LMFDB - Embedded newform 2695.2.a.t.1.3

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:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} - 8x^{6} + 26x^{5} + 15x^{4} - 60x^{3} - 2x^{2} + 37x - 9 $ x^8 - 3x^7 - 8x^6 + 26x^5 + 15x^4 - 60x^3 - 2x^2 + 37*x - 9
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			1.3
Root			$-1.06232$ 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)

$f(q)$	$=$	$q-1.06232 q^{2} -2.71455 q^{3} -0.871473 q^{4} +1.00000 q^{5} +2.88373 q^{6} +3.05043 q^{8} +4.36879 q^{9} +O(q^{10})$	\(q-1.06232 q^{2} -2.71455 q^{3} -0.871473 q^{4} +1.00000 q^{5} +2.88373 q^{6} +3.05043 q^{8} +4.36879 q^{9} -1.06232 q^{10} -1.00000 q^{11} +2.36566 q^{12} -2.49133 q^{13} -2.71455 q^{15} -1.49759 q^{16} +5.49343 q^{17} -4.64106 q^{18} -0.216024 q^{19} -0.871473 q^{20} +1.06232 q^{22} +4.35386 q^{23} -8.28054 q^{24} +1.00000 q^{25} +2.64659 q^{26} -3.71566 q^{27} +4.41251 q^{29} +2.88373 q^{30} +4.02441 q^{31} -4.50994 q^{32} +2.71455 q^{33} -5.83579 q^{34} -3.80729 q^{36} +0.990698 q^{37} +0.229486 q^{38} +6.76285 q^{39} +3.05043 q^{40} -10.0228 q^{41} +9.68882 q^{43} +0.871473 q^{44} +4.36879 q^{45} -4.62520 q^{46} -12.0473 q^{47} +4.06528 q^{48} -1.06232 q^{50} -14.9122 q^{51} +2.17113 q^{52} +0.434723 q^{53} +3.94722 q^{54} -1.00000 q^{55} +0.586407 q^{57} -4.68750 q^{58} -6.04323 q^{59} +2.36566 q^{60} -5.09412 q^{61} -4.27521 q^{62} +7.78618 q^{64} -2.49133 q^{65} -2.88373 q^{66} +0.385874 q^{67} -4.78738 q^{68} -11.8188 q^{69} -12.7026 q^{71} +13.3267 q^{72} +11.4439 q^{73} -1.05244 q^{74} -2.71455 q^{75} +0.188259 q^{76} -7.18432 q^{78} -9.34685 q^{79} -1.49759 q^{80} -3.02003 q^{81} +10.6474 q^{82} -7.72963 q^{83} +5.49343 q^{85} -10.2926 q^{86} -11.9780 q^{87} -3.05043 q^{88} +15.9499 q^{89} -4.64106 q^{90} -3.79427 q^{92} -10.9245 q^{93} +12.7981 q^{94} -0.216024 q^{95} +12.2425 q^{96} +6.56206 q^{97} -4.36879 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{2} + q^{3} + 9 q^{4} + 8 q^{5} - 3 q^{6} + 9 q^{8} + 19 q^{9}+O(q^{10}) $ 8 * q + 3 * q^2 + q^3 + 9 * q^4 + 8 * q^5 - 3 * q^6 + 9 * q^8 + 19 * q^9	$ 8 q + 3 q^{2} + q^{3} + 9 q^{4} + 8 q^{5} - 3 q^{6} + 9 q^{8} + 19 q^{9} + 3 q^{10} - 8 q^{11} + 9 q^{12} + 14 q^{13} + q^{15} + 7 q^{16} + 5 q^{17} + 27 q^{18} + q^{19} + 9 q^{20} - 3 q^{22} - 2 q^{23} - 24 q^{24} + 8 q^{25} + 21 q^{26} - 5 q^{27} + 26 q^{29} - 3 q^{30} + 2 q^{31} + 16 q^{32} - q^{33} - 26 q^{34} + 54 q^{36} - q^{37} - 31 q^{38} + 19 q^{39} + 9 q^{40} - 3 q^{41} + 4 q^{43} - 9 q^{44} + 19 q^{45} + 10 q^{46} + q^{47} - 21 q^{48} + 3 q^{50} + 3 q^{51} + 37 q^{52} + 26 q^{53} - 5 q^{54} - 8 q^{55} + 20 q^{57} - q^{58} - 19 q^{59} + 9 q^{60} - 26 q^{62} + q^{64} + 14 q^{65} + 3 q^{66} - 13 q^{67} + 15 q^{68} - 14 q^{69} - 9 q^{71} + 32 q^{72} + 11 q^{73} + 24 q^{74} + q^{75} - 18 q^{76} - 33 q^{78} - 8 q^{79} + 7 q^{80} + 52 q^{81} + 41 q^{82} + 32 q^{83} + 5 q^{85} + 28 q^{86} - 16 q^{87} - 9 q^{88} + 5 q^{89} + 27 q^{90} + 30 q^{92} - 14 q^{93} - 5 q^{94} + q^{95} + q^{96} + 9 q^{97} - 19 q^{99}+O(q^{100}) $ 8 * q + 3 * q^2 + q^3 + 9 * q^4 + 8 * q^5 - 3 * q^6 + 9 * q^8 + 19 * q^9 + 3 * q^10 - 8 * q^11 + 9 * q^12 + 14 * q^13 + q^15 + 7 * q^16 + 5 * q^17 + 27 * q^18 + q^19 + 9 * q^20 - 3 * q^22 - 2 * q^23 - 24 * q^24 + 8 * q^25 + 21 * q^26 - 5 * q^27 + 26 * q^29 - 3 * q^30 + 2 * q^31 + 16 * q^32 - q^33 - 26 * q^34 + 54 * q^36 - q^37 - 31 * q^38 + 19 * q^39 + 9 * q^40 - 3 * q^41 + 4 * q^43 - 9 * q^44 + 19 * q^45 + 10 * q^46 + q^47 - 21 * q^48 + 3 * q^50 + 3 * q^51 + 37 * q^52 + 26 * q^53 - 5 * q^54 - 8 * q^55 + 20 * q^57 - q^58 - 19 * q^59 + 9 * q^60 - 26 * q^62 + q^64 + 14 * q^65 + 3 * q^66 - 13 * q^67 + 15 * q^68 - 14 * q^69 - 9 * q^71 + 32 * q^72 + 11 * q^73 + 24 * q^74 + q^75 - 18 * q^76 - 33 * q^78 - 8 * q^79 + 7 * q^80 + 52 * q^81 + 41 * q^82 + 32 * q^83 + 5 * q^85 + 28 * q^86 - 16 * q^87 - 9 * q^88 + 5 * q^89 + 27 * q^90 + 30 * q^92 - 14 * q^93 - 5 * q^94 + q^95 + q^96 + 9 * q^97 - 19 * 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 $

$2$	−1.06232	−0.751175	−0.375587	−	0.926787i	$-0.622559\pi$
$2$	−1.06232	−0.751175	−0.375587	+	0.926787i	$0.622559\pi$
$3$	−2.71455	−1.56725	−0.783624	−	0.621236i	$-0.786631\pi$
$3$	−2.71455	−1.56725	−0.783624	+	0.621236i	$0.786631\pi$
$4$	−0.871473	−0.435737
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.88373	1.17728
$7$	0	0
$7$	0	0
$8$	3.05043	1.07849
$9$	4.36879	1.45626
$10$	−1.06232	−0.335936
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	2.36566	0.682907
$13$	−2.49133	−0.690971	−0.345485	−	0.938424i	$-0.612286\pi$
$13$	−2.49133	−0.690971	−0.345485	+	0.938424i	$0.612286\pi$
$14$	0	0
$15$	−2.71455	−0.700894
$16$	−1.49759	−0.374397
$17$	5.49343	1.33235	0.666177	−	0.745794i	$-0.267930\pi$
$17$	5.49343	1.33235	0.666177	+	0.745794i	$0.267930\pi$
$18$	−4.64106	−1.09391
$19$	−0.216024	−0.0495592	−0.0247796	−	0.999693i	$-0.507888\pi$
$19$	−0.216024	−0.0495592	−0.0247796	+	0.999693i	$0.507888\pi$
$20$	−0.871473	−0.194867
$21$	0	0
$22$	1.06232	0.226488
$23$	4.35386	0.907843	0.453921	−	0.891042i	$-0.350025\pi$
$23$	4.35386	0.907843	0.453921	+	0.891042i	$0.350025\pi$
$24$	−8.28054	−1.69026
$25$	1.00000	0.200000
$26$	2.64659	0.519040
$27$	−3.71566	−0.715078
$28$	0	0
$29$	4.41251	0.819382	0.409691	−	0.912224i	$-0.365636\pi$
$29$	4.41251	0.819382	0.409691	+	0.912224i	$0.365636\pi$
$30$	2.88373	0.526494
$31$	4.02441	0.722805	0.361402	−	0.932410i	$-0.382298\pi$
$31$	4.02441	0.722805	0.361402	+	0.932410i	$0.382298\pi$
$32$	−4.50994	−0.797251
$33$	2.71455	0.472543
$34$	−5.83579	−1.00083
$35$	0	0
$36$	−3.80729	−0.634548
$37$	0.990698	0.162870	0.0814349	−	0.996679i	$-0.474050\pi$
$37$	0.990698	0.162870	0.0814349	+	0.996679i	$0.474050\pi$
$38$	0.229486	0.0372276
$39$	6.76285	1.08292
$40$	3.05043	0.482315
$41$	−10.0228	−1.56529	−0.782647	−	0.622465i	$-0.786131\pi$
$41$	−10.0228	−1.56529	−0.782647	+	0.622465i	$0.786131\pi$
$42$	0	0
$43$	9.68882	1.47753	0.738766	−	0.673962i	$-0.235409\pi$
$43$	9.68882	1.47753	0.738766	+	0.673962i	$0.235409\pi$
$44$	0.871473	0.131380
$45$	4.36879	0.651261
$46$	−4.62520	−0.681948
$47$	−12.0473	−1.75728	−0.878638	−	0.477488i	$-0.841547\pi$
$47$	−12.0473	−1.75728	−0.878638	+	0.477488i	$0.841547\pi$
$48$	4.06528	0.586773
$49$	0	0
$50$	−1.06232	−0.150235
$51$	−14.9122	−2.08813
$52$	2.17113	0.301081
$53$	0.434723	0.0597138	0.0298569	−	0.999554i	$-0.490495\pi$
$53$	0.434723	0.0597138	0.0298569	+	0.999554i	$0.490495\pi$
$54$	3.94722	0.537149
$55$	−1.00000	−0.134840
$56$	0	0
$57$	0.586407	0.0776715
$58$	−4.68750	−0.615499
$59$	−6.04323	−0.786761	−0.393381	−	0.919376i	$-0.628695\pi$
$59$	−6.04323	−0.786761	−0.393381	+	0.919376i	$0.628695\pi$
$60$	2.36566	0.305405
$61$	−5.09412	−0.652235	−0.326118	−	0.945329i	$-0.605741\pi$
$61$	−5.09412	−0.652235	−0.326118	+	0.945329i	$0.605741\pi$
$62$	−4.27521	−0.542953
$63$	0	0
$64$	7.78618	0.973272
$65$	−2.49133	−0.309012
$66$	−2.88373	−0.354962
$67$	0.385874	0.0471420	0.0235710	−	0.999722i	$-0.492496\pi$
$67$	0.385874	0.0471420	0.0235710	+	0.999722i	$0.492496\pi$
$68$	−4.78738	−0.580555
$69$	−11.8188	−1.42281
$70$	0	0
$71$	−12.7026	−1.50752	−0.753762	−	0.657147i	$-0.771763\pi$
$71$	−12.7026	−1.50752	−0.753762	+	0.657147i	$0.771763\pi$
$72$	13.3267	1.57056
$73$	11.4439	1.33941	0.669703	−	0.742629i	$-0.266421\pi$
$73$	11.4439	1.33941	0.669703	+	0.742629i	$0.266421\pi$
$74$	−1.05244	−0.122344
$75$	−2.71455	−0.313449
$76$	0.188259	0.0215948
$77$	0	0
$78$	−7.18432	−0.813464
$79$	−9.34685	−1.05160	−0.525801	−	0.850607i	$-0.676234\pi$
$79$	−9.34685	−1.05160	−0.525801	+	0.850607i	$0.676234\pi$
$80$	−1.49759	−0.167435
$81$	−3.02003	−0.335559
$82$	10.6474	1.17581
$83$	−7.72963	−0.848437	−0.424219	−	0.905560i	$-0.639451\pi$
$83$	−7.72963	−0.848437	−0.424219	+	0.905560i	$0.639451\pi$
$84$	0	0
$85$	5.49343	0.595847
$86$	−10.2926	−1.10988
$87$	−11.9780	−1.28417
$88$	−3.05043	−0.325177
$89$	15.9499	1.69069	0.845344	−	0.534223i	$-0.179396\pi$
$89$	15.9499	1.69069	0.845344	+	0.534223i	$0.179396\pi$
$90$	−4.64106	−0.489211
$91$	0	0
$92$	−3.79427	−0.395580
$93$	−10.9245	−1.13281
$94$	12.7981	1.32002
$95$	−0.216024	−0.0221635
$96$	12.2425	1.24949
$97$	6.56206	0.666277	0.333138	−	0.942878i	$-0.391892\pi$
$97$	6.56206	0.666277	0.333138	+	0.942878i	$0.391892\pi$
$98$	0	0
$99$	−4.36879	−0.439080
$100$	−0.871473	−0.0871473
$101$	−17.8308	−1.77423	−0.887114	−	0.461550i	$-0.847293\pi$
$101$	−17.8308	−1.77423	−0.887114	+	0.461550i	$0.847293\pi$
$102$	15.8416	1.56855
$103$	−9.84517	−0.970073	−0.485037	−	0.874494i	$-0.661194\pi$
$103$	−9.84517	−0.970073	−0.485037	+	0.874494i	$0.661194\pi$
$104$	−7.59962	−0.745204
$105$	0	0
$106$	−0.461816	−0.0448555
$107$	11.3089	1.09328	0.546638	−	0.837369i	$-0.315907\pi$
$107$	11.3089	1.09328	0.546638	+	0.837369i	$0.315907\pi$
$108$	3.23810	0.311586
$109$	10.3329	0.989708	0.494854	−	0.868976i	$-0.335222\pi$
$109$	10.3329	0.989708	0.494854	+	0.868976i	$0.335222\pi$
$110$	1.06232	0.101288
$111$	−2.68930	−0.255257
$112$	0	0
$113$	14.7643	1.38891	0.694457	−	0.719535i	$-0.255645\pi$
$113$	14.7643	1.38891	0.694457	+	0.719535i	$0.255645\pi$
$114$	−0.622953	−0.0583449
$115$	4.35386	0.406000
$116$	−3.84538	−0.357035
$117$	−10.8841	−1.00624
$118$	6.41985	0.590995
$119$	0	0
$120$	−8.28054	−0.755907
$121$	1.00000	0.0909091
$122$	5.41159	0.489943
$123$	27.2073	2.45320
$124$	−3.50716	−0.314952
$125$	1.00000	0.0894427
$126$	0	0
$127$	−2.10124	−0.186455	−0.0932275	−	0.995645i	$-0.529718\pi$
$127$	−2.10124	−0.186455	−0.0932275	+	0.995645i	$0.529718\pi$
$128$	0.748449	0.0661542
$129$	−26.3008	−2.31566
$130$	2.64659	0.232122
$131$	15.3344	1.33977	0.669886	−	0.742464i	$-0.266343\pi$
$131$	15.3344	1.33977	0.669886	+	0.742464i	$0.266343\pi$
$132$	−2.36566	−0.205904
$133$	0	0
$134$	−0.409922	−0.0354119
$135$	−3.71566	−0.319793
$136$	16.7573	1.43693
$137$	4.55718	0.389346	0.194673	−	0.980868i	$-0.437635\pi$
$137$	4.55718	0.389346	0.194673	+	0.980868i	$0.437635\pi$
$138$	12.5553	1.06878
$139$	−13.8225	−1.17241	−0.586203	−	0.810164i	$-0.699378\pi$
$139$	−13.8225	−1.17241	−0.586203	+	0.810164i	$0.699378\pi$
$140$	0	0
$141$	32.7030	2.75409
$142$	13.4943	1.13241
$143$	2.49133	0.208336
$144$	−6.54265	−0.545221
$145$	4.41251	0.366439
$146$	−12.1571	−1.00613
$147$	0	0
$148$	−0.863367	−0.0709683
$149$	9.61008	0.787288	0.393644	−	0.919263i	$-0.371214\pi$
$149$	9.61008	0.787288	0.393644	+	0.919263i	$0.371214\pi$
$150$	2.88373	0.235455
$151$	−0.306738	−0.0249620	−0.0124810	−	0.999922i	$-0.503973\pi$
$151$	−0.306738	−0.0249620	−0.0124810	+	0.999922i	$0.503973\pi$
$152$	−0.658964	−0.0534491
$153$	23.9997	1.94026
$154$	0	0
$155$	4.02441	0.323248
$156$	−5.89364	−0.471869
$157$	−16.3999	−1.30886	−0.654429	−	0.756124i	$-0.727091\pi$
$157$	−16.3999	−1.30886	−0.654429	+	0.756124i	$0.727091\pi$
$158$	9.92935	0.789937
$159$	−1.18008	−0.0935863
$160$	−4.50994	−0.356542
$161$	0	0
$162$	3.20825	0.252064
$163$	10.1339	0.793748	0.396874	−	0.917873i	$-0.370095\pi$
$163$	10.1339	0.793748	0.396874	+	0.917873i	$0.370095\pi$
$164$	8.73458	0.682056
$165$	2.71455	0.211328
$166$	8.21135	0.637325
$167$	11.3927	0.881590	0.440795	−	0.897608i	$-0.354697\pi$
$167$	11.3927	0.881590	0.440795	+	0.897608i	$0.354697\pi$
$168$	0	0
$169$	−6.79327	−0.522559
$170$	−5.83579	−0.447585
$171$	−0.943762	−0.0721713
$172$	−8.44355	−0.643814
$173$	−0.166483	−0.0126575	−0.00632874	−	0.999980i	$-0.502015\pi$
$173$	−0.166483	−0.0126575	−0.00632874	+	0.999980i	$0.502015\pi$
$174$	12.7245	0.964639
$175$	0	0
$176$	1.49759	0.112885
$177$	16.4047	1.23305
$178$	−16.9439	−1.27000
$179$	16.5554	1.23741	0.618705	−	0.785624i	$-0.287658\pi$
$179$	16.5554	1.23741	0.618705	+	0.785624i	$0.287658\pi$
$180$	−3.80729	−0.283778
$181$	12.2225	0.908493	0.454247	−	0.890876i	$-0.349909\pi$
$181$	12.2225	0.908493	0.454247	+	0.890876i	$0.349909\pi$
$182$	0	0
$183$	13.8283	1.02221
$184$	13.2811	0.979098
$185$	0.990698	0.0728376
$186$	11.6053	0.850941
$187$	−5.49343	−0.401720
$188$	10.4989	0.765710
$189$	0	0
$190$	0.229486	0.0166487
$191$	11.0092	0.796598	0.398299	−	0.917256i	$-0.369601\pi$
$191$	11.0092	0.796598	0.398299	+	0.917256i	$0.369601\pi$
$192$	−21.1360	−1.52536
$193$	18.9673	1.36530	0.682649	−	0.730746i	$-0.260828\pi$
$193$	18.9673	1.36530	0.682649	+	0.730746i	$0.260828\pi$
$194$	−6.97102	−0.500490
$195$	6.76285	0.484297
$196$	0	0
$197$	15.3718	1.09519	0.547596	−	0.836743i	$-0.315543\pi$
$197$	15.3718	1.09519	0.547596	+	0.836743i	$0.315543\pi$
$198$	4.64106	0.329826
$199$	−8.00558	−0.567501	−0.283750	−	0.958898i	$-0.591579\pi$
$199$	−8.00558	−0.567501	−0.283750	+	0.958898i	$0.591579\pi$
$200$	3.05043	0.215698
$201$	−1.04748	−0.0738832
$202$	18.9420	1.33276
$203$	0	0
$204$	12.9956	0.909874
$205$	−10.0228	−0.700021
$206$	10.4587	0.728694
$207$	19.0211	1.32206
$208$	3.73099	0.258697
$209$	0.216024	0.0149427
$210$	0	0
$211$	−11.3174	−0.779123	−0.389561	−	0.921001i	$-0.627373\pi$
$211$	−11.3174	−0.779123	−0.389561	+	0.921001i	$0.627373\pi$
$212$	−0.378850	−0.0260195
$213$	34.4819	2.36266
$214$	−12.0137	−0.821241
$215$	9.68882	0.660772
$216$	−11.3343	−0.771204
$217$	0	0
$218$	−10.9768	−0.743444
$219$	−31.0650	−2.09918
$220$	0.871473	0.0587547
$221$	−13.6860	−0.920617
$222$	2.85690	0.191743
$223$	24.4418	1.63674	0.818370	−	0.574691i	$-0.194878\pi$
$223$	24.4418	1.63674	0.818370	+	0.574691i	$0.194878\pi$
$224$	0	0
$225$	4.36879	0.291253
$226$	−15.6845	−1.04332
$227$	−4.56549	−0.303022	−0.151511	−	0.988456i	$-0.548414\pi$
$227$	−4.56549	−0.303022	−0.151511	+	0.988456i	$0.548414\pi$
$228$	−0.511038	−0.0338443
$229$	5.18545	0.342664	0.171332	−	0.985213i	$-0.445193\pi$
$229$	5.18545	0.342664	0.171332	+	0.985213i	$0.445193\pi$
$230$	−4.62520	−0.304977
$231$	0	0
$232$	13.4600	0.883695
$233$	4.92653	0.322748	0.161374	−	0.986893i	$-0.448408\pi$
$233$	4.92653	0.322748	0.161374	+	0.986893i	$0.448408\pi$
$234$	11.5624	0.755859
$235$	−12.0473	−0.785878
$236$	5.26651	0.342821
$237$	25.3725	1.64812
$238$	0	0
$239$	−19.0096	−1.22963	−0.614813	−	0.788673i	$-0.710769\pi$
$239$	−19.0096	−1.22963	−0.614813	+	0.788673i	$0.710769\pi$
$240$	4.06528	0.262413
$241$	1.67870	0.108134	0.0540672	−	0.998537i	$-0.482781\pi$
$241$	1.67870	0.108134	0.0540672	+	0.998537i	$0.482781\pi$
$242$	−1.06232	−0.0682886
$243$	19.3450	1.24098
$244$	4.43939	0.284203
$245$	0	0
$246$	−28.9029	−1.84278
$247$	0.538186	0.0342440
$248$	12.2762	0.779537
$249$	20.9825	1.32971
$250$	−1.06232	−0.0671871
$251$	−24.8596	−1.56912	−0.784562	−	0.620051i	$-0.787112\pi$
$251$	−24.8596	−1.56912	−0.784562	+	0.620051i	$0.787112\pi$
$252$	0	0
$253$	−4.35386	−0.273725
$254$	2.23219	0.140060
$255$	−14.9122	−0.933839
$256$	−16.3674	−1.02297
$257$	24.9206	1.55450	0.777252	−	0.629190i	$-0.216613\pi$
$257$	24.9206	1.55450	0.777252	+	0.629190i	$0.216613\pi$
$258$	27.9399	1.73946
$259$	0	0
$260$	2.17113	0.134648
$261$	19.2773	1.19324
$262$	−16.2901	−1.00640
$263$	1.06154	0.0654572	0.0327286	−	0.999464i	$-0.489580\pi$
$263$	1.06154	0.0654572	0.0327286	+	0.999464i	$0.489580\pi$
$264$	8.28054	0.509632
$265$	0.434723	0.0267048
$266$	0	0
$267$	−43.2969	−2.64972
$268$	−0.336279	−0.0205415
$269$	10.2732	0.626368	0.313184	−	0.949693i	$-0.398604\pi$
$269$	10.2732	0.626368	0.313184	+	0.949693i	$0.398604\pi$
$270$	3.94722	0.240220
$271$	−8.55150	−0.519467	−0.259733	−	0.965680i	$-0.583635\pi$
$271$	−8.55150	−0.519467	−0.259733	+	0.965680i	$0.583635\pi$
$272$	−8.22690	−0.498829
$273$	0	0
$274$	−4.84119	−0.292467
$275$	−1.00000	−0.0603023
$276$	10.2998	0.619972
$277$	−7.31171	−0.439318	−0.219659	−	0.975577i	$-0.570494\pi$
$277$	−7.31171	−0.439318	−0.219659	+	0.975577i	$0.570494\pi$
$278$	14.6839	0.880682
$279$	17.5818	1.05259
$280$	0	0
$281$	23.2429	1.38655	0.693276	−	0.720672i	$-0.256167\pi$
$281$	23.2429	1.38655	0.693276	+	0.720672i	$0.256167\pi$
$282$	−34.7411	−2.06880
$283$	2.17195	0.129109	0.0645546	−	0.997914i	$-0.479437\pi$
$283$	2.17195	0.129109	0.0645546	+	0.997914i	$0.479437\pi$
$284$	11.0700	0.656884
$285$	0.586407	0.0347358
$286$	−2.64659	−0.156496
$287$	0	0
$288$	−19.7030	−1.16101
$289$	13.1778	0.775166
$290$	−4.68750	−0.275260
$291$	−17.8131	−1.04422
$292$	−9.97305	−0.583629
$293$	−12.1315	−0.708727	−0.354364	−	0.935108i	$-0.615302\pi$
$293$	−12.1315	−0.708727	−0.354364	+	0.935108i	$0.615302\pi$
$294$	0	0
$295$	−6.04323	−0.351850
$296$	3.02205	0.175653
$297$	3.71566	0.215604
$298$	−10.2090	−0.591391
$299$	−10.8469	−0.627293
$300$	2.36566	0.136581
$301$	0	0
$302$	0.325855	0.0187508
$303$	48.4026	2.78065
$304$	0.323514	0.0185548
$305$	−5.09412	−0.291688
$306$	−25.4954	−1.45747
$307$	−31.0266	−1.77078	−0.885390	−	0.464848i	$-0.846109\pi$
$307$	−31.0266	−1.77078	−0.885390	+	0.464848i	$0.846109\pi$
$308$	0	0
$309$	26.7252	1.52034
$310$	−4.27521	−0.242816
$311$	6.65682	0.377473	0.188737	−	0.982028i	$-0.439561\pi$
$311$	6.65682	0.377473	0.188737	+	0.982028i	$0.439561\pi$
$312$	20.6296	1.16792
$313$	24.5863	1.38970	0.694849	−	0.719155i	$-0.255471\pi$
$313$	24.5863	1.38970	0.694849	+	0.719155i	$0.255471\pi$
$314$	17.4220	0.983181
$315$	0	0
$316$	8.14553	0.458222
$317$	−29.4517	−1.65417	−0.827087	−	0.562073i	$-0.810004\pi$
$317$	−29.4517	−1.65417	−0.827087	+	0.562073i	$0.810004\pi$
$318$	1.25362	0.0702997
$319$	−4.41251	−0.247053
$320$	7.78618	0.435260
$321$	−30.6987	−1.71343
$322$	0	0
$323$	−1.18671	−0.0660304
$324$	2.63188	0.146215
$325$	−2.49133	−0.138194
$326$	−10.7655	−0.596244
$327$	−28.0491	−1.55112
$328$	−30.5737	−1.68815
$329$	0	0
$330$	−2.88373	−0.158744
$331$	4.76001	0.261634	0.130817	−	0.991407i	$-0.458240\pi$
$331$	4.76001	0.261634	0.130817	+	0.991407i	$0.458240\pi$
$332$	6.73617	0.369695
$333$	4.32815	0.237181
$334$	−12.1027	−0.662228
$335$	0.385874	0.0210826
$336$	0	0
$337$	23.2559	1.26683	0.633416	−	0.773811i	$-0.281652\pi$
$337$	23.2559	1.26683	0.633416	+	0.773811i	$0.281652\pi$
$338$	7.21664	0.392533
$339$	−40.0786	−2.17677
$340$	−4.78738	−0.259632
$341$	−4.02441	−0.217934
$342$	1.00258	0.0542132
$343$	0	0
$344$	29.5550	1.59350
$345$	−11.8188	−0.636302
$346$	0.176859	0.00950798
$347$	0.524059	0.0281330	0.0140665	−	0.999901i	$-0.495522\pi$
$347$	0.524059	0.0281330	0.0140665	+	0.999901i	$0.495522\pi$
$348$	10.4385	0.559562
$349$	26.7599	1.43242	0.716211	−	0.697884i	$-0.245875\pi$
$349$	26.7599	1.43242	0.716211	+	0.697884i	$0.245875\pi$
$350$	0	0
$351$	9.25693	0.494098
$352$	4.50994	0.240380
$353$	10.0681	0.535870	0.267935	−	0.963437i	$-0.413659\pi$
$353$	10.0681	0.535870	0.267935	+	0.963437i	$0.413659\pi$
$354$	−17.4270	−0.926236
$355$	−12.7026	−0.674185
$356$	−13.8999	−0.736694
$357$	0	0
$358$	−17.5872	−0.929511
$359$	1.47579	0.0778894	0.0389447	−	0.999241i	$-0.487600\pi$
$359$	1.47579	0.0778894	0.0389447	+	0.999241i	$0.487600\pi$
$360$	13.3267	0.702378
$361$	−18.9533	−0.997544
$362$	−12.9842	−0.682437
$363$	−2.71455	−0.142477
$364$	0	0
$365$	11.4439	0.599001
$366$	−14.6900	−0.767861
$367$	18.0425	0.941813	0.470907	−	0.882183i	$-0.343927\pi$
$367$	18.0425	0.941813	0.470907	+	0.882183i	$0.343927\pi$
$368$	−6.52029	−0.339893
$369$	−43.7874	−2.27948
$370$	−1.05244	−0.0547137
$371$	0	0
$372$	9.52037	0.493608
$373$	−9.05936	−0.469076	−0.234538	−	0.972107i	$-0.575358\pi$
$373$	−9.05936	−0.469076	−0.234538	+	0.972107i	$0.575358\pi$
$374$	5.83579	0.301762
$375$	−2.71455	−0.140179
$376$	−36.7494	−1.89520
$377$	−10.9930	−0.566169
$378$	0	0
$379$	−10.1597	−0.521868	−0.260934	−	0.965357i	$-0.584030\pi$
$379$	−10.1597	−0.521868	−0.260934	+	0.965357i	$0.584030\pi$
$380$	0.188259	0.00965747
$381$	5.70393	0.292221
$382$	−11.6953	−0.598384
$383$	17.3331	0.885681	0.442841	−	0.896600i	$-0.353971\pi$
$383$	17.3331	0.885681	0.442841	+	0.896600i	$0.353971\pi$
$384$	−2.03170	−0.103680
$385$	0	0
$386$	−20.1494	−1.02558
$387$	42.3284	2.15168
$388$	−5.71866	−0.290321
$389$	0.364497	0.0184807	0.00924036	−	0.999957i	$-0.497059\pi$
$389$	0.364497	0.0184807	0.00924036	+	0.999957i	$0.497059\pi$
$390$	−7.18432	−0.363792
$391$	23.9176	1.20957
$392$	0	0
$393$	−41.6260	−2.09975
$394$	−16.3297	−0.822681
$395$	−9.34685	−0.470291
$396$	3.80729	0.191323
$397$	−3.02936	−0.152039	−0.0760197	−	0.997106i	$-0.524221\pi$
$397$	−3.02936	−0.152039	−0.0760197	+	0.997106i	$0.524221\pi$
$398$	8.50450	0.426292
$399$	0	0
$400$	−1.49759	−0.0748794
$401$	27.9546	1.39599	0.697994	−	0.716104i	$-0.254076\pi$
$401$	27.9546	1.39599	0.697994	+	0.716104i	$0.254076\pi$
$402$	1.11276	0.0554992
$403$	−10.0261	−0.499437
$404$	15.5390	0.773096
$405$	−3.02003	−0.150067
$406$	0	0
$407$	−0.990698	−0.0491071
$408$	−45.4886	−2.25202
$409$	−6.35425	−0.314197	−0.157099	−	0.987583i	$-0.550214\pi$
$409$	−6.35425	−0.314197	−0.157099	+	0.987583i	$0.550214\pi$
$410$	10.6474	0.525838
$411$	−12.3707	−0.610201
$412$	8.57980	0.422696
$413$	0	0
$414$	−20.2065	−0.993097
$415$	−7.72963	−0.379433
$416$	11.2357	0.550877
$417$	37.5218	1.83745
$418$	−0.229486	−0.0112245
$419$	13.4218	0.655700	0.327850	−	0.944730i	$-0.393676\pi$
$419$	13.4218	0.655700	0.327850	+	0.944730i	$0.393676\pi$
$420$	0	0
$421$	−9.40394	−0.458320	−0.229160	−	0.973389i	$-0.573598\pi$
$421$	−9.40394	−0.458320	−0.229160	+	0.973389i	$0.573598\pi$
$422$	12.0227	0.585257
$423$	−52.6321	−2.55906
$424$	1.32609	0.0644007
$425$	5.49343	0.266471
$426$	−36.6309	−1.77477
$427$	0	0
$428$	−9.85544	−0.476381
$429$	−6.76285	−0.326513
$430$	−10.2926	−0.496355
$431$	11.2775	0.543217	0.271609	−	0.962408i	$-0.412444\pi$
$431$	11.2775	0.543217	0.271609	+	0.962408i	$0.412444\pi$
$432$	5.56452	0.267723
$433$	30.4381	1.46276	0.731381	−	0.681969i	$-0.238876\pi$
$433$	30.4381	1.46276	0.731381	+	0.681969i	$0.238876\pi$
$434$	0	0
$435$	−11.9780	−0.574300
$436$	−9.00481	−0.431252
$437$	−0.940536	−0.0449920
$438$	33.0011	1.57685
$439$	12.8126	0.611513	0.305757	−	0.952110i	$-0.401091\pi$
$439$	12.8126	0.611513	0.305757	+	0.952110i	$0.401091\pi$
$440$	−3.05043	−0.145423
$441$	0	0
$442$	14.5389	0.691544
$443$	−35.6694	−1.69471	−0.847353	−	0.531031i	$-0.821805\pi$
$443$	−35.6694	−1.69471	−0.847353	+	0.531031i	$0.821805\pi$
$444$	2.34365	0.111225
$445$	15.9499	0.756098
$446$	−25.9650	−1.22948
$447$	−26.0871	−1.23388
$448$	0	0
$449$	40.4845	1.91058	0.955290	−	0.295671i	$-0.0955431\pi$
$449$	40.4845	1.91058	0.955290	+	0.295671i	$0.0955431\pi$
$450$	−4.64106	−0.218782
$451$	10.0228	0.471954
$452$	−12.8667	−0.605200
$453$	0.832658	0.0391217
$454$	4.85002	0.227623
$455$	0	0
$456$	1.78879	0.0837679
$457$	29.4160	1.37602	0.688012	−	0.725700i	$-0.258484\pi$
$457$	29.4160	1.37602	0.688012	+	0.725700i	$0.258484\pi$
$458$	−5.50862	−0.257401
$459$	−20.4117	−0.952737
$460$	−3.79427	−0.176909
$461$	−18.9682	−0.883436	−0.441718	−	0.897154i	$-0.645631\pi$
$461$	−18.9682	−0.883436	−0.441718	+	0.897154i	$0.645631\pi$
$462$	0	0
$463$	−15.8564	−0.736910	−0.368455	−	0.929646i	$-0.620113\pi$
$463$	−15.8564	−0.736910	−0.368455	+	0.929646i	$0.620113\pi$
$464$	−6.60812	−0.306774
$465$	−10.9245	−0.506610
$466$	−5.23356	−0.242440
$467$	−13.4090	−0.620495	−0.310247	−	0.950656i	$-0.600412\pi$
$467$	−13.4090	−0.620495	−0.310247	+	0.950656i	$0.600412\pi$
$468$	9.48521	0.438454
$469$	0	0
$470$	12.7981	0.590332
$471$	44.5185	2.05130
$472$	−18.4344	−0.848514
$473$	−9.68882	−0.445492
$474$	−26.9537	−1.23803
$475$	−0.216024	−0.00991184
$476$	0	0
$477$	1.89922	0.0869591
$478$	20.1943	0.923664
$479$	12.3443	0.564025	0.282013	−	0.959411i	$-0.408998\pi$
$479$	12.3443	0.564025	0.282013	+	0.959411i	$0.408998\pi$
$480$	12.2425	0.558789
$481$	−2.46816	−0.112538
$482$	−1.78332	−0.0812278
$483$	0	0
$484$	−0.871473	−0.0396124
$485$	6.56206	0.297968
$486$	−20.5506	−0.932195
$487$	−36.9283	−1.67338	−0.836691	−	0.547675i	$-0.815513\pi$
$487$	−36.9283	−1.67338	−0.836691	+	0.547675i	$0.815513\pi$
$488$	−15.5392	−0.703429
$489$	−27.5090	−1.24400
$490$	0	0
$491$	17.0641	0.770092	0.385046	−	0.922897i	$-0.374186\pi$
$491$	17.0641	0.770092	0.385046	+	0.922897i	$0.374186\pi$
$492$	−23.7105	−1.06895
$493$	24.2398	1.09171
$494$	−0.571727	−0.0257232
$495$	−4.36879	−0.196363
$496$	−6.02690	−0.270616
$497$	0	0
$498$	−22.2901	−0.998845
$499$	12.0106	0.537670	0.268835	−	0.963186i	$-0.413361\pi$
$499$	12.0106	0.537670	0.268835	+	0.963186i	$0.413361\pi$
$500$	−0.871473	−0.0389735
$501$	−30.9260	−1.38167
$502$	26.4089	1.17869
$503$	35.3880	1.57787	0.788936	−	0.614476i	$-0.210632\pi$
$503$	35.3880	1.57787	0.788936	+	0.614476i	$0.210632\pi$
$504$	0	0
$505$	−17.8308	−0.793459
$506$	4.62520	0.205615
$507$	18.4407	0.818980
$508$	1.83118	0.0812453
$509$	22.3055	0.988675	0.494337	−	0.869270i	$-0.335411\pi$
$509$	22.3055	0.988675	0.494337	+	0.869270i	$0.335411\pi$
$510$	15.8416	0.701476
$511$	0	0
$512$	15.8906	0.702271
$513$	0.802669	0.0354387
$514$	−26.4737	−1.16770
$515$	−9.84517	−0.433830
$516$	22.9204	1.00902
$517$	12.0473	0.529839
$518$	0	0
$519$	0.451927	0.0198374
$520$	−7.59962	−0.333266
$521$	1.45745	0.0638519	0.0319259	−	0.999490i	$-0.489836\pi$
$521$	1.45745	0.0638519	0.0319259	+	0.999490i	$0.489836\pi$
$522$	−20.4787	−0.896329
$523$	13.2178	0.577975	0.288987	−	0.957333i	$-0.406681\pi$
$523$	13.2178	0.577975	0.288987	+	0.957333i	$0.406681\pi$
$524$	−13.3635	−0.583788
$525$	0	0
$526$	−1.12769	−0.0491698
$527$	22.1078	0.963031
$528$	−4.06528	−0.176919
$529$	−4.04390	−0.175822
$530$	−0.461816	−0.0200600
$531$	−26.4016	−1.14573
$532$	0	0
$533$	24.9700	1.08157
$534$	45.9952	1.99041
$535$	11.3089	0.488928
$536$	1.17708	0.0508421
$537$	−44.9405	−1.93933
$538$	−10.9134	−0.470512
$539$	0	0
$540$	3.23810	0.139345
$541$	−38.2843	−1.64597	−0.822985	−	0.568063i	$-0.807693\pi$
$541$	−38.2843	−1.64597	−0.822985	+	0.568063i	$0.807693\pi$
$542$	9.08445	0.390210
$543$	−33.1787	−1.42383
$544$	−24.7750	−1.06222
$545$	10.3329	0.442611
$546$	0	0
$547$	−17.7989	−0.761027	−0.380513	−	0.924775i	$-0.624253\pi$
$547$	−17.7989	−0.761027	−0.380513	+	0.924775i	$0.624253\pi$
$548$	−3.97146	−0.169652
$549$	−22.2552	−0.949827
$550$	1.06232	0.0452975
$551$	−0.953206	−0.0406079
$552$	−36.0523	−1.53449
$553$	0	0
$554$	7.76739	0.330005
$555$	−2.68930	−0.114154
$556$	12.0459	0.510860
$557$	−19.2718	−0.816571	−0.408285	−	0.912854i	$-0.633873\pi$
$557$	−19.2718	−0.816571	−0.408285	+	0.912854i	$0.633873\pi$
$558$	−18.6775	−0.790682
$559$	−24.1381	−1.02093
$560$	0	0
$561$	14.9122	0.629594
$562$	−24.6914	−1.04154
$563$	17.8855	0.753785	0.376892	−	0.926257i	$-0.376993\pi$
$563$	17.8855	0.753785	0.376892	+	0.926257i	$0.376993\pi$
$564$	−28.4998	−1.20006
$565$	14.7643	0.621141
$566$	−2.30731	−0.0969836
$567$	0	0
$568$	−38.7484	−1.62585
$569$	−15.8226	−0.663318	−0.331659	−	0.943399i	$-0.607608\pi$
$569$	−15.8226	−0.663318	−0.331659	+	0.943399i	$0.607608\pi$
$570$	−0.622953	−0.0260926
$571$	−6.94544	−0.290658	−0.145329	−	0.989383i	$-0.546424\pi$
$571$	−6.94544	−0.290658	−0.145329	+	0.989383i	$0.546424\pi$
$572$	−2.17113	−0.0907794
$573$	−29.8851	−1.24847
$574$	0	0
$575$	4.35386	0.181569
$576$	34.0162	1.41734
$577$	39.6172	1.64929	0.824643	−	0.565654i	$-0.191376\pi$
$577$	39.6172	1.64929	0.824643	+	0.565654i	$0.191376\pi$
$578$	−13.9991	−0.582285
$579$	−51.4878	−2.13976
$580$	−3.84538	−0.159671
$581$	0	0
$582$	18.9232	0.784392
$583$	−0.434723	−0.0180044
$584$	34.9088	1.44454
$585$	−10.8841	−0.450002
$586$	12.8875	0.532378
$587$	7.62489	0.314713	0.157356	−	0.987542i	$-0.449703\pi$
$587$	7.62489	0.314713	0.157356	+	0.987542i	$0.449703\pi$
$588$	0	0
$589$	−0.869366	−0.0358216
$590$	6.41985	0.264301
$591$	−41.7274	−1.71644
$592$	−1.48366	−0.0609779
$593$	−47.8526	−1.96507	−0.982536	−	0.186072i	$-0.940424\pi$
$593$	−47.8526	−1.96507	−0.982536	+	0.186072i	$0.940424\pi$
$594$	−3.94722	−0.161956
$595$	0	0
$596$	−8.37493	−0.343050
$597$	21.7316	0.889414
$598$	11.5229	0.471206
$599$	11.4235	0.466753	0.233376	−	0.972386i	$-0.425023\pi$
$599$	11.4235	0.466753	0.233376	+	0.972386i	$0.425023\pi$
$600$	−8.28054	−0.338052
$601$	35.8382	1.46187	0.730936	−	0.682446i	$-0.239084\pi$
$601$	35.8382	1.46187	0.730936	+	0.682446i	$0.239084\pi$
$602$	0	0
$603$	1.68580	0.0686512
$604$	0.267314	0.0108769
$605$	1.00000	0.0406558
$606$	−51.4191	−2.08876
$607$	14.2678	0.579114	0.289557	−	0.957161i	$-0.406492\pi$
$607$	14.2678	0.579114	0.289557	+	0.957161i	$0.406492\pi$
$608$	0.974252	0.0395111
$609$	0	0
$610$	5.41159	0.219109
$611$	30.0138	1.21423
$612$	−20.9151	−0.845442
$613$	−7.14292	−0.288500	−0.144250	−	0.989541i	$-0.546077\pi$
$613$	−7.14292	−0.288500	−0.144250	+	0.989541i	$0.546077\pi$
$614$	32.9602	1.33017
$615$	27.2073	1.09711
$616$	0	0
$617$	−38.3359	−1.54335	−0.771673	−	0.636019i	$-0.780580\pi$
$617$	−38.3359	−1.54335	−0.771673	+	0.636019i	$0.780580\pi$
$618$	−28.3908	−1.14204
$619$	−24.5098	−0.985134	−0.492567	−	0.870275i	$-0.663941\pi$
$619$	−24.5098	−0.985134	−0.492567	+	0.870275i	$0.663941\pi$
$620$	−3.50716	−0.140851
$621$	−16.1774	−0.649179
$622$	−7.07168	−0.283549
$623$	0	0
$624$	−10.1280	−0.405443
$625$	1.00000	0.0400000
$626$	−26.1185	−1.04391
$627$	−0.586407	−0.0234188
$628$	14.2921	0.570317
$629$	5.44234	0.217000
$630$	0	0
$631$	27.2067	1.08308	0.541540	−	0.840675i	$-0.317841\pi$
$631$	27.2067	1.08308	0.541540	+	0.840675i	$0.317841\pi$
$632$	−28.5119	−1.13414
$633$	30.7217	1.22108
$634$	31.2872	1.24257
$635$	−2.10124	−0.0833852
$636$	1.02841	0.0407790
$637$	0	0
$638$	4.68750	0.185580
$639$	−55.4951	−2.19535
$640$	0.748449	0.0295851
$641$	0.305631	0.0120717	0.00603584	−	0.999982i	$-0.498079\pi$
$641$	0.305631	0.0120717	0.00603584	+	0.999982i	$0.498079\pi$
$642$	32.6119	1.28709
$643$	30.0896	1.18662	0.593309	−	0.804974i	$-0.297821\pi$
$643$	30.0896	1.18662	0.593309	+	0.804974i	$0.297821\pi$
$644$	0	0
$645$	−26.3008	−1.03559
$646$	1.26067	0.0496003
$647$	6.54621	0.257358	0.128679	−	0.991686i	$-0.458926\pi$
$647$	6.54621	0.257358	0.128679	+	0.991686i	$0.458926\pi$
$648$	−9.21239	−0.361897
$649$	6.04323	0.237218
$650$	2.64659	0.103808
$651$	0	0
$652$	−8.83142	−0.345865
$653$	−8.88098	−0.347540	−0.173770	−	0.984786i	$-0.555595\pi$
$653$	−8.88098	−0.347540	−0.173770	+	0.984786i	$0.555595\pi$
$654$	29.7971	1.16516
$655$	15.3344	0.599164
$656$	15.0100	0.586041
$657$	49.9960	1.95053
$658$	0	0
$659$	44.0609	1.71637	0.858185	−	0.513341i	$-0.171592\pi$
$659$	44.0609	1.71637	0.858185	+	0.513341i	$0.171592\pi$
$660$	−2.36566	−0.0920832
$661$	21.1571	0.822915	0.411457	−	0.911429i	$-0.365020\pi$
$661$	21.1571	0.822915	0.411457	+	0.911429i	$0.365020\pi$
$662$	−5.05666	−0.196533
$663$	37.1513	1.44284
$664$	−23.5787	−0.915030
$665$	0	0
$666$	−4.59789	−0.178165
$667$	19.2114	0.743870
$668$	−9.92839	−0.384141
$669$	−66.3484	−2.56518
$670$	−0.409922	−0.0158367
$671$	5.09412	0.196656
$672$	0	0
$673$	14.7120	0.567107	0.283554	−	0.958956i	$-0.408487\pi$
$673$	14.7120	0.567107	0.283554	+	0.958956i	$0.408487\pi$
$674$	−24.7053	−0.951612
$675$	−3.71566	−0.143016
$676$	5.92016	0.227698
$677$	−19.6135	−0.753807	−0.376904	−	0.926253i	$-0.623011\pi$
$677$	−19.6135	−0.753807	−0.376904	+	0.926253i	$0.623011\pi$
$678$	42.5763	1.63513
$679$	0	0
$680$	16.7573	0.642614
$681$	12.3933	0.474911
$682$	4.27521	0.163706
$683$	48.2304	1.84548	0.922742	−	0.385417i	$-0.125942\pi$
$683$	48.2304	1.84548	0.922742	+	0.385417i	$0.125942\pi$
$684$	0.822463	0.0314477
$685$	4.55718	0.174121
$686$	0	0
$687$	−14.0762	−0.537040
$688$	−14.5099	−0.553183
$689$	−1.08304	−0.0412605
$690$	12.5553	0.477974
$691$	−37.6060	−1.43060	−0.715300	−	0.698818i	$-0.753710\pi$
$691$	−37.6060	−1.43060	−0.715300	+	0.698818i	$0.753710\pi$
$692$	0.145086	0.00551533
$693$	0	0
$694$	−0.556720	−0.0211328
$695$	−13.8225	−0.524316
$696$	−36.5380	−1.38497
$697$	−55.0595	−2.08553
$698$	−28.4276	−1.07600
$699$	−13.3733	−0.505825
$700$	0	0
$701$	38.1263	1.44001	0.720005	−	0.693969i	$-0.244140\pi$
$701$	38.1263	1.44001	0.720005	+	0.693969i	$0.244140\pi$
$702$	−9.83383	−0.371154
$703$	−0.214014	−0.00807170
$704$	−7.78618	−0.293453
$705$	32.7030	1.23167
$706$	−10.6955	−0.402532
$707$	0	0
$708$	−14.2962	−0.537285
$709$	−2.86879	−0.107740	−0.0538699	−	0.998548i	$-0.517156\pi$
$709$	−2.86879	−0.107740	−0.0538699	+	0.998548i	$0.517156\pi$
$710$	13.4943	0.506431
$711$	−40.8344	−1.53141
$712$	48.6540	1.82339
$713$	17.5217	0.656193
$714$	0	0
$715$	2.49133	0.0931705
$716$	−14.4276	−0.539185
$717$	51.6024	1.92713
$718$	−1.56777	−0.0585086
$719$	−10.9552	−0.408559	−0.204280	−	0.978913i	$-0.565485\pi$
$719$	−10.9552	−0.408559	−0.204280	+	0.978913i	$0.565485\pi$
$720$	−6.54265	−0.243830
$721$	0	0
$722$	20.1345	0.749330
$723$	−4.55691	−0.169473
$724$	−10.6516	−0.395864
$725$	4.41251	0.163876
$726$	2.88373	0.107025
$727$	−36.6999	−1.36112	−0.680562	−	0.732691i	$-0.738264\pi$
$727$	−36.6999	−1.36112	−0.680562	+	0.732691i	$0.738264\pi$
$728$	0	0
$729$	−43.4529	−1.60937
$730$	−12.1571	−0.449954
$731$	53.2249	1.96859
$732$	−12.0510	−0.445416
$733$	−4.19330	−0.154883	−0.0774416	−	0.996997i	$-0.524675\pi$
$733$	−4.19330	−0.154883	−0.0774416	+	0.996997i	$0.524675\pi$
$734$	−19.1670	−0.707466
$735$	0	0
$736$	−19.6356	−0.723779
$737$	−0.385874	−0.0142139
$738$	46.5163	1.71229
$739$	39.2463	1.44370	0.721849	−	0.692051i	$-0.243292\pi$
$739$	39.2463	1.44370	0.721849	+	0.692051i	$0.243292\pi$
$740$	−0.863367	−0.0317380
$741$	−1.46093	−0.0536688
$742$	0	0
$743$	−31.7254	−1.16389	−0.581946	−	0.813227i	$-0.697708\pi$
$743$	−31.7254	−1.16389	−0.581946	+	0.813227i	$0.697708\pi$
$744$	−33.3243	−1.22173
$745$	9.61008	0.352086
$746$	9.62395	0.352358
$747$	−33.7692	−1.23555
$748$	4.78738	0.175044
$749$	0	0
$750$	2.88373	0.105299
$751$	−48.9023	−1.78447	−0.892236	−	0.451570i	$-0.850864\pi$
$751$	−48.9023	−1.78447	−0.892236	+	0.451570i	$0.850864\pi$
$752$	18.0419	0.657919
$753$	67.4826	2.45920
$754$	11.6781	0.425292
$755$	−0.306738	−0.0111634
$756$	0	0
$757$	−45.1542	−1.64116	−0.820578	−	0.571535i	$-0.806348\pi$
$757$	−45.1542	−1.64116	−0.820578	+	0.571535i	$0.806348\pi$
$758$	10.7928	0.392014
$759$	11.8188	0.428995
$760$	−0.658964	−0.0239031
$761$	13.8386	0.501648	0.250824	−	0.968033i	$-0.419298\pi$
$761$	13.8386	0.501648	0.250824	+	0.968033i	$0.419298\pi$
$762$	−6.05941	−0.219509
$763$	0	0
$764$	−9.59423	−0.347107
$765$	23.9997	0.867710
$766$	−18.4133	−0.665301
$767$	15.0557	0.543629
$768$	44.4303	1.60324
$769$	18.2700	0.658832	0.329416	−	0.944185i	$-0.393148\pi$
$769$	18.2700	0.658832	0.329416	+	0.944185i	$0.393148\pi$
$770$	0	0
$771$	−67.6482	−2.43629
$772$	−16.5295	−0.594911
$773$	34.2030	1.23020	0.615099	−	0.788450i	$-0.289116\pi$
$773$	34.2030	1.23020	0.615099	+	0.788450i	$0.289116\pi$
$774$	−44.9664	−1.61628
$775$	4.02441	0.144561
$776$	20.0171	0.718572
$777$	0	0
$778$	−0.387213	−0.0138822
$779$	2.16516	0.0775747
$780$	−5.89364	−0.211026
$781$	12.7026	0.454536
$782$	−25.4082	−0.908596
$783$	−16.3954	−0.585923
$784$	0	0
$785$	−16.3999	−0.585339
$786$	44.2202	1.57728
$787$	30.2458	1.07815	0.539073	−	0.842259i	$-0.318775\pi$
$787$	30.2458	1.07815	0.539073	+	0.842259i	$0.318775\pi$
$788$	−13.3961	−0.477215
$789$	−2.88160	−0.102588
$790$	9.92935	0.353271
$791$	0	0
$792$	−13.3267	−0.473543
$793$	12.6911	0.450675
$794$	3.21816	0.114208
$795$	−1.18008	−0.0418531
$796$	6.97665	0.247281
$797$	3.77585	0.133748	0.0668738	−	0.997761i	$-0.478698\pi$
$797$	3.77585	0.133748	0.0668738	+	0.997761i	$0.478698\pi$
$798$	0	0
$799$	−66.1810	−2.34131
$800$	−4.50994	−0.159450
$801$	69.6818	2.46209
$802$	−29.6968	−1.04863
$803$	−11.4439	−0.403846
$804$	0.912847	0.0321936
$805$	0	0
$806$	10.6510	0.375164
$807$	−27.8871	−0.981673
$808$	−54.3915	−1.91349
$809$	16.5871	0.583170	0.291585	−	0.956545i	$-0.405817\pi$
$809$	16.5871	0.583170	0.291585	+	0.956545i	$0.405817\pi$
$810$	3.20825	0.112726
$811$	15.7522	0.553135	0.276567	−	0.960995i	$-0.410803\pi$
$811$	15.7522	0.553135	0.276567	+	0.960995i	$0.410803\pi$
$812$	0	0
$813$	23.2135	0.814133
$814$	1.05244	0.0368880
$815$	10.1339	0.354975
$816$	22.3323	0.781789
$817$	−2.09301	−0.0732253
$818$	6.75025	0.236017
$819$	0	0
$820$	8.73458	0.305025
$821$	8.28882	0.289282	0.144641	−	0.989484i	$-0.453797\pi$
$821$	8.28882	0.289282	0.144641	+	0.989484i	$0.453797\pi$
$822$	13.1417	0.458368
$823$	20.4320	0.712213	0.356107	−	0.934445i	$-0.384104\pi$
$823$	20.4320	0.712213	0.356107	+	0.934445i	$0.384104\pi$
$824$	−30.0320	−1.04621
$825$	2.71455	0.0945086
$826$	0	0
$827$	47.3196	1.64546	0.822732	−	0.568429i	$-0.192449\pi$
$827$	47.3196	1.64546	0.822732	+	0.568429i	$0.192449\pi$
$828$	−16.5764	−0.576069
$829$	−36.8950	−1.28142	−0.640708	−	0.767785i	$-0.721359\pi$
$829$	−36.8950	−1.28142	−0.640708	+	0.767785i	$0.721359\pi$
$830$	8.21135	0.285020
$831$	19.8480	0.688520
$832$	−19.3979	−0.672503
$833$	0	0
$834$	−39.8602	−1.38025
$835$	11.3927	0.394259
$836$	−0.188259	−0.00651107
$837$	−14.9533	−0.516862
$838$	−14.2583	−0.492545
$839$	13.3898	0.462269	0.231134	−	0.972922i	$-0.425756\pi$
$839$	13.3898	0.462269	0.231134	+	0.972922i	$0.425756\pi$
$840$	0	0
$841$	−9.52977	−0.328613
$842$	9.99000	0.344278
$843$	−63.0939	−2.17307
$844$	9.86282	0.339492
$845$	−6.79327	−0.233696
$846$	55.9122	1.92230
$847$	0	0
$848$	−0.651036	−0.0223567
$849$	−5.89588	−0.202346
$850$	−5.83579	−0.200166
$851$	4.31336	0.147860
$852$	−30.0501	−1.02950
$853$	25.6968	0.879841	0.439920	−	0.898037i	$-0.355007\pi$
$853$	25.6968	0.879841	0.439920	+	0.898037i	$0.355007\pi$
$854$	0	0
$855$	−0.943762	−0.0322760
$856$	34.4971	1.17909
$857$	−17.0406	−0.582096	−0.291048	−	0.956708i	$-0.594004\pi$
$857$	−17.0406	−0.582096	−0.291048	+	0.956708i	$0.594004\pi$
$858$	7.18432	0.245269
$859$	17.1003	0.583453	0.291727	−	0.956502i	$-0.405770\pi$
$859$	17.1003	0.583453	0.291727	+	0.956502i	$0.405770\pi$
$860$	−8.44355	−0.287923
$861$	0	0
$862$	−11.9803	−0.408051
$863$	26.6684	0.907804	0.453902	−	0.891052i	$-0.350032\pi$
$863$	26.6684	0.907804	0.453902	+	0.891052i	$0.350032\pi$
$864$	16.7574	0.570097
$865$	−0.166483	−0.00566060
$866$	−32.3351	−1.09879
$867$	−35.7719	−1.21488
$868$	0	0
$869$	9.34685	0.317070
$870$	12.7245	0.431400
$871$	−0.961340	−0.0325738
$872$	31.5196	1.06739
$873$	28.6683	0.970275
$874$	0.999152	0.0337968
$875$	0	0
$876$	27.0724	0.914690
$877$	−49.7814	−1.68100	−0.840499	−	0.541813i	$-0.817738\pi$
$877$	−49.7814	−1.68100	−0.840499	+	0.541813i	$0.817738\pi$
$878$	−13.6111	−0.459353
$879$	32.9315	1.11075
$880$	1.49759	0.0504837
$881$	12.6033	0.424615	0.212307	−	0.977203i	$-0.431902\pi$
$881$	12.6033	0.424615	0.212307	+	0.977203i	$0.431902\pi$
$882$	0	0
$883$	3.37550	0.113595	0.0567973	−	0.998386i	$-0.481911\pi$
$883$	3.37550	0.113595	0.0567973	+	0.998386i	$0.481911\pi$
$884$	11.9270	0.401147
$885$	16.4047	0.551437
$886$	37.8924	1.27302
$887$	41.6350	1.39797	0.698983	−	0.715138i	$-0.253636\pi$
$887$	41.6350	1.39797	0.698983	+	0.715138i	$0.253636\pi$
$888$	−8.20352	−0.275292
$889$	0	0
$890$	−16.9439	−0.567962
$891$	3.02003	0.101175
$892$	−21.3003	−0.713188
$893$	2.60250	0.0870892
$894$	27.7128	0.926856
$895$	16.5554	0.553386
$896$	0	0
$897$	29.4445	0.983123
$898$	−43.0075	−1.43518
$899$	17.7577	0.592253
$900$	−3.80729	−0.126910
$901$	2.38812	0.0795599
$902$	−10.6474	−0.354520
$903$	0	0
$904$	45.0376	1.49793
$905$	12.2225	0.406290
$906$	−0.884550	−0.0293872
$907$	−29.8985	−0.992763	−0.496382	−	0.868104i	$-0.665338\pi$
$907$	−29.8985	−0.992763	−0.496382	+	0.868104i	$0.665338\pi$
$908$	3.97870	0.132038
$909$	−77.8989	−2.58374
$910$	0	0
$911$	27.2007	0.901199	0.450599	−	0.892726i	$-0.351210\pi$
$911$	27.2007	0.901199	0.450599	+	0.892726i	$0.351210\pi$
$912$	−0.878196	−0.0290800
$913$	7.72963	0.255813
$914$	−31.2493	−1.03363
$915$	13.8283	0.457148
$916$	−4.51898	−0.149311
$917$	0	0
$918$	21.6838	0.715672
$919$	13.1506	0.433800	0.216900	−	0.976194i	$-0.430405\pi$
$919$	13.1506	0.433800	0.216900	+	0.976194i	$0.430405\pi$
$920$	13.2811	0.437866
$921$	84.2233	2.77525
$922$	20.1503	0.663615
$923$	31.6464	1.04166
$924$	0	0
$925$	0.990698	0.0325740
$926$	16.8446	0.553548
$927$	−43.0115	−1.41268
$928$	−19.9001	−0.653254
$929$	53.2656	1.74759	0.873794	−	0.486296i	$-0.161652\pi$
$929$	53.2656	1.74759	0.873794	+	0.486296i	$0.161652\pi$
$930$	11.6053	0.380552
$931$	0	0
$932$	−4.29334	−0.140633
$933$	−18.0703	−0.591594
$934$	14.2447	0.466100
$935$	−5.49343	−0.179655
$936$	−33.2012	−1.08521
$937$	15.8292	0.517119	0.258559	−	0.965995i	$-0.416752\pi$
$937$	15.8292	0.517119	0.258559	+	0.965995i	$0.416752\pi$
$938$	0	0
$939$	−66.7407	−2.17800
$940$	10.4989	0.342436
$941$	−52.0842	−1.69790	−0.848949	−	0.528475i	$-0.822764\pi$
$941$	−52.0842	−1.69790	−0.848949	+	0.528475i	$0.822764\pi$
$942$	−47.2929	−1.54089
$943$	−43.6378	−1.42104
$944$	9.05027	0.294561
$945$	0	0
$946$	10.2926	0.334643
$947$	−36.6232	−1.19009	−0.595047	−	0.803691i	$-0.702867\pi$
$947$	−36.6232	−1.19009	−0.595047	+	0.803691i	$0.702867\pi$
$948$	−22.1115	−0.718147
$949$	−28.5105	−0.925491
$950$	0.229486	0.00744552
$951$	79.9483	2.59250
$952$	0	0
$953$	37.9581	1.22958	0.614791	−	0.788690i	$-0.289240\pi$
$953$	37.9581	1.22958	0.614791	+	0.788690i	$0.289240\pi$
$954$	−2.01758	−0.0653215
$955$	11.0092	0.356250
$956$	16.5663	0.535793
$957$	11.9780	0.387193
$958$	−13.1136	−0.423682
$959$	0	0
$960$	−21.1360	−0.682161
$961$	−14.8042	−0.477553
$962$	2.62198	0.0845359
$963$	49.4064	1.59210
$964$	−1.46294	−0.0471181
$965$	18.9673	0.610580
$966$	0	0
$967$	−1.62261	−0.0521796	−0.0260898	−	0.999660i	$-0.508306\pi$
$967$	−1.62261	−0.0521796	−0.0260898	+	0.999660i	$0.508306\pi$
$968$	3.05043	0.0980445
$969$	3.22139	0.103486
$970$	−6.97102	−0.223826
$971$	−38.2756	−1.22832	−0.614161	−	0.789181i	$-0.710505\pi$
$971$	−38.2756	−1.22832	−0.614161	+	0.789181i	$0.710505\pi$
$972$	−16.8587	−0.540742
$973$	0	0
$974$	39.2298	1.25700
$975$	6.76285	0.216584
$976$	7.62889	0.244195
$977$	17.9523	0.574346	0.287173	−	0.957879i	$-0.407285\pi$
$977$	17.9523	0.574346	0.287173	+	0.957879i	$0.407285\pi$
$978$	29.2234	0.934461
$979$	−15.9499	−0.509761
$980$	0	0
$981$	45.1421	1.44128
$982$	−18.1276	−0.578474
$983$	−5.11816	−0.163244	−0.0816219	−	0.996663i	$-0.526010\pi$
$983$	−5.11816	−0.163244	−0.0816219	+	0.996663i	$0.526010\pi$
$984$	82.9940	2.64575
$985$	15.3718	0.489785
$986$	−25.7505	−0.820063
$987$	0	0
$988$	−0.469015	−0.0149213
$989$	42.1838	1.34137
$990$	4.64106	0.147503
$991$	59.5099	1.89039	0.945197	−	0.326501i	$-0.105870\pi$
$991$	59.5099	1.89039	0.945197	+	0.326501i	$0.105870\pi$
$992$	−18.1498	−0.576257
$993$	−12.9213	−0.410045
$994$	0	0
$995$	−8.00558	−0.253794
$996$	−18.2857	−0.579404
$997$	44.4170	1.40670	0.703351	−	0.710843i	$-0.251686\pi$
$997$	44.4170	1.40670	0.703351	+	0.710843i	$0.251686\pi$
$998$	−12.7592	−0.403884
$999$	−3.68109	−0.116465

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2695.2.a.t.1.3		8
7.2	even	3		385.2.i.c.221.6	✓	16
7.4	even	3		385.2.i.c.331.6	yes	16
7.6	odd	2		2695.2.a.s.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.i.c.221.6	✓	16	7.2	even	3
385.2.i.c.331.6	yes	16	7.4	even	3
2695.2.a.s.1.3		8	7.6	odd	2
2695.2.a.t.1.3		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:	\( N \)	\(=\)	\( 2695 = 5 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2695.a (trivial)

\(f(q)\)	\(=\)	\(q-1.06232 q^{2} -2.71455 q^{3} -0.871473 q^{4} +1.00000 q^{5} +2.88373 q^{6} +3.05043 q^{8} +4.36879 q^{9} +O(q^{10})\)	\(q-1.06232 q^{2} -2.71455 q^{3} -0.871473 q^{4} +1.00000 q^{5} +2.88373 q^{6} +3.05043 q^{8} +4.36879 q^{9} -1.06232 q^{10} -1.00000 q^{11} +2.36566 q^{12} -2.49133 q^{13} -2.71455 q^{15} -1.49759 q^{16} +5.49343 q^{17} -4.64106 q^{18} -0.216024 q^{19} -0.871473 q^{20} +1.06232 q^{22} +4.35386 q^{23} -8.28054 q^{24} +1.00000 q^{25} +2.64659 q^{26} -3.71566 q^{27} +4.41251 q^{29} +2.88373 q^{30} +4.02441 q^{31} -4.50994 q^{32} +2.71455 q^{33} -5.83579 q^{34} -3.80729 q^{36} +0.990698 q^{37} +0.229486 q^{38} +6.76285 q^{39} +3.05043 q^{40} -10.0228 q^{41} +9.68882 q^{43} +0.871473 q^{44} +4.36879 q^{45} -4.62520 q^{46} -12.0473 q^{47} +4.06528 q^{48} -1.06232 q^{50} -14.9122 q^{51} +2.17113 q^{52} +0.434723 q^{53} +3.94722 q^{54} -1.00000 q^{55} +0.586407 q^{57} -4.68750 q^{58} -6.04323 q^{59} +2.36566 q^{60} -5.09412 q^{61} -4.27521 q^{62} +7.78618 q^{64} -2.49133 q^{65} -2.88373 q^{66} +0.385874 q^{67} -4.78738 q^{68} -11.8188 q^{69} -12.7026 q^{71} +13.3267 q^{72} +11.4439 q^{73} -1.05244 q^{74} -2.71455 q^{75} +0.188259 q^{76} -7.18432 q^{78} -9.34685 q^{79} -1.49759 q^{80} -3.02003 q^{81} +10.6474 q^{82} -7.72963 q^{83} +5.49343 q^{85} -10.2926 q^{86} -11.9780 q^{87} -3.05043 q^{88} +15.9499 q^{89} -4.64106 q^{90} -3.79427 q^{92} -10.9245 q^{93} +12.7981 q^{94} -0.216024 q^{95} +12.2425 q^{96} +6.56206 q^{97} -4.36879 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} + q^{3} + 9 q^{4} + 8 q^{5} - 3 q^{6} + 9 q^{8} + 19 q^{9}+O(q^{10}) \) 8 * q + 3 * q^2 + q^3 + 9 * q^4 + 8 * q^5 - 3 * q^6 + 9 * q^8 + 19 * q^9	\( 8 q + 3 q^{2} + q^{3} + 9 q^{4} + 8 q^{5} - 3 q^{6} + 9 q^{8} + 19 q^{9} + 3 q^{10} - 8 q^{11} + 9 q^{12} + 14 q^{13} + q^{15} + 7 q^{16} + 5 q^{17} + 27 q^{18} + q^{19} + 9 q^{20} - 3 q^{22} - 2 q^{23} - 24 q^{24} + 8 q^{25} + 21 q^{26} - 5 q^{27} + 26 q^{29} - 3 q^{30} + 2 q^{31} + 16 q^{32} - q^{33} - 26 q^{34} + 54 q^{36} - q^{37} - 31 q^{38} + 19 q^{39} + 9 q^{40} - 3 q^{41} + 4 q^{43} - 9 q^{44} + 19 q^{45} + 10 q^{46} + q^{47} - 21 q^{48} + 3 q^{50} + 3 q^{51} + 37 q^{52} + 26 q^{53} - 5 q^{54} - 8 q^{55} + 20 q^{57} - q^{58} - 19 q^{59} + 9 q^{60} - 26 q^{62} + q^{64} + 14 q^{65} + 3 q^{66} - 13 q^{67} + 15 q^{68} - 14 q^{69} - 9 q^{71} + 32 q^{72} + 11 q^{73} + 24 q^{74} + q^{75} - 18 q^{76} - 33 q^{78} - 8 q^{79} + 7 q^{80} + 52 q^{81} + 41 q^{82} + 32 q^{83} + 5 q^{85} + 28 q^{86} - 16 q^{87} - 9 q^{88} + 5 q^{89} + 27 q^{90} + 30 q^{92} - 14 q^{93} - 5 q^{94} + q^{95} + q^{96} + 9 q^{97} - 19 q^{99}+O(q^{100}) \) 8 * q + 3 * q^2 + q^3 + 9 * q^4 + 8 * q^5 - 3 * q^6 + 9 * q^8 + 19 * q^9 + 3 * q^10 - 8 * q^11 + 9 * q^12 + 14 * q^13 + q^15 + 7 * q^16 + 5 * q^17 + 27 * q^18 + q^19 + 9 * q^20 - 3 * q^22 - 2 * q^23 - 24 * q^24 + 8 * q^25 + 21 * q^26 - 5 * q^27 + 26 * q^29 - 3 * q^30 + 2 * q^31 + 16 * q^32 - q^33 - 26 * q^34 + 54 * q^36 - q^37 - 31 * q^38 + 19 * q^39 + 9 * q^40 - 3 * q^41 + 4 * q^43 - 9 * q^44 + 19 * q^45 + 10 * q^46 + q^47 - 21 * q^48 + 3 * q^50 + 3 * q^51 + 37 * q^52 + 26 * q^53 - 5 * q^54 - 8 * q^55 + 20 * q^57 - q^58 - 19 * q^59 + 9 * q^60 - 26 * q^62 + q^64 + 14 * q^65 + 3 * q^66 - 13 * q^67 + 15 * q^68 - 14 * q^69 - 9 * q^71 + 32 * q^72 + 11 * q^73 + 24 * q^74 + q^75 - 18 * q^76 - 33 * q^78 - 8 * q^79 + 7 * q^80 + 52 * q^81 + 41 * q^82 + 32 * q^83 + 5 * q^85 + 28 * q^86 - 16 * q^87 - 9 * q^88 + 5 * q^89 + 27 * q^90 + 30 * q^92 - 14 * q^93 - 5 * q^94 + q^95 + q^96 + 9 * q^97 - 19 * q^99

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