LMFDB - Embedded newform 3381.2.a.bi.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	$-0.856788\pi$
$5$	−4.02709	−1.80097	−0.900485	+	0.434887i	$0.856788\pi$
$6$	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	$-0.708874\pi$
$13$	−4.39956	−1.22022	−0.610109	+	0.792318i	$0.708874\pi$
$14$	0	0
$15$	4.02709	1.03979
$16$	0.800870	0.200218
$17$	−2.24965	−0.545621	−0.272810	−	0.962068i	$-0.587953\pi$
$17$	−2.24965	−0.545621	−0.272810	+	0.962068i	$0.587953\pi$
$18$	−0.769091	−0.181276
$19$	3.56152	0.817069	0.408534	−	0.912743i	$-0.366040\pi$
$19$	3.56152	0.817069	0.408534	+	0.912743i	$0.366040\pi$
$20$	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	$-0.896250\pi$
$31$	−10.5492	−1.89470	−0.947350	+	0.320198i	$0.896250\pi$
$32$	−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	$-0.600542\pi$
$41$	−3.97807	−0.621270	−0.310635	+	0.950529i	$0.600542\pi$
$42$	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	$-0.512036\pi$
$47$	−0.518350	−0.0756091	−0.0378046	+	0.999285i	$0.512036\pi$
$48$	−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	$-0.482526\pi$
$59$	0.842890	0.109735	0.0548675	+	0.998494i	$0.482526\pi$
$60$	−5.67216	−0.732272
$61$	9.00931	1.15352	0.576762	−	0.816912i	$-0.304316\pi$
$61$	9.00931	1.15352	0.576762	+	0.816912i	$0.304316\pi$
$62$	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	$-0.399107\pi$
$73$	5.32607	0.623370	0.311685	+	0.950186i	$0.399107\pi$
$74$	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	$-0.440304\pi$
$83$	3.39713	0.372883	0.186442	+	0.982466i	$0.440304\pi$
$84$	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	$-0.257687\pi$
$89$	13.0156	1.37965	0.689826	+	0.723975i	$0.257687\pi$
$90$	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	$-0.604585\pi$
$97$	−6.35615	−0.645369	−0.322684	+	0.946507i	$0.604585\pi$
$98$	0	0
$99$	5.47113	0.549870
$100$	−15.7998	−1.57998
$101$	2.83587	0.282180	0.141090	−	0.989997i	$-0.454939\pi$
$101$	2.83587	0.282180	0.141090	+	0.989997i	$0.454939\pi$
$102$	−1.73019	−0.171314
$103$	10.5894	1.04340	0.521701	−	0.853128i	$-0.325298\pi$
$103$	10.5894	1.04340	0.521701	+	0.853128i	$0.325298\pi$
$104$	−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	$-0.704684\pi$
$131$	−13.7260	−1.19925	−0.599625	+	0.800281i	$0.704684\pi$
$132$	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	$-0.496195\pi$
$139$	0.281873	0.0239081	0.0119541	+	0.999929i	$0.496195\pi$
$140$	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	$-0.267137\pi$
$157$	16.7408	1.33606	0.668032	+	0.744133i	$0.267137\pi$
$158$	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	$-0.659312\pi$
$167$	−12.4022	−0.959714	−0.479857	+	0.877347i	$0.659312\pi$
$168$	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	$-0.538903\pi$
$173$	−3.20701	−0.243824	−0.121912	+	0.992541i	$0.538903\pi$
$174$	−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	$-0.257606\pi$
$181$	18.5663	1.38002	0.690011	+	0.723799i	$0.257606\pi$
$182$	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	$-0.236003\pi$
$199$	20.8076	1.47501	0.737506	+	0.675340i	$0.236003\pi$
$200$	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	$-0.512833\pi$
$223$	−1.20377	−0.0806102	−0.0403051	+	0.999187i	$0.512833\pi$
$224$	0	0
$225$	11.2175	0.747831
$226$	0.999657	0.0664962
$227$	14.2531	0.946015	0.473007	−	0.881059i	$-0.343168\pi$
$227$	14.2531	0.946015	0.473007	+	0.881059i	$0.343168\pi$
$228$	5.01640	0.332219
$229$	12.3571	0.816578	0.408289	−	0.912853i	$-0.366125\pi$
$229$	12.3571	0.816578	0.408289	+	0.912853i	$0.366125\pi$
$230$	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	$-0.494873\pi$
$241$	0.500065	0.0322120	0.0161060	+	0.999870i	$0.494873\pi$
$242$	−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	$-0.448535\pi$
$251$	5.10076	0.321957	0.160978	+	0.986958i	$0.448535\pi$
$252$	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	$-0.589114\pi$
$257$	−8.85942	−0.552635	−0.276318	+	0.961066i	$0.589114\pi$
$258$	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	$-0.659493\pi$
$269$	−15.7569	−0.960714	−0.480357	+	0.877073i	$0.659493\pi$
$270$	−3.09720	−0.188489
$271$	−5.95116	−0.361507	−0.180754	−	0.983528i	$-0.557854\pi$
$271$	−5.95116	−0.361507	−0.180754	+	0.983528i	$0.557854\pi$
$272$	−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	$-0.702615\pi$
$283$	−19.9991	−1.18882	−0.594412	+	0.804161i	$0.702615\pi$
$284$	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	$-0.670055\pi$
$293$	−17.4319	−1.01838	−0.509191	+	0.860653i	$0.670055\pi$
$294$	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	$-0.717691\pi$
$307$	−22.1407	−1.26363	−0.631817	+	0.775117i	$0.717691\pi$
$308$	0	0
$309$	−10.5894	−0.602409
$310$	−32.6731	−1.85571
$311$	−6.89035	−0.390716	−0.195358	−	0.980732i	$-0.562587\pi$
$311$	−6.89035	−0.390716	−0.195358	+	0.980732i	$0.562587\pi$
$312$	11.5332	0.652939
$313$	13.5739	0.767241	0.383620	−	0.923491i	$-0.374677\pi$
$313$	13.5739	0.767241	0.383620	+	0.923491i	$0.374677\pi$
$314$	−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	$-0.368783\pi$
$349$	14.9697	0.801308	0.400654	+	0.916229i	$0.368783\pi$
$350$	0	0
$351$	4.39956	0.234831
$352$	−32.0545	−1.70851
$353$	2.73206	0.145413	0.0727064	−	0.997353i	$-0.476836\pi$
$353$	2.73206	0.145413	0.0727064	+	0.997353i	$0.476836\pi$
$354$	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	$-0.761795\pi$
$367$	−28.0775	−1.46563	−0.732817	+	0.680426i	$0.761795\pi$
$368$	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	$-0.446138\pi$
$383$	6.59155	0.336813	0.168406	+	0.985718i	$0.446138\pi$
$384$	−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	$-0.520396\pi$
$397$	−2.55171	−0.128067	−0.0640334	+	0.997948i	$0.520396\pi$
$398$	−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	$-0.585817\pi$
$409$	−10.7730	−0.532693	−0.266346	+	0.963877i	$0.585817\pi$
$410$	−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	$-0.339147\pi$
$419$	19.8186	0.968200	0.484100	+	0.875013i	$0.339147\pi$
$420$	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	$-0.200689\pi$
$433$	33.6161	1.61549	0.807743	+	0.589535i	$0.200689\pi$
$434$	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	$-0.517534\pi$
$439$	−2.30712	−0.110113	−0.0550565	+	0.998483i	$0.517534\pi$
$440$	−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	$-0.202009\pi$
$461$	34.5807	1.61058	0.805291	+	0.592880i	$0.202009\pi$
$462$	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	$-0.601027\pi$
$467$	−13.4884	−0.624167	−0.312083	+	0.950055i	$0.601027\pi$
$468$	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	$-0.546042\pi$
$479$	−6.30939	−0.288283	−0.144142	+	0.989557i	$0.546042\pi$
$480$	−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	$-0.237168\pi$
$503$	32.9700	1.47006	0.735029	+	0.678035i	$0.237168\pi$
$504$	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	$-0.337766\pi$
$509$	22.0147	0.975783	0.487892	+	0.872904i	$0.337766\pi$
$510$	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	$-0.630456\pi$
$521$	−18.1901	−0.796922	−0.398461	+	0.917185i	$0.630456\pi$
$522$	3.62197	0.158529
$523$	39.1642	1.71253	0.856265	−	0.516537i	$-0.172779\pi$
$523$	39.1642	1.71253	0.856265	+	0.516537i	$0.172779\pi$
$524$	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	$-0.320746\pi$
$563$	25.3338	1.06769	0.533845	+	0.845582i	$0.320746\pi$
$564$	−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	$-0.181654\pi$
$577$	40.4286	1.68306	0.841532	+	0.540208i	$0.181654\pi$
$578$	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	$-0.919389\pi$
$587$	−46.9106	−1.93621	−0.968104	+	0.250547i	$0.919389\pi$
$588$	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	$-0.462763\pi$
$593$	5.68443	0.233432	0.116716	+	0.993165i	$0.462763\pi$
$594$	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	$-0.441722\pi$
$601$	8.92677	0.364131	0.182065	+	0.983286i	$0.441722\pi$
$602$	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	$-0.478506\pi$
$607$	3.32483	0.134951	0.0674753	+	0.997721i	$0.478506\pi$
$608$	−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	$-0.461541\pi$
$619$	5.99740	0.241056	0.120528	+	0.992710i	$0.461541\pi$
$620$	−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	$-0.628059\pi$
$643$	−19.8571	−0.783088	−0.391544	+	0.920159i	$0.628059\pi$
$644$	0	0
$645$	10.5142	0.413997
$646$	6.16209	0.242444
$647$	−29.4130	−1.15634	−0.578172	−	0.815915i	$-0.696234\pi$
$647$	−29.4130	−1.15634	−0.578172	+	0.815915i	$0.696234\pi$
$648$	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	$-0.405408\pi$
$661$	15.0565	0.585628	0.292814	+	0.956169i	$0.405408\pi$
$662$	−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	$-0.552758\pi$
$677$	−8.58560	−0.329971	−0.164986	+	0.986296i	$0.552758\pi$
$678$	−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	$-0.632642\pi$
$691$	−21.2793	−0.809503	−0.404751	+	0.914427i	$0.632642\pi$
$692$	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	$-0.393009\pi$
$719$	17.6882	0.659658	0.329829	+	0.944041i	$0.393009\pi$
$720$	−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	$-0.346255\pi$
$727$	25.0455	0.928885	0.464442	+	0.885603i	$0.346255\pi$
$728$	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	$-0.405840\pi$
$733$	15.7850	0.583033	0.291517	+	0.956566i	$0.405840\pi$
$734$	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	$-0.423372\pi$
$761$	13.1540	0.476831	0.238416	+	0.971163i	$0.423372\pi$
$762$	−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	$-0.641295\pi$
$769$	−23.8184	−0.858915	−0.429457	+	0.903087i	$0.641295\pi$
$770$	0	0
$771$	8.85942	0.319064
$772$	14.2674	0.513496
$773$	−1.79587	−0.0645929	−0.0322965	−	0.999478i	$-0.510282\pi$
$773$	−1.79587	−0.0645929	−0.0322965	+	0.999478i	$0.510282\pi$
$774$	−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	$-0.586588\pi$
$787$	−15.0749	−0.537362	−0.268681	+	0.963229i	$0.586588\pi$
$788$	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	$-0.379108\pi$
$797$	20.9322	0.741456	0.370728	+	0.928742i	$0.379108\pi$
$798$	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	$-0.303197\pi$
$811$	33.0135	1.15926	0.579630	+	0.814880i	$0.303197\pi$
$812$	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	$-0.174014\pi$
$829$	49.1920	1.70851	0.854255	+	0.519854i	$0.174014\pi$
$830$	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	$-0.481196\pi$
$839$	3.42024	0.118080	0.0590399	+	0.998256i	$0.481196\pi$
$840$	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	$-0.347322\pi$
$853$	26.9555	0.922939	0.461469	+	0.887156i	$0.347322\pi$
$854$	0	0
$855$	−14.3426	−0.490505
$856$	−49.4248	−1.68931
$857$	21.1442	0.722273	0.361137	−	0.932513i	$-0.382389\pi$
$857$	21.1442	0.722273	0.361137	+	0.932513i	$0.382389\pi$
$858$	−18.5124	−0.632004
$859$	41.3331	1.41027	0.705133	−	0.709075i	$-0.250887\pi$
$859$	41.3331	1.41027	0.705133	+	0.709075i	$0.250887\pi$
$860$	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	$-0.833340\pi$
$881$	−51.4107	−1.73207	−0.866036	+	0.499982i	$0.833340\pi$
$882$	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	$-0.586728\pi$
$887$	−16.0293	−0.538212	−0.269106	+	0.963111i	$0.586728\pi$
$888$	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	$-0.707238\pi$
$929$	−36.9429	−1.21206	−0.606028	+	0.795443i	$0.707238\pi$
$930$	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	$-0.540661\pi$
$937$	−7.79921	−0.254789	−0.127395	+	0.991852i	$0.540661\pi$
$938$	0	0
$939$	−13.5739	−0.442967
$940$	−2.94016	−0.0958975
$941$	−23.3080	−0.759820	−0.379910	−	0.925023i	$-0.624045\pi$
$941$	−23.3080	−0.759820	−0.379910	+	0.925023i	$0.624045\pi$
$942$	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	$-0.578408\pi$
$971$	−15.1966	−0.487683	−0.243841	+	0.969815i	$0.578408\pi$
$972$	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	$-0.567857\pi$
$983$	−13.2666	−0.423139	−0.211570	+	0.977363i	$0.567857\pi$
$984$	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	$-0.449019\pi$
$997$	10.0710	0.318953	0.159477	+	0.987202i	$0.449019\pi$
$998$	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.bi.1.4		10
7.2	even	3		483.2.i.h.277.7	✓	20
7.4	even	3		483.2.i.h.415.7	yes	20
7.6	odd	2		3381.2.a.bj.1.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.i.h.277.7	✓	20	7.2	even	3
483.2.i.h.415.7	yes	20	7.4	even	3
3381.2.a.bi.1.4		10	1.1	even	1	trivial
3381.2.a.bj.1.4		10	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3381 = 3 \cdot 7^{2} \cdot 23 \)
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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