LMFDB - Embedded newform 2695.2.a.r.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2695,2,Mod(1,2695)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2695, 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("2695.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2695 = 5 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2695.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:	$21.5196833447$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.15751800.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 8x^{4} + 6x^{3} + 16x^{2} - 7x - 1 $ x^6 - x^5 - 8x^4 + 6x^3 + 16x^2 - 7x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 385)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.66208$ of defining polynomial
Character	$\chi$	$=$	2695.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.05680 q^{2} -1.66208 q^{3} +2.23042 q^{4} -1.00000 q^{5} +3.41857 q^{6} -0.473937 q^{8} -0.237484 q^{9} +O(q^{10})$	\(q-2.05680 q^{2} -1.66208 q^{3} +2.23042 q^{4} -1.00000 q^{5} +3.41857 q^{6} -0.473937 q^{8} -0.237484 q^{9} +2.05680 q^{10} -1.00000 q^{11} -3.70715 q^{12} +1.53780 q^{13} +1.66208 q^{15} -3.48606 q^{16} -1.88888 q^{17} +0.488457 q^{18} +3.08668 q^{19} -2.23042 q^{20} +2.05680 q^{22} +0.952738 q^{23} +0.787722 q^{24} +1.00000 q^{25} -3.16294 q^{26} +5.38096 q^{27} -8.17403 q^{29} -3.41857 q^{30} -3.77997 q^{31} +8.11799 q^{32} +1.66208 q^{33} +3.88505 q^{34} -0.529690 q^{36} +2.40821 q^{37} -6.34868 q^{38} -2.55594 q^{39} +0.473937 q^{40} +2.20800 q^{41} -3.36988 q^{43} -2.23042 q^{44} +0.237484 q^{45} -1.95959 q^{46} +7.68887 q^{47} +5.79411 q^{48} -2.05680 q^{50} +3.13947 q^{51} +3.42994 q^{52} +1.64899 q^{53} -11.0676 q^{54} +1.00000 q^{55} -5.13031 q^{57} +16.8123 q^{58} -7.32489 q^{59} +3.70715 q^{60} +11.0714 q^{61} +7.77465 q^{62} -9.72497 q^{64} -1.53780 q^{65} -3.41857 q^{66} -3.91838 q^{67} -4.21300 q^{68} -1.58353 q^{69} -9.15592 q^{71} +0.112552 q^{72} +9.42931 q^{73} -4.95320 q^{74} -1.66208 q^{75} +6.88461 q^{76} +5.25706 q^{78} +6.45208 q^{79} +3.48606 q^{80} -8.23115 q^{81} -4.54142 q^{82} +10.8285 q^{83} +1.88888 q^{85} +6.93116 q^{86} +13.5859 q^{87} +0.473937 q^{88} -12.1979 q^{89} -0.488457 q^{90} +2.12501 q^{92} +6.28263 q^{93} -15.8145 q^{94} -3.08668 q^{95} -13.4928 q^{96} +12.1284 q^{97} +0.237484 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} + q^{3} + 5 q^{4} - 6 q^{5} - 5 q^{6} - 9 q^{8} - q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 + q^3 + 5 * q^4 - 6 * q^5 - 5 * q^6 - 9 * q^8 - q^9	$ 6 q - 3 q^{2} + q^{3} + 5 q^{4} - 6 q^{5} - 5 q^{6} - 9 q^{8} - q^{9} + 3 q^{10} - 6 q^{11} + 9 q^{12} + 14 q^{13} - q^{15} + 11 q^{16} + 3 q^{17} - 9 q^{18} - 3 q^{19} - 5 q^{20} + 3 q^{22} - 10 q^{23} - 10 q^{24} + 6 q^{25} - 17 q^{26} + q^{27} - 16 q^{29} + 5 q^{30} + 2 q^{31} - 26 q^{32} - q^{33} + 30 q^{34} + 8 q^{36} + 5 q^{37} + q^{38} + 3 q^{39} + 9 q^{40} - 9 q^{41} - 20 q^{43} - 5 q^{44} + q^{45} - 20 q^{46} + q^{47} + 41 q^{48} - 3 q^{50} - 5 q^{51} + 23 q^{52} - 24 q^{53} - 7 q^{54} + 6 q^{55} - 30 q^{57} + 31 q^{58} - 7 q^{59} - 9 q^{60} - 14 q^{61} + 24 q^{62} + 15 q^{64} - 14 q^{65} + 5 q^{66} + q^{67} - 25 q^{68} - 4 q^{69} - 9 q^{71} - 26 q^{72} + 13 q^{73} - 40 q^{74} + q^{75} - 10 q^{76} - 33 q^{78} - 4 q^{79} - 11 q^{80} - 26 q^{81} - 27 q^{82} + 8 q^{83} - 3 q^{85} + 36 q^{86} - 2 q^{87} + 9 q^{88} - 13 q^{89} + 9 q^{90} - 18 q^{92} - 36 q^{93} - q^{94} + 3 q^{95} - 89 q^{96} - 3 q^{97} + q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 + q^3 + 5 * q^4 - 6 * q^5 - 5 * q^6 - 9 * q^8 - q^9 + 3 * q^10 - 6 * q^11 + 9 * q^12 + 14 * q^13 - q^15 + 11 * q^16 + 3 * q^17 - 9 * q^18 - 3 * q^19 - 5 * q^20 + 3 * q^22 - 10 * q^23 - 10 * q^24 + 6 * q^25 - 17 * q^26 + q^27 - 16 * q^29 + 5 * q^30 + 2 * q^31 - 26 * q^32 - q^33 + 30 * q^34 + 8 * q^36 + 5 * q^37 + q^38 + 3 * q^39 + 9 * q^40 - 9 * q^41 - 20 * q^43 - 5 * q^44 + q^45 - 20 * q^46 + q^47 + 41 * q^48 - 3 * q^50 - 5 * q^51 + 23 * q^52 - 24 * q^53 - 7 * q^54 + 6 * q^55 - 30 * q^57 + 31 * q^58 - 7 * q^59 - 9 * q^60 - 14 * q^61 + 24 * q^62 + 15 * q^64 - 14 * q^65 + 5 * q^66 + q^67 - 25 * q^68 - 4 * q^69 - 9 * q^71 - 26 * q^72 + 13 * q^73 - 40 * q^74 + q^75 - 10 * q^76 - 33 * q^78 - 4 * q^79 - 11 * q^80 - 26 * q^81 - 27 * q^82 + 8 * q^83 - 3 * q^85 + 36 * q^86 - 2 * q^87 + 9 * q^88 - 13 * q^89 + 9 * q^90 - 18 * q^92 - 36 * q^93 - q^94 + 3 * q^95 - 89 * q^96 - 3 * q^97 + 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 $

$2$	−2.05680	−1.45438	−0.727188	−	0.686438i	$-0.759173\pi$
$2$	−2.05680	−1.45438	−0.727188	+	0.686438i	$0.759173\pi$
$3$	−1.66208	−0.959603	−0.479802	−	0.877377i	$-0.659291\pi$
$3$	−1.66208	−0.959603	−0.479802	+	0.877377i	$0.659291\pi$
$4$	2.23042	1.11521
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	3.41857	1.39563
$7$	0	0
$7$	0	0
$8$	−0.473937	−0.167562
$9$	−0.237484	−0.0791613
$10$	2.05680	0.650417
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−3.70715	−1.07016
$13$	1.53780	0.426508	0.213254	−	0.976997i	$-0.431594\pi$
$13$	1.53780	0.426508	0.213254	+	0.976997i	$0.431594\pi$
$14$	0	0
$15$	1.66208	0.429148
$16$	−3.48606	−0.871514
$17$	−1.88888	−0.458121	−0.229060	−	0.973412i	$-0.573565\pi$
$17$	−1.88888	−0.458121	−0.229060	+	0.973412i	$0.573565\pi$
$18$	0.488457	0.115130
$19$	3.08668	0.708133	0.354066	−	0.935220i	$-0.384799\pi$
$19$	3.08668	0.708133	0.354066	+	0.935220i	$0.384799\pi$
$20$	−2.23042	−0.498738
$21$	0	0
$22$	2.05680	0.438511
$23$	0.952738	0.198660	0.0993298	−	0.995055i	$-0.468330\pi$
$23$	0.952738	0.198660	0.0993298	+	0.995055i	$0.468330\pi$
$24$	0.787722	0.160793
$25$	1.00000	0.200000
$26$	−3.16294	−0.620303
$27$	5.38096	1.03557
$28$	0	0
$29$	−8.17403	−1.51788	−0.758939	−	0.651161i	$-0.774282\pi$
$29$	−8.17403	−1.51788	−0.758939	+	0.651161i	$0.774282\pi$
$30$	−3.41857	−0.624142
$31$	−3.77997	−0.678903	−0.339452	−	0.940623i	$-0.610242\pi$
$31$	−3.77997	−0.678903	−0.339452	+	0.940623i	$0.610242\pi$
$32$	8.11799	1.43507
$33$	1.66208	0.289331
$34$	3.88505	0.666280
$35$	0	0
$36$	−0.529690	−0.0882817
$37$	2.40821	0.395907	0.197953	−	0.980211i	$-0.436571\pi$
$37$	2.40821	0.395907	0.197953	+	0.980211i	$0.436571\pi$
$38$	−6.34868	−1.02989
$39$	−2.55594	−0.409278
$40$	0.473937	0.0749360
$41$	2.20800	0.344832	0.172416	−	0.985024i	$-0.444843\pi$
$41$	2.20800	0.344832	0.172416	+	0.985024i	$0.444843\pi$
$42$	0	0
$43$	−3.36988	−0.513901	−0.256951	−	0.966425i	$-0.582718\pi$
$43$	−3.36988	−0.513901	−0.256951	+	0.966425i	$0.582718\pi$
$44$	−2.23042	−0.336249
$45$	0.237484	0.0354020
$46$	−1.95959	−0.288926
$47$	7.68887	1.12154	0.560769	−	0.827973i	$-0.310506\pi$
$47$	7.68887	1.12154	0.560769	+	0.827973i	$0.310506\pi$
$48$	5.79411	0.836308
$49$	0	0
$50$	−2.05680	−0.290875
$51$	3.13947	0.439614
$52$	3.42994	0.475647
$53$	1.64899	0.226507	0.113253	−	0.993566i	$-0.463873\pi$
$53$	1.64899	0.226507	0.113253	+	0.993566i	$0.463873\pi$
$54$	−11.0676	−1.50610
$55$	1.00000	0.134840
$56$	0	0
$57$	−5.13031	−0.679527
$58$	16.8123	2.20757
$59$	−7.32489	−0.953619	−0.476810	−	0.879007i	$-0.658207\pi$
$59$	−7.32489	−0.953619	−0.476810	+	0.879007i	$0.658207\pi$
$60$	3.70715	0.478591
$61$	11.0714	1.41755	0.708774	−	0.705436i	$-0.249249\pi$
$61$	11.0714	1.41755	0.708774	+	0.705436i	$0.249249\pi$
$62$	7.77465	0.987382
$63$	0	0
$64$	−9.72497	−1.21562
$65$	−1.53780	−0.190740
$66$	−3.41857	−0.420797
$67$	−3.91838	−0.478706	−0.239353	−	0.970933i	$-0.576935\pi$
$67$	−3.91838	−0.478706	−0.239353	+	0.970933i	$0.576935\pi$
$68$	−4.21300	−0.510902
$69$	−1.58353	−0.190634
$70$	0	0
$71$	−9.15592	−1.08661	−0.543304	−	0.839536i	$-0.682827\pi$
$71$	−9.15592	−1.08661	−0.543304	+	0.839536i	$0.682827\pi$
$72$	0.112552	0.0132644
$73$	9.42931	1.10362	0.551809	−	0.833971i	$-0.313938\pi$
$73$	9.42931	1.10362	0.551809	+	0.833971i	$0.313938\pi$
$74$	−4.95320	−0.575798
$75$	−1.66208	−0.191921
$76$	6.88461	0.789719
$77$	0	0
$78$	5.25706	0.595245
$79$	6.45208	0.725915	0.362958	−	0.931806i	$-0.381767\pi$
$79$	6.45208	0.725915	0.362958	+	0.931806i	$0.381767\pi$
$80$	3.48606	0.389753
$81$	−8.23115	−0.914572
$82$	−4.54142	−0.501516
$83$	10.8285	1.18859	0.594293	−	0.804249i	$-0.297432\pi$
$83$	10.8285	1.18859	0.594293	+	0.804249i	$0.297432\pi$
$84$	0	0
$85$	1.88888	0.204878
$86$	6.93116	0.747406
$87$	13.5859	1.45656
$88$	0.473937	0.0505219
$89$	−12.1979	−1.29297	−0.646486	−	0.762926i	$-0.723762\pi$
$89$	−12.1979	−1.29297	−0.646486	+	0.762926i	$0.723762\pi$
$90$	−0.488457	−0.0514879
$91$	0	0
$92$	2.12501	0.221548
$93$	6.28263	0.651478
$94$	−15.8145	−1.63114
$95$	−3.08668	−0.316687
$96$	−13.4928	−1.37710
$97$	12.1284	1.23145	0.615725	−	0.787961i	$-0.288863\pi$
$97$	12.1284	1.23145	0.615725	+	0.787961i	$0.288863\pi$
$98$	0	0
$99$	0.237484	0.0238680
$100$	2.23042	0.223042
$101$	12.1639	1.21035	0.605177	−	0.796091i	$-0.293103\pi$
$101$	12.1639	1.21035	0.605177	+	0.796091i	$0.293103\pi$
$102$	−6.45726	−0.639364
$103$	−1.80703	−0.178052	−0.0890261	−	0.996029i	$-0.528375\pi$
$103$	−1.80703	−0.178052	−0.0890261	+	0.996029i	$0.528375\pi$
$104$	−0.728819	−0.0714666
$105$	0	0
$106$	−3.39165	−0.329426
$107$	−10.8223	−1.04623	−0.523115	−	0.852262i	$-0.675230\pi$
$107$	−10.8223	−1.04623	−0.523115	+	0.852262i	$0.675230\pi$
$108$	12.0018	1.15488
$109$	17.0414	1.63227	0.816134	−	0.577862i	$-0.196113\pi$
$109$	17.0414	1.63227	0.816134	+	0.577862i	$0.196113\pi$
$110$	−2.05680	−0.196108
$111$	−4.00264	−0.379913
$112$	0	0
$113$	17.2417	1.62196	0.810980	−	0.585074i	$-0.198935\pi$
$113$	17.2417	1.62196	0.810980	+	0.585074i	$0.198935\pi$
$114$	10.5520	0.988288
$115$	−0.952738	−0.0888433
$116$	−18.2315	−1.69276
$117$	−0.365202	−0.0337629
$118$	15.0658	1.38692
$119$	0	0
$120$	−0.787722	−0.0719089
$121$	1.00000	0.0909091
$122$	−22.7716	−2.06165
$123$	−3.66988	−0.330902
$124$	−8.43095	−0.757122
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	5.39923	0.479104	0.239552	−	0.970884i	$-0.422999\pi$
$127$	5.39923	0.479104	0.239552	+	0.970884i	$0.422999\pi$
$128$	3.76633	0.332900
$129$	5.60101	0.493141
$130$	3.16294	0.277408
$131$	13.9374	1.21772	0.608860	−	0.793278i	$-0.291627\pi$
$131$	13.9374	1.21772	0.608860	+	0.793278i	$0.291627\pi$
$132$	3.70715	0.322666
$133$	0	0
$134$	8.05932	0.696219
$135$	−5.38096	−0.463120
$136$	0.895210	0.0767636
$137$	−16.7222	−1.42867	−0.714336	−	0.699803i	$-0.753271\pi$
$137$	−16.7222	−1.42867	−0.714336	+	0.699803i	$0.753271\pi$
$138$	3.25700	0.277254
$139$	−14.5504	−1.23414	−0.617072	−	0.786906i	$-0.711681\pi$
$139$	−14.5504	−1.23414	−0.617072	+	0.786906i	$0.711681\pi$
$140$	0	0
$141$	−12.7795	−1.07623
$142$	18.8319	1.58034
$143$	−1.53780	−0.128597
$144$	0.827882	0.0689902
$145$	8.17403	0.678816
$146$	−19.3942	−1.60508
$147$	0	0
$148$	5.37132	0.441520
$149$	−21.1611	−1.73359	−0.866794	−	0.498666i	$-0.833823\pi$
$149$	−21.1611	−1.73359	−0.866794	+	0.498666i	$0.833823\pi$
$150$	3.41857	0.279125
$151$	−8.60389	−0.700175	−0.350087	−	0.936717i	$-0.613848\pi$
$151$	−8.60389	−0.700175	−0.350087	+	0.936717i	$0.613848\pi$
$152$	−1.46289	−0.118656
$153$	0.448578	0.0362654
$154$	0	0
$155$	3.77997	0.303615
$156$	−5.70084	−0.456432
$157$	5.41597	0.432242	0.216121	−	0.976367i	$-0.430659\pi$
$157$	5.41597	0.432242	0.216121	+	0.976367i	$0.430659\pi$
$158$	−13.2706	−1.05575
$159$	−2.74076	−0.217357
$160$	−8.11799	−0.641784
$161$	0	0
$162$	16.9298	1.33013
$163$	6.20940	0.486358	0.243179	−	0.969981i	$-0.421810\pi$
$163$	6.20940	0.486358	0.243179	+	0.969981i	$0.421810\pi$
$164$	4.92479	0.384561
$165$	−1.66208	−0.129393
$166$	−22.2721	−1.72865
$167$	2.53431	0.196110	0.0980552	−	0.995181i	$-0.468738\pi$
$167$	2.53431	0.196110	0.0980552	+	0.995181i	$0.468738\pi$
$168$	0	0
$169$	−10.6352	−0.818091
$170$	−3.88505	−0.297969
$171$	−0.733037	−0.0560567
$172$	−7.51625	−0.573109
$173$	−22.3297	−1.69770	−0.848848	−	0.528637i	$-0.822703\pi$
$173$	−22.3297	−1.69770	−0.848848	+	0.528637i	$0.822703\pi$
$174$	−27.9435	−2.11839
$175$	0	0
$176$	3.48606	0.262771
$177$	12.1746	0.915096
$178$	25.0886	1.88047
$179$	21.8910	1.63621	0.818104	−	0.575071i	$-0.195025\pi$
$179$	21.8910	1.63621	0.818104	+	0.575071i	$0.195025\pi$
$180$	0.529690	0.0394808
$181$	−20.9562	−1.55766	−0.778829	−	0.627236i	$-0.784186\pi$
$181$	−20.9562	−1.55766	−0.778829	+	0.627236i	$0.784186\pi$
$182$	0	0
$183$	−18.4016	−1.36028
$184$	−0.451538	−0.0332878
$185$	−2.40821	−0.177055
$186$	−12.9221	−0.947495
$187$	1.88888	0.138129
$188$	17.1494	1.25075
$189$	0	0
$190$	6.34868	0.460582
$191$	−2.48105	−0.179523	−0.0897613	−	0.995963i	$-0.528610\pi$
$191$	−2.48105	−0.179523	−0.0897613	+	0.995963i	$0.528610\pi$
$192$	16.1637	1.16651
$193$	16.3290	1.17539	0.587693	−	0.809084i	$-0.300036\pi$
$193$	16.3290	1.17539	0.587693	+	0.809084i	$0.300036\pi$
$194$	−24.9456	−1.79099
$195$	2.55594	0.183035
$196$	0	0
$197$	−24.9926	−1.78065	−0.890326	−	0.455324i	$-0.849523\pi$
$197$	−24.9926	−1.78065	−0.890326	+	0.455324i	$0.849523\pi$
$198$	−0.488457	−0.0347131
$199$	−13.3049	−0.943161	−0.471581	−	0.881823i	$-0.656316\pi$
$199$	−13.3049	−0.943161	−0.471581	+	0.881823i	$0.656316\pi$
$200$	−0.473937	−0.0335124
$201$	6.51267	0.459368
$202$	−25.0187	−1.76031
$203$	0	0
$204$	7.00236	0.490263
$205$	−2.20800	−0.154214
$206$	3.71670	0.258955
$207$	−0.226260	−0.0157262
$208$	−5.36084	−0.371708
$209$	−3.08668	−0.213510
$210$	0	0
$211$	1.59145	0.109560	0.0547800	−	0.998498i	$-0.482554\pi$
$211$	1.59145	0.109560	0.0547800	+	0.998498i	$0.482554\pi$
$212$	3.67796	0.252603
$213$	15.2179	1.04271
$214$	22.2593	1.52161
$215$	3.36988	0.229824
$216$	−2.55024	−0.173522
$217$	0	0
$218$	−35.0507	−2.37393
$219$	−15.6723	−1.05904
$220$	2.23042	0.150375
$221$	−2.90471	−0.195392
$222$	8.23262	0.552537
$223$	4.68366	0.313641	0.156821	−	0.987627i	$-0.449876\pi$
$223$	4.68366	0.313641	0.156821	+	0.987627i	$0.449876\pi$
$224$	0	0
$225$	−0.237484	−0.0158323
$226$	−35.4627	−2.35894
$227$	1.41973	0.0942311	0.0471155	−	0.998889i	$-0.484997\pi$
$227$	1.41973	0.0942311	0.0471155	+	0.998889i	$0.484997\pi$
$228$	−11.4428	−0.757817
$229$	13.0004	0.859092	0.429546	−	0.903045i	$-0.358674\pi$
$229$	13.0004	0.859092	0.429546	+	0.903045i	$0.358674\pi$
$230$	1.95959	0.129212
$231$	0	0
$232$	3.87397	0.254339
$233$	−19.5832	−1.28294	−0.641470	−	0.767148i	$-0.721675\pi$
$233$	−19.5832	−1.28294	−0.641470	+	0.767148i	$0.721675\pi$
$234$	0.751147	0.0491040
$235$	−7.68887	−0.501567
$236$	−16.3376	−1.06349
$237$	−10.7239	−0.696591
$238$	0	0
$239$	5.73323	0.370852	0.185426	−	0.982658i	$-0.440634\pi$
$239$	5.73323	0.370852	0.185426	+	0.982658i	$0.440634\pi$
$240$	−5.79411	−0.374008
$241$	−18.1562	−1.16954	−0.584772	−	0.811198i	$-0.698816\pi$
$241$	−18.1562	−1.16954	−0.584772	+	0.811198i	$0.698816\pi$
$242$	−2.05680	−0.132216
$243$	−2.46205	−0.157940
$244$	24.6939	1.58087
$245$	0	0
$246$	7.54822	0.481257
$247$	4.74668	0.302024
$248$	1.79147	0.113758
$249$	−17.9979	−1.14057
$250$	2.05680	0.130083
$251$	−0.546995	−0.0345260	−0.0172630	−	0.999851i	$-0.505495\pi$
$251$	−0.546995	−0.0345260	−0.0172630	+	0.999851i	$0.505495\pi$
$252$	0	0
$253$	−0.952738	−0.0598981
$254$	−11.1051	−0.696798
$255$	−3.13947	−0.196601
$256$	11.7033	0.731459
$257$	−7.23058	−0.451031	−0.225516	−	0.974240i	$-0.572407\pi$
$257$	−7.23058	−0.451031	−0.225516	+	0.974240i	$0.572407\pi$
$258$	−11.5202	−0.717213
$259$	0	0
$260$	−3.42994	−0.212716
$261$	1.94120	0.120157
$262$	−28.6665	−1.77102
$263$	−23.0524	−1.42147	−0.710736	−	0.703459i	$-0.751638\pi$
$263$	−23.0524	−1.42147	−0.710736	+	0.703459i	$0.751638\pi$
$264$	−0.787722	−0.0484810
$265$	−1.64899	−0.101297
$266$	0	0
$267$	20.2739	1.24074
$268$	−8.73965	−0.533859
$269$	−21.8423	−1.33175	−0.665873	−	0.746065i	$-0.731941\pi$
$269$	−21.8423	−1.33175	−0.665873	+	0.746065i	$0.731941\pi$
$270$	11.0676	0.673550
$271$	−2.07091	−0.125799	−0.0628993	−	0.998020i	$-0.520035\pi$
$271$	−2.07091	−0.125799	−0.0628993	+	0.998020i	$0.520035\pi$
$272$	6.58474	0.399258
$273$	0	0
$274$	34.3942	2.07783
$275$	−1.00000	−0.0603023
$276$	−3.53194	−0.212598
$277$	−11.9778	−0.719677	−0.359839	−	0.933015i	$-0.617168\pi$
$277$	−11.9778	−0.719677	−0.359839	+	0.933015i	$0.617168\pi$
$278$	29.9272	1.79491
$279$	0.897683	0.0537429
$280$	0	0
$281$	−17.8620	−1.06556	−0.532779	−	0.846255i	$-0.678852\pi$
$281$	−17.8620	−1.06556	−0.532779	+	0.846255i	$0.678852\pi$
$282$	26.2849	1.56525
$283$	8.64067	0.513635	0.256817	−	0.966460i	$-0.417326\pi$
$283$	8.64067	0.513635	0.256817	+	0.966460i	$0.417326\pi$
$284$	−20.4216	−1.21180
$285$	5.13031	0.303894
$286$	3.16294	0.187028
$287$	0	0
$288$	−1.92789	−0.113602
$289$	−13.4321	−0.790126
$290$	−16.8123	−0.987254
$291$	−20.1583	−1.18170
$292$	21.0314	1.23077
$293$	15.1338	0.884128	0.442064	−	0.896984i	$-0.354246\pi$
$293$	15.1338	0.884128	0.442064	+	0.896984i	$0.354246\pi$
$294$	0	0
$295$	7.32489	0.426472
$296$	−1.14134	−0.0663390
$297$	−5.38096	−0.312235
$298$	43.5242	2.52129
$299$	1.46512	0.0847299
$300$	−3.70715	−0.214032
$301$	0	0
$302$	17.6965	1.01832
$303$	−20.2174	−1.16146
$304$	−10.7603	−0.617148
$305$	−11.0714	−0.633946
$306$	−0.922636	−0.0527436
$307$	−14.4369	−0.823959	−0.411979	−	0.911193i	$-0.635162\pi$
$307$	−14.4369	−0.823959	−0.411979	+	0.911193i	$0.635162\pi$
$308$	0	0
$309$	3.00343	0.170859
$310$	−7.77465	−0.441570
$311$	27.2342	1.54431	0.772155	−	0.635434i	$-0.219179\pi$
$311$	27.2342	1.54431	0.772155	+	0.635434i	$0.219179\pi$
$312$	1.21136	0.0685795
$313$	7.54192	0.426294	0.213147	−	0.977020i	$-0.431629\pi$
$313$	7.54192	0.426294	0.213147	+	0.977020i	$0.431629\pi$
$314$	−11.1396	−0.628642
$315$	0	0
$316$	14.3909	0.809550
$317$	−29.0331	−1.63066	−0.815331	−	0.578995i	$-0.803445\pi$
$317$	−29.0331	−1.63066	−0.815331	+	0.578995i	$0.803445\pi$
$318$	5.63720	0.316118
$319$	8.17403	0.457658
$320$	9.72497	0.543642
$321$	17.9875	1.00397
$322$	0	0
$323$	−5.83037	−0.324410
$324$	−18.3590	−1.01994
$325$	1.53780	0.0853016
$326$	−12.7715	−0.707348
$327$	−28.3242	−1.56633
$328$	−1.04646	−0.0577808
$329$	0	0
$330$	3.41857	0.188186
$331$	−10.0827	−0.554194	−0.277097	−	0.960842i	$-0.589372\pi$
$331$	−10.0827	−0.554194	−0.277097	+	0.960842i	$0.589372\pi$
$332$	24.1522	1.32553
$333$	−0.571910	−0.0313405
$334$	−5.21256	−0.285218
$335$	3.91838	0.214084
$336$	0	0
$337$	−32.3875	−1.76426	−0.882131	−	0.471004i	$-0.843892\pi$
$337$	−32.3875	−1.76426	−0.882131	+	0.471004i	$0.843892\pi$
$338$	21.8744	1.18981
$339$	−28.6571	−1.55644
$340$	4.21300	0.228482
$341$	3.77997	0.204697
$342$	1.50771	0.0815276
$343$	0	0
$344$	1.59711	0.0861104
$345$	1.58353	0.0852543
$346$	45.9277	2.46909
$347$	−25.9758	−1.39445	−0.697227	−	0.716851i	$-0.745583\pi$
$347$	−25.9758	−1.39445	−0.697227	+	0.716851i	$0.745583\pi$
$348$	30.3023	1.62438
$349$	−34.1782	−1.82952	−0.914758	−	0.404002i	$-0.867619\pi$
$349$	−34.1782	−1.82952	−0.914758	+	0.404002i	$0.867619\pi$
$350$	0	0
$351$	8.27482	0.441677
$352$	−8.11799	−0.432690
$353$	−0.706402	−0.0375980	−0.0187990	−	0.999823i	$-0.505984\pi$
$353$	−0.706402	−0.0375980	−0.0187990	+	0.999823i	$0.505984\pi$
$354$	−25.0406	−1.33089
$355$	9.15592	0.485946
$356$	−27.2064	−1.44194
$357$	0	0
$358$	−45.0253	−2.37966
$359$	−26.8435	−1.41675	−0.708373	−	0.705839i	$-0.750570\pi$
$359$	−26.8435	−1.41675	−0.708373	+	0.705839i	$0.750570\pi$
$360$	−0.112552	−0.00593204
$361$	−9.47241	−0.498548
$362$	43.1026	2.26542
$363$	−1.66208	−0.0872367
$364$	0	0
$365$	−9.42931	−0.493553
$366$	37.8483	1.97836
$367$	14.9519	0.780484	0.390242	−	0.920712i	$-0.372391\pi$
$367$	14.9519	0.780484	0.390242	+	0.920712i	$0.372391\pi$
$368$	−3.32130	−0.173135
$369$	−0.524366	−0.0272974
$370$	4.95320	0.257505
$371$	0	0
$372$	14.0129	0.726536
$373$	2.56312	0.132713	0.0663566	−	0.997796i	$-0.478863\pi$
$373$	2.56312	0.132713	0.0663566	+	0.997796i	$0.478863\pi$
$374$	−3.88505	−0.200891
$375$	1.66208	0.0858295
$376$	−3.64404	−0.187927
$377$	−12.5700	−0.647387
$378$	0	0
$379$	12.0592	0.619438	0.309719	−	0.950828i	$-0.399765\pi$
$379$	12.0592	0.619438	0.309719	+	0.950828i	$0.399765\pi$
$380$	−6.88461	−0.353173
$381$	−8.97396	−0.459750
$382$	5.10303	0.261094
$383$	27.1088	1.38520	0.692598	−	0.721324i	$-0.256466\pi$
$383$	27.1088	1.38520	0.692598	+	0.721324i	$0.256466\pi$
$384$	−6.25995	−0.319452
$385$	0	0
$386$	−33.5854	−1.70945
$387$	0.800291	0.0406811
$388$	27.0514	1.37333
$389$	21.0496	1.06726	0.533628	−	0.845719i	$-0.320828\pi$
$389$	21.0496	1.06726	0.533628	+	0.845719i	$0.320828\pi$
$390$	−5.25706	−0.266202
$391$	−1.79961	−0.0910101
$392$	0	0
$393$	−23.1652	−1.16853
$394$	51.4048	2.58974
$395$	−6.45208	−0.324639
$396$	0.529690	0.0266179
$397$	−11.4205	−0.573176	−0.286588	−	0.958054i	$-0.592521\pi$
$397$	−11.4205	−0.573176	−0.286588	+	0.958054i	$0.592521\pi$
$398$	27.3656	1.37171
$399$	0	0
$400$	−3.48606	−0.174303
$401$	7.91780	0.395396	0.197698	−	0.980263i	$-0.436653\pi$
$401$	7.91780	0.395396	0.197698	+	0.980263i	$0.436653\pi$
$402$	−13.3953	−0.668094
$403$	−5.81283	−0.289558
$404$	27.1307	1.34980
$405$	8.23115	0.409009
$406$	0	0
$407$	−2.40821	−0.119370
$408$	−1.48791	−0.0736626
$409$	−25.2042	−1.24627	−0.623134	−	0.782115i	$-0.714141\pi$
$409$	−25.2042	−1.24627	−0.623134	+	0.782115i	$0.714141\pi$
$410$	4.54142	0.224285
$411$	27.7936	1.37096
$412$	−4.03045	−0.198566
$413$	0	0
$414$	0.465372	0.0228718
$415$	−10.8285	−0.531552
$416$	12.4838	0.612069
$417$	24.1839	1.18429
$418$	6.34868	0.310524
$419$	21.9670	1.07316	0.536580	−	0.843849i	$-0.319716\pi$
$419$	21.9670	1.07316	0.536580	+	0.843849i	$0.319716\pi$
$420$	0	0
$421$	22.7516	1.10884	0.554422	−	0.832235i	$-0.312939\pi$
$421$	22.7516	1.10884	0.554422	+	0.832235i	$0.312939\pi$
$422$	−3.27329	−0.159341
$423$	−1.82598	−0.0887824
$424$	−0.781519	−0.0379539
$425$	−1.88888	−0.0916241
$426$	−31.3001	−1.51650
$427$	0	0
$428$	−24.1383	−1.16677
$429$	2.55594	0.123402
$430$	−6.93116	−0.334250
$431$	−27.4412	−1.32180	−0.660898	−	0.750476i	$-0.729824\pi$
$431$	−27.4412	−1.32180	−0.660898	+	0.750476i	$0.729824\pi$
$432$	−18.7583	−0.902511
$433$	11.5414	0.554646	0.277323	−	0.960777i	$-0.410553\pi$
$433$	11.5414	0.554646	0.277323	+	0.960777i	$0.410553\pi$
$434$	0	0
$435$	−13.5859	−0.651394
$436$	38.0095	1.82033
$437$	2.94080	0.140677
$438$	32.2348	1.54024
$439$	−6.50534	−0.310483	−0.155241	−	0.987877i	$-0.549616\pi$
$439$	−6.50534	−0.310483	−0.155241	+	0.987877i	$0.549616\pi$
$440$	−0.473937	−0.0225941
$441$	0	0
$442$	5.97441	0.284174
$443$	19.1349	0.909124	0.454562	−	0.890715i	$-0.349796\pi$
$443$	19.1349	0.909124	0.454562	+	0.890715i	$0.349796\pi$
$444$	−8.92758	−0.423684
$445$	12.1979	0.578235
$446$	−9.63335	−0.456152
$447$	35.1716	1.66356
$448$	0	0
$449$	−37.8605	−1.78675	−0.893373	−	0.449315i	$-0.851668\pi$
$449$	−37.8605	−1.78675	−0.893373	+	0.449315i	$0.851668\pi$
$450$	0.488457	0.0230261
$451$	−2.20800	−0.103971
$452$	38.4562	1.80883
$453$	14.3004	0.671890
$454$	−2.92011	−0.137047
$455$	0	0
$456$	2.43145	0.113863
$457$	−9.22256	−0.431413	−0.215707	−	0.976458i	$-0.569205\pi$
$457$	−9.22256	−0.431413	−0.215707	+	0.976458i	$0.569205\pi$
$458$	−26.7393	−1.24944
$459$	−10.1640	−0.474414
$460$	−2.12501	−0.0990791
$461$	−32.8271	−1.52891	−0.764455	−	0.644677i	$-0.776992\pi$
$461$	−32.8271	−1.52891	−0.764455	+	0.644677i	$0.776992\pi$
$462$	0	0
$463$	13.0795	0.607856	0.303928	−	0.952695i	$-0.401702\pi$
$463$	13.0795	0.607856	0.303928	+	0.952695i	$0.401702\pi$
$464$	28.4951	1.32285
$465$	−6.28263	−0.291350
$466$	40.2788	1.86588
$467$	−26.1302	−1.20916	−0.604580	−	0.796544i	$-0.706659\pi$
$467$	−26.1302	−1.20916	−0.604580	+	0.796544i	$0.706659\pi$
$468$	−0.814555	−0.0376528
$469$	0	0
$470$	15.8145	0.729467
$471$	−9.00179	−0.414781
$472$	3.47154	0.159790
$473$	3.36988	0.154947
$474$	22.0569	1.01311
$475$	3.08668	0.141627
$476$	0	0
$477$	−0.391610	−0.0179306
$478$	−11.7921	−0.539358
$479$	−17.3134	−0.791070	−0.395535	−	0.918451i	$-0.629441\pi$
$479$	−17.3134	−0.791070	−0.395535	+	0.918451i	$0.629441\pi$
$480$	13.4928	0.615858
$481$	3.70333	0.168857
$482$	37.3436	1.70096
$483$	0	0
$484$	2.23042	0.101383
$485$	−12.1284	−0.550721
$486$	5.06393	0.229705
$487$	30.0929	1.36364	0.681820	−	0.731520i	$-0.261189\pi$
$487$	30.0929	1.36364	0.681820	+	0.731520i	$0.261189\pi$
$488$	−5.24715	−0.237527
$489$	−10.3205	−0.466711
$490$	0	0
$491$	17.1429	0.773647	0.386823	−	0.922154i	$-0.373572\pi$
$491$	17.1429	0.773647	0.386823	+	0.922154i	$0.373572\pi$
$492$	−8.18540	−0.369026
$493$	15.4397	0.695371
$494$	−9.76298	−0.439257
$495$	−0.237484	−0.0106741
$496$	13.1772	0.591674
$497$	0	0
$498$	37.0181	1.65882
$499$	1.28577	0.0575589	0.0287794	−	0.999586i	$-0.490838\pi$
$499$	1.28577	0.0575589	0.0287794	+	0.999586i	$0.490838\pi$
$500$	−2.23042	−0.0997476
$501$	−4.21222	−0.188188
$502$	1.12506	0.0502138
$503$	−1.47083	−0.0655812	−0.0327906	−	0.999462i	$-0.510439\pi$
$503$	−1.47083	−0.0655812	−0.0327906	+	0.999462i	$0.510439\pi$
$504$	0	0
$505$	−12.1639	−0.541286
$506$	1.95959	0.0871145
$507$	17.6765	0.785043
$508$	12.0426	0.534302
$509$	24.4002	1.08152	0.540760	−	0.841177i	$-0.318137\pi$
$509$	24.4002	1.08152	0.540760	+	0.841177i	$0.318137\pi$
$510$	6.45726	0.285932
$511$	0	0
$512$	−31.6041	−1.39672
$513$	16.6093	0.733319
$514$	14.8719	0.655970
$515$	1.80703	0.0796273
$516$	12.4926	0.549957
$517$	−7.68887	−0.338156
$518$	0	0
$519$	37.1138	1.62911
$520$	0.728819	0.0319608
$521$	13.3591	0.585272	0.292636	−	0.956224i	$-0.405468\pi$
$521$	13.3591	0.585272	0.292636	+	0.956224i	$0.405468\pi$
$522$	−3.99266	−0.174754
$523$	28.5702	1.24929	0.624644	−	0.780910i	$-0.285244\pi$
$523$	28.5702	1.24929	0.624644	+	0.780910i	$0.285244\pi$
$524$	31.0864	1.35802
$525$	0	0
$526$	47.4142	2.06736
$527$	7.13992	0.311020
$528$	−5.79411	−0.252156
$529$	−22.0923	−0.960534
$530$	3.39165	0.147324
$531$	1.73954	0.0754898
$532$	0	0
$533$	3.39546	0.147074
$534$	−41.6993	−1.80450
$535$	10.8223	0.467889
$536$	1.85707	0.0802130
$537$	−36.3846	−1.57011
$538$	44.9251	1.93686
$539$	0	0
$540$	−12.0018	−0.516477
$541$	30.3814	1.30620	0.653099	−	0.757273i	$-0.273469\pi$
$541$	30.3814	1.30620	0.653099	+	0.757273i	$0.273469\pi$
$542$	4.25944	0.182959
$543$	34.8308	1.49473
$544$	−15.3339	−0.657436
$545$	−17.0414	−0.729973
$546$	0	0
$547$	18.4132	0.787291	0.393646	−	0.919262i	$-0.371214\pi$
$547$	18.4132	0.787291	0.393646	+	0.919262i	$0.371214\pi$
$548$	−37.2976	−1.59327
$549$	−2.62928	−0.112215
$550$	2.05680	0.0877022
$551$	−25.2306	−1.07486
$552$	0.750493	0.0319431
$553$	0	0
$554$	24.6360	1.04668
$555$	4.00264	0.169902
$556$	−32.4535	−1.37633
$557$	16.9136	0.716653	0.358327	−	0.933596i	$-0.383347\pi$
$557$	16.9136	0.716653	0.358327	+	0.933596i	$0.383347\pi$
$558$	−1.84635	−0.0781624
$559$	−5.18218	−0.219183
$560$	0	0
$561$	−3.13947	−0.132549
$562$	36.7385	1.54972
$563$	−21.3381	−0.899292	−0.449646	−	0.893207i	$-0.648450\pi$
$563$	−21.3381	−0.899292	−0.449646	+	0.893207i	$0.648450\pi$
$564$	−28.5038	−1.20023
$565$	−17.2417	−0.725362
$566$	−17.7721	−0.747019
$567$	0	0
$568$	4.33933	0.182074
$569$	−25.3259	−1.06172	−0.530859	−	0.847460i	$-0.678131\pi$
$569$	−25.3259	−1.06172	−0.530859	+	0.847460i	$0.678131\pi$
$570$	−10.5520	−0.441976
$571$	25.1085	1.05076	0.525379	−	0.850868i	$-0.323924\pi$
$571$	25.1085	1.05076	0.525379	+	0.850868i	$0.323924\pi$
$572$	−3.42994	−0.143413
$573$	4.12371	0.172271
$574$	0	0
$575$	0.952738	0.0397319
$576$	2.30952	0.0962302
$577$	−11.7223	−0.488007	−0.244003	−	0.969774i	$-0.578461\pi$
$577$	−11.7223	−0.488007	−0.244003	+	0.969774i	$0.578461\pi$
$578$	27.6272	1.14914
$579$	−27.1401	−1.12790
$580$	18.2315	0.757024
$581$	0	0
$582$	41.4617	1.71864
$583$	−1.64899	−0.0682943
$584$	−4.46890	−0.184924
$585$	0.365202	0.0150992
$586$	−31.1272	−1.28585
$587$	−28.2807	−1.16727	−0.583634	−	0.812017i	$-0.698370\pi$
$587$	−28.2807	−1.16727	−0.583634	+	0.812017i	$0.698370\pi$
$588$	0	0
$589$	−11.6676	−0.480754
$590$	−15.0658	−0.620250
$591$	41.5398	1.70872
$592$	−8.39514	−0.345038
$593$	−24.6749	−1.01328	−0.506639	−	0.862158i	$-0.669112\pi$
$593$	−24.6749	−1.01328	−0.506639	+	0.862158i	$0.669112\pi$
$594$	11.0676	0.454108
$595$	0	0
$596$	−47.1983	−1.93332
$597$	22.1139	0.905061
$598$	−3.01345	−0.123229
$599$	4.26724	0.174355	0.0871774	−	0.996193i	$-0.472215\pi$
$599$	4.26724	0.174355	0.0871774	+	0.996193i	$0.472215\pi$
$600$	0.787722	0.0321586
$601$	29.4863	1.20277	0.601385	−	0.798959i	$-0.294616\pi$
$601$	29.4863	1.20277	0.601385	+	0.798959i	$0.294616\pi$
$602$	0	0
$603$	0.930552	0.0378950
$604$	−19.1903	−0.780843
$605$	−1.00000	−0.0406558
$606$	41.5831	1.68920
$607$	34.0537	1.38220	0.691098	−	0.722761i	$-0.257127\pi$
$607$	34.0537	1.38220	0.691098	+	0.722761i	$0.257127\pi$
$608$	25.0576	1.01622
$609$	0	0
$610$	22.7716	0.921997
$611$	11.8239	0.478345
$612$	1.00052	0.0404436
$613$	15.6895	0.633691	0.316846	−	0.948477i	$-0.397376\pi$
$613$	15.6895	0.633691	0.316846	+	0.948477i	$0.397376\pi$
$614$	29.6939	1.19835
$615$	3.66988	0.147984
$616$	0	0
$617$	−17.9888	−0.724200	−0.362100	−	0.932139i	$-0.617940\pi$
$617$	−17.9888	−0.724200	−0.362100	+	0.932139i	$0.617940\pi$
$618$	−6.17746	−0.248494
$619$	−9.40476	−0.378009	−0.189005	−	0.981976i	$-0.560526\pi$
$619$	−9.40476	−0.378009	−0.189005	+	0.981976i	$0.560526\pi$
$620$	8.43095	0.338595
$621$	5.12665	0.205725
$622$	−56.0153	−2.24601
$623$	0	0
$624$	8.91016	0.356692
$625$	1.00000	0.0400000
$626$	−15.5122	−0.619993
$627$	5.13031	0.204885
$628$	12.0799	0.482041
$629$	−4.54881	−0.181373
$630$	0	0
$631$	41.7606	1.66246	0.831231	−	0.555927i	$-0.187637\pi$
$631$	41.7606	1.66246	0.831231	+	0.555927i	$0.187637\pi$
$632$	−3.05788	−0.121636
$633$	−2.64512	−0.105134
$634$	59.7153	2.37160
$635$	−5.39923	−0.214262
$636$	−6.11306	−0.242399
$637$	0	0
$638$	−16.8123	−0.665607
$639$	2.17438	0.0860173
$640$	−3.76633	−0.148877
$641$	10.8686	0.429285	0.214643	−	0.976693i	$-0.431141\pi$
$641$	10.8686	0.429285	0.214643	+	0.976693i	$0.431141\pi$
$642$	−36.9968	−1.46015
$643$	−43.1506	−1.70169	−0.850846	−	0.525415i	$-0.823910\pi$
$643$	−43.1506	−1.70169	−0.850846	+	0.525415i	$0.823910\pi$
$644$	0	0
$645$	−5.60101	−0.220540
$646$	11.9919	0.471815
$647$	8.87111	0.348759	0.174380	−	0.984679i	$-0.444208\pi$
$647$	8.87111	0.348759	0.174380	+	0.984679i	$0.444208\pi$
$648$	3.90105	0.153248
$649$	7.32489	0.287527
$650$	−3.16294	−0.124061
$651$	0	0
$652$	13.8496	0.542393
$653$	−38.3080	−1.49911	−0.749554	−	0.661944i	$-0.769732\pi$
$653$	−38.3080	−1.49911	−0.749554	+	0.661944i	$0.769732\pi$
$654$	58.2572	2.27804
$655$	−13.9374	−0.544581
$656$	−7.69723	−0.300526
$657$	−2.23931	−0.0873638
$658$	0	0
$659$	18.4905	0.720288	0.360144	−	0.932897i	$-0.382727\pi$
$659$	18.4905	0.720288	0.360144	+	0.932897i	$0.382727\pi$
$660$	−3.70715	−0.144301
$661$	−21.8787	−0.850984	−0.425492	−	0.904962i	$-0.639899\pi$
$661$	−21.8787	−0.850984	−0.425492	+	0.904962i	$0.639899\pi$
$662$	20.7380	0.806007
$663$	4.82787	0.187499
$664$	−5.13204	−0.199162
$665$	0	0
$666$	1.17631	0.0455809
$667$	−7.78771	−0.301541
$668$	5.65258	0.218705
$669$	−7.78463	−0.300971
$670$	−8.05932	−0.311359
$671$	−11.0714	−0.427407
$672$	0	0
$673$	−20.2680	−0.781272	−0.390636	−	0.920545i	$-0.627745\pi$
$673$	−20.2680	−0.781272	−0.390636	+	0.920545i	$0.627745\pi$
$674$	66.6147	2.56590
$675$	5.38096	0.207113
$676$	−23.7210	−0.912345
$677$	−23.2148	−0.892216	−0.446108	−	0.894979i	$-0.647190\pi$
$677$	−23.2148	−0.892216	−0.446108	+	0.894979i	$0.647190\pi$
$678$	58.9418	2.26365
$679$	0	0
$680$	−0.895210	−0.0343297
$681$	−2.35971	−0.0904244
$682$	−7.77465	−0.297707
$683$	15.2884	0.584994	0.292497	−	0.956266i	$-0.405514\pi$
$683$	15.2884	0.584994	0.292497	+	0.956266i	$0.405514\pi$
$684$	−1.63498	−0.0625152
$685$	16.7222	0.638922
$686$	0	0
$687$	−21.6078	−0.824388
$688$	11.7476	0.447872
$689$	2.53582	0.0966069
$690$	−3.25700	−0.123992
$691$	26.9911	1.02679	0.513394	−	0.858153i	$-0.328388\pi$
$691$	26.9911	1.02679	0.513394	+	0.858153i	$0.328388\pi$
$692$	−49.8047	−1.89329
$693$	0	0
$694$	53.4270	2.02806
$695$	14.5504	0.551926
$696$	−6.43886	−0.244064
$697$	−4.17065	−0.157975
$698$	70.2977	2.66081
$699$	32.5489	1.23111
$700$	0	0
$701$	49.9046	1.88487	0.942435	−	0.334390i	$-0.108530\pi$
$701$	49.9046	1.88487	0.942435	+	0.334390i	$0.108530\pi$
$702$	−17.0197	−0.642366
$703$	7.43336	0.280355
$704$	9.72497	0.366524
$705$	12.7795	0.481305
$706$	1.45293	0.0546817
$707$	0	0
$708$	27.1544	1.02053
$709$	27.1742	1.02055	0.510273	−	0.860012i	$-0.329544\pi$
$709$	27.1742	1.02055	0.510273	+	0.860012i	$0.329544\pi$
$710$	−18.8319	−0.706748
$711$	−1.53226	−0.0574644
$712$	5.78103	0.216653
$713$	−3.60133	−0.134871
$714$	0	0
$715$	1.53780	0.0575103
$716$	48.8261	1.82472
$717$	−9.52909	−0.355870
$718$	55.2117	2.06048
$719$	−22.2658	−0.830375	−0.415188	−	0.909736i	$-0.636284\pi$
$719$	−22.2658	−0.830375	−0.415188	+	0.909736i	$0.636284\pi$
$720$	−0.827882	−0.0308533
$721$	0	0
$722$	19.4828	0.725076
$723$	30.1771	1.12230
$724$	−46.7411	−1.73712
$725$	−8.17403	−0.303576
$726$	3.41857	0.126875
$727$	−39.6395	−1.47015	−0.735074	−	0.677987i	$-0.762853\pi$
$727$	−39.6395	−1.47015	−0.735074	+	0.677987i	$0.762853\pi$
$728$	0	0
$729$	28.7856	1.06613
$730$	19.3942	0.717812
$731$	6.36529	0.235429
$732$	−41.0433	−1.51700
$733$	35.4728	1.31022	0.655109	−	0.755534i	$-0.272623\pi$
$733$	35.4728	1.31022	0.655109	+	0.755534i	$0.272623\pi$
$734$	−30.7531	−1.13512
$735$	0	0
$736$	7.73432	0.285091
$737$	3.91838	0.144335
$738$	1.07852	0.0397007
$739$	3.66856	0.134950	0.0674751	−	0.997721i	$-0.478506\pi$
$739$	3.66856	0.134950	0.0674751	+	0.997721i	$0.478506\pi$
$740$	−5.37132	−0.197454
$741$	−7.88938	−0.289824
$742$	0	0
$743$	27.6855	1.01568	0.507841	−	0.861451i	$-0.330444\pi$
$743$	27.6855	1.01568	0.507841	+	0.861451i	$0.330444\pi$
$744$	−2.97757	−0.109163
$745$	21.1611	0.775284
$746$	−5.27182	−0.193015
$747$	−2.57160	−0.0940900
$748$	4.21300	0.154043
$749$	0	0
$750$	−3.41857	−0.124828
$751$	−24.2817	−0.886050	−0.443025	−	0.896509i	$-0.646095\pi$
$751$	−24.2817	−0.886050	−0.443025	+	0.896509i	$0.646095\pi$
$752$	−26.8038	−0.977435
$753$	0.909150	0.0331313
$754$	25.8539	0.941545
$755$	8.60389	0.313128
$756$	0	0
$757$	−30.4600	−1.10709	−0.553544	−	0.832820i	$-0.686725\pi$
$757$	−30.4600	−1.10709	−0.553544	+	0.832820i	$0.686725\pi$
$758$	−24.8033	−0.900896
$759$	1.58353	0.0574785
$760$	1.46289	0.0530647
$761$	−27.6255	−1.00142	−0.500712	−	0.865614i	$-0.666929\pi$
$761$	−27.6255	−1.00142	−0.500712	+	0.865614i	$0.666929\pi$
$762$	18.4576	0.668649
$763$	0	0
$764$	−5.53380	−0.200206
$765$	−0.448578	−0.0162184
$766$	−55.7574	−2.01460
$767$	−11.2642	−0.406726
$768$	−19.4519	−0.701911
$769$	−24.7230	−0.891535	−0.445767	−	0.895149i	$-0.647069\pi$
$769$	−24.7230	−0.891535	−0.445767	+	0.895149i	$0.647069\pi$
$770$	0	0
$771$	12.0178	0.432811
$772$	36.4205	1.31080
$773$	−18.0338	−0.648632	−0.324316	−	0.945949i	$-0.605134\pi$
$773$	−18.0338	−0.648632	−0.324316	+	0.945949i	$0.605134\pi$
$774$	−1.64604	−0.0591656
$775$	−3.77997	−0.135781
$776$	−5.74809	−0.206344
$777$	0	0
$778$	−43.2948	−1.55219
$779$	6.81540	0.244187
$780$	5.70084	0.204123
$781$	9.15592	0.327625
$782$	3.70143	0.132363
$783$	−43.9841	−1.57186
$784$	0	0
$785$	−5.41597	−0.193304
$786$	47.6461	1.69948
$787$	−24.5896	−0.876524	−0.438262	−	0.898847i	$-0.644406\pi$
$787$	−24.5896	−0.876524	−0.438262	+	0.898847i	$0.644406\pi$
$788$	−55.7442	−1.98580
$789$	38.3150	1.36405
$790$	13.2706	0.472148
$791$	0	0
$792$	−0.112552	−0.00399938
$793$	17.0256	0.604595
$794$	23.4896	0.833614
$795$	2.74076	0.0972048
$796$	−29.6756	−1.05183
$797$	36.9099	1.30742	0.653708	−	0.756747i	$-0.273212\pi$
$797$	36.9099	1.30742	0.653708	+	0.756747i	$0.273212\pi$
$798$	0	0
$799$	−14.5234	−0.513799
$800$	8.11799	0.287014
$801$	2.89680	0.102353
$802$	−16.2853	−0.575055
$803$	−9.42931	−0.332753
$804$	14.5260	0.512293
$805$	0	0
$806$	11.9558	0.421126
$807$	36.3036	1.27795
$808$	−5.76492	−0.202809
$809$	25.0166	0.879538	0.439769	−	0.898111i	$-0.355060\pi$
$809$	25.0166	0.879538	0.439769	+	0.898111i	$0.355060\pi$
$810$	−16.9298	−0.594853
$811$	−35.5675	−1.24894	−0.624471	−	0.781048i	$-0.714686\pi$
$811$	−35.5675	−1.24894	−0.624471	+	0.781048i	$0.714686\pi$
$812$	0	0
$813$	3.44202	0.120717
$814$	4.95320	0.173610
$815$	−6.20940	−0.217506
$816$	−10.9444	−0.383130
$817$	−10.4017	−0.363910
$818$	51.8400	1.81254
$819$	0	0
$820$	−4.92479	−0.171981
$821$	−6.05119	−0.211188	−0.105594	−	0.994409i	$-0.533674\pi$
$821$	−6.05119	−0.211188	−0.105594	+	0.994409i	$0.533674\pi$
$822$	−57.1659	−1.99389
$823$	−32.9409	−1.14825	−0.574123	−	0.818769i	$-0.694657\pi$
$823$	−32.9409	−1.14825	−0.574123	+	0.818769i	$0.694657\pi$
$824$	0.856419	0.0298348
$825$	1.66208	0.0578663
$826$	0	0
$827$	−41.1297	−1.43022	−0.715110	−	0.699012i	$-0.753624\pi$
$827$	−41.1297	−1.43022	−0.715110	+	0.699012i	$0.753624\pi$
$828$	−0.504656	−0.0175380
$829$	−2.85519	−0.0991647	−0.0495823	−	0.998770i	$-0.515789\pi$
$829$	−2.85519	−0.0991647	−0.0495823	+	0.998770i	$0.515789\pi$
$830$	22.2721	0.773077
$831$	19.9081	0.690605
$832$	−14.9550	−0.518472
$833$	0	0
$834$	−49.7414	−1.72240
$835$	−2.53431	−0.0877033
$836$	−6.88461	−0.238109
$837$	−20.3399	−0.703050
$838$	−45.1818	−1.56078
$839$	−45.8337	−1.58235	−0.791177	−	0.611587i	$-0.790532\pi$
$839$	−45.8337	−1.58235	−0.791177	+	0.611587i	$0.790532\pi$
$840$	0	0
$841$	37.8147	1.30396
$842$	−46.7955	−1.61268
$843$	29.6881	1.02251
$844$	3.54961	0.122183
$845$	10.6352	0.365861
$846$	3.75568	0.129123
$847$	0	0
$848$	−5.74848	−0.197404
$849$	−14.3615	−0.492886
$850$	3.88505	0.133256
$851$	2.29439	0.0786507
$852$	33.9423	1.16285
$853$	1.37150	0.0469593	0.0234797	−	0.999724i	$-0.492526\pi$
$853$	1.37150	0.0469593	0.0234797	+	0.999724i	$0.492526\pi$
$854$	0	0
$855$	0.733037	0.0250693
$856$	5.12909	0.175309
$857$	13.1240	0.448306	0.224153	−	0.974554i	$-0.428038\pi$
$857$	13.1240	0.448306	0.224153	+	0.974554i	$0.428038\pi$
$858$	−5.25706	−0.179473
$859$	49.2330	1.67981	0.839905	−	0.542734i	$-0.182611\pi$
$859$	49.2330	1.67981	0.839905	+	0.542734i	$0.182611\pi$
$860$	7.51625	0.256302
$861$	0	0
$862$	56.4411	1.92239
$863$	−0.944120	−0.0321382	−0.0160691	−	0.999871i	$-0.505115\pi$
$863$	−0.944120	−0.0321382	−0.0160691	+	0.999871i	$0.505115\pi$
$864$	43.6826	1.48611
$865$	22.3297	0.759233
$866$	−23.7384	−0.806665
$867$	22.3253	0.758207
$868$	0	0
$869$	−6.45208	−0.218872
$870$	27.9435	0.947372
$871$	−6.02567	−0.204172
$872$	−8.07655	−0.273506
$873$	−2.88029	−0.0974832
$874$	−6.04863	−0.204598
$875$	0	0
$876$	−34.9559	−1.18105
$877$	5.23551	0.176791	0.0883954	−	0.996085i	$-0.471826\pi$
$877$	5.23551	0.176791	0.0883954	+	0.996085i	$0.471826\pi$
$878$	13.3802	0.451559
$879$	−25.1537	−0.848412
$880$	−3.48606	−0.117515
$881$	30.6327	1.03204	0.516022	−	0.856576i	$-0.327412\pi$
$881$	30.6327	1.03204	0.516022	+	0.856576i	$0.327412\pi$
$882$	0	0
$883$	22.4867	0.756738	0.378369	−	0.925655i	$-0.376485\pi$
$883$	22.4867	0.756738	0.378369	+	0.925655i	$0.376485\pi$
$884$	−6.47874	−0.217904
$885$	−12.1746	−0.409244
$886$	−39.3566	−1.32221
$887$	−8.11607	−0.272511	−0.136256	−	0.990674i	$-0.543507\pi$
$887$	−8.11607	−0.272511	−0.136256	+	0.990674i	$0.543507\pi$
$888$	1.89700	0.0636591
$889$	0	0
$890$	−25.0886	−0.840971
$891$	8.23115	0.275754
$892$	10.4466	0.349776
$893$	23.7331	0.794197
$894$	−72.3408	−2.41944
$895$	−21.8910	−0.731734
$896$	0	0
$897$	−2.43514	−0.0813071
$898$	77.8714	2.59860
$899$	30.8976	1.03049
$900$	−0.529690	−0.0176563
$901$	−3.11475	−0.103767
$902$	4.54142	0.151213
$903$	0	0
$904$	−8.17147	−0.271779
$905$	20.9562	0.696606
$906$	−29.4130	−0.977181
$907$	−18.9356	−0.628746	−0.314373	−	0.949300i	$-0.601794\pi$
$907$	−18.9356	−0.628746	−0.314373	+	0.949300i	$0.601794\pi$
$908$	3.16661	0.105088
$909$	−2.88873	−0.0958131
$910$	0	0
$911$	−4.96615	−0.164536	−0.0822680	−	0.996610i	$-0.526216\pi$
$911$	−4.96615	−0.164536	−0.0822680	+	0.996610i	$0.526216\pi$
$912$	17.8846	0.592217
$913$	−10.8285	−0.358372
$914$	18.9690	0.627438
$915$	18.4016	0.608337
$916$	28.9965	0.958070
$917$	0	0
$918$	20.9053	0.689977
$919$	−55.1828	−1.82031	−0.910156	−	0.414266i	$-0.864038\pi$
$919$	−55.1828	−1.82031	−0.910156	+	0.414266i	$0.864038\pi$
$920$	0.451538	0.0148868
$921$	23.9953	0.790674
$922$	67.5187	2.22361
$923$	−14.0799	−0.463447
$924$	0	0
$925$	2.40821	0.0791813
$926$	−26.9019	−0.884051
$927$	0.429141	0.0140948
$928$	−66.3567	−2.17826
$929$	−21.2477	−0.697113	−0.348557	−	0.937288i	$-0.613328\pi$
$929$	−21.2477	−0.697113	−0.348557	+	0.937288i	$0.613328\pi$
$930$	12.9221	0.423733
$931$	0	0
$932$	−43.6789	−1.43075
$933$	−45.2655	−1.48193
$934$	53.7445	1.75858
$935$	−1.88888	−0.0617730
$936$	0.173083	0.00565739
$937$	−16.2888	−0.532133	−0.266067	−	0.963955i	$-0.585724\pi$
$937$	−16.2888	−0.532133	−0.266067	+	0.963955i	$0.585724\pi$
$938$	0	0
$939$	−12.5353	−0.409073
$940$	−17.1494	−0.559353
$941$	−29.0004	−0.945386	−0.472693	−	0.881227i	$-0.656718\pi$
$941$	−29.0004	−0.945386	−0.472693	+	0.881227i	$0.656718\pi$
$942$	18.5149	0.603247
$943$	2.10365	0.0685043
$944$	25.5350	0.831092
$945$	0	0
$946$	−6.93116	−0.225351
$947$	43.3256	1.40789	0.703946	−	0.710253i	$-0.251420\pi$
$947$	43.3256	1.40789	0.703946	+	0.710253i	$0.251420\pi$
$948$	−23.9188	−0.776847
$949$	14.5004	0.470702
$950$	−6.34868	−0.205978
$951$	48.2554	1.56479
$952$	0	0
$953$	24.9429	0.807980	0.403990	−	0.914763i	$-0.367623\pi$
$953$	24.9429	0.807980	0.403990	+	0.914763i	$0.367623\pi$
$954$	0.805462	0.0260778
$955$	2.48105	0.0802850
$956$	12.7875	0.413578
$957$	−13.5859	−0.439170
$958$	35.6102	1.15051
$959$	0	0
$960$	−16.1637	−0.521681
$961$	−16.7118	−0.539090
$962$	−7.61701	−0.245582
$963$	2.57012	0.0828210
$964$	−40.4960	−1.30429
$965$	−16.3290	−0.525648
$966$	0	0
$967$	9.28042	0.298438	0.149219	−	0.988804i	$-0.452324\pi$
$967$	9.28042	0.298438	0.149219	+	0.988804i	$0.452324\pi$
$968$	−0.473937	−0.0152329
$969$	9.69054	0.311305
$970$	24.9456	0.800956
$971$	−14.7416	−0.473082	−0.236541	−	0.971622i	$-0.576014\pi$
$971$	−14.7416	−0.473082	−0.236541	+	0.971622i	$0.576014\pi$
$972$	−5.49141	−0.176137
$973$	0	0
$974$	−61.8951	−1.98325
$975$	−2.55594	−0.0818557
$976$	−38.5955	−1.23541
$977$	−7.10918	−0.227443	−0.113721	−	0.993513i	$-0.536277\pi$
$977$	−7.10918	−0.227443	−0.113721	+	0.993513i	$0.536277\pi$
$978$	21.2273	0.678774
$979$	12.1979	0.389846
$980$	0	0
$981$	−4.04706	−0.129213
$982$	−35.2594	−1.12517
$983$	53.5528	1.70807	0.854035	−	0.520215i	$-0.174148\pi$
$983$	53.5528	1.70807	0.854035	+	0.520215i	$0.174148\pi$
$984$	1.73929	0.0554467
$985$	24.9926	0.796332
$986$	−31.7565	−1.01133
$987$	0	0
$988$	10.5871	0.336821
$989$	−3.21061	−0.102091
$990$	0.488457	0.0155242
$991$	−60.6478	−1.92654	−0.963271	−	0.268531i	$-0.913462\pi$
$991$	−60.6478	−1.92654	−0.963271	+	0.268531i	$0.913462\pi$
$992$	−30.6858	−0.974275
$993$	16.7582	0.531806
$994$	0	0
$995$	13.3049	0.421795
$996$	−40.1430	−1.27198
$997$	−35.5152	−1.12478	−0.562390	−	0.826872i	$-0.690118\pi$
$997$	−35.5152	−1.12478	−0.562390	+	0.826872i	$0.690118\pi$
$998$	−2.64457	−0.0837123
$999$	12.9585	0.409988

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2695.2.a.r.1.2		6
7.2	even	3		385.2.i.b.221.5	✓	12
7.4	even	3		385.2.i.b.331.5	yes	12
7.6	odd	2		2695.2.a.q.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.i.b.221.5	✓	12	7.2	even	3
385.2.i.b.331.5	yes	12	7.4	even	3
2695.2.a.q.1.2		6	7.6	odd	2
2695.2.a.r.1.2		6	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:	\( N \)	\(=\)	\( 2695 = 5 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2695.a (trivial)

\(f(q)\)	\(=\)	\(q-2.05680 q^{2} -1.66208 q^{3} +2.23042 q^{4} -1.00000 q^{5} +3.41857 q^{6} -0.473937 q^{8} -0.237484 q^{9} +O(q^{10})\)	\(q-2.05680 q^{2} -1.66208 q^{3} +2.23042 q^{4} -1.00000 q^{5} +3.41857 q^{6} -0.473937 q^{8} -0.237484 q^{9} +2.05680 q^{10} -1.00000 q^{11} -3.70715 q^{12} +1.53780 q^{13} +1.66208 q^{15} -3.48606 q^{16} -1.88888 q^{17} +0.488457 q^{18} +3.08668 q^{19} -2.23042 q^{20} +2.05680 q^{22} +0.952738 q^{23} +0.787722 q^{24} +1.00000 q^{25} -3.16294 q^{26} +5.38096 q^{27} -8.17403 q^{29} -3.41857 q^{30} -3.77997 q^{31} +8.11799 q^{32} +1.66208 q^{33} +3.88505 q^{34} -0.529690 q^{36} +2.40821 q^{37} -6.34868 q^{38} -2.55594 q^{39} +0.473937 q^{40} +2.20800 q^{41} -3.36988 q^{43} -2.23042 q^{44} +0.237484 q^{45} -1.95959 q^{46} +7.68887 q^{47} +5.79411 q^{48} -2.05680 q^{50} +3.13947 q^{51} +3.42994 q^{52} +1.64899 q^{53} -11.0676 q^{54} +1.00000 q^{55} -5.13031 q^{57} +16.8123 q^{58} -7.32489 q^{59} +3.70715 q^{60} +11.0714 q^{61} +7.77465 q^{62} -9.72497 q^{64} -1.53780 q^{65} -3.41857 q^{66} -3.91838 q^{67} -4.21300 q^{68} -1.58353 q^{69} -9.15592 q^{71} +0.112552 q^{72} +9.42931 q^{73} -4.95320 q^{74} -1.66208 q^{75} +6.88461 q^{76} +5.25706 q^{78} +6.45208 q^{79} +3.48606 q^{80} -8.23115 q^{81} -4.54142 q^{82} +10.8285 q^{83} +1.88888 q^{85} +6.93116 q^{86} +13.5859 q^{87} +0.473937 q^{88} -12.1979 q^{89} -0.488457 q^{90} +2.12501 q^{92} +6.28263 q^{93} -15.8145 q^{94} -3.08668 q^{95} -13.4928 q^{96} +12.1284 q^{97} +0.237484 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} + q^{3} + 5 q^{4} - 6 q^{5} - 5 q^{6} - 9 q^{8} - q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 + q^3 + 5 * q^4 - 6 * q^5 - 5 * q^6 - 9 * q^8 - q^9	\( 6 q - 3 q^{2} + q^{3} + 5 q^{4} - 6 q^{5} - 5 q^{6} - 9 q^{8} - q^{9} + 3 q^{10} - 6 q^{11} + 9 q^{12} + 14 q^{13} - q^{15} + 11 q^{16} + 3 q^{17} - 9 q^{18} - 3 q^{19} - 5 q^{20} + 3 q^{22} - 10 q^{23} - 10 q^{24} + 6 q^{25} - 17 q^{26} + q^{27} - 16 q^{29} + 5 q^{30} + 2 q^{31} - 26 q^{32} - q^{33} + 30 q^{34} + 8 q^{36} + 5 q^{37} + q^{38} + 3 q^{39} + 9 q^{40} - 9 q^{41} - 20 q^{43} - 5 q^{44} + q^{45} - 20 q^{46} + q^{47} + 41 q^{48} - 3 q^{50} - 5 q^{51} + 23 q^{52} - 24 q^{53} - 7 q^{54} + 6 q^{55} - 30 q^{57} + 31 q^{58} - 7 q^{59} - 9 q^{60} - 14 q^{61} + 24 q^{62} + 15 q^{64} - 14 q^{65} + 5 q^{66} + q^{67} - 25 q^{68} - 4 q^{69} - 9 q^{71} - 26 q^{72} + 13 q^{73} - 40 q^{74} + q^{75} - 10 q^{76} - 33 q^{78} - 4 q^{79} - 11 q^{80} - 26 q^{81} - 27 q^{82} + 8 q^{83} - 3 q^{85} + 36 q^{86} - 2 q^{87} + 9 q^{88} - 13 q^{89} + 9 q^{90} - 18 q^{92} - 36 q^{93} - q^{94} + 3 q^{95} - 89 q^{96} - 3 q^{97} + q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 + q^3 + 5 * q^4 - 6 * q^5 - 5 * q^6 - 9 * q^8 - q^9 + 3 * q^10 - 6 * q^11 + 9 * q^12 + 14 * q^13 - q^15 + 11 * q^16 + 3 * q^17 - 9 * q^18 - 3 * q^19 - 5 * q^20 + 3 * q^22 - 10 * q^23 - 10 * q^24 + 6 * q^25 - 17 * q^26 + q^27 - 16 * q^29 + 5 * q^30 + 2 * q^31 - 26 * q^32 - q^33 + 30 * q^34 + 8 * q^36 + 5 * q^37 + q^38 + 3 * q^39 + 9 * q^40 - 9 * q^41 - 20 * q^43 - 5 * q^44 + q^45 - 20 * q^46 + q^47 + 41 * q^48 - 3 * q^50 - 5 * q^51 + 23 * q^52 - 24 * q^53 - 7 * q^54 + 6 * q^55 - 30 * q^57 + 31 * q^58 - 7 * q^59 - 9 * q^60 - 14 * q^61 + 24 * q^62 + 15 * q^64 - 14 * q^65 + 5 * q^66 + q^67 - 25 * q^68 - 4 * q^69 - 9 * q^71 - 26 * q^72 + 13 * q^73 - 40 * q^74 + q^75 - 10 * q^76 - 33 * q^78 - 4 * q^79 - 11 * q^80 - 26 * q^81 - 27 * q^82 + 8 * q^83 - 3 * q^85 + 36 * q^86 - 2 * q^87 + 9 * q^88 - 13 * q^89 + 9 * q^90 - 18 * q^92 - 36 * q^93 - q^94 + 3 * q^95 - 89 * q^96 - 3 * q^97 + q^99

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