LMFDB - Embedded newform 7399.2.a.e.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7399,2,Mod(1,7399)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7399, 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("7399.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7399 = 7^{2} \cdot 151 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7399.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:	$59.0813124555$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.4838537.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 7x^{4} + 3x^{3} + 13x^{2} + 3x - 1 $ x^6 - x^5 - 7x^4 + 3x^3 + 13x^2 + 3x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 151)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$0.183668$ of defining polynomial
Character	$\chi$	$=$	7399.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.183668 q^{2} +3.29466 q^{3} -1.96627 q^{4} -3.71611 q^{5} +0.605125 q^{6} -0.728478 q^{8} +7.85477 q^{9} +O(q^{10})$	\(q+0.183668 q^{2} +3.29466 q^{3} -1.96627 q^{4} -3.71611 q^{5} +0.605125 q^{6} -0.728478 q^{8} +7.85477 q^{9} -0.682533 q^{10} -0.912147 q^{11} -6.47817 q^{12} +1.27865 q^{13} -12.2433 q^{15} +3.79873 q^{16} -1.65822 q^{17} +1.44267 q^{18} -3.74742 q^{19} +7.30687 q^{20} -0.167533 q^{22} -0.248713 q^{23} -2.40009 q^{24} +8.80951 q^{25} +0.234848 q^{26} +15.9948 q^{27} +1.93860 q^{29} -2.24871 q^{30} +5.44267 q^{31} +2.15466 q^{32} -3.00521 q^{33} -0.304563 q^{34} -15.4446 q^{36} -4.41526 q^{37} -0.688284 q^{38} +4.21272 q^{39} +2.70711 q^{40} -8.64880 q^{41} +1.41210 q^{43} +1.79352 q^{44} -29.1892 q^{45} -0.0456807 q^{46} -2.19095 q^{47} +12.5155 q^{48} +1.61803 q^{50} -5.46328 q^{51} -2.51417 q^{52} -10.4493 q^{53} +2.93774 q^{54} +3.38964 q^{55} -12.3465 q^{57} +0.356059 q^{58} +0.862276 q^{59} +24.0736 q^{60} +2.48235 q^{61} +0.999648 q^{62} -7.20172 q^{64} -4.75161 q^{65} -0.551962 q^{66} -13.4435 q^{67} +3.26051 q^{68} -0.819424 q^{69} +8.78436 q^{71} -5.72203 q^{72} +14.3562 q^{73} -0.810944 q^{74} +29.0243 q^{75} +7.36843 q^{76} +0.773744 q^{78} -10.1620 q^{79} -14.1165 q^{80} +29.1331 q^{81} -1.58851 q^{82} -7.06074 q^{83} +6.16215 q^{85} +0.259358 q^{86} +6.38702 q^{87} +0.664479 q^{88} -11.7770 q^{89} -5.36114 q^{90} +0.489036 q^{92} +17.9317 q^{93} -0.402409 q^{94} +13.9259 q^{95} +7.09888 q^{96} +0.860838 q^{97} -7.16470 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} + 5 q^{3} + 3 q^{4} - 6 q^{5} + 2 q^{6} + 9 q^{8} + 15 q^{9}+O(q^{10}) $ 6 * q + q^2 + 5 * q^3 + 3 * q^4 - 6 * q^5 + 2 * q^6 + 9 * q^8 + 15 * q^9	$ 6 q + q^{2} + 5 q^{3} + 3 q^{4} - 6 q^{5} + 2 q^{6} + 9 q^{8} + 15 q^{9} - 8 q^{10} + 8 q^{11} + 11 q^{12} + q^{13} - 18 q^{15} - 3 q^{16} - 9 q^{17} - 16 q^{18} + 6 q^{19} - 3 q^{20} - 12 q^{22} - 4 q^{23} - q^{24} - 4 q^{25} + 7 q^{26} + 2 q^{27} - 2 q^{29} - 16 q^{30} + 8 q^{31} - 11 q^{32} - 3 q^{33} + 9 q^{34} - 25 q^{36} - 12 q^{37} + 3 q^{38} - 22 q^{39} - 9 q^{40} - 41 q^{41} + q^{43} - 12 q^{45} - 17 q^{46} - 28 q^{47} - 9 q^{48} + 15 q^{50} - 31 q^{51} - 15 q^{52} + 14 q^{53} - 27 q^{54} - q^{55} - 28 q^{57} + q^{58} - 12 q^{59} + 17 q^{60} - 5 q^{61} + 9 q^{62} - 27 q^{64} + 13 q^{65} - 8 q^{66} - 15 q^{67} - 11 q^{68} - 33 q^{69} - 2 q^{71} + q^{72} + 7 q^{73} + 53 q^{74} + 32 q^{75} + 3 q^{76} + 16 q^{78} - 9 q^{79} - 16 q^{80} + 66 q^{81} - 10 q^{82} + 11 q^{83} - 10 q^{85} - 26 q^{86} + 26 q^{87} + 24 q^{88} - 36 q^{89} - 19 q^{90} - 38 q^{92} - q^{93} - 42 q^{94} + 32 q^{95} + 34 q^{96} - 11 q^{97} + 17 q^{99}+O(q^{100}) $ 6 * q + q^2 + 5 * q^3 + 3 * q^4 - 6 * q^5 + 2 * q^6 + 9 * q^8 + 15 * q^9 - 8 * q^10 + 8 * q^11 + 11 * q^12 + q^13 - 18 * q^15 - 3 * q^16 - 9 * q^17 - 16 * q^18 + 6 * q^19 - 3 * q^20 - 12 * q^22 - 4 * q^23 - q^24 - 4 * q^25 + 7 * q^26 + 2 * q^27 - 2 * q^29 - 16 * q^30 + 8 * q^31 - 11 * q^32 - 3 * q^33 + 9 * q^34 - 25 * q^36 - 12 * q^37 + 3 * q^38 - 22 * q^39 - 9 * q^40 - 41 * q^41 + q^43 - 12 * q^45 - 17 * q^46 - 28 * q^47 - 9 * q^48 + 15 * q^50 - 31 * q^51 - 15 * q^52 + 14 * q^53 - 27 * q^54 - q^55 - 28 * q^57 + q^58 - 12 * q^59 + 17 * q^60 - 5 * q^61 + 9 * q^62 - 27 * q^64 + 13 * q^65 - 8 * q^66 - 15 * q^67 - 11 * q^68 - 33 * q^69 - 2 * q^71 + q^72 + 7 * q^73 + 53 * q^74 + 32 * q^75 + 3 * q^76 + 16 * q^78 - 9 * q^79 - 16 * q^80 + 66 * q^81 - 10 * q^82 + 11 * q^83 - 10 * q^85 - 26 * q^86 + 26 * q^87 + 24 * q^88 - 36 * q^89 - 19 * q^90 - 38 * q^92 - q^93 - 42 * q^94 + 32 * q^95 + 34 * q^96 - 11 * q^97 + 17 * 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 $

$2$	0.183668	0.129873	0.0649366	−	0.997889i	$-0.479315\pi$
$2$	0.183668	0.129873	0.0649366	+	0.997889i	$0.479315\pi$
$3$	3.29466	1.90217	0.951086	−	0.308927i	$-0.0999698\pi$
$3$	3.29466	1.90217	0.951086	+	0.308927i	$0.0999698\pi$
$4$	−1.96627	−0.983133
$5$	−3.71611	−1.66190	−0.830948	−	0.556349i	$-0.812202\pi$
$5$	−3.71611	−1.66190	−0.830948	+	0.556349i	$0.812202\pi$
$6$	0.605125	0.247041
$7$	0	0
$7$	0	0
$8$	−0.728478	−0.257556
$9$	7.85477	2.61826
$10$	−0.682533	−0.215836
$11$	−0.912147	−0.275023	−0.137511	−	0.990500i	$-0.543910\pi$
$11$	−0.912147	−0.275023	−0.137511	+	0.990500i	$0.543910\pi$
$12$	−6.47817	−1.87009
$13$	1.27865	0.354634	0.177317	−	0.984154i	$-0.443258\pi$
$13$	1.27865	0.354634	0.177317	+	0.984154i	$0.443258\pi$
$14$	0	0
$15$	−12.2433	−3.16121
$16$	3.79873	0.949683
$17$	−1.65822	−0.402178	−0.201089	−	0.979573i	$-0.564448\pi$
$17$	−1.65822	−0.402178	−0.201089	+	0.979573i	$0.564448\pi$
$18$	1.44267	0.340041
$19$	−3.74742	−0.859718	−0.429859	−	0.902896i	$-0.641437\pi$
$19$	−3.74742	−0.859718	−0.429859	+	0.902896i	$0.641437\pi$
$20$	7.30687	1.63387
$21$	0	0
$22$	−0.167533	−0.0357181
$23$	−0.248713	−0.0518602	−0.0259301	−	0.999664i	$-0.508255\pi$
$23$	−0.248713	−0.0518602	−0.0259301	+	0.999664i	$0.508255\pi$
$24$	−2.40009	−0.489915
$25$	8.80951	1.76190
$26$	0.234848	0.0460575
$27$	15.9948	3.07820
$28$	0	0
$29$	1.93860	0.359989	0.179994	−	0.983668i	$-0.442392\pi$
$29$	1.93860	0.359989	0.179994	+	0.983668i	$0.442392\pi$
$30$	−2.24871	−0.410557
$31$	5.44267	0.977533	0.488767	−	0.872415i	$-0.337447\pi$
$31$	5.44267	0.977533	0.488767	+	0.872415i	$0.337447\pi$
$32$	2.15466	0.380894
$33$	−3.00521	−0.523140
$34$	−0.304563	−0.0522322
$35$	0	0
$36$	−15.4446	−2.57409
$37$	−4.41526	−0.725864	−0.362932	−	0.931816i	$-0.618224\pi$
$37$	−4.41526	−0.725864	−0.362932	+	0.931816i	$0.618224\pi$
$38$	−0.688284	−0.111654
$39$	4.21272	0.674575
$40$	2.70711	0.428031
$41$	−8.64880	−1.35072	−0.675358	−	0.737490i	$-0.736011\pi$
$41$	−8.64880	−1.35072	−0.675358	+	0.737490i	$0.736011\pi$
$42$	0	0
$43$	1.41210	0.215343	0.107671	−	0.994187i	$-0.465661\pi$
$43$	1.41210	0.215343	0.107671	+	0.994187i	$0.465661\pi$
$44$	1.79352	0.270384
$45$	−29.1892	−4.35127
$46$	−0.0456807	−0.00673526
$47$	−2.19095	−0.319583	−0.159791	−	0.987151i	$-0.551082\pi$
$47$	−2.19095	−0.319583	−0.159791	+	0.987151i	$0.551082\pi$
$48$	12.5155	1.80646
$49$	0	0
$50$	1.61803	0.228824
$51$	−5.46328	−0.765012
$52$	−2.51417	−0.348652
$53$	−10.4493	−1.43532	−0.717661	−	0.696393i	$-0.754787\pi$
$53$	−10.4493	−1.43532	−0.717661	+	0.696393i	$0.754787\pi$
$54$	2.93774	0.399776
$55$	3.38964	0.457059
$56$	0	0
$57$	−12.3465	−1.63533
$58$	0.356059	0.0467529
$59$	0.862276	0.112259	0.0561294	−	0.998424i	$-0.482124\pi$
$59$	0.862276	0.112259	0.0561294	+	0.998424i	$0.482124\pi$
$60$	24.0736	3.10789
$61$	2.48235	0.317833	0.158916	−	0.987292i	$-0.449200\pi$
$61$	2.48235	0.317833	0.158916	+	0.987292i	$0.449200\pi$
$62$	0.999648	0.126955
$63$	0	0
$64$	−7.20172	−0.900215
$65$	−4.75161	−0.589365
$66$	−0.551962	−0.0679419
$67$	−13.4435	−1.64239	−0.821195	−	0.570647i	$-0.806692\pi$
$67$	−13.4435	−1.64239	−0.821195	+	0.570647i	$0.806692\pi$
$68$	3.26051	0.395395
$69$	−0.819424	−0.0986471
$70$	0	0
$71$	8.78436	1.04251	0.521256	−	0.853400i	$-0.325464\pi$
$71$	8.78436	1.04251	0.521256	+	0.853400i	$0.325464\pi$
$72$	−5.72203	−0.674347
$73$	14.3562	1.68026	0.840131	−	0.542383i	$-0.182478\pi$
$73$	14.3562	1.68026	0.840131	+	0.542383i	$0.182478\pi$
$74$	−0.810944	−0.0942703
$75$	29.0243	3.35144
$76$	7.36843	0.845217
$77$	0	0
$78$	0.773744	0.0876092
$79$	−10.1620	−1.14331	−0.571655	−	0.820494i	$-0.693698\pi$
$79$	−10.1620	−1.14331	−0.571655	+	0.820494i	$0.693698\pi$
$80$	−14.1165	−1.57828
$81$	29.1331	3.23701
$82$	−1.58851	−0.175422
$83$	−7.06074	−0.775017	−0.387509	−	0.921866i	$-0.626664\pi$
$83$	−7.06074	−0.775017	−0.387509	+	0.921866i	$0.626664\pi$
$84$	0	0
$85$	6.16215	0.668378
$86$	0.259358	0.0279673
$87$	6.38702	0.684760
$88$	0.664479	0.0708337
$89$	−11.7770	−1.24836	−0.624180	−	0.781280i	$-0.714567\pi$
$89$	−11.7770	−1.24836	−0.624180	+	0.781280i	$0.714567\pi$
$90$	−5.36114	−0.565114
$91$	0	0
$92$	0.489036	0.0509855
$93$	17.9317	1.85944
$94$	−0.402409	−0.0415053
$95$	13.9259	1.42876
$96$	7.09888	0.724526
$97$	0.860838	0.0874048	0.0437024	−	0.999045i	$-0.486085\pi$
$97$	0.860838	0.0874048	0.0437024	+	0.999045i	$0.486085\pi$
$98$	0	0
$99$	−7.16470	−0.720080
$100$	−17.3218	−1.73218
$101$	7.72970	0.769134	0.384567	−	0.923097i	$-0.374351\pi$
$101$	7.72970	0.769134	0.384567	+	0.923097i	$0.374351\pi$
$102$	−1.00343	−0.0993545
$103$	−1.97534	−0.194636	−0.0973179	−	0.995253i	$-0.531026\pi$
$103$	−1.97534	−0.194636	−0.0973179	+	0.995253i	$0.531026\pi$
$104$	−0.931469	−0.0913381
$105$	0	0
$106$	−1.91921	−0.186410
$107$	−0.319598	−0.0308967	−0.0154484	−	0.999881i	$-0.504918\pi$
$107$	−0.319598	−0.0308967	−0.0154484	+	0.999881i	$0.504918\pi$
$108$	−31.4501	−3.02628
$109$	12.6271	1.20945	0.604727	−	0.796433i	$-0.293282\pi$
$109$	12.6271	1.20945	0.604727	+	0.796433i	$0.293282\pi$
$110$	0.622570	0.0593597
$111$	−14.5468	−1.38072
$112$	0	0
$113$	−13.1810	−1.23997	−0.619984	−	0.784615i	$-0.712861\pi$
$113$	−13.1810	−1.23997	−0.619984	+	0.784615i	$0.712861\pi$
$114$	−2.26766	−0.212386
$115$	0.924246	0.0861864
$116$	−3.81180	−0.353917
$117$	10.0435	0.928523
$118$	0.158373	0.0145794
$119$	0	0
$120$	8.91899	0.814189
$121$	−10.1680	−0.924363
$122$	0.455930	0.0412780
$123$	−28.4948	−2.56929
$124$	−10.7017	−0.961045
$125$	−14.1566	−1.26620
$126$	0	0
$127$	0.830524	0.0736971	0.0368485	−	0.999321i	$-0.488268\pi$
$127$	0.830524	0.0736971	0.0368485	+	0.999321i	$0.488268\pi$
$128$	−5.63206	−0.497808
$129$	4.65238	0.409619
$130$	−0.872722	−0.0765428
$131$	−9.31948	−0.814247	−0.407124	−	0.913373i	$-0.633468\pi$
$131$	−9.31948	−0.814247	−0.407124	+	0.913373i	$0.633468\pi$
$132$	5.90904	0.514316
$133$	0	0
$134$	−2.46916	−0.213303
$135$	−59.4385	−5.11566
$136$	1.20798	0.103583
$137$	4.27610	0.365332	0.182666	−	0.983175i	$-0.441527\pi$
$137$	4.27610	0.365332	0.182666	+	0.983175i	$0.441527\pi$
$138$	−0.150502	−0.0128116
$139$	−11.8522	−1.00529	−0.502645	−	0.864493i	$-0.667640\pi$
$139$	−11.8522	−1.00529	−0.502645	+	0.864493i	$0.667640\pi$
$140$	0	0
$141$	−7.21843	−0.607902
$142$	1.61341	0.135394
$143$	−1.16632	−0.0975323
$144$	29.8382	2.48652
$145$	−7.20405	−0.598264
$146$	2.63678	0.218221
$147$	0	0
$148$	8.68158	0.713621
$149$	−21.2817	−1.74347	−0.871734	−	0.489979i	$-0.837004\pi$
$149$	−21.2817	−1.74347	−0.871734	+	0.489979i	$0.837004\pi$
$150$	5.33085	0.435262
$151$	1.00000	0.0813788
$151$	1.00000	0.0813788
$152$	2.72992	0.221425
$153$	−13.0250	−1.05301
$154$	0	0
$155$	−20.2256	−1.62456
$156$	−8.28332	−0.663197
$157$	15.8157	1.26223	0.631115	−	0.775689i	$-0.282597\pi$
$157$	15.8157	1.26223	0.631115	+	0.775689i	$0.282597\pi$
$158$	−1.86643	−0.148485
$159$	−34.4269	−2.73023
$160$	−8.00698	−0.633007
$161$	0	0
$162$	5.35084	0.420401
$163$	−13.1212	−1.02773	−0.513866	−	0.857871i	$-0.671787\pi$
$163$	−13.1212	−1.02773	−0.513866	+	0.857871i	$0.671787\pi$
$164$	17.0058	1.32793
$165$	11.1677	0.869405
$166$	−1.29684	−0.100654
$167$	−20.1890	−1.56227	−0.781134	−	0.624363i	$-0.785359\pi$
$167$	−20.1890	−1.56227	−0.781134	+	0.624363i	$0.785359\pi$
$168$	0	0
$169$	−11.3651	−0.874235
$170$	1.13179	0.0868045
$171$	−29.4352	−2.25096
$172$	−2.77656	−0.211711
$173$	−0.672028	−0.0510933	−0.0255467	−	0.999674i	$-0.508133\pi$
$173$	−0.672028	−0.0510933	−0.0255467	+	0.999674i	$0.508133\pi$
$174$	1.17309	0.0889320
$175$	0	0
$176$	−3.46500	−0.261184
$177$	2.84091	0.213536
$178$	−2.16307	−0.162129
$179$	−2.07329	−0.154965	−0.0774823	−	0.996994i	$-0.524688\pi$
$179$	−2.07329	−0.154965	−0.0774823	+	0.996994i	$0.524688\pi$
$180$	57.3938	4.27788
$181$	−2.78471	−0.206985	−0.103493	−	0.994630i	$-0.533002\pi$
$181$	−2.78471	−0.206985	−0.103493	+	0.994630i	$0.533002\pi$
$182$	0	0
$183$	8.17850	0.604572
$184$	0.181182	0.0133569
$185$	16.4076	1.20631
$186$	3.29350	0.241491
$187$	1.51254	0.110608
$188$	4.30799	0.314193
$189$	0	0
$190$	2.55774	0.185558
$191$	12.6722	0.916930	0.458465	−	0.888712i	$-0.348399\pi$
$191$	12.6722	0.916930	0.458465	+	0.888712i	$0.348399\pi$
$192$	−23.7272	−1.71236
$193$	−6.20943	−0.446964	−0.223482	−	0.974708i	$-0.571742\pi$
$193$	−6.20943	−0.446964	−0.223482	+	0.974708i	$0.571742\pi$
$194$	0.158109	0.0113515
$195$	−15.6549	−1.12107
$196$	0	0
$197$	−14.8505	−1.05805	−0.529027	−	0.848605i	$-0.677443\pi$
$197$	−14.8505	−1.05805	−0.529027	+	0.848605i	$0.677443\pi$
$198$	−1.31593	−0.0935191
$199$	−15.0571	−1.06737	−0.533685	−	0.845683i	$-0.679193\pi$
$199$	−15.0571	−1.06737	−0.533685	+	0.845683i	$0.679193\pi$
$200$	−6.41753	−0.453788
$201$	−44.2919	−3.12411
$202$	1.41970	0.0998899
$203$	0	0
$204$	10.7423	0.752108
$205$	32.1399	2.24475
$206$	−0.362807	−0.0252780
$207$	−1.95358	−0.135783
$208$	4.85725	0.336790
$209$	3.41820	0.236442
$210$	0	0
$211$	−14.1331	−0.972961	−0.486481	−	0.873691i	$-0.661720\pi$
$211$	−14.1331	−0.972961	−0.486481	+	0.873691i	$0.661720\pi$
$212$	20.5461	1.41111
$213$	28.9415	1.98304
$214$	−0.0587001	−0.00401266
$215$	−5.24751	−0.357878
$216$	−11.6519	−0.792809
$217$	0	0
$218$	2.31919	0.157076
$219$	47.2987	3.19615
$220$	−6.66493	−0.449350
$221$	−2.12029	−0.142626
$222$	−2.67178	−0.179318
$223$	9.31277	0.623629	0.311815	−	0.950143i	$-0.399063\pi$
$223$	9.31277	0.623629	0.311815	+	0.950143i	$0.399063\pi$
$224$	0	0
$225$	69.1967	4.61311
$226$	−2.42094	−0.161039
$227$	−0.485548	−0.0322270	−0.0161135	−	0.999870i	$-0.505129\pi$
$227$	−0.485548	−0.0322270	−0.0161135	+	0.999870i	$0.505129\pi$
$228$	24.2765	1.60775
$229$	−15.3956	−1.01737	−0.508685	−	0.860953i	$-0.669868\pi$
$229$	−15.3956	−1.01737	−0.508685	+	0.860953i	$0.669868\pi$
$230$	0.169755	0.0111933
$231$	0	0
$232$	−1.41223	−0.0927172
$233$	−20.5505	−1.34631	−0.673154	−	0.739502i	$-0.735061\pi$
$233$	−20.5505	−1.34631	−0.673154	+	0.739502i	$0.735061\pi$
$234$	1.84468	0.120590
$235$	8.14182	0.531114
$236$	−1.69546	−0.110365
$237$	−33.4802	−2.17477
$238$	0	0
$239$	−2.85049	−0.184383	−0.0921915	−	0.995741i	$-0.529387\pi$
$239$	−2.85049	−0.184383	−0.0921915	+	0.995741i	$0.529387\pi$
$240$	−46.5091	−3.00215
$241$	−11.0331	−0.710707	−0.355354	−	0.934732i	$-0.615640\pi$
$241$	−11.0331	−0.710707	−0.355354	+	0.934732i	$0.615640\pi$
$242$	−1.86754	−0.120050
$243$	47.9992	3.07915
$244$	−4.88097	−0.312472
$245$	0	0
$246$	−5.23360	−0.333682
$247$	−4.79165	−0.304885
$248$	−3.96487	−0.251769
$249$	−23.2627	−1.47422
$250$	−2.60011	−0.164446
$251$	14.4565	0.912486	0.456243	−	0.889855i	$-0.349195\pi$
$251$	14.4565	0.912486	0.456243	+	0.889855i	$0.349195\pi$
$252$	0	0
$253$	0.226863	0.0142627
$254$	0.152541	0.00957127
$255$	20.3022	1.27137
$256$	13.3690	0.835563
$257$	−28.0657	−1.75069	−0.875345	−	0.483500i	$-0.839365\pi$
$257$	−28.0657	−1.75069	−0.875345	+	0.483500i	$0.839365\pi$
$258$	0.854495	0.0531985
$259$	0	0
$260$	9.34294	0.579424
$261$	15.2272	0.942543
$262$	−1.71170	−0.105749
$263$	−10.9878	−0.677537	−0.338768	−	0.940870i	$-0.610010\pi$
$263$	−10.9878	−0.677537	−0.338768	+	0.940870i	$0.610010\pi$
$264$	2.18923	0.134738
$265$	38.8308	2.38536
$266$	0	0
$267$	−38.8012	−2.37460
$268$	26.4336	1.61469
$269$	14.6293	0.891965	0.445983	−	0.895042i	$-0.352854\pi$
$269$	14.6293	0.891965	0.445983	+	0.895042i	$0.352854\pi$
$270$	−10.9170	−0.664387
$271$	31.9043	1.93805	0.969025	−	0.246964i	$-0.0794330\pi$
$271$	31.9043	1.93805	0.969025	+	0.246964i	$0.0794330\pi$
$272$	−6.29915	−0.381942
$273$	0	0
$274$	0.785384	0.0474468
$275$	−8.03556	−0.484562
$276$	1.61121	0.0969832
$277$	14.7225	0.884588	0.442294	−	0.896870i	$-0.354165\pi$
$277$	14.7225	0.884588	0.442294	+	0.896870i	$0.354165\pi$
$278$	−2.17687	−0.130560
$279$	42.7510	2.55943
$280$	0	0
$281$	27.3492	1.63152	0.815758	−	0.578394i	$-0.196320\pi$
$281$	27.3492	1.63152	0.815758	+	0.578394i	$0.196320\pi$
$282$	−1.32580	−0.0789502
$283$	−26.2831	−1.56237	−0.781183	−	0.624302i	$-0.785384\pi$
$283$	−26.2831	−1.56237	−0.781183	+	0.624302i	$0.785384\pi$
$284$	−17.2724	−1.02493
$285$	45.8809	2.71775
$286$	−0.214216	−0.0126668
$287$	0	0
$288$	16.9244	0.997279
$289$	−14.2503	−0.838253
$290$	−1.32316	−0.0776985
$291$	2.83617	0.166259
$292$	−28.2280	−1.65192
$293$	−16.2252	−0.947884	−0.473942	−	0.880556i	$-0.657169\pi$
$293$	−16.2252	−0.947884	−0.473942	+	0.880556i	$0.657169\pi$
$294$	0	0
$295$	−3.20432	−0.186563
$296$	3.21642	0.186951
$297$	−14.5896	−0.846575
$298$	−3.90879	−0.226430
$299$	−0.318017	−0.0183914
$300$	−57.0695	−3.29491
$301$	0	0
$302$	0.183668	0.0105689
$303$	25.4667	1.46302
$304$	−14.2355	−0.816460
$305$	−9.22471	−0.528205
$306$	−2.39227	−0.136757
$307$	−0.0943867	−0.00538693	−0.00269347	−	0.999996i	$-0.500857\pi$
$307$	−0.0943867	−0.00538693	−0.00269347	+	0.999996i	$0.500857\pi$
$308$	0	0
$309$	−6.50806	−0.370231
$310$	−3.71480	−0.210987
$311$	13.8783	0.786968	0.393484	−	0.919332i	$-0.371270\pi$
$311$	13.8783	0.786968	0.393484	+	0.919332i	$0.371270\pi$
$312$	−3.06887	−0.173741
$313$	13.4879	0.762379	0.381190	−	0.924497i	$-0.375514\pi$
$313$	13.4879	0.762379	0.381190	+	0.924497i	$0.375514\pi$
$314$	2.90485	0.163930
$315$	0	0
$316$	19.9811	1.12403
$317$	−2.90664	−0.163253	−0.0816267	−	0.996663i	$-0.526012\pi$
$317$	−2.90664	−0.163253	−0.0816267	+	0.996663i	$0.526012\pi$
$318$	−6.32313	−0.354583
$319$	−1.76829	−0.0990050
$320$	26.7624	1.49607
$321$	−1.05297	−0.0587709
$322$	0	0
$323$	6.21406	0.345760
$324$	−57.2835	−3.18241
$325$	11.2643	0.624830
$326$	−2.40995	−0.133475
$327$	41.6019	2.30059
$328$	6.30046	0.347885
$329$	0	0
$330$	2.05116	0.112912
$331$	−11.1032	−0.610288	−0.305144	−	0.952306i	$-0.598705\pi$
$331$	−11.1032	−0.610288	−0.305144	+	0.952306i	$0.598705\pi$
$332$	13.8833	0.761945
$333$	−34.6809	−1.90050
$334$	−3.70808	−0.202897
$335$	49.9578	2.72948
$336$	0	0
$337$	−0.880266	−0.0479512	−0.0239756	−	0.999713i	$-0.507632\pi$
$337$	−0.880266	−0.0479512	−0.0239756	+	0.999713i	$0.507632\pi$
$338$	−2.08740	−0.113540
$339$	−43.4270	−2.35863
$340$	−12.1164	−0.657105
$341$	−4.96452	−0.268844
$342$	−5.40631	−0.292340
$343$	0	0
$344$	−1.02868	−0.0554628
$345$	3.04507	0.163941
$346$	−0.123430	−0.00663565
$347$	34.5128	1.85275	0.926373	−	0.376608i	$-0.122910\pi$
$347$	34.5128	1.85275	0.926373	+	0.376608i	$0.122910\pi$
$348$	−12.5586	−0.673210
$349$	28.8423	1.54389	0.771947	−	0.635687i	$-0.219283\pi$
$349$	28.8423	1.54389	0.771947	+	0.635687i	$0.219283\pi$
$350$	0	0
$351$	20.4518	1.09164
$352$	−1.96537	−0.104755
$353$	−23.9585	−1.27518	−0.637591	−	0.770375i	$-0.720069\pi$
$353$	−23.9585	−1.27518	−0.637591	+	0.770375i	$0.720069\pi$
$354$	0.521785	0.0277326
$355$	−32.6437	−1.73255
$356$	23.1567	1.22730
$357$	0	0
$358$	−0.380797	−0.0201258
$359$	−1.51542	−0.0799807	−0.0399904	−	0.999200i	$-0.512733\pi$
$359$	−1.51542	−0.0799807	−0.0399904	+	0.999200i	$0.512733\pi$
$360$	21.2637	1.12070
$361$	−4.95681	−0.260885
$362$	−0.511463	−0.0268819
$363$	−33.5000	−1.75830
$364$	0	0
$365$	−53.3492	−2.79242
$366$	1.50213	0.0785178
$367$	7.67846	0.400812	0.200406	−	0.979713i	$-0.435774\pi$
$367$	7.67846	0.400812	0.200406	+	0.979713i	$0.435774\pi$
$368$	−0.944794	−0.0492508
$369$	−67.9343	−3.53652
$370$	3.01356	0.156668
$371$	0	0
$372$	−35.2586	−1.82807
$373$	23.5390	1.21880	0.609402	−	0.792861i	$-0.291409\pi$
$373$	23.5390	1.21880	0.609402	+	0.792861i	$0.291409\pi$
$374$	0.277806	0.0143650
$375$	−46.6410	−2.40853
$376$	1.59606	0.0823105
$377$	2.47879	0.127664
$378$	0	0
$379$	−23.0030	−1.18159	−0.590793	−	0.806823i	$-0.701185\pi$
$379$	−23.0030	−1.18159	−0.590793	+	0.806823i	$0.701185\pi$
$380$	−27.3819	−1.40466
$381$	2.73629	0.140184
$382$	2.32749	0.119085
$383$	−20.8953	−1.06770	−0.533851	−	0.845579i	$-0.679256\pi$
$383$	−20.8953	−1.06770	−0.533851	+	0.845579i	$0.679256\pi$
$384$	−18.5557	−0.946917
$385$	0	0
$386$	−1.14048	−0.0580487
$387$	11.0917	0.563823
$388$	−1.69264	−0.0859306
$389$	15.5215	0.786971	0.393486	−	0.919331i	$-0.371269\pi$
$389$	15.5215	0.786971	0.393486	+	0.919331i	$0.371269\pi$
$390$	−2.87532	−0.145597
$391$	0.412422	0.0208571
$392$	0	0
$393$	−30.7045	−1.54884
$394$	−2.72757	−0.137413
$395$	37.7630	1.90006
$396$	14.0877	0.707934
$397$	32.1277	1.61244	0.806222	−	0.591614i	$-0.201509\pi$
$397$	32.1277	1.61244	0.806222	+	0.591614i	$0.201509\pi$
$398$	−2.76552	−0.138623
$399$	0	0
$400$	33.4650	1.67325
$401$	1.10536	0.0551989	0.0275994	−	0.999619i	$-0.491214\pi$
$401$	1.10536	0.0551989	0.0275994	+	0.999619i	$0.491214\pi$
$402$	−8.13502	−0.405738
$403$	6.95928	0.346667
$404$	−15.1986	−0.756161
$405$	−108.262	−5.37958
$406$	0	0
$407$	4.02736	0.199629
$408$	3.97988	0.197033
$409$	−30.4605	−1.50617	−0.753086	−	0.657922i	$-0.771436\pi$
$409$	−30.4605	−1.50617	−0.753086	+	0.657922i	$0.771436\pi$
$410$	5.90309	0.291533
$411$	14.0883	0.694924
$412$	3.88404	0.191353
$413$	0	0
$414$	−0.358812	−0.0176346
$415$	26.2385	1.28800
$416$	2.75506	0.135078
$417$	−39.0489	−1.91223
$418$	0.627816	0.0307075
$419$	−12.4139	−0.606459	−0.303230	−	0.952917i	$-0.598065\pi$
$419$	−12.4139	−0.606459	−0.303230	+	0.952917i	$0.598065\pi$
$420$	0	0
$421$	14.3449	0.699126	0.349563	−	0.936913i	$-0.386330\pi$
$421$	14.3449	0.699126	0.349563	+	0.936913i	$0.386330\pi$
$422$	−2.59580	−0.126362
$423$	−17.2094	−0.836750
$424$	7.61208	0.369675
$425$	−14.6081	−0.708598
$426$	5.31564	0.257543
$427$	0	0
$428$	0.628415	0.0303756
$429$	−3.84262	−0.185523
$430$	−0.963803	−0.0464787
$431$	−40.0541	−1.92934	−0.964668	−	0.263468i	$-0.915134\pi$
$431$	−40.0541	−1.92934	−0.964668	+	0.263468i	$0.915134\pi$
$432$	60.7600	2.92332
$433$	−30.1463	−1.44874	−0.724369	−	0.689412i	$-0.757869\pi$
$433$	−30.1463	−1.44874	−0.724369	+	0.689412i	$0.757869\pi$
$434$	0	0
$435$	−23.7349	−1.13800
$436$	−24.8282	−1.18905
$437$	0.932033	0.0445852
$438$	8.68727	0.415094
$439$	−18.4456	−0.880359	−0.440179	−	0.897910i	$-0.645085\pi$
$439$	−18.4456	−0.880359	−0.440179	+	0.897910i	$0.645085\pi$
$440$	−2.46928	−0.117718
$441$	0	0
$442$	−0.389430	−0.0185233
$443$	4.84442	0.230165	0.115083	−	0.993356i	$-0.463287\pi$
$443$	4.84442	0.230165	0.115083	+	0.993356i	$0.463287\pi$
$444$	28.6028	1.35743
$445$	43.7647	2.07465
$446$	1.71046	0.0809928
$447$	−70.1161	−3.31638
$448$	0	0
$449$	−21.8751	−1.03235	−0.516174	−	0.856484i	$-0.672644\pi$
$449$	−21.8751	−1.03235	−0.516174	+	0.856484i	$0.672644\pi$
$450$	12.7092	0.599119
$451$	7.88897	0.371477
$452$	25.9174	1.21905
$453$	3.29466	0.154797
$454$	−0.0891800	−0.00418542
$455$	0	0
$456$	8.99414	0.421189
$457$	0.383056	0.0179186	0.00895930	−	0.999960i	$-0.497148\pi$
$457$	0.383056	0.0179186	0.00895930	+	0.999960i	$0.497148\pi$
$458$	−2.82768	−0.132129
$459$	−26.5230	−1.23799
$460$	−1.81731	−0.0847327
$461$	−34.9368	−1.62717	−0.813585	−	0.581447i	$-0.802487\pi$
$461$	−34.9368	−1.62717	−0.813585	+	0.581447i	$0.802487\pi$
$462$	0	0
$463$	13.6404	0.633925	0.316963	−	0.948438i	$-0.397337\pi$
$463$	13.6404	0.633925	0.316963	+	0.948438i	$0.397337\pi$
$464$	7.36422	0.341875
$465$	−66.6364	−3.09019
$466$	−3.77448	−0.174849
$467$	30.3922	1.40638	0.703192	−	0.711000i	$-0.251757\pi$
$467$	30.3922	1.40638	0.703192	+	0.711000i	$0.251757\pi$
$468$	−19.7482	−0.912862
$469$	0	0
$470$	1.49540	0.0689775
$471$	52.1073	2.40098
$472$	−0.628149	−0.0289129
$473$	−1.28804	−0.0592241
$474$	−6.14925	−0.282444
$475$	−33.0130	−1.51474
$476$	0	0
$477$	−82.0768	−3.75804
$478$	−0.523545	−0.0239464
$479$	23.2203	1.06096	0.530482	−	0.847696i	$-0.322011\pi$
$479$	23.2203	1.06096	0.530482	+	0.847696i	$0.322011\pi$
$480$	−26.3802	−1.20409
$481$	−5.64558	−0.257416
$482$	−2.02644	−0.0923019
$483$	0	0
$484$	19.9930	0.908771
$485$	−3.19897	−0.145258
$486$	8.81594	0.399899
$487$	23.9343	1.08457	0.542284	−	0.840195i	$-0.317560\pi$
$487$	23.9343	1.08457	0.542284	+	0.840195i	$0.317560\pi$
$488$	−1.80834	−0.0818597
$489$	−43.2298	−1.95492
$490$	0	0
$491$	14.5262	0.655557	0.327778	−	0.944755i	$-0.393700\pi$
$491$	14.5262	0.655557	0.327778	+	0.944755i	$0.393700\pi$
$492$	56.0284	2.52596
$493$	−3.21463	−0.144780
$494$	−0.880075	−0.0395964
$495$	26.6249	1.19670
$496$	20.6753	0.928347
$497$	0	0
$498$	−4.27263	−0.191461
$499$	19.6649	0.880322	0.440161	−	0.897919i	$-0.354921\pi$
$499$	19.6649	0.880322	0.440161	+	0.897919i	$0.354921\pi$
$500$	27.8356	1.24484
$501$	−66.5157	−2.97170
$502$	2.65520	0.118508
$503$	−7.56135	−0.337144	−0.168572	−	0.985689i	$-0.553916\pi$
$503$	−7.56135	−0.337144	−0.168572	+	0.985689i	$0.553916\pi$
$504$	0	0
$505$	−28.7244	−1.27822
$506$	0.0416675	0.00185235
$507$	−37.4440	−1.66294
$508$	−1.63303	−0.0724540
$509$	4.07748	0.180731	0.0903656	−	0.995909i	$-0.471196\pi$
$509$	4.07748	0.180731	0.0903656	+	0.995909i	$0.471196\pi$
$510$	3.72887	0.165117
$511$	0	0
$512$	13.7196	0.606326
$513$	−59.9393	−2.64639
$514$	−5.15478	−0.227368
$515$	7.34058	0.323465
$516$	−9.14781	−0.402710
$517$	1.99847	0.0878925
$518$	0	0
$519$	−2.21410	−0.0971883
$520$	3.46145	0.151794
$521$	33.7144	1.47706	0.738528	−	0.674223i	$-0.235521\pi$
$521$	33.7144	1.47706	0.738528	+	0.674223i	$0.235521\pi$
$522$	2.79677	0.122411
$523$	36.7350	1.60631	0.803154	−	0.595772i	$-0.203154\pi$
$523$	36.7350	1.60631	0.803154	+	0.595772i	$0.203154\pi$
$524$	18.3246	0.800513
$525$	0	0
$526$	−2.01811	−0.0879939
$527$	−9.02517	−0.393142
$528$	−11.4160	−0.496817
$529$	−22.9381	−0.997311
$530$	7.13199	0.309794
$531$	6.77298	0.293922
$532$	0	0
$533$	−11.0588	−0.479010
$534$	−7.12656	−0.308396
$535$	1.18766	0.0513472
$536$	9.79333	0.423007
$537$	−6.83077	−0.294769
$538$	2.68694	0.115842
$539$	0	0
$540$	116.872	5.02937
$541$	17.3851	0.747442	0.373721	−	0.927541i	$-0.378082\pi$
$541$	17.3851	0.747442	0.373721	+	0.927541i	$0.378082\pi$
$542$	5.85982	0.251701
$543$	−9.17465	−0.393722
$544$	−3.57291	−0.153187
$545$	−46.9236	−2.00999
$546$	0	0
$547$	27.2857	1.16665	0.583326	−	0.812238i	$-0.301751\pi$
$547$	27.2857	1.16665	0.583326	+	0.812238i	$0.301751\pi$
$548$	−8.40795	−0.359170
$549$	19.4983	0.832168
$550$	−1.47588	−0.0629317
$551$	−7.26475	−0.309489
$552$	0.596933	0.0254071
$553$	0	0
$554$	2.70406	0.114884
$555$	54.0575	2.29461
$556$	23.3045	0.988333
$557$	22.0118	0.932669	0.466335	−	0.884608i	$-0.345574\pi$
$557$	22.0118	0.932669	0.466335	+	0.884608i	$0.345574\pi$
$558$	7.85200	0.332402
$559$	1.80558	0.0763679
$560$	0	0
$561$	4.98331	0.210395
$562$	5.02318	0.211890
$563$	34.7867	1.46609	0.733043	−	0.680183i	$-0.238100\pi$
$563$	34.7867	1.46609	0.733043	+	0.680183i	$0.238100\pi$
$564$	14.1934	0.597648
$565$	48.9822	2.06070
$566$	−4.82737	−0.202910
$567$	0	0
$568$	−6.39922	−0.268505
$569$	4.70112	0.197081	0.0985407	−	0.995133i	$-0.468583\pi$
$569$	4.70112	0.197081	0.0985407	+	0.995133i	$0.468583\pi$
$570$	8.42688	0.352963
$571$	−10.1822	−0.426112	−0.213056	−	0.977040i	$-0.568342\pi$
$571$	−10.1822	−0.426112	−0.213056	+	0.977040i	$0.568342\pi$
$572$	2.29329	0.0958873
$573$	41.7506	1.74416
$574$	0	0
$575$	−2.19104	−0.0913726
$576$	−56.5679	−2.35700
$577$	−20.5479	−0.855422	−0.427711	−	0.903916i	$-0.640680\pi$
$577$	−20.5479	−0.855422	−0.427711	+	0.903916i	$0.640680\pi$
$578$	−2.61733	−0.108867
$579$	−20.4579	−0.850203
$580$	14.1651	0.588173
$581$	0	0
$582$	0.520914	0.0215926
$583$	9.53129	0.394746
$584$	−10.4582	−0.432761
$585$	−37.3228	−1.54311
$586$	−2.98005	−0.123105
$587$	−8.40929	−0.347088	−0.173544	−	0.984826i	$-0.555522\pi$
$587$	−8.40929	−0.347088	−0.173544	+	0.984826i	$0.555522\pi$
$588$	0	0
$589$	−20.3960	−0.840403
$590$	−0.588532	−0.0242295
$591$	−48.9273	−2.01260
$592$	−16.7724	−0.689341
$593$	7.48556	0.307395	0.153697	−	0.988118i	$-0.450882\pi$
$593$	7.48556	0.307395	0.153697	+	0.988118i	$0.450882\pi$
$594$	−2.67965	−0.109947
$595$	0	0
$596$	41.8456	1.71406
$597$	−49.6080	−2.03032
$598$	−0.0584097	−0.00238855
$599$	4.69324	0.191760	0.0958802	−	0.995393i	$-0.469433\pi$
$599$	4.69324	0.191760	0.0958802	+	0.995393i	$0.469433\pi$
$600$	−21.1436	−0.863183
$601$	1.89605	0.0773416	0.0386708	−	0.999252i	$-0.487688\pi$
$601$	1.89605	0.0773416	0.0386708	+	0.999252i	$0.487688\pi$
$602$	0	0
$603$	−105.596	−4.30020
$604$	−1.96627	−0.0800062
$605$	37.7854	1.53620
$606$	4.67743	0.190008
$607$	19.6483	0.797501	0.398751	−	0.917059i	$-0.369444\pi$
$607$	19.6483	0.797501	0.398751	+	0.917059i	$0.369444\pi$
$608$	−8.07444	−0.327462
$609$	0	0
$610$	−1.69429	−0.0685997
$611$	−2.80146	−0.113335
$612$	25.6105	1.03524
$613$	−17.3399	−0.700352	−0.350176	−	0.936684i	$-0.613878\pi$
$613$	−17.3399	−0.700352	−0.350176	+	0.936684i	$0.613878\pi$
$614$	−0.0173359	−0.000699619 0
$615$	105.890	4.26990
$616$	0	0
$617$	6.60055	0.265728	0.132864	−	0.991134i	$-0.457583\pi$
$617$	6.60055	0.265728	0.132864	+	0.991134i	$0.457583\pi$
$618$	−1.19533	−0.0480830
$619$	6.67297	0.268209	0.134105	−	0.990967i	$-0.457184\pi$
$619$	6.67297	0.268209	0.134105	+	0.990967i	$0.457184\pi$
$620$	39.7689	1.59716
$621$	−3.97812	−0.159636
$622$	2.54901	0.102206
$623$	0	0
$624$	16.0030	0.640632
$625$	8.55986	0.342394
$626$	2.47730	0.0990127
$627$	11.2618	0.449753
$628$	−31.0979	−1.24094
$629$	7.32149	0.291927
$630$	0	0
$631$	16.7963	0.668651	0.334325	−	0.942458i	$-0.391492\pi$
$631$	16.7963	0.668651	0.334325	+	0.942458i	$0.391492\pi$
$632$	7.40276	0.294466
$633$	−46.5637	−1.85074
$634$	−0.533859	−0.0212022
$635$	−3.08632	−0.122477
$636$	67.6924	2.68418
$637$	0	0
$638$	−0.324778	−0.0128581
$639$	68.9992	2.72956
$640$	20.9294	0.827306
$641$	20.5409	0.811316	0.405658	−	0.914025i	$-0.367042\pi$
$641$	20.5409	0.811316	0.405658	+	0.914025i	$0.367042\pi$
$642$	−0.193397	−0.00763277
$643$	−1.06457	−0.0419825	−0.0209913	−	0.999780i	$-0.506682\pi$
$643$	−1.06457	−0.0419825	−0.0209913	+	0.999780i	$0.506682\pi$
$644$	0	0
$645$	−17.2888	−0.680745
$646$	1.14133	0.0449049
$647$	−29.6687	−1.16640	−0.583198	−	0.812330i	$-0.698199\pi$
$647$	−29.6687	−1.16640	−0.583198	+	0.812330i	$0.698199\pi$
$648$	−21.2228	−0.833712
$649$	−0.786522	−0.0308737
$650$	2.06889	0.0811487
$651$	0	0
$652$	25.7998	1.01040
$653$	−20.1399	−0.788137	−0.394069	−	0.919081i	$-0.628933\pi$
$653$	−20.1399	−0.788137	−0.394069	+	0.919081i	$0.628933\pi$
$654$	7.64095	0.298785
$655$	34.6323	1.35319
$656$	−32.8545	−1.28275
$657$	112.764	4.39936
$658$	0	0
$659$	36.5416	1.42346	0.711730	−	0.702453i	$-0.247912\pi$
$659$	36.5416	1.42346	0.711730	+	0.702453i	$0.247912\pi$
$660$	−21.9587	−0.854740
$661$	−22.1043	−0.859758	−0.429879	−	0.902886i	$-0.641444\pi$
$661$	−22.1043	−0.859758	−0.429879	+	0.902886i	$0.641444\pi$
$662$	−2.03931	−0.0792600
$663$	−6.98563	−0.271299
$664$	5.14360	0.199610
$665$	0	0
$666$	−6.36978	−0.246824
$667$	−0.482155	−0.0186691
$668$	39.6969	1.53592
$669$	30.6824	1.18625
$670$	9.17567	0.354487
$671$	−2.26427	−0.0874111
$672$	0	0
$673$	30.5471	1.17750	0.588751	−	0.808314i	$-0.299620\pi$
$673$	30.5471	1.17750	0.588751	+	0.808314i	$0.299620\pi$
$674$	−0.161677	−0.00622757
$675$	140.906	5.42349
$676$	22.3467	0.859489
$677$	−24.5063	−0.941854	−0.470927	−	0.882172i	$-0.656080\pi$
$677$	−24.5063	−0.941854	−0.470927	+	0.882172i	$0.656080\pi$
$678$	−7.97617	−0.306323
$679$	0	0
$680$	−4.48899	−0.172145
$681$	−1.59972	−0.0613013
$682$	−0.911825	−0.0349156
$683$	−36.8637	−1.41055	−0.705275	−	0.708933i	$-0.749177\pi$
$683$	−36.8637	−1.41055	−0.705275	+	0.708933i	$0.749177\pi$
$684$	57.8774	2.21300
$685$	−15.8905	−0.607144
$686$	0	0
$687$	−50.7232	−1.93521
$688$	5.36418	0.204507
$689$	−13.3610	−0.509014
$690$	0.559284	0.0212916
$691$	12.4203	0.472492	0.236246	−	0.971693i	$-0.424083\pi$
$691$	12.4203	0.472492	0.236246	+	0.971693i	$0.424083\pi$
$692$	1.32139	0.0502315
$693$	0	0
$694$	6.33892	0.240622
$695$	44.0441	1.67069
$696$	−4.65280	−0.176364
$697$	14.3416	0.543228
$698$	5.29743	0.200511
$699$	−67.7069	−2.56091
$700$	0	0
$701$	28.1266	1.06233	0.531164	−	0.847269i	$-0.321755\pi$
$701$	28.1266	1.06233	0.531164	+	0.847269i	$0.321755\pi$
$702$	3.75635	0.141774
$703$	16.5459	0.624039
$704$	6.56903	0.247579
$705$	26.8245	1.01027
$706$	−4.40042	−0.165612
$707$	0	0
$708$	−5.58598	−0.209934
$709$	1.43051	0.0537241	0.0268620	−	0.999639i	$-0.491449\pi$
$709$	1.43051	0.0537241	0.0268620	+	0.999639i	$0.491449\pi$
$710$	−5.99562	−0.225012
$711$	−79.8198	−2.99348
$712$	8.57929	0.321523
$713$	−1.35366	−0.0506951
$714$	0	0
$715$	4.33417	0.162089
$716$	4.07663	0.152351
$717$	−9.39139	−0.350728
$718$	−0.278335	−0.0103874
$719$	−16.8995	−0.630244	−0.315122	−	0.949051i	$-0.602045\pi$
$719$	−16.8995	−0.630244	−0.315122	+	0.949051i	$0.602045\pi$
$720$	−110.882	−4.13233
$721$	0	0
$722$	−0.910409	−0.0338819
$723$	−36.3504	−1.35189
$724$	5.47547	0.203494
$725$	17.0781	0.634265
$726$	−6.15290	−0.228356
$727$	−26.9422	−0.999233	−0.499616	−	0.866247i	$-0.666526\pi$
$727$	−26.9422	−0.999233	−0.499616	+	0.866247i	$0.666526\pi$
$728$	0	0
$729$	70.7417	2.62006
$730$	−9.79856	−0.362661
$731$	−2.34157	−0.0866062
$732$	−16.0811	−0.594375
$733$	9.89979	0.365657	0.182829	−	0.983145i	$-0.441475\pi$
$733$	9.89979	0.365657	0.182829	+	0.983145i	$0.441475\pi$
$734$	1.41029	0.0520548
$735$	0	0
$736$	−0.535893	−0.0197533
$737$	12.2625	0.451694
$738$	−12.4774	−0.459299
$739$	36.7085	1.35034	0.675171	−	0.737661i	$-0.264070\pi$
$739$	36.7085	1.35034	0.675171	+	0.737661i	$0.264070\pi$
$740$	−32.2617	−1.18596
$741$	−15.7868	−0.579944
$742$	0	0
$743$	−40.2612	−1.47704	−0.738521	−	0.674231i	$-0.764475\pi$
$743$	−40.2612	−1.47704	−0.738521	+	0.674231i	$0.764475\pi$
$744$	−13.0629	−0.478909
$745$	79.0854	2.89746
$746$	4.32338	0.158290
$747$	−55.4605	−2.02919
$748$	−2.97406	−0.108742
$749$	0	0
$750$	−8.56648	−0.312804
$751$	20.0555	0.731836	0.365918	−	0.930647i	$-0.380755\pi$
$751$	20.0555	0.731836	0.365918	+	0.930647i	$0.380755\pi$
$752$	−8.32284	−0.303503
$753$	47.6292	1.73571
$754$	0.455276	0.0165802
$755$	−3.71611	−0.135243
$756$	0	0
$757$	38.8419	1.41173	0.705867	−	0.708345i	$-0.250558\pi$
$757$	38.8419	1.41173	0.705867	+	0.708345i	$0.250558\pi$
$758$	−4.22493	−0.153456
$759$	0.747435	0.0271302
$760$	−10.1447	−0.367986
$761$	−9.26836	−0.335978	−0.167989	−	0.985789i	$-0.553727\pi$
$761$	−9.26836	−0.335978	−0.167989	+	0.985789i	$0.553727\pi$
$762$	0.502570	0.0182062
$763$	0	0
$764$	−24.9170	−0.901464
$765$	48.4022	1.74999
$766$	−3.83781	−0.138666
$767$	1.10255	0.0398108
$768$	44.0463	1.58939
$769$	8.24686	0.297389	0.148695	−	0.988883i	$-0.452493\pi$
$769$	8.24686	0.297389	0.148695	+	0.988883i	$0.452493\pi$
$770$	0	0
$771$	−92.4668	−3.33011
$772$	12.2094	0.439425
$773$	17.9148	0.644352	0.322176	−	0.946680i	$-0.395586\pi$
$773$	17.9148	0.644352	0.322176	+	0.946680i	$0.395586\pi$
$774$	2.03720	0.0732255
$775$	47.9473	1.72232
$776$	−0.627102	−0.0225116
$777$	0	0
$778$	2.85081	0.102206
$779$	32.4107	1.16123
$780$	30.7818	1.10216
$781$	−8.01263	−0.286714
$782$	0.0757488	0.00270877
$783$	31.0075	1.10812
$784$	0	0
$785$	−58.7730	−2.09770
$786$	−5.63945	−0.201153
$787$	−37.4489	−1.33491	−0.667454	−	0.744651i	$-0.732616\pi$
$787$	−37.4489	−1.33491	−0.667454	+	0.744651i	$0.732616\pi$
$788$	29.2000	1.04021
$789$	−36.2010	−1.28879
$790$	6.93587	0.246767
$791$	0	0
$792$	5.21933	0.185461
$793$	3.17406	0.112714
$794$	5.90085	0.209413
$795$	127.934	4.53736
$796$	29.6063	1.04937
$797$	6.56429	0.232519	0.116259	−	0.993219i	$-0.462910\pi$
$797$	6.56429	0.232519	0.116259	+	0.993219i	$0.462910\pi$
$798$	0	0
$799$	3.63308	0.128529
$800$	18.9815	0.671098
$801$	−92.5057	−3.26853
$802$	0.203019	0.00716886
$803$	−13.0949	−0.462110
$804$	87.0896	3.07141
$805$	0	0
$806$	1.27820	0.0450227
$807$	48.1986	1.69667
$808$	−5.63091	−0.198095
$809$	12.8394	0.451409	0.225704	−	0.974196i	$-0.427532\pi$
$809$	12.8394	0.451409	0.225704	+	0.974196i	$0.427532\pi$
$810$	−19.8843	−0.698664
$811$	1.31098	0.0460347	0.0230174	−	0.999735i	$-0.492673\pi$
$811$	1.31098	0.0460347	0.0230174	+	0.999735i	$0.492673\pi$
$812$	0	0
$813$	105.114	3.68650
$814$	0.739700	0.0259265
$815$	48.7598	1.70798
$816$	−20.7535	−0.726519
$817$	−5.29173	−0.185134
$818$	−5.59463	−0.195612
$819$	0	0
$820$	−63.1956	−2.20689
$821$	−46.1086	−1.60920	−0.804600	−	0.593817i	$-0.797620\pi$
$821$	−46.1086	−1.60920	−0.804600	+	0.593817i	$0.797620\pi$
$822$	2.58757	0.0902520
$823$	6.36527	0.221879	0.110940	−	0.993827i	$-0.464614\pi$
$823$	6.36527	0.221879	0.110940	+	0.993827i	$0.464614\pi$
$824$	1.43899	0.0501296
$825$	−26.4744	−0.921721
$826$	0	0
$827$	18.4051	0.640009	0.320004	−	0.947416i	$-0.396316\pi$
$827$	18.4051	0.640009	0.320004	+	0.947416i	$0.396316\pi$
$828$	3.84127	0.133493
$829$	−0.214845	−0.00746186	−0.00373093	−	0.999993i	$-0.501188\pi$
$829$	−0.214845	−0.00746186	−0.00373093	+	0.999993i	$0.501188\pi$
$830$	4.81919	0.167277
$831$	48.5055	1.68264
$832$	−9.20849	−0.319247
$833$	0	0
$834$	−7.17205	−0.248348
$835$	75.0245	2.59633
$836$	−6.72109	−0.232454
$837$	87.0545	3.00905
$838$	−2.28004	−0.0787628
$839$	−8.66817	−0.299259	−0.149629	−	0.988742i	$-0.547808\pi$
$839$	−8.66817	−0.299259	−0.149629	+	0.988742i	$0.547808\pi$
$840$	0	0
$841$	−25.2418	−0.870408
$842$	2.63470	0.0907977
$843$	90.1062	3.10342
$844$	27.7894	0.956550
$845$	42.2338	1.45289
$846$	−3.16083	−0.108671
$847$	0	0
$848$	−39.6941	−1.36310
$849$	−86.5938	−2.97189
$850$	−2.68305	−0.0920279
$851$	1.09813	0.0376435
$852$	−56.9066	−1.94959
$853$	22.5241	0.771211	0.385605	−	0.922664i	$-0.373993\pi$
$853$	22.5241	0.771211	0.385605	+	0.922664i	$0.373993\pi$
$854$	0	0
$855$	109.384	3.74087
$856$	0.232820	0.00795764
$857$	45.0950	1.54041	0.770207	−	0.637794i	$-0.220153\pi$
$857$	45.0950	1.54041	0.770207	+	0.637794i	$0.220153\pi$
$858$	−0.705768	−0.0240945
$859$	21.0436	0.718000	0.359000	−	0.933338i	$-0.383118\pi$
$859$	21.0436	0.718000	0.359000	+	0.933338i	$0.383118\pi$
$860$	10.3180	0.351841
$861$	0	0
$862$	−7.35667	−0.250569
$863$	−2.01110	−0.0684587	−0.0342293	−	0.999414i	$-0.510898\pi$
$863$	−2.01110	−0.0684587	−0.0342293	+	0.999414i	$0.510898\pi$
$864$	34.4634	1.17247
$865$	2.49733	0.0849118
$866$	−5.53693	−0.188152
$867$	−46.9499	−1.59450
$868$	0	0
$869$	9.26919	0.314436
$870$	−4.35935	−0.147796
$871$	−17.1896	−0.582448
$872$	−9.19854	−0.311502
$873$	6.76168	0.228848
$874$	0.171185	0.00579042
$875$	0	0
$876$	−93.0018	−3.14224
$877$	0.542916	0.0183330	0.00916648	−	0.999958i	$-0.497082\pi$
$877$	0.542916	0.0183330	0.00916648	+	0.999958i	$0.497082\pi$
$878$	−3.38787	−0.114335
$879$	−53.4563	−1.80304
$880$	12.8763	0.434061
$881$	8.69333	0.292886	0.146443	−	0.989219i	$-0.453218\pi$
$881$	8.69333	0.292886	0.146443	+	0.989219i	$0.453218\pi$
$882$	0	0
$883$	35.6778	1.20065	0.600327	−	0.799755i	$-0.295037\pi$
$883$	35.6778	1.20065	0.600327	+	0.799755i	$0.295037\pi$
$884$	4.16905	0.140220
$885$	−10.5571	−0.354874
$886$	0.889767	0.0298923
$887$	−13.8237	−0.464154	−0.232077	−	0.972697i	$-0.574552\pi$
$887$	−13.8237	−0.464154	−0.232077	+	0.972697i	$0.574552\pi$
$888$	10.5970	0.355612
$889$	0	0
$890$	8.03820	0.269441
$891$	−26.5737	−0.890251
$892$	−18.3114	−0.613111
$893$	8.21042	0.274751
$894$	−12.8781	−0.430708
$895$	7.70457	0.257535
$896$	0	0
$897$	−1.04776	−0.0349836
$898$	−4.01776	−0.134074
$899$	10.5512	0.351901
$900$	−136.059	−4.53530
$901$	17.3273	0.577255
$902$	1.44896	0.0482449
$903$	0	0
$904$	9.60209	0.319361
$905$	10.3483	0.343989
$906$	0.605125	0.0201039
$907$	3.22925	0.107225	0.0536127	−	0.998562i	$-0.482926\pi$
$907$	3.22925	0.107225	0.0536127	+	0.998562i	$0.482926\pi$
$908$	0.954717	0.0316834
$909$	60.7150	2.01379
$910$	0	0
$911$	−36.7510	−1.21761	−0.608807	−	0.793318i	$-0.708352\pi$
$911$	−36.7510	−1.21761	−0.608807	+	0.793318i	$0.708352\pi$
$912$	−46.9010	−1.55305
$913$	6.44043	0.213147
$914$	0.0703553	0.00232715
$915$	−30.3923	−1.00474
$916$	30.2718	1.00021
$917$	0	0
$918$	−4.87143	−0.160781
$919$	−50.3548	−1.66105	−0.830526	−	0.556980i	$-0.811960\pi$
$919$	−50.3548	−1.66105	−0.830526	+	0.556980i	$0.811960\pi$
$920$	−0.673293	−0.0221978
$921$	−0.310972	−0.0102469
$922$	−6.41679	−0.211326
$923$	11.2321	0.369710
$924$	0	0
$925$	−38.8963	−1.27890
$926$	2.50532	0.0823299
$927$	−15.5158	−0.509606
$928$	4.17703	0.137118
$929$	−49.9006	−1.63719	−0.818593	−	0.574374i	$-0.805245\pi$
$929$	−49.9006	−1.63719	−0.818593	+	0.574374i	$0.805245\pi$
$930$	−12.2390	−0.401333
$931$	0	0
$932$	40.4078	1.32360
$933$	45.7243	1.49695
$934$	5.58209	0.182652
$935$	−5.62078	−0.183819
$936$	−7.31648	−0.239147
$937$	39.6375	1.29490	0.647451	−	0.762107i	$-0.275835\pi$
$937$	39.6375	1.29490	0.647451	+	0.762107i	$0.275835\pi$
$938$	0	0
$939$	44.4379	1.45018
$940$	−16.0090	−0.522156
$941$	−25.3577	−0.826637	−0.413318	−	0.910587i	$-0.635630\pi$
$941$	−25.3577	−0.826637	−0.413318	+	0.910587i	$0.635630\pi$
$942$	9.57048	0.311823
$943$	2.15107	0.0700484
$944$	3.27556	0.106610
$945$	0	0
$946$	−0.236572	−0.00769163
$947$	5.89253	0.191481	0.0957407	−	0.995406i	$-0.469478\pi$
$947$	5.89253	0.191481	0.0957407	+	0.995406i	$0.469478\pi$
$948$	65.8309	2.13809
$949$	18.3565	0.595878
$950$	−6.06344	−0.196724
$951$	−9.57639	−0.310536
$952$	0	0
$953$	10.0351	0.325070	0.162535	−	0.986703i	$-0.448033\pi$
$953$	10.0351	0.325070	0.162535	+	0.986703i	$0.448033\pi$
$954$	−15.0749	−0.488069
$955$	−47.0914	−1.52384
$956$	5.60482	0.181273
$957$	−5.82590	−0.188325
$958$	4.26484	0.137791
$959$	0	0
$960$	88.1730	2.84577
$961$	−1.37730	−0.0444291
$962$	−1.03691	−0.0334315
$963$	−2.51037	−0.0808956
$964$	21.6941	0.698720
$965$	23.0749	0.742809
$966$	0	0
$967$	−45.6262	−1.46724	−0.733620	−	0.679560i	$-0.762171\pi$
$967$	−45.6262	−1.46724	−0.733620	+	0.679560i	$0.762171\pi$
$968$	7.40716	0.238075
$969$	20.4732	0.657695
$970$	−0.587550	−0.0188651
$971$	−50.0563	−1.60638	−0.803191	−	0.595721i	$-0.796866\pi$
$971$	−50.0563	−1.60638	−0.803191	+	0.595721i	$0.796866\pi$
$972$	−94.3792	−3.02722
$973$	0	0
$974$	4.39598	0.140856
$975$	37.1120	1.18853
$976$	9.42980	0.301840
$977$	16.8418	0.538817	0.269409	−	0.963026i	$-0.413172\pi$
$977$	16.8418	0.538817	0.269409	+	0.963026i	$0.413172\pi$
$978$	−7.93996	−0.253892
$979$	10.7424	0.343327
$980$	0	0
$981$	99.1827	3.16666
$982$	2.66800	0.0851393
$983$	54.2760	1.73114	0.865568	−	0.500792i	$-0.166958\pi$
$983$	54.2760	1.73114	0.865568	+	0.500792i	$0.166958\pi$
$984$	20.7579	0.661736
$985$	55.1862	1.75838
$986$	−0.590426	−0.0188030
$987$	0	0
$988$	9.42166	0.299743
$989$	−0.351207	−0.0111677
$990$	4.89015	0.155419
$991$	−5.73279	−0.182108	−0.0910540	−	0.995846i	$-0.529024\pi$
$991$	−5.73279	−0.182108	−0.0910540	+	0.995846i	$0.529024\pi$
$992$	11.7271	0.372337
$993$	−36.5813	−1.16087
$994$	0	0
$995$	55.9539	1.77386
$996$	45.7407	1.44935
$997$	−19.9095	−0.630541	−0.315270	−	0.949002i	$-0.602095\pi$
$997$	−19.9095	−0.630541	−0.315270	+	0.949002i	$0.602095\pi$
$998$	3.61182	0.114330
$999$	−70.6213	−2.23436

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7399.2.a.e.1.4		6
7.6	odd	2		151.2.a.c.1.4	✓	6
21.20	even	2		1359.2.a.i.1.3		6
28.27	even	2		2416.2.a.o.1.6		6
35.34	odd	2		3775.2.a.p.1.3		6
56.13	odd	2		9664.2.a.bh.1.6		6
56.27	even	2		9664.2.a.bc.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
151.2.a.c.1.4	✓	6	7.6	odd	2
1359.2.a.i.1.3		6	21.20	even	2
2416.2.a.o.1.6		6	28.27	even	2
3775.2.a.p.1.3		6	35.34	odd	2
7399.2.a.e.1.4		6	1.1	even	1	trivial
9664.2.a.bc.1.1		6	56.27	even	2
9664.2.a.bh.1.6		6	56.13	odd	2

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:	\( N \)	\(=\)	\( 7399 = 7^{2} \cdot 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7399.a (trivial)

\(f(q)\)	\(=\)	\(q+0.183668 q^{2} +3.29466 q^{3} -1.96627 q^{4} -3.71611 q^{5} +0.605125 q^{6} -0.728478 q^{8} +7.85477 q^{9} +O(q^{10})\)	\(q+0.183668 q^{2} +3.29466 q^{3} -1.96627 q^{4} -3.71611 q^{5} +0.605125 q^{6} -0.728478 q^{8} +7.85477 q^{9} -0.682533 q^{10} -0.912147 q^{11} -6.47817 q^{12} +1.27865 q^{13} -12.2433 q^{15} +3.79873 q^{16} -1.65822 q^{17} +1.44267 q^{18} -3.74742 q^{19} +7.30687 q^{20} -0.167533 q^{22} -0.248713 q^{23} -2.40009 q^{24} +8.80951 q^{25} +0.234848 q^{26} +15.9948 q^{27} +1.93860 q^{29} -2.24871 q^{30} +5.44267 q^{31} +2.15466 q^{32} -3.00521 q^{33} -0.304563 q^{34} -15.4446 q^{36} -4.41526 q^{37} -0.688284 q^{38} +4.21272 q^{39} +2.70711 q^{40} -8.64880 q^{41} +1.41210 q^{43} +1.79352 q^{44} -29.1892 q^{45} -0.0456807 q^{46} -2.19095 q^{47} +12.5155 q^{48} +1.61803 q^{50} -5.46328 q^{51} -2.51417 q^{52} -10.4493 q^{53} +2.93774 q^{54} +3.38964 q^{55} -12.3465 q^{57} +0.356059 q^{58} +0.862276 q^{59} +24.0736 q^{60} +2.48235 q^{61} +0.999648 q^{62} -7.20172 q^{64} -4.75161 q^{65} -0.551962 q^{66} -13.4435 q^{67} +3.26051 q^{68} -0.819424 q^{69} +8.78436 q^{71} -5.72203 q^{72} +14.3562 q^{73} -0.810944 q^{74} +29.0243 q^{75} +7.36843 q^{76} +0.773744 q^{78} -10.1620 q^{79} -14.1165 q^{80} +29.1331 q^{81} -1.58851 q^{82} -7.06074 q^{83} +6.16215 q^{85} +0.259358 q^{86} +6.38702 q^{87} +0.664479 q^{88} -11.7770 q^{89} -5.36114 q^{90} +0.489036 q^{92} +17.9317 q^{93} -0.402409 q^{94} +13.9259 q^{95} +7.09888 q^{96} +0.860838 q^{97} -7.16470 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} + 5 q^{3} + 3 q^{4} - 6 q^{5} + 2 q^{6} + 9 q^{8} + 15 q^{9}+O(q^{10}) \) 6 * q + q^2 + 5 * q^3 + 3 * q^4 - 6 * q^5 + 2 * q^6 + 9 * q^8 + 15 * q^9	\( 6 q + q^{2} + 5 q^{3} + 3 q^{4} - 6 q^{5} + 2 q^{6} + 9 q^{8} + 15 q^{9} - 8 q^{10} + 8 q^{11} + 11 q^{12} + q^{13} - 18 q^{15} - 3 q^{16} - 9 q^{17} - 16 q^{18} + 6 q^{19} - 3 q^{20} - 12 q^{22} - 4 q^{23} - q^{24} - 4 q^{25} + 7 q^{26} + 2 q^{27} - 2 q^{29} - 16 q^{30} + 8 q^{31} - 11 q^{32} - 3 q^{33} + 9 q^{34} - 25 q^{36} - 12 q^{37} + 3 q^{38} - 22 q^{39} - 9 q^{40} - 41 q^{41} + q^{43} - 12 q^{45} - 17 q^{46} - 28 q^{47} - 9 q^{48} + 15 q^{50} - 31 q^{51} - 15 q^{52} + 14 q^{53} - 27 q^{54} - q^{55} - 28 q^{57} + q^{58} - 12 q^{59} + 17 q^{60} - 5 q^{61} + 9 q^{62} - 27 q^{64} + 13 q^{65} - 8 q^{66} - 15 q^{67} - 11 q^{68} - 33 q^{69} - 2 q^{71} + q^{72} + 7 q^{73} + 53 q^{74} + 32 q^{75} + 3 q^{76} + 16 q^{78} - 9 q^{79} - 16 q^{80} + 66 q^{81} - 10 q^{82} + 11 q^{83} - 10 q^{85} - 26 q^{86} + 26 q^{87} + 24 q^{88} - 36 q^{89} - 19 q^{90} - 38 q^{92} - q^{93} - 42 q^{94} + 32 q^{95} + 34 q^{96} - 11 q^{97} + 17 q^{99}+O(q^{100}) \) 6 * q + q^2 + 5 * q^3 + 3 * q^4 - 6 * q^5 + 2 * q^6 + 9 * q^8 + 15 * q^9 - 8 * q^10 + 8 * q^11 + 11 * q^12 + q^13 - 18 * q^15 - 3 * q^16 - 9 * q^17 - 16 * q^18 + 6 * q^19 - 3 * q^20 - 12 * q^22 - 4 * q^23 - q^24 - 4 * q^25 + 7 * q^26 + 2 * q^27 - 2 * q^29 - 16 * q^30 + 8 * q^31 - 11 * q^32 - 3 * q^33 + 9 * q^34 - 25 * q^36 - 12 * q^37 + 3 * q^38 - 22 * q^39 - 9 * q^40 - 41 * q^41 + q^43 - 12 * q^45 - 17 * q^46 - 28 * q^47 - 9 * q^48 + 15 * q^50 - 31 * q^51 - 15 * q^52 + 14 * q^53 - 27 * q^54 - q^55 - 28 * q^57 + q^58 - 12 * q^59 + 17 * q^60 - 5 * q^61 + 9 * q^62 - 27 * q^64 + 13 * q^65 - 8 * q^66 - 15 * q^67 - 11 * q^68 - 33 * q^69 - 2 * q^71 + q^72 + 7 * q^73 + 53 * q^74 + 32 * q^75 + 3 * q^76 + 16 * q^78 - 9 * q^79 - 16 * q^80 + 66 * q^81 - 10 * q^82 + 11 * q^83 - 10 * q^85 - 26 * q^86 + 26 * q^87 + 24 * q^88 - 36 * q^89 - 19 * q^90 - 38 * q^92 - q^93 - 42 * q^94 + 32 * q^95 + 34 * q^96 - 11 * q^97 + 17 * q^99

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