LMFDB - Embedded newform 6015.2.a.e.1.30

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, 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("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.0300168158$
Analytic rank:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.30
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.58233 q^{2} -1.00000 q^{3} +4.66843 q^{4} -1.00000 q^{5} -2.58233 q^{6} +3.06134 q^{7} +6.89076 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.58233 q^{2} -1.00000 q^{3} +4.66843 q^{4} -1.00000 q^{5} -2.58233 q^{6} +3.06134 q^{7} +6.89076 q^{8} +1.00000 q^{9} -2.58233 q^{10} -3.14312 q^{11} -4.66843 q^{12} -3.68576 q^{13} +7.90538 q^{14} +1.00000 q^{15} +8.45736 q^{16} +5.47911 q^{17} +2.58233 q^{18} +5.73621 q^{19} -4.66843 q^{20} -3.06134 q^{21} -8.11659 q^{22} +6.14658 q^{23} -6.89076 q^{24} +1.00000 q^{25} -9.51785 q^{26} -1.00000 q^{27} +14.2916 q^{28} +1.14385 q^{29} +2.58233 q^{30} +1.01258 q^{31} +8.05818 q^{32} +3.14312 q^{33} +14.1489 q^{34} -3.06134 q^{35} +4.66843 q^{36} -3.17427 q^{37} +14.8128 q^{38} +3.68576 q^{39} -6.89076 q^{40} -4.54986 q^{41} -7.90538 q^{42} -8.58692 q^{43} -14.6735 q^{44} -1.00000 q^{45} +15.8725 q^{46} +3.46745 q^{47} -8.45736 q^{48} +2.37177 q^{49} +2.58233 q^{50} -5.47911 q^{51} -17.2067 q^{52} +8.71221 q^{53} -2.58233 q^{54} +3.14312 q^{55} +21.0949 q^{56} -5.73621 q^{57} +2.95379 q^{58} -4.58566 q^{59} +4.66843 q^{60} +9.12204 q^{61} +2.61480 q^{62} +3.06134 q^{63} +3.89415 q^{64} +3.68576 q^{65} +8.11659 q^{66} +3.42581 q^{67} +25.5789 q^{68} -6.14658 q^{69} -7.90538 q^{70} +11.1121 q^{71} +6.89076 q^{72} +7.13079 q^{73} -8.19701 q^{74} -1.00000 q^{75} +26.7791 q^{76} -9.62216 q^{77} +9.51785 q^{78} +3.94578 q^{79} -8.45736 q^{80} +1.00000 q^{81} -11.7492 q^{82} +2.72829 q^{83} -14.2916 q^{84} -5.47911 q^{85} -22.1743 q^{86} -1.14385 q^{87} -21.6585 q^{88} +5.32227 q^{89} -2.58233 q^{90} -11.2833 q^{91} +28.6948 q^{92} -1.01258 q^{93} +8.95410 q^{94} -5.73621 q^{95} -8.05818 q^{96} -2.04840 q^{97} +6.12470 q^{98} -3.14312 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 6 q^{2} - 31 q^{3} + 24 q^{4} - 31 q^{5} - 6 q^{6} - 4 q^{7} + 15 q^{8} + 31 q^{9}+O(q^{10}) $ 31 * q + 6 * q^2 - 31 * q^3 + 24 * q^4 - 31 * q^5 - 6 * q^6 - 4 * q^7 + 15 * q^8 + 31 * q^9	\( 31 q + 6 q^{2} - 31 q^{3} + 24 q^{4} - 31 q^{5} - 6 q^{6} - 4 q^{7} + 15 q^{8} + 31 q^{9} - 6 q^{10} - q^{11} - 24 q^{12} + 8 q^{13} + 8 q^{14} + 31 q^{15} + 10 q^{16} + 42 q^{17} + 6 q^{18} - 19 q^{19} - 24 q^{20} + 4 q^{21} + 17 q^{22} + 26 q^{23} - 15 q^{24} + 31 q^{25} + 4 q^{26} - 31 q^{27} - 16 q^{28} - 11 q^{29} + 6 q^{30} - 3 q^{31} + 41 q^{32} + q^{33} + 6 q^{34} + 4 q^{35} + 24 q^{36} + 10 q^{37} + 12 q^{38} - 8 q^{39} - 15 q^{40} + 27 q^{41} - 8 q^{42} - 37 q^{43} - 9 q^{44} - 31 q^{45} - 23 q^{46} + 48 q^{47} - 10 q^{48} + 31 q^{49} + 6 q^{50} - 42 q^{51} + 18 q^{52} + 35 q^{53} - 6 q^{54} + q^{55} + 7 q^{56} + 19 q^{57} - 26 q^{58} - 3 q^{59} + 24 q^{60} + 11 q^{61} + 49 q^{62} - 4 q^{63} - 27 q^{64} - 8 q^{65} - 17 q^{66} - 44 q^{67} + 72 q^{68} - 26 q^{69} - 8 q^{70} + 6 q^{71} + 15 q^{72} + 49 q^{73} - 6 q^{74} - 31 q^{75} - 36 q^{76} + 66 q^{77} - 4 q^{78} - 41 q^{79} - 10 q^{80} + 31 q^{81} + 9 q^{82} + 53 q^{83} + 16 q^{84} - 42 q^{85} + 3 q^{86} + 11 q^{87} + 21 q^{88} + 31 q^{89} - 6 q^{90} - 45 q^{91} + 45 q^{92} + 3 q^{93} - 4 q^{94} + 19 q^{95} - 41 q^{96} + 37 q^{97} + 41 q^{98} - q^{99}+O(q^{100}) \) 31 * q + 6 * q^2 - 31 * q^3 + 24 * q^4 - 31 * q^5 - 6 * q^6 - 4 * q^7 + 15 * q^8 + 31 * q^9 - 6 * q^10 - q^11 - 24 * q^12 + 8 * q^13 + 8 * q^14 + 31 * q^15 + 10 * q^16 + 42 * q^17 + 6 * q^18 - 19 * q^19 - 24 * q^20 + 4 * q^21 + 17 * q^22 + 26 * q^23 - 15 * q^24 + 31 * q^25 + 4 * q^26 - 31 * q^27 - 16 * q^28 - 11 * q^29 + 6 * q^30 - 3 * q^31 + 41 * q^32 + q^33 + 6 * q^34 + 4 * q^35 + 24 * q^36 + 10 * q^37 + 12 * q^38 - 8 * q^39 - 15 * q^40 + 27 * q^41 - 8 * q^42 - 37 * q^43 - 9 * q^44 - 31 * q^45 - 23 * q^46 + 48 * q^47 - 10 * q^48 + 31 * q^49 + 6 * q^50 - 42 * q^51 + 18 * q^52 + 35 * q^53 - 6 * q^54 + q^55 + 7 * q^56 + 19 * q^57 - 26 * q^58 - 3 * q^59 + 24 * q^60 + 11 * q^61 + 49 * q^62 - 4 * q^63 - 27 * q^64 - 8 * q^65 - 17 * q^66 - 44 * q^67 + 72 * q^68 - 26 * q^69 - 8 * q^70 + 6 * q^71 + 15 * q^72 + 49 * q^73 - 6 * q^74 - 31 * q^75 - 36 * q^76 + 66 * q^77 - 4 * q^78 - 41 * q^79 - 10 * q^80 + 31 * q^81 + 9 * q^82 + 53 * q^83 + 16 * q^84 - 42 * q^85 + 3 * q^86 + 11 * q^87 + 21 * q^88 + 31 * q^89 - 6 * q^90 - 45 * q^91 + 45 * q^92 + 3 * q^93 - 4 * q^94 + 19 * q^95 - 41 * q^96 + 37 * q^97 + 41 * q^98 - 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 $

$2$	2.58233	1.82598	0.912991	−	0.407979i	$-0.133766\pi$
$2$	2.58233	1.82598	0.912991	+	0.407979i	$0.133766\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.66843	2.33421
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.58233	−1.05423
$7$	3.06134	1.15708	0.578538	−	0.815655i	$-0.303623\pi$
$7$	3.06134	1.15708	0.578538	+	0.815655i	$0.303623\pi$
$8$	6.89076	2.43625
$9$	1.00000	0.333333
$10$	−2.58233	−0.816604
$11$	−3.14312	−0.947688	−0.473844	−	0.880609i	$-0.657134\pi$
$11$	−3.14312	−0.947688	−0.473844	+	0.880609i	$0.657134\pi$
$12$	−4.66843	−1.34766
$13$	−3.68576	−1.02225	−0.511123	−	0.859508i	$-0.670770\pi$
$13$	−3.68576	−1.02225	−0.511123	+	0.859508i	$0.670770\pi$
$14$	7.90538	2.11280
$15$	1.00000	0.258199
$16$	8.45736	2.11434
$17$	5.47911	1.32888	0.664440	−	0.747341i	$-0.268670\pi$
$17$	5.47911	1.32888	0.664440	+	0.747341i	$0.268670\pi$
$18$	2.58233	0.608661
$19$	5.73621	1.31598	0.657988	−	0.753028i	$-0.271408\pi$
$19$	5.73621	1.31598	0.657988	+	0.753028i	$0.271408\pi$
$20$	−4.66843	−1.04389
$21$	−3.06134	−0.668038
$22$	−8.11659	−1.73046
$23$	6.14658	1.28165	0.640825	−	0.767687i	$-0.278592\pi$
$23$	6.14658	1.28165	0.640825	+	0.767687i	$0.278592\pi$
$24$	−6.89076	−1.40657
$25$	1.00000	0.200000
$26$	−9.51785	−1.86660
$27$	−1.00000	−0.192450
$28$	14.2916	2.70086
$29$	1.14385	0.212407	0.106204	−	0.994344i	$-0.466130\pi$
$29$	1.14385	0.212407	0.106204	+	0.994344i	$0.466130\pi$
$30$	2.58233	0.471467
$31$	1.01258	0.181864	0.0909320	−	0.995857i	$-0.471015\pi$
$31$	1.01258	0.181864	0.0909320	+	0.995857i	$0.471015\pi$
$32$	8.05818	1.42450
$33$	3.14312	0.547148
$34$	14.1489	2.42651
$35$	−3.06134	−0.517460
$36$	4.66843	0.778071
$37$	−3.17427	−0.521847	−0.260923	−	0.965359i	$-0.584027\pi$
$37$	−3.17427	−0.521847	−0.260923	+	0.965359i	$0.584027\pi$
$38$	14.8128	2.40295
$39$	3.68576	0.590194
$40$	−6.89076	−1.08952
$41$	−4.54986	−0.710569	−0.355285	−	0.934758i	$-0.615616\pi$
$41$	−4.54986	−0.710569	−0.355285	+	0.934758i	$0.615616\pi$
$42$	−7.90538	−1.21983
$43$	−8.58692	−1.30949	−0.654746	−	0.755849i	$-0.727225\pi$
$43$	−8.58692	−1.30949	−0.654746	+	0.755849i	$0.727225\pi$
$44$	−14.6735	−2.21211
$45$	−1.00000	−0.149071
$46$	15.8725	2.34027
$47$	3.46745	0.505780	0.252890	−	0.967495i	$-0.418619\pi$
$47$	3.46745	0.505780	0.252890	+	0.967495i	$0.418619\pi$
$48$	−8.45736	−1.22071
$49$	2.37177	0.338825
$50$	2.58233	0.365197
$51$	−5.47911	−0.767230
$52$	−17.2067	−2.38614
$53$	8.71221	1.19671	0.598357	−	0.801229i	$-0.295820\pi$
$53$	8.71221	1.19671	0.598357	+	0.801229i	$0.295820\pi$
$54$	−2.58233	−0.351411
$55$	3.14312	0.423819
$56$	21.0949	2.81893
$57$	−5.73621	−0.759780
$58$	2.95379	0.387852
$59$	−4.58566	−0.597002	−0.298501	−	0.954409i	$-0.596487\pi$
$59$	−4.58566	−0.597002	−0.298501	+	0.954409i	$0.596487\pi$
$60$	4.66843	0.602691
$61$	9.12204	1.16796	0.583979	−	0.811769i	$-0.301495\pi$
$61$	9.12204	1.16796	0.583979	+	0.811769i	$0.301495\pi$
$62$	2.61480	0.332080
$63$	3.06134	0.385692
$64$	3.89415	0.486768
$65$	3.68576	0.457162
$66$	8.11659	0.999083
$67$	3.42581	0.418529	0.209265	−	0.977859i	$-0.432893\pi$
$67$	3.42581	0.418529	0.209265	+	0.977859i	$0.432893\pi$
$68$	25.5789	3.10189
$69$	−6.14658	−0.739961
$70$	−7.90538	−0.944873
$71$	11.1121	1.31876	0.659379	−	0.751810i	$-0.270819\pi$
$71$	11.1121	1.31876	0.659379	+	0.751810i	$0.270819\pi$
$72$	6.89076	0.812084
$73$	7.13079	0.834596	0.417298	−	0.908770i	$-0.362977\pi$
$73$	7.13079	0.834596	0.417298	+	0.908770i	$0.362977\pi$
$74$	−8.19701	−0.952884
$75$	−1.00000	−0.115470
$76$	26.7791	3.07177
$77$	−9.62216	−1.09655
$78$	9.51785	1.07768
$79$	3.94578	0.443935	0.221968	−	0.975054i	$-0.428752\pi$
$79$	3.94578	0.443935	0.221968	+	0.975054i	$0.428752\pi$
$80$	−8.45736	−0.945562
$81$	1.00000	0.111111
$82$	−11.7492	−1.29749
$83$	2.72829	0.299469	0.149734	−	0.988726i	$-0.452158\pi$
$83$	2.72829	0.299469	0.149734	+	0.988726i	$0.452158\pi$
$84$	−14.2916	−1.55934
$85$	−5.47911	−0.594293
$86$	−22.1743	−2.39111
$87$	−1.14385	−0.122633
$88$	−21.6585	−2.30881
$89$	5.32227	0.564160	0.282080	−	0.959391i	$-0.408976\pi$
$89$	5.32227	0.564160	0.282080	+	0.959391i	$0.408976\pi$
$90$	−2.58233	−0.272201
$91$	−11.2833	−1.18282
$92$	28.6948	2.99164
$93$	−1.01258	−0.104999
$94$	8.95410	0.923545
$95$	−5.73621	−0.588523
$96$	−8.05818	−0.822434
$97$	−2.04840	−0.207983	−0.103992	−	0.994578i	$-0.533162\pi$
$97$	−2.04840	−0.207983	−0.103992	+	0.994578i	$0.533162\pi$
$98$	6.12470	0.618689
$99$	−3.14312	−0.315896
$100$	4.66843	0.466843
$101$	13.2576	1.31918	0.659588	−	0.751627i	$-0.270731\pi$
$101$	13.2576	1.31918	0.659588	+	0.751627i	$0.270731\pi$
$102$	−14.1489	−1.40095
$103$	9.59287	0.945214	0.472607	−	0.881273i	$-0.343313\pi$
$103$	9.59287	0.945214	0.472607	+	0.881273i	$0.343313\pi$
$104$	−25.3977	−2.49045
$105$	3.06134	0.298756
$106$	22.4978	2.18518
$107$	−3.48452	−0.336861	−0.168430	−	0.985714i	$-0.553870\pi$
$107$	−3.48452	−0.336861	−0.168430	+	0.985714i	$0.553870\pi$
$108$	−4.66843	−0.449220
$109$	4.02961	0.385967	0.192983	−	0.981202i	$-0.438184\pi$
$109$	4.02961	0.385967	0.192983	+	0.981202i	$0.438184\pi$
$110$	8.11659	0.773886
$111$	3.17427	0.301288
$112$	25.8908	2.44645
$113$	−3.30593	−0.310996	−0.155498	−	0.987836i	$-0.549698\pi$
$113$	−3.30593	−0.310996	−0.155498	+	0.987836i	$0.549698\pi$
$114$	−14.8128	−1.38734
$115$	−6.14658	−0.573171
$116$	5.33997	0.495803
$117$	−3.68576	−0.340749
$118$	−11.8417	−1.09012
$119$	16.7734	1.53762
$120$	6.89076	0.629037
$121$	−1.12077	−0.101888
$122$	23.5561	2.13267
$123$	4.54986	0.410247
$124$	4.72714	0.424509
$125$	−1.00000	−0.0894427
$126$	7.90538	0.704267
$127$	2.31061	0.205033	0.102517	−	0.994731i	$-0.467310\pi$
$127$	2.31061	0.205033	0.102517	+	0.994731i	$0.467310\pi$
$128$	−6.06038	−0.535667
$129$	8.58692	0.756036
$130$	9.51785	0.834770
$131$	−6.84916	−0.598414	−0.299207	−	0.954188i	$-0.596722\pi$
$131$	−6.84916	−0.598414	−0.299207	+	0.954188i	$0.596722\pi$
$132$	14.6735	1.27716
$133$	17.5605	1.52269
$134$	8.84657	0.764227
$135$	1.00000	0.0860663
$136$	37.7553	3.23749
$137$	−22.0580	−1.88454	−0.942270	−	0.334854i	$-0.891313\pi$
$137$	−22.0580	−1.88454	−0.942270	+	0.334854i	$0.891313\pi$
$138$	−15.8725	−1.35116
$139$	−3.15299	−0.267433	−0.133717	−	0.991020i	$-0.542691\pi$
$139$	−3.15299	−0.267433	−0.133717	+	0.991020i	$0.542691\pi$
$140$	−14.2916	−1.20786
$141$	−3.46745	−0.292012
$142$	28.6950	2.40803
$143$	11.5848	0.968770
$144$	8.45736	0.704780
$145$	−1.14385	−0.0949913
$146$	18.4141	1.52396
$147$	−2.37177	−0.195621
$148$	−14.8189	−1.21810
$149$	−6.05251	−0.495841	−0.247920	−	0.968780i	$-0.579747\pi$
$149$	−6.05251	−0.495841	−0.247920	+	0.968780i	$0.579747\pi$
$150$	−2.58233	−0.210846
$151$	19.5468	1.59069	0.795347	−	0.606154i	$-0.207288\pi$
$151$	19.5468	1.59069	0.795347	+	0.606154i	$0.207288\pi$
$152$	39.5269	3.20605
$153$	5.47911	0.442960
$154$	−24.8476	−2.00228
$155$	−1.01258	−0.0813320
$156$	17.2067	1.37764
$157$	−7.10600	−0.567121	−0.283560	−	0.958954i	$-0.591516\pi$
$157$	−7.10600	−0.567121	−0.283560	+	0.958954i	$0.591516\pi$
$158$	10.1893	0.810618
$159$	−8.71221	−0.690923
$160$	−8.05818	−0.637055
$161$	18.8167	1.48297
$162$	2.58233	0.202887
$163$	−8.21772	−0.643662	−0.321831	−	0.946797i	$-0.604298\pi$
$163$	−8.21772	−0.643662	−0.321831	+	0.946797i	$0.604298\pi$
$164$	−21.2407	−1.65862
$165$	−3.14312	−0.244692
$166$	7.04534	0.546825
$167$	−9.11841	−0.705603	−0.352802	−	0.935698i	$-0.614771\pi$
$167$	−9.11841	−0.705603	−0.352802	+	0.935698i	$0.614771\pi$
$168$	−21.0949	−1.62751
$169$	0.584826	0.0449866
$170$	−14.1489	−1.08517
$171$	5.73621	0.438659
$172$	−40.0874	−3.05664
$173$	17.9027	1.36112	0.680559	−	0.732693i	$-0.261737\pi$
$173$	17.9027	1.36112	0.680559	+	0.732693i	$0.261737\pi$
$174$	−2.95379	−0.223926
$175$	3.06134	0.231415
$176$	−26.5825	−2.00373
$177$	4.58566	0.344679
$178$	13.7439	1.03015
$179$	−12.3910	−0.926148	−0.463074	−	0.886320i	$-0.653254\pi$
$179$	−12.3910	−0.926148	−0.463074	+	0.886320i	$0.653254\pi$
$180$	−4.66843	−0.347964
$181$	−14.0390	−1.04351	−0.521755	−	0.853095i	$-0.674723\pi$
$181$	−14.0390	−1.04351	−0.521755	+	0.853095i	$0.674723\pi$
$182$	−29.1373	−2.15980
$183$	−9.12204	−0.674321
$184$	42.3546	3.12242
$185$	3.17427	0.233377
$186$	−2.61480	−0.191727
$187$	−17.2215	−1.25936
$188$	16.1875	1.18060
$189$	−3.06134	−0.222679
$190$	−14.8128	−1.07463
$191$	−4.69022	−0.339372	−0.169686	−	0.985498i	$-0.554275\pi$
$191$	−4.69022	−0.339372	−0.169686	+	0.985498i	$0.554275\pi$
$192$	−3.89415	−0.281036
$193$	−16.6381	−1.19764	−0.598819	−	0.800884i	$-0.704363\pi$
$193$	−16.6381	−1.19764	−0.598819	+	0.800884i	$0.704363\pi$
$194$	−5.28964	−0.379774
$195$	−3.68576	−0.263943
$196$	11.0725	0.790890
$197$	−8.38547	−0.597440	−0.298720	−	0.954341i	$-0.596560\pi$
$197$	−8.38547	−0.597440	−0.298720	+	0.954341i	$0.596560\pi$
$198$	−8.11659	−0.576821
$199$	10.3854	0.736200	0.368100	−	0.929786i	$-0.380008\pi$
$199$	10.3854	0.736200	0.368100	+	0.929786i	$0.380008\pi$
$200$	6.89076	0.487250
$201$	−3.42581	−0.241638
$202$	34.2354	2.40879
$203$	3.50170	0.245771
$204$	−25.5789	−1.79088
$205$	4.54986	0.317776
$206$	24.7720	1.72594
$207$	6.14658	0.427217
$208$	−31.1718	−2.16138
$209$	−18.0296	−1.24714
$210$	7.90538	0.545523
$211$	1.34991	0.0929313	0.0464657	−	0.998920i	$-0.485204\pi$
$211$	1.34991	0.0929313	0.0464657	+	0.998920i	$0.485204\pi$
$212$	40.6723	2.79339
$213$	−11.1121	−0.761386
$214$	−8.99817	−0.615102
$215$	8.58692	0.585623
$216$	−6.89076	−0.468857
$217$	3.09983	0.210430
$218$	10.4058	0.704769
$219$	−7.13079	−0.481854
$220$	14.6735	0.989284
$221$	−20.1947	−1.35844
$222$	8.19701	0.550148
$223$	22.7354	1.52247	0.761236	−	0.648475i	$-0.224593\pi$
$223$	22.7354	1.52247	0.761236	+	0.648475i	$0.224593\pi$
$224$	24.6688	1.64825
$225$	1.00000	0.0666667
$226$	−8.53700	−0.567873
$227$	3.97258	0.263669	0.131835	−	0.991272i	$-0.457913\pi$
$227$	3.97258	0.263669	0.131835	+	0.991272i	$0.457913\pi$
$228$	−26.7791	−1.77349
$229$	−8.93610	−0.590514	−0.295257	−	0.955418i	$-0.595405\pi$
$229$	−8.93610	−0.590514	−0.295257	+	0.955418i	$0.595405\pi$
$230$	−15.8725	−1.04660
$231$	9.62216	0.633092
$232$	7.88198	0.517477
$233$	8.64475	0.566337	0.283168	−	0.959070i	$-0.408614\pi$
$233$	8.64475	0.566337	0.283168	+	0.959070i	$0.408614\pi$
$234$	−9.51785	−0.622201
$235$	−3.46745	−0.226192
$236$	−21.4078	−1.39353
$237$	−3.94578	−0.256306
$238$	43.3145	2.80766
$239$	21.2804	1.37652	0.688258	−	0.725466i	$-0.258376\pi$
$239$	21.2804	1.37652	0.688258	+	0.725466i	$0.258376\pi$
$240$	8.45736	0.545920
$241$	−21.2859	−1.37115	−0.685573	−	0.728004i	$-0.740448\pi$
$241$	−21.2859	−1.37115	−0.685573	+	0.728004i	$0.740448\pi$
$242$	−2.89419	−0.186046
$243$	−1.00000	−0.0641500
$244$	42.5856	2.72626
$245$	−2.37177	−0.151527
$246$	11.7492	0.749105
$247$	−21.1423	−1.34525
$248$	6.97742	0.443066
$249$	−2.72829	−0.172898
$250$	−2.58233	−0.163321
$251$	14.1341	0.892135	0.446068	−	0.894999i	$-0.352824\pi$
$251$	14.1341	0.892135	0.446068	+	0.894999i	$0.352824\pi$
$252$	14.2916	0.900288
$253$	−19.3195	−1.21460
$254$	5.96676	0.374388
$255$	5.47911	0.343115
$256$	−23.4382	−1.46489
$257$	−0.941843	−0.0587505	−0.0293753	−	0.999568i	$-0.509352\pi$
$257$	−0.941843	−0.0587505	−0.0293753	+	0.999568i	$0.509352\pi$
$258$	22.1743	1.38051
$259$	−9.71751	−0.603817
$260$	17.2067	1.06711
$261$	1.14385	0.0708024
$262$	−17.6868	−1.09269
$263$	8.85572	0.546067	0.273034	−	0.962005i	$-0.411973\pi$
$263$	8.85572	0.546067	0.273034	+	0.962005i	$0.411973\pi$
$264$	21.6585	1.33299
$265$	−8.71221	−0.535187
$266$	45.3469	2.78040
$267$	−5.32227	−0.325718
$268$	15.9931	0.976937
$269$	30.6204	1.86696	0.933481	−	0.358628i	$-0.116755\pi$
$269$	30.6204	1.86696	0.933481	+	0.358628i	$0.116755\pi$
$270$	2.58233	0.157156
$271$	3.54423	0.215296	0.107648	−	0.994189i	$-0.465668\pi$
$271$	3.54423	0.215296	0.107648	+	0.994189i	$0.465668\pi$
$272$	46.3389	2.80971
$273$	11.2833	0.682899
$274$	−56.9610	−3.44114
$275$	−3.14312	−0.189538
$276$	−28.6948	−1.72723
$277$	26.4148	1.58711	0.793555	−	0.608498i	$-0.208228\pi$
$277$	26.4148	1.58711	0.793555	+	0.608498i	$0.208228\pi$
$278$	−8.14206	−0.488328
$279$	1.01258	0.0606213
$280$	−21.0949	−1.26066
$281$	−16.8191	−1.00335	−0.501673	−	0.865057i	$-0.667282\pi$
$281$	−16.8191	−1.00335	−0.501673	+	0.865057i	$0.667282\pi$
$282$	−8.95410	−0.533209
$283$	−6.70571	−0.398613	−0.199307	−	0.979937i	$-0.563869\pi$
$283$	−6.70571	−0.398613	−0.199307	+	0.979937i	$0.563869\pi$
$284$	51.8758	3.07827
$285$	5.73621	0.339784
$286$	29.9158	1.76896
$287$	−13.9287	−0.822183
$288$	8.05818	0.474833
$289$	13.0207	0.765923
$290$	−2.95379	−0.173453
$291$	2.04840	0.120079
$292$	33.2896	1.94813
$293$	15.6765	0.915830	0.457915	−	0.888996i	$-0.348596\pi$
$293$	15.6765	0.915830	0.457915	+	0.888996i	$0.348596\pi$
$294$	−6.12470	−0.357200
$295$	4.58566	0.266988
$296$	−21.8731	−1.27135
$297$	3.14312	0.182383
$298$	−15.6296	−0.905397
$299$	−22.6548	−1.31016
$300$	−4.66843	−0.269532
$301$	−26.2874	−1.51518
$302$	50.4762	2.90458
$303$	−13.2576	−0.761627
$304$	48.5132	2.78242
$305$	−9.12204	−0.522326
$306$	14.1489	0.808838
$307$	−6.30668	−0.359941	−0.179971	−	0.983672i	$-0.557600\pi$
$307$	−6.30668	−0.359941	−0.179971	+	0.983672i	$0.557600\pi$
$308$	−44.9204	−2.55957
$309$	−9.59287	−0.545719
$310$	−2.61480	−0.148511
$311$	−0.607951	−0.0344737	−0.0172369	−	0.999851i	$-0.505487\pi$
$311$	−0.607951	−0.0344737	−0.0172369	+	0.999851i	$0.505487\pi$
$312$	25.3977	1.43786
$313$	−4.49675	−0.254171	−0.127086	−	0.991892i	$-0.540562\pi$
$313$	−4.49675	−0.254171	−0.127086	+	0.991892i	$0.540562\pi$
$314$	−18.3500	−1.03555
$315$	−3.06134	−0.172487
$316$	18.4206	1.03624
$317$	−6.26481	−0.351867	−0.175933	−	0.984402i	$-0.556294\pi$
$317$	−6.26481	−0.351867	−0.175933	+	0.984402i	$0.556294\pi$
$318$	−22.4978	−1.26161
$319$	−3.59525	−0.201296
$320$	−3.89415	−0.217689
$321$	3.48452	0.194487
$322$	48.5910	2.70787
$323$	31.4294	1.74878
$324$	4.66843	0.259357
$325$	−3.68576	−0.204449
$326$	−21.2209	−1.17532
$327$	−4.02961	−0.222838
$328$	−31.3520	−1.73113
$329$	10.6150	0.585226
$330$	−8.11659	−0.446803
$331$	−30.2655	−1.66354	−0.831771	−	0.555118i	$-0.812673\pi$
$331$	−30.2655	−1.66354	−0.831771	+	0.555118i	$0.812673\pi$
$332$	12.7368	0.699024
$333$	−3.17427	−0.173949
$334$	−23.5467	−1.28842
$335$	−3.42581	−0.187172
$336$	−25.8908	−1.41246
$337$	−29.1284	−1.58672	−0.793362	−	0.608750i	$-0.791671\pi$
$337$	−29.1284	−1.58672	−0.793362	+	0.608750i	$0.791671\pi$
$338$	1.51021	0.0821448
$339$	3.30593	0.179553
$340$	−25.5789	−1.38721
$341$	−3.18265	−0.172350
$342$	14.8128	0.800984
$343$	−14.1686	−0.765030
$344$	−59.1704	−3.19025
$345$	6.14658	0.330921
$346$	46.2307	2.48538
$347$	−29.0470	−1.55932	−0.779662	−	0.626200i	$-0.784609\pi$
$347$	−29.0470	−1.55932	−0.779662	+	0.626200i	$0.784609\pi$
$348$	−5.33997	−0.286252
$349$	−36.1788	−1.93661	−0.968303	−	0.249779i	$-0.919642\pi$
$349$	−36.1788	−1.93661	−0.968303	+	0.249779i	$0.919642\pi$
$350$	7.90538	0.422560
$351$	3.68576	0.196731
$352$	−25.3279	−1.34998
$353$	8.51198	0.453047	0.226524	−	0.974006i	$-0.427264\pi$
$353$	8.51198	0.453047	0.226524	+	0.974006i	$0.427264\pi$
$354$	11.8417	0.629379
$355$	−11.1121	−0.589767
$356$	24.8466	1.31687
$357$	−16.7734	−0.887743
$358$	−31.9977	−1.69113
$359$	−11.6784	−0.616362	−0.308181	−	0.951328i	$-0.599720\pi$
$359$	−11.6784	−0.616362	−0.308181	+	0.951328i	$0.599720\pi$
$360$	−6.89076	−0.363175
$361$	13.9041	0.731795
$362$	−36.2533	−1.90543
$363$	1.12077	0.0588250
$364$	−52.6755	−2.76095
$365$	−7.13079	−0.373243
$366$	−23.5561	−1.23130
$367$	9.20312	0.480399	0.240199	−	0.970724i	$-0.422787\pi$
$367$	9.20312	0.480399	0.240199	+	0.970724i	$0.422787\pi$
$368$	51.9838	2.70984
$369$	−4.54986	−0.236856
$370$	8.19701	0.426142
$371$	26.6710	1.38469
$372$	−4.72714	−0.245091
$373$	−12.4584	−0.645073	−0.322536	−	0.946557i	$-0.604535\pi$
$373$	−12.4584	−0.645073	−0.322536	+	0.946557i	$0.604535\pi$
$374$	−44.4717	−2.29958
$375$	1.00000	0.0516398
$376$	23.8934	1.23221
$377$	−4.21595	−0.217132
$378$	−7.90538	−0.406609
$379$	−27.5396	−1.41461	−0.707307	−	0.706907i	$-0.750090\pi$
$379$	−27.5396	−1.41461	−0.707307	+	0.706907i	$0.750090\pi$
$380$	−26.7791	−1.37374
$381$	−2.31061	−0.118376
$382$	−12.1117	−0.619688
$383$	−24.4920	−1.25148	−0.625741	−	0.780031i	$-0.715203\pi$
$383$	−24.4920	−1.25148	−0.625741	+	0.780031i	$0.715203\pi$
$384$	6.06038	0.309268
$385$	9.62216	0.490391
$386$	−42.9651	−2.18687
$387$	−8.58692	−0.436498
$388$	−9.56280	−0.485477
$389$	23.2156	1.17708	0.588539	−	0.808469i	$-0.299703\pi$
$389$	23.2156	1.17708	0.588539	+	0.808469i	$0.299703\pi$
$390$	−9.51785	−0.481955
$391$	33.6778	1.70316
$392$	16.3433	0.825463
$393$	6.84916	0.345495
$394$	−21.6540	−1.09091
$395$	−3.94578	−0.198534
$396$	−14.6735	−0.737369
$397$	−29.0214	−1.45654	−0.728270	−	0.685290i	$-0.759675\pi$
$397$	−29.0214	−1.45654	−0.728270	+	0.685290i	$0.759675\pi$
$398$	26.8185	1.34429
$399$	−17.5605	−0.879123
$400$	8.45736	0.422868
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	−8.84657	−0.441227
$403$	−3.73211	−0.185910
$404$	61.8920	3.07924
$405$	−1.00000	−0.0496904
$406$	9.04254	0.448774
$407$	9.97713	0.494548
$408$	−37.7553	−1.86916
$409$	−17.9523	−0.887684	−0.443842	−	0.896105i	$-0.646385\pi$
$409$	−17.9523	−0.887684	−0.443842	+	0.896105i	$0.646385\pi$
$410$	11.7492	0.580254
$411$	22.0580	1.08804
$412$	44.7836	2.20633
$413$	−14.0382	−0.690777
$414$	15.8725	0.780090
$415$	−2.72829	−0.133926
$416$	−29.7005	−1.45619
$417$	3.15299	0.154403
$418$	−46.5584	−2.27725
$419$	13.6978	0.669180	0.334590	−	0.942364i	$-0.391402\pi$
$419$	13.6978	0.669180	0.334590	+	0.942364i	$0.391402\pi$
$420$	14.2916	0.697360
$421$	−1.69633	−0.0826739	−0.0413370	−	0.999145i	$-0.513162\pi$
$421$	−1.69633	−0.0826739	−0.0413370	+	0.999145i	$0.513162\pi$
$422$	3.48590	0.169691
$423$	3.46745	0.168593
$424$	60.0338	2.91550
$425$	5.47911	0.265776
$426$	−28.6950	−1.39028
$427$	27.9256	1.35142
$428$	−16.2672	−0.786305
$429$	−11.5848	−0.559320
$430$	22.1743	1.06934
$431$	13.9067	0.669863	0.334931	−	0.942242i	$-0.391287\pi$
$431$	13.9067	0.669863	0.334931	+	0.942242i	$0.391287\pi$
$432$	−8.45736	−0.406905
$433$	19.2795	0.926515	0.463258	−	0.886224i	$-0.346680\pi$
$433$	19.2795	0.926515	0.463258	+	0.886224i	$0.346680\pi$
$434$	8.00479	0.384242
$435$	1.14385	0.0548433
$436$	18.8120	0.900929
$437$	35.2581	1.68662
$438$	−18.4141	−0.879858
$439$	−31.4847	−1.50268	−0.751341	−	0.659914i	$-0.770593\pi$
$439$	−31.4847	−1.50268	−0.751341	+	0.659914i	$0.770593\pi$
$440$	21.6585	1.03253
$441$	2.37177	0.112942
$442$	−52.1494	−2.48049
$443$	−31.0780	−1.47656	−0.738281	−	0.674493i	$-0.764362\pi$
$443$	−31.0780	−1.47656	−0.738281	+	0.674493i	$0.764362\pi$
$444$	14.8189	0.703272
$445$	−5.32227	−0.252300
$446$	58.7102	2.78001
$447$	6.05251	0.286274
$448$	11.9213	0.563228
$449$	1.26901	0.0598881	0.0299440	−	0.999552i	$-0.490467\pi$
$449$	1.26901	0.0598881	0.0299440	+	0.999552i	$0.490467\pi$
$450$	2.58233	0.121732
$451$	14.3008	0.673398
$452$	−15.4335	−0.725930
$453$	−19.5468	−0.918388
$454$	10.2585	0.481455
$455$	11.2833	0.528971
$456$	−39.5269	−1.85101
$457$	9.38668	0.439091	0.219545	−	0.975602i	$-0.429543\pi$
$457$	9.38668	0.439091	0.219545	+	0.975602i	$0.429543\pi$
$458$	−23.0760	−1.07827
$459$	−5.47911	−0.255743
$460$	−28.6948	−1.33790
$461$	4.22896	0.196962	0.0984812	−	0.995139i	$-0.468602\pi$
$461$	4.22896	0.196962	0.0984812	+	0.995139i	$0.468602\pi$
$462$	24.8476	1.15601
$463$	−14.6594	−0.681280	−0.340640	−	0.940194i	$-0.610644\pi$
$463$	−14.6594	−0.681280	−0.340640	+	0.940194i	$0.610644\pi$
$464$	9.67393	0.449101
$465$	1.01258	0.0469571
$466$	22.3236	1.03412
$467$	−4.29536	−0.198766	−0.0993828	−	0.995049i	$-0.531687\pi$
$467$	−4.29536	−0.198766	−0.0993828	+	0.995049i	$0.531687\pi$
$468$	−17.2067	−0.795380
$469$	10.4876	0.484270
$470$	−8.95410	−0.413022
$471$	7.10600	0.327427
$472$	−31.5987	−1.45445
$473$	26.9898	1.24099
$474$	−10.1893	−0.468011
$475$	5.73621	0.263195
$476$	78.3054	3.58912
$477$	8.71221	0.398905
$478$	54.9531	2.51349
$479$	18.6143	0.850510	0.425255	−	0.905074i	$-0.360184\pi$
$479$	18.6143	0.850510	0.425255	+	0.905074i	$0.360184\pi$
$480$	8.05818	0.367804
$481$	11.6996	0.533456
$482$	−54.9672	−2.50369
$483$	−18.8167	−0.856191
$484$	−5.23222	−0.237828
$485$	2.04840	0.0930130
$486$	−2.58233	−0.117137
$487$	1.46514	0.0663917	0.0331958	−	0.999449i	$-0.489431\pi$
$487$	1.46514	0.0663917	0.0331958	+	0.999449i	$0.489431\pi$
$488$	62.8578	2.84544
$489$	8.21772	0.371618
$490$	−6.12470	−0.276686
$491$	36.4137	1.64333	0.821663	−	0.569973i	$-0.193046\pi$
$491$	36.4137	1.64333	0.821663	+	0.569973i	$0.193046\pi$
$492$	21.2407	0.957605
$493$	6.26727	0.282264
$494$	−54.5964	−2.45641
$495$	3.14312	0.141273
$496$	8.56372	0.384522
$497$	34.0177	1.52590
$498$	−7.04534	−0.315709
$499$	−20.8327	−0.932598	−0.466299	−	0.884627i	$-0.654413\pi$
$499$	−20.8327	−0.932598	−0.466299	+	0.884627i	$0.654413\pi$
$500$	−4.66843	−0.208778
$501$	9.11841	0.407380
$502$	36.4989	1.62902
$503$	−1.43383	−0.0639311	−0.0319656	−	0.999489i	$-0.510177\pi$
$503$	−1.43383	−0.0639311	−0.0319656	+	0.999489i	$0.510177\pi$
$504$	21.0949	0.939643
$505$	−13.2576	−0.589954
$506$	−49.8892	−2.21785
$507$	−0.584826	−0.0259730
$508$	10.7869	0.478592
$509$	−16.6690	−0.738840	−0.369420	−	0.929262i	$-0.620444\pi$
$509$	−16.6690	−0.738840	−0.369420	+	0.929262i	$0.620444\pi$
$510$	14.1489	0.626523
$511$	21.8297	0.965691
$512$	−48.4044	−2.13919
$513$	−5.73621	−0.253260
$514$	−2.43215	−0.107278
$515$	−9.59287	−0.422712
$516$	40.0874	1.76475
$517$	−10.8986	−0.479321
$518$	−25.0938	−1.10256
$519$	−17.9027	−0.785842
$520$	25.3977	1.11376
$521$	11.6732	0.511411	0.255705	−	0.966755i	$-0.417692\pi$
$521$	11.6732	0.511411	0.255705	+	0.966755i	$0.417692\pi$
$522$	2.95379	0.129284
$523$	6.78510	0.296692	0.148346	−	0.988936i	$-0.452605\pi$
$523$	6.78510	0.296692	0.148346	+	0.988936i	$0.452605\pi$
$524$	−31.9748	−1.39683
$525$	−3.06134	−0.133608
$526$	22.8684	0.997109
$527$	5.54802	0.241675
$528$	26.5825	1.15686
$529$	14.7804	0.642626
$530$	−22.4978	−0.977242
$531$	−4.58566	−0.199001
$532$	81.9798	3.55427
$533$	16.7697	0.726377
$534$	−13.7439	−0.594755
$535$	3.48452	0.150649
$536$	23.6064	1.01964
$537$	12.3910	0.534712
$538$	79.0721	3.40904
$539$	−7.45478	−0.321100
$540$	4.66843	0.200897
$541$	−30.0482	−1.29187	−0.645936	−	0.763392i	$-0.723533\pi$
$541$	−30.0482	−1.29187	−0.645936	+	0.763392i	$0.723533\pi$
$542$	9.15236	0.393128
$543$	14.0390	0.602471
$544$	44.1517	1.89299
$545$	−4.02961	−0.172610
$546$	29.1373	1.24696
$547$	6.65403	0.284506	0.142253	−	0.989830i	$-0.454565\pi$
$547$	6.65403	0.284506	0.142253	+	0.989830i	$0.454565\pi$
$548$	−102.976	−4.39892
$549$	9.12204	0.389319
$550$	−8.11659	−0.346092
$551$	6.56135	0.279523
$552$	−42.3546	−1.80273
$553$	12.0794	0.513667
$554$	68.2117	2.89804
$555$	−3.17427	−0.134740
$556$	−14.7195	−0.624246
$557$	−24.0638	−1.01962	−0.509808	−	0.860288i	$-0.670284\pi$
$557$	−24.0638	−1.01962	−0.509808	+	0.860288i	$0.670284\pi$
$558$	2.61480	0.110693
$559$	31.6493	1.33862
$560$	−25.8908	−1.09409
$561$	17.2215	0.727094
$562$	−43.4326	−1.83209
$563$	−25.3928	−1.07018	−0.535089	−	0.844796i	$-0.679722\pi$
$563$	−25.3928	−1.07018	−0.535089	+	0.844796i	$0.679722\pi$
$564$	−16.1875	−0.681618
$565$	3.30593	0.139082
$566$	−17.3164	−0.727861
$567$	3.06134	0.128564
$568$	76.5705	3.21283
$569$	6.26404	0.262602	0.131301	−	0.991343i	$-0.458085\pi$
$569$	6.26404	0.262602	0.131301	+	0.991343i	$0.458085\pi$
$570$	14.8128	0.620439
$571$	0.825079	0.0345285	0.0172642	−	0.999851i	$-0.494504\pi$
$571$	0.825079	0.0345285	0.0172642	+	0.999851i	$0.494504\pi$
$572$	54.0828	2.26132
$573$	4.69022	0.195937
$574$	−35.9684	−1.50129
$575$	6.14658	0.256330
$576$	3.89415	0.162256
$577$	−33.9605	−1.41379	−0.706897	−	0.707316i	$-0.749906\pi$
$577$	−33.9605	−1.41379	−0.706897	+	0.707316i	$0.749906\pi$
$578$	33.6237	1.39856
$579$	16.6381	0.691457
$580$	−5.33997	−0.221730
$581$	8.35221	0.346508
$582$	5.28964	0.219263
$583$	−27.3836	−1.13411
$584$	49.1366	2.03329
$585$	3.68576	0.152387
$586$	40.4819	1.67229
$587$	21.3978	0.883181	0.441591	−	0.897217i	$-0.354414\pi$
$587$	21.3978	0.883181	0.441591	+	0.897217i	$0.354414\pi$
$588$	−11.0725	−0.456620
$589$	5.80835	0.239329
$590$	11.8417	0.487515
$591$	8.38547	0.344932
$592$	−26.8460	−1.10336
$593$	−7.54505	−0.309838	−0.154919	−	0.987927i	$-0.549512\pi$
$593$	−7.54505	−0.309838	−0.154919	+	0.987927i	$0.549512\pi$
$594$	8.11659	0.333028
$595$	−16.7734	−0.687643
$596$	−28.2557	−1.15740
$597$	−10.3854	−0.425045
$598$	−58.5022	−2.39233
$599$	2.40070	0.0980899	0.0490450	−	0.998797i	$-0.484382\pi$
$599$	2.40070	0.0980899	0.0490450	+	0.998797i	$0.484382\pi$
$600$	−6.89076	−0.281314
$601$	−3.27703	−0.133673	−0.0668364	−	0.997764i	$-0.521291\pi$
$601$	−3.27703	−0.133673	−0.0668364	+	0.997764i	$0.521291\pi$
$602$	−67.8828	−2.76670
$603$	3.42581	0.139510
$604$	91.2527	3.71302
$605$	1.12077	0.0455656
$606$	−34.2354	−1.39072
$607$	26.4306	1.07278	0.536391	−	0.843969i	$-0.319787\pi$
$607$	26.4306	1.07278	0.536391	+	0.843969i	$0.319787\pi$
$608$	46.2234	1.87461
$609$	−3.50170	−0.141896
$610$	−23.5561	−0.953759
$611$	−12.7802	−0.517031
$612$	25.5789	1.03396
$613$	−30.2991	−1.22377	−0.611885	−	0.790947i	$-0.709588\pi$
$613$	−30.2991	−1.22377	−0.611885	+	0.790947i	$0.709588\pi$
$614$	−16.2859	−0.657247
$615$	−4.54986	−0.183468
$616$	−66.3040	−2.67146
$617$	44.2574	1.78174	0.890868	−	0.454263i	$-0.150097\pi$
$617$	44.2574	1.78174	0.890868	+	0.454263i	$0.150097\pi$
$618$	−24.7720	−0.996474
$619$	31.7740	1.27710	0.638552	−	0.769578i	$-0.279534\pi$
$619$	31.7740	1.27710	0.638552	+	0.769578i	$0.279534\pi$
$620$	−4.72714	−0.189846
$621$	−6.14658	−0.246654
$622$	−1.56993	−0.0629485
$623$	16.2933	0.652776
$624$	31.1718	1.24787
$625$	1.00000	0.0400000
$626$	−11.6121	−0.464113
$627$	18.0296	0.720034
$628$	−33.1738	−1.32378
$629$	−17.3922	−0.693472
$630$	−7.90538	−0.314958
$631$	−30.3359	−1.20765	−0.603827	−	0.797115i	$-0.706358\pi$
$631$	−30.3359	−1.20765	−0.603827	+	0.797115i	$0.706358\pi$
$632$	27.1894	1.08154
$633$	−1.34991	−0.0536539
$634$	−16.1778	−0.642503
$635$	−2.31061	−0.0916938
$636$	−40.6723	−1.61276
$637$	−8.74179	−0.346362
$638$	−9.28413	−0.367562
$639$	11.1121	0.439586
$640$	6.06038	0.239558
$641$	28.6280	1.13074	0.565369	−	0.824838i	$-0.308734\pi$
$641$	28.6280	1.13074	0.565369	+	0.824838i	$0.308734\pi$
$642$	8.99817	0.355129
$643$	16.5322	0.651967	0.325983	−	0.945375i	$-0.394305\pi$
$643$	16.5322	0.651967	0.325983	+	0.945375i	$0.394305\pi$
$644$	87.8446	3.46156
$645$	−8.58692	−0.338110
$646$	81.1610	3.19324
$647$	−16.2993	−0.640791	−0.320396	−	0.947284i	$-0.603816\pi$
$647$	−16.2993	−0.640791	−0.320396	+	0.947284i	$0.603816\pi$
$648$	6.89076	0.270695
$649$	14.4133	0.565772
$650$	−9.51785	−0.373321
$651$	−3.09983	−0.121492
$652$	−38.3638	−1.50244
$653$	8.70844	0.340788	0.170394	−	0.985376i	$-0.445496\pi$
$653$	8.70844	0.340788	0.170394	+	0.985376i	$0.445496\pi$
$654$	−10.4058	−0.406898
$655$	6.84916	0.267619
$656$	−38.4798	−1.50239
$657$	7.13079	0.278199
$658$	27.4115	1.06861
$659$	−34.3051	−1.33634	−0.668168	−	0.744010i	$-0.732921\pi$
$659$	−34.3051	−1.33634	−0.668168	+	0.744010i	$0.732921\pi$
$660$	−14.6735	−0.571163
$661$	35.4523	1.37893	0.689466	−	0.724318i	$-0.257845\pi$
$661$	35.4523	1.37893	0.689466	+	0.724318i	$0.257845\pi$
$662$	−78.1555	−3.03760
$663$	20.1947	0.784297
$664$	18.8000	0.729581
$665$	−17.5605	−0.680966
$666$	−8.19701	−0.317628
$667$	7.03074	0.272231
$668$	−42.5686	−1.64703
$669$	−22.7354	−0.879000
$670$	−8.84657	−0.341773
$671$	−28.6717	−1.10686
$672$	−24.6688	−0.951619
$673$	−29.1083	−1.12204	−0.561022	−	0.827801i	$-0.689592\pi$
$673$	−29.1083	−1.12204	−0.561022	+	0.827801i	$0.689592\pi$
$674$	−75.2191	−2.89733
$675$	−1.00000	−0.0384900
$676$	2.73022	0.105008
$677$	41.1777	1.58259	0.791293	−	0.611437i	$-0.209408\pi$
$677$	41.1777	1.58259	0.791293	+	0.611437i	$0.209408\pi$
$678$	8.53700	0.327862
$679$	−6.27083	−0.240652
$680$	−37.7553	−1.44785
$681$	−3.97258	−0.152229
$682$	−8.21866	−0.314709
$683$	11.6776	0.446832	0.223416	−	0.974723i	$-0.428279\pi$
$683$	11.6776	0.446832	0.223416	+	0.974723i	$0.428279\pi$
$684$	26.7791	1.02392
$685$	22.0580	0.842792
$686$	−36.5879	−1.39693
$687$	8.93610	0.340933
$688$	−72.6227	−2.76871
$689$	−32.1111	−1.22334
$690$	15.8725	0.604255
$691$	−10.4792	−0.398648	−0.199324	−	0.979934i	$-0.563875\pi$
$691$	−10.4792	−0.398648	−0.199324	+	0.979934i	$0.563875\pi$
$692$	83.5775	3.17714
$693$	−9.62216	−0.365516
$694$	−75.0090	−2.84730
$695$	3.15299	0.119600
$696$	−7.88198	−0.298766
$697$	−24.9292	−0.944262
$698$	−93.4255	−3.53621
$699$	−8.64475	−0.326975
$700$	14.2916	0.540173
$701$	−29.4400	−1.11193	−0.555967	−	0.831204i	$-0.687652\pi$
$701$	−29.4400	−1.11193	−0.555967	+	0.831204i	$0.687652\pi$
$702$	9.51785	0.359228
$703$	−18.2083	−0.686738
$704$	−12.2398	−0.461304
$705$	3.46745	0.130592
$706$	21.9807	0.827256
$707$	40.5858	1.52639
$708$	21.4078	0.804556
$709$	6.61577	0.248461	0.124230	−	0.992253i	$-0.460354\pi$
$709$	6.61577	0.248461	0.124230	+	0.992253i	$0.460354\pi$
$710$	−28.6950	−1.07690
$711$	3.94578	0.147978
$712$	36.6745	1.37444
$713$	6.22387	0.233086
$714$	−43.3145	−1.62100
$715$	−11.5848	−0.433247
$716$	−57.8465	−2.16183
$717$	−21.2804	−0.794732
$718$	−30.1574	−1.12547
$719$	3.96677	0.147936	0.0739678	−	0.997261i	$-0.476434\pi$
$719$	3.96677	0.147936	0.0739678	+	0.997261i	$0.476434\pi$
$720$	−8.45736	−0.315187
$721$	29.3670	1.09368
$722$	35.9050	1.33625
$723$	21.2859	0.791631
$724$	−65.5401	−2.43578
$725$	1.14385	0.0424814
$726$	2.89419	0.107413
$727$	−46.5259	−1.72555	−0.862775	−	0.505588i	$-0.831275\pi$
$727$	−46.5259	−1.72555	−0.862775	+	0.505588i	$0.831275\pi$
$728$	−77.7508	−2.88164
$729$	1.00000	0.0370370
$730$	−18.4141	−0.681535
$731$	−47.0487	−1.74016
$732$	−42.5856	−1.57401
$733$	−14.9288	−0.551407	−0.275703	−	0.961243i	$-0.588911\pi$
$733$	−14.9288	−0.551407	−0.275703	+	0.961243i	$0.588911\pi$
$734$	23.7655	0.877200
$735$	2.37177	0.0874842
$736$	49.5302	1.82571
$737$	−10.7677	−0.396635
$738$	−11.7492	−0.432496
$739$	−31.0839	−1.14344	−0.571719	−	0.820449i	$-0.693723\pi$
$739$	−31.0839	−1.14344	−0.571719	+	0.820449i	$0.693723\pi$
$740$	14.8189	0.544752
$741$	21.1423	0.776682
$742$	68.8733	2.52842
$743$	16.6681	0.611495	0.305747	−	0.952113i	$-0.401094\pi$
$743$	16.6681	0.611495	0.305747	+	0.952113i	$0.401094\pi$
$744$	−6.97742	−0.255804
$745$	6.05251	0.221747
$746$	−32.1718	−1.17789
$747$	2.72829	0.0998229
$748$	−80.3975	−2.93962
$749$	−10.6673	−0.389774
$750$	2.58233	0.0942934
$751$	−27.8804	−1.01737	−0.508685	−	0.860953i	$-0.669868\pi$
$751$	−27.8804	−1.01737	−0.508685	+	0.860953i	$0.669868\pi$
$752$	29.3255	1.06939
$753$	−14.1341	−0.515074
$754$	−10.8870	−0.396480
$755$	−19.5468	−0.711380
$756$	−14.2916	−0.519781
$757$	−9.23434	−0.335628	−0.167814	−	0.985819i	$-0.553671\pi$
$757$	−9.23434	−0.335628	−0.167814	+	0.985819i	$0.553671\pi$
$758$	−71.1163	−2.58306
$759$	19.3195	0.701252
$760$	−39.5269	−1.43379
$761$	−7.76983	−0.281656	−0.140828	−	0.990034i	$-0.544976\pi$
$761$	−7.76983	−0.281656	−0.140828	+	0.990034i	$0.544976\pi$
$762$	−5.96676	−0.216153
$763$	12.3360	0.446593
$764$	−21.8959	−0.792167
$765$	−5.47911	−0.198098
$766$	−63.2464	−2.28518
$767$	16.9016	0.610283
$768$	23.4382	0.845753
$769$	−39.7691	−1.43411	−0.717055	−	0.697016i	$-0.754510\pi$
$769$	−39.7691	−1.43411	−0.717055	+	0.697016i	$0.754510\pi$
$770$	24.8476	0.895445
$771$	0.941843	0.0339196
$772$	−77.6738	−2.79554
$773$	33.3944	1.20111	0.600556	−	0.799583i	$-0.294946\pi$
$773$	33.3944	1.20111	0.600556	+	0.799583i	$0.294946\pi$
$774$	−22.1743	−0.797037
$775$	1.01258	0.0363728
$776$	−14.1150	−0.506700
$777$	9.71751	0.348614
$778$	59.9504	2.14933
$779$	−26.0990	−0.935093
$780$	−17.2067	−0.616099
$781$	−34.9266	−1.24977
$782$	86.9672	3.10994
$783$	−1.14385	−0.0408778
$784$	20.0590	0.716391
$785$	7.10600	0.253624
$786$	17.6868	0.630867
$787$	−18.6423	−0.664526	−0.332263	−	0.943187i	$-0.607812\pi$
$787$	−18.6423	−0.664526	−0.332263	+	0.943187i	$0.607812\pi$
$788$	−39.1469	−1.39455
$789$	−8.85572	−0.315272
$790$	−10.1893	−0.362519
$791$	−10.1206	−0.359846
$792$	−21.6585	−0.769602
$793$	−33.6216	−1.19394
$794$	−74.9427	−2.65962
$795$	8.71221	0.308990
$796$	48.4834	1.71845
$797$	−17.5135	−0.620361	−0.310181	−	0.950678i	$-0.600389\pi$
$797$	−17.5135	−0.620361	−0.310181	+	0.950678i	$0.600389\pi$
$798$	−45.3469	−1.60526
$799$	18.9986	0.672121
$800$	8.05818	0.284900
$801$	5.32227	0.188053
$802$	2.58233	0.0911852
$803$	−22.4130	−0.790936
$804$	−15.9931	−0.564035
$805$	−18.8167	−0.663203
$806$	−9.63754	−0.339468
$807$	−30.6204	−1.07789
$808$	91.3547	3.21385
$809$	−12.0529	−0.423758	−0.211879	−	0.977296i	$-0.567958\pi$
$809$	−12.0529	−0.423758	−0.211879	+	0.977296i	$0.567958\pi$
$810$	−2.58233	−0.0907338
$811$	−34.4472	−1.20960	−0.604802	−	0.796376i	$-0.706748\pi$
$811$	−34.4472	−1.20960	−0.604802	+	0.796376i	$0.706748\pi$
$812$	16.3474	0.573682
$813$	−3.54423	−0.124301
$814$	25.7642	0.903036
$815$	8.21772	0.287854
$816$	−46.3389	−1.62218
$817$	−49.2564	−1.72326
$818$	−46.3588	−1.62090
$819$	−11.2833	−0.394272
$820$	21.2407	0.741758
$821$	−30.0428	−1.04850	−0.524251	−	0.851564i	$-0.675654\pi$
$821$	−30.0428	−1.04850	−0.524251	+	0.851564i	$0.675654\pi$
$822$	56.9610	1.98674
$823$	5.05995	0.176379	0.0881893	−	0.996104i	$-0.471892\pi$
$823$	5.05995	0.176379	0.0881893	+	0.996104i	$0.471892\pi$
$824$	66.1022	2.30278
$825$	3.14312	0.109430
$826$	−36.2514	−1.26135
$827$	0.718930	0.0249997	0.0124998	−	0.999922i	$-0.496021\pi$
$827$	0.718930	0.0249997	0.0124998	+	0.999922i	$0.496021\pi$
$828$	28.6948	0.997215
$829$	45.5849	1.58323	0.791614	−	0.611022i	$-0.209241\pi$
$829$	45.5849	1.58323	0.791614	+	0.611022i	$0.209241\pi$
$830$	−7.04534	−0.244547
$831$	−26.4148	−0.916319
$832$	−14.3529	−0.497597
$833$	12.9952	0.450258
$834$	8.14206	0.281937
$835$	9.11841	0.315555
$836$	−84.1700	−2.91108
$837$	−1.01258	−0.0349997
$838$	35.3722	1.22191
$839$	−49.6943	−1.71564	−0.857819	−	0.513952i	$-0.828181\pi$
$839$	−49.6943	−1.71564	−0.857819	+	0.513952i	$0.828181\pi$
$840$	21.0949	0.727844
$841$	−27.6916	−0.954883
$842$	−4.38048	−0.150961
$843$	16.8191	0.579282
$844$	6.30193	0.216922
$845$	−0.584826	−0.0201186
$846$	8.95410	0.307848
$847$	−3.43104	−0.117892
$848$	73.6823	2.53026
$849$	6.70571	0.230139
$850$	14.1489	0.485303
$851$	−19.5109	−0.668825
$852$	−51.8758	−1.77724
$853$	8.95422	0.306587	0.153293	−	0.988181i	$-0.451012\pi$
$853$	8.95422	0.306587	0.153293	+	0.988181i	$0.451012\pi$
$854$	72.1132	2.46766
$855$	−5.73621	−0.196174
$856$	−24.0110	−0.820678
$857$	45.6396	1.55902	0.779509	−	0.626390i	$-0.215468\pi$
$857$	45.6396	1.55902	0.779509	+	0.626390i	$0.215468\pi$
$858$	−29.9158	−1.02131
$859$	43.5963	1.48749	0.743744	−	0.668465i	$-0.233048\pi$
$859$	43.5963	1.48749	0.743744	+	0.668465i	$0.233048\pi$
$860$	40.0874	1.36697
$861$	13.9287	0.474687
$862$	35.9117	1.22316
$863$	16.0733	0.547141	0.273570	−	0.961852i	$-0.411795\pi$
$863$	16.0733	0.547141	0.273570	+	0.961852i	$0.411795\pi$
$864$	−8.05818	−0.274145
$865$	−17.9027	−0.608710
$866$	49.7861	1.69180
$867$	−13.0207	−0.442206
$868$	14.4713	0.491190
$869$	−12.4021	−0.420712
$870$	2.95379	0.100143
$871$	−12.6267	−0.427840
$872$	27.7671	0.940312
$873$	−2.04840	−0.0693278
$874$	91.0479	3.07974
$875$	−3.06134	−0.103492
$876$	−33.2896	−1.12475
$877$	54.0206	1.82415	0.912073	−	0.410029i	$-0.134481\pi$
$877$	54.0206	1.82415	0.912073	+	0.410029i	$0.134481\pi$
$878$	−81.3038	−2.74387
$879$	−15.6765	−0.528755
$880$	26.5825	0.896097
$881$	30.2061	1.01767	0.508835	−	0.860864i	$-0.330076\pi$
$881$	30.2061	1.01767	0.508835	+	0.860864i	$0.330076\pi$
$882$	6.12470	0.206230
$883$	12.7219	0.428126	0.214063	−	0.976820i	$-0.431330\pi$
$883$	12.7219	0.428126	0.214063	+	0.976820i	$0.431330\pi$
$884$	−94.2775	−3.17090
$885$	−4.58566	−0.154145
$886$	−80.2537	−2.69618
$887$	−55.8965	−1.87682	−0.938410	−	0.345524i	$-0.887701\pi$
$887$	−55.8965	−1.87682	−0.938410	+	0.345524i	$0.887701\pi$
$888$	21.8731	0.734014
$889$	7.07355	0.237239
$890$	−13.7439	−0.460695
$891$	−3.14312	−0.105299
$892$	106.138	3.55378
$893$	19.8900	0.665594
$894$	15.6296	0.522731
$895$	12.3910	0.414186
$896$	−18.5529	−0.619808
$897$	22.6548	0.756422
$898$	3.27699	0.109355
$899$	1.15823	0.0386292
$900$	4.66843	0.155614
$901$	47.7352	1.59029
$902$	36.9294	1.22961
$903$	26.2874	0.874791
$904$	−22.7804	−0.757664
$905$	14.0390	0.466672
$906$	−50.4762	−1.67696
$907$	−11.8246	−0.392628	−0.196314	−	0.980541i	$-0.562897\pi$
$907$	−11.8246	−0.392628	−0.196314	+	0.980541i	$0.562897\pi$
$908$	18.5457	0.615460
$909$	13.2576	0.439726
$910$	29.1373	0.965893
$911$	−1.81711	−0.0602034	−0.0301017	−	0.999547i	$-0.509583\pi$
$911$	−1.81711	−0.0602034	−0.0301017	+	0.999547i	$0.509583\pi$
$912$	−48.5132	−1.60643
$913$	−8.57535	−0.283803
$914$	24.2395	0.801772
$915$	9.12204	0.301565
$916$	−41.7175	−1.37839
$917$	−20.9676	−0.692411
$918$	−14.1489	−0.466983
$919$	−50.5368	−1.66705	−0.833527	−	0.552478i	$-0.813682\pi$
$919$	−50.5368	−1.66705	−0.833527	+	0.552478i	$0.813682\pi$
$920$	−42.3546	−1.39639
$921$	6.30668	0.207812
$922$	10.9206	0.359650
$923$	−40.9564	−1.34810
$924$	44.9204	1.47777
$925$	−3.17427	−0.104369
$926$	−37.8554	−1.24401
$927$	9.59287	0.315071
$928$	9.21732	0.302573
$929$	13.1932	0.432854	0.216427	−	0.976299i	$-0.430560\pi$
$929$	13.1932	0.432854	0.216427	+	0.976299i	$0.430560\pi$
$930$	2.61480	0.0857428
$931$	13.6050	0.445886
$932$	40.3574	1.32195
$933$	0.607951	0.0199034
$934$	−11.0920	−0.362942
$935$	17.2215	0.563205
$936$	−25.3977	−0.830149
$937$	1.11966	0.0365777	0.0182889	−	0.999833i	$-0.494178\pi$
$937$	1.11966	0.0365777	0.0182889	+	0.999833i	$0.494178\pi$
$938$	27.0823	0.884269
$939$	4.49675	0.146746
$940$	−16.1875	−0.527979
$941$	−37.6674	−1.22792	−0.613961	−	0.789336i	$-0.710425\pi$
$941$	−37.6674	−1.22792	−0.613961	+	0.789336i	$0.710425\pi$
$942$	18.3500	0.597877
$943$	−27.9661	−0.910701
$944$	−38.7826	−1.26227
$945$	3.06134	0.0995852
$946$	69.6965	2.26603
$947$	−30.0752	−0.977312	−0.488656	−	0.872476i	$-0.662513\pi$
$947$	−30.0752	−0.977312	−0.488656	+	0.872476i	$0.662513\pi$
$948$	−18.4206	−0.598273
$949$	−26.2824	−0.853162
$950$	14.8128	0.480590
$951$	6.26481	0.203150
$952$	115.582	3.74602
$953$	7.83602	0.253834	0.126917	−	0.991913i	$-0.459492\pi$
$953$	7.83602	0.253834	0.126917	+	0.991913i	$0.459492\pi$
$954$	22.4978	0.728393
$955$	4.69022	0.151772
$956$	99.3461	3.21308
$957$	3.59525	0.116218
$958$	48.0683	1.55302
$959$	−67.5269	−2.18056
$960$	3.89415	0.125683
$961$	−29.9747	−0.966926
$962$	30.2122	0.974081
$963$	−3.48452	−0.112287
$964$	−99.3717	−3.20055
$965$	16.6381	0.535600
$966$	−48.5910	−1.56339
$967$	2.86255	0.0920535	0.0460267	−	0.998940i	$-0.485344\pi$
$967$	2.86255	0.0920535	0.0460267	+	0.998940i	$0.485344\pi$
$968$	−7.72293	−0.248224
$969$	−31.4294	−1.00966
$970$	5.28964	0.169840
$971$	−56.4996	−1.81316	−0.906579	−	0.422035i	$-0.861316\pi$
$971$	−56.4996	−1.81316	−0.906579	+	0.422035i	$0.861316\pi$
$972$	−4.66843	−0.149740
$973$	−9.65236	−0.309441
$974$	3.78347	0.121230
$975$	3.68576	0.118039
$976$	77.1484	2.46946
$977$	53.1346	1.69993	0.849963	−	0.526842i	$-0.176624\pi$
$977$	53.1346	1.69993	0.849963	+	0.526842i	$0.176624\pi$
$978$	21.2209	0.678569
$979$	−16.7286	−0.534647
$980$	−11.0725	−0.353697
$981$	4.02961	0.128656
$982$	94.0322	3.00069
$983$	−20.6102	−0.657364	−0.328682	−	0.944441i	$-0.606605\pi$
$983$	−20.6102	−0.657364	−0.328682	+	0.944441i	$0.606605\pi$
$984$	31.3520	0.999466
$985$	8.38547	0.267183
$986$	16.1842	0.515409
$987$	−10.6150	−0.337880
$988$	−98.7013	−3.14011
$989$	−52.7802	−1.67831
$990$	8.11659	0.257962
$991$	59.5199	1.89071	0.945356	−	0.326039i	$-0.105714\pi$
$991$	59.5199	1.89071	0.945356	+	0.326039i	$0.105714\pi$
$992$	8.15951	0.259065
$993$	30.2655	0.960447
$994$	87.8450	2.78628
$995$	−10.3854	−0.329239
$996$	−12.7368	−0.403582
$997$	−9.86083	−0.312296	−0.156148	−	0.987734i	$-0.549908\pi$
$997$	−9.86083	−0.312296	−0.156148	+	0.987734i	$0.549908\pi$
$998$	−53.7968	−1.70291
$999$	3.17427	0.100429

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.e.1.30	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.e.1.30	✓	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q+2.58233 q^{2} -1.00000 q^{3} +4.66843 q^{4} -1.00000 q^{5} -2.58233 q^{6} +3.06134 q^{7} +6.89076 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.58233 q^{2} -1.00000 q^{3} +4.66843 q^{4} -1.00000 q^{5} -2.58233 q^{6} +3.06134 q^{7} +6.89076 q^{8} +1.00000 q^{9} -2.58233 q^{10} -3.14312 q^{11} -4.66843 q^{12} -3.68576 q^{13} +7.90538 q^{14} +1.00000 q^{15} +8.45736 q^{16} +5.47911 q^{17} +2.58233 q^{18} +5.73621 q^{19} -4.66843 q^{20} -3.06134 q^{21} -8.11659 q^{22} +6.14658 q^{23} -6.89076 q^{24} +1.00000 q^{25} -9.51785 q^{26} -1.00000 q^{27} +14.2916 q^{28} +1.14385 q^{29} +2.58233 q^{30} +1.01258 q^{31} +8.05818 q^{32} +3.14312 q^{33} +14.1489 q^{34} -3.06134 q^{35} +4.66843 q^{36} -3.17427 q^{37} +14.8128 q^{38} +3.68576 q^{39} -6.89076 q^{40} -4.54986 q^{41} -7.90538 q^{42} -8.58692 q^{43} -14.6735 q^{44} -1.00000 q^{45} +15.8725 q^{46} +3.46745 q^{47} -8.45736 q^{48} +2.37177 q^{49} +2.58233 q^{50} -5.47911 q^{51} -17.2067 q^{52} +8.71221 q^{53} -2.58233 q^{54} +3.14312 q^{55} +21.0949 q^{56} -5.73621 q^{57} +2.95379 q^{58} -4.58566 q^{59} +4.66843 q^{60} +9.12204 q^{61} +2.61480 q^{62} +3.06134 q^{63} +3.89415 q^{64} +3.68576 q^{65} +8.11659 q^{66} +3.42581 q^{67} +25.5789 q^{68} -6.14658 q^{69} -7.90538 q^{70} +11.1121 q^{71} +6.89076 q^{72} +7.13079 q^{73} -8.19701 q^{74} -1.00000 q^{75} +26.7791 q^{76} -9.62216 q^{77} +9.51785 q^{78} +3.94578 q^{79} -8.45736 q^{80} +1.00000 q^{81} -11.7492 q^{82} +2.72829 q^{83} -14.2916 q^{84} -5.47911 q^{85} -22.1743 q^{86} -1.14385 q^{87} -21.6585 q^{88} +5.32227 q^{89} -2.58233 q^{90} -11.2833 q^{91} +28.6948 q^{92} -1.01258 q^{93} +8.95410 q^{94} -5.73621 q^{95} -8.05818 q^{96} -2.04840 q^{97} +6.12470 q^{98} -3.14312 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 6 q^{2} - 31 q^{3} + 24 q^{4} - 31 q^{5} - 6 q^{6} - 4 q^{7} + 15 q^{8} + 31 q^{9}+O(q^{10}) \) 31 * q + 6 * q^2 - 31 * q^3 + 24 * q^4 - 31 * q^5 - 6 * q^6 - 4 * q^7 + 15 * q^8 + 31 * q^9	\( 31 q + 6 q^{2} - 31 q^{3} + 24 q^{4} - 31 q^{5} - 6 q^{6} - 4 q^{7} + 15 q^{8} + 31 q^{9} - 6 q^{10} - q^{11} - 24 q^{12} + 8 q^{13} + 8 q^{14} + 31 q^{15} + 10 q^{16} + 42 q^{17} + 6 q^{18} - 19 q^{19} - 24 q^{20} + 4 q^{21} + 17 q^{22} + 26 q^{23} - 15 q^{24} + 31 q^{25} + 4 q^{26} - 31 q^{27} - 16 q^{28} - 11 q^{29} + 6 q^{30} - 3 q^{31} + 41 q^{32} + q^{33} + 6 q^{34} + 4 q^{35} + 24 q^{36} + 10 q^{37} + 12 q^{38} - 8 q^{39} - 15 q^{40} + 27 q^{41} - 8 q^{42} - 37 q^{43} - 9 q^{44} - 31 q^{45} - 23 q^{46} + 48 q^{47} - 10 q^{48} + 31 q^{49} + 6 q^{50} - 42 q^{51} + 18 q^{52} + 35 q^{53} - 6 q^{54} + q^{55} + 7 q^{56} + 19 q^{57} - 26 q^{58} - 3 q^{59} + 24 q^{60} + 11 q^{61} + 49 q^{62} - 4 q^{63} - 27 q^{64} - 8 q^{65} - 17 q^{66} - 44 q^{67} + 72 q^{68} - 26 q^{69} - 8 q^{70} + 6 q^{71} + 15 q^{72} + 49 q^{73} - 6 q^{74} - 31 q^{75} - 36 q^{76} + 66 q^{77} - 4 q^{78} - 41 q^{79} - 10 q^{80} + 31 q^{81} + 9 q^{82} + 53 q^{83} + 16 q^{84} - 42 q^{85} + 3 q^{86} + 11 q^{87} + 21 q^{88} + 31 q^{89} - 6 q^{90} - 45 q^{91} + 45 q^{92} + 3 q^{93} - 4 q^{94} + 19 q^{95} - 41 q^{96} + 37 q^{97} + 41 q^{98} - q^{99}+O(q^{100}) \) 31 * q + 6 * q^2 - 31 * q^3 + 24 * q^4 - 31 * q^5 - 6 * q^6 - 4 * q^7 + 15 * q^8 + 31 * q^9 - 6 * q^10 - q^11 - 24 * q^12 + 8 * q^13 + 8 * q^14 + 31 * q^15 + 10 * q^16 + 42 * q^17 + 6 * q^18 - 19 * q^19 - 24 * q^20 + 4 * q^21 + 17 * q^22 + 26 * q^23 - 15 * q^24 + 31 * q^25 + 4 * q^26 - 31 * q^27 - 16 * q^28 - 11 * q^29 + 6 * q^30 - 3 * q^31 + 41 * q^32 + q^33 + 6 * q^34 + 4 * q^35 + 24 * q^36 + 10 * q^37 + 12 * q^38 - 8 * q^39 - 15 * q^40 + 27 * q^41 - 8 * q^42 - 37 * q^43 - 9 * q^44 - 31 * q^45 - 23 * q^46 + 48 * q^47 - 10 * q^48 + 31 * q^49 + 6 * q^50 - 42 * q^51 + 18 * q^52 + 35 * q^53 - 6 * q^54 + q^55 + 7 * q^56 + 19 * q^57 - 26 * q^58 - 3 * q^59 + 24 * q^60 + 11 * q^61 + 49 * q^62 - 4 * q^63 - 27 * q^64 - 8 * q^65 - 17 * q^66 - 44 * q^67 + 72 * q^68 - 26 * q^69 - 8 * q^70 + 6 * q^71 + 15 * q^72 + 49 * q^73 - 6 * q^74 - 31 * q^75 - 36 * q^76 + 66 * q^77 - 4 * q^78 - 41 * q^79 - 10 * q^80 + 31 * q^81 + 9 * q^82 + 53 * q^83 + 16 * q^84 - 42 * q^85 + 3 * q^86 + 11 * q^87 + 21 * q^88 + 31 * q^89 - 6 * q^90 - 45 * q^91 + 45 * q^92 + 3 * q^93 - 4 * q^94 + 19 * q^95 - 41 * q^96 + 37 * q^97 + 41 * q^98 - q^99

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