LMFDB - Embedded newform 3381.2.a.bf.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3381,2,Mod(1,3381)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3381, 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("3381.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3381 = 3 \cdot 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3381.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:	$26.9974209234$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 15x^{6} + 11x^{5} + 75x^{4} - 35x^{3} - 141x^{2} + 37x + 80 $ x^8 - x^7 - 15x^6 + 11x^5 + 75x^4 - 35x^3 - 141x^2 + 37x + 80
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 483)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.55222$ of defining polynomial
Character	$\chi$	$=$	3381.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.55222 q^{2} +1.00000 q^{3} +4.51383 q^{4} +0.648159 q^{5} -2.55222 q^{6} -6.41586 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.55222 q^{2} +1.00000 q^{3} +4.51383 q^{4} +0.648159 q^{5} -2.55222 q^{6} -6.41586 q^{8} +1.00000 q^{9} -1.65425 q^{10} -2.98015 q^{11} +4.51383 q^{12} -3.87158 q^{13} +0.648159 q^{15} +7.34703 q^{16} +6.73221 q^{17} -2.55222 q^{18} -6.97725 q^{19} +2.92568 q^{20} +7.60600 q^{22} -1.00000 q^{23} -6.41586 q^{24} -4.57989 q^{25} +9.88114 q^{26} +1.00000 q^{27} +4.40182 q^{29} -1.65425 q^{30} +2.21646 q^{31} -5.91953 q^{32} -2.98015 q^{33} -17.1821 q^{34} +4.51383 q^{36} -4.41093 q^{37} +17.8075 q^{38} -3.87158 q^{39} -4.15850 q^{40} -0.194472 q^{41} -1.37588 q^{43} -13.4519 q^{44} +0.648159 q^{45} +2.55222 q^{46} -2.48832 q^{47} +7.34703 q^{48} +11.6889 q^{50} +6.73221 q^{51} -17.4757 q^{52} +9.46929 q^{53} -2.55222 q^{54} -1.93161 q^{55} -6.97725 q^{57} -11.2344 q^{58} +6.80034 q^{59} +2.92568 q^{60} +8.72332 q^{61} -5.65689 q^{62} +0.413880 q^{64} -2.50940 q^{65} +7.60600 q^{66} -0.893854 q^{67} +30.3881 q^{68} -1.00000 q^{69} +15.2489 q^{71} -6.41586 q^{72} +0.943428 q^{73} +11.2577 q^{74} -4.57989 q^{75} -31.4942 q^{76} +9.88114 q^{78} +14.1495 q^{79} +4.76204 q^{80} +1.00000 q^{81} +0.496336 q^{82} +14.6280 q^{83} +4.36354 q^{85} +3.51154 q^{86} +4.40182 q^{87} +19.1202 q^{88} -15.7461 q^{89} -1.65425 q^{90} -4.51383 q^{92} +2.21646 q^{93} +6.35075 q^{94} -4.52237 q^{95} -5.91953 q^{96} +3.23421 q^{97} -2.98015 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + 8 q^{3} + 15 q^{4} + 5 q^{5} + q^{6} + 9 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + q^2 + 8 * q^3 + 15 * q^4 + 5 * q^5 + q^6 + 9 * q^8 + 8 * q^9	$ 8 q + q^{2} + 8 q^{3} + 15 q^{4} + 5 q^{5} + q^{6} + 9 q^{8} + 8 q^{9} - 3 q^{10} + 10 q^{11} + 15 q^{12} - 6 q^{13} + 5 q^{15} + 13 q^{16} + 21 q^{17} + q^{18} + 5 q^{19} - q^{20} + 18 q^{22} - 8 q^{23} + 9 q^{24} + 27 q^{25} + 3 q^{26} + 8 q^{27} + 2 q^{29} - 3 q^{30} - 13 q^{31} + 29 q^{32} + 10 q^{33} - 19 q^{34} + 15 q^{36} + 13 q^{37} - 6 q^{38} - 6 q^{39} + 7 q^{40} + 16 q^{41} + 15 q^{43} + 24 q^{44} + 5 q^{45} - q^{46} - q^{47} + 13 q^{48} + 16 q^{50} + 21 q^{51} - 19 q^{52} + 3 q^{53} + q^{54} - 10 q^{55} + 5 q^{57} - 40 q^{58} + 26 q^{59} - q^{60} - 14 q^{61} - 14 q^{62} + 49 q^{64} - 3 q^{65} + 18 q^{66} + 38 q^{67} + 43 q^{68} - 8 q^{69} + 9 q^{71} + 9 q^{72} - 6 q^{73} + 32 q^{74} + 27 q^{75} - 14 q^{76} + 3 q^{78} + 23 q^{79} - 17 q^{80} + 8 q^{81} + 20 q^{82} + 30 q^{83} - 37 q^{85} - 28 q^{86} + 2 q^{87} + 86 q^{88} + 12 q^{89} - 3 q^{90} - 15 q^{92} - 13 q^{93} - 45 q^{94} + 16 q^{95} + 29 q^{96} + 14 q^{97} + 10 q^{99}+O(q^{100}) $ 8 * q + q^2 + 8 * q^3 + 15 * q^4 + 5 * q^5 + q^6 + 9 * q^8 + 8 * q^9 - 3 * q^10 + 10 * q^11 + 15 * q^12 - 6 * q^13 + 5 * q^15 + 13 * q^16 + 21 * q^17 + q^18 + 5 * q^19 - q^20 + 18 * q^22 - 8 * q^23 + 9 * q^24 + 27 * q^25 + 3 * q^26 + 8 * q^27 + 2 * q^29 - 3 * q^30 - 13 * q^31 + 29 * q^32 + 10 * q^33 - 19 * q^34 + 15 * q^36 + 13 * q^37 - 6 * q^38 - 6 * q^39 + 7 * q^40 + 16 * q^41 + 15 * q^43 + 24 * q^44 + 5 * q^45 - q^46 - q^47 + 13 * q^48 + 16 * q^50 + 21 * q^51 - 19 * q^52 + 3 * q^53 + q^54 - 10 * q^55 + 5 * q^57 - 40 * q^58 + 26 * q^59 - q^60 - 14 * q^61 - 14 * q^62 + 49 * q^64 - 3 * q^65 + 18 * q^66 + 38 * q^67 + 43 * q^68 - 8 * q^69 + 9 * q^71 + 9 * q^72 - 6 * q^73 + 32 * q^74 + 27 * q^75 - 14 * q^76 + 3 * q^78 + 23 * q^79 - 17 * q^80 + 8 * q^81 + 20 * q^82 + 30 * q^83 - 37 * q^85 - 28 * q^86 + 2 * q^87 + 86 * q^88 + 12 * q^89 - 3 * q^90 - 15 * q^92 - 13 * q^93 - 45 * q^94 + 16 * q^95 + 29 * q^96 + 14 * q^97 + 10 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.55222	−1.80469	−0.902347	−	0.431011i	$-0.858157\pi$
$2$	−2.55222	−1.80469	−0.902347	+	0.431011i	$0.858157\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.51383	2.25692
$5$	0.648159	0.289866	0.144933	−	0.989442i	$-0.453703\pi$
$5$	0.648159	0.289866	0.144933	+	0.989442i	$0.453703\pi$
$6$	−2.55222	−1.04194
$7$	0	0
$7$	0	0
$8$	−6.41586	−2.26835
$9$	1.00000	0.333333
$10$	−1.65425	−0.523118
$11$	−2.98015	−0.898549	−0.449274	−	0.893394i	$-0.648317\pi$
$11$	−2.98015	−0.898549	−0.449274	+	0.893394i	$0.648317\pi$
$12$	4.51383	1.30303
$13$	−3.87158	−1.07378	−0.536892	−	0.843651i	$-0.680402\pi$
$13$	−3.87158	−1.07378	−0.536892	+	0.843651i	$0.680402\pi$
$14$	0	0
$15$	0.648159	0.167354
$16$	7.34703	1.83676
$17$	6.73221	1.63280	0.816400	−	0.577486i	$-0.195966\pi$
$17$	6.73221	1.63280	0.816400	+	0.577486i	$0.195966\pi$
$18$	−2.55222	−0.601564
$19$	−6.97725	−1.60069	−0.800346	−	0.599538i	$-0.795351\pi$
$19$	−6.97725	−1.60069	−0.800346	+	0.599538i	$0.795351\pi$
$20$	2.92568	0.654203
$21$	0	0
$22$	7.60600	1.62160
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−6.41586	−1.30963
$25$	−4.57989	−0.915978
$26$	9.88114	1.93785
$27$	1.00000	0.192450
$28$	0	0
$29$	4.40182	0.817397	0.408699	−	0.912669i	$-0.365983\pi$
$29$	4.40182	0.817397	0.408699	+	0.912669i	$0.365983\pi$
$30$	−1.65425	−0.302023
$31$	2.21646	0.398088	0.199044	−	0.979991i	$-0.436216\pi$
$31$	2.21646	0.398088	0.199044	+	0.979991i	$0.436216\pi$
$32$	−5.91953	−1.04643
$33$	−2.98015	−0.518777
$34$	−17.1821	−2.94670
$35$	0	0
$36$	4.51383	0.752306
$37$	−4.41093	−0.725153	−0.362576	−	0.931954i	$-0.618103\pi$
$37$	−4.41093	−0.725153	−0.362576	+	0.931954i	$0.618103\pi$
$38$	17.8075	2.88876
$39$	−3.87158	−0.619950
$40$	−4.15850	−0.657516
$41$	−0.194472	−0.0303714	−0.0151857	−	0.999885i	$-0.504834\pi$
$41$	−0.194472	−0.0303714	−0.0151857	+	0.999885i	$0.504834\pi$
$42$	0	0
$43$	−1.37588	−0.209819	−0.104910	−	0.994482i	$-0.533455\pi$
$43$	−1.37588	−0.209819	−0.104910	+	0.994482i	$0.533455\pi$
$44$	−13.4519	−2.02795
$45$	0.648159	0.0966219
$46$	2.55222	0.376305
$47$	−2.48832	−0.362959	−0.181479	−	0.983395i	$-0.558089\pi$
$47$	−2.48832	−0.362959	−0.181479	+	0.983395i	$0.558089\pi$
$48$	7.34703	1.06045
$49$	0	0
$50$	11.6889	1.65306
$51$	6.73221	0.942698
$52$	−17.4757	−2.42344
$53$	9.46929	1.30071	0.650353	−	0.759632i	$-0.274621\pi$
$53$	9.46929	1.30071	0.650353	+	0.759632i	$0.274621\pi$
$54$	−2.55222	−0.347313
$55$	−1.93161	−0.260458
$56$	0	0
$57$	−6.97725	−0.924160
$58$	−11.2344	−1.47515
$59$	6.80034	0.885329	0.442664	−	0.896687i	$-0.354033\pi$
$59$	6.80034	0.885329	0.442664	+	0.896687i	$0.354033\pi$
$60$	2.92568	0.377704
$61$	8.72332	1.11691	0.558453	−	0.829536i	$-0.311395\pi$
$61$	8.72332	1.11691	0.558453	+	0.829536i	$0.311395\pi$
$62$	−5.65689	−0.718426
$63$	0	0
$64$	0.413880	0.0517349
$65$	−2.50940	−0.311253
$66$	7.60600	0.936234
$67$	−0.893854	−0.109202	−0.0546008	−	0.998508i	$-0.517389\pi$
$67$	−0.893854	−0.109202	−0.0546008	+	0.998508i	$0.517389\pi$
$68$	30.3881	3.68510
$69$	−1.00000	−0.120386
$70$	0	0
$71$	15.2489	1.80971	0.904856	−	0.425718i	$-0.139979\pi$
$71$	15.2489	1.80971	0.904856	+	0.425718i	$0.139979\pi$
$72$	−6.41586	−0.756117
$73$	0.943428	0.110420	0.0552099	−	0.998475i	$-0.482417\pi$
$73$	0.943428	0.110420	0.0552099	+	0.998475i	$0.482417\pi$
$74$	11.2577	1.30868
$75$	−4.57989	−0.528840
$76$	−31.4942	−3.61263
$77$	0	0
$78$	9.88114	1.11882
$79$	14.1495	1.59194	0.795971	−	0.605335i	$-0.206961\pi$
$79$	14.1495	1.59194	0.795971	+	0.605335i	$0.206961\pi$
$80$	4.76204	0.532413
$81$	1.00000	0.111111
$82$	0.496336	0.0548111
$83$	14.6280	1.60563	0.802815	−	0.596228i	$-0.203335\pi$
$83$	14.6280	1.60563	0.802815	+	0.596228i	$0.203335\pi$
$84$	0	0
$85$	4.36354	0.473293
$86$	3.51154	0.378659
$87$	4.40182	0.471924
$88$	19.1202	2.03822
$89$	−15.7461	−1.66908	−0.834541	−	0.550946i	$-0.814267\pi$
$89$	−15.7461	−1.66908	−0.834541	+	0.550946i	$0.814267\pi$
$90$	−1.65425	−0.174373
$91$	0	0
$92$	−4.51383	−0.470600
$93$	2.21646	0.229836
$94$	6.35075	0.655029
$95$	−4.52237	−0.463985
$96$	−5.91953	−0.604159
$97$	3.23421	0.328384	0.164192	−	0.986428i	$-0.447498\pi$
$97$	3.23421	0.328384	0.164192	+	0.986428i	$0.447498\pi$
$98$	0	0
$99$	−2.98015	−0.299516
$100$	−20.6729	−2.06729
$101$	3.00663	0.299171	0.149585	−	0.988749i	$-0.452206\pi$
$101$	3.00663	0.299171	0.149585	+	0.988749i	$0.452206\pi$
$102$	−17.1821	−1.70128
$103$	13.9595	1.37547	0.687733	−	0.725964i	$-0.258606\pi$
$103$	13.9595	1.37547	0.687733	+	0.725964i	$0.258606\pi$
$104$	24.8395	2.43572
$105$	0	0
$106$	−24.1677	−2.34738
$107$	−1.22874	−0.118787	−0.0593933	−	0.998235i	$-0.518917\pi$
$107$	−1.22874	−0.118787	−0.0593933	+	0.998235i	$0.518917\pi$
$108$	4.51383	0.434344
$109$	16.1711	1.54891	0.774454	−	0.632631i	$-0.218025\pi$
$109$	16.1711	1.54891	0.774454	+	0.632631i	$0.218025\pi$
$110$	4.92990	0.470047
$111$	−4.41093	−0.418667
$112$	0	0
$113$	−4.70467	−0.442578	−0.221289	−	0.975208i	$-0.571026\pi$
$113$	−4.70467	−0.442578	−0.221289	+	0.975208i	$0.571026\pi$
$114$	17.8075	1.66782
$115$	−0.648159	−0.0604412
$116$	19.8691	1.84480
$117$	−3.87158	−0.357928
$118$	−17.3560	−1.59775
$119$	0	0
$120$	−4.15850	−0.379617
$121$	−2.11872	−0.192611
$122$	−22.2638	−2.01567
$123$	−0.194472	−0.0175349
$124$	10.0047	0.898451
$125$	−6.20929	−0.555376
$126$	0	0
$127$	15.9640	1.41657	0.708287	−	0.705924i	$-0.249468\pi$
$127$	15.9640	1.41657	0.708287	+	0.705924i	$0.249468\pi$
$128$	10.7827	0.953069
$129$	−1.37588	−0.121139
$130$	6.40455	0.561716
$131$	15.5926	1.36233	0.681166	−	0.732129i	$-0.261473\pi$
$131$	15.5926	1.36233	0.681166	+	0.732129i	$0.261473\pi$
$132$	−13.4519	−1.17084
$133$	0	0
$134$	2.28131	0.197075
$135$	0.648159	0.0557847
$136$	−43.1929	−3.70376
$137$	10.7255	0.916345	0.458173	−	0.888863i	$-0.348504\pi$
$137$	10.7255	0.916345	0.458173	+	0.888863i	$0.348504\pi$
$138$	2.55222	0.217260
$139$	21.4287	1.81756	0.908781	−	0.417273i	$-0.137014\pi$
$139$	21.4287	1.81756	0.908781	+	0.417273i	$0.137014\pi$
$140$	0	0
$141$	−2.48832	−0.209554
$142$	−38.9186	−3.26597
$143$	11.5379	0.964847
$144$	7.34703	0.612253
$145$	2.85308	0.236935
$146$	−2.40784	−0.199274
$147$	0	0
$148$	−19.9102	−1.63661
$149$	−10.3525	−0.848111	−0.424055	−	0.905636i	$-0.639394\pi$
$149$	−10.3525	−0.848111	−0.424055	+	0.905636i	$0.639394\pi$
$150$	11.6889	0.954394
$151$	−8.80577	−0.716603	−0.358302	−	0.933606i	$-0.616644\pi$
$151$	−8.80577	−0.716603	−0.358302	+	0.933606i	$0.616644\pi$
$152$	44.7651	3.63093
$153$	6.73221	0.544267
$154$	0	0
$155$	1.43662	0.115392
$156$	−17.4757	−1.39917
$157$	−9.33096	−0.744692	−0.372346	−	0.928094i	$-0.621447\pi$
$157$	−9.33096	−0.744692	−0.372346	+	0.928094i	$0.621447\pi$
$158$	−36.1126	−2.87297
$159$	9.46929	0.750964
$160$	−3.83679	−0.303325
$161$	0	0
$162$	−2.55222	−0.200521
$163$	0.463122	0.0362745	0.0181373	−	0.999836i	$-0.494226\pi$
$163$	0.463122	0.0362745	0.0181373	+	0.999836i	$0.494226\pi$
$164$	−0.877814	−0.0685458
$165$	−1.93161	−0.150376
$166$	−37.3339	−2.89767
$167$	2.40385	0.186015	0.0930076	−	0.995665i	$-0.470352\pi$
$167$	2.40385	0.186015	0.0930076	+	0.995665i	$0.470352\pi$
$168$	0	0
$169$	1.98916	0.153012
$170$	−11.1367	−0.854148
$171$	−6.97725	−0.533564
$172$	−6.21048	−0.473544
$173$	5.14814	0.391406	0.195703	−	0.980663i	$-0.437301\pi$
$173$	5.14814	0.391406	0.195703	+	0.980663i	$0.437301\pi$
$174$	−11.2344	−0.851679
$175$	0	0
$176$	−21.8952	−1.65042
$177$	6.80034	0.511145
$178$	40.1875	3.01218
$179$	−7.77885	−0.581419	−0.290709	−	0.956811i	$-0.593891\pi$
$179$	−7.77885	−0.581419	−0.290709	+	0.956811i	$0.593891\pi$
$180$	2.92568	0.218068
$181$	−7.61327	−0.565890	−0.282945	−	0.959136i	$-0.591311\pi$
$181$	−7.61327	−0.565890	−0.282945	+	0.959136i	$0.591311\pi$
$182$	0	0
$183$	8.72332	0.644846
$184$	6.41586	0.472984
$185$	−2.85899	−0.210197
$186$	−5.65689	−0.414784
$187$	−20.0630	−1.46715
$188$	−11.2319	−0.819168
$189$	0	0
$190$	11.5421	0.837351
$191$	−0.738878	−0.0534633	−0.0267317	−	0.999643i	$-0.508510\pi$
$191$	−0.738878	−0.0534633	−0.0267317	+	0.999643i	$0.508510\pi$
$192$	0.413880	0.0298692
$193$	−15.9702	−1.14956	−0.574781	−	0.818307i	$-0.694913\pi$
$193$	−15.9702	−1.14956	−0.574781	+	0.818307i	$0.694913\pi$
$194$	−8.25441	−0.592632
$195$	−2.50940	−0.179702
$196$	0	0
$197$	−9.50195	−0.676986	−0.338493	−	0.940969i	$-0.609917\pi$
$197$	−9.50195	−0.676986	−0.338493	+	0.940969i	$0.609917\pi$
$198$	7.60600	0.540535
$199$	−16.6593	−1.18095	−0.590473	−	0.807057i	$-0.701059\pi$
$199$	−16.6593	−1.18095	−0.590473	+	0.807057i	$0.701059\pi$
$200$	29.3839	2.07776
$201$	−0.893854	−0.0630476
$202$	−7.67358	−0.539911
$203$	0	0
$204$	30.3881	2.12759
$205$	−0.126049	−0.00880363
$206$	−35.6276	−2.48229
$207$	−1.00000	−0.0695048
$208$	−28.4446	−1.97228
$209$	20.7933	1.43830
$210$	0	0
$211$	19.6449	1.35241	0.676207	−	0.736712i	$-0.263623\pi$
$211$	19.6449	1.35241	0.676207	+	0.736712i	$0.263623\pi$
$212$	42.7428	2.93559
$213$	15.2489	1.04484
$214$	3.13601	0.214373
$215$	−0.891787	−0.0608193
$216$	−6.41586	−0.436544
$217$	0	0
$218$	−41.2721	−2.79530
$219$	0.943428	0.0637509
$220$	−8.71897	−0.587833
$221$	−26.0643	−1.75328
$222$	11.2577	0.755565
$223$	−17.5246	−1.17353	−0.586766	−	0.809757i	$-0.699599\pi$
$223$	−17.5246	−1.17353	−0.586766	+	0.809757i	$0.699599\pi$
$224$	0	0
$225$	−4.57989	−0.305326
$226$	12.0074	0.798718
$227$	−10.6921	−0.709662	−0.354831	−	0.934930i	$-0.615462\pi$
$227$	−10.6921	−0.709662	−0.354831	+	0.934930i	$0.615462\pi$
$228$	−31.4942	−2.08575
$229$	9.30000	0.614561	0.307281	−	0.951619i	$-0.400581\pi$
$229$	9.30000	0.614561	0.307281	+	0.951619i	$0.400581\pi$
$230$	1.65425	0.109078
$231$	0	0
$232$	−28.2415	−1.85414
$233$	−23.7260	−1.55434	−0.777172	−	0.629288i	$-0.783347\pi$
$233$	−23.7260	−1.55434	−0.777172	+	0.629288i	$0.783347\pi$
$234$	9.88114	0.645950
$235$	−1.61283	−0.105209
$236$	30.6956	1.99811
$237$	14.1495	0.919108
$238$	0	0
$239$	26.6326	1.72272	0.861360	−	0.507994i	$-0.169613\pi$
$239$	26.6326	1.72272	0.861360	+	0.507994i	$0.169613\pi$
$240$	4.76204	0.307389
$241$	11.6859	0.752754	0.376377	−	0.926466i	$-0.377170\pi$
$241$	11.6859	0.752754	0.376377	+	0.926466i	$0.377170\pi$
$242$	5.40743	0.347603
$243$	1.00000	0.0641500
$244$	39.3756	2.52076
$245$	0	0
$246$	0.496336	0.0316452
$247$	27.0130	1.71880
$248$	−14.2205	−0.903002
$249$	14.6280	0.927011
$250$	15.8475	1.00228
$251$	−12.0271	−0.759142	−0.379571	−	0.925163i	$-0.623928\pi$
$251$	−12.0271	−0.759142	−0.379571	+	0.925163i	$0.623928\pi$
$252$	0	0
$253$	2.98015	0.187360
$254$	−40.7436	−2.55648
$255$	4.36354	0.273256
$256$	−28.3477	−1.77173
$257$	−10.1840	−0.635261	−0.317631	−	0.948215i	$-0.602887\pi$
$257$	−10.1840	−0.635261	−0.317631	+	0.948215i	$0.602887\pi$
$258$	3.51154	0.218619
$259$	0	0
$260$	−11.3270	−0.702472
$261$	4.40182	0.272466
$262$	−39.7958	−2.45859
$263$	20.8565	1.28607	0.643033	−	0.765839i	$-0.277676\pi$
$263$	20.8565	1.28607	0.643033	+	0.765839i	$0.277676\pi$
$264$	19.1202	1.17677
$265$	6.13761	0.377030
$266$	0	0
$267$	−15.7461	−0.963645
$268$	−4.03471	−0.246459
$269$	−20.4710	−1.24814	−0.624071	−	0.781368i	$-0.714522\pi$
$269$	−20.4710	−1.24814	−0.624071	+	0.781368i	$0.714522\pi$
$270$	−1.65425	−0.100674
$271$	−18.8557	−1.14540	−0.572700	−	0.819765i	$-0.694104\pi$
$271$	−18.8557	−1.14540	−0.572700	+	0.819765i	$0.694104\pi$
$272$	49.4617	2.99906
$273$	0	0
$274$	−27.3740	−1.65372
$275$	13.6488	0.823051
$276$	−4.51383	−0.271701
$277$	−4.96206	−0.298141	−0.149070	−	0.988827i	$-0.547628\pi$
$277$	−4.96206	−0.298141	−0.149070	+	0.988827i	$0.547628\pi$
$278$	−54.6909	−3.28014
$279$	2.21646	0.132696
$280$	0	0
$281$	9.56605	0.570663	0.285331	−	0.958429i	$-0.407896\pi$
$281$	9.56605	0.570663	0.285331	+	0.958429i	$0.407896\pi$
$282$	6.35075	0.378181
$283$	7.41833	0.440974	0.220487	−	0.975390i	$-0.429235\pi$
$283$	7.41833	0.440974	0.220487	+	0.975390i	$0.429235\pi$
$284$	68.8310	4.08437
$285$	−4.52237	−0.267882
$286$	−29.4473	−1.74125
$287$	0	0
$288$	−5.91953	−0.348811
$289$	28.3226	1.66604
$290$	−7.28169	−0.427595
$291$	3.23421	0.189593
$292$	4.25848	0.249208
$293$	9.37108	0.547464	0.273732	−	0.961806i	$-0.411742\pi$
$293$	9.37108	0.547464	0.273732	+	0.961806i	$0.411742\pi$
$294$	0	0
$295$	4.40770	0.256626
$296$	28.2999	1.64490
$297$	−2.98015	−0.172926
$298$	26.4219	1.53058
$299$	3.87158	0.223899
$300$	−20.6729	−1.19355
$301$	0	0
$302$	22.4743	1.29325
$303$	3.00663	0.172726
$304$	−51.2621	−2.94008
$305$	5.65410	0.323753
$306$	−17.1821	−0.982235
$307$	−0.0388797	−0.00221898	−0.00110949	−	0.999999i	$-0.500353\pi$
$307$	−0.0388797	−0.00221898	−0.00110949	+	0.999999i	$0.500353\pi$
$308$	0	0
$309$	13.9595	0.794125
$310$	−3.66657	−0.208247
$311$	9.13847	0.518195	0.259098	−	0.965851i	$-0.416575\pi$
$311$	9.13847	0.518195	0.259098	+	0.965851i	$0.416575\pi$
$312$	24.8395	1.40626
$313$	−12.8762	−0.727803	−0.363902	−	0.931437i	$-0.618556\pi$
$313$	−12.8762	−0.727803	−0.363902	+	0.931437i	$0.618556\pi$
$314$	23.8147	1.34394
$315$	0	0
$316$	63.8684	3.59288
$317$	10.7871	0.605864	0.302932	−	0.953012i	$-0.402034\pi$
$317$	10.7871	0.605864	0.302932	+	0.953012i	$0.402034\pi$
$318$	−24.1677	−1.35526
$319$	−13.1181	−0.734471
$320$	0.268260	0.0149962
$321$	−1.22874	−0.0685814
$322$	0	0
$323$	−46.9723	−2.61361
$324$	4.51383	0.250769
$325$	17.7314	0.983563
$326$	−1.18199	−0.0654644
$327$	16.1711	0.894262
$328$	1.24771	0.0688930
$329$	0	0
$330$	4.92990	0.271382
$331$	22.5766	1.24092	0.620461	−	0.784237i	$-0.286945\pi$
$331$	22.5766	1.24092	0.620461	+	0.784237i	$0.286945\pi$
$332$	66.0283	3.62377
$333$	−4.41093	−0.241718
$334$	−6.13515	−0.335700
$335$	−0.579360	−0.0316538
$336$	0	0
$337$	−6.39947	−0.348601	−0.174301	−	0.984693i	$-0.555766\pi$
$337$	−6.39947	−0.348601	−0.174301	+	0.984693i	$0.555766\pi$
$338$	−5.07678	−0.276140
$339$	−4.70467	−0.255523
$340$	19.6963	1.06818
$341$	−6.60538	−0.357701
$342$	17.8075	0.962919
$343$	0	0
$344$	8.82743	0.475943
$345$	−0.648159	−0.0348957
$346$	−13.1392	−0.706368
$347$	33.3198	1.78870	0.894351	−	0.447366i	$-0.147638\pi$
$347$	33.3198	1.78870	0.894351	+	0.447366i	$0.147638\pi$
$348$	19.8691	1.06509
$349$	−28.5439	−1.52792	−0.763961	−	0.645262i	$-0.776748\pi$
$349$	−28.5439	−1.52792	−0.763961	+	0.645262i	$0.776748\pi$
$350$	0	0
$351$	−3.87158	−0.206650
$352$	17.6411	0.940272
$353$	−0.153112	−0.00814932	−0.00407466	−	0.999992i	$-0.501297\pi$
$353$	−0.153112	−0.00814932	−0.00407466	+	0.999992i	$0.501297\pi$
$354$	−17.3560	−0.922459
$355$	9.88371	0.524573
$356$	−71.0752	−3.76698
$357$	0	0
$358$	19.8534	1.04928
$359$	21.6852	1.14450	0.572250	−	0.820079i	$-0.306071\pi$
$359$	21.6852	1.14450	0.572250	+	0.820079i	$0.306071\pi$
$360$	−4.15850	−0.219172
$361$	29.6821	1.56221
$362$	19.4307	1.02126
$363$	−2.11872	−0.111204
$364$	0	0
$365$	0.611491	0.0320069
$366$	−22.2638	−1.16375
$367$	3.04207	0.158795	0.0793974	−	0.996843i	$-0.474700\pi$
$367$	3.04207	0.158795	0.0793974	+	0.996843i	$0.474700\pi$
$368$	−7.34703	−0.382990
$369$	−0.194472	−0.0101238
$370$	7.29676	0.379341
$371$	0	0
$372$	10.0047	0.518721
$373$	27.6137	1.42978	0.714892	−	0.699235i	$-0.246476\pi$
$373$	27.6137	1.42978	0.714892	+	0.699235i	$0.246476\pi$
$374$	51.2052	2.64776
$375$	−6.20929	−0.320647
$376$	15.9647	0.823318
$377$	−17.0420	−0.877708
$378$	0	0
$379$	24.0119	1.23341	0.616705	−	0.787194i	$-0.288467\pi$
$379$	24.0119	1.23341	0.616705	+	0.787194i	$0.288467\pi$
$380$	−20.4132	−1.04718
$381$	15.9640	0.817860
$382$	1.88578	0.0964849
$383$	−11.0118	−0.562677	−0.281339	−	0.959609i	$-0.590778\pi$
$383$	−11.0118	−0.562677	−0.281339	+	0.959609i	$0.590778\pi$
$384$	10.7827	0.550254
$385$	0	0
$386$	40.7596	2.07461
$387$	−1.37588	−0.0699397
$388$	14.5987	0.741135
$389$	35.0954	1.77941	0.889704	−	0.456538i	$-0.150911\pi$
$389$	35.0954	1.77941	0.889704	+	0.456538i	$0.150911\pi$
$390$	6.40455	0.324307
$391$	−6.73221	−0.340462
$392$	0	0
$393$	15.5926	0.786543
$394$	24.2511	1.22175
$395$	9.17112	0.461449
$396$	−13.4519	−0.675983
$397$	15.2283	0.764287	0.382144	−	0.924103i	$-0.375186\pi$
$397$	15.2283	0.764287	0.382144	+	0.924103i	$0.375186\pi$
$398$	42.5182	2.13124
$399$	0	0
$400$	−33.6486	−1.68243
$401$	−18.9860	−0.948116	−0.474058	−	0.880494i	$-0.657211\pi$
$401$	−18.9860	−0.948116	−0.474058	+	0.880494i	$0.657211\pi$
$402$	2.28131	0.113782
$403$	−8.58121	−0.427460
$404$	13.5714	0.675203
$405$	0.648159	0.0322073
$406$	0	0
$407$	13.1452	0.651585
$408$	−43.1929	−2.13837
$409$	7.45476	0.368614	0.184307	−	0.982869i	$-0.440996\pi$
$409$	7.45476	0.368614	0.184307	+	0.982869i	$0.440996\pi$
$410$	0.321704	0.0158878
$411$	10.7255	0.529052
$412$	63.0106	3.10431
$413$	0	0
$414$	2.55222	0.125435
$415$	9.48127	0.465417
$416$	22.9179	1.12364
$417$	21.4287	1.04937
$418$	−53.0690	−2.59569
$419$	3.17379	0.155050	0.0775248	−	0.996990i	$-0.475298\pi$
$419$	3.17379	0.155050	0.0775248	+	0.996990i	$0.475298\pi$
$420$	0	0
$421$	15.1064	0.736239	0.368120	−	0.929778i	$-0.380002\pi$
$421$	15.1064	0.736239	0.368120	+	0.929778i	$0.380002\pi$
$422$	−50.1382	−2.44069
$423$	−2.48832	−0.120986
$424$	−60.7537	−2.95046
$425$	−30.8328	−1.49561
$426$	−38.9186	−1.88561
$427$	0	0
$428$	−5.54632	−0.268091
$429$	11.5379	0.557055
$430$	2.27604	0.109760
$431$	25.0272	1.20552	0.602760	−	0.797923i	$-0.294068\pi$
$431$	25.0272	1.20552	0.602760	+	0.797923i	$0.294068\pi$
$432$	7.34703	0.353484
$433$	−27.5871	−1.32575	−0.662876	−	0.748729i	$-0.730664\pi$
$433$	−27.5871	−1.32575	−0.662876	+	0.748729i	$0.730664\pi$
$434$	0	0
$435$	2.85308	0.136795
$436$	72.9935	3.49576
$437$	6.97725	0.333767
$438$	−2.40784	−0.115051
$439$	−20.3867	−0.973002	−0.486501	−	0.873680i	$-0.661727\pi$
$439$	−20.3867	−0.973002	−0.486501	+	0.873680i	$0.661727\pi$
$440$	12.3929	0.590810
$441$	0	0
$442$	66.5219	3.16412
$443$	27.8743	1.32435	0.662173	−	0.749351i	$-0.269634\pi$
$443$	27.8743	1.32435	0.662173	+	0.749351i	$0.269634\pi$
$444$	−19.9102	−0.944897
$445$	−10.2060	−0.483809
$446$	44.7266	2.11786
$447$	−10.3525	−0.489657
$448$	0	0
$449$	−12.5841	−0.593882	−0.296941	−	0.954896i	$-0.595966\pi$
$449$	−12.5841	−0.593882	−0.296941	+	0.954896i	$0.595966\pi$
$450$	11.6889	0.551020
$451$	0.579555	0.0272902
$452$	−21.2361	−0.998863
$453$	−8.80577	−0.413731
$454$	27.2887	1.28072
$455$	0	0
$456$	44.7651	2.09632
$457$	−21.2928	−0.996037	−0.498019	−	0.867166i	$-0.665939\pi$
$457$	−21.2928	−0.996037	−0.498019	+	0.867166i	$0.665939\pi$
$458$	−23.7357	−1.10909
$459$	6.73221	0.314233
$460$	−2.92568	−0.136411
$461$	−3.83733	−0.178722	−0.0893612	−	0.995999i	$-0.528483\pi$
$461$	−3.83733	−0.178722	−0.0893612	+	0.995999i	$0.528483\pi$
$462$	0	0
$463$	−40.4632	−1.88048	−0.940242	−	0.340508i	$-0.889401\pi$
$463$	−40.4632	−1.88048	−0.940242	+	0.340508i	$0.889401\pi$
$464$	32.3403	1.50136
$465$	1.43662	0.0666216
$466$	60.5541	2.80512
$467$	−1.77203	−0.0819998	−0.0409999	−	0.999159i	$-0.513054\pi$
$467$	−1.77203	−0.0819998	−0.0409999	+	0.999159i	$0.513054\pi$
$468$	−17.4757	−0.807814
$469$	0	0
$470$	4.11629	0.189870
$471$	−9.33096	−0.429948
$472$	−43.6300	−2.00823
$473$	4.10031	0.188533
$474$	−36.1126	−1.65871
$475$	31.9551	1.46620
$476$	0	0
$477$	9.46929	0.433569
$478$	−67.9723	−3.10898
$479$	−14.0198	−0.640580	−0.320290	−	0.947319i	$-0.603780\pi$
$479$	−14.0198	−0.640580	−0.320290	+	0.947319i	$0.603780\pi$
$480$	−3.83679	−0.175125
$481$	17.0773	0.778657
$482$	−29.8250	−1.35849
$483$	0	0
$484$	−9.56353	−0.434706
$485$	2.09628	0.0951872
$486$	−2.55222	−0.115771
$487$	−26.7790	−1.21347	−0.606736	−	0.794903i	$-0.707522\pi$
$487$	−26.7790	−1.21347	−0.606736	+	0.794903i	$0.707522\pi$
$488$	−55.9676	−2.53353
$489$	0.463122	0.0209431
$490$	0	0
$491$	36.1444	1.63117	0.815587	−	0.578635i	$-0.196414\pi$
$491$	36.1444	1.63117	0.815587	+	0.578635i	$0.196414\pi$
$492$	−0.877814	−0.0395749
$493$	29.6340	1.33465
$494$	−68.9432	−3.10190
$495$	−1.93161	−0.0868194
$496$	16.2844	0.731191
$497$	0	0
$498$	−37.3339	−1.67297
$499$	38.0321	1.70255	0.851274	−	0.524721i	$-0.175830\pi$
$499$	38.0321	1.70255	0.851274	+	0.524721i	$0.175830\pi$
$500$	−28.0277	−1.25344
$501$	2.40385	0.107396
$502$	30.6957	1.37002
$503$	−13.8143	−0.615947	−0.307974	−	0.951395i	$-0.599651\pi$
$503$	−13.8143	−0.615947	−0.307974	+	0.951395i	$0.599651\pi$
$504$	0	0
$505$	1.94877	0.0867193
$506$	−7.60600	−0.338128
$507$	1.98916	0.0883417
$508$	72.0588	3.19709
$509$	8.38094	0.371479	0.185739	−	0.982599i	$-0.440532\pi$
$509$	8.38094	0.371479	0.185739	+	0.982599i	$0.440532\pi$
$510$	−11.1367	−0.493143
$511$	0	0
$512$	50.7841	2.24436
$513$	−6.97725	−0.308053
$514$	25.9919	1.14645
$515$	9.04795	0.398700
$516$	−6.21048	−0.273401
$517$	7.41557	0.326136
$518$	0	0
$519$	5.14814	0.225978
$520$	16.1000	0.706031
$521$	−0.350341	−0.0153487	−0.00767436	−	0.999971i	$-0.502443\pi$
$521$	−0.350341	−0.0153487	−0.00767436	+	0.999971i	$0.502443\pi$
$522$	−11.2344	−0.491717
$523$	−39.2807	−1.71763	−0.858813	−	0.512289i	$-0.828798\pi$
$523$	−39.2807	−1.71763	−0.858813	+	0.512289i	$0.828798\pi$
$524$	70.3824	3.07467
$525$	0	0
$526$	−53.2304	−2.32095
$527$	14.9217	0.649998
$528$	−21.8952	−0.952868
$529$	1.00000	0.0434783
$530$	−15.6645	−0.680424
$531$	6.80034	0.295110
$532$	0	0
$533$	0.752915	0.0326123
$534$	40.1875	1.73908
$535$	−0.796417	−0.0344321
$536$	5.73484	0.247707
$537$	−7.77885	−0.335682
$538$	52.2466	2.25251
$539$	0	0
$540$	2.92568	0.125901
$541$	−19.0989	−0.821126	−0.410563	−	0.911832i	$-0.634668\pi$
$541$	−19.0989	−0.821126	−0.410563	+	0.911832i	$0.634668\pi$
$542$	48.1239	2.06710
$543$	−7.61327	−0.326717
$544$	−39.8515	−1.70862
$545$	10.4814	0.448975
$546$	0	0
$547$	−14.2276	−0.608330	−0.304165	−	0.952619i	$-0.598377\pi$
$547$	−14.2276	−0.608330	−0.304165	+	0.952619i	$0.598377\pi$
$548$	48.4133	2.06811
$549$	8.72332	0.372302
$550$	−34.8346	−1.48535
$551$	−30.7126	−1.30840
$552$	6.41586	0.273077
$553$	0	0
$554$	12.6643	0.538053
$555$	−2.85899	−0.121357
$556$	96.7258	4.10209
$557$	−13.7605	−0.583050	−0.291525	−	0.956563i	$-0.594163\pi$
$557$	−13.7605	−0.583050	−0.291525	+	0.956563i	$0.594163\pi$
$558$	−5.65689	−0.239475
$559$	5.32682	0.225300
$560$	0	0
$561$	−20.0630	−0.847060
$562$	−24.4147	−1.02987
$563$	−23.4218	−0.987111	−0.493555	−	0.869714i	$-0.664303\pi$
$563$	−23.4218	−0.987111	−0.493555	+	0.869714i	$0.664303\pi$
$564$	−11.2319	−0.472947
$565$	−3.04938	−0.128288
$566$	−18.9332	−0.795823
$567$	0	0
$568$	−97.8348	−4.10506
$569$	16.9478	0.710490	0.355245	−	0.934773i	$-0.384397\pi$
$569$	16.9478	0.710490	0.355245	+	0.934773i	$0.384397\pi$
$570$	11.5421	0.483445
$571$	23.3857	0.978660	0.489330	−	0.872099i	$-0.337241\pi$
$571$	23.3857	0.978660	0.489330	+	0.872099i	$0.337241\pi$
$572$	52.0801	2.17758
$573$	−0.738878	−0.0308671
$574$	0	0
$575$	4.57989	0.190995
$576$	0.413880	0.0172450
$577$	−18.6601	−0.776831	−0.388415	−	0.921484i	$-0.626977\pi$
$577$	−18.6601	−0.776831	−0.388415	+	0.921484i	$0.626977\pi$
$578$	−72.2856	−3.00669
$579$	−15.9702	−0.663700
$580$	12.8783	0.534743
$581$	0	0
$582$	−8.25441	−0.342156
$583$	−28.2199	−1.16875
$584$	−6.05290	−0.250471
$585$	−2.50940	−0.103751
$586$	−23.9171	−0.988005
$587$	36.1742	1.49307	0.746535	−	0.665346i	$-0.231716\pi$
$587$	36.1742	1.49307	0.746535	+	0.665346i	$0.231716\pi$
$588$	0	0
$589$	−15.4648	−0.637216
$590$	−11.2494	−0.463132
$591$	−9.50195	−0.390858
$592$	−32.4072	−1.33193
$593$	29.0739	1.19392	0.596961	−	0.802270i	$-0.296375\pi$
$593$	29.0739	1.19392	0.596961	+	0.802270i	$0.296375\pi$
$594$	7.60600	0.312078
$595$	0	0
$596$	−46.7295	−1.91412
$597$	−16.6593	−0.681819
$598$	−9.88114	−0.404070
$599$	39.3093	1.60613	0.803066	−	0.595889i	$-0.203200\pi$
$599$	39.3093	1.60613	0.803066	+	0.595889i	$0.203200\pi$
$600$	29.3839	1.19959
$601$	45.2577	1.84610	0.923049	−	0.384682i	$-0.125689\pi$
$601$	45.2577	1.84610	0.923049	+	0.384682i	$0.125689\pi$
$602$	0	0
$603$	−0.893854	−0.0364005
$604$	−39.7478	−1.61731
$605$	−1.37326	−0.0558312
$606$	−7.67358	−0.311718
$607$	−45.5528	−1.84893	−0.924466	−	0.381265i	$-0.875488\pi$
$607$	−45.5528	−1.84893	−0.924466	+	0.381265i	$0.875488\pi$
$608$	41.3020	1.67502
$609$	0	0
$610$	−14.4305	−0.584274
$611$	9.63374	0.389740
$612$	30.3881	1.22837
$613$	5.94205	0.239997	0.119999	−	0.992774i	$-0.461711\pi$
$613$	5.94205	0.239997	0.119999	+	0.992774i	$0.461711\pi$
$614$	0.0992296	0.00400458
$615$	−0.126049	−0.00508278
$616$	0	0
$617$	7.63295	0.307291	0.153646	−	0.988126i	$-0.450899\pi$
$617$	7.63295	0.307291	0.153646	+	0.988126i	$0.450899\pi$
$618$	−35.6276	−1.43315
$619$	12.7641	0.513034	0.256517	−	0.966540i	$-0.417425\pi$
$619$	12.7641	0.513034	0.256517	+	0.966540i	$0.417425\pi$
$620$	6.48466	0.260430
$621$	−1.00000	−0.0401286
$622$	−23.3234	−0.935183
$623$	0	0
$624$	−28.4446	−1.13870
$625$	18.8748	0.754994
$626$	32.8628	1.31346
$627$	20.7933	0.830403
$628$	−42.1184	−1.68071
$629$	−29.6953	−1.18403
$630$	0	0
$631$	−23.8685	−0.950192	−0.475096	−	0.879934i	$-0.657587\pi$
$631$	−23.8685	−0.950192	−0.475096	+	0.879934i	$0.657587\pi$
$632$	−90.7811	−3.61108
$633$	19.6449	0.780816
$634$	−27.5311	−1.09340
$635$	10.3472	0.410616
$636$	42.7428	1.69486
$637$	0	0
$638$	33.4802	1.32549
$639$	15.2489	0.603237
$640$	6.98893	0.276262
$641$	24.7914	0.979202	0.489601	−	0.871947i	$-0.337142\pi$
$641$	24.7914	0.979202	0.489601	+	0.871947i	$0.337142\pi$
$642$	3.13601	0.123768
$643$	40.8527	1.61107	0.805537	−	0.592546i	$-0.201877\pi$
$643$	40.8527	1.61107	0.805537	+	0.592546i	$0.201877\pi$
$644$	0	0
$645$	−0.891787	−0.0351141
$646$	119.884	4.71676
$647$	−28.6316	−1.12562	−0.562811	−	0.826585i	$-0.690280\pi$
$647$	−28.6316	−1.12562	−0.562811	+	0.826585i	$0.690280\pi$
$648$	−6.41586	−0.252039
$649$	−20.2660	−0.795511
$650$	−45.2545	−1.77503
$651$	0	0
$652$	2.09046	0.0818686
$653$	−20.9254	−0.818874	−0.409437	−	0.912338i	$-0.634275\pi$
$653$	−20.9254	−0.818874	−0.409437	+	0.912338i	$0.634275\pi$
$654$	−41.2721	−1.61387
$655$	10.1065	0.394893
$656$	−1.42879	−0.0557849
$657$	0.943428	0.0368066
$658$	0	0
$659$	−12.2792	−0.478329	−0.239165	−	0.970979i	$-0.576874\pi$
$659$	−12.2792	−0.478329	−0.239165	+	0.970979i	$0.576874\pi$
$660$	−8.71897	−0.339385
$661$	27.3262	1.06286	0.531432	−	0.847101i	$-0.321654\pi$
$661$	27.3262	1.06286	0.531432	+	0.847101i	$0.321654\pi$
$662$	−57.6205	−2.23948
$663$	−26.0643	−1.01225
$664$	−93.8512	−3.64213
$665$	0	0
$666$	11.2577	0.436226
$667$	−4.40182	−0.170439
$668$	10.8506	0.419821
$669$	−17.5246	−0.677539
$670$	1.47865	0.0571254
$671$	−25.9968	−1.00359
$672$	0	0
$673$	9.75358	0.375973	0.187986	−	0.982172i	$-0.439804\pi$
$673$	9.75358	0.375973	0.187986	+	0.982172i	$0.439804\pi$
$674$	16.3329	0.629118
$675$	−4.57989	−0.176280
$676$	8.97874	0.345336
$677$	3.26332	0.125419	0.0627097	−	0.998032i	$-0.480026\pi$
$677$	3.26332	0.125419	0.0627097	+	0.998032i	$0.480026\pi$
$678$	12.0074	0.461140
$679$	0	0
$680$	−27.9959	−1.07359
$681$	−10.6921	−0.409724
$682$	16.8584	0.645541
$683$	−28.5540	−1.09259	−0.546294	−	0.837594i	$-0.683962\pi$
$683$	−28.5540	−1.09259	−0.546294	+	0.837594i	$0.683962\pi$
$684$	−31.4942	−1.20421
$685$	6.95186	0.265617
$686$	0	0
$687$	9.30000	0.354817
$688$	−10.1086	−0.385387
$689$	−36.6611	−1.39668
$690$	1.65425	0.0629761
$691$	46.2116	1.75797	0.878985	−	0.476849i	$-0.158221\pi$
$691$	46.2116	1.75797	0.878985	+	0.476849i	$0.158221\pi$
$692$	23.2379	0.883371
$693$	0	0
$694$	−85.0396	−3.22806
$695$	13.8892	0.526849
$696$	−28.2415	−1.07049
$697$	−1.30923	−0.0495905
$698$	72.8505	2.75743
$699$	−23.7260	−0.897401
$700$	0	0
$701$	29.0091	1.09566	0.547830	−	0.836590i	$-0.315454\pi$
$701$	29.0091	1.09566	0.547830	+	0.836590i	$0.315454\pi$
$702$	9.88114	0.372940
$703$	30.7762	1.16075
$704$	−1.23342	−0.0464864
$705$	−1.61283	−0.0607426
$706$	0.390775	0.0147070
$707$	0	0
$708$	30.6956	1.15361
$709$	49.2148	1.84830	0.924150	−	0.382030i	$-0.124775\pi$
$709$	49.2148	1.84830	0.924150	+	0.382030i	$0.124775\pi$
$710$	−25.2254	−0.946693
$711$	14.1495	0.530647
$712$	101.025	3.78606
$713$	−2.21646	−0.0830070
$714$	0	0
$715$	7.47839	0.279676
$716$	−35.1124	−1.31221
$717$	26.6326	0.994613
$718$	−55.3454	−2.06547
$719$	19.1086	0.712629	0.356314	−	0.934366i	$-0.384033\pi$
$719$	19.1086	0.712629	0.356314	+	0.934366i	$0.384033\pi$
$720$	4.76204	0.177471
$721$	0	0
$722$	−75.7552	−2.81932
$723$	11.6859	0.434603
$724$	−34.3650	−1.27717
$725$	−20.1598	−0.748718
$726$	5.40743	0.200689
$727$	3.03289	0.112483	0.0562417	−	0.998417i	$-0.482088\pi$
$727$	3.03289	0.112483	0.0562417	+	0.998417i	$0.482088\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−1.56066	−0.0577627
$731$	−9.26268	−0.342593
$732$	39.3756	1.45536
$733$	−0.824326	−0.0304472	−0.0152236	−	0.999884i	$-0.504846\pi$
$733$	−0.824326	−0.0304472	−0.0152236	+	0.999884i	$0.504846\pi$
$734$	−7.76404	−0.286576
$735$	0	0
$736$	5.91953	0.218197
$737$	2.66382	0.0981230
$738$	0.496336	0.0182704
$739$	−10.2193	−0.375924	−0.187962	−	0.982176i	$-0.560188\pi$
$739$	−10.2193	−0.375924	−0.187962	+	0.982176i	$0.560188\pi$
$740$	−12.9050	−0.474397
$741$	27.0130	0.992348
$742$	0	0
$743$	10.5624	0.387496	0.193748	−	0.981051i	$-0.437936\pi$
$743$	10.5624	0.387496	0.193748	+	0.981051i	$0.437936\pi$
$744$	−14.2205	−0.521349
$745$	−6.71008	−0.245838
$746$	−70.4763	−2.58032
$747$	14.6280	0.535210
$748$	−90.5610	−3.31124
$749$	0	0
$750$	15.8475	0.578669
$751$	−41.1035	−1.49989	−0.749944	−	0.661501i	$-0.769920\pi$
$751$	−41.1035	−1.49989	−0.749944	+	0.661501i	$0.769920\pi$
$752$	−18.2818	−0.666668
$753$	−12.0271	−0.438291
$754$	43.4950	1.58399
$755$	−5.70754	−0.207719
$756$	0	0
$757$	−34.3157	−1.24723	−0.623613	−	0.781733i	$-0.714336\pi$
$757$	−34.3157	−1.24723	−0.623613	+	0.781733i	$0.714336\pi$
$758$	−61.2838	−2.22593
$759$	2.98015	0.108173
$760$	29.0149	1.05248
$761$	−5.79240	−0.209974	−0.104987	−	0.994474i	$-0.533480\pi$
$761$	−5.79240	−0.209974	−0.104987	+	0.994474i	$0.533480\pi$
$762$	−40.7436	−1.47599
$763$	0	0
$764$	−3.33517	−0.120662
$765$	4.36354	0.157764
$766$	28.1046	1.01546
$767$	−26.3281	−0.950652
$768$	−28.3477	−1.02291
$769$	−27.9852	−1.00917	−0.504586	−	0.863361i	$-0.668355\pi$
$769$	−27.9852	−1.00917	−0.504586	+	0.863361i	$0.668355\pi$
$770$	0	0
$771$	−10.1840	−0.366768
$772$	−72.0870	−2.59447
$773$	−35.3270	−1.27063	−0.635313	−	0.772255i	$-0.719129\pi$
$773$	−35.3270	−1.27063	−0.635313	+	0.772255i	$0.719129\pi$
$774$	3.51154	0.126220
$775$	−10.1511	−0.364640
$776$	−20.7502	−0.744889
$777$	0	0
$778$	−89.5712	−3.21128
$779$	1.35688	0.0486153
$780$	−11.3270	−0.405573
$781$	−45.4440	−1.62611
$782$	17.1821	0.614430
$783$	4.40182	0.157308
$784$	0	0
$785$	−6.04795	−0.215861
$786$	−39.7958	−1.41947
$787$	−34.3989	−1.22619	−0.613094	−	0.790010i	$-0.710075\pi$
$787$	−34.3989	−1.22619	−0.613094	+	0.790010i	$0.710075\pi$
$788$	−42.8902	−1.52790
$789$	20.8565	0.742510
$790$	−23.4067	−0.832774
$791$	0	0
$792$	19.1202	0.679407
$793$	−33.7730	−1.19932
$794$	−38.8660	−1.37930
$795$	6.13761	0.217678
$796$	−75.1973	−2.66530
$797$	−22.2714	−0.788894	−0.394447	−	0.918919i	$-0.629064\pi$
$797$	−22.2714	−0.788894	−0.394447	+	0.918919i	$0.629064\pi$
$798$	0	0
$799$	−16.7519	−0.592640
$800$	27.1108	0.958511
$801$	−15.7461	−0.556361
$802$	48.4565	1.71106
$803$	−2.81155	−0.0992176
$804$	−4.03471	−0.142293
$805$	0	0
$806$	21.9011	0.771435
$807$	−20.4710	−0.720615
$808$	−19.2901	−0.678624
$809$	−34.2698	−1.20486	−0.602431	−	0.798171i	$-0.705801\pi$
$809$	−34.2698	−1.20486	−0.602431	+	0.798171i	$0.705801\pi$
$810$	−1.65425	−0.0581243
$811$	−52.1588	−1.83154	−0.915772	−	0.401698i	$-0.868420\pi$
$811$	−52.1588	−1.83154	−0.915772	+	0.401698i	$0.868420\pi$
$812$	0	0
$813$	−18.8557	−0.661297
$814$	−33.5495	−1.17591
$815$	0.300177	0.0105147
$816$	49.4617	1.73151
$817$	9.59984	0.335856
$818$	−19.0262	−0.665235
$819$	0	0
$820$	−0.568963	−0.0198691
$821$	−17.7363	−0.619003	−0.309501	−	0.950899i	$-0.600162\pi$
$821$	−17.7363	−0.619003	−0.309501	+	0.950899i	$0.600162\pi$
$822$	−27.3740	−0.954777
$823$	−0.590118	−0.0205702	−0.0102851	−	0.999947i	$-0.503274\pi$
$823$	−0.590118	−0.0205702	−0.0102851	+	0.999947i	$0.503274\pi$
$824$	−89.5619	−3.12004
$825$	13.6488	0.475189
$826$	0	0
$827$	50.4841	1.75550	0.877752	−	0.479114i	$-0.159042\pi$
$827$	50.4841	1.75550	0.877752	+	0.479114i	$0.159042\pi$
$828$	−4.51383	−0.156867
$829$	−28.1085	−0.976248	−0.488124	−	0.872774i	$-0.662319\pi$
$829$	−28.1085	−0.976248	−0.488124	+	0.872774i	$0.662319\pi$
$830$	−24.1983	−0.839935
$831$	−4.96206	−0.172132
$832$	−1.60237	−0.0555522
$833$	0	0
$834$	−54.6909	−1.89379
$835$	1.55807	0.0539194
$836$	93.8573	3.24612
$837$	2.21646	0.0766120
$838$	−8.10021	−0.279817
$839$	−22.3730	−0.772401	−0.386200	−	0.922415i	$-0.626213\pi$
$839$	−22.3730	−0.772401	−0.386200	+	0.922415i	$0.626213\pi$
$840$	0	0
$841$	−9.62400	−0.331862
$842$	−38.5548	−1.32869
$843$	9.56605	0.329472
$844$	88.6740	3.05228
$845$	1.28929	0.0443530
$846$	6.35075	0.218343
$847$	0	0
$848$	69.5712	2.38908
$849$	7.41833	0.254597
$850$	78.6921	2.69912
$851$	4.41093	0.151205
$852$	68.8310	2.35811
$853$	39.3664	1.34788	0.673940	−	0.738786i	$-0.264601\pi$
$853$	39.3664	1.34788	0.673940	+	0.738786i	$0.264601\pi$
$854$	0	0
$855$	−4.52237	−0.154662
$856$	7.88341	0.269449
$857$	23.9320	0.817501	0.408751	−	0.912646i	$-0.365965\pi$
$857$	23.9320	0.817501	0.408751	+	0.912646i	$0.365965\pi$
$858$	−29.4473	−1.00531
$859$	26.1879	0.893521	0.446761	−	0.894654i	$-0.352578\pi$
$859$	26.1879	0.893521	0.446761	+	0.894654i	$0.352578\pi$
$860$	−4.02538	−0.137264
$861$	0	0
$862$	−63.8751	−2.17559
$863$	−17.7501	−0.604221	−0.302111	−	0.953273i	$-0.597691\pi$
$863$	−17.7501	−0.604221	−0.302111	+	0.953273i	$0.597691\pi$
$864$	−5.91953	−0.201386
$865$	3.33681	0.113455
$866$	70.4084	2.39258
$867$	28.3226	0.961887
$868$	0	0
$869$	−42.1676	−1.43044
$870$	−7.28169	−0.246872
$871$	3.46063	0.117259
$872$	−103.751	−3.51346
$873$	3.23421	0.109461
$874$	−17.8075	−0.602348
$875$	0	0
$876$	4.25848	0.143881
$877$	0.981287	0.0331357	0.0165679	−	0.999863i	$-0.494726\pi$
$877$	0.981287	0.0331357	0.0165679	+	0.999863i	$0.494726\pi$
$878$	52.0313	1.75597
$879$	9.37108	0.316079
$880$	−14.1916	−0.478399
$881$	52.6379	1.77341	0.886707	−	0.462331i	$-0.152987\pi$
$881$	52.6379	1.77341	0.886707	+	0.462331i	$0.152987\pi$
$882$	0	0
$883$	22.2550	0.748939	0.374469	−	0.927239i	$-0.377825\pi$
$883$	22.2550	0.748939	0.374469	+	0.927239i	$0.377825\pi$
$884$	−117.650	−3.95700
$885$	4.40770	0.148163
$886$	−71.1413	−2.39004
$887$	−33.2977	−1.11803	−0.559014	−	0.829158i	$-0.688820\pi$
$887$	−33.2977	−1.11803	−0.559014	+	0.829158i	$0.688820\pi$
$888$	28.2999	0.949683
$889$	0	0
$890$	26.0479	0.873127
$891$	−2.98015	−0.0998387
$892$	−79.1030	−2.64856
$893$	17.3616	0.580985
$894$	26.4219	0.883681
$895$	−5.04193	−0.168533
$896$	0	0
$897$	3.87158	0.129268
$898$	32.1175	1.07177
$899$	9.75645	0.325396
$900$	−20.6729	−0.689095
$901$	63.7492	2.12380
$902$	−1.47915	−0.0492504
$903$	0	0
$904$	30.1845	1.00392
$905$	−4.93461	−0.164032
$906$	22.4743	0.746658
$907$	6.18355	0.205321	0.102661	−	0.994716i	$-0.467264\pi$
$907$	6.18355	0.205321	0.102661	+	0.994716i	$0.467264\pi$
$908$	−48.2625	−1.60165
$909$	3.00663	0.0997235
$910$	0	0
$911$	15.7337	0.521282	0.260641	−	0.965436i	$-0.416066\pi$
$911$	15.7337	0.521282	0.260641	+	0.965436i	$0.416066\pi$
$912$	−51.2621	−1.69746
$913$	−43.5936	−1.44274
$914$	54.3441	1.79754
$915$	5.65410	0.186919
$916$	41.9787	1.38701
$917$	0	0
$918$	−17.1821	−0.567093
$919$	11.4879	0.378949	0.189475	−	0.981886i	$-0.439322\pi$
$919$	11.4879	0.378949	0.189475	+	0.981886i	$0.439322\pi$
$920$	4.15850	0.137102
$921$	−0.0388797	−0.00128113
$922$	9.79372	0.322539
$923$	−59.0374	−1.94324
$924$	0	0
$925$	20.2016	0.664224
$926$	103.271	3.39370
$927$	13.9595	0.458489
$928$	−26.0567	−0.855352
$929$	10.2883	0.337549	0.168775	−	0.985655i	$-0.446019\pi$
$929$	10.2883	0.337549	0.168775	+	0.985655i	$0.446019\pi$
$930$	−3.66657	−0.120231
$931$	0	0
$932$	−107.095	−3.50803
$933$	9.13847	0.299180
$934$	4.52261	0.147984
$935$	−13.0040	−0.425276
$936$	24.8395	0.811906
$937$	−5.44863	−0.177999	−0.0889994	−	0.996032i	$-0.528367\pi$
$937$	−5.44863	−0.177999	−0.0889994	+	0.996032i	$0.528367\pi$
$938$	0	0
$939$	−12.8762	−0.420197
$940$	−7.28004	−0.237449
$941$	−27.8487	−0.907841	−0.453921	−	0.891042i	$-0.649975\pi$
$941$	−27.8487	−0.907841	−0.453921	+	0.891042i	$0.649975\pi$
$942$	23.8147	0.775924
$943$	0.194472	0.00633288
$944$	49.9623	1.62613
$945$	0	0
$946$	−10.4649	−0.340244
$947$	−48.3043	−1.56968	−0.784840	−	0.619699i	$-0.787255\pi$
$947$	−48.3043	−1.56968	−0.784840	+	0.619699i	$0.787255\pi$
$948$	63.8684	2.07435
$949$	−3.65256	−0.118567
$950$	−81.5564	−2.64604
$951$	10.7871	0.349796
$952$	0	0
$953$	−17.0509	−0.552334	−0.276167	−	0.961110i	$-0.589064\pi$
$953$	−17.0509	−0.552334	−0.276167	+	0.961110i	$0.589064\pi$
$954$	−24.1677	−0.782459
$955$	−0.478910	−0.0154972
$956$	120.215	3.88804
$957$	−13.1181	−0.424047
$958$	35.7816	1.15605
$959$	0	0
$960$	0.268260	0.00865805
$961$	−26.0873	−0.841526
$962$	−43.5850	−1.40524
$963$	−1.22874	−0.0395955
$964$	52.7482	1.69890
$965$	−10.3513	−0.333219
$966$	0	0
$967$	46.1833	1.48515	0.742577	−	0.669761i	$-0.233603\pi$
$967$	46.1833	1.48515	0.742577	+	0.669761i	$0.233603\pi$
$968$	13.5934	0.436908
$969$	−46.9723	−1.50897
$970$	−5.35017	−0.171784
$971$	−2.22985	−0.0715594	−0.0357797	−	0.999360i	$-0.511391\pi$
$971$	−2.22985	−0.0715594	−0.0357797	+	0.999360i	$0.511391\pi$
$972$	4.51383	0.144781
$973$	0	0
$974$	68.3459	2.18995
$975$	17.7314	0.567860
$976$	64.0905	2.05149
$977$	−47.9767	−1.53491	−0.767456	−	0.641102i	$-0.778478\pi$
$977$	−47.9767	−1.53491	−0.767456	+	0.641102i	$0.778478\pi$
$978$	−1.18199	−0.0377959
$979$	46.9257	1.49975
$980$	0	0
$981$	16.1711	0.516302
$982$	−92.2485	−2.94377
$983$	−56.4597	−1.80079	−0.900393	−	0.435078i	$-0.856721\pi$
$983$	−56.4597	−1.80079	−0.900393	+	0.435078i	$0.856721\pi$
$984$	1.24771	0.0397754
$985$	−6.15877	−0.196235
$986$	−75.6324	−2.40863
$987$	0	0
$988$	121.932	3.87918
$989$	1.37588	0.0437503
$990$	4.92990	0.156682
$991$	23.2425	0.738322	0.369161	−	0.929366i	$-0.379645\pi$
$991$	23.2425	0.738322	0.369161	+	0.929366i	$0.379645\pi$
$992$	−13.1204	−0.416573
$993$	22.5766	0.716447
$994$	0	0
$995$	−10.7979	−0.342316
$996$	66.0283	2.09219
$997$	−55.7275	−1.76491	−0.882454	−	0.470398i	$-0.844110\pi$
$997$	−55.7275	−1.76491	−0.882454	+	0.470398i	$0.844110\pi$
$998$	−97.0662	−3.07258
$999$	−4.41093	−0.139556

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3381.2.a.bf.1.1		8
7.2	even	3		483.2.i.g.277.8	✓	16
7.4	even	3		483.2.i.g.415.8	yes	16
7.6	odd	2		3381.2.a.be.1.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.i.g.277.8	✓	16	7.2	even	3
483.2.i.g.415.8	yes	16	7.4	even	3
3381.2.a.be.1.1		8	7.6	odd	2
3381.2.a.bf.1.1		8	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3381 = 3 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3381.a (trivial)

\(f(q)\)	\(=\)	\(q-2.55222 q^{2} +1.00000 q^{3} +4.51383 q^{4} +0.648159 q^{5} -2.55222 q^{6} -6.41586 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.55222 q^{2} +1.00000 q^{3} +4.51383 q^{4} +0.648159 q^{5} -2.55222 q^{6} -6.41586 q^{8} +1.00000 q^{9} -1.65425 q^{10} -2.98015 q^{11} +4.51383 q^{12} -3.87158 q^{13} +0.648159 q^{15} +7.34703 q^{16} +6.73221 q^{17} -2.55222 q^{18} -6.97725 q^{19} +2.92568 q^{20} +7.60600 q^{22} -1.00000 q^{23} -6.41586 q^{24} -4.57989 q^{25} +9.88114 q^{26} +1.00000 q^{27} +4.40182 q^{29} -1.65425 q^{30} +2.21646 q^{31} -5.91953 q^{32} -2.98015 q^{33} -17.1821 q^{34} +4.51383 q^{36} -4.41093 q^{37} +17.8075 q^{38} -3.87158 q^{39} -4.15850 q^{40} -0.194472 q^{41} -1.37588 q^{43} -13.4519 q^{44} +0.648159 q^{45} +2.55222 q^{46} -2.48832 q^{47} +7.34703 q^{48} +11.6889 q^{50} +6.73221 q^{51} -17.4757 q^{52} +9.46929 q^{53} -2.55222 q^{54} -1.93161 q^{55} -6.97725 q^{57} -11.2344 q^{58} +6.80034 q^{59} +2.92568 q^{60} +8.72332 q^{61} -5.65689 q^{62} +0.413880 q^{64} -2.50940 q^{65} +7.60600 q^{66} -0.893854 q^{67} +30.3881 q^{68} -1.00000 q^{69} +15.2489 q^{71} -6.41586 q^{72} +0.943428 q^{73} +11.2577 q^{74} -4.57989 q^{75} -31.4942 q^{76} +9.88114 q^{78} +14.1495 q^{79} +4.76204 q^{80} +1.00000 q^{81} +0.496336 q^{82} +14.6280 q^{83} +4.36354 q^{85} +3.51154 q^{86} +4.40182 q^{87} +19.1202 q^{88} -15.7461 q^{89} -1.65425 q^{90} -4.51383 q^{92} +2.21646 q^{93} +6.35075 q^{94} -4.52237 q^{95} -5.91953 q^{96} +3.23421 q^{97} -2.98015 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + 8 q^{3} + 15 q^{4} + 5 q^{5} + q^{6} + 9 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + q^2 + 8 * q^3 + 15 * q^4 + 5 * q^5 + q^6 + 9 * q^8 + 8 * q^9	\( 8 q + q^{2} + 8 q^{3} + 15 q^{4} + 5 q^{5} + q^{6} + 9 q^{8} + 8 q^{9} - 3 q^{10} + 10 q^{11} + 15 q^{12} - 6 q^{13} + 5 q^{15} + 13 q^{16} + 21 q^{17} + q^{18} + 5 q^{19} - q^{20} + 18 q^{22} - 8 q^{23} + 9 q^{24} + 27 q^{25} + 3 q^{26} + 8 q^{27} + 2 q^{29} - 3 q^{30} - 13 q^{31} + 29 q^{32} + 10 q^{33} - 19 q^{34} + 15 q^{36} + 13 q^{37} - 6 q^{38} - 6 q^{39} + 7 q^{40} + 16 q^{41} + 15 q^{43} + 24 q^{44} + 5 q^{45} - q^{46} - q^{47} + 13 q^{48} + 16 q^{50} + 21 q^{51} - 19 q^{52} + 3 q^{53} + q^{54} - 10 q^{55} + 5 q^{57} - 40 q^{58} + 26 q^{59} - q^{60} - 14 q^{61} - 14 q^{62} + 49 q^{64} - 3 q^{65} + 18 q^{66} + 38 q^{67} + 43 q^{68} - 8 q^{69} + 9 q^{71} + 9 q^{72} - 6 q^{73} + 32 q^{74} + 27 q^{75} - 14 q^{76} + 3 q^{78} + 23 q^{79} - 17 q^{80} + 8 q^{81} + 20 q^{82} + 30 q^{83} - 37 q^{85} - 28 q^{86} + 2 q^{87} + 86 q^{88} + 12 q^{89} - 3 q^{90} - 15 q^{92} - 13 q^{93} - 45 q^{94} + 16 q^{95} + 29 q^{96} + 14 q^{97} + 10 q^{99}+O(q^{100}) \) 8 * q + q^2 + 8 * q^3 + 15 * q^4 + 5 * q^5 + q^6 + 9 * q^8 + 8 * q^9 - 3 * q^10 + 10 * q^11 + 15 * q^12 - 6 * q^13 + 5 * q^15 + 13 * q^16 + 21 * q^17 + q^18 + 5 * q^19 - q^20 + 18 * q^22 - 8 * q^23 + 9 * q^24 + 27 * q^25 + 3 * q^26 + 8 * q^27 + 2 * q^29 - 3 * q^30 - 13 * q^31 + 29 * q^32 + 10 * q^33 - 19 * q^34 + 15 * q^36 + 13 * q^37 - 6 * q^38 - 6 * q^39 + 7 * q^40 + 16 * q^41 + 15 * q^43 + 24 * q^44 + 5 * q^45 - q^46 - q^47 + 13 * q^48 + 16 * q^50 + 21 * q^51 - 19 * q^52 + 3 * q^53 + q^54 - 10 * q^55 + 5 * q^57 - 40 * q^58 + 26 * q^59 - q^60 - 14 * q^61 - 14 * q^62 + 49 * q^64 - 3 * q^65 + 18 * q^66 + 38 * q^67 + 43 * q^68 - 8 * q^69 + 9 * q^71 + 9 * q^72 - 6 * q^73 + 32 * q^74 + 27 * q^75 - 14 * q^76 + 3 * q^78 + 23 * q^79 - 17 * q^80 + 8 * q^81 + 20 * q^82 + 30 * q^83 - 37 * q^85 - 28 * q^86 + 2 * q^87 + 86 * q^88 + 12 * q^89 - 3 * q^90 - 15 * q^92 - 13 * q^93 - 45 * q^94 + 16 * q^95 + 29 * q^96 + 14 * q^97 + 10 * q^99

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