LMFDB - Embedded newform 189.4.e.h.163.5

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			163.5
Root			$-0.178435 - 0.309059i$ of defining polynomial
Character	$\chi$	$=$	189.163
Dual form			189.4.e.h.109.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.884622 - 1.53221i) q^{2} +(2.43489 + 4.21735i) q^{4} +(-6.52561 + 11.3027i) q^{5} +(-18.4950 + 0.966772i) q^{7} +22.7698 q^{8} +O(q^{10})$	\(q+(0.884622 - 1.53221i) q^{2} +(2.43489 + 4.21735i) q^{4} +(-6.52561 + 11.3027i) q^{5} +(-18.4950 + 0.966772i) q^{7} +22.7698 q^{8} +(11.5454 + 19.9972i) q^{10} +(-26.4705 - 45.8483i) q^{11} -71.7001 q^{13} +(-14.8798 + 29.1935i) q^{14} +(0.663570 - 1.14934i) q^{16} +(-53.2866 - 92.2950i) q^{17} +(-26.9643 + 46.7035i) q^{19} -63.5565 q^{20} -93.6656 q^{22} +(-9.32943 + 16.1590i) q^{23} +(-22.6672 - 39.2608i) q^{25} +(-63.4275 + 109.860i) q^{26} +(-49.1105 - 75.6459i) q^{28} +261.806 q^{29} +(61.1632 + 105.938i) q^{31} +(89.9051 + 155.720i) q^{32} -188.554 q^{34} +(109.764 - 215.352i) q^{35} +(-139.069 + 240.874i) q^{37} +(47.7064 + 82.6298i) q^{38} +(-148.587 + 257.360i) q^{40} -31.3788 q^{41} -347.239 q^{43} +(128.905 - 223.271i) q^{44} +(16.5060 + 28.5893i) q^{46} +(-271.109 + 469.575i) q^{47} +(341.131 - 35.7609i) q^{49} -80.2078 q^{50} +(-174.582 - 302.384i) q^{52} +(128.528 + 222.618i) q^{53} +690.945 q^{55} +(-421.127 + 22.0132i) q^{56} +(231.599 - 401.142i) q^{58} +(-157.810 - 273.335i) q^{59} +(-69.4019 + 120.208i) q^{61} +216.425 q^{62} +328.745 q^{64} +(467.887 - 810.405i) q^{65} +(-198.950 - 344.592i) q^{67} +(259.493 - 449.456i) q^{68} +(-232.865 - 358.687i) q^{70} -843.419 q^{71} +(436.140 + 755.417i) q^{73} +(246.047 + 426.165i) q^{74} -262.620 q^{76} +(533.897 + 822.373i) q^{77} +(277.456 - 480.568i) q^{79} +(8.66040 + 15.0002i) q^{80} +(-27.7584 + 48.0789i) q^{82} -297.114 q^{83} +1390.91 q^{85} +(-307.176 + 532.044i) q^{86} +(-602.728 - 1043.96i) q^{88} +(-51.2419 + 88.7536i) q^{89} +(1326.09 - 69.3177i) q^{91} -90.8644 q^{92} +(479.659 + 830.793i) q^{94} +(-351.916 - 609.537i) q^{95} -515.437 q^{97} +(246.979 - 554.319i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.884622	−	1.53221i	0.312761	−	0.541718i	−0.666198	−	0.745775i	$-0.732079\pi$
$2$	0.884622	−	1.53221i	0.312761	−	0.541718i	0.978959	+	0.204057i	$0.0654127\pi$
$3$		0			0
$3$		0			0
$4$	2.43489	+	4.21735i	0.304361	+	0.527168i
$5$	−6.52561	+	11.3027i	−0.583669	+	1.01094i	0.411371	+	0.911468i	$0.365050\pi$
$5$	−6.52561	+	11.3027i	−0.583669	+	1.01094i	−0.995040	+	0.0994757i	$0.968283\pi$
$6$		0			0
$7$	−18.4950	+	0.966772i	−0.998637	+	0.0522008i
$7$	−18.4950	+	0.966772i	−0.998637	+	0.0522008i
$8$	22.7698			1.00629
$9$		0			0
$10$	11.5454	+	19.9972i	0.365098	+	0.632368i
$11$	−26.4705	−	45.8483i	−0.725560	−	1.25671i	−0.958743	−	0.284274i	$-0.908248\pi$
$11$	−26.4705	−	45.8483i	−0.725560	−	1.25671i	0.233183	−	0.972433i	$-0.425086\pi$
$12$		0			0
$13$	−71.7001			−1.52970			−0.764848	−	0.644211i	$-0.777186\pi$
$13$	−71.7001			−1.52970			−0.764848	+	0.644211i	$0.777186\pi$
$14$	−14.8798	+	29.1935i	−0.284057	+	0.557306i
$15$		0			0
$16$	0.663570	−	1.14934i	0.0103683	−	0.0179584i
$17$	−53.2866	−	92.2950i	−0.760229	−	1.31676i	−0.942732	−	0.333550i	$-0.891753\pi$
$17$	−53.2866	−	92.2950i	−0.760229	−	1.31676i	0.182504	−	0.983205i	$-0.441580\pi$
$18$		0			0
$19$	−26.9643	+	46.7035i	−0.325580	+	0.563921i	−0.981630	−	0.190797i	$-0.938893\pi$
$19$	−26.9643	+	46.7035i	−0.325580	+	0.563921i	0.656049	+	0.754718i	$0.272226\pi$
$20$	−63.5565			−0.710583
$21$		0			0
$22$	−93.6656			−0.907708
$23$	−9.32943	+	16.1590i	−0.0845792	+	0.146495i	−0.905212	−	0.424961i	$-0.860288\pi$
$23$	−9.32943	+	16.1590i	−0.0845792	+	0.146495i	0.820633	+	0.571456i	$0.193621\pi$
$24$		0			0
$25$	−22.6672	−	39.2608i	−0.181338	−	0.314086i
$26$	−63.4275	+	109.860i	−0.478429	+	0.828664i
$27$		0			0
$28$	−49.1105	−	75.6459i	−0.331464	−	0.510562i
$29$	261.806			1.67642			0.838208	−	0.545350i	$-0.183603\pi$
$29$	261.806			1.67642			0.838208	+	0.545350i	$0.183603\pi$
$30$		0			0
$31$	61.1632	+	105.938i	0.354362	+	0.613773i	0.987009	−	0.160667i	$-0.0513646\pi$
$31$	61.1632	+	105.938i	0.354362	+	0.613773i	−0.632646	+	0.774441i	$0.718031\pi$
$32$	89.9051	+	155.720i	0.496660	+	0.860241i
$33$		0			0
$34$	−188.554			−0.951081
$35$	109.764	−	215.352i	0.530101	−	1.04003i
$36$		0			0
$37$	−139.069	+	240.874i	−0.617912	+	1.07026i	0.371954	+	0.928251i	$0.378688\pi$
$37$	−139.069	+	240.874i	−0.617912	+	1.07026i	−0.989866	+	0.142004i	$0.954645\pi$
$38$	47.7064	+	82.6298i	0.203658	+	0.352746i
$39$		0			0
$40$	−148.587	+	257.360i	−0.587341	+	1.01730i
$41$	−31.3788			−0.119525			−0.0597627	−	0.998213i	$-0.519034\pi$
$41$	−31.3788			−0.119525			−0.0597627	+	0.998213i	$0.519034\pi$
$42$		0			0
$43$	−347.239			−1.23148			−0.615739	−	0.787951i	$-0.711142\pi$
$43$	−347.239			−1.23148			−0.615739	+	0.787951i	$0.711142\pi$
$44$	128.905	−	223.271i	0.441664	−	0.764984i
$45$		0			0
$46$	16.5060	+	28.5893i	0.0529062	+	0.0916362i
$47$	−271.109	+	469.575i	−0.841390	+	1.45733i	0.0473295	+	0.998879i	$0.484929\pi$
$47$	−271.109	+	469.575i	−0.841390	+	1.45733i	−0.888720	+	0.458451i	$0.848404\pi$
$48$		0			0
$49$	341.131	−	35.7609i	0.994550	−	0.104259i
$50$	−80.2078			−0.226862
$51$		0			0
$52$	−174.582	−	302.384i	−0.465579	−	0.806407i
$53$	128.528	+	222.618i	0.333108	+	0.576960i	0.983120	−	0.182964i	$-0.0585693\pi$
$53$	128.528	+	222.618i	0.333108	+	0.576960i	−0.650012	+	0.759924i	$0.725236\pi$
$54$		0			0
$55$	690.945			1.69395
$56$	−421.127	+	22.0132i	−1.00492	+	0.0525292i
$57$		0			0
$58$	231.599	−	401.142i	0.524318	−	0.908146i
$59$	−157.810	−	273.335i	−0.348223	−	0.603139i	0.637711	−	0.770276i	$-0.279881\pi$
$59$	−157.810	−	273.335i	−0.348223	−	0.603139i	−0.985934	+	0.167136i	$0.946548\pi$
$60$		0			0
$61$	−69.4019	+	120.208i	−0.145672	+	0.252312i	−0.929624	−	0.368511i	$-0.879868\pi$
$61$	−69.4019	+	120.208i	−0.145672	+	0.252312i	0.783951	+	0.620822i	$0.213201\pi$
$62$	216.425			0.443323
$63$		0			0
$64$	328.745			0.642081
$65$	467.887	−	810.405i	0.892835	−	1.54644i
$66$		0			0
$67$	−198.950	−	344.592i	−0.362771	−	0.628338i	0.625645	−	0.780108i	$-0.284836\pi$
$67$	−198.950	−	344.592i	−0.362771	−	0.628338i	−0.988416	+	0.151770i	$0.951503\pi$
$68$	259.493	−	449.456i	0.462768	−	0.801537i
$69$		0			0
$70$	−232.865	−	358.687i	−0.397610	−	0.612447i
$71$	−843.419			−1.40979			−0.704897	−	0.709309i	$-0.749007\pi$
$71$	−843.419			−1.40979			−0.704897	+	0.709309i	$0.749007\pi$
$72$		0			0
$73$	436.140	+	755.417i	0.699265	+	1.21116i	0.968721	+	0.248151i	$0.0798228\pi$
$73$	436.140	+	755.417i	0.699265	+	1.21116i	−0.269456	+	0.963013i	$0.586844\pi$
$74$	246.047	+	426.165i	0.386518	+	0.669469i
$75$		0			0
$76$	−262.620			−0.396375
$77$	533.897	+	822.373i	0.790172	+	1.21712i
$78$		0			0
$79$	277.456	−	480.568i	0.395143	−	0.684407i	−0.597977	−	0.801513i	$-0.704029\pi$
$79$	277.456	−	480.568i	0.395143	−	0.684407i	0.993119	+	0.117106i	$0.0373619\pi$
$80$	8.66040	+	15.0002i	0.0121033	+	0.0209635i
$81$		0			0
$82$	−27.7584	+	48.0789i	−0.0373829	+	0.0647492i
$83$	−297.114			−0.392921			−0.196461	−	0.980512i	$-0.562945\pi$
$83$	−297.114			−0.392921			−0.196461	+	0.980512i	$0.562945\pi$
$84$		0			0
$85$	1390.91			1.77489
$86$	−307.176	+	532.044i	−0.385158	+	0.667114i
$87$		0			0
$88$	−602.728	−	1043.96i	−0.730125	−	1.26461i
$89$	−51.2419	+	88.7536i	−0.0610295	+	0.105706i	−0.894926	−	0.446215i	$-0.852772\pi$
$89$	−51.2419	+	88.7536i	−0.0610295	+	0.105706i	0.833896	+	0.551921i	$0.186105\pi$
$90$		0			0
$91$	1326.09	−	69.3177i	1.52761	−	0.0798513i
$92$	−90.8644			−0.102970
$93$		0			0
$94$	479.659	+	830.793i	0.526308	+	0.911593i
$95$	−351.916	−	609.537i	−0.380062	−	0.658286i
$96$		0			0
$97$	−515.437			−0.539533			−0.269766	−	0.962926i	$-0.586947\pi$
$97$	−515.437			−0.539533			−0.269766	+	0.962926i	$0.586947\pi$
$98$	246.979	−	554.319i	0.254578	−	0.571374i
$99$		0			0
$100$	110.384	−	191.191i	0.110384	−	0.191191i
$101$	−550.975	−	954.317i	−0.542813	−	0.940179i	−0.998741	−	0.0501625i	$-0.984026\pi$
$101$	−550.975	−	954.317i	−0.542813	−	0.940179i	0.455929	−	0.890016i	$-0.349307\pi$
$102$		0			0
$103$	176.814	−	306.251i	0.169146	−	0.292969i	−0.768974	−	0.639280i	$-0.779233\pi$
$103$	176.814	−	306.251i	0.169146	−	0.292969i	0.938120	+	0.346311i	$0.112566\pi$
$104$	−1632.60			−1.53932
$105$		0			0
$106$	454.796			0.416733
$107$	155.332	−	269.042i	0.140341	−	0.243077i	−0.787284	−	0.616590i	$-0.788514\pi$
$107$	155.332	−	269.042i	0.140341	−	0.243077i	0.927625	+	0.373513i	$0.121847\pi$
$108$		0			0
$109$	257.492	+	445.989i	0.226268	+	0.391909i	0.956699	−	0.291078i	$-0.0940140\pi$
$109$	257.492	+	445.989i	0.226268	+	0.391909i	−0.730431	+	0.682987i	$0.760681\pi$
$110$	611.226	−	1058.67i	0.529801	−	0.917642i
$111$		0			0
$112$	−11.1616	+	21.8985i	−0.00941670	+	0.0184751i
$113$	1106.59			0.921233			0.460616	−	0.887599i	$-0.347628\pi$
$113$	1106.59			0.921233			0.460616	+	0.887599i	$0.347628\pi$
$114$		0			0
$115$	−121.760	−	210.895i	−0.0987324	−	0.171009i
$116$	637.467	+	1104.13i	0.510236	+	0.883754i
$117$		0			0
$118$	−558.410			−0.435642
$119$	1074.76	+	1655.48i	0.827928	+	1.27528i
$120$		0			0
$121$	−735.876	+	1274.57i	−0.552875	+	0.957607i
$122$	122.789	+	212.677i	0.0911212	+	0.157827i
$123$		0			0
$124$	−297.851	+	515.893i	−0.215708	+	0.373617i
$125$	−1039.73			−0.743972
$126$		0			0
$127$	1591.62			1.11207			0.556037	−	0.831158i	$-0.312321\pi$
$127$	1591.62			1.11207			0.556037	+	0.831158i	$0.312321\pi$
$128$	−428.425	+	742.054i	−0.295842	+	0.512414i
$129$		0			0
$130$	−827.807	−	1433.80i	−0.558488	−	0.967330i
$131$	408.628	−	707.764i	0.272534	−	0.472043i	−0.696976	−	0.717095i	$-0.745472\pi$
$131$	408.628	−	707.764i	0.272534	−	0.472043i	0.969510	+	0.245052i	$0.0788049\pi$
$132$		0			0
$133$	453.552	−	889.849i	0.295699	−	0.580148i
$134$	−703.984			−0.453843
$135$		0			0
$136$	−1213.32	−	2101.54i	−0.765012	−	1.32504i
$137$	−514.067	−	890.390i	−0.320582	−	0.555264i	0.660026	−	0.751242i	$-0.270545\pi$
$137$	−514.067	−	890.390i	−0.320582	−	0.555264i	−0.980608	+	0.195978i	$0.937212\pi$
$138$		0			0
$139$	−607.307			−0.370583			−0.185292	−	0.982684i	$-0.559323\pi$
$139$	−607.307			−0.370583			−0.185292	+	0.982684i	$0.559323\pi$
$140$	1175.48	−	61.4446i	0.709614	−	0.0370930i
$141$		0			0
$142$	−746.107	+	1292.30i	−0.440929	+	0.763712i
$143$	1897.94	+	3287.33i	1.10989	+	1.92238i
$144$		0			0
$145$	−1708.44	+	2959.11i	−0.978472	+	1.69476i
$146$	1543.28			0.874813
$147$		0			0
$148$	−1354.47			−0.752273
$149$	610.031	−	1056.60i	0.335407	−	0.580942i	−0.648156	−	0.761508i	$-0.724459\pi$
$149$	610.031	−	1056.60i	0.335407	−	0.580942i	0.983563	+	0.180566i	$0.0577928\pi$
$150$		0			0
$151$	−976.718	−	1691.73i	−0.526386	−	0.911726i	−0.999527	−	0.0307402i	$-0.990214\pi$
$151$	−976.718	−	1691.73i	−0.526386	−	0.911726i	0.473142	−	0.880986i	$-0.343120\pi$
$152$	−613.970	+	1063.43i	−0.327629	+	0.567469i
$153$		0			0
$154$	1732.35	−	90.5533i	0.906471	−	0.0473831i
$155$	−1596.51			−0.827320
$156$		0			0
$157$	765.394	+	1325.70i	0.389077	+	0.673901i	0.992326	−	0.123652i	$-0.0394606\pi$
$157$	765.394	+	1325.70i	0.389077	+	0.673901i	−0.603249	+	0.797553i	$0.706127\pi$
$158$	−490.888	−	850.243i	−0.247171	−	0.428112i
$159$		0			0
$160$	−2346.74			−1.15954
$161$	156.926	−	307.881i	0.0768167	−	0.150711i
$162$		0			0
$163$	−1141.60	+	1977.31i	−0.548570	+	0.950151i	0.449803	+	0.893128i	$0.351494\pi$
$163$	−1141.60	+	1977.31i	−0.548570	+	0.950151i	−0.998373	+	0.0570230i	$0.981839\pi$
$164$	−76.4038	−	132.335i	−0.0363789	−	0.0630100i
$165$		0			0
$166$	−262.833	+	455.241i	−0.122891	+	0.212853i
$167$	1071.13			0.496325			0.248162	−	0.968718i	$-0.420173\pi$
$167$	1071.13			0.496325			0.248162	+	0.968718i	$0.420173\pi$
$168$		0			0
$169$	2943.91			1.33997
$170$	1230.43	−	2131.17i	0.555116	−	0.961489i
$171$		0			0
$172$	−845.488	−	1464.43i	−0.374813	−	0.649196i
$173$	−1829.44	+	3168.68i	−0.803985	+	1.39254i	0.112989	+	0.993596i	$0.463958\pi$
$173$	−1829.44	+	3168.68i	−0.803985	+	1.39254i	−0.916974	+	0.398947i	$0.869376\pi$
$174$		0			0
$175$	457.187	+	704.215i	0.197486	+	0.304192i
$176$	−70.2601			−0.0300912
$177$		0			0
$178$	90.6595	+	157.027i	0.0381754	+	0.0661217i
$179$	−405.117	−	701.683i	−0.169161	−	0.292996i	0.768964	−	0.639292i	$-0.220772\pi$
$179$	−405.117	−	701.683i	−0.169161	−	0.292996i	−0.938125	+	0.346296i	$0.887439\pi$
$180$		0			0
$181$	−1730.05			−0.710462			−0.355231	−	0.934779i	$-0.615598\pi$
$181$	−1730.05			−0.710462			−0.355231	+	0.934779i	$0.615598\pi$
$182$	1066.88	−	2093.18i	0.434520	−	0.852509i
$183$		0			0
$184$	−212.429	+	367.938i	−0.0851113	+	0.147417i
$185$	−1815.02	−	3143.70i	−0.721312	−	1.24935i
$186$		0			0
$187$	−2821.05	+	4886.19i	−1.10318	+	1.91077i
$188$	−2640.48			−1.02434
$189$		0			0
$190$	−1245.25			−0.475474
$191$	−537.799	+	931.495i	−0.203737	+	0.352883i	−0.949730	−	0.313071i	$-0.898642\pi$
$191$	−537.799	+	931.495i	−0.203737	+	0.352883i	0.745993	+	0.665954i	$0.231975\pi$
$192$		0			0
$193$	−2246.86	−	3891.67i	−0.837992	−	1.45144i	−0.891571	−	0.452881i	$-0.850396\pi$
$193$	−2246.86	−	3891.67i	−0.837992	−	1.45144i	0.0535795	−	0.998564i	$-0.482937\pi$
$194$	−455.967	+	789.758i	−0.168745	+	0.292275i
$195$		0			0
$196$	981.431	+	1351.59i	0.357664	+	0.492563i
$197$	−101.961			−0.0368753			−0.0184377	−	0.999830i	$-0.505869\pi$
$197$	−101.961			−0.0368753			−0.0184377	+	0.999830i	$0.505869\pi$
$198$		0			0
$199$	267.794	+	463.832i	0.0953940	+	0.165227i	0.909773	−	0.415106i	$-0.136256\pi$
$199$	267.794	+	463.832i	0.0953940	+	0.165227i	−0.814379	+	0.580333i	$0.802922\pi$
$200$	−516.128	−	893.960i	−0.182479	−	0.316063i
$201$		0			0
$202$	−1949.62			−0.679083
$203$	−4842.10	+	253.106i	−1.67413	+	0.0875103i
$204$		0			0
$205$	204.766	−	354.665i	0.0697633	−	0.120834i
$206$	−312.827	−	541.832i	−0.105804	−	0.183259i
$207$		0			0
$208$	−47.5780	+	82.4076i	−0.0158603	+	0.0274709i
$209$	2855.03			0.944912
$210$		0			0
$211$	1247.47			0.407012			0.203506	−	0.979074i	$-0.434766\pi$
$211$	1247.47			0.407012			0.203506	+	0.979074i	$0.434766\pi$
$212$	−625.904	+	1084.10i	−0.202770	+	0.351208i
$213$		0			0
$214$	−274.820	−	476.001i	−0.0877863	−	0.152050i
$215$	2265.95	−	3924.74i	0.718774	−	1.24495i
$216$		0			0
$217$	−1233.63	−	1900.19i	−0.385919	−	0.594439i
$218$	911.133			0.283072
$219$		0			0
$220$	1682.37	+	2913.96i	0.515571	+	0.892995i
$221$	3820.65	+	6617.57i	1.16292	+	2.01423i
$222$		0			0
$223$	2573.28			0.772734			0.386367	−	0.922345i	$-0.373730\pi$
$223$	2573.28			0.772734			0.386367	+	0.922345i	$0.373730\pi$
$224$	−1813.34	−	2793.13i	−0.540888	−	0.833142i
$225$		0			0
$226$	978.915	−	1695.53i	0.288126	−	0.499049i
$227$	−744.416	−	1289.37i	−0.217659	−	0.376997i	0.736433	−	0.676511i	$-0.236509\pi$
$227$	−744.416	−	1289.37i	−0.217659	−	0.376997i	−0.954092	+	0.299514i	$0.903175\pi$
$228$		0			0
$229$	1605.20	−	2780.28i	0.463207	−	0.802297i	−0.535912	−	0.844274i	$-0.680032\pi$
$229$	1605.20	−	2780.28i	0.463207	−	0.802297i	0.999119	+	0.0419764i	$0.0133654\pi$
$230$	−430.848			−0.123519
$231$		0			0
$232$	5961.26			1.68696
$233$	−1463.84	+	2535.45i	−0.411586	+	0.712888i	−0.995063	−	0.0992415i	$-0.968358\pi$
$233$	−1463.84	+	2535.45i	−0.411586	+	0.712888i	0.583477	+	0.812129i	$0.301692\pi$
$234$		0			0
$235$	−3538.31	−	6128.53i	−0.982186	−	1.70120i
$236$	768.500	−	1331.08i	0.211971	−	0.367144i
$237$		0			0
$238$	3487.31	−	182.289i	0.949784	−	0.0496472i
$239$	4263.99			1.15404			0.577019	−	0.816731i	$-0.304216\pi$
$239$	4263.99			1.15404			0.577019	+	0.816731i	$0.304216\pi$
$240$		0			0
$241$	2158.04	+	3737.84i	0.576813	+	0.999069i	0.995842	+	0.0910964i	$0.0290371\pi$
$241$	2158.04	+	3737.84i	0.576813	+	0.999069i	−0.419029	+	0.907973i	$0.637630\pi$
$242$	1301.94	+	2255.03i	0.345835	+	0.599005i
$243$		0			0
$244$	−675.943			−0.177348
$245$	−1821.89	+	4089.06i	−0.475087	+	1.06629i
$246$		0			0
$247$	1933.34	−	3348.64i	0.498038	−	0.862628i
$248$	1392.67	+	2412.18i	0.356592	+	0.617635i
$249$		0			0
$250$	−919.771	+	1593.09i	−0.232686	+	0.403023i
$251$	2107.60			0.530001			0.265001	−	0.964248i	$-0.414628\pi$
$251$	2107.60			0.530001			0.265001	+	0.964248i	$0.414628\pi$
$252$		0			0
$253$	987.819			0.245469
$254$	1407.98	−	2438.70i	0.347814	−	0.602431i
$255$		0			0
$256$	2072.97	+	3590.49i	0.506096	+	0.876585i
$257$	−1410.31	+	2442.73i	−0.342307	+	0.592893i	−0.984861	−	0.173348i	$-0.944542\pi$
$257$	−1410.31	+	2442.73i	−0.342307	+	0.592893i	0.642554	+	0.766241i	$0.277875\pi$
$258$		0			0
$259$	2339.21	−	4589.42i	0.561202	−	1.10105i
$260$	4557.01			1.08698
$261$		0			0
$262$	−722.963	−	1252.21i	−0.170476	−	0.295274i
$263$	−2976.21	−	5154.95i	−0.697799	−	1.20862i	−0.969228	−	0.246165i	$-0.920829\pi$
$263$	−2976.21	−	5154.95i	−0.697799	−	1.20862i	0.271429	−	0.962459i	$-0.412504\pi$
$264$		0			0
$265$	−3354.90			−0.777698
$266$	−962.214	−	1482.12i	−0.221794	−	0.341634i
$267$		0			0
$268$	968.843	−	1678.09i	0.220827	−	0.382483i
$269$	−3321.51	−	5753.02i	−0.752847	−	1.30397i	−0.946438	−	0.322887i	$-0.895347\pi$
$269$	−3321.51	−	5753.02i	−0.752847	−	1.30397i	0.193590	−	0.981082i	$-0.437987\pi$
$270$		0			0
$271$	−480.913	+	832.966i	−0.107799	+	0.186713i	−0.914878	−	0.403730i	$-0.867713\pi$
$271$	−480.913	+	832.966i	−0.107799	+	0.186713i	0.807080	+	0.590443i	$0.201047\pi$
$272$	−141.437			−0.0315291
$273$		0			0
$274$	−1819.02			−0.401062
$275$	−1200.03	+	2078.51i	−0.263143	+	0.455777i
$276$		0			0
$277$	2800.06	+	4849.84i	0.607362	+	1.05198i	0.991673	+	0.128778i	$0.0411055\pi$
$277$	2800.06	+	4849.84i	0.607362	+	1.05198i	−0.384312	+	0.923203i	$0.625561\pi$
$278$	−537.237	+	930.522i	−0.115904	+	0.200752i
$279$		0			0
$280$	2499.31	−	4903.52i	0.533436	−	1.04658i
$281$	−1044.12			−0.221661			−0.110831	−	0.993839i	$-0.535351\pi$
$281$	−1044.12			−0.221661			−0.110831	+	0.993839i	$0.535351\pi$
$282$		0			0
$283$	−1161.99	−	2012.62i	−0.244074	−	0.422749i	0.717797	−	0.696253i	$-0.245151\pi$
$283$	−1161.99	−	2012.62i	−0.244074	−	0.422749i	−0.961871	+	0.273504i	$0.911817\pi$
$284$	−2053.63	−	3556.99i	−0.429086	−	0.743199i
$285$		0			0
$286$	6715.84			1.38852
$287$	580.351	−	30.3361i	0.119363	−	0.00623932i
$288$		0			0
$289$	−3222.42	+	5581.39i	−0.655896	+	1.13605i
$290$	3022.65	+	5235.39i	0.612056	+	1.06011i
$291$		0			0
$292$	−2123.90	+	3678.71i	−0.425658	+	0.737261i
$293$	4140.37			0.825540			0.412770	−	0.910835i	$-0.364561\pi$
$293$	4140.37			0.825540			0.412770	+	0.910835i	$0.364561\pi$
$294$		0			0
$295$	4119.23			0.812986
$296$	−3166.56	+	5484.65i	−0.621800	+	1.07699i
$297$		0			0
$298$	−1079.29	−	1869.39i	−0.209805	−	0.363392i
$299$	668.921	−	1158.61i	0.129380	−	0.224093i
$300$		0			0
$301$	6422.20	−	335.701i	1.22980	−	0.0642841i
$302$	−3456.11			−0.658532
$303$		0			0
$304$	35.7853	+	61.9820i	0.00675141	+	0.0116938i
$305$	−905.780	−	1568.86i	−0.170049	−	0.294533i
$306$		0			0
$307$	3074.68			0.571600			0.285800	−	0.958289i	$-0.407741\pi$
$307$	3074.68			0.571600			0.285800	+	0.958289i	$0.407741\pi$
$308$	−2168.25	+	4254.01i	−0.401129	+	0.786997i
$309$		0			0
$310$	−1412.31	+	2446.19i	−0.258754	+	0.448175i
$311$	1159.17	+	2007.74i	0.211352	+	0.366073i	0.952138	−	0.305669i	$-0.0988800\pi$
$311$	1159.17	+	2007.74i	0.211352	+	0.366073i	−0.740786	+	0.671741i	$0.765547\pi$
$312$		0			0
$313$	−947.953	+	1641.90i	−0.171187	+	0.296504i	−0.938835	−	0.344367i	$-0.888094\pi$
$313$	−947.953	+	1641.90i	−0.171187	+	0.296504i	0.767648	+	0.640871i	$0.221427\pi$
$314$	2708.34			0.486753
$315$		0			0
$316$	2702.30			0.481064
$317$	486.154	−	842.043i	0.0861360	−	0.149192i	−0.819739	−	0.572738i	$-0.805881\pi$
$317$	486.154	−	842.043i	0.0861360	−	0.149192i	0.905875	+	0.423546i	$0.139215\pi$
$318$		0			0
$319$	−6930.13	−	12003.3i	−1.21634	−	2.10676i
$320$	−2145.27	+	3715.71i	−0.374762	+	0.649108i
$321$		0			0
$322$	−332.919	−	512.802i	−0.0576175	−	0.0887495i
$323$	5747.33			0.990062
$324$		0			0
$325$	1625.24	+	2815.00i	0.277392	+	0.480456i
$326$	2019.77	+	3498.34i	0.343143	+	0.594341i
$327$		0			0
$328$	−714.488			−0.120277
$329$	4560.19	−	8946.89i	0.764169	−	1.49926i
$330$		0			0
$331$	2234.82	−	3870.82i	0.371108	−	0.642779i	−0.618628	−	0.785684i	$-0.712311\pi$
$331$	2234.82	−	3870.82i	0.371108	−	0.642779i	0.989736	+	0.142905i	$0.0456445\pi$
$332$	−723.438	−	1253.03i	−0.119590	−	0.207136i
$333$		0			0
$334$	947.542	−	1641.19i	0.155231	−	0.268868i
$335$	5193.09			0.846952
$336$		0			0
$337$	−8494.45			−1.37306			−0.686532	−	0.727100i	$-0.740868\pi$
$337$	−8494.45			−1.37306			−0.686532	+	0.727100i	$0.740868\pi$
$338$	2604.25	−	4510.69i	0.419090	−	0.725885i
$339$		0			0
$340$	3386.71	+	5865.95i	0.540206	+	0.935664i
$341$	3238.04	−	5608.45i	0.514222	−	0.890659i
$342$		0			0
$343$	−6274.64	+	991.194i	−0.987752	+	0.156033i
$344$	−7906.56			−1.23923
$345$		0			0
$346$	3236.72	+	5606.16i	0.502911	+	0.871067i
$347$	−4230.65	−	7327.70i	−0.654505	−	1.13364i	−0.982018	−	0.188789i	$-0.939544\pi$
$347$	−4230.65	−	7327.70i	−0.654505	−	1.13364i	0.327513	−	0.944847i	$-0.393790\pi$
$348$		0			0
$349$	−5910.68			−0.906566			−0.453283	−	0.891367i	$-0.649747\pi$
$349$	−5910.68			−0.906566			−0.453283	+	0.891367i	$0.649747\pi$
$350$	1483.44	−	77.5426i	0.226553	−	0.0118424i
$351$		0			0
$352$	4759.67	−	8243.99i	0.720714	−	1.24831i
$353$	3023.09	+	5236.14i	0.455815	+	0.789494i	0.998735	−	0.0502901i	$-0.0160146\pi$
$353$	3023.09	+	5236.14i	0.455815	+	0.789494i	−0.542920	+	0.839785i	$0.682681\pi$
$354$		0			0
$355$	5503.82	−	9532.90i	0.822853	−	1.42522i
$356$	−499.073			−0.0743000
$357$		0			0
$358$	−1433.50			−0.211628
$359$	−5448.34	+	9436.81i	−0.800982	+	1.38734i	0.117988	+	0.993015i	$0.462355\pi$
$359$	−5448.34	+	9436.81i	−0.800982	+	1.38734i	−0.918970	+	0.394327i	$0.870978\pi$
$360$		0			0
$361$	1975.36	+	3421.42i	0.287995	+	0.498822i
$362$	−1530.44	+	2650.80i	−0.222205	+	0.384870i
$363$		0			0
$364$	3521.23	+	5423.82i	0.507040	+	0.781004i
$365$	−11384.3			−1.63256
$366$		0			0
$367$	−3887.83	−	6733.92i	−0.552979	−	0.957787i	−0.998058	−	0.0622958i	$-0.980158\pi$
$367$	−3887.83	−	6733.92i	−0.552979	−	0.957787i	0.445079	−	0.895491i	$-0.353176\pi$
$368$	12.3815	+	21.4453i	0.00175388	+	0.00303781i
$369$		0			0
$370$	−6422.42			−0.902394
$371$	−2592.35	−	3993.06i	−0.362772	−	0.558785i
$372$		0			0
$373$	−5964.54	+	10330.9i	−0.827969	+	1.43408i	0.0716601	+	0.997429i	$0.477170\pi$
$373$	−5964.54	+	10330.9i	−0.827969	+	1.43408i	−0.899629	+	0.436655i	$0.856163\pi$
$374$	4991.12	+	8644.87i	0.690066	+	1.19523i
$375$		0			0
$376$	−6173.10	+	10692.1i	−0.846684	+	1.46650i
$377$	−18771.5			−2.56441
$378$		0			0
$379$	−8130.56			−1.10195			−0.550975	−	0.834522i	$-0.685744\pi$
$379$	−8130.56			−1.10195			−0.550975	+	0.834522i	$0.685744\pi$
$380$	1713.75	−	2968.31i	0.231352	−	0.400713i
$381$		0			0
$382$	951.498	+	1648.04i	0.127442	+	0.220736i
$383$	5425.88	−	9397.90i	0.723889	−	1.25381i	−0.235540	−	0.971865i	$-0.575686\pi$
$383$	5425.88	−	9397.90i	0.723889	−	1.25381i	0.959429	−	0.281949i	$-0.0909808\pi$
$384$		0			0
$385$	−12779.0	+	667.986i	−1.69164	+	0.0884253i
$386$	−7950.49			−1.04837
$387$		0			0
$388$	−1255.03	−	2173.78i	−0.164213	−	0.284425i
$389$	−5884.87	−	10192.9i	−0.767031	−	1.32854i	−0.939166	−	0.343463i	$-0.888400\pi$
$389$	−5884.87	−	10192.9i	−0.767031	−	1.32854i	0.172135	−	0.985073i	$-0.444933\pi$
$390$		0			0
$391$	1988.53			0.257198
$392$	7767.47	−	814.268i	1.00081	−	0.104915i
$393$		0			0
$394$	−90.1972	+	156.226i	−0.0115332	+	0.0199760i
$395$	3621.14	+	6272.00i	0.461265	+	0.798934i
$396$		0			0
$397$	−5066.25	+	8774.99i	−0.640472	+	1.10933i	0.344855	+	0.938656i	$0.387928\pi$
$397$	−5066.25	+	8774.99i	−0.640472	+	1.10933i	−0.985327	+	0.170675i	$0.945405\pi$
$398$	947.586			0.119342
$399$		0			0
$400$	−60.1652			−0.00752064
$401$	−2402.12	+	4160.60i	−0.299143	+	0.518130i	−0.975940	−	0.218039i	$-0.930034\pi$
$401$	−2402.12	+	4160.60i	−0.299143	+	0.518130i	0.676797	+	0.736169i	$0.263367\pi$
$402$		0			0
$403$	−4385.41	−	7595.75i	−0.542066	−	0.938886i
$404$	2683.12	−	4647.31i	0.330422	−	0.572307i
$405$		0			0
$406$	−3895.62	+	7643.02i	−0.476197	+	0.934278i
$407$	14724.9			1.79333
$408$		0			0
$409$	4418.75	+	7653.50i	0.534213	+	0.925284i	0.999201	+	0.0399668i	$0.0127252\pi$
$409$	4418.75	+	7653.50i	0.534213	+	0.925284i	−0.464988	+	0.885317i	$0.653941\pi$
$410$	−362.281	−	627.489i	−0.0436385	−	0.0755841i
$411$		0			0
$412$	1722.09			0.205925
$413$	3182.95	+	4902.77i	0.379232	+	0.584139i
$414$		0			0
$415$	1938.85	−	3358.18i	0.229336	−	0.397221i
$416$	−6446.21	−	11165.2i	−0.759739	−	1.31591i
$417$		0			0
$418$	2525.62	−	4374.51i	0.295532	−	0.511876i
$419$	−5730.73			−0.668173			−0.334086	−	0.942542i	$-0.608428\pi$
$419$	−5730.73			−0.668173			−0.334086	+	0.942542i	$0.608428\pi$
$420$		0			0
$421$	1841.98			0.213236			0.106618	−	0.994300i	$-0.465998\pi$
$421$	1841.98			0.213236			0.106618	+	0.994300i	$0.465998\pi$
$422$	1103.54	−	1911.39i	0.127298	−	0.220486i
$423$		0			0
$424$	2926.56	+	5068.95i	0.335204	+	0.580590i
$425$	−2415.72	+	4184.15i	−0.275717	+	0.477555i
$426$		0			0
$427$	1167.38	−	2290.34i	0.132303	−	0.259572i
$428$	1512.86			0.170857
$429$		0			0
$430$	−4009.02	−	6943.83i	−0.449610	−	0.778747i
$431$	4573.50	+	7921.54i	0.511132	+	0.885307i	0.999917	+	0.0129023i	$0.00410704\pi$
$431$	4573.50	+	7921.54i	0.511132	+	0.885307i	−0.488785	+	0.872404i	$0.662560\pi$
$432$		0			0
$433$	−2469.71			−0.274103			−0.137052	−	0.990564i	$-0.543763\pi$
$433$	−2469.71			−0.274103			−0.137052	+	0.990564i	$0.543763\pi$
$434$	−4002.79	+	209.234i	−0.442719	+	0.0231418i
$435$		0			0
$436$	−1253.93	+	2171.87i	−0.137734	+	0.238563i
$437$	−503.122	−	871.433i	−0.0550746	−	0.0953920i
$438$		0			0
$439$	1852.20	−	3208.10i	0.201368	−	0.348779i	−0.747602	−	0.664147i	$-0.768795\pi$
$439$	1852.20	−	3208.10i	0.201368	−	0.348779i	0.948969	+	0.315368i	$0.102128\pi$
$440$	15732.7			1.70460
$441$		0			0
$442$	13519.3			1.45486
$443$	−675.693	+	1170.33i	−0.0724676	+	0.125517i	−0.899982	−	0.435927i	$-0.856421\pi$
$443$	−675.693	+	1170.33i	−0.0724676	+	0.125517i	0.827515	+	0.561444i	$0.189754\pi$
$444$		0			0
$445$	−668.769	−	1158.34i	−0.0712421	−	0.123395i
$446$	2276.38	−	3942.81i	0.241681	−	0.418604i
$447$		0			0
$448$	−6080.15	+	317.822i	−0.641205	+	0.0335171i
$449$	15461.0			1.62505			0.812526	−	0.582926i	$-0.198092\pi$
$449$	15461.0			1.62505			0.812526	+	0.582926i	$0.198092\pi$
$450$		0			0
$451$	830.613	+	1438.66i	0.0867229	+	0.150208i
$452$	2694.42	+	4666.88i	0.280387	+	0.485645i
$453$		0			0
$454$	−2634.11			−0.272301
$455$	−7870.10	+	15440.8i	−0.810893	+	1.59093i
$456$		0			0
$457$	−6784.81	+	11751.6i	−0.694486	+	1.20288i	0.275868	+	0.961196i	$0.411035\pi$
$457$	−6784.81	+	11751.6i	−0.694486	+	1.20288i	−0.970354	+	0.241689i	$0.922299\pi$
$458$	−2839.98	−	4919.00i	−0.289746	−	0.501855i
$459$		0			0
$460$	592.946	−	1027.01i	0.0601005	−	0.104097i
$461$	7979.72			0.806188			0.403094	−	0.915159i	$-0.367935\pi$
$461$	7979.72			0.806188			0.403094	+	0.915159i	$0.367935\pi$
$462$		0			0
$463$	−18086.2			−1.81542			−0.907709	−	0.419600i	$-0.862170\pi$
$463$	−18086.2			−1.81542			−0.907709	+	0.419600i	$0.862170\pi$
$464$	173.726	−	300.903i	0.0173816	−	0.0301057i
$465$		0			0
$466$	2589.90	+	4485.83i	0.257456	+	0.445927i
$467$	−2902.27	+	5026.88i	−0.287583	+	0.498108i	−0.973232	−	0.229824i	$-0.926185\pi$
$467$	−2902.27	+	5026.88i	−0.287583	+	0.498108i	0.685649	+	0.727932i	$0.259518\pi$
$468$		0			0
$469$	4012.73	+	6180.90i	0.395076	+	0.608544i
$470$	−12520.3			−1.22876
$471$		0			0
$472$	−3593.30	−	6223.78i	−0.350414	−	0.606934i
$473$	9191.60	+	15920.3i	0.893510	+	1.54761i
$474$		0			0
$475$	2444.82			0.236160
$476$	−4364.81	+	8563.56i	−0.420296	+	0.824601i
$477$		0			0
$478$	3772.02	−	6533.34i	0.360938	−	0.625163i
$479$	−2172.94	−	3763.65i	−0.207274	−	0.359009i	0.743581	−	0.668646i	$-0.233126\pi$
$479$	−2172.94	−	3763.65i	−0.207274	−	0.359009i	−0.950855	+	0.309637i	$0.899793\pi$
$480$		0			0
$481$	9971.24	−	17270.7i	0.945217	−	1.63716i
$482$	7636.22			0.721619
$483$		0			0
$484$	−7167.10			−0.673093
$485$	3363.54	−	5825.83i	0.314908	−	0.545437i
$486$		0			0
$487$	9390.55	+	16264.9i	0.873771	+	1.51342i	0.858066	+	0.513540i	$0.171666\pi$
$487$	9390.55	+	16264.9i	0.873771	+	1.51342i	0.0157056	+	0.999877i	$0.495001\pi$
$488$	−1580.27	+	2737.10i	−0.146589	+	0.253899i
$489$		0			0
$490$	4653.61	+	6408.80i	0.429038	+	0.590857i
$491$	−7552.56			−0.694180			−0.347090	−	0.937832i	$-0.612830\pi$
$491$	−7552.56			−0.694180			−0.347090	+	0.937832i	$0.612830\pi$
$492$		0			0
$493$	−13950.7	−	24163.4i	−1.27446	−	2.20743i
$494$	−3420.55	−	5924.57i	−0.311534	−	0.539593i
$495$		0			0
$496$	162.344			0.0146965
$497$	15599.0	−	815.394i	1.40787	−	0.0735924i
$498$		0			0
$499$	−4450.95	+	7709.27i	−0.399302	+	0.691612i	−0.993640	−	0.112604i	$-0.964081\pi$
$499$	−4450.95	+	7709.27i	−0.399302	+	0.691612i	0.594338	+	0.804216i	$0.297414\pi$
$500$	−2531.63	−	4384.91i	−0.226436	−	0.392199i
$501$		0			0
$502$	1864.43	−	3229.28i	0.165764	−	0.287111i
$503$	−18241.5			−1.61700			−0.808498	−	0.588500i	$-0.799719\pi$
$503$	−18241.5			−1.61700			−0.808498	+	0.588500i	$0.799719\pi$
$504$		0			0
$505$	14381.8			1.26729
$506$	873.847	−	1513.55i	0.0767732	−	0.132975i
$507$		0			0
$508$	3875.41	+	6712.41i	0.338472	+	0.586250i
$509$	4492.39	−	7781.04i	0.391201	−	0.677581i	−0.601407	−	0.798943i	$-0.705393\pi$
$509$	4492.39	−	7781.04i	0.391201	−	0.677581i	0.992608	+	0.121362i	$0.0387263\pi$
$510$		0			0
$511$	−8796.74	−	13549.8i	−0.761536	−	1.17301i
$512$	480.383			0.0414651
$513$		0			0
$514$	2495.19	+	4321.79i	0.214121	+	0.370868i
$515$	2307.64	+	3996.95i	0.197450	+	0.341993i
$516$		0			0
$517$	28705.6			2.44192
$518$	−4962.64	−	7644.06i	−0.420938	−	0.648380i
$519$		0			0
$520$	10653.7	−	18452.7i	0.898452	−	1.55617i
$521$	−4444.36	−	7697.87i	−0.373726	−	0.647312i	0.616410	−	0.787426i	$-0.288587\pi$
$521$	−4444.36	−	7697.87i	−0.373726	−	0.647312i	−0.990135	+	0.140114i	$0.955253\pi$
$522$		0			0
$523$	10519.5	−	18220.2i	0.879510	−	1.52336i	0.0276313	−	0.999618i	$-0.491204\pi$
$523$	10519.5	−	18220.2i	0.879510	−	1.52336i	0.851879	−	0.523738i	$-0.175463\pi$
$524$	3979.85			0.331795
$525$		0			0
$526$	−10531.3			−0.872978
$527$	6518.35	−	11290.1i	0.538793	−	0.933217i
$528$		0			0
$529$	5909.42	+	10235.4i	0.485693	+	0.841244i
$530$	−2967.82	+	5140.42i	−0.243234	+	0.421294i
$531$		0			0
$532$	4857.15	−	253.893i	0.395835	−	0.0206911i
$533$	2249.86			0.182838
$534$		0			0
$535$	2027.27	+	3511.33i	0.163825	+	0.283753i
$536$	−4530.06	−	7846.29i	−0.365053	−	0.632291i
$537$		0			0
$538$	−11753.1			−0.941846
$539$	−10669.5	−	14693.6i	−0.852629	−	1.17421i
$540$		0			0
$541$	−4003.07	+	6933.51i	−0.318124	+	0.551007i	−0.980097	−	0.198521i	$-0.936386\pi$
$541$	−4003.07	+	6933.51i	−0.318124	+	0.551007i	0.661972	+	0.749528i	$0.269720\pi$
$542$	850.854	+	1473.72i	0.0674304	+	0.116793i
$543$		0			0
$544$	9581.47	−	16595.6i	0.755151	−	1.30796i
$545$	−6721.17			−0.528263
$546$		0			0
$547$	22259.4			1.73993			0.869965	−	0.493114i	$-0.164141\pi$
$547$	22259.4			1.73993			0.869965	+	0.493114i	$0.164141\pi$
$548$	2503.39	−	4336.00i	0.195145	−	0.338001i
$549$		0			0
$550$	2123.14	+	3677.39i	0.164602	+	0.285099i
$551$	−7059.39	+	12227.2i	−0.545808	+	0.945367i
$552$		0			0
$553$	−4666.95	+	9156.35i	−0.358877	+	0.704101i
$554$	9907.98			0.759837
$555$		0			0
$556$	−1478.72	−	2561.22i	−0.112791	−	0.195360i
$557$	3741.96	+	6481.27i	0.284653	+	0.493034i	0.972525	−	0.232798i	$-0.0747881\pi$
$557$	3741.96	+	6481.27i	0.284653	+	0.493034i	−0.687872	+	0.725832i	$0.741455\pi$
$558$		0			0
$559$	24897.1			1.88378
$560$	−174.676	−	269.057i	−0.0131811	−	0.0203031i
$561$		0			0
$562$	−923.649	+	1599.81i	−0.0693270	+	0.120078i
$563$	−3146.34	−	5449.63i	−0.235529	−	0.407947i	0.723898	−	0.689907i	$-0.242349\pi$
$563$	−3146.34	−	5449.63i	−0.235529	−	0.407947i	−0.959426	+	0.281960i	$0.909015\pi$
$564$		0			0
$565$	−7221.18	+	12507.5i	−0.537695	+	0.931314i
$566$	−4111.69			−0.305348
$567$		0			0
$568$	−19204.5			−1.41866
$569$	−5169.22	+	8953.36i	−0.380853	+	0.659656i	−0.991184	−	0.132490i	$-0.957703\pi$
$569$	−5169.22	+	8953.36i	−0.380853	+	0.659656i	0.610332	+	0.792146i	$0.291036\pi$
$570$		0			0
$571$	7269.81	+	12591.7i	0.532806	+	0.922847i	0.999266	+	0.0383046i	$0.0121957\pi$
$571$	7269.81	+	12591.7i	0.532806	+	0.922847i	−0.466460	+	0.884542i	$0.654471\pi$
$572$	−9242.53	+	16008.5i	−0.675611	+	1.17019i
$573$		0			0
$574$	466.910	−	916.056i	0.0339520	−	0.0666123i
$575$	845.889			0.0613496
$576$		0			0
$577$	5972.54	+	10344.7i	0.430919	+	0.746373i	0.996953	−	0.0780089i	$-0.0248562\pi$
$577$	5972.54	+	10344.7i	0.430919	+	0.746373i	−0.566034	+	0.824382i	$0.691523\pi$
$578$	5701.25	+	9874.85i	0.410278	+	0.710622i
$579$		0			0
$580$	−16639.4			−1.19123
$581$	5495.12	−	287.241i	0.392385	−	0.0205108i
$582$		0			0
$583$	6804.42	−	11785.6i	0.483380	−	0.837238i
$584$	9930.82	+	17200.7i	0.703665	+	1.21878i
$585$		0			0
$586$	3662.67	−	6343.93i	0.258197	−	0.447210i
$587$	−27431.6			−1.92883			−0.964414	−	0.264398i	$-0.914827\pi$
$587$	−27431.6			−1.92883			−0.964414	+	0.264398i	$0.914827\pi$
$588$		0			0
$589$	−6596.88			−0.461493
$590$	3643.97	−	6311.53i	0.254271	−	0.440410i
$591$		0			0
$592$	184.564	+	319.673i	0.0128134	+	0.0221934i
$593$	−1824.41	+	3159.98i	−0.126340	+	0.218827i	−0.922256	−	0.386580i	$-0.873656\pi$
$593$	−1824.41	+	3159.98i	−0.126340	+	0.218827i	0.795916	+	0.605407i	$0.206990\pi$
$594$		0			0
$595$	−25724.9	+	1344.69i	−1.77247	+	0.0926505i
$596$	5941.42			0.408339
$597$		0			0
$598$	−1183.49	−	2049.86i	−0.0809303	−	0.140175i
$599$	5424.85	+	9396.12i	0.370039	+	0.640927i	0.989571	−	0.144045i	$-0.0460109\pi$
$599$	5424.85	+	9396.12i	0.370039	+	0.640927i	−0.619532	+	0.784971i	$0.712678\pi$
$600$		0			0
$601$	23865.9			1.61982			0.809908	−	0.586557i	$-0.199517\pi$
$601$	23865.9			1.61982			0.809908	+	0.586557i	$0.199517\pi$
$602$	5166.85	−	10137.1i	0.349809	−	0.686310i
$603$		0			0
$604$	4756.40	−	8238.32i	0.320422	−	0.554988i
$605$	−9604.08	−	16634.8i	−0.645391	−	1.11785i
$606$		0			0
$607$	10759.9	−	18636.8i	0.719493	−	1.24620i	−0.241708	−	0.970349i	$-0.577708\pi$
$607$	10759.9	−	18636.8i	0.719493	−	1.24620i	0.961201	−	0.275849i	$-0.0889591\pi$
$608$	−9696.89			−0.646811
$609$		0			0
$610$	−3205.09			−0.212738
$611$	19438.6	−	33668.6i	1.28707	−	2.22927i
$612$		0			0
$613$	−3089.48	−	5351.13i	−0.203561	−	0.352578i	0.746112	−	0.665820i	$-0.231918\pi$
$613$	−3089.48	−	5351.13i	−0.203561	−	0.352578i	−0.949673	+	0.313242i	$0.898585\pi$
$614$	2719.93	−	4711.06i	0.178774	−	0.309646i
$615$		0			0
$616$	12156.7	+	18725.3i	0.795143	+	1.22478i
$617$	1011.92			0.0660267			0.0330134	−	0.999455i	$-0.489490\pi$
$617$	1011.92			0.0660267			0.0330134	+	0.999455i	$0.489490\pi$
$618$		0			0
$619$	1984.27	+	3436.86i	0.128844	+	0.223165i	0.923229	−	0.384250i	$-0.125540\pi$
$619$	1984.27	+	3436.86i	0.128844	+	0.223165i	−0.794385	+	0.607415i	$0.792207\pi$
$620$	−3887.32	−	6733.03i	−0.251804	−	0.436137i
$621$		0			0
$622$	4101.71			0.264411
$623$	861.915	−	1691.04i	0.0554284	−	0.108748i
$624$		0			0
$625$	9618.30	−	16659.4i	0.615571	−	1.06620i
$626$	1677.16	+	2904.93i	0.107081	+	0.185470i
$627$		0			0
$628$	−3727.30	+	6455.86i	−0.236840	+	0.410218i
$629$	29642.0			1.87902
$630$		0			0
$631$	9288.00			0.585974			0.292987	−	0.956116i	$-0.405351\pi$
$631$	9288.00			0.585974			0.292987	+	0.956116i	$0.405351\pi$
$632$	6317.62	−	10942.4i	0.397629	−	0.688713i
$633$		0			0
$634$	−860.125	−	1489.78i	−0.0538800	−	0.0933229i
$635$	−10386.3	+	17989.6i	−0.649082	+	1.12424i
$636$		0			0
$637$	−24459.1	+	2564.06i	−1.52136	+	0.159485i
$638$	−24522.2			−1.52170
$639$		0			0
$640$	−5591.47	−	9684.72i	−0.345348	−	0.598159i
$641$	1629.43	+	2822.26i	0.100404	+	0.173904i	0.911851	−	0.410521i	$-0.134653\pi$
$641$	1629.43	+	2822.26i	0.100404	+	0.173904i	−0.811447	+	0.584425i	$0.801320\pi$
$642$		0			0
$643$	−17217.9			−1.05600			−0.528001	−	0.849244i	$-0.677058\pi$
$643$	−17217.9			−1.05600			−0.528001	+	0.849244i	$0.677058\pi$
$644$	1680.54	−	87.8451i	0.102830	−	0.00537513i
$645$		0			0
$646$	5084.22	−	8806.12i	0.309653	−	0.536335i
$647$	5015.34	+	8686.82i	0.304750	+	0.527843i	0.977206	−	0.212295i	$-0.0680937\pi$
$647$	5015.34	+	8686.82i	0.304750	+	0.527843i	−0.672456	+	0.740138i	$0.734760\pi$
$648$		0			0
$649$	−8354.63	+	14470.6i	−0.505313	+	0.875227i
$650$	5750.91			0.347030
$651$		0			0
$652$	−11118.6			−0.667852
$653$	−15601.8	+	27023.1i	−0.934986	+	1.61944i	−0.160328	+	0.987064i	$0.551255\pi$
$653$	−15601.8	+	27023.1i	−0.934986	+	1.61944i	−0.774658	+	0.632380i	$0.782078\pi$
$654$		0			0
$655$	5333.09	+	9237.19i	0.318139	+	0.551033i
$656$	−20.8220	+	36.0648i	−0.00123927	+	0.00214648i
$657$		0			0
$658$	−9674.48	−	14901.8i	−0.573177	−	0.882876i
$659$	−2666.60			−0.157627			−0.0788133	−	0.996889i	$-0.525113\pi$
$659$	−2666.60			−0.157627			−0.0788133	+	0.996889i	$0.525113\pi$
$660$		0			0
$661$	10161.2	+	17599.6i	0.597917	+	1.03562i	0.993128	+	0.117032i	$0.0373381\pi$
$661$	10161.2	+	17599.6i	0.597917	+	1.03562i	−0.395211	+	0.918590i	$0.629329\pi$
$662$	−3953.95	−	6848.44i	−0.232137	−	0.402073i
$663$		0			0
$664$	−6765.21			−0.395393
$665$	7097.98	+	10933.2i	0.413907	+	0.637549i
$666$		0			0
$667$	−2442.50	+	4230.53i	−0.141790	+	0.245587i
$668$	2608.07	+	4517.31i	0.151062	+	0.261647i
$669$		0			0
$670$	4593.93	−	7956.91i	0.264894	−	0.458810i
$671$	7348.42			0.422776
$672$		0			0
$673$	−16480.1			−0.943922			−0.471961	−	0.881619i	$-0.656454\pi$
$673$	−16480.1			−0.943922			−0.471961	+	0.881619i	$0.656454\pi$
$674$	−7514.38	+	13015.3i	−0.429441	+	0.743814i
$675$		0			0
$676$	7168.08	+	12415.5i	0.407834	+	0.706388i
$677$	9832.02	−	17029.6i	0.558161	−	0.966764i	−0.439489	−	0.898248i	$-0.644840\pi$
$677$	9832.02	−	17029.6i	0.558161	−	0.966764i	0.997650	−	0.0685158i	$-0.0218264\pi$
$678$		0			0
$679$	9533.01	−	498.310i	0.538797	−	0.0281640i
$680$	31670.7			1.78605
$681$		0			0
$682$	−5728.89	−	9922.73i	−0.321658	−	0.557127i
$683$	−6034.92	−	10452.8i	−0.338096	−	0.585600i	0.645978	−	0.763356i	$-0.276450\pi$
$683$	−6034.92	−	10452.8i	−0.338096	−	0.585600i	−0.984075	+	0.177756i	$0.943116\pi$
$684$		0			0
$685$	13418.4			0.748454
$686$	−4031.97	+	10490.9i	−0.224404	+	0.583885i
$687$		0			0
$688$	−230.418	+	399.095i	−0.0127683	+	0.0221153i
$689$	−9215.50	−	15961.7i	−0.509554	−	0.882573i
$690$		0			0
$691$	541.776	−	938.384i	0.0298265	−	0.0516611i	−0.850727	−	0.525608i	$-0.823838\pi$
$691$	541.776	−	938.384i	0.0298265	−	0.0516611i	0.880553	+	0.473947i	$0.157171\pi$
$692$	−17817.9			−0.978806
$693$		0			0
$694$	−14970.1			−0.818815
$695$	3963.05	−	6864.20i	0.216298	−	0.374639i
$696$		0			0
$697$	1672.07	+	2896.11i	0.0908667	+	0.157386i
$698$	−5228.72	+	9056.42i	−0.283539	+	0.491104i
$699$		0			0
$700$	−1856.72	+	3642.80i	−0.100253	+	0.196693i
$701$	−19478.9			−1.04951			−0.524755	−	0.851253i	$-0.675843\pi$
$701$	−19478.9			−1.04951			−0.524755	+	0.851253i	$0.675843\pi$
$702$		0			0
$703$	−7499.77	−	12990.0i	−0.402360	−	0.696908i
$704$	−8702.06	−	15072.4i	−0.465868	−	0.806907i
$705$		0			0
$706$	10697.2			0.570245
$707$	11112.9	+	17117.4i	0.591151	+	0.910562i
$708$		0			0
$709$	−13813.4	+	23925.5i	−0.731695	+	1.26733i	0.224463	+	0.974483i	$0.427937\pi$
$709$	−13813.4	+	23925.5i	−0.731695	+	1.26733i	−0.956158	+	0.292851i	$0.905396\pi$
$710$	−9737.61	−	16866.0i	−0.514713	−	0.891509i
$711$		0			0
$712$	−1166.77	+	2020.90i	−0.0614135	+	0.106371i
$713$	−2282.47			−0.119887
$714$		0			0
$715$	−49540.9			−2.59122
$716$	1972.83	−	3417.03i	0.102972	−	0.178353i
$717$		0			0
$718$	9639.45	+	16696.0i	0.501032	+	0.867813i
$719$	−1067.47	+	1848.91i	−0.0553684	+	0.0959009i	−0.892381	−	0.451283i	$-0.850967\pi$
$719$	−1067.47	+	1848.91i	−0.0553684	+	0.0959009i	0.837013	+	0.547183i	$0.184300\pi$
$720$		0			0
$721$	−2974.10	+	5835.05i	−0.153622	+	0.301399i
$722$	6989.79			0.360295
$723$		0			0
$724$	−4212.47	−	7296.22i	−0.216237	−	0.374533i
$725$	−5934.41	−	10278.7i	−0.303998	−	0.526540i
$726$		0			0
$727$	12294.4			0.627198			0.313599	−	0.949556i	$-0.398465\pi$
$727$	12294.4			0.627198			0.313599	+	0.949556i	$0.398465\pi$
$728$	30194.9	−	1578.35i	1.53722	−	0.0803537i
$729$		0			0
$730$	−10070.8	+	17443.2i	−0.510601	+	0.884386i
$731$	18503.2	+	32048.5i	0.936204	+	1.62155i
$732$		0			0
$733$	9103.87	−	15768.4i	0.458744	−	0.794567i	−0.540151	−	0.841568i	$-0.681633\pi$
$733$	9103.87	−	15768.4i	0.458744	−	0.794567i	0.998895	+	0.0470008i	$0.0149663\pi$
$734$	−13757.1			−0.691801
$735$		0			0
$736$	−3355.05			−0.168028
$737$	−10532.6	+	18243.1i	−0.526424	+	0.911794i
$738$		0			0
$739$	−1268.68	−	2197.42i	−0.0631519	−	0.109382i	0.832721	−	0.553693i	$-0.186782\pi$
$739$	−1268.68	−	2197.42i	−0.0631519	−	0.109382i	−0.895873	+	0.444311i	$0.853449\pi$
$740$	8838.72	−	15309.1i	0.439078	−	0.760506i
$741$		0			0
$742$	−8411.46	+	439.684i	−0.416165	+	0.0217538i
$743$	20574.2			1.01587			0.507937	−	0.861394i	$-0.330408\pi$
$743$	20574.2			1.01587			0.507937	+	0.861394i	$0.330408\pi$
$744$		0			0
$745$	7961.65	+	13790.0i	0.391533	+	0.678155i
$746$	10552.7	+	18277.9i	0.517913	+	0.897052i
$747$		0			0
$748$	−27475.7			−1.34306
$749$	−2612.76	+	5126.11i	−0.127461	+	0.250072i
$750$		0			0
$751$	−12473.3	+	21604.3i	−0.606067	+	1.04974i	0.385815	+	0.922576i	$0.373920\pi$
$751$	−12473.3	+	21604.3i	−0.606067	+	1.04974i	−0.991882	+	0.127163i	$0.959413\pi$
$752$	359.800	+	623.191i	0.0174475	+	0.0302200i
$753$		0			0
$754$	−16605.7	+	28761.9i	−0.802047	+	1.38919i
$755$	25494.7			1.22894
$756$		0			0
$757$	−24686.4			−1.18526			−0.592631	−	0.805474i	$-0.701911\pi$
$757$	−24686.4			−1.18526			−0.592631	+	0.805474i	$0.701911\pi$
$758$	−7192.47	+	12457.7i	−0.344647	+	0.596946i
$759$		0			0
$760$	−8013.06	−	13879.0i	−0.382453	−	0.662428i
$761$	19715.7	−	34148.5i	0.939148	−	1.62665i	0.172084	−	0.985082i	$-0.444950\pi$
$761$	19715.7	−	34148.5i	0.939148	−	1.62665i	0.767064	−	0.641570i	$-0.221717\pi$
$762$		0			0
$763$	−5193.49	−	7999.64i	−0.246418	−	0.379563i
$764$	−5237.91			−0.248038
$765$		0			0
$766$	−9599.72	−	16627.2i	−0.452809	−	0.784289i
$767$	11315.0	+	19598.2i	0.532675	+	0.922619i
$768$		0			0
$769$	−2762.60			−0.129547			−0.0647736	−	0.997900i	$-0.520633\pi$
$769$	−2762.60			−0.129547			−0.0647736	+	0.997900i	$0.520633\pi$
$770$	−10281.1	+	20171.1i	−0.481177	+	0.944047i
$771$		0			0
$772$	10941.7	−	18951.6i	0.510104	−	0.883525i
$773$	−371.442	−	643.357i	−0.0172831	−	0.0299352i	0.857254	−	0.514893i	$-0.172168\pi$
$773$	−371.442	−	643.357i	−0.0172831	−	0.0299352i	−0.874538	+	0.484958i	$0.838835\pi$
$774$		0			0
$775$	2772.80	−	4802.63i	0.128519	−	0.222601i
$776$	−11736.4			−0.542927
$777$		0			0
$778$	−20823.6			−0.959590
$779$	846.106	−	1465.50i	0.0389151	−	0.0674030i
$780$

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)

\(f(q)\)	\(=\)	\(q+(0.884622 - 1.53221i) q^{2} +(2.43489 + 4.21735i) q^{4} +(-6.52561 + 11.3027i) q^{5} +(-18.4950 + 0.966772i) q^{7} +22.7698 q^{8} +O(q^{10})\)	\(q+(0.884622 - 1.53221i) q^{2} +(2.43489 + 4.21735i) q^{4} +(-6.52561 + 11.3027i) q^{5} +(-18.4950 + 0.966772i) q^{7} +22.7698 q^{8} +(11.5454 + 19.9972i) q^{10} +(-26.4705 - 45.8483i) q^{11} -71.7001 q^{13} +(-14.8798 + 29.1935i) q^{14} +(0.663570 - 1.14934i) q^{16} +(-53.2866 - 92.2950i) q^{17} +(-26.9643 + 46.7035i) q^{19} -63.5565 q^{20} -93.6656 q^{22} +(-9.32943 + 16.1590i) q^{23} +(-22.6672 - 39.2608i) q^{25} +(-63.4275 + 109.860i) q^{26} +(-49.1105 - 75.6459i) q^{28} +261.806 q^{29} +(61.1632 + 105.938i) q^{31} +(89.9051 + 155.720i) q^{32} -188.554 q^{34} +(109.764 - 215.352i) q^{35} +(-139.069 + 240.874i) q^{37} +(47.7064 + 82.6298i) q^{38} +(-148.587 + 257.360i) q^{40} -31.3788 q^{41} -347.239 q^{43} +(128.905 - 223.271i) q^{44} +(16.5060 + 28.5893i) q^{46} +(-271.109 + 469.575i) q^{47} +(341.131 - 35.7609i) q^{49} -80.2078 q^{50} +(-174.582 - 302.384i) q^{52} +(128.528 + 222.618i) q^{53} +690.945 q^{55} +(-421.127 + 22.0132i) q^{56} +(231.599 - 401.142i) q^{58} +(-157.810 - 273.335i) q^{59} +(-69.4019 + 120.208i) q^{61} +216.425 q^{62} +328.745 q^{64} +(467.887 - 810.405i) q^{65} +(-198.950 - 344.592i) q^{67} +(259.493 - 449.456i) q^{68} +(-232.865 - 358.687i) q^{70} -843.419 q^{71} +(436.140 + 755.417i) q^{73} +(246.047 + 426.165i) q^{74} -262.620 q^{76} +(533.897 + 822.373i) q^{77} +(277.456 - 480.568i) q^{79} +(8.66040 + 15.0002i) q^{80} +(-27.7584 + 48.0789i) q^{82} -297.114 q^{83} +1390.91 q^{85} +(-307.176 + 532.044i) q^{86} +(-602.728 - 1043.96i) q^{88} +(-51.2419 + 88.7536i) q^{89} +(1326.09 - 69.3177i) q^{91} -90.8644 q^{92} +(479.659 + 830.793i) q^{94} +(-351.916 - 609.537i) q^{95} -515.437 q^{97} +(246.979 - 554.319i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 48 q^{4} - 60 q^{7}+O(q^{10}) \) 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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