LMFDB - Embedded newform 8015.2.a.l.1.52

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, 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("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$0$
Dimension:	$62$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.52
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.01854 q^{2} -0.120356 q^{3} +2.07451 q^{4} -1.00000 q^{5} -0.242944 q^{6} -1.00000 q^{7} +0.150396 q^{8} -2.98551 q^{9} +O(q^{10})$	\(q+2.01854 q^{2} -0.120356 q^{3} +2.07451 q^{4} -1.00000 q^{5} -0.242944 q^{6} -1.00000 q^{7} +0.150396 q^{8} -2.98551 q^{9} -2.01854 q^{10} +2.98599 q^{11} -0.249680 q^{12} -0.821835 q^{13} -2.01854 q^{14} +0.120356 q^{15} -3.84543 q^{16} -1.51410 q^{17} -6.02638 q^{18} -2.64727 q^{19} -2.07451 q^{20} +0.120356 q^{21} +6.02734 q^{22} -3.02307 q^{23} -0.0181011 q^{24} +1.00000 q^{25} -1.65891 q^{26} +0.720394 q^{27} -2.07451 q^{28} +0.285570 q^{29} +0.242944 q^{30} +10.8458 q^{31} -8.06296 q^{32} -0.359383 q^{33} -3.05627 q^{34} +1.00000 q^{35} -6.19347 q^{36} +8.77302 q^{37} -5.34363 q^{38} +0.0989130 q^{39} -0.150396 q^{40} +4.58429 q^{41} +0.242944 q^{42} +11.3637 q^{43} +6.19446 q^{44} +2.98551 q^{45} -6.10218 q^{46} -4.30252 q^{47} +0.462822 q^{48} +1.00000 q^{49} +2.01854 q^{50} +0.182231 q^{51} -1.70490 q^{52} -14.5128 q^{53} +1.45414 q^{54} -2.98599 q^{55} -0.150396 q^{56} +0.318616 q^{57} +0.576434 q^{58} +7.32785 q^{59} +0.249680 q^{60} -7.06064 q^{61} +21.8926 q^{62} +2.98551 q^{63} -8.58454 q^{64} +0.821835 q^{65} -0.725428 q^{66} +13.8295 q^{67} -3.14101 q^{68} +0.363845 q^{69} +2.01854 q^{70} +2.79792 q^{71} -0.449009 q^{72} +14.0562 q^{73} +17.7087 q^{74} -0.120356 q^{75} -5.49179 q^{76} -2.98599 q^{77} +0.199660 q^{78} -9.81451 q^{79} +3.84543 q^{80} +8.86984 q^{81} +9.25358 q^{82} +8.73512 q^{83} +0.249680 q^{84} +1.51410 q^{85} +22.9381 q^{86} -0.0343701 q^{87} +0.449080 q^{88} +5.44007 q^{89} +6.02638 q^{90} +0.821835 q^{91} -6.27137 q^{92} -1.30535 q^{93} -8.68482 q^{94} +2.64727 q^{95} +0.970427 q^{96} -0.253552 q^{97} +2.01854 q^{98} -8.91472 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) $ 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.01854	1.42732	0.713662	−	0.700490i	$-0.247035\pi$
$2$	2.01854	1.42732	0.713662	+	0.700490i	$0.247035\pi$
$3$	−0.120356	−0.0694877	−0.0347439	−	0.999396i	$-0.511062\pi$
$3$	−0.120356	−0.0694877	−0.0347439	+	0.999396i	$0.511062\pi$
$4$	2.07451	1.03725
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.242944	−0.0991815
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	0.150396	0.0531729
$9$	−2.98551	−0.995171
$10$	−2.01854	−0.638319
$11$	2.98599	0.900310	0.450155	−	0.892950i	$-0.351369\pi$
$11$	2.98599	0.900310	0.450155	+	0.892950i	$0.351369\pi$
$12$	−0.249680	−0.0720764
$13$	−0.821835	−0.227936	−0.113968	−	0.993484i	$-0.536356\pi$
$13$	−0.821835	−0.227936	−0.113968	+	0.993484i	$0.536356\pi$
$14$	−2.01854	−0.539478
$15$	0.120356	0.0310758
$16$	−3.84543	−0.961359
$17$	−1.51410	−0.367223	−0.183612	−	0.982999i	$-0.558779\pi$
$17$	−1.51410	−0.367223	−0.183612	+	0.982999i	$0.558779\pi$
$18$	−6.02638	−1.42043
$19$	−2.64727	−0.607326	−0.303663	−	0.952779i	$-0.598210\pi$
$19$	−2.64727	−0.607326	−0.303663	+	0.952779i	$0.598210\pi$
$20$	−2.07451	−0.463874
$21$	0.120356	0.0262639
$22$	6.02734	1.28503
$23$	−3.02307	−0.630353	−0.315176	−	0.949033i	$-0.602064\pi$
$23$	−3.02307	−0.630353	−0.315176	+	0.949033i	$0.602064\pi$
$24$	−0.0181011	−0.00369486
$25$	1.00000	0.200000
$26$	−1.65891	−0.325339
$27$	0.720394	0.138640
$28$	−2.07451	−0.392045
$29$	0.285570	0.0530290	0.0265145	−	0.999648i	$-0.491559\pi$
$29$	0.285570	0.0530290	0.0265145	+	0.999648i	$0.491559\pi$
$30$	0.242944	0.0443553
$31$	10.8458	1.94796	0.973978	−	0.226643i	$-0.0727750\pi$
$31$	10.8458	1.94796	0.973978	+	0.226643i	$0.0727750\pi$
$32$	−8.06296	−1.42534
$33$	−0.359383	−0.0625605
$34$	−3.05627	−0.524147
$35$	1.00000	0.169031
$36$	−6.19347	−1.03225
$37$	8.77302	1.44228	0.721138	−	0.692792i	$-0.243620\pi$
$37$	8.77302	1.44228	0.721138	+	0.692792i	$0.243620\pi$
$38$	−5.34363	−0.866851
$39$	0.0989130	0.0158388
$40$	−0.150396	−0.0237797
$41$	4.58429	0.715946	0.357973	−	0.933732i	$-0.383468\pi$
$41$	4.58429	0.715946	0.357973	+	0.933732i	$0.383468\pi$
$42$	0.242944	0.0374871
$43$	11.3637	1.73295	0.866476	−	0.499219i	$-0.166380\pi$
$43$	11.3637	1.73295	0.866476	+	0.499219i	$0.166380\pi$
$44$	6.19446	0.933850
$45$	2.98551	0.445054
$46$	−6.10218	−0.899718
$47$	−4.30252	−0.627587	−0.313794	−	0.949491i	$-0.601600\pi$
$47$	−4.30252	−0.627587	−0.313794	+	0.949491i	$0.601600\pi$
$48$	0.462822	0.0668026
$49$	1.00000	0.142857
$50$	2.01854	0.285465
$51$	0.182231	0.0255175
$52$	−1.70490	−0.236427
$53$	−14.5128	−1.99349	−0.996743	−	0.0806401i	$-0.974304\pi$
$53$	−14.5128	−1.99349	−0.996743	+	0.0806401i	$0.974304\pi$
$54$	1.45414	0.197884
$55$	−2.98599	−0.402631
$56$	−0.150396	−0.0200975
$57$	0.318616	0.0422017
$58$	0.576434	0.0756895
$59$	7.32785	0.954005	0.477002	−	0.878902i	$-0.341723\pi$
$59$	7.32785	0.954005	0.477002	+	0.878902i	$0.341723\pi$
$60$	0.249680	0.0322335
$61$	−7.06064	−0.904022	−0.452011	−	0.892012i	$-0.649293\pi$
$61$	−7.06064	−0.904022	−0.452011	+	0.892012i	$0.649293\pi$
$62$	21.8926	2.78036
$63$	2.98551	0.376139
$64$	−8.58454	−1.07307
$65$	0.821835	0.101936
$66$	−0.725428	−0.0892941
$67$	13.8295	1.68954	0.844772	−	0.535127i	$-0.179736\pi$
$67$	13.8295	1.68954	0.844772	+	0.535127i	$0.179736\pi$
$68$	−3.14101	−0.380904
$69$	0.363845	0.0438018
$70$	2.01854	0.241262
$71$	2.79792	0.332052	0.166026	−	0.986121i	$-0.446906\pi$
$71$	2.79792	0.332052	0.166026	+	0.986121i	$0.446906\pi$
$72$	−0.449009	−0.0529162
$73$	14.0562	1.64515	0.822577	−	0.568654i	$-0.192536\pi$
$73$	14.0562	1.64515	0.822577	+	0.568654i	$0.192536\pi$
$74$	17.7087	2.05859
$75$	−0.120356	−0.0138975
$76$	−5.49179	−0.629951
$77$	−2.98599	−0.340285
$78$	0.199660	0.0226070
$79$	−9.81451	−1.10422	−0.552109	−	0.833772i	$-0.686177\pi$
$79$	−9.81451	−1.10422	−0.552109	+	0.833772i	$0.686177\pi$
$80$	3.84543	0.429933
$81$	8.86984	0.985538
$82$	9.25358	1.02189
$83$	8.73512	0.958804	0.479402	−	0.877596i	$-0.340854\pi$
$83$	8.73512	0.958804	0.479402	+	0.877596i	$0.340854\pi$
$84$	0.249680	0.0272423
$85$	1.51410	0.164227
$86$	22.9381	2.47348
$87$	−0.0343701	−0.00368486
$88$	0.449080	0.0478721
$89$	5.44007	0.576646	0.288323	−	0.957533i	$-0.406902\pi$
$89$	5.44007	0.576646	0.288323	+	0.957533i	$0.406902\pi$
$90$	6.02638	0.635237
$91$	0.821835	0.0861517
$92$	−6.27137	−0.653836
$93$	−1.30535	−0.135359
$94$	−8.68482	−0.895771
$95$	2.64727	0.271605
$96$	0.970427	0.0990438
$97$	−0.253552	−0.0257443	−0.0128722	−	0.999917i	$-0.504097\pi$
$97$	−0.253552	−0.0257443	−0.0128722	+	0.999917i	$0.504097\pi$
$98$	2.01854	0.203903
$99$	−8.91472	−0.895963
$100$	2.07451	0.207451
$101$	11.9362	1.18769	0.593847	−	0.804578i	$-0.297608\pi$
$101$	11.9362	1.18769	0.593847	+	0.804578i	$0.297608\pi$
$102$	0.367842	0.0364217
$103$	−10.7124	−1.05552	−0.527761	−	0.849393i	$-0.676969\pi$
$103$	−10.7124	−1.05552	−0.527761	+	0.849393i	$0.676969\pi$
$104$	−0.123600	−0.0121200
$105$	−0.120356	−0.0117456
$106$	−29.2947	−2.84535
$107$	2.14088	0.206967	0.103484	−	0.994631i	$-0.467001\pi$
$107$	2.14088	0.206967	0.103484	+	0.994631i	$0.467001\pi$
$108$	1.49446	0.143805
$109$	3.50768	0.335975	0.167988	−	0.985789i	$-0.446273\pi$
$109$	3.50768	0.335975	0.167988	+	0.985789i	$0.446273\pi$
$110$	−6.02734	−0.574685
$111$	−1.05589	−0.100220
$112$	3.84543	0.363359
$113$	−7.79191	−0.733001	−0.366501	−	0.930418i	$-0.619444\pi$
$113$	−7.79191	−0.733001	−0.366501	+	0.930418i	$0.619444\pi$
$114$	0.643139	0.0602355
$115$	3.02307	0.281902
$116$	0.592417	0.0550045
$117$	2.45360	0.226835
$118$	14.7916	1.36167
$119$	1.51410	0.138797
$120$	0.0181011	0.00165239
$121$	−2.08386	−0.189442
$122$	−14.2522	−1.29033
$123$	−0.551748	−0.0497494
$124$	22.4996	2.02052
$125$	−1.00000	−0.0894427
$126$	6.02638	0.536873
$127$	19.1524	1.69950	0.849749	−	0.527187i	$-0.176753\pi$
$127$	19.1524	1.69950	0.849749	+	0.527187i	$0.176753\pi$
$128$	−1.20233	−0.106272
$129$	−1.36769	−0.120419
$130$	1.65891	0.145496
$131$	−4.72072	−0.412452	−0.206226	−	0.978504i	$-0.566118\pi$
$131$	−4.72072	−0.412452	−0.206226	+	0.978504i	$0.566118\pi$
$132$	−0.745542	−0.0648911
$133$	2.64727	0.229548
$134$	27.9154	2.41153
$135$	−0.720394	−0.0620016
$136$	−0.227714	−0.0195263
$137$	4.06542	0.347332	0.173666	−	0.984805i	$-0.444439\pi$
$137$	4.06542	0.347332	0.173666	+	0.984805i	$0.444439\pi$
$138$	0.734436	0.0625193
$139$	11.0486	0.937129	0.468565	−	0.883429i	$-0.344771\pi$
$139$	11.0486	0.937129	0.468565	+	0.883429i	$0.344771\pi$
$140$	2.07451	0.175328
$141$	0.517835	0.0436096
$142$	5.64772	0.473946
$143$	−2.45399	−0.205213
$144$	11.4806	0.956717
$145$	−0.285570	−0.0237153
$146$	28.3730	2.34817
$147$	−0.120356	−0.00992681
$148$	18.1997	1.49601
$149$	−22.9093	−1.87680	−0.938402	−	0.345545i	$-0.887694\pi$
$149$	−22.9093	−1.87680	−0.938402	+	0.345545i	$0.887694\pi$
$150$	−0.242944	−0.0198363
$151$	−0.773441	−0.0629418	−0.0314709	−	0.999505i	$-0.510019\pi$
$151$	−0.773441	−0.0629418	−0.0314709	+	0.999505i	$0.510019\pi$
$152$	−0.398139	−0.0322933
$153$	4.52037	0.365450
$154$	−6.02734	−0.485697
$155$	−10.8458	−0.871152
$156$	0.205196	0.0164288
$157$	12.7942	1.02109	0.510546	−	0.859851i	$-0.329443\pi$
$157$	12.7942	1.02109	0.510546	+	0.859851i	$0.329443\pi$
$158$	−19.8110	−1.57608
$159$	1.74671	0.138523
$160$	8.06296	0.637433
$161$	3.02307	0.238251
$162$	17.9041	1.40668
$163$	10.1285	0.793322	0.396661	−	0.917965i	$-0.370169\pi$
$163$	10.1285	0.793322	0.396661	+	0.917965i	$0.370169\pi$
$164$	9.51014	0.742617
$165$	0.359383	0.0279779
$166$	17.6322	1.36852
$167$	14.3083	1.10721	0.553604	−	0.832780i	$-0.313252\pi$
$167$	14.3083	1.10721	0.553604	+	0.832780i	$0.313252\pi$
$168$	0.0181011	0.00139653
$169$	−12.3246	−0.948045
$170$	3.05627	0.234405
$171$	7.90347	0.604394
$172$	23.5741	1.79751
$173$	−0.230042	−0.0174897	−0.00874487	−	0.999962i	$-0.502784\pi$
$173$	−0.230042	−0.0174897	−0.00874487	+	0.999962i	$0.502784\pi$
$174$	−0.0693775	−0.00525949
$175$	−1.00000	−0.0755929
$176$	−11.4824	−0.865521
$177$	−0.881952	−0.0662916
$178$	10.9810	0.823061
$179$	2.12800	0.159054	0.0795270	−	0.996833i	$-0.474659\pi$
$179$	2.12800	0.159054	0.0795270	+	0.996833i	$0.474659\pi$
$180$	6.19347	0.461634
$181$	−4.12887	−0.306897	−0.153448	−	0.988157i	$-0.549038\pi$
$181$	−4.12887	−0.306897	−0.153448	+	0.988157i	$0.549038\pi$
$182$	1.65891	0.122966
$183$	0.849792	0.0628184
$184$	−0.454656	−0.0335177
$185$	−8.77302	−0.645005
$186$	−2.63491	−0.193201
$187$	−4.52109	−0.330615
$188$	−8.92561	−0.650967
$189$	−0.720394	−0.0524009
$190$	5.34363	0.387668
$191$	−17.8444	−1.29118	−0.645589	−	0.763685i	$-0.723388\pi$
$191$	−17.8444	−1.29118	−0.645589	+	0.763685i	$0.723388\pi$
$192$	1.03320	0.0745650
$193$	14.3542	1.03324	0.516620	−	0.856215i	$-0.327190\pi$
$193$	14.3542	1.03324	0.516620	+	0.856215i	$0.327190\pi$
$194$	−0.511805	−0.0367455
$195$	−0.0989130	−0.00708330
$196$	2.07451	0.148179
$197$	−5.18092	−0.369125	−0.184563	−	0.982821i	$-0.559087\pi$
$197$	−5.18092	−0.369125	−0.184563	+	0.982821i	$0.559087\pi$
$198$	−17.9947	−1.27883
$199$	13.9001	0.985349	0.492675	−	0.870214i	$-0.336019\pi$
$199$	13.9001	0.985349	0.492675	+	0.870214i	$0.336019\pi$
$200$	0.150396	0.0106346
$201$	−1.66447	−0.117402
$202$	24.0937	1.69523
$203$	−0.285570	−0.0200431
$204$	0.378040	0.0264681
$205$	−4.58429	−0.320181
$206$	−21.6234	−1.50657
$207$	9.02541	0.627309
$208$	3.16031	0.219128
$209$	−7.90473	−0.546782
$210$	−0.242944	−0.0167647
$211$	13.9829	0.962623	0.481311	−	0.876550i	$-0.340161\pi$
$211$	13.9829	0.962623	0.481311	+	0.876550i	$0.340161\pi$
$212$	−30.1069	−2.06775
$213$	−0.336747	−0.0230735
$214$	4.32146	0.295409
$215$	−11.3637	−0.774999
$216$	0.108344	0.00737189
$217$	−10.8458	−0.736258
$218$	7.08040	0.479545
$219$	−1.69175	−0.114318
$220$	−6.19446	−0.417630
$221$	1.24434	0.0837034
$222$	−2.13135	−0.143047
$223$	−1.92404	−0.128843	−0.0644217	−	0.997923i	$-0.520520\pi$
$223$	−1.92404	−0.128843	−0.0644217	+	0.997923i	$0.520520\pi$
$224$	8.06296	0.538729
$225$	−2.98551	−0.199034
$226$	−15.7283	−1.04623
$227$	−25.9778	−1.72421	−0.862105	−	0.506730i	$-0.830854\pi$
$227$	−25.9778	−1.72421	−0.862105	+	0.506730i	$0.830854\pi$
$228$	0.660971	0.0437739
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	6.10218	0.402366
$231$	0.359383	0.0236456
$232$	0.0429485	0.00281971
$233$	3.83628	0.251323	0.125662	−	0.992073i	$-0.459895\pi$
$233$	3.83628	0.251323	0.125662	+	0.992073i	$0.459895\pi$
$234$	4.95269	0.323768
$235$	4.30252	0.280666
$236$	15.2017	0.989545
$237$	1.18124	0.0767296
$238$	3.05627	0.198109
$239$	2.97210	0.192249	0.0961247	−	0.995369i	$-0.469355\pi$
$239$	2.97210	0.192249	0.0961247	+	0.995369i	$0.469355\pi$
$240$	−0.462822	−0.0298750
$241$	−8.38102	−0.539869	−0.269934	−	0.962879i	$-0.587002\pi$
$241$	−8.38102	−0.539869	−0.269934	+	0.962879i	$0.587002\pi$
$242$	−4.20636	−0.270395
$243$	−3.22872	−0.207123
$244$	−14.6473	−0.937700
$245$	−1.00000	−0.0638877
$246$	−1.11373	−0.0710086
$247$	2.17562	0.138432
$248$	1.63116	0.103579
$249$	−1.05133	−0.0666251
$250$	−2.01854	−0.127664
$251$	−10.8118	−0.682433	−0.341217	−	0.939985i	$-0.610839\pi$
$251$	−10.8118	−0.682433	−0.341217	+	0.939985i	$0.610839\pi$
$252$	6.19347	0.390152
$253$	−9.02685	−0.567513
$254$	38.6599	2.42574
$255$	−0.182231	−0.0114118
$256$	14.7421	0.921383
$257$	−2.99285	−0.186689	−0.0933443	−	0.995634i	$-0.529756\pi$
$257$	−2.99285	−0.186689	−0.0933443	+	0.995634i	$0.529756\pi$
$258$	−2.76075	−0.171877
$259$	−8.77302	−0.545129
$260$	1.70490	0.105734
$261$	−0.852573	−0.0527729
$262$	−9.52898	−0.588702
$263$	−9.74849	−0.601117	−0.300559	−	0.953763i	$-0.597173\pi$
$263$	−9.74849	−0.601117	−0.300559	+	0.953763i	$0.597173\pi$
$264$	−0.0540496	−0.00332652
$265$	14.5128	0.891514
$266$	5.34363	0.327639
$267$	−0.654746	−0.0400698
$268$	28.6894	1.75248
$269$	14.7391	0.898659	0.449330	−	0.893366i	$-0.351663\pi$
$269$	14.7391	0.898659	0.449330	+	0.893366i	$0.351663\pi$
$270$	−1.45414	−0.0884964
$271$	28.1816	1.71191	0.855954	−	0.517052i	$-0.172971\pi$
$271$	28.1816	1.71191	0.855954	+	0.517052i	$0.172971\pi$
$272$	5.82237	0.353033
$273$	−0.0989130	−0.00598649
$274$	8.20621	0.495755
$275$	2.98599	0.180062
$276$	0.754799	0.0454335
$277$	−25.0942	−1.50776	−0.753882	−	0.657009i	$-0.771821\pi$
$277$	−25.0942	−1.50776	−0.753882	+	0.657009i	$0.771821\pi$
$278$	22.3020	1.33759
$279$	−32.3802	−1.93855
$280$	0.150396	0.00898786
$281$	1.34593	0.0802917	0.0401458	−	0.999194i	$-0.487218\pi$
$281$	1.34593	0.0802917	0.0401458	+	0.999194i	$0.487218\pi$
$282$	1.04527	0.0622450
$283$	4.90900	0.291809	0.145905	−	0.989299i	$-0.453391\pi$
$283$	4.90900	0.291809	0.145905	+	0.989299i	$0.453391\pi$
$284$	5.80430	0.344422
$285$	−0.318616	−0.0188732
$286$	−4.95348	−0.292906
$287$	−4.58429	−0.270602
$288$	24.0721	1.41846
$289$	−14.7075	−0.865147
$290$	−0.576434	−0.0338494
$291$	0.0305166	0.00178891
$292$	29.1597	1.70644
$293$	−4.75988	−0.278075	−0.139038	−	0.990287i	$-0.544401\pi$
$293$	−4.75988	−0.278075	−0.139038	+	0.990287i	$0.544401\pi$
$294$	−0.242944	−0.0141688
$295$	−7.32785	−0.426644
$296$	1.31942	0.0766900
$297$	2.15109	0.124819
$298$	−46.2434	−2.67881
$299$	2.48446	0.143680
$300$	−0.249680	−0.0144153
$301$	−11.3637	−0.654994
$302$	−1.56122	−0.0898383
$303$	−1.43659	−0.0825302
$304$	10.1799	0.583858
$305$	7.06064	0.404291
$306$	9.12455	0.521616
$307$	6.36296	0.363153	0.181577	−	0.983377i	$-0.441880\pi$
$307$	6.36296	0.363153	0.181577	+	0.983377i	$0.441880\pi$
$308$	−6.19446	−0.352962
$309$	1.28930	0.0733459
$310$	−21.8926	−1.24342
$311$	7.14344	0.405067	0.202534	−	0.979275i	$-0.435082\pi$
$311$	7.14344	0.405067	0.202534	+	0.979275i	$0.435082\pi$
$312$	0.0148761	0.000842193 0
$313$	32.8188	1.85503	0.927515	−	0.373785i	$-0.121940\pi$
$313$	32.8188	1.85503	0.927515	+	0.373785i	$0.121940\pi$
$314$	25.8257	1.45743
$315$	−2.98551	−0.168215
$316$	−20.3603	−1.14535
$317$	20.8644	1.17186	0.585931	−	0.810361i	$-0.300729\pi$
$317$	20.8644	1.17186	0.585931	+	0.810361i	$0.300729\pi$
$318$	3.52580	0.197717
$319$	0.852709	0.0477425
$320$	8.58454	0.479890
$321$	−0.257669	−0.0143817
$322$	6.10218	0.340061
$323$	4.00824	0.223024
$324$	18.4005	1.02225
$325$	−0.821835	−0.0455872
$326$	20.4447	1.13233
$327$	−0.422172	−0.0233461
$328$	0.689458	0.0380689
$329$	4.30252	0.237206
$330$	0.725428	0.0399335
$331$	22.7009	1.24775	0.623877	−	0.781523i	$-0.285557\pi$
$331$	22.7009	1.24775	0.623877	+	0.781523i	$0.285557\pi$
$332$	18.1211	0.994523
$333$	−26.1920	−1.43531
$334$	28.8819	1.58034
$335$	−13.8295	−0.755587
$336$	−0.462822	−0.0252490
$337$	26.0804	1.42069	0.710346	−	0.703852i	$-0.248538\pi$
$337$	26.0804	1.42069	0.710346	+	0.703852i	$0.248538\pi$
$338$	−24.8777	−1.35317
$339$	0.937805	0.0509346
$340$	3.14101	0.170345
$341$	32.3853	1.75376
$342$	15.9535	0.862666
$343$	−1.00000	−0.0539949
$344$	1.70905	0.0921461
$345$	−0.363845	−0.0195887
$346$	−0.464348	−0.0249635
$347$	26.9574	1.44715	0.723574	−	0.690247i	$-0.242498\pi$
$347$	26.9574	1.44715	0.723574	+	0.690247i	$0.242498\pi$
$348$	−0.0713010	−0.00382214
$349$	−12.6296	−0.676049	−0.338024	−	0.941137i	$-0.609759\pi$
$349$	−12.6296	−0.676049	−0.338024	+	0.941137i	$0.609759\pi$
$350$	−2.01854	−0.107896
$351$	−0.592045	−0.0316010
$352$	−24.0759	−1.28325
$353$	−24.6136	−1.31005	−0.655025	−	0.755607i	$-0.727342\pi$
$353$	−24.6136	−1.31005	−0.655025	+	0.755607i	$0.727342\pi$
$354$	−1.78026	−0.0946196
$355$	−2.79792	−0.148498
$356$	11.2855	0.598128
$357$	−0.182231	−0.00964471
$358$	4.29545	0.227022
$359$	−27.3321	−1.44253	−0.721266	−	0.692658i	$-0.756439\pi$
$359$	−27.3321	−1.44253	−0.721266	+	0.692658i	$0.756439\pi$
$360$	0.449009	0.0236648
$361$	−11.9919	−0.631155
$362$	−8.33430	−0.438041
$363$	0.250806	0.0131639
$364$	1.70490	0.0893612
$365$	−14.0562	−0.735735
$366$	1.71534	0.0896623
$367$	4.72242	0.246508	0.123254	−	0.992375i	$-0.460667\pi$
$367$	4.72242	0.246508	0.123254	+	0.992375i	$0.460667\pi$
$368$	11.6250	0.605995
$369$	−13.6865	−0.712489
$370$	−17.7087	−0.920631
$371$	14.5128	0.753467
$372$	−2.70797	−0.140402
$373$	−27.7541	−1.43705	−0.718526	−	0.695500i	$-0.755183\pi$
$373$	−27.7541	−1.43705	−0.718526	+	0.695500i	$0.755183\pi$
$374$	−9.12600	−0.471894
$375$	0.120356	0.00621517
$376$	−0.647081	−0.0333707
$377$	−0.234691	−0.0120872
$378$	−1.45414	−0.0747931
$379$	−11.8613	−0.609273	−0.304636	−	0.952469i	$-0.598535\pi$
$379$	−11.8613	−0.609273	−0.304636	+	0.952469i	$0.598535\pi$
$380$	5.49179	0.281723
$381$	−2.30511	−0.118094
$382$	−36.0197	−1.84293
$383$	−3.24910	−0.166021	−0.0830106	−	0.996549i	$-0.526454\pi$
$383$	−3.24910	−0.166021	−0.0830106	+	0.996549i	$0.526454\pi$
$384$	0.144708	0.00738460
$385$	2.98599	0.152180
$386$	28.9746	1.47477
$387$	−33.9266	−1.72458
$388$	−0.525996	−0.0267034
$389$	−27.5946	−1.39910	−0.699550	−	0.714583i	$-0.746616\pi$
$389$	−27.5946	−1.39910	−0.699550	+	0.714583i	$0.746616\pi$
$390$	−0.199660	−0.0101102
$391$	4.57723	0.231480
$392$	0.150396	0.00759613
$393$	0.568169	0.0286603
$394$	−10.4579	−0.526861
$395$	9.81451	0.493821
$396$	−18.4936	−0.929341
$397$	23.7727	1.19312	0.596559	−	0.802570i	$-0.296534\pi$
$397$	23.7727	1.19312	0.596559	+	0.802570i	$0.296534\pi$
$398$	28.0578	1.40641
$399$	−0.318616	−0.0159507
$400$	−3.84543	−0.192272
$401$	−1.62548	−0.0811728	−0.0405864	−	0.999176i	$-0.512923\pi$
$401$	−1.62548	−0.0811728	−0.0405864	+	0.999176i	$0.512923\pi$
$402$	−3.35980	−0.167571
$403$	−8.91343	−0.444009
$404$	24.7617	1.23194
$405$	−8.86984	−0.440746
$406$	−0.576434	−0.0286080
$407$	26.1961	1.29849
$408$	0.0274068	0.00135684
$409$	−11.1149	−0.549596	−0.274798	−	0.961502i	$-0.588611\pi$
$409$	−11.1149	−0.549596	−0.274798	+	0.961502i	$0.588611\pi$
$410$	−9.25358	−0.457002
$411$	−0.489298	−0.0241353
$412$	−22.2229	−1.09484
$413$	−7.32785	−0.360580
$414$	18.2182	0.895373
$415$	−8.73512	−0.428790
$416$	6.62642	0.324887
$417$	−1.32977	−0.0651190
$418$	−15.9560	−0.780435
$419$	36.4669	1.78152	0.890762	−	0.454470i	$-0.150171\pi$
$419$	36.4669	1.78152	0.890762	+	0.454470i	$0.150171\pi$
$420$	−0.249680	−0.0121831
$421$	−6.47846	−0.315741	−0.157870	−	0.987460i	$-0.550463\pi$
$421$	−6.47846	−0.315741	−0.157870	+	0.987460i	$0.550463\pi$
$422$	28.2251	1.37397
$423$	12.8452	0.624557
$424$	−2.18266	−0.105999
$425$	−1.51410	−0.0734447
$426$	−0.679738	−0.0329334
$427$	7.06064	0.341688
$428$	4.44128	0.214677
$429$	0.295353	0.0142598
$430$	−22.9381	−1.10618
$431$	0.605717	0.0291764	0.0145882	−	0.999894i	$-0.495356\pi$
$431$	0.605717	0.0291764	0.0145882	+	0.999894i	$0.495356\pi$
$432$	−2.77023	−0.133283
$433$	40.0413	1.92426	0.962132	−	0.272585i	$-0.0878786\pi$
$433$	40.0413	1.92426	0.962132	+	0.272585i	$0.0878786\pi$
$434$	−21.8926	−1.05088
$435$	0.0343701	0.00164792
$436$	7.27672	0.348491
$437$	8.00288	0.382830
$438$	−3.41487	−0.163169
$439$	14.0004	0.668201	0.334101	−	0.942537i	$-0.391567\pi$
$439$	14.0004	0.668201	0.334101	+	0.942537i	$0.391567\pi$
$440$	−0.449080	−0.0214091
$441$	−2.98551	−0.142167
$442$	2.51175	0.119472
$443$	30.6569	1.45655	0.728277	−	0.685283i	$-0.240321\pi$
$443$	30.6569	1.45655	0.728277	+	0.685283i	$0.240321\pi$
$444$	−2.19045	−0.103954
$445$	−5.44007	−0.257884
$446$	−3.88376	−0.183901
$447$	2.75728	0.130415
$448$	8.58454	0.405581
$449$	20.4269	0.964006	0.482003	−	0.876170i	$-0.339909\pi$
$449$	20.4269	0.964006	0.482003	+	0.876170i	$0.339909\pi$
$450$	−6.02638	−0.284086
$451$	13.6886	0.644573
$452$	−16.1644	−0.760308
$453$	0.0930885	0.00437368
$454$	−52.4373	−2.46101
$455$	−0.821835	−0.0385282
$456$	0.0479185	0.00224399
$457$	−26.9185	−1.25920	−0.629598	−	0.776921i	$-0.716780\pi$
$457$	−26.9185	−1.25920	−0.629598	+	0.776921i	$0.716780\pi$
$458$	2.01854	0.0943202
$459$	−1.09075	−0.0509118
$460$	6.27137	0.292404
$461$	40.7205	1.89654	0.948271	−	0.317462i	$-0.102830\pi$
$461$	40.7205	1.89654	0.948271	+	0.317462i	$0.102830\pi$
$462$	0.725428	0.0337500
$463$	−19.8876	−0.924256	−0.462128	−	0.886813i	$-0.652914\pi$
$463$	−19.8876	−0.924256	−0.462128	+	0.886813i	$0.652914\pi$
$464$	−1.09814	−0.0509799
$465$	1.30535	0.0605344
$466$	7.74369	0.358720
$467$	−19.1949	−0.888232	−0.444116	−	0.895969i	$-0.646482\pi$
$467$	−19.1949	−0.888232	−0.444116	+	0.895969i	$0.646482\pi$
$468$	5.09001	0.235286
$469$	−13.8295	−0.638587
$470$	8.68482	0.400601
$471$	−1.53987	−0.0709533
$472$	1.10208	0.0507272
$473$	33.9320	1.56019
$474$	2.38438	0.109518
$475$	−2.64727	−0.121465
$476$	3.14101	0.143968
$477$	43.3282	1.98386
$478$	5.99931	0.274402
$479$	−13.0349	−0.595579	−0.297789	−	0.954632i	$-0.596249\pi$
$479$	−13.0349	−0.595579	−0.297789	+	0.954632i	$0.596249\pi$
$480$	−0.970427	−0.0442937
$481$	−7.20997	−0.328747
$482$	−16.9174	−0.770567
$483$	−0.363845	−0.0165555
$484$	−4.32299	−0.196499
$485$	0.253552	0.0115132
$486$	−6.51731	−0.295631
$487$	−1.39679	−0.0632944	−0.0316472	−	0.999499i	$-0.510075\pi$
$487$	−1.39679	−0.0632944	−0.0316472	+	0.999499i	$0.510075\pi$
$488$	−1.06189	−0.0480695
$489$	−1.21902	−0.0551261
$490$	−2.01854	−0.0911884
$491$	19.4386	0.877251	0.438625	−	0.898670i	$-0.355465\pi$
$491$	19.4386	0.877251	0.438625	+	0.898670i	$0.355465\pi$
$492$	−1.14461	−0.0516028
$493$	−0.432381	−0.0194735
$494$	4.39158	0.197587
$495$	8.91472	0.400687
$496$	−41.7067	−1.87268
$497$	−2.79792	−0.125504
$498$	−2.12214	−0.0950956
$499$	16.8089	0.752470	0.376235	−	0.926524i	$-0.377219\pi$
$499$	16.8089	0.752470	0.376235	+	0.926524i	$0.377219\pi$
$500$	−2.07451	−0.0927748
$501$	−1.72209	−0.0769374
$502$	−21.8240	−0.974054
$503$	40.5525	1.80815	0.904073	−	0.427378i	$-0.140562\pi$
$503$	40.5525	1.80815	0.904073	+	0.427378i	$0.140562\pi$
$504$	0.449009	0.0200004
$505$	−11.9362	−0.531153
$506$	−18.2211	−0.810025
$507$	1.48334	0.0658775
$508$	39.7317	1.76281
$509$	−0.740309	−0.0328136	−0.0164068	−	0.999865i	$-0.505223\pi$
$509$	−0.740309	−0.0328136	−0.0164068	+	0.999865i	$0.505223\pi$
$510$	−0.367842	−0.0162883
$511$	−14.0562	−0.621810
$512$	32.1622	1.42138
$513$	−1.90708	−0.0841996
$514$	−6.04118	−0.266465
$515$	10.7124	0.472044
$516$	−2.83729	−0.124905
$517$	−12.8473	−0.565023
$518$	−17.7087	−0.778075
$519$	0.0276869	0.00121532
$520$	0.123600	0.00542024
$521$	−35.4362	−1.55249	−0.776245	−	0.630432i	$-0.782878\pi$
$521$	−35.4362	−1.55249	−0.776245	+	0.630432i	$0.782878\pi$
$522$	−1.72095	−0.0753241
$523$	11.4006	0.498513	0.249257	−	0.968437i	$-0.419814\pi$
$523$	11.4006	0.498513	0.249257	+	0.968437i	$0.419814\pi$
$524$	−9.79318	−0.427817
$525$	0.120356	0.00525278
$526$	−19.6777	−0.857989
$527$	−16.4216	−0.715335
$528$	1.38198	0.0601430
$529$	−13.8611	−0.602655
$530$	29.2947	1.27248
$531$	−21.8774	−0.949398
$532$	5.49179	0.238099
$533$	−3.76753	−0.163190
$534$	−1.32163	−0.0571926
$535$	−2.14088	−0.0925585
$536$	2.07990	0.0898380
$537$	−0.256118	−0.0110523
$538$	29.7515	1.28268
$539$	2.98599	0.128616
$540$	−1.49446	−0.0643114
$541$	23.4058	1.00629	0.503146	−	0.864201i	$-0.332176\pi$
$541$	23.4058	1.00629	0.503146	+	0.864201i	$0.332176\pi$
$542$	56.8856	2.44345
$543$	0.496935	0.0213255
$544$	12.2081	0.523419
$545$	−3.50768	−0.150253
$546$	−0.199660	−0.00854465
$547$	−13.1125	−0.560649	−0.280325	−	0.959905i	$-0.590442\pi$
$547$	−13.1125	−0.560649	−0.280325	+	0.959905i	$0.590442\pi$
$548$	8.43374	0.360271
$549$	21.0796	0.899657
$550$	6.02734	0.257007
$551$	−0.755981	−0.0322059
$552$	0.0547207	0.00232907
$553$	9.81451	0.417355
$554$	−50.6537	−2.15207
$555$	1.05589	0.0448199
$556$	22.9204	0.972041
$557$	4.01859	0.170273	0.0851365	−	0.996369i	$-0.472867\pi$
$557$	4.01859	0.170273	0.0851365	+	0.996369i	$0.472867\pi$
$558$	−65.3607	−2.76694
$559$	−9.33910	−0.395002
$560$	−3.84543	−0.162499
$561$	0.544141	0.0229737
$562$	2.71682	0.114602
$563$	23.6255	0.995695	0.497847	−	0.867265i	$-0.334124\pi$
$563$	23.6255	0.995695	0.497847	+	0.867265i	$0.334124\pi$
$564$	1.07425	0.0452342
$565$	7.79191	0.327808
$566$	9.90901	0.416507
$567$	−8.86984	−0.372498
$568$	0.420795	0.0176562
$569$	0.466002	0.0195358	0.00976792	−	0.999952i	$-0.496891\pi$
$569$	0.466002	0.0195358	0.00976792	+	0.999952i	$0.496891\pi$
$570$	−0.643139	−0.0269381
$571$	9.13380	0.382238	0.191119	−	0.981567i	$-0.438788\pi$
$571$	9.13380	0.382238	0.191119	+	0.981567i	$0.438788\pi$
$572$	−5.09082	−0.212858
$573$	2.14769	0.0897211
$574$	−9.25358	−0.386237
$575$	−3.02307	−0.126071
$576$	25.6293	1.06789
$577$	17.2137	0.716616	0.358308	−	0.933604i	$-0.383354\pi$
$577$	17.2137	0.716616	0.358308	+	0.933604i	$0.383354\pi$
$578$	−29.6877	−1.23485
$579$	−1.72762	−0.0717975
$580$	−0.592417	−0.0245988
$581$	−8.73512	−0.362394
$582$	0.0615990	0.00255336
$583$	−43.3351	−1.79476
$584$	2.11399	0.0874776
$585$	−2.45360	−0.101444
$586$	−9.60801	−0.396903
$587$	13.5138	0.557775	0.278887	−	0.960324i	$-0.410034\pi$
$587$	13.5138	0.557775	0.278887	+	0.960324i	$0.410034\pi$
$588$	−0.249680	−0.0102966
$589$	−28.7117	−1.18304
$590$	−14.7916	−0.608959
$591$	0.623556	0.0256497
$592$	−33.7361	−1.38654
$593$	−21.3194	−0.875484	−0.437742	−	0.899101i	$-0.644222\pi$
$593$	−21.3194	−0.875484	−0.437742	+	0.899101i	$0.644222\pi$
$594$	4.34206	0.178157
$595$	−1.51410	−0.0620721
$596$	−47.5255	−1.94672
$597$	−1.67296	−0.0684696
$598$	5.01499	0.205078
$599$	−23.9550	−0.978775	−0.489388	−	0.872066i	$-0.662780\pi$
$599$	−23.9550	−0.978775	−0.489388	+	0.872066i	$0.662780\pi$
$600$	−0.0181011	−0.000738973 0
$601$	20.0702	0.818681	0.409340	−	0.912382i	$-0.365759\pi$
$601$	20.0702	0.818681	0.409340	+	0.912382i	$0.365759\pi$
$602$	−22.9381	−0.934889
$603$	−41.2882	−1.68139
$604$	−1.60451	−0.0652866
$605$	2.08386	0.0847210
$606$	−2.89982	−0.117797
$607$	5.41787	0.219905	0.109952	−	0.993937i	$-0.464930\pi$
$607$	5.41787	0.219905	0.109952	+	0.993937i	$0.464930\pi$
$608$	21.3449	0.865648
$609$	0.0343701	0.00139275
$610$	14.2522	0.577054
$611$	3.53596	0.143050
$612$	9.37754	0.379064
$613$	−10.8001	−0.436213	−0.218106	−	0.975925i	$-0.569988\pi$
$613$	−10.8001	−0.436213	−0.218106	+	0.975925i	$0.569988\pi$
$614$	12.8439	0.518337
$615$	0.551748	0.0222486
$616$	−0.449080	−0.0180940
$617$	−6.15143	−0.247647	−0.123824	−	0.992304i	$-0.539516\pi$
$617$	−6.15143	−0.247647	−0.123824	+	0.992304i	$0.539516\pi$
$618$	2.60251	0.104688
$619$	11.3119	0.454665	0.227333	−	0.973817i	$-0.427000\pi$
$619$	11.3119	0.454665	0.227333	+	0.973817i	$0.427000\pi$
$620$	−22.4996	−0.903606
$621$	−2.17780	−0.0873920
$622$	14.4193	0.578162
$623$	−5.44007	−0.217952
$624$	−0.380363	−0.0152267
$625$	1.00000	0.0400000
$626$	66.2462	2.64773
$627$	0.951384	0.0379946
$628$	26.5417	1.05913
$629$	−13.2832	−0.529637
$630$	−6.02638	−0.240097
$631$	−31.9598	−1.27230	−0.636150	−	0.771566i	$-0.719474\pi$
$631$	−31.9598	−1.27230	−0.636150	+	0.771566i	$0.719474\pi$
$632$	−1.47606	−0.0587145
$633$	−1.68293	−0.0668904
$634$	42.1157	1.67263
$635$	−19.1524	−0.760039
$636$	3.62355	0.143683
$637$	−0.821835	−0.0325623
$638$	1.72123	0.0681440
$639$	−8.35323	−0.330449
$640$	1.20233	0.0475263
$641$	−1.77275	−0.0700196	−0.0350098	−	0.999387i	$-0.511146\pi$
$641$	−1.77275	−0.0700196	−0.0350098	+	0.999387i	$0.511146\pi$
$642$	−0.520115	−0.0205273
$643$	−8.92532	−0.351980	−0.175990	−	0.984392i	$-0.556313\pi$
$643$	−8.92532	−0.351980	−0.175990	+	0.984392i	$0.556313\pi$
$644$	6.27137	0.247127
$645$	1.36769	0.0538529
$646$	8.09079	0.318328
$647$	−33.4910	−1.31667	−0.658334	−	0.752726i	$-0.728739\pi$
$647$	−33.4910	−1.31667	−0.658334	+	0.752726i	$0.728739\pi$
$648$	1.33399	0.0524039
$649$	21.8809	0.858900
$650$	−1.65891	−0.0650677
$651$	1.30535	0.0511609
$652$	21.0115	0.822876
$653$	24.1848	0.946426	0.473213	−	0.880948i	$-0.343094\pi$
$653$	24.1848	0.946426	0.473213	+	0.880948i	$0.343094\pi$
$654$	−0.852171	−0.0333225
$655$	4.72072	0.184454
$656$	−17.6286	−0.688281
$657$	−41.9650	−1.63721
$658$	8.68482	0.338569
$659$	−24.4776	−0.953512	−0.476756	−	0.879036i	$-0.658187\pi$
$659$	−24.4776	−0.953512	−0.476756	+	0.879036i	$0.658187\pi$
$660$	0.745542	0.0290202
$661$	36.2043	1.40818	0.704091	−	0.710109i	$-0.251355\pi$
$661$	36.2043	1.40818	0.704091	+	0.710109i	$0.251355\pi$
$662$	45.8227	1.78095
$663$	−0.149764	−0.00581636
$664$	1.31372	0.0509824
$665$	−2.64727	−0.102657
$666$	−52.8696	−2.04865
$667$	−0.863296	−0.0334270
$668$	29.6826	1.14846
$669$	0.231571	0.00895303
$670$	−27.9154	−1.07847
$671$	−21.0830	−0.813900
$672$	−0.970427	−0.0374350
$673$	−10.8707	−0.419034	−0.209517	−	0.977805i	$-0.567189\pi$
$673$	−10.8707	−0.419034	−0.209517	+	0.977805i	$0.567189\pi$
$674$	52.6444	2.02779
$675$	0.720394	0.0277280
$676$	−25.5674	−0.983363
$677$	−13.4130	−0.515503	−0.257752	−	0.966211i	$-0.582982\pi$
$677$	−13.4130	−0.515503	−0.257752	+	0.966211i	$0.582982\pi$
$678$	1.89300	0.0727002
$679$	0.253552	0.00973044
$680$	0.227714	0.00873244
$681$	3.12659	0.119811
$682$	65.3711	2.50319
$683$	28.0061	1.07162	0.535811	−	0.844338i	$-0.320006\pi$
$683$	28.0061	1.07162	0.535811	+	0.844338i	$0.320006\pi$
$684$	16.3958	0.626910
$685$	−4.06542	−0.155332
$686$	−2.01854	−0.0770682
$687$	−0.120356	−0.00459188
$688$	−43.6984	−1.66599
$689$	11.9271	0.454387
$690$	−0.734436	−0.0279595
$691$	−41.6412	−1.58411	−0.792053	−	0.610452i	$-0.790988\pi$
$691$	−41.6412	−1.58411	−0.792053	+	0.610452i	$0.790988\pi$
$692$	−0.477223	−0.0181413
$693$	8.91472	0.338642
$694$	54.4146	2.06555
$695$	−11.0486	−0.419097
$696$	−0.00516912	−0.000195935 0
$697$	−6.94108	−0.262912
$698$	−25.4934	−0.964941
$699$	−0.461721	−0.0174639
$700$	−2.07451	−0.0784090
$701$	−13.0563	−0.493129	−0.246564	−	0.969126i	$-0.579302\pi$
$701$	−13.0563	−0.493129	−0.246564	+	0.969126i	$0.579302\pi$
$702$	−1.19507	−0.0451049
$703$	−23.2246	−0.875932
$704$	−25.6334	−0.966093
$705$	−0.517835	−0.0195028
$706$	−49.6836	−1.86987
$707$	−11.9362	−0.448906
$708$	−1.82962	−0.0687612
$709$	−35.4715	−1.33216	−0.666081	−	0.745879i	$-0.732030\pi$
$709$	−35.4715	−1.33216	−0.666081	+	0.745879i	$0.732030\pi$
$710$	−5.64772	−0.211955
$711$	29.3014	1.09889
$712$	0.818163	0.0306620
$713$	−32.7874	−1.22790
$714$	−0.367842	−0.0137661
$715$	2.45399	0.0917741
$716$	4.41455	0.164979
$717$	−0.357711	−0.0133590
$718$	−55.1709	−2.05896
$719$	3.15811	0.117778	0.0588889	−	0.998265i	$-0.481244\pi$
$719$	3.15811	0.117778	0.0588889	+	0.998265i	$0.481244\pi$
$720$	−11.4806	−0.427857
$721$	10.7124	0.398950
$722$	−24.2062	−0.900862
$723$	1.00871	0.0375142
$724$	−8.56537	−0.318330
$725$	0.285570	0.0106058
$726$	0.506262	0.0187891
$727$	−2.07992	−0.0771401	−0.0385701	−	0.999256i	$-0.512280\pi$
$727$	−2.07992	−0.0771401	−0.0385701	+	0.999256i	$0.512280\pi$
$728$	0.123600	0.00458094
$729$	−26.2209	−0.971145
$730$	−28.3730	−1.05013
$731$	−17.2058	−0.636380
$732$	1.76290	0.0651586
$733$	−16.5428	−0.611022	−0.305511	−	0.952189i	$-0.598827\pi$
$733$	−16.5428	−0.611022	−0.305511	+	0.952189i	$0.598827\pi$
$734$	9.53239	0.351847
$735$	0.120356	0.00443941
$736$	24.3749	0.898469
$737$	41.2948	1.52111
$738$	−27.6267	−1.01695
$739$	17.3838	0.639472	0.319736	−	0.947507i	$-0.396406\pi$
$739$	17.3838	0.639472	0.319736	+	0.947507i	$0.396406\pi$
$740$	−18.1997	−0.669034
$741$	−0.261850	−0.00961929
$742$	29.2947	1.07544
$743$	−7.12855	−0.261521	−0.130761	−	0.991414i	$-0.541742\pi$
$743$	−7.12855	−0.261521	−0.130761	+	0.991414i	$0.541742\pi$
$744$	−0.196320	−0.00719743
$745$	22.9093	0.839332
$746$	−56.0228	−2.05114
$747$	−26.0788	−0.954174
$748$	−9.37903	−0.342931
$749$	−2.14088	−0.0782262
$750$	0.242944	0.00887106
$751$	−45.6608	−1.66618	−0.833092	−	0.553134i	$-0.813432\pi$
$751$	−45.6608	−1.66618	−0.833092	+	0.553134i	$0.813432\pi$
$752$	16.5451	0.603337
$753$	1.30126	0.0474207
$754$	−0.473734	−0.0172524
$755$	0.773441	0.0281484
$756$	−1.49446	−0.0543531
$757$	23.3090	0.847180	0.423590	−	0.905854i	$-0.360770\pi$
$757$	23.3090	0.847180	0.423590	+	0.905854i	$0.360770\pi$
$758$	−23.9425	−0.869630
$759$	1.08644	0.0394352
$760$	0.398139	0.0144420
$761$	36.5513	1.32498	0.662492	−	0.749069i	$-0.269499\pi$
$761$	36.5513	1.32498	0.662492	+	0.749069i	$0.269499\pi$
$762$	−4.65296	−0.168559
$763$	−3.50768	−0.126987
$764$	−37.0184	−1.33928
$765$	−4.52037	−0.163434
$766$	−6.55844	−0.236966
$767$	−6.02228	−0.217452
$768$	−1.77431	−0.0640248
$769$	32.8931	1.18616	0.593078	−	0.805145i	$-0.297913\pi$
$769$	32.8931	1.18616	0.593078	+	0.805145i	$0.297913\pi$
$770$	6.02734	0.217210
$771$	0.360208	0.0129726
$772$	29.7780	1.07173
$773$	−22.2418	−0.799981	−0.399991	−	0.916519i	$-0.630987\pi$
$773$	−22.2418	−0.799981	−0.399991	+	0.916519i	$0.630987\pi$
$774$	−68.4821	−2.46154
$775$	10.8458	0.389591
$776$	−0.0381332	−0.00136890
$777$	1.05589	0.0378798
$778$	−55.7008	−1.99697
$779$	−12.1359	−0.434813
$780$	−0.205196	−0.00734718
$781$	8.35456	0.298950
$782$	9.23932	0.330397
$783$	0.205723	0.00735193
$784$	−3.84543	−0.137337
$785$	−12.7942	−0.456646
$786$	1.14687	0.0409076
$787$	1.42465	0.0507831	0.0253916	−	0.999678i	$-0.491917\pi$
$787$	1.42465	0.0507831	0.0253916	+	0.999678i	$0.491917\pi$
$788$	−10.7479	−0.382877
$789$	1.17329	0.0417703
$790$	19.8110	0.704843
$791$	7.79191	0.277049
$792$	−1.34074	−0.0476410
$793$	5.80268	0.206059
$794$	47.9861	1.70296
$795$	−1.74671	−0.0619493
$796$	28.8358	1.02206
$797$	−37.2617	−1.31988	−0.659939	−	0.751319i	$-0.729418\pi$
$797$	−37.2617	−1.31988	−0.659939	+	0.751319i	$0.729418\pi$
$798$	−0.643139	−0.0227669
$799$	6.51445	0.230465
$800$	−8.06296	−0.285069
$801$	−16.2414	−0.573862
$802$	−3.28110	−0.115860
$803$	41.9717	1.48115
$804$	−3.45295	−0.121776
$805$	−3.02307	−0.106549
$806$	−17.9921	−0.633745
$807$	−1.77394	−0.0624458
$808$	1.79515	0.0631532
$809$	−19.9105	−0.700016	−0.350008	−	0.936747i	$-0.613821\pi$
$809$	−19.9105	−0.700016	−0.350008	+	0.936747i	$0.613821\pi$
$810$	−17.9041	−0.629087
$811$	17.9295	0.629589	0.314795	−	0.949160i	$-0.398064\pi$
$811$	17.9295	0.629589	0.314795	+	0.949160i	$0.398064\pi$
$812$	−0.592417	−0.0207897
$813$	−3.39183	−0.118957
$814$	52.8780	1.85337
$815$	−10.1285	−0.354784
$816$	−0.700759	−0.0245315
$817$	−30.0829	−1.05247
$818$	−22.4358	−0.784451
$819$	−2.45360	−0.0857357
$820$	−9.51014	−0.332109
$821$	−5.29890	−0.184933	−0.0924664	−	0.995716i	$-0.529475\pi$
$821$	−5.29890	−0.184933	−0.0924664	+	0.995716i	$0.529475\pi$
$822$	−0.987669	−0.0344489
$823$	−12.2789	−0.428017	−0.214008	−	0.976832i	$-0.568652\pi$
$823$	−12.2789	−0.428017	−0.214008	+	0.976832i	$0.568652\pi$
$824$	−1.61110	−0.0561252
$825$	−0.359383	−0.0125121
$826$	−14.7916	−0.514664
$827$	29.5684	1.02819	0.514097	−	0.857732i	$-0.328127\pi$
$827$	29.5684	1.02819	0.514097	+	0.857732i	$0.328127\pi$
$828$	18.7233	0.650679
$829$	−31.3691	−1.08950	−0.544748	−	0.838600i	$-0.683375\pi$
$829$	−31.3691	−1.08950	−0.544748	+	0.838600i	$0.683375\pi$
$830$	−17.6322	−0.612022
$831$	3.02024	0.104771
$832$	7.05508	0.244591
$833$	−1.51410	−0.0524605
$834$	−2.68419	−0.0929459
$835$	−14.3083	−0.495159
$836$	−16.3984	−0.567151
$837$	7.81322	0.270064
$838$	73.6099	2.54281
$839$	34.7611	1.20009	0.600044	−	0.799967i	$-0.295150\pi$
$839$	34.7611	1.20009	0.600044	+	0.799967i	$0.295150\pi$
$840$	−0.0181011	−0.000624546 0
$841$	−28.9184	−0.997188
$842$	−13.0770	−0.450665
$843$	−0.161992	−0.00557928
$844$	29.0076	0.998484
$845$	12.3246	0.423979
$846$	25.9286	0.891445
$847$	2.08386	0.0716023
$848$	55.8080	1.91646
$849$	−0.590828	−0.0202772
$850$	−3.05627	−0.104829
$851$	−26.5214	−0.909142
$852$	−0.698584	−0.0239331
$853$	−32.0906	−1.09876	−0.549381	−	0.835572i	$-0.685137\pi$
$853$	−32.0906	−1.09876	−0.549381	+	0.835572i	$0.685137\pi$
$854$	14.2522	0.487700
$855$	−7.90347	−0.270293
$856$	0.321980	0.0110050
$857$	37.3455	1.27570	0.637849	−	0.770161i	$-0.279824\pi$
$857$	37.3455	1.27570	0.637849	+	0.770161i	$0.279824\pi$
$858$	0.596182	0.0203533
$859$	−48.6768	−1.66083	−0.830416	−	0.557144i	$-0.811897\pi$
$859$	−48.6768	−1.66083	−0.830416	+	0.557144i	$0.811897\pi$
$860$	−23.5741	−0.803871
$861$	0.551748	0.0188035
$862$	1.22266	0.0416441
$863$	3.21053	0.109288	0.0546438	−	0.998506i	$-0.482598\pi$
$863$	3.21053	0.109288	0.0546438	+	0.998506i	$0.482598\pi$
$864$	−5.80851	−0.197609
$865$	0.230042	0.00782165
$866$	80.8251	2.74655
$867$	1.77014	0.0601171
$868$	−22.4996	−0.763686
$869$	−29.3060	−0.994139
$870$	0.0693775	0.00235212
$871$	−11.3656	−0.385108
$872$	0.527541	0.0178648
$873$	0.756984	0.0256200
$874$	16.1541	0.546422
$875$	1.00000	0.0338062
$876$	−3.50955	−0.118577
$877$	18.4976	0.624621	0.312310	−	0.949980i	$-0.398897\pi$
$877$	18.4976	0.624621	0.312310	+	0.949980i	$0.398897\pi$
$878$	28.2603	0.953740
$879$	0.572881	0.0193228
$880$	11.4824	0.387073
$881$	18.7894	0.633032	0.316516	−	0.948587i	$-0.397487\pi$
$881$	18.7894	0.633032	0.316516	+	0.948587i	$0.397487\pi$
$882$	−6.02638	−0.202919
$883$	−10.1513	−0.341618	−0.170809	−	0.985304i	$-0.554638\pi$
$883$	−10.1513	−0.341618	−0.170809	+	0.985304i	$0.554638\pi$
$884$	2.58139	0.0868217
$885$	0.881952	0.0296465
$886$	61.8823	2.07897
$887$	15.7594	0.529149	0.264575	−	0.964365i	$-0.414768\pi$
$887$	15.7594	0.529149	0.264575	+	0.964365i	$0.414768\pi$
$888$	−0.158801	−0.00532901
$889$	−19.1524	−0.642350
$890$	−10.9810	−0.368084
$891$	26.4853	0.887289
$892$	−3.99144	−0.133643
$893$	11.3900	0.381150
$894$	5.56568	0.186144
$895$	−2.12800	−0.0711311
$896$	1.20233	0.0401671
$897$	−0.299020	−0.00998400
$898$	41.2326	1.37595
$899$	3.09722	0.103298
$900$	−6.19347	−0.206449
$901$	21.9738	0.732055
$902$	27.6311	0.920015
$903$	1.36769	0.0455140
$904$	−1.17187	−0.0389758
$905$	4.12887	0.137248
$906$	0.187903	0.00624266
$907$	−45.6118	−1.51451	−0.757257	−	0.653117i	$-0.773461\pi$
$907$	−45.6118	−1.51451	−0.757257	+	0.653117i	$0.773461\pi$
$908$	−53.8912	−1.78844
$909$	−35.6356	−1.18196
$910$	−1.65891	−0.0549923
$911$	13.9943	0.463651	0.231826	−	0.972757i	$-0.425530\pi$
$911$	13.9943	0.463651	0.231826	+	0.972757i	$0.425530\pi$
$912$	−1.22522	−0.0405710
$913$	26.0830	0.863221
$914$	−54.3362	−1.79728
$915$	−0.849792	−0.0280933
$916$	2.07451	0.0685436
$917$	4.72072	0.155892
$918$	−2.20172	−0.0726676
$919$	20.6800	0.682170	0.341085	−	0.940033i	$-0.389206\pi$
$919$	20.6800	0.682170	0.341085	+	0.940033i	$0.389206\pi$
$920$	0.454656	0.0149896
$921$	−0.765821	−0.0252347
$922$	82.1960	2.70698
$923$	−2.29943	−0.0756866
$924$	0.745542	0.0245265
$925$	8.77302	0.288455
$926$	−40.1440	−1.31921
$927$	31.9820	1.05043
$928$	−2.30254	−0.0755845
$929$	−7.05111	−0.231339	−0.115670	−	0.993288i	$-0.536901\pi$
$929$	−7.05111	−0.231339	−0.115670	+	0.993288i	$0.536901\pi$
$930$	2.63491	0.0864022
$931$	−2.64727	−0.0867609
$932$	7.95840	0.260686
$933$	−0.859757	−0.0281472
$934$	−38.7456	−1.26780
$935$	4.52109	0.147855
$936$	0.369011	0.0120615
$937$	18.9884	0.620325	0.310163	−	0.950684i	$-0.399617\pi$
$937$	18.9884	0.620325	0.310163	+	0.950684i	$0.399617\pi$
$938$	−27.9154	−0.911471
$939$	−3.94995	−0.128902
$940$	8.92561	0.291121
$941$	5.49813	0.179234	0.0896170	−	0.995976i	$-0.471436\pi$
$941$	5.49813	0.179234	0.0896170	+	0.995976i	$0.471436\pi$
$942$	−3.10828	−0.101273
$943$	−13.8586	−0.451299
$944$	−28.1788	−0.917140
$945$	0.720394	0.0234344
$946$	68.4930	2.22690
$947$	60.6523	1.97093	0.985467	−	0.169868i	$-0.0543342\pi$
$947$	60.6523	1.97093	0.985467	+	0.169868i	$0.0543342\pi$
$948$	2.45048	0.0795881
$949$	−11.5519	−0.374990
$950$	−5.34363	−0.173370
$951$	−2.51116	−0.0814300
$952$	0.227714	0.00738026
$953$	−32.2600	−1.04500	−0.522502	−	0.852638i	$-0.675001\pi$
$953$	−32.2600	−1.04500	−0.522502	+	0.852638i	$0.675001\pi$
$954$	87.4597	2.83161
$955$	17.8444	0.577433
$956$	6.16565	0.199411
$957$	−0.102629	−0.00331752
$958$	−26.3114	−0.850084
$959$	−4.06542	−0.131279
$960$	−1.03320	−0.0333465
$961$	86.6305	2.79453
$962$	−14.5536	−0.469228
$963$	−6.39164	−0.205968
$964$	−17.3865	−0.559981
$965$	−14.3542	−0.462079
$966$	−0.734436	−0.0236301
$967$	2.64984	0.0852132	0.0426066	−	0.999092i	$-0.486434\pi$
$967$	2.64984	0.0852132	0.0426066	+	0.999092i	$0.486434\pi$
$968$	−0.313404	−0.0100732
$969$	−0.482416	−0.0154974
$970$	0.511805	0.0164331
$971$	−10.1530	−0.325825	−0.162913	−	0.986640i	$-0.552089\pi$
$971$	−10.1530	−0.325825	−0.162913	+	0.986640i	$0.552089\pi$
$972$	−6.69801	−0.214839
$973$	−11.0486	−0.354202
$974$	−2.81947	−0.0903416
$975$	0.0989130	0.00316775
$976$	27.1512	0.869090
$977$	44.2425	1.41544	0.707722	−	0.706491i	$-0.249723\pi$
$977$	44.2425	1.41544	0.707722	+	0.706491i	$0.249723\pi$
$978$	−2.46065	−0.0786828
$979$	16.2440	0.519160
$980$	−2.07451	−0.0662677
$981$	−10.4722	−0.334353
$982$	39.2376	1.25212
$983$	32.2834	1.02968	0.514840	−	0.857286i	$-0.327851\pi$
$983$	32.2834	1.02968	0.514840	+	0.857286i	$0.327851\pi$
$984$	−0.0829805	−0.00264532
$985$	5.18092	0.165078
$986$	−0.872779	−0.0277950
$987$	−0.517835	−0.0164829
$988$	4.51334	0.143589
$989$	−34.3533	−1.09237
$990$	17.9947	0.571910
$991$	−5.92942	−0.188354	−0.0941770	−	0.995555i	$-0.530022\pi$
$991$	−5.92942	−0.188354	−0.0941770	+	0.995555i	$0.530022\pi$
$992$	−87.4489	−2.77651
$993$	−2.73219	−0.0867035
$994$	−5.64772	−0.179135
$995$	−13.9001	−0.440662
$996$	−2.18098	−0.0691071
$997$	11.2013	0.354748	0.177374	−	0.984143i	$-0.443240\pi$
$997$	11.2013	0.354748	0.177374	+	0.984143i	$0.443240\pi$
$998$	33.9295	1.07402
$999$	6.32003	0.199957

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.l.1.52	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.l.1.52	✓	62	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q+2.01854 q^{2} -0.120356 q^{3} +2.07451 q^{4} -1.00000 q^{5} -0.242944 q^{6} -1.00000 q^{7} +0.150396 q^{8} -2.98551 q^{9} +O(q^{10})\)	\(q+2.01854 q^{2} -0.120356 q^{3} +2.07451 q^{4} -1.00000 q^{5} -0.242944 q^{6} -1.00000 q^{7} +0.150396 q^{8} -2.98551 q^{9} -2.01854 q^{10} +2.98599 q^{11} -0.249680 q^{12} -0.821835 q^{13} -2.01854 q^{14} +0.120356 q^{15} -3.84543 q^{16} -1.51410 q^{17} -6.02638 q^{18} -2.64727 q^{19} -2.07451 q^{20} +0.120356 q^{21} +6.02734 q^{22} -3.02307 q^{23} -0.0181011 q^{24} +1.00000 q^{25} -1.65891 q^{26} +0.720394 q^{27} -2.07451 q^{28} +0.285570 q^{29} +0.242944 q^{30} +10.8458 q^{31} -8.06296 q^{32} -0.359383 q^{33} -3.05627 q^{34} +1.00000 q^{35} -6.19347 q^{36} +8.77302 q^{37} -5.34363 q^{38} +0.0989130 q^{39} -0.150396 q^{40} +4.58429 q^{41} +0.242944 q^{42} +11.3637 q^{43} +6.19446 q^{44} +2.98551 q^{45} -6.10218 q^{46} -4.30252 q^{47} +0.462822 q^{48} +1.00000 q^{49} +2.01854 q^{50} +0.182231 q^{51} -1.70490 q^{52} -14.5128 q^{53} +1.45414 q^{54} -2.98599 q^{55} -0.150396 q^{56} +0.318616 q^{57} +0.576434 q^{58} +7.32785 q^{59} +0.249680 q^{60} -7.06064 q^{61} +21.8926 q^{62} +2.98551 q^{63} -8.58454 q^{64} +0.821835 q^{65} -0.725428 q^{66} +13.8295 q^{67} -3.14101 q^{68} +0.363845 q^{69} +2.01854 q^{70} +2.79792 q^{71} -0.449009 q^{72} +14.0562 q^{73} +17.7087 q^{74} -0.120356 q^{75} -5.49179 q^{76} -2.98599 q^{77} +0.199660 q^{78} -9.81451 q^{79} +3.84543 q^{80} +8.86984 q^{81} +9.25358 q^{82} +8.73512 q^{83} +0.249680 q^{84} +1.51410 q^{85} +22.9381 q^{86} -0.0343701 q^{87} +0.449080 q^{88} +5.44007 q^{89} +6.02638 q^{90} +0.821835 q^{91} -6.27137 q^{92} -1.30535 q^{93} -8.68482 q^{94} +2.64727 q^{95} +0.970427 q^{96} -0.253552 q^{97} +2.01854 q^{98} -8.91472 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * q^99

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