LMFDB - Embedded newform 324.3.j.a.307.13

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			307.13
Character	$\chi$	$=$	324.307
Dual form			324.3.j.a.19.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.518880 - 1.93152i) q^{2} +(-3.46153 + 2.00445i) q^{4} +(-1.09499 + 6.21002i) q^{5} +(-5.65814 - 6.74311i) q^{7} +(5.66776 + 5.64593i) q^{8} +O(q^{10})$	\(q+(-0.518880 - 1.93152i) q^{2} +(-3.46153 + 2.00445i) q^{4} +(-1.09499 + 6.21002i) q^{5} +(-5.65814 - 6.74311i) q^{7} +(5.66776 + 5.64593i) q^{8} +(12.5629 - 1.10726i) q^{10} +(-3.98532 + 0.702720i) q^{11} +(11.3127 - 4.11749i) q^{13} +(-10.0885 + 14.4277i) q^{14} +(7.96433 - 13.8769i) q^{16} +(7.63358 - 13.2217i) q^{17} +(20.6326 - 11.9123i) q^{19} +(-8.65735 - 23.6910i) q^{20} +(3.42522 + 7.33310i) q^{22} +(11.4927 - 13.6965i) q^{23} +(-13.8730 - 5.04937i) q^{25} +(-13.8229 - 19.7142i) q^{26} +(33.1021 + 12.0000i) q^{28} +(40.6859 + 14.8084i) q^{29} +(31.8949 - 38.0109i) q^{31} +(-30.9361 - 8.18277i) q^{32} +(-29.4990 - 7.88389i) q^{34} +(48.0705 - 27.7535i) q^{35} +(-14.4238 + 24.9828i) q^{37} +(-33.7146 - 33.6713i) q^{38} +(-41.2675 + 29.0146i) q^{40} +(-40.7670 + 14.8380i) q^{41} +(-19.2340 + 3.39148i) q^{43} +(12.3867 - 10.4209i) q^{44} +(-32.4184 - 15.0916i) q^{46} +(-2.31031 - 2.75332i) q^{47} +(-4.94621 + 28.0514i) q^{49} +(-2.55450 + 29.4160i) q^{50} +(-30.9059 + 36.9286i) q^{52} -81.1632 q^{53} -25.5184i q^{55} +(6.00214 - 70.1638i) q^{56} +(7.49168 - 86.2693i) q^{58} +(48.7001 + 8.58715i) q^{59} +(79.8933 - 67.0384i) q^{61} +(-89.9683 - 41.8825i) q^{62} +(0.246975 + 63.9995i) q^{64} +(13.1823 + 74.7607i) q^{65} +(23.6170 + 64.8871i) q^{67} +(0.0785545 + 61.0686i) q^{68} +(-78.5492 - 78.4483i) q^{70} +(-48.4794 - 27.9896i) q^{71} +(12.9295 + 22.3946i) q^{73} +(55.7389 + 14.8968i) q^{74} +(-47.5428 + 82.5917i) q^{76} +(27.2880 + 22.8974i) q^{77} +(28.9877 - 79.6430i) q^{79} +(77.4552 + 64.6538i) q^{80} +(49.8130 + 71.0430i) q^{82} +(21.4076 - 58.8168i) q^{83} +(73.7486 + 61.8824i) q^{85} +(16.5309 + 35.3911i) q^{86} +(-26.5554 - 18.5180i) q^{88} +(11.6524 + 20.1826i) q^{89} +(-91.7735 - 52.9855i) q^{91} +(-12.3284 + 70.4475i) q^{92} +(-4.11931 + 5.89104i) q^{94} +(51.3827 + 141.173i) q^{95} +(-16.4127 - 93.0811i) q^{97} +(56.7482 - 5.00160i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−0.518880	−	1.93152i	−0.259440	−	0.965759i
$2$	−0.518880	−	1.93152i	−0.259440	−	0.965759i
$3$		0			0
$3$		0			0
$4$	−3.46153	+	2.00445i	−0.865382	+	0.501114i
$5$	−1.09499	+	6.21002i	−0.218999	+	1.24200i	0.654832	+	0.755774i	$0.272739\pi$
$5$	−1.09499	+	6.21002i	−0.218999	+	1.24200i	−0.873831	+	0.486230i	$0.838372\pi$
$6$		0			0
$7$	−5.65814	−	6.74311i	−0.808306	−	0.963301i	0.191529	−	0.981487i	$-0.438655\pi$
$7$	−5.65814	−	6.74311i	−0.808306	−	0.963301i	−0.999835	+	0.0181856i	$0.994211\pi$
$8$	5.66776	+	5.64593i	0.708470	+	0.705741i
$9$		0			0
$10$	12.5629	−	1.10726i	1.25629	−	0.110726i
$11$	−3.98532	+	0.702720i	−0.362302	+	0.0638836i	−0.351836	−	0.936062i	$-0.614443\pi$
$11$	−3.98532	+	0.702720i	−0.362302	+	0.0638836i	−0.0104659	+	0.999945i	$0.503331\pi$
$12$		0			0
$13$	11.3127	−	4.11749i	0.870208	−	0.316730i	0.131956	−	0.991256i	$-0.457874\pi$
$13$	11.3127	−	4.11749i	0.870208	−	0.316730i	0.738251	+	0.674526i	$0.235652\pi$
$14$	−10.0885	+	14.4277i	−0.720610	+	1.03055i
$15$		0			0
$16$	7.96433	−	13.8769i	0.497770	−	0.867309i
$17$	7.63358	−	13.2217i	0.449034	−	0.777750i	−0.549289	−	0.835632i	$-0.685101\pi$
$17$	7.63358	−	13.2217i	0.449034	−	0.777750i	0.998323	+	0.0578824i	$0.0184348\pi$
$18$		0			0
$19$	20.6326	−	11.9123i	1.08593	−	0.626961i	0.153438	−	0.988158i	$-0.450965\pi$
$19$	20.6326	−	11.9123i	1.08593	−	0.626961i	0.932489	+	0.361198i	$0.117632\pi$
$20$	−8.65735	−	23.6910i	−0.432868	−	1.18455i
$21$		0			0
$22$	3.42522	+	7.33310i	0.155692	+	0.333323i
$23$	11.4927	−	13.6965i	0.499684	−	0.595501i	−0.455969	−	0.889996i	$-0.650707\pi$
$23$	11.4927	−	13.6965i	0.499684	−	0.595501i	0.955653	+	0.294495i	$0.0951515\pi$
$24$		0			0
$25$	−13.8730	−	5.04937i	−0.554921	−	0.201975i
$26$	−13.8229	−	19.7142i	−0.531652	−	0.758239i
$27$		0			0
$28$	33.1021	+	12.0000i	1.18222	+	0.428570i
$29$	40.6859	+	14.8084i	1.40296	+	0.510636i	0.929056	−	0.369940i	$-0.120622\pi$
$29$	40.6859	+	14.8084i	1.40296	+	0.510636i	0.473905	+	0.880576i	$0.342844\pi$
$30$		0			0
$31$	31.8949	−	38.0109i	1.02887	−	1.22616i	0.0551316	−	0.998479i	$-0.482442\pi$
$31$	31.8949	−	38.0109i	1.02887	−	1.22616i	0.973736	−	0.227678i	$-0.0731134\pi$
$32$	−30.9361	−	8.18277i	−0.966753	−	0.255711i
$33$		0			0
$34$	−29.4990	−	7.88389i	−0.867617	−	0.231879i
$35$	48.0705	−	27.7535i	1.37344	−	0.792957i
$36$		0			0
$37$	−14.4238	+	24.9828i	−0.389833	+	0.675210i	−0.992427	−	0.122838i	$-0.960800\pi$
$37$	−14.4238	+	24.9828i	−0.389833	+	0.675210i	0.602594	+	0.798048i	$0.294134\pi$
$38$	−33.7146	−	33.6713i	−0.887226	−	0.886086i
$39$		0			0
$40$	−41.2675	+	29.0146i	−1.03169	+	0.725366i
$41$	−40.7670	+	14.8380i	−0.994316	+	0.361902i	−0.787390	−	0.616455i	$-0.788568\pi$
$41$	−40.7670	+	14.8380i	−0.994316	+	0.361902i	−0.206926	+	0.978357i	$0.566346\pi$
$42$		0			0
$43$	−19.2340	+	3.39148i	−0.447303	+	0.0788716i	−0.392762	−	0.919640i	$-0.628481\pi$
$43$	−19.2340	+	3.39148i	−0.447303	+	0.0788716i	−0.0545406	+	0.998512i	$0.517369\pi$
$44$	12.3867	−	10.4209i	0.281517	−	0.236838i
$45$		0			0
$46$	−32.4184	−	15.0916i	−0.704748	−	0.328078i
$47$	−2.31031	−	2.75332i	−0.0491555	−	0.0585812i	0.740907	−	0.671608i	$-0.234396\pi$
$47$	−2.31031	−	2.75332i	−0.0491555	−	0.0585812i	−0.790062	+	0.613027i	$0.789952\pi$
$48$		0			0
$49$	−4.94621	+	28.0514i	−0.100943	+	0.572477i
$50$	−2.55450	+	29.4160i	−0.0510901	+	0.588320i
$51$		0			0
$52$	−30.9059	+	36.9286i	−0.594344	+	0.710165i
$53$	−81.1632			−1.53138			−0.765690	−	0.643209i	$-0.777602\pi$
$53$	−81.1632			−1.53138			−0.765690	+	0.643209i	$0.777602\pi$
$54$		0			0
$55$		−	25.5184i		−	0.463971i
$56$	6.00214	−	70.1638i	0.107181	−	1.25292i
$57$		0			0
$58$	7.49168	−	86.2693i	0.129167	−	1.48740i
$59$	48.7001	+	8.58715i	0.825426	+	0.145545i	0.570377	−	0.821383i	$-0.306797\pi$
$59$	48.7001	+	8.58715i	0.825426	+	0.145545i	0.255049	+	0.966928i	$0.417908\pi$
$60$		0			0
$61$	79.8933	−	67.0384i	1.30973	−	1.09899i	0.321350	−	0.946961i	$-0.395863\pi$
$61$	79.8933	−	67.0384i	1.30973	−	1.09899i	0.988376	−	0.152030i	$-0.0485809\pi$
$62$	−89.9683	−	41.8825i	−1.45110	−	0.675524i
$63$		0			0
$64$	0.246975	+	63.9995i	0.00385898	+	0.999993i
$65$	13.1823	+	74.7607i	0.202805	+	1.15016i
$66$		0			0
$67$	23.6170	+	64.8871i	0.352492	+	0.968464i	0.981567	+	0.191119i	$0.0612116\pi$
$67$	23.6170	+	64.8871i	0.352492	+	0.968464i	−0.629075	+	0.777345i	$0.716566\pi$
$68$	0.0785545	+	61.0686i	0.00115521	+	0.898067i
$69$		0			0
$70$	−78.5492	−	78.4483i	−1.12213	−	1.12069i
$71$	−48.4794	−	27.9896i	−0.682808	−	0.394219i	0.118104	−	0.993001i	$-0.462318\pi$
$71$	−48.4794	−	27.9896i	−0.682808	−	0.394219i	−0.800912	+	0.598782i	$0.795652\pi$
$72$		0			0
$73$	12.9295	+	22.3946i	0.177117	+	0.306776i	0.940892	−	0.338707i	$-0.109990\pi$
$73$	12.9295	+	22.3946i	0.177117	+	0.306776i	−0.763775	+	0.645483i	$0.776656\pi$
$74$	55.7389	+	14.8968i	0.753229	+	0.201308i
$75$		0			0
$76$	−47.5428	+	82.5917i	−0.625563	+	1.08673i
$77$	27.2880	+	22.8974i	0.354390	+	0.297369i
$78$		0			0
$79$	28.9877	−	79.6430i	0.366933	−	1.00814i	−0.609589	−	0.792718i	$-0.708665\pi$
$79$	28.9877	−	79.6430i	0.366933	−	1.00814i	0.976521	−	0.215421i	$-0.0691125\pi$
$80$	77.4552	+	64.6538i	0.968190	+	0.808172i
$81$		0			0
$82$	49.8130	+	71.0430i	0.607476	+	0.866378i
$83$	21.4076	−	58.8168i	0.257922	−	0.708636i	−0.741373	−	0.671094i	$-0.765825\pi$
$83$	21.4076	−	58.8168i	0.257922	−	0.708636i	0.999295	−	0.0375425i	$-0.0119530\pi$
$84$		0			0
$85$	73.7486	+	61.8824i	0.867631	+	0.728028i
$86$	16.5309	+	35.3911i	0.192219	+	0.411524i
$87$		0			0
$88$	−26.5554	−	18.5180i	−0.301765	−	0.210432i
$89$	11.6524	+	20.1826i	0.130926	+	0.226771i	0.924034	−	0.382311i	$-0.124872\pi$
$89$	11.6524	+	20.1826i	0.130926	+	0.226771i	−0.793108	+	0.609081i	$0.791538\pi$
$90$		0			0
$91$	−91.7735	−	52.9855i	−1.00850	−	0.582258i
$92$	−12.3284	+	70.4475i	−0.134004	+	0.765734i
$93$		0			0
$94$	−4.11931	+	5.89104i	−0.0438224	+	0.0626706i
$95$	51.3827	+	141.173i	0.540871	+	1.48603i
$96$		0			0
$97$	−16.4127	−	93.0811i	−0.169203	−	0.959599i	−0.944624	−	0.328154i	$-0.893573\pi$
$97$	−16.4127	−	93.0811i	−0.169203	−	0.959599i	0.775421	−	0.631445i	$-0.217538\pi$
$98$	56.7482	−	5.00160i	0.579063	−	0.0510368i
$99$		0			0
$100$	58.1430	−	10.3293i	0.581430	−	0.103293i
$101$	103.010	−	86.4360i	1.01990	−	0.855802i	0.0302891	−	0.999541i	$-0.490357\pi$
$101$	103.010	−	86.4360i	1.01990	−	0.855802i	0.989616	+	0.143740i	$0.0459128\pi$
$102$		0			0
$103$	−63.9321	−	11.2730i	−0.620700	−	0.109446i	−0.145550	−	0.989351i	$-0.546495\pi$
$103$	−63.9321	−	11.2730i	−0.620700	−	0.109446i	−0.475150	+	0.879905i	$0.657606\pi$
$104$	87.3647	+	40.5338i	0.840045	+	0.389748i
$105$		0			0
$106$	42.1140	+	156.768i	0.397302	+	1.47894i
$107$			53.0300i			0.495608i	0.968810	+	0.247804i	$0.0797089\pi$
$107$			53.0300i			0.495608i	−0.968810	+	0.247804i	$0.920291\pi$
$108$		0			0
$109$	193.535			1.77555			0.887773	−	0.460281i	$-0.152251\pi$
$109$	193.535			1.77555			0.887773	+	0.460281i	$0.152251\pi$
$110$	−49.2893	+	13.2410i	−0.448084	+	0.120373i
$111$		0			0
$112$	−138.637	+	24.8134i	−1.23783	+	0.221548i
$113$	13.0720	−	74.1349i	0.115681	−	0.656061i	−0.870729	−	0.491762i	$-0.836353\pi$
$113$	13.0720	−	74.1349i	0.115681	−	0.656061i	0.986411	−	0.164299i	$-0.0525360\pi$
$114$		0			0
$115$	72.4711	+	86.3677i	0.630184	+	0.751024i
$116$	−170.518	+	30.2931i	−1.46998	+	0.261148i
$117$		0			0
$118$	−8.68332	−	98.5209i	−0.0735874	−	0.834923i
$119$	−132.348	+	23.3364i	−1.11216	+	0.196105i
$120$		0			0
$121$	−98.3138	+	35.7833i	−0.812511	+	0.295730i
$122$	−170.941	−	119.530i	−1.40116	−	0.979757i
$123$		0			0
$124$	−34.2140	+	195.508i	−0.275919	+	1.57667i
$125$	−32.2752	+	55.9023i	−0.258202	+	0.447218i
$126$		0			0
$127$	−27.2780	+	15.7489i	−0.214787	+	0.124007i	−0.603534	−	0.797337i	$-0.706241\pi$
$127$	−27.2780	+	15.7489i	−0.214787	+	0.124007i	0.388747	+	0.921345i	$0.372908\pi$
$128$	123.488	−	33.6851i	0.964751	−	0.263165i
$129$		0			0
$130$	137.562	−	64.2538i	1.05817	−	0.494260i
$131$	52.0385	−	62.0171i	0.397240	−	0.473413i	−0.529936	−	0.848038i	$-0.677784\pi$
$131$	52.0385	−	62.0171i	0.397240	−	0.473413i	0.927176	+	0.374625i	$0.122229\pi$
$132$		0			0
$133$	−197.068	−	71.7269i	−1.48171	−	0.539300i
$134$	113.076	−	79.2852i	0.843852	−	0.591681i
$135$		0			0
$136$	117.914	−	31.8390i	0.867017	−	0.234111i
$137$	95.7424	+	34.8474i	0.698850	+	0.254360i	0.666920	−	0.745130i	$-0.267612\pi$
$137$	95.7424	+	34.8474i	0.698850	+	0.254360i	0.0319300	+	0.999490i	$0.489835\pi$
$138$		0			0
$139$	−141.211	+	168.289i	−1.01591	+	1.21071i	−0.0385168	+	0.999258i	$0.512263\pi$
$139$	−141.211	+	168.289i	−1.01591	+	1.21071i	−0.977389	+	0.211451i	$0.932181\pi$
$140$	−110.767	+	192.425i	−0.791190	+	1.37446i
$141$		0			0
$142$	−28.9074	+	108.162i	−0.203573	+	0.761704i
$143$	−42.1913	+	24.3592i	−0.295044	+	0.170344i
$144$		0			0
$145$	−136.512	+	236.445i	−0.941459	+	1.63065i
$146$	36.5467	−	36.5938i	0.250320	−	0.250642i
$147$		0			0
$148$	−0.148430	−	115.390i	−0.00100291	−	0.779665i
$149$	109.046	−	39.6894i	0.731850	−	0.266372i	0.0509025	−	0.998704i	$-0.483790\pi$
$149$	109.046	−	39.6894i	0.731850	−	0.266372i	0.680948	+	0.732332i	$0.261568\pi$
$150$		0			0
$151$	113.127	−	19.9473i	0.749183	−	0.132101i	0.213996	−	0.976835i	$-0.431352\pi$
$151$	113.127	−	19.9473i	0.749183	−	0.132101i	0.535188	+	0.844733i	$0.320241\pi$
$152$	184.196	+	48.9746i	1.21182	+	0.322201i
$153$		0			0
$154$	30.0675	−	64.5883i	0.195243	−	0.419405i
$155$	201.124	+	239.690i	1.29757	+	1.54639i
$156$		0			0
$157$	−3.14219	+	17.8203i	−0.0200140	+	0.113505i	−0.993178	−	0.116607i	$-0.962798\pi$
$157$	−3.14219	+	17.8203i	−0.0200140	+	0.113505i	0.973164	+	0.230112i	$0.0739093\pi$
$158$	−168.873	−	14.6650i	−1.06882	−	0.0928167i
$159$		0			0
$160$	84.6900	−	183.154i	0.529312	−	1.14471i
$161$	−157.385			−0.977544
$162$		0			0
$163$		−	111.870i		−	0.686322i	−0.939277	−	0.343161i	$-0.888502\pi$
$163$		−	111.870i		−	0.686322i	0.939277	−	0.343161i	$-0.111498\pi$
$164$	111.374	−	133.078i	0.679109	−	0.811448i
$165$		0			0
$166$	−124.714	−	10.8302i	−0.751287	−	0.0652423i
$167$	58.4844	+	10.3124i	0.350206	+	0.0617508i	0.345984	−	0.938240i	$-0.387545\pi$
$167$	58.4844	+	10.3124i	0.350206	+	0.0617508i	0.00422188	+	0.999991i	$0.498656\pi$
$168$		0			0
$169$	−18.4380	+	15.4713i	−0.109101	+	0.0915463i
$170$	81.2603	−	174.556i	0.478002	−	1.02680i
$171$		0			0
$172$	59.7810	−	50.2934i	0.347564	−	0.292404i
$173$	15.8732	+	90.0212i	0.0917524	+	0.520354i	0.995694	+	0.0926984i	$0.0295492\pi$
$173$	15.8732	+	90.0212i	0.0917524	+	0.520354i	−0.903942	+	0.427656i	$0.859340\pi$
$174$		0			0
$175$	44.4471	+	122.117i	0.253983	+	0.697813i
$176$	−21.9888	+	60.9008i	−0.124936	+	0.346027i
$177$		0			0
$178$	32.9368	−	32.9792i	0.185038	−	0.185277i
$179$	−272.538	−	157.350i	−1.52256	−	0.879050i	−0.999644	−	0.0266652i	$-0.991511\pi$
$179$	−272.538	−	157.350i	−1.52256	−	0.879050i	−0.522915	−	0.852385i	$-0.675155\pi$
$180$		0			0
$181$	−102.558	−	177.636i	−0.566621	−	0.981416i	−0.996897	−	0.0787186i	$-0.974917\pi$
$181$	−102.558	−	177.636i	−0.566621	−	0.981416i	0.430276	−	0.902697i	$-0.358416\pi$
$182$	−54.7229	+	204.755i	−0.300675	+	1.12503i
$183$		0			0
$184$	142.468	−	12.7413i	0.774280	−	0.0692464i
$185$	−139.350	−	116.928i	−0.753241	−	0.632044i
$186$		0			0
$187$	−21.1311	+	58.0572i	−0.113000	+	0.310466i
$188$	13.5161	+	4.89977i	0.0718940	+	0.0260626i
$189$		0			0
$190$	246.016	−	172.499i	1.29482	−	0.907887i
$191$	−10.6521	+	29.2664i	−0.0557702	+	0.153227i	−0.964449	−	0.264268i	$-0.914870\pi$
$191$	−10.6521	+	29.2664i	−0.0557702	+	0.153227i	0.908679	+	0.417495i	$0.137092\pi$
$192$		0			0
$193$	148.161	+	124.322i	0.767673	+	0.644154i	0.940112	−	0.340866i	$-0.110720\pi$
$193$	148.161	+	124.322i	0.767673	+	0.644154i	−0.172439	+	0.985020i	$0.555165\pi$
$194$	−171.272	+	79.9994i	−0.882843	+	0.412368i
$195$		0			0
$196$	−39.1062	−	107.015i	−0.199522	−	0.545995i
$197$	−133.002	−	230.367i	−0.675139	−	1.16938i	−0.976428	−	0.215842i	$-0.930750\pi$
$197$	−133.002	−	230.367i	−0.675139	−	1.16938i	0.301289	−	0.953533i	$-0.402583\pi$
$198$		0			0
$199$	25.7924	+	14.8913i	0.129610	+	0.0748305i	0.563403	−	0.826182i	$-0.309492\pi$
$199$	25.7924	+	14.8913i	0.129610	+	0.0748305i	−0.433793	+	0.901013i	$0.642825\pi$
$200$	−50.1206	−	106.945i	−0.250603	−	0.534723i
$201$		0			0
$202$	−220.403	−	154.116i	−1.09110	−	0.762953i
$203$	−130.351	−	358.138i	−0.642125	−	1.76422i
$204$		0			0
$205$	−47.5045	−	269.411i	−0.231729	−	1.31420i
$206$	11.3992	+	129.335i	0.0553359	+	0.627842i
$207$		0			0
$208$	32.9599	−	189.779i	0.158461	−	0.912398i
$209$	−73.8567	+	61.9731i	−0.353381	+	0.296522i
$210$		0			0
$211$	−110.858	−	19.5472i	−0.525393	−	0.0926409i	−0.0953402	−	0.995445i	$-0.530394\pi$
$211$	−110.858	−	19.5472i	−0.525393	−	0.0926409i	−0.430053	+	0.902804i	$0.641505\pi$
$212$	280.948	−	162.688i	1.32523	−	0.767396i
$213$		0			0
$214$	102.428	−	27.5162i	0.478638	−	0.128581i
$215$		−	123.157i		−	0.572825i
$216$		0			0
$217$	−436.777			−2.01280
$218$	−100.421	−	373.816i	−0.460648	−	1.71475i
$219$		0			0
$220$	51.1505	+	88.3326i	0.232502	+	0.401512i
$221$	31.9160	−	181.005i	0.144416	−	0.819026i
$222$		0			0
$223$	−31.4443	−	37.4738i	−0.141006	−	0.168044i	0.690920	−	0.722931i	$-0.257206\pi$
$223$	−31.4443	−	37.4738i	−0.141006	−	0.168044i	−0.831925	+	0.554887i	$0.812761\pi$
$224$	119.864	+	254.905i	0.535105	+	1.13797i
$225$		0			0
$226$	−149.976	+	13.2184i	−0.663609	+	0.0584884i
$227$	−347.917	+	61.3471i	−1.53267	+	0.270251i	−0.875399	−	0.483401i	$-0.839401\pi$
$227$	−347.917	+	61.3471i	−1.53267	+	0.270251i	−0.657273	+	0.753652i	$0.728290\pi$
$228$		0			0
$229$	203.515	−	74.0734i	0.888712	−	0.323465i	0.142992	−	0.989724i	$-0.454328\pi$
$229$	203.515	−	74.0734i	0.888712	−	0.323465i	0.745720	+	0.666259i	$0.232106\pi$
$230$	129.217	−	184.794i	0.561813	−	0.803452i
$231$		0			0
$232$	146.990	+	313.640i	0.633579	+	1.35190i
$233$	−8.68589	+	15.0444i	−0.0372785	+	0.0645682i	−0.884063	−	0.467368i	$-0.845202\pi$
$233$	−8.68589	+	15.0444i	−0.0372785	+	0.0645682i	0.846784	+	0.531937i	$0.178536\pi$
$234$		0			0
$235$	19.6279	−	11.3322i	0.0835231	−	0.0482221i
$236$	−185.789	+	67.8926i	−0.787243	+	0.287680i
$237$		0			0
$238$	113.747	+	243.523i	0.477930	+	1.02321i
$239$	−85.0177	+	101.320i	−0.355722	+	0.423934i	−0.913996	−	0.405724i	$-0.867020\pi$
$239$	−85.0177	+	101.320i	−0.355722	+	0.423934i	0.558273	+	0.829657i	$0.311464\pi$
$240$		0			0
$241$	241.722	+	87.9795i	1.00299	+	0.365060i	0.790739	−	0.612154i	$-0.209697\pi$
$241$	241.722	+	87.9795i	1.00299	+	0.365060i	0.212256	+	0.977214i	$0.431919\pi$
$242$	120.129	+	171.328i	0.496402	+	0.707966i
$243$		0			0
$244$	−142.177	+	392.198i	−0.582693	+	1.60737i
$245$	−168.783	−	61.4321i	−0.688912	−	0.250743i
$246$		0			0
$247$	184.362	−	219.714i	0.746406	−	0.889532i
$248$	395.379	−	35.3601i	1.59427	−	0.142581i
$249$		0			0
$250$	124.723	+	33.3335i	0.498893	+	0.133334i
$251$	−40.4851	+	23.3741i	−0.161295	+	0.0931237i	−0.578475	−	0.815700i	$-0.696352\pi$
$251$	−40.4851	+	23.3741i	−0.161295	+	0.0931237i	0.417180	+	0.908824i	$0.363019\pi$
$252$		0			0
$253$	−36.1775	+	62.6612i	−0.142994	+	0.247673i
$254$	44.5734	+	44.5161i	0.175486	+	0.175260i
$255$		0			0
$256$	−129.139	−	221.041i	−0.504449	−	0.863441i
$257$	214.289	−	77.9949i	0.833810	−	0.303482i	0.110388	−	0.993889i	$-0.464791\pi$
$257$	214.289	−	77.9949i	0.833810	−	0.303482i	0.723422	+	0.690407i	$0.242568\pi$
$258$		0			0
$259$	250.074	−	44.0947i	0.965535	−	0.170250i
$260$	−195.485	−	232.363i	−0.751867	−	0.893703i
$261$		0			0
$262$	−146.789	−	68.3338i	−0.560263	−	0.260816i
$263$	−99.5544	−	118.644i	−0.378534	−	0.451119i	0.542817	−	0.839851i	$-0.317358\pi$
$263$	−99.5544	−	118.644i	−0.378534	−	0.451119i	−0.921351	+	0.388732i	$0.872913\pi$
$264$		0			0
$265$	88.8732	−	504.025i	0.335371	−	1.90198i
$266$	−36.2870	+	417.858i	−0.136417	+	1.57089i
$267$		0			0
$268$	−211.814	−	177.269i	−0.790350	−	0.661452i
$269$	−69.6193			−0.258808			−0.129404	−	0.991592i	$-0.541306\pi$
$269$	−69.6193			−0.258808			−0.129404	+	0.991592i	$0.541306\pi$
$270$		0			0
$271$			237.786i			0.877438i	0.898624	+	0.438719i	$0.144568\pi$
$271$			237.786i			0.877438i	−0.898624	+	0.438719i	$0.855432\pi$
$272$	−122.681	−	211.233i	−0.451034	−	0.776592i
$273$		0			0
$274$	17.6295	−	203.010i	0.0643412	−	0.740912i
$275$	58.8367	+	10.3745i	0.213952	+	0.0377255i
$276$		0			0
$277$	−133.236	+	111.798i	−0.480995	+	0.403603i	−0.850786	−	0.525512i	$-0.823874\pi$
$277$	−133.236	+	111.798i	−0.480995	+	0.403603i	0.369791	+	0.929115i	$0.379429\pi$
$278$	398.324	+	185.430i	1.43282	+	0.667013i
$279$		0			0
$280$	429.146	+	114.102i	1.53266	+	0.407508i
$281$	47.2360	+	267.889i	0.168100	+	0.953341i	0.945811	+	0.324719i	$0.105270\pi$
$281$	47.2360	+	267.889i	0.168100	+	0.953341i	−0.777711	+	0.628622i	$0.783619\pi$
$282$		0			0
$283$	160.917	+	442.115i	0.568610	+	1.56224i	0.806675	+	0.590995i	$0.201265\pi$
$283$	160.917	+	442.115i	0.568610	+	1.56224i	−0.238065	+	0.971249i	$0.576513\pi$
$284$	223.916	−	0.288031i	0.788438	−	0.00101419i
$285$		0			0
$286$	68.9424	+	68.8538i	0.241057	+	0.240748i
$287$	330.719	+	190.941i	1.15233	+	0.665299i
$288$		0			0
$289$	27.9569	+	48.4228i	0.0967367	+	0.167553i
$290$	527.531	+	140.988i	1.81907	+	0.486165i
$291$		0			0
$292$	−89.6449	−	51.6029i	−0.307003	−	0.176722i
$293$	−262.820	−	220.532i	−0.896996	−	0.752669i	0.0726053	−	0.997361i	$-0.476869\pi$
$293$	−262.820	−	220.532i	−0.896996	−	0.752669i	−0.969601	+	0.244692i	$0.921313\pi$
$294$		0			0
$295$	−106.653	+	293.026i	−0.361535	+	0.993308i
$296$	−222.802	+	60.1605i	−0.752708	+	0.203245i
$297$		0			0
$298$	−133.242	−	190.030i	−0.447122	−	0.637684i
$299$	73.6187	−	202.266i	0.246216	−	0.676474i
$300$		0			0
$301$	131.698	+	110.508i	0.437535	+	0.367135i
$302$	−97.2278	−	208.156i	−0.321946	−	0.689258i
$303$		0			0
$304$	−0.980677	−	381.191i	−0.00322591	−	1.25392i
$305$	328.827	+	569.545i	1.07812	+	1.86736i
$306$		0			0
$307$	−251.000	−	144.915i	−0.817589	−	0.472035i	0.0319956	−	0.999488i	$-0.489814\pi$
$307$	−251.000	−	144.915i	−0.817589	−	0.472035i	−0.849584	+	0.527453i	$0.823147\pi$
$308$	−140.355	−	24.5623i	−0.455698	−	0.0797476i
$309$		0			0
$310$	358.606	−	512.844i	1.15679	−	1.65434i
$311$	116.870	+	321.097i	0.375787	+	1.03247i	0.973085	+	0.230446i	$0.0740187\pi$
$311$	116.870	+	321.097i	0.375787	+	1.03247i	−0.597298	+	0.802019i	$0.703759\pi$
$312$		0			0
$313$	48.4649	+	274.858i	0.154840	+	0.878141i	0.958932	+	0.283636i	$0.0915408\pi$
$313$	48.4649	+	274.858i	0.154840	+	0.878141i	−0.804092	+	0.594505i	$0.797348\pi$
$314$	36.0506	−	3.17738i	0.114811	−	0.0101191i
$315$		0			0
$316$	59.2991	+	333.791i	0.187656	+	1.05630i
$317$	176.584	−	148.172i	0.557048	−	0.467419i	−0.320271	−	0.947326i	$-0.603774\pi$
$317$	176.584	−	148.172i	0.557048	−	0.467419i	0.877319	+	0.479907i	$0.159330\pi$
$318$		0			0
$319$	−172.552	−	30.4257i	−0.540917	−	0.0953782i
$320$	−397.709	−	68.5454i	−1.24284	−	0.214204i
$321$		0			0
$322$	81.6638	+	303.991i	0.253614	+	0.944072i
$323$		−	363.733i		−	1.12611i
$324$		0			0
$325$	−177.732			−0.546868
$326$	−216.080	+	58.0474i	−0.662821	+	0.178059i
$327$		0			0
$328$	−314.831	−	146.069i	−0.959852	−	0.445334i
$329$	−5.49387	+	31.1573i	−0.0166987	+	0.0947030i
$330$		0			0
$331$	−65.1143	−	77.6002i	−0.196720	−	0.234442i	0.658663	−	0.752438i	$-0.271122\pi$
$331$	−65.1143	−	77.6002i	−0.196720	−	0.234442i	−0.855383	+	0.517997i	$0.826678\pi$
$332$	43.7927	+	246.506i	0.131906	+	0.742489i
$333$		0			0
$334$	−10.4279	−	118.315i	−0.0312212	−	0.354236i
$335$	−428.810	+	75.6108i	−1.28003	+	0.225704i
$336$		0			0
$337$	−191.992	+	69.8794i	−0.569709	+	0.207357i	−0.610782	−	0.791799i	$-0.709145\pi$
$337$	−191.992	+	69.8794i	−0.569709	+	0.207357i	0.0410724	+	0.999156i	$0.486923\pi$
$338$	39.4503	+	27.5856i	0.116717	+	0.0816141i
$339$		0			0
$340$	−379.323	−	66.3819i	−1.11566	−	0.195241i
$341$	−100.400	+	173.899i	−0.294430	+	0.509967i
$342$		0			0
$343$	−156.397	+	90.2957i	−0.455967	+	0.263253i
$344$	−128.162	−	89.3719i	−0.372564	−	0.259802i
$345$		0			0
$346$	165.641	−	77.3696i	0.478732	−	0.223612i
$347$	−144.591	+	172.317i	−0.416688	+	0.496589i	−0.933033	−	0.359791i	$-0.882848\pi$
$347$	−144.591	+	172.317i	−0.416688	+	0.496589i	0.516345	+	0.856381i	$0.327292\pi$
$348$		0			0
$349$	308.560	+	112.307i	0.884127	+	0.321796i	0.743874	−	0.668320i	$-0.232986\pi$
$349$	308.560	+	112.307i	0.884127	+	0.321796i	0.140253	+	0.990116i	$0.455208\pi$
$350$	212.809	−	149.215i	0.608026	−	0.426328i
$351$		0			0
$352$	129.041	+	10.8716i	0.366592	+	0.0308851i
$353$	−28.8261	−	10.4918i	−0.0816603	−	0.0297219i	0.300867	−	0.953666i	$-0.402724\pi$
$353$	−28.8261	−	10.4918i	−0.0816603	−	0.0297219i	−0.382527	+	0.923944i	$0.624946\pi$
$354$		0			0
$355$	226.900	−	270.409i	0.639156	−	0.761716i
$356$	−80.7903	−	46.5058i	−0.226939	−	0.130634i
$357$		0			0
$358$	−162.510	+	608.058i	−0.453937	+	1.69849i
$359$	285.024	−	164.559i	0.793939	−	0.458381i	−0.0474081	−	0.998876i	$-0.515096\pi$
$359$	285.024	−	164.559i	0.793939	−	0.458381i	0.841348	+	0.540494i	$0.181763\pi$
$360$		0			0
$361$	103.304	−	178.927i	0.286159	−	0.495643i
$362$	−289.892	+	290.265i	−0.800807	+	0.801838i
$363$		0			0
$364$	423.883	−	0.545255i	1.16451	−	0.00149795i
$365$	−153.229	+	55.7707i	−0.419805	+	0.152797i
$366$		0			0
$367$	−187.339	+	33.0330i	−0.510461	+	0.0900081i	−0.422946	−	0.906155i	$-0.639004\pi$
$367$	−187.339	+	33.0330i	−0.510461	+	0.0900081i	−0.0875156	+	0.996163i	$0.527893\pi$
$368$	−98.5338	−	268.568i	−0.267755	−	0.729803i
$369$		0			0
$370$	−153.543	+	329.828i	−0.414981	+	0.891427i
$371$	459.233	+	547.292i	1.23782	+	1.47518i
$372$		0			0
$373$	21.9716	−	124.607i	0.0589052	−	0.334068i	−0.941086	−	0.338166i	$-0.890193\pi$
$373$	21.9716	−	124.607i	0.0589052	−	0.334068i	0.999992	+	0.00409830i	$0.00130453\pi$
$374$	123.103	+	10.6903i	0.329153	+	0.0285838i
$375$		0			0
$376$	2.45077	−	28.6490i	0.00651800	−	0.0761940i
$377$	521.241			1.38260
$378$		0			0
$379$		−	101.688i		−	0.268305i	−0.990961	−	0.134153i	$-0.957169\pi$
$379$		−	101.688i		−	0.268305i	0.990961	−	0.134153i	$-0.0428312\pi$
$380$	−460.837	−	385.679i	−1.21273	−	1.01495i
$381$		0			0
$382$	62.0558	+	5.38896i	0.162450	+	0.0141072i
$383$	−43.3604	−	7.64562i	−0.113213	−	0.0199624i	0.116755	−	0.993161i	$-0.462751\pi$
$383$	−43.3604	−	7.64562i	−0.113213	−	0.0199624i	−0.229967	+	0.973198i	$0.573862\pi$
$384$		0			0
$385$	−172.073	+	144.387i	−0.446944	+	0.375030i
$386$	163.252	−	350.683i	0.422932	−	0.908506i
$387$		0			0
$388$	243.390	+	289.304i	0.627293	+	0.745629i
$389$	−79.7241	−	452.138i	−0.204946	−	1.16231i	−0.897524	−	0.440965i	$-0.854636\pi$
$389$	−79.7241	−	452.138i	−0.204946	−	1.16231i	0.692578	−	0.721343i	$-0.256475\pi$
$390$		0			0
$391$	−93.3611	−	256.508i	−0.238775	−	0.656029i
$392$	−186.410	+	131.062i	−0.475536	+	0.334343i
$393$		0			0
$394$	−375.946	+	376.429i	−0.954176	+	0.955405i
$395$	462.843	+	267.223i	1.17176	+	0.676513i
$396$		0			0
$397$	38.9350	+	67.4374i	0.0980731	+	0.169868i	0.910887	−	0.412656i	$-0.135399\pi$
$397$	38.9350	+	67.4374i	0.0980731	+	0.169868i	−0.812814	+	0.582523i	$0.802065\pi$
$398$	15.3796	−	57.5453i	0.0386421	−	0.144586i
$399$		0			0
$400$	−180.559	+	152.300i	−0.451398	+	0.380751i
$401$	430.076	+	360.877i	1.07251	+	0.899943i	0.995278	−	0.0970705i	$-0.0309472\pi$
$401$	430.076	+	360.877i	1.07251	+	0.899943i	0.0772323	+	0.997013i	$0.475392\pi$
$402$		0			0
$403$	204.308	−	561.332i	0.506969	−	1.39288i
$404$	−183.316	+	505.680i	−0.453753	+	1.25168i
$405$		0			0
$406$	−624.112	+	437.607i	−1.53722	+	1.07785i
$407$	39.9276	−	109.700i	0.0981023	−	0.269534i
$408$		0			0
$409$	286.590	+	240.478i	0.700710	+	0.587966i	0.921976	−	0.387248i	$-0.126574\pi$
$409$	286.590	+	240.478i	0.700710	+	0.587966i	−0.221265	+	0.975214i	$0.571019\pi$
$410$	−495.724	+	231.548i	−1.20908	+	0.564751i
$411$		0			0
$412$	243.899	−	89.1274i	0.591987	−	0.216329i
$413$	−217.648	−	376.978i	−0.526993	−	0.912779i
$414$		0			0
$415$	341.812	+	197.345i	0.823644	+	0.475531i
$416$	−383.663	+	34.8098i	−0.922268	+	0.0836774i
$417$		0			0
$418$	158.025	+	110.499i	0.378050	+	0.264351i
$419$	119.164	+	327.401i	0.284402	+	0.781388i	0.996824	+	0.0796365i	$0.0253760\pi$
$419$	119.164	+	327.401i	0.284402	+	0.781388i	−0.712422	+	0.701751i	$0.752402\pi$
$420$		0			0
$421$	28.8481	+	163.606i	0.0685227	+	0.388612i	0.999710	+	0.0240712i	$0.00766283\pi$
$421$	28.8481	+	163.606i	0.0685227	+	0.388612i	−0.931188	+	0.364541i	$0.881226\pi$
$422$	19.7661	+	224.267i	0.0468392	+	0.531438i
$423$		0			0
$424$	−460.013	−	458.241i	−1.08494	−	1.08076i
$425$	−172.662	+	144.881i	−0.406264	+	0.340896i
$426$		0			0
$427$	−904.095	−	159.416i	−2.11732	−	0.373340i
$428$	−106.296	−	183.565i	−0.248356	−	0.428890i
$429$		0			0
$430$	−237.881	+	63.9039i	−0.553211	+	0.148614i
$431$			149.947i			0.347904i	0.984754	+	0.173952i	$0.0556538\pi$
$431$			149.947i			0.347904i	−0.984754	+	0.173952i	$0.944346\pi$
$432$		0			0
$433$	−117.205			−0.270681			−0.135341	−	0.990799i	$-0.543213\pi$
$433$	−117.205			−0.270681			−0.135341	+	0.990799i	$0.543213\pi$
$434$	226.635	+	843.644i	0.522201	+	1.94388i
$435$		0			0
$436$	−669.925	+	387.931i	−1.53653	+	0.889751i
$437$	73.9691	−	419.499i	0.169266	−	0.959953i
$438$		0			0
$439$	−88.8615	−	105.901i	−0.202418	−	0.241232i	0.655280	−	0.755386i	$-0.272551\pi$
$439$	−88.8615	−	105.901i	−0.202418	−	0.241232i	−0.857698	+	0.514154i	$0.828106\pi$
$440$	144.075	−	144.632i	0.327443	−	0.328709i
$441$		0			0
$442$	−366.175	+	32.2735i	−0.828450	+	0.0730169i
$443$	528.154	−	93.1279i	1.19222	−	0.210221i	0.457888	−	0.889010i	$-0.348606\pi$
$443$	528.154	−	93.1279i	1.19222	−	0.210221i	0.734334	+	0.678789i	$0.237495\pi$
$444$		0			0
$445$	−138.094	+	50.2620i	−0.310323	+	0.112948i
$446$	−56.0655	+	80.1796i	−0.125707	+	0.179775i
$447$		0			0
$448$	430.158	−	363.784i	0.960175	−	0.812017i
$449$	−228.269	+	395.373i	−0.508394	+	0.880564i	0.491559	+	0.870844i	$0.336427\pi$
$449$	−228.269	+	395.373i	−0.508394	+	0.880564i	−0.999953	+	0.00971998i	$0.996906\pi$
$450$		0			0
$451$	152.043	−	87.7818i	0.337123	−	0.194638i
$452$	103.351	+	282.822i	0.228653	+	0.625712i
$453$		0			0
$454$	299.020	+	640.175i	0.658635	+	1.41008i
$455$	429.532	−	511.897i	0.944027	−	1.12505i
$456$		0			0
$457$	−544.589	−	198.214i	−1.19166	−	0.433729i	−0.331354	−	0.943506i	$-0.607505\pi$
$457$	−544.589	−	198.214i	−1.19166	−	0.433729i	−0.860306	+	0.509778i	$0.829728\pi$
$458$	−248.674	−	354.658i	−0.542956	−	0.774362i
$459$		0			0
$460$	−423.981	−	153.699i	−0.921698	−	0.334128i
$461$	−377.847	−	137.525i	−0.819624	−	0.298319i	−0.102031	−	0.994781i	$-0.532534\pi$
$461$	−377.847	−	137.525i	−0.819624	−	0.298319i	−0.717593	+	0.696463i	$0.754756\pi$
$462$		0			0
$463$	542.788	−	646.870i	1.17233	−	1.39713i	0.271786	−	0.962358i	$-0.412386\pi$
$463$	542.788	−	646.870i	1.17233	−	1.39713i	0.900542	−	0.434769i	$-0.143170\pi$
$464$	529.531	−	446.656i	1.14123	−	0.962621i
$465$		0			0
$466$	33.5655	+	8.97071i	0.0720289	+	0.0192504i
$467$	−592.887	+	342.304i	−1.26957	+	0.732984i	−0.974906	−	0.222618i	$-0.928540\pi$
$467$	−592.887	+	342.304i	−1.26957	+	0.732984i	−0.294660	+	0.955602i	$0.595207\pi$
$468$		0			0
$469$	303.912	−	526.392i	0.648001	−	1.12237i
$470$	−32.0729	−	32.0316i	−0.0682401	−	0.0681524i
$471$		0			0
$472$	227.538	+	323.627i	0.482073	+	0.685651i
$473$	74.2705	−	27.0323i	0.157020	−	0.0571507i
$474$		0			0
$475$	−346.386	+	61.0772i	−0.729234	+	0.128584i
$476$	411.348	−	346.064i	0.864176	−	0.727026i
$477$		0			0
$478$	239.816	+	111.640i	0.501706	+	0.233557i
$479$	−311.792	−	371.580i	−0.650924	−	0.775740i	0.335129	−	0.942172i	$-0.391220\pi$
$479$	−311.792	−	371.580i	−0.650924	−	0.775740i	−0.986053	+	0.166432i	$0.946775\pi$
$480$		0			0
$481$	−60.3060	+	342.012i	−0.125376	+	0.711045i
$482$	44.5094	−	512.541i	0.0923431	−	1.06336i
$483$		0			0
$484$	268.590	−	320.930i	0.554938	−	0.663079i
$485$	596.007			1.22888
$486$		0			0
$487$			77.9383i			0.160038i	0.996793	+	0.0800188i	$0.0254980\pi$
$487$			77.9383i			0.160038i	−0.996793	+	0.0800188i	$0.974502\pi$
$488$	831.310	+	71.1142i	1.70350	+	0.145726i
$489$		0			0
$490$	−31.0789	+	357.884i	−0.0634263	+	0.730376i
$491$	−398.433	−	70.2545i	−0.811473	−	0.143085i	−0.247511	−	0.968885i	$-0.579613\pi$
$491$	−398.433	−	70.2545i	−0.811473	−	0.143085i	−0.563962	+	0.825801i	$0.690724\pi$
$492$		0			0
$493$	506.372	−	424.897i	1.02712	−	0.861860i
$494$	−520.044	−	242.094i	−1.05272	−	0.490068i
$495$		0			0
$496$	−273.453	−	745.335i	−0.551317	−	1.50269i
$497$	85.5663	+	485.271i	0.172166	+	0.976399i
$498$		0			0
$499$	246.492	+	677.231i	0.493971	+	1.35718i	0.897017	+	0.441996i	$0.145729\pi$
$499$	246.492	+	677.231i	0.493971	+	1.35718i	−0.403046	+	0.915180i	$0.632048\pi$
$500$	−0.332133	−	258.201i	−0.000664265	−	0.516403i
$501$		0			0
$502$	66.1543	+	66.0693i	0.131782	+	0.131612i
$503$	−204.980	−	118.346i	−0.407516	−	0.235279i	0.282206	−	0.959354i	$-0.408934\pi$
$503$	−204.980	−	118.346i	−0.407516	−	0.235279i	−0.689722	+	0.724074i	$0.742267\pi$
$504$		0			0
$505$	423.973	+	734.343i	0.839551	+	1.45415i
$506$	139.803	+	37.3638i	0.276291	+	0.0738414i
$507$		0			0
$508$	62.8554	−	109.193i	0.123731	−	0.214947i
$509$	472.945	+	396.848i	0.929165	+	0.779662i	0.975667	−	0.219256i	$-0.0703630\pi$
$509$	472.945	+	396.848i	0.929165	+	0.779662i	−0.0465023	+	0.998918i	$0.514807\pi$
$510$		0			0
$511$	77.8522	−	213.897i	0.152353	−	0.418586i
$512$	−359.937	+	364.128i	−0.703002	+	0.711188i
$513$		0			0
$514$	−261.839	−	373.433i	−0.509414	−	0.726524i
$515$	140.011	−	384.676i	0.271865	−	0.746943i
$516$		0			0
$517$	11.1421	+	9.34935i	0.0215515	+	0.0180839i
$518$	−214.928	−	460.142i	−0.414919	−	0.888304i
$519$		0			0
$520$	−347.379	+	498.152i	−0.668037	+	0.957985i
$521$	−188.649	−	326.750i	−0.362090	−	0.627159i	0.626214	−	0.779651i	$-0.284603\pi$
$521$	−188.649	−	326.750i	−0.362090	−	0.627159i	−0.988305	+	0.152492i	$0.951270\pi$
$522$		0			0
$523$	718.669	+	414.924i	1.37413	+	0.793353i	0.991445	−	0.130527i	$-0.0416669\pi$
$523$	718.669	+	414.924i	1.37413	+	0.793353i	0.382683	+	0.923880i	$0.375000\pi$
$524$	−55.8222	+	318.982i	−0.106531	+	0.608745i
$525$		0			0
$526$	−177.507	+	253.853i	−0.337466	+	0.482611i
$527$	−259.098	−	711.865i	−0.491647	−	1.35079i
$528$		0			0
$529$	36.3485	+	206.142i	0.0687117	+	0.389683i
$530$	−1019.65	+	89.8685i	−1.92386	+	0.169563i
$531$		0			0
$532$	825.929	−	146.729i	1.55250	−	0.275807i
$533$	−400.089	+	335.715i	−0.750637	+	0.629859i
$534$		0			0
$535$	−329.318	−	58.0676i	−0.615547	−	0.108538i
$536$	−232.492	+	501.104i	−0.433755	+	0.934895i
$537$		0			0
$538$	36.1241	+	134.471i	0.0671452	+	0.249946i
$539$		−	115.270i		−	0.213858i
$540$		0			0
$541$	947.380			1.75116			0.875582	−	0.483069i	$-0.160478\pi$
$541$	947.380			1.75116			0.875582	+	0.483069i	$0.160478\pi$
$542$	459.288	−	123.382i	0.847394	−	0.227643i
$543$		0			0
$544$	−344.344	+	346.566i	−0.632985	+	0.637069i
$545$	−211.919	+	1201.85i	−0.388843	+	2.20524i
$546$		0			0
$547$	202.576	+	241.421i	0.370341	+	0.441355i	0.918741	−	0.394861i	$-0.129207\pi$
$547$	202.576	+	241.421i	0.370341	+	0.441355i	−0.548400	+	0.836216i	$0.684763\pi$
$548$	−401.265	+	71.2861i	−0.732235	+	0.130084i
$549$		0			0
$550$	−10.4907	−	119.027i	−0.0190740	−	0.216413i
$551$	1015.86	−	179.123i	1.84366	−	0.325087i
$552$		0			0
$553$	−701.058	+	255.164i	−1.26774	+	0.461418i
$554$	285.073	+	199.337i	0.514573	+	0.359815i
$555$		0			0
$556$	151.478	−	865.586i	0.272443	−	1.55681i
$557$	197.912	−	342.794i	0.355318	−	0.615429i	−0.631854	−	0.775087i	$-0.717706\pi$
$557$	197.912	−	342.794i	0.355318	−	0.615429i	0.987172	+	0.159659i	$0.0510393\pi$
$558$		0			0
$559$	−203.624	+	117.563i	−0.364266	+	0.210309i
$560$	−2.28481	−	888.109i	−0.00408002	−	1.58591i
$561$		0			0
$562$	492.922	−	230.239i	0.877086	−	0.409679i
$563$	−14.0883	+	16.7898i	−0.0250236	+	0.0298219i	−0.778411	−	0.627755i	$-0.783974\pi$
$563$	−14.0883	+	16.7898i	−0.0250236	+	0.0298219i	0.753388	+	0.657577i	$0.228418\pi$
$564$		0			0
$565$	446.065	+	162.355i	0.789496	+	0.287353i
$566$	770.457	−	540.219i	1.36123	−	0.954450i
$567$		0			0
$568$	−116.742	−	432.349i	−0.205532	−	0.761178i
$569$	−71.8483	−	26.1506i	−0.126271	−	0.0459589i	0.278112	−	0.960549i	$-0.410291\pi$
$569$	−71.8483	−	26.1506i	−0.126271	−	0.0459589i	−0.404383	+	0.914590i	$0.632514\pi$
$570$		0			0
$571$	551.758	−	657.560i	0.966301	−	1.15159i	−0.0221043	−	0.999756i	$-0.507037\pi$
$571$	551.758	−	657.560i	0.966301	−	1.15159i	0.988406	−	0.151837i	$-0.0485190\pi$
$572$	97.2195	−	168.890i	0.169964	−	0.295263i
$573$		0			0
$574$	197.202	−	737.866i	0.343558	−	1.28548i
$575$	−228.598	+	131.981i	−0.397561	+	0.229532i
$576$		0			0
$577$	358.886	−	621.609i	0.621986	−	1.07731i	−0.367129	−	0.930170i	$-0.619659\pi$
$577$	358.886	−	621.609i	0.621986	−	1.07731i	0.989115	−	0.147142i	$-0.0470075\pi$
$578$	79.0232	−	79.1249i	0.136718	−	0.136894i
$579$		0			0
$580$	−1.40479	−	1092.09i	−0.00242205	−	1.88292i
$581$	−517.735	+	188.440i	−0.891110	+	0.324338i
$582$		0			0
$583$	323.461	−	57.0350i	0.554822	−	0.0978301i
$584$	−53.1569	+	199.927i	−0.0910221	+	0.342340i
$585$		0			0
$586$	−289.589	+	622.071i	−0.494180	+	1.06155i
$587$	296.445	+	353.290i	0.505017	+	0.601856i	0.956970	−	0.290186i	$-0.0937170\pi$
$587$	296.445	+	353.290i	0.505017	+	0.601856i	−0.451953	+	0.892042i	$0.649273\pi$
$588$		0			0
$589$	205.281	−	1164.20i	0.348524	−	1.97658i
$590$	621.325	+	53.9563i	1.05309	+	0.0914513i
$591$		0			0
$592$	231.809	+	399.129i	0.391568	+	0.674205i
$593$	−680.046			−1.14679			−0.573395	−	0.819279i	$-0.694374\pi$
$593$	−680.046			−1.14679			−0.573395	+	0.819279i	$0.694374\pi$
$594$		0			0
$595$		−	847.434i		−	1.42426i
$596$	−297.909	+	355.963i	−0.499847	+	0.597253i
$597$		0			0
$598$	−428.879	−	37.2441i	−0.717189	−	0.0622812i
$599$	401.294	+	70.7590i	0.669941	+	0.118129i	0.498265	−	0.867025i	$-0.333971\pi$
$599$	401.294	+	70.7590i	0.669941	+	0.118129i	0.171676	+	0.985153i	$0.445082\pi$
$600$		0			0
$601$	−95.1408	+	79.8326i	−0.158304	+	0.132833i	−0.718499	−	0.695528i	$-0.755171\pi$
$601$	−95.1408	+	79.8326i	−0.158304	+	0.132833i	0.560195	+	0.828361i	$0.310726\pi$
$602$	145.112	−	311.717i	0.241050	−	0.517803i
$603$		0			0
$604$	−351.608	+	295.805i	−0.582132	+	0.489744i
$605$	−114.562	−	649.713i	−0.189359	−	1.07391i
$606$		0			0
$607$	72.4290	+	198.997i	0.119323	+	0.327837i	0.984947	−	0.172858i	$-0.0553001\pi$
$607$	72.4290	+	198.997i	0.119323	+	0.327837i	−0.865624	+	0.500695i	$0.833078\pi$
$608$	−735.768	+	199.687i	−1.21015	+	0.328432i
$609$		0			0
$610$	929.465	−	930.662i	1.52371	−	1.52568i
$611$	−37.4725	−	21.6348i	−0.0613299	−	0.0354088i
$612$		0			0
$613$	−348.189	−	603.082i	−0.568009	−	0.983820i	−0.996763	−	0.0803988i	$-0.974381\pi$
$613$	−348.189	−	603.082i	−0.568009	−	0.983820i	0.428754	−	0.903421i	$-0.358953\pi$
$614$	−149.667	+	560.004i	−0.243757	+	0.912058i
$615$		0			0
$616$	25.3850	+	283.843i	0.0412094	+	0.460784i
$617$	−164.966	−	138.423i	−0.267368	−	0.224349i	0.499240	−	0.866464i	$-0.333613\pi$
$617$	−164.966	−	138.423i	−0.267368	−	0.224349i	−0.766608	+	0.642115i	$0.778057\pi$
$618$		0			0
$619$	−275.355	+	756.532i	−0.444839	+	1.22218i	0.491435	+	0.870914i	$0.336472\pi$
$619$	−275.355	+	756.532i	−0.444839	+	1.22218i	−0.936274	+	0.351270i	$0.885750\pi$
$620$	−1176.64	−	426.549i	−1.89781	−	0.687983i
$621$		0			0
$622$	559.563	−	392.347i	0.899619	−	0.630783i
$623$	70.1624	−	192.770i	0.112620	−	0.309421i
$624$		0			0
$625$	−594.548	−	498.885i	−0.951277	−	0.798216i
$626$	505.746	−	236.229i	0.807901	−	0.377363i
$627$		0			0
$628$	−24.8431	−	67.9837i	−0.0395591	−	0.108254i
$629$	220.211	+	381.416i	0.350096	+	0.606385i
$630$		0			0
$631$	−834.435	−	481.761i	−1.32240	−	0.763488i	−0.338289	−	0.941042i	$-0.609848\pi$
$631$	−834.435	−	481.761i	−1.32240	−	0.763488i	−0.984111	+	0.177554i	$0.943182\pi$
$632$	613.954	−	287.735i	0.971446	−	0.455277i
$633$		0			0
$634$	−377.823	−	264.192i	−0.595935	−	0.416707i
$635$	−67.9321	−	186.642i	−0.106980	−	0.293924i
$636$		0			0
$637$	59.5461	+	337.703i	0.0934789	+	0.530145i
$638$	30.7664	+	349.076i	0.0482232	+	0.547140i
$639$		0			0
$640$	73.9667	+	803.749i	0.115573	+	1.25586i
$641$	661.366	−	554.952i	1.03177	−	0.865760i	0.0407115	−	0.999171i	$-0.487038\pi$
$641$	661.366	−	554.952i	1.03177	−	0.865760i	0.991061	+	0.133411i	$0.0425931\pi$
$642$		0			0
$643$	883.667	+	155.814i	1.37429	+	0.242324i	0.811536	−	0.584302i	$-0.198632\pi$
$643$	883.667	+	155.814i	1.37429	+	0.242324i	0.562751	+	0.826626i	$0.309743\pi$
$644$	544.791	−	315.470i	0.845949	−	0.489861i
$645$		0			0
$646$	−702.556	+	188.734i	−1.08755	+	0.292157i
$647$			878.052i			1.35711i	0.734549	+	0.678556i	$0.237394\pi$
$647$			878.052i			1.35711i	−0.734549	+	0.678556i	$0.762606\pi$
$648$		0			0
$649$	−200.120			−0.308352
$650$	92.2217	+	343.293i	0.141880	+	0.528143i
$651$		0			0
$652$	224.239	+	387.242i	0.343925	+	0.593930i
$653$	−52.9434	+	300.257i	−0.0810771	+	0.459811i	0.917057	+	0.398756i	$0.130558\pi$
$653$	−52.9434	+	300.257i	−0.0810771	+	0.459811i	−0.998134	+	0.0610557i	$0.980553\pi$
$654$		0			0
$655$	328.145	+	391.068i	0.500985	+	0.597051i
$656$	−118.776	+	683.895i	−0.181061	+	1.04252i
$657$		0			0
$658$	63.0316	−	5.55540i	0.0957926	−	0.00844286i
$659$	−985.857	+	173.833i	−1.49599	+	0.263783i	−0.860947	−	0.508694i	$-0.830128\pi$
$659$	−985.857	+	173.833i	−1.49599	+	0.263783i	−0.635042	+	0.772478i	$0.719017\pi$
$660$		0			0
$661$	−944.242	+	343.676i	−1.42850	+	0.519933i	−0.936503	−	0.350661i	$-0.885957\pi$
$661$	−944.242	+	343.676i	−1.42850	+	0.519933i	−0.492002	+	0.870594i	$0.663735\pi$
$662$	−116.100	+	166.035i	−0.175377	+	0.250808i
$663$		0			0
$664$	453.408	−	212.494i	0.682844	−	0.320021i
$665$	661.214	−	1145.26i	0.994306	−	1.72219i
$666$		0			0
$667$	670.416	−	387.065i	1.00512	−	0.580307i
$668$	−223.116	+	81.5328i	−0.334006	+	0.122055i
$669$		0			0
$670$	368.545	+	789.022i	0.550067	+	1.17764i
$671$	−271.291	+	323.312i	−0.404309	+	0.481836i
$672$		0			0
$673$	−557.788	−	203.018i	−0.828808	−	0.301662i	−0.107439	−	0.994212i	$-0.534265\pi$
$673$	−557.788	−	203.018i	−0.828808	−	0.301662i	−0.721370	+	0.692550i	$0.756487\pi$
$674$	234.594	+	334.577i	0.348063	+	0.496405i
$675$		0			0
$676$	32.8121	−	90.5125i	0.0485386	−	0.133894i
$677$	419.692	+	152.755i	0.619929	+	0.225636i	0.632842	−	0.774281i	$-0.281888\pi$
$677$	419.692	+	152.755i	0.619929	+	0.225636i	−0.0129131	+	0.999917i	$0.504110\pi$
$678$		0			0
$679$	−534.791	+	637.339i	−0.787615	+	0.938643i
$680$	68.6055	+	767.114i	0.100890	+	1.12811i
$681$		0			0
$682$	387.985	+	103.693i	0.568892	+	0.152042i
$683$	740.219	−	427.366i	1.08378	−	0.625718i	0.151863	−	0.988402i	$-0.451473\pi$
$683$	740.219	−	427.366i	1.08378	−	0.625718i	0.931912	+	0.362683i	$0.118139\pi$
$684$		0			0
$685$	−321.240	+	556.405i	−0.468964	+	0.812269i
$686$	255.559	+	255.230i	0.372535	+	0.372056i
$687$		0			0
$688$	−106.123	+	293.920i	−0.154248	+	0.427210i
$689$	−918.175	+	334.188i	−1.33262	+	0.485034i
$690$		0			0
$691$	−1014.01	+	178.797i	−1.46745	+	0.258750i	−0.849550	−	0.527509i	$-0.823126\pi$
$691$	−1014.01	+	178.797i	−1.46745	+	0.258750i	−0.617897	+	0.786259i	$0.712015\pi$
$692$	−235.389	−	279.794i	−0.340157	−	0.404326i
$693$		0			0
$694$	407.858	+	189.868i	0.587691	+	0.273585i
$695$	−890.450	−	1061.20i	−1.28122	−	1.52690i
$696$		0			0
$697$	−115.014	+	652.277i	−0.165013	+	0.935836i
$698$	56.8167	−	654.264i	0.0813992	−	0.937341i
$699$		0			0
$700$	−398.633	−	333.620i	−0.569476	−	0.476600i
$701$	164.190			0.234222			0.117111	−	0.993119i	$-0.462637\pi$
$701$	164.190			0.234222			0.117111	+	0.993119i	$0.462637\pi$
$702$		0			0
$703$			687.280i			0.977639i
$704$	−45.9580	−	254.885i	−0.0652813	−	0.362053i
$705$		0			0
$706$	−5.30788	+	61.1221i	−0.00751825	+	0.0865752i
$707$	−1165.69	−	205.543i	−1.64879	−	0.290726i
$708$		0			0
$709$	−199.551	+	167.443i	−0.281454	+	0.236168i	−0.772575	−	0.634924i	$-0.781032\pi$
$709$	−199.551	+	167.443i	−0.281454	+	0.236168i	0.491121	+	0.871091i	$0.336587\pi$
$710$	−640.035	−	297.952i	−0.901457	−	0.419651i
$711$		0			0
$712$	−47.9064	+	180.179i	−0.0672842	+	0.253060i
$713$	−154.057	−	873.698i	−0.216068	−	1.22538i
$714$		0			0
$715$	−105.072	−	288.682i	−0.146953	−	0.403751i
$716$	1258.80	−	1.61923i	1.75810	−	0.00226150i
$717$		0			0
$718$	−465.742	−	465.143i	−0.648666	−	0.647832i
$719$	−129.283	−	74.6416i	−0.179809	−	0.103813i	0.407394	−	0.913253i	$-0.366438\pi$
$719$	−129.283	−	74.6416i	−0.179809	−	0.103813i	−0.587203	+	0.809440i	$0.699771\pi$
$720$		0			0
$721$	285.722	+	494.885i	0.396286	+	0.686387i
$722$	−399.203	−	106.691i	−0.552913	−	0.147771i
$723$		0			0
$724$	711.072	+	409.319i	0.982144	+	0.565358i
$725$	−489.663	−	410.876i	−0.675397	−	0.566725i
$726$		0			0
$727$	−18.1243	+	49.7962i	−0.0249303	+	0.0684954i	−0.951533	−	0.307545i	$-0.900492\pi$
$727$	−18.1243	+	49.7962i	−0.0249303	+	0.0684954i	0.926603	+	0.376041i	$0.122715\pi$
$728$	−220.998	−	818.456i	−0.303569	−	1.12425i
$729$		0			0
$730$	187.230	+	267.026i	0.256479	+	0.365789i
$731$	−101.983	+	280.197i	−0.139512	+	0.383306i
$732$		0			0
$733$	−68.7825	−	57.7154i	−0.0938370	−	0.0787386i	0.594662	−	0.803976i	$-0.297286\pi$
$733$	−68.7825	−	57.7154i	−0.0938370	−	0.0787386i	−0.688499	+	0.725237i	$0.741730\pi$
$734$	161.010	+	344.709i	0.219360	+	0.469631i
$735$		0			0
$736$	−467.616	+	329.674i	−0.635348	+	0.447927i
$737$	−139.719	−	242.000i	−0.189577	−	0.328358i
$738$		0			0
$739$	190.957	+	110.249i	0.258399	+	0.149187i	0.623604	−	0.781740i	$-0.285668\pi$
$739$	190.957	+	110.249i	0.258399	+	0.149187i	−0.365205	+	0.930927i	$0.619001\pi$
$740$	716.739	+	125.430i	0.968566	+	0.169500i
$741$		0			0
$742$	818.818	−	1171.00i	1.10353	−	1.57816i
$743$	117.725	+	323.447i	0.158445	+	0.435325i	0.993359	−	0.115056i	$-0.0367047\pi$
$743$	117.725	+	323.447i	0.158445	+	0.435325i	−0.834914	+	0.550381i	$0.814482\pi$
$744$		0			0
$745$	127.068	+	720.636i	0.170560	+	0.967296i
$746$	−252.082	+	22.2177i	−0.337911	+	0.0297824i
$747$		0			0
$748$	−43.2272	−	243.323i	−0.0577903	−	0.325298i
$749$	357.587	−	300.051i	0.477420	−	0.400603i
$750$		0			0
$751$	−577.725	−	101.868i	−0.769274	−	0.135644i	−0.224781	−	0.974409i	$-0.572167\pi$
$751$	−577.725	−	101.868i	−0.769274	−	0.135644i	−0.544493	+	0.838765i	$0.683278\pi$
$752$	−56.6076	+	10.1317i	−0.0752761	+	0.0134730i
$753$		0			0
$754$	−270.462	−	1006.79i	−0.358702	−	1.33526i
$755$			724.361i			0.959419i
$756$		0			0
$757$	352.312			0.465406			0.232703	−	0.972548i	$-0.425243\pi$
$757$	352.312			0.465406			0.232703	+	0.972548i	$0.425243\pi$
$758$	−196.412	+	52.7637i	−0.259118	+	0.0696091i
$759$		0			0
$760$	−505.827	+	1090.24i	−0.665562	+	1.43452i
$761$	−43.3833	+	246.039i	−0.0570083	+	0.323310i	−0.999954	−	0.00963779i	$-0.996932\pi$
$761$	−43.3833	+	246.039i	−0.0570083	+	0.323310i	0.942945	+	0.332948i	$0.108043\pi$
$762$		0			0
$763$	−1095.05	−	1305.03i	−1.43518	−	1.71039i
$764$	−21.7907	−	122.658i	−0.0285218	−	0.160547i
$765$		0			0
$766$	7.73124	+	87.7186i	0.0100930	+	0.114515i
$767$	586.288	−	103.378i	0.764391	−	0.134783i
$768$		0			0
$769$	−1188.05	+	432.413i	−1.54492	+	0.562306i	−0.967220	−	0.253941i	$-0.918273\pi$
$769$	−1188.05	+	432.413i	−1.54492	+	0.562306i	−0.577703	+	0.816247i	$0.696051\pi$
$770$	368.171	+	257.443i	0.478144	+	0.334342i
$771$		0			0
$772$	−762.060	−	133.361i	−0.987124	−	0.172748i
$773$	748.700	−	1296.79i	0.968564	−	1.67760i	0.268845	−	0.963183i	$-0.413358\pi$
$773$	748.700	−	1296.79i	0.968564	−	1.67760i	0.699719	−	0.714419i	$-0.253309\pi$
$774$		0			0
$775$	−634.410	+	366.277i	−0.818593	+	0.472615i
$776$	432.506	−	620.226i	0.557353	−	0.799261i
$777$		0			0
$778$	−831.945	+	388.594i	−1.06934	+	0.499478i
$779$	−664.376	+	791.773i	−0.852858	+	1.01640i
$780$		0			0
$781$	212.875	+	77.4800i	0.272567	+	0.0992062i
$782$	−447.006	+	313.425i	−0.571619	+	0.400800i
$783$		0			0
$784$	349.874	+	292.048i	0.446268	+	0.372511i
$785$	−107.224	−	39.0262i	−0.136591	−	0.0497149i
$786$		0			0
$787$	−346.942	+	413.469i	−0.440841	+	0.525373i	−0.940017	−	0.341127i	$-0.889191\pi$
$787$	−346.942	+	413.469i	−0.440841	+	0.525373i	0.499177	+	0.866500i	$0.333636\pi$
$788$	922.151	+	530.824i	1.17024	+	0.673634i
$789$		0			0
$790$	275.985	−	1032.65i	0.349348	−	1.30715i
$791$	−573.863	+	331.320i	−0.725490	+	0.418862i
$792$		0			0
$793$	627.779	−	1087.34i	0.791651	−	1.37118i
$794$	110.054	−	110.196i	0.138607	−	0.138785i
$795$		0			0
$796$	−119.130	+	0.153241i	−0.149661	+	0.000192513i
$797$	311.665	−	113.437i	0.391048	−	0.142330i	−0.139011	−	0.990291i	$-0.544392\pi$
$797$	311.665	−	113.437i	0.391048	−	0.142330i	0.530058	+	0.847961i	$0.322170\pi$
$798$		0			0
$799$	−54.0396	+	9.52863i	−0.0676340	+	0.0119257i
$800$	387.859	+	269.727i	0.484824	+	0.337159i
$801$		0			0
$802$	473.882	−	1017.95i	0.590876	−	1.26927i
$803$	−67.2655	−	80.1639i	−0.0837678	−	0.0998306i
$804$		0			0
$805$	172.335	−	977.362i	0.214081	−	1.21411i
$806$	−1190.24	−	103.361i	−1.47672	−	0.128239i
$807$		0			0
$808$	1071.85	+	91.6910i	1.32655	+	0.113479i
$809$	−34.7466			−0.0429501			−0.0214750	−	0.999769i	$-0.506836\pi$
$809$	−34.7466			−0.0429501			−0.0214750	+	0.999769i	$0.506836\pi$
$810$		0			0
$811$			873.324i			1.07685i	0.842674	+	0.538424i	$0.180980\pi$
$811$			873.324i			1.07685i	−0.842674	+	0.538424i	$0.819020\pi$
$812$	1169.09	+	978.419i	1.43976	+	1.20495i
$813$		0			0
$814$	−232.606	−	20.1996i	−0.285756	−	0.0248153i
$815$	694.717	+	122.497i	0.852414	+	0.150304i
$816$		0			0
$817$	−356.448	+	299.096i	−0.436289	+	0.366090i
$818$	315.781	−	678.334i	0.386041	−	0.829259i
$819$		0			0
$820$	704.460	+	837.353i	0.859098	+	1.02116i
$821$	210.789	+	1195.44i	0.256747	+	1.45608i	0.791548	+	0.611106i	$0.209275\pi$
$821$	210.789	+	1195.44i	0.256747	+	1.45608i	−0.534802	+	0.844978i	$0.679614\pi$
$822$		0			0
$823$	248.432	+	682.560i	0.301861	+	0.829357i	0.994177	+	0.107762i	$0.0343684\pi$
$823$	248.432	+	682.560i	0.301861	+	0.829357i	−0.692316	+	0.721595i	$0.743409\pi$
$824$	−298.705	−	424.849i	−0.362507	−	0.515593i
$825$		0			0
$826$	−615.206	+	615.998i	−0.744802	+	0.745760i
$827$	−194.573	−	112.337i	−0.235276	−	0.135837i	0.377728	−	0.925917i	$-0.376706\pi$
$827$	−194.573	−	112.337i	−0.235276	−	0.135837i	−0.613004	+	0.790080i	$0.710039\pi$
$828$		0			0
$829$	−206.345	−	357.399i	−0.248908	−	0.431121i	0.714315	−	0.699824i	$-0.246738\pi$
$829$	−206.345	−	357.399i	−0.248908	−	0.431121i	−0.963223	+	0.268703i	$0.913405\pi$
$830$	203.817	−	762.616i	0.245562	−	0.918814i
$831$		0			0
$832$	266.311	+	722.991i	0.320085	+	0.868979i
$833$	333.131	+	279.530i	0.399917	+	0.335570i
$834$		0			0
$835$	−128.080	+	351.898i	−0.153390	+	0.421434i
$836$	131.435	−	362.564i	0.157218	−	0.433689i
$837$		0			0
$838$	570.550	−	400.050i	0.680847	−	0.477387i
$839$	−440.665	+	1210.72i	−0.525226	+	1.44305i	0.339406	+	0.940640i	$0.389774\pi$
$839$	−440.665	+	1210.72i	−0.525226	+	1.44305i	−0.864632	+	0.502406i	$0.832448\pi$
$840$		0			0
$841$	791.806	+	664.404i	0.941506	+	0.790017i
$842$	301.038	−	140.612i	0.357528	−	0.166998i
$843$		0			0
$844$	422.919	−	154.546i	0.501089	−	0.183112i
$845$	−75.8877	−	131.441i	−0.0898079	−	0.155552i
$846$		0			0
$847$	797.564	+	460.474i	0.941634	+	0.543653i
$848$	−646.410	+	1126.30i	−0.762276	+	1.32818i
$849$		0			0
$850$	369.431	+	258.324i	0.434625	+	0.303911i
$851$	176.408	+	484.676i	0.207295	+	0.569537i
$852$		0			0
$853$	−184.006	−	1043.55i	−0.215717	−	1.22339i	−0.879658	−	0.475606i	$-0.842229\pi$
$853$	−184.006	−	1043.55i	−0.215717	−	1.22339i	0.663942	−	0.747784i	$-0.268882\pi$
$854$	161.202	+	1828.99i	0.188761	+	2.14168i
$855$		0			0
$856$	−299.404	+	300.561i	−0.349771	+	0.351123i
$857$	−362.506	+	304.178i	−0.422994	+	0.354934i	−0.829301	−	0.558803i	$-0.811261\pi$
$857$	−362.506	+	304.178i	−0.422994	+	0.354934i	0.406307	+	0.913737i	$0.366816\pi$
$858$		0			0
$859$	318.137	+	56.0961i	0.370357	+	0.0653039i	0.355729	−	0.934589i	$-0.384233\pi$
$859$	318.137	+	56.0961i	0.370357	+	0.0653039i	0.0146277	+	0.999893i	$0.495344\pi$
$860$	246.863	+	426.312i	0.287050	+	0.495712i
$861$		0			0
$862$	289.625	−	77.8044i	0.335992	−	0.0902604i
$863$			1003.38i			1.16266i	0.813668	+	0.581330i	$0.197468\pi$
$863$			1003.38i			1.16266i	−0.813668	+	0.581330i	$0.802532\pi$
$864$		0			0
$865$	−576.415			−0.666375
$866$	60.8153	+	226.383i	0.0702256	+	0.261413i
$867$		0			0
$868$	1511.92	−	875.500i	1.74184	−	1.00864i
$869$	−59.5585	+	337.773i	−0.0685369	+	0.388692i
$870$		0			0
$871$	534.343	+	636.805i	0.613482	+	0.731120i
$872$	1096.91	+	1092.68i	1.25792	+	1.25308i
$873$		0			0
$874$	−848.652	+	74.7975i	−0.970998	+	0.0855806i
$875$	559.573	−	98.6678i	0.639512	−	0.112763i
$876$		0			0
$877$	375.169	−	136.550i	0.427787	−	0.155702i	−0.119149	−	0.992876i	$-0.538017\pi$
$877$	375.169	−	136.550i	0.427787	−	0.155702i	0.546935	+	0.837175i	$0.315794\pi$
$878$	−158.441	+	226.588i	−0.180457	+	0.258072i
$879$		0			0
$880$	−354.117	−	203.237i	−0.402406	−	0.230951i
$881$	−628.998	+	1089.46i	−0.713959	+	1.23661i	0.249400	+	0.968401i	$0.419767\pi$
$881$	−628.998	+	1089.46i	−0.713959	+	1.23661i	−0.963360	+	0.268213i	$0.913567\pi$
$882$		0			0
$883$	−26.0807	+	15.0577i	−0.0295365	+	0.0170529i	−0.514696	−	0.857373i	$-0.672095\pi$
$883$	−26.0807	+	15.0577i	−0.0295365	+	0.0170529i	0.485159	+	0.874426i	$0.338762\pi$
$884$	252.338	+	690.527i	0.285450	+	0.781139i
$885$		0			0
$886$	−453.927	−	971.818i	−0.512333	−	1.09686i
$887$	208.670	−	248.683i	0.235253	−	0.280364i	−0.635482	−	0.772115i	$-0.719199\pi$
$887$	208.670	−	248.683i	0.235253	−	0.280364i	0.870736	+	0.491752i	$0.163643\pi$
$888$		0			0
$889$	260.540	+	94.8287i	0.293070	+	0.106669i
$890$	168.736	+	240.650i	0.189591	+	0.270394i
$891$		0			0
$892$	183.960	+	66.6880i	0.206233	+	0.0747623i
$893$	−80.4659	−	29.2872i	−0.0901074	−	0.0327964i
$894$		0			0
$895$	1275.57	−	1520.17i	1.42522	−	1.69851i
$896$	−925.856	−	642.099i	−1.03332	−	0.716628i
$897$		0			0
$898$	882.115	+	235.754i	0.982311	+	0.262532i
$899$	1860.55	−	1074.19i	2.06958	−	1.19487i
$900$		0			0
$901$	−619.566	+	1073.12i	−0.687642	+	1.19103i
$902$	−248.444	−	248.125i	−0.275437	−	0.275083i
$903$		0			0
$904$	492.649	−	346.375i	0.544966	−	0.383158i
$905$	1215.43	−	442.379i	1.34301	−	0.488816i
$906$		0			0
$907$	−1332.50	+	234.956i	−1.46913	+	0.259047i	−0.850226	−	0.526418i	$-0.823535\pi$
$907$	−1332.50	+	234.956i	−1.46913	+	0.259047i	−0.618905	+	0.785465i	$0.712424\pi$
$908$	1081.35	−	909.737i	1.19092	−	1.00191i
$909$		0			0
$910$	−1211.61	−	564.036i	−1.33144	−	0.619820i
$911$	−433.248	−	516.324i	−0.475574	−	0.566767i	0.473914	−	0.880571i	$-0.342841\pi$
$911$	−433.248	−	516.324i	−0.475574	−	0.566767i	−0.949488	+	0.313805i	$0.898396\pi$
$912$		0			0
$913$	−43.9843	+	249.447i	−0.0481756	+	0.273217i
$914$	−100.278	+	1154.73i	−0.109713	+	1.26338i
$915$		0			0
$916$	−555.996	+	664.343i	−0.606982	+	0.725266i
$917$	−712.629			−0.777131
$918$		0			0
$919$			1384.80i			1.50685i	0.657534	+	0.753425i	$0.271600\pi$
$919$			1384.80i			1.50685i	−0.657534	+	0.753425i	$0.728400\pi$
$920$	−76.8772	+	898.678i	−0.0835622	+	0.976824i
$921$		0			0
$922$	−69.5747	+	801.177i	−0.0754606	+	0.868955i
$923$	−663.679	−	117.025i	−0.719046	−	0.126787i
$924$		0			0
$925$	326.249	−	273.755i	0.352702	−	0.295952i
$926$	−1531.08	−	712.757i	−1.65344	−	0.769716i
$927$		0			0
$928$	−1137.49	−	791.038i	−1.22574	−	0.852412i
$929$	−218.722	−	1240.43i	−0.235438	−	1.33523i	−0.841690	−	0.539961i	$-0.818439\pi$
$929$	−218.722	−	1240.43i	−0.235438	−	1.33523i	0.606252	−	0.795272i	$-0.292672\pi$
$930$		0			0
$931$	232.102	+	637.694i	0.249303	+	0.684956i
$932$	−0.0893834	−	69.4871i	−9.59049e−5	−	0.0745569i
$933$		0			0
$934$	968.804	+	967.558i	1.03726	+	1.03593i
$935$	−337.398	−	194.797i	−0.360853	−	0.208339i
$936$		0			0
$937$	−429.804	−	744.443i	−0.458703	−	0.794496i	0.540190	−	0.841543i	$-0.318352\pi$
$937$	−429.804	−	744.443i	−0.458703	−	0.794496i	−0.998893	+	0.0470467i	$0.985019\pi$
$938$	−1174.43	−	313.878i	−1.25206	−	0.334625i
$939$		0			0
$940$	−45.2277	+	78.5699i	−0.0481146	+	0.0835850i
$941$	109.878	+	92.1984i	0.116767	+	0.0979791i	0.699302	−	0.714827i	$-0.253494\pi$
$941$	109.878	+	92.1984i	0.116767	+	0.0979791i	−0.582535	+	0.812806i	$0.697939\pi$
$942$		0			0
$943$	−265.296	+	728.894i	−0.281332	+	0.772953i
$944$	507.027	−	607.418i	0.537105	−	0.643452i
$945$		0			0
$946$	−90.7509	−	129.428i	−0.0959311	−	0.136816i
$947$	−302.546	+	831.238i	−0.319478	+	0.877759i	0.671168	+	0.741305i	$0.265793\pi$
$947$	−302.546	+	831.238i	−0.319478	+	0.877759i	−0.990646	+	0.136454i	$0.956429\pi$
$948$		0			0
$949$	238.478	+	200.106i	0.251294	+	0.210860i
$950$	297.705	+	637.359i	0.313373	+	0.670905i
$951$		0			0
$952$	−881.870	−	614.960i	−0.926334	−	0.645966i
$953$	376.513	+	652.140i	0.395082	+	0.684302i	0.993112	−	0.117172i	$-0.0373828\pi$
$953$	376.513	+	652.140i	0.395082	+	0.684302i	−0.598030	+	0.801474i	$0.704049\pi$
$954$		0			0
$955$	−170.081	−	98.1963i	−0.178095	−	0.102823i
$956$	91.1993	−	521.136i	0.0953968	−	0.545122i
$957$		0			0
$958$	−555.930	+	795.038i	−0.580303	+	0.829894i
$959$	−306.744	−	842.773i	−0.319859	−	0.878804i
$960$		0			0
$961$	−260.665	−	1478.31i	−0.271244	−	1.53830i
$962$	691.895	−	60.9814i	0.719225	−	0.0633902i
$963$		0			0
$964$	−1013.08	+	179.977i	−1.05091	+	0.186698i
$965$	−934.275	+	783.950i	−0.968161	+	0.812383i
$966$		0			0
$967$	−1807.24	−	318.666i	−1.86892	−	0.329541i	−0.879646	−	0.475628i	$-0.842221\pi$
$967$	−1807.24	−	318.666i	−1.86892	−	0.329541i	−0.989272	+	0.146087i	$0.953332\pi$
$968$	−759.249	−	352.262i	−0.784348	−	0.363907i
$969$		0			0
$970$	−309.257	−	1151.20i	−0.318821	−	1.18680i
$971$		−	1398.13i		−	1.43989i	−0.694031	−	0.719945i	$-0.744167\pi$
$971$		−	1398.13i		−	1.43989i	0.694031	−	0.719945i	$-0.255833\pi$
$972$		0			0
$973$	1933.78			1.98744
$974$	150.539	−	40.4407i	0.154558	−	0.0415202i
$975$		0			0
$976$	−293.992	−	1642.59i	−0.301221	−	1.68298i
$977$	−27.4421	+	155.632i	−0.0280881	+	0.159296i	−0.995626	−	0.0934315i	$-0.970216\pi$
$977$	−27.4421	+	155.632i	−0.0280881	+	0.159296i	0.967538	+	0.252727i	$0.0813275\pi$
$978$		0			0
$979$	−60.6214	−	72.2457i	−0.0619217	−	0.0737955i
$980$	707.386	−	125.670i	0.721823	−	0.128234i
$981$		0			0
$982$	71.0413	+	806.035i	0.0723435	+	0.820809i
$983$	972.425	−	171.465i	0.989242	−	0.174430i	0.344464	−	0.938800i	$-0.388061\pi$
$983$	972.425	−	171.465i	0.989242	−	0.174430i	0.644779	+	0.764369i	$0.276950\pi$
$984$		0			0
$985$	1576.22	−	573.697i	1.60022	−	0.582434i
$986$	−1083.44	−	757.597i	−1.09883	−	0.768354i
$987$		0			0
$988$	−197.767	+	1130.09i	−0.200169	+	1.14382i
$989$	−174.600	+	302.416i	−0.176542	+	0.305780i
$990$		0			0
$991$	528.087	−	304.891i	0.532883	−	0.307660i	−0.209307	−	0.977850i	$-0.567121\pi$
$991$	528.087	−	304.891i	0.532883	−	0.307660i	0.742190	+	0.670190i	$0.233787\pi$
$992$	−1297.74	+	914.920i	−1.30820	+	0.922298i
$993$		0			0
$994$	892.910	−	417.070i	0.898300	−	0.419588i
$995$	−120.718	+	143.866i	−0.121324	+	0.144589i
$996$		0			0
$997$	183.098	+	66.6423i	0.183649	+	0.0668428i	0.432208	−	0.901774i	$-0.357735\pi$
$997$	183.098	+	66.6423i	0.183649	+	0.0668428i	−0.248559	+	0.968617i	$0.579957\pi$
$998$	1180.18	−	827.505i	1.18255	−	0.829163i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.j.a.307.13		204
3.2	odd	2		108.3.j.a.31.22	yes	204
4.3	odd	2	inner	324.3.j.a.307.6		204
12.11	even	2		108.3.j.a.31.29	yes	204
27.7	even	9	inner	324.3.j.a.19.6		204
27.20	odd	18		108.3.j.a.7.29	yes	204
108.7	odd	18	inner	324.3.j.a.19.13		204
108.47	even	18		108.3.j.a.7.22	✓	204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.j.a.7.22	✓	204	108.47	even	18
108.3.j.a.7.29	yes	204	27.20	odd	18
108.3.j.a.31.22	yes	204	3.2	odd	2
108.3.j.a.31.29	yes	204	12.11	even	2
324.3.j.a.19.6		204	27.7	even	9	inner
324.3.j.a.19.13		204	108.7	odd	18	inner
324.3.j.a.307.6		204	4.3	odd	2	inner
324.3.j.a.307.13		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)

\(f(q)\)	\(=\)	\(q+(-0.518880 - 1.93152i) q^{2} +(-3.46153 + 2.00445i) q^{4} +(-1.09499 + 6.21002i) q^{5} +(-5.65814 - 6.74311i) q^{7} +(5.66776 + 5.64593i) q^{8} +O(q^{10})\)	\(q+(-0.518880 - 1.93152i) q^{2} +(-3.46153 + 2.00445i) q^{4} +(-1.09499 + 6.21002i) q^{5} +(-5.65814 - 6.74311i) q^{7} +(5.66776 + 5.64593i) q^{8} +(12.5629 - 1.10726i) q^{10} +(-3.98532 + 0.702720i) q^{11} +(11.3127 - 4.11749i) q^{13} +(-10.0885 + 14.4277i) q^{14} +(7.96433 - 13.8769i) q^{16} +(7.63358 - 13.2217i) q^{17} +(20.6326 - 11.9123i) q^{19} +(-8.65735 - 23.6910i) q^{20} +(3.42522 + 7.33310i) q^{22} +(11.4927 - 13.6965i) q^{23} +(-13.8730 - 5.04937i) q^{25} +(-13.8229 - 19.7142i) q^{26} +(33.1021 + 12.0000i) q^{28} +(40.6859 + 14.8084i) q^{29} +(31.8949 - 38.0109i) q^{31} +(-30.9361 - 8.18277i) q^{32} +(-29.4990 - 7.88389i) q^{34} +(48.0705 - 27.7535i) q^{35} +(-14.4238 + 24.9828i) q^{37} +(-33.7146 - 33.6713i) q^{38} +(-41.2675 + 29.0146i) q^{40} +(-40.7670 + 14.8380i) q^{41} +(-19.2340 + 3.39148i) q^{43} +(12.3867 - 10.4209i) q^{44} +(-32.4184 - 15.0916i) q^{46} +(-2.31031 - 2.75332i) q^{47} +(-4.94621 + 28.0514i) q^{49} +(-2.55450 + 29.4160i) q^{50} +(-30.9059 + 36.9286i) q^{52} -81.1632 q^{53} -25.5184i q^{55} +(6.00214 - 70.1638i) q^{56} +(7.49168 - 86.2693i) q^{58} +(48.7001 + 8.58715i) q^{59} +(79.8933 - 67.0384i) q^{61} +(-89.9683 - 41.8825i) q^{62} +(0.246975 + 63.9995i) q^{64} +(13.1823 + 74.7607i) q^{65} +(23.6170 + 64.8871i) q^{67} +(0.0785545 + 61.0686i) q^{68} +(-78.5492 - 78.4483i) q^{70} +(-48.4794 - 27.9896i) q^{71} +(12.9295 + 22.3946i) q^{73} +(55.7389 + 14.8968i) q^{74} +(-47.5428 + 82.5917i) q^{76} +(27.2880 + 22.8974i) q^{77} +(28.9877 - 79.6430i) q^{79} +(77.4552 + 64.6538i) q^{80} +(49.8130 + 71.0430i) q^{82} +(21.4076 - 58.8168i) q^{83} +(73.7486 + 61.8824i) q^{85} +(16.5309 + 35.3911i) q^{86} +(-26.5554 - 18.5180i) q^{88} +(11.6524 + 20.1826i) q^{89} +(-91.7735 - 52.9855i) q^{91} +(-12.3284 + 70.4475i) q^{92} +(-4.11931 + 5.89104i) q^{94} +(51.3827 + 141.173i) q^{95} +(-16.4127 - 93.0811i) q^{97} +(56.7482 - 5.00160i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) \) 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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