LMFDB - Embedded newform 3381.2.a.bj.1.4

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:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 3x^{9} - 13x^{8} + 41x^{7} + 47x^{6} - 165x^{5} - 45x^{4} + 207x^{3} + 12x^{2} - 76x - 2 $ x^10 - 3x^9 - 13x^8 + 41x^7 + 47x^6 - 165x^5 - 45x^4 + 207x^3 + 12x^2 - 76*x - 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			1.4
Root			$-0.769091$ 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)

$f(q)$	$=$	$q-0.769091 q^{2} +1.00000 q^{3} -1.40850 q^{4} +4.02709 q^{5} -0.769091 q^{6} +2.62145 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.769091 q^{2} +1.00000 q^{3} -1.40850 q^{4} +4.02709 q^{5} -0.769091 q^{6} +2.62145 q^{8} +1.00000 q^{9} -3.09720 q^{10} +5.47113 q^{11} -1.40850 q^{12} +4.39956 q^{13} +4.02709 q^{15} +0.800870 q^{16} +2.24965 q^{17} -0.769091 q^{18} -3.56152 q^{19} -5.67216 q^{20} -4.20780 q^{22} +1.00000 q^{23} +2.62145 q^{24} +11.2175 q^{25} -3.38366 q^{26} +1.00000 q^{27} -4.70941 q^{29} -3.09720 q^{30} +10.5492 q^{31} -5.85883 q^{32} +5.47113 q^{33} -1.73019 q^{34} -1.40850 q^{36} -3.92549 q^{37} +2.73913 q^{38} +4.39956 q^{39} +10.5568 q^{40} +3.97807 q^{41} +2.61087 q^{43} -7.70609 q^{44} +4.02709 q^{45} -0.769091 q^{46} +0.518350 q^{47} +0.800870 q^{48} -8.62724 q^{50} +2.24965 q^{51} -6.19677 q^{52} -12.6363 q^{53} -0.769091 q^{54} +22.0328 q^{55} -3.56152 q^{57} +3.62197 q^{58} -0.842890 q^{59} -5.67216 q^{60} -9.00931 q^{61} -8.11333 q^{62} +2.90423 q^{64} +17.7174 q^{65} -4.20780 q^{66} -1.39968 q^{67} -3.16863 q^{68} +1.00000 q^{69} -7.10801 q^{71} +2.62145 q^{72} -5.32607 q^{73} +3.01906 q^{74} +11.2175 q^{75} +5.01640 q^{76} -3.38366 q^{78} -13.4434 q^{79} +3.22518 q^{80} +1.00000 q^{81} -3.05950 q^{82} -3.39713 q^{83} +9.05955 q^{85} -2.00800 q^{86} -4.70941 q^{87} +14.3423 q^{88} -13.0156 q^{89} -3.09720 q^{90} -1.40850 q^{92} +10.5492 q^{93} -0.398658 q^{94} -14.3426 q^{95} -5.85883 q^{96} +6.35615 q^{97} +5.47113 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 3 q^{2} + 10 q^{3} + 15 q^{4} + 5 q^{5} + 3 q^{6} + 9 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 3 * q^2 + 10 * q^3 + 15 * q^4 + 5 * q^5 + 3 * q^6 + 9 * q^8 + 10 * q^9	$ 10 q + 3 q^{2} + 10 q^{3} + 15 q^{4} + 5 q^{5} + 3 q^{6} + 9 q^{8} + 10 q^{9} - 11 q^{10} + 8 q^{11} + 15 q^{12} + 5 q^{15} + 37 q^{16} + 11 q^{17} + 3 q^{18} - q^{19} + 15 q^{20} + 6 q^{22} + 10 q^{23} + 9 q^{24} + 21 q^{25} - q^{26} + 10 q^{27} + 22 q^{29} - 11 q^{30} + 3 q^{31} + 11 q^{32} + 8 q^{33} + 3 q^{34} + 15 q^{36} - 3 q^{37} - 16 q^{38} - 39 q^{40} + 26 q^{41} + 27 q^{43} + 16 q^{44} + 5 q^{45} + 3 q^{46} - 11 q^{47} + 37 q^{48} + 2 q^{50} + 11 q^{51} - 29 q^{52} + 5 q^{53} + 3 q^{54} + 18 q^{55} - q^{57} + 16 q^{58} + 10 q^{59} + 15 q^{60} - 22 q^{61} + 32 q^{62} + 69 q^{64} - 11 q^{65} + 6 q^{66} - 2 q^{67} + 21 q^{68} + 10 q^{69} + 27 q^{71} + 9 q^{72} + 8 q^{73} + 14 q^{74} + 21 q^{75} + 22 q^{76} - q^{78} + 21 q^{79} + 53 q^{80} + 10 q^{81} - 36 q^{82} + 12 q^{83} + 23 q^{85} + 18 q^{86} + 22 q^{87} - 10 q^{88} - 6 q^{89} - 11 q^{90} + 15 q^{92} + 3 q^{93} - 35 q^{94} + 44 q^{95} + 11 q^{96} - 6 q^{97} + 8 q^{99}+O(q^{100}) $ 10 * q + 3 * q^2 + 10 * q^3 + 15 * q^4 + 5 * q^5 + 3 * q^6 + 9 * q^8 + 10 * q^9 - 11 * q^10 + 8 * q^11 + 15 * q^12 + 5 * q^15 + 37 * q^16 + 11 * q^17 + 3 * q^18 - q^19 + 15 * q^20 + 6 * q^22 + 10 * q^23 + 9 * q^24 + 21 * q^25 - q^26 + 10 * q^27 + 22 * q^29 - 11 * q^30 + 3 * q^31 + 11 * q^32 + 8 * q^33 + 3 * q^34 + 15 * q^36 - 3 * q^37 - 16 * q^38 - 39 * q^40 + 26 * q^41 + 27 * q^43 + 16 * q^44 + 5 * q^45 + 3 * q^46 - 11 * q^47 + 37 * q^48 + 2 * q^50 + 11 * q^51 - 29 * q^52 + 5 * q^53 + 3 * q^54 + 18 * q^55 - q^57 + 16 * q^58 + 10 * q^59 + 15 * q^60 - 22 * q^61 + 32 * q^62 + 69 * q^64 - 11 * q^65 + 6 * q^66 - 2 * q^67 + 21 * q^68 + 10 * q^69 + 27 * q^71 + 9 * q^72 + 8 * q^73 + 14 * q^74 + 21 * q^75 + 22 * q^76 - q^78 + 21 * q^79 + 53 * q^80 + 10 * q^81 - 36 * q^82 + 12 * q^83 + 23 * q^85 + 18 * q^86 + 22 * q^87 - 10 * q^88 - 6 * q^89 - 11 * q^90 + 15 * q^92 + 3 * q^93 - 35 * q^94 + 44 * q^95 + 11 * q^96 - 6 * q^97 + 8 * 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 $

$2$	−0.769091	−0.543829	−0.271915	−	0.962321i	$-0.587657\pi$
$2$	−0.769091	−0.543829	−0.271915	+	0.962321i	$0.587657\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.40850	−0.704250
$5$	4.02709	1.80097	0.900485	−	0.434887i	$-0.143212\pi$
$5$	4.02709	1.80097	0.900485	+	0.434887i	$0.143212\pi$
$6$	−0.769091	−0.313980
$7$	0	0
$7$	0	0
$8$	2.62145	0.926821
$9$	1.00000	0.333333
$10$	−3.09720	−0.979420
$11$	5.47113	1.64961	0.824804	−	0.565418i	$-0.191285\pi$
$11$	5.47113	1.64961	0.824804	+	0.565418i	$0.191285\pi$
$12$	−1.40850	−0.406599
$13$	4.39956	1.22022	0.610109	−	0.792318i	$-0.291126\pi$
$13$	4.39956	1.22022	0.610109	+	0.792318i	$0.291126\pi$
$14$	0	0
$15$	4.02709	1.03979
$16$	0.800870	0.200218
$17$	2.24965	0.545621	0.272810	−	0.962068i	$-0.412047\pi$
$17$	2.24965	0.545621	0.272810	+	0.962068i	$0.412047\pi$
$18$	−0.769091	−0.181276
$19$	−3.56152	−0.817069	−0.408534	−	0.912743i	$-0.633960\pi$
$19$	−3.56152	−0.817069	−0.408534	+	0.912743i	$0.633960\pi$
$20$	−5.67216	−1.26833
$21$	0	0
$22$	−4.20780	−0.897105
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	2.62145	0.535100
$25$	11.2175	2.24349
$26$	−3.38366	−0.663590
$27$	1.00000	0.192450
$28$	0	0
$29$	−4.70941	−0.874516	−0.437258	−	0.899336i	$-0.644050\pi$
$29$	−4.70941	−0.874516	−0.437258	+	0.899336i	$0.644050\pi$
$30$	−3.09720	−0.565468
$31$	10.5492	1.89470	0.947350	−	0.320198i	$-0.103750\pi$
$31$	10.5492	1.89470	0.947350	+	0.320198i	$0.103750\pi$
$32$	−5.85883	−1.03570
$33$	5.47113	0.952402
$34$	−1.73019	−0.296724
$35$	0	0
$36$	−1.40850	−0.234750
$37$	−3.92549	−0.645347	−0.322673	−	0.946510i	$-0.604582\pi$
$37$	−3.92549	−0.645347	−0.322673	+	0.946510i	$0.604582\pi$
$38$	2.73913	0.444346
$39$	4.39956	0.704493
$40$	10.5568	1.66918
$41$	3.97807	0.621270	0.310635	−	0.950529i	$-0.399458\pi$
$41$	3.97807	0.621270	0.310635	+	0.950529i	$0.399458\pi$
$42$	0	0
$43$	2.61087	0.398155	0.199077	−	0.979984i	$-0.436206\pi$
$43$	2.61087	0.398155	0.199077	+	0.979984i	$0.436206\pi$
$44$	−7.70609	−1.16174
$45$	4.02709	0.600323
$46$	−0.769091	−0.113396
$47$	0.518350	0.0756091	0.0378046	−	0.999285i	$-0.487964\pi$
$47$	0.518350	0.0756091	0.0378046	+	0.999285i	$0.487964\pi$
$48$	0.800870	0.115596
$49$	0	0
$50$	−8.62724	−1.22008
$51$	2.24965	0.315014
$52$	−6.19677	−0.859338
$53$	−12.6363	−1.73573	−0.867865	−	0.496799i	$-0.834508\pi$
$53$	−12.6363	−1.73573	−0.867865	+	0.496799i	$0.834508\pi$
$54$	−0.769091	−0.104660
$55$	22.0328	2.97090
$56$	0	0
$57$	−3.56152	−0.471735
$58$	3.62197	0.475587
$59$	−0.842890	−0.109735	−0.0548675	−	0.998494i	$-0.517474\pi$
$59$	−0.842890	−0.109735	−0.0548675	+	0.998494i	$0.517474\pi$
$60$	−5.67216	−0.732272
$61$	−9.00931	−1.15352	−0.576762	−	0.816912i	$-0.695684\pi$
$61$	−9.00931	−1.15352	−0.576762	+	0.816912i	$0.695684\pi$
$62$	−8.11333	−1.03039
$63$	0	0
$64$	2.90423	0.363029
$65$	17.7174	2.19757
$66$	−4.20780	−0.517944
$67$	−1.39968	−0.170999	−0.0854993	−	0.996338i	$-0.527249\pi$
$67$	−1.39968	−0.170999	−0.0854993	+	0.996338i	$0.527249\pi$
$68$	−3.16863	−0.384253
$69$	1.00000	0.120386
$70$	0	0
$71$	−7.10801	−0.843565	−0.421783	−	0.906697i	$-0.638596\pi$
$71$	−7.10801	−0.843565	−0.421783	+	0.906697i	$0.638596\pi$
$72$	2.62145	0.308940
$73$	−5.32607	−0.623370	−0.311685	−	0.950186i	$-0.600893\pi$
$73$	−5.32607	−0.623370	−0.311685	+	0.950186i	$0.600893\pi$
$74$	3.01906	0.350958
$75$	11.2175	1.29528
$76$	5.01640	0.575420
$77$	0	0
$78$	−3.38366	−0.383124
$79$	−13.4434	−1.51250	−0.756251	−	0.654281i	$-0.772971\pi$
$79$	−13.4434	−1.51250	−0.756251	+	0.654281i	$0.772971\pi$
$80$	3.22518	0.360586
$81$	1.00000	0.111111
$82$	−3.05950	−0.337865
$83$	−3.39713	−0.372883	−0.186442	−	0.982466i	$-0.559696\pi$
$83$	−3.39713	−0.372883	−0.186442	+	0.982466i	$0.559696\pi$
$84$	0	0
$85$	9.05955	0.982646
$86$	−2.00800	−0.216528
$87$	−4.70941	−0.504902
$88$	14.3423	1.52889
$89$	−13.0156	−1.37965	−0.689826	−	0.723975i	$-0.742313\pi$
$89$	−13.0156	−1.37965	−0.689826	+	0.723975i	$0.742313\pi$
$90$	−3.09720	−0.326473
$91$	0	0
$92$	−1.40850	−0.146846
$93$	10.5492	1.09391
$94$	−0.398658	−0.0411185
$95$	−14.3426	−1.47152
$96$	−5.85883	−0.597965
$97$	6.35615	0.645369	0.322684	−	0.946507i	$-0.395415\pi$
$97$	6.35615	0.645369	0.322684	+	0.946507i	$0.395415\pi$
$98$	0	0
$99$	5.47113	0.549870
$100$	−15.7998	−1.57998
$101$	−2.83587	−0.282180	−0.141090	−	0.989997i	$-0.545061\pi$
$101$	−2.83587	−0.282180	−0.141090	+	0.989997i	$0.545061\pi$
$102$	−1.73019	−0.171314
$103$	−10.5894	−1.04340	−0.521701	−	0.853128i	$-0.674702\pi$
$103$	−10.5894	−1.04340	−0.521701	+	0.853128i	$0.674702\pi$
$104$	11.5332	1.13092
$105$	0	0
$106$	9.71847	0.943941
$107$	−18.8540	−1.82269	−0.911344	−	0.411646i	$-0.864954\pi$
$107$	−18.8540	−1.82269	−0.911344	+	0.411646i	$0.864954\pi$
$108$	−1.40850	−0.135533
$109$	11.1344	1.06649	0.533243	−	0.845962i	$-0.320973\pi$
$109$	11.1344	1.06649	0.533243	+	0.845962i	$0.320973\pi$
$110$	−16.9452	−1.61566
$111$	−3.92549	−0.372591
$112$	0	0
$113$	−1.29979	−0.122274	−0.0611370	−	0.998129i	$-0.519473\pi$
$113$	−1.29979	−0.122274	−0.0611370	+	0.998129i	$0.519473\pi$
$114$	2.73913	0.256543
$115$	4.02709	0.375528
$116$	6.63321	0.615878
$117$	4.39956	0.406739
$118$	0.648259	0.0596771
$119$	0	0
$120$	10.5568	0.963699
$121$	18.9333	1.72121
$122$	6.92898	0.627320
$123$	3.97807	0.358691
$124$	−14.8586	−1.33434
$125$	25.0383	2.23949
$126$	0	0
$127$	−0.0947076	−0.00840394	−0.00420197	−	0.999991i	$-0.501338\pi$
$127$	−0.0947076	−0.00840394	−0.00420197	+	0.999991i	$0.501338\pi$
$128$	9.48405	0.838279
$129$	2.61087	0.229875
$130$	−13.6263	−1.19511
$131$	13.7260	1.19925	0.599625	−	0.800281i	$-0.295316\pi$
$131$	13.7260	1.19925	0.599625	+	0.800281i	$0.295316\pi$
$132$	−7.70609	−0.670729
$133$	0	0
$134$	1.07648	0.0929941
$135$	4.02709	0.346597
$136$	5.89734	0.505693
$137$	−1.03182	−0.0881541	−0.0440771	−	0.999028i	$-0.514035\pi$
$137$	−1.03182	−0.0881541	−0.0440771	+	0.999028i	$0.514035\pi$
$138$	−0.769091	−0.0654693
$139$	−0.281873	−0.0239081	−0.0119541	−	0.999929i	$-0.503805\pi$
$139$	−0.281873	−0.0239081	−0.0119541	+	0.999929i	$0.503805\pi$
$140$	0	0
$141$	0.518350	0.0436530
$142$	5.46670	0.458756
$143$	24.0706	2.01288
$144$	0.800870	0.0667392
$145$	−18.9652	−1.57498
$146$	4.09623	0.339007
$147$	0	0
$148$	5.52905	0.454485
$149$	−5.70250	−0.467167	−0.233584	−	0.972337i	$-0.575045\pi$
$149$	−5.70250	−0.467167	−0.233584	+	0.972337i	$0.575045\pi$
$150$	−8.62724	−0.704412
$151$	2.87628	0.234069	0.117034	−	0.993128i	$-0.462661\pi$
$151$	2.87628	0.234069	0.117034	+	0.993128i	$0.462661\pi$
$152$	−9.33633	−0.757276
$153$	2.24965	0.181874
$154$	0	0
$155$	42.4828	3.41230
$156$	−6.19677	−0.496139
$157$	−16.7408	−1.33606	−0.668032	−	0.744133i	$-0.732863\pi$
$157$	−16.7408	−1.33606	−0.668032	+	0.744133i	$0.732863\pi$
$158$	10.3392	0.822543
$159$	−12.6363	−1.00212
$160$	−23.5940	−1.86527
$161$	0	0
$162$	−0.769091	−0.0604255
$163$	−0.687374	−0.0538393	−0.0269197	−	0.999638i	$-0.508570\pi$
$163$	−0.687374	−0.0538393	−0.0269197	+	0.999638i	$0.508570\pi$
$164$	−5.60311	−0.437529
$165$	22.0328	1.71525
$166$	2.61270	0.202785
$167$	12.4022	0.959714	0.479857	−	0.877347i	$-0.340688\pi$
$167$	12.4022	0.959714	0.479857	+	0.877347i	$0.340688\pi$
$168$	0	0
$169$	6.35609	0.488930
$170$	−6.96762	−0.534392
$171$	−3.56152	−0.272356
$172$	−3.67742	−0.280400
$173$	3.20701	0.243824	0.121912	−	0.992541i	$-0.461097\pi$
$173$	3.20701	0.243824	0.121912	+	0.992541i	$0.461097\pi$
$174$	3.62197	0.274581
$175$	0	0
$176$	4.38167	0.330281
$177$	−0.842890	−0.0633555
$178$	10.0102	0.750295
$179$	11.1472	0.833178	0.416589	−	0.909095i	$-0.363225\pi$
$179$	11.1472	0.833178	0.416589	+	0.909095i	$0.363225\pi$
$180$	−5.67216	−0.422778
$181$	−18.5663	−1.38002	−0.690011	−	0.723799i	$-0.742394\pi$
$181$	−18.5663	−1.38002	−0.690011	+	0.723799i	$0.742394\pi$
$182$	0	0
$183$	−9.00931	−0.665988
$184$	2.62145	0.193255
$185$	−15.8083	−1.16225
$186$	−8.11333	−0.594898
$187$	12.3081	0.900060
$188$	−0.730096	−0.0532477
$189$	0	0
$190$	11.0307	0.800253
$191$	−22.9387	−1.65978	−0.829892	−	0.557924i	$-0.811598\pi$
$191$	−22.9387	−1.65978	−0.829892	+	0.557924i	$0.811598\pi$
$192$	2.90423	0.209595
$193$	−10.1295	−0.729139	−0.364569	−	0.931176i	$-0.618784\pi$
$193$	−10.1295	−0.729139	−0.364569	+	0.931176i	$0.618784\pi$
$194$	−4.88845	−0.350970
$195$	17.7174	1.26877
$196$	0	0
$197$	−4.51568	−0.321729	−0.160864	−	0.986977i	$-0.551428\pi$
$197$	−4.51568	−0.321729	−0.160864	+	0.986977i	$0.551428\pi$
$198$	−4.20780	−0.299035
$199$	−20.8076	−1.47501	−0.737506	−	0.675340i	$-0.763997\pi$
$199$	−20.8076	−1.47501	−0.737506	+	0.675340i	$0.763997\pi$
$200$	29.4060	2.07932
$201$	−1.39968	−0.0987261
$202$	2.18104	0.153458
$203$	0	0
$204$	−3.16863	−0.221849
$205$	16.0201	1.11889
$206$	8.14419	0.567433
$207$	1.00000	0.0695048
$208$	3.52347	0.244309
$209$	−19.4856	−1.34784
$210$	0	0
$211$	26.2315	1.80585	0.902925	−	0.429799i	$-0.141416\pi$
$211$	26.2315	1.80585	0.902925	+	0.429799i	$0.141416\pi$
$212$	17.7982	1.22239
$213$	−7.10801	−0.487033
$214$	14.5005	0.991231
$215$	10.5142	0.717064
$216$	2.62145	0.178367
$217$	0	0
$218$	−8.56339	−0.579986
$219$	−5.32607	−0.359903
$220$	−31.0331	−2.09225
$221$	9.89747	0.665776
$222$	3.01906	0.202626
$223$	1.20377	0.0806102	0.0403051	−	0.999187i	$-0.487167\pi$
$223$	1.20377	0.0806102	0.0403051	+	0.999187i	$0.487167\pi$
$224$	0	0
$225$	11.2175	0.747831
$226$	0.999657	0.0664962
$227$	−14.2531	−0.946015	−0.473007	−	0.881059i	$-0.656832\pi$
$227$	−14.2531	−0.946015	−0.473007	+	0.881059i	$0.656832\pi$
$228$	5.01640	0.332219
$229$	−12.3571	−0.816578	−0.408289	−	0.912853i	$-0.633875\pi$
$229$	−12.3571	−0.816578	−0.408289	+	0.912853i	$0.633875\pi$
$230$	−3.09720	−0.204223
$231$	0	0
$232$	−12.3455	−0.810520
$233$	11.9828	0.785017	0.392508	−	0.919748i	$-0.371607\pi$
$233$	11.9828	0.785017	0.392508	+	0.919748i	$0.371607\pi$
$234$	−3.38366	−0.221197
$235$	2.08744	0.136170
$236$	1.18721	0.0772808
$237$	−13.4434	−0.873244
$238$	0	0
$239$	6.53934	0.422995	0.211497	−	0.977379i	$-0.432166\pi$
$239$	6.53934	0.422995	0.211497	+	0.977379i	$0.432166\pi$
$240$	3.22518	0.208184
$241$	−0.500065	−0.0322120	−0.0161060	−	0.999870i	$-0.505127\pi$
$241$	−0.500065	−0.0322120	−0.0161060	+	0.999870i	$0.505127\pi$
$242$	−14.5614	−0.936044
$243$	1.00000	0.0641500
$244$	12.6896	0.812369
$245$	0	0
$246$	−3.05950	−0.195066
$247$	−15.6691	−0.997001
$248$	27.6543	1.75605
$249$	−3.39713	−0.215284
$250$	−19.2567	−1.21790
$251$	−5.10076	−0.321957	−0.160978	−	0.986958i	$-0.551465\pi$
$251$	−5.10076	−0.321957	−0.160978	+	0.986958i	$0.551465\pi$
$252$	0	0
$253$	5.47113	0.343967
$254$	0.0728387	0.00457031
$255$	9.05955	0.567331
$256$	−13.1026	−0.818910
$257$	8.85942	0.552635	0.276318	−	0.961066i	$-0.410886\pi$
$257$	8.85942	0.552635	0.276318	+	0.961066i	$0.410886\pi$
$258$	−2.00800	−0.125013
$259$	0	0
$260$	−24.9550	−1.54764
$261$	−4.70941	−0.291505
$262$	−10.5566	−0.652187
$263$	26.1608	1.61315	0.806573	−	0.591135i	$-0.201320\pi$
$263$	26.1608	1.61315	0.806573	+	0.591135i	$0.201320\pi$
$264$	14.3423	0.882706
$265$	−50.8876	−3.12600
$266$	0	0
$267$	−13.0156	−0.796542
$268$	1.97146	0.120426
$269$	15.7569	0.960714	0.480357	−	0.877073i	$-0.340507\pi$
$269$	15.7569	0.960714	0.480357	+	0.877073i	$0.340507\pi$
$270$	−3.09720	−0.188489
$271$	5.95116	0.361507	0.180754	−	0.983528i	$-0.442146\pi$
$271$	5.95116	0.361507	0.180754	+	0.983528i	$0.442146\pi$
$272$	1.80168	0.109243
$273$	0	0
$274$	0.793561	0.0479408
$275$	61.3722	3.70088
$276$	−1.40850	−0.0847817
$277$	15.2365	0.915475	0.457738	−	0.889087i	$-0.348660\pi$
$277$	15.2365	0.915475	0.457738	+	0.889087i	$0.348660\pi$
$278$	0.216786	0.0130019
$279$	10.5492	0.631567
$280$	0	0
$281$	1.78254	0.106338	0.0531688	−	0.998586i	$-0.483068\pi$
$281$	1.78254	0.106338	0.0531688	+	0.998586i	$0.483068\pi$
$282$	−0.398658	−0.0237398
$283$	19.9991	1.18882	0.594412	−	0.804161i	$-0.297385\pi$
$283$	19.9991	1.18882	0.594412	+	0.804161i	$0.297385\pi$
$284$	10.0116	0.594081
$285$	−14.3426	−0.849580
$286$	−18.5124	−1.09466
$287$	0	0
$288$	−5.85883	−0.345235
$289$	−11.9391	−0.702298
$290$	14.5860	0.856519
$291$	6.35615	0.372604
$292$	7.50177	0.439008
$293$	17.4319	1.01838	0.509191	−	0.860653i	$-0.329945\pi$
$293$	17.4319	1.01838	0.509191	+	0.860653i	$0.329945\pi$
$294$	0	0
$295$	−3.39439	−0.197629
$296$	−10.2905	−0.598121
$297$	5.47113	0.317467
$298$	4.38574	0.254059
$299$	4.39956	0.254433
$300$	−15.7998	−0.912201
$301$	0	0
$302$	−2.21212	−0.127293
$303$	−2.83587	−0.162916
$304$	−2.85232	−0.163592
$305$	−36.2813	−2.07746
$306$	−1.73019	−0.0989081
$307$	22.1407	1.26363	0.631817	−	0.775117i	$-0.282309\pi$
$307$	22.1407	1.26363	0.631817	+	0.775117i	$0.282309\pi$
$308$	0	0
$309$	−10.5894	−0.602409
$310$	−32.6731	−1.85571
$311$	6.89035	0.390716	0.195358	−	0.980732i	$-0.437413\pi$
$311$	6.89035	0.390716	0.195358	+	0.980732i	$0.437413\pi$
$312$	11.5332	0.652939
$313$	−13.5739	−0.767241	−0.383620	−	0.923491i	$-0.625323\pi$
$313$	−13.5739	−0.767241	−0.383620	+	0.923491i	$0.625323\pi$
$314$	12.8752	0.726591
$315$	0	0
$316$	18.9350	1.06518
$317$	−24.6587	−1.38497	−0.692486	−	0.721431i	$-0.743485\pi$
$317$	−24.6587	−1.38497	−0.692486	+	0.721431i	$0.743485\pi$
$318$	9.71847	0.544985
$319$	−25.7658	−1.44261
$320$	11.6956	0.653804
$321$	−18.8540	−1.05233
$322$	0	0
$323$	−8.01218	−0.445810
$324$	−1.40850	−0.0782500
$325$	49.3518	2.73755
$326$	0.528653	0.0292794
$327$	11.1344	0.615736
$328$	10.4283	0.575806
$329$	0	0
$330$	−16.9452	−0.932802
$331$	22.9676	1.26241	0.631207	−	0.775615i	$-0.282560\pi$
$331$	22.9676	1.26241	0.631207	+	0.775615i	$0.282560\pi$
$332$	4.78486	0.262603
$333$	−3.92549	−0.215116
$334$	−9.53845	−0.521921
$335$	−5.63666	−0.307963
$336$	0	0
$337$	−19.9238	−1.08532	−0.542659	−	0.839953i	$-0.682582\pi$
$337$	−19.9238	−1.08532	−0.542659	+	0.839953i	$0.682582\pi$
$338$	−4.88841	−0.265894
$339$	−1.29979	−0.0705950
$340$	−12.7604	−0.692028
$341$	57.7163	3.12552
$342$	2.73913	0.148115
$343$	0	0
$344$	6.84426	0.369018
$345$	4.02709	0.216811
$346$	−2.46648	−0.132599
$347$	12.6315	0.678093	0.339046	−	0.940770i	$-0.389896\pi$
$347$	12.6315	0.678093	0.339046	+	0.940770i	$0.389896\pi$
$348$	6.63321	0.355577
$349$	−14.9697	−0.801308	−0.400654	−	0.916229i	$-0.631217\pi$
$349$	−14.9697	−0.801308	−0.400654	+	0.916229i	$0.631217\pi$
$350$	0	0
$351$	4.39956	0.234831
$352$	−32.0545	−1.70851
$353$	−2.73206	−0.145413	−0.0727064	−	0.997353i	$-0.523164\pi$
$353$	−2.73206	−0.145413	−0.0727064	+	0.997353i	$0.523164\pi$
$354$	0.648259	0.0344546
$355$	−28.6246	−1.51924
$356$	18.3325	0.971619
$357$	0	0
$358$	−8.57318	−0.453107
$359$	16.6777	0.880217	0.440108	−	0.897945i	$-0.354940\pi$
$359$	16.6777	0.880217	0.440108	+	0.897945i	$0.354940\pi$
$360$	10.5568	0.556392
$361$	−6.31558	−0.332399
$362$	14.2792	0.750497
$363$	18.9333	0.993740
$364$	0	0
$365$	−21.4486	−1.12267
$366$	6.92898	0.362184
$367$	28.0775	1.46563	0.732817	−	0.680426i	$-0.238205\pi$
$367$	28.0775	1.46563	0.732817	+	0.680426i	$0.238205\pi$
$368$	0.800870	0.0417483
$369$	3.97807	0.207090
$370$	12.1580	0.632066
$371$	0	0
$372$	−14.8586	−0.770383
$373$	22.3398	1.15671	0.578356	−	0.815785i	$-0.303695\pi$
$373$	22.3398	1.15671	0.578356	+	0.815785i	$0.303695\pi$
$374$	−9.46608	−0.489479
$375$	25.0383	1.29297
$376$	1.35883	0.0700761
$377$	−20.7193	−1.06710
$378$	0	0
$379$	27.7949	1.42773	0.713864	−	0.700284i	$-0.246943\pi$
$379$	27.7949	1.42773	0.713864	+	0.700284i	$0.246943\pi$
$380$	20.2015	1.03631
$381$	−0.0947076	−0.00485202
$382$	17.6419	0.902639
$383$	−6.59155	−0.336813	−0.168406	−	0.985718i	$-0.553862\pi$
$383$	−6.59155	−0.336813	−0.168406	+	0.985718i	$0.553862\pi$
$384$	9.48405	0.483981
$385$	0	0
$386$	7.79052	0.396527
$387$	2.61087	0.132718
$388$	−8.95263	−0.454501
$389$	8.98913	0.455767	0.227883	−	0.973688i	$-0.426819\pi$
$389$	8.98913	0.455767	0.227883	+	0.973688i	$0.426819\pi$
$390$	−13.6263	−0.689994
$391$	2.24965	0.113770
$392$	0	0
$393$	13.7260	0.692387
$394$	3.47296	0.174965
$395$	−54.1379	−2.72397
$396$	−7.70609	−0.387246
$397$	2.55171	0.128067	0.0640334	−	0.997948i	$-0.479604\pi$
$397$	2.55171	0.128067	0.0640334	+	0.997948i	$0.479604\pi$
$398$	16.0029	0.802155
$399$	0	0
$400$	8.98373	0.449187
$401$	37.3623	1.86578	0.932892	−	0.360157i	$-0.117277\pi$
$401$	37.3623	1.86578	0.932892	+	0.360157i	$0.117277\pi$
$402$	1.07648	0.0536902
$403$	46.4120	2.31195
$404$	3.99432	0.198725
$405$	4.02709	0.200108
$406$	0	0
$407$	−21.4769	−1.06457
$408$	5.89734	0.291962
$409$	10.7730	0.532693	0.266346	−	0.963877i	$-0.414183\pi$
$409$	10.7730	0.532693	0.266346	+	0.963877i	$0.414183\pi$
$410$	−12.3209	−0.608485
$411$	−1.03182	−0.0508958
$412$	14.9151	0.734816
$413$	0	0
$414$	−0.769091	−0.0377987
$415$	−13.6806	−0.671552
$416$	−25.7763	−1.26379
$417$	−0.281873	−0.0138034
$418$	14.9862	0.732997
$419$	−19.8186	−0.968200	−0.484100	−	0.875013i	$-0.660853\pi$
$419$	−19.8186	−0.968200	−0.484100	+	0.875013i	$0.660853\pi$
$420$	0	0
$421$	3.68979	0.179830	0.0899148	−	0.995949i	$-0.471341\pi$
$421$	3.68979	0.179830	0.0899148	+	0.995949i	$0.471341\pi$
$422$	−20.1744	−0.982074
$423$	0.518350	0.0252030
$424$	−33.1254	−1.60871
$425$	25.2354	1.22410
$426$	5.46670	0.264863
$427$	0	0
$428$	26.5559	1.28363
$429$	24.0706	1.16214
$430$	−8.08639	−0.389961
$431$	9.19005	0.442669	0.221335	−	0.975198i	$-0.428959\pi$
$431$	9.19005	0.442669	0.221335	+	0.975198i	$0.428959\pi$
$432$	0.800870	0.0385319
$433$	−33.6161	−1.61549	−0.807743	−	0.589535i	$-0.799311\pi$
$433$	−33.6161	−1.61549	−0.807743	+	0.589535i	$0.799311\pi$
$434$	0	0
$435$	−18.9652	−0.909313
$436$	−15.6829	−0.751073
$437$	−3.56152	−0.170371
$438$	4.09623	0.195726
$439$	2.30712	0.110113	0.0550565	−	0.998483i	$-0.482466\pi$
$439$	2.30712	0.110113	0.0550565	+	0.998483i	$0.482466\pi$
$440$	57.7576	2.75349
$441$	0	0
$442$	−7.61205	−0.362068
$443$	−11.3956	−0.541422	−0.270711	−	0.962661i	$-0.587259\pi$
$443$	−11.3956	−0.541422	−0.270711	+	0.962661i	$0.587259\pi$
$444$	5.52905	0.262397
$445$	−52.4150	−2.48471
$446$	−0.925805	−0.0438382
$447$	−5.70250	−0.269719
$448$	0	0
$449$	3.16307	0.149275	0.0746373	−	0.997211i	$-0.476220\pi$
$449$	3.16307	0.149275	0.0746373	+	0.997211i	$0.476220\pi$
$450$	−8.62724	−0.406692
$451$	21.7646	1.02485
$452$	1.83076	0.0861115
$453$	2.87628	0.135140
$454$	10.9620	0.514470
$455$	0	0
$456$	−9.33633	−0.437214
$457$	10.9136	0.510518	0.255259	−	0.966873i	$-0.417839\pi$
$457$	10.9136	0.510518	0.255259	+	0.966873i	$0.417839\pi$
$458$	9.50371	0.444079
$459$	2.24965	0.105005
$460$	−5.67216	−0.264466
$461$	−34.5807	−1.61058	−0.805291	−	0.592880i	$-0.797991\pi$
$461$	−34.5807	−1.61058	−0.805291	+	0.592880i	$0.797991\pi$
$462$	0	0
$463$	−1.07364	−0.0498961	−0.0249480	−	0.999689i	$-0.507942\pi$
$463$	−1.07364	−0.0498961	−0.0249480	+	0.999689i	$0.507942\pi$
$464$	−3.77163	−0.175094
$465$	42.4828	1.97009
$466$	−9.21583	−0.426915
$467$	13.4884	0.624167	0.312083	−	0.950055i	$-0.398973\pi$
$467$	13.4884	0.624167	0.312083	+	0.950055i	$0.398973\pi$
$468$	−6.19677	−0.286446
$469$	0	0
$470$	−1.60543	−0.0740531
$471$	−16.7408	−0.771377
$472$	−2.20959	−0.101705
$473$	14.2844	0.656799
$474$	10.3392	0.474895
$475$	−39.9512	−1.83309
$476$	0	0
$477$	−12.6363	−0.578577
$478$	−5.02935	−0.230037
$479$	6.30939	0.288283	0.144142	−	0.989557i	$-0.453958\pi$
$479$	6.30939	0.288283	0.144142	+	0.989557i	$0.453958\pi$
$480$	−23.5940	−1.07692
$481$	−17.2704	−0.787463
$482$	0.384595	0.0175178
$483$	0	0
$484$	−26.6675	−1.21216
$485$	25.5968	1.16229
$486$	−0.769091	−0.0348867
$487$	−18.5968	−0.842703	−0.421352	−	0.906897i	$-0.638444\pi$
$487$	−18.5968	−0.842703	−0.421352	+	0.906897i	$0.638444\pi$
$488$	−23.6174	−1.06911
$489$	−0.687374	−0.0310841
$490$	0	0
$491$	−27.5620	−1.24386	−0.621928	−	0.783074i	$-0.713651\pi$
$491$	−27.5620	−1.24386	−0.621928	+	0.783074i	$0.713651\pi$
$492$	−5.60311	−0.252608
$493$	−10.5945	−0.477154
$494$	12.0510	0.542198
$495$	22.0328	0.990299
$496$	8.44858	0.379352
$497$	0	0
$498$	2.61270	0.117078
$499$	−9.33757	−0.418007	−0.209004	−	0.977915i	$-0.567022\pi$
$499$	−9.33757	−0.418007	−0.209004	+	0.977915i	$0.567022\pi$
$500$	−35.2664	−1.57716
$501$	12.4022	0.554091
$502$	3.92294	0.175090
$503$	−32.9700	−1.47006	−0.735029	−	0.678035i	$-0.762832\pi$
$503$	−32.9700	−1.47006	−0.735029	+	0.678035i	$0.762832\pi$
$504$	0	0
$505$	−11.4203	−0.508197
$506$	−4.20780	−0.187059
$507$	6.35609	0.282284
$508$	0.133396	0.00591847
$509$	−22.0147	−0.975783	−0.487892	−	0.872904i	$-0.662234\pi$
$509$	−22.0147	−0.975783	−0.487892	+	0.872904i	$0.662234\pi$
$510$	−6.96762	−0.308531
$511$	0	0
$512$	−8.89104	−0.392932
$513$	−3.56152	−0.157245
$514$	−6.81370	−0.300539
$515$	−42.6444	−1.87914
$516$	−3.67742	−0.161889
$517$	2.83596	0.124725
$518$	0	0
$519$	3.20701	0.140772
$520$	46.4452	2.03676
$521$	18.1901	0.796922	0.398461	−	0.917185i	$-0.369544\pi$
$521$	18.1901	0.796922	0.398461	+	0.917185i	$0.369544\pi$
$522$	3.62197	0.158529
$523$	−39.1642	−1.71253	−0.856265	−	0.516537i	$-0.827221\pi$
$523$	−39.1642	−1.71253	−0.856265	+	0.516537i	$0.827221\pi$
$524$	−19.3331	−0.844572
$525$	0	0
$526$	−20.1200	−0.877276
$527$	23.7321	1.03379
$528$	4.38167	0.190688
$529$	1.00000	0.0434783
$530$	39.1372	1.70001
$531$	−0.842890	−0.0365783
$532$	0	0
$533$	17.5017	0.758085
$534$	10.0102	0.433183
$535$	−75.9269	−3.28261
$536$	−3.66920	−0.158485
$537$	11.1472	0.481036
$538$	−12.1185	−0.522464
$539$	0	0
$540$	−5.67216	−0.244091
$541$	12.4131	0.533681	0.266841	−	0.963741i	$-0.414020\pi$
$541$	12.4131	0.533681	0.266841	+	0.963741i	$0.414020\pi$
$542$	−4.57698	−0.196598
$543$	−18.5663	−0.796757
$544$	−13.1803	−0.565102
$545$	44.8394	1.92071
$546$	0	0
$547$	25.5889	1.09410	0.547052	−	0.837099i	$-0.315750\pi$
$547$	25.5889	1.09410	0.547052	+	0.837099i	$0.315750\pi$
$548$	1.45331	0.0620825
$549$	−9.00931	−0.384508
$550$	−47.2008	−2.01265
$551$	16.7727	0.714540
$552$	2.62145	0.111576
$553$	0	0
$554$	−11.7183	−0.497862
$555$	−15.8083	−0.671026
$556$	0.397018	0.0168373
$557$	27.5846	1.16880	0.584398	−	0.811468i	$-0.301331\pi$
$557$	27.5846	1.16880	0.584398	+	0.811468i	$0.301331\pi$
$558$	−8.11333	−0.343465
$559$	11.4867	0.485835
$560$	0	0
$561$	12.3081	0.519650
$562$	−1.37094	−0.0578295
$563$	−25.3338	−1.06769	−0.533845	−	0.845582i	$-0.679254\pi$
$563$	−25.3338	−1.06769	−0.533845	+	0.845582i	$0.679254\pi$
$564$	−0.730096	−0.0307426
$565$	−5.23438	−0.220212
$566$	−15.3811	−0.646517
$567$	0	0
$568$	−18.6333	−0.781834
$569$	−22.2054	−0.930900	−0.465450	−	0.885074i	$-0.654108\pi$
$569$	−22.2054	−0.930900	−0.465450	+	0.885074i	$0.654108\pi$
$570$	11.0307	0.462027
$571$	8.66454	0.362600	0.181300	−	0.983428i	$-0.441970\pi$
$571$	8.66454	0.362600	0.181300	+	0.983428i	$0.441970\pi$
$572$	−33.9034	−1.41757
$573$	−22.9387	−0.958277
$574$	0	0
$575$	11.2175	0.467800
$576$	2.90423	0.121010
$577$	−40.4286	−1.68306	−0.841532	−	0.540208i	$-0.818346\pi$
$577$	−40.4286	−1.68306	−0.841532	+	0.540208i	$0.818346\pi$
$578$	9.18223	0.381930
$579$	−10.1295	−0.420969
$580$	26.7125	1.10918
$581$	0	0
$582$	−4.88845	−0.202633
$583$	−69.1349	−2.86328
$584$	−13.9620	−0.577752
$585$	17.7174	0.732525
$586$	−13.4067	−0.553826
$587$	46.9106	1.93621	0.968104	−	0.250547i	$-0.0806106\pi$
$587$	46.9106	1.93621	0.968104	+	0.250547i	$0.0806106\pi$
$588$	0	0
$589$	−37.5714	−1.54810
$590$	2.61060	0.107477
$591$	−4.51568	−0.185750
$592$	−3.14381	−0.129210
$593$	−5.68443	−0.233432	−0.116716	−	0.993165i	$-0.537237\pi$
$593$	−5.68443	−0.233432	−0.116716	+	0.993165i	$0.537237\pi$
$594$	−4.20780	−0.172648
$595$	0	0
$596$	8.03197	0.329002
$597$	−20.8076	−0.851599
$598$	−3.38366	−0.138368
$599$	4.80057	0.196146	0.0980730	−	0.995179i	$-0.468732\pi$
$599$	4.80057	0.196146	0.0980730	+	0.995179i	$0.468732\pi$
$600$	29.4060	1.20049
$601$	−8.92677	−0.364131	−0.182065	−	0.983286i	$-0.558278\pi$
$601$	−8.92677	−0.364131	−0.182065	+	0.983286i	$0.558278\pi$
$602$	0	0
$603$	−1.39968	−0.0569996
$604$	−4.05124	−0.164843
$605$	76.2461	3.09985
$606$	2.18104	0.0885987
$607$	−3.32483	−0.134951	−0.0674753	−	0.997721i	$-0.521494\pi$
$607$	−3.32483	−0.134951	−0.0674753	+	0.997721i	$0.521494\pi$
$608$	20.8663	0.846242
$609$	0	0
$610$	27.9036	1.12978
$611$	2.28051	0.0922596
$612$	−3.16863	−0.128084
$613$	25.6252	1.03499	0.517497	−	0.855685i	$-0.326864\pi$
$613$	25.6252	1.03499	0.517497	+	0.855685i	$0.326864\pi$
$614$	−17.0282	−0.687201
$615$	16.0201	0.645991
$616$	0	0
$617$	29.3425	1.18128	0.590642	−	0.806934i	$-0.298875\pi$
$617$	29.3425	1.18128	0.590642	+	0.806934i	$0.298875\pi$
$618$	8.14419	0.327607
$619$	−5.99740	−0.241056	−0.120528	−	0.992710i	$-0.538459\pi$
$619$	−5.99740	−0.241056	−0.120528	+	0.992710i	$0.538459\pi$
$620$	−59.8370	−2.40311
$621$	1.00000	0.0401286
$622$	−5.29930	−0.212483
$623$	0	0
$624$	3.52347	0.141052
$625$	44.7441	1.78977
$626$	10.4395	0.417248
$627$	−19.4856	−0.778178
$628$	23.5795	0.940923
$629$	−8.83099	−0.352115
$630$	0	0
$631$	16.3993	0.652846	0.326423	−	0.945224i	$-0.394157\pi$
$631$	16.3993	0.652846	0.326423	+	0.945224i	$0.394157\pi$
$632$	−35.2412	−1.40182
$633$	26.2315	1.04261
$634$	18.9648	0.753189
$635$	−0.381396	−0.0151352
$636$	17.7982	0.705746
$637$	0	0
$638$	19.8163	0.784533
$639$	−7.10801	−0.281188
$640$	38.1931	1.50972
$641$	−48.4652	−1.91426	−0.957130	−	0.289658i	$-0.906458\pi$
$641$	−48.4652	−1.91426	−0.957130	+	0.289658i	$0.906458\pi$
$642$	14.5005	0.572287
$643$	19.8571	0.783088	0.391544	−	0.920159i	$-0.371941\pi$
$643$	19.8571	0.783088	0.391544	+	0.920159i	$0.371941\pi$
$644$	0	0
$645$	10.5142	0.413997
$646$	6.16209	0.242444
$647$	29.4130	1.15634	0.578172	−	0.815915i	$-0.303766\pi$
$647$	29.4130	1.15634	0.578172	+	0.815915i	$0.303766\pi$
$648$	2.62145	0.102980
$649$	−4.61156	−0.181020
$650$	−37.9560	−1.48876
$651$	0	0
$652$	0.968166	0.0379163
$653$	23.1788	0.907057	0.453528	−	0.891242i	$-0.350165\pi$
$653$	23.1788	0.907057	0.453528	+	0.891242i	$0.350165\pi$
$654$	−8.56339	−0.334855
$655$	55.2760	2.15981
$656$	3.18592	0.124389
$657$	−5.32607	−0.207790
$658$	0	0
$659$	33.1492	1.29131	0.645654	−	0.763630i	$-0.276585\pi$
$659$	33.1492	1.29131	0.645654	+	0.763630i	$0.276585\pi$
$660$	−31.0331	−1.20796
$661$	−15.0565	−0.585628	−0.292814	−	0.956169i	$-0.594592\pi$
$661$	−15.0565	−0.585628	−0.292814	+	0.956169i	$0.594592\pi$
$662$	−17.6642	−0.686537
$663$	9.89747	0.384386
$664$	−8.90539	−0.345596
$665$	0	0
$666$	3.01906	0.116986
$667$	−4.70941	−0.182349
$668$	−17.4686	−0.675879
$669$	1.20377	0.0465403
$670$	4.33510	0.167480
$671$	−49.2912	−1.90286
$672$	0	0
$673$	−23.8903	−0.920904	−0.460452	−	0.887684i	$-0.652313\pi$
$673$	−23.8903	−0.920904	−0.460452	+	0.887684i	$0.652313\pi$
$674$	15.3232	0.590228
$675$	11.2175	0.431760
$676$	−8.95255	−0.344329
$677$	8.58560	0.329971	0.164986	−	0.986296i	$-0.447242\pi$
$677$	8.58560	0.329971	0.164986	+	0.986296i	$0.447242\pi$
$678$	0.999657	0.0383916
$679$	0	0
$680$	23.7491	0.910737
$681$	−14.2531	−0.546182
$682$	−44.3891	−1.69975
$683$	−9.38317	−0.359037	−0.179518	−	0.983755i	$-0.557454\pi$
$683$	−9.38317	−0.359037	−0.179518	+	0.983755i	$0.557454\pi$
$684$	5.01640	0.191807
$685$	−4.15522	−0.158763
$686$	0	0
$687$	−12.3571	−0.471452
$688$	2.09097	0.0797176
$689$	−55.5942	−2.11797
$690$	−3.09720	−0.117908
$691$	21.2793	0.809503	0.404751	−	0.914427i	$-0.367358\pi$
$691$	21.2793	0.809503	0.404751	+	0.914427i	$0.367358\pi$
$692$	−4.51707	−0.171713
$693$	0	0
$694$	−9.71474	−0.368767
$695$	−1.13513	−0.0430578
$696$	−12.3455	−0.467954
$697$	8.94927	0.338978
$698$	11.5130	0.435775
$699$	11.9828	0.453230
$700$	0	0
$701$	−4.27651	−0.161521	−0.0807607	−	0.996734i	$-0.525735\pi$
$701$	−4.27651	−0.161521	−0.0807607	+	0.996734i	$0.525735\pi$
$702$	−3.38366	−0.127708
$703$	13.9807	0.527293
$704$	15.8894	0.598856
$705$	2.08744	0.0786177
$706$	2.10120	0.0790797
$707$	0	0
$708$	1.18721	0.0446181
$709$	−13.7316	−0.515702	−0.257851	−	0.966185i	$-0.583014\pi$
$709$	−13.7316	−0.515702	−0.257851	+	0.966185i	$0.583014\pi$
$710$	22.0149	0.826205
$711$	−13.4434	−0.504168
$712$	−34.1197	−1.27869
$713$	10.5492	0.395072
$714$	0	0
$715$	96.9343	3.62514
$716$	−15.7008	−0.586765
$717$	6.53934	0.244216
$718$	−12.8267	−0.478687
$719$	−17.6882	−0.659658	−0.329829	−	0.944041i	$-0.606991\pi$
$719$	−17.6882	−0.659658	−0.329829	+	0.944041i	$0.606991\pi$
$720$	3.22518	0.120195
$721$	0	0
$722$	4.85725	0.180768
$723$	−0.500065	−0.0185976
$724$	26.1506	0.971881
$725$	−52.8277	−1.96197
$726$	−14.5614	−0.540425
$727$	−25.0455	−0.928885	−0.464442	−	0.885603i	$-0.653745\pi$
$727$	−25.0455	−0.928885	−0.464442	+	0.885603i	$0.653745\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	16.4959	0.610541
$731$	5.87356	0.217241
$732$	12.6896	0.469022
$733$	−15.7850	−0.583033	−0.291517	−	0.956566i	$-0.594160\pi$
$733$	−15.7850	−0.583033	−0.291517	+	0.956566i	$0.594160\pi$
$734$	−21.5942	−0.797055
$735$	0	0
$736$	−5.85883	−0.215959
$737$	−7.65786	−0.282081
$738$	−3.05950	−0.112622
$739$	−9.99859	−0.367804	−0.183902	−	0.982945i	$-0.558873\pi$
$739$	−9.99859	−0.367804	−0.183902	+	0.982945i	$0.558873\pi$
$740$	22.2660	0.818515
$741$	−15.6691	−0.575619
$742$	0	0
$743$	−7.14322	−0.262059	−0.131030	−	0.991378i	$-0.541828\pi$
$743$	−7.14322	−0.262059	−0.131030	+	0.991378i	$0.541828\pi$
$744$	27.6543	1.01385
$745$	−22.9645	−0.841354
$746$	−17.1813	−0.629053
$747$	−3.39713	−0.124294
$748$	−17.3360	−0.633867
$749$	0	0
$750$	−19.2567	−0.703156
$751$	−21.3619	−0.779507	−0.389754	−	0.920919i	$-0.627440\pi$
$751$	−21.3619	−0.779507	−0.389754	+	0.920919i	$0.627440\pi$
$752$	0.415131	0.0151383
$753$	−5.10076	−0.185882
$754$	15.9350	0.580320
$755$	11.5831	0.421550
$756$	0	0
$757$	−6.60015	−0.239887	−0.119943	−	0.992781i	$-0.538271\pi$
$757$	−6.60015	−0.239887	−0.119943	+	0.992781i	$0.538271\pi$
$758$	−21.3768	−0.776440
$759$	5.47113	0.198590
$760$	−37.5982	−1.36383
$761$	−13.1540	−0.476831	−0.238416	−	0.971163i	$-0.576628\pi$
$761$	−13.1540	−0.476831	−0.238416	+	0.971163i	$0.576628\pi$
$762$	0.0728387	0.00263867
$763$	0	0
$764$	32.3091	1.16890
$765$	9.05955	0.327549
$766$	5.06950	0.183169
$767$	−3.70834	−0.133900
$768$	−13.1026	−0.472798
$769$	23.8184	0.858915	0.429457	−	0.903087i	$-0.358705\pi$
$769$	23.8184	0.858915	0.429457	+	0.903087i	$0.358705\pi$
$770$	0	0
$771$	8.85942	0.319064
$772$	14.2674	0.513496
$773$	1.79587	0.0645929	0.0322965	−	0.999478i	$-0.489718\pi$
$773$	1.79587	0.0645929	0.0322965	+	0.999478i	$0.489718\pi$
$774$	−2.00800	−0.0721760
$775$	118.336	4.25075
$776$	16.6623	0.598141
$777$	0	0
$778$	−6.91345	−0.247859
$779$	−14.1680	−0.507621
$780$	−24.9550	−0.893531
$781$	−38.8889	−1.39155
$782$	−1.73019	−0.0618713
$783$	−4.70941	−0.168301
$784$	0	0
$785$	−67.4169	−2.40621
$786$	−10.5566	−0.376540
$787$	15.0749	0.537362	0.268681	−	0.963229i	$-0.413412\pi$
$787$	15.0749	0.537362	0.268681	+	0.963229i	$0.413412\pi$
$788$	6.36033	0.226577
$789$	26.1608	0.931350
$790$	41.6369	1.48138
$791$	0	0
$792$	14.3423	0.509631
$793$	−39.6370	−1.40755
$794$	−1.96250	−0.0696465
$795$	−50.8876	−1.80480
$796$	29.3075	1.03878
$797$	−20.9322	−0.741456	−0.370728	−	0.928742i	$-0.620892\pi$
$797$	−20.9322	−0.741456	−0.370728	+	0.928742i	$0.620892\pi$
$798$	0	0
$799$	1.16611	0.0412539
$800$	−65.7212	−2.32360
$801$	−13.0156	−0.459884
$802$	−28.7350	−1.01467
$803$	−29.1397	−1.02832
$804$	1.97146	0.0695279
$805$	0	0
$806$	−35.6950	−1.25730
$807$	15.7569	0.554668
$808$	−7.43408	−0.261530
$809$	24.8986	0.875388	0.437694	−	0.899124i	$-0.355795\pi$
$809$	24.8986	0.875388	0.437694	+	0.899124i	$0.355795\pi$
$810$	−3.09720	−0.108824
$811$	−33.0135	−1.15926	−0.579630	−	0.814880i	$-0.696803\pi$
$811$	−33.0135	−1.15926	−0.579630	+	0.814880i	$0.696803\pi$
$812$	0	0
$813$	5.95116	0.208716
$814$	16.5177	0.578944
$815$	−2.76812	−0.0969630
$816$	1.80168	0.0630714
$817$	−9.29868	−0.325320
$818$	−8.28545	−0.289694
$819$	0	0
$820$	−22.5642	−0.787977
$821$	7.06657	0.246625	0.123312	−	0.992368i	$-0.460648\pi$
$821$	7.06657	0.246625	0.123312	+	0.992368i	$0.460648\pi$
$822$	0.793561	0.0276786
$823$	38.3257	1.33595	0.667975	−	0.744183i	$-0.267161\pi$
$823$	38.3257	1.33595	0.667975	+	0.744183i	$0.267161\pi$
$824$	−27.7595	−0.967047
$825$	61.3722	2.13671
$826$	0	0
$827$	−18.8543	−0.655629	−0.327815	−	0.944742i	$-0.606312\pi$
$827$	−18.8543	−0.655629	−0.327815	+	0.944742i	$0.606312\pi$
$828$	−1.40850	−0.0489487
$829$	−49.1920	−1.70851	−0.854255	−	0.519854i	$-0.825986\pi$
$829$	−49.1920	−1.70851	−0.854255	+	0.519854i	$0.825986\pi$
$830$	10.5216	0.365210
$831$	15.2365	0.528550
$832$	12.7773	0.442974
$833$	0	0
$834$	0.216786	0.00750668
$835$	49.9450	1.72842
$836$	27.4454	0.949219
$837$	10.5492	0.364635
$838$	15.2423	0.526535
$839$	−3.42024	−0.118080	−0.0590399	−	0.998256i	$-0.518804\pi$
$839$	−3.42024	−0.118080	−0.0590399	+	0.998256i	$0.518804\pi$
$840$	0	0
$841$	−6.82142	−0.235222
$842$	−2.83779	−0.0977966
$843$	1.78254	0.0613941
$844$	−36.9470	−1.27177
$845$	25.5966	0.880548
$846$	−0.398658	−0.0137062
$847$	0	0
$848$	−10.1200	−0.347524
$849$	19.9991	0.686368
$850$	−19.4083	−0.665699
$851$	−3.92549	−0.134564
$852$	10.0116	0.342993
$853$	−26.9555	−0.922939	−0.461469	−	0.887156i	$-0.652678\pi$
$853$	−26.9555	−0.922939	−0.461469	+	0.887156i	$0.652678\pi$
$854$	0	0
$855$	−14.3426	−0.490505
$856$	−49.4248	−1.68931
$857$	−21.1442	−0.722273	−0.361137	−	0.932513i	$-0.617611\pi$
$857$	−21.1442	−0.722273	−0.361137	+	0.932513i	$0.617611\pi$
$858$	−18.5124	−0.632004
$859$	−41.3331	−1.41027	−0.705133	−	0.709075i	$-0.749113\pi$
$859$	−41.3331	−1.41027	−0.705133	+	0.709075i	$0.749113\pi$
$860$	−14.8093	−0.504992
$861$	0	0
$862$	−7.06798	−0.240736
$863$	−1.37678	−0.0468661	−0.0234331	−	0.999725i	$-0.507460\pi$
$863$	−1.37678	−0.0468661	−0.0234331	+	0.999725i	$0.507460\pi$
$864$	−5.85883	−0.199322
$865$	12.9149	0.439120
$866$	25.8538	0.878549
$867$	−11.9391	−0.405472
$868$	0	0
$869$	−73.5507	−2.49504
$870$	14.5860	0.494511
$871$	−6.15799	−0.208656
$872$	29.1883	0.988441
$873$	6.35615	0.215123
$874$	2.73913	0.0926525
$875$	0	0
$876$	7.50177	0.253461
$877$	−22.4325	−0.757490	−0.378745	−	0.925501i	$-0.623644\pi$
$877$	−22.4325	−0.757490	−0.378745	+	0.925501i	$0.623644\pi$
$878$	−1.77439	−0.0598826
$879$	17.4319	0.587963
$880$	17.6454	0.594826
$881$	51.4107	1.73207	0.866036	−	0.499982i	$-0.166660\pi$
$881$	51.4107	1.73207	0.866036	+	0.499982i	$0.166660\pi$
$882$	0	0
$883$	47.4947	1.59833	0.799163	−	0.601115i	$-0.205277\pi$
$883$	47.4947	1.59833	0.799163	+	0.601115i	$0.205277\pi$
$884$	−13.9406	−0.468872
$885$	−3.39439	−0.114101
$886$	8.76426	0.294441
$887$	16.0293	0.538212	0.269106	−	0.963111i	$-0.413272\pi$
$887$	16.0293	0.538212	0.269106	+	0.963111i	$0.413272\pi$
$888$	−10.2905	−0.345325
$889$	0	0
$890$	40.3119	1.35126
$891$	5.47113	0.183290
$892$	−1.69550	−0.0567697
$893$	−1.84611	−0.0617779
$894$	4.38574	0.146681
$895$	44.8906	1.50053
$896$	0	0
$897$	4.39956	0.146897
$898$	−2.43269	−0.0811799
$899$	−49.6808	−1.65695
$900$	−15.7998	−0.526660
$901$	−28.4273	−0.947050
$902$	−16.7389	−0.557345
$903$	0	0
$904$	−3.40733	−0.113326
$905$	−74.7682	−2.48538
$906$	−2.21212	−0.0734928
$907$	−28.8875	−0.959194	−0.479597	−	0.877489i	$-0.659217\pi$
$907$	−28.8875	−0.959194	−0.479597	+	0.877489i	$0.659217\pi$
$908$	20.0756	0.666231
$909$	−2.83587	−0.0940599
$910$	0	0
$911$	41.9126	1.38863	0.694314	−	0.719672i	$-0.255708\pi$
$911$	41.9126	1.38863	0.694314	+	0.719672i	$0.255708\pi$
$912$	−2.85232	−0.0944496
$913$	−18.5862	−0.615112
$914$	−8.39357	−0.277634
$915$	−36.2813	−1.19942
$916$	17.4049	0.575075
$917$	0	0
$918$	−1.73019	−0.0571046
$919$	4.98999	0.164605	0.0823023	−	0.996607i	$-0.473773\pi$
$919$	4.98999	0.164605	0.0823023	+	0.996607i	$0.473773\pi$
$920$	10.5568	0.348047
$921$	22.1407	0.729560
$922$	26.5957	0.875882
$923$	−31.2721	−1.02933
$924$	0	0
$925$	−44.0341	−1.44783
$926$	0.825723	0.0271350
$927$	−10.5894	−0.347801
$928$	27.5917	0.905741
$929$	36.9429	1.21206	0.606028	−	0.795443i	$-0.292762\pi$
$929$	36.9429	1.21206	0.606028	+	0.795443i	$0.292762\pi$
$930$	−32.6731	−1.07139
$931$	0	0
$932$	−16.8777	−0.552848
$933$	6.89035	0.225580
$934$	−10.3738	−0.339440
$935$	49.5660	1.62098
$936$	11.5332	0.376974
$937$	7.79921	0.254789	0.127395	−	0.991852i	$-0.459339\pi$
$937$	7.79921	0.254789	0.127395	+	0.991852i	$0.459339\pi$
$938$	0	0
$939$	−13.5739	−0.442967
$940$	−2.94016	−0.0958975
$941$	23.3080	0.759820	0.379910	−	0.925023i	$-0.375955\pi$
$941$	23.3080	0.759820	0.379910	+	0.925023i	$0.375955\pi$
$942$	12.8752	0.419497
$943$	3.97807	0.129544
$944$	−0.675046	−0.0219709
$945$	0	0
$946$	−10.9860	−0.357187
$947$	37.5586	1.22049	0.610244	−	0.792213i	$-0.291071\pi$
$947$	37.5586	1.22049	0.610244	+	0.792213i	$0.291071\pi$
$948$	18.9350	0.614982
$949$	−23.4324	−0.760647
$950$	30.7261	0.996886
$951$	−24.6587	−0.799614
$952$	0	0
$953$	−16.0283	−0.519209	−0.259604	−	0.965715i	$-0.583592\pi$
$953$	−16.0283	−0.519209	−0.259604	+	0.965715i	$0.583592\pi$
$954$	9.71847	0.314647
$955$	−92.3761	−2.98922
$956$	−9.21066	−0.297894
$957$	−25.7658	−0.832891
$958$	−4.85249	−0.156777
$959$	0	0
$960$	11.6956	0.377474
$961$	80.2866	2.58989
$962$	13.2825	0.428246
$963$	−18.8540	−0.607563
$964$	0.704341	0.0226853
$965$	−40.7925	−1.31316
$966$	0	0
$967$	−49.3526	−1.58707	−0.793536	−	0.608523i	$-0.791762\pi$
$967$	−49.3526	−1.58707	−0.793536	+	0.608523i	$0.791762\pi$
$968$	49.6326	1.59525
$969$	−8.01218	−0.257388
$970$	−19.6862	−0.632087
$971$	15.1966	0.487683	0.243841	−	0.969815i	$-0.421592\pi$
$971$	15.1966	0.487683	0.243841	+	0.969815i	$0.421592\pi$
$972$	−1.40850	−0.0451776
$973$	0	0
$974$	14.3027	0.458287
$975$	49.3518	1.58052
$976$	−7.21529	−0.230956
$977$	−48.2766	−1.54451	−0.772253	−	0.635315i	$-0.780870\pi$
$977$	−48.2766	−1.54451	−0.772253	+	0.635315i	$0.780870\pi$
$978$	0.528653	0.0169045
$979$	−71.2101	−2.27589
$980$	0	0
$981$	11.1344	0.355495
$982$	21.1977	0.676446
$983$	13.2666	0.423139	0.211570	−	0.977363i	$-0.432143\pi$
$983$	13.2666	0.423139	0.211570	+	0.977363i	$0.432143\pi$
$984$	10.4283	0.332442
$985$	−18.1850	−0.579423
$986$	8.14816	0.259490
$987$	0	0
$988$	22.0699	0.702138
$989$	2.61087	0.0830210
$990$	−16.9452	−0.538553
$991$	1.40433	0.0446100	0.0223050	−	0.999751i	$-0.492900\pi$
$991$	1.40433	0.0446100	0.0223050	+	0.999751i	$0.492900\pi$
$992$	−61.8063	−1.96235
$993$	22.9676	0.728855
$994$	0	0
$995$	−83.7942	−2.65645
$996$	4.78486	0.151614
$997$	−10.0710	−0.318953	−0.159477	−	0.987202i	$-0.550981\pi$
$997$	−10.0710	−0.318953	−0.159477	+	0.987202i	$0.550981\pi$
$998$	7.18144	0.227324
$999$	−3.92549	−0.124197

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3381.2.a.bj.1.4		10
7.3	odd	6		483.2.i.h.415.7	yes	20
7.5	odd	6		483.2.i.h.277.7	✓	20
7.6	odd	2		3381.2.a.bi.1.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.i.h.277.7	✓	20	7.5	odd	6
483.2.i.h.415.7	yes	20	7.3	odd	6
3381.2.a.bi.1.4		10	7.6	odd	2
3381.2.a.bj.1.4		10	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)

\(f(q)\)	\(=\)	\(q-0.769091 q^{2} +1.00000 q^{3} -1.40850 q^{4} +4.02709 q^{5} -0.769091 q^{6} +2.62145 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.769091 q^{2} +1.00000 q^{3} -1.40850 q^{4} +4.02709 q^{5} -0.769091 q^{6} +2.62145 q^{8} +1.00000 q^{9} -3.09720 q^{10} +5.47113 q^{11} -1.40850 q^{12} +4.39956 q^{13} +4.02709 q^{15} +0.800870 q^{16} +2.24965 q^{17} -0.769091 q^{18} -3.56152 q^{19} -5.67216 q^{20} -4.20780 q^{22} +1.00000 q^{23} +2.62145 q^{24} +11.2175 q^{25} -3.38366 q^{26} +1.00000 q^{27} -4.70941 q^{29} -3.09720 q^{30} +10.5492 q^{31} -5.85883 q^{32} +5.47113 q^{33} -1.73019 q^{34} -1.40850 q^{36} -3.92549 q^{37} +2.73913 q^{38} +4.39956 q^{39} +10.5568 q^{40} +3.97807 q^{41} +2.61087 q^{43} -7.70609 q^{44} +4.02709 q^{45} -0.769091 q^{46} +0.518350 q^{47} +0.800870 q^{48} -8.62724 q^{50} +2.24965 q^{51} -6.19677 q^{52} -12.6363 q^{53} -0.769091 q^{54} +22.0328 q^{55} -3.56152 q^{57} +3.62197 q^{58} -0.842890 q^{59} -5.67216 q^{60} -9.00931 q^{61} -8.11333 q^{62} +2.90423 q^{64} +17.7174 q^{65} -4.20780 q^{66} -1.39968 q^{67} -3.16863 q^{68} +1.00000 q^{69} -7.10801 q^{71} +2.62145 q^{72} -5.32607 q^{73} +3.01906 q^{74} +11.2175 q^{75} +5.01640 q^{76} -3.38366 q^{78} -13.4434 q^{79} +3.22518 q^{80} +1.00000 q^{81} -3.05950 q^{82} -3.39713 q^{83} +9.05955 q^{85} -2.00800 q^{86} -4.70941 q^{87} +14.3423 q^{88} -13.0156 q^{89} -3.09720 q^{90} -1.40850 q^{92} +10.5492 q^{93} -0.398658 q^{94} -14.3426 q^{95} -5.85883 q^{96} +6.35615 q^{97} +5.47113 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 3 q^{2} + 10 q^{3} + 15 q^{4} + 5 q^{5} + 3 q^{6} + 9 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 3 * q^2 + 10 * q^3 + 15 * q^4 + 5 * q^5 + 3 * q^6 + 9 * q^8 + 10 * q^9	\( 10 q + 3 q^{2} + 10 q^{3} + 15 q^{4} + 5 q^{5} + 3 q^{6} + 9 q^{8} + 10 q^{9} - 11 q^{10} + 8 q^{11} + 15 q^{12} + 5 q^{15} + 37 q^{16} + 11 q^{17} + 3 q^{18} - q^{19} + 15 q^{20} + 6 q^{22} + 10 q^{23} + 9 q^{24} + 21 q^{25} - q^{26} + 10 q^{27} + 22 q^{29} - 11 q^{30} + 3 q^{31} + 11 q^{32} + 8 q^{33} + 3 q^{34} + 15 q^{36} - 3 q^{37} - 16 q^{38} - 39 q^{40} + 26 q^{41} + 27 q^{43} + 16 q^{44} + 5 q^{45} + 3 q^{46} - 11 q^{47} + 37 q^{48} + 2 q^{50} + 11 q^{51} - 29 q^{52} + 5 q^{53} + 3 q^{54} + 18 q^{55} - q^{57} + 16 q^{58} + 10 q^{59} + 15 q^{60} - 22 q^{61} + 32 q^{62} + 69 q^{64} - 11 q^{65} + 6 q^{66} - 2 q^{67} + 21 q^{68} + 10 q^{69} + 27 q^{71} + 9 q^{72} + 8 q^{73} + 14 q^{74} + 21 q^{75} + 22 q^{76} - q^{78} + 21 q^{79} + 53 q^{80} + 10 q^{81} - 36 q^{82} + 12 q^{83} + 23 q^{85} + 18 q^{86} + 22 q^{87} - 10 q^{88} - 6 q^{89} - 11 q^{90} + 15 q^{92} + 3 q^{93} - 35 q^{94} + 44 q^{95} + 11 q^{96} - 6 q^{97} + 8 q^{99}+O(q^{100}) \) 10 * q + 3 * q^2 + 10 * q^3 + 15 * q^4 + 5 * q^5 + 3 * q^6 + 9 * q^8 + 10 * q^9 - 11 * q^10 + 8 * q^11 + 15 * q^12 + 5 * q^15 + 37 * q^16 + 11 * q^17 + 3 * q^18 - q^19 + 15 * q^20 + 6 * q^22 + 10 * q^23 + 9 * q^24 + 21 * q^25 - q^26 + 10 * q^27 + 22 * q^29 - 11 * q^30 + 3 * q^31 + 11 * q^32 + 8 * q^33 + 3 * q^34 + 15 * q^36 - 3 * q^37 - 16 * q^38 - 39 * q^40 + 26 * q^41 + 27 * q^43 + 16 * q^44 + 5 * q^45 + 3 * q^46 - 11 * q^47 + 37 * q^48 + 2 * q^50 + 11 * q^51 - 29 * q^52 + 5 * q^53 + 3 * q^54 + 18 * q^55 - q^57 + 16 * q^58 + 10 * q^59 + 15 * q^60 - 22 * q^61 + 32 * q^62 + 69 * q^64 - 11 * q^65 + 6 * q^66 - 2 * q^67 + 21 * q^68 + 10 * q^69 + 27 * q^71 + 9 * q^72 + 8 * q^73 + 14 * q^74 + 21 * q^75 + 22 * q^76 - q^78 + 21 * q^79 + 53 * q^80 + 10 * q^81 - 36 * q^82 + 12 * q^83 + 23 * q^85 + 18 * q^86 + 22 * q^87 - 10 * q^88 - 6 * q^89 - 11 * q^90 + 15 * q^92 + 3 * q^93 - 35 * q^94 + 44 * q^95 + 11 * q^96 - 6 * q^97 + 8 * q^99

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Database

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