LMFDB - Embedded newform 4015.2.a.f.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4015,2,Mod(1,4015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4015, 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("4015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4015 = 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4015.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:	$32.0599364115$
Analytic rank:	$1$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	4015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.69949 q^{2} -0.262694 q^{3} +0.888269 q^{4} -1.00000 q^{5} +0.446447 q^{6} +0.253523 q^{7} +1.88938 q^{8} -2.93099 q^{9} +O(q^{10})$	\(q-1.69949 q^{2} -0.262694 q^{3} +0.888269 q^{4} -1.00000 q^{5} +0.446447 q^{6} +0.253523 q^{7} +1.88938 q^{8} -2.93099 q^{9} +1.69949 q^{10} +1.00000 q^{11} -0.233343 q^{12} -3.64072 q^{13} -0.430860 q^{14} +0.262694 q^{15} -4.98752 q^{16} +3.34510 q^{17} +4.98119 q^{18} -5.39157 q^{19} -0.888269 q^{20} -0.0665991 q^{21} -1.69949 q^{22} -0.224160 q^{23} -0.496329 q^{24} +1.00000 q^{25} +6.18737 q^{26} +1.55804 q^{27} +0.225197 q^{28} +8.47296 q^{29} -0.446447 q^{30} +9.14702 q^{31} +4.69749 q^{32} -0.262694 q^{33} -5.68497 q^{34} -0.253523 q^{35} -2.60351 q^{36} +4.30101 q^{37} +9.16292 q^{38} +0.956397 q^{39} -1.88938 q^{40} +3.52724 q^{41} +0.113185 q^{42} +1.36543 q^{43} +0.888269 q^{44} +2.93099 q^{45} +0.380957 q^{46} -7.60813 q^{47} +1.31019 q^{48} -6.93573 q^{49} -1.69949 q^{50} -0.878739 q^{51} -3.23394 q^{52} -6.79151 q^{53} -2.64787 q^{54} -1.00000 q^{55} +0.479001 q^{56} +1.41633 q^{57} -14.3997 q^{58} -7.00691 q^{59} +0.233343 q^{60} -11.8025 q^{61} -15.5453 q^{62} -0.743074 q^{63} +1.99170 q^{64} +3.64072 q^{65} +0.446447 q^{66} +15.0892 q^{67} +2.97135 q^{68} +0.0588855 q^{69} +0.430860 q^{70} -4.31695 q^{71} -5.53775 q^{72} +1.00000 q^{73} -7.30952 q^{74} -0.262694 q^{75} -4.78916 q^{76} +0.253523 q^{77} -1.62539 q^{78} +0.496408 q^{79} +4.98752 q^{80} +8.38369 q^{81} -5.99452 q^{82} +6.69921 q^{83} -0.0591579 q^{84} -3.34510 q^{85} -2.32053 q^{86} -2.22580 q^{87} +1.88938 q^{88} +10.6799 q^{89} -4.98119 q^{90} -0.923007 q^{91} -0.199114 q^{92} -2.40287 q^{93} +12.9299 q^{94} +5.39157 q^{95} -1.23400 q^{96} -14.2221 q^{97} +11.7872 q^{98} -2.93099 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q - 7 q^{2} - 4 q^{3} + 39 q^{4} - 31 q^{5} - 5 q^{6} - 11 q^{7} - 24 q^{8} + 31 q^{9}+O(q^{10}) $ 31 * q - 7 * q^2 - 4 * q^3 + 39 * q^4 - 31 * q^5 - 5 * q^6 - 11 * q^7 - 24 * q^8 + 31 * q^9	\( 31 q - 7 q^{2} - 4 q^{3} + 39 q^{4} - 31 q^{5} - 5 q^{6} - 11 q^{7} - 24 q^{8} + 31 q^{9} + 7 q^{10} + 31 q^{11} - 4 q^{12} - 24 q^{13} - 9 q^{14} + 4 q^{15} + 43 q^{16} - 49 q^{17} - 35 q^{18} - 22 q^{19} - 39 q^{20} - 8 q^{21} - 7 q^{22} - q^{23} - 13 q^{24} + 31 q^{25} - 9 q^{26} - 22 q^{27} - 34 q^{28} - 12 q^{29} + 5 q^{30} + 4 q^{31} - 45 q^{32} - 4 q^{33} + 2 q^{34} + 11 q^{35} + 34 q^{36} - 18 q^{37} - 7 q^{38} - q^{39} + 24 q^{40} - 58 q^{41} - 21 q^{42} - 41 q^{43} + 39 q^{44} - 31 q^{45} + 23 q^{46} - 31 q^{47} - 29 q^{48} + 44 q^{49} - 7 q^{50} + 8 q^{51} - 89 q^{52} - 46 q^{53} - 47 q^{54} - 31 q^{55} + 10 q^{56} - 47 q^{57} - 34 q^{58} - 9 q^{59} + 4 q^{60} - 5 q^{61} - 50 q^{62} - 61 q^{63} + 78 q^{64} + 24 q^{65} - 5 q^{66} + q^{67} - 115 q^{68} - 19 q^{69} + 9 q^{70} - 8 q^{71} - 93 q^{72} + 31 q^{73} - 19 q^{74} - 4 q^{75} - 7 q^{76} - 11 q^{77} + 57 q^{78} - 43 q^{80} + 43 q^{81} + 20 q^{82} - 29 q^{83} - 32 q^{84} + 49 q^{85} + 25 q^{86} - 62 q^{87} - 24 q^{88} - 77 q^{89} + 35 q^{90} - 11 q^{91} - 25 q^{92} - 38 q^{94} + 22 q^{95} - 23 q^{96} - 39 q^{97} - 65 q^{98} + 31 q^{99}+O(q^{100}) \) 31 * q - 7 * q^2 - 4 * q^3 + 39 * q^4 - 31 * q^5 - 5 * q^6 - 11 * q^7 - 24 * q^8 + 31 * q^9 + 7 * q^10 + 31 * q^11 - 4 * q^12 - 24 * q^13 - 9 * q^14 + 4 * q^15 + 43 * q^16 - 49 * q^17 - 35 * q^18 - 22 * q^19 - 39 * q^20 - 8 * q^21 - 7 * q^22 - q^23 - 13 * q^24 + 31 * q^25 - 9 * q^26 - 22 * q^27 - 34 * q^28 - 12 * q^29 + 5 * q^30 + 4 * q^31 - 45 * q^32 - 4 * q^33 + 2 * q^34 + 11 * q^35 + 34 * q^36 - 18 * q^37 - 7 * q^38 - q^39 + 24 * q^40 - 58 * q^41 - 21 * q^42 - 41 * q^43 + 39 * q^44 - 31 * q^45 + 23 * q^46 - 31 * q^47 - 29 * q^48 + 44 * q^49 - 7 * q^50 + 8 * q^51 - 89 * q^52 - 46 * q^53 - 47 * q^54 - 31 * q^55 + 10 * q^56 - 47 * q^57 - 34 * q^58 - 9 * q^59 + 4 * q^60 - 5 * q^61 - 50 * q^62 - 61 * q^63 + 78 * q^64 + 24 * q^65 - 5 * q^66 + q^67 - 115 * q^68 - 19 * q^69 + 9 * q^70 - 8 * q^71 - 93 * q^72 + 31 * q^73 - 19 * q^74 - 4 * q^75 - 7 * q^76 - 11 * q^77 + 57 * q^78 - 43 * q^80 + 43 * q^81 + 20 * q^82 - 29 * q^83 - 32 * q^84 + 49 * q^85 + 25 * q^86 - 62 * q^87 - 24 * q^88 - 77 * q^89 + 35 * q^90 - 11 * q^91 - 25 * q^92 - 38 * q^94 + 22 * q^95 - 23 * q^96 - 39 * q^97 - 65 * q^98 + 31 * 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 $

$2$	−1.69949	−1.20172	−0.600861	−	0.799354i	$-0.705175\pi$
$2$	−1.69949	−1.20172	−0.600861	+	0.799354i	$0.705175\pi$
$3$	−0.262694	−0.151667	−0.0758333	−	0.997121i	$-0.524162\pi$
$3$	−0.262694	−0.151667	−0.0758333	+	0.997121i	$0.524162\pi$
$4$	0.888269	0.444135
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.446447	0.182261
$7$	0.253523	0.0958228	0.0479114	−	0.998852i	$-0.484743\pi$
$7$	0.253523	0.0958228	0.0479114	+	0.998852i	$0.484743\pi$
$8$	1.88938	0.667995
$9$	−2.93099	−0.976997
$10$	1.69949	0.537426
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.233343	−0.0673604
$13$	−3.64072	−1.00975	−0.504877	−	0.863191i	$-0.668462\pi$
$13$	−3.64072	−1.00975	−0.504877	+	0.863191i	$0.668462\pi$
$14$	−0.430860	−0.115152
$15$	0.262694	0.0678274
$16$	−4.98752	−1.24688
$17$	3.34510	0.811306	0.405653	−	0.914027i	$-0.367044\pi$
$17$	3.34510	0.811306	0.405653	+	0.914027i	$0.367044\pi$
$18$	4.98119	1.17408
$19$	−5.39157	−1.23691	−0.618455	−	0.785820i	$-0.712241\pi$
$19$	−5.39157	−1.23691	−0.618455	+	0.785820i	$0.712241\pi$
$20$	−0.888269	−0.198623
$21$	−0.0665991	−0.0145331
$22$	−1.69949	−0.362333
$23$	−0.224160	−0.0467405	−0.0233703	−	0.999727i	$-0.507440\pi$
$23$	−0.224160	−0.0467405	−0.0233703	+	0.999727i	$0.507440\pi$
$24$	−0.496329	−0.101313
$25$	1.00000	0.200000
$26$	6.18737	1.21344
$27$	1.55804	0.299845
$28$	0.225197	0.0425582
$29$	8.47296	1.57339	0.786695	−	0.617342i	$-0.211791\pi$
$29$	8.47296	1.57339	0.786695	+	0.617342i	$0.211791\pi$
$30$	−0.446447	−0.0815096
$31$	9.14702	1.64285	0.821427	−	0.570314i	$-0.193179\pi$
$31$	9.14702	1.64285	0.821427	+	0.570314i	$0.193179\pi$
$32$	4.69749	0.830406
$33$	−0.262694	−0.0457292
$34$	−5.68497	−0.974964
$35$	−0.253523	−0.0428532
$36$	−2.60351	−0.433918
$37$	4.30101	0.707081	0.353541	−	0.935419i	$-0.384978\pi$
$37$	4.30101	0.707081	0.353541	+	0.935419i	$0.384978\pi$
$38$	9.16292	1.48642
$39$	0.956397	0.153146
$40$	−1.88938	−0.298737
$41$	3.52724	0.550863	0.275432	−	0.961321i	$-0.411179\pi$
$41$	3.52724	0.550863	0.275432	+	0.961321i	$0.411179\pi$
$42$	0.113185	0.0174648
$43$	1.36543	0.208226	0.104113	−	0.994565i	$-0.466800\pi$
$43$	1.36543	0.208226	0.104113	+	0.994565i	$0.466800\pi$
$44$	0.888269	0.133912
$45$	2.93099	0.436926
$46$	0.380957	0.0561691
$47$	−7.60813	−1.10976	−0.554880	−	0.831931i	$-0.687236\pi$
$47$	−7.60813	−1.10976	−0.554880	+	0.831931i	$0.687236\pi$
$48$	1.31019	0.189110
$49$	−6.93573	−0.990818
$50$	−1.69949	−0.240344
$51$	−0.878739	−0.123048
$52$	−3.23394	−0.448467
$53$	−6.79151	−0.932886	−0.466443	−	0.884551i	$-0.654465\pi$
$53$	−6.79151	−0.932886	−0.466443	+	0.884551i	$0.654465\pi$
$54$	−2.64787	−0.360330
$55$	−1.00000	−0.134840
$56$	0.479001	0.0640092
$57$	1.41633	0.187598
$58$	−14.3997	−1.89078
$59$	−7.00691	−0.912222	−0.456111	−	0.889923i	$-0.650758\pi$
$59$	−7.00691	−0.912222	−0.456111	+	0.889923i	$0.650758\pi$
$60$	0.233343	0.0301245
$61$	−11.8025	−1.51116	−0.755578	−	0.655059i	$-0.772644\pi$
$61$	−11.8025	−1.51116	−0.755578	+	0.655059i	$0.772644\pi$
$62$	−15.5453	−1.97425
$63$	−0.743074	−0.0936186
$64$	1.99170	0.248962
$65$	3.64072	0.451576
$66$	0.446447	0.0549538
$67$	15.0892	1.84344	0.921718	−	0.387860i	$-0.126786\pi$
$67$	15.0892	1.84344	0.921718	+	0.387860i	$0.126786\pi$
$68$	2.97135	0.360329
$69$	0.0588855	0.00708898
$70$	0.430860	0.0514977
$71$	−4.31695	−0.512328	−0.256164	−	0.966633i	$-0.582459\pi$
$71$	−4.31695	−0.512328	−0.256164	+	0.966633i	$0.582459\pi$
$72$	−5.53775	−0.652630
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	−7.30952	−0.849715
$75$	−0.262694	−0.0303333
$76$	−4.78916	−0.549355
$77$	0.253523	0.0288916
$78$	−1.62539	−0.184039
$79$	0.496408	0.0558503	0.0279251	−	0.999610i	$-0.491110\pi$
$79$	0.496408	0.0558503	0.0279251	+	0.999610i	$0.491110\pi$
$80$	4.98752	0.557621
$81$	8.38369	0.931521
$82$	−5.99452	−0.661984
$83$	6.69921	0.735334	0.367667	−	0.929957i	$-0.380157\pi$
$83$	6.69921	0.735334	0.367667	+	0.929957i	$0.380157\pi$
$84$	−0.0591579	−0.00645466
$85$	−3.34510	−0.362827
$86$	−2.32053	−0.250229
$87$	−2.22580	−0.238631
$88$	1.88938	0.201408
$89$	10.6799	1.13207	0.566036	−	0.824381i	$-0.308476\pi$
$89$	10.6799	1.13207	0.566036	+	0.824381i	$0.308476\pi$
$90$	−4.98119	−0.525064
$91$	−0.923007	−0.0967574
$92$	−0.199114	−0.0207591
$93$	−2.40287	−0.249166
$94$	12.9299	1.33362
$95$	5.39157	0.553163
$96$	−1.23400	−0.125945
$97$	−14.2221	−1.44403	−0.722015	−	0.691877i	$-0.756784\pi$
$97$	−14.2221	−1.44403	−0.722015	+	0.691877i	$0.756784\pi$
$98$	11.7872	1.19069
$99$	−2.93099	−0.294576
$100$	0.888269	0.0888269
$101$	10.4989	1.04468	0.522338	−	0.852739i	$-0.325060\pi$
$101$	10.4989	1.04468	0.522338	+	0.852739i	$0.325060\pi$
$102$	1.49341	0.147870
$103$	0.644401	0.0634947	0.0317473	−	0.999496i	$-0.489893\pi$
$103$	0.644401	0.0634947	0.0317473	+	0.999496i	$0.489893\pi$
$104$	−6.87869	−0.674511
$105$	0.0665991	0.00649941
$106$	11.5421	1.12107
$107$	14.5441	1.40603	0.703014	−	0.711176i	$-0.251837\pi$
$107$	14.5441	1.40603	0.703014	+	0.711176i	$0.251837\pi$
$108$	1.38396	0.133171
$109$	−1.86446	−0.178583	−0.0892913	−	0.996006i	$-0.528460\pi$
$109$	−1.86446	−0.178583	−0.0892913	+	0.996006i	$0.528460\pi$
$110$	1.69949	0.162040
$111$	−1.12985	−0.107241
$112$	−1.26445	−0.119479
$113$	−10.6118	−0.998275	−0.499137	−	0.866523i	$-0.666350\pi$
$113$	−10.6118	−0.998275	−0.499137	+	0.866523i	$0.666350\pi$
$114$	−2.40705	−0.225441
$115$	0.224160	0.0209030
$116$	7.52627	0.698797
$117$	10.6709	0.986527
$118$	11.9082	1.09624
$119$	0.848061	0.0777416
$120$	0.496329	0.0453084
$121$	1.00000	0.0909091
$122$	20.0582	1.81599
$123$	−0.926587	−0.0835476
$124$	8.12501	0.729648
$125$	−1.00000	−0.0894427
$126$	1.26285	0.112503
$127$	6.97084	0.618562	0.309281	−	0.950971i	$-0.399912\pi$
$127$	6.97084	0.618562	0.309281	+	0.950971i	$0.399912\pi$
$128$	−12.7798	−1.12959
$129$	−0.358690	−0.0315809
$130$	−6.18737	−0.542668
$131$	−7.91189	−0.691265	−0.345632	−	0.938370i	$-0.612336\pi$
$131$	−7.91189	−0.691265	−0.345632	+	0.938370i	$0.612336\pi$
$132$	−0.233343	−0.0203099
$133$	−1.36689	−0.118524
$134$	−25.6439	−2.21530
$135$	−1.55804	−0.134095
$136$	6.32015	0.541949
$137$	7.95796	0.679895	0.339947	−	0.940444i	$-0.389591\pi$
$137$	7.95796	0.679895	0.339947	+	0.940444i	$0.389591\pi$
$138$	−0.100075	−0.00851898
$139$	−10.1565	−0.861467	−0.430734	−	0.902479i	$-0.641745\pi$
$139$	−10.1565	−0.861467	−0.430734	+	0.902479i	$0.641745\pi$
$140$	−0.225197	−0.0190326
$141$	1.99861	0.168313
$142$	7.33662	0.615675
$143$	−3.64072	−0.304452
$144$	14.6184	1.21820
$145$	−8.47296	−0.703641
$146$	−1.69949	−0.140651
$147$	1.82198	0.150274
$148$	3.82045	0.314039
$149$	23.9329	1.96066	0.980332	−	0.197356i	$-0.0632356\pi$
$149$	23.9329	1.96066	0.980332	+	0.197356i	$0.0632356\pi$
$150$	0.446447	0.0364522
$151$	7.39131	0.601496	0.300748	−	0.953704i	$-0.402764\pi$
$151$	7.39131	0.601496	0.300748	+	0.953704i	$0.402764\pi$
$152$	−10.1867	−0.826251
$153$	−9.80446	−0.792644
$154$	−0.430860	−0.0347197
$155$	−9.14702	−0.734706
$156$	0.849538	0.0680175
$157$	2.96835	0.236900	0.118450	−	0.992960i	$-0.462208\pi$
$157$	2.96835	0.236900	0.118450	+	0.992960i	$0.462208\pi$
$158$	−0.843641	−0.0671165
$159$	1.78409	0.141488
$160$	−4.69749	−0.371369
$161$	−0.0568297	−0.00447881
$162$	−14.2480	−1.11943
$163$	−23.9200	−1.87356	−0.936778	−	0.349925i	$-0.886207\pi$
$163$	−23.9200	−1.87356	−0.936778	+	0.349925i	$0.886207\pi$
$164$	3.13314	0.244657
$165$	0.262694	0.0204507
$166$	−11.3853	−0.883667
$167$	−16.6477	−1.28823	−0.644117	−	0.764927i	$-0.722775\pi$
$167$	−16.6477	−1.28823	−0.644117	+	0.764927i	$0.722775\pi$
$168$	−0.125831	−0.00970806
$169$	0.254849	0.0196038
$170$	5.68497	0.436017
$171$	15.8026	1.20846
$172$	1.21287	0.0924802
$173$	−17.3927	−1.32234	−0.661169	−	0.750237i	$-0.729940\pi$
$173$	−17.3927	−1.32234	−0.661169	+	0.750237i	$0.729940\pi$
$174$	3.78273	0.286768
$175$	0.253523	0.0191646
$176$	−4.98752	−0.375948
$177$	1.84068	0.138354
$178$	−18.1505	−1.36044
$179$	4.40197	0.329018	0.164509	−	0.986376i	$-0.447396\pi$
$179$	4.40197	0.329018	0.164509	+	0.986376i	$0.447396\pi$
$180$	2.60351	0.194054
$181$	2.24072	0.166552	0.0832759	−	0.996527i	$-0.473462\pi$
$181$	2.24072	0.166552	0.0832759	+	0.996527i	$0.473462\pi$
$182$	1.56864	0.116275
$183$	3.10045	0.229192
$184$	−0.423522	−0.0312225
$185$	−4.30101	−0.316216
$186$	4.08366	0.299428
$187$	3.34510	0.244618
$188$	−6.75806	−0.492882
$189$	0.394999	0.0287319
$190$	−9.16292	−0.664748
$191$	2.62314	0.189804	0.0949018	−	0.995487i	$-0.469746\pi$
$191$	2.62314	0.189804	0.0949018	+	0.995487i	$0.469746\pi$
$192$	−0.523208	−0.0377593
$193$	12.1643	0.875605	0.437803	−	0.899071i	$-0.355757\pi$
$193$	12.1643	0.875605	0.437803	+	0.899071i	$0.355757\pi$
$194$	24.1703	1.73532
$195$	−0.956397	−0.0684890
$196$	−6.16079	−0.440057
$197$	−23.0890	−1.64502	−0.822512	−	0.568748i	$-0.807428\pi$
$197$	−23.0890	−1.64502	−0.822512	+	0.568748i	$0.807428\pi$
$198$	4.98119	0.353998
$199$	−5.08792	−0.360673	−0.180337	−	0.983605i	$-0.557719\pi$
$199$	−5.08792	−0.360673	−0.180337	+	0.983605i	$0.557719\pi$
$200$	1.88938	0.133599
$201$	−3.96384	−0.279588
$202$	−17.8427	−1.25541
$203$	2.14809	0.150767
$204$	−0.780557	−0.0546499
$205$	−3.52724	−0.246353
$206$	−1.09515	−0.0763029
$207$	0.657010	0.0456654
$208$	18.1582	1.25904
$209$	−5.39157	−0.372943
$210$	−0.113185	−0.00781048
$211$	20.7644	1.42948	0.714740	−	0.699390i	$-0.246545\pi$
$211$	20.7644	1.42948	0.714740	+	0.699390i	$0.246545\pi$
$212$	−6.03269	−0.414327
$213$	1.13404	0.0777030
$214$	−24.7175	−1.68966
$215$	−1.36543	−0.0931213
$216$	2.94372	0.200295
$217$	2.31898	0.157423
$218$	3.16863	0.214607
$219$	−0.262694	−0.0177512
$220$	−0.888269	−0.0598871
$221$	−12.1786	−0.819220
$222$	1.92017	0.128873
$223$	−7.30757	−0.489351	−0.244676	−	0.969605i	$-0.578681\pi$
$223$	−7.30757	−0.489351	−0.244676	+	0.969605i	$0.578681\pi$
$224$	1.19092	0.0795718
$225$	−2.93099	−0.195399
$226$	18.0347	1.19965
$227$	−17.4047	−1.15519	−0.577595	−	0.816323i	$-0.696009\pi$
$227$	−17.4047	−1.15519	−0.577595	+	0.816323i	$0.696009\pi$
$228$	1.25809	0.0833188
$229$	18.1215	1.19750	0.598751	−	0.800935i	$-0.295664\pi$
$229$	18.1215	1.19750	0.598751	+	0.800935i	$0.295664\pi$
$230$	−0.380957	−0.0251196
$231$	−0.0665991	−0.00438190
$232$	16.0086	1.05102
$233$	−16.5789	−1.08612	−0.543061	−	0.839693i	$-0.682735\pi$
$233$	−16.5789	−1.08612	−0.543061	+	0.839693i	$0.682735\pi$
$234$	−18.1351	−1.18553
$235$	7.60813	0.496299
$236$	−6.22402	−0.405149
$237$	−0.130404	−0.00847062
$238$	−1.44127	−0.0934237
$239$	−6.33571	−0.409823	−0.204912	−	0.978780i	$-0.565691\pi$
$239$	−6.33571	−0.409823	−0.204912	+	0.978780i	$0.565691\pi$
$240$	−1.31019	−0.0845726
$241$	6.08751	0.392131	0.196066	−	0.980591i	$-0.437183\pi$
$241$	6.08751	0.392131	0.196066	+	0.980591i	$0.437183\pi$
$242$	−1.69949	−0.109247
$243$	−6.87646	−0.441125
$244$	−10.4838	−0.671156
$245$	6.93573	0.443107
$246$	1.57473	0.100401
$247$	19.6292	1.24898
$248$	17.2822	1.09742
$249$	−1.75985	−0.111526
$250$	1.69949	0.107485
$251$	−17.9974	−1.13598	−0.567991	−	0.823034i	$-0.692279\pi$
$251$	−17.9974	−1.13598	−0.567991	+	0.823034i	$0.692279\pi$
$252$	−0.660050	−0.0415792
$253$	−0.224160	−0.0140928
$254$	−11.8469	−0.743339
$255$	0.878739	0.0550288
$256$	17.7358	1.10849
$257$	−21.0852	−1.31526	−0.657630	−	0.753341i	$-0.728441\pi$
$257$	−21.0852	−1.31526	−0.657630	+	0.753341i	$0.728441\pi$
$258$	0.609590	0.0379514
$259$	1.09040	0.0677545
$260$	3.23394	0.200560
$261$	−24.8342	−1.53720
$262$	13.4462	0.830708
$263$	−29.2819	−1.80560	−0.902799	−	0.430062i	$-0.858492\pi$
$263$	−29.2819	−1.80560	−0.902799	+	0.430062i	$0.858492\pi$
$264$	−0.496329	−0.0305469
$265$	6.79151	0.417199
$266$	2.32301	0.142433
$267$	−2.80556	−0.171698
$268$	13.4032	0.818734
$269$	2.84681	0.173573	0.0867865	−	0.996227i	$-0.472340\pi$
$269$	2.84681	0.173573	0.0867865	+	0.996227i	$0.472340\pi$
$270$	2.64787	0.161144
$271$	15.9195	0.967040	0.483520	−	0.875333i	$-0.339358\pi$
$271$	15.9195	0.967040	0.483520	+	0.875333i	$0.339358\pi$
$272$	−16.6837	−1.01160
$273$	0.242469	0.0146749
$274$	−13.5245	−0.817044
$275$	1.00000	0.0603023
$276$	0.0523062	0.00314846
$277$	−21.7560	−1.30719	−0.653596	−	0.756843i	$-0.726741\pi$
$277$	−21.7560	−1.30719	−0.653596	+	0.756843i	$0.726741\pi$
$278$	17.2610	1.03524
$279$	−26.8098	−1.60506
$280$	−0.479001	−0.0286258
$281$	4.41629	0.263454	0.131727	−	0.991286i	$-0.457948\pi$
$281$	4.41629	0.263454	0.131727	+	0.991286i	$0.457948\pi$
$282$	−3.39662	−0.202266
$283$	−23.9172	−1.42173	−0.710865	−	0.703328i	$-0.751696\pi$
$283$	−23.9172	−1.42173	−0.710865	+	0.703328i	$0.751696\pi$
$284$	−3.83461	−0.227542
$285$	−1.41633	−0.0838964
$286$	6.18737	0.365867
$287$	0.894238	0.0527852
$288$	−13.7683	−0.811304
$289$	−5.81030	−0.341782
$290$	14.3997	0.845581
$291$	3.73605	0.219011
$292$	0.888269	0.0519820
$293$	−15.2115	−0.888666	−0.444333	−	0.895862i	$-0.646559\pi$
$293$	−15.2115	−0.888666	−0.444333	+	0.895862i	$0.646559\pi$
$294$	−3.09643	−0.180588
$295$	7.00691	0.407958
$296$	8.12622	0.472327
$297$	1.55804	0.0904065
$298$	−40.6738	−2.35617
$299$	0.816103	0.0471965
$300$	−0.233343	−0.0134721
$301$	0.346167	0.0199528
$302$	−12.5615	−0.722831
$303$	−2.75799	−0.158442
$304$	26.8905	1.54228
$305$	11.8025	0.675809
$306$	16.6626	0.952537
$307$	−3.23580	−0.184677	−0.0923383	−	0.995728i	$-0.529434\pi$
$307$	−3.23580	−0.184677	−0.0923383	+	0.995728i	$0.529434\pi$
$308$	0.225197	0.0128318
$309$	−0.169280	−0.00963003
$310$	15.5453	0.882912
$311$	−6.03837	−0.342404	−0.171202	−	0.985236i	$-0.554765\pi$
$311$	−6.03837	−0.342404	−0.171202	+	0.985236i	$0.554765\pi$
$312$	1.80699	0.102301
$313$	−16.3785	−0.925766	−0.462883	−	0.886419i	$-0.653185\pi$
$313$	−16.3785	−0.925766	−0.462883	+	0.886419i	$0.653185\pi$
$314$	−5.04468	−0.284688
$315$	0.743074	0.0418675
$316$	0.440944	0.0248050
$317$	5.38776	0.302607	0.151303	−	0.988487i	$-0.451653\pi$
$317$	5.38776	0.302607	0.151303	+	0.988487i	$0.451653\pi$
$318$	−3.03205	−0.170029
$319$	8.47296	0.474395
$320$	−1.99170	−0.111339
$321$	−3.82065	−0.213248
$322$	0.0965815	0.00538228
$323$	−18.0353	−1.00351
$324$	7.44697	0.413721
$325$	−3.64072	−0.201951
$326$	40.6517	2.25149
$327$	0.489783	0.0270850
$328$	6.66429	0.367974
$329$	−1.92884	−0.106340
$330$	−0.446447	−0.0245761
$331$	−12.2855	−0.675275	−0.337637	−	0.941276i	$-0.609628\pi$
$331$	−12.2855	−0.675275	−0.337637	+	0.941276i	$0.609628\pi$
$332$	5.95070	0.326587
$333$	−12.6062	−0.690816
$334$	28.2925	1.54810
$335$	−15.0892	−0.824410
$336$	0.332164	0.0181210
$337$	13.4226	0.731177	0.365588	−	0.930777i	$-0.380868\pi$
$337$	13.4226	0.731177	0.365588	+	0.930777i	$0.380868\pi$
$338$	−0.433113	−0.0235583
$339$	2.78766	0.151405
$340$	−2.97135	−0.161144
$341$	9.14702	0.495339
$342$	−26.8564	−1.45223
$343$	−3.53303	−0.190766
$344$	2.57980	0.139094
$345$	−0.0588855	−0.00317029
$346$	29.5587	1.58908
$347$	−19.6323	−1.05392	−0.526958	−	0.849891i	$-0.676667\pi$
$347$	−19.6323	−1.05392	−0.526958	+	0.849891i	$0.676667\pi$
$348$	−1.97711	−0.105984
$349$	11.0682	0.592467	0.296233	−	0.955116i	$-0.404269\pi$
$349$	11.0682	0.592467	0.296233	+	0.955116i	$0.404269\pi$
$350$	−0.430860	−0.0230305
$351$	−5.67238	−0.302769
$352$	4.69749	0.250377
$353$	−24.4101	−1.29922	−0.649610	−	0.760267i	$-0.725068\pi$
$353$	−24.4101	−1.29922	−0.649610	+	0.760267i	$0.725068\pi$
$354$	−3.12821	−0.166263
$355$	4.31695	0.229120
$356$	9.48667	0.502792
$357$	−0.222781	−0.0117908
$358$	−7.48110	−0.395389
$359$	−33.2188	−1.75322	−0.876610	−	0.481201i	$-0.840201\pi$
$359$	−33.2188	−1.75322	−0.876610	+	0.481201i	$0.840201\pi$
$360$	5.53775	0.291865
$361$	10.0690	0.529948
$362$	−3.80809	−0.200149
$363$	−0.262694	−0.0137879
$364$	−0.819879	−0.0429733
$365$	−1.00000	−0.0523424
$366$	−5.26919	−0.275425
$367$	34.0716	1.77852	0.889262	−	0.457399i	$-0.151219\pi$
$367$	34.0716	1.77852	0.889262	+	0.457399i	$0.151219\pi$
$368$	1.11800	0.0582798
$369$	−10.3383	−0.538192
$370$	7.30952	0.380004
$371$	−1.72181	−0.0893917
$372$	−2.13440	−0.110663
$373$	18.2653	0.945742	0.472871	−	0.881132i	$-0.343218\pi$
$373$	18.2653	0.945742	0.472871	+	0.881132i	$0.343218\pi$
$374$	−5.68497	−0.293963
$375$	0.262694	0.0135655
$376$	−14.3746	−0.741314
$377$	−30.8477	−1.58874
$378$	−0.671297	−0.0345278
$379$	17.9581	0.922446	0.461223	−	0.887284i	$-0.347411\pi$
$379$	17.9581	0.922446	0.461223	+	0.887284i	$0.347411\pi$
$380$	4.78916	0.245679
$381$	−1.83120	−0.0938152
$382$	−4.45800	−0.228091
$383$	−38.3869	−1.96148	−0.980738	−	0.195327i	$-0.937423\pi$
$383$	−38.3869	−1.96148	−0.980738	+	0.195327i	$0.937423\pi$
$384$	3.35719	0.171321
$385$	−0.253523	−0.0129207
$386$	−20.6731	−1.05223
$387$	−4.00205	−0.203436
$388$	−12.6330	−0.641344
$389$	4.41477	0.223838	0.111919	−	0.993717i	$-0.464300\pi$
$389$	4.41477	0.223838	0.111919	+	0.993717i	$0.464300\pi$
$390$	1.62539	0.0823047
$391$	−0.749837	−0.0379209
$392$	−13.1042	−0.661862
$393$	2.07841	0.104842
$394$	39.2396	1.97686
$395$	−0.496408	−0.0249770
$396$	−2.60351	−0.130831
$397$	24.1525	1.21218	0.606089	−	0.795397i	$-0.292738\pi$
$397$	24.1525	1.21218	0.606089	+	0.795397i	$0.292738\pi$
$398$	8.64688	0.433429
$399$	0.359074	0.0179762
$400$	−4.98752	−0.249376
$401$	18.1872	0.908226	0.454113	−	0.890944i	$-0.349956\pi$
$401$	18.1872	0.908226	0.454113	+	0.890944i	$0.349956\pi$
$402$	6.73651	0.335987
$403$	−33.3017	−1.65888
$404$	9.32581	0.463976
$405$	−8.38369	−0.416589
$406$	−3.65066	−0.181179
$407$	4.30101	0.213193
$408$	−1.66027	−0.0821956
$409$	−26.8691	−1.32859	−0.664295	−	0.747471i	$-0.731268\pi$
$409$	−26.8691	−1.32859	−0.664295	+	0.747471i	$0.731268\pi$
$410$	5.99452	0.296048
$411$	−2.09051	−0.103117
$412$	0.572401	0.0282002
$413$	−1.77641	−0.0874116
$414$	−1.11658	−0.0548771
$415$	−6.69921	−0.328851
$416$	−17.1022	−0.838506
$417$	2.66807	0.130656
$418$	9.16292	0.448173
$419$	2.31976	0.113328	0.0566639	−	0.998393i	$-0.481954\pi$
$419$	2.31976	0.113328	0.0566639	+	0.998393i	$0.481954\pi$
$420$	0.0591579	0.00288661
$421$	0.303017	0.0147681	0.00738407	−	0.999973i	$-0.497650\pi$
$421$	0.303017	0.0147681	0.00738407	+	0.999973i	$0.497650\pi$
$422$	−35.2889	−1.71784
$423$	22.2994	1.08423
$424$	−12.8317	−0.623164
$425$	3.34510	0.162261
$426$	−1.92729	−0.0933774
$427$	−2.99221	−0.144803
$428$	12.9191	0.624466
$429$	0.956397	0.0461753
$430$	2.32053	0.111906
$431$	−26.4489	−1.27400	−0.637000	−	0.770864i	$-0.719825\pi$
$431$	−26.4489	−1.27400	−0.637000	+	0.770864i	$0.719825\pi$
$432$	−7.77074	−0.373870
$433$	17.9278	0.861556	0.430778	−	0.902458i	$-0.358239\pi$
$433$	17.9278	0.861556	0.430778	+	0.902458i	$0.358239\pi$
$434$	−3.94109	−0.189178
$435$	2.22580	0.106719
$436$	−1.65614	−0.0793147
$437$	1.20857	0.0578139
$438$	0.446447	0.0213320
$439$	−32.1568	−1.53476	−0.767379	−	0.641193i	$-0.778440\pi$
$439$	−32.1568	−1.53476	−0.767379	+	0.641193i	$0.778440\pi$
$440$	−1.88938	−0.0900725
$441$	20.3286	0.968026
$442$	20.6974	0.984474
$443$	22.9839	1.09200	0.546000	−	0.837785i	$-0.316150\pi$
$443$	22.9839	1.09200	0.546000	+	0.837785i	$0.316150\pi$
$444$	−1.00361	−0.0476293
$445$	−10.6799	−0.506278
$446$	12.4192	0.588064
$447$	−6.28705	−0.297367
$448$	0.504942	0.0238563
$449$	−0.744929	−0.0351554	−0.0175777	−	0.999846i	$-0.505595\pi$
$449$	−0.744929	−0.0351554	−0.0175777	+	0.999846i	$0.505595\pi$
$450$	4.98119	0.234816
$451$	3.52724	0.166091
$452$	−9.42614	−0.443368
$453$	−1.94166	−0.0912269
$454$	29.5791	1.38822
$455$	0.923007	0.0432712
$456$	2.67599	0.125315
$457$	−25.4157	−1.18890	−0.594448	−	0.804134i	$-0.702629\pi$
$457$	−25.4157	−1.18890	−0.594448	+	0.804134i	$0.702629\pi$
$458$	−30.7973	−1.43906
$459$	5.21180	0.243266
$460$	0.199114	0.00928374
$461$	−2.88744	−0.134482	−0.0672408	−	0.997737i	$-0.521420\pi$
$461$	−2.88744	−0.134482	−0.0672408	+	0.997737i	$0.521420\pi$
$462$	0.113185	0.00526582
$463$	−25.8098	−1.19948	−0.599742	−	0.800193i	$-0.704730\pi$
$463$	−25.8098	−1.19948	−0.599742	+	0.800193i	$0.704730\pi$
$464$	−42.2590	−1.96183
$465$	2.40287	0.111430
$466$	28.1757	1.30522
$467$	−37.0419	−1.71409	−0.857047	−	0.515239i	$-0.827703\pi$
$467$	−37.0419	−1.71409	−0.857047	+	0.515239i	$0.827703\pi$
$468$	9.47865	0.438151
$469$	3.82546	0.176643
$470$	−12.9299	−0.596414
$471$	−0.779768	−0.0359298
$472$	−13.2387	−0.609360
$473$	1.36543	0.0627824
$474$	0.221620	0.0101793
$475$	−5.39157	−0.247382
$476$	0.753306	0.0345277
$477$	19.9059	0.911427
$478$	10.7675	0.492493
$479$	−1.01877	−0.0465488	−0.0232744	−	0.999729i	$-0.507409\pi$
$479$	−1.01877	−0.0465488	−0.0232744	+	0.999729i	$0.507409\pi$
$480$	1.23400	0.0563243
$481$	−15.6588	−0.713978
$482$	−10.3457	−0.471232
$483$	0.0149288	0.000679286 0
$484$	0.888269	0.0403759
$485$	14.2221	0.645790
$486$	11.6865	0.530110
$487$	15.8883	0.719966	0.359983	−	0.932959i	$-0.382783\pi$
$487$	15.8883	0.719966	0.359983	+	0.932959i	$0.382783\pi$
$488$	−22.2994	−1.00945
$489$	6.28364	0.284156
$490$	−11.7872	−0.532492
$491$	0.0252588	0.00113991	0.000569957	−	1.00000i	$-0.499819\pi$
$491$	0.0252588	0.00113991	0.000569957		1.00000i	$0.499819\pi$
$492$	−0.823059	−0.0371064
$493$	28.3429	1.27650
$494$	−33.3596	−1.50092
$495$	2.93099	0.131738
$496$	−45.6209	−2.04844
$497$	−1.09445	−0.0490927
$498$	2.99084	0.134023
$499$	41.6840	1.86603	0.933015	−	0.359837i	$-0.117168\pi$
$499$	41.6840	1.86603	0.933015	+	0.359837i	$0.117168\pi$
$500$	−0.888269	−0.0397246
$501$	4.37325	0.195382
$502$	30.5863	1.36513
$503$	−18.1581	−0.809631	−0.404816	−	0.914398i	$-0.632664\pi$
$503$	−18.1581	−0.809631	−0.404816	+	0.914398i	$0.632664\pi$
$504$	−1.40395	−0.0625368
$505$	−10.4989	−0.467193
$506$	0.380957	0.0169356
$507$	−0.0669474	−0.00297324
$508$	6.19198	0.274725
$509$	−22.2855	−0.987788	−0.493894	−	0.869522i	$-0.664427\pi$
$509$	−22.2855	−0.987788	−0.493894	+	0.869522i	$0.664427\pi$
$510$	−1.49341	−0.0661293
$511$	0.253523	0.0112152
$512$	−4.58219	−0.202506
$513$	−8.40027	−0.370881
$514$	35.8342	1.58058
$515$	−0.644401	−0.0283957
$516$	−0.318613	−0.0140262
$517$	−7.60813	−0.334605
$518$	−1.85313	−0.0814220
$519$	4.56895	0.200555
$520$	6.87869	0.301651
$521$	41.3449	1.81135	0.905676	−	0.423970i	$-0.139364\pi$
$521$	41.3449	1.81135	0.905676	+	0.423970i	$0.139364\pi$
$522$	42.2055	1.84728
$523$	38.1582	1.66854	0.834270	−	0.551356i	$-0.185889\pi$
$523$	38.1582	1.66854	0.834270	+	0.551356i	$0.185889\pi$
$524$	−7.02789	−0.307015
$525$	−0.0665991	−0.00290662
$526$	49.7643	2.16983
$527$	30.5977	1.33286
$528$	1.31019	0.0570188
$529$	−22.9498	−0.997815
$530$	−11.5421	−0.501357
$531$	20.5372	0.891239
$532$	−1.21416	−0.0526407
$533$	−12.8417	−0.556236
$534$	4.76803	0.206333
$535$	−14.5441	−0.628795
$536$	28.5091	1.23141
$537$	−1.15637	−0.0499011
$538$	−4.83812	−0.208586
$539$	−6.93573	−0.298743
$540$	−1.38396	−0.0595560
$541$	−37.9637	−1.63219	−0.816094	−	0.577919i	$-0.803865\pi$
$541$	−37.9637	−1.63219	−0.816094	+	0.577919i	$0.803865\pi$
$542$	−27.0550	−1.16211
$543$	−0.588626	−0.0252604
$544$	15.7136	0.673713
$545$	1.86446	0.0798646
$546$	−0.412073	−0.0176351
$547$	−22.9958	−0.983230	−0.491615	−	0.870813i	$-0.663593\pi$
$547$	−22.9958	−0.983230	−0.491615	+	0.870813i	$0.663593\pi$
$548$	7.06881	0.301965
$549$	34.5930	1.47639
$550$	−1.69949	−0.0724665
$551$	−45.6825	−1.94614
$552$	0.111257	0.00473541
$553$	0.125851	0.00535172
$554$	36.9742	1.57088
$555$	1.12985	0.0479595
$556$	−9.02175	−0.382607
$557$	24.4901	1.03768	0.518839	−	0.854872i	$-0.326364\pi$
$557$	24.4901	1.03768	0.518839	+	0.854872i	$0.326364\pi$
$558$	45.5631	1.92884
$559$	−4.97114	−0.210257
$560$	1.26445	0.0534328
$561$	−0.878739	−0.0371004
$562$	−7.50544	−0.316598
$563$	9.35642	0.394326	0.197163	−	0.980371i	$-0.436827\pi$
$563$	9.35642	0.394326	0.197163	+	0.980371i	$0.436827\pi$
$564$	1.77531	0.0747538
$565$	10.6118	0.446442
$566$	40.6471	1.70852
$567$	2.12546	0.0892609
$568$	−8.15634	−0.342233
$569$	41.9493	1.75860	0.879302	−	0.476264i	$-0.158009\pi$
$569$	41.9493	1.75860	0.879302	+	0.476264i	$0.158009\pi$
$570$	2.40705	0.100820
$571$	17.4472	0.730143	0.365071	−	0.930980i	$-0.381045\pi$
$571$	17.4472	0.730143	0.365071	+	0.930980i	$0.381045\pi$
$572$	−3.23394	−0.135218
$573$	−0.689084	−0.0287869
$574$	−1.51975	−0.0634331
$575$	−0.224160	−0.00934811
$576$	−5.83765	−0.243236
$577$	−6.97833	−0.290512	−0.145256	−	0.989394i	$-0.546401\pi$
$577$	−6.97833	−0.290512	−0.145256	+	0.989394i	$0.546401\pi$
$578$	9.87455	0.410727
$579$	−3.19549	−0.132800
$580$	−7.52627	−0.312511
$581$	1.69841	0.0704617
$582$	−6.34939	−0.263191
$583$	−6.79151	−0.281276
$584$	1.88938	0.0781830
$585$	−10.6709	−0.441188
$586$	25.8518	1.06793
$587$	−21.6303	−0.892779	−0.446390	−	0.894839i	$-0.647290\pi$
$587$	−21.6303	−0.892779	−0.446390	+	0.894839i	$0.647290\pi$
$588$	1.61841	0.0667419
$589$	−49.3168	−2.03206
$590$	−11.9082	−0.490252
$591$	6.06535	0.249495
$592$	−21.4513	−0.881645
$593$	−17.1121	−0.702709	−0.351355	−	0.936242i	$-0.614279\pi$
$593$	−17.1121	−0.702709	−0.351355	+	0.936242i	$0.614279\pi$
$594$	−2.64787	−0.108643
$595$	−0.848061	−0.0347671
$596$	21.2589	0.870799
$597$	1.33657	0.0547021
$598$	−1.38696	−0.0567170
$599$	−25.9462	−1.06013	−0.530067	−	0.847956i	$-0.677833\pi$
$599$	−25.9462	−1.06013	−0.530067	+	0.847956i	$0.677833\pi$
$600$	−0.496329	−0.0202625
$601$	−42.9610	−1.75241	−0.876207	−	0.481934i	$-0.839934\pi$
$601$	−42.9610	−1.75241	−0.876207	+	0.481934i	$0.839934\pi$
$602$	−0.588308	−0.0239776
$603$	−44.2262	−1.80103
$604$	6.56547	0.267145
$605$	−1.00000	−0.0406558
$606$	4.68718	0.190404
$607$	−0.323687	−0.0131380	−0.00656902	−	0.999978i	$-0.502091\pi$
$607$	−0.323687	−0.0131380	−0.00656902	+	0.999978i	$0.502091\pi$
$608$	−25.3268	−1.02714
$609$	−0.564292	−0.0228663
$610$	−20.0582	−0.812135
$611$	27.6991	1.12058
$612$	−8.70900	−0.352041
$613$	−20.1640	−0.814415	−0.407208	−	0.913336i	$-0.633497\pi$
$613$	−20.1640	−0.814415	−0.407208	+	0.913336i	$0.633497\pi$
$614$	5.49921	0.221930
$615$	0.926587	0.0373636
$616$	0.479001	0.0192995
$617$	44.2883	1.78298	0.891490	−	0.453041i	$-0.149661\pi$
$617$	44.2883	1.78298	0.891490	+	0.453041i	$0.149661\pi$
$618$	0.287691	0.0115726
$619$	−18.1346	−0.728890	−0.364445	−	0.931225i	$-0.618741\pi$
$619$	−18.1346	−0.728890	−0.364445	+	0.931225i	$0.618741\pi$
$620$	−8.12501	−0.326308
$621$	−0.349249	−0.0140149
$622$	10.2621	0.411475
$623$	2.70761	0.108478
$624$	−4.77005	−0.190955
$625$	1.00000	0.0400000
$626$	27.8351	1.11251
$627$	1.41633	0.0565630
$628$	2.63669	0.105215
$629$	14.3873	0.573659
$630$	−1.26285	−0.0503131
$631$	12.9446	0.515316	0.257658	−	0.966236i	$-0.417049\pi$
$631$	12.9446	0.515316	0.257658	+	0.966236i	$0.417049\pi$
$632$	0.937901	0.0373077
$633$	−5.45469	−0.216804
$634$	−9.15645	−0.363649
$635$	−6.97084	−0.276629
$636$	1.58475	0.0628396
$637$	25.2510	1.00048
$638$	−14.3997	−0.570090
$639$	12.6529	0.500543
$640$	12.7798	0.505168
$641$	−41.1366	−1.62480	−0.812399	−	0.583101i	$-0.801839\pi$
$641$	−41.1366	−1.62480	−0.812399	+	0.583101i	$0.801839\pi$
$642$	6.49316	0.256264
$643$	−16.8226	−0.663417	−0.331708	−	0.943382i	$-0.607625\pi$
$643$	−16.8226	−0.663417	−0.331708	+	0.943382i	$0.607625\pi$
$644$	−0.0504800	−0.00198919
$645$	0.358690	0.0141234
$646$	30.6509	1.20594
$647$	5.91410	0.232507	0.116254	−	0.993220i	$-0.462911\pi$
$647$	5.91410	0.232507	0.116254	+	0.993220i	$0.462911\pi$
$648$	15.8399	0.622252
$649$	−7.00691	−0.275045
$650$	6.18737	0.242689
$651$	−0.609183	−0.0238758
$652$	−21.2474	−0.832111
$653$	−18.1836	−0.711581	−0.355790	−	0.934566i	$-0.615788\pi$
$653$	−18.1836	−0.711581	−0.355790	+	0.934566i	$0.615788\pi$
$654$	−0.832381	−0.0325487
$655$	7.91189	0.309143
$656$	−17.5922	−0.686860
$657$	−2.93099	−0.114349
$658$	3.27804	0.127791
$659$	12.7305	0.495909	0.247955	−	0.968772i	$-0.420242\pi$
$659$	12.7305	0.495909	0.247955	+	0.968772i	$0.420242\pi$
$660$	0.233343	0.00908288
$661$	−16.4406	−0.639466	−0.319733	−	0.947508i	$-0.603593\pi$
$661$	−16.4406	−0.639466	−0.319733	+	0.947508i	$0.603593\pi$
$662$	20.8792	0.811492
$663$	3.19924	0.124248
$664$	12.6573	0.491200
$665$	1.36689	0.0530056
$666$	21.4241	0.830169
$667$	−1.89930	−0.0735411
$668$	−14.7876	−0.572149
$669$	1.91966	0.0742183
$670$	25.6439	0.990711
$671$	−11.8025	−0.455631
$672$	−0.312848	−0.0120684
$673$	−25.0757	−0.966598	−0.483299	−	0.875455i	$-0.660562\pi$
$673$	−25.0757	−0.966598	−0.483299	+	0.875455i	$0.660562\pi$
$674$	−22.8116	−0.878671
$675$	1.55804	0.0599689
$676$	0.226374	0.00870671
$677$	−0.752095	−0.0289054	−0.0144527	−	0.999896i	$-0.504601\pi$
$677$	−0.752095	−0.0289054	−0.0144527	+	0.999896i	$0.504601\pi$
$678$	−4.73761	−0.181947
$679$	−3.60562	−0.138371
$680$	−6.32015	−0.242367
$681$	4.57212	0.175204
$682$	−15.5453	−0.595259
$683$	48.5093	1.85616	0.928079	−	0.372383i	$-0.121459\pi$
$683$	48.5093	1.85616	0.928079	+	0.372383i	$0.121459\pi$
$684$	14.0370	0.536718
$685$	−7.95796	−0.304058
$686$	6.00435	0.229247
$687$	−4.76042	−0.181621
$688$	−6.81009	−0.259632
$689$	24.7260	0.941986
$690$	0.100075	0.00380980
$691$	20.8362	0.792645	0.396323	−	0.918111i	$-0.370286\pi$
$691$	20.8362	0.792645	0.396323	+	0.918111i	$0.370286\pi$
$692$	−15.4494	−0.587296
$693$	−0.743074	−0.0282271
$694$	33.3649	1.26651
$695$	10.1565	0.385260
$696$	−4.20537	−0.159404
$697$	11.7990	0.446919
$698$	−18.8103	−0.711980
$699$	4.35519	0.164729
$700$	0.225197	0.00851164
$701$	−49.8553	−1.88301	−0.941504	−	0.337003i	$-0.890587\pi$
$701$	−49.8553	−1.88301	−0.941504	+	0.337003i	$0.890587\pi$
$702$	9.64016	0.363844
$703$	−23.1892	−0.874596
$704$	1.99170	0.0750650
$705$	−1.99861	−0.0752721
$706$	41.4848	1.56130
$707$	2.66170	0.100104
$708$	1.63502	0.0614477
$709$	−14.8937	−0.559345	−0.279672	−	0.960095i	$-0.590226\pi$
$709$	−14.8937	−0.559345	−0.279672	+	0.960095i	$0.590226\pi$
$710$	−7.33662	−0.275338
$711$	−1.45497	−0.0545655
$712$	20.1784	0.756219
$713$	−2.05039	−0.0767878
$714$	0.378614	0.0141693
$715$	3.64072	0.136155
$716$	3.91013	0.146128
$717$	1.66436	0.0621565
$718$	56.4550	2.10688
$719$	−53.2904	−1.98740	−0.993698	−	0.112088i	$-0.964246\pi$
$719$	−53.2904	−1.98740	−0.993698	+	0.112088i	$0.964246\pi$
$720$	−14.6184	−0.544794
$721$	0.163370	0.00608423
$722$	−17.1122	−0.636849
$723$	−1.59915	−0.0594732
$724$	1.99037	0.0739714
$725$	8.47296	0.314678
$726$	0.446447	0.0165692
$727$	12.8929	0.478169	0.239085	−	0.970999i	$-0.423153\pi$
$727$	12.8929	0.478169	0.239085	+	0.970999i	$0.423153\pi$
$728$	−1.74391	−0.0646335
$729$	−23.3447	−0.864617
$730$	1.69949	0.0629010
$731$	4.56749	0.168935
$732$	2.75404	0.101792
$733$	24.8552	0.918050	0.459025	−	0.888423i	$-0.348199\pi$
$733$	24.8552	0.918050	0.459025	+	0.888423i	$0.348199\pi$
$734$	−57.9044	−2.13729
$735$	−1.82198	−0.0672046
$736$	−1.05299	−0.0388136
$737$	15.0892	0.555817
$738$	17.5699	0.646757
$739$	−41.1289	−1.51295	−0.756475	−	0.654022i	$-0.773080\pi$
$739$	−41.1289	−1.51295	−0.756475	+	0.654022i	$0.773080\pi$
$740$	−3.82045	−0.140443
$741$	−5.15648	−0.189428
$742$	2.92619	0.107424
$743$	−30.5589	−1.12110	−0.560549	−	0.828121i	$-0.689410\pi$
$743$	−30.5589	−1.12110	−0.560549	+	0.828121i	$0.689410\pi$
$744$	−4.53993	−0.166442
$745$	−23.9329	−0.876835
$746$	−31.0417	−1.13652
$747$	−19.6353	−0.718420
$748$	2.97135	0.108643
$749$	3.68726	0.134730
$750$	−0.446447	−0.0163019
$751$	35.0675	1.27963	0.639816	−	0.768528i	$-0.279010\pi$
$751$	35.0675	1.27963	0.639816	+	0.768528i	$0.279010\pi$
$752$	37.9457	1.38374
$753$	4.72780	0.172291
$754$	52.4254	1.90922
$755$	−7.39131	−0.268997
$756$	0.350865	0.0127608
$757$	−26.9422	−0.979230	−0.489615	−	0.871939i	$-0.662863\pi$
$757$	−26.9422	−0.979230	−0.489615	+	0.871939i	$0.662863\pi$
$758$	−30.5197	−1.10852
$759$	0.0588855	0.00213741
$760$	10.1867	0.369510
$761$	−42.8362	−1.55281	−0.776405	−	0.630234i	$-0.782959\pi$
$761$	−42.8362	−1.55281	−0.776405	+	0.630234i	$0.782959\pi$
$762$	3.11211	0.112740
$763$	−0.472683	−0.0171123
$764$	2.33005	0.0842984
$765$	9.80446	0.354481
$766$	65.2381	2.35715
$767$	25.5102	0.921120
$768$	−4.65910	−0.168121
$769$	12.5049	0.450938	0.225469	−	0.974250i	$-0.427609\pi$
$769$	12.5049	0.450938	0.225469	+	0.974250i	$0.427609\pi$
$770$	0.430860	0.0155271
$771$	5.53897	0.199481
$772$	10.8052	0.388887
$773$	27.6792	0.995551	0.497776	−	0.867306i	$-0.334150\pi$
$773$	27.6792	0.995551	0.497776	+	0.867306i	$0.334150\pi$
$774$	6.80145	0.244473
$775$	9.14702	0.328571
$776$	−26.8708	−0.964606
$777$	−0.286443	−0.0102761
$778$	−7.50286	−0.268990
$779$	−19.0174	−0.681368
$780$	−0.849538	−0.0304183
$781$	−4.31695	−0.154473
$782$	1.27434	0.0455703
$783$	13.2012	0.471772
$784$	34.5920	1.23543
$785$	−2.96835	−0.105945
$786$	−3.53224	−0.125991
$787$	27.7302	0.988475	0.494237	−	0.869327i	$-0.335447\pi$
$787$	27.7302	0.988475	0.494237	+	0.869327i	$0.335447\pi$
$788$	−20.5093	−0.730612
$789$	7.69219	0.273849
$790$	0.843641	0.0300154
$791$	−2.69034	−0.0956575
$792$	−5.53775	−0.196775
$793$	42.9696	1.52590
$794$	−41.0469	−1.45670
$795$	−1.78409	−0.0632752
$796$	−4.51944	−0.160187
$797$	28.2990	1.00240	0.501201	−	0.865331i	$-0.332892\pi$
$797$	28.2990	1.00240	0.501201	+	0.865331i	$0.332892\pi$
$798$	−0.610242	−0.0216023
$799$	−25.4500	−0.900355
$800$	4.69749	0.166081
$801$	−31.3028	−1.10603
$802$	−30.9090	−1.09143
$803$	1.00000	0.0352892
$804$	−3.52096	−0.124175
$805$	0.0568297	0.00200298
$806$	56.5960	1.99351
$807$	−0.747841	−0.0263252
$808$	19.8363	0.697838
$809$	−9.83411	−0.345749	−0.172875	−	0.984944i	$-0.555306\pi$
$809$	−9.83411	−0.345749	−0.172875	+	0.984944i	$0.555306\pi$
$810$	14.2480	0.500624
$811$	44.5948	1.56594	0.782968	−	0.622061i	$-0.213705\pi$
$811$	44.5948	1.56594	0.782968	+	0.622061i	$0.213705\pi$
$812$	1.90808	0.0669606
$813$	−4.18196	−0.146668
$814$	−7.30952	−0.256199
$815$	23.9200	0.837880
$816$	4.38273	0.153426
$817$	−7.36179	−0.257556
$818$	45.6637	1.59659
$819$	2.70533	0.0945317
$820$	−3.13314	−0.109414
$821$	−6.11207	−0.213313	−0.106656	−	0.994296i	$-0.534014\pi$
$821$	−6.11207	−0.213313	−0.106656	+	0.994296i	$0.534014\pi$
$822$	3.55281	0.123918
$823$	37.1845	1.29617	0.648086	−	0.761567i	$-0.275570\pi$
$823$	37.1845	1.29617	0.648086	+	0.761567i	$0.275570\pi$
$824$	1.21752	0.0424142
$825$	−0.262694	−0.00914584
$826$	3.01900	0.105044
$827$	0.642666	0.0223477	0.0111739	−	0.999938i	$-0.496443\pi$
$827$	0.642666	0.0223477	0.0111739	+	0.999938i	$0.496443\pi$
$828$	0.583602	0.0202816
$829$	33.0024	1.14622	0.573111	−	0.819478i	$-0.305737\pi$
$829$	33.0024	1.14622	0.573111	+	0.819478i	$0.305737\pi$
$830$	11.3853	0.395188
$831$	5.71518	0.198258
$832$	−7.25122	−0.251391
$833$	−23.2007	−0.803857
$834$	−4.53436	−0.157012
$835$	16.6477	0.576116
$836$	−4.78916	−0.165637
$837$	14.2514	0.492601
$838$	−3.94242	−0.136189
$839$	18.3245	0.632632	0.316316	−	0.948654i	$-0.397554\pi$
$839$	18.3245	0.632632	0.316316	+	0.948654i	$0.397554\pi$
$840$	0.125831	0.00434157
$841$	42.7911	1.47555
$842$	−0.514974	−0.0177472
$843$	−1.16013	−0.0399571
$844$	18.4444	0.634882
$845$	−0.254849	−0.00876707
$846$	−37.8975	−1.30294
$847$	0.253523	0.00871116
$848$	33.8728	1.16320
$849$	6.28291	0.215629
$850$	−5.68497	−0.194993
$851$	−0.964112	−0.0330493
$852$	1.00733	0.0345106
$853$	−2.72352	−0.0932514	−0.0466257	−	0.998912i	$-0.514847\pi$
$853$	−2.72352	−0.0932514	−0.0466257	+	0.998912i	$0.514847\pi$
$854$	5.08523	0.174013
$855$	−15.8026	−0.540439
$856$	27.4792	0.939221
$857$	−29.4914	−1.00741	−0.503703	−	0.863877i	$-0.668030\pi$
$857$	−29.4914	−1.00741	−0.503703	+	0.863877i	$0.668030\pi$
$858$	−1.62539	−0.0554898
$859$	1.03619	0.0353543	0.0176772	−	0.999844i	$-0.494373\pi$
$859$	1.03619	0.0353543	0.0176772	+	0.999844i	$0.494373\pi$
$860$	−1.21287	−0.0413584
$861$	−0.234911	−0.00800576
$862$	44.9497	1.53099
$863$	−9.40313	−0.320086	−0.160043	−	0.987110i	$-0.551163\pi$
$863$	−9.40313	−0.320086	−0.160043	+	0.987110i	$0.551163\pi$
$864$	7.31886	0.248993
$865$	17.3927	0.591368
$866$	−30.4681	−1.03535
$867$	1.52633	0.0518370
$868$	2.05988	0.0699169
$869$	0.496408	0.0168395
$870$	−3.78273	−0.128246
$871$	−54.9355	−1.86142
$872$	−3.52266	−0.119292
$873$	41.6847	1.41081
$874$	−2.05396	−0.0694761
$875$	−0.253523	−0.00857065
$876$	−0.233343	−0.00788394
$877$	−46.8882	−1.58330	−0.791650	−	0.610974i	$-0.790778\pi$
$877$	−46.8882	−1.58330	−0.791650	+	0.610974i	$0.790778\pi$
$878$	54.6501	1.84435
$879$	3.99598	0.134781
$880$	4.98752	0.168129
$881$	44.3487	1.49415	0.747073	−	0.664742i	$-0.231458\pi$
$881$	44.3487	1.49415	0.747073	+	0.664742i	$0.231458\pi$
$882$	−34.5482	−1.16330
$883$	14.1928	0.477624	0.238812	−	0.971066i	$-0.423242\pi$
$883$	14.1928	0.477624	0.238812	+	0.971066i	$0.423242\pi$
$884$	−10.8179	−0.363844
$885$	−1.84068	−0.0618737
$886$	−39.0610	−1.31228
$887$	10.8271	0.363537	0.181768	−	0.983341i	$-0.441818\pi$
$887$	10.8271	0.363537	0.181768	+	0.983341i	$0.441818\pi$
$888$	−2.13471	−0.0716363
$889$	1.76727	0.0592723
$890$	18.1505	0.608405
$891$	8.38369	0.280864
$892$	−6.49109	−0.217338
$893$	41.0197	1.37267
$894$	10.6848	0.357353
$895$	−4.40197	−0.147142
$896$	−3.23999	−0.108240
$897$	−0.214386	−0.00715813
$898$	1.26600	0.0422470
$899$	77.5023	2.58485
$900$	−2.60351	−0.0867836
$901$	−22.7183	−0.756856
$902$	−5.99452	−0.199596
$903$	−0.0909362	−0.00302617
$904$	−20.0497	−0.666843
$905$	−2.24072	−0.0744842
$906$	3.29983	0.109629
$907$	−24.0885	−0.799846	−0.399923	−	0.916549i	$-0.630963\pi$
$907$	−24.0885	−0.799846	−0.399923	+	0.916549i	$0.630963\pi$
$908$	−15.4601	−0.513060
$909$	−30.7721	−1.02064
$910$	−1.56864	−0.0520000
$911$	37.4609	1.24114	0.620568	−	0.784152i	$-0.286902\pi$
$911$	37.4609	1.24114	0.620568	+	0.784152i	$0.286902\pi$
$912$	−7.06399	−0.233912
$913$	6.69921	0.221712
$914$	43.1937	1.42872
$915$	−3.10045	−0.102498
$916$	16.0968	0.531852
$917$	−2.00585	−0.0662389
$918$	−8.85740	−0.292338
$919$	14.9563	0.493363	0.246682	−	0.969097i	$-0.420660\pi$
$919$	14.9563	0.493363	0.246682	+	0.969097i	$0.420660\pi$
$920$	0.423522	0.0139631
$921$	0.850025	0.0280093
$922$	4.90718	0.161609
$923$	15.7168	0.517325
$924$	−0.0591579	−0.00194615
$925$	4.30101	0.141416
$926$	43.8636	1.44145
$927$	−1.88873	−0.0620341
$928$	39.8016	1.30655
$929$	−17.1452	−0.562517	−0.281258	−	0.959632i	$-0.590752\pi$
$929$	−17.1452	−0.562517	−0.281258	+	0.959632i	$0.590752\pi$
$930$	−4.08366	−0.133908
$931$	37.3944	1.22555
$932$	−14.7266	−0.482384
$933$	1.58624	0.0519313
$934$	62.9523	2.05986
$935$	−3.34510	−0.109397
$936$	20.1614	0.658996
$937$	−12.9470	−0.422961	−0.211481	−	0.977382i	$-0.567829\pi$
$937$	−12.9470	−0.422961	−0.211481	+	0.977382i	$0.567829\pi$
$938$	−6.50133	−0.212276
$939$	4.30253	0.140408
$940$	6.75806	0.220424
$941$	37.7476	1.23054	0.615268	−	0.788318i	$-0.289048\pi$
$941$	37.7476	1.23054	0.615268	+	0.788318i	$0.289048\pi$
$942$	1.32521	0.0431776
$943$	−0.790666	−0.0257476
$944$	34.9471	1.13743
$945$	−0.394999	−0.0128493
$946$	−2.32053	−0.0754469
$947$	−48.2070	−1.56652	−0.783259	−	0.621696i	$-0.786444\pi$
$947$	−48.2070	−1.56652	−0.783259	+	0.621696i	$0.786444\pi$
$948$	−0.115833	−0.00376210
$949$	−3.64072	−0.118183
$950$	9.16292	0.297284
$951$	−1.41533	−0.0458954
$952$	1.60231	0.0519310
$953$	14.8350	0.480552	0.240276	−	0.970705i	$-0.422762\pi$
$953$	14.8350	0.480552	0.240276	+	0.970705i	$0.422762\pi$
$954$	−33.8298	−1.09528
$955$	−2.62314	−0.0848828
$956$	−5.62782	−0.182017
$957$	−2.22580	−0.0719499
$958$	1.73139	0.0559388
$959$	2.01753	0.0651494
$960$	0.523208	0.0168865
$961$	52.6680	1.69897
$962$	26.6119	0.858003
$963$	−42.6286	−1.37369
$964$	5.40735	0.174159
$965$	−12.1643	−0.391583
$966$	−0.0253714	−0.000816312 0
$967$	−9.77045	−0.314196	−0.157098	−	0.987583i	$-0.550214\pi$
$967$	−9.77045	−0.314196	−0.157098	+	0.987583i	$0.550214\pi$
$968$	1.88938	0.0607269
$969$	4.73778	0.152199
$970$	−24.1703	−0.776060
$971$	37.9742	1.21865	0.609325	−	0.792920i	$-0.291440\pi$
$971$	37.9742	1.21865	0.609325	+	0.792920i	$0.291440\pi$
$972$	−6.10815	−0.195919
$973$	−2.57492	−0.0825481
$974$	−27.0019	−0.865198
$975$	0.956397	0.0306292
$976$	58.8652	1.88423
$977$	41.8399	1.33858	0.669289	−	0.743002i	$-0.266599\pi$
$977$	41.8399	1.33858	0.669289	+	0.743002i	$0.266599\pi$
$978$	−10.6790	−0.341476
$979$	10.6799	0.341333
$980$	6.16079	0.196799
$981$	5.46471	0.174475
$982$	−0.0429271	−0.00136986
$983$	0.773051	0.0246565	0.0123282	−	0.999924i	$-0.496076\pi$
$983$	0.773051	0.0246565	0.0123282	+	0.999924i	$0.496076\pi$
$984$	−1.75067	−0.0558094
$985$	23.0890	0.735677
$986$	−48.1685	−1.53400
$987$	0.506694	0.0161283
$988$	17.4360	0.554713
$989$	−0.306074	−0.00973258
$990$	−4.98119	−0.158313
$991$	30.4974	0.968782	0.484391	−	0.874852i	$-0.339041\pi$
$991$	30.4974	0.968782	0.484391	+	0.874852i	$0.339041\pi$
$992$	42.9680	1.36423
$993$	3.22734	0.102417
$994$	1.86000	0.0589957
$995$	5.08792	0.161298
$996$	−1.56322	−0.0495324
$997$	−9.40107	−0.297735	−0.148867	−	0.988857i	$-0.547563\pi$
$997$	−9.40107	−0.297735	−0.148867	+	0.988857i	$0.547563\pi$
$998$	−70.8415	−2.24245
$999$	6.70113	0.212014

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.f.1.9	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.f.1.9	✓	31	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:	\( N \)	\(=\)	\( 4015 = 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4015.a (trivial)

\(f(q)\)	\(=\)	\(q-1.69949 q^{2} -0.262694 q^{3} +0.888269 q^{4} -1.00000 q^{5} +0.446447 q^{6} +0.253523 q^{7} +1.88938 q^{8} -2.93099 q^{9} +O(q^{10})\)	\(q-1.69949 q^{2} -0.262694 q^{3} +0.888269 q^{4} -1.00000 q^{5} +0.446447 q^{6} +0.253523 q^{7} +1.88938 q^{8} -2.93099 q^{9} +1.69949 q^{10} +1.00000 q^{11} -0.233343 q^{12} -3.64072 q^{13} -0.430860 q^{14} +0.262694 q^{15} -4.98752 q^{16} +3.34510 q^{17} +4.98119 q^{18} -5.39157 q^{19} -0.888269 q^{20} -0.0665991 q^{21} -1.69949 q^{22} -0.224160 q^{23} -0.496329 q^{24} +1.00000 q^{25} +6.18737 q^{26} +1.55804 q^{27} +0.225197 q^{28} +8.47296 q^{29} -0.446447 q^{30} +9.14702 q^{31} +4.69749 q^{32} -0.262694 q^{33} -5.68497 q^{34} -0.253523 q^{35} -2.60351 q^{36} +4.30101 q^{37} +9.16292 q^{38} +0.956397 q^{39} -1.88938 q^{40} +3.52724 q^{41} +0.113185 q^{42} +1.36543 q^{43} +0.888269 q^{44} +2.93099 q^{45} +0.380957 q^{46} -7.60813 q^{47} +1.31019 q^{48} -6.93573 q^{49} -1.69949 q^{50} -0.878739 q^{51} -3.23394 q^{52} -6.79151 q^{53} -2.64787 q^{54} -1.00000 q^{55} +0.479001 q^{56} +1.41633 q^{57} -14.3997 q^{58} -7.00691 q^{59} +0.233343 q^{60} -11.8025 q^{61} -15.5453 q^{62} -0.743074 q^{63} +1.99170 q^{64} +3.64072 q^{65} +0.446447 q^{66} +15.0892 q^{67} +2.97135 q^{68} +0.0588855 q^{69} +0.430860 q^{70} -4.31695 q^{71} -5.53775 q^{72} +1.00000 q^{73} -7.30952 q^{74} -0.262694 q^{75} -4.78916 q^{76} +0.253523 q^{77} -1.62539 q^{78} +0.496408 q^{79} +4.98752 q^{80} +8.38369 q^{81} -5.99452 q^{82} +6.69921 q^{83} -0.0591579 q^{84} -3.34510 q^{85} -2.32053 q^{86} -2.22580 q^{87} +1.88938 q^{88} +10.6799 q^{89} -4.98119 q^{90} -0.923007 q^{91} -0.199114 q^{92} -2.40287 q^{93} +12.9299 q^{94} +5.39157 q^{95} -1.23400 q^{96} -14.2221 q^{97} +11.7872 q^{98} -2.93099 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q - 7 q^{2} - 4 q^{3} + 39 q^{4} - 31 q^{5} - 5 q^{6} - 11 q^{7} - 24 q^{8} + 31 q^{9}+O(q^{10}) \) 31 * q - 7 * q^2 - 4 * q^3 + 39 * q^4 - 31 * q^5 - 5 * q^6 - 11 * q^7 - 24 * q^8 + 31 * q^9	\( 31 q - 7 q^{2} - 4 q^{3} + 39 q^{4} - 31 q^{5} - 5 q^{6} - 11 q^{7} - 24 q^{8} + 31 q^{9} + 7 q^{10} + 31 q^{11} - 4 q^{12} - 24 q^{13} - 9 q^{14} + 4 q^{15} + 43 q^{16} - 49 q^{17} - 35 q^{18} - 22 q^{19} - 39 q^{20} - 8 q^{21} - 7 q^{22} - q^{23} - 13 q^{24} + 31 q^{25} - 9 q^{26} - 22 q^{27} - 34 q^{28} - 12 q^{29} + 5 q^{30} + 4 q^{31} - 45 q^{32} - 4 q^{33} + 2 q^{34} + 11 q^{35} + 34 q^{36} - 18 q^{37} - 7 q^{38} - q^{39} + 24 q^{40} - 58 q^{41} - 21 q^{42} - 41 q^{43} + 39 q^{44} - 31 q^{45} + 23 q^{46} - 31 q^{47} - 29 q^{48} + 44 q^{49} - 7 q^{50} + 8 q^{51} - 89 q^{52} - 46 q^{53} - 47 q^{54} - 31 q^{55} + 10 q^{56} - 47 q^{57} - 34 q^{58} - 9 q^{59} + 4 q^{60} - 5 q^{61} - 50 q^{62} - 61 q^{63} + 78 q^{64} + 24 q^{65} - 5 q^{66} + q^{67} - 115 q^{68} - 19 q^{69} + 9 q^{70} - 8 q^{71} - 93 q^{72} + 31 q^{73} - 19 q^{74} - 4 q^{75} - 7 q^{76} - 11 q^{77} + 57 q^{78} - 43 q^{80} + 43 q^{81} + 20 q^{82} - 29 q^{83} - 32 q^{84} + 49 q^{85} + 25 q^{86} - 62 q^{87} - 24 q^{88} - 77 q^{89} + 35 q^{90} - 11 q^{91} - 25 q^{92} - 38 q^{94} + 22 q^{95} - 23 q^{96} - 39 q^{97} - 65 q^{98} + 31 q^{99}+O(q^{100}) \) 31 * q - 7 * q^2 - 4 * q^3 + 39 * q^4 - 31 * q^5 - 5 * q^6 - 11 * q^7 - 24 * q^8 + 31 * q^9 + 7 * q^10 + 31 * q^11 - 4 * q^12 - 24 * q^13 - 9 * q^14 + 4 * q^15 + 43 * q^16 - 49 * q^17 - 35 * q^18 - 22 * q^19 - 39 * q^20 - 8 * q^21 - 7 * q^22 - q^23 - 13 * q^24 + 31 * q^25 - 9 * q^26 - 22 * q^27 - 34 * q^28 - 12 * q^29 + 5 * q^30 + 4 * q^31 - 45 * q^32 - 4 * q^33 + 2 * q^34 + 11 * q^35 + 34 * q^36 - 18 * q^37 - 7 * q^38 - q^39 + 24 * q^40 - 58 * q^41 - 21 * q^42 - 41 * q^43 + 39 * q^44 - 31 * q^45 + 23 * q^46 - 31 * q^47 - 29 * q^48 + 44 * q^49 - 7 * q^50 + 8 * q^51 - 89 * q^52 - 46 * q^53 - 47 * q^54 - 31 * q^55 + 10 * q^56 - 47 * q^57 - 34 * q^58 - 9 * q^59 + 4 * q^60 - 5 * q^61 - 50 * q^62 - 61 * q^63 + 78 * q^64 + 24 * q^65 - 5 * q^66 + q^67 - 115 * q^68 - 19 * q^69 + 9 * q^70 - 8 * q^71 - 93 * q^72 + 31 * q^73 - 19 * q^74 - 4 * q^75 - 7 * q^76 - 11 * q^77 + 57 * q^78 - 43 * q^80 + 43 * q^81 + 20 * q^82 - 29 * q^83 - 32 * q^84 + 49 * q^85 + 25 * q^86 - 62 * q^87 - 24 * q^88 - 77 * q^89 + 35 * q^90 - 11 * q^91 - 25 * q^92 - 38 * q^94 + 22 * q^95 - 23 * q^96 - 39 * q^97 - 65 * q^98 + 31 * q^99

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