LMFDB - Embedded newform 189.4.e.h.109.2

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			109.2
Root			$1.03883 - 1.79930i$ of defining polynomial
Character	$\chi$	$=$	189.109
Dual form			189.4.e.h.163.2

$q$-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 $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.74618	−	3.02447i	−0.617368	−	1.06931i	−0.989964	−	0.141319i	$-0.954866\pi$
$2$	−1.74618	−	3.02447i	−0.617368	−	1.06931i	0.372596	−	0.927994i	$-0.378468\pi$
$3$		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	$-0.0521022\pi$
$5$	3.93765	+	6.82022i	0.352195	+	0.610019i	−0.634439	+	0.772973i	$0.718769\pi$
$6$		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	0.212318	+	0.977201i	$0.431899\pi$
$11$	−27.0018	+	46.7684i	−0.740122	+	1.28193i	−0.952439	+	0.304728i	$0.901434\pi$
$12$		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	0.279475	+	0.960153i	$0.409840\pi$
$17$	−48.4888	+	83.9850i	−0.691780	+	1.19820i	−0.971254	+	0.238044i	$0.923494\pi$
$18$		0			0
$19$	71.1636	+	123.259i	0.859266	+	1.48829i	0.872631	+	0.488381i	$0.162412\pi$
$19$	71.1636	+	123.259i	0.859266	+	1.48829i	−0.0133650	+	0.999911i	$0.504254\pi$
$20$	−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	$-0.322578\pi$
$23$	−51.8936	−	89.8823i	−0.470459	−	0.814859i	−0.999429	+	0.0337813i	$0.989245\pi$
$24$		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	$-0.474972\pi$
$29$	24.5329			0.157091			0.0785456	+	0.996911i	$0.474972\pi$
$30$		0			0
$31$	−93.6897	+	162.275i	−0.542812	+	0.940177i	0.455930	+	0.890016i	$0.349307\pi$
$31$	−93.6897	+	162.275i	−0.542812	+	0.940177i	−0.998741	+	0.0501613i	$0.984026\pi$
$32$	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	0.656044	−	0.754723i	$-0.272229\pi$
$37$	−73.2774	−	126.920i	−0.325587	−	0.563933i	−0.981631	+	0.190789i	$0.938895\pi$
$38$	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	$-0.295814\pi$
$41$	314.180			1.19675			0.598374	+	0.801217i	$0.295814\pi$
$42$		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	$-0.0348885\pi$
$47$	129.617	+	224.504i	0.402269	+	0.696749i	−0.591731	+	0.806136i	$0.701555\pi$
$48$		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	0.112059	+	0.993702i	$0.464256\pi$
$53$	−310.429	+	537.679i	−0.804541	+	1.39351i	−0.916600	+	0.399805i	$0.869078\pi$
$54$		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	$-0.670738\pi$
$59$	221.555	−	383.745i	0.488882	−	0.846768i	0.999918	+	0.0127908i	$0.00407155\pi$
$60$		0			0
$61$	−56.6478	−	98.1168i	−0.118902	−	0.205944i	0.800431	−	0.599425i	$-0.204604\pi$
$61$	−56.6478	−	98.1168i	−0.118902	−	0.205944i	−0.919333	+	0.393481i	$0.871271\pi$
$62$	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	0.422764	+	0.906240i	$0.361060\pi$
$67$	−314.488	+	544.708i	−0.573444	+	0.993235i	−0.996209	+	0.0869950i	$0.972274\pi$
$68$	−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	$-0.489010\pi$
$71$	41.3042			0.0690410			0.0345205	+	0.999404i	$0.489010\pi$
$72$		0			0
$73$	−223.555	+	387.209i	−0.358427	+	0.620814i	−0.987698	−	0.156372i	$-0.950020\pi$
$73$	−223.555	+	387.209i	−0.358427	+	0.620814i	0.629271	+	0.777186i	$0.283353\pi$
$74$	−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	0.668717	−	0.743517i	$-0.266844\pi$
$79$	−217.353	−	376.467i	−0.309546	−	0.536149i	−0.978263	+	0.207368i	$0.933510\pi$
$80$	−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	$-0.569839\pi$
$83$	−329.158			−0.435299			−0.217649	+	0.976027i	$0.569839\pi$
$84$		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	$-0.161952\pi$
$89$	12.4354	+	21.5388i	0.0148107	+	0.0256529i	−0.858525	+	0.512772i	$0.828619\pi$
$90$		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	$-0.792758\pi$
$101$	129.038	−	223.501i	0.127127	−	0.220190i	0.922562	+	0.385848i	$0.126091\pi$
$102$		0			0
$103$	−480.159	−	831.659i	−0.459334	−	0.795590i	0.539592	−	0.841927i	$-0.318579\pi$
$103$	−480.159	−	831.659i	−0.459334	−	0.795590i	−0.998926	+	0.0463365i	$0.985245\pi$
$104$	649.716			0.612595
$105$		0			0
$106$	2168.26			1.98679
$107$	−1027.13	−	1779.04i	−0.928004	−	1.60735i	−0.786657	−	0.617391i	$-0.788190\pi$
$107$	−1027.13	−	1779.04i	−0.928004	−	1.60735i	−0.141347	−	0.989960i	$-0.545143\pi$
$108$		0			0
$109$	−892.052	+	1545.08i	−0.783881	+	1.35772i	0.145784	+	0.989316i	$0.453430\pi$
$109$	−892.052	+	1545.08i	−0.783881	+	1.35772i	−0.929665	+	0.368406i	$0.879904\pi$
$110$	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	$-0.318573\pi$
$113$	1296.36			1.07921			0.539607	+	0.841917i	$0.318573\pi$
$114$		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	$-0.157827\pi$
$131$	41.6352	+	72.1143i	0.0277686	+	0.0480966i	−0.851807	+	0.523855i	$0.824493\pi$
$132$		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	0.0893421	−	0.996001i	$-0.471524\pi$
$137$	1454.79	−	2519.77i	0.907233	−	1.57137i	0.817891	−	0.575373i	$-0.195143\pi$
$138$		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	0.992651	+	0.121012i	$0.0386141\pi$
$149$	1093.31	+	1893.67i	0.601125	+	1.04118i	−0.391526	+	0.920167i	$0.628053\pi$
$150$		0			0
$151$	−819.629	+	1419.64i	−0.441725	+	0.765090i	−0.997818	−	0.0660304i	$-0.978967\pi$
$151$	−819.629	+	1419.64i	−0.441725	+	0.765090i	0.556093	+	0.831120i	$0.312300\pi$
$152$	−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	−0.980486	−	0.196588i	$-0.937014\pi$
$157$	−629.491	+	1090.31i	−0.319993	+	0.554244i	0.660493	+	0.750832i	$0.270347\pi$
$158$	−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	0.943364	+	0.331761i	$0.107643\pi$
$163$	1579.50	+	2735.78i	0.758995	+	1.31462i	−0.184368	+	0.982857i	$0.559024\pi$
$164$	−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	$-0.359092\pi$
$167$	1848.90			0.856718			0.428359	+	0.903609i	$0.359092\pi$
$168$		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	$-0.210390\pi$
$173$	−311.578	−	539.669i	−0.136930	−	0.237169i	−0.926333	+	0.376706i	$0.877057\pi$
$174$		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	$-0.995857\pi$
$179$	−1170.33	+	2027.07i	−0.488685	+	0.846427i	0.511230	+	0.859444i	$0.329190\pi$
$180$		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	−0.999984	−	0.00572288i	$-0.998178\pi$
$191$	−1332.90	−	2308.65i	−0.504948	−	0.874596i	0.495036	−	0.868873i	$-0.335155\pi$
$192$		0			0
$193$	−65.2845	+	113.076i	−0.0243486	+	0.0421730i	−0.877943	−	0.478765i	$-0.841085\pi$
$193$	−65.2845	+	113.076i	−0.0243486	+	0.0421730i	0.853594	+	0.520938i	$0.174418\pi$
$194$	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	$-0.735601\pi$
$197$	−3729.51			−1.34882			−0.674408	+	0.738359i	$0.735601\pi$
$198$		0			0
$199$	1886.38	−	3267.30i	0.671968	−	1.16388i	−0.305377	−	0.952232i	$-0.598782\pi$
$199$	1886.38	−	3267.30i	0.671968	−	1.16388i	0.977345	−	0.211652i	$-0.0678842\pi$
$200$	−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	$-0.773934\pi$
$227$	634.521	−	1099.02i	0.185527	−	0.321342i	0.943754	+	0.330649i	$0.107267\pi$
$228$		0			0
$229$	1025.74	+	1776.63i	0.295995	+	0.512678i	0.975216	−	0.221256i	$-0.0710155\pi$
$229$	1025.74	+	1776.63i	0.295995	+	0.512678i	−0.679221	+	0.733934i	$0.737682\pi$
$230$	−2854.50			−0.818349
$231$		0			0
$232$	−325.868			−0.0922169
$233$	2475.22	+	4287.20i	0.695953	+	1.20543i	0.969859	+	0.243669i	$0.0783510\pi$
$233$	2475.22	+	4287.20i	0.695953	+	1.20543i	−0.273906	+	0.961756i	$0.588316\pi$
$234$		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	$-0.511317\pi$
$239$	−262.671			−0.0710910			−0.0355455	+	0.999368i	$0.511317\pi$
$240$		0			0
$241$	−1451.19	+	2513.53i	−0.387880	+	0.671829i	−0.992164	−	0.124941i	$-0.960126\pi$
$241$	−1451.19	+	2513.53i	−0.387880	+	0.671829i	0.604284	+	0.796769i	$0.293459\pi$
$242$	−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	$-0.211209\pi$
$251$	6265.68			1.57564			0.787821	+	0.615904i	$0.211209\pi$
$252$		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	$-0.302942\pi$
$257$	−1710.48	−	2962.64i	−0.415163	−	0.719083i	−0.995446	+	0.0953322i	$0.969609\pi$
$258$		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	0.251435	−	0.967874i	$-0.419098\pi$
$263$	4111.26	−	7120.91i	0.963921	−	1.66956i	0.712486	−	0.701686i	$-0.247569\pi$
$264$		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	0.366453	+	0.930436i	$0.380572\pi$
$269$	−2746.67	+	4757.37i	−0.622555	+	1.07830i	−0.989008	+	0.147860i	$0.952761\pi$
$270$		0			0
$271$	548.242	+	949.584i	0.122891	+	0.212853i	0.920906	−	0.389784i	$-0.127450\pi$
$271$	548.242	+	949.584i	0.122891	+	0.212853i	−0.798016	+	0.602637i	$0.794117\pi$
$272$	−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	−0.769264	−	0.638931i	$-0.779377\pi$
$277$	777.736	−	1347.08i	0.168699	−	0.292195i	0.937963	+	0.346736i	$0.112710\pi$
$278$	−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	$-0.533714\pi$
$281$	−995.950			−0.211435			−0.105718	+	0.994396i	$0.533714\pi$
$282$		0			0
$283$	4317.74	−	7478.54i	0.906936	−	1.57086i	0.0886383	−	0.996064i	$-0.471748\pi$
$283$	4317.74	−	7478.54i	0.906936	−	1.57086i	0.818297	−	0.574795i	$-0.194918\pi$
$284$	−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	$-0.569736\pi$
$293$	−2180.01			−0.434667			−0.217333	+	0.976097i	$0.569736\pi$
$294$		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	$-0.961474\pi$
$311$	−2148.74	+	3721.72i	−0.391780	+	0.678584i	0.600904	+	0.799321i	$0.294807\pi$
$312$		0			0
$313$	1180.48	+	2044.65i	0.213178	+	0.369235i	0.952707	−	0.303889i	$-0.0982852\pi$
$313$	1180.48	+	2044.65i	0.213178	+	0.369235i	−0.739529	+	0.673124i	$0.764952\pi$
$314$	4396.82			0.790213
$315$		0			0
$316$	1824.28			0.324759
$317$	4546.33	+	7874.47i	0.805512	+	1.39519i	0.915945	+	0.401304i	$0.131443\pi$
$317$	4546.33	+	7874.47i	0.805512	+	1.39519i	−0.110433	+	0.993884i	$0.535224\pi$
$318$		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	0.624964	−	0.780653i	$-0.285114\pi$
$331$	−2189.51	−	3792.34i	−0.363584	−	0.629745i	−0.988548	+	0.150908i	$0.951780\pi$
$332$	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	0.318512	+	0.947919i	$0.396817\pi$
$347$	−4276.94	+	7407.87i	−0.661666	+	1.14604i	−0.980178	+	0.198120i	$0.936517\pi$
$348$		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	$-0.679295\pi$
$353$	3085.71	−	5344.60i	0.465257	−	0.805848i	0.999213	+	0.0396640i	$0.0126287\pi$
$354$		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	0.967844	+	0.251552i	$0.0809409\pi$
$359$	4773.51	+	8267.96i	0.701772	+	1.21551i	−0.266072	+	0.963953i	$0.585726\pi$
$360$		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	−0.686467	−	0.727161i	$-0.740839\pi$
$367$	2014.34	−	3488.94i	0.286506	−	0.496243i	0.972973	+	0.230918i	$0.0741728\pi$
$368$	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	0.865329	−	0.501205i	$-0.167110\pi$
$373$	−10.0254	−	17.3646i	−0.00139168	−	0.00241046i	−0.866720	+	0.498794i	$0.833776\pi$
$374$	−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	−0.999222	−	0.0394450i	$-0.987441\pi$
$383$	−4000.86	−	6929.69i	−0.533771	−	0.924519i	0.465451	−	0.885074i	$-0.345892\pi$
$384$		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	$-0.906255\pi$
$389$	−1742.32	+	3017.79i	−0.227093	+	0.393336i	0.729852	+	0.683605i	$0.239589\pi$
$390$		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	0.998042	−	0.0625455i	$-0.0199218\pi$
$397$	3518.88	+	6094.88i	0.444855	+	0.770512i	−0.553187	+	0.833057i	$0.686589\pi$
$398$	−13175.8			−1.65941
$399$		0			0
$400$	5035.93			0.629491
$401$	4194.86	+	7265.72i	0.522398	+	0.904820i	0.999660	+	0.0260589i	$0.00829573\pi$
$401$	4194.86	+	7265.72i	0.522398	+	0.904820i	−0.477263	+	0.878761i	$0.658371\pi$
$402$		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	−0.0877604	−	0.996142i	$-0.527971\pi$
$409$	6772.75	−	11730.7i	0.818804	−	1.41821i	0.906564	−	0.422068i	$-0.138696\pi$
$410$	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	$-0.473057\pi$
$419$	1450.22			0.169089			0.0845443	+	0.996420i	$0.473057\pi$
$420$		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	$-0.811292\pi$
$431$	619.105	−	1072.32i	0.0691908	−	0.119842i	0.898545	+	0.438881i	$0.144625\pi$
$432$		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	0.760368	−	0.649493i	$-0.225019\pi$
$439$	−1676.75	−	2904.21i	−0.182293	−	0.315741i	−0.942661	+	0.333752i	$0.891685\pi$
$440$	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	$-0.309509\pi$
$443$	−4045.18	−	7006.46i	−0.433843	−	0.751438i	−0.997200	+	0.0747756i	$0.976176\pi$
$444$		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	$-0.428966\pi$
$449$	4211.19			0.442625			0.221312	+	0.975203i	$0.428966\pi$
$450$		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	1.00000		0.000477301i	$0.000151930\pi$
$457$	4888.81	+	8467.67i	0.500413	+	0.866741i	−0.499587	+	0.866264i	$0.666515\pi$
$458$	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	$-0.285351\pi$
$461$	12360.4			1.24876			0.624381	+	0.781120i	$0.285351\pi$
$462$		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	−0.978428	−	0.206588i	$-0.933764\pi$
$467$	−6742.68	−	11678.7i	−0.668125	−	1.15723i	0.310303	−	0.950638i	$-0.399569\pi$
$468$		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	$-0.839269\pi$
$479$	−195.482	+	338.585i	−0.0186468	+	0.0322972i	0.856551	+	0.516062i	$0.172602\pi$
$480$		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	−0.220179	−	0.975460i	$-0.570664\pi$
$487$	7895.75	−	13675.8i	0.734683	−	1.27251i	0.954862	−	0.297049i	$-0.0960026\pi$
$488$	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	$-0.502803\pi$
$491$	−191.606			−0.0176111			−0.00880557	+	0.999961i	$0.502803\pi$
$492$		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	0.711979	−	0.702201i	$-0.247799\pi$
$499$	−2810.50	−	4867.93i	−0.252135	−	0.436710i	−0.964113	+	0.265491i	$0.914466\pi$
$500$	−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	$-0.229742\pi$
$503$	16936.3			1.50129			0.750647	+	0.660704i	$0.229742\pi$
$504$		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	$-0.225569\pi$
$509$	−2112.88	−	3659.62i	−0.183992	−	0.318684i	−0.943236	+	0.332122i	$0.892235\pi$
$510$		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	$-0.778402\pi$
$521$	2042.06	−	3536.95i	0.171716	−	0.297421i	0.939020	+	0.343863i	$0.111735\pi$
$522$		0			0
$523$	−8485.69	−	14697.7i	−0.709471	−	1.22884i	−0.965054	−	0.262053i	$-0.915601\pi$
$523$	−8485.69	−	14697.7i	−0.709471	−	1.22884i	0.255582	−	0.966787i	$-0.417733\pi$
$524$	−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	0.853217	−	0.521556i	$-0.174648\pi$
$541$	−315.493	−	546.451i	−0.0250723	−	0.0434265i	−0.878289	+	0.478130i	$0.841315\pi$
$542$	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	$-0.994490\pi$
$557$	−6374.78	+	11041.4i	−0.484934	+	0.839930i	0.514917	+	0.857240i	$0.327823\pi$
$558$		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	−0.472504	−	0.881328i	$-0.656650\pi$
$563$	7040.02	−	12193.7i	0.527001	−	0.912792i	0.999505	−	0.0314637i	$-0.0100169\pi$
$564$		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	$-0.178136\pi$
$569$	−488.954	−	846.893i	−0.0360246	−	0.0623965i	−0.883476	+	0.468477i	$0.844803\pi$
$570$		0			0
$571$	2438.76	−	4224.06i	0.178737	−	0.309582i	−0.762711	−	0.646740i	$-0.776132\pi$
$571$	2438.76	−	4224.06i	0.178737	−	0.309582i	0.941448	+	0.337157i	$0.109465\pi$
$572$	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	−0.980512	−	0.196459i	$-0.937056\pi$
$577$	−4436.83	+	7684.82i	−0.320117	+	0.554460i	0.660395	+	0.750919i	$0.270389\pi$
$578$	−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	$-0.289479\pi$
$587$	17470.2			1.22840			0.614201	+	0.789150i	$0.289479\pi$
$588$		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	0.991508	+	0.130044i	$0.0415119\pi$
$593$	8785.24	+	15216.5i	0.608376	+	1.05374i	−0.383133	+	0.923693i	$0.625155\pi$
$594$		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	$-0.860187\pi$
$599$	−1235.30	+	2139.61i	−0.0842623	+	0.145947i	0.820814	+	0.571195i	$0.193520\pi$
$600$		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	0.930879	+	0.365328i	$0.119043\pi$
$607$	11692.1	+	20251.3i	0.781823	+	1.35416i	−0.149056	+	0.988829i	$0.547623\pi$
$608$	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	0.343150	+	0.939280i	$0.388506\pi$
$613$	−9741.70	+	16873.1i	−0.641865	+	1.11174i	−0.985016	+	0.172463i	$0.944827\pi$
$614$	−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	$-0.618816\pi$
$617$	−11177.6			−0.729327			−0.364664	+	0.931139i	$0.618816\pi$
$618$		0			0
$619$	−3126.64	+	5415.50i	−0.203021	+	0.351643i	−0.949500	−	0.313766i	$-0.898409\pi$
$619$	−3126.64	+	5415.50i	−0.203021	+	0.351643i	0.746479	+	0.665409i	$0.231743\pi$
$620$	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	$-0.831923\pi$
$641$	71.8842	−	124.507i	0.00442941	−	0.00767197i	0.868232	+	0.496159i	$0.165257\pi$
$642$		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	0.237493	+	0.971389i	$0.423674\pi$
$647$	−11890.4	+	20594.7i	−0.722501	+	1.25141i	−0.959994	+	0.280020i	$0.909659\pi$
$648$		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	$-0.183285\pi$
$653$	−870.797	−	1508.26i	−0.0521851	−	0.0903873i	−0.890938	+	0.454125i	$0.849952\pi$
$654$		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	$-0.580769\pi$
$659$	−8493.45			−0.502061			−0.251030	+	0.967979i	$0.580769\pi$
$660$		0			0
$661$	−12507.4	+	21663.4i	−0.735976	+	1.27475i	0.218318	+	0.975878i	$0.429943\pi$
$661$	−12507.4	+	21663.4i	−0.735976	+	1.27475i	−0.954294	+	0.298869i	$0.903390\pi$
$662$	−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	$-0.133054\pi$
$677$	1856.63	+	3215.78i	0.105401	+	0.182559i	−0.808501	+	0.588495i	$0.799721\pi$
$678$		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	−0.295743	−	0.955268i	$-0.595567\pi$
$683$	12127.3	−	21005.2i	0.679414	−	1.17678i	0.975157	−	0.221513i	$-0.0710994\pi$
$684$		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	0.599325	−	0.800506i	$-0.295436\pi$
$691$	−7149.36	−	12383.1i	−0.393595	−	0.681727i	−0.992921	+	0.118778i	$0.962102\pi$
$692$	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	$-0.215770\pi$
$701$	28913.3			1.55783			0.778916	+	0.627128i	$0.215770\pi$
$702$		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	0.691321	−	0.722548i	$-0.257029\pi$
$709$	−5287.60	−	9158.39i	−0.280085	−	0.485121i	−0.971405	+	0.237427i	$0.923696\pi$
$710$	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	$-0.210952\pi$
$719$	−2673.63	−	4630.87i	−0.138678	−	0.240198i	−0.926997	+	0.375070i	$0.877619\pi$
$720$		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	0.834139	−	0.551554i	$-0.185965\pi$
$733$	−1202.43	−	2082.68i	−0.0605906	−	0.104946i	−0.894730	+	0.446608i	$0.852632\pi$
$734$	−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	−0.519175	−	0.854668i	$-0.673761\pi$
$739$	9654.49	−	16722.1i	0.480577	−	0.832383i	0.999752	+	0.0222847i	$0.00709403\pi$
$740$	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	$-0.493703\pi$
$743$	801.314			0.0395658			0.0197829	+	0.999804i	$0.493703\pi$
$744$		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	0.626853	−	0.779138i	$-0.284343\pi$
$751$	−7436.36	−	12880.2i	−0.361327	−	0.625837i	−0.988180	+	0.153301i	$0.951010\pi$
$752$	−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	0.953304	+	0.302014i	$0.0976588\pi$
$761$	15497.2	+	26841.9i	0.738203	+	1.27861i	−0.215100	+	0.976592i	$0.569008\pi$
$762$		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	0.307625	+	0.951508i	$0.400466\pi$
$773$	−14404.1	+	24948.6i	−0.670217	+	1.16085i	−0.977842	+	0.209343i	$0.932868\pi$
$774$		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
$780$		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)

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