LMFDB - Embedded newform 2695.2.a.u.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:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 13x^{8} + 24x^{7} + 56x^{6} - 92x^{5} - 86x^{4} + 116x^{3} + 31x^{2} - 30x - 7 $ x^10 - 2x^9 - 13x^8 + 24x^7 + 56x^6 - 92x^5 - 86x^4 + 116x^3 + 31x^2 - 30*x - 7
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.18262$ 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)

$f(q)$	$=$	$q-2.18262 q^{2} +1.88048 q^{3} +2.76381 q^{4} +1.00000 q^{5} -4.10437 q^{6} -1.66711 q^{8} +0.536219 q^{9} +O(q^{10})$	\(q-2.18262 q^{2} +1.88048 q^{3} +2.76381 q^{4} +1.00000 q^{5} -4.10437 q^{6} -1.66711 q^{8} +0.536219 q^{9} -2.18262 q^{10} +1.00000 q^{11} +5.19731 q^{12} +6.34275 q^{13} +1.88048 q^{15} -1.88896 q^{16} -4.44210 q^{17} -1.17036 q^{18} -4.08467 q^{19} +2.76381 q^{20} -2.18262 q^{22} -8.44940 q^{23} -3.13498 q^{24} +1.00000 q^{25} -13.8438 q^{26} -4.63310 q^{27} -9.91812 q^{29} -4.10437 q^{30} -6.27647 q^{31} +7.45710 q^{32} +1.88048 q^{33} +9.69540 q^{34} +1.48201 q^{36} -9.91659 q^{37} +8.91526 q^{38} +11.9274 q^{39} -1.66711 q^{40} -6.04416 q^{41} +3.33404 q^{43} +2.76381 q^{44} +0.536219 q^{45} +18.4418 q^{46} -2.32408 q^{47} -3.55216 q^{48} -2.18262 q^{50} -8.35329 q^{51} +17.5302 q^{52} -1.48134 q^{53} +10.1123 q^{54} +1.00000 q^{55} -7.68115 q^{57} +21.6475 q^{58} +0.280240 q^{59} +5.19731 q^{60} +6.85909 q^{61} +13.6991 q^{62} -12.4981 q^{64} +6.34275 q^{65} -4.10437 q^{66} -15.6288 q^{67} -12.2771 q^{68} -15.8890 q^{69} +8.88528 q^{71} -0.893937 q^{72} +5.52879 q^{73} +21.6441 q^{74} +1.88048 q^{75} -11.2893 q^{76} -26.0330 q^{78} -4.56853 q^{79} -1.88896 q^{80} -10.3211 q^{81} +13.1921 q^{82} +1.45664 q^{83} -4.44210 q^{85} -7.27693 q^{86} -18.6509 q^{87} -1.66711 q^{88} -8.08870 q^{89} -1.17036 q^{90} -23.3526 q^{92} -11.8028 q^{93} +5.07256 q^{94} -4.08467 q^{95} +14.0230 q^{96} -3.43717 q^{97} +0.536219 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} - 8 q^{3} + 10 q^{4} + 10 q^{5} - 4 q^{6} - 6 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q - 2 * q^2 - 8 * q^3 + 10 * q^4 + 10 * q^5 - 4 * q^6 - 6 * q^8 + 10 * q^9	$ 10 q - 2 q^{2} - 8 q^{3} + 10 q^{4} + 10 q^{5} - 4 q^{6} - 6 q^{8} + 10 q^{9} - 2 q^{10} + 10 q^{11} - 20 q^{12} - 8 q^{13} - 8 q^{15} + 6 q^{16} - 28 q^{17} - 14 q^{18} + 10 q^{20} - 2 q^{22} - 16 q^{23} + 8 q^{24} + 10 q^{25} - 20 q^{26} - 32 q^{27} - 4 q^{30} - 20 q^{31} - 14 q^{32} - 8 q^{33} + 4 q^{34} + 42 q^{36} - 36 q^{37} - 24 q^{38} + 24 q^{39} - 6 q^{40} - 36 q^{41} - 4 q^{43} + 10 q^{44} + 10 q^{45} - 4 q^{46} - 12 q^{47} - 40 q^{48} - 2 q^{50} + 20 q^{51} - 4 q^{52} - 16 q^{53} + 48 q^{54} + 10 q^{55} + 4 q^{57} + 16 q^{58} - 32 q^{59} - 20 q^{60} + 16 q^{61} + 4 q^{62} - 34 q^{64} - 8 q^{65} - 4 q^{66} - 20 q^{67} - 32 q^{68} - 28 q^{69} + 12 q^{71} - 2 q^{72} - 20 q^{73} + 32 q^{74} - 8 q^{75} - 12 q^{76} + 20 q^{78} + 12 q^{79} + 6 q^{80} + 42 q^{81} + 40 q^{82} - 8 q^{83} - 28 q^{85} - 4 q^{86} - 28 q^{87} - 6 q^{88} - 68 q^{89} - 14 q^{90} + 32 q^{92} - 32 q^{93} - 16 q^{94} + 80 q^{96} - 36 q^{97} + 10 q^{99}+O(q^{100}) $ 10 * q - 2 * q^2 - 8 * q^3 + 10 * q^4 + 10 * q^5 - 4 * q^6 - 6 * q^8 + 10 * q^9 - 2 * q^10 + 10 * q^11 - 20 * q^12 - 8 * q^13 - 8 * q^15 + 6 * q^16 - 28 * q^17 - 14 * q^18 + 10 * q^20 - 2 * q^22 - 16 * q^23 + 8 * q^24 + 10 * q^25 - 20 * q^26 - 32 * q^27 - 4 * q^30 - 20 * q^31 - 14 * q^32 - 8 * q^33 + 4 * q^34 + 42 * q^36 - 36 * q^37 - 24 * q^38 + 24 * q^39 - 6 * q^40 - 36 * q^41 - 4 * q^43 + 10 * q^44 + 10 * q^45 - 4 * q^46 - 12 * q^47 - 40 * q^48 - 2 * q^50 + 20 * q^51 - 4 * q^52 - 16 * q^53 + 48 * q^54 + 10 * q^55 + 4 * q^57 + 16 * q^58 - 32 * q^59 - 20 * q^60 + 16 * q^61 + 4 * q^62 - 34 * q^64 - 8 * q^65 - 4 * q^66 - 20 * q^67 - 32 * q^68 - 28 * q^69 + 12 * q^71 - 2 * q^72 - 20 * q^73 + 32 * q^74 - 8 * q^75 - 12 * q^76 + 20 * q^78 + 12 * q^79 + 6 * q^80 + 42 * q^81 + 40 * q^82 - 8 * q^83 - 28 * q^85 - 4 * q^86 - 28 * q^87 - 6 * q^88 - 68 * q^89 - 14 * q^90 + 32 * q^92 - 32 * q^93 - 16 * q^94 + 80 * q^96 - 36 * q^97 + 10 * 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 $

$2$	−2.18262	−1.54334	−0.771671	−	0.636021i	$-0.780579\pi$
$2$	−2.18262	−1.54334	−0.771671	+	0.636021i	$0.780579\pi$
$3$	1.88048	1.08570	0.542849	−	0.839830i	$-0.317346\pi$
$3$	1.88048	1.08570	0.542849	+	0.839830i	$0.317346\pi$
$4$	2.76381	1.38191
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−4.10437	−1.67560
$7$	0	0
$7$	0	0
$8$	−1.66711	−0.589413
$9$	0.536219	0.178740
$10$	−2.18262	−0.690204
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	5.19731	1.50033
$13$	6.34275	1.75916	0.879581	−	0.475750i	$-0.157823\pi$
$13$	6.34275	1.75916	0.879581	+	0.475750i	$0.157823\pi$
$14$	0	0
$15$	1.88048	0.485539
$16$	−1.88896	−0.472240
$17$	−4.44210	−1.07737	−0.538684	−	0.842508i	$-0.681078\pi$
$17$	−4.44210	−1.07737	−0.538684	+	0.842508i	$0.681078\pi$
$18$	−1.17036	−0.275857
$19$	−4.08467	−0.937087	−0.468543	−	0.883441i	$-0.655221\pi$
$19$	−4.08467	−0.937087	−0.468543	+	0.883441i	$0.655221\pi$
$20$	2.76381	0.618008
$21$	0	0
$22$	−2.18262	−0.465335
$23$	−8.44940	−1.76182	−0.880911	−	0.473283i	$-0.843069\pi$
$23$	−8.44940	−1.76182	−0.880911	+	0.473283i	$0.843069\pi$
$24$	−3.13498	−0.639925
$25$	1.00000	0.200000
$26$	−13.8438	−2.71499
$27$	−4.63310	−0.891641
$28$	0	0
$29$	−9.91812	−1.84175	−0.920874	−	0.389859i	$-0.872524\pi$
$29$	−9.91812	−1.84175	−0.920874	+	0.389859i	$0.872524\pi$
$30$	−4.10437	−0.749353
$31$	−6.27647	−1.12729	−0.563643	−	0.826018i	$-0.690601\pi$
$31$	−6.27647	−1.12729	−0.563643	+	0.826018i	$0.690601\pi$
$32$	7.45710	1.31824
$33$	1.88048	0.327350
$34$	9.69540	1.66275
$35$	0	0
$36$	1.48201	0.247002
$37$	−9.91659	−1.63028	−0.815139	−	0.579265i	$-0.803339\pi$
$37$	−9.91659	−1.63028	−0.815139	+	0.579265i	$0.803339\pi$
$38$	8.91526	1.44625
$39$	11.9274	1.90992
$40$	−1.66711	−0.263594
$41$	−6.04416	−0.943938	−0.471969	−	0.881615i	$-0.656457\pi$
$41$	−6.04416	−0.943938	−0.471969	+	0.881615i	$0.656457\pi$
$42$	0	0
$43$	3.33404	0.508436	0.254218	−	0.967147i	$-0.418182\pi$
$43$	3.33404	0.508436	0.254218	+	0.967147i	$0.418182\pi$
$44$	2.76381	0.416661
$45$	0.536219	0.0799348
$46$	18.4418	2.71909
$47$	−2.32408	−0.339001	−0.169501	−	0.985530i	$-0.554215\pi$
$47$	−2.32408	−0.339001	−0.169501	+	0.985530i	$0.554215\pi$
$48$	−3.55216	−0.512710
$49$	0	0
$50$	−2.18262	−0.308669
$51$	−8.35329	−1.16969
$52$	17.5302	2.43100
$53$	−1.48134	−0.203477	−0.101739	−	0.994811i	$-0.532441\pi$
$53$	−1.48134	−0.203477	−0.101739	+	0.994811i	$0.532441\pi$
$54$	10.1123	1.37611
$55$	1.00000	0.134840
$56$	0	0
$57$	−7.68115	−1.01739
$58$	21.6475	2.84245
$59$	0.280240	0.0364842	0.0182421	−	0.999834i	$-0.494193\pi$
$59$	0.280240	0.0364842	0.0182421	+	0.999834i	$0.494193\pi$
$60$	5.19731	0.670969
$61$	6.85909	0.878216	0.439108	−	0.898434i	$-0.355295\pi$
$61$	6.85909	0.878216	0.439108	+	0.898434i	$0.355295\pi$
$62$	13.6991	1.73979
$63$	0	0
$64$	−12.4981	−1.56226
$65$	6.34275	0.786721
$66$	−4.10437	−0.505214
$67$	−15.6288	−1.90937	−0.954683	−	0.297624i	$-0.903806\pi$
$67$	−15.6288	−1.90937	−0.954683	+	0.297624i	$0.903806\pi$
$68$	−12.2771	−1.48882
$69$	−15.8890	−1.91281
$70$	0	0
$71$	8.88528	1.05449	0.527244	−	0.849714i	$-0.323225\pi$
$71$	8.88528	1.05449	0.527244	+	0.849714i	$0.323225\pi$
$72$	−0.893937	−0.105351
$73$	5.52879	0.647096	0.323548	−	0.946212i	$-0.395124\pi$
$73$	5.52879	0.647096	0.323548	+	0.946212i	$0.395124\pi$
$74$	21.6441	2.51608
$75$	1.88048	0.217140
$76$	−11.2893	−1.29497
$77$	0	0
$78$	−26.0330	−2.94766
$79$	−4.56853	−0.514000	−0.257000	−	0.966411i	$-0.582734\pi$
$79$	−4.56853	−0.514000	−0.257000	+	0.966411i	$0.582734\pi$
$80$	−1.88896	−0.211192
$81$	−10.3211	−1.14679
$82$	13.1921	1.45682
$83$	1.45664	0.159887	0.0799435	−	0.996799i	$-0.474526\pi$
$83$	1.45664	0.159887	0.0799435	+	0.996799i	$0.474526\pi$
$84$	0	0
$85$	−4.44210	−0.481813
$86$	−7.27693	−0.784692
$87$	−18.6509	−1.99958
$88$	−1.66711	−0.177715
$89$	−8.08870	−0.857401	−0.428701	−	0.903447i	$-0.641028\pi$
$89$	−8.08870	−0.857401	−0.428701	+	0.903447i	$0.641028\pi$
$90$	−1.17036	−0.123367
$91$	0	0
$92$	−23.3526	−2.43467
$93$	−11.8028	−1.22389
$94$	5.07256	0.523195
$95$	−4.08467	−0.419078
$96$	14.0230	1.43121
$97$	−3.43717	−0.348991	−0.174496	−	0.984658i	$-0.555830\pi$
$97$	−3.43717	−0.348991	−0.174496	+	0.984658i	$0.555830\pi$
$98$	0	0
$99$	0.536219	0.0538920
$100$	2.76381	0.276381
$101$	11.1639	1.11085	0.555426	−	0.831566i	$-0.312555\pi$
$101$	11.1639	1.11085	0.555426	+	0.831566i	$0.312555\pi$
$102$	18.2320	1.80524
$103$	18.3192	1.80505	0.902523	−	0.430641i	$-0.141713\pi$
$103$	18.3192	1.80505	0.902523	+	0.430641i	$0.141713\pi$
$104$	−10.5741	−1.03687
$105$	0	0
$106$	3.23319	0.314035
$107$	2.37100	0.229213	0.114607	−	0.993411i	$-0.463439\pi$
$107$	2.37100	0.229213	0.114607	+	0.993411i	$0.463439\pi$
$108$	−12.8050	−1.23216
$109$	6.47609	0.620297	0.310148	−	0.950688i	$-0.399621\pi$
$109$	6.47609	0.620297	0.310148	+	0.950688i	$0.399621\pi$
$110$	−2.18262	−0.208104
$111$	−18.6480	−1.76999
$112$	0	0
$113$	−17.5144	−1.64762	−0.823810	−	0.566867i	$-0.808155\pi$
$113$	−17.5144	−1.64762	−0.823810	+	0.566867i	$0.808155\pi$
$114$	16.7650	1.57019
$115$	−8.44940	−0.787910
$116$	−27.4118	−2.54513
$117$	3.40110	0.314432
$118$	−0.611657	−0.0563076
$119$	0	0
$120$	−3.13498	−0.286183
$121$	1.00000	0.0909091
$122$	−14.9708	−1.35539
$123$	−11.3659	−1.02483
$124$	−17.3470	−1.55780
$125$	1.00000	0.0894427
$126$	0	0
$127$	0.321917	0.0285655	0.0142827	−	0.999898i	$-0.495454\pi$
$127$	0.321917	0.0285655	0.0142827	+	0.999898i	$0.495454\pi$
$128$	12.3643	1.09286
$129$	6.26961	0.552008
$130$	−13.8438	−1.21418
$131$	9.44254	0.824998	0.412499	−	0.910958i	$-0.364656\pi$
$131$	9.44254	0.824998	0.412499	+	0.910958i	$0.364656\pi$
$132$	5.19731	0.452367
$133$	0	0
$134$	34.1118	2.94681
$135$	−4.63310	−0.398754
$136$	7.40548	0.635014
$137$	6.37191	0.544389	0.272195	−	0.962242i	$-0.412251\pi$
$137$	6.37191	0.544389	0.272195	+	0.962242i	$0.412251\pi$
$138$	34.6795	2.95211
$139$	18.4605	1.56580	0.782900	−	0.622147i	$-0.213739\pi$
$139$	18.4605	1.56580	0.782900	+	0.622147i	$0.213739\pi$
$140$	0	0
$141$	−4.37039	−0.368053
$142$	−19.3932	−1.62744
$143$	6.34275	0.530407
$144$	−1.01290	−0.0844081
$145$	−9.91812	−0.823655
$146$	−12.0672	−0.998691
$147$	0	0
$148$	−27.4076	−2.25289
$149$	3.27701	0.268463	0.134231	−	0.990950i	$-0.457143\pi$
$149$	3.27701	0.268463	0.134231	+	0.990950i	$0.457143\pi$
$150$	−4.10437	−0.335121
$151$	−5.25573	−0.427705	−0.213852	−	0.976866i	$-0.568601\pi$
$151$	−5.25573	−0.427705	−0.213852	+	0.976866i	$0.568601\pi$
$152$	6.80960	0.552331
$153$	−2.38194	−0.192568
$154$	0	0
$155$	−6.27647	−0.504138
$156$	32.9652	2.63933
$157$	7.86246	0.627493	0.313746	−	0.949507i	$-0.398416\pi$
$157$	7.86246	0.627493	0.313746	+	0.949507i	$0.398416\pi$
$158$	9.97135	0.793278
$159$	−2.78563	−0.220915
$160$	7.45710	0.589536
$161$	0	0
$162$	22.5271	1.76989
$163$	15.5171	1.21540	0.607698	−	0.794168i	$-0.292093\pi$
$163$	15.5171	1.21540	0.607698	+	0.794168i	$0.292093\pi$
$164$	−16.7049	−1.30444
$165$	1.88048	0.146395
$166$	−3.17929	−0.246761
$167$	−9.88147	−0.764651	−0.382325	−	0.924028i	$-0.624877\pi$
$167$	−9.88147	−0.764651	−0.382325	+	0.924028i	$0.624877\pi$
$168$	0	0
$169$	27.2304	2.09465
$170$	9.69540	0.743603
$171$	−2.19028	−0.167495
$172$	9.21467	0.702612
$173$	−24.4302	−1.85739	−0.928697	−	0.370839i	$-0.879070\pi$
$173$	−24.4302	−1.85739	−0.928697	+	0.370839i	$0.879070\pi$
$174$	40.7077	3.08604
$175$	0	0
$176$	−1.88896	−0.142386
$177$	0.526988	0.0396108
$178$	17.6545	1.32326
$179$	24.7106	1.84696	0.923478	−	0.383653i	$-0.125334\pi$
$179$	24.7106	1.84696	0.923478	+	0.383653i	$0.125334\pi$
$180$	1.48201	0.110462
$181$	−0.825212	−0.0613375	−0.0306688	−	0.999530i	$-0.509764\pi$
$181$	−0.825212	−0.0613375	−0.0306688	+	0.999530i	$0.509764\pi$
$182$	0	0
$183$	12.8984	0.953477
$184$	14.0861	1.03844
$185$	−9.91659	−0.729082
$186$	25.7610	1.88889
$187$	−4.44210	−0.324838
$188$	−6.42331	−0.468468
$189$	0	0
$190$	8.91526	0.646781
$191$	6.83487	0.494554	0.247277	−	0.968945i	$-0.420464\pi$
$191$	6.83487	0.494554	0.247277	+	0.968945i	$0.420464\pi$
$192$	−23.5024	−1.69614
$193$	1.24078	0.0893133	0.0446567	−	0.999002i	$-0.485781\pi$
$193$	1.24078	0.0893133	0.0446567	+	0.999002i	$0.485781\pi$
$194$	7.50202	0.538613
$195$	11.9274	0.854141
$196$	0	0
$197$	−3.11573	−0.221987	−0.110993	−	0.993821i	$-0.535403\pi$
$197$	−3.11573	−0.221987	−0.110993	+	0.993821i	$0.535403\pi$
$198$	−1.17036	−0.0831739
$199$	8.74399	0.619845	0.309923	−	0.950762i	$-0.399697\pi$
$199$	8.74399	0.619845	0.309923	+	0.950762i	$0.399697\pi$
$200$	−1.66711	−0.117883
$201$	−29.3898	−2.07299
$202$	−24.3665	−1.71442
$203$	0	0
$204$	−23.0869	−1.61641
$205$	−6.04416	−0.422142
$206$	−39.9838	−2.78581
$207$	−4.53073	−0.314907
$208$	−11.9812	−0.830747
$209$	−4.08467	−0.282542
$210$	0	0
$211$	0.431054	0.0296750	0.0148375	−	0.999890i	$-0.495277\pi$
$211$	0.431054	0.0296750	0.0148375	+	0.999890i	$0.495277\pi$
$212$	−4.09414	−0.281186
$213$	16.7086	1.14486
$214$	−5.17498	−0.353755
$215$	3.33404	0.227380
$216$	7.72390	0.525545
$217$	0	0
$218$	−14.1348	−0.957330
$219$	10.3968	0.702551
$220$	2.76381	0.186336
$221$	−28.1751	−1.89526
$222$	40.7014	2.73170
$223$	−15.4899	−1.03728	−0.518640	−	0.854993i	$-0.673562\pi$
$223$	−15.4899	−1.03728	−0.518640	+	0.854993i	$0.673562\pi$
$224$	0	0
$225$	0.536219	0.0357479
$226$	38.2273	2.54284
$227$	−3.61706	−0.240073	−0.120037	−	0.992769i	$-0.538301\pi$
$227$	−3.61706	−0.240073	−0.120037	+	0.992769i	$0.538301\pi$
$228$	−21.2293	−1.40594
$229$	−0.956048	−0.0631774	−0.0315887	−	0.999501i	$-0.510057\pi$
$229$	−0.956048	−0.0631774	−0.0315887	+	0.999501i	$0.510057\pi$
$230$	18.4418	1.21602
$231$	0	0
$232$	16.5346	1.08555
$233$	16.2130	1.06215	0.531073	−	0.847326i	$-0.321789\pi$
$233$	16.2130	1.06215	0.531073	+	0.847326i	$0.321789\pi$
$234$	−7.42330	−0.485276
$235$	−2.32408	−0.151606
$236$	0.774532	0.0504178
$237$	−8.59104	−0.558048
$238$	0	0
$239$	18.5098	1.19730	0.598649	−	0.801011i	$-0.295704\pi$
$239$	18.5098	1.19730	0.598649	+	0.801011i	$0.295704\pi$
$240$	−3.55216	−0.229291
$241$	−12.8169	−0.825610	−0.412805	−	0.910819i	$-0.635451\pi$
$241$	−12.8169	−0.825610	−0.412805	+	0.910819i	$0.635451\pi$
$242$	−2.18262	−0.140304
$243$	−5.50941	−0.353429
$244$	18.9572	1.21361
$245$	0	0
$246$	24.8075	1.58167
$247$	−25.9080	−1.64849
$248$	10.4636	0.664438
$249$	2.73919	0.173589
$250$	−2.18262	−0.138041
$251$	5.01952	0.316829	0.158415	−	0.987373i	$-0.449362\pi$
$251$	5.01952	0.316829	0.158415	+	0.987373i	$0.449362\pi$
$252$	0	0
$253$	−8.44940	−0.531209
$254$	−0.702621	−0.0440864
$255$	−8.35329	−0.523103
$256$	−1.99035	−0.124397
$257$	−25.1035	−1.56591	−0.782957	−	0.622076i	$-0.786290\pi$
$257$	−25.1035	−1.56591	−0.782957	+	0.622076i	$0.786290\pi$
$258$	−13.6841	−0.851938
$259$	0	0
$260$	17.5302	1.08718
$261$	−5.31828	−0.329194
$262$	−20.6094	−1.27326
$263$	−14.7000	−0.906439	−0.453220	−	0.891399i	$-0.649725\pi$
$263$	−14.7000	−0.906439	−0.453220	+	0.891399i	$0.649725\pi$
$264$	−3.13498	−0.192945
$265$	−1.48134	−0.0909977
$266$	0	0
$267$	−15.2107	−0.930878
$268$	−43.1952	−2.63857
$269$	−6.51564	−0.397265	−0.198633	−	0.980074i	$-0.563650\pi$
$269$	−6.51564	−0.397265	−0.198633	+	0.980074i	$0.563650\pi$
$270$	10.1123	0.615414
$271$	16.7945	1.02019	0.510096	−	0.860118i	$-0.329610\pi$
$271$	16.7945	1.02019	0.510096	+	0.860118i	$0.329610\pi$
$272$	8.39095	0.508776
$273$	0	0
$274$	−13.9074	−0.840179
$275$	1.00000	0.0603023
$276$	−43.9141	−2.64332
$277$	17.2683	1.03755	0.518777	−	0.854910i	$-0.326388\pi$
$277$	17.2683	1.03755	0.518777	+	0.854910i	$0.326388\pi$
$278$	−40.2922	−2.41657
$279$	−3.36556	−0.201491
$280$	0	0
$281$	3.26449	0.194743	0.0973716	−	0.995248i	$-0.468956\pi$
$281$	3.26449	0.194743	0.0973716	+	0.995248i	$0.468956\pi$
$282$	9.53887	0.568032
$283$	13.6919	0.813898	0.406949	−	0.913451i	$-0.366593\pi$
$283$	13.6919	0.813898	0.406949	+	0.913451i	$0.366593\pi$
$284$	24.5573	1.45721
$285$	−7.68115	−0.454992
$286$	−13.8438	−0.818600
$287$	0	0
$288$	3.99864	0.235622
$289$	2.73224	0.160720
$290$	21.6475	1.27118
$291$	−6.46354	−0.378899
$292$	15.2805	0.894226
$293$	−21.3339	−1.24634	−0.623170	−	0.782086i	$-0.714156\pi$
$293$	−21.3339	−1.24634	−0.623170	+	0.782086i	$0.714156\pi$
$294$	0	0
$295$	0.280240	0.0163162
$296$	16.5321	0.960907
$297$	−4.63310	−0.268840
$298$	−7.15244	−0.414330
$299$	−53.5924	−3.09933
$300$	5.19731	0.300067
$301$	0	0
$302$	11.4712	0.660095
$303$	20.9936	1.20605
$304$	7.71578	0.442530
$305$	6.85909	0.392750
$306$	5.19885	0.297199
$307$	5.35795	0.305794	0.152897	−	0.988242i	$-0.451140\pi$
$307$	5.35795	0.305794	0.152897	+	0.988242i	$0.451140\pi$
$308$	0	0
$309$	34.4490	1.95973
$310$	13.6991	0.778058
$311$	−15.7203	−0.891415	−0.445708	−	0.895179i	$-0.647048\pi$
$311$	−15.7203	−0.891415	−0.445708	+	0.895179i	$0.647048\pi$
$312$	−19.8844	−1.12573
$313$	21.9052	1.23816	0.619078	−	0.785330i	$-0.287507\pi$
$313$	21.9052	1.23816	0.619078	+	0.785330i	$0.287507\pi$
$314$	−17.1607	−0.968437
$315$	0	0
$316$	−12.6266	−0.710300
$317$	21.6944	1.21848	0.609238	−	0.792987i	$-0.291475\pi$
$317$	21.6944	1.21848	0.609238	+	0.792987i	$0.291475\pi$
$318$	6.07996	0.340947
$319$	−9.91812	−0.555308
$320$	−12.4981	−0.698663
$321$	4.45863	0.248856
$322$	0	0
$323$	18.1445	1.00959
$324$	−28.5257	−1.58476
$325$	6.34275	0.351832
$326$	−33.8680	−1.87577
$327$	12.1782	0.673455
$328$	10.0763	0.556370
$329$	0	0
$330$	−4.10437	−0.225938
$331$	−3.31751	−0.182347	−0.0911735	−	0.995835i	$-0.529062\pi$
$331$	−3.31751	−0.182347	−0.0911735	+	0.995835i	$0.529062\pi$
$332$	4.02588	0.220949
$333$	−5.31746	−0.291395
$334$	21.5675	1.18012
$335$	−15.6288	−0.853895
$336$	0	0
$337$	20.2870	1.10510	0.552552	−	0.833478i	$-0.313654\pi$
$337$	20.2870	1.10510	0.552552	+	0.833478i	$0.313654\pi$
$338$	−59.4336	−3.23276
$339$	−32.9356	−1.78882
$340$	−12.2771	−0.665821
$341$	−6.27647	−0.339890
$342$	4.78053	0.258501
$343$	0	0
$344$	−5.55822	−0.299679
$345$	−15.8890	−0.855432
$346$	53.3218	2.86660
$347$	−15.8800	−0.852481	−0.426241	−	0.904610i	$-0.640162\pi$
$347$	−15.8800	−0.852481	−0.426241	+	0.904610i	$0.640162\pi$
$348$	−51.5475	−2.76324
$349$	−11.0943	−0.593862	−0.296931	−	0.954899i	$-0.595963\pi$
$349$	−11.0943	−0.593862	−0.296931	+	0.954899i	$0.595963\pi$
$350$	0	0
$351$	−29.3866	−1.56854
$352$	7.45710	0.397465
$353$	−36.3369	−1.93402	−0.967010	−	0.254739i	$-0.918010\pi$
$353$	−36.3369	−1.93402	−0.967010	+	0.254739i	$0.918010\pi$
$354$	−1.15021	−0.0611331
$355$	8.88528	0.471582
$356$	−22.3557	−1.18485
$357$	0	0
$358$	−53.9337	−2.85048
$359$	−15.1277	−0.798411	−0.399206	−	0.916861i	$-0.630714\pi$
$359$	−15.1277	−0.798411	−0.399206	+	0.916861i	$0.630714\pi$
$360$	−0.893937	−0.0471146
$361$	−2.31550	−0.121869
$362$	1.80112	0.0946648
$363$	1.88048	0.0986998
$364$	0	0
$365$	5.52879	0.289390
$366$	−28.1523	−1.47154
$367$	−18.8857	−0.985823	−0.492912	−	0.870079i	$-0.664067\pi$
$367$	−18.8857	−0.985823	−0.492912	+	0.870079i	$0.664067\pi$
$368$	15.9606	0.832003
$369$	−3.24099	−0.168719
$370$	21.6441	1.12522
$371$	0	0
$372$	−32.6207	−1.69131
$373$	−30.4335	−1.57578	−0.787892	−	0.615813i	$-0.788828\pi$
$373$	−30.4335	−1.57578	−0.787892	+	0.615813i	$0.788828\pi$
$374$	9.69540	0.501337
$375$	1.88048	0.0971078
$376$	3.87449	0.199812
$377$	−62.9081	−3.23993
$378$	0	0
$379$	31.9881	1.64312	0.821558	−	0.570125i	$-0.193105\pi$
$379$	31.9881	1.64312	0.821558	+	0.570125i	$0.193105\pi$
$380$	−11.2893	−0.579127
$381$	0.605359	0.0310135
$382$	−14.9179	−0.763266
$383$	−11.3175	−0.578295	−0.289148	−	0.957285i	$-0.593372\pi$
$383$	−11.3175	−0.578295	−0.289148	+	0.957285i	$0.593372\pi$
$384$	23.2508	1.18651
$385$	0	0
$386$	−2.70815	−0.137841
$387$	1.78778	0.0908777
$388$	−9.49969	−0.482274
$389$	−30.9541	−1.56944	−0.784718	−	0.619853i	$-0.787192\pi$
$389$	−30.9541	−1.56944	−0.784718	+	0.619853i	$0.787192\pi$
$390$	−26.0330	−1.31823
$391$	37.5330	1.89813
$392$	0	0
$393$	17.7565	0.895699
$394$	6.80044	0.342601
$395$	−4.56853	−0.229868
$396$	1.48201	0.0744738
$397$	−2.48261	−0.124599	−0.0622994	−	0.998058i	$-0.519843\pi$
$397$	−2.48261	−0.124599	−0.0622994	+	0.998058i	$0.519843\pi$
$398$	−19.0848	−0.956633
$399$	0	0
$400$	−1.88896	−0.0944481
$401$	−0.196290	−0.00980225	−0.00490112	−	0.999988i	$-0.501560\pi$
$401$	−0.196290	−0.00980225	−0.00490112	+	0.999988i	$0.501560\pi$
$402$	64.1466	3.19934
$403$	−39.8100	−1.98308
$404$	30.8550	1.53509
$405$	−10.3211	−0.512861
$406$	0	0
$407$	−9.91659	−0.491547
$408$	13.9259	0.689434
$409$	5.25573	0.259879	0.129939	−	0.991522i	$-0.458522\pi$
$409$	5.25573	0.259879	0.129939	+	0.991522i	$0.458522\pi$
$410$	13.1921	0.651510
$411$	11.9823	0.591042
$412$	50.6309	2.49441
$413$	0	0
$414$	9.88884	0.486010
$415$	1.45664	0.0715037
$416$	47.2985	2.31900
$417$	34.7147	1.69999
$418$	8.91526	0.436060
$419$	−14.3240	−0.699775	−0.349888	−	0.936792i	$-0.613780\pi$
$419$	−14.3240	−0.699775	−0.349888	+	0.936792i	$0.613780\pi$
$420$	0	0
$421$	28.2385	1.37626	0.688129	−	0.725588i	$-0.258432\pi$
$421$	28.2385	1.37626	0.688129	+	0.725588i	$0.258432\pi$
$422$	−0.940826	−0.0457987
$423$	−1.24621	−0.0605930
$424$	2.46955	0.119932
$425$	−4.44210	−0.215473
$426$	−36.4685	−1.76691
$427$	0	0
$428$	6.55300	0.316751
$429$	11.9274	0.575862
$430$	−7.27693	−0.350925
$431$	13.3193	0.641566	0.320783	−	0.947153i	$-0.396054\pi$
$431$	13.3193	0.641566	0.320783	+	0.947153i	$0.396054\pi$
$432$	8.75175	0.421069
$433$	−28.0919	−1.35001	−0.675005	−	0.737814i	$-0.735858\pi$
$433$	−28.0919	−1.35001	−0.675005	+	0.737814i	$0.735858\pi$
$434$	0	0
$435$	−18.6509	−0.894241
$436$	17.8987	0.857192
$437$	34.5130	1.65098
$438$	−22.6922	−1.08428
$439$	−10.0506	−0.479690	−0.239845	−	0.970811i	$-0.577097\pi$
$439$	−10.0506	−0.479690	−0.239845	+	0.970811i	$0.577097\pi$
$440$	−1.66711	−0.0794765
$441$	0	0
$442$	61.4954	2.92504
$443$	−12.5698	−0.597209	−0.298605	−	0.954377i	$-0.596521\pi$
$443$	−12.5698	−0.597209	−0.298605	+	0.954377i	$0.596521\pi$
$444$	−51.5396	−2.44596
$445$	−8.08870	−0.383441
$446$	33.8085	1.60088
$447$	6.16235	0.291469
$448$	0	0
$449$	7.43556	0.350906	0.175453	−	0.984488i	$-0.443861\pi$
$449$	7.43556	0.350906	0.175453	+	0.984488i	$0.443861\pi$
$450$	−1.17036	−0.0551713
$451$	−6.04416	−0.284608
$452$	−48.4066	−2.27686
$453$	−9.88331	−0.464358
$454$	7.89466	0.370515
$455$	0	0
$456$	12.8053	0.599665
$457$	27.5374	1.28814	0.644072	−	0.764965i	$-0.277244\pi$
$457$	27.5374	1.28814	0.644072	+	0.764965i	$0.277244\pi$
$458$	2.08669	0.0975045
$459$	20.5807	0.960624
$460$	−23.3526	−1.08882
$461$	−9.07024	−0.422443	−0.211222	−	0.977438i	$-0.567744\pi$
$461$	−9.07024	−0.422443	−0.211222	+	0.977438i	$0.567744\pi$
$462$	0	0
$463$	10.8883	0.506022	0.253011	−	0.967463i	$-0.418579\pi$
$463$	10.8883	0.506022	0.253011	+	0.967463i	$0.418579\pi$
$464$	18.7349	0.869748
$465$	−11.8028	−0.547341
$466$	−35.3867	−1.63926
$467$	−34.1172	−1.57875	−0.789377	−	0.613909i	$-0.789596\pi$
$467$	−34.1172	−1.57875	−0.789377	+	0.613909i	$0.789596\pi$
$468$	9.40001	0.434516
$469$	0	0
$470$	5.07256	0.233980
$471$	14.7852	0.681268
$472$	−0.467192	−0.0215043
$473$	3.33404	0.153299
$474$	18.7510	0.861260
$475$	−4.08467	−0.187417
$476$	0	0
$477$	−0.794320	−0.0363694
$478$	−40.3997	−1.84784
$479$	20.6442	0.943257	0.471628	−	0.881797i	$-0.343666\pi$
$479$	20.6442	0.943257	0.471628	+	0.881797i	$0.343666\pi$
$480$	14.0230	0.640058
$481$	−62.8984	−2.86792
$482$	27.9744	1.27420
$483$	0	0
$484$	2.76381	0.125628
$485$	−3.43717	−0.156074
$486$	12.0249	0.545462
$487$	−10.7232	−0.485916	−0.242958	−	0.970037i	$-0.578118\pi$
$487$	−10.7232	−0.485916	−0.242958	+	0.970037i	$0.578118\pi$
$488$	−11.4349	−0.517632
$489$	29.1797	1.31955
$490$	0	0
$491$	31.2569	1.41060	0.705302	−	0.708907i	$-0.250811\pi$
$491$	31.2569	1.41060	0.705302	+	0.708907i	$0.250811\pi$
$492$	−31.4133	−1.41622
$493$	44.0573	1.98424
$494$	56.5472	2.54418
$495$	0.536219	0.0241012
$496$	11.8560	0.532350
$497$	0	0
$498$	−5.97860	−0.267907
$499$	−3.58205	−0.160355	−0.0801773	−	0.996781i	$-0.525549\pi$
$499$	−3.58205	−0.160355	−0.0801773	+	0.996781i	$0.525549\pi$
$500$	2.76381	0.123602
$501$	−18.5819	−0.830180
$502$	−10.9557	−0.488976
$503$	15.1179	0.674072	0.337036	−	0.941492i	$-0.390576\pi$
$503$	15.1179	0.674072	0.337036	+	0.941492i	$0.390576\pi$
$504$	0	0
$505$	11.1639	0.496788
$506$	18.4418	0.819838
$507$	51.2064	2.27416
$508$	0.889718	0.0394749
$509$	24.5873	1.08981	0.544907	−	0.838496i	$-0.316565\pi$
$509$	24.5873	1.08981	0.544907	+	0.838496i	$0.316565\pi$
$510$	18.2320	0.807328
$511$	0	0
$512$	−20.3844	−0.900872
$513$	18.9247	0.835544
$514$	54.7913	2.41674
$515$	18.3192	0.807241
$516$	17.3280	0.762824
$517$	−2.32408	−0.102213
$518$	0	0
$519$	−45.9406	−2.01657
$520$	−10.5741	−0.463704
$521$	0.678173	0.0297113	0.0148556	−	0.999890i	$-0.495271\pi$
$521$	0.678173	0.0297113	0.0148556	+	0.999890i	$0.495271\pi$
$522$	11.6078	0.508058
$523$	−27.2539	−1.19173	−0.595864	−	0.803085i	$-0.703190\pi$
$523$	−27.2539	−1.19173	−0.595864	+	0.803085i	$0.703190\pi$
$524$	26.0974	1.14007
$525$	0	0
$526$	32.0844	1.39895
$527$	27.8807	1.21450
$528$	−3.55216	−0.154588
$529$	48.3923	2.10401
$530$	3.23319	0.140441
$531$	0.150270	0.00652117
$532$	0	0
$533$	−38.3365	−1.66054
$534$	33.1991	1.43666
$535$	2.37100	0.102507
$536$	26.0550	1.12541
$537$	46.4678	2.00523
$538$	14.2211	0.613117
$539$	0	0
$540$	−12.8050	−0.551041
$541$	−24.5703	−1.05636	−0.528180	−	0.849133i	$-0.677125\pi$
$541$	−24.5703	−1.05636	−0.528180	+	0.849133i	$0.677125\pi$
$542$	−36.6559	−1.57451
$543$	−1.55180	−0.0665940
$544$	−33.1252	−1.42023
$545$	6.47609	0.277405
$546$	0	0
$547$	−29.6145	−1.26623	−0.633113	−	0.774059i	$-0.718223\pi$
$547$	−29.6145	−1.26623	−0.633113	+	0.774059i	$0.718223\pi$
$548$	17.6108	0.752295
$549$	3.67797	0.156972
$550$	−2.18262	−0.0930671
$551$	40.5122	1.72588
$552$	26.4887	1.12743
$553$	0	0
$554$	−37.6901	−1.60130
$555$	−18.6480	−0.791563
$556$	51.0214	2.16379
$557$	2.47449	0.104848	0.0524239	−	0.998625i	$-0.483305\pi$
$557$	2.47449	0.104848	0.0524239	+	0.998625i	$0.483305\pi$
$558$	7.34572	0.310969
$559$	21.1470	0.894422
$560$	0	0
$561$	−8.35329	−0.352676
$562$	−7.12513	−0.300555
$563$	−13.3585	−0.562995	−0.281498	−	0.959562i	$-0.590831\pi$
$563$	−13.3585	−0.562995	−0.281498	+	0.959562i	$0.590831\pi$
$564$	−12.0789	−0.508615
$565$	−17.5144	−0.736838
$566$	−29.8841	−1.25612
$567$	0	0
$568$	−14.8128	−0.621530
$569$	−38.9693	−1.63368	−0.816840	−	0.576865i	$-0.804276\pi$
$569$	−38.9693	−1.63368	−0.816840	+	0.576865i	$0.804276\pi$
$570$	16.7650	0.702209
$571$	−15.1631	−0.634555	−0.317277	−	0.948333i	$-0.602769\pi$
$571$	−15.1631	−0.634555	−0.317277	+	0.948333i	$0.602769\pi$
$572$	17.5302	0.732973
$573$	12.8529	0.536936
$574$	0	0
$575$	−8.44940	−0.352364
$576$	−6.70170	−0.279238
$577$	0.190258	0.00792055	0.00396027	−	0.999992i	$-0.498739\pi$
$577$	0.190258	0.00792055	0.00396027	+	0.999992i	$0.498739\pi$
$578$	−5.96342	−0.248046
$579$	2.33327	0.0969673
$580$	−27.4118	−1.13821
$581$	0	0
$582$	14.1074	0.584771
$583$	−1.48134	−0.0613507
$584$	−9.21711	−0.381407
$585$	3.40110	0.140618
$586$	46.5637	1.92353
$587$	−9.09439	−0.375366	−0.187683	−	0.982230i	$-0.560098\pi$
$587$	−9.09439	−0.375366	−0.187683	+	0.982230i	$0.560098\pi$
$588$	0	0
$589$	25.6373	1.05637
$590$	−0.611657	−0.0251815
$591$	−5.85908	−0.241010
$592$	18.7321	0.769883
$593$	29.9184	1.22860	0.614302	−	0.789071i	$-0.289438\pi$
$593$	29.9184	1.22860	0.614302	+	0.789071i	$0.289438\pi$
$594$	10.1123	0.414912
$595$	0	0
$596$	9.05703	0.370990
$597$	16.4429	0.672964
$598$	116.972	4.78332
$599$	−5.05270	−0.206448	−0.103224	−	0.994658i	$-0.532916\pi$
$599$	−5.05270	−0.206448	−0.103224	+	0.994658i	$0.532916\pi$
$600$	−3.13498	−0.127985
$601$	31.0105	1.26494	0.632472	−	0.774583i	$-0.282040\pi$
$601$	31.0105	1.26494	0.632472	+	0.774583i	$0.282040\pi$
$602$	0	0
$603$	−8.38048	−0.341279
$604$	−14.5258	−0.591048
$605$	1.00000	0.0406558
$606$	−45.8209	−1.86135
$607$	22.7532	0.923525	0.461763	−	0.887004i	$-0.347217\pi$
$607$	22.7532	0.923525	0.461763	+	0.887004i	$0.347217\pi$
$608$	−30.4598	−1.23531
$609$	0	0
$610$	−14.9708	−0.606148
$611$	−14.7410	−0.596358
$612$	−6.58323	−0.266111
$613$	−9.10859	−0.367893	−0.183946	−	0.982936i	$-0.558887\pi$
$613$	−9.10859	−0.367893	−0.183946	+	0.982936i	$0.558887\pi$
$614$	−11.6943	−0.471945
$615$	−11.3659	−0.458319
$616$	0	0
$617$	22.3737	0.900732	0.450366	−	0.892844i	$-0.351293\pi$
$617$	22.3737	0.900732	0.450366	+	0.892844i	$0.351293\pi$
$618$	−75.1889	−3.02454
$619$	−46.5027	−1.86910	−0.934551	−	0.355829i	$-0.884198\pi$
$619$	−46.5027	−1.86910	−0.934551	+	0.355829i	$0.884198\pi$
$620$	−17.3470	−0.696672
$621$	39.1469	1.57091
$622$	34.3113	1.37576
$623$	0	0
$624$	−22.5305	−0.901940
$625$	1.00000	0.0400000
$626$	−47.8106	−1.91090
$627$	−7.68115	−0.306755
$628$	21.7304	0.867137
$629$	44.0505	1.75641
$630$	0	0
$631$	2.84446	0.113236	0.0566180	−	0.998396i	$-0.481968\pi$
$631$	2.84446	0.113236	0.0566180	+	0.998396i	$0.481968\pi$
$632$	7.61625	0.302958
$633$	0.810591	0.0322181
$634$	−47.3505	−1.88053
$635$	0.321917	0.0127749
$636$	−7.69896	−0.305283
$637$	0	0
$638$	21.6475	0.857031
$639$	4.76446	0.188479
$640$	12.3643	0.488741
$641$	−2.25725	−0.0891561	−0.0445780	−	0.999006i	$-0.514194\pi$
$641$	−2.25725	−0.0891561	−0.0445780	+	0.999006i	$0.514194\pi$
$642$	−9.73147	−0.384071
$643$	−0.952559	−0.0375653	−0.0187826	−	0.999824i	$-0.505979\pi$
$643$	−0.952559	−0.0375653	−0.0187826	+	0.999824i	$0.505979\pi$
$644$	0	0
$645$	6.26961	0.246866
$646$	−39.6025	−1.55814
$647$	−8.41825	−0.330956	−0.165478	−	0.986214i	$-0.552917\pi$
$647$	−8.41825	−0.330956	−0.165478	+	0.986214i	$0.552917\pi$
$648$	17.2065	0.675934
$649$	0.280240	0.0110004
$650$	−13.8438	−0.542998
$651$	0	0
$652$	42.8865	1.67956
$653$	−23.3965	−0.915575	−0.457787	−	0.889062i	$-0.651358\pi$
$653$	−23.3965	−0.915575	−0.457787	+	0.889062i	$0.651358\pi$
$654$	−26.5803	−1.03937
$655$	9.44254	0.368951
$656$	11.4172	0.445766
$657$	2.96464	0.115662
$658$	0	0
$659$	−7.40377	−0.288410	−0.144205	−	0.989548i	$-0.546062\pi$
$659$	−7.40377	−0.288410	−0.144205	+	0.989548i	$0.546062\pi$
$660$	5.19731	0.202305
$661$	4.29764	0.167159	0.0835795	−	0.996501i	$-0.473365\pi$
$661$	4.29764	0.167159	0.0835795	+	0.996501i	$0.473365\pi$
$662$	7.24086	0.281424
$663$	−52.9828	−2.05768
$664$	−2.42838	−0.0942396
$665$	0	0
$666$	11.6060	0.449723
$667$	83.8021	3.24483
$668$	−27.3105	−1.05668
$669$	−29.1285	−1.12617
$670$	34.1118	1.31785
$671$	6.85909	0.264792
$672$	0	0
$673$	−12.7730	−0.492364	−0.246182	−	0.969224i	$-0.579176\pi$
$673$	−12.7730	−0.492364	−0.246182	+	0.969224i	$0.579176\pi$
$674$	−44.2788	−1.70555
$675$	−4.63310	−0.178328
$676$	75.2599	2.89461
$677$	−16.9257	−0.650509	−0.325254	−	0.945627i	$-0.605450\pi$
$677$	−16.9257	−0.650509	−0.325254	+	0.945627i	$0.605450\pi$
$678$	71.8858	2.76076
$679$	0	0
$680$	7.40548	0.283987
$681$	−6.80183	−0.260647
$682$	13.6991	0.524566
$683$	−9.17559	−0.351094	−0.175547	−	0.984471i	$-0.556169\pi$
$683$	−9.17559	−0.351094	−0.175547	+	0.984471i	$0.556169\pi$
$684$	−6.05351	−0.231462
$685$	6.37191	0.243458
$686$	0	0
$687$	−1.79783	−0.0685916
$688$	−6.29787	−0.240104
$689$	−9.39574	−0.357949
$690$	34.6795	1.32023
$691$	17.4936	0.665489	0.332745	−	0.943017i	$-0.392025\pi$
$691$	17.4936	0.665489	0.332745	+	0.943017i	$0.392025\pi$
$692$	−67.5205	−2.56675
$693$	0	0
$694$	34.6599	1.31567
$695$	18.4605	0.700247
$696$	31.0931	1.17858
$697$	26.8487	1.01697
$698$	24.2145	0.916532
$699$	30.4882	1.15317
$700$	0	0
$701$	−23.3058	−0.880247	−0.440123	−	0.897937i	$-0.645065\pi$
$701$	−23.3058	−0.880247	−0.440123	+	0.897937i	$0.645065\pi$
$702$	64.1396	2.42079
$703$	40.5060	1.52771
$704$	−12.4981	−0.471039
$705$	−4.37039	−0.164598
$706$	79.3096	2.98486
$707$	0	0
$708$	1.45650	0.0547385
$709$	−14.4476	−0.542591	−0.271296	−	0.962496i	$-0.587452\pi$
$709$	−14.4476	−0.542591	−0.271296	+	0.962496i	$0.587452\pi$
$710$	−19.3932	−0.727812
$711$	−2.44973	−0.0918721
$712$	13.4848	0.505363
$713$	53.0323	1.98608
$714$	0	0
$715$	6.34275	0.237205
$716$	68.2954	2.55232
$717$	34.8073	1.29990
$718$	33.0180	1.23222
$719$	21.2074	0.790902	0.395451	−	0.918487i	$-0.370588\pi$
$719$	21.2074	0.790902	0.395451	+	0.918487i	$0.370588\pi$
$720$	−1.01290	−0.0377484
$721$	0	0
$722$	5.05386	0.188085
$723$	−24.1020	−0.896363
$724$	−2.28073	−0.0847628
$725$	−9.91812	−0.368350
$726$	−4.10437	−0.152328
$727$	27.7995	1.03103	0.515513	−	0.856882i	$-0.327601\pi$
$727$	27.7995	1.03103	0.515513	+	0.856882i	$0.327601\pi$
$728$	0	0
$729$	20.6030	0.763075
$730$	−12.0672	−0.446628
$731$	−14.8101	−0.547773
$732$	35.6488	1.31762
$733$	−7.37206	−0.272293	−0.136147	−	0.990689i	$-0.543472\pi$
$733$	−7.37206	−0.272293	−0.136147	+	0.990689i	$0.543472\pi$
$734$	41.2201	1.52146
$735$	0	0
$736$	−63.0080	−2.32251
$737$	−15.6288	−0.575696
$738$	7.07384	0.260392
$739$	−46.4766	−1.70967	−0.854835	−	0.518899i	$-0.826342\pi$
$739$	−46.4766	−1.70967	−0.854835	+	0.518899i	$0.826342\pi$
$740$	−27.4076	−1.00752
$741$	−48.7196	−1.78976
$742$	0	0
$743$	−9.77466	−0.358597	−0.179299	−	0.983795i	$-0.557383\pi$
$743$	−9.77466	−0.358597	−0.179299	+	0.983795i	$0.557383\pi$
$744$	19.6766	0.721378
$745$	3.27701	0.120060
$746$	66.4246	2.43198
$747$	0.781078	0.0285782
$748$	−12.2771	−0.448896
$749$	0	0
$750$	−4.10437	−0.149871
$751$	15.0625	0.549637	0.274819	−	0.961496i	$-0.411382\pi$
$751$	15.0625	0.549637	0.274819	+	0.961496i	$0.411382\pi$
$752$	4.39009	0.160090
$753$	9.43912	0.343981
$754$	137.304	5.00033
$755$	−5.25573	−0.191275
$756$	0	0
$757$	20.8790	0.758861	0.379430	−	0.925220i	$-0.376120\pi$
$757$	20.8790	0.758861	0.379430	+	0.925220i	$0.376120\pi$
$758$	−69.8176	−2.53589
$759$	−15.8890	−0.576732
$760$	6.80960	0.247010
$761$	31.1101	1.12774	0.563870	−	0.825864i	$-0.309312\pi$
$761$	31.1101	1.12774	0.563870	+	0.825864i	$0.309312\pi$
$762$	−1.32127	−0.0478645
$763$	0	0
$764$	18.8903	0.683427
$765$	−2.38194	−0.0861191
$766$	24.7017	0.892508
$767$	1.77749	0.0641816
$768$	−3.74283	−0.135058
$769$	−16.6936	−0.601988	−0.300994	−	0.953626i	$-0.597318\pi$
$769$	−16.6936	−0.601988	−0.300994	+	0.953626i	$0.597318\pi$
$770$	0	0
$771$	−47.2067	−1.70011
$772$	3.42928	0.123423
$773$	−46.1780	−1.66091	−0.830453	−	0.557088i	$-0.811919\pi$
$773$	−46.1780	−1.66091	−0.830453	+	0.557088i	$0.811919\pi$
$774$	−3.90203	−0.140255
$775$	−6.27647	−0.225457
$776$	5.73014	0.205700
$777$	0	0
$778$	67.5610	2.42218
$779$	24.6884	0.884552
$780$	32.9652	1.18034
$781$	8.88528	0.317940
$782$	−81.9202	−2.92946
$783$	45.9517	1.64218
$784$	0	0
$785$	7.86246	0.280623
$786$	−38.7557	−1.38237
$787$	34.7028	1.23702	0.618511	−	0.785776i	$-0.287736\pi$
$787$	34.7028	1.23702	0.618511	+	0.785776i	$0.287736\pi$
$788$	−8.61130	−0.306765
$789$	−27.6431	−0.984119
$790$	9.97135	0.354765
$791$	0	0
$792$	−0.893937	−0.0317647
$793$	43.5055	1.54492
$794$	5.41859	0.192299
$795$	−2.78563	−0.0987960
$796$	24.1668	0.856568
$797$	−27.4398	−0.971967	−0.485983	−	0.873968i	$-0.661538\pi$
$797$	−27.4398	−0.971967	−0.485983	+	0.873968i	$0.661538\pi$
$798$	0	0
$799$	10.3238	0.365229
$800$	7.45710	0.263648
$801$	−4.33732	−0.153252
$802$	0.428425	0.0151282
$803$	5.52879	0.195107
$804$	−81.2279	−2.86469
$805$	0	0
$806$	86.8900	3.06057
$807$	−12.2526	−0.431310
$808$	−18.6115	−0.654750
$809$	12.6833	0.445921	0.222960	−	0.974828i	$-0.428428\pi$
$809$	12.6833	0.445921	0.222960	+	0.974828i	$0.428428\pi$
$810$	22.5271	0.791520
$811$	−28.3414	−0.995200	−0.497600	−	0.867407i	$-0.665785\pi$
$811$	−28.3414	−0.995200	−0.497600	+	0.867407i	$0.665785\pi$
$812$	0	0
$813$	31.5817	1.10762
$814$	21.6441	0.758626
$815$	15.5171	0.543542
$816$	15.7790	0.552377
$817$	−13.6184	−0.476449
$818$	−11.4712	−0.401082
$819$	0	0
$820$	−16.7049	−0.583361
$821$	43.4373	1.51597	0.757986	−	0.652271i	$-0.226183\pi$
$821$	43.4373	1.51597	0.757986	+	0.652271i	$0.226183\pi$
$822$	−26.1527	−0.912181
$823$	44.4238	1.54852	0.774259	−	0.632869i	$-0.218123\pi$
$823$	44.4238	1.54852	0.774259	+	0.632869i	$0.218123\pi$
$824$	−30.5402	−1.06392
$825$	1.88048	0.0654700
$826$	0	0
$827$	10.0387	0.349081	0.174541	−	0.984650i	$-0.444156\pi$
$827$	10.0387	0.349081	0.174541	+	0.984650i	$0.444156\pi$
$828$	−12.5221	−0.435172
$829$	−44.0115	−1.52858	−0.764291	−	0.644871i	$-0.776911\pi$
$829$	−44.0115	−1.52858	−0.764291	+	0.644871i	$0.776911\pi$
$830$	−3.17929	−0.110355
$831$	32.4728	1.12647
$832$	−79.2721	−2.74827
$833$	0	0
$834$	−75.7689	−2.62366
$835$	−9.88147	−0.341962
$836$	−11.2893	−0.390447
$837$	29.0795	1.00513
$838$	31.2639	1.07999
$839$	−7.01935	−0.242335	−0.121167	−	0.992632i	$-0.538664\pi$
$839$	−7.01935	−0.242335	−0.121167	+	0.992632i	$0.538664\pi$
$840$	0	0
$841$	69.3691	2.39204
$842$	−61.6337	−2.12404
$843$	6.13882	0.211432
$844$	1.19135	0.0410081
$845$	27.2304	0.936755
$846$	2.72000	0.0935157
$847$	0	0
$848$	2.79819	0.0960901
$849$	25.7474	0.883647
$850$	9.69540	0.332549
$851$	83.7892	2.87226
$852$	46.1795	1.58208
$853$	−27.5019	−0.941646	−0.470823	−	0.882228i	$-0.656043\pi$
$853$	−27.5019	−0.941646	−0.470823	+	0.882228i	$0.656043\pi$
$854$	0	0
$855$	−2.19028	−0.0749058
$856$	−3.95272	−0.135101
$857$	−11.0998	−0.379162	−0.189581	−	0.981865i	$-0.560713\pi$
$857$	−11.0998	−0.379162	−0.189581	+	0.981865i	$0.560713\pi$
$858$	−26.0330	−0.888752
$859$	−50.5883	−1.72605	−0.863025	−	0.505161i	$-0.831433\pi$
$859$	−50.5883	−1.72605	−0.863025	+	0.505161i	$0.831433\pi$
$860$	9.21467	0.314218
$861$	0	0
$862$	−29.0708	−0.990156
$863$	28.5355	0.971358	0.485679	−	0.874137i	$-0.338572\pi$
$863$	28.5355	0.971358	0.485679	+	0.874137i	$0.338572\pi$
$864$	−34.5495	−1.17540
$865$	−24.4302	−0.830652
$866$	61.3138	2.08353
$867$	5.13792	0.174493
$868$	0	0
$869$	−4.56853	−0.154977
$870$	40.7077	1.38012
$871$	−99.1298	−3.35888
$872$	−10.7964	−0.365611
$873$	−1.84307	−0.0623786
$874$	−75.3286	−2.54803
$875$	0	0
$876$	28.7348	0.970860
$877$	49.7765	1.68083	0.840417	−	0.541941i	$-0.182310\pi$
$877$	49.7765	1.68083	0.840417	+	0.541941i	$0.182310\pi$
$878$	21.9366	0.740326
$879$	−40.1181	−1.35315
$880$	−1.88896	−0.0636769
$881$	20.5112	0.691040	0.345520	−	0.938411i	$-0.387703\pi$
$881$	20.5112	0.691040	0.345520	+	0.938411i	$0.387703\pi$
$882$	0	0
$883$	−7.30501	−0.245833	−0.122917	−	0.992417i	$-0.539225\pi$
$883$	−7.30501	−0.245833	−0.122917	+	0.992417i	$0.539225\pi$
$884$	−77.8707	−2.61908
$885$	0.526988	0.0177145
$886$	27.4350	0.921698
$887$	18.4385	0.619105	0.309552	−	0.950882i	$-0.399821\pi$
$887$	18.4385	0.619105	0.309552	+	0.950882i	$0.399821\pi$
$888$	31.0883	1.04325
$889$	0	0
$890$	17.6545	0.591781
$891$	−10.3211	−0.345771
$892$	−42.8112	−1.43342
$893$	9.49307	0.317674
$894$	−13.4501	−0.449837
$895$	24.7106	0.825983
$896$	0	0
$897$	−100.780	−3.36493
$898$	−16.2290	−0.541568
$899$	62.2507	2.07618
$900$	1.48201	0.0494003
$901$	6.58024	0.219220
$902$	13.1921	0.439248
$903$	0	0
$904$	29.1985	0.971128
$905$	−0.825212	−0.0274310
$906$	21.5715	0.716664
$907$	−42.2812	−1.40392	−0.701962	−	0.712215i	$-0.747692\pi$
$907$	−42.2812	−1.40392	−0.701962	+	0.712215i	$0.747692\pi$
$908$	−9.99689	−0.331759
$909$	5.98630	0.198553
$910$	0	0
$911$	−9.30528	−0.308298	−0.154149	−	0.988048i	$-0.549264\pi$
$911$	−9.30528	−0.308298	−0.154149	+	0.988048i	$0.549264\pi$
$912$	14.5094	0.480454
$913$	1.45664	0.0482078
$914$	−60.1036	−1.98805
$915$	12.8984	0.426408
$916$	−2.64234	−0.0873053
$917$	0	0
$918$	−44.9197	−1.48257
$919$	−36.2054	−1.19431	−0.597153	−	0.802127i	$-0.703702\pi$
$919$	−36.2054	−1.19431	−0.597153	+	0.802127i	$0.703702\pi$
$920$	14.0861	0.464405
$921$	10.0755	0.332000
$922$	19.7969	0.651975
$923$	56.3571	1.85502
$924$	0	0
$925$	−9.91659	−0.326056
$926$	−23.7650	−0.780965
$927$	9.82311	0.322633
$928$	−73.9604	−2.42787
$929$	16.9112	0.554837	0.277418	−	0.960749i	$-0.410521\pi$
$929$	16.9112	0.554837	0.277418	+	0.960749i	$0.410521\pi$
$930$	25.7610	0.844735
$931$	0	0
$932$	44.8096	1.46779
$933$	−29.5617	−0.967808
$934$	74.4647	2.43656
$935$	−4.44210	−0.145272
$936$	−5.67002	−0.185330
$937$	−47.0269	−1.53630	−0.768150	−	0.640269i	$-0.778823\pi$
$937$	−47.0269	−1.53630	−0.768150	+	0.640269i	$0.778823\pi$
$938$	0	0
$939$	41.1924	1.34426
$940$	−6.42331	−0.209505
$941$	−19.3334	−0.630251	−0.315125	−	0.949050i	$-0.602047\pi$
$941$	−19.3334	−0.630251	−0.315125	+	0.949050i	$0.602047\pi$
$942$	−32.2705	−1.05143
$943$	51.0695	1.66305
$944$	−0.529363	−0.0172293
$945$	0	0
$946$	−7.27693	−0.236593
$947$	−28.3649	−0.921736	−0.460868	−	0.887469i	$-0.652462\pi$
$947$	−28.3649	−0.921736	−0.460868	+	0.887469i	$0.652462\pi$
$948$	−23.7440	−0.771171
$949$	35.0677	1.13835
$950$	8.91526	0.289249
$951$	40.7959	1.32290
$952$	0	0
$953$	−5.76868	−0.186866	−0.0934330	−	0.995626i	$-0.529784\pi$
$953$	−5.76868	−0.186866	−0.0934330	+	0.995626i	$0.529784\pi$
$954$	1.73370	0.0561305
$955$	6.83487	0.221171
$956$	51.1576	1.65455
$957$	−18.6509	−0.602897
$958$	−45.0583	−1.45577
$959$	0	0
$960$	−23.5024	−0.758537
$961$	8.39402	0.270775
$962$	137.283	4.42619
$963$	1.27138	0.0409695
$964$	−35.4236	−1.14092
$965$	1.24078	0.0399421
$966$	0	0
$967$	59.8621	1.92503	0.962517	−	0.271222i	$-0.0874276\pi$
$967$	59.8621	1.92503	0.962517	+	0.271222i	$0.0874276\pi$
$968$	−1.66711	−0.0535830
$969$	34.1204	1.09611
$970$	7.50202	0.240875
$971$	−5.24548	−0.168335	−0.0841677	−	0.996452i	$-0.526823\pi$
$971$	−5.24548	−0.168335	−0.0841677	+	0.996452i	$0.526823\pi$
$972$	−15.2270	−0.488406
$973$	0	0
$974$	23.4047	0.749935
$975$	11.9274	0.381984
$976$	−12.9565	−0.414729
$977$	−12.7614	−0.408274	−0.204137	−	0.978942i	$-0.565439\pi$
$977$	−12.7614	−0.408274	−0.204137	+	0.978942i	$0.565439\pi$
$978$	−63.6882	−2.03652
$979$	−8.08870	−0.258516
$980$	0	0
$981$	3.47260	0.110872
$982$	−68.2218	−2.17705
$983$	−34.9490	−1.11470	−0.557349	−	0.830278i	$-0.688182\pi$
$983$	−34.9490	−1.11470	−0.557349	+	0.830278i	$0.688182\pi$
$984$	18.9483	0.604049
$985$	−3.11573	−0.0992754
$986$	−96.1601	−3.06236
$987$	0	0
$988$	−71.6049	−2.27806
$989$	−28.1706	−0.895774
$990$	−1.17036	−0.0371965
$991$	−12.8766	−0.409037	−0.204519	−	0.978863i	$-0.565563\pi$
$991$	−12.8766	−0.409037	−0.204519	+	0.978863i	$0.565563\pi$
$992$	−46.8042	−1.48604
$993$	−6.23853	−0.197974
$994$	0	0
$995$	8.74399	0.277203
$996$	7.57061	0.239884
$997$	−50.6110	−1.60287	−0.801433	−	0.598085i	$-0.795929\pi$
$997$	−50.6110	−1.60287	−0.801433	+	0.598085i	$0.795929\pi$
$998$	7.81824	0.247482
$999$	45.9446	1.45362

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2695.2.a.u.1.2	✓	10
7.6	odd	2		2695.2.a.v.1.2	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2695.2.a.u.1.2	✓	10	1.1	even	1	trivial
2695.2.a.v.1.2	yes	10	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2695 = 5 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2695.a (trivial)

\(f(q)\)	\(=\)	\(q-2.18262 q^{2} +1.88048 q^{3} +2.76381 q^{4} +1.00000 q^{5} -4.10437 q^{6} -1.66711 q^{8} +0.536219 q^{9} +O(q^{10})\)	\(q-2.18262 q^{2} +1.88048 q^{3} +2.76381 q^{4} +1.00000 q^{5} -4.10437 q^{6} -1.66711 q^{8} +0.536219 q^{9} -2.18262 q^{10} +1.00000 q^{11} +5.19731 q^{12} +6.34275 q^{13} +1.88048 q^{15} -1.88896 q^{16} -4.44210 q^{17} -1.17036 q^{18} -4.08467 q^{19} +2.76381 q^{20} -2.18262 q^{22} -8.44940 q^{23} -3.13498 q^{24} +1.00000 q^{25} -13.8438 q^{26} -4.63310 q^{27} -9.91812 q^{29} -4.10437 q^{30} -6.27647 q^{31} +7.45710 q^{32} +1.88048 q^{33} +9.69540 q^{34} +1.48201 q^{36} -9.91659 q^{37} +8.91526 q^{38} +11.9274 q^{39} -1.66711 q^{40} -6.04416 q^{41} +3.33404 q^{43} +2.76381 q^{44} +0.536219 q^{45} +18.4418 q^{46} -2.32408 q^{47} -3.55216 q^{48} -2.18262 q^{50} -8.35329 q^{51} +17.5302 q^{52} -1.48134 q^{53} +10.1123 q^{54} +1.00000 q^{55} -7.68115 q^{57} +21.6475 q^{58} +0.280240 q^{59} +5.19731 q^{60} +6.85909 q^{61} +13.6991 q^{62} -12.4981 q^{64} +6.34275 q^{65} -4.10437 q^{66} -15.6288 q^{67} -12.2771 q^{68} -15.8890 q^{69} +8.88528 q^{71} -0.893937 q^{72} +5.52879 q^{73} +21.6441 q^{74} +1.88048 q^{75} -11.2893 q^{76} -26.0330 q^{78} -4.56853 q^{79} -1.88896 q^{80} -10.3211 q^{81} +13.1921 q^{82} +1.45664 q^{83} -4.44210 q^{85} -7.27693 q^{86} -18.6509 q^{87} -1.66711 q^{88} -8.08870 q^{89} -1.17036 q^{90} -23.3526 q^{92} -11.8028 q^{93} +5.07256 q^{94} -4.08467 q^{95} +14.0230 q^{96} -3.43717 q^{97} +0.536219 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} - 8 q^{3} + 10 q^{4} + 10 q^{5} - 4 q^{6} - 6 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q - 2 * q^2 - 8 * q^3 + 10 * q^4 + 10 * q^5 - 4 * q^6 - 6 * q^8 + 10 * q^9	\( 10 q - 2 q^{2} - 8 q^{3} + 10 q^{4} + 10 q^{5} - 4 q^{6} - 6 q^{8} + 10 q^{9} - 2 q^{10} + 10 q^{11} - 20 q^{12} - 8 q^{13} - 8 q^{15} + 6 q^{16} - 28 q^{17} - 14 q^{18} + 10 q^{20} - 2 q^{22} - 16 q^{23} + 8 q^{24} + 10 q^{25} - 20 q^{26} - 32 q^{27} - 4 q^{30} - 20 q^{31} - 14 q^{32} - 8 q^{33} + 4 q^{34} + 42 q^{36} - 36 q^{37} - 24 q^{38} + 24 q^{39} - 6 q^{40} - 36 q^{41} - 4 q^{43} + 10 q^{44} + 10 q^{45} - 4 q^{46} - 12 q^{47} - 40 q^{48} - 2 q^{50} + 20 q^{51} - 4 q^{52} - 16 q^{53} + 48 q^{54} + 10 q^{55} + 4 q^{57} + 16 q^{58} - 32 q^{59} - 20 q^{60} + 16 q^{61} + 4 q^{62} - 34 q^{64} - 8 q^{65} - 4 q^{66} - 20 q^{67} - 32 q^{68} - 28 q^{69} + 12 q^{71} - 2 q^{72} - 20 q^{73} + 32 q^{74} - 8 q^{75} - 12 q^{76} + 20 q^{78} + 12 q^{79} + 6 q^{80} + 42 q^{81} + 40 q^{82} - 8 q^{83} - 28 q^{85} - 4 q^{86} - 28 q^{87} - 6 q^{88} - 68 q^{89} - 14 q^{90} + 32 q^{92} - 32 q^{93} - 16 q^{94} + 80 q^{96} - 36 q^{97} + 10 q^{99}+O(q^{100}) \) 10 * q - 2 * q^2 - 8 * q^3 + 10 * q^4 + 10 * q^5 - 4 * q^6 - 6 * q^8 + 10 * q^9 - 2 * q^10 + 10 * q^11 - 20 * q^12 - 8 * q^13 - 8 * q^15 + 6 * q^16 - 28 * q^17 - 14 * q^18 + 10 * q^20 - 2 * q^22 - 16 * q^23 + 8 * q^24 + 10 * q^25 - 20 * q^26 - 32 * q^27 - 4 * q^30 - 20 * q^31 - 14 * q^32 - 8 * q^33 + 4 * q^34 + 42 * q^36 - 36 * q^37 - 24 * q^38 + 24 * q^39 - 6 * q^40 - 36 * q^41 - 4 * q^43 + 10 * q^44 + 10 * q^45 - 4 * q^46 - 12 * q^47 - 40 * q^48 - 2 * q^50 + 20 * q^51 - 4 * q^52 - 16 * q^53 + 48 * q^54 + 10 * q^55 + 4 * q^57 + 16 * q^58 - 32 * q^59 - 20 * q^60 + 16 * q^61 + 4 * q^62 - 34 * q^64 - 8 * q^65 - 4 * q^66 - 20 * q^67 - 32 * q^68 - 28 * q^69 + 12 * q^71 - 2 * q^72 - 20 * q^73 + 32 * q^74 - 8 * q^75 - 12 * q^76 + 20 * q^78 + 12 * q^79 + 6 * q^80 + 42 * q^81 + 40 * q^82 - 8 * q^83 - 28 * q^85 - 4 * q^86 - 28 * q^87 - 6 * q^88 - 68 * q^89 - 14 * q^90 + 32 * q^92 - 32 * q^93 - 16 * q^94 + 80 * q^96 - 36 * q^97 + 10 * q^99

Introduction

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