LMFDB - Embedded newform 6045.2.a.t.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6045,2,Mod(1,6045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6045, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6045.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6045 = 3 \cdot 5 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6045.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:	$48.2695680219$
Analytic rank:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 3x^{8} - 7x^{7} + 22x^{6} + 14x^{5} - 52x^{4} - 5x^{3} + 41x^{2} - 4x - 5 $ x^9 - 3x^8 - 7x^7 + 22x^6 + 14x^5 - 52x^4 - 5x^3 + 41x^2 - 4x - 5
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-0.316933$ of defining polynomial
Character	$\chi$	$=$	6045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.31693 q^{2} +1.00000 q^{3} -0.265687 q^{4} +1.00000 q^{5} -1.31693 q^{6} +1.83326 q^{7} +2.98376 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.31693 q^{2} +1.00000 q^{3} -0.265687 q^{4} +1.00000 q^{5} -1.31693 q^{6} +1.83326 q^{7} +2.98376 q^{8} +1.00000 q^{9} -1.31693 q^{10} -3.89286 q^{11} -0.265687 q^{12} +1.00000 q^{13} -2.41428 q^{14} +1.00000 q^{15} -3.39804 q^{16} -5.72477 q^{17} -1.31693 q^{18} +3.17003 q^{19} -0.265687 q^{20} +1.83326 q^{21} +5.12663 q^{22} +4.42705 q^{23} +2.98376 q^{24} +1.00000 q^{25} -1.31693 q^{26} +1.00000 q^{27} -0.487073 q^{28} -7.39297 q^{29} -1.31693 q^{30} +1.00000 q^{31} -1.49253 q^{32} -3.89286 q^{33} +7.53913 q^{34} +1.83326 q^{35} -0.265687 q^{36} -4.72451 q^{37} -4.17472 q^{38} +1.00000 q^{39} +2.98376 q^{40} -7.37356 q^{41} -2.41428 q^{42} +3.88737 q^{43} +1.03428 q^{44} +1.00000 q^{45} -5.83013 q^{46} +7.26773 q^{47} -3.39804 q^{48} -3.63917 q^{49} -1.31693 q^{50} -5.72477 q^{51} -0.265687 q^{52} -3.54826 q^{53} -1.31693 q^{54} -3.89286 q^{55} +5.47000 q^{56} +3.17003 q^{57} +9.73605 q^{58} -7.51919 q^{59} -0.265687 q^{60} -7.62391 q^{61} -1.31693 q^{62} +1.83326 q^{63} +8.76164 q^{64} +1.00000 q^{65} +5.12663 q^{66} -12.3435 q^{67} +1.52100 q^{68} +4.42705 q^{69} -2.41428 q^{70} -0.175800 q^{71} +2.98376 q^{72} +10.7300 q^{73} +6.22186 q^{74} +1.00000 q^{75} -0.842237 q^{76} -7.13661 q^{77} -1.31693 q^{78} +5.79903 q^{79} -3.39804 q^{80} +1.00000 q^{81} +9.71048 q^{82} +4.95740 q^{83} -0.487073 q^{84} -5.72477 q^{85} -5.11941 q^{86} -7.39297 q^{87} -11.6154 q^{88} +0.109851 q^{89} -1.31693 q^{90} +1.83326 q^{91} -1.17621 q^{92} +1.00000 q^{93} -9.57112 q^{94} +3.17003 q^{95} -1.49253 q^{96} +10.4997 q^{97} +4.79254 q^{98} -3.89286 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 6 q^{2} + 9 q^{3} + 8 q^{4} + 9 q^{5} - 6 q^{6} - 12 q^{7} - 21 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q - 6 * q^2 + 9 * q^3 + 8 * q^4 + 9 * q^5 - 6 * q^6 - 12 * q^7 - 21 * q^8 + 9 * q^9	\( 9 q - 6 q^{2} + 9 q^{3} + 8 q^{4} + 9 q^{5} - 6 q^{6} - 12 q^{7} - 21 q^{8} + 9 q^{9} - 6 q^{10} - 10 q^{11} + 8 q^{12} + 9 q^{13} - 9 q^{14} + 9 q^{15} + 30 q^{16} - 17 q^{17} - 6 q^{18} + 6 q^{19} + 8 q^{20} - 12 q^{21} + 15 q^{22} - 23 q^{23} - 21 q^{24} + 9 q^{25} - 6 q^{26} + 9 q^{27} + 2 q^{28} - 4 q^{29} - 6 q^{30} + 9 q^{31} - 38 q^{32} - 10 q^{33} + 15 q^{34} - 12 q^{35} + 8 q^{36} + 11 q^{37} - 16 q^{38} + 9 q^{39} - 21 q^{40} - 8 q^{41} - 9 q^{42} - 15 q^{43} - q^{44} + 9 q^{45} + 26 q^{46} - 33 q^{47} + 30 q^{48} + 15 q^{49} - 6 q^{50} - 17 q^{51} + 8 q^{52} - 38 q^{53} - 6 q^{54} - 10 q^{55} + 37 q^{56} + 6 q^{57} - 26 q^{58} - 25 q^{59} + 8 q^{60} - 10 q^{61} - 6 q^{62} - 12 q^{63} + 47 q^{64} + 9 q^{65} + 15 q^{66} - 19 q^{67} + 7 q^{68} - 23 q^{69} - 9 q^{70} - 43 q^{71} - 21 q^{72} + q^{73} + 4 q^{74} + 9 q^{75} - 26 q^{76} + 2 q^{77} - 6 q^{78} - 9 q^{79} + 30 q^{80} + 9 q^{81} + 15 q^{82} - 12 q^{83} + 2 q^{84} - 17 q^{85} - 30 q^{86} - 4 q^{87} + q^{88} - 5 q^{89} - 6 q^{90} - 12 q^{91} - 57 q^{92} + 9 q^{93} + 40 q^{94} + 6 q^{95} - 38 q^{96} - 4 q^{97} + 34 q^{98} - 10 q^{99}+O(q^{100}) \) 9 * q - 6 * q^2 + 9 * q^3 + 8 * q^4 + 9 * q^5 - 6 * q^6 - 12 * q^7 - 21 * q^8 + 9 * q^9 - 6 * q^10 - 10 * q^11 + 8 * q^12 + 9 * q^13 - 9 * q^14 + 9 * q^15 + 30 * q^16 - 17 * q^17 - 6 * q^18 + 6 * q^19 + 8 * q^20 - 12 * q^21 + 15 * q^22 - 23 * q^23 - 21 * q^24 + 9 * q^25 - 6 * q^26 + 9 * q^27 + 2 * q^28 - 4 * q^29 - 6 * q^30 + 9 * q^31 - 38 * q^32 - 10 * q^33 + 15 * q^34 - 12 * q^35 + 8 * q^36 + 11 * q^37 - 16 * q^38 + 9 * q^39 - 21 * q^40 - 8 * q^41 - 9 * q^42 - 15 * q^43 - q^44 + 9 * q^45 + 26 * q^46 - 33 * q^47 + 30 * q^48 + 15 * q^49 - 6 * q^50 - 17 * q^51 + 8 * q^52 - 38 * q^53 - 6 * q^54 - 10 * q^55 + 37 * q^56 + 6 * q^57 - 26 * q^58 - 25 * q^59 + 8 * q^60 - 10 * q^61 - 6 * q^62 - 12 * q^63 + 47 * q^64 + 9 * q^65 + 15 * q^66 - 19 * q^67 + 7 * q^68 - 23 * q^69 - 9 * q^70 - 43 * q^71 - 21 * q^72 + q^73 + 4 * q^74 + 9 * q^75 - 26 * q^76 + 2 * q^77 - 6 * q^78 - 9 * q^79 + 30 * q^80 + 9 * q^81 + 15 * q^82 - 12 * q^83 + 2 * q^84 - 17 * q^85 - 30 * q^86 - 4 * q^87 + q^88 - 5 * q^89 - 6 * q^90 - 12 * q^91 - 57 * q^92 + 9 * q^93 + 40 * q^94 + 6 * q^95 - 38 * q^96 - 4 * q^97 + 34 * q^98 - 10 * 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 $

$2$	−1.31693	−0.931212	−0.465606	−	0.884992i	$-0.654164\pi$
$2$	−1.31693	−0.931212	−0.465606	+	0.884992i	$0.654164\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.265687	−0.132844
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.31693	−0.537636
$7$	1.83326	0.692906	0.346453	−	0.938067i	$-0.387386\pi$
$7$	1.83326	0.692906	0.346453	+	0.938067i	$0.387386\pi$
$8$	2.98376	1.05492
$9$	1.00000	0.333333
$10$	−1.31693	−0.416451
$11$	−3.89286	−1.17374	−0.586871	−	0.809681i	$-0.699640\pi$
$11$	−3.89286	−1.17374	−0.586871	+	0.809681i	$0.699640\pi$
$12$	−0.265687	−0.0766973
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−2.41428	−0.645243
$15$	1.00000	0.258199
$16$	−3.39804	−0.849509
$17$	−5.72477	−1.38846	−0.694230	−	0.719753i	$-0.744255\pi$
$17$	−5.72477	−1.38846	−0.694230	+	0.719753i	$0.744255\pi$
$18$	−1.31693	−0.310404
$19$	3.17003	0.727255	0.363627	−	0.931544i	$-0.381538\pi$
$19$	3.17003	0.727255	0.363627	+	0.931544i	$0.381538\pi$
$20$	−0.265687	−0.0594095
$21$	1.83326	0.400050
$22$	5.12663	1.09300
$23$	4.42705	0.923104	0.461552	−	0.887113i	$-0.347293\pi$
$23$	4.42705	0.923104	0.461552	+	0.887113i	$0.347293\pi$
$24$	2.98376	0.609057
$25$	1.00000	0.200000
$26$	−1.31693	−0.258272
$27$	1.00000	0.192450
$28$	−0.487073	−0.0920482
$29$	−7.39297	−1.37284	−0.686420	−	0.727205i	$-0.740819\pi$
$29$	−7.39297	−1.37284	−0.686420	+	0.727205i	$0.740819\pi$
$30$	−1.31693	−0.240438
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−1.49253	−0.263845
$33$	−3.89286	−0.677660
$34$	7.53913	1.29295
$35$	1.83326	0.309877
$36$	−0.265687	−0.0442812
$37$	−4.72451	−0.776704	−0.388352	−	0.921511i	$-0.626956\pi$
$37$	−4.72451	−0.776704	−0.388352	+	0.921511i	$0.626956\pi$
$38$	−4.17472	−0.677229
$39$	1.00000	0.160128
$40$	2.98376	0.471774
$41$	−7.37356	−1.15156	−0.575778	−	0.817606i	$-0.695301\pi$
$41$	−7.37356	−1.15156	−0.575778	+	0.817606i	$0.695301\pi$
$42$	−2.41428	−0.372531
$43$	3.88737	0.592819	0.296409	−	0.955061i	$-0.404211\pi$
$43$	3.88737	0.592819	0.296409	+	0.955061i	$0.404211\pi$
$44$	1.03428	0.155924
$45$	1.00000	0.149071
$46$	−5.83013	−0.859606
$47$	7.26773	1.06011	0.530054	−	0.847964i	$-0.322172\pi$
$47$	7.26773	1.06011	0.530054	+	0.847964i	$0.322172\pi$
$48$	−3.39804	−0.490464
$49$	−3.63917	−0.519881
$50$	−1.31693	−0.186242
$51$	−5.72477	−0.801628
$52$	−0.265687	−0.0368442
$53$	−3.54826	−0.487391	−0.243696	−	0.969852i	$-0.578360\pi$
$53$	−3.54826	−0.487391	−0.243696	+	0.969852i	$0.578360\pi$
$54$	−1.31693	−0.179212
$55$	−3.89286	−0.524913
$56$	5.47000	0.730959
$57$	3.17003	0.419881
$58$	9.73605	1.27841
$59$	−7.51919	−0.978916	−0.489458	−	0.872027i	$-0.662805\pi$
$59$	−7.51919	−0.978916	−0.489458	+	0.872027i	$0.662805\pi$
$60$	−0.265687	−0.0343001
$61$	−7.62391	−0.976141	−0.488071	−	0.872804i	$-0.662299\pi$
$61$	−7.62391	−0.976141	−0.488071	+	0.872804i	$0.662299\pi$
$62$	−1.31693	−0.167251
$63$	1.83326	0.230969
$64$	8.76164	1.09520
$65$	1.00000	0.124035
$66$	5.12663	0.631045
$67$	−12.3435	−1.50800	−0.754000	−	0.656874i	$-0.771878\pi$
$67$	−12.3435	−1.50800	−0.754000	+	0.656874i	$0.771878\pi$
$68$	1.52100	0.184448
$69$	4.42705	0.532954
$70$	−2.41428	−0.288561
$71$	−0.175800	−0.0208636	−0.0104318	−	0.999946i	$-0.503321\pi$
$71$	−0.175800	−0.0208636	−0.0104318	+	0.999946i	$0.503321\pi$
$72$	2.98376	0.351639
$73$	10.7300	1.25585	0.627926	−	0.778273i	$-0.283904\pi$
$73$	10.7300	1.25585	0.627926	+	0.778273i	$0.283904\pi$
$74$	6.22186	0.723276
$75$	1.00000	0.115470
$76$	−0.842237	−0.0966112
$77$	−7.13661	−0.813292
$78$	−1.31693	−0.149113
$79$	5.79903	0.652442	0.326221	−	0.945294i	$-0.394225\pi$
$79$	5.79903	0.652442	0.326221	+	0.945294i	$0.394225\pi$
$80$	−3.39804	−0.379912
$81$	1.00000	0.111111
$82$	9.71048	1.07234
$83$	4.95740	0.544145	0.272072	−	0.962277i	$-0.412291\pi$
$83$	4.95740	0.544145	0.272072	+	0.962277i	$0.412291\pi$
$84$	−0.487073	−0.0531440
$85$	−5.72477	−0.620938
$86$	−5.11941	−0.552040
$87$	−7.39297	−0.792610
$88$	−11.6154	−1.23820
$89$	0.109851	0.0116442	0.00582208	−	0.999983i	$-0.498147\pi$
$89$	0.109851	0.0116442	0.00582208	+	0.999983i	$0.498147\pi$
$90$	−1.31693	−0.138817
$91$	1.83326	0.192178
$92$	−1.17621	−0.122629
$93$	1.00000	0.103695
$94$	−9.57112	−0.987185
$95$	3.17003	0.325238
$96$	−1.49253	−0.152331
$97$	10.4997	1.06608	0.533042	−	0.846089i	$-0.321049\pi$
$97$	10.4997	1.06608	0.533042	+	0.846089i	$0.321049\pi$
$98$	4.79254	0.484120
$99$	−3.89286	−0.391247
$100$	−0.265687	−0.0265687
$101$	−16.4722	−1.63904	−0.819520	−	0.573050i	$-0.805760\pi$
$101$	−16.4722	−1.63904	−0.819520	+	0.573050i	$0.805760\pi$
$102$	7.53913	0.746485
$103$	−4.87961	−0.480803	−0.240401	−	0.970674i	$-0.577279\pi$
$103$	−4.87961	−0.480803	−0.240401	+	0.970674i	$0.577279\pi$
$104$	2.98376	0.292582
$105$	1.83326	0.178908
$106$	4.67282	0.453865
$107$	−9.26315	−0.895503	−0.447751	−	0.894158i	$-0.647775\pi$
$107$	−9.26315	−0.895503	−0.447751	+	0.894158i	$0.647775\pi$
$108$	−0.265687	−0.0255658
$109$	−15.9780	−1.53041	−0.765207	−	0.643785i	$-0.777363\pi$
$109$	−15.9780	−1.53041	−0.765207	+	0.643785i	$0.777363\pi$
$110$	5.12663	0.488805
$111$	−4.72451	−0.448430
$112$	−6.22947	−0.588630
$113$	−13.6457	−1.28368	−0.641838	−	0.766840i	$-0.721828\pi$
$113$	−13.6457	−1.28368	−0.641838	+	0.766840i	$0.721828\pi$
$114$	−4.17472	−0.390998
$115$	4.42705	0.412825
$116$	1.96422	0.182373
$117$	1.00000	0.0924500
$118$	9.90228	0.911578
$119$	−10.4950	−0.962072
$120$	2.98376	0.272379
$121$	4.15435	0.377668
$122$	10.0402	0.908995
$123$	−7.37356	−0.664851
$124$	−0.265687	−0.0238594
$125$	1.00000	0.0894427
$126$	−2.41428	−0.215081
$127$	3.73186	0.331149	0.165575	−	0.986197i	$-0.447052\pi$
$127$	3.73186	0.331149	0.165575	+	0.986197i	$0.447052\pi$
$128$	−8.55342	−0.756023
$129$	3.88737	0.342264
$130$	−1.31693	−0.115503
$131$	8.74286	0.763867	0.381934	−	0.924190i	$-0.375258\pi$
$131$	8.74286	0.763867	0.381934	+	0.924190i	$0.375258\pi$
$132$	1.03428	0.0900228
$133$	5.81148	0.503919
$134$	16.2556	1.40427
$135$	1.00000	0.0860663
$136$	−17.0813	−1.46471
$137$	−12.5386	−1.07124	−0.535621	−	0.844459i	$-0.679922\pi$
$137$	−12.5386	−1.07124	−0.535621	+	0.844459i	$0.679922\pi$
$138$	−5.83013	−0.496294
$139$	−4.00573	−0.339762	−0.169881	−	0.985465i	$-0.554338\pi$
$139$	−4.00573	−0.339762	−0.169881	+	0.985465i	$0.554338\pi$
$140$	−0.487073	−0.0411652
$141$	7.26773	0.612054
$142$	0.231517	0.0194284
$143$	−3.89286	−0.325537
$144$	−3.39804	−0.283170
$145$	−7.39297	−0.613953
$146$	−14.1307	−1.16946
$147$	−3.63917	−0.300153
$148$	1.25524	0.103180
$149$	−2.67110	−0.218825	−0.109412	−	0.993996i	$-0.534897\pi$
$149$	−2.67110	−0.218825	−0.109412	+	0.993996i	$0.534897\pi$
$150$	−1.31693	−0.107527
$151$	−16.1248	−1.31221	−0.656107	−	0.754668i	$-0.727798\pi$
$151$	−16.1248	−1.31221	−0.656107	+	0.754668i	$0.727798\pi$
$152$	9.45861	0.767194
$153$	−5.72477	−0.462820
$154$	9.39844	0.757348
$155$	1.00000	0.0803219
$156$	−0.265687	−0.0212720
$157$	−11.7798	−0.940129	−0.470065	−	0.882632i	$-0.655769\pi$
$157$	−11.7798	−0.940129	−0.470065	+	0.882632i	$0.655769\pi$
$158$	−7.63694	−0.607562
$159$	−3.54826	−0.281395
$160$	−1.49253	−0.117995
$161$	8.11593	0.639625
$162$	−1.31693	−0.103468
$163$	9.75303	0.763917	0.381958	−	0.924180i	$-0.375250\pi$
$163$	9.75303	0.763917	0.381958	+	0.924180i	$0.375250\pi$
$164$	1.95906	0.152977
$165$	−3.89286	−0.303059
$166$	−6.52856	−0.506714
$167$	22.6516	1.75283	0.876417	−	0.481552i	$-0.159927\pi$
$167$	22.6516	1.75283	0.876417	+	0.481552i	$0.159927\pi$
$168$	5.47000	0.422019
$169$	1.00000	0.0769231
$170$	7.53913	0.578225
$171$	3.17003	0.242418
$172$	−1.03283	−0.0787522
$173$	17.6251	1.34001	0.670005	−	0.742357i	$-0.266292\pi$
$173$	17.6251	1.34001	0.670005	+	0.742357i	$0.266292\pi$
$174$	9.73605	0.738088
$175$	1.83326	0.138581
$176$	13.2281	0.997104
$177$	−7.51919	−0.565177
$178$	−0.144666	−0.0108432
$179$	−1.56562	−0.117020	−0.0585099	−	0.998287i	$-0.518635\pi$
$179$	−1.56562	−0.117020	−0.0585099	+	0.998287i	$0.518635\pi$
$180$	−0.265687	−0.0198032
$181$	−19.8169	−1.47298	−0.736490	−	0.676448i	$-0.763518\pi$
$181$	−19.8169	−1.47298	−0.736490	+	0.676448i	$0.763518\pi$
$182$	−2.41428	−0.178958
$183$	−7.62391	−0.563575
$184$	13.2093	0.973799
$185$	−4.72451	−0.347353
$186$	−1.31693	−0.0965622
$187$	22.2857	1.62969
$188$	−1.93094	−0.140829
$189$	1.83326	0.133350
$190$	−4.17472	−0.302866
$191$	24.1750	1.74924	0.874619	−	0.484810i	$-0.161111\pi$
$191$	24.1750	1.74924	0.874619	+	0.484810i	$0.161111\pi$
$192$	8.76164	0.632317
$193$	3.50150	0.252043	0.126022	−	0.992027i	$-0.459779\pi$
$193$	3.50150	0.252043	0.126022	+	0.992027i	$0.459779\pi$
$194$	−13.8274	−0.992750
$195$	1.00000	0.0716115
$196$	0.966881	0.0690629
$197$	2.91265	0.207518	0.103759	−	0.994602i	$-0.466913\pi$
$197$	2.91265	0.207518	0.103759	+	0.994602i	$0.466913\pi$
$198$	5.12663	0.364334
$199$	13.1828	0.934505	0.467253	−	0.884124i	$-0.345244\pi$
$199$	13.1828	0.934505	0.467253	+	0.884124i	$0.345244\pi$
$200$	2.98376	0.210984
$201$	−12.3435	−0.870645
$202$	21.6927	1.52630
$203$	−13.5532	−0.951249
$204$	1.52100	0.106491
$205$	−7.37356	−0.514991
$206$	6.42612	0.447729
$207$	4.42705	0.307701
$208$	−3.39804	−0.235611
$209$	−12.3405	−0.853609
$210$	−2.41428	−0.166601
$211$	−24.9284	−1.71615	−0.858073	−	0.513528i	$-0.828338\pi$
$211$	−24.9284	−1.71615	−0.858073	+	0.513528i	$0.828338\pi$
$212$	0.942728	0.0647468
$213$	−0.175800	−0.0120456
$214$	12.1990	0.833903
$215$	3.88737	0.265117
$216$	2.98376	0.203019
$217$	1.83326	0.124450
$218$	21.0419	1.42514
$219$	10.7300	0.725066
$220$	1.03428	0.0697314
$221$	−5.72477	−0.385089
$222$	6.22186	0.417584
$223$	13.8012	0.924196	0.462098	−	0.886829i	$-0.347097\pi$
$223$	13.8012	0.924196	0.462098	+	0.886829i	$0.347097\pi$
$224$	−2.73619	−0.182820
$225$	1.00000	0.0666667
$226$	17.9704	1.19537
$227$	−13.1487	−0.872707	−0.436354	−	0.899775i	$-0.643730\pi$
$227$	−13.1487	−0.872707	−0.436354	+	0.899775i	$0.643730\pi$
$228$	−0.842237	−0.0557785
$229$	13.9464	0.921604	0.460802	−	0.887503i	$-0.347562\pi$
$229$	13.9464	0.921604	0.460802	+	0.887503i	$0.347562\pi$
$230$	−5.83013	−0.384427
$231$	−7.13661	−0.469555
$232$	−22.0588	−1.44823
$233$	−26.8345	−1.75798	−0.878992	−	0.476836i	$-0.841783\pi$
$233$	−26.8345	−1.75798	−0.878992	+	0.476836i	$0.841783\pi$
$234$	−1.31693	−0.0860906
$235$	7.26773	0.474095
$236$	1.99775	0.130043
$237$	5.79903	0.376688
$238$	13.8212	0.895893
$239$	21.5769	1.39569	0.697847	−	0.716247i	$-0.254142\pi$
$239$	21.5769	1.39569	0.697847	+	0.716247i	$0.254142\pi$
$240$	−3.39804	−0.219342
$241$	5.57174	0.358907	0.179454	−	0.983766i	$-0.442567\pi$
$241$	5.57174	0.358907	0.179454	+	0.983766i	$0.442567\pi$
$242$	−5.47100	−0.351689
$243$	1.00000	0.0641500
$244$	2.02558	0.129674
$245$	−3.63917	−0.232498
$246$	9.71048	0.619118
$247$	3.17003	0.201704
$248$	2.98376	0.189469
$249$	4.95740	0.314162
$250$	−1.31693	−0.0832902
$251$	−17.3139	−1.09285	−0.546423	−	0.837510i	$-0.684011\pi$
$251$	−17.3139	−1.09285	−0.546423	+	0.837510i	$0.684011\pi$
$252$	−0.487073	−0.0306827
$253$	−17.2339	−1.08349
$254$	−4.91461	−0.308370
$255$	−5.72477	−0.358499
$256$	−6.25898	−0.391186
$257$	28.7400	1.79275	0.896375	−	0.443296i	$-0.146191\pi$
$257$	28.7400	1.79275	0.896375	+	0.443296i	$0.146191\pi$
$258$	−5.11941	−0.318721
$259$	−8.66123	−0.538183
$260$	−0.265687	−0.0164772
$261$	−7.39297	−0.457613
$262$	−11.5138	−0.711323
$263$	5.48114	0.337981	0.168991	−	0.985618i	$-0.445949\pi$
$263$	5.48114	0.337981	0.168991	+	0.985618i	$0.445949\pi$
$264$	−11.6154	−0.714875
$265$	−3.54826	−0.217968
$266$	−7.65333	−0.469256
$267$	0.109851	0.00672276
$268$	3.27952	0.200328
$269$	−22.4921	−1.37137	−0.685685	−	0.727899i	$-0.740497\pi$
$269$	−22.4921	−1.37137	−0.685685	+	0.727899i	$0.740497\pi$
$270$	−1.31693	−0.0801460
$271$	−2.62954	−0.159733	−0.0798665	−	0.996806i	$-0.525449\pi$
$271$	−2.62954	−0.159733	−0.0798665	+	0.996806i	$0.525449\pi$
$272$	19.4530	1.17951
$273$	1.83326	0.110954
$274$	16.5124	0.997553
$275$	−3.89286	−0.234748
$276$	−1.17621	−0.0707996
$277$	5.01527	0.301338	0.150669	−	0.988584i	$-0.451857\pi$
$277$	5.01527	0.301338	0.150669	+	0.988584i	$0.451857\pi$
$278$	5.27528	0.316390
$279$	1.00000	0.0598684
$280$	5.47000	0.326895
$281$	−10.9882	−0.655501	−0.327751	−	0.944764i	$-0.606291\pi$
$281$	−10.9882	−0.655501	−0.327751	+	0.944764i	$0.606291\pi$
$282$	−9.57112	−0.569952
$283$	24.6137	1.46314	0.731568	−	0.681769i	$-0.238789\pi$
$283$	24.6137	1.46314	0.731568	+	0.681769i	$0.238789\pi$
$284$	0.0467078	0.00277160
$285$	3.17003	0.187776
$286$	5.12663	0.303144
$287$	−13.5176	−0.797920
$288$	−1.49253	−0.0879483
$289$	15.7729	0.927820
$290$	9.73605	0.571720
$291$	10.4997	0.615503
$292$	−2.85083	−0.166832
$293$	−14.3727	−0.839664	−0.419832	−	0.907602i	$-0.637911\pi$
$293$	−14.3727	−0.839664	−0.419832	+	0.907602i	$0.637911\pi$
$294$	4.79254	0.279507
$295$	−7.51919	−0.437784
$296$	−14.0968	−0.819359
$297$	−3.89286	−0.225887
$298$	3.51766	0.203772
$299$	4.42705	0.256023
$300$	−0.265687	−0.0153395
$301$	7.12655	0.410768
$302$	21.2352	1.22195
$303$	−16.4722	−0.946301
$304$	−10.7719	−0.617810
$305$	−7.62391	−0.436544
$306$	7.53913	0.430984
$307$	16.0750	0.917450	0.458725	−	0.888578i	$-0.348306\pi$
$307$	16.0750	0.917450	0.458725	+	0.888578i	$0.348306\pi$
$308$	1.89611	0.108041
$309$	−4.87961	−0.277591
$310$	−1.31693	−0.0747968
$311$	25.9814	1.47327	0.736636	−	0.676289i	$-0.236413\pi$
$311$	25.9814	1.47327	0.736636	+	0.676289i	$0.236413\pi$
$312$	2.98376	0.168922
$313$	13.6524	0.771681	0.385841	−	0.922565i	$-0.373911\pi$
$313$	13.6524	0.771681	0.385841	+	0.922565i	$0.373911\pi$
$314$	15.5132	0.875460
$315$	1.83326	0.103292
$316$	−1.54073	−0.0866728
$317$	−27.6422	−1.55254	−0.776271	−	0.630400i	$-0.782891\pi$
$317$	−27.6422	−1.55254	−0.776271	+	0.630400i	$0.782891\pi$
$318$	4.67282	0.262039
$319$	28.7798	1.61136
$320$	8.76164	0.489790
$321$	−9.26315	−0.517019
$322$	−10.6881	−0.595626
$323$	−18.1477	−1.00976
$324$	−0.265687	−0.0147604
$325$	1.00000	0.0554700
$326$	−12.8441	−0.711369
$327$	−15.9780	−0.883584
$328$	−22.0009	−1.21480
$329$	13.3236	0.734555
$330$	5.12663	0.282212
$331$	13.7458	0.755535	0.377768	−	0.925900i	$-0.376692\pi$
$331$	13.7458	0.755535	0.377768	+	0.925900i	$0.376692\pi$
$332$	−1.31712	−0.0722862
$333$	−4.72451	−0.258901
$334$	−29.8307	−1.63226
$335$	−12.3435	−0.674399
$336$	−6.22947	−0.339846
$337$	26.1699	1.42556	0.712782	−	0.701386i	$-0.247435\pi$
$337$	26.1699	1.42556	0.712782	+	0.701386i	$0.247435\pi$
$338$	−1.31693	−0.0716317
$339$	−13.6457	−0.741131
$340$	1.52100	0.0824877
$341$	−3.89286	−0.210810
$342$	−4.17472	−0.225743
$343$	−19.5043	−1.05313
$344$	11.5990	0.625375
$345$	4.42705	0.238344
$346$	−23.2110	−1.24783
$347$	−10.9068	−0.585510	−0.292755	−	0.956187i	$-0.594572\pi$
$347$	−10.9068	−0.585510	−0.292755	+	0.956187i	$0.594572\pi$
$348$	1.96422	0.105293
$349$	−5.83137	−0.312146	−0.156073	−	0.987746i	$-0.549884\pi$
$349$	−5.83137	−0.312146	−0.156073	+	0.987746i	$0.549884\pi$
$350$	−2.41428	−0.129049
$351$	1.00000	0.0533761
$352$	5.81021	0.309685
$353$	−12.3476	−0.657196	−0.328598	−	0.944470i	$-0.606576\pi$
$353$	−12.3476	−0.657196	−0.328598	+	0.944470i	$0.606576\pi$
$354$	9.90228	0.526300
$355$	−0.175800	−0.00933049
$356$	−0.0291860	−0.00154685
$357$	−10.4950	−0.555453
$358$	2.06181	0.108970
$359$	−21.7983	−1.15047	−0.575236	−	0.817988i	$-0.695090\pi$
$359$	−21.7983	−1.15047	−0.575236	+	0.817988i	$0.695090\pi$
$360$	2.98376	0.157258
$361$	−8.95090	−0.471100
$362$	26.0976	1.37166
$363$	4.15435	0.218047
$364$	−0.487073	−0.0255296
$365$	10.7300	0.561634
$366$	10.0402	0.524808
$367$	−28.1058	−1.46711	−0.733555	−	0.679630i	$-0.762140\pi$
$367$	−28.1058	−1.46711	−0.733555	+	0.679630i	$0.762140\pi$
$368$	−15.0433	−0.784185
$369$	−7.37356	−0.383852
$370$	6.22186	0.323459
$371$	−6.50487	−0.337716
$372$	−0.265687	−0.0137752
$373$	25.8579	1.33887	0.669437	−	0.742869i	$-0.266536\pi$
$373$	25.8579	1.33887	0.669437	+	0.742869i	$0.266536\pi$
$374$	−29.3488	−1.51759
$375$	1.00000	0.0516398
$376$	21.6852	1.11833
$377$	−7.39297	−0.380757
$378$	−2.41428	−0.124177
$379$	−26.9102	−1.38228	−0.691141	−	0.722720i	$-0.742892\pi$
$379$	−26.9102	−1.38228	−0.691141	+	0.722720i	$0.742892\pi$
$380$	−0.842237	−0.0432058
$381$	3.73186	0.191189
$382$	−31.8368	−1.62891
$383$	−33.7922	−1.72670	−0.863350	−	0.504606i	$-0.831638\pi$
$383$	−33.7922	−1.72670	−0.863350	+	0.504606i	$0.831638\pi$
$384$	−8.55342	−0.436490
$385$	−7.13661	−0.363715
$386$	−4.61124	−0.234706
$387$	3.88737	0.197606
$388$	−2.78964	−0.141622
$389$	−32.5407	−1.64988	−0.824939	−	0.565221i	$-0.808791\pi$
$389$	−32.5407	−1.64988	−0.824939	+	0.565221i	$0.808791\pi$
$390$	−1.31693	−0.0666855
$391$	−25.3438	−1.28169
$392$	−10.8584	−0.548432
$393$	8.74286	0.441019
$394$	−3.83577	−0.193243
$395$	5.79903	0.291781
$396$	1.03428	0.0519747
$397$	−8.73498	−0.438396	−0.219198	−	0.975680i	$-0.570344\pi$
$397$	−8.73498	−0.438396	−0.219198	+	0.975680i	$0.570344\pi$
$398$	−17.3609	−0.870223
$399$	5.81148	0.290938
$400$	−3.39804	−0.169902
$401$	−7.55158	−0.377108	−0.188554	−	0.982063i	$-0.560380\pi$
$401$	−7.55158	−0.377108	−0.188554	+	0.982063i	$0.560380\pi$
$402$	16.2556	0.810755
$403$	1.00000	0.0498135
$404$	4.37644	0.217736
$405$	1.00000	0.0496904
$406$	17.8487	0.885815
$407$	18.3918	0.911649
$408$	−17.0813	−0.845651
$409$	33.8451	1.67353	0.836766	−	0.547560i	$-0.184443\pi$
$409$	33.8451	1.67353	0.836766	+	0.547560i	$0.184443\pi$
$410$	9.71048	0.479566
$411$	−12.5386	−0.618481
$412$	1.29645	0.0638716
$413$	−13.7846	−0.678297
$414$	−5.83013	−0.286535
$415$	4.95740	0.243349
$416$	−1.49253	−0.0731774
$417$	−4.00573	−0.196161
$418$	16.2516	0.794891
$419$	−21.9138	−1.07056	−0.535279	−	0.844675i	$-0.679794\pi$
$419$	−21.9138	−1.07056	−0.535279	+	0.844675i	$0.679794\pi$
$420$	−0.487073	−0.0237667
$421$	18.6398	0.908446	0.454223	−	0.890888i	$-0.349917\pi$
$421$	18.6398	0.908446	0.454223	+	0.890888i	$0.349917\pi$
$422$	32.8291	1.59810
$423$	7.26773	0.353369
$424$	−10.5872	−0.514158
$425$	−5.72477	−0.277692
$426$	0.231517	0.0112170
$427$	−13.9766	−0.676374
$428$	2.46110	0.118962
$429$	−3.89286	−0.187949
$430$	−5.11941	−0.246880
$431$	−9.20412	−0.443347	−0.221673	−	0.975121i	$-0.571152\pi$
$431$	−9.20412	−0.443347	−0.221673	+	0.975121i	$0.571152\pi$
$432$	−3.39804	−0.163488
$433$	10.1046	0.485597	0.242799	−	0.970077i	$-0.421935\pi$
$433$	10.1046	0.485597	0.242799	+	0.970077i	$0.421935\pi$
$434$	−2.41428	−0.115889
$435$	−7.39297	−0.354466
$436$	4.24515	0.203306
$437$	14.0339	0.671332
$438$	−14.1307	−0.675191
$439$	6.22418	0.297064	0.148532	−	0.988908i	$-0.452545\pi$
$439$	6.22418	0.297064	0.148532	+	0.988908i	$0.452545\pi$
$440$	−11.6154	−0.553740
$441$	−3.63917	−0.173294
$442$	7.53913	0.358600
$443$	−33.8955	−1.61042	−0.805212	−	0.592987i	$-0.797949\pi$
$443$	−33.8955	−1.61042	−0.805212	+	0.592987i	$0.797949\pi$
$444$	1.25524	0.0595711
$445$	0.109851	0.00520743
$446$	−18.1752	−0.860623
$447$	−2.67110	−0.126339
$448$	16.0623	0.758874
$449$	−15.4618	−0.729689	−0.364845	−	0.931068i	$-0.618878\pi$
$449$	−15.4618	−0.729689	−0.364845	+	0.931068i	$0.618878\pi$
$450$	−1.31693	−0.0620808
$451$	28.7042	1.35163
$452$	3.62548	0.170528
$453$	−16.1248	−0.757607
$454$	17.3159	0.812676
$455$	1.83326	0.0859444
$456$	9.45861	0.442940
$457$	−28.9629	−1.35483	−0.677414	−	0.735602i	$-0.736899\pi$
$457$	−28.9629	−1.35483	−0.677414	+	0.735602i	$0.736899\pi$
$458$	−18.3665	−0.858209
$459$	−5.72477	−0.267209
$460$	−1.17621	−0.0548411
$461$	−33.7308	−1.57100	−0.785501	−	0.618861i	$-0.787595\pi$
$461$	−33.7308	−1.57100	−0.785501	+	0.618861i	$0.787595\pi$
$462$	9.39844	0.437255
$463$	−33.4426	−1.55421	−0.777104	−	0.629372i	$-0.783312\pi$
$463$	−33.4426	−1.55421	−0.777104	+	0.629372i	$0.783312\pi$
$464$	25.1216	1.16624
$465$	1.00000	0.0463739
$466$	35.3392	1.63706
$467$	−26.3613	−1.21986	−0.609928	−	0.792456i	$-0.708802\pi$
$467$	−26.3613	−1.21986	−0.609928	+	0.792456i	$0.708802\pi$
$468$	−0.265687	−0.0122814
$469$	−22.6288	−1.04490
$470$	−9.57112	−0.441483
$471$	−11.7798	−0.542784
$472$	−22.4355	−1.03268
$473$	−15.1330	−0.695816
$474$	−7.63694	−0.350776
$475$	3.17003	0.145451
$476$	2.78838	0.127805
$477$	−3.54826	−0.162464
$478$	−28.4153	−1.29969
$479$	−0.696968	−0.0318453	−0.0159226	−	0.999873i	$-0.505069\pi$
$479$	−0.696968	−0.0318453	−0.0159226	+	0.999873i	$0.505069\pi$
$480$	−1.49253	−0.0681244
$481$	−4.72451	−0.215419
$482$	−7.33761	−0.334219
$483$	8.11593	0.369287
$484$	−1.10376	−0.0501708
$485$	10.4997	0.476767
$486$	−1.31693	−0.0597373
$487$	−19.0073	−0.861305	−0.430652	−	0.902518i	$-0.641716\pi$
$487$	−19.0073	−0.861305	−0.430652	+	0.902518i	$0.641716\pi$
$488$	−22.7479	−1.02975
$489$	9.75303	0.441047
$490$	4.79254	0.216505
$491$	18.9983	0.857381	0.428691	−	0.903451i	$-0.358975\pi$
$491$	18.9983	0.857381	0.428691	+	0.903451i	$0.358975\pi$
$492$	1.95906	0.0883212
$493$	42.3230	1.90613
$494$	−4.17472	−0.187829
$495$	−3.89286	−0.174971
$496$	−3.39804	−0.152576
$497$	−0.322286	−0.0144565
$498$	−6.52856	−0.292552
$499$	−7.30687	−0.327100	−0.163550	−	0.986535i	$-0.552295\pi$
$499$	−7.30687	−0.327100	−0.163550	+	0.986535i	$0.552295\pi$
$500$	−0.265687	−0.0118819
$501$	22.6516	1.01200
$502$	22.8013	1.01767
$503$	−27.0806	−1.20747	−0.603733	−	0.797187i	$-0.706321\pi$
$503$	−27.0806	−1.20747	−0.603733	+	0.797187i	$0.706321\pi$
$504$	5.47000	0.243653
$505$	−16.4722	−0.733001
$506$	22.6959	1.00895
$507$	1.00000	0.0444116
$508$	−0.991508	−0.0439911
$509$	42.0665	1.86457	0.932283	−	0.361729i	$-0.117814\pi$
$509$	42.0665	1.86457	0.932283	+	0.361729i	$0.117814\pi$
$510$	7.53913	0.333838
$511$	19.6709	0.870187
$512$	25.3495	1.12030
$513$	3.17003	0.139960
$514$	−37.8486	−1.66943
$515$	−4.87961	−0.215021
$516$	−1.03283	−0.0454676
$517$	−28.2923	−1.24429
$518$	11.4063	0.501163
$519$	17.6251	0.773655
$520$	2.98376	0.130846
$521$	29.9656	1.31282	0.656408	−	0.754406i	$-0.272075\pi$
$521$	29.9656	1.31282	0.656408	+	0.754406i	$0.272075\pi$
$522$	9.73605	0.426135
$523$	−1.26204	−0.0551850	−0.0275925	−	0.999619i	$-0.508784\pi$
$523$	−1.26204	−0.0551850	−0.0275925	+	0.999619i	$0.508784\pi$
$524$	−2.32287	−0.101475
$525$	1.83326	0.0800099
$526$	−7.21829	−0.314732
$527$	−5.72477	−0.249375
$528$	13.2281	0.575678
$529$	−3.40121	−0.147879
$530$	4.67282	0.202974
$531$	−7.51919	−0.326305
$532$	−1.54404	−0.0669425
$533$	−7.37356	−0.319384
$534$	−0.144666	−0.00626032
$535$	−9.26315	−0.400481
$536$	−36.8301	−1.59082
$537$	−1.56562	−0.0675614
$538$	29.6206	1.27704
$539$	14.1668	0.610206
$540$	−0.265687	−0.0114334
$541$	18.8232	0.809273	0.404636	−	0.914478i	$-0.367398\pi$
$541$	18.8232	0.809273	0.404636	+	0.914478i	$0.367398\pi$
$542$	3.46293	0.148745
$543$	−19.8169	−0.850426
$544$	8.54439	0.366338
$545$	−15.9780	−0.684422
$546$	−2.41428	−0.103322
$547$	−9.72033	−0.415611	−0.207806	−	0.978170i	$-0.566632\pi$
$547$	−9.72033	−0.415611	−0.207806	+	0.978170i	$0.566632\pi$
$548$	3.33134	0.142308
$549$	−7.62391	−0.325380
$550$	5.12663	0.218600
$551$	−23.4359	−0.998405
$552$	13.2093	0.562223
$553$	10.6311	0.452081
$554$	−6.60477	−0.280610
$555$	−4.72451	−0.200544
$556$	1.06427	0.0451352
$557$	24.5751	1.04128	0.520641	−	0.853776i	$-0.325693\pi$
$557$	24.5751	1.04128	0.520641	+	0.853776i	$0.325693\pi$
$558$	−1.31693	−0.0557502
$559$	3.88737	0.164418
$560$	−6.22947	−0.263243
$561$	22.2857	0.940903
$562$	14.4707	0.610411
$563$	−2.36519	−0.0996808	−0.0498404	−	0.998757i	$-0.515871\pi$
$563$	−2.36519	−0.0996808	−0.0498404	+	0.998757i	$0.515871\pi$
$564$	−1.93094	−0.0813074
$565$	−13.6457	−0.574077
$566$	−32.4147	−1.36249
$567$	1.83326	0.0769896
$568$	−0.524544	−0.0220094
$569$	42.4506	1.77962	0.889811	−	0.456330i	$-0.150836\pi$
$569$	42.4506	1.77962	0.889811	+	0.456330i	$0.150836\pi$
$570$	−4.17472	−0.174860
$571$	−14.0738	−0.588972	−0.294486	−	0.955656i	$-0.595148\pi$
$571$	−14.0738	−0.588972	−0.294486	+	0.955656i	$0.595148\pi$
$572$	1.03428	0.0432456
$573$	24.1750	1.00992
$574$	17.8018	0.743033
$575$	4.42705	0.184621
$576$	8.76164	0.365068
$577$	27.8951	1.16129	0.580644	−	0.814158i	$-0.302801\pi$
$577$	27.8951	1.16129	0.580644	+	0.814158i	$0.302801\pi$
$578$	−20.7719	−0.863998
$579$	3.50150	0.145517
$580$	1.96422	0.0815597
$581$	9.08818	0.377041
$582$	−13.8274	−0.573164
$583$	13.8129	0.572071
$584$	32.0157	1.32482
$585$	1.00000	0.0413449
$586$	18.9279	0.781905
$587$	29.0028	1.19707	0.598537	−	0.801095i	$-0.295749\pi$
$587$	29.0028	1.19707	0.598537	+	0.801095i	$0.295749\pi$
$588$	0.966881	0.0398735
$589$	3.17003	0.130619
$590$	9.90228	0.407670
$591$	2.91265	0.119811
$592$	16.0540	0.659817
$593$	−36.8538	−1.51341	−0.756703	−	0.653759i	$-0.773191\pi$
$593$	−36.8538	−1.51341	−0.756703	+	0.653759i	$0.773191\pi$
$594$	5.12663	0.210348
$595$	−10.4950	−0.430252
$596$	0.709676	0.0290695
$597$	13.1828	0.539537
$598$	−5.83013	−0.238412
$599$	3.42719	0.140031	0.0700157	−	0.997546i	$-0.477695\pi$
$599$	3.42719	0.140031	0.0700157	+	0.997546i	$0.477695\pi$
$600$	2.98376	0.121811
$601$	4.10567	0.167474	0.0837369	−	0.996488i	$-0.473314\pi$
$601$	4.10567	0.167474	0.0837369	+	0.996488i	$0.473314\pi$
$602$	−9.38520	−0.382512
$603$	−12.3435	−0.502667
$604$	4.28414	0.174319
$605$	4.15435	0.168898
$606$	21.6927	0.881207
$607$	35.7049	1.44922	0.724608	−	0.689161i	$-0.242021\pi$
$607$	35.7049	1.44922	0.724608	+	0.689161i	$0.242021\pi$
$608$	−4.73137	−0.191882
$609$	−13.5532	−0.549204
$610$	10.0402	0.406515
$611$	7.26773	0.294021
$612$	1.52100	0.0614827
$613$	−23.1335	−0.934355	−0.467177	−	0.884164i	$-0.654729\pi$
$613$	−23.1335	−0.934355	−0.467177	+	0.884164i	$0.654729\pi$
$614$	−21.1697	−0.854340
$615$	−7.37356	−0.297330
$616$	−21.2939	−0.857957
$617$	−33.3797	−1.34381	−0.671907	−	0.740635i	$-0.734525\pi$
$617$	−33.3797	−1.34381	−0.671907	+	0.740635i	$0.734525\pi$
$618$	6.42612	0.258497
$619$	36.5219	1.46794	0.733970	−	0.679182i	$-0.237665\pi$
$619$	36.5219	1.46794	0.733970	+	0.679182i	$0.237665\pi$
$620$	−0.265687	−0.0106703
$621$	4.42705	0.177651
$622$	−34.2158	−1.37193
$623$	0.201385	0.00806832
$624$	−3.39804	−0.136030
$625$	1.00000	0.0400000
$626$	−17.9793	−0.718599
$627$	−12.3405	−0.492831
$628$	3.12974	0.124890
$629$	27.0467	1.07842
$630$	−2.41428	−0.0961871
$631$	−15.2450	−0.606896	−0.303448	−	0.952848i	$-0.598138\pi$
$631$	−15.2450	−0.606896	−0.303448	+	0.952848i	$0.598138\pi$
$632$	17.3029	0.688273
$633$	−24.9284	−0.990817
$634$	36.4030	1.44575
$635$	3.73186	0.148094
$636$	0.942728	0.0373816
$637$	−3.63917	−0.144189
$638$	−37.9011	−1.50052
$639$	−0.175800	−0.00695453
$640$	−8.55342	−0.338104
$641$	13.7609	0.543523	0.271762	−	0.962365i	$-0.412394\pi$
$641$	13.7609	0.543523	0.271762	+	0.962365i	$0.412394\pi$
$642$	12.1990	0.481454
$643$	−40.7341	−1.60640	−0.803199	−	0.595711i	$-0.796870\pi$
$643$	−40.7341	−1.60640	−0.803199	+	0.595711i	$0.796870\pi$
$644$	−2.15630	−0.0849701
$645$	3.88737	0.153065
$646$	23.8993	0.940305
$647$	−32.0469	−1.25989	−0.629946	−	0.776639i	$-0.716923\pi$
$647$	−32.0469	−1.25989	−0.629946	+	0.776639i	$0.716923\pi$
$648$	2.98376	0.117213
$649$	29.2712	1.14899
$650$	−1.31693	−0.0516544
$651$	1.83326	0.0718510
$652$	−2.59126	−0.101481
$653$	−23.1664	−0.906572	−0.453286	−	0.891365i	$-0.649748\pi$
$653$	−23.1664	−0.906572	−0.453286	+	0.891365i	$0.649748\pi$
$654$	21.0419	0.822805
$655$	8.74286	0.341612
$656$	25.0556	0.978257
$657$	10.7300	0.418617
$658$	−17.5463	−0.684027
$659$	1.05802	0.0412144	0.0206072	−	0.999788i	$-0.493440\pi$
$659$	1.05802	0.0412144	0.0206072	+	0.999788i	$0.493440\pi$
$660$	1.03428	0.0402594
$661$	−16.5092	−0.642132	−0.321066	−	0.947057i	$-0.604041\pi$
$661$	−16.5092	−0.642132	−0.321066	+	0.947057i	$0.604041\pi$
$662$	−18.1022	−0.703563
$663$	−5.72477	−0.222331
$664$	14.7917	0.574028
$665$	5.81148	0.225360
$666$	6.22186	0.241092
$667$	−32.7291	−1.26727
$668$	−6.01825	−0.232853
$669$	13.8012	0.533585
$670$	16.2556	0.628008
$671$	29.6788	1.14574
$672$	−2.73619	−0.105551
$673$	23.2719	0.897065	0.448533	−	0.893766i	$-0.351947\pi$
$673$	23.2719	0.897065	0.448533	+	0.893766i	$0.351947\pi$
$674$	−34.4640	−1.32750
$675$	1.00000	0.0384900
$676$	−0.265687	−0.0102187
$677$	−37.1528	−1.42790	−0.713949	−	0.700197i	$-0.753095\pi$
$677$	−37.1528	−1.42790	−0.713949	+	0.700197i	$0.753095\pi$
$678$	17.9704	0.690150
$679$	19.2487	0.738696
$680$	−17.0813	−0.655039
$681$	−13.1487	−0.503858
$682$	5.12663	0.196309
$683$	−18.5188	−0.708604	−0.354302	−	0.935131i	$-0.615281\pi$
$683$	−18.5188	−0.708604	−0.354302	+	0.935131i	$0.615281\pi$
$684$	−0.842237	−0.0322037
$685$	−12.5386	−0.479074
$686$	25.6859	0.980692
$687$	13.9464	0.532088
$688$	−13.2094	−0.503605
$689$	−3.54826	−0.135178
$690$	−5.83013	−0.221949
$691$	7.83730	0.298145	0.149072	−	0.988826i	$-0.452371\pi$
$691$	7.83730	0.298145	0.149072	+	0.988826i	$0.452371\pi$
$692$	−4.68276	−0.178012
$693$	−7.13661	−0.271097
$694$	14.3636	0.545234
$695$	−4.00573	−0.151946
$696$	−22.0588	−0.836138
$697$	42.2119	1.59889
$698$	7.67952	0.290674
$699$	−26.8345	−1.01497
$700$	−0.487073	−0.0184096
$701$	46.6155	1.76064	0.880321	−	0.474379i	$-0.157327\pi$
$701$	46.6155	1.76064	0.880321	+	0.474379i	$0.157327\pi$
$702$	−1.31693	−0.0497044
$703$	−14.9768	−0.564862
$704$	−34.1078	−1.28549
$705$	7.26773	0.273719
$706$	16.2610	0.611989
$707$	−30.1977	−1.13570
$708$	1.99775	0.0750802
$709$	35.9285	1.34932	0.674662	−	0.738126i	$-0.264289\pi$
$709$	35.9285	1.34932	0.674662	+	0.738126i	$0.264289\pi$
$710$	0.231517	0.00868866
$711$	5.79903	0.217481
$712$	0.327768	0.0122836
$713$	4.42705	0.165794
$714$	13.8212	0.517244
$715$	−3.89286	−0.145585
$716$	0.415965	0.0155453
$717$	21.5769	0.805804
$718$	28.7069	1.07133
$719$	−18.5307	−0.691078	−0.345539	−	0.938404i	$-0.612304\pi$
$719$	−18.5307	−0.691078	−0.345539	+	0.938404i	$0.612304\pi$
$720$	−3.39804	−0.126637
$721$	−8.94559	−0.333151
$722$	11.7877	0.438694
$723$	5.57174	0.207215
$724$	5.26511	0.195676
$725$	−7.39297	−0.274568
$726$	−5.47100	−0.203048
$727$	35.6972	1.32393	0.661967	−	0.749533i	$-0.269722\pi$
$727$	35.6972	1.32393	0.661967	+	0.749533i	$0.269722\pi$
$728$	5.47000	0.202732
$729$	1.00000	0.0370370
$730$	−14.1307	−0.523000
$731$	−22.2543	−0.823105
$732$	2.02558	0.0748674
$733$	−48.8083	−1.80278	−0.901389	−	0.433011i	$-0.857451\pi$
$733$	−48.8083	−1.80278	−0.901389	+	0.433011i	$0.857451\pi$
$734$	37.0134	1.36619
$735$	−3.63917	−0.134233
$736$	−6.60751	−0.243556
$737$	48.0516	1.77000
$738$	9.71048	0.357448
$739$	−4.37904	−0.161085	−0.0805427	−	0.996751i	$-0.525665\pi$
$739$	−4.37904	−0.161085	−0.0805427	+	0.996751i	$0.525665\pi$
$740$	1.25524	0.0461436
$741$	3.17003	0.116454
$742$	8.56648	0.314486
$743$	3.93542	0.144376	0.0721882	−	0.997391i	$-0.477002\pi$
$743$	3.93542	0.144376	0.0721882	+	0.997391i	$0.477002\pi$
$744$	2.98376	0.109390
$745$	−2.67110	−0.0978614
$746$	−34.0532	−1.24678
$747$	4.95740	0.181382
$748$	−5.92103	−0.216494
$749$	−16.9817	−0.620499
$750$	−1.31693	−0.0480876
$751$	3.94611	0.143995	0.0719977	−	0.997405i	$-0.477063\pi$
$751$	3.94611	0.143995	0.0719977	+	0.997405i	$0.477063\pi$
$752$	−24.6960	−0.900571
$753$	−17.3139	−0.630955
$754$	9.73605	0.354566
$755$	−16.1248	−0.586840
$756$	−0.487073	−0.0177147
$757$	−29.5626	−1.07447	−0.537236	−	0.843432i	$-0.680532\pi$
$757$	−29.5626	−1.07447	−0.537236	+	0.843432i	$0.680532\pi$
$758$	35.4389	1.28720
$759$	−17.2339	−0.625551
$760$	9.45861	0.343100
$761$	−33.7704	−1.22418	−0.612089	−	0.790789i	$-0.709671\pi$
$761$	−33.7704	−1.22418	−0.612089	+	0.790789i	$0.709671\pi$
$762$	−4.91461	−0.178038
$763$	−29.2918	−1.06043
$764$	−6.42298	−0.232375
$765$	−5.72477	−0.206979
$766$	44.5020	1.60792
$767$	−7.51919	−0.271502
$768$	−6.25898	−0.225852
$769$	13.0941	0.472187	0.236093	−	0.971730i	$-0.424133\pi$
$769$	13.0941	0.472187	0.236093	+	0.971730i	$0.424133\pi$
$770$	9.39844	0.338696
$771$	28.7400	1.03505
$772$	−0.930304	−0.0334824
$773$	7.06049	0.253948	0.126974	−	0.991906i	$-0.459474\pi$
$773$	7.06049	0.253948	0.126974	+	0.991906i	$0.459474\pi$
$774$	−5.11941	−0.184013
$775$	1.00000	0.0359211
$776$	31.3286	1.12463
$777$	−8.66123	−0.310720
$778$	42.8539	1.53639
$779$	−23.3744	−0.837475
$780$	−0.265687	−0.00951313
$781$	0.684364	0.0244885
$782$	33.3761	1.19353
$783$	−7.39297	−0.264203
$784$	12.3660	0.441644
$785$	−11.7798	−0.420439
$786$	−11.5138	−0.410682
$787$	16.7469	0.596962	0.298481	−	0.954416i	$-0.403520\pi$
$787$	16.7469	0.596962	0.298481	+	0.954416i	$0.403520\pi$
$788$	−0.773855	−0.0275674
$789$	5.48114	0.195134
$790$	−7.63694	−0.271710
$791$	−25.0160	−0.889467
$792$	−11.6154	−0.412734
$793$	−7.62391	−0.270733
$794$	11.5034	0.408240
$795$	−3.54826	−0.125844
$796$	−3.50251	−0.124143
$797$	37.5702	1.33081	0.665403	−	0.746485i	$-0.268260\pi$
$797$	37.5702	1.33081	0.665403	+	0.746485i	$0.268260\pi$
$798$	−7.65333	−0.270925
$799$	−41.6061	−1.47192
$800$	−1.49253	−0.0527690
$801$	0.109851	0.00388139
$802$	9.94492	0.351167
$803$	−41.7704	−1.47404
$804$	3.27952	0.115660
$805$	8.11593	0.286049
$806$	−1.31693	−0.0463870
$807$	−22.4921	−0.791761
$808$	−49.1489	−1.72905
$809$	−41.2918	−1.45174	−0.725871	−	0.687831i	$-0.758563\pi$
$809$	−41.2918	−1.45174	−0.725871	+	0.687831i	$0.758563\pi$
$810$	−1.31693	−0.0462723
$811$	0.885400	0.0310906	0.0155453	−	0.999879i	$-0.495052\pi$
$811$	0.885400	0.0310906	0.0155453	+	0.999879i	$0.495052\pi$
$812$	3.60092	0.126367
$813$	−2.62954	−0.0922219
$814$	−24.2208	−0.848939
$815$	9.75303	0.341634
$816$	19.4530	0.680990
$817$	12.3231	0.431130
$818$	−44.5717	−1.55841
$819$	1.83326	0.0640592
$820$	1.95906	0.0684133
$821$	−56.0475	−1.95607	−0.978036	−	0.208434i	$-0.933163\pi$
$821$	−56.0475	−1.95607	−0.978036	+	0.208434i	$0.933163\pi$
$822$	16.5124	0.575937
$823$	−39.2714	−1.36892	−0.684458	−	0.729052i	$-0.739961\pi$
$823$	−39.2714	−1.36892	−0.684458	+	0.729052i	$0.739961\pi$
$824$	−14.5596	−0.507207
$825$	−3.89286	−0.135532
$826$	18.1534	0.631638
$827$	45.8138	1.59310	0.796551	−	0.604572i	$-0.206656\pi$
$827$	45.8138	1.59310	0.796551	+	0.604572i	$0.206656\pi$
$828$	−1.17621	−0.0408762
$829$	−51.4382	−1.78652	−0.893261	−	0.449538i	$-0.851589\pi$
$829$	−51.4382	−1.78652	−0.893261	+	0.449538i	$0.851589\pi$
$830$	−6.52856	−0.226610
$831$	5.01527	0.173978
$832$	8.76164	0.303755
$833$	20.8334	0.721834
$834$	5.27528	0.182668
$835$	22.6516	0.783892
$836$	3.27871	0.113397
$837$	1.00000	0.0345651
$838$	28.8590	0.996918
$839$	−4.73272	−0.163391	−0.0816957	−	0.996657i	$-0.526034\pi$
$839$	−4.73272	−0.163391	−0.0816957	+	0.996657i	$0.526034\pi$
$840$	5.47000	0.188733
$841$	25.6560	0.884690
$842$	−24.5473	−0.845956
$843$	−10.9882	−0.378454
$844$	6.62317	0.227979
$845$	1.00000	0.0344010
$846$	−9.57112	−0.329062
$847$	7.61599	0.261689
$848$	12.0571	0.414043
$849$	24.6137	0.844741
$850$	7.53913	0.258590
$851$	−20.9156	−0.716979
$852$	0.0467078	0.00160018
$853$	−31.5554	−1.08044	−0.540219	−	0.841525i	$-0.681659\pi$
$853$	−31.5554	−1.08044	−0.540219	+	0.841525i	$0.681659\pi$
$854$	18.4062	0.629848
$855$	3.17003	0.108413
$856$	−27.6390	−0.944682
$857$	29.9368	1.02262	0.511311	−	0.859396i	$-0.329160\pi$
$857$	29.9368	1.02262	0.511311	+	0.859396i	$0.329160\pi$
$858$	5.12663	0.175020
$859$	18.5443	0.632725	0.316362	−	0.948638i	$-0.397538\pi$
$859$	18.5443	0.632725	0.316362	+	0.948638i	$0.397538\pi$
$860$	−1.03283	−0.0352191
$861$	−13.5176	−0.460679
$862$	12.1212	0.412850
$863$	−48.1287	−1.63832	−0.819160	−	0.573565i	$-0.805560\pi$
$863$	−48.1287	−1.63832	−0.819160	+	0.573565i	$0.805560\pi$
$864$	−1.49253	−0.0507770
$865$	17.6251	0.599270
$866$	−13.3071	−0.452194
$867$	15.7729	0.535677
$868$	−0.487073	−0.0165323
$869$	−22.5748	−0.765798
$870$	9.73605	0.330083
$871$	−12.3435	−0.418244
$872$	−47.6744	−1.61446
$873$	10.4997	0.355361
$874$	−18.4817	−0.625153
$875$	1.83326	0.0619754
$876$	−2.85083	−0.0963205
$877$	−48.3659	−1.63320	−0.816600	−	0.577204i	$-0.804144\pi$
$877$	−48.3659	−1.63320	−0.816600	+	0.577204i	$0.804144\pi$
$878$	−8.19683	−0.276629
$879$	−14.3727	−0.484780
$880$	13.2281	0.445918
$881$	4.02867	0.135729	0.0678647	−	0.997695i	$-0.478381\pi$
$881$	4.02867	0.135729	0.0678647	+	0.997695i	$0.478381\pi$
$882$	4.79254	0.161373
$883$	−7.88164	−0.265238	−0.132619	−	0.991167i	$-0.542339\pi$
$883$	−7.88164	−0.265238	−0.132619	+	0.991167i	$0.542339\pi$
$884$	1.52100	0.0511567
$885$	−7.51919	−0.252755
$886$	44.6381	1.49965
$887$	−51.9861	−1.74552	−0.872761	−	0.488148i	$-0.837673\pi$
$887$	−51.9861	−1.74552	−0.872761	+	0.488148i	$0.837673\pi$
$888$	−14.0968	−0.473057
$889$	6.84146	0.229455
$890$	−0.144666	−0.00484922
$891$	−3.89286	−0.130416
$892$	−3.66680	−0.122774
$893$	23.0389	0.770969
$894$	3.51766	0.117648
$895$	−1.56562	−0.0523328
$896$	−15.6806	−0.523853
$897$	4.42705	0.147815
$898$	20.3622	0.679496
$899$	−7.39297	−0.246569
$900$	−0.265687	−0.00885624
$901$	20.3130	0.676723
$902$	−37.8015	−1.25865
$903$	7.12655	0.237157
$904$	−40.7154	−1.35417
$905$	−19.8169	−0.658737
$906$	21.2352	0.705493
$907$	54.7628	1.81837	0.909184	−	0.416395i	$-0.136706\pi$
$907$	54.7628	1.81837	0.909184	+	0.416395i	$0.136706\pi$
$908$	3.49343	0.115934
$909$	−16.4722	−0.546347
$910$	−2.41428	−0.0800325
$911$	19.4090	0.643050	0.321525	−	0.946901i	$-0.395805\pi$
$911$	19.4090	0.643050	0.321525	+	0.946901i	$0.395805\pi$
$912$	−10.7719	−0.356693
$913$	−19.2984	−0.638685
$914$	38.1422	1.26163
$915$	−7.62391	−0.252039
$916$	−3.70538	−0.122429
$917$	16.0279	0.529288
$918$	7.53913	0.248828
$919$	9.83312	0.324365	0.162182	−	0.986761i	$-0.448147\pi$
$919$	9.83312	0.324365	0.162182	+	0.986761i	$0.448147\pi$
$920$	13.2093	0.435496
$921$	16.0750	0.529690
$922$	44.4212	1.46294
$923$	−0.175800	−0.00578652
$924$	1.89611	0.0623773
$925$	−4.72451	−0.155341
$926$	44.0416	1.44730
$927$	−4.87961	−0.160268
$928$	11.0342	0.362217
$929$	42.4098	1.39142	0.695709	−	0.718323i	$-0.255090\pi$
$929$	42.4098	1.39142	0.695709	+	0.718323i	$0.255090\pi$
$930$	−1.31693	−0.0431839
$931$	−11.5363	−0.378086
$932$	7.12958	0.233537
$933$	25.9814	0.850594
$934$	34.7161	1.13595
$935$	22.2857	0.728821
$936$	2.98376	0.0975272
$937$	11.4402	0.373734	0.186867	−	0.982385i	$-0.440167\pi$
$937$	11.4402	0.373734	0.186867	+	0.982385i	$0.440167\pi$
$938$	29.8007	0.973027
$939$	13.6524	0.445530
$940$	−1.93094	−0.0629805
$941$	−22.3849	−0.729728	−0.364864	−	0.931061i	$-0.618885\pi$
$941$	−22.3849	−0.729728	−0.364864	+	0.931061i	$0.618885\pi$
$942$	15.5132	0.505447
$943$	−32.6431	−1.06301
$944$	25.5505	0.831598
$945$	1.83326	0.0596359
$946$	19.9291	0.647952
$947$	14.0927	0.457952	0.228976	−	0.973432i	$-0.426462\pi$
$947$	14.0927	0.457952	0.228976	+	0.973432i	$0.426462\pi$
$948$	−1.54073	−0.0500406
$949$	10.7300	0.348311
$950$	−4.17472	−0.135446
$951$	−27.6422	−0.896360
$952$	−31.3145	−1.01491
$953$	44.4476	1.43980	0.719900	−	0.694078i	$-0.244188\pi$
$953$	44.4476	1.43980	0.719900	+	0.694078i	$0.244188\pi$
$954$	4.67282	0.151288
$955$	24.1750	0.782283
$956$	−5.73271	−0.185409
$957$	28.7798	0.930319
$958$	0.917860	0.0296547
$959$	−22.9864	−0.742270
$960$	8.76164	0.282781
$961$	1.00000	0.0322581
$962$	6.22186	0.200601
$963$	−9.26315	−0.298501
$964$	−1.48034	−0.0476785
$965$	3.50150	0.112717
$966$	−10.6881	−0.343885
$967$	−29.8140	−0.958754	−0.479377	−	0.877609i	$-0.659137\pi$
$967$	−29.8140	−0.958754	−0.479377	+	0.877609i	$0.659137\pi$
$968$	12.3956	0.398409
$969$	−18.1477	−0.582988
$970$	−13.8274	−0.443971
$971$	33.7640	1.08354	0.541769	−	0.840528i	$-0.317755\pi$
$971$	33.7640	1.08354	0.541769	+	0.840528i	$0.317755\pi$
$972$	−0.265687	−0.00852192
$973$	−7.34354	−0.235423
$974$	25.0314	0.802057
$975$	1.00000	0.0320256
$976$	25.9063	0.829241
$977$	−52.0825	−1.66627	−0.833133	−	0.553072i	$-0.813455\pi$
$977$	−52.0825	−1.66627	−0.833133	+	0.553072i	$0.813455\pi$
$978$	−12.8441	−0.410709
$979$	−0.427634	−0.0136672
$980$	0.966881	0.0308859
$981$	−15.9780	−0.510138
$982$	−25.0195	−0.798404
$983$	−4.46865	−0.142528	−0.0712639	−	0.997457i	$-0.522703\pi$
$983$	−4.46865	−0.142528	−0.0712639	+	0.997457i	$0.522703\pi$
$984$	−22.0009	−0.701363
$985$	2.91265	0.0928048
$986$	−55.7366	−1.77501
$987$	13.3236	0.424096
$988$	−0.842237	−0.0267951
$989$	17.2096	0.547233
$990$	5.12663	0.162935
$991$	−39.6337	−1.25901	−0.629503	−	0.776998i	$-0.716742\pi$
$991$	−39.6337	−1.25901	−0.629503	+	0.776998i	$0.716742\pi$
$992$	−1.49253	−0.0473879
$993$	13.7458	0.436208
$994$	0.424430	0.0134621
$995$	13.1828	0.417923
$996$	−1.31712	−0.0417345
$997$	42.2666	1.33860	0.669299	−	0.742994i	$-0.266595\pi$
$997$	42.2666	1.33860	0.669299	+	0.742994i	$0.266595\pi$
$998$	9.62266	0.304600
$999$	−4.72451	−0.149477

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6045.2.a.t.1.4	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6045.2.a.t.1.4	✓	9	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6045 = 3 \cdot 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6045.a (trivial)

\(f(q)\)	\(=\)	\(q-1.31693 q^{2} +1.00000 q^{3} -0.265687 q^{4} +1.00000 q^{5} -1.31693 q^{6} +1.83326 q^{7} +2.98376 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.31693 q^{2} +1.00000 q^{3} -0.265687 q^{4} +1.00000 q^{5} -1.31693 q^{6} +1.83326 q^{7} +2.98376 q^{8} +1.00000 q^{9} -1.31693 q^{10} -3.89286 q^{11} -0.265687 q^{12} +1.00000 q^{13} -2.41428 q^{14} +1.00000 q^{15} -3.39804 q^{16} -5.72477 q^{17} -1.31693 q^{18} +3.17003 q^{19} -0.265687 q^{20} +1.83326 q^{21} +5.12663 q^{22} +4.42705 q^{23} +2.98376 q^{24} +1.00000 q^{25} -1.31693 q^{26} +1.00000 q^{27} -0.487073 q^{28} -7.39297 q^{29} -1.31693 q^{30} +1.00000 q^{31} -1.49253 q^{32} -3.89286 q^{33} +7.53913 q^{34} +1.83326 q^{35} -0.265687 q^{36} -4.72451 q^{37} -4.17472 q^{38} +1.00000 q^{39} +2.98376 q^{40} -7.37356 q^{41} -2.41428 q^{42} +3.88737 q^{43} +1.03428 q^{44} +1.00000 q^{45} -5.83013 q^{46} +7.26773 q^{47} -3.39804 q^{48} -3.63917 q^{49} -1.31693 q^{50} -5.72477 q^{51} -0.265687 q^{52} -3.54826 q^{53} -1.31693 q^{54} -3.89286 q^{55} +5.47000 q^{56} +3.17003 q^{57} +9.73605 q^{58} -7.51919 q^{59} -0.265687 q^{60} -7.62391 q^{61} -1.31693 q^{62} +1.83326 q^{63} +8.76164 q^{64} +1.00000 q^{65} +5.12663 q^{66} -12.3435 q^{67} +1.52100 q^{68} +4.42705 q^{69} -2.41428 q^{70} -0.175800 q^{71} +2.98376 q^{72} +10.7300 q^{73} +6.22186 q^{74} +1.00000 q^{75} -0.842237 q^{76} -7.13661 q^{77} -1.31693 q^{78} +5.79903 q^{79} -3.39804 q^{80} +1.00000 q^{81} +9.71048 q^{82} +4.95740 q^{83} -0.487073 q^{84} -5.72477 q^{85} -5.11941 q^{86} -7.39297 q^{87} -11.6154 q^{88} +0.109851 q^{89} -1.31693 q^{90} +1.83326 q^{91} -1.17621 q^{92} +1.00000 q^{93} -9.57112 q^{94} +3.17003 q^{95} -1.49253 q^{96} +10.4997 q^{97} +4.79254 q^{98} -3.89286 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 6 q^{2} + 9 q^{3} + 8 q^{4} + 9 q^{5} - 6 q^{6} - 12 q^{7} - 21 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q - 6 * q^2 + 9 * q^3 + 8 * q^4 + 9 * q^5 - 6 * q^6 - 12 * q^7 - 21 * q^8 + 9 * q^9	\( 9 q - 6 q^{2} + 9 q^{3} + 8 q^{4} + 9 q^{5} - 6 q^{6} - 12 q^{7} - 21 q^{8} + 9 q^{9} - 6 q^{10} - 10 q^{11} + 8 q^{12} + 9 q^{13} - 9 q^{14} + 9 q^{15} + 30 q^{16} - 17 q^{17} - 6 q^{18} + 6 q^{19} + 8 q^{20} - 12 q^{21} + 15 q^{22} - 23 q^{23} - 21 q^{24} + 9 q^{25} - 6 q^{26} + 9 q^{27} + 2 q^{28} - 4 q^{29} - 6 q^{30} + 9 q^{31} - 38 q^{32} - 10 q^{33} + 15 q^{34} - 12 q^{35} + 8 q^{36} + 11 q^{37} - 16 q^{38} + 9 q^{39} - 21 q^{40} - 8 q^{41} - 9 q^{42} - 15 q^{43} - q^{44} + 9 q^{45} + 26 q^{46} - 33 q^{47} + 30 q^{48} + 15 q^{49} - 6 q^{50} - 17 q^{51} + 8 q^{52} - 38 q^{53} - 6 q^{54} - 10 q^{55} + 37 q^{56} + 6 q^{57} - 26 q^{58} - 25 q^{59} + 8 q^{60} - 10 q^{61} - 6 q^{62} - 12 q^{63} + 47 q^{64} + 9 q^{65} + 15 q^{66} - 19 q^{67} + 7 q^{68} - 23 q^{69} - 9 q^{70} - 43 q^{71} - 21 q^{72} + q^{73} + 4 q^{74} + 9 q^{75} - 26 q^{76} + 2 q^{77} - 6 q^{78} - 9 q^{79} + 30 q^{80} + 9 q^{81} + 15 q^{82} - 12 q^{83} + 2 q^{84} - 17 q^{85} - 30 q^{86} - 4 q^{87} + q^{88} - 5 q^{89} - 6 q^{90} - 12 q^{91} - 57 q^{92} + 9 q^{93} + 40 q^{94} + 6 q^{95} - 38 q^{96} - 4 q^{97} + 34 q^{98} - 10 q^{99}+O(q^{100}) \) 9 * q - 6 * q^2 + 9 * q^3 + 8 * q^4 + 9 * q^5 - 6 * q^6 - 12 * q^7 - 21 * q^8 + 9 * q^9 - 6 * q^10 - 10 * q^11 + 8 * q^12 + 9 * q^13 - 9 * q^14 + 9 * q^15 + 30 * q^16 - 17 * q^17 - 6 * q^18 + 6 * q^19 + 8 * q^20 - 12 * q^21 + 15 * q^22 - 23 * q^23 - 21 * q^24 + 9 * q^25 - 6 * q^26 + 9 * q^27 + 2 * q^28 - 4 * q^29 - 6 * q^30 + 9 * q^31 - 38 * q^32 - 10 * q^33 + 15 * q^34 - 12 * q^35 + 8 * q^36 + 11 * q^37 - 16 * q^38 + 9 * q^39 - 21 * q^40 - 8 * q^41 - 9 * q^42 - 15 * q^43 - q^44 + 9 * q^45 + 26 * q^46 - 33 * q^47 + 30 * q^48 + 15 * q^49 - 6 * q^50 - 17 * q^51 + 8 * q^52 - 38 * q^53 - 6 * q^54 - 10 * q^55 + 37 * q^56 + 6 * q^57 - 26 * q^58 - 25 * q^59 + 8 * q^60 - 10 * q^61 - 6 * q^62 - 12 * q^63 + 47 * q^64 + 9 * q^65 + 15 * q^66 - 19 * q^67 + 7 * q^68 - 23 * q^69 - 9 * q^70 - 43 * q^71 - 21 * q^72 + q^73 + 4 * q^74 + 9 * q^75 - 26 * q^76 + 2 * q^77 - 6 * q^78 - 9 * q^79 + 30 * q^80 + 9 * q^81 + 15 * q^82 - 12 * q^83 + 2 * q^84 - 17 * q^85 - 30 * q^86 - 4 * q^87 + q^88 - 5 * q^89 - 6 * q^90 - 12 * q^91 - 57 * q^92 + 9 * q^93 + 40 * q^94 + 6 * q^95 - 38 * q^96 - 4 * q^97 + 34 * q^98 - 10 * q^99

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