
$59$	−31.4856	−	86.5061i	−0.533655	−	1.46620i	0.321036	−	0.947067i	$-0.395969\pi$
$60$		0			0
$61$	−17.4186	−	98.7856i	−0.285550	−	1.61944i	−0.703314	−	0.710880i	$-0.748297\pi$
$61$	−17.4186	−	98.7856i	−0.285550	−	1.61944i	0.417764	−	0.908556i	$-0.362814\pi$
$62$	95.0675	+	0.697304i	1.53335	+	0.0112468i
$63$		0			0
$64$	34.4074	−	53.9642i	0.537616	−	0.843190i
$65$	18.8731	+	6.86925i	0.290356	+	0.105681i
$66$		0			0
$67$	−18.1558	+	21.6372i	−0.270982	+	0.322943i	−0.884324	−	0.466874i	$-0.845380\pi$
$67$	−18.1558	+	21.6372i	−0.270982	+	0.322943i	0.613342	+	0.789817i	$0.289825\pi$
$68$	13.2055	−	68.9606i	0.194198	−	1.01413i
$69$		0			0
$70$	16.8916	−	13.9639i	0.241308	−	0.199484i
$71$	−40.2696	−	23.2497i	−0.567177	−	0.327460i	0.188844	−	0.982007i	$-0.439526\pi$
$71$	−40.2696	−	23.2497i	−0.567177	−	0.327460i	−0.756021	+	0.654547i	$0.772859\pi$
$72$		0			0
$73$	−18.0611	−	31.2827i	−0.247412	−	0.428531i	0.715395	−	0.698720i	$-0.246247\pi$
$73$	−18.0611	−	31.2827i	−0.247412	−	0.428531i	−0.962807	+	0.270190i	$0.912914\pi$
$74$	−32.1155	+	86.2627i	−0.433994	+	1.16571i
$75$		0			0
$76$	−40.4070	+	46.7452i	−0.531672	+	0.615068i
$77$	−1.07450	+	6.09379i	−0.0139545	+	0.0791402i
$78$		0			0
$79$	58.8468	+	70.1309i	0.744896	+	0.887733i	0.996793	−	0.0800214i	$-0.0254989\pi$
$79$	58.8468	+	70.1309i	0.744896	+	0.887733i	−0.251897	+	0.967754i	$0.581054\pi$
$80$	−35.6284	+	57.7301i	−0.445355	+	0.721626i
$81$		0			0
$82$	133.076	+	78.1382i	1.62287	+	0.952905i
$83$	50.7354	+	60.4641i	0.611270	+	0.728483i	0.979543	−	0.201234i	$-0.0644952\pi$
$83$	50.7354	+	60.4641i	0.611270	+	0.728483i	−0.368273	+	0.929718i	$0.620051\pi$
$84$		0			0
$85$	−12.9238	+	73.2948i	−0.152045	+	0.862292i
$86$	−11.8843	+	64.6238i	−0.138190	+	0.751440i
$87$		0			0
$88$	−2.91018	−	18.9313i	−0.0330702	−	0.215129i
$89$	31.6951	+	54.8975i	0.356124	+	0.616826i	0.987310	−	0.158806i	$-0.0507646\pi$
$89$	31.6951	+	54.8975i	0.356124	+	0.616826i	−0.631185	+	0.775632i	$0.717431\pi$
$90$		0			0
$91$	−10.6023	−	6.12126i	−0.116509	−	0.0672666i
$92$	−53.5028	+	8.62676i	−0.581552	+	0.0937691i
$93$		0			0
$94$	70.0426	−	24.9132i	0.745134	−	0.265034i
$95$	42.0995	−	50.1722i	0.443152	−	0.528128i
$96$		0			0
$97$	−74.9366	−	27.2747i	−0.772543	−	0.281183i	−0.0744832	−	0.997222i	$-0.523731\pi$
$97$	−74.9366	−	27.2747i	−0.772543	−	0.281183i	−0.698060	+	0.716040i	$0.745953\pi$
$98$	73.6096	−	41.7817i	0.751118	−	0.426344i
$99$		0			0
$100$	−14.4011	+	24.1193i	−0.144011	+	0.241193i
$101$	3.91355	+	22.1949i	0.0387480	+	0.219751i	0.998033	−	0.0626885i	$-0.0199675\pi$
$101$	3.91355	+	22.1949i	0.0387480	+	0.219751i	−0.959285	+	0.282440i	$0.908856\pi$
$102$		0			0
$103$	63.0772	+	173.303i	0.612400	+	1.68255i	0.724858	+	0.688898i	$0.241905\pi$
$103$	63.0772	+	173.303i	0.612400	+	1.68255i	−0.112458	+	0.993656i	$0.535873\pi$
$104$	37.1659	+	7.40001i	0.357365	+	0.0711539i
$105$		0			0
$106$	−69.8810	+	11.7941i	−0.659255	+	0.111265i
$107$			203.126i			1.89837i	0.314712	+	0.949187i	$0.398092\pi$
$107$			203.126i			1.89837i	−0.314712	+	0.949187i	$0.601908\pi$
$108$		0			0
$109$	−13.8141			−0.126735			−0.0633673	−	0.997990i	$-0.520184\pi$
$109$	−13.8141			−0.126735			−0.0633673	+	0.997990i	$0.520184\pi$
$110$	3.37877	+	20.0195i	0.0307161	+	0.181996i
$111$		0			0
$112$	27.4982	−	30.8839i	0.245519	−	0.275749i
$113$	−25.8778	+	9.41875i	−0.229007	+	0.0833518i	−0.453975	−	0.891014i	$-0.649994\pi$
$113$	−25.8778	+	9.41875i	−0.229007	+	0.0833518i	0.224968	+	0.974366i	$0.427772\pi$
$114$		0			0
$115$	56.5720	−	9.97517i	0.491930	−	0.0867406i
$116$	89.2519	−	149.481i	0.769413	−	1.28863i
$117$		0			0
$118$	90.8859	+	160.120i	0.770219	+	1.35695i
$119$	15.5162	−	42.6305i	0.130389	−	0.358240i
$120$		0			0
$121$	88.3002	+	74.0927i	0.729754	+	0.612336i
$122$	67.2312	+	189.018i	0.551075	+	1.54933i
$123$		0			0
$124$	−187.716	+	30.2672i	−1.51384	+	0.244090i
$125$	67.8876	−	117.585i	0.543101	−	0.940678i
$126$		0			0
$127$	17.4875	−	10.0964i	0.137697	−	0.0794993i	−0.429569	−	0.903034i	$-0.641335\pi$
$127$	17.4875	−	10.0964i	0.137697	−	0.0794993i	0.567266	+	0.823535i	$0.308001\pi$
$128$	−49.8937	+	117.875i	−0.389795	+	0.920902i
$129$		0			0
$130$	−39.5062	−	7.26518i	−0.303894	−	0.0558860i
$131$	104.468	+	18.4206i	0.797469	+	0.140615i	0.557513	−	0.830168i	$-0.311756\pi$
$131$	104.468	+	18.4206i	0.797469	+	0.140615i	0.239956	+	0.970784i	$0.422867\pi$
$132$		0			0
$133$	−30.5827	+	25.6620i	−0.229945	+	0.192947i
$134$	28.6034	−	48.7139i	0.213458	−	0.363537i
$135$		0			0
$136$	−3.08973	+	140.393i	−0.0227186	+	1.03230i
$137$	−68.1869	+	57.2156i	−0.497714	+	0.417632i	−0.856781	−	0.515680i	$-0.827539\pi$
$137$	−68.1869	+	57.2156i	−0.497714	+	0.417632i	0.359067	+	0.933312i	$0.383095\pi$
$138$		0			0
$139$	−194.732	−	34.3365i	−1.40095	−	0.247025i	−0.578417	−	0.815741i	$-0.696329\pi$
$139$	−194.732	−	34.3365i	−1.40095	−	0.247025i	−0.822534	+	0.568716i	$0.807440\pi$
$140$	−28.6643	+	33.1605i	−0.204745	+	0.236861i
$141$		0			0
$142$	87.1545	+	32.4475i	0.613764	+	0.228504i
$143$	9.82180	−	5.67062i	0.0686839	−	0.0396547i
$144$		0			0
$145$	−92.2714	+	159.819i	−0.636354	+	1.10220i
$146$	46.0306	+	55.6815i	0.315278	+	0.381380i
$147$		0			0
$148$	34.6236	−	180.809i	0.233943	−	1.22168i
$149$	−70.9348	−	59.5214i	−0.476072	−	0.399472i	0.372931	−	0.927859i	$-0.378353\pi$
$149$	−70.9348	−	59.5214i	−0.476072	−	0.399472i	−0.849004	+	0.528387i	$0.822797\pi$
$150$		0			0
$151$	25.3592	−	69.6739i	0.167942	−	0.461416i	−0.826960	−	0.562260i	$-0.809932\pi$
$151$	25.3592	−	69.6739i	0.167942	−	0.461416i	0.994902	+	0.100844i	$0.0321542\pi$
$152$	64.1284	−	105.636i	0.421898	−	0.694972i
$153$		0			0
$154$	0.0907705	−	12.3753i	0.000589419	−	0.0803589i
$155$	198.484	−	34.9981i	1.28054	−	0.225794i
$156$		0			0
$157$	210.559	−	76.6373i	1.34114	−	0.488135i	0.430969	−	0.902367i	$-0.358172\pi$
$157$	210.559	−	76.6373i	1.34114	−	0.488135i	0.910172	+	0.414231i	$0.135949\pi$
$158$	−139.395	−	118.719i	−0.882245	−	0.751387i
$159$		0			0
$160$	51.0481	−	125.709i	0.319051	−	0.785679i
$161$	−35.0157			−0.217489
$162$		0			0
$163$		−	164.898i		−	1.01164i	−0.862638	−	0.505822i	$-0.831189\pi$
$163$		−	164.898i		−	1.01164i	0.862638	−	0.505822i	$-0.168811\pi$
$164$	−288.447	−	109.804i	−1.75882	−	0.669538i
$165$		0			0
$166$	−120.181	−	102.355i	−0.723980	−	0.616597i
$167$	−41.2270	−	113.270i	−0.246868	−	0.678264i	−0.999797	−	0.0201622i	$-0.993582\pi$
$167$	−41.2270	−	113.270i	−0.246868	−	0.678264i	0.752929	−	0.658102i	$-0.228640\pi$
$168$		0			0
$169$	−25.4501	−	144.335i	−0.150592	−	0.854052i
$170$	1.09177	−	148.847i	0.00642216	−	0.875570i
$171$		0			0
$172$	1.92771	−	131.401i	0.0112076	−	0.763958i
$173$	2.93090	+	1.06676i	0.0169416	+	0.00616625i	0.350477	−	0.936571i	$-0.386019\pi$
$173$	2.93090	+	1.06676i	0.0169416	+	0.00616625i	−0.333535	+	0.942738i	$0.608242\pi$
$174$		0			0
$175$	−11.6669	+	13.9041i	−0.0666680	+	0.0794519i
$176$	12.0403	+	36.3660i	0.0684108	+	0.206625i
$177$		0			0
$178$	−80.7783	−	97.7145i	−0.453811	−	0.548958i
$179$	−204.401	−	118.011i	−1.14190	−	0.659278i	−0.195002	−	0.980803i	$-0.562471\pi$
$179$	−204.401	−	118.011i	−1.14190	−	0.659278i	−0.946901	+	0.321525i	$0.895805\pi$
$180$		0			0
$181$	65.9812	+	114.283i	0.364537	+	0.631397i	0.988702	−	0.149896i	$-0.0478939\pi$
$181$	65.9812	+	114.283i	0.364537	+	0.631397i	−0.624165	+	0.781293i	$0.714561\pi$
$182$	22.9464	+	8.54291i	0.126079	+	0.0469391i
$183$		0			0
$184$	102.642	−	34.8208i	0.557837	−	0.189244i
$185$	−33.8852	+	192.173i	−0.183163	+	1.03877i
$186$		0			0
$187$	27.0142	+	32.1942i	0.144461	+	0.172162i
$188$	−129.840	+	72.4445i	−0.690636	+	0.385343i
$189$		0			0
$190$	−66.3254	+	112.957i	−0.349081	+	0.594513i
$191$	50.3735	+	60.0328i	0.263736	+	0.314308i	0.881619	−	0.471962i	$-0.156454\pi$
$191$	50.3735	+	60.0328i	0.263736	+	0.314308i	−0.617883	+	0.786270i	$0.712010\pi$
$192$		0			0
$193$	−4.46923	+	25.3463i	−0.0231567	+	0.131328i	−0.994195	−	0.107598i	$-0.965684\pi$
$193$	−4.46923	+	25.3463i	−0.0231567	+	0.131328i	0.971038	+	0.238926i	$0.0767952\pi$
$194$	156.861	+	28.8468i	0.808564	+	0.148695i
$195$		0			0
$196$	−131.260	+	106.898i	−0.669692	+	0.545400i
$197$	71.9902	+	124.691i	0.365432	+	0.632947i	0.988845	−	0.148945i	$-0.0475878\pi$
$197$	71.9902	+	124.691i	0.365432	+	0.632947i	−0.623413	+	0.781893i	$0.714255\pi$
$198$		0			0
$199$	−201.908	−	116.571i	−1.01461	−	0.585786i	−0.102073	−	0.994777i	$-0.532548\pi$
$199$	−201.908	−	116.571i	−1.01461	−	0.585786i	−0.912539	+	0.408990i	$0.865881\pi$
$200$	20.3727	−	52.3592i	0.101863	−	0.261796i
$201$		0			0
$202$	−15.1053	−	42.4681i	−0.0747787	−	0.210238i
$203$	72.3066	−	86.1716i	0.356190	−	0.424491i
$204$		0			0
$205$	307.425	+	111.893i	1.49963	+	0.545821i
$206$	−182.077	−	320.778i	−0.883871	−	1.55718i
$207$		0			0
$208$	−75.7584	−	2.22330i	−0.364223	−	0.0106889i
$209$	−6.42217	−	36.4219i	−0.0307281	−	0.174268i
$210$		0			0
$211$	−7.12646	−	19.5798i	−0.0337747	−	0.0927953i	0.921659	−	0.388001i	$-0.126834\pi$
$211$	−7.12646	−	19.5798i	−0.0337747	−	0.0927953i	−0.955434	+	0.295205i	$0.904612\pi$
$212$	133.887	−	46.5185i	0.631544	−	0.219427i
$213$		0			0
$214$	−67.6086	−	400.587i	−0.315928	−	1.87190i
$215$			139.298i			0.647898i
$216$		0			0
$217$	−122.853			−0.566145
$218$	27.2429	−	4.59789i	0.124967	−	0.0210912i
$219$		0			0
$220$	−13.3266	−	38.3561i	−0.0605756	−	0.174346i
$221$	−78.1349	+	28.4388i	−0.353551	+	0.128682i
$222$		0			0
$223$	264.230	−	46.5908i	1.18489	−	0.208928i	0.453732	−	0.891138i	$-0.350092\pi$
$223$	264.230	−	46.5908i	1.18489	−	0.208928i	0.731155	+	0.682211i	$0.238981\pi$
$224$	−43.9500	+	70.0589i	−0.196205	+	0.312763i
$225$		0			0
$226$	47.8989	−	27.1880i	0.211942	−	0.120301i
$227$	−93.7660	+	257.620i	−0.413066	+	1.13489i	0.542485	+	0.840065i	$0.317483\pi$
$227$	−93.7660	+	257.620i	−0.413066	+	1.13489i	−0.955551	+	0.294824i	$0.904739\pi$
$228$		0			0
$229$	150.793	+	126.530i	0.658483	+	0.552533i	0.909632	−	0.415415i	$-0.136364\pi$
$229$	150.793	+	126.530i	0.658483	+	0.552533i	−0.251148	+	0.967949i	$0.580808\pi$
$230$	−108.246	+	38.5016i	−0.470635	+	0.167398i
$231$		0			0
$232$	−126.261	+	324.500i	−0.544229	+	1.39871i
$233$	−137.473	+	238.110i	−0.590012	+	1.02193i	0.404219	+	0.914662i	$0.367544\pi$
$233$	−137.473	+	238.110i	−0.590012	+	1.02193i	−0.994230	+	0.107268i	$0.965790\pi$
$234$		0			0
$235$	136.487	−	78.8007i	0.580795	−	0.335322i
$236$	−232.531	−	285.523i	−0.985302	−	1.20984i
$237$		0			0
$238$	−16.4106	+	89.2365i	−0.0689520	+	0.374943i
$239$	−245.841	−	43.3484i	−1.02862	−	0.181374i	−0.366225	−	0.930526i	$-0.619350\pi$
$239$	−245.841	−	43.3484i	−1.02862	−	0.181374i	−0.662398	+	0.749152i	$0.730461\pi$
$240$		0			0
$241$	−14.5817	+	12.2355i	−0.0605051	+	0.0507698i	−0.672539	−	0.740062i	$-0.734796\pi$
$241$	−14.5817	+	12.2355i	−0.0605051	+	0.0507698i	0.612034	+	0.790832i	$0.290352\pi$
$242$	−198.799	−	116.729i	−0.821483	−	0.482351i
$243$		0			0
$244$	−195.500	−	350.388i	−0.801230	−	1.43602i
$245$	137.456	−	115.339i	0.561046	−	0.470773i
$246$		0			0
$247$	72.0606	+	12.7062i	0.291743	+	0.0514422i
$248$	360.122	−	122.170i	1.45210	−	0.492619i
$249$		0			0
$250$	−94.7448	+	254.486i	−0.378979	+	1.01794i
$251$	−5.39896	+	3.11709i	−0.0215098	+	0.0124187i	−0.510716	−	0.859749i	$-0.670620\pi$
$251$	−5.39896	+	3.11709i	−0.0215098	+	0.0124187i	0.489207	+	0.872168i	$0.337286\pi$
$252$		0			0
$253$	16.2189	−	28.0920i	0.0641065	−	0.111036i
$254$	−31.1268	+	25.7318i	−0.122546	+	0.101306i
$255$		0			0
$256$	59.1622	−	249.070i	0.231102	−	0.972929i
$257$	149.042	+	125.061i	0.579930	+	0.486619i	0.884924	−	0.465735i	$-0.154210\pi$
$257$	149.042	+	125.061i	0.579930	+	0.486619i	−0.304994	+	0.952354i	$0.598655\pi$
$258$		0			0
$259$	40.6823	−	111.774i	0.157074	−	0.431558i
$260$	80.3287	+	1.17846i	0.308957	+	0.00453253i
$261$		0			0
$262$	−212.154	−	1.55612i	−0.809749	−	0.00593937i
$263$	194.704	−	34.3316i	0.740320	−	0.130538i	0.209245	−	0.977863i	$-0.432899\pi$
$263$	194.704	−	34.3316i	0.740320	−	0.130538i	0.531075	+	0.847325i	$0.321788\pi$
$264$		0			0
$265$	−141.180	+	51.3854i	−0.532756	+	0.193907i
$266$	51.7712	−	60.7874i	0.194628	−	0.228524i
$267$		0			0
$268$	−40.1951	+	105.590i	−0.149982	+	0.393991i
$269$	−253.937			−0.944004			−0.472002	−	0.881597i	$-0.656469\pi$
$269$	−253.937			−0.944004			−0.472002	+	0.881597i	$0.656469\pi$
$270$		0			0
$271$		−	205.121i		−	0.756905i	−0.925621	−	0.378452i	$-0.876456\pi$
$271$		−	205.121i		−	0.756905i	0.925621	−	0.378452i	$-0.123544\pi$
$272$	−40.6353	−	277.899i	−0.149395	−	1.02169i
$273$		0			0
$274$	115.428	−	135.531i	0.421271	−	0.494638i
$275$	−5.75081	−	15.8002i	−0.0209120	−	0.0574554i
$276$		0			0
$277$	−27.2346	−	154.455i	−0.0983197	−	0.557599i	−0.993679	−	0.112255i	$-0.964193\pi$
$277$	−27.2346	−	154.455i	−0.0983197	−	0.557599i	0.895360	−	0.445344i	$-0.146919\pi$
$278$	395.462	+	2.90064i	1.42252	+	0.0104340i
$279$		0			0
$280$	45.4920	−	74.9369i	0.162472	−	0.267632i
$281$	−19.5697	−	7.12277i	−0.0696429	−	0.0253479i	0.306964	−	0.951721i	$-0.400687\pi$
$281$	−19.5697	−	7.12277i	−0.0696429	−	0.0253479i	−0.376607	+	0.926373i	$0.622909\pi$
$282$		0			0
$283$	10.4696	−	12.4772i	0.0369951	−	0.0440890i	−0.747230	−	0.664566i	$-0.768616\pi$
$283$	10.4696	−	12.4772i	0.0369951	−	0.0440890i	0.784225	+	0.620477i	$0.213061\pi$
$284$	−182.678	−	34.9815i	−0.643232	−	0.123174i
$285$		0			0
$286$	−17.4822	+	14.4522i	−0.0611267	+	0.0505321i
$287$	−172.702	−	99.7094i	−0.601748	−	0.347419i
$288$		0			0
$289$	−9.56108	−	16.5603i	−0.0330833	−	0.0573020i
$290$	128.775	−	345.892i	0.444052	−	1.19273i
$291$		0			0
$292$	−109.311	−	94.4892i	−0.374351	−	0.323593i
$293$	31.7417	−	180.016i	0.108333	−	0.614389i	−0.881503	−	0.472178i	$-0.843468\pi$
$293$	31.7417	−	180.016i	0.108333	−	0.614389i	0.989836	−	0.142211i	$-0.0454210\pi$
$294$		0			0
$295$	250.893	+	299.003i	0.850485	+	1.01357i
$296$	−8.10100	+	368.099i	−0.0273682	+	1.24358i
$297$		0			0
$298$	159.702	+	93.7727i	0.535914	+	0.314673i
$299$	41.2529	+	49.1633i	0.137970	+	0.164426i
$300$		0			0
$301$	14.7445	−	83.6199i	0.0489849	−	0.277807i
$302$	−26.8209	+	145.845i	−0.0888108	+	0.482931i
$303$		0			0
$304$	−91.3085	+	229.670i	−0.300357	+	0.755493i
$305$	212.653	+	368.326i	0.697224	+	1.20763i
$306$		0			0
$307$	66.6563	+	38.4840i	0.217121	+	0.125355i	0.604617	−	0.796517i	$-0.293326\pi$
$307$	66.6563	+	38.4840i	0.217121	+	0.125355i	−0.387495	+	0.921872i	$0.626660\pi$
$308$	3.93998	+	24.4356i	0.0127921	+	0.0793364i
$309$		0			0
$310$	−379.783	+	135.084i	−1.22511	+	0.435753i
$311$	−103.312	+	123.123i	−0.332194	+	0.395893i	−0.906125	−	0.423011i	$-0.860973\pi$
$311$	−103.312	+	123.123i	−0.332194	+	0.395893i	0.573931	+	0.818904i	$0.305418\pi$
$312$		0			0
$313$	342.269	+	124.576i	1.09351	+	0.398006i	0.824921	−	0.565248i	$-0.191220\pi$
$313$	342.269	+	124.576i	1.09351	+	0.398006i	0.268591	+	0.963254i	$0.413442\pi$
$314$	−389.738	+	221.220i	−1.24120	+	0.704522i
$315$		0			0
$316$	314.416	+	187.731i	0.994988	+	0.594086i
$317$	−80.0708	−	454.104i	−0.252589	−	1.43251i	−0.802186	−	0.597075i	$-0.796330\pi$
$317$	−80.0708	−	454.104i	−0.252589	−	1.43251i	0.549596	−	0.835430i	$-0.314782\pi$
$318$		0			0
$319$	35.6411	+	97.9232i	0.111728	+	0.306969i
$320$	−58.8316	+	264.902i	−0.183849	+	0.827819i
$321$		0			0
$322$	69.0549	−	11.6547i	0.214456	−	0.0361946i
$323$			271.150i			0.839475i
$324$		0			0
$325$	33.2669			0.102360
$326$	54.8847	+	325.197i	0.168358	+	0.997536i
$327$		0			0
$328$	605.397	+	120.539i	1.84572	+	0.367497i
$329$	−90.2733	+	32.8568i	−0.274387	+	0.0998687i
$330$		0			0
$331$	−560.929	+	98.9068i	−1.69465	+	0.298812i	−0.935820	−	0.352479i	$-0.885339\pi$
$331$	−560.929	+	98.9068i	−1.69465	+	0.298812i	−0.758828	+	0.651291i	$0.774228\pi$
$332$	271.078	+	161.854i	0.816499	+	0.487513i
$333$		0			0
$334$	119.005	+	209.659i	0.356302	+	0.627722i
$335$	40.9599	−	112.536i	0.122268	−	0.335930i
$336$		0			0
$337$	−313.100	−	262.722i	−0.929079	−	0.779590i	0.0465731	−	0.998915i	$-0.485170\pi$
$337$	−313.100	−	262.722i	−0.929079	−	0.779590i	−0.975652	+	0.219325i	$0.929614\pi$
$338$	98.2309	+	276.173i	0.290624	+	0.817081i
$339$		0			0
$340$	47.3892	+	293.906i	0.139380	+	0.864429i
$341$	56.9045	−	98.5614i	0.166875	−	0.289036i
$342$		0			0
$343$	−204.396	+	118.008i	−0.595906	+	0.344047i
$344$	39.9339	+	259.779i	0.116087	+	0.755170i
$345$		0			0
$346$	−6.13513	−	1.12825i	−0.0177316	−	0.00326083i
$347$	67.6194	+	11.9231i	0.194868	+	0.0343606i	0.270230	−	0.962796i	$-0.412900\pi$
$347$	67.6194	+	11.9231i	0.194868	+	0.0343606i	−0.0753620	+	0.997156i	$0.524011\pi$
$348$		0			0
$349$	−301.507	+	252.994i	−0.863916	+	0.724912i	−0.962808	−	0.270186i	$-0.912915\pi$
$349$	−301.507	+	252.994i	−0.863916	+	0.724912i	0.0988917	+	0.995098i	$0.468470\pi$
$350$	18.3806	−	31.3036i	0.0525159	−	0.0894388i
$351$		0			0
$352$	−35.8489	−	67.7103i	−0.101843	−	0.192359i
$353$	64.2850	−	53.9415i	0.182110	−	0.152809i	−0.547175	−	0.837018i	$-0.684297\pi$
$353$	64.2850	−	53.9415i	0.182110	−	0.152809i	0.729286	+	0.684209i	$0.239852\pi$
$354$		0			0
$355$	194.159	+	34.2355i	0.546927	+	0.0964381i
$356$	191.827	+	165.817i	0.538840	+	0.465779i
$357$		0			0
$358$	442.379	+	164.697i	1.23570	+	0.460049i
$359$	516.172	−	298.012i	1.43781	−	0.830117i	0.440108	−	0.897945i	$-0.354940\pi$
$359$	516.172	−	298.012i	1.43781	−	0.830117i	0.997697	+	0.0678276i	$0.0216068\pi$
$360$		0			0
$361$	−61.1925	+	105.988i	−0.169508	+	0.293597i
$362$	−168.160	−	203.417i	−0.464531	−	0.561925i
$363$		0			0
$364$	−48.0962	−	9.21008i	−0.132132	−	0.0253024i
$365$	117.324	+	98.4468i	0.321437	+	0.269717i
$366$		0			0
$367$	54.1761	−	148.847i	0.147619	−	0.405579i	−0.843741	−	0.536751i	$-0.819652\pi$
$367$	54.1761	−	148.847i	0.147619	−	0.405579i	0.991360	+	0.131172i	$0.0418739\pi$
$368$	−190.832	+	102.834i	−0.518564	+	0.279440i
$369$		0			0
$370$	2.86252	−	390.264i	0.00773654	−	1.05477i
$371$	90.1889	−	15.9027i	0.243097	−	0.0428645i
$372$		0			0
$373$	13.0433	−	4.74739i	0.0349688	−	0.0127276i	−0.324477	−	0.945894i	$-0.605188\pi$
$373$	13.0433	−	4.74739i	0.0349688	−	0.0127276i	0.359445	+	0.933166i	$0.382966\pi$
$374$	−63.9905	−	54.4992i	−0.171098	−	0.145720i
$375$		0			0
$376$	231.945	−	186.084i	0.616876	−	0.494905i
$377$	−206.174			−0.546881
$378$		0			0
$379$			388.683i			1.02555i	0.858523	+	0.512774i	$0.171382\pi$
$379$			388.683i			1.02555i	−0.858523	+	0.512774i	$0.828618\pi$
$380$	93.2042	−	244.840i	0.245274	−	0.644317i
$381$		0			0
$382$	−119.323	−	101.625i	−0.312365	−	0.266034i
$383$	97.1646	+	266.958i	0.253694	+	0.697017i	0.999523	+	0.0308805i	$0.00983114\pi$
$383$	97.1646	+	266.958i	0.253694	+	0.697017i	−0.745829	+	0.666137i	$0.767947\pi$
$384$		0			0
$385$	−4.55582	−	25.8373i	−0.0118333	−	0.0671100i
$386$	0.377547	−	51.4732i	0.000978101	−	0.133350i
$387$		0			0
$388$	−318.949	−	4.67913i	−0.822034	−	0.0120596i
$389$	23.9834	+	8.72924i	0.0616540	+	0.0224402i	0.372663	−	0.927967i	$-0.378445\pi$
$389$	23.9834	+	8.72924i	0.0616540	+	0.0224402i	−0.311009	+	0.950407i	$0.600667\pi$
$390$		0			0
$391$	−152.869	+	182.182i	−0.390969	+	0.465938i
$392$	223.278	−	254.504i	0.569587	−	0.649244i
$393$		0			0
$394$	−183.475	−	221.942i	−0.465672	−	0.563305i
$395$	−336.160	−	194.082i	−0.851038	−	0.491347i
$396$		0			0
$397$	−211.963	−	367.130i	−0.533911	−	0.924761i	−0.999215	−	0.0396104i	$-0.987388\pi$
$397$	−211.963	−	367.130i	−0.533911	−	0.924761i	0.465304	−	0.885151i	$-0.345945\pi$
$398$	436.984	+	162.689i	1.09795	+	0.408766i
$399$		0			0
$400$	−22.7499	+	110.039i	−0.0568747	+	0.275097i
$401$	26.4342	−	149.916i	0.0659207	−	0.373855i	−0.933944	−	0.357419i	$-0.883657\pi$
$401$	26.4342	−	149.916i	0.0659207	−	0.373855i	0.999865	−	0.0164359i	$-0.00523196\pi$
$402$		0			0
$403$	144.737	+	172.490i	0.359148	+	0.428016i
$404$	43.9244	+	78.7241i	0.108724	+	0.194862i
$405$		0			0
$406$	−113.915	+	194.007i	−0.280579	+	0.477849i
$407$	70.8289	+	84.4106i	0.174027	+	0.207397i
$408$		0			0
$409$	57.5159	−	326.189i	0.140626	−	0.797528i	−0.830150	−	0.557540i	$-0.811745\pi$
$409$	57.5159	−	326.189i	0.140626	−	0.797528i	0.970776	−	0.239988i	$-0.0771435\pi$
$410$	−643.518	−	118.343i	−1.56956	−	0.288641i
$411$		0			0
$412$	465.845	+	572.007i	1.13069	+	1.38837i
$413$	−118.961	−	206.046i	−0.288041	−	0.498902i
$414$		0			0
$415$	−289.824	−	167.330i	−0.698372	−	0.403205i
$416$	150.144	−	20.8309i	0.360923	−	0.0500742i
$417$		0			0
$418$	24.7879	+	69.6905i	0.0593013	+	0.166724i
$419$	255.170	−	304.100i	0.608997	−	0.725775i	−0.370140	−	0.928976i	$-0.620690\pi$
$419$	255.170	−	304.100i	0.608997	−	0.725775i	0.979137	+	0.203201i	$0.0651346\pi$
$420$		0			0
$421$	612.453	+	222.915i	1.45476	+	0.529488i	0.943916	−	0.330187i	$-0.107112\pi$
$421$	612.453	+	222.915i	1.45476	+	0.529488i	0.510841	+	0.859675i	$0.329334\pi$
$422$	20.5711	+	36.2415i	0.0487467	+	0.0858804i
$423$		0			0
$424$	−248.557	+	136.303i	−0.586220	+	0.321469i
$425$	21.4065	+	121.403i	0.0503683	+	0.285653i
$426$		0			0
$427$	−88.6680	−	243.613i	−0.207654	−	0.570523i
$428$	266.663	+	767.499i	0.623045	+	1.79322i
$429$		0			0
$430$	−46.3641	−	274.711i	−0.107823	−	0.638863i
$431$		−	248.329i		−	0.576170i	−0.957605	−	0.288085i	$-0.906981\pi$
$431$		−	248.329i		−	0.576170i	0.957605	−	0.288085i	$-0.0930186\pi$
$432$		0			0
$433$	−426.359			−0.984663			−0.492332	−	0.870408i	$-0.663855\pi$
$433$	−426.359			−0.984663			−0.492332	+	0.870408i	$0.663855\pi$
$434$	242.280	−	40.8906i	0.558250	−	0.0942179i
$435$		0			0
$436$	−52.1956	+	18.1351i	−0.119715	+	0.0415942i
$437$	196.664	−	71.5798i	0.450032	−	0.163798i
$438$		0			0
$439$	−760.647	+	134.123i	−1.73268	+	0.305518i	−0.948914	−	0.315536i	$-0.897816\pi$
$439$	−760.647	+	134.123i	−1.73268	+	0.305518i	−0.783768	+	0.621054i	$0.786705\pi$
$440$	39.0481	+	71.2069i	0.0887456	+	0.161834i
$441$		0			0
$442$	144.625	−	82.0908i	0.327206	−	0.185726i
$443$	245.427	−	674.306i	0.554012	−	1.52213i	−0.274173	−	0.961680i	$-0.588404\pi$
$443$	245.427	−	674.306i	0.554012	−	1.52213i	0.828185	−	0.560455i	$-0.189374\pi$
$444$		0			0
$445$	−205.890	−	172.762i	−0.462675	−	0.388230i
$446$	−505.583	+	179.829i	−1.13359	+	0.403203i
$447$		0			0
$448$	63.3557	−	152.792i	0.141419	−	0.341054i
$449$	101.434	−	175.689i	0.225911	−	0.391289i	−0.730682	−	0.682718i	$-0.760798\pi$
$449$	101.434	−	175.689i	0.225911	−	0.391289i	0.956592	+	0.291430i	$0.0941309\pi$
$450$		0			0
$451$	159.987	−	92.3688i	0.354739	−	0.204809i
$452$	−85.4127	+	69.5604i	−0.188966	+	0.153895i
$453$		0			0
$454$	99.1705	−	539.264i	0.218437	−	1.18781i
$455$	51.1190	+	9.01366i	0.112350	+	0.0198102i
$456$		0			0
$457$	−619.478	+	519.804i	−1.35553	+	1.13743i	−0.378198	+	0.925725i	$0.623456\pi$
$457$	−619.478	+	519.804i	−1.35553	+	1.13743i	−0.977334	+	0.211702i	$0.932100\pi$
$458$	−339.494	−	199.341i	−0.741253	−	0.435243i
$459$		0			0
$460$	200.658	−	111.958i	0.436213	−	0.243387i
$461$	141.765	−	118.955i	0.307517	−	0.258037i	−0.475948	−	0.879473i	$-0.657895\pi$
$461$	141.765	−	118.955i	0.307517	−	0.258037i	0.783465	+	0.621436i	$0.213450\pi$
$462$		0			0
$463$	501.788	+	88.4787i	1.08377	+	0.191099i	0.686884	−	0.726767i	$-0.258978\pi$
$463$	501.788	+	88.4787i	1.08377	+	0.191099i	0.396891	+	0.917866i	$0.370089\pi$
$464$	140.994	−	681.975i	0.303867	−	1.46977i
$465$		0			0
$466$	191.859	−	515.335i	0.411714	−	1.10587i
$467$	−358.476	+	206.966i	−0.767615	+	0.443183i	−0.832023	−	0.554741i	$-0.812817\pi$
$467$	−358.476	+	206.966i	−0.767615	+	0.443183i	0.0644080	+	0.997924i	$0.479484\pi$
$468$		0			0
$469$	−36.4998	+	63.2195i	−0.0778248	+	0.134796i
$470$	−242.939	+	200.832i	−0.516891	+	0.427302i
$471$		0			0
$472$	553.611	+	485.687i	1.17290	+	1.02900i
$473$	60.2562	+	50.5609i	0.127392	+	0.106894i
$474$		0			0
$475$	37.1035	−	101.941i	0.0781127	−	0.214613i
$476$	2.66190	−	181.446i	0.00559222	−	0.381190i
$477$		0			0
$478$	499.254	+	3.66194i	1.04446	+	0.00766096i
$479$	−676.603	+	119.303i	−1.41253	+	0.249067i	−0.827283	−	0.561786i	$-0.810114\pi$
$479$	−676.603	+	119.303i	−1.41253	+	0.249067i	−0.585249	+	0.810853i	$0.699003\pi$
$480$		0			0
$481$	−204.863	+	74.5640i	−0.425911	+	0.155019i
$482$	24.6843	−	28.9832i	0.0512123	−	0.0601311i
$483$		0			0
$484$	430.905	+	164.034i	0.890300	+	0.338913i
$485$	338.118			0.697151
$486$		0			0
$487$		−	15.2210i		−	0.0312545i	−0.999878	−	0.0156273i	$-0.995025\pi$
$487$		−	15.2210i		−	0.0312545i	0.999878	−	0.0156273i	$-0.00497452\pi$
$488$	502.171	+	625.933i	1.02904	+	1.28265i
$489$		0			0
$490$	−232.689	+	273.213i	−0.474876	+	0.557578i
$491$	163.650	+	449.624i	0.333299	+	0.915732i	0.987248	+	0.159193i	$0.0508891\pi$
$491$	163.650	+	449.624i	0.333299	+	0.915732i	−0.653948	+	0.756539i	$0.726889\pi$
$492$		0			0
$493$	−132.669	−	752.402i	−0.269105	−	1.52617i
$494$	−146.341	−	1.07338i	−0.296236	−	0.00217284i
$495$		0			0
$496$	−669.536	+	360.795i	−1.34987	+	0.727409i
$497$	−112.929	−	41.1028i	−0.227221	−	0.0827018i
$498$		0			0
$499$	−321.114	+	382.689i	−0.643516	+	0.766913i	−0.984921	−	0.173004i	$-0.944653\pi$
$499$	−321.114	+	382.689i	−0.643516	+	0.766913i	0.341405	+	0.939916i	$0.389097\pi$
$500$	102.144	−	533.409i	0.204288	−	1.06682i
$501$		0			0
$502$	9.60984	−	7.94423i	0.0191431	−	0.0158252i
$503$	385.032	+	222.299i	0.765472	+	0.441946i	0.831257	−	0.555888i	$-0.187622\pi$
$503$	385.032	+	222.299i	0.765472	+	0.441946i	−0.0657849	+	0.997834i	$0.520955\pi$
$504$		0			0
$505$	−47.7783	−	82.7545i	−0.0946106	−	0.163870i
$506$	−22.6354	+	60.7989i	−0.0447339	+	0.120156i
$507$		0			0
$508$	52.8208	−	61.1061i	0.103978	−	0.120288i
$509$	115.845	−	656.990i	0.227594	−	1.29075i	−0.630071	−	0.776537i	$-0.716974\pi$
$509$	115.845	−	656.990i	0.227594	−	1.29075i	0.857665	−	0.514209i	$-0.171915\pi$
$510$		0			0
$511$	−60.0088	−	71.5157i	−0.117434	−	0.139953i
$512$	−33.7737	+	510.885i	−0.0659643	+	0.997822i
$513$		0			0
$514$	−335.553	−	197.027i	−0.652826	−	0.383321i
$515$	−502.630	−	599.011i	−0.975980	−	1.16313i
$516$		0			0
$517$	15.4537	−	87.6424i	0.0298911	−	0.169521i
$518$	−43.0271	+	233.971i	−0.0830639	+	0.451681i
$519$		0			0
$520$	−158.809	+	24.4126i	−0.305403	+	0.0469473i
$521$	−177.270	−	307.041i	−0.340250	−	0.589330i	0.644229	−	0.764833i	$-0.277178\pi$
$521$	−177.270	−	307.041i	−0.340250	−	0.589330i	−0.984479	+	0.175503i	$0.943845\pi$
$522$		0			0
$523$	826.762	+	477.331i	1.58081	+	0.912679i	0.994742	+	0.102415i	$0.0326571\pi$
$523$	826.762	+	477.331i	1.58081	+	0.912679i	0.586065	+	0.810264i	$0.300676\pi$
$524$	418.910	−	67.5447i	0.799446	−	0.128902i
$525$		0			0
$526$	−372.551	+	132.511i	−0.708272	+	0.251922i
$527$	−536.343	+	639.189i	−1.01773	+	1.21288i
$528$		0			0
$529$	−324.607	−	118.147i	−0.613623	−	0.223341i
$530$	261.320	−	148.328i	0.493056	−	0.279864i
$531$		0			0
$532$	−81.8659	+	137.111i	−0.153883	+	0.257727i
$533$	63.4688	+	359.949i	0.119078	+	0.675327i
$534$		0			0
$535$	−294.563	−	809.304i	−0.550584	−	1.51272i
$536$	44.1247	−	221.613i	0.0823223	−	0.413457i
$537$		0			0
$538$	500.792	−	84.5206i	0.930840	−	0.157102i
$539$		−	101.324i		−	0.187985i
$540$		0			0
$541$	705.012			1.30316			0.651582	−	0.758578i	$-0.274105\pi$
$541$	705.012			1.30316			0.651582	+	0.758578i	$0.274105\pi$
$542$	68.2727	+	404.522i	0.125964	+	0.746350i
$543$		0			0
$544$	172.633	+	534.523i	0.317341	+	0.982579i
$545$	55.0387	−	20.0324i	0.100988	−	0.0367568i
$546$		0			0
$547$	43.3865	−	7.65021i	0.0793172	−	0.0139858i	−0.133849	−	0.991002i	$-0.542734\pi$
$547$	43.3865	−	7.65021i	0.0793172	−	0.0139858i	0.213166	+	0.977016i	$0.431623\pi$
$548$	−182.527	+	305.701i	−0.333079	+	0.557848i
$549$		0			0
$550$	16.6002	+	29.2457i	0.0301822	+	0.0531740i
$551$	−229.952	+	631.788i	−0.417336	+	1.14662i
$552$		0			0
$553$	181.252	+	152.088i	0.327761	+	0.275024i
$554$	105.118	+	295.537i	0.189744	+	0.533461i
$555$		0			0
$556$	−780.860	+	125.905i	−1.40442	+	0.226448i
$557$	242.720	−	420.403i	0.435762	−	0.754762i	−0.561595	−	0.827412i	$-0.689812\pi$
$557$	242.720	−	420.403i	0.435762	−	0.754762i	0.997358	+	0.0726498i	$0.0231455\pi$
$558$		0			0
$559$	−134.776	+	77.8131i	−0.241102	+	0.139200i
$560$	−64.7732	+	162.925i	−0.115667	+	0.290938i
$561$		0			0
$562$	40.9643	+	7.53331i	0.0728901	+	0.0134045i
$563$	−269.918	−	47.5938i	−0.479428	−	0.0845360i	−0.0712885	−	0.997456i	$-0.522711\pi$
$563$	−269.918	−	47.5938i	−0.479428	−	0.0845360i	−0.408139	+	0.912920i	$0.633822\pi$
$564$		0			0
$565$	89.4449	−	75.0532i	0.158310	−	0.132838i
$566$	−16.4943	+	28.0911i	−0.0291419	+	0.0496309i
$567$		0			0
$568$	371.904	+	8.18474i	0.654761	+	0.0144098i
$569$	−534.345	+	448.369i	−0.939095	+	0.787995i	−0.977428	−	0.211270i	$-0.932240\pi$
$569$	−534.345	+	448.369i	−0.939095	+	0.787995i	0.0383322	+	0.999265i	$0.487795\pi$
$570$		0			0
$571$	145.993	+	25.7425i	0.255679	+	0.0450831i	0.300018	−	0.953933i	$-0.403007\pi$
$571$	145.993	+	25.7425i	0.255679	+	0.0450831i	−0.0443393	+	0.999017i	$0.514118\pi$
$572$	29.6666	−	34.3201i	0.0518648	−	0.0600001i
$573$		0			0
$574$	373.774	+	139.156i	0.651174	+	0.242432i
$575$	82.4015	−	47.5745i	0.143307	−	0.0827383i
$576$		0			0
$577$	398.974	−	691.043i	0.691462	−	1.19765i	−0.279896	−	0.960030i	$-0.590300\pi$
$577$	398.974	−	691.043i	0.691462	−	1.19765i	0.971359	−	0.237618i	$-0.0763666\pi$
$578$	24.3674	+	29.4764i	0.0421582	+	0.0509972i
$579$		0			0
$580$	−138.832	+	724.998i	−0.239365	+	1.25000i
$581$	156.268	+	131.125i	0.268965	+	0.225688i
$582$		0			0
$583$	−29.0163	+	79.7217i	−0.0497707	+	0.136744i
$584$	247.022	+	149.960i	0.422983	+	0.256781i
$585$		0			0
$586$	−2.68144	+	365.576i	−0.00457583	+	0.623850i
$587$	−1075.96	+	189.721i	−1.83298	+	0.323204i	−0.980039	−	0.198806i	$-0.936294\pi$
$587$	−1075.96	+	189.721i	−1.83298	+	0.323204i	−0.852940	+	0.522009i	$0.825183\pi$
$588$		0			0
$589$	689.999	−	251.139i	1.17148	−	0.426382i
$590$	−594.309	−	506.159i	−1.00730	−	0.857896i
$591$		0			0
$592$	−106.542	−	728.629i	−0.179970	−	1.23079i
$593$	−175.815			−0.296484			−0.148242	−	0.988951i	$-0.547361\pi$
$593$	−175.815			−0.296484			−0.148242	+	0.988951i	$0.547361\pi$
$594$		0			0
$595$			192.351i			0.323279i
$596$	−346.162	−	131.775i	−0.580808	−	0.221098i
$597$		0			0
$598$	−97.7189	−	83.2248i	−0.163409	−	0.139172i
$599$	−134.650	−	369.949i	−0.224792	−	0.617611i	0.775107	−	0.631830i	$-0.217696\pi$
$599$	−134.650	−	369.949i	−0.224792	−	0.617611i	−0.999899	+	0.0142191i	$0.995474\pi$
$600$		0			0
$601$	−140.037	−	794.189i	−0.233007	−	1.32145i	−0.846771	−	0.531957i	$-0.821457\pi$
$601$	−140.037	−	794.189i	−0.233007	−	1.32145i	0.613765	−	0.789489i	$-0.289654\pi$
$602$	−1.24557	+	169.815i	−0.00206905	+	0.282085i
$603$		0			0
$604$	4.35051	−	296.550i	0.00720284	−	0.490976i
$605$	−459.255	−	167.155i	−0.759099	−	0.276289i
$606$		0			0
$607$	747.526	−	890.867i	1.23151	−	1.46766i	0.395934	−	0.918279i	$-0.370421\pi$
$607$	747.526	−	890.867i	1.23151	−	1.46766i	0.835575	−	0.549376i	$-0.185135\pi$
$608$	103.627	−	483.325i	0.170439	−	0.794943i
$609$		0			0
$610$	−541.970	−	655.600i	−0.888475	−	1.07475i
$611$	152.485	+	88.0375i	0.249567	+	0.144088i
$612$		0			0
$613$	453.450	+	785.398i	0.739723	+	1.28124i	0.952620	+	0.304163i	$0.0983766\pi$
$613$	453.450	+	785.398i	0.739723	+	1.28124i	−0.212897	+	0.977075i	$0.568290\pi$
$614$	−144.263	−	53.7088i	−0.234955	−	0.0874736i
$615$		0			0
$616$	−15.9032	−	46.8783i	−0.0258169	−	0.0761011i
$617$	−117.850	+	668.362i	−0.191005	+	1.08324i	0.726988	+	0.686650i	$0.240919\pi$
$617$	−117.850	+	668.362i	−0.191005	+	1.08324i	−0.917994	+	0.396595i	$0.870192\pi$
$618$		0			0
$619$	−380.515	−	453.480i	−0.614725	−	0.732601i	0.365429	−	0.930839i	$-0.380922\pi$
$619$	−380.515	−	453.480i	−0.614725	−	0.732601i	−0.980154	+	0.198239i	$0.936478\pi$
$620$	704.013	−	392.807i	1.13550	−	0.633559i
$621$		0			0
$622$	162.763	−	277.198i	0.261677	−	0.445656i
$623$	105.308	+	125.502i	0.169034	+	0.201447i
$624$		0			0
$625$	−69.4779	+	394.029i	−0.111165	+	0.630446i
$626$	−716.457	−	131.756i	−1.14450	−	0.210473i
$627$		0			0
$628$	694.975	−	565.990i	1.10665	−	0.901258i
$629$	−403.935	−	699.636i	−0.642186	−	1.11230i
$630$		0			0
$631$	57.7491	+	33.3415i	0.0915200	+	0.0528391i	0.545062	−	0.838396i	$-0.316506\pi$
$631$	57.7491	+	33.3415i	0.0915200	+	0.0528391i	−0.453542	+	0.891235i	$0.649840\pi$
$632$	−682.548	−	265.576i	−1.07998	−	0.420215i
$633$		0			0
$634$	309.053	+	868.892i	0.487465	+	1.37049i
$635$	−55.0332	+	65.5860i	−0.0866664	+	0.103285i
$636$		0			0
$637$	188.379	+	68.5645i	0.295729	+	0.107637i
$638$	−102.881	−	181.252i	−0.161256	−	0.284095i
$639$		0			0
$640$	27.8522	−	541.998i	0.0435191	−	0.846871i
$641$	168.295	+	954.448i	0.262551	+	1.48900i	0.775920	+	0.630831i	$0.217286\pi$
$641$	168.295	+	954.448i	0.262551	+	1.48900i	−0.513370	+	0.858167i	$0.671603\pi$
$642$		0			0
$643$	57.0470	+	156.735i	0.0887201	+	0.243757i	0.976115	−	0.217253i	$-0.0697096\pi$
$643$	57.0470	+	156.735i	0.0887201	+	0.243757i	−0.887395	+	0.461009i	$0.847487\pi$
$644$	−132.305	+	45.9685i	−0.205442	+	0.0713797i
$645$		0			0
$646$	−90.2499	−	534.739i	−0.139706	−	0.827769i
$647$		−	453.807i		−	0.701402i	−0.936487	−	0.350701i	$-0.885943\pi$
$647$		−	453.807i		−	0.701402i	0.936487	−	0.350701i	$-0.114057\pi$
$648$		0			0
$649$	220.406			0.339609
$650$	−65.6060	+	11.0726i	−0.100932	+	0.0170347i
$651$		0			0
$652$	−216.477	−	623.056i	−0.332021	−	0.955607i
$653$	505.399	−	183.950i	0.773965	−	0.281700i	0.0753113	−	0.997160i	$-0.476005\pi$
$653$	505.399	−	183.950i	0.773965	−	0.281700i	0.698654	+	0.715460i	$0.253783\pi$
$654$		0			0
$655$	−442.940	+	78.1023i	−0.676245	+	0.119240i
$656$	−1234.03	−	36.2153i	−1.88114	−	0.0552063i
$657$		0			0
$658$	167.093	−	94.8438i	0.253940	−	0.144140i
$659$	54.5893	−	149.983i	0.0828366	−	0.227592i	−0.891359	−	0.453299i	$-0.850247\pi$
$659$	54.5893	−	149.983i	0.0828366	−	0.227592i	0.974195	+	0.225707i	$0.0724693\pi$
$660$		0			0
$661$	−159.965	−	134.227i	−0.242005	−	0.203066i	0.513716	−	0.857961i	$-0.328269\pi$
$661$	−159.965	−	134.227i	−0.242005	−	0.203066i	−0.755720	+	0.654894i	$0.772713\pi$
$662$	1073.29	−	381.755i	1.62129	−	0.576669i
$663$		0			0
$664$	−588.466	−	228.969i	−0.886245	−	0.344833i
$665$	84.6355	−	146.593i	0.127271	−	0.220441i
$666$		0			0
$667$	−510.690	+	294.847i	−0.765652	+	0.442049i
$668$	−304.474	−	373.861i	−0.455799	−	0.559672i
$669$		0			0
$670$	−43.3208	+	235.567i	−0.0646578	+	0.351593i
$671$	236.514	+	41.7037i	0.352479	+	0.0621516i
$672$		0			0
$673$	−894.100	+	750.239i	−1.32853	+	1.11477i	−0.344109	+	0.938930i	$0.611819\pi$
$673$	−894.100	+	750.239i	−1.32853	+	1.11477i	−0.984419	+	0.175838i	$0.943736\pi$
$674$	704.911	+	413.904i	1.04586	+	0.614101i
$675$		0			0
$676$	−285.644	−	511.949i	−0.422550	−	0.757321i
$677$	−88.3923	+	74.1700i	−0.130565	+	0.109557i	−0.705732	−	0.708479i	$-0.749382\pi$
$677$	−88.3923	+	74.1700i	−0.130565	+	0.109557i	0.575167	+	0.818036i	$0.304937\pi$
$678$		0			0
$679$	−202.971	−	35.7892i	−0.298926	−	0.0527087i
$680$	−191.281	−	563.842i	−0.281295	−	0.829179i
$681$		0			0
$682$	−79.4166	+	213.314i	−0.116447	+	0.312777i
$683$	1124.02	−	648.952i	1.64571	−	0.950150i	0.666956	−	0.745097i	$-0.267597\pi$
$683$	1124.02	−	648.952i	1.64571	−	0.950150i	0.978751	−	0.205053i	$-0.0657366\pi$
$684$		0			0
$685$	188.702	−	326.842i	0.275478	−	0.477141i
$686$	363.813	−	300.756i	0.530340	−	0.438420i
$687$		0			0
$688$	−165.219	−	499.020i	−0.240144	−	0.725320i
$689$	−128.582	−	107.893i	−0.186621	−	0.156593i
$690$		0			0
$691$	399.004	−	1096.25i	0.577430	−	1.58648i	−0.215067	−	0.976599i	$-0.568997\pi$
$691$	399.004	−	1096.25i	0.577430	−	1.58648i	0.792497	−	0.609876i	$-0.208781\pi$
$692$	12.4747	+	0.183009i	0.0180270	+	0.000264464i
$693$		0			0
$694$	−137.321	−	1.00723i	−0.197869	−	0.00145134i
$695$	825.653	−	145.585i	1.18799	−	0.209475i
$696$		0			0
$697$	−1272.74	+	463.240i	−1.82603	+	0.664619i
$698$	510.398	−	599.286i	0.731229	−	0.858576i
$699$		0			0
$700$	−25.8294	+	67.8519i	−0.0368992	+	0.0969313i
$701$	188.390			0.268744			0.134372	−	0.990931i	$-0.457098\pi$
$701$	188.390			0.268744			0.134372	+	0.990931i	$0.457098\pi$
$702$		0			0
$703$			710.934i			1.01129i
$704$	93.2347	+	121.600i	0.132436	+	0.172728i
$705$		0			0
$706$	−108.823	+	127.775i	−0.154140	+	0.180985i
$707$	19.9217	+	54.7344i	0.0281778	+	0.0774178i
$708$		0			0
$709$	79.4255	+	450.444i	0.112025	+	0.635323i	0.988180	+	0.153295i	$0.0489885\pi$
$709$	79.4255	+	450.444i	0.112025	+	0.635323i	−0.876156	+	0.482028i	$0.839900\pi$
$710$	−394.298	−	2.89211i	−0.555350	−	0.00407339i
$711$		0			0
$712$	−433.495	−	263.162i	−0.608841	−	0.369610i
$713$	605.186	+	220.270i	0.848789	+	0.308934i
$714$		0			0
$715$	−30.9092	+	36.8362i	−0.0432297	+	0.0515191i
$716$	−927.239	−	177.559i	−1.29503	−	0.247988i
$717$		0			0
$718$	−918.757	+	759.516i	−1.27961	+	1.05782i
$719$	905.273	+	522.660i	1.25907	+	0.726926i	0.972894	−	0.231251i	$-0.0742818\pi$
$719$	905.273	+	522.660i	1.25907	+	0.726926i	0.286178	+	0.958176i	$0.407615\pi$
$720$		0			0
$721$	238.322	+	412.786i	0.330544	+	0.572518i
$722$	85.4010	−	229.388i	0.118284	−	0.317712i
$723$		0			0
$724$	399.336	+	345.190i	0.551569	+	0.476782i
$725$	−53.0789	+	301.025i	−0.0732123	+	0.415207i
$726$		0			0
$727$	29.5874	+	35.2609i	0.0406979	+	0.0485019i	0.786009	−	0.618214i	$-0.212144\pi$
$727$	29.5874	+	35.2609i	0.0406979	+	0.0485019i	−0.745312	+	0.666716i	$0.767699\pi$
$728$	97.9165	+	2.15491i	0.134501	+	0.00296004i
$729$		0			0
$730$	−264.144	−	155.098i	−0.361841	−	0.212463i
$731$	−370.693	−	441.774i	−0.507103	−	0.604342i
$732$		0			0
$733$	−179.034	+	1015.35i	−0.244248	+	1.38520i	0.577983	+	0.816049i	$0.303840\pi$
$733$	−179.034	+	1015.35i	−0.244248	+	1.38520i	−0.822232	+	0.569153i	$0.807271\pi$
$734$	−57.2986	+	311.576i	−0.0780635	+	0.424490i
$735$		0			0
$736$	342.114	−	266.316i	0.464828	−	0.361843i
$737$	−33.8127	−	58.5653i	−0.0458788	−	0.0794645i
$738$		0			0
$739$	477.275	+	275.555i	0.645839	+	0.372875i	0.786860	−	0.617131i	$-0.211705\pi$
$739$	477.275	+	275.555i	0.645839	+	0.372875i	−0.141021	+	0.990007i	$0.545039\pi$
$740$	124.251	+	770.596i	0.167906	+	1.04135i
$741$		0			0
$742$	−172.569	+	61.3804i	−0.232573	+	0.0827230i
$743$	309.908	−	369.334i	0.417104	−	0.497085i	−0.516052	−	0.856557i	$-0.672599\pi$
$743$	309.908	−	369.334i	0.417104	−	0.497085i	0.933156	+	0.359473i	$0.117043\pi$
$744$		0			0
$745$	368.936	+	134.282i	0.495216	+	0.180244i
$746$	−24.1428	+	13.7037i	−0.0323630	+	0.0183696i
$747$		0			0
$748$	144.336	+	86.1797i	0.192962	+	0.115214i
$749$	91.1611	+	517.000i	0.121710	+	0.690254i
$750$		0			0
$751$	−289.824	−	796.286i	−0.385918	−	1.06030i	−0.968822	−	0.247760i	$-0.920306\pi$
$751$	−289.824	−	796.286i	−0.385918	−	1.06030i	0.582903	−	0.812541i	$-0.301917\pi$
$752$	−395.485	+	444.180i	−0.525911	+	0.590664i
$753$		0			0
$754$	406.598	−	68.6232i	0.539255	−	0.0910122i
$755$			314.372i			0.416387i
$756$		0			0
$757$	774.769			1.02347			0.511736	−	0.859143i	$-0.329002\pi$
$757$	774.769			1.02347			0.511736	+	0.859143i	$0.329002\pi$
$758$	−129.369	−	766.526i	−0.170672	−	1.01125i
$759$		0			0
$760$	−102.316	+	513.874i	−0.134626	+	0.676150i
$761$	−496.314	+	180.644i	−0.652187	+	0.237377i	−0.646860	−	0.762609i	$-0.723918\pi$
$761$	−496.314	+	180.644i	−0.652187	+	0.237377i	−0.00532749	+	0.999986i	$0.501696\pi$
$762$		0			0
$763$	−35.1598	+	6.19963i	−0.0460810	+	0.00812533i
$764$	269.144	+	160.700i	0.352283	+	0.210340i
$765$		0			0
$766$	−280.474	−	494.130i	−0.366154	−	0.645078i
$767$	−149.145	+	409.774i	−0.194453	+	0.534255i
$768$		0			0
$769$	795.277	+	667.317i	1.03417	+	0.867772i	0.991341	−	0.131310i	$-0.0419185\pi$
$769$	795.277	+	667.317i	1.03417	+	0.867772i	0.0428291	+	0.999082i	$0.486363\pi$
$770$	17.5843	+	49.4377i	0.0228367	+	0.0642048i
$771$		0			0
$772$	16.3878	+	101.636i	0.0212277	+	0.131653i
$773$	−176.398	+	305.531i	−0.228200	+	0.395253i	−0.957275	−	0.289181i	$-0.906617\pi$
$773$	−176.398	+	305.531i	−0.228200	+	0.395253i	0.729075	+	0.684434i	$0.239951\pi$
$774$		0			0
$775$	289.107	−	166.916i	0.373042	−	0.215376i
$776$	630.560	−	96.9315i	0.812578	−	0.124912i
$777$		0			0
$778$	−50.2033	−	9.23237i	−0.0645287	−	0.0118668i
$779$	1173.80	+	206.972i	1.50680	+	0.265689i
$780$		0			0
$781$	85.2831	−	71.5610i	0.109197	−	0.0916275i
$782$	240.836	−	410.164i	0.307975	−	0.524506i
$783$		0			0
$784$	−355.620	+	576.225i	−0.453597	+	0.734981i
$785$	−727.784	+	610.683i	−0.927113	+	0.777940i
$786$		0			0
$787$	−580.832	−	102.416i	−0.738033	−	0.130135i	−0.208020	−	0.978125i	$-0.566702\pi$
$787$	−580.832	−	102.416i	−0.738033	−	0.130135i	−0.530013	+	0.847990i	$0.677813\pi$
$788$	435.703	+	376.627i	0.552923	+	0.477953i
$789$		0			0
$790$	727.543	+	270.863i	0.920940	+	0.342865i
$791$	−61.6376	+	35.5865i	−0.0779236	+	0.0449892i
$792$		0			0
$793$	−237.580	+	411.500i	−0.299596	+	0.518916i
$794$	540.210	+	653.471i	0.680365	+	0.823012i
$795$		0			0
$796$	−915.930	−	175.394i	−1.15067	−	0.220344i
$797$	−731.347	−	613.673i	−0.917625	−	0.769979i	0.0559292	−	0.998435i	$-0.482188\pi$
$797$	−731.347	−	613.673i	−0.917625	−	0.769979i	−0.973554	+	0.228456i	$0.926632\pi$
$798$		0			0
$799$	−223.158	+	613.123i	−0.279297	+	0.767363i
$800$	8.23986	−	224.581i	0.0102998	−	0.280726i
$801$		0			0
$802$	−2.23308	+	304.449i	−0.00278439	+	0.379612i
$803$	85.1703	−	15.0178i	0.106065	−	0.0187022i
$804$		0			0
$805$	139.511	−	50.7779i	0.173306	−	0.0630782i
$806$	−342.848	−	291.996i	−0.425370	−	0.362278i
$807$		0			0
$808$	−112.826	−	140.633i	−0.139637	−	0.174050i
$809$	303.198			0.374781			0.187390	−	0.982286i	$-0.439997\pi$
$809$	303.198			0.374781			0.187390	+	0.982286i	$0.439997\pi$
$810$		0			0
$811$			655.791i			0.808620i	0.914622	+	0.404310i	$0.132488\pi$
$811$			655.791i			0.808620i	−0.914622	+	0.404310i	$0.867512\pi$
$812$	160.080	−	420.518i	0.197143	−	0.517879i
$813$		0			0
$814$	−167.778	−	142.892i	−0.206115	−	0.175543i
$815$	239.126	+	656.994i	0.293406	+	0.806127i
$816$		0			0
$817$	88.1260	+	499.787i	0.107865	+	0.611735i
$818$	−4.85877	+	662.424i	−0.00593981	+	0.809809i
$819$		0			0
$820$	1308.48	+	19.1959i	1.59570	+	0.0234097i
$821$	603.451	+	219.638i	0.735020	+	0.267525i	0.682288	−	0.731083i	$-0.260985\pi$
$821$	603.451	+	219.638i	0.735020	+	0.267525i	0.0527318	+	0.998609i	$0.483207\pi$
$822$		0			0
$823$	191.436	−	228.144i	0.232607	−	0.277210i	−0.637097	−	0.770783i	$-0.719865\pi$
$823$	191.436	−	228.144i	0.232607	−	0.277210i	0.869704	+	0.493573i	$0.164309\pi$
$824$	−1109.08	−	973.008i	−1.34598	−	1.18084i
$825$		0			0
$826$	303.185	+	366.751i	0.367052	+	0.444008i
$827$	945.876	+	546.102i	1.14374	+	0.660340i	0.947355	−	0.320186i	$-0.103745\pi$
$827$	945.876	+	546.102i	1.14374	+	0.660340i	0.196388	+	0.980526i	$0.437079\pi$
$828$		0			0
$829$	−331.753	−	574.613i	−0.400184	−	0.693140i	0.593563	−	0.804787i	$-0.297721\pi$
$829$	−331.753	−	574.613i	−0.400184	−	0.693140i	−0.993748	+	0.111647i	$0.964387\pi$
$830$	627.259	+	233.528i	0.755734	+	0.281359i
$831$		0			0
$832$	−289.167	+	91.0547i	−0.347556	+	0.109441i
$833$	−128.998	+	731.582i	−0.154859	+	0.878250i
$834$		0			0
$835$	328.517	+	391.511i	0.393433	+	0.468875i
$836$	−72.0804	−	129.187i	−0.0862205	−	0.154530i
$837$		0			0
$838$	−402.006	+	684.649i	−0.479721	+	0.817003i
$839$	105.043	+	125.185i	0.125200	+	0.149207i	0.825003	−	0.565128i	$-0.191173\pi$
$839$	105.043	+	125.185i	0.125200	+	0.149207i	−0.699803	+	0.714336i	$0.746729\pi$
$840$		0			0
$841$	182.923	−	1037.41i	0.217506	−	1.23354i
$842$	−1282.02	−	235.763i	−1.52259	−	0.280003i
$843$		0			0
$844$	−52.6312	−	64.6254i	−0.0623592	−	0.0765704i
$845$	310.706	+	538.159i	0.367700	+	0.636874i
$846$		0			0
$847$	257.995	+	148.954i	0.304599	+	0.175860i
$848$	444.816	−	351.534i	0.524547	−	0.414545i
$849$		0			0
$850$	−82.6237	−	232.294i	−0.0972044	−	0.273287i
$851$	−400.809	+	477.665i	−0.470986	+	0.561299i
$852$		0			0
$853$	443.225	+	161.321i	0.519607	+	0.189121i	0.588492	−	0.808503i	$-0.299722\pi$
$853$	443.225	+	161.321i	0.519607	+	0.189121i	−0.0688849	+	0.997625i	$0.521944\pi$
$854$	255.948	+	450.920i	0.299704	+	0.528010i
$855$		0			0
$856$	−781.344	−	1424.84i	−0.912785	−	1.66453i
$857$	−164.122	−	930.785i	−0.191508	−	1.08610i	−0.917304	−	0.398187i	$-0.869640\pi$
$857$	−164.122	−	930.785i	−0.191508	−	1.08610i	0.725796	−	0.687910i	$-0.241472\pi$
$858$		0			0
$859$	326.269	+	896.417i	0.379824	+	1.04356i	0.971429	+	0.237330i	$0.0762724\pi$
$859$	326.269	+	896.417i	0.379824	+	1.04356i	−0.591605	+	0.806228i	$0.701505\pi$
$860$	182.870	+	526.329i	0.212640	+	0.612010i
$861$		0			0
$862$	82.6541	+	489.733i	0.0958865	+	0.568136i
$863$		−	1620.35i		−	1.87758i	−0.344486	−	0.938791i	$-0.611947\pi$
$863$		−	1620.35i		−	1.87758i	0.344486	−	0.938791i	$-0.388053\pi$
$864$		0			0
$865$	−13.2244			−0.0152883
$866$	840.827	−	141.910i	0.970932	−	0.163868i
$867$		0			0
$868$	−464.193	+	161.281i	−0.534785	+	0.185808i
$869$	−205.970	+	74.9669i	−0.237020	+	0.0862681i
$870$		0			0
$871$	131.764	−	23.2335i	0.151279	−	0.0266745i
$872$	96.8993	−	53.1372i	0.111123	−	0.0609371i
$873$		0			0
$874$	−364.018	+	206.621i	−0.416497	+	0.236408i
$875$	120.018	−	329.746i	0.137163	−	0.376853i
$876$		0			0
$877$	−736.316	−	617.843i	−0.839585	−	0.704496i	0.117885	−	0.993027i	$-0.462389\pi$
$877$	−736.316	−	617.843i	−0.839585	−	0.704496i	−0.957470	+	0.288532i	$0.906833\pi$
$878$	1455.44	−	517.679i	1.65767	−	0.589611i
$879$		0			0
$880$	−100.708	−	127.431i	−0.114440	−	0.144808i
$881$	−692.400	+	1199.27i	−0.785925	+	1.36126i	0.142520	+	0.989792i	$0.454480\pi$
$881$	−692.400	+	1199.27i	−0.785925	+	1.36126i	−0.928445	+	0.371470i	$0.878854\pi$
$882$		0			0
$883$	810.077	−	467.698i	0.917415	−	0.529670i	0.0346053	−	0.999401i	$-0.488983\pi$
$883$	810.077	−	467.698i	0.917415	−	0.529670i	0.882809	+	0.469731i	$0.155649\pi$
$884$	−257.893	+	210.029i	−0.291734	+	0.237590i
$885$		0			0
$886$	−259.573	+	1411.49i	−0.292972	+	1.59311i
$887$	−815.590	−	143.810i	−0.919492	−	0.162131i	−0.306182	−	0.951973i	$-0.599052\pi$
$887$	−815.590	−	143.810i	−0.919492	−	0.162131i	−0.613311	+	0.789842i	$0.710163\pi$
$888$		0			0
$889$	39.9783	−	33.5458i	0.0449700	−	0.0377343i
$890$	463.541	+	272.178i	0.520832	+	0.305818i
$891$		0			0
$892$	937.211	−	522.920i	1.05068	−	0.586234i
$893$	439.848	−	369.077i	0.492551	−	0.413300i
$894$		0			0
$895$	985.515	+	173.773i	1.10113	+	0.194160i
$896$	−74.0890	+	322.410i	−0.0826886	+	0.359833i
$897$		0			0
$898$	−141.562	+	380.239i	−0.157642	+	0.423428i
$899$	−1791.77	+	1034.48i	−1.99306	+	1.15070i
$900$		0			0
$901$	310.999	−	538.667i	0.345171	−	0.597854i
$902$	−284.769	+	235.412i	−0.315708	+	0.260989i
$903$		0			0
$904$	145.291	−	165.610i	0.160720	−	0.183196i
$905$	−428.612	−	359.648i	−0.473604	−	0.397401i
$906$		0			0
$907$	185.561	−	509.825i	0.204588	−	0.562100i	−0.794385	−	0.607414i	$-0.792207\pi$
$907$	185.561	−	509.825i	0.204588	−	0.562100i	0.998973	+	0.0453144i	$0.0144290\pi$
$908$	−16.0861	+	1096.50i	−0.0177159	+	1.20759i
$909$		0			0
$910$	−103.812	−	0.761446i	−0.114080	−	0.000836754i
$911$	33.3668	−	5.88346i	0.0366265	−	0.00645824i	−0.155305	−	0.987867i	$-0.549636\pi$
$911$	33.3668	−	5.88346i	0.0366265	−	0.00645824i	0.191931	+	0.981408i	$0.438525\pi$
$912$		0			0
$913$	−177.579	+	64.6336i	−0.194501	+	0.0707925i
$914$	1048.67	−	1231.30i	1.14734	−	1.34715i
$915$		0			0
$916$	735.868	+	280.126i	0.803350	+	0.305814i
$917$	274.162			0.298977
$918$		0			0
$919$		−	745.594i		−	0.811310i	−0.914026	−	0.405655i	$-0.867044\pi$
$919$		−	745.594i		−	0.811310i	0.914026	−	0.405655i	$-0.132956\pi$
$920$	−358.456	+	287.581i	−0.389626	+	0.312588i
$921$		0			0
$922$	−239.984	+	281.778i	−0.260286	+	0.305616i
$923$	75.3348	+	206.981i	0.0816195	+	0.224248i
$924$		0			0
$925$	56.1261	+	318.307i	0.0606769	+	0.344116i
$926$	−1019.03	−	7.47441i	−1.10046	−	0.00807171i
$927$		0			0
$928$	−51.0672	+	1391.86i	−0.0550293	+	1.49985i
$929$	669.948	+	243.841i	0.721149	+	0.262477i	0.676414	−	0.736522i	$-0.263533\pi$
$929$	669.948	+	243.841i	0.721149	+	0.262477i	0.0447356	+	0.998999i	$0.485755\pi$
$930$		0			0
$931$	420.210	−	500.787i	0.451354	−	0.537902i
$932$	−206.842	+	1080.16i	−0.221933	+	1.15897i
$933$		0			0
$934$	638.068	−	527.476i	0.683156	−	0.564749i
$935$	−154.317	−	89.0952i	−0.165045	−	0.0952890i
$936$		0			0
$937$	−430.456	−	745.572i	−0.459398	−	0.795701i	0.539531	−	0.841966i	$-0.318602\pi$
$937$	−430.456	−	745.572i	−0.459398	−	0.795701i	−0.998929	+	0.0462645i	$0.985268\pi$
$938$	50.9396	−	136.824i	0.0543066	−	0.145868i
$939$		0			0
$940$	412.257	−	476.923i	0.438572	−	0.507365i
$941$	−87.2608	+	494.881i	−0.0927320	+	0.525909i	0.902687	+	0.430298i	$0.141592\pi$
$941$	−87.2608	+	494.881i	−0.0927320	+	0.525909i	−0.995419	+	0.0956111i	$0.969519\pi$
$942$		0			0
$943$	671.970	+	800.823i	0.712587	+	0.849229i
$944$	−1253.44	−	773.565i	−1.32779	−	0.819454i
$945$		0			0
$946$	−135.661	−	79.6560i	−0.143404	−	0.0842030i
$947$	−157.029	−	187.140i	−0.165817	−	0.197613i	0.676737	−	0.736225i	$-0.263393\pi$
$947$	−157.029	−	187.140i	−0.165817	−	0.197613i	−0.842554	+	0.538612i	$0.818949\pi$
$948$		0			0
$949$	−29.7127	+	168.509i	−0.0313095	+	0.177565i
$950$	−39.2421	+	213.389i	−0.0413075	+	0.224620i
$951$		0			0
$952$	55.1432	+	358.718i	0.0579235	+	0.376805i
$953$	−263.010	−	455.547i	−0.275981	−	0.478014i	0.694401	−	0.719588i	$-0.255669\pi$
$953$	−263.010	−	455.547i	−0.275981	−	0.478014i	−0.970382	+	0.241575i	$0.922336\pi$
$954$		0			0
$955$	−287.757	−	166.136i	−0.301316	−	0.173965i
$956$	−985.802	+	158.950i	−1.03117	+	0.166266i
$957$		0			0
$958$	1294.63	−	460.480i	1.35138	−	0.480668i
$959$	−147.873	+	176.228i	−0.154195	+	0.183762i
$960$		0			0
$961$	1220.26	+	444.140i	1.26978	+	0.462164i
$962$	379.194	−	215.235i	0.394173	−	0.223737i
$963$		0			0
$964$	−39.0334	+	65.3740i	−0.0404911	+	0.0678154i
$965$	−18.9493	−	107.467i	−0.0196366	−	0.111365i
$966$		0			0
$967$	569.494	+	1564.67i	0.588929	+	1.61807i	0.772467	+	0.635055i	$0.219023\pi$
$967$	569.494	+	1564.67i	0.588929	+	1.61807i	−0.183538	+	0.983013i	$0.558755\pi$
$968$	−904.390	−	180.071i	−0.934287	−	0.186023i
$969$		0			0
$970$	−666.806	+	112.539i	−0.687429	+	0.116020i
$971$			25.8021i			0.0265727i	0.999912	+	0.0132863i	$0.00422930\pi$
$971$			25.8021i			0.0265727i	−0.999912	+	0.0132863i	$0.995771\pi$
$972$		0			0
$973$	−511.046			−0.525227
$974$	5.06615	+	30.0174i	0.00520139	+	0.0308187i
$975$		0			0
$976$	−1198.67	−	1067.26i	−1.22815	−	1.09351i
$977$	677.223	−	246.489i	0.693165	−	0.252292i	0.0286755	−	0.999589i	$-0.490871\pi$
$977$	677.223	−	246.489i	0.693165	−	0.252292i	0.664490	+	0.747297i	$0.268649\pi$
$978$		0			0
$979$	−149.464	+	26.3545i	−0.152670	+	0.0269198i
$980$	367.952	−	616.255i	0.375461	−	0.628831i
$981$		0			0
$982$	−472.389	−	832.239i	−0.481048	−	0.847494i
$983$	−212.414	+	583.604i	−0.216088	+	0.593697i	−0.999617	−	0.0276579i	$-0.991195\pi$
$983$	−212.414	+	583.604i	−0.216088	+	0.593697i	0.783530	+	0.621355i	$0.213417\pi$
$984$		0			0
$985$	−467.646	−	392.402i	−0.474768	−	0.398377i
$986$	512.067	+	1439.66i	0.519338	+	1.46010i
$987$		0			0
$988$	288.957	−	46.5913i	0.292467	−	0.0471571i
$989$	−222.559	+	385.483i	−0.225034	+	0.389771i
$990$		0			0
$991$	−441.847	+	255.101i	−0.445860	+	0.257417i	−0.706080	−	0.708132i	$-0.749538\pi$
$991$	−441.847	+	255.101i	−0.445860	+	0.257417i	0.260220	+	0.965549i	$0.416205\pi$
$992$	1200.31	−	934.376i	1.20999	−	0.941911i
$993$		0			0
$994$	236.389	+	43.4719i	0.237816	+	0.0437343i
$995$	973.496	+	171.654i	0.978388	+	0.172516i
$996$		0			0
$997$	−698.282	+	585.928i	−0.700383	+	0.587691i	−0.921883	−	0.387469i	$-0.873349\pi$
$997$	−698.282	+	585.928i	−0.700383	+	0.587691i	0.221499	+	0.975161i	$0.428905\pi$
$998$	505.898	−	861.585i	0.506912	−	0.863312i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.j.a.199.2		204
3.2	odd	2		108.3.j.a.103.33	yes	204
4.3	odd	2	inner	324.3.j.a.199.13		204
12.11	even	2		108.3.j.a.103.22	yes	204
27.11	odd	18		108.3.j.a.43.22	✓	204
27.16	even	9	inner	324.3.j.a.127.13		204
108.11	even	18		108.3.j.a.43.33	yes	204
108.43	odd	18	inner	324.3.j.a.127.2		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.j.a.43.22	✓	204	27.11	odd	18
108.3.j.a.43.33	yes	204	108.11	even	18
108.3.j.a.103.22	yes	204	12.11	even	2
108.3.j.a.103.33	yes	204	3.2	odd	2
324.3.j.a.127.2		204	108.43	odd	18	inner
324.3.j.a.127.13		204	27.16	even	9	inner
324.3.j.a.199.2		204	1.1	even	1	trivial
324.3.j.a.199.13		204	4.3	odd	2	inner

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)

\(f(q)\)	\(=\)	\(q+(-1.97211 + 0.332841i) q^{2} +(3.77843 - 1.31280i) q^{4} +(-3.98424 + 1.45015i) q^{5} +(2.54522 - 0.448791i) q^{7} +(-7.01454 + 3.84660i) q^{8} +O(q^{10})\)	\(q+(-1.97211 + 0.332841i) q^{2} +(3.77843 - 1.31280i) q^{4} +(-3.98424 + 1.45015i) q^{5} +(2.54522 - 0.448791i) q^{7} +(-7.01454 + 3.84660i) q^{8} +(7.37470 - 4.18597i) q^{10} +(-0.818869 + 2.24982i) q^{11} +(-3.62870 - 3.04484i) q^{13} +(-4.87007 + 1.73222i) q^{14} +(12.5531 - 9.92063i) q^{16} +(8.77670 - 15.2017i) q^{17} +(-13.3776 + 7.72359i) q^{19} +(-13.1505 + 10.7098i) q^{20} +(0.866067 - 4.70945i) q^{22} +(-13.3426 - 2.35266i) q^{23} +(-5.37983 + 4.51422i) q^{25} +(8.16965 + 4.79699i) q^{26} +(9.02777 - 5.03708i) q^{28} +(33.3419 - 27.9772i) q^{29} +(-46.8128 - 8.25437i) q^{31} +(-21.4542 + 23.7428i) q^{32} +(-12.2489 + 32.9007i) q^{34} +(-9.48996 + 5.47903i) q^{35} +(23.0118 - 39.8576i) q^{37} +(23.8115 - 19.6844i) q^{38} +(22.3695 - 25.4979i) q^{40} +(-59.1080 - 49.5975i) q^{41} +(11.2366 - 30.8724i) q^{43} +(-0.140482 + 9.57582i) q^{44} +(27.0962 + 0.198746i) q^{46} +(-36.6059 + 6.45461i) q^{47} +(-39.7682 + 14.4744i) q^{49} +(9.10711 - 10.6932i) q^{50} +(-17.7081 - 6.74099i) q^{52} +35.4346 q^{53} -10.1513i q^{55} +(-16.1272 + 12.9385i) q^{56} +(-56.4420 + 66.2717i) q^{58} +(-31.4856 - 86.5061i) q^{59} +(-17.4186 - 98.7856i) q^{61} +(95.0675 + 0.697304i) q^{62} +(34.4074 - 53.9642i) q^{64} +(18.8731 + 6.86925i) q^{65} +(-18.1558 + 21.6372i) q^{67} +(13.2055 - 68.9606i) q^{68} +(16.8916 - 13.9639i) q^{70} +(-40.2696 - 23.2497i) q^{71} +(-18.0611 - 31.2827i) q^{73} +(-32.1155 + 86.2627i) q^{74} +(-40.4070 + 46.7452i) q^{76} +(-1.07450 + 6.09379i) q^{77} +(58.8468 + 70.1309i) q^{79} +(-35.6284 + 57.7301i) q^{80} +(133.076 + 78.1382i) q^{82} +(50.7354 + 60.4641i) q^{83} +(-12.9238 + 73.2948i) q^{85} +(-11.8843 + 64.6238i) q^{86} +(-2.91018 - 18.9313i) q^{88} +(31.6951 + 54.8975i) q^{89} +(-10.6023 - 6.12126i) q^{91} +(-53.5028 + 8.62676i) q^{92} +(70.0426 - 24.9132i) q^{94} +(42.0995 - 50.1722i) q^{95} +(-74.9366 - 27.2747i) q^{97} +(73.6096 - 41.7817i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) \) 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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