LMFDB - Embedded newform 2541.2.a.bm.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2541,2,Mod(1,2541)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2541, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2541.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2541 = 3 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2541.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:	$20.2899871536$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.725.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 3x^{2} + x + 1 $ x^4 - x^3 - 3*x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 231)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.477260$ of defining polynomial
Character	$\chi$	$=$	2541.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.77222 q^{2} -1.00000 q^{3} +1.14077 q^{4} +0.589926 q^{5} +1.77222 q^{6} +1.00000 q^{7} +1.52274 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.77222 q^{2} -1.00000 q^{3} +1.14077 q^{4} +0.589926 q^{5} +1.77222 q^{6} +1.00000 q^{7} +1.52274 q^{8} +1.00000 q^{9} -1.04548 q^{10} -1.14077 q^{12} +1.54445 q^{13} -1.77222 q^{14} -0.589926 q^{15} -4.98018 q^{16} -7.14511 q^{17} -1.77222 q^{18} +6.19059 q^{19} +0.672972 q^{20} -1.00000 q^{21} +3.76314 q^{23} -1.52274 q^{24} -4.65199 q^{25} -2.73710 q^{26} -1.00000 q^{27} +1.14077 q^{28} -0.607298 q^{29} +1.04548 q^{30} -6.87147 q^{31} +5.78051 q^{32} +12.6627 q^{34} +0.589926 q^{35} +1.14077 q^{36} -7.70693 q^{37} -10.9711 q^{38} -1.54445 q^{39} +0.898304 q^{40} -7.48287 q^{41} +1.77222 q^{42} +10.9537 q^{43} +0.589926 q^{45} -6.66913 q^{46} -10.2072 q^{47} +4.98018 q^{48} +1.00000 q^{49} +8.24436 q^{50} +7.14511 q^{51} +1.76186 q^{52} +7.04469 q^{53} +1.77222 q^{54} +1.52274 q^{56} -6.19059 q^{57} +1.07627 q^{58} -3.35386 q^{59} -0.672972 q^{60} +3.37044 q^{61} +12.1778 q^{62} +1.00000 q^{63} -0.283993 q^{64} +0.911108 q^{65} -2.19138 q^{67} -8.15095 q^{68} -3.76314 q^{69} -1.04548 q^{70} -13.9430 q^{71} +1.52274 q^{72} +2.58993 q^{73} +13.6584 q^{74} +4.65199 q^{75} +7.06206 q^{76} +2.73710 q^{78} +4.66351 q^{79} -2.93794 q^{80} +1.00000 q^{81} +13.2613 q^{82} +3.50970 q^{83} -1.14077 q^{84} -4.21508 q^{85} -19.4125 q^{86} +0.607298 q^{87} +8.15095 q^{89} -1.04548 q^{90} +1.54445 q^{91} +4.29289 q^{92} +6.87147 q^{93} +18.0894 q^{94} +3.65199 q^{95} -5.78051 q^{96} -4.79710 q^{97} -1.77222 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - 4 q^{3} + 3 q^{4} - 4 q^{5} + q^{6} + 4 q^{7} + 9 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - q^2 - 4 * q^3 + 3 * q^4 - 4 * q^5 + q^6 + 4 * q^7 + 9 * q^8 + 4 * q^9	$ 4 q - q^{2} - 4 q^{3} + 3 q^{4} - 4 q^{5} + q^{6} + 4 q^{7} + 9 q^{8} + 4 q^{9} - 10 q^{10} - 3 q^{12} - 6 q^{13} - q^{14} + 4 q^{15} - 3 q^{16} - 8 q^{17} - q^{18} + 10 q^{19} - 4 q^{21} - 10 q^{23} - 9 q^{24} + 12 q^{25} - 20 q^{26} - 4 q^{27} + 3 q^{28} + 10 q^{30} - 18 q^{31} + 2 q^{32} + 18 q^{34} - 4 q^{35} + 3 q^{36} - 2 q^{37} - 8 q^{38} + 6 q^{39} - 6 q^{40} - 10 q^{41} + q^{42} + 4 q^{43} - 4 q^{45} - 11 q^{46} + 4 q^{47} + 3 q^{48} + 4 q^{49} + 9 q^{50} + 8 q^{51} - 20 q^{52} + q^{54} + 9 q^{56} - 10 q^{57} + 14 q^{58} - 16 q^{59} - 14 q^{61} + 4 q^{63} - 11 q^{64} + 28 q^{65} - 28 q^{67} + 16 q^{68} + 10 q^{69} - 10 q^{70} - 18 q^{71} + 9 q^{72} + 4 q^{73} + 41 q^{74} - 12 q^{75} + 4 q^{76} + 20 q^{78} + 20 q^{79} - 36 q^{80} + 4 q^{81} - 24 q^{82} - 6 q^{83} - 3 q^{84} + 20 q^{85} - 20 q^{86} - 16 q^{89} - 10 q^{90} - 6 q^{91} - 22 q^{92} + 18 q^{93} + 16 q^{94} - 16 q^{95} - 2 q^{96} + 32 q^{97} - q^{98}+O(q^{100}) $ 4 * q - q^2 - 4 * q^3 + 3 * q^4 - 4 * q^5 + q^6 + 4 * q^7 + 9 * q^8 + 4 * q^9 - 10 * q^10 - 3 * q^12 - 6 * q^13 - q^14 + 4 * q^15 - 3 * q^16 - 8 * q^17 - q^18 + 10 * q^19 - 4 * q^21 - 10 * q^23 - 9 * q^24 + 12 * q^25 - 20 * q^26 - 4 * q^27 + 3 * q^28 + 10 * q^30 - 18 * q^31 + 2 * q^32 + 18 * q^34 - 4 * q^35 + 3 * q^36 - 2 * q^37 - 8 * q^38 + 6 * q^39 - 6 * q^40 - 10 * q^41 + q^42 + 4 * q^43 - 4 * q^45 - 11 * q^46 + 4 * q^47 + 3 * q^48 + 4 * q^49 + 9 * q^50 + 8 * q^51 - 20 * q^52 + q^54 + 9 * q^56 - 10 * q^57 + 14 * q^58 - 16 * q^59 - 14 * q^61 + 4 * q^63 - 11 * q^64 + 28 * q^65 - 28 * q^67 + 16 * q^68 + 10 * q^69 - 10 * q^70 - 18 * q^71 + 9 * q^72 + 4 * q^73 + 41 * q^74 - 12 * q^75 + 4 * q^76 + 20 * q^78 + 20 * q^79 - 36 * q^80 + 4 * q^81 - 24 * q^82 - 6 * q^83 - 3 * q^84 + 20 * q^85 - 20 * q^86 - 16 * q^89 - 10 * q^90 - 6 * q^91 - 22 * q^92 + 18 * q^93 + 16 * q^94 - 16 * q^95 - 2 * q^96 + 32 * q^97 - q^98

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 $

$2$	−1.77222	−1.25315	−0.626575	−	0.779361i	$-0.715544\pi$
$2$	−1.77222	−1.25315	−0.626575	+	0.779361i	$0.715544\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.14077	0.570387
$5$	0.589926	0.263823	0.131911	−	0.991262i	$-0.457889\pi$
$5$	0.589926	0.263823	0.131911	+	0.991262i	$0.457889\pi$
$6$	1.77222	0.723507
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.52274	0.538370
$9$	1.00000	0.333333
$10$	−1.04548	−0.330610
$11$	0	0
$11$	0	0
$12$	−1.14077	−0.329313
$13$	1.54445	0.428352	0.214176	−	0.976795i	$-0.431293\pi$
$13$	1.54445	0.428352	0.214176	+	0.976795i	$0.431293\pi$
$14$	−1.77222	−0.473646
$15$	−0.589926	−0.152318
$16$	−4.98018	−1.24505
$17$	−7.14511	−1.73294	−0.866472	−	0.499226i	$-0.833618\pi$
$17$	−7.14511	−1.73294	−0.866472	+	0.499226i	$0.833618\pi$
$18$	−1.77222	−0.417717
$19$	6.19059	1.42022	0.710109	−	0.704092i	$-0.248646\pi$
$19$	6.19059	1.42022	0.710109	+	0.704092i	$0.248646\pi$
$20$	0.672972	0.150481
$21$	−1.00000	−0.218218
$22$	0	0
$23$	3.76314	0.784669	0.392335	−	0.919823i	$-0.371668\pi$
$23$	3.76314	0.784669	0.392335	+	0.919823i	$0.371668\pi$
$24$	−1.52274	−0.310828
$25$	−4.65199	−0.930398
$26$	−2.73710	−0.536790
$27$	−1.00000	−0.192450
$28$	1.14077	0.215586
$29$	−0.607298	−0.112772	−0.0563862	−	0.998409i	$-0.517958\pi$
$29$	−0.607298	−0.112772	−0.0563862	+	0.998409i	$0.517958\pi$
$30$	1.04548	0.190878
$31$	−6.87147	−1.23415	−0.617077	−	0.786903i	$-0.711683\pi$
$31$	−6.87147	−1.23415	−0.617077	+	0.786903i	$0.711683\pi$
$32$	5.78051	1.02186
$33$	0	0
$34$	12.6627	2.17164
$35$	0.589926	0.0997157
$36$	1.14077	0.190129
$37$	−7.70693	−1.26701	−0.633505	−	0.773738i	$-0.718385\pi$
$37$	−7.70693	−1.26701	−0.633505	+	0.773738i	$0.718385\pi$
$38$	−10.9711	−1.77975
$39$	−1.54445	−0.247309
$40$	0.898304	0.142034
$41$	−7.48287	−1.16863	−0.584314	−	0.811528i	$-0.698636\pi$
$41$	−7.48287	−1.16863	−0.584314	+	0.811528i	$0.698636\pi$
$42$	1.77222	0.273460
$43$	10.9537	1.67043	0.835214	−	0.549925i	$-0.185344\pi$
$43$	10.9537	1.67043	0.835214	+	0.549925i	$0.185344\pi$
$44$	0	0
$45$	0.589926	0.0879409
$46$	−6.66913	−0.983309
$47$	−10.2072	−1.48887	−0.744434	−	0.667696i	$-0.767281\pi$
$47$	−10.2072	−1.48887	−0.744434	+	0.667696i	$0.767281\pi$
$48$	4.98018	0.718827
$49$	1.00000	0.142857
$50$	8.24436	1.16593
$51$	7.14511	1.00052
$52$	1.76186	0.244327
$53$	7.04469	0.967663	0.483831	−	0.875161i	$-0.339245\pi$
$53$	7.04469	0.967663	0.483831	+	0.875161i	$0.339245\pi$
$54$	1.77222	0.241169
$55$	0	0
$56$	1.52274	0.203485
$57$	−6.19059	−0.819963
$58$	1.07627	0.141321
$59$	−3.35386	−0.436635	−0.218318	−	0.975878i	$-0.570057\pi$
$59$	−3.35386	−0.436635	−0.218318	+	0.975878i	$0.570057\pi$
$60$	−0.672972	−0.0868803
$61$	3.37044	0.431541	0.215770	−	0.976444i	$-0.430774\pi$
$61$	3.37044	0.431541	0.215770	+	0.976444i	$0.430774\pi$
$62$	12.1778	1.54658
$63$	1.00000	0.125988
$64$	−0.283993	−0.0354992
$65$	0.911108	0.113009
$66$	0	0
$67$	−2.19138	−0.267719	−0.133860	−	0.991000i	$-0.542737\pi$
$67$	−2.19138	−0.267719	−0.133860	+	0.991000i	$0.542737\pi$
$68$	−8.15095	−0.988448
$69$	−3.76314	−0.453029
$70$	−1.04548	−0.124959
$71$	−13.9430	−1.65473	−0.827364	−	0.561665i	$-0.810161\pi$
$71$	−13.9430	−1.65473	−0.827364	+	0.561665i	$0.810161\pi$
$72$	1.52274	0.179457
$73$	2.58993	0.303128	0.151564	−	0.988447i	$-0.451569\pi$
$73$	2.58993	0.303128	0.151564	+	0.988447i	$0.451569\pi$
$74$	13.6584	1.58776
$75$	4.65199	0.537165
$76$	7.06206	0.810074
$77$	0	0
$78$	2.73710	0.309916
$79$	4.66351	0.524686	0.262343	−	0.964975i	$-0.415505\pi$
$79$	4.66351	0.524686	0.262343	+	0.964975i	$0.415505\pi$
$80$	−2.93794	−0.328471
$81$	1.00000	0.111111
$82$	13.2613	1.46447
$83$	3.50970	0.385240	0.192620	−	0.981273i	$-0.438302\pi$
$83$	3.50970	0.385240	0.192620	+	0.981273i	$0.438302\pi$
$84$	−1.14077	−0.124469
$85$	−4.21508	−0.457190
$86$	−19.4125	−2.09330
$87$	0.607298	0.0651091
$88$	0	0
$89$	8.15095	0.863999	0.432000	−	0.901874i	$-0.357808\pi$
$89$	8.15095	0.863999	0.432000	+	0.901874i	$0.357808\pi$
$90$	−1.04548	−0.110203
$91$	1.54445	0.161902
$92$	4.29289	0.447565
$93$	6.87147	0.712539
$94$	18.0894	1.86578
$95$	3.65199	0.374686
$96$	−5.78051	−0.589971
$97$	−4.79710	−0.487071	−0.243536	−	0.969892i	$-0.578307\pi$
$97$	−4.79710	−0.487071	−0.243536	+	0.969892i	$0.578307\pi$
$98$	−1.77222	−0.179022
$99$	0	0
$100$	−5.30687	−0.530687
$101$	1.42666	0.141958	0.0709788	−	0.997478i	$-0.477388\pi$
$101$	1.42666	0.141958	0.0709788	+	0.997478i	$0.477388\pi$
$102$	−12.6627	−1.25380
$103$	17.6172	1.73588	0.867939	−	0.496670i	$-0.165444\pi$
$103$	17.6172	1.73588	0.867939	+	0.496670i	$0.165444\pi$
$104$	2.35179	0.230612
$105$	−0.589926	−0.0575709
$106$	−12.4848	−1.21263
$107$	7.20005	0.696055	0.348027	−	0.937484i	$-0.386852\pi$
$107$	7.20005	0.696055	0.348027	+	0.937484i	$0.386852\pi$
$108$	−1.14077	−0.109771
$109$	8.88678	0.851199	0.425599	−	0.904912i	$-0.360063\pi$
$109$	8.88678	0.851199	0.425599	+	0.904912i	$0.360063\pi$
$110$	0	0
$111$	7.70693	0.731509
$112$	−4.98018	−0.470583
$113$	−7.80862	−0.734573	−0.367287	−	0.930108i	$-0.619713\pi$
$113$	−7.80862	−0.734573	−0.367287	+	0.930108i	$0.619713\pi$
$114$	10.9711	1.02754
$115$	2.21997	0.207014
$116$	−0.692789	−0.0643239
$117$	1.54445	0.142784
$118$	5.94378	0.547170
$119$	−7.14511	−0.654991
$120$	−0.898304	−0.0820035
$121$	0	0
$122$	−5.97317	−0.540785
$123$	7.48287	0.674708
$124$	−7.83880	−0.703945
$125$	−5.69396	−0.509283
$126$	−1.77222	−0.157882
$127$	−8.25186	−0.732234	−0.366117	−	0.930569i	$-0.619313\pi$
$127$	−8.25186	−0.732234	−0.366117	+	0.930569i	$0.619313\pi$
$128$	−11.0577	−0.977374
$129$	−10.9537	−0.964422
$130$	−1.61469	−0.141617
$131$	−12.1162	−1.05860	−0.529299	−	0.848435i	$-0.677545\pi$
$131$	−12.1162	−1.05860	−0.529299	+	0.848435i	$0.677545\pi$
$132$	0	0
$133$	6.19059	0.536792
$134$	3.88361	0.335493
$135$	−0.589926	−0.0507727
$136$	−10.8801	−0.932964
$137$	−17.4548	−1.49126	−0.745631	−	0.666360i	$-0.767852\pi$
$137$	−17.4548	−1.49126	−0.745631	+	0.666360i	$0.767852\pi$
$138$	6.66913	0.567714
$139$	−14.7624	−1.25213	−0.626063	−	0.779772i	$-0.715335\pi$
$139$	−14.7624	−1.25213	−0.626063	+	0.779772i	$0.715335\pi$
$140$	0.672972	0.0568765
$141$	10.2072	0.859599
$142$	24.7101	2.07362
$143$	0	0
$144$	−4.98018	−0.415015
$145$	−0.358261	−0.0297519
$146$	−4.58993	−0.379865
$147$	−1.00000	−0.0824786
$148$	−8.79186	−0.722686
$149$	−12.5258	−1.02615	−0.513077	−	0.858343i	$-0.671494\pi$
$149$	−12.5258	−1.02615	−0.513077	+	0.858343i	$0.671494\pi$
$150$	−8.24436	−0.673149
$151$	−0.328572	−0.0267388	−0.0133694	−	0.999911i	$-0.504256\pi$
$151$	−0.328572	−0.0267388	−0.0133694	+	0.999911i	$0.504256\pi$
$152$	9.42666	0.764603
$153$	−7.14511	−0.577648
$154$	0	0
$155$	−4.05366	−0.325598
$156$	−1.76186	−0.141062
$157$	−2.68089	−0.213958	−0.106979	−	0.994261i	$-0.534118\pi$
$157$	−2.68089	−0.213958	−0.106979	+	0.994261i	$0.534118\pi$
$158$	−8.26479	−0.657511
$159$	−7.04469	−0.558680
$160$	3.41007	0.269590
$161$	3.76314	0.296577
$162$	−1.77222	−0.139239
$163$	−0.891668	−0.0698408	−0.0349204	−	0.999390i	$-0.511118\pi$
$163$	−0.891668	−0.0698408	−0.0349204	+	0.999390i	$0.511118\pi$
$164$	−8.53627	−0.666570
$165$	0	0
$166$	−6.21997	−0.482764
$167$	−11.5610	−0.894619	−0.447310	−	0.894379i	$-0.647618\pi$
$167$	−11.5610	−0.894619	−0.447310	+	0.894379i	$0.647618\pi$
$168$	−1.52274	−0.117482
$169$	−10.6147	−0.816514
$170$	7.47007	0.572928
$171$	6.19059	0.473406
$172$	12.4957	0.952790
$173$	−8.98926	−0.683441	−0.341721	−	0.939802i	$-0.611010\pi$
$173$	−8.98926	−0.683441	−0.341721	+	0.939802i	$0.611010\pi$
$174$	−1.07627	−0.0815916
$175$	−4.65199	−0.351657
$176$	0	0
$177$	3.35386	0.252091
$178$	−14.4453	−1.08272
$179$	−6.14590	−0.459366	−0.229683	−	0.973265i	$-0.573769\pi$
$179$	−6.14590	−0.459366	−0.229683	+	0.973265i	$0.573769\pi$
$180$	0.672972	0.0501604
$181$	14.9662	1.11243	0.556215	−	0.831039i	$-0.312253\pi$
$181$	14.9662	1.11243	0.556215	+	0.831039i	$0.312253\pi$
$182$	−2.73710	−0.202888
$183$	−3.37044	−0.249150
$184$	5.73029	0.422442
$185$	−4.54651	−0.334266
$186$	−12.1778	−0.892918
$187$	0	0
$188$	−11.6441	−0.849231
$189$	−1.00000	−0.0727393
$190$	−6.47214	−0.469538
$191$	9.87351	0.714422	0.357211	−	0.934024i	$-0.383728\pi$
$191$	9.87351	0.714422	0.357211	+	0.934024i	$0.383728\pi$
$192$	0.283993	0.0204955
$193$	6.18113	0.444927	0.222464	−	0.974941i	$-0.428590\pi$
$193$	6.18113	0.444927	0.222464	+	0.974941i	$0.428590\pi$
$194$	8.50152	0.610374
$195$	−0.911108	−0.0652458
$196$	1.14077	0.0814839
$197$	19.0720	1.35882	0.679412	−	0.733757i	$-0.262235\pi$
$197$	19.0720	1.35882	0.679412	+	0.733757i	$0.262235\pi$
$198$	0	0
$199$	−11.8479	−0.839878	−0.419939	−	0.907552i	$-0.637948\pi$
$199$	−11.8479	−0.839878	−0.419939	+	0.907552i	$0.637948\pi$
$200$	−7.08377	−0.500898
$201$	2.19138	0.154568
$202$	−2.52835	−0.177894
$203$	−0.607298	−0.0426239
$204$	8.15095	0.570681
$205$	−4.41434	−0.308311
$206$	−31.2217	−2.17532
$207$	3.76314	0.261556
$208$	−7.69162	−0.533318
$209$	0	0
$210$	1.04548	0.0721450
$211$	20.9810	1.44439	0.722197	−	0.691687i	$-0.243132\pi$
$211$	20.9810	1.44439	0.722197	+	0.691687i	$0.243132\pi$
$212$	8.03640	0.551942
$213$	13.9430	0.955358
$214$	−12.7601	−0.872262
$215$	6.46189	0.440697
$216$	−1.52274	−0.103609
$217$	−6.87147	−0.466466
$218$	−15.7493	−1.06668
$219$	−2.58993	−0.175011
$220$	0	0
$221$	−11.0352	−0.742310
$222$	−13.6584	−0.916691
$223$	3.38860	0.226918	0.113459	−	0.993543i	$-0.463807\pi$
$223$	3.38860	0.226918	0.113459	+	0.993543i	$0.463807\pi$
$224$	5.78051	0.386227
$225$	−4.65199	−0.310133
$226$	13.8386	0.920531
$227$	−19.3973	−1.28744	−0.643721	−	0.765260i	$-0.722610\pi$
$227$	−19.3973	−1.28744	−0.643721	+	0.765260i	$0.722610\pi$
$228$	−7.06206	−0.467696
$229$	−9.86405	−0.651835	−0.325917	−	0.945398i	$-0.605673\pi$
$229$	−9.86405	−0.651835	−0.325917	+	0.945398i	$0.605673\pi$
$230$	−3.93429	−0.259419
$231$	0	0
$232$	−0.924756	−0.0607132
$233$	−7.12619	−0.466852	−0.233426	−	0.972375i	$-0.574994\pi$
$233$	−7.12619	−0.466852	−0.233426	+	0.972375i	$0.574994\pi$
$234$	−2.73710	−0.178930
$235$	−6.02147	−0.392798
$236$	−3.82599	−0.249051
$237$	−4.66351	−0.302928
$238$	12.6627	0.820802
$239$	−22.2894	−1.44178	−0.720892	−	0.693048i	$-0.756267\pi$
$239$	−22.2894	−1.44178	−0.720892	+	0.693048i	$0.756267\pi$
$240$	2.93794	0.189643
$241$	−14.8753	−0.958199	−0.479100	−	0.877761i	$-0.659037\pi$
$241$	−14.8753	−0.958199	−0.479100	+	0.877761i	$0.659037\pi$
$242$	0	0
$243$	−1.00000	−0.0641500
$244$	3.84491	0.246145
$245$	0.589926	0.0376890
$246$	−13.2613	−0.845511
$247$	9.56103	0.608354
$248$	−10.4635	−0.664431
$249$	−3.50970	−0.222418
$250$	10.0910	0.638208
$251$	−25.9233	−1.63626	−0.818132	−	0.575031i	$-0.804990\pi$
$251$	−25.9233	−1.63626	−0.818132	+	0.575031i	$0.804990\pi$
$252$	1.14077	0.0718620
$253$	0	0
$254$	14.6241	0.917600
$255$	4.21508	0.263959
$256$	20.1647	1.26030
$257$	0.871474	0.0543610	0.0271805	−	0.999631i	$-0.491347\pi$
$257$	0.871474	0.0543610	0.0271805	+	0.999631i	$0.491347\pi$
$258$	19.4125	1.20857
$259$	−7.70693	−0.478885
$260$	1.03937	0.0644589
$261$	−0.607298	−0.0375908
$262$	21.4726	1.32658
$263$	−26.8873	−1.65794	−0.828970	−	0.559293i	$-0.811073\pi$
$263$	−26.8873	−1.65794	−0.828970	+	0.559293i	$0.811073\pi$
$264$	0	0
$265$	4.15584	0.255291
$266$	−10.9711	−0.672681
$267$	−8.15095	−0.498830
$268$	−2.49987	−0.152704
$269$	−0.992574	−0.0605183	−0.0302592	−	0.999542i	$-0.509633\pi$
$269$	−0.992574	−0.0605183	−0.0302592	+	0.999542i	$0.509633\pi$
$270$	1.04548	0.0636259
$271$	−26.8650	−1.63193	−0.815966	−	0.578099i	$-0.803795\pi$
$271$	−26.8650	−1.63193	−0.815966	+	0.578099i	$0.803795\pi$
$272$	35.5839	2.15759
$273$	−1.54445	−0.0934741
$274$	30.9337	1.86878
$275$	0	0
$276$	−4.29289	−0.258402
$277$	27.6302	1.66014	0.830069	−	0.557660i	$-0.188301\pi$
$277$	27.6302	1.66014	0.830069	+	0.557660i	$0.188301\pi$
$278$	26.1622	1.56910
$279$	−6.87147	−0.411384
$280$	0.898304	0.0536839
$281$	−23.8418	−1.42228	−0.711141	−	0.703050i	$-0.751821\pi$
$281$	−23.8418	−1.42228	−0.711141	+	0.703050i	$0.751821\pi$
$282$	−18.0894	−1.07721
$283$	−8.74735	−0.519976	−0.259988	−	0.965612i	$-0.583719\pi$
$283$	−8.74735	−0.519976	−0.259988	+	0.965612i	$0.583719\pi$
$284$	−15.9058	−0.943836
$285$	−3.65199	−0.216325
$286$	0	0
$287$	−7.48287	−0.441700
$288$	5.78051	0.340620
$289$	34.0526	2.00309
$290$	0.634918	0.0372836
$291$	4.79710	0.281211
$292$	2.95452	0.172900
$293$	19.6252	1.14651	0.573257	−	0.819376i	$-0.305680\pi$
$293$	19.6252	1.14651	0.573257	+	0.819376i	$0.305680\pi$
$294$	1.77222	0.103358
$295$	−1.97853	−0.115194
$296$	−11.7356	−0.682120
$297$	0	0
$298$	22.1985	1.28592
$299$	5.81197	0.336115
$300$	5.30687	0.306392
$301$	10.9537	0.631362
$302$	0.582303	0.0335078
$303$	−1.42666	−0.0819592
$304$	−30.8303	−1.76824
$305$	1.98831	0.113850
$306$	12.6627	0.723880
$307$	17.0835	0.975009	0.487504	−	0.873121i	$-0.337907\pi$
$307$	17.0835	0.975009	0.487504	+	0.873121i	$0.337907\pi$
$308$	0	0
$309$	−17.6172	−1.00221
$310$	7.18399	0.408023
$311$	−7.23351	−0.410175	−0.205087	−	0.978744i	$-0.565748\pi$
$311$	−7.23351	−0.410175	−0.205087	+	0.978744i	$0.565748\pi$
$312$	−2.35179	−0.133144
$313$	13.7784	0.778804	0.389402	−	0.921068i	$-0.372682\pi$
$313$	13.7784	0.778804	0.389402	+	0.921068i	$0.372682\pi$
$314$	4.75113	0.268122
$315$	0.589926	0.0332386
$316$	5.32002	0.299274
$317$	−6.95629	−0.390704	−0.195352	−	0.980733i	$-0.562585\pi$
$317$	−6.95629	−0.390704	−0.195352	+	0.980733i	$0.562585\pi$
$318$	12.4848	0.700111
$319$	0	0
$320$	−0.167535	−0.00936550
$321$	−7.20005	−0.401867
$322$	−6.66913	−0.371656
$323$	−44.2324	−2.46116
$324$	1.14077	0.0633763
$325$	−7.18474	−0.398538
$326$	1.58023	0.0875211
$327$	−8.88678	−0.491440
$328$	−11.3945	−0.629154
$329$	−10.2072	−0.562739
$330$	0	0
$331$	−29.6698	−1.63080	−0.815401	−	0.578896i	$-0.803484\pi$
$331$	−29.6698	−1.63080	−0.815401	+	0.578896i	$0.803484\pi$
$332$	4.00378	0.219736
$333$	−7.70693	−0.422337
$334$	20.4887	1.12109
$335$	−1.29275	−0.0706305
$336$	4.98018	0.271691
$337$	−19.5714	−1.06612	−0.533062	−	0.846076i	$-0.678959\pi$
$337$	−19.5714	−1.06612	−0.533062	+	0.846076i	$0.678959\pi$
$338$	18.8116	1.02322
$339$	7.80862	0.424106
$340$	−4.80846	−0.260775
$341$	0	0
$342$	−10.9711	−0.593249
$343$	1.00000	0.0539949
$344$	16.6797	0.899308
$345$	−2.21997	−0.119519
$346$	15.9310	0.856455
$347$	6.49184	0.348500	0.174250	−	0.984701i	$-0.444250\pi$
$347$	6.49184	0.348500	0.174250	+	0.984701i	$0.444250\pi$
$348$	0.692789	0.0371374
$349$	−7.87965	−0.421788	−0.210894	−	0.977509i	$-0.567638\pi$
$349$	−7.87965	−0.421788	−0.210894	+	0.977509i	$0.567638\pi$
$350$	8.24436	0.440680
$351$	−1.54445	−0.0824364
$352$	0	0
$353$	−5.34594	−0.284536	−0.142268	−	0.989828i	$-0.545439\pi$
$353$	−5.34594	−0.284536	−0.142268	+	0.989828i	$0.545439\pi$
$354$	−5.94378	−0.315909
$355$	−8.22533	−0.436555
$356$	9.29840	0.492814
$357$	7.14511	0.378159
$358$	10.8919	0.575655
$359$	17.8515	0.942169	0.471084	−	0.882088i	$-0.343863\pi$
$359$	17.8515	0.942169	0.471084	+	0.882088i	$0.343863\pi$
$360$	0.898304	0.0473448
$361$	19.3234	1.01702
$362$	−26.5235	−1.39404
$363$	0	0
$364$	1.76186	0.0923467
$365$	1.52786	0.0799721
$366$	5.97317	0.312223
$367$	−29.9357	−1.56263	−0.781316	−	0.624135i	$-0.785451\pi$
$367$	−29.9357	−1.56263	−0.781316	+	0.624135i	$0.785451\pi$
$368$	−18.7411	−0.976949
$369$	−7.48287	−0.389543
$370$	8.05744	0.418886
$371$	7.04469	0.365742
$372$	7.83880	0.406423
$373$	−23.4915	−1.21635	−0.608173	−	0.793805i	$-0.708097\pi$
$373$	−23.4915	−1.21635	−0.608173	+	0.793805i	$0.708097\pi$
$374$	0	0
$375$	5.69396	0.294035
$376$	−15.5429	−0.801562
$377$	−0.937938	−0.0483063
$378$	1.77222	0.0911533
$379$	−31.4532	−1.61564	−0.807821	−	0.589428i	$-0.799353\pi$
$379$	−31.4532	−1.61564	−0.807821	+	0.589428i	$0.799353\pi$
$380$	4.16609	0.213716
$381$	8.25186	0.422756
$382$	−17.4981	−0.895278
$383$	−5.62749	−0.287551	−0.143776	−	0.989610i	$-0.545924\pi$
$383$	−5.62749	−0.287551	−0.143776	+	0.989610i	$0.545924\pi$
$384$	11.0577	0.564287
$385$	0	0
$386$	−10.9543	−0.557561
$387$	10.9537	0.556809
$388$	−5.47240	−0.277819
$389$	26.1072	1.32369	0.661845	−	0.749641i	$-0.269774\pi$
$389$	26.1072	1.32369	0.661845	+	0.749641i	$0.269774\pi$
$390$	1.61469	0.0817629
$391$	−26.8881	−1.35979
$392$	1.52274	0.0769100
$393$	12.1162	0.611182
$394$	−33.7998	−1.70281
$395$	2.75113	0.138424
$396$	0	0
$397$	10.3828	0.521096	0.260548	−	0.965461i	$-0.416097\pi$
$397$	10.3828	0.521096	0.260548	+	0.965461i	$0.416097\pi$
$398$	20.9972	1.05249
$399$	−6.19059	−0.309917
$400$	23.1677	1.15839
$401$	3.68876	0.184208	0.0921040	−	0.995749i	$-0.470641\pi$
$401$	3.68876	0.184208	0.0921040	+	0.995749i	$0.470641\pi$
$402$	−3.88361	−0.193697
$403$	−10.6126	−0.528652
$404$	1.62749	0.0809708
$405$	0.589926	0.0293136
$406$	1.07627	0.0534142
$407$	0	0
$408$	10.8801	0.538647
$409$	−1.08022	−0.0534136	−0.0267068	−	0.999643i	$-0.508502\pi$
$409$	−1.08022	−0.0534136	−0.0267068	+	0.999643i	$0.508502\pi$
$410$	7.82319	0.386360
$411$	17.4548	0.860980
$412$	20.0973	0.990123
$413$	−3.35386	−0.165033
$414$	−6.66913	−0.327770
$415$	2.07046	0.101635
$416$	8.92769	0.437716
$417$	14.7624	0.722915
$418$	0	0
$419$	10.0766	0.492273	0.246136	−	0.969235i	$-0.420839\pi$
$419$	10.0766	0.492273	0.246136	+	0.969235i	$0.420839\pi$
$420$	−0.672972	−0.0328377
$421$	11.9757	0.583658	0.291829	−	0.956470i	$-0.405736\pi$
$421$	11.9757	0.583658	0.291829	+	0.956470i	$0.405736\pi$
$422$	−37.1831	−1.81004
$423$	−10.2072	−0.496290
$424$	10.7272	0.520960
$425$	33.2390	1.61233
$426$	−24.7101	−1.19721
$427$	3.37044	0.163107
$428$	8.21363	0.397021
$429$	0	0
$430$	−11.4519	−0.552260
$431$	0.548547	0.0264226	0.0132113	−	0.999913i	$-0.495795\pi$
$431$	0.548547	0.0264226	0.0132113	+	0.999913i	$0.495795\pi$
$432$	4.98018	0.239609
$433$	19.5879	0.941332	0.470666	−	0.882311i	$-0.344014\pi$
$433$	19.5879	0.941332	0.470666	+	0.882311i	$0.344014\pi$
$434$	12.1778	0.584552
$435$	0.358261	0.0171773
$436$	10.1378	0.485513
$437$	23.2961	1.11440
$438$	4.58993	0.219315
$439$	−37.4069	−1.78533	−0.892667	−	0.450716i	$-0.851169\pi$
$439$	−37.4069	−1.78533	−0.892667	+	0.450716i	$0.851169\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	19.5569	0.930226
$443$	21.4478	1.01902	0.509508	−	0.860466i	$-0.329827\pi$
$443$	21.4478	1.01902	0.509508	+	0.860466i	$0.329827\pi$
$444$	8.79186	0.417243
$445$	4.80846	0.227943
$446$	−6.00536	−0.284362
$447$	12.5258	0.592450
$448$	−0.283993	−0.0134174
$449$	6.39904	0.301989	0.150995	−	0.988535i	$-0.451752\pi$
$449$	6.39904	0.301989	0.150995	+	0.988535i	$0.451752\pi$
$450$	8.24436	0.388643
$451$	0	0
$452$	−8.90787	−0.418991
$453$	0.328572	0.0154377
$454$	34.3763	1.61336
$455$	0.911108	0.0427134
$456$	−9.42666	−0.441444
$457$	36.9430	1.72812	0.864060	−	0.503389i	$-0.167914\pi$
$457$	36.9430	1.72812	0.864060	+	0.503389i	$0.167914\pi$
$458$	17.4813	0.816847
$459$	7.14511	0.333505
$460$	2.53249	0.118078
$461$	−7.39825	−0.344571	−0.172285	−	0.985047i	$-0.555115\pi$
$461$	−7.39825	−0.344571	−0.172285	+	0.985047i	$0.555115\pi$
$462$	0	0
$463$	−14.3717	−0.667910	−0.333955	−	0.942589i	$-0.608383\pi$
$463$	−14.3717	−0.667910	−0.333955	+	0.942589i	$0.608383\pi$
$464$	3.02445	0.140407
$465$	4.05366	0.187984
$466$	12.6292	0.585036
$467$	36.1626	1.67341	0.836704	−	0.547656i	$-0.184480\pi$
$467$	36.1626	1.67341	0.836704	+	0.547656i	$0.184480\pi$
$468$	1.76186	0.0814422
$469$	−2.19138	−0.101188
$470$	10.6714	0.492235
$471$	2.68089	0.123529
$472$	−5.10705	−0.235071
$473$	0	0
$474$	8.26479	0.379614
$475$	−28.7985	−1.32137
$476$	−8.15095	−0.373598
$477$	7.04469	0.322554
$478$	39.5018	1.80677
$479$	−16.0252	−0.732212	−0.366106	−	0.930573i	$-0.619309\pi$
$479$	−16.0252	−0.732212	−0.366106	+	0.930573i	$0.619309\pi$
$480$	−3.41007	−0.155648
$481$	−11.9029	−0.542727
$482$	26.3623	1.20077
$483$	−3.76314	−0.171229
$484$	0	0
$485$	−2.82993	−0.128501
$486$	1.77222	0.0803897
$487$	1.55059	0.0702641	0.0351320	−	0.999383i	$-0.488815\pi$
$487$	1.55059	0.0702641	0.0351320	+	0.999383i	$0.488815\pi$
$488$	5.13230	0.232328
$489$	0.891668	0.0403226
$490$	−1.04548	−0.0472300
$491$	0.0331635	0.00149665	0.000748324	−	1.00000i	$-0.499762\pi$
$491$	0.0331635	0.00149665	0.000748324		1.00000i	$0.499762\pi$
$492$	8.53627	0.384845
$493$	4.33921	0.195428
$494$	−16.9443	−0.762359
$495$	0	0
$496$	34.2212	1.53658
$497$	−13.9430	−0.625429
$498$	6.21997	0.278724
$499$	−27.0314	−1.21009	−0.605046	−	0.796190i	$-0.706845\pi$
$499$	−27.0314	−1.21009	−0.605046	+	0.796190i	$0.706845\pi$
$500$	−6.49552	−0.290488
$501$	11.5610	0.516509
$502$	45.9418	2.05048
$503$	29.3341	1.30794	0.653972	−	0.756519i	$-0.273101\pi$
$503$	29.3341	1.30794	0.653972	+	0.756519i	$0.273101\pi$
$504$	1.52274	0.0678282
$505$	0.841621	0.0374516
$506$	0	0
$507$	10.6147	0.471415
$508$	−9.41351	−0.417657
$509$	−16.6329	−0.737239	−0.368620	−	0.929580i	$-0.620169\pi$
$509$	−16.6329	−0.737239	−0.368620	+	0.929580i	$0.620169\pi$
$510$	−7.47007	−0.330780
$511$	2.58993	0.114572
$512$	−13.6210	−0.601967
$513$	−6.19059	−0.273321
$514$	−1.54445	−0.0681226
$515$	10.3929	0.457964
$516$	−12.4957	−0.550094
$517$	0	0
$518$	13.6584	0.600115
$519$	8.98926	0.394585
$520$	1.38738	0.0608407
$521$	35.8923	1.57247	0.786236	−	0.617927i	$-0.212027\pi$
$521$	35.8923	1.57247	0.786236	+	0.617927i	$0.212027\pi$
$522$	1.07627	0.0471069
$523$	−7.27873	−0.318276	−0.159138	−	0.987256i	$-0.550872\pi$
$523$	−7.27873	−0.318276	−0.159138	+	0.987256i	$0.550872\pi$
$524$	−13.8219	−0.603811
$525$	4.65199	0.203029
$526$	47.6502	2.07765
$527$	49.0974	2.13872
$528$	0	0
$529$	−8.83876	−0.384294
$530$	−7.36508	−0.319919
$531$	−3.35386	−0.145545
$532$	7.06206	0.306179
$533$	−11.5569	−0.500585
$534$	14.4453	0.625110
$535$	4.24749	0.183635
$536$	−3.33690	−0.144132
$537$	6.14590	0.265215
$538$	1.75906	0.0758386
$539$	0	0
$540$	−0.672972	−0.0289601
$541$	10.4709	0.450177	0.225089	−	0.974338i	$-0.427733\pi$
$541$	10.4709	0.450177	0.225089	+	0.974338i	$0.427733\pi$
$542$	47.6108	2.04506
$543$	−14.9662	−0.642262
$544$	−41.3024	−1.77083
$545$	5.24254	0.224566
$546$	2.73710	0.117137
$547$	−8.16609	−0.349157	−0.174578	−	0.984643i	$-0.555856\pi$
$547$	−8.16609	−0.349157	−0.174578	+	0.984643i	$0.555856\pi$
$548$	−19.9119	−0.850596
$549$	3.37044	0.143847
$550$	0	0
$551$	−3.75953	−0.160161
$552$	−5.73029	−0.243897
$553$	4.66351	0.198313
$554$	−48.9669	−2.08040
$555$	4.54651	0.192989
$556$	−16.8405	−0.714197
$557$	−11.8765	−0.503225	−0.251612	−	0.967828i	$-0.580961\pi$
$557$	−11.8765	−0.503225	−0.251612	+	0.967828i	$0.580961\pi$
$558$	12.1778	0.515527
$559$	16.9174	0.715532
$560$	−2.93794	−0.124151
$561$	0	0
$562$	42.2530	1.78233
$563$	−4.83929	−0.203952	−0.101976	−	0.994787i	$-0.532516\pi$
$563$	−4.83929	−0.203952	−0.101976	+	0.994787i	$0.532516\pi$
$564$	11.6441	0.490304
$565$	−4.60651	−0.193797
$566$	15.5023	0.651608
$567$	1.00000	0.0419961
$568$	−21.2316	−0.890856
$569$	−6.52993	−0.273749	−0.136875	−	0.990588i	$-0.543706\pi$
$569$	−6.52993	−0.273749	−0.136875	+	0.990588i	$0.543706\pi$
$570$	6.47214	0.271088
$571$	33.8691	1.41738	0.708689	−	0.705521i	$-0.249287\pi$
$571$	33.8691	1.41738	0.708689	+	0.705521i	$0.249287\pi$
$572$	0	0
$573$	−9.87351	−0.412472
$574$	13.2613	0.553517
$575$	−17.5061	−0.730054
$576$	−0.283993	−0.0118331
$577$	−37.3609	−1.55536	−0.777678	−	0.628662i	$-0.783603\pi$
$577$	−37.3609	−1.55536	−0.777678	+	0.628662i	$0.783603\pi$
$578$	−60.3487	−2.51018
$579$	−6.18113	−0.256879
$580$	−0.408694	−0.0169701
$581$	3.50970	0.145607
$582$	−8.50152	−0.352399
$583$	0	0
$584$	3.94378	0.163195
$585$	0.911108	0.0376697
$586$	−34.7802	−1.43675
$587$	−2.07974	−0.0858399	−0.0429199	−	0.999079i	$-0.513666\pi$
$587$	−2.07974	−0.0858399	−0.0429199	+	0.999079i	$0.513666\pi$
$588$	−1.14077	−0.0470447
$589$	−42.5385	−1.75277
$590$	3.50639	0.144356
$591$	−19.0720	−0.784518
$592$	38.3819	1.57749
$593$	−6.54983	−0.268969	−0.134485	−	0.990916i	$-0.542938\pi$
$593$	−6.54983	−0.268969	−0.134485	+	0.990916i	$0.542938\pi$
$594$	0	0
$595$	−4.21508	−0.172802
$596$	−14.2891	−0.585304
$597$	11.8479	0.484904
$598$	−10.3001	−0.421203
$599$	−4.98187	−0.203554	−0.101777	−	0.994807i	$-0.532453\pi$
$599$	−4.98187	−0.203554	−0.101777	+	0.994807i	$0.532453\pi$
$600$	7.08377	0.289194
$601$	32.4713	1.32453	0.662266	−	0.749269i	$-0.269595\pi$
$601$	32.4713	1.32453	0.662266	+	0.749269i	$0.269595\pi$
$602$	−19.4125	−0.791192
$603$	−2.19138	−0.0892398
$604$	−0.374827	−0.0152515
$605$	0	0
$606$	2.52835	0.102707
$607$	−3.13388	−0.127200	−0.0636002	−	0.997975i	$-0.520258\pi$
$607$	−3.13388	−0.127200	−0.0636002	+	0.997975i	$0.520258\pi$
$608$	35.7848	1.45126
$609$	0.607298	0.0246089
$610$	−3.52373	−0.142672
$611$	−15.7644	−0.637760
$612$	−8.15095	−0.329483
$613$	−46.8484	−1.89219	−0.946094	−	0.323892i	$-0.895009\pi$
$613$	−46.8484	−1.89219	−0.946094	+	0.323892i	$0.895009\pi$
$614$	−30.2758	−1.22183
$615$	4.41434	0.178003
$616$	0	0
$617$	26.5924	1.07057	0.535286	−	0.844671i	$-0.320204\pi$
$617$	26.5924	1.07057	0.535286	+	0.844671i	$0.320204\pi$
$618$	31.2217	1.25592
$619$	−32.9765	−1.32544	−0.662718	−	0.748869i	$-0.730597\pi$
$619$	−32.9765	−1.32544	−0.662718	+	0.748869i	$0.730597\pi$
$620$	−4.62431	−0.185717
$621$	−3.76314	−0.151010
$622$	12.8194	0.514011
$623$	8.15095	0.326561
$624$	7.69162	0.307911
$625$	19.9009	0.796037
$626$	−24.4185	−0.975959
$627$	0	0
$628$	−3.05828	−0.122039
$629$	55.0668	2.19566
$630$	−1.04548	−0.0416529
$631$	11.1721	0.444754	0.222377	−	0.974961i	$-0.428618\pi$
$631$	11.1721	0.444754	0.222377	+	0.974961i	$0.428618\pi$
$632$	7.10132	0.282475
$633$	−20.9810	−0.833922
$634$	12.3281	0.489611
$635$	−4.86798	−0.193180
$636$	−8.03640	−0.318664
$637$	1.54445	0.0611932
$638$	0	0
$639$	−13.9430	−0.551576
$640$	−6.52324	−0.257854
$641$	−41.9153	−1.65556	−0.827778	−	0.561056i	$-0.810395\pi$
$641$	−41.9153	−1.65556	−0.827778	+	0.561056i	$0.810395\pi$
$642$	12.7601	0.503600
$643$	29.0873	1.14709	0.573546	−	0.819173i	$-0.305567\pi$
$643$	29.0873	1.14709	0.573546	+	0.819173i	$0.305567\pi$
$644$	4.29289	0.169164
$645$	−6.46189	−0.254437
$646$	78.3897	3.08420
$647$	1.89804	0.0746196	0.0373098	−	0.999304i	$-0.488121\pi$
$647$	1.89804	0.0746196	0.0373098	+	0.999304i	$0.488121\pi$
$648$	1.52274	0.0598189
$649$	0	0
$650$	12.7330	0.499428
$651$	6.87147	0.269314
$652$	−1.01719	−0.0398363
$653$	20.2519	0.792517	0.396258	−	0.918139i	$-0.370308\pi$
$653$	20.2519	0.792517	0.396258	+	0.918139i	$0.370308\pi$
$654$	15.7493	0.615848
$655$	−7.14766	−0.279282
$656$	37.2661	1.45500
$657$	2.58993	0.101043
$658$	18.0894	0.705197
$659$	11.5620	0.450392	0.225196	−	0.974314i	$-0.427698\pi$
$659$	11.5620	0.450392	0.225196	+	0.974314i	$0.427698\pi$
$660$	0	0
$661$	−32.6894	−1.27147	−0.635735	−	0.771907i	$-0.719303\pi$
$661$	−32.6894	−1.27147	−0.635735	+	0.771907i	$0.719303\pi$
$662$	52.5816	2.04364
$663$	11.0352	0.428573
$664$	5.34436	0.207402
$665$	3.65199	0.141618
$666$	13.6584	0.529252
$667$	−2.28535	−0.0884890
$668$	−13.1885	−0.510279
$669$	−3.38860	−0.131011
$670$	2.29104	0.0885107
$671$	0	0
$672$	−5.78051	−0.222988
$673$	20.1249	0.775758	0.387879	−	0.921710i	$-0.373208\pi$
$673$	20.1249	0.775758	0.387879	+	0.921710i	$0.373208\pi$
$674$	34.6850	1.33601
$675$	4.65199	0.179055
$676$	−12.1090	−0.465729
$677$	−23.5746	−0.906045	−0.453022	−	0.891499i	$-0.649654\pi$
$677$	−23.5746	−0.906045	−0.453022	+	0.891499i	$0.649654\pi$
$678$	−13.8386	−0.531469
$679$	−4.79710	−0.184096
$680$	−6.41848	−0.246137
$681$	19.3973	0.743305
$682$	0	0
$683$	11.5812	0.443143	0.221572	−	0.975144i	$-0.428881\pi$
$683$	11.5812	0.443143	0.221572	+	0.975144i	$0.428881\pi$
$684$	7.06206	0.270025
$685$	−10.2970	−0.393429
$686$	−1.77222	−0.0676638
$687$	9.86405	0.376337
$688$	−54.5516	−2.07976
$689$	10.8801	0.414500
$690$	3.93429	0.149776
$691$	43.8164	1.66685	0.833426	−	0.552630i	$-0.186376\pi$
$691$	43.8164	1.66685	0.833426	+	0.552630i	$0.186376\pi$
$692$	−10.2547	−0.389826
$693$	0	0
$694$	−11.5050	−0.436723
$695$	−8.70869	−0.330340
$696$	0.924756	0.0350528
$697$	53.4659	2.02517
$698$	13.9645	0.528564
$699$	7.12619	0.269537
$700$	−5.30687	−0.200581
$701$	22.8165	0.861769	0.430884	−	0.902407i	$-0.358202\pi$
$701$	22.8165	0.861769	0.430884	+	0.902407i	$0.358202\pi$
$702$	2.73710	0.103305
$703$	−47.7104	−1.79943
$704$	0	0
$705$	6.02147	0.226782
$706$	9.47420	0.356566
$707$	1.42666	0.0536549
$708$	3.82599	0.143790
$709$	39.9746	1.50128	0.750638	−	0.660713i	$-0.229746\pi$
$709$	39.9746	1.50128	0.750638	+	0.660713i	$0.229746\pi$
$710$	14.5771	0.547070
$711$	4.66351	0.174895
$712$	12.4118	0.465151
$713$	−25.8583	−0.968402
$714$	−12.6627	−0.473891
$715$	0	0
$716$	−7.01108	−0.262016
$717$	22.2894	0.832414
$718$	−31.6369	−1.18068
$719$	−26.2200	−0.977840	−0.488920	−	0.872329i	$-0.662609\pi$
$719$	−26.2200	−0.977840	−0.488920	+	0.872329i	$0.662609\pi$
$720$	−2.93794	−0.109490
$721$	17.6172	0.656100
$722$	−34.2453	−1.27448
$723$	14.8753	0.553217
$724$	17.0731	0.634515
$725$	2.82514	0.104923
$726$	0	0
$727$	−22.2366	−0.824708	−0.412354	−	0.911024i	$-0.635293\pi$
$727$	−22.2366	−0.824708	−0.412354	+	0.911024i	$0.635293\pi$
$728$	2.35179	0.0871631
$729$	1.00000	0.0370370
$730$	−2.70772	−0.100217
$731$	−78.2656	−2.89476
$732$	−3.84491	−0.142112
$733$	21.1284	0.780395	0.390197	−	0.920731i	$-0.372407\pi$
$733$	21.1284	0.780395	0.390197	+	0.920731i	$0.372407\pi$
$734$	53.0528	1.95821
$735$	−0.589926	−0.0217597
$736$	21.7529	0.801822
$737$	0	0
$738$	13.2613	0.488156
$739$	−37.5036	−1.37959	−0.689795	−	0.724004i	$-0.742299\pi$
$739$	−37.5036	−1.37959	−0.689795	+	0.724004i	$0.742299\pi$
$740$	−5.18655	−0.190661
$741$	−9.56103	−0.351233
$742$	−12.4848	−0.458330
$743$	36.1464	1.32608	0.663041	−	0.748583i	$-0.269265\pi$
$743$	36.1464	1.32608	0.663041	+	0.748583i	$0.269265\pi$
$744$	10.4635	0.383609
$745$	−7.38929	−0.270723
$746$	41.6322	1.52426
$747$	3.50970	0.128413
$748$	0	0
$749$	7.20005	0.263084
$750$	−10.0910	−0.368470
$751$	−43.5533	−1.58928	−0.794641	−	0.607080i	$-0.792341\pi$
$751$	−43.5533	−1.58928	−0.794641	+	0.607080i	$0.792341\pi$
$752$	50.8336	1.85371
$753$	25.9233	0.944697
$754$	1.66224	0.0605351
$755$	−0.193833	−0.00705431
$756$	−1.14077	−0.0414895
$757$	−44.4442	−1.61535	−0.807675	−	0.589628i	$-0.799274\pi$
$757$	−44.4442	−1.61535	−0.807675	+	0.589628i	$0.799274\pi$
$758$	55.7421	2.02464
$759$	0	0
$760$	5.56103	0.201720
$761$	15.9613	0.578598	0.289299	−	0.957239i	$-0.406578\pi$
$761$	15.9613	0.578598	0.289299	+	0.957239i	$0.406578\pi$
$762$	−14.6241	−0.529777
$763$	8.88678	0.321723
$764$	11.2634	0.407497
$765$	−4.21508	−0.152397
$766$	9.97317	0.360345
$767$	−5.17985	−0.187034
$768$	−20.1647	−0.727633
$769$	−5.19899	−0.187480	−0.0937402	−	0.995597i	$-0.529882\pi$
$769$	−5.19899	−0.187480	−0.0937402	+	0.995597i	$0.529882\pi$
$770$	0	0
$771$	−0.871474	−0.0313854
$772$	7.05127	0.253781
$773$	−12.1614	−0.437416	−0.218708	−	0.975790i	$-0.570184\pi$
$773$	−12.1614	−0.437416	−0.218708	+	0.975790i	$0.570184\pi$
$774$	−19.4125	−0.697766
$775$	31.9660	1.14825
$776$	−7.30473	−0.262224
$777$	7.70693	0.276484
$778$	−46.2678	−1.65878
$779$	−46.3234	−1.65971
$780$	−1.03937	−0.0372154
$781$	0	0
$782$	47.6516	1.70402
$783$	0.607298	0.0217030
$784$	−4.98018	−0.177864
$785$	−1.58152	−0.0564470
$786$	−21.4726	−0.765903
$787$	39.6430	1.41312	0.706559	−	0.707654i	$-0.250246\pi$
$787$	39.6430	1.41312	0.706559	+	0.707654i	$0.250246\pi$
$788$	21.7569	0.775056
$789$	26.8873	0.957212
$790$	−4.87561	−0.173466
$791$	−7.80862	−0.277643
$792$	0	0
$793$	5.20546	0.184851
$794$	−18.4006	−0.653011
$795$	−4.15584	−0.147393
$796$	−13.5158	−0.479055
$797$	−35.1118	−1.24372	−0.621862	−	0.783127i	$-0.713624\pi$
$797$	−35.1118	−1.24372	−0.621862	+	0.783127i	$0.713624\pi$
$798$	10.9711	0.388373
$799$	72.9313	2.58012
$800$	−26.8909	−0.950736
$801$	8.15095	0.288000
$802$	−6.53731	−0.230840
$803$	0	0
$804$	2.49987	0.0881635
$805$	2.21997	0.0782438
$806$	18.8079	0.662481
$807$	0.992574	0.0349403
$808$	2.17243	0.0764257
$809$	41.7873	1.46916	0.734581	−	0.678521i	$-0.237379\pi$
$809$	41.7873	1.46916	0.734581	+	0.678521i	$0.237379\pi$
$810$	−1.04548	−0.0367344
$811$	9.89879	0.347594	0.173797	−	0.984782i	$-0.444396\pi$
$811$	9.89879	0.347594	0.173797	+	0.984782i	$0.444396\pi$
$812$	−0.692789	−0.0243121
$813$	26.8650	0.942197
$814$	0	0
$815$	−0.526018	−0.0184256
$816$	−35.5839	−1.24569
$817$	67.8100	2.37237
$818$	1.91440	0.0669353
$819$	1.54445	0.0539673
$820$	−5.03576	−0.175856
$821$	−16.1936	−0.565161	−0.282580	−	0.959244i	$-0.591190\pi$
$821$	−16.1936	−0.565161	−0.282580	+	0.959244i	$0.591190\pi$
$822$	−30.9337	−1.07894
$823$	−3.86642	−0.134775	−0.0673874	−	0.997727i	$-0.521466\pi$
$823$	−3.86642	−0.134775	−0.0673874	+	0.997727i	$0.521466\pi$
$824$	26.8265	0.934545
$825$	0	0
$826$	5.94378	0.206811
$827$	46.8179	1.62802	0.814009	−	0.580852i	$-0.197280\pi$
$827$	46.8179	1.62802	0.814009	+	0.580852i	$0.197280\pi$
$828$	4.29289	0.149188
$829$	−41.5599	−1.44344	−0.721718	−	0.692187i	$-0.756647\pi$
$829$	−41.5599	−1.44344	−0.721718	+	0.692187i	$0.756647\pi$
$830$	−3.66932	−0.127364
$831$	−27.6302	−0.958481
$832$	−0.438613	−0.0152062
$833$	−7.14511	−0.247563
$834$	−26.1622	−0.905922
$835$	−6.82015	−0.236021
$836$	0	0
$837$	6.87147	0.237513
$838$	−17.8579	−0.616892
$839$	5.14119	0.177494	0.0887469	−	0.996054i	$-0.471714\pi$
$839$	5.14119	0.177494	0.0887469	+	0.996054i	$0.471714\pi$
$840$	−0.898304	−0.0309944
$841$	−28.6312	−0.987282
$842$	−21.2236	−0.731412
$843$	23.8418	0.821155
$844$	23.9346	0.823864
$845$	−6.26188	−0.215415
$846$	18.0894	0.621926
$847$	0	0
$848$	−35.0838	−1.20478
$849$	8.74735	0.300208
$850$	−58.9068	−2.02049
$851$	−29.0023	−0.994184
$852$	15.9058	0.544924
$853$	−6.69649	−0.229283	−0.114642	−	0.993407i	$-0.536572\pi$
$853$	−6.69649	−0.229283	−0.114642	+	0.993407i	$0.536572\pi$
$854$	−5.97317	−0.204398
$855$	3.65199	0.124895
$856$	10.9638	0.374735
$857$	36.1064	1.23337	0.616686	−	0.787209i	$-0.288475\pi$
$857$	36.1064	1.23337	0.616686	+	0.787209i	$0.288475\pi$
$858$	0	0
$859$	−37.1034	−1.26595	−0.632976	−	0.774171i	$-0.718167\pi$
$859$	−37.1034	−1.26595	−0.632976	+	0.774171i	$0.718167\pi$
$860$	7.37155	0.251368
$861$	7.48287	0.255016
$862$	−0.972147	−0.0331115
$863$	38.3724	1.30621	0.653105	−	0.757267i	$-0.273466\pi$
$863$	38.3724	1.30621	0.653105	+	0.757267i	$0.273466\pi$
$864$	−5.78051	−0.196657
$865$	−5.30300	−0.180307
$866$	−34.7140	−1.17963
$867$	−34.0526	−1.15649
$868$	−7.83880	−0.266066
$869$	0	0
$870$	−0.634918	−0.0215257
$871$	−3.38446	−0.114678
$872$	13.5323	0.458260
$873$	−4.79710	−0.162357
$874$	−41.2858	−1.39651
$875$	−5.69396	−0.192491
$876$	−2.95452	−0.0998240
$877$	0.811156	0.0273908	0.0136954	−	0.999906i	$-0.495640\pi$
$877$	0.811156	0.0273908	0.0136954	+	0.999906i	$0.495640\pi$
$878$	66.2934	2.23729
$879$	−19.6252	−0.661940
$880$	0	0
$881$	−32.5076	−1.09521	−0.547605	−	0.836737i	$-0.684460\pi$
$881$	−32.5076	−1.09521	−0.547605	+	0.836737i	$0.684460\pi$
$882$	−1.77222	−0.0596738
$883$	48.0995	1.61868	0.809338	−	0.587343i	$-0.199826\pi$
$883$	48.0995	1.61868	0.809338	+	0.587343i	$0.199826\pi$
$884$	−12.5887	−0.423404
$885$	1.97853	0.0665075
$886$	−38.0103	−1.27698
$887$	−11.3847	−0.382260	−0.191130	−	0.981565i	$-0.561215\pi$
$887$	−11.3847	−0.382260	−0.191130	+	0.981565i	$0.561215\pi$
$888$	11.7356	0.393822
$889$	−8.25186	−0.276758
$890$	−8.52166	−0.285647
$891$	0	0
$892$	3.86563	0.129431
$893$	−63.1884	−2.11452
$894$	−22.1985	−0.742429
$895$	−3.62562	−0.121191
$896$	−11.0577	−0.369413
$897$	−5.81197	−0.194056
$898$	−11.3405	−0.378438
$899$	4.17303	0.139178
$900$	−5.30687	−0.176896
$901$	−50.3351	−1.67690
$902$	0	0
$903$	−10.9537	−0.364517
$904$	−11.8905	−0.395472
$905$	8.82895	0.293484
$906$	−0.582303	−0.0193457
$907$	13.4259	0.445799	0.222899	−	0.974841i	$-0.428448\pi$
$907$	13.4259	0.445799	0.222899	+	0.974841i	$0.428448\pi$
$908$	−22.1279	−0.734340
$909$	1.42666	0.0473192
$910$	−1.61469	−0.0535264
$911$	3.39303	0.112416	0.0562080	−	0.998419i	$-0.482099\pi$
$911$	3.39303	0.112416	0.0562080	+	0.998419i	$0.482099\pi$
$912$	30.8303	1.02089
$913$	0	0
$914$	−65.4712	−2.16560
$915$	−1.98831	−0.0657315
$916$	−11.2526	−0.371798
$917$	−12.1162	−0.400112
$918$	−12.6627	−0.417932
$919$	44.5668	1.47012	0.735062	−	0.678000i	$-0.237153\pi$
$919$	44.5668	1.47012	0.735062	+	0.678000i	$0.237153\pi$
$920$	3.38044	0.111450
$921$	−17.0835	−0.562922
$922$	13.1113	0.431799
$923$	−21.5342	−0.708807
$924$	0	0
$925$	35.8525	1.17882
$926$	25.4699	0.836992
$927$	17.6172	0.578626
$928$	−3.51049	−0.115238
$929$	−7.15205	−0.234651	−0.117325	−	0.993094i	$-0.537432\pi$
$929$	−7.15205	−0.234651	−0.117325	+	0.993094i	$0.537432\pi$
$930$	−7.18399	−0.235572
$931$	6.19059	0.202888
$932$	−8.12937	−0.266287
$933$	7.23351	0.236815
$934$	−64.0883	−2.09703
$935$	0	0
$936$	2.35179	0.0768706
$937$	1.30811	0.0427342	0.0213671	−	0.999772i	$-0.493198\pi$
$937$	1.30811	0.0427342	0.0213671	+	0.999772i	$0.493198\pi$
$938$	3.88361	0.126804
$939$	−13.7784	−0.449643
$940$	−6.86914	−0.224047
$941$	22.1225	0.721174	0.360587	−	0.932726i	$-0.382576\pi$
$941$	22.1225	0.721174	0.360587	+	0.932726i	$0.382576\pi$
$942$	−4.75113	−0.154800
$943$	−28.1591	−0.916987
$944$	16.7028	0.543631
$945$	−0.589926	−0.0191903
$946$	0	0
$947$	−17.6842	−0.574658	−0.287329	−	0.957832i	$-0.592767\pi$
$947$	−17.6842	−0.574658	−0.287329	+	0.957832i	$0.592767\pi$
$948$	−5.32002	−0.172786
$949$	4.00000	0.129845
$950$	51.0374	1.65587
$951$	6.95629	0.225573
$952$	−10.8801	−0.352627
$953$	23.7741	0.770118	0.385059	−	0.922892i	$-0.374181\pi$
$953$	23.7741	0.770118	0.385059	+	0.922892i	$0.374181\pi$
$954$	−12.4848	−0.404209
$955$	5.82464	0.188481
$956$	−25.4272	−0.822374
$957$	0	0
$958$	28.4003	0.917573
$959$	−17.4548	−0.563644
$960$	0.167535	0.00540717
$961$	16.2172	0.523134
$962$	21.0946	0.680119
$963$	7.20005	0.232018
$964$	−16.9693	−0.546544
$965$	3.64641	0.117382
$966$	6.66913	0.214576
$967$	−21.1829	−0.681195	−0.340597	−	0.940209i	$-0.610629\pi$
$967$	−21.1829	−0.681195	−0.340597	+	0.940209i	$0.610629\pi$
$968$	0	0
$969$	44.2324	1.42095
$970$	5.01527	0.161031
$971$	−47.4360	−1.52229	−0.761147	−	0.648579i	$-0.775363\pi$
$971$	−47.4360	−1.52229	−0.761147	+	0.648579i	$0.775363\pi$
$972$	−1.14077	−0.0365903
$973$	−14.7624	−0.473259
$974$	−2.74800	−0.0880515
$975$	7.18474	0.230096
$976$	−16.7854	−0.537288
$977$	−13.1860	−0.421858	−0.210929	−	0.977501i	$-0.567649\pi$
$977$	−13.1860	−0.421858	−0.210929	+	0.977501i	$0.567649\pi$
$978$	−1.58023	−0.0505303
$979$	0	0
$980$	0.672972	0.0214973
$981$	8.88678	0.283733
$982$	−0.0587731	−0.00187553
$983$	−4.07740	−0.130049	−0.0650244	−	0.997884i	$-0.520713\pi$
$983$	−4.07740	−0.130049	−0.0650244	+	0.997884i	$0.520713\pi$
$984$	11.3945	0.363242
$985$	11.2511	0.358489
$986$	−7.69004	−0.244901
$987$	10.2072	0.324898
$988$	10.9070	0.346997
$989$	41.2204	1.31073
$990$	0	0
$991$	−5.49154	−0.174445	−0.0872223	−	0.996189i	$-0.527799\pi$
$991$	−5.49154	−0.174445	−0.0872223	+	0.996189i	$0.527799\pi$
$992$	−39.7206	−1.26113
$993$	29.6698	0.941544
$994$	24.7101	0.783757
$995$	−6.98940	−0.221579
$996$	−4.00378	−0.126865
$997$	−22.9725	−0.727548	−0.363774	−	0.931487i	$-0.618512\pi$
$997$	−22.9725	−0.727548	−0.363774	+	0.931487i	$0.618512\pi$
$998$	47.9057	1.51643
$999$	7.70693	0.243836

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2541.2.a.bm.1.1		4
3.2	odd	2		7623.2.a.cl.1.4		4
11.2	odd	10		231.2.j.f.169.1	✓	8
11.6	odd	10		231.2.j.f.190.1	yes	8
11.10	odd	2		2541.2.a.bn.1.4		4
33.2	even	10		693.2.m.f.631.2		8
33.17	even	10		693.2.m.f.190.2		8
33.32	even	2		7623.2.a.ci.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.j.f.169.1	✓	8	11.2	odd	10
231.2.j.f.190.1	yes	8	11.6	odd	10
693.2.m.f.190.2		8	33.17	even	10
693.2.m.f.631.2		8	33.2	even	10
2541.2.a.bm.1.1		4	1.1	even	1	trivial
2541.2.a.bn.1.4		4	11.10	odd	2
7623.2.a.ci.1.1		4	33.32	even	2
7623.2.a.cl.1.4		4	3.2	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:	\( N \)	\(=\)	\( 2541 = 3 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2541.a (trivial)

\(f(q)\)	\(=\)	\(q-1.77222 q^{2} -1.00000 q^{3} +1.14077 q^{4} +0.589926 q^{5} +1.77222 q^{6} +1.00000 q^{7} +1.52274 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.77222 q^{2} -1.00000 q^{3} +1.14077 q^{4} +0.589926 q^{5} +1.77222 q^{6} +1.00000 q^{7} +1.52274 q^{8} +1.00000 q^{9} -1.04548 q^{10} -1.14077 q^{12} +1.54445 q^{13} -1.77222 q^{14} -0.589926 q^{15} -4.98018 q^{16} -7.14511 q^{17} -1.77222 q^{18} +6.19059 q^{19} +0.672972 q^{20} -1.00000 q^{21} +3.76314 q^{23} -1.52274 q^{24} -4.65199 q^{25} -2.73710 q^{26} -1.00000 q^{27} +1.14077 q^{28} -0.607298 q^{29} +1.04548 q^{30} -6.87147 q^{31} +5.78051 q^{32} +12.6627 q^{34} +0.589926 q^{35} +1.14077 q^{36} -7.70693 q^{37} -10.9711 q^{38} -1.54445 q^{39} +0.898304 q^{40} -7.48287 q^{41} +1.77222 q^{42} +10.9537 q^{43} +0.589926 q^{45} -6.66913 q^{46} -10.2072 q^{47} +4.98018 q^{48} +1.00000 q^{49} +8.24436 q^{50} +7.14511 q^{51} +1.76186 q^{52} +7.04469 q^{53} +1.77222 q^{54} +1.52274 q^{56} -6.19059 q^{57} +1.07627 q^{58} -3.35386 q^{59} -0.672972 q^{60} +3.37044 q^{61} +12.1778 q^{62} +1.00000 q^{63} -0.283993 q^{64} +0.911108 q^{65} -2.19138 q^{67} -8.15095 q^{68} -3.76314 q^{69} -1.04548 q^{70} -13.9430 q^{71} +1.52274 q^{72} +2.58993 q^{73} +13.6584 q^{74} +4.65199 q^{75} +7.06206 q^{76} +2.73710 q^{78} +4.66351 q^{79} -2.93794 q^{80} +1.00000 q^{81} +13.2613 q^{82} +3.50970 q^{83} -1.14077 q^{84} -4.21508 q^{85} -19.4125 q^{86} +0.607298 q^{87} +8.15095 q^{89} -1.04548 q^{90} +1.54445 q^{91} +4.29289 q^{92} +6.87147 q^{93} +18.0894 q^{94} +3.65199 q^{95} -5.78051 q^{96} -4.79710 q^{97} -1.77222 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - 4 q^{3} + 3 q^{4} - 4 q^{5} + q^{6} + 4 q^{7} + 9 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - q^2 - 4 * q^3 + 3 * q^4 - 4 * q^5 + q^6 + 4 * q^7 + 9 * q^8 + 4 * q^9	\( 4 q - q^{2} - 4 q^{3} + 3 q^{4} - 4 q^{5} + q^{6} + 4 q^{7} + 9 q^{8} + 4 q^{9} - 10 q^{10} - 3 q^{12} - 6 q^{13} - q^{14} + 4 q^{15} - 3 q^{16} - 8 q^{17} - q^{18} + 10 q^{19} - 4 q^{21} - 10 q^{23} - 9 q^{24} + 12 q^{25} - 20 q^{26} - 4 q^{27} + 3 q^{28} + 10 q^{30} - 18 q^{31} + 2 q^{32} + 18 q^{34} - 4 q^{35} + 3 q^{36} - 2 q^{37} - 8 q^{38} + 6 q^{39} - 6 q^{40} - 10 q^{41} + q^{42} + 4 q^{43} - 4 q^{45} - 11 q^{46} + 4 q^{47} + 3 q^{48} + 4 q^{49} + 9 q^{50} + 8 q^{51} - 20 q^{52} + q^{54} + 9 q^{56} - 10 q^{57} + 14 q^{58} - 16 q^{59} - 14 q^{61} + 4 q^{63} - 11 q^{64} + 28 q^{65} - 28 q^{67} + 16 q^{68} + 10 q^{69} - 10 q^{70} - 18 q^{71} + 9 q^{72} + 4 q^{73} + 41 q^{74} - 12 q^{75} + 4 q^{76} + 20 q^{78} + 20 q^{79} - 36 q^{80} + 4 q^{81} - 24 q^{82} - 6 q^{83} - 3 q^{84} + 20 q^{85} - 20 q^{86} - 16 q^{89} - 10 q^{90} - 6 q^{91} - 22 q^{92} + 18 q^{93} + 16 q^{94} - 16 q^{95} - 2 q^{96} + 32 q^{97} - q^{98}+O(q^{100}) \) 4 * q - q^2 - 4 * q^3 + 3 * q^4 - 4 * q^5 + q^6 + 4 * q^7 + 9 * q^8 + 4 * q^9 - 10 * q^10 - 3 * q^12 - 6 * q^13 - q^14 + 4 * q^15 - 3 * q^16 - 8 * q^17 - q^18 + 10 * q^19 - 4 * q^21 - 10 * q^23 - 9 * q^24 + 12 * q^25 - 20 * q^26 - 4 * q^27 + 3 * q^28 + 10 * q^30 - 18 * q^31 + 2 * q^32 + 18 * q^34 - 4 * q^35 + 3 * q^36 - 2 * q^37 - 8 * q^38 + 6 * q^39 - 6 * q^40 - 10 * q^41 + q^42 + 4 * q^43 - 4 * q^45 - 11 * q^46 + 4 * q^47 + 3 * q^48 + 4 * q^49 + 9 * q^50 + 8 * q^51 - 20 * q^52 + q^54 + 9 * q^56 - 10 * q^57 + 14 * q^58 - 16 * q^59 - 14 * q^61 + 4 * q^63 - 11 * q^64 + 28 * q^65 - 28 * q^67 + 16 * q^68 + 10 * q^69 - 10 * q^70 - 18 * q^71 + 9 * q^72 + 4 * q^73 + 41 * q^74 - 12 * q^75 + 4 * q^76 + 20 * q^78 + 20 * q^79 - 36 * q^80 + 4 * q^81 - 24 * q^82 - 6 * q^83 - 3 * q^84 + 20 * q^85 - 20 * q^86 - 16 * q^89 - 10 * q^90 - 6 * q^91 - 22 * q^92 + 18 * q^93 + 16 * q^94 - 16 * q^95 - 2 * q^96 + 32 * q^97 - q^98

Introduction

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