LMFDB - Embedded newform 9386.2.a.t.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9386,2,Mod(1,9386)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9386, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("9386.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9386 = 2 \cdot 13 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9386.a (trivial)

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:	yes
Analytic conductor:	$74.9475873372$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{6}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 6 $ x^2 - 6
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 494)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-2.44949$ of defining polynomial
Character	$\chi$	$=$	9386.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.44949 q^{5} +1.00000 q^{6} -4.89898 q^{7} +1.00000 q^{8} -2.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.44949 q^{5} +1.00000 q^{6} -4.89898 q^{7} +1.00000 q^{8} -2.00000 q^{9} +2.44949 q^{10} -5.44949 q^{11} +1.00000 q^{12} +1.00000 q^{13} -4.89898 q^{14} +2.44949 q^{15} +1.00000 q^{16} +4.00000 q^{17} -2.00000 q^{18} +2.44949 q^{20} -4.89898 q^{21} -5.44949 q^{22} +6.89898 q^{23} +1.00000 q^{24} +1.00000 q^{25} +1.00000 q^{26} -5.00000 q^{27} -4.89898 q^{28} -3.55051 q^{29} +2.44949 q^{30} +3.55051 q^{31} +1.00000 q^{32} -5.44949 q^{33} +4.00000 q^{34} -12.0000 q^{35} -2.00000 q^{36} +1.10102 q^{37} +1.00000 q^{39} +2.44949 q^{40} +3.44949 q^{41} -4.89898 q^{42} +6.00000 q^{43} -5.44949 q^{44} -4.89898 q^{45} +6.89898 q^{46} +4.00000 q^{47} +1.00000 q^{48} +17.0000 q^{49} +1.00000 q^{50} +4.00000 q^{51} +1.00000 q^{52} +11.3485 q^{53} -5.00000 q^{54} -13.3485 q^{55} -4.89898 q^{56} -3.55051 q^{58} -6.34847 q^{59} +2.44949 q^{60} +13.7980 q^{61} +3.55051 q^{62} +9.79796 q^{63} +1.00000 q^{64} +2.44949 q^{65} -5.44949 q^{66} +13.4495 q^{67} +4.00000 q^{68} +6.89898 q^{69} -12.0000 q^{70} -6.00000 q^{71} -2.00000 q^{72} +7.44949 q^{73} +1.10102 q^{74} +1.00000 q^{75} +26.6969 q^{77} +1.00000 q^{78} -4.44949 q^{79} +2.44949 q^{80} +1.00000 q^{81} +3.44949 q^{82} -11.4495 q^{83} -4.89898 q^{84} +9.79796 q^{85} +6.00000 q^{86} -3.55051 q^{87} -5.44949 q^{88} -6.89898 q^{89} -4.89898 q^{90} -4.89898 q^{91} +6.89898 q^{92} +3.55051 q^{93} +4.00000 q^{94} +1.00000 q^{96} -4.34847 q^{97} +17.0000 q^{98} +10.8990 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{6} + 2 q^{8} - 4 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^6 + 2 * q^8 - 4 * q^9	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{6} + 2 q^{8} - 4 q^{9} - 6 q^{11} + 2 q^{12} + 2 q^{13} + 2 q^{16} + 8 q^{17} - 4 q^{18} - 6 q^{22} + 4 q^{23} + 2 q^{24} + 2 q^{25} + 2 q^{26} - 10 q^{27} - 12 q^{29} + 12 q^{31} + 2 q^{32} - 6 q^{33} + 8 q^{34} - 24 q^{35} - 4 q^{36} + 12 q^{37} + 2 q^{39} + 2 q^{41} + 12 q^{43} - 6 q^{44} + 4 q^{46} + 8 q^{47} + 2 q^{48} + 34 q^{49} + 2 q^{50} + 8 q^{51} + 2 q^{52} + 8 q^{53} - 10 q^{54} - 12 q^{55} - 12 q^{58} + 2 q^{59} + 8 q^{61} + 12 q^{62} + 2 q^{64} - 6 q^{66} + 22 q^{67} + 8 q^{68} + 4 q^{69} - 24 q^{70} - 12 q^{71} - 4 q^{72} + 10 q^{73} + 12 q^{74} + 2 q^{75} + 24 q^{77} + 2 q^{78} - 4 q^{79} + 2 q^{81} + 2 q^{82} - 18 q^{83} + 12 q^{86} - 12 q^{87} - 6 q^{88} - 4 q^{89} + 4 q^{92} + 12 q^{93} + 8 q^{94} + 2 q^{96} + 6 q^{97} + 34 q^{98} + 12 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^6 + 2 * q^8 - 4 * q^9 - 6 * q^11 + 2 * q^12 + 2 * q^13 + 2 * q^16 + 8 * q^17 - 4 * q^18 - 6 * q^22 + 4 * q^23 + 2 * q^24 + 2 * q^25 + 2 * q^26 - 10 * q^27 - 12 * q^29 + 12 * q^31 + 2 * q^32 - 6 * q^33 + 8 * q^34 - 24 * q^35 - 4 * q^36 + 12 * q^37 + 2 * q^39 + 2 * q^41 + 12 * q^43 - 6 * q^44 + 4 * q^46 + 8 * q^47 + 2 * q^48 + 34 * q^49 + 2 * q^50 + 8 * q^51 + 2 * q^52 + 8 * q^53 - 10 * q^54 - 12 * q^55 - 12 * q^58 + 2 * q^59 + 8 * q^61 + 12 * q^62 + 2 * q^64 - 6 * q^66 + 22 * q^67 + 8 * q^68 + 4 * q^69 - 24 * q^70 - 12 * q^71 - 4 * q^72 + 10 * q^73 + 12 * q^74 + 2 * q^75 + 24 * q^77 + 2 * q^78 - 4 * q^79 + 2 * q^81 + 2 * q^82 - 18 * q^83 + 12 * q^86 - 12 * q^87 - 6 * q^88 - 4 * q^89 + 4 * q^92 + 12 * q^93 + 8 * q^94 + 2 * q^96 + 6 * q^97 + 34 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350	0.288675	−	0.957427i	$-0.406785\pi$
$3$	1.00000	0.577350	0.288675	+	0.957427i	$0.406785\pi$
$4$	1.00000	0.500000
$5$	2.44949	1.09545	0.547723	−	0.836660i	$-0.315495\pi$
$5$	2.44949	1.09545	0.547723	+	0.836660i	$0.315495\pi$
$6$	1.00000	0.408248
$7$	−4.89898	−1.85164	−0.925820	−	0.377964i	$-0.876624\pi$
$7$	−4.89898	−1.85164	−0.925820	+	0.377964i	$0.876624\pi$
$8$	1.00000	0.353553
$9$	−2.00000	−0.666667
$10$	2.44949	0.774597
$11$	−5.44949	−1.64308	−0.821541	−	0.570149i	$-0.806886\pi$
$11$	−5.44949	−1.64308	−0.821541	+	0.570149i	$0.806886\pi$
$12$	1.00000	0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−4.89898	−1.30931
$15$	2.44949	0.632456
$16$	1.00000	0.250000
$17$	4.00000	0.970143	0.485071	−	0.874475i	$-0.338794\pi$
$17$	4.00000	0.970143	0.485071	+	0.874475i	$0.338794\pi$
$18$	−2.00000	−0.471405
$19$	0	0
$19$	0	0
$20$	2.44949	0.547723
$21$	−4.89898	−1.06904
$22$	−5.44949	−1.16184
$23$	6.89898	1.43854	0.719268	−	0.694732i	$-0.244477\pi$
$23$	6.89898	1.43854	0.719268	+	0.694732i	$0.244477\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	1.00000	0.196116
$27$	−5.00000	−0.962250
$28$	−4.89898	−0.925820
$29$	−3.55051	−0.659313	−0.329657	−	0.944101i	$-0.606933\pi$
$29$	−3.55051	−0.659313	−0.329657	+	0.944101i	$0.606933\pi$
$30$	2.44949	0.447214
$31$	3.55051	0.637690	0.318845	−	0.947807i	$-0.396705\pi$
$31$	3.55051	0.637690	0.318845	+	0.947807i	$0.396705\pi$
$32$	1.00000	0.176777
$33$	−5.44949	−0.948634
$34$	4.00000	0.685994
$35$	−12.0000	−2.02837
$36$	−2.00000	−0.333333
$37$	1.10102	0.181007	0.0905033	−	0.995896i	$-0.471152\pi$
$37$	1.10102	0.181007	0.0905033	+	0.995896i	$0.471152\pi$
$38$	0	0
$39$	1.00000	0.160128
$40$	2.44949	0.387298
$41$	3.44949	0.538720	0.269360	−	0.963040i	$-0.413188\pi$
$41$	3.44949	0.538720	0.269360	+	0.963040i	$0.413188\pi$
$42$	−4.89898	−0.755929
$43$	6.00000	0.914991	0.457496	−	0.889212i	$-0.348747\pi$
$43$	6.00000	0.914991	0.457496	+	0.889212i	$0.348747\pi$
$44$	−5.44949	−0.821541
$45$	−4.89898	−0.730297
$46$	6.89898	1.01720
$47$	4.00000	0.583460	0.291730	−	0.956501i	$-0.405769\pi$
$47$	4.00000	0.583460	0.291730	+	0.956501i	$0.405769\pi$
$48$	1.00000	0.144338
$49$	17.0000	2.42857
$50$	1.00000	0.141421
$51$	4.00000	0.560112
$52$	1.00000	0.138675
$53$	11.3485	1.55883	0.779416	−	0.626507i	$-0.215516\pi$
$53$	11.3485	1.55883	0.779416	+	0.626507i	$0.215516\pi$
$54$	−5.00000	−0.680414
$55$	−13.3485	−1.79991
$56$	−4.89898	−0.654654
$57$	0	0
$58$	−3.55051	−0.466205
$59$	−6.34847	−0.826500	−0.413250	−	0.910618i	$-0.635606\pi$
$59$	−6.34847	−0.826500	−0.413250	+	0.910618i	$0.635606\pi$
$60$	2.44949	0.316228
$61$	13.7980	1.76665	0.883324	−	0.468763i	$-0.155300\pi$
$61$	13.7980	1.76665	0.883324	+	0.468763i	$0.155300\pi$
$62$	3.55051	0.450915
$63$	9.79796	1.23443
$64$	1.00000	0.125000
$65$	2.44949	0.303822
$66$	−5.44949	−0.670786
$67$	13.4495	1.64312	0.821558	−	0.570124i	$-0.193105\pi$
$67$	13.4495	1.64312	0.821558	+	0.570124i	$0.193105\pi$
$68$	4.00000	0.485071
$69$	6.89898	0.830540
$70$	−12.0000	−1.43427
$71$	−6.00000	−0.712069	−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000	−0.712069	−0.356034	+	0.934473i	$0.615871\pi$
$72$	−2.00000	−0.235702
$73$	7.44949	0.871897	0.435948	−	0.899972i	$-0.356413\pi$
$73$	7.44949	0.871897	0.435948	+	0.899972i	$0.356413\pi$
$74$	1.10102	0.127991
$75$	1.00000	0.115470
$76$	0	0
$77$	26.6969	3.04240
$78$	1.00000	0.113228
$79$	−4.44949	−0.500607	−0.250303	−	0.968167i	$-0.580530\pi$
$79$	−4.44949	−0.500607	−0.250303	+	0.968167i	$0.580530\pi$
$80$	2.44949	0.273861
$81$	1.00000	0.111111
$82$	3.44949	0.380932
$83$	−11.4495	−1.25674	−0.628372	−	0.777913i	$-0.716279\pi$
$83$	−11.4495	−1.25674	−0.628372	+	0.777913i	$0.716279\pi$
$84$	−4.89898	−0.534522
$85$	9.79796	1.06274
$86$	6.00000	0.646997
$87$	−3.55051	−0.380655
$88$	−5.44949	−0.580918
$89$	−6.89898	−0.731290	−0.365645	−	0.930754i	$-0.619152\pi$
$89$	−6.89898	−0.731290	−0.365645	+	0.930754i	$0.619152\pi$
$90$	−4.89898	−0.516398
$91$	−4.89898	−0.513553
$92$	6.89898	0.719268
$93$	3.55051	0.368171
$94$	4.00000	0.412568
$95$	0	0
$96$	1.00000	0.102062
$97$	−4.34847	−0.441520	−0.220760	−	0.975328i	$-0.570854\pi$
$97$	−4.34847	−0.441520	−0.220760	+	0.975328i	$0.570854\pi$
$98$	17.0000	1.71726
$99$	10.8990	1.09539
$100$	1.00000	0.100000
$101$	2.65153	0.263837	0.131919	−	0.991261i	$-0.457886\pi$
$101$	2.65153	0.263837	0.131919	+	0.991261i	$0.457886\pi$
$102$	4.00000	0.396059
$103$	−2.44949	−0.241355	−0.120678	−	0.992692i	$-0.538507\pi$
$103$	−2.44949	−0.241355	−0.120678	+	0.992692i	$0.538507\pi$
$104$	1.00000	0.0980581
$105$	−12.0000	−1.17108
$106$	11.3485	1.10226
$107$	7.79796	0.753857	0.376929	−	0.926242i	$-0.376980\pi$
$107$	7.79796	0.753857	0.376929	+	0.926242i	$0.376980\pi$
$108$	−5.00000	−0.481125
$109$	13.5505	1.29790	0.648952	−	0.760830i	$-0.275208\pi$
$109$	13.5505	1.29790	0.648952	+	0.760830i	$0.275208\pi$
$110$	−13.3485	−1.27273
$111$	1.10102	0.104504
$112$	−4.89898	−0.462910
$113$	−2.10102	−0.197647	−0.0988237	−	0.995105i	$-0.531508\pi$
$113$	−2.10102	−0.197647	−0.0988237	+	0.995105i	$0.531508\pi$
$114$	0	0
$115$	16.8990	1.57584
$116$	−3.55051	−0.329657
$117$	−2.00000	−0.184900
$118$	−6.34847	−0.584424
$119$	−19.5959	−1.79635
$120$	2.44949	0.223607
$121$	18.6969	1.69972
$122$	13.7980	1.24921
$123$	3.44949	0.311030
$124$	3.55051	0.318845
$125$	−9.79796	−0.876356
$126$	9.79796	0.872872
$127$	−8.24745	−0.731843	−0.365921	−	0.930646i	$-0.619246\pi$
$127$	−8.24745	−0.731843	−0.365921	+	0.930646i	$0.619246\pi$
$128$	1.00000	0.0883883
$129$	6.00000	0.528271
$130$	2.44949	0.214834
$131$	3.00000	0.262111	0.131056	−	0.991375i	$-0.458163\pi$
$131$	3.00000	0.262111	0.131056	+	0.991375i	$0.458163\pi$
$132$	−5.44949	−0.474317
$133$	0	0
$134$	13.4495	1.16186
$135$	−12.2474	−1.05409
$136$	4.00000	0.342997
$137$	10.5505	0.901391	0.450695	−	0.892678i	$-0.351176\pi$
$137$	10.5505	0.901391	0.450695	+	0.892678i	$0.351176\pi$
$138$	6.89898	0.587280
$139$	−8.10102	−0.687120	−0.343560	−	0.939131i	$-0.611633\pi$
$139$	−8.10102	−0.687120	−0.343560	+	0.939131i	$0.611633\pi$
$140$	−12.0000	−1.01419
$141$	4.00000	0.336861
$142$	−6.00000	−0.503509
$143$	−5.44949	−0.455709
$144$	−2.00000	−0.166667
$145$	−8.69694	−0.722241
$146$	7.44949	0.616524
$147$	17.0000	1.40214
$148$	1.10102	0.0905033
$149$	3.79796	0.311141	0.155570	−	0.987825i	$-0.450278\pi$
$149$	3.79796	0.311141	0.155570	+	0.987825i	$0.450278\pi$
$150$	1.00000	0.0816497
$151$	−10.0000	−0.813788	−0.406894	−	0.913475i	$-0.633388\pi$
$151$	−10.0000	−0.813788	−0.406894	+	0.913475i	$0.633388\pi$
$152$	0	0
$153$	−8.00000	−0.646762
$154$	26.6969	2.15130
$155$	8.69694	0.698555
$156$	1.00000	0.0800641
$157$	4.00000	0.319235	0.159617	−	0.987179i	$-0.448974\pi$
$157$	4.00000	0.319235	0.159617	+	0.987179i	$0.448974\pi$
$158$	−4.44949	−0.353982
$159$	11.3485	0.899992
$160$	2.44949	0.193649
$161$	−33.7980	−2.66365
$162$	1.00000	0.0785674
$163$	8.55051	0.669728	0.334864	−	0.942267i	$-0.391310\pi$
$163$	8.55051	0.669728	0.334864	+	0.942267i	$0.391310\pi$
$164$	3.44949	0.269360
$165$	−13.3485	−1.03918
$166$	−11.4495	−0.888653
$167$	25.1464	1.94589	0.972945	−	0.231039i	$-0.0742125\pi$
$167$	25.1464	1.94589	0.972945	+	0.231039i	$0.0742125\pi$
$168$	−4.89898	−0.377964
$169$	1.00000	0.0769231
$170$	9.79796	0.751469
$171$	0	0
$172$	6.00000	0.457496
$173$	1.10102	0.0837090	0.0418545	−	0.999124i	$-0.486673\pi$
$173$	1.10102	0.0837090	0.0418545	+	0.999124i	$0.486673\pi$
$174$	−3.55051	−0.269163
$175$	−4.89898	−0.370328
$176$	−5.44949	−0.410771
$177$	−6.34847	−0.477180
$178$	−6.89898	−0.517100
$179$	13.8990	1.03886	0.519429	−	0.854513i	$-0.326145\pi$
$179$	13.8990	1.03886	0.519429	+	0.854513i	$0.326145\pi$
$180$	−4.89898	−0.365148
$181$	−13.5505	−1.00720	−0.503601	−	0.863937i	$-0.667992\pi$
$181$	−13.5505	−1.00720	−0.503601	+	0.863937i	$0.667992\pi$
$182$	−4.89898	−0.363137
$183$	13.7980	1.01997
$184$	6.89898	0.508600
$185$	2.69694	0.198283
$186$	3.55051	0.260336
$187$	−21.7980	−1.59402
$188$	4.00000	0.291730
$189$	24.4949	1.78174
$190$	0	0
$191$	−5.34847	−0.387002	−0.193501	−	0.981100i	$-0.561984\pi$
$191$	−5.34847	−0.387002	−0.193501	+	0.981100i	$0.561984\pi$
$192$	1.00000	0.0721688
$193$	1.10102	0.0792532	0.0396266	−	0.999215i	$-0.487383\pi$
$193$	1.10102	0.0792532	0.0396266	+	0.999215i	$0.487383\pi$
$194$	−4.34847	−0.312202
$195$	2.44949	0.175412
$196$	17.0000	1.21429
$197$	−15.5505	−1.10793	−0.553964	−	0.832541i	$-0.686885\pi$
$197$	−15.5505	−1.10793	−0.553964	+	0.832541i	$0.686885\pi$
$198$	10.8990	0.774557
$199$	1.55051	0.109913	0.0549564	−	0.998489i	$-0.482498\pi$
$199$	1.55051	0.109913	0.0549564	+	0.998489i	$0.482498\pi$
$200$	1.00000	0.0707107
$201$	13.4495	0.948654
$202$	2.65153	0.186561
$203$	17.3939	1.22081
$204$	4.00000	0.280056
$205$	8.44949	0.590138
$206$	−2.44949	−0.170664
$207$	−13.7980	−0.959024
$208$	1.00000	0.0693375
$209$	0	0
$210$	−12.0000	−0.828079
$211$	25.5959	1.76210	0.881048	−	0.473027i	$-0.156839\pi$
$211$	25.5959	1.76210	0.881048	+	0.473027i	$0.156839\pi$
$212$	11.3485	0.779416
$213$	−6.00000	−0.411113
$214$	7.79796	0.533058
$215$	14.6969	1.00232
$216$	−5.00000	−0.340207
$217$	−17.3939	−1.18077
$218$	13.5505	0.917756
$219$	7.44949	0.503390
$220$	−13.3485	−0.899954
$221$	4.00000	0.269069
$222$	1.10102	0.0738957
$223$	11.7980	0.790050	0.395025	−	0.918670i	$-0.370736\pi$
$223$	11.7980	0.790050	0.395025	+	0.918670i	$0.370736\pi$
$224$	−4.89898	−0.327327
$225$	−2.00000	−0.133333
$226$	−2.10102	−0.139758
$227$	−4.34847	−0.288618	−0.144309	−	0.989533i	$-0.546096\pi$
$227$	−4.34847	−0.288618	−0.144309	+	0.989533i	$0.546096\pi$
$228$	0	0
$229$	−10.6969	−0.706874	−0.353437	−	0.935458i	$-0.614987\pi$
$229$	−10.6969	−0.706874	−0.353437	+	0.935458i	$0.614987\pi$
$230$	16.8990	1.11429
$231$	26.6969	1.75653
$232$	−3.55051	−0.233102
$233$	16.5959	1.08723	0.543617	−	0.839333i	$-0.317054\pi$
$233$	16.5959	1.08723	0.543617	+	0.839333i	$0.317054\pi$
$234$	−2.00000	−0.130744
$235$	9.79796	0.639148
$236$	−6.34847	−0.413250
$237$	−4.44949	−0.289025
$238$	−19.5959	−1.27021
$239$	−13.1464	−0.850372	−0.425186	−	0.905106i	$-0.639791\pi$
$239$	−13.1464	−0.850372	−0.425186	+	0.905106i	$0.639791\pi$
$240$	2.44949	0.158114
$241$	19.2474	1.23984	0.619919	−	0.784666i	$-0.287166\pi$
$241$	19.2474	1.23984	0.619919	+	0.784666i	$0.287166\pi$
$242$	18.6969	1.20188
$243$	16.0000	1.02640
$244$	13.7980	0.883324
$245$	41.6413	2.66037
$246$	3.44949	0.219931
$247$	0	0
$248$	3.55051	0.225458
$249$	−11.4495	−0.725582
$250$	−9.79796	−0.619677
$251$	−21.6969	−1.36950	−0.684749	−	0.728779i	$-0.740088\pi$
$251$	−21.6969	−1.36950	−0.684749	+	0.728779i	$0.740088\pi$
$252$	9.79796	0.617213
$253$	−37.5959	−2.36364
$254$	−8.24745	−0.517491
$255$	9.79796	0.613572
$256$	1.00000	0.0625000
$257$	17.8990	1.11651	0.558254	−	0.829670i	$-0.311472\pi$
$257$	17.8990	1.11651	0.558254	+	0.829670i	$0.311472\pi$
$258$	6.00000	0.373544
$259$	−5.39388	−0.335159
$260$	2.44949	0.151911
$261$	7.10102	0.439542
$262$	3.00000	0.185341
$263$	14.6969	0.906252	0.453126	−	0.891446i	$-0.350309\pi$
$263$	14.6969	0.906252	0.453126	+	0.891446i	$0.350309\pi$
$264$	−5.44949	−0.335393
$265$	27.7980	1.70762
$266$	0	0
$267$	−6.89898	−0.422211
$268$	13.4495	0.821558
$269$	−19.1464	−1.16738	−0.583689	−	0.811977i	$-0.698391\pi$
$269$	−19.1464	−1.16738	−0.583689	+	0.811977i	$0.698391\pi$
$270$	−12.2474	−0.745356
$271$	−17.7980	−1.08115	−0.540575	−	0.841296i	$-0.681793\pi$
$271$	−17.7980	−1.08115	−0.540575	+	0.841296i	$0.681793\pi$
$272$	4.00000	0.242536
$273$	−4.89898	−0.296500
$274$	10.5505	0.637380
$275$	−5.44949	−0.328617
$276$	6.89898	0.415270
$277$	11.1464	0.669724	0.334862	−	0.942267i	$-0.391310\pi$
$277$	11.1464	0.669724	0.334862	+	0.942267i	$0.391310\pi$
$278$	−8.10102	−0.485867
$279$	−7.10102	−0.425127
$280$	−12.0000	−0.717137
$281$	−14.1464	−0.843905	−0.421953	−	0.906618i	$-0.638655\pi$
$281$	−14.1464	−0.843905	−0.421953	+	0.906618i	$0.638655\pi$
$282$	4.00000	0.238197
$283$	32.7980	1.94964	0.974818	−	0.223001i	$-0.0715854\pi$
$283$	32.7980	1.94964	0.974818	+	0.223001i	$0.0715854\pi$
$284$	−6.00000	−0.356034
$285$	0	0
$286$	−5.44949	−0.322235
$287$	−16.8990	−0.997515
$288$	−2.00000	−0.117851
$289$	−1.00000	−0.0588235
$290$	−8.69694	−0.510702
$291$	−4.34847	−0.254912
$292$	7.44949	0.435948
$293$	4.89898	0.286201	0.143101	−	0.989708i	$-0.454293\pi$
$293$	4.89898	0.286201	0.143101	+	0.989708i	$0.454293\pi$
$294$	17.0000	0.991460
$295$	−15.5505	−0.905386
$296$	1.10102	0.0639955
$297$	27.2474	1.58106
$298$	3.79796	0.220010
$299$	6.89898	0.398978
$300$	1.00000	0.0577350
$301$	−29.3939	−1.69423
$302$	−10.0000	−0.575435
$303$	2.65153	0.152326
$304$	0	0
$305$	33.7980	1.93527
$306$	−8.00000	−0.457330
$307$	0.752551	0.0429504	0.0214752	−	0.999769i	$-0.493164\pi$
$307$	0.752551	0.0429504	0.0214752	+	0.999769i	$0.493164\pi$
$308$	26.6969	1.52120
$309$	−2.44949	−0.139347
$310$	8.69694	0.493953
$311$	2.44949	0.138898	0.0694489	−	0.997586i	$-0.477876\pi$
$311$	2.44949	0.138898	0.0694489	+	0.997586i	$0.477876\pi$
$312$	1.00000	0.0566139
$313$	19.8990	1.12476	0.562378	−	0.826880i	$-0.309886\pi$
$313$	19.8990	1.12476	0.562378	+	0.826880i	$0.309886\pi$
$314$	4.00000	0.225733
$315$	24.0000	1.35225
$316$	−4.44949	−0.250303
$317$	4.44949	0.249908	0.124954	−	0.992163i	$-0.460122\pi$
$317$	4.44949	0.249908	0.124954	+	0.992163i	$0.460122\pi$
$318$	11.3485	0.636391
$319$	19.3485	1.08331
$320$	2.44949	0.136931
$321$	7.79796	0.435240
$322$	−33.7980	−1.88349
$323$	0	0
$324$	1.00000	0.0555556
$325$	1.00000	0.0554700
$326$	8.55051	0.473569
$327$	13.5505	0.749345
$328$	3.44949	0.190466
$329$	−19.5959	−1.08036
$330$	−13.3485	−0.734809
$331$	26.3485	1.44824	0.724121	−	0.689673i	$-0.242246\pi$
$331$	26.3485	1.44824	0.724121	+	0.689673i	$0.242246\pi$
$332$	−11.4495	−0.628372
$333$	−2.20204	−0.120671
$334$	25.1464	1.37595
$335$	32.9444	1.79994
$336$	−4.89898	−0.267261
$337$	12.5959	0.686143	0.343072	−	0.939309i	$-0.388533\pi$
$337$	12.5959	0.686143	0.343072	+	0.939309i	$0.388533\pi$
$338$	1.00000	0.0543928
$339$	−2.10102	−0.114112
$340$	9.79796	0.531369
$341$	−19.3485	−1.04778
$342$	0	0
$343$	−48.9898	−2.64520
$344$	6.00000	0.323498
$345$	16.8990	0.909810
$346$	1.10102	0.0591912
$347$	−32.3939	−1.73899	−0.869497	−	0.493938i	$-0.835557\pi$
$347$	−32.3939	−1.73899	−0.869497	+	0.493938i	$0.835557\pi$
$348$	−3.55051	−0.190327
$349$	−35.3485	−1.89216	−0.946080	−	0.323933i	$-0.894995\pi$
$349$	−35.3485	−1.89216	−0.946080	+	0.323933i	$0.894995\pi$
$350$	−4.89898	−0.261861
$351$	−5.00000	−0.266880
$352$	−5.44949	−0.290459
$353$	27.2474	1.45024	0.725118	−	0.688625i	$-0.241785\pi$
$353$	27.2474	1.45024	0.725118	+	0.688625i	$0.241785\pi$
$354$	−6.34847	−0.337417
$355$	−14.6969	−0.780033
$356$	−6.89898	−0.365645
$357$	−19.5959	−1.03713
$358$	13.8990	0.734584
$359$	−5.59592	−0.295341	−0.147671	−	0.989037i	$-0.547178\pi$
$359$	−5.59592	−0.295341	−0.147671	+	0.989037i	$0.547178\pi$
$360$	−4.89898	−0.258199
$361$	0	0
$362$	−13.5505	−0.712199
$363$	18.6969	0.981335
$364$	−4.89898	−0.256776
$365$	18.2474	0.955115
$366$	13.7980	0.721231
$367$	−26.8990	−1.40412	−0.702058	−	0.712120i	$-0.747735\pi$
$367$	−26.8990	−1.40412	−0.702058	+	0.712120i	$0.747735\pi$
$368$	6.89898	0.359634
$369$	−6.89898	−0.359147
$370$	2.69694	0.140207
$371$	−55.5959	−2.88640
$372$	3.55051	0.184085
$373$	0.449490	0.0232737	0.0116368	−	0.999932i	$-0.496296\pi$
$373$	0.449490	0.0232737	0.0116368	+	0.999932i	$0.496296\pi$
$374$	−21.7980	−1.12715
$375$	−9.79796	−0.505964
$376$	4.00000	0.206284
$377$	−3.55051	−0.182861
$378$	24.4949	1.25988
$379$	−34.6969	−1.78226	−0.891131	−	0.453746i	$-0.850087\pi$
$379$	−34.6969	−1.78226	−0.891131	+	0.453746i	$0.850087\pi$
$380$	0	0
$381$	−8.24745	−0.422530
$382$	−5.34847	−0.273651
$383$	−28.4949	−1.45602	−0.728011	−	0.685566i	$-0.759555\pi$
$383$	−28.4949	−1.45602	−0.728011	+	0.685566i	$0.759555\pi$
$384$	1.00000	0.0510310
$385$	65.3939	3.33278
$386$	1.10102	0.0560405
$387$	−12.0000	−0.609994
$388$	−4.34847	−0.220760
$389$	−2.20204	−0.111648	−0.0558240	−	0.998441i	$-0.517779\pi$
$389$	−2.20204	−0.111648	−0.0558240	+	0.998441i	$0.517779\pi$
$390$	2.44949	0.124035
$391$	27.5959	1.39559
$392$	17.0000	0.858630
$393$	3.00000	0.151330
$394$	−15.5505	−0.783423
$395$	−10.8990	−0.548387
$396$	10.8990	0.547694
$397$	24.0454	1.20680	0.603402	−	0.797437i	$-0.293811\pi$
$397$	24.0454	1.20680	0.603402	+	0.797437i	$0.293811\pi$
$398$	1.55051	0.0777201
$399$	0	0
$400$	1.00000	0.0500000
$401$	33.9444	1.69510	0.847551	−	0.530714i	$-0.178076\pi$
$401$	33.9444	1.69510	0.847551	+	0.530714i	$0.178076\pi$
$402$	13.4495	0.670800
$403$	3.55051	0.176864
$404$	2.65153	0.131919
$405$	2.44949	0.121716
$406$	17.3939	0.863244
$407$	−6.00000	−0.297409
$408$	4.00000	0.198030
$409$	−29.2474	−1.44619	−0.723097	−	0.690747i	$-0.757282\pi$
$409$	−29.2474	−1.44619	−0.723097	+	0.690747i	$0.757282\pi$
$410$	8.44949	0.417291
$411$	10.5505	0.520418
$412$	−2.44949	−0.120678
$413$	31.1010	1.53038
$414$	−13.7980	−0.678133
$415$	−28.0454	−1.37669
$416$	1.00000	0.0490290
$417$	−8.10102	−0.396709
$418$	0	0
$419$	−22.8990	−1.11869	−0.559344	−	0.828936i	$-0.688947\pi$
$419$	−22.8990	−1.11869	−0.559344	+	0.828936i	$0.688947\pi$
$420$	−12.0000	−0.585540
$421$	2.24745	0.109534	0.0547670	−	0.998499i	$-0.482558\pi$
$421$	2.24745	0.109534	0.0547670	+	0.998499i	$0.482558\pi$
$422$	25.5959	1.24599
$423$	−8.00000	−0.388973
$424$	11.3485	0.551130
$425$	4.00000	0.194029
$426$	−6.00000	−0.290701
$427$	−67.5959	−3.27120
$428$	7.79796	0.376929
$429$	−5.44949	−0.263104
$430$	14.6969	0.708749
$431$	30.2474	1.45697	0.728484	−	0.685063i	$-0.240225\pi$
$431$	30.2474	1.45697	0.728484	+	0.685063i	$0.240225\pi$
$432$	−5.00000	−0.240563
$433$	−22.6969	−1.09075	−0.545373	−	0.838194i	$-0.683612\pi$
$433$	−22.6969	−1.09075	−0.545373	+	0.838194i	$0.683612\pi$
$434$	−17.3939	−0.834933
$435$	−8.69694	−0.416986
$436$	13.5505	0.648952
$437$	0	0
$438$	7.44949	0.355950
$439$	27.3939	1.30744	0.653719	−	0.756737i	$-0.273208\pi$
$439$	27.3939	1.30744	0.653719	+	0.756737i	$0.273208\pi$
$440$	−13.3485	−0.636363
$441$	−34.0000	−1.61905
$442$	4.00000	0.190261
$443$	26.3939	1.25401	0.627005	−	0.779015i	$-0.284280\pi$
$443$	26.3939	1.25401	0.627005	+	0.779015i	$0.284280\pi$
$444$	1.10102	0.0522521
$445$	−16.8990	−0.801088
$446$	11.7980	0.558650
$447$	3.79796	0.179637
$448$	−4.89898	−0.231455
$449$	−19.0454	−0.898808	−0.449404	−	0.893329i	$-0.648364\pi$
$449$	−19.0454	−0.898808	−0.449404	+	0.893329i	$0.648364\pi$
$450$	−2.00000	−0.0942809
$451$	−18.7980	−0.885161
$452$	−2.10102	−0.0988237
$453$	−10.0000	−0.469841
$454$	−4.34847	−0.204084
$455$	−12.0000	−0.562569
$456$	0	0
$457$	7.65153	0.357924	0.178962	−	0.983856i	$-0.442726\pi$
$457$	7.65153	0.357924	0.178962	+	0.983856i	$0.442726\pi$
$458$	−10.6969	−0.499835
$459$	−20.0000	−0.933520
$460$	16.8990	0.787919
$461$	8.44949	0.393532	0.196766	−	0.980450i	$-0.436956\pi$
$461$	8.44949	0.393532	0.196766	+	0.980450i	$0.436956\pi$
$462$	26.6969	1.24205
$463$	−4.69694	−0.218285	−0.109143	−	0.994026i	$-0.534811\pi$
$463$	−4.69694	−0.218285	−0.109143	+	0.994026i	$0.534811\pi$
$464$	−3.55051	−0.164828
$465$	8.69694	0.403311
$466$	16.5959	0.768791
$467$	−31.4949	−1.45741	−0.728705	−	0.684828i	$-0.759877\pi$
$467$	−31.4949	−1.45741	−0.728705	+	0.684828i	$0.759877\pi$
$468$	−2.00000	−0.0924500
$469$	−65.8888	−3.04246
$470$	9.79796	0.451946
$471$	4.00000	0.184310
$472$	−6.34847	−0.292212
$473$	−32.6969	−1.50341
$474$	−4.44949	−0.204372
$475$	0	0
$476$	−19.5959	−0.898177
$477$	−22.6969	−1.03922
$478$	−13.1464	−0.601304
$479$	25.5505	1.16743	0.583716	−	0.811958i	$-0.301598\pi$
$479$	25.5505	1.16743	0.583716	+	0.811958i	$0.301598\pi$
$480$	2.44949	0.111803
$481$	1.10102	0.0502022
$482$	19.2474	0.876697
$483$	−33.7980	−1.53786
$484$	18.6969	0.849861
$485$	−10.6515	−0.483661
$486$	16.0000	0.725775
$487$	−33.8434	−1.53359	−0.766795	−	0.641892i	$-0.778150\pi$
$487$	−33.8434	−1.53359	−0.766795	+	0.641892i	$0.778150\pi$
$488$	13.7980	0.624604
$489$	8.55051	0.386667
$490$	41.6413	1.88116
$491$	−19.7980	−0.893469	−0.446735	−	0.894666i	$-0.647413\pi$
$491$	−19.7980	−0.893469	−0.446735	+	0.894666i	$0.647413\pi$
$492$	3.44949	0.155515
$493$	−14.2020	−0.639628
$494$	0	0
$495$	26.6969	1.19994
$496$	3.55051	0.159423
$497$	29.3939	1.31850
$498$	−11.4495	−0.513064
$499$	4.14643	0.185620	0.0928098	−	0.995684i	$-0.470415\pi$
$499$	4.14643	0.185620	0.0928098	+	0.995684i	$0.470415\pi$
$500$	−9.79796	−0.438178
$501$	25.1464	1.12346
$502$	−21.6969	−0.968382
$503$	1.10102	0.0490921	0.0245460	−	0.999699i	$-0.492186\pi$
$503$	1.10102	0.0490921	0.0245460	+	0.999699i	$0.492186\pi$
$504$	9.79796	0.436436
$505$	6.49490	0.289019
$506$	−37.5959	−1.67134
$507$	1.00000	0.0444116
$508$	−8.24745	−0.365921
$509$	−3.59592	−0.159386	−0.0796931	−	0.996819i	$-0.525394\pi$
$509$	−3.59592	−0.159386	−0.0796931	+	0.996819i	$0.525394\pi$
$510$	9.79796	0.433861
$511$	−36.4949	−1.61444
$512$	1.00000	0.0441942
$513$	0	0
$514$	17.8990	0.789490
$515$	−6.00000	−0.264392
$516$	6.00000	0.264135
$517$	−21.7980	−0.958673
$518$	−5.39388	−0.236993
$519$	1.10102	0.0483294
$520$	2.44949	0.107417
$521$	20.5959	0.902324	0.451162	−	0.892442i	$-0.351010\pi$
$521$	20.5959	0.902324	0.451162	+	0.892442i	$0.351010\pi$
$522$	7.10102	0.310803
$523$	−40.2929	−1.76188	−0.880942	−	0.473225i	$-0.843090\pi$
$523$	−40.2929	−1.76188	−0.880942	+	0.473225i	$0.843090\pi$
$524$	3.00000	0.131056
$525$	−4.89898	−0.213809
$526$	14.6969	0.640817
$527$	14.2020	0.618651
$528$	−5.44949	−0.237159
$529$	24.5959	1.06939
$530$	27.7980	1.20747
$531$	12.6969	0.551000
$532$	0	0
$533$	3.44949	0.149414
$534$	−6.89898	−0.298548
$535$	19.1010	0.825809
$536$	13.4495	0.580929
$537$	13.8990	0.599785
$538$	−19.1464	−0.825461
$539$	−92.6413	−3.99034
$540$	−12.2474	−0.527046
$541$	6.69694	0.287924	0.143962	−	0.989583i	$-0.454016\pi$
$541$	6.69694	0.287924	0.143962	+	0.989583i	$0.454016\pi$
$542$	−17.7980	−0.764488
$543$	−13.5505	−0.581508
$544$	4.00000	0.171499
$545$	33.1918	1.42178
$546$	−4.89898	−0.209657
$547$	39.5959	1.69300	0.846500	−	0.532389i	$-0.178706\pi$
$547$	39.5959	1.69300	0.846500	+	0.532389i	$0.178706\pi$
$548$	10.5505	0.450695
$549$	−27.5959	−1.17777
$550$	−5.44949	−0.232367
$551$	0	0
$552$	6.89898	0.293640
$553$	21.7980	0.926944
$554$	11.1464	0.473566
$555$	2.69694	0.114479
$556$	−8.10102	−0.343560
$557$	10.0454	0.425638	0.212819	−	0.977092i	$-0.431736\pi$
$557$	10.0454	0.425638	0.212819	+	0.977092i	$0.431736\pi$
$558$	−7.10102	−0.300610
$559$	6.00000	0.253773
$560$	−12.0000	−0.507093
$561$	−21.7980	−0.920311
$562$	−14.1464	−0.596731
$563$	39.0000	1.64365	0.821827	−	0.569737i	$-0.192955\pi$
$563$	39.0000	1.64365	0.821827	+	0.569737i	$0.192955\pi$
$564$	4.00000	0.168430
$565$	−5.14643	−0.216512
$566$	32.7980	1.37860
$567$	−4.89898	−0.205738
$568$	−6.00000	−0.251754
$569$	−30.2929	−1.26994	−0.634971	−	0.772536i	$-0.718988\pi$
$569$	−30.2929	−1.26994	−0.634971	+	0.772536i	$0.718988\pi$
$570$	0	0
$571$	−39.0000	−1.63210	−0.816050	−	0.577982i	$-0.803840\pi$
$571$	−39.0000	−1.63210	−0.816050	+	0.577982i	$0.803840\pi$
$572$	−5.44949	−0.227855
$573$	−5.34847	−0.223436
$574$	−16.8990	−0.705350
$575$	6.89898	0.287707
$576$	−2.00000	−0.0833333
$577$	−4.55051	−0.189440	−0.0947201	−	0.995504i	$-0.530196\pi$
$577$	−4.55051	−0.189440	−0.0947201	+	0.995504i	$0.530196\pi$
$578$	−1.00000	−0.0415945
$579$	1.10102	0.0457569
$580$	−8.69694	−0.361121
$581$	56.0908	2.32704
$582$	−4.34847	−0.180250
$583$	−61.8434	−2.56129
$584$	7.44949	0.308262
$585$	−4.89898	−0.202548
$586$	4.89898	0.202375
$587$	−24.8990	−1.02769	−0.513845	−	0.857883i	$-0.671780\pi$
$587$	−24.8990	−1.02769	−0.513845	+	0.857883i	$0.671780\pi$
$588$	17.0000	0.701068
$589$	0	0
$590$	−15.5505	−0.640204
$591$	−15.5505	−0.639663
$592$	1.10102	0.0452517
$593$	−16.3485	−0.671351	−0.335676	−	0.941978i	$-0.608965\pi$
$593$	−16.3485	−0.671351	−0.335676	+	0.941978i	$0.608965\pi$
$594$	27.2474	1.11798
$595$	−48.0000	−1.96781
$596$	3.79796	0.155570
$597$	1.55051	0.0634582
$598$	6.89898	0.282120
$599$	−15.7980	−0.645487	−0.322744	−	0.946486i	$-0.604605\pi$
$599$	−15.7980	−0.645487	−0.322744	+	0.946486i	$0.604605\pi$
$600$	1.00000	0.0408248
$601$	0.101021	0.00412071	0.00206036	−	0.999998i	$-0.499344\pi$
$601$	0.101021	0.00412071	0.00206036	+	0.999998i	$0.499344\pi$
$602$	−29.3939	−1.19800
$603$	−26.8990	−1.09541
$604$	−10.0000	−0.406894
$605$	45.7980	1.86195
$606$	2.65153	0.107711
$607$	18.2020	0.738798	0.369399	−	0.929271i	$-0.379564\pi$
$607$	18.2020	0.738798	0.369399	+	0.929271i	$0.379564\pi$
$608$	0	0
$609$	17.3939	0.704835
$610$	33.7980	1.36844
$611$	4.00000	0.161823
$612$	−8.00000	−0.323381
$613$	3.79796	0.153398	0.0766991	−	0.997054i	$-0.475562\pi$
$613$	3.79796	0.153398	0.0766991	+	0.997054i	$0.475562\pi$
$614$	0.752551	0.0303705
$615$	8.44949	0.340716
$616$	26.6969	1.07565
$617$	7.24745	0.291771	0.145886	−	0.989301i	$-0.453397\pi$
$617$	7.24745	0.291771	0.145886	+	0.989301i	$0.453397\pi$
$618$	−2.44949	−0.0985329
$619$	−15.5959	−0.626853	−0.313426	−	0.949612i	$-0.601477\pi$
$619$	−15.5959	−0.626853	−0.313426	+	0.949612i	$0.601477\pi$
$620$	8.69694	0.349277
$621$	−34.4949	−1.38423
$622$	2.44949	0.0982156
$623$	33.7980	1.35409
$624$	1.00000	0.0400320
$625$	−29.0000	−1.16000
$626$	19.8990	0.795323
$627$	0	0
$628$	4.00000	0.159617
$629$	4.40408	0.175602
$630$	24.0000	0.956183
$631$	−29.5505	−1.17639	−0.588194	−	0.808720i	$-0.700161\pi$
$631$	−29.5505	−1.17639	−0.588194	+	0.808720i	$0.700161\pi$
$632$	−4.44949	−0.176991
$633$	25.5959	1.01735
$634$	4.44949	0.176712
$635$	−20.2020	−0.801694
$636$	11.3485	0.449996
$637$	17.0000	0.673565
$638$	19.3485	0.766013
$639$	12.0000	0.474713
$640$	2.44949	0.0968246
$641$	−35.6969	−1.40994	−0.704972	−	0.709235i	$-0.749041\pi$
$641$	−35.6969	−1.40994	−0.704972	+	0.709235i	$0.749041\pi$
$642$	7.79796	0.307761
$643$	15.9444	0.628785	0.314393	−	0.949293i	$-0.398199\pi$
$643$	15.9444	0.628785	0.314393	+	0.949293i	$0.398199\pi$
$644$	−33.7980	−1.33183
$645$	14.6969	0.578691
$646$	0	0
$647$	34.8990	1.37202	0.686010	−	0.727592i	$-0.259361\pi$
$647$	34.8990	1.37202	0.686010	+	0.727592i	$0.259361\pi$
$648$	1.00000	0.0392837
$649$	34.5959	1.35801
$650$	1.00000	0.0392232
$651$	−17.3939	−0.681720
$652$	8.55051	0.334864
$653$	−21.3485	−0.835430	−0.417715	−	0.908578i	$-0.637169\pi$
$653$	−21.3485	−0.835430	−0.417715	+	0.908578i	$0.637169\pi$
$654$	13.5505	0.529867
$655$	7.34847	0.287128
$656$	3.44949	0.134680
$657$	−14.8990	−0.581265
$658$	−19.5959	−0.763928
$659$	30.8990	1.20365	0.601827	−	0.798627i	$-0.294440\pi$
$659$	30.8990	1.20365	0.601827	+	0.798627i	$0.294440\pi$
$660$	−13.3485	−0.519588
$661$	35.1918	1.36880	0.684402	−	0.729105i	$-0.260063\pi$
$661$	35.1918	1.36880	0.684402	+	0.729105i	$0.260063\pi$
$662$	26.3485	1.02406
$663$	4.00000	0.155347
$664$	−11.4495	−0.444326
$665$	0	0
$666$	−2.20204	−0.0853274
$667$	−24.4949	−0.948446
$668$	25.1464	0.972945
$669$	11.7980	0.456135
$670$	32.9444	1.27275
$671$	−75.1918	−2.90275
$672$	−4.89898	−0.188982
$673$	35.5959	1.37212	0.686061	−	0.727544i	$-0.259338\pi$
$673$	35.5959	1.37212	0.686061	+	0.727544i	$0.259338\pi$
$674$	12.5959	0.485177
$675$	−5.00000	−0.192450
$676$	1.00000	0.0384615
$677$	40.2929	1.54858	0.774290	−	0.632831i	$-0.218107\pi$
$677$	40.2929	1.54858	0.774290	+	0.632831i	$0.218107\pi$
$678$	−2.10102	−0.0806892
$679$	21.3031	0.817536
$680$	9.79796	0.375735
$681$	−4.34847	−0.166634
$682$	−19.3485	−0.740891
$683$	34.0000	1.30097	0.650487	−	0.759517i	$-0.274565\pi$
$683$	34.0000	1.30097	0.650487	+	0.759517i	$0.274565\pi$
$684$	0	0
$685$	25.8434	0.987424
$686$	−48.9898	−1.87044
$687$	−10.6969	−0.408114
$688$	6.00000	0.228748
$689$	11.3485	0.432342
$690$	16.8990	0.643333
$691$	3.59592	0.136795	0.0683976	−	0.997658i	$-0.478211\pi$
$691$	3.59592	0.136795	0.0683976	+	0.997658i	$0.478211\pi$
$692$	1.10102	0.0418545
$693$	−53.3939	−2.02827
$694$	−32.3939	−1.22965
$695$	−19.8434	−0.752702
$696$	−3.55051	−0.134582
$697$	13.7980	0.522635
$698$	−35.3485	−1.33796
$699$	16.5959	0.627715
$700$	−4.89898	−0.185164
$701$	4.40408	0.166340	0.0831699	−	0.996535i	$-0.473496\pi$
$701$	4.40408	0.166340	0.0831699	+	0.996535i	$0.473496\pi$
$702$	−5.00000	−0.188713
$703$	0	0
$704$	−5.44949	−0.205385
$705$	9.79796	0.369012
$706$	27.2474	1.02547
$707$	−12.9898	−0.488532
$708$	−6.34847	−0.238590
$709$	−42.2474	−1.58664	−0.793318	−	0.608807i	$-0.791648\pi$
$709$	−42.2474	−1.58664	−0.793318	+	0.608807i	$0.791648\pi$
$710$	−14.6969	−0.551566
$711$	8.89898	0.333738
$712$	−6.89898	−0.258550
$713$	24.4949	0.917341
$714$	−19.5959	−0.733359
$715$	−13.3485	−0.499204
$716$	13.8990	0.519429
$717$	−13.1464	−0.490962
$718$	−5.59592	−0.208838
$719$	−19.3031	−0.719883	−0.359941	−	0.932975i	$-0.617203\pi$
$719$	−19.3031	−0.719883	−0.359941	+	0.932975i	$0.617203\pi$
$720$	−4.89898	−0.182574
$721$	12.0000	0.446903
$722$	0	0
$723$	19.2474	0.715820
$724$	−13.5505	−0.503601
$725$	−3.55051	−0.131863
$726$	18.6969	0.693908
$727$	26.7423	0.991819	0.495909	−	0.868374i	$-0.334835\pi$
$727$	26.7423	0.991819	0.495909	+	0.868374i	$0.334835\pi$
$728$	−4.89898	−0.181568
$729$	13.0000	0.481481
$730$	18.2474	0.675368
$731$	24.0000	0.887672
$732$	13.7980	0.509987
$733$	−31.1464	−1.15042	−0.575210	−	0.818006i	$-0.695080\pi$
$733$	−31.1464	−1.15042	−0.575210	+	0.818006i	$0.695080\pi$
$734$	−26.8990	−0.992859
$735$	41.6413	1.53596
$736$	6.89898	0.254300
$737$	−73.2929	−2.69978
$738$	−6.89898	−0.253955
$739$	24.1464	0.888241	0.444120	−	0.895967i	$-0.353516\pi$
$739$	24.1464	0.888241	0.444120	+	0.895967i	$0.353516\pi$
$740$	2.69694	0.0991414
$741$	0	0
$742$	−55.5959	−2.04099
$743$	16.4495	0.603473	0.301737	−	0.953391i	$-0.402434\pi$
$743$	16.4495	0.603473	0.301737	+	0.953391i	$0.402434\pi$
$744$	3.55051	0.130168
$745$	9.30306	0.340838
$746$	0.449490	0.0164570
$747$	22.8990	0.837830
$748$	−21.7980	−0.797012
$749$	−38.2020	−1.39587
$750$	−9.79796	−0.357771
$751$	−8.20204	−0.299297	−0.149648	−	0.988739i	$-0.547814\pi$
$751$	−8.20204	−0.299297	−0.149648	+	0.988739i	$0.547814\pi$
$752$	4.00000	0.145865
$753$	−21.6969	−0.790680
$754$	−3.55051	−0.129302
$755$	−24.4949	−0.891461
$756$	24.4949	0.890871
$757$	17.1464	0.623198	0.311599	−	0.950214i	$-0.399136\pi$
$757$	17.1464	0.623198	0.311599	+	0.950214i	$0.399136\pi$
$758$	−34.6969	−1.26025
$759$	−37.5959	−1.36465
$760$	0	0
$761$	23.9444	0.867983	0.433992	−	0.900917i	$-0.357105\pi$
$761$	23.9444	0.867983	0.433992	+	0.900917i	$0.357105\pi$
$762$	−8.24745	−0.298774
$763$	−66.3837	−2.40325
$764$	−5.34847	−0.193501
$765$	−19.5959	−0.708492
$766$	−28.4949	−1.02956
$767$	−6.34847	−0.229230
$768$	1.00000	0.0360844
$769$	16.6969	0.602107	0.301054	−	0.953607i	$-0.402662\pi$
$769$	16.6969	0.602107	0.301054	+	0.953607i	$0.402662\pi$
$770$	65.3939	2.35663
$771$	17.8990	0.644616
$772$	1.10102	0.0396266
$773$	12.2474	0.440510	0.220255	−	0.975442i	$-0.429311\pi$
$773$	12.2474	0.440510	0.220255	+	0.975442i	$0.429311\pi$
$774$	−12.0000	−0.431331
$775$	3.55051	0.127538
$776$	−4.34847	−0.156101
$777$	−5.39388	−0.193504
$778$	−2.20204	−0.0789470
$779$	0	0
$780$	2.44949	0.0877058
$781$	32.6969	1.16999
$782$	27.5959	0.986828
$783$	17.7526	0.634424
$784$	17.0000	0.607143
$785$	9.79796	0.349704
$786$	3.00000	0.107006
$787$	−31.2474	−1.11385	−0.556926	−	0.830562i	$-0.688019\pi$
$787$	−31.2474	−1.11385	−0.556926	+	0.830562i	$0.688019\pi$
$788$	−15.5505	−0.553964
$789$	14.6969	0.523225
$790$	−10.8990	−0.387768
$791$	10.2929	0.365972
$792$	10.8990	0.387278
$793$	13.7980	0.489980
$794$	24.0454	0.853340
$795$	27.7980	0.985892
$796$	1.55051	0.0549564
$797$	−23.7980	−0.842967	−0.421483	−	0.906836i	$-0.638490\pi$
$797$	−23.7980	−0.842967	−0.421483	+	0.906836i	$0.638490\pi$
$798$	0	0
$799$	16.0000	0.566039
$800$	1.00000	0.0353553
$801$	13.7980	0.487527
$802$	33.9444	1.19862
$803$	−40.5959	−1.43260
$804$	13.4495	0.474327
$805$	−82.7878	−2.91788
$806$	3.55051	0.125061
$807$	−19.1464	−0.673986
$808$	2.65153	0.0932805
$809$	−0.303062	−0.0106551	−0.00532754	−	0.999986i	$-0.501696\pi$
$809$	−0.303062	−0.0106551	−0.00532754	+	0.999986i	$0.501696\pi$
$810$	2.44949	0.0860663
$811$	−17.5959	−0.617876	−0.308938	−	0.951082i	$-0.599974\pi$
$811$	−17.5959	−0.617876	−0.308938	+	0.951082i	$0.599974\pi$
$812$	17.3939	0.610405
$813$	−17.7980	−0.624202
$814$	−6.00000	−0.210300
$815$	20.9444	0.733650
$816$	4.00000	0.140028
$817$	0	0
$818$	−29.2474	−1.02261
$819$	9.79796	0.342368
$820$	8.44949	0.295069
$821$	6.49490	0.226673	0.113337	−	0.993557i	$-0.463846\pi$
$821$	6.49490	0.226673	0.113337	+	0.993557i	$0.463846\pi$
$822$	10.5505	0.367991
$823$	−21.1464	−0.737118	−0.368559	−	0.929604i	$-0.620149\pi$
$823$	−21.1464	−0.737118	−0.368559	+	0.929604i	$0.620149\pi$
$824$	−2.44949	−0.0853320
$825$	−5.44949	−0.189727
$826$	31.1010	1.08214
$827$	−49.4495	−1.71953	−0.859764	−	0.510692i	$-0.829389\pi$
$827$	−49.4495	−1.71953	−0.859764	+	0.510692i	$0.829389\pi$
$828$	−13.7980	−0.479512
$829$	35.5959	1.23630	0.618149	−	0.786061i	$-0.287883\pi$
$829$	35.5959	1.23630	0.618149	+	0.786061i	$0.287883\pi$
$830$	−28.0454	−0.973470
$831$	11.1464	0.386665
$832$	1.00000	0.0346688
$833$	68.0000	2.35606
$834$	−8.10102	−0.280515
$835$	61.5959	2.13161
$836$	0	0
$837$	−17.7526	−0.613618
$838$	−22.8990	−0.791032
$839$	−20.8990	−0.721513	−0.360756	−	0.932660i	$-0.617481\pi$
$839$	−20.8990	−0.721513	−0.360756	+	0.932660i	$0.617481\pi$
$840$	−12.0000	−0.414039
$841$	−16.3939	−0.565306
$842$	2.24745	0.0774522
$843$	−14.1464	−0.487229
$844$	25.5959	0.881048
$845$	2.44949	0.0842650
$846$	−8.00000	−0.275046
$847$	−91.5959	−3.14727
$848$	11.3485	0.389708
$849$	32.7980	1.12562
$850$	4.00000	0.137199
$851$	7.59592	0.260385
$852$	−6.00000	−0.205557
$853$	12.0454	0.412427	0.206213	−	0.978507i	$-0.433886\pi$
$853$	12.0454	0.412427	0.206213	+	0.978507i	$0.433886\pi$
$854$	−67.5959	−2.31308
$855$	0	0
$856$	7.79796	0.266529
$857$	−42.1918	−1.44125	−0.720623	−	0.693327i	$-0.756144\pi$
$857$	−42.1918	−1.44125	−0.720623	+	0.693327i	$0.756144\pi$
$858$	−5.44949	−0.186043
$859$	−20.1010	−0.685838	−0.342919	−	0.939365i	$-0.611416\pi$
$859$	−20.1010	−0.685838	−0.342919	+	0.939365i	$0.611416\pi$
$860$	14.6969	0.501161
$861$	−16.8990	−0.575916
$862$	30.2474	1.03023
$863$	3.30306	0.112438	0.0562188	−	0.998418i	$-0.482096\pi$
$863$	3.30306	0.112438	0.0562188	+	0.998418i	$0.482096\pi$
$864$	−5.00000	−0.170103
$865$	2.69694	0.0916987
$866$	−22.6969	−0.771273
$867$	−1.00000	−0.0339618
$868$	−17.3939	−0.590387
$869$	24.2474	0.822538
$870$	−8.69694	−0.294854
$871$	13.4495	0.455719
$872$	13.5505	0.458878
$873$	8.69694	0.294347
$874$	0	0
$875$	48.0000	1.62270
$876$	7.44949	0.251695
$877$	−16.6515	−0.562282	−0.281141	−	0.959666i	$-0.590713\pi$
$877$	−16.6515	−0.562282	−0.281141	+	0.959666i	$0.590713\pi$
$878$	27.3939	0.924499
$879$	4.89898	0.165238
$880$	−13.3485	−0.449977
$881$	2.39388	0.0806518	0.0403259	−	0.999187i	$-0.487160\pi$
$881$	2.39388	0.0806518	0.0403259	+	0.999187i	$0.487160\pi$
$882$	−34.0000	−1.14484
$883$	31.0000	1.04323	0.521617	−	0.853180i	$-0.325329\pi$
$883$	31.0000	1.04323	0.521617	+	0.853180i	$0.325329\pi$
$884$	4.00000	0.134535
$885$	−15.5505	−0.522725
$886$	26.3939	0.886720
$887$	18.6515	0.626257	0.313129	−	0.949711i	$-0.398623\pi$
$887$	18.6515	0.626257	0.313129	+	0.949711i	$0.398623\pi$
$888$	1.10102	0.0369478
$889$	40.4041	1.35511
$890$	−16.8990	−0.566455
$891$	−5.44949	−0.182565
$892$	11.7980	0.395025
$893$	0	0
$894$	3.79796	0.127023
$895$	34.0454	1.13801
$896$	−4.89898	−0.163663
$897$	6.89898	0.230350
$898$	−19.0454	−0.635553
$899$	−12.6061	−0.420438
$900$	−2.00000	−0.0666667
$901$	45.3939	1.51229
$902$	−18.7980	−0.625904
$903$	−29.3939	−0.978167
$904$	−2.10102	−0.0698789
$905$	−33.1918	−1.10333
$906$	−10.0000	−0.332228
$907$	12.5959	0.418241	0.209120	−	0.977890i	$-0.432940\pi$
$907$	12.5959	0.418241	0.209120	+	0.977890i	$0.432940\pi$
$908$	−4.34847	−0.144309
$909$	−5.30306	−0.175891
$910$	−12.0000	−0.397796
$911$	−36.7423	−1.21733	−0.608664	−	0.793428i	$-0.708294\pi$
$911$	−36.7423	−1.21733	−0.608664	+	0.793428i	$0.708294\pi$
$912$	0	0
$913$	62.3939	2.06494
$914$	7.65153	0.253090
$915$	33.7980	1.11733
$916$	−10.6969	−0.353437
$917$	−14.6969	−0.485336
$918$	−20.0000	−0.660098
$919$	38.4949	1.26983	0.634915	−	0.772582i	$-0.281035\pi$
$919$	38.4949	1.26983	0.634915	+	0.772582i	$0.281035\pi$
$920$	16.8990	0.557143
$921$	0.752551	0.0247974
$922$	8.44949	0.278269
$923$	−6.00000	−0.197492
$924$	26.6969	0.878265
$925$	1.10102	0.0362013
$926$	−4.69694	−0.154351
$927$	4.89898	0.160904
$928$	−3.55051	−0.116551
$929$	−17.0454	−0.559242	−0.279621	−	0.960111i	$-0.590209\pi$
$929$	−17.0454	−0.559242	−0.279621	+	0.960111i	$0.590209\pi$
$930$	8.69694	0.285184
$931$	0	0
$932$	16.5959	0.543617
$933$	2.44949	0.0801927
$934$	−31.4949	−1.03054
$935$	−53.3939	−1.74617
$936$	−2.00000	−0.0653720
$937$	12.7980	0.418091	0.209046	−	0.977906i	$-0.432964\pi$
$937$	12.7980	0.418091	0.209046	+	0.977906i	$0.432964\pi$
$938$	−65.8888	−2.15134
$939$	19.8990	0.649379
$940$	9.79796	0.319574
$941$	32.9444	1.07396	0.536978	−	0.843596i	$-0.319566\pi$
$941$	32.9444	1.07396	0.536978	+	0.843596i	$0.319566\pi$
$942$	4.00000	0.130327
$943$	23.7980	0.774968
$944$	−6.34847	−0.206625
$945$	60.0000	1.95180
$946$	−32.6969	−1.06307
$947$	49.1918	1.59852	0.799260	−	0.600985i	$-0.205225\pi$
$947$	49.1918	1.59852	0.799260	+	0.600985i	$0.205225\pi$
$948$	−4.44949	−0.144513
$949$	7.44949	0.241821
$950$	0	0
$951$	4.44949	0.144285
$952$	−19.5959	−0.635107
$953$	33.4949	1.08501	0.542503	−	0.840054i	$-0.317477\pi$
$953$	33.4949	1.08501	0.542503	+	0.840054i	$0.317477\pi$
$954$	−22.6969	−0.734841
$955$	−13.1010	−0.423939
$956$	−13.1464	−0.425186
$957$	19.3485	0.625447
$958$	25.5505	0.825500
$959$	−51.6867	−1.66905
$960$	2.44949	0.0790569
$961$	−18.3939	−0.593351
$962$	1.10102	0.0354983
$963$	−15.5959	−0.502571
$964$	19.2474	0.619919
$965$	2.69694	0.0868175
$966$	−33.7980	−1.08743
$967$	−7.14643	−0.229814	−0.114907	−	0.993376i	$-0.536657\pi$
$967$	−7.14643	−0.229814	−0.114907	+	0.993376i	$0.536657\pi$
$968$	18.6969	0.600942
$969$	0	0
$970$	−10.6515	−0.342000
$971$	46.3939	1.48885	0.744425	−	0.667706i	$-0.232724\pi$
$971$	46.3939	1.48885	0.744425	+	0.667706i	$0.232724\pi$
$972$	16.0000	0.513200
$973$	39.6867	1.27230
$974$	−33.8434	−1.08441
$975$	1.00000	0.0320256
$976$	13.7980	0.441662
$977$	−13.9444	−0.446120	−0.223060	−	0.974805i	$-0.571605\pi$
$977$	−13.9444	−0.446120	−0.223060	+	0.974805i	$0.571605\pi$
$978$	8.55051	0.273415
$979$	37.5959	1.20157
$980$	41.6413	1.33018
$981$	−27.1010	−0.865269
$982$	−19.7980	−0.631778
$983$	29.7980	0.950407	0.475204	−	0.879876i	$-0.342374\pi$
$983$	29.7980	0.950407	0.475204	+	0.879876i	$0.342374\pi$
$984$	3.44949	0.109966
$985$	−38.0908	−1.21367
$986$	−14.2020	−0.452285
$987$	−19.5959	−0.623745
$988$	0	0
$989$	41.3939	1.31625
$990$	26.6969	0.848484
$991$	−2.20204	−0.0699501	−0.0349751	−	0.999388i	$-0.511135\pi$
$991$	−2.20204	−0.0699501	−0.0349751	+	0.999388i	$0.511135\pi$
$992$	3.55051	0.112729
$993$	26.3485	0.836143
$994$	29.3939	0.932317
$995$	3.79796	0.120403
$996$	−11.4495	−0.362791
$997$	4.89898	0.155152	0.0775761	−	0.996986i	$-0.475282\pi$
$997$	4.89898	0.155152	0.0775761	+	0.996986i	$0.475282\pi$
$998$	4.14643	0.131253
$999$	−5.50510	−0.174174

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9386.2.a.t.1.2		2
19.8	odd	6		494.2.f.g.235.1	✓	4
19.12	odd	6		494.2.f.g.391.1	yes	4
19.18	odd	2		9386.2.a.o.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
494.2.f.g.235.1	✓	4	19.8	odd	6
494.2.f.g.391.1	yes	4	19.12	odd	6
9386.2.a.o.1.2		2	19.18	odd	2
9386.2.a.t.1.2		2	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 9386 = 2 \cdot 13 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9386.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.44949 q^{5} +1.00000 q^{6} -4.89898 q^{7} +1.00000 q^{8} -2.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.44949 q^{5} +1.00000 q^{6} -4.89898 q^{7} +1.00000 q^{8} -2.00000 q^{9} +2.44949 q^{10} -5.44949 q^{11} +1.00000 q^{12} +1.00000 q^{13} -4.89898 q^{14} +2.44949 q^{15} +1.00000 q^{16} +4.00000 q^{17} -2.00000 q^{18} +2.44949 q^{20} -4.89898 q^{21} -5.44949 q^{22} +6.89898 q^{23} +1.00000 q^{24} +1.00000 q^{25} +1.00000 q^{26} -5.00000 q^{27} -4.89898 q^{28} -3.55051 q^{29} +2.44949 q^{30} +3.55051 q^{31} +1.00000 q^{32} -5.44949 q^{33} +4.00000 q^{34} -12.0000 q^{35} -2.00000 q^{36} +1.10102 q^{37} +1.00000 q^{39} +2.44949 q^{40} +3.44949 q^{41} -4.89898 q^{42} +6.00000 q^{43} -5.44949 q^{44} -4.89898 q^{45} +6.89898 q^{46} +4.00000 q^{47} +1.00000 q^{48} +17.0000 q^{49} +1.00000 q^{50} +4.00000 q^{51} +1.00000 q^{52} +11.3485 q^{53} -5.00000 q^{54} -13.3485 q^{55} -4.89898 q^{56} -3.55051 q^{58} -6.34847 q^{59} +2.44949 q^{60} +13.7980 q^{61} +3.55051 q^{62} +9.79796 q^{63} +1.00000 q^{64} +2.44949 q^{65} -5.44949 q^{66} +13.4495 q^{67} +4.00000 q^{68} +6.89898 q^{69} -12.0000 q^{70} -6.00000 q^{71} -2.00000 q^{72} +7.44949 q^{73} +1.10102 q^{74} +1.00000 q^{75} +26.6969 q^{77} +1.00000 q^{78} -4.44949 q^{79} +2.44949 q^{80} +1.00000 q^{81} +3.44949 q^{82} -11.4495 q^{83} -4.89898 q^{84} +9.79796 q^{85} +6.00000 q^{86} -3.55051 q^{87} -5.44949 q^{88} -6.89898 q^{89} -4.89898 q^{90} -4.89898 q^{91} +6.89898 q^{92} +3.55051 q^{93} +4.00000 q^{94} +1.00000 q^{96} -4.34847 q^{97} +17.0000 q^{98} +10.8990 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{6} + 2 q^{8} - 4 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^6 + 2 * q^8 - 4 * q^9	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{6} + 2 q^{8} - 4 q^{9} - 6 q^{11} + 2 q^{12} + 2 q^{13} + 2 q^{16} + 8 q^{17} - 4 q^{18} - 6 q^{22} + 4 q^{23} + 2 q^{24} + 2 q^{25} + 2 q^{26} - 10 q^{27} - 12 q^{29} + 12 q^{31} + 2 q^{32} - 6 q^{33} + 8 q^{34} - 24 q^{35} - 4 q^{36} + 12 q^{37} + 2 q^{39} + 2 q^{41} + 12 q^{43} - 6 q^{44} + 4 q^{46} + 8 q^{47} + 2 q^{48} + 34 q^{49} + 2 q^{50} + 8 q^{51} + 2 q^{52} + 8 q^{53} - 10 q^{54} - 12 q^{55} - 12 q^{58} + 2 q^{59} + 8 q^{61} + 12 q^{62} + 2 q^{64} - 6 q^{66} + 22 q^{67} + 8 q^{68} + 4 q^{69} - 24 q^{70} - 12 q^{71} - 4 q^{72} + 10 q^{73} + 12 q^{74} + 2 q^{75} + 24 q^{77} + 2 q^{78} - 4 q^{79} + 2 q^{81} + 2 q^{82} - 18 q^{83} + 12 q^{86} - 12 q^{87} - 6 q^{88} - 4 q^{89} + 4 q^{92} + 12 q^{93} + 8 q^{94} + 2 q^{96} + 6 q^{97} + 34 q^{98} + 12 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^6 + 2 * q^8 - 4 * q^9 - 6 * q^11 + 2 * q^12 + 2 * q^13 + 2 * q^16 + 8 * q^17 - 4 * q^18 - 6 * q^22 + 4 * q^23 + 2 * q^24 + 2 * q^25 + 2 * q^26 - 10 * q^27 - 12 * q^29 + 12 * q^31 + 2 * q^32 - 6 * q^33 + 8 * q^34 - 24 * q^35 - 4 * q^36 + 12 * q^37 + 2 * q^39 + 2 * q^41 + 12 * q^43 - 6 * q^44 + 4 * q^46 + 8 * q^47 + 2 * q^48 + 34 * q^49 + 2 * q^50 + 8 * q^51 + 2 * q^52 + 8 * q^53 - 10 * q^54 - 12 * q^55 - 12 * q^58 + 2 * q^59 + 8 * q^61 + 12 * q^62 + 2 * q^64 - 6 * q^66 + 22 * q^67 + 8 * q^68 + 4 * q^69 - 24 * q^70 - 12 * q^71 - 4 * q^72 + 10 * q^73 + 12 * q^74 + 2 * q^75 + 24 * q^77 + 2 * q^78 - 4 * q^79 + 2 * q^81 + 2 * q^82 - 18 * q^83 + 12 * q^86 - 12 * q^87 - 6 * q^88 - 4 * q^89 + 4 * q^92 + 12 * q^93 + 8 * q^94 + 2 * q^96 + 6 * q^97 + 34 * q^98 + 12 * q^99

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