LMFDB - Embedded newform 324.3.j.a.307.6

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			307.6
Character	$\chi$	$=$	324.307
Dual form			324.3.j.a.19.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.63904 + 1.14610i) q^{2} +(1.37291 - 3.75701i) q^{4} +(-1.09499 + 6.21002i) q^{5} +(5.65814 + 6.74311i) q^{7} +(2.05564 + 7.73139i) q^{8} +O(q^{10})$	\(q+(-1.63904 + 1.14610i) q^{2} +(1.37291 - 3.75701i) q^{4} +(-1.09499 + 6.21002i) q^{5} +(5.65814 + 6.74311i) q^{7} +(2.05564 + 7.73139i) q^{8} +(-5.32256 - 11.4335i) q^{10} +(3.98532 - 0.702720i) q^{11} +(11.3127 - 4.11749i) q^{13} +(-17.0022 - 4.56745i) q^{14} +(-12.2302 - 10.3161i) q^{16} +(7.63358 - 13.2217i) q^{17} +(-20.6326 + 11.9123i) q^{19} +(21.8278 + 12.6397i) q^{20} +(-5.72672 + 5.71936i) q^{22} +(-11.4927 + 13.6965i) q^{23} +(-13.8730 - 5.04937i) q^{25} +(-13.8229 + 19.7142i) q^{26} +(33.1021 - 12.0000i) q^{28} +(40.6859 + 14.8084i) q^{29} +(-31.8949 + 38.0109i) q^{31} +(31.8691 + 2.89148i) q^{32} +(2.64168 + 30.4198i) q^{34} +(-48.0705 + 27.7535i) q^{35} +(-14.4238 + 24.9828i) q^{37} +(20.1651 - 43.1717i) q^{38} +(-50.2630 + 4.29973i) q^{40} +(-40.7670 + 14.8380i) q^{41} +(19.2340 - 3.39148i) q^{43} +(2.83138 - 15.9377i) q^{44} +(3.13952 - 35.6210i) q^{46} +(2.31031 + 2.75332i) q^{47} +(-4.94621 + 28.0514i) q^{49} +(28.5255 - 7.62373i) q^{50} +(0.0619431 - 48.1549i) q^{52} -81.1632 q^{53} +25.5184i q^{55} +(-40.5025 + 57.6067i) q^{56} +(-83.6578 + 22.3584i) q^{58} +(-48.7001 - 8.58715i) q^{59} +(79.8933 - 67.0384i) q^{61} +(8.71286 - 98.8561i) q^{62} +(-55.5487 + 31.7859i) q^{64} +(13.1823 + 74.7607i) q^{65} +(-23.6170 - 64.8871i) q^{67} +(-39.1940 - 46.8317i) q^{68} +(46.9813 - 100.583i) q^{70} +(48.4794 + 27.9896i) q^{71} +(12.9295 + 22.3946i) q^{73} +(-4.99150 - 57.4789i) q^{74} +(16.4276 + 93.8714i) q^{76} +(27.2880 + 22.8974i) q^{77} +(-28.9877 + 79.6430i) q^{79} +(77.4552 - 64.6538i) q^{80} +(49.8130 - 71.0430i) q^{82} +(-21.4076 + 58.8168i) q^{83} +(73.7486 + 61.8824i) q^{85} +(-27.6384 + 27.6029i) q^{86} +(13.6254 + 29.3675i) q^{88} +(11.6524 + 20.1826i) q^{89} +(91.7735 + 52.9855i) q^{91} +(35.6794 + 61.9824i) q^{92} +(-6.94226 - 1.86496i) q^{94} +(-51.3827 - 141.173i) q^{95} +(-16.4127 - 93.0811i) q^{97} +(-24.0426 - 51.6462i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.63904	+	1.14610i	−0.819521	+	0.573049i
$2$	−1.63904	+	1.14610i	−0.819521	+	0.573049i
$3$		0			0
$3$		0			0
$4$	1.37291	−	3.75701i	0.343229	−	0.939252i
$5$	−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	0.999835	−	0.0181856i	$-0.00578896\pi$
$7$	5.65814	+	6.74311i	0.808306	+	0.963301i	−0.191529	+	0.981487i	$0.561345\pi$
$8$	2.05564	+	7.73139i	0.256955	+	0.966423i
$9$		0			0
$10$	−5.32256	−	11.4335i	−0.532256	−	1.14335i
$11$	3.98532	−	0.702720i	0.362302	−	0.0638836i	0.0104659	−	0.999945i	$-0.496669\pi$
$11$	3.98532	−	0.702720i	0.362302	−	0.0638836i	0.351836	+	0.936062i	$0.385557\pi$
$12$		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	$0.235652\pi$
$14$	−17.0022	−	4.56745i	−1.21444	−	0.326246i
$15$		0			0
$16$	−12.2302	−	10.3161i	−0.764388	−	0.644756i
$17$	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	−0.932489	−	0.361198i	$-0.882368\pi$
$19$	−20.6326	+	11.9123i	−1.08593	+	0.626961i	−0.153438	+	0.988158i	$0.549035\pi$
$20$	21.8278	+	12.6397i	1.09139	+	0.631986i
$21$		0			0
$22$	−5.72672	+	5.71936i	−0.260306	+	0.259971i
$23$	−11.4927	+	13.6965i	−0.499684	+	0.595501i	−0.955653	−	0.294495i	$-0.904848\pi$
$23$	−11.4927	+	13.6965i	−0.499684	+	0.595501i	0.455969	+	0.889996i	$0.349293\pi$
$24$		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	$0.517558\pi$
$31$	−31.8949	+	38.0109i	−1.02887	+	1.22616i	−0.973736	+	0.227678i	$0.926887\pi$
$32$	31.8691	+	2.89148i	0.995909	+	0.0903589i
$33$		0			0
$34$	2.64168	+	30.4198i	0.0776964	+	0.894701i
$35$	−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	$0.294134\pi$
$38$	20.1651	−	43.1717i	0.530661	−	1.13610i
$39$		0			0
$40$	−50.2630	+	4.29973i	−1.25657	+	0.107493i
$41$	−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	0.0545406	−	0.998512i	$-0.482631\pi$
$43$	19.2340	−	3.39148i	0.447303	−	0.0788716i	0.392762	+	0.919640i	$0.371519\pi$
$44$	2.83138	−	15.9377i	0.0643496	−	0.362220i
$45$		0			0
$46$	3.13952	−	35.6210i	0.0682504	−	0.774369i
$47$	2.31031	+	2.75332i	0.0491555	+	0.0585812i	0.790062	−	0.613027i	$-0.210048\pi$
$47$	2.31031	+	2.75332i	0.0491555	+	0.0585812i	−0.740907	+	0.671608i	$0.765604\pi$
$48$		0			0
$49$	−4.94621	+	28.0514i	−0.100943	+	0.572477i
$50$	28.5255	−	7.62373i	0.570511	−	0.152475i
$51$		0			0
$52$	0.0619431	−	48.1549i	0.00119121	−	0.926055i
$53$	−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
$56$	−40.5025	+	57.6067i	−0.723259	+	1.02869i
$57$		0			0
$58$	−83.6578	+	22.3584i	−1.44238	+	0.385489i
$59$	−48.7001	−	8.58715i	−0.825426	−	0.145545i	−0.255049	−	0.966928i	$-0.582092\pi$
$59$	−48.7001	−	8.58715i	−0.825426	−	0.145545i	−0.570377	+	0.821383i	$0.693203\pi$
$60$		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	$-0.0485809\pi$
$62$	8.71286	−	98.8561i	0.140530	−	1.59445i
$63$		0			0
$64$	−55.5487	+	31.7859i	−0.867948	+	0.496654i
$65$	13.1823	+	74.7607i	0.202805	+	1.15016i
$66$		0			0
$67$	−23.6170	−	64.8871i	−0.352492	−	0.968464i	−0.981567	−	0.191119i	$-0.938788\pi$
$67$	−23.6170	−	64.8871i	−0.352492	−	0.968464i	0.629075	−	0.777345i	$-0.283434\pi$
$68$	−39.1940	−	46.8317i	−0.576382	−	0.688702i
$69$		0			0
$70$	46.9813	−	100.583i	0.671161	−	1.43690i
$71$	48.4794	+	27.9896i	0.682808	+	0.394219i	0.800912	−	0.598782i	$-0.204348\pi$
$71$	48.4794	+	27.9896i	0.682808	+	0.394219i	−0.118104	+	0.993001i	$0.537682\pi$
$72$		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	$0.776656\pi$
$74$	−4.99150	−	57.4789i	−0.0674528	−	0.776742i
$75$		0			0
$76$	16.4276	+	93.8714i	0.216153	+	1.23515i
$77$	27.2880	+	22.8974i	0.354390	+	0.297369i
$78$		0			0
$79$	−28.9877	+	79.6430i	−0.366933	+	1.00814i	0.609589	+	0.792718i	$0.291335\pi$
$79$	−28.9877	+	79.6430i	−0.366933	+	1.00814i	−0.976521	+	0.215421i	$0.930888\pi$
$80$	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	$0.234175\pi$
$83$	−21.4076	+	58.8168i	−0.257922	+	0.708636i	−0.999295	+	0.0375425i	$0.988047\pi$
$84$		0			0
$85$	73.7486	+	61.8824i	0.867631	+	0.728028i
$86$	−27.6384	+	27.6029i	−0.321377	+	0.320964i
$87$		0			0
$88$	13.6254	+	29.3675i	0.154834	+	0.333722i
$89$	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
$92$	35.6794	+	61.9824i	0.387819	+	0.673722i
$93$		0			0
$94$	−6.94226	−	1.86496i	−0.0738538	−	0.0198400i
$95$	−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	$-0.217538\pi$
$98$	−24.0426	−	51.6462i	−0.245333	−	0.527002i
$99$		0			0
$100$	−38.0170	+	45.1887i	−0.380170	+	0.451887i
$101$	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	0.475150	−	0.879905i	$-0.342394\pi$
$103$	63.9321	+	11.2730i	0.620700	+	0.109446i	0.145550	+	0.989351i	$0.453505\pi$
$104$	55.0887	+	78.9988i	0.529699	+	0.759604i
$105$		0			0
$106$	133.030	−	93.0210i	1.25500	−	0.877557i
$107$		−	53.0300i		−	0.495608i	−0.968810	−	0.247804i	$-0.920291\pi$
$107$		−	53.0300i		−	0.495608i	0.968810	−	0.247804i	$-0.0797089\pi$
$108$		0			0
$109$	193.535			1.77555			0.887773	−	0.460281i	$-0.152251\pi$
$109$	193.535			1.77555			0.887773	+	0.460281i	$0.152251\pi$
$110$	−29.2466	−	41.8257i	−0.265878	−	0.380234i
$111$		0			0
$112$	0.362334	−	140.840i	0.00323512	−	1.25750i
$113$	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
$116$	111.494	−	132.526i	0.961152	−	1.14247i
$117$		0			0
$118$	89.6633	−	41.7405i	0.759858	−	0.353733i
$119$	132.348	−	23.3364i	1.11216	−	0.196105i
$120$		0			0
$121$	−98.3138	+	35.7833i	−0.812511	+	0.295730i
$122$	−54.1157	+	201.444i	−0.443572	+	1.65118i
$123$		0			0
$124$	99.0182	+	172.015i	0.798533	+	1.38722i
$125$	−32.2752	+	55.9023i	−0.258202	+	0.447218i
$126$		0			0
$127$	27.2780	−	15.7489i	0.214787	−	0.124007i	−0.388747	−	0.921345i	$-0.627092\pi$
$127$	27.2780	−	15.7489i	0.214787	−	0.124007i	0.603534	+	0.797337i	$0.293759\pi$
$128$	54.6169	−	115.763i	0.426694	−	0.904396i
$129$		0			0
$130$	−107.290	−	107.428i	−0.825304	−	0.826367i
$131$	−52.0385	+	62.0171i	−0.397240	+	0.473413i	−0.927176	−	0.374625i	$-0.877771\pi$
$131$	−52.0385	+	62.0171i	−0.397240	+	0.473413i	0.529936	+	0.848038i	$0.322216\pi$
$132$		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	$-0.487737\pi$
$139$	141.211	−	168.289i	1.01591	−	1.21071i	0.977389	−	0.211451i	$-0.0678189\pi$
$140$	38.2735	+	218.704i	0.273382	+	1.56217i
$141$		0			0
$142$	−111.538	+	9.68607i	−0.785482	+	0.0682118i
$143$	42.1913	−	24.3592i	0.295044	−	0.170344i
$144$		0			0
$145$	−136.512	+	236.445i	−0.941459	+	1.63065i
$146$	−46.8585	−	21.8872i	−0.320949	−	0.149912i
$147$		0			0
$148$	74.0578	+	88.4896i	0.500391	+	0.597902i
$149$	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	−0.535188	−	0.844733i	$-0.679759\pi$
$151$	−113.127	+	19.9473i	−0.749183	+	0.132101i	−0.213996	+	0.976835i	$0.568648\pi$
$152$	−134.511	−	135.032i	−0.884944	−	0.888365i
$153$		0			0
$154$	−70.9689	−	6.25497i	−0.460837	−	0.0406167i
$155$	−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	$0.0739093\pi$
$158$	−43.7667	−	163.761i	−0.277005	−	1.03646i
$159$		0			0
$160$	−52.8526	+	194.742i	−0.330329	+	1.21713i
$161$	−157.385			−0.977544
$162$		0			0
$163$			111.870i			0.686322i	0.939277	+	0.343161i	$0.111498\pi$
$163$			111.870i			0.686322i	−0.939277	+	0.343161i	$0.888502\pi$
$164$	−0.223221	+	173.533i	−0.00136110	+	1.05813i
$165$		0			0
$166$	−32.3220	−	120.938i	−0.194711	−	0.728544i
$167$	−58.4844	−	10.3124i	−0.350206	−	0.0617508i	−0.00422188	−	0.999991i	$-0.501344\pi$
$167$	−58.4844	−	10.3124i	−0.350206	−	0.0617508i	−0.345984	+	0.938240i	$0.612455\pi$
$168$		0			0
$169$	−18.4380	+	15.4713i	−0.109101	+	0.0915463i
$170$	−191.800	−	16.9047i	−1.12824	−	0.0994392i
$171$		0			0
$172$	13.6649	−	76.9186i	0.0794469	−	0.447201i
$173$	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
$176$	−55.9907	−	32.5186i	−0.318129	−	0.184765i
$177$		0			0
$178$	−42.2301	−	19.7253i	−0.237248	−	0.110816i
$179$	272.538	+	157.350i	1.52256	+	0.879050i	0.999644	+	0.0266652i	$0.00848882\pi$
$179$	272.538	+	157.350i	1.52256	+	0.879050i	0.522915	+	0.852385i	$0.324845\pi$
$180$		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	$-0.358416\pi$
$182$	−211.147	+	18.3362i	−1.16015	+	0.100748i
$183$		0			0
$184$	−129.518	−	60.6997i	−0.703902	−	0.329890i
$185$	−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	−0.908679	−	0.417495i	$-0.862908\pi$
$191$	10.6521	−	29.2664i	0.0557702	−	0.153227i	0.964449	+	0.264268i	$0.0851303\pi$
$192$		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	$0.555165\pi$
$194$	133.581	+	133.753i	0.688563	+	0.689449i
$195$		0			0
$196$	98.5984	+	57.0951i	0.503053	+	0.291301i
$197$	−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	0.433793	−	0.901013i	$-0.357175\pi$
$199$	−25.7924	−	14.8913i	−0.129610	−	0.0748305i	−0.563403	+	0.826182i	$0.690508\pi$
$200$	10.5207	−	117.637i	0.0526035	−	0.588187i
$201$		0			0
$202$	−69.7741	+	259.732i	−0.345416	+	1.28580i
$203$	130.351	+	358.138i	0.642125	+	1.76422i
$204$		0			0
$205$	−47.5045	−	269.411i	−0.231729	−	1.31420i
$206$	−117.707	+	54.7957i	−0.571395	+	0.265998i
$207$		0			0
$208$	−180.833	−	66.3452i	−0.869390	−	0.318967i
$209$	−73.8567	+	61.9731i	−0.353381	+	0.296522i
$210$		0			0
$211$	110.858	+	19.5472i	0.525393	+	0.0926409i	0.430053	−	0.902804i	$-0.358495\pi$
$211$	110.858	+	19.5472i	0.525393	+	0.0926409i	0.0953402	+	0.995445i	$0.469606\pi$
$212$	−111.430	+	304.931i	−0.525614	+	1.43835i
$213$		0			0
$214$	60.7777	+	86.9184i	0.284008	+	0.406161i
$215$			123.157i			0.572825i
$216$		0			0
$217$	−436.777			−2.01280
$218$	−317.211	+	221.810i	−1.45510	+	1.01748i
$219$		0			0
$220$	95.8728	+	35.0346i	0.435786	+	0.159248i
$221$	31.9160	−	181.005i	0.144416	−	0.819026i
$222$		0			0
$223$	31.4443	+	37.4738i	0.141006	+	0.168044i	0.831925	−	0.554887i	$-0.187239\pi$
$223$	31.4443	+	37.4738i	0.141006	+	0.168044i	−0.690920	+	0.722931i	$0.742794\pi$
$224$	160.822	+	231.257i	0.717956	+	1.03240i
$225$		0			0
$226$	63.5404	+	136.492i	0.281152	+	0.603947i
$227$	347.917	−	61.3471i	1.53267	−	0.270251i	0.657273	−	0.753652i	$-0.271710\pi$
$227$	347.917	−	61.3471i	1.53267	−	0.270251i	0.875399	+	0.483401i	$0.160599\pi$
$228$		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	$0.232106\pi$
$230$	217.769	+	58.5012i	0.946822	+	0.254353i
$231$		0			0
$232$	−30.8544	+	344.999i	−0.132993	+	1.48706i
$233$	−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
$236$	−99.1231	+	171.177i	−0.420013	+	0.725328i
$237$		0			0
$238$	−190.177	+	189.933i	−0.799064	+	0.798037i
$239$	85.0177	−	101.320i	0.355722	−	0.423934i	−0.558273	−	0.829657i	$-0.688536\pi$
$239$	85.0177	−	101.320i	0.355722	−	0.423934i	0.913996	+	0.405724i	$0.132980\pi$
$240$		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
$248$	−359.441	−	168.455i	−1.44936	−	0.679255i
$249$		0			0
$250$	−11.1692	−	128.617i	−0.0446766	−	0.514467i
$251$	40.4851	−	23.3741i	0.161295	−	0.0931237i	−0.417180	−	0.908824i	$-0.636981\pi$
$251$	40.4851	−	23.3741i	0.161295	−	0.0931237i	0.578475	+	0.815700i	$0.303648\pi$
$252$		0			0
$253$	−36.1775	+	62.6612i	−0.142994	+	0.247673i
$254$	−26.6599	+	57.0764i	−0.104960	+	0.224710i
$255$		0			0
$256$	43.1562	+	252.336i	0.168579	+	0.985688i
$257$	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
$260$	298.975	+	53.1140i	1.14990	+	0.204284i
$261$		0			0
$262$	14.2156	−	161.290i	0.0542579	−	0.615610i
$263$	99.5544	+	118.644i	0.378534	+	0.451119i	0.921351	−	0.388732i	$-0.127087\pi$
$263$	99.5544	+	118.644i	0.378534	+	0.451119i	−0.542817	+	0.839851i	$0.682642\pi$
$264$		0			0
$265$	88.8732	−	504.025i	0.335371	−	1.90198i
$266$	405.209	−	108.296i	1.52334	−	0.407128i
$267$		0			0
$268$	−276.205	−	0.355292i	−1.03062	−	0.00132571i
$269$	−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	$-0.855432\pi$
$271$		−	237.786i		−	0.877438i	0.898624	−	0.438719i	$-0.144568\pi$
$272$	−229.757	+	82.9560i	−0.844696	+	0.304985i
$273$		0			0
$274$	−196.864	+	52.6140i	−0.718483	+	0.192022i
$275$	−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	$0.379429\pi$
$278$	−38.5751	+	437.674i	−0.138759	+	1.57437i
$279$		0			0
$280$	−313.389	−	314.600i	−1.11925	−	1.12357i
$281$	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	$-0.798735\pi$
$283$	−160.917	−	442.115i	−0.568610	−	1.56224i	0.238065	−	0.971249i	$-0.423487\pi$
$284$	171.715	−	143.710i	0.604630	−	0.506021i
$285$		0			0
$286$	−41.2353	+	88.2811i	−0.144179	+	0.308675i
$287$	−330.719	−	190.941i	−1.15233	−	0.665299i
$288$		0			0
$289$	27.9569	+	48.4228i	0.0967367	+	0.167553i
$290$	−47.2412	−	543.999i	−0.162901	−	1.87586i
$291$		0			0
$292$	101.888	−	17.8305i	0.348931	−	0.0610633i
$293$	−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
$302$	162.558	−	162.349i	0.538271	−	0.537579i
$303$		0			0
$304$	375.229	+	67.1589i	1.23431	+	0.220917i
$305$	328.827	+	569.545i	1.07812	+	1.86736i
$306$		0			0
$307$	251.000	+	144.915i	0.817589	+	0.472035i	0.849584	−	0.527453i	$-0.176853\pi$
$307$	251.000	+	144.915i	0.817589	+	0.472035i	−0.0319956	+	0.999488i	$0.510186\pi$
$308$	123.490	−	71.0852i	0.400941	−	0.230796i
$309$		0			0
$310$	604.358	+	162.354i	1.94954	+	0.523722i
$311$	−116.870	−	321.097i	−0.375787	−	1.03247i	−0.973085	−	0.230446i	$-0.925981\pi$
$311$	−116.870	−	321.097i	−0.375787	−	1.03247i	0.597298	−	0.802019i	$-0.296241\pi$
$312$		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	$0.797348\pi$
$314$	−15.2736	−	32.8094i	−0.0486421	−	0.104489i
$315$		0			0
$316$	259.422	+	218.250i	0.820955	+	0.690664i
$317$	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
$320$	−136.565	−	379.764i	−0.426767	−	1.18676i
$321$		0			0
$322$	257.960	−	180.378i	0.801118	−	0.560181i
$323$			363.733i			1.12611i
$324$		0			0
$325$	−177.732			−0.546868
$326$	−128.215	−	183.360i	−0.393296	−	0.562455i
$327$		0			0
$328$	−198.520	−	284.684i	−0.605245	−	0.867938i
$329$	−5.49387	+	31.1573i	−0.0166987	+	0.0947030i
$330$		0			0
$331$	65.1143	+	77.6002i	0.196720	+	0.234442i	0.855383	−	0.517997i	$-0.173322\pi$
$331$	65.1143	+	77.6002i	0.196720	+	0.234442i	−0.658663	+	0.752438i	$0.728878\pi$
$332$	191.584	+	161.179i	0.577061	+	0.485478i
$333$		0			0
$334$	107.677	−	50.1265i	0.322388	−	0.150079i
$335$	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	$0.486923\pi$
$338$	12.4890	−	46.4899i	0.0369497	−	0.137544i
$339$		0			0
$340$	333.743	−	192.115i	0.981598	−	0.565043i
$341$	−100.400	+	173.899i	−0.294430	+	0.509967i
$342$		0			0
$343$	156.397	−	90.2957i	0.455967	−	0.263253i
$344$	65.7590	+	141.734i	0.191160	+	0.412018i
$345$		0			0
$346$	−129.190	−	129.356i	−0.373382	−	0.373862i
$347$	144.591	−	172.317i	0.416688	−	0.496589i	−0.516345	−	0.856381i	$-0.672708\pi$
$347$	144.591	−	172.317i	0.416688	−	0.496589i	0.933033	+	0.359791i	$0.117152\pi$
$348$		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
$356$	91.8239	−	16.0693i	0.257932	−	0.0451384i
$357$		0			0
$358$	−627.040	+	54.4525i	−1.75151	+	0.152102i
$359$	−285.024	+	164.559i	−0.793939	+	0.458381i	−0.841348	−	0.540494i	$-0.818237\pi$
$359$	−285.024	+	164.559i	−0.793939	+	0.458381i	0.0474081	+	0.998876i	$0.484904\pi$
$360$		0			0
$361$	103.304	−	178.927i	0.286159	−	0.495643i
$362$	371.686	+	173.611i	1.02676	+	0.479589i
$363$		0			0
$364$	325.064	−	272.049i	0.893033	−	0.747388i
$365$	−153.229	+	55.7707i	−0.419805	+	0.152797i
$366$		0			0
$367$	187.339	−	33.0330i	0.510461	−	0.0900081i	0.0875156	−	0.996163i	$-0.472107\pi$
$367$	187.339	−	33.0330i	0.510461	−	0.0900081i	0.422946	+	0.906155i	$0.360996\pi$
$368$	281.853	−	48.9510i	0.765905	−	0.133019i
$369$		0			0
$370$	362.411	+	31.9417i	0.979489	+	0.0863290i
$371$	−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	$0.00130453\pi$
$374$	31.9046	+	119.376i	0.0853063	+	0.319188i
$375$		0			0
$376$	−16.5378	+	23.5217i	−0.0439835	+	0.0625577i
$377$	521.241			1.38260
$378$		0			0
$379$			101.688i			0.268305i	0.990961	+	0.134153i	$0.0428312\pi$
$379$			101.688i			0.268305i	−0.990961	+	0.134153i	$0.957169\pi$
$380$	−600.932	−	0.772997i	−1.58140	−	0.00203420i
$381$		0			0
$382$	16.0830	+	60.1772i	0.0421020	+	0.157532i
$383$	43.3604	+	7.64562i	0.113213	+	0.0199624i	0.229967	−	0.973198i	$-0.426138\pi$
$383$	43.3604	+	7.64562i	0.113213	+	0.0199624i	−0.116755	+	0.993161i	$0.537249\pi$
$384$		0			0
$385$	−172.073	+	144.387i	−0.446944	+	0.375030i
$386$	−385.327	−	33.9615i	−0.998256	−	0.0879830i
$387$		0			0
$388$	−372.240	−	66.1297i	−0.959380	−	0.170437i
$389$	−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
$392$	−227.044	+	19.4224i	−0.579193	+	0.0495469i
$393$		0			0
$394$	482.020	+	225.147i	1.22340	+	0.571439i
$395$	−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	$0.802065\pi$
$398$	59.3417	−	5.15327i	0.149100	−	0.0129479i
$399$		0			0
$400$	117.580	+	204.870i	0.293951	+	0.512176i
$401$	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	$0.571019\pi$
$410$	386.634	+	387.131i	0.943009	+	0.944223i
$411$		0			0
$412$	130.126	−	224.717i	0.315840	−	0.545429i
$413$	−217.648	−	376.978i	−0.526993	−	0.912779i
$414$		0			0
$415$	−341.812	−	197.345i	−0.823644	−	0.475531i
$416$	372.431	−	98.5101i	0.895267	−	0.236803i
$417$		0			0
$418$	50.0269	−	186.224i	0.119681	−	0.445511i
$419$	−119.164	−	327.401i	−0.284402	−	0.781388i	−0.996824	−	0.0796365i	$-0.974624\pi$
$419$	−119.164	−	327.401i	−0.284402	−	0.781388i	0.712422	−	0.701751i	$-0.247598\pi$
$420$		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	$0.881226\pi$
$422$	−204.104	+	95.0154i	−0.483658	+	0.225155i
$423$		0			0
$424$	−166.842	−	627.504i	−0.393496	−	1.47996i
$425$	−172.662	+	144.881i	−0.406264	+	0.340896i
$426$		0			0
$427$	904.095	+	159.416i	2.11732	+	0.373340i
$428$	−199.234	−	72.8057i	−0.465500	−	0.170107i
$429$		0			0
$430$	−141.150	−	201.860i	−0.328257	−	0.469442i
$431$		−	149.947i		−	0.347904i	−0.984754	−	0.173952i	$-0.944346\pi$
$431$		−	149.947i		−	0.347904i	0.984754	−	0.173952i	$-0.0556538\pi$
$432$		0			0
$433$	−117.205			−0.270681			−0.135341	−	0.990799i	$-0.543213\pi$
$433$	−117.205			−0.270681			−0.135341	+	0.990799i	$0.543213\pi$
$434$	715.896	−	500.590i	1.64953	−	1.15343i
$435$		0			0
$436$	265.706	−	727.111i	0.609418	−	1.66769i
$437$	73.9691	−	419.499i	0.169266	−	0.959953i
$438$		0			0
$439$	88.8615	+	105.901i	0.202418	+	0.241232i	0.857698	−	0.514154i	$-0.171894\pi$
$439$	88.8615	+	105.901i	0.202418	+	0.241232i	−0.655280	+	0.755386i	$0.727449\pi$
$440$	−197.293	+	52.4566i	−0.448392	+	0.119220i
$441$		0			0
$442$	155.138	+	333.253i	0.350990	+	0.753967i
$443$	−528.154	+	93.1279i	−1.19222	+	0.210221i	−0.734334	−	0.678789i	$-0.762505\pi$
$443$	−528.154	+	93.1279i	−1.19222	+	0.210221i	−0.457888	+	0.889010i	$0.651394\pi$
$444$		0			0
$445$	−138.094	+	50.2620i	−0.310323	+	0.112948i
$446$	−94.4871	−	25.3829i	−0.211855	−	0.0569123i
$447$		0			0
$448$	−528.638	−	194.722i	−1.18000	−	0.434647i
$449$	−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
$452$	−260.579	−	150.892i	−0.576501	−	0.333833i
$453$		0			0
$454$	−499.940	+	499.297i	−1.10119	+	1.09977i
$455$	−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	$0.587614\pi$
$463$	−542.788	+	646.870i	−1.17233	+	1.39713i	−0.900542	+	0.434769i	$0.856830\pi$
$464$	−344.831	−	600.830i	−0.743171	−	1.29489i
$465$		0			0
$466$	−3.00584	−	34.6133i	−0.00645030	−	0.0742774i
$467$	592.887	−	342.304i	1.26957	−	0.732984i	0.294660	−	0.955602i	$-0.404793\pi$
$467$	592.887	−	342.304i	1.26957	−	0.732984i	0.974906	+	0.222618i	$0.0714601\pi$
$468$		0			0
$469$	303.912	−	526.392i	0.648001	−	1.12237i
$470$	19.1832	−	41.0695i	0.0408153	−	0.0873818i
$471$		0			0
$472$	−33.7193	−	394.172i	−0.0714392	−	0.835110i
$473$	74.2705	−	27.0323i	0.157020	−	0.0571507i
$474$		0			0
$475$	346.386	−	61.0772i	0.729234	−	0.128584i
$476$	94.0267	−	529.270i	0.197535	−	1.11191i
$477$		0			0
$478$	−23.2246	+	263.507i	−0.0485871	+	0.551269i
$479$	311.792	+	371.580i	0.650924	+	0.775740i	0.986053	−	0.166432i	$-0.0532245\pi$
$479$	311.792	+	371.580i	0.650924	+	0.775740i	−0.335129	+	0.942172i	$0.608780\pi$
$480$		0			0
$481$	−60.3060	+	342.012i	−0.125376	+	0.711045i
$482$	−497.025	+	132.835i	−1.03117	+	0.275591i
$483$		0			0
$484$	−0.538321	+	418.493i	−0.00111223	+	0.864655i
$485$	596.007			1.22888
$486$		0			0
$487$		−	77.9383i		−	0.160038i	−0.996793	−	0.0800188i	$-0.974502\pi$
$487$		−	77.9383i		−	0.160038i	0.996793	−	0.0800188i	$-0.0254980\pi$
$488$	682.532	+	479.879i	1.39863	+	0.983359i
$489$		0			0
$490$	347.050	−	92.7527i	0.708266	−	0.189291i
$491$	398.433	+	70.2545i	0.811473	+	0.143085i	0.563962	−	0.825801i	$-0.309276\pi$
$491$	398.433	+	70.2545i	0.811473	+	0.143085i	0.247511	+	0.968885i	$0.420387\pi$
$492$		0			0
$493$	506.372	−	424.897i	1.02712	−	0.861860i
$494$	50.3630	−	571.418i	0.101949	−	1.15672i
$495$		0			0
$496$	782.205	−	135.850i	1.57703	−	0.273891i
$497$	85.5663	+	485.271i	0.172166	+	0.976399i
$498$		0			0
$499$	−246.492	−	677.231i	−0.493971	−	1.35718i	−0.897017	−	0.441996i	$-0.854271\pi$
$499$	−246.492	−	677.231i	−0.493971	−	1.35718i	0.403046	−	0.915180i	$-0.367952\pi$
$500$	165.714	+	198.007i	0.331428	+	0.396015i
$501$		0			0
$502$	−39.5677	+	84.7109i	−0.0788201	+	0.168747i
$503$	204.980	+	118.346i	0.407516	+	0.235279i	0.689722	−	0.724074i	$-0.257733\pi$
$503$	204.980	+	118.346i	0.407516	+	0.235279i	−0.282206	+	0.959354i	$0.591066\pi$
$504$		0			0
$505$	423.973	+	734.343i	0.839551	+	1.45415i
$506$	−12.5196	−	144.167i	−0.0247422	−	0.284916i
$507$		0			0
$508$	−21.7186	−	124.106i	−0.0427531	−	0.244302i
$509$	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
$518$	359.344	−	358.882i	0.693714	−	0.692822i
$519$		0			0
$520$	−550.906	+	255.599i	−1.05943	+	0.491536i
$521$	−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	−0.382683	−	0.923880i	$-0.625000\pi$
$523$	−718.669	−	414.924i	−1.37413	−	0.793353i	−0.991445	+	0.130527i	$0.958333\pi$
$524$	161.554	+	280.653i	0.308309	+	0.535597i
$525$		0			0
$526$	−299.152	−	80.3638i	−0.568730	−	0.152783i
$527$	259.098	+	711.865i	0.491647	+	1.35079i
$528$		0			0
$529$	36.3485	+	206.142i	0.0687117	+	0.389683i
$530$	431.996	+	927.975i	0.815086	+	1.75090i
$531$		0			0
$532$	−540.036	+	641.911i	−1.01510	+	1.20660i
$533$	−400.089	+	335.715i	−0.750637	+	0.629859i
$534$		0			0
$535$	329.318	+	58.0676i	0.615547	+	0.108538i
$536$	453.119	−	315.976i	0.845371	−	0.589508i
$537$		0			0
$538$	114.109	−	79.7907i	0.212099	−	0.148310i
$539$			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	$0.160478\pi$
$542$	272.526	+	389.741i	0.502816	+	0.719079i
$543$		0			0
$544$	281.506	−	399.293i	0.517474	−	0.733994i
$545$	−211.919	+	1201.85i	−0.388843	+	2.20524i
$546$		0			0
$547$	−202.576	−	241.421i	−0.370341	−	0.441355i	0.548400	−	0.836216i	$-0.315237\pi$
$547$	−202.576	−	241.421i	−0.370341	−	0.441355i	−0.918741	+	0.394861i	$0.870793\pi$
$548$	262.368	−	311.862i	0.478774	−	0.569092i
$549$		0			0
$550$	108.326	−	50.4285i	0.196957	−	0.0916882i
$551$	−1015.86	+	179.123i	−1.84366	+	0.325087i
$552$		0			0
$553$	−701.058	+	255.164i	−1.26774	+	0.461418i
$554$	90.2473	−	335.943i	0.162901	−	0.606395i
$555$		0			0
$556$	−438.391	−	761.576i	−0.788473	−	1.36974i
$557$	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
$560$	874.220	+	156.469i	1.56111	+	0.279408i
$561$		0			0
$562$	−384.449	−	384.944i	−0.684073	−	0.684953i
$563$	14.0883	−	16.7898i	0.0250236	−	0.0298219i	−0.753388	−	0.657577i	$-0.771582\pi$
$563$	14.0883	−	16.7898i	0.0250236	−	0.0298219i	0.778411	+	0.627755i	$0.216026\pi$
$564$		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	$0.492963\pi$
$571$	−551.758	+	657.560i	−0.966301	+	1.15159i	−0.988406	+	0.151837i	$0.951481\pi$
$572$	−33.5925	−	191.956i	−0.0587282	−	0.335588i
$573$		0			0
$574$	760.900	−	66.0770i	1.32561	−	0.115117i
$575$	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	$-0.0470075\pi$
$578$	−101.320	−	47.3256i	−0.175294	−	0.0818782i
$579$		0			0
$580$	700.907	+	837.493i	1.20846	+	1.44395i
$581$	−517.735	+	188.440i	−0.891110	+	0.324338i
$582$		0			0
$583$	−323.461	+	57.0350i	−0.554822	+	0.0978301i
$584$	−146.563	+	145.999i	−0.250964	+	0.249997i
$585$		0			0
$586$	683.524	+	60.2436i	1.16642	+	0.102805i
$587$	−296.445	−	353.290i	−0.505017	−	0.601856i	0.451953	−	0.892042i	$-0.350727\pi$
$587$	−296.445	−	353.290i	−0.505017	−	0.601856i	−0.956970	+	0.290186i	$0.906283\pi$
$588$		0			0
$589$	205.281	−	1164.20i	0.348524	−	1.97658i
$590$	161.029	+	602.516i	0.272930	+	1.02121i
$591$		0			0
$592$	434.131	−	156.747i	0.733329	−	0.264776i
$593$	−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
$596$	0.597084	−	464.176i	0.00100182	−	0.778818i
$597$		0			0
$598$	−111.152	−	415.896i	−0.185874	−	0.695479i
$599$	−401.294	−	70.7590i	−0.669941	−	0.118129i	−0.171676	−	0.985153i	$-0.554918\pi$
$599$	−401.294	−	70.7590i	−0.669941	−	0.118129i	−0.498265	+	0.867025i	$0.666029\pi$
$600$		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	$0.310726\pi$
$602$	−342.511	−	30.1878i	−0.568955	−	0.0501459i
$603$		0			0
$604$	−80.3712	+	452.404i	−0.133065	+	0.749013i
$605$	−114.562	−	649.713i	−0.189359	−	1.07391i
$606$		0			0
$607$	−72.4290	−	198.997i	−0.119323	−	0.327837i	0.865624	−	0.500695i	$-0.166922\pi$
$607$	−72.4290	−	198.997i	−0.119323	−	0.327837i	−0.984947	+	0.172858i	$0.944700\pi$
$608$	−691.987	+	319.974i	−1.13814	+	0.526273i
$609$		0			0
$610$	−1191.72	−	556.640i	−1.95363	−	0.912525i
$611$	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	$-0.358953\pi$
$614$	−577.486	+	50.1492i	−0.940530	+	0.0816762i
$615$		0			0
$616$	−120.934	+	258.043i	−0.196322	+	0.418901i
$617$	−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	$-0.663528\pi$
$619$	275.355	−	756.532i	0.444839	−	1.22218i	0.936274	−	0.351270i	$-0.114250\pi$
$620$	−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
$626$	−394.451	−	394.958i	−0.630113	−	0.630924i
$627$		0			0
$628$	62.6369	+	36.2710i	0.0997403	+	0.0577563i
$629$	220.211	+	381.416i	0.350096	+	0.606385i
$630$		0			0
$631$	834.435	+	481.761i	1.32240	+	0.763488i	0.984111	−	0.177554i	$-0.0568184\pi$
$631$	834.435	+	481.761i	1.32240	+	0.763488i	0.338289	+	0.941042i	$0.390152\pi$
$632$	−675.339	−	60.3978i	−1.06857	−	0.0955661i
$633$		0			0
$634$	−119.609	+	445.243i	−0.188658	+	0.702276i
$635$	67.9321	+	186.642i	0.106980	+	0.293924i
$636$		0			0
$637$	59.5461	+	337.703i	0.0934789	+	0.530145i
$638$	−317.691	+	147.893i	−0.497949	+	0.231808i
$639$		0			0
$640$	659.083	+	465.931i	1.02982	+	0.728018i
$641$	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	−0.562751	−	0.826626i	$-0.690257\pi$
$643$	−883.667	−	155.814i	−1.37429	−	0.242324i	−0.811536	+	0.584302i	$0.801368\pi$
$644$	−216.076	+	591.295i	−0.335521	+	0.918160i
$645$		0			0
$646$	−416.873	−	596.173i	−0.645315	−	0.922868i
$647$		−	878.052i		−	1.35711i	−0.734549	−	0.678556i	$-0.762606\pi$
$647$		−	878.052i		−	1.35711i	0.734549	−	0.678556i	$-0.237394\pi$
$648$		0			0
$649$	−200.120			−0.308352
$650$	291.310	−	203.698i	0.448169	−	0.313382i
$651$		0			0
$652$	420.298	+	153.588i	0.644629	+	0.235565i
$653$	−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
$656$	651.659	+	239.085i	0.993382	+	0.364458i
$657$		0			0
$658$	−26.7047	−	57.3646i	−0.0405846	−	0.0871803i
$659$	985.857	−	173.833i	1.49599	−	0.263783i	0.635042	−	0.772478i	$-0.280983\pi$
$659$	985.857	−	173.833i	1.49599	−	0.263783i	0.860947	+	0.508694i	$0.169872\pi$
$660$		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	$0.663735\pi$
$662$	−195.663	−	52.5625i	−0.295563	−	0.0793996i
$663$		0			0
$664$	−498.742	−	44.6041i	−0.751117	−	0.0671748i
$665$	661.214	−	1145.26i	0.994306	−	1.72219i
$666$		0			0
$667$	−670.416	+	387.065i	−1.00512	+	0.580307i
$668$	−119.038	+	205.568i	−0.178200	+	0.307737i
$669$		0			0
$670$	−616.180	+	615.388i	−0.919672	+	0.918490i
$671$	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
$680$	−326.836	+	697.387i	−0.480642	+	1.02557i
$681$		0			0
$682$	−34.7446	−	400.096i	−0.0509452	−	0.586651i
$683$	−740.219	+	427.366i	−1.08378	+	0.625718i	−0.931912	−	0.362683i	$-0.881861\pi$
$683$	−740.219	+	427.366i	−1.08378	+	0.625718i	−0.151863	+	0.988402i	$0.548527\pi$
$684$		0			0
$685$	−321.240	+	556.405i	−0.468964	+	0.812269i
$686$	−152.853	+	327.244i	−0.222818	+	0.477033i
$687$		0			0
$688$	−270.223	−	156.942i	−0.392766	−	0.228113i
$689$	−918.175	+	334.188i	−1.33262	+	0.485034i
$690$		0			0
$691$	1014.01	−	178.797i	1.46745	−	0.258750i	0.617897	−	0.786259i	$-0.287985\pi$
$691$	1014.01	−	178.797i	1.46745	−	0.258750i	0.849550	+	0.527509i	$0.176874\pi$
$692$	360.003	+	63.9558i	0.520235	+	0.0924217i
$693$		0			0
$694$	−39.4984	+	448.149i	−0.0569142	+	0.645748i
$695$	890.450	+	1061.20i	1.28122	+	1.52690i
$696$		0			0
$697$	−115.014	+	652.277i	−0.165013	+	0.935836i
$698$	−634.458	+	169.565i	−0.908965	+	0.242930i
$699$		0			0
$700$	−519.818	−	0.668658i	−0.742597	−	0.000955226i
$701$	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
$704$	−199.043	+	165.712i	−0.282731	+	0.235387i
$705$		0			0
$706$	59.2718	−	15.8410i	0.0839544	−	0.0224377i
$707$	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	$0.336587\pi$
$710$	61.9833	−	703.262i	0.0873004	−	0.990510i
$711$		0			0
$712$	−132.086	+	131.578i	−0.185514	+	0.184800i
$713$	−154.057	−	873.698i	−0.216068	−	1.22538i
$714$		0			0
$715$	105.072	+	288.682i	0.146953	+	0.403751i
$716$	965.337	−	807.900i	1.34824	−	1.12835i
$717$		0			0
$718$	278.566	−	596.385i	0.387975	−	0.830619i
$719$	129.283	+	74.6416i	0.179809	+	0.103813i	0.587203	−	0.809440i	$-0.300229\pi$
$719$	129.283	+	74.6416i	0.179809	+	0.103813i	−0.407394	+	0.913253i	$0.633562\pi$
$720$		0			0
$721$	285.722	+	494.885i	0.396286	+	0.686387i
$722$	35.7492	+	411.665i	0.0495142	+	0.570173i
$723$		0			0
$724$	−808.185	+	141.433i	−1.11628	+	0.195350i
$725$	−489.663	−	410.876i	−0.675397	−	0.566725i
$726$		0			0
$727$	18.1243	−	49.7962i	0.0249303	−	0.0684954i	−0.926603	−	0.376041i	$-0.877285\pi$
$727$	18.1243	−	49.7962i	0.0249303	−	0.0684954i	0.951533	+	0.307545i	$0.0995075\pi$
$728$	−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	$0.741730\pi$
$734$	−269.198	+	268.852i	−0.366755	+	0.366283i
$735$		0			0
$736$	−405.866	+	403.264i	−0.551449	+	0.547914i
$737$	−139.719	−	242.000i	−0.189577	−	0.328358i
$738$		0			0
$739$	−190.957	−	110.249i	−0.258399	−	0.149187i	0.365205	−	0.930927i	$-0.380999\pi$
$739$	−190.957	−	110.249i	−0.258399	−	0.149187i	−0.623604	+	0.781740i	$0.714332\pi$
$740$	−630.615	+	363.005i	−0.852182	+	0.490547i
$741$		0			0
$742$	1379.95	+	370.709i	1.85977	+	0.499607i
$743$	−117.725	−	323.447i	−0.158445	−	0.435325i	0.834914	−	0.550381i	$-0.185518\pi$
$743$	−117.725	−	323.447i	−0.158445	−	0.435325i	−0.993359	+	0.115056i	$0.963295\pi$
$744$		0			0
$745$	127.068	+	720.636i	0.170560	+	0.967296i
$746$	106.800	+	229.418i	0.143163	+	0.307531i
$747$		0			0
$748$	−189.110	−	159.097i	−0.252821	−	0.212697i
$749$	357.587	−	300.051i	0.477420	−	0.400603i
$750$		0			0
$751$	577.725	+	101.868i	0.769274	+	0.135644i	0.544493	−	0.838765i	$-0.316722\pi$
$751$	577.725	+	101.868i	0.769274	+	0.135644i	0.224781	+	0.974409i	$0.427833\pi$
$752$	0.147946	−	57.5070i	0.000196737	−	0.0764721i
$753$		0			0
$754$	−854.335	+	597.393i	−1.13307	+	0.792299i
$755$		−	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	$0.425243\pi$
$758$	−116.544	−	166.670i	−0.153752	−	0.219882i
$759$		0			0
$760$	985.838	−	687.460i	1.29716	−	0.904553i
$761$	−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
$764$	−95.3297	−	80.2003i	−0.124777	−	0.104974i
$765$		0			0
$766$	−79.8322	+	37.1639i	−0.104220	+	0.0485168i
$767$	−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	$0.696051\pi$
$770$	116.554	−	433.869i	0.151369	−	0.563466i
$771$		0			0
$772$	670.490	−	385.958i	0.868510	−	0.499946i
$773$	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
$776$	685.907	−	318.234i	0.883901	−	0.410095i
$777$		0			0
$778$	648.866	+	649.701i	0.834018	+	0.835091i
$779$	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	−0.499177	−	0.866500i	$-0.666364\pi$
$787$	346.942	−	413.469i	0.440841	−	0.525373i	0.940017	+	0.341127i	$0.110809\pi$
$788$	−1048.09	+	183.417i	−1.33006	+	0.232763i
$789$		0			0
$790$	1064.88	−	92.4751i	1.34795	−	0.117057i
$791$	573.863	−	331.320i	0.725490	−	0.418862i
$792$		0			0
$793$	627.779	−	1087.34i	0.791651	−	1.37118i
$794$	−141.106	−	65.9094i	−0.177715	−	0.0830093i
$795$		0			0
$796$	−91.3574	+	76.4579i	−0.114771	+	0.0960526i
$797$	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
$800$	−427.520	−	201.032i	−0.534401	−	0.251290i
$801$		0			0
$802$	−1118.51	−	98.5822i	−1.39466	−	0.122920i
$803$	67.2655	+	80.1639i	0.0837678	+	0.0998306i
$804$		0			0
$805$	172.335	−	977.362i	0.214081	−	1.21411i
$806$	−308.473	−	1154.20i	−0.382721	−	1.43202i
$807$		0			0
$808$	880.022	+	618.732i	1.08914	+	0.765757i
$809$	−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	$-0.819020\pi$
$811$		−	873.324i		−	1.07685i	0.842674	−	0.538424i	$-0.180980\pi$
$812$	1524.49	+	1.96100i	1.87745	+	0.00241502i
$813$		0			0
$814$	−60.2843	−	225.564i	−0.0740594	−	0.277106i
$815$	−694.717	−	122.497i	−0.852414	−	0.150304i
$816$		0			0
$817$	−356.448	+	299.096i	−0.436289	+	0.366090i
$818$	−745.345	−	65.6923i	−0.911180	−	0.0803085i
$819$		0			0
$820$	−1077.40	−	191.404i	−1.31390	−	0.233419i
$821$	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	$-0.965632\pi$
$823$	−248.432	−	682.560i	−0.301861	−	0.829357i	0.692316	−	0.721595i	$-0.256591\pi$
$824$	44.2657	+	517.457i	0.0537205	+	0.627982i
$825$		0			0
$826$	788.788	+	368.436i	0.954949	+	0.446048i
$827$	194.573	+	112.337i	0.235276	+	0.135837i	0.613004	−	0.790080i	$-0.289961\pi$
$827$	194.573	+	112.337i	0.235276	+	0.135837i	−0.377728	+	0.925917i	$0.623294\pi$
$828$		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	$0.913405\pi$
$830$	786.422	−	68.2934i	0.947496	−	0.0822812i
$831$		0			0
$832$	−497.528	+	588.305i	−0.597990	+	0.707098i
$833$	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	$-0.610226\pi$
$839$	440.665	−	1210.72i	0.525226	−	1.44305i	0.864632	−	0.502406i	$-0.167552\pi$
$840$		0			0
$841$	791.806	+	664.404i	0.941506	+	0.790017i
$842$	−234.791	−	235.094i	−0.278850	−	0.279208i
$843$		0			0
$844$	225.637	−	389.657i	0.267343	−	0.461679i
$845$	−75.8877	−	131.441i	−0.0898079	−	0.155552i
$846$		0			0
$847$	−797.564	−	460.474i	−0.941634	−	0.543653i
$848$	992.643	+	837.287i	1.17057	+	0.987367i
$849$		0			0
$850$	116.953	−	435.354i	0.137592	−	0.512181i
$851$	−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	$-0.268882\pi$
$854$	−1664.56	+	774.892i	−1.94913	+	0.907368i
$855$		0			0
$856$	409.996	−	109.011i	0.478967	−	0.127349i
$857$	−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	−0.0146277	−	0.999893i	$-0.504656\pi$
$859$	−318.137	−	56.0961i	−0.370357	−	0.0653039i	−0.355729	+	0.934589i	$0.615767\pi$
$860$	462.703	+	169.084i	0.538027	+	0.196610i
$861$		0			0
$862$	171.854	+	245.769i	0.199366	+	0.285115i
$863$		−	1003.38i		−	1.16266i	−0.813668	−	0.581330i	$-0.802532\pi$
$863$		−	1003.38i		−	1.16266i	0.813668	−	0.581330i	$-0.197468\pi$
$864$		0			0
$865$	−576.415			−0.666375
$866$	192.104	−	134.328i	0.221829	−	0.155114i
$867$		0			0
$868$	−599.658	+	1640.98i	−0.690850	+	1.89053i
$869$	−59.5585	+	337.773i	−0.0685369	+	0.388692i
$870$		0			0
$871$	−534.343	−	636.805i	−0.613482	−	0.731120i
$872$	397.837	+	1496.29i	0.456235	+	1.71593i
$873$		0			0
$874$	359.549	+	772.353i	0.411384	+	0.883699i
$875$	−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	$0.315794\pi$
$878$	−267.021	−	71.7321i	−0.304124	−	0.0816994i
$879$		0			0
$880$	263.250	−	312.095i	0.299148	−	0.354654i
$881$	−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	−0.485159	−	0.874426i	$-0.661238\pi$
$883$	26.0807	−	15.0577i	0.0295365	−	0.0170529i	0.514696	+	0.857373i	$0.327905\pi$
$884$	−636.219	−	368.413i	−0.719704	−	0.416757i
$885$		0			0
$886$	758.933	−	757.958i	0.856584	−	0.855483i
$887$	−208.670	+	248.683i	−0.235253	+	0.280364i	−0.870736	−	0.491752i	$-0.836357\pi$
$887$	−208.670	+	248.683i	−0.235253	+	0.280364i	0.635482	+	0.772115i	$0.280801\pi$
$888$		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
$896$	1089.63	−	286.714i	1.21611	−	0.319993i
$897$		0			0
$898$	−78.9948	−	909.652i	−0.0879674	−	1.01298i
$899$	−1860.55	+	1074.19i	−2.06958	+	1.19487i
$900$		0			0
$901$	−619.566	+	1073.12i	−0.687642	+	1.19103i
$902$	148.597	−	318.134i	0.164742	−	0.352698i
$903$		0			0
$904$	600.037	−	51.3300i	0.663758	−	0.0567810i
$905$	1215.43	−	442.379i	1.34301	−	0.488816i
$906$		0			0
$907$	1332.50	−	234.956i	1.46913	−	0.259047i	0.618905	−	0.785465i	$-0.287576\pi$
$907$	1332.50	−	234.956i	1.46913	−	0.259047i	0.850226	+	0.526418i	$0.176465\pi$
$908$	247.178	−	1391.35i	0.272223	−	1.53232i
$909$		0			0
$910$	117.337	−	1331.31i	0.128942	−	1.46297i
$911$	433.248	+	516.324i	0.475574	+	0.566767i	0.949488	−	0.313805i	$-0.101604\pi$
$911$	433.248	+	516.324i	0.475574	+	0.566767i	−0.473914	+	0.880571i	$0.657159\pi$
$912$		0			0
$913$	−43.9843	+	249.447i	−0.0481756	+	0.273217i
$914$	1119.78	−	299.271i	1.22514	−	0.327430i
$915$		0			0
$916$	1.11435	−	866.304i	0.00121654	−	0.945746i
$917$	−712.629			−0.777131
$918$		0			0
$919$		−	1384.80i		−	1.50685i	−0.657534	−	0.753425i	$-0.728400\pi$
$919$		−	1384.80i		−	1.50685i	0.657534	−	0.753425i	$-0.271600\pi$
$920$	518.768	−	737.843i	0.563878	−	0.802004i
$921$		0			0
$922$	776.923	−	207.641i	0.842650	−	0.225207i
$923$	663.679	+	117.025i	0.719046	+	0.126787i
$924$		0			0
$925$	326.249	−	273.755i	0.352702	−	0.295952i
$926$	148.276	−	1682.33i	0.160125	−	1.81678i
$927$		0			0
$928$	1253.80	+	589.574i	1.35108	+	0.635317i
$929$	−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
$932$	44.5969	+	53.2876i	0.0478508	+	0.0571756i
$933$		0			0
$934$	−579.453	+	1240.56i	−0.620400	+	1.32822i
$935$	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	$0.985019\pi$
$938$	105.172	+	1211.09i	0.112124	+	1.29114i
$939$		0			0
$940$	15.6276	+	89.3004i	0.0166252	+	0.0950004i
$941$	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	$-0.734207\pi$
$947$	302.546	−	831.238i	0.319478	−	0.877759i	0.990646	−	0.136454i	$-0.0435705\pi$
$948$		0			0
$949$	238.478	+	200.106i	0.251294	+	0.210860i
$950$	−497.741	+	497.101i	−0.523938	+	0.523264i
$951$		0			0
$952$	452.482	+	975.259i	0.475296	+	1.02443i
$953$	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
$956$	−263.938	−	458.516i	−0.276086	−	0.479619i
$957$		0			0
$958$	−936.908	−	251.690i	−0.977983	−	0.262724i
$959$	306.744	+	842.773i	0.319859	+	0.878804i
$960$		0			0
$961$	−260.665	−	1478.31i	−0.271244	−	1.53830i
$962$	−293.136	−	629.689i	−0.304715	−	0.654563i
$963$		0			0
$964$	662.403	−	787.362i	0.687140	−	0.816766i
$965$	−934.275	+	783.950i	−0.968161	+	0.812383i
$966$		0			0
$967$	1807.24	+	318.666i	1.86892	+	0.329541i	0.989272	−	0.146087i	$-0.0466681\pi$
$967$	1807.24	+	318.666i	1.86892	+	0.329541i	0.879646	+	0.475628i	$0.157779\pi$
$968$	−478.752	−	686.545i	−0.494579	−	0.709240i
$969$		0			0
$970$	−976.881	+	683.083i	−1.00709	+	0.704210i
$971$			1398.13i			1.43989i	0.694031	+	0.719945i	$0.255833\pi$
$971$			1398.13i			1.43989i	−0.694031	+	0.719945i	$0.744167\pi$
$972$		0			0
$973$	1933.78			1.98744
$974$	89.3250	+	127.744i	0.0917095	+	0.131154i
$975$		0			0
$976$	−1668.69	−	4.29298i	−1.70972	−	0.00439854i
$977$	−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
$980$	−462.526	+	549.780i	−0.471966	+	0.561000i
$981$		0			0
$982$	−733.567	+	341.494i	−0.747013	+	0.347753i
$983$	−972.425	+	171.465i	−0.989242	+	0.174430i	−0.644779	−	0.764369i	$-0.723050\pi$
$983$	−972.425	+	171.465i	−0.989242	+	0.174430i	−0.344464	+	0.938800i	$0.611939\pi$
$984$		0			0
$985$	1576.22	−	573.697i	1.60022	−	0.582434i
$986$	−342.991	+	1276.78i	−0.347862	+	1.29490i
$987$		0			0
$988$	572.355	+	994.299i	0.579307	+	1.00638i
$989$	−174.600	+	302.416i	−0.176542	+	0.305780i
$990$		0			0
$991$	−528.087	+	304.891i	−0.532883	+	0.307660i	−0.742190	−	0.670190i	$-0.766213\pi$
$991$	−528.087	+	304.891i	−0.532883	+	0.307660i	0.209307	+	0.977850i	$0.432879\pi$
$992$	−1126.37	+	1119.15i	−1.13545	+	1.12817i
$993$		0			0
$994$	−696.415	−	697.311i	−0.700618	−	0.701520i
$995$	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.307.6		204
3.2	odd	2		108.3.j.a.31.29	yes	204
4.3	odd	2	inner	324.3.j.a.307.13		204
12.11	even	2		108.3.j.a.31.22	yes	204
27.7	even	9	inner	324.3.j.a.19.13		204
27.20	odd	18		108.3.j.a.7.22	✓	204
108.7	odd	18	inner	324.3.j.a.19.6		204
108.47	even	18		108.3.j.a.7.29	yes	204

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

\(f(q)\)	\(=\)	\(q+(-1.63904 + 1.14610i) q^{2} +(1.37291 - 3.75701i) q^{4} +(-1.09499 + 6.21002i) q^{5} +(5.65814 + 6.74311i) q^{7} +(2.05564 + 7.73139i) q^{8} +O(q^{10})\)	\(q+(-1.63904 + 1.14610i) q^{2} +(1.37291 - 3.75701i) q^{4} +(-1.09499 + 6.21002i) q^{5} +(5.65814 + 6.74311i) q^{7} +(2.05564 + 7.73139i) q^{8} +(-5.32256 - 11.4335i) q^{10} +(3.98532 - 0.702720i) q^{11} +(11.3127 - 4.11749i) q^{13} +(-17.0022 - 4.56745i) q^{14} +(-12.2302 - 10.3161i) q^{16} +(7.63358 - 13.2217i) q^{17} +(-20.6326 + 11.9123i) q^{19} +(21.8278 + 12.6397i) q^{20} +(-5.72672 + 5.71936i) q^{22} +(-11.4927 + 13.6965i) q^{23} +(-13.8730 - 5.04937i) q^{25} +(-13.8229 + 19.7142i) q^{26} +(33.1021 - 12.0000i) q^{28} +(40.6859 + 14.8084i) q^{29} +(-31.8949 + 38.0109i) q^{31} +(31.8691 + 2.89148i) q^{32} +(2.64168 + 30.4198i) q^{34} +(-48.0705 + 27.7535i) q^{35} +(-14.4238 + 24.9828i) q^{37} +(20.1651 - 43.1717i) q^{38} +(-50.2630 + 4.29973i) q^{40} +(-40.7670 + 14.8380i) q^{41} +(19.2340 - 3.39148i) q^{43} +(2.83138 - 15.9377i) q^{44} +(3.13952 - 35.6210i) q^{46} +(2.31031 + 2.75332i) q^{47} +(-4.94621 + 28.0514i) q^{49} +(28.5255 - 7.62373i) q^{50} +(0.0619431 - 48.1549i) q^{52} -81.1632 q^{53} +25.5184i q^{55} +(-40.5025 + 57.6067i) q^{56} +(-83.6578 + 22.3584i) q^{58} +(-48.7001 - 8.58715i) q^{59} +(79.8933 - 67.0384i) q^{61} +(8.71286 - 98.8561i) q^{62} +(-55.5487 + 31.7859i) q^{64} +(13.1823 + 74.7607i) q^{65} +(-23.6170 - 64.8871i) q^{67} +(-39.1940 - 46.8317i) q^{68} +(46.9813 - 100.583i) q^{70} +(48.4794 + 27.9896i) q^{71} +(12.9295 + 22.3946i) q^{73} +(-4.99150 - 57.4789i) q^{74} +(16.4276 + 93.8714i) q^{76} +(27.2880 + 22.8974i) q^{77} +(-28.9877 + 79.6430i) q^{79} +(77.4552 - 64.6538i) q^{80} +(49.8130 - 71.0430i) q^{82} +(-21.4076 + 58.8168i) q^{83} +(73.7486 + 61.8824i) q^{85} +(-27.6384 + 27.6029i) q^{86} +(13.6254 + 29.3675i) q^{88} +(11.6524 + 20.1826i) q^{89} +(91.7735 + 52.9855i) q^{91} +(35.6794 + 61.9824i) q^{92} +(-6.94226 - 1.86496i) q^{94} +(-51.3827 - 141.173i) q^{95} +(-16.4127 - 93.0811i) q^{97} +(-24.0426 - 51.6462i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) \) 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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