LMFDB - Embedded newform 3381.2.a.bi.1.9

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			1.9
Root			$2.51520$ 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)

$f(q)$	$=$	$q+2.51520 q^{2} -1.00000 q^{3} +4.32625 q^{4} +4.31735 q^{5} -2.51520 q^{6} +5.85100 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.51520 q^{2} -1.00000 q^{3} +4.32625 q^{4} +4.31735 q^{5} -2.51520 q^{6} +5.85100 q^{8} +1.00000 q^{9} +10.8590 q^{10} +1.72915 q^{11} -4.32625 q^{12} -2.88941 q^{13} -4.31735 q^{15} +6.06395 q^{16} -4.93124 q^{17} +2.51520 q^{18} +2.44156 q^{19} +18.6780 q^{20} +4.34917 q^{22} +1.00000 q^{23} -5.85100 q^{24} +13.6396 q^{25} -7.26746 q^{26} -1.00000 q^{27} +8.05817 q^{29} -10.8590 q^{30} +0.915859 q^{31} +3.55007 q^{32} -1.72915 q^{33} -12.4031 q^{34} +4.32625 q^{36} -9.15581 q^{37} +6.14102 q^{38} +2.88941 q^{39} +25.2608 q^{40} -6.60783 q^{41} +10.7440 q^{43} +7.48074 q^{44} +4.31735 q^{45} +2.51520 q^{46} -0.399649 q^{47} -6.06395 q^{48} +34.3063 q^{50} +4.93124 q^{51} -12.5003 q^{52} +6.54512 q^{53} -2.51520 q^{54} +7.46536 q^{55} -2.44156 q^{57} +20.2679 q^{58} -1.83508 q^{59} -18.6780 q^{60} -1.30126 q^{61} +2.30357 q^{62} -3.19874 q^{64} -12.4746 q^{65} -4.34917 q^{66} -10.2140 q^{67} -21.3338 q^{68} -1.00000 q^{69} -9.00190 q^{71} +5.85100 q^{72} -2.61716 q^{73} -23.0287 q^{74} -13.6396 q^{75} +10.5628 q^{76} +7.26746 q^{78} +10.1870 q^{79} +26.1802 q^{80} +1.00000 q^{81} -16.6200 q^{82} -10.8838 q^{83} -21.2899 q^{85} +27.0234 q^{86} -8.05817 q^{87} +10.1173 q^{88} +14.9862 q^{89} +10.8590 q^{90} +4.32625 q^{92} -0.915859 q^{93} -1.00520 q^{94} +10.5411 q^{95} -3.55007 q^{96} -3.07116 q^{97} +1.72915 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.51520	1.77852	0.889259	−	0.457404i	$-0.151221\pi$
$2$	2.51520	1.77852	0.889259	+	0.457404i	$0.151221\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.32625	2.16313
$5$	4.31735	1.93078	0.965390	−	0.260811i	$-0.0839900\pi$
$5$	4.31735	1.93078	0.965390	+	0.260811i	$0.0839900\pi$
$6$	−2.51520	−1.02683
$7$	0	0
$7$	0	0
$8$	5.85100	2.06864
$9$	1.00000	0.333333
$10$	10.8590	3.43393
$11$	1.72915	0.521359	0.260679	−	0.965425i	$-0.416053\pi$
$11$	1.72915	0.521359	0.260679	+	0.965425i	$0.416053\pi$
$12$	−4.32625	−1.24888
$13$	−2.88941	−0.801378	−0.400689	−	0.916214i	$-0.631229\pi$
$13$	−2.88941	−0.801378	−0.400689	+	0.916214i	$0.631229\pi$
$14$	0	0
$15$	−4.31735	−1.11474
$16$	6.06395	1.51599
$17$	−4.93124	−1.19600	−0.598001	−	0.801495i	$-0.704038\pi$
$17$	−4.93124	−1.19600	−0.598001	+	0.801495i	$0.704038\pi$
$18$	2.51520	0.592839
$19$	2.44156	0.560132	0.280066	−	0.959981i	$-0.409644\pi$
$19$	2.44156	0.560132	0.280066	+	0.959981i	$0.409644\pi$
$20$	18.6780	4.17652
$21$	0	0
$22$	4.34917	0.927245
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−5.85100	−1.19433
$25$	13.6396	2.72791
$26$	−7.26746	−1.42527
$27$	−1.00000	−0.192450
$28$	0	0
$29$	8.05817	1.49636	0.748182	−	0.663493i	$-0.230927\pi$
$29$	8.05817	1.49636	0.748182	+	0.663493i	$0.230927\pi$
$30$	−10.8590	−1.98258
$31$	0.915859	0.164493	0.0822466	−	0.996612i	$-0.473790\pi$
$31$	0.915859	0.164493	0.0822466	+	0.996612i	$0.473790\pi$
$32$	3.55007	0.627570
$33$	−1.72915	−0.301007
$34$	−12.4031	−2.12711
$35$	0	0
$36$	4.32625	0.721042
$37$	−9.15581	−1.50521	−0.752603	−	0.658475i	$-0.771202\pi$
$37$	−9.15581	−1.50521	−0.752603	+	0.658475i	$0.771202\pi$
$38$	6.14102	0.996205
$39$	2.88941	0.462676
$40$	25.2608	3.99409
$41$	−6.60783	−1.03197	−0.515985	−	0.856598i	$-0.672574\pi$
$41$	−6.60783	−1.03197	−0.515985	+	0.856598i	$0.672574\pi$
$42$	0	0
$43$	10.7440	1.63845	0.819223	−	0.573475i	$-0.194405\pi$
$43$	10.7440	1.63845	0.819223	+	0.573475i	$0.194405\pi$
$44$	7.48074	1.12776
$45$	4.31735	0.643593
$46$	2.51520	0.370847
$47$	−0.399649	−0.0582948	−0.0291474	−	0.999575i	$-0.509279\pi$
$47$	−0.399649	−0.0582948	−0.0291474	+	0.999575i	$0.509279\pi$
$48$	−6.06395	−0.875255
$49$	0	0
$50$	34.3063	4.85164
$51$	4.93124	0.690512
$52$	−12.5003	−1.73348
$53$	6.54512	0.899042	0.449521	−	0.893270i	$-0.351595\pi$
$53$	6.54512	0.899042	0.449521	+	0.893270i	$0.351595\pi$
$54$	−2.51520	−0.342276
$55$	7.46536	1.00663
$56$	0	0
$57$	−2.44156	−0.323393
$58$	20.2679	2.66131
$59$	−1.83508	−0.238907	−0.119454	−	0.992840i	$-0.538114\pi$
$59$	−1.83508	−0.238907	−0.119454	+	0.992840i	$0.538114\pi$
$60$	−18.6780	−2.41131
$61$	−1.30126	−0.166609	−0.0833045	−	0.996524i	$-0.526547\pi$
$61$	−1.30126	−0.166609	−0.0833045	+	0.996524i	$0.526547\pi$
$62$	2.30357	0.292554
$63$	0	0
$64$	−3.19874	−0.399843
$65$	−12.4746	−1.54728
$66$	−4.34917	−0.535345
$67$	−10.2140	−1.24784	−0.623918	−	0.781490i	$-0.714460\pi$
$67$	−10.2140	−1.24784	−0.623918	+	0.781490i	$0.714460\pi$
$68$	−21.3338	−2.58710
$69$	−1.00000	−0.120386
$70$	0	0
$71$	−9.00190	−1.06833	−0.534164	−	0.845381i	$-0.679374\pi$
$71$	−9.00190	−1.06833	−0.534164	+	0.845381i	$0.679374\pi$
$72$	5.85100	0.689547
$73$	−2.61716	−0.306315	−0.153158	−	0.988202i	$-0.548944\pi$
$73$	−2.61716	−0.306315	−0.153158	+	0.988202i	$0.548944\pi$
$74$	−23.0287	−2.67703
$75$	−13.6396	−1.57496
$76$	10.5628	1.21164
$77$	0	0
$78$	7.26746	0.822877
$79$	10.1870	1.14613	0.573064	−	0.819510i	$-0.305755\pi$
$79$	10.1870	1.14613	0.573064	+	0.819510i	$0.305755\pi$
$80$	26.1802	2.92704
$81$	1.00000	0.111111
$82$	−16.6200	−1.83538
$83$	−10.8838	−1.19465	−0.597327	−	0.801998i	$-0.703771\pi$
$83$	−10.8838	−1.19465	−0.597327	+	0.801998i	$0.703771\pi$
$84$	0	0
$85$	−21.2899	−2.30922
$86$	27.0234	2.91400
$87$	−8.05817	−0.863926
$88$	10.1173	1.07850
$89$	14.9862	1.58854	0.794269	−	0.607566i	$-0.207854\pi$
$89$	14.9862	1.58854	0.794269	+	0.607566i	$0.207854\pi$
$90$	10.8590	1.14464
$91$	0	0
$92$	4.32625	0.451043
$93$	−0.915859	−0.0949702
$94$	−1.00520	−0.103678
$95$	10.5411	1.08149
$96$	−3.55007	−0.362328
$97$	−3.07116	−0.311829	−0.155914	−	0.987771i	$-0.549832\pi$
$97$	−3.07116	−0.311829	−0.155914	+	0.987771i	$0.549832\pi$
$98$	0	0
$99$	1.72915	0.173786
$100$	59.0081	5.90081
$101$	1.08810	0.108270	0.0541349	−	0.998534i	$-0.482760\pi$
$101$	1.08810	0.108270	0.0541349	+	0.998534i	$0.482760\pi$
$102$	12.4031	1.22809
$103$	−3.23110	−0.318369	−0.159185	−	0.987249i	$-0.550887\pi$
$103$	−3.23110	−0.318369	−0.159185	+	0.987249i	$0.550887\pi$
$104$	−16.9059	−1.65776
$105$	0	0
$106$	16.4623	1.59896
$107$	−0.936899	−0.0905734	−0.0452867	−	0.998974i	$-0.514420\pi$
$107$	−0.936899	−0.0905734	−0.0452867	+	0.998974i	$0.514420\pi$
$108$	−4.32625	−0.416294
$109$	−14.9782	−1.43465	−0.717324	−	0.696739i	$-0.754633\pi$
$109$	−14.9782	−1.43465	−0.717324	+	0.696739i	$0.754633\pi$
$110$	18.7769	1.79031
$111$	9.15581	0.869031
$112$	0	0
$113$	−14.1424	−1.33040	−0.665201	−	0.746665i	$-0.731654\pi$
$113$	−14.1424	−1.33040	−0.665201	+	0.746665i	$0.731654\pi$
$114$	−6.14102	−0.575159
$115$	4.31735	0.402595
$116$	34.8617	3.23682
$117$	−2.88941	−0.267126
$118$	−4.61560	−0.424901
$119$	0	0
$120$	−25.2608	−2.30599
$121$	−8.01004	−0.728185
$122$	−3.27293	−0.296317
$123$	6.60783	0.595808
$124$	3.96224	0.355819
$125$	37.3000	3.33621
$126$	0	0
$127$	−1.77968	−0.157921	−0.0789604	−	0.996878i	$-0.525160\pi$
$127$	−1.77968	−0.157921	−0.0789604	+	0.996878i	$0.525160\pi$
$128$	−15.1456	−1.33870
$129$	−10.7440	−0.945957
$130$	−31.3762	−2.75187
$131$	8.89264	0.776954	0.388477	−	0.921459i	$-0.373001\pi$
$131$	8.89264	0.776954	0.388477	+	0.921459i	$0.373001\pi$
$132$	−7.48074	−0.651115
$133$	0	0
$134$	−25.6902	−2.21930
$135$	−4.31735	−0.371579
$136$	−28.8527	−2.47410
$137$	0.247404	0.0211371	0.0105686	−	0.999944i	$-0.496636\pi$
$137$	0.247404	0.0211371	0.0105686	+	0.999944i	$0.496636\pi$
$138$	−2.51520	−0.214108
$139$	−8.59949	−0.729399	−0.364699	−	0.931125i	$-0.618828\pi$
$139$	−8.59949	−0.729399	−0.364699	+	0.931125i	$0.618828\pi$
$140$	0	0
$141$	0.399649	0.0336565
$142$	−22.6416	−1.90004
$143$	−4.99623	−0.417805
$144$	6.06395	0.505329
$145$	34.7900	2.88915
$146$	−6.58268	−0.544787
$147$	0	0
$148$	−39.6103	−3.25595
$149$	4.50669	0.369202	0.184601	−	0.982814i	$-0.440901\pi$
$149$	4.50669	0.369202	0.184601	+	0.982814i	$0.440901\pi$
$150$	−34.3063	−2.80109
$151$	−4.52766	−0.368455	−0.184228	−	0.982884i	$-0.558978\pi$
$151$	−4.52766	−0.368455	−0.184228	+	0.982884i	$0.558978\pi$
$152$	14.2856	1.15871
$153$	−4.93124	−0.398667
$154$	0	0
$155$	3.95409	0.317600
$156$	12.5003	1.00083
$157$	−3.26727	−0.260757	−0.130378	−	0.991464i	$-0.541619\pi$
$157$	−3.26727	−0.260757	−0.130378	+	0.991464i	$0.541619\pi$
$158$	25.6224	2.03841
$159$	−6.54512	−0.519062
$160$	15.3269	1.21170
$161$	0	0
$162$	2.51520	0.197613
$163$	10.6420	0.833549	0.416774	−	0.909010i	$-0.363160\pi$
$163$	10.6420	0.833549	0.416774	+	0.909010i	$0.363160\pi$
$164$	−28.5871	−2.23228
$165$	−7.46536	−0.581177
$166$	−27.3750	−2.12471
$167$	2.99812	0.232001	0.116001	−	0.993249i	$-0.462993\pi$
$167$	2.99812	0.232001	0.116001	+	0.993249i	$0.462993\pi$
$168$	0	0
$169$	−4.65131	−0.357793
$170$	−53.5485	−4.10698
$171$	2.44156	0.186711
$172$	46.4813	3.54416
$173$	−13.2996	−1.01115	−0.505576	−	0.862782i	$-0.668720\pi$
$173$	−13.2996	−1.01115	−0.505576	+	0.862782i	$0.668720\pi$
$174$	−20.2679	−1.53651
$175$	0	0
$176$	10.4855	0.790373
$177$	1.83508	0.137933
$178$	37.6934	2.82524
$179$	19.6297	1.46719	0.733596	−	0.679585i	$-0.237840\pi$
$179$	19.6297	1.46719	0.733596	+	0.679585i	$0.237840\pi$
$180$	18.6780	1.39217
$181$	19.2095	1.42783	0.713915	−	0.700232i	$-0.246920\pi$
$181$	19.2095	1.42783	0.713915	+	0.700232i	$0.246920\pi$
$182$	0	0
$183$	1.30126	0.0961917
$184$	5.85100	0.431341
$185$	−39.5289	−2.90622
$186$	−2.30357	−0.168906
$187$	−8.52686	−0.623546
$188$	−1.72898	−0.126099
$189$	0	0
$190$	26.5130	1.92345
$191$	−7.15375	−0.517627	−0.258814	−	0.965927i	$-0.583332\pi$
$191$	−7.15375	−0.517627	−0.258814	+	0.965927i	$0.583332\pi$
$192$	3.19874	0.230849
$193$	−21.9573	−1.58052	−0.790259	−	0.612772i	$-0.790054\pi$
$193$	−21.9573	−1.58052	−0.790259	+	0.612772i	$0.790054\pi$
$194$	−7.72458	−0.554593
$195$	12.4746	0.893325
$196$	0	0
$197$	3.21028	0.228723	0.114361	−	0.993439i	$-0.463518\pi$
$197$	3.21028	0.228723	0.114361	+	0.993439i	$0.463518\pi$
$198$	4.34917	0.309082
$199$	12.7170	0.901483	0.450741	−	0.892655i	$-0.351160\pi$
$199$	12.7170	0.901483	0.450741	+	0.892655i	$0.351160\pi$
$200$	79.8050	5.64306
$201$	10.2140	0.720438
$202$	2.73679	0.192560
$203$	0	0
$204$	21.3338	1.49366
$205$	−28.5283	−1.99251
$206$	−8.12686	−0.566225
$207$	1.00000	0.0695048
$208$	−17.5212	−1.21488
$209$	4.22183	0.292030
$210$	0	0
$211$	−17.0500	−1.17377	−0.586884	−	0.809671i	$-0.699646\pi$
$211$	−17.0500	−1.17377	−0.586884	+	0.809671i	$0.699646\pi$
$212$	28.3159	1.94474
$213$	9.00190	0.616800
$214$	−2.35649	−0.161086
$215$	46.3857	3.16348
$216$	−5.85100	−0.398110
$217$	0	0
$218$	−37.6732	−2.55155
$219$	2.61716	0.176851
$220$	32.2970	2.17746
$221$	14.2484	0.958450
$222$	23.0287	1.54559
$223$	23.3278	1.56215	0.781073	−	0.624440i	$-0.214673\pi$
$223$	23.3278	1.56215	0.781073	+	0.624440i	$0.214673\pi$
$224$	0	0
$225$	13.6396	0.909303
$226$	−35.5709	−2.36614
$227$	−7.67594	−0.509470	−0.254735	−	0.967011i	$-0.581988\pi$
$227$	−7.67594	−0.509470	−0.254735	+	0.967011i	$0.581988\pi$
$228$	−10.5628	−0.699539
$229$	−22.8736	−1.51153	−0.755766	−	0.654842i	$-0.772735\pi$
$229$	−22.8736	−1.51153	−0.755766	+	0.654842i	$0.772735\pi$
$230$	10.8590	0.716023
$231$	0	0
$232$	47.1483	3.09544
$233$	23.5559	1.54320	0.771599	−	0.636110i	$-0.219457\pi$
$233$	23.5559	1.54320	0.771599	+	0.636110i	$0.219457\pi$
$234$	−7.26746	−0.475089
$235$	−1.72543	−0.112554
$236$	−7.93902	−0.516786
$237$	−10.1870	−0.661718
$238$	0	0
$239$	13.1829	0.852732	0.426366	−	0.904551i	$-0.359794\pi$
$239$	13.1829	0.852732	0.426366	+	0.904551i	$0.359794\pi$
$240$	−26.1802	−1.68993
$241$	−17.2670	−1.11227	−0.556134	−	0.831093i	$-0.687716\pi$
$241$	−17.2670	−1.11227	−0.556134	+	0.831093i	$0.687716\pi$
$242$	−20.1469	−1.29509
$243$	−1.00000	−0.0641500
$244$	−5.62957	−0.360396
$245$	0	0
$246$	16.6200	1.05966
$247$	−7.05467	−0.448878
$248$	5.35869	0.340277
$249$	10.8838	0.689734
$250$	93.8171	5.93352
$251$	4.74956	0.299790	0.149895	−	0.988702i	$-0.452106\pi$
$251$	4.74956	0.299790	0.149895	+	0.988702i	$0.452106\pi$
$252$	0	0
$253$	1.72915	0.108711
$254$	−4.47625	−0.280865
$255$	21.2899	1.33323
$256$	−31.6969	−1.98105
$257$	1.42884	0.0891283	0.0445641	−	0.999007i	$-0.485810\pi$
$257$	1.42884	0.0891283	0.0445641	+	0.999007i	$0.485810\pi$
$258$	−27.0234	−1.68240
$259$	0	0
$260$	−53.9683	−3.34697
$261$	8.05817	0.498788
$262$	22.3668	1.38183
$263$	8.81746	0.543708	0.271854	−	0.962339i	$-0.412363\pi$
$263$	8.81746	0.543708	0.271854	+	0.962339i	$0.412363\pi$
$264$	−10.1173	−0.622674
$265$	28.2576	1.73585
$266$	0	0
$267$	−14.9862	−0.917143
$268$	−44.1882	−2.69922
$269$	−12.9185	−0.787658	−0.393829	−	0.919184i	$-0.628850\pi$
$269$	−12.9185	−0.787658	−0.393829	+	0.919184i	$0.628850\pi$
$270$	−10.8590	−0.660859
$271$	13.3485	0.810865	0.405433	−	0.914125i	$-0.367121\pi$
$271$	13.3485	0.810865	0.405433	+	0.914125i	$0.367121\pi$
$272$	−29.9028	−1.81312
$273$	0	0
$274$	0.622271	0.0375927
$275$	23.5848	1.42222
$276$	−4.32625	−0.260410
$277$	−15.4986	−0.931221	−0.465610	−	0.884990i	$-0.654165\pi$
$277$	−15.4986	−0.931221	−0.465610	+	0.884990i	$0.654165\pi$
$278$	−21.6295	−1.29725
$279$	0.915859	0.0548311
$280$	0	0
$281$	23.6088	1.40838	0.704192	−	0.710009i	$-0.251309\pi$
$281$	23.6088	1.40838	0.704192	+	0.710009i	$0.251309\pi$
$282$	1.00520	0.0598587
$283$	23.6814	1.40772	0.703858	−	0.710341i	$-0.251459\pi$
$283$	23.6814	1.40772	0.703858	+	0.710341i	$0.251459\pi$
$284$	−38.9445	−2.31093
$285$	−10.5411	−0.624400
$286$	−12.5665	−0.743074
$287$	0	0
$288$	3.55007	0.209190
$289$	7.31715	0.430421
$290$	87.5039	5.13840
$291$	3.07116	0.180034
$292$	−11.3225	−0.662598
$293$	21.1268	1.23424	0.617121	−	0.786868i	$-0.288299\pi$
$293$	21.1268	1.23424	0.617121	+	0.786868i	$0.288299\pi$
$294$	0	0
$295$	−7.92270	−0.461277
$296$	−53.5706	−3.11373
$297$	−1.72915	−0.100336
$298$	11.3352	0.656633
$299$	−2.88941	−0.167099
$300$	−59.0081	−3.40684
$301$	0	0
$302$	−11.3880	−0.655305
$303$	−1.08810	−0.0625096
$304$	14.8055	0.849153
$305$	−5.61799	−0.321685
$306$	−12.4031	−0.709037
$307$	−1.97923	−0.112961	−0.0564804	−	0.998404i	$-0.517988\pi$
$307$	−1.97923	−0.112961	−0.0564804	+	0.998404i	$0.517988\pi$
$308$	0	0
$309$	3.23110	0.183811
$310$	9.94534	0.564857
$311$	−3.89679	−0.220967	−0.110483	−	0.993878i	$-0.535240\pi$
$311$	−3.89679	−0.220967	−0.110483	+	0.993878i	$0.535240\pi$
$312$	16.9059	0.957110
$313$	17.6584	0.998111	0.499056	−	0.866570i	$-0.333680\pi$
$313$	17.6584	0.998111	0.499056	+	0.866570i	$0.333680\pi$
$314$	−8.21786	−0.463761
$315$	0	0
$316$	44.0716	2.47922
$317$	−12.3323	−0.692652	−0.346326	−	0.938114i	$-0.612571\pi$
$317$	−12.3323	−0.692652	−0.346326	+	0.938114i	$0.612571\pi$
$318$	−16.4623	−0.923161
$319$	13.9338	0.780142
$320$	−13.8101	−0.772008
$321$	0.936899	0.0522926
$322$	0	0
$323$	−12.0399	−0.669919
$324$	4.32625	0.240347
$325$	−39.4103	−2.18609
$326$	26.7669	1.48248
$327$	14.9782	0.828295
$328$	−38.6624	−2.13477
$329$	0	0
$330$	−18.7769	−1.03363
$331$	5.80565	0.319107	0.159554	−	0.987189i	$-0.448995\pi$
$331$	5.80565	0.319107	0.159554	+	0.987189i	$0.448995\pi$
$332$	−47.0861	−2.58419
$333$	−9.15581	−0.501735
$334$	7.54087	0.412618
$335$	−44.0973	−2.40930
$336$	0	0
$337$	−22.5441	−1.22805	−0.614027	−	0.789285i	$-0.710452\pi$
$337$	−22.5441	−1.22805	−0.614027	+	0.789285i	$0.710452\pi$
$338$	−11.6990	−0.636341
$339$	14.1424	0.768108
$340$	−92.1056	−4.99512
$341$	1.58366	0.0857599
$342$	6.14102	0.332068
$343$	0	0
$344$	62.8631	3.38935
$345$	−4.31735	−0.232439
$346$	−33.4513	−1.79835
$347$	−7.49730	−0.402476	−0.201238	−	0.979542i	$-0.564497\pi$
$347$	−7.49730	−0.402476	−0.201238	+	0.979542i	$0.564497\pi$
$348$	−34.8617	−1.86878
$349$	−7.97347	−0.426810	−0.213405	−	0.976964i	$-0.568455\pi$
$349$	−7.97347	−0.426810	−0.213405	+	0.976964i	$0.568455\pi$
$350$	0	0
$351$	2.88941	0.154225
$352$	6.13861	0.327189
$353$	−29.5289	−1.57167	−0.785833	−	0.618439i	$-0.787765\pi$
$353$	−29.5289	−1.57167	−0.785833	+	0.618439i	$0.787765\pi$
$354$	4.61560	0.245317
$355$	−38.8644	−2.06271
$356$	64.8342	3.43621
$357$	0	0
$358$	49.3727	2.60943
$359$	−13.1206	−0.692481	−0.346241	−	0.938146i	$-0.612542\pi$
$359$	−13.1206	−0.692481	−0.346241	+	0.938146i	$0.612542\pi$
$360$	25.2608	1.33136
$361$	−13.0388	−0.686252
$362$	48.3158	2.53942
$363$	8.01004	0.420418
$364$	0	0
$365$	−11.2992	−0.591427
$366$	3.27293	0.171079
$367$	5.26368	0.274762	0.137381	−	0.990518i	$-0.456132\pi$
$367$	5.26368	0.274762	0.137381	+	0.990518i	$0.456132\pi$
$368$	6.06395	0.316105
$369$	−6.60783	−0.343990
$370$	−99.4232	−5.16876
$371$	0	0
$372$	−3.96224	−0.205432
$373$	−12.6495	−0.654968	−0.327484	−	0.944857i	$-0.606201\pi$
$373$	−12.6495	−0.654968	−0.327484	+	0.944857i	$0.606201\pi$
$374$	−21.4468	−1.10899
$375$	−37.3000	−1.92616
$376$	−2.33834	−0.120591
$377$	−23.2834	−1.19915
$378$	0	0
$379$	12.7987	0.657426	0.328713	−	0.944430i	$-0.393385\pi$
$379$	12.7987	0.657426	0.328713	+	0.944430i	$0.393385\pi$
$380$	45.6034	2.33940
$381$	1.77968	0.0911756
$382$	−17.9931	−0.920609
$383$	−16.6269	−0.849595	−0.424797	−	0.905288i	$-0.639655\pi$
$383$	−16.6269	−0.849595	−0.424797	+	0.905288i	$0.639655\pi$
$384$	15.1456	0.772897
$385$	0	0
$386$	−55.2270	−2.81098
$387$	10.7440	0.546149
$388$	−13.2866	−0.674525
$389$	−29.8703	−1.51448	−0.757242	−	0.653134i	$-0.773454\pi$
$389$	−29.8703	−1.51448	−0.757242	+	0.653134i	$0.773454\pi$
$390$	31.3762	1.58880
$391$	−4.93124	−0.249384
$392$	0	0
$393$	−8.89264	−0.448574
$394$	8.07450	0.406787
$395$	43.9810	2.21292
$396$	7.48074	0.375921
$397$	−5.98437	−0.300347	−0.150173	−	0.988660i	$-0.547983\pi$
$397$	−5.98437	−0.300347	−0.150173	+	0.988660i	$0.547983\pi$
$398$	31.9858	1.60330
$399$	0	0
$400$	82.7095	4.13548
$401$	−15.8635	−0.792185	−0.396092	−	0.918211i	$-0.629634\pi$
$401$	−15.8635	−0.792185	−0.396092	+	0.918211i	$0.629634\pi$
$402$	25.6902	1.28131
$403$	−2.64629	−0.131821
$404$	4.70738	0.234201
$405$	4.31735	0.214531
$406$	0	0
$407$	−15.8318	−0.784752
$408$	28.8527	1.42842
$409$	24.9384	1.23313	0.616563	−	0.787306i	$-0.288525\pi$
$409$	24.9384	1.23313	0.616563	+	0.787306i	$0.288525\pi$
$410$	−71.7546	−3.54371
$411$	−0.247404	−0.0122035
$412$	−13.9785	−0.688673
$413$	0	0
$414$	2.51520	0.123616
$415$	−46.9893	−2.30661
$416$	−10.2576	−0.502921
$417$	8.59949	0.421119
$418$	10.6188	0.519380
$419$	−13.2262	−0.646140	−0.323070	−	0.946375i	$-0.604715\pi$
$419$	−13.2262	−0.646140	−0.323070	+	0.946375i	$0.604715\pi$
$420$	0	0
$421$	−5.82168	−0.283731	−0.141866	−	0.989886i	$-0.545310\pi$
$421$	−5.82168	−0.283731	−0.141866	+	0.989886i	$0.545310\pi$
$422$	−42.8841	−2.08757
$423$	−0.399649	−0.0194316
$424$	38.2955	1.85979
$425$	−67.2599	−3.26259
$426$	22.6416	1.09699
$427$	0	0
$428$	−4.05326	−0.195922
$429$	4.99623	0.241220
$430$	116.669	5.62630
$431$	6.21912	0.299565	0.149782	−	0.988719i	$-0.452143\pi$
$431$	6.21912	0.299565	0.149782	+	0.988719i	$0.452143\pi$
$432$	−6.06395	−0.291752
$433$	−2.16316	−0.103955	−0.0519774	−	0.998648i	$-0.516552\pi$
$433$	−2.16316	−0.103955	−0.0519774	+	0.998648i	$0.516552\pi$
$434$	0	0
$435$	−34.7900	−1.66805
$436$	−64.7993	−3.10333
$437$	2.44156	0.116796
$438$	6.58268	0.314533
$439$	11.5256	0.550085	0.275042	−	0.961432i	$-0.411308\pi$
$439$	11.5256	0.550085	0.275042	+	0.961432i	$0.411308\pi$
$440$	43.6798	2.08235
$441$	0	0
$442$	35.8376	1.70462
$443$	9.13040	0.433799	0.216899	−	0.976194i	$-0.430406\pi$
$443$	9.13040	0.433799	0.216899	+	0.976194i	$0.430406\pi$
$444$	39.6103	1.87982
$445$	64.7009	3.06712
$446$	58.6742	2.77830
$447$	−4.50669	−0.213159
$448$	0	0
$449$	−20.6827	−0.976079	−0.488039	−	0.872822i	$-0.662288\pi$
$449$	−20.6827	−0.976079	−0.488039	+	0.872822i	$0.662288\pi$
$450$	34.3063	1.61721
$451$	−11.4259	−0.538026
$452$	−61.1834	−2.87783
$453$	4.52766	0.212728
$454$	−19.3066	−0.906102
$455$	0	0
$456$	−14.2856	−0.668983
$457$	24.5958	1.15054	0.575271	−	0.817963i	$-0.304897\pi$
$457$	24.5958	1.15054	0.575271	+	0.817963i	$0.304897\pi$
$458$	−57.5318	−2.68829
$459$	4.93124	0.230171
$460$	18.6780	0.870864
$461$	−3.35047	−0.156047	−0.0780235	−	0.996952i	$-0.524861\pi$
$461$	−3.35047	−0.156047	−0.0780235	+	0.996952i	$0.524861\pi$
$462$	0	0
$463$	−30.2309	−1.40495	−0.702476	−	0.711708i	$-0.747922\pi$
$463$	−30.2309	−1.40495	−0.702476	+	0.711708i	$0.747922\pi$
$464$	48.8643	2.26847
$465$	−3.95409	−0.183366
$466$	59.2479	2.74460
$467$	−30.1416	−1.39479	−0.697394	−	0.716688i	$-0.745657\pi$
$467$	−30.1416	−1.39479	−0.697394	+	0.716688i	$0.745657\pi$
$468$	−12.5003	−0.577827
$469$	0	0
$470$	−4.33980	−0.200180
$471$	3.26727	0.150548
$472$	−10.7371	−0.494213
$473$	18.5780	0.854218
$474$	−25.6224	−1.17688
$475$	33.3018	1.52799
$476$	0	0
$477$	6.54512	0.299681
$478$	33.1577	1.51660
$479$	29.0344	1.32662	0.663308	−	0.748347i	$-0.269152\pi$
$479$	29.0344	1.32662	0.663308	+	0.748347i	$0.269152\pi$
$480$	−15.3269	−0.699575
$481$	26.4549	1.20624
$482$	−43.4301	−1.97819
$483$	0	0
$484$	−34.6534	−1.57516
$485$	−13.2593	−0.602072
$486$	−2.51520	−0.114092
$487$	−17.3057	−0.784195	−0.392097	−	0.919924i	$-0.628250\pi$
$487$	−17.3057	−0.784195	−0.392097	+	0.919924i	$0.628250\pi$
$488$	−7.61365	−0.344654
$489$	−10.6420	−0.481250
$490$	0	0
$491$	14.2287	0.642133	0.321067	−	0.947057i	$-0.395959\pi$
$491$	14.2287	0.642133	0.321067	+	0.947057i	$0.395959\pi$
$492$	28.5871	1.28881
$493$	−39.7368	−1.78965
$494$	−17.7439	−0.798337
$495$	7.46536	0.335543
$496$	5.55372	0.249369
$497$	0	0
$498$	27.3750	1.22670
$499$	11.1172	0.497672	0.248836	−	0.968546i	$-0.419952\pi$
$499$	11.1172	0.497672	0.248836	+	0.968546i	$0.419952\pi$
$500$	161.369	7.21665
$501$	−2.99812	−0.133946
$502$	11.9461	0.533181
$503$	25.5401	1.13878	0.569389	−	0.822068i	$-0.307180\pi$
$503$	25.5401	1.13878	0.569389	+	0.822068i	$0.307180\pi$
$504$	0	0
$505$	4.69770	0.209045
$506$	4.34917	0.193344
$507$	4.65131	0.206572
$508$	−7.69933	−0.341602
$509$	30.3594	1.34566	0.672829	−	0.739798i	$-0.265079\pi$
$509$	30.3594	1.34566	0.672829	+	0.739798i	$0.265079\pi$
$510$	53.5485	2.37117
$511$	0	0
$512$	−49.4328	−2.18464
$513$	−2.44156	−0.107798
$514$	3.59381	0.158516
$515$	−13.9498	−0.614701
$516$	−46.4813	−2.04622
$517$	−0.691053	−0.0303925
$518$	0	0
$519$	13.2996	0.583789
$520$	−72.9889	−3.20077
$521$	−24.7007	−1.08216	−0.541079	−	0.840972i	$-0.681984\pi$
$521$	−24.7007	−1.08216	−0.541079	+	0.840972i	$0.681984\pi$
$522$	20.2679	0.887104
$523$	−28.5353	−1.24776	−0.623881	−	0.781519i	$-0.714445\pi$
$523$	−28.5353	−1.24776	−0.623881	+	0.781519i	$0.714445\pi$
$524$	38.4718	1.68065
$525$	0	0
$526$	22.1777	0.966994
$527$	−4.51632	−0.196734
$528$	−10.4855	−0.456322
$529$	1.00000	0.0434783
$530$	71.0737	3.08724
$531$	−1.83508	−0.0796357
$532$	0	0
$533$	19.0927	0.826998
$534$	−37.6934	−1.63115
$535$	−4.04493	−0.174877
$536$	−59.7619	−2.58132
$537$	−19.6297	−0.847084
$538$	−32.4928	−1.40086
$539$	0	0
$540$	−18.6780	−0.803771
$541$	−7.74392	−0.332937	−0.166469	−	0.986047i	$-0.553236\pi$
$541$	−7.74392	−0.332937	−0.166469	+	0.986047i	$0.553236\pi$
$542$	33.5743	1.44214
$543$	−19.2095	−0.824358
$544$	−17.5063	−0.750575
$545$	−64.6661	−2.76999
$546$	0	0
$547$	36.8996	1.57771	0.788856	−	0.614578i	$-0.210674\pi$
$547$	36.8996	1.57771	0.788856	+	0.614578i	$0.210674\pi$
$548$	1.07033	0.0457222
$549$	−1.30126	−0.0555363
$550$	59.3207	2.52944
$551$	19.6745	0.838162
$552$	−5.85100	−0.249035
$553$	0	0
$554$	−38.9821	−1.65619
$555$	39.5289	1.67791
$556$	−37.2035	−1.57778
$557$	28.2645	1.19760	0.598802	−	0.800897i	$-0.295644\pi$
$557$	28.2645	1.19760	0.598802	+	0.800897i	$0.295644\pi$
$558$	2.30357	0.0975180
$559$	−31.0438	−1.31301
$560$	0	0
$561$	8.52686	0.360004
$562$	59.3810	2.50484
$563$	−9.62212	−0.405524	−0.202762	−	0.979228i	$-0.564992\pi$
$563$	−9.62212	−0.405524	−0.202762	+	0.979228i	$0.564992\pi$
$564$	1.72898	0.0728032
$565$	−61.0576	−2.56871
$566$	59.5637	2.50365
$567$	0	0
$568$	−52.6701	−2.20999
$569$	−15.7146	−0.658791	−0.329396	−	0.944192i	$-0.606845\pi$
$569$	−15.7146	−0.658791	−0.329396	+	0.944192i	$0.606845\pi$
$570$	−26.5130	−1.11051
$571$	11.3442	0.474739	0.237369	−	0.971419i	$-0.423715\pi$
$571$	11.3442	0.474739	0.237369	+	0.971419i	$0.423715\pi$
$572$	−21.6149	−0.903766
$573$	7.15375	0.298852
$574$	0	0
$575$	13.6396	0.568809
$576$	−3.19874	−0.133281
$577$	−7.95051	−0.330984	−0.165492	−	0.986211i	$-0.552921\pi$
$577$	−7.95051	−0.330984	−0.165492	+	0.986211i	$0.552921\pi$
$578$	18.4041	0.765511
$579$	21.9573	0.912513
$580$	150.510	6.24959
$581$	0	0
$582$	7.72458	0.320194
$583$	11.3175	0.468723
$584$	−15.3130	−0.633655
$585$	−12.4746	−0.515762
$586$	53.1383	2.19512
$587$	21.2897	0.878718	0.439359	−	0.898311i	$-0.355206\pi$
$587$	21.2897	0.878718	0.439359	+	0.898311i	$0.355206\pi$
$588$	0	0
$589$	2.23613	0.0921379
$590$	−19.9272	−0.820390
$591$	−3.21028	−0.132053
$592$	−55.5203	−2.28187
$593$	−9.67715	−0.397393	−0.198696	−	0.980061i	$-0.563671\pi$
$593$	−9.67715	−0.397393	−0.198696	+	0.980061i	$0.563671\pi$
$594$	−4.34917	−0.178448
$595$	0	0
$596$	19.4971	0.798631
$597$	−12.7170	−0.520471
$598$	−7.26746	−0.297188
$599$	25.9792	1.06148	0.530740	−	0.847535i	$-0.321914\pi$
$599$	25.9792	1.06148	0.530740	+	0.847535i	$0.321914\pi$
$600$	−79.8050	−3.25802
$601$	31.2857	1.27617	0.638084	−	0.769967i	$-0.279727\pi$
$601$	31.2857	1.27617	0.638084	+	0.769967i	$0.279727\pi$
$602$	0	0
$603$	−10.2140	−0.415945
$604$	−19.5878	−0.797015
$605$	−34.5822	−1.40597
$606$	−2.73679	−0.111174
$607$	28.9163	1.17368	0.586838	−	0.809704i	$-0.300372\pi$
$607$	28.9163	1.17368	0.586838	+	0.809704i	$0.300372\pi$
$608$	8.66771	0.351522
$609$	0	0
$610$	−14.1304	−0.572123
$611$	1.15475	0.0467162
$612$	−21.3338	−0.862367
$613$	−47.9848	−1.93809	−0.969043	−	0.246892i	$-0.920591\pi$
$613$	−47.9848	−1.93809	−0.969043	+	0.246892i	$0.920591\pi$
$614$	−4.97818	−0.200903
$615$	28.5283	1.15037
$616$	0	0
$617$	41.9964	1.69071	0.845355	−	0.534205i	$-0.179389\pi$
$617$	41.9964	1.69071	0.845355	+	0.534205i	$0.179389\pi$
$618$	8.12686	0.326910
$619$	−9.42381	−0.378775	−0.189388	−	0.981902i	$-0.560650\pi$
$619$	−9.42381	−0.378775	−0.189388	+	0.981902i	$0.560650\pi$
$620$	17.1064	0.687009
$621$	−1.00000	−0.0401286
$622$	−9.80123	−0.392994
$623$	0	0
$624$	17.5212	0.701411
$625$	92.8396	3.71358
$626$	44.4144	1.77516
$627$	−4.22183	−0.168603
$628$	−14.1350	−0.564050
$629$	45.1495	1.80023
$630$	0	0
$631$	6.84273	0.272405	0.136202	−	0.990681i	$-0.456510\pi$
$631$	6.84273	0.272405	0.136202	+	0.990681i	$0.456510\pi$
$632$	59.6042	2.37093
$633$	17.0500	0.677675
$634$	−31.0183	−1.23189
$635$	−7.68350	−0.304910
$636$	−28.3159	−1.12280
$637$	0	0
$638$	35.0463	1.38750
$639$	−9.00190	−0.356110
$640$	−65.3891	−2.58473
$641$	7.02021	0.277282	0.138641	−	0.990343i	$-0.455727\pi$
$641$	7.02021	0.277282	0.138641	+	0.990343i	$0.455727\pi$
$642$	2.35649	0.0930033
$643$	−47.1743	−1.86037	−0.930185	−	0.367090i	$-0.880354\pi$
$643$	−47.1743	−1.86037	−0.930185	+	0.367090i	$0.880354\pi$
$644$	0	0
$645$	−46.3857	−1.82643
$646$	−30.2829	−1.19146
$647$	23.9670	0.942239	0.471119	−	0.882070i	$-0.343850\pi$
$647$	23.9670	0.942239	0.471119	+	0.882070i	$0.343850\pi$
$648$	5.85100	0.229849
$649$	−3.17313	−0.124556
$650$	−99.1249	−3.88800
$651$	0	0
$652$	46.0401	1.80307
$653$	−18.3313	−0.717359	−0.358679	−	0.933461i	$-0.616773\pi$
$653$	−18.3313	−0.717359	−0.358679	+	0.933461i	$0.616773\pi$
$654$	37.6732	1.47314
$655$	38.3927	1.50013
$656$	−40.0695	−1.56445
$657$	−2.61716	−0.102105
$658$	0	0
$659$	16.4341	0.640183	0.320092	−	0.947387i	$-0.396286\pi$
$659$	16.4341	0.640183	0.320092	+	0.947387i	$0.396286\pi$
$660$	−32.2970	−1.25716
$661$	−30.0350	−1.16823	−0.584113	−	0.811672i	$-0.698558\pi$
$661$	−30.0350	−1.16823	−0.584113	+	0.811672i	$0.698558\pi$
$662$	14.6024	0.567538
$663$	−14.2484	−0.553361
$664$	−63.6812	−2.47131
$665$	0	0
$666$	−23.0287	−0.892345
$667$	8.05817	0.312014
$668$	12.9706	0.501848
$669$	−23.3278	−0.901906
$670$	−110.914	−4.28497
$671$	−2.25007	−0.0868630
$672$	0	0
$673$	17.0642	0.657776	0.328888	−	0.944369i	$-0.393326\pi$
$673$	17.0642	0.657776	0.328888	+	0.944369i	$0.393326\pi$
$674$	−56.7030	−2.18412
$675$	−13.6396	−0.524987
$676$	−20.1227	−0.773951
$677$	−37.6555	−1.44722	−0.723610	−	0.690209i	$-0.757518\pi$
$677$	−37.6555	−1.44722	−0.723610	+	0.690209i	$0.757518\pi$
$678$	35.5709	1.36609
$679$	0	0
$680$	−124.567	−4.77694
$681$	7.67594	0.294143
$682$	3.98322	0.152526
$683$	−40.7749	−1.56021	−0.780104	−	0.625649i	$-0.784834\pi$
$683$	−40.7749	−1.56021	−0.780104	+	0.625649i	$0.784834\pi$
$684$	10.5628	0.403879
$685$	1.06813	0.0408111
$686$	0	0
$687$	22.8736	0.872683
$688$	65.1511	2.48386
$689$	−18.9116	−0.720473
$690$	−10.8590	−0.413396
$691$	3.98906	0.151751	0.0758756	−	0.997117i	$-0.475825\pi$
$691$	3.98906	0.151751	0.0758756	+	0.997117i	$0.475825\pi$
$692$	−57.5376	−2.18725
$693$	0	0
$694$	−18.8572	−0.715811
$695$	−37.1270	−1.40831
$696$	−47.1483	−1.78715
$697$	32.5848	1.23424
$698$	−20.0549	−0.759089
$699$	−23.5559	−0.890965
$700$	0	0
$701$	3.27653	0.123753	0.0618763	−	0.998084i	$-0.480292\pi$
$701$	3.27653	0.123753	0.0618763	+	0.998084i	$0.480292\pi$
$702$	7.26746	0.274292
$703$	−22.3545	−0.843114
$704$	−5.53111	−0.208461
$705$	1.72543	0.0649833
$706$	−74.2712	−2.79523
$707$	0	0
$708$	7.93902	0.298367
$709$	−7.16279	−0.269004	−0.134502	−	0.990913i	$-0.542944\pi$
$709$	−7.16279	−0.269004	−0.134502	+	0.990913i	$0.542944\pi$
$710$	−97.7519	−3.66856
$711$	10.1870	0.382043
$712$	87.6844	3.28611
$713$	0.915859	0.0342992
$714$	0	0
$715$	−21.5705	−0.806690
$716$	84.9230	3.17372
$717$	−13.1829	−0.492325
$718$	−33.0011	−1.23159
$719$	49.3742	1.84135	0.920673	−	0.390335i	$-0.127641\pi$
$719$	49.3742	1.84135	0.920673	+	0.390335i	$0.127641\pi$
$720$	26.1802	0.975679
$721$	0	0
$722$	−32.7952	−1.22051
$723$	17.2670	0.642168
$724$	83.1051	3.08858
$725$	109.910	4.08195
$726$	20.1469	0.747721
$727$	−15.4034	−0.571281	−0.285640	−	0.958337i	$-0.592206\pi$
$727$	−15.4034	−0.571281	−0.285640	+	0.958337i	$0.592206\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−28.4198	−1.05186
$731$	−52.9813	−1.95958
$732$	5.62957	0.208075
$733$	12.2110	0.451025	0.225512	−	0.974240i	$-0.427594\pi$
$733$	12.2110	0.451025	0.225512	+	0.974240i	$0.427594\pi$
$734$	13.2392	0.488669
$735$	0	0
$736$	3.55007	0.130857
$737$	−17.6615	−0.650570
$738$	−16.6200	−0.611792
$739$	32.4803	1.19481	0.597404	−	0.801940i	$-0.296199\pi$
$739$	32.4803	1.19481	0.597404	+	0.801940i	$0.296199\pi$
$740$	−171.012	−6.28652
$741$	7.05467	0.259160
$742$	0	0
$743$	−40.1671	−1.47359	−0.736795	−	0.676117i	$-0.763662\pi$
$743$	−40.1671	−1.47359	−0.736795	+	0.676117i	$0.763662\pi$
$744$	−5.35869	−0.196459
$745$	19.4570	0.712848
$746$	−31.8162	−1.16487
$747$	−10.8838	−0.398218
$748$	−36.8893	−1.34881
$749$	0	0
$750$	−93.8171	−3.42572
$751$	44.3036	1.61666	0.808330	−	0.588729i	$-0.200372\pi$
$751$	44.3036	1.61666	0.808330	+	0.588729i	$0.200372\pi$
$752$	−2.42345	−0.0883741
$753$	−4.74956	−0.173084
$754$	−58.5624	−2.13272
$755$	−19.5475	−0.711406
$756$	0	0
$757$	41.4696	1.50724	0.753620	−	0.657311i	$-0.228306\pi$
$757$	41.4696	1.50724	0.753620	+	0.657311i	$0.228306\pi$
$758$	32.1914	1.16924
$759$	−1.72915	−0.0627642
$760$	61.6758	2.23722
$761$	−3.17300	−0.115021	−0.0575107	−	0.998345i	$-0.518316\pi$
$761$	−3.17300	−0.115021	−0.0575107	+	0.998345i	$0.518316\pi$
$762$	4.47625	0.162157
$763$	0	0
$764$	−30.9489	−1.11969
$765$	−21.2899	−0.769739
$766$	−41.8200	−1.51102
$767$	5.30230	0.191455
$768$	31.6969	1.14376
$769$	−13.6487	−0.492184	−0.246092	−	0.969246i	$-0.579147\pi$
$769$	−13.6487	−0.492184	−0.246092	+	0.969246i	$0.579147\pi$
$770$	0	0
$771$	−1.42884	−0.0514582
$772$	−94.9927	−3.41886
$773$	−28.4748	−1.02417	−0.512083	−	0.858936i	$-0.671126\pi$
$773$	−28.4748	−1.02417	−0.512083	+	0.858936i	$0.671126\pi$
$774$	27.0234	0.971335
$775$	12.4919	0.448723
$776$	−17.9693	−0.645061
$777$	0	0
$778$	−75.1299	−2.69354
$779$	−16.1334	−0.578040
$780$	53.9683	1.93237
$781$	−15.5656	−0.556982
$782$	−12.4031	−0.443533
$783$	−8.05817	−0.287975
$784$	0	0
$785$	−14.1060	−0.503464
$786$	−22.3668	−0.797797
$787$	48.0679	1.71343	0.856717	−	0.515786i	$-0.172500\pi$
$787$	48.0679	1.71343	0.856717	+	0.515786i	$0.172500\pi$
$788$	13.8885	0.494756
$789$	−8.81746	−0.313910
$790$	110.621	3.93572
$791$	0	0
$792$	10.1173	0.359501
$793$	3.75987	0.133517
$794$	−15.0519	−0.534172
$795$	−28.2576	−1.00219
$796$	55.0168	1.95002
$797$	−28.0705	−0.994308	−0.497154	−	0.867662i	$-0.665622\pi$
$797$	−28.0705	−0.994308	−0.497154	+	0.867662i	$0.665622\pi$
$798$	0	0
$799$	1.97077	0.0697207
$800$	48.4214	1.71195
$801$	14.9862	0.529513
$802$	−39.8999	−1.40892
$803$	−4.52546	−0.159700
$804$	44.1882	1.55840
$805$	0	0
$806$	−6.65597	−0.234446
$807$	12.9185	0.454754
$808$	6.36645	0.223971
$809$	42.7600	1.50336	0.751681	−	0.659527i	$-0.229243\pi$
$809$	42.7600	1.50336	0.751681	+	0.659527i	$0.229243\pi$
$810$	10.8590	0.381547
$811$	50.7214	1.78107	0.890534	−	0.454916i	$-0.150331\pi$
$811$	50.7214	1.78107	0.890534	+	0.454916i	$0.150331\pi$
$812$	0	0
$813$	−13.3485	−0.468153
$814$	−39.8201	−1.39569
$815$	45.9455	1.60940
$816$	29.9028	1.04681
$817$	26.2321	0.917746
$818$	62.7252	2.19314
$819$	0	0
$820$	−123.421	−4.31004
$821$	42.2837	1.47571	0.737856	−	0.674959i	$-0.235839\pi$
$821$	42.2837	1.47571	0.737856	+	0.674959i	$0.235839\pi$
$822$	−0.622271	−0.0217042
$823$	−16.4856	−0.574650	−0.287325	−	0.957833i	$-0.592766\pi$
$823$	−16.4856	−0.574650	−0.287325	+	0.957833i	$0.592766\pi$
$824$	−18.9051	−0.658591
$825$	−23.5848	−0.821119
$826$	0	0
$827$	21.3447	0.742229	0.371115	−	0.928587i	$-0.378976\pi$
$827$	21.3447	0.742229	0.371115	+	0.928587i	$0.378976\pi$
$828$	4.32625	0.150348
$829$	8.82638	0.306553	0.153276	−	0.988183i	$-0.451018\pi$
$829$	8.82638	0.306553	0.153276	+	0.988183i	$0.451018\pi$
$830$	−118.188	−4.10235
$831$	15.4986	0.537640
$832$	9.24248	0.320425
$833$	0	0
$834$	21.6295	0.748967
$835$	12.9439	0.447943
$836$	18.2647	0.631697
$837$	−0.915859	−0.0316567
$838$	−33.2665	−1.14917
$839$	−32.7270	−1.12986	−0.564932	−	0.825138i	$-0.691097\pi$
$839$	−32.7270	−1.12986	−0.564932	+	0.825138i	$0.691097\pi$
$840$	0	0
$841$	35.9341	1.23911
$842$	−14.6427	−0.504621
$843$	−23.6088	−0.813131
$844$	−73.7624	−2.53901
$845$	−20.0813	−0.690819
$846$	−1.00520	−0.0345594
$847$	0	0
$848$	39.6893	1.36294
$849$	−23.6814	−0.812745
$850$	−169.172	−5.80257
$851$	−9.15581	−0.313857
$852$	38.9445	1.33422
$853$	8.42097	0.288329	0.144164	−	0.989554i	$-0.453951\pi$
$853$	8.42097	0.288329	0.144164	+	0.989554i	$0.453951\pi$
$854$	0	0
$855$	10.5411	0.360497
$856$	−5.48179	−0.187364
$857$	−5.60723	−0.191539	−0.0957697	−	0.995404i	$-0.530531\pi$
$857$	−5.60723	−0.191539	−0.0957697	+	0.995404i	$0.530531\pi$
$858$	12.5665	0.429014
$859$	6.20674	0.211771	0.105886	−	0.994378i	$-0.466232\pi$
$859$	6.20674	0.211771	0.105886	+	0.994378i	$0.466232\pi$
$860$	200.676	6.84300
$861$	0	0
$862$	15.6424	0.532781
$863$	−7.30992	−0.248833	−0.124416	−	0.992230i	$-0.539706\pi$
$863$	−7.30992	−0.248833	−0.124416	+	0.992230i	$0.539706\pi$
$864$	−3.55007	−0.120776
$865$	−57.4192	−1.95231
$866$	−5.44079	−0.184886
$867$	−7.31715	−0.248504
$868$	0	0
$869$	17.6149	0.597544
$870$	−87.5039	−2.96666
$871$	29.5124	0.999988
$872$	−87.6372	−2.96777
$873$	−3.07116	−0.103943
$874$	6.14102	0.207723
$875$	0	0
$876$	11.3225	0.382551
$877$	−32.7872	−1.10715	−0.553573	−	0.832801i	$-0.686736\pi$
$877$	−32.7872	−1.10715	−0.553573	+	0.832801i	$0.686736\pi$
$878$	28.9891	0.978335
$879$	−21.1268	−0.712590
$880$	45.2695	1.52604
$881$	17.0828	0.575533	0.287767	−	0.957701i	$-0.407087\pi$
$881$	17.0828	0.575533	0.287767	+	0.957701i	$0.407087\pi$
$882$	0	0
$883$	26.9824	0.908030	0.454015	−	0.890994i	$-0.349991\pi$
$883$	26.9824	0.908030	0.454015	+	0.890994i	$0.349991\pi$
$884$	61.6421	2.07325
$885$	7.92270	0.266319
$886$	22.9648	0.771518
$887$	6.80466	0.228478	0.114239	−	0.993453i	$-0.463557\pi$
$887$	6.80466	0.228478	0.114239	+	0.993453i	$0.463557\pi$
$888$	53.5706	1.79771
$889$	0	0
$890$	162.736	5.45492
$891$	1.72915	0.0579287
$892$	100.922	3.37912
$893$	−0.975766	−0.0326528
$894$	−11.3352	−0.379107
$895$	84.7484	2.83283
$896$	0	0
$897$	2.88941	0.0964746
$898$	−52.0213	−1.73597
$899$	7.38015	0.246142
$900$	59.0081	1.96694
$901$	−32.2756	−1.07526
$902$	−28.7386	−0.956889
$903$	0	0
$904$	−82.7469	−2.75212
$905$	82.9342	2.75683
$906$	11.3880	0.378340
$907$	−5.42913	−0.180271	−0.0901357	−	0.995929i	$-0.528730\pi$
$907$	−5.42913	−0.180271	−0.0901357	+	0.995929i	$0.528730\pi$
$908$	−33.2081	−1.10205
$909$	1.08810	0.0360899
$910$	0	0
$911$	−15.8106	−0.523829	−0.261914	−	0.965091i	$-0.584354\pi$
$911$	−15.8106	−0.523829	−0.261914	+	0.965091i	$0.584354\pi$
$912$	−14.8055	−0.490259
$913$	−18.8198	−0.622843
$914$	61.8634	2.04626
$915$	5.61799	0.185725
$916$	−98.9571	−3.26963
$917$	0	0
$918$	12.4031	0.409363
$919$	37.3581	1.23233	0.616165	−	0.787617i	$-0.288686\pi$
$919$	37.3581	1.23233	0.616165	+	0.787617i	$0.288686\pi$
$920$	25.2608	0.832825
$921$	1.97923	0.0652180
$922$	−8.42712	−0.277532
$923$	26.0102	0.856135
$924$	0	0
$925$	−124.881	−4.10607
$926$	−76.0370	−2.49873
$927$	−3.23110	−0.106123
$928$	28.6071	0.939073
$929$	32.7069	1.07308	0.536539	−	0.843875i	$-0.319731\pi$
$929$	32.7069	1.07308	0.536539	+	0.843875i	$0.319731\pi$
$930$	−9.94534	−0.326121
$931$	0	0
$932$	101.909	3.33813
$933$	3.89679	0.127575
$934$	−75.8123	−2.48065
$935$	−36.8135	−1.20393
$936$	−16.9059	−0.552588
$937$	49.2657	1.60944	0.804721	−	0.593654i	$-0.202315\pi$
$937$	49.2657	1.60944	0.804721	+	0.593654i	$0.202315\pi$
$938$	0	0
$939$	−17.6584	−0.576260
$940$	−7.46462	−0.243469
$941$	−10.8684	−0.354299	−0.177149	−	0.984184i	$-0.556688\pi$
$941$	−10.8684	−0.354299	−0.177149	+	0.984184i	$0.556688\pi$
$942$	8.21786	0.267752
$943$	−6.60783	−0.215181
$944$	−11.1278	−0.362180
$945$	0	0
$946$	46.7275	1.51924
$947$	31.5907	1.02656	0.513279	−	0.858222i	$-0.328431\pi$
$947$	31.5907	1.02656	0.513279	+	0.858222i	$0.328431\pi$
$948$	−44.0716	−1.43138
$949$	7.56204	0.245474
$950$	83.7608	2.71756
$951$	12.3323	0.399903
$952$	0	0
$953$	−7.60480	−0.246344	−0.123172	−	0.992385i	$-0.539307\pi$
$953$	−7.60480	−0.246344	−0.123172	+	0.992385i	$0.539307\pi$
$954$	16.4623	0.532987
$955$	−30.8853	−0.999424
$956$	57.0326	1.84457
$957$	−13.9338	−0.450415
$958$	73.0274	2.35941
$959$	0	0
$960$	13.8101	0.445719
$961$	−30.1612	−0.972942
$962$	66.5394	2.14532
$963$	−0.936899	−0.0301911
$964$	−74.7015	−2.40597
$965$	−94.7973	−3.05163
$966$	0	0
$967$	10.3379	0.332446	0.166223	−	0.986088i	$-0.446843\pi$
$967$	10.3379	0.332446	0.166223	+	0.986088i	$0.446843\pi$
$968$	−46.8667	−1.50635
$969$	12.0399	0.386778
$970$	−33.3498	−1.07080
$971$	19.7589	0.634095	0.317047	−	0.948410i	$-0.397309\pi$
$971$	19.7589	0.634095	0.317047	+	0.948410i	$0.397309\pi$
$972$	−4.32625	−0.138765
$973$	0	0
$974$	−43.5273	−1.39470
$975$	39.4103	1.26214
$976$	−7.89075	−0.252577
$977$	−19.6177	−0.627626	−0.313813	−	0.949485i	$-0.601607\pi$
$977$	−19.6177	−0.627626	−0.313813	+	0.949485i	$0.601607\pi$
$978$	−26.7669	−0.855911
$979$	25.9135	0.828198
$980$	0	0
$981$	−14.9782	−0.478216
$982$	35.7881	1.14205
$983$	−15.1056	−0.481794	−0.240897	−	0.970551i	$-0.577442\pi$
$983$	−15.1056	−0.481794	−0.240897	+	0.970551i	$0.577442\pi$
$984$	38.6624	1.23251
$985$	13.8599	0.441613
$986$	−99.9461	−3.18293
$987$	0	0
$988$	−30.5203	−0.970979
$989$	10.7440	0.341640
$990$	18.7769	0.596769
$991$	41.2825	1.31138	0.655690	−	0.755030i	$-0.272378\pi$
$991$	41.2825	1.31138	0.655690	+	0.755030i	$0.272378\pi$
$992$	3.25136	0.103231
$993$	−5.80565	−0.184237
$994$	0	0
$995$	54.9037	1.74056
$996$	47.0861	1.49198
$997$	18.5381	0.587107	0.293554	−	0.955943i	$-0.405162\pi$
$997$	18.5381	0.587107	0.293554	+	0.955943i	$0.405162\pi$
$998$	27.9619	0.885119
$999$	9.15581	0.289677

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3381.2.a.bi.1.9		10
7.2	even	3		483.2.i.h.277.2	✓	20
7.4	even	3		483.2.i.h.415.2	yes	20
7.6	odd	2		3381.2.a.bj.1.9		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.i.h.277.2	✓	20	7.2	even	3
483.2.i.h.415.2	yes	20	7.4	even	3
3381.2.a.bi.1.9		10	1.1	even	1	trivial
3381.2.a.bj.1.9		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)

\(f(q)\)	\(=\)	\(q+2.51520 q^{2} -1.00000 q^{3} +4.32625 q^{4} +4.31735 q^{5} -2.51520 q^{6} +5.85100 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.51520 q^{2} -1.00000 q^{3} +4.32625 q^{4} +4.31735 q^{5} -2.51520 q^{6} +5.85100 q^{8} +1.00000 q^{9} +10.8590 q^{10} +1.72915 q^{11} -4.32625 q^{12} -2.88941 q^{13} -4.31735 q^{15} +6.06395 q^{16} -4.93124 q^{17} +2.51520 q^{18} +2.44156 q^{19} +18.6780 q^{20} +4.34917 q^{22} +1.00000 q^{23} -5.85100 q^{24} +13.6396 q^{25} -7.26746 q^{26} -1.00000 q^{27} +8.05817 q^{29} -10.8590 q^{30} +0.915859 q^{31} +3.55007 q^{32} -1.72915 q^{33} -12.4031 q^{34} +4.32625 q^{36} -9.15581 q^{37} +6.14102 q^{38} +2.88941 q^{39} +25.2608 q^{40} -6.60783 q^{41} +10.7440 q^{43} +7.48074 q^{44} +4.31735 q^{45} +2.51520 q^{46} -0.399649 q^{47} -6.06395 q^{48} +34.3063 q^{50} +4.93124 q^{51} -12.5003 q^{52} +6.54512 q^{53} -2.51520 q^{54} +7.46536 q^{55} -2.44156 q^{57} +20.2679 q^{58} -1.83508 q^{59} -18.6780 q^{60} -1.30126 q^{61} +2.30357 q^{62} -3.19874 q^{64} -12.4746 q^{65} -4.34917 q^{66} -10.2140 q^{67} -21.3338 q^{68} -1.00000 q^{69} -9.00190 q^{71} +5.85100 q^{72} -2.61716 q^{73} -23.0287 q^{74} -13.6396 q^{75} +10.5628 q^{76} +7.26746 q^{78} +10.1870 q^{79} +26.1802 q^{80} +1.00000 q^{81} -16.6200 q^{82} -10.8838 q^{83} -21.2899 q^{85} +27.0234 q^{86} -8.05817 q^{87} +10.1173 q^{88} +14.9862 q^{89} +10.8590 q^{90} +4.32625 q^{92} -0.915859 q^{93} -1.00520 q^{94} +10.5411 q^{95} -3.55007 q^{96} -3.07116 q^{97} +1.72915 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 3 q^{2} - 10 q^{3} + 15 q^{4} - 5 q^{5} - 3 q^{6} + 9 q^{8} + 10 q^{9}+O(q^{10}) \) 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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