LMFDB - Embedded newform 2695.2.a.y.1.9

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:	$10$
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} - 3x^{9} - 13x^{8} + 41x^{7} + 51x^{6} - 184x^{5} - 45x^{4} + 297x^{3} - 59x^{2} - 109x + 21 $ x^10 - 3x^9 - 13x^8 + 41x^7 + 51x^6 - 184x^5 - 45x^4 + 297x^3 - 59x^2 - 109*x + 21
Coefficient ring:	$\Z[a_1, a_2, a_3]$
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			1.9
Root			$2.63370$ 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)

$f(q)$	$=$	$q+2.63370 q^{2} +2.48035 q^{3} +4.93639 q^{4} -1.00000 q^{5} +6.53251 q^{6} +7.73356 q^{8} +3.15215 q^{9} +O(q^{10})$	\(q+2.63370 q^{2} +2.48035 q^{3} +4.93639 q^{4} -1.00000 q^{5} +6.53251 q^{6} +7.73356 q^{8} +3.15215 q^{9} -2.63370 q^{10} +1.00000 q^{11} +12.2440 q^{12} -2.05210 q^{13} -2.48035 q^{15} +10.4951 q^{16} +3.17488 q^{17} +8.30181 q^{18} -6.57586 q^{19} -4.93639 q^{20} +2.63370 q^{22} +4.76082 q^{23} +19.1820 q^{24} +1.00000 q^{25} -5.40461 q^{26} +0.377374 q^{27} -7.72026 q^{29} -6.53251 q^{30} +10.2304 q^{31} +12.1739 q^{32} +2.48035 q^{33} +8.36169 q^{34} +15.5602 q^{36} +3.77295 q^{37} -17.3189 q^{38} -5.08992 q^{39} -7.73356 q^{40} -8.85946 q^{41} +2.01269 q^{43} +4.93639 q^{44} -3.15215 q^{45} +12.5386 q^{46} +1.20548 q^{47} +26.0316 q^{48} +2.63370 q^{50} +7.87482 q^{51} -10.1299 q^{52} +5.96845 q^{53} +0.993892 q^{54} -1.00000 q^{55} -16.3105 q^{57} -20.3329 q^{58} -8.97158 q^{59} -12.2440 q^{60} -11.6236 q^{61} +26.9438 q^{62} +11.0722 q^{64} +2.05210 q^{65} +6.53251 q^{66} +8.25535 q^{67} +15.6724 q^{68} +11.8085 q^{69} -2.10238 q^{71} +24.3773 q^{72} -2.40137 q^{73} +9.93682 q^{74} +2.48035 q^{75} -32.4610 q^{76} -13.4053 q^{78} -15.9432 q^{79} -10.4951 q^{80} -8.52042 q^{81} -23.3332 q^{82} +4.70352 q^{83} -3.17488 q^{85} +5.30083 q^{86} -19.1490 q^{87} +7.73356 q^{88} +1.09849 q^{89} -8.30181 q^{90} +23.5012 q^{92} +25.3750 q^{93} +3.17488 q^{94} +6.57586 q^{95} +30.1956 q^{96} -11.7031 q^{97} +3.15215 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 3 q^{2} - 3 q^{3} + 15 q^{4} - 10 q^{5} + 5 q^{6} + 9 q^{8} + 19 q^{9}+O(q^{10}) $ 10 * q + 3 * q^2 - 3 * q^3 + 15 * q^4 - 10 * q^5 + 5 * q^6 + 9 * q^8 + 19 * q^9	$ 10 q + 3 q^{2} - 3 q^{3} + 15 q^{4} - 10 q^{5} + 5 q^{6} + 9 q^{8} + 19 q^{9} - 3 q^{10} + 10 q^{11} - 3 q^{12} - 6 q^{13} + 3 q^{15} + 21 q^{16} - 5 q^{17} + q^{18} + q^{19} - 15 q^{20} + 3 q^{22} + 18 q^{23} + 10 q^{24} + 10 q^{25} + 13 q^{26} - 15 q^{27} + 14 q^{29} - 5 q^{30} + 10 q^{31} + 46 q^{32} - 3 q^{33} - 2 q^{34} + 26 q^{36} + 13 q^{37} + 9 q^{38} + 3 q^{39} - 9 q^{40} - 7 q^{41} + 6 q^{43} + 15 q^{44} - 19 q^{45} + 10 q^{46} + q^{47} - 35 q^{48} + 3 q^{50} + 9 q^{51} - 17 q^{52} + 16 q^{53} + 73 q^{54} - 10 q^{55} + 12 q^{57} - 9 q^{58} + 13 q^{59} + 3 q^{60} + 18 q^{61} + 14 q^{62} + 43 q^{64} + 6 q^{65} + 5 q^{66} + 29 q^{67} + 13 q^{68} + 19 q^{71} - 48 q^{72} - 31 q^{73} - 8 q^{74} - 3 q^{75} - 8 q^{76} + 3 q^{78} - 21 q^{80} + 42 q^{81} + q^{82} - 2 q^{83} + 5 q^{85} + 10 q^{86} - 50 q^{87} + 9 q^{88} + 23 q^{89} - q^{90} + 14 q^{92} + 4 q^{93} - 5 q^{94} - q^{95} + 39 q^{96} - 43 q^{97} + 19 q^{99}+O(q^{100}) $ 10 * q + 3 * q^2 - 3 * q^3 + 15 * q^4 - 10 * q^5 + 5 * q^6 + 9 * q^8 + 19 * q^9 - 3 * q^10 + 10 * q^11 - 3 * q^12 - 6 * q^13 + 3 * q^15 + 21 * q^16 - 5 * q^17 + q^18 + q^19 - 15 * q^20 + 3 * q^22 + 18 * q^23 + 10 * q^24 + 10 * q^25 + 13 * q^26 - 15 * q^27 + 14 * q^29 - 5 * q^30 + 10 * q^31 + 46 * q^32 - 3 * q^33 - 2 * q^34 + 26 * q^36 + 13 * q^37 + 9 * q^38 + 3 * q^39 - 9 * q^40 - 7 * q^41 + 6 * q^43 + 15 * q^44 - 19 * q^45 + 10 * q^46 + q^47 - 35 * q^48 + 3 * q^50 + 9 * q^51 - 17 * q^52 + 16 * q^53 + 73 * q^54 - 10 * q^55 + 12 * q^57 - 9 * q^58 + 13 * q^59 + 3 * q^60 + 18 * q^61 + 14 * q^62 + 43 * q^64 + 6 * q^65 + 5 * q^66 + 29 * q^67 + 13 * q^68 + 19 * q^71 - 48 * q^72 - 31 * q^73 - 8 * q^74 - 3 * q^75 - 8 * q^76 + 3 * q^78 - 21 * q^80 + 42 * q^81 + q^82 - 2 * q^83 + 5 * q^85 + 10 * q^86 - 50 * q^87 + 9 * q^88 + 23 * q^89 - q^90 + 14 * q^92 + 4 * q^93 - 5 * q^94 - q^95 + 39 * q^96 - 43 * 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 $

$2$	2.63370	1.86231	0.931154	−	0.364626i	$-0.118803\pi$
$2$	2.63370	1.86231	0.931154	+	0.364626i	$0.118803\pi$
$3$	2.48035	1.43203	0.716016	−	0.698084i	$-0.245964\pi$
$3$	2.48035	1.43203	0.716016	+	0.698084i	$0.245964\pi$
$4$	4.93639	2.46819
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	6.53251	2.66688
$7$	0	0
$7$	0	0
$8$	7.73356	2.73423
$9$	3.15215	1.05072
$10$	−2.63370	−0.832850
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	12.2440	3.53453
$13$	−2.05210	−0.569149	−0.284574	−	0.958654i	$-0.591852\pi$
$13$	−2.05210	−0.569149	−0.284574	+	0.958654i	$0.591852\pi$
$14$	0	0
$15$	−2.48035	−0.640424
$16$	10.4951	2.62378
$17$	3.17488	0.770021	0.385011	−	0.922912i	$-0.374198\pi$
$17$	3.17488	0.770021	0.385011	+	0.922912i	$0.374198\pi$
$18$	8.30181	1.95676
$19$	−6.57586	−1.50861	−0.754303	−	0.656526i	$-0.772025\pi$
$19$	−6.57586	−1.50861	−0.754303	+	0.656526i	$0.772025\pi$
$20$	−4.93639	−1.10381
$21$	0	0
$22$	2.63370	0.561507
$23$	4.76082	0.992699	0.496349	−	0.868123i	$-0.334674\pi$
$23$	4.76082	0.992699	0.496349	+	0.868123i	$0.334674\pi$
$24$	19.1820	3.91550
$25$	1.00000	0.200000
$26$	−5.40461	−1.05993
$27$	0.377374	0.0726257
$28$	0	0
$29$	−7.72026	−1.43362	−0.716809	−	0.697270i	$-0.754398\pi$
$29$	−7.72026	−1.43362	−0.716809	+	0.697270i	$0.754398\pi$
$30$	−6.53251	−1.19267
$31$	10.2304	1.83743	0.918717	−	0.394917i	$-0.129227\pi$
$31$	10.2304	1.83743	0.918717	+	0.394917i	$0.129227\pi$
$32$	12.1739	2.15206
$33$	2.48035	0.431774
$34$	8.36169	1.43402
$35$	0	0
$36$	15.5602	2.59337
$37$	3.77295	0.620269	0.310134	−	0.950693i	$-0.399626\pi$
$37$	3.77295	0.620269	0.310134	+	0.950693i	$0.399626\pi$
$38$	−17.3189	−2.80949
$39$	−5.08992	−0.815039
$40$	−7.73356	−1.22278
$41$	−8.85946	−1.38362	−0.691808	−	0.722082i	$-0.743185\pi$
$41$	−8.85946	−1.38362	−0.691808	+	0.722082i	$0.743185\pi$
$42$	0	0
$43$	2.01269	0.306933	0.153466	−	0.988154i	$-0.450956\pi$
$43$	2.01269	0.306933	0.153466	+	0.988154i	$0.450956\pi$
$44$	4.93639	0.744188
$45$	−3.15215	−0.469894
$46$	12.5386	1.84871
$47$	1.20548	0.175838	0.0879188	−	0.996128i	$-0.471978\pi$
$47$	1.20548	0.175838	0.0879188	+	0.996128i	$0.471978\pi$
$48$	26.0316	3.75734
$49$	0	0
$50$	2.63370	0.372462
$51$	7.87482	1.10270
$52$	−10.1299	−1.40477
$53$	5.96845	0.819829	0.409915	−	0.912124i	$-0.365558\pi$
$53$	5.96845	0.819829	0.409915	+	0.912124i	$0.365558\pi$
$54$	0.993892	0.135252
$55$	−1.00000	−0.134840
$56$	0	0
$57$	−16.3105	−2.16037
$58$	−20.3329	−2.66984
$59$	−8.97158	−1.16800	−0.584000	−	0.811753i	$-0.698513\pi$
$59$	−8.97158	−1.16800	−0.584000	+	0.811753i	$0.698513\pi$
$60$	−12.2440	−1.58069
$61$	−11.6236	−1.48825	−0.744127	−	0.668038i	$-0.767134\pi$
$61$	−11.6236	−1.48825	−0.744127	+	0.668038i	$0.767134\pi$
$62$	26.9438	3.42187
$63$	0	0
$64$	11.0722	1.38403
$65$	2.05210	0.254531
$66$	6.53251	0.804096
$67$	8.25535	1.00855	0.504276	−	0.863543i	$-0.331760\pi$
$67$	8.25535	1.00855	0.504276	+	0.863543i	$0.331760\pi$
$68$	15.6724	1.90056
$69$	11.8085	1.42158
$70$	0	0
$71$	−2.10238	−0.249507	−0.124753	−	0.992188i	$-0.539814\pi$
$71$	−2.10238	−0.249507	−0.124753	+	0.992188i	$0.539814\pi$
$72$	24.3773	2.87289
$73$	−2.40137	−0.281059	−0.140530	−	0.990076i	$-0.544881\pi$
$73$	−2.40137	−0.281059	−0.140530	+	0.990076i	$0.544881\pi$
$74$	9.93682	1.15513
$75$	2.48035	0.286406
$76$	−32.4610	−3.72353
$77$	0	0
$78$	−13.4053	−1.51785
$79$	−15.9432	−1.79375	−0.896873	−	0.442288i	$-0.854167\pi$
$79$	−15.9432	−1.79375	−0.896873	+	0.442288i	$0.854167\pi$
$80$	−10.4951	−1.17339
$81$	−8.52042	−0.946713
$82$	−23.3332	−2.57672
$83$	4.70352	0.516278	0.258139	−	0.966108i	$-0.416891\pi$
$83$	4.70352	0.516278	0.258139	+	0.966108i	$0.416891\pi$
$84$	0	0
$85$	−3.17488	−0.344364
$86$	5.30083	0.571604
$87$	−19.1490	−2.05299
$88$	7.73356	0.824401
$89$	1.09849	0.116440	0.0582199	−	0.998304i	$-0.481458\pi$
$89$	1.09849	0.116440	0.0582199	+	0.998304i	$0.481458\pi$
$90$	−8.30181	−0.875088
$91$	0	0
$92$	23.5012	2.45017
$93$	25.3750	2.63126
$94$	3.17488	0.327464
$95$	6.57586	0.674669
$96$	30.1956	3.08182
$97$	−11.7031	−1.18827	−0.594137	−	0.804364i	$-0.702506\pi$
$97$	−11.7031	−1.18827	−0.594137	+	0.804364i	$0.702506\pi$
$98$	0	0
$99$	3.15215	0.316803
$100$	4.93639	0.493639
$101$	−6.61933	−0.658648	−0.329324	−	0.944217i	$-0.606821\pi$
$101$	−6.61933	−0.658648	−0.329324	+	0.944217i	$0.606821\pi$
$102$	20.7399	2.05356
$103$	1.85751	0.183026	0.0915128	−	0.995804i	$-0.470830\pi$
$103$	1.85751	0.183026	0.0915128	+	0.995804i	$0.470830\pi$
$104$	−15.8700	−1.55618
$105$	0	0
$106$	15.7191	1.52677
$107$	1.99151	0.192526	0.0962632	−	0.995356i	$-0.469311\pi$
$107$	1.99151	0.192526	0.0962632	+	0.995356i	$0.469311\pi$
$108$	1.86287	0.179254
$109$	−5.14954	−0.493236	−0.246618	−	0.969113i	$-0.579319\pi$
$109$	−5.14954	−0.493236	−0.246618	+	0.969113i	$0.579319\pi$
$110$	−2.63370	−0.251114
$111$	9.35823	0.888244
$112$	0	0
$113$	−11.9715	−1.12618	−0.563091	−	0.826395i	$-0.690388\pi$
$113$	−11.9715	−1.12618	−0.563091	+	0.826395i	$0.690388\pi$
$114$	−42.9569	−4.02328
$115$	−4.76082	−0.443948
$116$	−38.1102	−3.53844
$117$	−6.46850	−0.598013
$118$	−23.6285	−2.17518
$119$	0	0
$120$	−19.1820	−1.75107
$121$	1.00000	0.0909091
$122$	−30.6132	−2.77159
$123$	−21.9746	−1.98138
$124$	50.5012	4.53514
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	6.35086	0.563548	0.281774	−	0.959481i	$-0.409077\pi$
$127$	6.35086	0.563548	0.281774	+	0.959481i	$0.409077\pi$
$128$	4.81305	0.425417
$129$	4.99219	0.439538
$130$	5.40461	0.474015
$131$	−0.0109499	−0.000956694 0	−0.000478347	−	1.00000i	$-0.500152\pi$
$131$	−0.0109499	−0.000956694 0	−0.000478347		1.00000i	$0.500152\pi$
$132$	12.2440	1.06570
$133$	0	0
$134$	21.7421	1.87823
$135$	−0.377374	−0.0324792
$136$	24.5531	2.10541
$137$	20.9516	1.79002	0.895009	−	0.446049i	$-0.147169\pi$
$137$	20.9516	1.79002	0.895009	+	0.446049i	$0.147169\pi$
$138$	31.1001	2.64741
$139$	16.3556	1.38727	0.693633	−	0.720328i	$-0.256009\pi$
$139$	16.3556	1.38727	0.693633	+	0.720328i	$0.256009\pi$
$140$	0	0
$141$	2.99002	0.251805
$142$	−5.53704	−0.464658
$143$	−2.05210	−0.171605
$144$	33.0822	2.75685
$145$	7.72026	0.641133
$146$	−6.32450	−0.523419
$147$	0	0
$148$	18.6247	1.53094
$149$	8.28332	0.678596	0.339298	−	0.940679i	$-0.389811\pi$
$149$	8.28332	0.678596	0.339298	+	0.940679i	$0.389811\pi$
$150$	6.53251	0.533377
$151$	−16.5887	−1.34997	−0.674984	−	0.737832i	$-0.735850\pi$
$151$	−16.5887	−1.34997	−0.674984	+	0.737832i	$0.735850\pi$
$152$	−50.8549	−4.12487
$153$	10.0077	0.809073
$154$	0	0
$155$	−10.2304	−0.821725
$156$	−25.1258	−2.01167
$157$	7.71033	0.615352	0.307676	−	0.951491i	$-0.400449\pi$
$157$	7.71033	0.615352	0.307676	+	0.951491i	$0.400449\pi$
$158$	−41.9895	−3.34051
$159$	14.8038	1.17402
$160$	−12.1739	−0.962432
$161$	0	0
$162$	−22.4402	−1.76307
$163$	−9.88007	−0.773867	−0.386933	−	0.922108i	$-0.626466\pi$
$163$	−9.88007	−0.773867	−0.386933	+	0.922108i	$0.626466\pi$
$164$	−43.7337	−3.41503
$165$	−2.48035	−0.193095
$166$	12.3877	0.961469
$167$	17.9683	1.39043	0.695214	−	0.718803i	$-0.255310\pi$
$167$	17.9683	1.39043	0.695214	+	0.718803i	$0.255310\pi$
$168$	0	0
$169$	−8.78891	−0.676070
$170$	−8.36169	−0.641312
$171$	−20.7281	−1.58512
$172$	9.93543	0.757569
$173$	−4.60627	−0.350209	−0.175104	−	0.984550i	$-0.556026\pi$
$173$	−4.60627	−0.350209	−0.175104	+	0.984550i	$0.556026\pi$
$174$	−50.4327	−3.82329
$175$	0	0
$176$	10.4951	0.791100
$177$	−22.2527	−1.67261
$178$	2.89310	0.216847
$179$	6.70157	0.500899	0.250449	−	0.968130i	$-0.419422\pi$
$179$	6.70157	0.500899	0.250449	+	0.968130i	$0.419422\pi$
$180$	−15.5602	−1.15979
$181$	19.5420	1.45255	0.726273	−	0.687407i	$-0.241251\pi$
$181$	19.5420	1.45255	0.726273	+	0.687407i	$0.241251\pi$
$182$	0	0
$183$	−28.8307	−2.13123
$184$	36.8181	2.71426
$185$	−3.77295	−0.277393
$186$	66.8301	4.90022
$187$	3.17488	0.232170
$188$	5.95072	0.434001
$189$	0	0
$190$	17.3189	1.25644
$191$	−12.4900	−0.903744	−0.451872	−	0.892083i	$-0.649244\pi$
$191$	−12.4900	−0.903744	−0.451872	+	0.892083i	$0.649244\pi$
$192$	27.4630	1.98197
$193$	14.0470	1.01113	0.505563	−	0.862790i	$-0.331285\pi$
$193$	14.0470	1.01113	0.505563	+	0.862790i	$0.331285\pi$
$194$	−30.8226	−2.21293
$195$	5.08992	0.364497
$196$	0	0
$197$	−0.816272	−0.0581570	−0.0290785	−	0.999577i	$-0.509257\pi$
$197$	−0.816272	−0.0581570	−0.0290785	+	0.999577i	$0.509257\pi$
$198$	8.30181	0.589984
$199$	0.975611	0.0691592	0.0345796	−	0.999402i	$-0.488991\pi$
$199$	0.975611	0.0691592	0.0345796	+	0.999402i	$0.488991\pi$
$200$	7.73356	0.546846
$201$	20.4762	1.44428
$202$	−17.4333	−1.22661
$203$	0	0
$204$	38.8731	2.72166
$205$	8.85946	0.618771
$206$	4.89212	0.340850
$207$	15.0068	1.04304
$208$	−21.5370	−1.49332
$209$	−6.57586	−0.454862
$210$	0	0
$211$	17.9114	1.23307	0.616535	−	0.787328i	$-0.288536\pi$
$211$	17.9114	1.23307	0.616535	+	0.787328i	$0.288536\pi$
$212$	29.4626	2.02350
$213$	−5.21464	−0.357301
$214$	5.24504	0.358544
$215$	−2.01269	−0.137265
$216$	2.91845	0.198575
$217$	0	0
$218$	−13.5624	−0.918558
$219$	−5.95625	−0.402486
$220$	−4.93639	−0.332811
$221$	−6.51516	−0.438257
$222$	24.6468	1.65418
$223$	3.14967	0.210917	0.105459	−	0.994424i	$-0.466369\pi$
$223$	3.14967	0.210917	0.105459	+	0.994424i	$0.466369\pi$
$224$	0	0
$225$	3.15215	0.210143
$226$	−31.5293	−2.09730
$227$	4.64536	0.308323	0.154162	−	0.988046i	$-0.450732\pi$
$227$	4.64536	0.308323	0.154162	+	0.988046i	$0.450732\pi$
$228$	−80.5147	−5.33222
$229$	8.33888	0.551049	0.275524	−	0.961294i	$-0.411149\pi$
$229$	8.33888	0.551049	0.275524	+	0.961294i	$0.411149\pi$
$230$	−12.5386	−0.826769
$231$	0	0
$232$	−59.7052	−3.91984
$233$	28.2591	1.85132	0.925658	−	0.378360i	$-0.123512\pi$
$233$	28.2591	1.85132	0.925658	+	0.378360i	$0.123512\pi$
$234$	−17.0361	−1.11369
$235$	−1.20548	−0.0786370
$236$	−44.2872	−2.88285
$237$	−39.5447	−2.56870
$238$	0	0
$239$	−10.0199	−0.648134	−0.324067	−	0.946034i	$-0.605050\pi$
$239$	−10.0199	−0.648134	−0.324067	+	0.946034i	$0.605050\pi$
$240$	−26.0316	−1.68033
$241$	7.24968	0.466993	0.233496	−	0.972358i	$-0.424983\pi$
$241$	7.24968	0.466993	0.233496	+	0.972358i	$0.424983\pi$
$242$	2.63370	0.169301
$243$	−22.2658	−1.42835
$244$	−57.3788	−3.67330
$245$	0	0
$246$	−57.8745	−3.68994
$247$	13.4943	0.858621
$248$	79.1174	5.02396
$249$	11.6664	0.739327
$250$	−2.63370	−0.166570
$251$	20.1037	1.26893	0.634467	−	0.772950i	$-0.281220\pi$
$251$	20.1037	1.26893	0.634467	+	0.772950i	$0.281220\pi$
$252$	0	0
$253$	4.76082	0.299310
$254$	16.7263	1.04950
$255$	−7.87482	−0.493140
$256$	−9.46827	−0.591767
$257$	−18.7809	−1.17152	−0.585760	−	0.810484i	$-0.699204\pi$
$257$	−18.7809	−1.17152	−0.585760	+	0.810484i	$0.699204\pi$
$258$	13.1479	0.818555
$259$	0	0
$260$	10.1299	0.628232
$261$	−24.3354	−1.50632
$262$	−0.0288387	−0.00178166
$263$	−20.2106	−1.24624	−0.623119	−	0.782127i	$-0.714135\pi$
$263$	−20.2106	−1.24624	−0.623119	+	0.782127i	$0.714135\pi$
$264$	19.1820	1.18057
$265$	−5.96845	−0.366639
$266$	0	0
$267$	2.72464	0.166746
$268$	40.7516	2.48930
$269$	−0.138539	−0.00844686	−0.00422343	−	0.999991i	$-0.501344\pi$
$269$	−0.138539	−0.00844686	−0.00422343	+	0.999991i	$0.501344\pi$
$270$	−0.993892	−0.0604863
$271$	6.33211	0.384648	0.192324	−	0.981331i	$-0.438398\pi$
$271$	6.33211	0.384648	0.192324	+	0.981331i	$0.438398\pi$
$272$	33.3208	2.02037
$273$	0	0
$274$	55.1803	3.33356
$275$	1.00000	0.0603023
$276$	58.2913	3.50872
$277$	−32.2666	−1.93872	−0.969358	−	0.245654i	$-0.920997\pi$
$277$	−32.2666	−1.93872	−0.969358	+	0.245654i	$0.920997\pi$
$278$	43.0758	2.58352
$279$	32.2477	1.93062
$280$	0	0
$281$	10.2999	0.614439	0.307220	−	0.951639i	$-0.400601\pi$
$281$	10.2999	0.614439	0.307220	+	0.951639i	$0.400601\pi$
$282$	7.87482	0.468939
$283$	24.6789	1.46701	0.733503	−	0.679686i	$-0.237884\pi$
$283$	24.6789	1.46701	0.733503	+	0.679686i	$0.237884\pi$
$284$	−10.3782	−0.615830
$285$	16.3105	0.966148
$286$	−5.40461	−0.319581
$287$	0	0
$288$	38.3739	2.26121
$289$	−6.92014	−0.407067
$290$	20.3329	1.19399
$291$	−29.0279	−1.70165
$292$	−11.8541	−0.693708
$293$	−1.71789	−0.100360	−0.0501800	−	0.998740i	$-0.515980\pi$
$293$	−1.71789	−0.100360	−0.0501800	+	0.998740i	$0.515980\pi$
$294$	0	0
$295$	8.97158	0.522346
$296$	29.1783	1.69596
$297$	0.377374	0.0218975
$298$	21.8158	1.26375
$299$	−9.76965	−0.564993
$300$	12.2440	0.706906
$301$	0	0
$302$	−43.6897	−2.51406
$303$	−16.4183	−0.943205
$304$	−69.0145	−3.95825
$305$	11.6236	0.665568
$306$	26.3573	1.50674
$307$	−8.43303	−0.481299	−0.240649	−	0.970612i	$-0.577360\pi$
$307$	−8.43303	−0.481299	−0.240649	+	0.970612i	$0.577360\pi$
$308$	0	0
$309$	4.60727	0.262099
$310$	−26.9438	−1.53031
$311$	14.8001	0.839236	0.419618	−	0.907701i	$-0.362164\pi$
$311$	14.8001	0.839236	0.419618	+	0.907701i	$0.362164\pi$
$312$	−39.3632	−2.22850
$313$	16.2891	0.920716	0.460358	−	0.887733i	$-0.347721\pi$
$313$	16.2891	0.920716	0.460358	+	0.887733i	$0.347721\pi$
$314$	20.3067	1.14597
$315$	0	0
$316$	−78.7016	−4.42731
$317$	−27.9839	−1.57173	−0.785866	−	0.618396i	$-0.787783\pi$
$317$	−27.9839	−1.57173	−0.785866	+	0.618396i	$0.787783\pi$
$318$	38.9889	2.18639
$319$	−7.72026	−0.432252
$320$	−11.0722	−0.618955
$321$	4.93964	0.275704
$322$	0	0
$323$	−20.8776	−1.16166
$324$	−42.0601	−2.33667
$325$	−2.05210	−0.113830
$326$	−26.0212	−1.44118
$327$	−12.7727	−0.706330
$328$	−68.5152	−3.78312
$329$	0	0
$330$	−6.53251	−0.359603
$331$	29.2875	1.60979	0.804893	−	0.593421i	$-0.202223\pi$
$331$	29.2875	1.60979	0.804893	+	0.593421i	$0.202223\pi$
$332$	23.2184	1.27427
$333$	11.8929	0.651726
$334$	47.3231	2.58940
$335$	−8.25535	−0.451038
$336$	0	0
$337$	11.1900	0.609560	0.304780	−	0.952423i	$-0.401417\pi$
$337$	11.1900	0.609560	0.304780	+	0.952423i	$0.401417\pi$
$338$	−23.1474	−1.25905
$339$	−29.6935	−1.61273
$340$	−15.6724	−0.849957
$341$	10.2304	0.554007
$342$	−54.5916	−2.95197
$343$	0	0
$344$	15.5653	0.839224
$345$	−11.8085	−0.635748
$346$	−12.1316	−0.652196
$347$	13.6506	0.732805	0.366402	−	0.930457i	$-0.380589\pi$
$347$	13.6506	0.732805	0.366402	+	0.930457i	$0.380589\pi$
$348$	−94.5267	−5.06716
$349$	0.802668	0.0429658	0.0214829	−	0.999769i	$-0.493161\pi$
$349$	0.802668	0.0429658	0.0214829	+	0.999769i	$0.493161\pi$
$350$	0	0
$351$	−0.774408	−0.0413349
$352$	12.1739	0.648872
$353$	0.593298	0.0315780	0.0157890	−	0.999875i	$-0.494974\pi$
$353$	0.593298	0.0315780	0.0157890	+	0.999875i	$0.494974\pi$
$354$	−58.6069	−3.11492
$355$	2.10238	0.111583
$356$	5.42258	0.287396
$357$	0	0
$358$	17.6499	0.932828
$359$	−16.3532	−0.863088	−0.431544	−	0.902092i	$-0.642031\pi$
$359$	−16.3532	−0.863088	−0.431544	+	0.902092i	$0.642031\pi$
$360$	−24.3773	−1.28480
$361$	24.2420	1.27589
$362$	51.4678	2.70509
$363$	2.48035	0.130185
$364$	0	0
$365$	2.40137	0.125694
$366$	−75.9315	−3.96900
$367$	9.61994	0.502157	0.251078	−	0.967967i	$-0.419215\pi$
$367$	9.61994	0.502157	0.251078	+	0.967967i	$0.419215\pi$
$368$	49.9654	2.60462
$369$	−27.9263	−1.45379
$370$	−9.93682	−0.516590
$371$	0	0
$372$	125.261	6.49447
$373$	−23.2213	−1.20235	−0.601177	−	0.799116i	$-0.705301\pi$
$373$	−23.2213	−1.20235	−0.601177	+	0.799116i	$0.705301\pi$
$374$	8.36169	0.432373
$375$	−2.48035	−0.128085
$376$	9.32267	0.480780
$377$	15.8427	0.815941
$378$	0	0
$379$	−20.6496	−1.06070	−0.530351	−	0.847778i	$-0.677940\pi$
$379$	−20.6496	−1.06070	−0.530351	+	0.847778i	$0.677940\pi$
$380$	32.4610	1.66521
$381$	15.7524	0.807018
$382$	−32.8949	−1.68305
$383$	10.5377	0.538452	0.269226	−	0.963077i	$-0.413232\pi$
$383$	10.5377	0.538452	0.269226	+	0.963077i	$0.413232\pi$
$384$	11.9381	0.609211
$385$	0	0
$386$	36.9957	1.88303
$387$	6.34430	0.322499
$388$	−57.7712	−2.93289
$389$	−20.5132	−1.04006	−0.520030	−	0.854148i	$-0.674079\pi$
$389$	−20.5132	−1.04006	−0.520030	+	0.854148i	$0.674079\pi$
$390$	13.4053	0.678805
$391$	15.1150	0.764399
$392$	0	0
$393$	−0.0271595	−0.00137002
$394$	−2.14982	−0.108306
$395$	15.9432	0.802188
$396$	15.5602	0.781930
$397$	−23.9809	−1.20357	−0.601783	−	0.798659i	$-0.705543\pi$
$397$	−23.9809	−1.20357	−0.601783	+	0.798659i	$0.705543\pi$
$398$	2.56947	0.128796
$399$	0	0
$400$	10.4951	0.524756
$401$	9.78266	0.488523	0.244261	−	0.969709i	$-0.421454\pi$
$401$	9.78266	0.488523	0.244261	+	0.969709i	$0.421454\pi$
$402$	53.9281	2.68969
$403$	−20.9937	−1.04577
$404$	−32.6756	−1.62567
$405$	8.52042	0.423383
$406$	0	0
$407$	3.77295	0.187018
$408$	60.9004	3.01502
$409$	25.6426	1.26795	0.633973	−	0.773355i	$-0.281423\pi$
$409$	25.6426	1.26795	0.633973	+	0.773355i	$0.281423\pi$
$410$	23.3332	1.15234
$411$	51.9674	2.56336
$412$	9.16937	0.451743
$413$	0	0
$414$	39.5234	1.94247
$415$	−4.70352	−0.230887
$416$	−24.9820	−1.22484
$417$	40.5677	1.98661
$418$	−17.3189	−0.847093
$419$	−22.9516	−1.12126	−0.560630	−	0.828066i	$-0.689441\pi$
$419$	−22.9516	−1.12126	−0.560630	+	0.828066i	$0.689441\pi$
$420$	0	0
$421$	−14.5447	−0.708868	−0.354434	−	0.935081i	$-0.615326\pi$
$421$	−14.5447	−0.708868	−0.354434	+	0.935081i	$0.615326\pi$
$422$	47.1732	2.29636
$423$	3.79985	0.184755
$424$	46.1574	2.24160
$425$	3.17488	0.154004
$426$	−13.7338	−0.665405
$427$	0	0
$428$	9.83086	0.475192
$429$	−5.08992	−0.245744
$430$	−5.30083	−0.255629
$431$	−22.8952	−1.10282	−0.551411	−	0.834234i	$-0.685911\pi$
$431$	−22.8952	−1.10282	−0.551411	+	0.834234i	$0.685911\pi$
$432$	3.96059	0.190554
$433$	12.7694	0.613657	0.306829	−	0.951765i	$-0.400732\pi$
$433$	12.7694	0.613657	0.306829	+	0.951765i	$0.400732\pi$
$434$	0	0
$435$	19.1490	0.918123
$436$	−25.4201	−1.21740
$437$	−31.3065	−1.49759
$438$	−15.6870	−0.749553
$439$	−0.441326	−0.0210633	−0.0105317	−	0.999945i	$-0.503352\pi$
$439$	−0.441326	−0.0210633	−0.0105317	+	0.999945i	$0.503352\pi$
$440$	−7.73356	−0.368683
$441$	0	0
$442$	−17.1590	−0.816169
$443$	4.94126	0.234766	0.117383	−	0.993087i	$-0.462549\pi$
$443$	4.94126	0.234766	0.117383	+	0.993087i	$0.462549\pi$
$444$	46.1958	2.19236
$445$	−1.09849	−0.0520735
$446$	8.29529	0.392793
$447$	20.5455	0.971771
$448$	0	0
$449$	−10.6933	−0.504650	−0.252325	−	0.967643i	$-0.581195\pi$
$449$	−10.6933	−0.504650	−0.252325	+	0.967643i	$0.581195\pi$
$450$	8.30181	0.391351
$451$	−8.85946	−0.417176
$452$	−59.0958	−2.77963
$453$	−41.1458	−1.93320
$454$	12.2345	0.574193
$455$	0	0
$456$	−126.138	−5.90695
$457$	34.7108	1.62370	0.811852	−	0.583864i	$-0.198460\pi$
$457$	34.7108	1.62370	0.811852	+	0.583864i	$0.198460\pi$
$458$	21.9621	1.02622
$459$	1.19812	0.0559234
$460$	−23.5012	−1.09575
$461$	8.90420	0.414710	0.207355	−	0.978266i	$-0.433514\pi$
$461$	8.90420	0.414710	0.207355	+	0.978266i	$0.433514\pi$
$462$	0	0
$463$	16.6963	0.775944	0.387972	−	0.921671i	$-0.373176\pi$
$463$	16.6963	0.775944	0.387972	+	0.921671i	$0.373176\pi$
$464$	−81.0252	−3.76150
$465$	−25.3750	−1.17674
$466$	74.4261	3.44772
$467$	32.4807	1.50303	0.751514	−	0.659718i	$-0.229324\pi$
$467$	32.4807	1.50303	0.751514	+	0.659718i	$0.229324\pi$
$468$	−31.9310	−1.47601
$469$	0	0
$470$	−3.17488	−0.146446
$471$	19.1243	0.881203
$472$	−69.3823	−3.19358
$473$	2.01269	0.0925437
$474$	−104.149	−4.78371
$475$	−6.57586	−0.301721
$476$	0	0
$477$	18.8134	0.861407
$478$	−26.3895	−1.20703
$479$	36.5648	1.67069	0.835345	−	0.549727i	$-0.185268\pi$
$479$	36.5648	1.67069	0.835345	+	0.549727i	$0.185268\pi$
$480$	−30.1956	−1.37823
$481$	−7.74244	−0.353025
$482$	19.0935	0.869685
$483$	0	0
$484$	4.93639	0.224381
$485$	11.7031	0.531412
$486$	−58.6413	−2.66003
$487$	28.9781	1.31312	0.656562	−	0.754272i	$-0.272010\pi$
$487$	28.9781	1.31312	0.656562	+	0.754272i	$0.272010\pi$
$488$	−89.8921	−4.06923
$489$	−24.5061	−1.10820
$490$	0	0
$491$	2.73589	0.123469	0.0617344	−	0.998093i	$-0.480337\pi$
$491$	2.73589	0.123469	0.0617344	+	0.998093i	$0.480337\pi$
$492$	−108.475	−4.89043
$493$	−24.5109	−1.10392
$494$	35.5400	1.59902
$495$	−3.15215	−0.141678
$496$	107.369	4.82103
$497$	0	0
$498$	30.7258	1.37685
$499$	−15.9194	−0.712651	−0.356325	−	0.934362i	$-0.615971\pi$
$499$	−15.9194	−0.712651	−0.356325	+	0.934362i	$0.615971\pi$
$500$	−4.93639	−0.220762
$501$	44.5677	1.99114
$502$	52.9471	2.36315
$503$	1.61088	0.0718258	0.0359129	−	0.999355i	$-0.488566\pi$
$503$	1.61088	0.0718258	0.0359129	+	0.999355i	$0.488566\pi$
$504$	0	0
$505$	6.61933	0.294556
$506$	12.5386	0.557407
$507$	−21.7996	−0.968153
$508$	31.3503	1.39094
$509$	−37.1399	−1.64620	−0.823098	−	0.567900i	$-0.807756\pi$
$509$	−37.1399	−1.64620	−0.823098	+	0.567900i	$0.807756\pi$
$510$	−20.7399	−0.918379
$511$	0	0
$512$	−34.5627	−1.52747
$513$	−2.48156	−0.109564
$514$	−49.4633	−2.18173
$515$	−1.85751	−0.0818516
$516$	24.6434	1.08486
$517$	1.20548	0.0530170
$518$	0	0
$519$	−11.4252	−0.501510
$520$	15.8700	0.695946
$521$	−1.91587	−0.0839360	−0.0419680	−	0.999119i	$-0.513363\pi$
$521$	−1.91587	−0.0839360	−0.0419680	+	0.999119i	$0.513363\pi$
$522$	−64.0922	−2.80524
$523$	26.8585	1.17444	0.587221	−	0.809427i	$-0.300222\pi$
$523$	26.8585	1.17444	0.587221	+	0.809427i	$0.300222\pi$
$524$	−0.0540528	−0.00236131
$525$	0	0
$526$	−53.2286	−2.32088
$527$	32.4803	1.41486
$528$	26.0316	1.13288
$529$	−0.334638	−0.0145495
$530$	−15.7191	−0.682795
$531$	−28.2797	−1.22724
$532$	0	0
$533$	18.1805	0.787483
$534$	7.17590	0.310532
$535$	−1.99151	−0.0861005
$536$	63.8432	2.75761
$537$	16.6222	0.717303
$538$	−0.364870	−0.0157307
$539$	0	0
$540$	−1.86287	−0.0801650
$541$	6.10727	0.262572	0.131286	−	0.991345i	$-0.458089\pi$
$541$	6.10727	0.262572	0.131286	+	0.991345i	$0.458089\pi$
$542$	16.6769	0.716333
$543$	48.4710	2.08009
$544$	38.6507	1.65714
$545$	5.14954	0.220582
$546$	0	0
$547$	−0.397202	−0.0169831	−0.00849156	−	0.999964i	$-0.502703\pi$
$547$	−0.397202	−0.0169831	−0.00849156	+	0.999964i	$0.502703\pi$
$548$	103.425	4.41811
$549$	−36.6394	−1.56373
$550$	2.63370	0.112301
$551$	50.7674	2.16276
$552$	91.3218	3.88691
$553$	0	0
$554$	−84.9807	−3.61049
$555$	−9.35823	−0.397235
$556$	80.7377	3.42404
$557$	24.8387	1.05245	0.526226	−	0.850345i	$-0.323607\pi$
$557$	24.8387	1.05245	0.526226	+	0.850345i	$0.323607\pi$
$558$	84.9308	3.59541
$559$	−4.13024	−0.174690
$560$	0	0
$561$	7.87482	0.332475
$562$	27.1268	1.14428
$563$	27.6743	1.16633	0.583167	−	0.812352i	$-0.301813\pi$
$563$	27.6743	1.16633	0.583167	+	0.812352i	$0.301813\pi$
$564$	14.7599	0.621503
$565$	11.9715	0.503644
$566$	64.9968	2.73202
$567$	0	0
$568$	−16.2589	−0.682208
$569$	30.0012	1.25771	0.628857	−	0.777521i	$-0.283523\pi$
$569$	30.0012	1.25771	0.628857	+	0.777521i	$0.283523\pi$
$570$	42.9569	1.79927
$571$	−3.50555	−0.146703	−0.0733514	−	0.997306i	$-0.523369\pi$
$571$	−3.50555	−0.146703	−0.0733514	+	0.997306i	$0.523369\pi$
$572$	−10.1299	−0.423554
$573$	−30.9796	−1.29419
$574$	0	0
$575$	4.76082	0.198540
$576$	34.9012	1.45422
$577$	−34.7904	−1.44834	−0.724172	−	0.689619i	$-0.757778\pi$
$577$	−34.7904	−1.44834	−0.724172	+	0.689619i	$0.757778\pi$
$578$	−18.2256	−0.758084
$579$	34.8416	1.44797
$580$	38.1102	1.58244
$581$	0	0
$582$	−76.4509	−3.16899
$583$	5.96845	0.247188
$584$	−18.5712	−0.768480
$585$	6.46850	0.267440
$586$	−4.52440	−0.186901
$587$	5.13912	0.212114	0.106057	−	0.994360i	$-0.466177\pi$
$587$	5.13912	0.212114	0.106057	+	0.994360i	$0.466177\pi$
$588$	0	0
$589$	−67.2737	−2.77196
$590$	23.6285	0.972769
$591$	−2.02464	−0.0832826
$592$	39.5976	1.62745
$593$	1.48118	0.0608247	0.0304123	−	0.999537i	$-0.490318\pi$
$593$	1.48118	0.0608247	0.0304123	+	0.999537i	$0.490318\pi$
$594$	0.993892	0.0407799
$595$	0	0
$596$	40.8896	1.67491
$597$	2.41986	0.0990382
$598$	−25.7303	−1.05219
$599$	−32.7812	−1.33941	−0.669703	−	0.742629i	$-0.733578\pi$
$599$	−32.7812	−1.33941	−0.669703	+	0.742629i	$0.733578\pi$
$600$	19.1820	0.783100
$601$	−1.97212	−0.0804446	−0.0402223	−	0.999191i	$-0.512807\pi$
$601$	−1.97212	−0.0804446	−0.0402223	+	0.999191i	$0.512807\pi$
$602$	0	0
$603$	26.0221	1.05970
$604$	−81.8882	−3.33198
$605$	−1.00000	−0.0406558
$606$	−43.2408	−1.75654
$607$	27.2006	1.10404	0.552019	−	0.833831i	$-0.313858\pi$
$607$	27.2006	1.10404	0.552019	+	0.833831i	$0.313858\pi$
$608$	−80.0540	−3.24662
$609$	0	0
$610$	30.6132	1.23949
$611$	−2.47376	−0.100078
$612$	49.4018	1.99695
$613$	−26.5371	−1.07182	−0.535911	−	0.844275i	$-0.680032\pi$
$613$	−26.5371	−1.07182	−0.535911	+	0.844275i	$0.680032\pi$
$614$	−22.2101	−0.896326
$615$	21.9746	0.886100
$616$	0	0
$617$	26.5833	1.07020	0.535101	−	0.844788i	$-0.320274\pi$
$617$	26.5833	1.07020	0.535101	+	0.844788i	$0.320274\pi$
$618$	12.1342	0.488108
$619$	−19.0160	−0.764317	−0.382159	−	0.924097i	$-0.624819\pi$
$619$	−19.0160	−0.764317	−0.382159	+	0.924097i	$0.624819\pi$
$620$	−50.5012	−2.02818
$621$	1.79661	0.0720955
$622$	38.9790	1.56292
$623$	0	0
$624$	−53.4193	−2.13849
$625$	1.00000	0.0400000
$626$	42.9007	1.71466
$627$	−16.3105	−0.651377
$628$	38.0612	1.51881
$629$	11.9787	0.477620
$630$	0	0
$631$	30.5600	1.21658	0.608288	−	0.793717i	$-0.291857\pi$
$631$	30.5600	1.21658	0.608288	+	0.793717i	$0.291857\pi$
$632$	−123.297	−4.90451
$633$	44.4265	1.76579
$634$	−73.7013	−2.92705
$635$	−6.35086	−0.252026
$636$	73.0775	2.89771
$637$	0	0
$638$	−20.3329	−0.804986
$639$	−6.62701	−0.262160
$640$	−4.81305	−0.190252
$641$	25.5204	1.00800	0.503998	−	0.863705i	$-0.331862\pi$
$641$	25.5204	1.00800	0.503998	+	0.863705i	$0.331862\pi$
$642$	13.0096	0.513446
$643$	20.0480	0.790617	0.395308	−	0.918548i	$-0.370638\pi$
$643$	20.0480	0.790617	0.395308	+	0.918548i	$0.370638\pi$
$644$	0	0
$645$	−4.99219	−0.196567
$646$	−54.9853	−2.16337
$647$	−10.5200	−0.413586	−0.206793	−	0.978385i	$-0.566303\pi$
$647$	−10.5200	−0.413586	−0.206793	+	0.978385i	$0.566303\pi$
$648$	−65.8932	−2.58853
$649$	−8.97158	−0.352165
$650$	−5.40461	−0.211986
$651$	0	0
$652$	−48.7718	−1.91005
$653$	−3.85046	−0.150680	−0.0753400	−	0.997158i	$-0.524004\pi$
$653$	−3.85046	−0.150680	−0.0753400	+	0.997158i	$0.524004\pi$
$654$	−33.6394	−1.31540
$655$	0.0109499	0.000427847 0
$656$	−92.9812	−3.63030
$657$	−7.56947	−0.295313
$658$	0	0
$659$	−2.08244	−0.0811203	−0.0405601	−	0.999177i	$-0.512914\pi$
$659$	−2.08244	−0.0811203	−0.0405601	+	0.999177i	$0.512914\pi$
$660$	−12.2440	−0.476596
$661$	25.5530	0.993897	0.496949	−	0.867780i	$-0.334454\pi$
$661$	25.5530	0.993897	0.496949	+	0.867780i	$0.334454\pi$
$662$	77.1345	2.99792
$663$	−16.1599	−0.627598
$664$	36.3750	1.41162
$665$	0	0
$666$	31.3223	1.21371
$667$	−36.7548	−1.42315
$668$	88.6984	3.43184
$669$	7.81228	0.302040
$670$	−21.7421	−0.839971
$671$	−11.6236	−0.448726
$672$	0	0
$673$	3.13648	0.120903	0.0604513	−	0.998171i	$-0.480746\pi$
$673$	3.13648	0.120903	0.0604513	+	0.998171i	$0.480746\pi$
$674$	29.4712	1.13519
$675$	0.377374	0.0145251
$676$	−43.3854	−1.66867
$677$	−3.05938	−0.117581	−0.0587907	−	0.998270i	$-0.518724\pi$
$677$	−3.05938	−0.117581	−0.0587907	+	0.998270i	$0.518724\pi$
$678$	−78.2038	−3.00340
$679$	0	0
$680$	−24.5531	−0.941570
$681$	11.5221	0.441529
$682$	26.9438	1.03173
$683$	33.3431	1.27584	0.637918	−	0.770104i	$-0.279796\pi$
$683$	33.3431	1.27584	0.637918	+	0.770104i	$0.279796\pi$
$684$	−102.322	−3.91237
$685$	−20.9516	−0.800520
$686$	0	0
$687$	20.6834	0.789119
$688$	21.1235	0.805325
$689$	−12.2478	−0.466605
$690$	−31.1001	−1.18396
$691$	−14.3545	−0.546072	−0.273036	−	0.962004i	$-0.588028\pi$
$691$	−14.3545	−0.546072	−0.273036	+	0.962004i	$0.588028\pi$
$692$	−22.7383	−0.864382
$693$	0	0
$694$	35.9517	1.36471
$695$	−16.3556	−0.620404
$696$	−148.090	−5.61333
$697$	−28.1277	−1.06541
$698$	2.11399	0.0800156
$699$	70.0926	2.65114
$700$	0	0
$701$	50.8858	1.92193	0.960965	−	0.276670i	$-0.0892309\pi$
$701$	50.8858	1.92193	0.960965	+	0.276670i	$0.0892309\pi$
$702$	−2.03956	−0.0769782
$703$	−24.8104	−0.935741
$704$	11.0722	0.417299
$705$	−2.99002	−0.112611
$706$	1.56257	0.0588081
$707$	0	0
$708$	−109.848	−4.12833
$709$	−29.9705	−1.12557	−0.562783	−	0.826604i	$-0.690270\pi$
$709$	−29.9705	−1.12557	−0.562783	+	0.826604i	$0.690270\pi$
$710$	5.53704	0.207802
$711$	−50.2552	−1.88472
$712$	8.49525	0.318373
$713$	48.7050	1.82402
$714$	0	0
$715$	2.05210	0.0767440
$716$	33.0815	1.23631
$717$	−24.8529	−0.928149
$718$	−43.0694	−1.60734
$719$	−20.8650	−0.778131	−0.389066	−	0.921210i	$-0.627202\pi$
$719$	−20.8650	−0.778131	−0.389066	+	0.921210i	$0.627202\pi$
$720$	−33.0822	−1.23290
$721$	0	0
$722$	63.8461	2.37611
$723$	17.9818	0.668749
$724$	96.4668	3.58516
$725$	−7.72026	−0.286723
$726$	6.53251	0.242444
$727$	−30.7659	−1.14104	−0.570521	−	0.821283i	$-0.693259\pi$
$727$	−30.7659	−1.14104	−0.570521	+	0.821283i	$0.693259\pi$
$728$	0	0
$729$	−29.6657	−1.09873
$730$	6.32450	0.234080
$731$	6.39006	0.236345
$732$	−142.319	−5.26028
$733$	−33.8964	−1.25199	−0.625996	−	0.779826i	$-0.715307\pi$
$733$	−33.8964	−1.25199	−0.625996	+	0.779826i	$0.715307\pi$
$734$	25.3360	0.935171
$735$	0	0
$736$	57.9578	2.13635
$737$	8.25535	0.304090
$738$	−73.5496	−2.70740
$739$	−20.9944	−0.772291	−0.386146	−	0.922438i	$-0.626194\pi$
$739$	−20.9944	−0.772291	−0.386146	+	0.922438i	$0.626194\pi$
$740$	−18.6247	−0.684658
$741$	33.4706	1.22957
$742$	0	0
$743$	29.3854	1.07804	0.539022	−	0.842292i	$-0.318794\pi$
$743$	29.3854	1.07804	0.539022	+	0.842292i	$0.318794\pi$
$744$	196.239	7.19447
$745$	−8.28332	−0.303477
$746$	−61.1580	−2.23915
$747$	14.8262	0.542461
$748$	15.6724	0.573041
$749$	0	0
$750$	−6.53251	−0.238533
$751$	−10.4054	−0.379700	−0.189850	−	0.981813i	$-0.560800\pi$
$751$	−10.4054	−0.379700	−0.189850	+	0.981813i	$0.560800\pi$
$752$	12.6517	0.461360
$753$	49.8642	1.81715
$754$	41.7250	1.51953
$755$	16.5887	0.603724
$756$	0	0
$757$	−16.2195	−0.589508	−0.294754	−	0.955573i	$-0.595238\pi$
$757$	−16.2195	−0.589508	−0.294754	+	0.955573i	$0.595238\pi$
$758$	−54.3850	−1.97535
$759$	11.8085	0.428621
$760$	50.8549	1.84470
$761$	−41.8821	−1.51823	−0.759113	−	0.650959i	$-0.774367\pi$
$761$	−41.8821	−1.51823	−0.759113	+	0.650959i	$0.774367\pi$
$762$	41.4870	1.50292
$763$	0	0
$764$	−61.6554	−2.23061
$765$	−10.0077	−0.361829
$766$	27.7532	1.00276
$767$	18.4105	0.664766
$768$	−23.4846	−0.847429
$769$	−38.7049	−1.39573	−0.697867	−	0.716228i	$-0.745867\pi$
$769$	−38.7049	−1.39573	−0.697867	+	0.716228i	$0.745867\pi$
$770$	0	0
$771$	−46.5833	−1.67766
$772$	69.3415	2.49566
$773$	−24.8486	−0.893743	−0.446872	−	0.894598i	$-0.647462\pi$
$773$	−24.8486	−0.893743	−0.446872	+	0.894598i	$0.647462\pi$
$774$	16.7090	0.600593
$775$	10.2304	0.367487
$776$	−90.5070	−3.24901
$777$	0	0
$778$	−54.0257	−1.93691
$779$	58.2586	2.08733
$780$	25.1258	0.899648
$781$	−2.10238	−0.0752291
$782$	39.8084	1.42355
$783$	−2.91343	−0.104118
$784$	0	0
$785$	−7.71033	−0.275194
$786$	−0.0715301	−0.00255139
$787$	−26.1856	−0.933415	−0.466708	−	0.884412i	$-0.654560\pi$
$787$	−26.1856	−0.933415	−0.466708	+	0.884412i	$0.654560\pi$
$788$	−4.02943	−0.143543
$789$	−50.1293	−1.78465
$790$	41.9895	1.49392
$791$	0	0
$792$	24.3773	0.866210
$793$	23.8528	0.847038
$794$	−63.1585	−2.24141
$795$	−14.8038	−0.525038
$796$	4.81599	0.170698
$797$	18.6426	0.660353	0.330177	−	0.943919i	$-0.392892\pi$
$797$	18.6426	0.660353	0.330177	+	0.943919i	$0.392892\pi$
$798$	0	0
$799$	3.82726	0.135399
$800$	12.1739	0.430413
$801$	3.46260	0.122345
$802$	25.7646	0.909780
$803$	−2.40137	−0.0847426
$804$	101.078	3.56475
$805$	0	0
$806$	−55.2913	−1.94755
$807$	−0.343625	−0.0120962
$808$	−51.1910	−1.80089
$809$	8.68346	0.305294	0.152647	−	0.988281i	$-0.451220\pi$
$809$	8.68346	0.305294	0.152647	+	0.988281i	$0.451220\pi$
$810$	22.4402	0.788469
$811$	−7.11567	−0.249865	−0.124933	−	0.992165i	$-0.539871\pi$
$811$	−7.11567	−0.249865	−0.124933	+	0.992165i	$0.539871\pi$
$812$	0	0
$813$	15.7059	0.550828
$814$	9.93682	0.348285
$815$	9.88007	0.346084
$816$	82.6472	2.89323
$817$	−13.2352	−0.463041
$818$	67.5350	2.36131
$819$	0	0
$820$	43.7337	1.52725
$821$	−20.3518	−0.710282	−0.355141	−	0.934813i	$-0.615567\pi$
$821$	−20.3518	−0.710282	−0.355141	+	0.934813i	$0.615567\pi$
$822$	136.867	4.77377
$823$	22.1703	0.772809	0.386405	−	0.922329i	$-0.373717\pi$
$823$	22.1703	0.772809	0.386405	+	0.922329i	$0.373717\pi$
$824$	14.3652	0.500434
$825$	2.48035	0.0863548
$826$	0	0
$827$	−24.1200	−0.838735	−0.419367	−	0.907817i	$-0.637748\pi$
$827$	−24.1200	−0.838735	−0.419367	+	0.907817i	$0.637748\pi$
$828$	74.0793	2.57443
$829$	−4.74046	−0.164643	−0.0823215	−	0.996606i	$-0.526233\pi$
$829$	−4.74046	−0.164643	−0.0823215	+	0.996606i	$0.526233\pi$
$830$	−12.3877	−0.429982
$831$	−80.0326	−2.77630
$832$	−22.7212	−0.787716
$833$	0	0
$834$	106.843	3.69968
$835$	−17.9683	−0.621818
$836$	−32.4610	−1.12269
$837$	3.86069	0.133445
$838$	−60.4477	−2.08813
$839$	−4.74188	−0.163708	−0.0818539	−	0.996644i	$-0.526084\pi$
$839$	−4.74188	−0.163708	−0.0818539	+	0.996644i	$0.526084\pi$
$840$	0	0
$841$	30.6025	1.05526
$842$	−38.3065	−1.32013
$843$	25.5473	0.879897
$844$	88.4174	3.04345
$845$	8.78891	0.302348
$846$	10.0077	0.344071
$847$	0	0
$848$	62.6396	2.15105
$849$	61.2123	2.10080
$850$	8.36169	0.286803
$851$	17.9623	0.615740
$852$	−25.7415	−0.881889
$853$	−34.1583	−1.16956	−0.584779	−	0.811193i	$-0.698819\pi$
$853$	−34.1583	−1.16956	−0.584779	+	0.811193i	$0.698819\pi$
$854$	0	0
$855$	20.7281	0.708885
$856$	15.4015	0.526411
$857$	18.0239	0.615684	0.307842	−	0.951438i	$-0.400393\pi$
$857$	18.0239	0.615684	0.307842	+	0.951438i	$0.400393\pi$
$858$	−13.4053	−0.457650
$859$	−19.5576	−0.667296	−0.333648	−	0.942698i	$-0.608280\pi$
$859$	−19.5576	−0.667296	−0.333648	+	0.942698i	$0.608280\pi$
$860$	−9.93543	−0.338795
$861$	0	0
$862$	−60.2991	−2.05380
$863$	9.85177	0.335358	0.167679	−	0.985842i	$-0.446373\pi$
$863$	9.85177	0.335358	0.167679	+	0.985842i	$0.446373\pi$
$864$	4.59412	0.156295
$865$	4.60627	0.156618
$866$	33.6307	1.14282
$867$	−17.1644	−0.582933
$868$	0	0
$869$	−15.9432	−0.540835
$870$	50.4327	1.70983
$871$	−16.9408	−0.574016
$872$	−39.8243	−1.34862
$873$	−36.8900	−1.24854
$874$	−82.4519	−2.78898
$875$	0	0
$876$	−29.4023	−0.993412
$877$	46.5171	1.57077	0.785385	−	0.619007i	$-0.212465\pi$
$877$	46.5171	1.57077	0.785385	+	0.619007i	$0.212465\pi$
$878$	−1.16232	−0.0392264
$879$	−4.26097	−0.143719
$880$	−10.4951	−0.353791
$881$	−42.8947	−1.44516	−0.722580	−	0.691288i	$-0.757044\pi$
$881$	−42.8947	−1.44516	−0.722580	+	0.691288i	$0.757044\pi$
$882$	0	0
$883$	−34.5397	−1.16235	−0.581176	−	0.813778i	$-0.697407\pi$
$883$	−34.5397	−1.16235	−0.581176	+	0.813778i	$0.697407\pi$
$884$	−32.1613	−1.08170
$885$	22.2527	0.748016
$886$	13.0138	0.437207
$887$	−29.9278	−1.00488	−0.502438	−	0.864613i	$-0.667563\pi$
$887$	−29.9278	−1.00488	−0.502438	+	0.864613i	$0.667563\pi$
$888$	72.3725	2.42866
$889$	0	0
$890$	−2.89310	−0.0969769
$891$	−8.52042	−0.285445
$892$	15.5480	0.520585
$893$	−7.92708	−0.265270
$894$	54.1108	1.80974
$895$	−6.70157	−0.224009
$896$	0	0
$897$	−24.2322	−0.809088
$898$	−28.1631	−0.939813
$899$	−78.9814	−2.63418
$900$	15.5602	0.518673
$901$	18.9491	0.631286
$902$	−23.3332	−0.776910
$903$	0	0
$904$	−92.5822	−3.07924
$905$	−19.5420	−0.649598
$906$	−108.366	−3.60021
$907$	53.0922	1.76290	0.881449	−	0.472279i	$-0.156568\pi$
$907$	53.0922	1.76290	0.881449	+	0.472279i	$0.156568\pi$
$908$	22.9313	0.761002
$909$	−20.8651	−0.692052
$910$	0	0
$911$	26.2077	0.868300	0.434150	−	0.900841i	$-0.357049\pi$
$911$	26.2077	0.868300	0.434150	+	0.900841i	$0.357049\pi$
$912$	−171.180	−5.66835
$913$	4.70352	0.155664
$914$	91.4179	3.02384
$915$	28.8307	0.953114
$916$	41.1639	1.36009
$917$	0	0
$918$	3.15549	0.104147
$919$	3.32075	0.109542	0.0547708	−	0.998499i	$-0.482557\pi$
$919$	3.32075	0.109542	0.0547708	+	0.998499i	$0.482557\pi$
$920$	−36.8181	−1.21386
$921$	−20.9169	−0.689235
$922$	23.4510	0.772318
$923$	4.31428	0.142006
$924$	0	0
$925$	3.77295	0.124054
$926$	43.9731	1.44505
$927$	5.85513	0.192308
$928$	−93.9858	−3.08524
$929$	42.7202	1.40160	0.700801	−	0.713357i	$-0.252826\pi$
$929$	42.7202	1.40160	0.700801	+	0.713357i	$0.252826\pi$
$930$	−66.8301	−2.19145
$931$	0	0
$932$	139.498	4.56941
$933$	36.7094	1.20181
$934$	85.5445	2.79910
$935$	−3.17488	−0.103830
$936$	−50.0246	−1.63510
$937$	−0.739256	−0.0241504	−0.0120752	−	0.999927i	$-0.503844\pi$
$937$	−0.739256	−0.0241504	−0.0120752	+	0.999927i	$0.503844\pi$
$938$	0	0
$939$	40.4028	1.31849
$940$	−5.95072	−0.194091
$941$	5.29179	0.172507	0.0862536	−	0.996273i	$-0.472510\pi$
$941$	5.29179	0.172507	0.0862536	+	0.996273i	$0.472510\pi$
$942$	50.3678	1.64107
$943$	−42.1783	−1.37351
$944$	−94.1579	−3.06458
$945$	0	0
$946$	5.30083	0.172345
$947$	−24.8821	−0.808559	−0.404280	−	0.914635i	$-0.632478\pi$
$947$	−24.8821	−0.808559	−0.404280	+	0.914635i	$0.632478\pi$
$948$	−195.208	−6.34005
$949$	4.92784	0.159965
$950$	−17.3189	−0.561898
$951$	−69.4099	−2.25077
$952$	0	0
$953$	−3.40496	−0.110297	−0.0551487	−	0.998478i	$-0.517563\pi$
$953$	−3.40496	−0.110297	−0.0551487	+	0.998478i	$0.517563\pi$
$954$	49.5489	1.60421
$955$	12.4900	0.404166
$956$	−49.4622	−1.59972
$957$	−19.1490	−0.618998
$958$	96.3008	3.11134
$959$	0	0
$960$	−27.4630	−0.886363
$961$	73.6610	2.37616
$962$	−20.3913	−0.657442
$963$	6.27753	0.202291
$964$	35.7872	1.15263
$965$	−14.0470	−0.452190
$966$	0	0
$967$	15.1073	0.485817	0.242908	−	0.970049i	$-0.421899\pi$
$967$	15.1073	0.485817	0.242908	+	0.970049i	$0.421899\pi$
$968$	7.73356	0.248566
$969$	−51.7837	−1.66353
$970$	30.8226	0.989654
$971$	6.36774	0.204351	0.102175	−	0.994766i	$-0.467420\pi$
$971$	6.36774	0.204351	0.102175	+	0.994766i	$0.467420\pi$
$972$	−109.912	−3.52544
$973$	0	0
$974$	76.3197	2.44544
$975$	−5.08992	−0.163008
$976$	−121.992	−3.90486
$977$	34.9456	1.11801	0.559004	−	0.829165i	$-0.311184\pi$
$977$	34.9456	1.11801	0.559004	+	0.829165i	$0.311184\pi$
$978$	−64.5416	−2.06381
$979$	1.09849	0.0351079
$980$	0	0
$981$	−16.2321	−0.518251
$982$	7.20551	0.229937
$983$	33.0407	1.05383	0.526917	−	0.849917i	$-0.323348\pi$
$983$	33.0407	1.05383	0.526917	+	0.849917i	$0.323348\pi$
$984$	−169.942	−5.41755
$985$	0.816272	0.0260086
$986$	−64.5544	−2.05583
$987$	0	0
$988$	66.6130	2.11924
$989$	9.58206	0.304692
$990$	−8.30181	−0.263849
$991$	−10.7934	−0.342865	−0.171432	−	0.985196i	$-0.554840\pi$
$991$	−10.7934	−0.342865	−0.171432	+	0.985196i	$0.554840\pi$
$992$	124.544	3.95428
$993$	72.6432	2.30526
$994$	0	0
$995$	−0.975611	−0.0309290
$996$	57.5898	1.82480
$997$	8.78150	0.278113	0.139056	−	0.990284i	$-0.455593\pi$
$997$	8.78150	0.278113	0.139056	+	0.990284i	$0.455593\pi$
$998$	−41.9270	−1.32718
$999$	1.42381	0.0450475

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2695.2.a.y.1.9		10
7.2	even	3		385.2.i.d.221.2	✓	20
7.4	even	3		385.2.i.d.331.2	yes	20
7.6	odd	2		2695.2.a.z.1.9		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.i.d.221.2	✓	20	7.2	even	3
385.2.i.d.331.2	yes	20	7.4	even	3
2695.2.a.y.1.9		10	1.1	even	1	trivial
2695.2.a.z.1.9		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)

\(f(q)\)	\(=\)	\(q+2.63370 q^{2} +2.48035 q^{3} +4.93639 q^{4} -1.00000 q^{5} +6.53251 q^{6} +7.73356 q^{8} +3.15215 q^{9} +O(q^{10})\)	\(q+2.63370 q^{2} +2.48035 q^{3} +4.93639 q^{4} -1.00000 q^{5} +6.53251 q^{6} +7.73356 q^{8} +3.15215 q^{9} -2.63370 q^{10} +1.00000 q^{11} +12.2440 q^{12} -2.05210 q^{13} -2.48035 q^{15} +10.4951 q^{16} +3.17488 q^{17} +8.30181 q^{18} -6.57586 q^{19} -4.93639 q^{20} +2.63370 q^{22} +4.76082 q^{23} +19.1820 q^{24} +1.00000 q^{25} -5.40461 q^{26} +0.377374 q^{27} -7.72026 q^{29} -6.53251 q^{30} +10.2304 q^{31} +12.1739 q^{32} +2.48035 q^{33} +8.36169 q^{34} +15.5602 q^{36} +3.77295 q^{37} -17.3189 q^{38} -5.08992 q^{39} -7.73356 q^{40} -8.85946 q^{41} +2.01269 q^{43} +4.93639 q^{44} -3.15215 q^{45} +12.5386 q^{46} +1.20548 q^{47} +26.0316 q^{48} +2.63370 q^{50} +7.87482 q^{51} -10.1299 q^{52} +5.96845 q^{53} +0.993892 q^{54} -1.00000 q^{55} -16.3105 q^{57} -20.3329 q^{58} -8.97158 q^{59} -12.2440 q^{60} -11.6236 q^{61} +26.9438 q^{62} +11.0722 q^{64} +2.05210 q^{65} +6.53251 q^{66} +8.25535 q^{67} +15.6724 q^{68} +11.8085 q^{69} -2.10238 q^{71} +24.3773 q^{72} -2.40137 q^{73} +9.93682 q^{74} +2.48035 q^{75} -32.4610 q^{76} -13.4053 q^{78} -15.9432 q^{79} -10.4951 q^{80} -8.52042 q^{81} -23.3332 q^{82} +4.70352 q^{83} -3.17488 q^{85} +5.30083 q^{86} -19.1490 q^{87} +7.73356 q^{88} +1.09849 q^{89} -8.30181 q^{90} +23.5012 q^{92} +25.3750 q^{93} +3.17488 q^{94} +6.57586 q^{95} +30.1956 q^{96} -11.7031 q^{97} +3.15215 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 3 q^{2} - 3 q^{3} + 15 q^{4} - 10 q^{5} + 5 q^{6} + 9 q^{8} + 19 q^{9}+O(q^{10}) \) 10 * q + 3 * q^2 - 3 * q^3 + 15 * q^4 - 10 * q^5 + 5 * q^6 + 9 * q^8 + 19 * q^9	\( 10 q + 3 q^{2} - 3 q^{3} + 15 q^{4} - 10 q^{5} + 5 q^{6} + 9 q^{8} + 19 q^{9} - 3 q^{10} + 10 q^{11} - 3 q^{12} - 6 q^{13} + 3 q^{15} + 21 q^{16} - 5 q^{17} + q^{18} + q^{19} - 15 q^{20} + 3 q^{22} + 18 q^{23} + 10 q^{24} + 10 q^{25} + 13 q^{26} - 15 q^{27} + 14 q^{29} - 5 q^{30} + 10 q^{31} + 46 q^{32} - 3 q^{33} - 2 q^{34} + 26 q^{36} + 13 q^{37} + 9 q^{38} + 3 q^{39} - 9 q^{40} - 7 q^{41} + 6 q^{43} + 15 q^{44} - 19 q^{45} + 10 q^{46} + q^{47} - 35 q^{48} + 3 q^{50} + 9 q^{51} - 17 q^{52} + 16 q^{53} + 73 q^{54} - 10 q^{55} + 12 q^{57} - 9 q^{58} + 13 q^{59} + 3 q^{60} + 18 q^{61} + 14 q^{62} + 43 q^{64} + 6 q^{65} + 5 q^{66} + 29 q^{67} + 13 q^{68} + 19 q^{71} - 48 q^{72} - 31 q^{73} - 8 q^{74} - 3 q^{75} - 8 q^{76} + 3 q^{78} - 21 q^{80} + 42 q^{81} + q^{82} - 2 q^{83} + 5 q^{85} + 10 q^{86} - 50 q^{87} + 9 q^{88} + 23 q^{89} - q^{90} + 14 q^{92} + 4 q^{93} - 5 q^{94} - q^{95} + 39 q^{96} - 43 q^{97} + 19 q^{99}+O(q^{100}) \) 10 * q + 3 * q^2 - 3 * q^3 + 15 * q^4 - 10 * q^5 + 5 * q^6 + 9 * q^8 + 19 * q^9 - 3 * q^10 + 10 * q^11 - 3 * q^12 - 6 * q^13 + 3 * q^15 + 21 * q^16 - 5 * q^17 + q^18 + q^19 - 15 * q^20 + 3 * q^22 + 18 * q^23 + 10 * q^24 + 10 * q^25 + 13 * q^26 - 15 * q^27 + 14 * q^29 - 5 * q^30 + 10 * q^31 + 46 * q^32 - 3 * q^33 - 2 * q^34 + 26 * q^36 + 13 * q^37 + 9 * q^38 + 3 * q^39 - 9 * q^40 - 7 * q^41 + 6 * q^43 + 15 * q^44 - 19 * q^45 + 10 * q^46 + q^47 - 35 * q^48 + 3 * q^50 + 9 * q^51 - 17 * q^52 + 16 * q^53 + 73 * q^54 - 10 * q^55 + 12 * q^57 - 9 * q^58 + 13 * q^59 + 3 * q^60 + 18 * q^61 + 14 * q^62 + 43 * q^64 + 6 * q^65 + 5 * q^66 + 29 * q^67 + 13 * q^68 + 19 * q^71 - 48 * q^72 - 31 * q^73 - 8 * q^74 - 3 * q^75 - 8 * q^76 + 3 * q^78 - 21 * q^80 + 42 * q^81 + q^82 - 2 * q^83 + 5 * q^85 + 10 * q^86 - 50 * q^87 + 9 * q^88 + 23 * q^89 - q^90 + 14 * q^92 + 4 * q^93 - 5 * q^94 - q^95 + 39 * q^96 - 43 * q^97 + 19 * q^99

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