LMFDB - Embedded newform 6034.2.a.n.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.1817325796$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.920246 q^{3} +1.00000 q^{4} +2.96551 q^{5} +0.920246 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.15315 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.920246 q^{3} +1.00000 q^{4} +2.96551 q^{5} +0.920246 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.15315 q^{9} -2.96551 q^{10} -3.73387 q^{11} -0.920246 q^{12} -4.18929 q^{13} +1.00000 q^{14} -2.72900 q^{15} +1.00000 q^{16} +5.64502 q^{17} +2.15315 q^{18} +1.59892 q^{19} +2.96551 q^{20} +0.920246 q^{21} +3.73387 q^{22} +4.99189 q^{23} +0.920246 q^{24} +3.79427 q^{25} +4.18929 q^{26} +4.74216 q^{27} -1.00000 q^{28} -0.281679 q^{29} +2.72900 q^{30} -0.595843 q^{31} -1.00000 q^{32} +3.43608 q^{33} -5.64502 q^{34} -2.96551 q^{35} -2.15315 q^{36} -1.75109 q^{37} -1.59892 q^{38} +3.85518 q^{39} -2.96551 q^{40} +1.43359 q^{41} -0.920246 q^{42} +7.07586 q^{43} -3.73387 q^{44} -6.38519 q^{45} -4.99189 q^{46} -8.92805 q^{47} -0.920246 q^{48} +1.00000 q^{49} -3.79427 q^{50} -5.19480 q^{51} -4.18929 q^{52} -10.7665 q^{53} -4.74216 q^{54} -11.0729 q^{55} +1.00000 q^{56} -1.47140 q^{57} +0.281679 q^{58} +2.59695 q^{59} -2.72900 q^{60} -11.3867 q^{61} +0.595843 q^{62} +2.15315 q^{63} +1.00000 q^{64} -12.4234 q^{65} -3.43608 q^{66} -0.827398 q^{67} +5.64502 q^{68} -4.59377 q^{69} +2.96551 q^{70} -8.62062 q^{71} +2.15315 q^{72} +0.950530 q^{73} +1.75109 q^{74} -3.49166 q^{75} +1.59892 q^{76} +3.73387 q^{77} -3.85518 q^{78} +13.6713 q^{79} +2.96551 q^{80} +2.09549 q^{81} -1.43359 q^{82} +10.7904 q^{83} +0.920246 q^{84} +16.7404 q^{85} -7.07586 q^{86} +0.259214 q^{87} +3.73387 q^{88} -5.53491 q^{89} +6.38519 q^{90} +4.18929 q^{91} +4.99189 q^{92} +0.548322 q^{93} +8.92805 q^{94} +4.74161 q^{95} +0.920246 q^{96} +4.82510 q^{97} -1.00000 q^{98} +8.03958 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9}+O(q^{10}) $ 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9	\( 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9} - 8 q^{10} + 15 q^{11} + 7 q^{12} - 7 q^{13} + 24 q^{14} + 13 q^{15} + 24 q^{16} - 5 q^{17} - 19 q^{18} + 6 q^{19} + 8 q^{20} - 7 q^{21} - 15 q^{22} + 3 q^{23} - 7 q^{24} + 12 q^{25} + 7 q^{26} + 22 q^{27} - 24 q^{28} + 5 q^{29} - 13 q^{30} + 13 q^{31} - 24 q^{32} - 8 q^{33} + 5 q^{34} - 8 q^{35} + 19 q^{36} + 2 q^{37} - 6 q^{38} + 7 q^{39} - 8 q^{40} + 25 q^{41} + 7 q^{42} - 15 q^{43} + 15 q^{44} + 41 q^{45} - 3 q^{46} + 35 q^{47} + 7 q^{48} + 24 q^{49} - 12 q^{50} + 31 q^{51} - 7 q^{52} + 2 q^{53} - 22 q^{54} + 14 q^{55} + 24 q^{56} - 13 q^{57} - 5 q^{58} + 35 q^{59} + 13 q^{60} - 7 q^{61} - 13 q^{62} - 19 q^{63} + 24 q^{64} - 4 q^{65} + 8 q^{66} + 10 q^{67} - 5 q^{68} + 6 q^{69} + 8 q^{70} + 58 q^{71} - 19 q^{72} + 9 q^{73} - 2 q^{74} + 7 q^{75} + 6 q^{76} - 15 q^{77} - 7 q^{78} + 31 q^{79} + 8 q^{80} + 16 q^{81} - 25 q^{82} - q^{83} - 7 q^{84} - 4 q^{85} + 15 q^{86} + 30 q^{87} - 15 q^{88} + 45 q^{89} - 41 q^{90} + 7 q^{91} + 3 q^{92} + 25 q^{93} - 35 q^{94} - 10 q^{95} - 7 q^{96} - 9 q^{97} - 24 q^{98} + 64 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9 - 8 * q^10 + 15 * q^11 + 7 * q^12 - 7 * q^13 + 24 * q^14 + 13 * q^15 + 24 * q^16 - 5 * q^17 - 19 * q^18 + 6 * q^19 + 8 * q^20 - 7 * q^21 - 15 * q^22 + 3 * q^23 - 7 * q^24 + 12 * q^25 + 7 * q^26 + 22 * q^27 - 24 * q^28 + 5 * q^29 - 13 * q^30 + 13 * q^31 - 24 * q^32 - 8 * q^33 + 5 * q^34 - 8 * q^35 + 19 * q^36 + 2 * q^37 - 6 * q^38 + 7 * q^39 - 8 * q^40 + 25 * q^41 + 7 * q^42 - 15 * q^43 + 15 * q^44 + 41 * q^45 - 3 * q^46 + 35 * q^47 + 7 * q^48 + 24 * q^49 - 12 * q^50 + 31 * q^51 - 7 * q^52 + 2 * q^53 - 22 * q^54 + 14 * q^55 + 24 * q^56 - 13 * q^57 - 5 * q^58 + 35 * q^59 + 13 * q^60 - 7 * q^61 - 13 * q^62 - 19 * q^63 + 24 * q^64 - 4 * q^65 + 8 * q^66 + 10 * q^67 - 5 * q^68 + 6 * q^69 + 8 * q^70 + 58 * q^71 - 19 * q^72 + 9 * q^73 - 2 * q^74 + 7 * q^75 + 6 * q^76 - 15 * q^77 - 7 * q^78 + 31 * q^79 + 8 * q^80 + 16 * q^81 - 25 * q^82 - q^83 - 7 * q^84 - 4 * q^85 + 15 * q^86 + 30 * q^87 - 15 * q^88 + 45 * q^89 - 41 * q^90 + 7 * q^91 + 3 * q^92 + 25 * q^93 - 35 * q^94 - 10 * q^95 - 7 * q^96 - 9 * q^97 - 24 * q^98 + 64 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−0.920246	−0.531304	−0.265652	−	0.964069i	$-0.585587\pi$
$3$	−0.920246	−0.531304	−0.265652	+	0.964069i	$0.585587\pi$
$4$	1.00000	0.500000
$5$	2.96551	1.32622	0.663109	−	0.748523i	$-0.269237\pi$
$5$	2.96551	1.32622	0.663109	+	0.748523i	$0.269237\pi$
$6$	0.920246	0.375689
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	−2.15315	−0.717716
$10$	−2.96551	−0.937778
$11$	−3.73387	−1.12580	−0.562902	−	0.826523i	$-0.690315\pi$
$11$	−3.73387	−1.12580	−0.562902	+	0.826523i	$0.690315\pi$
$12$	−0.920246	−0.265652
$13$	−4.18929	−1.16190	−0.580950	−	0.813939i	$-0.697319\pi$
$13$	−4.18929	−1.16190	−0.580950	+	0.813939i	$0.697319\pi$
$14$	1.00000	0.267261
$15$	−2.72900	−0.704625
$16$	1.00000	0.250000
$17$	5.64502	1.36912	0.684559	−	0.728958i	$-0.259995\pi$
$17$	5.64502	1.36912	0.684559	+	0.728958i	$0.259995\pi$
$18$	2.15315	0.507502
$19$	1.59892	0.366817	0.183408	−	0.983037i	$-0.441287\pi$
$19$	1.59892	0.366817	0.183408	+	0.983037i	$0.441287\pi$
$20$	2.96551	0.663109
$21$	0.920246	0.200814
$22$	3.73387	0.796064
$23$	4.99189	1.04088	0.520441	−	0.853898i	$-0.325768\pi$
$23$	4.99189	1.04088	0.520441	+	0.853898i	$0.325768\pi$
$24$	0.920246	0.187844
$25$	3.79427	0.758854
$26$	4.18929	0.821588
$27$	4.74216	0.912630
$28$	−1.00000	−0.188982
$29$	−0.281679	−0.0523066	−0.0261533	−	0.999658i	$-0.508326\pi$
$29$	−0.281679	−0.0523066	−0.0261533	+	0.999658i	$0.508326\pi$
$30$	2.72900	0.498245
$31$	−0.595843	−0.107017	−0.0535083	−	0.998567i	$-0.517040\pi$
$31$	−0.595843	−0.107017	−0.0535083	+	0.998567i	$0.517040\pi$
$32$	−1.00000	−0.176777
$33$	3.43608	0.598145
$34$	−5.64502	−0.968112
$35$	−2.96551	−0.501263
$36$	−2.15315	−0.358858
$37$	−1.75109	−0.287878	−0.143939	−	0.989587i	$-0.545977\pi$
$37$	−1.75109	−0.287878	−0.143939	+	0.989587i	$0.545977\pi$
$38$	−1.59892	−0.259379
$39$	3.85518	0.617323
$40$	−2.96551	−0.468889
$41$	1.43359	0.223889	0.111945	−	0.993714i	$-0.464292\pi$
$41$	1.43359	0.223889	0.111945	+	0.993714i	$0.464292\pi$
$42$	−0.920246	−0.141997
$43$	7.07586	1.07906	0.539529	−	0.841967i	$-0.318602\pi$
$43$	7.07586	1.07906	0.539529	+	0.841967i	$0.318602\pi$
$44$	−3.73387	−0.562902
$45$	−6.38519	−0.951848
$46$	−4.99189	−0.736014
$47$	−8.92805	−1.30229	−0.651145	−	0.758953i	$-0.725711\pi$
$47$	−8.92805	−1.30229	−0.651145	+	0.758953i	$0.725711\pi$
$48$	−0.920246	−0.132826
$49$	1.00000	0.142857
$50$	−3.79427	−0.536591
$51$	−5.19480	−0.727418
$52$	−4.18929	−0.580950
$53$	−10.7665	−1.47889	−0.739447	−	0.673214i	$-0.764913\pi$
$53$	−10.7665	−1.47889	−0.739447	+	0.673214i	$0.764913\pi$
$54$	−4.74216	−0.645327
$55$	−11.0729	−1.49306
$56$	1.00000	0.133631
$57$	−1.47140	−0.194891
$58$	0.281679	0.0369863
$59$	2.59695	0.338094	0.169047	−	0.985608i	$-0.445931\pi$
$59$	2.59695	0.338094	0.169047	+	0.985608i	$0.445931\pi$
$60$	−2.72900	−0.352313
$61$	−11.3867	−1.45792	−0.728960	−	0.684556i	$-0.759996\pi$
$61$	−11.3867	−1.45792	−0.728960	+	0.684556i	$0.759996\pi$
$62$	0.595843	0.0756721
$63$	2.15315	0.271271
$64$	1.00000	0.125000
$65$	−12.4234	−1.54093
$66$	−3.43608	−0.422952
$67$	−0.827398	−0.101083	−0.0505414	−	0.998722i	$-0.516095\pi$
$67$	−0.827398	−0.101083	−0.0505414	+	0.998722i	$0.516095\pi$
$68$	5.64502	0.684559
$69$	−4.59377	−0.553025
$70$	2.96551	0.354447
$71$	−8.62062	−1.02308	−0.511540	−	0.859260i	$-0.670925\pi$
$71$	−8.62062	−1.02308	−0.511540	+	0.859260i	$0.670925\pi$
$72$	2.15315	0.253751
$73$	0.950530	0.111251	0.0556256	−	0.998452i	$-0.482285\pi$
$73$	0.950530	0.111251	0.0556256	+	0.998452i	$0.482285\pi$
$74$	1.75109	0.203561
$75$	−3.49166	−0.403182
$76$	1.59892	0.183408
$77$	3.73387	0.425514
$78$	−3.85518	−0.436513
$79$	13.6713	1.53814	0.769070	−	0.639165i	$-0.220720\pi$
$79$	13.6713	1.53814	0.769070	+	0.639165i	$0.220720\pi$
$80$	2.96551	0.331555
$81$	2.09549	0.232832
$82$	−1.43359	−0.158314
$83$	10.7904	1.18440	0.592199	−	0.805792i	$-0.298260\pi$
$83$	10.7904	1.18440	0.592199	+	0.805792i	$0.298260\pi$
$84$	0.920246	0.100407
$85$	16.7404	1.81575
$86$	−7.07586	−0.763009
$87$	0.259214	0.0277907
$88$	3.73387	0.398032
$89$	−5.53491	−0.586699	−0.293350	−	0.956005i	$-0.594770\pi$
$89$	−5.53491	−0.586699	−0.293350	+	0.956005i	$0.594770\pi$
$90$	6.38519	0.673058
$91$	4.18929	0.439157
$92$	4.99189	0.520441
$93$	0.548322	0.0568583
$94$	8.92805	0.920858
$95$	4.74161	0.486479
$96$	0.920246	0.0939222
$97$	4.82510	0.489914	0.244957	−	0.969534i	$-0.421226\pi$
$97$	4.82510	0.489914	0.244957	+	0.969534i	$0.421226\pi$
$98$	−1.00000	−0.101015
$99$	8.03958	0.808008
$100$	3.79427	0.379427
$101$	11.0551	1.10002	0.550010	−	0.835158i	$-0.314624\pi$
$101$	11.0551	1.10002	0.550010	+	0.835158i	$0.314624\pi$
$102$	5.19480	0.514362
$103$	14.8392	1.46215	0.731075	−	0.682297i	$-0.239019\pi$
$103$	14.8392	1.46215	0.731075	+	0.682297i	$0.239019\pi$
$104$	4.18929	0.410794
$105$	2.72900	0.266323
$106$	10.7665	1.04574
$107$	−5.78284	−0.559048	−0.279524	−	0.960139i	$-0.590177\pi$
$107$	−5.78284	−0.559048	−0.279524	+	0.960139i	$0.590177\pi$
$108$	4.74216	0.456315
$109$	−1.51331	−0.144949	−0.0724744	−	0.997370i	$-0.523090\pi$
$109$	−1.51331	−0.144949	−0.0724744	+	0.997370i	$0.523090\pi$
$110$	11.0729	1.05575
$111$	1.61144	0.152951
$112$	−1.00000	−0.0944911
$113$	3.08038	0.289777	0.144889	−	0.989448i	$-0.453718\pi$
$113$	3.08038	0.289777	0.144889	+	0.989448i	$0.453718\pi$
$114$	1.47140	0.137809
$115$	14.8035	1.38044
$116$	−0.281679	−0.0261533
$117$	9.02016	0.833914
$118$	−2.59695	−0.239069
$119$	−5.64502	−0.517478
$120$	2.72900	0.249123
$121$	2.94181	0.267437
$122$	11.3867	1.03091
$123$	−1.31926	−0.118953
$124$	−0.595843	−0.0535083
$125$	−3.57561	−0.319812
$126$	−2.15315	−0.191818
$127$	−0.225215	−0.0199846	−0.00999231	−	0.999950i	$-0.503181\pi$
$127$	−0.225215	−0.0199846	−0.00999231	+	0.999950i	$0.503181\pi$
$128$	−1.00000	−0.0883883
$129$	−6.51153	−0.573308
$130$	12.4234	1.08960
$131$	−12.8742	−1.12483	−0.562413	−	0.826857i	$-0.690127\pi$
$131$	−12.8742	−1.12483	−0.562413	+	0.826857i	$0.690127\pi$
$132$	3.43608	0.299072
$133$	−1.59892	−0.138644
$134$	0.827398	0.0714763
$135$	14.0629	1.21035
$136$	−5.64502	−0.484056
$137$	−11.8084	−1.00886	−0.504429	−	0.863453i	$-0.668297\pi$
$137$	−11.8084	−1.00886	−0.504429	+	0.863453i	$0.668297\pi$
$138$	4.59377	0.391048
$139$	−3.68604	−0.312646	−0.156323	−	0.987706i	$-0.549964\pi$
$139$	−3.68604	−0.312646	−0.156323	+	0.987706i	$0.549964\pi$
$140$	−2.96551	−0.250632
$141$	8.21601	0.691912
$142$	8.62062	0.723426
$143$	15.6423	1.30807
$144$	−2.15315	−0.179429
$145$	−0.835324	−0.0693699
$146$	−0.950530	−0.0786664
$147$	−0.920246	−0.0759006
$148$	−1.75109	−0.143939
$149$	3.42446	0.280543	0.140271	−	0.990113i	$-0.455202\pi$
$149$	3.42446	0.280543	0.140271	+	0.990113i	$0.455202\pi$
$150$	3.49166	0.285093
$151$	21.8871	1.78115	0.890575	−	0.454837i	$-0.150303\pi$
$151$	21.8871	1.78115	0.890575	+	0.454837i	$0.150303\pi$
$152$	−1.59892	−0.129689
$153$	−12.1546	−0.982637
$154$	−3.73387	−0.300884
$155$	−1.76698	−0.141927
$156$	3.85518	0.308661
$157$	2.80024	0.223484	0.111742	−	0.993737i	$-0.464357\pi$
$157$	2.80024	0.223484	0.111742	+	0.993737i	$0.464357\pi$
$158$	−13.6713	−1.08763
$159$	9.90784	0.785743
$160$	−2.96551	−0.234444
$161$	−4.99189	−0.393416
$162$	−2.09549	−0.164637
$163$	5.01493	0.392800	0.196400	−	0.980524i	$-0.437075\pi$
$163$	5.01493	0.392800	0.196400	+	0.980524i	$0.437075\pi$
$164$	1.43359	0.111945
$165$	10.1897	0.793271
$166$	−10.7904	−0.837495
$167$	4.31481	0.333890	0.166945	−	0.985966i	$-0.446610\pi$
$167$	4.31481	0.333890	0.166945	+	0.985966i	$0.446610\pi$
$168$	−0.920246	−0.0709985
$169$	4.55016	0.350012
$170$	−16.7404	−1.28393
$171$	−3.44270	−0.263270
$172$	7.07586	0.539529
$173$	9.90231	0.752858	0.376429	−	0.926445i	$-0.377152\pi$
$173$	9.90231	0.752858	0.376429	+	0.926445i	$0.377152\pi$
$174$	−0.259214	−0.0196510
$175$	−3.79427	−0.286820
$176$	−3.73387	−0.281451
$177$	−2.38983	−0.179631
$178$	5.53491	0.414859
$179$	17.3323	1.29548	0.647740	−	0.761861i	$-0.275714\pi$
$179$	17.3323	1.29548	0.647740	+	0.761861i	$0.275714\pi$
$180$	−6.38519	−0.475924
$181$	0.496174	0.0368803	0.0184402	−	0.999830i	$-0.494130\pi$
$181$	0.496174	0.0368803	0.0184402	+	0.999830i	$0.494130\pi$
$182$	−4.18929	−0.310531
$183$	10.4786	0.774599
$184$	−4.99189	−0.368007
$185$	−5.19290	−0.381789
$186$	−0.548322	−0.0402049
$187$	−21.0778	−1.54136
$188$	−8.92805	−0.651145
$189$	−4.74216	−0.344942
$190$	−4.74161	−0.343993
$191$	12.9619	0.937890	0.468945	−	0.883227i	$-0.344634\pi$
$191$	12.9619	0.937890	0.468945	+	0.883227i	$0.344634\pi$
$192$	−0.920246	−0.0664130
$193$	16.1898	1.16537	0.582685	−	0.812698i	$-0.302002\pi$
$193$	16.1898	1.16537	0.582685	+	0.812698i	$0.302002\pi$
$194$	−4.82510	−0.346422
$195$	11.4326	0.818704
$196$	1.00000	0.0714286
$197$	19.3336	1.37746	0.688731	−	0.725017i	$-0.258168\pi$
$197$	19.3336	1.37746	0.688731	+	0.725017i	$0.258168\pi$
$198$	−8.03958	−0.571348
$199$	−4.28872	−0.304019	−0.152010	−	0.988379i	$-0.548574\pi$
$199$	−4.28872	−0.304019	−0.152010	+	0.988379i	$0.548574\pi$
$200$	−3.79427	−0.268295
$201$	0.761410	0.0537057
$202$	−11.0551	−0.777832
$203$	0.281679	0.0197700
$204$	−5.19480	−0.363709
$205$	4.25133	0.296926
$206$	−14.8392	−1.03390
$207$	−10.7483	−0.747057
$208$	−4.18929	−0.290475
$209$	−5.97015	−0.412964
$210$	−2.72900	−0.188319
$211$	13.5601	0.933518	0.466759	−	0.884384i	$-0.345421\pi$
$211$	13.5601	0.933518	0.466759	+	0.884384i	$0.345421\pi$
$212$	−10.7665	−0.739447
$213$	7.93309	0.543566
$214$	5.78284	0.395307
$215$	20.9835	1.43107
$216$	−4.74216	−0.322663
$217$	0.595843	0.0404484
$218$	1.51331	0.102494
$219$	−0.874721	−0.0591082
$220$	−11.0729	−0.746531
$221$	−23.6486	−1.59078
$222$	−1.61144	−0.108153
$223$	12.1396	0.812926	0.406463	−	0.913667i	$-0.366762\pi$
$223$	12.1396	0.812926	0.406463	+	0.913667i	$0.366762\pi$
$224$	1.00000	0.0668153
$225$	−8.16963	−0.544642
$226$	−3.08038	−0.204904
$227$	13.9190	0.923840	0.461920	−	0.886922i	$-0.347161\pi$
$227$	13.9190	0.923840	0.461920	+	0.886922i	$0.347161\pi$
$228$	−1.47140	−0.0974456
$229$	−12.5004	−0.826048	−0.413024	−	0.910720i	$-0.635527\pi$
$229$	−12.5004	−0.826048	−0.413024	+	0.910720i	$0.635527\pi$
$230$	−14.8035	−0.976116
$231$	−3.43608	−0.226078
$232$	0.281679	0.0184932
$233$	−0.392089	−0.0256866	−0.0128433	−	0.999918i	$-0.504088\pi$
$233$	−0.392089	−0.0256866	−0.0128433	+	0.999918i	$0.504088\pi$
$234$	−9.02016	−0.589666
$235$	−26.4763	−1.72712
$236$	2.59695	0.169047
$237$	−12.5809	−0.817220
$238$	5.64502	0.365912
$239$	17.1919	1.11205	0.556026	−	0.831165i	$-0.312325\pi$
$239$	17.1919	1.11205	0.556026	+	0.831165i	$0.312325\pi$
$240$	−2.72900	−0.176156
$241$	−5.92629	−0.381746	−0.190873	−	0.981615i	$-0.561132\pi$
$241$	−5.92629	−0.381746	−0.190873	+	0.981615i	$0.561132\pi$
$242$	−2.94181	−0.189106
$243$	−16.1549	−1.03633
$244$	−11.3867	−0.728960
$245$	2.96551	0.189460
$246$	1.31926	0.0841127
$247$	−6.69833	−0.426204
$248$	0.595843	0.0378361
$249$	−9.92980	−0.629275
$250$	3.57561	0.226141
$251$	26.0565	1.64467	0.822336	−	0.569002i	$-0.192670\pi$
$251$	26.0565	1.64467	0.822336	+	0.569002i	$0.192670\pi$
$252$	2.15315	0.135636
$253$	−18.6391	−1.17183
$254$	0.225215	0.0141313
$255$	−15.4053	−0.964715
$256$	1.00000	0.0625000
$257$	−7.88491	−0.491847	−0.245923	−	0.969289i	$-0.579091\pi$
$257$	−7.88491	−0.491847	−0.245923	+	0.969289i	$0.579091\pi$
$258$	6.51153	0.405390
$259$	1.75109	0.108808
$260$	−12.4234	−0.770467
$261$	0.606497	0.0375412
$262$	12.8742	0.795371
$263$	3.97875	0.245340	0.122670	−	0.992447i	$-0.460854\pi$
$263$	3.97875	0.245340	0.122670	+	0.992447i	$0.460854\pi$
$264$	−3.43608	−0.211476
$265$	−31.9283	−1.96134
$266$	1.59892	0.0980359
$267$	5.09348	0.311716
$268$	−0.827398	−0.0505414
$269$	−7.78372	−0.474582	−0.237291	−	0.971439i	$-0.576259\pi$
$269$	−7.78372	−0.474582	−0.237291	+	0.971439i	$0.576259\pi$
$270$	−14.0629	−0.855844
$271$	13.3878	0.813254	0.406627	−	0.913594i	$-0.366705\pi$
$271$	13.3878	0.813254	0.406627	+	0.913594i	$0.366705\pi$
$272$	5.64502	0.342279
$273$	−3.85518	−0.233326
$274$	11.8084	0.713371
$275$	−14.1673	−0.854322
$276$	−4.59377	−0.276512
$277$	15.3841	0.924344	0.462172	−	0.886790i	$-0.347070\pi$
$277$	15.3841	0.924344	0.462172	+	0.886790i	$0.347070\pi$
$278$	3.68604	0.221074
$279$	1.28294	0.0768075
$280$	2.96551	0.177223
$281$	23.8750	1.42427	0.712133	−	0.702045i	$-0.247729\pi$
$281$	23.8750	1.42427	0.712133	+	0.702045i	$0.247729\pi$
$282$	−8.21601	−0.489256
$283$	−25.3162	−1.50489	−0.752445	−	0.658656i	$-0.771125\pi$
$283$	−25.3162	−1.50489	−0.752445	+	0.658656i	$0.771125\pi$
$284$	−8.62062	−0.511540
$285$	−4.36345	−0.258468
$286$	−15.6423	−0.924947
$287$	−1.43359	−0.0846222
$288$	2.15315	0.126875
$289$	14.8662	0.874483
$290$	0.835324	0.0490519
$291$	−4.44027	−0.260293
$292$	0.950530	0.0556256
$293$	−9.72297	−0.568022	−0.284011	−	0.958821i	$-0.591665\pi$
$293$	−9.72297	−0.568022	−0.284011	+	0.958821i	$0.591665\pi$
$294$	0.920246	0.0536698
$295$	7.70129	0.448387
$296$	1.75109	0.101780
$297$	−17.7066	−1.02744
$298$	−3.42446	−0.198374
$299$	−20.9125	−1.20940
$300$	−3.49166	−0.201591
$301$	−7.07586	−0.407846
$302$	−21.8871	−1.25946
$303$	−10.1734	−0.584446
$304$	1.59892	0.0917042
$305$	−33.7675	−1.93352
$306$	12.1546	0.694829
$307$	−16.3176	−0.931295	−0.465648	−	0.884970i	$-0.654179\pi$
$307$	−16.3176	−0.931295	−0.465648	+	0.884970i	$0.654179\pi$
$308$	3.73387	0.212757
$309$	−13.6557	−0.776846
$310$	1.76698	0.100358
$311$	30.4396	1.72607	0.863035	−	0.505144i	$-0.168561\pi$
$311$	30.4396	1.72607	0.863035	+	0.505144i	$0.168561\pi$
$312$	−3.85518	−0.218256
$313$	3.79828	0.214691	0.107346	−	0.994222i	$-0.465765\pi$
$313$	3.79828	0.214691	0.107346	+	0.994222i	$0.465765\pi$
$314$	−2.80024	−0.158027
$315$	6.38519	0.359765
$316$	13.6713	0.769070
$317$	31.4929	1.76882	0.884408	−	0.466715i	$-0.154563\pi$
$317$	31.4929	1.76882	0.884408	+	0.466715i	$0.154563\pi$
$318$	−9.90784	−0.555604
$319$	1.05176	0.0588870
$320$	2.96551	0.165777
$321$	5.32164	0.297025
$322$	4.99189	0.278187
$323$	9.02591	0.502215
$324$	2.09549	0.116416
$325$	−15.8953	−0.881713
$326$	−5.01493	−0.277751
$327$	1.39262	0.0770119
$328$	−1.43359	−0.0791568
$329$	8.92805	0.492220
$330$	−10.1897	−0.560927
$331$	17.6665	0.971041	0.485520	−	0.874225i	$-0.338630\pi$
$331$	17.6665	0.971041	0.485520	+	0.874225i	$0.338630\pi$
$332$	10.7904	0.592199
$333$	3.77037	0.206615
$334$	−4.31481	−0.236096
$335$	−2.45366	−0.134058
$336$	0.920246	0.0502035
$337$	34.6562	1.88785	0.943923	−	0.330166i	$-0.107105\pi$
$337$	34.6562	1.88785	0.943923	+	0.330166i	$0.107105\pi$
$338$	−4.55016	−0.247496
$339$	−2.83470	−0.153960
$340$	16.7404	0.907874
$341$	2.22480	0.120480
$342$	3.44270	0.186160
$343$	−1.00000	−0.0539949
$344$	−7.07586	−0.381505
$345$	−13.6229	−0.733431
$346$	−9.90231	−0.532351
$347$	−33.2148	−1.78306	−0.891532	−	0.452959i	$-0.850369\pi$
$347$	−33.2148	−1.78306	−0.891532	+	0.452959i	$0.850369\pi$
$348$	0.259214	0.0138953
$349$	7.55703	0.404518	0.202259	−	0.979332i	$-0.435172\pi$
$349$	7.55703	0.404518	0.202259	+	0.979332i	$0.435172\pi$
$350$	3.79427	0.202812
$351$	−19.8663	−1.06038
$352$	3.73387	0.199016
$353$	−15.2892	−0.813760	−0.406880	−	0.913482i	$-0.633383\pi$
$353$	−15.2892	−0.813760	−0.406880	+	0.913482i	$0.633383\pi$
$354$	2.38983	0.127018
$355$	−25.5646	−1.35683
$356$	−5.53491	−0.293350
$357$	5.19480	0.274938
$358$	−17.3323	−0.916043
$359$	6.70872	0.354073	0.177036	−	0.984204i	$-0.443349\pi$
$359$	6.70872	0.354073	0.177036	+	0.984204i	$0.443349\pi$
$360$	6.38519	0.336529
$361$	−16.4435	−0.865446
$362$	−0.496174	−0.0260783
$363$	−2.70718	−0.142090
$364$	4.18929	0.219579
$365$	2.81881	0.147543
$366$	−10.4786	−0.547724
$367$	14.1782	0.740094	0.370047	−	0.929013i	$-0.379342\pi$
$367$	14.1782	0.740094	0.370047	+	0.929013i	$0.379342\pi$
$368$	4.99189	0.260220
$369$	−3.08673	−0.160689
$370$	5.19290	0.269966
$371$	10.7665	0.558970
$372$	0.548322	0.0284292
$373$	−9.62992	−0.498618	−0.249309	−	0.968424i	$-0.580204\pi$
$373$	−9.62992	−0.498618	−0.249309	+	0.968424i	$0.580204\pi$
$374$	21.0778	1.08991
$375$	3.29044	0.169917
$376$	8.92805	0.460429
$377$	1.18004	0.0607750
$378$	4.74216	0.243911
$379$	0.704386	0.0361819	0.0180909	−	0.999836i	$-0.494241\pi$
$379$	0.704386	0.0361819	0.0180909	+	0.999836i	$0.494241\pi$
$380$	4.74161	0.243239
$381$	0.207253	0.0106179
$382$	−12.9619	−0.663188
$383$	11.5952	0.592489	0.296245	−	0.955112i	$-0.404266\pi$
$383$	11.5952	0.592489	0.296245	+	0.955112i	$0.404266\pi$
$384$	0.920246	0.0469611
$385$	11.0729	0.564325
$386$	−16.1898	−0.824040
$387$	−15.2354	−0.774457
$388$	4.82510	0.244957
$389$	−4.89619	−0.248247	−0.124123	−	0.992267i	$-0.539612\pi$
$389$	−4.89619	−0.248247	−0.124123	+	0.992267i	$0.539612\pi$
$390$	−11.4326	−0.578911
$391$	28.1793	1.42509
$392$	−1.00000	−0.0505076
$393$	11.8474	0.597624
$394$	−19.3336	−0.974013
$395$	40.5424	2.03991
$396$	8.03958	0.404004
$397$	23.3345	1.17112	0.585562	−	0.810627i	$-0.300874\pi$
$397$	23.3345	1.17112	0.585562	+	0.810627i	$0.300874\pi$
$398$	4.28872	0.214974
$399$	1.47140	0.0736620
$400$	3.79427	0.189714
$401$	24.8657	1.24173	0.620866	−	0.783917i	$-0.286781\pi$
$401$	24.8657	1.24173	0.620866	+	0.783917i	$0.286781\pi$
$402$	−0.761410	−0.0379757
$403$	2.49616	0.124343
$404$	11.0551	0.550010
$405$	6.21419	0.308786
$406$	−0.281679	−0.0139795
$407$	6.53837	0.324095
$408$	5.19480	0.257181
$409$	0.240956	0.0119145	0.00595726	−	0.999982i	$-0.498104\pi$
$409$	0.240956	0.0119145	0.00595726	+	0.999982i	$0.498104\pi$
$410$	−4.25133	−0.209958
$411$	10.8666	0.536011
$412$	14.8392	0.731075
$413$	−2.59695	−0.127788
$414$	10.7483	0.528249
$415$	31.9990	1.57077
$416$	4.18929	0.205397
$417$	3.39207	0.166110
$418$	5.97015	0.292010
$419$	6.22872	0.304293	0.152146	−	0.988358i	$-0.451381\pi$
$419$	6.22872	0.304293	0.152146	+	0.988358i	$0.451381\pi$
$420$	2.72900	0.133162
$421$	2.28185	0.111210	0.0556052	−	0.998453i	$-0.482291\pi$
$421$	2.28185	0.111210	0.0556052	+	0.998453i	$0.482291\pi$
$422$	−13.5601	−0.660097
$423$	19.2234	0.934674
$424$	10.7665	0.522868
$425$	21.4187	1.03896
$426$	−7.93309	−0.384360
$427$	11.3867	0.551042
$428$	−5.78284	−0.279524
$429$	−14.3947	−0.694985
$430$	−20.9835	−1.01192
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	4.74216	0.228157
$433$	−7.69716	−0.369902	−0.184951	−	0.982748i	$-0.559213\pi$
$433$	−7.69716	−0.369902	−0.184951	+	0.982748i	$0.559213\pi$
$434$	−0.595843	−0.0286014
$435$	0.768704	0.0368565
$436$	−1.51331	−0.0724744
$437$	7.98162	0.381813
$438$	0.874721	0.0417958
$439$	15.6183	0.745420	0.372710	−	0.927948i	$-0.378429\pi$
$439$	15.6183	0.745420	0.372710	+	0.927948i	$0.378429\pi$
$440$	11.0729	0.527877
$441$	−2.15315	−0.102531
$442$	23.6486	1.12485
$443$	21.4825	1.02067	0.510333	−	0.859977i	$-0.329522\pi$
$443$	21.4825	1.02067	0.510333	+	0.859977i	$0.329522\pi$
$444$	1.61144	0.0764755
$445$	−16.4139	−0.778091
$446$	−12.1396	−0.574825
$447$	−3.15135	−0.149054
$448$	−1.00000	−0.0472456
$449$	5.15008	0.243047	0.121524	−	0.992589i	$-0.461222\pi$
$449$	5.15008	0.243047	0.121524	+	0.992589i	$0.461222\pi$
$450$	8.16963	0.385120
$451$	−5.35285	−0.252056
$452$	3.08038	0.144889
$453$	−20.1415	−0.946332
$454$	−13.9190	−0.653253
$455$	12.4234	0.582418
$456$	1.47140	0.0689045
$457$	−24.1714	−1.13069	−0.565346	−	0.824854i	$-0.691257\pi$
$457$	−24.1714	−1.13069	−0.565346	+	0.824854i	$0.691257\pi$
$458$	12.5004	0.584104
$459$	26.7696	1.24950
$460$	14.8035	0.690218
$461$	−19.9699	−0.930090	−0.465045	−	0.885287i	$-0.653962\pi$
$461$	−19.9699	−0.930090	−0.465045	+	0.885287i	$0.653962\pi$
$462$	3.43608	0.159861
$463$	24.5172	1.13941	0.569706	−	0.821849i	$-0.307057\pi$
$463$	24.5172	1.13941	0.569706	+	0.821849i	$0.307057\pi$
$464$	−0.281679	−0.0130766
$465$	1.62606	0.0754065
$466$	0.392089	0.0181632
$467$	4.73023	0.218889	0.109444	−	0.993993i	$-0.465093\pi$
$467$	4.73023	0.218889	0.109444	+	0.993993i	$0.465093\pi$
$468$	9.02016	0.416957
$469$	0.827398	0.0382057
$470$	26.4763	1.22126
$471$	−2.57691	−0.118738
$472$	−2.59695	−0.119534
$473$	−26.4203	−1.21481
$474$	12.5809	0.577862
$475$	6.06672	0.278360
$476$	−5.64502	−0.258739
$477$	23.1819	1.06143
$478$	−17.1919	−0.786340
$479$	−15.6484	−0.714993	−0.357497	−	0.933914i	$-0.616370\pi$
$479$	−15.6484	−0.714993	−0.357497	+	0.933914i	$0.616370\pi$
$480$	2.72900	0.124561
$481$	7.33585	0.334486
$482$	5.92629	0.269935
$483$	4.59377	0.209024
$484$	2.94181	0.133718
$485$	14.3089	0.649733
$486$	16.1549	0.732799
$487$	−35.3945	−1.60388	−0.801939	−	0.597406i	$-0.796198\pi$
$487$	−35.3945	−1.60388	−0.801939	+	0.597406i	$0.796198\pi$
$488$	11.3867	0.515453
$489$	−4.61497	−0.208696
$490$	−2.96551	−0.133968
$491$	12.5717	0.567354	0.283677	−	0.958920i	$-0.408446\pi$
$491$	12.5717	0.567354	0.283677	+	0.958920i	$0.408446\pi$
$492$	−1.31926	−0.0594767
$493$	−1.59009	−0.0716138
$494$	6.69833	0.301372
$495$	23.8415	1.07159
$496$	−0.595843	−0.0267541
$497$	8.62062	0.386688
$498$	9.92980	0.444965
$499$	−23.1265	−1.03529	−0.517643	−	0.855597i	$-0.673190\pi$
$499$	−23.1265	−1.03529	−0.517643	+	0.855597i	$0.673190\pi$
$500$	−3.57561	−0.159906
$501$	−3.97069	−0.177397
$502$	−26.0565	−1.16296
$503$	−9.56311	−0.426398	−0.213199	−	0.977009i	$-0.568388\pi$
$503$	−9.56311	−0.426398	−0.213199	+	0.977009i	$0.568388\pi$
$504$	−2.15315	−0.0959088
$505$	32.7840	1.45887
$506$	18.6391	0.828609
$507$	−4.18726	−0.185963
$508$	−0.225215	−0.00999231
$509$	−7.03707	−0.311912	−0.155956	−	0.987764i	$-0.549846\pi$
$509$	−7.03707	−0.311912	−0.155956	+	0.987764i	$0.549846\pi$
$510$	15.4053	0.682156
$511$	−0.950530	−0.0420490
$512$	−1.00000	−0.0441942
$513$	7.58232	0.334768
$514$	7.88491	0.347788
$515$	44.0059	1.93913
$516$	−6.51153	−0.286654
$517$	33.3362	1.46613
$518$	−1.75109	−0.0769387
$519$	−9.11256	−0.399997
$520$	12.4234	0.544802
$521$	28.7774	1.26076	0.630380	−	0.776286i	$-0.282899\pi$
$521$	28.7774	1.26076	0.630380	+	0.776286i	$0.282899\pi$
$522$	−0.606497	−0.0265457
$523$	−9.00158	−0.393612	−0.196806	−	0.980442i	$-0.563057\pi$
$523$	−9.00158	−0.393612	−0.196806	+	0.980442i	$0.563057\pi$
$524$	−12.8742	−0.562413
$525$	3.49166	0.152389
$526$	−3.97875	−0.173482
$527$	−3.36354	−0.146518
$528$	3.43608	0.149536
$529$	1.91900	0.0834346
$530$	31.9283	1.38687
$531$	−5.59162	−0.242656
$532$	−1.59892	−0.0693218
$533$	−6.00573	−0.260137
$534$	−5.09348	−0.220416
$535$	−17.1491	−0.741420
$536$	0.827398	0.0357382
$537$	−15.9500	−0.688294
$538$	7.78372	0.335580
$539$	−3.73387	−0.160829
$540$	14.0629	0.605173
$541$	0.811603	0.0348935	0.0174468	−	0.999848i	$-0.494446\pi$
$541$	0.811603	0.0348935	0.0174468	+	0.999848i	$0.494446\pi$
$542$	−13.3878	−0.575057
$543$	−0.456602	−0.0195947
$544$	−5.64502	−0.242028
$545$	−4.48774	−0.192234
$546$	3.85518	0.164986
$547$	4.85868	0.207742	0.103871	−	0.994591i	$-0.466877\pi$
$547$	4.85868	0.207742	0.103871	+	0.994591i	$0.466877\pi$
$548$	−11.8084	−0.504429
$549$	24.5173	1.04637
$550$	14.1673	0.604097
$551$	−0.450382	−0.0191869
$552$	4.59377	0.195524
$553$	−13.6713	−0.581362
$554$	−15.3841	−0.653610
$555$	4.77874	0.202846
$556$	−3.68604	−0.156323
$557$	−42.9449	−1.81964	−0.909818	−	0.415008i	$-0.863779\pi$
$557$	−42.9449	−1.81964	−0.909818	+	0.415008i	$0.863779\pi$
$558$	−1.28294	−0.0543111
$559$	−29.6428	−1.25376
$560$	−2.96551	−0.125316
$561$	19.3967	0.818931
$562$	−23.8750	−1.00711
$563$	−17.0067	−0.716747	−0.358374	−	0.933578i	$-0.616669\pi$
$563$	−17.0067	−0.716747	−0.358374	+	0.933578i	$0.616669\pi$
$564$	8.21601	0.345956
$565$	9.13490	0.384308
$566$	25.3162	1.06412
$567$	−2.09549	−0.0880021
$568$	8.62062	0.361713
$569$	33.9507	1.42329	0.711644	−	0.702540i	$-0.247951\pi$
$569$	33.9507	1.42329	0.711644	+	0.702540i	$0.247951\pi$
$570$	4.36345	0.182765
$571$	−11.3356	−0.474378	−0.237189	−	0.971464i	$-0.576226\pi$
$571$	−11.3356	−0.474378	−0.237189	+	0.971464i	$0.576226\pi$
$572$	15.6423	0.654037
$573$	−11.9281	−0.498305
$574$	1.43359	0.0598369
$575$	18.9406	0.789877
$576$	−2.15315	−0.0897145
$577$	25.9991	1.08236	0.541179	−	0.840908i	$-0.317978\pi$
$577$	25.9991	1.08236	0.541179	+	0.840908i	$0.317978\pi$
$578$	−14.8662	−0.618353
$579$	−14.8986	−0.619166
$580$	−0.835324	−0.0346850
$581$	−10.7904	−0.447660
$582$	4.44027	0.184055
$583$	40.2008	1.66495
$584$	−0.950530	−0.0393332
$585$	26.7494	1.10595
$586$	9.72297	0.401652
$587$	32.4335	1.33867	0.669336	−	0.742960i	$-0.266579\pi$
$587$	32.4335	1.33867	0.669336	+	0.742960i	$0.266579\pi$
$588$	−0.920246	−0.0379503
$589$	−0.952703	−0.0392554
$590$	−7.70129	−0.317057
$591$	−17.7917	−0.731852
$592$	−1.75109	−0.0719696
$593$	8.70949	0.357656	0.178828	−	0.983880i	$-0.442769\pi$
$593$	8.70949	0.357656	0.178828	+	0.983880i	$0.442769\pi$
$594$	17.7066	0.726512
$595$	−16.7404	−0.686288
$596$	3.42446	0.140271
$597$	3.94668	0.161527
$598$	20.9125	0.855175
$599$	−30.4873	−1.24568	−0.622838	−	0.782351i	$-0.714021\pi$
$599$	−30.4873	−1.24568	−0.622838	+	0.782351i	$0.714021\pi$
$600$	3.49166	0.142547
$601$	−33.5614	−1.36900	−0.684499	−	0.729014i	$-0.739979\pi$
$601$	−33.5614	−1.36900	−0.684499	+	0.729014i	$0.739979\pi$
$602$	7.07586	0.288390
$603$	1.78151	0.0725487
$604$	21.8871	0.890575
$605$	8.72397	0.354680
$606$	10.1734	0.413265
$607$	23.0581	0.935898	0.467949	−	0.883756i	$-0.344993\pi$
$607$	23.0581	0.935898	0.467949	+	0.883756i	$0.344993\pi$
$608$	−1.59892	−0.0648446
$609$	−0.259214	−0.0105039
$610$	33.7675	1.36721
$611$	37.4022	1.51313
$612$	−12.1546	−0.491319
$613$	5.78694	0.233732	0.116866	−	0.993148i	$-0.462715\pi$
$613$	5.78694	0.233732	0.116866	+	0.993148i	$0.462715\pi$
$614$	16.3176	0.658525
$615$	−3.91227	−0.157758
$616$	−3.73387	−0.150442
$617$	7.82002	0.314822	0.157411	−	0.987533i	$-0.449685\pi$
$617$	7.82002	0.314822	0.157411	+	0.987533i	$0.449685\pi$
$618$	13.6557	0.549313
$619$	−38.0806	−1.53059	−0.765294	−	0.643681i	$-0.777407\pi$
$619$	−38.0806	−1.53059	−0.765294	+	0.643681i	$0.777407\pi$
$620$	−1.76698	−0.0709636
$621$	23.6724	0.949939
$622$	−30.4396	−1.22052
$623$	5.53491	0.221752
$624$	3.85518	0.154331
$625$	−29.5749	−1.18299
$626$	−3.79828	−0.151810
$627$	5.49401	0.219410
$628$	2.80024	0.111742
$629$	−9.88496	−0.394139
$630$	−6.38519	−0.254392
$631$	42.7598	1.70224	0.851121	−	0.524969i	$-0.175923\pi$
$631$	42.7598	1.70224	0.851121	+	0.524969i	$0.175923\pi$
$632$	−13.6713	−0.543815
$633$	−12.4787	−0.495982
$634$	−31.4929	−1.25074
$635$	−0.667879	−0.0265040
$636$	9.90784	0.392872
$637$	−4.18929	−0.165986
$638$	−1.05176	−0.0416394
$639$	18.5615	0.734280
$640$	−2.96551	−0.117222
$641$	−8.44630	−0.333609	−0.166804	−	0.985990i	$-0.553345\pi$
$641$	−8.44630	−0.333609	−0.166804	+	0.985990i	$0.553345\pi$
$642$	−5.32164	−0.210028
$643$	20.1993	0.796584	0.398292	−	0.917259i	$-0.369603\pi$
$643$	20.1993	0.796584	0.398292	+	0.917259i	$0.369603\pi$
$644$	−4.99189	−0.196708
$645$	−19.3100	−0.760332
$646$	−9.02591	−0.355120
$647$	18.1854	0.714943	0.357471	−	0.933924i	$-0.383639\pi$
$647$	18.1854	0.714943	0.357471	+	0.933924i	$0.383639\pi$
$648$	−2.09549	−0.0823185
$649$	−9.69668	−0.380628
$650$	15.8953	0.623465
$651$	−0.548322	−0.0214904
$652$	5.01493	0.196400
$653$	−19.3459	−0.757063	−0.378531	−	0.925588i	$-0.623571\pi$
$653$	−19.3459	−0.757063	−0.378531	+	0.925588i	$0.623571\pi$
$654$	−1.39262	−0.0544556
$655$	−38.1787	−1.49176
$656$	1.43359	0.0559723
$657$	−2.04663	−0.0798467
$658$	−8.92805	−0.348052
$659$	28.1137	1.09515	0.547576	−	0.836756i	$-0.315551\pi$
$659$	28.1137	1.09515	0.547576	+	0.836756i	$0.315551\pi$
$660$	10.1897	0.396635
$661$	33.8790	1.31774	0.658870	−	0.752256i	$-0.271035\pi$
$661$	33.8790	1.31774	0.658870	+	0.752256i	$0.271035\pi$
$662$	−17.6665	−0.686630
$663$	21.7625	0.845187
$664$	−10.7904	−0.418748
$665$	−4.74161	−0.183872
$666$	−3.77037	−0.146099
$667$	−1.40611	−0.0544449
$668$	4.31481	0.166945
$669$	−11.1714	−0.431911
$670$	2.45366	0.0947932
$671$	42.5166	1.64133
$672$	−0.920246	−0.0354993
$673$	−43.9445	−1.69394	−0.846969	−	0.531643i	$-0.821575\pi$
$673$	−43.9445	−1.69394	−0.846969	+	0.531643i	$0.821575\pi$
$674$	−34.6562	−1.33491
$675$	17.9931	0.692553
$676$	4.55016	0.175006
$677$	−29.0469	−1.11636	−0.558182	−	0.829718i	$-0.688501\pi$
$677$	−29.0469	−1.11636	−0.558182	+	0.829718i	$0.688501\pi$
$678$	2.83470	0.108866
$679$	−4.82510	−0.185170
$680$	−16.7404	−0.641964
$681$	−12.8089	−0.490840
$682$	−2.22480	−0.0851920
$683$	−4.86375	−0.186106	−0.0930531	−	0.995661i	$-0.529663\pi$
$683$	−4.86375	−0.186106	−0.0930531	+	0.995661i	$0.529663\pi$
$684$	−3.44270	−0.131635
$685$	−35.0179	−1.33797
$686$	1.00000	0.0381802
$687$	11.5034	0.438883
$688$	7.07586	0.269765
$689$	45.1041	1.71833
$690$	13.6229	0.518614
$691$	22.6241	0.860660	0.430330	−	0.902672i	$-0.358397\pi$
$691$	22.6241	0.860660	0.430330	+	0.902672i	$0.358397\pi$
$692$	9.90231	0.376429
$693$	−8.03958	−0.305398
$694$	33.2148	1.26082
$695$	−10.9310	−0.414637
$696$	−0.259214	−0.00982550
$697$	8.09265	0.306531
$698$	−7.55703	−0.286038
$699$	0.360819	0.0136474
$700$	−3.79427	−0.143410
$701$	−21.4443	−0.809939	−0.404969	−	0.914330i	$-0.632718\pi$
$701$	−21.4443	−0.809939	−0.404969	+	0.914330i	$0.632718\pi$
$702$	19.8663	0.749805
$703$	−2.79986	−0.105599
$704$	−3.73387	−0.140726
$705$	24.3647	0.917627
$706$	15.2892	0.575415
$707$	−11.0551	−0.415769
$708$	−2.38983	−0.0898154
$709$	36.4867	1.37029	0.685143	−	0.728408i	$-0.259740\pi$
$709$	36.4867	1.37029	0.685143	+	0.728408i	$0.259740\pi$
$710$	25.5646	0.959421
$711$	−29.4363	−1.10395
$712$	5.53491	0.207430
$713$	−2.97438	−0.111392
$714$	−5.19480	−0.194411
$715$	46.3874	1.73479
$716$	17.3323	0.647740
$717$	−15.8208	−0.590838
$718$	−6.70872	−0.250367
$719$	20.5648	0.766938	0.383469	−	0.923554i	$-0.374729\pi$
$719$	20.5648	0.766938	0.383469	+	0.923554i	$0.374729\pi$
$720$	−6.38519	−0.237962
$721$	−14.8392	−0.552641
$722$	16.4435	0.611962
$723$	5.45365	0.202823
$724$	0.496174	0.0184402
$725$	−1.06877	−0.0396931
$726$	2.70718	0.100473
$727$	3.06023	0.113497	0.0567487	−	0.998388i	$-0.481927\pi$
$727$	3.06023	0.113497	0.0567487	+	0.998388i	$0.481927\pi$
$728$	−4.18929	−0.155265
$729$	8.57998	0.317777
$730$	−2.81881	−0.104329
$731$	39.9433	1.47736
$732$	10.4786	0.387300
$733$	2.35676	0.0870491	0.0435245	−	0.999052i	$-0.486141\pi$
$733$	2.35676	0.0870491	0.0435245	+	0.999052i	$0.486141\pi$
$734$	−14.1782	−0.523326
$735$	−2.72900	−0.100661
$736$	−4.99189	−0.184004
$737$	3.08940	0.113799
$738$	3.08673	0.113624
$739$	−34.2481	−1.25984	−0.629918	−	0.776661i	$-0.716912\pi$
$739$	−34.2481	−1.25984	−0.629918	+	0.776661i	$0.716912\pi$
$740$	−5.19290	−0.190895
$741$	6.16411	0.226444
$742$	−10.7665	−0.395251
$743$	−26.3559	−0.966903	−0.483452	−	0.875371i	$-0.660617\pi$
$743$	−26.3559	−0.966903	−0.483452	+	0.875371i	$0.660617\pi$
$744$	−0.548322	−0.0201025
$745$	10.1553	0.372061
$746$	9.62992	0.352576
$747$	−23.2333	−0.850061
$748$	−21.0778	−0.770680
$749$	5.78284	0.211300
$750$	−3.29044	−0.120150
$751$	10.4102	0.379874	0.189937	−	0.981796i	$-0.439172\pi$
$751$	10.4102	0.379874	0.189937	+	0.981796i	$0.439172\pi$
$752$	−8.92805	−0.325573
$753$	−23.9784	−0.873821
$754$	−1.18004	−0.0429744
$755$	64.9066	2.36219
$756$	−4.74216	−0.172471
$757$	−11.1410	−0.404928	−0.202464	−	0.979290i	$-0.564895\pi$
$757$	−11.1410	−0.404928	−0.202464	+	0.979290i	$0.564895\pi$
$758$	−0.704386	−0.0255844
$759$	17.1525	0.622598
$760$	−4.74161	−0.171996
$761$	27.5200	0.997598	0.498799	−	0.866718i	$-0.333775\pi$
$761$	27.5200	0.997598	0.498799	+	0.866718i	$0.333775\pi$
$762$	−0.207253	−0.00750800
$763$	1.51331	0.0547855
$764$	12.9619	0.468945
$765$	−36.0445	−1.30319
$766$	−11.5952	−0.418953
$767$	−10.8794	−0.392832
$768$	−0.920246	−0.0332065
$769$	1.61368	0.0581907	0.0290953	−	0.999577i	$-0.490737\pi$
$769$	1.61368	0.0581907	0.0290953	+	0.999577i	$0.490737\pi$
$770$	−11.0729	−0.399038
$771$	7.25605	0.261320
$772$	16.1898	0.582685
$773$	23.5910	0.848510	0.424255	−	0.905543i	$-0.360536\pi$
$773$	23.5910	0.848510	0.424255	+	0.905543i	$0.360536\pi$
$774$	15.2354	0.547624
$775$	−2.26079	−0.0812099
$776$	−4.82510	−0.173211
$777$	−1.61144	−0.0578100
$778$	4.89619	0.175537
$779$	2.29219	0.0821263
$780$	11.4326	0.409352
$781$	32.1883	1.15179
$782$	−28.1793	−1.00769
$783$	−1.33577	−0.0477365
$784$	1.00000	0.0357143
$785$	8.30416	0.296388
$786$	−11.8474	−0.422584
$787$	−11.4838	−0.409353	−0.204676	−	0.978830i	$-0.565614\pi$
$787$	−11.4838	−0.409353	−0.204676	+	0.978830i	$0.565614\pi$
$788$	19.3336	0.688731
$789$	−3.66143	−0.130350
$790$	−40.5424	−1.44243
$791$	−3.08038	−0.109526
$792$	−8.03958	−0.285674
$793$	47.7023	1.69396
$794$	−23.3345	−0.828110
$795$	29.3818	1.04207
$796$	−4.28872	−0.152010
$797$	−13.7209	−0.486019	−0.243009	−	0.970024i	$-0.578135\pi$
$797$	−13.7209	−0.486019	−0.243009	+	0.970024i	$0.578135\pi$
$798$	−1.47140	−0.0520869
$799$	−50.3990	−1.78299
$800$	−3.79427	−0.134148
$801$	11.9175	0.421083
$802$	−24.8657	−0.878037
$803$	−3.54916	−0.125247
$804$	0.761410	0.0268528
$805$	−14.8035	−0.521756
$806$	−2.49616	−0.0879234
$807$	7.16293	0.252147
$808$	−11.0551	−0.388916
$809$	−13.7223	−0.482450	−0.241225	−	0.970469i	$-0.577549\pi$
$809$	−13.7223	−0.482450	−0.241225	+	0.970469i	$0.577549\pi$
$810$	−6.21419	−0.218344
$811$	11.5696	0.406265	0.203132	−	0.979151i	$-0.434888\pi$
$811$	11.5696	0.406265	0.203132	+	0.979151i	$0.434888\pi$
$812$	0.281679	0.00988501
$813$	−12.3201	−0.432085
$814$	−6.53837	−0.229170
$815$	14.8719	0.520938
$816$	−5.19480	−0.181854
$817$	11.3137	0.395817
$818$	−0.240956	−0.00842484
$819$	−9.02016	−0.315190
$820$	4.25133	0.148463
$821$	13.9858	0.488107	0.244054	−	0.969762i	$-0.421523\pi$
$821$	13.9858	0.488107	0.244054	+	0.969762i	$0.421523\pi$
$822$	−10.8666	−0.379017
$823$	−19.1504	−0.667542	−0.333771	−	0.942654i	$-0.608321\pi$
$823$	−19.1504	−0.667542	−0.333771	+	0.942654i	$0.608321\pi$
$824$	−14.8392	−0.516948
$825$	13.0374	0.453905
$826$	2.59695	0.0903595
$827$	49.3630	1.71652	0.858259	−	0.513216i	$-0.171546\pi$
$827$	49.3630	1.71652	0.858259	+	0.513216i	$0.171546\pi$
$828$	−10.7483	−0.373529
$829$	−2.76014	−0.0958635	−0.0479318	−	0.998851i	$-0.515263\pi$
$829$	−2.76014	−0.0958635	−0.0479318	+	0.998851i	$0.515263\pi$
$830$	−31.9990	−1.11070
$831$	−14.1572	−0.491108
$832$	−4.18929	−0.145238
$833$	5.64502	0.195588
$834$	−3.39207	−0.117458
$835$	12.7956	0.442811
$836$	−5.97015	−0.206482
$837$	−2.82558	−0.0976665
$838$	−6.22872	−0.215168
$839$	11.1669	0.385524	0.192762	−	0.981246i	$-0.438255\pi$
$839$	11.1669	0.385524	0.192762	+	0.981246i	$0.438255\pi$
$840$	−2.72900	−0.0941595
$841$	−28.9207	−0.997264
$842$	−2.28185	−0.0786376
$843$	−21.9709	−0.756718
$844$	13.5601	0.466759
$845$	13.4936	0.464192
$846$	−19.2234	−0.660915
$847$	−2.94181	−0.101082
$848$	−10.7665	−0.369724
$849$	23.2971	0.799554
$850$	−21.4187	−0.734656
$851$	−8.74128	−0.299647
$852$	7.93309	0.271783
$853$	−52.3890	−1.79376	−0.896882	−	0.442270i	$-0.854173\pi$
$853$	−52.3890	−1.79376	−0.896882	+	0.442270i	$0.854173\pi$
$854$	−11.3867	−0.389646
$855$	−10.2094	−0.349154
$856$	5.78284	0.197653
$857$	−0.850670	−0.0290583	−0.0145292	−	0.999894i	$-0.504625\pi$
$857$	−0.850670	−0.0290583	−0.0145292	+	0.999894i	$0.504625\pi$
$858$	14.3947	0.491428
$859$	−1.82823	−0.0623785	−0.0311892	−	0.999513i	$-0.509929\pi$
$859$	−1.82823	−0.0623785	−0.0311892	+	0.999513i	$0.509929\pi$
$860$	20.9835	0.715533
$861$	1.31926	0.0449601
$862$	−1.00000	−0.0340601
$863$	17.4958	0.595563	0.297782	−	0.954634i	$-0.403753\pi$
$863$	17.4958	0.595563	0.297782	+	0.954634i	$0.403753\pi$
$864$	−4.74216	−0.161332
$865$	29.3654	0.998455
$866$	7.69716	0.261560
$867$	−13.6806	−0.464616
$868$	0.595843	0.0202242
$869$	−51.0468	−1.73165
$870$	−0.768704	−0.0260615
$871$	3.46621	0.117448
$872$	1.51331	0.0512471
$873$	−10.3891	−0.351619
$874$	−7.98162	−0.269982
$875$	3.57561	0.120878
$876$	−0.874721	−0.0295541
$877$	−15.9725	−0.539354	−0.269677	−	0.962951i	$-0.586917\pi$
$877$	−15.9725	−0.539354	−0.269677	+	0.962951i	$0.586917\pi$
$878$	−15.6183	−0.527091
$879$	8.94752	0.301792
$880$	−11.0729	−0.373266
$881$	−7.31983	−0.246611	−0.123306	−	0.992369i	$-0.539350\pi$
$881$	−7.31983	−0.246611	−0.123306	+	0.992369i	$0.539350\pi$
$882$	2.15315	0.0725002
$883$	−41.2582	−1.38845	−0.694224	−	0.719759i	$-0.744252\pi$
$883$	−41.2582	−1.38845	−0.694224	+	0.719759i	$0.744252\pi$
$884$	−23.6486	−0.795389
$885$	−7.08708	−0.238230
$886$	−21.4825	−0.721720
$887$	−38.7293	−1.30040	−0.650202	−	0.759762i	$-0.725316\pi$
$887$	−38.7293	−1.30040	−0.650202	+	0.759762i	$0.725316\pi$
$888$	−1.61144	−0.0540763
$889$	0.225215	0.00755348
$890$	16.4139	0.550194
$891$	−7.82428	−0.262123
$892$	12.1396	0.406463
$893$	−14.2752	−0.477702
$894$	3.15135	0.105397
$895$	51.3993	1.71809
$896$	1.00000	0.0334077
$897$	19.2446	0.642560
$898$	−5.15008	−0.171860
$899$	0.167837	0.00559767
$900$	−8.16963	−0.272321
$901$	−60.7772	−2.02478
$902$	5.35285	0.178230
$903$	6.51153	0.216690
$904$	−3.08038	−0.102452
$905$	1.47141	0.0489113
$906$	20.1415	0.669158
$907$	3.54657	0.117762	0.0588810	−	0.998265i	$-0.481247\pi$
$907$	3.54657	0.117762	0.0588810	+	0.998265i	$0.481247\pi$
$908$	13.9190	0.461920
$909$	−23.8032	−0.789502
$910$	−12.4234	−0.411832
$911$	−13.1576	−0.435932	−0.217966	−	0.975956i	$-0.569942\pi$
$911$	−13.1576	−0.435932	−0.217966	+	0.975956i	$0.569942\pi$
$912$	−1.47140	−0.0487228
$913$	−40.2899	−1.33340
$914$	24.1714	0.799520
$915$	31.0744	1.02729
$916$	−12.5004	−0.413024
$917$	12.8742	0.425144
$918$	−26.7696	−0.883528
$919$	−24.0443	−0.793147	−0.396573	−	0.918003i	$-0.629801\pi$
$919$	−24.0443	−0.793147	−0.396573	+	0.918003i	$0.629801\pi$
$920$	−14.8035	−0.488058
$921$	15.0162	0.494801
$922$	19.9699	0.657673
$923$	36.1143	1.18872
$924$	−3.43608	−0.113039
$925$	−6.64413	−0.218458
$926$	−24.5172	−0.805686
$927$	−31.9510	−1.04941
$928$	0.281679	0.00924658
$929$	−9.38922	−0.308050	−0.154025	−	0.988067i	$-0.549224\pi$
$929$	−9.38922	−0.308050	−0.154025	+	0.988067i	$0.549224\pi$
$930$	−1.62606	−0.0533205
$931$	1.59892	0.0524024
$932$	−0.392089	−0.0128433
$933$	−28.0119	−0.917068
$934$	−4.73023	−0.154778
$935$	−62.5064	−2.04418
$936$	−9.02016	−0.294833
$937$	−22.4978	−0.734970	−0.367485	−	0.930030i	$-0.619781\pi$
$937$	−22.4978	−0.734970	−0.367485	+	0.930030i	$0.619781\pi$
$938$	−0.827398	−0.0270155
$939$	−3.49535	−0.114066
$940$	−26.4763	−0.863561
$941$	30.5767	0.996773	0.498386	−	0.866955i	$-0.333926\pi$
$941$	30.5767	0.996773	0.498386	+	0.866955i	$0.333926\pi$
$942$	2.57691	0.0839603
$943$	7.15633	0.233042
$944$	2.59695	0.0845235
$945$	−14.0629	−0.457468
$946$	26.4203	0.859000
$947$	−20.0129	−0.650331	−0.325166	−	0.945657i	$-0.605420\pi$
$947$	−20.0129	−0.650331	−0.325166	+	0.945657i	$0.605420\pi$
$948$	−12.5809	−0.408610
$949$	−3.98205	−0.129263
$950$	−6.06672	−0.196831
$951$	−28.9812	−0.939779
$952$	5.64502	0.182956
$953$	22.3561	0.724184	0.362092	−	0.932142i	$-0.382063\pi$
$953$	22.3561	0.724184	0.362092	+	0.932142i	$0.382063\pi$
$954$	−23.1819	−0.750542
$955$	38.4387	1.24385
$956$	17.1919	0.556026
$957$	−0.967874	−0.0312869
$958$	15.6484	0.505577
$959$	11.8084	0.381313
$960$	−2.72900	−0.0880782
$961$	−30.6450	−0.988547
$962$	−7.33585	−0.236517
$963$	12.4513	0.401238
$964$	−5.92629	−0.190873
$965$	48.0111	1.54553
$966$	−4.59377	−0.147802
$967$	−7.43118	−0.238971	−0.119485	−	0.992836i	$-0.538124\pi$
$967$	−7.43118	−0.238971	−0.119485	+	0.992836i	$0.538124\pi$
$968$	−2.94181	−0.0945532
$969$	−8.30606	−0.266829
$970$	−14.3089	−0.459431
$971$	14.4503	0.463731	0.231866	−	0.972748i	$-0.425517\pi$
$971$	14.4503	0.463731	0.231866	+	0.972748i	$0.425517\pi$
$972$	−16.1549	−0.518167
$973$	3.68604	0.118169
$974$	35.3945	1.13411
$975$	14.6276	0.468458
$976$	−11.3867	−0.364480
$977$	28.9904	0.927486	0.463743	−	0.885970i	$-0.346506\pi$
$977$	28.9904	0.927486	0.463743	+	0.885970i	$0.346506\pi$
$978$	4.61497	0.147571
$979$	20.6667	0.660509
$980$	2.96551	0.0947299
$981$	3.25838	0.104032
$982$	−12.5717	−0.401180
$983$	6.71003	0.214017	0.107008	−	0.994258i	$-0.465873\pi$
$983$	6.71003	0.214017	0.107008	+	0.994258i	$0.465873\pi$
$984$	1.31926	0.0420564
$985$	57.3341	1.82682
$986$	1.59009	0.0506386
$987$	−8.21601	−0.261518
$988$	−6.69833	−0.213102
$989$	35.3219	1.12317
$990$	−23.8415	−0.757732
$991$	−39.6410	−1.25924	−0.629619	−	0.776904i	$-0.716789\pi$
$991$	−39.6410	−1.25924	−0.629619	+	0.776904i	$0.716789\pi$
$992$	0.595843	0.0189180
$993$	−16.2576	−0.515918
$994$	−8.62062	−0.273430
$995$	−12.7183	−0.403196
$996$	−9.92980	−0.314638
$997$	−11.2595	−0.356592	−0.178296	−	0.983977i	$-0.557058\pi$
$997$	−11.2595	−0.356592	−0.178296	+	0.983977i	$0.557058\pi$
$998$	23.1265	0.732057
$999$	−8.30398	−0.262726

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.n.1.8	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.n.1.8	✓	24	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.920246 q^{3} +1.00000 q^{4} +2.96551 q^{5} +0.920246 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.15315 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.920246 q^{3} +1.00000 q^{4} +2.96551 q^{5} +0.920246 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.15315 q^{9} -2.96551 q^{10} -3.73387 q^{11} -0.920246 q^{12} -4.18929 q^{13} +1.00000 q^{14} -2.72900 q^{15} +1.00000 q^{16} +5.64502 q^{17} +2.15315 q^{18} +1.59892 q^{19} +2.96551 q^{20} +0.920246 q^{21} +3.73387 q^{22} +4.99189 q^{23} +0.920246 q^{24} +3.79427 q^{25} +4.18929 q^{26} +4.74216 q^{27} -1.00000 q^{28} -0.281679 q^{29} +2.72900 q^{30} -0.595843 q^{31} -1.00000 q^{32} +3.43608 q^{33} -5.64502 q^{34} -2.96551 q^{35} -2.15315 q^{36} -1.75109 q^{37} -1.59892 q^{38} +3.85518 q^{39} -2.96551 q^{40} +1.43359 q^{41} -0.920246 q^{42} +7.07586 q^{43} -3.73387 q^{44} -6.38519 q^{45} -4.99189 q^{46} -8.92805 q^{47} -0.920246 q^{48} +1.00000 q^{49} -3.79427 q^{50} -5.19480 q^{51} -4.18929 q^{52} -10.7665 q^{53} -4.74216 q^{54} -11.0729 q^{55} +1.00000 q^{56} -1.47140 q^{57} +0.281679 q^{58} +2.59695 q^{59} -2.72900 q^{60} -11.3867 q^{61} +0.595843 q^{62} +2.15315 q^{63} +1.00000 q^{64} -12.4234 q^{65} -3.43608 q^{66} -0.827398 q^{67} +5.64502 q^{68} -4.59377 q^{69} +2.96551 q^{70} -8.62062 q^{71} +2.15315 q^{72} +0.950530 q^{73} +1.75109 q^{74} -3.49166 q^{75} +1.59892 q^{76} +3.73387 q^{77} -3.85518 q^{78} +13.6713 q^{79} +2.96551 q^{80} +2.09549 q^{81} -1.43359 q^{82} +10.7904 q^{83} +0.920246 q^{84} +16.7404 q^{85} -7.07586 q^{86} +0.259214 q^{87} +3.73387 q^{88} -5.53491 q^{89} +6.38519 q^{90} +4.18929 q^{91} +4.99189 q^{92} +0.548322 q^{93} +8.92805 q^{94} +4.74161 q^{95} +0.920246 q^{96} +4.82510 q^{97} -1.00000 q^{98} +8.03958 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9}+O(q^{10}) \) 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9	\( 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9} - 8 q^{10} + 15 q^{11} + 7 q^{12} - 7 q^{13} + 24 q^{14} + 13 q^{15} + 24 q^{16} - 5 q^{17} - 19 q^{18} + 6 q^{19} + 8 q^{20} - 7 q^{21} - 15 q^{22} + 3 q^{23} - 7 q^{24} + 12 q^{25} + 7 q^{26} + 22 q^{27} - 24 q^{28} + 5 q^{29} - 13 q^{30} + 13 q^{31} - 24 q^{32} - 8 q^{33} + 5 q^{34} - 8 q^{35} + 19 q^{36} + 2 q^{37} - 6 q^{38} + 7 q^{39} - 8 q^{40} + 25 q^{41} + 7 q^{42} - 15 q^{43} + 15 q^{44} + 41 q^{45} - 3 q^{46} + 35 q^{47} + 7 q^{48} + 24 q^{49} - 12 q^{50} + 31 q^{51} - 7 q^{52} + 2 q^{53} - 22 q^{54} + 14 q^{55} + 24 q^{56} - 13 q^{57} - 5 q^{58} + 35 q^{59} + 13 q^{60} - 7 q^{61} - 13 q^{62} - 19 q^{63} + 24 q^{64} - 4 q^{65} + 8 q^{66} + 10 q^{67} - 5 q^{68} + 6 q^{69} + 8 q^{70} + 58 q^{71} - 19 q^{72} + 9 q^{73} - 2 q^{74} + 7 q^{75} + 6 q^{76} - 15 q^{77} - 7 q^{78} + 31 q^{79} + 8 q^{80} + 16 q^{81} - 25 q^{82} - q^{83} - 7 q^{84} - 4 q^{85} + 15 q^{86} + 30 q^{87} - 15 q^{88} + 45 q^{89} - 41 q^{90} + 7 q^{91} + 3 q^{92} + 25 q^{93} - 35 q^{94} - 10 q^{95} - 7 q^{96} - 9 q^{97} - 24 q^{98} + 64 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9 - 8 * q^10 + 15 * q^11 + 7 * q^12 - 7 * q^13 + 24 * q^14 + 13 * q^15 + 24 * q^16 - 5 * q^17 - 19 * q^18 + 6 * q^19 + 8 * q^20 - 7 * q^21 - 15 * q^22 + 3 * q^23 - 7 * q^24 + 12 * q^25 + 7 * q^26 + 22 * q^27 - 24 * q^28 + 5 * q^29 - 13 * q^30 + 13 * q^31 - 24 * q^32 - 8 * q^33 + 5 * q^34 - 8 * q^35 + 19 * q^36 + 2 * q^37 - 6 * q^38 + 7 * q^39 - 8 * q^40 + 25 * q^41 + 7 * q^42 - 15 * q^43 + 15 * q^44 + 41 * q^45 - 3 * q^46 + 35 * q^47 + 7 * q^48 + 24 * q^49 - 12 * q^50 + 31 * q^51 - 7 * q^52 + 2 * q^53 - 22 * q^54 + 14 * q^55 + 24 * q^56 - 13 * q^57 - 5 * q^58 + 35 * q^59 + 13 * q^60 - 7 * q^61 - 13 * q^62 - 19 * q^63 + 24 * q^64 - 4 * q^65 + 8 * q^66 + 10 * q^67 - 5 * q^68 + 6 * q^69 + 8 * q^70 + 58 * q^71 - 19 * q^72 + 9 * q^73 - 2 * q^74 + 7 * q^75 + 6 * q^76 - 15 * q^77 - 7 * q^78 + 31 * q^79 + 8 * q^80 + 16 * q^81 - 25 * q^82 - q^83 - 7 * q^84 - 4 * q^85 + 15 * q^86 + 30 * q^87 - 15 * q^88 + 45 * q^89 - 41 * q^90 + 7 * q^91 + 3 * q^92 + 25 * q^93 - 35 * q^94 - 10 * q^95 - 7 * q^96 - 9 * q^97 - 24 * q^98 + 64 * q^99

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