LMFDB - Embedded newform 3381.2.a.bd.1.3

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:	$1$
Dimension:	$6$
Coefficient field:	6.6.7997584.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 7x^{4} + 5x^{3} + 12x^{2} - 4x - 2 $ x^6 - x^5 - 7x^4 + 5x^3 + 12x^2 - 4x - 2
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			1.3
Root			$0.593528$ 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)

$f(q)$	$=$	$q-0.593528 q^{2} +1.00000 q^{3} -1.64772 q^{4} +3.15120 q^{5} -0.593528 q^{6} +2.16503 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.593528 q^{2} +1.00000 q^{3} -1.64772 q^{4} +3.15120 q^{5} -0.593528 q^{6} +2.16503 q^{8} +1.00000 q^{9} -1.87033 q^{10} -6.54534 q^{11} -1.64772 q^{12} +0.692965 q^{13} +3.15120 q^{15} +2.01044 q^{16} -6.84417 q^{17} -0.593528 q^{18} +2.91662 q^{19} -5.19231 q^{20} +3.88485 q^{22} -1.00000 q^{23} +2.16503 q^{24} +4.93009 q^{25} -0.411295 q^{26} +1.00000 q^{27} +2.94619 q^{29} -1.87033 q^{30} +0.539333 q^{31} -5.52331 q^{32} -6.54534 q^{33} +4.06221 q^{34} -1.64772 q^{36} -2.89613 q^{37} -1.73110 q^{38} +0.692965 q^{39} +6.82244 q^{40} -9.26871 q^{41} -4.27043 q^{43} +10.7849 q^{44} +3.15120 q^{45} +0.593528 q^{46} -10.4674 q^{47} +2.01044 q^{48} -2.92615 q^{50} -6.84417 q^{51} -1.14182 q^{52} +12.5749 q^{53} -0.593528 q^{54} -20.6257 q^{55} +2.91662 q^{57} -1.74865 q^{58} -6.70326 q^{59} -5.19231 q^{60} -5.30183 q^{61} -0.320109 q^{62} -0.742642 q^{64} +2.18368 q^{65} +3.88485 q^{66} -2.73628 q^{67} +11.2773 q^{68} -1.00000 q^{69} -0.587217 q^{71} +2.16503 q^{72} -10.5266 q^{73} +1.71893 q^{74} +4.93009 q^{75} -4.80579 q^{76} -0.411295 q^{78} -13.3870 q^{79} +6.33531 q^{80} +1.00000 q^{81} +5.50124 q^{82} +9.77501 q^{83} -21.5674 q^{85} +2.53462 q^{86} +2.94619 q^{87} -14.1708 q^{88} -2.92939 q^{89} -1.87033 q^{90} +1.64772 q^{92} +0.539333 q^{93} +6.21272 q^{94} +9.19088 q^{95} -5.52331 q^{96} +8.14170 q^{97} -6.54534 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{2} + 6 q^{3} + 3 q^{4} - 3 q^{5} - q^{6} - 3 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q - q^2 + 6 * q^3 + 3 * q^4 - 3 * q^5 - q^6 - 3 * q^8 + 6 * q^9	$ 6 q - q^{2} + 6 q^{3} + 3 q^{4} - 3 q^{5} - q^{6} - 3 q^{8} + 6 q^{9} + 3 q^{10} - 14 q^{11} + 3 q^{12} - 3 q^{15} - 7 q^{16} - 15 q^{17} - q^{18} + q^{19} - 17 q^{20} - 6 q^{22} - 6 q^{23} - 3 q^{24} + 9 q^{25} + 15 q^{26} + 6 q^{27} - 6 q^{29} + 3 q^{30} + 11 q^{31} + 3 q^{32} - 14 q^{33} - 15 q^{34} + 3 q^{36} - 5 q^{37} - 14 q^{38} + 17 q^{40} - 18 q^{41} - 37 q^{43} - 10 q^{44} - 3 q^{45} + q^{46} - 3 q^{47} - 7 q^{48} - 30 q^{50} - 15 q^{51} + 7 q^{52} - 15 q^{53} - q^{54} + 2 q^{55} + q^{57} + 4 q^{58} + 2 q^{59} - 17 q^{60} + 12 q^{61} - 36 q^{62} - 23 q^{64} - 17 q^{65} - 6 q^{66} - 10 q^{67} + q^{68} - 6 q^{69} - 21 q^{71} - 3 q^{72} + 8 q^{73} - 16 q^{74} + 9 q^{75} - 18 q^{76} + 15 q^{78} - 17 q^{79} - 3 q^{80} + 6 q^{81} + 48 q^{82} - 12 q^{83} - 13 q^{85} + 22 q^{86} - 6 q^{87} - 2 q^{88} - 18 q^{89} + 3 q^{90} - 3 q^{92} + 11 q^{93} - 3 q^{94} - 16 q^{95} + 3 q^{96} + 2 q^{97} - 14 q^{99}+O(q^{100}) $ 6 * q - q^2 + 6 * q^3 + 3 * q^4 - 3 * q^5 - q^6 - 3 * q^8 + 6 * q^9 + 3 * q^10 - 14 * q^11 + 3 * q^12 - 3 * q^15 - 7 * q^16 - 15 * q^17 - q^18 + q^19 - 17 * q^20 - 6 * q^22 - 6 * q^23 - 3 * q^24 + 9 * q^25 + 15 * q^26 + 6 * q^27 - 6 * q^29 + 3 * q^30 + 11 * q^31 + 3 * q^32 - 14 * q^33 - 15 * q^34 + 3 * q^36 - 5 * q^37 - 14 * q^38 + 17 * q^40 - 18 * q^41 - 37 * q^43 - 10 * q^44 - 3 * q^45 + q^46 - 3 * q^47 - 7 * q^48 - 30 * q^50 - 15 * q^51 + 7 * q^52 - 15 * q^53 - q^54 + 2 * q^55 + q^57 + 4 * q^58 + 2 * q^59 - 17 * q^60 + 12 * q^61 - 36 * q^62 - 23 * q^64 - 17 * q^65 - 6 * q^66 - 10 * q^67 + q^68 - 6 * q^69 - 21 * q^71 - 3 * q^72 + 8 * q^73 - 16 * q^74 + 9 * q^75 - 18 * q^76 + 15 * q^78 - 17 * q^79 - 3 * q^80 + 6 * q^81 + 48 * q^82 - 12 * q^83 - 13 * q^85 + 22 * q^86 - 6 * q^87 - 2 * q^88 - 18 * q^89 + 3 * q^90 - 3 * q^92 + 11 * q^93 - 3 * q^94 - 16 * q^95 + 3 * q^96 + 2 * q^97 - 14 * 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 $

$2$	−0.593528	−0.419688	−0.209844	−	0.977735i	$-0.567296\pi$
$2$	−0.593528	−0.419688	−0.209844	+	0.977735i	$0.567296\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.64772	−0.823862
$5$	3.15120	1.40926	0.704631	−	0.709574i	$-0.251113\pi$
$5$	3.15120	1.40926	0.704631	+	0.709574i	$0.251113\pi$
$6$	−0.593528	−0.242307
$7$	0	0
$7$	0	0
$8$	2.16503	0.765453
$9$	1.00000	0.333333
$10$	−1.87033	−0.591450
$11$	−6.54534	−1.97349	−0.986747	−	0.162266i	$-0.948120\pi$
$11$	−6.54534	−1.97349	−0.986747	+	0.162266i	$0.948120\pi$
$12$	−1.64772	−0.475657
$13$	0.692965	0.192194	0.0960970	−	0.995372i	$-0.469364\pi$
$13$	0.692965	0.192194	0.0960970	+	0.995372i	$0.469364\pi$
$14$	0	0
$15$	3.15120	0.813637
$16$	2.01044	0.502611
$17$	−6.84417	−1.65995	−0.829977	−	0.557797i	$-0.811647\pi$
$17$	−6.84417	−1.65995	−0.829977	+	0.557797i	$0.811647\pi$
$18$	−0.593528	−0.139896
$19$	2.91662	0.669120	0.334560	−	0.942375i	$-0.391412\pi$
$19$	2.91662	0.669120	0.334560	+	0.942375i	$0.391412\pi$
$20$	−5.19231	−1.16104
$21$	0	0
$22$	3.88485	0.828252
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	2.16503	0.441934
$25$	4.93009	0.986017
$26$	−0.411295	−0.0806615
$27$	1.00000	0.192450
$28$	0	0
$29$	2.94619	0.547094	0.273547	−	0.961859i	$-0.411803\pi$
$29$	2.94619	0.547094	0.273547	+	0.961859i	$0.411803\pi$
$30$	−1.87033	−0.341474
$31$	0.539333	0.0968671	0.0484335	−	0.998826i	$-0.484577\pi$
$31$	0.539333	0.0968671	0.0484335	+	0.998826i	$0.484577\pi$
$32$	−5.52331	−0.976393
$33$	−6.54534	−1.13940
$34$	4.06221	0.696663
$35$	0	0
$36$	−1.64772	−0.274621
$37$	−2.89613	−0.476120	−0.238060	−	0.971250i	$-0.576512\pi$
$37$	−2.89613	−0.476120	−0.238060	+	0.971250i	$0.576512\pi$
$38$	−1.73110	−0.280821
$39$	0.692965	0.110963
$40$	6.82244	1.07872
$41$	−9.26871	−1.44753	−0.723765	−	0.690047i	$-0.757590\pi$
$41$	−9.26871	−1.44753	−0.723765	+	0.690047i	$0.757590\pi$
$42$	0	0
$43$	−4.27043	−0.651235	−0.325617	−	0.945502i	$-0.605572\pi$
$43$	−4.27043	−0.651235	−0.325617	+	0.945502i	$0.605572\pi$
$44$	10.7849	1.62589
$45$	3.15120	0.469754
$46$	0.593528	0.0875110
$47$	−10.4674	−1.52683	−0.763416	−	0.645907i	$-0.776479\pi$
$47$	−10.4674	−1.52683	−0.763416	+	0.645907i	$0.776479\pi$
$48$	2.01044	0.290182
$49$	0	0
$50$	−2.92615	−0.413820
$51$	−6.84417	−0.958375
$52$	−1.14182	−0.158341
$53$	12.5749	1.72729	0.863647	−	0.504097i	$-0.168175\pi$
$53$	12.5749	1.72729	0.863647	+	0.504097i	$0.168175\pi$
$54$	−0.593528	−0.0807690
$55$	−20.6257	−2.78117
$56$	0	0
$57$	2.91662	0.386316
$58$	−1.74865	−0.229609
$59$	−6.70326	−0.872690	−0.436345	−	0.899779i	$-0.643727\pi$
$59$	−6.70326	−0.872690	−0.436345	+	0.899779i	$0.643727\pi$
$60$	−5.19231	−0.670325
$61$	−5.30183	−0.678830	−0.339415	−	0.940637i	$-0.610229\pi$
$61$	−5.30183	−0.678830	−0.339415	+	0.940637i	$0.610229\pi$
$62$	−0.320109	−0.0406539
$63$	0	0
$64$	−0.742642	−0.0928303
$65$	2.18368	0.270852
$66$	3.88485	0.478191
$67$	−2.73628	−0.334290	−0.167145	−	0.985932i	$-0.553455\pi$
$67$	−2.73628	−0.334290	−0.167145	+	0.985932i	$0.553455\pi$
$68$	11.2773	1.36757
$69$	−1.00000	−0.120386
$70$	0	0
$71$	−0.587217	−0.0696899	−0.0348449	−	0.999393i	$-0.511094\pi$
$71$	−0.587217	−0.0696899	−0.0348449	+	0.999393i	$0.511094\pi$
$72$	2.16503	0.255151
$73$	−10.5266	−1.23205	−0.616023	−	0.787728i	$-0.711257\pi$
$73$	−10.5266	−1.23205	−0.616023	+	0.787728i	$0.711257\pi$
$74$	1.71893	0.199822
$75$	4.93009	0.569277
$76$	−4.80579	−0.551262
$77$	0	0
$78$	−0.411295	−0.0465699
$79$	−13.3870	−1.50616	−0.753078	−	0.657931i	$-0.771432\pi$
$79$	−13.3870	−1.50616	−0.753078	+	0.657931i	$0.771432\pi$
$80$	6.33531	0.708310
$81$	1.00000	0.111111
$82$	5.50124	0.607511
$83$	9.77501	1.07295	0.536473	−	0.843917i	$-0.319756\pi$
$83$	9.77501	1.07295	0.536473	+	0.843917i	$0.319756\pi$
$84$	0	0
$85$	−21.5674	−2.33931
$86$	2.53462	0.273315
$87$	2.94619	0.315865
$88$	−14.1708	−1.51062
$89$	−2.92939	−0.310515	−0.155258	−	0.987874i	$-0.549621\pi$
$89$	−2.92939	−0.310515	−0.155258	+	0.987874i	$0.549621\pi$
$90$	−1.87033	−0.197150
$91$	0	0
$92$	1.64772	0.171787
$93$	0.539333	0.0559262
$94$	6.21272	0.640793
$95$	9.19088	0.942964
$96$	−5.52331	−0.563721
$97$	8.14170	0.826664	0.413332	−	0.910580i	$-0.364365\pi$
$97$	8.14170	0.826664	0.413332	+	0.910580i	$0.364365\pi$
$98$	0	0
$99$	−6.54534	−0.657831
$100$	−8.12342	−0.812342
$101$	0.133249	0.0132588	0.00662939	−	0.999978i	$-0.497890\pi$
$101$	0.133249	0.0132588	0.00662939	+	0.999978i	$0.497890\pi$
$102$	4.06221	0.402219
$103$	11.0107	1.08491	0.542456	−	0.840084i	$-0.317494\pi$
$103$	11.0107	1.08491	0.542456	+	0.840084i	$0.317494\pi$
$104$	1.50029	0.147115
$105$	0	0
$106$	−7.46355	−0.724924
$107$	−8.57510	−0.828986	−0.414493	−	0.910053i	$-0.636041\pi$
$107$	−8.57510	−0.828986	−0.414493	+	0.910053i	$0.636041\pi$
$108$	−1.64772	−0.158552
$109$	11.2823	1.08064	0.540322	−	0.841458i	$-0.318302\pi$
$109$	11.2823	1.08064	0.540322	+	0.841458i	$0.318302\pi$
$110$	12.2419	1.16722
$111$	−2.89613	−0.274888
$112$	0	0
$113$	3.14165	0.295541	0.147771	−	0.989022i	$-0.452790\pi$
$113$	3.14165	0.295541	0.147771	+	0.989022i	$0.452790\pi$
$114$	−1.73110	−0.162132
$115$	−3.15120	−0.293851
$116$	−4.85451	−0.450730
$117$	0.692965	0.0640647
$118$	3.97858	0.366258
$119$	0	0
$120$	6.82244	0.622801
$121$	31.8415	2.89468
$122$	3.14679	0.284897
$123$	−9.26871	−0.835731
$124$	−0.888672	−0.0798051
$125$	−0.220311	−0.0197052
$126$	0	0
$127$	−12.9337	−1.14768	−0.573841	−	0.818967i	$-0.694547\pi$
$127$	−12.9337	−1.14768	−0.573841	+	0.818967i	$0.694547\pi$
$128$	11.4874	1.01535
$129$	−4.27043	−0.375991
$130$	−1.29607	−0.113673
$131$	−6.14667	−0.537037	−0.268518	−	0.963275i	$-0.586534\pi$
$131$	−6.14667	−0.537037	−0.268518	+	0.963275i	$0.586534\pi$
$132$	10.7849	0.938706
$133$	0	0
$134$	1.62406	0.140298
$135$	3.15120	0.271212
$136$	−14.8178	−1.27062
$137$	−19.6122	−1.67558	−0.837792	−	0.545989i	$-0.816154\pi$
$137$	−19.6122	−1.67558	−0.837792	+	0.545989i	$0.816154\pi$
$138$	0.593528	0.0505245
$139$	11.8453	1.00470	0.502352	−	0.864663i	$-0.332468\pi$
$139$	11.8453	1.00470	0.502352	+	0.864663i	$0.332468\pi$
$140$	0	0
$141$	−10.4674	−0.881517
$142$	0.348530	0.0292480
$143$	−4.53569	−0.379294
$144$	2.01044	0.167537
$145$	9.28405	0.770999
$146$	6.24784	0.517075
$147$	0	0
$148$	4.77202	0.392258
$149$	−5.17374	−0.423849	−0.211925	−	0.977286i	$-0.567973\pi$
$149$	−5.17374	−0.423849	−0.211925	+	0.977286i	$0.567973\pi$
$150$	−2.92615	−0.238919
$151$	−5.05014	−0.410974	−0.205487	−	0.978660i	$-0.565878\pi$
$151$	−5.05014	−0.410974	−0.205487	+	0.978660i	$0.565878\pi$
$152$	6.31457	0.512180
$153$	−6.84417	−0.553318
$154$	0	0
$155$	1.69955	0.136511
$156$	−1.14182	−0.0914184
$157$	9.64814	0.770005	0.385003	−	0.922915i	$-0.374201\pi$
$157$	9.64814	0.770005	0.385003	+	0.922915i	$0.374201\pi$
$158$	7.94557	0.632116
$159$	12.5749	0.997253
$160$	−17.4051	−1.37599
$161$	0	0
$162$	−0.593528	−0.0466320
$163$	23.9325	1.87454	0.937271	−	0.348602i	$-0.113344\pi$
$163$	23.9325	1.87454	0.937271	+	0.348602i	$0.113344\pi$
$164$	15.2723	1.19256
$165$	−20.6257	−1.60571
$166$	−5.80174	−0.450303
$167$	−12.0368	−0.931435	−0.465718	−	0.884933i	$-0.654204\pi$
$167$	−12.0368	−0.931435	−0.465718	+	0.884933i	$0.654204\pi$
$168$	0	0
$169$	−12.5198	−0.963061
$170$	12.8009	0.981780
$171$	2.91662	0.223040
$172$	7.03649	0.536528
$173$	16.6038	1.26236	0.631182	−	0.775634i	$-0.282570\pi$
$173$	16.6038	1.26236	0.631182	+	0.775634i	$0.282570\pi$
$174$	−1.74865	−0.132565
$175$	0	0
$176$	−13.1590	−0.991899
$177$	−6.70326	−0.503848
$178$	1.73868	0.130320
$179$	3.24538	0.242571	0.121285	−	0.992618i	$-0.461298\pi$
$179$	3.24538	0.242571	0.121285	+	0.992618i	$0.461298\pi$
$180$	−5.19231	−0.387012
$181$	−14.3797	−1.06883	−0.534417	−	0.845221i	$-0.679469\pi$
$181$	−14.3797	−1.06883	−0.534417	+	0.845221i	$0.679469\pi$
$182$	0	0
$183$	−5.30183	−0.391923
$184$	−2.16503	−0.159608
$185$	−9.12629	−0.670978
$186$	−0.320109	−0.0234716
$187$	44.7974	3.27591
$188$	17.2474	1.25790
$189$	0	0
$190$	−5.45505	−0.395751
$191$	−9.88912	−0.715552	−0.357776	−	0.933808i	$-0.616465\pi$
$191$	−9.88912	−0.715552	−0.357776	+	0.933808i	$0.616465\pi$
$192$	−0.742642	−0.0535956
$193$	−3.59051	−0.258450	−0.129225	−	0.991615i	$-0.541249\pi$
$193$	−3.59051	−0.258450	−0.129225	+	0.991615i	$0.541249\pi$
$194$	−4.83233	−0.346941
$195$	2.18368	0.156376
$196$	0	0
$197$	8.21279	0.585137	0.292569	−	0.956245i	$-0.405490\pi$
$197$	8.21279	0.585137	0.292569	+	0.956245i	$0.405490\pi$
$198$	3.88485	0.276084
$199$	−2.24507	−0.159149	−0.0795743	−	0.996829i	$-0.525356\pi$
$199$	−2.24507	−0.159149	−0.0795743	+	0.996829i	$0.525356\pi$
$200$	10.6738	0.754750
$201$	−2.73628	−0.193003
$202$	−0.0790871	−0.00556455
$203$	0	0
$204$	11.2773	0.789569
$205$	−29.2076	−2.03995
$206$	−6.53514	−0.455325
$207$	−1.00000	−0.0695048
$208$	1.39317	0.0965987
$209$	−19.0903	−1.32050
$210$	0	0
$211$	−23.0784	−1.58878	−0.794392	−	0.607406i	$-0.792210\pi$
$211$	−23.0784	−1.58878	−0.794392	+	0.607406i	$0.792210\pi$
$212$	−20.7199	−1.42305
$213$	−0.587217	−0.0402355
$214$	5.08956	0.347915
$215$	−13.4570	−0.917760
$216$	2.16503	0.147311
$217$	0	0
$218$	−6.69634	−0.453533
$219$	−10.5266	−0.711322
$220$	33.9855	2.29130
$221$	−4.74277	−0.319033
$222$	1.71893	0.115367
$223$	−4.28573	−0.286993	−0.143497	−	0.989651i	$-0.545835\pi$
$223$	−4.28573	−0.286993	−0.143497	+	0.989651i	$0.545835\pi$
$224$	0	0
$225$	4.93009	0.328672
$226$	−1.86466	−0.124035
$227$	−10.9334	−0.725673	−0.362837	−	0.931853i	$-0.618192\pi$
$227$	−10.9334	−0.725673	−0.362837	+	0.931853i	$0.618192\pi$
$228$	−4.80579	−0.318271
$229$	−5.57751	−0.368572	−0.184286	−	0.982873i	$-0.558997\pi$
$229$	−5.57751	−0.368572	−0.184286	+	0.982873i	$0.558997\pi$
$230$	1.87033	0.123326
$231$	0	0
$232$	6.37859	0.418775
$233$	−22.2706	−1.45899	−0.729497	−	0.683984i	$-0.760246\pi$
$233$	−22.2706	−1.45899	−0.729497	+	0.683984i	$0.760246\pi$
$234$	−0.411295	−0.0268872
$235$	−32.9850	−2.15171
$236$	11.0451	0.718976
$237$	−13.3870	−0.869580
$238$	0	0
$239$	13.3901	0.866134	0.433067	−	0.901362i	$-0.357431\pi$
$239$	13.3901	0.866134	0.433067	+	0.901362i	$0.357431\pi$
$240$	6.33531	0.408943
$241$	3.28645	0.211699	0.105849	−	0.994382i	$-0.466244\pi$
$241$	3.28645	0.211699	0.105849	+	0.994382i	$0.466244\pi$
$242$	−18.8988	−1.21486
$243$	1.00000	0.0641500
$244$	8.73595	0.559262
$245$	0	0
$246$	5.50124	0.350746
$247$	2.02112	0.128601
$248$	1.16767	0.0741472
$249$	9.77501	0.619466
$250$	0.130761	0.00827004
$251$	−10.2769	−0.648672	−0.324336	−	0.945942i	$-0.605141\pi$
$251$	−10.2769	−0.648672	−0.324336	+	0.945942i	$0.605141\pi$
$252$	0	0
$253$	6.54534	0.411502
$254$	7.67653	0.481668
$255$	−21.5674	−1.35060
$256$	−5.33281	−0.333301
$257$	−23.4070	−1.46009	−0.730046	−	0.683398i	$-0.760501\pi$
$257$	−23.4070	−1.46009	−0.730046	+	0.683398i	$0.760501\pi$
$258$	2.53462	0.157799
$259$	0	0
$260$	−3.59809	−0.223144
$261$	2.94619	0.182365
$262$	3.64822	0.225388
$263$	−27.3656	−1.68744	−0.843719	−	0.536785i	$-0.819638\pi$
$263$	−27.3656	−1.68744	−0.843719	+	0.536785i	$0.819638\pi$
$264$	−14.1708	−0.872155
$265$	39.6260	2.43421
$266$	0	0
$267$	−2.92939	−0.179276
$268$	4.50864	0.275409
$269$	26.3771	1.60824	0.804119	−	0.594469i	$-0.202638\pi$
$269$	26.3771	1.60824	0.804119	+	0.594469i	$0.202638\pi$
$270$	−1.87033	−0.113825
$271$	−4.30436	−0.261471	−0.130736	−	0.991417i	$-0.541734\pi$
$271$	−4.30436	−0.261471	−0.130736	+	0.991417i	$0.541734\pi$
$272$	−13.7598	−0.834311
$273$	0	0
$274$	11.6404	0.703223
$275$	−32.2691	−1.94590
$276$	1.64772	0.0991813
$277$	−14.6493	−0.880192	−0.440096	−	0.897951i	$-0.645056\pi$
$277$	−14.6493	−0.880192	−0.440096	+	0.897951i	$0.645056\pi$
$278$	−7.03052	−0.421663
$279$	0.539333	0.0322890
$280$	0	0
$281$	17.0380	1.01640	0.508202	−	0.861238i	$-0.330310\pi$
$281$	17.0380	1.01640	0.508202	+	0.861238i	$0.330310\pi$
$282$	6.21272	0.369962
$283$	17.9128	1.06481	0.532403	−	0.846491i	$-0.321289\pi$
$283$	17.9128	1.06481	0.532403	+	0.846491i	$0.321289\pi$
$284$	0.967572	0.0574148
$285$	9.19088	0.544421
$286$	2.69206	0.159185
$287$	0	0
$288$	−5.52331	−0.325464
$289$	29.8427	1.75545
$290$	−5.51035	−0.323579
$291$	8.14170	0.477275
$292$	17.3449	1.01504
$293$	18.7699	1.09655	0.548273	−	0.836299i	$-0.315285\pi$
$293$	18.7699	1.09655	0.548273	+	0.836299i	$0.315285\pi$
$294$	0	0
$295$	−21.1233	−1.22985
$296$	−6.27020	−0.364448
$297$	−6.54534	−0.379799
$298$	3.07076	0.177884
$299$	−0.692965	−0.0400752
$300$	−8.12342	−0.469006
$301$	0	0
$302$	2.99740	0.172481
$303$	0.133249	0.00765496
$304$	5.86370	0.336307
$305$	−16.7071	−0.956648
$306$	4.06221	0.232221
$307$	1.42373	0.0812566	0.0406283	−	0.999174i	$-0.487064\pi$
$307$	1.42373	0.0812566	0.0406283	+	0.999174i	$0.487064\pi$
$308$	0	0
$309$	11.0107	0.626374
$310$	−1.00873	−0.0572920
$311$	4.42471	0.250902	0.125451	−	0.992100i	$-0.459962\pi$
$311$	4.42471	0.250902	0.125451	+	0.992100i	$0.459962\pi$
$312$	1.50029	0.0849372
$313$	−21.6865	−1.22580	−0.612898	−	0.790162i	$-0.709996\pi$
$313$	−21.6865	−1.22580	−0.612898	+	0.790162i	$0.709996\pi$
$314$	−5.72644	−0.323162
$315$	0	0
$316$	22.0581	1.24086
$317$	−11.6270	−0.653037	−0.326518	−	0.945191i	$-0.605875\pi$
$317$	−11.6270	−0.653037	−0.326518	+	0.945191i	$0.605875\pi$
$318$	−7.46355	−0.418535
$319$	−19.2838	−1.07969
$320$	−2.34022	−0.130822
$321$	−8.57510	−0.478615
$322$	0	0
$323$	−19.9619	−1.11071
$324$	−1.64772	−0.0915402
$325$	3.41638	0.189507
$326$	−14.2046	−0.786723
$327$	11.2823	0.623910
$328$	−20.0670	−1.10802
$329$	0	0
$330$	12.2419	0.673897
$331$	7.89484	0.433940	0.216970	−	0.976178i	$-0.430383\pi$
$331$	7.89484	0.433940	0.216970	+	0.976178i	$0.430383\pi$
$332$	−16.1065	−0.883960
$333$	−2.89613	−0.158707
$334$	7.14418	0.390912
$335$	−8.62259	−0.471102
$336$	0	0
$337$	12.1596	0.662378	0.331189	−	0.943565i	$-0.392550\pi$
$337$	12.1596	0.662378	0.331189	+	0.943565i	$0.392550\pi$
$338$	7.43086	0.404185
$339$	3.14165	0.170631
$340$	35.5371	1.92727
$341$	−3.53012	−0.191167
$342$	−1.73110	−0.0936071
$343$	0	0
$344$	−9.24561	−0.498490
$345$	−3.15120	−0.169655
$346$	−9.85484	−0.529799
$347$	14.0192	0.752588	0.376294	−	0.926500i	$-0.377198\pi$
$347$	14.0192	0.752588	0.376294	+	0.926500i	$0.377198\pi$
$348$	−4.85451	−0.260229
$349$	−2.94132	−0.157445	−0.0787226	−	0.996897i	$-0.525084\pi$
$349$	−2.94132	−0.157445	−0.0787226	+	0.996897i	$0.525084\pi$
$350$	0	0
$351$	0.692965	0.0369878
$352$	36.1519	1.92691
$353$	10.0734	0.536153	0.268076	−	0.963398i	$-0.413612\pi$
$353$	10.0734	0.536153	0.268076	+	0.963398i	$0.413612\pi$
$354$	3.97858	0.211459
$355$	−1.85044	−0.0982112
$356$	4.82683	0.255822
$357$	0	0
$358$	−1.92622	−0.101804
$359$	−32.4956	−1.71505	−0.857526	−	0.514441i	$-0.827999\pi$
$359$	−32.4956	−1.71505	−0.857526	+	0.514441i	$0.827999\pi$
$360$	6.82244	0.359574
$361$	−10.4933	−0.552279
$362$	8.53476	0.448577
$363$	31.8415	1.67124
$364$	0	0
$365$	−33.1715	−1.73627
$366$	3.14679	0.164485
$367$	−24.2742	−1.26710	−0.633552	−	0.773701i	$-0.718404\pi$
$367$	−24.2742	−1.26710	−0.633552	+	0.773701i	$0.718404\pi$
$368$	−2.01044	−0.104802
$369$	−9.26871	−0.482510
$370$	5.41671	0.281601
$371$	0	0
$372$	−0.888672	−0.0460755
$373$	−22.0627	−1.14236	−0.571181	−	0.820824i	$-0.693515\pi$
$373$	−22.0627	−1.14236	−0.571181	+	0.820824i	$0.693515\pi$
$374$	−26.5885	−1.37486
$375$	−0.220311	−0.0113768
$376$	−22.6623	−1.16872
$377$	2.04161	0.105148
$378$	0	0
$379$	0.844591	0.0433837	0.0216919	−	0.999765i	$-0.493095\pi$
$379$	0.844591	0.0433837	0.0216919	+	0.999765i	$0.493095\pi$
$380$	−15.1440	−0.776872
$381$	−12.9337	−0.662615
$382$	5.86947	0.300308
$383$	−33.0352	−1.68802	−0.844009	−	0.536329i	$-0.819811\pi$
$383$	−33.0352	−1.68802	−0.844009	+	0.536329i	$0.819811\pi$
$384$	11.4874	0.586214
$385$	0	0
$386$	2.13107	0.108469
$387$	−4.27043	−0.217078
$388$	−13.4153	−0.681057
$389$	0.772812	0.0391831	0.0195916	−	0.999808i	$-0.493763\pi$
$389$	0.772812	0.0391831	0.0195916	+	0.999808i	$0.493763\pi$
$390$	−1.29607	−0.0656292
$391$	6.84417	0.346125
$392$	0	0
$393$	−6.14667	−0.310058
$394$	−4.87453	−0.245575
$395$	−42.1852	−2.12257
$396$	10.7849	0.541962
$397$	21.1380	1.06089	0.530444	−	0.847720i	$-0.322025\pi$
$397$	21.1380	1.06089	0.530444	+	0.847720i	$0.322025\pi$
$398$	1.33251	0.0667928
$399$	0	0
$400$	9.91165	0.495583
$401$	28.3143	1.41395	0.706975	−	0.707238i	$-0.250059\pi$
$401$	28.3143	1.41395	0.706975	+	0.707238i	$0.250059\pi$
$402$	1.62406	0.0810009
$403$	0.373739	0.0186173
$404$	−0.219558	−0.0109234
$405$	3.15120	0.156585
$406$	0	0
$407$	18.9561	0.939621
$408$	−14.8178	−0.733591
$409$	22.3144	1.10338	0.551688	−	0.834051i	$-0.313984\pi$
$409$	22.3144	1.10338	0.551688	+	0.834051i	$0.313984\pi$
$410$	17.3355	0.856141
$411$	−19.6122	−0.967399
$412$	−18.1425	−0.893818
$413$	0	0
$414$	0.593528	0.0291703
$415$	30.8030	1.51206
$416$	−3.82746	−0.187657
$417$	11.8453	0.580067
$418$	11.3306	0.554199
$419$	5.99719	0.292982	0.146491	−	0.989212i	$-0.453202\pi$
$419$	5.99719	0.292982	0.146491	+	0.989212i	$0.453202\pi$
$420$	0	0
$421$	12.4472	0.606638	0.303319	−	0.952889i	$-0.401905\pi$
$421$	12.4472	0.606638	0.303319	+	0.952889i	$0.401905\pi$
$422$	13.6977	0.666793
$423$	−10.4674	−0.508944
$424$	27.2250	1.32216
$425$	−33.7423	−1.63674
$426$	0.348530	0.0168863
$427$	0	0
$428$	14.1294	0.682970
$429$	−4.53569	−0.218985
$430$	7.98712	0.385173
$431$	5.38995	0.259625	0.129812	−	0.991539i	$-0.458563\pi$
$431$	5.38995	0.259625	0.129812	+	0.991539i	$0.458563\pi$
$432$	2.01044	0.0967274
$433$	32.6738	1.57020	0.785102	−	0.619366i	$-0.212610\pi$
$433$	32.6738	1.57020	0.785102	+	0.619366i	$0.212610\pi$
$434$	0	0
$435$	9.28405	0.445136
$436$	−18.5900	−0.890302
$437$	−2.91662	−0.139521
$438$	6.24784	0.298533
$439$	−0.0288317	−0.00137606	−0.000688030	−	1.00000i	$-0.500219\pi$
$439$	−0.0288317	−0.00137606	−0.000688030		1.00000i	$0.500219\pi$
$440$	−44.6552	−2.12885
$441$	0	0
$442$	2.81497	0.133894
$443$	16.9327	0.804499	0.402249	−	0.915530i	$-0.368229\pi$
$443$	16.9327	0.804499	0.402249	+	0.915530i	$0.368229\pi$
$444$	4.77202	0.226470
$445$	−9.23112	−0.437597
$446$	2.54370	0.120448
$447$	−5.17374	−0.244709
$448$	0	0
$449$	20.8257	0.982825	0.491412	−	0.870927i	$-0.336481\pi$
$449$	20.8257	0.982825	0.491412	+	0.870927i	$0.336481\pi$
$450$	−2.92615	−0.137940
$451$	60.6669	2.85669
$452$	−5.17656	−0.243485
$453$	−5.05014	−0.237276
$454$	6.48927	0.304556
$455$	0	0
$456$	6.31457	0.295707
$457$	−14.3513	−0.671326	−0.335663	−	0.941982i	$-0.608960\pi$
$457$	−14.3513	−0.671326	−0.335663	+	0.941982i	$0.608960\pi$
$458$	3.31041	0.154685
$459$	−6.84417	−0.319458
$460$	5.19231	0.242093
$461$	3.54822	0.165257	0.0826286	−	0.996580i	$-0.473668\pi$
$461$	3.54822	0.165257	0.0826286	+	0.996580i	$0.473668\pi$
$462$	0	0
$463$	12.2267	0.568223	0.284111	−	0.958791i	$-0.408301\pi$
$463$	12.2267	0.568223	0.284111	+	0.958791i	$0.408301\pi$
$464$	5.92315	0.274975
$465$	1.69955	0.0788147
$466$	13.2182	0.612323
$467$	28.5860	1.32280	0.661401	−	0.750032i	$-0.269962\pi$
$467$	28.5860	1.32280	0.661401	+	0.750032i	$0.269962\pi$
$468$	−1.14182	−0.0527804
$469$	0	0
$470$	19.5776	0.903045
$471$	9.64814	0.444563
$472$	−14.5127	−0.668003
$473$	27.9514	1.28521
$474$	7.94557	0.364952
$475$	14.3792	0.659763
$476$	0	0
$477$	12.5749	0.575765
$478$	−7.94741	−0.363506
$479$	−30.2691	−1.38303	−0.691516	−	0.722361i	$-0.743057\pi$
$479$	−30.2691	−1.38303	−0.691516	+	0.722361i	$0.743057\pi$
$480$	−17.4051	−0.794430
$481$	−2.00692	−0.0915075
$482$	−1.95060	−0.0888474
$483$	0	0
$484$	−52.4660	−2.38482
$485$	25.6561	1.16499
$486$	−0.593528	−0.0269230
$487$	28.9369	1.31125	0.655627	−	0.755085i	$-0.272404\pi$
$487$	28.9369	1.31125	0.655627	+	0.755085i	$0.272404\pi$
$488$	−11.4786	−0.519612
$489$	23.9325	1.08227
$490$	0	0
$491$	−11.9185	−0.537876	−0.268938	−	0.963158i	$-0.586673\pi$
$491$	−11.9185	−0.537876	−0.268938	+	0.963158i	$0.586673\pi$
$492$	15.2723	0.688527
$493$	−20.1642	−0.908152
$494$	−1.19959	−0.0539722
$495$	−20.6257	−0.927056
$496$	1.08430	0.0486864
$497$	0	0
$498$	−5.80174	−0.259982
$499$	10.3738	0.464394	0.232197	−	0.972669i	$-0.425409\pi$
$499$	10.3738	0.464394	0.232197	+	0.972669i	$0.425409\pi$
$500$	0.363012	0.0162344
$501$	−12.0368	−0.537765
$502$	6.09963	0.272240
$503$	−22.4429	−1.00068	−0.500340	−	0.865829i	$-0.666791\pi$
$503$	−22.4429	−1.00068	−0.500340	+	0.865829i	$0.666791\pi$
$504$	0	0
$505$	0.419895	0.0186851
$506$	−3.88485	−0.172702
$507$	−12.5198	−0.556024
$508$	21.3112	0.945532
$509$	5.96381	0.264341	0.132171	−	0.991227i	$-0.457805\pi$
$509$	5.96381	0.264341	0.132171	+	0.991227i	$0.457805\pi$
$510$	12.8009	0.566831
$511$	0	0
$512$	−19.8096	−0.875470
$513$	2.91662	0.128772
$514$	13.8927	0.612783
$515$	34.6968	1.52892
$516$	7.03649	0.309764
$517$	68.5129	3.01319
$518$	0	0
$519$	16.6038	0.728827
$520$	4.72772	0.207324
$521$	−1.02187	−0.0447691	−0.0223845	−	0.999749i	$-0.507126\pi$
$521$	−1.02187	−0.0447691	−0.0223845	+	0.999749i	$0.507126\pi$
$522$	−1.74865	−0.0765363
$523$	−4.98369	−0.217922	−0.108961	−	0.994046i	$-0.534752\pi$
$523$	−4.98369	−0.217922	−0.108961	+	0.994046i	$0.534752\pi$
$524$	10.1280	0.442444
$525$	0	0
$526$	16.2423	0.708197
$527$	−3.69129	−0.160795
$528$	−13.1590	−0.572673
$529$	1.00000	0.0434783
$530$	−23.5192	−1.02161
$531$	−6.70326	−0.290897
$532$	0	0
$533$	−6.42289	−0.278206
$534$	1.73868	0.0752400
$535$	−27.0219	−1.16826
$536$	−5.92413	−0.255884
$537$	3.24538	0.140048
$538$	−15.6555	−0.674958
$539$	0	0
$540$	−5.19231	−0.223442
$541$	15.3340	0.659260	0.329630	−	0.944110i	$-0.393076\pi$
$541$	15.3340	0.659260	0.329630	+	0.944110i	$0.393076\pi$
$542$	2.55476	0.109736
$543$	−14.3797	−0.617092
$544$	37.8025	1.62077
$545$	35.5527	1.52291
$546$	0	0
$547$	−6.89796	−0.294935	−0.147468	−	0.989067i	$-0.547112\pi$
$547$	−6.89796	−0.294935	−0.147468	+	0.989067i	$0.547112\pi$
$548$	32.3155	1.38045
$549$	−5.30183	−0.226277
$550$	19.1526	0.816671
$551$	8.59294	0.366071
$552$	−2.16503	−0.0921497
$553$	0	0
$554$	8.69479	0.369406
$555$	−9.12629	−0.387389
$556$	−19.5178	−0.827738
$557$	29.4889	1.24949	0.624743	−	0.780830i	$-0.285204\pi$
$557$	29.4889	1.24949	0.624743	+	0.780830i	$0.285204\pi$
$558$	−0.320109	−0.0135513
$559$	−2.95926	−0.125163
$560$	0	0
$561$	44.7974	1.89135
$562$	−10.1126	−0.426573
$563$	7.22423	0.304465	0.152232	−	0.988345i	$-0.451354\pi$
$563$	7.22423	0.304465	0.152232	+	0.988345i	$0.451354\pi$
$564$	17.2474	0.726248
$565$	9.89996	0.416495
$566$	−10.6318	−0.446887
$567$	0	0
$568$	−1.27134	−0.0533443
$569$	−3.61375	−0.151496	−0.0757482	−	0.997127i	$-0.524135\pi$
$569$	−3.61375	−0.151496	−0.0757482	+	0.997127i	$0.524135\pi$
$570$	−5.45505	−0.228487
$571$	−2.53390	−0.106041	−0.0530203	−	0.998593i	$-0.516885\pi$
$571$	−2.53390	−0.106041	−0.0530203	+	0.998593i	$0.516885\pi$
$572$	7.47357	0.312486
$573$	−9.88912	−0.413124
$574$	0	0
$575$	−4.93009	−0.205599
$576$	−0.742642	−0.0309434
$577$	2.10686	0.0877097	0.0438548	−	0.999038i	$-0.486036\pi$
$577$	2.10686	0.0877097	0.0438548	+	0.999038i	$0.486036\pi$
$578$	−17.7125	−0.736741
$579$	−3.59051	−0.149216
$580$	−15.2976	−0.635196
$581$	0	0
$582$	−4.83233	−0.200306
$583$	−82.3069	−3.40880
$584$	−22.7904	−0.943073
$585$	2.18368	0.0902839
$586$	−11.1404	−0.460208
$587$	−3.01620	−0.124492	−0.0622460	−	0.998061i	$-0.519826\pi$
$587$	−3.01620	−0.124492	−0.0622460	+	0.998061i	$0.519826\pi$
$588$	0	0
$589$	1.57303	0.0648156
$590$	12.5373	0.516153
$591$	8.21279	0.337829
$592$	−5.82250	−0.239303
$593$	−10.4536	−0.429278	−0.214639	−	0.976693i	$-0.568857\pi$
$593$	−10.4536	−0.429278	−0.214639	+	0.976693i	$0.568857\pi$
$594$	3.88485	0.159397
$595$	0	0
$596$	8.52489	0.349193
$597$	−2.24507	−0.0918845
$598$	0.411295	0.0168191
$599$	−1.77010	−0.0723245	−0.0361623	−	0.999346i	$-0.511513\pi$
$599$	−1.77010	−0.0723245	−0.0361623	+	0.999346i	$0.511513\pi$
$600$	10.6738	0.435755
$601$	37.1024	1.51344	0.756720	−	0.653739i	$-0.226801\pi$
$601$	37.1024	1.51344	0.756720	+	0.653739i	$0.226801\pi$
$602$	0	0
$603$	−2.73628	−0.111430
$604$	8.32123	0.338586
$605$	100.339	4.07936
$606$	−0.0790871	−0.00321269
$607$	9.90037	0.401844	0.200922	−	0.979607i	$-0.435606\pi$
$607$	9.90037	0.401844	0.200922	+	0.979607i	$0.435606\pi$
$608$	−16.1094	−0.653323
$609$	0	0
$610$	9.91617	0.401494
$611$	−7.25357	−0.293448
$612$	11.2773	0.455858
$613$	−33.3962	−1.34886	−0.674430	−	0.738338i	$-0.735611\pi$
$613$	−33.3962	−1.34886	−0.674430	+	0.738338i	$0.735611\pi$
$614$	−0.845025	−0.0341024
$615$	−29.2076	−1.17776
$616$	0	0
$617$	−19.5997	−0.789054	−0.394527	−	0.918884i	$-0.629092\pi$
$617$	−19.5997	−0.789054	−0.394527	+	0.918884i	$0.629092\pi$
$618$	−6.53514	−0.262882
$619$	20.4682	0.822685	0.411342	−	0.911481i	$-0.365060\pi$
$619$	20.4682	0.822685	0.411342	+	0.911481i	$0.365060\pi$
$620$	−2.80039	−0.112466
$621$	−1.00000	−0.0401286
$622$	−2.62619	−0.105301
$623$	0	0
$624$	1.39317	0.0557713
$625$	−25.3447	−1.01379
$626$	12.8716	0.514452
$627$	−19.0903	−0.762393
$628$	−15.8975	−0.634378
$629$	19.8216	0.790338
$630$	0	0
$631$	−16.9942	−0.676529	−0.338265	−	0.941051i	$-0.609840\pi$
$631$	−16.9942	−0.676529	−0.338265	+	0.941051i	$0.609840\pi$
$632$	−28.9833	−1.15289
$633$	−23.0784	−0.917285
$634$	6.90095	0.274072
$635$	−40.7568	−1.61738
$636$	−20.7199	−0.821599
$637$	0	0
$638$	11.4455	0.453132
$639$	−0.587217	−0.0232300
$640$	36.1991	1.43090
$641$	10.9633	0.433023	0.216512	−	0.976280i	$-0.430532\pi$
$641$	10.9633	0.433023	0.216512	+	0.976280i	$0.430532\pi$
$642$	5.08956	0.200869
$643$	−11.7658	−0.463996	−0.231998	−	0.972716i	$-0.574526\pi$
$643$	−11.7658	−0.463996	−0.231998	+	0.972716i	$0.574526\pi$
$644$	0	0
$645$	−13.4570	−0.529869
$646$	11.8479	0.466151
$647$	−1.76940	−0.0695624	−0.0347812	−	0.999395i	$-0.511073\pi$
$647$	−1.76940	−0.0695624	−0.0347812	+	0.999395i	$0.511073\pi$
$648$	2.16503	0.0850503
$649$	43.8751	1.72225
$650$	−2.02772	−0.0795337
$651$	0	0
$652$	−39.4342	−1.54436
$653$	10.5678	0.413551	0.206776	−	0.978388i	$-0.433703\pi$
$653$	10.5678	0.413551	0.206776	+	0.978388i	$0.433703\pi$
$654$	−6.69634	−0.261848
$655$	−19.3694	−0.756825
$656$	−18.6342	−0.727543
$657$	−10.5266	−0.410682
$658$	0	0
$659$	−10.3840	−0.404504	−0.202252	−	0.979334i	$-0.564826\pi$
$659$	−10.3840	−0.404504	−0.202252	+	0.979334i	$0.564826\pi$
$660$	33.9855	1.32288
$661$	33.3468	1.29704	0.648521	−	0.761197i	$-0.275388\pi$
$661$	33.3468	1.29704	0.648521	+	0.761197i	$0.275388\pi$
$662$	−4.68581	−0.182119
$663$	−4.74277	−0.184194
$664$	21.1632	0.821290
$665$	0	0
$666$	1.71893	0.0666073
$667$	−2.94619	−0.114077
$668$	19.8333	0.767374
$669$	−4.28573	−0.165696
$670$	5.11775	0.197716
$671$	34.7023	1.33967
$672$	0	0
$673$	11.0030	0.424134	0.212067	−	0.977255i	$-0.431980\pi$
$673$	11.0030	0.424134	0.212067	+	0.977255i	$0.431980\pi$
$674$	−7.21709	−0.277992
$675$	4.93009	0.189759
$676$	20.6292	0.793430
$677$	−33.6967	−1.29507	−0.647536	−	0.762035i	$-0.724200\pi$
$677$	−33.6967	−1.29507	−0.647536	+	0.762035i	$0.724200\pi$
$678$	−1.86466	−0.0716117
$679$	0	0
$680$	−46.6940	−1.79063
$681$	−10.9334	−0.418968
$682$	2.09523	0.0802303
$683$	−47.1617	−1.80459	−0.902297	−	0.431115i	$-0.858120\pi$
$683$	−47.1617	−1.80459	−0.902297	+	0.431115i	$0.858120\pi$
$684$	−4.80579	−0.183754
$685$	−61.8021	−2.36134
$686$	0	0
$687$	−5.57751	−0.212795
$688$	−8.58546	−0.327318
$689$	8.71396	0.331975
$690$	1.87033	0.0712022
$691$	−23.8501	−0.907300	−0.453650	−	0.891180i	$-0.649878\pi$
$691$	−23.8501	−0.907300	−0.453650	+	0.891180i	$0.649878\pi$
$692$	−27.3585	−1.04001
$693$	0	0
$694$	−8.32077	−0.315852
$695$	37.3269	1.41589
$696$	6.37859	0.241780
$697$	63.4366	2.40283
$698$	1.74576	0.0660779
$699$	−22.2706	−0.842351
$700$	0	0
$701$	6.20352	0.234304	0.117152	−	0.993114i	$-0.462624\pi$
$701$	6.20352	0.234304	0.117152	+	0.993114i	$0.462624\pi$
$702$	−0.411295	−0.0155233
$703$	−8.44692	−0.318581
$704$	4.86085	0.183200
$705$	−32.9850	−1.24229
$706$	−5.97885	−0.225017
$707$	0	0
$708$	11.0451	0.415101
$709$	16.2491	0.610249	0.305124	−	0.952312i	$-0.401302\pi$
$709$	16.2491	0.610249	0.305124	+	0.952312i	$0.401302\pi$
$710$	1.09829	0.0412181
$711$	−13.3870	−0.502052
$712$	−6.34222	−0.237685
$713$	−0.539333	−0.0201982
$714$	0	0
$715$	−14.2929	−0.534524
$716$	−5.34749	−0.199845
$717$	13.3901	0.500063
$718$	19.2871	0.719786
$719$	−40.0502	−1.49362	−0.746811	−	0.665036i	$-0.768416\pi$
$719$	−40.0502	−1.49362	−0.746811	+	0.665036i	$0.768416\pi$
$720$	6.33531	0.236103
$721$	0	0
$722$	6.22807	0.231785
$723$	3.28645	0.122224
$724$	23.6938	0.880572
$725$	14.5250	0.539444
$726$	−18.8988	−0.701401
$727$	−40.4544	−1.50037	−0.750185	−	0.661228i	$-0.770036\pi$
$727$	−40.4544	−1.50037	−0.750185	+	0.661228i	$0.770036\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	19.6882	0.728693
$731$	29.2276	1.08102
$732$	8.73595	0.322890
$733$	53.0168	1.95822	0.979110	−	0.203332i	$-0.0651772\pi$
$733$	53.0168	1.95822	0.979110	+	0.203332i	$0.0651772\pi$
$734$	14.4074	0.531788
$735$	0	0
$736$	5.52331	0.203592
$737$	17.9099	0.659720
$738$	5.50124	0.202504
$739$	30.5517	1.12386	0.561930	−	0.827185i	$-0.310059\pi$
$739$	30.5517	1.12386	0.561930	+	0.827185i	$0.310059\pi$
$740$	15.0376	0.552793
$741$	2.02112	0.0742477
$742$	0	0
$743$	−49.1733	−1.80399	−0.901997	−	0.431743i	$-0.857899\pi$
$743$	−49.1733	−1.80399	−0.901997	+	0.431743i	$0.857899\pi$
$744$	1.16767	0.0428089
$745$	−16.3035	−0.597314
$746$	13.0948	0.479436
$747$	9.77501	0.357649
$748$	−73.8138	−2.69890
$749$	0	0
$750$	0.130761	0.00477471
$751$	41.5221	1.51516	0.757582	−	0.652740i	$-0.226381\pi$
$751$	41.5221	1.51516	0.757582	+	0.652740i	$0.226381\pi$
$752$	−21.0442	−0.767402
$753$	−10.2769	−0.374511
$754$	−1.21175	−0.0441294
$755$	−15.9140	−0.579170
$756$	0	0
$757$	−26.7837	−0.973470	−0.486735	−	0.873550i	$-0.661812\pi$
$757$	−26.7837	−0.973470	−0.486735	+	0.873550i	$0.661812\pi$
$758$	−0.501289	−0.0182076
$759$	6.54534	0.237581
$760$	19.8985	0.721795
$761$	23.6683	0.857976	0.428988	−	0.903310i	$-0.358870\pi$
$761$	23.6683	0.857976	0.428988	+	0.903310i	$0.358870\pi$
$762$	7.67653	0.278091
$763$	0	0
$764$	16.2945	0.589516
$765$	−21.5674	−0.779770
$766$	19.6073	0.708441
$767$	−4.64513	−0.167726
$768$	−5.33281	−0.192431
$769$	16.2072	0.584448	0.292224	−	0.956350i	$-0.405605\pi$
$769$	16.2072	0.584448	0.292224	+	0.956350i	$0.405605\pi$
$770$	0	0
$771$	−23.4070	−0.842984
$772$	5.91617	0.212927
$773$	−43.8899	−1.57861	−0.789305	−	0.614002i	$-0.789559\pi$
$773$	−43.8899	−1.57861	−0.789305	+	0.614002i	$0.789559\pi$
$774$	2.53462	0.0911052
$775$	2.65896	0.0955126
$776$	17.6270	0.632773
$777$	0	0
$778$	−0.458686	−0.0164447
$779$	−27.0333	−0.968570
$780$	−3.59809	−0.128832
$781$	3.84354	0.137533
$782$	−4.06221	−0.145264
$783$	2.94619	0.105288
$784$	0	0
$785$	30.4033	1.08514
$786$	3.64822	0.130128
$787$	25.7349	0.917351	0.458675	−	0.888604i	$-0.348324\pi$
$787$	25.7349	0.917351	0.458675	+	0.888604i	$0.348324\pi$
$788$	−13.5324	−0.482072
$789$	−27.3656	−0.974243
$790$	25.0381	0.890816
$791$	0	0
$792$	−14.1708	−0.503539
$793$	−3.67398	−0.130467
$794$	−12.5460	−0.445242
$795$	39.6260	1.40539
$796$	3.69925	0.131117
$797$	0.541418	0.0191780	0.00958901	−	0.999954i	$-0.496948\pi$
$797$	0.541418	0.0191780	0.00958901	+	0.999954i	$0.496948\pi$
$798$	0	0
$799$	71.6409	2.53447
$800$	−27.2304	−0.962740
$801$	−2.92939	−0.103505
$802$	−16.8054	−0.593418
$803$	68.9002	2.43143
$804$	4.50864	0.159008
$805$	0	0
$806$	−0.221825	−0.00781344
$807$	26.3771	0.928516
$808$	0.288488	0.0101490
$809$	−3.89720	−0.137018	−0.0685091	−	0.997650i	$-0.521824\pi$
$809$	−3.89720	−0.137018	−0.0685091	+	0.997650i	$0.521824\pi$
$810$	−1.87033	−0.0657167
$811$	−17.8242	−0.625892	−0.312946	−	0.949771i	$-0.601316\pi$
$811$	−17.8242	−0.625892	−0.312946	+	0.949771i	$0.601316\pi$
$812$	0	0
$813$	−4.30436	−0.150960
$814$	−11.2510	−0.394348
$815$	75.4163	2.64172
$816$	−13.7598	−0.481690
$817$	−12.4552	−0.435754
$818$	−13.2442	−0.463073
$819$	0	0
$820$	48.1261	1.68063
$821$	−18.6898	−0.652278	−0.326139	−	0.945322i	$-0.605748\pi$
$821$	−18.6898	−0.652278	−0.326139	+	0.945322i	$0.605748\pi$
$822$	11.6404	0.406006
$823$	3.44929	0.120235	0.0601174	−	0.998191i	$-0.480853\pi$
$823$	3.44929	0.120235	0.0601174	+	0.998191i	$0.480853\pi$
$824$	23.8384	0.830449
$825$	−32.2691	−1.12347
$826$	0	0
$827$	55.4418	1.92790	0.963950	−	0.266085i	$-0.0857301\pi$
$827$	55.4418	1.92790	0.963950	+	0.266085i	$0.0857301\pi$
$828$	1.64772	0.0572624
$829$	−36.7658	−1.27693	−0.638465	−	0.769651i	$-0.720430\pi$
$829$	−36.7658	−1.27693	−0.638465	+	0.769651i	$0.720430\pi$
$830$	−18.2825	−0.634594
$831$	−14.6493	−0.508179
$832$	−0.514625	−0.0178414
$833$	0	0
$834$	−7.03052	−0.243447
$835$	−37.9304	−1.31264
$836$	31.4555	1.08791
$837$	0.539333	0.0186421
$838$	−3.55950	−0.122961
$839$	25.3306	0.874508	0.437254	−	0.899338i	$-0.355951\pi$
$839$	25.3306	0.874508	0.437254	+	0.899338i	$0.355951\pi$
$840$	0	0
$841$	−20.3200	−0.700688
$842$	−7.38775	−0.254599
$843$	17.0380	0.586821
$844$	38.0269	1.30894
$845$	−39.4524	−1.35721
$846$	6.21272	0.213598
$847$	0	0
$848$	25.2811	0.868156
$849$	17.9128	0.614766
$850$	20.0270	0.686922
$851$	2.89613	0.0992780
$852$	0.967572	0.0331485
$853$	51.3694	1.75885	0.879427	−	0.476034i	$-0.157926\pi$
$853$	51.3694	1.75885	0.879427	+	0.476034i	$0.157926\pi$
$854$	0	0
$855$	9.19088	0.314321
$856$	−18.5653	−0.634550
$857$	−9.55532	−0.326403	−0.163202	−	0.986593i	$-0.552182\pi$
$857$	−9.55532	−0.326403	−0.163202	+	0.986593i	$0.552182\pi$
$858$	2.69206	0.0919055
$859$	3.63424	0.123999	0.0619994	−	0.998076i	$-0.480252\pi$
$859$	3.63424	0.123999	0.0619994	+	0.998076i	$0.480252\pi$
$860$	22.1734	0.756108
$861$	0	0
$862$	−3.19909	−0.108961
$863$	8.57788	0.291995	0.145997	−	0.989285i	$-0.453361\pi$
$863$	8.57788	0.291995	0.145997	+	0.989285i	$0.453361\pi$
$864$	−5.52331	−0.187907
$865$	52.3220	1.77900
$866$	−19.3929	−0.658996
$867$	29.8427	1.01351
$868$	0	0
$869$	87.6225	2.97239
$870$	−5.51035	−0.186818
$871$	−1.89615	−0.0642486
$872$	24.4264	0.827182
$873$	8.14170	0.275555
$874$	1.73110	0.0585553
$875$	0	0
$876$	17.3449	0.586031
$877$	45.6311	1.54085	0.770427	−	0.637528i	$-0.220043\pi$
$877$	45.6311	1.54085	0.770427	+	0.637528i	$0.220043\pi$
$878$	0.0171124	0.000577516 0
$879$	18.7699	0.633092
$880$	−41.4668	−1.39784
$881$	17.3176	0.583446	0.291723	−	0.956503i	$-0.405771\pi$
$881$	17.3176	0.583446	0.291723	+	0.956503i	$0.405771\pi$
$882$	0	0
$883$	14.3872	0.484166	0.242083	−	0.970256i	$-0.422169\pi$
$883$	14.3872	0.484166	0.242083	+	0.970256i	$0.422169\pi$
$884$	7.81478	0.262839
$885$	−21.1233	−0.710053
$886$	−10.0501	−0.337638
$887$	−2.17198	−0.0729278	−0.0364639	−	0.999335i	$-0.511609\pi$
$887$	−2.17198	−0.0729278	−0.0364639	+	0.999335i	$0.511609\pi$
$888$	−6.27020	−0.210414
$889$	0	0
$890$	5.47893	0.183654
$891$	−6.54534	−0.219277
$892$	7.06169	0.236443
$893$	−30.5296	−1.02163
$894$	3.07076	0.102702
$895$	10.2268	0.341846
$896$	0	0
$897$	−0.692965	−0.0231374
$898$	−12.3606	−0.412480
$899$	1.58898	0.0529954
$900$	−8.12342	−0.270781
$901$	−86.0647	−2.86723
$902$	−36.0075	−1.19892
$903$	0	0
$904$	6.80175	0.226223
$905$	−45.3134	−1.50627
$906$	2.99740	0.0995820
$907$	−12.8687	−0.427297	−0.213648	−	0.976911i	$-0.568535\pi$
$907$	−12.8687	−0.427297	−0.213648	+	0.976911i	$0.568535\pi$
$908$	18.0152	0.597855
$909$	0.133249	0.00441959
$910$	0	0
$911$	−4.61820	−0.153008	−0.0765039	−	0.997069i	$-0.524376\pi$
$911$	−4.61820	−0.153008	−0.0765039	+	0.997069i	$0.524376\pi$
$912$	5.86370	0.194167
$913$	−63.9807	−2.11745
$914$	8.51792	0.281748
$915$	−16.7071	−0.552321
$916$	9.19019	0.303652
$917$	0	0
$918$	4.06221	0.134073
$919$	−0.395383	−0.0130425	−0.00652124	−	0.999979i	$-0.502076\pi$
$919$	−0.395383	−0.0130425	−0.00652124	+	0.999979i	$0.502076\pi$
$920$	−6.82244	−0.224929
$921$	1.42373	0.0469135
$922$	−2.10597	−0.0693564
$923$	−0.406921	−0.0133940
$924$	0	0
$925$	−14.2782	−0.469463
$926$	−7.25689	−0.238476
$927$	11.0107	0.361637
$928$	−16.2727	−0.534179
$929$	36.6487	1.20240	0.601202	−	0.799097i	$-0.294689\pi$
$929$	36.6487	1.20240	0.601202	+	0.799097i	$0.294689\pi$
$930$	−1.00873	−0.0330776
$931$	0	0
$932$	36.6958	1.20201
$933$	4.42471	0.144859
$934$	−16.9666	−0.555164
$935$	141.166	4.61661
$936$	1.50029	0.0490385
$937$	37.1650	1.21413	0.607063	−	0.794654i	$-0.292348\pi$
$937$	37.1650	1.21413	0.607063	+	0.794654i	$0.292348\pi$
$938$	0	0
$939$	−21.6865	−0.707714
$940$	54.3502	1.77271
$941$	−21.3747	−0.696796	−0.348398	−	0.937347i	$-0.613274\pi$
$941$	−21.3747	−0.696796	−0.348398	+	0.937347i	$0.613274\pi$
$942$	−5.72644	−0.186578
$943$	9.26871	0.301831
$944$	−13.4765	−0.438623
$945$	0	0
$946$	−16.5900	−0.539386
$947$	58.0483	1.88632	0.943158	−	0.332345i	$-0.107840\pi$
$947$	58.0483	1.88632	0.943158	+	0.332345i	$0.107840\pi$
$948$	22.0581	0.716414
$949$	−7.29457	−0.236792
$950$	−8.53447	−0.276895
$951$	−11.6270	−0.377031
$952$	0	0
$953$	0.853059	0.0276333	0.0138166	−	0.999905i	$-0.495602\pi$
$953$	0.853059	0.0276333	0.0138166	+	0.999905i	$0.495602\pi$
$954$	−7.46355	−0.241641
$955$	−31.1626	−1.00840
$956$	−22.0632	−0.713575
$957$	−19.2838	−0.623358
$958$	17.9656	0.580442
$959$	0	0
$960$	−2.34022	−0.0755302
$961$	−30.7091	−0.990617
$962$	1.19116	0.0384046
$963$	−8.57510	−0.276329
$964$	−5.41516	−0.174410
$965$	−11.3144	−0.364224
$966$	0	0
$967$	38.6397	1.24257	0.621284	−	0.783585i	$-0.286611\pi$
$967$	38.6397	1.24257	0.621284	+	0.783585i	$0.286611\pi$
$968$	68.9377	2.21574
$969$	−19.9619	−0.641268
$970$	−15.2277	−0.488931
$971$	41.1365	1.32013	0.660066	−	0.751208i	$-0.270528\pi$
$971$	41.1365	1.32013	0.660066	+	0.751208i	$0.270528\pi$
$972$	−1.64772	−0.0528508
$973$	0	0
$974$	−17.1748	−0.550318
$975$	3.41638	0.109412
$976$	−10.6590	−0.341187
$977$	7.59884	0.243108	0.121554	−	0.992585i	$-0.461212\pi$
$977$	7.59884	0.243108	0.121554	+	0.992585i	$0.461212\pi$
$978$	−14.2046	−0.454214
$979$	19.1739	0.612800
$980$	0	0
$981$	11.2823	0.360215
$982$	7.07399	0.225740
$983$	−39.0631	−1.24592	−0.622959	−	0.782255i	$-0.714070\pi$
$983$	−39.0631	−1.24592	−0.622959	+	0.782255i	$0.714070\pi$
$984$	−20.0670	−0.639713
$985$	25.8802	0.824611
$986$	11.9680	0.381140
$987$	0	0
$988$	−3.33025	−0.105949
$989$	4.27043	0.135792
$990$	12.2419	0.389074
$991$	1.80629	0.0573786	0.0286893	−	0.999588i	$-0.490867\pi$
$991$	1.80629	0.0573786	0.0286893	+	0.999588i	$0.490867\pi$
$992$	−2.97890	−0.0945803
$993$	7.89484	0.250535
$994$	0	0
$995$	−7.07467	−0.224282
$996$	−16.1065	−0.510354
$997$	39.5007	1.25100	0.625499	−	0.780225i	$-0.284895\pi$
$997$	39.5007	1.25100	0.625499	+	0.780225i	$0.284895\pi$
$998$	−6.15714	−0.194901
$999$	−2.89613	−0.0916294

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3381.2.a.bd.1.3		6
7.3	odd	6		483.2.i.f.415.4	yes	12
7.5	odd	6		483.2.i.f.277.4	✓	12
7.6	odd	2		3381.2.a.bc.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.i.f.277.4	✓	12	7.5	odd	6
483.2.i.f.415.4	yes	12	7.3	odd	6
3381.2.a.bc.1.3		6	7.6	odd	2
3381.2.a.bd.1.3		6	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)

\(f(q)\)	\(=\)	\(q-0.593528 q^{2} +1.00000 q^{3} -1.64772 q^{4} +3.15120 q^{5} -0.593528 q^{6} +2.16503 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.593528 q^{2} +1.00000 q^{3} -1.64772 q^{4} +3.15120 q^{5} -0.593528 q^{6} +2.16503 q^{8} +1.00000 q^{9} -1.87033 q^{10} -6.54534 q^{11} -1.64772 q^{12} +0.692965 q^{13} +3.15120 q^{15} +2.01044 q^{16} -6.84417 q^{17} -0.593528 q^{18} +2.91662 q^{19} -5.19231 q^{20} +3.88485 q^{22} -1.00000 q^{23} +2.16503 q^{24} +4.93009 q^{25} -0.411295 q^{26} +1.00000 q^{27} +2.94619 q^{29} -1.87033 q^{30} +0.539333 q^{31} -5.52331 q^{32} -6.54534 q^{33} +4.06221 q^{34} -1.64772 q^{36} -2.89613 q^{37} -1.73110 q^{38} +0.692965 q^{39} +6.82244 q^{40} -9.26871 q^{41} -4.27043 q^{43} +10.7849 q^{44} +3.15120 q^{45} +0.593528 q^{46} -10.4674 q^{47} +2.01044 q^{48} -2.92615 q^{50} -6.84417 q^{51} -1.14182 q^{52} +12.5749 q^{53} -0.593528 q^{54} -20.6257 q^{55} +2.91662 q^{57} -1.74865 q^{58} -6.70326 q^{59} -5.19231 q^{60} -5.30183 q^{61} -0.320109 q^{62} -0.742642 q^{64} +2.18368 q^{65} +3.88485 q^{66} -2.73628 q^{67} +11.2773 q^{68} -1.00000 q^{69} -0.587217 q^{71} +2.16503 q^{72} -10.5266 q^{73} +1.71893 q^{74} +4.93009 q^{75} -4.80579 q^{76} -0.411295 q^{78} -13.3870 q^{79} +6.33531 q^{80} +1.00000 q^{81} +5.50124 q^{82} +9.77501 q^{83} -21.5674 q^{85} +2.53462 q^{86} +2.94619 q^{87} -14.1708 q^{88} -2.92939 q^{89} -1.87033 q^{90} +1.64772 q^{92} +0.539333 q^{93} +6.21272 q^{94} +9.19088 q^{95} -5.52331 q^{96} +8.14170 q^{97} -6.54534 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} + 6 q^{3} + 3 q^{4} - 3 q^{5} - q^{6} - 3 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q - q^2 + 6 * q^3 + 3 * q^4 - 3 * q^5 - q^6 - 3 * q^8 + 6 * q^9	\( 6 q - q^{2} + 6 q^{3} + 3 q^{4} - 3 q^{5} - q^{6} - 3 q^{8} + 6 q^{9} + 3 q^{10} - 14 q^{11} + 3 q^{12} - 3 q^{15} - 7 q^{16} - 15 q^{17} - q^{18} + q^{19} - 17 q^{20} - 6 q^{22} - 6 q^{23} - 3 q^{24} + 9 q^{25} + 15 q^{26} + 6 q^{27} - 6 q^{29} + 3 q^{30} + 11 q^{31} + 3 q^{32} - 14 q^{33} - 15 q^{34} + 3 q^{36} - 5 q^{37} - 14 q^{38} + 17 q^{40} - 18 q^{41} - 37 q^{43} - 10 q^{44} - 3 q^{45} + q^{46} - 3 q^{47} - 7 q^{48} - 30 q^{50} - 15 q^{51} + 7 q^{52} - 15 q^{53} - q^{54} + 2 q^{55} + q^{57} + 4 q^{58} + 2 q^{59} - 17 q^{60} + 12 q^{61} - 36 q^{62} - 23 q^{64} - 17 q^{65} - 6 q^{66} - 10 q^{67} + q^{68} - 6 q^{69} - 21 q^{71} - 3 q^{72} + 8 q^{73} - 16 q^{74} + 9 q^{75} - 18 q^{76} + 15 q^{78} - 17 q^{79} - 3 q^{80} + 6 q^{81} + 48 q^{82} - 12 q^{83} - 13 q^{85} + 22 q^{86} - 6 q^{87} - 2 q^{88} - 18 q^{89} + 3 q^{90} - 3 q^{92} + 11 q^{93} - 3 q^{94} - 16 q^{95} + 3 q^{96} + 2 q^{97} - 14 q^{99}+O(q^{100}) \) 6 * q - q^2 + 6 * q^3 + 3 * q^4 - 3 * q^5 - q^6 - 3 * q^8 + 6 * q^9 + 3 * q^10 - 14 * q^11 + 3 * q^12 - 3 * q^15 - 7 * q^16 - 15 * q^17 - q^18 + q^19 - 17 * q^20 - 6 * q^22 - 6 * q^23 - 3 * q^24 + 9 * q^25 + 15 * q^26 + 6 * q^27 - 6 * q^29 + 3 * q^30 + 11 * q^31 + 3 * q^32 - 14 * q^33 - 15 * q^34 + 3 * q^36 - 5 * q^37 - 14 * q^38 + 17 * q^40 - 18 * q^41 - 37 * q^43 - 10 * q^44 - 3 * q^45 + q^46 - 3 * q^47 - 7 * q^48 - 30 * q^50 - 15 * q^51 + 7 * q^52 - 15 * q^53 - q^54 + 2 * q^55 + q^57 + 4 * q^58 + 2 * q^59 - 17 * q^60 + 12 * q^61 - 36 * q^62 - 23 * q^64 - 17 * q^65 - 6 * q^66 - 10 * q^67 + q^68 - 6 * q^69 - 21 * q^71 - 3 * q^72 + 8 * q^73 - 16 * q^74 + 9 * q^75 - 18 * q^76 + 15 * q^78 - 17 * q^79 - 3 * q^80 + 6 * q^81 + 48 * q^82 - 12 * q^83 - 13 * q^85 + 22 * q^86 - 6 * q^87 - 2 * q^88 - 18 * q^89 + 3 * q^90 - 3 * q^92 + 11 * q^93 - 3 * q^94 - 16 * q^95 + 3 * q^96 + 2 * q^97 - 14 * q^99

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