LMFDB - Embedded newform 189.4.e.h.163.7

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			163.7
Root			$3.25730 + 5.64181i$ of defining polynomial
Character	$\chi$	$=$	189.163
Dual form			189.4.e.h.109.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.74618 - 3.02447i) q^{2} +(-2.09829 - 3.63435i) q^{4} +(-3.93765 + 6.82022i) q^{5} +(18.4135 + 1.98614i) q^{7} +13.2829 q^{8} +O(q^{10})$	\(q+(1.74618 - 3.02447i) q^{2} +(-2.09829 - 3.63435i) q^{4} +(-3.93765 + 6.82022i) q^{5} +(18.4135 + 1.98614i) q^{7} +13.2829 q^{8} +(13.7517 + 23.8187i) q^{10} +(27.0018 + 46.7684i) q^{11} -48.9137 q^{13} +(38.1602 - 52.2228i) q^{14} +(39.9807 - 69.2486i) q^{16} +(48.4888 + 83.9850i) q^{17} +(71.1636 - 123.259i) q^{19} +33.0494 q^{20} +188.600 q^{22} +(51.8936 - 89.8823i) q^{23} +(31.4897 + 54.5418i) q^{25} +(-85.4121 + 147.938i) q^{26} +(-31.4185 - 71.0884i) q^{28} -24.5329 q^{29} +(-93.6897 - 162.275i) q^{31} +(-86.4953 - 149.814i) q^{32} +338.680 q^{34} +(-86.0517 + 117.763i) q^{35} +(-73.2774 + 126.920i) q^{37} +(-248.529 - 430.465i) q^{38} +(-52.3035 + 90.5923i) q^{40} -314.180 q^{41} +173.165 q^{43} +(113.315 - 196.268i) q^{44} +(-181.231 - 313.901i) q^{46} +(-129.617 + 224.504i) q^{47} +(335.110 + 73.1434i) q^{49} +219.947 q^{50} +(102.635 + 177.769i) q^{52} +(310.429 + 537.679i) q^{53} -425.295 q^{55} +(244.584 + 26.3817i) q^{56} +(-42.8389 + 74.1991i) q^{58} +(-221.555 - 383.745i) q^{59} +(-56.6478 + 98.1168i) q^{61} -654.396 q^{62} +35.5454 q^{64} +(192.605 - 333.602i) q^{65} +(-314.488 - 544.708i) q^{67} +(203.487 - 352.450i) q^{68} +(205.909 + 465.897i) q^{70} -41.3042 q^{71} +(-223.555 - 387.209i) q^{73} +(255.911 + 443.251i) q^{74} -597.287 q^{76} +(404.307 + 914.798i) q^{77} +(-217.353 + 376.467i) q^{79} +(314.860 + 545.354i) q^{80} +(-548.615 + 950.229i) q^{82} +329.158 q^{83} -763.728 q^{85} +(302.378 - 523.734i) q^{86} +(358.662 + 621.221i) q^{88} +(-12.4354 + 21.5388i) q^{89} +(-900.670 - 97.1494i) q^{91} -435.551 q^{92} +(452.670 + 784.048i) q^{94} +(560.435 + 970.702i) q^{95} -499.239 q^{97} +(806.384 - 885.811i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.74618	−	3.02447i	0.617368	−	1.06931i	−0.372596	−	0.927994i	$-0.621532\pi$
$2$	1.74618	−	3.02447i	0.617368	−	1.06931i	0.989964	−	0.141319i	$-0.0451343\pi$
$3$		0			0
$3$		0			0
$4$	−2.09829	−	3.63435i	−0.262286	−	0.454293i
$5$	−3.93765	+	6.82022i	−0.352195	+	0.610019i	−0.986634	−	0.162954i	$-0.947898\pi$
$5$	−3.93765	+	6.82022i	−0.352195	+	0.610019i	0.634439	+	0.772973i	$0.281231\pi$
$6$		0			0
$7$	18.4135	+	1.98614i	0.994233	+	0.107242i
$7$	18.4135	+	1.98614i	0.994233	+	0.107242i
$8$	13.2829			0.587027
$9$		0			0
$10$	13.7517	+	23.8187i	0.434867	+	0.753212i
$11$	27.0018	+	46.7684i	0.740122	+	1.28193i	0.952439	+	0.304728i	$0.0985655\pi$
$11$	27.0018	+	46.7684i	0.740122	+	1.28193i	−0.212318	+	0.977201i	$0.568101\pi$
$12$		0			0
$13$	−48.9137			−1.04355			−0.521777	−	0.853082i	$-0.674731\pi$
$13$	−48.9137			−1.04355			−0.521777	+	0.853082i	$0.674731\pi$
$14$	38.1602	−	52.2228i	0.728482	−	0.996938i
$15$		0			0
$16$	39.9807	−	69.2486i	0.624698	−	1.08201i
$17$	48.4888	+	83.9850i	0.691780	+	1.19820i	0.971254	+	0.238044i	$0.0765063\pi$
$17$	48.4888	+	83.9850i	0.691780	+	1.19820i	−0.279475	+	0.960153i	$0.590160\pi$
$18$		0			0
$19$	71.1636	−	123.259i	0.859266	−	1.48829i	−0.0133650	−	0.999911i	$-0.504254\pi$
$19$	71.1636	−	123.259i	0.859266	−	1.48829i	0.872631	−	0.488381i	$-0.162412\pi$
$20$	33.0494			0.369503
$21$		0			0
$22$	188.600			1.82771
$23$	51.8936	−	89.8823i	0.470459	−	0.814859i	−0.528970	−	0.848640i	$-0.677422\pi$
$23$	51.8936	−	89.8823i	0.470459	−	0.814859i	0.999429	+	0.0337813i	$0.0107550\pi$
$24$		0			0
$25$	31.4897	+	54.5418i	0.251918	+	0.436335i
$26$	−85.4121	+	147.938i	−0.644257	+	1.11589i
$27$		0			0
$28$	−31.4185	−	71.0884i	−0.212055	−	0.479801i
$29$	−24.5329			−0.157091			−0.0785456	−	0.996911i	$-0.525028\pi$
$29$	−24.5329			−0.157091			−0.0785456	+	0.996911i	$0.525028\pi$
$30$		0			0
$31$	−93.6897	−	162.275i	−0.542812	−	0.940177i	−0.998741	−	0.0501613i	$-0.984026\pi$
$31$	−93.6897	−	162.275i	−0.542812	−	0.940177i	0.455930	−	0.890016i	$-0.349307\pi$
$32$	−86.4953	−	149.814i	−0.477824	−	0.827615i
$33$		0			0
$34$	338.680			1.70833
$35$	−86.0517	+	117.763i	−0.415583	+	0.568731i
$36$		0			0
$37$	−73.2774	+	126.920i	−0.325587	+	0.563933i	−0.981631	−	0.190789i	$-0.938895\pi$
$37$	−73.2774	+	126.920i	−0.325587	+	0.563933i	0.656044	+	0.754723i	$0.272229\pi$
$38$	−248.529	−	430.465i	−1.06097	−	1.83765i
$39$		0			0
$40$	−52.3035	+	90.5923i	−0.206748	+	0.358098i
$41$	−314.180			−1.19675			−0.598374	−	0.801217i	$-0.704186\pi$
$41$	−314.180			−1.19675			−0.598374	+	0.801217i	$0.704186\pi$
$42$		0			0
$43$	173.165			0.614127			0.307064	−	0.951689i	$-0.400654\pi$
$43$	173.165			0.614127			0.307064	+	0.951689i	$0.400654\pi$
$44$	113.315	−	196.268i	0.388248	−	0.672465i
$45$		0			0
$46$	−181.231	−	313.901i	−0.580893	−	1.00614i
$47$	−129.617	+	224.504i	−0.402269	+	0.696749i	−0.993999	−	0.109386i	$-0.965112\pi$
$47$	−129.617	+	224.504i	−0.402269	+	0.696749i	0.591731	+	0.806136i	$0.298445\pi$
$48$		0			0
$49$	335.110	+	73.1434i	0.976999	+	0.213246i
$50$	219.947			0.622104
$51$		0			0
$52$	102.635	+	177.769i	0.273710	+	0.474080i
$53$	310.429	+	537.679i	0.804541	+	1.39351i	0.916600	+	0.399805i	$0.130922\pi$
$53$	310.429	+	537.679i	0.804541	+	1.39351i	−0.112059	+	0.993702i	$0.535744\pi$
$54$		0			0
$55$	−425.295			−1.04267
$56$	244.584	+	26.3817i	0.583642	+	0.0629537i
$57$		0			0
$58$	−42.8389	+	74.1991i	−0.0969831	+	0.167980i
$59$	−221.555	−	383.745i	−0.488882	−	0.846768i	0.511036	−	0.859559i	$-0.329262\pi$
$59$	−221.555	−	383.745i	−0.488882	−	0.846768i	−0.999918	+	0.0127908i	$0.995928\pi$
$60$		0			0
$61$	−56.6478	+	98.1168i	−0.118902	+	0.205944i	−0.919333	−	0.393481i	$-0.871271\pi$
$61$	−56.6478	+	98.1168i	−0.118902	+	0.205944i	0.800431	+	0.599425i	$0.204604\pi$
$62$	−654.396			−1.34046
$63$		0			0
$64$	35.5454			0.0694245
$65$	192.605	−	333.602i	0.367534	−	0.636588i
$66$		0			0
$67$	−314.488	−	544.708i	−0.573444	−	0.993235i	−0.996209	−	0.0869950i	$-0.972274\pi$
$67$	−314.488	−	544.708i	−0.573444	−	0.993235i	0.422764	−	0.906240i	$-0.361060\pi$
$68$	203.487	−	352.450i	0.362889	−	0.628542i
$69$		0			0
$70$	205.909	+	465.897i	0.351584	+	0.795504i
$71$	−41.3042			−0.0690410			−0.0345205	−	0.999404i	$-0.510990\pi$
$71$	−41.3042			−0.0690410			−0.0345205	+	0.999404i	$0.510990\pi$
$72$		0			0
$73$	−223.555	−	387.209i	−0.358427	−	0.620814i	0.629271	−	0.777186i	$-0.283353\pi$
$73$	−223.555	−	387.209i	−0.358427	−	0.620814i	−0.987698	+	0.156372i	$0.950020\pi$
$74$	255.911	+	443.251i	0.402014	+	0.696309i
$75$		0			0
$76$	−597.287			−0.901494
$77$	404.307	+	914.798i	0.598378	+	1.35391i
$78$		0			0
$79$	−217.353	+	376.467i	−0.309546	+	0.536149i	−0.978263	−	0.207368i	$-0.933510\pi$
$79$	−217.353	+	376.467i	−0.309546	+	0.536149i	0.668717	+	0.743517i	$0.266844\pi$
$80$	314.860	+	545.354i	0.440031	+	0.762155i
$81$		0			0
$82$	−548.615	+	950.229i	−0.738834	+	1.27970i
$83$	329.158			0.435299			0.217649	−	0.976027i	$-0.430161\pi$
$83$	329.158			0.435299			0.217649	+	0.976027i	$0.430161\pi$
$84$		0			0
$85$	−763.728			−0.974564
$86$	302.378	−	523.734i	0.379143	−	0.656694i
$87$		0			0
$88$	358.662	+	621.221i	0.434472	+	0.752527i
$89$	−12.4354	+	21.5388i	−0.0148107	+	0.0256529i	−0.873336	−	0.487119i	$-0.838048\pi$
$89$	−12.4354	+	21.5388i	−0.0148107	+	0.0256529i	0.858525	+	0.512772i	$0.171381\pi$
$90$		0			0
$91$	−900.670	−	97.1494i	−1.03754	−	0.111912i
$92$	−435.551			−0.493580
$93$		0			0
$94$	452.670	+	784.048i	0.496695	+	0.860302i
$95$	560.435	+	970.702i	0.605257	+	1.04834i
$96$		0			0
$97$	−499.239			−0.522578			−0.261289	−	0.965261i	$-0.584148\pi$
$97$	−499.239			−0.522578			−0.261289	+	0.965261i	$0.584148\pi$
$98$	806.384	−	885.811i	0.831194	−	0.913066i
$99$		0			0
$100$	132.149	−	228.889i	0.132149	−	0.228889i
$101$	−129.038	−	223.501i	−0.127127	−	0.220190i	0.795436	−	0.606038i	$-0.207242\pi$
$101$	−129.038	−	223.501i	−0.127127	−	0.220190i	−0.922562	+	0.385848i	$0.873909\pi$
$102$		0			0
$103$	−480.159	+	831.659i	−0.459334	+	0.795590i	−0.998926	−	0.0463365i	$-0.985245\pi$
$103$	−480.159	+	831.659i	−0.459334	+	0.795590i	0.539592	+	0.841927i	$0.318579\pi$
$104$	−649.716			−0.612595
$105$		0			0
$106$	2168.26			1.98679
$107$	1027.13	−	1779.04i	0.928004	−	1.60735i	0.141347	−	0.989960i	$-0.454857\pi$
$107$	1027.13	−	1779.04i	0.928004	−	1.60735i	0.786657	−	0.617391i	$-0.211810\pi$
$108$		0			0
$109$	−892.052	−	1545.08i	−0.783881	−	1.35772i	−0.929665	−	0.368406i	$-0.879904\pi$
$109$	−892.052	−	1545.08i	−0.783881	−	1.35772i	0.145784	−	0.989316i	$-0.453430\pi$
$110$	−742.641	+	1286.29i	−0.643709	+	1.11494i
$111$		0			0
$112$	873.720	−	1195.70i	0.737132	−	1.00878i
$113$	−1296.36			−1.07921			−0.539607	−	0.841917i	$-0.681427\pi$
$113$	−1296.36			−1.07921			−0.539607	+	0.841917i	$0.681427\pi$
$114$		0			0
$115$	408.678	+	707.851i	0.331386	+	0.573978i
$116$	51.4772	+	89.1611i	0.0412029	+	0.0713655i
$117$		0			0
$118$	−1547.50			−1.20728
$119$	726.040	+	1642.76i	0.559294	+	1.26547i
$120$		0			0
$121$	−792.691	+	1372.98i	−0.595561	+	1.03154i
$122$	197.834	+	342.659i	0.146812	+	0.254286i
$123$		0			0
$124$	−393.176	+	681.001i	−0.284744	+	0.493191i
$125$	−1480.40			−1.05929
$126$		0			0
$127$	−312.058			−0.218037			−0.109018	−	0.994040i	$-0.534771\pi$
$127$	−312.058			−0.218037			−0.109018	+	0.994040i	$0.534771\pi$
$128$	754.031	−	1306.02i	0.520684	−	0.901851i
$129$		0			0
$130$	−672.647	−	1165.06i	−0.453808	−	0.786018i
$131$	−41.6352	+	72.1143i	−0.0277686	+	0.0480966i	−0.879576	−	0.475759i	$-0.842173\pi$
$131$	−41.6352	+	72.1143i	−0.0277686	+	0.0480966i	0.851807	+	0.523855i	$0.175507\pi$
$132$		0			0
$133$	1555.18	−	2128.28i	1.01392	−	1.38756i
$134$	−2196.61			−1.41610
$135$		0			0
$136$	644.072	+	1115.57i	0.406093	+	0.703374i
$137$	−1454.79	−	2519.77i	−0.907233	−	1.57137i	−0.817891	−	0.575373i	$-0.804857\pi$
$137$	−1454.79	−	2519.77i	−0.907233	−	1.57137i	−0.0893421	−	0.996001i	$-0.528476\pi$
$138$		0			0
$139$	1414.91			0.863392			0.431696	−	0.902019i	$-0.357915\pi$
$139$	1414.91			0.863392			0.431696	+	0.902019i	$0.357915\pi$
$140$	608.553	+	65.6407i	0.367372	+	0.0396261i
$141$		0			0
$142$	−72.1246	+	124.923i	−0.0426237	+	0.0738264i
$143$	−1320.76	−	2287.62i	−0.772358	−	1.33776i
$144$		0			0
$145$	96.6021	−	167.320i	0.0553267	−	0.0958286i
$146$	−1561.47			−0.885125
$147$		0			0
$148$	615.029			0.341588
$149$	−1093.31	+	1893.67i	−0.601125	+	1.04118i	0.391526	+	0.920167i	$0.371947\pi$
$149$	−1093.31	+	1893.67i	−0.601125	+	1.04118i	−0.992651	+	0.121012i	$0.961386\pi$
$150$		0			0
$151$	−819.629	−	1419.64i	−0.441725	−	0.765090i	0.556093	−	0.831120i	$-0.312300\pi$
$151$	−819.629	−	1419.64i	−0.441725	−	0.765090i	−0.997818	+	0.0660304i	$0.978967\pi$
$152$	945.259	−	1637.24i	0.504412	−	0.873668i
$153$		0			0
$154$	3472.77	+	374.586i	1.81717	+	0.196006i
$155$	1475.67			0.764701
$156$		0			0
$157$	−629.491	−	1090.31i	−0.319993	−	0.554244i	0.660493	−	0.750832i	$-0.270347\pi$
$157$	−629.491	−	1090.31i	−0.319993	−	0.554244i	−0.980486	+	0.196588i	$0.937014\pi$
$158$	759.075	+	1314.76i	0.382207	+	0.662003i
$159$		0			0
$160$	1362.35			0.673147
$161$	1134.06	−	1551.98i	0.555133	−	0.759707i
$162$		0			0
$163$	1579.50	−	2735.78i	0.758995	−	1.31462i	−0.184368	−	0.982857i	$-0.559024\pi$
$163$	1579.50	−	2735.78i	0.758995	−	1.31462i	0.943364	−	0.331761i	$-0.107643\pi$
$164$	659.241	+	1141.84i	0.313891	+	0.543675i
$165$		0			0
$166$	574.769	−	995.530i	0.268739	−	0.465470i
$167$	−1848.90			−0.856718			−0.428359	−	0.903609i	$-0.640908\pi$
$167$	−1848.90			−0.856718			−0.428359	+	0.903609i	$0.640908\pi$
$168$		0			0
$169$	195.548			0.0890068
$170$	−1333.61	+	2309.87i	−0.601665	+	1.04211i
$171$		0			0
$172$	−363.351	−	629.343i	−0.161077	−	0.278994i
$173$	311.578	−	539.669i	0.136930	−	0.237169i	−0.789403	−	0.613875i	$-0.789610\pi$
$173$	311.578	−	539.669i	0.136930	−	0.237169i	0.926333	+	0.376706i	$0.122943\pi$
$174$		0			0
$175$	471.507	+	1066.85i	0.203672	+	0.460834i
$176$	4318.20			1.84941
$177$		0			0
$178$	43.4290	+	75.2213i	0.0182873	+	0.0316746i
$179$	1170.33	+	2027.07i	0.488685	+	0.846427i	0.999915	−	0.0130168i	$-0.00414349\pi$
$179$	1170.33	+	2027.07i	0.488685	+	0.846427i	−0.511230	+	0.859444i	$0.670810\pi$
$180$		0			0
$181$	−461.896			−0.189682			−0.0948411	−	0.995492i	$-0.530234\pi$
$181$	−461.896			−0.189682			−0.0948411	+	0.995492i	$0.530234\pi$
$182$	−1866.56	+	2554.41i	−0.760211	+	1.04036i
$183$		0			0
$184$	689.298	−	1193.90i	0.276172	−	0.478345i
$185$	−577.082	−	999.535i	−0.229340	−	0.397229i
$186$		0			0
$187$	−2618.56	+	4535.49i	−1.02400	+	1.77362i
$188$	1087.90			0.422038
$189$		0			0
$190$	3914.48			1.49467
$191$	1332.90	−	2308.65i	0.504948	−	0.874596i	−0.495036	−	0.868873i	$-0.664845\pi$
$191$	1332.90	−	2308.65i	0.504948	−	0.874596i	0.999984	−	0.00572288i	$-0.00182166\pi$
$192$		0			0
$193$	−65.2845	−	113.076i	−0.0243486	−	0.0421730i	0.853594	−	0.520938i	$-0.174418\pi$
$193$	−65.2845	−	113.076i	−0.0243486	−	0.0421730i	−0.877943	+	0.478765i	$0.841085\pi$
$194$	−871.761	+	1509.93i	−0.322623	+	0.558799i
$195$		0			0
$196$	−437.331	−	1371.38i	−0.159377	−	0.499775i
$197$	3729.51			1.34882			0.674408	−	0.738359i	$-0.264399\pi$
$197$	3729.51			1.34882			0.674408	+	0.738359i	$0.264399\pi$
$198$		0			0
$199$	1886.38	+	3267.30i	0.671968	+	1.16388i	0.977345	+	0.211652i	$0.0678842\pi$
$199$	1886.38	+	3267.30i	0.671968	+	1.16388i	−0.305377	+	0.952232i	$0.598782\pi$
$200$	418.275	+	724.474i	0.147883	+	0.256140i
$201$		0			0
$202$	−901.296			−0.313935
$203$	−451.736	−	48.7258i	−0.156185	−	0.0168467i
$204$		0			0
$205$	1237.13	−	2142.78i	0.421488	−	0.730039i
$206$	1676.89	+	2904.45i	0.567157	+	0.982344i
$207$		0			0
$208$	−1955.60	+	3387.20i	−0.651907	+	1.12914i
$209$	7686.17			2.54384
$210$		0			0
$211$	2398.28			0.782484			0.391242	−	0.920288i	$-0.372046\pi$
$211$	2398.28			0.782484			0.391242	+	0.920288i	$0.372046\pi$
$212$	1302.74	−	2256.41i	0.422040	−	0.730995i
$213$		0			0
$214$	−3587.11	−	6213.06i	−1.14584	−	1.98465i
$215$	−681.866	+	1181.03i	−0.216292	+	0.374629i
$216$		0			0
$217$	−1402.85	−	3174.13i	−0.438855	−	0.992967i
$218$	−6230.73			−1.93577
$219$		0			0
$220$	892.392	+	1545.67i	0.273477	+	0.473677i
$221$	−2371.76	−	4108.02i	−0.721910	−	1.25038i
$222$		0			0
$223$	−3338.23			−1.00244			−0.501220	−	0.865320i	$-0.667115\pi$
$223$	−3338.23			−1.00244			−0.501220	+	0.865320i	$0.667115\pi$
$224$	−1295.12	−	2930.39i	−0.386313	−	0.874084i
$225$		0			0
$226$	−2263.68	+	3920.80i	−0.666272	+	1.15402i
$227$	−634.521	−	1099.02i	−0.185527	−	0.321342i	0.758227	−	0.651991i	$-0.226066\pi$
$227$	−634.521	−	1099.02i	−0.185527	−	0.321342i	−0.943754	+	0.330649i	$0.892733\pi$
$228$		0			0
$229$	1025.74	−	1776.63i	0.295995	−	0.512678i	−0.679221	−	0.733934i	$-0.737682\pi$
$229$	1025.74	−	1776.63i	0.295995	−	0.512678i	0.975216	+	0.221256i	$0.0710155\pi$
$230$	2854.50			0.818349
$231$		0			0
$232$	−325.868			−0.0922169
$233$	−2475.22	+	4287.20i	−0.695953	+	1.20543i	0.273906	+	0.961756i	$0.411684\pi$
$233$	−2475.22	+	4287.20i	−0.695953	+	1.20543i	−0.969859	+	0.243669i	$0.921649\pi$
$234$		0			0
$235$	−1020.78	−	1768.04i	−0.283354	−	0.490783i
$236$	−929.774	+	1610.42i	−0.256454	+	0.444192i
$237$		0			0
$238$	6236.28	+	672.667i	1.69848	+	0.183204i
$239$	262.671			0.0710910			0.0355455	−	0.999368i	$-0.488683\pi$
$239$	262.671			0.0710910			0.0355455	+	0.999368i	$0.488683\pi$
$240$		0			0
$241$	−1451.19	−	2513.53i	−0.387880	−	0.671829i	0.604284	−	0.796769i	$-0.293459\pi$
$241$	−1451.19	−	2513.53i	−0.387880	−	0.671829i	−0.992164	+	0.124941i	$0.960126\pi$
$242$	2768.36	+	4794.95i	0.735360	+	1.27368i
$243$		0			0
$244$	475.454			0.124745
$245$	−1818.40	+	1997.51i	−0.474178	+	0.520883i
$246$		0			0
$247$	−3480.87	+	6029.05i	−0.896691	+	1.55311i
$248$	−1244.47	−	2155.49i	−0.318645	−	0.551910i
$249$		0			0
$250$	−2585.04	+	4477.42i	−0.653969	+	1.13271i
$251$	−6265.68			−1.57564			−0.787821	−	0.615904i	$-0.788791\pi$
$251$	−6265.68			−1.57564			−0.787821	+	0.615904i	$0.788791\pi$
$252$		0			0
$253$	5604.87			1.39279
$254$	−544.909	+	943.810i	−0.134609	+	0.233149i
$255$		0			0
$256$	−2491.17	−	4314.83i	−0.608195	−	1.05342i
$257$	1710.48	−	2962.64i	0.415163	−	0.719083i	−0.580283	−	0.814415i	$-0.697058\pi$
$257$	1710.48	−	2962.64i	0.415163	−	0.719083i	0.995446	+	0.0953322i	$0.0303913\pi$
$258$		0			0
$259$	−1601.37	+	2191.50i	−0.384187	+	0.525765i
$260$	−1616.57			−0.385597
$261$		0			0
$262$	145.405	+	251.849i	0.0342869	+	0.0593866i
$263$	−4111.26	−	7120.91i	−0.963921	−	1.66956i	−0.712486	−	0.701686i	$-0.752431\pi$
$263$	−4111.26	−	7120.91i	−0.963921	−	1.66956i	−0.251435	−	0.967874i	$-0.580902\pi$
$264$		0			0
$265$	−4889.45			−1.13342
$266$	−3721.31	−	8419.95i	−0.857775	−	1.94083i
$267$		0			0
$268$	−1319.77	+	2285.91i	−0.300813	+	0.521024i
$269$	2746.67	+	4757.37i	0.622555	+	1.07830i	0.989008	+	0.147860i	$0.0472386\pi$
$269$	2746.67	+	4757.37i	0.622555	+	1.07830i	−0.366453	+	0.930436i	$0.619428\pi$
$270$		0			0
$271$	548.242	−	949.584i	0.122891	−	0.212853i	−0.798016	−	0.602637i	$-0.794117\pi$
$271$	548.242	−	949.584i	0.122891	−	0.212853i	0.920906	+	0.389784i	$0.127450\pi$
$272$	7754.45			1.72861
$273$		0			0
$274$	−10161.3			−2.24039
$275$	−1700.56	+	2945.45i	−0.372900	+	0.645882i
$276$		0			0
$277$	777.736	+	1347.08i	0.168699	+	0.292195i	0.937963	−	0.346736i	$-0.112710\pi$
$277$	777.736	+	1347.08i	0.168699	+	0.292195i	−0.769264	+	0.638931i	$0.779377\pi$
$278$	2470.70	−	4279.37i	0.533030	−	0.923236i
$279$		0			0
$280$	−1143.02	+	1564.24i	−0.243958	+	0.333861i
$281$	995.950			0.211435			0.105718	−	0.994396i	$-0.466286\pi$
$281$	995.950			0.211435			0.105718	+	0.994396i	$0.466286\pi$
$282$		0			0
$283$	4317.74	+	7478.54i	0.906936	+	1.57086i	0.818297	+	0.574795i	$0.194918\pi$
$283$	4317.74	+	7478.54i	0.906936	+	1.57086i	0.0886383	+	0.996064i	$0.471748\pi$
$284$	86.6683	+	150.114i	0.0181085	+	0.0313648i
$285$		0			0
$286$	−9225.11			−1.90732
$287$	−5785.14	−	624.006i	−1.18985	−	0.128341i
$288$		0			0
$289$	−2245.82	+	3889.87i	−0.457118	+	0.791751i
$290$	−337.369	−	584.341i	−0.0683139	−	0.118323i
$291$		0			0
$292$	−938.168	+	1624.95i	−0.188021	+	0.325662i
$293$	2180.01			0.434667			0.217333	−	0.976097i	$-0.430264\pi$
$293$	2180.01			0.434667			0.217333	+	0.976097i	$0.430264\pi$
$294$		0			0
$295$	3489.63			0.688726
$296$	−973.336	+	1685.87i	−0.191128	+	0.331044i
$297$		0			0
$298$	3818.24	+	6613.39i	0.742231	+	1.28558i
$299$	−2538.31	+	4396.48i	−0.490950	+	0.850350i
$300$		0			0
$301$	3188.57	+	343.931i	0.610586	+	0.0658600i
$302$	−5724.88			−1.09083
$303$		0			0
$304$	−5690.34	−	9855.95i	−1.07356	−	1.85947i
$305$	−446.119	−	772.700i	−0.0837531	−	0.145065i
$306$		0			0
$307$	5281.18			0.981800			0.490900	−	0.871216i	$-0.336668\pi$
$307$	5281.18			0.981800			0.490900	+	0.871216i	$0.336668\pi$
$308$	2476.34	−	3388.90i	0.458125	−	0.626950i
$309$		0			0
$310$	2576.79	−	4463.12i	0.472102	−	0.817705i
$311$	2148.74	+	3721.72i	0.391780	+	0.678584i	0.992684	−	0.120738i	$-0.0385260\pi$
$311$	2148.74	+	3721.72i	0.391780	+	0.678584i	−0.600904	+	0.799321i	$0.705193\pi$
$312$		0			0
$313$	1180.48	−	2044.65i	0.213178	−	0.369235i	−0.739529	−	0.673124i	$-0.764952\pi$
$313$	1180.48	−	2044.65i	0.213178	−	0.369235i	0.952707	+	0.303889i	$0.0982852\pi$
$314$	−4396.82			−0.790213
$315$		0			0
$316$	1824.28			0.324759
$317$	−4546.33	+	7874.47i	−0.805512	+	1.39519i	0.110433	+	0.993884i	$0.464776\pi$
$317$	−4546.33	+	7874.47i	−0.805512	+	1.39519i	−0.915945	+	0.401304i	$0.868557\pi$
$318$		0			0
$319$	−662.432	−	1147.37i	−0.116267	−	0.201380i
$320$	−139.965	+	242.427i	−0.0244509	+	0.0423503i
$321$		0			0
$322$	−2713.64	−	6139.96i	−0.469643	−	1.06263i
$323$	13802.5			2.37769
$324$		0			0
$325$	−1540.28	−	2667.84i	−0.262890	−	0.455339i
$326$	−5516.19	−	9554.33i	−0.937158	−	1.62321i
$327$		0			0
$328$	−4173.23			−0.702524
$329$	−2832.60	+	3876.45i	−0.474669	+	0.649591i
$330$		0			0
$331$	−2189.51	+	3792.34i	−0.363584	+	0.629745i	−0.988548	−	0.150908i	$-0.951780\pi$
$331$	−2189.51	+	3792.34i	−0.363584	+	0.629745i	0.624964	+	0.780653i	$0.285114\pi$
$332$	−690.669	−	1196.27i	−0.114173	−	0.197753i
$333$		0			0
$334$	−3228.51	+	5591.94i	−0.528910	+	0.916100i
$335$	4953.37			0.807856
$336$		0			0
$337$	3314.59			0.535778			0.267889	−	0.963450i	$-0.413674\pi$
$337$	3314.59			0.535778			0.267889	+	0.963450i	$0.413674\pi$
$338$	341.462	−	591.429i	0.0549499	−	0.0951760i
$339$		0			0
$340$	1602.52	+	2775.65i	0.255615	+	0.442738i
$341$	5059.57	−	8763.44i	0.803493	−	1.39169i
$342$		0			0
$343$	6025.27	+	2012.40i	0.948495	+	0.316791i
$344$	2300.14			0.360510
$345$		0			0
$346$	−1088.14	−	1884.72i	−0.169072	−	0.292842i
$347$	4276.94	+	7407.87i	0.661666	+	1.14604i	0.980178	+	0.198120i	$0.0634835\pi$
$347$	4276.94	+	7407.87i	0.661666	+	1.14604i	−0.318512	+	0.947919i	$0.603183\pi$
$348$		0			0
$349$	9832.96			1.50816			0.754078	−	0.656785i	$-0.228084\pi$
$349$	9832.96			1.50816			0.754078	+	0.656785i	$0.228084\pi$
$350$	4049.99	+	436.846i	0.618517	+	0.0667154i
$351$		0			0
$352$	4671.05	−	8090.50i	0.707295	−	1.22507i
$353$	−3085.71	−	5344.60i	−0.465257	−	0.805848i	0.533957	−	0.845512i	$-0.320705\pi$
$353$	−3085.71	−	5344.60i	−0.465257	−	0.805848i	−0.999213	+	0.0396640i	$0.987371\pi$
$354$		0			0
$355$	162.642	−	281.704i	0.0243159	−	0.0421163i
$356$	104.373			0.0155386
$357$		0			0
$358$	8174.43			1.20679
$359$	−4773.51	+	8267.96i	−0.701772	+	1.21551i	0.266072	+	0.963953i	$0.414274\pi$
$359$	−4773.51	+	8267.96i	−0.701772	+	1.21551i	−0.967844	+	0.251552i	$0.919059\pi$
$360$		0			0
$361$	−6699.01	−	11603.0i	−0.976675	−	1.69165i
$362$	−806.554	+	1396.99i	−0.117104	+	0.202830i
$363$		0			0
$364$	1536.79	+	3477.19i	0.221291	+	0.500699i
$365$	3521.14			0.504944
$366$		0			0
$367$	2014.34	+	3488.94i	0.286506	+	0.496243i	0.972973	−	0.230918i	$-0.0741728\pi$
$367$	2014.34	+	3488.94i	0.286506	+	0.496243i	−0.686467	+	0.727161i	$0.740839\pi$
$368$	−4149.48	−	7187.11i	−0.587790	−	1.01808i
$369$		0			0
$370$	−4030.76			−0.566349
$371$	4648.16	+	10517.1i	0.650460	+	1.47175i
$372$		0			0
$373$	−10.0254	+	17.3646i	−0.00139168	+	0.00241046i	−0.866720	−	0.498794i	$-0.833776\pi$
$373$	−10.0254	+	17.3646i	−0.00139168	+	0.00241046i	0.865329	+	0.501205i	$0.167110\pi$
$374$	9144.97	+	15839.6i	1.26437	+	2.18996i
$375$		0			0
$376$	−1721.69	+	2982.06i	−0.236143	+	0.409011i
$377$	1199.99			0.163933
$378$		0			0
$379$	−3787.79			−0.513366			−0.256683	−	0.966496i	$-0.582630\pi$
$379$	−3787.79			−0.513366			−0.256683	+	0.966496i	$0.582630\pi$
$380$	2351.91	−	4073.63i	0.317501	−	0.549929i
$381$		0			0
$382$	−4654.96	−	8062.62i	−0.623477	−	1.07989i
$383$	4000.86	−	6929.69i	0.533771	−	0.924519i	−0.465451	−	0.885074i	$-0.654108\pi$
$383$	4000.86	−	6929.69i	0.533771	−	0.924519i	0.999222	−	0.0394450i	$-0.0125590\pi$
$384$		0			0
$385$	−7831.14	−	844.695i	−1.03665	−	0.111817i
$386$	−455.994			−0.0601282
$387$		0			0
$388$	1047.55	+	1814.41i	0.137065	+	0.237404i
$389$	1742.32	+	3017.79i	0.227093	+	0.393336i	0.956945	−	0.290268i	$-0.0937446\pi$
$389$	1742.32	+	3017.79i	0.227093	+	0.393336i	−0.729852	+	0.683605i	$0.760411\pi$
$390$		0			0
$391$	10065.0			1.30182
$392$	4451.24	+	971.557i	0.573525	+	0.125181i
$393$		0			0
$394$	6512.40	−	11279.8i	0.832716	−	1.44231i
$395$	−1711.72	−	2964.79i	−0.218041	−	0.377658i
$396$		0			0
$397$	3518.88	−	6094.88i	0.444855	−	0.770512i	−0.553187	−	0.833057i	$-0.686589\pi$
$397$	3518.88	−	6094.88i	0.444855	−	0.770512i	0.998042	+	0.0625455i	$0.0199218\pi$
$398$	13175.8			1.65941
$399$		0			0
$400$	5035.93			0.629491
$401$	−4194.86	+	7265.72i	−0.522398	+	0.904820i	0.477263	+	0.878761i	$0.341629\pi$
$401$	−4194.86	+	7265.72i	−0.522398	+	0.904820i	−0.999660	+	0.0260589i	$0.991704\pi$
$402$		0			0
$403$	4582.71	+	7937.48i	0.566454	+	0.981126i
$404$	−541.519	+	937.939i	−0.0666871	+	0.115505i
$405$		0			0
$406$	−936.182	+	1281.18i	−0.114438	+	0.156610i
$407$	−7914.47			−0.963896
$408$		0			0
$409$	6772.75	+	11730.7i	0.818804	+	1.41821i	0.906564	+	0.422068i	$0.138696\pi$
$409$	6772.75	+	11730.7i	0.818804	+	1.41821i	−0.0877604	+	0.996142i	$0.527971\pi$
$410$	−4320.51	−	7483.35i	−0.520427	−	0.901406i
$411$		0			0
$412$	4030.05			0.481908
$413$	−3317.43	−	7506.11i	−0.395254	−	0.894313i
$414$		0			0
$415$	−1296.11	+	2244.93i	−0.153310	+	0.265540i
$416$	4230.80	+	7327.97i	0.498635	+	0.863661i
$417$		0			0
$418$	13421.4	−	23246.6i	1.57049	−	2.72017i
$419$	−1450.22			−0.169089			−0.0845443	−	0.996420i	$-0.526943\pi$
$419$	−1450.22			−0.169089			−0.0845443	+	0.996420i	$0.526943\pi$
$420$		0			0
$421$	−923.118			−0.106865			−0.0534324	−	0.998571i	$-0.517016\pi$
$421$	−923.118			−0.106865			−0.0534324	+	0.998571i	$0.517016\pi$
$422$	4187.82	−	7253.52i	0.483080	−	0.836720i
$423$		0			0
$424$	4123.40	+	7141.94i	0.472288	+	0.818026i
$425$	−3053.80	+	5289.33i	−0.348543	+	0.603695i
$426$		0			0
$427$	−1237.95	+	1694.16i	−0.140302	+	0.192005i
$428$	−8620.87			−0.973611
$429$		0			0
$430$	2381.32	+	4124.57i	0.267064	+	0.462568i
$431$	−619.105	−	1072.32i	−0.0691908	−	0.119842i	0.829355	−	0.558723i	$-0.188708\pi$
$431$	−619.105	−	1072.32i	−0.0691908	−	0.119842i	−0.898545	+	0.438881i	$0.855375\pi$
$432$		0			0
$433$	10786.5			1.19715			0.598575	−	0.801067i	$-0.295734\pi$
$433$	10786.5			1.19715			0.598575	+	0.801067i	$0.295734\pi$
$434$	−12049.7	−	1299.72i	−1.33273	−	0.143753i
$435$		0			0
$436$	−3743.57	+	6484.05i	−0.411203	+	0.712224i
$437$	−7385.87	−	12792.7i	−0.808499	−	1.40036i
$438$		0			0
$439$	−1676.75	+	2904.21i	−0.182293	+	0.315741i	−0.942661	−	0.333752i	$-0.891685\pi$
$439$	−1676.75	+	2904.21i	−0.182293	+	0.315741i	0.760368	+	0.649493i	$0.225019\pi$
$440$	−5649.15			−0.612074
$441$		0			0
$442$	−16566.1			−1.78274
$443$	4045.18	−	7006.46i	0.433843	−	0.751438i	−0.563358	−	0.826213i	$-0.690491\pi$
$443$	4045.18	−	7006.46i	0.433843	−	0.751438i	0.997200	+	0.0747756i	$0.0238240\pi$
$444$		0			0
$445$	−97.9329	−	169.625i	−0.0104325	−	0.0180696i
$446$	−5829.14	+	10096.4i	−0.618874	+	1.07192i
$447$		0			0
$448$	654.513	+	70.5981i	0.0690241	+	0.00744519i
$449$	−4211.19			−0.442625			−0.221312	−	0.975203i	$-0.571034\pi$
$449$	−4211.19			−0.442625			−0.221312	+	0.975203i	$0.571034\pi$
$450$		0			0
$451$	−8483.42	−	14693.7i	−0.885740	−	1.53415i
$452$	2720.14	+	4711.42i	0.283063	+	0.490280i
$453$		0			0
$454$	−4431.95			−0.458154
$455$	4209.11	−	5760.22i	0.433683	−	0.593502i
$456$		0			0
$457$	4888.81	−	8467.67i	0.500413	−	0.866741i	−0.499587	−	0.866264i	$-0.666515\pi$
$457$	4888.81	−	8467.67i	0.500413	−	0.866741i	1.00000		0.000477301i	$-0.000151930\pi$
$458$	−3582.26	−	6204.65i	−0.365476	−	0.633022i
$459$		0			0
$460$	1715.05	−	2970.55i	0.173836	−	0.301093i
$461$	−12360.4			−1.24876			−0.624381	−	0.781120i	$-0.714649\pi$
$461$	−12360.4			−1.24876			−0.624381	+	0.781120i	$0.714649\pi$
$462$		0			0
$463$	−16107.0			−1.61675			−0.808377	−	0.588666i	$-0.799653\pi$
$463$	−16107.0			−1.61675			−0.808377	+	0.588666i	$0.799653\pi$
$464$	−980.842	+	1698.87i	−0.0981346	+	0.169974i
$465$		0			0
$466$	8644.35	+	14972.5i	0.859318	+	1.48838i
$467$	6742.68	−	11678.7i	0.668125	−	1.15723i	−0.310303	−	0.950638i	$-0.600431\pi$
$467$	6742.68	−	11678.7i	0.668125	−	1.15723i	0.978428	−	0.206588i	$-0.0662360\pi$
$468$		0			0
$469$	−4708.93	−	10654.6i	−0.463621	−	1.04900i
$470$	−7129.84			−0.699734
$471$		0			0
$472$	−2942.90	−	5097.25i	−0.286987	−	0.497076i
$473$	4675.77	+	8098.68i	0.454529	+	0.787268i
$474$		0			0
$475$	8963.69			0.865858
$476$	4446.91	−	6085.67i	0.428202	−	0.586000i
$477$		0			0
$478$	458.670	−	794.440i	0.0438893	−	0.0760185i
$479$	195.482	+	338.585i	0.0186468	+	0.0322972i	0.875198	−	0.483764i	$-0.160731\pi$
$479$	195.482	+	338.585i	0.0186468	+	0.0322972i	−0.856551	+	0.516062i	$0.827398\pi$
$480$		0			0
$481$	3584.26	−	6208.13i	0.339768	−	0.588495i
$482$	−10136.1			−0.957860
$483$		0			0
$484$	6653.18			0.624830
$485$	1965.83	−	3404.92i	0.184049	−	0.318782i
$486$		0			0
$487$	7895.75	+	13675.8i	0.734683	+	1.27251i	0.954862	+	0.297049i	$0.0960026\pi$
$487$	7895.75	+	13675.8i	0.734683	+	1.27251i	−0.220179	+	0.975460i	$0.570664\pi$
$488$	−752.447	+	1303.28i	−0.0697985	+	0.120895i
$489$		0			0
$490$	2866.16	+	8987.73i	0.264245	+	0.828621i
$491$	191.606			0.0176111			0.00880557	−	0.999961i	$-0.497197\pi$
$491$	191.606			0.0176111			0.00880557	+	0.999961i	$0.497197\pi$
$492$		0			0
$493$	−1189.57	−	2060.40i	−0.108673	−	0.188226i
$494$	12156.5	+	21055.6i	1.10718	+	1.91769i
$495$		0			0
$496$	−14983.1			−1.35637
$497$	−760.553	−	82.0360i	−0.0686428	−	0.00740406i
$498$		0			0
$499$	−2810.50	+	4867.93i	−0.252135	+	0.436710i	−0.964113	−	0.265491i	$-0.914466\pi$
$499$	−2810.50	+	4867.93i	−0.252135	+	0.436710i	0.711979	+	0.702201i	$0.247799\pi$
$500$	3106.30	+	5380.27i	0.277836	+	0.481226i
$501$		0			0
$502$	−10941.0	+	18950.4i	−0.972751	+	1.68485i
$503$	−16936.3			−1.50129			−0.750647	−	0.660704i	$-0.770258\pi$
$503$	−16936.3			−1.50129			−0.750647	+	0.660704i	$0.770258\pi$
$504$		0			0
$505$	2032.43			0.179093
$506$	9787.12	−	16951.8i	0.859863	−	1.48933i
$507$		0			0
$508$	654.788	+	1134.13i	0.0571880	+	0.0990526i
$509$	2112.88	−	3659.62i	0.183992	−	0.318684i	−0.759244	−	0.650806i	$-0.774431\pi$
$509$	2112.88	−	3659.62i	0.183992	−	0.318684i	0.943236	+	0.332122i	$0.107765\pi$
$510$		0			0
$511$	−3347.37	−	7573.87i	−0.289783	−	0.655672i
$512$	−5335.61			−0.460552
$513$		0			0
$514$	−5973.61	−	10346.6i	−0.512616	−	0.887877i
$515$	−3781.40	−	6549.57i	−0.323550	−	0.560405i
$516$		0			0
$517$	−13999.6			−1.19091
$518$	3831.85	+	8670.05i	0.325022	+	0.735406i
$519$		0			0
$520$	2558.36	−	4431.20i	0.215753	−	0.373695i
$521$	−2042.06	−	3536.95i	−0.171716	−	0.297421i	0.767304	−	0.641284i	$-0.221598\pi$
$521$	−2042.06	−	3536.95i	−0.171716	−	0.297421i	−0.939020	+	0.343863i	$0.888265\pi$
$522$		0			0
$523$	−8485.69	+	14697.7i	−0.709471	+	1.22884i	0.255582	+	0.966787i	$0.417733\pi$
$523$	−8485.69	+	14697.7i	−0.709471	+	1.22884i	−0.965054	+	0.262053i	$0.915601\pi$
$524$	349.451			0.0291333
$525$		0			0
$526$	−28716.0			−2.38038
$527$	9085.79	−	15737.1i	0.751012	−	1.30079i
$528$		0			0
$529$	697.611	+	1208.30i	0.0573363	+	0.0993095i
$530$	−8537.86	+	14788.0i	−0.699737	+	1.21198i
$531$		0			0
$532$	−10998.1	−	1186.30i	−0.896295	−	0.0966776i
$533$	15367.7			1.24887
$534$		0			0
$535$	8088.97	+	14010.5i	0.653676	+	1.13220i
$536$	−4177.31	−	7235.31i	−0.336627	−	0.583056i
$537$		0			0
$538$	19184.7			1.53738
$539$	5627.77	+	17647.6i	0.449732	+	1.41027i
$540$		0			0
$541$	−315.493	+	546.451i	−0.0250723	+	0.0434265i	−0.878289	−	0.478130i	$-0.841315\pi$
$541$	−315.493	+	546.451i	−0.0250723	+	0.0434265i	0.853217	+	0.521556i	$0.174648\pi$
$542$	−1914.66	−	3316.29i	−0.151737	−	0.262817i
$543$		0			0
$544$	8388.10	−	14528.6i	0.661097	−	1.14505i
$545$	14050.4			1.10431
$546$		0			0
$547$	14377.3			1.12382			0.561910	−	0.827198i	$-0.310067\pi$
$547$	14377.3			1.12382			0.561910	+	0.827198i	$0.310067\pi$
$548$	−6105.14	+	10574.4i	−0.475910	+	0.824300i
$549$		0			0
$550$	5938.96	+	10286.6i	0.460433	+	0.797493i
$551$	−1745.85	+	3023.90i	−0.134983	+	0.233798i
$552$		0			0
$553$	−4749.94	+	6500.35i	−0.365258	+	0.499861i
$554$	5432.27			0.416598
$555$		0			0
$556$	−2968.90	−	5142.29i	−0.226456	−	0.392233i
$557$	6374.78	+	11041.4i	0.484934	+	0.839930i	0.999850	−	0.0173106i	$-0.00551041\pi$
$557$	6374.78	+	11041.4i	0.484934	+	0.839930i	−0.514917	+	0.857240i	$0.672177\pi$
$558$		0			0
$559$	−8470.16			−0.640876
$560$	4714.51	+	10667.2i	0.355758	+	0.804949i
$561$		0			0
$562$	1739.11	−	3012.22i	0.130533	−	0.226091i
$563$	−7040.02	−	12193.7i	−0.527001	−	0.912792i	−0.999505	−	0.0314637i	$-0.989983\pi$
$563$	−7040.02	−	12193.7i	−0.527001	−	0.912792i	0.472504	−	0.881328i	$-0.343350\pi$
$564$		0			0
$565$	5104.61	−	8841.45i	0.380093	−	0.658341i
$566$	30158.2			2.23965
$567$		0			0
$568$	−548.640			−0.0405289
$569$	488.954	−	846.893i	0.0360246	−	0.0623965i	−0.847451	−	0.530874i	$-0.821864\pi$
$569$	488.954	−	846.893i	0.0360246	−	0.0623965i	0.883476	+	0.468477i	$0.155197\pi$
$570$		0			0
$571$	2438.76	+	4224.06i	0.178737	+	0.309582i	0.941448	−	0.337157i	$-0.109465\pi$
$571$	2438.76	+	4224.06i	0.178737	+	0.309582i	−0.762711	+	0.646740i	$0.776132\pi$
$572$	−5542.66	+	9600.17i	−0.405158	+	0.701754i
$573$		0			0
$574$	−11989.2	+	16407.4i	−0.871810	+	1.19308i
$575$	6536.46			0.474068
$576$		0			0
$577$	−4436.83	−	7684.82i	−0.320117	−	0.554460i	0.660395	−	0.750919i	$-0.270389\pi$
$577$	−4436.83	−	7684.82i	−0.320117	−	0.554460i	−0.980512	+	0.196459i	$0.937056\pi$
$578$	7843.21	+	13584.8i	0.564420	+	0.977604i
$579$		0			0
$580$	−810.797			−0.0580457
$581$	6060.94	+	653.754i	0.432788	+	0.0466821i
$582$		0			0
$583$	−16764.3	+	29036.6i	−1.19092	+	2.06273i
$584$	−2969.47	−	5143.27i	−0.210406	−	0.364435i
$585$		0			0
$586$	3806.69	−	6593.37i	0.268349	−	0.464795i
$587$	−17470.2			−1.22840			−0.614201	−	0.789150i	$-0.710521\pi$
$587$	−17470.2			−1.22840			−0.614201	+	0.789150i	$0.710521\pi$
$588$		0			0
$589$	−26669.2			−1.86568
$590$	6093.53	−	10554.3i	0.425198	−	0.736464i
$591$		0			0
$592$	5859.36	+	10148.7i	0.406787	+	0.704576i
$593$	−8785.24	+	15216.5i	−0.608376	+	1.05374i	0.383133	+	0.923693i	$0.374845\pi$
$593$	−8785.24	+	15216.5i	−0.608376	+	1.05374i	−0.991508	+	0.130044i	$0.958488\pi$
$594$		0			0
$595$	−14062.9	−	1516.87i	−0.968944	−	0.104514i
$596$	9176.35			0.630668
$597$		0			0
$598$	8864.68	+	15354.1i	0.606194	+	1.04996i
$599$	1235.30	+	2139.61i	0.0842623	+	0.145947i	0.905077	−	0.425249i	$-0.139813\pi$
$599$	1235.30	+	2139.61i	0.0842623	+	0.145947i	−0.820814	+	0.571195i	$0.806480\pi$
$600$		0			0
$601$	−7760.05			−0.526688			−0.263344	−	0.964702i	$-0.584825\pi$
$601$	−7760.05			−0.526688			−0.263344	+	0.964702i	$0.584825\pi$
$602$	6608.03	−	9043.19i	0.447381	−	0.612247i
$603$		0			0
$604$	−3439.64	+	5957.63i	−0.231717	+	0.401345i
$605$	−6242.69	−	10812.7i	−0.419506	−	0.726606i
$606$		0			0
$607$	11692.1	−	20251.3i	0.781823	−	1.35416i	−0.149056	−	0.988829i	$-0.547623\pi$
$607$	11692.1	−	20251.3i	0.781823	−	1.35416i	0.930879	−	0.365328i	$-0.119043\pi$
$608$	−24621.3			−1.64231
$609$		0			0
$610$	−3116.01			−0.206826
$611$	6340.06	−	10981.3i	0.419789	−	0.727096i
$612$		0			0
$613$	−9741.70	−	16873.1i	−0.641865	−	1.11174i	−0.985016	−	0.172463i	$-0.944827\pi$
$613$	−9741.70	−	16873.1i	−0.641865	−	1.11174i	0.343150	−	0.939280i	$-0.388506\pi$
$614$	9221.89	−	15972.8i	0.606132	−	1.04985i
$615$		0			0
$616$	5370.37	+	12151.2i	0.351264	+	0.794781i
$617$	11177.6			0.729327			0.364664	−	0.931139i	$-0.381184\pi$
$617$	11177.6			0.729327			0.364664	+	0.931139i	$0.381184\pi$
$618$		0			0
$619$	−3126.64	−	5415.50i	−0.203021	−	0.351643i	0.746479	−	0.665409i	$-0.231743\pi$
$619$	−3126.64	−	5415.50i	−0.203021	−	0.351643i	−0.949500	+	0.313766i	$0.898409\pi$
$620$	−3096.38	−	5363.10i	−0.200571	−	0.347399i
$621$		0			0
$622$	15008.3			0.967491
$623$	−271.758	+	371.905i	−0.0174764	+	0.0239166i
$624$		0			0
$625$	1893.07	−	3278.90i	0.121157	−	0.209850i
$626$	−4122.67	−	7140.67i	−0.263219	−	0.455908i
$627$		0			0
$628$	−2641.71	+	4575.58i	−0.167859	+	0.290741i
$629$	−14212.5			−0.900938
$630$		0			0
$631$	−19733.2			−1.24496			−0.622478	−	0.782637i	$-0.713874\pi$
$631$	−19733.2			−1.24496			−0.622478	+	0.782637i	$0.713874\pi$
$632$	−2887.08	+	5000.57i	−0.181712	+	0.314734i
$633$		0			0
$634$	15877.4	+	27500.5i	0.994594	+	1.72269i
$635$	1228.78	−	2128.30i	0.0767913	−	0.133006i
$636$		0			0
$637$	−16391.5	−	3577.71i	−1.01955	−	0.222534i
$638$	−4626.90			−0.287117
$639$		0			0
$640$	5938.23	+	10285.3i	0.366764	+	0.635254i
$641$	−71.8842	−	124.507i	−0.00442941	−	0.00767197i	0.863802	−	0.503831i	$-0.168077\pi$
$641$	−71.8842	−	124.507i	−0.00442941	−	0.00767197i	−0.868232	+	0.496159i	$0.834743\pi$
$642$		0			0
$643$	29565.4			1.81329			0.906645	−	0.421894i	$-0.138634\pi$
$643$	29565.4			1.81329			0.906645	+	0.421894i	$0.138634\pi$
$644$	−8020.00	−	865.066i	−0.490734	−	0.0529323i
$645$		0			0
$646$	24101.7	−	41745.4i	1.46791	−	2.54249i
$647$	11890.4	+	20594.7i	0.722501	+	1.25141i	0.959994	+	0.280020i	$0.0903410\pi$
$647$	11890.4	+	20594.7i	0.722501	+	1.25141i	−0.237493	+	0.971389i	$0.576326\pi$
$648$		0			0
$649$	11964.8	−	20723.6i	0.723664	−	1.25342i
$650$	−10758.4			−0.649200
$651$		0			0
$652$	−13257.0			−0.796296
$653$	870.797	−	1508.26i	0.0521851	−	0.0903873i	−0.838753	−	0.544512i	$-0.816715\pi$
$653$	870.797	−	1508.26i	0.0521851	−	0.0903873i	0.890938	+	0.454125i	$0.150048\pi$
$654$		0			0
$655$	−327.890	−	567.923i	−0.0195599	−	0.0338787i
$656$	−12561.1	+	21756.5i	−0.747607	+	1.29489i
$657$		0			0
$658$	6777.99	+	15336.1i	0.401571	+	0.908607i
$659$	8493.45			0.502061			0.251030	−	0.967979i	$-0.419231\pi$
$659$	8493.45			0.502061			0.251030	+	0.967979i	$0.419231\pi$
$660$		0			0
$661$	−12507.4	−	21663.4i	−0.735976	−	1.27475i	−0.954294	−	0.298869i	$-0.903390\pi$
$661$	−12507.4	−	21663.4i	−0.735976	−	1.27475i	0.218318	−	0.975878i	$-0.429943\pi$
$662$	7646.55	+	13244.2i	0.448930	+	0.777569i
$663$		0			0
$664$	4372.18			0.255532
$665$	8391.60	+	18987.1i	0.489342	+	1.10720i
$666$		0			0
$667$	−1273.10	+	2205.08i	−0.0739050	+	0.128007i
$668$	3879.52	+	6719.53i	0.224706	+	0.389201i
$669$		0			0
$670$	8649.48	−	14981.3i	0.498744	−	0.863850i
$671$	−6118.36			−0.352007
$672$		0			0
$673$	29696.5			1.70091			0.850456	−	0.526046i	$-0.176326\pi$
$673$	29696.5			1.70091			0.850456	+	0.526046i	$0.176326\pi$
$674$	5787.87	−	10024.9i	0.330772	−	0.572914i
$675$		0			0
$676$	−410.316	−	710.688i	−0.0233453	−	0.0404352i
$677$	−1856.63	+	3215.78i	−0.105401	+	0.182559i	−0.913902	−	0.405935i	$-0.866946\pi$
$677$	−1856.63	+	3215.78i	−0.105401	+	0.182559i	0.808501	+	0.588495i	$0.200279\pi$
$678$		0			0
$679$	−9192.71	−	991.559i	−0.519564	−	0.0560420i
$680$	−10144.5			−0.572096
$681$		0			0
$682$	−17669.9	−	30605.1i	−0.992102	−	1.71837i
$683$	−12127.3	−	21005.2i	−0.679414	−	1.17678i	−0.975157	−	0.221513i	$-0.928901\pi$
$683$	−12127.3	−	21005.2i	−0.679414	−	1.17678i	0.295743	−	0.955268i	$-0.404433\pi$
$684$		0			0
$685$	22913.8			1.27809
$686$	16607.7	−	14709.2i	0.924319	−	0.818661i
$687$		0			0
$688$	6923.27	−	11991.5i	0.383644	−	0.664491i
$689$	−15184.2	−	26299.8i	−0.839583	−	1.45420i
$690$		0			0
$691$	−7149.36	+	12383.1i	−0.393595	+	0.681727i	−0.992921	−	0.118778i	$-0.962102\pi$
$691$	−7149.36	+	12383.1i	−0.393595	+	0.681727i	0.599325	+	0.800506i	$0.295436\pi$
$692$	−2615.13			−0.143659
$693$		0			0
$694$	29873.2			1.63396
$695$	−5571.45	+	9650.03i	−0.304082	+	0.526685i
$696$		0			0
$697$	−15234.2	−	26386.4i	−0.827886	−	1.43394i
$698$	17170.1	−	29739.5i	0.931087	−	1.61269i
$699$		0			0
$700$	2887.93	−	3952.17i	0.155934	−	0.213397i
$701$	−28913.3			−1.55783			−0.778916	−	0.627128i	$-0.784230\pi$
$701$	−28913.3			−1.55783			−0.778916	+	0.627128i	$0.784230\pi$
$702$		0			0
$703$	10429.4	+	18064.2i	0.559532	+	0.969137i
$704$	959.787	+	1662.40i	0.0513826	+	0.0889973i
$705$		0			0
$706$	−21552.8			−1.14894
$707$	−1932.14	−	4371.71i	−0.102780	−	0.232553i
$708$		0			0
$709$	−5287.60	+	9158.39i	−0.280085	+	0.485121i	−0.971405	−	0.237427i	$-0.923696\pi$
$709$	−5287.60	+	9158.39i	−0.280085	+	0.485121i	0.691321	+	0.722548i	$0.257029\pi$
$710$	−568.004	−	983.811i	−0.0300237	−	0.0520025i
$711$		0			0
$712$	−165.179	+	286.098i	−0.00869429	+	0.0150590i
$713$	−19447.6			−1.02148
$714$		0			0
$715$	20802.7			1.08808
$716$	4911.38	−	8506.77i	0.256351	−	0.444012i
$717$		0			0
$718$	16670.8	+	28874.7i	0.866503	+	1.50083i
$719$	2673.63	−	4630.87i	0.138678	−	0.240198i	−0.788318	−	0.615268i	$-0.789048\pi$
$719$	2673.63	−	4630.87i	0.138678	−	0.240198i	0.926997	+	0.375070i	$0.122381\pi$
$720$		0			0
$721$	−10493.2	+	14360.1i	−0.542006	+	0.741743i
$722$	−46790.7			−2.41187
$723$		0			0
$724$	969.193	+	1678.69i	0.0497511	+	0.0861714i
$725$	−772.535	−	1338.07i	−0.0395741	−	0.0685444i
$726$		0			0
$727$	−19629.1			−1.00138			−0.500689	−	0.865627i	$-0.666920\pi$
$727$	−19629.1			−1.00138			−0.500689	+	0.865627i	$0.666920\pi$
$728$	−11963.5	−	1290.43i	−0.609062	−	0.0656956i
$729$		0			0
$730$	6148.54	−	10649.6i	0.311736	−	0.539943i
$731$	8396.58	+	14543.3i	0.424841	+	0.735846i
$732$		0			0
$733$	−1202.43	+	2082.68i	−0.0605906	+	0.104946i	−0.894730	−	0.446608i	$-0.852632\pi$
$733$	−1202.43	+	2082.68i	−0.0605906	+	0.104946i	0.834139	+	0.551554i	$0.185965\pi$
$734$	14069.6			0.707519
$735$		0			0
$736$	−17954.2			−0.899186
$737$	16983.4	−	29416.2i	0.848837	−	1.47023i
$738$		0			0
$739$	9654.49	+	16722.1i	0.480577	+	0.832383i	0.999752	−	0.0222847i	$-0.00709403\pi$
$739$	9654.49	+	16722.1i	0.480577	+	0.832383i	−0.519175	+	0.854668i	$0.673761\pi$
$740$	−2421.77	+	4194.63i	−0.120305	+	0.208375i
$741$		0			0
$742$	39925.1	+	4306.47i	1.97533	+	0.213067i
$743$	−801.314			−0.0395658			−0.0197829	−	0.999804i	$-0.506297\pi$
$743$	−801.314			−0.0395658			−0.0197829	+	0.999804i	$0.506297\pi$
$744$		0			0
$745$	−8610.18	−	14913.3i	−0.423426	−	0.733396i
$746$	35.0124	+	60.6433i	0.00171836	+	0.00297629i
$747$		0			0
$748$	21978.0			1.07433
$749$	22446.4	−	30718.3i	1.09503	−	1.49856i
$750$		0			0
$751$	−7436.36	+	12880.2i	−0.361327	+	0.625837i	−0.988180	−	0.153301i	$-0.951010\pi$
$751$	−7436.36	+	12880.2i	−0.361327	+	0.625837i	0.626853	+	0.779138i	$0.284343\pi$
$752$	10364.4	+	17951.6i	0.502593	+	0.870516i
$753$		0			0
$754$	2095.41	−	3629.35i	0.101207	−	0.175296i
$755$	12909.7			0.622292
$756$		0			0
$757$	9127.52			0.438237			0.219118	−	0.975698i	$-0.429682\pi$
$757$	9127.52			0.438237			0.219118	+	0.975698i	$0.429682\pi$
$758$	−6614.16	+	11456.1i	−0.316935	+	0.548948i
$759$		0			0
$760$	7444.21	+	12893.8i	0.355303	+	0.615402i
$761$	−15497.2	+	26841.9i	−0.738203	+	1.27861i	0.215100	+	0.976592i	$0.430992\pi$
$761$	−15497.2	+	26841.9i	−0.738203	+	1.27861i	−0.953304	+	0.302014i	$0.902341\pi$
$762$		0			0
$763$	−13357.0	−	30222.0i	−0.633756	−	1.43396i
$764$	−11187.2			−0.529764
$765$		0			0
$766$	−13972.4	−	24201.0i	−0.659066	−	1.14154i
$767$	10837.1	+	18770.4i	0.510175	+	0.883649i
$768$		0			0
$769$	12979.5			0.608653			0.304326	−	0.952568i	$-0.401569\pi$
$769$	12979.5			0.608653			0.304326	+	0.952568i	$0.401569\pi$
$770$	−16229.3	+	22210.1i	−0.759565	+	1.03948i
$771$		0			0
$772$	−273.972	+	474.533i	−0.0127726	+	0.0221228i
$773$	14404.1	+	24948.6i	0.670217	+	1.16085i	0.977842	+	0.209343i	$0.0671325\pi$
$773$	14404.1	+	24948.6i	0.670217	+	1.16085i	−0.307625	+	0.951508i	$0.599534\pi$
$774$		0			0
$775$	5900.53	−	10220.0i	0.273488	−	0.473695i
$776$	−6631.35			−0.306767
$777$		0			0
$778$	12169.6			0.560799
$779$	−22358.2	+	38725.5i	−1.02832	+	1.78111i
$780$

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)

\(f(q)\)	\(=\)	\(q+(1.74618 - 3.02447i) q^{2} +(-2.09829 - 3.63435i) q^{4} +(-3.93765 + 6.82022i) q^{5} +(18.4135 + 1.98614i) q^{7} +13.2829 q^{8} +O(q^{10})\)	\(q+(1.74618 - 3.02447i) q^{2} +(-2.09829 - 3.63435i) q^{4} +(-3.93765 + 6.82022i) q^{5} +(18.4135 + 1.98614i) q^{7} +13.2829 q^{8} +(13.7517 + 23.8187i) q^{10} +(27.0018 + 46.7684i) q^{11} -48.9137 q^{13} +(38.1602 - 52.2228i) q^{14} +(39.9807 - 69.2486i) q^{16} +(48.4888 + 83.9850i) q^{17} +(71.1636 - 123.259i) q^{19} +33.0494 q^{20} +188.600 q^{22} +(51.8936 - 89.8823i) q^{23} +(31.4897 + 54.5418i) q^{25} +(-85.4121 + 147.938i) q^{26} +(-31.4185 - 71.0884i) q^{28} -24.5329 q^{29} +(-93.6897 - 162.275i) q^{31} +(-86.4953 - 149.814i) q^{32} +338.680 q^{34} +(-86.0517 + 117.763i) q^{35} +(-73.2774 + 126.920i) q^{37} +(-248.529 - 430.465i) q^{38} +(-52.3035 + 90.5923i) q^{40} -314.180 q^{41} +173.165 q^{43} +(113.315 - 196.268i) q^{44} +(-181.231 - 313.901i) q^{46} +(-129.617 + 224.504i) q^{47} +(335.110 + 73.1434i) q^{49} +219.947 q^{50} +(102.635 + 177.769i) q^{52} +(310.429 + 537.679i) q^{53} -425.295 q^{55} +(244.584 + 26.3817i) q^{56} +(-42.8389 + 74.1991i) q^{58} +(-221.555 - 383.745i) q^{59} +(-56.6478 + 98.1168i) q^{61} -654.396 q^{62} +35.5454 q^{64} +(192.605 - 333.602i) q^{65} +(-314.488 - 544.708i) q^{67} +(203.487 - 352.450i) q^{68} +(205.909 + 465.897i) q^{70} -41.3042 q^{71} +(-223.555 - 387.209i) q^{73} +(255.911 + 443.251i) q^{74} -597.287 q^{76} +(404.307 + 914.798i) q^{77} +(-217.353 + 376.467i) q^{79} +(314.860 + 545.354i) q^{80} +(-548.615 + 950.229i) q^{82} +329.158 q^{83} -763.728 q^{85} +(302.378 - 523.734i) q^{86} +(358.662 + 621.221i) q^{88} +(-12.4354 + 21.5388i) q^{89} +(-900.670 - 97.1494i) q^{91} -435.551 q^{92} +(452.670 + 784.048i) q^{94} +(560.435 + 970.702i) q^{95} -499.239 q^{97} +(806.384 - 885.811i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 48 q^{4} - 60 q^{7}+O(q^{10}) \) 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

Introduction

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