LMFDB - Embedded newform 2793.2.a.bm.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2793,2,Mod(1,2793)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2793, 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("2793.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2793 = 3 \cdot 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2793.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:	$22.3022172845$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 13x^{6} - x^{5} + 51x^{4} + 3x^{3} - 65x^{2} - 6x + 16 $ x^8 - 13x^6 - x^5 + 51x^4 + 3x^3 - 65x^2 - 6*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 399)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-2.28285$ of defining polynomial
Character	$\chi$	$=$	2793.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.28285 q^{2} -1.00000 q^{3} +3.21141 q^{4} -2.54525 q^{5} -2.28285 q^{6} +2.76546 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.28285 q^{2} -1.00000 q^{3} +3.21141 q^{4} -2.54525 q^{5} -2.28285 q^{6} +2.76546 q^{8} +1.00000 q^{9} -5.81043 q^{10} +3.29628 q^{11} -3.21141 q^{12} -4.96243 q^{13} +2.54525 q^{15} -0.109683 q^{16} +5.59636 q^{17} +2.28285 q^{18} -1.00000 q^{19} -8.17384 q^{20} +7.52492 q^{22} -5.81981 q^{23} -2.76546 q^{24} +1.47831 q^{25} -11.3285 q^{26} -1.00000 q^{27} -9.32850 q^{29} +5.81043 q^{30} -6.42307 q^{31} -5.78131 q^{32} -3.29628 q^{33} +12.7757 q^{34} +3.21141 q^{36} +7.70048 q^{37} -2.28285 q^{38} +4.96243 q^{39} -7.03879 q^{40} +6.13136 q^{41} -4.62835 q^{43} +10.5857 q^{44} -2.54525 q^{45} -13.2858 q^{46} -6.31439 q^{47} +0.109683 q^{48} +3.37477 q^{50} -5.59636 q^{51} -15.9364 q^{52} -9.16420 q^{53} -2.28285 q^{54} -8.38987 q^{55} +1.00000 q^{57} -21.2956 q^{58} +9.81110 q^{59} +8.17384 q^{60} -1.81589 q^{61} -14.6629 q^{62} -12.9785 q^{64} +12.6307 q^{65} -7.52492 q^{66} +3.36328 q^{67} +17.9722 q^{68} +5.81981 q^{69} +2.01667 q^{71} +2.76546 q^{72} -4.72568 q^{73} +17.5791 q^{74} -1.47831 q^{75} -3.21141 q^{76} +11.3285 q^{78} -12.8985 q^{79} +0.279170 q^{80} +1.00000 q^{81} +13.9970 q^{82} -0.743338 q^{83} -14.2442 q^{85} -10.5658 q^{86} +9.32850 q^{87} +9.11573 q^{88} -11.4048 q^{89} -5.81043 q^{90} -18.6898 q^{92} +6.42307 q^{93} -14.4148 q^{94} +2.54525 q^{95} +5.78131 q^{96} -16.9210 q^{97} +3.29628 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{3} + 10 q^{4} - 5 q^{5} - 3 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q - 8 * q^3 + 10 * q^4 - 5 * q^5 - 3 * q^8 + 8 * q^9	$ 8 q - 8 q^{3} + 10 q^{4} - 5 q^{5} - 3 q^{8} + 8 q^{9} - 3 q^{10} - 7 q^{11} - 10 q^{12} - 6 q^{13} + 5 q^{15} + 10 q^{16} - 8 q^{19} - 16 q^{20} + 18 q^{22} - 9 q^{23} + 3 q^{24} + 15 q^{25} - 12 q^{26} - 8 q^{27} + 4 q^{29} + 3 q^{30} - 11 q^{31} - 26 q^{32} + 7 q^{33} - 16 q^{34} + 10 q^{36} + 17 q^{37} + 6 q^{39} - 3 q^{40} - 17 q^{41} + 8 q^{43} - 31 q^{44} - 5 q^{45} + q^{46} - 29 q^{47} - 10 q^{48} + 30 q^{50} - 25 q^{52} - 6 q^{53} - 21 q^{55} + 8 q^{57} - 37 q^{58} - 7 q^{59} + 16 q^{60} - 2 q^{61} - 39 q^{62} + 29 q^{64} - 13 q^{65} - 18 q^{66} + 13 q^{67} + 14 q^{68} + 9 q^{69} + 18 q^{71} - 3 q^{72} - 20 q^{73} - 26 q^{74} - 15 q^{75} - 10 q^{76} + 12 q^{78} - 3 q^{79} - 35 q^{80} + 8 q^{81} - 5 q^{82} - 36 q^{83} + 5 q^{85} - 51 q^{86} - 4 q^{87} + 53 q^{88} - q^{89} - 3 q^{90} + 15 q^{92} + 11 q^{93} - 30 q^{94} + 5 q^{95} + 26 q^{96} + 3 q^{97} - 7 q^{99}+O(q^{100}) $ 8 * q - 8 * q^3 + 10 * q^4 - 5 * q^5 - 3 * q^8 + 8 * q^9 - 3 * q^10 - 7 * q^11 - 10 * q^12 - 6 * q^13 + 5 * q^15 + 10 * q^16 - 8 * q^19 - 16 * q^20 + 18 * q^22 - 9 * q^23 + 3 * q^24 + 15 * q^25 - 12 * q^26 - 8 * q^27 + 4 * q^29 + 3 * q^30 - 11 * q^31 - 26 * q^32 + 7 * q^33 - 16 * q^34 + 10 * q^36 + 17 * q^37 + 6 * q^39 - 3 * q^40 - 17 * q^41 + 8 * q^43 - 31 * q^44 - 5 * q^45 + q^46 - 29 * q^47 - 10 * q^48 + 30 * q^50 - 25 * q^52 - 6 * q^53 - 21 * q^55 + 8 * q^57 - 37 * q^58 - 7 * q^59 + 16 * q^60 - 2 * q^61 - 39 * q^62 + 29 * q^64 - 13 * q^65 - 18 * q^66 + 13 * q^67 + 14 * q^68 + 9 * q^69 + 18 * q^71 - 3 * q^72 - 20 * q^73 - 26 * q^74 - 15 * q^75 - 10 * q^76 + 12 * q^78 - 3 * q^79 - 35 * q^80 + 8 * q^81 - 5 * q^82 - 36 * q^83 + 5 * q^85 - 51 * q^86 - 4 * q^87 + 53 * q^88 - q^89 - 3 * q^90 + 15 * q^92 + 11 * q^93 - 30 * q^94 + 5 * q^95 + 26 * q^96 + 3 * q^97 - 7 * 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 $

$2$	2.28285	1.61422	0.807110	−	0.590402i	$-0.201031\pi$
$2$	2.28285	1.61422	0.807110	+	0.590402i	$0.201031\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.21141	1.60570
$5$	−2.54525	−1.13827	−0.569136	−	0.822244i	$-0.692722\pi$
$5$	−2.54525	−1.13827	−0.569136	+	0.822244i	$0.692722\pi$
$6$	−2.28285	−0.931970
$7$	0	0
$7$	0	0
$8$	2.76546	0.977737
$9$	1.00000	0.333333
$10$	−5.81043	−1.83742
$11$	3.29628	0.993866	0.496933	−	0.867789i	$-0.334459\pi$
$11$	3.29628	0.993866	0.496933	+	0.867789i	$0.334459\pi$
$12$	−3.21141	−0.927053
$13$	−4.96243	−1.37633	−0.688166	−	0.725553i	$-0.741584\pi$
$13$	−4.96243	−1.37633	−0.688166	+	0.725553i	$0.741584\pi$
$14$	0	0
$15$	2.54525	0.657181
$16$	−0.109683	−0.0274207
$17$	5.59636	1.35732	0.678658	−	0.734454i	$-0.262562\pi$
$17$	5.59636	1.35732	0.678658	+	0.734454i	$0.262562\pi$
$18$	2.28285	0.538073
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−8.17384	−1.82773
$21$	0	0
$22$	7.52492	1.60432
$23$	−5.81981	−1.21351	−0.606757	−	0.794887i	$-0.707530\pi$
$23$	−5.81981	−1.21351	−0.606757	+	0.794887i	$0.707530\pi$
$24$	−2.76546	−0.564497
$25$	1.47831	0.295662
$26$	−11.3285	−2.22170
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−9.32850	−1.73226	−0.866129	−	0.499820i	$-0.833399\pi$
$29$	−9.32850	−1.73226	−0.866129	+	0.499820i	$0.833399\pi$
$30$	5.81043	1.06083
$31$	−6.42307	−1.15362	−0.576809	−	0.816879i	$-0.695702\pi$
$31$	−6.42307	−1.15362	−0.576809	+	0.816879i	$0.695702\pi$
$32$	−5.78131	−1.02200
$33$	−3.29628	−0.573809
$34$	12.7757	2.19101
$35$	0	0
$36$	3.21141	0.535234
$37$	7.70048	1.26595	0.632976	−	0.774171i	$-0.281833\pi$
$37$	7.70048	1.26595	0.632976	+	0.774171i	$0.281833\pi$
$38$	−2.28285	−0.370327
$39$	4.96243	0.794625
$40$	−7.03879	−1.11293
$41$	6.13136	0.957558	0.478779	−	0.877936i	$-0.341080\pi$
$41$	6.13136	0.957558	0.478779	+	0.877936i	$0.341080\pi$
$42$	0	0
$43$	−4.62835	−0.705816	−0.352908	−	0.935658i	$-0.614807\pi$
$43$	−4.62835	−0.705816	−0.352908	+	0.935658i	$0.614807\pi$
$44$	10.5857	1.59585
$45$	−2.54525	−0.379424
$46$	−13.2858	−1.95888
$47$	−6.31439	−0.921049	−0.460524	−	0.887647i	$-0.652339\pi$
$47$	−6.31439	−0.921049	−0.460524	+	0.887647i	$0.652339\pi$
$48$	0.109683	0.0158313
$49$	0	0
$50$	3.37477	0.477264
$51$	−5.59636	−0.783647
$52$	−15.9364	−2.20998
$53$	−9.16420	−1.25880	−0.629400	−	0.777082i	$-0.716699\pi$
$53$	−9.16420	−1.25880	−0.629400	+	0.777082i	$0.716699\pi$
$54$	−2.28285	−0.310657
$55$	−8.38987	−1.13129
$56$	0	0
$57$	1.00000	0.132453
$58$	−21.2956	−2.79624
$59$	9.81110	1.27730	0.638649	−	0.769499i	$-0.279494\pi$
$59$	9.81110	1.27730	0.638649	+	0.769499i	$0.279494\pi$
$60$	8.17384	1.05524
$61$	−1.81589	−0.232501	−0.116251	−	0.993220i	$-0.537088\pi$
$61$	−1.81589	−0.232501	−0.116251	+	0.993220i	$0.537088\pi$
$62$	−14.6629	−1.86219
$63$	0	0
$64$	−12.9785	−1.62231
$65$	12.6307	1.56664
$66$	−7.52492	−0.926253
$67$	3.36328	0.410891	0.205445	−	0.978669i	$-0.434136\pi$
$67$	3.36328	0.410891	0.205445	+	0.978669i	$0.434136\pi$
$68$	17.9722	2.17945
$69$	5.81981	0.700623
$70$	0	0
$71$	2.01667	0.239335	0.119667	−	0.992814i	$-0.461817\pi$
$71$	2.01667	0.239335	0.119667	+	0.992814i	$0.461817\pi$
$72$	2.76546	0.325912
$73$	−4.72568	−0.553099	−0.276550	−	0.961000i	$-0.589191\pi$
$73$	−4.72568	−0.553099	−0.276550	+	0.961000i	$0.589191\pi$
$74$	17.5791	2.04352
$75$	−1.47831	−0.170701
$76$	−3.21141	−0.368374
$77$	0	0
$78$	11.3285	1.28270
$79$	−12.8985	−1.45120	−0.725599	−	0.688117i	$-0.758437\pi$
$79$	−12.8985	−1.45120	−0.725599	+	0.688117i	$0.758437\pi$
$80$	0.279170	0.0312122
$81$	1.00000	0.111111
$82$	13.9970	1.54571
$83$	−0.743338	−0.0815919	−0.0407960	−	0.999167i	$-0.512989\pi$
$83$	−0.743338	−0.0815919	−0.0407960	+	0.999167i	$0.512989\pi$
$84$	0	0
$85$	−14.2442	−1.54500
$86$	−10.5658	−1.13934
$87$	9.32850	1.00012
$88$	9.11573	0.971740
$89$	−11.4048	−1.20891	−0.604455	−	0.796639i	$-0.706609\pi$
$89$	−11.4048	−1.20891	−0.604455	+	0.796639i	$0.706609\pi$
$90$	−5.81043	−0.612473
$91$	0	0
$92$	−18.6898	−1.94854
$93$	6.42307	0.666042
$94$	−14.4148	−1.48677
$95$	2.54525	0.261137
$96$	5.78131	0.590052
$97$	−16.9210	−1.71807	−0.859035	−	0.511918i	$-0.828935\pi$
$97$	−16.9210	−1.71807	−0.859035	+	0.511918i	$0.828935\pi$
$98$	0	0
$99$	3.29628	0.331289
$100$	4.74746	0.474746
$101$	−10.8587	−1.08048	−0.540242	−	0.841510i	$-0.681667\pi$
$101$	−10.8587	−1.08048	−0.540242	+	0.841510i	$0.681667\pi$
$102$	−12.7757	−1.26498
$103$	4.17582	0.411456	0.205728	−	0.978609i	$-0.434044\pi$
$103$	4.17582	0.411456	0.205728	+	0.978609i	$0.434044\pi$
$104$	−13.7234	−1.34569
$105$	0	0
$106$	−20.9205	−2.03198
$107$	−3.64747	−0.352614	−0.176307	−	0.984335i	$-0.556415\pi$
$107$	−3.64747	−0.352614	−0.176307	+	0.984335i	$0.556415\pi$
$108$	−3.21141	−0.309018
$109$	14.1717	1.35740	0.678701	−	0.734414i	$-0.262543\pi$
$109$	14.1717	1.35740	0.678701	+	0.734414i	$0.262543\pi$
$110$	−19.1528	−1.82615
$111$	−7.70048	−0.730898
$112$	0	0
$113$	−9.20761	−0.866179	−0.433089	−	0.901351i	$-0.642577\pi$
$113$	−9.20761	−0.866179	−0.433089	+	0.901351i	$0.642577\pi$
$114$	2.28285	0.213809
$115$	14.8129	1.38131
$116$	−29.9576	−2.78149
$117$	−4.96243	−0.458777
$118$	22.3973	2.06184
$119$	0	0
$120$	7.03879	0.642551
$121$	−0.134531	−0.0122300
$122$	−4.14542	−0.375308
$123$	−6.13136	−0.552846
$124$	−20.6271	−1.85237
$125$	8.96359	0.801728
$126$	0	0
$127$	−5.26815	−0.467472	−0.233736	−	0.972300i	$-0.575095\pi$
$127$	−5.26815	−0.467472	−0.233736	+	0.972300i	$0.575095\pi$
$128$	−18.0653	−1.59677
$129$	4.62835	0.407503
$130$	28.8339	2.52890
$131$	−7.93634	−0.693402	−0.346701	−	0.937976i	$-0.612698\pi$
$131$	−7.93634	−0.693402	−0.346701	+	0.937976i	$0.612698\pi$
$132$	−10.5857	−0.921367
$133$	0	0
$134$	7.67788	0.663268
$135$	2.54525	0.219060
$136$	15.4765	1.32710
$137$	8.19651	0.700275	0.350138	−	0.936698i	$-0.386135\pi$
$137$	8.19651	0.700275	0.350138	+	0.936698i	$0.386135\pi$
$138$	13.2858	1.13096
$139$	9.20860	0.781063	0.390531	−	0.920590i	$-0.372291\pi$
$139$	9.20860	0.781063	0.390531	+	0.920590i	$0.372291\pi$
$140$	0	0
$141$	6.31439	0.531768
$142$	4.60376	0.386339
$143$	−16.3576	−1.36789
$144$	−0.109683	−0.00914023
$145$	23.7434	1.97178
$146$	−10.7880	−0.892823
$147$	0	0
$148$	24.7294	2.03274
$149$	4.79529	0.392845	0.196423	−	0.980519i	$-0.437068\pi$
$149$	4.79529	0.392845	0.196423	+	0.980519i	$0.437068\pi$
$150$	−3.37477	−0.275548
$151$	7.66081	0.623428	0.311714	−	0.950176i	$-0.399097\pi$
$151$	7.66081	0.623428	0.311714	+	0.950176i	$0.399097\pi$
$152$	−2.76546	−0.224308
$153$	5.59636	0.452439
$154$	0	0
$155$	16.3483	1.31313
$156$	15.9364	1.27593
$157$	−4.93606	−0.393940	−0.196970	−	0.980409i	$-0.563110\pi$
$157$	−4.93606	−0.393940	−0.196970	+	0.980409i	$0.563110\pi$
$158$	−29.4454	−2.34255
$159$	9.16420	0.726768
$160$	14.7149	1.16331
$161$	0	0
$162$	2.28285	0.179358
$163$	2.55111	0.199818	0.0999090	−	0.994997i	$-0.468145\pi$
$163$	2.55111	0.199818	0.0999090	+	0.994997i	$0.468145\pi$
$164$	19.6903	1.53755
$165$	8.38987	0.653150
$166$	−1.69693	−0.131707
$167$	−1.94706	−0.150668	−0.0753340	−	0.997158i	$-0.524002\pi$
$167$	−1.94706	−0.150668	−0.0753340	+	0.997158i	$0.524002\pi$
$168$	0	0
$169$	11.6258	0.894289
$170$	−32.5173	−2.49396
$171$	−1.00000	−0.0764719
$172$	−14.8635	−1.13333
$173$	15.0694	1.14571	0.572853	−	0.819658i	$-0.305836\pi$
$173$	15.0694	1.14571	0.572853	+	0.819658i	$0.305836\pi$
$174$	21.2956	1.61441
$175$	0	0
$176$	−0.361545	−0.0272525
$177$	−9.81110	−0.737448
$178$	−26.0355	−1.95145
$179$	23.3572	1.74580	0.872901	−	0.487897i	$-0.162236\pi$
$179$	23.3572	1.74580	0.872901	+	0.487897i	$0.162236\pi$
$180$	−8.17384	−0.609242
$181$	21.8279	1.62246	0.811228	−	0.584730i	$-0.198800\pi$
$181$	21.8279	1.62246	0.811228	+	0.584730i	$0.198800\pi$
$182$	0	0
$183$	1.81589	0.134235
$184$	−16.0944	−1.18650
$185$	−19.5997	−1.44100
$186$	14.6629	1.07514
$187$	18.4472	1.34899
$188$	−20.2781	−1.47893
$189$	0	0
$190$	5.81043	0.421533
$191$	−10.7351	−0.776763	−0.388381	−	0.921499i	$-0.626966\pi$
$191$	−10.7351	−0.776763	−0.388381	+	0.921499i	$0.626966\pi$
$192$	12.9785	0.936642
$193$	18.0206	1.29715	0.648575	−	0.761151i	$-0.275365\pi$
$193$	18.0206	1.29715	0.648575	+	0.761151i	$0.275365\pi$
$194$	−38.6282	−2.77334
$195$	−12.6307	−0.904500
$196$	0	0
$197$	−3.39251	−0.241706	−0.120853	−	0.992670i	$-0.538563\pi$
$197$	−3.39251	−0.241706	−0.120853	+	0.992670i	$0.538563\pi$
$198$	7.52492	0.534773
$199$	0.110913	0.00786243	0.00393121	−	0.999992i	$-0.498749\pi$
$199$	0.110913	0.00786243	0.00393121	+	0.999992i	$0.498749\pi$
$200$	4.08821	0.289080
$201$	−3.36328	−0.237228
$202$	−24.7888	−1.74414
$203$	0	0
$204$	−17.9722	−1.25830
$205$	−15.6059	−1.08996
$206$	9.53277	0.664180
$207$	−5.81981	−0.404505
$208$	0.544293	0.0377399
$209$	−3.29628	−0.228009
$210$	0	0
$211$	11.6596	0.802681	0.401340	−	0.915929i	$-0.368544\pi$
$211$	11.6596	0.802681	0.401340	+	0.915929i	$0.368544\pi$
$212$	−29.4300	−2.02126
$213$	−2.01667	−0.138180
$214$	−8.32662	−0.569196
$215$	11.7803	0.803410
$216$	−2.76546	−0.188166
$217$	0	0
$218$	32.3519	2.19115
$219$	4.72568	0.319332
$220$	−26.9433	−1.81652
$221$	−27.7716	−1.86812
$222$	−17.5791	−1.17983
$223$	13.8313	0.926214	0.463107	−	0.886302i	$-0.346735\pi$
$223$	13.8313	0.926214	0.463107	+	0.886302i	$0.346735\pi$
$224$	0	0
$225$	1.47831	0.0985541
$226$	−21.0196	−1.39820
$227$	13.7904	0.915299	0.457650	−	0.889133i	$-0.348691\pi$
$227$	13.7904	0.915299	0.457650	+	0.889133i	$0.348691\pi$
$228$	3.21141	0.212681
$229$	13.9644	0.922797	0.461398	−	0.887193i	$-0.347348\pi$
$229$	13.9644	0.922797	0.461398	+	0.887193i	$0.347348\pi$
$230$	33.8156	2.22973
$231$	0	0
$232$	−25.7976	−1.69369
$233$	−16.9838	−1.11264	−0.556322	−	0.830967i	$-0.687788\pi$
$233$	−16.9838	−1.11264	−0.556322	+	0.830967i	$0.687788\pi$
$234$	−11.3285	−0.740567
$235$	16.0717	1.04840
$236$	31.5074	2.05096
$237$	12.8985	0.837850
$238$	0	0
$239$	2.74352	0.177463	0.0887317	−	0.996056i	$-0.471719\pi$
$239$	2.74352	0.177463	0.0887317	+	0.996056i	$0.471719\pi$
$240$	−0.279170	−0.0180204
$241$	9.93214	0.639786	0.319893	−	0.947454i	$-0.396353\pi$
$241$	9.93214	0.639786	0.319893	+	0.947454i	$0.396353\pi$
$242$	−0.307113	−0.0197420
$243$	−1.00000	−0.0641500
$244$	−5.83157	−0.373328
$245$	0	0
$246$	−13.9970	−0.892415
$247$	4.96243	0.315752
$248$	−17.7628	−1.12794
$249$	0.743338	0.0471071
$250$	20.4625	1.29416
$251$	0.0936224	0.00590940	0.00295470	−	0.999996i	$-0.499059\pi$
$251$	0.0936224	0.00590940	0.00295470	+	0.999996i	$0.499059\pi$
$252$	0	0
$253$	−19.1837	−1.20607
$254$	−12.0264	−0.754603
$255$	14.2442	0.892004
$256$	−15.2835	−0.955219
$257$	10.6649	0.665260	0.332630	−	0.943057i	$-0.392064\pi$
$257$	10.6649	0.665260	0.332630	+	0.943057i	$0.392064\pi$
$258$	10.5658	0.657799
$259$	0	0
$260$	40.5621	2.51556
$261$	−9.32850	−0.577419
$262$	−18.1175	−1.11930
$263$	2.71193	0.167225	0.0836124	−	0.996498i	$-0.473354\pi$
$263$	2.71193	0.167225	0.0836124	+	0.996498i	$0.473354\pi$
$264$	−9.11573	−0.561034
$265$	23.3252	1.43286
$266$	0	0
$267$	11.4048	0.697965
$268$	10.8009	0.659768
$269$	−0.765987	−0.0467030	−0.0233515	−	0.999727i	$-0.507434\pi$
$269$	−0.765987	−0.0467030	−0.0233515	+	0.999727i	$0.507434\pi$
$270$	5.81043	0.353612
$271$	5.61998	0.341389	0.170695	−	0.985324i	$-0.445399\pi$
$271$	5.61998	0.341389	0.170695	+	0.985324i	$0.445399\pi$
$272$	−0.613824	−0.0372186
$273$	0	0
$274$	18.7114	1.13040
$275$	4.87293	0.293849
$276$	18.6898	1.12499
$277$	−28.3556	−1.70373	−0.851863	−	0.523765i	$-0.824527\pi$
$277$	−28.3556	−1.70373	−0.851863	+	0.523765i	$0.824527\pi$
$278$	21.0218	1.26081
$279$	−6.42307	−0.384539
$280$	0	0
$281$	−30.7742	−1.83583	−0.917916	−	0.396774i	$-0.870130\pi$
$281$	−30.7742	−1.83583	−0.917916	+	0.396774i	$0.870130\pi$
$282$	14.4148	0.858390
$283$	−15.4003	−0.915452	−0.457726	−	0.889093i	$-0.651336\pi$
$283$	−15.4003	−0.915452	−0.457726	+	0.889093i	$0.651336\pi$
$284$	6.47635	0.384301
$285$	−2.54525	−0.150768
$286$	−37.3419	−2.20807
$287$	0	0
$288$	−5.78131	−0.340667
$289$	14.3193	0.842309
$290$	54.2026	3.18289
$291$	16.9210	0.991928
$292$	−15.1761	−0.888113
$293$	−3.63257	−0.212217	−0.106109	−	0.994355i	$-0.533839\pi$
$293$	−3.63257	−0.212217	−0.106109	+	0.994355i	$0.533839\pi$
$294$	0	0
$295$	−24.9717	−1.45391
$296$	21.2954	1.23777
$297$	−3.29628	−0.191270
$298$	10.9469	0.634138
$299$	28.8804	1.67020
$300$	−4.74746	−0.274095
$301$	0	0
$302$	17.4885	1.00635
$303$	10.8587	0.623817
$304$	0.109683	0.00629074
$305$	4.62191	0.264650
$306$	12.7757	0.730336
$307$	20.4805	1.16888	0.584442	−	0.811436i	$-0.301314\pi$
$307$	20.4805	1.16888	0.584442	+	0.811436i	$0.301314\pi$
$308$	0	0
$309$	−4.17582	−0.237554
$310$	37.3208	2.11968
$311$	−22.8687	−1.29676	−0.648382	−	0.761315i	$-0.724554\pi$
$311$	−22.8687	−1.29676	−0.648382	+	0.761315i	$0.724554\pi$
$312$	13.7234	0.776935
$313$	−21.4524	−1.21256	−0.606279	−	0.795252i	$-0.707339\pi$
$313$	−21.4524	−1.21256	−0.606279	+	0.795252i	$0.707339\pi$
$314$	−11.2683	−0.635906
$315$	0	0
$316$	−41.4224	−2.33019
$317$	22.6472	1.27199	0.635996	−	0.771692i	$-0.280589\pi$
$317$	22.6472	1.27199	0.635996	+	0.771692i	$0.280589\pi$
$318$	20.9205	1.17316
$319$	−30.7493	−1.72163
$320$	33.0336	1.84663
$321$	3.64747	0.203582
$322$	0	0
$323$	−5.59636	−0.311390
$324$	3.21141	0.178411
$325$	−7.33603	−0.406930
$326$	5.82379	0.322550
$327$	−14.1717	−0.783697
$328$	16.9560	0.936240
$329$	0	0
$330$	19.1528	1.05433
$331$	28.7069	1.57787	0.788937	−	0.614474i	$-0.210632\pi$
$331$	28.7069	1.57787	0.788937	+	0.614474i	$0.210632\pi$
$332$	−2.38716	−0.131012
$333$	7.70048	0.421984
$334$	−4.44485	−0.243211
$335$	−8.56041	−0.467705
$336$	0	0
$337$	27.9822	1.52428	0.762142	−	0.647409i	$-0.224148\pi$
$337$	27.9822	1.52428	0.762142	+	0.647409i	$0.224148\pi$
$338$	26.5399	1.44358
$339$	9.20761	0.500089
$340$	−45.7438	−2.48080
$341$	−21.1723	−1.14654
$342$	−2.28285	−0.123442
$343$	0	0
$344$	−12.7995	−0.690103
$345$	−14.8129	−0.797499
$346$	34.4012	1.84942
$347$	18.1162	0.972531	0.486265	−	0.873811i	$-0.338359\pi$
$347$	18.1162	0.972531	0.486265	+	0.873811i	$0.338359\pi$
$348$	29.9576	1.60590
$349$	−16.1254	−0.863170	−0.431585	−	0.902072i	$-0.642046\pi$
$349$	−16.1254	−0.863170	−0.431585	+	0.902072i	$0.642046\pi$
$350$	0	0
$351$	4.96243	0.264875
$352$	−19.0568	−1.01573
$353$	−19.0378	−1.01328	−0.506641	−	0.862157i	$-0.669113\pi$
$353$	−19.0378	−1.01328	−0.506641	+	0.862157i	$0.669113\pi$
$354$	−22.3973	−1.19040
$355$	−5.13294	−0.272428
$356$	−36.6256	−1.94115
$357$	0	0
$358$	53.3211	2.81811
$359$	−5.17164	−0.272948	−0.136474	−	0.990644i	$-0.543577\pi$
$359$	−5.17164	−0.272948	−0.136474	+	0.990644i	$0.543577\pi$
$360$	−7.03879	−0.370977
$361$	1.00000	0.0526316
$362$	49.8299	2.61900
$363$	0.134531	0.00706102
$364$	0	0
$365$	12.0281	0.629577
$366$	4.14542	0.216684
$367$	5.62784	0.293771	0.146886	−	0.989153i	$-0.453075\pi$
$367$	5.62784	0.293771	0.146886	+	0.989153i	$0.453075\pi$
$368$	0.638332	0.0332754
$369$	6.13136	0.319186
$370$	−44.7431	−2.32609
$371$	0	0
$372$	20.6271	1.06947
$373$	3.59456	0.186119	0.0930596	−	0.995661i	$-0.470335\pi$
$373$	3.59456	0.186119	0.0930596	+	0.995661i	$0.470335\pi$
$374$	42.1122	2.17757
$375$	−8.96359	−0.462878
$376$	−17.4622	−0.900544
$377$	46.2920	2.38416
$378$	0	0
$379$	8.82165	0.453138	0.226569	−	0.973995i	$-0.427249\pi$
$379$	8.82165	0.453138	0.226569	+	0.973995i	$0.427249\pi$
$380$	8.17384	0.419309
$381$	5.26815	0.269895
$382$	−24.5066	−1.25387
$383$	−31.3248	−1.60062	−0.800311	−	0.599586i	$-0.795332\pi$
$383$	−31.3248	−1.60062	−0.800311	+	0.599586i	$0.795332\pi$
$384$	18.0653	0.921893
$385$	0	0
$386$	41.1383	2.09388
$387$	−4.62835	−0.235272
$388$	−54.3403	−2.75871
$389$	−0.245826	−0.0124639	−0.00623193	−	0.999981i	$-0.501984\pi$
$389$	−0.245826	−0.0124639	−0.00623193	+	0.999981i	$0.501984\pi$
$390$	−28.8339	−1.46006
$391$	−32.5697	−1.64712
$392$	0	0
$393$	7.93634	0.400336
$394$	−7.74458	−0.390166
$395$	32.8300	1.65186
$396$	10.5857	0.531951
$397$	−1.79530	−0.0901037	−0.0450519	−	0.998985i	$-0.514345\pi$
$397$	−1.79530	−0.0901037	−0.0450519	+	0.998985i	$0.514345\pi$
$398$	0.253198	0.0126917
$399$	0	0
$400$	−0.162145	−0.00810726
$401$	−24.5023	−1.22359	−0.611793	−	0.791018i	$-0.709552\pi$
$401$	−24.5023	−1.22359	−0.611793	+	0.791018i	$0.709552\pi$
$402$	−7.67788	−0.382938
$403$	31.8741	1.58776
$404$	−34.8718	−1.73493
$405$	−2.54525	−0.126475
$406$	0	0
$407$	25.3830	1.25819
$408$	−15.4765	−0.766201
$409$	27.1049	1.34025	0.670125	−	0.742248i	$-0.266240\pi$
$409$	27.1049	1.34025	0.670125	+	0.742248i	$0.266240\pi$
$410$	−35.6259	−1.75944
$411$	−8.19651	−0.404304
$412$	13.4103	0.660676
$413$	0	0
$414$	−13.2858	−0.652959
$415$	1.89198	0.0928738
$416$	28.6894	1.40661
$417$	−9.20860	−0.450947
$418$	−7.52492	−0.368056
$419$	−24.5949	−1.20154	−0.600771	−	0.799421i	$-0.705140\pi$
$419$	−24.5949	−1.20154	−0.600771	+	0.799421i	$0.705140\pi$
$420$	0	0
$421$	17.1191	0.834334	0.417167	−	0.908830i	$-0.363023\pi$
$421$	17.1191	0.834334	0.417167	+	0.908830i	$0.363023\pi$
$422$	26.6171	1.29570
$423$	−6.31439	−0.307016
$424$	−25.3432	−1.23078
$425$	8.27317	0.401308
$426$	−4.60376	−0.223053
$427$	0	0
$428$	−11.7135	−0.566193
$429$	16.3576	0.789751
$430$	26.8927	1.29688
$431$	−19.6284	−0.945467	−0.472733	−	0.881206i	$-0.656733\pi$
$431$	−19.6284	−0.945467	−0.472733	+	0.881206i	$0.656733\pi$
$432$	0.109683	0.00527711
$433$	30.0095	1.44216	0.721082	−	0.692850i	$-0.243645\pi$
$433$	30.0095	1.44216	0.721082	+	0.692850i	$0.243645\pi$
$434$	0	0
$435$	−23.7434	−1.13841
$436$	45.5111	2.17959
$437$	5.81981	0.278399
$438$	10.7880	0.515472
$439$	−11.6440	−0.555739	−0.277869	−	0.960619i	$-0.589628\pi$
$439$	−11.6440	−0.555739	−0.277869	+	0.960619i	$0.589628\pi$
$440$	−23.2018	−1.10610
$441$	0	0
$442$	−63.3984	−3.01555
$443$	−19.3379	−0.918771	−0.459386	−	0.888237i	$-0.651930\pi$
$443$	−19.3379	−0.918771	−0.459386	+	0.888237i	$0.651930\pi$
$444$	−24.7294	−1.17360
$445$	29.0282	1.37607
$446$	31.5749	1.49511
$447$	−4.79529	−0.226809
$448$	0	0
$449$	−34.8975	−1.64692	−0.823458	−	0.567377i	$-0.807958\pi$
$449$	−34.8975	−1.64692	−0.823458	+	0.567377i	$0.807958\pi$
$450$	3.37477	0.159088
$451$	20.2107	0.951684
$452$	−29.5694	−1.39083
$453$	−7.66081	−0.359936
$454$	31.4814	1.47749
$455$	0	0
$456$	2.76546	0.129504
$457$	−3.11205	−0.145576	−0.0727878	−	0.997347i	$-0.523190\pi$
$457$	−3.11205	−0.145576	−0.0727878	+	0.997347i	$0.523190\pi$
$458$	31.8787	1.48960
$459$	−5.59636	−0.261216
$460$	47.5702	2.21797
$461$	21.6573	1.00868	0.504341	−	0.863505i	$-0.331736\pi$
$461$	21.6573	1.00868	0.504341	+	0.863505i	$0.331736\pi$
$462$	0	0
$463$	−27.4240	−1.27450	−0.637252	−	0.770656i	$-0.719929\pi$
$463$	−27.4240	−1.27450	−0.637252	+	0.770656i	$0.719929\pi$
$464$	1.02317	0.0474997
$465$	−16.3483	−0.758137
$466$	−38.7714	−1.79605
$467$	−27.2546	−1.26119	−0.630595	−	0.776112i	$-0.717189\pi$
$467$	−27.2546	−1.26119	−0.630595	+	0.776112i	$0.717189\pi$
$468$	−15.9364	−0.736660
$469$	0	0
$470$	36.6893	1.69235
$471$	4.93606	0.227442
$472$	27.1322	1.24886
$473$	−15.2563	−0.701487
$474$	29.4454	1.35247
$475$	−1.47831	−0.0678296
$476$	0	0
$477$	−9.16420	−0.419600
$478$	6.26304	0.286465
$479$	−35.5989	−1.62655	−0.813277	−	0.581877i	$-0.802318\pi$
$479$	−35.5989	−1.62655	−0.813277	+	0.581877i	$0.802318\pi$
$480$	−14.7149	−0.671640
$481$	−38.2132	−1.74237
$482$	22.6736	1.03275
$483$	0	0
$484$	−0.432032	−0.0196378
$485$	43.0683	1.95563
$486$	−2.28285	−0.103552
$487$	21.5604	0.976996	0.488498	−	0.872565i	$-0.337545\pi$
$487$	21.5604	0.976996	0.488498	+	0.872565i	$0.337545\pi$
$488$	−5.02178	−0.227325
$489$	−2.55111	−0.115365
$490$	0	0
$491$	4.06065	0.183255	0.0916273	−	0.995793i	$-0.470793\pi$
$491$	4.06065	0.183255	0.0916273	+	0.995793i	$0.470793\pi$
$492$	−19.6903	−0.887707
$493$	−52.2056	−2.35122
$494$	11.3285	0.509693
$495$	−8.38987	−0.377097
$496$	0.704500	0.0316330
$497$	0	0
$498$	1.69693	0.0760412
$499$	−13.6822	−0.612498	−0.306249	−	0.951951i	$-0.599074\pi$
$499$	−13.6822	−0.612498	−0.306249	+	0.951951i	$0.599074\pi$
$500$	28.7857	1.28734
$501$	1.94706	0.0869882
$502$	0.213726	0.00953906
$503$	16.8353	0.750650	0.375325	−	0.926893i	$-0.377531\pi$
$503$	16.8353	0.750650	0.375325	+	0.926893i	$0.377531\pi$
$504$	0	0
$505$	27.6382	1.22988
$506$	−43.7936	−1.94686
$507$	−11.6258	−0.516318
$508$	−16.9182	−0.750622
$509$	4.18134	0.185335	0.0926673	−	0.995697i	$-0.470461\pi$
$509$	4.18134	0.185335	0.0926673	+	0.995697i	$0.470461\pi$
$510$	32.5173	1.43989
$511$	0	0
$512$	1.24076	0.0548342
$513$	1.00000	0.0441511
$514$	24.3464	1.07387
$515$	−10.6285	−0.468348
$516$	14.8635	0.654329
$517$	−20.8140	−0.915399
$518$	0	0
$519$	−15.0694	−0.661474
$520$	34.9295	1.53176
$521$	−12.7717	−0.559538	−0.279769	−	0.960067i	$-0.590258\pi$
$521$	−12.7717	−0.559538	−0.279769	+	0.960067i	$0.590258\pi$
$522$	−21.2956	−0.932081
$523$	−25.9317	−1.13391	−0.566957	−	0.823747i	$-0.691880\pi$
$523$	−25.9317	−1.13391	−0.566957	+	0.823747i	$0.691880\pi$
$524$	−25.4868	−1.11340
$525$	0	0
$526$	6.19093	0.269937
$527$	−35.9458	−1.56583
$528$	0.361545	0.0157342
$529$	10.8702	0.472616
$530$	53.2480	2.31294
$531$	9.81110	0.425766
$532$	0	0
$533$	−30.4265	−1.31792
$534$	26.0355	1.12667
$535$	9.28372	0.401370
$536$	9.30103	0.401743
$537$	−23.3572	−1.00794
$538$	−1.74863	−0.0753889
$539$	0	0
$540$	8.17384	0.351746
$541$	−22.8312	−0.981590	−0.490795	−	0.871275i	$-0.663294\pi$
$541$	−22.8312	−0.981590	−0.490795	+	0.871275i	$0.663294\pi$
$542$	12.8296	0.551077
$543$	−21.8279	−0.936725
$544$	−32.3543	−1.38718
$545$	−36.0706	−1.54509
$546$	0	0
$547$	−21.0599	−0.900455	−0.450227	−	0.892914i	$-0.648657\pi$
$547$	−21.0599	−0.900455	−0.450227	+	0.892914i	$0.648657\pi$
$548$	26.3223	1.12443
$549$	−1.81589	−0.0775005
$550$	11.1242	0.474336
$551$	9.32850	0.397407
$552$	16.0944	0.685025
$553$	0	0
$554$	−64.7317	−2.75019
$555$	19.5997	0.831960
$556$	29.5725	1.25416
$557$	43.5536	1.84543	0.922713	−	0.385488i	$-0.125967\pi$
$557$	43.5536	1.84543	0.922713	+	0.385488i	$0.125967\pi$
$558$	−14.6629	−0.620731
$559$	22.9679	0.971437
$560$	0	0
$561$	−18.4472	−0.778841
$562$	−70.2528	−2.96344
$563$	−21.5381	−0.907724	−0.453862	−	0.891072i	$-0.649954\pi$
$563$	−21.5381	−0.907724	−0.453862	+	0.891072i	$0.649954\pi$
$564$	20.2781	0.853861
$565$	23.4357	0.985947
$566$	−35.1566	−1.47774
$567$	0	0
$568$	5.57702	0.234007
$569$	13.8224	0.579464	0.289732	−	0.957108i	$-0.406434\pi$
$569$	13.8224	0.579464	0.289732	+	0.957108i	$0.406434\pi$
$570$	−5.81043	−0.243372
$571$	−6.37170	−0.266647	−0.133324	−	0.991073i	$-0.542565\pi$
$571$	−6.37170	−0.266647	−0.133324	+	0.991073i	$0.542565\pi$
$572$	−52.5308	−2.19642
$573$	10.7351	0.448464
$574$	0	0
$575$	−8.60349	−0.358790
$576$	−12.9785	−0.540771
$577$	18.3947	0.765780	0.382890	−	0.923794i	$-0.374929\pi$
$577$	18.3947	0.765780	0.382890	+	0.923794i	$0.374929\pi$
$578$	32.6887	1.35967
$579$	−18.0206	−0.748909
$580$	76.2496	3.16609
$581$	0	0
$582$	38.6282	1.60119
$583$	−30.2078	−1.25108
$584$	−13.0687	−0.540786
$585$	12.6307	0.522213
$586$	−8.29262	−0.342565
$587$	−28.7021	−1.18466	−0.592331	−	0.805695i	$-0.701792\pi$
$587$	−28.7021	−1.18466	−0.592331	+	0.805695i	$0.701792\pi$
$588$	0	0
$589$	6.42307	0.264658
$590$	−57.0068	−2.34693
$591$	3.39251	0.139549
$592$	−0.844610	−0.0347133
$593$	32.6544	1.34096	0.670478	−	0.741930i	$-0.266089\pi$
$593$	32.6544	1.34096	0.670478	+	0.741930i	$0.266089\pi$
$594$	−7.52492	−0.308751
$595$	0	0
$596$	15.3996	0.630793
$597$	−0.110913	−0.00453937
$598$	65.9297	2.69606
$599$	9.27154	0.378825	0.189412	−	0.981898i	$-0.439342\pi$
$599$	9.27154	0.378825	0.189412	+	0.981898i	$0.439342\pi$
$600$	−4.08821	−0.166901
$601$	6.44868	0.263047	0.131524	−	0.991313i	$-0.458013\pi$
$601$	6.44868	0.263047	0.131524	+	0.991313i	$0.458013\pi$
$602$	0	0
$603$	3.36328	0.136964
$604$	24.6020	1.00104
$605$	0.342414	0.0139211
$606$	24.7888	1.00698
$607$	−9.77185	−0.396627	−0.198314	−	0.980139i	$-0.563546\pi$
$607$	−9.77185	−0.396627	−0.198314	+	0.980139i	$0.563546\pi$
$608$	5.78131	0.234463
$609$	0	0
$610$	10.5511	0.427203
$611$	31.3348	1.26767
$612$	17.9722	0.726483
$613$	−44.6639	−1.80396	−0.901979	−	0.431781i	$-0.857885\pi$
$613$	−44.6639	−1.80396	−0.901979	+	0.431781i	$0.857885\pi$
$614$	46.7539	1.88683
$615$	15.6059	0.629289
$616$	0	0
$617$	−25.1695	−1.01329	−0.506643	−	0.862156i	$-0.669114\pi$
$617$	−25.1695	−1.01329	−0.506643	+	0.862156i	$0.669114\pi$
$618$	−9.53277	−0.383464
$619$	−39.4836	−1.58698	−0.793490	−	0.608583i	$-0.791738\pi$
$619$	−39.4836	−1.58698	−0.793490	+	0.608583i	$0.791738\pi$
$620$	52.5012	2.10850
$621$	5.81981	0.233541
$622$	−52.2058	−2.09326
$623$	0	0
$624$	−0.544293	−0.0217892
$625$	−30.2062	−1.20825
$626$	−48.9725	−1.95734
$627$	3.29628	0.131641
$628$	−15.8517	−0.632551
$629$	43.0947	1.71830
$630$	0	0
$631$	5.92164	0.235737	0.117868	−	0.993029i	$-0.462394\pi$
$631$	5.92164	0.235737	0.117868	+	0.993029i	$0.462394\pi$
$632$	−35.6704	−1.41889
$633$	−11.6596	−0.463428
$634$	51.7001	2.05327
$635$	13.4088	0.532110
$636$	29.4300	1.16697
$637$	0	0
$638$	−70.1962	−2.77909
$639$	2.01667	0.0797783
$640$	45.9809	1.81755
$641$	−15.1334	−0.597733	−0.298867	−	0.954295i	$-0.596609\pi$
$641$	−15.1334	−0.597733	−0.298867	+	0.954295i	$0.596609\pi$
$642$	8.32662	0.328625
$643$	14.5709	0.574619	0.287310	−	0.957838i	$-0.407239\pi$
$643$	14.5709	0.574619	0.287310	+	0.957838i	$0.407239\pi$
$644$	0	0
$645$	−11.7803	−0.463849
$646$	−12.7757	−0.502651
$647$	−2.91875	−0.114748	−0.0573739	−	0.998353i	$-0.518273\pi$
$647$	−2.91875	−0.114748	−0.0573739	+	0.998353i	$0.518273\pi$
$648$	2.76546	0.108637
$649$	32.3402	1.26946
$650$	−16.7471	−0.656873
$651$	0	0
$652$	8.19264	0.320848
$653$	−27.7398	−1.08554	−0.542770	−	0.839881i	$-0.682625\pi$
$653$	−27.7398	−1.08554	−0.542770	+	0.839881i	$0.682625\pi$
$654$	−32.3519	−1.26506
$655$	20.2000	0.789279
$656$	−0.672504	−0.0262569
$657$	−4.72568	−0.184366
$658$	0	0
$659$	14.7834	0.575880	0.287940	−	0.957648i	$-0.407030\pi$
$659$	14.7834	0.575880	0.287940	+	0.957648i	$0.407030\pi$
$660$	26.9433	1.04877
$661$	35.2532	1.37119	0.685596	−	0.727983i	$-0.259542\pi$
$661$	35.2532	1.37119	0.685596	+	0.727983i	$0.259542\pi$
$662$	65.5335	2.54703
$663$	27.7716	1.07856
$664$	−2.05567	−0.0797755
$665$	0	0
$666$	17.5791	0.681175
$667$	54.2901	2.10212
$668$	−6.25280	−0.241928
$669$	−13.8313	−0.534750
$670$	−19.5421	−0.754979
$671$	−5.98570	−0.231075
$672$	0	0
$673$	−22.4607	−0.865796	−0.432898	−	0.901443i	$-0.642509\pi$
$673$	−22.4607	−0.865796	−0.432898	+	0.901443i	$0.642509\pi$
$674$	63.8791	2.46053
$675$	−1.47831	−0.0569003
$676$	37.3350	1.43596
$677$	−9.28643	−0.356906	−0.178453	−	0.983948i	$-0.557109\pi$
$677$	−9.28643	−0.356906	−0.178453	+	0.983948i	$0.557109\pi$
$678$	21.0196	0.807253
$679$	0	0
$680$	−39.3916	−1.51060
$681$	−13.7904	−0.528448
$682$	−48.3331	−1.85077
$683$	19.2391	0.736162	0.368081	−	0.929794i	$-0.380015\pi$
$683$	19.2391	0.736162	0.368081	+	0.929794i	$0.380015\pi$
$684$	−3.21141	−0.122791
$685$	−20.8622	−0.797103
$686$	0	0
$687$	−13.9644	−0.532777
$688$	0.507649	0.0193540
$689$	45.4767	1.73253
$690$	−33.8156	−1.28734
$691$	23.0706	0.877646	0.438823	−	0.898573i	$-0.355395\pi$
$691$	23.0706	0.877646	0.438823	+	0.898573i	$0.355395\pi$
$692$	48.3940	1.83967
$693$	0	0
$694$	41.3567	1.56988
$695$	−23.4382	−0.889062
$696$	25.7976	0.977855
$697$	34.3133	1.29971
$698$	−36.8118	−1.39335
$699$	16.9838	0.642385
$700$	0	0
$701$	−18.6485	−0.704344	−0.352172	−	0.935935i	$-0.614557\pi$
$701$	−18.6485	−0.704344	−0.352172	+	0.935935i	$0.614557\pi$
$702$	11.3285	0.427567
$703$	−7.70048	−0.290429
$704$	−42.7808	−1.61236
$705$	−16.0717	−0.605296
$706$	−43.4605	−1.63566
$707$	0	0
$708$	−31.5074	−1.18412
$709$	44.5115	1.67166	0.835832	−	0.548986i	$-0.184986\pi$
$709$	44.5115	1.67166	0.835832	+	0.548986i	$0.184986\pi$
$710$	−11.7177	−0.439759
$711$	−12.8985	−0.483733
$712$	−31.5396	−1.18200
$713$	37.3811	1.39993
$714$	0	0
$715$	41.6342	1.55703
$716$	75.0096	2.80324
$717$	−2.74352	−0.102459
$718$	−11.8061	−0.440599
$719$	23.7966	0.887465	0.443733	−	0.896159i	$-0.353654\pi$
$719$	23.7966	0.887465	0.443733	+	0.896159i	$0.353654\pi$
$720$	0.279170	0.0104041
$721$	0	0
$722$	2.28285	0.0849589
$723$	−9.93214	−0.369380
$724$	70.0983	2.60518
$725$	−13.7904	−0.512164
$726$	0.307113	0.0113980
$727$	−28.5209	−1.05778	−0.528891	−	0.848689i	$-0.677392\pi$
$727$	−28.5209	−1.05778	−0.528891	+	0.848689i	$0.677392\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	27.4582	1.01628
$731$	−25.9019	−0.958016
$732$	5.83157	0.215541
$733$	−16.2788	−0.601270	−0.300635	−	0.953739i	$-0.597199\pi$
$733$	−16.2788	−0.601270	−0.300635	+	0.953739i	$0.597199\pi$
$734$	12.8475	0.474211
$735$	0	0
$736$	33.6461	1.24021
$737$	11.0863	0.408370
$738$	13.9970	0.515236
$739$	52.4917	1.93094	0.965470	−	0.260516i	$-0.0838927\pi$
$739$	52.4917	1.93094	0.965470	+	0.260516i	$0.0838927\pi$
$740$	−62.9425	−2.31381
$741$	−4.96243	−0.182300
$742$	0	0
$743$	−31.9433	−1.17189	−0.585944	−	0.810352i	$-0.699276\pi$
$743$	−31.9433	−1.17189	−0.585944	+	0.810352i	$0.699276\pi$
$744$	17.7628	0.651214
$745$	−12.2052	−0.447165
$746$	8.20584	0.300437
$747$	−0.743338	−0.0271973
$748$	59.2414	2.16608
$749$	0	0
$750$	−20.4625	−0.747186
$751$	−6.80983	−0.248494	−0.124247	−	0.992251i	$-0.539652\pi$
$751$	−6.80983	−0.248494	−0.124247	+	0.992251i	$0.539652\pi$
$752$	0.692580	0.0252558
$753$	−0.0936224	−0.00341179
$754$	105.678	3.84856
$755$	−19.4987	−0.709630
$756$	0	0
$757$	9.00239	0.327198	0.163599	−	0.986527i	$-0.447690\pi$
$757$	9.00239	0.327198	0.163599	+	0.986527i	$0.447690\pi$
$758$	20.1385	0.731464
$759$	19.1837	0.696325
$760$	7.03879	0.255324
$761$	5.17963	0.187762	0.0938808	−	0.995583i	$-0.470073\pi$
$761$	5.17963	0.187762	0.0938808	+	0.995583i	$0.470073\pi$
$762$	12.0264	0.435670
$763$	0	0
$764$	−34.4747	−1.24725
$765$	−14.2442	−0.514998
$766$	−71.5098	−2.58375
$767$	−48.6870	−1.75798
$768$	15.2835	0.551496
$769$	41.5253	1.49744	0.748720	−	0.662886i	$-0.230669\pi$
$769$	41.5253	1.49744	0.748720	+	0.662886i	$0.230669\pi$
$770$	0	0
$771$	−10.6649	−0.384088
$772$	57.8714	2.08284
$773$	−2.83802	−0.102076	−0.0510382	−	0.998697i	$-0.516253\pi$
$773$	−2.83802	−0.102076	−0.0510382	+	0.998697i	$0.516253\pi$
$774$	−10.5658	−0.379781
$775$	−9.49531	−0.341082
$776$	−46.7944	−1.67982
$777$	0	0
$778$	−0.561183	−0.0201194
$779$	−6.13136	−0.219679
$780$	−40.5621	−1.45236
$781$	6.64752	0.237867
$782$	−74.3519	−2.65882
$783$	9.32850	0.333373
$784$	0	0
$785$	12.5635	0.448411
$786$	18.1175	0.646229
$787$	−41.4975	−1.47923	−0.739614	−	0.673032i	$-0.764992\pi$
$787$	−41.4975	−1.47923	−0.739614	+	0.673032i	$0.764992\pi$
$788$	−10.8947	−0.388108
$789$	−2.71193	−0.0965472
$790$	74.9461	2.66646
$791$	0	0
$792$	9.11573	0.323913
$793$	9.01126	0.319999
$794$	−4.09841	−0.145447
$795$	−23.3252	−0.827260
$796$	0.356187	0.0126247
$797$	−34.7178	−1.22977	−0.614884	−	0.788618i	$-0.710797\pi$
$797$	−34.7178	−1.22977	−0.614884	+	0.788618i	$0.710797\pi$
$798$	0	0
$799$	−35.3376	−1.25016
$800$	−8.54658	−0.302167
$801$	−11.4048	−0.402970
$802$	−55.9351	−1.97514
$803$	−15.5772	−0.549706
$804$	−10.8009	−0.380917
$805$	0	0
$806$	72.7638	2.56299
$807$	0.765987	0.0269640
$808$	−30.0293	−1.05643
$809$	−36.8670	−1.29617	−0.648087	−	0.761566i	$-0.724431\pi$
$809$	−36.8670	−1.29617	−0.648087	+	0.761566i	$0.724431\pi$
$810$	−5.81043	−0.204158
$811$	−45.4803	−1.59703	−0.798515	−	0.601974i	$-0.794381\pi$
$811$	−45.4803	−1.59703	−0.798515	+	0.601974i	$0.794381\pi$
$812$	0	0
$813$	−5.61998	−0.197101
$814$	57.9455	2.03099
$815$	−6.49321	−0.227447
$816$	0.613824	0.0214881
$817$	4.62835	0.161925
$818$	61.8764	2.16346
$819$	0	0
$820$	−50.1168	−1.75015
$821$	25.5522	0.891776	0.445888	−	0.895089i	$-0.352888\pi$
$821$	25.5522	0.891776	0.445888	+	0.895089i	$0.352888\pi$
$822$	−18.7114	−0.652635
$823$	7.55183	0.263240	0.131620	−	0.991300i	$-0.457982\pi$
$823$	7.55183	0.263240	0.131620	+	0.991300i	$0.457982\pi$
$824$	11.5481	0.402296
$825$	−4.87293	−0.169654
$826$	0	0
$827$	−30.8901	−1.07415	−0.537077	−	0.843533i	$-0.680472\pi$
$827$	−30.8901	−1.07415	−0.537077	+	0.843533i	$0.680472\pi$
$828$	−18.6898	−0.649514
$829$	26.3786	0.916167	0.458084	−	0.888909i	$-0.348536\pi$
$829$	26.3786	0.916167	0.458084	+	0.888909i	$0.348536\pi$
$830$	4.31911	0.149919
$831$	28.3556	0.983647
$832$	64.4049	2.23284
$833$	0	0
$834$	−21.0218	−0.727927
$835$	4.95576	0.171501
$836$	−10.5857	−0.366114
$837$	6.42307	0.222014
$838$	−56.1466	−1.93955
$839$	−2.55457	−0.0881935	−0.0440968	−	0.999027i	$-0.514041\pi$
$839$	−2.55457	−0.0881935	−0.0440968	+	0.999027i	$0.514041\pi$
$840$	0	0
$841$	58.0208	2.00072
$842$	39.0803	1.34680
$843$	30.7742	1.05992
$844$	37.4437	1.28887
$845$	−29.5905	−1.01794
$846$	−14.4148	−0.495591
$847$	0	0
$848$	1.00515	0.0345171
$849$	15.4003	0.528537
$850$	18.8864	0.647798
$851$	−44.8153	−1.53625
$852$	−6.47635	−0.221876
$853$	−52.1083	−1.78416	−0.892078	−	0.451882i	$-0.850753\pi$
$853$	−52.1083	−1.78416	−0.892078	+	0.451882i	$0.850753\pi$
$854$	0	0
$855$	2.54525	0.0870458
$856$	−10.0869	−0.344764
$857$	−7.45507	−0.254660	−0.127330	−	0.991860i	$-0.540641\pi$
$857$	−7.45507	−0.254660	−0.127330	+	0.991860i	$0.540641\pi$
$858$	37.3419	1.27483
$859$	−29.9401	−1.02154	−0.510772	−	0.859716i	$-0.670640\pi$
$859$	−29.9401	−1.02154	−0.510772	+	0.859716i	$0.670640\pi$
$860$	37.8314	1.29004
$861$	0	0
$862$	−44.8087	−1.52619
$863$	−14.3896	−0.489828	−0.244914	−	0.969545i	$-0.578760\pi$
$863$	−14.3896	−0.489828	−0.244914	+	0.969545i	$0.578760\pi$
$864$	5.78131	0.196684
$865$	−38.3555	−1.30413
$866$	68.5071	2.32797
$867$	−14.3193	−0.486308
$868$	0	0
$869$	−42.5172	−1.44230
$870$	−54.2026	−1.83764
$871$	−16.6901	−0.565522
$872$	39.1913	1.32718
$873$	−16.9210	−0.572690
$874$	13.2858	0.449397
$875$	0	0
$876$	15.1761	0.512752
$877$	54.7996	1.85045	0.925226	−	0.379416i	$-0.123875\pi$
$877$	54.7996	1.85045	0.925226	+	0.379416i	$0.123875\pi$
$878$	−26.5816	−0.897084
$879$	3.63257	0.122524
$880$	0.920224	0.0310207
$881$	−20.3805	−0.686638	−0.343319	−	0.939219i	$-0.611551\pi$
$881$	−20.3805	−0.686638	−0.343319	+	0.939219i	$0.611551\pi$
$882$	0	0
$883$	−20.1615	−0.678488	−0.339244	−	0.940698i	$-0.610171\pi$
$883$	−20.1615	−0.678488	−0.339244	+	0.940698i	$0.610171\pi$
$884$	−89.1858	−2.99964
$885$	24.9717	0.839416
$886$	−44.1455	−1.48310
$887$	−45.0043	−1.51110	−0.755549	−	0.655092i	$-0.772630\pi$
$887$	−45.0043	−1.51110	−0.755549	+	0.655092i	$0.772630\pi$
$888$	−21.2954	−0.714626
$889$	0	0
$890$	66.2670	2.22128
$891$	3.29628	0.110430
$892$	44.4180	1.48723
$893$	6.31439	0.211303
$894$	−10.9469	−0.366120
$895$	−59.4501	−1.98720
$896$	0	0
$897$	−28.8804	−0.964289
$898$	−79.6659	−2.65848
$899$	59.9176	1.99836
$900$	4.74746	0.158249
$901$	−51.2862	−1.70859
$902$	46.1380	1.53623
$903$	0	0
$904$	−25.4633	−0.846895
$905$	−55.5575	−1.84680
$906$	−17.4885	−0.581016
$907$	−25.8676	−0.858919	−0.429459	−	0.903086i	$-0.641296\pi$
$907$	−25.8676	−0.858919	−0.429459	+	0.903086i	$0.641296\pi$
$908$	44.2865	1.46970
$909$	−10.8587	−0.360161
$910$	0	0
$911$	−8.50711	−0.281853	−0.140927	−	0.990020i	$-0.545008\pi$
$911$	−8.50711	−0.281853	−0.140927	+	0.990020i	$0.545008\pi$
$912$	−0.109683	−0.00363196
$913$	−2.45025	−0.0810915
$914$	−7.10435	−0.234991
$915$	−4.62191	−0.152796
$916$	44.8455	1.48174
$917$	0	0
$918$	−12.7757	−0.421659
$919$	27.7168	0.914292	0.457146	−	0.889392i	$-0.348872\pi$
$919$	27.7168	0.914292	0.457146	+	0.889392i	$0.348872\pi$
$920$	40.9644	1.35056
$921$	−20.4805	−0.674855
$922$	49.4404	1.62823
$923$	−10.0076	−0.329404
$924$	0	0
$925$	11.3837	0.374294
$926$	−62.6050	−2.05733
$927$	4.17582	0.137152
$928$	53.9309	1.77037
$929$	−19.6853	−0.645855	−0.322928	−	0.946424i	$-0.604667\pi$
$929$	−19.6853	−0.645855	−0.322928	+	0.946424i	$0.604667\pi$
$930$	−37.3208	−1.22380
$931$	0	0
$932$	−54.5418	−1.78658
$933$	22.8687	0.748687
$934$	−62.2181	−2.03584
$935$	−46.9527	−1.53552
$936$	−13.7234	−0.448564
$937$	39.0825	1.27677	0.638385	−	0.769717i	$-0.279603\pi$
$937$	39.0825	1.27677	0.638385	+	0.769717i	$0.279603\pi$
$938$	0	0
$939$	21.4524	0.700071
$940$	51.6128	1.68343
$941$	46.1337	1.50392	0.751958	−	0.659210i	$-0.229109\pi$
$941$	46.1337	1.50392	0.751958	+	0.659210i	$0.229109\pi$
$942$	11.2683	0.367140
$943$	−35.6833	−1.16201
$944$	−1.07611	−0.0350244
$945$	0	0
$946$	−34.8279	−1.13235
$947$	9.84967	0.320071	0.160036	−	0.987111i	$-0.448839\pi$
$947$	9.84967	0.320071	0.160036	+	0.987111i	$0.448839\pi$
$948$	41.4224	1.34534
$949$	23.4509	0.761248
$950$	−3.37477	−0.109492
$951$	−22.6472	−0.734385
$952$	0	0
$953$	23.5275	0.762131	0.381066	−	0.924548i	$-0.375557\pi$
$953$	23.5275	0.762131	0.381066	+	0.924548i	$0.375557\pi$
$954$	−20.9205	−0.677326
$955$	27.3235	0.884167
$956$	8.81055	0.284954
$957$	30.7493	0.993985
$958$	−81.2669	−2.62561
$959$	0	0
$960$	−33.0336	−1.06615
$961$	10.2559	0.330835
$962$	−87.2349	−2.81257
$963$	−3.64747	−0.117538
$964$	31.8961	1.02731
$965$	−45.8669	−1.47651
$966$	0	0
$967$	19.3664	0.622783	0.311391	−	0.950282i	$-0.399205\pi$
$967$	19.3664	0.622783	0.311391	+	0.950282i	$0.399205\pi$
$968$	−0.372039	−0.0119578
$969$	5.59636	0.179781
$970$	98.3184	3.15681
$971$	−39.1062	−1.25498	−0.627488	−	0.778626i	$-0.715917\pi$
$971$	−39.1062	−1.25498	−0.627488	+	0.778626i	$0.715917\pi$
$972$	−3.21141	−0.103006
$973$	0	0
$974$	49.2192	1.57709
$975$	7.33603	0.234941
$976$	0.199172	0.00637535
$977$	43.2545	1.38383	0.691917	−	0.721977i	$-0.256766\pi$
$977$	43.2545	1.38383	0.691917	+	0.721977i	$0.256766\pi$
$978$	−5.82379	−0.186224
$979$	−37.5935	−1.20149
$980$	0	0
$981$	14.1717	0.452468
$982$	9.26986	0.295813
$983$	−0.143918	−0.00459027	−0.00229513	−	0.999997i	$-0.500731\pi$
$983$	−0.143918	−0.00459027	−0.00229513	+	0.999997i	$0.500731\pi$
$984$	−16.9560	−0.540538
$985$	8.63478	0.275127
$986$	−119.178	−3.79539
$987$	0	0
$988$	15.9364	0.507004
$989$	26.9361	0.856518
$990$	−19.1528	−0.608716
$991$	12.6827	0.402880	0.201440	−	0.979501i	$-0.435438\pi$
$991$	12.6827	0.402880	0.201440	+	0.979501i	$0.435438\pi$
$992$	37.1338	1.17900
$993$	−28.7069	−0.910986
$994$	0	0
$995$	−0.282302	−0.00894958
$996$	2.38716	0.0756401
$997$	−22.3602	−0.708156	−0.354078	−	0.935216i	$-0.615205\pi$
$997$	−22.3602	−0.708156	−0.354078	+	0.935216i	$0.615205\pi$
$998$	−31.2343	−0.988706
$999$	−7.70048	−0.243633

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2793.2.a.bm.1.7		8
3.2	odd	2		8379.2.a.cr.1.2		8
7.2	even	3		399.2.j.g.172.2	yes	16
7.4	even	3		399.2.j.g.58.2	✓	16
7.6	odd	2		2793.2.a.bn.1.7		8
21.2	odd	6		1197.2.j.m.172.7		16
21.11	odd	6		1197.2.j.m.856.7		16
21.20	even	2		8379.2.a.cq.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
399.2.j.g.58.2	✓	16	7.4	even	3
399.2.j.g.172.2	yes	16	7.2	even	3
1197.2.j.m.172.7		16	21.2	odd	6
1197.2.j.m.856.7		16	21.11	odd	6
2793.2.a.bm.1.7		8	1.1	even	1	trivial
2793.2.a.bn.1.7		8	7.6	odd	2
8379.2.a.cq.1.2		8	21.20	even	2
8379.2.a.cr.1.2		8	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:	\( N \)	\(=\)	\( 2793 = 3 \cdot 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2793.a (trivial)

\(f(q)\)	\(=\)	\(q+2.28285 q^{2} -1.00000 q^{3} +3.21141 q^{4} -2.54525 q^{5} -2.28285 q^{6} +2.76546 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.28285 q^{2} -1.00000 q^{3} +3.21141 q^{4} -2.54525 q^{5} -2.28285 q^{6} +2.76546 q^{8} +1.00000 q^{9} -5.81043 q^{10} +3.29628 q^{11} -3.21141 q^{12} -4.96243 q^{13} +2.54525 q^{15} -0.109683 q^{16} +5.59636 q^{17} +2.28285 q^{18} -1.00000 q^{19} -8.17384 q^{20} +7.52492 q^{22} -5.81981 q^{23} -2.76546 q^{24} +1.47831 q^{25} -11.3285 q^{26} -1.00000 q^{27} -9.32850 q^{29} +5.81043 q^{30} -6.42307 q^{31} -5.78131 q^{32} -3.29628 q^{33} +12.7757 q^{34} +3.21141 q^{36} +7.70048 q^{37} -2.28285 q^{38} +4.96243 q^{39} -7.03879 q^{40} +6.13136 q^{41} -4.62835 q^{43} +10.5857 q^{44} -2.54525 q^{45} -13.2858 q^{46} -6.31439 q^{47} +0.109683 q^{48} +3.37477 q^{50} -5.59636 q^{51} -15.9364 q^{52} -9.16420 q^{53} -2.28285 q^{54} -8.38987 q^{55} +1.00000 q^{57} -21.2956 q^{58} +9.81110 q^{59} +8.17384 q^{60} -1.81589 q^{61} -14.6629 q^{62} -12.9785 q^{64} +12.6307 q^{65} -7.52492 q^{66} +3.36328 q^{67} +17.9722 q^{68} +5.81981 q^{69} +2.01667 q^{71} +2.76546 q^{72} -4.72568 q^{73} +17.5791 q^{74} -1.47831 q^{75} -3.21141 q^{76} +11.3285 q^{78} -12.8985 q^{79} +0.279170 q^{80} +1.00000 q^{81} +13.9970 q^{82} -0.743338 q^{83} -14.2442 q^{85} -10.5658 q^{86} +9.32850 q^{87} +9.11573 q^{88} -11.4048 q^{89} -5.81043 q^{90} -18.6898 q^{92} +6.42307 q^{93} -14.4148 q^{94} +2.54525 q^{95} +5.78131 q^{96} -16.9210 q^{97} +3.29628 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{3} + 10 q^{4} - 5 q^{5} - 3 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^3 + 10 * q^4 - 5 * q^5 - 3 * q^8 + 8 * q^9	\( 8 q - 8 q^{3} + 10 q^{4} - 5 q^{5} - 3 q^{8} + 8 q^{9} - 3 q^{10} - 7 q^{11} - 10 q^{12} - 6 q^{13} + 5 q^{15} + 10 q^{16} - 8 q^{19} - 16 q^{20} + 18 q^{22} - 9 q^{23} + 3 q^{24} + 15 q^{25} - 12 q^{26} - 8 q^{27} + 4 q^{29} + 3 q^{30} - 11 q^{31} - 26 q^{32} + 7 q^{33} - 16 q^{34} + 10 q^{36} + 17 q^{37} + 6 q^{39} - 3 q^{40} - 17 q^{41} + 8 q^{43} - 31 q^{44} - 5 q^{45} + q^{46} - 29 q^{47} - 10 q^{48} + 30 q^{50} - 25 q^{52} - 6 q^{53} - 21 q^{55} + 8 q^{57} - 37 q^{58} - 7 q^{59} + 16 q^{60} - 2 q^{61} - 39 q^{62} + 29 q^{64} - 13 q^{65} - 18 q^{66} + 13 q^{67} + 14 q^{68} + 9 q^{69} + 18 q^{71} - 3 q^{72} - 20 q^{73} - 26 q^{74} - 15 q^{75} - 10 q^{76} + 12 q^{78} - 3 q^{79} - 35 q^{80} + 8 q^{81} - 5 q^{82} - 36 q^{83} + 5 q^{85} - 51 q^{86} - 4 q^{87} + 53 q^{88} - q^{89} - 3 q^{90} + 15 q^{92} + 11 q^{93} - 30 q^{94} + 5 q^{95} + 26 q^{96} + 3 q^{97} - 7 q^{99}+O(q^{100}) \) 8 * q - 8 * q^3 + 10 * q^4 - 5 * q^5 - 3 * q^8 + 8 * q^9 - 3 * q^10 - 7 * q^11 - 10 * q^12 - 6 * q^13 + 5 * q^15 + 10 * q^16 - 8 * q^19 - 16 * q^20 + 18 * q^22 - 9 * q^23 + 3 * q^24 + 15 * q^25 - 12 * q^26 - 8 * q^27 + 4 * q^29 + 3 * q^30 - 11 * q^31 - 26 * q^32 + 7 * q^33 - 16 * q^34 + 10 * q^36 + 17 * q^37 + 6 * q^39 - 3 * q^40 - 17 * q^41 + 8 * q^43 - 31 * q^44 - 5 * q^45 + q^46 - 29 * q^47 - 10 * q^48 + 30 * q^50 - 25 * q^52 - 6 * q^53 - 21 * q^55 + 8 * q^57 - 37 * q^58 - 7 * q^59 + 16 * q^60 - 2 * q^61 - 39 * q^62 + 29 * q^64 - 13 * q^65 - 18 * q^66 + 13 * q^67 + 14 * q^68 + 9 * q^69 + 18 * q^71 - 3 * q^72 - 20 * q^73 - 26 * q^74 - 15 * q^75 - 10 * q^76 + 12 * q^78 - 3 * q^79 - 35 * q^80 + 8 * q^81 - 5 * q^82 - 36 * q^83 + 5 * q^85 - 51 * q^86 - 4 * q^87 + 53 * q^88 - q^89 - 3 * q^90 + 15 * q^92 + 11 * q^93 - 30 * q^94 + 5 * q^95 + 26 * q^96 + 3 * q^97 - 7 * q^99

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