LMFDB - Embedded newform 4015.2.a.e.1.5

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			1.5
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)

$f(q)$	$=$	$q-1.64001 q^{2} +1.19849 q^{3} +0.689644 q^{4} -1.00000 q^{5} -1.96554 q^{6} -2.90687 q^{7} +2.14900 q^{8} -1.56361 q^{9} +O(q^{10})$	\(q-1.64001 q^{2} +1.19849 q^{3} +0.689644 q^{4} -1.00000 q^{5} -1.96554 q^{6} -2.90687 q^{7} +2.14900 q^{8} -1.56361 q^{9} +1.64001 q^{10} +1.00000 q^{11} +0.826534 q^{12} -4.40756 q^{13} +4.76731 q^{14} -1.19849 q^{15} -4.90368 q^{16} -3.56485 q^{17} +2.56435 q^{18} -3.72929 q^{19} -0.689644 q^{20} -3.48387 q^{21} -1.64001 q^{22} -6.43105 q^{23} +2.57556 q^{24} +1.00000 q^{25} +7.22846 q^{26} -5.46946 q^{27} -2.00471 q^{28} -7.11552 q^{29} +1.96554 q^{30} -6.72666 q^{31} +3.74410 q^{32} +1.19849 q^{33} +5.84641 q^{34} +2.90687 q^{35} -1.07834 q^{36} +8.74751 q^{37} +6.11609 q^{38} -5.28243 q^{39} -2.14900 q^{40} +7.21453 q^{41} +5.71359 q^{42} +12.0139 q^{43} +0.689644 q^{44} +1.56361 q^{45} +10.5470 q^{46} -0.194346 q^{47} -5.87703 q^{48} +1.44992 q^{49} -1.64001 q^{50} -4.27245 q^{51} -3.03965 q^{52} -0.243416 q^{53} +8.96999 q^{54} -1.00000 q^{55} -6.24688 q^{56} -4.46953 q^{57} +11.6695 q^{58} -3.10798 q^{59} -0.826534 q^{60} +11.3820 q^{61} +11.0318 q^{62} +4.54523 q^{63} +3.66699 q^{64} +4.40756 q^{65} -1.96554 q^{66} -4.95163 q^{67} -2.45848 q^{68} -7.70757 q^{69} -4.76731 q^{70} -10.7183 q^{71} -3.36021 q^{72} -1.00000 q^{73} -14.3460 q^{74} +1.19849 q^{75} -2.57189 q^{76} -2.90687 q^{77} +8.66326 q^{78} -5.81786 q^{79} +4.90368 q^{80} -1.86427 q^{81} -11.8319 q^{82} +11.3689 q^{83} -2.40263 q^{84} +3.56485 q^{85} -19.7029 q^{86} -8.52790 q^{87} +2.14900 q^{88} -2.86370 q^{89} -2.56435 q^{90} +12.8122 q^{91} -4.43514 q^{92} -8.06186 q^{93} +0.318729 q^{94} +3.72929 q^{95} +4.48728 q^{96} +2.45325 q^{97} -2.37789 q^{98} -1.56361 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.64001	−1.15966	−0.579832	−	0.814736i	$-0.696882\pi$
$2$	−1.64001	−1.15966	−0.579832	+	0.814736i	$0.696882\pi$
$3$	1.19849	0.691950	0.345975	−	0.938244i	$-0.387548\pi$
$3$	1.19849	0.691950	0.345975	+	0.938244i	$0.387548\pi$
$4$	0.689644	0.344822
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.96554	−0.802430
$7$	−2.90687	−1.09870	−0.549348	−	0.835594i	$-0.685124\pi$
$7$	−2.90687	−1.09870	−0.549348	+	0.835594i	$0.685124\pi$
$8$	2.14900	0.759787
$9$	−1.56361	−0.521205
$10$	1.64001	0.518618
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.826534	0.238600
$13$	−4.40756	−1.22244	−0.611219	−	0.791462i	$-0.709320\pi$
$13$	−4.40756	−1.22244	−0.611219	+	0.791462i	$0.709320\pi$
$14$	4.76731	1.27412
$15$	−1.19849	−0.309450
$16$	−4.90368	−1.22592
$17$	−3.56485	−0.864604	−0.432302	−	0.901729i	$-0.642299\pi$
$17$	−3.56485	−0.864604	−0.432302	+	0.901729i	$0.642299\pi$
$18$	2.56435	0.604423
$19$	−3.72929	−0.855559	−0.427779	−	0.903883i	$-0.640704\pi$
$19$	−3.72929	−0.855559	−0.427779	+	0.903883i	$0.640704\pi$
$20$	−0.689644	−0.154209
$21$	−3.48387	−0.760243
$22$	−1.64001	−0.349652
$23$	−6.43105	−1.34097	−0.670484	−	0.741924i	$-0.733913\pi$
$23$	−6.43105	−1.34097	−0.670484	+	0.741924i	$0.733913\pi$
$24$	2.57556	0.525735
$25$	1.00000	0.200000
$26$	7.22846	1.41762
$27$	−5.46946	−1.05260
$28$	−2.00471	−0.378854
$29$	−7.11552	−1.32132	−0.660659	−	0.750686i	$-0.729723\pi$
$29$	−7.11552	−1.32132	−0.660659	+	0.750686i	$0.729723\pi$
$30$	1.96554	0.358858
$31$	−6.72666	−1.20814	−0.604072	−	0.796930i	$-0.706456\pi$
$31$	−6.72666	−1.20814	−0.604072	+	0.796930i	$0.706456\pi$
$32$	3.74410	0.661869
$33$	1.19849	0.208631
$34$	5.84641	1.00265
$35$	2.90687	0.491351
$36$	−1.07834	−0.179723
$37$	8.74751	1.43808	0.719041	−	0.694968i	$-0.244581\pi$
$37$	8.74751	1.43808	0.719041	+	0.694968i	$0.244581\pi$
$38$	6.11609	0.992161
$39$	−5.28243	−0.845866
$40$	−2.14900	−0.339787
$41$	7.21453	1.12672	0.563360	−	0.826212i	$-0.309508\pi$
$41$	7.21453	1.12672	0.563360	+	0.826212i	$0.309508\pi$
$42$	5.71359	0.881626
$43$	12.0139	1.83210	0.916048	−	0.401069i	$-0.131361\pi$
$43$	12.0139	1.83210	0.916048	+	0.401069i	$0.131361\pi$
$44$	0.689644	0.103968
$45$	1.56361	0.233090
$46$	10.5470	1.55507
$47$	−0.194346	−0.0283482	−0.0141741	−	0.999900i	$-0.504512\pi$
$47$	−0.194346	−0.0283482	−0.0141741	+	0.999900i	$0.504512\pi$
$48$	−5.87703	−0.848276
$49$	1.44992	0.207131
$50$	−1.64001	−0.231933
$51$	−4.27245	−0.598263
$52$	−3.03965	−0.421523
$53$	−0.243416	−0.0334358	−0.0167179	−	0.999860i	$-0.505322\pi$
$53$	−0.243416	−0.0334358	−0.0167179	+	0.999860i	$0.505322\pi$
$54$	8.96999	1.22066
$55$	−1.00000	−0.134840
$56$	−6.24688	−0.834774
$57$	−4.46953	−0.592004
$58$	11.6695	1.53229
$59$	−3.10798	−0.404625	−0.202312	−	0.979321i	$-0.564846\pi$
$59$	−3.10798	−0.404625	−0.202312	+	0.979321i	$0.564846\pi$
$60$	−0.826534	−0.106705
$61$	11.3820	1.45732	0.728659	−	0.684877i	$-0.240144\pi$
$61$	11.3820	1.45732	0.728659	+	0.684877i	$0.240144\pi$
$62$	11.0318	1.40104
$63$	4.54523	0.572645
$64$	3.66699	0.458373
$65$	4.40756	0.546691
$66$	−1.96554	−0.241942
$67$	−4.95163	−0.604937	−0.302469	−	0.953159i	$-0.597811\pi$
$67$	−4.95163	−0.604937	−0.302469	+	0.953159i	$0.597811\pi$
$68$	−2.45848	−0.298135
$69$	−7.70757	−0.927883
$70$	−4.76731	−0.569803
$71$	−10.7183	−1.27203	−0.636013	−	0.771678i	$-0.719418\pi$
$71$	−10.7183	−1.27203	−0.636013	+	0.771678i	$0.719418\pi$
$72$	−3.36021	−0.396004
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	−14.3460	−1.66769
$75$	1.19849	0.138390
$76$	−2.57189	−0.295016
$77$	−2.90687	−0.331269
$78$	8.66326	0.980921
$79$	−5.81786	−0.654560	−0.327280	−	0.944927i	$-0.606132\pi$
$79$	−5.81786	−0.654560	−0.327280	+	0.944927i	$0.606132\pi$
$80$	4.90368	0.548248
$81$	−1.86427	−0.207141
$82$	−11.8319	−1.30662
$83$	11.3689	1.24790	0.623951	−	0.781463i	$-0.285526\pi$
$83$	11.3689	1.24790	0.623951	+	0.781463i	$0.285526\pi$
$84$	−2.40263	−0.262148
$85$	3.56485	0.386663
$86$	−19.7029	−2.12462
$87$	−8.52790	−0.914287
$88$	2.14900	0.229084
$89$	−2.86370	−0.303552	−0.151776	−	0.988415i	$-0.548499\pi$
$89$	−2.86370	−0.303552	−0.151776	+	0.988415i	$0.548499\pi$
$90$	−2.56435	−0.270306
$91$	12.8122	1.34309
$92$	−4.43514	−0.462395
$93$	−8.06186	−0.835976
$94$	0.318729	0.0328744
$95$	3.72929	0.382617
$96$	4.48728	0.457981
$97$	2.45325	0.249090	0.124545	−	0.992214i	$-0.460253\pi$
$97$	2.45325	0.249090	0.124545	+	0.992214i	$0.460253\pi$
$98$	−2.37789	−0.240203
$99$	−1.56361	−0.157149
$100$	0.689644	0.0689644
$101$	−1.67397	−0.166567	−0.0832833	−	0.996526i	$-0.526541\pi$
$101$	−1.67397	−0.166567	−0.0832833	+	0.996526i	$0.526541\pi$
$102$	7.00688	0.693784
$103$	−3.50370	−0.345229	−0.172615	−	0.984989i	$-0.555222\pi$
$103$	−3.50370	−0.345229	−0.172615	+	0.984989i	$0.555222\pi$
$104$	−9.47185	−0.928791
$105$	3.48387	0.339991
$106$	0.399206	0.0387743
$107$	3.28104	0.317190	0.158595	−	0.987344i	$-0.449304\pi$
$107$	3.28104	0.317190	0.158595	+	0.987344i	$0.449304\pi$
$108$	−3.77198	−0.362959
$109$	−0.735054	−0.0704054	−0.0352027	−	0.999380i	$-0.511208\pi$
$109$	−0.735054	−0.0704054	−0.0352027	+	0.999380i	$0.511208\pi$
$110$	1.64001	0.156369
$111$	10.4838	0.995082
$112$	14.2544	1.34691
$113$	6.19839	0.583096	0.291548	−	0.956556i	$-0.405830\pi$
$113$	6.19839	0.583096	0.291548	+	0.956556i	$0.405830\pi$
$114$	7.33009	0.686526
$115$	6.43105	0.599699
$116$	−4.90718	−0.455620
$117$	6.89172	0.637140
$118$	5.09713	0.469229
$119$	10.3626	0.949936
$120$	−2.57556	−0.235116
$121$	1.00000	0.0909091
$122$	−18.6667	−1.69000
$123$	8.64656	0.779634
$124$	−4.63900	−0.416595
$125$	−1.00000	−0.0894427
$126$	−7.45424	−0.664076
$127$	−16.8771	−1.49760	−0.748802	−	0.662794i	$-0.769370\pi$
$127$	−16.8771	−1.49760	−0.748802	+	0.662794i	$0.769370\pi$
$128$	−13.5021	−1.19343
$129$	14.3985	1.26772
$130$	−7.22846	−0.633978
$131$	−3.52176	−0.307698	−0.153849	−	0.988094i	$-0.549167\pi$
$131$	−3.52176	−0.307698	−0.153849	+	0.988094i	$0.549167\pi$
$132$	0.826534	0.0719405
$133$	10.8406	0.939998
$134$	8.12073	0.701525
$135$	5.46946	0.470736
$136$	−7.66087	−0.656915
$137$	−11.9746	−1.02306	−0.511528	−	0.859266i	$-0.670921\pi$
$137$	−11.9746	−1.02306	−0.511528	+	0.859266i	$0.670921\pi$
$138$	12.6405	1.07603
$139$	7.19331	0.610128	0.305064	−	0.952332i	$-0.401322\pi$
$139$	7.19331	0.610128	0.305064	+	0.952332i	$0.401322\pi$
$140$	2.00471	0.169429
$141$	−0.232922	−0.0196156
$142$	17.5781	1.47512
$143$	−4.40756	−0.368579
$144$	7.66746	0.638955
$145$	7.11552	0.590912
$146$	1.64001	0.135728
$147$	1.73772	0.143325
$148$	6.03267	0.495883
$149$	−2.35782	−0.193160	−0.0965801	−	0.995325i	$-0.530790\pi$
$149$	−2.35782	−0.193160	−0.0965801	+	0.995325i	$0.530790\pi$
$150$	−1.96554	−0.160486
$151$	−6.04021	−0.491546	−0.245773	−	0.969327i	$-0.579042\pi$
$151$	−6.04021	−0.491546	−0.245773	+	0.969327i	$0.579042\pi$
$152$	−8.01425	−0.650042
$153$	5.57406	0.450636
$154$	4.76731	0.384161
$155$	6.72666	0.540299
$156$	−3.64300	−0.291673
$157$	3.83203	0.305829	0.152914	−	0.988239i	$-0.451134\pi$
$157$	3.83203	0.305829	0.152914	+	0.988239i	$0.451134\pi$
$158$	9.54137	0.759070
$159$	−0.291733	−0.0231359
$160$	−3.74410	−0.295997
$161$	18.6943	1.47331
$162$	3.05742	0.240214
$163$	−0.288978	−0.0226345	−0.0113172	−	0.999936i	$-0.503602\pi$
$163$	−0.288978	−0.0226345	−0.0113172	+	0.999936i	$0.503602\pi$
$164$	4.97546	0.388518
$165$	−1.19849	−0.0933026
$166$	−18.6452	−1.44715
$167$	−13.6346	−1.05508	−0.527538	−	0.849531i	$-0.676885\pi$
$167$	−13.6346	−1.05508	−0.527538	+	0.849531i	$0.676885\pi$
$168$	−7.48684	−0.577622
$169$	6.42659	0.494353
$170$	−5.84641	−0.448399
$171$	5.83118	0.445921
$172$	8.28529	0.631747
$173$	25.6843	1.95274	0.976369	−	0.216109i	$-0.0693367\pi$
$173$	25.6843	1.95274	0.976369	+	0.216109i	$0.0693367\pi$
$174$	13.9859	1.06027
$175$	−2.90687	−0.219739
$176$	−4.90368	−0.369629
$177$	−3.72489	−0.279980
$178$	4.69651	0.352019
$179$	14.1832	1.06010	0.530050	−	0.847967i	$-0.322173\pi$
$179$	14.1832	1.06010	0.530050	+	0.847967i	$0.322173\pi$
$180$	1.07834	0.0803745
$181$	−17.3668	−1.29086	−0.645431	−	0.763819i	$-0.723322\pi$
$181$	−17.3668	−1.29086	−0.645431	+	0.763819i	$0.723322\pi$
$182$	−21.0122	−1.55753
$183$	13.6413	1.00839
$184$	−13.8203	−1.01885
$185$	−8.74751	−0.643130
$186$	13.2216	0.969452
$187$	−3.56485	−0.260688
$188$	−0.134029	−0.00977509
$189$	15.8990	1.15648
$190$	−6.11609	−0.443708
$191$	24.0535	1.74045	0.870226	−	0.492653i	$-0.163973\pi$
$191$	24.0535	1.74045	0.870226	+	0.492653i	$0.163973\pi$
$192$	4.39486	0.317172
$193$	4.47200	0.321902	0.160951	−	0.986962i	$-0.448544\pi$
$193$	4.47200	0.321902	0.160951	+	0.986962i	$0.448544\pi$
$194$	−4.02336	−0.288861
$195$	5.28243	0.378283
$196$	0.999929	0.0714235
$197$	2.43123	0.173218	0.0866090	−	0.996242i	$-0.472397\pi$
$197$	2.43123	0.173218	0.0866090	+	0.996242i	$0.472397\pi$
$198$	2.56435	0.182240
$199$	1.80642	0.128054	0.0640268	−	0.997948i	$-0.479606\pi$
$199$	1.80642	0.128054	0.0640268	+	0.997948i	$0.479606\pi$
$200$	2.14900	0.151957
$201$	−5.93449	−0.418587
$202$	2.74534	0.193161
$203$	20.6839	1.45173
$204$	−2.94647	−0.206294
$205$	−7.21453	−0.503884
$206$	5.74611	0.400350
$207$	10.0557	0.698919
$208$	21.6133	1.49861
$209$	−3.72929	−0.257961
$210$	−5.71359	−0.394275
$211$	22.9798	1.58199	0.790996	−	0.611822i	$-0.209563\pi$
$211$	22.9798	1.58199	0.790996	+	0.611822i	$0.209563\pi$
$212$	−0.167871	−0.0115294
$213$	−12.8458	−0.880179
$214$	−5.38095	−0.367834
$215$	−12.0139	−0.819338
$216$	−11.7539	−0.799750
$217$	19.5536	1.32738
$218$	1.20550	0.0816466
$219$	−1.19849	−0.0809867
$220$	−0.689644	−0.0464958
$221$	15.7123	1.05692
$222$	−17.1936	−1.15396
$223$	−9.14620	−0.612475	−0.306237	−	0.951955i	$-0.599070\pi$
$223$	−9.14620	−0.612475	−0.306237	+	0.951955i	$0.599070\pi$
$224$	−10.8836	−0.727193
$225$	−1.56361	−0.104241
$226$	−10.1655	−0.676196
$227$	3.12992	0.207740	0.103870	−	0.994591i	$-0.466877\pi$
$227$	3.12992	0.207740	0.103870	+	0.994591i	$0.466877\pi$
$228$	−3.08239	−0.204136
$229$	−9.87817	−0.652768	−0.326384	−	0.945237i	$-0.605830\pi$
$229$	−9.87817	−0.652768	−0.326384	+	0.945237i	$0.605830\pi$
$230$	−10.5470	−0.695450
$231$	−3.48387	−0.229222
$232$	−15.2913	−1.00392
$233$	9.14967	0.599415	0.299708	−	0.954031i	$-0.403111\pi$
$233$	9.14967	0.599415	0.299708	+	0.954031i	$0.403111\pi$
$234$	−11.3025	−0.738869
$235$	0.194346	0.0126777
$236$	−2.14340	−0.139524
$237$	−6.97266	−0.452923
$238$	−16.9948	−1.10161
$239$	4.48123	0.289867	0.144933	−	0.989441i	$-0.453703\pi$
$239$	4.48123	0.289867	0.144933	+	0.989441i	$0.453703\pi$
$240$	5.87703	0.379360
$241$	−26.9902	−1.73859	−0.869295	−	0.494294i	$-0.835427\pi$
$241$	−26.9902	−1.73859	−0.869295	+	0.494294i	$0.835427\pi$
$242$	−1.64001	−0.105424
$243$	14.1741	0.909267
$244$	7.84954	0.502515
$245$	−1.44992	−0.0926320
$246$	−14.1805	−0.904114
$247$	16.4371	1.04587
$248$	−14.4556	−0.917932
$249$	13.6256	0.863486
$250$	1.64001	0.103724
$251$	−22.0637	−1.39265	−0.696323	−	0.717729i	$-0.745182\pi$
$251$	−22.0637	−1.39265	−0.696323	+	0.717729i	$0.745182\pi$
$252$	3.13459	0.197461
$253$	−6.43105	−0.404317
$254$	27.6787	1.73672
$255$	4.27245	0.267551
$256$	14.8097	0.925604
$257$	11.5069	0.717782	0.358891	−	0.933380i	$-0.383155\pi$
$257$	11.5069	0.717782	0.358891	+	0.933380i	$0.383155\pi$
$258$	−23.6138	−1.47013
$259$	−25.4279	−1.58001
$260$	3.03965	0.188511
$261$	11.1259	0.688678
$262$	5.77574	0.356826
$263$	0.698396	0.0430649	0.0215325	−	0.999768i	$-0.493145\pi$
$263$	0.698396	0.0430649	0.0215325	+	0.999768i	$0.493145\pi$
$264$	2.57556	0.158515
$265$	0.243416	0.0149529
$266$	−17.7787	−1.09008
$267$	−3.43213	−0.210043
$268$	−3.41486	−0.208596
$269$	3.68994	0.224980	0.112490	−	0.993653i	$-0.464117\pi$
$269$	3.68994	0.224980	0.112490	+	0.993653i	$0.464117\pi$
$270$	−8.96999	−0.545896
$271$	10.9115	0.662826	0.331413	−	0.943486i	$-0.392475\pi$
$271$	10.9115	0.662826	0.331413	+	0.943486i	$0.392475\pi$
$272$	17.4809	1.05994
$273$	15.3554	0.929349
$274$	19.6385	1.18640
$275$	1.00000	0.0603023
$276$	−5.31548	−0.319955
$277$	4.00587	0.240689	0.120345	−	0.992732i	$-0.461600\pi$
$277$	4.00587	0.240689	0.120345	+	0.992732i	$0.461600\pi$
$278$	−11.7971	−0.707544
$279$	10.5179	0.629690
$280$	6.24688	0.373322
$281$	−3.44895	−0.205747	−0.102873	−	0.994694i	$-0.532804\pi$
$281$	−3.44895	−0.205747	−0.102873	+	0.994694i	$0.532804\pi$
$282$	0.381995	0.0227475
$283$	10.1975	0.606180	0.303090	−	0.952962i	$-0.401982\pi$
$283$	10.1975	0.606180	0.303090	+	0.952962i	$0.401982\pi$
$284$	−7.39181	−0.438623
$285$	4.46953	0.264752
$286$	7.22846	0.427428
$287$	−20.9717	−1.23792
$288$	−5.85433	−0.344969
$289$	−4.29182	−0.252460
$290$	−11.6695	−0.685259
$291$	2.94020	0.172358
$292$	−0.689644	−0.0403584
$293$	23.8723	1.39464	0.697318	−	0.716762i	$-0.254377\pi$
$293$	23.8723	1.39464	0.697318	+	0.716762i	$0.254377\pi$
$294$	−2.84988	−0.166209
$295$	3.10798	0.180954
$296$	18.7984	1.09264
$297$	−5.46946	−0.317370
$298$	3.86686	0.224001
$299$	28.3453	1.63925
$300$	0.826534	0.0477200
$301$	−34.9228	−2.01292
$302$	9.90603	0.570028
$303$	−2.00625	−0.115256
$304$	18.2873	1.04885
$305$	−11.3820	−0.651732
$306$	−9.14153	−0.522586
$307$	31.3232	1.78771	0.893854	−	0.448358i	$-0.147991\pi$
$307$	31.3232	1.78771	0.893854	+	0.448358i	$0.147991\pi$
$308$	−2.00471	−0.114229
$309$	−4.19916	−0.238882
$310$	−11.0318	−0.626565
$311$	−20.6345	−1.17008	−0.585038	−	0.811006i	$-0.698920\pi$
$311$	−20.6345	−1.17008	−0.585038	+	0.811006i	$0.698920\pi$
$312$	−11.3519	−0.642678
$313$	−13.8357	−0.782039	−0.391019	−	0.920382i	$-0.627877\pi$
$313$	−13.8357	−0.782039	−0.391019	+	0.920382i	$0.627877\pi$
$314$	−6.28457	−0.354659
$315$	−4.54523	−0.256095
$316$	−4.01225	−0.225707
$317$	20.6698	1.16093	0.580466	−	0.814285i	$-0.302870\pi$
$317$	20.6698	1.16093	0.580466	+	0.814285i	$0.302870\pi$
$318$	0.478446	0.0268299
$319$	−7.11552	−0.398393
$320$	−3.66699	−0.204991
$321$	3.93230	0.219480
$322$	−30.6589	−1.70855
$323$	13.2944	0.739719
$324$	−1.28568	−0.0714268
$325$	−4.40756	−0.244487
$326$	0.473927	0.0262484
$327$	−0.880957	−0.0487170
$328$	15.5040	0.856067
$329$	0.564938	0.0311460
$330$	1.96554	0.108200
$331$	−3.84828	−0.211521	−0.105760	−	0.994392i	$-0.533728\pi$
$331$	−3.84828	−0.211521	−0.105760	+	0.994392i	$0.533728\pi$
$332$	7.84052	0.430304
$333$	−13.6777	−0.749535
$334$	22.3609	1.22353
$335$	4.95163	0.270536
$336$	17.0838	0.931996
$337$	−16.1249	−0.878382	−0.439191	−	0.898394i	$-0.644735\pi$
$337$	−16.1249	−0.878382	−0.439191	+	0.898394i	$0.644735\pi$
$338$	−10.5397	−0.573284
$339$	7.42873	0.403473
$340$	2.45848	0.133330
$341$	−6.72666	−0.364269
$342$	−9.56321	−0.517119
$343$	16.1334	0.871121
$344$	25.8178	1.39200
$345$	7.70757	0.414962
$346$	−42.1225	−2.26452
$347$	−26.5397	−1.42472	−0.712362	−	0.701812i	$-0.752375\pi$
$347$	−26.5397	−1.42472	−0.712362	+	0.701812i	$0.752375\pi$
$348$	−5.88122	−0.315266
$349$	−8.58174	−0.459370	−0.229685	−	0.973265i	$-0.573770\pi$
$349$	−8.58174	−0.459370	−0.229685	+	0.973265i	$0.573770\pi$
$350$	4.76731	0.254824
$351$	24.1070	1.28674
$352$	3.74410	0.199561
$353$	17.9554	0.955669	0.477834	−	0.878450i	$-0.341422\pi$
$353$	17.9554	0.955669	0.477834	+	0.878450i	$0.341422\pi$
$354$	6.10888	0.324683
$355$	10.7183	0.568868
$356$	−1.97494	−0.104671
$357$	12.4195	0.657309
$358$	−23.2606	−1.22936
$359$	−34.9635	−1.84530	−0.922651	−	0.385635i	$-0.873982\pi$
$359$	−34.9635	−1.84530	−0.922651	+	0.385635i	$0.873982\pi$
$360$	3.36021	0.177099
$361$	−5.09237	−0.268020
$362$	28.4817	1.49697
$363$	1.19849	0.0629046
$364$	8.83588	0.463126
$365$	1.00000	0.0523424
$366$	−22.3719	−1.16940
$367$	−14.9756	−0.781718	−0.390859	−	0.920451i	$-0.627822\pi$
$367$	−14.9756	−0.781718	−0.390859	+	0.920451i	$0.627822\pi$
$368$	31.5358	1.64392
$369$	−11.2807	−0.587252
$370$	14.3460	0.745815
$371$	0.707581	0.0367358
$372$	−5.55981	−0.288263
$373$	−32.5534	−1.68555	−0.842777	−	0.538263i	$-0.819081\pi$
$373$	−32.5534	−1.68555	−0.842777	+	0.538263i	$0.819081\pi$
$374$	5.84641	0.302311
$375$	−1.19849	−0.0618899
$376$	−0.417649	−0.0215386
$377$	31.3621	1.61523
$378$	−26.0746	−1.34113
$379$	7.59841	0.390304	0.195152	−	0.980773i	$-0.437480\pi$
$379$	7.59841	0.390304	0.195152	+	0.980773i	$0.437480\pi$
$380$	2.57189	0.131935
$381$	−20.2271	−1.03627
$382$	−39.4481	−2.01834
$383$	18.6413	0.952527	0.476263	−	0.879303i	$-0.341991\pi$
$383$	18.6413	0.952527	0.476263	+	0.879303i	$0.341991\pi$
$384$	−16.1822	−0.825793
$385$	2.90687	0.148148
$386$	−7.33415	−0.373298
$387$	−18.7850	−0.954897
$388$	1.69187	0.0858917
$389$	−10.4363	−0.529139	−0.264569	−	0.964367i	$-0.585230\pi$
$389$	−10.4363	−0.529139	−0.264569	+	0.964367i	$0.585230\pi$
$390$	−8.66326	−0.438681
$391$	22.9258	1.15941
$392$	3.11588	0.157376
$393$	−4.22081	−0.212912
$394$	−3.98725	−0.200875
$395$	5.81786	0.292728
$396$	−1.07834	−0.0541885
$397$	−17.8750	−0.897121	−0.448560	−	0.893752i	$-0.648063\pi$
$397$	−17.8750	−0.897121	−0.448560	+	0.893752i	$0.648063\pi$
$398$	−2.96255	−0.148499
$399$	12.9924	0.650432
$400$	−4.90368	−0.245184
$401$	24.3578	1.21637	0.608186	−	0.793795i	$-0.291898\pi$
$401$	24.3578	1.21637	0.608186	+	0.793795i	$0.291898\pi$
$402$	9.73264	0.485420
$403$	29.6482	1.47688
$404$	−1.15445	−0.0574359
$405$	1.86427	0.0926362
$406$	−33.9219	−1.68352
$407$	8.74751	0.433598
$408$	−9.18151	−0.454552
$409$	−13.6028	−0.672617	−0.336309	−	0.941752i	$-0.609179\pi$
$409$	−13.6028	−0.672617	−0.336309	+	0.941752i	$0.609179\pi$
$410$	11.8319	0.584337
$411$	−14.3514	−0.707905
$412$	−2.41630	−0.119043
$413$	9.03451	0.444559
$414$	−16.4915	−0.810511
$415$	−11.3689	−0.558079
$416$	−16.5023	−0.809094
$417$	8.62113	0.422179
$418$	6.11609	0.299148
$419$	−9.50398	−0.464300	−0.232150	−	0.972680i	$-0.574576\pi$
$419$	−9.50398	−0.464300	−0.232150	+	0.972680i	$0.574576\pi$
$420$	2.40263	0.117236
$421$	−11.5011	−0.560528	−0.280264	−	0.959923i	$-0.590422\pi$
$421$	−11.5011	−0.560528	−0.280264	+	0.959923i	$0.590422\pi$
$422$	−37.6871	−1.83458
$423$	0.303881	0.0147752
$424$	−0.523102	−0.0254041
$425$	−3.56485	−0.172921
$426$	21.0673	1.02071
$427$	−33.0861	−1.60115
$428$	2.26275	0.109374
$429$	−5.28243	−0.255038
$430$	19.7029	0.950158
$431$	−4.86110	−0.234151	−0.117075	−	0.993123i	$-0.537352\pi$
$431$	−4.86110	−0.234151	−0.117075	+	0.993123i	$0.537352\pi$
$432$	26.8205	1.29040
$433$	−24.2345	−1.16464	−0.582318	−	0.812961i	$-0.697854\pi$
$433$	−24.2345	−1.16464	−0.582318	+	0.812961i	$0.697854\pi$
$434$	−32.0681	−1.53932
$435$	8.52790	0.408882
$436$	−0.506926	−0.0242773
$437$	23.9833	1.14728
$438$	1.96554	0.0939174
$439$	40.7636	1.94554	0.972770	−	0.231771i	$-0.0744520\pi$
$439$	40.7636	1.94554	0.972770	+	0.231771i	$0.0744520\pi$
$440$	−2.14900	−0.102450
$441$	−2.26711	−0.107958
$442$	−25.7684	−1.22568
$443$	22.0020	1.04535	0.522673	−	0.852533i	$-0.324935\pi$
$443$	22.0020	1.04535	0.522673	+	0.852533i	$0.324935\pi$
$444$	7.23012	0.343126
$445$	2.86370	0.135753
$446$	14.9999	0.710265
$447$	−2.82583	−0.133657
$448$	−10.6595	−0.503613
$449$	−3.99692	−0.188626	−0.0943131	−	0.995543i	$-0.530065\pi$
$449$	−3.99692	−0.188626	−0.0943131	+	0.995543i	$0.530065\pi$
$450$	2.56435	0.120885
$451$	7.21453	0.339719
$452$	4.27469	0.201064
$453$	−7.23915	−0.340125
$454$	−5.13310	−0.240909
$455$	−12.8122	−0.600646
$456$	−9.60503	−0.449797
$457$	7.32175	0.342497	0.171249	−	0.985228i	$-0.445220\pi$
$457$	7.32175	0.342497	0.171249	+	0.985228i	$0.445220\pi$
$458$	16.2003	0.756991
$459$	19.4978	0.910081
$460$	4.43514	0.206789
$461$	38.2375	1.78090	0.890448	−	0.455085i	$-0.150391\pi$
$461$	38.2375	1.78090	0.890448	+	0.455085i	$0.150391\pi$
$462$	5.71359	0.265820
$463$	22.8863	1.06362	0.531809	−	0.846864i	$-0.321512\pi$
$463$	22.8863	1.06362	0.531809	+	0.846864i	$0.321512\pi$
$464$	34.8922	1.61983
$465$	8.06186	0.373860
$466$	−15.0056	−0.695121
$467$	25.2463	1.16826	0.584130	−	0.811660i	$-0.301436\pi$
$467$	25.2463	1.16826	0.584130	+	0.811660i	$0.301436\pi$
$468$	4.75284	0.219700
$469$	14.3938	0.664642
$470$	−0.318729	−0.0147019
$471$	4.59266	0.211618
$472$	−6.67905	−0.307428
$473$	12.0139	0.552398
$474$	11.4353	0.525239
$475$	−3.72929	−0.171112
$476$	7.14650	0.327559
$477$	0.380609	0.0174269
$478$	−7.34928	−0.336148
$479$	−23.6095	−1.07875	−0.539373	−	0.842067i	$-0.681339\pi$
$479$	−23.6095	−1.07875	−0.539373	+	0.842067i	$0.681339\pi$
$480$	−4.48728	−0.204815
$481$	−38.5552	−1.75797
$482$	44.2642	2.01618
$483$	22.4050	1.01946
$484$	0.689644	0.0313475
$485$	−2.45325	−0.111396
$486$	−23.2457	−1.05444
$487$	−14.3963	−0.652360	−0.326180	−	0.945308i	$-0.605762\pi$
$487$	−14.3963	−0.652360	−0.326180	+	0.945308i	$0.605762\pi$
$488$	24.4600	1.10725
$489$	−0.346338	−0.0156619
$490$	2.37789	0.107422
$491$	−24.7939	−1.11893	−0.559466	−	0.828853i	$-0.688994\pi$
$491$	−24.7939	−1.11893	−0.559466	+	0.828853i	$0.688994\pi$
$492$	5.96305	0.268835
$493$	25.3658	1.14242
$494$	−26.9570	−1.21285
$495$	1.56361	0.0702792
$496$	32.9854	1.48109
$497$	31.1567	1.39757
$498$	−22.3461	−1.00135
$499$	15.5113	0.694383	0.347192	−	0.937794i	$-0.387135\pi$
$499$	15.5113	0.694383	0.347192	+	0.937794i	$0.387135\pi$
$500$	−0.689644	−0.0308418
$501$	−16.3410	−0.730061
$502$	36.1847	1.61500
$503$	38.5010	1.71668	0.858338	−	0.513084i	$-0.171497\pi$
$503$	38.5010	1.71668	0.858338	+	0.513084i	$0.171497\pi$
$504$	9.76770	0.435088
$505$	1.67397	0.0744908
$506$	10.5470	0.468872
$507$	7.70222	0.342068
$508$	−11.6392	−0.516407
$509$	6.31519	0.279916	0.139958	−	0.990157i	$-0.455303\pi$
$509$	6.31519	0.279916	0.139958	+	0.990157i	$0.455303\pi$
$510$	−7.00688	−0.310270
$511$	2.90687	0.128593
$512$	2.71617	0.120039
$513$	20.3972	0.900559
$514$	−18.8715	−0.832386
$515$	3.50370	0.154391
$516$	9.92986	0.437138
$517$	−0.194346	−0.00854731
$518$	41.7021	1.83229
$519$	30.7824	1.35120
$520$	9.47185	0.415368
$521$	11.6507	0.510426	0.255213	−	0.966885i	$-0.417854\pi$
$521$	11.6507	0.510426	0.255213	+	0.966885i	$0.417854\pi$
$522$	−18.2467	−0.798635
$523$	34.5351	1.51011	0.755057	−	0.655660i	$-0.227609\pi$
$523$	34.5351	1.51011	0.755057	+	0.655660i	$0.227609\pi$
$524$	−2.42876	−0.106101
$525$	−3.48387	−0.152049
$526$	−1.14538	−0.0499409
$527$	23.9796	1.04457
$528$	−5.87703	−0.255765
$529$	18.3585	0.798194
$530$	−0.399206	−0.0173404
$531$	4.85968	0.210892
$532$	7.47615	0.324132
$533$	−31.7985	−1.37734
$534$	5.62874	0.243579
$535$	−3.28104	−0.141852
$536$	−10.6411	−0.459623
$537$	16.9984	0.733536
$538$	−6.05156	−0.260901
$539$	1.44992	0.0624525
$540$	3.77198	0.162320
$541$	15.9840	0.687205	0.343603	−	0.939115i	$-0.388353\pi$
$541$	15.9840	0.687205	0.343603	+	0.939115i	$0.388353\pi$
$542$	−17.8950	−0.768656
$543$	−20.8139	−0.893212
$544$	−13.3472	−0.572255
$545$	0.735054	0.0314862
$546$	−25.1830	−1.07773
$547$	−8.31924	−0.355705	−0.177852	−	0.984057i	$-0.556915\pi$
$547$	−8.31924	−0.355705	−0.177852	+	0.984057i	$0.556915\pi$
$548$	−8.25820	−0.352773
$549$	−17.7971	−0.759561
$550$	−1.64001	−0.0699304
$551$	26.5359	1.13047
$552$	−16.5636	−0.704993
$553$	16.9118	0.719162
$554$	−6.56968	−0.279119
$555$	−10.4838	−0.445014
$556$	4.96082	0.210386
$557$	47.1753	1.99888	0.999442	−	0.0334114i	$-0.0106371\pi$
$557$	47.1753	1.99888	0.999442	+	0.0334114i	$0.0106371\pi$
$558$	−17.2495	−0.730230
$559$	−52.9518	−2.23962
$560$	−14.2544	−0.602358
$561$	−4.27245	−0.180383
$562$	5.65632	0.238597
$563$	−6.43274	−0.271108	−0.135554	−	0.990770i	$-0.543281\pi$
$563$	−6.43274	−0.271108	−0.135554	+	0.990770i	$0.543281\pi$
$564$	−0.160633	−0.00676388
$565$	−6.19839	−0.260768
$566$	−16.7241	−0.702965
$567$	5.41919	0.227585
$568$	−23.0336	−0.966469
$569$	−28.8809	−1.21075	−0.605376	−	0.795940i	$-0.706977\pi$
$569$	−28.8809	−1.21075	−0.605376	+	0.795940i	$0.706977\pi$
$570$	−7.33009	−0.307024
$571$	−15.4847	−0.648014	−0.324007	−	0.946055i	$-0.605030\pi$
$571$	−15.4847	−0.648014	−0.324007	+	0.946055i	$0.605030\pi$
$572$	−3.03965	−0.127094
$573$	28.8280	1.20431
$574$	34.3939	1.43557
$575$	−6.43105	−0.268194
$576$	−5.73375	−0.238906
$577$	−25.3450	−1.05513	−0.527563	−	0.849516i	$-0.676894\pi$
$577$	−25.3450	−1.05513	−0.527563	+	0.849516i	$0.676894\pi$
$578$	7.03864	0.292769
$579$	5.35966	0.222740
$580$	4.90718	0.203759
$581$	−33.0481	−1.37106
$582$	−4.82197	−0.199877
$583$	−0.243416	−0.0100813
$584$	−2.14900	−0.0889263
$585$	−6.89172	−0.284938
$586$	−39.1509	−1.61731
$587$	37.3404	1.54120	0.770602	−	0.637316i	$-0.219956\pi$
$587$	37.3404	1.54120	0.770602	+	0.637316i	$0.219956\pi$
$588$	1.19841	0.0494215
$589$	25.0857	1.03364
$590$	−5.09713	−0.209846
$591$	2.91381	0.119858
$592$	−42.8950	−1.76297
$593$	5.24612	0.215432	0.107716	−	0.994182i	$-0.465646\pi$
$593$	5.24612	0.215432	0.107716	+	0.994182i	$0.465646\pi$
$594$	8.96999	0.368043
$595$	−10.3626	−0.424824
$596$	−1.62606	−0.0666059
$597$	2.16498	0.0886067
$598$	−46.4866	−1.90098
$599$	−29.1875	−1.19257	−0.596285	−	0.802773i	$-0.703357\pi$
$599$	−29.1875	−1.19257	−0.596285	+	0.802773i	$0.703357\pi$
$600$	2.57556	0.105147
$601$	19.8127	0.808178	0.404089	−	0.914720i	$-0.367589\pi$
$601$	19.8127	0.808178	0.404089	+	0.914720i	$0.367589\pi$
$602$	57.2738	2.33431
$603$	7.74243	0.315296
$604$	−4.16560	−0.169496
$605$	−1.00000	−0.0406558
$606$	3.29027	0.133658
$607$	26.8983	1.09177	0.545884	−	0.837861i	$-0.316194\pi$
$607$	26.8983	1.09177	0.545884	+	0.837861i	$0.316194\pi$
$608$	−13.9628	−0.566268
$609$	24.7895	1.00452
$610$	18.6667	0.755791
$611$	0.856590	0.0346539
$612$	3.84412	0.155389
$613$	25.5489	1.03191	0.515956	−	0.856615i	$-0.327437\pi$
$613$	25.5489	1.03191	0.515956	+	0.856615i	$0.327437\pi$
$614$	−51.3704	−2.07314
$615$	−8.64656	−0.348663
$616$	−6.24688	−0.251694
$617$	−9.01038	−0.362744	−0.181372	−	0.983415i	$-0.558054\pi$
$617$	−9.01038	−0.362744	−0.181372	+	0.983415i	$0.558054\pi$
$618$	6.88667	0.277023
$619$	−41.2756	−1.65900	−0.829502	−	0.558503i	$-0.811376\pi$
$619$	−41.2756	−1.65900	−0.829502	+	0.558503i	$0.811376\pi$
$620$	4.63900	0.186307
$621$	35.1744	1.41150
$622$	33.8409	1.35690
$623$	8.32443	0.333511
$624$	25.9033	1.03696
$625$	1.00000	0.0400000
$626$	22.6907	0.906903
$627$	−4.46953	−0.178496
$628$	2.64273	0.105457
$629$	−31.1836	−1.24337
$630$	7.45424	0.296984
$631$	−33.1859	−1.32111	−0.660554	−	0.750778i	$-0.729679\pi$
$631$	−33.1859	−1.32111	−0.660554	+	0.750778i	$0.729679\pi$
$632$	−12.5026	−0.497326
$633$	27.5411	1.09466
$634$	−33.8988	−1.34629
$635$	16.8771	0.669748
$636$	−0.201192	−0.00797778
$637$	−6.39061	−0.253205
$638$	11.6695	0.462002
$639$	16.7593	0.662986
$640$	13.5021	0.533718
$641$	40.9385	1.61697	0.808486	−	0.588515i	$-0.200287\pi$
$641$	40.9385	1.61697	0.808486	+	0.588515i	$0.200287\pi$
$642$	−6.44903	−0.254523
$643$	−18.7990	−0.741360	−0.370680	−	0.928761i	$-0.620875\pi$
$643$	−18.7990	−0.741360	−0.370680	+	0.928761i	$0.620875\pi$
$644$	12.8924	0.508032
$645$	−14.3985	−0.566941
$646$	−21.8030	−0.857826
$647$	−9.98580	−0.392582	−0.196291	−	0.980546i	$-0.562890\pi$
$647$	−9.98580	−0.392582	−0.196291	+	0.980546i	$0.562890\pi$
$648$	−4.00631	−0.157383
$649$	−3.10798	−0.121999
$650$	7.22846	0.283523
$651$	23.4348	0.918483
$652$	−0.199292	−0.00780487
$653$	22.1120	0.865311	0.432655	−	0.901559i	$-0.357577\pi$
$653$	22.1120	0.865311	0.432655	+	0.901559i	$0.357577\pi$
$654$	1.44478	0.0564954
$655$	3.52176	0.137607
$656$	−35.3777	−1.38127
$657$	1.56361	0.0610024
$658$	−0.926506	−0.0361190
$659$	42.3014	1.64783	0.823914	−	0.566714i	$-0.191786\pi$
$659$	42.3014	1.64783	0.823914	+	0.566714i	$0.191786\pi$
$660$	−0.826534	−0.0321728
$661$	−34.7120	−1.35014	−0.675071	−	0.737753i	$-0.735887\pi$
$661$	−34.7120	−1.35014	−0.675071	+	0.737753i	$0.735887\pi$
$662$	6.31124	0.245293
$663$	18.8311	0.731339
$664$	24.4318	0.948139
$665$	−10.8406	−0.420380
$666$	22.4317	0.869210
$667$	45.7603	1.77185
$668$	−9.40302	−0.363814
$669$	−10.9617	−0.423802
$670$	−8.12073	−0.313731
$671$	11.3820	0.439398
$672$	−13.0439	−0.503181
$673$	30.4849	1.17510	0.587552	−	0.809186i	$-0.300092\pi$
$673$	30.4849	1.17510	0.587552	+	0.809186i	$0.300092\pi$
$674$	26.4451	1.01863
$675$	−5.46946	−0.210520
$676$	4.43206	0.170464
$677$	11.6262	0.446830	0.223415	−	0.974723i	$-0.428280\pi$
$677$	11.6262	0.446830	0.223415	+	0.974723i	$0.428280\pi$
$678$	−12.1832	−0.467894
$679$	−7.13129	−0.273674
$680$	7.66087	0.293781
$681$	3.75118	0.143746
$682$	11.0318	0.422430
$683$	−36.6692	−1.40311	−0.701554	−	0.712617i	$-0.747510\pi$
$683$	−36.6692	−1.40311	−0.701554	+	0.712617i	$0.747510\pi$
$684$	4.02144	0.153763
$685$	11.9746	0.457525
$686$	−26.4590	−1.01021
$687$	−11.8389	−0.451683
$688$	−58.9121	−2.24600
$689$	1.07287	0.0408732
$690$	−12.6405	−0.481217
$691$	−1.51545	−0.0576506	−0.0288253	−	0.999584i	$-0.509177\pi$
$691$	−1.51545	−0.0576506	−0.0288253	+	0.999584i	$0.509177\pi$
$692$	17.7130	0.673347
$693$	4.54523	0.172659
$694$	43.5254	1.65220
$695$	−7.19331	−0.272858
$696$	−18.3265	−0.694663
$697$	−25.7187	−0.974166
$698$	14.0742	0.532715
$699$	10.9658	0.414766
$700$	−2.00471	−0.0757709
$701$	−16.2021	−0.611946	−0.305973	−	0.952040i	$-0.598982\pi$
$701$	−16.2021	−0.611946	−0.305973	+	0.952040i	$0.598982\pi$
$702$	−39.5358	−1.49218
$703$	−32.6220	−1.23036
$704$	3.66699	0.138205
$705$	0.232922	0.00877234
$706$	−29.4471	−1.10826
$707$	4.86603	0.183006
$708$	−2.56885	−0.0965434
$709$	37.1813	1.39637	0.698186	−	0.715916i	$-0.253991\pi$
$709$	37.1813	1.39637	0.698186	+	0.715916i	$0.253991\pi$
$710$	−17.5781	−0.659696
$711$	9.09689	0.341160
$712$	−6.15410	−0.230635
$713$	43.2595	1.62008
$714$	−20.3681	−0.762258
$715$	4.40756	0.164833
$716$	9.78134	0.365546
$717$	5.37072	0.200573
$718$	57.3406	2.13993
$719$	−22.6408	−0.844359	−0.422180	−	0.906512i	$-0.638735\pi$
$719$	−22.6408	−0.844359	−0.422180	+	0.906512i	$0.638735\pi$
$720$	−7.66746	−0.285749
$721$	10.1848	0.379302
$722$	8.35156	0.310813
$723$	−32.3475	−1.20302
$724$	−11.9769	−0.445118
$725$	−7.11552	−0.264264
$726$	−1.96554	−0.0729482
$727$	−30.6101	−1.13527	−0.567633	−	0.823282i	$-0.692141\pi$
$727$	−30.6101	−1.13527	−0.567633	+	0.823282i	$0.692141\pi$
$728$	27.5335	1.02046
$729$	22.5803	0.836308
$730$	−1.64001	−0.0606996
$731$	−42.8276	−1.58404
$732$	9.40762	0.347716
$733$	3.44006	0.127062	0.0635308	−	0.997980i	$-0.479764\pi$
$733$	3.44006	0.127062	0.0635308	+	0.997980i	$0.479764\pi$
$734$	24.5601	0.906531
$735$	−1.73772	−0.0640967
$736$	−24.0785	−0.887545
$737$	−4.95163	−0.182396
$738$	18.5006	0.681015
$739$	5.74996	0.211516	0.105758	−	0.994392i	$-0.466273\pi$
$739$	5.74996	0.211516	0.105758	+	0.994392i	$0.466273\pi$
$740$	−6.03267	−0.221765
$741$	19.6997	0.723688
$742$	−1.16044	−0.0426012
$743$	−42.7645	−1.56888	−0.784438	−	0.620207i	$-0.787049\pi$
$743$	−42.7645	−1.56888	−0.784438	+	0.620207i	$0.787049\pi$
$744$	−17.3249	−0.635163
$745$	2.35782	0.0863839
$746$	53.3881	1.95468
$747$	−17.7766	−0.650413
$748$	−2.45848	−0.0898910
$749$	−9.53757	−0.348495
$750$	1.96554	0.0717716
$751$	−21.6061	−0.788418	−0.394209	−	0.919021i	$-0.628981\pi$
$751$	−21.6061	−0.788418	−0.394209	+	0.919021i	$0.628981\pi$
$752$	0.953008	0.0347526
$753$	−26.4431	−0.963642
$754$	−51.4342	−1.87312
$755$	6.04021	0.219826
$756$	10.9647	0.398782
$757$	14.7417	0.535796	0.267898	−	0.963447i	$-0.413671\pi$
$757$	14.7417	0.535796	0.267898	+	0.963447i	$0.413671\pi$
$758$	−12.4615	−0.452622
$759$	−7.70757	−0.279767
$760$	8.01425	0.290708
$761$	23.1405	0.838842	0.419421	−	0.907792i	$-0.362233\pi$
$761$	23.1405	0.838842	0.419421	+	0.907792i	$0.362233\pi$
$762$	33.1728	1.20172
$763$	2.13671	0.0773541
$764$	16.5884	0.600146
$765$	−5.57406	−0.201530
$766$	−30.5720	−1.10461
$767$	13.6986	0.494628
$768$	17.7493	0.640472
$769$	21.8663	0.788519	0.394259	−	0.918999i	$-0.371001\pi$
$769$	21.8663	0.788519	0.394259	+	0.918999i	$0.371001\pi$
$770$	−4.76731	−0.171802
$771$	13.7910	0.496669
$772$	3.08409	0.110999
$773$	−46.0277	−1.65550	−0.827750	−	0.561097i	$-0.810380\pi$
$773$	−46.0277	−1.65550	−0.827750	+	0.561097i	$0.810380\pi$
$774$	30.8077	1.10736
$775$	−6.72666	−0.241629
$776$	5.27204	0.189255
$777$	−30.4752	−1.09329
$778$	17.1156	0.613624
$779$	−26.9051	−0.963975
$780$	3.64300	0.130440
$781$	−10.7183	−0.383530
$782$	−37.5986	−1.34452
$783$	38.9181	1.39082
$784$	−7.10994	−0.253926
$785$	−3.83203	−0.136771
$786$	6.92218	0.246906
$787$	−22.0990	−0.787745	−0.393872	−	0.919165i	$-0.628865\pi$
$787$	−22.0990	−0.787745	−0.393872	+	0.919165i	$0.628865\pi$
$788$	1.67668	0.0597294
$789$	0.837023	0.0297988
$790$	−9.54137	−0.339467
$791$	−18.0180	−0.640645
$792$	−3.36021	−0.119400
$793$	−50.1669	−1.78148
$794$	29.3153	1.04036
$795$	0.291733	0.0103467
$796$	1.24579	0.0441557
$797$	38.5117	1.36415	0.682077	−	0.731281i	$-0.261077\pi$
$797$	38.5117	1.36415	0.682077	+	0.731281i	$0.261077\pi$
$798$	−21.3077	−0.754283
$799$	0.692813	0.0245100
$800$	3.74410	0.132374
$801$	4.47773	0.158213
$802$	−39.9472	−1.41058
$803$	−1.00000	−0.0352892
$804$	−4.09269	−0.144338
$805$	−18.6943	−0.658886
$806$	−48.6234	−1.71269
$807$	4.42237	0.155675
$808$	−3.59737	−0.126555
$809$	−22.2678	−0.782894	−0.391447	−	0.920201i	$-0.628025\pi$
$809$	−22.2678	−0.782894	−0.391447	+	0.920201i	$0.628025\pi$
$810$	−3.05742	−0.107427
$811$	14.6070	0.512923	0.256461	−	0.966554i	$-0.417443\pi$
$811$	14.6070	0.512923	0.256461	+	0.966554i	$0.417443\pi$
$812$	14.2645	0.500588
$813$	13.0774	0.458643
$814$	−14.3460	−0.502828
$815$	0.288978	0.0101224
$816$	20.9507	0.733423
$817$	−44.8032	−1.56747
$818$	22.3088	0.780011
$819$	−20.0334	−0.700023
$820$	−4.97546	−0.173751
$821$	−35.4413	−1.23691	−0.618455	−	0.785820i	$-0.712241\pi$
$821$	−35.4413	−1.23691	−0.618455	+	0.785820i	$0.712241\pi$
$822$	23.5366	0.820932
$823$	4.87436	0.169910	0.0849548	−	0.996385i	$-0.472925\pi$
$823$	4.87436	0.169910	0.0849548	+	0.996385i	$0.472925\pi$
$824$	−7.52945	−0.262301
$825$	1.19849	0.0417262
$826$	−14.8167	−0.515540
$827$	17.7499	0.617225	0.308613	−	0.951188i	$-0.400135\pi$
$827$	17.7499	0.617225	0.308613	+	0.951188i	$0.400135\pi$
$828$	6.93485	0.241003
$829$	−52.5374	−1.82470	−0.912349	−	0.409413i	$-0.865733\pi$
$829$	−52.5374	−1.82470	−0.912349	+	0.409413i	$0.865733\pi$
$830$	18.6452	0.647184
$831$	4.80101	0.166545
$832$	−16.1625	−0.560333
$833$	−5.16875	−0.179087
$834$	−14.1388	−0.489586
$835$	13.6346	0.471845
$836$	−2.57189	−0.0889505
$837$	36.7912	1.27169
$838$	15.5866	0.538432
$839$	−8.43690	−0.291274	−0.145637	−	0.989338i	$-0.546523\pi$
$839$	−8.43690	−0.291274	−0.145637	+	0.989338i	$0.546523\pi$
$840$	7.48684	0.258320
$841$	21.6306	0.745883
$842$	18.8619	0.650025
$843$	−4.13354	−0.142367
$844$	15.8479	0.545506
$845$	−6.42659	−0.221081
$846$	−0.498370	−0.0171343
$847$	−2.90687	−0.0998814
$848$	1.19364	0.0409896
$849$	12.2217	0.419446
$850$	5.84641	0.200530
$851$	−56.2557	−1.92842
$852$	−8.85903	−0.303505
$853$	−30.2932	−1.03722	−0.518610	−	0.855011i	$-0.673550\pi$
$853$	−30.2932	−1.03722	−0.518610	+	0.855011i	$0.673550\pi$
$854$	54.2616	1.85679
$855$	−5.83118	−0.199422
$856$	7.05096	0.240997
$857$	−41.2490	−1.40904	−0.704519	−	0.709685i	$-0.748837\pi$
$857$	−41.2490	−1.40904	−0.704519	+	0.709685i	$0.748837\pi$
$858$	8.66326	0.295759
$859$	−49.5480	−1.69056	−0.845278	−	0.534326i	$-0.820565\pi$
$859$	−49.5480	−1.69056	−0.845278	+	0.534326i	$0.820565\pi$
$860$	−8.28529	−0.282526
$861$	−25.1345	−0.856580
$862$	7.97227	0.271537
$863$	−44.5606	−1.51686	−0.758431	−	0.651753i	$-0.774034\pi$
$863$	−44.5606	−1.51686	−0.758431	+	0.651753i	$0.774034\pi$
$864$	−20.4782	−0.696682
$865$	−25.6843	−0.873291
$866$	39.7449	1.35059
$867$	−5.14372	−0.174690
$868$	13.4850	0.457711
$869$	−5.81786	−0.197357
$870$	−13.9859	−0.474166
$871$	21.8246	0.739498
$872$	−1.57963	−0.0534931
$873$	−3.83594	−0.129827
$874$	−39.3329	−1.33046
$875$	2.90687	0.0982703
$876$	−0.826534	−0.0279260
$877$	−5.58231	−0.188501	−0.0942506	−	0.995549i	$-0.530045\pi$
$877$	−5.58231	−0.188501	−0.0942506	+	0.995549i	$0.530045\pi$
$878$	−66.8529	−2.25617
$879$	28.6108	0.965019
$880$	4.90368	0.165303
$881$	−46.7145	−1.57385	−0.786926	−	0.617047i	$-0.788329\pi$
$881$	−46.7145	−1.57385	−0.786926	+	0.617047i	$0.788329\pi$
$882$	3.71810	0.125195
$883$	−28.6264	−0.963356	−0.481678	−	0.876348i	$-0.659972\pi$
$883$	−28.6264	−0.963356	−0.481678	+	0.876348i	$0.659972\pi$
$884$	10.8359	0.364451
$885$	3.72489	0.125211
$886$	−36.0836	−1.21225
$887$	26.9445	0.904707	0.452354	−	0.891839i	$-0.350584\pi$
$887$	26.9445	0.904707	0.452354	+	0.891839i	$0.350584\pi$
$888$	22.5298	0.756050
$889$	49.0597	1.64541
$890$	−4.69651	−0.157428
$891$	−1.86427	−0.0624553
$892$	−6.30762	−0.211195
$893$	0.724771	0.0242535
$894$	4.63440	0.154998
$895$	−14.1832	−0.474091
$896$	39.2489	1.31121
$897$	33.9716	1.13428
$898$	6.55500	0.218743
$899$	47.8637	1.59634
$900$	−1.07834	−0.0359446
$901$	0.867743	0.0289087
$902$	−11.8319	−0.393960
$903$	−41.8547	−1.39284
$904$	13.3204	0.443028
$905$	17.3668	0.577291
$906$	11.8723	0.394431
$907$	11.6282	0.386109	0.193054	−	0.981188i	$-0.438161\pi$
$907$	11.6282	0.386109	0.193054	+	0.981188i	$0.438161\pi$
$908$	2.15853	0.0716333
$909$	2.61745	0.0868153
$910$	21.0122	0.696548
$911$	32.2710	1.06919	0.534593	−	0.845109i	$-0.320465\pi$
$911$	32.2710	1.06919	0.534593	+	0.845109i	$0.320465\pi$
$912$	21.9172	0.725749
$913$	11.3689	0.376257
$914$	−12.0078	−0.397182
$915$	−13.6413	−0.450966
$916$	−6.81242	−0.225089
$917$	10.2373	0.338066
$918$	−31.9767	−1.05539
$919$	−19.8182	−0.653741	−0.326870	−	0.945069i	$-0.605994\pi$
$919$	−19.8182	−0.653741	−0.326870	+	0.945069i	$0.605994\pi$
$920$	13.8203	0.455643
$921$	37.5406	1.23700
$922$	−62.7100	−2.06524
$923$	47.2415	1.55497
$924$	−2.40263	−0.0790407
$925$	8.74751	0.287616
$926$	−37.5339	−1.23344
$927$	5.47843	0.179935
$928$	−26.6412	−0.874540
$929$	28.0891	0.921572	0.460786	−	0.887511i	$-0.347568\pi$
$929$	28.0891	0.921572	0.460786	+	0.887511i	$0.347568\pi$
$930$	−13.2216	−0.433552
$931$	−5.40718	−0.177213
$932$	6.31002	0.206692
$933$	−24.7303	−0.809635
$934$	−41.4043	−1.35479
$935$	3.56485	0.116583
$936$	14.8103	0.484091
$937$	−6.59834	−0.215558	−0.107779	−	0.994175i	$-0.534374\pi$
$937$	−6.59834	−0.215558	−0.107779	+	0.994175i	$0.534374\pi$
$938$	−23.6060	−0.770762
$939$	−16.5820	−0.541132
$940$	0.134029	0.00437155
$941$	19.4201	0.633078	0.316539	−	0.948580i	$-0.397479\pi$
$941$	19.4201	0.633078	0.316539	+	0.948580i	$0.397479\pi$
$942$	−7.53202	−0.245406
$943$	−46.3970	−1.51089
$944$	15.2405	0.496037
$945$	−15.8990	−0.517196
$946$	−19.7029	−0.640596
$947$	9.98560	0.324489	0.162244	−	0.986751i	$-0.448127\pi$
$947$	9.98560	0.324489	0.162244	+	0.986751i	$0.448127\pi$
$948$	−4.80866	−0.156178
$949$	4.40756	0.143075
$950$	6.11609	0.198432
$951$	24.7726	0.803307
$952$	22.2692	0.721749
$953$	−36.7368	−1.19002	−0.595011	−	0.803717i	$-0.702852\pi$
$953$	−36.7368	−1.19002	−0.595011	+	0.803717i	$0.702852\pi$
$954$	−0.624204	−0.0202094
$955$	−24.0535	−0.778354
$956$	3.09045	0.0999524
$957$	−8.52790	−0.275668
$958$	38.7199	1.25098
$959$	34.8086	1.12403
$960$	−4.39486	−0.141843
$961$	14.2480	0.459613
$962$	63.2310	2.03865
$963$	−5.13028	−0.165321
$964$	−18.6136	−0.599504
$965$	−4.47200	−0.143959
$966$	−36.7444	−1.18223
$967$	26.1891	0.842184	0.421092	−	0.907018i	$-0.361647\pi$
$967$	26.1891	0.842184	0.421092	+	0.907018i	$0.361647\pi$
$968$	2.14900	0.0690715
$969$	15.9332	0.511849
$970$	4.02336	0.129182
$971$	−6.68065	−0.214392	−0.107196	−	0.994238i	$-0.534187\pi$
$971$	−6.68065	−0.214392	−0.107196	+	0.994238i	$0.534187\pi$
$972$	9.77507	0.313535
$973$	−20.9100	−0.670345
$974$	23.6102	0.756519
$975$	−5.28243	−0.169173
$976$	−55.8137	−1.78655
$977$	−15.6472	−0.500598	−0.250299	−	0.968169i	$-0.580529\pi$
$977$	−15.6472	−0.500598	−0.250299	+	0.968169i	$0.580529\pi$
$978$	0.567999	0.0181626
$979$	−2.86370	−0.0915244
$980$	−0.999929	−0.0319416
$981$	1.14934	0.0366956
$982$	40.6623	1.29759
$983$	−9.90640	−0.315965	−0.157982	−	0.987442i	$-0.550499\pi$
$983$	−9.90640	−0.315965	−0.157982	+	0.987442i	$0.550499\pi$
$984$	18.5815	0.592356
$985$	−2.43123	−0.0774654
$986$	−41.6002	−1.32482
$987$	0.677074	0.0215515
$988$	11.3357	0.360638
$989$	−77.2618	−2.45678
$990$	−2.56435	−0.0815003
$991$	−26.2878	−0.835060	−0.417530	−	0.908663i	$-0.637104\pi$
$991$	−26.2878	−0.835060	−0.417530	+	0.908663i	$0.637104\pi$
$992$	−25.1853	−0.799634
$993$	−4.61214	−0.146362
$994$	−51.0974	−1.62071
$995$	−1.80642	−0.0572673
$996$	9.39681	0.297749
$997$	17.9982	0.570008	0.285004	−	0.958526i	$-0.408005\pi$
$997$	17.9982	0.570008	0.285004	+	0.958526i	$0.408005\pi$
$998$	−25.4388	−0.805252
$999$	−47.8442	−1.51372

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.e.1.5	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.e.1.5	✓	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)

\(f(q)\)	\(=\)	\(q-1.64001 q^{2} +1.19849 q^{3} +0.689644 q^{4} -1.00000 q^{5} -1.96554 q^{6} -2.90687 q^{7} +2.14900 q^{8} -1.56361 q^{9} +O(q^{10})\)	\(q-1.64001 q^{2} +1.19849 q^{3} +0.689644 q^{4} -1.00000 q^{5} -1.96554 q^{6} -2.90687 q^{7} +2.14900 q^{8} -1.56361 q^{9} +1.64001 q^{10} +1.00000 q^{11} +0.826534 q^{12} -4.40756 q^{13} +4.76731 q^{14} -1.19849 q^{15} -4.90368 q^{16} -3.56485 q^{17} +2.56435 q^{18} -3.72929 q^{19} -0.689644 q^{20} -3.48387 q^{21} -1.64001 q^{22} -6.43105 q^{23} +2.57556 q^{24} +1.00000 q^{25} +7.22846 q^{26} -5.46946 q^{27} -2.00471 q^{28} -7.11552 q^{29} +1.96554 q^{30} -6.72666 q^{31} +3.74410 q^{32} +1.19849 q^{33} +5.84641 q^{34} +2.90687 q^{35} -1.07834 q^{36} +8.74751 q^{37} +6.11609 q^{38} -5.28243 q^{39} -2.14900 q^{40} +7.21453 q^{41} +5.71359 q^{42} +12.0139 q^{43} +0.689644 q^{44} +1.56361 q^{45} +10.5470 q^{46} -0.194346 q^{47} -5.87703 q^{48} +1.44992 q^{49} -1.64001 q^{50} -4.27245 q^{51} -3.03965 q^{52} -0.243416 q^{53} +8.96999 q^{54} -1.00000 q^{55} -6.24688 q^{56} -4.46953 q^{57} +11.6695 q^{58} -3.10798 q^{59} -0.826534 q^{60} +11.3820 q^{61} +11.0318 q^{62} +4.54523 q^{63} +3.66699 q^{64} +4.40756 q^{65} -1.96554 q^{66} -4.95163 q^{67} -2.45848 q^{68} -7.70757 q^{69} -4.76731 q^{70} -10.7183 q^{71} -3.36021 q^{72} -1.00000 q^{73} -14.3460 q^{74} +1.19849 q^{75} -2.57189 q^{76} -2.90687 q^{77} +8.66326 q^{78} -5.81786 q^{79} +4.90368 q^{80} -1.86427 q^{81} -11.8319 q^{82} +11.3689 q^{83} -2.40263 q^{84} +3.56485 q^{85} -19.7029 q^{86} -8.52790 q^{87} +2.14900 q^{88} -2.86370 q^{89} -2.56435 q^{90} +12.8122 q^{91} -4.43514 q^{92} -8.06186 q^{93} +0.318729 q^{94} +3.72929 q^{95} +4.48728 q^{96} +2.45325 q^{97} -2.37789 q^{98} -1.56361 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q + 6 q^{2} + 5 q^{3} + 22 q^{4} - 27 q^{5} + 7 q^{6} + 10 q^{7} + 15 q^{8} + 24 q^{9}+O(q^{10}) \) 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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