LMFDB - Embedded newform 4015.2.a.e.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4015 = 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4015.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.0599364115$
Analytic rank:	$0$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	4015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.0560878 q^{2} -2.46183 q^{3} -1.99685 q^{4} -1.00000 q^{5} +0.138079 q^{6} -2.79584 q^{7} +0.224175 q^{8} +3.06062 q^{9} +O(q^{10})$	\(q-0.0560878 q^{2} -2.46183 q^{3} -1.99685 q^{4} -1.00000 q^{5} +0.138079 q^{6} -2.79584 q^{7} +0.224175 q^{8} +3.06062 q^{9} +0.0560878 q^{10} +1.00000 q^{11} +4.91592 q^{12} +0.990143 q^{13} +0.156813 q^{14} +2.46183 q^{15} +3.98113 q^{16} +5.14135 q^{17} -0.171663 q^{18} -4.29197 q^{19} +1.99685 q^{20} +6.88289 q^{21} -0.0560878 q^{22} -7.79959 q^{23} -0.551881 q^{24} +1.00000 q^{25} -0.0555350 q^{26} -0.149231 q^{27} +5.58289 q^{28} -3.65994 q^{29} -0.138079 q^{30} -9.15274 q^{31} -0.671643 q^{32} -2.46183 q^{33} -0.288367 q^{34} +2.79584 q^{35} -6.11161 q^{36} +4.07061 q^{37} +0.240727 q^{38} -2.43757 q^{39} -0.224175 q^{40} -9.69865 q^{41} -0.386046 q^{42} -8.93499 q^{43} -1.99685 q^{44} -3.06062 q^{45} +0.437462 q^{46} -11.1909 q^{47} -9.80089 q^{48} +0.816732 q^{49} -0.0560878 q^{50} -12.6571 q^{51} -1.97717 q^{52} -0.865476 q^{53} +0.00837006 q^{54} -1.00000 q^{55} -0.626757 q^{56} +10.5661 q^{57} +0.205278 q^{58} +2.27866 q^{59} -4.91592 q^{60} -2.70852 q^{61} +0.513357 q^{62} -8.55700 q^{63} -7.92460 q^{64} -0.990143 q^{65} +0.138079 q^{66} -3.78861 q^{67} -10.2665 q^{68} +19.2013 q^{69} -0.156813 q^{70} +0.804524 q^{71} +0.686113 q^{72} -1.00000 q^{73} -0.228312 q^{74} -2.46183 q^{75} +8.57044 q^{76} -2.79584 q^{77} +0.136718 q^{78} +3.13945 q^{79} -3.98113 q^{80} -8.81447 q^{81} +0.543976 q^{82} +11.9876 q^{83} -13.7441 q^{84} -5.14135 q^{85} +0.501144 q^{86} +9.01015 q^{87} +0.224175 q^{88} +16.0593 q^{89} +0.171663 q^{90} -2.76828 q^{91} +15.5747 q^{92} +22.5325 q^{93} +0.627672 q^{94} +4.29197 q^{95} +1.65347 q^{96} +3.08198 q^{97} -0.0458087 q^{98} +3.06062 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q + 6 q^{2} + 5 q^{3} + 22 q^{4} - 27 q^{5} + 7 q^{6} + 10 q^{7} + 15 q^{8} + 24 q^{9}+O(q^{10}) $ 27 * q + 6 * q^2 + 5 * q^3 + 22 * q^4 - 27 * q^5 + 7 * q^6 + 10 * q^7 + 15 * q^8 + 24 * q^9	\( 27 q + 6 q^{2} + 5 q^{3} + 22 q^{4} - 27 q^{5} + 7 q^{6} + 10 q^{7} + 15 q^{8} + 24 q^{9} - 6 q^{10} + 27 q^{11} + 28 q^{12} + 21 q^{13} + 11 q^{14} - 5 q^{15} + 12 q^{16} + 30 q^{17} + 10 q^{18} + 20 q^{19} - 22 q^{20} - 14 q^{21} + 6 q^{22} + 16 q^{23} + 23 q^{24} + 27 q^{25} + 13 q^{26} + 17 q^{27} + 6 q^{28} - 2 q^{29} - 7 q^{30} - 6 q^{31} + 41 q^{32} + 5 q^{33} + 8 q^{34} - 10 q^{35} + 13 q^{36} + 20 q^{37} + 11 q^{38} - 10 q^{39} - 15 q^{40} + 38 q^{41} - 33 q^{42} + 29 q^{43} + 22 q^{44} - 24 q^{45} + 23 q^{46} + 17 q^{47} + 37 q^{48} + 21 q^{49} + 6 q^{50} + 13 q^{51} + 29 q^{52} + 4 q^{53} + q^{54} - 27 q^{55} + 28 q^{56} + 51 q^{57} - 6 q^{58} + 35 q^{59} - 28 q^{60} - 13 q^{61} + 28 q^{62} + 41 q^{63} - 5 q^{64} - 21 q^{65} + 7 q^{66} + 10 q^{67} + 65 q^{68} - 12 q^{69} - 11 q^{70} + 22 q^{71} - 12 q^{72} - 27 q^{73} - 5 q^{74} + 5 q^{75} + 13 q^{76} + 10 q^{77} - 9 q^{78} - 18 q^{79} - 12 q^{80} + 39 q^{81} + 20 q^{82} + 54 q^{83} - 50 q^{84} - 30 q^{85} + 3 q^{86} + 15 q^{87} + 15 q^{88} + 89 q^{89} - 10 q^{90} - 18 q^{91} + 57 q^{92} + 20 q^{93} - 29 q^{94} - 20 q^{95} + 105 q^{96} + 35 q^{97} + 10 q^{98} + 24 q^{99}+O(q^{100}) \) 27 * q + 6 * q^2 + 5 * q^3 + 22 * q^4 - 27 * q^5 + 7 * q^6 + 10 * q^7 + 15 * q^8 + 24 * q^9 - 6 * q^10 + 27 * q^11 + 28 * q^12 + 21 * q^13 + 11 * q^14 - 5 * q^15 + 12 * q^16 + 30 * q^17 + 10 * q^18 + 20 * q^19 - 22 * q^20 - 14 * q^21 + 6 * q^22 + 16 * q^23 + 23 * q^24 + 27 * q^25 + 13 * q^26 + 17 * q^27 + 6 * q^28 - 2 * q^29 - 7 * q^30 - 6 * q^31 + 41 * q^32 + 5 * q^33 + 8 * q^34 - 10 * q^35 + 13 * q^36 + 20 * q^37 + 11 * q^38 - 10 * q^39 - 15 * q^40 + 38 * q^41 - 33 * q^42 + 29 * q^43 + 22 * q^44 - 24 * q^45 + 23 * q^46 + 17 * q^47 + 37 * q^48 + 21 * q^49 + 6 * q^50 + 13 * q^51 + 29 * q^52 + 4 * q^53 + q^54 - 27 * q^55 + 28 * q^56 + 51 * q^57 - 6 * q^58 + 35 * q^59 - 28 * q^60 - 13 * q^61 + 28 * q^62 + 41 * q^63 - 5 * q^64 - 21 * q^65 + 7 * q^66 + 10 * q^67 + 65 * q^68 - 12 * q^69 - 11 * q^70 + 22 * q^71 - 12 * q^72 - 27 * q^73 - 5 * q^74 + 5 * q^75 + 13 * q^76 + 10 * q^77 - 9 * q^78 - 18 * q^79 - 12 * q^80 + 39 * q^81 + 20 * q^82 + 54 * q^83 - 50 * q^84 - 30 * q^85 + 3 * q^86 + 15 * q^87 + 15 * q^88 + 89 * q^89 - 10 * q^90 - 18 * q^91 + 57 * q^92 + 20 * q^93 - 29 * q^94 - 20 * q^95 + 105 * q^96 + 35 * q^97 + 10 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−0.0560878	−0.0396601	−0.0198300	−	0.999803i	$-0.506313\pi$
$2$	−0.0560878	−0.0396601	−0.0198300	+	0.999803i	$0.506313\pi$
$3$	−2.46183	−1.42134	−0.710670	−	0.703526i	$-0.751608\pi$
$3$	−2.46183	−1.42134	−0.710670	+	0.703526i	$0.751608\pi$
$4$	−1.99685	−0.998427
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.138079	0.0563704
$7$	−2.79584	−1.05673	−0.528364	−	0.849018i	$-0.677195\pi$
$7$	−2.79584	−1.05673	−0.528364	+	0.849018i	$0.677195\pi$
$8$	0.224175	0.0792578
$9$	3.06062	1.02021
$10$	0.0560878	0.0177365
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	4.91592	1.41910
$13$	0.990143	0.274616	0.137308	−	0.990528i	$-0.456155\pi$
$13$	0.990143	0.274616	0.137308	+	0.990528i	$0.456155\pi$
$14$	0.156813	0.0419099
$15$	2.46183	0.635642
$16$	3.98113	0.995284
$17$	5.14135	1.24696	0.623481	−	0.781839i	$-0.285718\pi$
$17$	5.14135	1.24696	0.623481	+	0.781839i	$0.285718\pi$
$18$	−0.171663	−0.0404614
$19$	−4.29197	−0.984646	−0.492323	−	0.870413i	$-0.663852\pi$
$19$	−4.29197	−0.984646	−0.492323	+	0.870413i	$0.663852\pi$
$20$	1.99685	0.446510
$21$	6.88289	1.50197
$22$	−0.0560878	−0.0119580
$23$	−7.79959	−1.62633	−0.813164	−	0.582035i	$-0.802257\pi$
$23$	−7.79959	−1.62633	−0.813164	+	0.582035i	$0.802257\pi$
$24$	−0.551881	−0.112652
$25$	1.00000	0.200000
$26$	−0.0555350	−0.0108913
$27$	−0.149231	−0.0287196
$28$	5.58289	1.05507
$29$	−3.65994	−0.679633	−0.339816	−	0.940492i	$-0.610365\pi$
$29$	−3.65994	−0.679633	−0.339816	+	0.940492i	$0.610365\pi$
$30$	−0.138079	−0.0252096
$31$	−9.15274	−1.64388	−0.821941	−	0.569573i	$-0.807108\pi$
$31$	−9.15274	−1.64388	−0.821941	+	0.569573i	$0.807108\pi$
$32$	−0.671643	−0.118731
$33$	−2.46183	−0.428550
$34$	−0.288367	−0.0494546
$35$	2.79584	0.472584
$36$	−6.11161	−1.01860
$37$	4.07061	0.669204	0.334602	−	0.942360i	$-0.391398\pi$
$37$	4.07061	0.669204	0.334602	+	0.942360i	$0.391398\pi$
$38$	0.240727	0.0390511
$39$	−2.43757	−0.390323
$40$	−0.224175	−0.0354451
$41$	−9.69865	−1.51467	−0.757337	−	0.653024i	$-0.773500\pi$
$41$	−9.69865	−1.51467	−0.757337	+	0.653024i	$0.773500\pi$
$42$	−0.386046	−0.0595683
$43$	−8.93499	−1.36257	−0.681287	−	0.732017i	$-0.738579\pi$
$43$	−8.93499	−1.36257	−0.681287	+	0.732017i	$0.738579\pi$
$44$	−1.99685	−0.301037
$45$	−3.06062	−0.456250
$46$	0.437462	0.0645003
$47$	−11.1909	−1.63236	−0.816179	−	0.577799i	$-0.803912\pi$
$47$	−11.1909	−1.63236	−0.816179	+	0.577799i	$0.803912\pi$
$48$	−9.80089	−1.41464
$49$	0.816732	0.116676
$50$	−0.0560878	−0.00793201
$51$	−12.6571	−1.77236
$52$	−1.97717	−0.274184
$53$	−0.865476	−0.118882	−0.0594411	−	0.998232i	$-0.518932\pi$
$53$	−0.865476	−0.118882	−0.0594411	+	0.998232i	$0.518932\pi$
$54$	0.00837006	0.00113902
$55$	−1.00000	−0.134840
$56$	−0.626757	−0.0837540
$57$	10.5661	1.39952
$58$	0.205278	0.0269543
$59$	2.27866	0.296657	0.148328	−	0.988938i	$-0.452611\pi$
$59$	2.27866	0.296657	0.148328	+	0.988938i	$0.452611\pi$
$60$	−4.91592	−0.634643
$61$	−2.70852	−0.346790	−0.173395	−	0.984852i	$-0.555474\pi$
$61$	−2.70852	−0.346790	−0.173395	+	0.984852i	$0.555474\pi$
$62$	0.513357	0.0651964
$63$	−8.55700	−1.07808
$64$	−7.92460	−0.990575
$65$	−0.990143	−0.122812
$66$	0.138079	0.0169963
$67$	−3.78861	−0.462853	−0.231426	−	0.972852i	$-0.574339\pi$
$67$	−3.78861	−0.462853	−0.231426	+	0.972852i	$0.574339\pi$
$68$	−10.2665	−1.24500
$69$	19.2013	2.31156
$70$	−0.156813	−0.0187427
$71$	0.804524	0.0954794	0.0477397	−	0.998860i	$-0.484798\pi$
$71$	0.804524	0.0954794	0.0477397	+	0.998860i	$0.484798\pi$
$72$	0.686113	0.0808592
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	−0.228312	−0.0265407
$75$	−2.46183	−0.284268
$76$	8.57044	0.983097
$77$	−2.79584	−0.318616
$78$	0.136718	0.0154802
$79$	3.13945	0.353215	0.176608	−	0.984281i	$-0.443488\pi$
$79$	3.13945	0.353215	0.176608	+	0.984281i	$0.443488\pi$
$80$	−3.98113	−0.445104
$81$	−8.81447	−0.979386
$82$	0.543976	0.0600721
$83$	11.9876	1.31581	0.657904	−	0.753102i	$-0.271443\pi$
$83$	11.9876	1.31581	0.657904	+	0.753102i	$0.271443\pi$
$84$	−13.7441	−1.49961
$85$	−5.14135	−0.557658
$86$	0.501144	0.0540398
$87$	9.01015	0.965989
$88$	0.224175	0.0238971
$89$	16.0593	1.70228	0.851141	−	0.524937i	$-0.175911\pi$
$89$	16.0593	1.70228	0.851141	+	0.524937i	$0.175911\pi$
$90$	0.171663	0.0180949
$91$	−2.76828	−0.290195
$92$	15.5747	1.62377
$93$	22.5325	2.33651
$94$	0.627672	0.0647395
$95$	4.29197	0.440347
$96$	1.65347	0.168757
$97$	3.08198	0.312927	0.156464	−	0.987684i	$-0.449991\pi$
$97$	3.08198	0.312927	0.156464	+	0.987684i	$0.449991\pi$
$98$	−0.0458087	−0.00462738
$99$	3.06062	0.307604
$100$	−1.99685	−0.199685
$101$	−9.23097	−0.918516	−0.459258	−	0.888303i	$-0.651885\pi$
$101$	−9.23097	−0.918516	−0.459258	+	0.888303i	$0.651885\pi$
$102$	0.709912	0.0702917
$103$	−11.6071	−1.14368	−0.571840	−	0.820365i	$-0.693770\pi$
$103$	−11.6071	−1.14368	−0.571840	+	0.820365i	$0.693770\pi$
$104$	0.221965	0.0217655
$105$	−6.88289	−0.671702
$106$	0.0485426	0.00471488
$107$	−0.944480	−0.0913063	−0.0456532	−	0.998957i	$-0.514537\pi$
$107$	−0.944480	−0.0913063	−0.0456532	+	0.998957i	$0.514537\pi$
$108$	0.297993	0.0286744
$109$	−10.3683	−0.993105	−0.496552	−	0.868007i	$-0.665401\pi$
$109$	−10.3683	−0.993105	−0.496552	+	0.868007i	$0.665401\pi$
$110$	0.0560878	0.00534776
$111$	−10.0212	−0.951166
$112$	−11.1306	−1.05175
$113$	−12.5090	−1.17675	−0.588375	−	0.808588i	$-0.700232\pi$
$113$	−12.5090	−1.17675	−0.588375	+	0.808588i	$0.700232\pi$
$114$	−0.592630	−0.0555049
$115$	7.79959	0.727316
$116$	7.30836	0.678564
$117$	3.03045	0.280165
$118$	−0.127805	−0.0117654
$119$	−14.3744	−1.31770
$120$	0.551881	0.0503796
$121$	1.00000	0.0909091
$122$	0.151915	0.0137537
$123$	23.8764	2.15287
$124$	18.2767	1.64130
$125$	−1.00000	−0.0894427
$126$	0.479944	0.0427568
$127$	19.7455	1.75213	0.876067	−	0.482190i	$-0.160158\pi$
$127$	19.7455	1.75213	0.876067	+	0.482190i	$0.160158\pi$
$128$	1.78776	0.158017
$129$	21.9964	1.93668
$130$	0.0555350	0.00487074
$131$	−15.6225	−1.36494	−0.682471	−	0.730913i	$-0.739094\pi$
$131$	−15.6225	−1.36494	−0.682471	+	0.730913i	$0.739094\pi$
$132$	4.91592	0.427876
$133$	11.9997	1.04050
$134$	0.212495	0.0183568
$135$	0.149231	0.0128438
$136$	1.15256	0.0988314
$137$	18.4522	1.57648	0.788239	−	0.615369i	$-0.210993\pi$
$137$	18.4522	1.57648	0.788239	+	0.615369i	$0.210993\pi$
$138$	−1.07696	−0.0916768
$139$	−4.37310	−0.370921	−0.185461	−	0.982652i	$-0.559378\pi$
$139$	−4.37310	−0.370921	−0.185461	+	0.982652i	$0.559378\pi$
$140$	−5.58289	−0.471840
$141$	27.5501	2.32014
$142$	−0.0451240	−0.00378672
$143$	0.990143	0.0827999
$144$	12.1847	1.01539
$145$	3.65994	0.303941
$146$	0.0560878	0.00464186
$147$	−2.01066	−0.165836
$148$	−8.12841	−0.668151
$149$	−22.9939	−1.88374	−0.941868	−	0.335983i	$-0.890932\pi$
$149$	−22.9939	−1.88374	−0.941868	+	0.335983i	$0.890932\pi$
$150$	0.138079	0.0112741
$151$	−2.09563	−0.170540	−0.0852699	−	0.996358i	$-0.527175\pi$
$151$	−2.09563	−0.170540	−0.0852699	+	0.996358i	$0.527175\pi$
$152$	−0.962152	−0.0780408
$153$	15.7357	1.27216
$154$	0.156813	0.0126363
$155$	9.15274	0.735166
$156$	4.86747	0.389709
$157$	18.9145	1.50955	0.754773	−	0.655986i	$-0.227747\pi$
$157$	18.9145	1.50955	0.754773	+	0.655986i	$0.227747\pi$
$158$	−0.176085	−0.0140085
$159$	2.13066	0.168972
$160$	0.671643	0.0530980
$161$	21.8064	1.71859
$162$	0.494384	0.0388425
$163$	2.71180	0.212405	0.106202	−	0.994345i	$-0.466131\pi$
$163$	2.71180	0.212405	0.106202	+	0.994345i	$0.466131\pi$
$164$	19.3668	1.51229
$165$	2.46183	0.191653
$166$	−0.672357	−0.0521850
$167$	−11.9476	−0.924530	−0.462265	−	0.886742i	$-0.652963\pi$
$167$	−11.9476	−0.924530	−0.462265	+	0.886742i	$0.652963\pi$
$168$	1.54297	0.119043
$169$	−12.0196	−0.924586
$170$	0.288367	0.0221168
$171$	−13.1361	−1.00454
$172$	17.8419	1.36043
$173$	6.18880	0.470526	0.235263	−	0.971932i	$-0.424405\pi$
$173$	6.18880	0.470526	0.235263	+	0.971932i	$0.424405\pi$
$174$	−0.505359	−0.0383112
$175$	−2.79584	−0.211346
$176$	3.98113	0.300089
$177$	−5.60968	−0.421650
$178$	−0.900731	−0.0675126
$179$	−20.7906	−1.55396	−0.776980	−	0.629526i	$-0.783249\pi$
$179$	−20.7906	−1.55396	−0.776980	+	0.629526i	$0.783249\pi$
$180$	6.11161	0.455532
$181$	−6.80941	−0.506140	−0.253070	−	0.967448i	$-0.581440\pi$
$181$	−6.80941	−0.506140	−0.253070	+	0.967448i	$0.581440\pi$
$182$	0.155267	0.0115092
$183$	6.66792	0.492906
$184$	−1.74847	−0.128899
$185$	−4.07061	−0.299277
$186$	−1.26380	−0.0926663
$187$	5.14135	0.375973
$188$	22.3466	1.62979
$189$	0.417227	0.0303488
$190$	−0.240727	−0.0174642
$191$	−24.7931	−1.79397	−0.896983	−	0.442065i	$-0.854246\pi$
$191$	−24.7931	−1.79397	−0.896983	+	0.442065i	$0.854246\pi$
$192$	19.5090	1.40794
$193$	7.01656	0.505063	0.252532	−	0.967589i	$-0.418737\pi$
$193$	7.01656	0.505063	0.252532	+	0.967589i	$0.418737\pi$
$194$	−0.172861	−0.0124107
$195$	2.43757	0.174558
$196$	−1.63089	−0.116492
$197$	15.0537	1.07253	0.536266	−	0.844049i	$-0.319834\pi$
$197$	15.0537	1.07253	0.536266	+	0.844049i	$0.319834\pi$
$198$	−0.171663	−0.0121996
$199$	3.35991	0.238178	0.119089	−	0.992884i	$-0.462003\pi$
$199$	3.35991	0.238178	0.119089	+	0.992884i	$0.462003\pi$
$200$	0.224175	0.0158516
$201$	9.32693	0.657871
$202$	0.517745	0.0364284
$203$	10.2326	0.718188
$204$	25.2745	1.76957
$205$	9.69865	0.677383
$206$	0.651015	0.0453584
$207$	−23.8716	−1.65919
$208$	3.94189	0.273321
$209$	−4.29197	−0.296882
$210$	0.386046	0.0266397
$211$	25.8924	1.78251	0.891254	−	0.453504i	$-0.149826\pi$
$211$	25.8924	1.78251	0.891254	+	0.453504i	$0.149826\pi$
$212$	1.72823	0.118695
$213$	−1.98060	−0.135709
$214$	0.0529738	0.00362122
$215$	8.93499	0.609361
$216$	−0.0334539	−0.00227625
$217$	25.5896	1.73714
$218$	0.581536	0.0393866
$219$	2.46183	0.166355
$220$	1.99685	0.134628
$221$	5.09068	0.342436
$222$	0.562065	0.0377233
$223$	−17.3142	−1.15945	−0.579723	−	0.814814i	$-0.696839\pi$
$223$	−17.3142	−1.15945	−0.579723	+	0.814814i	$0.696839\pi$
$224$	1.87781	0.125466
$225$	3.06062	0.204041
$226$	0.701604	0.0466700
$227$	1.19331	0.0792025	0.0396012	−	0.999216i	$-0.487391\pi$
$227$	1.19331	0.0792025	0.0396012	+	0.999216i	$0.487391\pi$
$228$	−21.0990	−1.39731
$229$	4.25026	0.280865	0.140432	−	0.990090i	$-0.455151\pi$
$229$	4.25026	0.280865	0.140432	+	0.990090i	$0.455151\pi$
$230$	−0.437462	−0.0288454
$231$	6.88289	0.452861
$232$	−0.820465	−0.0538662
$233$	10.6184	0.695637	0.347818	−	0.937562i	$-0.386923\pi$
$233$	10.6184	0.695637	0.347818	+	0.937562i	$0.386923\pi$
$234$	−0.169971	−0.0111114
$235$	11.1909	0.730013
$236$	−4.55016	−0.296190
$237$	−7.72879	−0.502039
$238$	0.806229	0.0522601
$239$	−13.5677	−0.877623	−0.438812	−	0.898579i	$-0.644600\pi$
$239$	−13.5677	−0.877623	−0.438812	+	0.898579i	$0.644600\pi$
$240$	9.80089	0.632644
$241$	14.7246	0.948492	0.474246	−	0.880392i	$-0.342721\pi$
$241$	14.7246	0.948492	0.474246	+	0.880392i	$0.342721\pi$
$242$	−0.0560878	−0.00360546
$243$	22.1474	1.42076
$244$	5.40851	0.346245
$245$	−0.816732	−0.0521791
$246$	−1.33918	−0.0853828
$247$	−4.24967	−0.270400
$248$	−2.05181	−0.130290
$249$	−29.5114	−1.87021
$250$	0.0560878	0.00354730
$251$	−18.7450	−1.18317	−0.591585	−	0.806242i	$-0.701498\pi$
$251$	−18.7450	−1.18317	−0.591585	+	0.806242i	$0.701498\pi$
$252$	17.0871	1.07639
$253$	−7.79959	−0.490356
$254$	−1.10748	−0.0694897
$255$	12.6571	0.792621
$256$	15.7489	0.984308
$257$	−20.3632	−1.27022	−0.635110	−	0.772421i	$-0.719045\pi$
$257$	−20.3632	−1.27022	−0.635110	+	0.772421i	$0.719045\pi$
$258$	−1.23373	−0.0768088
$259$	−11.3808	−0.707167
$260$	1.97717	0.122619
$261$	−11.2017	−0.693366
$262$	0.876230	0.0541337
$263$	−18.5538	−1.14408	−0.572039	−	0.820226i	$-0.693848\pi$
$263$	−18.5538	−1.14408	−0.572039	+	0.820226i	$0.693848\pi$
$264$	−0.551881	−0.0339659
$265$	0.865476	0.0531658
$266$	−0.673036	−0.0412665
$267$	−39.5353	−2.41952
$268$	7.56530	0.462125
$269$	30.0249	1.83065	0.915326	−	0.402713i	$-0.131933\pi$
$269$	30.0249	1.83065	0.915326	+	0.402713i	$0.131933\pi$
$270$	−0.00837006	−0.000509386 0
$271$	23.4279	1.42314	0.711572	−	0.702614i	$-0.247984\pi$
$271$	23.4279	1.42314	0.711572	+	0.702614i	$0.247984\pi$
$272$	20.4684	1.24108
$273$	6.81505	0.412466
$274$	−1.03494	−0.0625232
$275$	1.00000	0.0603023
$276$	−38.3422	−2.30793
$277$	−19.4616	−1.16933	−0.584667	−	0.811273i	$-0.698775\pi$
$277$	−19.4616	−1.16933	−0.584667	+	0.811273i	$0.698775\pi$
$278$	0.245277	0.0147108
$279$	−28.0130	−1.67710
$280$	0.626757	0.0374559
$281$	−24.9436	−1.48801	−0.744005	−	0.668174i	$-0.767076\pi$
$281$	−24.9436	−1.48801	−0.744005	+	0.668174i	$0.767076\pi$
$282$	−1.54522	−0.0920167
$283$	3.78280	0.224864	0.112432	−	0.993659i	$-0.464136\pi$
$283$	3.78280	0.224864	0.112432	+	0.993659i	$0.464136\pi$
$284$	−1.60652	−0.0953292
$285$	−10.5661	−0.625883
$286$	−0.0555350	−0.00328385
$287$	27.1159	1.60060
$288$	−2.05564	−0.121130
$289$	9.43351	0.554913
$290$	−0.205278	−0.0120543
$291$	−7.58731	−0.444776
$292$	1.99685	0.116857
$293$	1.92171	0.112268	0.0561338	−	0.998423i	$-0.482123\pi$
$293$	1.92171	0.112268	0.0561338	+	0.998423i	$0.482123\pi$
$294$	0.112773	0.00657707
$295$	−2.27866	−0.132669
$296$	0.912528	0.0530396
$297$	−0.149231	−0.00865928
$298$	1.28968	0.0747091
$299$	−7.72272	−0.446616
$300$	4.91592	0.283821
$301$	24.9808	1.43987
$302$	0.117539	0.00676362
$303$	22.7251	1.30552
$304$	−17.0869	−0.980002
$305$	2.70852	0.155089
$306$	−0.882582	−0.0504539
$307$	2.28914	0.130648	0.0653242	−	0.997864i	$-0.479192\pi$
$307$	2.28914	0.130648	0.0653242	+	0.997864i	$0.479192\pi$
$308$	5.58289	0.318115
$309$	28.5747	1.62556
$310$	−0.513357	−0.0291567
$311$	26.5213	1.50389	0.751943	−	0.659228i	$-0.229117\pi$
$311$	26.5213	1.50389	0.751943	+	0.659228i	$0.229117\pi$
$312$	−0.546441	−0.0309361
$313$	−21.9701	−1.24182	−0.620912	−	0.783880i	$-0.713238\pi$
$313$	−21.9701	−1.24182	−0.620912	+	0.783880i	$0.713238\pi$
$314$	−1.06088	−0.0598687
$315$	8.55700	0.482133
$316$	−6.26901	−0.352660
$317$	−20.6370	−1.15909	−0.579545	−	0.814940i	$-0.696770\pi$
$317$	−20.6370	−1.15909	−0.579545	+	0.814940i	$0.696770\pi$
$318$	−0.119504	−0.00670144
$319$	−3.65994	−0.204917
$320$	7.92460	0.442999
$321$	2.32515	0.129777
$322$	−1.22308	−0.0681593
$323$	−22.0665	−1.22782
$324$	17.6012	0.977845
$325$	0.990143	0.0549233
$326$	−0.152099	−0.00842398
$327$	25.5251	1.41154
$328$	−2.17419	−0.120050
$329$	31.2880	1.72496
$330$	−0.138079	−0.00760099
$331$	17.9114	0.984500	0.492250	−	0.870454i	$-0.336175\pi$
$331$	17.9114	0.984500	0.492250	+	0.870454i	$0.336175\pi$
$332$	−23.9374	−1.31374
$333$	12.4586	0.682726
$334$	0.670112	0.0366669
$335$	3.78861	0.206994
$336$	27.4017	1.49489
$337$	−12.0801	−0.658045	−0.329022	−	0.944322i	$-0.606719\pi$
$337$	−12.0801	−0.658045	−0.329022	+	0.944322i	$0.606719\pi$
$338$	0.674154	0.0366691
$339$	30.7951	1.67256
$340$	10.2665	0.556781
$341$	−9.15274	−0.495649
$342$	0.736774	0.0398402
$343$	17.2874	0.933434
$344$	−2.00300	−0.107995
$345$	−19.2013	−1.03376
$346$	−0.347116	−0.0186611
$347$	23.9504	1.28572	0.642862	−	0.765982i	$-0.277747\pi$
$347$	23.9504	1.28572	0.642862	+	0.765982i	$0.277747\pi$
$348$	−17.9920	−0.964470
$349$	−14.3641	−0.768891	−0.384446	−	0.923148i	$-0.625607\pi$
$349$	−14.3641	−0.768891	−0.384446	+	0.923148i	$0.625607\pi$
$350$	0.156813	0.00838199
$351$	−0.147760	−0.00788687
$352$	−0.671643	−0.0357987
$353$	21.6820	1.15401	0.577007	−	0.816739i	$-0.304221\pi$
$353$	21.6820	1.15401	0.577007	+	0.816739i	$0.304221\pi$
$354$	0.314635	0.0167227
$355$	−0.804524	−0.0426997
$356$	−32.0681	−1.69960
$357$	35.3874	1.87290
$358$	1.16610	0.0616301
$359$	37.4726	1.97773	0.988865	−	0.148816i	$-0.0475463\pi$
$359$	37.4726	1.97773	0.988865	+	0.148816i	$0.0475463\pi$
$360$	−0.686113	−0.0361614
$361$	−0.578975	−0.0304724
$362$	0.381925	0.0200735
$363$	−2.46183	−0.129213
$364$	5.52786	0.289739
$365$	1.00000	0.0523424
$366$	−0.373989	−0.0195487
$367$	18.6721	0.974675	0.487338	−	0.873214i	$-0.337968\pi$
$367$	18.6721	0.974675	0.487338	+	0.873214i	$0.337968\pi$
$368$	−31.0512	−1.61866
$369$	−29.6839	−1.54528
$370$	0.228312	0.0118694
$371$	2.41973	0.125626
$372$	−44.9941	−2.33284
$373$	−13.1886	−0.682879	−0.341440	−	0.939904i	$-0.610915\pi$
$373$	−13.1886	−0.682879	−0.341440	+	0.939904i	$0.610915\pi$
$374$	−0.288367	−0.0149111
$375$	2.46183	0.127128
$376$	−2.50871	−0.129377
$377$	−3.62386	−0.186638
$378$	−0.0234014	−0.00120364
$379$	3.24102	0.166480	0.0832401	−	0.996530i	$-0.473473\pi$
$379$	3.24102	0.166480	0.0832401	+	0.996530i	$0.473473\pi$
$380$	−8.57044	−0.439654
$381$	−48.6102	−2.49038
$382$	1.39059	0.0711488
$383$	−14.5681	−0.744393	−0.372196	−	0.928154i	$-0.621395\pi$
$383$	−14.5681	−0.744393	−0.372196	+	0.928154i	$0.621395\pi$
$384$	−4.40116	−0.224596
$385$	2.79584	0.142489
$386$	−0.393544	−0.0200308
$387$	−27.3466	−1.39011
$388$	−6.15426	−0.312435
$389$	25.7876	1.30748	0.653742	−	0.756717i	$-0.273198\pi$
$389$	25.7876	1.30748	0.653742	+	0.756717i	$0.273198\pi$
$390$	−0.136718	−0.00692297
$391$	−40.1005	−2.02797
$392$	0.183091	0.00924747
$393$	38.4599	1.94004
$394$	−0.844330	−0.0425367
$395$	−3.13945	−0.157963
$396$	−6.11161	−0.307120
$397$	16.1763	0.811866	0.405933	−	0.913903i	$-0.366947\pi$
$397$	16.1763	0.811866	0.405933	+	0.913903i	$0.366947\pi$
$398$	−0.188450	−0.00944614
$399$	−29.5412	−1.47891
$400$	3.98113	0.199057
$401$	37.5366	1.87449	0.937245	−	0.348671i	$-0.113367\pi$
$401$	37.5366	1.87449	0.937245	+	0.348671i	$0.113367\pi$
$402$	−0.523127	−0.0260912
$403$	−9.06253	−0.451437
$404$	18.4329	0.917071
$405$	8.81447	0.437995
$406$	−0.573924	−0.0284834
$407$	4.07061	0.201773
$408$	−2.83741	−0.140473
$409$	−22.5371	−1.11439	−0.557194	−	0.830382i	$-0.688122\pi$
$409$	−22.5371	−1.11439	−0.557194	+	0.830382i	$0.688122\pi$
$410$	−0.543976	−0.0268651
$411$	−45.4262	−2.24071
$412$	23.1776	1.14188
$413$	−6.37078	−0.313486
$414$	1.33890	0.0658036
$415$	−11.9876	−0.588447
$416$	−0.665023	−0.0326054
$417$	10.7658	0.527205
$418$	0.240727	0.0117744
$419$	−5.04504	−0.246466	−0.123233	−	0.992378i	$-0.539326\pi$
$419$	−5.04504	−0.246466	−0.123233	+	0.992378i	$0.539326\pi$
$420$	13.7441	0.670645
$421$	−32.2239	−1.57049	−0.785247	−	0.619182i	$-0.787464\pi$
$421$	−32.2239	−1.57049	−0.785247	+	0.619182i	$0.787464\pi$
$422$	−1.45225	−0.0706944
$423$	−34.2510	−1.66534
$424$	−0.194018	−0.00942234
$425$	5.14135	0.249392
$426$	0.111088	0.00538221
$427$	7.57259	0.366463
$428$	1.88599	0.0911627
$429$	−2.43757	−0.117687
$430$	−0.501144	−0.0241673
$431$	1.22603	0.0590559	0.0295279	−	0.999564i	$-0.490600\pi$
$431$	1.22603	0.0590559	0.0295279	+	0.999564i	$0.490600\pi$
$432$	−0.594110	−0.0285841
$433$	−17.8867	−0.859581	−0.429791	−	0.902929i	$-0.641413\pi$
$433$	−17.8867	−0.859581	−0.429791	+	0.902929i	$0.641413\pi$
$434$	−1.43527	−0.0688950
$435$	−9.01015	−0.432004
$436$	20.7040	0.991543
$437$	33.4756	1.60136
$438$	−0.138079	−0.00659766
$439$	10.1741	0.485584	0.242792	−	0.970078i	$-0.421937\pi$
$439$	10.1741	0.485584	0.242792	+	0.970078i	$0.421937\pi$
$440$	−0.224175	−0.0106871
$441$	2.49970	0.119034
$442$	−0.285525	−0.0135810
$443$	39.9046	1.89593	0.947963	−	0.318381i	$-0.103139\pi$
$443$	39.9046	1.89593	0.947963	+	0.318381i	$0.103139\pi$
$444$	20.0108	0.949670
$445$	−16.0593	−0.761284
$446$	0.971116	0.0459837
$447$	56.6072	2.67743
$448$	22.1559	1.04677
$449$	−16.7752	−0.791668	−0.395834	−	0.918322i	$-0.629545\pi$
$449$	−16.7752	−0.791668	−0.395834	+	0.918322i	$0.629545\pi$
$450$	−0.171663	−0.00809229
$451$	−9.69865	−0.456692
$452$	24.9787	1.17490
$453$	5.15908	0.242395
$454$	−0.0669299	−0.00314118
$455$	2.76828	0.129779
$456$	2.36866	0.110923
$457$	26.4348	1.23657	0.618284	−	0.785955i	$-0.287828\pi$
$457$	26.4348	1.23657	0.618284	+	0.785955i	$0.287828\pi$
$458$	−0.238388	−0.0111391
$459$	−0.767251	−0.0358122
$460$	−15.5747	−0.726172
$461$	−14.2057	−0.661625	−0.330813	−	0.943696i	$-0.607323\pi$
$461$	−14.2057	−0.661625	−0.330813	+	0.943696i	$0.607323\pi$
$462$	−0.386046	−0.0179605
$463$	2.32075	0.107855	0.0539273	−	0.998545i	$-0.482826\pi$
$463$	2.32075	0.107855	0.0539273	+	0.998545i	$0.482826\pi$
$464$	−14.5707	−0.676428
$465$	−22.5325	−1.04492
$466$	−0.595565	−0.0275890
$467$	29.1274	1.34786	0.673929	−	0.738796i	$-0.264605\pi$
$467$	29.1274	1.34786	0.673929	+	0.738796i	$0.264605\pi$
$468$	−6.05137	−0.279725
$469$	10.5924	0.489110
$470$	−0.627672	−0.0289524
$471$	−46.5644	−2.14558
$472$	0.510819	0.0235123
$473$	−8.93499	−0.410831
$474$	0.433491	0.0199109
$475$	−4.29197	−0.196929
$476$	28.7036	1.31563
$477$	−2.64889	−0.121284
$478$	0.760984	0.0348066
$479$	−15.0760	−0.688841	−0.344420	−	0.938816i	$-0.611925\pi$
$479$	−15.0760	−0.688841	−0.344420	+	0.938816i	$0.611925\pi$
$480$	−1.65347	−0.0754703
$481$	4.03049	0.183774
$482$	−0.825868	−0.0376173
$483$	−53.6838	−2.44270
$484$	−1.99685	−0.0907661
$485$	−3.08198	−0.139945
$486$	−1.24220	−0.0563474
$487$	8.64660	0.391815	0.195908	−	0.980622i	$-0.437235\pi$
$487$	8.64660	0.391815	0.195908	+	0.980622i	$0.437235\pi$
$488$	−0.607181	−0.0274858
$489$	−6.67600	−0.301899
$490$	0.0458087	0.00206943
$491$	−43.1881	−1.94905	−0.974525	−	0.224278i	$-0.927998\pi$
$491$	−43.1881	−1.94905	−0.974525	+	0.224278i	$0.927998\pi$
$492$	−47.6778	−2.14948
$493$	−18.8170	−0.847476
$494$	0.238355	0.0107241
$495$	−3.06062	−0.137565
$496$	−36.4383	−1.63613
$497$	−2.24932	−0.100896
$498$	1.65523	0.0741726
$499$	3.79176	0.169743	0.0848713	−	0.996392i	$-0.472952\pi$
$499$	3.79176	0.169743	0.0848713	+	0.996392i	$0.472952\pi$
$500$	1.99685	0.0893020
$501$	29.4129	1.31407
$502$	1.05136	0.0469246
$503$	12.2071	0.544289	0.272144	−	0.962256i	$-0.412267\pi$
$503$	12.2071	0.544289	0.272144	+	0.962256i	$0.412267\pi$
$504$	−1.91826	−0.0854463
$505$	9.23097	0.410773
$506$	0.437462	0.0194476
$507$	29.5903	1.31415
$508$	−39.4290	−1.74938
$509$	−11.1077	−0.492338	−0.246169	−	0.969227i	$-0.579172\pi$
$509$	−11.1077	−0.492338	−0.246169	+	0.969227i	$0.579172\pi$
$510$	−0.709912	−0.0314354
$511$	2.79584	0.123681
$512$	−4.45884	−0.197055
$513$	0.640497	0.0282786
$514$	1.14213	0.0503771
$515$	11.6071	0.511469
$516$	−43.9237	−1.93363
$517$	−11.1909	−0.492175
$518$	0.638323	0.0280463
$519$	−15.2358	−0.668777
$520$	−0.221965	−0.00973382
$521$	21.8232	0.956091	0.478045	−	0.878335i	$-0.341345\pi$
$521$	21.8232	0.956091	0.478045	+	0.878335i	$0.341345\pi$
$522$	0.628277	0.0274989
$523$	8.19039	0.358141	0.179070	−	0.983836i	$-0.442691\pi$
$523$	8.19039	0.358141	0.179070	+	0.983836i	$0.442691\pi$
$524$	31.1958	1.36279
$525$	6.88289	0.300394
$526$	1.04064	0.0453742
$527$	−47.0575	−2.04986
$528$	−9.80089	−0.426529
$529$	37.8337	1.64494
$530$	−0.0485426	−0.00210856
$531$	6.97411	0.302651
$532$	−23.9616	−1.03887
$533$	−9.60305	−0.415954
$534$	2.21745	0.0959584
$535$	0.944480	0.0408334
$536$	−0.849311	−0.0366847
$537$	51.1829	2.20870
$538$	−1.68403	−0.0726038
$539$	0.816732	0.0351791
$540$	−0.297993	−0.0128236
$541$	3.83533	0.164894	0.0824470	−	0.996595i	$-0.473726\pi$
$541$	3.83533	0.164894	0.0824470	+	0.996595i	$0.473726\pi$
$542$	−1.31402	−0.0564420
$543$	16.7636	0.719397
$544$	−3.45315	−0.148053
$545$	10.3683	0.444130
$546$	−0.382241	−0.0163584
$547$	15.0153	0.642006	0.321003	−	0.947078i	$-0.395980\pi$
$547$	15.0153	0.642006	0.321003	+	0.947078i	$0.395980\pi$
$548$	−36.8464	−1.57400
$549$	−8.28974	−0.353797
$550$	−0.0560878	−0.00239159
$551$	15.7083	0.669198
$552$	4.30445	0.183209
$553$	−8.77739	−0.373253
$554$	1.09156	0.0463759
$555$	10.0212	0.425374
$556$	8.73243	0.370338
$557$	6.45220	0.273389	0.136694	−	0.990613i	$-0.456352\pi$
$557$	6.45220	0.273389	0.136694	+	0.990613i	$0.456352\pi$
$558$	1.57119	0.0665138
$559$	−8.84692	−0.374185
$560$	11.1306	0.470355
$561$	−12.6571	−0.534385
$562$	1.39903	0.0590146
$563$	8.99453	0.379074	0.189537	−	0.981874i	$-0.439301\pi$
$563$	8.99453	0.379074	0.189537	+	0.981874i	$0.439301\pi$
$564$	−55.0135	−2.31649
$565$	12.5090	0.526259
$566$	−0.212169	−0.00891812
$567$	24.6439	1.03495
$568$	0.180354	0.00756748
$569$	8.30662	0.348232	0.174116	−	0.984725i	$-0.444293\pi$
$569$	8.30662	0.348232	0.174116	+	0.984725i	$0.444293\pi$
$570$	0.592630	0.0248226
$571$	1.77776	0.0743967	0.0371984	−	0.999308i	$-0.488157\pi$
$571$	1.77776	0.0743967	0.0371984	+	0.999308i	$0.488157\pi$
$572$	−1.97717	−0.0826697
$573$	61.0365	2.54983
$574$	−1.52087	−0.0634799
$575$	−7.79959	−0.325266
$576$	−24.2542	−1.01059
$577$	3.31510	0.138010	0.0690048	−	0.997616i	$-0.478018\pi$
$577$	3.31510	0.138010	0.0690048	+	0.997616i	$0.478018\pi$
$578$	−0.529105	−0.0220079
$579$	−17.2736	−0.717866
$580$	−7.30836	−0.303463
$581$	−33.5154	−1.39045
$582$	0.425555	0.0176398
$583$	−0.865476	−0.0358443
$584$	−0.224175	−0.00927642
$585$	−3.03045	−0.125294
$586$	−0.107785	−0.00445254
$587$	−5.83643	−0.240895	−0.120448	−	0.992720i	$-0.538433\pi$
$587$	−5.83643	−0.240895	−0.120448	+	0.992720i	$0.538433\pi$
$588$	4.01499	0.165575
$589$	39.2833	1.61864
$590$	0.127805	0.00526166
$591$	−37.0597	−1.52443
$592$	16.2056	0.666048
$593$	−43.4944	−1.78610	−0.893051	−	0.449955i	$-0.851440\pi$
$593$	−43.4944	−1.78610	−0.893051	+	0.449955i	$0.851440\pi$
$594$	0.00837006	0.000343428 0
$595$	14.3744	0.589293
$596$	45.9155	1.88077
$597$	−8.27154	−0.338531
$598$	0.433150	0.0177128
$599$	43.4189	1.77405	0.887025	−	0.461722i	$-0.152768\pi$
$599$	43.4189	1.77405	0.887025	+	0.461722i	$0.152768\pi$
$600$	−0.551881	−0.0225304
$601$	22.1420	0.903191	0.451596	−	0.892223i	$-0.350855\pi$
$601$	22.1420	0.903191	0.451596	+	0.892223i	$0.350855\pi$
$602$	−1.40112	−0.0571054
$603$	−11.5955	−0.472205
$604$	4.18466	0.170272
$605$	−1.00000	−0.0406558
$606$	−1.27460	−0.0517771
$607$	31.1307	1.26355	0.631777	−	0.775150i	$-0.282326\pi$
$607$	31.1307	1.26355	0.631777	+	0.775150i	$0.282326\pi$
$608$	2.88267	0.116908
$609$	−25.1909	−1.02079
$610$	−0.151915	−0.00615085
$611$	−11.0806	−0.448272
$612$	−31.4219	−1.27016
$613$	−34.0142	−1.37382	−0.686910	−	0.726743i	$-0.741033\pi$
$613$	−34.0142	−1.37382	−0.686910	+	0.726743i	$0.741033\pi$
$614$	−0.128393	−0.00518152
$615$	−23.8764	−0.962791
$616$	−0.626757	−0.0252528
$617$	34.6402	1.39456	0.697281	−	0.716798i	$-0.254393\pi$
$617$	34.6402	1.39456	0.697281	+	0.716798i	$0.254393\pi$
$618$	−1.60269	−0.0644697
$619$	18.0375	0.724988	0.362494	−	0.931986i	$-0.381925\pi$
$619$	18.0375	0.724988	0.362494	+	0.931986i	$0.381925\pi$
$620$	−18.2767	−0.734010
$621$	1.16394	0.0467075
$622$	−1.48752	−0.0596442
$623$	−44.8993	−1.79885
$624$	−9.70428	−0.388482
$625$	1.00000	0.0400000
$626$	1.23226	0.0492508
$627$	10.5661	0.421970
$628$	−37.7696	−1.50717
$629$	20.9284	0.834472
$630$	−0.479944	−0.0191214
$631$	−32.0003	−1.27391	−0.636956	−	0.770900i	$-0.719807\pi$
$631$	−32.0003	−1.27391	−0.636956	+	0.770900i	$0.719807\pi$
$632$	0.703785	0.0279950
$633$	−63.7428	−2.53355
$634$	1.15748	0.0459696
$635$	−19.7455	−0.783578
$636$	−4.25461	−0.168706
$637$	0.808681	0.0320411
$638$	0.205278	0.00812702
$639$	2.46234	0.0974087
$640$	−1.78776	−0.0706674
$641$	4.23711	0.167356	0.0836779	−	0.996493i	$-0.473333\pi$
$641$	4.23711	0.167356	0.0836779	+	0.996493i	$0.473333\pi$
$642$	−0.130413	−0.00514698
$643$	22.6640	0.893779	0.446889	−	0.894589i	$-0.352532\pi$
$643$	22.6640	0.893779	0.446889	+	0.894589i	$0.352532\pi$
$644$	−43.5443	−1.71588
$645$	−21.9964	−0.866109
$646$	1.23766	0.0486952
$647$	−17.0464	−0.670162	−0.335081	−	0.942189i	$-0.608764\pi$
$647$	−17.0464	−0.670162	−0.335081	+	0.942189i	$0.608764\pi$
$648$	−1.97598	−0.0776239
$649$	2.27866	0.0894453
$650$	−0.0555350	−0.00217826
$651$	−62.9974	−2.46906
$652$	−5.41507	−0.212070
$653$	38.3700	1.50153	0.750767	−	0.660567i	$-0.229684\pi$
$653$	38.3700	1.50153	0.750767	+	0.660567i	$0.229684\pi$
$654$	−1.43164	−0.0559817
$655$	15.6225	0.610420
$656$	−38.6116	−1.50753
$657$	−3.06062	−0.119406
$658$	−1.75487	−0.0684121
$659$	−37.3807	−1.45615	−0.728073	−	0.685500i	$-0.759584\pi$
$659$	−37.3807	−1.45615	−0.728073	+	0.685500i	$0.759584\pi$
$660$	−4.91592	−0.191352
$661$	−40.0466	−1.55763	−0.778816	−	0.627252i	$-0.784180\pi$
$661$	−40.0466	−1.55763	−0.778816	+	0.627252i	$0.784180\pi$
$662$	−1.00461	−0.0390453
$663$	−12.5324	−0.486718
$664$	2.68731	0.104288
$665$	−11.9997	−0.465327
$666$	−0.698775	−0.0270770
$667$	28.5460	1.10531
$668$	23.8575	0.923076
$669$	42.6247	1.64797
$670$	−0.212495	−0.00820939
$671$	−2.70852	−0.104561
$672$	−4.62285	−0.178330
$673$	4.55711	0.175664	0.0878319	−	0.996135i	$-0.472006\pi$
$673$	4.55711	0.175664	0.0878319	+	0.996135i	$0.472006\pi$
$674$	0.677546	0.0260981
$675$	−0.149231	−0.00574392
$676$	24.0014	0.923132
$677$	30.5144	1.17276	0.586381	−	0.810035i	$-0.300552\pi$
$677$	30.5144	1.17276	0.586381	+	0.810035i	$0.300552\pi$
$678$	−1.72723	−0.0663339
$679$	−8.61672	−0.330679
$680$	−1.15256	−0.0441987
$681$	−2.93772	−0.112574
$682$	0.513357	0.0196575
$683$	7.06532	0.270347	0.135173	−	0.990822i	$-0.456841\pi$
$683$	7.06532	0.270347	0.135173	+	0.990822i	$0.456841\pi$
$684$	26.2309	1.00296
$685$	−18.4522	−0.705022
$686$	−0.969615	−0.0370201
$687$	−10.4634	−0.399204
$688$	−35.5714	−1.35615
$689$	−0.856945	−0.0326470
$690$	1.07696	0.0409991
$691$	36.3362	1.38229	0.691147	−	0.722714i	$-0.257106\pi$
$691$	36.3362	1.38229	0.691147	+	0.722714i	$0.257106\pi$
$692$	−12.3581	−0.469786
$693$	−8.55700	−0.325054
$694$	−1.34332	−0.0509919
$695$	4.37310	0.165881
$696$	2.01985	0.0765621
$697$	−49.8642	−1.88874
$698$	0.805650	0.0304943
$699$	−26.1408	−0.988736
$700$	5.58289	0.211013
$701$	−4.06952	−0.153704	−0.0768518	−	0.997043i	$-0.524487\pi$
$701$	−4.06952	−0.153704	−0.0768518	+	0.997043i	$0.524487\pi$
$702$	0.00828756	0.000312794 0
$703$	−17.4709	−0.658929
$704$	−7.92460	−0.298670
$705$	−27.5501	−1.03760
$706$	−1.21609	−0.0457683
$707$	25.8083	0.970623
$708$	11.2017	0.420986
$709$	−28.5763	−1.07321	−0.536603	−	0.843835i	$-0.680293\pi$
$709$	−28.5763	−1.07321	−0.536603	+	0.843835i	$0.680293\pi$
$710$	0.0451240	0.00169347
$711$	9.60864	0.360352
$712$	3.60009	0.134919
$713$	71.3877	2.67349
$714$	−1.98480	−0.0742793
$715$	−0.990143	−0.0370293
$716$	41.5157	1.55152
$717$	33.4015	1.24740
$718$	−2.10176	−0.0784369
$719$	−0.0246582	−0.000919597 0	−0.000459798	−	1.00000i	$-0.500146\pi$
$719$	−0.0246582	−0.000919597 0	−0.000459798		1.00000i	$0.500146\pi$
$720$	−12.1847	−0.454098
$721$	32.4515	1.20856
$722$	0.0324734	0.00120854
$723$	−36.2494	−1.34813
$724$	13.5974	0.505344
$725$	−3.65994	−0.135927
$726$	0.138079	0.00512458
$727$	−3.59951	−0.133499	−0.0667493	−	0.997770i	$-0.521263\pi$
$727$	−3.59951	−0.133499	−0.0667493	+	0.997770i	$0.521263\pi$
$728$	−0.620580	−0.0230002
$729$	−28.0799	−1.04000
$730$	−0.0560878	−0.00207590
$731$	−45.9379	−1.69908
$732$	−13.3149	−0.492131
$733$	−17.5089	−0.646706	−0.323353	−	0.946278i	$-0.604810\pi$
$733$	−17.5089	−0.646706	−0.323353	+	0.946278i	$0.604810\pi$
$734$	−1.04728	−0.0386557
$735$	2.01066	0.0741642
$736$	5.23854	0.193095
$737$	−3.78861	−0.139555
$738$	1.66490	0.0612859
$739$	−44.4562	−1.63535	−0.817674	−	0.575681i	$-0.804737\pi$
$739$	−44.4562	−1.63535	−0.817674	+	0.575681i	$0.804737\pi$
$740$	8.12841	0.298806
$741$	10.4620	0.384330
$742$	−0.135718	−0.00498235
$743$	−8.21659	−0.301437	−0.150719	−	0.988577i	$-0.548159\pi$
$743$	−8.21659	−0.301437	−0.150719	+	0.988577i	$0.548159\pi$
$744$	5.05122	0.185187
$745$	22.9939	0.842432
$746$	0.739719	0.0270830
$747$	36.6894	1.34239
$748$	−10.2665	−0.375382
$749$	2.64062	0.0964860
$750$	−0.138079	−0.00504192
$751$	6.15349	0.224544	0.112272	−	0.993678i	$-0.464187\pi$
$751$	6.15349	0.224544	0.112272	+	0.993678i	$0.464187\pi$
$752$	−44.5524	−1.62466
$753$	46.1469	1.68169
$754$	0.203254	0.00740209
$755$	2.09563	0.0762677
$756$	−0.833142	−0.0303011
$757$	−32.7282	−1.18953	−0.594764	−	0.803901i	$-0.702754\pi$
$757$	−32.7282	−1.18953	−0.594764	+	0.803901i	$0.702754\pi$
$758$	−0.181782	−0.00660261
$759$	19.2013	0.696963
$760$	0.962152	0.0349009
$761$	24.3068	0.881121	0.440561	−	0.897723i	$-0.354780\pi$
$761$	24.3068	0.881121	0.440561	+	0.897723i	$0.354780\pi$
$762$	2.72644	0.0987685
$763$	28.9882	1.04944
$764$	49.5082	1.79114
$765$	−15.7357	−0.568926
$766$	0.817090	0.0295227
$767$	2.25620	0.0814667
$768$	−38.7712	−1.39904
$769$	31.6234	1.14037	0.570185	−	0.821516i	$-0.306872\pi$
$769$	31.6234	1.14037	0.570185	+	0.821516i	$0.306872\pi$
$770$	−0.156813	−0.00565114
$771$	50.1308	1.80542
$772$	−14.0111	−0.504269
$773$	40.5806	1.45958	0.729792	−	0.683669i	$-0.239617\pi$
$773$	40.5806	1.45958	0.729792	+	0.683669i	$0.239617\pi$
$774$	1.53381	0.0551317
$775$	−9.15274	−0.328776
$776$	0.690901	0.0248019
$777$	28.0176	1.00512
$778$	−1.44637	−0.0518549
$779$	41.6263	1.49142
$780$	−4.86747	−0.174283
$781$	0.804524	0.0287881
$782$	2.24915	0.0804294
$783$	0.546177	0.0195188
$784$	3.25152	0.116126
$785$	−18.9145	−0.675089
$786$	−2.15713	−0.0769423
$787$	−7.02732	−0.250497	−0.125248	−	0.992125i	$-0.539973\pi$
$787$	−7.02732	−0.250497	−0.125248	+	0.992125i	$0.539973\pi$
$788$	−30.0601	−1.07085
$789$	45.6764	1.62612
$790$	0.176085	0.00626481
$791$	34.9733	1.24351
$792$	0.686113	0.0243800
$793$	−2.68182	−0.0952342
$794$	−0.907294	−0.0321987
$795$	−2.13066	−0.0755666
$796$	−6.70925	−0.237803
$797$	−22.1922	−0.786087	−0.393044	−	0.919520i	$-0.628578\pi$
$797$	−22.1922	−0.786087	−0.393044	+	0.919520i	$0.628578\pi$
$798$	1.65690	0.0586536
$799$	−57.5363	−2.03549
$800$	−0.671643	−0.0237462
$801$	49.1514	1.73668
$802$	−2.10535	−0.0743424
$803$	−1.00000	−0.0352892
$804$	−18.6245	−0.656836
$805$	−21.8064	−0.768576
$806$	0.508297	0.0179040
$807$	−73.9163	−2.60198
$808$	−2.06935	−0.0727995
$809$	−0.290276	−0.0102056	−0.00510278	−	0.999987i	$-0.501624\pi$
$809$	−0.290276	−0.0102056	−0.00510278	+	0.999987i	$0.501624\pi$
$810$	−0.494384	−0.0173709
$811$	−13.9692	−0.490526	−0.245263	−	0.969457i	$-0.578874\pi$
$811$	−13.9692	−0.490526	−0.245263	+	0.969457i	$0.578874\pi$
$812$	−20.4330	−0.717058
$813$	−57.6755	−2.02277
$814$	−0.228312	−0.00800232
$815$	−2.71180	−0.0949902
$816$	−50.3898	−1.76400
$817$	38.3487	1.34165
$818$	1.26406	0.0441967
$819$	−8.47266	−0.296059
$820$	−19.3668	−0.676318
$821$	−12.9029	−0.450314	−0.225157	−	0.974323i	$-0.572289\pi$
$821$	−12.9029	−0.450314	−0.225157	+	0.974323i	$0.572289\pi$
$822$	2.54786	0.0888667
$823$	25.2297	0.879452	0.439726	−	0.898132i	$-0.355076\pi$
$823$	25.2297	0.879452	0.439726	+	0.898132i	$0.355076\pi$
$824$	−2.60201	−0.0906454
$825$	−2.46183	−0.0857100
$826$	0.357323	0.0124329
$827$	8.54864	0.297265	0.148633	−	0.988892i	$-0.452513\pi$
$827$	8.54864	0.297265	0.148633	+	0.988892i	$0.452513\pi$
$828$	47.6681	1.65658
$829$	−34.8467	−1.21028	−0.605138	−	0.796121i	$-0.706882\pi$
$829$	−34.8467	−1.21028	−0.605138	+	0.796121i	$0.706882\pi$
$830$	0.672357	0.0233378
$831$	47.9112	1.66202
$832$	−7.84649	−0.272028
$833$	4.19911	0.145490
$834$	−0.603832	−0.0209090
$835$	11.9476	0.413462
$836$	8.57044	0.296415
$837$	1.36588	0.0472116
$838$	0.282965	0.00977487
$839$	40.1059	1.38461	0.692304	−	0.721606i	$-0.256596\pi$
$839$	40.1059	1.38461	0.692304	+	0.721606i	$0.256596\pi$
$840$	−1.54297	−0.0532376
$841$	−15.6049	−0.538099
$842$	1.80737	0.0622859
$843$	61.4069	2.11497
$844$	−51.7034	−1.77970
$845$	12.0196	0.413487
$846$	1.92107	0.0660476
$847$	−2.79584	−0.0960663
$848$	−3.44558	−0.118322
$849$	−9.31262	−0.319608
$850$	−0.288367	−0.00989091
$851$	−31.7491	−1.08835
$852$	3.95497	0.135495
$853$	−44.3509	−1.51855	−0.759274	−	0.650772i	$-0.774446\pi$
$853$	−44.3509	−1.51855	−0.759274	+	0.650772i	$0.774446\pi$
$854$	−0.424730	−0.0145340
$855$	13.1361	0.449245
$856$	−0.211729	−0.00723674
$857$	20.2453	0.691565	0.345782	−	0.938315i	$-0.387614\pi$
$857$	20.2453	0.691565	0.345782	+	0.938315i	$0.387614\pi$
$858$	0.136718	0.00466747
$859$	−34.2638	−1.16906	−0.584532	−	0.811371i	$-0.698722\pi$
$859$	−34.2638	−1.16906	−0.584532	+	0.811371i	$0.698722\pi$
$860$	−17.8419	−0.608403
$861$	−66.7548	−2.27500
$862$	−0.0687654	−0.00234216
$863$	−32.5774	−1.10895	−0.554474	−	0.832201i	$-0.687080\pi$
$863$	−32.5774	−1.10895	−0.554474	+	0.832201i	$0.687080\pi$
$864$	0.100230	0.00340990
$865$	−6.18880	−0.210425
$866$	1.00323	0.0340911
$867$	−23.2237	−0.788719
$868$	−51.0987	−1.73440
$869$	3.13945	0.106498
$870$	0.505359	0.0171333
$871$	−3.75127	−0.127107
$872$	−2.32432	−0.0787113
$873$	9.43275	0.319250
$874$	−1.87758	−0.0635099
$875$	2.79584	0.0945167
$876$	−4.91592	−0.166094
$877$	−37.0167	−1.24996	−0.624982	−	0.780639i	$-0.714894\pi$
$877$	−37.0167	−1.24996	−0.624982	+	0.780639i	$0.714894\pi$
$878$	−0.570644	−0.0192583
$879$	−4.73093	−0.159570
$880$	−3.98113	−0.134204
$881$	−29.4656	−0.992722	−0.496361	−	0.868116i	$-0.665331\pi$
$881$	−29.4656	−0.992722	−0.496361	+	0.868116i	$0.665331\pi$
$882$	−0.140203	−0.00472088
$883$	21.4644	0.722336	0.361168	−	0.932501i	$-0.382378\pi$
$883$	21.4644	0.722336	0.361168	+	0.932501i	$0.382378\pi$
$884$	−10.1653	−0.341897
$885$	5.60968	0.188567
$886$	−2.23816	−0.0751925
$887$	−55.2157	−1.85396	−0.926981	−	0.375107i	$-0.877606\pi$
$887$	−55.2157	−1.85396	−0.926981	+	0.375107i	$0.877606\pi$
$888$	−2.24649	−0.0753873
$889$	−55.2054	−1.85153
$890$	0.900731	0.0301926
$891$	−8.81447	−0.295296
$892$	34.5740	1.15762
$893$	48.0310	1.60730
$894$	−3.17497	−0.106187
$895$	20.7906	0.694952
$896$	−4.99829	−0.166981
$897$	19.0120	0.634793
$898$	0.940882	0.0313976
$899$	33.4984	1.11724
$900$	−6.11161	−0.203720
$901$	−4.44972	−0.148242
$902$	0.543976	0.0181124
$903$	−61.4986	−2.04655
$904$	−2.80421	−0.0932666
$905$	6.80941	0.226353
$906$	−0.289362	−0.00961340
$907$	−20.2585	−0.672672	−0.336336	−	0.941742i	$-0.609188\pi$
$907$	−20.2585	−0.672672	−0.336336	+	0.941742i	$0.609188\pi$
$908$	−2.38286	−0.0790779
$909$	−28.2525	−0.937076
$910$	−0.155267	−0.00514705
$911$	−4.97994	−0.164993	−0.0824963	−	0.996591i	$-0.526289\pi$
$911$	−4.97994	−0.164993	−0.0824963	+	0.996591i	$0.526289\pi$
$912$	42.0651	1.39292
$913$	11.9876	0.396731
$914$	−1.48267	−0.0490424
$915$	−6.66792	−0.220434
$916$	−8.48714	−0.280423
$917$	43.6779	1.44237
$918$	0.0430334	0.00142032
$919$	0.0584999	0.00192973	0.000964867	−	1.00000i	$-0.499693\pi$
$919$	0.0584999	0.00192973	0.000964867		1.00000i	$0.499693\pi$
$920$	1.74847	0.0576454
$921$	−5.63549	−0.185696
$922$	0.796766	0.0262401
$923$	0.796594	0.0262202
$924$	−13.7441	−0.452149
$925$	4.07061	0.133841
$926$	−0.130166	−0.00427752
$927$	−35.5248	−1.16679
$928$	2.45817	0.0806934
$929$	−15.8807	−0.521028	−0.260514	−	0.965470i	$-0.583892\pi$
$929$	−15.8807	−0.521028	−0.260514	+	0.965470i	$0.583892\pi$
$930$	1.26380	0.0414416
$931$	−3.50539	−0.114885
$932$	−21.2035	−0.694542
$933$	−65.2910	−2.13753
$934$	−1.63369	−0.0534561
$935$	−5.14135	−0.168140
$936$	0.679351	0.0222053
$937$	29.2102	0.954256	0.477128	−	0.878834i	$-0.341678\pi$
$937$	29.2102	0.954256	0.477128	+	0.878834i	$0.341678\pi$
$938$	−0.594102	−0.0193981
$939$	54.0867	1.76505
$940$	−22.3466	−0.728865
$941$	−60.1399	−1.96050	−0.980252	−	0.197753i	$-0.936636\pi$
$941$	−60.1399	−1.96050	−0.980252	+	0.197753i	$0.936636\pi$
$942$	2.61170	0.0850937
$943$	75.6455	2.46336
$944$	9.07166	0.295257
$945$	−0.417227	−0.0135724
$946$	0.501144	0.0162936
$947$	−30.6197	−0.995006	−0.497503	−	0.867462i	$-0.665750\pi$
$947$	−30.6197	−0.995006	−0.497503	+	0.867462i	$0.665750\pi$
$948$	15.4333	0.501249
$949$	−0.990143	−0.0321414
$950$	0.240727	0.00781023
$951$	50.8048	1.64746
$952$	−3.22238	−0.104438
$953$	4.14920	0.134406	0.0672029	−	0.997739i	$-0.478593\pi$
$953$	4.14920	0.134406	0.0672029	+	0.997739i	$0.478593\pi$
$954$	0.148571	0.00481015
$955$	24.7931	0.802286
$956$	27.0928	0.876243
$957$	9.01015	0.291257
$958$	0.845581	0.0273195
$959$	−51.5894	−1.66591
$960$	−19.5090	−0.629651
$961$	52.7727	1.70234
$962$	−0.226061	−0.00728850
$963$	−2.89069	−0.0931513
$964$	−29.4028	−0.947000
$965$	−7.01656	−0.225871
$966$	3.01101	0.0968775
$967$	55.3933	1.78133	0.890664	−	0.454663i	$-0.150240\pi$
$967$	55.3933	1.78133	0.890664	+	0.454663i	$0.150240\pi$
$968$	0.224175	0.00720525
$969$	54.3241	1.74514
$970$	0.172861	0.00555024
$971$	18.4033	0.590592	0.295296	−	0.955406i	$-0.404582\pi$
$971$	18.4033	0.590592	0.295296	+	0.955406i	$0.404582\pi$
$972$	−44.2252	−1.41852
$973$	12.2265	0.391963
$974$	−0.484969	−0.0155394
$975$	−2.43757	−0.0780646
$976$	−10.7830	−0.345155
$977$	41.3442	1.32272	0.661359	−	0.750069i	$-0.269980\pi$
$977$	41.3442	1.32272	0.661359	+	0.750069i	$0.269980\pi$
$978$	0.374442	0.0119733
$979$	16.0593	0.513257
$980$	1.63089	0.0520970
$981$	−31.7335	−1.01317
$982$	2.42232	0.0772995
$983$	40.3152	1.28586	0.642928	−	0.765926i	$-0.277719\pi$
$983$	40.3152	1.28586	0.642928	+	0.765926i	$0.277719\pi$
$984$	5.35250	0.170631
$985$	−15.0537	−0.479651
$986$	1.05541	0.0336110
$987$	−77.0257	−2.45175
$988$	8.48597	0.269975
$989$	69.6893	2.21599
$990$	0.171663	0.00545582
$991$	−25.0639	−0.796181	−0.398090	−	0.917346i	$-0.630327\pi$
$991$	−25.0639	−0.796181	−0.398090	+	0.917346i	$0.630327\pi$
$992$	6.14737	0.195179
$993$	−44.0949	−1.39931
$994$	0.126160	0.00400154
$995$	−3.35991	−0.106516
$996$	58.9299	1.86727
$997$	2.14271	0.0678603	0.0339302	−	0.999424i	$-0.489198\pi$
$997$	2.14271	0.0678603	0.0339302	+	0.999424i	$0.489198\pi$
$998$	−0.212672	−0.00673200
$999$	−0.607463	−0.0192193

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.e.1.13	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.e.1.13	✓	27	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4015 = 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4015.a (trivial)

\(f(q)\)	\(=\)	\(q-0.0560878 q^{2} -2.46183 q^{3} -1.99685 q^{4} -1.00000 q^{5} +0.138079 q^{6} -2.79584 q^{7} +0.224175 q^{8} +3.06062 q^{9} +O(q^{10})\)	\(q-0.0560878 q^{2} -2.46183 q^{3} -1.99685 q^{4} -1.00000 q^{5} +0.138079 q^{6} -2.79584 q^{7} +0.224175 q^{8} +3.06062 q^{9} +0.0560878 q^{10} +1.00000 q^{11} +4.91592 q^{12} +0.990143 q^{13} +0.156813 q^{14} +2.46183 q^{15} +3.98113 q^{16} +5.14135 q^{17} -0.171663 q^{18} -4.29197 q^{19} +1.99685 q^{20} +6.88289 q^{21} -0.0560878 q^{22} -7.79959 q^{23} -0.551881 q^{24} +1.00000 q^{25} -0.0555350 q^{26} -0.149231 q^{27} +5.58289 q^{28} -3.65994 q^{29} -0.138079 q^{30} -9.15274 q^{31} -0.671643 q^{32} -2.46183 q^{33} -0.288367 q^{34} +2.79584 q^{35} -6.11161 q^{36} +4.07061 q^{37} +0.240727 q^{38} -2.43757 q^{39} -0.224175 q^{40} -9.69865 q^{41} -0.386046 q^{42} -8.93499 q^{43} -1.99685 q^{44} -3.06062 q^{45} +0.437462 q^{46} -11.1909 q^{47} -9.80089 q^{48} +0.816732 q^{49} -0.0560878 q^{50} -12.6571 q^{51} -1.97717 q^{52} -0.865476 q^{53} +0.00837006 q^{54} -1.00000 q^{55} -0.626757 q^{56} +10.5661 q^{57} +0.205278 q^{58} +2.27866 q^{59} -4.91592 q^{60} -2.70852 q^{61} +0.513357 q^{62} -8.55700 q^{63} -7.92460 q^{64} -0.990143 q^{65} +0.138079 q^{66} -3.78861 q^{67} -10.2665 q^{68} +19.2013 q^{69} -0.156813 q^{70} +0.804524 q^{71} +0.686113 q^{72} -1.00000 q^{73} -0.228312 q^{74} -2.46183 q^{75} +8.57044 q^{76} -2.79584 q^{77} +0.136718 q^{78} +3.13945 q^{79} -3.98113 q^{80} -8.81447 q^{81} +0.543976 q^{82} +11.9876 q^{83} -13.7441 q^{84} -5.14135 q^{85} +0.501144 q^{86} +9.01015 q^{87} +0.224175 q^{88} +16.0593 q^{89} +0.171663 q^{90} -2.76828 q^{91} +15.5747 q^{92} +22.5325 q^{93} +0.627672 q^{94} +4.29197 q^{95} +1.65347 q^{96} +3.08198 q^{97} -0.0458087 q^{98} +3.06062 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q + 6 q^{2} + 5 q^{3} + 22 q^{4} - 27 q^{5} + 7 q^{6} + 10 q^{7} + 15 q^{8} + 24 q^{9}+O(q^{10}) \) 27 * q + 6 * q^2 + 5 * q^3 + 22 * q^4 - 27 * q^5 + 7 * q^6 + 10 * q^7 + 15 * q^8 + 24 * q^9	\( 27 q + 6 q^{2} + 5 q^{3} + 22 q^{4} - 27 q^{5} + 7 q^{6} + 10 q^{7} + 15 q^{8} + 24 q^{9} - 6 q^{10} + 27 q^{11} + 28 q^{12} + 21 q^{13} + 11 q^{14} - 5 q^{15} + 12 q^{16} + 30 q^{17} + 10 q^{18} + 20 q^{19} - 22 q^{20} - 14 q^{21} + 6 q^{22} + 16 q^{23} + 23 q^{24} + 27 q^{25} + 13 q^{26} + 17 q^{27} + 6 q^{28} - 2 q^{29} - 7 q^{30} - 6 q^{31} + 41 q^{32} + 5 q^{33} + 8 q^{34} - 10 q^{35} + 13 q^{36} + 20 q^{37} + 11 q^{38} - 10 q^{39} - 15 q^{40} + 38 q^{41} - 33 q^{42} + 29 q^{43} + 22 q^{44} - 24 q^{45} + 23 q^{46} + 17 q^{47} + 37 q^{48} + 21 q^{49} + 6 q^{50} + 13 q^{51} + 29 q^{52} + 4 q^{53} + q^{54} - 27 q^{55} + 28 q^{56} + 51 q^{57} - 6 q^{58} + 35 q^{59} - 28 q^{60} - 13 q^{61} + 28 q^{62} + 41 q^{63} - 5 q^{64} - 21 q^{65} + 7 q^{66} + 10 q^{67} + 65 q^{68} - 12 q^{69} - 11 q^{70} + 22 q^{71} - 12 q^{72} - 27 q^{73} - 5 q^{74} + 5 q^{75} + 13 q^{76} + 10 q^{77} - 9 q^{78} - 18 q^{79} - 12 q^{80} + 39 q^{81} + 20 q^{82} + 54 q^{83} - 50 q^{84} - 30 q^{85} + 3 q^{86} + 15 q^{87} + 15 q^{88} + 89 q^{89} - 10 q^{90} - 18 q^{91} + 57 q^{92} + 20 q^{93} - 29 q^{94} - 20 q^{95} + 105 q^{96} + 35 q^{97} + 10 q^{98} + 24 q^{99}+O(q^{100}) \) 27 * q + 6 * q^2 + 5 * q^3 + 22 * q^4 - 27 * q^5 + 7 * q^6 + 10 * q^7 + 15 * q^8 + 24 * q^9 - 6 * q^10 + 27 * q^11 + 28 * q^12 + 21 * q^13 + 11 * q^14 - 5 * q^15 + 12 * q^16 + 30 * q^17 + 10 * q^18 + 20 * q^19 - 22 * q^20 - 14 * q^21 + 6 * q^22 + 16 * q^23 + 23 * q^24 + 27 * q^25 + 13 * q^26 + 17 * q^27 + 6 * q^28 - 2 * q^29 - 7 * q^30 - 6 * q^31 + 41 * q^32 + 5 * q^33 + 8 * q^34 - 10 * q^35 + 13 * q^36 + 20 * q^37 + 11 * q^38 - 10 * q^39 - 15 * q^40 + 38 * q^41 - 33 * q^42 + 29 * q^43 + 22 * q^44 - 24 * q^45 + 23 * q^46 + 17 * q^47 + 37 * q^48 + 21 * q^49 + 6 * q^50 + 13 * q^51 + 29 * q^52 + 4 * q^53 + q^54 - 27 * q^55 + 28 * q^56 + 51 * q^57 - 6 * q^58 + 35 * q^59 - 28 * q^60 - 13 * q^61 + 28 * q^62 + 41 * q^63 - 5 * q^64 - 21 * q^65 + 7 * q^66 + 10 * q^67 + 65 * q^68 - 12 * q^69 - 11 * q^70 + 22 * q^71 - 12 * q^72 - 27 * q^73 - 5 * q^74 + 5 * q^75 + 13 * q^76 + 10 * q^77 - 9 * q^78 - 18 * q^79 - 12 * q^80 + 39 * q^81 + 20 * q^82 + 54 * q^83 - 50 * q^84 - 30 * q^85 + 3 * q^86 + 15 * q^87 + 15 * q^88 + 89 * q^89 - 10 * q^90 - 18 * q^91 + 57 * q^92 + 20 * q^93 - 29 * q^94 - 20 * q^95 + 105 * q^96 + 35 * q^97 + 10 * q^98 + 24 * q^99

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