LMFDB - Embedded newform 189.4.e.h.109.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,4,Mod(109,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("189.109");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	189.e (of order $3$, degree $2$, 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:	$11.1513609911$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 54 x^{14} - 12 x^{13} + 2361 x^{12} - 966 x^{11} + 29570 x^{10} - 65952 x^{9} + 300096 x^{8} + \cdots + 81 $ x^16 + 54x^14 - 12x^13 + 2361x^12 - 966x^11 + 29570x^10 - 65952x^9 + 300096x^8 - 356610x^7 + 531858x^6 + 80070x^5 + 77197x^4 - 216x^3 + 4878x^2 + 486x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{9}\cdot 7^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			109.3
Root			$-0.0640761 + 0.110983i$ of defining polynomial
Character	$\chi$	$=$	189.109
Dual form			189.4.e.h.163.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.64637 - 2.85159i) q^{2} +(-1.42105 + 2.46133i) q^{4} +(-10.8582 - 18.8070i) q^{5} +(1.08769 - 18.4883i) q^{7} -16.9836 q^{8} +O(q^{10})$	\(q+(-1.64637 - 2.85159i) q^{2} +(-1.42105 + 2.46133i) q^{4} +(-10.8582 - 18.8070i) q^{5} +(1.08769 - 18.4883i) q^{7} -16.9836 q^{8} +(-35.7533 + 61.9265i) q^{10} +(20.9820 - 36.3419i) q^{11} +46.0329 q^{13} +(-54.5118 + 27.3369i) q^{14} +(39.3296 + 68.1209i) q^{16} +(-1.00882 + 1.74732i) q^{17} +(-36.6244 - 63.4352i) q^{19} +61.7204 q^{20} -138.176 q^{22} +(12.0838 + 20.9298i) q^{23} +(-173.303 + 300.169i) q^{25} +(-75.7871 - 131.267i) q^{26} +(43.9602 + 28.9500i) q^{28} +90.7240 q^{29} +(-26.6026 + 46.0771i) q^{31} +(61.5677 - 106.638i) q^{32} +6.64353 q^{34} +(-359.520 + 180.294i) q^{35} +(-33.9309 - 58.7701i) q^{37} +(-120.594 + 208.875i) q^{38} +(184.412 + 319.411i) q^{40} +341.211 q^{41} +509.713 q^{43} +(59.6330 + 103.287i) q^{44} +(39.7889 - 68.9164i) q^{46} +(-19.2351 - 33.3162i) q^{47} +(-340.634 - 40.2191i) q^{49} +1141.28 q^{50} +(-65.4151 + 113.302i) q^{52} +(-194.694 + 337.220i) q^{53} -911.311 q^{55} +(-18.4729 + 313.998i) q^{56} +(-149.365 - 258.708i) q^{58} +(-225.310 + 390.249i) q^{59} +(-112.951 - 195.638i) q^{61} +175.191 q^{62} +223.822 q^{64} +(-499.836 - 865.742i) q^{65} +(386.006 - 668.582i) q^{67} +(-2.86716 - 4.96606i) q^{68} +(1106.03 + 728.374i) q^{70} -962.655 q^{71} +(526.897 - 912.612i) q^{73} +(-111.726 + 193.514i) q^{74} +208.180 q^{76} +(-649.078 - 427.450i) q^{77} +(-16.7953 - 29.0904i) q^{79} +(854.101 - 1479.35i) q^{80} +(-561.759 - 972.995i) q^{82} +446.386 q^{83} +43.8159 q^{85} +(-839.175 - 1453.49i) q^{86} +(-356.350 + 617.216i) q^{88} +(-244.899 - 424.178i) q^{89} +(50.0695 - 851.070i) q^{91} -68.6870 q^{92} +(-63.3361 + 109.701i) q^{94} +(-795.352 + 1377.59i) q^{95} +460.958 q^{97} +(446.120 + 1037.56i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 48 q^{4} - 60 q^{7}+O(q^{10}) $ 16 * q - 48 * q^4 - 60 * q^7	$ 16 q - 48 q^{4} - 60 q^{7} - 44 q^{10} - 168 q^{13} - 156 q^{16} - 12 q^{19} + 448 q^{22} - 408 q^{25} - 152 q^{28} - 800 q^{31} - 1896 q^{34} - 692 q^{37} - 96 q^{40} + 2912 q^{43} - 1524 q^{46} + 2020 q^{49} - 1972 q^{52} - 2560 q^{55} - 2372 q^{58} - 216 q^{61} + 9928 q^{64} - 684 q^{67} + 4316 q^{70} + 4564 q^{73} - 760 q^{76} - 556 q^{79} - 3340 q^{82} + 2592 q^{85} - 6696 q^{88} - 184 q^{91} + 492 q^{94} + 1168 q^{97}+O(q^{100}) $ 16 * q - 48 * q^4 - 60 * q^7 - 44 * q^10 - 168 * q^13 - 156 * q^16 - 12 * q^19 + 448 * q^22 - 408 * q^25 - 152 * q^28 - 800 * q^31 - 1896 * q^34 - 692 * q^37 - 96 * q^40 + 2912 * q^43 - 1524 * q^46 + 2020 * q^49 - 1972 * q^52 - 2560 * q^55 - 2372 * q^58 - 216 * q^61 + 9928 * q^64 - 684 * q^67 + 4316 * q^70 + 4564 * q^73 - 760 * q^76 - 556 * q^79 - 3340 * q^82 + 2592 * q^85 - 6696 * q^88 - 184 * q^91 + 492 * q^94 + 1168 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.64637	−	2.85159i	−0.582079	−	1.00819i	−0.995233	−	0.0975288i	$-0.968906\pi$
$2$	−1.64637	−	2.85159i	−0.582079	−	1.00819i	0.413154	−	0.910661i	$-0.364427\pi$
$3$		0			0
$3$		0			0
$4$	−1.42105	+	2.46133i	−0.177631	+	0.307667i
$5$	−10.8582	−	18.8070i	−0.971190	−	1.68215i	−0.691973	−	0.721923i	$-0.743258\pi$
$5$	−10.8582	−	18.8070i	−0.971190	−	1.68215i	−0.279217	−	0.960228i	$-0.590075\pi$
$6$		0			0
$7$	1.08769	−	18.4883i	0.0587298	−	0.998274i
$7$	1.08769	−	18.4883i	0.0587298	−	0.998274i
$8$	−16.9836			−0.750576
$9$		0			0
$10$	−35.7533	+	61.9265i	−1.13062	+	1.95829i
$11$	20.9820	−	36.3419i	0.575119	−	0.996136i	−0.420909	−	0.907103i	$-0.638289\pi$
$11$	20.9820	−	36.3419i	0.575119	−	0.996136i	0.996029	−	0.0890334i	$-0.0283778\pi$
$12$		0			0
$13$	46.0329			0.982095			0.491047	−	0.871133i	$-0.336614\pi$
$13$	46.0329			0.982095			0.491047	+	0.871133i	$0.336614\pi$
$14$	−54.5118	+	27.3369i	−1.04064	+	0.521863i
$15$		0			0
$16$	39.3296	+	68.1209i	0.614526	+	1.06439i
$17$	−1.00882	+	1.74732i	−0.0143926	+	0.0249287i	−0.873132	−	0.487484i	$-0.837915\pi$
$17$	−1.00882	+	1.74732i	−0.0143926	+	0.0249287i	0.858739	+	0.512413i	$0.171248\pi$
$18$		0			0
$19$	−36.6244	−	63.4352i	−0.442221	−	0.765950i	0.555633	−	0.831428i	$-0.312476\pi$
$19$	−36.6244	−	63.4352i	−0.442221	−	0.765950i	−0.997854	+	0.0654782i	$0.979143\pi$
$20$	61.7204			0.690055
$21$		0			0
$22$	−138.176			−1.33906
$23$	12.0838	+	20.9298i	0.109550	+	0.189747i	0.915588	−	0.402117i	$-0.131726\pi$
$23$	12.0838	+	20.9298i	0.109550	+	0.189747i	−0.806038	+	0.591864i	$0.798392\pi$
$24$		0			0
$25$	−173.303	+	300.169i	−1.38642	+	2.40135i
$26$	−75.7871	−	131.267i	−0.571656	−	0.990138i
$27$		0			0
$28$	43.9602	+	28.9500i	0.296703	+	0.195394i
$29$	90.7240			0.580932			0.290466	−	0.956885i	$-0.406190\pi$
$29$	90.7240			0.580932			0.290466	+	0.956885i	$0.406190\pi$
$30$		0			0
$31$	−26.6026	+	46.0771i	−0.154128	+	0.266958i	−0.932741	−	0.360547i	$-0.882590\pi$
$31$	−26.6026	+	46.0771i	−0.154128	+	0.266958i	0.778613	+	0.627504i	$0.215923\pi$
$32$	61.5677	−	106.638i	0.340117	−	0.589099i
$33$		0			0
$34$	6.64353			0.0335105
$35$	−359.520	+	180.294i	−1.73629	+	0.870722i
$36$		0			0
$37$	−33.9309	−	58.7701i	−0.150762	−	0.261128i	0.780745	−	0.624849i	$-0.214840\pi$
$37$	−33.9309	−	58.7701i	−0.150762	−	0.261128i	−0.931508	+	0.363721i	$0.881506\pi$
$38$	−120.594	+	208.875i	−0.514815	+	0.891686i
$39$		0			0
$40$	184.412	+	319.411i	0.728952	+	1.26258i
$41$	341.211			1.29971			0.649856	−	0.760057i	$-0.274829\pi$
$41$	341.211			1.29971			0.649856	+	0.760057i	$0.274829\pi$
$42$		0			0
$43$	509.713			1.80769			0.903843	−	0.427863i	$-0.140734\pi$
$43$	509.713			1.80769			0.903843	+	0.427863i	$0.140734\pi$
$44$	59.6330	+	103.287i	0.204318	+	0.353890i
$45$		0			0
$46$	39.7889	−	68.9164i	0.127534	−	0.220895i
$47$	−19.2351	−	33.3162i	−0.0596963	−	0.103397i	0.834633	−	0.550807i	$-0.185680\pi$
$47$	−19.2351	−	33.3162i	−0.0596963	−	0.103397i	−0.894329	+	0.447410i	$0.852347\pi$
$48$		0			0
$49$	−340.634	−	40.2191i	−0.993102	−	0.117257i
$50$	1141.28			3.22803
$51$		0			0
$52$	−65.4151	+	113.302i	−0.174451	+	0.302158i
$53$	−194.694	+	337.220i	−0.504590	+	0.873976i	0.495396	+	0.868668i	$0.335023\pi$
$53$	−194.694	+	337.220i	−0.504590	+	0.873976i	−0.999986	+	0.00530861i	$0.998310\pi$
$54$		0			0
$55$	−911.311			−2.23420
$56$	−18.4729	+	313.998i	−0.0440811	+	0.749280i
$57$		0			0
$58$	−149.365	−	258.708i	−0.338148	−	0.585690i
$59$	−225.310	+	390.249i	−0.497168	+	0.861120i	−0.999995	−	0.00326692i	$-0.998960\pi$
$59$	−225.310	+	390.249i	−0.497168	+	0.861120i	0.502827	+	0.864387i	$0.332293\pi$
$60$		0			0
$61$	−112.951	−	195.638i	−0.237081	−	0.410636i	0.722794	−	0.691063i	$-0.242857\pi$
$61$	−112.951	−	195.638i	−0.237081	−	0.410636i	−0.959875	+	0.280427i	$0.909524\pi$
$62$	175.191			0.358859
$63$		0			0
$64$	223.822			0.437152
$65$	−499.836	−	865.742i	−0.953801	−	1.65203i
$66$		0			0
$67$	386.006	−	668.582i	0.703853	−	1.21911i	−0.263251	−	0.964727i	$-0.584795\pi$
$67$	386.006	−	668.582i	0.703853	−	1.21911i	0.967104	−	0.254382i	$-0.0818719\pi$
$68$	−2.86716	−	4.96606i	−0.00511315	−	0.00885623i
$69$		0			0
$70$	1106.03	+	728.374i	1.88851	+	1.24368i
$71$	−962.655			−1.60910			−0.804550	−	0.593885i	$-0.797593\pi$
$71$	−962.655			−1.60910			−0.804550	+	0.593885i	$0.797593\pi$
$72$		0			0
$73$	526.897	−	912.612i	0.844775	−	1.46319i	−0.0410408	−	0.999157i	$-0.513067\pi$
$73$	526.897	−	912.612i	0.844775	−	1.46319i	0.885816	−	0.464036i	$-0.153599\pi$
$74$	−111.726	+	193.514i	−0.175511	+	0.303994i
$75$		0			0
$76$	208.180			0.314209
$77$	−649.078	−	427.450i	−0.960640	−	0.632630i
$78$		0			0
$79$	−16.7953	−	29.0904i	−0.0239193	−	0.0414294i	0.853818	−	0.520572i	$-0.174281\pi$
$79$	−16.7953	−	29.0904i	−0.0239193	−	0.0414294i	−0.877737	+	0.479142i	$0.840948\pi$
$80$	854.101	−	1479.35i	1.19364	−	2.06745i
$81$		0			0
$82$	−561.759	−	972.995i	−0.756535	−	1.31036i
$83$	446.386			0.590328			0.295164	−	0.955447i	$-0.404626\pi$
$83$	446.386			0.590328			0.295164	+	0.955447i	$0.404626\pi$
$84$		0			0
$85$	43.8159			0.0559117
$86$	−839.175	−	1453.49i	−1.05222	−	1.82249i
$87$		0			0
$88$	−356.350	+	617.216i	−0.431671	+	0.747676i
$89$	−244.899	−	424.178i	−0.291677	−	0.505199i	0.682529	−	0.730858i	$-0.260880\pi$
$89$	−244.899	−	424.178i	−0.291677	−	0.505199i	−0.974206	+	0.225659i	$0.927547\pi$
$90$		0			0
$91$	50.0695	−	851.070i	0.0576782	−	0.980399i
$92$	−68.6870			−0.0778382
$93$		0			0
$94$	−63.3361	+	109.701i	−0.0694959	+	0.120370i
$95$	−795.352	+	1377.59i	−0.858962	+	1.48777i
$96$		0			0
$97$	460.958			0.482507			0.241253	−	0.970462i	$-0.422441\pi$
$97$	460.958			0.482507			0.241253	+	0.970462i	$0.422441\pi$
$98$	446.120	+	1037.56i	0.459846	+	1.06949i
$99$		0			0
$100$	−492.544	−	853.111i	−0.492544	−	0.853111i
$101$	771.372	−	1336.06i	0.759945	−	1.31626i	−0.182934	−	0.983125i	$-0.558559\pi$
$101$	771.372	−	1336.06i	0.759945	−	1.31626i	0.942878	−	0.333137i	$-0.108107\pi$
$102$		0			0
$103$	−571.318	−	989.552i	−0.546540	−	0.946635i	−0.998508	−	0.0546011i	$-0.982611\pi$
$103$	−571.318	−	989.552i	−0.546540	−	0.946635i	0.451968	−	0.892034i	$-0.350722\pi$
$104$	−781.804			−0.737136
$105$		0			0
$106$	1282.15			1.17485
$107$	401.280	+	695.038i	0.362554	+	0.627961i	0.988380	−	0.152001i	$-0.0485717\pi$
$107$	401.280	+	695.038i	0.362554	+	0.627961i	−0.625827	+	0.779962i	$0.715238\pi$
$108$		0			0
$109$	−749.480	+	1298.14i	−0.658598	+	1.14073i	0.322380	+	0.946610i	$0.395517\pi$
$109$	−749.480	+	1298.14i	−0.658598	+	1.14073i	−0.980979	+	0.194115i	$0.937816\pi$
$110$	1500.35	+	2598.69i	1.30048	+	2.25250i
$111$		0			0
$112$	1302.22	−	653.043i	1.09864	−	0.550954i
$113$	−651.941			−0.542738			−0.271369	−	0.962475i	$-0.587476\pi$
$113$	−651.941			−0.542738			−0.271369	+	0.962475i	$0.587476\pi$
$114$		0			0
$115$	262.418	−	454.522i	0.212788	−	0.368560i
$116$	−128.923	+	223.302i	−0.103192	+	0.178733i
$117$		0			0
$118$	1483.77			1.15756
$119$	31.2077	+	20.5518i	0.0240404	+	0.0158318i
$120$		0			0
$121$	−214.990	−	372.373i	−0.161525	−	0.279769i
$122$	−371.919	+	644.182i	−0.276000	+	0.478045i
$123$		0			0
$124$	−75.6073	−	130.956i	−0.0547559	−	0.0948401i
$125$	4812.49			3.44354
$126$		0			0
$127$	−634.311			−0.443197			−0.221598	−	0.975138i	$-0.571127\pi$
$127$	−634.311			−0.443197			−0.221598	+	0.975138i	$0.571127\pi$
$128$	−861.035	−	1491.36i	−0.594574	−	1.02983i
$129$		0			0
$130$	−1645.83	+	2850.66i	−1.11037	+	1.92322i
$131$	1145.08	+	1983.33i	0.763709	+	1.32278i	0.940926	+	0.338611i	$0.109957\pi$
$131$	1145.08	+	1983.33i	0.763709	+	1.32278i	−0.177217	+	0.984172i	$0.556709\pi$
$132$		0			0
$133$	−1212.65	+	608.124i	−0.790599	+	0.396474i
$134$	−2542.03			−1.63879
$135$		0			0
$136$	17.1333	−	29.6758i	0.0108027	−	0.0187109i
$137$	−365.175	+	632.501i	−0.227730	+	0.394440i	−0.957135	−	0.289642i	$-0.906464\pi$
$137$	−365.175	+	632.501i	−0.227730	+	0.394440i	0.729405	+	0.684082i	$0.239797\pi$
$138$		0			0
$139$	−1195.39			−0.729436			−0.364718	−	0.931118i	$-0.618835\pi$
$139$	−1195.39			−0.729436			−0.364718	+	0.931118i	$0.618835\pi$
$140$	67.1327	−	1141.11i	0.0405268	−	0.688864i
$141$		0			0
$142$	1584.88	+	2745.10i	0.936623	+	1.62228i
$143$	965.863	−	1672.92i	0.564822	−	0.978300i
$144$		0			0
$145$	−985.103	−	1706.25i	−0.564195	−	0.977215i
$146$	−3469.86			−1.96690
$147$		0			0
$148$	192.870			0.107121
$149$	−634.691	−	1099.32i	−0.348966	−	0.604427i	0.637100	−	0.770781i	$-0.280134\pi$
$149$	−634.691	−	1099.32i	−0.348966	−	0.604427i	−0.986066	+	0.166354i	$0.946800\pi$
$150$		0			0
$151$	−219.486	+	380.160i	−0.118288	+	0.204881i	−0.919089	−	0.394049i	$-0.871074\pi$
$151$	−219.486	+	380.160i	−0.118288	+	0.204881i	0.800801	+	0.598930i	$0.204407\pi$
$152$	622.013	+	1077.36i	0.331921	+	0.574903i
$153$		0			0
$154$	−150.293	+	2554.65i	−0.0786426	+	1.33675i
$155$	1155.43			0.598751
$156$		0			0
$157$	893.137	−	1546.96i	0.454013	−	0.786374i	−0.544618	−	0.838685i	$-0.683325\pi$
$157$	893.137	−	1546.96i	0.454013	−	0.786374i	0.998631	+	0.0523103i	$0.0166585\pi$
$158$	−55.3026	+	95.7870i	−0.0278458	+	0.0482304i
$159$		0			0
$160$	−2674.07			−1.32127
$161$	400.100	−	200.644i	0.195853	−	0.0982174i
$162$		0			0
$163$	423.616	+	733.724i	0.203559	+	0.352575i	0.949673	−	0.313244i	$-0.101416\pi$
$163$	423.616	+	733.724i	0.203559	+	0.352575i	−0.746114	+	0.665819i	$0.768082\pi$
$164$	−484.878	+	839.834i	−0.230870	+	0.399878i
$165$		0			0
$166$	−734.915	−	1272.91i	−0.343617	−	0.595163i
$167$	1454.66			0.674040			0.337020	−	0.941498i	$-0.390581\pi$
$167$	1454.66			0.674040			0.337020	+	0.941498i	$0.390581\pi$
$168$		0			0
$169$	−77.9721			−0.0354903
$170$	−72.1370	−	124.945i	−0.0325450	−	0.0563696i
$171$		0			0
$172$	−724.328	+	1254.57i	−0.321102	+	0.556165i
$173$	−424.755	−	735.698i	−0.186668	−	0.323318i	0.757469	−	0.652871i	$-0.226436\pi$
$173$	−424.755	−	735.698i	−0.186668	−	0.323318i	−0.944137	+	0.329552i	$0.893102\pi$
$174$		0			0
$175$	5361.11	+	3530.56i	2.31578	+	1.52506i
$176$	3300.86			1.41370
$177$		0			0
$178$	−806.388	+	1396.70i	−0.339558	+	0.588132i
$179$	−660.009	+	1143.17i	−0.275595	+	0.477344i	−0.970285	−	0.241965i	$-0.922208\pi$
$179$	−660.009	+	1143.17i	−0.275595	+	0.477344i	0.694690	+	0.719309i	$0.255541\pi$
$180$		0			0
$181$	−4005.73			−1.64499			−0.822495	−	0.568772i	$-0.807419\pi$
$181$	−4005.73			−1.64499			−0.822495	+	0.568772i	$0.807419\pi$
$182$	−2509.34	+	1258.40i	−1.02200	+	0.512519i
$183$		0			0
$184$	−205.227	−	355.464i	−0.0822257	−	0.142419i
$185$	−736.861	+	1276.28i	−0.292838	+	0.507211i
$186$		0			0
$187$	42.3340	+	73.3246i	0.0165549	+	0.0286739i
$188$	109.336			0.0424157
$189$		0			0
$190$	5237.77			1.99993
$191$	855.755	+	1482.21i	0.324190	+	0.561514i	0.981348	−	0.192239i	$-0.0615750\pi$
$191$	855.755	+	1482.21i	0.324190	+	0.561514i	−0.657158	+	0.753753i	$0.728242\pi$
$192$		0			0
$193$	−2191.97	+	3796.61i	−0.817521	+	1.41599i	0.0899819	+	0.995943i	$0.471319\pi$
$193$	−2191.97	+	3796.61i	−0.817521	+	1.41599i	−0.907503	+	0.420045i	$0.862014\pi$
$194$	−758.906	−	1314.46i	−0.280857	−	0.486459i
$195$		0			0
$196$	583.050	−	781.260i	0.212482	−	0.284716i
$197$	−1269.36			−0.459076			−0.229538	−	0.973300i	$-0.573721\pi$
$197$	−1269.36			−0.459076			−0.229538	+	0.973300i	$0.573721\pi$
$198$		0			0
$199$	−293.283	+	507.981i	−0.104474	+	0.180954i	−0.913523	−	0.406787i	$-0.866649\pi$
$199$	−293.283	+	507.981i	−0.104474	+	0.180954i	0.809049	+	0.587741i	$0.199983\pi$
$200$	2943.30	−	5097.95i	1.04061	−	1.80240i
$201$		0			0
$202$	−5079.85			−1.76939
$203$	98.6796	−	1677.33i	0.0341180	−	0.579929i
$204$		0			0
$205$	−3704.95	−	6417.16i	−1.26227	−	2.18631i
$206$	−1881.20	+	3258.33i	−0.636259	+	1.10203i
$207$		0			0
$208$	1810.46	+	3135.80i	0.603522	+	1.04533i
$209$	−3073.81			−1.01732
$210$		0			0
$211$	1037.46			0.338491			0.169246	−	0.985574i	$-0.445867\pi$
$211$	1037.46			0.338491			0.169246	+	0.985574i	$0.445867\pi$
$212$	−553.340	−	958.414i	−0.179262	−	0.310491i
$213$		0			0
$214$	1321.31	−	2288.58i	0.422069	−	0.731046i
$215$	−5534.59	−	9586.19i	−1.75561	−	3.04080i
$216$		0			0
$217$	822.951	+	541.954i	0.257445	+	0.169540i
$218$	4935.68			1.53342
$219$		0			0
$220$	1295.02	−	2243.04i	0.396864	−	0.687389i
$221$	−46.4387	+	80.4342i	−0.0141349	+	0.0244823i
$222$		0			0
$223$	5421.68			1.62808			0.814041	−	0.580807i	$-0.197263\pi$
$223$	5421.68			1.62808			0.814041	+	0.580807i	$0.197263\pi$
$224$	−1904.59	−	1254.27i	−0.568107	−	0.374127i
$225$		0			0
$226$	1073.33	+	1859.07i	0.315916	+	0.547183i
$227$	915.300	−	1585.35i	0.267624	−	0.463538i	−0.700624	−	0.713531i	$-0.747095\pi$
$227$	915.300	−	1585.35i	0.267624	−	0.463538i	0.968248	+	0.249993i	$0.0804282\pi$
$228$		0			0
$229$	−34.3935	−	59.5713i	−0.00992483	−	0.0171903i	0.861020	−	0.508571i	$-0.169826\pi$
$229$	−34.3935	−	59.5713i	−0.00992483	−	0.0171903i	−0.870945	+	0.491380i	$0.836493\pi$
$230$	−1728.15			−0.495438
$231$		0			0
$232$	−1540.82			−0.436033
$233$	2435.97	+	4219.22i	0.684916	+	1.18631i	0.973463	+	0.228844i	$0.0734945\pi$
$233$	2435.97	+	4219.22i	0.684916	+	1.18631i	−0.288547	+	0.957466i	$0.593172\pi$
$234$		0			0
$235$	−417.719	+	723.510i	−0.115953	+	0.200836i
$236$	−640.355	−	1109.13i	−0.176625	−	0.305924i
$237$		0			0
$238$	7.22610	−	122.827i	0.00196806	−	0.0334526i
$239$	−3786.86			−1.02490			−0.512451	−	0.858716i	$-0.671263\pi$
$239$	−3786.86			−1.02490			−0.512451	+	0.858716i	$0.671263\pi$
$240$		0			0
$241$	−903.300	+	1564.56i	−0.241438	+	0.418184i	−0.961124	−	0.276116i	$-0.910953\pi$
$241$	−903.300	+	1564.56i	−0.241438	+	0.418184i	0.719686	+	0.694300i	$0.244286\pi$
$242$	−707.904	+	1226.12i	−0.188040	+	0.325695i
$243$		0			0
$244$	642.039			0.168452
$245$	2942.28	+	6843.02i	0.767247	+	1.78443i
$246$		0			0
$247$	−1685.93	−	2920.11i	−0.434303	−	0.752235i
$248$	451.808	−	782.554i	0.115685	−	0.200372i
$249$		0			0
$250$	−7923.12	−	13723.3i	−2.00441	−	3.47174i
$251$	235.616			0.0592508			0.0296254	−	0.999561i	$-0.490569\pi$
$251$	235.616			0.0592508			0.0296254	+	0.999561i	$0.490569\pi$
$252$		0			0
$253$	1014.17			0.252018
$254$	1044.31	+	1808.80i	0.257975	+	0.446826i
$255$		0			0
$256$	−1939.87	+	3359.96i	−0.473601	+	0.820302i
$257$	−1042.18	−	1805.10i	−0.252954	−	0.438129i	0.711384	−	0.702804i	$-0.248069\pi$
$257$	−1042.18	−	1805.10i	−0.252954	−	0.438129i	−0.964338	+	0.264675i	$0.914735\pi$
$258$		0			0
$259$	−1123.47	+	563.401i	−0.269532	+	0.135166i
$260$	2841.17			0.677700
$261$		0			0
$262$	3770.44	−	6530.59i	0.889078	−	1.53993i
$263$	2942.36	−	5096.32i	0.689862	−	1.19488i	−0.282020	−	0.959408i	$-0.591005\pi$
$263$	2942.36	−	5096.32i	0.689862	−	1.19488i	0.971882	−	0.235468i	$-0.0756621\pi$
$264$		0			0
$265$	8456.14			1.96021
$266$	3730.58	+	2456.77i	0.859912	+	0.566295i
$267$		0			0
$268$	1097.07	+	1900.18i	0.250053	+	0.433104i
$269$	−3538.31	+	6128.53i	−0.801987	+	1.38908i	0.116320	+	0.993212i	$0.462890\pi$
$269$	−3538.31	+	6128.53i	−0.801987	+	1.38908i	−0.918306	+	0.395870i	$0.870443\pi$
$270$		0			0
$271$	−1409.33	−	2441.03i	−0.315907	−	0.547167i	0.663723	−	0.747978i	$-0.268975\pi$
$271$	−1409.33	−	2441.03i	−0.315907	−	0.547167i	−0.979630	+	0.200812i	$0.935642\pi$
$272$	−158.705			−0.0353784
$273$		0			0
$274$	2404.85			0.530227
$275$	7272.48	+	12596.3i	1.59472	+	2.76213i
$276$		0			0
$277$	−2184.43	+	3783.55i	−0.473826	+	0.820691i	−0.999551	−	0.0299636i	$-0.990461\pi$
$277$	−2184.43	+	3783.55i	−0.473826	+	0.820691i	0.525725	+	0.850655i	$0.323794\pi$
$278$	1968.05	+	3408.76i	0.424589	+	0.735410i
$279$		0			0
$280$	6105.94	−	3062.04i	1.30321	−	0.653543i
$281$	520.957			0.110597			0.0552984	−	0.998470i	$-0.482389\pi$
$281$	520.957			0.110597			0.0552984	+	0.998470i	$0.482389\pi$
$282$		0			0
$283$	1416.36	−	2453.20i	0.297504	−	0.515292i	−0.678060	−	0.735006i	$-0.737179\pi$
$283$	1416.36	−	2453.20i	0.297504	−	0.515292i	0.975564	+	0.219714i	$0.0705124\pi$
$284$	1367.98	−	2369.41i	0.285827	−	0.495066i
$285$		0			0
$286$	−6360.66			−1.31508
$287$	371.132	−	6308.41i	0.0763318	−	1.29747i
$288$		0			0
$289$	2454.46	+	4251.26i	0.499586	+	0.865308i
$290$	−3243.68	+	5618.22i	−0.656812	+	1.13763i
$291$		0			0
$292$	1497.49	+	2593.74i	0.300117	+	0.519818i
$293$	3591.98			0.716196			0.358098	−	0.933684i	$-0.383425\pi$
$293$	3591.98			0.716196			0.358098	+	0.933684i	$0.383425\pi$
$294$		0			0
$295$	9785.90			1.93138
$296$	576.269	+	998.128i	0.113159	+	0.195997i
$297$		0			0
$298$	−2089.87	+	3619.76i	−0.406251	+	0.703648i
$299$	556.254	+	963.461i	0.107589	+	0.186349i
$300$		0			0
$301$	554.410	−	9423.73i	0.106165	−	1.80457i
$302$	1445.42			0.275412
$303$		0			0
$304$	2880.84	−	4989.77i	0.543512	−	0.941391i
$305$	−2452.91	+	4248.56i	−0.460502	+	0.797612i
$306$		0			0
$307$	2168.14			0.403069			0.201535	−	0.979481i	$-0.435407\pi$
$307$	2168.14			0.403069			0.201535	+	0.979481i	$0.435407\pi$
$308$	1974.47	−	990.168i	0.365279	−	0.183182i
$309$		0			0
$310$	−1902.26	−	3294.81i	−0.348520	−	0.603654i
$311$	3609.01	−	6250.99i	0.658032	−	1.13975i	−0.323092	−	0.946368i	$-0.604722\pi$
$311$	3609.01	−	6250.99i	0.658032	−	1.13975i	0.981124	−	0.193378i	$-0.0619443\pi$
$312$		0			0
$313$	−1522.27	−	2636.64i	−0.274900	−	0.476140i	0.695210	−	0.718807i	$-0.255311\pi$
$313$	−1522.27	−	2636.64i	−0.274900	−	0.476140i	−0.970110	+	0.242666i	$0.921978\pi$
$314$	−5881.73			−1.05709
$315$		0			0
$316$	95.4682			0.0169953
$317$	−3055.39	−	5292.08i	−0.541349	−	0.937644i	−0.998827	−	0.0484229i	$-0.984580\pi$
$317$	−3055.39	−	5292.08i	−0.541349	−	0.937644i	0.457478	−	0.889221i	$-0.348753\pi$
$318$		0			0
$319$	1903.57	−	3297.08i	0.334105	−	0.578687i
$320$	−2430.31	−	4209.43i	−0.424558	−	0.735356i
$321$		0			0
$322$	−1230.87	−	810.588i	−0.213024	−	0.140287i
$323$	147.789			0.0254588
$324$		0			0
$325$	−7977.63	+	13817.7i	−1.36160	+	2.35836i
$326$	1394.85	−	2415.96i	0.236975	−	0.410453i
$327$		0			0
$328$	−5794.99			−0.975533
$329$	−636.881	+	319.386i	−0.106725	+	0.0535208i
$330$		0			0
$331$	−748.710	−	1296.80i	−0.124329	−	0.215344i	0.797142	−	0.603792i	$-0.206344\pi$
$331$	−748.710	−	1296.80i	−0.124329	−	0.215344i	−0.921470	+	0.388449i	$0.873011\pi$
$332$	−634.337	+	1098.70i	−0.104861	+	0.181624i
$333$		0			0
$334$	−2394.90	−	4148.09i	−0.392344	−	0.679560i
$335$	−16765.4			−2.73430
$336$		0			0
$337$	−8157.61			−1.31861			−0.659307	−	0.751873i	$-0.729150\pi$
$337$	−8157.61			−1.31861			−0.659307	+	0.751873i	$0.729150\pi$
$338$	128.371	+	222.345i	0.0206581	+	0.0357809i
$339$		0			0
$340$	−62.2646	+	107.845i	−0.00993168	+	0.0172022i
$341$	1116.35	+	1933.58i	0.177284	+	0.307065i
$342$		0			0
$343$	−1114.09	+	6253.99i	−0.175379	+	0.984501i
$344$	−8656.76			−1.35681
$345$		0			0
$346$	−1398.61	+	2422.46i	−0.217311	+	0.376394i
$347$	4566.56	−	7909.51i	0.706472	−	1.22364i	−0.259686	−	0.965693i	$-0.583619\pi$
$347$	4566.56	−	7909.51i	0.706472	−	1.22364i	0.966158	−	0.257952i	$-0.0830475\pi$
$348$		0			0
$349$	−9528.48			−1.46145			−0.730727	−	0.682670i	$-0.760819\pi$
$349$	−9528.48			−1.46145			−0.730727	+	0.682670i	$0.760819\pi$
$350$	1241.36	−	21100.3i	0.189581	−	3.22245i
$351$		0			0
$352$	−2583.63	−	4474.97i	−0.391215	−	0.677605i
$353$	1678.67	−	2907.55i	0.253107	−	0.438394i	−0.711273	−	0.702916i	$-0.751881\pi$
$353$	1678.67	−	2907.55i	0.253107	−	0.438394i	0.964380	+	0.264522i	$0.0852143\pi$
$354$		0			0
$355$	10452.7	+	18104.7i	1.56274	+	2.70675i
$356$	1392.06			0.207244
$357$		0			0
$358$	4346.47			0.641671
$359$	−46.4867	−	80.5174i	−0.00683420	−	0.0118372i	0.862588	−	0.505907i	$-0.168842\pi$
$359$	−46.4867	−	80.5174i	−0.00683420	−	0.0118372i	−0.869422	+	0.494070i	$0.835509\pi$
$360$		0			0
$361$	746.814	−	1293.52i	0.108881	−	0.188587i
$362$	6594.90	+	11422.7i	0.957514	+	1.65846i
$363$		0			0
$364$	2023.61	+	1332.65i	0.291391	+	0.191895i
$365$	−22884.7			−3.28175
$366$		0			0
$367$	3392.95	−	5876.77i	0.482590	−	0.835871i	−0.517210	−	0.855859i	$-0.673029\pi$
$367$	3392.95	−	5876.77i	0.482590	−	0.835871i	0.999800	+	0.0199876i	$0.00636268\pi$
$368$	−950.506	+	1646.32i	−0.134643	+	0.233208i
$369$		0			0
$370$	4852.57			0.681820
$371$	6022.86	+	3966.35i	0.842833	+	0.555048i
$372$		0			0
$373$	3725.53	+	6452.80i	0.517159	+	0.895746i	0.999801	+	0.0199284i	$0.00634382\pi$
$373$	3725.53	+	6452.80i	0.517159	+	0.895746i	−0.482642	+	0.875818i	$0.660323\pi$
$374$	139.395	−	241.438i	0.0192725	−	0.0333810i
$375$		0			0
$376$	326.681	+	565.828i	0.0448066	+	0.0776073i
$377$	4176.29			0.570530
$378$		0			0
$379$	4014.67			0.544115			0.272058	−	0.962281i	$-0.412296\pi$
$379$	4014.67			0.544115			0.272058	+	0.962281i	$0.412296\pi$
$380$	−2260.47	−	3915.25i	−0.305157	−	0.528548i
$381$		0			0
$382$	2817.78	−	4880.53i	0.377408	−	0.653690i
$383$	3232.44	+	5598.74i	0.431253	+	0.746951i	0.996981	−	0.0776399i	$-0.0247384\pi$
$383$	3232.44	+	5598.74i	0.431253	+	0.746951i	−0.565729	+	0.824591i	$0.691405\pi$
$384$		0			0
$385$	−991.224	+	16848.6i	−0.131214	+	2.23035i
$386$	14435.2			1.90345
$387$		0			0
$388$	−655.044	+	1134.57i	−0.0857084	+	0.148451i
$389$	3472.03	−	6013.73i	0.452542	−	0.783826i	−0.546001	−	0.837785i	$-0.683850\pi$
$389$	3472.03	−	6013.73i	0.452542	−	0.783826i	0.998543	+	0.0539584i	$0.0171838\pi$
$390$		0			0
$391$	−48.7615			−0.00630684
$392$	5785.19	+	683.064i	0.745398	+	0.0880101i
$393$		0			0
$394$	2089.83	+	3619.69i	0.267218	+	0.462835i
$395$	−364.736	+	631.741i	−0.0464604	+	0.0804717i
$396$		0			0
$397$	−681.535	−	1180.45i	−0.0861594	−	0.149232i	0.819725	−	0.572757i	$-0.194126\pi$
$397$	−681.535	−	1180.45i	−0.0861594	−	0.149232i	−0.905885	+	0.423524i	$0.860793\pi$
$398$	1931.41			0.243248
$399$		0			0
$400$	−27263.7			−3.40797
$401$	−1944.54	−	3368.04i	−0.242158	−	0.419431i	0.719170	−	0.694834i	$-0.244522\pi$
$401$	−1944.54	−	3368.04i	−0.242158	−	0.419431i	−0.961329	+	0.275403i	$0.911189\pi$
$402$		0			0
$403$	−1224.60	+	2121.06i	−0.151368	+	0.262178i
$404$	2192.32	+	3797.21i	0.269980	+	0.467619i
$405$		0			0
$406$	−4945.53	+	2480.11i	−0.604538	+	0.303167i
$407$	−2847.76			−0.346826
$408$		0			0
$409$	4186.88	−	7251.88i	0.506180	−	0.876730i	−0.493794	−	0.869579i	$-0.664390\pi$
$409$	4186.88	−	7251.88i	0.506180	−	0.876730i	0.999974	−	0.00715125i	$-0.00227633\pi$
$410$	−12199.4	+	21130.0i	−1.46948	+	2.54521i
$411$		0			0
$412$	3247.49			0.388331
$413$	6969.97	+	4590.07i	0.830435	+	0.546883i
$414$		0			0
$415$	−4846.97	−	8395.19i	−0.573321	−	0.993021i
$416$	2834.14	−	4908.87i	0.334027	−	0.578551i
$417$		0			0
$418$	5060.62	+	8765.25i	0.592160	+	1.02565i
$419$	−11115.8			−1.29604			−0.648022	−	0.761621i	$-0.724404\pi$
$419$	−11115.8			−1.29604			−0.648022	+	0.761621i	$0.724404\pi$
$420$		0			0
$421$	9201.47			1.06521			0.532604	−	0.846365i	$-0.321214\pi$
$421$	9201.47			1.06521			0.532604	+	0.846365i	$0.321214\pi$
$422$	−1708.04	−	2958.41i	−0.197028	−	0.341263i
$423$		0			0
$424$	3306.60	−	5727.21i	0.378733	−	0.655985i
$425$	−349.661	−	605.631i	−0.0399084	−	0.0691233i
$426$		0			0
$427$	−3739.86	+	1875.48i	−0.423851	+	0.212555i
$428$	−2280.96			−0.257603
$429$		0			0
$430$	−18223.9	+	31564.8i	−2.04380	+	3.53997i
$431$	−1498.56	+	2595.58i	−0.167478	+	0.290081i	−0.937533	−	0.347898i	$-0.886896\pi$
$431$	−1498.56	+	2595.58i	−0.167478	+	0.290081i	0.770054	+	0.637978i	$0.220229\pi$
$432$		0			0
$433$	−4285.85			−0.475669			−0.237835	−	0.971306i	$-0.576438\pi$
$433$	−4285.85			−0.475669			−0.237835	+	0.971306i	$0.576438\pi$
$434$	190.553	−	3238.98i	0.0210757	−	0.358239i
$435$		0			0
$436$	−2130.10	−	3689.44i	−0.233975	−	0.405257i
$437$	885.126	−	1533.08i	0.0968909	−	0.167820i
$438$		0			0
$439$	−1525.58	−	2642.37i	−0.165858	−	0.287275i	0.771102	−	0.636712i	$-0.219706\pi$
$439$	−1525.58	−	2642.37i	−0.165858	−	0.287275i	−0.936960	+	0.349437i	$0.886373\pi$
$440$	15477.3			1.67694
$441$		0			0
$442$	305.821			0.0329104
$443$	5785.50	+	10020.8i	0.620491	+	1.07472i	0.989394	+	0.145254i	$0.0463998\pi$
$443$	5785.50	+	10020.8i	0.620491	+	1.07472i	−0.368904	+	0.929468i	$0.620267\pi$
$444$		0			0
$445$	−5318.35	+	9211.65i	−0.566548	+	0.981290i
$446$	−8926.07	−	15460.4i	−0.947672	−	1.64142i
$447$		0			0
$448$	243.449	−	4138.09i	0.0256739	−	0.436398i
$449$	−3588.18			−0.377142			−0.188571	−	0.982060i	$-0.560386\pi$
$449$	−3588.18			−0.377142			−0.188571	+	0.982060i	$0.560386\pi$
$450$		0			0
$451$	7159.29	−	12400.3i	0.747490	−	1.29469i
$452$	926.441	−	1604.64i	0.0964073	−	0.166982i
$453$		0			0
$454$	−6027.68			−0.623113
$455$	−16549.8	+	8299.46i	−1.70520	+	0.855131i
$456$		0			0
$457$	4683.70	+	8112.41i	0.479419	+	0.830377i	0.999721	−	0.0236044i	$-0.00751421\pi$
$457$	4683.70	+	8112.41i	0.479419	+	0.830377i	−0.520303	+	0.853982i	$0.674181\pi$
$458$	−113.249	+	196.152i	−0.0115541	+	0.0200122i
$459$		0			0
$460$	745.820	+	1291.80i	0.0755957	+	0.130936i
$461$	1091.46			0.110269			0.0551346	−	0.998479i	$-0.482441\pi$
$461$	1091.46			0.110269			0.0551346	+	0.998479i	$0.482441\pi$
$462$		0			0
$463$	13226.1			1.32758			0.663790	−	0.747919i	$-0.268947\pi$
$463$	13226.1			1.32758			0.663790	+	0.747919i	$0.268947\pi$
$464$	3568.14	+	6180.20i	0.356997	+	0.618338i
$465$		0			0
$466$	8020.99	−	13892.8i	0.797350	−	1.38105i
$467$	5670.70	+	9821.95i	0.561903	+	0.973245i	0.997330	+	0.0730211i	$0.0232640\pi$
$467$	5670.70	+	9821.95i	0.561903	+	0.973245i	−0.435427	+	0.900224i	$0.643403\pi$
$468$		0			0
$469$	−11941.1	−	7863.80i	−1.17567	−	0.774236i
$470$	2750.87			0.269975
$471$		0			0
$472$	3826.58	−	6627.83i	0.373162	−	0.646336i
$473$	10694.8	−	18523.9i	1.03964	−	1.80070i
$474$		0			0
$475$	25388.4			2.45242
$476$	−94.9326	+	47.6073i	−0.00914124	+	0.00458420i
$477$		0			0
$478$	6234.57	+	10798.6i	0.596574	+	1.03330i
$479$	8512.21	−	14743.6i	0.811968	−	1.40637i	−0.0995168	−	0.995036i	$-0.531730\pi$
$479$	8512.21	−	14743.6i	0.811968	−	1.40637i	0.911485	−	0.411334i	$-0.134937\pi$
$480$		0			0
$481$	−1561.94	−	2705.36i	−0.148063	−	0.256453i
$482$	5948.66			0.562145
$483$		0			0
$484$	1222.04			0.114767
$485$	−5005.19	−	8669.24i	−0.468606	−	0.811650i
$486$		0			0
$487$	−4862.35	+	8421.84i	−0.452431	+	0.783634i	−0.998536	−	0.0540825i	$-0.982777\pi$
$487$	−4862.35	+	8421.84i	−0.452431	+	0.783634i	0.546105	+	0.837717i	$0.316110\pi$
$488$	1918.32	+	3322.63i	0.177947	+	0.308214i
$489$		0			0
$490$	14669.4	−	19656.3i	1.35244	−	1.81221i
$491$	16363.4			1.50402			0.752008	−	0.659154i	$-0.229085\pi$
$491$	16363.4			1.50402			0.752008	+	0.659154i	$0.229085\pi$
$492$		0			0
$493$	−91.5238	+	158.524i	−0.00836111	+	0.0144819i
$494$	−5551.30	+	9615.14i	−0.505597	+	0.875720i
$495$		0			0
$496$	−4185.08			−0.378862
$497$	−1047.07	+	17797.8i	−0.0945020	+	1.60632i
$498$		0			0
$499$	2726.23	+	4721.96i	0.244575	+	0.423616i	0.962012	−	0.273007i	$-0.0880184\pi$
$499$	2726.23	+	4721.96i	0.244575	+	0.423616i	−0.717437	+	0.696623i	$0.754685\pi$
$500$	−6838.79	+	11845.1i	−0.611680	+	1.05946i
$501$		0			0
$502$	−387.910	−	671.880i	−0.0344886	−	0.0597360i
$503$	3703.99			0.328336			0.164168	−	0.986432i	$-0.447506\pi$
$503$	3703.99			0.328336			0.164168	+	0.986432i	$0.447506\pi$
$504$		0			0
$505$	−33503.0			−2.95220
$506$	−1669.70	−	2892.01i	−0.146694	−	0.254082i
$507$		0			0
$508$	901.388	−	1561.25i	0.0787256	−	0.136357i
$509$	826.843	+	1432.13i	0.0720023	+	0.124712i	0.899779	−	0.436346i	$-0.143728\pi$
$509$	826.843	+	1432.13i	0.0720023	+	0.124712i	−0.827776	+	0.561058i	$0.810394\pi$
$510$		0			0
$511$	−16299.5	−	10734.1i	−1.41105	−	0.929250i
$512$	−1001.60			−0.0864546
$513$		0			0
$514$	−3431.61	+	5943.72i	−0.294478	+	0.510051i
$515$	−12407.0	+	21489.6i	−1.06159	+	1.83873i
$516$		0			0
$517$	−1614.36			−0.137330
$518$	3456.23	+	2276.10i	0.293162	+	0.193062i
$519$		0			0
$520$	8489.01	+	14703.4i	0.715900	+	1.23997i
$521$	−1550.15	+	2684.94i	−0.130352	+	0.225776i	−0.923812	−	0.382846i	$-0.874944\pi$
$521$	−1550.15	+	2684.94i	−0.130352	+	0.225776i	0.793460	+	0.608622i	$0.208277\pi$
$522$		0			0
$523$	1562.72	+	2706.70i	0.130655	+	0.226302i	0.923929	−	0.382563i	$-0.124958\pi$
$523$	1562.72	+	2706.70i	0.130655	+	0.226302i	−0.793274	+	0.608865i	$0.791625\pi$
$524$	−6508.85			−0.542635
$525$		0			0
$526$	−19376.8			−1.60622
$527$	−53.6743	−	92.9666i	−0.00443660	−	0.00768442i
$528$		0			0
$529$	5791.46	−	10031.1i	0.475997	−	0.824452i
$530$	−13921.9	−	24113.5i	−1.14100	−	1.97627i
$531$		0			0
$532$	226.436	−	3848.90i	0.0184534	−	0.313667i
$533$	15706.9			1.27644
$534$		0			0
$535$	8714.39	−	15093.8i	0.704217	−	1.21974i
$536$	−6555.77	+	11354.9i	−0.528295	+	0.915034i
$537$		0			0
$538$	23301.4			1.86728
$539$	−8608.82	+	11535.4i	−0.687956	+	0.921828i
$540$		0			0
$541$	−10757.2	−	18632.0i	−0.854874	−	1.48069i	−0.876762	−	0.480925i	$-0.840301\pi$
$541$	−10757.2	−	18632.0i	−0.854874	−	1.48069i	0.0218880	−	0.999760i	$-0.493032\pi$
$542$	−4640.55	+	8037.67i	−0.367765	+	0.636988i
$543$		0			0
$544$	124.221	+	215.157i	0.00979031	+	0.0169573i
$545$	32552.2			2.55850
$546$		0			0
$547$	−13104.4			−1.02432			−0.512161	−	0.858889i	$-0.671155\pi$
$547$	−13104.4			−1.02432			−0.512161	+	0.858889i	$0.671155\pi$
$548$	−1037.86	−	1797.63i	−0.0809039	−	0.140130i
$549$		0			0
$550$	23946.3	−	41476.3i	1.85650	−	3.21555i
$551$	−3322.71	−	5755.10i	−0.256900	−	0.444965i
$552$		0			0
$553$	−556.100	+	278.876i	−0.0427627	+	0.0214449i
$554$	14385.5			1.10322
$555$		0			0
$556$	1698.71	−	2942.25i	0.129571	−	0.224423i
$557$	9397.45	−	16276.9i	0.714870	−	1.23819i	−0.248139	−	0.968724i	$-0.579819\pi$
$557$	9397.45	−	16276.9i	0.714870	−	1.23819i	0.963009	−	0.269467i	$-0.0868477\pi$
$558$		0			0
$559$	23463.6			1.77532
$560$	−26421.6	−	17399.9i	−1.99378	−	1.31300i
$561$		0			0
$562$	−857.687	−	1485.56i	−0.0643761	−	0.111503i
$563$	8724.85	−	15111.9i	0.653124	−	1.13124i	−0.329237	−	0.944247i	$-0.606792\pi$
$563$	8724.85	−	15111.9i	0.653124	−	1.13124i	0.982361	−	0.186996i	$-0.0598751\pi$
$564$		0			0
$565$	7078.93	+	12261.1i	0.527102	+	0.912968i
$566$	−9327.38			−0.692684
$567$		0			0
$568$	16349.3			1.20775
$569$	−11420.4	−	19780.8i	−0.841423	−	1.45739i	−0.888691	−	0.458506i	$-0.848385\pi$
$569$	−11420.4	−	19780.8i	−0.841423	−	1.45739i	0.0472680	−	0.998882i	$-0.484949\pi$
$570$		0			0
$571$	−448.021	+	775.995i	−0.0328355	+	0.0568728i	−0.881976	−	0.471294i	$-0.843787\pi$
$571$	−448.021	+	775.995i	−0.0328355	+	0.0568728i	0.849141	+	0.528167i	$0.177120\pi$
$572$	2745.08	+	4754.62i	0.200660	+	0.347553i
$573$		0			0
$574$	−18600.0	+	9327.64i	−1.35253	+	0.678272i
$575$	−8376.65			−0.607531
$576$		0			0
$577$	1483.10	−	2568.80i	0.107005	−	0.185339i	−0.807550	−	0.589799i	$-0.799207\pi$
$577$	1483.10	−	2568.80i	0.107005	−	0.185339i	0.914556	+	0.404460i	$0.132540\pi$
$578$	8081.90	−	13998.3i	0.581596	−	1.00735i
$579$		0			0
$580$	5599.52			0.400875
$581$	485.530	−	8252.92i	0.0346698	−	0.589309i
$582$		0			0
$583$	8170.15	+	14151.1i	0.580399	+	1.00528i
$584$	−8948.60	+	15499.4i	−0.634068	+	1.09824i
$585$		0			0
$586$	−5913.71	−	10242.8i	−0.416882	−	0.722062i
$587$	1872.80			0.131684			0.0658420	−	0.997830i	$-0.479027\pi$
$587$	1872.80			0.131684			0.0658420	+	0.997830i	$0.479027\pi$
$588$		0			0
$589$	3897.21			0.272635
$590$	−16111.2	−	27905.4i	−1.12421	−	1.94720i
$591$		0			0
$592$	2668.98	−	4622.81i	0.185295	−	0.320940i
$593$	−8549.50	−	14808.2i	−0.592051	−	1.02546i	−0.993956	−	0.109781i	$-0.964985\pi$
$593$	−8549.50	−	14808.2i	−0.592051	−	1.02546i	0.401905	−	0.915681i	$-0.368348\pi$
$594$		0			0
$595$	47.6581	−	810.080i	0.00328368	−	0.0558152i
$596$	3607.71			0.247949
$597$		0			0
$598$	1831.60	−	3172.42i	0.125250	−	0.216940i
$599$	5709.09	−	9888.44i	0.389428	−	0.674509i	−0.602945	−	0.797783i	$-0.706006\pi$
$599$	5709.09	−	9888.44i	0.389428	−	0.674509i	0.992373	+	0.123274i	$0.0393395\pi$
$600$		0			0
$601$	−10231.6			−0.694432			−0.347216	−	0.937785i	$-0.612873\pi$
$601$	−10231.6			−0.694432			−0.347216	+	0.937785i	$0.612873\pi$
$602$	−27785.4	+	13934.0i	−1.88114	+	0.943365i
$603$		0			0
$604$	−623.800	−	1080.45i	−0.0420233	−	0.0727865i
$605$	−4668.82	+	8086.63i	−0.313743	+	0.543418i
$606$		0			0
$607$	6095.70	+	10558.1i	0.407606	+	0.705995i	0.994621	−	0.103582i	$-0.0330303\pi$
$607$	6095.70	+	10558.1i	0.407606	+	0.705995i	−0.587015	+	0.809576i	$0.699697\pi$
$608$	−9019.51			−0.601627
$609$		0			0
$610$	16153.5			1.07219
$611$	−885.447	−	1533.64i	−0.0586274	−	0.101546i
$612$		0			0
$613$	3824.87	−	6624.88i	0.252015	−	0.436503i	−0.712065	−	0.702113i	$-0.752240\pi$
$613$	3824.87	−	6624.88i	0.252015	−	0.436503i	0.964080	+	0.265610i	$0.0855734\pi$
$614$	−3569.55	−	6182.65i	−0.234618	−	0.406370i
$615$		0			0
$616$	11023.7	+	7259.64i	0.721033	+	0.474836i
$617$	19107.4			1.24673			0.623367	−	0.781929i	$-0.285764\pi$
$617$	19107.4			1.24673			0.623367	+	0.781929i	$0.285764\pi$
$618$		0			0
$619$	−8831.65	+	15296.9i	−0.573464	+	0.993269i	0.422743	+	0.906250i	$0.361067\pi$
$619$	−8831.65	+	15296.9i	−0.573464	+	0.993269i	−0.996207	+	0.0870189i	$0.972266\pi$
$620$	−1641.92	+	2843.90i	−0.106357	+	0.184216i
$621$		0			0
$622$	−23767.0			−1.53211
$623$	−8108.70	+	4066.39i	−0.521458	+	0.261503i
$624$		0			0
$625$	−30592.3	−	52987.4i	−1.95791	−	3.39120i
$626$	−5012.42	+	8681.77i	−0.320027	+	0.554303i
$627$		0			0
$628$	2538.39	+	4396.61i	0.161294	+	0.279369i
$629$	136.920			0.00867944
$630$		0			0
$631$	5523.07			0.348447			0.174223	−	0.984706i	$-0.444259\pi$
$631$	5523.07			0.348447			0.174223	+	0.984706i	$0.444259\pi$
$632$	285.245	+	494.059i	0.0179532	+	0.0310959i
$633$		0			0
$634$	−10060.6	+	17425.4i	−0.630215	+	1.09157i
$635$	6887.50	+	11929.5i	0.430428	+	0.745524i
$636$		0			0
$637$	−15680.4	−	1851.40i	−0.975320	−	0.115157i
$638$	−12535.9			−0.777902
$639$		0			0
$640$	−18698.6	+	32387.0i	−1.15489	+	2.00033i
$641$	−8727.00	+	15115.6i	−0.537747	+	0.931405i	0.461278	+	0.887256i	$0.347391\pi$
$641$	−8727.00	+	15115.6i	−0.537747	+	0.931405i	−0.999025	+	0.0441491i	$0.985942\pi$
$642$		0			0
$643$	−8175.22			−0.501398			−0.250699	−	0.968065i	$-0.580660\pi$
$643$	−8175.22			−0.501398			−0.250699	+	0.968065i	$0.580660\pi$
$644$	−74.7102	+	1269.91i	−0.00457142	+	0.0777039i
$645$		0			0
$646$	−243.315	−	421.434i	−0.0148190	−	0.0256673i
$647$	12500.3	−	21651.2i	0.759564	−	1.31560i	−0.183509	−	0.983018i	$-0.558746\pi$
$647$	12500.3	−	21651.2i	0.759564	−	1.31560i	0.943073	−	0.332586i	$-0.107921\pi$
$648$		0			0
$649$	9454.93	+	16376.4i	0.571862	+	0.990494i
$650$	52536.4			3.17023
$651$		0			0
$652$	−2407.92			−0.144634
$653$	384.545	+	666.052i	0.0230451	+	0.0399152i	0.877318	−	0.479910i	$-0.159331\pi$
$653$	384.545	+	666.052i	0.0230451	+	0.0399152i	−0.854273	+	0.519825i	$0.825997\pi$
$654$		0			0
$655$	24867.1	−	43071.0i	1.48341	−	2.56935i
$656$	13419.7	+	23243.6i	0.798707	+	1.38340i
$657$		0			0
$658$	1959.30	+	1290.30i	0.116081	+	0.0764453i
$659$	7037.98			0.416025			0.208013	−	0.978126i	$-0.433300\pi$
$659$	7037.98			0.416025			0.208013	+	0.978126i	$0.433300\pi$
$660$		0			0
$661$	−2044.87	+	3541.82i	−0.120327	+	0.208413i	−0.919897	−	0.392161i	$-0.871728\pi$
$661$	−2044.87	+	3541.82i	−0.120327	+	0.208413i	0.799569	+	0.600574i	$0.205061\pi$
$662$	−2465.30	+	4270.03i	−0.144738	+	0.250694i
$663$		0			0
$664$	−7581.24			−0.443086
$665$	24604.2	+	16203.1i	1.43475	+	0.944855i
$666$		0			0
$667$	1096.29	+	1898.84i	0.0636412	+	0.110230i
$668$	−2067.14	+	3580.39i	−0.119731	+	0.207379i
$669$		0			0
$670$	27602.0	+	47808.0i	1.59158	+	2.75669i
$671$	−9479.79			−0.545400
$672$		0			0
$673$	2151.39			0.123224			0.0616121	−	0.998100i	$-0.480376\pi$
$673$	2151.39			0.123224			0.0616121	+	0.998100i	$0.480376\pi$
$674$	13430.4	+	23262.2i	0.767538	+	1.32941i
$675$		0			0
$676$	110.802	−	191.915i	0.00630418	−	0.0109192i
$677$	3837.80	+	6647.27i	0.217871	+	0.377364i	0.954157	−	0.299307i	$-0.0967554\pi$
$677$	3837.80	+	6647.27i	0.217871	+	0.377364i	−0.736286	+	0.676671i	$0.763422\pi$
$678$		0			0
$679$	501.379	−	8522.32i	0.0283375	−	0.481674i
$680$	−744.151			−0.0419660
$681$		0			0
$682$	3675.85	−	6366.76i	0.206387	−	0.357472i
$683$	−8049.29	+	13941.8i	−0.450948	+	0.781065i	−0.998445	−	0.0557429i	$-0.982247\pi$
$683$	−8049.29	+	13941.8i	−0.450948	+	0.781065i	0.547497	+	0.836807i	$0.315581\pi$
$684$		0			0
$685$	15860.6			0.884676
$686$	19668.0	−	7119.45i	1.09465	−	0.396242i
$687$		0			0
$688$	20046.8	+	34722.1i	1.11087	+	1.92408i
$689$	−8962.33	+	15523.2i	−0.495555	+	0.858327i
$690$		0			0
$691$	−9541.91	−	16527.1i	−0.525313	−	0.909869i	−0.999565	−	0.0294802i	$-0.990615\pi$
$691$	−9541.91	−	16527.1i	−0.525313	−	0.909869i	0.474252	−	0.880389i	$-0.342719\pi$
$692$	2414.40			0.132632
$693$		0			0
$694$	−30072.9			−1.64489
$695$	12979.8	+	22481.7i	0.708421	+	1.22702i
$696$		0			0
$697$	−344.219	+	596.205i	−0.0187062	+	0.0324001i
$698$	15687.4	+	27171.3i	0.850682	+	1.47342i
$699$		0			0
$700$	−16308.3	+	8178.37i	−0.880565	+	0.441591i
$701$	−29898.7			−1.61093			−0.805463	−	0.592646i	$-0.798083\pi$
$701$	−29898.7			−1.61093			−0.805463	+	0.592646i	$0.798083\pi$
$702$		0			0
$703$	−2485.40	+	4304.83i	−0.133341	+	0.230953i
$704$	4696.24	−	8134.12i	0.251415	−	0.435463i
$705$		0			0
$706$	−11054.8			−0.589312
$707$	−23862.4	−	15714.6i	−1.26936	−	0.835937i
$708$		0			0
$709$	−9939.56	−	17215.8i	−0.526500	−	0.911924i	−0.999523	−	0.0308743i	$-0.990171\pi$
$709$	−9939.56	−	17215.8i	−0.526500	−	0.911924i	0.473024	−	0.881050i	$-0.343162\pi$
$710$	34418.1	−	59613.9i	1.81928	−	3.15108i
$711$		0			0
$712$	4159.27	+	7204.06i	0.218926	+	0.379190i
$713$	−1285.85			−0.0675390
$714$		0			0
$715$	−41950.3			−2.19420
$716$	−1875.81	−	3249.00i	−0.0979085	−	0.169582i
$717$		0			0
$718$	−153.069	+	265.122i	−0.00795608	+	0.0137803i
$719$	6820.25	+	11813.0i	0.353758	+	0.612728i	0.986905	−	0.161305i	$-0.0515702\pi$
$719$	6820.25	+	11813.0i	0.353758	+	0.612728i	−0.633146	+	0.774032i	$0.718237\pi$
$720$		0			0
$721$	−18916.5	+	9486.37i	−0.977099	+	0.490001i
$722$	−4918.12			−0.253509
$723$		0			0
$724$	5692.34	−	9859.42i	0.292202	−	0.506108i
$725$	−15722.7	+	27232.5i	−0.805416	+	1.39502i
$726$		0			0
$727$	−10021.8			−0.511262			−0.255631	−	0.966774i	$-0.582283\pi$
$727$	−10021.8			−0.511262			−0.255631	+	0.966774i	$0.582283\pi$
$728$	−850.361	+	14454.2i	−0.0432918	+	0.735864i
$729$		0			0
$730$	37676.6	+	65257.8i	1.91024	+	3.30863i
$731$	−514.207	+	890.632i	−0.0260173	+	0.0450632i
$732$		0			0
$733$	12044.0	+	20860.8i	0.606898	+	1.05118i	0.991749	+	0.128199i	$0.0409195\pi$
$733$	12044.0	+	20860.8i	0.606898	+	1.05118i	−0.384851	+	0.922979i	$0.625747\pi$
$734$	−22344.2			−1.12362
$735$		0			0
$736$	2975.90			0.149039
$737$	−16198.4	−	28056.4i	−0.809599	−	1.40227i
$738$		0			0
$739$	−12328.9	+	21354.4i	−0.613705	+	1.06297i	0.376906	+	0.926252i	$0.376988\pi$
$739$	−12328.9	+	21354.4i	−0.613705	+	1.06297i	−0.990610	+	0.136716i	$0.956345\pi$
$740$	−2094.23	−	3627.32i	−0.104034	−	0.180193i
$741$		0			0
$742$	1394.58	−	23704.8i	0.0689984	−	1.17282i
$743$	−13467.0			−0.664948			−0.332474	−	0.943112i	$-0.607883\pi$
$743$	−13467.0			−0.664948			−0.332474	+	0.943112i	$0.607883\pi$
$744$		0			0
$745$	−13783.3	+	23873.3i	−0.677825	+	1.17403i
$746$	12267.2	−	21247.4i	0.602055	−	1.04279i
$747$		0			0
$748$	−240.635			−0.0117627
$749$	13286.5	−	6663.00i	0.648170	−	0.325048i
$750$		0			0
$751$	3440.08	+	5958.39i	0.167151	+	0.289513i	0.937417	−	0.348209i	$-0.113210\pi$
$751$	3440.08	+	5958.39i	0.167151	+	0.289513i	−0.770266	+	0.637722i	$0.779877\pi$
$752$	1513.02	−	2620.63i	0.0733698	−	0.127080i
$753$		0			0
$754$	−6875.71	−	11909.1i	−0.332093	−	0.575203i
$755$	9532.91			0.459521
$756$		0			0
$757$	33528.2			1.60978			0.804889	−	0.593425i	$-0.202225\pi$
$757$	33528.2			1.60978			0.804889	+	0.593425i	$0.202225\pi$
$758$	−6609.62	−	11448.2i	−0.316718	−	0.548572i
$759$		0			0
$760$	13507.9	−	23396.4i	0.644716	−	1.11668i
$761$	−545.457	−	944.759i	−0.0259826	−	0.0450033i	0.852742	−	0.522333i	$-0.174938\pi$
$761$	−545.457	−	944.759i	−0.0259826	−	0.0450033i	−0.878724	+	0.477330i	$0.841605\pi$
$762$		0			0
$763$	23185.2	+	15268.6i	1.10008	+	0.724456i
$764$	−4864.29			−0.230345
$765$		0			0
$766$	10643.6	−	18435.2i	0.502046	−	0.869569i
$767$	−10371.7	+	17964.3i	−0.488266	+	0.845702i
$768$		0			0
$769$	30520.8			1.43122			0.715609	−	0.698501i	$-0.246149\pi$
$769$	30520.8			1.43122			0.715609	+	0.698501i	$0.246149\pi$
$770$	49677.2	−	24912.4i	2.32499	−	1.16595i
$771$		0			0
$772$	−6229.81	−	10790.3i	−0.290435	−	0.503048i
$773$	−3924.15	+	6796.82i	−0.182590	+	0.316255i	−0.942762	−	0.333467i	$-0.891781\pi$
$773$	−3924.15	+	6796.82i	−0.182590	+	0.316255i	0.760172	+	0.649722i	$0.225115\pi$
$774$		0			0
$775$	−9220.61	−	15970.6i	−0.427373	−	0.740231i
$776$	−7828.72			−0.362158
$777$		0			0
$778$	−22865.0			−1.05366
$779$	−12496.6	−	21644.8i	−0.574760	−	0.995514i
$780$		0

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	189.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.64637 - 2.85159i) q^{2} +(-1.42105 + 2.46133i) q^{4} +(-10.8582 - 18.8070i) q^{5} +(1.08769 - 18.4883i) q^{7} -16.9836 q^{8} +O(q^{10})\)	\(q+(-1.64637 - 2.85159i) q^{2} +(-1.42105 + 2.46133i) q^{4} +(-10.8582 - 18.8070i) q^{5} +(1.08769 - 18.4883i) q^{7} -16.9836 q^{8} +(-35.7533 + 61.9265i) q^{10} +(20.9820 - 36.3419i) q^{11} +46.0329 q^{13} +(-54.5118 + 27.3369i) q^{14} +(39.3296 + 68.1209i) q^{16} +(-1.00882 + 1.74732i) q^{17} +(-36.6244 - 63.4352i) q^{19} +61.7204 q^{20} -138.176 q^{22} +(12.0838 + 20.9298i) q^{23} +(-173.303 + 300.169i) q^{25} +(-75.7871 - 131.267i) q^{26} +(43.9602 + 28.9500i) q^{28} +90.7240 q^{29} +(-26.6026 + 46.0771i) q^{31} +(61.5677 - 106.638i) q^{32} +6.64353 q^{34} +(-359.520 + 180.294i) q^{35} +(-33.9309 - 58.7701i) q^{37} +(-120.594 + 208.875i) q^{38} +(184.412 + 319.411i) q^{40} +341.211 q^{41} +509.713 q^{43} +(59.6330 + 103.287i) q^{44} +(39.7889 - 68.9164i) q^{46} +(-19.2351 - 33.3162i) q^{47} +(-340.634 - 40.2191i) q^{49} +1141.28 q^{50} +(-65.4151 + 113.302i) q^{52} +(-194.694 + 337.220i) q^{53} -911.311 q^{55} +(-18.4729 + 313.998i) q^{56} +(-149.365 - 258.708i) q^{58} +(-225.310 + 390.249i) q^{59} +(-112.951 - 195.638i) q^{61} +175.191 q^{62} +223.822 q^{64} +(-499.836 - 865.742i) q^{65} +(386.006 - 668.582i) q^{67} +(-2.86716 - 4.96606i) q^{68} +(1106.03 + 728.374i) q^{70} -962.655 q^{71} +(526.897 - 912.612i) q^{73} +(-111.726 + 193.514i) q^{74} +208.180 q^{76} +(-649.078 - 427.450i) q^{77} +(-16.7953 - 29.0904i) q^{79} +(854.101 - 1479.35i) q^{80} +(-561.759 - 972.995i) q^{82} +446.386 q^{83} +43.8159 q^{85} +(-839.175 - 1453.49i) q^{86} +(-356.350 + 617.216i) q^{88} +(-244.899 - 424.178i) q^{89} +(50.0695 - 851.070i) q^{91} -68.6870 q^{92} +(-63.3361 + 109.701i) q^{94} +(-795.352 + 1377.59i) q^{95} +460.958 q^{97} +(446.120 + 1037.56i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 48 q^{4} - 60 q^{7}+O(q^{10}) \) 16 * q - 48 * q^4 - 60 * q^7	\( 16 q - 48 q^{4} - 60 q^{7} - 44 q^{10} - 168 q^{13} - 156 q^{16} - 12 q^{19} + 448 q^{22} - 408 q^{25} - 152 q^{28} - 800 q^{31} - 1896 q^{34} - 692 q^{37} - 96 q^{40} + 2912 q^{43} - 1524 q^{46} + 2020 q^{49} - 1972 q^{52} - 2560 q^{55} - 2372 q^{58} - 216 q^{61} + 9928 q^{64} - 684 q^{67} + 4316 q^{70} + 4564 q^{73} - 760 q^{76} - 556 q^{79} - 3340 q^{82} + 2592 q^{85} - 6696 q^{88} - 184 q^{91} + 492 q^{94} + 1168 q^{97}+O(q^{100}) \) 16 * q - 48 * q^4 - 60 * q^7 - 44 * q^10 - 168 * q^13 - 156 * q^16 - 12 * q^19 + 448 * q^22 - 408 * q^25 - 152 * q^28 - 800 * q^31 - 1896 * q^34 - 692 * q^37 - 96 * q^40 + 2912 * q^43 - 1524 * q^46 + 2020 * q^49 - 1972 * q^52 - 2560 * q^55 - 2372 * q^58 - 216 * q^61 + 9928 * q^64 - 684 * q^67 + 4316 * q^70 + 4564 * q^73 - 760 * q^76 - 556 * q^79 - 3340 * q^82 + 2592 * q^85 - 6696 * q^88 - 184 * q^91 + 492 * q^94 + 1168 * q^97

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