LMFDB - Embedded newform 6027.2.a.bc.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6027,2,Mod(1,6027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6027, 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("6027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6027 = 3 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6027.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:	$48.1258372982$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.8.7457527933.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} - 6x^{6} + 23x^{5} - 4x^{4} - 27x^{3} + 8x^{2} + 8x + 1 $ x^8 - 3x^7 - 6x^6 + 23x^5 - 4x^4 - 27x^3 + 8x^2 + 8*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 861)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-2.52358$ of defining polynomial
Character	$\chi$	$=$	6027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.07710 q^{2} +1.00000 q^{3} +2.31436 q^{4} -2.30039 q^{5} +2.07710 q^{6} +0.652949 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.07710 q^{2} +1.00000 q^{3} +2.31436 q^{4} -2.30039 q^{5} +2.07710 q^{6} +0.652949 q^{8} +1.00000 q^{9} -4.77814 q^{10} -2.24173 q^{11} +2.31436 q^{12} +4.05386 q^{13} -2.30039 q^{15} -3.27247 q^{16} +1.22520 q^{17} +2.07710 q^{18} +4.41144 q^{19} -5.32392 q^{20} -4.65630 q^{22} +6.56124 q^{23} +0.652949 q^{24} +0.291790 q^{25} +8.42028 q^{26} +1.00000 q^{27} +3.41695 q^{29} -4.77814 q^{30} -1.07464 q^{31} -8.10315 q^{32} -2.24173 q^{33} +2.54488 q^{34} +2.31436 q^{36} -1.63983 q^{37} +9.16300 q^{38} +4.05386 q^{39} -1.50204 q^{40} +1.00000 q^{41} -4.67207 q^{43} -5.18815 q^{44} -2.30039 q^{45} +13.6284 q^{46} +10.9409 q^{47} -3.27247 q^{48} +0.606078 q^{50} +1.22520 q^{51} +9.38207 q^{52} -3.43644 q^{53} +2.07710 q^{54} +5.15684 q^{55} +4.41144 q^{57} +7.09735 q^{58} +9.90021 q^{59} -5.32392 q^{60} +5.18833 q^{61} -2.23214 q^{62} -10.2861 q^{64} -9.32545 q^{65} -4.65630 q^{66} +10.9161 q^{67} +2.83556 q^{68} +6.56124 q^{69} -5.24347 q^{71} +0.652949 q^{72} +5.69973 q^{73} -3.40610 q^{74} +0.291790 q^{75} +10.2096 q^{76} +8.42028 q^{78} +3.55265 q^{79} +7.52795 q^{80} +1.00000 q^{81} +2.07710 q^{82} +2.44743 q^{83} -2.81845 q^{85} -9.70437 q^{86} +3.41695 q^{87} -1.46373 q^{88} +5.51735 q^{89} -4.77814 q^{90} +15.1850 q^{92} -1.07464 q^{93} +22.7254 q^{94} -10.1480 q^{95} -8.10315 q^{96} -3.88945 q^{97} -2.24173 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + 8 q^{3} + 13 q^{4} + 7 q^{5} + q^{6} + 6 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + q^2 + 8 * q^3 + 13 * q^4 + 7 * q^5 + q^6 + 6 * q^8 + 8 * q^9	$ 8 q + q^{2} + 8 q^{3} + 13 q^{4} + 7 q^{5} + q^{6} + 6 q^{8} + 8 q^{9} + 8 q^{10} + 11 q^{11} + 13 q^{12} + 10 q^{13} + 7 q^{15} - 17 q^{16} + 3 q^{17} + q^{18} + 6 q^{19} + 11 q^{20} + 15 q^{22} + 14 q^{23} + 6 q^{24} + 25 q^{25} + 24 q^{26} + 8 q^{27} + 2 q^{29} + 8 q^{30} + 16 q^{31} + 3 q^{32} + 11 q^{33} - 4 q^{34} + 13 q^{36} - 20 q^{37} + 10 q^{38} + 10 q^{39} - 3 q^{40} + 8 q^{41} + 7 q^{43} + 7 q^{45} - 5 q^{46} + 14 q^{47} - 17 q^{48} - 5 q^{50} + 3 q^{51} + 23 q^{52} + 7 q^{53} + q^{54} + 48 q^{55} + 6 q^{57} - 20 q^{58} + 22 q^{59} + 11 q^{60} - 33 q^{62} - 10 q^{64} - 14 q^{65} + 15 q^{66} + 12 q^{67} - 27 q^{68} + 14 q^{69} - 5 q^{71} + 6 q^{72} + 2 q^{73} + 6 q^{74} + 25 q^{75} + 43 q^{76} + 24 q^{78} - 15 q^{79} - 7 q^{80} + 8 q^{81} + q^{82} + 15 q^{83} - 43 q^{85} + 31 q^{86} + 2 q^{87} + 17 q^{88} + 29 q^{89} + 8 q^{90} + 19 q^{92} + 16 q^{93} + 20 q^{94} + 14 q^{95} + 3 q^{96} + 19 q^{97} + 11 q^{99}+O(q^{100}) $ 8 * q + q^2 + 8 * q^3 + 13 * q^4 + 7 * q^5 + q^6 + 6 * q^8 + 8 * q^9 + 8 * q^10 + 11 * q^11 + 13 * q^12 + 10 * q^13 + 7 * q^15 - 17 * q^16 + 3 * q^17 + q^18 + 6 * q^19 + 11 * q^20 + 15 * q^22 + 14 * q^23 + 6 * q^24 + 25 * q^25 + 24 * q^26 + 8 * q^27 + 2 * q^29 + 8 * q^30 + 16 * q^31 + 3 * q^32 + 11 * q^33 - 4 * q^34 + 13 * q^36 - 20 * q^37 + 10 * q^38 + 10 * q^39 - 3 * q^40 + 8 * q^41 + 7 * q^43 + 7 * q^45 - 5 * q^46 + 14 * q^47 - 17 * q^48 - 5 * q^50 + 3 * q^51 + 23 * q^52 + 7 * q^53 + q^54 + 48 * q^55 + 6 * q^57 - 20 * q^58 + 22 * q^59 + 11 * q^60 - 33 * q^62 - 10 * q^64 - 14 * q^65 + 15 * q^66 + 12 * q^67 - 27 * q^68 + 14 * q^69 - 5 * q^71 + 6 * q^72 + 2 * q^73 + 6 * q^74 + 25 * q^75 + 43 * q^76 + 24 * q^78 - 15 * q^79 - 7 * q^80 + 8 * q^81 + q^82 + 15 * q^83 - 43 * q^85 + 31 * q^86 + 2 * q^87 + 17 * q^88 + 29 * q^89 + 8 * q^90 + 19 * q^92 + 16 * q^93 + 20 * q^94 + 14 * q^95 + 3 * q^96 + 19 * q^97 + 11 * 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 $

$2$	2.07710	1.46873	0.734367	−	0.678753i	$-0.237479\pi$
$2$	2.07710	1.46873	0.734367	+	0.678753i	$0.237479\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.31436	1.15718
$5$	−2.30039	−1.02877	−0.514383	−	0.857561i	$-0.671979\pi$
$5$	−2.30039	−1.02877	−0.514383	+	0.857561i	$0.671979\pi$
$6$	2.07710	0.847974
$7$	0	0
$7$	0	0
$8$	0.652949	0.230852
$9$	1.00000	0.333333
$10$	−4.77814	−1.51098
$11$	−2.24173	−0.675906	−0.337953	−	0.941163i	$-0.609735\pi$
$11$	−2.24173	−0.675906	−0.337953	+	0.941163i	$0.609735\pi$
$12$	2.31436	0.668097
$13$	4.05386	1.12434	0.562169	−	0.827022i	$-0.309967\pi$
$13$	4.05386	1.12434	0.562169	+	0.827022i	$0.309967\pi$
$14$	0	0
$15$	−2.30039	−0.593958
$16$	−3.27247	−0.818117
$17$	1.22520	0.297156	0.148578	−	0.988901i	$-0.452530\pi$
$17$	1.22520	0.297156	0.148578	+	0.988901i	$0.452530\pi$
$18$	2.07710	0.489578
$19$	4.41144	1.01205	0.506026	−	0.862518i	$-0.331114\pi$
$19$	4.41144	1.01205	0.506026	+	0.862518i	$0.331114\pi$
$20$	−5.32392	−1.19046
$21$	0	0
$22$	−4.65630	−0.992726
$23$	6.56124	1.36811	0.684056	−	0.729429i	$-0.260214\pi$
$23$	6.56124	1.36811	0.684056	+	0.729429i	$0.260214\pi$
$24$	0.652949	0.133283
$25$	0.291790	0.0583580
$26$	8.42028	1.65135
$27$	1.00000	0.192450
$28$	0	0
$29$	3.41695	0.634511	0.317255	−	0.948340i	$-0.397239\pi$
$29$	3.41695	0.634511	0.317255	+	0.948340i	$0.397239\pi$
$30$	−4.77814	−0.872366
$31$	−1.07464	−0.193011	−0.0965056	−	0.995332i	$-0.530767\pi$
$31$	−1.07464	−0.193011	−0.0965056	+	0.995332i	$0.530767\pi$
$32$	−8.10315	−1.43245
$33$	−2.24173	−0.390235
$34$	2.54488	0.436443
$35$	0	0
$36$	2.31436	0.385726
$37$	−1.63983	−0.269587	−0.134793	−	0.990874i	$-0.543037\pi$
$37$	−1.63983	−0.269587	−0.134793	+	0.990874i	$0.543037\pi$
$38$	9.16300	1.48644
$39$	4.05386	0.649137
$40$	−1.50204	−0.237493
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	−4.67207	−0.712484	−0.356242	−	0.934394i	$-0.615942\pi$
$43$	−4.67207	−0.712484	−0.356242	+	0.934394i	$0.615942\pi$
$44$	−5.18815	−0.782144
$45$	−2.30039	−0.342922
$46$	13.6284	2.00939
$47$	10.9409	1.59589	0.797947	−	0.602727i	$-0.205919\pi$
$47$	10.9409	1.59589	0.797947	+	0.602727i	$0.205919\pi$
$48$	−3.27247	−0.472340
$49$	0	0
$50$	0.606078	0.0857123
$51$	1.22520	0.171563
$52$	9.38207	1.30106
$53$	−3.43644	−0.472032	−0.236016	−	0.971749i	$-0.575842\pi$
$53$	−3.43644	−0.472032	−0.236016	+	0.971749i	$0.575842\pi$
$54$	2.07710	0.282658
$55$	5.15684	0.695349
$56$	0	0
$57$	4.41144	0.584309
$58$	7.09735	0.931927
$59$	9.90021	1.28890	0.644449	−	0.764648i	$-0.277087\pi$
$59$	9.90021	1.28890	0.644449	+	0.764648i	$0.277087\pi$
$60$	−5.32392	−0.687315
$61$	5.18833	0.664298	0.332149	−	0.943227i	$-0.392226\pi$
$61$	5.18833	0.664298	0.332149	+	0.943227i	$0.392226\pi$
$62$	−2.23214	−0.283482
$63$	0	0
$64$	−10.2861	−1.28577
$65$	−9.32545	−1.15668
$66$	−4.65630	−0.573151
$67$	10.9161	1.33361	0.666806	−	0.745231i	$-0.267661\pi$
$67$	10.9161	1.33361	0.666806	+	0.745231i	$0.267661\pi$
$68$	2.83556	0.343862
$69$	6.56124	0.789880
$70$	0	0
$71$	−5.24347	−0.622286	−0.311143	−	0.950363i	$-0.600712\pi$
$71$	−5.24347	−0.622286	−0.311143	+	0.950363i	$0.600712\pi$
$72$	0.652949	0.0769507
$73$	5.69973	0.667103	0.333551	−	0.942732i	$-0.391753\pi$
$73$	5.69973	0.667103	0.333551	+	0.942732i	$0.391753\pi$
$74$	−3.40610	−0.395951
$75$	0.291790	0.0336930
$76$	10.2096	1.17112
$77$	0	0
$78$	8.42028	0.953409
$79$	3.55265	0.399704	0.199852	−	0.979826i	$-0.435954\pi$
$79$	3.55265	0.399704	0.199852	+	0.979826i	$0.435954\pi$
$80$	7.52795	0.841651
$81$	1.00000	0.111111
$82$	2.07710	0.229378
$83$	2.44743	0.268640	0.134320	−	0.990938i	$-0.457115\pi$
$83$	2.44743	0.268640	0.134320	+	0.990938i	$0.457115\pi$
$84$	0	0
$85$	−2.81845	−0.305703
$86$	−9.70437	−1.04645
$87$	3.41695	0.366335
$88$	−1.46373	−0.156034
$89$	5.51735	0.584837	0.292419	−	0.956290i	$-0.405540\pi$
$89$	5.51735	0.584837	0.292419	+	0.956290i	$0.405540\pi$
$90$	−4.77814	−0.503661
$91$	0	0
$92$	15.1850	1.58315
$93$	−1.07464	−0.111435
$94$	22.7254	2.34394
$95$	−10.1480	−1.04116
$96$	−8.10315	−0.827025
$97$	−3.88945	−0.394914	−0.197457	−	0.980312i	$-0.563268\pi$
$97$	−3.88945	−0.394914	−0.197457	+	0.980312i	$0.563268\pi$
$98$	0	0
$99$	−2.24173	−0.225302
$100$	0.675306	0.0675306
$101$	11.7539	1.16956	0.584780	−	0.811192i	$-0.301181\pi$
$101$	11.7539	1.16956	0.584780	+	0.811192i	$0.301181\pi$
$102$	2.54488	0.251980
$103$	−7.81801	−0.770331	−0.385165	−	0.922848i	$-0.625856\pi$
$103$	−7.81801	−0.770331	−0.385165	+	0.922848i	$0.625856\pi$
$104$	2.64696	0.259556
$105$	0	0
$106$	−7.13785	−0.693289
$107$	14.9202	1.44239	0.721193	−	0.692734i	$-0.243594\pi$
$107$	14.9202	1.44239	0.721193	+	0.692734i	$0.243594\pi$
$108$	2.31436	0.222699
$109$	−2.44790	−0.234466	−0.117233	−	0.993104i	$-0.537402\pi$
$109$	−2.44790	−0.234466	−0.117233	+	0.993104i	$0.537402\pi$
$110$	10.7113	1.02128
$111$	−1.63983	−0.155646
$112$	0	0
$113$	−5.66753	−0.533156	−0.266578	−	0.963813i	$-0.585893\pi$
$113$	−5.66753	−0.533156	−0.266578	+	0.963813i	$0.585893\pi$
$114$	9.16300	0.858194
$115$	−15.0934	−1.40747
$116$	7.90803	0.734242
$117$	4.05386	0.374779
$118$	20.5637	1.89305
$119$	0	0
$120$	−1.50204	−0.137116
$121$	−5.97466	−0.543151
$122$	10.7767	0.975676
$123$	1.00000	0.0901670
$124$	−2.48710	−0.223348
$125$	10.8307	0.968729
$126$	0	0
$127$	5.81071	0.515617	0.257809	−	0.966196i	$-0.417000\pi$
$127$	5.81071	0.515617	0.257809	+	0.966196i	$0.417000\pi$
$128$	−5.15907	−0.456001
$129$	−4.67207	−0.411353
$130$	−19.3699	−1.69885
$131$	14.4403	1.26165	0.630826	−	0.775925i	$-0.282716\pi$
$131$	14.4403	1.26165	0.630826	+	0.775925i	$0.282716\pi$
$132$	−5.18815	−0.451571
$133$	0	0
$134$	22.6738	1.95872
$135$	−2.30039	−0.197986
$136$	0.799996	0.0685991
$137$	7.95642	0.679762	0.339881	−	0.940468i	$-0.389613\pi$
$137$	7.95642	0.679762	0.339881	+	0.940468i	$0.389613\pi$
$138$	13.6284	1.16012
$139$	−8.96101	−0.760063	−0.380031	−	0.924974i	$-0.624087\pi$
$139$	−8.96101	−0.760063	−0.380031	+	0.924974i	$0.624087\pi$
$140$	0	0
$141$	10.9409	0.921390
$142$	−10.8912	−0.913972
$143$	−9.08764	−0.759947
$144$	−3.27247	−0.272706
$145$	−7.86030	−0.652763
$146$	11.8389	0.979796
$147$	0	0
$148$	−3.79515	−0.311960
$149$	−3.54749	−0.290622	−0.145311	−	0.989386i	$-0.546418\pi$
$149$	−3.54749	−0.290622	−0.145311	+	0.989386i	$0.546418\pi$
$150$	0.606078	0.0494860
$151$	−8.99035	−0.731624	−0.365812	−	0.930689i	$-0.619209\pi$
$151$	−8.99035	−0.731624	−0.365812	+	0.930689i	$0.619209\pi$
$152$	2.88044	0.233635
$153$	1.22520	0.0990519
$154$	0	0
$155$	2.47209	0.198563
$156$	9.38207	0.751166
$157$	−7.01626	−0.559958	−0.279979	−	0.960006i	$-0.590328\pi$
$157$	−7.01626	−0.559958	−0.279979	+	0.960006i	$0.590328\pi$
$158$	7.37921	0.587059
$159$	−3.43644	−0.272528
$160$	18.6404	1.47365
$161$	0	0
$162$	2.07710	0.163193
$163$	18.5576	1.45355	0.726773	−	0.686878i	$-0.241019\pi$
$163$	18.5576	1.45355	0.726773	+	0.686878i	$0.241019\pi$
$164$	2.31436	0.180721
$165$	5.15684	0.401460
$166$	5.08356	0.394561
$167$	14.8071	1.14581	0.572905	−	0.819622i	$-0.305816\pi$
$167$	14.8071	1.14581	0.572905	+	0.819622i	$0.305816\pi$
$168$	0	0
$169$	3.43376	0.264135
$170$	−5.85420	−0.448997
$171$	4.41144	0.337351
$172$	−10.8128	−0.824470
$173$	−21.1741	−1.60984	−0.804920	−	0.593383i	$-0.797792\pi$
$173$	−21.1741	−1.60984	−0.804920	+	0.593383i	$0.797792\pi$
$174$	7.09735	0.538049
$175$	0	0
$176$	7.33598	0.552971
$177$	9.90021	0.744145
$178$	11.4601	0.858970
$179$	7.08941	0.529887	0.264944	−	0.964264i	$-0.414647\pi$
$179$	7.08941	0.529887	0.264944	+	0.964264i	$0.414647\pi$
$180$	−5.32392	−0.396821
$181$	24.0383	1.78675	0.893375	−	0.449312i	$-0.148331\pi$
$181$	24.0383	1.78675	0.893375	+	0.449312i	$0.148331\pi$
$182$	0	0
$183$	5.18833	0.383532
$184$	4.28415	0.315832
$185$	3.77225	0.277341
$186$	−2.23214	−0.163668
$187$	−2.74657	−0.200849
$188$	25.3211	1.84673
$189$	0	0
$190$	−21.0785	−1.52919
$191$	19.7740	1.43080	0.715399	−	0.698716i	$-0.246245\pi$
$191$	19.7740	1.43080	0.715399	+	0.698716i	$0.246245\pi$
$192$	−10.2861	−0.742338
$193$	−10.7386	−0.772985	−0.386492	−	0.922293i	$-0.626313\pi$
$193$	−10.7386	−0.772985	−0.386492	+	0.922293i	$0.626313\pi$
$194$	−8.07879	−0.580023
$195$	−9.32545	−0.667809
$196$	0	0
$197$	−25.6837	−1.82989	−0.914944	−	0.403580i	$-0.867766\pi$
$197$	−25.6837	−1.82989	−0.914944	+	0.403580i	$0.867766\pi$
$198$	−4.65630	−0.330909
$199$	12.3661	0.876611	0.438305	−	0.898826i	$-0.355579\pi$
$199$	12.3661	0.876611	0.438305	+	0.898826i	$0.355579\pi$
$200$	0.190524	0.0134721
$201$	10.9161	0.769961
$202$	24.4141	1.71777
$203$	0	0
$204$	2.83556	0.198529
$205$	−2.30039	−0.160666
$206$	−16.2388	−1.13141
$207$	6.56124	0.456037
$208$	−13.2661	−0.919840
$209$	−9.88923	−0.684053
$210$	0	0
$211$	−12.7379	−0.876916	−0.438458	−	0.898752i	$-0.644475\pi$
$211$	−12.7379	−0.876916	−0.438458	+	0.898752i	$0.644475\pi$
$212$	−7.95315	−0.546225
$213$	−5.24347	−0.359277
$214$	30.9907	2.11848
$215$	10.7476	0.732979
$216$	0.652949	0.0444275
$217$	0	0
$218$	−5.08454	−0.344368
$219$	5.69973	0.385152
$220$	11.9348	0.804642
$221$	4.96680	0.334103
$222$	−3.40610	−0.228602
$223$	−14.5408	−0.973721	−0.486861	−	0.873480i	$-0.661858\pi$
$223$	−14.5408	−0.973721	−0.486861	+	0.873480i	$0.661858\pi$
$224$	0	0
$225$	0.291790	0.0194527
$226$	−11.7720	−0.783064
$227$	−12.7598	−0.846898	−0.423449	−	0.905920i	$-0.639181\pi$
$227$	−12.7598	−0.846898	−0.423449	+	0.905920i	$0.639181\pi$
$228$	10.2096	0.676149
$229$	−16.3536	−1.08067	−0.540337	−	0.841448i	$-0.681703\pi$
$229$	−16.3536	−1.08067	−0.540337	+	0.841448i	$0.681703\pi$
$230$	−31.3505	−2.06719
$231$	0	0
$232$	2.23109	0.146478
$233$	25.6813	1.68244	0.841218	−	0.540696i	$-0.181839\pi$
$233$	25.6813	1.68244	0.841218	+	0.540696i	$0.181839\pi$
$234$	8.42028	0.550451
$235$	−25.1683	−1.64180
$236$	22.9126	1.49148
$237$	3.55265	0.230769
$238$	0	0
$239$	−6.68343	−0.432315	−0.216158	−	0.976359i	$-0.569352\pi$
$239$	−6.68343	−0.432315	−0.216158	+	0.976359i	$0.569352\pi$
$240$	7.52795	0.485927
$241$	−12.8119	−0.825289	−0.412645	−	0.910892i	$-0.635395\pi$
$241$	−12.8119	−0.825289	−0.412645	+	0.910892i	$0.635395\pi$
$242$	−12.4100	−0.797744
$243$	1.00000	0.0641500
$244$	12.0076	0.768711
$245$	0	0
$246$	2.07710	0.132431
$247$	17.8833	1.13789
$248$	−0.701685	−0.0445570
$249$	2.44743	0.155099
$250$	22.4965	1.42280
$251$	−20.6747	−1.30498	−0.652488	−	0.757799i	$-0.726275\pi$
$251$	−20.6747	−1.30498	−0.652488	+	0.757799i	$0.726275\pi$
$252$	0	0
$253$	−14.7085	−0.924716
$254$	12.0694	0.757304
$255$	−2.81845	−0.176498
$256$	9.85637	0.616023
$257$	26.3985	1.64669	0.823345	−	0.567541i	$-0.192105\pi$
$257$	26.3985	1.64669	0.823345	+	0.567541i	$0.192105\pi$
$258$	−9.70437	−0.604167
$259$	0	0
$260$	−21.5824	−1.33848
$261$	3.41695	0.211504
$262$	29.9939	1.85303
$263$	−4.26169	−0.262787	−0.131393	−	0.991330i	$-0.541945\pi$
$263$	−4.26169	−0.262787	−0.131393	+	0.991330i	$0.541945\pi$
$264$	−1.46373	−0.0900865
$265$	7.90516	0.485610
$266$	0	0
$267$	5.51735	0.337656
$268$	25.2637	1.54323
$269$	−14.8791	−0.907193	−0.453597	−	0.891207i	$-0.649859\pi$
$269$	−14.8791	−0.907193	−0.453597	+	0.891207i	$0.649859\pi$
$270$	−4.77814	−0.290789
$271$	−24.8652	−1.51045	−0.755225	−	0.655465i	$-0.772473\pi$
$271$	−24.8652	−1.51045	−0.755225	+	0.655465i	$0.772473\pi$
$272$	−4.00944	−0.243108
$273$	0	0
$274$	16.5263	0.998390
$275$	−0.654114	−0.0394445
$276$	15.1850	0.914032
$277$	−24.1746	−1.45251	−0.726256	−	0.687425i	$-0.758741\pi$
$277$	−24.1746	−1.45251	−0.726256	+	0.687425i	$0.758741\pi$
$278$	−18.6129	−1.11633
$279$	−1.07464	−0.0643370
$280$	0	0
$281$	−11.0063	−0.656583	−0.328291	−	0.944576i	$-0.606473\pi$
$281$	−11.0063	−0.656583	−0.328291	+	0.944576i	$0.606473\pi$
$282$	22.7254	1.35328
$283$	−16.1057	−0.957387	−0.478694	−	0.877982i	$-0.658890\pi$
$283$	−16.1057	−0.957387	−0.478694	+	0.877982i	$0.658890\pi$
$284$	−12.1353	−0.720095
$285$	−10.1480	−0.601117
$286$	−18.8760	−1.11616
$287$	0	0
$288$	−8.10315	−0.477483
$289$	−15.4989	−0.911698
$290$	−16.3267	−0.958735
$291$	−3.88945	−0.228004
$292$	13.1912	0.771957
$293$	12.6292	0.737808	0.368904	−	0.929467i	$-0.379733\pi$
$293$	12.6292	0.737808	0.368904	+	0.929467i	$0.379733\pi$
$294$	0	0
$295$	−22.7743	−1.32597
$296$	−1.07073	−0.0622347
$297$	−2.24173	−0.130078
$298$	−7.36851	−0.426846
$299$	26.5983	1.53822
$300$	0.675306	0.0389888
$301$	0	0
$302$	−18.6739	−1.07456
$303$	11.7539	0.675246
$304$	−14.4363	−0.827978
$305$	−11.9352	−0.683406
$306$	2.54488	0.145481
$307$	−23.2927	−1.32939	−0.664693	−	0.747116i	$-0.731438\pi$
$307$	−23.2927	−1.32939	−0.664693	+	0.747116i	$0.731438\pi$
$308$	0	0
$309$	−7.81801	−0.444751
$310$	5.13479	0.291636
$311$	8.17595	0.463616	0.231808	−	0.972762i	$-0.425536\pi$
$311$	8.17595	0.463616	0.231808	+	0.972762i	$0.425536\pi$
$312$	2.64696	0.149855
$313$	16.9412	0.957576	0.478788	−	0.877931i	$-0.341076\pi$
$313$	16.9412	0.957576	0.478788	+	0.877931i	$0.341076\pi$
$314$	−14.5735	−0.822429
$315$	0	0
$316$	8.22209	0.462529
$317$	10.8754	0.610824	0.305412	−	0.952220i	$-0.401206\pi$
$317$	10.8754	0.610824	0.305412	+	0.952220i	$0.401206\pi$
$318$	−7.13785	−0.400271
$319$	−7.65986	−0.428870
$320$	23.6621	1.32275
$321$	14.9202	0.832762
$322$	0	0
$323$	5.40491	0.300737
$324$	2.31436	0.128575
$325$	1.18288	0.0656141
$326$	38.5461	2.13487
$327$	−2.44790	−0.135369
$328$	0.652949	0.0360531
$329$	0	0
$330$	10.7113	0.589637
$331$	−12.5272	−0.688557	−0.344278	−	0.938868i	$-0.611876\pi$
$331$	−12.5272	−0.688557	−0.344278	+	0.938868i	$0.611876\pi$
$332$	5.66422	0.310864
$333$	−1.63983	−0.0898622
$334$	30.7559	1.68289
$335$	−25.1112	−1.37197
$336$	0	0
$337$	15.0009	0.817152	0.408576	−	0.912724i	$-0.366026\pi$
$337$	15.0009	0.817152	0.408576	+	0.912724i	$0.366026\pi$
$338$	7.13227	0.387944
$339$	−5.66753	−0.307818
$340$	−6.52289	−0.353753
$341$	2.40905	0.130457
$342$	9.16300	0.495479
$343$	0	0
$344$	−3.05062	−0.164478
$345$	−15.0934	−0.812601
$346$	−43.9809	−2.36443
$347$	−35.5777	−1.90991	−0.954955	−	0.296752i	$-0.904097\pi$
$347$	−35.5777	−1.90991	−0.954955	+	0.296752i	$0.904097\pi$
$348$	7.90803	0.423915
$349$	−24.7802	−1.32646	−0.663228	−	0.748418i	$-0.730814\pi$
$349$	−24.7802	−1.32646	−0.663228	+	0.748418i	$0.730814\pi$
$350$	0	0
$351$	4.05386	0.216379
$352$	18.1651	0.968201
$353$	−8.42011	−0.448157	−0.224079	−	0.974571i	$-0.571937\pi$
$353$	−8.42011	−0.448157	−0.224079	+	0.974571i	$0.571937\pi$
$354$	20.5637	1.09295
$355$	12.0620	0.640186
$356$	12.7691	0.676761
$357$	0	0
$358$	14.7254	0.778263
$359$	20.6533	1.09004	0.545019	−	0.838424i	$-0.316522\pi$
$359$	20.6533	1.09004	0.545019	+	0.838424i	$0.316522\pi$
$360$	−1.50204	−0.0791642
$361$	0.460761	0.0242506
$362$	49.9299	2.62426
$363$	−5.97466	−0.313588
$364$	0	0
$365$	−13.1116	−0.686292
$366$	10.7767	0.563307
$367$	29.3148	1.53022	0.765111	−	0.643898i	$-0.222684\pi$
$367$	29.3148	1.53022	0.765111	+	0.643898i	$0.222684\pi$
$368$	−21.4714	−1.11928
$369$	1.00000	0.0520579
$370$	7.83535	0.407340
$371$	0	0
$372$	−2.48710	−0.128950
$373$	−25.6244	−1.32678	−0.663391	−	0.748273i	$-0.730883\pi$
$373$	−25.6244	−1.32678	−0.663391	+	0.748273i	$0.730883\pi$
$374$	−5.70492	−0.294994
$375$	10.8307	0.559296
$376$	7.14385	0.368416
$377$	13.8518	0.713405
$378$	0	0
$379$	−9.09331	−0.467092	−0.233546	−	0.972346i	$-0.575033\pi$
$379$	−9.09331	−0.467092	−0.233546	+	0.972346i	$0.575033\pi$
$380$	−23.4861	−1.20481
$381$	5.81071	0.297692
$382$	41.0727	2.10146
$383$	−10.4624	−0.534603	−0.267302	−	0.963613i	$-0.586132\pi$
$383$	−10.4624	−0.534603	−0.267302	+	0.963613i	$0.586132\pi$
$384$	−5.15907	−0.263272
$385$	0	0
$386$	−22.3053	−1.13531
$387$	−4.67207	−0.237495
$388$	−9.00158	−0.456986
$389$	−22.4569	−1.13861	−0.569304	−	0.822127i	$-0.692787\pi$
$389$	−22.4569	−1.13861	−0.569304	+	0.822127i	$0.692787\pi$
$390$	−19.3699	−0.980834
$391$	8.03886	0.406542
$392$	0	0
$393$	14.4403	0.728415
$394$	−53.3477	−2.68762
$395$	−8.17247	−0.411202
$396$	−5.18815	−0.260715
$397$	34.0978	1.71132	0.855659	−	0.517540i	$-0.173152\pi$
$397$	34.0978	1.71132	0.855659	+	0.517540i	$0.173152\pi$
$398$	25.6857	1.28751
$399$	0	0
$400$	−0.954874	−0.0477437
$401$	26.2661	1.31167	0.655833	−	0.754906i	$-0.272318\pi$
$401$	26.2661	1.31167	0.655833	+	0.754906i	$0.272318\pi$
$402$	22.6738	1.13087
$403$	−4.35644	−0.217010
$404$	27.2028	1.35339
$405$	−2.30039	−0.114307
$406$	0	0
$407$	3.67605	0.182215
$408$	0.799996	0.0396057
$409$	−13.7222	−0.678517	−0.339259	−	0.940693i	$-0.610176\pi$
$409$	−13.7222	−0.678517	−0.339259	+	0.940693i	$0.610176\pi$
$410$	−4.77814	−0.235976
$411$	7.95642	0.392461
$412$	−18.0936	−0.891410
$413$	0	0
$414$	13.6284	0.669797
$415$	−5.63004	−0.276368
$416$	−32.8490	−1.61056
$417$	−8.96101	−0.438823
$418$	−20.5410	−1.00469
$419$	−5.03172	−0.245815	−0.122908	−	0.992418i	$-0.539222\pi$
$419$	−5.03172	−0.245815	−0.122908	+	0.992418i	$0.539222\pi$
$420$	0	0
$421$	35.3421	1.72247	0.861234	−	0.508209i	$-0.169692\pi$
$421$	35.3421	1.72247	0.861234	+	0.508209i	$0.169692\pi$
$422$	−26.4580	−1.28796
$423$	10.9409	0.531965
$424$	−2.24382	−0.108970
$425$	0.357502	0.0173414
$426$	−10.8912	−0.527682
$427$	0	0
$428$	34.5305	1.66910
$429$	−9.08764	−0.438755
$430$	22.3238	1.07655
$431$	−10.0032	−0.481838	−0.240919	−	0.970545i	$-0.577449\pi$
$431$	−10.0032	−0.481838	−0.240919	+	0.970545i	$0.577449\pi$
$432$	−3.27247	−0.157447
$433$	0.228599	0.0109858	0.00549289	−	0.999985i	$-0.498252\pi$
$433$	0.228599	0.0109858	0.00549289	+	0.999985i	$0.498252\pi$
$434$	0	0
$435$	−7.86030	−0.376873
$436$	−5.66531	−0.271319
$437$	28.9445	1.38460
$438$	11.8389	0.565686
$439$	−6.63796	−0.316812	−0.158406	−	0.987374i	$-0.550636\pi$
$439$	−6.63796	−0.316812	−0.158406	+	0.987374i	$0.550636\pi$
$440$	3.36715	0.160523
$441$	0	0
$442$	10.3166	0.490709
$443$	−34.2893	−1.62913	−0.814567	−	0.580069i	$-0.803025\pi$
$443$	−34.2893	−1.62913	−0.814567	+	0.580069i	$0.803025\pi$
$444$	−3.79515	−0.180110
$445$	−12.6920	−0.601660
$446$	−30.2026	−1.43014
$447$	−3.54749	−0.167791
$448$	0	0
$449$	−23.8006	−1.12322	−0.561609	−	0.827403i	$-0.689817\pi$
$449$	−23.8006	−1.12322	−0.561609	+	0.827403i	$0.689817\pi$
$450$	0.606078	0.0285708
$451$	−2.24173	−0.105559
$452$	−13.1167	−0.616956
$453$	−8.99035	−0.422403
$454$	−26.5034	−1.24387
$455$	0	0
$456$	2.88044	0.134889
$457$	3.89804	0.182343	0.0911713	−	0.995835i	$-0.470939\pi$
$457$	3.89804	0.182343	0.0911713	+	0.995835i	$0.470939\pi$
$458$	−33.9681	−1.58722
$459$	1.22520	0.0571876
$460$	−34.9315	−1.62869
$461$	8.82325	0.410940	0.205470	−	0.978663i	$-0.434128\pi$
$461$	8.82325	0.410940	0.205470	+	0.978663i	$0.434128\pi$
$462$	0	0
$463$	−27.1088	−1.25985	−0.629925	−	0.776656i	$-0.716915\pi$
$463$	−27.1088	−1.25985	−0.629925	+	0.776656i	$0.716915\pi$
$464$	−11.1819	−0.519104
$465$	2.47209	0.114640
$466$	53.3426	2.47105
$467$	39.6617	1.83532	0.917662	−	0.397361i	$-0.130074\pi$
$467$	39.6617	1.83532	0.917662	+	0.397361i	$0.130074\pi$
$468$	9.38207	0.433686
$469$	0	0
$470$	−52.2772	−2.41137
$471$	−7.01626	−0.323292
$472$	6.46433	0.297545
$473$	10.4735	0.481572
$474$	7.37921	0.338938
$475$	1.28721	0.0590614
$476$	0	0
$477$	−3.43644	−0.157344
$478$	−13.8822	−0.634956
$479$	−0.661325	−0.0302167	−0.0151084	−	0.999886i	$-0.504809\pi$
$479$	−0.661325	−0.0302167	−0.0151084	+	0.999886i	$0.504809\pi$
$480$	18.6404	0.850814
$481$	−6.64764	−0.303106
$482$	−26.6117	−1.21213
$483$	0	0
$484$	−13.8275	−0.628522
$485$	8.94725	0.406274
$486$	2.07710	0.0942193
$487$	−12.0841	−0.547582	−0.273791	−	0.961789i	$-0.588278\pi$
$487$	−12.0841	−0.547582	−0.273791	+	0.961789i	$0.588278\pi$
$488$	3.38771	0.153355
$489$	18.5576	0.839205
$490$	0	0
$491$	−5.89624	−0.266094	−0.133047	−	0.991110i	$-0.542476\pi$
$491$	−5.89624	−0.266094	−0.133047	+	0.991110i	$0.542476\pi$
$492$	2.31436	0.104339
$493$	4.18646	0.188549
$494$	37.1455	1.67126
$495$	5.15684	0.231783
$496$	3.51673	0.157906
$497$	0	0
$498$	5.08356	0.227800
$499$	−9.66766	−0.432784	−0.216392	−	0.976307i	$-0.569429\pi$
$499$	−9.66766	−0.432784	−0.216392	+	0.976307i	$0.569429\pi$
$500$	25.0661	1.12099
$501$	14.8071	0.661534
$502$	−42.9435	−1.91666
$503$	−35.1796	−1.56858	−0.784290	−	0.620395i	$-0.786972\pi$
$503$	−35.1796	−1.56858	−0.784290	+	0.620395i	$0.786972\pi$
$504$	0	0
$505$	−27.0386	−1.20320
$506$	−30.5511	−1.35816
$507$	3.43376	0.152499
$508$	13.4481	0.596661
$509$	2.79729	0.123988	0.0619938	−	0.998077i	$-0.480254\pi$
$509$	2.79729	0.123988	0.0619938	+	0.998077i	$0.480254\pi$
$510$	−5.85420	−0.259228
$511$	0	0
$512$	30.7908	1.36078
$513$	4.41144	0.194770
$514$	54.8323	2.41855
$515$	17.9845	0.792490
$516$	−10.8128	−0.476008
$517$	−24.5265	−1.07867
$518$	0	0
$519$	−21.1741	−0.929442
$520$	−6.08904	−0.267022
$521$	−29.5199	−1.29329	−0.646645	−	0.762791i	$-0.723829\pi$
$521$	−29.5199	−1.29329	−0.646645	+	0.762791i	$0.723829\pi$
$522$	7.09735	0.310642
$523$	−29.5127	−1.29050	−0.645250	−	0.763971i	$-0.723247\pi$
$523$	−29.5127	−1.29050	−0.645250	+	0.763971i	$0.723247\pi$
$524$	33.4199	1.45995
$525$	0	0
$526$	−8.85196	−0.385964
$527$	−1.31665	−0.0573544
$528$	7.33598	0.319258
$529$	20.0498	0.871732
$530$	16.4198	0.713232
$531$	9.90021	0.429632
$532$	0	0
$533$	4.05386	0.175592
$534$	11.4601	0.495927
$535$	−34.3222	−1.48388
$536$	7.12764	0.307867
$537$	7.08941	0.305930
$538$	−30.9054	−1.33242
$539$	0	0
$540$	−5.32392	−0.229105
$541$	35.9810	1.54695	0.773473	−	0.633830i	$-0.218518\pi$
$541$	35.9810	1.54695	0.773473	+	0.633830i	$0.218518\pi$
$542$	−51.6475	−2.21845
$543$	24.0383	1.03158
$544$	−9.92802	−0.425660
$545$	5.63112	0.241211
$546$	0	0
$547$	19.5998	0.838028	0.419014	−	0.907980i	$-0.362376\pi$
$547$	19.5998	0.838028	0.419014	+	0.907980i	$0.362376\pi$
$548$	18.4140	0.786606
$549$	5.18833	0.221433
$550$	−1.35866	−0.0579335
$551$	15.0736	0.642158
$552$	4.28415	0.182346
$553$	0	0
$554$	−50.2131	−2.13335
$555$	3.77225	0.160123
$556$	−20.7390	−0.879528
$557$	14.9938	0.635306	0.317653	−	0.948207i	$-0.397105\pi$
$557$	14.9938	0.635306	0.317653	+	0.948207i	$0.397105\pi$
$558$	−2.23214	−0.0944939
$559$	−18.9399	−0.801072
$560$	0	0
$561$	−2.74657	−0.115960
$562$	−22.8613	−0.964345
$563$	35.7951	1.50858	0.754291	−	0.656540i	$-0.227981\pi$
$563$	35.7951	1.50858	0.754291	+	0.656540i	$0.227981\pi$
$564$	25.3211	1.06621
$565$	13.0375	0.548492
$566$	−33.4533	−1.40615
$567$	0	0
$568$	−3.42372	−0.143656
$569$	25.4501	1.06692	0.533461	−	0.845825i	$-0.320891\pi$
$569$	25.4501	1.06692	0.533461	+	0.845825i	$0.320891\pi$
$570$	−21.0785	−0.882880
$571$	−22.1799	−0.928200	−0.464100	−	0.885783i	$-0.653622\pi$
$571$	−22.1799	−0.928200	−0.464100	+	0.885783i	$0.653622\pi$
$572$	−21.0320	−0.879393
$573$	19.7740	0.826072
$574$	0	0
$575$	1.91450	0.0798403
$576$	−10.2861	−0.428589
$577$	30.2462	1.25917	0.629583	−	0.776933i	$-0.283226\pi$
$577$	30.2462	1.25917	0.629583	+	0.776933i	$0.283226\pi$
$578$	−32.1928	−1.33904
$579$	−10.7386	−0.446283
$580$	−18.1915	−0.755363
$581$	0	0
$582$	−8.07879	−0.334877
$583$	7.70357	0.319049
$584$	3.72163	0.154002
$585$	−9.32545	−0.385560
$586$	26.2322	1.08364
$587$	−2.37388	−0.0979804	−0.0489902	−	0.998799i	$-0.515600\pi$
$587$	−2.37388	−0.0979804	−0.0489902	+	0.998799i	$0.515600\pi$
$588$	0	0
$589$	−4.74071	−0.195337
$590$	−47.3046	−1.94750
$591$	−25.6837	−1.05649
$592$	5.36630	0.220553
$593$	11.6657	0.479051	0.239525	−	0.970890i	$-0.423008\pi$
$593$	11.6657	0.479051	0.239525	+	0.970890i	$0.423008\pi$
$594$	−4.65630	−0.191050
$595$	0	0
$596$	−8.21016	−0.336301
$597$	12.3661	0.506112
$598$	55.2474	2.25924
$599$	15.5533	0.635489	0.317744	−	0.948176i	$-0.397075\pi$
$599$	15.5533	0.635489	0.317744	+	0.948176i	$0.397075\pi$
$600$	0.190524	0.00777811
$601$	−22.3375	−0.911166	−0.455583	−	0.890193i	$-0.650569\pi$
$601$	−22.3375	−0.911166	−0.455583	+	0.890193i	$0.650569\pi$
$602$	0	0
$603$	10.9161	0.444537
$604$	−20.8069	−0.846619
$605$	13.7440	0.558775
$606$	24.4141	0.991756
$607$	−37.4654	−1.52067	−0.760337	−	0.649528i	$-0.774966\pi$
$607$	−37.4654	−1.52067	−0.760337	+	0.649528i	$0.774966\pi$
$608$	−35.7465	−1.44971
$609$	0	0
$610$	−24.7906	−1.00374
$611$	44.3528	1.79432
$612$	2.83556	0.114621
$613$	47.2820	1.90970	0.954852	−	0.297083i	$-0.0960139\pi$
$613$	47.2820	1.90970	0.954852	+	0.297083i	$0.0960139\pi$
$614$	−48.3814	−1.95251
$615$	−2.30039	−0.0927606
$616$	0	0
$617$	−6.52799	−0.262807	−0.131404	−	0.991329i	$-0.541948\pi$
$617$	−6.52799	−0.262807	−0.131404	+	0.991329i	$0.541948\pi$
$618$	−16.2388	−0.653220
$619$	43.1677	1.73506	0.867528	−	0.497389i	$-0.165708\pi$
$619$	43.1677	1.73506	0.867528	+	0.497389i	$0.165708\pi$
$620$	5.72130	0.229773
$621$	6.56124	0.263293
$622$	16.9823	0.680928
$623$	0	0
$624$	−13.2661	−0.531070
$625$	−26.3738	−1.05495
$626$	35.1887	1.40642
$627$	−9.88923	−0.394938
$628$	−16.2381	−0.647971
$629$	−2.00913	−0.0801092
$630$	0	0
$631$	34.2725	1.36437	0.682183	−	0.731182i	$-0.261031\pi$
$631$	34.2725	1.36437	0.682183	+	0.731182i	$0.261031\pi$
$632$	2.31970	0.0922725
$633$	−12.7379	−0.506288
$634$	22.5893	0.897137
$635$	−13.3669	−0.530449
$636$	−7.95315	−0.315363
$637$	0	0
$638$	−15.9103	−0.629895
$639$	−5.24347	−0.207429
$640$	11.8679	0.469118
$641$	29.6706	1.17192	0.585960	−	0.810340i	$-0.300718\pi$
$641$	29.6706	1.17192	0.585960	+	0.810340i	$0.300718\pi$
$642$	30.9907	1.22311
$643$	0.491928	0.0193997	0.00969987	−	0.999953i	$-0.496912\pi$
$643$	0.491928	0.0193997	0.00969987	+	0.999953i	$0.496912\pi$
$644$	0	0
$645$	10.7476	0.423185
$646$	11.2266	0.441703
$647$	−17.2939	−0.679895	−0.339948	−	0.940444i	$-0.610409\pi$
$647$	−17.2939	−0.679895	−0.339948	+	0.940444i	$0.610409\pi$
$648$	0.652949	0.0256502
$649$	−22.1936	−0.871174
$650$	2.45695	0.0963696
$651$	0	0
$652$	42.9489	1.68201
$653$	−5.95097	−0.232879	−0.116440	−	0.993198i	$-0.537148\pi$
$653$	−5.95097	−0.232879	−0.116440	+	0.993198i	$0.537148\pi$
$654$	−5.08454	−0.198821
$655$	−33.2182	−1.29794
$656$	−3.27247	−0.127768
$657$	5.69973	0.222368
$658$	0	0
$659$	48.3637	1.88398	0.941992	−	0.335635i	$-0.108951\pi$
$659$	48.3637	1.88398	0.941992	+	0.335635i	$0.108951\pi$
$660$	11.9348	0.464560
$661$	−15.9158	−0.619054	−0.309527	−	0.950891i	$-0.600171\pi$
$661$	−15.9158	−0.619054	−0.309527	+	0.950891i	$0.600171\pi$
$662$	−26.0203	−1.01131
$663$	4.96680	0.192895
$664$	1.59804	0.0620162
$665$	0	0
$666$	−3.40610	−0.131984
$667$	22.4194	0.868082
$668$	34.2690	1.32591
$669$	−14.5408	−0.562178
$670$	−52.1586	−2.01506
$671$	−11.6308	−0.449003
$672$	0	0
$673$	−21.6199	−0.833387	−0.416693	−	0.909047i	$-0.636811\pi$
$673$	−21.6199	−0.833387	−0.416693	+	0.909047i	$0.636811\pi$
$674$	31.1584	1.20018
$675$	0.291790	0.0112310
$676$	7.94694	0.305651
$677$	−10.1041	−0.388331	−0.194166	−	0.980969i	$-0.562200\pi$
$677$	−10.1041	−0.388331	−0.194166	+	0.980969i	$0.562200\pi$
$678$	−11.7720	−0.452102
$679$	0	0
$680$	−1.84030	−0.0705723
$681$	−12.7598	−0.488957
$682$	5.00385	0.191607
$683$	−44.1322	−1.68867	−0.844336	−	0.535813i	$-0.820005\pi$
$683$	−44.1322	−1.68867	−0.844336	+	0.535813i	$0.820005\pi$
$684$	10.2096	0.390375
$685$	−18.3029	−0.699316
$686$	0	0
$687$	−16.3536	−0.623928
$688$	15.2892	0.582895
$689$	−13.9309	−0.530723
$690$	−31.3505	−1.19349
$691$	−6.85734	−0.260865	−0.130433	−	0.991457i	$-0.541637\pi$
$691$	−6.85734	−0.260865	−0.130433	+	0.991457i	$0.541637\pi$
$692$	−49.0045	−1.86287
$693$	0	0
$694$	−73.8985	−2.80515
$695$	20.6138	0.781926
$696$	2.23109	0.0845693
$697$	1.22520	0.0464079
$698$	−51.4711	−1.94821
$699$	25.6813	0.971355
$700$	0	0
$701$	49.8246	1.88185	0.940925	−	0.338615i	$-0.109958\pi$
$701$	49.8246	1.88185	0.940925	+	0.338615i	$0.109958\pi$
$702$	8.42028	0.317803
$703$	−7.23401	−0.272836
$704$	23.0587	0.869058
$705$	−25.1683	−0.947894
$706$	−17.4894	−0.658223
$707$	0	0
$708$	22.9126	0.861108
$709$	−46.7512	−1.75578	−0.877889	−	0.478865i	$-0.841048\pi$
$709$	−46.7512	−1.75578	−0.877889	+	0.478865i	$0.841048\pi$
$710$	25.0541	0.940263
$711$	3.55265	0.133235
$712$	3.60254	0.135011
$713$	−7.05097	−0.264061
$714$	0	0
$715$	20.9051	0.781807
$716$	16.4074	0.613174
$717$	−6.68343	−0.249597
$718$	42.8990	1.60098
$719$	−17.2085	−0.641769	−0.320884	−	0.947118i	$-0.603980\pi$
$719$	−17.2085	−0.641769	−0.320884	+	0.947118i	$0.603980\pi$
$720$	7.52795	0.280550
$721$	0	0
$722$	0.957049	0.0356177
$723$	−12.8119	−0.476481
$724$	55.6331	2.06759
$725$	0.997031	0.0370288
$726$	−12.4100	−0.460578
$727$	−14.0624	−0.521547	−0.260773	−	0.965400i	$-0.583978\pi$
$727$	−14.0624	−0.521547	−0.260773	+	0.965400i	$0.583978\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−27.2341	−1.00798
$731$	−5.72424	−0.211719
$732$	12.0076	0.443815
$733$	44.3042	1.63641	0.818206	−	0.574925i	$-0.194969\pi$
$733$	44.3042	1.63641	0.818206	+	0.574925i	$0.194969\pi$
$734$	60.8899	2.24749
$735$	0	0
$736$	−53.1667	−1.95975
$737$	−24.4709	−0.901397
$738$	2.07710	0.0764592
$739$	37.1616	1.36701	0.683506	−	0.729945i	$-0.260455\pi$
$739$	37.1616	1.36701	0.683506	+	0.729945i	$0.260455\pi$
$740$	8.73033	0.320933
$741$	17.8833	0.656960
$742$	0	0
$743$	17.6676	0.648161	0.324080	−	0.946030i	$-0.394945\pi$
$743$	17.6676	0.648161	0.324080	+	0.946030i	$0.394945\pi$
$744$	−0.701685	−0.0257250
$745$	8.16062	0.298982
$746$	−53.2246	−1.94869
$747$	2.44743	0.0895467
$748$	−6.35655	−0.232418
$749$	0	0
$750$	22.4965	0.821456
$751$	23.3385	0.851635	0.425817	−	0.904809i	$-0.359987\pi$
$751$	23.3385	0.851635	0.425817	+	0.904809i	$0.359987\pi$
$752$	−35.8038	−1.30563
$753$	−20.6747	−0.753428
$754$	28.7716	1.04780
$755$	20.6813	0.752670
$756$	0	0
$757$	−2.81661	−0.102371	−0.0511857	−	0.998689i	$-0.516300\pi$
$757$	−2.81661	−0.102371	−0.0511857	+	0.998689i	$0.516300\pi$
$758$	−18.8877	−0.686034
$759$	−14.7085	−0.533885
$760$	−6.62613	−0.240355
$761$	−25.8866	−0.938389	−0.469194	−	0.883095i	$-0.655456\pi$
$761$	−25.8866	−0.938389	−0.469194	+	0.883095i	$0.655456\pi$
$762$	12.0694	0.437230
$763$	0	0
$764$	45.7641	1.65569
$765$	−2.81845	−0.101901
$766$	−21.7315	−0.785189
$767$	40.1340	1.44916
$768$	9.85637	0.355661
$769$	21.1931	0.764243	0.382121	−	0.924112i	$-0.375194\pi$
$769$	21.1931	0.764243	0.382121	+	0.924112i	$0.375194\pi$
$770$	0	0
$771$	26.3985	0.950717
$772$	−24.8530	−0.894481
$773$	−30.2026	−1.08631	−0.543155	−	0.839632i	$-0.682771\pi$
$773$	−30.2026	−1.08631	−0.543155	+	0.839632i	$0.682771\pi$
$774$	−9.70437	−0.348816
$775$	−0.313569	−0.0112637
$776$	−2.53961	−0.0911668
$777$	0	0
$778$	−46.6452	−1.67231
$779$	4.41144	0.158056
$780$	−21.5824	−0.772774
$781$	11.7544	0.420607
$782$	16.6975	0.597102
$783$	3.41695	0.122112
$784$	0	0
$785$	16.1401	0.576066
$786$	29.9939	1.06985
$787$	−22.0228	−0.785027	−0.392513	−	0.919746i	$-0.628394\pi$
$787$	−22.0228	−0.785027	−0.392513	+	0.919746i	$0.628394\pi$
$788$	−59.4412	−2.11751
$789$	−4.26169	−0.151720
$790$	−16.9751	−0.603945
$791$	0	0
$792$	−1.46373	−0.0520115
$793$	21.0328	0.746895
$794$	70.8245	2.51347
$795$	7.90516	0.280367
$796$	28.6196	1.01439
$797$	−16.6446	−0.589583	−0.294791	−	0.955562i	$-0.595250\pi$
$797$	−16.6446	−0.589583	−0.294791	+	0.955562i	$0.595250\pi$
$798$	0	0
$799$	13.4048	0.474229
$800$	−2.36442	−0.0835948
$801$	5.51735	0.194946
$802$	54.5573	1.92649
$803$	−12.7772	−0.450899
$804$	25.2637	0.890982
$805$	0	0
$806$	−9.04877	−0.318729
$807$	−14.8791	−0.523768
$808$	7.67472	0.269996
$809$	−20.1468	−0.708323	−0.354162	−	0.935184i	$-0.615234\pi$
$809$	−20.1468	−0.708323	−0.354162	+	0.935184i	$0.615234\pi$
$810$	−4.77814	−0.167887
$811$	34.5884	1.21456	0.607282	−	0.794487i	$-0.292260\pi$
$811$	34.5884	1.21456	0.607282	+	0.794487i	$0.292260\pi$
$812$	0	0
$813$	−24.8652	−0.872059
$814$	7.63554	0.267626
$815$	−42.6898	−1.49536
$816$	−4.00944	−0.140359
$817$	−20.6105	−0.721071
$818$	−28.5024	−0.996561
$819$	0	0
$820$	−5.32392	−0.185919
$821$	−31.8361	−1.11109	−0.555543	−	0.831488i	$-0.687490\pi$
$821$	−31.8361	−1.11109	−0.555543	+	0.831488i	$0.687490\pi$
$822$	16.5263	0.576421
$823$	3.12481	0.108924	0.0544620	−	0.998516i	$-0.482656\pi$
$823$	3.12481	0.108924	0.0544620	+	0.998516i	$0.482656\pi$
$824$	−5.10476	−0.177833
$825$	−0.654114	−0.0227733
$826$	0	0
$827$	9.35195	0.325199	0.162600	−	0.986692i	$-0.448012\pi$
$827$	9.35195	0.325199	0.162600	+	0.986692i	$0.448012\pi$
$828$	15.1850	0.527716
$829$	12.0702	0.419215	0.209608	−	0.977786i	$-0.432781\pi$
$829$	12.0702	0.419215	0.209608	+	0.977786i	$0.432781\pi$
$830$	−11.6942	−0.405910
$831$	−24.1746	−0.838608
$832$	−41.6985	−1.44564
$833$	0	0
$834$	−18.6129	−0.644513
$835$	−34.0622	−1.17877
$836$	−22.8872	−0.791570
$837$	−1.07464	−0.0371450
$838$	−10.4514	−0.361037
$839$	14.1488	0.488472	0.244236	−	0.969716i	$-0.421463\pi$
$839$	14.1488	0.488472	0.244236	+	0.969716i	$0.421463\pi$
$840$	0	0
$841$	−17.3245	−0.597396
$842$	73.4091	2.52985
$843$	−11.0063	−0.379078
$844$	−29.4801	−1.01475
$845$	−7.89898	−0.271733
$846$	22.7254	0.781314
$847$	0	0
$848$	11.2457	0.386178
$849$	−16.1057	−0.552748
$850$	0.742569	0.0254699
$851$	−10.7593	−0.368825
$852$	−12.1353	−0.415747
$853$	51.9016	1.77708	0.888538	−	0.458804i	$-0.151722\pi$
$853$	51.9016	1.77708	0.888538	+	0.458804i	$0.151722\pi$
$854$	0	0
$855$	−10.1480	−0.347055
$856$	9.74210	0.332978
$857$	26.5421	0.906662	0.453331	−	0.891342i	$-0.350236\pi$
$857$	26.5421	0.906662	0.453331	+	0.891342i	$0.350236\pi$
$858$	−18.8760	−0.644415
$859$	24.1629	0.824427	0.412214	−	0.911087i	$-0.364756\pi$
$859$	24.1629	0.824427	0.412214	+	0.911087i	$0.364756\pi$
$860$	24.8737	0.848187
$861$	0	0
$862$	−20.7777	−0.707692
$863$	49.6475	1.69002	0.845011	−	0.534749i	$-0.179594\pi$
$863$	49.6475	1.69002	0.845011	+	0.534749i	$0.179594\pi$
$864$	−8.10315	−0.275675
$865$	48.7088	1.65615
$866$	0.474824	0.0161352
$867$	−15.4989	−0.526369
$868$	0	0
$869$	−7.96406	−0.270162
$870$	−16.3267	−0.553526
$871$	44.2523	1.49943
$872$	−1.59835	−0.0541270
$873$	−3.88945	−0.131638
$874$	60.1206	2.03361
$875$	0	0
$876$	13.1912	0.445689
$877$	−0.127968	−0.00432118	−0.00216059	−	0.999998i	$-0.500688\pi$
$877$	−0.127968	−0.00432118	−0.00216059	+	0.999998i	$0.500688\pi$
$878$	−13.7877	−0.465313
$879$	12.6292	0.425974
$880$	−16.8756	−0.568877
$881$	−35.9413	−1.21089	−0.605446	−	0.795886i	$-0.707005\pi$
$881$	−35.9413	−1.21089	−0.605446	+	0.795886i	$0.707005\pi$
$882$	0	0
$883$	12.5574	0.422590	0.211295	−	0.977422i	$-0.432232\pi$
$883$	12.5574	0.422590	0.211295	+	0.977422i	$0.432232\pi$
$884$	11.4949	0.386617
$885$	−22.7743	−0.765551
$886$	−71.2224	−2.39276
$887$	−13.9193	−0.467364	−0.233682	−	0.972313i	$-0.575078\pi$
$887$	−13.9193	−0.467364	−0.233682	+	0.972313i	$0.575078\pi$
$888$	−1.07073	−0.0359312
$889$	0	0
$890$	−26.3627	−0.883679
$891$	−2.24173	−0.0751007
$892$	−33.6525	−1.12677
$893$	48.2651	1.61513
$894$	−7.36851	−0.246440
$895$	−16.3084	−0.545129
$896$	0	0
$897$	26.5983	0.888092
$898$	−49.4362	−1.64971
$899$	−3.67199	−0.122468
$900$	0.675306	0.0225102
$901$	−4.21035	−0.140267
$902$	−4.65630	−0.155038
$903$	0	0
$904$	−3.70060	−0.123080
$905$	−55.2974	−1.83815
$906$	−18.6739	−0.620398
$907$	−44.7454	−1.48575	−0.742874	−	0.669431i	$-0.766538\pi$
$907$	−44.7454	−1.48575	−0.742874	+	0.669431i	$0.766538\pi$
$908$	−29.5307	−0.980011
$909$	11.7539	0.389853
$910$	0	0
$911$	−10.4251	−0.345400	−0.172700	−	0.984975i	$-0.555249\pi$
$911$	−10.4251	−0.345400	−0.172700	+	0.984975i	$0.555249\pi$
$912$	−14.4363	−0.478033
$913$	−5.48647	−0.181576
$914$	8.09663	0.267813
$915$	−11.9352	−0.394565
$916$	−37.8480	−1.25053
$917$	0	0
$918$	2.54488	0.0839934
$919$	24.6925	0.814532	0.407266	−	0.913310i	$-0.366482\pi$
$919$	24.6925	0.814532	0.407266	+	0.913310i	$0.366482\pi$
$920$	−9.85521	−0.324917
$921$	−23.2927	−0.767522
$922$	18.3268	0.603561
$923$	−21.2563	−0.699659
$924$	0	0
$925$	−0.478486	−0.0157325
$926$	−56.3077	−1.85039
$927$	−7.81801	−0.256777
$928$	−27.6880	−0.908904
$929$	0.159923	0.00524692	0.00262346	−	0.999997i	$-0.499165\pi$
$929$	0.159923	0.00524692	0.00262346	+	0.999997i	$0.499165\pi$
$930$	5.13479	0.168376
$931$	0	0
$932$	59.4356	1.94688
$933$	8.17595	0.267669
$934$	82.3814	2.69560
$935$	6.31819	0.206627
$936$	2.64696	0.0865186
$937$	−28.2710	−0.923572	−0.461786	−	0.886991i	$-0.652791\pi$
$937$	−28.2710	−0.923572	−0.461786	+	0.886991i	$0.652791\pi$
$938$	0	0
$939$	16.9412	0.552857
$940$	−58.2485	−1.89986
$941$	−12.0075	−0.391434	−0.195717	−	0.980660i	$-0.562703\pi$
$941$	−12.0075	−0.391434	−0.195717	+	0.980660i	$0.562703\pi$
$942$	−14.5735	−0.474830
$943$	6.56124	0.213663
$944$	−32.3981	−1.05447
$945$	0	0
$946$	21.7545	0.707301
$947$	1.30006	0.0422463	0.0211232	−	0.999777i	$-0.493276\pi$
$947$	1.30006	0.0422463	0.0211232	+	0.999777i	$0.493276\pi$
$948$	8.22209	0.267041
$949$	23.1059	0.750049
$950$	2.67367	0.0867454
$951$	10.8754	0.352659
$952$	0	0
$953$	−58.2749	−1.88771	−0.943854	−	0.330363i	$-0.892829\pi$
$953$	−58.2749	−1.88771	−0.943854	+	0.330363i	$0.892829\pi$
$954$	−7.13785	−0.231096
$955$	−45.4880	−1.47196
$956$	−15.4678	−0.500265
$957$	−7.65986	−0.247608
$958$	−1.37364	−0.0443803
$959$	0	0
$960$	23.6621	0.763692
$961$	−29.8451	−0.962747
$962$	−13.8078	−0.445182
$963$	14.9202	0.480795
$964$	−29.6514	−0.955006
$965$	24.7031	0.795220
$966$	0	0
$967$	39.2902	1.26349	0.631743	−	0.775178i	$-0.282340\pi$
$967$	39.2902	1.26349	0.631743	+	0.775178i	$0.282340\pi$
$968$	−3.90115	−0.125388
$969$	5.40491	0.173631
$970$	18.5844	0.596708
$971$	56.1663	1.80246	0.901232	−	0.433338i	$-0.142664\pi$
$971$	56.1663	1.80246	0.901232	+	0.433338i	$0.142664\pi$
$972$	2.31436	0.0742330
$973$	0	0
$974$	−25.0999	−0.804251
$975$	1.18288	0.0378823
$976$	−16.9787	−0.543474
$977$	−14.6676	−0.469259	−0.234629	−	0.972085i	$-0.575388\pi$
$977$	−14.6676	−0.469259	−0.234629	+	0.972085i	$0.575388\pi$
$978$	38.5461	1.23257
$979$	−12.3684	−0.395295
$980$	0	0
$981$	−2.44790	−0.0781554
$982$	−12.2471	−0.390821
$983$	−29.8488	−0.952027	−0.476014	−	0.879438i	$-0.657919\pi$
$983$	−29.8488	−0.952027	−0.476014	+	0.879438i	$0.657919\pi$
$984$	0.652949	0.0208152
$985$	59.0825	1.88253
$986$	8.69570	0.276928
$987$	0	0
$988$	41.3884	1.31674
$989$	−30.6546	−0.974758
$990$	10.7113	0.340427
$991$	−48.8390	−1.55142	−0.775710	−	0.631089i	$-0.782608\pi$
$991$	−48.8390	−1.55142	−0.775710	+	0.631089i	$0.782608\pi$
$992$	8.70797	0.276478
$993$	−12.5272	−0.397539
$994$	0	0
$995$	−28.4469	−0.901827
$996$	5.66422	0.179478
$997$	−43.4145	−1.37495	−0.687475	−	0.726208i	$-0.741281\pi$
$997$	−43.4145	−1.37495	−0.687475	+	0.726208i	$0.741281\pi$
$998$	−20.0807	−0.635644
$999$	−1.63983	−0.0518820

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bc.1.7		8
7.3	odd	6		861.2.i.d.247.2	✓	16
7.5	odd	6		861.2.i.d.739.2	yes	16
7.6	odd	2		6027.2.a.bb.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.i.d.247.2	✓	16	7.3	odd	6
861.2.i.d.739.2	yes	16	7.5	odd	6
6027.2.a.bb.1.7		8	7.6	odd	2
6027.2.a.bc.1.7		8	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6027.a (trivial)

\(f(q)\)	\(=\)	\(q+2.07710 q^{2} +1.00000 q^{3} +2.31436 q^{4} -2.30039 q^{5} +2.07710 q^{6} +0.652949 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.07710 q^{2} +1.00000 q^{3} +2.31436 q^{4} -2.30039 q^{5} +2.07710 q^{6} +0.652949 q^{8} +1.00000 q^{9} -4.77814 q^{10} -2.24173 q^{11} +2.31436 q^{12} +4.05386 q^{13} -2.30039 q^{15} -3.27247 q^{16} +1.22520 q^{17} +2.07710 q^{18} +4.41144 q^{19} -5.32392 q^{20} -4.65630 q^{22} +6.56124 q^{23} +0.652949 q^{24} +0.291790 q^{25} +8.42028 q^{26} +1.00000 q^{27} +3.41695 q^{29} -4.77814 q^{30} -1.07464 q^{31} -8.10315 q^{32} -2.24173 q^{33} +2.54488 q^{34} +2.31436 q^{36} -1.63983 q^{37} +9.16300 q^{38} +4.05386 q^{39} -1.50204 q^{40} +1.00000 q^{41} -4.67207 q^{43} -5.18815 q^{44} -2.30039 q^{45} +13.6284 q^{46} +10.9409 q^{47} -3.27247 q^{48} +0.606078 q^{50} +1.22520 q^{51} +9.38207 q^{52} -3.43644 q^{53} +2.07710 q^{54} +5.15684 q^{55} +4.41144 q^{57} +7.09735 q^{58} +9.90021 q^{59} -5.32392 q^{60} +5.18833 q^{61} -2.23214 q^{62} -10.2861 q^{64} -9.32545 q^{65} -4.65630 q^{66} +10.9161 q^{67} +2.83556 q^{68} +6.56124 q^{69} -5.24347 q^{71} +0.652949 q^{72} +5.69973 q^{73} -3.40610 q^{74} +0.291790 q^{75} +10.2096 q^{76} +8.42028 q^{78} +3.55265 q^{79} +7.52795 q^{80} +1.00000 q^{81} +2.07710 q^{82} +2.44743 q^{83} -2.81845 q^{85} -9.70437 q^{86} +3.41695 q^{87} -1.46373 q^{88} +5.51735 q^{89} -4.77814 q^{90} +15.1850 q^{92} -1.07464 q^{93} +22.7254 q^{94} -10.1480 q^{95} -8.10315 q^{96} -3.88945 q^{97} -2.24173 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + 8 q^{3} + 13 q^{4} + 7 q^{5} + q^{6} + 6 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + q^2 + 8 * q^3 + 13 * q^4 + 7 * q^5 + q^6 + 6 * q^8 + 8 * q^9	\( 8 q + q^{2} + 8 q^{3} + 13 q^{4} + 7 q^{5} + q^{6} + 6 q^{8} + 8 q^{9} + 8 q^{10} + 11 q^{11} + 13 q^{12} + 10 q^{13} + 7 q^{15} - 17 q^{16} + 3 q^{17} + q^{18} + 6 q^{19} + 11 q^{20} + 15 q^{22} + 14 q^{23} + 6 q^{24} + 25 q^{25} + 24 q^{26} + 8 q^{27} + 2 q^{29} + 8 q^{30} + 16 q^{31} + 3 q^{32} + 11 q^{33} - 4 q^{34} + 13 q^{36} - 20 q^{37} + 10 q^{38} + 10 q^{39} - 3 q^{40} + 8 q^{41} + 7 q^{43} + 7 q^{45} - 5 q^{46} + 14 q^{47} - 17 q^{48} - 5 q^{50} + 3 q^{51} + 23 q^{52} + 7 q^{53} + q^{54} + 48 q^{55} + 6 q^{57} - 20 q^{58} + 22 q^{59} + 11 q^{60} - 33 q^{62} - 10 q^{64} - 14 q^{65} + 15 q^{66} + 12 q^{67} - 27 q^{68} + 14 q^{69} - 5 q^{71} + 6 q^{72} + 2 q^{73} + 6 q^{74} + 25 q^{75} + 43 q^{76} + 24 q^{78} - 15 q^{79} - 7 q^{80} + 8 q^{81} + q^{82} + 15 q^{83} - 43 q^{85} + 31 q^{86} + 2 q^{87} + 17 q^{88} + 29 q^{89} + 8 q^{90} + 19 q^{92} + 16 q^{93} + 20 q^{94} + 14 q^{95} + 3 q^{96} + 19 q^{97} + 11 q^{99}+O(q^{100}) \) 8 * q + q^2 + 8 * q^3 + 13 * q^4 + 7 * q^5 + q^6 + 6 * q^8 + 8 * q^9 + 8 * q^10 + 11 * q^11 + 13 * q^12 + 10 * q^13 + 7 * q^15 - 17 * q^16 + 3 * q^17 + q^18 + 6 * q^19 + 11 * q^20 + 15 * q^22 + 14 * q^23 + 6 * q^24 + 25 * q^25 + 24 * q^26 + 8 * q^27 + 2 * q^29 + 8 * q^30 + 16 * q^31 + 3 * q^32 + 11 * q^33 - 4 * q^34 + 13 * q^36 - 20 * q^37 + 10 * q^38 + 10 * q^39 - 3 * q^40 + 8 * q^41 + 7 * q^43 + 7 * q^45 - 5 * q^46 + 14 * q^47 - 17 * q^48 - 5 * q^50 + 3 * q^51 + 23 * q^52 + 7 * q^53 + q^54 + 48 * q^55 + 6 * q^57 - 20 * q^58 + 22 * q^59 + 11 * q^60 - 33 * q^62 - 10 * q^64 - 14 * q^65 + 15 * q^66 + 12 * q^67 - 27 * q^68 + 14 * q^69 - 5 * q^71 + 6 * q^72 + 2 * q^73 + 6 * q^74 + 25 * q^75 + 43 * q^76 + 24 * q^78 - 15 * q^79 - 7 * q^80 + 8 * q^81 + q^82 + 15 * q^83 - 43 * q^85 + 31 * q^86 + 2 * q^87 + 17 * q^88 + 29 * q^89 + 8 * q^90 + 19 * q^92 + 16 * q^93 + 20 * q^94 + 14 * q^95 + 3 * q^96 + 19 * q^97 + 11 * q^99

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