LMFDB - Embedded newform 3381.2.a.bc.1.5

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			1.5
Root			$-1.36549$ 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)

$f(q)$	$=$	$q+1.36549 q^{2} -1.00000 q^{3} -0.135449 q^{4} -1.32621 q^{5} -1.36549 q^{6} -2.91593 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.36549 q^{2} -1.00000 q^{3} -0.135449 q^{4} -1.32621 q^{5} -1.36549 q^{6} -2.91593 q^{8} +1.00000 q^{9} -1.81092 q^{10} -1.42009 q^{11} +0.135449 q^{12} +3.16661 q^{13} +1.32621 q^{15} -3.71076 q^{16} +1.15960 q^{17} +1.36549 q^{18} +8.57886 q^{19} +0.179634 q^{20} -1.93911 q^{22} -1.00000 q^{23} +2.91593 q^{24} -3.24116 q^{25} +4.32396 q^{26} -1.00000 q^{27} +7.45480 q^{29} +1.81092 q^{30} +1.86642 q^{31} +0.764868 q^{32} +1.42009 q^{33} +1.58342 q^{34} -0.135449 q^{36} -7.79838 q^{37} +11.7143 q^{38} -3.16661 q^{39} +3.86713 q^{40} -11.2258 q^{41} -11.8479 q^{43} +0.192350 q^{44} -1.32621 q^{45} -1.36549 q^{46} +1.73650 q^{47} +3.71076 q^{48} -4.42576 q^{50} -1.15960 q^{51} -0.428914 q^{52} -4.14898 q^{53} -1.36549 q^{54} +1.88333 q^{55} -8.57886 q^{57} +10.1794 q^{58} +12.6871 q^{59} -0.179634 q^{60} -13.8148 q^{61} +2.54857 q^{62} +8.46593 q^{64} -4.19959 q^{65} +1.93911 q^{66} -8.09295 q^{67} -0.157067 q^{68} +1.00000 q^{69} -5.18979 q^{71} -2.91593 q^{72} -11.3686 q^{73} -10.6486 q^{74} +3.24116 q^{75} -1.16200 q^{76} -4.32396 q^{78} -11.7365 q^{79} +4.92124 q^{80} +1.00000 q^{81} -15.3286 q^{82} +5.70566 q^{83} -1.53788 q^{85} -16.1781 q^{86} -7.45480 q^{87} +4.14087 q^{88} -6.35511 q^{89} -1.81092 q^{90} +0.135449 q^{92} -1.86642 q^{93} +2.37116 q^{94} -11.3774 q^{95} -0.764868 q^{96} +0.408396 q^{97} -1.42009 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.36549	0.965544	0.482772	−	0.875746i	$-0.339630\pi$
$2$	1.36549	0.965544	0.482772	+	0.875746i	$0.339630\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.135449	−0.0677246
$5$	−1.32621	−0.593100	−0.296550	−	0.955017i	$-0.595836\pi$
$5$	−1.32621	−0.593100	−0.296550	+	0.955017i	$0.595836\pi$
$6$	−1.36549	−0.557457
$7$	0	0
$7$	0	0
$8$	−2.91593	−1.03094
$9$	1.00000	0.333333
$10$	−1.81092	−0.572664
$11$	−1.42009	−0.428172	−0.214086	−	0.976815i	$-0.568677\pi$
$11$	−1.42009	−0.428172	−0.214086	+	0.976815i	$0.568677\pi$
$12$	0.135449	0.0391008
$13$	3.16661	0.878259	0.439129	−	0.898424i	$-0.355287\pi$
$13$	3.16661	0.878259	0.439129	+	0.898424i	$0.355287\pi$
$14$	0	0
$15$	1.32621	0.342426
$16$	−3.71076	−0.927689
$17$	1.15960	0.281245	0.140623	−	0.990063i	$-0.455090\pi$
$17$	1.15960	0.281245	0.140623	+	0.990063i	$0.455090\pi$
$18$	1.36549	0.321848
$19$	8.57886	1.96813	0.984063	−	0.177822i	$-0.0569051\pi$
$19$	8.57886	1.96813	0.984063	+	0.177822i	$0.0569051\pi$
$20$	0.179634	0.0401674
$21$	0	0
$22$	−1.93911	−0.413419
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	2.91593	0.595211
$25$	−3.24116	−0.648233
$26$	4.32396	0.847998
$27$	−1.00000	−0.192450
$28$	0	0
$29$	7.45480	1.38432	0.692161	−	0.721743i	$-0.256659\pi$
$29$	7.45480	1.38432	0.692161	+	0.721743i	$0.256659\pi$
$30$	1.81092	0.330628
$31$	1.86642	0.335219	0.167609	−	0.985853i	$-0.446395\pi$
$31$	1.86642	0.335219	0.167609	+	0.985853i	$0.446395\pi$
$32$	0.764868	0.135211
$33$	1.42009	0.247205
$34$	1.58342	0.271555
$35$	0	0
$36$	−0.135449	−0.0225749
$37$	−7.79838	−1.28205	−0.641023	−	0.767522i	$-0.721490\pi$
$37$	−7.79838	−1.28205	−0.641023	+	0.767522i	$0.721490\pi$
$38$	11.7143	1.90031
$39$	−3.16661	−0.507063
$40$	3.86713	0.611447
$41$	−11.2258	−1.75317	−0.876584	−	0.481248i	$-0.840183\pi$
$41$	−11.2258	−1.75317	−0.876584	+	0.481248i	$0.840183\pi$
$42$	0	0
$43$	−11.8479	−1.80679	−0.903393	−	0.428814i	$-0.858932\pi$
$43$	−11.8479	−1.80679	−0.903393	+	0.428814i	$0.858932\pi$
$44$	0.192350	0.0289978
$45$	−1.32621	−0.197700
$46$	−1.36549	−0.201330
$47$	1.73650	0.253294	0.126647	−	0.991948i	$-0.459578\pi$
$47$	1.73650	0.253294	0.126647	+	0.991948i	$0.459578\pi$
$48$	3.71076	0.535601
$49$	0	0
$50$	−4.42576	−0.625897
$51$	−1.15960	−0.162377
$52$	−0.428914	−0.0594797
$53$	−4.14898	−0.569906	−0.284953	−	0.958541i	$-0.591978\pi$
$53$	−4.14898	−0.569906	−0.284953	+	0.958541i	$0.591978\pi$
$54$	−1.36549	−0.185819
$55$	1.88333	0.253949
$56$	0	0
$57$	−8.57886	−1.13630
$58$	10.1794	1.33662
$59$	12.6871	1.65172	0.825862	−	0.563872i	$-0.190689\pi$
$59$	12.6871	1.65172	0.825862	+	0.563872i	$0.190689\pi$
$60$	−0.179634	−0.0231907
$61$	−13.8148	−1.76880	−0.884399	−	0.466731i	$-0.845432\pi$
$61$	−13.8148	−1.76880	−0.884399	+	0.466731i	$0.845432\pi$
$62$	2.54857	0.323669
$63$	0	0
$64$	8.46593	1.05824
$65$	−4.19959	−0.520895
$66$	1.93911	0.238688
$67$	−8.09295	−0.988711	−0.494355	−	0.869260i	$-0.664596\pi$
$67$	−8.09295	−0.988711	−0.494355	+	0.869260i	$0.664596\pi$
$68$	−0.157067	−0.0190472
$69$	1.00000	0.120386
$70$	0	0
$71$	−5.18979	−0.615915	−0.307957	−	0.951400i	$-0.599645\pi$
$71$	−5.18979	−0.615915	−0.307957	+	0.951400i	$0.599645\pi$
$72$	−2.91593	−0.343645
$73$	−11.3686	−1.33059	−0.665297	−	0.746579i	$-0.731695\pi$
$73$	−11.3686	−1.33059	−0.665297	+	0.746579i	$0.731695\pi$
$74$	−10.6486	−1.23787
$75$	3.24116	0.374257
$76$	−1.16200	−0.133291
$77$	0	0
$78$	−4.32396	−0.489592
$79$	−11.7365	−1.32046	−0.660228	−	0.751065i	$-0.729540\pi$
$79$	−11.7365	−1.32046	−0.660228	+	0.751065i	$0.729540\pi$
$80$	4.92124	0.550212
$81$	1.00000	0.111111
$82$	−15.3286	−1.69276
$83$	5.70566	0.626277	0.313139	−	0.949707i	$-0.398620\pi$
$83$	5.70566	0.626277	0.313139	+	0.949707i	$0.398620\pi$
$84$	0	0
$85$	−1.53788	−0.166806
$86$	−16.1781	−1.74453
$87$	−7.45480	−0.799238
$88$	4.14087	0.441418
$89$	−6.35511	−0.673641	−0.336820	−	0.941569i	$-0.609352\pi$
$89$	−6.35511	−0.673641	−0.336820	+	0.941569i	$0.609352\pi$
$90$	−1.81092	−0.190888
$91$	0	0
$92$	0.135449	0.0141216
$93$	−1.86642	−0.193539
$94$	2.37116	0.244567
$95$	−11.3774	−1.16729
$96$	−0.764868	−0.0780640
$97$	0.408396	0.0414663	0.0207331	−	0.999785i	$-0.493400\pi$
$97$	0.408396	0.0414663	0.0207331	+	0.999785i	$0.493400\pi$
$98$	0	0
$99$	−1.42009	−0.142724
$100$	0.439013	0.0439013
$101$	−0.723827	−0.0720235	−0.0360117	−	0.999351i	$-0.511465\pi$
$101$	−0.723827	−0.0720235	−0.0360117	+	0.999351i	$0.511465\pi$
$102$	−1.58342	−0.156782
$103$	−14.2739	−1.40645	−0.703225	−	0.710967i	$-0.748257\pi$
$103$	−14.2739	−1.40645	−0.703225	+	0.710967i	$0.748257\pi$
$104$	−9.23359	−0.905428
$105$	0	0
$106$	−5.66537	−0.550270
$107$	13.9959	1.35304	0.676520	−	0.736425i	$-0.263487\pi$
$107$	13.9959	1.35304	0.676520	+	0.736425i	$0.263487\pi$
$108$	0.135449	0.0130336
$109$	2.90945	0.278675	0.139338	−	0.990245i	$-0.455503\pi$
$109$	2.90945	0.278675	0.139338	+	0.990245i	$0.455503\pi$
$110$	2.57167	0.245199
$111$	7.79838	0.740190
$112$	0	0
$113$	18.6624	1.75561	0.877804	−	0.479020i	$-0.159008\pi$
$113$	18.6624	1.75561	0.877804	+	0.479020i	$0.159008\pi$
$114$	−11.7143	−1.09715
$115$	1.32621	0.123670
$116$	−1.00975	−0.0937526
$117$	3.16661	0.292753
$118$	17.3241	1.59481
$119$	0	0
$120$	−3.86713	−0.353019
$121$	−8.98335	−0.816669
$122$	−18.8639	−1.70785
$123$	11.2258	1.01219
$124$	−0.252805	−0.0227026
$125$	10.9295	0.977566
$126$	0	0
$127$	1.06631	0.0946196	0.0473098	−	0.998880i	$-0.484935\pi$
$127$	1.06631	0.0946196	0.0473098	+	0.998880i	$0.484935\pi$
$128$	10.0304	0.886567
$129$	11.8479	1.04315
$130$	−5.73448	−0.502947
$131$	−16.0144	−1.39919	−0.699593	−	0.714541i	$-0.746635\pi$
$131$	−16.0144	−1.39919	−0.699593	+	0.714541i	$0.746635\pi$
$132$	−0.192350	−0.0167419
$133$	0	0
$134$	−11.0508	−0.954644
$135$	1.32621	0.114142
$136$	−3.38132	−0.289946
$137$	0.927579	0.0792484	0.0396242	−	0.999215i	$-0.487384\pi$
$137$	0.927579	0.0792484	0.0396242	+	0.999215i	$0.487384\pi$
$138$	1.36549	0.116238
$139$	−4.22569	−0.358418	−0.179209	−	0.983811i	$-0.557354\pi$
$139$	−4.22569	−0.358418	−0.179209	+	0.983811i	$0.557354\pi$
$140$	0	0
$141$	−1.73650	−0.146239
$142$	−7.08658	−0.594693
$143$	−4.49686	−0.376046
$144$	−3.71076	−0.309230
$145$	−9.88664	−0.821040
$146$	−15.5237	−1.28475
$147$	0	0
$148$	1.05628	0.0868261
$149$	−16.4464	−1.34734	−0.673670	−	0.739032i	$-0.735283\pi$
$149$	−16.4464	−1.34734	−0.673670	+	0.739032i	$0.735283\pi$
$150$	4.42576	0.361362
$151$	−8.18838	−0.666361	−0.333180	−	0.942863i	$-0.608122\pi$
$151$	−8.18838	−0.666361	−0.333180	+	0.942863i	$0.608122\pi$
$152$	−25.0153	−2.02901
$153$	1.15960	0.0937484
$154$	0	0
$155$	−2.47527	−0.198818
$156$	0.428914	0.0343406
$157$	22.5151	1.79690	0.898452	−	0.439072i	$-0.144693\pi$
$157$	22.5151	1.79690	0.898452	+	0.439072i	$0.144693\pi$
$158$	−16.0260	−1.27496
$159$	4.14898	0.329036
$160$	−1.01438	−0.0801935
$161$	0	0
$162$	1.36549	0.107283
$163$	−1.46151	−0.114474	−0.0572370	−	0.998361i	$-0.518229\pi$
$163$	−1.46151	−0.114474	−0.0572370	+	0.998361i	$0.518229\pi$
$164$	1.52052	0.118733
$165$	−1.88333	−0.146617
$166$	7.79099	0.604698
$167$	2.76301	0.213808	0.106904	−	0.994269i	$-0.465906\pi$
$167$	2.76301	0.213808	0.106904	+	0.994269i	$0.465906\pi$
$168$	0	0
$169$	−2.97260	−0.228661
$170$	−2.09995	−0.161059
$171$	8.57886	0.656042
$172$	1.60479	0.122364
$173$	18.8661	1.43436	0.717182	−	0.696886i	$-0.245432\pi$
$173$	18.8661	1.43436	0.717182	+	0.696886i	$0.245432\pi$
$174$	−10.1794	−0.771700
$175$	0	0
$176$	5.26959	0.397210
$177$	−12.6871	−0.953623
$178$	−8.67782	−0.650430
$179$	−20.7182	−1.54855	−0.774276	−	0.632847i	$-0.781886\pi$
$179$	−20.7182	−1.54855	−0.774276	+	0.632847i	$0.781886\pi$
$180$	0.179634	0.0133891
$181$	0.686865	0.0510543	0.0255271	−	0.999674i	$-0.491874\pi$
$181$	0.686865	0.0510543	0.0255271	+	0.999674i	$0.491874\pi$
$182$	0	0
$183$	13.8148	1.02122
$184$	2.91593	0.214965
$185$	10.3423	0.760381
$186$	−2.54857	−0.186870
$187$	−1.64674	−0.120421
$188$	−0.235207	−0.0171542
$189$	0	0
$190$	−15.5356	−1.12707
$191$	1.09300	0.0790868	0.0395434	−	0.999218i	$-0.487410\pi$
$191$	1.09300	0.0790868	0.0395434	+	0.999218i	$0.487410\pi$
$192$	−8.46593	−0.610976
$193$	7.41394	0.533667	0.266833	−	0.963743i	$-0.414023\pi$
$193$	7.41394	0.533667	0.266833	+	0.963743i	$0.414023\pi$
$194$	0.557658	0.0400375
$195$	4.19959	0.300739
$196$	0	0
$197$	3.16080	0.225198	0.112599	−	0.993641i	$-0.464082\pi$
$197$	3.16080	0.225198	0.112599	+	0.993641i	$0.464082\pi$
$198$	−1.93911	−0.137806
$199$	−1.80928	−0.128257	−0.0641283	−	0.997942i	$-0.520427\pi$
$199$	−1.80928	−0.128257	−0.0641283	+	0.997942i	$0.520427\pi$
$200$	9.45099	0.668286
$201$	8.09295	0.570833
$202$	−0.988375	−0.0695419
$203$	0	0
$204$	0.157067	0.0109969
$205$	14.8877	1.03980
$206$	−19.4908	−1.35799
$207$	−1.00000	−0.0695048
$208$	−11.7505	−0.814751
$209$	−12.1827	−0.842696
$210$	0	0
$211$	−22.5516	−1.55252	−0.776260	−	0.630413i	$-0.782885\pi$
$211$	−22.5516	−1.55252	−0.776260	+	0.630413i	$0.782885\pi$
$212$	0.561976	0.0385967
$213$	5.18979	0.355599
$214$	19.1113	1.30642
$215$	15.7128	1.07160
$216$	2.91593	0.198404
$217$	0	0
$218$	3.97282	0.269073
$219$	11.3686	0.768218
$220$	−0.255096	−0.0171986
$221$	3.67201	0.247006
$222$	10.6486	0.714686
$223$	−14.4484	−0.967535	−0.483767	−	0.875197i	$-0.660732\pi$
$223$	−14.4484	−0.967535	−0.483767	+	0.875197i	$0.660732\pi$
$224$	0	0
$225$	−3.24116	−0.216078
$226$	25.4832	1.69512
$227$	−3.27881	−0.217622	−0.108811	−	0.994062i	$-0.534704\pi$
$227$	−3.27881	−0.217622	−0.108811	+	0.994062i	$0.534704\pi$
$228$	1.16200	0.0769553
$229$	−0.263933	−0.0174412	−0.00872059	−	0.999962i	$-0.502776\pi$
$229$	−0.263933	−0.0174412	−0.00872059	+	0.999962i	$0.502776\pi$
$230$	1.81092	0.119409
$231$	0	0
$232$	−21.7376	−1.42715
$233$	17.8509	1.16945	0.584727	−	0.811230i	$-0.301202\pi$
$233$	17.8509	1.16945	0.584727	+	0.811230i	$0.301202\pi$
$234$	4.32396	0.282666
$235$	−2.30296	−0.150229
$236$	−1.71846	−0.111862
$237$	11.7365	0.762366
$238$	0	0
$239$	1.68846	0.109217	0.0546086	−	0.998508i	$-0.482609\pi$
$239$	1.68846	0.109217	0.0546086	+	0.998508i	$0.482609\pi$
$240$	−4.92124	−0.317665
$241$	19.0420	1.22660	0.613300	−	0.789850i	$-0.289842\pi$
$241$	19.0420	1.22660	0.613300	+	0.789850i	$0.289842\pi$
$242$	−12.2666	−0.788530
$243$	−1.00000	−0.0641500
$244$	1.87120	0.119791
$245$	0	0
$246$	15.3286	0.977316
$247$	27.1659	1.72852
$248$	−5.44234	−0.345589
$249$	−5.70566	−0.361581
$250$	14.9241	0.943883
$251$	−20.3390	−1.28379	−0.641895	−	0.766793i	$-0.721851\pi$
$251$	−20.3390	−1.28379	−0.641895	+	0.766793i	$0.721851\pi$
$252$	0	0
$253$	1.42009	0.0892801
$254$	1.45603	0.0913594
$255$	1.53788	0.0963057
$256$	−3.23553	−0.202221
$257$	−9.62955	−0.600675	−0.300337	−	0.953833i	$-0.597099\pi$
$257$	−9.62955	−0.600675	−0.300337	+	0.953833i	$0.597099\pi$
$258$	16.1781	1.00721
$259$	0	0
$260$	0.568831	0.0352774
$261$	7.45480	0.461440
$262$	−21.8675	−1.35098
$263$	−4.85507	−0.299377	−0.149688	−	0.988733i	$-0.547827\pi$
$263$	−4.85507	−0.299377	−0.149688	+	0.988733i	$0.547827\pi$
$264$	−4.14087	−0.254853
$265$	5.50243	0.338011
$266$	0	0
$267$	6.35511	0.388927
$268$	1.09618	0.0669601
$269$	12.7386	0.776684	0.388342	−	0.921515i	$-0.373048\pi$
$269$	12.7386	0.776684	0.388342	+	0.921515i	$0.373048\pi$
$270$	1.81092	0.110209
$271$	−22.0021	−1.33653	−0.668265	−	0.743923i	$-0.732963\pi$
$271$	−22.0021	−1.33653	−0.668265	+	0.743923i	$0.732963\pi$
$272$	−4.30301	−0.260908
$273$	0	0
$274$	1.26660	0.0765179
$275$	4.60273	0.277555
$276$	−0.135449	−0.00815308
$277$	0.165444	0.00994059	0.00497030	−	0.999988i	$-0.498418\pi$
$277$	0.165444	0.00994059	0.00497030	+	0.999988i	$0.498418\pi$
$278$	−5.77012	−0.346069
$279$	1.86642	0.111740
$280$	0	0
$281$	−20.9797	−1.25155	−0.625773	−	0.780006i	$-0.715216\pi$
$281$	−20.9797	−1.25155	−0.625773	+	0.780006i	$0.715216\pi$
$282$	−2.37116	−0.141201
$283$	−0.814822	−0.0484362	−0.0242181	−	0.999707i	$-0.507710\pi$
$283$	−0.814822	−0.0484362	−0.0242181	+	0.999707i	$0.507710\pi$
$284$	0.702953	0.0417126
$285$	11.3774	0.673938
$286$	−6.14039	−0.363089
$287$	0	0
$288$	0.764868	0.0450703
$289$	−15.6553	−0.920901
$290$	−13.5001	−0.792751
$291$	−0.408396	−0.0239406
$292$	1.53987	0.0901139
$293$	−12.6589	−0.739543	−0.369771	−	0.929123i	$-0.620564\pi$
$293$	−12.6589	−0.739543	−0.369771	+	0.929123i	$0.620564\pi$
$294$	0	0
$295$	−16.8258	−0.979637
$296$	22.7395	1.32171
$297$	1.42009	0.0824018
$298$	−22.4573	−1.30092
$299$	−3.16661	−0.183130
$300$	−0.439013	−0.0253464
$301$	0	0
$302$	−11.1811	−0.643401
$303$	0.723827	0.0415828
$304$	−31.8340	−1.82581
$305$	18.3213	1.04907
$306$	1.58342	0.0905182
$307$	−3.03467	−0.173198	−0.0865989	−	0.996243i	$-0.527600\pi$
$307$	−3.03467	−0.173198	−0.0865989	+	0.996243i	$0.527600\pi$
$308$	0	0
$309$	14.2739	0.812014
$310$	−3.37994	−0.191968
$311$	27.4766	1.55806	0.779029	−	0.626988i	$-0.215713\pi$
$311$	27.4766	1.55806	0.779029	+	0.626988i	$0.215713\pi$
$312$	9.23359	0.522749
$313$	1.34203	0.0758558	0.0379279	−	0.999280i	$-0.487924\pi$
$313$	1.34203	0.0758558	0.0379279	+	0.999280i	$0.487924\pi$
$314$	30.7441	1.73499
$315$	0	0
$316$	1.58970	0.0894274
$317$	0.508616	0.0285667	0.0142834	−	0.999898i	$-0.495453\pi$
$317$	0.508616	0.0285667	0.0142834	+	0.999898i	$0.495453\pi$
$318$	5.66537	0.317698
$319$	−10.5865	−0.592728
$320$	−11.2276	−0.627642
$321$	−13.9959	−0.781178
$322$	0	0
$323$	9.94808	0.553526
$324$	−0.135449	−0.00752496
$325$	−10.2635	−0.569316
$326$	−1.99566	−0.110530
$327$	−2.90945	−0.160893
$328$	32.7335	1.80740
$329$	0	0
$330$	−2.57167	−0.141566
$331$	6.19033	0.340252	0.170126	−	0.985422i	$-0.445583\pi$
$331$	6.19033	0.340252	0.170126	+	0.985422i	$0.445583\pi$
$332$	−0.772827	−0.0424144
$333$	−7.79838	−0.427349
$334$	3.77284	0.206441
$335$	10.7330	0.586404
$336$	0	0
$337$	−5.07603	−0.276509	−0.138254	−	0.990397i	$-0.544149\pi$
$337$	−5.07603	−0.276509	−0.138254	+	0.990397i	$0.544149\pi$
$338$	−4.05904	−0.220783
$339$	−18.6624	−1.01360
$340$	0.208305	0.0112969
$341$	−2.65048	−0.143531
$342$	11.7143	0.633437
$343$	0	0
$344$	34.5476	1.86268
$345$	−1.32621	−0.0714008
$346$	25.7614	1.38494
$347$	−25.4952	−1.36865	−0.684326	−	0.729176i	$-0.739903\pi$
$347$	−25.4952	−1.36865	−0.684326	+	0.729176i	$0.739903\pi$
$348$	1.00975	0.0541281
$349$	−11.0135	−0.589541	−0.294771	−	0.955568i	$-0.595243\pi$
$349$	−11.0135	−0.589541	−0.294771	+	0.955568i	$0.595243\pi$
$350$	0	0
$351$	−3.16661	−0.169021
$352$	−1.08618	−0.0578935
$353$	−6.64781	−0.353827	−0.176914	−	0.984226i	$-0.556611\pi$
$353$	−6.64781	−0.353827	−0.176914	+	0.984226i	$0.556611\pi$
$354$	−17.3241	−0.920765
$355$	6.88276	0.365299
$356$	0.860795	0.0456221
$357$	0	0
$358$	−28.2904	−1.49520
$359$	−7.85473	−0.414557	−0.207278	−	0.978282i	$-0.566461\pi$
$359$	−7.85473	−0.414557	−0.207278	+	0.978282i	$0.566461\pi$
$360$	3.86713	0.203816
$361$	54.5968	2.87352
$362$	0.937905	0.0492952
$363$	8.98335	0.471504
$364$	0	0
$365$	15.0772	0.789174
$366$	18.8639	0.986029
$367$	1.87237	0.0977369	0.0488684	−	0.998805i	$-0.484438\pi$
$367$	1.87237	0.0977369	0.0488684	+	0.998805i	$0.484438\pi$
$368$	3.71076	0.193436
$369$	−11.2258	−0.584389
$370$	14.1223	0.734182
$371$	0	0
$372$	0.252805	0.0131073
$373$	−23.3775	−1.21044	−0.605220	−	0.796058i	$-0.706915\pi$
$373$	−23.3775	−1.21044	−0.605220	+	0.796058i	$0.706915\pi$
$374$	−2.24860	−0.116272
$375$	−10.9295	−0.564398
$376$	−5.06350	−0.261130
$377$	23.6064	1.21579
$378$	0	0
$379$	20.9257	1.07488	0.537441	−	0.843301i	$-0.319391\pi$
$379$	20.9257	1.07488	0.537441	+	0.843301i	$0.319391\pi$
$380$	1.54106	0.0790546
$381$	−1.06631	−0.0546287
$382$	1.49248	0.0763618
$383$	−26.8189	−1.37038	−0.685191	−	0.728363i	$-0.740281\pi$
$383$	−26.8189	−1.37038	−0.685191	+	0.728363i	$0.740281\pi$
$384$	−10.0304	−0.511860
$385$	0	0
$386$	10.1236	0.515279
$387$	−11.8479	−0.602262
$388$	−0.0553169	−0.00280829
$389$	−25.6338	−1.29968	−0.649842	−	0.760070i	$-0.725165\pi$
$389$	−25.6338	−1.29968	−0.649842	+	0.760070i	$0.725165\pi$
$390$	5.73448	0.290377
$391$	−1.15960	−0.0586437
$392$	0	0
$393$	16.0144	0.807821
$394$	4.31603	0.217439
$395$	15.5650	0.783162
$396$	0.192350	0.00966593
$397$	10.1904	0.511444	0.255722	−	0.966750i	$-0.417687\pi$
$397$	10.1904	0.511444	0.255722	+	0.966750i	$0.417687\pi$
$398$	−2.47055	−0.123837
$399$	0	0
$400$	12.0272	0.601358
$401$	23.7815	1.18759	0.593796	−	0.804615i	$-0.297629\pi$
$401$	23.7815	1.18759	0.593796	+	0.804615i	$0.297629\pi$
$402$	11.0508	0.551164
$403$	5.91022	0.294409
$404$	0.0980418	0.00487776
$405$	−1.32621	−0.0659000
$406$	0	0
$407$	11.0744	0.548937
$408$	3.38132	0.167400
$409$	−14.4367	−0.713849	−0.356925	−	0.934133i	$-0.616175\pi$
$409$	−14.4367	−0.713849	−0.356925	+	0.934133i	$0.616175\pi$
$410$	20.3290	1.00398
$411$	−0.927579	−0.0457541
$412$	1.93339	0.0952513
$413$	0	0
$414$	−1.36549	−0.0671100
$415$	−7.56691	−0.371445
$416$	2.42204	0.118750
$417$	4.22569	0.206933
$418$	−16.6353	−0.813661
$419$	18.5772	0.907558	0.453779	−	0.891114i	$-0.350076\pi$
$419$	18.5772	0.907558	0.453779	+	0.891114i	$0.350076\pi$
$420$	0	0
$421$	−7.98595	−0.389211	−0.194606	−	0.980882i	$-0.562343\pi$
$421$	−7.98595	−0.389211	−0.194606	+	0.980882i	$0.562343\pi$
$422$	−30.7939	−1.49903
$423$	1.73650	0.0844314
$424$	12.0981	0.587537
$425$	−3.75847	−0.182312
$426$	7.08658	0.343346
$427$	0	0
$428$	−1.89574	−0.0916340
$429$	4.49686	0.217110
$430$	21.4556	1.03468
$431$	−18.0343	−0.868680	−0.434340	−	0.900749i	$-0.643018\pi$
$431$	−18.0343	−0.868680	−0.434340	+	0.900749i	$0.643018\pi$
$432$	3.71076	0.178534
$433$	−13.6502	−0.655989	−0.327995	−	0.944680i	$-0.606373\pi$
$433$	−13.6502	−0.655989	−0.327995	+	0.944680i	$0.606373\pi$
$434$	0	0
$435$	9.88664	0.474028
$436$	−0.394083	−0.0188732
$437$	−8.57886	−0.410383
$438$	15.5237	0.741749
$439$	10.8654	0.518578	0.259289	−	0.965800i	$-0.416512\pi$
$439$	10.8654	0.518578	0.259289	+	0.965800i	$0.416512\pi$
$440$	−5.49166	−0.261805
$441$	0	0
$442$	5.01408	0.238495
$443$	15.1123	0.718006	0.359003	−	0.933336i	$-0.383117\pi$
$443$	15.1123	0.718006	0.359003	+	0.933336i	$0.383117\pi$
$444$	−1.05628	−0.0501291
$445$	8.42822	0.399536
$446$	−19.7290	−0.934197
$447$	16.4464	0.777887
$448$	0	0
$449$	6.14432	0.289968	0.144984	−	0.989434i	$-0.453687\pi$
$449$	6.14432	0.289968	0.144984	+	0.989434i	$0.453687\pi$
$450$	−4.42576	−0.208632
$451$	15.9415	0.750658
$452$	−2.52780	−0.118898
$453$	8.18838	0.384724
$454$	−4.47717	−0.210124
$455$	0	0
$456$	25.0153	1.17145
$457$	29.5848	1.38392	0.691960	−	0.721936i	$-0.256747\pi$
$457$	29.5848	1.38392	0.691960	+	0.721936i	$0.256747\pi$
$458$	−0.360396	−0.0168402
$459$	−1.15960	−0.0541257
$460$	−0.179634	−0.00837549
$461$	−34.7997	−1.62078	−0.810391	−	0.585890i	$-0.800745\pi$
$461$	−34.7997	−1.62078	−0.810391	+	0.585890i	$0.800745\pi$
$462$	0	0
$463$	15.8969	0.738793	0.369397	−	0.929272i	$-0.379564\pi$
$463$	15.8969	0.738793	0.369397	+	0.929272i	$0.379564\pi$
$464$	−27.6629	−1.28422
$465$	2.47527	0.114788
$466$	24.3752	1.12916
$467$	7.28616	0.337163	0.168582	−	0.985688i	$-0.446081\pi$
$467$	7.28616	0.337163	0.168582	+	0.985688i	$0.446081\pi$
$468$	−0.428914	−0.0198266
$469$	0	0
$470$	−3.14466	−0.145052
$471$	−22.5151	−1.03744
$472$	−36.9947	−1.70282
$473$	16.8250	0.773615
$474$	16.0260	0.736098
$475$	−27.8055	−1.27580
$476$	0	0
$477$	−4.14898	−0.189969
$478$	2.30556	0.105454
$479$	−18.6156	−0.850569	−0.425285	−	0.905060i	$-0.639826\pi$
$479$	−18.6156	−0.850569	−0.425285	+	0.905060i	$0.639826\pi$
$480$	1.01438	0.0462997
$481$	−24.6944	−1.12597
$482$	26.0015	1.18434
$483$	0	0
$484$	1.21679	0.0553086
$485$	−0.541619	−0.0245936
$486$	−1.36549	−0.0619397
$487$	9.62891	0.436328	0.218164	−	0.975912i	$-0.429993\pi$
$487$	9.62891	0.436328	0.218164	+	0.975912i	$0.429993\pi$
$488$	40.2828	1.82352
$489$	1.46151	0.0660915
$490$	0	0
$491$	−4.61117	−0.208099	−0.104050	−	0.994572i	$-0.533180\pi$
$491$	−4.61117	−0.208099	−0.104050	+	0.994572i	$0.533180\pi$
$492$	−1.52052	−0.0685503
$493$	8.64461	0.389334
$494$	37.0946	1.66897
$495$	1.88333	0.0846496
$496$	−6.92583	−0.310979
$497$	0	0
$498$	−7.79099	−0.349123
$499$	12.8567	0.575543	0.287771	−	0.957699i	$-0.407086\pi$
$499$	12.8567	0.575543	0.287771	+	0.957699i	$0.407086\pi$
$500$	−1.48040	−0.0662053
$501$	−2.76301	−0.123442
$502$	−27.7727	−1.23955
$503$	15.4383	0.688360	0.344180	−	0.938904i	$-0.388157\pi$
$503$	15.4383	0.688360	0.344180	+	0.938904i	$0.388157\pi$
$504$	0	0
$505$	0.959948	0.0427171
$506$	1.93911	0.0862038
$507$	2.97260	0.132018
$508$	−0.144431	−0.00640807
$509$	11.4032	0.505439	0.252720	−	0.967540i	$-0.418675\pi$
$509$	11.4032	0.505439	0.252720	+	0.967540i	$0.418675\pi$
$510$	2.09995	0.0929874
$511$	0	0
$512$	−24.4788	−1.08182
$513$	−8.57886	−0.378766
$514$	−13.1490	−0.579978
$515$	18.9302	0.834165
$516$	−1.60479	−0.0706468
$517$	−2.46598	−0.108454
$518$	0	0
$519$	−18.8661	−0.828131
$520$	12.2457	0.537009
$521$	14.9757	0.656097	0.328049	−	0.944661i	$-0.393609\pi$
$521$	14.9757	0.656097	0.328049	+	0.944661i	$0.393609\pi$
$522$	10.1794	0.445541
$523$	−11.4151	−0.499147	−0.249573	−	0.968356i	$-0.580290\pi$
$523$	−11.4151	−0.499147	−0.249573	+	0.968356i	$0.580290\pi$
$524$	2.16914	0.0947593
$525$	0	0
$526$	−6.62953	−0.289061
$527$	2.16431	0.0942787
$528$	−5.26959	−0.229330
$529$	1.00000	0.0434783
$530$	7.51348	0.326365
$531$	12.6871	0.550575
$532$	0	0
$533$	−35.5476	−1.53974
$534$	8.67782	0.375526
$535$	−18.5616	−0.802487
$536$	23.5984	1.01930
$537$	20.7182	0.894057
$538$	17.3943	0.749923
$539$	0	0
$540$	−0.179634	−0.00773023
$541$	18.1297	0.779455	0.389727	−	0.920930i	$-0.372569\pi$
$541$	18.1297	0.779455	0.389727	+	0.920930i	$0.372569\pi$
$542$	−30.0435	−1.29048
$543$	−0.686865	−0.0294762
$544$	0.886943	0.0380274
$545$	−3.85855	−0.165282
$546$	0	0
$547$	−13.0632	−0.558543	−0.279271	−	0.960212i	$-0.590093\pi$
$547$	−13.0632	−0.558543	−0.279271	+	0.960212i	$0.590093\pi$
$548$	−0.125640	−0.00536707
$549$	−13.8148	−0.589599
$550$	6.28497	0.267992
$551$	63.9537	2.72452
$552$	−2.91593	−0.124110
$553$	0	0
$554$	0.225912	0.00959808
$555$	−10.3423	−0.439006
$556$	0.572366	0.0242737
$557$	−26.8913	−1.13942	−0.569711	−	0.821845i	$-0.692945\pi$
$557$	−26.8913	−1.13942	−0.569711	+	0.821845i	$0.692945\pi$
$558$	2.54857	0.107890
$559$	−37.5176	−1.58683
$560$	0	0
$561$	1.64674	0.0695253
$562$	−28.6475	−1.20842
$563$	9.77405	0.411927	0.205963	−	0.978560i	$-0.433967\pi$
$563$	9.77405	0.411927	0.205963	+	0.978560i	$0.433967\pi$
$564$	0.235207	0.00990401
$565$	−24.7502	−1.04125
$566$	−1.11263	−0.0467673
$567$	0	0
$568$	15.1330	0.634968
$569$	−43.9890	−1.84411	−0.922057	−	0.387054i	$-0.873493\pi$
$569$	−43.9890	−1.84411	−0.922057	+	0.387054i	$0.873493\pi$
$570$	15.5356	0.650717
$571$	6.19921	0.259429	0.129714	−	0.991551i	$-0.458594\pi$
$571$	6.19921	0.259429	0.129714	+	0.991551i	$0.458594\pi$
$572$	0.609096	0.0254676
$573$	−1.09300	−0.0456608
$574$	0	0
$575$	3.24116	0.135166
$576$	8.46593	0.352747
$577$	14.5603	0.606154	0.303077	−	0.952966i	$-0.401986\pi$
$577$	14.5603	0.606154	0.303077	+	0.952966i	$0.401986\pi$
$578$	−21.3771	−0.889171
$579$	−7.41394	−0.308113
$580$	1.33914	0.0556046
$581$	0	0
$582$	−0.557658	−0.0231157
$583$	5.89191	0.244018
$584$	33.1500	1.37176
$585$	−4.19959	−0.173632
$586$	−17.2856	−0.714061
$587$	−16.3784	−0.676009	−0.338004	−	0.941145i	$-0.609752\pi$
$587$	−16.3784	−0.676009	−0.338004	+	0.941145i	$0.609752\pi$
$588$	0	0
$589$	16.0118	0.659753
$590$	−22.9754	−0.945883
$591$	−3.16080	−0.130018
$592$	28.9379	1.18934
$593$	27.2314	1.11826	0.559129	−	0.829081i	$-0.311136\pi$
$593$	27.2314	1.11826	0.559129	+	0.829081i	$0.311136\pi$
$594$	1.93911	0.0795625
$595$	0	0
$596$	2.22765	0.0912481
$597$	1.80928	0.0740490
$598$	−4.32396	−0.176820
$599$	40.5288	1.65596	0.827981	−	0.560756i	$-0.189489\pi$
$599$	40.5288	1.65596	0.827981	+	0.560756i	$0.189489\pi$
$600$	−9.45099	−0.385835
$601$	8.69739	0.354774	0.177387	−	0.984141i	$-0.443236\pi$
$601$	8.69739	0.354774	0.177387	+	0.984141i	$0.443236\pi$
$602$	0	0
$603$	−8.09295	−0.329570
$604$	1.10911	0.0451290
$605$	11.9138	0.484366
$606$	0.988375	0.0401500
$607$	20.0430	0.813522	0.406761	−	0.913535i	$-0.366658\pi$
$607$	20.0430	0.813522	0.406761	+	0.913535i	$0.366658\pi$
$608$	6.56169	0.266112
$609$	0	0
$610$	25.0175	1.01293
$611$	5.49881	0.222458
$612$	−0.157067	−0.00634907
$613$	−20.0601	−0.810221	−0.405111	−	0.914268i	$-0.632767\pi$
$613$	−20.0601	−0.810221	−0.405111	+	0.914268i	$0.632767\pi$
$614$	−4.14380	−0.167230
$615$	−14.8877	−0.600331
$616$	0	0
$617$	35.9585	1.44764	0.723818	−	0.689991i	$-0.242385\pi$
$617$	35.9585	1.44764	0.723818	+	0.689991i	$0.242385\pi$
$618$	19.4908	0.784036
$619$	−14.8199	−0.595663	−0.297832	−	0.954618i	$-0.596263\pi$
$619$	−14.8199	−0.595663	−0.297832	+	0.954618i	$0.596263\pi$
$620$	0.335273	0.0134649
$621$	1.00000	0.0401286
$622$	37.5190	1.50437
$623$	0	0
$624$	11.7505	0.470397
$625$	1.71096	0.0684386
$626$	1.83252	0.0732421
$627$	12.1827	0.486531
$628$	−3.04966	−0.121695
$629$	−9.04303	−0.360569
$630$	0	0
$631$	−25.6933	−1.02284	−0.511418	−	0.859332i	$-0.670880\pi$
$631$	−25.6933	−1.02284	−0.511418	+	0.859332i	$0.670880\pi$
$632$	34.2227	1.36130
$633$	22.5516	0.896347
$634$	0.694508	0.0275825
$635$	−1.41415	−0.0561189
$636$	−0.561976	−0.0222838
$637$	0	0
$638$	−14.4557	−0.572305
$639$	−5.18979	−0.205305
$640$	−13.3024	−0.525823
$641$	19.7597	0.780460	0.390230	−	0.920717i	$-0.372395\pi$
$641$	19.7597	0.780460	0.390230	+	0.920717i	$0.372395\pi$
$642$	−19.1113	−0.754261
$643$	−6.27845	−0.247598	−0.123799	−	0.992307i	$-0.539508\pi$
$643$	−6.27845	−0.247598	−0.123799	+	0.992307i	$0.539508\pi$
$644$	0	0
$645$	−15.7128	−0.618691
$646$	13.5840	0.534454
$647$	−46.9083	−1.84416	−0.922078	−	0.387004i	$-0.873510\pi$
$647$	−46.9083	−1.84416	−0.922078	+	0.387004i	$0.873510\pi$
$648$	−2.91593	−0.114548
$649$	−18.0168	−0.707222
$650$	−14.0147	−0.549700
$651$	0	0
$652$	0.197960	0.00775270
$653$	29.3176	1.14729	0.573643	−	0.819105i	$-0.305530\pi$
$653$	29.3176	1.14729	0.573643	+	0.819105i	$0.305530\pi$
$654$	−3.97282	−0.155349
$655$	21.2385	0.829857
$656$	41.6560	1.62639
$657$	−11.3686	−0.443531
$658$	0	0
$659$	−8.04283	−0.313304	−0.156652	−	0.987654i	$-0.550070\pi$
$659$	−8.04283	−0.313304	−0.156652	+	0.987654i	$0.550070\pi$
$660$	0.255096	0.00992960
$661$	12.8774	0.500872	0.250436	−	0.968133i	$-0.419426\pi$
$661$	12.8774	0.500872	0.250436	+	0.968133i	$0.419426\pi$
$662$	8.45281	0.328528
$663$	−3.67201	−0.142609
$664$	−16.6373	−0.645651
$665$	0	0
$666$	−10.6486	−0.412624
$667$	−7.45480	−0.288651
$668$	−0.374247	−0.0144800
$669$	14.4484	0.558606
$670$	14.6557	0.566199
$671$	19.6181	0.757350
$672$	0	0
$673$	42.5924	1.64182	0.820909	−	0.571059i	$-0.193467\pi$
$673$	42.5924	1.64182	0.820909	+	0.571059i	$0.193467\pi$
$674$	−6.93124	−0.266981
$675$	3.24116	0.124752
$676$	0.402636	0.0154860
$677$	11.6245	0.446766	0.223383	−	0.974731i	$-0.428290\pi$
$677$	11.6245	0.446766	0.223383	+	0.974731i	$0.428290\pi$
$678$	−25.4832	−0.978676
$679$	0	0
$680$	4.48434	0.171967
$681$	3.27881	0.125644
$682$	−3.61919	−0.138586
$683$	8.84158	0.338314	0.169157	−	0.985589i	$-0.445896\pi$
$683$	8.84158	0.338314	0.169157	+	0.985589i	$0.445896\pi$
$684$	−1.16200	−0.0444302
$685$	−1.23017	−0.0470022
$686$	0	0
$687$	0.263933	0.0100697
$688$	43.9646	1.67614
$689$	−13.1382	−0.500525
$690$	−1.81092	−0.0689406
$691$	25.2677	0.961230	0.480615	−	0.876932i	$-0.340413\pi$
$691$	25.2677	0.961230	0.480615	+	0.876932i	$0.340413\pi$
$692$	−2.55540	−0.0971417
$693$	0	0
$694$	−34.8133	−1.32149
$695$	5.60416	0.212578
$696$	21.7376	0.823963
$697$	−13.0174	−0.493070
$698$	−15.0388	−0.569228
$699$	−17.8509	−0.675184
$700$	0	0
$701$	17.9512	0.678009	0.339005	−	0.940785i	$-0.389910\pi$
$701$	17.9512	0.678009	0.339005	+	0.940785i	$0.389910\pi$
$702$	−4.32396	−0.163197
$703$	−66.9012	−2.52323
$704$	−12.0223	−0.453109
$705$	2.30296	0.0867346
$706$	−9.07748	−0.341636
$707$	0	0
$708$	1.71846	0.0645838
$709$	−37.4627	−1.40694	−0.703470	−	0.710725i	$-0.748367\pi$
$709$	−37.4627	−1.40694	−0.703470	+	0.710725i	$0.748367\pi$
$710$	9.39831	0.352712
$711$	−11.7365	−0.440152
$712$	18.5310	0.694480
$713$	−1.86642	−0.0698980
$714$	0	0
$715$	5.96378	0.223033
$716$	2.80627	0.104875
$717$	−1.68846	−0.0630566
$718$	−10.7255	−0.400273
$719$	31.6182	1.17916	0.589580	−	0.807710i	$-0.299293\pi$
$719$	31.6182	1.17916	0.589580	+	0.807710i	$0.299293\pi$
$720$	4.92124	0.183404
$721$	0	0
$722$	74.5512	2.77451
$723$	−19.0420	−0.708178
$724$	−0.0930354	−0.00345763
$725$	−24.1622	−0.897362
$726$	12.2666	0.455258
$727$	0.00894509	0.000331755 0	0.000165878	−	1.00000i	$-0.499947\pi$
$727$	0.00894509	0.000331755 0	0.000165878		1.00000i	$0.499947\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	20.5876	0.761983
$731$	−13.7389	−0.508150
$732$	−1.87120	−0.0691615
$733$	25.7110	0.949656	0.474828	−	0.880079i	$-0.342510\pi$
$733$	25.7110	0.949656	0.474828	+	0.880079i	$0.342510\pi$
$734$	2.55669	0.0943693
$735$	0	0
$736$	−0.764868	−0.0281934
$737$	11.4927	0.423339
$738$	−15.3286	−0.564254
$739$	−16.7658	−0.616739	−0.308370	−	0.951267i	$-0.599783\pi$
$739$	−16.7658	−0.616739	−0.308370	+	0.951267i	$0.599783\pi$
$740$	−1.40086	−0.0514965
$741$	−27.1659	−0.997964
$742$	0	0
$743$	13.6484	0.500712	0.250356	−	0.968154i	$-0.419452\pi$
$743$	13.6484	0.500712	0.250356	+	0.968154i	$0.419452\pi$
$744$	5.44234	0.199526
$745$	21.8114	0.799107
$746$	−31.9216	−1.16873
$747$	5.70566	0.208759
$748$	0.223049	0.00815549
$749$	0	0
$750$	−14.9241	−0.544951
$751$	−19.5144	−0.712092	−0.356046	−	0.934468i	$-0.615875\pi$
$751$	−19.5144	−0.712092	−0.356046	+	0.934468i	$0.615875\pi$
$752$	−6.44372	−0.234978
$753$	20.3390	0.741196
$754$	32.2342	1.17390
$755$	10.8595	0.395218
$756$	0	0
$757$	11.1059	0.403652	0.201826	−	0.979421i	$-0.435312\pi$
$757$	11.1059	0.403652	0.201826	+	0.979421i	$0.435312\pi$
$758$	28.5738	1.03785
$759$	−1.42009	−0.0515459
$760$	33.1756	1.20340
$761$	29.3210	1.06288	0.531442	−	0.847095i	$-0.321650\pi$
$761$	29.3210	1.06288	0.531442	+	0.847095i	$0.321650\pi$
$762$	−1.45603	−0.0527464
$763$	0	0
$764$	−0.148046	−0.00535613
$765$	−1.53788	−0.0556021
$766$	−36.6208	−1.32316
$767$	40.1752	1.45064
$768$	3.23553	0.116752
$769$	−9.29965	−0.335354	−0.167677	−	0.985842i	$-0.553627\pi$
$769$	−9.29965	−0.335354	−0.167677	+	0.985842i	$0.553627\pi$
$770$	0	0
$771$	9.62955	0.346800
$772$	−1.00421	−0.0361424
$773$	33.5436	1.20648	0.603240	−	0.797559i	$-0.293876\pi$
$773$	33.5436	1.20648	0.603240	+	0.797559i	$0.293876\pi$
$774$	−16.1781	−0.581511
$775$	−6.04937	−0.217300
$776$	−1.19085	−0.0427491
$777$	0	0
$778$	−35.0025	−1.25490
$779$	−96.3042	−3.45046
$780$	−0.568831	−0.0203674
$781$	7.36995	0.263718
$782$	−1.58342	−0.0566231
$783$	−7.45480	−0.266413
$784$	0	0
$785$	−29.8598	−1.06574
$786$	21.8675	0.779986
$787$	−30.5190	−1.08789	−0.543943	−	0.839122i	$-0.683069\pi$
$787$	−30.5190	−1.08789	−0.543943	+	0.839122i	$0.683069\pi$
$788$	−0.428128	−0.0152514
$789$	4.85507	0.172845
$790$	21.2538	0.756177
$791$	0	0
$792$	4.14087	0.147139
$793$	−43.7459	−1.55346
$794$	13.9149	0.493821
$795$	−5.50243	−0.195151
$796$	0.245066	0.00868613
$797$	−41.6491	−1.47529	−0.737643	−	0.675191i	$-0.764061\pi$
$797$	−41.6491	−1.47529	−0.737643	+	0.675191i	$0.764061\pi$
$798$	0	0
$799$	2.01365	0.0712378
$800$	−2.47906	−0.0876481
$801$	−6.35511	−0.224547
$802$	32.4733	1.14667
$803$	16.1444	0.569723
$804$	−1.09618	−0.0386594
$805$	0	0
$806$	8.07032	0.284265
$807$	−12.7386	−0.448419
$808$	2.11063	0.0742515
$809$	−31.5420	−1.10896	−0.554479	−	0.832198i	$-0.687082\pi$
$809$	−31.5420	−1.10896	−0.554479	+	0.832198i	$0.687082\pi$
$810$	−1.81092	−0.0636293
$811$	−22.0480	−0.774211	−0.387106	−	0.922035i	$-0.626525\pi$
$811$	−22.0480	−0.774211	−0.387106	+	0.922035i	$0.626525\pi$
$812$	0	0
$813$	22.0021	0.771646
$814$	15.1219	0.530022
$815$	1.93826	0.0678944
$816$	4.30301	0.150635
$817$	−101.641	−3.55598
$818$	−19.7131	−0.689253
$819$	0	0
$820$	−2.01653	−0.0704203
$821$	52.0995	1.81828	0.909142	−	0.416487i	$-0.136739\pi$
$821$	52.0995	1.81828	0.909142	+	0.416487i	$0.136739\pi$
$822$	−1.26660	−0.0441776
$823$	−38.4976	−1.34194	−0.670970	−	0.741484i	$-0.734122\pi$
$823$	−38.4976	−1.34194	−0.670970	+	0.741484i	$0.734122\pi$
$824$	41.6217	1.44996
$825$	−4.60273	−0.160247
$826$	0	0
$827$	−36.5676	−1.27158	−0.635790	−	0.771862i	$-0.719325\pi$
$827$	−36.5676	−1.27158	−0.635790	+	0.771862i	$0.719325\pi$
$828$	0.135449	0.00470719
$829$	27.5191	0.955777	0.477888	−	0.878421i	$-0.341402\pi$
$829$	27.5191	0.955777	0.477888	+	0.878421i	$0.341402\pi$
$830$	−10.3325	−0.358646
$831$	−0.165444	−0.00573921
$832$	26.8083	0.929409
$833$	0	0
$834$	5.77012	0.199803
$835$	−3.66433	−0.126809
$836$	1.65014	0.0570713
$837$	−1.86642	−0.0645129
$838$	25.3670	0.876287
$839$	2.02614	0.0699502	0.0349751	−	0.999388i	$-0.488865\pi$
$839$	2.02614	0.0699502	0.0349751	+	0.999388i	$0.488865\pi$
$840$	0	0
$841$	26.5740	0.916345
$842$	−10.9047	−0.375801
$843$	20.9797	0.722580
$844$	3.05460	0.105144
$845$	3.94229	0.135619
$846$	2.37116	0.0815222
$847$	0	0
$848$	15.3959	0.528696
$849$	0.814822	0.0279646
$850$	−5.13213	−0.176031
$851$	7.79838	0.267325
$852$	−0.702953	−0.0240828
$853$	−38.6105	−1.32200	−0.660999	−	0.750387i	$-0.729867\pi$
$853$	−38.6105	−1.32200	−0.660999	+	0.750387i	$0.729867\pi$
$854$	0	0
$855$	−11.3774	−0.389098
$856$	−40.8111	−1.39490
$857$	41.9796	1.43399	0.716997	−	0.697076i	$-0.245516\pi$
$857$	41.9796	1.43399	0.716997	+	0.697076i	$0.245516\pi$
$858$	6.14039	0.209630
$859$	40.8629	1.39422	0.697111	−	0.716963i	$-0.254468\pi$
$859$	40.8629	1.39422	0.697111	+	0.716963i	$0.254468\pi$
$860$	−2.12829	−0.0725740
$861$	0	0
$862$	−24.6255	−0.838748
$863$	−33.2645	−1.13234	−0.566169	−	0.824289i	$-0.691575\pi$
$863$	−33.2645	−1.13234	−0.566169	+	0.824289i	$0.691575\pi$
$864$	−0.764868	−0.0260213
$865$	−25.0205	−0.850721
$866$	−18.6392	−0.633386
$867$	15.6553	0.531683
$868$	0	0
$869$	16.6668	0.565382
$870$	13.5001	0.457695
$871$	−25.6272	−0.868344
$872$	−8.48375	−0.287296
$873$	0.408396	0.0138221
$874$	−11.7143	−0.396242
$875$	0	0
$876$	−1.53987	−0.0520273
$877$	18.2687	0.616892	0.308446	−	0.951242i	$-0.400191\pi$
$877$	18.2687	0.616892	0.308446	+	0.951242i	$0.400191\pi$
$878$	14.8366	0.500710
$879$	12.6589	0.426975
$880$	−6.98859	−0.235585
$881$	27.6269	0.930775	0.465387	−	0.885107i	$-0.345915\pi$
$881$	27.6269	0.930775	0.465387	+	0.885107i	$0.345915\pi$
$882$	0	0
$883$	−46.7892	−1.57458	−0.787290	−	0.616582i	$-0.788517\pi$
$883$	−46.7892	−1.57458	−0.787290	+	0.616582i	$0.788517\pi$
$884$	−0.497371	−0.0167284
$885$	16.8258	0.565594
$886$	20.6356	0.693267
$887$	−21.8623	−0.734064	−0.367032	−	0.930208i	$-0.619626\pi$
$887$	−21.8623	−0.734064	−0.367032	+	0.930208i	$0.619626\pi$
$888$	−22.7395	−0.763088
$889$	0	0
$890$	11.5086	0.385770
$891$	−1.42009	−0.0475747
$892$	1.95702	0.0655259
$893$	14.8972	0.498515
$894$	22.4573	0.751084
$895$	27.4767	0.918446
$896$	0	0
$897$	3.16661	0.105730
$898$	8.38998	0.279977
$899$	13.9138	0.464051
$900$	0.439013	0.0146338
$901$	−4.81117	−0.160283
$902$	21.7679	0.724793
$903$	0	0
$904$	−54.4181	−1.80992
$905$	−0.910928	−0.0302803
$906$	11.1811	0.371468
$907$	−51.1525	−1.69849	−0.849246	−	0.527998i	$-0.822943\pi$
$907$	−51.1525	−1.69849	−0.849246	+	0.527998i	$0.822943\pi$
$908$	0.444112	0.0147384
$909$	−0.723827	−0.0240078
$910$	0	0
$911$	−26.2401	−0.869373	−0.434686	−	0.900582i	$-0.643141\pi$
$911$	−26.2401	−0.869373	−0.434686	+	0.900582i	$0.643141\pi$
$912$	31.8340	1.05413
$913$	−8.10253	−0.268155
$914$	40.3977	1.33624
$915$	−18.3213	−0.605683
$916$	0.0357495	0.00118120
$917$	0	0
$918$	−1.58342	−0.0522607
$919$	31.9401	1.05361	0.526803	−	0.849987i	$-0.323390\pi$
$919$	31.9401	1.05361	0.526803	+	0.849987i	$0.323390\pi$
$920$	−3.86713	−0.127496
$921$	3.03467	0.0999957
$922$	−47.5184	−1.56494
$923$	−16.4340	−0.540933
$924$	0	0
$925$	25.2758	0.831065
$926$	21.7070	0.713337
$927$	−14.2739	−0.468817
$928$	5.70193	0.187175
$929$	−13.4153	−0.440140	−0.220070	−	0.975484i	$-0.570629\pi$
$929$	−13.4153	−0.440140	−0.220070	+	0.975484i	$0.570629\pi$
$930$	3.37994	0.110833
$931$	0	0
$932$	−2.41789	−0.0792008
$933$	−27.4766	−0.899545
$934$	9.94915	0.325546
$935$	2.18392	0.0714219
$936$	−9.23359	−0.301809
$937$	21.3033	0.695950	0.347975	−	0.937504i	$-0.386869\pi$
$937$	21.3033	0.695950	0.347975	+	0.937504i	$0.386869\pi$
$938$	0	0
$939$	−1.34203	−0.0437954
$940$	0.311934	0.0101742
$941$	5.22573	0.170354	0.0851770	−	0.996366i	$-0.472854\pi$
$941$	5.22573	0.170354	0.0851770	+	0.996366i	$0.472854\pi$
$942$	−30.7441	−1.00170
$943$	11.2258	0.365561
$944$	−47.0788	−1.53229
$945$	0	0
$946$	22.9743	0.746960
$947$	−14.7609	−0.479664	−0.239832	−	0.970814i	$-0.577092\pi$
$947$	−14.7609	−0.479664	−0.239832	+	0.970814i	$0.577092\pi$
$948$	−1.58970	−0.0516309
$949$	−35.9999	−1.16861
$950$	−37.9680	−1.23184
$951$	−0.508616	−0.0164930
$952$	0	0
$953$	−33.6944	−1.09147	−0.545735	−	0.837958i	$-0.683749\pi$
$953$	−33.6944	−1.09147	−0.545735	+	0.837958i	$0.683749\pi$
$954$	−5.66537	−0.183423
$955$	−1.44955	−0.0469064
$956$	−0.228700	−0.00739669
$957$	10.5865	0.342212
$958$	−25.4193	−0.821262
$959$	0	0
$960$	11.2276	0.362369
$961$	−27.5165	−0.887628
$962$	−33.7199	−1.08717
$963$	13.9959	0.451013
$964$	−2.57922	−0.0830710
$965$	−9.83244	−0.316518
$966$	0	0
$967$	49.9879	1.60750	0.803751	−	0.594966i	$-0.202835\pi$
$967$	49.9879	1.60750	0.803751	+	0.594966i	$0.202835\pi$
$968$	26.1948	0.841932
$969$	−9.94808	−0.319578
$970$	−0.739573	−0.0237462
$971$	−11.4283	−0.366751	−0.183375	−	0.983043i	$-0.558702\pi$
$971$	−11.4283	−0.366751	−0.183375	+	0.983043i	$0.558702\pi$
$972$	0.135449	0.00434454
$973$	0	0
$974$	13.1481	0.421294
$975$	10.2635	0.328695
$976$	51.2632	1.64089
$977$	4.98782	0.159575	0.0797873	−	0.996812i	$-0.474576\pi$
$977$	4.98782	0.159575	0.0797873	+	0.996812i	$0.474576\pi$
$978$	1.99566	0.0638143
$979$	9.02481	0.288434
$980$	0	0
$981$	2.90945	0.0928917
$982$	−6.29649	−0.200929
$983$	45.8555	1.46256	0.731282	−	0.682075i	$-0.238922\pi$
$983$	45.8555	1.46256	0.731282	+	0.682075i	$0.238922\pi$
$984$	−32.7335	−1.04350
$985$	−4.19189	−0.133565
$986$	11.8041	0.375919
$987$	0	0
$988$	−3.67960	−0.117064
$989$	11.8479	0.376741
$990$	2.57167	0.0817329
$991$	33.4065	1.06119	0.530596	−	0.847625i	$-0.321968\pi$
$991$	33.4065	1.06119	0.530596	+	0.847625i	$0.321968\pi$
$992$	1.42756	0.0453252
$993$	−6.19033	−0.196444
$994$	0	0
$995$	2.39949	0.0760690
$996$	0.772827	0.0244880
$997$	−21.8973	−0.693494	−0.346747	−	0.937959i	$-0.612714\pi$
$997$	−21.8973	−0.693494	−0.346747	+	0.937959i	$0.612714\pi$
$998$	17.5556	0.555712
$999$	7.79838	0.246730

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3381.2.a.bc.1.5		6
7.2	even	3		483.2.i.f.277.2	✓	12
7.4	even	3		483.2.i.f.415.2	yes	12
7.6	odd	2		3381.2.a.bd.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.i.f.277.2	✓	12	7.2	even	3
483.2.i.f.415.2	yes	12	7.4	even	3
3381.2.a.bc.1.5		6	1.1	even	1	trivial
3381.2.a.bd.1.5		6	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)

\(f(q)\)	\(=\)	\(q+1.36549 q^{2} -1.00000 q^{3} -0.135449 q^{4} -1.32621 q^{5} -1.36549 q^{6} -2.91593 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.36549 q^{2} -1.00000 q^{3} -0.135449 q^{4} -1.32621 q^{5} -1.36549 q^{6} -2.91593 q^{8} +1.00000 q^{9} -1.81092 q^{10} -1.42009 q^{11} +0.135449 q^{12} +3.16661 q^{13} +1.32621 q^{15} -3.71076 q^{16} +1.15960 q^{17} +1.36549 q^{18} +8.57886 q^{19} +0.179634 q^{20} -1.93911 q^{22} -1.00000 q^{23} +2.91593 q^{24} -3.24116 q^{25} +4.32396 q^{26} -1.00000 q^{27} +7.45480 q^{29} +1.81092 q^{30} +1.86642 q^{31} +0.764868 q^{32} +1.42009 q^{33} +1.58342 q^{34} -0.135449 q^{36} -7.79838 q^{37} +11.7143 q^{38} -3.16661 q^{39} +3.86713 q^{40} -11.2258 q^{41} -11.8479 q^{43} +0.192350 q^{44} -1.32621 q^{45} -1.36549 q^{46} +1.73650 q^{47} +3.71076 q^{48} -4.42576 q^{50} -1.15960 q^{51} -0.428914 q^{52} -4.14898 q^{53} -1.36549 q^{54} +1.88333 q^{55} -8.57886 q^{57} +10.1794 q^{58} +12.6871 q^{59} -0.179634 q^{60} -13.8148 q^{61} +2.54857 q^{62} +8.46593 q^{64} -4.19959 q^{65} +1.93911 q^{66} -8.09295 q^{67} -0.157067 q^{68} +1.00000 q^{69} -5.18979 q^{71} -2.91593 q^{72} -11.3686 q^{73} -10.6486 q^{74} +3.24116 q^{75} -1.16200 q^{76} -4.32396 q^{78} -11.7365 q^{79} +4.92124 q^{80} +1.00000 q^{81} -15.3286 q^{82} +5.70566 q^{83} -1.53788 q^{85} -16.1781 q^{86} -7.45480 q^{87} +4.14087 q^{88} -6.35511 q^{89} -1.81092 q^{90} +0.135449 q^{92} -1.86642 q^{93} +2.37116 q^{94} -11.3774 q^{95} -0.764868 q^{96} +0.408396 q^{97} -1.42009 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} - 6 q^{3} + 3 q^{4} + 3 q^{5} + q^{6} - 3 q^{8} + 6 q^{9}+O(q^{10}) \) 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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