LMFDB - Embedded newform 2695.2.a.y.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:	$0$
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			1.2
Root			$-2.10414$ 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)

$f(q)$	$=$	$q-2.10414 q^{2} +1.86644 q^{3} +2.42740 q^{4} -1.00000 q^{5} -3.92725 q^{6} -0.899305 q^{8} +0.483603 q^{9} +O(q^{10})$	\(q-2.10414 q^{2} +1.86644 q^{3} +2.42740 q^{4} -1.00000 q^{5} -3.92725 q^{6} -0.899305 q^{8} +0.483603 q^{9} +2.10414 q^{10} +1.00000 q^{11} +4.53060 q^{12} -4.19694 q^{13} -1.86644 q^{15} -2.96253 q^{16} -6.50001 q^{17} -1.01757 q^{18} -3.44403 q^{19} -2.42740 q^{20} -2.10414 q^{22} -3.61204 q^{23} -1.67850 q^{24} +1.00000 q^{25} +8.83095 q^{26} -4.69671 q^{27} +6.70712 q^{29} +3.92725 q^{30} +4.42755 q^{31} +8.03219 q^{32} +1.86644 q^{33} +13.6769 q^{34} +1.17390 q^{36} +6.51275 q^{37} +7.24671 q^{38} -7.83335 q^{39} +0.899305 q^{40} +4.37238 q^{41} +9.77275 q^{43} +2.42740 q^{44} -0.483603 q^{45} +7.60022 q^{46} +3.08915 q^{47} -5.52940 q^{48} -2.10414 q^{50} -12.1319 q^{51} -10.1877 q^{52} +13.3676 q^{53} +9.88252 q^{54} -1.00000 q^{55} -6.42807 q^{57} -14.1127 q^{58} +8.72633 q^{59} -4.53060 q^{60} -3.73684 q^{61} -9.31619 q^{62} -10.9758 q^{64} +4.19694 q^{65} -3.92725 q^{66} -4.60749 q^{67} -15.7781 q^{68} -6.74165 q^{69} +10.4120 q^{71} -0.434907 q^{72} +6.66072 q^{73} -13.7037 q^{74} +1.86644 q^{75} -8.36002 q^{76} +16.4825 q^{78} -3.30337 q^{79} +2.96253 q^{80} -10.2169 q^{81} -9.20009 q^{82} -3.04340 q^{83} +6.50001 q^{85} -20.5632 q^{86} +12.5184 q^{87} -0.899305 q^{88} +17.4926 q^{89} +1.01757 q^{90} -8.76785 q^{92} +8.26377 q^{93} -6.50001 q^{94} +3.44403 q^{95} +14.9916 q^{96} +10.5411 q^{97} +0.483603 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.10414	−1.48785	−0.743925	−	0.668263i	$-0.767038\pi$
$2$	−2.10414	−1.48785	−0.743925	+	0.668263i	$0.767038\pi$
$3$	1.86644	1.07759	0.538795	−	0.842437i	$-0.318880\pi$
$3$	1.86644	1.07759	0.538795	+	0.842437i	$0.318880\pi$
$4$	2.42740	1.21370
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−3.92725	−1.60329
$7$	0	0
$7$	0	0
$8$	−0.899305	−0.317952
$9$	0.483603	0.161201
$10$	2.10414	0.665387
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	4.53060	1.30787
$13$	−4.19694	−1.16402	−0.582011	−	0.813181i	$-0.697734\pi$
$13$	−4.19694	−1.16402	−0.582011	+	0.813181i	$0.697734\pi$
$14$	0	0
$15$	−1.86644	−0.481913
$16$	−2.96253	−0.740634
$17$	−6.50001	−1.57648	−0.788242	−	0.615366i	$-0.789008\pi$
$17$	−6.50001	−1.57648	−0.788242	+	0.615366i	$0.789008\pi$
$18$	−1.01757	−0.239843
$19$	−3.44403	−0.790114	−0.395057	−	0.918657i	$-0.629275\pi$
$19$	−3.44403	−0.790114	−0.395057	+	0.918657i	$0.629275\pi$
$20$	−2.42740	−0.542783
$21$	0	0
$22$	−2.10414	−0.448604
$23$	−3.61204	−0.753162	−0.376581	−	0.926384i	$-0.622900\pi$
$23$	−3.61204	−0.753162	−0.376581	+	0.926384i	$0.622900\pi$
$24$	−1.67850	−0.342622
$25$	1.00000	0.200000
$26$	8.83095	1.73189
$27$	−4.69671	−0.903882
$28$	0	0
$29$	6.70712	1.24548	0.622741	−	0.782428i	$-0.286019\pi$
$29$	6.70712	1.24548	0.622741	+	0.782428i	$0.286019\pi$
$30$	3.92725	0.717015
$31$	4.42755	0.795212	0.397606	−	0.917556i	$-0.369841\pi$
$31$	4.42755	0.795212	0.397606	+	0.917556i	$0.369841\pi$
$32$	8.03219	1.41990
$33$	1.86644	0.324906
$34$	13.6769	2.34557
$35$	0	0
$36$	1.17390	0.195650
$37$	6.51275	1.07069	0.535345	−	0.844633i	$-0.320182\pi$
$37$	6.51275	1.07069	0.535345	+	0.844633i	$0.320182\pi$
$38$	7.24671	1.17557
$39$	−7.83335	−1.25434
$40$	0.899305	0.142193
$41$	4.37238	0.682851	0.341426	−	0.939909i	$-0.389090\pi$
$41$	4.37238	0.682851	0.341426	+	0.939909i	$0.389090\pi$
$42$	0	0
$43$	9.77275	1.49033	0.745165	−	0.666880i	$-0.232371\pi$
$43$	9.77275	1.49033	0.745165	+	0.666880i	$0.232371\pi$
$44$	2.42740	0.365944
$45$	−0.483603	−0.0720913
$46$	7.60022	1.12059
$47$	3.08915	0.450599	0.225300	−	0.974289i	$-0.427664\pi$
$47$	3.08915	0.450599	0.225300	+	0.974289i	$0.427664\pi$
$48$	−5.52940	−0.798100
$49$	0	0
$50$	−2.10414	−0.297570
$51$	−12.1319	−1.69880
$52$	−10.1877	−1.41277
$53$	13.3676	1.83619	0.918093	−	0.396365i	$-0.129729\pi$
$53$	13.3676	1.83619	0.918093	+	0.396365i	$0.129729\pi$
$54$	9.88252	1.34484
$55$	−1.00000	−0.134840
$56$	0	0
$57$	−6.42807	−0.851419
$58$	−14.1127	−1.85309
$59$	8.72633	1.13607	0.568036	−	0.823004i	$-0.307704\pi$
$59$	8.72633	1.13607	0.568036	+	0.823004i	$0.307704\pi$
$60$	−4.53060	−0.584897
$61$	−3.73684	−0.478453	−0.239227	−	0.970964i	$-0.576894\pi$
$61$	−3.73684	−0.478453	−0.239227	+	0.970964i	$0.576894\pi$
$62$	−9.31619	−1.18316
$63$	0	0
$64$	−10.9758	−1.37197
$65$	4.19694	0.520567
$66$	−3.92725	−0.483411
$67$	−4.60749	−0.562894	−0.281447	−	0.959577i	$-0.590814\pi$
$67$	−4.60749	−0.562894	−0.281447	+	0.959577i	$0.590814\pi$
$68$	−15.7781	−1.91338
$69$	−6.74165	−0.811600
$70$	0	0
$71$	10.4120	1.23568	0.617840	−	0.786304i	$-0.288008\pi$
$71$	10.4120	1.23568	0.617840	+	0.786304i	$0.288008\pi$
$72$	−0.434907	−0.0512543
$73$	6.66072	0.779579	0.389789	−	0.920904i	$-0.372548\pi$
$73$	6.66072	0.779579	0.389789	+	0.920904i	$0.372548\pi$
$74$	−13.7037	−1.59303
$75$	1.86644	0.215518
$76$	−8.36002	−0.958960
$77$	0	0
$78$	16.4825	1.86627
$79$	−3.30337	−0.371659	−0.185829	−	0.982582i	$-0.559497\pi$
$79$	−3.30337	−0.371659	−0.185829	+	0.982582i	$0.559497\pi$
$80$	2.96253	0.331221
$81$	−10.2169	−1.13522
$82$	−9.20009	−1.01598
$83$	−3.04340	−0.334057	−0.167029	−	0.985952i	$-0.553417\pi$
$83$	−3.04340	−0.334057	−0.167029	+	0.985952i	$0.553417\pi$
$84$	0	0
$85$	6.50001	0.705025
$86$	−20.5632	−2.21739
$87$	12.5184	1.34212
$88$	−0.899305	−0.0958662
$89$	17.4926	1.85421	0.927105	−	0.374803i	$-0.122290\pi$
$89$	17.4926	1.85421	0.927105	+	0.374803i	$0.122290\pi$
$90$	1.01757	0.107261
$91$	0	0
$92$	−8.76785	−0.914112
$93$	8.26377	0.856913
$94$	−6.50001	−0.670425
$95$	3.44403	0.353350
$96$	14.9916	1.53008
$97$	10.5411	1.07028	0.535142	−	0.844762i	$-0.320258\pi$
$97$	10.5411	1.07028	0.535142	+	0.844762i	$0.320258\pi$
$98$	0	0
$99$	0.483603	0.0486039
$100$	2.42740	0.242740
$101$	−6.67593	−0.664280	−0.332140	−	0.943230i	$-0.607771\pi$
$101$	−6.67593	−0.664280	−0.332140	+	0.943230i	$0.607771\pi$
$102$	25.5272	2.52757
$103$	5.36479	0.528609	0.264304	−	0.964439i	$-0.414858\pi$
$103$	5.36479	0.528609	0.264304	+	0.964439i	$0.414858\pi$
$104$	3.77433	0.370104
$105$	0	0
$106$	−28.1274	−2.73197
$107$	−1.23010	−0.118918	−0.0594591	−	0.998231i	$-0.518938\pi$
$107$	−1.23010	−0.118918	−0.0594591	+	0.998231i	$0.518938\pi$
$108$	−11.4008	−1.09704
$109$	−5.02522	−0.481329	−0.240664	−	0.970608i	$-0.577365\pi$
$109$	−5.02522	−0.481329	−0.240664	+	0.970608i	$0.577365\pi$
$110$	2.10414	0.200622
$111$	12.1557	1.15377
$112$	0	0
$113$	11.3073	1.06370	0.531849	−	0.846839i	$-0.321497\pi$
$113$	11.3073	1.06370	0.531849	+	0.846839i	$0.321497\pi$
$114$	13.5256	1.26678
$115$	3.61204	0.336824
$116$	16.2809	1.51164
$117$	−2.02966	−0.187642
$118$	−18.3614	−1.69030
$119$	0	0
$120$	1.67850	0.153225
$121$	1.00000	0.0909091
$122$	7.86282	0.711867
$123$	8.16079	0.735834
$124$	10.7474	0.965148
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	−9.02990	−0.801274	−0.400637	−	0.916237i	$-0.631211\pi$
$127$	−9.02990	−0.801274	−0.400637	+	0.916237i	$0.631211\pi$
$128$	7.03017	0.621385
$129$	18.2403	1.60597
$130$	−8.83095	−0.774526
$131$	3.27445	0.286090	0.143045	−	0.989716i	$-0.454311\pi$
$131$	3.27445	0.286090	0.143045	+	0.989716i	$0.454311\pi$
$132$	4.53060	0.394338
$133$	0	0
$134$	9.69479	0.837502
$135$	4.69671	0.404228
$136$	5.84549	0.501247
$137$	−18.2364	−1.55804	−0.779019	−	0.627000i	$-0.784282\pi$
$137$	−18.2364	−1.55804	−0.779019	+	0.627000i	$0.784282\pi$
$138$	14.1854	1.20754
$139$	19.9100	1.68875	0.844374	−	0.535754i	$-0.179973\pi$
$139$	19.9100	1.68875	0.844374	+	0.535754i	$0.179973\pi$
$140$	0	0
$141$	5.76573	0.485562
$142$	−21.9083	−1.83851
$143$	−4.19694	−0.350966
$144$	−1.43269	−0.119391
$145$	−6.70712	−0.556996
$146$	−14.0151	−1.15990
$147$	0	0
$148$	15.8090	1.29950
$149$	14.3715	1.17736	0.588679	−	0.808367i	$-0.299648\pi$
$149$	14.3715	1.17736	0.588679	+	0.808367i	$0.299648\pi$
$150$	−3.92725	−0.320659
$151$	−7.23141	−0.588484	−0.294242	−	0.955731i	$-0.595067\pi$
$151$	−7.23141	−0.588484	−0.294242	+	0.955731i	$0.595067\pi$
$152$	3.09723	0.251219
$153$	−3.14342	−0.254131
$154$	0	0
$155$	−4.42755	−0.355630
$156$	−19.0147	−1.52239
$157$	−20.1386	−1.60724	−0.803619	−	0.595144i	$-0.797095\pi$
$157$	−20.1386	−1.60724	−0.803619	+	0.595144i	$0.797095\pi$
$158$	6.95075	0.552972
$159$	24.9499	1.97866
$160$	−8.03219	−0.635001
$161$	0	0
$162$	21.4979	1.68903
$163$	3.09489	0.242411	0.121205	−	0.992627i	$-0.461324\pi$
$163$	3.09489	0.242411	0.121205	+	0.992627i	$0.461324\pi$
$164$	10.6135	0.828776
$165$	−1.86644	−0.145302
$166$	6.40374	0.497027
$167$	10.4324	0.807282	0.403641	−	0.914917i	$-0.367745\pi$
$167$	10.4324	0.807282	0.403641	+	0.914917i	$0.367745\pi$
$168$	0	0
$169$	4.61434	0.354949
$170$	−13.6769	−1.04897
$171$	−1.66554	−0.127367
$172$	23.7224	1.80881
$173$	−21.5289	−1.63682	−0.818408	−	0.574638i	$-0.805143\pi$
$173$	−21.5289	−1.63682	−0.818408	+	0.574638i	$0.805143\pi$
$174$	−26.3405	−1.99687
$175$	0	0
$176$	−2.96253	−0.223309
$177$	16.2872	1.22422
$178$	−36.8068	−2.75879
$179$	22.6527	1.69314	0.846571	−	0.532276i	$-0.178663\pi$
$179$	22.6527	1.69314	0.846571	+	0.532276i	$0.178663\pi$
$180$	−1.17390	−0.0874972
$181$	−5.01411	−0.372696	−0.186348	−	0.982484i	$-0.559665\pi$
$181$	−5.01411	−0.372696	−0.186348	+	0.982484i	$0.559665\pi$
$182$	0	0
$183$	−6.97459	−0.515576
$184$	3.24832	0.239470
$185$	−6.51275	−0.478827
$186$	−17.3881	−1.27496
$187$	−6.50001	−0.475328
$188$	7.49861	0.546892
$189$	0	0
$190$	−7.24671	−0.525731
$191$	19.1411	1.38500	0.692499	−	0.721419i	$-0.256510\pi$
$191$	19.1411	1.38500	0.692499	+	0.721419i	$0.256510\pi$
$192$	−20.4856	−1.47842
$193$	−20.8159	−1.49836	−0.749179	−	0.662368i	$-0.769552\pi$
$193$	−20.8159	−1.49836	−0.749179	+	0.662368i	$0.769552\pi$
$194$	−22.1799	−1.59242
$195$	7.83335	0.560958
$196$	0	0
$197$	−10.0934	−0.719125	−0.359563	−	0.933121i	$-0.617074\pi$
$197$	−10.0934	−0.719125	−0.359563	+	0.933121i	$0.617074\pi$
$198$	−1.01757	−0.0723154
$199$	−10.2188	−0.724392	−0.362196	−	0.932102i	$-0.617973\pi$
$199$	−10.2188	−0.724392	−0.362196	+	0.932102i	$0.617973\pi$
$200$	−0.899305	−0.0635905
$201$	−8.59960	−0.606569
$202$	14.0471	0.988349
$203$	0	0
$204$	−29.4489	−2.06184
$205$	−4.37238	−0.305380
$206$	−11.2883	−0.786491
$207$	−1.74679	−0.121410
$208$	12.4336	0.862114
$209$	−3.44403	−0.238228
$210$	0	0
$211$	−3.54668	−0.244164	−0.122082	−	0.992520i	$-0.538957\pi$
$211$	−3.54668	−0.244164	−0.122082	+	0.992520i	$0.538957\pi$
$212$	32.4486	2.22858
$213$	19.4334	1.33156
$214$	2.58830	0.176932
$215$	−9.77275	−0.666496
$216$	4.22377	0.287391
$217$	0	0
$218$	10.5738	0.716145
$219$	12.4318	0.840066
$220$	−2.42740	−0.163655
$221$	27.2802	1.83506
$222$	−25.5772	−1.71663
$223$	−9.79279	−0.655774	−0.327887	−	0.944717i	$-0.606337\pi$
$223$	−9.79279	−0.655774	−0.327887	+	0.944717i	$0.606337\pi$
$224$	0	0
$225$	0.483603	0.0322402
$226$	−23.7921	−1.58262
$227$	−12.6460	−0.839347	−0.419673	−	0.907675i	$-0.637855\pi$
$227$	−12.6460	−0.839347	−0.419673	+	0.907675i	$0.637855\pi$
$228$	−15.6035	−1.03337
$229$	12.9349	0.854765	0.427383	−	0.904071i	$-0.359436\pi$
$229$	12.9349	0.854765	0.427383	+	0.904071i	$0.359436\pi$
$230$	−7.60022	−0.501144
$231$	0	0
$232$	−6.03175	−0.396004
$233$	14.3727	0.941589	0.470795	−	0.882243i	$-0.343967\pi$
$233$	14.3727	0.941589	0.470795	+	0.882243i	$0.343967\pi$
$234$	4.27068	0.279183
$235$	−3.08915	−0.201514
$236$	21.1823	1.37885
$237$	−6.16555	−0.400496
$238$	0	0
$239$	−1.79879	−0.116354	−0.0581769	−	0.998306i	$-0.518529\pi$
$239$	−1.79879	−0.116354	−0.0581769	+	0.998306i	$0.518529\pi$
$240$	5.52940	0.356921
$241$	−8.07730	−0.520305	−0.260152	−	0.965568i	$-0.583773\pi$
$241$	−8.07730	−0.520305	−0.260152	+	0.965568i	$0.583773\pi$
$242$	−2.10414	−0.135259
$243$	−4.97919	−0.319415
$244$	−9.07079	−0.580698
$245$	0	0
$246$	−17.1714	−1.09481
$247$	14.4544	0.919710
$248$	−3.98172	−0.252840
$249$	−5.68034	−0.359977
$250$	2.10414	0.133077
$251$	−12.1815	−0.768889	−0.384444	−	0.923148i	$-0.625607\pi$
$251$	−12.1815	−0.768889	−0.384444	+	0.923148i	$0.625607\pi$
$252$	0	0
$253$	−3.61204	−0.227087
$254$	19.0002	1.19218
$255$	12.1319	0.759728
$256$	7.15911	0.447444
$257$	−21.4894	−1.34047	−0.670235	−	0.742149i	$-0.733807\pi$
$257$	−21.4894	−1.34047	−0.670235	+	0.742149i	$0.733807\pi$
$258$	−38.3800	−2.38944
$259$	0	0
$260$	10.1877	0.631811
$261$	3.24359	0.200773
$262$	−6.88990	−0.425660
$263$	20.0262	1.23487	0.617433	−	0.786623i	$-0.288173\pi$
$263$	20.0262	1.23487	0.617433	+	0.786623i	$0.288173\pi$
$264$	−1.67850	−0.103305
$265$	−13.3676	−0.821167
$266$	0	0
$267$	32.6489	1.99808
$268$	−11.1842	−0.683184
$269$	19.0089	1.15899	0.579497	−	0.814974i	$-0.303249\pi$
$269$	19.0089	1.15899	0.579497	+	0.814974i	$0.303249\pi$
$270$	−9.88252	−0.601431
$271$	−7.42832	−0.451238	−0.225619	−	0.974216i	$-0.572440\pi$
$271$	−7.42832	−0.451238	−0.225619	+	0.974216i	$0.572440\pi$
$272$	19.2565	1.16760
$273$	0	0
$274$	38.3718	2.31813
$275$	1.00000	0.0603023
$276$	−16.3647	−0.985038
$277$	19.5903	1.17707	0.588534	−	0.808472i	$-0.299705\pi$
$277$	19.5903	1.17707	0.588534	+	0.808472i	$0.299705\pi$
$278$	−41.8935	−2.51260
$279$	2.14118	0.128189
$280$	0	0
$281$	1.86618	0.111327	0.0556634	−	0.998450i	$-0.482273\pi$
$281$	1.86618	0.111327	0.0556634	+	0.998450i	$0.482273\pi$
$282$	−12.1319	−0.722443
$283$	−1.43767	−0.0854607	−0.0427304	−	0.999087i	$-0.513606\pi$
$283$	−1.43767	−0.0854607	−0.0427304	+	0.999087i	$0.513606\pi$
$284$	25.2741	1.49974
$285$	6.42807	0.380766
$286$	8.83095	0.522185
$287$	0	0
$288$	3.88439	0.228890
$289$	25.2501	1.48530
$290$	14.1127	0.828727
$291$	19.6743	1.15333
$292$	16.1682	0.946174
$293$	−9.40155	−0.549244	−0.274622	−	0.961552i	$-0.588553\pi$
$293$	−9.40155	−0.549244	−0.274622	+	0.961552i	$0.588553\pi$
$294$	0	0
$295$	−8.72633	−0.508067
$296$	−5.85695	−0.340428
$297$	−4.69671	−0.272531
$298$	−30.2396	−1.75173
$299$	15.1595	0.876697
$300$	4.53060	0.261574
$301$	0	0
$302$	15.2159	0.875576
$303$	−12.4602	−0.715821
$304$	10.2030	0.585185
$305$	3.73684	0.213971
$306$	6.61420	0.378109
$307$	3.47734	0.198462	0.0992312	−	0.995064i	$-0.468362\pi$
$307$	3.47734	0.198462	0.0992312	+	0.995064i	$0.468362\pi$
$308$	0	0
$309$	10.0131	0.569624
$310$	9.31619	0.529124
$311$	8.24409	0.467479	0.233740	−	0.972299i	$-0.424904\pi$
$311$	8.24409	0.467479	0.233740	+	0.972299i	$0.424904\pi$
$312$	7.04457	0.398820
$313$	−18.5229	−1.04698	−0.523488	−	0.852033i	$-0.675369\pi$
$313$	−18.5229	−1.04698	−0.523488	+	0.852033i	$0.675369\pi$
$314$	42.3745	2.39133
$315$	0	0
$316$	−8.01860	−0.451082
$317$	−5.65053	−0.317366	−0.158683	−	0.987330i	$-0.550725\pi$
$317$	−5.65053	−0.317366	−0.158683	+	0.987330i	$0.550725\pi$
$318$	−52.4980	−2.94394
$319$	6.70712	0.375527
$320$	10.9758	0.613564
$321$	−2.29591	−0.128145
$322$	0	0
$323$	22.3862	1.24560
$324$	−24.8006	−1.37781
$325$	−4.19694	−0.232805
$326$	−6.51208	−0.360671
$327$	−9.37928	−0.518675
$328$	−3.93210	−0.217114
$329$	0	0
$330$	3.92725	0.216188
$331$	−6.42845	−0.353339	−0.176670	−	0.984270i	$-0.556532\pi$
$331$	−6.42845	−0.353339	−0.176670	+	0.984270i	$0.556532\pi$
$332$	−7.38756	−0.405445
$333$	3.14959	0.172596
$334$	−21.9512	−1.20111
$335$	4.60749	0.251734
$336$	0	0
$337$	−10.2967	−0.560896	−0.280448	−	0.959869i	$-0.590483\pi$
$337$	−10.2967	−0.560896	−0.280448	+	0.959869i	$0.590483\pi$
$338$	−9.70920	−0.528111
$339$	21.1044	1.14623
$340$	15.7781	0.855688
$341$	4.42755	0.239766
$342$	3.50453	0.189503
$343$	0	0
$344$	−8.78868	−0.473854
$345$	6.74165	0.362958
$346$	45.2999	2.43534
$347$	17.3638	0.932138	0.466069	−	0.884748i	$-0.345670\pi$
$347$	17.3638	0.932138	0.466069	+	0.884748i	$0.345670\pi$
$348$	30.3873	1.62893
$349$	31.7306	1.69850	0.849249	−	0.527993i	$-0.177055\pi$
$349$	31.7306	1.69850	0.849249	+	0.527993i	$0.177055\pi$
$350$	0	0
$351$	19.7118	1.05214
$352$	8.03219	0.428117
$353$	−2.16658	−0.115315	−0.0576577	−	0.998336i	$-0.518363\pi$
$353$	−2.16658	−0.115315	−0.0576577	+	0.998336i	$0.518363\pi$
$354$	−34.2705	−1.82146
$355$	−10.4120	−0.552613
$356$	42.4614	2.25045
$357$	0	0
$358$	−47.6644	−2.51914
$359$	11.2739	0.595014	0.297507	−	0.954720i	$-0.403845\pi$
$359$	11.2739	0.595014	0.297507	+	0.954720i	$0.403845\pi$
$360$	0.434907	0.0229216
$361$	−7.13868	−0.375720
$362$	10.5504	0.554516
$363$	1.86644	0.0979628
$364$	0	0
$365$	−6.66072	−0.348638
$366$	14.6755	0.767101
$367$	33.7930	1.76398	0.881989	−	0.471270i	$-0.156204\pi$
$367$	33.7930	1.76398	0.881989	+	0.471270i	$0.156204\pi$
$368$	10.7008	0.557817
$369$	2.11450	0.110076
$370$	13.7037	0.712423
$371$	0	0
$372$	20.0595	1.04003
$373$	−13.0934	−0.677951	−0.338976	−	0.940795i	$-0.610080\pi$
$373$	−13.0934	−0.677951	−0.338976	+	0.940795i	$0.610080\pi$
$374$	13.6769	0.707217
$375$	−1.86644	−0.0963826
$376$	−2.77809	−0.143269
$377$	−28.1494	−1.44977
$378$	0	0
$379$	−18.7657	−0.963928	−0.481964	−	0.876191i	$-0.660076\pi$
$379$	−18.7657	−0.963928	−0.481964	+	0.876191i	$0.660076\pi$
$380$	8.36002	0.428860
$381$	−16.8538	−0.863445
$382$	−40.2754	−2.06067
$383$	2.11251	0.107944	0.0539722	−	0.998542i	$-0.482812\pi$
$383$	2.11251	0.107944	0.0539722	+	0.998542i	$0.482812\pi$
$384$	13.1214	0.669598
$385$	0	0
$386$	43.7994	2.22933
$387$	4.72613	0.240243
$388$	25.5874	1.29900
$389$	28.8121	1.46083	0.730415	−	0.683004i	$-0.239327\pi$
$389$	28.8121	1.46083	0.730415	+	0.683004i	$0.239327\pi$
$390$	−16.4825	−0.834621
$391$	23.4783	1.18735
$392$	0	0
$393$	6.11158	0.308288
$394$	21.2379	1.06995
$395$	3.30337	0.166211
$396$	1.17390	0.0589906
$397$	−8.23798	−0.413452	−0.206726	−	0.978399i	$-0.566281\pi$
$397$	−8.23798	−0.413452	−0.206726	+	0.978399i	$0.566281\pi$
$398$	21.5018	1.07779
$399$	0	0
$400$	−2.96253	−0.148127
$401$	24.9519	1.24604	0.623019	−	0.782207i	$-0.285906\pi$
$401$	24.9519	1.24604	0.623019	+	0.782207i	$0.285906\pi$
$402$	18.0948	0.902484
$403$	−18.5822	−0.925645
$404$	−16.2051	−0.806235
$405$	10.2169	0.507684
$406$	0	0
$407$	6.51275	0.322825
$408$	10.9103	0.540139
$409$	−22.6563	−1.12028	−0.560140	−	0.828398i	$-0.689253\pi$
$409$	−22.6563	−1.12028	−0.560140	+	0.828398i	$0.689253\pi$
$410$	9.20009	0.454360
$411$	−34.0371	−1.67893
$412$	13.0225	0.641572
$413$	0	0
$414$	3.67549	0.180641
$415$	3.04340	0.149395
$416$	−33.7107	−1.65280
$417$	37.1609	1.81978
$418$	7.24671	0.354448
$419$	35.1034	1.71491	0.857456	−	0.514558i	$-0.172044\pi$
$419$	35.1034	1.71491	0.857456	+	0.514558i	$0.172044\pi$
$420$	0	0
$421$	14.4014	0.701882	0.350941	−	0.936398i	$-0.385862\pi$
$421$	14.4014	0.701882	0.350941	+	0.936398i	$0.385862\pi$
$422$	7.46272	0.363279
$423$	1.49392	0.0726371
$424$	−12.0216	−0.583820
$425$	−6.50001	−0.315297
$426$	−40.8906	−1.98116
$427$	0	0
$428$	−2.98594	−0.144331
$429$	−7.83335	−0.378198
$430$	20.5632	0.991646
$431$	−16.6205	−0.800580	−0.400290	−	0.916388i	$-0.631091\pi$
$431$	−16.6205	−0.800580	−0.400290	+	0.916388i	$0.631091\pi$
$432$	13.9142	0.669445
$433$	−5.53993	−0.266232	−0.133116	−	0.991100i	$-0.542498\pi$
$433$	−5.53993	−0.266232	−0.133116	+	0.991100i	$0.542498\pi$
$434$	0	0
$435$	−12.5184	−0.600214
$436$	−12.1982	−0.584188
$437$	12.4399	0.595083
$438$	−26.1583	−1.24989
$439$	−30.2632	−1.44438	−0.722192	−	0.691693i	$-0.756865\pi$
$439$	−30.2632	−1.44438	−0.722192	+	0.691693i	$0.756865\pi$
$440$	0.899305	0.0428727
$441$	0	0
$442$	−57.4013	−2.73030
$443$	35.5792	1.69042	0.845209	−	0.534436i	$-0.179476\pi$
$443$	35.5792	1.69042	0.845209	+	0.534436i	$0.179476\pi$
$444$	29.5067	1.40032
$445$	−17.4926	−0.829228
$446$	20.6054	0.975693
$447$	26.8235	1.26871
$448$	0	0
$449$	−7.82372	−0.369224	−0.184612	−	0.982811i	$-0.559103\pi$
$449$	−7.82372	−0.369224	−0.184612	+	0.982811i	$0.559103\pi$
$450$	−1.01757	−0.0479686
$451$	4.37238	0.205887
$452$	27.4472	1.29101
$453$	−13.4970	−0.634144
$454$	26.6090	1.24882
$455$	0	0
$456$	5.78080	0.270711
$457$	−12.2840	−0.574619	−0.287310	−	0.957838i	$-0.592761\pi$
$457$	−12.2840	−0.574619	−0.287310	+	0.957838i	$0.592761\pi$
$458$	−27.2169	−1.27176
$459$	30.5286	1.42495
$460$	8.76785	0.408803
$461$	11.3217	0.527306	0.263653	−	0.964618i	$-0.415073\pi$
$461$	11.3217	0.527306	0.263653	+	0.964618i	$0.415073\pi$
$462$	0	0
$463$	−8.43729	−0.392114	−0.196057	−	0.980592i	$-0.562814\pi$
$463$	−8.43729	−0.392114	−0.196057	+	0.980592i	$0.562814\pi$
$464$	−19.8701	−0.922445
$465$	−8.26377	−0.383223
$466$	−30.2422	−1.40094
$467$	20.2878	0.938807	0.469404	−	0.882984i	$-0.344469\pi$
$467$	20.2878	0.938807	0.469404	+	0.882984i	$0.344469\pi$
$468$	−4.92678	−0.227741
$469$	0	0
$470$	6.50001	0.299823
$471$	−37.5876	−1.73194
$472$	−7.84763	−0.361217
$473$	9.77275	0.449352
$474$	12.9732	0.595878
$475$	−3.44403	−0.158023
$476$	0	0
$477$	6.46463	0.295995
$478$	3.78489	0.173117
$479$	−0.211909	−0.00968235	−0.00484117	−	0.999988i	$-0.501541\pi$
$479$	−0.211909	−0.00968235	−0.00484117	+	0.999988i	$0.501541\pi$
$480$	−14.9916	−0.684270
$481$	−27.3337	−1.24631
$482$	16.9958	0.774136
$483$	0	0
$484$	2.42740	0.110336
$485$	−10.5411	−0.478646
$486$	10.4769	0.475242
$487$	−6.42265	−0.291038	−0.145519	−	0.989355i	$-0.546485\pi$
$487$	−6.42265	−0.291038	−0.145519	+	0.989355i	$0.546485\pi$
$488$	3.36056	0.152125
$489$	5.77643	0.261219
$490$	0	0
$491$	2.10815	0.0951396	0.0475698	−	0.998868i	$-0.484852\pi$
$491$	2.10815	0.0951396	0.0475698	+	0.998868i	$0.484852\pi$
$492$	19.8095	0.893081
$493$	−43.5963	−1.96348
$494$	−30.4140	−1.36839
$495$	−0.483603	−0.0217363
$496$	−13.1168	−0.588961
$497$	0	0
$498$	11.9522	0.535591
$499$	3.16574	0.141718	0.0708590	−	0.997486i	$-0.477426\pi$
$499$	3.16574	0.141718	0.0708590	+	0.997486i	$0.477426\pi$
$500$	−2.42740	−0.108557
$501$	19.4714	0.869919
$502$	25.6315	1.14399
$503$	−22.2628	−0.992647	−0.496324	−	0.868138i	$-0.665317\pi$
$503$	−22.2628	−0.992647	−0.496324	+	0.868138i	$0.665317\pi$
$504$	0	0
$505$	6.67593	0.297075
$506$	7.60022	0.337871
$507$	8.61239	0.382490
$508$	−21.9192	−0.972506
$509$	−19.3466	−0.857524	−0.428762	−	0.903418i	$-0.641050\pi$
$509$	−19.3466	−0.857524	−0.428762	+	0.903418i	$0.641050\pi$
$510$	−25.5272	−1.13036
$511$	0	0
$512$	−29.1241	−1.28712
$513$	16.1756	0.714169
$514$	45.2166	1.99442
$515$	−5.36479	−0.236401
$516$	44.2764	1.94916
$517$	3.08915	0.135861
$518$	0	0
$519$	−40.1825	−1.76382
$520$	−3.77433	−0.165515
$521$	19.5682	0.857297	0.428648	−	0.903471i	$-0.358990\pi$
$521$	19.5682	0.857297	0.428648	+	0.903471i	$0.358990\pi$
$522$	−6.82495	−0.298720
$523$	8.19390	0.358294	0.179147	−	0.983822i	$-0.442666\pi$
$523$	8.19390	0.358294	0.179147	+	0.983822i	$0.442666\pi$
$524$	7.94840	0.347228
$525$	0	0
$526$	−42.1378	−1.83730
$527$	−28.7791	−1.25364
$528$	−5.52940	−0.240636
$529$	−9.95319	−0.432748
$530$	28.1274	1.22177
$531$	4.22008	0.183136
$532$	0	0
$533$	−18.3506	−0.794854
$534$	−68.6977	−2.97284
$535$	1.23010	0.0531818
$536$	4.14354	0.178973
$537$	42.2799	1.82451
$538$	−39.9974	−1.72441
$539$	0	0
$540$	11.4008	0.490611
$541$	33.7105	1.44933	0.724663	−	0.689104i	$-0.241996\pi$
$541$	33.7105	1.44933	0.724663	+	0.689104i	$0.241996\pi$
$542$	15.6302	0.671375
$543$	−9.35854	−0.401613
$544$	−52.2093	−2.23846
$545$	5.02522	0.215257
$546$	0	0
$547$	2.68593	0.114842	0.0574211	−	0.998350i	$-0.481712\pi$
$547$	2.68593	0.114842	0.0574211	+	0.998350i	$0.481712\pi$
$548$	−44.2669	−1.89099
$549$	−1.80715	−0.0771271
$550$	−2.10414	−0.0897208
$551$	−23.0995	−0.984072
$552$	6.06280	0.258050
$553$	0	0
$554$	−41.2207	−1.75130
$555$	−12.1557	−0.515980
$556$	48.3296	2.04963
$557$	−43.5467	−1.84513	−0.922566	−	0.385839i	$-0.873912\pi$
$557$	−43.5467	−1.84513	−0.922566	+	0.385839i	$0.873912\pi$
$558$	−4.50534	−0.190726
$559$	−41.0157	−1.73478
$560$	0	0
$561$	−12.1319	−0.512209
$562$	−3.92670	−0.165638
$563$	−13.4436	−0.566580	−0.283290	−	0.959034i	$-0.591426\pi$
$563$	−13.4436	−0.566580	−0.283290	+	0.959034i	$0.591426\pi$
$564$	13.9957	0.589326
$565$	−11.3073	−0.475700
$566$	3.02506	0.127153
$567$	0	0
$568$	−9.36358	−0.392887
$569$	28.2879	1.18589	0.592945	−	0.805243i	$-0.297965\pi$
$569$	28.2879	1.18589	0.592945	+	0.805243i	$0.297965\pi$
$570$	−13.5256	−0.566523
$571$	4.79859	0.200815	0.100407	−	0.994946i	$-0.467985\pi$
$571$	4.79859	0.200815	0.100407	+	0.994946i	$0.467985\pi$
$572$	−10.1877	−0.425967
$573$	35.7257	1.49246
$574$	0	0
$575$	−3.61204	−0.150632
$576$	−5.30792	−0.221163
$577$	43.3120	1.80310	0.901552	−	0.432671i	$-0.142429\pi$
$577$	43.3120	1.80310	0.901552	+	0.432671i	$0.142429\pi$
$578$	−53.1297	−2.20991
$579$	−38.8516	−1.61462
$580$	−16.2809	−0.676026
$581$	0	0
$582$	−41.3975	−1.71598
$583$	13.3676	0.553631
$584$	−5.99002	−0.247869
$585$	2.02966	0.0839159
$586$	19.7822	0.817194
$587$	−33.7995	−1.39506	−0.697528	−	0.716558i	$-0.745717\pi$
$587$	−33.7995	−1.39506	−0.697528	+	0.716558i	$0.745717\pi$
$588$	0	0
$589$	−15.2486	−0.628308
$590$	18.3614	0.755927
$591$	−18.8387	−0.774923
$592$	−19.2943	−0.792989
$593$	34.4021	1.41272	0.706362	−	0.707851i	$-0.250335\pi$
$593$	34.4021	1.41272	0.706362	+	0.707851i	$0.250335\pi$
$594$	9.88252	0.405485
$595$	0	0
$596$	34.8853	1.42896
$597$	−19.0728	−0.780598
$598$	−31.8977	−1.30439
$599$	−30.8397	−1.26008	−0.630039	−	0.776564i	$-0.716961\pi$
$599$	−30.8397	−1.26008	−0.630039	+	0.776564i	$0.716961\pi$
$600$	−1.67850	−0.0685245
$601$	−24.5546	−1.00160	−0.500801	−	0.865563i	$-0.666961\pi$
$601$	−24.5546	−1.00160	−0.500801	+	0.865563i	$0.666961\pi$
$602$	0	0
$603$	−2.22819	−0.0907391
$604$	−17.5535	−0.714242
$605$	−1.00000	−0.0406558
$606$	26.2180	1.06503
$607$	36.7968	1.49354	0.746769	−	0.665084i	$-0.231604\pi$
$607$	36.7968	1.49354	0.746769	+	0.665084i	$0.231604\pi$
$608$	−27.6631	−1.12189
$609$	0	0
$610$	−7.86282	−0.318356
$611$	−12.9650	−0.524508
$612$	−7.63034	−0.308438
$613$	46.7911	1.88988	0.944938	−	0.327250i	$-0.106122\pi$
$613$	46.7911	1.88988	0.944938	+	0.327250i	$0.106122\pi$
$614$	−7.31681	−0.295282
$615$	−8.16079	−0.329075
$616$	0	0
$617$	−14.4526	−0.581838	−0.290919	−	0.956748i	$-0.593961\pi$
$617$	−14.4526	−0.581838	−0.290919	+	0.956748i	$0.593961\pi$
$618$	−21.0689	−0.847515
$619$	−9.82899	−0.395061	−0.197530	−	0.980297i	$-0.563292\pi$
$619$	−9.82899	−0.395061	−0.197530	+	0.980297i	$0.563292\pi$
$620$	−10.7474	−0.431627
$621$	16.9647	0.680769
$622$	−17.3467	−0.695539
$623$	0	0
$624$	23.2066	0.929006
$625$	1.00000	0.0400000
$626$	38.9747	1.55774
$627$	−6.42807	−0.256712
$628$	−48.8845	−1.95070
$629$	−42.3330	−1.68793
$630$	0	0
$631$	0.300251	0.0119528	0.00597639	−	0.999982i	$-0.498098\pi$
$631$	0.300251	0.0119528	0.00597639	+	0.999982i	$0.498098\pi$
$632$	2.97074	0.118170
$633$	−6.61968	−0.263109
$634$	11.8895	0.472193
$635$	9.02990	0.358341
$636$	60.5634	2.40149
$637$	0	0
$638$	−14.1127	−0.558728
$639$	5.03528	0.199193
$640$	−7.03017	−0.277892
$641$	42.3064	1.67100	0.835501	−	0.549489i	$-0.185178\pi$
$641$	42.3064	1.67100	0.835501	+	0.549489i	$0.185178\pi$
$642$	4.83091	0.190661
$643$	39.1601	1.54433	0.772163	−	0.635425i	$-0.219175\pi$
$643$	39.1601	1.54433	0.772163	+	0.635425i	$0.219175\pi$
$644$	0	0
$645$	−18.2403	−0.718210
$646$	−47.1037	−1.85327
$647$	−30.5041	−1.19924	−0.599620	−	0.800285i	$-0.704682\pi$
$647$	−30.5041	−1.19924	−0.599620	+	0.800285i	$0.704682\pi$
$648$	9.18814	0.360944
$649$	8.72633	0.342538
$650$	8.83095	0.346378
$651$	0	0
$652$	7.51254	0.294214
$653$	−39.1077	−1.53040	−0.765200	−	0.643792i	$-0.777360\pi$
$653$	−39.1077	−1.53040	−0.765200	+	0.643792i	$0.777360\pi$
$654$	19.7353	0.771711
$655$	−3.27445	−0.127943
$656$	−12.9533	−0.505742
$657$	3.22115	0.125669
$658$	0	0
$659$	19.0063	0.740379	0.370189	−	0.928956i	$-0.379293\pi$
$659$	19.0063	0.740379	0.370189	+	0.928956i	$0.379293\pi$
$660$	−4.53060	−0.176353
$661$	8.57854	0.333667	0.166833	−	0.985985i	$-0.446646\pi$
$661$	8.57854	0.333667	0.166833	+	0.985985i	$0.446646\pi$
$662$	13.5263	0.525716
$663$	50.9168	1.97745
$664$	2.73695	0.106214
$665$	0	0
$666$	−6.62717	−0.256798
$667$	−24.2264	−0.938049
$668$	25.3235	0.979797
$669$	−18.2777	−0.706656
$670$	−9.69479	−0.374542
$671$	−3.73684	−0.144259
$672$	0	0
$673$	37.5047	1.44570	0.722850	−	0.691005i	$-0.242832\pi$
$673$	37.5047	1.44570	0.722850	+	0.691005i	$0.242832\pi$
$674$	21.6657	0.834530
$675$	−4.69671	−0.180776
$676$	11.2008	0.430801
$677$	5.31174	0.204147	0.102073	−	0.994777i	$-0.467452\pi$
$677$	5.31174	0.204147	0.102073	+	0.994777i	$0.467452\pi$
$678$	−44.4065	−1.70542
$679$	0	0
$680$	−5.84549	−0.224164
$681$	−23.6031	−0.904472
$682$	−9.31619	−0.356735
$683$	−11.3094	−0.432743	−0.216372	−	0.976311i	$-0.569422\pi$
$683$	−11.3094	−0.432743	−0.216372	+	0.976311i	$0.569422\pi$
$684$	−4.04293	−0.154585
$685$	18.2364	0.696776
$686$	0	0
$687$	24.1423	0.921087
$688$	−28.9521	−1.10379
$689$	−56.1032	−2.13736
$690$	−14.1854	−0.540028
$691$	−12.3698	−0.470569	−0.235284	−	0.971927i	$-0.575602\pi$
$691$	−12.3698	−0.470569	−0.235284	+	0.971927i	$0.575602\pi$
$692$	−52.2593	−1.98660
$693$	0	0
$694$	−36.5359	−1.38688
$695$	−19.9100	−0.755231
$696$	−11.2579	−0.426730
$697$	−28.4205	−1.07650
$698$	−66.7655	−2.52711
$699$	26.8259	1.01465
$700$	0	0
$701$	−25.8456	−0.976173	−0.488086	−	0.872795i	$-0.662305\pi$
$701$	−25.8456	−0.976173	−0.488086	+	0.872795i	$0.662305\pi$
$702$	−41.4764	−1.56543
$703$	−22.4301	−0.845967
$704$	−10.9758	−0.413665
$705$	−5.76573	−0.217150
$706$	4.55879	0.171572
$707$	0	0
$708$	39.5355	1.48583
$709$	−19.3602	−0.727087	−0.363544	−	0.931577i	$-0.618433\pi$
$709$	−19.3602	−0.727087	−0.363544	+	0.931577i	$0.618433\pi$
$710$	21.9083	0.822205
$711$	−1.59752	−0.0599117
$712$	−15.7312	−0.589550
$713$	−15.9925	−0.598923
$714$	0	0
$715$	4.19694	0.156957
$716$	54.9871	2.05497
$717$	−3.35733	−0.125382
$718$	−23.7218	−0.885291
$719$	38.1292	1.42198	0.710990	−	0.703202i	$-0.248247\pi$
$719$	38.1292	1.42198	0.710990	+	0.703202i	$0.248247\pi$
$720$	1.43269	0.0533932
$721$	0	0
$722$	15.0208	0.559016
$723$	−15.0758	−0.560675
$724$	−12.1712	−0.452340
$725$	6.70712	0.249096
$726$	−3.92725	−0.145754
$727$	9.77825	0.362655	0.181328	−	0.983423i	$-0.441961\pi$
$727$	9.77825	0.362655	0.181328	+	0.983423i	$0.441961\pi$
$728$	0	0
$729$	21.3574	0.791016
$730$	14.0151	0.518721
$731$	−63.5230	−2.34948
$732$	−16.9301	−0.625755
$733$	−32.4579	−1.19886	−0.599430	−	0.800427i	$-0.704606\pi$
$733$	−32.4579	−1.19886	−0.599430	+	0.800427i	$0.704606\pi$
$734$	−71.1051	−2.62454
$735$	0	0
$736$	−29.0126	−1.06942
$737$	−4.60749	−0.169719
$738$	−4.44919	−0.163777
$739$	−34.2474	−1.25981	−0.629906	−	0.776671i	$-0.716907\pi$
$739$	−34.2474	−1.25981	−0.629906	+	0.776671i	$0.716907\pi$
$740$	−15.8090	−0.581152
$741$	26.9783	0.991071
$742$	0	0
$743$	8.51091	0.312235	0.156118	−	0.987738i	$-0.450102\pi$
$743$	8.51091	0.312235	0.156118	+	0.987738i	$0.450102\pi$
$744$	−7.43165	−0.272458
$745$	−14.3715	−0.526530
$746$	27.5504	1.00869
$747$	−1.47180	−0.0538504
$748$	−15.7781	−0.576905
$749$	0	0
$750$	3.92725	0.143403
$751$	14.8113	0.540473	0.270236	−	0.962794i	$-0.412898\pi$
$751$	14.8113	0.540473	0.270236	+	0.962794i	$0.412898\pi$
$752$	−9.15173	−0.333729
$753$	−22.7360	−0.828547
$754$	59.2303	2.15704
$755$	7.23141	0.263178
$756$	0	0
$757$	30.7959	1.11930	0.559648	−	0.828730i	$-0.310936\pi$
$757$	30.7959	1.11930	0.559648	+	0.828730i	$0.310936\pi$
$758$	39.4856	1.43418
$759$	−6.74165	−0.244707
$760$	−3.09723	−0.112348
$761$	12.0178	0.435645	0.217823	−	0.975988i	$-0.430105\pi$
$761$	12.0178	0.435645	0.217823	+	0.975988i	$0.430105\pi$
$762$	35.4627	1.28468
$763$	0	0
$764$	46.4630	1.68097
$765$	3.14342	0.113651
$766$	−4.44502	−0.160605
$767$	−36.6239	−1.32241
$768$	13.3621	0.482162
$769$	35.9200	1.29531	0.647654	−	0.761935i	$-0.275750\pi$
$769$	35.9200	1.29531	0.647654	+	0.761935i	$0.275750\pi$
$770$	0	0
$771$	−40.1086	−1.44448
$772$	−50.5284	−1.81856
$773$	26.4220	0.950334	0.475167	−	0.879896i	$-0.342388\pi$
$773$	26.4220	0.950334	0.475167	+	0.879896i	$0.342388\pi$
$774$	−9.94444	−0.357445
$775$	4.42755	0.159042
$776$	−9.47965	−0.340299
$777$	0	0
$778$	−60.6246	−2.17350
$779$	−15.0586	−0.539530
$780$	19.0147	0.680834
$781$	10.4120	0.372571
$782$	−49.4015	−1.76659
$783$	−31.5014	−1.12577
$784$	0	0
$785$	20.1386	0.718779
$786$	−12.8596	−0.458687
$787$	−21.8039	−0.777224	−0.388612	−	0.921402i	$-0.627045\pi$
$787$	−21.8039	−0.777224	−0.388612	+	0.921402i	$0.627045\pi$
$788$	−24.5007	−0.872802
$789$	37.3777	1.33068
$790$	−6.95075	−0.247297
$791$	0	0
$792$	−0.434907	−0.0154537
$793$	15.6833	0.556930
$794$	17.3338	0.615155
$795$	−24.9499	−0.884882
$796$	−24.8051	−0.879194
$797$	−50.2248	−1.77905	−0.889527	−	0.456883i	$-0.848966\pi$
$797$	−50.2248	−1.77905	−0.889527	+	0.456883i	$0.848966\pi$
$798$	0	0
$799$	−20.0795	−0.710363
$800$	8.03219	0.283981
$801$	8.45947	0.298901
$802$	−52.5022	−1.85392
$803$	6.66072	0.235052
$804$	−20.8747	−0.736192
$805$	0	0
$806$	39.0995	1.37722
$807$	35.4790	1.24892
$808$	6.00369	0.211209
$809$	9.28287	0.326368	0.163184	−	0.986596i	$-0.447824\pi$
$809$	9.28287	0.326368	0.163184	+	0.986596i	$0.447824\pi$
$810$	−21.4979	−0.755357
$811$	20.8961	0.733763	0.366881	−	0.930268i	$-0.380425\pi$
$811$	20.8961	0.733763	0.366881	+	0.930268i	$0.380425\pi$
$812$	0	0
$813$	−13.8645	−0.486250
$814$	−13.7037	−0.480316
$815$	−3.09489	−0.108409
$816$	35.9411	1.25819
$817$	−33.6576	−1.17753
$818$	47.6719	1.66681
$819$	0	0
$820$	−10.6135	−0.370640
$821$	34.6170	1.20814	0.604070	−	0.796931i	$-0.293545\pi$
$821$	34.6170	1.20814	0.604070	+	0.796931i	$0.293545\pi$
$822$	71.6188	2.49799
$823$	−26.0278	−0.907272	−0.453636	−	0.891187i	$-0.649873\pi$
$823$	−26.0278	−0.907272	−0.453636	+	0.891187i	$0.649873\pi$
$824$	−4.82458	−0.168072
$825$	1.86644	0.0649811
$826$	0	0
$827$	52.2977	1.81857	0.909284	−	0.416176i	$-0.136630\pi$
$827$	52.2977	1.81857	0.909284	+	0.416176i	$0.136630\pi$
$828$	−4.24016	−0.147356
$829$	7.57959	0.263250	0.131625	−	0.991300i	$-0.457981\pi$
$829$	7.57959	0.263250	0.131625	+	0.991300i	$0.457981\pi$
$830$	−6.40374	−0.222277
$831$	36.5642	1.26840
$832$	46.0647	1.59701
$833$	0	0
$834$	−78.1917	−2.70756
$835$	−10.4324	−0.361027
$836$	−8.36002	−0.289137
$837$	−20.7949	−0.718778
$838$	−73.8623	−2.55153
$839$	−37.0706	−1.27982	−0.639910	−	0.768450i	$-0.721028\pi$
$839$	−37.0706	−1.27982	−0.639910	+	0.768450i	$0.721028\pi$
$840$	0	0
$841$	15.9855	0.551224
$842$	−30.3026	−1.04430
$843$	3.48311	0.119965
$844$	−8.60922	−0.296341
$845$	−4.61434	−0.158738
$846$	−3.14342	−0.108073
$847$	0	0
$848$	−39.6021	−1.35994
$849$	−2.68333	−0.0920916
$850$	13.6769	0.469114
$851$	−23.5243	−0.806403
$852$	47.1726	1.61611
$853$	−5.00166	−0.171253	−0.0856267	−	0.996327i	$-0.527289\pi$
$853$	−5.00166	−0.171253	−0.0856267	+	0.996327i	$0.527289\pi$
$854$	0	0
$855$	1.66554	0.0569603
$856$	1.10623	0.0378103
$857$	50.2512	1.71655	0.858273	−	0.513193i	$-0.171537\pi$
$857$	50.2512	1.71655	0.858273	+	0.513193i	$0.171537\pi$
$858$	16.4825	0.562702
$859$	30.1739	1.02952	0.514761	−	0.857334i	$-0.327881\pi$
$859$	30.1739	1.02952	0.514761	+	0.857334i	$0.327881\pi$
$860$	−23.7224	−0.808926
$861$	0	0
$862$	34.9718	1.19114
$863$	48.6500	1.65607	0.828033	−	0.560680i	$-0.189460\pi$
$863$	48.6500	1.65607	0.828033	+	0.560680i	$0.189460\pi$
$864$	−37.7249	−1.28343
$865$	21.5289	0.732006
$866$	11.6568	0.396113
$867$	47.1278	1.60055
$868$	0	0
$869$	−3.30337	−0.112059
$870$	26.3405	0.893028
$871$	19.3374	0.655221
$872$	4.51921	0.153040
$873$	5.09770	0.172531
$874$	−26.1754	−0.885395
$875$	0	0
$876$	30.1770	1.01959
$877$	−39.9528	−1.34911	−0.674555	−	0.738225i	$-0.735664\pi$
$877$	−39.9528	−1.34911	−0.674555	+	0.738225i	$0.735664\pi$
$878$	63.6780	2.14903
$879$	−17.5474	−0.591861
$880$	2.96253	0.0998670
$881$	−5.40624	−0.182141	−0.0910704	−	0.995844i	$-0.529029\pi$
$881$	−5.40624	−0.182141	−0.0910704	+	0.995844i	$0.529029\pi$
$882$	0	0
$883$	48.8546	1.64409	0.822044	−	0.569425i	$-0.192834\pi$
$883$	48.8546	1.64409	0.822044	+	0.569425i	$0.192834\pi$
$884$	66.2198	2.22721
$885$	−16.2872	−0.547488
$886$	−74.8635	−2.51509
$887$	0.538022	0.0180650	0.00903250	−	0.999959i	$-0.497125\pi$
$887$	0.538022	0.0180650	0.00903250	+	0.999959i	$0.497125\pi$
$888$	−10.9317	−0.366842
$889$	0	0
$890$	36.8068	1.23377
$891$	−10.2169	−0.342280
$892$	−23.7710	−0.795912
$893$	−10.6391	−0.356025
$894$	−56.4404	−1.88765
$895$	−22.6527	−0.757196
$896$	0	0
$897$	28.2943	0.944721
$898$	16.4622	0.549350
$899$	29.6961	0.990422
$900$	1.17390	0.0391299
$901$	−86.8897	−2.89472
$902$	−9.20009	−0.306330
$903$	0	0
$904$	−10.1687	−0.338205
$905$	5.01411	0.166675
$906$	28.3995	0.943512
$907$	45.6538	1.51591	0.757954	−	0.652307i	$-0.226199\pi$
$907$	45.6538	1.51591	0.757954	+	0.652307i	$0.226199\pi$
$908$	−30.6970	−1.01871
$909$	−3.22850	−0.107083
$910$	0	0
$911$	−51.6072	−1.70982	−0.854912	−	0.518773i	$-0.826389\pi$
$911$	−51.6072	−1.70982	−0.854912	+	0.518773i	$0.826389\pi$
$912$	19.0434	0.630589
$913$	−3.04340	−0.100722
$914$	25.8471	0.854947
$915$	6.97459	0.230573
$916$	31.3983	1.03743
$917$	0	0
$918$	−64.2365	−2.12012
$919$	−12.7553	−0.420757	−0.210378	−	0.977620i	$-0.567470\pi$
$919$	−12.7553	−0.420757	−0.210378	+	0.977620i	$0.567470\pi$
$920$	−3.24832	−0.107094
$921$	6.49025	0.213861
$922$	−23.8225	−0.784553
$923$	−43.6987	−1.43836
$924$	0	0
$925$	6.51275	0.214138
$926$	17.7532	0.583407
$927$	2.59443	0.0852123
$928$	53.8729	1.76846
$929$	−5.79744	−0.190208	−0.0951039	−	0.995467i	$-0.530318\pi$
$929$	−5.79744	−0.190208	−0.0951039	+	0.995467i	$0.530318\pi$
$930$	17.3881	0.570179
$931$	0	0
$932$	34.8884	1.14281
$933$	15.3871	0.503751
$934$	−42.6883	−1.39680
$935$	6.50001	0.212573
$936$	1.82528	0.0596611
$937$	43.6703	1.42665	0.713324	−	0.700835i	$-0.247189\pi$
$937$	43.6703	1.42665	0.713324	+	0.700835i	$0.247189\pi$
$938$	0	0
$939$	−34.5719	−1.12821
$940$	−7.49861	−0.244578
$941$	−25.3386	−0.826015	−0.413008	−	0.910728i	$-0.635522\pi$
$941$	−25.3386	−0.826015	−0.413008	+	0.910728i	$0.635522\pi$
$942$	79.0895	2.57687
$943$	−15.7932	−0.514297
$944$	−25.8521	−0.841413
$945$	0	0
$946$	−20.5632	−0.668568
$947$	−7.17984	−0.233313	−0.116657	−	0.993172i	$-0.537218\pi$
$947$	−7.17984	−0.233313	−0.116657	+	0.993172i	$0.537218\pi$
$948$	−14.9662	−0.486081
$949$	−27.9547	−0.907447
$950$	7.24671	0.235114
$951$	−10.5464	−0.341990
$952$	0	0
$953$	−2.34189	−0.0758614	−0.0379307	−	0.999280i	$-0.512077\pi$
$953$	−2.34189	−0.0758614	−0.0379307	+	0.999280i	$0.512077\pi$
$954$	−13.6025	−0.440396
$955$	−19.1411	−0.619390
$956$	−4.36637	−0.141218
$957$	12.5184	0.404664
$958$	0.445885	0.0144059
$959$	0	0
$960$	20.4856	0.661171
$961$	−11.3968	−0.367638
$962$	57.5138	1.85432
$963$	−0.594880	−0.0191697
$964$	−19.6068	−0.631493
$965$	20.8159	0.670086
$966$	0	0
$967$	−54.4531	−1.75109	−0.875547	−	0.483133i	$-0.839499\pi$
$967$	−54.4531	−1.75109	−0.875547	+	0.483133i	$0.839499\pi$
$968$	−0.899305	−0.0289048
$969$	41.7825	1.34225
$970$	22.1799	0.712153
$971$	15.5362	0.498581	0.249290	−	0.968429i	$-0.419803\pi$
$971$	15.5362	0.498581	0.249290	+	0.968429i	$0.419803\pi$
$972$	−12.0865	−0.387674
$973$	0	0
$974$	13.5142	0.433021
$975$	−7.83335	−0.250868
$976$	11.0705	0.354358
$977$	13.4785	0.431216	0.215608	−	0.976480i	$-0.430827\pi$
$977$	13.4785	0.431216	0.215608	+	0.976480i	$0.430827\pi$
$978$	−12.1544	−0.388655
$979$	17.4926	0.559065
$980$	0	0
$981$	−2.43021	−0.0775907
$982$	−4.43585	−0.141554
$983$	−8.58930	−0.273956	−0.136978	−	0.990574i	$-0.543739\pi$
$983$	−8.58930	−0.273956	−0.136978	+	0.990574i	$0.543739\pi$
$984$	−7.33904	−0.233960
$985$	10.0934	0.321603
$986$	91.7327	2.92137
$987$	0	0
$988$	35.0865	1.11625
$989$	−35.2995	−1.12246
$990$	1.01757	0.0323404
$991$	50.1627	1.59347	0.796736	−	0.604328i	$-0.206558\pi$
$991$	50.1627	1.59347	0.796736	+	0.604328i	$0.206558\pi$
$992$	35.5630	1.12913
$993$	−11.9983	−0.380755
$994$	0	0
$995$	10.2188	0.323958
$996$	−13.7884	−0.436903
$997$	−3.53154	−0.111845	−0.0559226	−	0.998435i	$-0.517810\pi$
$997$	−3.53154	−0.111845	−0.0559226	+	0.998435i	$0.517810\pi$
$998$	−6.66115	−0.210855
$999$	−30.5885	−0.967777

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2695.2.a.y.1.2		10
7.2	even	3		385.2.i.d.221.9	✓	20
7.4	even	3		385.2.i.d.331.9	yes	20
7.6	odd	2		2695.2.a.z.1.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.i.d.221.9	✓	20	7.2	even	3
385.2.i.d.331.9	yes	20	7.4	even	3
2695.2.a.y.1.2		10	1.1	even	1	trivial
2695.2.a.z.1.2		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)

\(f(q)\)	\(=\)	\(q-2.10414 q^{2} +1.86644 q^{3} +2.42740 q^{4} -1.00000 q^{5} -3.92725 q^{6} -0.899305 q^{8} +0.483603 q^{9} +O(q^{10})\)	\(q-2.10414 q^{2} +1.86644 q^{3} +2.42740 q^{4} -1.00000 q^{5} -3.92725 q^{6} -0.899305 q^{8} +0.483603 q^{9} +2.10414 q^{10} +1.00000 q^{11} +4.53060 q^{12} -4.19694 q^{13} -1.86644 q^{15} -2.96253 q^{16} -6.50001 q^{17} -1.01757 q^{18} -3.44403 q^{19} -2.42740 q^{20} -2.10414 q^{22} -3.61204 q^{23} -1.67850 q^{24} +1.00000 q^{25} +8.83095 q^{26} -4.69671 q^{27} +6.70712 q^{29} +3.92725 q^{30} +4.42755 q^{31} +8.03219 q^{32} +1.86644 q^{33} +13.6769 q^{34} +1.17390 q^{36} +6.51275 q^{37} +7.24671 q^{38} -7.83335 q^{39} +0.899305 q^{40} +4.37238 q^{41} +9.77275 q^{43} +2.42740 q^{44} -0.483603 q^{45} +7.60022 q^{46} +3.08915 q^{47} -5.52940 q^{48} -2.10414 q^{50} -12.1319 q^{51} -10.1877 q^{52} +13.3676 q^{53} +9.88252 q^{54} -1.00000 q^{55} -6.42807 q^{57} -14.1127 q^{58} +8.72633 q^{59} -4.53060 q^{60} -3.73684 q^{61} -9.31619 q^{62} -10.9758 q^{64} +4.19694 q^{65} -3.92725 q^{66} -4.60749 q^{67} -15.7781 q^{68} -6.74165 q^{69} +10.4120 q^{71} -0.434907 q^{72} +6.66072 q^{73} -13.7037 q^{74} +1.86644 q^{75} -8.36002 q^{76} +16.4825 q^{78} -3.30337 q^{79} +2.96253 q^{80} -10.2169 q^{81} -9.20009 q^{82} -3.04340 q^{83} +6.50001 q^{85} -20.5632 q^{86} +12.5184 q^{87} -0.899305 q^{88} +17.4926 q^{89} +1.01757 q^{90} -8.76785 q^{92} +8.26377 q^{93} -6.50001 q^{94} +3.44403 q^{95} +14.9916 q^{96} +10.5411 q^{97} +0.483603 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 3 q^{2} - 3 q^{3} + 15 q^{4} - 10 q^{5} + 5 q^{6} + 9 q^{8} + 19 q^{9}+O(q^{10}) \) 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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