LMFDB - Embedded newform 3381.2.a.bd.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3381, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("3381.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$26.9974209234$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.7997584.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 7x^{4} + 5x^{3} + 12x^{2} - 4x - 2 $ x^6 - x^5 - 7x^4 + 5x^3 + 12x^2 - 4x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 483)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.27267$ of defining polynomial
Character	$\chi$	$=$	3381.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.27267 q^{2} +1.00000 q^{3} +3.16503 q^{4} -4.15120 q^{5} -2.27267 q^{6} -2.64772 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.27267 q^{2} +1.00000 q^{3} +3.16503 q^{4} -4.15120 q^{5} -2.27267 q^{6} -2.64772 q^{8} +1.00000 q^{9} +9.43432 q^{10} -3.18706 q^{11} +3.16503 q^{12} -0.175661 q^{13} -4.15120 q^{15} -0.312654 q^{16} +1.32687 q^{17} -2.27267 q^{18} -0.0504261 q^{19} -13.1387 q^{20} +7.24313 q^{22} -1.00000 q^{23} -2.64772 q^{24} +12.2325 q^{25} +0.399220 q^{26} +1.00000 q^{27} +1.10049 q^{29} +9.43432 q^{30} +8.71037 q^{31} +6.00601 q^{32} -3.18706 q^{33} -3.01553 q^{34} +3.16503 q^{36} +3.76233 q^{37} +0.114602 q^{38} -0.175661 q^{39} +10.9912 q^{40} -4.84719 q^{41} -10.5958 q^{43} -10.0871 q^{44} -4.15120 q^{45} +2.27267 q^{46} +8.95013 q^{47} -0.312654 q^{48} -27.8004 q^{50} +1.32687 q^{51} -0.555973 q^{52} -9.97629 q^{53} -2.27267 q^{54} +13.2301 q^{55} -0.0504261 q^{57} -2.50105 q^{58} +6.38897 q^{59} -13.1387 q^{60} +7.23261 q^{61} -19.7958 q^{62} -13.0244 q^{64} +0.729206 q^{65} +7.24313 q^{66} +6.02059 q^{67} +4.19957 q^{68} -1.00000 q^{69} +6.71519 q^{71} -2.64772 q^{72} +4.61372 q^{73} -8.55052 q^{74} +12.2325 q^{75} -0.159600 q^{76} +0.399220 q^{78} -15.4854 q^{79} +1.29789 q^{80} +1.00000 q^{81} +11.0161 q^{82} -7.21102 q^{83} -5.50809 q^{85} +24.0807 q^{86} +1.10049 q^{87} +8.43845 q^{88} +1.94147 q^{89} +9.43432 q^{90} -3.16503 q^{92} +8.71037 q^{93} -20.3407 q^{94} +0.209329 q^{95} +6.00601 q^{96} +12.7879 q^{97} -3.18706 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{2} + 6 q^{3} + 3 q^{4} - 3 q^{5} - q^{6} - 3 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q - q^2 + 6 * q^3 + 3 * q^4 - 3 * q^5 - q^6 - 3 * q^8 + 6 * q^9	$ 6 q - q^{2} + 6 q^{3} + 3 q^{4} - 3 q^{5} - q^{6} - 3 q^{8} + 6 q^{9} + 3 q^{10} - 14 q^{11} + 3 q^{12} - 3 q^{15} - 7 q^{16} - 15 q^{17} - q^{18} + q^{19} - 17 q^{20} - 6 q^{22} - 6 q^{23} - 3 q^{24} + 9 q^{25} + 15 q^{26} + 6 q^{27} - 6 q^{29} + 3 q^{30} + 11 q^{31} + 3 q^{32} - 14 q^{33} - 15 q^{34} + 3 q^{36} - 5 q^{37} - 14 q^{38} + 17 q^{40} - 18 q^{41} - 37 q^{43} - 10 q^{44} - 3 q^{45} + q^{46} - 3 q^{47} - 7 q^{48} - 30 q^{50} - 15 q^{51} + 7 q^{52} - 15 q^{53} - q^{54} + 2 q^{55} + q^{57} + 4 q^{58} + 2 q^{59} - 17 q^{60} + 12 q^{61} - 36 q^{62} - 23 q^{64} - 17 q^{65} - 6 q^{66} - 10 q^{67} + q^{68} - 6 q^{69} - 21 q^{71} - 3 q^{72} + 8 q^{73} - 16 q^{74} + 9 q^{75} - 18 q^{76} + 15 q^{78} - 17 q^{79} - 3 q^{80} + 6 q^{81} + 48 q^{82} - 12 q^{83} - 13 q^{85} + 22 q^{86} - 6 q^{87} - 2 q^{88} - 18 q^{89} + 3 q^{90} - 3 q^{92} + 11 q^{93} - 3 q^{94} - 16 q^{95} + 3 q^{96} + 2 q^{97} - 14 q^{99}+O(q^{100}) $ 6 * q - q^2 + 6 * q^3 + 3 * q^4 - 3 * q^5 - q^6 - 3 * q^8 + 6 * q^9 + 3 * q^10 - 14 * q^11 + 3 * q^12 - 3 * q^15 - 7 * q^16 - 15 * q^17 - q^18 + q^19 - 17 * q^20 - 6 * q^22 - 6 * q^23 - 3 * q^24 + 9 * q^25 + 15 * q^26 + 6 * q^27 - 6 * q^29 + 3 * q^30 + 11 * q^31 + 3 * q^32 - 14 * q^33 - 15 * q^34 + 3 * q^36 - 5 * q^37 - 14 * q^38 + 17 * q^40 - 18 * q^41 - 37 * q^43 - 10 * q^44 - 3 * q^45 + q^46 - 3 * q^47 - 7 * q^48 - 30 * q^50 - 15 * q^51 + 7 * q^52 - 15 * q^53 - q^54 + 2 * q^55 + q^57 + 4 * q^58 + 2 * q^59 - 17 * q^60 + 12 * q^61 - 36 * q^62 - 23 * q^64 - 17 * q^65 - 6 * q^66 - 10 * q^67 + q^68 - 6 * q^69 - 21 * q^71 - 3 * q^72 + 8 * q^73 - 16 * q^74 + 9 * q^75 - 18 * q^76 + 15 * q^78 - 17 * q^79 - 3 * q^80 + 6 * q^81 + 48 * q^82 - 12 * q^83 - 13 * q^85 + 22 * q^86 - 6 * q^87 - 2 * q^88 - 18 * q^89 + 3 * q^90 - 3 * q^92 + 11 * q^93 - 3 * q^94 - 16 * q^95 + 3 * q^96 + 2 * q^97 - 14 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.27267	−1.60702	−0.803510	−	0.595291i	$-0.797037\pi$
$2$	−2.27267	−1.60702	−0.803510	+	0.595291i	$0.797037\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.16503	1.58251
$5$	−4.15120	−1.85647	−0.928237	−	0.371988i	$-0.878676\pi$
$5$	−4.15120	−1.85647	−0.928237	+	0.371988i	$0.878676\pi$
$6$	−2.27267	−0.927814
$7$	0	0
$7$	0	0
$8$	−2.64772	−0.936112
$9$	1.00000	0.333333
$10$	9.43432	2.98339
$11$	−3.18706	−0.960934	−0.480467	−	0.877013i	$-0.659533\pi$
$11$	−3.18706	−0.960934	−0.480467	+	0.877013i	$0.659533\pi$
$12$	3.16503	0.913665
$13$	−0.175661	−0.0487197	−0.0243598	−	0.999703i	$-0.507755\pi$
$13$	−0.175661	−0.0487197	−0.0243598	+	0.999703i	$0.507755\pi$
$14$	0	0
$15$	−4.15120	−1.07184
$16$	−0.312654	−0.0781634
$17$	1.32687	0.321812	0.160906	−	0.986970i	$-0.448558\pi$
$17$	1.32687	0.321812	0.160906	+	0.986970i	$0.448558\pi$
$18$	−2.27267	−0.535673
$19$	−0.0504261	−0.0115685	−0.00578427	−	0.999983i	$-0.501841\pi$
$19$	−0.0504261	−0.0115685	−0.00578427	+	0.999983i	$0.501841\pi$
$20$	−13.1387	−2.93790
$21$	0	0
$22$	7.24313	1.54424
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−2.64772	−0.540464
$25$	12.2325	2.44650
$26$	0.399220	0.0782935
$27$	1.00000	0.192450
$28$	0	0
$29$	1.10049	0.204356	0.102178	−	0.994766i	$-0.467419\pi$
$29$	1.10049	0.204356	0.102178	+	0.994766i	$0.467419\pi$
$30$	9.43432	1.72246
$31$	8.71037	1.56443	0.782214	−	0.623010i	$-0.214090\pi$
$31$	8.71037	1.56443	0.782214	+	0.623010i	$0.214090\pi$
$32$	6.00601	1.06172
$33$	−3.18706	−0.554795
$34$	−3.01553	−0.517159
$35$	0	0
$36$	3.16503	0.527505
$37$	3.76233	0.618523	0.309261	−	0.950977i	$-0.399918\pi$
$37$	3.76233	0.618523	0.309261	+	0.950977i	$0.399918\pi$
$38$	0.114602	0.0185909
$39$	−0.175661	−0.0281283
$40$	10.9912	1.73787
$41$	−4.84719	−0.757004	−0.378502	−	0.925601i	$-0.623561\pi$
$41$	−4.84719	−0.757004	−0.378502	+	0.925601i	$0.623561\pi$
$42$	0	0
$43$	−10.5958	−1.61584	−0.807920	−	0.589293i	$-0.799406\pi$
$43$	−10.5958	−1.61584	−0.807920	+	0.589293i	$0.799406\pi$
$44$	−10.0871	−1.52069
$45$	−4.15120	−0.618825
$46$	2.27267	0.335087
$47$	8.95013	1.30551	0.652755	−	0.757569i	$-0.273613\pi$
$47$	8.95013	1.30551	0.652755	+	0.757569i	$0.273613\pi$
$48$	−0.312654	−0.0451277
$49$	0	0
$50$	−27.8004	−3.93157
$51$	1.32687	0.185798
$52$	−0.555973	−0.0770996
$53$	−9.97629	−1.37035	−0.685175	−	0.728379i	$-0.740274\pi$
$53$	−9.97629	−1.37035	−0.685175	+	0.728379i	$0.740274\pi$
$54$	−2.27267	−0.309271
$55$	13.2301	1.78395
$56$	0	0
$57$	−0.0504261	−0.00667910
$58$	−2.50105	−0.328404
$59$	6.38897	0.831774	0.415887	−	0.909416i	$-0.363471\pi$
$59$	6.38897	0.831774	0.415887	+	0.909416i	$0.363471\pi$
$60$	−13.1387	−1.69620
$61$	7.23261	0.926041	0.463021	−	0.886348i	$-0.346766\pi$
$61$	7.23261	0.926041	0.463021	+	0.886348i	$0.346766\pi$
$62$	−19.7958	−2.51407
$63$	0	0
$64$	−13.0244	−1.62805
$65$	0.729206	0.0904468
$66$	7.24313	0.891567
$67$	6.02059	0.735533	0.367766	−	0.929918i	$-0.380123\pi$
$67$	6.02059	0.735533	0.367766	+	0.929918i	$0.380123\pi$
$68$	4.19957	0.509272
$69$	−1.00000	−0.120386
$70$	0	0
$71$	6.71519	0.796947	0.398473	−	0.917180i	$-0.369540\pi$
$71$	6.71519	0.796947	0.398473	+	0.917180i	$0.369540\pi$
$72$	−2.64772	−0.312037
$73$	4.61372	0.539995	0.269998	−	0.962861i	$-0.412977\pi$
$73$	4.61372	0.539995	0.269998	+	0.962861i	$0.412977\pi$
$74$	−8.55052	−0.993978
$75$	12.2325	1.41249
$76$	−0.159600	−0.0183074
$77$	0	0
$78$	0.399220	0.0452028
$79$	−15.4854	−1.74225	−0.871124	−	0.491064i	$-0.836608\pi$
$79$	−15.4854	−1.74225	−0.871124	+	0.491064i	$0.836608\pi$
$80$	1.29789	0.145108
$81$	1.00000	0.111111
$82$	11.0161	1.21652
$83$	−7.21102	−0.791512	−0.395756	−	0.918356i	$-0.629517\pi$
$83$	−7.21102	−0.791512	−0.395756	+	0.918356i	$0.629517\pi$
$84$	0	0
$85$	−5.50809	−0.597436
$86$	24.0807	2.59669
$87$	1.10049	0.117985
$88$	8.43845	0.899541
$89$	1.94147	0.205795	0.102898	−	0.994692i	$-0.467189\pi$
$89$	1.94147	0.205795	0.102898	+	0.994692i	$0.467189\pi$
$90$	9.43432	0.994464
$91$	0	0
$92$	−3.16503	−0.329977
$93$	8.71037	0.903223
$94$	−20.3407	−2.09798
$95$	0.209329	0.0214767
$96$	6.00601	0.612985
$97$	12.7879	1.29841	0.649207	−	0.760612i	$-0.275101\pi$
$97$	12.7879	1.29841	0.649207	+	0.760612i	$0.275101\pi$
$98$	0	0
$99$	−3.18706	−0.320311
$100$	38.7162	3.87162
$101$	1.64583	0.163766	0.0818831	−	0.996642i	$-0.473907\pi$
$101$	1.64583	0.163766	0.0818831	+	0.996642i	$0.473907\pi$
$102$	−3.01553	−0.298582
$103$	−8.99275	−0.886082	−0.443041	−	0.896501i	$-0.646100\pi$
$103$	−8.99275	−0.886082	−0.443041	+	0.896501i	$0.646100\pi$
$104$	0.465103	0.0456071
$105$	0	0
$106$	22.6728	2.20218
$107$	−18.9831	−1.83516	−0.917581	−	0.397549i	$-0.869861\pi$
$107$	−18.9831	−1.83516	−0.917581	+	0.397549i	$0.869861\pi$
$108$	3.16503	0.304555
$109$	−11.7183	−1.12241	−0.561203	−	0.827678i	$-0.689661\pi$
$109$	−11.7183	−1.12241	−0.561203	+	0.827678i	$0.689661\pi$
$110$	−30.0677	−2.86684
$111$	3.76233	0.357104
$112$	0	0
$113$	16.6028	1.56186	0.780931	−	0.624617i	$-0.214745\pi$
$113$	16.6028	1.56186	0.780931	+	0.624617i	$0.214745\pi$
$114$	0.114602	0.0107335
$115$	4.15120	0.387102
$116$	3.48308	0.323396
$117$	−0.175661	−0.0162399
$118$	−14.5200	−1.33668
$119$	0	0
$120$	10.9912	1.00336
$121$	−0.842668	−0.0766062
$122$	−16.4373	−1.48817
$123$	−4.84719	−0.437056
$124$	27.5686	2.47573
$125$	−30.0236	−2.68539
$126$	0	0
$127$	17.8466	1.58363	0.791815	−	0.610761i	$-0.209136\pi$
$127$	17.8466	1.58363	0.791815	+	0.610761i	$0.209136\pi$
$128$	17.5881	1.55458
$129$	−10.5958	−0.932905
$130$	−1.65724	−0.145350
$131$	−21.5620	−1.88388	−0.941940	−	0.335781i	$-0.891000\pi$
$131$	−21.5620	−1.88388	−0.941940	+	0.335781i	$0.891000\pi$
$132$	−10.0871	−0.877971
$133$	0	0
$134$	−13.6828	−1.18202
$135$	−4.15120	−0.357279
$136$	−3.51317	−0.301252
$137$	0.565532	0.0483166	0.0241583	−	0.999708i	$-0.492309\pi$
$137$	0.565532	0.0483166	0.0241583	+	0.999708i	$0.492309\pi$
$138$	2.27267	0.193463
$139$	19.5670	1.65965	0.829825	−	0.558024i	$-0.188440\pi$
$139$	19.5670	1.65965	0.829825	+	0.558024i	$0.188440\pi$
$140$	0	0
$141$	8.95013	0.753737
$142$	−15.2614	−1.28071
$143$	0.559842	0.0468164
$144$	−0.312654	−0.0260545
$145$	−4.56836	−0.379382
$146$	−10.4855	−0.867783
$147$	0	0
$148$	11.9079	0.978821
$149$	7.52726	0.616657	0.308329	−	0.951280i	$-0.400230\pi$
$149$	7.52726	0.616657	0.308329	+	0.951280i	$0.400230\pi$
$150$	−27.8004	−2.26989
$151$	−21.3621	−1.73843	−0.869213	−	0.494437i	$-0.835374\pi$
$151$	−21.3621	−1.73843	−0.869213	+	0.494437i	$0.835374\pi$
$152$	0.133514	0.0108294
$153$	1.32687	0.107271
$154$	0	0
$155$	−36.1585	−2.90432
$156$	−0.555973	−0.0445135
$157$	−11.7594	−0.938503	−0.469251	−	0.883065i	$-0.655476\pi$
$157$	−11.7594	−0.938503	−0.469251	+	0.883065i	$0.655476\pi$
$158$	35.1933	2.79983
$159$	−9.97629	−0.791171
$160$	−24.9322	−1.97106
$161$	0	0
$162$	−2.27267	−0.178558
$163$	−15.3219	−1.20010	−0.600051	−	0.799962i	$-0.704853\pi$
$163$	−15.3219	−1.20010	−0.600051	+	0.799962i	$0.704853\pi$
$164$	−15.3415	−1.19797
$165$	13.2301	1.02996
$166$	16.3883	1.27198
$167$	8.02472	0.620972	0.310486	−	0.950578i	$-0.399508\pi$
$167$	8.02472	0.620972	0.310486	+	0.950578i	$0.399508\pi$
$168$	0	0
$169$	−12.9691	−0.997626
$170$	12.5181	0.960092
$171$	−0.0504261	−0.00385618
$172$	−33.5359	−2.55709
$173$	−15.5225	−1.18016	−0.590078	−	0.807346i	$-0.700903\pi$
$173$	−15.5225	−1.18016	−0.590078	+	0.807346i	$0.700903\pi$
$174$	−2.50105	−0.189604
$175$	0	0
$176$	0.996445	0.0751099
$177$	6.38897	0.480225
$178$	−4.41232	−0.330717
$179$	8.28280	0.619086	0.309543	−	0.950885i	$-0.399824\pi$
$179$	8.28280	0.619086	0.309543	+	0.950885i	$0.399824\pi$
$180$	−13.1387	−0.979299
$181$	5.71189	0.424561	0.212281	−	0.977209i	$-0.431911\pi$
$181$	5.71189	0.424561	0.212281	+	0.977209i	$0.431911\pi$
$182$	0	0
$183$	7.23261	0.534650
$184$	2.64772	0.195193
$185$	−15.6182	−1.14827
$186$	−19.7958	−1.45150
$187$	−4.22880	−0.309240
$188$	28.3274	2.06599
$189$	0	0
$190$	−0.475736	−0.0345135
$191$	−1.55152	−0.112264	−0.0561322	−	0.998423i	$-0.517877\pi$
$191$	−1.55152	−0.112264	−0.0561322	+	0.998423i	$0.517877\pi$
$192$	−13.0244	−0.939952
$193$	7.32290	0.527114	0.263557	−	0.964644i	$-0.415104\pi$
$193$	7.32290	0.527114	0.263557	+	0.964644i	$0.415104\pi$
$194$	−29.0626	−2.08658
$195$	0.729206	0.0522195
$196$	0	0
$197$	−6.84137	−0.487427	−0.243714	−	0.969847i	$-0.578366\pi$
$197$	−6.84137	−0.487427	−0.243714	+	0.969847i	$0.578366\pi$
$198$	7.24313	0.514747
$199$	−7.64366	−0.541845	−0.270922	−	0.962601i	$-0.587329\pi$
$199$	−7.64366	−0.541845	−0.270922	+	0.962601i	$0.587329\pi$
$200$	−32.3883	−2.29020
$201$	6.02059	0.424660
$202$	−3.74043	−0.263176
$203$	0	0
$204$	4.19957	0.294028
$205$	20.1217	1.40536
$206$	20.4376	1.42395
$207$	−1.00000	−0.0695048
$208$	0.0549212	0.00380810
$209$	0.160711	0.0111166
$210$	0	0
$211$	−4.69603	−0.323288	−0.161644	−	0.986849i	$-0.551680\pi$
$211$	−4.69603	−0.323288	−0.161644	+	0.986849i	$0.551680\pi$
$212$	−31.5752	−2.16860
$213$	6.71519	0.460117
$214$	43.1422	2.94914
$215$	43.9852	2.99976
$216$	−2.64772	−0.180155
$217$	0	0
$218$	26.6318	1.80373
$219$	4.61372	0.311766
$220$	41.8737	2.82313
$221$	−0.233079	−0.0156786
$222$	−8.55052	−0.573874
$223$	−24.2891	−1.62652	−0.813260	−	0.581900i	$-0.802310\pi$
$223$	−24.2891	−1.62652	−0.813260	+	0.581900i	$0.802310\pi$
$224$	0	0
$225$	12.2325	0.815500
$226$	−37.7327	−2.50994
$227$	−4.33303	−0.287593	−0.143797	−	0.989607i	$-0.545931\pi$
$227$	−4.33303	−0.287593	−0.143797	+	0.989607i	$0.545931\pi$
$228$	−0.159600	−0.0105698
$229$	12.4437	0.822303	0.411152	−	0.911567i	$-0.365127\pi$
$229$	12.4437	0.822303	0.411152	+	0.911567i	$0.365127\pi$
$230$	−9.43432	−0.622080
$231$	0	0
$232$	−2.91380	−0.191300
$233$	3.24764	0.212760	0.106380	−	0.994326i	$-0.466074\pi$
$233$	3.24764	0.212760	0.106380	+	0.994326i	$0.466074\pi$
$234$	0.399220	0.0260978
$235$	−37.1538	−2.42365
$236$	20.2213	1.31629
$237$	−15.4854	−1.00589
$238$	0	0
$239$	26.4823	1.71300	0.856500	−	0.516147i	$-0.172634\pi$
$239$	26.4823	1.71300	0.856500	+	0.516147i	$0.172634\pi$
$240$	1.29789	0.0837784
$241$	−2.56149	−0.165000	−0.0825001	−	0.996591i	$-0.526290\pi$
$241$	−2.56149	−0.165000	−0.0825001	+	0.996591i	$0.526290\pi$
$242$	1.91511	0.123108
$243$	1.00000	0.0641500
$244$	22.8914	1.46547
$245$	0	0
$246$	11.0161	0.702358
$247$	0.00885791	0.000563616 0
$248$	−23.0626	−1.46448
$249$	−7.21102	−0.456980
$250$	68.2336	4.31547
$251$	−14.6123	−0.922317	−0.461159	−	0.887318i	$-0.652566\pi$
$251$	−14.6123	−0.922317	−0.461159	+	0.887318i	$0.652566\pi$
$252$	0	0
$253$	3.18706	0.200369
$254$	−40.5594	−2.54493
$255$	−5.50809	−0.344930
$256$	−13.9231	−0.870196
$257$	5.12857	0.319911	0.159956	−	0.987124i	$-0.448865\pi$
$257$	5.12857	0.319911	0.159956	+	0.987124i	$0.448865\pi$
$258$	24.0807	1.49920
$259$	0	0
$260$	2.30796	0.143133
$261$	1.10049	0.0681187
$262$	49.0033	3.02743
$263$	3.24813	0.200288	0.100144	−	0.994973i	$-0.468070\pi$
$263$	3.24813	0.200288	0.100144	+	0.994973i	$0.468070\pi$
$264$	8.43845	0.519351
$265$	41.4136	2.54402
$266$	0	0
$267$	1.94147	0.118816
$268$	19.0553	1.16399
$269$	4.83101	0.294552	0.147276	−	0.989095i	$-0.452950\pi$
$269$	4.83101	0.294552	0.147276	+	0.989095i	$0.452950\pi$
$270$	9.43432	0.574154
$271$	12.1239	0.736473	0.368236	−	0.929732i	$-0.379962\pi$
$271$	12.1239	0.736473	0.368236	+	0.929732i	$0.379962\pi$
$272$	−0.414849	−0.0251539
$273$	0	0
$274$	−1.28527	−0.0776458
$275$	−38.9857	−2.35092
$276$	−3.16503	−0.190512
$277$	−21.9014	−1.31593	−0.657964	−	0.753050i	$-0.728582\pi$
$277$	−21.9014	−1.31593	−0.657964	+	0.753050i	$0.728582\pi$
$278$	−44.4693	−2.66709
$279$	8.71037	0.521476
$280$	0	0
$281$	−24.2364	−1.44582	−0.722912	−	0.690940i	$-0.757197\pi$
$281$	−24.2364	−1.44582	−0.722912	+	0.690940i	$0.757197\pi$
$282$	−20.3407	−1.21127
$283$	−5.14581	−0.305887	−0.152943	−	0.988235i	$-0.548875\pi$
$283$	−5.14581	−0.305887	−0.152943	+	0.988235i	$0.548875\pi$
$284$	21.2538	1.26118
$285$	0.209329	0.0123996
$286$	−1.27234	−0.0752349
$287$	0	0
$288$	6.00601	0.353907
$289$	−15.2394	−0.896437
$290$	10.3824	0.609674
$291$	12.7879	0.749639
$292$	14.6026	0.854550
$293$	24.5374	1.43349	0.716745	−	0.697335i	$-0.245631\pi$
$293$	24.5374	1.43349	0.716745	+	0.697335i	$0.245631\pi$
$294$	0	0
$295$	−26.5219	−1.54417
$296$	−9.96160	−0.579006
$297$	−3.18706	−0.184932
$298$	−17.1070	−0.990981
$299$	0.175661	0.0101588
$300$	38.7162	2.23528
$301$	0	0
$302$	48.5491	2.79369
$303$	1.64583	0.0945505
$304$	0.0157659	0.000904237 0
$305$	−30.0241	−1.71917
$306$	−3.01553	−0.172386
$307$	−7.16659	−0.409019	−0.204509	−	0.978865i	$-0.565560\pi$
$307$	−7.16659	−0.409019	−0.204509	+	0.978865i	$0.565560\pi$
$308$	0	0
$309$	−8.99275	−0.511580
$310$	82.1764	4.66730
$311$	−5.87280	−0.333016	−0.166508	−	0.986040i	$-0.553249\pi$
$311$	−5.87280	−0.333016	−0.166508	+	0.986040i	$0.553249\pi$
$312$	0.465103	0.0263312
$313$	3.80364	0.214994	0.107497	−	0.994205i	$-0.465716\pi$
$313$	3.80364	0.214994	0.107497	+	0.994205i	$0.465716\pi$
$314$	26.7252	1.50819
$315$	0	0
$316$	−49.0118	−2.75713
$317$	9.80284	0.550582	0.275291	−	0.961361i	$-0.411226\pi$
$317$	9.80284	0.550582	0.275291	+	0.961361i	$0.411226\pi$
$318$	22.6728	1.27143
$319$	−3.50733	−0.196373
$320$	54.0668	3.02243
$321$	−18.9831	−1.05953
$322$	0	0
$323$	−0.0669087	−0.00372290
$324$	3.16503	0.175835
$325$	−2.14878	−0.119193
$326$	34.8216	1.92859
$327$	−11.7183	−0.648022
$328$	12.8340	0.708640
$329$	0	0
$330$	−30.0677	−1.65517
$331$	−11.1896	−0.615036	−0.307518	−	0.951542i	$-0.599499\pi$
$331$	−11.1896	−0.615036	−0.307518	+	0.951542i	$0.599499\pi$
$332$	−22.8231	−1.25258
$333$	3.76233	0.206174
$334$	−18.2375	−0.997914
$335$	−24.9927	−1.36550
$336$	0	0
$337$	−31.7991	−1.73221	−0.866103	−	0.499865i	$-0.833383\pi$
$337$	−31.7991	−1.73221	−0.866103	+	0.499865i	$0.833383\pi$
$338$	29.4746	1.60321
$339$	16.6028	0.901742
$340$	−17.4333	−0.945451
$341$	−27.7604	−1.50331
$342$	0.114602	0.00619696
$343$	0	0
$344$	28.0547	1.51261
$345$	4.15120	0.223493
$346$	35.2776	1.89653
$347$	−1.37388	−0.0737539	−0.0368770	−	0.999320i	$-0.511741\pi$
$347$	−1.37388	−0.0737539	−0.0368770	+	0.999320i	$0.511741\pi$
$348$	3.48308	0.186713
$349$	6.43146	0.344268	0.172134	−	0.985074i	$-0.444934\pi$
$349$	6.43146	0.344268	0.172134	+	0.985074i	$0.444934\pi$
$350$	0	0
$351$	−0.175661	−0.00937611
$352$	−19.1415	−1.02024
$353$	−25.7366	−1.36982	−0.684910	−	0.728628i	$-0.740158\pi$
$353$	−25.7366	−1.36982	−0.684910	+	0.728628i	$0.740158\pi$
$354$	−14.5200	−0.771731
$355$	−27.8761	−1.47951
$356$	6.14480	0.325674
$357$	0	0
$358$	−18.8241	−0.994883
$359$	−23.9634	−1.26474	−0.632369	−	0.774667i	$-0.717918\pi$
$359$	−23.9634	−1.26474	−0.632369	+	0.774667i	$0.717918\pi$
$360$	10.9912	0.579289
$361$	−18.9975	−0.999866
$362$	−12.9812	−0.682278
$363$	−0.842668	−0.0442286
$364$	0	0
$365$	−19.1525	−1.00249
$366$	−16.4373	−0.859194
$367$	−25.6783	−1.34040	−0.670199	−	0.742181i	$-0.733791\pi$
$367$	−25.6783	−1.34040	−0.670199	+	0.742181i	$0.733791\pi$
$368$	0.312654	0.0162982
$369$	−4.84719	−0.252335
$370$	35.4950	1.84530
$371$	0	0
$372$	27.5686	1.42936
$373$	5.80092	0.300360	0.150180	−	0.988659i	$-0.452015\pi$
$373$	5.80092	0.300360	0.150180	+	0.988659i	$0.452015\pi$
$374$	9.61066	0.496955
$375$	−30.0236	−1.55041
$376$	−23.6975	−1.22210
$377$	−0.193314	−0.00995616
$378$	0	0
$379$	21.0504	1.08129	0.540643	−	0.841252i	$-0.318181\pi$
$379$	21.0504	1.08129	0.540643	+	0.841252i	$0.318181\pi$
$380$	0.662532	0.0339872
$381$	17.8466	0.914309
$382$	3.52610	0.180411
$383$	4.82289	0.246438	0.123219	−	0.992379i	$-0.460678\pi$
$383$	4.82289	0.246438	0.123219	+	0.992379i	$0.460678\pi$
$384$	17.5881	0.897537
$385$	0	0
$386$	−16.6425	−0.847083
$387$	−10.5958	−0.538613
$388$	40.4740	2.05476
$389$	−19.5414	−0.990790	−0.495395	−	0.868668i	$-0.664977\pi$
$389$	−19.5414	−0.990790	−0.495395	+	0.868668i	$0.664977\pi$
$390$	−1.65724	−0.0839178
$391$	−1.32687	−0.0671025
$392$	0	0
$393$	−21.5620	−1.08766
$394$	15.5482	0.783305
$395$	64.2832	3.23444
$396$	−10.0871	−0.506897
$397$	−36.5849	−1.83614	−0.918072	−	0.396413i	$-0.870255\pi$
$397$	−36.5849	−1.83614	−0.918072	+	0.396413i	$0.870255\pi$
$398$	17.3715	0.870756
$399$	0	0
$400$	−3.82454	−0.191227
$401$	−4.67488	−0.233452	−0.116726	−	0.993164i	$-0.537240\pi$
$401$	−4.67488	−0.233452	−0.116726	+	0.993164i	$0.537240\pi$
$402$	−13.6828	−0.682437
$403$	−1.53007	−0.0762184
$404$	5.20910	0.259162
$405$	−4.15120	−0.206275
$406$	0	0
$407$	−11.9907	−0.594359
$408$	−3.51317	−0.173928
$409$	−11.0059	−0.544208	−0.272104	−	0.962268i	$-0.587720\pi$
$409$	−11.0059	−0.544208	−0.272104	+	0.962268i	$0.587720\pi$
$410$	−45.7299	−2.25844
$411$	0.565532	0.0278956
$412$	−28.4623	−1.40224
$413$	0	0
$414$	2.27267	0.111696
$415$	29.9344	1.46942
$416$	−1.05502	−0.0517267
$417$	19.5670	0.958199
$418$	−0.365243	−0.0178646
$419$	−18.8771	−0.922206	−0.461103	−	0.887347i	$-0.652546\pi$
$419$	−18.8771	−0.922206	−0.461103	+	0.887347i	$0.652546\pi$
$420$	0	0
$421$	−10.1341	−0.493905	−0.246952	−	0.969028i	$-0.579429\pi$
$421$	−10.1341	−0.493905	−0.246952	+	0.969028i	$0.579429\pi$
$422$	10.6725	0.519531
$423$	8.95013	0.435170
$424$	26.4145	1.28280
$425$	16.2309	0.787313
$426$	−15.2614	−0.739418
$427$	0	0
$428$	−60.0819	−2.90417
$429$	0.559842	0.0270295
$430$	−99.9638	−4.82068
$431$	7.87183	0.379173	0.189586	−	0.981864i	$-0.439285\pi$
$431$	7.87183	0.379173	0.189586	+	0.981864i	$0.439285\pi$
$432$	−0.312654	−0.0150426
$433$	20.5867	0.989335	0.494668	−	0.869082i	$-0.335290\pi$
$433$	20.5867	0.989335	0.494668	+	0.869082i	$0.335290\pi$
$434$	0	0
$435$	−4.56836	−0.219036
$436$	−37.0886	−1.77622
$437$	0.0504261	0.00241221
$438$	−10.4855	−0.501015
$439$	−33.6678	−1.60687	−0.803437	−	0.595389i	$-0.796998\pi$
$439$	−33.6678	−1.60687	−0.803437	+	0.595389i	$0.796998\pi$
$440$	−35.0297	−1.66998
$441$	0	0
$442$	0.529711	0.0251958
$443$	7.33528	0.348510	0.174255	−	0.984701i	$-0.444248\pi$
$443$	7.33528	0.348510	0.174255	+	0.984701i	$0.444248\pi$
$444$	11.9079	0.565122
$445$	−8.05943	−0.382054
$446$	55.2012	2.61385
$447$	7.52726	0.356027
$448$	0	0
$449$	−21.1508	−0.998170	−0.499085	−	0.866553i	$-0.666330\pi$
$449$	−21.1508	−0.998170	−0.499085	+	0.866553i	$0.666330\pi$
$450$	−27.8004	−1.31052
$451$	15.4483	0.727431
$452$	52.5484	2.47167
$453$	−21.3621	−1.00368
$454$	9.84755	0.462168
$455$	0	0
$456$	0.133514	0.00625239
$457$	8.96782	0.419497	0.209748	−	0.977755i	$-0.432736\pi$
$457$	8.96782	0.419497	0.209748	+	0.977755i	$0.432736\pi$
$458$	−28.2804	−1.32146
$459$	1.32687	0.0619328
$460$	13.1387	0.612594
$461$	−6.30195	−0.293511	−0.146756	−	0.989173i	$-0.546883\pi$
$461$	−6.30195	−0.293511	−0.146756	+	0.989173i	$0.546883\pi$
$462$	0	0
$463$	−15.1092	−0.702183	−0.351092	−	0.936341i	$-0.614189\pi$
$463$	−15.1092	−0.702183	−0.351092	+	0.936341i	$0.614189\pi$
$464$	−0.344072	−0.0159732
$465$	−36.1585	−1.67681
$466$	−7.38081	−0.341909
$467$	18.9605	0.877387	0.438694	−	0.898637i	$-0.355441\pi$
$467$	18.9605	0.877387	0.438694	+	0.898637i	$0.355441\pi$
$468$	−0.555973	−0.0256999
$469$	0	0
$470$	84.4384	3.89485
$471$	−11.7594	−0.541845
$472$	−16.9162	−0.778633
$473$	33.7693	1.55271
$474$	35.1933	1.61648
$475$	−0.616837	−0.0283024
$476$	0	0
$477$	−9.97629	−0.456783
$478$	−60.1856	−2.75283
$479$	28.5772	1.30572	0.652862	−	0.757477i	$-0.273568\pi$
$479$	28.5772	1.30572	0.652862	+	0.757477i	$0.273568\pi$
$480$	−24.9322	−1.13799
$481$	−0.660895	−0.0301342
$482$	5.82143	0.265159
$483$	0	0
$484$	−2.66707	−0.121230
$485$	−53.0851	−2.41047
$486$	−2.27267	−0.103090
$487$	24.9927	1.13253	0.566264	−	0.824224i	$-0.308388\pi$
$487$	24.9927	1.13253	0.566264	+	0.824224i	$0.308388\pi$
$488$	−19.1500	−0.866878
$489$	−15.3219	−0.692879
$490$	0	0
$491$	−22.0515	−0.995170	−0.497585	−	0.867415i	$-0.665780\pi$
$491$	−22.0515	−0.995170	−0.497585	+	0.867415i	$0.665780\pi$
$492$	−15.3415	−0.691648
$493$	1.46020	0.0657642
$494$	−0.0201311	−0.000905742 0
$495$	13.2301	0.594650
$496$	−2.72333	−0.122281
$497$	0	0
$498$	16.3883	0.734376
$499$	−39.4251	−1.76491	−0.882455	−	0.470397i	$-0.844111\pi$
$499$	−39.4251	−1.76491	−0.882455	+	0.470397i	$0.844111\pi$
$500$	−95.0254	−4.24967
$501$	8.02472	0.358518
$502$	33.2088	1.48218
$503$	31.3079	1.39595	0.697975	−	0.716122i	$-0.254085\pi$
$503$	31.3079	1.39595	0.697975	+	0.716122i	$0.254085\pi$
$504$	0	0
$505$	−6.83218	−0.304028
$506$	−7.24313	−0.321996
$507$	−12.9691	−0.575980
$508$	56.4850	2.50612
$509$	−15.4660	−0.685519	−0.342760	−	0.939423i	$-0.611362\pi$
$509$	−15.4660	−0.685519	−0.342760	+	0.939423i	$0.611362\pi$
$510$	12.5181	0.554309
$511$	0	0
$512$	−3.53344	−0.156158
$513$	−0.0504261	−0.00222637
$514$	−11.6555	−0.514104
$515$	37.3308	1.64499
$516$	−33.5359	−1.47634
$517$	−28.5246	−1.25451
$518$	0	0
$519$	−15.5225	−0.681363
$520$	−1.93074	−0.0846684
$521$	6.81604	0.298616	0.149308	−	0.988791i	$-0.452295\pi$
$521$	6.81604	0.298616	0.149308	+	0.988791i	$0.452295\pi$
$522$	−2.50105	−0.109468
$523$	8.53560	0.373236	0.186618	−	0.982433i	$-0.440247\pi$
$523$	8.53560	0.373236	0.186618	+	0.982433i	$0.440247\pi$
$524$	−68.2443	−2.98127
$525$	0	0
$526$	−7.38192	−0.321867
$527$	11.5575	0.503452
$528$	0.996445	0.0433647
$529$	1.00000	0.0434783
$530$	−94.1195	−4.08829
$531$	6.38897	0.277258
$532$	0	0
$533$	0.851464	0.0368810
$534$	−4.41232	−0.190940
$535$	78.8026	3.40693
$536$	−15.9409	−0.688541
$537$	8.28280	0.357429
$538$	−10.9793	−0.473350
$539$	0	0
$540$	−13.1387	−0.565399
$541$	1.23462	0.0530806	0.0265403	−	0.999648i	$-0.491551\pi$
$541$	1.23462	0.0530806	0.0265403	+	0.999648i	$0.491551\pi$
$542$	−27.5536	−1.18353
$543$	5.71189	0.245121
$544$	7.96916	0.341675
$545$	48.6449	2.08372
$546$	0	0
$547$	26.1193	1.11678	0.558390	−	0.829578i	$-0.311419\pi$
$547$	26.1193	1.11678	0.558390	+	0.829578i	$0.311419\pi$
$548$	1.78992	0.0764618
$549$	7.23261	0.308680
$550$	88.6015	3.77798
$551$	−0.0554935	−0.00236410
$552$	2.64772	0.112695
$553$	0	0
$554$	49.7746	2.11472
$555$	−15.6182	−0.662955
$556$	61.9301	2.62642
$557$	−25.7744	−1.09210	−0.546049	−	0.837753i	$-0.683869\pi$
$557$	−25.7744	−1.09210	−0.546049	+	0.837753i	$0.683869\pi$
$558$	−19.7958	−0.838023
$559$	1.86127	0.0787232
$560$	0	0
$561$	−4.22880	−0.178540
$562$	55.0814	2.32347
$563$	−11.1504	−0.469932	−0.234966	−	0.972004i	$-0.575498\pi$
$563$	−11.1504	−0.469932	−0.234966	+	0.972004i	$0.575498\pi$
$564$	28.3274	1.19280
$565$	−68.9217	−2.89956
$566$	11.6947	0.491567
$567$	0	0
$568$	−17.7800	−0.746031
$569$	−9.49752	−0.398157	−0.199078	−	0.979984i	$-0.563795\pi$
$569$	−9.49752	−0.398157	−0.199078	+	0.979984i	$0.563795\pi$
$570$	−0.475736	−0.0199264
$571$	−25.5625	−1.06976	−0.534878	−	0.844929i	$-0.679643\pi$
$571$	−25.5625	−1.06976	−0.534878	+	0.844929i	$0.679643\pi$
$572$	1.77192	0.0740876
$573$	−1.55152	−0.0648159
$574$	0	0
$575$	−12.2325	−0.510130
$576$	−13.0244	−0.542682
$577$	−15.3566	−0.639302	−0.319651	−	0.947535i	$-0.603566\pi$
$577$	−15.3566	−0.639302	−0.319651	+	0.947535i	$0.603566\pi$
$578$	34.6342	1.44059
$579$	7.32290	0.304330
$580$	−14.4590	−0.600377
$581$	0	0
$582$	−29.0626	−1.20469
$583$	31.7950	1.31681
$584$	−12.2159	−0.505496
$585$	0.729206	0.0301489
$586$	−55.7654	−2.30365
$587$	2.88985	0.119277	0.0596384	−	0.998220i	$-0.481005\pi$
$587$	2.88985	0.119277	0.0596384	+	0.998220i	$0.481005\pi$
$588$	0	0
$589$	−0.439230	−0.0180982
$590$	60.2756	2.48151
$591$	−6.84137	−0.281416
$592$	−1.17631	−0.0483458
$593$	−20.9778	−0.861454	−0.430727	−	0.902482i	$-0.641743\pi$
$593$	−20.9778	−0.861454	−0.430727	+	0.902482i	$0.641743\pi$
$594$	7.24313	0.297189
$595$	0	0
$596$	23.8240	0.975869
$597$	−7.64366	−0.312834
$598$	−0.399220	−0.0163253
$599$	8.10812	0.331289	0.165644	−	0.986186i	$-0.447030\pi$
$599$	8.10812	0.331289	0.165644	+	0.986186i	$0.447030\pi$
$600$	−32.3883	−1.32225
$601$	−31.3113	−1.27721	−0.638607	−	0.769533i	$-0.720489\pi$
$601$	−31.3113	−1.27721	−0.638607	+	0.769533i	$0.720489\pi$
$602$	0	0
$603$	6.02059	0.245178
$604$	−67.6118	−2.75108
$605$	3.49809	0.142217
$606$	−3.74043	−0.151945
$607$	25.6566	1.04137	0.520685	−	0.853749i	$-0.325677\pi$
$607$	25.6566	1.04137	0.520685	+	0.853749i	$0.325677\pi$
$608$	−0.302860	−0.0122826
$609$	0	0
$610$	68.2348	2.76274
$611$	−1.57219	−0.0636041
$612$	4.19957	0.169757
$613$	29.3962	1.18730	0.593651	−	0.804722i	$-0.297686\pi$
$613$	29.3962	1.18730	0.593651	+	0.804722i	$0.297686\pi$
$614$	16.2873	0.657301
$615$	20.1217	0.811384
$616$	0	0
$617$	36.1711	1.45619	0.728097	−	0.685474i	$-0.240405\pi$
$617$	36.1711	1.45619	0.728097	+	0.685474i	$0.240405\pi$
$618$	20.4376	0.822119
$619$	22.9578	0.922752	0.461376	−	0.887205i	$-0.347356\pi$
$619$	22.9578	0.922752	0.461376	+	0.887205i	$0.347356\pi$
$620$	−114.443	−4.59613
$621$	−1.00000	−0.0401286
$622$	13.3469	0.535163
$623$	0	0
$624$	0.0549212	0.00219861
$625$	63.4715	2.53886
$626$	−8.64441	−0.345500
$627$	0.160711	0.00641817
$628$	−37.2188	−1.48519
$629$	4.99210	0.199048
$630$	0	0
$631$	−13.3609	−0.531890	−0.265945	−	0.963988i	$-0.585684\pi$
$631$	−13.3609	−0.531890	−0.265945	+	0.963988i	$0.585684\pi$
$632$	41.0012	1.63094
$633$	−4.69603	−0.186651
$634$	−22.2786	−0.884797
$635$	−74.0849	−2.93997
$636$	−31.5752	−1.25204
$637$	0	0
$638$	7.97099	0.315575
$639$	6.71519	0.265649
$640$	−73.0116	−2.88604
$641$	−35.0959	−1.38620	−0.693102	−	0.720840i	$-0.743756\pi$
$641$	−35.0959	−1.38620	−0.693102	+	0.720840i	$0.743756\pi$
$642$	43.1422	1.70269
$643$	−15.1822	−0.598726	−0.299363	−	0.954139i	$-0.596774\pi$
$643$	−15.1822	−0.598726	−0.299363	+	0.954139i	$0.596774\pi$
$644$	0	0
$645$	43.9852	1.73191
$646$	0.152061	0.00598277
$647$	−20.0656	−0.788861	−0.394430	−	0.918926i	$-0.629058\pi$
$647$	−20.0656	−0.788861	−0.394430	+	0.918926i	$0.629058\pi$
$648$	−2.64772	−0.104012
$649$	−20.3620	−0.799279
$650$	4.88346	0.191545
$651$	0	0
$652$	−48.4942	−1.89918
$653$	−4.13765	−0.161919	−0.0809594	−	0.996717i	$-0.525798\pi$
$653$	−4.13765	−0.161919	−0.0809594	+	0.996717i	$0.525798\pi$
$654$	26.6318	1.04138
$655$	89.5083	3.49738
$656$	1.51549	0.0591700
$657$	4.61372	0.179998
$658$	0	0
$659$	14.7450	0.574383	0.287192	−	0.957873i	$-0.407278\pi$
$659$	14.7450	0.574383	0.287192	+	0.957873i	$0.407278\pi$
$660$	41.8737	1.62993
$661$	−25.9992	−1.01125	−0.505625	−	0.862753i	$-0.668738\pi$
$661$	−25.9992	−1.01125	−0.505625	+	0.862753i	$0.668738\pi$
$662$	25.4303	0.988376
$663$	−0.233079	−0.00905203
$664$	19.0928	0.740944
$665$	0	0
$666$	−8.55052	−0.331326
$667$	−1.10049	−0.0426112
$668$	25.3985	0.982697
$669$	−24.2891	−0.939072
$670$	56.8002	2.19438
$671$	−23.0507	−0.889864
$672$	0	0
$673$	8.46300	0.326225	0.163112	−	0.986608i	$-0.447847\pi$
$673$	8.46300	0.326225	0.163112	+	0.986608i	$0.447847\pi$
$674$	72.2688	2.78369
$675$	12.2325	0.470829
$676$	−41.0477	−1.57876
$677$	−18.7230	−0.719583	−0.359791	−	0.933033i	$-0.617152\pi$
$677$	−18.7230	−0.719583	−0.359791	+	0.933033i	$0.617152\pi$
$678$	−37.7327	−1.44912
$679$	0	0
$680$	14.5839	0.559267
$681$	−4.33303	−0.166042
$682$	63.0903	2.41585
$683$	−0.301855	−0.0115502	−0.00577508	−	0.999983i	$-0.501838\pi$
$683$	−0.301855	−0.0115502	−0.00577508	+	0.999983i	$0.501838\pi$
$684$	−0.159600	−0.00610246
$685$	−2.34764	−0.0896986
$686$	0	0
$687$	12.4437	0.474757
$688$	3.31281	0.126300
$689$	1.75245	0.0667630
$690$	−9.43432	−0.359158
$691$	31.5237	1.19922	0.599610	−	0.800293i	$-0.295323\pi$
$691$	31.5237	1.19922	0.599610	+	0.800293i	$0.295323\pi$
$692$	−49.1292	−1.86761
$693$	0	0
$694$	3.12238	0.118524
$695$	−81.2266	−3.08110
$696$	−2.91380	−0.110447
$697$	−6.43157	−0.243613
$698$	−14.6166	−0.553246
$699$	3.24764	0.122837
$700$	0	0
$701$	−17.6579	−0.666928	−0.333464	−	0.942763i	$-0.608218\pi$
$701$	−17.6579	−0.666928	−0.333464	+	0.942763i	$0.608218\pi$
$702$	0.399220	0.0150676
$703$	−0.189719	−0.00715540
$704$	41.5094	1.56444
$705$	−37.1538	−1.39929
$706$	58.4907	2.20133
$707$	0	0
$708$	20.2213	0.759962
$709$	7.73921	0.290652	0.145326	−	0.989384i	$-0.453577\pi$
$709$	7.73921	0.290652	0.145326	+	0.989384i	$0.453577\pi$
$710$	63.3532	2.37760
$711$	−15.4854	−0.580749
$712$	−5.14047	−0.192647
$713$	−8.71037	−0.326206
$714$	0	0
$715$	−2.32402	−0.0869134
$716$	26.2153	0.979712
$717$	26.4823	0.989001
$718$	54.4608	2.03246
$719$	23.4142	0.873203	0.436602	−	0.899655i	$-0.356182\pi$
$719$	23.4142	0.873203	0.436602	+	0.899655i	$0.356182\pi$
$720$	1.29789	0.0483695
$721$	0	0
$722$	43.1749	1.60681
$723$	−2.56149	−0.0952630
$724$	18.0783	0.671874
$725$	13.4617	0.499957
$726$	1.91511	0.0710763
$727$	43.6574	1.61916	0.809582	−	0.587007i	$-0.199694\pi$
$727$	43.6574	1.61916	0.809582	+	0.587007i	$0.199694\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	43.5273	1.61102
$731$	−14.0592	−0.519997
$732$	22.8914	0.846091
$733$	42.2476	1.56045	0.780226	−	0.625497i	$-0.215104\pi$
$733$	42.2476	1.56045	0.780226	+	0.625497i	$0.215104\pi$
$734$	58.3584	2.15405
$735$	0	0
$736$	−6.00601	−0.221384
$737$	−19.1880	−0.706798
$738$	11.0161	0.405507
$739$	−39.2506	−1.44386	−0.721929	−	0.691967i	$-0.756744\pi$
$739$	−39.2506	−1.44386	−0.721929	+	0.691967i	$0.756744\pi$
$740$	−49.4320	−1.81716
$741$	0.00885791	0.000325404 0
$742$	0	0
$743$	20.7027	0.759507	0.379754	−	0.925088i	$-0.376009\pi$
$743$	20.7027	0.759507	0.379754	+	0.925088i	$0.376009\pi$
$744$	−23.0626	−0.845518
$745$	−31.2472	−1.14481
$746$	−13.1836	−0.482685
$747$	−7.21102	−0.263837
$748$	−13.3843	−0.489377
$749$	0	0
$750$	68.2336	2.49154
$751$	−0.0631626	−0.00230484	−0.00115242	−	0.999999i	$-0.500367\pi$
$751$	−0.0631626	−0.00230484	−0.00115242	+	0.999999i	$0.500367\pi$
$752$	−2.79829	−0.102043
$753$	−14.6123	−0.532500
$754$	0.439338	0.0159997
$755$	88.6786	3.22735
$756$	0	0
$757$	37.1805	1.35135	0.675673	−	0.737201i	$-0.263853\pi$
$757$	37.1805	1.35135	0.675673	+	0.737201i	$0.263853\pi$
$758$	−47.8406	−1.73765
$759$	3.18706	0.115683
$760$	−0.554246	−0.0201046
$761$	28.3067	1.02612	0.513059	−	0.858353i	$-0.328512\pi$
$761$	28.3067	1.02612	0.513059	+	0.858353i	$0.328512\pi$
$762$	−40.5594	−1.46931
$763$	0	0
$764$	−4.91062	−0.177660
$765$	−5.50809	−0.199145
$766$	−10.9608	−0.396031
$767$	−1.12230	−0.0405237
$768$	−13.9231	−0.502408
$769$	−7.54568	−0.272104	−0.136052	−	0.990702i	$-0.543441\pi$
$769$	−7.54568	−0.272104	−0.136052	+	0.990702i	$0.543441\pi$
$770$	0	0
$771$	5.12857	0.184701
$772$	23.1772	0.834166
$773$	18.3951	0.661626	0.330813	−	0.943696i	$-0.392677\pi$
$773$	18.3951	0.661626	0.330813	+	0.943696i	$0.392677\pi$
$774$	24.0807	0.865562
$775$	106.550	3.82737
$776$	−33.8588	−1.21546
$777$	0	0
$778$	44.4112	1.59222
$779$	0.244425	0.00875743
$780$	2.30796	0.0826381
$781$	−21.4017	−0.765813
$782$	3.01553	0.107835
$783$	1.10049	0.0393283
$784$	0	0
$785$	48.8157	1.74231
$786$	49.0033	1.74789
$787$	−17.2390	−0.614502	−0.307251	−	0.951628i	$-0.599409\pi$
$787$	−17.2390	−0.614502	−0.307251	+	0.951628i	$0.599409\pi$
$788$	−21.6531	−0.771360
$789$	3.24813	0.115636
$790$	−146.094	−5.19781
$791$	0	0
$792$	8.43845	0.299847
$793$	−1.27049	−0.0451164
$794$	83.1455	2.95072
$795$	41.4136	1.46879
$796$	−24.1924	−0.857477
$797$	52.7371	1.86804	0.934021	−	0.357217i	$-0.116274\pi$
$797$	52.7371	1.86804	0.934021	+	0.357217i	$0.116274\pi$
$798$	0	0
$799$	11.8756	0.420129
$800$	73.4684	2.59750
$801$	1.94147	0.0685984
$802$	10.6245	0.375163
$803$	−14.7042	−0.518900
$804$	19.0553	0.672030
$805$	0	0
$806$	3.47735	0.122485
$807$	4.83101	0.170059
$808$	−4.35770	−0.153303
$809$	6.01310	0.211409	0.105705	−	0.994398i	$-0.466290\pi$
$809$	6.01310	0.211409	0.105705	+	0.994398i	$0.466290\pi$
$810$	9.43432	0.331488
$811$	−24.3539	−0.855181	−0.427591	−	0.903972i	$-0.640638\pi$
$811$	−24.3539	−0.855181	−0.427591	+	0.903972i	$0.640638\pi$
$812$	0	0
$813$	12.1239	0.425203
$814$	27.2510	0.955147
$815$	63.6042	2.22796
$816$	−0.414849	−0.0145226
$817$	0.534303	0.0186929
$818$	25.0128	0.874554
$819$	0	0
$820$	63.6857	2.22400
$821$	0.111893	0.00390508	0.00195254	−	0.999998i	$-0.499378\pi$
$821$	0.111893	0.00390508	0.00195254	+	0.999998i	$0.499378\pi$
$822$	−1.28527	−0.0448288
$823$	19.9376	0.694983	0.347491	−	0.937683i	$-0.387034\pi$
$823$	19.9376	0.694983	0.347491	+	0.937683i	$0.387034\pi$
$824$	23.8103	0.829472
$825$	−38.9857	−1.35731
$826$	0	0
$827$	−48.7394	−1.69483	−0.847417	−	0.530928i	$-0.821843\pi$
$827$	−48.7394	−1.69483	−0.847417	+	0.530928i	$0.821843\pi$
$828$	−3.16503	−0.109992
$829$	−11.3338	−0.393638	−0.196819	−	0.980440i	$-0.563061\pi$
$829$	−11.3338	−0.393638	−0.196819	+	0.980440i	$0.563061\pi$
$830$	−68.0310	−2.36139
$831$	−21.9014	−0.759751
$832$	2.28788	0.0793178
$833$	0	0
$834$	−44.4693	−1.53985
$835$	−33.3123	−1.15282
$836$	0.508654	0.0175922
$837$	8.71037	0.301074
$838$	42.9014	1.48200
$839$	−42.1263	−1.45436	−0.727182	−	0.686445i	$-0.759170\pi$
$839$	−42.1263	−1.45436	−0.727182	+	0.686445i	$0.759170\pi$
$840$	0	0
$841$	−27.7889	−0.958239
$842$	23.0314	0.793715
$843$	−24.2364	−0.834747
$844$	−14.8631	−0.511608
$845$	53.8376	1.85207
$846$	−20.3407	−0.699327
$847$	0	0
$848$	3.11912	0.107111
$849$	−5.14581	−0.176604
$850$	−36.8874	−1.26523
$851$	−3.76233	−0.128971
$852$	21.2538	0.728142
$853$	37.5528	1.28578	0.642891	−	0.765957i	$-0.277735\pi$
$853$	37.5528	1.28578	0.642891	+	0.765957i	$0.277735\pi$
$854$	0	0
$855$	0.209329	0.00715890
$856$	50.2619	1.71792
$857$	−58.0721	−1.98370	−0.991852	−	0.127397i	$-0.959338\pi$
$857$	−58.0721	−1.98370	−0.991852	+	0.127397i	$0.959338\pi$
$858$	−1.27234	−0.0434369
$859$	24.9857	0.852501	0.426250	−	0.904605i	$-0.359834\pi$
$859$	24.9857	0.852501	0.426250	+	0.904605i	$0.359834\pi$
$860$	139.214	4.74717
$861$	0	0
$862$	−17.8901	−0.609338
$863$	−13.9209	−0.473875	−0.236937	−	0.971525i	$-0.576144\pi$
$863$	−13.9209	−0.473875	−0.236937	+	0.971525i	$0.576144\pi$
$864$	6.00601	0.204328
$865$	64.4372	2.19093
$866$	−46.7868	−1.58988
$867$	−15.2394	−0.517558
$868$	0	0
$869$	49.3530	1.67418
$870$	10.3824	0.351996
$871$	−1.05759	−0.0358349
$872$	31.0267	1.05070
$873$	12.7879	0.432804
$874$	−0.114602	−0.00387647
$875$	0	0
$876$	14.6026	0.493375
$877$	−7.97539	−0.269310	−0.134655	−	0.990893i	$-0.542993\pi$
$877$	−7.97539	−0.269310	−0.134655	+	0.990893i	$0.542993\pi$
$878$	76.5157	2.58228
$879$	24.5374	0.827626
$880$	−4.13645	−0.139440
$881$	33.6800	1.13471	0.567354	−	0.823474i	$-0.307967\pi$
$881$	33.6800	1.13471	0.567354	+	0.823474i	$0.307967\pi$
$882$	0	0
$883$	32.7638	1.10259	0.551294	−	0.834311i	$-0.314134\pi$
$883$	32.7638	1.10259	0.551294	+	0.834311i	$0.314134\pi$
$884$	−0.737701	−0.0248116
$885$	−26.5219	−0.891525
$886$	−16.6707	−0.560062
$887$	−9.33788	−0.313535	−0.156768	−	0.987635i	$-0.550107\pi$
$887$	−9.33788	−0.313535	−0.156768	+	0.987635i	$0.550107\pi$
$888$	−9.96160	−0.334289
$889$	0	0
$890$	18.3164	0.613968
$891$	−3.18706	−0.106770
$892$	−76.8758	−2.57399
$893$	−0.451320	−0.0151029
$894$	−17.1070	−0.572143
$895$	−34.3836	−1.14932
$896$	0	0
$897$	0.175661	0.00586516
$898$	48.0689	1.60408
$899$	9.58568	0.319700
$900$	38.7162	1.29054
$901$	−13.2372	−0.440995
$902$	−35.1088	−1.16900
$903$	0	0
$904$	−43.9597	−1.46208
$905$	−23.7112	−0.788187
$906$	48.5491	1.61294
$907$	19.1938	0.637320	0.318660	−	0.947869i	$-0.396767\pi$
$907$	19.1938	0.637320	0.318660	+	0.947869i	$0.396767\pi$
$908$	−13.7142	−0.455121
$909$	1.64583	0.0545887
$910$	0	0
$911$	−18.4406	−0.610963	−0.305481	−	0.952198i	$-0.598817\pi$
$911$	−18.4406	−0.610963	−0.305481	+	0.952198i	$0.598817\pi$
$912$	0.0157659	0.000522061 0
$913$	22.9819	0.760591
$914$	−20.3809	−0.674140
$915$	−30.0241	−0.992565
$916$	39.3847	1.30131
$917$	0	0
$918$	−3.01553	−0.0995272
$919$	−30.6905	−1.01239	−0.506194	−	0.862420i	$-0.668948\pi$
$919$	−30.6905	−1.01239	−0.506194	+	0.862420i	$0.668948\pi$
$920$	−10.9912	−0.362371
$921$	−7.16659	−0.236147
$922$	14.3223	0.471679
$923$	−1.17960	−0.0388270
$924$	0	0
$925$	46.0226	1.51321
$926$	34.3382	1.12842
$927$	−8.99275	−0.295361
$928$	6.60955	0.216969
$929$	4.18918	0.137443	0.0687213	−	0.997636i	$-0.478108\pi$
$929$	4.18918	0.137443	0.0687213	+	0.997636i	$0.478108\pi$
$930$	82.1764	2.69467
$931$	0	0
$932$	10.2789	0.336696
$933$	−5.87280	−0.192267
$934$	−43.0910	−1.40998
$935$	17.5546	0.574097
$936$	0.465103	0.0152024
$937$	−31.8927	−1.04189	−0.520945	−	0.853590i	$-0.674420\pi$
$937$	−31.8927	−1.04189	−0.520945	+	0.853590i	$0.674420\pi$
$938$	0	0
$939$	3.80364	0.124127
$940$	−117.593	−3.83546
$941$	30.3580	0.989643	0.494822	−	0.868995i	$-0.335233\pi$
$941$	30.3580	0.989643	0.494822	+	0.868995i	$0.335233\pi$
$942$	26.7252	0.870756
$943$	4.84719	0.157846
$944$	−1.99754	−0.0650143
$945$	0	0
$946$	−76.7465	−2.49524
$947$	33.7676	1.09730	0.548650	−	0.836052i	$-0.315142\pi$
$947$	33.7676	1.09730	0.548650	+	0.836052i	$0.315142\pi$
$948$	−49.0118	−1.59183
$949$	−0.810452	−0.0263084
$950$	1.40187	0.0454826
$951$	9.80284	0.317879
$952$	0	0
$953$	6.62261	0.214527	0.107264	−	0.994231i	$-0.465791\pi$
$953$	6.62261	0.214527	0.107264	+	0.994231i	$0.465791\pi$
$954$	22.6728	0.734060
$955$	6.44070	0.208416
$956$	83.8173	2.71085
$957$	−3.50733	−0.113376
$958$	−64.9465	−2.09833
$959$	0	0
$960$	54.0668	1.74500
$961$	44.8705	1.44744
$962$	1.50200	0.0484263
$963$	−18.9831	−0.611721
$964$	−8.10720	−0.261115
$965$	−30.3989	−0.978574
$966$	0	0
$967$	−49.1558	−1.58074	−0.790372	−	0.612628i	$-0.790113\pi$
$967$	−49.1558	−1.58074	−0.790372	+	0.612628i	$0.790113\pi$
$968$	2.23115	0.0717120
$969$	−0.0669087	−0.00214942
$970$	120.645	3.87368
$971$	8.76315	0.281223	0.140611	−	0.990065i	$-0.455093\pi$
$971$	8.76315	0.281223	0.140611	+	0.990065i	$0.455093\pi$
$972$	3.16503	0.101518
$973$	0	0
$974$	−56.8002	−1.82000
$975$	−2.14878	−0.0688159
$976$	−2.26130	−0.0723826
$977$	−0.347523	−0.0111183	−0.00555913	−	0.999985i	$-0.501770\pi$
$977$	−0.347523	−0.0111183	−0.00555913	+	0.999985i	$0.501770\pi$
$978$	34.8216	1.11347
$979$	−6.18757	−0.197756
$980$	0	0
$981$	−11.7183	−0.374136
$982$	50.1158	1.59926
$983$	53.3283	1.70091	0.850454	−	0.526050i	$-0.176328\pi$
$983$	53.3283	1.70091	0.850454	+	0.526050i	$0.176328\pi$
$984$	12.8340	0.409134
$985$	28.3999	0.904896
$986$	−3.31856	−0.105684
$987$	0	0
$988$	0.0280355	0.000891930 0
$989$	10.5958	0.336926
$990$	−30.0677	−0.955614
$991$	−5.82924	−0.185172	−0.0925860	−	0.995705i	$-0.529513\pi$
$991$	−5.82924	−0.185172	−0.0925860	+	0.995705i	$0.529513\pi$
$992$	52.3145	1.66099
$993$	−11.1896	−0.355091
$994$	0	0
$995$	31.7304	1.00592
$996$	−22.8231	−0.723177
$997$	31.9358	1.01142	0.505708	−	0.862705i	$-0.331231\pi$
$997$	31.9358	1.01142	0.505708	+	0.862705i	$0.331231\pi$
$998$	89.6002	2.83625
$999$	3.76233	0.119035

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3381.2.a.bd.1.1		6
7.3	odd	6		483.2.i.f.415.6	yes	12
7.5	odd	6		483.2.i.f.277.6	✓	12
7.6	odd	2		3381.2.a.bc.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.i.f.277.6	✓	12	7.5	odd	6
483.2.i.f.415.6	yes	12	7.3	odd	6
3381.2.a.bc.1.1		6	7.6	odd	2
3381.2.a.bd.1.1		6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.27267 q^{2} +1.00000 q^{3} +3.16503 q^{4} -4.15120 q^{5} -2.27267 q^{6} -2.64772 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.27267 q^{2} +1.00000 q^{3} +3.16503 q^{4} -4.15120 q^{5} -2.27267 q^{6} -2.64772 q^{8} +1.00000 q^{9} +9.43432 q^{10} -3.18706 q^{11} +3.16503 q^{12} -0.175661 q^{13} -4.15120 q^{15} -0.312654 q^{16} +1.32687 q^{17} -2.27267 q^{18} -0.0504261 q^{19} -13.1387 q^{20} +7.24313 q^{22} -1.00000 q^{23} -2.64772 q^{24} +12.2325 q^{25} +0.399220 q^{26} +1.00000 q^{27} +1.10049 q^{29} +9.43432 q^{30} +8.71037 q^{31} +6.00601 q^{32} -3.18706 q^{33} -3.01553 q^{34} +3.16503 q^{36} +3.76233 q^{37} +0.114602 q^{38} -0.175661 q^{39} +10.9912 q^{40} -4.84719 q^{41} -10.5958 q^{43} -10.0871 q^{44} -4.15120 q^{45} +2.27267 q^{46} +8.95013 q^{47} -0.312654 q^{48} -27.8004 q^{50} +1.32687 q^{51} -0.555973 q^{52} -9.97629 q^{53} -2.27267 q^{54} +13.2301 q^{55} -0.0504261 q^{57} -2.50105 q^{58} +6.38897 q^{59} -13.1387 q^{60} +7.23261 q^{61} -19.7958 q^{62} -13.0244 q^{64} +0.729206 q^{65} +7.24313 q^{66} +6.02059 q^{67} +4.19957 q^{68} -1.00000 q^{69} +6.71519 q^{71} -2.64772 q^{72} +4.61372 q^{73} -8.55052 q^{74} +12.2325 q^{75} -0.159600 q^{76} +0.399220 q^{78} -15.4854 q^{79} +1.29789 q^{80} +1.00000 q^{81} +11.0161 q^{82} -7.21102 q^{83} -5.50809 q^{85} +24.0807 q^{86} +1.10049 q^{87} +8.43845 q^{88} +1.94147 q^{89} +9.43432 q^{90} -3.16503 q^{92} +8.71037 q^{93} -20.3407 q^{94} +0.209329 q^{95} +6.00601 q^{96} +12.7879 q^{97} -3.18706 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} + 6 q^{3} + 3 q^{4} - 3 q^{5} - q^{6} - 3 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q - q^2 + 6 * q^3 + 3 * q^4 - 3 * q^5 - q^6 - 3 * q^8 + 6 * q^9	\( 6 q - q^{2} + 6 q^{3} + 3 q^{4} - 3 q^{5} - q^{6} - 3 q^{8} + 6 q^{9} + 3 q^{10} - 14 q^{11} + 3 q^{12} - 3 q^{15} - 7 q^{16} - 15 q^{17} - q^{18} + q^{19} - 17 q^{20} - 6 q^{22} - 6 q^{23} - 3 q^{24} + 9 q^{25} + 15 q^{26} + 6 q^{27} - 6 q^{29} + 3 q^{30} + 11 q^{31} + 3 q^{32} - 14 q^{33} - 15 q^{34} + 3 q^{36} - 5 q^{37} - 14 q^{38} + 17 q^{40} - 18 q^{41} - 37 q^{43} - 10 q^{44} - 3 q^{45} + q^{46} - 3 q^{47} - 7 q^{48} - 30 q^{50} - 15 q^{51} + 7 q^{52} - 15 q^{53} - q^{54} + 2 q^{55} + q^{57} + 4 q^{58} + 2 q^{59} - 17 q^{60} + 12 q^{61} - 36 q^{62} - 23 q^{64} - 17 q^{65} - 6 q^{66} - 10 q^{67} + q^{68} - 6 q^{69} - 21 q^{71} - 3 q^{72} + 8 q^{73} - 16 q^{74} + 9 q^{75} - 18 q^{76} + 15 q^{78} - 17 q^{79} - 3 q^{80} + 6 q^{81} + 48 q^{82} - 12 q^{83} - 13 q^{85} + 22 q^{86} - 6 q^{87} - 2 q^{88} - 18 q^{89} + 3 q^{90} - 3 q^{92} + 11 q^{93} - 3 q^{94} - 16 q^{95} + 3 q^{96} + 2 q^{97} - 14 q^{99}+O(q^{100}) \) 6 * q - q^2 + 6 * q^3 + 3 * q^4 - 3 * q^5 - q^6 - 3 * q^8 + 6 * q^9 + 3 * q^10 - 14 * q^11 + 3 * q^12 - 3 * q^15 - 7 * q^16 - 15 * q^17 - q^18 + q^19 - 17 * q^20 - 6 * q^22 - 6 * q^23 - 3 * q^24 + 9 * q^25 + 15 * q^26 + 6 * q^27 - 6 * q^29 + 3 * q^30 + 11 * q^31 + 3 * q^32 - 14 * q^33 - 15 * q^34 + 3 * q^36 - 5 * q^37 - 14 * q^38 + 17 * q^40 - 18 * q^41 - 37 * q^43 - 10 * q^44 - 3 * q^45 + q^46 - 3 * q^47 - 7 * q^48 - 30 * q^50 - 15 * q^51 + 7 * q^52 - 15 * q^53 - q^54 + 2 * q^55 + q^57 + 4 * q^58 + 2 * q^59 - 17 * q^60 + 12 * q^61 - 36 * q^62 - 23 * q^64 - 17 * q^65 - 6 * q^66 - 10 * q^67 + q^68 - 6 * q^69 - 21 * q^71 - 3 * q^72 + 8 * q^73 - 16 * q^74 + 9 * q^75 - 18 * q^76 + 15 * q^78 - 17 * q^79 - 3 * q^80 + 6 * q^81 + 48 * q^82 - 12 * q^83 - 13 * q^85 + 22 * q^86 - 6 * q^87 - 2 * q^88 - 18 * q^89 + 3 * q^90 - 3 * q^92 + 11 * q^93 - 3 * q^94 - 16 * q^95 + 3 * q^96 + 2 * q^97 - 14 * q^99

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