LMFDB - Embedded newform 4015.2.a.b.1.17

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:	$1$
Dimension:	$23$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
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)

$f(q)$	$=$	$q+1.18208 q^{2} -1.23608 q^{3} -0.602686 q^{4} +1.00000 q^{5} -1.46115 q^{6} -1.06876 q^{7} -3.07658 q^{8} -1.47210 q^{9} +O(q^{10})$	\(q+1.18208 q^{2} -1.23608 q^{3} -0.602686 q^{4} +1.00000 q^{5} -1.46115 q^{6} -1.06876 q^{7} -3.07658 q^{8} -1.47210 q^{9} +1.18208 q^{10} +1.00000 q^{11} +0.744971 q^{12} +2.90515 q^{13} -1.26336 q^{14} -1.23608 q^{15} -2.43140 q^{16} -3.32274 q^{17} -1.74014 q^{18} +4.84260 q^{19} -0.602686 q^{20} +1.32108 q^{21} +1.18208 q^{22} +2.67478 q^{23} +3.80291 q^{24} +1.00000 q^{25} +3.43413 q^{26} +5.52789 q^{27} +0.644129 q^{28} +3.76077 q^{29} -1.46115 q^{30} +1.91364 q^{31} +3.27906 q^{32} -1.23608 q^{33} -3.92775 q^{34} -1.06876 q^{35} +0.887214 q^{36} +5.64583 q^{37} +5.72435 q^{38} -3.59101 q^{39} -3.07658 q^{40} -6.93643 q^{41} +1.56162 q^{42} -10.3066 q^{43} -0.602686 q^{44} -1.47210 q^{45} +3.16181 q^{46} -4.16361 q^{47} +3.00541 q^{48} -5.85775 q^{49} +1.18208 q^{50} +4.10719 q^{51} -1.75090 q^{52} -3.36535 q^{53} +6.53440 q^{54} +1.00000 q^{55} +3.28814 q^{56} -5.98586 q^{57} +4.44553 q^{58} -11.8935 q^{59} +0.744971 q^{60} -7.39584 q^{61} +2.26207 q^{62} +1.57332 q^{63} +8.73891 q^{64} +2.90515 q^{65} -1.46115 q^{66} -0.772136 q^{67} +2.00257 q^{68} -3.30626 q^{69} -1.26336 q^{70} +5.01506 q^{71} +4.52904 q^{72} -1.00000 q^{73} +6.67382 q^{74} -1.23608 q^{75} -2.91857 q^{76} -1.06876 q^{77} -4.24486 q^{78} -14.3679 q^{79} -2.43140 q^{80} -2.41663 q^{81} -8.19941 q^{82} -16.0563 q^{83} -0.796197 q^{84} -3.32274 q^{85} -12.1832 q^{86} -4.64863 q^{87} -3.07658 q^{88} -14.3329 q^{89} -1.74014 q^{90} -3.10492 q^{91} -1.61206 q^{92} -2.36542 q^{93} -4.92172 q^{94} +4.84260 q^{95} -4.05319 q^{96} +6.92681 q^{97} -6.92432 q^{98} -1.47210 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 23 q - 5 q^{2} - 3 q^{3} + 15 q^{4} + 23 q^{5} - 15 q^{6} - 10 q^{7} - 12 q^{8} + 8 q^{9}+O(q^{10}) $ 23 * q - 5 * q^2 - 3 * q^3 + 15 * q^4 + 23 * q^5 - 15 * q^6 - 10 * q^7 - 12 * q^8 + 8 * q^9	\( 23 q - 5 q^{2} - 3 q^{3} + 15 q^{4} + 23 q^{5} - 15 q^{6} - 10 q^{7} - 12 q^{8} + 8 q^{9} - 5 q^{10} + 23 q^{11} + 4 q^{12} - 19 q^{13} - 5 q^{14} - 3 q^{15} - q^{16} - 26 q^{17} + 5 q^{18} - 34 q^{19} + 15 q^{20} - 26 q^{21} - 5 q^{22} - 4 q^{23} - 23 q^{24} + 23 q^{25} - 13 q^{26} - 3 q^{27} - 28 q^{28} - 36 q^{29} - 15 q^{30} - 24 q^{31} - 19 q^{32} - 3 q^{33} - 4 q^{34} - 10 q^{35} - 14 q^{36} + 4 q^{37} - 15 q^{38} - 34 q^{39} - 12 q^{40} - 74 q^{41} + 7 q^{42} - 15 q^{43} + 15 q^{44} + 8 q^{45} + 3 q^{46} + q^{47} + 29 q^{48} + q^{49} - 5 q^{50} - 47 q^{51} - 23 q^{52} - 6 q^{53} - 11 q^{54} + 23 q^{55} - 20 q^{56} - 19 q^{57} + 22 q^{58} - 17 q^{59} + 4 q^{60} - 59 q^{61} + 38 q^{62} - 21 q^{63} - 18 q^{64} - 19 q^{65} - 15 q^{66} + 12 q^{67} + 5 q^{68} - 8 q^{69} - 5 q^{70} - 34 q^{71} + 21 q^{72} - 23 q^{73} - 9 q^{74} - 3 q^{75} - 53 q^{76} - 10 q^{77} + 23 q^{78} - 62 q^{79} - q^{80} + 7 q^{81} + 24 q^{82} - 8 q^{83} + 46 q^{84} - 26 q^{85} - 11 q^{86} + q^{87} - 12 q^{88} - 77 q^{89} + 5 q^{90} - 6 q^{91} + 47 q^{92} - 32 q^{94} - 34 q^{95} - 53 q^{96} - 21 q^{97} - 3 q^{98} + 8 q^{99}+O(q^{100}) \) 23 * q - 5 * q^2 - 3 * q^3 + 15 * q^4 + 23 * q^5 - 15 * q^6 - 10 * q^7 - 12 * q^8 + 8 * q^9 - 5 * q^10 + 23 * q^11 + 4 * q^12 - 19 * q^13 - 5 * q^14 - 3 * q^15 - q^16 - 26 * q^17 + 5 * q^18 - 34 * q^19 + 15 * q^20 - 26 * q^21 - 5 * q^22 - 4 * q^23 - 23 * q^24 + 23 * q^25 - 13 * q^26 - 3 * q^27 - 28 * q^28 - 36 * q^29 - 15 * q^30 - 24 * q^31 - 19 * q^32 - 3 * q^33 - 4 * q^34 - 10 * q^35 - 14 * q^36 + 4 * q^37 - 15 * q^38 - 34 * q^39 - 12 * q^40 - 74 * q^41 + 7 * q^42 - 15 * q^43 + 15 * q^44 + 8 * q^45 + 3 * q^46 + q^47 + 29 * q^48 + q^49 - 5 * q^50 - 47 * q^51 - 23 * q^52 - 6 * q^53 - 11 * q^54 + 23 * q^55 - 20 * q^56 - 19 * q^57 + 22 * q^58 - 17 * q^59 + 4 * q^60 - 59 * q^61 + 38 * q^62 - 21 * q^63 - 18 * q^64 - 19 * q^65 - 15 * q^66 + 12 * q^67 + 5 * q^68 - 8 * q^69 - 5 * q^70 - 34 * q^71 + 21 * q^72 - 23 * q^73 - 9 * q^74 - 3 * q^75 - 53 * q^76 - 10 * q^77 + 23 * q^78 - 62 * q^79 - q^80 + 7 * q^81 + 24 * q^82 - 8 * q^83 + 46 * q^84 - 26 * q^85 - 11 * q^86 + q^87 - 12 * q^88 - 77 * q^89 + 5 * q^90 - 6 * q^91 + 47 * q^92 - 32 * q^94 - 34 * q^95 - 53 * q^96 - 21 * q^97 - 3 * q^98 + 8 * 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 $

$2$	1.18208	0.835857	0.417928	−	0.908480i	$-0.362756\pi$
$2$	1.18208	0.835857	0.417928	+	0.908480i	$0.362756\pi$
$3$	−1.23608	−0.713653	−0.356826	−	0.934171i	$-0.616141\pi$
$3$	−1.23608	−0.713653	−0.356826	+	0.934171i	$0.616141\pi$
$4$	−0.602686	−0.301343
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.46115	−0.596512
$7$	−1.06876	−0.403955	−0.201977	−	0.979390i	$-0.564737\pi$
$7$	−1.06876	−0.403955	−0.201977	+	0.979390i	$0.564737\pi$
$8$	−3.07658	−1.08774
$9$	−1.47210	−0.490700
$10$	1.18208	0.373807
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.744971	0.215054
$13$	2.90515	0.805745	0.402872	−	0.915256i	$-0.368012\pi$
$13$	2.90515	0.805745	0.402872	+	0.915256i	$0.368012\pi$
$14$	−1.26336	−0.337648
$15$	−1.23608	−0.319155
$16$	−2.43140	−0.607849
$17$	−3.32274	−0.805884	−0.402942	−	0.915226i	$-0.632012\pi$
$17$	−3.32274	−0.805884	−0.402942	+	0.915226i	$0.632012\pi$
$18$	−1.74014	−0.410155
$19$	4.84260	1.11097	0.555485	−	0.831527i	$-0.312533\pi$
$19$	4.84260	1.11097	0.555485	+	0.831527i	$0.312533\pi$
$20$	−0.602686	−0.134765
$21$	1.32108	0.288283
$22$	1.18208	0.252020
$23$	2.67478	0.557731	0.278866	−	0.960330i	$-0.410042\pi$
$23$	2.67478	0.557731	0.278866	+	0.960330i	$0.410042\pi$
$24$	3.80291	0.776266
$25$	1.00000	0.200000
$26$	3.43413	0.673487
$27$	5.52789	1.06384
$28$	0.644129	0.121729
$29$	3.76077	0.698358	0.349179	−	0.937056i	$-0.386461\pi$
$29$	3.76077	0.698358	0.349179	+	0.937056i	$0.386461\pi$
$30$	−1.46115	−0.266768
$31$	1.91364	0.343700	0.171850	−	0.985123i	$-0.445026\pi$
$31$	1.91364	0.343700	0.171850	+	0.985123i	$0.445026\pi$
$32$	3.27906	0.579662
$33$	−1.23608	−0.215174
$34$	−3.92775	−0.673603
$35$	−1.06876	−0.180654
$36$	0.887214	0.147869
$37$	5.64583	0.928169	0.464084	−	0.885791i	$-0.346383\pi$
$37$	5.64583	0.928169	0.464084	+	0.885791i	$0.346383\pi$
$38$	5.72435	0.928612
$39$	−3.59101	−0.575022
$40$	−3.07658	−0.486451
$41$	−6.93643	−1.08329	−0.541644	−	0.840608i	$-0.682198\pi$
$41$	−6.93643	−1.08329	−0.541644	+	0.840608i	$0.682198\pi$
$42$	1.56162	0.240964
$43$	−10.3066	−1.57174	−0.785868	−	0.618395i	$-0.787783\pi$
$43$	−10.3066	−1.57174	−0.785868	+	0.618395i	$0.787783\pi$
$44$	−0.602686	−0.0908584
$45$	−1.47210	−0.219448
$46$	3.16181	0.466183
$47$	−4.16361	−0.607325	−0.303662	−	0.952780i	$-0.598210\pi$
$47$	−4.16361	−0.607325	−0.303662	+	0.952780i	$0.598210\pi$
$48$	3.00541	0.433793
$49$	−5.85775	−0.836821
$50$	1.18208	0.167171
$51$	4.10719	0.575121
$52$	−1.75090	−0.242806
$53$	−3.36535	−0.462266	−0.231133	−	0.972922i	$-0.574243\pi$
$53$	−3.36535	−0.462266	−0.231133	+	0.972922i	$0.574243\pi$
$54$	6.53440	0.889220
$55$	1.00000	0.134840
$56$	3.28814	0.439396
$57$	−5.98586	−0.792847
$58$	4.44553	0.583727
$59$	−11.8935	−1.54840	−0.774198	−	0.632943i	$-0.781847\pi$
$59$	−11.8935	−1.54840	−0.774198	+	0.632943i	$0.781847\pi$
$60$	0.744971	0.0961753
$61$	−7.39584	−0.946940	−0.473470	−	0.880810i	$-0.656999\pi$
$61$	−7.39584	−0.946940	−0.473470	+	0.880810i	$0.656999\pi$
$62$	2.26207	0.287284
$63$	1.57332	0.198220
$64$	8.73891	1.09236
$65$	2.90515	0.360340
$66$	−1.46115	−0.179855
$67$	−0.772136	−0.0943315	−0.0471657	−	0.998887i	$-0.515019\pi$
$67$	−0.772136	−0.0943315	−0.0471657	+	0.998887i	$0.515019\pi$
$68$	2.00257	0.242848
$69$	−3.30626	−0.398026
$70$	−1.26336	−0.151001
$71$	5.01506	0.595178	0.297589	−	0.954694i	$-0.403817\pi$
$71$	5.01506	0.595178	0.297589	+	0.954694i	$0.403817\pi$
$72$	4.52904	0.533752
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	6.67382	0.775816
$75$	−1.23608	−0.142731
$76$	−2.91857	−0.334783
$77$	−1.06876	−0.121797
$78$	−4.24486	−0.480636
$79$	−14.3679	−1.61652	−0.808258	−	0.588829i	$-0.799589\pi$
$79$	−14.3679	−1.61652	−0.808258	+	0.588829i	$0.799589\pi$
$80$	−2.43140	−0.271838
$81$	−2.41663	−0.268514
$82$	−8.19941	−0.905474
$83$	−16.0563	−1.76240	−0.881202	−	0.472740i	$-0.843265\pi$
$83$	−16.0563	−1.76240	−0.881202	+	0.472740i	$0.843265\pi$
$84$	−0.796197	−0.0868722
$85$	−3.32274	−0.360402
$86$	−12.1832	−1.31375
$87$	−4.64863	−0.498385
$88$	−3.07658	−0.327965
$89$	−14.3329	−1.51928	−0.759642	−	0.650342i	$-0.774626\pi$
$89$	−14.3329	−1.51928	−0.759642	+	0.650342i	$0.774626\pi$
$90$	−1.74014	−0.183427
$91$	−3.10492	−0.325484
$92$	−1.61206	−0.168068
$93$	−2.36542	−0.245282
$94$	−4.92172	−0.507637
$95$	4.84260	0.496841
$96$	−4.05319	−0.413677
$97$	6.92681	0.703311	0.351656	−	0.936129i	$-0.385619\pi$
$97$	6.92681	0.703311	0.351656	+	0.936129i	$0.385619\pi$
$98$	−6.92432	−0.699462
$99$	−1.47210	−0.147951
$100$	−0.602686	−0.0602686
$101$	4.59132	0.456854	0.228427	−	0.973561i	$-0.426642\pi$
$101$	4.59132	0.456854	0.228427	+	0.973561i	$0.426642\pi$
$102$	4.85502	0.480719
$103$	10.2005	1.00508	0.502541	−	0.864553i	$-0.332399\pi$
$103$	10.2005	1.00508	0.502541	+	0.864553i	$0.332399\pi$
$104$	−8.93795	−0.876438
$105$	1.32108	0.128924
$106$	−3.97811	−0.386388
$107$	−1.59542	−0.154235	−0.0771173	−	0.997022i	$-0.524572\pi$
$107$	−1.59542	−0.154235	−0.0771173	+	0.997022i	$0.524572\pi$
$108$	−3.33158	−0.320582
$109$	7.00933	0.671372	0.335686	−	0.941974i	$-0.391032\pi$
$109$	7.00933	0.671372	0.335686	+	0.941974i	$0.391032\pi$
$110$	1.18208	0.112707
$111$	−6.97872	−0.662390
$112$	2.59859	0.245543
$113$	−0.563829	−0.0530406	−0.0265203	−	0.999648i	$-0.508443\pi$
$113$	−0.563829	−0.0530406	−0.0265203	+	0.999648i	$0.508443\pi$
$114$	−7.07577	−0.662706
$115$	2.67478	0.249425
$116$	−2.26657	−0.210445
$117$	−4.27667	−0.395379
$118$	−14.0590	−1.29424
$119$	3.55123	0.325540
$120$	3.80291	0.347157
$121$	1.00000	0.0909091
$122$	−8.74247	−0.791506
$123$	8.57400	0.773091
$124$	−1.15332	−0.103572
$125$	1.00000	0.0894427
$126$	1.85980	0.165684
$127$	−11.8499	−1.05151	−0.525755	−	0.850636i	$-0.676217\pi$
$127$	−11.8499	−1.05151	−0.525755	+	0.850636i	$0.676217\pi$
$128$	3.77196	0.333398
$129$	12.7398	1.12167
$130$	3.43413	0.301193
$131$	−4.84206	−0.423052	−0.211526	−	0.977372i	$-0.567843\pi$
$131$	−4.84206	−0.423052	−0.211526	+	0.977372i	$0.567843\pi$
$132$	0.744971	0.0648414
$133$	−5.17560	−0.448781
$134$	−0.912727	−0.0788476
$135$	5.52789	0.475765
$136$	10.2227	0.876589
$137$	9.77487	0.835124	0.417562	−	0.908649i	$-0.362885\pi$
$137$	9.77487	0.835124	0.417562	+	0.908649i	$0.362885\pi$
$138$	−3.90826	−0.332693
$139$	18.4692	1.56653	0.783267	−	0.621685i	$-0.213552\pi$
$139$	18.4692	1.56653	0.783267	+	0.621685i	$0.213552\pi$
$140$	0.644129	0.0544388
$141$	5.14657	0.433419
$142$	5.92820	0.497484
$143$	2.90515	0.242941
$144$	3.57925	0.298271
$145$	3.76077	0.312315
$146$	−1.18208	−0.0978297
$147$	7.24066	0.597200
$148$	−3.40267	−0.279697
$149$	−15.4824	−1.26837	−0.634183	−	0.773183i	$-0.718663\pi$
$149$	−15.4824	−1.26837	−0.634183	+	0.773183i	$0.718663\pi$
$150$	−1.46115	−0.119302
$151$	−9.73669	−0.792361	−0.396180	−	0.918173i	$-0.629664\pi$
$151$	−9.73669	−0.792361	−0.396180	+	0.918173i	$0.629664\pi$
$152$	−14.8987	−1.20844
$153$	4.89141	0.395447
$154$	−1.26336	−0.101805
$155$	1.91364	0.153707
$156$	2.16425	0.173279
$157$	2.24716	0.179343	0.0896716	−	0.995971i	$-0.471418\pi$
$157$	2.24716	0.179343	0.0896716	+	0.995971i	$0.471418\pi$
$158$	−16.9840	−1.35118
$159$	4.15985	0.329898
$160$	3.27906	0.259233
$161$	−2.85871	−0.225298
$162$	−2.85665	−0.224440
$163$	8.11255	0.635424	0.317712	−	0.948187i	$-0.397086\pi$
$163$	8.11255	0.635424	0.317712	+	0.948187i	$0.397086\pi$
$164$	4.18049	0.326441
$165$	−1.23608	−0.0962289
$166$	−18.9798	−1.47312
$167$	21.2907	1.64752	0.823762	−	0.566935i	$-0.191871\pi$
$167$	21.2907	1.64752	0.823762	+	0.566935i	$0.191871\pi$
$168$	−4.06441	−0.313576
$169$	−4.56008	−0.350775
$170$	−3.92775	−0.301245
$171$	−7.12879	−0.545152
$172$	6.21162	0.473632
$173$	−16.0156	−1.21764	−0.608820	−	0.793308i	$-0.708357\pi$
$173$	−16.0156	−1.21764	−0.608820	+	0.793308i	$0.708357\pi$
$174$	−5.49505	−0.416579
$175$	−1.06876	−0.0807909
$176$	−2.43140	−0.183273
$177$	14.7013	1.10502
$178$	−16.9426	−1.26990
$179$	−15.1966	−1.13585	−0.567923	−	0.823082i	$-0.692253\pi$
$179$	−15.1966	−1.13585	−0.567923	+	0.823082i	$0.692253\pi$
$180$	0.887214	0.0661290
$181$	2.48691	0.184851	0.0924254	−	0.995720i	$-0.470538\pi$
$181$	2.48691	0.184851	0.0924254	+	0.995720i	$0.470538\pi$
$182$	−3.67027	−0.272058
$183$	9.14187	0.675786
$184$	−8.22920	−0.606665
$185$	5.64583	0.415090
$186$	−2.79611	−0.205021
$187$	−3.32274	−0.242983
$188$	2.50935	0.183013
$189$	−5.90800	−0.429744
$190$	5.72435	0.415288
$191$	−22.5937	−1.63482	−0.817412	−	0.576053i	$-0.804592\pi$
$191$	−22.5937	−1.63482	−0.817412	+	0.576053i	$0.804592\pi$
$192$	−10.8020	−0.779568
$193$	−4.94096	−0.355658	−0.177829	−	0.984061i	$-0.556907\pi$
$193$	−4.94096	−0.355658	−0.177829	+	0.984061i	$0.556907\pi$
$194$	8.18805	0.587868
$195$	−3.59101	−0.257158
$196$	3.53038	0.252170
$197$	−26.5804	−1.89377	−0.946887	−	0.321565i	$-0.895791\pi$
$197$	−26.5804	−1.89377	−0.946887	+	0.321565i	$0.895791\pi$
$198$	−1.74014	−0.123666
$199$	−5.46205	−0.387195	−0.193597	−	0.981081i	$-0.562016\pi$
$199$	−5.46205	−0.387195	−0.193597	+	0.981081i	$0.562016\pi$
$200$	−3.07658	−0.217547
$201$	0.954425	0.0673199
$202$	5.42731	0.381864
$203$	−4.01938	−0.282105
$204$	−2.47535	−0.173309
$205$	−6.93643	−0.484461
$206$	12.0578	0.840105
$207$	−3.93755	−0.273678
$208$	−7.06358	−0.489771
$209$	4.84260	0.334970
$210$	1.56162	0.107762
$211$	15.1631	1.04387	0.521935	−	0.852985i	$-0.325210\pi$
$211$	15.1631	1.04387	0.521935	+	0.852985i	$0.325210\pi$
$212$	2.02825	0.139301
$213$	−6.19903	−0.424751
$214$	−1.88591	−0.128918
$215$	−10.3066	−0.702901
$216$	−17.0070	−1.15718
$217$	−2.04523	−0.138839
$218$	8.28559	0.561171
$219$	1.23608	0.0835268
$220$	−0.602686	−0.0406331
$221$	−9.65308	−0.649337
$222$	−8.24940	−0.553664
$223$	−23.8012	−1.59385	−0.796924	−	0.604079i	$-0.793541\pi$
$223$	−23.8012	−1.59385	−0.796924	+	0.604079i	$0.793541\pi$
$224$	−3.50454	−0.234157
$225$	−1.47210	−0.0981399
$226$	−0.666492	−0.0443344
$227$	16.0214	1.06338	0.531689	−	0.846940i	$-0.321558\pi$
$227$	16.0214	1.06338	0.531689	+	0.846940i	$0.321558\pi$
$228$	3.60760	0.238919
$229$	1.35981	0.0898587	0.0449293	−	0.998990i	$-0.485694\pi$
$229$	1.35981	0.0898587	0.0449293	+	0.998990i	$0.485694\pi$
$230$	3.16181	0.208484
$231$	1.32108	0.0869207
$232$	−11.5703	−0.759630
$233$	−0.972144	−0.0636872	−0.0318436	−	0.999493i	$-0.510138\pi$
$233$	−0.972144	−0.0636872	−0.0318436	+	0.999493i	$0.510138\pi$
$234$	−5.05537	−0.330480
$235$	−4.16361	−0.271604
$236$	7.16802	0.466599
$237$	17.7599	1.15363
$238$	4.19783	0.272105
$239$	15.6832	1.01446	0.507232	−	0.861810i	$-0.330669\pi$
$239$	15.6832	1.01446	0.507232	+	0.861810i	$0.330669\pi$
$240$	3.00541	0.193998
$241$	11.3646	0.732061	0.366030	−	0.930603i	$-0.380717\pi$
$241$	11.3646	0.732061	0.366030	+	0.930603i	$0.380717\pi$
$242$	1.18208	0.0759870
$243$	−13.5965	−0.872216
$244$	4.45737	0.285354
$245$	−5.85775	−0.374238
$246$	10.1352	0.646194
$247$	14.0685	0.895158
$248$	−5.88747	−0.373855
$249$	19.8469	1.25774
$250$	1.18208	0.0747613
$251$	−6.71866	−0.424078	−0.212039	−	0.977261i	$-0.568010\pi$
$251$	−6.71866	−0.424078	−0.212039	+	0.977261i	$0.568010\pi$
$252$	−0.948222	−0.0597323
$253$	2.67478	0.168162
$254$	−14.0075	−0.878912
$255$	4.10719	0.257202
$256$	−13.0191	−0.813691
$257$	11.6664	0.727727	0.363864	−	0.931452i	$-0.381457\pi$
$257$	11.6664	0.727727	0.363864	+	0.931452i	$0.381457\pi$
$258$	15.0594	0.937559
$259$	−6.03406	−0.374938
$260$	−1.75090	−0.108586
$261$	−5.53623	−0.342684
$262$	−5.72370	−0.353611
$263$	−11.5203	−0.710375	−0.355187	−	0.934795i	$-0.615583\pi$
$263$	−11.5203	−0.710375	−0.355187	+	0.934795i	$0.615583\pi$
$264$	3.80291	0.234053
$265$	−3.36535	−0.206732
$266$	−6.11797	−0.375117
$267$	17.7166	1.08424
$268$	0.465356	0.0284261
$269$	−12.9318	−0.788468	−0.394234	−	0.919010i	$-0.628990\pi$
$269$	−12.9318	−0.788468	−0.394234	+	0.919010i	$0.628990\pi$
$270$	6.53440	0.397671
$271$	−22.5709	−1.37109	−0.685543	−	0.728032i	$-0.740435\pi$
$271$	−22.5709	−1.37109	−0.685543	+	0.728032i	$0.740435\pi$
$272$	8.07891	0.489856
$273$	3.83794	0.232283
$274$	11.5547	0.698044
$275$	1.00000	0.0603023
$276$	1.99264	0.119943
$277$	−10.2849	−0.617960	−0.308980	−	0.951069i	$-0.599988\pi$
$277$	−10.2849	−0.617960	−0.308980	+	0.951069i	$0.599988\pi$
$278$	21.8320	1.30940
$279$	−2.81706	−0.168653
$280$	3.28814	0.196504
$281$	10.6697	0.636504	0.318252	−	0.948006i	$-0.396904\pi$
$281$	10.6697	0.636504	0.318252	+	0.948006i	$0.396904\pi$
$282$	6.08366	0.362276
$283$	−14.8222	−0.881089	−0.440544	−	0.897731i	$-0.645215\pi$
$283$	−14.8222	−0.881089	−0.440544	+	0.897731i	$0.645215\pi$
$284$	−3.02251	−0.179353
$285$	−5.98586	−0.354572
$286$	3.43413	0.203064
$287$	7.41340	0.437599
$288$	−4.82710	−0.284440
$289$	−5.95938	−0.350552
$290$	4.44553	0.261051
$291$	−8.56212	−0.501920
$292$	0.602686	0.0352696
$293$	−18.8443	−1.10089	−0.550447	−	0.834870i	$-0.685543\pi$
$293$	−18.8443	−1.10089	−0.550447	+	0.834870i	$0.685543\pi$
$294$	8.55904	0.499173
$295$	−11.8935	−0.692464
$296$	−17.3699	−1.00960
$297$	5.52789	0.320760
$298$	−18.3014	−1.06017
$299$	7.77066	0.449389
$300$	0.744971	0.0430109
$301$	11.0153	0.634910
$302$	−11.5095	−0.662300
$303$	−5.67526	−0.326035
$304$	−11.7743	−0.675302
$305$	−7.39584	−0.423484
$306$	5.78203	0.330537
$307$	28.0541	1.60113	0.800565	−	0.599246i	$-0.204533\pi$
$307$	28.0541	1.60113	0.800565	+	0.599246i	$0.204533\pi$
$308$	0.644129	0.0367027
$309$	−12.6086	−0.717280
$310$	2.26207	0.128477
$311$	17.1220	0.970898	0.485449	−	0.874265i	$-0.338656\pi$
$311$	17.1220	0.970898	0.485449	+	0.874265i	$0.338656\pi$
$312$	11.0480	0.625473
$313$	−9.83915	−0.556142	−0.278071	−	0.960561i	$-0.589695\pi$
$313$	−9.83915	−0.556142	−0.278071	+	0.960561i	$0.589695\pi$
$314$	2.65633	0.149905
$315$	1.57332	0.0886468
$316$	8.65934	0.487126
$317$	−4.90054	−0.275242	−0.137621	−	0.990485i	$-0.543946\pi$
$317$	−4.90054	−0.275242	−0.137621	+	0.990485i	$0.543946\pi$
$318$	4.91728	0.275747
$319$	3.76077	0.210563
$320$	8.73891	0.488520
$321$	1.97207	0.110070
$322$	−3.37923	−0.188317
$323$	−16.0907	−0.895312
$324$	1.45647	0.0809150
$325$	2.90515	0.161149
$326$	9.58968	0.531123
$327$	−8.66411	−0.479127
$328$	21.3405	1.17833
$329$	4.44991	0.245332
$330$	−1.46115	−0.0804336
$331$	24.4455	1.34365	0.671824	−	0.740711i	$-0.265511\pi$
$331$	24.4455	1.34365	0.671824	+	0.740711i	$0.265511\pi$
$332$	9.67690	0.531089
$333$	−8.31122	−0.455452
$334$	25.1673	1.37710
$335$	−0.772136	−0.0421863
$336$	−3.21207	−0.175233
$337$	17.2651	0.940493	0.470246	−	0.882535i	$-0.344165\pi$
$337$	17.2651	0.940493	0.470246	+	0.882535i	$0.344165\pi$
$338$	−5.39038	−0.293198
$339$	0.696940	0.0378526
$340$	2.00257	0.108605
$341$	1.91364	0.103629
$342$	−8.42680	−0.455669
$343$	13.7419	0.741992
$344$	31.7090	1.70963
$345$	−3.30626	−0.178003
$346$	−18.9317	−1.01777
$347$	18.1318	0.973364	0.486682	−	0.873579i	$-0.338207\pi$
$347$	18.1318	0.973364	0.486682	+	0.873579i	$0.338207\pi$
$348$	2.80166	0.150185
$349$	−6.01759	−0.322114	−0.161057	−	0.986945i	$-0.551490\pi$
$349$	−6.01759	−0.322114	−0.161057	+	0.986945i	$0.551490\pi$
$350$	−1.26336	−0.0675296
$351$	16.0594	0.857185
$352$	3.27906	0.174775
$353$	−12.8494	−0.683903	−0.341952	−	0.939718i	$-0.611088\pi$
$353$	−12.8494	−0.683903	−0.341952	+	0.939718i	$0.611088\pi$
$354$	17.3781	0.923636
$355$	5.01506	0.266172
$356$	8.63824	0.457826
$357$	−4.38961	−0.232323
$358$	−17.9636	−0.949404
$359$	6.78899	0.358309	0.179154	−	0.983821i	$-0.442664\pi$
$359$	6.78899	0.358309	0.179154	+	0.983821i	$0.442664\pi$
$360$	4.52904	0.238701
$361$	4.45082	0.234254
$362$	2.93973	0.154509
$363$	−1.23608	−0.0648775
$364$	1.87129	0.0980825
$365$	−1.00000	−0.0523424
$366$	10.8064	0.564861
$367$	33.8572	1.76733	0.883665	−	0.468120i	$-0.155068\pi$
$367$	33.8572	1.76733	0.883665	+	0.468120i	$0.155068\pi$
$368$	−6.50346	−0.339016
$369$	10.2111	0.531569
$370$	6.67382	0.346956
$371$	3.59676	0.186734
$372$	1.42560	0.0739141
$373$	−10.8937	−0.564054	−0.282027	−	0.959407i	$-0.591007\pi$
$373$	−10.8937	−0.564054	−0.282027	+	0.959407i	$0.591007\pi$
$374$	−3.92775	−0.203099
$375$	−1.23608	−0.0638311
$376$	12.8097	0.660610
$377$	10.9256	0.562698
$378$	−6.98373	−0.359204
$379$	−2.89524	−0.148719	−0.0743593	−	0.997232i	$-0.523691\pi$
$379$	−2.89524	−0.148719	−0.0743593	+	0.997232i	$0.523691\pi$
$380$	−2.91857	−0.149720
$381$	14.6475	0.750413
$382$	−26.7076	−1.36648
$383$	8.64378	0.441676	0.220838	−	0.975310i	$-0.429121\pi$
$383$	8.64378	0.441676	0.220838	+	0.975310i	$0.429121\pi$
$384$	−4.66246	−0.237930
$385$	−1.06876	−0.0544692
$386$	−5.84061	−0.297279
$387$	15.1723	0.771250
$388$	−4.17470	−0.211938
$389$	−20.9849	−1.06398	−0.531989	−	0.846751i	$-0.678555\pi$
$389$	−20.9849	−1.06398	−0.531989	+	0.846751i	$0.678555\pi$
$390$	−4.24486	−0.214947
$391$	−8.88762	−0.449466
$392$	18.0218	0.910241
$393$	5.98518	0.301913
$394$	−31.4202	−1.58292
$395$	−14.3679	−0.722928
$396$	0.887214	0.0445842
$397$	−4.53468	−0.227589	−0.113795	−	0.993504i	$-0.536301\pi$
$397$	−4.53468	−0.227589	−0.113795	+	0.993504i	$0.536301\pi$
$398$	−6.45658	−0.323639
$399$	6.39747	0.320274
$400$	−2.43140	−0.121570
$401$	8.66984	0.432951	0.216476	−	0.976288i	$-0.430544\pi$
$401$	8.66984	0.432951	0.216476	+	0.976288i	$0.430544\pi$
$402$	1.12821	0.0562698
$403$	5.55941	0.276934
$404$	−2.76713	−0.137670
$405$	−2.41663	−0.120083
$406$	−4.75122	−0.235799
$407$	5.64583	0.279853
$408$	−12.6361	−0.625580
$409$	−22.9530	−1.13495	−0.567477	−	0.823389i	$-0.692080\pi$
$409$	−22.9530	−1.13495	−0.567477	+	0.823389i	$0.692080\pi$
$410$	−8.19941	−0.404940
$411$	−12.0826	−0.595988
$412$	−6.14769	−0.302875
$413$	12.7113	0.625482
$414$	−4.65449	−0.228756
$415$	−16.0563	−0.788171
$416$	9.52618	0.467060
$417$	−22.8294	−1.11796
$418$	5.72435	0.279987
$419$	−12.6586	−0.618413	−0.309207	−	0.950995i	$-0.600063\pi$
$419$	−12.6586	−0.618413	−0.309207	+	0.950995i	$0.600063\pi$
$420$	−0.796197	−0.0388504
$421$	−25.4687	−1.24127	−0.620634	−	0.784100i	$-0.713125\pi$
$421$	−25.4687	−1.24127	−0.620634	+	0.784100i	$0.713125\pi$
$422$	17.9240	0.872526
$423$	6.12924	0.298014
$424$	10.3538	0.502824
$425$	−3.32274	−0.161177
$426$	−7.32775	−0.355031
$427$	7.90440	0.382521
$428$	0.961535	0.0464776
$429$	−3.59101	−0.173376
$430$	−12.1832	−0.587525
$431$	6.48825	0.312528	0.156264	−	0.987715i	$-0.450055\pi$
$431$	6.48825	0.312528	0.156264	+	0.987715i	$0.450055\pi$
$432$	−13.4405	−0.646655
$433$	20.1950	0.970510	0.485255	−	0.874373i	$-0.338727\pi$
$433$	20.1950	0.970510	0.485255	+	0.874373i	$0.338727\pi$
$434$	−2.41762	−0.116050
$435$	−4.64863	−0.222885
$436$	−4.22443	−0.202313
$437$	12.9529	0.619622
$438$	1.46115	0.0698164
$439$	−16.7565	−0.799744	−0.399872	−	0.916571i	$-0.630945\pi$
$439$	−16.7565	−0.799744	−0.399872	+	0.916571i	$0.630945\pi$
$440$	−3.07658	−0.146670
$441$	8.62318	0.410628
$442$	−11.4107	−0.542752
$443$	25.9783	1.23426	0.617132	−	0.786859i	$-0.288294\pi$
$443$	25.9783	1.23426	0.617132	+	0.786859i	$0.288294\pi$
$444$	4.20598	0.199607
$445$	−14.3329	−0.679444
$446$	−28.1350	−1.33223
$447$	19.1375	0.905172
$448$	−9.33982	−0.441265
$449$	2.06084	0.0972572	0.0486286	−	0.998817i	$-0.484515\pi$
$449$	2.06084	0.0972572	0.0486286	+	0.998817i	$0.484515\pi$
$450$	−1.74014	−0.0820309
$451$	−6.93643	−0.326624
$452$	0.339812	0.0159834
$453$	12.0354	0.565470
$454$	18.9386	0.888832
$455$	−3.10492	−0.145561
$456$	18.4160	0.862409
$457$	−26.1090	−1.22133	−0.610663	−	0.791891i	$-0.709097\pi$
$457$	−26.1090	−1.22133	−0.610663	+	0.791891i	$0.709097\pi$
$458$	1.60740	0.0751090
$459$	−18.3677	−0.857333
$460$	−1.61206	−0.0751625
$461$	−6.32696	−0.294676	−0.147338	−	0.989086i	$-0.547071\pi$
$461$	−6.32696	−0.294676	−0.147338	+	0.989086i	$0.547071\pi$
$462$	1.56162	0.0726533
$463$	24.7801	1.15163	0.575815	−	0.817580i	$-0.304685\pi$
$463$	24.7801	1.15163	0.575815	+	0.817580i	$0.304685\pi$
$464$	−9.14393	−0.424496
$465$	−2.36542	−0.109694
$466$	−1.14915	−0.0532334
$467$	7.58936	0.351194	0.175597	−	0.984462i	$-0.443814\pi$
$467$	7.58936	0.351194	0.175597	+	0.984462i	$0.443814\pi$
$468$	2.57749	0.119145
$469$	0.825231	0.0381056
$470$	−4.92172	−0.227022
$471$	−2.77768	−0.127989
$472$	36.5912	1.68425
$473$	−10.3066	−0.473896
$474$	20.9936	0.964270
$475$	4.84260	0.222194
$476$	−2.14028	−0.0980994
$477$	4.95412	0.226834
$478$	18.5388	0.847946
$479$	−5.55521	−0.253824	−0.126912	−	0.991914i	$-0.540507\pi$
$479$	−5.55521	−0.253824	−0.126912	+	0.991914i	$0.540507\pi$
$480$	−4.05319	−0.185002
$481$	16.4020	0.747867
$482$	13.4339	0.611898
$483$	3.53360	0.160785
$484$	−0.602686	−0.0273948
$485$	6.92681	0.314530
$486$	−16.0722	−0.729048
$487$	−1.56751	−0.0710308	−0.0355154	−	0.999369i	$-0.511307\pi$
$487$	−1.56751	−0.0710308	−0.0355154	+	0.999369i	$0.511307\pi$
$488$	22.7539	1.03002
$489$	−10.0278	−0.453472
$490$	−6.92432	−0.312809
$491$	−15.3922	−0.694641	−0.347321	−	0.937746i	$-0.612908\pi$
$491$	−15.3922	−0.694641	−0.347321	+	0.937746i	$0.612908\pi$
$492$	−5.16743	−0.232966
$493$	−12.4961	−0.562795
$494$	16.6301	0.748224
$495$	−1.47210	−0.0661659
$496$	−4.65281	−0.208917
$497$	−5.35991	−0.240425
$498$	23.4606	1.05129
$499$	−12.4886	−0.559066	−0.279533	−	0.960136i	$-0.590180\pi$
$499$	−12.4886	−0.559066	−0.279533	+	0.960136i	$0.590180\pi$
$500$	−0.602686	−0.0269530
$501$	−26.3171	−1.17576
$502$	−7.94200	−0.354469
$503$	24.4996	1.09238	0.546191	−	0.837660i	$-0.316077\pi$
$503$	24.4996	1.09238	0.546191	+	0.837660i	$0.316077\pi$
$504$	−4.84047	−0.215612
$505$	4.59132	0.204311
$506$	3.16181	0.140560
$507$	5.63664	0.250332
$508$	7.14178	0.316865
$509$	9.41099	0.417135	0.208567	−	0.978008i	$-0.433120\pi$
$509$	9.41099	0.417135	0.208567	+	0.978008i	$0.433120\pi$
$510$	4.85502	0.214984
$511$	1.06876	0.0472793
$512$	−22.9335	−1.01353
$513$	26.7694	1.18190
$514$	13.7906	0.608276
$515$	10.2005	0.449487
$516$	−7.67808	−0.338009
$517$	−4.16361	−0.183115
$518$	−7.13274	−0.313395
$519$	19.7966	0.868973
$520$	−8.93795	−0.391955
$521$	−11.5000	−0.503824	−0.251912	−	0.967750i	$-0.581059\pi$
$521$	−11.5000	−0.503824	−0.251912	+	0.967750i	$0.581059\pi$
$522$	−6.54427	−0.286435
$523$	−42.0963	−1.84074	−0.920372	−	0.391043i	$-0.872114\pi$
$523$	−42.0963	−1.84074	−0.920372	+	0.391043i	$0.872114\pi$
$524$	2.91824	0.127484
$525$	1.32108	0.0576567
$526$	−13.6180	−0.593772
$527$	−6.35853	−0.276982
$528$	3.00541	0.130794
$529$	−15.8455	−0.688936
$530$	−3.97811	−0.172798
$531$	17.5083	0.759797
$532$	3.11926	0.135237
$533$	−20.1514	−0.872853
$534$	20.9425	0.906270
$535$	−1.59542	−0.0689758
$536$	2.37554	0.102608
$537$	18.7842	0.810599
$538$	−15.2865	−0.659046
$539$	−5.85775	−0.252311
$540$	−3.33158	−0.143368
$541$	−27.5193	−1.18315	−0.591574	−	0.806250i	$-0.701493\pi$
$541$	−27.5193	−1.18315	−0.591574	+	0.806250i	$0.701493\pi$
$542$	−26.6806	−1.14603
$543$	−3.07403	−0.131919
$544$	−10.8955	−0.467140
$545$	7.00933	0.300247
$546$	4.53675	0.194155
$547$	−9.61778	−0.411226	−0.205613	−	0.978633i	$-0.565919\pi$
$547$	−9.61778	−0.411226	−0.205613	+	0.978633i	$0.565919\pi$
$548$	−5.89118	−0.251659
$549$	10.8874	0.464663
$550$	1.18208	0.0504041
$551$	18.2119	0.775854
$552$	10.1720	0.432948
$553$	15.3559	0.652999
$554$	−12.1576	−0.516526
$555$	−6.97872	−0.296230
$556$	−11.1311	−0.472065
$557$	−14.3333	−0.607323	−0.303662	−	0.952780i	$-0.598209\pi$
$557$	−14.3333	−0.607323	−0.303662	+	0.952780i	$0.598209\pi$
$558$	−3.33000	−0.140970
$559$	−29.9421	−1.26642
$560$	2.59859	0.109810
$561$	4.10719	0.173406
$562$	12.6125	0.532026
$563$	−38.3145	−1.61476	−0.807382	−	0.590029i	$-0.799116\pi$
$563$	−38.3145	−1.61476	−0.807382	+	0.590029i	$0.799116\pi$
$564$	−3.10177	−0.130608
$565$	−0.563829	−0.0237205
$566$	−17.5210	−0.736464
$567$	2.58281	0.108468
$568$	−15.4293	−0.647397
$569$	−12.0399	−0.504741	−0.252370	−	0.967631i	$-0.581210\pi$
$569$	−12.0399	−0.504741	−0.252370	+	0.967631i	$0.581210\pi$
$570$	−7.07577	−0.296371
$571$	42.1069	1.76212	0.881059	−	0.473007i	$-0.156831\pi$
$571$	42.1069	1.76212	0.881059	+	0.473007i	$0.156831\pi$
$572$	−1.75090	−0.0732087
$573$	27.9277	1.16670
$574$	8.76323	0.365770
$575$	2.67478	0.111546
$576$	−12.8645	−0.536022
$577$	−3.40550	−0.141773	−0.0708865	−	0.997484i	$-0.522583\pi$
$577$	−3.40550	−0.141773	−0.0708865	+	0.997484i	$0.522583\pi$
$578$	−7.04446	−0.293011
$579$	6.10744	0.253816
$580$	−2.26657	−0.0941141
$581$	17.1603	0.711931
$582$	−10.1211	−0.419533
$583$	−3.36535	−0.139378
$584$	3.07658	0.127310
$585$	−4.27667	−0.176819
$586$	−22.2754	−0.920190
$587$	−14.9464	−0.616905	−0.308453	−	0.951240i	$-0.599811\pi$
$587$	−14.9464	−0.616905	−0.308453	+	0.951240i	$0.599811\pi$
$588$	−4.36385	−0.179962
$589$	9.26699	0.381840
$590$	−14.0590	−0.578801
$591$	32.8556	1.35150
$592$	−13.7272	−0.564186
$593$	38.6917	1.58888	0.794439	−	0.607344i	$-0.207765\pi$
$593$	38.6917	1.58888	0.794439	+	0.607344i	$0.207765\pi$
$594$	6.53440	0.268110
$595$	3.55123	0.145586
$596$	9.33101	0.382213
$597$	6.75155	0.276323
$598$	9.18554	0.375625
$599$	8.67538	0.354466	0.177233	−	0.984169i	$-0.443285\pi$
$599$	8.67538	0.354466	0.177233	+	0.984169i	$0.443285\pi$
$600$	3.80291	0.155253
$601$	21.9316	0.894609	0.447305	−	0.894382i	$-0.352384\pi$
$601$	21.9316	0.894609	0.447305	+	0.894382i	$0.352384\pi$
$602$	13.0209	0.530694
$603$	1.13666	0.0462884
$604$	5.86817	0.238772
$605$	1.00000	0.0406558
$606$	−6.70861	−0.272519
$607$	41.2402	1.67389	0.836944	−	0.547289i	$-0.184340\pi$
$607$	41.2402	1.67389	0.836944	+	0.547289i	$0.184340\pi$
$608$	15.8792	0.643987
$609$	4.96828	0.201325
$610$	−8.74247	−0.353972
$611$	−12.0959	−0.489349
$612$	−2.94798	−0.119165
$613$	−21.4302	−0.865557	−0.432779	−	0.901500i	$-0.642467\pi$
$613$	−21.4302	−0.865557	−0.432779	+	0.901500i	$0.642467\pi$
$614$	33.1622	1.33832
$615$	8.57400	0.345737
$616$	3.28814	0.132483
$617$	−14.4887	−0.583294	−0.291647	−	0.956526i	$-0.594203\pi$
$617$	−14.4887	−0.583294	−0.291647	+	0.956526i	$0.594203\pi$
$618$	−14.9044	−0.599543
$619$	11.3300	0.455392	0.227696	−	0.973732i	$-0.426881\pi$
$619$	11.3300	0.455392	0.227696	+	0.973732i	$0.426881\pi$
$620$	−1.15332	−0.0463186
$621$	14.7859	0.593338
$622$	20.2396	0.811532
$623$	15.3185	0.613721
$624$	8.73117	0.349527
$625$	1.00000	0.0400000
$626$	−11.6307	−0.464855
$627$	−5.98586	−0.239052
$628$	−1.35434	−0.0540439
$629$	−18.7596	−0.747996
$630$	1.85980	0.0740961
$631$	−25.6773	−1.02220	−0.511099	−	0.859522i	$-0.670762\pi$
$631$	−25.6773	−1.02220	−0.511099	+	0.859522i	$0.670762\pi$
$632$	44.2041	1.75834
$633$	−18.7428	−0.744961
$634$	−5.79283	−0.230063
$635$	−11.8499	−0.470250
$636$	−2.50708	−0.0994124
$637$	−17.0177	−0.674264
$638$	4.44553	0.176000
$639$	−7.38266	−0.292054
$640$	3.77196	0.149100
$641$	−0.943956	−0.0372840	−0.0186420	−	0.999826i	$-0.505934\pi$
$641$	−0.943956	−0.0372840	−0.0186420	+	0.999826i	$0.505934\pi$
$642$	2.33114	0.0920028
$643$	−6.04158	−0.238257	−0.119128	−	0.992879i	$-0.538010\pi$
$643$	−6.04158	−0.238257	−0.119128	+	0.992879i	$0.538010\pi$
$644$	1.72291	0.0678920
$645$	12.7398	0.501628
$646$	−19.0205	−0.748353
$647$	40.4193	1.58905	0.794523	−	0.607234i	$-0.207721\pi$
$647$	40.4193	1.58905	0.794523	+	0.607234i	$0.207721\pi$
$648$	7.43497	0.292073
$649$	−11.8935	−0.466859
$650$	3.43413	0.134697
$651$	2.52807	0.0990828
$652$	−4.88932	−0.191481
$653$	12.2209	0.478242	0.239121	−	0.970990i	$-0.423141\pi$
$653$	12.2209	0.478242	0.239121	+	0.970990i	$0.423141\pi$
$654$	−10.2417	−0.400481
$655$	−4.84206	−0.189195
$656$	16.8652	0.658475
$657$	1.47210	0.0574320
$658$	5.26015	0.205062
$659$	19.7198	0.768173	0.384087	−	0.923297i	$-0.374516\pi$
$659$	19.7198	0.768173	0.384087	+	0.923297i	$0.374516\pi$
$660$	0.744971	0.0289979
$661$	11.5757	0.450243	0.225122	−	0.974331i	$-0.427722\pi$
$661$	11.5757	0.450243	0.225122	+	0.974331i	$0.427722\pi$
$662$	28.8966	1.12310
$663$	11.9320	0.463401
$664$	49.3985	1.91703
$665$	−5.17560	−0.200701
$666$	−9.82453	−0.380693
$667$	10.0593	0.389496
$668$	−12.8316	−0.496470
$669$	29.4203	1.13745
$670$	−0.912727	−0.0352617
$671$	−7.39584	−0.285513
$672$	4.33191	0.167107
$673$	−5.72345	−0.220623	−0.110311	−	0.993897i	$-0.535185\pi$
$673$	−5.72345	−0.220623	−0.110311	+	0.993897i	$0.535185\pi$
$674$	20.4088	0.786117
$675$	5.52789	0.212768
$676$	2.74830	0.105704
$677$	−13.0078	−0.499929	−0.249964	−	0.968255i	$-0.580419\pi$
$677$	−13.0078	−0.499929	−0.249964	+	0.968255i	$0.580419\pi$
$678$	0.823839	0.0316393
$679$	−7.40312	−0.284106
$680$	10.2227	0.392023
$681$	−19.8038	−0.758883
$682$	2.26207	0.0866193
$683$	34.5630	1.32252	0.661259	−	0.750158i	$-0.270022\pi$
$683$	34.5630	1.32252	0.661259	+	0.750158i	$0.270022\pi$
$684$	4.29643	0.164278
$685$	9.77487	0.373479
$686$	16.2440	0.620199
$687$	−1.68084	−0.0641279
$688$	25.0593	0.955378
$689$	−9.77685	−0.372468
$690$	−3.90826	−0.148785
$691$	13.6408	0.518919	0.259459	−	0.965754i	$-0.416456\pi$
$691$	13.6408	0.518919	0.259459	+	0.965754i	$0.416456\pi$
$692$	9.65236	0.366928
$693$	1.57332	0.0597657
$694$	21.4332	0.813593
$695$	18.4692	0.700576
$696$	14.3019	0.542112
$697$	23.0480	0.873004
$698$	−7.11328	−0.269242
$699$	1.20165	0.0454506
$700$	0.644129	0.0243458
$701$	3.87019	0.146175	0.0730876	−	0.997326i	$-0.476715\pi$
$701$	3.87019	0.146175	0.0730876	+	0.997326i	$0.476715\pi$
$702$	18.9835	0.716484
$703$	27.3405	1.03117
$704$	8.73891	0.329360
$705$	5.14657	0.193831
$706$	−15.1890	−0.571645
$707$	−4.90704	−0.184548
$708$	−8.86027	−0.332989
$709$	−6.77740	−0.254531	−0.127265	−	0.991869i	$-0.540620\pi$
$709$	−6.77740	−0.254531	−0.127265	+	0.991869i	$0.540620\pi$
$710$	5.92820	0.222481
$711$	21.1510	0.793223
$712$	44.0963	1.65258
$713$	5.11857	0.191692
$714$	−5.18887	−0.194189
$715$	2.90515	0.108647
$716$	9.15877	0.342279
$717$	−19.3858	−0.723975
$718$	8.02512	0.299495
$719$	−4.95652	−0.184847	−0.0924235	−	0.995720i	$-0.529461\pi$
$719$	−4.95652	−0.184847	−0.0924235	+	0.995720i	$0.529461\pi$
$720$	3.57925	0.133391
$721$	−10.9019	−0.406008
$722$	5.26123	0.195803
$723$	−14.0476	−0.522437
$724$	−1.49883	−0.0557036
$725$	3.76077	0.139672
$726$	−1.46115	−0.0542283
$727$	−12.5196	−0.464328	−0.232164	−	0.972677i	$-0.574581\pi$
$727$	−12.5196	−0.464328	−0.232164	+	0.972677i	$0.574581\pi$
$728$	9.55255	0.354041
$729$	24.0563	0.890974
$730$	−1.18208	−0.0437508
$731$	34.2460	1.26664
$732$	−5.50968	−0.203644
$733$	−26.9829	−0.996635	−0.498318	−	0.866995i	$-0.666049\pi$
$733$	−26.9829	−0.996635	−0.498318	+	0.866995i	$0.666049\pi$
$734$	40.0219	1.47724
$735$	7.24066	0.267076
$736$	8.77078	0.323295
$737$	−0.772136	−0.0284420
$738$	12.0703	0.444315
$739$	−12.1949	−0.448597	−0.224298	−	0.974521i	$-0.572009\pi$
$739$	−12.1949	−0.448597	−0.224298	+	0.974521i	$0.572009\pi$
$740$	−3.40267	−0.125084
$741$	−17.3899	−0.638832
$742$	4.25166	0.156083
$743$	−5.22863	−0.191820	−0.0959100	−	0.995390i	$-0.530576\pi$
$743$	−5.22863	−0.191820	−0.0959100	+	0.995390i	$0.530576\pi$
$744$	7.27740	0.266802
$745$	−15.4824	−0.567230
$746$	−12.8772	−0.471468
$747$	23.6364	0.864811
$748$	2.00257	0.0732213
$749$	1.70512	0.0623038
$750$	−1.46115	−0.0533536
$751$	−23.3132	−0.850710	−0.425355	−	0.905027i	$-0.639851\pi$
$751$	−23.3132	−0.850710	−0.425355	+	0.905027i	$0.639851\pi$
$752$	10.1234	0.369162
$753$	8.30482	0.302645
$754$	12.9150	0.470335
$755$	−9.73669	−0.354354
$756$	3.56067	0.129500
$757$	−15.7268	−0.571601	−0.285801	−	0.958289i	$-0.592260\pi$
$757$	−15.7268	−0.571601	−0.285801	+	0.958289i	$0.592260\pi$
$758$	−3.42241	−0.124308
$759$	−3.30626	−0.120009
$760$	−14.8987	−0.540432
$761$	−35.9559	−1.30340	−0.651700	−	0.758477i	$-0.725944\pi$
$761$	−35.9559	−1.30340	−0.651700	+	0.758477i	$0.725944\pi$
$762$	17.3145	0.627238
$763$	−7.49131	−0.271204
$764$	13.6169	0.492643
$765$	4.89141	0.176849
$766$	10.2176	0.369178
$767$	−34.5523	−1.24761
$768$	16.0926	0.580693
$769$	−20.9897	−0.756908	−0.378454	−	0.925620i	$-0.623544\pi$
$769$	−20.9897	−0.756908	−0.378454	+	0.925620i	$0.623544\pi$
$770$	−1.26336	−0.0455285
$771$	−14.4206	−0.519345
$772$	2.97785	0.107175
$773$	24.9569	0.897638	0.448819	−	0.893623i	$-0.351845\pi$
$773$	24.9569	0.897638	0.448819	+	0.893623i	$0.351845\pi$
$774$	17.9348	0.644655
$775$	1.91364	0.0687399
$776$	−21.3109	−0.765018
$777$	7.45859	0.267576
$778$	−24.8059	−0.889333
$779$	−33.5904	−1.20350
$780$	2.16425	0.0774927
$781$	5.01506	0.179453
$782$	−10.5059	−0.375689
$783$	20.7891	0.742943
$784$	14.2425	0.508661
$785$	2.24716	0.0802047
$786$	7.07497	0.252356
$787$	35.8846	1.27915	0.639573	−	0.768730i	$-0.279111\pi$
$787$	35.8846	1.27915	0.639573	+	0.768730i	$0.279111\pi$
$788$	16.0196	0.570676
$789$	14.2401	0.506961
$790$	−16.9840	−0.604264
$791$	0.602600	0.0214260
$792$	4.52904	0.160932
$793$	−21.4860	−0.762992
$794$	−5.36036	−0.190232
$795$	4.15985	0.147535
$796$	3.29190	0.116678
$797$	−26.7391	−0.947149	−0.473575	−	0.880754i	$-0.657037\pi$
$797$	−26.7391	−0.947149	−0.473575	+	0.880754i	$0.657037\pi$
$798$	7.56232	0.267703
$799$	13.8346	0.489433
$800$	3.27906	0.115932
$801$	21.0994	0.745512
$802$	10.2484	0.361885
$803$	−1.00000	−0.0352892
$804$	−0.575219	−0.0202864
$805$	−2.85871	−0.100756
$806$	6.57167	0.231477
$807$	15.9848	0.562692
$808$	−14.1256	−0.496937
$809$	−3.77090	−0.132578	−0.0662889	−	0.997800i	$-0.521116\pi$
$809$	−3.77090	−0.132578	−0.0662889	+	0.997800i	$0.521116\pi$
$810$	−2.85665	−0.100372
$811$	46.3116	1.62622	0.813110	−	0.582110i	$-0.197773\pi$
$811$	46.3116	1.62622	0.813110	+	0.582110i	$0.197773\pi$
$812$	2.42242	0.0850104
$813$	27.8995	0.978480
$814$	6.67382	0.233917
$815$	8.11255	0.284170
$816$	−9.98620	−0.349587
$817$	−49.9106	−1.74615
$818$	−27.1323	−0.948659
$819$	4.57075	0.159715
$820$	4.18049	0.145989
$821$	−27.7941	−0.970019	−0.485010	−	0.874509i	$-0.661184\pi$
$821$	−27.7941	−0.970019	−0.485010	+	0.874509i	$0.661184\pi$
$822$	−14.2825	−0.498161
$823$	−16.1252	−0.562090	−0.281045	−	0.959695i	$-0.590681\pi$
$823$	−16.1252	−0.562090	−0.281045	+	0.959695i	$0.590681\pi$
$824$	−31.3826	−1.09327
$825$	−1.23608	−0.0430349
$826$	15.0258	0.522813
$827$	13.5786	0.472176	0.236088	−	0.971732i	$-0.424135\pi$
$827$	13.5786	0.472176	0.236088	+	0.971732i	$0.424135\pi$
$828$	2.37311	0.0824711
$829$	37.5379	1.30375	0.651873	−	0.758329i	$-0.273984\pi$
$829$	37.5379	1.30375	0.651873	+	0.758329i	$0.273984\pi$
$830$	−18.9798	−0.658798
$831$	12.7130	0.441009
$832$	25.3879	0.880166
$833$	19.4638	0.674380
$834$	−26.9862	−0.934456
$835$	21.2907	0.736796
$836$	−2.91857	−0.100941
$837$	10.5784	0.365642
$838$	−14.9635	−0.516905
$839$	51.2836	1.77051	0.885254	−	0.465109i	$-0.153985\pi$
$839$	51.2836	1.77051	0.885254	+	0.465109i	$0.153985\pi$
$840$	−4.06441	−0.140236
$841$	−14.8566	−0.512296
$842$	−30.1061	−1.03752
$843$	−13.1887	−0.454243
$844$	−9.13859	−0.314563
$845$	−4.56008	−0.156872
$846$	7.24526	0.249097
$847$	−1.06876	−0.0367231
$848$	8.18249	0.280988
$849$	18.3215	0.628792
$850$	−3.92775	−0.134721
$851$	15.1014	0.517668
$852$	3.73607	0.127996
$853$	−35.2076	−1.20548	−0.602742	−	0.797936i	$-0.705925\pi$
$853$	−35.2076	−1.20548	−0.602742	+	0.797936i	$0.705925\pi$
$854$	9.34363	0.319732
$855$	−7.12879	−0.243800
$856$	4.90843	0.167767
$857$	26.7009	0.912086	0.456043	−	0.889958i	$-0.349266\pi$
$857$	26.7009	0.912086	0.456043	+	0.889958i	$0.349266\pi$
$858$	−4.24486	−0.144917
$859$	−51.7514	−1.76574	−0.882868	−	0.469621i	$-0.844391\pi$
$859$	−51.7514	−1.76574	−0.882868	+	0.469621i	$0.844391\pi$
$860$	6.21162	0.211815
$861$	−9.16357	−0.312294
$862$	7.66963	0.261229
$863$	46.5217	1.58362	0.791809	−	0.610769i	$-0.209140\pi$
$863$	46.5217	1.58362	0.791809	+	0.610769i	$0.209140\pi$
$864$	18.1263	0.616669
$865$	−16.0156	−0.544545
$866$	23.8721	0.811207
$867$	7.36629	0.250172
$868$	1.23263	0.0418382
$869$	−14.3679	−0.487398
$870$	−5.49505	−0.186300
$871$	−2.24317	−0.0760071
$872$	−21.5648	−0.730276
$873$	−10.1970	−0.345115
$874$	15.3114	0.517916
$875$	−1.06876	−0.0361308
$876$	−0.744971	−0.0251702
$877$	−10.6376	−0.359205	−0.179603	−	0.983739i	$-0.557481\pi$
$877$	−10.6376	−0.359205	−0.179603	+	0.983739i	$0.557481\pi$
$878$	−19.8075	−0.668471
$879$	23.2931	0.785656
$880$	−2.43140	−0.0819623
$881$	−37.6897	−1.26980	−0.634899	−	0.772595i	$-0.718958\pi$
$881$	−37.6897	−1.26980	−0.634899	+	0.772595i	$0.718958\pi$
$882$	10.1933	0.343226
$883$	−16.1111	−0.542182	−0.271091	−	0.962554i	$-0.587384\pi$
$883$	−16.1111	−0.542182	−0.271091	+	0.962554i	$0.587384\pi$
$884$	5.81778	0.195673
$885$	14.7013	0.494179
$886$	30.7084	1.03167
$887$	−8.56552	−0.287602	−0.143801	−	0.989607i	$-0.545933\pi$
$887$	−8.56552	−0.287602	−0.143801	+	0.989607i	$0.545933\pi$
$888$	21.4706	0.720506
$889$	12.6648	0.424762
$890$	−16.9426	−0.567918
$891$	−2.41663	−0.0809601
$892$	14.3447	0.480295
$893$	−20.1627	−0.674720
$894$	22.6221	0.756595
$895$	−15.1966	−0.507966
$896$	−4.03134	−0.134677
$897$	−9.60518	−0.320708
$898$	2.43608	0.0812931
$899$	7.19676	0.240025
$900$	0.887214	0.0295738
$901$	11.1822	0.372533
$902$	−8.19941	−0.273011
$903$	−13.6158	−0.453105
$904$	1.73467	0.0576942
$905$	2.48691	0.0826678
$906$	14.2268	0.472652
$907$	34.0089	1.12925	0.564624	−	0.825348i	$-0.309021\pi$
$907$	34.0089	1.12925	0.564624	+	0.825348i	$0.309021\pi$
$908$	−9.65588	−0.320442
$909$	−6.75888	−0.224178
$910$	−3.67027	−0.121668
$911$	11.7347	0.388786	0.194393	−	0.980924i	$-0.437726\pi$
$911$	11.7347	0.388786	0.194393	+	0.980924i	$0.437726\pi$
$912$	14.5540	0.481931
$913$	−16.0563	−0.531385
$914$	−30.8629	−1.02085
$915$	9.14187	0.302221
$916$	−0.819538	−0.0270783
$917$	5.17501	0.170894
$918$	−21.7121	−0.716608
$919$	55.1131	1.81801	0.909006	−	0.416783i	$-0.136842\pi$
$919$	55.1131	1.81801	0.909006	+	0.416783i	$0.136842\pi$
$920$	−8.22920	−0.271309
$921$	−34.6772	−1.14265
$922$	−7.47898	−0.246307
$923$	14.5695	0.479562
$924$	−0.796197	−0.0261930
$925$	5.64583	0.185634
$926$	29.2921	0.962599
$927$	−15.0161	−0.493193
$928$	12.3318	0.404811
$929$	3.59760	0.118034	0.0590168	−	0.998257i	$-0.481203\pi$
$929$	3.59760	0.118034	0.0590168	+	0.998257i	$0.481203\pi$
$930$	−2.79611	−0.0916881
$931$	−28.3667	−0.929682
$932$	0.585898	0.0191917
$933$	−21.1642	−0.692884
$934$	8.97123	0.293548
$935$	−3.32274	−0.108665
$936$	13.1575	0.430068
$937$	53.2906	1.74093	0.870464	−	0.492231i	$-0.163819\pi$
$937$	53.2906	1.74093	0.870464	+	0.492231i	$0.163819\pi$
$938$	0.975489	0.0318508
$939$	12.1620	0.396892
$940$	2.50935	0.0818460
$941$	7.59818	0.247694	0.123847	−	0.992301i	$-0.460477\pi$
$941$	7.59818	0.247694	0.123847	+	0.992301i	$0.460477\pi$
$942$	−3.28344	−0.106980
$943$	−18.5534	−0.604183
$944$	28.9177	0.941191
$945$	−5.90800	−0.192187
$946$	−12.1832	−0.396109
$947$	−27.0385	−0.878633	−0.439316	−	0.898332i	$-0.644779\pi$
$947$	−27.0385	−0.878633	−0.439316	+	0.898332i	$0.644779\pi$
$948$	−10.7037	−0.347639
$949$	−2.90515	−0.0943053
$950$	5.72435	0.185722
$951$	6.05748	0.196427
$952$	−10.9256	−0.354102
$953$	23.8290	0.771896	0.385948	−	0.922521i	$-0.373874\pi$
$953$	23.8290	0.771896	0.385948	+	0.922521i	$0.373874\pi$
$954$	5.85617	0.189601
$955$	−22.5937	−0.731116
$956$	−9.45207	−0.305702
$957$	−4.64863	−0.150269
$958$	−6.56671	−0.212161
$959$	−10.4470	−0.337352
$960$	−10.8020	−0.348634
$961$	−27.3380	−0.881871
$962$	19.3885	0.625110
$963$	2.34861	0.0756829
$964$	−6.84931	−0.220602
$965$	−4.94096	−0.159055
$966$	4.17700	0.134393
$967$	15.0485	0.483928	0.241964	−	0.970285i	$-0.422208\pi$
$967$	15.0485	0.483928	0.241964	+	0.970285i	$0.422208\pi$
$968$	−3.07658	−0.0988852
$969$	19.8895	0.638942
$970$	8.18805	0.262902
$971$	−34.2061	−1.09772	−0.548862	−	0.835913i	$-0.684939\pi$
$971$	−34.2061	−1.09772	−0.548862	+	0.835913i	$0.684939\pi$
$972$	8.19443	0.262836
$973$	−19.7392	−0.632809
$974$	−1.85293	−0.0593716
$975$	−3.59101	−0.115004
$976$	17.9822	0.575596
$977$	14.6513	0.468738	0.234369	−	0.972148i	$-0.424698\pi$
$977$	14.6513	0.468738	0.234369	+	0.972148i	$0.424698\pi$
$978$	−11.8536	−0.379038
$979$	−14.3329	−0.458081
$980$	3.53038	0.112774
$981$	−10.3184	−0.329442
$982$	−18.1948	−0.580621
$983$	28.7152	0.915872	0.457936	−	0.888985i	$-0.348589\pi$
$983$	28.7152	0.915872	0.457936	+	0.888985i	$0.348589\pi$
$984$	−26.3786	−0.840920
$985$	−26.5804	−0.846922
$986$	−14.7714	−0.470416
$987$	−5.50046	−0.175082
$988$	−8.47890	−0.269750
$989$	−27.5678	−0.876606
$990$	−1.74014	−0.0553052
$991$	−39.2671	−1.24736	−0.623680	−	0.781680i	$-0.714363\pi$
$991$	−39.2671	−1.24736	−0.623680	+	0.781680i	$0.714363\pi$
$992$	6.27494	0.199230
$993$	−30.2167	−0.958898
$994$	−6.33584	−0.200961
$995$	−5.46205	−0.173159
$996$	−11.9614	−0.379013
$997$	24.5248	0.776709	0.388354	−	0.921510i	$-0.373044\pi$
$997$	24.5248	0.776709	0.388354	+	0.921510i	$0.373044\pi$
$998$	−14.7625	−0.467299
$999$	31.2095	0.987425

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.b.1.17	✓	23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.b.1.17	✓	23	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)

\(f(q)\)	\(=\)	\(q+1.18208 q^{2} -1.23608 q^{3} -0.602686 q^{4} +1.00000 q^{5} -1.46115 q^{6} -1.06876 q^{7} -3.07658 q^{8} -1.47210 q^{9} +O(q^{10})\)	\(q+1.18208 q^{2} -1.23608 q^{3} -0.602686 q^{4} +1.00000 q^{5} -1.46115 q^{6} -1.06876 q^{7} -3.07658 q^{8} -1.47210 q^{9} +1.18208 q^{10} +1.00000 q^{11} +0.744971 q^{12} +2.90515 q^{13} -1.26336 q^{14} -1.23608 q^{15} -2.43140 q^{16} -3.32274 q^{17} -1.74014 q^{18} +4.84260 q^{19} -0.602686 q^{20} +1.32108 q^{21} +1.18208 q^{22} +2.67478 q^{23} +3.80291 q^{24} +1.00000 q^{25} +3.43413 q^{26} +5.52789 q^{27} +0.644129 q^{28} +3.76077 q^{29} -1.46115 q^{30} +1.91364 q^{31} +3.27906 q^{32} -1.23608 q^{33} -3.92775 q^{34} -1.06876 q^{35} +0.887214 q^{36} +5.64583 q^{37} +5.72435 q^{38} -3.59101 q^{39} -3.07658 q^{40} -6.93643 q^{41} +1.56162 q^{42} -10.3066 q^{43} -0.602686 q^{44} -1.47210 q^{45} +3.16181 q^{46} -4.16361 q^{47} +3.00541 q^{48} -5.85775 q^{49} +1.18208 q^{50} +4.10719 q^{51} -1.75090 q^{52} -3.36535 q^{53} +6.53440 q^{54} +1.00000 q^{55} +3.28814 q^{56} -5.98586 q^{57} +4.44553 q^{58} -11.8935 q^{59} +0.744971 q^{60} -7.39584 q^{61} +2.26207 q^{62} +1.57332 q^{63} +8.73891 q^{64} +2.90515 q^{65} -1.46115 q^{66} -0.772136 q^{67} +2.00257 q^{68} -3.30626 q^{69} -1.26336 q^{70} +5.01506 q^{71} +4.52904 q^{72} -1.00000 q^{73} +6.67382 q^{74} -1.23608 q^{75} -2.91857 q^{76} -1.06876 q^{77} -4.24486 q^{78} -14.3679 q^{79} -2.43140 q^{80} -2.41663 q^{81} -8.19941 q^{82} -16.0563 q^{83} -0.796197 q^{84} -3.32274 q^{85} -12.1832 q^{86} -4.64863 q^{87} -3.07658 q^{88} -14.3329 q^{89} -1.74014 q^{90} -3.10492 q^{91} -1.61206 q^{92} -2.36542 q^{93} -4.92172 q^{94} +4.84260 q^{95} -4.05319 q^{96} +6.92681 q^{97} -6.92432 q^{98} -1.47210 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 23 q - 5 q^{2} - 3 q^{3} + 15 q^{4} + 23 q^{5} - 15 q^{6} - 10 q^{7} - 12 q^{8} + 8 q^{9}+O(q^{10}) \) 23 * q - 5 * q^2 - 3 * q^3 + 15 * q^4 + 23 * q^5 - 15 * q^6 - 10 * q^7 - 12 * q^8 + 8 * q^9	\( 23 q - 5 q^{2} - 3 q^{3} + 15 q^{4} + 23 q^{5} - 15 q^{6} - 10 q^{7} - 12 q^{8} + 8 q^{9} - 5 q^{10} + 23 q^{11} + 4 q^{12} - 19 q^{13} - 5 q^{14} - 3 q^{15} - q^{16} - 26 q^{17} + 5 q^{18} - 34 q^{19} + 15 q^{20} - 26 q^{21} - 5 q^{22} - 4 q^{23} - 23 q^{24} + 23 q^{25} - 13 q^{26} - 3 q^{27} - 28 q^{28} - 36 q^{29} - 15 q^{30} - 24 q^{31} - 19 q^{32} - 3 q^{33} - 4 q^{34} - 10 q^{35} - 14 q^{36} + 4 q^{37} - 15 q^{38} - 34 q^{39} - 12 q^{40} - 74 q^{41} + 7 q^{42} - 15 q^{43} + 15 q^{44} + 8 q^{45} + 3 q^{46} + q^{47} + 29 q^{48} + q^{49} - 5 q^{50} - 47 q^{51} - 23 q^{52} - 6 q^{53} - 11 q^{54} + 23 q^{55} - 20 q^{56} - 19 q^{57} + 22 q^{58} - 17 q^{59} + 4 q^{60} - 59 q^{61} + 38 q^{62} - 21 q^{63} - 18 q^{64} - 19 q^{65} - 15 q^{66} + 12 q^{67} + 5 q^{68} - 8 q^{69} - 5 q^{70} - 34 q^{71} + 21 q^{72} - 23 q^{73} - 9 q^{74} - 3 q^{75} - 53 q^{76} - 10 q^{77} + 23 q^{78} - 62 q^{79} - q^{80} + 7 q^{81} + 24 q^{82} - 8 q^{83} + 46 q^{84} - 26 q^{85} - 11 q^{86} + q^{87} - 12 q^{88} - 77 q^{89} + 5 q^{90} - 6 q^{91} + 47 q^{92} - 32 q^{94} - 34 q^{95} - 53 q^{96} - 21 q^{97} - 3 q^{98} + 8 q^{99}+O(q^{100}) \) 23 * q - 5 * q^2 - 3 * q^3 + 15 * q^4 + 23 * q^5 - 15 * q^6 - 10 * q^7 - 12 * q^8 + 8 * q^9 - 5 * q^10 + 23 * q^11 + 4 * q^12 - 19 * q^13 - 5 * q^14 - 3 * q^15 - q^16 - 26 * q^17 + 5 * q^18 - 34 * q^19 + 15 * q^20 - 26 * q^21 - 5 * q^22 - 4 * q^23 - 23 * q^24 + 23 * q^25 - 13 * q^26 - 3 * q^27 - 28 * q^28 - 36 * q^29 - 15 * q^30 - 24 * q^31 - 19 * q^32 - 3 * q^33 - 4 * q^34 - 10 * q^35 - 14 * q^36 + 4 * q^37 - 15 * q^38 - 34 * q^39 - 12 * q^40 - 74 * q^41 + 7 * q^42 - 15 * q^43 + 15 * q^44 + 8 * q^45 + 3 * q^46 + q^47 + 29 * q^48 + q^49 - 5 * q^50 - 47 * q^51 - 23 * q^52 - 6 * q^53 - 11 * q^54 + 23 * q^55 - 20 * q^56 - 19 * q^57 + 22 * q^58 - 17 * q^59 + 4 * q^60 - 59 * q^61 + 38 * q^62 - 21 * q^63 - 18 * q^64 - 19 * q^65 - 15 * q^66 + 12 * q^67 + 5 * q^68 - 8 * q^69 - 5 * q^70 - 34 * q^71 + 21 * q^72 - 23 * q^73 - 9 * q^74 - 3 * q^75 - 53 * q^76 - 10 * q^77 + 23 * q^78 - 62 * q^79 - q^80 + 7 * q^81 + 24 * q^82 - 8 * q^83 + 46 * q^84 - 26 * q^85 - 11 * q^86 + q^87 - 12 * q^88 - 77 * q^89 + 5 * q^90 - 6 * q^91 + 47 * q^92 - 32 * q^94 - 34 * q^95 - 53 * q^96 - 21 * q^97 - 3 * q^98 + 8 * q^99

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