LMFDB - Embedded newform 324.3.j.a.199.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("324.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.82836056527$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			199.17
Character	$\chi$	$=$	324.199
Dual form			324.3.j.a.127.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.00794476 - 1.99998i) q^{2} +(-3.99987 - 0.0317788i) q^{4} +(-7.18780 + 2.61614i) q^{5} +(5.65258 - 0.996703i) q^{7} +(-0.0953352 + 7.99943i) q^{8} +O(q^{10})$	\(q+(0.00794476 - 1.99998i) q^{2} +(-3.99987 - 0.0317788i) q^{4} +(-7.18780 + 2.61614i) q^{5} +(5.65258 - 0.996703i) q^{7} +(-0.0953352 + 7.99943i) q^{8} +(5.17514 + 14.3963i) q^{10} +(2.01574 - 5.53819i) q^{11} +(8.25839 + 6.92961i) q^{13} +(-1.94848 - 11.3130i) q^{14} +(15.9980 + 0.254222i) q^{16} +(-10.4844 + 18.1596i) q^{17} +(21.5373 - 12.4346i) q^{19} +(28.8334 - 10.2358i) q^{20} +(-11.0603 - 4.07544i) q^{22} +(20.5338 + 3.62067i) q^{23} +(25.6691 - 21.5389i) q^{25} +(13.9247 - 16.4616i) q^{26} +(-22.6413 + 3.80705i) q^{28} +(30.1767 - 25.3212i) q^{29} +(10.3697 + 1.82845i) q^{31} +(0.635541 - 31.9937i) q^{32} +(36.2355 + 21.1130i) q^{34} +(-38.0221 + 21.9521i) q^{35} +(-1.83871 + 3.18474i) q^{37} +(-24.6978 - 43.1730i) q^{38} +(-20.2424 - 57.7477i) q^{40} +(51.1323 + 42.9051i) q^{41} +(-28.3547 + 77.9040i) q^{43} +(-8.23869 + 22.0880i) q^{44} +(7.40442 - 41.0386i) q^{46} +(-33.3947 + 5.88839i) q^{47} +(-15.0867 + 5.49110i) q^{49} +(-42.8736 - 51.5089i) q^{50} +(-32.8123 - 27.9800i) q^{52} +43.9772 q^{53} +45.0808i q^{55} +(7.43417 + 45.3125i) q^{56} +(-50.4023 - 60.5540i) q^{58} +(-9.37752 - 25.7645i) q^{59} +(-1.47945 - 8.39040i) q^{61} +(3.73926 - 20.7246i) q^{62} +(-63.9818 - 1.52525i) q^{64} +(-77.4885 - 28.2035i) q^{65} +(31.0935 - 37.0558i) q^{67} +(42.5135 - 72.3028i) q^{68} +(43.6017 + 76.2180i) q^{70} +(24.2168 + 13.9816i) q^{71} +(43.5064 + 75.3554i) q^{73} +(6.35483 + 3.70270i) q^{74} +(-86.5416 + 49.0522i) q^{76} +(5.87418 - 33.3142i) q^{77} +(11.6931 + 13.9353i) q^{79} +(-115.655 + 40.0257i) q^{80} +(86.2157 - 101.923i) q^{82} +(8.95501 + 10.6722i) q^{83} +(27.8519 - 157.956i) q^{85} +(155.581 + 57.3279i) q^{86} +(44.1102 + 16.6527i) q^{88} +(81.2903 + 140.799i) q^{89} +(53.5880 + 30.9390i) q^{91} +(-82.0177 - 15.1348i) q^{92} +(11.5114 + 66.8357i) q^{94} +(-122.275 + 145.722i) q^{95} +(39.6511 + 14.4318i) q^{97} +(10.8623 + 30.2167i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) $ 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8	$ 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8} - 3 q^{10} - 12 q^{13} - 39 q^{14} - 6 q^{16} + 6 q^{17} + 69 q^{20} - 6 q^{22} - 12 q^{25} + 174 q^{26} - 12 q^{28} - 60 q^{29} + 96 q^{32} + 6 q^{34} - 6 q^{37} - 72 q^{38} + 69 q^{40} + 192 q^{41} + 219 q^{44} - 3 q^{46} - 12 q^{49} + 165 q^{50} + 21 q^{52} + 24 q^{53} - 99 q^{56} - 141 q^{58} - 12 q^{61} - 294 q^{62} - 3 q^{64} + 156 q^{65} - 375 q^{68} - 165 q^{70} - 6 q^{73} - 447 q^{74} - 54 q^{76} - 132 q^{77} - 798 q^{80} - 12 q^{82} + 138 q^{85} - 606 q^{86} - 198 q^{88} + 114 q^{89} - 723 q^{92} - 357 q^{94} + 168 q^{97} - 510 q^{98}+O(q^{100}) $ 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8 - 3 * q^10 - 12 * q^13 - 39 * q^14 - 6 * q^16 + 6 * q^17 + 69 * q^20 - 6 * q^22 - 12 * q^25 + 174 * q^26 - 12 * q^28 - 60 * q^29 + 96 * q^32 + 6 * q^34 - 6 * q^37 - 72 * q^38 + 69 * q^40 + 192 * q^41 + 219 * q^44 - 3 * q^46 - 12 * q^49 + 165 * q^50 + 21 * q^52 + 24 * q^53 - 99 * q^56 - 141 * q^58 - 12 * q^61 - 294 * q^62 - 3 * q^64 + 156 * q^65 - 375 * q^68 - 165 * q^70 - 6 * q^73 - 447 * q^74 - 54 * q^76 - 132 * q^77 - 798 * q^80 - 12 * q^82 + 138 * q^85 - 606 * q^86 - 198 * q^88 + 114 * q^89 - 723 * q^92 - 357 * q^94 + 168 * q^97 - 510 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.00794476	−	1.99998i	0.00397238	−	0.999992i
$2$	0.00794476	−	1.99998i	0.00397238	−	0.999992i
$3$		0			0
$3$		0			0
$4$	−3.99987	−	0.0317788i	−0.999968	−	0.00794470i
$5$	−7.18780	+	2.61614i	−1.43756	+	0.523229i	−0.939088	−	0.343677i	$-0.888327\pi$
$5$	−7.18780	+	2.61614i	−1.43756	+	0.523229i	−0.498471	+	0.866906i	$0.666105\pi$
$6$		0			0
$7$	5.65258	−	0.996703i	0.807512	−	0.142386i	0.245373	−	0.969429i	$-0.421090\pi$
$7$	5.65258	−	0.996703i	0.807512	−	0.142386i	0.562139	+	0.827043i	$0.309979\pi$
$8$	−0.0953352	+	7.99943i	−0.0119169	+	0.999929i
$9$		0			0
$10$	5.17514	+	14.3963i	0.517514	+	1.43963i
$11$	2.01574	−	5.53819i	0.183249	−	0.503472i	−0.813722	−	0.581255i	$-0.802562\pi$
$11$	2.01574	−	5.53819i	0.183249	−	0.503472i	0.996970	+	0.0777831i	$0.0247842\pi$
$12$		0			0
$13$	8.25839	+	6.92961i	0.635261	+	0.533047i	0.902559	−	0.430567i	$-0.141686\pi$
$13$	8.25839	+	6.92961i	0.635261	+	0.533047i	−0.267298	+	0.963614i	$0.586131\pi$
$14$	−1.94848	−	11.3130i	−0.139177	−	0.808071i
$15$		0			0
$16$	15.9980	+	0.254222i	0.999874	+	0.0158889i
$17$	−10.4844	+	18.1596i	−0.616731	+	1.06821i	0.373347	+	0.927692i	$0.378210\pi$
$17$	−10.4844	+	18.1596i	−0.616731	+	1.06821i	−0.990078	+	0.140518i	$0.955123\pi$
$18$		0			0
$19$	21.5373	−	12.4346i	1.13354	−	0.654450i	0.188718	−	0.982031i	$-0.439567\pi$
$19$	21.5373	−	12.4346i	1.13354	−	0.654450i	0.944823	+	0.327581i	$0.106233\pi$
$20$	28.8334	−	10.2358i	1.44167	−	0.511791i
$21$		0			0
$22$	−11.0603	−	4.07544i	−0.502740	−	0.185247i
$23$	20.5338	+	3.62067i	0.892776	+	0.157420i	0.601173	−	0.799119i	$-0.294700\pi$
$23$	20.5338	+	3.62067i	0.892776	+	0.157420i	0.291603	+	0.956539i	$0.405811\pi$
$24$		0			0
$25$	25.6691	−	21.5389i	1.02676	−	0.861557i
$26$	13.9247	−	16.4616i	0.535566	−	0.633138i
$27$		0			0
$28$	−22.6413	+	3.80705i	−0.808617	+	0.135966i
$29$	30.1767	−	25.3212i	1.04058	−	0.873146i	0.0485038	−	0.998823i	$-0.484555\pi$
$29$	30.1767	−	25.3212i	1.04058	−	0.873146i	0.992071	+	0.125677i	$0.0401102\pi$
$30$		0			0
$31$	10.3697	+	1.82845i	0.334505	+	0.0589823i	0.338378	−	0.941010i	$-0.390122\pi$
$31$	10.3697	+	1.82845i	0.334505	+	0.0589823i	−0.00387293	+	0.999993i	$0.501233\pi$
$32$	0.635541	−	31.9937i	0.0198607	−	0.999803i
$33$		0			0
$34$	36.2355	+	21.1130i	1.06575	+	0.620969i
$35$	−38.0221	+	21.9521i	−1.08635	+	0.627202i
$36$		0			0
$37$	−1.83871	+	3.18474i	−0.0496950	+	0.0860742i	−0.889803	−	0.456345i	$-0.849158\pi$
$37$	−1.83871	+	3.18474i	−0.0496950	+	0.0860742i	0.840108	+	0.542419i	$0.182492\pi$
$38$	−24.6978	−	43.1730i	−0.649942	−	1.13613i
$39$		0			0
$40$	−20.2424	−	57.7477i	−0.506060	−	1.44369i
$41$	51.1323	+	42.9051i	1.24713	+	1.04647i	0.996932	+	0.0782699i	$0.0249396\pi$
$41$	51.1323	+	42.9051i	1.24713	+	1.04647i	0.250196	+	0.968195i	$0.419505\pi$
$42$		0			0
$43$	−28.3547	+	77.9040i	−0.659412	+	1.81172i	−0.0798268	+	0.996809i	$0.525437\pi$
$43$	−28.3547	+	77.9040i	−0.659412	+	1.81172i	−0.579585	+	0.814912i	$0.696785\pi$
$44$	−8.23869	+	22.0880i	−0.187243	+	0.502000i
$45$		0			0
$46$	7.40442	−	41.0386i	0.160966	−	0.892143i
$47$	−33.3947	+	5.88839i	−0.710526	+	0.125285i	−0.517219	−	0.855853i	$-0.673033\pi$
$47$	−33.3947	+	5.88839i	−0.710526	+	0.125285i	−0.193308	+	0.981138i	$0.561922\pi$
$48$		0			0
$49$	−15.0867	+	5.49110i	−0.307891	+	0.112063i
$50$	−42.8736	−	51.5089i	−0.857471	−	1.03018i
$51$		0			0
$52$	−32.8123	−	27.9800i	−0.631006	−	0.538077i
$53$	43.9772			0.829758			0.414879	−	0.909877i	$-0.363824\pi$
$53$	43.9772			0.829758			0.414879	+	0.909877i	$0.363824\pi$
$54$		0			0
$55$			45.0808i			0.819651i
$56$	7.43417	+	45.3125i	0.132753	+	0.809151i
$57$		0			0
$58$	−50.4023	−	60.5540i	−0.869006	−	1.04404i
$59$	−9.37752	−	25.7645i	−0.158941	−	0.436687i	0.834503	−	0.551003i	$-0.185755\pi$
$59$	−9.37752	−	25.7645i	−0.158941	−	0.436687i	−0.993444	+	0.114316i	$0.963532\pi$
$60$		0			0
$61$	−1.47945	−	8.39040i	−0.0242533	−	0.137548i	0.970277	−	0.241998i	$-0.0778028\pi$
$61$	−1.47945	−	8.39040i	−0.0242533	−	0.137548i	−0.994530	+	0.104450i	$0.966692\pi$
$62$	3.73926	−	20.7246i	0.0603106	−	0.334268i
$63$		0			0
$64$	−63.9818	−	1.52525i	−0.999716	−	0.0238321i
$65$	−77.4885	−	28.2035i	−1.19213	−	0.433900i
$66$		0			0
$67$	31.0935	−	37.0558i	0.464083	−	0.553072i	−0.482348	−	0.875980i	$-0.660216\pi$
$67$	31.0935	−	37.0558i	0.464083	−	0.553072i	0.946431	+	0.322908i	$0.104660\pi$
$68$	42.5135	−	72.3028i	0.625198	−	1.06328i
$69$		0			0
$70$	43.6017	+	76.2180i	0.622881	+	1.08883i
$71$	24.2168	+	13.9816i	0.341082	+	0.196924i	0.660751	−	0.750606i	$-0.270238\pi$
$71$	24.2168	+	13.9816i	0.341082	+	0.196924i	−0.319668	+	0.947530i	$0.603571\pi$
$72$		0			0
$73$	43.5064	+	75.3554i	0.595979	+	1.03227i	0.993408	+	0.114633i	$0.0365691\pi$
$73$	43.5064	+	75.3554i	0.595979	+	1.03227i	−0.397429	+	0.917633i	$0.630098\pi$
$74$	6.35483	+	3.70270i	0.0858761	+	0.0500365i
$75$		0			0
$76$	−86.5416	+	49.0522i	−1.13870	+	0.645424i
$77$	5.87418	−	33.3142i	0.0762881	−	0.432651i
$78$		0			0
$79$	11.6931	+	13.9353i	0.148014	+	0.176396i	0.834957	−	0.550315i	$-0.185492\pi$
$79$	11.6931	+	13.9353i	0.148014	+	0.176396i	−0.686943	+	0.726711i	$0.741048\pi$
$80$	−115.655	+	40.0257i	−1.44569	+	0.500321i
$81$		0			0
$82$	86.2157	−	101.923i	1.05141	−	1.24296i
$83$	8.95501	+	10.6722i	0.107892	+	0.128580i	0.817288	−	0.576230i	$-0.195477\pi$
$83$	8.95501	+	10.6722i	0.107892	+	0.128580i	−0.709396	+	0.704810i	$0.751032\pi$
$84$		0			0
$85$	27.8519	−	157.956i	0.327669	−	1.85831i
$86$	155.581	+	57.3279i	1.80909	+	0.666604i
$87$		0			0
$88$	44.1102	+	16.6527i	0.501252	+	0.189236i
$89$	81.2903	+	140.799i	0.913374	+	1.58201i	0.809264	+	0.587445i	$0.199866\pi$
$89$	81.2903	+	140.799i	0.913374	+	1.58201i	0.104110	+	0.994566i	$0.466801\pi$
$90$		0			0
$91$	53.5880	+	30.9390i	0.588879	+	0.339989i
$92$	−82.0177	−	15.1348i	−0.891497	−	0.164508i
$93$		0			0
$94$	11.5114	+	66.8357i	0.122462	+	0.711019i
$95$	−122.275	+	145.722i	−1.28711	+	1.53391i
$96$		0			0
$97$	39.6511	+	14.4318i	0.408775	+	0.148782i	0.538219	−	0.842805i	$-0.319097\pi$
$97$	39.6511	+	14.4318i	0.408775	+	0.148782i	−0.129445	+	0.991587i	$0.541319\pi$
$98$	10.8623	+	30.2167i	0.110839	+	0.308334i
$99$		0			0
$100$	−103.358	+	85.3372i	−1.03358	+	0.853372i
$101$	−19.0016	−	107.763i	−0.188134	−	1.06696i	−0.921862	−	0.387519i	$-0.873332\pi$
$101$	−19.0016	−	107.763i	−0.188134	−	1.06696i	0.733728	−	0.679444i	$-0.237779\pi$
$102$		0			0
$103$	0.336017	+	0.923198i	0.00326230	+	0.00896309i	0.941313	−	0.337535i	$-0.109593\pi$
$103$	0.336017	+	0.923198i	0.00326230	+	0.00896309i	−0.938051	+	0.346498i	$0.887371\pi$
$104$	−56.2203	+	65.4018i	−0.540579	+	0.628863i
$105$		0			0
$106$	0.349388	−	87.9536i	0.00329612	−	0.829751i
$107$		−	129.179i		−	1.20728i	−0.797258	−	0.603639i	$-0.793717\pi$
$107$		−	129.179i		−	1.20728i	0.797258	−	0.603639i	$-0.206283\pi$
$108$		0			0
$109$	−160.479			−1.47229			−0.736144	−	0.676825i	$-0.763355\pi$
$109$	−160.479			−1.47229			−0.736144	+	0.676825i	$0.763355\pi$
$110$	90.1609	+	0.358157i	0.819645	+	0.00325597i
$111$		0			0
$112$	90.6833	−	14.5082i	0.809672	−	0.129538i
$113$	−61.3383	+	22.3253i	−0.542817	+	0.197569i	−0.598852	−	0.800860i	$-0.704376\pi$
$113$	−61.3383	+	22.3253i	−0.542817	+	0.197569i	0.0560354	+	0.998429i	$0.482154\pi$
$114$		0			0
$115$	−157.065	+	27.6948i	−1.36578	+	0.240825i
$116$	−121.508	+	100.323i	−1.04748	+	0.864852i
$117$		0			0
$118$	−51.6031	+	18.5502i	−0.437315	+	0.157205i
$119$	−41.1644	+	113.098i	−0.345919	+	0.950405i
$120$		0			0
$121$	66.0830	+	55.4502i	0.546141	+	0.458267i
$122$	−16.7924	+	2.89223i	−0.137643	+	0.0237068i
$123$		0			0
$124$	−41.4192	−	7.64311i	−0.334026	−	0.0616380i
$125$	−32.5416	+	56.3637i	−0.260333	+	0.450909i
$126$		0			0
$127$	−42.9918	+	24.8213i	−0.338518	+	0.195443i	−0.659616	−	0.751602i	$-0.729281\pi$
$127$	−42.9918	+	24.8213i	−0.338518	+	0.195443i	0.321099	+	0.947046i	$0.395948\pi$
$128$	−3.55880	+	127.951i	−0.0278032	+	0.999613i
$129$		0			0
$130$	−57.0222	+	154.752i	−0.438632	+	1.19040i
$131$	170.857	+	30.1266i	1.30425	+	0.229974i	0.782246	−	0.622970i	$-0.214074\pi$
$131$	170.857	+	30.1266i	1.30425	+	0.229974i	0.522002	+	0.852944i	$0.325185\pi$
$132$		0			0
$133$	109.348	−	91.7536i	0.822163	−	0.689877i
$134$	−73.8641	−	62.4810i	−0.551224	−	0.466276i
$135$		0			0
$136$	−144.267	−	85.6007i	−1.06078	−	0.629417i
$137$	−38.4087	+	32.2287i	−0.280356	+	0.235246i	−0.772112	−	0.635487i	$-0.780800\pi$
$137$	−38.4087	+	32.2287i	−0.280356	+	0.235246i	0.491756	+	0.870733i	$0.336355\pi$
$138$		0			0
$139$	−183.877	−	32.4224i	−1.32285	−	0.233255i	−0.532773	−	0.846258i	$-0.678850\pi$
$139$	−183.877	−	32.4224i	−1.32285	−	0.233255i	−0.790081	+	0.613003i	$0.789961\pi$
$140$	152.781	−	86.5972i	1.09129	−	0.618551i
$141$		0			0
$142$	28.1554	−	48.3222i	0.198277	−	0.340297i
$143$	55.0242	−	31.7682i	0.384785	−	0.222156i
$144$		0			0
$145$	−150.660	+	260.950i	−1.03903	+	1.79966i
$146$	151.055	−	86.4135i	1.03462	−	0.591873i
$147$		0			0
$148$	7.45583	−	12.6801i	0.0503772	−	0.0856767i
$149$	−29.7807	−	24.9890i	−0.199871	−	0.167711i	0.537359	−	0.843354i	$-0.319422\pi$
$149$	−29.7807	−	24.9890i	−0.199871	−	0.167711i	−0.737230	+	0.675642i	$0.763866\pi$
$150$		0			0
$151$	97.1070	−	266.799i	0.643093	−	1.76688i	0.00130597	−	0.999999i	$-0.499584\pi$
$151$	97.1070	−	266.799i	0.643093	−	1.76688i	0.641787	−	0.766883i	$-0.278193\pi$
$152$	97.4161	+	173.471i	0.640896	+	1.14126i
$153$		0			0
$154$	−66.5811	−	12.0129i	−0.432345	−	0.0780062i
$155$	−79.3185	+	13.9860i	−0.511732	+	0.0902322i
$156$		0			0
$157$	137.397	−	50.0085i	0.875141	−	0.318525i	0.134894	−	0.990860i	$-0.456931\pi$
$157$	137.397	−	50.0085i	0.875141	−	0.318525i	0.740247	+	0.672335i	$0.234708\pi$
$158$	27.9632	−	23.2753i	0.176982	−	0.147312i
$159$		0			0
$160$	79.1319	+	231.627i	0.494575	+	1.44767i
$161$	119.678			0.743341
$162$		0			0
$163$			55.1271i			0.338203i	0.985599	+	0.169102i	$0.0540866\pi$
$163$			55.1271i			0.338203i	−0.985599	+	0.169102i	$0.945913\pi$
$164$	−203.159	−	173.240i	−1.23878	−	1.05634i
$165$		0			0
$166$	21.4153	−	17.8251i	0.129008	−	0.107380i
$167$	58.1117	+	159.661i	0.347974	+	0.956051i	0.983007	+	0.183566i	$0.0587642\pi$
$167$	58.1117	+	159.661i	0.347974	+	0.956051i	−0.635033	+	0.772485i	$0.719014\pi$
$168$		0			0
$169$	−9.16507	−	51.9777i	−0.0542312	−	0.307560i
$170$	−315.688	−	56.9583i	−1.85699	−	0.335049i
$171$		0			0
$172$	115.891	−	310.705i	0.673785	−	1.80642i
$173$	−87.8563	−	31.9771i	−0.507840	−	0.184839i	0.0753771	−	0.997155i	$-0.475984\pi$
$173$	−87.8563	−	31.9771i	−0.507840	−	0.184839i	−0.583217	+	0.812317i	$0.698206\pi$
$174$		0			0
$175$	123.629	−	147.335i	0.706450	−	0.841914i
$176$	33.6556	−	88.0874i	0.191225	−	0.500497i
$177$		0			0
$178$	282.241	−	161.461i	1.58563	−	0.907083i
$179$	130.749	+	75.4882i	0.730444	+	0.421722i	0.818585	−	0.574386i	$-0.194759\pi$
$179$	130.749	+	75.4882i	0.730444	+	0.421722i	−0.0881407	+	0.996108i	$0.528092\pi$
$180$		0			0
$181$	9.82485	+	17.0171i	0.0542809	+	0.0940173i	0.891889	−	0.452254i	$-0.149380\pi$
$181$	9.82485	+	17.0171i	0.0542809	+	0.0940173i	−0.837608	+	0.546272i	$0.816047\pi$
$182$	62.3033	−	106.929i	0.342326	−	0.587524i
$183$		0			0
$184$	−30.9209	+	163.914i	−0.168048	+	0.890836i
$185$	4.88455	−	27.7016i	0.0264029	−	0.149739i
$186$		0			0
$187$	79.4372	+	94.6696i	0.424798	+	0.506255i
$188$	133.762	−	22.4916i	0.711499	−	0.119636i
$189$		0			0
$190$	290.470	+	245.706i	1.52879	+	1.29319i
$191$	−161.522	−	192.495i	−0.845667	−	1.00783i	−0.999804	−	0.0197775i	$-0.993704\pi$
$191$	−161.522	−	192.495i	−0.845667	−	1.00783i	0.154137	−	0.988049i	$-0.450740\pi$
$192$		0			0
$193$	2.54996	−	14.4615i	0.0132122	−	0.0749303i	−0.977489	−	0.210988i	$-0.932332\pi$
$193$	2.54996	−	14.4615i	0.0132122	−	0.0749303i	0.990701	+	0.136057i	$0.0434431\pi$
$194$	29.1785	−	79.1870i	0.150404	−	0.408180i
$195$		0			0
$196$	60.5193	−	21.4843i	0.308772	−	0.109614i
$197$	−104.711	−	181.365i	−0.531528	−	0.920634i	−0.999323	−	0.0367968i	$-0.988285\pi$
$197$	−104.711	−	181.365i	−0.531528	−	0.920634i	0.467794	−	0.883837i	$-0.345049\pi$
$198$		0			0
$199$	−4.56353	−	2.63476i	−0.0229323	−	0.0132400i	0.488490	−	0.872569i	$-0.337548\pi$
$199$	−4.56353	−	2.63476i	−0.0229323	−	0.0132400i	−0.511422	+	0.859330i	$0.670881\pi$
$200$	169.852	+	207.392i	0.849260	+	1.03696i
$201$		0			0
$202$	−215.676	+	37.1467i	−1.06770	+	0.183894i
$203$	145.338	−	173.208i	0.715953	−	0.853239i
$204$		0			0
$205$	−479.774	−	174.623i	−2.34036	−	0.851822i
$206$	1.84905	−	0.664693i	0.00897598	−	0.00322667i
$207$		0			0
$208$	130.356	+	112.959i	0.626711	+	0.543073i
$209$	−25.4514	−	144.342i	−0.121777	−	0.690633i
$210$		0			0
$211$	−30.7845	−	84.5797i	−0.145898	−	0.400852i	0.845120	−	0.534576i	$-0.179529\pi$
$211$	−30.7845	−	84.5797i	−0.145898	−	0.400852i	−0.991019	+	0.133724i	$0.957306\pi$
$212$	−175.903	−	1.39754i	−0.829732	−	0.00659218i
$213$		0			0
$214$	−258.355	−	1.02629i	−1.20727	−	0.00479577i
$215$		−	634.138i		−	2.94948i
$216$		0			0
$217$	60.4378			0.278515
$218$	−1.27497	+	320.956i	−0.00584849	+	1.47228i
$219$		0			0
$220$	1.43261	−	180.318i	0.00651189	−	0.819625i
$221$	−212.423	+	77.3157i	−0.961191	+	0.349845i
$222$		0			0
$223$	−233.603	+	41.1905i	−1.04755	+	0.184711i	−0.670825	−	0.741616i	$-0.734060\pi$
$223$	−233.603	+	41.1905i	−1.04755	+	0.184711i	−0.376722	+	0.926326i	$0.622949\pi$
$224$	−28.2957	−	181.480i	−0.126320	−	0.810180i
$225$		0			0
$226$	44.1629	+	122.853i	0.195411	+	0.543597i
$227$	92.2846	−	253.550i	0.406540	−	1.11696i	−0.552456	−	0.833542i	$-0.686309\pi$
$227$	92.2846	−	253.550i	0.406540	−	1.11696i	0.958996	−	0.283418i	$-0.0914684\pi$
$228$		0			0
$229$	132.829	+	111.457i	0.580039	+	0.486710i	0.884960	−	0.465667i	$-0.154186\pi$
$229$	132.829	+	111.457i	0.580039	+	0.486710i	−0.304921	+	0.952378i	$0.598630\pi$
$230$	54.1414	+	314.348i	0.235397	+	1.36673i
$231$		0			0
$232$	199.679	+	243.810i	0.860684	+	1.05091i
$233$	85.3765	−	147.877i	0.366423	−	0.634663i	−0.622580	−	0.782556i	$-0.713916\pi$
$233$	85.3765	−	147.877i	0.366423	−	0.634663i	0.989003	+	0.147893i	$0.0472490\pi$
$234$		0			0
$235$	224.630	−	129.690i	0.955871	−	0.551872i
$236$	36.6901	+	103.353i	0.155467	+	0.437936i
$237$		0			0
$238$	225.868	+	83.2267i	0.949024	+	0.349692i
$239$	126.129	+	22.2400i	0.527738	+	0.0930544i	0.431168	−	0.902272i	$-0.358102\pi$
$239$	126.129	+	22.2400i	0.527738	+	0.0930544i	0.0965700	+	0.995326i	$0.469213\pi$
$240$		0			0
$241$	−126.565	+	106.201i	−0.525167	+	0.440668i	−0.866429	−	0.499301i	$-0.833590\pi$
$241$	−126.565	+	106.201i	−0.525167	+	0.440668i	0.341261	+	0.939968i	$0.389146\pi$
$242$	111.425	−	131.724i	0.460432	−	0.544316i
$243$		0			0
$244$	5.65099	+	33.6076i	0.0231598	+	0.137736i
$245$	94.0744	−	78.9378i	0.383977	−	0.322195i
$246$		0			0
$247$	264.030	+	46.5556i	1.06895	+	0.188484i
$248$	−15.6152	+	82.7771i	−0.0629644	+	0.333779i
$249$		0			0
$250$	112.468	+	65.5304i	0.449872	+	0.262122i
$251$	−114.384	+	66.0395i	−0.455712	+	0.263106i	−0.710240	−	0.703960i	$-0.751413\pi$
$251$	−114.384	+	66.0395i	−0.455712	+	0.263106i	0.254527	+	0.967066i	$0.418080\pi$
$252$		0			0
$253$	61.4428	−	106.422i	0.242857	−	0.420640i
$254$	49.3007	+	86.1801i	0.194097	+	0.339292i
$255$		0			0
$256$	255.871	+	8.13409i	0.999495	+	0.0317738i
$257$	−7.69515	−	6.45700i	−0.0299422	−	0.0251245i	0.627694	−	0.778460i	$-0.283999\pi$
$257$	−7.69515	−	6.45700i	−0.0299422	−	0.0251245i	−0.657636	+	0.753336i	$0.728443\pi$
$258$		0			0
$259$	−7.21923	+	19.8347i	−0.0278735	+	0.0765818i
$260$	309.048	+	115.273i	1.18865	+	0.443357i
$261$		0			0
$262$	61.6102	−	341.471i	0.235153	−	1.30332i
$263$	−97.1175	+	17.1244i	−0.369268	+	0.0651119i	−0.355203	−	0.934789i	$-0.615588\pi$
$263$	−97.1175	+	17.1244i	−0.369268	+	0.0651119i	−0.0140650	+	0.999901i	$0.504477\pi$
$264$		0			0
$265$	−316.099	+	115.051i	−1.19283	+	0.434153i
$266$	−182.637	−	219.423i	−0.686605	−	0.824897i
$267$		0			0
$268$	−125.548	+	147.231i	−0.468462	+	0.549368i
$269$	−39.0655			−0.145225			−0.0726125	−	0.997360i	$-0.523134\pi$
$269$	−39.0655			−0.145225			−0.0726125	+	0.997360i	$0.523134\pi$
$270$		0			0
$271$		−	286.162i		−	1.05595i	−0.849260	−	0.527975i	$-0.822951\pi$
$271$		−	286.162i		−	1.05595i	0.849260	−	0.527975i	$-0.177049\pi$
$272$	−172.346	+	287.851i	−0.633626	+	1.05828i
$273$		0			0
$274$	64.1518	+	77.0729i	0.234131	+	0.281288i
$275$	−67.5445	−	185.577i	−0.245616	−	0.674826i
$276$		0			0
$277$	11.2278	+	63.6758i	0.0405334	+	0.229877i	0.998344	−	0.0575231i	$-0.0183203\pi$
$277$	11.2278	+	63.6758i	0.0405334	+	0.229877i	−0.957811	+	0.287400i	$0.907209\pi$
$278$	−66.3052	+	367.493i	−0.238508	+	1.32192i
$279$		0			0
$280$	−171.979	−	306.248i	−0.614211	−	1.09374i
$281$	370.748	+	134.941i	1.31939	+	0.480219i	0.903263	−	0.429088i	$-0.141165\pi$
$281$	370.748	+	134.941i	1.31939	+	0.480219i	0.416127	+	0.909307i	$0.363387\pi$
$282$		0			0
$283$	31.3644	−	37.3786i	0.110828	−	0.132080i	−0.707778	−	0.706435i	$-0.750302\pi$
$283$	31.3644	−	37.3786i	0.110828	−	0.132080i	0.818607	+	0.574355i	$0.194747\pi$
$284$	−96.4200	−	56.6942i	−0.339507	−	0.199628i
$285$		0			0
$286$	−63.0988	−	110.300i	−0.220625	−	0.385664i
$287$	331.793	+	191.561i	1.15607	+	0.667459i
$288$		0			0
$289$	−75.3464	−	130.504i	−0.260714	−	0.451570i
$290$	520.700	+	303.390i	1.79552	+	1.04617i
$291$		0			0
$292$	−171.626	−	302.795i	−0.587759	−	1.03697i
$293$	−95.7393	+	542.964i	−0.326755	+	1.85312i	0.170287	+	0.985395i	$0.445531\pi$
$293$	−95.7393	+	542.964i	−0.326755	+	1.85312i	−0.497042	+	0.867727i	$0.665580\pi$
$294$		0			0
$295$	134.807	+	160.657i	0.456974	+	0.544600i
$296$	−25.3009	−	15.0123i	−0.0854759	−	0.0507172i
$297$		0			0
$298$	−50.2142	+	59.3625i	−0.168504	+	0.199203i
$299$	144.487	+	172.192i	0.483233	+	0.575894i
$300$		0			0
$301$	−82.6303	+	468.620i	−0.274519	+	1.55688i
$302$	−532.823	−	196.332i	−1.76431	−	0.650106i
$303$		0			0
$304$	347.714	−	193.453i	1.14380	−	0.636357i
$305$	32.5845	+	56.4380i	0.106834	+	0.185043i
$306$		0			0
$307$	256.843	+	148.288i	0.836622	+	0.483024i	0.856115	−	0.516786i	$-0.172872\pi$
$307$	256.843	+	148.288i	0.836622	+	0.483024i	−0.0194923	+	0.999810i	$0.506205\pi$
$308$	−24.5547	+	133.066i	−0.0797230	+	0.432032i
$309$		0			0
$310$	27.3416	+	158.747i	0.0881987	+	0.512087i
$311$	96.9784	−	115.574i	0.311828	−	0.371622i	−0.587254	−	0.809403i	$-0.699791\pi$
$311$	96.9784	−	115.574i	0.311828	−	0.371622i	0.899082	+	0.437781i	$0.144235\pi$
$312$		0			0
$313$	−290.511	−	105.737i	−0.928150	−	0.337819i	−0.166674	−	0.986012i	$-0.553303\pi$
$313$	−290.511	−	105.737i	−0.928150	−	0.337819i	−0.761476	+	0.648193i	$0.775525\pi$
$314$	−98.9246	−	275.189i	−0.315046	−	0.876399i
$315$		0			0
$316$	−46.3280	−	56.1109i	−0.146608	−	0.177566i
$317$	−26.3539	−	149.461i	−0.0831355	−	0.471485i	−0.997743	−	0.0671428i	$-0.978612\pi$
$317$	−26.3539	−	149.461i	−0.0831355	−	0.471485i	0.914608	−	0.404342i	$-0.132499\pi$
$318$		0			0
$319$	−79.4056	−	218.165i	−0.248920	−	0.683903i
$320$	463.879	−	156.422i	1.44962	−	0.488820i
$321$		0			0
$322$	0.950813	−	239.354i	0.00295284	−	0.743335i
$323$			521.477i			1.61448i
$324$		0			0
$325$	361.242			1.11151
$326$	110.253	+	0.437972i	0.338201	+	0.00134347i
$327$		0			0
$328$	−348.091	+	404.939i	−1.06125	+	1.23457i
$329$	−182.898	+	66.5693i	−0.555920	+	0.202338i
$330$		0			0
$331$	−569.180	+	100.362i	−1.71958	+	0.303208i	−0.944464	−	0.328614i	$-0.893419\pi$
$331$	−569.180	+	100.362i	−1.71958	+	0.303208i	−0.775114	+	0.631822i	$0.782308\pi$
$332$	−35.4798	−	42.9719i	−0.106867	−	0.129433i
$333$		0			0
$334$	319.780	−	114.954i	0.957426	−	0.344174i
$335$	−126.551	+	347.695i	−0.377763	+	1.03790i
$336$		0			0
$337$	340.126	+	285.400i	1.00928	+	0.846883i	0.988242	−	0.152896i	$-0.0488599\pi$
$337$	340.126	+	285.400i	1.00928	+	0.846883i	0.0210336	+	0.999779i	$0.493304\pi$
$338$	−104.027	+	17.9170i	−0.307773	+	0.0530090i
$339$		0			0
$340$	−116.424	+	630.919i	−0.342423	+	1.85564i
$341$	31.0288	−	53.7435i	0.0909936	−	0.157606i
$342$		0			0
$343$	−323.375	+	186.700i	−0.942783	+	0.544316i
$344$	−620.484	−	234.249i	−1.80373	−	0.680956i
$345$		0			0
$346$	−64.6516	+	175.457i	−0.186854	+	0.507101i
$347$	−539.222	−	95.0793i	−1.55395	−	0.274004i	−0.670280	−	0.742108i	$-0.733826\pi$
$347$	−539.222	−	95.0793i	−1.55395	−	0.274004i	−0.883673	+	0.468105i	$0.844937\pi$
$348$		0			0
$349$	308.273	−	258.672i	0.883305	−	0.741181i	−0.0835512	−	0.996503i	$-0.526626\pi$
$349$	308.273	−	258.672i	0.883305	−	0.741181i	0.966856	+	0.255323i	$0.0821818\pi$
$350$	−293.685	−	248.426i	−0.839101	−	0.709789i
$351$		0			0
$352$	−175.906	−	68.0106i	−0.499733	−	0.193212i
$353$	87.4208	−	73.3547i	0.247651	−	0.207804i	−0.510509	−	0.859872i	$-0.670543\pi$
$353$	87.4208	−	73.3547i	0.247651	−	0.207804i	0.758160	+	0.652069i	$0.226099\pi$
$354$		0			0
$355$	−210.644	−	37.1421i	−0.593362	−	0.104626i
$356$	−320.677	−	565.761i	−0.900777	−	1.58922i
$357$		0			0
$358$	152.014	−	260.897i	0.424620	−	0.728763i
$359$	−441.999	+	255.188i	−1.23120	+	0.710831i	−0.967279	−	0.253715i	$-0.918348\pi$
$359$	−441.999	+	255.188i	−1.23120	+	0.710831i	−0.263916	+	0.964546i	$0.585014\pi$
$360$		0			0
$361$	128.736	−	222.978i	0.356610	−	0.617667i
$362$	34.1120	−	19.5143i	0.0942322	−	0.0539070i
$363$		0			0
$364$	−213.362	−	125.455i	−0.586159	−	0.344657i
$365$	−509.856	−	427.820i	−1.39687	−	1.17211i
$366$		0			0
$367$	−18.6859	+	51.3391i	−0.0509152	+	0.139888i	−0.962544	−	0.271127i	$-0.912604\pi$
$367$	−18.6859	+	51.3391i	−0.0509152	+	0.139888i	0.911628	+	0.411016i	$0.134826\pi$
$368$	327.580	+	63.1436i	0.890162	+	0.171586i
$369$		0			0
$370$	−55.3640	−	9.98910i	−0.149632	−	0.0269976i
$371$	248.585	−	43.8322i	0.670039	−	0.118146i
$372$		0			0
$373$	620.992	−	226.023i	1.66486	−	0.605959i	0.673744	−	0.738965i	$-0.264685\pi$
$373$	620.992	−	226.023i	1.66486	−	0.605959i	0.991115	+	0.133006i	$0.0424629\pi$
$374$	189.969	−	158.121i	0.507938	−	0.422784i
$375$		0			0
$376$	−43.9201	−	267.700i	−0.116809	−	0.711969i
$377$	424.677			1.12646
$378$		0			0
$379$			294.012i			0.775757i	0.921711	+	0.387878i	$0.126792\pi$
$379$			294.012i			0.775757i	−0.921711	+	0.387878i	$0.873208\pi$
$380$	493.715	−	578.983i	1.29925	−	1.52364i
$381$		0			0
$382$	−386.270	+	321.513i	−1.01118	+	0.841657i
$383$	178.617	+	490.746i	0.466362	+	1.28132i	0.920624	+	0.390451i	$0.127681\pi$
$383$	178.617	+	490.746i	0.466362	+	1.28132i	−0.454261	+	0.890869i	$0.650097\pi$
$384$		0			0
$385$	44.9322	+	254.823i	0.116707	+	0.661878i
$386$	−28.9026	−	5.21477i	−0.0748772	−	0.0135098i
$387$		0			0
$388$	−158.141	−	58.9856i	−0.407580	−	0.152025i
$389$	−101.361	−	36.8924i	−0.260568	−	0.0948391i	0.208433	−	0.978037i	$-0.433164\pi$
$389$	−101.361	−	36.8924i	−0.260568	−	0.0948391i	−0.469001	+	0.883198i	$0.655386\pi$
$390$		0			0
$391$	−281.035	+	334.925i	−0.718760	+	0.856585i
$392$	−42.4874	−	121.208i	−0.108386	−	0.309205i
$393$		0			0
$394$	−363.559	+	207.980i	−0.922738	+	0.527867i
$395$	−120.504	−	69.5731i	−0.305074	−	0.176134i
$396$		0			0
$397$	−197.478	−	342.043i	−0.497427	−	0.861568i	0.502569	−	0.864537i	$-0.332388\pi$
$397$	−197.478	−	342.043i	−0.497427	−	0.861568i	−0.999996	+	0.00296877i	$0.999055\pi$
$398$	−5.30573	+	9.10606i	−0.0133310	+	0.0228796i
$399$		0			0
$400$	416.129	−	338.054i	1.04032	−	0.845134i
$401$	−5.45754	+	30.9512i	−0.0136098	+	0.0771851i	−0.990856	−	0.134922i	$-0.956922\pi$
$401$	−5.45754	+	30.9512i	−0.0136098	+	0.0771851i	0.977246	+	0.212107i	$0.0680326\pi$
$402$		0			0
$403$	72.9663	+	86.9578i	0.181058	+	0.215776i
$404$	72.5792	+	431.643i	0.179652	+	1.06842i
$405$		0			0
$406$	−345.258	−	292.051i	−0.850388	−	0.719336i
$407$	13.9314	+	16.6027i	0.0342294	+	0.0407930i
$408$		0			0
$409$	36.6237	−	207.703i	0.0895445	−	0.507832i	−0.906739	−	0.421693i	$-0.861436\pi$
$409$	36.6237	−	207.703i	0.0895445	−	0.507832i	0.996283	−	0.0861391i	$-0.0274529\pi$
$410$	−353.056	+	958.153i	−0.861112	+	2.33696i
$411$		0			0
$412$	−1.31469	−	3.70335i	−0.00319099	−	0.00898872i
$413$	−78.6867	−	136.289i	−0.190525	−	0.329999i
$414$		0			0
$415$	−92.2867	−	53.2817i	−0.222378	−	0.128390i
$416$	226.952	−	259.812i	0.545559	−	0.624549i
$417$		0			0
$418$	−288.885	+	49.7557i	−0.691111	+	0.119033i
$419$	26.3541	−	31.4075i	0.0628975	−	0.0749583i	−0.733678	−	0.679497i	$-0.762198\pi$
$419$	26.3541	−	31.4075i	0.0628975	−	0.0749583i	0.796576	+	0.604539i	$0.206643\pi$
$420$		0			0
$421$	180.665	+	65.7568i	0.429134	+	0.156192i	0.547551	−	0.836772i	$-0.315560\pi$
$421$	180.665	+	65.7568i	0.429134	+	0.156192i	−0.118418	+	0.992964i	$0.537782\pi$
$422$	−169.403	+	60.8966i	−0.401428	+	0.144305i
$423$		0			0
$424$	−4.19257	+	351.792i	−0.00988814	+	0.829699i
$425$	122.012	+	691.962i	0.287086	+	1.62815i
$426$		0			0
$427$	−16.7255	−	45.9529i	−0.0391697	−	0.107618i
$428$	−4.10515	+	516.699i	−0.00959146	+	1.20724i
$429$		0			0
$430$	−1268.27	−	5.03808i	−2.94946	−	0.0117165i
$431$		−	427.089i		−	0.990927i	−0.868629	−	0.495463i	$-0.834998\pi$
$431$		−	427.089i		−	0.990927i	0.868629	−	0.495463i	$-0.165002\pi$
$432$		0			0
$433$	−265.388			−0.612906			−0.306453	−	0.951886i	$-0.599142\pi$
$433$	−265.388			−0.612906			−0.306453	+	0.951886i	$0.599142\pi$
$434$	0.480164	−	120.875i	0.00110637	−	0.278513i
$435$		0			0
$436$	641.897	+	5.09984i	1.47224	+	0.0116969i
$437$	487.265	−	177.350i	1.11502	−	0.405835i
$438$		0			0
$439$	553.109	−	97.5280i	1.25993	−	0.222159i	0.496492	−	0.868041i	$-0.334621\pi$
$439$	553.109	−	97.5280i	1.25993	−	0.222159i	0.763437	+	0.645882i	$0.223510\pi$
$440$	−360.621	−	4.29779i	−0.819593	−	0.00976770i
$441$		0			0
$442$	152.943	+	425.457i	0.346024	+	0.962573i
$443$	−111.741	+	307.006i	−0.252237	+	0.693016i	0.747354	+	0.664426i	$0.231324\pi$
$443$	−111.741	+	307.006i	−0.252237	+	0.693016i	−0.999591	+	0.0285901i	$0.990898\pi$
$444$		0			0
$445$	−952.648	−	799.367i	−2.14078	−	1.79633i
$446$	80.5245	+	467.530i	0.180548	+	1.04827i
$447$		0			0
$448$	−363.183	+	55.1492i	−0.810676	+	0.123101i
$449$	−97.3394	+	168.597i	−0.216791	+	0.375494i	−0.953825	−	0.300362i	$-0.902892\pi$
$449$	−97.3394	+	168.597i	−0.216791	+	0.375494i	0.737034	+	0.675856i	$0.236226\pi$
$450$		0			0
$451$	340.686	−	196.695i	0.755400	−	0.436131i
$452$	246.055	−	87.3491i	0.544369	−	0.193250i
$453$		0			0
$454$	−506.363	−	186.582i	−1.11534	−	0.410974i
$455$	−466.120	−	82.1896i	−1.02444	−	0.180636i
$456$		0			0
$457$	237.405	−	199.206i	0.519486	−	0.435900i	−0.344967	−	0.938615i	$-0.612110\pi$
$457$	237.405	−	199.206i	0.519486	−	0.435900i	0.864452	+	0.502715i	$0.167665\pi$
$458$	223.967	−	264.770i	0.489010	−	0.578101i
$459$		0			0
$460$	629.121	−	105.785i	1.36765	−	0.229966i
$461$	−308.002	+	258.445i	−0.668118	+	0.560617i	−0.912508	−	0.409060i	$-0.865857\pi$
$461$	−308.002	+	258.445i	−0.668118	+	0.560617i	0.244390	+	0.969677i	$0.421412\pi$
$462$		0			0
$463$	−66.1231	−	11.6593i	−0.142814	−	0.0251820i	0.101784	−	0.994807i	$-0.467545\pi$
$463$	−66.1231	−	11.6593i	−0.142814	−	0.0251820i	−0.244598	+	0.969624i	$0.578656\pi$
$464$	489.203	−	397.417i	1.05432	−	0.856502i
$465$		0			0
$466$	−295.072	−	171.927i	−0.633203	−	0.368941i
$467$	−309.740	+	178.828i	−0.663254	+	0.382930i	−0.793516	−	0.608550i	$-0.791752\pi$
$467$	−309.740	+	178.828i	−0.663254	+	0.382930i	0.130261	+	0.991480i	$0.458418\pi$
$468$		0			0
$469$	138.825	−	240.452i	0.296002	−	0.512691i
$470$	−257.593	−	450.286i	−0.548071	−	0.958056i
$471$		0			0
$472$	206.995	−	72.5585i	0.438550	−	0.153726i
$473$	374.291	+	314.068i	0.791313	+	0.663991i
$474$		0			0
$475$	285.015	−	783.074i	0.600033	−	1.64858i
$476$	168.246	−	451.071i	0.353459	−	0.947627i
$477$		0			0
$478$	45.4817	−	252.080i	0.0951501	−	0.527364i
$479$	7.06355	−	1.24549i	0.0147464	−	0.00260020i	−0.166270	−	0.986080i	$-0.553172\pi$
$479$	7.06355	−	1.24549i	0.0147464	−	0.00260020i	0.181017	+	0.983480i	$0.442061\pi$
$480$		0			0
$481$	−37.2539	+	13.5593i	−0.0774508	+	0.0281898i
$482$	211.395	+	253.972i	0.438578	+	0.526914i
$483$		0			0
$484$	−262.562	−	223.894i	−0.542483	−	0.462591i
$485$	−322.760			−0.665485
$486$		0			0
$487$			432.322i			0.887725i	0.896095	+	0.443862i	$0.146392\pi$
$487$			432.322i			0.887725i	−0.896095	+	0.443862i	$0.853608\pi$
$488$	67.2595	−	11.0349i	0.137827	−	0.0226125i
$489$		0			0
$490$	−157.127	−	188.775i	−0.320667	−	0.385254i
$491$	61.1331	+	167.962i	0.124507	+	0.342081i	0.986249	−	0.165266i	$-0.0528484\pi$
$491$	61.1331	+	167.962i	0.124507	+	0.342081i	−0.861742	+	0.507347i	$0.830626\pi$
$492$		0			0
$493$	143.437	+	813.474i	0.290948	+	1.65005i
$494$	95.2081	−	527.686i	0.192729	−	1.06819i
$495$		0			0
$496$	165.429	+	31.8877i	0.333526	+	0.0642898i
$497$	150.823	+	54.8951i	0.303467	+	0.110453i
$498$		0			0
$499$	−413.773	+	493.116i	−0.829205	+	0.988208i	0.170791	+	0.985307i	$0.445368\pi$
$499$	−413.773	+	493.116i	−0.829205	+	0.988208i	−0.999996	+	0.00290072i	$0.999077\pi$
$500$	131.953	−	224.413i	0.263907	−	0.448827i
$501$		0			0
$502$	131.169	+	229.290i	0.261293	+	0.456754i
$503$	306.467	+	176.939i	0.609279	+	0.351767i	0.772683	−	0.634792i	$-0.218914\pi$
$503$	306.467	+	176.939i	0.609279	+	0.351767i	−0.163404	+	0.986559i	$0.552248\pi$
$504$		0			0
$505$	418.503	+	724.869i	0.828719	+	1.43538i
$506$	−212.354	−	123.730i	−0.419672	−	0.244526i
$507$		0			0
$508$	172.750	−	97.9159i	0.340060	−	0.192748i
$509$	94.0125	−	533.171i	0.184700	−	1.04749i	−0.741639	−	0.670799i	$-0.765951\pi$
$509$	94.0125	−	533.171i	0.184700	−	1.04749i	0.926340	−	0.376689i	$-0.122937\pi$
$510$		0			0
$511$	321.031	+	382.589i	0.628240	+	0.748707i
$512$	18.3009	−	511.673i	0.0357439	−	0.999361i
$513$		0			0
$514$	−12.9750	+	15.3389i	−0.0252432	+	0.0298422i
$515$	−4.83044	−	5.75669i	−0.00937949	−	0.0111780i
$516$		0			0
$517$	−34.7039	+	196.816i	−0.0671256	+	0.380688i
$518$	39.6117	+	14.5959i	0.0764705	+	0.0281775i
$519$		0			0
$520$	232.999	−	617.175i	0.448076	−	1.18687i
$521$	−3.55297	−	6.15392i	−0.00681952	−	0.0118118i	0.862596	−	0.505894i	$-0.168837\pi$
$521$	−3.55297	−	6.15392i	−0.00681952	−	0.0118118i	−0.869415	+	0.494082i	$0.835504\pi$
$522$		0			0
$523$	−26.6849	−	15.4065i	−0.0510227	−	0.0294580i	0.474272	−	0.880379i	$-0.342711\pi$
$523$	−26.6849	−	15.4065i	−0.0510227	−	0.0294580i	−0.525294	+	0.850921i	$0.676045\pi$
$524$	−682.447	−	125.932i	−1.30238	−	0.240329i
$525$		0			0
$526$	33.4770	+	194.370i	0.0636445	+	0.369524i
$527$	−141.924	+	169.138i	−0.269305	+	0.320945i
$528$		0			0
$529$	−88.5681	−	32.2361i	−0.167425	−	0.0609379i
$530$	227.588	+	633.107i	0.429411	+	1.19454i
$531$		0			0
$532$	−440.293	+	363.528i	−0.827618	+	0.683323i
$533$	124.955	+	708.653i	0.234437	+	1.32956i
$534$		0			0
$535$	337.950	+	928.510i	0.631682	+	1.73553i
$536$	293.461	+	252.263i	0.547503	+	0.470641i
$537$		0			0
$538$	−0.310366	+	78.1304i	−0.000576889	+	0.145224i
$539$			94.6215i			0.175550i
$540$		0			0
$541$	74.8336			0.138325			0.0691623	−	0.997605i	$-0.477967\pi$
$541$	74.8336			0.138325			0.0691623	+	0.997605i	$0.477967\pi$
$542$	−572.320	−	2.27349i	−1.05594	−	0.00419464i
$543$		0			0
$544$	574.328	+	346.977i	1.05575	+	0.637825i
$545$	1153.49	−	419.837i	2.11650	−	0.770343i
$546$		0			0
$547$	290.555	−	51.2327i	0.531179	−	0.0936612i	0.0983754	−	0.995149i	$-0.468635\pi$
$547$	290.555	−	51.2327i	0.531179	−	0.0936612i	0.432804	+	0.901488i	$0.357524\pi$
$548$	154.654	−	127.690i	0.282216	−	0.233011i
$549$		0			0
$550$	−371.688	+	133.614i	−0.675796	+	0.242934i
$551$	335.065	−	920.584i	0.608104	−	1.67075i
$552$		0			0
$553$	79.9854	+	67.1157i	0.144639	+	0.121367i
$554$	127.440	−	21.9495i	0.230036	−	0.0396200i
$555$		0			0
$556$	734.453	+	135.529i	1.32096	+	0.243757i
$557$	73.4754	−	127.263i	0.131913	−	0.228480i	−0.792501	−	0.609870i	$-0.791221\pi$
$557$	73.4754	−	127.263i	0.131913	−	0.228480i	0.924414	+	0.381391i	$0.124555\pi$
$558$		0			0
$559$	−774.009	+	446.874i	−1.38463	+	0.799417i
$560$	−613.857	+	341.523i	−1.09617	+	0.609862i
$561$		0			0
$562$	272.826	−	740.419i	0.485456	−	1.31747i
$563$	286.120	+	50.4507i	0.508207	+	0.0896105i	0.421871	−	0.906656i	$-0.361373\pi$
$563$	286.120	+	50.4507i	0.508207	+	0.0896105i	0.0863350	+	0.996266i	$0.472484\pi$
$564$		0			0
$565$	382.481	−	320.939i	0.676957	−	0.568034i
$566$	−74.5075	−	63.0253i	−0.131639	−	0.111352i
$567$		0			0
$568$	−114.154	+	192.388i	−0.200975	+	0.338711i
$569$	37.1059	−	31.1355i	0.0652125	−	0.0547198i	−0.609599	−	0.792710i	$-0.708669\pi$
$569$	37.1059	−	31.1355i	0.0652125	−	0.0547198i	0.674811	+	0.737990i	$0.264225\pi$
$570$		0			0
$571$	860.734	+	151.771i	1.50741	+	0.265798i	0.865473	−	0.500956i	$-0.167018\pi$
$571$	860.734	+	151.771i	1.50741	+	0.265798i	0.641941	+	0.766754i	$0.278129\pi$
$572$	−221.099	+	125.320i	−0.386538	+	0.219092i
$573$		0			0
$574$	385.754	−	662.059i	0.672046	−	1.15341i
$575$	605.070	−	349.337i	1.05230	−	0.607543i
$576$		0			0
$577$	−92.1639	+	159.633i	−0.159730	+	0.276660i	−0.934771	−	0.355251i	$-0.884396\pi$
$577$	−92.1639	+	159.633i	−0.159730	+	0.276660i	0.775042	+	0.631910i	$0.217729\pi$
$578$	−261.604	+	149.655i	−0.452602	+	0.258918i
$579$		0			0
$580$	610.913	−	1038.98i	1.05330	−	1.79135i
$581$	61.2559	+	51.3998i	0.105432	+	0.0884678i
$582$		0			0
$583$	88.6464	−	243.554i	0.152052	−	0.417760i
$584$	−606.948	+	340.843i	−1.03929	+	0.583635i
$585$		0			0
$586$	1085.16	+	195.791i	1.85181	+	0.334114i
$587$	−624.158	+	110.056i	−1.06330	+	0.187489i	−0.677821	−	0.735227i	$-0.737076\pi$
$587$	−624.158	+	110.056i	−1.06330	+	0.187489i	−0.385481	+	0.922716i	$0.625965\pi$
$588$		0			0
$589$	246.070	−	89.5623i	0.417777	−	0.152058i
$590$	322.383	−	268.336i	0.546411	−	0.454807i
$591$		0			0
$592$	−30.2253	+	50.4820i	−0.0510563	+	0.0852737i
$593$	−445.495			−0.751256			−0.375628	−	0.926771i	$-0.622573\pi$
$593$	−445.495			−0.751256			−0.375628	+	0.926771i	$0.622573\pi$
$594$		0			0
$595$		−	920.619i		−	1.54726i
$596$	118.325	+	100.899i	0.198532	+	0.169294i
$597$		0			0
$598$	345.530	−	287.603i	0.577809	−	0.480941i
$599$	−304.954	−	837.855i	−0.509105	−	1.39876i	−0.882162	−	0.470947i	$-0.843912\pi$
$599$	−304.954	−	837.855i	−0.509105	−	1.39876i	0.373056	−	0.927809i	$-0.378310\pi$
$600$		0			0
$601$	174.212	+	988.005i	0.289870	+	1.64393i	0.687352	+	0.726325i	$0.258773\pi$
$601$	174.212	+	988.005i	0.289870	+	1.64393i	−0.397482	+	0.917610i	$0.630116\pi$
$602$	936.576	+	168.982i	1.55577	+	0.280702i
$603$		0			0
$604$	−396.894	+	1064.08i	−0.657110	+	1.76172i
$605$	−620.057	−	225.682i	−1.02489	−	0.373029i
$606$		0			0
$607$	522.302	−	622.455i	0.860464	−	1.02546i	−0.138918	−	0.990304i	$-0.544362\pi$
$607$	522.302	−	622.455i	0.860464	−	1.02546i	0.999382	−	0.0351573i	$-0.0111932\pi$
$608$	−384.139	−	696.960i	−0.631808	−	1.14632i
$609$		0			0
$610$	113.134	−	64.7201i	0.185466	−	0.106099i
$611$	−316.591	−	182.784i	−0.518152	−	0.299155i
$612$		0			0
$613$	−176.799	−	306.225i	−0.288416	−	0.499551i	0.685016	−	0.728528i	$-0.259795\pi$
$613$	−176.799	−	306.225i	−0.288416	−	0.499551i	−0.973432	+	0.228977i	$0.926462\pi$
$614$	298.615	−	512.504i	0.486344	−	0.834697i
$615$		0			0
$616$	265.934	+	50.1661i	0.431712	+	0.0814385i
$617$	−14.8981	+	84.4914i	−0.0241460	+	0.136939i	−0.994498	−	0.104758i	$-0.966593\pi$
$617$	−14.8981	+	84.4914i	−0.0241460	+	0.136939i	0.970352	+	0.241697i	$0.0777042\pi$
$618$		0			0
$619$	409.962	+	488.574i	0.662298	+	0.789296i	0.987714	−	0.156275i	$-0.0499487\pi$
$619$	409.962	+	488.574i	0.662298	+	0.789296i	−0.325416	+	0.945571i	$0.605504\pi$
$620$	317.709	−	53.4216i	0.512433	−	0.0861638i
$621$		0			0
$622$	−230.376	−	194.874i	−0.370380	−	0.313302i
$623$	599.835	+	714.855i	0.962817	+	1.14744i
$624$		0			0
$625$	−59.0210	+	334.725i	−0.0944335	+	0.535559i
$626$	−213.781	+	580.177i	−0.341503	+	0.926801i
$627$		0			0
$628$	−551.160	+	195.661i	−0.877644	+	0.311562i
$629$	−38.5557	−	66.7804i	−0.0612968	−	0.106169i
$630$		0			0
$631$	−1010.86	−	583.618i	−1.60199	−	0.924909i	−0.991089	−	0.133203i	$-0.957474\pi$
$631$	−1010.86	−	583.618i	−1.60199	−	0.924909i	−0.610901	−	0.791707i	$-0.709193\pi$
$632$	−112.589	+	92.2094i	−0.178147	+	0.145901i
$633$		0			0
$634$	−299.128	+	51.5201i	−0.471811	+	0.0812619i
$635$	244.080	−	290.883i	0.384378	−	0.458084i
$636$		0			0
$637$	−162.643	−	59.1971i	−0.255326	−	0.0929312i
$638$	−436.958	+	157.077i	−0.684886	+	0.246202i
$639$		0			0
$640$	−309.157	−	928.993i	−0.483058	−	1.45155i
$641$	−80.0762	−	454.134i	−0.124924	−	0.708478i	−0.981353	−	0.192214i	$-0.938433\pi$
$641$	−80.0762	−	454.134i	−0.124924	−	0.708478i	0.856429	−	0.516264i	$-0.172678\pi$
$642$		0			0
$643$	27.9088	+	76.6788i	0.0434040	+	0.119252i	0.959501	−	0.281705i	$-0.0909000\pi$
$643$	27.9088	+	76.6788i	0.0434040	+	0.119252i	−0.916097	+	0.400957i	$0.868678\pi$
$644$	−478.697	−	3.80322i	−0.743318	−	0.00590562i
$645$		0			0
$646$	1042.95	+	4.14301i	1.61447	+	0.00641333i
$647$			360.614i			0.557363i	0.960384	+	0.278682i	$0.0898974\pi$
$647$			360.614i			0.557363i	−0.960384	+	0.278682i	$0.910103\pi$
$648$		0			0
$649$	−161.591			−0.248985
$650$	2.86998	−	722.478i	0.00441535	−	1.11150i
$651$		0			0
$652$	1.75187	−	220.502i	0.00268692	−	0.338193i
$653$	−114.976	+	41.8479i	−0.176074	+	0.0640857i	−0.428553	−	0.903517i	$-0.640976\pi$
$653$	−114.976	+	41.8479i	−0.176074	+	0.0640857i	0.252479	+	0.967602i	$0.418754\pi$
$654$		0			0
$655$	−1306.90	+	230.441i	−1.99526	+	0.351819i
$656$	807.106	+	699.393i	1.23034	+	1.06615i
$657$		0			0
$658$	131.684	+	366.321i	0.200128	+	0.556719i
$659$	19.5137	−	53.6136i	0.0296111	−	0.0813560i	−0.924006	−	0.382378i	$-0.875105\pi$
$659$	19.5137	−	53.6136i	0.0296111	−	0.0813560i	0.953617	+	0.301022i	$0.0973276\pi$
$660$		0			0
$661$	−716.089	−	600.870i	−1.08334	−	0.909031i	−0.0871475	−	0.996195i	$-0.527775\pi$
$661$	−716.089	−	600.870i	−1.08334	−	0.909031i	−0.996194	+	0.0871639i	$0.972220\pi$
$662$	196.200	+	1139.15i	0.296375	+	1.72077i
$663$		0			0
$664$	−86.2250	+	70.6176i	−0.129857	+	0.106352i
$665$	−545.928	+	945.575i	−0.820945	+	1.42192i
$666$		0			0
$667$	711.323	−	410.682i	1.06645	−	0.615716i
$668$	−227.366	−	640.469i	−0.340368	−	0.958785i
$669$		0			0
$670$	694.379	+	255.862i	1.03639	+	0.381883i
$671$	−49.4498	−	8.71934i	−0.0736957	−	0.0129945i
$672$		0			0
$673$	48.9893	−	41.1069i	0.0727924	−	0.0610801i	−0.605666	−	0.795719i	$-0.707093\pi$
$673$	48.9893	−	41.1069i	0.0727924	−	0.0610801i	0.678458	+	0.734639i	$0.262649\pi$
$674$	573.497	−	677.979i	0.850886	−	1.00590i
$675$		0			0
$676$	35.0073	+	208.195i	0.0517860	+	0.307981i
$677$	453.503	−	380.534i	0.669872	−	0.562089i	−0.243156	−	0.969987i	$-0.578183\pi$
$677$	453.503	−	380.534i	0.669872	−	0.562089i	0.913028	+	0.407898i	$0.133738\pi$
$678$		0			0
$679$	238.516	+	42.0567i	0.351275	+	0.0619392i
$680$	1260.90	+	237.858i	1.85427	+	0.349791i
$681$		0			0
$682$	−107.240	−	62.4841i	−0.157243	−	0.0916189i
$683$	187.818	−	108.437i	0.274990	−	0.158766i	−0.356163	−	0.934424i	$-0.615915\pi$
$683$	187.818	−	108.437i	0.274990	−	0.158766i	0.631153	+	0.775658i	$0.282582\pi$
$684$		0			0
$685$	191.759	−	332.136i	0.279940	−	0.484870i
$686$	370.829	+	648.228i	0.540567	+	0.944938i
$687$		0			0
$688$	−473.423	+	1239.10i	−0.688115	+	1.80101i
$689$	363.181	+	304.745i	0.527112	+	0.442300i
$690$		0			0
$691$	444.760	−	1221.97i	0.643647	−	1.76841i	0.00369336	−	0.999993i	$-0.498824\pi$
$691$	444.760	−	1221.97i	0.643647	−	1.76841i	0.639954	−	0.768413i	$-0.278953\pi$
$692$	350.398	+	130.696i	0.506355	+	0.188867i
$693$		0			0
$694$	−194.441	+	1077.68i	−0.280175	+	1.55285i
$695$	1406.49	−	248.002i	2.02373	−	0.356838i
$696$		0			0
$697$	−1315.23	+	478.704i	−1.88699	+	0.686807i
$698$	−514.891	−	618.597i	−0.737666	−	0.886242i
$699$		0			0
$700$	−499.181	+	585.392i	−0.713116	+	0.836275i
$701$	−937.091			−1.33679			−0.668396	−	0.743806i	$-0.733019\pi$
$701$	−937.091			−1.33679			−0.668396	+	0.743806i	$0.733019\pi$
$702$		0			0
$703$			91.4543i			0.130092i
$704$	−137.418	+	351.269i	−0.195195	+	0.498962i
$705$		0			0
$706$	−146.014	−	175.423i	−0.206818	−	0.248474i
$707$	−214.816	−	590.201i	−0.303841	−	0.834797i
$708$		0			0
$709$	−223.970	−	1270.20i	−0.315896	−	1.79153i	−0.567152	−	0.823613i	$-0.691955\pi$
$709$	−223.970	−	1270.20i	−0.315896	−	1.79153i	0.251256	−	0.967921i	$-0.419156\pi$
$710$	−75.9572	+	420.989i	−0.106982	+	0.592942i
$711$		0			0
$712$	−1134.06	+	636.853i	−1.59278	+	0.894457i
$713$	206.309	+	75.0903i	0.289353	+	0.105316i
$714$		0			0
$715$	−312.393	+	372.295i	−0.436913	+	0.520692i
$716$	−520.582	−	306.098i	−0.727070	−	0.427512i
$717$		0			0
$718$	506.861	+	886.019i	0.705935	+	1.23401i
$719$	−843.005	−	486.709i	−1.17247	−	0.676925i	−0.218209	−	0.975902i	$-0.570021\pi$
$719$	−843.005	−	486.709i	−1.17247	−	0.676925i	−0.954260	+	0.298977i	$0.903355\pi$
$720$		0			0
$721$	2.81952	+	4.88354i	0.00391056	+	0.00677329i
$722$	−444.930	−	259.242i	−0.616246	−	0.359061i
$723$		0			0
$724$	−38.7574	−	68.3786i	−0.0535323	−	0.0944456i
$725$	229.216	−	1299.95i	0.316159	−	1.79303i
$726$		0			0
$727$	632.891	+	754.250i	0.870551	+	1.03748i	0.998952	+	0.0457605i	$0.0145711\pi$
$727$	632.891	+	754.250i	0.870551	+	1.03748i	−0.128401	+	0.991722i	$0.540984\pi$
$728$	−252.603	+	425.724i	−0.346983	+	0.584785i
$729$		0			0
$730$	−859.684	+	1016.30i	−1.17765	+	1.39220i
$731$	−1117.42	−	1331.69i	−1.52862	−	1.82173i
$732$		0			0
$733$	102.753	−	582.739i	0.140181	−	0.795006i	−0.830930	−	0.556377i	$-0.812191\pi$
$733$	102.753	−	582.739i	0.140181	−	0.795006i	0.971111	−	0.238629i	$-0.0766979\pi$
$734$	102.529	+	37.7794i	0.139685	+	0.0514705i
$735$		0			0
$736$	128.889	−	654.652i	0.175120	−	0.889473i
$737$	−142.546	−	246.897i	−0.193414	−	0.335002i
$738$		0			0
$739$	−722.804	−	417.311i	−0.978084	−	0.564697i	−0.0763932	−	0.997078i	$-0.524340\pi$
$739$	−722.804	−	417.311i	−0.978084	−	0.564697i	−0.901691	+	0.432380i	$0.857674\pi$
$740$	−20.4179	+	110.648i	−0.0275917	+	0.149524i
$741$		0			0
$742$	−85.6887	−	497.513i	−0.115483	−	0.670503i
$743$	−374.265	+	446.031i	−0.503721	+	0.600311i	−0.956652	−	0.291234i	$-0.905934\pi$
$743$	−374.265	+	446.031i	−0.503721	+	0.600311i	0.452931	+	0.891546i	$0.350378\pi$
$744$		0			0
$745$	279.433	+	101.705i	0.375077	+	0.136517i
$746$	−447.108	−	1243.77i	−0.599341	−	1.66725i
$747$		0			0
$748$	−314.730	−	381.191i	−0.420763	−	0.509613i
$749$	−128.753	−	730.193i	−0.171900	−	0.974891i
$750$		0			0
$751$	−383.766	−	1054.39i	−0.511006	−	1.40398i	−0.880190	−	0.474622i	$-0.842585\pi$
$751$	−383.766	−	1054.39i	−0.511006	−	1.40398i	0.369183	−	0.929357i	$-0.379638\pi$
$752$	−535.745	+	85.7127i	−0.712427	+	0.113980i
$753$		0			0
$754$	3.37396	−	849.347i	0.00447475	−	1.12646i
$755$			2171.74i			2.87648i
$756$		0			0
$757$	84.4056			0.111500			0.0557501	−	0.998445i	$-0.482245\pi$
$757$	84.4056			0.111500			0.0557501	+	0.998445i	$0.482245\pi$
$758$	588.019	+	2.33585i	0.775750	+	0.00308160i
$759$		0			0
$760$	−1154.03	−	992.023i	−1.51847	−	1.30529i
$761$	−1003.11	+	365.103i	−1.31815	+	0.479768i	−0.902865	−	0.429924i	$-0.858540\pi$
$761$	−1003.11	+	365.103i	−1.31815	+	0.479768i	−0.415285	+	0.909691i	$0.636318\pi$
$762$		0			0
$763$	−907.123	+	159.950i	−1.18889	+	0.209633i
$764$	639.952	+	775.089i	0.837634	+	1.01451i
$765$		0			0
$766$	982.902	−	353.332i	1.28316	−	0.461269i
$767$	101.095	−	277.756i	0.131806	−	0.362133i
$768$		0			0
$769$	121.602	+	102.037i	0.158131	+	0.132687i	0.718420	−	0.695610i	$-0.244866\pi$
$769$	121.602	+	102.037i	0.158131	+	0.132687i	−0.560289	+	0.828297i	$0.689310\pi$
$770$	509.999	−	87.8391i	0.662336	−	0.114077i
$771$		0			0
$772$	−10.6591	+	57.7633i	−0.0138071	+	0.0748229i
$773$	371.280	−	643.076i	0.480310	−	0.831922i	−0.519434	−	0.854510i	$-0.673857\pi$
$773$	371.280	−	643.076i	0.480310	−	0.831922i	0.999745	+	0.0225883i	$0.00719069\pi$
$774$		0			0
$775$	305.563	−	176.417i	0.394274	−	0.227634i
$776$	−119.227	+	315.811i	−0.153643	+	0.406973i
$777$		0			0
$778$	−74.5895	+	202.427i	−0.0958734	+	0.260190i
$779$	1634.76	+	288.252i	2.09853	+	0.370028i
$780$		0			0
$781$	126.247	−	105.934i	0.161649	−	0.135639i
$782$	667.612	+	564.727i	0.853723	+	0.722157i
$783$		0			0
$784$	−242.752	+	84.0112i	−0.309633	+	0.107157i
$785$	−856.753	+	718.901i	−1.09141	+	0.915798i
$786$		0			0
$787$	−754.529	−	133.044i	−0.958741	−	0.169052i	−0.327683	−	0.944788i	$-0.606268\pi$
$787$	−754.529	−	133.044i	−0.958741	−	0.169052i	−0.631058	+	0.775736i	$0.717379\pi$
$788$	413.068	+	728.764i	0.524197	+	0.924828i
$789$		0			0
$790$	−140.102	+	240.454i	−0.177345	+	0.304372i
$791$	−324.468	+	187.332i	−0.410200	+	0.236829i
$792$		0			0
$793$	45.9243	−	79.5432i	0.0579121	−	0.100307i
$794$	−685.649	+	392.236i	−0.863538	+	0.494000i
$795$		0			0
$796$	18.1698	+	10.6837i	0.0228264	+	0.0134218i
$797$	772.076	+	647.848i	0.968727	+	0.812859i	0.982351	−	0.187048i	$-0.0598921\pi$
$797$	772.076	+	647.848i	0.968727	+	0.812859i	−0.0136233	+	0.999907i	$0.504337\pi$
$798$		0			0
$799$	243.194	−	668.170i	0.304373	−	0.836258i
$800$	−672.796	−	834.938i	−0.840995	−	1.04367i
$801$		0			0
$802$	61.8586	+	11.1609i	0.0771304	+	0.0139163i
$803$	505.030	−	89.0504i	0.628929	−	0.110897i
$804$		0			0
$805$	−860.221	+	313.095i	−1.06860	+	0.388937i
$806$	174.494	−	145.240i	0.216494	−	0.180199i
$807$		0			0
$808$	863.856	−	141.728i	1.06913	−	0.175406i
$809$	−909.106			−1.12374			−0.561870	−	0.827226i	$-0.689918\pi$
$809$	−909.106			−1.12374			−0.561870	+	0.827226i	$0.689918\pi$
$810$		0			0
$811$			241.760i			0.298101i	0.988830	+	0.149051i	$0.0476217\pi$
$811$			241.760i			0.298101i	−0.988830	+	0.149051i	$0.952378\pi$
$812$	−586.840	+	688.190i	−0.722709	+	0.847524i
$813$		0			0
$814$	33.3159	−	27.7306i	0.0409286	−	0.0340671i
$815$	−144.220	−	396.243i	−0.176958	−	0.486187i
$816$		0			0
$817$	358.018	+	2030.42i	0.438210	+	2.48521i
$818$	−415.112	−	74.8970i	−0.507472	−	0.0915611i
$819$		0			0
$820$	1913.49	+	713.719i	2.33352	+	0.870388i
$821$	−381.889	−	138.996i	−0.465151	−	0.169301i	0.0988038	−	0.995107i	$-0.468498\pi$
$821$	−381.889	−	138.996i	−0.465151	−	0.169301i	−0.563954	+	0.825806i	$0.690721\pi$
$822$		0			0
$823$	−30.4525	+	36.2919i	−0.0370019	+	0.0440971i	−0.784228	−	0.620473i	$-0.786941\pi$
$823$	−30.4525	+	36.2919i	−0.0370019	+	0.0440971i	0.747226	+	0.664570i	$0.231385\pi$
$824$	−7.41709	+	2.59993i	−0.00900133	+	0.00315525i
$825$		0			0
$826$	−273.202	+	156.289i	−0.330753	+	0.189212i
$827$	310.818	+	179.451i	0.375839	+	0.216991i	0.676006	−	0.736896i	$-0.263709\pi$
$827$	310.818	+	179.451i	0.375839	+	0.216991i	−0.300168	+	0.953886i	$0.597043\pi$
$828$		0			0
$829$	95.4686	+	165.356i	0.115161	+	0.199465i	0.917844	−	0.396941i	$-0.129928\pi$
$829$	95.4686	+	165.356i	0.115161	+	0.199465i	−0.802683	+	0.596406i	$0.796595\pi$
$830$	−107.296	+	184.149i	−0.129272	+	0.221866i
$831$		0			0
$832$	−517.817	−	455.965i	−0.622377	−	0.548035i
$833$	58.4592	−	331.538i	0.0701791	−	0.398005i
$834$		0			0
$835$	−835.390	−	995.579i	−1.00047	−	1.19231i
$836$	97.2155	+	578.160i	0.116287	+	0.691579i
$837$		0			0
$838$	−62.6052	−	52.9572i	−0.0747079	−	0.0631948i
$839$	826.157	+	984.575i	0.984692	+	1.17351i	0.984832	+	0.173511i	$0.0555111\pi$
$839$	826.157	+	984.575i	0.984692	+	1.17351i	−0.000139714		1.00000i	$0.500044\pi$
$840$		0			0
$841$	123.429	−	699.998i	0.146764	−	0.832340i
$842$	132.948	−	360.805i	0.157895	−	0.428510i
$843$		0			0
$844$	120.446	+	339.287i	0.142709	+	0.401998i
$845$	201.858	+	349.628i	0.238885	+	0.413761i
$846$		0			0
$847$	428.807	+	247.572i	0.506266	+	0.292293i
$848$	703.546	+	11.1800i	0.829653	+	0.0131839i
$849$		0			0
$850$	1384.88	−	238.524i	1.62927	−	0.280616i
$851$	−49.2868	+	58.7377i	−0.0579163	+	0.0690219i
$852$		0			0
$853$	508.554	+	185.098i	0.596194	+	0.216997i	0.622452	−	0.782658i	$-0.286137\pi$
$853$	508.554	+	185.098i	0.596194	+	0.216997i	−0.0262574	+	0.999655i	$0.508359\pi$
$854$	−92.0379	+	33.0856i	−0.107773	+	0.0387419i
$855$		0			0
$856$	1033.36	+	12.3153i	1.20719	+	0.0143870i
$857$	−27.5580	−	156.289i	−0.0321563	−	0.182367i	0.964499	−	0.264086i	$-0.0850703\pi$
$857$	−27.5580	−	156.289i	−0.0321563	−	0.182367i	−0.996655	+	0.0817185i	$0.973959\pi$
$858$		0			0
$859$	360.358	+	990.074i	0.419508	+	1.15259i	0.951985	+	0.306145i	$0.0990392\pi$
$859$	360.358	+	990.074i	0.419508	+	1.15259i	−0.532477	+	0.846445i	$0.678739\pi$
$860$	−20.1521	+	2536.47i	−0.0234327	+	2.94939i
$861$		0			0
$862$	−854.172	−	3.39313i	−0.990919	−	0.00393634i
$863$		−	251.308i		−	0.291203i	−0.989343	−	0.145601i	$-0.953488\pi$
$863$		−	251.308i		−	0.291203i	0.989343	−	0.145601i	$-0.0465117\pi$
$864$		0			0
$865$	715.149			0.826762
$866$	−2.10845	+	530.772i	−0.00243470	+	0.612901i
$867$		0			0
$868$	−241.744	−	1.92064i	−0.278506	−	0.00221272i
$869$	100.746	−	36.6686i	0.115934	−	0.0421964i
$870$		0			0
$871$	513.565	−	90.5554i	0.589627	−	0.103967i
$872$	15.2993	−	1283.74i	0.0175451	−	1.47218i
$873$		0			0
$874$	−350.826	−	975.930i	−0.401402	−	1.11663i
$875$	−127.766	+	351.035i	−0.146018	+	0.401182i
$876$		0			0
$877$	−153.816	−	129.067i	−0.175389	−	0.147168i	0.550868	−	0.834593i	$-0.314297\pi$
$877$	−153.816	−	129.067i	−0.175389	−	0.147168i	−0.726256	+	0.687424i	$0.758741\pi$
$878$	−190.660	−	1106.98i	−0.217153	−	1.26080i
$879$		0			0
$880$	−11.4606	+	721.202i	−0.0130234	+	0.819548i
$881$	402.080	−	696.424i	0.456391	−	0.790492i	−0.542376	−	0.840136i	$-0.682475\pi$
$881$	402.080	−	696.424i	0.456391	−	0.790492i	0.998767	+	0.0496435i	$0.0158085\pi$
$882$		0			0
$883$	−1490.79	+	860.707i	−1.68832	+	0.974753i	−0.732518	+	0.680747i	$0.761655\pi$
$883$	−1490.79	+	860.707i	−1.68832	+	0.974753i	−0.955804	+	0.294006i	$0.905011\pi$
$884$	852.123	−	302.502i	0.963940	−	0.342197i
$885$		0			0
$886$	613.120	+	225.920i	0.692009	+	0.254988i
$887$	−1284.01	−	226.405i	−1.44759	−	0.255248i	−0.606040	−	0.795434i	$-0.707243\pi$
$887$	−1284.01	−	226.405i	−1.44759	−	0.255248i	−0.841546	+	0.540186i	$0.818354\pi$
$888$		0			0
$889$	−218.275	+	183.154i	−0.245529	+	0.206023i
$890$	−1606.29	+	1898.93i	−1.80482	+	2.13363i
$891$		0			0
$892$	935.692	−	157.333i	1.04898	−	0.176383i
$893$	−646.012	+	542.069i	−0.723418	+	0.607020i
$894$		0			0
$895$	−1137.29	−	200.535i	−1.27071	−	0.224061i
$896$	107.412	+	726.798i	0.119880	+	0.811158i
$897$		0			0
$898$	336.417	+	196.017i	0.374630	+	0.218281i
$899$	359.221	−	207.396i	0.399578	−	0.230696i
$900$		0			0
$901$	−461.075	+	798.606i	−0.511737	+	0.886355i
$902$	−390.680	−	682.928i	−0.433126	−	0.757127i
$903$		0			0
$904$	−172.742	−	492.800i	−0.191086	−	0.545132i
$905$	−115.138	−	96.6125i	−0.127225	−	0.106754i
$906$		0			0
$907$	−329.124	+	904.260i	−0.362871	+	0.996979i	0.615139	+	0.788419i	$0.289100\pi$
$907$	−329.124	+	904.260i	−0.362871	+	0.996979i	−0.978010	+	0.208560i	$0.933122\pi$
$908$	−377.184	+	1011.23i	−0.415401	+	1.11369i
$909$		0			0
$910$	−168.081	+	931.580i	−0.184705	+	1.02371i
$911$	145.176	−	25.5984i	0.159359	−	0.0280992i	−0.0933996	−	0.995629i	$-0.529773\pi$
$911$	145.176	−	25.5984i	0.159359	−	0.0280992i	0.252758	+	0.967529i	$0.418662\pi$
$912$		0			0
$913$	77.1554	−	28.0823i	0.0845076	−	0.0307582i
$914$	−396.524	−	476.389i	−0.433833	−	0.521213i
$915$		0			0
$916$	−527.757	−	450.034i	−0.576153	−	0.491303i
$917$	995.808			1.08594
$918$		0			0
$919$		−	1373.16i		−	1.49419i	−0.664720	−	0.747093i	$-0.731449\pi$
$919$		−	1373.16i		−	1.49419i	0.664720	−	0.747093i	$-0.268551\pi$
$920$	−206.569	−	1259.07i	−0.224532	−	1.36856i
$921$		0			0
$922$	514.438	+	618.053i	0.557959	+	0.670339i
$923$	103.105	+	283.279i	0.111706	+	0.306911i
$924$		0			0
$925$	21.3979	+	121.353i	0.0231328	+	0.131193i
$926$	−23.8437	+	132.153i	−0.0257492	+	0.142713i
$927$		0			0
$928$	−790.941	−	981.556i	−0.852307	−	1.05771i
$929$	1478.64	+	538.182i	1.59165	+	0.579313i	0.977695	−	0.210029i	$-0.0673557\pi$
$929$	1478.64	+	538.182i	1.59165	+	0.579313i	0.613954	+	0.789342i	$0.289578\pi$
$930$		0			0
$931$	−256.647	+	305.860i	−0.275668	+	0.328528i
$932$	−346.195	+	588.774i	−0.371454	+	0.631732i
$933$		0			0
$934$	355.193	+	620.895i	0.380292	+	0.664770i
$935$	−818.648	−	472.647i	−0.875559	−	0.505504i
$936$		0			0
$937$	−829.427	−	1436.61i	−0.885195	−	1.53320i	−0.845491	−	0.533990i	$-0.820692\pi$
$937$	−829.427	−	1436.61i	−0.885195	−	1.53320i	−0.0397040	−	0.999211i	$-0.512641\pi$
$938$	−479.798	−	279.558i	−0.511511	−	0.298037i
$939$		0			0
$940$	−902.612	+	511.605i	−0.960225	+	0.544261i
$941$	48.3337	−	274.114i	0.0513642	−	0.291301i	−0.948295	−	0.317389i	$-0.897194\pi$
$941$	48.3337	−	274.114i	0.0513642	−	0.291301i	0.999660	+	0.0260881i	$0.00830503\pi$
$942$		0			0
$943$	894.597	+	1066.14i	0.948671	+	1.13058i
$944$	−143.471	−	414.564i	−0.151982	−	0.439157i
$945$		0			0
$946$	631.104	−	746.081i	0.667129	−	0.788670i
$947$	−84.4477	−	100.641i	−0.0891739	−	0.106273i	0.719612	−	0.694376i	$-0.244320\pi$
$947$	−84.4477	−	100.641i	−0.0891739	−	0.106273i	−0.808786	+	0.588103i	$0.799875\pi$
$948$		0			0
$949$	−162.890	+	923.797i	−0.171644	+	0.973442i
$950$	−1563.87	−	576.248i	−1.64618	−	0.606577i
$951$		0			0
$952$	−900.797	−	340.074i	−0.946216	−	0.357221i
$953$	−107.243	−	185.750i	−0.112532	−	0.194911i	0.804258	−	0.594280i	$-0.202563\pi$
$953$	−107.243	−	185.750i	−0.112532	−	0.194911i	−0.916791	+	0.399368i	$0.869229\pi$
$954$		0			0
$955$	1664.58	+	961.048i	1.74302	+	1.00633i
$956$	−503.795	−	92.9655i	−0.526982	−	0.0972442i
$957$		0			0
$958$	−2.43485	−	14.1369i	−0.00254160	−	0.0147567i
$959$	−184.986	+	220.458i	−0.192895	+	0.229883i
$960$		0			0
$961$	−798.858	−	290.761i	−0.831278	−	0.302560i
$962$	26.8224	+	74.6148i	0.0278819	+	0.0775622i
$963$		0			0
$964$	509.620	−	420.768i	0.528652	−	0.436482i
$965$	19.5049	+	110.618i	0.0202123	+	0.114630i
$966$		0			0
$967$	−551.943	−	1516.45i	−0.570779	−	1.56820i	−0.803277	−	0.595605i	$-0.796912\pi$
$967$	−551.943	−	1516.45i	−0.570779	−	1.56820i	0.232499	−	0.972597i	$-0.425310\pi$
$968$	−449.871	+	523.340i	−0.464742	+	0.540641i
$969$		0			0
$970$	−2.56425	+	645.515i	−0.00264356	+	0.665479i
$971$		−	981.080i		−	1.01038i	−0.863008	−	0.505190i	$-0.831422\pi$
$971$		−	981.080i		−	1.01038i	0.863008	−	0.505190i	$-0.168578\pi$
$972$		0			0
$973$	−1071.69			−1.10143
$974$	864.637	+	3.43470i	0.887718	+	0.00352638i
$975$		0			0
$976$	−21.5353	−	134.606i	−0.0220648	−	0.137916i
$977$	−109.248	+	39.7629i	−0.111820	+	0.0406990i	−0.397324	−	0.917678i	$-0.630061\pi$
$977$	−109.248	+	39.7629i	−0.111820	+	0.0406990i	0.285504	+	0.958377i	$0.407839\pi$
$978$		0			0
$979$	943.631	−	166.388i	0.963872	−	0.169957i
$980$	−378.794	+	312.752i	−0.386525	+	0.319134i
$981$		0			0
$982$	336.406	−	120.931i	0.342573	−	0.123147i
$983$	−318.542	+	875.187i	−0.324051	+	0.890322i	0.665534	+	0.746368i	$0.268204\pi$
$983$	−318.542	+	875.187i	−0.324051	+	0.890322i	−0.989584	+	0.143954i	$0.954018\pi$
$984$		0			0
$985$	1227.12	+	1029.67i	1.24581	+	1.04536i
$986$	1628.07	−	280.410i	1.65119	−	0.284391i
$987$		0			0
$988$	−1054.61	−	194.607i	−1.06742	−	0.196971i
$989$	−864.296	+	1497.00i	−0.873909	+	1.51365i
$990$		0			0
$991$	509.689	−	294.269i	0.514318	−	0.296941i	−0.220289	−	0.975435i	$-0.570700\pi$
$991$	509.689	−	294.269i	0.514318	−	0.296941i	0.734607	+	0.678493i	$0.237367\pi$
$992$	65.0893	−	330.602i	0.0656142	−	0.333268i
$993$		0			0
$994$	110.988	−	301.208i	0.111658	−	0.303026i
$995$	39.6946	+	6.99924i	0.0398941	+	0.00703441i
$996$		0			0
$997$	−89.4084	+	75.0226i	−0.0896774	+	0.0752483i	−0.686524	−	0.727107i	$-0.740864\pi$
$997$	−89.4084	+	75.0226i	−0.0896774	+	0.0752483i	0.596847	+	0.802355i	$0.296420\pi$
$998$	982.937	+	831.458i	0.984906	+	0.833124i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.j.a.199.17		204
3.2	odd	2		108.3.j.a.103.18	yes	204
4.3	odd	2	inner	324.3.j.a.199.33		204
12.11	even	2		108.3.j.a.103.2	yes	204
27.11	odd	18		108.3.j.a.43.2	✓	204
27.16	even	9	inner	324.3.j.a.127.33		204
108.11	even	18		108.3.j.a.43.18	yes	204
108.43	odd	18	inner	324.3.j.a.127.17		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.j.a.43.2	✓	204	27.11	odd	18
108.3.j.a.43.18	yes	204	108.11	even	18
108.3.j.a.103.2	yes	204	12.11	even	2
108.3.j.a.103.18	yes	204	3.2	odd	2
324.3.j.a.127.17		204	108.43	odd	18	inner
324.3.j.a.127.33		204	27.16	even	9	inner
324.3.j.a.199.17		204	1.1	even	1	trivial
324.3.j.a.199.33		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)

\(f(q)\)	\(=\)	\(q+(0.00794476 - 1.99998i) q^{2} +(-3.99987 - 0.0317788i) q^{4} +(-7.18780 + 2.61614i) q^{5} +(5.65258 - 0.996703i) q^{7} +(-0.0953352 + 7.99943i) q^{8} +O(q^{10})\)	\(q+(0.00794476 - 1.99998i) q^{2} +(-3.99987 - 0.0317788i) q^{4} +(-7.18780 + 2.61614i) q^{5} +(5.65258 - 0.996703i) q^{7} +(-0.0953352 + 7.99943i) q^{8} +(5.17514 + 14.3963i) q^{10} +(2.01574 - 5.53819i) q^{11} +(8.25839 + 6.92961i) q^{13} +(-1.94848 - 11.3130i) q^{14} +(15.9980 + 0.254222i) q^{16} +(-10.4844 + 18.1596i) q^{17} +(21.5373 - 12.4346i) q^{19} +(28.8334 - 10.2358i) q^{20} +(-11.0603 - 4.07544i) q^{22} +(20.5338 + 3.62067i) q^{23} +(25.6691 - 21.5389i) q^{25} +(13.9247 - 16.4616i) q^{26} +(-22.6413 + 3.80705i) q^{28} +(30.1767 - 25.3212i) q^{29} +(10.3697 + 1.82845i) q^{31} +(0.635541 - 31.9937i) q^{32} +(36.2355 + 21.1130i) q^{34} +(-38.0221 + 21.9521i) q^{35} +(-1.83871 + 3.18474i) q^{37} +(-24.6978 - 43.1730i) q^{38} +(-20.2424 - 57.7477i) q^{40} +(51.1323 + 42.9051i) q^{41} +(-28.3547 + 77.9040i) q^{43} +(-8.23869 + 22.0880i) q^{44} +(7.40442 - 41.0386i) q^{46} +(-33.3947 + 5.88839i) q^{47} +(-15.0867 + 5.49110i) q^{49} +(-42.8736 - 51.5089i) q^{50} +(-32.8123 - 27.9800i) q^{52} +43.9772 q^{53} +45.0808i q^{55} +(7.43417 + 45.3125i) q^{56} +(-50.4023 - 60.5540i) q^{58} +(-9.37752 - 25.7645i) q^{59} +(-1.47945 - 8.39040i) q^{61} +(3.73926 - 20.7246i) q^{62} +(-63.9818 - 1.52525i) q^{64} +(-77.4885 - 28.2035i) q^{65} +(31.0935 - 37.0558i) q^{67} +(42.5135 - 72.3028i) q^{68} +(43.6017 + 76.2180i) q^{70} +(24.2168 + 13.9816i) q^{71} +(43.5064 + 75.3554i) q^{73} +(6.35483 + 3.70270i) q^{74} +(-86.5416 + 49.0522i) q^{76} +(5.87418 - 33.3142i) q^{77} +(11.6931 + 13.9353i) q^{79} +(-115.655 + 40.0257i) q^{80} +(86.2157 - 101.923i) q^{82} +(8.95501 + 10.6722i) q^{83} +(27.8519 - 157.956i) q^{85} +(155.581 + 57.3279i) q^{86} +(44.1102 + 16.6527i) q^{88} +(81.2903 + 140.799i) q^{89} +(53.5880 + 30.9390i) q^{91} +(-82.0177 - 15.1348i) q^{92} +(11.5114 + 66.8357i) q^{94} +(-122.275 + 145.722i) q^{95} +(39.6511 + 14.4318i) q^{97} +(10.8623 + 30.2167i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) \) 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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