LMFDB - Embedded newform 6041.2.a.f.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6041,2,Mod(1,6041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6041, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6041 = 7 \cdot 863 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6041.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:	$48.2376278611$
Analytic rank:	$0$
Dimension:	$132$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	6041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.56875 q^{2} -3.19690 q^{3} +4.59849 q^{4} -1.91049 q^{5} +8.21205 q^{6} +1.00000 q^{7} -6.67489 q^{8} +7.22017 q^{9} +O(q^{10})$	\(q-2.56875 q^{2} -3.19690 q^{3} +4.59849 q^{4} -1.91049 q^{5} +8.21205 q^{6} +1.00000 q^{7} -6.67489 q^{8} +7.22017 q^{9} +4.90758 q^{10} +5.45473 q^{11} -14.7009 q^{12} -2.75875 q^{13} -2.56875 q^{14} +6.10765 q^{15} +7.94917 q^{16} -1.52927 q^{17} -18.5468 q^{18} +2.74225 q^{19} -8.78538 q^{20} -3.19690 q^{21} -14.0119 q^{22} -8.61124 q^{23} +21.3390 q^{24} -1.35002 q^{25} +7.08656 q^{26} -13.4914 q^{27} +4.59849 q^{28} -3.64687 q^{29} -15.6890 q^{30} -6.70859 q^{31} -7.06966 q^{32} -17.4382 q^{33} +3.92833 q^{34} -1.91049 q^{35} +33.2019 q^{36} +4.87651 q^{37} -7.04417 q^{38} +8.81946 q^{39} +12.7523 q^{40} +5.17648 q^{41} +8.21205 q^{42} +5.42937 q^{43} +25.0835 q^{44} -13.7941 q^{45} +22.1202 q^{46} +10.0340 q^{47} -25.4127 q^{48} +1.00000 q^{49} +3.46788 q^{50} +4.88893 q^{51} -12.6861 q^{52} -3.15331 q^{53} +34.6562 q^{54} -10.4212 q^{55} -6.67489 q^{56} -8.76671 q^{57} +9.36790 q^{58} -6.50781 q^{59} +28.0860 q^{60} +4.62860 q^{61} +17.2327 q^{62} +7.22017 q^{63} +2.26189 q^{64} +5.27058 q^{65} +44.7945 q^{66} +4.17921 q^{67} -7.03236 q^{68} +27.5293 q^{69} +4.90758 q^{70} -7.98204 q^{71} -48.1938 q^{72} +3.87065 q^{73} -12.5266 q^{74} +4.31589 q^{75} +12.6102 q^{76} +5.45473 q^{77} -22.6550 q^{78} +10.2824 q^{79} -15.1868 q^{80} +21.4703 q^{81} -13.2971 q^{82} -7.69439 q^{83} -14.7009 q^{84} +2.92166 q^{85} -13.9467 q^{86} +11.6587 q^{87} -36.4097 q^{88} -6.10370 q^{89} +35.4335 q^{90} -2.75875 q^{91} -39.5987 q^{92} +21.4467 q^{93} -25.7749 q^{94} -5.23905 q^{95} +22.6010 q^{96} -7.71647 q^{97} -2.56875 q^{98} +39.3840 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9}+O(q^{10}) $ 132 * q + 8 * q^2 + 10 * q^3 + 174 * q^4 + 11 * q^5 + 16 * q^6 + 132 * q^7 + 30 * q^8 + 178 * q^9	\( 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9} + 22 q^{10} + 32 q^{11} + 30 q^{12} + 16 q^{13} + 8 q^{14} + 59 q^{15} + 254 q^{16} + 11 q^{17} + 33 q^{18} + 40 q^{19} + 4 q^{20} + 10 q^{21} + 66 q^{22} + 62 q^{23} + 36 q^{24} + 235 q^{25} + 25 q^{26} + 37 q^{27} + 174 q^{28} + 28 q^{29} + 45 q^{30} + 121 q^{31} + 53 q^{32} - 13 q^{33} + 44 q^{34} + 11 q^{35} + 274 q^{36} + 61 q^{37} - 28 q^{38} + 114 q^{39} + 32 q^{40} - q^{41} + 16 q^{42} + 105 q^{43} + 54 q^{44} + 29 q^{45} + 104 q^{46} + 33 q^{47} + 16 q^{48} + 132 q^{49} - 14 q^{50} + 53 q^{51} - 11 q^{52} + 48 q^{53} + 11 q^{54} + 118 q^{55} + 30 q^{56} + 93 q^{57} + 87 q^{58} + 12 q^{59} + 41 q^{60} + 54 q^{61} - 28 q^{62} + 178 q^{63} + 376 q^{64} + 22 q^{65} + 6 q^{66} + 123 q^{67} - 47 q^{68} + 58 q^{69} + 22 q^{70} + 108 q^{71} + 97 q^{72} + q^{73} - 10 q^{74} + 23 q^{75} + 71 q^{76} + 32 q^{77} + 5 q^{78} + 204 q^{79} - 10 q^{80} + 296 q^{81} + 80 q^{82} - 10 q^{83} + 30 q^{84} + 94 q^{85} + 48 q^{86} + 4 q^{87} + 155 q^{88} + q^{89} - 66 q^{90} + 16 q^{91} + 49 q^{92} + 90 q^{93} + 79 q^{94} + 100 q^{95} + q^{96} + 18 q^{97} + 8 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q + 8 * q^2 + 10 * q^3 + 174 * q^4 + 11 * q^5 + 16 * q^6 + 132 * q^7 + 30 * q^8 + 178 * q^9 + 22 * q^10 + 32 * q^11 + 30 * q^12 + 16 * q^13 + 8 * q^14 + 59 * q^15 + 254 * q^16 + 11 * q^17 + 33 * q^18 + 40 * q^19 + 4 * q^20 + 10 * q^21 + 66 * q^22 + 62 * q^23 + 36 * q^24 + 235 * q^25 + 25 * q^26 + 37 * q^27 + 174 * q^28 + 28 * q^29 + 45 * q^30 + 121 * q^31 + 53 * q^32 - 13 * q^33 + 44 * q^34 + 11 * q^35 + 274 * q^36 + 61 * q^37 - 28 * q^38 + 114 * q^39 + 32 * q^40 - q^41 + 16 * q^42 + 105 * q^43 + 54 * q^44 + 29 * q^45 + 104 * q^46 + 33 * q^47 + 16 * q^48 + 132 * q^49 - 14 * q^50 + 53 * q^51 - 11 * q^52 + 48 * q^53 + 11 * q^54 + 118 * q^55 + 30 * q^56 + 93 * q^57 + 87 * q^58 + 12 * q^59 + 41 * q^60 + 54 * q^61 - 28 * q^62 + 178 * q^63 + 376 * q^64 + 22 * q^65 + 6 * q^66 + 123 * q^67 - 47 * q^68 + 58 * q^69 + 22 * q^70 + 108 * q^71 + 97 * q^72 + q^73 - 10 * q^74 + 23 * q^75 + 71 * q^76 + 32 * q^77 + 5 * q^78 + 204 * q^79 - 10 * q^80 + 296 * q^81 + 80 * q^82 - 10 * q^83 + 30 * q^84 + 94 * q^85 + 48 * q^86 + 4 * q^87 + 155 * q^88 + q^89 - 66 * q^90 + 16 * q^91 + 49 * q^92 + 90 * q^93 + 79 * q^94 + 100 * q^95 + q^96 + 18 * q^97 + 8 * q^98 + 96 * 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 $

$2$	−2.56875	−1.81638	−0.908192	−	0.418555i	$-0.862537\pi$
$2$	−2.56875	−1.81638	−0.908192	+	0.418555i	$0.862537\pi$
$3$	−3.19690	−1.84573	−0.922865	−	0.385123i	$-0.874159\pi$
$3$	−3.19690	−1.84573	−0.922865	+	0.385123i	$0.874159\pi$
$4$	4.59849	2.29925
$5$	−1.91049	−0.854398	−0.427199	−	0.904158i	$-0.640500\pi$
$5$	−1.91049	−0.854398	−0.427199	+	0.904158i	$0.640500\pi$
$6$	8.21205	3.35255
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−6.67489	−2.35993
$9$	7.22017	2.40672
$10$	4.90758	1.55191
$11$	5.45473	1.64466	0.822331	−	0.569009i	$-0.192673\pi$
$11$	5.45473	1.64466	0.822331	+	0.569009i	$0.192673\pi$
$12$	−14.7009	−4.24379
$13$	−2.75875	−0.765141	−0.382570	−	0.923926i	$-0.624961\pi$
$13$	−2.75875	−0.765141	−0.382570	+	0.923926i	$0.624961\pi$
$14$	−2.56875	−0.686528
$15$	6.10765	1.57699
$16$	7.94917	1.98729
$17$	−1.52927	−0.370903	−0.185452	−	0.982653i	$-0.559375\pi$
$17$	−1.52927	−0.370903	−0.185452	+	0.982653i	$0.559375\pi$
$18$	−18.5468	−4.37153
$19$	2.74225	0.629116	0.314558	−	0.949238i	$-0.398144\pi$
$19$	2.74225	0.629116	0.314558	+	0.949238i	$0.398144\pi$
$20$	−8.78538	−1.96447
$21$	−3.19690	−0.697621
$22$	−14.0119	−2.98734
$23$	−8.61124	−1.79557	−0.897784	−	0.440436i	$-0.854824\pi$
$23$	−8.61124	−1.79557	−0.897784	+	0.440436i	$0.854824\pi$
$24$	21.3390	4.35580
$25$	−1.35002	−0.270005
$26$	7.08656	1.38979
$27$	−13.4914	−2.59643
$28$	4.59849	0.869034
$29$	−3.64687	−0.677206	−0.338603	−	0.940929i	$-0.609954\pi$
$29$	−3.64687	−0.677206	−0.338603	+	0.940929i	$0.609954\pi$
$30$	−15.6890	−2.86441
$31$	−6.70859	−1.20490	−0.602449	−	0.798157i	$-0.705808\pi$
$31$	−6.70859	−1.20490	−0.602449	+	0.798157i	$0.705808\pi$
$32$	−7.06966	−1.24975
$33$	−17.4382	−3.03560
$34$	3.92833	0.673702
$35$	−1.91049	−0.322932
$36$	33.2019	5.53365
$37$	4.87651	0.801693	0.400847	−	0.916145i	$-0.368716\pi$
$37$	4.87651	0.801693	0.400847	+	0.916145i	$0.368716\pi$
$38$	−7.04417	−1.14272
$39$	8.81946	1.41224
$40$	12.7523	2.01632
$41$	5.17648	0.808431	0.404215	−	0.914664i	$-0.367545\pi$
$41$	5.17648	0.808431	0.404215	+	0.914664i	$0.367545\pi$
$42$	8.21205	1.26715
$43$	5.42937	0.827971	0.413986	−	0.910283i	$-0.364136\pi$
$43$	5.42937	0.827971	0.413986	+	0.910283i	$0.364136\pi$
$44$	25.0835	3.78149
$45$	−13.7941	−2.05630
$46$	22.1202	3.26144
$47$	10.0340	1.46361	0.731807	−	0.681512i	$-0.238677\pi$
$47$	10.0340	1.46361	0.731807	+	0.681512i	$0.238677\pi$
$48$	−25.4127	−3.66800
$49$	1.00000	0.142857
$50$	3.46788	0.490432
$51$	4.88893	0.684588
$52$	−12.6861	−1.75925
$53$	−3.15331	−0.433140	−0.216570	−	0.976267i	$-0.569487\pi$
$53$	−3.15331	−0.433140	−0.216570	+	0.976267i	$0.569487\pi$
$54$	34.6562	4.71611
$55$	−10.4212	−1.40520
$56$	−6.67489	−0.891970
$57$	−8.76671	−1.16118
$58$	9.36790	1.23007
$59$	−6.50781	−0.847245	−0.423622	−	0.905839i	$-0.639242\pi$
$59$	−6.50781	−0.847245	−0.423622	+	0.905839i	$0.639242\pi$
$60$	28.0860	3.62589
$61$	4.62860	0.592632	0.296316	−	0.955090i	$-0.404242\pi$
$61$	4.62860	0.592632	0.296316	+	0.955090i	$0.404242\pi$
$62$	17.2327	2.18856
$63$	7.22017	0.909655
$64$	2.26189	0.282736
$65$	5.27058	0.653734
$66$	44.7945	5.51382
$67$	4.17921	0.510572	0.255286	−	0.966866i	$-0.417830\pi$
$67$	4.17921	0.510572	0.255286	+	0.966866i	$0.417830\pi$
$68$	−7.03236	−0.852798
$69$	27.5293	3.31413
$70$	4.90758	0.586568
$71$	−7.98204	−0.947294	−0.473647	−	0.880715i	$-0.657063\pi$
$71$	−7.98204	−0.947294	−0.473647	+	0.880715i	$0.657063\pi$
$72$	−48.1938	−5.67970
$73$	3.87065	0.453025	0.226512	−	0.974008i	$-0.427268\pi$
$73$	3.87065	0.453025	0.226512	+	0.974008i	$0.427268\pi$
$74$	−12.5266	−1.45618
$75$	4.31589	0.498356
$76$	12.6102	1.44649
$77$	5.45473	0.621624
$78$	−22.6550	−2.56518
$79$	10.2824	1.15686	0.578432	−	0.815731i	$-0.303665\pi$
$79$	10.2824	1.15686	0.578432	+	0.815731i	$0.303665\pi$
$80$	−15.1868	−1.69794
$81$	21.4703	2.38559
$82$	−13.2971	−1.46842
$83$	−7.69439	−0.844569	−0.422285	−	0.906463i	$-0.638772\pi$
$83$	−7.69439	−0.844569	−0.422285	+	0.906463i	$0.638772\pi$
$84$	−14.7009	−1.60400
$85$	2.92166	0.316899
$86$	−13.9467	−1.50391
$87$	11.6587	1.24994
$88$	−36.4097	−3.88129
$89$	−6.10370	−0.646991	−0.323495	−	0.946230i	$-0.604858\pi$
$89$	−6.10370	−0.646991	−0.323495	+	0.946230i	$0.604858\pi$
$90$	35.4335	3.73502
$91$	−2.75875	−0.289196
$92$	−39.5987	−4.12845
$93$	21.4467	2.22392
$94$	−25.7749	−2.65848
$95$	−5.23905	−0.537515
$96$	22.6010	2.30670
$97$	−7.71647	−0.783489	−0.391744	−	0.920074i	$-0.628128\pi$
$97$	−7.71647	−0.783489	−0.391744	+	0.920074i	$0.628128\pi$
$98$	−2.56875	−0.259483
$99$	39.3840	3.95824
$100$	−6.20808	−0.620808
$101$	0.454038	0.0451785	0.0225893	−	0.999745i	$-0.492809\pi$
$101$	0.454038	0.0451785	0.0225893	+	0.999745i	$0.492809\pi$
$102$	−12.5585	−1.24347
$103$	−7.54078	−0.743015	−0.371508	−	0.928430i	$-0.621159\pi$
$103$	−7.54078	−0.743015	−0.371508	+	0.928430i	$0.621159\pi$
$104$	18.4144	1.80568
$105$	6.10765	0.596045
$106$	8.10007	0.786748
$107$	−7.86993	−0.760815	−0.380408	−	0.924819i	$-0.624216\pi$
$107$	−7.86993	−0.760815	−0.380408	+	0.924819i	$0.624216\pi$
$108$	−62.0404	−5.96984
$109$	13.5078	1.29381	0.646906	−	0.762570i	$-0.276063\pi$
$109$	13.5078	1.29381	0.646906	+	0.762570i	$0.276063\pi$
$110$	26.7695	2.55237
$111$	−15.5897	−1.47971
$112$	7.94917	0.751126
$113$	13.1272	1.23490	0.617451	−	0.786610i	$-0.288165\pi$
$113$	13.1272	1.23490	0.617451	+	0.786610i	$0.288165\pi$
$114$	22.5195	2.10915
$115$	16.4517	1.53413
$116$	−16.7701	−1.55706
$117$	−19.9187	−1.84148
$118$	16.7170	1.53892
$119$	−1.52927	−0.140188
$120$	−40.7679	−3.72158
$121$	18.7541	1.70491
$122$	−11.8897	−1.07645
$123$	−16.5487	−1.49215
$124$	−30.8494	−2.77036
$125$	12.1317	1.08509
$126$	−18.5468	−1.65228
$127$	4.84167	0.429629	0.214815	−	0.976655i	$-0.431085\pi$
$127$	4.84167	0.429629	0.214815	+	0.976655i	$0.431085\pi$
$128$	8.32909	0.736195
$129$	−17.3572	−1.52821
$130$	−13.5388	−1.18743
$131$	−15.0343	−1.31355	−0.656775	−	0.754086i	$-0.728080\pi$
$131$	−15.0343	−1.31355	−0.656775	+	0.754086i	$0.728080\pi$
$132$	−80.1895	−6.97960
$133$	2.74225	0.237784
$134$	−10.7354	−0.927395
$135$	25.7753	2.21838
$136$	10.2077	0.875306
$137$	−18.6789	−1.59584	−0.797922	−	0.602761i	$-0.794067\pi$
$137$	−18.6789	−1.59584	−0.797922	+	0.602761i	$0.794067\pi$
$138$	−70.7159	−6.01974
$139$	−1.84353	−0.156366	−0.0781829	−	0.996939i	$-0.524912\pi$
$139$	−1.84353	−0.156366	−0.0781829	+	0.996939i	$0.524912\pi$
$140$	−8.78538	−0.742500
$141$	−32.0778	−2.70144
$142$	20.5039	1.72065
$143$	−15.0483	−1.25840
$144$	57.3943	4.78286
$145$	6.96730	0.578603
$146$	−9.94274	−0.822867
$147$	−3.19690	−0.263676
$148$	22.4246	1.84329
$149$	22.7532	1.86401	0.932006	−	0.362442i	$-0.118057\pi$
$149$	22.7532	1.86401	0.932006	+	0.362442i	$0.118057\pi$
$150$	−11.0865	−0.905206
$151$	−15.1476	−1.23269	−0.616345	−	0.787476i	$-0.711387\pi$
$151$	−15.1476	−1.23269	−0.616345	+	0.787476i	$0.711387\pi$
$152$	−18.3043	−1.48467
$153$	−11.0416	−0.892661
$154$	−14.0119	−1.12911
$155$	12.8167	1.02946
$156$	40.5562	3.24710
$157$	−3.72481	−0.297272	−0.148636	−	0.988892i	$-0.547488\pi$
$157$	−3.72481	−0.297272	−0.148636	+	0.988892i	$0.547488\pi$
$158$	−26.4130	−2.10131
$159$	10.0808	0.799460
$160$	13.5065	1.06778
$161$	−8.61124	−0.678661
$162$	−55.1519	−4.33314
$163$	18.9092	1.48108	0.740542	−	0.672010i	$-0.234569\pi$
$163$	18.9092	1.48108	0.740542	+	0.672010i	$0.234569\pi$
$164$	23.8040	1.85878
$165$	33.3156	2.59361
$166$	19.7650	1.53406
$167$	17.4820	1.35280	0.676400	−	0.736535i	$-0.263539\pi$
$167$	17.4820	1.35280	0.676400	+	0.736535i	$0.263539\pi$
$168$	21.3390	1.64634
$169$	−5.38928	−0.414560
$170$	−7.50503	−0.575610
$171$	19.7995	1.51411
$172$	24.9669	1.90371
$173$	−24.0918	−1.83166	−0.915831	−	0.401564i	$-0.868467\pi$
$173$	−24.0918	−1.83166	−0.915831	+	0.401564i	$0.868467\pi$
$174$	−29.9482	−2.27037
$175$	−1.35002	−0.102052
$176$	43.3605	3.26842
$177$	20.8048	1.56379
$178$	15.6789	1.17518
$179$	−20.0774	−1.50066	−0.750329	−	0.661065i	$-0.770105\pi$
$179$	−20.0774	−1.50066	−0.750329	+	0.661065i	$0.770105\pi$
$180$	−63.4319	−4.72794
$181$	4.12601	0.306684	0.153342	−	0.988173i	$-0.450996\pi$
$181$	4.12601	0.306684	0.153342	+	0.988173i	$0.450996\pi$
$182$	7.08656	0.525291
$183$	−14.7972	−1.09384
$184$	57.4791	4.23742
$185$	−9.31653	−0.684965
$186$	−55.0912	−4.03949
$187$	−8.34177	−0.610011
$188$	46.1414	3.36521
$189$	−13.4914	−0.981358
$190$	13.4578	0.976334
$191$	−0.642613	−0.0464979	−0.0232489	−	0.999730i	$-0.507401\pi$
$191$	−0.642613	−0.0464979	−0.0232489	+	0.999730i	$0.507401\pi$
$192$	−7.23102	−0.521854
$193$	23.2420	1.67300	0.836499	−	0.547968i	$-0.184598\pi$
$193$	23.2420	1.67300	0.836499	+	0.547968i	$0.184598\pi$
$194$	19.8217	1.42312
$195$	−16.8495	−1.20662
$196$	4.59849	0.328464
$197$	−20.1155	−1.43317	−0.716584	−	0.697500i	$-0.754296\pi$
$197$	−20.1155	−1.43317	−0.716584	+	0.697500i	$0.754296\pi$
$198$	−101.168	−7.18969
$199$	3.99916	0.283493	0.141747	−	0.989903i	$-0.454728\pi$
$199$	3.99916	0.283493	0.141747	+	0.989903i	$0.454728\pi$
$200$	9.01127	0.637193
$201$	−13.3605	−0.942379
$202$	−1.16631	−0.0820615
$203$	−3.64687	−0.255960
$204$	22.4817	1.57404
$205$	−9.88962	−0.690721
$206$	19.3704	1.34960
$207$	−62.1746	−4.32143
$208$	−21.9298	−1.52056
$209$	14.9582	1.03468
$210$	−15.6890	−1.08265
$211$	12.0797	0.831604	0.415802	−	0.909455i	$-0.363501\pi$
$211$	12.0797	0.831604	0.415802	+	0.909455i	$0.363501\pi$
$212$	−14.5005	−0.995896
$213$	25.5178	1.74845
$214$	20.2159	1.38193
$215$	−10.3728	−0.707417
$216$	90.0540	6.12740
$217$	−6.70859	−0.455409
$218$	−34.6982	−2.35006
$219$	−12.3741	−0.836162
$220$	−47.9219	−3.23089
$221$	4.21889	0.283793
$222$	40.0461	2.68772
$223$	27.5569	1.84535	0.922673	−	0.385583i	$-0.126000\pi$
$223$	27.5569	1.84535	0.922673	+	0.385583i	$0.126000\pi$
$224$	−7.06966	−0.472362
$225$	−9.74740	−0.649827
$226$	−33.7205	−2.24305
$227$	−5.03708	−0.334323	−0.167161	−	0.985930i	$-0.553460\pi$
$227$	−5.03708	−0.334323	−0.167161	+	0.985930i	$0.553460\pi$
$228$	−40.3137	−2.66984
$229$	24.9859	1.65112	0.825558	−	0.564318i	$-0.190861\pi$
$229$	24.9859	1.65112	0.825558	+	0.564318i	$0.190861\pi$
$230$	−42.2604	−2.78657
$231$	−17.4382	−1.14735
$232$	24.3424	1.59816
$233$	5.15979	0.338029	0.169014	−	0.985614i	$-0.445942\pi$
$233$	5.15979	0.338029	0.169014	+	0.985614i	$0.445942\pi$
$234$	51.1661	3.34484
$235$	−19.1699	−1.25051
$236$	−29.9261	−1.94802
$237$	−32.8719	−2.13526
$238$	3.92833	0.254636
$239$	6.30611	0.407908	0.203954	−	0.978980i	$-0.434621\pi$
$239$	6.30611	0.407908	0.203954	+	0.978980i	$0.434621\pi$
$240$	48.5507	3.13393
$241$	−20.1600	−1.29862	−0.649309	−	0.760524i	$-0.724942\pi$
$241$	−20.1600	−1.29862	−0.649309	+	0.760524i	$0.724942\pi$
$242$	−48.1745	−3.09678
$243$	−28.1641	−1.80673
$244$	21.2846	1.36261
$245$	−1.91049	−0.122057
$246$	42.5095	2.71031
$247$	−7.56520	−0.481362
$248$	44.7791	2.84348
$249$	24.5982	1.55885
$250$	−31.1633	−1.97094
$251$	−21.0740	−1.33018	−0.665089	−	0.746764i	$-0.731607\pi$
$251$	−21.0740	−1.33018	−0.665089	+	0.746764i	$0.731607\pi$
$252$	33.2019	2.09152
$253$	−46.9720	−2.95310
$254$	−12.4371	−0.780371
$255$	−9.34026	−0.584910
$256$	−25.9192	−1.61995
$257$	−19.3546	−1.20731	−0.603654	−	0.797246i	$-0.706289\pi$
$257$	−19.3546	−1.20731	−0.603654	+	0.797246i	$0.706289\pi$
$258$	44.5862	2.77582
$259$	4.87651	0.303012
$260$	24.2367	1.50310
$261$	−26.3310	−1.62985
$262$	38.6193	2.38591
$263$	1.00432	0.0619291	0.0309645	−	0.999520i	$-0.490142\pi$
$263$	1.00432	0.0619291	0.0309645	+	0.999520i	$0.490142\pi$
$264$	116.398	7.16382
$265$	6.02437	0.370074
$266$	−7.04417	−0.431906
$267$	19.5129	1.19417
$268$	19.2181	1.17393
$269$	−25.1647	−1.53432	−0.767159	−	0.641457i	$-0.778330\pi$
$269$	−25.1647	−1.53432	−0.767159	+	0.641457i	$0.778330\pi$
$270$	−66.2104	−4.02943
$271$	11.2076	0.680815	0.340407	−	0.940278i	$-0.389435\pi$
$271$	11.2076	0.680815	0.340407	+	0.940278i	$0.389435\pi$
$272$	−12.1564	−0.737093
$273$	8.81946	0.533778
$274$	47.9814	2.89866
$275$	−7.36401	−0.444067
$276$	126.593	7.62002
$277$	−8.45410	−0.507958	−0.253979	−	0.967210i	$-0.581739\pi$
$277$	−8.45410	−0.507958	−0.253979	+	0.967210i	$0.581739\pi$
$278$	4.73556	0.284020
$279$	−48.4371	−2.89985
$280$	12.7523	0.762097
$281$	18.3157	1.09262	0.546311	−	0.837583i	$-0.316032\pi$
$281$	18.3157	1.09262	0.546311	+	0.837583i	$0.316032\pi$
$282$	82.3999	4.90684
$283$	−12.7408	−0.757360	−0.378680	−	0.925528i	$-0.623622\pi$
$283$	−12.7408	−0.757360	−0.378680	+	0.925528i	$0.623622\pi$
$284$	−36.7054	−2.17806
$285$	16.7487	0.992109
$286$	38.6553	2.28573
$287$	5.17648	0.305558
$288$	−51.0441	−3.00780
$289$	−14.6613	−0.862431
$290$	−17.8973	−1.05096
$291$	24.6688	1.44611
$292$	17.7992	1.04162
$293$	−4.58838	−0.268056	−0.134028	−	0.990978i	$-0.542791\pi$
$293$	−4.58838	−0.268056	−0.134028	+	0.990978i	$0.542791\pi$
$294$	8.21205	0.478936
$295$	12.4331	0.723884
$296$	−32.5502	−1.89194
$297$	−73.5922	−4.27025
$298$	−58.4473	−3.38576
$299$	23.7563	1.37386
$300$	19.8466	1.14584
$301$	5.42937	0.312944
$302$	38.9103	2.23904
$303$	−1.45151	−0.0833873
$304$	21.7986	1.25024
$305$	−8.84290	−0.506343
$306$	28.3632	1.62141
$307$	−5.64280	−0.322052	−0.161026	−	0.986950i	$-0.551480\pi$
$307$	−5.64280	−0.322052	−0.161026	+	0.986950i	$0.551480\pi$
$308$	25.0835	1.42927
$309$	24.1071	1.37141
$310$	−32.9229	−1.86990
$311$	16.3065	0.924656	0.462328	−	0.886709i	$-0.347014\pi$
$311$	16.3065	0.924656	0.462328	+	0.886709i	$0.347014\pi$
$312$	−58.8690	−3.33280
$313$	−27.4240	−1.55010	−0.775049	−	0.631901i	$-0.782275\pi$
$313$	−27.4240	−1.55010	−0.775049	+	0.631901i	$0.782275\pi$
$314$	9.56812	0.539960
$315$	−13.7941	−0.777207
$316$	47.2837	2.65992
$317$	9.00618	0.505838	0.252919	−	0.967488i	$-0.418609\pi$
$317$	9.00618	0.505838	0.252919	+	0.967488i	$0.418609\pi$
$318$	−25.8951	−1.45213
$319$	−19.8927	−1.11378
$320$	−4.32131	−0.241569
$321$	25.1594	1.40426
$322$	22.1202	1.23271
$323$	−4.19366	−0.233341
$324$	98.7311	5.48506
$325$	3.72438	0.206592
$326$	−48.5731	−2.69022
$327$	−43.1831	−2.38803
$328$	−34.5525	−1.90784
$329$	10.0340	0.553194
$330$	−85.5795	−4.71099
$331$	−24.5290	−1.34824	−0.674118	−	0.738624i	$-0.735476\pi$
$331$	−24.5290	−1.34824	−0.674118	+	0.738624i	$0.735476\pi$
$332$	−35.3826	−1.94187
$333$	35.2092	1.92945
$334$	−44.9070	−2.45720
$335$	−7.98435	−0.436232
$336$	−25.4127	−1.38638
$337$	24.7723	1.34943	0.674717	−	0.738077i	$-0.264266\pi$
$337$	24.7723	1.34943	0.674717	+	0.738077i	$0.264266\pi$
$338$	13.8437	0.752999
$339$	−41.9663	−2.27930
$340$	13.4353	0.728629
$341$	−36.5935	−1.98165
$342$	−50.8601	−2.75020
$343$	1.00000	0.0539949
$344$	−36.2405	−1.95395
$345$	−52.5944	−2.83159
$346$	61.8858	3.32700
$347$	−9.62086	−0.516475	−0.258238	−	0.966081i	$-0.583142\pi$
$347$	−9.62086	−0.516475	−0.258238	+	0.966081i	$0.583142\pi$
$348$	53.6123	2.87392
$349$	−0.971712	−0.0520146	−0.0260073	−	0.999662i	$-0.508279\pi$
$349$	−0.971712	−0.0520146	−0.0260073	+	0.999662i	$0.508279\pi$
$350$	3.46788	0.185366
$351$	37.2196	1.98663
$352$	−38.5631	−2.05542
$353$	−3.44080	−0.183135	−0.0915677	−	0.995799i	$-0.529188\pi$
$353$	−3.44080	−0.183135	−0.0915677	+	0.995799i	$0.529188\pi$
$354$	−53.4424	−2.84043
$355$	15.2496	0.809366
$356$	−28.0678	−1.48759
$357$	4.88893	0.258750
$358$	51.5740	2.72577
$359$	36.2705	1.91429	0.957143	−	0.289616i	$-0.0935275\pi$
$359$	36.2705	1.91429	0.957143	+	0.289616i	$0.0935275\pi$
$360$	92.0739	4.85272
$361$	−11.4800	−0.604213
$362$	−10.5987	−0.557055
$363$	−59.9548	−3.14681
$364$	−12.6861	−0.664933
$365$	−7.39484	−0.387063
$366$	38.0103	1.98683
$367$	−27.2921	−1.42464	−0.712319	−	0.701856i	$-0.752355\pi$
$367$	−27.2921	−1.42464	−0.712319	+	0.701856i	$0.752355\pi$
$368$	−68.4522	−3.56832
$369$	37.3751	1.94567
$370$	23.9319	1.24416
$371$	−3.15331	−0.163712
$372$	98.6224	5.11334
$373$	9.03245	0.467683	0.233841	−	0.972275i	$-0.424870\pi$
$373$	9.03245	0.467683	0.233841	+	0.972275i	$0.424870\pi$
$374$	21.4280	1.10801
$375$	−38.7837	−2.00278
$376$	−66.9761	−3.45403
$377$	10.0608	0.518158
$378$	34.6562	1.78252
$379$	−23.5625	−1.21032	−0.605161	−	0.796103i	$-0.706891\pi$
$379$	−23.5625	−1.21032	−0.605161	+	0.796103i	$0.706891\pi$
$380$	−24.0918	−1.23588
$381$	−15.4783	−0.792980
$382$	1.65071	0.0844579
$383$	13.8731	0.708880	0.354440	−	0.935079i	$-0.384672\pi$
$383$	13.8731	0.708880	0.354440	+	0.935079i	$0.384672\pi$
$384$	−26.6273	−1.35882
$385$	−10.4212	−0.531114
$386$	−59.7031	−3.03881
$387$	39.2010	1.99270
$388$	−35.4841	−1.80143
$389$	−19.1588	−0.971390	−0.485695	−	0.874128i	$-0.661433\pi$
$389$	−19.1588	−0.971390	−0.485695	+	0.874128i	$0.661433\pi$
$390$	43.2822	2.19168
$391$	13.1689	0.665982
$392$	−6.67489	−0.337133
$393$	48.0631	2.42446
$394$	51.6717	2.60318
$395$	−19.6445	−0.988421
$396$	181.107	9.10098
$397$	2.53541	0.127249	0.0636243	−	0.997974i	$-0.479734\pi$
$397$	2.53541	0.127249	0.0636243	+	0.997974i	$0.479734\pi$
$398$	−10.2729	−0.514932
$399$	−8.76671	−0.438884
$400$	−10.7316	−0.536578
$401$	12.3799	0.618223	0.309111	−	0.951026i	$-0.399968\pi$
$401$	12.3799	0.618223	0.309111	+	0.951026i	$0.399968\pi$
$402$	34.3199	1.71172
$403$	18.5073	0.921916
$404$	2.08789	0.103877
$405$	−41.0188	−2.03824
$406$	9.36790	0.464921
$407$	26.6000	1.31851
$408$	−32.6331	−1.61558
$409$	15.1585	0.749539	0.374770	−	0.927118i	$-0.377722\pi$
$409$	15.1585	0.749539	0.374770	+	0.927118i	$0.377722\pi$
$410$	25.4040	1.25461
$411$	59.7145	2.94550
$412$	−34.6762	−1.70838
$413$	−6.50781	−0.320228
$414$	159.711	7.84938
$415$	14.7001	0.721598
$416$	19.5035	0.956236
$417$	5.89357	0.288609
$418$	−38.4241	−1.87938
$419$	22.0922	1.07927	0.539636	−	0.841898i	$-0.318562\pi$
$419$	22.0922	1.07927	0.539636	+	0.841898i	$0.318562\pi$
$420$	28.0860	1.37046
$421$	−4.78276	−0.233098	−0.116549	−	0.993185i	$-0.537183\pi$
$421$	−4.78276	−0.233098	−0.116549	+	0.993185i	$0.537183\pi$
$422$	−31.0299	−1.51051
$423$	72.4474	3.52251
$424$	21.0480	1.02218
$425$	2.06456	0.100146
$426$	−65.5489	−3.17585
$427$	4.62860	0.223994
$428$	−36.1899	−1.74930
$429$	48.1077	2.32266
$430$	26.6451	1.28494
$431$	14.4177	0.694475	0.347237	−	0.937777i	$-0.387120\pi$
$431$	14.4177	0.694475	0.347237	+	0.937777i	$0.387120\pi$
$432$	−107.246	−5.15986
$433$	−14.9463	−0.718272	−0.359136	−	0.933285i	$-0.616929\pi$
$433$	−14.9463	−0.718272	−0.359136	+	0.933285i	$0.616929\pi$
$434$	17.2327	0.827196
$435$	−22.2738	−1.06795
$436$	62.1155	2.97479
$437$	−23.6142	−1.12962
$438$	31.7859	1.51879
$439$	−15.6274	−0.745857	−0.372928	−	0.927860i	$-0.621646\pi$
$439$	−15.6274	−0.745857	−0.372928	+	0.927860i	$0.621646\pi$
$440$	69.5604	3.31616
$441$	7.22017	0.343817
$442$	−10.8373	−0.515477
$443$	33.5131	1.59225	0.796127	−	0.605129i	$-0.206879\pi$
$443$	33.5131	1.59225	0.796127	+	0.605129i	$0.206879\pi$
$444$	−71.6892	−3.40222
$445$	11.6611	0.552787
$446$	−70.7869	−3.35186
$447$	−72.7396	−3.44047
$448$	2.26189	0.106864
$449$	2.68273	0.126606	0.0633029	−	0.997994i	$-0.479837\pi$
$449$	2.68273	0.126606	0.0633029	+	0.997994i	$0.479837\pi$
$450$	25.0387	1.18033
$451$	28.2363	1.32960
$452$	60.3653	2.83934
$453$	48.4252	2.27521
$454$	12.9390	0.607258
$455$	5.27058	0.247088
$456$	58.5169	2.74030
$457$	28.4747	1.33199	0.665995	−	0.745956i	$-0.268007\pi$
$457$	28.4747	1.33199	0.665995	+	0.745956i	$0.268007\pi$
$458$	−64.1826	−2.99906
$459$	20.6321	0.963025
$460$	75.6531	3.52734
$461$	2.40870	0.112184	0.0560921	−	0.998426i	$-0.482136\pi$
$461$	2.40870	0.112184	0.0560921	+	0.998426i	$0.482136\pi$
$462$	44.7945	2.08403
$463$	17.3148	0.804688	0.402344	−	0.915489i	$-0.368196\pi$
$463$	17.3148	0.804688	0.402344	+	0.915489i	$0.368196\pi$
$464$	−28.9895	−1.34581
$465$	−40.9737	−1.90011
$466$	−13.2542	−0.613990
$467$	7.81206	0.361499	0.180749	−	0.983529i	$-0.442148\pi$
$467$	7.81206	0.361499	0.180749	+	0.983529i	$0.442148\pi$
$468$	−91.5959	−4.23402
$469$	4.17921	0.192978
$470$	49.2428	2.27140
$471$	11.9078	0.548685
$472$	43.4389	1.99944
$473$	29.6157	1.36173
$474$	84.4398	3.87845
$475$	−3.70211	−0.169864
$476$	−7.03236	−0.322328
$477$	−22.7674	−1.04245
$478$	−16.1988	−0.740917
$479$	−11.9759	−0.547192	−0.273596	−	0.961845i	$-0.588213\pi$
$479$	−11.9759	−0.547192	−0.273596	+	0.961845i	$0.588213\pi$
$480$	−43.1790	−1.97084
$481$	−13.4531	−0.613408
$482$	51.7860	2.35879
$483$	27.5293	1.25263
$484$	86.2404	3.92002
$485$	14.7422	0.669411
$486$	72.3465	3.28170
$487$	19.5404	0.885461	0.442731	−	0.896655i	$-0.354010\pi$
$487$	19.5404	0.885461	0.442731	+	0.896655i	$0.354010\pi$
$488$	−30.8954	−1.39857
$489$	−60.4508	−2.73368
$490$	4.90758	0.221702
$491$	18.6232	0.840453	0.420226	−	0.907419i	$-0.361951\pi$
$491$	18.6232	0.840453	0.420226	+	0.907419i	$0.361951\pi$
$492$	−76.0991	−3.43081
$493$	5.57705	0.251178
$494$	19.4331	0.874339
$495$	−75.2429	−3.38191
$496$	−53.3277	−2.39448
$497$	−7.98204	−0.358043
$498$	−63.1867	−2.83146
$499$	−22.0268	−0.986053	−0.493026	−	0.870014i	$-0.664109\pi$
$499$	−22.0268	−0.986053	−0.493026	+	0.870014i	$0.664109\pi$
$500$	55.7874	2.49489
$501$	−55.8883	−2.49690
$502$	54.1339	2.41611
$503$	34.5399	1.54006	0.770030	−	0.638008i	$-0.220241\pi$
$503$	34.5399	1.54006	0.770030	+	0.638008i	$0.220241\pi$
$504$	−48.1938	−2.14672
$505$	−0.867436	−0.0386004
$506$	120.659	5.36397
$507$	17.2290	0.765166
$508$	22.2644	0.987823
$509$	−32.5629	−1.44332	−0.721661	−	0.692246i	$-0.756621\pi$
$509$	−32.5629	−1.44332	−0.721661	+	0.692246i	$0.756621\pi$
$510$	23.9928	1.06242
$511$	3.87065	0.171227
$512$	49.9218	2.20625
$513$	−36.9970	−1.63346
$514$	49.7173	2.19293
$515$	14.4066	0.634830
$516$	−79.8168	−3.51374
$517$	54.7329	2.40715
$518$	−12.5266	−0.550385
$519$	77.0189	3.38076
$520$	−35.1805	−1.54277
$521$	−26.2070	−1.14815	−0.574075	−	0.818803i	$-0.694638\pi$
$521$	−26.2070	−1.14815	−0.574075	+	0.818803i	$0.694638\pi$
$522$	67.6378	2.96043
$523$	−3.44571	−0.150671	−0.0753353	−	0.997158i	$-0.524003\pi$
$523$	−3.44571	−0.150671	−0.0753353	+	0.997158i	$0.524003\pi$
$524$	−69.1350	−3.02018
$525$	4.31589	0.188361
$526$	−2.57985	−0.112487
$527$	10.2593	0.446901
$528$	−138.619	−6.03263
$529$	51.1535	2.22406
$530$	−15.4751	−0.672196
$531$	−46.9875	−2.03908
$532$	12.6102	0.546723
$533$	−14.2806	−0.618563
$534$	−50.1238	−2.16907
$535$	15.0354	0.650039
$536$	−27.8958	−1.20491
$537$	64.1855	2.76981
$538$	64.6418	2.78691
$539$	5.45473	0.234952
$540$	118.528	5.10061
$541$	−0.978042	−0.0420493	−0.0210247	−	0.999779i	$-0.506693\pi$
$541$	−0.978042	−0.0420493	−0.0210247	+	0.999779i	$0.506693\pi$
$542$	−28.7896	−1.23662
$543$	−13.1904	−0.566055
$544$	10.8114	0.463537
$545$	−25.8065	−1.10543
$546$	−22.6550	−0.969545
$547$	1.89014	0.0808167	0.0404084	−	0.999183i	$-0.487134\pi$
$547$	1.89014	0.0808167	0.0404084	+	0.999183i	$0.487134\pi$
$548$	−85.8947	−3.66924
$549$	33.4193	1.42630
$550$	18.9163	0.806595
$551$	−10.0006	−0.426041
$552$	−183.755	−7.82113
$553$	10.2824	0.437253
$554$	21.7165	0.922646
$555$	29.7840	1.26426
$556$	−8.47744	−0.359524
$557$	−30.7042	−1.30098	−0.650489	−	0.759516i	$-0.725436\pi$
$557$	−30.7042	−1.30098	−0.650489	+	0.759516i	$0.725436\pi$
$558$	124.423	5.26725
$559$	−14.9783	−0.633514
$560$	−15.1868	−0.641760
$561$	26.6678	1.12592
$562$	−47.0485	−1.98462
$563$	−8.17735	−0.344634	−0.172317	−	0.985042i	$-0.555125\pi$
$563$	−8.17735	−0.344634	−0.172317	+	0.985042i	$0.555125\pi$
$564$	−147.510	−6.21127
$565$	−25.0794	−1.05510
$566$	32.7279	1.37566
$567$	21.4703	0.901668
$568$	53.2793	2.23555
$569$	−37.3294	−1.56493	−0.782464	−	0.622696i	$-0.786037\pi$
$569$	−37.3294	−1.56493	−0.782464	+	0.622696i	$0.786037\pi$
$570$	−43.0233	−1.80205
$571$	27.2548	1.14058	0.570289	−	0.821444i	$-0.306831\pi$
$571$	27.2548	1.14058	0.570289	+	0.821444i	$0.306831\pi$
$572$	−69.1993	−2.89337
$573$	2.05437	0.0858225
$574$	−13.2971	−0.555011
$575$	11.6254	0.484812
$576$	16.3312	0.680467
$577$	−32.2780	−1.34375	−0.671875	−	0.740665i	$-0.734511\pi$
$577$	−32.2780	−1.34375	−0.671875	+	0.740665i	$0.734511\pi$
$578$	37.6613	1.56650
$579$	−74.3025	−3.08790
$580$	32.0391	1.33035
$581$	−7.69439	−0.319217
$582$	−63.3680	−2.62669
$583$	−17.2004	−0.712369
$584$	−25.8362	−1.06911
$585$	38.0544	1.57336
$586$	11.7864	0.486893
$587$	−16.5558	−0.683329	−0.341665	−	0.939822i	$-0.610991\pi$
$587$	−16.5558	−0.683329	−0.341665	+	0.939822i	$0.610991\pi$
$588$	−14.7009	−0.606256
$589$	−18.3966	−0.758021
$590$	−31.9376	−1.31485
$591$	64.3072	2.64524
$592$	38.7642	1.59320
$593$	24.0201	0.986387	0.493194	−	0.869920i	$-0.335829\pi$
$593$	24.0201	0.986387	0.493194	+	0.869920i	$0.335829\pi$
$594$	189.040	7.75641
$595$	2.92166	0.119777
$596$	104.630	4.28583
$597$	−12.7849	−0.523252
$598$	−61.0241	−2.49546
$599$	−2.68332	−0.109637	−0.0548187	−	0.998496i	$-0.517458\pi$
$599$	−2.68332	−0.109637	−0.0548187	+	0.998496i	$0.517458\pi$
$600$	−28.8081	−1.17609
$601$	−12.0529	−0.491647	−0.245824	−	0.969315i	$-0.579058\pi$
$601$	−12.0529	−0.491647	−0.245824	+	0.969315i	$0.579058\pi$
$602$	−13.9467	−0.568426
$603$	30.1746	1.22881
$604$	−69.6559	−2.83426
$605$	−35.8294	−1.45667
$606$	3.72858	0.151463
$607$	20.7008	0.840220	0.420110	−	0.907473i	$-0.361991\pi$
$607$	20.7008	0.840220	0.420110	+	0.907473i	$0.361991\pi$
$608$	−19.3868	−0.786239
$609$	11.6587	0.472433
$610$	22.7152	0.919713
$611$	−27.6814	−1.11987
$612$	−50.7748	−2.05245
$613$	−7.26437	−0.293405	−0.146702	−	0.989181i	$-0.546866\pi$
$613$	−7.26437	−0.293405	−0.146702	+	0.989181i	$0.546866\pi$
$614$	14.4950	0.584969
$615$	31.6161	1.27489
$616$	−36.4097	−1.46699
$617$	45.1295	1.81684	0.908422	−	0.418055i	$-0.137288\pi$
$617$	45.1295	1.81684	0.908422	+	0.418055i	$0.137288\pi$
$618$	−61.9252	−2.49100
$619$	7.39544	0.297248	0.148624	−	0.988894i	$-0.452516\pi$
$619$	7.39544	0.297248	0.148624	+	0.988894i	$0.452516\pi$
$620$	58.9375	2.36699
$621$	116.178	4.66207
$622$	−41.8873	−1.67953
$623$	−6.10370	−0.244539
$624$	70.1073	2.80654
$625$	−16.4273	−0.657093
$626$	70.4456	2.81557
$627$	−47.8200	−1.90975
$628$	−17.1285	−0.683503
$629$	−7.45752	−0.297351
$630$	35.4335	1.41171
$631$	−27.0224	−1.07574	−0.537872	−	0.843027i	$-0.680771\pi$
$631$	−27.0224	−1.07574	−0.537872	+	0.843027i	$0.680771\pi$
$632$	−68.6341	−2.73012
$633$	−38.6177	−1.53492
$634$	−23.1347	−0.918795
$635$	−9.24997	−0.367074
$636$	46.3565	1.83816
$637$	−2.75875	−0.109306
$638$	51.0993	2.02304
$639$	−57.6317	−2.27987
$640$	−15.9127	−0.629003
$641$	−49.4139	−1.95173	−0.975865	−	0.218375i	$-0.929924\pi$
$641$	−49.4139	−1.95173	−0.975865	+	0.218375i	$0.929924\pi$
$642$	−64.6283	−2.55067
$643$	16.5617	0.653128	0.326564	−	0.945175i	$-0.394109\pi$
$643$	16.5617	0.653128	0.326564	+	0.945175i	$0.394109\pi$
$644$	−39.5987	−1.56041
$645$	33.1607	1.30570
$646$	10.7725	0.423837
$647$	19.8062	0.778661	0.389331	−	0.921098i	$-0.372706\pi$
$647$	19.8062	0.778661	0.389331	+	0.921098i	$0.372706\pi$
$648$	−143.312	−5.62983
$649$	−35.4983	−1.39343
$650$	−9.56703	−0.375250
$651$	21.4467	0.840562
$652$	86.9539	3.40538
$653$	−18.8671	−0.738326	−0.369163	−	0.929365i	$-0.620356\pi$
$653$	−18.8671	−0.738326	−0.369163	+	0.929365i	$0.620356\pi$
$654$	110.927	4.33757
$655$	28.7228	1.12229
$656$	41.1487	1.60659
$657$	27.9467	1.09031
$658$	−25.7749	−1.00481
$659$	14.9081	0.580739	0.290370	−	0.956915i	$-0.406222\pi$
$659$	14.9081	0.580739	0.290370	+	0.956915i	$0.406222\pi$
$660$	153.201	5.96336
$661$	−27.6019	−1.07359	−0.536795	−	0.843713i	$-0.680365\pi$
$661$	−27.6019	−1.07359	−0.536795	+	0.843713i	$0.680365\pi$
$662$	63.0090	2.44891
$663$	−13.4874	−0.523806
$664$	51.3593	1.99313
$665$	−5.23905	−0.203162
$666$	−90.4438	−3.50463
$667$	31.4040	1.21597
$668$	80.3910	3.11042
$669$	−88.0966	−3.40601
$670$	20.5098	0.792364
$671$	25.2478	0.974679
$672$	22.6010	0.871852
$673$	−26.3053	−1.01399	−0.506997	−	0.861948i	$-0.669245\pi$
$673$	−26.3053	−1.01399	−0.506997	+	0.861948i	$0.669245\pi$
$674$	−63.6339	−2.45109
$675$	18.2138	0.701049
$676$	−24.7826	−0.953175
$677$	−14.3770	−0.552551	−0.276276	−	0.961078i	$-0.589100\pi$
$677$	−14.3770	−0.552551	−0.276276	+	0.961078i	$0.589100\pi$
$678$	107.801	4.14007
$679$	−7.71647	−0.296131
$680$	−19.5018	−0.747859
$681$	16.1030	0.617070
$682$	93.9997	3.59944
$683$	−10.7321	−0.410652	−0.205326	−	0.978694i	$-0.565825\pi$
$683$	−10.7321	−0.410652	−0.205326	+	0.978694i	$0.565825\pi$
$684$	91.0480	3.48131
$685$	35.6858	1.36348
$686$	−2.56875	−0.0980755
$687$	−79.8774	−3.04751
$688$	43.1590	1.64542
$689$	8.69920	0.331413
$690$	135.102	5.14325
$691$	−5.04768	−0.192023	−0.0960113	−	0.995380i	$-0.530609\pi$
$691$	−5.04768	−0.192023	−0.0960113	+	0.995380i	$0.530609\pi$
$692$	−110.786	−4.21144
$693$	39.3840	1.49608
$694$	24.7136	0.938116
$695$	3.52204	0.133599
$696$	−77.8203	−2.94977
$697$	−7.91626	−0.299850
$698$	2.49609	0.0944784
$699$	−16.4953	−0.623910
$700$	−6.20808	−0.234643
$701$	−15.7907	−0.596406	−0.298203	−	0.954503i	$-0.596387\pi$
$701$	−15.7907	−0.596406	−0.298203	+	0.954503i	$0.596387\pi$
$702$	−95.6079	−3.60849
$703$	13.3726	0.504358
$704$	12.3380	0.465005
$705$	61.2843	2.30810
$706$	8.83857	0.332644
$707$	0.454038	0.0170759
$708$	95.6708	3.59553
$709$	−30.7089	−1.15330	−0.576649	−	0.816992i	$-0.695640\pi$
$709$	−30.7089	−1.15330	−0.576649	+	0.816992i	$0.695640\pi$
$710$	−39.1725	−1.47012
$711$	74.2408	2.78425
$712$	40.7415	1.52685
$713$	57.7693	2.16348
$714$	−12.5585	−0.469989
$715$	28.7496	1.07517
$716$	−92.3260	−3.45038
$717$	−20.1600	−0.752888
$718$	−93.1701	−3.47708
$719$	40.5149	1.51095	0.755475	−	0.655178i	$-0.227406\pi$
$719$	40.5149	1.51095	0.755475	+	0.655178i	$0.227406\pi$
$720$	−109.651	−4.08646
$721$	−7.54078	−0.280833
$722$	29.4894	1.09748
$723$	64.4495	2.39690
$724$	18.9734	0.705141
$725$	4.92336	0.182849
$726$	154.009	5.71582
$727$	34.3785	1.27503	0.637514	−	0.770438i	$-0.279963\pi$
$727$	34.3785	1.27503	0.637514	+	0.770438i	$0.279963\pi$
$728$	18.4144	0.682483
$729$	25.6268	0.949139
$730$	18.9955	0.703055
$731$	−8.30299	−0.307097
$732$	−68.0447	−2.51501
$733$	13.7131	0.506504	0.253252	−	0.967400i	$-0.418500\pi$
$733$	13.7131	0.506504	0.253252	+	0.967400i	$0.418500\pi$
$734$	70.1067	2.58769
$735$	6.10765	0.225284
$736$	60.8786	2.24401
$737$	22.7965	0.839719
$738$	−96.0073	−3.53408
$739$	52.7242	1.93949	0.969745	−	0.244120i	$-0.0784991\pi$
$739$	52.7242	1.93949	0.969745	+	0.244120i	$0.0784991\pi$
$740$	−42.8420	−1.57490
$741$	24.1852	0.888465
$742$	8.10007	0.297363
$743$	33.1565	1.21639	0.608197	−	0.793786i	$-0.291893\pi$
$743$	33.1565	1.21639	0.608197	+	0.793786i	$0.291893\pi$
$744$	−143.154	−5.24829
$745$	−43.4697	−1.59261
$746$	−23.2021	−0.849491
$747$	−55.5548	−2.03264
$748$	−38.3596	−1.40257
$749$	−7.86993	−0.287561
$750$	99.6258	3.63782
$751$	49.9148	1.82142	0.910709	−	0.413049i	$-0.135536\pi$
$751$	49.9148	1.82142	0.910709	+	0.413049i	$0.135536\pi$
$752$	79.7621	2.90863
$753$	67.3714	2.45515
$754$	−25.8437	−0.941173
$755$	28.9393	1.05321
$756$	−62.0404	−2.25639
$757$	4.92985	0.179178	0.0895892	−	0.995979i	$-0.471445\pi$
$757$	4.92985	0.179178	0.0895892	+	0.995979i	$0.471445\pi$
$758$	60.5262	2.19841
$759$	150.165	5.45063
$760$	34.9701	1.26850
$761$	7.91919	0.287071	0.143535	−	0.989645i	$-0.454153\pi$
$761$	7.91919	0.287071	0.143535	+	0.989645i	$0.454153\pi$
$762$	39.7600	1.44035
$763$	13.5078	0.489015
$764$	−2.95505	−0.106910
$765$	21.0949	0.762688
$766$	−35.6365	−1.28760
$767$	17.9534	0.648261
$768$	82.8610	2.98999
$769$	53.3536	1.92398	0.961990	−	0.273084i	$-0.0880437\pi$
$769$	53.3536	1.92398	0.961990	+	0.273084i	$0.0880437\pi$
$770$	26.7695	0.964706
$771$	61.8748	2.22837
$772$	106.878	3.84664
$773$	25.4336	0.914783	0.457392	−	0.889265i	$-0.348784\pi$
$773$	25.4336	0.914783	0.457392	+	0.889265i	$0.348784\pi$
$774$	−100.698	−3.61950
$775$	9.05675	0.325328
$776$	51.5066	1.84898
$777$	−15.5897	−0.559278
$778$	49.2143	1.76442
$779$	14.1952	0.508597
$780$	−77.4823	−2.77431
$781$	−43.5399	−1.55798
$782$	−33.8278	−1.20968
$783$	49.2015	1.75832
$784$	7.94917	0.283899
$785$	7.11622	0.253989
$786$	−123.462	−4.40375
$787$	−21.0090	−0.748890	−0.374445	−	0.927249i	$-0.622167\pi$
$787$	−21.0090	−0.748890	−0.374445	+	0.927249i	$0.622167\pi$
$788$	−92.5009	−3.29521
$789$	−3.21071	−0.114304
$790$	50.4618	1.79535
$791$	13.1272	0.466749
$792$	−262.884	−9.34119
$793$	−12.7692	−0.453447
$794$	−6.51285	−0.231132
$795$	−19.2593	−0.683057
$796$	18.3901	0.651821
$797$	−12.3246	−0.436560	−0.218280	−	0.975886i	$-0.570045\pi$
$797$	−12.3246	−0.436560	−0.218280	+	0.975886i	$0.570045\pi$
$798$	22.5195	0.797182
$799$	−15.3448	−0.542859
$800$	9.54421	0.337439
$801$	−44.0697	−1.55713
$802$	−31.8009	−1.12293
$803$	21.1133	0.745073
$804$	−61.4383	−2.16676
$805$	16.4517	0.579846
$806$	−47.5408	−1.67455
$807$	80.4489	2.83194
$808$	−3.03066	−0.106618
$809$	18.3583	0.645443	0.322722	−	0.946494i	$-0.395402\pi$
$809$	18.3583	0.645443	0.322722	+	0.946494i	$0.395402\pi$
$810$	105.367	3.70223
$811$	−33.1118	−1.16271	−0.581356	−	0.813649i	$-0.697478\pi$
$811$	−33.1118	−1.16271	−0.581356	+	0.813649i	$0.697478\pi$
$812$	−16.7701	−0.588515
$813$	−35.8296	−1.25660
$814$	−68.3289	−2.39493
$815$	−36.1259	−1.26543
$816$	38.8629	1.36048
$817$	14.8887	0.520890
$818$	−38.9384	−1.36145
$819$	−19.9187	−0.696014
$820$	−45.4774	−1.58814
$821$	44.5159	1.55361	0.776807	−	0.629739i	$-0.216838\pi$
$821$	44.5159	1.55361	0.776807	+	0.629739i	$0.216838\pi$
$822$	−153.392	−5.35015
$823$	49.9970	1.74278	0.871392	−	0.490587i	$-0.163218\pi$
$823$	49.9970	1.74278	0.871392	+	0.490587i	$0.163218\pi$
$824$	50.3339	1.75346
$825$	23.5420	0.819628
$826$	16.7170	0.581657
$827$	−35.1271	−1.22149	−0.610744	−	0.791828i	$-0.709130\pi$
$827$	−35.1271	−1.22149	−0.610744	+	0.791828i	$0.709130\pi$
$828$	−285.910	−9.93604
$829$	−39.1375	−1.35930	−0.679650	−	0.733536i	$-0.737869\pi$
$829$	−39.1375	−1.35930	−0.679650	+	0.733536i	$0.737869\pi$
$830$	−37.7609	−1.31070
$831$	27.0269	0.937553
$832$	−6.23999	−0.216333
$833$	−1.52927	−0.0529862
$834$	−15.1391	−0.524225
$835$	−33.3992	−1.15583
$836$	68.7854	2.37899
$837$	90.5085	3.12843
$838$	−56.7493	−1.96037
$839$	23.3994	0.807838	0.403919	−	0.914795i	$-0.367648\pi$
$839$	23.3994	0.807838	0.403919	+	0.914795i	$0.367648\pi$
$840$	−40.7679	−1.40663
$841$	−15.7004	−0.541392
$842$	12.2857	0.423394
$843$	−58.5534	−2.01669
$844$	55.5486	1.91206
$845$	10.2962	0.354199
$846$	−186.099	−6.39823
$847$	18.7541	0.644397
$848$	−25.0662	−0.860776
$849$	40.7309	1.39788
$850$	−5.30334	−0.181903
$851$	−41.9928	−1.43949
$852$	117.343	4.02012
$853$	−0.274564	−0.00940088	−0.00470044	−	0.999989i	$-0.501496\pi$
$853$	−0.274564	−0.00940088	−0.00470044	+	0.999989i	$0.501496\pi$
$854$	−11.8897	−0.406858
$855$	−37.8268	−1.29365
$856$	52.5310	1.79547
$857$	18.4628	0.630679	0.315339	−	0.948979i	$-0.397882\pi$
$857$	18.4628	0.630679	0.315339	+	0.948979i	$0.397882\pi$
$858$	−123.577	−4.21885
$859$	−5.05933	−0.172622	−0.0863111	−	0.996268i	$-0.527508\pi$
$859$	−5.05933	−0.172622	−0.0863111	+	0.996268i	$0.527508\pi$
$860$	−47.6991	−1.62653
$861$	−16.5487	−0.563978
$862$	−37.0355	−1.26143
$863$	−1.00000	−0.0340404
$863$	−1.00000	−0.0340404
$864$	95.3800	3.24489
$865$	46.0271	1.56497
$866$	38.3933	1.30466
$867$	46.8708	1.59181
$868$	−30.8494	−1.04710
$869$	56.0878	1.90265
$870$	57.2158	1.93980
$871$	−11.5294	−0.390660
$872$	−90.1631	−3.05331
$873$	−55.7142	−1.88564
$874$	60.6591	2.05182
$875$	12.1317	0.410125
$876$	−56.9021	−1.92254
$877$	1.82136	0.0615030	0.0307515	−	0.999527i	$-0.490210\pi$
$877$	1.82136	0.0615030	0.0307515	+	0.999527i	$0.490210\pi$
$878$	40.1430	1.35476
$879$	14.6686	0.494760
$880$	−82.8399	−2.79253
$881$	−22.2482	−0.749560	−0.374780	−	0.927114i	$-0.622282\pi$
$881$	−22.2482	−0.749560	−0.374780	+	0.927114i	$0.622282\pi$
$882$	−18.5468	−0.624504
$883$	−10.7783	−0.362720	−0.181360	−	0.983417i	$-0.558050\pi$
$883$	−10.7783	−0.362720	−0.181360	+	0.983417i	$0.558050\pi$
$884$	19.4005	0.652511
$885$	−39.7474	−1.33609
$886$	−86.0868	−2.89214
$887$	−53.5965	−1.79959	−0.899797	−	0.436308i	$-0.856286\pi$
$887$	−53.5965	−1.79959	−0.899797	+	0.436308i	$0.856286\pi$
$888$	104.060	3.49201
$889$	4.84167	0.162385
$890$	−29.9544	−1.00407
$891$	117.115	3.92349
$892$	126.720	4.24291
$893$	27.5159	0.920783
$894$	186.850	6.24920
$895$	38.3578	1.28216
$896$	8.32909	0.278255
$897$	−75.9465	−2.53578
$898$	−6.89127	−0.229965
$899$	24.4653	0.815964
$900$	−44.8234	−1.49411
$901$	4.82227	0.160653
$902$	−72.5321	−2.41505
$903$	−17.3572	−0.577610
$904$	−87.6225	−2.91428
$905$	−7.88270	−0.262030
$906$	−124.392	−4.13266
$907$	−49.6902	−1.64994	−0.824968	−	0.565179i	$-0.808807\pi$
$907$	−49.6902	−1.64994	−0.824968	+	0.565179i	$0.808807\pi$
$908$	−23.1630	−0.768691
$909$	3.27823	0.108732
$910$	−13.5388	−0.448807
$911$	−25.5240	−0.845647	−0.422823	−	0.906212i	$-0.638961\pi$
$911$	−25.5240	−0.845647	−0.422823	+	0.906212i	$0.638961\pi$
$912$	−69.6880	−2.30760
$913$	−41.9708	−1.38903
$914$	−73.1445	−2.41940
$915$	28.2699	0.934573
$916$	114.898	3.79632
$917$	−15.0343	−0.496475
$918$	−52.9988	−1.74922
$919$	−2.50207	−0.0825358	−0.0412679	−	0.999148i	$-0.513140\pi$
$919$	−2.50207	−0.0825358	−0.0412679	+	0.999148i	$0.513140\pi$
$920$	−109.813	−3.62044
$921$	18.0395	0.594421
$922$	−6.18735	−0.203770
$923$	22.0205	0.724813
$924$	−80.1895	−2.63804
$925$	−6.58341	−0.216461
$926$	−44.4775	−1.46162
$927$	−54.4457	−1.78823
$928$	25.7821	0.846339
$929$	44.1712	1.44921	0.724606	−	0.689164i	$-0.242022\pi$
$929$	44.1712	1.44921	0.724606	+	0.689164i	$0.242022\pi$
$930$	105.251	3.45133
$931$	2.74225	0.0898737
$932$	23.7273	0.777212
$933$	−52.1302	−1.70667
$934$	−20.0672	−0.656620
$935$	15.9369	0.521192
$936$	132.955	4.34577
$937$	46.7473	1.52717	0.763584	−	0.645708i	$-0.223438\pi$
$937$	46.7473	1.52717	0.763584	+	0.645708i	$0.223438\pi$
$938$	−10.7354	−0.350522
$939$	87.6719	2.86106
$940$	−88.1528	−2.87523
$941$	13.1809	0.429687	0.214843	−	0.976649i	$-0.431076\pi$
$941$	13.1809	0.429687	0.214843	+	0.976649i	$0.431076\pi$
$942$	−30.5883	−0.996622
$943$	−44.5759	−1.45159
$944$	−51.7317	−1.68372
$945$	25.7753	0.838470
$946$	−76.0755	−2.47343
$947$	40.6263	1.32018	0.660088	−	0.751188i	$-0.270519\pi$
$947$	40.6263	1.32018	0.660088	+	0.751188i	$0.270519\pi$
$948$	−151.161	−4.90949
$949$	−10.6782	−0.346628
$950$	9.50980	0.308539
$951$	−28.7919	−0.933640
$952$	10.2077	0.330835
$953$	24.5735	0.796012	0.398006	−	0.917383i	$-0.369702\pi$
$953$	24.5735	0.796012	0.398006	+	0.917383i	$0.369702\pi$
$954$	58.4839	1.89348
$955$	1.22771	0.0397277
$956$	28.9986	0.937882
$957$	63.5948	2.05573
$958$	30.7631	0.993911
$959$	−18.6789	−0.603172
$960$	13.8148	0.445871
$961$	14.0051	0.451779
$962$	34.5577	1.11418
$963$	−56.8222	−1.83107
$964$	−92.7056	−2.98585
$965$	−44.4037	−1.42941
$966$	−70.7159	−2.27525
$967$	36.7244	1.18098	0.590488	−	0.807046i	$-0.298935\pi$
$967$	36.7244	1.18098	0.590488	+	0.807046i	$0.298935\pi$
$968$	−125.181	−4.02348
$969$	13.4067	0.430685
$970$	−37.8692	−1.21591
$971$	−32.5720	−1.04529	−0.522643	−	0.852552i	$-0.675054\pi$
$971$	−32.5720	−1.04529	−0.522643	+	0.852552i	$0.675054\pi$
$972$	−129.512	−4.15411
$973$	−1.84353	−0.0591007
$974$	−50.1945	−1.60834
$975$	−11.9065	−0.381313
$976$	36.7935	1.17773
$977$	−58.0328	−1.85663	−0.928317	−	0.371789i	$-0.878745\pi$
$977$	−58.0328	−1.85663	−0.928317	+	0.371789i	$0.878745\pi$
$978$	155.283	4.96541
$979$	−33.2940	−1.06408
$980$	−8.78538	−0.280639
$981$	97.5285	3.11385
$982$	−47.8384	−1.52658
$983$	12.3076	0.392551	0.196275	−	0.980549i	$-0.437115\pi$
$983$	12.3076	0.392551	0.196275	+	0.980549i	$0.437115\pi$
$984$	110.461	3.52136
$985$	38.4304	1.22450
$986$	−14.3261	−0.456235
$987$	−32.0778	−1.02105
$988$	−34.7886	−1.10677
$989$	−46.7536	−1.48668
$990$	193.280	6.14285
$991$	14.2905	0.453951	0.226976	−	0.973900i	$-0.427116\pi$
$991$	14.2905	0.453951	0.226976	+	0.973900i	$0.427116\pi$
$992$	47.4274	1.50582
$993$	78.4168	2.48848
$994$	20.5039	0.650344
$995$	−7.64036	−0.242216
$996$	113.115	3.58418
$997$	16.1716	0.512159	0.256079	−	0.966656i	$-0.417569\pi$
$997$	16.1716	0.512159	0.256079	+	0.966656i	$0.417569\pi$
$998$	56.5813	1.79105
$999$	−65.7912	−2.08154

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6041.2.a.f.1.12	✓	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6041.2.a.f.1.12	✓	132	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:	\( N \)	\(=\)	\( 6041 = 7 \cdot 863 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.56875 q^{2} -3.19690 q^{3} +4.59849 q^{4} -1.91049 q^{5} +8.21205 q^{6} +1.00000 q^{7} -6.67489 q^{8} +7.22017 q^{9} +O(q^{10})\)	\(q-2.56875 q^{2} -3.19690 q^{3} +4.59849 q^{4} -1.91049 q^{5} +8.21205 q^{6} +1.00000 q^{7} -6.67489 q^{8} +7.22017 q^{9} +4.90758 q^{10} +5.45473 q^{11} -14.7009 q^{12} -2.75875 q^{13} -2.56875 q^{14} +6.10765 q^{15} +7.94917 q^{16} -1.52927 q^{17} -18.5468 q^{18} +2.74225 q^{19} -8.78538 q^{20} -3.19690 q^{21} -14.0119 q^{22} -8.61124 q^{23} +21.3390 q^{24} -1.35002 q^{25} +7.08656 q^{26} -13.4914 q^{27} +4.59849 q^{28} -3.64687 q^{29} -15.6890 q^{30} -6.70859 q^{31} -7.06966 q^{32} -17.4382 q^{33} +3.92833 q^{34} -1.91049 q^{35} +33.2019 q^{36} +4.87651 q^{37} -7.04417 q^{38} +8.81946 q^{39} +12.7523 q^{40} +5.17648 q^{41} +8.21205 q^{42} +5.42937 q^{43} +25.0835 q^{44} -13.7941 q^{45} +22.1202 q^{46} +10.0340 q^{47} -25.4127 q^{48} +1.00000 q^{49} +3.46788 q^{50} +4.88893 q^{51} -12.6861 q^{52} -3.15331 q^{53} +34.6562 q^{54} -10.4212 q^{55} -6.67489 q^{56} -8.76671 q^{57} +9.36790 q^{58} -6.50781 q^{59} +28.0860 q^{60} +4.62860 q^{61} +17.2327 q^{62} +7.22017 q^{63} +2.26189 q^{64} +5.27058 q^{65} +44.7945 q^{66} +4.17921 q^{67} -7.03236 q^{68} +27.5293 q^{69} +4.90758 q^{70} -7.98204 q^{71} -48.1938 q^{72} +3.87065 q^{73} -12.5266 q^{74} +4.31589 q^{75} +12.6102 q^{76} +5.45473 q^{77} -22.6550 q^{78} +10.2824 q^{79} -15.1868 q^{80} +21.4703 q^{81} -13.2971 q^{82} -7.69439 q^{83} -14.7009 q^{84} +2.92166 q^{85} -13.9467 q^{86} +11.6587 q^{87} -36.4097 q^{88} -6.10370 q^{89} +35.4335 q^{90} -2.75875 q^{91} -39.5987 q^{92} +21.4467 q^{93} -25.7749 q^{94} -5.23905 q^{95} +22.6010 q^{96} -7.71647 q^{97} -2.56875 q^{98} +39.3840 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9}+O(q^{10}) \) 132 * q + 8 * q^2 + 10 * q^3 + 174 * q^4 + 11 * q^5 + 16 * q^6 + 132 * q^7 + 30 * q^8 + 178 * q^9	\( 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9} + 22 q^{10} + 32 q^{11} + 30 q^{12} + 16 q^{13} + 8 q^{14} + 59 q^{15} + 254 q^{16} + 11 q^{17} + 33 q^{18} + 40 q^{19} + 4 q^{20} + 10 q^{21} + 66 q^{22} + 62 q^{23} + 36 q^{24} + 235 q^{25} + 25 q^{26} + 37 q^{27} + 174 q^{28} + 28 q^{29} + 45 q^{30} + 121 q^{31} + 53 q^{32} - 13 q^{33} + 44 q^{34} + 11 q^{35} + 274 q^{36} + 61 q^{37} - 28 q^{38} + 114 q^{39} + 32 q^{40} - q^{41} + 16 q^{42} + 105 q^{43} + 54 q^{44} + 29 q^{45} + 104 q^{46} + 33 q^{47} + 16 q^{48} + 132 q^{49} - 14 q^{50} + 53 q^{51} - 11 q^{52} + 48 q^{53} + 11 q^{54} + 118 q^{55} + 30 q^{56} + 93 q^{57} + 87 q^{58} + 12 q^{59} + 41 q^{60} + 54 q^{61} - 28 q^{62} + 178 q^{63} + 376 q^{64} + 22 q^{65} + 6 q^{66} + 123 q^{67} - 47 q^{68} + 58 q^{69} + 22 q^{70} + 108 q^{71} + 97 q^{72} + q^{73} - 10 q^{74} + 23 q^{75} + 71 q^{76} + 32 q^{77} + 5 q^{78} + 204 q^{79} - 10 q^{80} + 296 q^{81} + 80 q^{82} - 10 q^{83} + 30 q^{84} + 94 q^{85} + 48 q^{86} + 4 q^{87} + 155 q^{88} + q^{89} - 66 q^{90} + 16 q^{91} + 49 q^{92} + 90 q^{93} + 79 q^{94} + 100 q^{95} + q^{96} + 18 q^{97} + 8 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q + 8 * q^2 + 10 * q^3 + 174 * q^4 + 11 * q^5 + 16 * q^6 + 132 * q^7 + 30 * q^8 + 178 * q^9 + 22 * q^10 + 32 * q^11 + 30 * q^12 + 16 * q^13 + 8 * q^14 + 59 * q^15 + 254 * q^16 + 11 * q^17 + 33 * q^18 + 40 * q^19 + 4 * q^20 + 10 * q^21 + 66 * q^22 + 62 * q^23 + 36 * q^24 + 235 * q^25 + 25 * q^26 + 37 * q^27 + 174 * q^28 + 28 * q^29 + 45 * q^30 + 121 * q^31 + 53 * q^32 - 13 * q^33 + 44 * q^34 + 11 * q^35 + 274 * q^36 + 61 * q^37 - 28 * q^38 + 114 * q^39 + 32 * q^40 - q^41 + 16 * q^42 + 105 * q^43 + 54 * q^44 + 29 * q^45 + 104 * q^46 + 33 * q^47 + 16 * q^48 + 132 * q^49 - 14 * q^50 + 53 * q^51 - 11 * q^52 + 48 * q^53 + 11 * q^54 + 118 * q^55 + 30 * q^56 + 93 * q^57 + 87 * q^58 + 12 * q^59 + 41 * q^60 + 54 * q^61 - 28 * q^62 + 178 * q^63 + 376 * q^64 + 22 * q^65 + 6 * q^66 + 123 * q^67 - 47 * q^68 + 58 * q^69 + 22 * q^70 + 108 * q^71 + 97 * q^72 + q^73 - 10 * q^74 + 23 * q^75 + 71 * q^76 + 32 * q^77 + 5 * q^78 + 204 * q^79 - 10 * q^80 + 296 * q^81 + 80 * q^82 - 10 * q^83 + 30 * q^84 + 94 * q^85 + 48 * q^86 + 4 * q^87 + 155 * q^88 + q^89 - 66 * q^90 + 16 * q^91 + 49 * q^92 + 90 * q^93 + 79 * q^94 + 100 * q^95 + q^96 + 18 * q^97 + 8 * q^98 + 96 * q^99

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