LMFDB - Embedded newform 8043.2.a.t.1.26

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8043,2,Mod(1,8043)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8043, 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("8043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8043 = 3 \cdot 7 \cdot 383 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8043.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:	$64.2236783457$
Analytic rank:	$0$
Dimension:	$52$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.26
Character	$\chi$	$=$	8043.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.00957487 q^{2} -1.00000 q^{3} -1.99991 q^{4} +2.93567 q^{5} -0.00957487 q^{6} +1.00000 q^{7} -0.0382986 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.00957487 q^{2} -1.00000 q^{3} -1.99991 q^{4} +2.93567 q^{5} -0.00957487 q^{6} +1.00000 q^{7} -0.0382986 q^{8} +1.00000 q^{9} +0.0281086 q^{10} +3.26445 q^{11} +1.99991 q^{12} +1.37591 q^{13} +0.00957487 q^{14} -2.93567 q^{15} +3.99945 q^{16} +7.20883 q^{17} +0.00957487 q^{18} -0.675813 q^{19} -5.87106 q^{20} -1.00000 q^{21} +0.0312566 q^{22} -0.624915 q^{23} +0.0382986 q^{24} +3.61813 q^{25} +0.0131741 q^{26} -1.00000 q^{27} -1.99991 q^{28} +1.21510 q^{29} -0.0281086 q^{30} -8.43543 q^{31} +0.114891 q^{32} -3.26445 q^{33} +0.0690236 q^{34} +2.93567 q^{35} -1.99991 q^{36} +7.68213 q^{37} -0.00647082 q^{38} -1.37591 q^{39} -0.112432 q^{40} +11.7660 q^{41} -0.00957487 q^{42} +6.99983 q^{43} -6.52859 q^{44} +2.93567 q^{45} -0.00598348 q^{46} +1.23164 q^{47} -3.99945 q^{48} +1.00000 q^{49} +0.0346431 q^{50} -7.20883 q^{51} -2.75169 q^{52} +11.1748 q^{53} -0.00957487 q^{54} +9.58332 q^{55} -0.0382986 q^{56} +0.675813 q^{57} +0.0116344 q^{58} +4.38876 q^{59} +5.87106 q^{60} +12.4714 q^{61} -0.0807681 q^{62} +1.00000 q^{63} -7.99780 q^{64} +4.03921 q^{65} -0.0312566 q^{66} -9.87493 q^{67} -14.4170 q^{68} +0.624915 q^{69} +0.0281086 q^{70} -0.850252 q^{71} -0.0382986 q^{72} -11.4811 q^{73} +0.0735553 q^{74} -3.61813 q^{75} +1.35156 q^{76} +3.26445 q^{77} -0.0131741 q^{78} -6.90025 q^{79} +11.7410 q^{80} +1.00000 q^{81} +0.112657 q^{82} -8.51766 q^{83} +1.99991 q^{84} +21.1627 q^{85} +0.0670224 q^{86} -1.21510 q^{87} -0.125024 q^{88} +10.5378 q^{89} +0.0281086 q^{90} +1.37591 q^{91} +1.24977 q^{92} +8.43543 q^{93} +0.0117928 q^{94} -1.98396 q^{95} -0.114891 q^{96} -2.72874 q^{97} +0.00957487 q^{98} +3.26445 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 3 q^{2} - 52 q^{3} + 61 q^{4} - 7 q^{5} - 3 q^{6} + 52 q^{7} + 24 q^{8} + 52 q^{9}+O(q^{10}) $ 52 * q + 3 * q^2 - 52 * q^3 + 61 * q^4 - 7 * q^5 - 3 * q^6 + 52 * q^7 + 24 * q^8 + 52 * q^9	\( 52 q + 3 q^{2} - 52 q^{3} + 61 q^{4} - 7 q^{5} - 3 q^{6} + 52 q^{7} + 24 q^{8} + 52 q^{9} - 2 q^{10} + 9 q^{11} - 61 q^{12} + 44 q^{13} + 3 q^{14} + 7 q^{15} + 95 q^{16} - 6 q^{17} + 3 q^{18} + 7 q^{19} - 21 q^{20} - 52 q^{21} + 19 q^{22} - 4 q^{23} - 24 q^{24} + 83 q^{25} - 5 q^{26} - 52 q^{27} + 61 q^{28} + 31 q^{29} + 2 q^{30} + 11 q^{31} + 71 q^{32} - 9 q^{33} + 17 q^{34} - 7 q^{35} + 61 q^{36} + 71 q^{37} - 8 q^{38} - 44 q^{39} + 20 q^{40} - 25 q^{41} - 3 q^{42} + 75 q^{43} + 14 q^{44} - 7 q^{45} + 36 q^{46} - 20 q^{47} - 95 q^{48} + 52 q^{49} + 26 q^{50} + 6 q^{51} + 88 q^{52} + 70 q^{53} - 3 q^{54} + 12 q^{55} + 24 q^{56} - 7 q^{57} + 48 q^{58} - 27 q^{59} + 21 q^{60} + 59 q^{61} - 23 q^{62} + 52 q^{63} + 138 q^{64} + 44 q^{65} - 19 q^{66} + 65 q^{67} - 8 q^{68} + 4 q^{69} - 2 q^{70} - 11 q^{71} + 24 q^{72} + 34 q^{73} + 38 q^{74} - 83 q^{75} + 31 q^{76} + 9 q^{77} + 5 q^{78} + 74 q^{79} - 5 q^{80} + 52 q^{81} + 51 q^{82} - 30 q^{83} - 61 q^{84} + 70 q^{85} + 29 q^{86} - 31 q^{87} + 90 q^{88} - q^{89} - 2 q^{90} + 44 q^{91} + 34 q^{92} - 11 q^{93} + 27 q^{94} + 9 q^{95} - 71 q^{96} + 73 q^{97} + 3 q^{98} + 9 q^{99}+O(q^{100}) \) 52 * q + 3 * q^2 - 52 * q^3 + 61 * q^4 - 7 * q^5 - 3 * q^6 + 52 * q^7 + 24 * q^8 + 52 * q^9 - 2 * q^10 + 9 * q^11 - 61 * q^12 + 44 * q^13 + 3 * q^14 + 7 * q^15 + 95 * q^16 - 6 * q^17 + 3 * q^18 + 7 * q^19 - 21 * q^20 - 52 * q^21 + 19 * q^22 - 4 * q^23 - 24 * q^24 + 83 * q^25 - 5 * q^26 - 52 * q^27 + 61 * q^28 + 31 * q^29 + 2 * q^30 + 11 * q^31 + 71 * q^32 - 9 * q^33 + 17 * q^34 - 7 * q^35 + 61 * q^36 + 71 * q^37 - 8 * q^38 - 44 * q^39 + 20 * q^40 - 25 * q^41 - 3 * q^42 + 75 * q^43 + 14 * q^44 - 7 * q^45 + 36 * q^46 - 20 * q^47 - 95 * q^48 + 52 * q^49 + 26 * q^50 + 6 * q^51 + 88 * q^52 + 70 * q^53 - 3 * q^54 + 12 * q^55 + 24 * q^56 - 7 * q^57 + 48 * q^58 - 27 * q^59 + 21 * q^60 + 59 * q^61 - 23 * q^62 + 52 * q^63 + 138 * q^64 + 44 * q^65 - 19 * q^66 + 65 * q^67 - 8 * q^68 + 4 * q^69 - 2 * q^70 - 11 * q^71 + 24 * q^72 + 34 * q^73 + 38 * q^74 - 83 * q^75 + 31 * q^76 + 9 * q^77 + 5 * q^78 + 74 * q^79 - 5 * q^80 + 52 * q^81 + 51 * q^82 - 30 * q^83 - 61 * q^84 + 70 * q^85 + 29 * q^86 - 31 * q^87 + 90 * q^88 - q^89 - 2 * q^90 + 44 * q^91 + 34 * q^92 - 11 * q^93 + 27 * q^94 + 9 * q^95 - 71 * q^96 + 73 * q^97 + 3 * q^98 + 9 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.00957487	0.00677045	0.00338523	−	0.999994i	$-0.498922\pi$
$2$	0.00957487	0.00677045	0.00338523	+	0.999994i	$0.498922\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.99991	−0.999954
$5$	2.93567	1.31287	0.656435	−	0.754383i	$-0.272064\pi$
$5$	2.93567	1.31287	0.656435	+	0.754383i	$0.272064\pi$
$6$	−0.00957487	−0.00390892
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−0.0382986	−0.0135406
$9$	1.00000	0.333333
$10$	0.0281086	0.00888872
$11$	3.26445	0.984268	0.492134	−	0.870520i	$-0.336217\pi$
$11$	3.26445	0.984268	0.492134	+	0.870520i	$0.336217\pi$
$12$	1.99991	0.577324
$13$	1.37591	0.381609	0.190804	−	0.981628i	$-0.438890\pi$
$13$	1.37591	0.381609	0.190804	+	0.981628i	$0.438890\pi$
$14$	0.00957487	0.00255899
$15$	−2.93567	−0.757985
$16$	3.99945	0.999862
$17$	7.20883	1.74840	0.874199	−	0.485568i	$-0.161387\pi$
$17$	7.20883	1.74840	0.874199	+	0.485568i	$0.161387\pi$
$18$	0.00957487	0.00225682
$19$	−0.675813	−0.155042	−0.0775211	−	0.996991i	$-0.524700\pi$
$19$	−0.675813	−0.155042	−0.0775211	+	0.996991i	$0.524700\pi$
$20$	−5.87106	−1.31281
$21$	−1.00000	−0.218218
$22$	0.0312566	0.00666394
$23$	−0.624915	−0.130304	−0.0651519	−	0.997875i	$-0.520753\pi$
$23$	−0.624915	−0.130304	−0.0651519	+	0.997875i	$0.520753\pi$
$24$	0.0382986	0.00781767
$25$	3.61813	0.723626
$26$	0.0131741	0.00258366
$27$	−1.00000	−0.192450
$28$	−1.99991	−0.377947
$29$	1.21510	0.225639	0.112819	−	0.993616i	$-0.464012\pi$
$29$	1.21510	0.225639	0.112819	+	0.993616i	$0.464012\pi$
$30$	−0.0281086	−0.00513191
$31$	−8.43543	−1.51505	−0.757524	−	0.652807i	$-0.773591\pi$
$31$	−8.43543	−1.51505	−0.757524	+	0.652807i	$0.773591\pi$
$32$	0.114891	0.0203101
$33$	−3.26445	−0.568267
$34$	0.0690236	0.0118374
$35$	2.93567	0.496218
$36$	−1.99991	−0.333318
$37$	7.68213	1.26293	0.631467	−	0.775403i	$-0.282453\pi$
$37$	7.68213	1.26293	0.631467	+	0.775403i	$0.282453\pi$
$38$	−0.00647082	−0.00104971
$39$	−1.37591	−0.220322
$40$	−0.112432	−0.0177770
$41$	11.7660	1.83753	0.918767	−	0.394800i	$-0.129186\pi$
$41$	11.7660	1.83753	0.918767	+	0.394800i	$0.129186\pi$
$42$	−0.00957487	−0.00147743
$43$	6.99983	1.06746	0.533732	−	0.845654i	$-0.320789\pi$
$43$	6.99983	1.06746	0.533732	+	0.845654i	$0.320789\pi$
$44$	−6.52859	−0.984222
$45$	2.93567	0.437623
$46$	−0.00598348	−0.000882215 0
$47$	1.23164	0.179653	0.0898267	−	0.995957i	$-0.471369\pi$
$47$	1.23164	0.179653	0.0898267	+	0.995957i	$0.471369\pi$
$48$	−3.99945	−0.577271
$49$	1.00000	0.142857
$50$	0.0346431	0.00489928
$51$	−7.20883	−1.00944
$52$	−2.75169	−0.381591
$53$	11.1748	1.53497	0.767487	−	0.641064i	$-0.221507\pi$
$53$	11.1748	1.53497	0.767487	+	0.641064i	$0.221507\pi$
$54$	−0.00957487	−0.00130297
$55$	9.58332	1.29221
$56$	−0.0382986	−0.00511786
$57$	0.675813	0.0895136
$58$	0.0116344	0.00152768
$59$	4.38876	0.571368	0.285684	−	0.958324i	$-0.407779\pi$
$59$	4.38876	0.571368	0.285684	+	0.958324i	$0.407779\pi$
$60$	5.87106	0.757951
$61$	12.4714	1.59680	0.798398	−	0.602130i	$-0.205681\pi$
$61$	12.4714	1.59680	0.798398	+	0.602130i	$0.205681\pi$
$62$	−0.0807681	−0.0102576
$63$	1.00000	0.125988
$64$	−7.99780	−0.999725
$65$	4.03921	0.501002
$66$	−0.0312566	−0.00384743
$67$	−9.87493	−1.20641	−0.603207	−	0.797585i	$-0.706111\pi$
$67$	−9.87493	−1.20641	−0.603207	+	0.797585i	$0.706111\pi$
$68$	−14.4170	−1.74832
$69$	0.624915	0.0752309
$70$	0.0281086	0.00335962
$71$	−0.850252	−0.100906	−0.0504532	−	0.998726i	$-0.516067\pi$
$71$	−0.850252	−0.100906	−0.0504532	+	0.998726i	$0.516067\pi$
$72$	−0.0382986	−0.00451353
$73$	−11.4811	−1.34376	−0.671881	−	0.740659i	$-0.734513\pi$
$73$	−11.4811	−1.34376	−0.671881	+	0.740659i	$0.734513\pi$
$74$	0.0735553	0.00855063
$75$	−3.61813	−0.417786
$76$	1.35156	0.155035
$77$	3.26445	0.372018
$78$	−0.0131741	−0.00149168
$79$	−6.90025	−0.776339	−0.388170	−	0.921588i	$-0.626893\pi$
$79$	−6.90025	−0.776339	−0.388170	+	0.921588i	$0.626893\pi$
$80$	11.7410	1.31269
$81$	1.00000	0.111111
$82$	0.112657	0.0124409
$83$	−8.51766	−0.934935	−0.467467	−	0.884010i	$-0.654834\pi$
$83$	−8.51766	−0.934935	−0.467467	+	0.884010i	$0.654834\pi$
$84$	1.99991	0.218208
$85$	21.1627	2.29542
$86$	0.0670224	0.00722721
$87$	−1.21510	−0.130273
$88$	−0.125024	−0.0133276
$89$	10.5378	1.11700	0.558500	−	0.829504i	$-0.311377\pi$
$89$	10.5378	1.11700	0.558500	+	0.829504i	$0.311377\pi$
$90$	0.0281086	0.00296291
$91$	1.37591	0.144234
$92$	1.24977	0.130298
$93$	8.43543	0.874714
$94$	0.0117928	0.00121634
$95$	−1.98396	−0.203550
$96$	−0.114891	−0.0117261
$97$	−2.72874	−0.277062	−0.138531	−	0.990358i	$-0.544238\pi$
$97$	−2.72874	−0.277062	−0.138531	+	0.990358i	$0.544238\pi$
$98$	0.00957487	0.000967208 0
$99$	3.26445	0.328089
$100$	−7.23593	−0.723593
$101$	−16.9282	−1.68442	−0.842209	−	0.539151i	$-0.818745\pi$
$101$	−16.9282	−1.68442	−0.842209	+	0.539151i	$0.818745\pi$
$102$	−0.0690236	−0.00683435
$103$	−11.2058	−1.10414	−0.552069	−	0.833799i	$-0.686161\pi$
$103$	−11.2058	−1.10414	−0.552069	+	0.833799i	$0.686161\pi$
$104$	−0.0526954	−0.00516721
$105$	−2.93567	−0.286492
$106$	0.106997	0.0103925
$107$	14.1473	1.36767	0.683834	−	0.729638i	$-0.260311\pi$
$107$	14.1473	1.36767	0.683834	+	0.729638i	$0.260311\pi$
$108$	1.99991	0.192441
$109$	−2.43283	−0.233023	−0.116512	−	0.993189i	$-0.537171\pi$
$109$	−2.43283	−0.233023	−0.116512	+	0.993189i	$0.537171\pi$
$110$	0.0917590	0.00874888
$111$	−7.68213	−0.729155
$112$	3.99945	0.377912
$113$	3.54653	0.333629	0.166815	−	0.985988i	$-0.446652\pi$
$113$	3.54653	0.333629	0.166815	+	0.985988i	$0.446652\pi$
$114$	0.00647082	0.000606048 0
$115$	−1.83454	−0.171072
$116$	−2.43009	−0.225628
$117$	1.37591	0.127203
$118$	0.0420218	0.00386842
$119$	7.20883	0.660832
$120$	0.112432	0.0102636
$121$	−0.343391	−0.0312173
$122$	0.119412	0.0108110
$123$	−11.7660	−1.06090
$124$	16.8701	1.51498
$125$	−4.05671	−0.362843
$126$	0.00957487	0.000852997 0
$127$	−1.65445	−0.146808	−0.0734042	−	0.997302i	$-0.523386\pi$
$127$	−1.65445	−0.146808	−0.0734042	+	0.997302i	$0.523386\pi$
$128$	−0.306361	−0.0270787
$129$	−6.99983	−0.616300
$130$	0.0386749	0.00339201
$131$	−10.0463	−0.877751	−0.438875	−	0.898548i	$-0.644623\pi$
$131$	−10.0463	−0.877751	−0.438875	+	0.898548i	$0.644623\pi$
$132$	6.52859	0.568241
$133$	−0.675813	−0.0586004
$134$	−0.0945511	−0.00816797
$135$	−2.93567	−0.252662
$136$	−0.276088	−0.0236743
$137$	10.5023	0.897271	0.448635	−	0.893715i	$-0.351910\pi$
$137$	10.5023	0.897271	0.448635	+	0.893715i	$0.351910\pi$
$138$	0.00598348	0.000509347 0
$139$	3.14450	0.266713	0.133357	−	0.991068i	$-0.457424\pi$
$139$	3.14450	0.266713	0.133357	+	0.991068i	$0.457424\pi$
$140$	−5.87106	−0.496195
$141$	−1.23164	−0.103723
$142$	−0.00814105	−0.000683181 0
$143$	4.49158	0.375605
$144$	3.99945	0.333287
$145$	3.56713	0.296234
$146$	−0.109930	−0.00909788
$147$	−1.00000	−0.0824786
$148$	−15.3635	−1.26288
$149$	−1.49156	−0.122194	−0.0610969	−	0.998132i	$-0.519460\pi$
$149$	−1.49156	−0.122194	−0.0610969	+	0.998132i	$0.519460\pi$
$150$	−0.0346431	−0.00282860
$151$	−17.8782	−1.45491	−0.727455	−	0.686155i	$-0.759297\pi$
$151$	−17.8782	−1.45491	−0.727455	+	0.686155i	$0.759297\pi$
$152$	0.0258827	0.00209936
$153$	7.20883	0.582799
$154$	0.0312566	0.00251873
$155$	−24.7636	−1.98906
$156$	2.75169	0.220312
$157$	−11.8918	−0.949069	−0.474535	−	0.880237i	$-0.657384\pi$
$157$	−11.8918	−0.949069	−0.474535	+	0.880237i	$0.657384\pi$
$158$	−0.0660690	−0.00525617
$159$	−11.1748	−0.886218
$160$	0.337283	0.0266645
$161$	−0.624915	−0.0492502
$162$	0.00957487	0.000752273 0
$163$	−15.4408	−1.20942	−0.604709	−	0.796447i	$-0.706710\pi$
$163$	−15.4408	−1.20942	−0.604709	+	0.796447i	$0.706710\pi$
$164$	−23.5308	−1.83745
$165$	−9.58332	−0.746061
$166$	−0.0815555	−0.00632993
$167$	8.38834	0.649109	0.324555	−	0.945867i	$-0.394786\pi$
$167$	8.38834	0.649109	0.324555	+	0.945867i	$0.394786\pi$
$168$	0.0382986	0.00295480
$169$	−11.1069	−0.854375
$170$	0.202630	0.0155410
$171$	−0.675813	−0.0516807
$172$	−13.9990	−1.06741
$173$	13.4744	1.02444	0.512219	−	0.858855i	$-0.328823\pi$
$173$	13.4744	1.02444	0.512219	+	0.858855i	$0.328823\pi$
$174$	−0.0116344	−0.000882004 0
$175$	3.61813	0.273505
$176$	13.0560	0.984132
$177$	−4.38876	−0.329879
$178$	0.100898	0.00756260
$179$	−13.5981	−1.01637	−0.508184	−	0.861248i	$-0.669683\pi$
$179$	−13.5981	−1.01637	−0.508184	+	0.861248i	$0.669683\pi$
$180$	−5.87106	−0.437603
$181$	2.92062	0.217088	0.108544	−	0.994092i	$-0.465381\pi$
$181$	2.92062	0.217088	0.108544	+	0.994092i	$0.465381\pi$
$182$	0.0131741	0.000976533 0
$183$	−12.4714	−0.921911
$184$	0.0239334	0.00176439
$185$	22.5522	1.65807
$186$	0.0807681	0.00592221
$187$	23.5328	1.72089
$188$	−2.46317	−0.179645
$189$	−1.00000	−0.0727393
$190$	−0.0189962	−0.00137813
$191$	20.3994	1.47605	0.738024	−	0.674775i	$-0.235759\pi$
$191$	20.3994	1.47605	0.738024	+	0.674775i	$0.235759\pi$
$192$	7.99780	0.577191
$193$	−26.2084	−1.88652	−0.943261	−	0.332051i	$-0.892259\pi$
$193$	−26.2084	−1.88652	−0.943261	+	0.332051i	$0.892259\pi$
$194$	−0.0261274	−0.00187584
$195$	−4.03921	−0.289254
$196$	−1.99991	−0.142851
$197$	−7.16837	−0.510725	−0.255362	−	0.966845i	$-0.582195\pi$
$197$	−7.16837	−0.510725	−0.255362	+	0.966845i	$0.582195\pi$
$198$	0.0312566	0.00222131
$199$	18.8060	1.33313	0.666563	−	0.745449i	$-0.267765\pi$
$199$	18.8060	1.33313	0.666563	+	0.745449i	$0.267765\pi$
$200$	−0.138569	−0.00979833
$201$	9.87493	0.696524
$202$	−0.162085	−0.0114043
$203$	1.21510	0.0852834
$204$	14.4170	1.00939
$205$	34.5409	2.41244
$206$	−0.107294	−0.00747551
$207$	−0.624915	−0.0434346
$208$	5.50288	0.381556
$209$	−2.20615	−0.152603
$210$	−0.0281086	−0.00193968
$211$	17.3344	1.19335	0.596676	−	0.802482i	$-0.296488\pi$
$211$	17.3344	1.19335	0.596676	+	0.802482i	$0.296488\pi$
$212$	−22.3485	−1.53490
$213$	0.850252	0.0582583
$214$	0.135458	0.00925973
$215$	20.5491	1.40144
$216$	0.0382986	0.00260589
$217$	−8.43543	−0.572635
$218$	−0.0232941	−0.00157767
$219$	11.4811	0.775821
$220$	−19.1658	−1.29216
$221$	9.91869	0.667203
$222$	−0.0735553	−0.00493671
$223$	−20.0658	−1.34371	−0.671853	−	0.740685i	$-0.734501\pi$
$223$	−20.0658	−1.34371	−0.671853	+	0.740685i	$0.734501\pi$
$224$	0.114891	0.00767650
$225$	3.61813	0.241209
$226$	0.0339575	0.00225882
$227$	−5.77153	−0.383070	−0.191535	−	0.981486i	$-0.561346\pi$
$227$	−5.77153	−0.383070	−0.191535	+	0.981486i	$0.561346\pi$
$228$	−1.35156	−0.0895095
$229$	−10.9586	−0.724166	−0.362083	−	0.932146i	$-0.617934\pi$
$229$	−10.9586	−0.724166	−0.362083	+	0.932146i	$0.617934\pi$
$230$	−0.0175655	−0.00115823
$231$	−3.26445	−0.214785
$232$	−0.0465367	−0.00305528
$233$	12.1947	0.798903	0.399451	−	0.916754i	$-0.369201\pi$
$233$	12.1947	0.798903	0.399451	+	0.916754i	$0.369201\pi$
$234$	0.0131741	0.000861221 0
$235$	3.61569	0.235861
$236$	−8.77712	−0.571342
$237$	6.90025	0.448220
$238$	0.0690236	0.00447413
$239$	−10.8767	−0.703558	−0.351779	−	0.936083i	$-0.614423\pi$
$239$	−10.8767	−0.703558	−0.351779	+	0.936083i	$0.614423\pi$
$240$	−11.7410	−0.757881
$241$	21.7677	1.40218	0.701092	−	0.713071i	$-0.252696\pi$
$241$	21.7677	1.40218	0.701092	+	0.713071i	$0.252696\pi$
$242$	−0.00328792	−0.000211356 0
$243$	−1.00000	−0.0641500
$244$	−24.9416	−1.59672
$245$	2.93567	0.187553
$246$	−0.112657	−0.00718278
$247$	−0.929857	−0.0591654
$248$	0.323065	0.0205147
$249$	8.51766	0.539785
$250$	−0.0388424	−0.00245661
$251$	−3.87558	−0.244625	−0.122312	−	0.992492i	$-0.539031\pi$
$251$	−3.87558	−0.244625	−0.122312	+	0.992492i	$0.539031\pi$
$252$	−1.99991	−0.125982
$253$	−2.04000	−0.128254
$254$	−0.0158411	−0.000993959 0
$255$	−21.1627	−1.32526
$256$	15.9927	0.999542
$257$	−2.26668	−0.141391	−0.0706957	−	0.997498i	$-0.522522\pi$
$257$	−2.26668	−0.141391	−0.0706957	+	0.997498i	$0.522522\pi$
$258$	−0.0670224	−0.00417263
$259$	7.68213	0.477344
$260$	−8.07805	−0.500979
$261$	1.21510	0.0752129
$262$	−0.0961922	−0.00594277
$263$	25.0405	1.54407	0.772033	−	0.635583i	$-0.219240\pi$
$263$	25.0405	1.54407	0.772033	+	0.635583i	$0.219240\pi$
$264$	0.125024	0.00769468
$265$	32.8054	2.01522
$266$	−0.00647082	−0.000396751 0
$267$	−10.5378	−0.644900
$268$	19.7489	1.20636
$269$	18.1088	1.10411	0.552056	−	0.833807i	$-0.313844\pi$
$269$	18.1088	1.10411	0.552056	+	0.833807i	$0.313844\pi$
$270$	−0.0281086	−0.00171064
$271$	−15.1902	−0.922739	−0.461370	−	0.887208i	$-0.652642\pi$
$271$	−15.1902	−0.922739	−0.461370	+	0.887208i	$0.652642\pi$
$272$	28.8313	1.74816
$273$	−1.37591	−0.0832738
$274$	0.100558	0.00607493
$275$	11.8112	0.712242
$276$	−1.24977	−0.0752275
$277$	−29.2199	−1.75565	−0.877827	−	0.478977i	$-0.841008\pi$
$277$	−29.2199	−1.75565	−0.877827	+	0.478977i	$0.841008\pi$
$278$	0.0301082	0.00180577
$279$	−8.43543	−0.505016
$280$	−0.112432	−0.00671909
$281$	14.3520	0.856169	0.428084	−	0.903739i	$-0.359189\pi$
$281$	14.3520	0.856169	0.428084	+	0.903739i	$0.359189\pi$
$282$	−0.0117928	−0.000702251 0
$283$	−24.4425	−1.45296	−0.726479	−	0.687189i	$-0.758844\pi$
$283$	−24.4425	−1.45296	−0.726479	+	0.687189i	$0.758844\pi$
$284$	1.70043	0.100902
$285$	1.98396	0.117520
$286$	0.0430063	0.00254302
$287$	11.7660	0.694523
$288$	0.114891	0.00677004
$289$	34.9672	2.05689
$290$	0.0341548	0.00200564
$291$	2.72874	0.159962
$292$	22.9612	1.34370
$293$	−3.95897	−0.231285	−0.115643	−	0.993291i	$-0.536893\pi$
$293$	−3.95897	−0.231285	−0.115643	+	0.993291i	$0.536893\pi$
$294$	−0.00957487	−0.000558418 0
$295$	12.8839	0.750131
$296$	−0.294215	−0.0171009
$297$	−3.26445	−0.189422
$298$	−0.0142815	−0.000827307 0
$299$	−0.859826	−0.0497250
$300$	7.23593	0.417767
$301$	6.99983	0.403463
$302$	−0.171182	−0.00985040
$303$	16.9282	0.972499
$304$	−2.70288	−0.155021
$305$	36.6118	2.09638
$306$	0.0690236	0.00394581
$307$	21.4446	1.22391	0.611955	−	0.790892i	$-0.290383\pi$
$307$	21.4446	1.22391	0.611955	+	0.790892i	$0.290383\pi$
$308$	−6.52859	−0.372001
$309$	11.2058	0.637474
$310$	−0.237108	−0.0134668
$311$	7.15945	0.405975	0.202988	−	0.979181i	$-0.434935\pi$
$311$	7.15945	0.405975	0.202988	+	0.979181i	$0.434935\pi$
$312$	0.0526954	0.00298329
$313$	14.3379	0.810429	0.405214	−	0.914222i	$-0.367197\pi$
$313$	14.3379	0.810429	0.405214	+	0.914222i	$0.367197\pi$
$314$	−0.113862	−0.00642563
$315$	2.93567	0.165406
$316$	13.7999	0.776304
$317$	−4.97956	−0.279680	−0.139840	−	0.990174i	$-0.544659\pi$
$317$	−4.97956	−0.279680	−0.139840	+	0.990174i	$0.544659\pi$
$318$	−0.106997	−0.00600010
$319$	3.96663	0.222089
$320$	−23.4789	−1.31251
$321$	−14.1473	−0.789623
$322$	−0.00598348	−0.000333446 0
$323$	−4.87182	−0.271075
$324$	−1.99991	−0.111106
$325$	4.97822	0.276142
$326$	−0.147844	−0.00818830
$327$	2.43283	0.134536
$328$	−0.450620	−0.0248813
$329$	1.23164	0.0679026
$330$	−0.0917590	−0.00505117
$331$	−17.2252	−0.946780	−0.473390	−	0.880853i	$-0.656970\pi$
$331$	−17.2252	−0.946780	−0.473390	+	0.880853i	$0.656970\pi$
$332$	17.0345	0.934892
$333$	7.68213	0.420978
$334$	0.0803173	0.00439477
$335$	−28.9895	−1.58386
$336$	−3.99945	−0.218188
$337$	−23.3193	−1.27028	−0.635142	−	0.772396i	$-0.719058\pi$
$337$	−23.3193	−1.27028	−0.635142	+	0.772396i	$0.719058\pi$
$338$	−0.106347	−0.00578451
$339$	−3.54653	−0.192621
$340$	−42.3235	−2.29531
$341$	−27.5370	−1.49121
$342$	−0.00647082	−0.000349902 0
$343$	1.00000	0.0539949
$344$	−0.268083	−0.0144541
$345$	1.83454	0.0987683
$346$	0.129015	0.00693592
$347$	25.8535	1.38789	0.693944	−	0.720029i	$-0.255871\pi$
$347$	25.8535	1.38789	0.693944	+	0.720029i	$0.255871\pi$
$348$	2.43009	0.130267
$349$	30.8309	1.65034	0.825170	−	0.564885i	$-0.191079\pi$
$349$	30.8309	1.65034	0.825170	+	0.564885i	$0.191079\pi$
$350$	0.0346431	0.00185175
$351$	−1.37591	−0.0734406
$352$	0.375057	0.0199906
$353$	−16.9403	−0.901639	−0.450820	−	0.892615i	$-0.648868\pi$
$353$	−16.9403	−0.901639	−0.450820	+	0.892615i	$0.648868\pi$
$354$	−0.0420218	−0.00223343
$355$	−2.49605	−0.132477
$356$	−21.0745	−1.11695
$357$	−7.20883	−0.381532
$358$	−0.130200	−0.00688128
$359$	36.6998	1.93694	0.968470	−	0.249130i	$-0.0801447\pi$
$359$	36.6998	1.93694	0.968470	+	0.249130i	$0.0801447\pi$
$360$	−0.112432	−0.00592568
$361$	−18.5433	−0.975962
$362$	0.0279645	0.00146978
$363$	0.343391	0.0180233
$364$	−2.75169	−0.144228
$365$	−33.7047	−1.76418
$366$	−0.119412	−0.00624175
$367$	25.9488	1.35452	0.677258	−	0.735745i	$-0.263168\pi$
$367$	25.9488	1.35452	0.677258	+	0.735745i	$0.263168\pi$
$368$	−2.49932	−0.130286
$369$	11.7660	0.612511
$370$	0.215934	0.0112259
$371$	11.1748	0.580166
$372$	−16.8701	−0.874674
$373$	−3.63787	−0.188362	−0.0941808	−	0.995555i	$-0.530023\pi$
$373$	−3.63787	−0.188362	−0.0941808	+	0.995555i	$0.530023\pi$
$374$	0.225324	0.0116512
$375$	4.05671	0.209487
$376$	−0.0471701	−0.00243261
$377$	1.67187	0.0861056
$378$	−0.00957487	−0.000492478 0
$379$	3.43684	0.176539	0.0882694	−	0.996097i	$-0.471866\pi$
$379$	3.43684	0.176539	0.0882694	+	0.996097i	$0.471866\pi$
$380$	3.96774	0.203541
$381$	1.65445	0.0847598
$382$	0.195321	0.00999351
$383$	−1.00000	−0.0510976
$383$	−1.00000	−0.0510976
$384$	0.306361	0.0156339
$385$	9.58332	0.488411
$386$	−0.250942	−0.0127726
$387$	6.99983	0.355821
$388$	5.45724	0.277049
$389$	−19.1868	−0.972807	−0.486403	−	0.873734i	$-0.661691\pi$
$389$	−19.1868	−0.972807	−0.486403	+	0.873734i	$0.661691\pi$
$390$	−0.0386749	−0.00195838
$391$	−4.50490	−0.227823
$392$	−0.0382986	−0.00193437
$393$	10.0463	0.506770
$394$	−0.0686361	−0.00345784
$395$	−20.2568	−1.01923
$396$	−6.52859	−0.328074
$397$	−17.1572	−0.861096	−0.430548	−	0.902568i	$-0.641680\pi$
$397$	−17.1572	−0.861096	−0.430548	+	0.902568i	$0.641680\pi$
$398$	0.180065	0.00902586
$399$	0.675813	0.0338330
$400$	14.4705	0.723527
$401$	34.2037	1.70805	0.854025	−	0.520231i	$-0.174154\pi$
$401$	34.2037	1.70805	0.854025	+	0.520231i	$0.174154\pi$
$402$	0.0945511	0.00471578
$403$	−11.6064	−0.578155
$404$	33.8548	1.68434
$405$	2.93567	0.145874
$406$	0.0116344	0.000577407 0
$407$	25.0779	1.24306
$408$	0.276088	0.0136684
$409$	4.93982	0.244259	0.122129	−	0.992514i	$-0.461028\pi$
$409$	4.93982	0.244259	0.122129	+	0.992514i	$0.461028\pi$
$410$	0.330725	0.0163333
$411$	−10.5023	−0.518040
$412$	22.4105	1.10409
$413$	4.38876	0.215957
$414$	−0.00598348	−0.000294072 0
$415$	−25.0050	−1.22745
$416$	0.158080	0.00775051
$417$	−3.14450	−0.153987
$418$	−0.0211236	−0.00103319
$419$	13.4288	0.656037	0.328019	−	0.944671i	$-0.393619\pi$
$419$	13.4288	0.656037	0.328019	+	0.944671i	$0.393619\pi$
$420$	5.87106	0.286478
$421$	−35.2044	−1.71576	−0.857878	−	0.513854i	$-0.828217\pi$
$421$	−35.2044	−1.71576	−0.857878	+	0.513854i	$0.828217\pi$
$422$	0.165975	0.00807954
$423$	1.23164	0.0598845
$424$	−0.427979	−0.0207845
$425$	26.0825	1.26519
$426$	0.00814105	0.000394435 0
$427$	12.4714	0.603532
$428$	−28.2932	−1.36760
$429$	−4.49158	−0.216856
$430$	0.196755	0.00948838
$431$	36.3074	1.74887	0.874433	−	0.485147i	$-0.161234\pi$
$431$	36.3074	1.74887	0.874433	+	0.485147i	$0.161234\pi$
$432$	−3.99945	−0.192424
$433$	30.7933	1.47983	0.739915	−	0.672701i	$-0.234866\pi$
$433$	30.7933	1.47983	0.739915	+	0.672701i	$0.234866\pi$
$434$	−0.0807681	−0.00387700
$435$	−3.56713	−0.171031
$436$	4.86544	0.233013
$437$	0.422325	0.0202026
$438$	0.109930	0.00525266
$439$	−11.8707	−0.566559	−0.283280	−	0.959037i	$-0.591422\pi$
$439$	−11.8707	−0.566559	−0.283280	+	0.959037i	$0.591422\pi$
$440$	−0.367028	−0.0174974
$441$	1.00000	0.0476190
$442$	0.0949702	0.00451727
$443$	−14.5443	−0.691022	−0.345511	−	0.938415i	$-0.612294\pi$
$443$	−14.5443	−0.691022	−0.345511	+	0.938415i	$0.612294\pi$
$444$	15.3635	0.729122
$445$	30.9353	1.46648
$446$	−0.192127	−0.00909749
$447$	1.49156	0.0705486
$448$	−7.99780	−0.377861
$449$	4.22457	0.199370	0.0996849	−	0.995019i	$-0.468217\pi$
$449$	4.22457	0.199370	0.0996849	+	0.995019i	$0.468217\pi$
$450$	0.0346431	0.00163309
$451$	38.4093	1.80863
$452$	−7.09273	−0.333614
$453$	17.8782	0.839993
$454$	−0.0552616	−0.00259356
$455$	4.03921	0.189361
$456$	−0.0258827	−0.00121207
$457$	20.8580	0.975694	0.487847	−	0.872929i	$-0.337782\pi$
$457$	20.8580	0.975694	0.487847	+	0.872929i	$0.337782\pi$
$458$	−0.104927	−0.00490293
$459$	−7.20883	−0.336479
$460$	3.66891	0.171064
$461$	−9.18937	−0.427992	−0.213996	−	0.976835i	$-0.568648\pi$
$461$	−9.18937	−0.427992	−0.213996	+	0.976835i	$0.568648\pi$
$462$	−0.0312566	−0.00145419
$463$	−14.9252	−0.693632	−0.346816	−	0.937933i	$-0.612737\pi$
$463$	−14.9252	−0.693632	−0.346816	+	0.937933i	$0.612737\pi$
$464$	4.85974	0.225608
$465$	24.7636	1.14838
$466$	0.116763	0.00540893
$467$	12.6661	0.586119	0.293059	−	0.956094i	$-0.405327\pi$
$467$	12.6661	0.586119	0.293059	+	0.956094i	$0.405327\pi$
$468$	−2.75169	−0.127197
$469$	−9.87493	−0.455982
$470$	0.0346197	0.00159689
$471$	11.8918	0.547945
$472$	−0.168083	−0.00773666
$473$	22.8506	1.05067
$474$	0.0660690	0.00303465
$475$	−2.44518	−0.112193
$476$	−14.4170	−0.660802
$477$	11.1748	0.511658
$478$	−0.104143	−0.00476341
$479$	−18.6701	−0.853057	−0.426528	−	0.904474i	$-0.640264\pi$
$479$	−18.6701	−0.853057	−0.426528	+	0.904474i	$0.640264\pi$
$480$	−0.337283	−0.0153948
$481$	10.5699	0.481946
$482$	0.208423	0.00949342
$483$	0.624915	0.0284346
$484$	0.686750	0.0312159
$485$	−8.01068	−0.363746
$486$	−0.00957487	−0.000434325 0
$487$	8.78591	0.398127	0.199064	−	0.979987i	$-0.436210\pi$
$487$	8.78591	0.398127	0.199064	+	0.979987i	$0.436210\pi$
$488$	−0.477636	−0.0216216
$489$	15.4408	0.698257
$490$	0.0281086	0.00126982
$491$	−36.8800	−1.66437	−0.832186	−	0.554496i	$-0.812911\pi$
$491$	−36.8800	−1.66437	−0.832186	+	0.554496i	$0.812911\pi$
$492$	23.5308	1.06085
$493$	8.75945	0.394506
$494$	−0.00890326	−0.000400577 0
$495$	9.58332	0.430738
$496$	−33.7371	−1.51484
$497$	−0.850252	−0.0381390
$498$	0.0815555	0.00365459
$499$	−2.91126	−0.130326	−0.0651630	−	0.997875i	$-0.520757\pi$
$499$	−2.91126	−0.130326	−0.0651630	+	0.997875i	$0.520757\pi$
$500$	8.11304	0.362826
$501$	−8.38834	−0.374764
$502$	−0.0371082	−0.00165622
$503$	15.5348	0.692663	0.346332	−	0.938112i	$-0.387427\pi$
$503$	15.5348	0.692663	0.346332	+	0.938112i	$0.387427\pi$
$504$	−0.0382986	−0.00170595
$505$	−49.6955	−2.21142
$506$	−0.0195327	−0.000868336 0
$507$	11.1069	0.493274
$508$	3.30874	0.146802
$509$	15.8418	0.702174	0.351087	−	0.936343i	$-0.385812\pi$
$509$	15.8418	0.702174	0.351087	+	0.936343i	$0.385812\pi$
$510$	−0.202630	−0.00897261
$511$	−11.4811	−0.507894
$512$	0.765849	0.0338461
$513$	0.675813	0.0298379
$514$	−0.0217031	−0.000957284 0
$515$	−32.8964	−1.44959
$516$	13.9990	0.616272
$517$	4.02063	0.176827
$518$	0.0735553	0.00323184
$519$	−13.4744	−0.591460
$520$	−0.154696	−0.00678387
$521$	−5.12425	−0.224498	−0.112249	−	0.993680i	$-0.535805\pi$
$521$	−5.12425	−0.224498	−0.112249	+	0.993680i	$0.535805\pi$
$522$	0.0116344	0.000509225 0
$523$	−2.97582	−0.130123	−0.0650617	−	0.997881i	$-0.520724\pi$
$523$	−2.97582	−0.130123	−0.0650617	+	0.997881i	$0.520724\pi$
$524$	20.0917	0.877711
$525$	−3.61813	−0.157908
$526$	0.239760	0.0104540
$527$	−60.8096	−2.64891
$528$	−13.0560	−0.568189
$529$	−22.6095	−0.983021
$530$	0.314108	0.0136440
$531$	4.38876	0.190456
$532$	1.35156	0.0585977
$533$	16.1889	0.701219
$534$	−0.100898	−0.00436627
$535$	41.5316	1.79557
$536$	0.378196	0.0163356
$537$	13.5981	0.586801
$538$	0.173389	0.00747534
$539$	3.26445	0.140610
$540$	5.87106	0.252650
$541$	−13.7023	−0.589107	−0.294554	−	0.955635i	$-0.595171\pi$
$541$	−13.7023	−0.589107	−0.294554	+	0.955635i	$0.595171\pi$
$542$	−0.145444	−0.00624736
$543$	−2.92062	−0.125336
$544$	0.828232	0.0355102
$545$	−7.14199	−0.305929
$546$	−0.0131741	−0.000563801 0
$547$	13.8442	0.591934	0.295967	−	0.955198i	$-0.404358\pi$
$547$	13.8442	0.591934	0.295967	+	0.955198i	$0.404358\pi$
$548$	−21.0036	−0.897230
$549$	12.4714	0.532265
$550$	0.113091	0.00482220
$551$	−0.821181	−0.0349835
$552$	−0.0239334	−0.00101867
$553$	−6.90025	−0.293429
$554$	−0.279777	−0.0118866
$555$	−22.5522	−0.957286
$556$	−6.28872	−0.266701
$557$	12.4124	0.525930	0.262965	−	0.964805i	$-0.415300\pi$
$557$	12.4124	0.525930	0.262965	+	0.964805i	$0.415300\pi$
$558$	−0.0807681	−0.00341919
$559$	9.63112	0.407353
$560$	11.7410	0.496150
$561$	−23.5328	−0.993557
$562$	0.137419	0.00579665
$563$	−22.6911	−0.956316	−0.478158	−	0.878274i	$-0.658695\pi$
$563$	−22.6911	−0.956316	−0.478158	+	0.878274i	$0.658695\pi$
$564$	2.46317	0.103718
$565$	10.4114	0.438012
$566$	−0.234034	−0.00983718
$567$	1.00000	0.0419961
$568$	0.0325634	0.00136633
$569$	−30.2115	−1.26653	−0.633267	−	0.773933i	$-0.718286\pi$
$569$	−30.2115	−1.26653	−0.633267	+	0.773933i	$0.718286\pi$
$570$	0.0189962	0.000795661 0
$571$	46.0726	1.92808	0.964039	−	0.265762i	$-0.0856234\pi$
$571$	46.0726	1.92808	0.964039	+	0.265762i	$0.0856234\pi$
$572$	−8.98275	−0.375588
$573$	−20.3994	−0.852197
$574$	0.112657	0.00470223
$575$	−2.26102	−0.0942912
$576$	−7.99780	−0.333242
$577$	24.6098	1.02452	0.512259	−	0.858831i	$-0.328809\pi$
$577$	24.6098	1.02452	0.512259	+	0.858831i	$0.328809\pi$
$578$	0.334806	0.0139261
$579$	26.2084	1.08918
$580$	−7.13393	−0.296220
$581$	−8.51766	−0.353372
$582$	0.0261274	0.00108301
$583$	36.4795	1.51083
$584$	0.439710	0.0181953
$585$	4.03921	0.167001
$586$	−0.0379066	−0.00156591
$587$	−9.27851	−0.382965	−0.191483	−	0.981496i	$-0.561330\pi$
$587$	−9.27851	−0.382965	−0.191483	+	0.981496i	$0.561330\pi$
$588$	1.99991	0.0824748
$589$	5.70077	0.234896
$590$	0.123362	0.00507873
$591$	7.16837	0.294867
$592$	30.7243	1.26276
$593$	−36.1768	−1.48560	−0.742801	−	0.669512i	$-0.766503\pi$
$593$	−36.1768	−1.48560	−0.742801	+	0.669512i	$0.766503\pi$
$594$	−0.0312566	−0.00128248
$595$	21.1627	0.867586
$596$	2.98299	0.122188
$597$	−18.8060	−0.769680
$598$	−0.00823272	−0.000336661 0
$599$	23.5769	0.963326	0.481663	−	0.876356i	$-0.340033\pi$
$599$	23.5769	0.963326	0.481663	+	0.876356i	$0.340033\pi$
$600$	0.138569	0.00565707
$601$	−25.0996	−1.02383	−0.511917	−	0.859035i	$-0.671064\pi$
$601$	−25.0996	−1.02383	−0.511917	+	0.859035i	$0.671064\pi$
$602$	0.0670224	0.00273163
$603$	−9.87493	−0.402138
$604$	35.7548	1.45484
$605$	−1.00808	−0.0409843
$606$	0.162085	0.00658426
$607$	21.0048	0.852560	0.426280	−	0.904591i	$-0.359824\pi$
$607$	21.0048	0.852560	0.426280	+	0.904591i	$0.359824\pi$
$608$	−0.0776451	−0.00314892
$609$	−1.21510	−0.0492384
$610$	0.350553	0.0141935
$611$	1.69463	0.0685573
$612$	−14.4170	−0.582772
$613$	12.4791	0.504027	0.252014	−	0.967724i	$-0.418907\pi$
$613$	12.4791	0.504027	0.252014	+	0.967724i	$0.418907\pi$
$614$	0.205330	0.00828643
$615$	−34.5409	−1.39282
$616$	−0.125024	−0.00503735
$617$	−3.36585	−0.135504	−0.0677520	−	0.997702i	$-0.521583\pi$
$617$	−3.36585	−0.135504	−0.0677520	+	0.997702i	$0.521583\pi$
$618$	0.107294	0.00431599
$619$	9.31428	0.374372	0.187186	−	0.982324i	$-0.440063\pi$
$619$	9.31428	0.374372	0.187186	+	0.982324i	$0.440063\pi$
$620$	49.5249	1.98897
$621$	0.624915	0.0250770
$622$	0.0685508	0.00274864
$623$	10.5378	0.422186
$624$	−5.50288	−0.220292
$625$	−29.9998	−1.19999
$626$	0.137284	0.00548697
$627$	2.20615	0.0881053
$628$	23.7825	0.949026
$629$	55.3791	2.20811
$630$	0.0281086	0.00111987
$631$	−30.9783	−1.23323	−0.616614	−	0.787266i	$-0.711496\pi$
$631$	−30.9783	−1.23323	−0.616614	+	0.787266i	$0.711496\pi$
$632$	0.264270	0.0105121
$633$	−17.3344	−0.688982
$634$	−0.0476786	−0.00189356
$635$	−4.85690	−0.192740
$636$	22.3485	0.886177
$637$	1.37591	0.0545155
$638$	0.0379800	0.00150364
$639$	−0.850252	−0.0336354
$640$	−0.899372	−0.0355508
$641$	0.922725	0.0364455	0.0182227	−	0.999834i	$-0.494199\pi$
$641$	0.922725	0.0364455	0.0182227	+	0.999834i	$0.494199\pi$
$642$	−0.135458	−0.00534611
$643$	−37.9150	−1.49522	−0.747610	−	0.664138i	$-0.768799\pi$
$643$	−37.9150	−1.49522	−0.747610	+	0.664138i	$0.768799\pi$
$644$	1.24977	0.0492479
$645$	−20.5491	−0.809122
$646$	−0.0466470	−0.00183530
$647$	8.72525	0.343025	0.171512	−	0.985182i	$-0.445135\pi$
$647$	8.72525	0.343025	0.171512	+	0.985182i	$0.445135\pi$
$648$	−0.0382986	−0.00150451
$649$	14.3269	0.562379
$650$	0.0476658	0.00186961
$651$	8.43543	0.330611
$652$	30.8802	1.20936
$653$	−17.3791	−0.680096	−0.340048	−	0.940408i	$-0.610443\pi$
$653$	−17.3791	−0.680096	−0.340048	+	0.940408i	$0.610443\pi$
$654$	0.0232941	0.000910870 0
$655$	−29.4926	−1.15237
$656$	47.0574	1.83728
$657$	−11.4811	−0.447921
$658$	0.0117928	0.000459731 0
$659$	−21.2032	−0.825960	−0.412980	−	0.910740i	$-0.635512\pi$
$659$	−21.2032	−0.825960	−0.412980	+	0.910740i	$0.635512\pi$
$660$	19.1658	0.746026
$661$	−16.5951	−0.645474	−0.322737	−	0.946489i	$-0.604603\pi$
$661$	−16.5951	−0.645474	−0.322737	+	0.946489i	$0.604603\pi$
$662$	−0.164929	−0.00641013
$663$	−9.91869	−0.385210
$664$	0.326214	0.0126596
$665$	−1.98396	−0.0769347
$666$	0.0735553	0.00285021
$667$	−0.759335	−0.0294016
$668$	−16.7759	−0.649080
$669$	20.0658	0.775789
$670$	−0.277570	−0.0107235
$671$	40.7121	1.57167
$672$	−0.114891	−0.00443203
$673$	−5.90255	−0.227527	−0.113763	−	0.993508i	$-0.536291\pi$
$673$	−5.90255	−0.227527	−0.113763	+	0.993508i	$0.536291\pi$
$674$	−0.223279	−0.00860039
$675$	−3.61813	−0.139262
$676$	22.2127	0.854336
$677$	−1.09122	−0.0419390	−0.0209695	−	0.999780i	$-0.506675\pi$
$677$	−1.09122	−0.0419390	−0.0209695	+	0.999780i	$0.506675\pi$
$678$	−0.0339575	−0.00130413
$679$	−2.72874	−0.104720
$680$	−0.810502	−0.0310813
$681$	5.77153	0.221165
$682$	−0.263663	−0.0100962
$683$	14.4540	0.553068	0.276534	−	0.961004i	$-0.410814\pi$
$683$	14.4540	0.553068	0.276534	+	0.961004i	$0.410814\pi$
$684$	1.35156	0.0516783
$685$	30.8312	1.17800
$686$	0.00957487	0.000365570 0
$687$	10.9586	0.418098
$688$	27.9955	1.06732
$689$	15.3755	0.585760
$690$	0.0175655	0.000668706 0
$691$	24.9406	0.948786	0.474393	−	0.880313i	$-0.342668\pi$
$691$	24.9406	0.948786	0.474393	+	0.880313i	$0.342668\pi$
$692$	−26.9475	−1.02439
$693$	3.26445	0.124006
$694$	0.247544	0.00939664
$695$	9.23121	0.350160
$696$	0.0465367	0.00176397
$697$	84.8188	3.21274
$698$	0.295202	0.0111735
$699$	−12.1947	−0.461247
$700$	−7.23593	−0.273492
$701$	17.6278	0.665791	0.332896	−	0.942964i	$-0.391974\pi$
$701$	17.6278	0.665791	0.332896	+	0.942964i	$0.391974\pi$
$702$	−0.0131741	−0.000497226 0
$703$	−5.19168	−0.195808
$704$	−26.1084	−0.983997
$705$	−3.61569	−0.136175
$706$	−0.162201	−0.00610451
$707$	−16.9282	−0.636650
$708$	8.77712	0.329864
$709$	25.1119	0.943099	0.471549	−	0.881840i	$-0.343695\pi$
$709$	25.1119	0.943099	0.471549	+	0.881840i	$0.343695\pi$
$710$	−0.0238994	−0.000896928 0
$711$	−6.90025	−0.258780
$712$	−0.403581	−0.0151248
$713$	5.27143	0.197416
$714$	−0.0690236	−0.00258314
$715$	13.1858	0.493120
$716$	27.1949	1.01632
$717$	10.8767	0.406199
$718$	0.351395	0.0131140
$719$	1.96828	0.0734044	0.0367022	−	0.999326i	$-0.488315\pi$
$719$	1.96828	0.0734044	0.0367022	+	0.999326i	$0.488315\pi$
$720$	11.7410	0.437563
$721$	−11.2058	−0.417325
$722$	−0.177549	−0.00660770
$723$	−21.7677	−0.809551
$724$	−5.84097	−0.217078
$725$	4.39639	0.163278
$726$	0.00328792	0.000122026 0
$727$	−19.9347	−0.739337	−0.369668	−	0.929164i	$-0.620529\pi$
$727$	−19.9347	−0.739337	−0.369668	+	0.929164i	$0.620529\pi$
$728$	−0.0526954	−0.00195302
$729$	1.00000	0.0370370
$730$	−0.322718	−0.0119443
$731$	50.4605	1.86635
$732$	24.9416	0.921868
$733$	11.9455	0.441217	0.220608	−	0.975362i	$-0.429196\pi$
$733$	11.9455	0.441217	0.220608	+	0.975362i	$0.429196\pi$
$734$	0.248456	0.00917069
$735$	−2.93567	−0.108284
$736$	−0.0717973	−0.00264648
$737$	−32.2362	−1.18743
$738$	0.112657	0.00414698
$739$	12.0147	0.441969	0.220985	−	0.975277i	$-0.429073\pi$
$739$	12.0147	0.441969	0.220985	+	0.975277i	$0.429073\pi$
$740$	−45.1022	−1.65799
$741$	0.929857	0.0341592
$742$	0.106997	0.00392799
$743$	−27.4729	−1.00788	−0.503942	−	0.863738i	$-0.668117\pi$
$743$	−27.4729	−1.00788	−0.503942	+	0.863738i	$0.668117\pi$
$744$	−0.323065	−0.0118441
$745$	−4.37873	−0.160424
$746$	−0.0348321	−0.00127529
$747$	−8.51766	−0.311645
$748$	−47.0635	−1.72081
$749$	14.1473	0.516930
$750$	0.0388424	0.00141832
$751$	53.2368	1.94264	0.971319	−	0.237781i	$-0.0764200\pi$
$751$	53.2368	1.94264	0.971319	+	0.237781i	$0.0764200\pi$
$752$	4.92589	0.179629
$753$	3.87558	0.141234
$754$	0.0160079	0.000582974 0
$755$	−52.4845	−1.91011
$756$	1.99991	0.0727360
$757$	−14.1553	−0.514484	−0.257242	−	0.966347i	$-0.582814\pi$
$757$	−14.1553	−0.514484	−0.257242	+	0.966347i	$0.582814\pi$
$758$	0.0329073	0.00119525
$759$	2.04000	0.0740473
$760$	0.0759829	0.00275619
$761$	−19.9326	−0.722557	−0.361278	−	0.932458i	$-0.617660\pi$
$761$	−19.9326	−0.722557	−0.361278	+	0.932458i	$0.617660\pi$
$762$	0.0158411	0.000573863 0
$763$	−2.43283	−0.0880745
$764$	−40.7969	−1.47598
$765$	21.1627	0.765139
$766$	−0.00957487	−0.000345954 0
$767$	6.03853	0.218039
$768$	−15.9927	−0.577086
$769$	32.2519	1.16303	0.581516	−	0.813535i	$-0.302460\pi$
$769$	32.2519	1.16303	0.581516	+	0.813535i	$0.302460\pi$
$770$	0.0917590	0.00330677
$771$	2.26668	0.0816324
$772$	52.4144	1.88644
$773$	41.1986	1.48181	0.740905	−	0.671610i	$-0.234397\pi$
$773$	41.1986	1.48181	0.740905	+	0.671610i	$0.234397\pi$
$774$	0.0670224	0.00240907
$775$	−30.5205	−1.09633
$776$	0.104507	0.00375159
$777$	−7.68213	−0.275595
$778$	−0.183711	−0.00658634
$779$	−7.95159	−0.284895
$780$	8.07805	0.289240
$781$	−2.77560	−0.0993188
$782$	−0.0431338	−0.00154246
$783$	−1.21510	−0.0434242
$784$	3.99945	0.142837
$785$	−34.9103	−1.24600
$786$	0.0961922	0.00343106
$787$	2.92647	0.104317	0.0521587	−	0.998639i	$-0.483390\pi$
$787$	2.92647	0.104317	0.0521587	+	0.998639i	$0.483390\pi$
$788$	14.3361	0.510701
$789$	−25.0405	−0.891467
$790$	−0.193956	−0.00690066
$791$	3.54653	0.126100
$792$	−0.125024	−0.00444252
$793$	17.1595	0.609351
$794$	−0.164278	−0.00583001
$795$	−32.8054	−1.16349
$796$	−37.6104	−1.33306
$797$	16.2599	0.575955	0.287978	−	0.957637i	$-0.407017\pi$
$797$	16.2599	0.575955	0.287978	+	0.957637i	$0.407017\pi$
$798$	0.00647082	0.000229064 0
$799$	8.87869	0.314106
$800$	0.415692	0.0146969
$801$	10.5378	0.372333
$802$	0.327496	0.0115643
$803$	−37.4795	−1.32262
$804$	−19.7489	−0.696492
$805$	−1.83454	−0.0646591
$806$	−0.111130	−0.00391437
$807$	−18.1088	−0.637459
$808$	0.648326	0.0228080
$809$	−23.7156	−0.833797	−0.416898	−	0.908953i	$-0.636883\pi$
$809$	−23.7156	−0.833797	−0.416898	+	0.908953i	$0.636883\pi$
$810$	0.0281086	0.000987636 0
$811$	13.7864	0.484105	0.242052	−	0.970263i	$-0.422179\pi$
$811$	13.7864	0.484105	0.242052	+	0.970263i	$0.422179\pi$
$812$	−2.43009	−0.0852795
$813$	15.1902	0.532744
$814$	0.240117	0.00841611
$815$	−45.3290	−1.58781
$816$	−28.8313	−1.00930
$817$	−4.73057	−0.165502
$818$	0.0472981	0.00165374
$819$	1.37591	0.0480782
$820$	−69.0787	−2.41233
$821$	35.6679	1.24482	0.622410	−	0.782692i	$-0.286154\pi$
$821$	35.6679	1.24482	0.622410	+	0.782692i	$0.286154\pi$
$822$	−0.100558	−0.00350736
$823$	1.36840	0.0476993	0.0238496	−	0.999716i	$-0.492408\pi$
$823$	1.36840	0.0476993	0.0238496	+	0.999716i	$0.492408\pi$
$824$	0.429165	0.0149507
$825$	−11.8112	−0.411213
$826$	0.0420218	0.00146212
$827$	−6.90795	−0.240213	−0.120107	−	0.992761i	$-0.538324\pi$
$827$	−6.90795	−0.240213	−0.120107	+	0.992761i	$0.538324\pi$
$828$	1.24977	0.0434326
$829$	4.88635	0.169710	0.0848550	−	0.996393i	$-0.472957\pi$
$829$	4.88635	0.169710	0.0848550	+	0.996393i	$0.472957\pi$
$830$	−0.239420	−0.00831038
$831$	29.2199	1.01363
$832$	−11.0042	−0.381504
$833$	7.20883	0.249771
$834$	−0.0301082	−0.00104256
$835$	24.6254	0.852196
$836$	4.41211	0.152596
$837$	8.43543	0.291571
$838$	0.128579	0.00444167
$839$	−0.377657	−0.0130382	−0.00651908	−	0.999979i	$-0.502075\pi$
$839$	−0.377657	−0.0130382	−0.00651908	+	0.999979i	$0.502075\pi$
$840$	0.112432	0.00387927
$841$	−27.5235	−0.949087
$842$	−0.337077	−0.0116164
$843$	−14.3520	−0.494309
$844$	−34.6673	−1.19330
$845$	−32.6061	−1.12168
$846$	0.0117928	0.000405445 0
$847$	−0.343391	−0.0117990
$848$	44.6930	1.53476
$849$	24.4425	0.838866
$850$	0.249736	0.00856588
$851$	−4.80067	−0.164565
$852$	−1.70043	−0.0582556
$853$	30.1680	1.03293	0.516467	−	0.856307i	$-0.327247\pi$
$853$	30.1680	1.03293	0.516467	+	0.856307i	$0.327247\pi$
$854$	0.119412	0.00408619
$855$	−1.98396	−0.0678500
$856$	−0.541820	−0.0185190
$857$	14.5164	0.495872	0.247936	−	0.968776i	$-0.420248\pi$
$857$	14.5164	0.495872	0.247936	+	0.968776i	$0.420248\pi$
$858$	−0.0430063	−0.00146821
$859$	−24.3921	−0.832246	−0.416123	−	0.909308i	$-0.636611\pi$
$859$	−24.3921	−0.832246	−0.416123	+	0.909308i	$0.636611\pi$
$860$	−41.0964	−1.40138
$861$	−11.7660	−0.400983
$862$	0.347638	0.0118406
$863$	0.769782	0.0262037	0.0131018	−	0.999914i	$-0.495829\pi$
$863$	0.769782	0.0262037	0.0131018	+	0.999914i	$0.495829\pi$
$864$	−0.114891	−0.00390868
$865$	39.5563	1.34495
$866$	0.294841	0.0100191
$867$	−34.9672	−1.18755
$868$	16.8701	0.572608
$869$	−22.5255	−0.764125
$870$	−0.0341548	−0.00115796
$871$	−13.5870	−0.460378
$872$	0.0931741	0.00315527
$873$	−2.72874	−0.0923540
$874$	0.00404371	0.000136781 0
$875$	−4.05671	−0.137142
$876$	−22.9612	−0.775786
$877$	40.4071	1.36445	0.682225	−	0.731143i	$-0.261013\pi$
$877$	40.4071	1.36445	0.682225	+	0.731143i	$0.261013\pi$
$878$	−0.113661	−0.00383586
$879$	3.95897	0.133533
$880$	38.3280	1.29204
$881$	10.6084	0.357405	0.178702	−	0.983903i	$-0.442810\pi$
$881$	10.6084	0.357405	0.178702	+	0.983903i	$0.442810\pi$
$882$	0.00957487	0.000322403 0
$883$	−41.5572	−1.39851	−0.699255	−	0.714872i	$-0.746485\pi$
$883$	−41.5572	−1.39851	−0.699255	+	0.714872i	$0.746485\pi$
$884$	−19.8365	−0.667173
$885$	−12.8839	−0.433088
$886$	−0.139260	−0.00467853
$887$	3.42586	0.115029	0.0575146	−	0.998345i	$-0.481682\pi$
$887$	3.42586	0.115029	0.0575146	+	0.998345i	$0.481682\pi$
$888$	0.294215	0.00987320
$889$	−1.65445	−0.0554883
$890$	0.296202	0.00992870
$891$	3.26445	0.109363
$892$	40.1298	1.34364
$893$	−0.832359	−0.0278538
$894$	0.0142815	0.000477646 0
$895$	−39.9194	−1.33436
$896$	−0.306361	−0.0102348
$897$	0.859826	0.0287088
$898$	0.0404497	0.00134982
$899$	−10.2499	−0.341853
$900$	−7.23593	−0.241198
$901$	80.5571	2.68375
$902$	0.367764	0.0122452
$903$	−6.99983	−0.232940
$904$	−0.135827	−0.00451754
$905$	8.57396	0.285008
$906$	0.171182	0.00568713
$907$	27.4593	0.911770	0.455885	−	0.890039i	$-0.349323\pi$
$907$	27.4593	0.911770	0.455885	+	0.890039i	$0.349323\pi$
$908$	11.5425	0.383052
$909$	−16.9282	−0.561473
$910$	0.0386749	0.00128206
$911$	−31.9488	−1.05851	−0.529255	−	0.848463i	$-0.677529\pi$
$911$	−31.9488	−1.05851	−0.529255	+	0.848463i	$0.677529\pi$
$912$	2.70288	0.0895013
$913$	−27.8055	−0.920226
$914$	0.199712	0.00660589
$915$	−36.6118	−1.21035
$916$	21.9162	0.724133
$917$	−10.0463	−0.331759
$918$	−0.0690236	−0.00227812
$919$	30.5881	1.00901	0.504504	−	0.863409i	$-0.331675\pi$
$919$	30.5881	1.00901	0.504504	+	0.863409i	$0.331675\pi$
$920$	0.0702603	0.00231641
$921$	−21.4446	−0.706625
$922$	−0.0879870	−0.00289770
$923$	−1.16987	−0.0385067
$924$	6.52859	0.214775
$925$	27.7949	0.913892
$926$	−0.142907	−0.00469620
$927$	−11.2058	−0.368046
$928$	0.139605	0.00458275
$929$	−7.35328	−0.241253	−0.120627	−	0.992698i	$-0.538490\pi$
$929$	−7.35328	−0.241253	−0.120627	+	0.992698i	$0.538490\pi$
$930$	0.237108	0.00777509
$931$	−0.675813	−0.0221489
$932$	−24.3883	−0.798866
$933$	−7.15945	−0.234390
$934$	0.121277	0.00396829
$935$	69.0845	2.25931
$936$	−0.0526954	−0.00172240
$937$	−38.5231	−1.25850	−0.629248	−	0.777204i	$-0.716637\pi$
$937$	−38.5231	−1.25850	−0.629248	+	0.777204i	$0.716637\pi$
$938$	−0.0945511	−0.00308720
$939$	−14.3379	−0.467901
$940$	−7.23104	−0.235851
$941$	−6.99131	−0.227910	−0.113955	−	0.993486i	$-0.536352\pi$
$941$	−6.99131	−0.227910	−0.113955	+	0.993486i	$0.536352\pi$
$942$	0.113862	0.00370984
$943$	−7.35272	−0.239438
$944$	17.5526	0.571289
$945$	−2.93567	−0.0954972
$946$	0.218791	0.00711351
$947$	26.3141	0.855094	0.427547	−	0.903993i	$-0.359378\pi$
$947$	26.3141	0.855094	0.427547	+	0.903993i	$0.359378\pi$
$948$	−13.7999	−0.448199
$949$	−15.7970	−0.512791
$950$	−0.0234123	−0.000759594 0
$951$	4.97956	0.161473
$952$	−0.276088	−0.00894806
$953$	−58.3441	−1.88995	−0.944976	−	0.327141i	$-0.893915\pi$
$953$	−58.3441	−1.88995	−0.944976	+	0.327141i	$0.893915\pi$
$954$	0.106997	0.00346416
$955$	59.8858	1.93786
$956$	21.7525	0.703526
$957$	−3.96663	−0.128223
$958$	−0.178763	−0.00577558
$959$	10.5023	0.339136
$960$	23.4789	0.757777
$961$	40.1565	1.29537
$962$	0.101205	0.00326300
$963$	14.1473	0.455889
$964$	−43.5335	−1.40212
$965$	−76.9391	−2.47676
$966$	0.00598348	0.000192515 0
$967$	18.6308	0.599125	0.299562	−	0.954077i	$-0.403159\pi$
$967$	18.6308	0.599125	0.299562	+	0.954077i	$0.403159\pi$
$968$	0.0131514	0.000422701 0
$969$	4.87182	0.156505
$970$	−0.0767012	−0.00246273
$971$	31.2241	1.00203	0.501015	−	0.865439i	$-0.332960\pi$
$971$	31.2241	1.00203	0.501015	+	0.865439i	$0.332960\pi$
$972$	1.99991	0.0641471
$973$	3.14450	0.100808
$974$	0.0841239	0.00269550
$975$	−4.97822	−0.159431
$976$	49.8786	1.59658
$977$	31.3693	1.00359	0.501797	−	0.864986i	$-0.332673\pi$
$977$	31.3693	1.00359	0.501797	+	0.864986i	$0.332673\pi$
$978$	0.147844	0.00472752
$979$	34.3999	1.09943
$980$	−5.87106	−0.187544
$981$	−2.43283	−0.0776744
$982$	−0.353121	−0.0112686
$983$	32.6984	1.04292	0.521458	−	0.853277i	$-0.325388\pi$
$983$	32.6984	1.04292	0.521458	+	0.853277i	$0.325388\pi$
$984$	0.450620	0.0143652
$985$	−21.0439	−0.670515
$986$	0.0838706	0.00267098
$987$	−1.23164	−0.0392036
$988$	1.85963	0.0591627
$989$	−4.37429	−0.139094
$990$	0.0917590	0.00291629
$991$	29.0188	0.921812	0.460906	−	0.887449i	$-0.347525\pi$
$991$	29.0188	0.921812	0.460906	+	0.887449i	$0.347525\pi$
$992$	−0.969159	−0.0307708
$993$	17.2252	0.546624
$994$	−0.00814105	−0.000258218 0
$995$	55.2083	1.75022
$996$	−17.0345	−0.539760
$997$	36.2025	1.14654	0.573272	−	0.819365i	$-0.305674\pi$
$997$	36.2025	1.14654	0.573272	+	0.819365i	$0.305674\pi$
$998$	−0.0278750	−0.000882367 0
$999$	−7.68213	−0.243052

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.t.1.26	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.t.1.26	✓	52	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:	\( N \)	\(=\)	\( 8043 = 3 \cdot 7 \cdot 383 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8043.a (trivial)

\(f(q)\)	\(=\)	\(q+0.00957487 q^{2} -1.00000 q^{3} -1.99991 q^{4} +2.93567 q^{5} -0.00957487 q^{6} +1.00000 q^{7} -0.0382986 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.00957487 q^{2} -1.00000 q^{3} -1.99991 q^{4} +2.93567 q^{5} -0.00957487 q^{6} +1.00000 q^{7} -0.0382986 q^{8} +1.00000 q^{9} +0.0281086 q^{10} +3.26445 q^{11} +1.99991 q^{12} +1.37591 q^{13} +0.00957487 q^{14} -2.93567 q^{15} +3.99945 q^{16} +7.20883 q^{17} +0.00957487 q^{18} -0.675813 q^{19} -5.87106 q^{20} -1.00000 q^{21} +0.0312566 q^{22} -0.624915 q^{23} +0.0382986 q^{24} +3.61813 q^{25} +0.0131741 q^{26} -1.00000 q^{27} -1.99991 q^{28} +1.21510 q^{29} -0.0281086 q^{30} -8.43543 q^{31} +0.114891 q^{32} -3.26445 q^{33} +0.0690236 q^{34} +2.93567 q^{35} -1.99991 q^{36} +7.68213 q^{37} -0.00647082 q^{38} -1.37591 q^{39} -0.112432 q^{40} +11.7660 q^{41} -0.00957487 q^{42} +6.99983 q^{43} -6.52859 q^{44} +2.93567 q^{45} -0.00598348 q^{46} +1.23164 q^{47} -3.99945 q^{48} +1.00000 q^{49} +0.0346431 q^{50} -7.20883 q^{51} -2.75169 q^{52} +11.1748 q^{53} -0.00957487 q^{54} +9.58332 q^{55} -0.0382986 q^{56} +0.675813 q^{57} +0.0116344 q^{58} +4.38876 q^{59} +5.87106 q^{60} +12.4714 q^{61} -0.0807681 q^{62} +1.00000 q^{63} -7.99780 q^{64} +4.03921 q^{65} -0.0312566 q^{66} -9.87493 q^{67} -14.4170 q^{68} +0.624915 q^{69} +0.0281086 q^{70} -0.850252 q^{71} -0.0382986 q^{72} -11.4811 q^{73} +0.0735553 q^{74} -3.61813 q^{75} +1.35156 q^{76} +3.26445 q^{77} -0.0131741 q^{78} -6.90025 q^{79} +11.7410 q^{80} +1.00000 q^{81} +0.112657 q^{82} -8.51766 q^{83} +1.99991 q^{84} +21.1627 q^{85} +0.0670224 q^{86} -1.21510 q^{87} -0.125024 q^{88} +10.5378 q^{89} +0.0281086 q^{90} +1.37591 q^{91} +1.24977 q^{92} +8.43543 q^{93} +0.0117928 q^{94} -1.98396 q^{95} -0.114891 q^{96} -2.72874 q^{97} +0.00957487 q^{98} +3.26445 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 3 q^{2} - 52 q^{3} + 61 q^{4} - 7 q^{5} - 3 q^{6} + 52 q^{7} + 24 q^{8} + 52 q^{9}+O(q^{10}) \) 52 * q + 3 * q^2 - 52 * q^3 + 61 * q^4 - 7 * q^5 - 3 * q^6 + 52 * q^7 + 24 * q^8 + 52 * q^9	\( 52 q + 3 q^{2} - 52 q^{3} + 61 q^{4} - 7 q^{5} - 3 q^{6} + 52 q^{7} + 24 q^{8} + 52 q^{9} - 2 q^{10} + 9 q^{11} - 61 q^{12} + 44 q^{13} + 3 q^{14} + 7 q^{15} + 95 q^{16} - 6 q^{17} + 3 q^{18} + 7 q^{19} - 21 q^{20} - 52 q^{21} + 19 q^{22} - 4 q^{23} - 24 q^{24} + 83 q^{25} - 5 q^{26} - 52 q^{27} + 61 q^{28} + 31 q^{29} + 2 q^{30} + 11 q^{31} + 71 q^{32} - 9 q^{33} + 17 q^{34} - 7 q^{35} + 61 q^{36} + 71 q^{37} - 8 q^{38} - 44 q^{39} + 20 q^{40} - 25 q^{41} - 3 q^{42} + 75 q^{43} + 14 q^{44} - 7 q^{45} + 36 q^{46} - 20 q^{47} - 95 q^{48} + 52 q^{49} + 26 q^{50} + 6 q^{51} + 88 q^{52} + 70 q^{53} - 3 q^{54} + 12 q^{55} + 24 q^{56} - 7 q^{57} + 48 q^{58} - 27 q^{59} + 21 q^{60} + 59 q^{61} - 23 q^{62} + 52 q^{63} + 138 q^{64} + 44 q^{65} - 19 q^{66} + 65 q^{67} - 8 q^{68} + 4 q^{69} - 2 q^{70} - 11 q^{71} + 24 q^{72} + 34 q^{73} + 38 q^{74} - 83 q^{75} + 31 q^{76} + 9 q^{77} + 5 q^{78} + 74 q^{79} - 5 q^{80} + 52 q^{81} + 51 q^{82} - 30 q^{83} - 61 q^{84} + 70 q^{85} + 29 q^{86} - 31 q^{87} + 90 q^{88} - q^{89} - 2 q^{90} + 44 q^{91} + 34 q^{92} - 11 q^{93} + 27 q^{94} + 9 q^{95} - 71 q^{96} + 73 q^{97} + 3 q^{98} + 9 q^{99}+O(q^{100}) \) 52 * q + 3 * q^2 - 52 * q^3 + 61 * q^4 - 7 * q^5 - 3 * q^6 + 52 * q^7 + 24 * q^8 + 52 * q^9 - 2 * q^10 + 9 * q^11 - 61 * q^12 + 44 * q^13 + 3 * q^14 + 7 * q^15 + 95 * q^16 - 6 * q^17 + 3 * q^18 + 7 * q^19 - 21 * q^20 - 52 * q^21 + 19 * q^22 - 4 * q^23 - 24 * q^24 + 83 * q^25 - 5 * q^26 - 52 * q^27 + 61 * q^28 + 31 * q^29 + 2 * q^30 + 11 * q^31 + 71 * q^32 - 9 * q^33 + 17 * q^34 - 7 * q^35 + 61 * q^36 + 71 * q^37 - 8 * q^38 - 44 * q^39 + 20 * q^40 - 25 * q^41 - 3 * q^42 + 75 * q^43 + 14 * q^44 - 7 * q^45 + 36 * q^46 - 20 * q^47 - 95 * q^48 + 52 * q^49 + 26 * q^50 + 6 * q^51 + 88 * q^52 + 70 * q^53 - 3 * q^54 + 12 * q^55 + 24 * q^56 - 7 * q^57 + 48 * q^58 - 27 * q^59 + 21 * q^60 + 59 * q^61 - 23 * q^62 + 52 * q^63 + 138 * q^64 + 44 * q^65 - 19 * q^66 + 65 * q^67 - 8 * q^68 + 4 * q^69 - 2 * q^70 - 11 * q^71 + 24 * q^72 + 34 * q^73 + 38 * q^74 - 83 * q^75 + 31 * q^76 + 9 * q^77 + 5 * q^78 + 74 * q^79 - 5 * q^80 + 52 * q^81 + 51 * q^82 - 30 * q^83 - 61 * q^84 + 70 * q^85 + 29 * q^86 - 31 * q^87 + 90 * q^88 - q^89 - 2 * q^90 + 44 * q^91 + 34 * q^92 - 11 * q^93 + 27 * q^94 + 9 * q^95 - 71 * q^96 + 73 * q^97 + 3 * q^98 + 9 * q^99

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