LMFDB - Embedded newform 241.2.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [241,2,Mod(1,241)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(241, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("241.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	241.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:	$1.92439468871$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	7.7.31056073.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 3x^{5} + 11x^{4} + x^{3} - 9x^{2} + 1 $ x^7 - 3x^6 - 3x^5 + 11x^4 + x^3 - 9x^2 + 1
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			1.3
Root			$-0.356270$ of defining polynomial
Character	$\chi$	$=$	241.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.35627 q^{2} -2.45059 q^{3} -0.160532 q^{4} +2.74184 q^{5} +3.32366 q^{6} -0.283608 q^{7} +2.93026 q^{8} +3.00540 q^{9} +O(q^{10})$	\(q-1.35627 q^{2} -2.45059 q^{3} -0.160532 q^{4} +2.74184 q^{5} +3.32366 q^{6} -0.283608 q^{7} +2.93026 q^{8} +3.00540 q^{9} -3.71867 q^{10} -4.12582 q^{11} +0.393399 q^{12} +0.0271909 q^{13} +0.384649 q^{14} -6.71913 q^{15} -3.65317 q^{16} -1.28740 q^{17} -4.07613 q^{18} -5.72717 q^{19} -0.440153 q^{20} +0.695007 q^{21} +5.59572 q^{22} -5.97702 q^{23} -7.18088 q^{24} +2.51768 q^{25} -0.0368782 q^{26} -0.0132278 q^{27} +0.0455281 q^{28} -2.55610 q^{29} +9.11295 q^{30} -2.02967 q^{31} -0.905851 q^{32} +10.1107 q^{33} +1.74607 q^{34} -0.777607 q^{35} -0.482463 q^{36} +2.42844 q^{37} +7.76759 q^{38} -0.0666338 q^{39} +8.03431 q^{40} -11.0324 q^{41} -0.942617 q^{42} +10.4984 q^{43} +0.662326 q^{44} +8.24032 q^{45} +8.10645 q^{46} +4.54349 q^{47} +8.95242 q^{48} -6.91957 q^{49} -3.41465 q^{50} +3.15490 q^{51} -0.00436502 q^{52} -9.30751 q^{53} +0.0179405 q^{54} -11.3123 q^{55} -0.831046 q^{56} +14.0350 q^{57} +3.46676 q^{58} -9.94762 q^{59} +1.07864 q^{60} +8.17350 q^{61} +2.75279 q^{62} -0.852354 q^{63} +8.53491 q^{64} +0.0745531 q^{65} -13.7128 q^{66} +4.40964 q^{67} +0.206670 q^{68} +14.6472 q^{69} +1.05464 q^{70} -3.80954 q^{71} +8.80661 q^{72} -15.6571 q^{73} -3.29362 q^{74} -6.16980 q^{75} +0.919395 q^{76} +1.17011 q^{77} +0.0903734 q^{78} +6.69229 q^{79} -10.0164 q^{80} -8.98378 q^{81} +14.9629 q^{82} -4.32880 q^{83} -0.111571 q^{84} -3.52985 q^{85} -14.2386 q^{86} +6.26396 q^{87} -12.0897 q^{88} +0.746861 q^{89} -11.1761 q^{90} -0.00771155 q^{91} +0.959503 q^{92} +4.97390 q^{93} -6.16219 q^{94} -15.7030 q^{95} +2.21987 q^{96} +11.9245 q^{97} +9.38480 q^{98} -12.3997 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 4 q^{2} - 3 q^{3} + 2 q^{4} - 8 q^{5} - 5 q^{6} - 7 q^{7} - 6 q^{8} - 2 q^{9}+O(q^{10}) $ 7 * q - 4 * q^2 - 3 * q^3 + 2 * q^4 - 8 * q^5 - 5 * q^6 - 7 * q^7 - 6 * q^8 - 2 * q^9	\( 7 q - 4 q^{2} - 3 q^{3} + 2 q^{4} - 8 q^{5} - 5 q^{6} - 7 q^{7} - 6 q^{8} - 2 q^{9} + 3 q^{10} - 18 q^{11} + q^{12} - q^{13} - 6 q^{14} - 11 q^{15} + 4 q^{16} - 2 q^{17} + 8 q^{18} - 6 q^{19} - 8 q^{20} - 2 q^{21} + 10 q^{22} - 22 q^{23} - 3 q^{24} + 5 q^{25} + 8 q^{26} + 3 q^{27} + 9 q^{28} - 16 q^{29} + 29 q^{30} - 18 q^{31} - 6 q^{32} + 4 q^{33} + 11 q^{34} + 7 q^{35} - 7 q^{36} + 8 q^{37} + 16 q^{38} - 9 q^{39} + 14 q^{40} - 15 q^{41} + 19 q^{42} + 14 q^{43} - 4 q^{44} + 3 q^{45} + 11 q^{46} - 10 q^{47} + 31 q^{48} + 6 q^{49} - 4 q^{50} + 13 q^{51} + 27 q^{52} + 15 q^{53} + 16 q^{54} + 29 q^{55} + 13 q^{56} + 14 q^{57} + 17 q^{58} - 18 q^{59} + 15 q^{60} + 4 q^{61} + 13 q^{62} - 16 q^{63} + 2 q^{64} - 7 q^{65} + 16 q^{66} + 18 q^{67} - 15 q^{68} + 26 q^{69} + 8 q^{70} - 50 q^{71} + 30 q^{72} + 10 q^{74} + 16 q^{75} - 20 q^{76} + 17 q^{77} - 32 q^{78} - 15 q^{79} - 11 q^{80} - 9 q^{81} + 45 q^{82} - 24 q^{83} + 6 q^{84} - 2 q^{85} - 23 q^{86} + 12 q^{87} + 8 q^{88} - 13 q^{89} - 39 q^{90} - 12 q^{91} - 10 q^{92} + 14 q^{93} - 32 q^{94} - 41 q^{95} - 15 q^{96} + q^{97} + 9 q^{98} - 20 q^{99}+O(q^{100}) \) 7 * q - 4 * q^2 - 3 * q^3 + 2 * q^4 - 8 * q^5 - 5 * q^6 - 7 * q^7 - 6 * q^8 - 2 * q^9 + 3 * q^10 - 18 * q^11 + q^12 - q^13 - 6 * q^14 - 11 * q^15 + 4 * q^16 - 2 * q^17 + 8 * q^18 - 6 * q^19 - 8 * q^20 - 2 * q^21 + 10 * q^22 - 22 * q^23 - 3 * q^24 + 5 * q^25 + 8 * q^26 + 3 * q^27 + 9 * q^28 - 16 * q^29 + 29 * q^30 - 18 * q^31 - 6 * q^32 + 4 * q^33 + 11 * q^34 + 7 * q^35 - 7 * q^36 + 8 * q^37 + 16 * q^38 - 9 * q^39 + 14 * q^40 - 15 * q^41 + 19 * q^42 + 14 * q^43 - 4 * q^44 + 3 * q^45 + 11 * q^46 - 10 * q^47 + 31 * q^48 + 6 * q^49 - 4 * q^50 + 13 * q^51 + 27 * q^52 + 15 * q^53 + 16 * q^54 + 29 * q^55 + 13 * q^56 + 14 * q^57 + 17 * q^58 - 18 * q^59 + 15 * q^60 + 4 * q^61 + 13 * q^62 - 16 * q^63 + 2 * q^64 - 7 * q^65 + 16 * q^66 + 18 * q^67 - 15 * q^68 + 26 * q^69 + 8 * q^70 - 50 * q^71 + 30 * q^72 + 10 * q^74 + 16 * q^75 - 20 * q^76 + 17 * q^77 - 32 * q^78 - 15 * q^79 - 11 * q^80 - 9 * q^81 + 45 * q^82 - 24 * q^83 + 6 * q^84 - 2 * q^85 - 23 * q^86 + 12 * q^87 + 8 * q^88 - 13 * q^89 - 39 * q^90 - 12 * q^91 - 10 * q^92 + 14 * q^93 - 32 * q^94 - 41 * q^95 - 15 * q^96 + q^97 + 9 * q^98 - 20 * 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 $

$2$	−1.35627	−0.959028	−0.479514	−	0.877534i	$-0.659187\pi$
$2$	−1.35627	−0.959028	−0.479514	+	0.877534i	$0.659187\pi$
$3$	−2.45059	−1.41485	−0.707425	−	0.706789i	$-0.750143\pi$
$3$	−2.45059	−1.41485	−0.707425	+	0.706789i	$0.750143\pi$
$4$	−0.160532	−0.0802661
$5$	2.74184	1.22619	0.613094	−	0.790010i	$-0.289925\pi$
$5$	2.74184	1.22619	0.613094	+	0.790010i	$0.289925\pi$
$6$	3.32366	1.35688
$7$	−0.283608	−0.107194	−0.0535968	−	0.998563i	$-0.517069\pi$
$7$	−0.283608	−0.107194	−0.0535968	+	0.998563i	$0.517069\pi$
$8$	2.93026	1.03600
$9$	3.00540	1.00180
$10$	−3.71867	−1.17595
$11$	−4.12582	−1.24398	−0.621990	−	0.783025i	$-0.713676\pi$
$11$	−4.12582	−1.24398	−0.621990	+	0.783025i	$0.713676\pi$
$12$	0.393399	0.113564
$13$	0.0271909	0.00754140	0.00377070	−	0.999993i	$-0.498800\pi$
$13$	0.0271909	0.00754140	0.00377070	+	0.999993i	$0.498800\pi$
$14$	0.384649	0.102802
$15$	−6.71913	−1.73487
$16$	−3.65317	−0.913291
$17$	−1.28740	−0.312241	−0.156121	−	0.987738i	$-0.549899\pi$
$17$	−1.28740	−0.312241	−0.156121	+	0.987738i	$0.549899\pi$
$18$	−4.07613	−0.960753
$19$	−5.72717	−1.31390	−0.656952	−	0.753933i	$-0.728154\pi$
$19$	−5.72717	−1.31390	−0.656952	+	0.753933i	$0.728154\pi$
$20$	−0.440153	−0.0984212
$21$	0.695007	0.151663
$22$	5.59572	1.19301
$23$	−5.97702	−1.24629	−0.623147	−	0.782104i	$-0.714146\pi$
$23$	−5.97702	−1.24629	−0.623147	+	0.782104i	$0.714146\pi$
$24$	−7.18088	−1.46579
$25$	2.51768	0.503536
$26$	−0.0368782	−0.00723241
$27$	−0.0132278	−0.00254570
$28$	0.0455281	0.00860401
$29$	−2.55610	−0.474656	−0.237328	−	0.971430i	$-0.576272\pi$
$29$	−2.55610	−0.474656	−0.237328	+	0.971430i	$0.576272\pi$
$30$	9.11295	1.66379
$31$	−2.02967	−0.364540	−0.182270	−	0.983248i	$-0.558345\pi$
$31$	−2.02967	−0.364540	−0.182270	+	0.983248i	$0.558345\pi$
$32$	−0.905851	−0.160133
$33$	10.1107	1.76005
$34$	1.74607	0.299448
$35$	−0.777607	−0.131440
$36$	−0.482463	−0.0804105
$37$	2.42844	0.399233	0.199617	−	0.979874i	$-0.436030\pi$
$37$	2.42844	0.399233	0.199617	+	0.979874i	$0.436030\pi$
$38$	7.76759	1.26007
$39$	−0.0666338	−0.0106700
$40$	8.03431	1.27034
$41$	−11.0324	−1.72297	−0.861483	−	0.507786i	$-0.830464\pi$
$41$	−11.0324	−1.72297	−0.861483	+	0.507786i	$0.830464\pi$
$42$	−0.942617	−0.145449
$43$	10.4984	1.60099	0.800493	−	0.599342i	$-0.204571\pi$
$43$	10.4984	1.60099	0.800493	+	0.599342i	$0.204571\pi$
$44$	0.662326	0.0998494
$45$	8.24032	1.22839
$46$	8.10645	1.19523
$47$	4.54349	0.662736	0.331368	−	0.943502i	$-0.392490\pi$
$47$	4.54349	0.662736	0.331368	+	0.943502i	$0.392490\pi$
$48$	8.95242	1.29217
$49$	−6.91957	−0.988510
$50$	−3.41465	−0.482904
$51$	3.15490	0.441774
$52$	−0.00436502	−0.000605319 0
$53$	−9.30751	−1.27848	−0.639242	−	0.769005i	$-0.720752\pi$
$53$	−9.30751	−1.27848	−0.639242	+	0.769005i	$0.720752\pi$
$54$	0.0179405	0.00244140
$55$	−11.3123	−1.52535
$56$	−0.831046	−0.111053
$57$	14.0350	1.85898
$58$	3.46676	0.455208
$59$	−9.94762	−1.29507	−0.647535	−	0.762036i	$-0.724200\pi$
$59$	−9.94762	−1.29507	−0.647535	+	0.762036i	$0.724200\pi$
$60$	1.07864	0.139251
$61$	8.17350	1.04651	0.523255	−	0.852176i	$-0.324718\pi$
$61$	8.17350	1.04651	0.523255	+	0.852176i	$0.324718\pi$
$62$	2.75279	0.349604
$63$	−0.852354	−0.107387
$64$	8.53491	1.06686
$65$	0.0745531	0.00924717
$66$	−13.7128	−1.68793
$67$	4.40964	0.538723	0.269361	−	0.963039i	$-0.413187\pi$
$67$	4.40964	0.538723	0.269361	+	0.963039i	$0.413187\pi$
$68$	0.206670	0.0250624
$69$	14.6472	1.76332
$70$	1.05464	0.126054
$71$	−3.80954	−0.452109	−0.226054	−	0.974115i	$-0.572583\pi$
$71$	−3.80954	−0.452109	−0.226054	+	0.974115i	$0.572583\pi$
$72$	8.80661	1.03787
$73$	−15.6571	−1.83252	−0.916261	−	0.400583i	$-0.868808\pi$
$73$	−15.6571	−1.83252	−0.916261	+	0.400583i	$0.868808\pi$
$74$	−3.29362	−0.382876
$75$	−6.16980	−0.712427
$76$	0.919395	0.105462
$77$	1.17011	0.133347
$78$	0.0903734	0.0102328
$79$	6.69229	0.752942	0.376471	−	0.926428i	$-0.377138\pi$
$79$	6.69229	0.752942	0.376471	+	0.926428i	$0.377138\pi$
$80$	−10.0164	−1.11987
$81$	−8.98378	−0.998197
$82$	14.9629	1.65237
$83$	−4.32880	−0.475147	−0.237574	−	0.971370i	$-0.576352\pi$
$83$	−4.32880	−0.475147	−0.237574	+	0.971370i	$0.576352\pi$
$84$	−0.111571	−0.0121734
$85$	−3.52985	−0.382866
$86$	−14.2386	−1.53539
$87$	6.26396	0.671567
$88$	−12.0897	−1.28877
$89$	0.746861	0.0791671	0.0395835	−	0.999216i	$-0.487397\pi$
$89$	0.746861	0.0791671	0.0395835	+	0.999216i	$0.487397\pi$
$90$	−11.1761	−1.17806
$91$	−0.00771155	−0.000808391 0
$92$	0.959503	0.100035
$93$	4.97390	0.515770
$94$	−6.16219	−0.635582
$95$	−15.7030	−1.61109
$96$	2.21987	0.226565
$97$	11.9245	1.21075	0.605373	−	0.795942i	$-0.293024\pi$
$97$	11.9245	1.21075	0.605373	+	0.795942i	$0.293024\pi$
$98$	9.38480	0.948008
$99$	−12.3997	−1.24622
$100$	−0.404168	−0.0404168
$101$	17.7456	1.76576	0.882878	−	0.469603i	$-0.155603\pi$
$101$	17.7456	1.76576	0.882878	+	0.469603i	$0.155603\pi$
$102$	−4.27890	−0.423674
$103$	5.10848	0.503354	0.251677	−	0.967811i	$-0.419018\pi$
$103$	5.10848	0.503354	0.251677	+	0.967811i	$0.419018\pi$
$104$	0.0796766	0.00781293
$105$	1.90560	0.185967
$106$	12.6235	1.22610
$107$	−0.619213	−0.0598615	−0.0299308	−	0.999552i	$-0.509529\pi$
$107$	−0.619213	−0.0598615	−0.0299308	+	0.999552i	$0.509529\pi$
$108$	0.00212349	0.000204333 0
$109$	3.34125	0.320034	0.160017	−	0.987114i	$-0.448845\pi$
$109$	3.34125	0.320034	0.160017	+	0.987114i	$0.448845\pi$
$110$	15.3426	1.46286
$111$	−5.95112	−0.564855
$112$	1.03607	0.0978990
$113$	−3.42957	−0.322627	−0.161313	−	0.986903i	$-0.551573\pi$
$113$	−3.42957	−0.322627	−0.161313	+	0.986903i	$0.551573\pi$
$114$	−19.0352	−1.78281
$115$	−16.3880	−1.52819
$116$	0.410336	0.0380988
$117$	0.0817195	0.00755497
$118$	13.4917	1.24201
$119$	0.365118	0.0334703
$120$	−19.6888	−1.79733
$121$	6.02237	0.547488
$122$	−11.0855	−1.00363
$123$	27.0358	2.43774
$124$	0.325828	0.0292602
$125$	−6.80613	−0.608758
$126$	1.15602	0.102987
$127$	8.11791	0.720348	0.360174	−	0.932885i	$-0.382717\pi$
$127$	8.11791	0.720348	0.360174	+	0.932885i	$0.382717\pi$
$128$	−9.76394	−0.863018
$129$	−25.7272	−2.26516
$130$	−0.101114	−0.00886830
$131$	2.73258	0.238747	0.119373	−	0.992849i	$-0.461911\pi$
$131$	2.73258	0.238747	0.119373	+	0.992849i	$0.461911\pi$
$132$	−1.62309	−0.141272
$133$	1.62427	0.140842
$134$	−5.98066	−0.516650
$135$	−0.0362686	−0.00312151
$136$	−3.77243	−0.323483
$137$	5.47355	0.467637	0.233819	−	0.972280i	$-0.424878\pi$
$137$	5.47355	0.467637	0.233819	+	0.972280i	$0.424878\pi$
$138$	−19.8656	−1.69107
$139$	−16.3761	−1.38901	−0.694503	−	0.719490i	$-0.744376\pi$
$139$	−16.3761	−1.38901	−0.694503	+	0.719490i	$0.744376\pi$
$140$	0.124831	0.0105501
$141$	−11.1342	−0.937671
$142$	5.16676	0.433585
$143$	−0.112185	−0.00938136
$144$	−10.9792	−0.914935
$145$	−7.00842	−0.582017
$146$	21.2352	1.75744
$147$	16.9570	1.39859
$148$	−0.389843	−0.0320449
$149$	−15.2495	−1.24929	−0.624645	−	0.780909i	$-0.714756\pi$
$149$	−15.2495	−1.24929	−0.624645	+	0.780909i	$0.714756\pi$
$150$	8.36791	0.683237
$151$	−3.19011	−0.259607	−0.129804	−	0.991540i	$-0.541435\pi$
$151$	−3.19011	−0.259607	−0.129804	+	0.991540i	$0.541435\pi$
$152$	−16.7821	−1.36121
$153$	−3.86916	−0.312803
$154$	−1.58699	−0.127883
$155$	−5.56504	−0.446995
$156$	0.0106969	0.000856435 0
$157$	12.7755	1.01959	0.509797	−	0.860295i	$-0.329721\pi$
$157$	12.7755	1.01959	0.509797	+	0.860295i	$0.329721\pi$
$158$	−9.07655	−0.722092
$159$	22.8089	1.80886
$160$	−2.48370	−0.196354
$161$	1.69513	0.133595
$162$	12.1844	0.957299
$163$	−14.1420	−1.10769	−0.553844	−	0.832620i	$-0.686840\pi$
$163$	−14.1420	−1.10769	−0.553844	+	0.832620i	$0.686840\pi$
$164$	1.77105	0.138296
$165$	27.7219	2.15815
$166$	5.87102	0.455679
$167$	9.14541	0.707693	0.353846	−	0.935304i	$-0.384874\pi$
$167$	9.14541	0.707693	0.353846	+	0.935304i	$0.384874\pi$
$168$	2.03655	0.157124
$169$	−12.9993	−0.999943
$170$	4.78743	0.367179
$171$	−17.2124	−1.31627
$172$	−1.68533	−0.128505
$173$	14.0992	1.07194	0.535970	−	0.844237i	$-0.319946\pi$
$173$	14.0992	1.07194	0.535970	+	0.844237i	$0.319946\pi$
$174$	−8.49562	−0.644051
$175$	−0.714033	−0.0539758
$176$	15.0723	1.13612
$177$	24.3776	1.83233
$178$	−1.01294	−0.0759234
$179$	23.3458	1.74495	0.872474	−	0.488660i	$-0.162514\pi$
$179$	23.3458	1.74495	0.872474	+	0.488660i	$0.162514\pi$
$180$	−1.32284	−0.0985983
$181$	19.8207	1.47326	0.736631	−	0.676295i	$-0.236415\pi$
$181$	19.8207	1.47326	0.736631	+	0.676295i	$0.236415\pi$
$182$	0.0104589	0.000775269 0
$183$	−20.0299	−1.48065
$184$	−17.5142	−1.29117
$185$	6.65839	0.489535
$186$	−6.74595	−0.494637
$187$	5.31159	0.388422
$188$	−0.729375	−0.0531952
$189$	0.00375152	0.000272883 0
$190$	21.2975	1.54508
$191$	1.89196	0.136898	0.0684488	−	0.997655i	$-0.478195\pi$
$191$	1.89196	0.136898	0.0684488	+	0.997655i	$0.478195\pi$
$192$	−20.9156	−1.50945
$193$	17.2319	1.24038	0.620189	−	0.784452i	$-0.287056\pi$
$193$	17.2319	1.24038	0.620189	+	0.784452i	$0.287056\pi$
$194$	−16.1728	−1.16114
$195$	−0.182699	−0.0130834
$196$	1.11081	0.0793438
$197$	4.62238	0.329331	0.164665	−	0.986349i	$-0.447346\pi$
$197$	4.62238	0.329331	0.164665	+	0.986349i	$0.447346\pi$
$198$	16.8174	1.19516
$199$	−17.7065	−1.25518	−0.627589	−	0.778545i	$-0.715958\pi$
$199$	−17.7065	−1.25518	−0.627589	+	0.778545i	$0.715958\pi$
$200$	7.37746	0.521665
$201$	−10.8062	−0.762212
$202$	−24.0679	−1.69341
$203$	0.724930	0.0508801
$204$	−0.506463	−0.0354595
$205$	−30.2490	−2.11268
$206$	−6.92848	−0.482730
$207$	−17.9633	−1.24854
$208$	−0.0993329	−0.00688750
$209$	23.6293	1.63447
$210$	−2.58450	−0.178348
$211$	−11.1970	−0.770834	−0.385417	−	0.922742i	$-0.625942\pi$
$211$	−11.1970	−0.770834	−0.385417	+	0.922742i	$0.625942\pi$
$212$	1.49415	0.102619
$213$	9.33561	0.639666
$214$	0.839819	0.0574089
$215$	28.7848	1.96311
$216$	−0.0387611	−0.00263736
$217$	0.575631	0.0390764
$218$	−4.53164	−0.306921
$219$	38.3691	2.59274
$220$	1.81599	0.122434
$221$	−0.0350057	−0.00235474
$222$	8.07132	0.541711
$223$	−2.90292	−0.194394	−0.0971969	−	0.995265i	$-0.530988\pi$
$223$	−2.90292	−0.194394	−0.0971969	+	0.995265i	$0.530988\pi$
$224$	0.256906	0.0171653
$225$	7.56662	0.504442
$226$	4.65142	0.309408
$227$	21.4022	1.42051	0.710255	−	0.703944i	$-0.248579\pi$
$227$	21.4022	1.42051	0.710255	+	0.703944i	$0.248579\pi$
$228$	−2.25306	−0.149213
$229$	17.5833	1.16194	0.580968	−	0.813926i	$-0.302674\pi$
$229$	17.5833	1.16194	0.580968	+	0.813926i	$0.302674\pi$
$230$	22.2266	1.46558
$231$	−2.86747	−0.188666
$232$	−7.49005	−0.491746
$233$	−28.8991	−1.89324	−0.946621	−	0.322348i	$-0.895528\pi$
$233$	−28.8991	−1.89324	−0.946621	+	0.322348i	$0.895528\pi$
$234$	−0.110834	−0.00724543
$235$	12.4575	0.812638
$236$	1.59691	0.103950
$237$	−16.4001	−1.06530
$238$	−0.495198	−0.0320989
$239$	25.6630	1.66000	0.830000	−	0.557763i	$-0.188340\pi$
$239$	25.6630	1.66000	0.830000	+	0.557763i	$0.188340\pi$
$240$	24.5461	1.58444
$241$	−1.00000	−0.0644157
$241$	−1.00000	−0.0644157
$242$	−8.16796	−0.525056
$243$	22.0553	1.41484
$244$	−1.31211	−0.0839992
$245$	−18.9723	−1.21210
$246$	−36.6679	−2.33786
$247$	−0.155727	−0.00990868
$248$	−5.94748	−0.377665
$249$	10.6081	0.672262
$250$	9.23094	0.583816
$251$	−28.3138	−1.78715	−0.893576	−	0.448913i	$-0.851811\pi$
$251$	−28.3138	−1.78715	−0.893576	+	0.448913i	$0.851811\pi$
$252$	0.136830	0.00861949
$253$	24.6601	1.55037
$254$	−11.0101	−0.690833
$255$	8.65022	0.541698
$256$	−3.82728	−0.239205
$257$	−17.0359	−1.06267	−0.531336	−	0.847161i	$-0.678310\pi$
$257$	−17.0359	−1.06267	−0.531336	+	0.847161i	$0.678310\pi$
$258$	34.8931	2.17235
$259$	−0.688725	−0.0427953
$260$	−0.0119682	−0.000742234 0
$261$	−7.68210	−0.475510
$262$	−3.70611	−0.228965
$263$	−21.9895	−1.35593	−0.677966	−	0.735094i	$-0.737138\pi$
$263$	−21.9895	−1.35593	−0.677966	+	0.735094i	$0.737138\pi$
$264$	29.6270	1.82342
$265$	−25.5197	−1.56766
$266$	−2.20295	−0.135071
$267$	−1.83025	−0.112009
$268$	−0.707888	−0.0432412
$269$	8.91005	0.543255	0.271628	−	0.962402i	$-0.412438\pi$
$269$	8.91005	0.543255	0.271628	+	0.962402i	$0.412438\pi$
$270$	0.0491900	0.00299361
$271$	29.9968	1.82218	0.911088	−	0.412213i	$-0.135244\pi$
$271$	29.9968	1.82218	0.911088	+	0.412213i	$0.135244\pi$
$272$	4.70310	0.285167
$273$	0.0188979	0.00114375
$274$	−7.42362	−0.448477
$275$	−10.3875	−0.626389
$276$	−2.35135	−0.141535
$277$	−14.9125	−0.896007	−0.448003	−	0.894032i	$-0.647865\pi$
$277$	−14.9125	−0.896007	−0.448003	+	0.894032i	$0.647865\pi$
$278$	22.2105	1.33210
$279$	−6.09998	−0.365196
$280$	−2.27859	−0.136172
$281$	−28.8871	−1.72326	−0.861631	−	0.507535i	$-0.830557\pi$
$281$	−28.8871	−1.72326	−0.861631	+	0.507535i	$0.830557\pi$
$282$	15.1010	0.899253
$283$	−16.5841	−0.985820	−0.492910	−	0.870080i	$-0.664067\pi$
$283$	−16.5841	−0.985820	−0.492910	+	0.870080i	$0.664067\pi$
$284$	0.611553	0.0362890
$285$	38.4816	2.27945
$286$	0.152153	0.00899698
$287$	3.12886	0.184691
$288$	−2.72244	−0.160422
$289$	−15.3426	−0.902505
$290$	9.50531	0.558171
$291$	−29.2220	−1.71302
$292$	2.51346	0.147089
$293$	−11.2756	−0.658729	−0.329364	−	0.944203i	$-0.606834\pi$
$293$	−11.2756	−0.658729	−0.329364	+	0.944203i	$0.606834\pi$
$294$	−22.9983	−1.34129
$295$	−27.2748	−1.58800
$296$	7.11597	0.413608
$297$	0.0545757	0.00316680
$298$	20.6825	1.19810
$299$	−0.162521	−0.00939881
$300$	0.990451	0.0571837
$301$	−2.97742	−0.171616
$302$	4.32665	0.248971
$303$	−43.4873	−2.49828
$304$	20.9223	1.19998
$305$	22.4104	1.28322
$306$	5.24762	0.299987
$307$	−1.24678	−0.0711575	−0.0355787	−	0.999367i	$-0.511327\pi$
$307$	−1.24678	−0.0711575	−0.0355787	+	0.999367i	$0.511327\pi$
$308$	−0.187841	−0.0107032
$309$	−12.5188	−0.712170
$310$	7.54769	0.428680
$311$	−17.8941	−1.01468	−0.507340	−	0.861746i	$-0.669371\pi$
$311$	−17.8941	−1.01468	−0.507340	+	0.861746i	$0.669371\pi$
$312$	−0.195255	−0.0110541
$313$	−30.0820	−1.70033	−0.850166	−	0.526514i	$-0.823499\pi$
$313$	−30.0820	−1.70033	−0.850166	+	0.526514i	$0.823499\pi$
$314$	−17.3270	−0.977818
$315$	−2.33702	−0.131676
$316$	−1.07433	−0.0604357
$317$	−8.17835	−0.459342	−0.229671	−	0.973268i	$-0.573765\pi$
$317$	−8.17835	−0.459342	−0.229671	+	0.973268i	$0.573765\pi$
$318$	−30.9350	−1.73475
$319$	10.5460	0.590463
$320$	23.4013	1.30817
$321$	1.51744	0.0846951
$322$	−2.29905	−0.128121
$323$	7.37318	0.410255
$324$	1.44218	0.0801214
$325$	0.0684580	0.00379736
$326$	19.1804	1.06230
$327$	−8.18805	−0.452800
$328$	−32.3278	−1.78500
$329$	−1.28857	−0.0710410
$330$	−37.5984	−2.06972
$331$	13.4643	0.740067	0.370034	−	0.929018i	$-0.379346\pi$
$331$	13.4643	0.740067	0.370034	+	0.929018i	$0.379346\pi$
$332$	0.694911	0.0381382
$333$	7.29843	0.399952
$334$	−12.4036	−0.678697
$335$	12.0905	0.660575
$336$	−2.53897	−0.138512
$337$	−6.06342	−0.330295	−0.165148	−	0.986269i	$-0.552810\pi$
$337$	−6.06342	−0.330295	−0.165148	+	0.986269i	$0.552810\pi$
$338$	17.6305	0.958973
$339$	8.40448	0.456469
$340$	0.566655	0.0307312
$341$	8.37407	0.453481
$342$	23.3447	1.26234
$343$	3.94770	0.213156
$344$	30.7630	1.65863
$345$	40.1603	2.16216
$346$	−19.1223	−1.02802
$347$	23.7297	1.27388	0.636938	−	0.770915i	$-0.280201\pi$
$347$	23.7297	1.27388	0.636938	+	0.770915i	$0.280201\pi$
$348$	−1.00557	−0.0539040
$349$	8.46091	0.452902	0.226451	−	0.974023i	$-0.427288\pi$
$349$	8.46091	0.452902	0.226451	+	0.974023i	$0.427288\pi$
$350$	0.968421	0.0517643
$351$	−0.000359677 0	−1.91982e−5 0
$352$	3.73738	0.199203
$353$	6.66847	0.354927	0.177463	−	0.984127i	$-0.443211\pi$
$353$	6.66847	0.354927	0.177463	+	0.984127i	$0.443211\pi$
$354$	−33.0625	−1.75725
$355$	−10.4451	−0.554370
$356$	−0.119895	−0.00635443
$357$	−0.894754	−0.0473554
$358$	−31.6632	−1.67345
$359$	−28.3212	−1.49474	−0.747369	−	0.664409i	$-0.768683\pi$
$359$	−28.3212	−1.49474	−0.747369	+	0.664409i	$0.768683\pi$
$360$	24.1463	1.27262
$361$	13.8005	0.726342
$362$	−26.8822	−1.41290
$363$	−14.7584	−0.774614
$364$	0.00123795	6.48863e−5 0
$365$	−42.9292	−2.24701
$366$	27.1660	1.41999
$367$	7.48573	0.390752	0.195376	−	0.980728i	$-0.437407\pi$
$367$	7.48573	0.390752	0.195376	+	0.980728i	$0.437407\pi$
$368$	21.8350	1.13823
$369$	−33.1566	−1.72607
$370$	−9.03058	−0.469477
$371$	2.63968	0.137045
$372$	−0.798471	−0.0413988
$373$	17.6125	0.911943	0.455972	−	0.889994i	$-0.349292\pi$
$373$	17.6125	0.911943	0.455972	+	0.889994i	$0.349292\pi$
$374$	−7.20395	−0.372507
$375$	16.6790	0.861302
$376$	13.3136	0.686597
$377$	−0.0695028	−0.00357957
$378$	−0.00508807	−0.000261702 0
$379$	7.61632	0.391224	0.195612	−	0.980681i	$-0.437331\pi$
$379$	7.61632	0.391224	0.195612	+	0.980681i	$0.437331\pi$
$380$	2.52083	0.129316
$381$	−19.8937	−1.01918
$382$	−2.56601	−0.131289
$383$	−27.2242	−1.39109	−0.695546	−	0.718482i	$-0.744837\pi$
$383$	−27.2242	−1.39109	−0.695546	+	0.718482i	$0.744837\pi$
$384$	23.9274	1.22104
$385$	3.20826	0.163508
$386$	−23.3711	−1.18956
$387$	31.5518	1.60387
$388$	−1.91426	−0.0971818
$389$	23.0380	1.16807	0.584036	−	0.811728i	$-0.301473\pi$
$389$	23.0380	1.16807	0.584036	+	0.811728i	$0.301473\pi$
$390$	0.247789	0.0125473
$391$	7.69483	0.389145
$392$	−20.2762	−1.02410
$393$	−6.69643	−0.337790
$394$	−6.26920	−0.315837
$395$	18.3492	0.923248
$396$	1.99055	0.100029
$397$	−17.0475	−0.855587	−0.427794	−	0.903876i	$-0.640709\pi$
$397$	−17.0475	−0.855587	−0.427794	+	0.903876i	$0.640709\pi$
$398$	24.0147	1.20375
$399$	−3.98042	−0.199270
$400$	−9.19749	−0.459875
$401$	6.19034	0.309131	0.154565	−	0.987983i	$-0.450602\pi$
$401$	6.19034	0.309131	0.154565	+	0.987983i	$0.450602\pi$
$402$	14.6561	0.730982
$403$	−0.0551887	−0.00274914
$404$	−2.84874	−0.141730
$405$	−24.6321	−1.22398
$406$	−0.983201	−0.0487954
$407$	−10.0193	−0.496638
$408$	9.24469	0.457680
$409$	11.3675	0.562088	0.281044	−	0.959695i	$-0.409319\pi$
$409$	11.3675	0.562088	0.281044	+	0.959695i	$0.409319\pi$
$410$	41.0258	2.02612
$411$	−13.4134	−0.661636
$412$	−0.820076	−0.0404022
$413$	2.82122	0.138823
$414$	24.3631	1.19738
$415$	−11.8689	−0.582620
$416$	−0.0246309	−0.00120763
$417$	40.1312	1.96523
$418$	−32.0477	−1.56750
$419$	4.14954	0.202718	0.101359	−	0.994850i	$-0.467681\pi$
$419$	4.14954	0.202718	0.101359	+	0.994850i	$0.467681\pi$
$420$	−0.305909	−0.0149268
$421$	−1.44805	−0.0705734	−0.0352867	−	0.999377i	$-0.511234\pi$
$421$	−1.44805	−0.0705734	−0.0352867	+	0.999377i	$0.511234\pi$
$422$	15.1862	0.739251
$423$	13.6550	0.663928
$424$	−27.2735	−1.32452
$425$	−3.24127	−0.157225
$426$	−12.6616	−0.613457
$427$	−2.31807	−0.112179
$428$	0.0994035	0.00480485
$429$	0.274919	0.0132732
$430$	−39.0400	−1.88268
$431$	−22.1450	−1.06669	−0.533344	−	0.845898i	$-0.679065\pi$
$431$	−22.1450	−1.06669	−0.533344	+	0.845898i	$0.679065\pi$
$432$	0.0483235	0.00232497
$433$	10.3894	0.499284	0.249642	−	0.968338i	$-0.419687\pi$
$433$	10.3894	0.499284	0.249642	+	0.968338i	$0.419687\pi$
$434$	−0.780711	−0.0374753
$435$	17.1748	0.823467
$436$	−0.536378	−0.0256879
$437$	34.2314	1.63751
$438$	−52.0388	−2.48651
$439$	39.5672	1.88844	0.944220	−	0.329316i	$-0.106818\pi$
$439$	39.5672	1.88844	0.944220	+	0.329316i	$0.106818\pi$
$440$	−33.1481	−1.58027
$441$	−20.7961	−0.990288
$442$	0.0474771	0.00225826
$443$	−2.60234	−0.123641	−0.0618203	−	0.998087i	$-0.519691\pi$
$443$	−2.60234	−0.123641	−0.0618203	+	0.998087i	$0.519691\pi$
$444$	0.955345	0.0453387
$445$	2.04777	0.0970737
$446$	3.93714	0.186429
$447$	37.3703	1.76756
$448$	−2.42057	−0.114361
$449$	−29.9486	−1.41336	−0.706681	−	0.707533i	$-0.749808\pi$
$449$	−29.9486	−1.41336	−0.706681	+	0.707533i	$0.749808\pi$
$450$	−10.2624	−0.483773
$451$	45.5175	2.14334
$452$	0.550556	0.0258960
$453$	7.81765	0.367305
$454$	−29.0271	−1.36231
$455$	−0.0211438	−0.000991238 0
$456$	41.1261	1.92591
$457$	−14.5052	−0.678526	−0.339263	−	0.940691i	$-0.610178\pi$
$457$	−14.5052	−0.678526	−0.339263	+	0.940691i	$0.610178\pi$
$458$	−23.8477	−1.11433
$459$	0.0170296	0.000794872 0
$460$	2.63080	0.122662
$461$	38.4334	1.79002	0.895011	−	0.446044i	$-0.147168\pi$
$461$	38.4334	1.79002	0.895011	+	0.446044i	$0.147168\pi$
$462$	3.88906	0.180936
$463$	36.2326	1.68387	0.841936	−	0.539578i	$-0.181416\pi$
$463$	36.2326	1.68387	0.841936	+	0.539578i	$0.181416\pi$
$464$	9.33786	0.433499
$465$	13.6376	0.632430
$466$	39.1950	1.81567
$467$	−25.1111	−1.16200	−0.581001	−	0.813903i	$-0.697339\pi$
$467$	−25.1111	−1.16200	−0.581001	+	0.813903i	$0.697339\pi$
$468$	−0.0131186	−0.000606408 0
$469$	−1.25061	−0.0577477
$470$	−16.8957	−0.779342
$471$	−31.3074	−1.44257
$472$	−29.1492	−1.34170
$473$	−43.3144	−1.99160
$474$	22.2429	1.02165
$475$	−14.4192	−0.661597
$476$	−0.0586131	−0.00268653
$477$	−27.9728	−1.28079
$478$	−34.8059	−1.59199
$479$	−22.0372	−1.00691	−0.503454	−	0.864022i	$-0.667938\pi$
$479$	−22.0372	−1.00691	−0.503454	+	0.864022i	$0.667938\pi$
$480$	6.08653	0.277811
$481$	0.0660315	0.00301078
$482$	1.35627	0.0617764
$483$	−4.15407	−0.189017
$484$	−0.966784	−0.0439447
$485$	32.6950	1.48460
$486$	−29.9129	−1.35688
$487$	−15.1309	−0.685649	−0.342824	−	0.939400i	$-0.611384\pi$
$487$	−15.1309	−0.685649	−0.342824	+	0.939400i	$0.611384\pi$
$488$	23.9505	1.08419
$489$	34.6563	1.56721
$490$	25.7316	1.16244
$491$	−40.4874	−1.82717	−0.913585	−	0.406649i	$-0.866697\pi$
$491$	−40.4874	−1.82717	−0.913585	+	0.406649i	$0.866697\pi$
$492$	−4.34012	−0.195668
$493$	3.29073	0.148207
$494$	0.211208	0.00950269
$495$	−33.9980	−1.52810
$496$	7.41473	0.332931
$497$	1.08041	0.0484632
$498$	−14.3875	−0.644718
$499$	−22.5598	−1.00992	−0.504959	−	0.863144i	$-0.668492\pi$
$499$	−22.5598	−1.00992	−0.504959	+	0.863144i	$0.668492\pi$
$500$	1.09260	0.0488626
$501$	−22.4117	−1.00128
$502$	38.4012	1.71393
$503$	25.5277	1.13823	0.569113	−	0.822259i	$-0.307287\pi$
$503$	25.5277	1.13823	0.569113	+	0.822259i	$0.307287\pi$
$504$	−2.49762	−0.111253
$505$	48.6556	2.16515
$506$	−33.4457	−1.48684
$507$	31.8559	1.41477
$508$	−1.30318	−0.0578195
$509$	−16.9047	−0.749287	−0.374643	−	0.927169i	$-0.622235\pi$
$509$	−16.9047	−0.749287	−0.374643	+	0.927169i	$0.622235\pi$
$510$	−11.7320	−0.519503
$511$	4.44047	0.196435
$512$	24.7187	1.09242
$513$	0.0757581	0.00334480
$514$	23.1053	1.01913
$515$	14.0066	0.617206
$516$	4.13004	0.181815
$517$	−18.7456	−0.824430
$518$	0.934096	0.0410418
$519$	−34.5513	−1.51663
$520$	0.218460	0.00958012
$521$	28.9409	1.26792	0.633961	−	0.773365i	$-0.281428\pi$
$521$	28.9409	1.26792	0.633961	+	0.773365i	$0.281428\pi$
$522$	10.4190	0.456027
$523$	15.3129	0.669586	0.334793	−	0.942292i	$-0.391334\pi$
$523$	15.3129	0.669586	0.334793	+	0.942292i	$0.391334\pi$
$524$	−0.438667	−0.0191632
$525$	1.74980	0.0763677
$526$	29.8237	1.30038
$527$	2.61301	0.113824
$528$	−36.9360	−1.60743
$529$	12.7248	0.553250
$530$	34.6116	1.50343
$531$	−29.8966	−1.29740
$532$	−0.260748	−0.0113048
$533$	−0.299980	−0.0129936
$534$	2.48231	0.107420
$535$	−1.69778	−0.0734015
$536$	12.9214	0.558120
$537$	−57.2111	−2.46884
$538$	−12.0844	−0.520997
$539$	28.5489	1.22969
$540$	0.00582228	0.000250551 0
$541$	11.0774	0.476253	0.238127	−	0.971234i	$-0.423467\pi$
$541$	11.0774	0.476253	0.238127	+	0.971234i	$0.423467\pi$
$542$	−40.6837	−1.74752
$543$	−48.5725	−2.08444
$544$	1.16620	0.0500002
$545$	9.16118	0.392422
$546$	−0.0256306	−0.00109689
$547$	4.93535	0.211020	0.105510	−	0.994418i	$-0.466352\pi$
$547$	4.93535	0.211020	0.105510	+	0.994418i	$0.466352\pi$
$548$	−0.878681	−0.0375354
$549$	24.5646	1.04839
$550$	14.0882	0.600724
$551$	14.6392	0.623652
$552$	42.9203	1.82681
$553$	−1.89799	−0.0807106
$554$	20.2254	0.859295
$555$	−16.3170	−0.692618
$556$	2.62890	0.111490
$557$	−14.0586	−0.595681	−0.297840	−	0.954616i	$-0.596266\pi$
$557$	−14.0586	−0.595681	−0.297840	+	0.954616i	$0.596266\pi$
$558$	8.27322	0.350233
$559$	0.285460	0.0120737
$560$	2.84073	0.120043
$561$	−13.0165	−0.549559
$562$	39.1788	1.65266
$563$	44.3164	1.86771	0.933856	−	0.357650i	$-0.116422\pi$
$563$	44.3164	1.86771	0.933856	+	0.357650i	$0.116422\pi$
$564$	1.78740	0.0752632
$565$	−9.40333	−0.395601
$566$	22.4925	0.945429
$567$	2.54787	0.107000
$568$	−11.1629	−0.468387
$569$	−6.64972	−0.278771	−0.139385	−	0.990238i	$-0.544513\pi$
$569$	−6.64972	−0.278771	−0.139385	+	0.990238i	$0.544513\pi$
$570$	−52.1914	−2.18606
$571$	−22.3573	−0.935625	−0.467812	−	0.883828i	$-0.654958\pi$
$571$	−22.3573	−0.935625	−0.467812	+	0.883828i	$0.654958\pi$
$572$	0.0180093	0.000753005 0
$573$	−4.63642	−0.193689
$574$	−4.24358	−0.177124
$575$	−15.0482	−0.627554
$576$	25.6508	1.06878
$577$	33.2047	1.38233	0.691165	−	0.722697i	$-0.257098\pi$
$577$	33.2047	1.38233	0.691165	+	0.722697i	$0.257098\pi$
$578$	20.8087	0.865528
$579$	−42.2283	−1.75495
$580$	1.12508	0.0467162
$581$	1.22768	0.0509328
$582$	39.6329	1.64284
$583$	38.4011	1.59041
$584$	−45.8794	−1.89850
$585$	0.224062	0.00926381
$586$	15.2928	0.631739
$587$	28.0737	1.15873	0.579363	−	0.815069i	$-0.303301\pi$
$587$	28.0737	1.15873	0.579363	+	0.815069i	$0.303301\pi$
$588$	−2.72215	−0.112259
$589$	11.6243	0.478971
$590$	36.9920	1.52293
$591$	−11.3276	−0.465954
$592$	−8.87150	−0.364616
$593$	−0.499968	−0.0205312	−0.0102656	−	0.999947i	$-0.503268\pi$
$593$	−0.499968	−0.0205312	−0.0102656	+	0.999947i	$0.503268\pi$
$594$	−0.0740193	−0.00303705
$595$	1.00109	0.0410408
$596$	2.44804	0.100276
$597$	43.3913	1.77589
$598$	0.220422	0.00901372
$599$	−5.66864	−0.231614	−0.115807	−	0.993272i	$-0.536945\pi$
$599$	−5.66864	−0.231614	−0.115807	+	0.993272i	$0.536945\pi$
$600$	−18.0791	−0.738078
$601$	22.5848	0.921252	0.460626	−	0.887594i	$-0.347625\pi$
$601$	22.5848	0.921252	0.460626	+	0.887594i	$0.347625\pi$
$602$	4.03818	0.164584
$603$	13.2527	0.539692
$604$	0.512115	0.0208377
$605$	16.5124	0.671323
$606$	58.9805	2.39592
$607$	−4.01260	−0.162867	−0.0814333	−	0.996679i	$-0.525950\pi$
$607$	−4.01260	−0.162867	−0.0814333	+	0.996679i	$0.525950\pi$
$608$	5.18797	0.210400
$609$	−1.77651	−0.0719877
$610$	−30.3946	−1.23064
$611$	0.123542	0.00499796
$612$	0.621124	0.0251075
$613$	−31.5947	−1.27610	−0.638048	−	0.769996i	$-0.720258\pi$
$613$	−31.5947	−1.27610	−0.638048	+	0.769996i	$0.720258\pi$
$614$	1.69097	0.0682420
$615$	74.1278	2.98912
$616$	3.42874	0.138148
$617$	−2.64125	−0.106333	−0.0531664	−	0.998586i	$-0.516931\pi$
$617$	−2.64125	−0.106333	−0.0531664	+	0.998586i	$0.516931\pi$
$618$	16.9789	0.682991
$619$	13.8609	0.557115	0.278558	−	0.960419i	$-0.410144\pi$
$619$	13.8609	0.557115	0.278558	+	0.960419i	$0.410144\pi$
$620$	0.893367	0.0358785
$621$	0.0790631	0.00317269
$622$	24.2692	0.973106
$623$	−0.211815	−0.00848621
$624$	0.243424	0.00974477
$625$	−31.2497	−1.24999
$626$	40.7992	1.63067
$627$	−57.9057	−2.31253
$628$	−2.05087	−0.0818387
$629$	−3.12638	−0.124657
$630$	3.16963	0.126281
$631$	−28.9779	−1.15359	−0.576795	−	0.816889i	$-0.695697\pi$
$631$	−28.9779	−1.15359	−0.576795	+	0.816889i	$0.695697\pi$
$632$	19.6102	0.780051
$633$	27.4393	1.09061
$634$	11.0921	0.440522
$635$	22.2580	0.883281
$636$	−3.66156	−0.145190
$637$	−0.188149	−0.00745475
$638$	−14.3032	−0.566271
$639$	−11.4492	−0.452922
$640$	−26.7711	−1.05822
$641$	−36.8202	−1.45431	−0.727154	−	0.686474i	$-0.759158\pi$
$641$	−36.8202	−1.45431	−0.727154	+	0.686474i	$0.759158\pi$
$642$	−2.05805	−0.0812249
$643$	14.9327	0.588890	0.294445	−	0.955668i	$-0.404865\pi$
$643$	14.9327	0.588890	0.294445	+	0.955668i	$0.404865\pi$
$644$	−0.272123	−0.0107231
$645$	−70.5399	−2.77751
$646$	−10.0000	−0.393446
$647$	1.09720	0.0431356	0.0215678	−	0.999767i	$-0.493134\pi$
$647$	1.09720	0.0431356	0.0215678	+	0.999767i	$0.493134\pi$
$648$	−26.3248	−1.03414
$649$	41.0421	1.61104
$650$	−0.0928475	−0.00364178
$651$	−1.41064	−0.0552872
$652$	2.27025	0.0889097
$653$	9.51269	0.372260	0.186130	−	0.982525i	$-0.440405\pi$
$653$	9.51269	0.372260	0.186130	+	0.982525i	$0.440405\pi$
$654$	11.1052	0.434248
$655$	7.49229	0.292748
$656$	40.3031	1.57357
$657$	−47.0557	−1.83582
$658$	1.74765	0.0681303
$659$	3.98928	0.155400	0.0777001	−	0.996977i	$-0.475242\pi$
$659$	3.98928	0.155400	0.0777001	+	0.996977i	$0.475242\pi$
$660$	−4.45025	−0.173226
$661$	−25.6014	−0.995780	−0.497890	−	0.867240i	$-0.665892\pi$
$661$	−25.6014	−0.995780	−0.497890	+	0.867240i	$0.665892\pi$
$662$	−18.2613	−0.709745
$663$	0.0857846	0.00333160
$664$	−12.6845	−0.492255
$665$	4.45349	0.172699
$666$	−9.89864	−0.383565
$667$	15.2779	0.591561
$668$	−1.46813	−0.0568037
$669$	7.11387	0.275038
$670$	−16.3980	−0.633510
$671$	−33.7224	−1.30184
$672$	−0.629573	−0.0242863
$673$	0.273027	0.0105244	0.00526221	−	0.999986i	$-0.498325\pi$
$673$	0.273027	0.0105244	0.00526221	+	0.999986i	$0.498325\pi$
$674$	8.22363	0.316762
$675$	−0.0333035	−0.00128185
$676$	2.08680	0.0802615
$677$	−5.73279	−0.220329	−0.110165	−	0.993913i	$-0.535138\pi$
$677$	−5.73279	−0.220329	−0.110165	+	0.993913i	$0.535138\pi$
$678$	−11.3987	−0.437766
$679$	−3.38187	−0.129784
$680$	−10.3434	−0.396651
$681$	−52.4479	−2.00981
$682$	−11.3575	−0.434901
$683$	−18.8046	−0.719538	−0.359769	−	0.933041i	$-0.617145\pi$
$683$	−18.8046	−0.719538	−0.359769	+	0.933041i	$0.617145\pi$
$684$	2.76315	0.105652
$685$	15.0076	0.573411
$686$	−5.35414	−0.204422
$687$	−43.0895	−1.64397
$688$	−38.3523	−1.46217
$689$	−0.253080	−0.00964157
$690$	−54.4683	−2.07357
$691$	15.8329	0.602310	0.301155	−	0.953575i	$-0.402628\pi$
$691$	15.8329	0.602310	0.301155	+	0.953575i	$0.402628\pi$
$692$	−2.26337	−0.0860403
$693$	3.51666	0.133587
$694$	−32.1838	−1.22168
$695$	−44.9007	−1.70318
$696$	18.3551	0.695747
$697$	14.2031	0.537981
$698$	−11.4753	−0.434346
$699$	70.8199	2.67865
$700$	0.114625	0.00433243
$701$	40.3523	1.52409	0.762043	−	0.647527i	$-0.224197\pi$
$701$	40.3523	1.52409	0.762043	+	0.647527i	$0.224197\pi$
$702$	0.000487819 0	1.84116e−5 0
$703$	−13.9081	−0.524554
$704$	−35.2135	−1.32716
$705$	−30.5283	−1.14976
$706$	−9.04425	−0.340385
$707$	−5.03280	−0.189278
$708$	−3.91338	−0.147074
$709$	−41.5401	−1.56007	−0.780036	−	0.625734i	$-0.784800\pi$
$709$	−41.5401	−1.56007	−0.780036	+	0.625734i	$0.784800\pi$
$710$	14.1664	0.531656
$711$	20.1130	0.754296
$712$	2.18850	0.0820175
$713$	12.1314	0.454325
$714$	1.21353	0.0454151
$715$	−0.307592	−0.0115033
$716$	−3.74775	−0.140060
$717$	−62.8895	−2.34865
$718$	38.4112	1.43349
$719$	−10.2324	−0.381603	−0.190801	−	0.981629i	$-0.561109\pi$
$719$	−10.2324	−0.381603	−0.190801	+	0.981629i	$0.561109\pi$
$720$	−30.1032	−1.12188
$721$	−1.44881	−0.0539563
$722$	−18.7172	−0.696582
$723$	2.45059	0.0911385
$724$	−3.18186	−0.118253
$725$	−6.43544	−0.239006
$726$	20.0163	0.742876
$727$	−45.5533	−1.68948	−0.844739	−	0.535178i	$-0.820244\pi$
$727$	−45.5533	−1.68948	−0.844739	+	0.535178i	$0.820244\pi$
$728$	−0.0225969	−0.000837497 0
$729$	−27.0971	−1.00360
$730$	58.2235	2.15495
$731$	−13.5156	−0.499894
$732$	3.21544	0.118846
$733$	−20.6241	−0.761770	−0.380885	−	0.924622i	$-0.624381\pi$
$733$	−20.6241	−0.761770	−0.380885	+	0.924622i	$0.624381\pi$
$734$	−10.1527	−0.374742
$735$	46.4934	1.71494
$736$	5.41429	0.199573
$737$	−18.1934	−0.670161
$738$	44.9694	1.65535
$739$	−17.1975	−0.632620	−0.316310	−	0.948656i	$-0.602444\pi$
$739$	−17.1975	−0.632620	−0.316310	+	0.948656i	$0.602444\pi$
$740$	−1.06889	−0.0392930
$741$	0.381623	0.0140193
$742$	−3.58012	−0.131430
$743$	−40.8356	−1.49811	−0.749056	−	0.662506i	$-0.769493\pi$
$743$	−40.8356	−1.49811	−0.749056	+	0.662506i	$0.769493\pi$
$744$	14.5748	0.534340
$745$	−41.8117	−1.53186
$746$	−23.8874	−0.874579
$747$	−13.0098	−0.476002
$748$	−0.852681	−0.0311771
$749$	0.175613	0.00641678
$750$	−22.6213	−0.826012
$751$	20.2798	0.740021	0.370010	−	0.929028i	$-0.379354\pi$
$751$	20.2798	0.740021	0.370010	+	0.929028i	$0.379354\pi$
$752$	−16.5981	−0.605271
$753$	69.3856	2.52855
$754$	0.0942645	0.00343291
$755$	−8.74676	−0.318327
$756$	−0.000602239 0	−2.19032e−5 0
$757$	13.7148	0.498473	0.249237	−	0.968443i	$-0.419820\pi$
$757$	13.7148	0.498473	0.249237	+	0.968443i	$0.419820\pi$
$758$	−10.3298	−0.375194
$759$	−60.4318	−2.19354
$760$	−46.0139	−1.66910
$761$	−6.41706	−0.232618	−0.116309	−	0.993213i	$-0.537106\pi$
$761$	−6.41706	−0.232618	−0.116309	+	0.993213i	$0.537106\pi$
$762$	26.9812	0.977425
$763$	−0.947605	−0.0343056
$764$	−0.303721	−0.0109882
$765$	−10.6086	−0.383555
$766$	36.9234	1.33410
$767$	−0.270485	−0.00976665
$768$	9.37911	0.338439
$769$	−27.8170	−1.00311	−0.501553	−	0.865127i	$-0.667238\pi$
$769$	−27.8170	−1.00311	−0.501553	+	0.865127i	$0.667238\pi$
$770$	−4.35127	−0.156809
$771$	41.7481	1.50352
$772$	−2.76627	−0.0995603
$773$	12.8524	0.462270	0.231135	−	0.972922i	$-0.425756\pi$
$773$	12.8524	0.462270	0.231135	+	0.972922i	$0.425756\pi$
$774$	−42.7927	−1.53815
$775$	−5.11007	−0.183559
$776$	34.9418	1.25434
$777$	1.68778	0.0605489
$778$	−31.2457	−1.12021
$779$	63.1843	2.26381
$780$	0.0293291	0.00105015
$781$	15.7174	0.562414
$782$	−10.4363	−0.373200
$783$	0.0338117	0.00120833
$784$	25.2783	0.902797
$785$	35.0283	1.25021
$786$	9.08217	0.323950
$787$	9.53803	0.339994	0.169997	−	0.985445i	$-0.445624\pi$
$787$	9.53803	0.339994	0.169997	+	0.985445i	$0.445624\pi$
$788$	−0.742040	−0.0264341
$789$	53.8873	1.91844
$790$	−24.8864	−0.885420
$791$	0.972653	0.0345836
$792$	−36.3345	−1.29109
$793$	0.222245	0.00789215
$794$	23.1209	0.820532
$795$	62.5383	2.21801
$796$	2.84246	0.100748
$797$	−7.72801	−0.273740	−0.136870	−	0.990589i	$-0.543704\pi$
$797$	−7.72801	−0.273740	−0.136870	+	0.990589i	$0.543704\pi$
$798$	5.39853	0.191106
$799$	−5.84930	−0.206933
$800$	−2.28064	−0.0806329
$801$	2.24461	0.0793095
$802$	−8.39577	−0.296465
$803$	64.5982	2.27962
$804$	1.73474	0.0611797
$805$	4.64777	0.163812
$806$	0.0748508	0.00263651
$807$	−21.8349	−0.768624
$808$	51.9994	1.82933
$809$	−1.99109	−0.0700030	−0.0350015	−	0.999387i	$-0.511144\pi$
$809$	−1.99109	−0.0700030	−0.0350015	+	0.999387i	$0.511144\pi$
$810$	33.4077	1.17383
$811$	28.5346	1.00198	0.500992	−	0.865452i	$-0.332969\pi$
$811$	28.5346	1.00198	0.500992	+	0.865452i	$0.332969\pi$
$812$	−0.116375	−0.00408395
$813$	−73.5099	−2.57810
$814$	13.5889	0.476290
$815$	−38.7751	−1.35823
$816$	−11.5254	−0.403469
$817$	−60.1260	−2.10354
$818$	−15.4174	−0.539058
$819$	−0.0231763	−0.000809845 0
$820$	4.85593	0.169576
$821$	48.3459	1.68728	0.843642	−	0.536907i	$-0.180407\pi$
$821$	48.3459	1.68728	0.843642	+	0.536907i	$0.180407\pi$
$822$	18.1922	0.634528
$823$	−36.4809	−1.27164	−0.635821	−	0.771836i	$-0.719338\pi$
$823$	−36.4809	−1.27164	−0.635821	+	0.771836i	$0.719338\pi$
$824$	14.9692	0.521477
$825$	25.4555	0.886246
$826$	−3.82634	−0.133135
$827$	23.2928	0.809971	0.404985	−	0.914323i	$-0.367277\pi$
$827$	23.2928	0.809971	0.404985	+	0.914323i	$0.367277\pi$
$828$	2.88369	0.100215
$829$	−29.8113	−1.03539	−0.517695	−	0.855565i	$-0.673210\pi$
$829$	−29.8113	−1.03539	−0.517695	+	0.855565i	$0.673210\pi$
$830$	16.0974	0.558748
$831$	36.5445	1.26771
$832$	0.232072	0.00804565
$833$	8.90827	0.308653
$834$	−54.4288	−1.88471
$835$	25.0752	0.867764
$836$	−3.79326	−0.131193
$837$	0.0268482	0.000928010 0
$838$	−5.62790	−0.194412
$839$	−48.3508	−1.66925	−0.834627	−	0.550815i	$-0.814317\pi$
$839$	−48.3508	−1.66925	−0.834627	+	0.550815i	$0.814317\pi$
$840$	5.58390	0.192663
$841$	−22.4663	−0.774702
$842$	1.96394	0.0676819
$843$	70.7906	2.43816
$844$	1.79748	0.0618718
$845$	−35.6419	−1.22612
$846$	−18.5198	−0.636725
$847$	−1.70799	−0.0586873
$848$	34.0019	1.16763
$849$	40.6408	1.39479
$850$	4.39603	0.150783
$851$	−14.5148	−0.497562
$852$	−1.49867	−0.0513434
$853$	5.13297	0.175750	0.0878748	−	0.996132i	$-0.471992\pi$
$853$	5.13297	0.175750	0.0878748	+	0.996132i	$0.471992\pi$
$854$	3.14393	0.107583
$855$	−47.1937	−1.61399
$856$	−1.81446	−0.0620168
$857$	20.8453	0.712062	0.356031	−	0.934474i	$-0.384130\pi$
$857$	20.8453	0.712062	0.356031	+	0.934474i	$0.384130\pi$
$858$	−0.372864	−0.0127294
$859$	24.4260	0.833403	0.416701	−	0.909043i	$-0.363186\pi$
$859$	24.4260	0.833403	0.416701	+	0.909043i	$0.363186\pi$
$860$	−4.62089	−0.157571
$861$	−7.66757	−0.261310
$862$	30.0346	1.02298
$863$	25.5588	0.870033	0.435017	−	0.900422i	$-0.356743\pi$
$863$	25.5588	0.870033	0.435017	+	0.900422i	$0.356743\pi$
$864$	0.0119825	0.000407652 0
$865$	38.6576	1.31440
$866$	−14.0909	−0.478827
$867$	37.5984	1.27691
$868$	−0.0924073	−0.00313651
$869$	−27.6112	−0.936645
$870$	−23.2936	−0.789728
$871$	0.119902	0.00406273
$872$	9.79076	0.331557
$873$	35.8378	1.21292
$874$	−46.4270	−1.57042
$875$	1.93027	0.0652550
$876$	−6.15947	−0.208109
$877$	−7.53456	−0.254424	−0.127212	−	0.991876i	$-0.540603\pi$
$877$	−7.53456	−0.254424	−0.127212	+	0.991876i	$0.540603\pi$
$878$	−53.6638	−1.81107
$879$	27.6319	0.932002
$880$	41.3258	1.39309
$881$	21.7361	0.732308	0.366154	−	0.930554i	$-0.380674\pi$
$881$	21.7361	0.732308	0.366154	+	0.930554i	$0.380674\pi$
$882$	28.2051	0.949714
$883$	−38.6202	−1.29967	−0.649837	−	0.760074i	$-0.725163\pi$
$883$	−38.6202	−1.29967	−0.649837	+	0.760074i	$0.725163\pi$
$884$	0.00561953	0.000189005 0
$885$	66.8393	2.24678
$886$	3.52947	0.118575
$887$	−14.3165	−0.480702	−0.240351	−	0.970686i	$-0.577262\pi$
$887$	−14.3165	−0.480702	−0.240351	+	0.970686i	$0.577262\pi$
$888$	−17.4383	−0.585193
$889$	−2.30230	−0.0772167
$890$	−2.77733	−0.0930963
$891$	37.0654	1.24174
$892$	0.466012	0.0156032
$893$	−26.0213	−0.870771
$894$	−50.6843	−1.69514
$895$	64.0105	2.13963
$896$	2.76913	0.0925101
$897$	0.398272	0.0132979
$898$	40.6184	1.35545
$899$	5.18805	0.173031
$900$	−1.21469	−0.0404895
$901$	11.9825	0.399196
$902$	−61.7341	−2.05552
$903$	7.29644	0.242810
$904$	−10.0496	−0.334243
$905$	54.3452	1.80650
$906$	−10.6028	−0.352256
$907$	−47.6042	−1.58067	−0.790336	−	0.612674i	$-0.790094\pi$
$907$	−47.6042	−1.58067	−0.790336	+	0.612674i	$0.790094\pi$
$908$	−3.43573	−0.114019
$909$	53.3327	1.76893
$910$	0.0286767	0.000950625 0
$911$	−40.1570	−1.33046	−0.665230	−	0.746639i	$-0.731666\pi$
$911$	−40.1570	−1.33046	−0.665230	+	0.746639i	$0.731666\pi$
$912$	−51.2720	−1.69779
$913$	17.8598	0.591074
$914$	19.6730	0.650726
$915$	−54.9188	−1.81556
$916$	−2.82268	−0.0932641
$917$	−0.774981	−0.0255921
$918$	−0.0230967	−0.000762305 0
$919$	−18.0383	−0.595029	−0.297514	−	0.954717i	$-0.596158\pi$
$919$	−18.0383	−0.595029	−0.297514	+	0.954717i	$0.596158\pi$
$920$	−48.0212	−1.58321
$921$	3.05535	0.100677
$922$	−52.1261	−1.71668
$923$	−0.103585	−0.00340953
$924$	0.460321	0.0151435
$925$	6.11403	0.201028
$926$	−49.1412	−1.61488
$927$	15.3530	0.504260
$928$	2.31545	0.0760083
$929$	−0.679116	−0.0222811	−0.0111405	−	0.999938i	$-0.503546\pi$
$929$	−0.679116	−0.0222811	−0.0111405	+	0.999938i	$0.503546\pi$
$930$	−18.4963	−0.606518
$931$	39.6295	1.29881
$932$	4.63923	0.151963
$933$	43.8510	1.43562
$934$	34.0574	1.11439
$935$	14.5635	0.476278
$936$	0.239460	0.00782699
$937$	−25.7202	−0.840243	−0.420122	−	0.907468i	$-0.638013\pi$
$937$	−25.7202	−0.840243	−0.420122	+	0.907468i	$0.638013\pi$
$938$	1.69616	0.0553816
$939$	73.7186	2.40571
$940$	−1.99983	−0.0652272
$941$	−41.9988	−1.36912	−0.684560	−	0.728956i	$-0.740006\pi$
$941$	−41.9988	−1.36912	−0.684560	+	0.728956i	$0.740006\pi$
$942$	42.4613	1.38347
$943$	65.9407	2.14732
$944$	36.3403	1.18278
$945$	0.0102861	0.000334606 0
$946$	58.7460	1.91000
$947$	−15.2367	−0.495128	−0.247564	−	0.968872i	$-0.579630\pi$
$947$	−15.2367	−0.495128	−0.247564	+	0.968872i	$0.579630\pi$
$948$	2.63274	0.0855074
$949$	−0.425730	−0.0138198
$950$	19.5563	0.634490
$951$	20.0418	0.649900
$952$	1.06989	0.0346754
$953$	43.1360	1.39731	0.698656	−	0.715457i	$-0.253782\pi$
$953$	43.1360	1.39731	0.698656	+	0.715457i	$0.253782\pi$
$954$	37.9386	1.22831
$955$	5.18745	0.167862
$956$	−4.11973	−0.133242
$957$	−25.8440	−0.835417
$958$	29.8885	0.965652
$959$	−1.55234	−0.0501277
$960$	−57.3471	−1.85087
$961$	−26.8804	−0.867110
$962$	−0.0895566	−0.00288742
$963$	−1.86098	−0.0599692
$964$	0.160532	0.00517039
$965$	47.2471	1.52094
$966$	5.63404	0.181272
$967$	45.6699	1.46864	0.734322	−	0.678801i	$-0.237500\pi$
$967$	45.6699	1.46864	0.734322	+	0.678801i	$0.237500\pi$
$968$	17.6471	0.567201
$969$	−18.0687	−0.580449
$970$	−44.3432	−1.42377
$971$	−2.32251	−0.0745330	−0.0372665	−	0.999305i	$-0.511865\pi$
$971$	−2.32251	−0.0745330	−0.0372665	+	0.999305i	$0.511865\pi$
$972$	−3.54058	−0.113564
$973$	4.64440	0.148893
$974$	20.5216	0.657556
$975$	−0.167762	−0.00537270
$976$	−29.8591	−0.955768
$977$	−50.8644	−1.62730	−0.813649	−	0.581357i	$-0.802522\pi$
$977$	−50.8644	−1.62730	−0.813649	+	0.581357i	$0.802522\pi$
$978$	−47.0033	−1.50300
$979$	−3.08141	−0.0984823
$980$	3.04567	0.0972903
$981$	10.0418	0.320610
$982$	54.9118	1.75231
$983$	−21.2587	−0.678047	−0.339023	−	0.940778i	$-0.610097\pi$
$983$	−21.2587	−0.678047	−0.339023	+	0.940778i	$0.610097\pi$
$984$	79.2221	2.52551
$985$	12.6738	0.403821
$986$	−4.46312	−0.142135
$987$	3.15775	0.100512
$988$	0.0249992	0.000795330 0
$989$	−62.7490	−1.99530
$990$	46.1105	1.46549
$991$	51.6637	1.64115	0.820575	−	0.571539i	$-0.193653\pi$
$991$	51.6637	1.64115	0.820575	+	0.571539i	$0.193653\pi$
$992$	1.83858	0.0583751
$993$	−32.9956	−1.04708
$994$	−1.46533	−0.0464775
$995$	−48.5483	−1.53908
$996$	−1.70294	−0.0539598
$997$	−32.2376	−1.02097	−0.510487	−	0.859885i	$-0.670535\pi$
$997$	−32.2376	−1.02097	−0.510487	+	0.859885i	$0.670535\pi$
$998$	30.5972	0.968538
$999$	−0.0321230	−0.00101633

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	241.2.a.a.1.3	✓	7
3.2	odd	2		2169.2.a.e.1.5		7
4.3	odd	2		3856.2.a.j.1.7		7
5.4	even	2		6025.2.a.f.1.5		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
241.2.a.a.1.3	✓	7	1.1	even	1	trivial
2169.2.a.e.1.5		7	3.2	odd	2
3856.2.a.j.1.7		7	4.3	odd	2
6025.2.a.f.1.5		7	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	241.a (trivial)

\(f(q)\)	\(=\)	\(q-1.35627 q^{2} -2.45059 q^{3} -0.160532 q^{4} +2.74184 q^{5} +3.32366 q^{6} -0.283608 q^{7} +2.93026 q^{8} +3.00540 q^{9} +O(q^{10})\)	\(q-1.35627 q^{2} -2.45059 q^{3} -0.160532 q^{4} +2.74184 q^{5} +3.32366 q^{6} -0.283608 q^{7} +2.93026 q^{8} +3.00540 q^{9} -3.71867 q^{10} -4.12582 q^{11} +0.393399 q^{12} +0.0271909 q^{13} +0.384649 q^{14} -6.71913 q^{15} -3.65317 q^{16} -1.28740 q^{17} -4.07613 q^{18} -5.72717 q^{19} -0.440153 q^{20} +0.695007 q^{21} +5.59572 q^{22} -5.97702 q^{23} -7.18088 q^{24} +2.51768 q^{25} -0.0368782 q^{26} -0.0132278 q^{27} +0.0455281 q^{28} -2.55610 q^{29} +9.11295 q^{30} -2.02967 q^{31} -0.905851 q^{32} +10.1107 q^{33} +1.74607 q^{34} -0.777607 q^{35} -0.482463 q^{36} +2.42844 q^{37} +7.76759 q^{38} -0.0666338 q^{39} +8.03431 q^{40} -11.0324 q^{41} -0.942617 q^{42} +10.4984 q^{43} +0.662326 q^{44} +8.24032 q^{45} +8.10645 q^{46} +4.54349 q^{47} +8.95242 q^{48} -6.91957 q^{49} -3.41465 q^{50} +3.15490 q^{51} -0.00436502 q^{52} -9.30751 q^{53} +0.0179405 q^{54} -11.3123 q^{55} -0.831046 q^{56} +14.0350 q^{57} +3.46676 q^{58} -9.94762 q^{59} +1.07864 q^{60} +8.17350 q^{61} +2.75279 q^{62} -0.852354 q^{63} +8.53491 q^{64} +0.0745531 q^{65} -13.7128 q^{66} +4.40964 q^{67} +0.206670 q^{68} +14.6472 q^{69} +1.05464 q^{70} -3.80954 q^{71} +8.80661 q^{72} -15.6571 q^{73} -3.29362 q^{74} -6.16980 q^{75} +0.919395 q^{76} +1.17011 q^{77} +0.0903734 q^{78} +6.69229 q^{79} -10.0164 q^{80} -8.98378 q^{81} +14.9629 q^{82} -4.32880 q^{83} -0.111571 q^{84} -3.52985 q^{85} -14.2386 q^{86} +6.26396 q^{87} -12.0897 q^{88} +0.746861 q^{89} -11.1761 q^{90} -0.00771155 q^{91} +0.959503 q^{92} +4.97390 q^{93} -6.16219 q^{94} -15.7030 q^{95} +2.21987 q^{96} +11.9245 q^{97} +9.38480 q^{98} -12.3997 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 4 q^{2} - 3 q^{3} + 2 q^{4} - 8 q^{5} - 5 q^{6} - 7 q^{7} - 6 q^{8} - 2 q^{9}+O(q^{10}) \) 7 * q - 4 * q^2 - 3 * q^3 + 2 * q^4 - 8 * q^5 - 5 * q^6 - 7 * q^7 - 6 * q^8 - 2 * q^9	\( 7 q - 4 q^{2} - 3 q^{3} + 2 q^{4} - 8 q^{5} - 5 q^{6} - 7 q^{7} - 6 q^{8} - 2 q^{9} + 3 q^{10} - 18 q^{11} + q^{12} - q^{13} - 6 q^{14} - 11 q^{15} + 4 q^{16} - 2 q^{17} + 8 q^{18} - 6 q^{19} - 8 q^{20} - 2 q^{21} + 10 q^{22} - 22 q^{23} - 3 q^{24} + 5 q^{25} + 8 q^{26} + 3 q^{27} + 9 q^{28} - 16 q^{29} + 29 q^{30} - 18 q^{31} - 6 q^{32} + 4 q^{33} + 11 q^{34} + 7 q^{35} - 7 q^{36} + 8 q^{37} + 16 q^{38} - 9 q^{39} + 14 q^{40} - 15 q^{41} + 19 q^{42} + 14 q^{43} - 4 q^{44} + 3 q^{45} + 11 q^{46} - 10 q^{47} + 31 q^{48} + 6 q^{49} - 4 q^{50} + 13 q^{51} + 27 q^{52} + 15 q^{53} + 16 q^{54} + 29 q^{55} + 13 q^{56} + 14 q^{57} + 17 q^{58} - 18 q^{59} + 15 q^{60} + 4 q^{61} + 13 q^{62} - 16 q^{63} + 2 q^{64} - 7 q^{65} + 16 q^{66} + 18 q^{67} - 15 q^{68} + 26 q^{69} + 8 q^{70} - 50 q^{71} + 30 q^{72} + 10 q^{74} + 16 q^{75} - 20 q^{76} + 17 q^{77} - 32 q^{78} - 15 q^{79} - 11 q^{80} - 9 q^{81} + 45 q^{82} - 24 q^{83} + 6 q^{84} - 2 q^{85} - 23 q^{86} + 12 q^{87} + 8 q^{88} - 13 q^{89} - 39 q^{90} - 12 q^{91} - 10 q^{92} + 14 q^{93} - 32 q^{94} - 41 q^{95} - 15 q^{96} + q^{97} + 9 q^{98} - 20 q^{99}+O(q^{100}) \) 7 * q - 4 * q^2 - 3 * q^3 + 2 * q^4 - 8 * q^5 - 5 * q^6 - 7 * q^7 - 6 * q^8 - 2 * q^9 + 3 * q^10 - 18 * q^11 + q^12 - q^13 - 6 * q^14 - 11 * q^15 + 4 * q^16 - 2 * q^17 + 8 * q^18 - 6 * q^19 - 8 * q^20 - 2 * q^21 + 10 * q^22 - 22 * q^23 - 3 * q^24 + 5 * q^25 + 8 * q^26 + 3 * q^27 + 9 * q^28 - 16 * q^29 + 29 * q^30 - 18 * q^31 - 6 * q^32 + 4 * q^33 + 11 * q^34 + 7 * q^35 - 7 * q^36 + 8 * q^37 + 16 * q^38 - 9 * q^39 + 14 * q^40 - 15 * q^41 + 19 * q^42 + 14 * q^43 - 4 * q^44 + 3 * q^45 + 11 * q^46 - 10 * q^47 + 31 * q^48 + 6 * q^49 - 4 * q^50 + 13 * q^51 + 27 * q^52 + 15 * q^53 + 16 * q^54 + 29 * q^55 + 13 * q^56 + 14 * q^57 + 17 * q^58 - 18 * q^59 + 15 * q^60 + 4 * q^61 + 13 * q^62 - 16 * q^63 + 2 * q^64 - 7 * q^65 + 16 * q^66 + 18 * q^67 - 15 * q^68 + 26 * q^69 + 8 * q^70 - 50 * q^71 + 30 * q^72 + 10 * q^74 + 16 * q^75 - 20 * q^76 + 17 * q^77 - 32 * q^78 - 15 * q^79 - 11 * q^80 - 9 * q^81 + 45 * q^82 - 24 * q^83 + 6 * q^84 - 2 * q^85 - 23 * q^86 + 12 * q^87 + 8 * q^88 - 13 * q^89 - 39 * q^90 - 12 * q^91 - 10 * q^92 + 14 * q^93 - 32 * q^94 - 41 * q^95 - 15 * q^96 + q^97 + 9 * q^98 - 20 * q^99

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