LMFDB - Embedded newform 6015.2.a.f.1.16

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:	$1$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
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)

$f(q)$	$=$	$q-0.823088 q^{2} -1.00000 q^{3} -1.32253 q^{4} -1.00000 q^{5} +0.823088 q^{6} +2.12642 q^{7} +2.73473 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.823088 q^{2} -1.00000 q^{3} -1.32253 q^{4} -1.00000 q^{5} +0.823088 q^{6} +2.12642 q^{7} +2.73473 q^{8} +1.00000 q^{9} +0.823088 q^{10} +5.61912 q^{11} +1.32253 q^{12} -4.36975 q^{13} -1.75023 q^{14} +1.00000 q^{15} +0.394125 q^{16} -0.824615 q^{17} -0.823088 q^{18} -2.24566 q^{19} +1.32253 q^{20} -2.12642 q^{21} -4.62503 q^{22} +5.33491 q^{23} -2.73473 q^{24} +1.00000 q^{25} +3.59669 q^{26} -1.00000 q^{27} -2.81225 q^{28} -4.27540 q^{29} -0.823088 q^{30} +2.01462 q^{31} -5.79386 q^{32} -5.61912 q^{33} +0.678731 q^{34} -2.12642 q^{35} -1.32253 q^{36} -3.56036 q^{37} +1.84838 q^{38} +4.36975 q^{39} -2.73473 q^{40} -2.66841 q^{41} +1.75023 q^{42} -4.77874 q^{43} -7.43143 q^{44} -1.00000 q^{45} -4.39110 q^{46} -10.8470 q^{47} -0.394125 q^{48} -2.47833 q^{49} -0.823088 q^{50} +0.824615 q^{51} +5.77911 q^{52} +9.40727 q^{53} +0.823088 q^{54} -5.61912 q^{55} +5.81520 q^{56} +2.24566 q^{57} +3.51903 q^{58} -4.59276 q^{59} -1.32253 q^{60} +6.24330 q^{61} -1.65821 q^{62} +2.12642 q^{63} +3.98061 q^{64} +4.36975 q^{65} +4.62503 q^{66} -1.57496 q^{67} +1.09057 q^{68} -5.33491 q^{69} +1.75023 q^{70} +9.49758 q^{71} +2.73473 q^{72} -10.0459 q^{73} +2.93049 q^{74} -1.00000 q^{75} +2.96995 q^{76} +11.9486 q^{77} -3.59669 q^{78} -6.16131 q^{79} -0.394125 q^{80} +1.00000 q^{81} +2.19633 q^{82} +0.220150 q^{83} +2.81225 q^{84} +0.824615 q^{85} +3.93332 q^{86} +4.27540 q^{87} +15.3668 q^{88} +11.0229 q^{89} +0.823088 q^{90} -9.29194 q^{91} -7.05555 q^{92} -2.01462 q^{93} +8.92804 q^{94} +2.24566 q^{95} +5.79386 q^{96} -4.83238 q^{97} +2.03988 q^{98} +5.61912 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 7 q^{2} - 36 q^{3} + 45 q^{4} - 36 q^{5} + 7 q^{6} + 2 q^{7} - 24 q^{8} + 36 q^{9}+O(q^{10}) $ 36 * q - 7 * q^2 - 36 * q^3 + 45 * q^4 - 36 * q^5 + 7 * q^6 + 2 * q^7 - 24 * q^8 + 36 * q^9	\( 36 q - 7 q^{2} - 36 q^{3} + 45 q^{4} - 36 q^{5} + 7 q^{6} + 2 q^{7} - 24 q^{8} + 36 q^{9} + 7 q^{10} - q^{11} - 45 q^{12} - 8 q^{13} - 4 q^{14} + 36 q^{15} + 63 q^{16} - 50 q^{17} - 7 q^{18} + 15 q^{19} - 45 q^{20} - 2 q^{21} + 7 q^{22} - 32 q^{23} + 24 q^{24} + 36 q^{25} - 12 q^{26} - 36 q^{27} - 10 q^{28} + 7 q^{29} - 7 q^{30} + 7 q^{31} - 50 q^{32} + q^{33} + 8 q^{34} - 2 q^{35} + 45 q^{36} - 10 q^{37} - 48 q^{38} + 8 q^{39} + 24 q^{40} - 31 q^{41} + 4 q^{42} + 27 q^{43} - 9 q^{44} - 36 q^{45} + 23 q^{46} - 46 q^{47} - 63 q^{48} + 48 q^{49} - 7 q^{50} + 50 q^{51} - 14 q^{52} - 39 q^{53} + 7 q^{54} + q^{55} - 29 q^{56} - 15 q^{57} - 26 q^{58} - 9 q^{59} + 45 q^{60} + 5 q^{61} - 65 q^{62} + 2 q^{63} + 90 q^{64} + 8 q^{65} - 7 q^{66} + 18 q^{67} - 128 q^{68} + 32 q^{69} + 4 q^{70} + 4 q^{71} - 24 q^{72} - 45 q^{73} - 22 q^{74} - 36 q^{75} + 26 q^{76} - 38 q^{77} + 12 q^{78} + 25 q^{79} - 63 q^{80} + 36 q^{81} - 5 q^{82} - 71 q^{83} + 10 q^{84} + 50 q^{85} + 3 q^{86} - 7 q^{87} - 9 q^{88} - 39 q^{89} + 7 q^{90} + 19 q^{91} - 95 q^{92} - 7 q^{93} + 16 q^{94} - 15 q^{95} + 50 q^{96} - 61 q^{97} - 76 q^{98} - q^{99}+O(q^{100}) \) 36 * q - 7 * q^2 - 36 * q^3 + 45 * q^4 - 36 * q^5 + 7 * q^6 + 2 * q^7 - 24 * q^8 + 36 * q^9 + 7 * q^10 - q^11 - 45 * q^12 - 8 * q^13 - 4 * q^14 + 36 * q^15 + 63 * q^16 - 50 * q^17 - 7 * q^18 + 15 * q^19 - 45 * q^20 - 2 * q^21 + 7 * q^22 - 32 * q^23 + 24 * q^24 + 36 * q^25 - 12 * q^26 - 36 * q^27 - 10 * q^28 + 7 * q^29 - 7 * q^30 + 7 * q^31 - 50 * q^32 + q^33 + 8 * q^34 - 2 * q^35 + 45 * q^36 - 10 * q^37 - 48 * q^38 + 8 * q^39 + 24 * q^40 - 31 * q^41 + 4 * q^42 + 27 * q^43 - 9 * q^44 - 36 * q^45 + 23 * q^46 - 46 * q^47 - 63 * q^48 + 48 * q^49 - 7 * q^50 + 50 * q^51 - 14 * q^52 - 39 * q^53 + 7 * q^54 + q^55 - 29 * q^56 - 15 * q^57 - 26 * q^58 - 9 * q^59 + 45 * q^60 + 5 * q^61 - 65 * q^62 + 2 * q^63 + 90 * q^64 + 8 * q^65 - 7 * q^66 + 18 * q^67 - 128 * q^68 + 32 * q^69 + 4 * q^70 + 4 * q^71 - 24 * q^72 - 45 * q^73 - 22 * q^74 - 36 * q^75 + 26 * q^76 - 38 * q^77 + 12 * q^78 + 25 * q^79 - 63 * q^80 + 36 * q^81 - 5 * q^82 - 71 * q^83 + 10 * q^84 + 50 * q^85 + 3 * q^86 - 7 * q^87 - 9 * q^88 - 39 * q^89 + 7 * q^90 + 19 * q^91 - 95 * q^92 - 7 * q^93 + 16 * q^94 - 15 * q^95 + 50 * q^96 - 61 * q^97 - 76 * 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 $

$2$	−0.823088	−0.582011	−0.291006	−	0.956721i	$-0.593990\pi$
$2$	−0.823088	−0.582011	−0.291006	+	0.956721i	$0.593990\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.32253	−0.661263
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.823088	0.336024
$7$	2.12642	0.803712	0.401856	−	0.915703i	$-0.368365\pi$
$7$	2.12642	0.803712	0.401856	+	0.915703i	$0.368365\pi$
$8$	2.73473	0.966874
$9$	1.00000	0.333333
$10$	0.823088	0.260283
$11$	5.61912	1.69423	0.847114	−	0.531411i	$-0.178338\pi$
$11$	5.61912	1.69423	0.847114	+	0.531411i	$0.178338\pi$
$12$	1.32253	0.381780
$13$	−4.36975	−1.21195	−0.605975	−	0.795483i	$-0.707217\pi$
$13$	−4.36975	−1.21195	−0.605975	+	0.795483i	$0.707217\pi$
$14$	−1.75023	−0.467770
$15$	1.00000	0.258199
$16$	0.394125	0.0985314
$17$	−0.824615	−0.199998	−0.0999992	−	0.994988i	$-0.531884\pi$
$17$	−0.824615	−0.199998	−0.0999992	+	0.994988i	$0.531884\pi$
$18$	−0.823088	−0.194004
$19$	−2.24566	−0.515190	−0.257595	−	0.966253i	$-0.582930\pi$
$19$	−2.24566	−0.515190	−0.257595	+	0.966253i	$0.582930\pi$
$20$	1.32253	0.295726
$21$	−2.12642	−0.464023
$22$	−4.62503	−0.986060
$23$	5.33491	1.11241	0.556203	−	0.831047i	$-0.312258\pi$
$23$	5.33491	1.11241	0.556203	+	0.831047i	$0.312258\pi$
$24$	−2.73473	−0.558225
$25$	1.00000	0.200000
$26$	3.59669	0.705369
$27$	−1.00000	−0.192450
$28$	−2.81225	−0.531465
$29$	−4.27540	−0.793921	−0.396961	−	0.917836i	$-0.629935\pi$
$29$	−4.27540	−0.793921	−0.396961	+	0.917836i	$0.629935\pi$
$30$	−0.823088	−0.150275
$31$	2.01462	0.361837	0.180918	−	0.983498i	$-0.442093\pi$
$31$	2.01462	0.361837	0.180918	+	0.983498i	$0.442093\pi$
$32$	−5.79386	−1.02422
$33$	−5.61912	−0.978163
$34$	0.678731	0.116401
$35$	−2.12642	−0.359431
$36$	−1.32253	−0.220421
$37$	−3.56036	−0.585319	−0.292660	−	0.956217i	$-0.594540\pi$
$37$	−3.56036	−0.585319	−0.292660	+	0.956217i	$0.594540\pi$
$38$	1.84838	0.299847
$39$	4.36975	0.699720
$40$	−2.73473	−0.432399
$41$	−2.66841	−0.416735	−0.208368	−	0.978051i	$-0.566815\pi$
$41$	−2.66841	−0.416735	−0.208368	+	0.978051i	$0.566815\pi$
$42$	1.75023	0.270067
$43$	−4.77874	−0.728751	−0.364375	−	0.931252i	$-0.618718\pi$
$43$	−4.77874	−0.728751	−0.364375	+	0.931252i	$0.618718\pi$
$44$	−7.43143	−1.12033
$45$	−1.00000	−0.149071
$46$	−4.39110	−0.647433
$47$	−10.8470	−1.58220	−0.791099	−	0.611688i	$-0.790491\pi$
$47$	−10.8470	−1.58220	−0.791099	+	0.611688i	$0.790491\pi$
$48$	−0.394125	−0.0568871
$49$	−2.47833	−0.354047
$50$	−0.823088	−0.116402
$51$	0.824615	0.115469
$52$	5.77911	0.801418
$53$	9.40727	1.29219	0.646094	−	0.763258i	$-0.276401\pi$
$53$	9.40727	1.29219	0.646094	+	0.763258i	$0.276401\pi$
$54$	0.823088	0.112008
$55$	−5.61912	−0.757682
$56$	5.81520	0.777088
$57$	2.24566	0.297445
$58$	3.51903	0.462071
$59$	−4.59276	−0.597926	−0.298963	−	0.954265i	$-0.596641\pi$
$59$	−4.59276	−0.597926	−0.298963	+	0.954265i	$0.596641\pi$
$60$	−1.32253	−0.170737
$61$	6.24330	0.799373	0.399687	−	0.916652i	$-0.369119\pi$
$61$	6.24330	0.799373	0.399687	+	0.916652i	$0.369119\pi$
$62$	−1.65821	−0.210593
$63$	2.12642	0.267904
$64$	3.98061	0.497576
$65$	4.36975	0.542001
$66$	4.62503	0.569302
$67$	−1.57496	−0.192413	−0.0962063	−	0.995361i	$-0.530671\pi$
$67$	−1.57496	−0.192413	−0.0962063	+	0.995361i	$0.530671\pi$
$68$	1.09057	0.132252
$69$	−5.33491	−0.642248
$70$	1.75023	0.209193
$71$	9.49758	1.12716	0.563578	−	0.826063i	$-0.309424\pi$
$71$	9.49758	1.12716	0.563578	+	0.826063i	$0.309424\pi$
$72$	2.73473	0.322291
$73$	−10.0459	−1.17578	−0.587891	−	0.808941i	$-0.700041\pi$
$73$	−10.0459	−1.17578	−0.587891	+	0.808941i	$0.700041\pi$
$74$	2.93049	0.340662
$75$	−1.00000	−0.115470
$76$	2.96995	0.340676
$77$	11.9486	1.36167
$78$	−3.59669	−0.407245
$79$	−6.16131	−0.693201	−0.346601	−	0.938013i	$-0.612664\pi$
$79$	−6.16131	−0.693201	−0.346601	+	0.938013i	$0.612664\pi$
$80$	−0.394125	−0.0440646
$81$	1.00000	0.111111
$82$	2.19633	0.242545
$83$	0.220150	0.0241646	0.0120823	−	0.999927i	$-0.496154\pi$
$83$	0.220150	0.0241646	0.0120823	+	0.999927i	$0.496154\pi$
$84$	2.81225	0.306841
$85$	0.824615	0.0894420
$86$	3.93332	0.424141
$87$	4.27540	0.458371
$88$	15.3668	1.63810
$89$	11.0229	1.16843	0.584215	−	0.811599i	$-0.301402\pi$
$89$	11.0229	1.16843	0.584215	+	0.811599i	$0.301402\pi$
$90$	0.823088	0.0867611
$91$	−9.29194	−0.974060
$92$	−7.05555	−0.735592
$93$	−2.01462	−0.208907
$94$	8.92804	0.920857
$95$	2.24566	0.230400
$96$	5.79386	0.591334
$97$	−4.83238	−0.490654	−0.245327	−	0.969440i	$-0.578895\pi$
$97$	−4.83238	−0.490654	−0.245327	+	0.969440i	$0.578895\pi$
$98$	2.03988	0.206059
$99$	5.61912	0.564743
$100$	−1.32253	−0.132253
$101$	−5.19043	−0.516467	−0.258233	−	0.966083i	$-0.583140\pi$
$101$	−5.19043	−0.516467	−0.258233	+	0.966083i	$0.583140\pi$
$102$	−0.678731	−0.0672043
$103$	3.57367	0.352124	0.176062	−	0.984379i	$-0.443664\pi$
$103$	3.57367	0.352124	0.176062	+	0.984379i	$0.443664\pi$
$104$	−11.9501	−1.17180
$105$	2.12642	0.207518
$106$	−7.74301	−0.752068
$107$	−9.84230	−0.951491	−0.475745	−	0.879583i	$-0.657822\pi$
$107$	−9.84230	−0.951491	−0.475745	+	0.879583i	$0.657822\pi$
$108$	1.32253	0.127260
$109$	8.05857	0.771871	0.385936	−	0.922526i	$-0.373879\pi$
$109$	8.05857	0.771871	0.385936	+	0.922526i	$0.373879\pi$
$110$	4.62503	0.440979
$111$	3.56036	0.337934
$112$	0.838077	0.0791909
$113$	6.09565	0.573431	0.286715	−	0.958016i	$-0.407437\pi$
$113$	6.09565	0.573431	0.286715	+	0.958016i	$0.407437\pi$
$114$	−1.84838	−0.173116
$115$	−5.33491	−0.497483
$116$	5.65432	0.524990
$117$	−4.36975	−0.403984
$118$	3.78025	0.348000
$119$	−1.75348	−0.160741
$120$	2.73473	0.249646
$121$	20.5745	1.87041
$122$	−5.13879	−0.465244
$123$	2.66841	0.240602
$124$	−2.66439	−0.239269
$125$	−1.00000	−0.0894427
$126$	−1.75023	−0.155923
$127$	4.58276	0.406654	0.203327	−	0.979111i	$-0.434824\pi$
$127$	4.58276	0.406654	0.203327	+	0.979111i	$0.434824\pi$
$128$	8.31133	0.734625
$129$	4.77874	0.420745
$130$	−3.59669	−0.315451
$131$	12.1713	1.06341	0.531704	−	0.846930i	$-0.321552\pi$
$131$	12.1713	1.06341	0.531704	+	0.846930i	$0.321552\pi$
$132$	7.43143	0.646823
$133$	−4.77523	−0.414065
$134$	1.29634	0.111986
$135$	1.00000	0.0860663
$136$	−2.25510	−0.193373
$137$	−14.9123	−1.27404	−0.637021	−	0.770847i	$-0.719833\pi$
$137$	−14.9123	−1.27404	−0.637021	+	0.770847i	$0.719833\pi$
$138$	4.39110	0.373795
$139$	−16.3041	−1.38289	−0.691446	−	0.722428i	$-0.743026\pi$
$139$	−16.3041	−1.38289	−0.691446	+	0.722428i	$0.743026\pi$
$140$	2.81225	0.237678
$141$	10.8470	0.913483
$142$	−7.81735	−0.656017
$143$	−24.5541	−2.05332
$144$	0.394125	0.0328438
$145$	4.27540	0.355052
$146$	8.26864	0.684318
$147$	2.47833	0.204409
$148$	4.70866	0.387050
$149$	−2.17568	−0.178239	−0.0891193	−	0.996021i	$-0.528405\pi$
$149$	−2.17568	−0.178239	−0.0891193	+	0.996021i	$0.528405\pi$
$150$	0.823088	0.0672049
$151$	−21.8986	−1.78208	−0.891041	−	0.453923i	$-0.850024\pi$
$151$	−21.8986	−1.78208	−0.891041	+	0.453923i	$0.850024\pi$
$152$	−6.14128	−0.498124
$153$	−0.824615	−0.0666661
$154$	−9.83477	−0.792508
$155$	−2.01462	−0.161818
$156$	−5.77911	−0.462699
$157$	22.1903	1.77098	0.885491	−	0.464657i	$-0.153822\pi$
$157$	22.1903	1.77098	0.885491	+	0.464657i	$0.153822\pi$
$158$	5.07130	0.403451
$159$	−9.40727	−0.746045
$160$	5.79386	0.458045
$161$	11.3443	0.894054
$162$	−0.823088	−0.0646679
$163$	20.4243	1.59976	0.799879	−	0.600162i	$-0.204897\pi$
$163$	20.4243	1.59976	0.799879	+	0.600162i	$0.204897\pi$
$164$	3.52904	0.275572
$165$	5.61912	0.437448
$166$	−0.181203	−0.0140641
$167$	−14.6440	−1.13319	−0.566595	−	0.823997i	$-0.691739\pi$
$167$	−14.6440	−1.13319	−0.566595	+	0.823997i	$0.691739\pi$
$168$	−5.81520	−0.448652
$169$	6.09472	0.468825
$170$	−0.678731	−0.0520563
$171$	−2.24566	−0.171730
$172$	6.32001	0.481896
$173$	−2.18596	−0.166196	−0.0830978	−	0.996541i	$-0.526481\pi$
$173$	−2.18596	−0.166196	−0.0830978	+	0.996541i	$0.526481\pi$
$174$	−3.51903	−0.266777
$175$	2.12642	0.160742
$176$	2.21464	0.166935
$177$	4.59276	0.345213
$178$	−9.07286	−0.680039
$179$	−1.27627	−0.0953932	−0.0476966	−	0.998862i	$-0.515188\pi$
$179$	−1.27627	−0.0953932	−0.0476966	+	0.998862i	$0.515188\pi$
$180$	1.32253	0.0985752
$181$	−4.69881	−0.349260	−0.174630	−	0.984634i	$-0.555873\pi$
$181$	−4.69881	−0.349260	−0.174630	+	0.984634i	$0.555873\pi$
$182$	7.64808	0.566914
$183$	−6.24330	−0.461518
$184$	14.5895	1.07556
$185$	3.56036	0.261763
$186$	1.65821	0.121586
$187$	−4.63361	−0.338843
$188$	14.3454	1.04625
$189$	−2.12642	−0.154674
$190$	−1.84838	−0.134095
$191$	−7.05829	−0.510720	−0.255360	−	0.966846i	$-0.582194\pi$
$191$	−7.05829	−0.510720	−0.255360	+	0.966846i	$0.582194\pi$
$192$	−3.98061	−0.287276
$193$	19.8016	1.42535	0.712676	−	0.701493i	$-0.247483\pi$
$193$	19.8016	1.42535	0.712676	+	0.701493i	$0.247483\pi$
$194$	3.97748	0.285566
$195$	−4.36975	−0.312924
$196$	3.27765	0.234118
$197$	−1.54881	−0.110348	−0.0551742	−	0.998477i	$-0.517571\pi$
$197$	−1.54881	−0.110348	−0.0551742	+	0.998477i	$0.517571\pi$
$198$	−4.62503	−0.328687
$199$	14.0551	0.996338	0.498169	−	0.867080i	$-0.334006\pi$
$199$	14.0551	0.996338	0.498169	+	0.867080i	$0.334006\pi$
$200$	2.73473	0.193375
$201$	1.57496	0.111089
$202$	4.27218	0.300590
$203$	−9.09130	−0.638084
$204$	−1.09057	−0.0763554
$205$	2.66841	0.186370
$206$	−2.94144	−0.204940
$207$	5.33491	0.370802
$208$	−1.72223	−0.119415
$209$	−12.6186	−0.872850
$210$	−1.75023	−0.120778
$211$	19.1926	1.32128	0.660638	−	0.750705i	$-0.270286\pi$
$211$	19.1926	1.32128	0.660638	+	0.750705i	$0.270286\pi$
$212$	−12.4414	−0.854476
$213$	−9.49758	−0.650764
$214$	8.10108	0.553778
$215$	4.77874	0.325907
$216$	−2.73473	−0.186075
$217$	4.28394	0.290813
$218$	−6.63291	−0.449238
$219$	10.0459	0.678838
$220$	7.43143	0.501027
$221$	3.60336	0.242388
$222$	−2.93049	−0.196681
$223$	−18.5188	−1.24011	−0.620054	−	0.784559i	$-0.712889\pi$
$223$	−18.5188	−1.24011	−0.620054	+	0.784559i	$0.712889\pi$
$224$	−12.3202	−0.823178
$225$	1.00000	0.0666667
$226$	−5.01726	−0.333743
$227$	−21.0154	−1.39484	−0.697421	−	0.716662i	$-0.745669\pi$
$227$	−21.0154	−1.39484	−0.697421	+	0.716662i	$0.745669\pi$
$228$	−2.96995	−0.196689
$229$	22.9011	1.51335	0.756674	−	0.653793i	$-0.226823\pi$
$229$	22.9011	1.51335	0.756674	+	0.653793i	$0.226823\pi$
$230$	4.39110	0.289541
$231$	−11.9486	−0.786161
$232$	−11.6921	−0.767621
$233$	27.0186	1.77005	0.885024	−	0.465545i	$-0.154142\pi$
$233$	27.0186	1.77005	0.885024	+	0.465545i	$0.154142\pi$
$234$	3.59669	0.235123
$235$	10.8470	0.707581
$236$	6.07404	0.395386
$237$	6.16131	0.400220
$238$	1.44327	0.0935532
$239$	−25.4430	−1.64577	−0.822886	−	0.568206i	$-0.807638\pi$
$239$	−25.4430	−1.64577	−0.822886	+	0.568206i	$0.807638\pi$
$240$	0.394125	0.0254407
$241$	−11.7215	−0.755049	−0.377524	−	0.926000i	$-0.623225\pi$
$241$	−11.7215	−0.755049	−0.377524	+	0.926000i	$0.623225\pi$
$242$	−16.9346	−1.08860
$243$	−1.00000	−0.0641500
$244$	−8.25693	−0.528596
$245$	2.47833	0.158335
$246$	−2.19633	−0.140033
$247$	9.81298	0.624385
$248$	5.50945	0.349851
$249$	−0.220150	−0.0139514
$250$	0.823088	0.0520567
$251$	−14.0198	−0.884920	−0.442460	−	0.896788i	$-0.645894\pi$
$251$	−14.0198	−0.884920	−0.442460	+	0.896788i	$0.645894\pi$
$252$	−2.81225	−0.177155
$253$	29.9775	1.88467
$254$	−3.77202	−0.236677
$255$	−0.824615	−0.0516394
$256$	−14.8022	−0.925136
$257$	−26.5404	−1.65554	−0.827771	−	0.561066i	$-0.810391\pi$
$257$	−26.5404	−1.65554	−0.827771	+	0.561066i	$0.810391\pi$
$258$	−3.93332	−0.244878
$259$	−7.57082	−0.470428
$260$	−5.77911	−0.358405
$261$	−4.27540	−0.264640
$262$	−10.0180	−0.618915
$263$	−4.87462	−0.300582	−0.150291	−	0.988642i	$-0.548021\pi$
$263$	−4.87462	−0.300582	−0.150291	+	0.988642i	$0.548021\pi$
$264$	−15.3668	−0.945760
$265$	−9.40727	−0.577884
$266$	3.93043	0.240990
$267$	−11.0229	−0.674593
$268$	2.08293	0.127235
$269$	8.44099	0.514656	0.257328	−	0.966324i	$-0.417158\pi$
$269$	8.44099	0.514656	0.257328	+	0.966324i	$0.417158\pi$
$270$	−0.823088	−0.0500916
$271$	14.1005	0.856543	0.428272	−	0.903650i	$-0.359123\pi$
$271$	14.1005	0.856543	0.428272	+	0.903650i	$0.359123\pi$
$272$	−0.325002	−0.0197061
$273$	9.29194	0.562374
$274$	12.2741	0.741506
$275$	5.61912	0.338846
$276$	7.05555	0.424695
$277$	−22.5912	−1.35738	−0.678688	−	0.734427i	$-0.737451\pi$
$277$	−22.5912	−1.35738	−0.678688	+	0.734427i	$0.737451\pi$
$278$	13.4197	0.804859
$279$	2.01462	0.120612
$280$	−5.81520	−0.347524
$281$	−16.3543	−0.975618	−0.487809	−	0.872950i	$-0.662204\pi$
$281$	−16.3543	−0.975618	−0.487809	+	0.872950i	$0.662204\pi$
$282$	−8.92804	−0.531657
$283$	−3.57092	−0.212269	−0.106135	−	0.994352i	$-0.533847\pi$
$283$	−3.57092	−0.212269	−0.106135	+	0.994352i	$0.533847\pi$
$284$	−12.5608	−0.745346
$285$	−2.24566	−0.133022
$286$	20.2102	1.19506
$287$	−5.67416	−0.334935
$288$	−5.79386	−0.341407
$289$	−16.3200	−0.960001
$290$	−3.51903	−0.206644
$291$	4.83238	0.283279
$292$	13.2859	0.777500
$293$	−6.53099	−0.381545	−0.190772	−	0.981634i	$-0.561099\pi$
$293$	−6.53099	−0.381545	−0.190772	+	0.981634i	$0.561099\pi$
$294$	−2.03988	−0.118968
$295$	4.59276	0.267401
$296$	−9.73662	−0.565930
$297$	−5.61912	−0.326054
$298$	1.79078	0.103737
$299$	−23.3122	−1.34818
$300$	1.32253	0.0763561
$301$	−10.1616	−0.585706
$302$	18.0245	1.03719
$303$	5.19043	0.298182
$304$	−0.885073	−0.0507624
$305$	−6.24330	−0.357491
$306$	0.678731	0.0388004
$307$	25.9756	1.48251	0.741253	−	0.671226i	$-0.234232\pi$
$307$	25.9756	1.48251	0.741253	+	0.671226i	$0.234232\pi$
$308$	−15.8024	−0.900423
$309$	−3.57367	−0.203299
$310$	1.65821	0.0941801
$311$	−21.8580	−1.23945	−0.619726	−	0.784818i	$-0.712756\pi$
$311$	−21.8580	−1.23945	−0.619726	+	0.784818i	$0.712756\pi$
$312$	11.9501	0.676541
$313$	−30.9619	−1.75007	−0.875035	−	0.484060i	$-0.839162\pi$
$313$	−30.9619	−1.75007	−0.875035	+	0.484060i	$0.839162\pi$
$314$	−18.2646	−1.03073
$315$	−2.12642	−0.119810
$316$	8.14849	0.458388
$317$	−15.0637	−0.846064	−0.423032	−	0.906115i	$-0.639034\pi$
$317$	−15.0637	−0.846064	−0.423032	+	0.906115i	$0.639034\pi$
$318$	7.74301	0.434207
$319$	−24.0240	−1.34508
$320$	−3.98061	−0.222523
$321$	9.84230	0.549344
$322$	−9.33734	−0.520349
$323$	1.85181	0.103037
$324$	−1.32253	−0.0734736
$325$	−4.36975	−0.242390
$326$	−16.8110	−0.931077
$327$	−8.05857	−0.445640
$328$	−7.29738	−0.402930
$329$	−23.0653	−1.27163
$330$	−4.62503	−0.254600
$331$	23.6553	1.30021	0.650105	−	0.759844i	$-0.274725\pi$
$331$	23.6553	1.30021	0.650105	+	0.759844i	$0.274725\pi$
$332$	−0.291154	−0.0159791
$333$	−3.56036	−0.195106
$334$	12.0533	0.659529
$335$	1.57496	0.0860495
$336$	−0.838077	−0.0457209
$337$	−34.2363	−1.86497	−0.932486	−	0.361207i	$-0.882365\pi$
$337$	−34.2363	−1.86497	−0.932486	+	0.361207i	$0.882365\pi$
$338$	−5.01649	−0.272861
$339$	−6.09565	−0.331070
$340$	−1.09057	−0.0591447
$341$	11.3204	0.613034
$342$	1.84838	0.0999488
$343$	−20.1549	−1.08826
$344$	−13.0686	−0.704610
$345$	5.33491	0.287222
$346$	1.79924	0.0967277
$347$	27.9473	1.50029	0.750144	−	0.661274i	$-0.229984\pi$
$347$	27.9473	1.50029	0.750144	+	0.661274i	$0.229984\pi$
$348$	−5.65432	−0.303103
$349$	10.9490	0.586084	0.293042	−	0.956100i	$-0.405332\pi$
$349$	10.9490	0.586084	0.293042	+	0.956100i	$0.405332\pi$
$350$	−1.75023	−0.0935539
$351$	4.36975	0.233240
$352$	−32.5564	−1.73526
$353$	−4.17323	−0.222118	−0.111059	−	0.993814i	$-0.535424\pi$
$353$	−4.17323	−0.222118	−0.111059	+	0.993814i	$0.535424\pi$
$354$	−3.78025	−0.200918
$355$	−9.49758	−0.504079
$356$	−14.5781	−0.772639
$357$	1.75348	0.0928039
$358$	1.05049	0.0555199
$359$	5.58894	0.294973	0.147486	−	0.989064i	$-0.452882\pi$
$359$	5.58894	0.294973	0.147486	+	0.989064i	$0.452882\pi$
$360$	−2.73473	−0.144133
$361$	−13.9570	−0.734579
$362$	3.86753	0.203273
$363$	−20.5745	−1.07988
$364$	12.2888	0.644109
$365$	10.0459	0.525825
$366$	5.13879	0.268609
$367$	−16.1132	−0.841102	−0.420551	−	0.907269i	$-0.638163\pi$
$367$	−16.1132	−0.841102	−0.420551	+	0.907269i	$0.638163\pi$
$368$	2.10262	0.109607
$369$	−2.66841	−0.138912
$370$	−2.93049	−0.152349
$371$	20.0038	1.03855
$372$	2.66439	0.138142
$373$	−15.9201	−0.824309	−0.412155	−	0.911114i	$-0.635224\pi$
$373$	−15.9201	−0.824309	−0.412155	+	0.911114i	$0.635224\pi$
$374$	3.81387	0.197210
$375$	1.00000	0.0516398
$376$	−29.6637	−1.52979
$377$	18.6824	0.962193
$378$	1.75023	0.0900223
$379$	−28.3755	−1.45755	−0.728775	−	0.684753i	$-0.759910\pi$
$379$	−28.3755	−1.45755	−0.728775	+	0.684753i	$0.759910\pi$
$380$	−2.96995	−0.152355
$381$	−4.58276	−0.234782
$382$	5.80960	0.297245
$383$	−35.7476	−1.82662	−0.913309	−	0.407267i	$-0.866482\pi$
$383$	−35.7476	−1.82662	−0.913309	+	0.407267i	$0.866482\pi$
$384$	−8.31133	−0.424136
$385$	−11.9486	−0.608958
$386$	−16.2985	−0.829571
$387$	−4.77874	−0.242917
$388$	6.39095	0.324451
$389$	−4.99316	−0.253163	−0.126582	−	0.991956i	$-0.540401\pi$
$389$	−4.99316	−0.253163	−0.126582	+	0.991956i	$0.540401\pi$
$390$	3.59669	0.182126
$391$	−4.39924	−0.222479
$392$	−6.77756	−0.342319
$393$	−12.1713	−0.613959
$394$	1.27481	0.0642240
$395$	6.16131	0.310009
$396$	−7.43143	−0.373443
$397$	20.2498	1.01631	0.508154	−	0.861266i	$-0.330328\pi$
$397$	20.2498	1.01631	0.508154	+	0.861266i	$0.330328\pi$
$398$	−11.5686	−0.579880
$399$	4.77523	0.239060
$400$	0.394125	0.0197063
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	−1.29634	−0.0646553
$403$	−8.80340	−0.438529
$404$	6.86447	0.341520
$405$	−1.00000	−0.0496904
$406$	7.48294	0.371372
$407$	−20.0061	−0.991664
$408$	2.25510	0.111644
$409$	20.1180	0.994770	0.497385	−	0.867530i	$-0.334294\pi$
$409$	20.1180	0.994770	0.497385	+	0.867530i	$0.334294\pi$
$410$	−2.19633	−0.108469
$411$	14.9123	0.735568
$412$	−4.72626	−0.232846
$413$	−9.76614	−0.480561
$414$	−4.39110	−0.215811
$415$	−0.220150	−0.0108067
$416$	25.3177	1.24130
$417$	16.3041	0.798413
$418$	10.3863	0.508008
$419$	18.8651	0.921619	0.460809	−	0.887499i	$-0.347559\pi$
$419$	18.8651	0.921619	0.460809	+	0.887499i	$0.347559\pi$
$420$	−2.81225	−0.137224
$421$	27.0044	1.31611	0.658057	−	0.752968i	$-0.271379\pi$
$421$	27.0044	1.31611	0.658057	+	0.752968i	$0.271379\pi$
$422$	−15.7972	−0.768997
$423$	−10.8470	−0.527399
$424$	25.7264	1.24938
$425$	−0.824615	−0.0399997
$426$	7.81735	0.378752
$427$	13.2759	0.642466
$428$	13.0167	0.629186
$429$	24.5541	1.18549
$430$	−3.93332	−0.189682
$431$	−8.04688	−0.387605	−0.193802	−	0.981041i	$-0.562082\pi$
$431$	−8.04688	−0.387605	−0.193802	+	0.981041i	$0.562082\pi$
$432$	−0.394125	−0.0189624
$433$	19.7306	0.948194	0.474097	−	0.880473i	$-0.342775\pi$
$433$	19.7306	0.948194	0.474097	+	0.880473i	$0.342775\pi$
$434$	−3.52606	−0.169256
$435$	−4.27540	−0.204990
$436$	−10.6577	−0.510410
$437$	−11.9804	−0.573100
$438$	−8.26864	−0.395091
$439$	−19.5849	−0.934735	−0.467367	−	0.884063i	$-0.654797\pi$
$439$	−19.5849	−0.934735	−0.467367	+	0.884063i	$0.654797\pi$
$440$	−15.3668	−0.732583
$441$	−2.47833	−0.118016
$442$	−2.96588	−0.141073
$443$	−18.6256	−0.884928	−0.442464	−	0.896786i	$-0.645896\pi$
$443$	−18.6256	−0.884928	−0.442464	+	0.896786i	$0.645896\pi$
$444$	−4.70866	−0.223463
$445$	−11.0229	−0.522538
$446$	15.2426	0.721757
$447$	2.17568	0.102906
$448$	8.46446	0.399908
$449$	6.49010	0.306287	0.153143	−	0.988204i	$-0.451060\pi$
$449$	6.49010	0.306287	0.153143	+	0.988204i	$0.451060\pi$
$450$	−0.823088	−0.0388008
$451$	−14.9941	−0.706044
$452$	−8.06166	−0.379188
$453$	21.8986	1.02889
$454$	17.2975	0.811814
$455$	9.29194	0.435613
$456$	6.14128	0.287592
$457$	21.0518	0.984762	0.492381	−	0.870380i	$-0.336127\pi$
$457$	21.0518	0.984762	0.492381	+	0.870380i	$0.336127\pi$
$458$	−18.8496	−0.880785
$459$	0.824615	0.0384897
$460$	7.05555	0.328967
$461$	−29.3930	−1.36897	−0.684483	−	0.729029i	$-0.739972\pi$
$461$	−29.3930	−1.36897	−0.684483	+	0.729029i	$0.739972\pi$
$462$	9.83477	0.457555
$463$	−39.5949	−1.84013	−0.920066	−	0.391764i	$-0.871865\pi$
$463$	−39.5949	−1.84013	−0.920066	+	0.391764i	$0.871865\pi$
$464$	−1.68504	−0.0782261
$465$	2.01462	0.0934259
$466$	−22.2387	−1.03019
$467$	−20.2894	−0.938882	−0.469441	−	0.882964i	$-0.655544\pi$
$467$	−20.2894	−0.938882	−0.469441	+	0.882964i	$0.655544\pi$
$468$	5.77911	0.267139
$469$	−3.34904	−0.154644
$470$	−8.92804	−0.411820
$471$	−22.1903	−1.02248
$472$	−12.5600	−0.578119
$473$	−26.8523	−1.23467
$474$	−5.07130	−0.232933
$475$	−2.24566	−0.103038
$476$	2.31902	0.106292
$477$	9.40727	0.430729
$478$	20.9419	0.957858
$479$	−1.06541	−0.0486801	−0.0243400	−	0.999704i	$-0.507748\pi$
$479$	−1.06541	−0.0486801	−0.0243400	+	0.999704i	$0.507748\pi$
$480$	−5.79386	−0.264453
$481$	15.5579	0.709378
$482$	9.64784	0.439447
$483$	−11.3443	−0.516182
$484$	−27.2103	−1.23683
$485$	4.83238	0.219427
$486$	0.823088	0.0373360
$487$	4.74651	0.215085	0.107542	−	0.994200i	$-0.465702\pi$
$487$	4.74651	0.215085	0.107542	+	0.994200i	$0.465702\pi$
$488$	17.0738	0.772893
$489$	−20.4243	−0.923620
$490$	−2.03988	−0.0921525
$491$	2.90373	0.131044	0.0655218	−	0.997851i	$-0.479129\pi$
$491$	2.90373	0.131044	0.0655218	+	0.997851i	$0.479129\pi$
$492$	−3.52904	−0.159101
$493$	3.52555	0.158783
$494$	−8.07695	−0.363399
$495$	−5.61912	−0.252561
$496$	0.794014	0.0356523
$497$	20.1959	0.905909
$498$	0.181203	0.00811989
$499$	−1.53459	−0.0686978	−0.0343489	−	0.999410i	$-0.510936\pi$
$499$	−1.53459	−0.0686978	−0.0343489	+	0.999410i	$0.510936\pi$
$500$	1.32253	0.0591451
$501$	14.6440	0.654247
$502$	11.5395	0.515034
$503$	−8.69929	−0.387882	−0.193941	−	0.981013i	$-0.562127\pi$
$503$	−8.69929	−0.387882	−0.193941	+	0.981013i	$0.562127\pi$
$504$	5.81520	0.259029
$505$	5.19043	0.230971
$506$	−24.6741	−1.09690
$507$	−6.09472	−0.270676
$508$	−6.06082	−0.268905
$509$	16.0658	0.712104	0.356052	−	0.934466i	$-0.384123\pi$
$509$	16.0658	0.712104	0.356052	+	0.934466i	$0.384123\pi$
$510$	0.678731	0.0300547
$511$	−21.3618	−0.944990
$512$	−4.43916	−0.196185
$513$	2.24566	0.0991484
$514$	21.8451	0.963544
$515$	−3.57367	−0.157475
$516$	−6.32001	−0.278223
$517$	−60.9506	−2.68060
$518$	6.23146	0.273794
$519$	2.18596	0.0959530
$520$	11.9501	0.524046
$521$	18.2633	0.800128	0.400064	−	0.916487i	$-0.368988\pi$
$521$	18.2633	0.800128	0.400064	+	0.916487i	$0.368988\pi$
$522$	3.51903	0.154024
$523$	−14.0213	−0.613107	−0.306553	−	0.951853i	$-0.599176\pi$
$523$	−14.0213	−0.613107	−0.306553	+	0.951853i	$0.599176\pi$
$524$	−16.0968	−0.703192
$525$	−2.12642	−0.0928047
$526$	4.01224	0.174942
$527$	−1.66129	−0.0723668
$528$	−2.21464	−0.0963797
$529$	5.46126	0.237446
$530$	7.74301	0.336335
$531$	−4.59276	−0.199309
$532$	6.31536	0.273806
$533$	11.6603	0.505063
$534$	9.07286	0.392621
$535$	9.84230	0.425520
$536$	−4.30711	−0.186039
$537$	1.27627	0.0550753
$538$	−6.94768	−0.299536
$539$	−13.9260	−0.599836
$540$	−1.32253	−0.0569124
$541$	3.90514	0.167895	0.0839476	−	0.996470i	$-0.473247\pi$
$541$	3.90514	0.167895	0.0839476	+	0.996470i	$0.473247\pi$
$542$	−11.6059	−0.498518
$543$	4.69881	0.201645
$544$	4.77770	0.204842
$545$	−8.05857	−0.345191
$546$	−7.64808	−0.327308
$547$	3.36694	0.143960	0.0719800	−	0.997406i	$-0.477068\pi$
$547$	3.36694	0.143960	0.0719800	+	0.997406i	$0.477068\pi$
$548$	19.7219	0.842476
$549$	6.24330	0.266458
$550$	−4.62503	−0.197212
$551$	9.60109	0.409020
$552$	−14.5895	−0.620972
$553$	−13.1015	−0.557134
$554$	18.5946	0.790008
$555$	−3.56036	−0.151129
$556$	21.5625	0.914455
$557$	−32.1272	−1.36127	−0.680636	−	0.732622i	$-0.738297\pi$
$557$	−32.1272	−1.36127	−0.680636	+	0.732622i	$0.738297\pi$
$558$	−1.65821	−0.0701977
$559$	20.8819	0.883210
$560$	−0.838077	−0.0354152
$561$	4.63361	0.195631
$562$	13.4611	0.567821
$563$	−46.4471	−1.95751	−0.978756	−	0.205028i	$-0.934271\pi$
$563$	−46.4471	−1.95751	−0.978756	+	0.205028i	$0.934271\pi$
$564$	−14.3454	−0.604052
$565$	−6.09565	−0.256446
$566$	2.93918	0.123543
$567$	2.12642	0.0893014
$568$	25.9733	1.08982
$569$	−2.63391	−0.110419	−0.0552096	−	0.998475i	$-0.517583\pi$
$569$	−2.63391	−0.110419	−0.0552096	+	0.998475i	$0.517583\pi$
$570$	1.84838	0.0774200
$571$	6.55656	0.274383	0.137192	−	0.990545i	$-0.456192\pi$
$571$	6.55656	0.274383	0.137192	+	0.990545i	$0.456192\pi$
$572$	32.4735	1.35778
$573$	7.05829	0.294864
$574$	4.67034	0.194936
$575$	5.33491	0.222481
$576$	3.98061	0.165859
$577$	20.2229	0.841891	0.420946	−	0.907086i	$-0.361698\pi$
$577$	20.2229	0.841891	0.420946	+	0.907086i	$0.361698\pi$
$578$	13.4328	0.558731
$579$	−19.8016	−0.822928
$580$	−5.65432	−0.234783
$581$	0.468131	0.0194214
$582$	−3.97748	−0.164872
$583$	52.8605	2.18926
$584$	−27.4728	−1.13683
$585$	4.36975	0.180667
$586$	5.37559	0.222063
$587$	47.9112	1.97751	0.988753	−	0.149560i	$-0.0477858\pi$
$587$	47.9112	1.97751	0.988753	+	0.149560i	$0.0477858\pi$
$588$	−3.27765	−0.135168
$589$	−4.52416	−0.186415
$590$	−3.78025	−0.155630
$591$	1.54881	0.0637097
$592$	−1.40323	−0.0576723
$593$	−19.1550	−0.786600	−0.393300	−	0.919410i	$-0.628667\pi$
$593$	−19.1550	−0.786600	−0.393300	+	0.919410i	$0.628667\pi$
$594$	4.62503	0.189767
$595$	1.75348	0.0718856
$596$	2.87739	0.117863
$597$	−14.0551	−0.575236
$598$	19.1880	0.784656
$599$	15.0190	0.613658	0.306829	−	0.951765i	$-0.400732\pi$
$599$	15.0190	0.613658	0.306829	+	0.951765i	$0.400732\pi$
$600$	−2.73473	−0.111645
$601$	16.3949	0.668760	0.334380	−	0.942438i	$-0.391473\pi$
$601$	16.3949	0.668760	0.334380	+	0.942438i	$0.391473\pi$
$602$	8.36391	0.340888
$603$	−1.57496	−0.0641375
$604$	28.9614	1.17842
$605$	−20.5745	−0.836472
$606$	−4.27218	−0.173545
$607$	7.96962	0.323477	0.161738	−	0.986834i	$-0.448290\pi$
$607$	7.96962	0.323477	0.161738	+	0.986834i	$0.448290\pi$
$608$	13.0111	0.527668
$609$	9.09130	0.368398
$610$	5.13879	0.208064
$611$	47.3987	1.91755
$612$	1.09057	0.0440838
$613$	−36.0800	−1.45726	−0.728628	−	0.684909i	$-0.759842\pi$
$613$	−36.0800	−1.45726	−0.728628	+	0.684909i	$0.759842\pi$
$614$	−21.3802	−0.862835
$615$	−2.66841	−0.107601
$616$	32.6763	1.31656
$617$	44.5335	1.79285	0.896425	−	0.443195i	$-0.146155\pi$
$617$	44.5335	1.79285	0.896425	+	0.443195i	$0.146155\pi$
$618$	2.94144	0.118322
$619$	11.9013	0.478355	0.239178	−	0.970976i	$-0.423122\pi$
$619$	11.9013	0.478355	0.239178	+	0.970976i	$0.423122\pi$
$620$	2.66439	0.107004
$621$	−5.33491	−0.214083
$622$	17.9910	0.721375
$623$	23.4394	0.939081
$624$	1.72223	0.0689444
$625$	1.00000	0.0400000
$626$	25.4844	1.01856
$627$	12.6186	0.503940
$628$	−29.3473	−1.17108
$629$	2.93592	0.117063
$630$	1.75023	0.0697310
$631$	35.0581	1.39564	0.697820	−	0.716273i	$-0.254154\pi$
$631$	35.0581	1.39564	0.697820	+	0.716273i	$0.254154\pi$
$632$	−16.8495	−0.670238
$633$	−19.1926	−0.762839
$634$	12.3988	0.492419
$635$	−4.58276	−0.181861
$636$	12.4414	0.493332
$637$	10.8297	0.429087
$638$	19.7738	0.782854
$639$	9.49758	0.375719
$640$	−8.31133	−0.328534
$641$	−30.0107	−1.18535	−0.592676	−	0.805441i	$-0.701929\pi$
$641$	−30.0107	−1.18535	−0.592676	+	0.805441i	$0.701929\pi$
$642$	−8.10108	−0.319724
$643$	16.7954	0.662345	0.331173	−	0.943570i	$-0.392556\pi$
$643$	16.7954	0.662345	0.331173	+	0.943570i	$0.392556\pi$
$644$	−15.0031	−0.591205
$645$	−4.77874	−0.188163
$646$	−1.52420	−0.0599688
$647$	−39.6961	−1.56062	−0.780308	−	0.625395i	$-0.784938\pi$
$647$	−39.6961	−1.56062	−0.780308	+	0.625395i	$0.784938\pi$
$648$	2.73473	0.107430
$649$	−25.8072	−1.01302
$650$	3.59669	0.141074
$651$	−4.28394	−0.167901
$652$	−27.0117	−1.05786
$653$	16.9530	0.663421	0.331711	−	0.943381i	$-0.392374\pi$
$653$	16.9530	0.663421	0.331711	+	0.943381i	$0.392374\pi$
$654$	6.63291	0.259367
$655$	−12.1713	−0.475570
$656$	−1.05169	−0.0410615
$657$	−10.0459	−0.391927
$658$	18.9848	0.740104
$659$	−7.25765	−0.282718	−0.141359	−	0.989958i	$-0.545147\pi$
$659$	−7.25765	−0.282718	−0.141359	+	0.989958i	$0.545147\pi$
$660$	−7.43143	−0.289268
$661$	−5.70846	−0.222033	−0.111017	−	0.993819i	$-0.535411\pi$
$661$	−5.70846	−0.222033	−0.111017	+	0.993819i	$0.535411\pi$
$662$	−19.4704	−0.756737
$663$	−3.60336	−0.139943
$664$	0.602050	0.0233641
$665$	4.77523	0.185175
$666$	2.93049	0.113554
$667$	−22.8089	−0.883162
$668$	19.3671	0.749336
$669$	18.5188	0.715977
$670$	−1.29634	−0.0500818
$671$	35.0819	1.35432
$672$	12.3202	0.475262
$673$	−30.0084	−1.15674	−0.578370	−	0.815774i	$-0.696311\pi$
$673$	−30.0084	−1.15674	−0.578370	+	0.815774i	$0.696311\pi$
$674$	28.1795	1.08543
$675$	−1.00000	−0.0384900
$676$	−8.06042	−0.310016
$677$	−46.4341	−1.78461	−0.892303	−	0.451437i	$-0.850912\pi$
$677$	−46.4341	−1.78461	−0.892303	+	0.451437i	$0.850912\pi$
$678$	5.01726	0.192687
$679$	−10.2757	−0.394345
$680$	2.25510	0.0864791
$681$	21.0154	0.805312
$682$	−9.31769	−0.356793
$683$	24.8683	0.951557	0.475779	−	0.879565i	$-0.342166\pi$
$683$	24.8683	0.951557	0.475779	+	0.879565i	$0.342166\pi$
$684$	2.96995	0.113559
$685$	14.9123	0.569769
$686$	16.5893	0.633382
$687$	−22.9011	−0.873731
$688$	−1.88342	−0.0718048
$689$	−41.1074	−1.56607
$690$	−4.39110	−0.167166
$691$	13.9109	0.529196	0.264598	−	0.964359i	$-0.414761\pi$
$691$	13.9109	0.529196	0.264598	+	0.964359i	$0.414761\pi$
$692$	2.89099	0.109899
$693$	11.9486	0.453890
$694$	−23.0031	−0.873185
$695$	16.3041	0.618448
$696$	11.6921	0.443186
$697$	2.20041	0.0833464
$698$	−9.01196	−0.341108
$699$	−27.0186	−1.02194
$700$	−2.81225	−0.106293
$701$	16.7956	0.634361	0.317181	−	0.948365i	$-0.397264\pi$
$701$	16.7956	0.634361	0.317181	+	0.948365i	$0.397264\pi$
$702$	−3.59669	−0.135748
$703$	7.99536	0.301551
$704$	22.3675	0.843008
$705$	−10.8470	−0.408522
$706$	3.43493	0.129275
$707$	−11.0370	−0.415091
$708$	−6.07404	−0.228276
$709$	−13.7848	−0.517700	−0.258850	−	0.965917i	$-0.583344\pi$
$709$	−13.7848	−0.517700	−0.258850	+	0.965917i	$0.583344\pi$
$710$	7.81735	0.293380
$711$	−6.16131	−0.231067
$712$	30.1448	1.12972
$713$	10.7478	0.402509
$714$	−1.44327	−0.0540129
$715$	24.5541	0.918273
$716$	1.68791	0.0630800
$717$	25.4430	0.950187
$718$	−4.60019	−0.171678
$719$	−22.8748	−0.853085	−0.426542	−	0.904468i	$-0.640269\pi$
$719$	−22.8748	−0.853085	−0.426542	+	0.904468i	$0.640269\pi$
$720$	−0.394125	−0.0146882
$721$	7.59912	0.283006
$722$	11.4878	0.427533
$723$	11.7215	0.435928
$724$	6.21429	0.230952
$725$	−4.27540	−0.158784
$726$	16.9346	0.628503
$727$	−39.9160	−1.48040	−0.740202	−	0.672385i	$-0.765270\pi$
$727$	−39.9160	−1.48040	−0.740202	+	0.672385i	$0.765270\pi$
$728$	−25.4110	−0.941793
$729$	1.00000	0.0370370
$730$	−8.26864	−0.306036
$731$	3.94062	0.145749
$732$	8.25693	0.305185
$733$	−17.1762	−0.634416	−0.317208	−	0.948356i	$-0.602745\pi$
$733$	−17.1762	−0.634416	−0.317208	+	0.948356i	$0.602745\pi$
$734$	13.2626	0.489531
$735$	−2.47833	−0.0914145
$736$	−30.9097	−1.13935
$737$	−8.84991	−0.325991
$738$	2.19633	0.0808482
$739$	35.3449	1.30018	0.650092	−	0.759856i	$-0.274730\pi$
$739$	35.3449	1.30018	0.650092	+	0.759856i	$0.274730\pi$
$740$	−4.70866	−0.173094
$741$	−9.81298	−0.360489
$742$	−16.4649	−0.604446
$743$	−36.1723	−1.32703	−0.663516	−	0.748162i	$-0.730937\pi$
$743$	−36.1723	−1.32703	−0.663516	+	0.748162i	$0.730937\pi$
$744$	−5.50945	−0.201986
$745$	2.17568	0.0797107
$746$	13.1036	0.479757
$747$	0.220150	0.00805486
$748$	6.12806	0.224064
$749$	−20.9289	−0.764725
$750$	−0.823088	−0.0300549
$751$	1.10315	0.0402545	0.0201272	−	0.999797i	$-0.493593\pi$
$751$	1.10315	0.0402545	0.0201272	+	0.999797i	$0.493593\pi$
$752$	−4.27508	−0.155896
$753$	14.0198	0.510909
$754$	−15.3773	−0.560007
$755$	21.8986	0.796971
$756$	2.81225	0.102280
$757$	25.8515	0.939590	0.469795	−	0.882775i	$-0.344328\pi$
$757$	25.8515	0.939590	0.469795	+	0.882775i	$0.344328\pi$
$758$	23.3555	0.848311
$759$	−29.9775	−1.08811
$760$	6.14128	0.222768
$761$	−23.3759	−0.847374	−0.423687	−	0.905809i	$-0.639264\pi$
$761$	−23.3759	−0.847374	−0.423687	+	0.905809i	$0.639264\pi$
$762$	3.77202	0.136646
$763$	17.1359	0.620362
$764$	9.33477	0.337720
$765$	0.824615	0.0298140
$766$	29.4235	1.06311
$767$	20.0692	0.724657
$768$	14.8022	0.534128
$769$	−2.53101	−0.0912705	−0.0456352	−	0.998958i	$-0.514531\pi$
$769$	−2.53101	−0.0912705	−0.0456352	+	0.998958i	$0.514531\pi$
$770$	9.83477	0.354420
$771$	26.5404	0.955828
$772$	−26.1882	−0.942533
$773$	−34.6297	−1.24554	−0.622772	−	0.782403i	$-0.713994\pi$
$773$	−34.6297	−1.24554	−0.622772	+	0.782403i	$0.713994\pi$
$774$	3.93332	0.141380
$775$	2.01462	0.0723674
$776$	−13.2153	−0.474400
$777$	7.57082	0.271602
$778$	4.10981	0.147344
$779$	5.99234	0.214698
$780$	5.77911	0.206925
$781$	53.3680	1.90966
$782$	3.62097	0.129485
$783$	4.27540	0.152790
$784$	−0.976772	−0.0348847
$785$	−22.1903	−0.792007
$786$	10.0180	0.357331
$787$	8.01005	0.285527	0.142764	−	0.989757i	$-0.454401\pi$
$787$	8.01005	0.285527	0.142764	+	0.989757i	$0.454401\pi$
$788$	2.04835	0.0729693
$789$	4.87462	0.173541
$790$	−5.07130	−0.180429
$791$	12.9619	0.460873
$792$	15.3668	0.546035
$793$	−27.2817	−0.968801
$794$	−16.6674	−0.591503
$795$	9.40727	0.333641
$796$	−18.5882	−0.658841
$797$	25.8145	0.914396	0.457198	−	0.889365i	$-0.348853\pi$
$797$	25.8145	0.914396	0.457198	+	0.889365i	$0.348853\pi$
$798$	−3.93043	−0.139136
$799$	8.94460	0.316437
$800$	−5.79386	−0.204844
$801$	11.0229	0.389477
$802$	0.823088	0.0290643
$803$	−56.4490	−1.99204
$804$	−2.08293	−0.0734593
$805$	−11.3443	−0.399833
$806$	7.24597	0.255229
$807$	−8.44099	−0.297137
$808$	−14.1944	−0.499358
$809$	7.34647	0.258288	0.129144	−	0.991626i	$-0.458777\pi$
$809$	7.34647	0.258288	0.129144	+	0.991626i	$0.458777\pi$
$810$	0.823088	0.0289204
$811$	−11.3875	−0.399870	−0.199935	−	0.979809i	$-0.564073\pi$
$811$	−11.3875	−0.399870	−0.199935	+	0.979809i	$0.564073\pi$
$812$	12.0235	0.421941
$813$	−14.1005	−0.494525
$814$	16.4668	0.577159
$815$	−20.4243	−0.715433
$816$	0.325002	0.0113773
$817$	10.7314	0.375445
$818$	−16.5589	−0.578967
$819$	−9.29194	−0.324687
$820$	−3.52904	−0.123239
$821$	−30.8910	−1.07810	−0.539051	−	0.842273i	$-0.681217\pi$
$821$	−30.8910	−1.07810	−0.539051	+	0.842273i	$0.681217\pi$
$822$	−12.2741	−0.428109
$823$	49.1726	1.71405	0.857025	−	0.515274i	$-0.172310\pi$
$823$	49.1726	1.71405	0.857025	+	0.515274i	$0.172310\pi$
$824$	9.77302	0.340459
$825$	−5.61912	−0.195633
$826$	8.03840	0.279692
$827$	−15.9647	−0.555147	−0.277574	−	0.960704i	$-0.589530\pi$
$827$	−15.9647	−0.555147	−0.277574	+	0.960704i	$0.589530\pi$
$828$	−7.05555	−0.245197
$829$	28.9064	1.00396	0.501981	−	0.864879i	$-0.332605\pi$
$829$	28.9064	1.00396	0.501981	+	0.864879i	$0.332605\pi$
$830$	0.181203	0.00628964
$831$	22.5912	0.783681
$832$	−17.3943	−0.603038
$833$	2.04366	0.0708088
$834$	−13.4197	−0.464686
$835$	14.6440	0.506778
$836$	16.6885	0.577183
$837$	−2.01462	−0.0696356
$838$	−15.5276	−0.536392
$839$	−0.348164	−0.0120200	−0.00600998	−	0.999982i	$-0.501913\pi$
$839$	−0.348164	−0.0120200	−0.00600998	+	0.999982i	$0.501913\pi$
$840$	5.81520	0.200643
$841$	−10.7210	−0.369689
$842$	−22.2270	−0.765993
$843$	16.3543	0.563273
$844$	−25.3827	−0.873710
$845$	−6.09472	−0.209665
$846$	8.92804	0.306952
$847$	43.7500	1.50327
$848$	3.70764	0.127321
$849$	3.57092	0.122554
$850$	0.678731	0.0232803
$851$	−18.9942	−0.651112
$852$	12.5608	0.430326
$853$	−2.64492	−0.0905603	−0.0452801	−	0.998974i	$-0.514418\pi$
$853$	−2.64492	−0.0905603	−0.0452801	+	0.998974i	$0.514418\pi$
$854$	−10.9272	−0.373922
$855$	2.24566	0.0768000
$856$	−26.9160	−0.919972
$857$	29.2355	0.998664	0.499332	−	0.866411i	$-0.333579\pi$
$857$	29.2355	0.998664	0.499332	+	0.866411i	$0.333579\pi$
$858$	−20.2102	−0.689966
$859$	−12.1818	−0.415638	−0.207819	−	0.978167i	$-0.566636\pi$
$859$	−12.1818	−0.415638	−0.207819	+	0.978167i	$0.566636\pi$
$860$	−6.32001	−0.215510
$861$	5.67416	0.193375
$862$	6.62329	0.225590
$863$	−55.2434	−1.88051	−0.940254	−	0.340475i	$-0.889412\pi$
$863$	−55.2434	−1.88051	−0.940254	+	0.340475i	$0.889412\pi$
$864$	5.79386	0.197111
$865$	2.18596	0.0743249
$866$	−16.2401	−0.551859
$867$	16.3200	0.554257
$868$	−5.66562	−0.192304
$869$	−34.6211	−1.17444
$870$	3.51903	0.119306
$871$	6.88220	0.233195
$872$	22.0380	0.746302
$873$	−4.83238	−0.163551
$874$	9.86093	0.333551
$875$	−2.12642	−0.0718862
$876$	−13.2859	−0.448890
$877$	−9.22020	−0.311344	−0.155672	−	0.987809i	$-0.549754\pi$
$877$	−9.22020	−0.311344	−0.155672	+	0.987809i	$0.549754\pi$
$878$	16.1201	0.544026
$879$	6.53099	0.220285
$880$	−2.21464	−0.0746554
$881$	−20.7039	−0.697531	−0.348766	−	0.937210i	$-0.613399\pi$
$881$	−20.7039	−0.697531	−0.348766	+	0.937210i	$0.613399\pi$
$882$	2.03988	0.0686864
$883$	15.0406	0.506157	0.253078	−	0.967446i	$-0.418557\pi$
$883$	15.0406	0.506157	0.253078	+	0.967446i	$0.418557\pi$
$884$	−4.76554	−0.160282
$885$	−4.59276	−0.154384
$886$	15.3305	0.515038
$887$	36.2741	1.21796	0.608982	−	0.793184i	$-0.291578\pi$
$887$	36.2741	1.21796	0.608982	+	0.793184i	$0.291578\pi$
$888$	9.73662	0.326740
$889$	9.74489	0.326833
$890$	9.07286	0.304123
$891$	5.61912	0.188248
$892$	24.4915	0.820038
$893$	24.3587	0.815133
$894$	−1.79078	−0.0598925
$895$	1.27627	0.0426611
$896$	17.6734	0.590427
$897$	23.3122	0.778373
$898$	−5.34192	−0.178262
$899$	−8.61331	−0.287270
$900$	−1.32253	−0.0440842
$901$	−7.75737	−0.258435
$902$	12.3415	0.410926
$903$	10.1616	0.338158
$904$	16.6700	0.554435
$905$	4.69881	0.156194
$906$	−18.0245	−0.598823
$907$	−26.9050	−0.893367	−0.446684	−	0.894692i	$-0.647395\pi$
$907$	−26.9050	−0.893367	−0.446684	+	0.894692i	$0.647395\pi$
$908$	27.7934	0.922357
$909$	−5.19043	−0.172156
$910$	−7.64808	−0.253532
$911$	26.1689	0.867015	0.433508	−	0.901150i	$-0.357276\pi$
$911$	26.1689	0.867015	0.433508	+	0.901150i	$0.357276\pi$
$912$	0.885073	0.0293077
$913$	1.23705	0.0409403
$914$	−17.3275	−0.573143
$915$	6.24330	0.206397
$916$	−30.2873	−1.00072
$917$	25.8812	0.854674
$918$	−0.678731	−0.0224014
$919$	16.5407	0.545628	0.272814	−	0.962067i	$-0.412046\pi$
$919$	16.5407	0.545628	0.272814	+	0.962067i	$0.412046\pi$
$920$	−14.5895	−0.481003
$921$	−25.9756	−0.855925
$922$	24.1930	0.796754
$923$	−41.5021	−1.36606
$924$	15.8024	0.519859
$925$	−3.56036	−0.117064
$926$	32.5901	1.07098
$927$	3.57367	0.117375
$928$	24.7711	0.813150
$929$	9.83907	0.322809	0.161405	−	0.986888i	$-0.448398\pi$
$929$	9.83907	0.322809	0.161405	+	0.986888i	$0.448398\pi$
$930$	−1.65821	−0.0543749
$931$	5.56549	0.182401
$932$	−35.7328	−1.17047
$933$	21.8580	0.715598
$934$	16.7000	0.546440
$935$	4.63361	0.151535
$936$	−11.9501	−0.390601
$937$	−21.7603	−0.710878	−0.355439	−	0.934699i	$-0.615669\pi$
$937$	−21.7603	−0.710878	−0.355439	+	0.934699i	$0.615669\pi$
$938$	2.75656	0.0900048
$939$	30.9619	1.01040
$940$	−14.3454	−0.467897
$941$	−7.97262	−0.259900	−0.129950	−	0.991521i	$-0.541482\pi$
$941$	−7.97262	−0.259900	−0.129950	+	0.991521i	$0.541482\pi$
$942$	18.2646	0.595093
$943$	−14.2357	−0.463579
$944$	−1.81012	−0.0589145
$945$	2.12642	0.0691725
$946$	22.1018	0.718592
$947$	−2.10754	−0.0684857	−0.0342428	−	0.999414i	$-0.510902\pi$
$947$	−2.10754	−0.0684857	−0.0342428	+	0.999414i	$0.510902\pi$
$948$	−8.14849	−0.264651
$949$	43.8980	1.42499
$950$	1.84838	0.0599693
$951$	15.0637	0.488475
$952$	−4.79529	−0.155416
$953$	11.3491	0.367634	0.183817	−	0.982961i	$-0.441155\pi$
$953$	11.3491	0.367634	0.183817	+	0.982961i	$0.441155\pi$
$954$	−7.74301	−0.250689
$955$	7.05829	0.228401
$956$	33.6491	1.08829
$957$	24.0240	0.776584
$958$	0.876931	0.0283323
$959$	−31.7098	−1.02396
$960$	3.98061	0.128474
$961$	−26.9413	−0.869074
$962$	−12.8055	−0.412866
$963$	−9.84230	−0.317164
$964$	15.5020	0.499286
$965$	−19.8016	−0.637437
$966$	9.33734	0.300424
$967$	13.3593	0.429606	0.214803	−	0.976657i	$-0.431089\pi$
$967$	13.3593	0.429606	0.214803	+	0.976657i	$0.431089\pi$
$968$	56.2657	1.80845
$969$	−1.85181	−0.0594886
$970$	−3.97748	−0.127709
$971$	11.1160	0.356731	0.178365	−	0.983964i	$-0.442919\pi$
$971$	11.1160	0.356731	0.178365	+	0.983964i	$0.442919\pi$
$972$	1.32253	0.0424200
$973$	−34.6693	−1.11145
$974$	−3.90680	−0.125182
$975$	4.36975	0.139944
$976$	2.46065	0.0787633
$977$	21.9907	0.703544	0.351772	−	0.936086i	$-0.385579\pi$
$977$	21.9907	0.703544	0.351772	+	0.936086i	$0.385579\pi$
$978$	16.8110	0.537558
$979$	61.9392	1.97959
$980$	−3.27765	−0.104701
$981$	8.05857	0.257290
$982$	−2.39003	−0.0762689
$983$	−0.0709205	−0.00226201	−0.00113101	−	0.999999i	$-0.500360\pi$
$983$	−0.0709205	−0.00226201	−0.00113101	+	0.999999i	$0.500360\pi$
$984$	7.29738	0.232632
$985$	1.54881	0.0493493
$986$	−2.90184	−0.0924135
$987$	23.0653	0.734177
$988$	−12.9779	−0.412883
$989$	−25.4941	−0.810667
$990$	4.62503	0.146993
$991$	25.2112	0.800860	0.400430	−	0.916327i	$-0.368861\pi$
$991$	25.2112	0.800860	0.400430	+	0.916327i	$0.368861\pi$
$992$	−11.6725	−0.370601
$993$	−23.6553	−0.750677
$994$	−16.6230	−0.527249
$995$	−14.0551	−0.445576
$996$	0.291154	0.00922556
$997$	−52.4249	−1.66031	−0.830157	−	0.557530i	$-0.811749\pi$
$997$	−52.4249	−1.66031	−0.830157	+	0.557530i	$0.811749\pi$
$998$	1.26311	0.0399829
$999$	3.56036	0.112645

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.f.1.16	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.f.1.16	✓	36	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)

\(f(q)\)	\(=\)	\(q-0.823088 q^{2} -1.00000 q^{3} -1.32253 q^{4} -1.00000 q^{5} +0.823088 q^{6} +2.12642 q^{7} +2.73473 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.823088 q^{2} -1.00000 q^{3} -1.32253 q^{4} -1.00000 q^{5} +0.823088 q^{6} +2.12642 q^{7} +2.73473 q^{8} +1.00000 q^{9} +0.823088 q^{10} +5.61912 q^{11} +1.32253 q^{12} -4.36975 q^{13} -1.75023 q^{14} +1.00000 q^{15} +0.394125 q^{16} -0.824615 q^{17} -0.823088 q^{18} -2.24566 q^{19} +1.32253 q^{20} -2.12642 q^{21} -4.62503 q^{22} +5.33491 q^{23} -2.73473 q^{24} +1.00000 q^{25} +3.59669 q^{26} -1.00000 q^{27} -2.81225 q^{28} -4.27540 q^{29} -0.823088 q^{30} +2.01462 q^{31} -5.79386 q^{32} -5.61912 q^{33} +0.678731 q^{34} -2.12642 q^{35} -1.32253 q^{36} -3.56036 q^{37} +1.84838 q^{38} +4.36975 q^{39} -2.73473 q^{40} -2.66841 q^{41} +1.75023 q^{42} -4.77874 q^{43} -7.43143 q^{44} -1.00000 q^{45} -4.39110 q^{46} -10.8470 q^{47} -0.394125 q^{48} -2.47833 q^{49} -0.823088 q^{50} +0.824615 q^{51} +5.77911 q^{52} +9.40727 q^{53} +0.823088 q^{54} -5.61912 q^{55} +5.81520 q^{56} +2.24566 q^{57} +3.51903 q^{58} -4.59276 q^{59} -1.32253 q^{60} +6.24330 q^{61} -1.65821 q^{62} +2.12642 q^{63} +3.98061 q^{64} +4.36975 q^{65} +4.62503 q^{66} -1.57496 q^{67} +1.09057 q^{68} -5.33491 q^{69} +1.75023 q^{70} +9.49758 q^{71} +2.73473 q^{72} -10.0459 q^{73} +2.93049 q^{74} -1.00000 q^{75} +2.96995 q^{76} +11.9486 q^{77} -3.59669 q^{78} -6.16131 q^{79} -0.394125 q^{80} +1.00000 q^{81} +2.19633 q^{82} +0.220150 q^{83} +2.81225 q^{84} +0.824615 q^{85} +3.93332 q^{86} +4.27540 q^{87} +15.3668 q^{88} +11.0229 q^{89} +0.823088 q^{90} -9.29194 q^{91} -7.05555 q^{92} -2.01462 q^{93} +8.92804 q^{94} +2.24566 q^{95} +5.79386 q^{96} -4.83238 q^{97} +2.03988 q^{98} +5.61912 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 7 q^{2} - 36 q^{3} + 45 q^{4} - 36 q^{5} + 7 q^{6} + 2 q^{7} - 24 q^{8} + 36 q^{9}+O(q^{10}) \) 36 * q - 7 * q^2 - 36 * q^3 + 45 * q^4 - 36 * q^5 + 7 * q^6 + 2 * q^7 - 24 * q^8 + 36 * q^9	\( 36 q - 7 q^{2} - 36 q^{3} + 45 q^{4} - 36 q^{5} + 7 q^{6} + 2 q^{7} - 24 q^{8} + 36 q^{9} + 7 q^{10} - q^{11} - 45 q^{12} - 8 q^{13} - 4 q^{14} + 36 q^{15} + 63 q^{16} - 50 q^{17} - 7 q^{18} + 15 q^{19} - 45 q^{20} - 2 q^{21} + 7 q^{22} - 32 q^{23} + 24 q^{24} + 36 q^{25} - 12 q^{26} - 36 q^{27} - 10 q^{28} + 7 q^{29} - 7 q^{30} + 7 q^{31} - 50 q^{32} + q^{33} + 8 q^{34} - 2 q^{35} + 45 q^{36} - 10 q^{37} - 48 q^{38} + 8 q^{39} + 24 q^{40} - 31 q^{41} + 4 q^{42} + 27 q^{43} - 9 q^{44} - 36 q^{45} + 23 q^{46} - 46 q^{47} - 63 q^{48} + 48 q^{49} - 7 q^{50} + 50 q^{51} - 14 q^{52} - 39 q^{53} + 7 q^{54} + q^{55} - 29 q^{56} - 15 q^{57} - 26 q^{58} - 9 q^{59} + 45 q^{60} + 5 q^{61} - 65 q^{62} + 2 q^{63} + 90 q^{64} + 8 q^{65} - 7 q^{66} + 18 q^{67} - 128 q^{68} + 32 q^{69} + 4 q^{70} + 4 q^{71} - 24 q^{72} - 45 q^{73} - 22 q^{74} - 36 q^{75} + 26 q^{76} - 38 q^{77} + 12 q^{78} + 25 q^{79} - 63 q^{80} + 36 q^{81} - 5 q^{82} - 71 q^{83} + 10 q^{84} + 50 q^{85} + 3 q^{86} - 7 q^{87} - 9 q^{88} - 39 q^{89} + 7 q^{90} + 19 q^{91} - 95 q^{92} - 7 q^{93} + 16 q^{94} - 15 q^{95} + 50 q^{96} - 61 q^{97} - 76 q^{98} - q^{99}+O(q^{100}) \) 36 * q - 7 * q^2 - 36 * q^3 + 45 * q^4 - 36 * q^5 + 7 * q^6 + 2 * q^7 - 24 * q^8 + 36 * q^9 + 7 * q^10 - q^11 - 45 * q^12 - 8 * q^13 - 4 * q^14 + 36 * q^15 + 63 * q^16 - 50 * q^17 - 7 * q^18 + 15 * q^19 - 45 * q^20 - 2 * q^21 + 7 * q^22 - 32 * q^23 + 24 * q^24 + 36 * q^25 - 12 * q^26 - 36 * q^27 - 10 * q^28 + 7 * q^29 - 7 * q^30 + 7 * q^31 - 50 * q^32 + q^33 + 8 * q^34 - 2 * q^35 + 45 * q^36 - 10 * q^37 - 48 * q^38 + 8 * q^39 + 24 * q^40 - 31 * q^41 + 4 * q^42 + 27 * q^43 - 9 * q^44 - 36 * q^45 + 23 * q^46 - 46 * q^47 - 63 * q^48 + 48 * q^49 - 7 * q^50 + 50 * q^51 - 14 * q^52 - 39 * q^53 + 7 * q^54 + q^55 - 29 * q^56 - 15 * q^57 - 26 * q^58 - 9 * q^59 + 45 * q^60 + 5 * q^61 - 65 * q^62 + 2 * q^63 + 90 * q^64 + 8 * q^65 - 7 * q^66 + 18 * q^67 - 128 * q^68 + 32 * q^69 + 4 * q^70 + 4 * q^71 - 24 * q^72 - 45 * q^73 - 22 * q^74 - 36 * q^75 + 26 * q^76 - 38 * q^77 + 12 * q^78 + 25 * q^79 - 63 * q^80 + 36 * q^81 - 5 * q^82 - 71 * q^83 + 10 * q^84 + 50 * q^85 + 3 * q^86 - 7 * q^87 - 9 * q^88 - 39 * q^89 + 7 * q^90 + 19 * q^91 - 95 * q^92 - 7 * q^93 + 16 * q^94 - 15 * q^95 + 50 * q^96 - 61 * q^97 - 76 * q^98 - q^99

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