LMFDB - Embedded newform 189.4.e.h.109.5

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			109.5
Root			$-0.178435 + 0.309059i$ of defining polynomial
Character	$\chi$	$=$	189.109
Dual form			189.4.e.h.163.5

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

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

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 $

$2$	0.884622	+	1.53221i	0.312761	+	0.541718i	0.978959	−	0.204057i	$-0.0654127\pi$
$2$	0.884622	+	1.53221i	0.312761	+	0.541718i	−0.666198	+	0.745775i	$0.732079\pi$
$3$		0			0
$3$		0			0
$4$	2.43489	−	4.21735i	0.304361	−	0.527168i
$5$	−6.52561	−	11.3027i	−0.583669	−	1.01094i	−0.995040	−	0.0994757i	$-0.968283\pi$
$5$	−6.52561	−	11.3027i	−0.583669	−	1.01094i	0.411371	−	0.911468i	$-0.365050\pi$
$6$		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	0.233183	+	0.972433i	$0.425086\pi$
$11$	−26.4705	+	45.8483i	−0.725560	+	1.25671i	−0.958743	+	0.284274i	$0.908248\pi$
$12$		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	0.182504	+	0.983205i	$0.441580\pi$
$17$	−53.2866	+	92.2950i	−0.760229	+	1.31676i	−0.942732	+	0.333550i	$0.891753\pi$
$18$		0			0
$19$	−26.9643	−	46.7035i	−0.325580	−	0.563921i	0.656049	−	0.754718i	$-0.272226\pi$
$19$	−26.9643	−	46.7035i	−0.325580	−	0.563921i	−0.981630	+	0.190797i	$0.938893\pi$
$20$	−63.5565			−0.710583
$21$		0			0
$22$	−93.6656			−0.907708
$23$	−9.32943	−	16.1590i	−0.0845792	−	0.146495i	0.820633	−	0.571456i	$-0.193621\pi$
$23$	−9.32943	−	16.1590i	−0.0845792	−	0.146495i	−0.905212	+	0.424961i	$0.860288\pi$
$24$		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	−0.632646	−	0.774441i	$-0.718031\pi$
$31$	61.1632	−	105.938i	0.354362	−	0.613773i	0.987009	+	0.160667i	$0.0513646\pi$
$32$	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	−0.989866	−	0.142004i	$-0.954645\pi$
$37$	−139.069	−	240.874i	−0.617912	−	1.07026i	0.371954	−	0.928251i	$-0.378688\pi$
$38$	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	−0.888720	−	0.458451i	$-0.848404\pi$
$47$	−271.109	−	469.575i	−0.841390	−	1.45733i	0.0473295	−	0.998879i	$-0.484929\pi$
$48$		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	−0.650012	−	0.759924i	$-0.725236\pi$
$53$	128.528	−	222.618i	0.333108	−	0.576960i	0.983120	+	0.182964i	$0.0585693\pi$
$54$		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	−0.985934	−	0.167136i	$-0.946548\pi$
$59$	−157.810	+	273.335i	−0.348223	+	0.603139i	0.637711	+	0.770276i	$0.279881\pi$
$60$		0			0
$61$	−69.4019	−	120.208i	−0.145672	−	0.252312i	0.783951	−	0.620822i	$-0.213201\pi$
$61$	−69.4019	−	120.208i	−0.145672	−	0.252312i	−0.929624	+	0.368511i	$0.879868\pi$
$62$	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	−0.988416	−	0.151770i	$-0.951503\pi$
$67$	−198.950	+	344.592i	−0.362771	+	0.628338i	0.625645	+	0.780108i	$0.284836\pi$
$68$	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	−0.269456	−	0.963013i	$-0.586844\pi$
$73$	436.140	−	755.417i	0.699265	−	1.21116i	0.968721	−	0.248151i	$-0.0798228\pi$
$74$	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	0.993119	−	0.117106i	$-0.0373619\pi$
$79$	277.456	+	480.568i	0.395143	+	0.684407i	−0.597977	+	0.801513i	$0.704029\pi$
$80$	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	0.833896	−	0.551921i	$-0.186105\pi$
$89$	−51.2419	−	88.7536i	−0.0610295	−	0.105706i	−0.894926	+	0.446215i	$0.852772\pi$
$90$		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	0.455929	+	0.890016i	$0.349307\pi$
$101$	−550.975	+	954.317i	−0.542813	+	0.940179i	−0.998741	+	0.0501625i	$0.984026\pi$
$102$		0			0
$103$	176.814	+	306.251i	0.169146	+	0.292969i	0.938120	−	0.346311i	$-0.112566\pi$
$103$	176.814	+	306.251i	0.169146	+	0.292969i	−0.768974	+	0.639280i	$0.779233\pi$
$104$	−1632.60			−1.53932
$105$		0			0
$106$	454.796			0.416733
$107$	155.332	+	269.042i	0.140341	+	0.243077i	0.927625	−	0.373513i	$-0.121847\pi$
$107$	155.332	+	269.042i	0.140341	+	0.243077i	−0.787284	+	0.616590i	$0.788514\pi$
$108$		0			0
$109$	257.492	−	445.989i	0.226268	−	0.391909i	−0.730431	−	0.682987i	$-0.760681\pi$
$109$	257.492	−	445.989i	0.226268	−	0.391909i	0.956699	+	0.291078i	$0.0940140\pi$
$110$	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	0.969510	−	0.245052i	$-0.0788049\pi$
$131$	408.628	+	707.764i	0.272534	+	0.472043i	−0.696976	+	0.717095i	$0.745472\pi$
$132$		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	−0.980608	−	0.195978i	$-0.937212\pi$
$137$	−514.067	+	890.390i	−0.320582	+	0.555264i	0.660026	+	0.751242i	$0.270545\pi$
$138$		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	0.983563	−	0.180566i	$-0.0577928\pi$
$149$	610.031	+	1056.60i	0.335407	+	0.580942i	−0.648156	+	0.761508i	$0.724459\pi$
$150$		0			0
$151$	−976.718	+	1691.73i	−0.526386	+	0.911726i	0.473142	+	0.880986i	$0.343120\pi$
$151$	−976.718	+	1691.73i	−0.526386	+	0.911726i	−0.999527	+	0.0307402i	$0.990214\pi$
$152$	−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	−0.603249	−	0.797553i	$-0.706127\pi$
$157$	765.394	−	1325.70i	0.389077	−	0.673901i	0.992326	+	0.123652i	$0.0394606\pi$
$158$	−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	−0.998373	−	0.0570230i	$-0.981839\pi$
$163$	−1141.60	−	1977.31i	−0.548570	−	0.950151i	0.449803	−	0.893128i	$-0.351494\pi$
$164$	−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	−0.916974	−	0.398947i	$-0.869376\pi$
$173$	−1829.44	−	3168.68i	−0.803985	−	1.39254i	0.112989	−	0.993596i	$-0.463958\pi$
$174$		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	−0.938125	−	0.346296i	$-0.887439\pi$
$179$	−405.117	+	701.683i	−0.169161	+	0.292996i	0.768964	+	0.639292i	$0.220772\pi$
$180$		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	0.745993	−	0.665954i	$-0.231975\pi$
$191$	−537.799	−	931.495i	−0.203737	−	0.352883i	−0.949730	+	0.313071i	$0.898642\pi$
$192$		0			0
$193$	−2246.86	+	3891.67i	−0.837992	+	1.45144i	0.0535795	+	0.998564i	$0.482937\pi$
$193$	−2246.86	+	3891.67i	−0.837992	+	1.45144i	−0.891571	+	0.452881i	$0.850396\pi$
$194$	−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	−0.814379	−	0.580333i	$-0.802922\pi$
$199$	267.794	−	463.832i	0.0953940	−	0.165227i	0.909773	+	0.415106i	$0.136256\pi$
$200$	−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	−0.954092	−	0.299514i	$-0.903175\pi$
$227$	−744.416	+	1289.37i	−0.217659	+	0.376997i	0.736433	+	0.676511i	$0.236509\pi$
$228$		0			0
$229$	1605.20	+	2780.28i	0.463207	+	0.802297i	0.999119	−	0.0419764i	$-0.0133654\pi$
$229$	1605.20	+	2780.28i	0.463207	+	0.802297i	−0.535912	+	0.844274i	$0.680032\pi$
$230$	−430.848			−0.123519
$231$		0			0
$232$	5961.26			1.68696
$233$	−1463.84	−	2535.45i	−0.411586	−	0.712888i	0.583477	−	0.812129i	$-0.301692\pi$
$233$	−1463.84	−	2535.45i	−0.411586	−	0.712888i	−0.995063	+	0.0992415i	$0.968358\pi$
$234$		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	−0.419029	−	0.907973i	$-0.637630\pi$
$241$	2158.04	−	3737.84i	0.576813	−	0.999069i	0.995842	−	0.0910964i	$-0.0290371\pi$
$242$	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	0.642554	−	0.766241i	$-0.277875\pi$
$257$	−1410.31	−	2442.73i	−0.342307	−	0.592893i	−0.984861	+	0.173348i	$0.944542\pi$
$258$		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	0.271429	+	0.962459i	$0.412504\pi$
$263$	−2976.21	+	5154.95i	−0.697799	+	1.20862i	−0.969228	+	0.246165i	$0.920829\pi$
$264$		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	0.193590	+	0.981082i	$0.437987\pi$
$269$	−3321.51	+	5753.02i	−0.752847	+	1.30397i	−0.946438	+	0.322887i	$0.895347\pi$
$270$		0			0
$271$	−480.913	−	832.966i	−0.107799	−	0.186713i	0.807080	−	0.590443i	$-0.201047\pi$
$271$	−480.913	−	832.966i	−0.107799	−	0.186713i	−0.914878	+	0.403730i	$0.867713\pi$
$272$	−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	−0.384312	−	0.923203i	$-0.625561\pi$
$277$	2800.06	−	4849.84i	0.607362	−	1.05198i	0.991673	−	0.128778i	$-0.0411055\pi$
$278$	−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	−0.961871	−	0.273504i	$-0.911817\pi$
$283$	−1161.99	+	2012.62i	−0.244074	+	0.422749i	0.717797	+	0.696253i	$0.245151\pi$
$284$	−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	−0.740786	−	0.671741i	$-0.765547\pi$
$311$	1159.17	−	2007.74i	0.211352	−	0.366073i	0.952138	+	0.305669i	$0.0988800\pi$
$312$		0			0
$313$	−947.953	−	1641.90i	−0.171187	−	0.296504i	0.767648	−	0.640871i	$-0.221427\pi$
$313$	−947.953	−	1641.90i	−0.171187	−	0.296504i	−0.938835	+	0.344367i	$0.888094\pi$
$314$	2708.34			0.486753
$315$		0			0
$316$	2702.30			0.481064
$317$	486.154	+	842.043i	0.0861360	+	0.149192i	0.905875	−	0.423546i	$-0.139215\pi$
$317$	486.154	+	842.043i	0.0861360	+	0.149192i	−0.819739	+	0.572738i	$0.805881\pi$
$318$		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	0.989736	−	0.142905i	$-0.0456445\pi$
$331$	2234.82	+	3870.82i	0.371108	+	0.642779i	−0.618628	+	0.785684i	$0.712311\pi$
$332$	−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	0.327513	+	0.944847i	$0.393790\pi$
$347$	−4230.65	+	7327.70i	−0.654505	+	1.13364i	−0.982018	+	0.188789i	$0.939544\pi$
$348$		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	−0.542920	−	0.839785i	$-0.682681\pi$
$353$	3023.09	−	5236.14i	0.455815	−	0.789494i	0.998735	+	0.0502901i	$0.0160146\pi$
$354$		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	−0.918970	−	0.394327i	$-0.870978\pi$
$359$	−5448.34	−	9436.81i	−0.800982	−	1.38734i	0.117988	−	0.993015i	$-0.462355\pi$
$360$		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	0.445079	+	0.895491i	$0.353176\pi$
$367$	−3887.83	+	6733.92i	−0.552979	+	0.957787i	−0.998058	+	0.0622958i	$0.980158\pi$
$368$	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	−0.899629	−	0.436655i	$-0.856163\pi$
$373$	−5964.54	−	10330.9i	−0.827969	−	1.43408i	0.0716601	−	0.997429i	$-0.477170\pi$
$374$	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	0.959429	+	0.281949i	$0.0909808\pi$
$383$	5425.88	+	9397.90i	0.723889	+	1.25381i	−0.235540	+	0.971865i	$0.575686\pi$
$384$		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	0.172135	+	0.985073i	$0.444933\pi$
$389$	−5884.87	+	10192.9i	−0.767031	+	1.32854i	−0.939166	+	0.343463i	$0.888400\pi$
$390$		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	−0.985327	−	0.170675i	$-0.945405\pi$
$397$	−5066.25	−	8774.99i	−0.640472	−	1.10933i	0.344855	−	0.938656i	$-0.387928\pi$
$398$	947.586			0.119342
$399$		0			0
$400$	−60.1652			−0.00752064
$401$	−2402.12	−	4160.60i	−0.299143	−	0.518130i	0.676797	−	0.736169i	$-0.263367\pi$
$401$	−2402.12	−	4160.60i	−0.299143	−	0.518130i	−0.975940	+	0.218039i	$0.930034\pi$
$402$		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	−0.464988	−	0.885317i	$-0.653941\pi$
$409$	4418.75	−	7653.50i	0.534213	−	0.925284i	0.999201	−	0.0399668i	$-0.0127252\pi$
$410$	−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	−0.488785	−	0.872404i	$-0.662560\pi$
$431$	4573.50	−	7921.54i	0.511132	−	0.885307i	0.999917	−	0.0129023i	$-0.00410704\pi$
$432$		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	0.948969	−	0.315368i	$-0.102128\pi$
$439$	1852.20	+	3208.10i	0.201368	+	0.348779i	−0.747602	+	0.664147i	$0.768795\pi$
$440$	15732.7			1.70460
$441$		0			0
$442$	13519.3			1.45486
$443$	−675.693	−	1170.33i	−0.0724676	−	0.125517i	0.827515	−	0.561444i	$-0.189754\pi$
$443$	−675.693	−	1170.33i	−0.0724676	−	0.125517i	−0.899982	+	0.435927i	$0.856421\pi$
$444$		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	−0.970354	−	0.241689i	$-0.922299\pi$
$457$	−6784.81	−	11751.6i	−0.694486	−	1.20288i	0.275868	−	0.961196i	$-0.411035\pi$
$458$	−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	0.685649	−	0.727932i	$-0.259518\pi$
$467$	−2902.27	−	5026.88i	−0.287583	−	0.498108i	−0.973232	+	0.229824i	$0.926185\pi$
$468$		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	−0.950855	−	0.309637i	$-0.899793\pi$
$479$	−2172.94	+	3763.65i	−0.207274	+	0.359009i	0.743581	+	0.668646i	$0.233126\pi$
$480$		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	0.0157056	−	0.999877i	$-0.495001\pi$
$487$	9390.55	−	16264.9i	0.873771	−	1.51342i	0.858066	−	0.513540i	$-0.171666\pi$
$488$	−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	0.594338	−	0.804216i	$-0.297414\pi$
$499$	−4450.95	−	7709.27i	−0.399302	−	0.691612i	−0.993640	+	0.112604i	$0.964081\pi$
$500$	−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	0.992608	−	0.121362i	$-0.0387263\pi$
$509$	4492.39	+	7781.04i	0.391201	+	0.677581i	−0.601407	+	0.798943i	$0.705393\pi$
$510$		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	−0.990135	−	0.140114i	$-0.955253\pi$
$521$	−4444.36	+	7697.87i	−0.373726	+	0.647312i	0.616410	+	0.787426i	$0.288587\pi$
$522$		0			0
$523$	10519.5	+	18220.2i	0.879510	+	1.52336i	0.851879	+	0.523738i	$0.175463\pi$
$523$	10519.5	+	18220.2i	0.879510	+	1.52336i	0.0276313	+	0.999618i	$0.491204\pi$
$524$	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	0.661972	−	0.749528i	$-0.269720\pi$
$541$	−4003.07	−	6933.51i	−0.318124	−	0.551007i	−0.980097	+	0.198521i	$0.936386\pi$
$542$	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	−0.687872	−	0.725832i	$-0.741455\pi$
$557$	3741.96	−	6481.27i	0.284653	−	0.493034i	0.972525	+	0.232798i	$0.0747881\pi$
$558$		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	−0.959426	−	0.281960i	$-0.909015\pi$
$563$	−3146.34	+	5449.63i	−0.235529	+	0.407947i	0.723898	+	0.689907i	$0.242349\pi$
$564$		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	0.610332	−	0.792146i	$-0.291036\pi$
$569$	−5169.22	−	8953.36i	−0.380853	−	0.659656i	−0.991184	+	0.132490i	$0.957703\pi$
$570$		0			0
$571$	7269.81	−	12591.7i	0.532806	−	0.922847i	−0.466460	−	0.884542i	$-0.654471\pi$
$571$	7269.81	−	12591.7i	0.532806	−	0.922847i	0.999266	−	0.0383046i	$-0.0121957\pi$
$572$	−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	−0.566034	−	0.824382i	$-0.691523\pi$
$577$	5972.54	−	10344.7i	0.430919	−	0.746373i	0.996953	+	0.0780089i	$0.0248562\pi$
$578$	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	0.795916	−	0.605407i	$-0.206990\pi$
$593$	−1824.41	−	3159.98i	−0.126340	−	0.218827i	−0.922256	+	0.386580i	$0.873656\pi$
$594$		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	−0.619532	−	0.784971i	$-0.712678\pi$
$599$	5424.85	−	9396.12i	0.370039	−	0.640927i	0.989571	+	0.144045i	$0.0460109\pi$
$600$		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	0.961201	+	0.275849i	$0.0889591\pi$
$607$	10759.9	+	18636.8i	0.719493	+	1.24620i	−0.241708	+	0.970349i	$0.577708\pi$
$608$	−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	−0.949673	−	0.313242i	$-0.898585\pi$
$613$	−3089.48	+	5351.13i	−0.203561	+	0.352578i	0.746112	+	0.665820i	$0.231918\pi$
$614$	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	−0.794385	−	0.607415i	$-0.792207\pi$
$619$	1984.27	−	3436.86i	0.128844	−	0.223165i	0.923229	+	0.384250i	$0.125540\pi$
$620$	−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	−0.811447	−	0.584425i	$-0.801320\pi$
$641$	1629.43	−	2822.26i	0.100404	−	0.173904i	0.911851	+	0.410521i	$0.134653\pi$
$642$		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	−0.672456	−	0.740138i	$-0.734760\pi$
$647$	5015.34	−	8686.82i	0.304750	−	0.527843i	0.977206	+	0.212295i	$0.0680937\pi$
$648$		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	−0.774658	−	0.632380i	$-0.782078\pi$
$653$	−15601.8	−	27023.1i	−0.934986	−	1.61944i	−0.160328	−	0.987064i	$-0.551255\pi$
$654$		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	−0.395211	−	0.918590i	$-0.629329\pi$
$661$	10161.2	−	17599.6i	0.597917	−	1.03562i	0.993128	−	0.117032i	$-0.0373381\pi$
$662$	−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	0.997650	+	0.0685158i	$0.0218264\pi$
$677$	9832.02	+	17029.6i	0.558161	+	0.966764i	−0.439489	+	0.898248i	$0.644840\pi$
$678$		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	−0.984075	−	0.177756i	$-0.943116\pi$
$683$	−6034.92	+	10452.8i	−0.338096	+	0.585600i	0.645978	+	0.763356i	$0.276450\pi$
$684$		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	0.880553	−	0.473947i	$-0.157171\pi$
$691$	541.776	+	938.384i	0.0298265	+	0.0516611i	−0.850727	+	0.525608i	$0.823838\pi$
$692$	−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	−0.956158	−	0.292851i	$-0.905396\pi$
$709$	−13813.4	−	23925.5i	−0.731695	−	1.26733i	0.224463	−	0.974483i	$-0.427937\pi$
$710$	−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	0.837013	−	0.547183i	$-0.184300\pi$
$719$	−1067.47	−	1848.91i	−0.0553684	−	0.0959009i	−0.892381	+	0.451283i	$0.850967\pi$
$720$		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	0.998895	−	0.0470008i	$-0.0149663\pi$
$733$	9103.87	+	15768.4i	0.458744	+	0.794567i	−0.540151	+	0.841568i	$0.681633\pi$
$734$	−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	−0.895873	−	0.444311i	$-0.853449\pi$
$739$	−1268.68	+	2197.42i	−0.0631519	+	0.109382i	0.832721	+	0.553693i	$0.186782\pi$
$740$	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	−0.991882	−	0.127163i	$-0.959413\pi$
$751$	−12473.3	−	21604.3i	−0.606067	−	1.04974i	0.385815	−	0.922576i	$-0.373920\pi$
$752$	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	0.767064	+	0.641570i	$0.221717\pi$
$761$	19715.7	+	34148.5i	0.939148	+	1.62665i	0.172084	+	0.985082i	$0.444950\pi$
$762$		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	−0.874538	−	0.484958i	$-0.838835\pi$
$773$	−371.442	+	643.357i	−0.0172831	+	0.0299352i	0.857254	+	0.514893i	$0.172168\pi$
$774$		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

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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