LMFDB - Embedded newform 8049.2.a.d.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8049,2,Mod(1,8049)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8049, 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("8049.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8049 = 3 \cdot 2683 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8049.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.2715885869$
Analytic rank:	$0$
Dimension:	$129$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	8049.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.57732 q^{2} +1.00000 q^{3} +4.64257 q^{4} -1.35723 q^{5} -2.57732 q^{6} +3.16714 q^{7} -6.81075 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.57732 q^{2} +1.00000 q^{3} +4.64257 q^{4} -1.35723 q^{5} -2.57732 q^{6} +3.16714 q^{7} -6.81075 q^{8} +1.00000 q^{9} +3.49801 q^{10} +5.90037 q^{11} +4.64257 q^{12} -4.84826 q^{13} -8.16272 q^{14} -1.35723 q^{15} +8.26834 q^{16} -3.32860 q^{17} -2.57732 q^{18} +3.47256 q^{19} -6.30102 q^{20} +3.16714 q^{21} -15.2071 q^{22} -0.769102 q^{23} -6.81075 q^{24} -3.15794 q^{25} +12.4955 q^{26} +1.00000 q^{27} +14.7037 q^{28} +4.45549 q^{29} +3.49801 q^{30} +8.32619 q^{31} -7.68864 q^{32} +5.90037 q^{33} +8.57887 q^{34} -4.29852 q^{35} +4.64257 q^{36} +0.282935 q^{37} -8.94990 q^{38} -4.84826 q^{39} +9.24373 q^{40} -5.22352 q^{41} -8.16272 q^{42} +9.44935 q^{43} +27.3929 q^{44} -1.35723 q^{45} +1.98222 q^{46} -3.56041 q^{47} +8.26834 q^{48} +3.03076 q^{49} +8.13901 q^{50} -3.32860 q^{51} -22.5084 q^{52} -10.0611 q^{53} -2.57732 q^{54} -8.00814 q^{55} -21.5706 q^{56} +3.47256 q^{57} -11.4832 q^{58} -15.2852 q^{59} -6.30102 q^{60} +5.90600 q^{61} -21.4593 q^{62} +3.16714 q^{63} +3.27940 q^{64} +6.58018 q^{65} -15.2071 q^{66} +9.33613 q^{67} -15.4533 q^{68} -0.769102 q^{69} +11.0787 q^{70} +7.12267 q^{71} -6.81075 q^{72} -2.80574 q^{73} -0.729214 q^{74} -3.15794 q^{75} +16.1216 q^{76} +18.6873 q^{77} +12.4955 q^{78} +8.43060 q^{79} -11.2220 q^{80} +1.00000 q^{81} +13.4627 q^{82} +13.8345 q^{83} +14.7037 q^{84} +4.51767 q^{85} -24.3540 q^{86} +4.45549 q^{87} -40.1860 q^{88} +1.76229 q^{89} +3.49801 q^{90} -15.3551 q^{91} -3.57061 q^{92} +8.32619 q^{93} +9.17631 q^{94} -4.71305 q^{95} -7.68864 q^{96} -16.7429 q^{97} -7.81124 q^{98} +5.90037 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 129 q + 8 q^{2} + 129 q^{3} + 158 q^{4} + 11 q^{5} + 8 q^{6} + 40 q^{7} + 18 q^{8} + 129 q^{9}+O(q^{10}) $ 129 * q + 8 * q^2 + 129 * q^3 + 158 * q^4 + 11 * q^5 + 8 * q^6 + 40 * q^7 + 18 * q^8 + 129 * q^9	\( 129 q + 8 q^{2} + 129 q^{3} + 158 q^{4} + 11 q^{5} + 8 q^{6} + 40 q^{7} + 18 q^{8} + 129 q^{9} + 20 q^{10} + 48 q^{11} + 158 q^{12} + 77 q^{13} + 13 q^{14} + 11 q^{15} + 212 q^{16} + 9 q^{17} + 8 q^{18} + 68 q^{19} + 19 q^{20} + 40 q^{21} + 45 q^{22} + 64 q^{23} + 18 q^{24} + 188 q^{25} + 19 q^{26} + 129 q^{27} + 69 q^{28} + 23 q^{29} + 20 q^{30} + 133 q^{31} + 24 q^{32} + 48 q^{33} + 63 q^{34} + 26 q^{35} + 158 q^{36} + 147 q^{37} + 9 q^{38} + 77 q^{39} + 58 q^{40} + 21 q^{41} + 13 q^{42} + 76 q^{43} + 110 q^{44} + 11 q^{45} + 48 q^{46} + 85 q^{47} + 212 q^{48} + 213 q^{49} + 17 q^{50} + 9 q^{51} + 139 q^{52} + 30 q^{53} + 8 q^{54} + 103 q^{55} + 19 q^{56} + 68 q^{57} + 94 q^{58} + 64 q^{59} + 19 q^{60} + 110 q^{61} - 10 q^{62} + 40 q^{63} + 288 q^{64} - 8 q^{65} + 45 q^{66} + 118 q^{67} - 15 q^{68} + 64 q^{69} + 75 q^{70} + 154 q^{71} + 18 q^{72} + 137 q^{73} + 28 q^{74} + 188 q^{75} + 156 q^{76} + 17 q^{77} + 19 q^{78} + 157 q^{79} + 2 q^{80} + 129 q^{81} + 72 q^{82} + 39 q^{83} + 69 q^{84} + 127 q^{85} + 54 q^{86} + 23 q^{87} + 97 q^{88} + 31 q^{89} + 20 q^{90} + 137 q^{91} + 82 q^{92} + 133 q^{93} + 40 q^{94} + 68 q^{95} + 24 q^{96} + 170 q^{97} - 21 q^{98} + 48 q^{99}+O(q^{100}) \) 129 * q + 8 * q^2 + 129 * q^3 + 158 * q^4 + 11 * q^5 + 8 * q^6 + 40 * q^7 + 18 * q^8 + 129 * q^9 + 20 * q^10 + 48 * q^11 + 158 * q^12 + 77 * q^13 + 13 * q^14 + 11 * q^15 + 212 * q^16 + 9 * q^17 + 8 * q^18 + 68 * q^19 + 19 * q^20 + 40 * q^21 + 45 * q^22 + 64 * q^23 + 18 * q^24 + 188 * q^25 + 19 * q^26 + 129 * q^27 + 69 * q^28 + 23 * q^29 + 20 * q^30 + 133 * q^31 + 24 * q^32 + 48 * q^33 + 63 * q^34 + 26 * q^35 + 158 * q^36 + 147 * q^37 + 9 * q^38 + 77 * q^39 + 58 * q^40 + 21 * q^41 + 13 * q^42 + 76 * q^43 + 110 * q^44 + 11 * q^45 + 48 * q^46 + 85 * q^47 + 212 * q^48 + 213 * q^49 + 17 * q^50 + 9 * q^51 + 139 * q^52 + 30 * q^53 + 8 * q^54 + 103 * q^55 + 19 * q^56 + 68 * q^57 + 94 * q^58 + 64 * q^59 + 19 * q^60 + 110 * q^61 - 10 * q^62 + 40 * q^63 + 288 * q^64 - 8 * q^65 + 45 * q^66 + 118 * q^67 - 15 * q^68 + 64 * q^69 + 75 * q^70 + 154 * q^71 + 18 * q^72 + 137 * q^73 + 28 * q^74 + 188 * q^75 + 156 * q^76 + 17 * q^77 + 19 * q^78 + 157 * q^79 + 2 * q^80 + 129 * q^81 + 72 * q^82 + 39 * q^83 + 69 * q^84 + 127 * q^85 + 54 * q^86 + 23 * q^87 + 97 * q^88 + 31 * q^89 + 20 * q^90 + 137 * q^91 + 82 * q^92 + 133 * q^93 + 40 * q^94 + 68 * q^95 + 24 * q^96 + 170 * q^97 - 21 * q^98 + 48 * 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 $

$2$	−2.57732	−1.82244	−0.911220	−	0.411920i	$-0.864858\pi$
$2$	−2.57732	−1.82244	−0.911220	+	0.411920i	$0.864858\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.64257	2.32129
$5$	−1.35723	−0.606970	−0.303485	−	0.952836i	$-0.598150\pi$
$5$	−1.35723	−0.606970	−0.303485	+	0.952836i	$0.598150\pi$
$6$	−2.57732	−1.05219
$7$	3.16714	1.19707	0.598533	−	0.801098i	$-0.295751\pi$
$7$	3.16714	1.19707	0.598533	+	0.801098i	$0.295751\pi$
$8$	−6.81075	−2.40797
$9$	1.00000	0.333333
$10$	3.49801	1.10617
$11$	5.90037	1.77903	0.889514	−	0.456907i	$-0.151043\pi$
$11$	5.90037	1.77903	0.889514	+	0.456907i	$0.151043\pi$
$12$	4.64257	1.34020
$13$	−4.84826	−1.34466	−0.672332	−	0.740250i	$-0.734707\pi$
$13$	−4.84826	−1.34466	−0.672332	+	0.740250i	$0.734707\pi$
$14$	−8.16272	−2.18158
$15$	−1.35723	−0.350434
$16$	8.26834	2.06708
$17$	−3.32860	−0.807305	−0.403652	−	0.914912i	$-0.632259\pi$
$17$	−3.32860	−0.807305	−0.403652	+	0.914912i	$0.632259\pi$
$18$	−2.57732	−0.607480
$19$	3.47256	0.796660	0.398330	−	0.917242i	$-0.369590\pi$
$19$	3.47256	0.796660	0.398330	+	0.917242i	$0.369590\pi$
$20$	−6.30102	−1.40895
$21$	3.16714	0.691126
$22$	−15.2071	−3.24217
$23$	−0.769102	−0.160369	−0.0801844	−	0.996780i	$-0.525551\pi$
$23$	−0.769102	−0.160369	−0.0801844	+	0.996780i	$0.525551\pi$
$24$	−6.81075	−1.39024
$25$	−3.15794	−0.631587
$26$	12.4955	2.45057
$27$	1.00000	0.192450
$28$	14.7037	2.77873
$29$	4.45549	0.827364	0.413682	−	0.910421i	$-0.364243\pi$
$29$	4.45549	0.827364	0.413682	+	0.910421i	$0.364243\pi$
$30$	3.49801	0.638645
$31$	8.32619	1.49543	0.747714	−	0.664021i	$-0.231151\pi$
$31$	8.32619	1.49543	0.747714	+	0.664021i	$0.231151\pi$
$32$	−7.68864	−1.35917
$33$	5.90037	1.02712
$34$	8.57887	1.47126
$35$	−4.29852	−0.726583
$36$	4.64257	0.773762
$37$	0.282935	0.0465142	0.0232571	−	0.999730i	$-0.492596\pi$
$37$	0.282935	0.0465142	0.0232571	+	0.999730i	$0.492596\pi$
$38$	−8.94990	−1.45187
$39$	−4.84826	−0.776342
$40$	9.24373	1.46156
$41$	−5.22352	−0.815777	−0.407889	−	0.913032i	$-0.633735\pi$
$41$	−5.22352	−0.815777	−0.407889	+	0.913032i	$0.633735\pi$
$42$	−8.16272	−1.25954
$43$	9.44935	1.44101	0.720506	−	0.693449i	$-0.243910\pi$
$43$	9.44935	1.44101	0.720506	+	0.693449i	$0.243910\pi$
$44$	27.3929	4.12964
$45$	−1.35723	−0.202323
$46$	1.98222	0.292262
$47$	−3.56041	−0.519339	−0.259670	−	0.965698i	$-0.583614\pi$
$47$	−3.56041	−0.519339	−0.259670	+	0.965698i	$0.583614\pi$
$48$	8.26834	1.19343
$49$	3.03076	0.432966
$50$	8.13901	1.15103
$51$	−3.32860	−0.466098
$52$	−22.5084	−3.12135
$53$	−10.0611	−1.38199	−0.690997	−	0.722857i	$-0.742828\pi$
$53$	−10.0611	−1.38199	−0.690997	+	0.722857i	$0.742828\pi$
$54$	−2.57732	−0.350729
$55$	−8.00814	−1.07982
$56$	−21.5706	−2.88249
$57$	3.47256	0.459952
$58$	−11.4832	−1.50782
$59$	−15.2852	−1.98997	−0.994985	−	0.100027i	$-0.968107\pi$
$59$	−15.2852	−1.98997	−0.994985	+	0.100027i	$0.968107\pi$
$60$	−6.30102	−0.813459
$61$	5.90600	0.756186	0.378093	−	0.925768i	$-0.376580\pi$
$61$	5.90600	0.756186	0.378093	+	0.925768i	$0.376580\pi$
$62$	−21.4593	−2.72533
$63$	3.16714	0.399022
$64$	3.27940	0.409925
$65$	6.58018	0.816171
$66$	−15.2071	−1.87187
$67$	9.33613	1.14059	0.570295	−	0.821440i	$-0.306829\pi$
$67$	9.33613	1.14059	0.570295	+	0.821440i	$0.306829\pi$
$68$	−15.4533	−1.87399
$69$	−0.769102	−0.0925889
$70$	11.0787	1.32415
$71$	7.12267	0.845306	0.422653	−	0.906292i	$-0.361099\pi$
$71$	7.12267	0.845306	0.422653	+	0.906292i	$0.361099\pi$
$72$	−6.81075	−0.802655
$73$	−2.80574	−0.328387	−0.164193	−	0.986428i	$-0.552502\pi$
$73$	−2.80574	−0.328387	−0.164193	+	0.986428i	$0.552502\pi$
$74$	−0.729214	−0.0847694
$75$	−3.15794	−0.364647
$76$	16.1216	1.84928
$77$	18.6873	2.12961
$78$	12.4955	1.41484
$79$	8.43060	0.948516	0.474258	−	0.880386i	$-0.342716\pi$
$79$	8.43060	0.948516	0.474258	+	0.880386i	$0.342716\pi$
$80$	−11.2220	−1.25466
$81$	1.00000	0.111111
$82$	13.4627	1.48671
$83$	13.8345	1.51854	0.759268	−	0.650777i	$-0.225557\pi$
$83$	13.8345	1.51854	0.759268	+	0.650777i	$0.225557\pi$
$84$	14.7037	1.60430
$85$	4.51767	0.490010
$86$	−24.3540	−2.62616
$87$	4.45549	0.477679
$88$	−40.1860	−4.28384
$89$	1.76229	0.186803	0.0934013	−	0.995629i	$-0.470226\pi$
$89$	1.76229	0.186803	0.0934013	+	0.995629i	$0.470226\pi$
$90$	3.49801	0.368722
$91$	−15.3551	−1.60965
$92$	−3.57061	−0.372262
$93$	8.32619	0.863386
$94$	9.17631	0.946464
$95$	−4.71305	−0.483549
$96$	−7.68864	−0.784719
$97$	−16.7429	−1.69998	−0.849991	−	0.526798i	$-0.823393\pi$
$97$	−16.7429	−1.69998	−0.849991	+	0.526798i	$0.823393\pi$
$98$	−7.81124	−0.789054
$99$	5.90037	0.593010
$100$	−14.6610	−1.46610
$101$	−9.28778	−0.924168	−0.462084	−	0.886836i	$-0.652898\pi$
$101$	−9.28778	−0.924168	−0.462084	+	0.886836i	$0.652898\pi$
$102$	8.57887	0.849435
$103$	8.78308	0.865422	0.432711	−	0.901533i	$-0.357557\pi$
$103$	8.78308	0.865422	0.432711	+	0.901533i	$0.357557\pi$
$104$	33.0203	3.23791
$105$	−4.29852	−0.419493
$106$	25.9306	2.51860
$107$	−3.28022	−0.317111	−0.158556	−	0.987350i	$-0.550684\pi$
$107$	−3.28022	−0.317111	−0.158556	+	0.987350i	$0.550684\pi$
$108$	4.64257	0.446732
$109$	12.2806	1.17627	0.588135	−	0.808763i	$-0.299863\pi$
$109$	12.2806	1.17627	0.588135	+	0.808763i	$0.299863\pi$
$110$	20.6395	1.96790
$111$	0.282935	0.0268550
$112$	26.1870	2.47444
$113$	2.10709	0.198219	0.0991093	−	0.995077i	$-0.468401\pi$
$113$	2.10709	0.198219	0.0991093	+	0.995077i	$0.468401\pi$
$114$	−8.94990	−0.838235
$115$	1.04384	0.0973390
$116$	20.6849	1.92055
$117$	−4.84826	−0.448221
$118$	39.3950	3.62660
$119$	−10.5421	−0.966397
$120$	9.24373	0.843834
$121$	23.8144	2.16494
$122$	−15.2216	−1.37810
$123$	−5.22352	−0.470989
$124$	38.6550	3.47132
$125$	11.0722	0.990325
$126$	−8.16272	−0.727193
$127$	12.0709	1.07112	0.535560	−	0.844497i	$-0.320100\pi$
$127$	12.0709	1.07112	0.535560	+	0.844497i	$0.320100\pi$
$128$	6.92522	0.612109
$129$	9.44935	0.831969
$130$	−16.9592	−1.48742
$131$	9.10645	0.795634	0.397817	−	0.917465i	$-0.369768\pi$
$131$	9.10645	0.795634	0.397817	+	0.917465i	$0.369768\pi$
$132$	27.3929	2.38425
$133$	10.9981	0.953655
$134$	−24.0622	−2.07866
$135$	−1.35723	−0.116811
$136$	22.6703	1.94396
$137$	−18.4071	−1.57262	−0.786311	−	0.617831i	$-0.788012\pi$
$137$	−18.4071	−1.57262	−0.786311	+	0.617831i	$0.788012\pi$
$138$	1.98222	0.168738
$139$	16.9927	1.44130	0.720650	−	0.693299i	$-0.243843\pi$
$139$	16.9927	1.44130	0.720650	+	0.693299i	$0.243843\pi$
$140$	−19.9562	−1.68661
$141$	−3.56041	−0.299841
$142$	−18.3574	−1.54052
$143$	−28.6065	−2.39220
$144$	8.26834	0.689028
$145$	−6.04711	−0.502185
$146$	7.23128	0.598465
$147$	3.03076	0.249973
$148$	1.31355	0.107973
$149$	16.8079	1.37696	0.688478	−	0.725257i	$-0.258279\pi$
$149$	16.8079	1.37696	0.688478	+	0.725257i	$0.258279\pi$
$150$	8.13901	0.664547
$151$	−9.45786	−0.769670	−0.384835	−	0.922985i	$-0.625742\pi$
$151$	−9.45786	−0.769670	−0.384835	+	0.922985i	$0.625742\pi$
$152$	−23.6508	−1.91833
$153$	−3.32860	−0.269102
$154$	−48.1631	−3.88109
$155$	−11.3005	−0.907680
$156$	−22.5084	−1.80211
$157$	4.15717	0.331778	0.165889	−	0.986144i	$-0.446951\pi$
$157$	4.15717	0.331778	0.165889	+	0.986144i	$0.446951\pi$
$158$	−21.7283	−1.72861
$159$	−10.0611	−0.797895
$160$	10.4352	0.824977
$161$	−2.43585	−0.191972
$162$	−2.57732	−0.202493
$163$	−7.39555	−0.579264	−0.289632	−	0.957138i	$-0.593533\pi$
$163$	−7.39555	−0.579264	−0.289632	+	0.957138i	$0.593533\pi$
$164$	−24.2506	−1.89365
$165$	−8.00814	−0.623433
$166$	−35.6560	−2.76744
$167$	13.3015	1.02930	0.514650	−	0.857400i	$-0.327922\pi$
$167$	13.3015	1.02930	0.514650	+	0.857400i	$0.327922\pi$
$168$	−21.5706	−1.66421
$169$	10.5056	0.808123
$170$	−11.6435	−0.893013
$171$	3.47256	0.265553
$172$	43.8693	3.34500
$173$	−3.08225	−0.234339	−0.117170	−	0.993112i	$-0.537382\pi$
$173$	−3.08225	−0.234339	−0.117170	+	0.993112i	$0.537382\pi$
$174$	−11.4832	−0.870541
$175$	−10.0016	−0.756051
$176$	48.7863	3.67740
$177$	−15.2852	−1.14891
$178$	−4.54199	−0.340436
$179$	18.1880	1.35943	0.679716	−	0.733475i	$-0.262103\pi$
$179$	18.1880	1.35943	0.679716	+	0.733475i	$0.262103\pi$
$180$	−6.30102	−0.469651
$181$	0.552935	0.0410993	0.0205497	−	0.999789i	$-0.493458\pi$
$181$	0.552935	0.0410993	0.0205497	+	0.999789i	$0.493458\pi$
$182$	39.5750	2.93349
$183$	5.90600	0.436584
$184$	5.23816	0.386162
$185$	−0.384007	−0.0282327
$186$	−21.4593	−1.57347
$187$	−19.6400	−1.43622
$188$	−16.5295	−1.20553
$189$	3.16714	0.230375
$190$	12.1470	0.881239
$191$	−9.98096	−0.722197	−0.361098	−	0.932528i	$-0.617598\pi$
$191$	−9.98096	−0.722197	−0.361098	+	0.932528i	$0.617598\pi$
$192$	3.27940	0.236670
$193$	19.1313	1.37710	0.688550	−	0.725189i	$-0.258247\pi$
$193$	19.1313	1.37710	0.688550	+	0.725189i	$0.258247\pi$
$194$	43.1517	3.09811
$195$	6.58018	0.471217
$196$	14.0705	1.00504
$197$	−15.2255	−1.08478	−0.542388	−	0.840128i	$-0.682480\pi$
$197$	−15.2255	−1.08478	−0.542388	+	0.840128i	$0.682480\pi$
$198$	−15.2071	−1.08072
$199$	9.95465	0.705666	0.352833	−	0.935686i	$-0.385218\pi$
$199$	9.95465	0.705666	0.352833	+	0.935686i	$0.385218\pi$
$200$	21.5079	1.52084
$201$	9.33613	0.658520
$202$	23.9376	1.68424
$203$	14.1112	0.990409
$204$	−15.4533	−1.08195
$205$	7.08950	0.495152
$206$	−22.6368	−1.57718
$207$	−0.769102	−0.0534563
$208$	−40.0870	−2.77954
$209$	20.4894	1.41728
$210$	11.0787	0.764500
$211$	2.15275	0.148201	0.0741006	−	0.997251i	$-0.476391\pi$
$211$	2.15275	0.148201	0.0741006	+	0.997251i	$0.476391\pi$
$212$	−46.7093	−3.20801
$213$	7.12267	0.488038
$214$	8.45418	0.577916
$215$	−12.8249	−0.874651
$216$	−6.81075	−0.463413
$217$	26.3702	1.79013
$218$	−31.6511	−2.14368
$219$	−2.80574	−0.189594
$220$	−37.1784	−2.50657
$221$	16.1379	1.08555
$222$	−0.729214	−0.0489416
$223$	−29.5333	−1.97770	−0.988848	−	0.148926i	$-0.952418\pi$
$223$	−29.5333	−1.97770	−0.988848	+	0.148926i	$0.952418\pi$
$224$	−24.3510	−1.62702
$225$	−3.15794	−0.210529
$226$	−5.43065	−0.361242
$227$	−20.3102	−1.34804	−0.674019	−	0.738714i	$-0.735433\pi$
$227$	−20.3102	−1.34804	−0.674019	+	0.738714i	$0.735433\pi$
$228$	16.1216	1.06768
$229$	−0.867426	−0.0573211	−0.0286605	−	0.999589i	$-0.509124\pi$
$229$	−0.867426	−0.0573211	−0.0286605	+	0.999589i	$0.509124\pi$
$230$	−2.69032	−0.177395
$231$	18.6873	1.22953
$232$	−30.3453	−1.99226
$233$	11.1687	0.731684	0.365842	−	0.930677i	$-0.380781\pi$
$233$	11.1687	0.731684	0.365842	+	0.930677i	$0.380781\pi$
$234$	12.4955	0.816857
$235$	4.83228	0.315223
$236$	−70.9629	−4.61929
$237$	8.43060	0.547626
$238$	27.1705	1.76120
$239$	9.06409	0.586307	0.293154	−	0.956065i	$-0.405295\pi$
$239$	9.06409	0.586307	0.293154	+	0.956065i	$0.405295\pi$
$240$	−11.2220	−0.724378
$241$	−2.23418	−0.143916	−0.0719582	−	0.997408i	$-0.522925\pi$
$241$	−2.23418	−0.143916	−0.0719582	+	0.997408i	$0.522925\pi$
$242$	−61.3772	−3.94548
$243$	1.00000	0.0641500
$244$	27.4190	1.75532
$245$	−4.11343	−0.262797
$246$	13.4627	0.858350
$247$	−16.8359	−1.07124
$248$	−56.7076	−3.60094
$249$	13.8345	0.876728
$250$	−28.5365	−1.80481
$251$	25.9463	1.63772	0.818858	−	0.573996i	$-0.194607\pi$
$251$	25.9463	1.63772	0.818858	+	0.573996i	$0.194607\pi$
$252$	14.7037	0.926244
$253$	−4.53798	−0.285301
$254$	−31.1106	−1.95205
$255$	4.51767	0.282907
$256$	−24.4073	−1.52546
$257$	26.2301	1.63619	0.818095	−	0.575084i	$-0.195030\pi$
$257$	26.2301	1.63619	0.818095	+	0.575084i	$0.195030\pi$
$258$	−24.3540	−1.51621
$259$	0.896094	0.0556806
$260$	30.5490	1.89457
$261$	4.45549	0.275788
$262$	−23.4702	−1.44999
$263$	−12.5540	−0.774110	−0.387055	−	0.922057i	$-0.626508\pi$
$263$	−12.5540	−0.774110	−0.387055	+	0.922057i	$0.626508\pi$
$264$	−40.1860	−2.47328
$265$	13.6552	0.838829
$266$	−28.3456	−1.73798
$267$	1.76229	0.107850
$268$	43.3437	2.64763
$269$	−0.905154	−0.0551882	−0.0275941	−	0.999619i	$-0.508785\pi$
$269$	−0.905154	−0.0551882	−0.0275941	+	0.999619i	$0.508785\pi$
$270$	3.49801	0.212882
$271$	−8.32690	−0.505823	−0.252912	−	0.967489i	$-0.581388\pi$
$271$	−8.32690	−0.505823	−0.252912	+	0.967489i	$0.581388\pi$
$272$	−27.5220	−1.66877
$273$	−15.3551	−0.929333
$274$	47.4409	2.86601
$275$	−18.6330	−1.12361
$276$	−3.57061	−0.214925
$277$	12.1314	0.728907	0.364453	−	0.931222i	$-0.381256\pi$
$277$	12.1314	0.728907	0.364453	+	0.931222i	$0.381256\pi$
$278$	−43.7956	−2.62668
$279$	8.32619	0.498476
$280$	29.2762	1.74959
$281$	−28.1054	−1.67663	−0.838313	−	0.545190i	$-0.816458\pi$
$281$	−28.1054	−1.67663	−0.838313	+	0.545190i	$0.816458\pi$
$282$	9.17631	0.546441
$283$	−1.13119	−0.0672425	−0.0336212	−	0.999435i	$-0.510704\pi$
$283$	−1.13119	−0.0672425	−0.0336212	+	0.999435i	$0.510704\pi$
$284$	33.0675	1.96220
$285$	−4.71305	−0.279177
$286$	73.7281	4.35963
$287$	−16.5436	−0.976539
$288$	−7.68864	−0.453057
$289$	−5.92041	−0.348259
$290$	15.5853	0.915202
$291$	−16.7429	−0.981485
$292$	−13.0258	−0.762280
$293$	−4.45876	−0.260484	−0.130242	−	0.991482i	$-0.541575\pi$
$293$	−4.45876	−0.260484	−0.130242	+	0.991482i	$0.541575\pi$
$294$	−7.81124	−0.455561
$295$	20.7455	1.20785
$296$	−1.92700	−0.112005
$297$	5.90037	0.342374
$298$	−43.3193	−2.50942
$299$	3.72880	0.215642
$300$	−14.6610	−0.846450
$301$	29.9274	1.72499
$302$	24.3759	1.40268
$303$	−9.28778	−0.533569
$304$	28.7123	1.64676
$305$	−8.01578	−0.458982
$306$	8.57887	0.490421
$307$	23.4377	1.33766	0.668831	−	0.743414i	$-0.266795\pi$
$307$	23.4377	1.33766	0.668831	+	0.743414i	$0.266795\pi$
$308$	86.7571	4.94344
$309$	8.78308	0.499652
$310$	29.1251	1.65419
$311$	17.7535	1.00671	0.503356	−	0.864079i	$-0.332099\pi$
$311$	17.7535	1.00671	0.503356	+	0.864079i	$0.332099\pi$
$312$	33.0203	1.86941
$313$	−9.31118	−0.526299	−0.263150	−	0.964755i	$-0.584761\pi$
$313$	−9.31118	−0.526299	−0.263150	+	0.964755i	$0.584761\pi$
$314$	−10.7143	−0.604646
$315$	−4.29852	−0.242194
$316$	39.1397	2.20178
$317$	18.7900	1.05535	0.527676	−	0.849446i	$-0.323064\pi$
$317$	18.7900	1.05535	0.527676	+	0.849446i	$0.323064\pi$
$318$	25.9306	1.45412
$319$	26.2891	1.47190
$320$	−4.45089	−0.248812
$321$	−3.28022	−0.183084
$322$	6.27796	0.349857
$323$	−11.5588	−0.643148
$324$	4.64257	0.257921
$325$	15.3105	0.849273
$326$	19.0607	1.05567
$327$	12.2806	0.679119
$328$	35.5761	1.96436
$329$	−11.2763	−0.621683
$330$	20.6395	1.13617
$331$	31.0198	1.70500	0.852500	−	0.522727i	$-0.175085\pi$
$331$	31.0198	1.70500	0.852500	+	0.522727i	$0.175085\pi$
$332$	64.2278	3.52496
$333$	0.282935	0.0155047
$334$	−34.2822	−1.87584
$335$	−12.6712	−0.692304
$336$	26.1870	1.42862
$337$	−11.7245	−0.638672	−0.319336	−	0.947642i	$-0.603460\pi$
$337$	−11.7245	−0.638672	−0.319336	+	0.947642i	$0.603460\pi$
$338$	−27.0763	−1.47275
$339$	2.10709	0.114442
$340$	20.9736	1.13745
$341$	49.1276	2.66041
$342$	−8.94990	−0.483955
$343$	−12.5711	−0.678777
$344$	−64.3572	−3.46991
$345$	1.04384	0.0561987
$346$	7.94395	0.427069
$347$	2.93079	0.157333	0.0786666	−	0.996901i	$-0.474934\pi$
$347$	2.93079	0.157333	0.0786666	+	0.996901i	$0.474934\pi$
$348$	20.6849	1.10883
$349$	−21.5328	−1.15263	−0.576313	−	0.817229i	$-0.695509\pi$
$349$	−21.5328	−1.15263	−0.576313	+	0.817229i	$0.695509\pi$
$350$	25.7774	1.37786
$351$	−4.84826	−0.258781
$352$	−45.3658	−2.41801
$353$	35.2220	1.87468	0.937340	−	0.348416i	$-0.113280\pi$
$353$	35.2220	1.87468	0.937340	+	0.348416i	$0.113280\pi$
$354$	39.3950	2.09382
$355$	−9.66708	−0.513075
$356$	8.18157	0.433622
$357$	−10.5421	−0.557949
$358$	−46.8762	−2.47748
$359$	−0.773368	−0.0408168	−0.0204084	−	0.999792i	$-0.506497\pi$
$359$	−0.773368	−0.0408168	−0.0204084	+	0.999792i	$0.506497\pi$
$360$	9.24373	0.487188
$361$	−6.94131	−0.365332
$362$	−1.42509	−0.0749011
$363$	23.8144	1.24993
$364$	−71.2872	−3.73646
$365$	3.80802	0.199321
$366$	−15.2216	−0.795648
$367$	11.4243	0.596344	0.298172	−	0.954512i	$-0.403623\pi$
$367$	11.4243	0.596344	0.298172	+	0.954512i	$0.403623\pi$
$368$	−6.35919	−0.331496
$369$	−5.22352	−0.271926
$370$	0.989708	0.0514525
$371$	−31.8648	−1.65434
$372$	38.6550	2.00417
$373$	−9.15533	−0.474045	−0.237022	−	0.971504i	$-0.576172\pi$
$373$	−9.15533	−0.474045	−0.237022	+	0.971504i	$0.576172\pi$
$374$	50.6185	2.61742
$375$	11.0722	0.571764
$376$	24.2491	1.25055
$377$	−21.6014	−1.11253
$378$	−8.16272	−0.419845
$379$	23.0791	1.18549	0.592746	−	0.805390i	$-0.298044\pi$
$379$	23.0791	1.18549	0.592746	+	0.805390i	$0.298044\pi$
$380$	−21.8807	−1.12246
$381$	12.0709	0.618412
$382$	25.7241	1.31616
$383$	14.7428	0.753320	0.376660	−	0.926352i	$-0.377073\pi$
$383$	14.7428	0.753320	0.376660	+	0.926352i	$0.377073\pi$
$384$	6.92522	0.353401
$385$	−25.3629	−1.29261
$386$	−49.3074	−2.50968
$387$	9.44935	0.480337
$388$	−77.7300	−3.94614
$389$	29.1707	1.47901	0.739507	−	0.673149i	$-0.235059\pi$
$389$	29.1707	1.47901	0.739507	+	0.673149i	$0.235059\pi$
$390$	−16.9592	−0.858764
$391$	2.56003	0.129466
$392$	−20.6418	−1.04257
$393$	9.10645	0.459359
$394$	39.2411	1.97694
$395$	−11.4422	−0.575721
$396$	27.3929	1.37655
$397$	−28.9236	−1.45163	−0.725816	−	0.687889i	$-0.758538\pi$
$397$	−28.9236	−1.45163	−0.725816	+	0.687889i	$0.758538\pi$
$398$	−25.6563	−1.28603
$399$	10.9981	0.550593
$400$	−26.1109	−1.30554
$401$	−17.9163	−0.894699	−0.447350	−	0.894359i	$-0.647632\pi$
$401$	−17.9163	−0.894699	−0.447350	+	0.894359i	$0.647632\pi$
$402$	−24.0622	−1.20011
$403$	−40.3675	−2.01085
$404$	−43.1192	−2.14526
$405$	−1.35723	−0.0674411
$406$	−36.3690	−1.80496
$407$	1.66942	0.0827502
$408$	22.6703	1.12235
$409$	−37.8634	−1.87223	−0.936113	−	0.351699i	$-0.885604\pi$
$409$	−37.8634	−1.87223	−0.936113	+	0.351699i	$0.885604\pi$
$410$	−18.2719	−0.902386
$411$	−18.4071	−0.907954
$412$	40.7761	2.00889
$413$	−48.4105	−2.38212
$414$	1.98222	0.0974208
$415$	−18.7766	−0.921707
$416$	37.2765	1.82763
$417$	16.9927	0.832135
$418$	−52.8077	−2.58291
$419$	−18.1366	−0.886033	−0.443016	−	0.896514i	$-0.646092\pi$
$419$	−18.1366	−0.886033	−0.443016	+	0.896514i	$0.646092\pi$
$420$	−19.9562	−0.973763
$421$	−0.245628	−0.0119712	−0.00598559	−	0.999982i	$-0.501905\pi$
$421$	−0.245628	−0.0119712	−0.00598559	+	0.999982i	$0.501905\pi$
$422$	−5.54831	−0.270088
$423$	−3.56041	−0.173113
$424$	68.5235	3.32779
$425$	10.5115	0.509883
$426$	−18.3574	−0.889419
$427$	18.7051	0.905204
$428$	−15.2287	−0.736106
$429$	−28.6065	−1.38114
$430$	33.0539	1.59400
$431$	−29.4967	−1.42081	−0.710404	−	0.703794i	$-0.751488\pi$
$431$	−29.4967	−1.42081	−0.710404	+	0.703794i	$0.751488\pi$
$432$	8.26834	0.397811
$433$	6.89926	0.331558	0.165779	−	0.986163i	$-0.446986\pi$
$433$	6.89926	0.331558	0.165779	+	0.986163i	$0.446986\pi$
$434$	−67.9644	−3.26240
$435$	−6.04711	−0.289937
$436$	57.0136	2.73046
$437$	−2.67075	−0.127759
$438$	7.23128	0.345524
$439$	−18.4854	−0.882260	−0.441130	−	0.897443i	$-0.645422\pi$
$439$	−18.4854	−0.882260	−0.441130	+	0.897443i	$0.645422\pi$
$440$	54.5415	2.60016
$441$	3.03076	0.144322
$442$	−41.5926	−1.97836
$443$	−18.1854	−0.864015	−0.432007	−	0.901870i	$-0.642195\pi$
$443$	−18.1854	−0.864015	−0.432007	+	0.901870i	$0.642195\pi$
$444$	1.31355	0.0623382
$445$	−2.39183	−0.113384
$446$	76.1168	3.60423
$447$	16.8079	0.794986
$448$	10.3863	0.490707
$449$	31.9730	1.50890	0.754450	−	0.656357i	$-0.227904\pi$
$449$	31.9730	1.50890	0.754450	+	0.656357i	$0.227904\pi$
$450$	8.13901	0.383677
$451$	−30.8207	−1.45129
$452$	9.78233	0.460122
$453$	−9.45786	−0.444369
$454$	52.3460	2.45672
$455$	20.8403	0.977010
$456$	−23.6508	−1.10755
$457$	1.14790	0.0536967	0.0268483	−	0.999640i	$-0.491453\pi$
$457$	1.14790	0.0536967	0.0268483	+	0.999640i	$0.491453\pi$
$458$	2.23563	0.104464
$459$	−3.32860	−0.155366
$460$	4.84613	0.225952
$461$	−4.92560	−0.229408	−0.114704	−	0.993400i	$-0.536592\pi$
$461$	−4.92560	−0.229408	−0.114704	+	0.993400i	$0.536592\pi$
$462$	−48.1631	−2.24075
$463$	32.1486	1.49407	0.747037	−	0.664782i	$-0.231476\pi$
$463$	32.1486	1.49407	0.747037	+	0.664782i	$0.231476\pi$
$464$	36.8395	1.71023
$465$	−11.3005	−0.524049
$466$	−28.7852	−1.33345
$467$	−6.53959	−0.302616	−0.151308	−	0.988487i	$-0.548349\pi$
$467$	−6.53959	−0.302616	−0.151308	+	0.988487i	$0.548349\pi$
$468$	−22.5084	−1.04045
$469$	29.5688	1.36536
$470$	−12.4543	−0.574476
$471$	4.15717	0.191552
$472$	104.104	4.79178
$473$	55.7547	2.56360
$474$	−21.7283	−0.998015
$475$	−10.9661	−0.503161
$476$	−48.9427	−2.24328
$477$	−10.0611	−0.460665
$478$	−23.3611	−1.06851
$479$	−21.2000	−0.968652	−0.484326	−	0.874888i	$-0.660935\pi$
$479$	−21.2000	−0.968652	−0.484326	+	0.874888i	$0.660935\pi$
$480$	10.4352	0.476301
$481$	−1.37174	−0.0625460
$482$	5.75820	0.262279
$483$	−2.43585	−0.110835
$484$	110.560	5.02545
$485$	22.7239	1.03184
$486$	−2.57732	−0.116910
$487$	−33.0839	−1.49918	−0.749588	−	0.661905i	$-0.769748\pi$
$487$	−33.0839	−1.49918	−0.749588	+	0.661905i	$0.769748\pi$
$488$	−40.2243	−1.82087
$489$	−7.39555	−0.334438
$490$	10.6016	0.478932
$491$	−39.9902	−1.80473	−0.902366	−	0.430971i	$-0.858171\pi$
$491$	−39.9902	−1.80473	−0.902366	+	0.430971i	$0.858171\pi$
$492$	−24.2506	−1.09330
$493$	−14.8306	−0.667935
$494$	43.3914	1.95227
$495$	−8.00814	−0.359939
$496$	68.8438	3.09118
$497$	22.5585	1.01189
$498$	−35.6560	−1.59778
$499$	13.1050	0.586659	0.293330	−	0.956011i	$-0.405237\pi$
$499$	13.1050	0.586659	0.293330	+	0.956011i	$0.405237\pi$
$500$	51.4033	2.29883
$501$	13.3015	0.594267
$502$	−66.8719	−2.98464
$503$	−17.4351	−0.777392	−0.388696	−	0.921366i	$-0.627074\pi$
$503$	−17.4351	−0.777392	−0.388696	+	0.921366i	$0.627074\pi$
$504$	−21.5706	−0.960831
$505$	12.6056	0.560942
$506$	11.6958	0.519943
$507$	10.5056	0.466570
$508$	56.0401	2.48638
$509$	21.5923	0.957063	0.478532	−	0.878070i	$-0.341169\pi$
$509$	21.5923	0.957063	0.478532	+	0.878070i	$0.341169\pi$
$510$	−11.6435	−0.515581
$511$	−8.88616	−0.393101
$512$	49.0550	2.16794
$513$	3.47256	0.153317
$514$	−67.6034	−2.98186
$515$	−11.9206	−0.525285
$516$	43.8693	1.93124
$517$	−21.0077	−0.923919
$518$	−2.30952	−0.101475
$519$	−3.08225	−0.135296
$520$	−44.8160	−1.96531
$521$	7.53919	0.330298	0.165149	−	0.986269i	$-0.447190\pi$
$521$	7.53919	0.330298	0.165149	+	0.986269i	$0.447190\pi$
$522$	−11.4832	−0.502607
$523$	−14.0435	−0.614082	−0.307041	−	0.951696i	$-0.599339\pi$
$523$	−14.0435	−0.614082	−0.307041	+	0.951696i	$0.599339\pi$
$524$	42.2773	1.84689
$525$	−10.0016	−0.436506
$526$	32.3556	1.41077
$527$	−27.7146	−1.20727
$528$	48.7863	2.12315
$529$	−22.4085	−0.974282
$530$	−35.1937	−1.52872
$531$	−15.2852	−0.663323
$532$	51.0594	2.21371
$533$	25.3250	1.09695
$534$	−4.54199	−0.196551
$535$	4.45201	0.192477
$536$	−63.5861	−2.74650
$537$	18.1880	0.784869
$538$	2.33287	0.100577
$539$	17.8826	0.770259
$540$	−6.30102	−0.271153
$541$	−10.5773	−0.454753	−0.227377	−	0.973807i	$-0.573015\pi$
$541$	−10.5773	−0.454753	−0.227377	+	0.973807i	$0.573015\pi$
$542$	21.4611	0.921832
$543$	0.552935	0.0237287
$544$	25.5924	1.09727
$545$	−16.6676	−0.713960
$546$	39.5750	1.69365
$547$	−38.4339	−1.64331	−0.821657	−	0.569982i	$-0.806950\pi$
$547$	−38.4339	−1.64331	−0.821657	+	0.569982i	$0.806950\pi$
$548$	−85.4562	−3.65051
$549$	5.90600	0.252062
$550$	48.0232	2.04771
$551$	15.4720	0.659128
$552$	5.23816	0.222951
$553$	26.7009	1.13544
$554$	−31.2666	−1.32839
$555$	−0.384007	−0.0163002
$556$	78.8898	3.34567
$557$	40.5232	1.71702	0.858512	−	0.512793i	$-0.171389\pi$
$557$	40.5232	1.71702	0.858512	+	0.512793i	$0.171389\pi$
$558$	−21.4593	−0.908443
$559$	−45.8129	−1.93768
$560$	−35.5416	−1.50191
$561$	−19.6400	−0.829201
$562$	72.4365	3.05555
$563$	−41.4611	−1.74738	−0.873689	−	0.486484i	$-0.838279\pi$
$563$	−41.4611	−1.74738	−0.873689	+	0.486484i	$0.838279\pi$
$564$	−16.5295	−0.696016
$565$	−2.85980	−0.120313
$566$	2.91545	0.122545
$567$	3.16714	0.133007
$568$	−48.5108	−2.03547
$569$	16.6735	0.698990	0.349495	−	0.936938i	$-0.386353\pi$
$569$	16.6735	0.698990	0.349495	+	0.936938i	$0.386353\pi$
$570$	12.1470	0.508784
$571$	8.31425	0.347941	0.173970	−	0.984751i	$-0.444340\pi$
$571$	8.31425	0.347941	0.173970	+	0.984751i	$0.444340\pi$
$572$	−132.808	−5.55297
$573$	−9.98096	−0.416960
$574$	42.6382	1.77968
$575$	2.42877	0.101287
$576$	3.27940	0.136642
$577$	41.6623	1.73443	0.867213	−	0.497938i	$-0.165909\pi$
$577$	41.6623	1.73443	0.867213	+	0.497938i	$0.165909\pi$
$578$	15.2588	0.634681
$579$	19.1313	0.795069
$580$	−28.0742	−1.16572
$581$	43.8159	1.81779
$582$	43.1517	1.78870
$583$	−59.3641	−2.45861
$584$	19.1092	0.790744
$585$	6.58018	0.272057
$586$	11.4917	0.474716
$587$	−10.3713	−0.428069	−0.214035	−	0.976826i	$-0.568661\pi$
$587$	−10.3713	−0.428069	−0.214035	+	0.976826i	$0.568661\pi$
$588$	14.0705	0.580259
$589$	28.9132	1.19135
$590$	−53.4679	−2.20124
$591$	−15.2255	−0.626295
$592$	2.33940	0.0961489
$593$	30.7130	1.26123	0.630617	−	0.776094i	$-0.282802\pi$
$593$	30.7130	1.26123	0.630617	+	0.776094i	$0.282802\pi$
$594$	−15.2071	−0.623956
$595$	14.3081	0.586574
$596$	78.0319	3.19631
$597$	9.95465	0.407417
$598$	−9.61031	−0.392995
$599$	24.4652	0.999622	0.499811	−	0.866135i	$-0.333403\pi$
$599$	24.4652	0.999622	0.499811	+	0.866135i	$0.333403\pi$
$600$	21.5079	0.878058
$601$	4.35063	0.177466	0.0887330	−	0.996055i	$-0.471718\pi$
$601$	4.35063	0.177466	0.0887330	+	0.996055i	$0.471718\pi$
$602$	−77.1324	−3.14368
$603$	9.33613	0.380196
$604$	−43.9088	−1.78662
$605$	−32.3215	−1.31406
$606$	23.9376	0.972397
$607$	5.41224	0.219676	0.109838	−	0.993949i	$-0.464967\pi$
$607$	5.41224	0.219676	0.109838	+	0.993949i	$0.464967\pi$
$608$	−26.6993	−1.08280
$609$	14.1112	0.571813
$610$	20.6592	0.836467
$611$	17.2618	0.698337
$612$	−15.4533	−0.624662
$613$	2.69566	0.108877	0.0544383	−	0.998517i	$-0.482663\pi$
$613$	2.69566	0.108877	0.0544383	+	0.998517i	$0.482663\pi$
$614$	−60.4066	−2.43781
$615$	7.08950	0.285876
$616$	−127.275	−5.12804
$617$	25.3573	1.02085	0.510423	−	0.859923i	$-0.329489\pi$
$617$	25.3573	1.02085	0.510423	+	0.859923i	$0.329489\pi$
$618$	−22.6368	−0.910585
$619$	4.73565	0.190342	0.0951709	−	0.995461i	$-0.469660\pi$
$619$	4.73565	0.190342	0.0951709	+	0.995461i	$0.469660\pi$
$620$	−52.4635	−2.10699
$621$	−0.769102	−0.0308630
$622$	−45.7565	−1.83467
$623$	5.58142	0.223615
$624$	−40.0870	−1.60477
$625$	0.762246	0.0304899
$626$	23.9979	0.959148
$627$	20.4894	0.818268
$628$	19.3000	0.770152
$629$	−0.941778	−0.0375512
$630$	11.0787	0.441385
$631$	−7.73291	−0.307842	−0.153921	−	0.988083i	$-0.549190\pi$
$631$	−7.73291	−0.307842	−0.153921	+	0.988083i	$0.549190\pi$
$632$	−57.4187	−2.28399
$633$	2.15275	0.0855640
$634$	−48.4278	−1.92331
$635$	−16.3830	−0.650138
$636$	−46.7093	−1.85214
$637$	−14.6939	−0.582194
$638$	−67.7553	−2.68246
$639$	7.12267	0.281769
$640$	−9.39910	−0.371532
$641$	44.8219	1.77036	0.885179	−	0.465251i	$-0.154036\pi$
$641$	44.8219	1.77036	0.885179	+	0.465251i	$0.154036\pi$
$642$	8.45418	0.333660
$643$	−5.11028	−0.201530	−0.100765	−	0.994910i	$-0.532129\pi$
$643$	−5.11028	−0.201530	−0.100765	+	0.994910i	$0.532129\pi$
$644$	−11.3086	−0.445622
$645$	−12.8249	−0.504980
$646$	29.7907	1.17210
$647$	39.6507	1.55883	0.779415	−	0.626508i	$-0.215516\pi$
$647$	39.6507	1.55883	0.779415	+	0.626508i	$0.215516\pi$
$648$	−6.81075	−0.267552
$649$	−90.1886	−3.54021
$650$	−39.4600	−1.54775
$651$	26.3702	1.03353
$652$	−34.3344	−1.34464
$653$	−18.9423	−0.741268	−0.370634	−	0.928779i	$-0.620860\pi$
$653$	−18.9423	−0.741268	−0.370634	+	0.928779i	$0.620860\pi$
$654$	−31.6511	−1.23765
$655$	−12.3595	−0.482926
$656$	−43.1899	−1.68628
$657$	−2.80574	−0.109462
$658$	29.0626	1.13298
$659$	47.7481	1.86000	0.930000	−	0.367559i	$-0.119806\pi$
$659$	47.7481	1.86000	0.930000	+	0.367559i	$0.119806\pi$
$660$	−37.1784	−1.44717
$661$	21.8690	0.850607	0.425303	−	0.905051i	$-0.360167\pi$
$661$	21.8690	0.850607	0.425303	+	0.905051i	$0.360167\pi$
$662$	−79.9478	−3.10726
$663$	16.1379	0.626745
$664$	−94.2236	−3.65658
$665$	−14.9269	−0.578840
$666$	−0.729214	−0.0282565
$667$	−3.42673	−0.132683
$668$	61.7531	2.38930
$669$	−29.5333	−1.14182
$670$	32.6578	1.26168
$671$	34.8476	1.34528
$672$	−24.3510	−0.939359
$673$	−20.3316	−0.783725	−0.391863	−	0.920024i	$-0.628169\pi$
$673$	−20.3316	−0.783725	−0.391863	+	0.920024i	$0.628169\pi$
$674$	30.2176	1.16394
$675$	−3.15794	−0.121549
$676$	48.7730	1.87588
$677$	17.3725	0.667679	0.333839	−	0.942630i	$-0.391656\pi$
$677$	17.3725	0.667679	0.333839	+	0.942630i	$0.391656\pi$
$678$	−5.43065	−0.208563
$679$	−53.0270	−2.03499
$680$	−30.7687	−1.17993
$681$	−20.3102	−0.778290
$682$	−126.618	−4.84844
$683$	34.8996	1.33540	0.667698	−	0.744432i	$-0.267280\pi$
$683$	34.8996	1.33540	0.667698	+	0.744432i	$0.267280\pi$
$684$	16.1216	0.616426
$685$	24.9826	0.954535
$686$	32.3998	1.23703
$687$	−0.867426	−0.0330943
$688$	78.1304	2.97869
$689$	48.7787	1.85832
$690$	−2.69032	−0.102419
$691$	3.40302	0.129457	0.0647285	−	0.997903i	$-0.479382\pi$
$691$	3.40302	0.129457	0.0647285	+	0.997903i	$0.479382\pi$
$692$	−14.3096	−0.543969
$693$	18.6873	0.709871
$694$	−7.55359	−0.286730
$695$	−23.0629	−0.874826
$696$	−30.3453	−1.15023
$697$	17.3870	0.658581
$698$	55.4970	2.10059
$699$	11.1687	0.422438
$700$	−46.4333	−1.75501
$701$	−11.3387	−0.428255	−0.214128	−	0.976806i	$-0.568691\pi$
$701$	−11.3387	−0.428255	−0.214128	+	0.976806i	$0.568691\pi$
$702$	12.4955	0.471612
$703$	0.982510	0.0370561
$704$	19.3497	0.729268
$705$	4.83228	0.181994
$706$	−90.7784	−3.41649
$707$	−29.4157	−1.10629
$708$	−70.9629	−2.66695
$709$	−14.0131	−0.526275	−0.263137	−	0.964758i	$-0.584757\pi$
$709$	−14.0131	−0.526275	−0.263137	+	0.964758i	$0.584757\pi$
$710$	24.9152	0.935049
$711$	8.43060	0.316172
$712$	−12.0025	−0.449814
$713$	−6.40369	−0.239820
$714$	27.1705	1.01683
$715$	38.8255	1.45199
$716$	84.4390	3.15563
$717$	9.06409	0.338505
$718$	1.99322	0.0743861
$719$	12.2296	0.456088	0.228044	−	0.973651i	$-0.426767\pi$
$719$	12.2296	0.456088	0.228044	+	0.973651i	$0.426767\pi$
$720$	−11.2220	−0.418220
$721$	27.8172	1.03597
$722$	17.8900	0.665796
$723$	−2.23418	−0.0830902
$724$	2.56704	0.0954034
$725$	−14.0702	−0.522553
$726$	−61.3772	−2.27792
$727$	23.0667	0.855497	0.427749	−	0.903898i	$-0.359307\pi$
$727$	23.0667	0.855497	0.427749	+	0.903898i	$0.359307\pi$
$728$	104.580	3.87598
$729$	1.00000	0.0370370
$730$	−9.81449	−0.363251
$731$	−31.4531	−1.16334
$732$	27.4190	1.01344
$733$	6.95651	0.256944	0.128472	−	0.991713i	$-0.458993\pi$
$733$	6.95651	0.256944	0.128472	+	0.991713i	$0.458993\pi$
$734$	−29.4441	−1.08680
$735$	−4.11343	−0.151726
$736$	5.91334	0.217969
$737$	55.0866	2.02914
$738$	13.4627	0.495568
$739$	37.8374	1.39187	0.695935	−	0.718105i	$-0.254990\pi$
$739$	37.8374	1.39187	0.695935	+	0.718105i	$0.254990\pi$
$740$	−1.78278	−0.0655363
$741$	−16.8359	−0.618481
$742$	82.1258	3.01493
$743$	14.7713	0.541907	0.270954	−	0.962592i	$-0.412661\pi$
$743$	14.7713	0.541907	0.270954	+	0.962592i	$0.412661\pi$
$744$	−56.7076	−2.07900
$745$	−22.8121	−0.835771
$746$	23.5962	0.863918
$747$	13.8345	0.506179
$748$	−91.1801	−3.33387
$749$	−10.3889	−0.379603
$750$	−28.5365	−1.04201
$751$	−16.6342	−0.606991	−0.303496	−	0.952833i	$-0.598154\pi$
$751$	−16.6342	−0.606991	−0.303496	+	0.952833i	$0.598154\pi$
$752$	−29.4387	−1.07352
$753$	25.9463	0.945536
$754$	55.6736	2.02751
$755$	12.8365	0.467166
$756$	14.7037	0.534767
$757$	24.7401	0.899193	0.449596	−	0.893232i	$-0.351568\pi$
$757$	24.7401	0.899193	0.449596	+	0.893232i	$0.351568\pi$
$758$	−59.4821	−2.16049
$759$	−4.53798	−0.164718
$760$	32.0994	1.16437
$761$	6.62279	0.240076	0.120038	−	0.992769i	$-0.461698\pi$
$761$	6.62279	0.240076	0.120038	+	0.992769i	$0.461698\pi$
$762$	−31.1106	−1.12702
$763$	38.8944	1.40807
$764$	−46.3373	−1.67643
$765$	4.51767	0.163337
$766$	−37.9968	−1.37288
$767$	74.1068	2.67584
$768$	−24.4073	−0.880723
$769$	−24.5788	−0.886333	−0.443166	−	0.896439i	$-0.646145\pi$
$769$	−24.5788	−0.886333	−0.443166	+	0.896439i	$0.646145\pi$
$770$	65.3682	2.35571
$771$	26.2301	0.944654
$772$	88.8184	3.19664
$773$	34.2094	1.23043	0.615214	−	0.788360i	$-0.289070\pi$
$773$	34.2094	1.23043	0.615214	+	0.788360i	$0.289070\pi$
$774$	−24.3540	−0.875386
$775$	−26.2936	−0.944494
$776$	114.032	4.09350
$777$	0.896094	0.0321472
$778$	−75.1822	−2.69541
$779$	−18.1390	−0.649898
$780$	30.5490	1.09383
$781$	42.0264	1.50382
$782$	−6.59802	−0.235945
$783$	4.45549	0.159226
$784$	25.0594	0.894977
$785$	−5.64222	−0.201379
$786$	−23.4702	−0.837155
$787$	−32.8462	−1.17084	−0.585421	−	0.810729i	$-0.699071\pi$
$787$	−32.8462	−1.17084	−0.585421	+	0.810729i	$0.699071\pi$
$788$	−70.6857	−2.51807
$789$	−12.5540	−0.446933
$790$	29.4903	1.04922
$791$	6.67345	0.237281
$792$	−40.1860	−1.42795
$793$	−28.6338	−1.01682
$794$	74.5453	2.64551
$795$	13.6552	0.484298
$796$	46.2152	1.63805
$797$	4.98506	0.176580	0.0882900	−	0.996095i	$-0.471860\pi$
$797$	4.98506	0.176580	0.0882900	+	0.996095i	$0.471860\pi$
$798$	−28.3456	−1.00342
$799$	11.8512	0.419265
$800$	24.2802	0.858436
$801$	1.76229	0.0622675
$802$	46.1761	1.63054
$803$	−16.5549	−0.584210
$804$	43.3437	1.52861
$805$	3.30600	0.116521
$806$	104.040	3.66465
$807$	−0.905154	−0.0318629
$808$	63.2568	2.22536
$809$	50.4668	1.77432	0.887159	−	0.461463i	$-0.152675\pi$
$809$	50.4668	1.77432	0.887159	+	0.461463i	$0.152675\pi$
$810$	3.49801	0.122907
$811$	−18.7930	−0.659910	−0.329955	−	0.943997i	$-0.607034\pi$
$811$	−18.7930	−0.659910	−0.329955	+	0.943997i	$0.607034\pi$
$812$	65.5121	2.29902
$813$	−8.32690	−0.292037
$814$	−4.30263	−0.150807
$815$	10.0374	0.351596
$816$	−27.5220	−0.963463
$817$	32.8135	1.14800
$818$	97.5862	3.41202
$819$	−15.3551	−0.536550
$820$	32.9135	1.14939
$821$	−38.6536	−1.34902	−0.674511	−	0.738265i	$-0.735645\pi$
$821$	−38.6536	−1.34902	−0.674511	+	0.738265i	$0.735645\pi$
$822$	47.4409	1.65469
$823$	24.1443	0.841619	0.420809	−	0.907149i	$-0.361746\pi$
$823$	24.1443	0.841619	0.420809	+	0.907149i	$0.361746\pi$
$824$	−59.8194	−2.08391
$825$	−18.6330	−0.648718
$826$	124.769	4.34128
$827$	23.1472	0.804908	0.402454	−	0.915440i	$-0.368157\pi$
$827$	23.1472	0.804908	0.402454	+	0.915440i	$0.368157\pi$
$828$	−3.57061	−0.124087
$829$	−39.7048	−1.37900	−0.689502	−	0.724284i	$-0.742171\pi$
$829$	−39.7048	−1.37900	−0.689502	+	0.724284i	$0.742171\pi$
$830$	48.3933	1.67975
$831$	12.1314	0.420835
$832$	−15.8994	−0.551211
$833$	−10.0882	−0.349535
$834$	−43.7956	−1.51652
$835$	−18.0531	−0.624754
$836$	95.1236	3.28992
$837$	8.32619	0.287795
$838$	46.7439	1.61474
$839$	−16.6673	−0.575419	−0.287710	−	0.957718i	$-0.592894\pi$
$839$	−16.6673	−0.575419	−0.287710	+	0.957718i	$0.592894\pi$
$840$	29.2762	1.01012
$841$	−9.14859	−0.315469
$842$	0.633062	0.0218168
$843$	−28.1054	−0.968000
$844$	9.99428	0.344017
$845$	−14.2585	−0.490506
$846$	9.17631	0.315488
$847$	75.4234	2.59158
$848$	−83.1884	−2.85670
$849$	−1.13119	−0.0388225
$850$	−27.0915	−0.929232
$851$	−0.217606	−0.00745943
$852$	33.0675	1.13288
$853$	11.6264	0.398082	0.199041	−	0.979991i	$-0.436217\pi$
$853$	11.6264	0.398082	0.199041	+	0.979991i	$0.436217\pi$
$854$	−48.2091	−1.64968
$855$	−4.71305	−0.161183
$856$	22.3408	0.763593
$857$	−41.5252	−1.41847	−0.709236	−	0.704971i	$-0.750960\pi$
$857$	−41.5252	−1.41847	−0.709236	+	0.704971i	$0.750960\pi$
$858$	73.7281	2.51704
$859$	−16.0419	−0.547342	−0.273671	−	0.961823i	$-0.588238\pi$
$859$	−16.0419	−0.547342	−0.273671	+	0.961823i	$0.588238\pi$
$860$	−59.5406	−2.03032
$861$	−16.5436	−0.563805
$862$	76.0225	2.58934
$863$	−7.30521	−0.248672	−0.124336	−	0.992240i	$-0.539680\pi$
$863$	−7.30521	−0.248672	−0.124336	+	0.992240i	$0.539680\pi$
$864$	−7.68864	−0.261573
$865$	4.18332	0.142237
$866$	−17.7816	−0.604244
$867$	−5.92041	−0.201067
$868$	122.426	4.15539
$869$	49.7436	1.68744
$870$	15.5853	0.528392
$871$	−45.2639	−1.53371
$872$	−83.6402	−2.83242
$873$	−16.7429	−0.566660
$874$	6.88338	0.232834
$875$	35.0671	1.18548
$876$	−13.0258	−0.440103
$877$	11.4563	0.386852	0.193426	−	0.981115i	$-0.438040\pi$
$877$	11.4563	0.386852	0.193426	+	0.981115i	$0.438040\pi$
$878$	47.6428	1.60787
$879$	−4.45876	−0.150390
$880$	−66.2140	−2.23207
$881$	−37.0364	−1.24779	−0.623894	−	0.781509i	$-0.714450\pi$
$881$	−37.0364	−1.24779	−0.623894	+	0.781509i	$0.714450\pi$
$882$	−7.81124	−0.263018
$883$	−43.6842	−1.47009	−0.735045	−	0.678019i	$-0.762839\pi$
$883$	−43.6842	−1.47009	−0.735045	+	0.678019i	$0.762839\pi$
$884$	74.9215	2.51988
$885$	20.7455	0.697354
$886$	46.8696	1.57462
$887$	−58.5617	−1.96631	−0.983154	−	0.182777i	$-0.941491\pi$
$887$	−58.5617	−1.96631	−0.983154	+	0.182777i	$0.941491\pi$
$888$	−1.92700	−0.0646659
$889$	38.2303	1.28220
$890$	6.16450	0.206635
$891$	5.90037	0.197670
$892$	−137.111	−4.59080
$893$	−12.3637	−0.413737
$894$	−43.3193	−1.44881
$895$	−24.6852	−0.825135
$896$	21.9331	0.732735
$897$	3.72880	0.124501
$898$	−82.4047	−2.74988
$899$	37.0973	1.23726
$900$	−14.6610	−0.488698
$901$	33.4893	1.11569
$902$	79.4348	2.64489
$903$	29.9274	0.995921
$904$	−14.3509	−0.477304
$905$	−0.750458	−0.0249461
$906$	24.3759	0.809836
$907$	4.22246	0.140204	0.0701022	−	0.997540i	$-0.477667\pi$
$907$	4.22246	0.140204	0.0701022	+	0.997540i	$0.477667\pi$
$908$	−94.2918	−3.12918
$909$	−9.28778	−0.308056
$910$	−53.7122	−1.78054
$911$	14.5556	0.482249	0.241124	−	0.970494i	$-0.422484\pi$
$911$	14.5556	0.482249	0.241124	+	0.970494i	$0.422484\pi$
$912$	28.7123	0.950760
$913$	81.6289	2.70152
$914$	−2.95851	−0.0978590
$915$	−8.01578	−0.264994
$916$	−4.02709	−0.133059
$917$	28.8414	0.952426
$918$	8.57887	0.283145
$919$	13.9832	0.461264	0.230632	−	0.973041i	$-0.425921\pi$
$919$	13.9832	0.461264	0.230632	+	0.973041i	$0.425921\pi$
$920$	−7.10937	−0.234389
$921$	23.4377	0.772300
$922$	12.6948	0.418082
$923$	−34.5326	−1.13665
$924$	86.7571	2.85410
$925$	−0.893491	−0.0293778
$926$	−82.8573	−2.72286
$927$	8.78308	0.288474
$928$	−34.2567	−1.12453
$929$	27.5506	0.903907	0.451953	−	0.892042i	$-0.350727\pi$
$929$	27.5506	0.903907	0.451953	+	0.892042i	$0.350727\pi$
$930$	29.1251	0.955048
$931$	10.5245	0.344927
$932$	51.8514	1.69845
$933$	17.7535	0.581225
$934$	16.8546	0.551499
$935$	26.6559	0.871741
$936$	33.0203	1.07930
$937$	49.1517	1.60572	0.802858	−	0.596170i	$-0.203312\pi$
$937$	49.1517	1.60572	0.802858	+	0.596170i	$0.203312\pi$
$938$	−76.2082	−2.48829
$939$	−9.31118	−0.303859
$940$	22.4342	0.731724
$941$	−32.5710	−1.06178	−0.530892	−	0.847439i	$-0.678143\pi$
$941$	−32.5710	−1.06178	−0.530892	+	0.847439i	$0.678143\pi$
$942$	−10.7143	−0.349092
$943$	4.01742	0.130825
$944$	−126.384	−4.11344
$945$	−4.29852	−0.139831
$946$	−143.698	−4.67201
$947$	38.8954	1.26393	0.631965	−	0.774997i	$-0.282249\pi$
$947$	38.8954	1.26393	0.631965	+	0.774997i	$0.282249\pi$
$948$	39.1397	1.27120
$949$	13.6029	0.441570
$950$	28.2632	0.916980
$951$	18.7900	0.609307
$952$	71.7999	2.32705
$953$	−14.7233	−0.476935	−0.238467	−	0.971150i	$-0.576645\pi$
$953$	−14.7233	−0.476935	−0.238467	+	0.971150i	$0.576645\pi$
$954$	25.9306	0.839534
$955$	13.5464	0.438352
$956$	42.0807	1.36099
$957$	26.2891	0.849804
$958$	54.6391	1.76531
$959$	−58.2977	−1.88253
$960$	−4.45089	−0.143652
$961$	38.3255	1.23631
$962$	3.53542	0.113986
$963$	−3.28022	−0.105704
$964$	−10.3724	−0.334071
$965$	−25.9655	−0.835859
$966$	6.27796	0.201990
$967$	38.3287	1.23257	0.616283	−	0.787524i	$-0.288638\pi$
$967$	38.3287	1.23257	0.616283	+	0.787524i	$0.288638\pi$
$968$	−162.194	−5.21311
$969$	−11.5588	−0.371322
$970$	−58.5667	−1.88046
$971$	−15.5045	−0.497563	−0.248782	−	0.968560i	$-0.580030\pi$
$971$	−15.5045	−0.497563	−0.248782	+	0.968560i	$0.580030\pi$
$972$	4.64257	0.148911
$973$	53.8182	1.72533
$974$	85.2679	2.73216
$975$	15.3105	0.490328
$976$	48.8328	1.56310
$977$	−32.6158	−1.04347	−0.521736	−	0.853107i	$-0.674715\pi$
$977$	−32.6158	−1.04347	−0.521736	+	0.853107i	$0.674715\pi$
$978$	19.0607	0.609494
$979$	10.3982	0.332327
$980$	−19.0969	−0.610028
$981$	12.2806	0.392090
$982$	103.067	3.28902
$983$	−14.7081	−0.469116	−0.234558	−	0.972102i	$-0.575364\pi$
$983$	−14.7081	−0.469116	−0.234558	+	0.972102i	$0.575364\pi$
$984$	35.5761	1.13413
$985$	20.6645	0.658426
$986$	38.2231	1.21727
$987$	−11.2763	−0.358929
$988$	−78.1618	−2.48666
$989$	−7.26751	−0.231093
$990$	20.6395	0.655967
$991$	57.8117	1.83645	0.918224	−	0.396061i	$-0.129623\pi$
$991$	57.8117	1.83645	0.918224	+	0.396061i	$0.129623\pi$
$992$	−64.0171	−2.03254
$993$	31.0198	0.984382
$994$	−58.1404	−1.84410
$995$	−13.5107	−0.428318
$996$	64.2278	2.03514
$997$	3.96896	0.125698	0.0628491	−	0.998023i	$-0.479981\pi$
$997$	3.96896	0.125698	0.0628491	+	0.998023i	$0.479981\pi$
$998$	−33.7757	−1.06915
$999$	0.282935	0.00895167

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8049.2.a.d.1.11	✓	129

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8049.2.a.d.1.11	✓	129	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:	\( N \)	\(=\)	\( 8049 = 3 \cdot 2683 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8049.a (trivial)

\(f(q)\)	\(=\)	\(q-2.57732 q^{2} +1.00000 q^{3} +4.64257 q^{4} -1.35723 q^{5} -2.57732 q^{6} +3.16714 q^{7} -6.81075 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.57732 q^{2} +1.00000 q^{3} +4.64257 q^{4} -1.35723 q^{5} -2.57732 q^{6} +3.16714 q^{7} -6.81075 q^{8} +1.00000 q^{9} +3.49801 q^{10} +5.90037 q^{11} +4.64257 q^{12} -4.84826 q^{13} -8.16272 q^{14} -1.35723 q^{15} +8.26834 q^{16} -3.32860 q^{17} -2.57732 q^{18} +3.47256 q^{19} -6.30102 q^{20} +3.16714 q^{21} -15.2071 q^{22} -0.769102 q^{23} -6.81075 q^{24} -3.15794 q^{25} +12.4955 q^{26} +1.00000 q^{27} +14.7037 q^{28} +4.45549 q^{29} +3.49801 q^{30} +8.32619 q^{31} -7.68864 q^{32} +5.90037 q^{33} +8.57887 q^{34} -4.29852 q^{35} +4.64257 q^{36} +0.282935 q^{37} -8.94990 q^{38} -4.84826 q^{39} +9.24373 q^{40} -5.22352 q^{41} -8.16272 q^{42} +9.44935 q^{43} +27.3929 q^{44} -1.35723 q^{45} +1.98222 q^{46} -3.56041 q^{47} +8.26834 q^{48} +3.03076 q^{49} +8.13901 q^{50} -3.32860 q^{51} -22.5084 q^{52} -10.0611 q^{53} -2.57732 q^{54} -8.00814 q^{55} -21.5706 q^{56} +3.47256 q^{57} -11.4832 q^{58} -15.2852 q^{59} -6.30102 q^{60} +5.90600 q^{61} -21.4593 q^{62} +3.16714 q^{63} +3.27940 q^{64} +6.58018 q^{65} -15.2071 q^{66} +9.33613 q^{67} -15.4533 q^{68} -0.769102 q^{69} +11.0787 q^{70} +7.12267 q^{71} -6.81075 q^{72} -2.80574 q^{73} -0.729214 q^{74} -3.15794 q^{75} +16.1216 q^{76} +18.6873 q^{77} +12.4955 q^{78} +8.43060 q^{79} -11.2220 q^{80} +1.00000 q^{81} +13.4627 q^{82} +13.8345 q^{83} +14.7037 q^{84} +4.51767 q^{85} -24.3540 q^{86} +4.45549 q^{87} -40.1860 q^{88} +1.76229 q^{89} +3.49801 q^{90} -15.3551 q^{91} -3.57061 q^{92} +8.32619 q^{93} +9.17631 q^{94} -4.71305 q^{95} -7.68864 q^{96} -16.7429 q^{97} -7.81124 q^{98} +5.90037 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 129 q + 8 q^{2} + 129 q^{3} + 158 q^{4} + 11 q^{5} + 8 q^{6} + 40 q^{7} + 18 q^{8} + 129 q^{9}+O(q^{10}) \) 129 * q + 8 * q^2 + 129 * q^3 + 158 * q^4 + 11 * q^5 + 8 * q^6 + 40 * q^7 + 18 * q^8 + 129 * q^9	\( 129 q + 8 q^{2} + 129 q^{3} + 158 q^{4} + 11 q^{5} + 8 q^{6} + 40 q^{7} + 18 q^{8} + 129 q^{9} + 20 q^{10} + 48 q^{11} + 158 q^{12} + 77 q^{13} + 13 q^{14} + 11 q^{15} + 212 q^{16} + 9 q^{17} + 8 q^{18} + 68 q^{19} + 19 q^{20} + 40 q^{21} + 45 q^{22} + 64 q^{23} + 18 q^{24} + 188 q^{25} + 19 q^{26} + 129 q^{27} + 69 q^{28} + 23 q^{29} + 20 q^{30} + 133 q^{31} + 24 q^{32} + 48 q^{33} + 63 q^{34} + 26 q^{35} + 158 q^{36} + 147 q^{37} + 9 q^{38} + 77 q^{39} + 58 q^{40} + 21 q^{41} + 13 q^{42} + 76 q^{43} + 110 q^{44} + 11 q^{45} + 48 q^{46} + 85 q^{47} + 212 q^{48} + 213 q^{49} + 17 q^{50} + 9 q^{51} + 139 q^{52} + 30 q^{53} + 8 q^{54} + 103 q^{55} + 19 q^{56} + 68 q^{57} + 94 q^{58} + 64 q^{59} + 19 q^{60} + 110 q^{61} - 10 q^{62} + 40 q^{63} + 288 q^{64} - 8 q^{65} + 45 q^{66} + 118 q^{67} - 15 q^{68} + 64 q^{69} + 75 q^{70} + 154 q^{71} + 18 q^{72} + 137 q^{73} + 28 q^{74} + 188 q^{75} + 156 q^{76} + 17 q^{77} + 19 q^{78} + 157 q^{79} + 2 q^{80} + 129 q^{81} + 72 q^{82} + 39 q^{83} + 69 q^{84} + 127 q^{85} + 54 q^{86} + 23 q^{87} + 97 q^{88} + 31 q^{89} + 20 q^{90} + 137 q^{91} + 82 q^{92} + 133 q^{93} + 40 q^{94} + 68 q^{95} + 24 q^{96} + 170 q^{97} - 21 q^{98} + 48 q^{99}+O(q^{100}) \) 129 * q + 8 * q^2 + 129 * q^3 + 158 * q^4 + 11 * q^5 + 8 * q^6 + 40 * q^7 + 18 * q^8 + 129 * q^9 + 20 * q^10 + 48 * q^11 + 158 * q^12 + 77 * q^13 + 13 * q^14 + 11 * q^15 + 212 * q^16 + 9 * q^17 + 8 * q^18 + 68 * q^19 + 19 * q^20 + 40 * q^21 + 45 * q^22 + 64 * q^23 + 18 * q^24 + 188 * q^25 + 19 * q^26 + 129 * q^27 + 69 * q^28 + 23 * q^29 + 20 * q^30 + 133 * q^31 + 24 * q^32 + 48 * q^33 + 63 * q^34 + 26 * q^35 + 158 * q^36 + 147 * q^37 + 9 * q^38 + 77 * q^39 + 58 * q^40 + 21 * q^41 + 13 * q^42 + 76 * q^43 + 110 * q^44 + 11 * q^45 + 48 * q^46 + 85 * q^47 + 212 * q^48 + 213 * q^49 + 17 * q^50 + 9 * q^51 + 139 * q^52 + 30 * q^53 + 8 * q^54 + 103 * q^55 + 19 * q^56 + 68 * q^57 + 94 * q^58 + 64 * q^59 + 19 * q^60 + 110 * q^61 - 10 * q^62 + 40 * q^63 + 288 * q^64 - 8 * q^65 + 45 * q^66 + 118 * q^67 - 15 * q^68 + 64 * q^69 + 75 * q^70 + 154 * q^71 + 18 * q^72 + 137 * q^73 + 28 * q^74 + 188 * q^75 + 156 * q^76 + 17 * q^77 + 19 * q^78 + 157 * q^79 + 2 * q^80 + 129 * q^81 + 72 * q^82 + 39 * q^83 + 69 * q^84 + 127 * q^85 + 54 * q^86 + 23 * q^87 + 97 * q^88 + 31 * q^89 + 20 * q^90 + 137 * q^91 + 82 * q^92 + 133 * q^93 + 40 * q^94 + 68 * q^95 + 24 * q^96 + 170 * q^97 - 21 * q^98 + 48 * q^99

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