LMFDB - Embedded newform 3381.2.a.be.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	$-0.546297\pi$
$5$	−0.648159	−0.289866	−0.144933	+	0.989442i	$0.546297\pi$
$6$	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	$-0.319598\pi$
$13$	3.87158	1.07378	0.536892	+	0.843651i	$0.319598\pi$
$14$	0	0
$15$	0.648159	0.167354
$16$	7.34703	1.83676
$17$	−6.73221	−1.63280	−0.816400	−	0.577486i	$-0.804034\pi$
$17$	−6.73221	−1.63280	−0.816400	+	0.577486i	$0.804034\pi$
$18$	−2.55222	−0.601564
$19$	6.97725	1.60069	0.800346	−	0.599538i	$-0.204649\pi$
$19$	6.97725	1.60069	0.800346	+	0.599538i	$0.204649\pi$
$20$	−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	$-0.563784\pi$
$31$	−2.21646	−0.398088	−0.199044	+	0.979991i	$0.563784\pi$
$32$	−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	$-0.495166\pi$
$41$	0.194472	0.0303714	0.0151857	+	0.999885i	$0.495166\pi$
$42$	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	$-0.441911\pi$
$47$	2.48832	0.362959	0.181479	+	0.983395i	$0.441911\pi$
$48$	−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	$-0.645967\pi$
$59$	−6.80034	−0.885329	−0.442664	+	0.896687i	$0.645967\pi$
$60$	2.92568	0.377704
$61$	−8.72332	−1.11691	−0.558453	−	0.829536i	$-0.688605\pi$
$61$	−8.72332	−1.11691	−0.558453	+	0.829536i	$0.688605\pi$
$62$	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	$-0.517583\pi$
$73$	−0.943428	−0.110420	−0.0552099	+	0.998475i	$0.517583\pi$
$74$	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	$-0.796665\pi$
$83$	−14.6280	−1.60563	−0.802815	+	0.596228i	$0.796665\pi$
$84$	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	$-0.185733\pi$
$89$	15.7461	1.66908	0.834541	+	0.550946i	$0.185733\pi$
$90$	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	$-0.552502\pi$
$97$	−3.23421	−0.328384	−0.164192	+	0.986428i	$0.552502\pi$
$98$	0	0
$99$	−2.98015	−0.299516
$100$	−20.6729	−2.06729
$101$	−3.00663	−0.299171	−0.149585	−	0.988749i	$-0.547794\pi$
$101$	−3.00663	−0.299171	−0.149585	+	0.988749i	$0.547794\pi$
$102$	−17.1821	−1.70128
$103$	−13.9595	−1.37547	−0.687733	−	0.725964i	$-0.741394\pi$
$103$	−13.9595	−1.37547	−0.687733	+	0.725964i	$0.741394\pi$
$104$	−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	$-0.738527\pi$
$131$	−15.5926	−1.36233	−0.681166	+	0.732129i	$0.738527\pi$
$132$	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	$-0.862986\pi$
$139$	−21.4287	−1.81756	−0.908781	+	0.417273i	$0.862986\pi$
$140$	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	$-0.378553\pi$
$157$	9.33096	0.744692	0.372346	+	0.928094i	$0.378553\pi$
$158$	−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	$-0.529648\pi$
$167$	−2.40385	−0.186015	−0.0930076	+	0.995665i	$0.529648\pi$
$168$	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	$-0.562699\pi$
$173$	−5.14814	−0.391406	−0.195703	+	0.980663i	$0.562699\pi$
$174$	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	$-0.408689\pi$
$181$	7.61327	0.565890	0.282945	+	0.959136i	$0.408689\pi$
$182$	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	$-0.298941\pi$
$199$	16.6593	1.18095	0.590473	+	0.807057i	$0.298941\pi$
$200$	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	$-0.300401\pi$
$223$	17.5246	1.17353	0.586766	+	0.809757i	$0.300401\pi$
$224$	0	0
$225$	−4.57989	−0.305326
$226$	12.0074	0.798718
$227$	10.6921	0.709662	0.354831	−	0.934930i	$-0.384538\pi$
$227$	10.6921	0.709662	0.354831	+	0.934930i	$0.384538\pi$
$228$	−31.4942	−2.08575
$229$	−9.30000	−0.614561	−0.307281	−	0.951619i	$-0.599419\pi$
$229$	−9.30000	−0.614561	−0.307281	+	0.951619i	$0.599419\pi$
$230$	−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	$-0.622830\pi$
$241$	−11.6859	−0.752754	−0.376377	+	0.926466i	$0.622830\pi$
$242$	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	$-0.376072\pi$
$251$	12.0271	0.759142	0.379571	+	0.925163i	$0.376072\pi$
$252$	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	$-0.397113\pi$
$257$	10.1840	0.635261	0.317631	+	0.948215i	$0.397113\pi$
$258$	−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	$-0.285478\pi$
$269$	20.4710	1.24814	0.624071	+	0.781368i	$0.285478\pi$
$270$	−1.65425	−0.100674
$271$	18.8557	1.14540	0.572700	−	0.819765i	$-0.305896\pi$
$271$	18.8557	1.14540	0.572700	+	0.819765i	$0.305896\pi$
$272$	−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	$-0.570765\pi$
$283$	−7.41833	−0.440974	−0.220487	+	0.975390i	$0.570765\pi$
$284$	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	$-0.588258\pi$
$293$	−9.37108	−0.547464	−0.273732	+	0.961806i	$0.588258\pi$
$294$	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	$-0.499647\pi$
$307$	0.0388797	0.00221898	0.00110949	+	0.999999i	$0.499647\pi$
$308$	0	0
$309$	13.9595	0.794125
$310$	−3.66657	−0.208247
$311$	−9.13847	−0.518195	−0.259098	−	0.965851i	$-0.583425\pi$
$311$	−9.13847	−0.518195	−0.259098	+	0.965851i	$0.583425\pi$
$312$	24.8395	1.40626
$313$	12.8762	0.727803	0.363902	−	0.931437i	$-0.381444\pi$
$313$	12.8762	0.727803	0.363902	+	0.931437i	$0.381444\pi$
$314$	−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	$-0.223252\pi$
$349$	28.5439	1.52792	0.763961	+	0.645262i	$0.223252\pi$
$350$	0	0
$351$	−3.87158	−0.206650
$352$	17.6411	0.940272
$353$	0.153112	0.00814932	0.00407466	−	0.999992i	$-0.498703\pi$
$353$	0.153112	0.00814932	0.00407466	+	0.999992i	$0.498703\pi$
$354$	−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	$-0.525300\pi$
$367$	−3.04207	−0.158795	−0.0793974	+	0.996843i	$0.525300\pi$
$368$	−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	$-0.409222\pi$
$383$	11.0118	0.562677	0.281339	+	0.959609i	$0.409222\pi$
$384$	−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	$-0.624814\pi$
$397$	−15.2283	−0.764287	−0.382144	+	0.924103i	$0.624814\pi$
$398$	−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	$-0.559004\pi$
$409$	−7.45476	−0.368614	−0.184307	+	0.982869i	$0.559004\pi$
$410$	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	$-0.524702\pi$
$419$	−3.17379	−0.155050	−0.0775248	+	0.996990i	$0.524702\pi$
$420$	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	$-0.269336\pi$
$433$	27.5871	1.32575	0.662876	+	0.748729i	$0.269336\pi$
$434$	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	$-0.338273\pi$
$439$	20.3867	0.973002	0.486501	+	0.873680i	$0.338273\pi$
$440$	−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	$-0.471517\pi$
$461$	3.83733	0.178722	0.0893612	+	0.995999i	$0.471517\pi$
$462$	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	$-0.486946\pi$
$467$	1.77203	0.0819998	0.0409999	+	0.999159i	$0.486946\pi$
$468$	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	$-0.396220\pi$
$479$	14.0198	0.640580	0.320290	+	0.947319i	$0.396220\pi$
$480$	−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	$-0.400349\pi$
$503$	13.8143	0.615947	0.307974	+	0.951395i	$0.400349\pi$
$504$	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	$-0.559468\pi$
$509$	−8.38094	−0.371479	−0.185739	+	0.982599i	$0.559468\pi$
$510$	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	$-0.497557\pi$
$521$	0.350341	0.0153487	0.00767436	+	0.999971i	$0.497557\pi$
$522$	−11.2344	−0.491717
$523$	39.2807	1.71763	0.858813	−	0.512289i	$-0.171202\pi$
$523$	39.2807	1.71763	0.858813	+	0.512289i	$0.171202\pi$
$524$	−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	$-0.335697\pi$
$563$	23.4218	0.987111	0.493555	+	0.869714i	$0.335697\pi$
$564$	−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	$-0.373023\pi$
$577$	18.6601	0.776831	0.388415	+	0.921484i	$0.373023\pi$
$578$	−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	$-0.768284\pi$
$587$	−36.1742	−1.49307	−0.746535	+	0.665346i	$0.768284\pi$
$588$	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	$-0.703625\pi$
$593$	−29.0739	−1.19392	−0.596961	+	0.802270i	$0.703625\pi$
$594$	−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	$-0.874311\pi$
$601$	−45.2577	−1.84610	−0.923049	+	0.384682i	$0.874311\pi$
$602$	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	$-0.124512\pi$
$607$	45.5528	1.84893	0.924466	+	0.381265i	$0.124512\pi$
$608$	−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	$-0.582575\pi$
$619$	−12.7641	−0.513034	−0.256517	+	0.966540i	$0.582575\pi$
$620$	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	$-0.798123\pi$
$643$	−40.8527	−1.61107	−0.805537	+	0.592546i	$0.798123\pi$
$644$	0	0
$645$	−0.891787	−0.0351141
$646$	119.884	4.71676
$647$	28.6316	1.12562	0.562811	−	0.826585i	$-0.309720\pi$
$647$	28.6316	1.12562	0.562811	+	0.826585i	$0.309720\pi$
$648$	−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	$-0.678346\pi$
$661$	−27.3262	−1.06286	−0.531432	+	0.847101i	$0.678346\pi$
$662$	−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	$-0.519974\pi$
$677$	−3.26332	−0.125419	−0.0627097	+	0.998032i	$0.519974\pi$
$678$	−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	$-0.841779\pi$
$691$	−46.2116	−1.75797	−0.878985	+	0.476849i	$0.841779\pi$
$692$	−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	$-0.615967\pi$
$719$	−19.1086	−0.712629	−0.356314	+	0.934366i	$0.615967\pi$
$720$	−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	$-0.517912\pi$
$727$	−3.03289	−0.112483	−0.0562417	+	0.998417i	$0.517912\pi$
$728$	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	$-0.495154\pi$
$733$	0.824326	0.0304472	0.0152236	+	0.999884i	$0.495154\pi$
$734$	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	$-0.466520\pi$
$761$	5.79240	0.209974	0.104987	+	0.994474i	$0.466520\pi$
$762$	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	$-0.331645\pi$
$769$	27.9852	1.00917	0.504586	+	0.863361i	$0.331645\pi$
$770$	0	0
$771$	−10.1840	−0.366768
$772$	−72.0870	−2.59447
$773$	35.3270	1.27063	0.635313	−	0.772255i	$-0.280871\pi$
$773$	35.3270	1.27063	0.635313	+	0.772255i	$0.280871\pi$
$774$	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	$-0.289925\pi$
$787$	34.3989	1.22619	0.613094	+	0.790010i	$0.289925\pi$
$788$	−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	$-0.370936\pi$
$797$	22.2714	0.788894	0.394447	+	0.918919i	$0.370936\pi$
$798$	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	$-0.131580\pi$
$811$	52.1588	1.83154	0.915772	+	0.401698i	$0.131580\pi$
$812$	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	$-0.337681\pi$
$829$	28.1085	0.976248	0.488124	+	0.872774i	$0.337681\pi$
$830$	−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	$-0.373787\pi$
$839$	22.3730	0.772401	0.386200	+	0.922415i	$0.373787\pi$
$840$	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	$-0.735399\pi$
$853$	−39.3664	−1.34788	−0.673940	+	0.738786i	$0.735399\pi$
$854$	0	0
$855$	−4.52237	−0.154662
$856$	7.88341	0.269449
$857$	−23.9320	−0.817501	−0.408751	−	0.912646i	$-0.634035\pi$
$857$	−23.9320	−0.817501	−0.408751	+	0.912646i	$0.634035\pi$
$858$	−29.4473	−1.00531
$859$	−26.1879	−0.893521	−0.446761	−	0.894654i	$-0.647422\pi$
$859$	−26.1879	−0.893521	−0.446761	+	0.894654i	$0.647422\pi$
$860$	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	$-0.847013\pi$
$881$	−52.6379	−1.77341	−0.886707	+	0.462331i	$0.847013\pi$
$882$	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	$-0.311180\pi$
$887$	33.2977	1.11803	0.559014	+	0.829158i	$0.311180\pi$
$888$	−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	$-0.553981\pi$
$929$	−10.2883	−0.337549	−0.168775	+	0.985655i	$0.553981\pi$
$930$	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	$-0.471633\pi$
$937$	5.44863	0.177999	0.0889994	+	0.996032i	$0.471633\pi$
$938$	0	0
$939$	−12.8762	−0.420197
$940$	−7.28004	−0.237449
$941$	27.8487	0.907841	0.453921	−	0.891042i	$-0.350025\pi$
$941$	27.8487	0.907841	0.453921	+	0.891042i	$0.350025\pi$
$942$	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	$-0.488609\pi$
$971$	2.22985	0.0715594	0.0357797	+	0.999360i	$0.488609\pi$
$972$	−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	$-0.143279\pi$
$983$	56.4597	1.80079	0.900393	+	0.435078i	$0.143279\pi$
$984$	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	$-0.155890\pi$
$997$	55.7275	1.76491	0.882454	+	0.470398i	$0.155890\pi$
$998$	−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.be.1.1		8
7.3	odd	6		483.2.i.g.415.8	yes	16
7.5	odd	6		483.2.i.g.277.8	✓	16
7.6	odd	2		3381.2.a.bf.1.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.i.g.277.8	✓	16	7.5	odd	6
483.2.i.g.415.8	yes	16	7.3	odd	6
3381.2.a.be.1.1		8	1.1	even	1	trivial
3381.2.a.bf.1.1		8	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:	\( N \)	\(=\)	\( 3381 = 3 \cdot 7^{2} \cdot 23 \)
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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