LMFDB - Embedded newform 6002.2.a.c.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6002,2,Mod(1,6002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6002, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6002 = 2 \cdot 3001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6002.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:	$47.9262112932$
Analytic rank:	$0$
Dimension:	$69$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	6002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.29088 q^{3} +1.00000 q^{4} +2.54707 q^{5} +2.29088 q^{6} +4.39407 q^{7} -1.00000 q^{8} +2.24813 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.29088 q^{3} +1.00000 q^{4} +2.54707 q^{5} +2.29088 q^{6} +4.39407 q^{7} -1.00000 q^{8} +2.24813 q^{9} -2.54707 q^{10} -2.27231 q^{11} -2.29088 q^{12} +4.31854 q^{13} -4.39407 q^{14} -5.83502 q^{15} +1.00000 q^{16} -4.05210 q^{17} -2.24813 q^{18} +0.428446 q^{19} +2.54707 q^{20} -10.0663 q^{21} +2.27231 q^{22} -2.43932 q^{23} +2.29088 q^{24} +1.48754 q^{25} -4.31854 q^{26} +1.72245 q^{27} +4.39407 q^{28} -6.34012 q^{29} +5.83502 q^{30} -5.50772 q^{31} -1.00000 q^{32} +5.20558 q^{33} +4.05210 q^{34} +11.1920 q^{35} +2.24813 q^{36} -7.84885 q^{37} -0.428446 q^{38} -9.89324 q^{39} -2.54707 q^{40} +0.720227 q^{41} +10.0663 q^{42} +0.149014 q^{43} -2.27231 q^{44} +5.72613 q^{45} +2.43932 q^{46} +6.22749 q^{47} -2.29088 q^{48} +12.3079 q^{49} -1.48754 q^{50} +9.28288 q^{51} +4.31854 q^{52} -0.586944 q^{53} -1.72245 q^{54} -5.78771 q^{55} -4.39407 q^{56} -0.981518 q^{57} +6.34012 q^{58} +7.04607 q^{59} -5.83502 q^{60} +9.20473 q^{61} +5.50772 q^{62} +9.87843 q^{63} +1.00000 q^{64} +10.9996 q^{65} -5.20558 q^{66} +4.47892 q^{67} -4.05210 q^{68} +5.58819 q^{69} -11.1920 q^{70} +1.38597 q^{71} -2.24813 q^{72} +7.58850 q^{73} +7.84885 q^{74} -3.40778 q^{75} +0.428446 q^{76} -9.98468 q^{77} +9.89324 q^{78} +16.2556 q^{79} +2.54707 q^{80} -10.6903 q^{81} -0.720227 q^{82} -8.28928 q^{83} -10.0663 q^{84} -10.3210 q^{85} -0.149014 q^{86} +14.5244 q^{87} +2.27231 q^{88} +11.0556 q^{89} -5.72613 q^{90} +18.9760 q^{91} -2.43932 q^{92} +12.6175 q^{93} -6.22749 q^{94} +1.09128 q^{95} +2.29088 q^{96} -8.77266 q^{97} -12.3079 q^{98} -5.10843 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 69 q - 69 q^{2} + 11 q^{3} + 69 q^{4} - 2 q^{5} - 11 q^{6} + 23 q^{7} - 69 q^{8} + 72 q^{9}+O(q^{10}) $ 69 * q - 69 * q^2 + 11 * q^3 + 69 * q^4 - 2 * q^5 - 11 * q^6 + 23 * q^7 - 69 * q^8 + 72 * q^9	\( 69 q - 69 q^{2} + 11 q^{3} + 69 q^{4} - 2 q^{5} - 11 q^{6} + 23 q^{7} - 69 q^{8} + 72 q^{9} + 2 q^{10} - 14 q^{11} + 11 q^{12} + 31 q^{13} - 23 q^{14} + 34 q^{15} + 69 q^{16} - 4 q^{17} - 72 q^{18} + 17 q^{19} - 2 q^{20} - 11 q^{21} + 14 q^{22} + 33 q^{23} - 11 q^{24} + 119 q^{25} - 31 q^{26} + 44 q^{27} + 23 q^{28} - 25 q^{29} - 34 q^{30} + 49 q^{31} - 69 q^{32} + 10 q^{33} + 4 q^{34} - 11 q^{35} + 72 q^{36} + 73 q^{37} - 17 q^{38} + 31 q^{39} + 2 q^{40} - 46 q^{41} + 11 q^{42} + 76 q^{43} - 14 q^{44} + 9 q^{45} - 33 q^{46} + 23 q^{47} + 11 q^{48} + 100 q^{49} - 119 q^{50} + 25 q^{51} + 31 q^{52} + 30 q^{53} - 44 q^{54} + 81 q^{55} - 23 q^{56} + 12 q^{57} + 25 q^{58} - 3 q^{59} + 34 q^{60} + 13 q^{61} - 49 q^{62} + 65 q^{63} + 69 q^{64} - 27 q^{65} - 10 q^{66} + 105 q^{67} - 4 q^{68} + 19 q^{69} + 11 q^{70} + 51 q^{71} - 72 q^{72} + 43 q^{73} - 73 q^{74} + 77 q^{75} + 17 q^{76} - 19 q^{77} - 31 q^{78} + 89 q^{79} - 2 q^{80} + 73 q^{81} + 46 q^{82} - 10 q^{83} - 11 q^{84} + 44 q^{85} - 76 q^{86} + 57 q^{87} + 14 q^{88} - 28 q^{89} - 9 q^{90} + 76 q^{91} + 33 q^{92} + 59 q^{93} - 23 q^{94} + 72 q^{95} - 11 q^{96} + 89 q^{97} - 100 q^{98} - 17 q^{99}+O(q^{100}) \) 69 * q - 69 * q^2 + 11 * q^3 + 69 * q^4 - 2 * q^5 - 11 * q^6 + 23 * q^7 - 69 * q^8 + 72 * q^9 + 2 * q^10 - 14 * q^11 + 11 * q^12 + 31 * q^13 - 23 * q^14 + 34 * q^15 + 69 * q^16 - 4 * q^17 - 72 * q^18 + 17 * q^19 - 2 * q^20 - 11 * q^21 + 14 * q^22 + 33 * q^23 - 11 * q^24 + 119 * q^25 - 31 * q^26 + 44 * q^27 + 23 * q^28 - 25 * q^29 - 34 * q^30 + 49 * q^31 - 69 * q^32 + 10 * q^33 + 4 * q^34 - 11 * q^35 + 72 * q^36 + 73 * q^37 - 17 * q^38 + 31 * q^39 + 2 * q^40 - 46 * q^41 + 11 * q^42 + 76 * q^43 - 14 * q^44 + 9 * q^45 - 33 * q^46 + 23 * q^47 + 11 * q^48 + 100 * q^49 - 119 * q^50 + 25 * q^51 + 31 * q^52 + 30 * q^53 - 44 * q^54 + 81 * q^55 - 23 * q^56 + 12 * q^57 + 25 * q^58 - 3 * q^59 + 34 * q^60 + 13 * q^61 - 49 * q^62 + 65 * q^63 + 69 * q^64 - 27 * q^65 - 10 * q^66 + 105 * q^67 - 4 * q^68 + 19 * q^69 + 11 * q^70 + 51 * q^71 - 72 * q^72 + 43 * q^73 - 73 * q^74 + 77 * q^75 + 17 * q^76 - 19 * q^77 - 31 * q^78 + 89 * q^79 - 2 * q^80 + 73 * q^81 + 46 * q^82 - 10 * q^83 - 11 * q^84 + 44 * q^85 - 76 * q^86 + 57 * q^87 + 14 * q^88 - 28 * q^89 - 9 * q^90 + 76 * q^91 + 33 * q^92 + 59 * q^93 - 23 * q^94 + 72 * q^95 - 11 * q^96 + 89 * q^97 - 100 * q^98 - 17 * 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
$3$	−2.29088	−1.32264	−0.661320	−	0.750104i	$-0.730003\pi$
$3$	−2.29088	−1.32264	−0.661320	+	0.750104i	$0.730003\pi$
$4$	1.00000	0.500000
$5$	2.54707	1.13908	0.569541	−	0.821963i	$-0.307121\pi$
$5$	2.54707	1.13908	0.569541	+	0.821963i	$0.307121\pi$
$6$	2.29088	0.935247
$7$	4.39407	1.66080	0.830402	−	0.557165i	$-0.188111\pi$
$7$	4.39407	1.66080	0.830402	+	0.557165i	$0.188111\pi$
$8$	−1.00000	−0.353553
$9$	2.24813	0.749376
$10$	−2.54707	−0.805453
$11$	−2.27231	−0.685126	−0.342563	−	0.939495i	$-0.611295\pi$
$11$	−2.27231	−0.685126	−0.342563	+	0.939495i	$0.611295\pi$
$12$	−2.29088	−0.661320
$13$	4.31854	1.19775	0.598873	−	0.800844i	$-0.295615\pi$
$13$	4.31854	1.19775	0.598873	+	0.800844i	$0.295615\pi$
$14$	−4.39407	−1.17437
$15$	−5.83502	−1.50660
$16$	1.00000	0.250000
$17$	−4.05210	−0.982780	−0.491390	−	0.870940i	$-0.663511\pi$
$17$	−4.05210	−0.982780	−0.491390	+	0.870940i	$0.663511\pi$
$18$	−2.24813	−0.529889
$19$	0.428446	0.0982923	0.0491461	−	0.998792i	$-0.484350\pi$
$19$	0.428446	0.0982923	0.0491461	+	0.998792i	$0.484350\pi$
$20$	2.54707	0.569541
$21$	−10.0663	−2.19664
$22$	2.27231	0.484457
$23$	−2.43932	−0.508634	−0.254317	−	0.967121i	$-0.581851\pi$
$23$	−2.43932	−0.508634	−0.254317	+	0.967121i	$0.581851\pi$
$24$	2.29088	0.467624
$25$	1.48754	0.297508
$26$	−4.31854	−0.846935
$27$	1.72245	0.331486
$28$	4.39407	0.830402
$29$	−6.34012	−1.17733	−0.588665	−	0.808377i	$-0.700346\pi$
$29$	−6.34012	−1.17733	−0.588665	+	0.808377i	$0.700346\pi$
$30$	5.83502	1.06532
$31$	−5.50772	−0.989216	−0.494608	−	0.869116i	$-0.664688\pi$
$31$	−5.50772	−0.989216	−0.494608	+	0.869116i	$0.664688\pi$
$32$	−1.00000	−0.176777
$33$	5.20558	0.906175
$34$	4.05210	0.694930
$35$	11.1920	1.89179
$36$	2.24813	0.374688
$37$	−7.84885	−1.29034	−0.645172	−	0.764038i	$-0.723214\pi$
$37$	−7.84885	−1.29034	−0.645172	+	0.764038i	$0.723214\pi$
$38$	−0.428446	−0.0695031
$39$	−9.89324	−1.58419
$40$	−2.54707	−0.402726
$41$	0.720227	0.112481	0.0562403	−	0.998417i	$-0.482089\pi$
$41$	0.720227	0.112481	0.0562403	+	0.998417i	$0.482089\pi$
$42$	10.0663	1.55326
$43$	0.149014	0.0227245	0.0113622	−	0.999935i	$-0.496383\pi$
$43$	0.149014	0.0227245	0.0113622	+	0.999935i	$0.496383\pi$
$44$	−2.27231	−0.342563
$45$	5.72613	0.853600
$46$	2.43932	0.359659
$47$	6.22749	0.908372	0.454186	−	0.890907i	$-0.349930\pi$
$47$	6.22749	0.908372	0.454186	+	0.890907i	$0.349930\pi$
$48$	−2.29088	−0.330660
$49$	12.3079	1.75827
$50$	−1.48754	−0.210370
$51$	9.28288	1.29986
$52$	4.31854	0.598873
$53$	−0.586944	−0.0806230	−0.0403115	−	0.999187i	$-0.512835\pi$
$53$	−0.586944	−0.0806230	−0.0403115	+	0.999187i	$0.512835\pi$
$54$	−1.72245	−0.234396
$55$	−5.78771	−0.780415
$56$	−4.39407	−0.587183
$57$	−0.981518	−0.130005
$58$	6.34012	0.832499
$59$	7.04607	0.917320	0.458660	−	0.888612i	$-0.348330\pi$
$59$	7.04607	0.917320	0.458660	+	0.888612i	$0.348330\pi$
$60$	−5.83502	−0.753298
$61$	9.20473	1.17855	0.589273	−	0.807934i	$-0.299414\pi$
$61$	9.20473	1.17855	0.589273	+	0.807934i	$0.299414\pi$
$62$	5.50772	0.699481
$63$	9.87843	1.24457
$64$	1.00000	0.125000
$65$	10.9996	1.36433
$66$	−5.20558	−0.640762
$67$	4.47892	0.547187	0.273593	−	0.961845i	$-0.411788\pi$
$67$	4.47892	0.547187	0.273593	+	0.961845i	$0.411788\pi$
$68$	−4.05210	−0.491390
$69$	5.58819	0.672740
$70$	−11.1920	−1.33770
$71$	1.38597	0.164484	0.0822421	−	0.996612i	$-0.473792\pi$
$71$	1.38597	0.164484	0.0822421	+	0.996612i	$0.473792\pi$
$72$	−2.24813	−0.264944
$73$	7.58850	0.888167	0.444084	−	0.895985i	$-0.353529\pi$
$73$	7.58850	0.888167	0.444084	+	0.895985i	$0.353529\pi$
$74$	7.84885	0.912411
$75$	−3.40778	−0.393496
$76$	0.428446	0.0491461
$77$	−9.98468	−1.13786
$78$	9.89324	1.12019
$79$	16.2556	1.82890	0.914449	−	0.404701i	$-0.132624\pi$
$79$	16.2556	1.82890	0.914449	+	0.404701i	$0.132624\pi$
$80$	2.54707	0.284771
$81$	−10.6903	−1.18781
$82$	−0.720227	−0.0795358
$83$	−8.28928	−0.909867	−0.454933	−	0.890526i	$-0.650337\pi$
$83$	−8.28928	−0.909867	−0.454933	+	0.890526i	$0.650337\pi$
$84$	−10.0663	−1.09832
$85$	−10.3210	−1.11947
$86$	−0.149014	−0.0160686
$87$	14.5244	1.55718
$88$	2.27231	0.242229
$89$	11.0556	1.17190	0.585948	−	0.810349i	$-0.300722\pi$
$89$	11.0556	1.17190	0.585948	+	0.810349i	$0.300722\pi$
$90$	−5.72613	−0.603587
$91$	18.9760	1.98922
$92$	−2.43932	−0.254317
$93$	12.6175	1.30838
$94$	−6.22749	−0.642316
$95$	1.09128	0.111963
$96$	2.29088	0.233812
$97$	−8.77266	−0.890729	−0.445364	−	0.895349i	$-0.646926\pi$
$97$	−8.77266	−0.890729	−0.445364	+	0.895349i	$0.646926\pi$
$98$	−12.3079	−1.24328
$99$	−5.10843	−0.513417
$100$	1.48754	0.148754
$101$	7.95661	0.791713	0.395856	−	0.918312i	$-0.370448\pi$
$101$	7.95661	0.791713	0.395856	+	0.918312i	$0.370448\pi$
$102$	−9.28288	−0.919142
$103$	0.913978	0.0900570	0.0450285	−	0.998986i	$-0.485662\pi$
$103$	0.913978	0.0900570	0.0450285	+	0.998986i	$0.485662\pi$
$104$	−4.31854	−0.423467
$105$	−25.6395	−2.50216
$106$	0.586944	0.0570091
$107$	−0.321413	−0.0310721	−0.0155361	−	0.999879i	$-0.504945\pi$
$107$	−0.321413	−0.0310721	−0.0155361	+	0.999879i	$0.504945\pi$
$108$	1.72245	0.165743
$109$	16.6429	1.59410	0.797050	−	0.603913i	$-0.206392\pi$
$109$	16.6429	1.59410	0.797050	+	0.603913i	$0.206392\pi$
$110$	5.78771	0.551837
$111$	17.9808	1.70666
$112$	4.39407	0.415201
$113$	0.476063	0.0447843	0.0223921	−	0.999749i	$-0.492872\pi$
$113$	0.476063	0.0447843	0.0223921	+	0.999749i	$0.492872\pi$
$114$	0.981518	0.0919276
$115$	−6.21312	−0.579376
$116$	−6.34012	−0.588665
$117$	9.70862	0.897562
$118$	−7.04607	−0.648643
$119$	−17.8052	−1.63220
$120$	5.83502	0.532662
$121$	−5.83663	−0.530602
$122$	−9.20473	−0.833357
$123$	−1.64995	−0.148771
$124$	−5.50772	−0.494608
$125$	−8.94646	−0.800196
$126$	−9.87843	−0.880041
$127$	18.6447	1.65445	0.827224	−	0.561872i	$-0.189919\pi$
$127$	18.6447	1.65445	0.827224	+	0.561872i	$0.189919\pi$
$128$	−1.00000	−0.0883883
$129$	−0.341374	−0.0300563
$130$	−10.9996	−0.964728
$131$	12.0996	1.05715	0.528575	−	0.848887i	$-0.322727\pi$
$131$	12.0996	1.05715	0.528575	+	0.848887i	$0.322727\pi$
$132$	5.20558	0.453087
$133$	1.88262	0.163244
$134$	−4.47892	−0.386919
$135$	4.38719	0.377589
$136$	4.05210	0.347465
$137$	14.9682	1.27882	0.639409	−	0.768867i	$-0.279179\pi$
$137$	14.9682	1.27882	0.639409	+	0.768867i	$0.279179\pi$
$138$	−5.58819	−0.475699
$139$	11.5112	0.976366	0.488183	−	0.872741i	$-0.337660\pi$
$139$	11.5112	0.976366	0.488183	+	0.872741i	$0.337660\pi$
$140$	11.1920	0.945896
$141$	−14.2664	−1.20145
$142$	−1.38597	−0.116308
$143$	−9.81304	−0.820607
$144$	2.24813	0.187344
$145$	−16.1487	−1.34108
$146$	−7.58850	−0.628029
$147$	−28.1958	−2.32555
$148$	−7.84885	−0.645172
$149$	−7.61531	−0.623870	−0.311935	−	0.950103i	$-0.600977\pi$
$149$	−7.61531	−0.623870	−0.311935	+	0.950103i	$0.600977\pi$
$150$	3.40778	0.278244
$151$	19.6573	1.59969	0.799843	−	0.600209i	$-0.204916\pi$
$151$	19.6573	1.59969	0.799843	+	0.600209i	$0.204916\pi$
$152$	−0.428446	−0.0347516
$153$	−9.10965	−0.736471
$154$	9.98468	0.804588
$155$	−14.0285	−1.12680
$156$	−9.89324	−0.792093
$157$	−2.40883	−0.192245	−0.0961226	−	0.995370i	$-0.530644\pi$
$157$	−2.40883	−0.192245	−0.0961226	+	0.995370i	$0.530644\pi$
$158$	−16.2556	−1.29323
$159$	1.34462	0.106635
$160$	−2.54707	−0.201363
$161$	−10.7186	−0.844741
$162$	10.6903	0.839910
$163$	−12.4717	−0.976863	−0.488431	−	0.872602i	$-0.662431\pi$
$163$	−12.4717	−0.976863	−0.488431	+	0.872602i	$0.662431\pi$
$164$	0.720227	0.0562403
$165$	13.2589	1.03221
$166$	8.28928	0.643373
$167$	6.40112	0.495334	0.247667	−	0.968845i	$-0.420336\pi$
$167$	6.40112	0.495334	0.247667	+	0.968845i	$0.420336\pi$
$168$	10.0663	0.776631
$169$	5.64976	0.434597
$170$	10.3210	0.791583
$171$	0.963201	0.0736579
$172$	0.149014	0.0113622
$173$	−3.93812	−0.299410	−0.149705	−	0.988731i	$-0.547832\pi$
$173$	−3.93812	−0.299410	−0.149705	+	0.988731i	$0.547832\pi$
$174$	−14.5244	−1.10110
$175$	6.53636	0.494102
$176$	−2.27231	−0.171281
$177$	−16.1417	−1.21328
$178$	−11.0556	−0.828656
$179$	15.8322	1.18336	0.591678	−	0.806174i	$-0.298466\pi$
$179$	15.8322	1.18336	0.591678	+	0.806174i	$0.298466\pi$
$180$	5.72613	0.426800
$181$	18.9224	1.40649	0.703245	−	0.710947i	$-0.251734\pi$
$181$	18.9224	1.40649	0.703245	+	0.710947i	$0.251734\pi$
$182$	−18.9760	−1.40659
$183$	−21.0869	−1.55879
$184$	2.43932	0.179829
$185$	−19.9915	−1.46981
$186$	−12.6175	−0.925162
$187$	9.20762	0.673328
$188$	6.22749	0.454186
$189$	7.56857	0.550532
$190$	−1.09128	−0.0791698
$191$	−20.5247	−1.48511	−0.742557	−	0.669783i	$-0.766387\pi$
$191$	−20.5247	−1.48511	−0.742557	+	0.669783i	$0.766387\pi$
$192$	−2.29088	−0.165330
$193$	4.64688	0.334490	0.167245	−	0.985915i	$-0.446513\pi$
$193$	4.64688	0.334490	0.167245	+	0.985915i	$0.446513\pi$
$194$	8.77266	0.629840
$195$	−25.1987	−1.80452
$196$	12.3079	0.879134
$197$	−8.47829	−0.604053	−0.302026	−	0.953300i	$-0.597663\pi$
$197$	−8.47829	−0.604053	−0.302026	+	0.953300i	$0.597663\pi$
$198$	5.10843	0.363040
$199$	23.9297	1.69633	0.848167	−	0.529729i	$-0.177706\pi$
$199$	23.9297	1.69633	0.848167	+	0.529729i	$0.177706\pi$
$200$	−1.48754	−0.105185
$201$	−10.2607	−0.723731
$202$	−7.95661	−0.559825
$203$	−27.8589	−1.95531
$204$	9.28288	0.649932
$205$	1.83447	0.128125
$206$	−0.913978	−0.0636799
$207$	−5.48391	−0.381158
$208$	4.31854	0.299437
$209$	−0.973561	−0.0673426
$210$	25.6395	1.76929
$211$	−26.7814	−1.84371	−0.921855	−	0.387535i	$-0.873327\pi$
$211$	−26.7814	−1.84371	−0.921855	+	0.387535i	$0.873327\pi$
$212$	−0.586944	−0.0403115
$213$	−3.17508	−0.217553
$214$	0.321413	0.0219713
$215$	0.379549	0.0258851
$216$	−1.72245	−0.117198
$217$	−24.2013	−1.64289
$218$	−16.6429	−1.12720
$219$	−17.3843	−1.17472
$220$	−5.78771	−0.390207
$221$	−17.4992	−1.17712
$222$	−17.9808	−1.20679
$223$	3.89073	0.260543	0.130271	−	0.991478i	$-0.458415\pi$
$223$	3.89073	0.260543	0.130271	+	0.991478i	$0.458415\pi$
$224$	−4.39407	−0.293591
$225$	3.34418	0.222945
$226$	−0.476063	−0.0316673
$227$	20.2891	1.34664	0.673319	−	0.739352i	$-0.264868\pi$
$227$	20.2891	1.34664	0.673319	+	0.739352i	$0.264868\pi$
$228$	−0.981518	−0.0650026
$229$	−4.05636	−0.268052	−0.134026	−	0.990978i	$-0.542791\pi$
$229$	−4.05636	−0.268052	−0.134026	+	0.990978i	$0.542791\pi$
$230$	6.21312	0.409681
$231$	22.8737	1.50498
$232$	6.34012	0.416249
$233$	−21.2947	−1.39506	−0.697532	−	0.716554i	$-0.745718\pi$
$233$	−21.2947	−1.39506	−0.697532	+	0.716554i	$0.745718\pi$
$234$	−9.70862	−0.634672
$235$	15.8618	1.03471
$236$	7.04607	0.458660
$237$	−37.2396	−2.41897
$238$	17.8052	1.15414
$239$	−18.7033	−1.20982	−0.604908	−	0.796295i	$-0.706790\pi$
$239$	−18.7033	−1.20982	−0.604908	+	0.796295i	$0.706790\pi$
$240$	−5.83502	−0.376649
$241$	−11.5431	−0.743558	−0.371779	−	0.928321i	$-0.621252\pi$
$241$	−11.5431	−0.743558	−0.371779	+	0.928321i	$0.621252\pi$
$242$	5.83663	0.375193
$243$	19.3228	1.23956
$244$	9.20473	0.589273
$245$	31.3489	2.00281
$246$	1.64995	0.105197
$247$	1.85026	0.117729
$248$	5.50772	0.349741
$249$	18.9897	1.20343
$250$	8.94646	0.565824
$251$	19.0291	1.20110	0.600552	−	0.799586i	$-0.294948\pi$
$251$	19.0291	1.20110	0.600552	+	0.799586i	$0.294948\pi$
$252$	9.87843	0.622283
$253$	5.54289	0.348478
$254$	−18.6447	−1.16987
$255$	23.6441	1.48065
$256$	1.00000	0.0625000
$257$	15.4163	0.961641	0.480821	−	0.876819i	$-0.340339\pi$
$257$	15.4163	0.961641	0.480821	+	0.876819i	$0.340339\pi$
$258$	0.341374	0.0212530
$259$	−34.4884	−2.14301
$260$	10.9996	0.682166
$261$	−14.2534	−0.882263
$262$	−12.0996	−0.747517
$263$	15.0898	0.930477	0.465238	−	0.885185i	$-0.345969\pi$
$263$	15.0898	0.930477	0.465238	+	0.885185i	$0.345969\pi$
$264$	−5.20558	−0.320381
$265$	−1.49498	−0.0918362
$266$	−1.88262	−0.115431
$267$	−25.3271	−1.55000
$268$	4.47892	0.273593
$269$	−9.55736	−0.582723	−0.291361	−	0.956613i	$-0.594108\pi$
$269$	−9.55736	−0.582723	−0.291361	+	0.956613i	$0.594108\pi$
$270$	−4.38719	−0.266996
$271$	1.75076	0.106351	0.0531757	−	0.998585i	$-0.483066\pi$
$271$	1.75076	0.106351	0.0531757	+	0.998585i	$0.483066\pi$
$272$	−4.05210	−0.245695
$273$	−43.4716	−2.63102
$274$	−14.9682	−0.904260
$275$	−3.38015	−0.203831
$276$	5.58819	0.336370
$277$	23.2596	1.39754	0.698768	−	0.715348i	$-0.253732\pi$
$277$	23.2596	1.39754	0.698768	+	0.715348i	$0.253732\pi$
$278$	−11.5112	−0.690395
$279$	−12.3821	−0.741294
$280$	−11.1920	−0.668849
$281$	−16.2462	−0.969169	−0.484584	−	0.874744i	$-0.661029\pi$
$281$	−16.2462	−0.969169	−0.484584	+	0.874744i	$0.661029\pi$
$282$	14.2664	0.849553
$283$	16.2194	0.964144	0.482072	−	0.876131i	$-0.339884\pi$
$283$	16.2194	0.964144	0.482072	+	0.876131i	$0.339884\pi$
$284$	1.38597	0.0822421
$285$	−2.49999	−0.148087
$286$	9.81304	0.580257
$287$	3.16473	0.186808
$288$	−2.24813	−0.132472
$289$	−0.580450	−0.0341441
$290$	16.1487	0.948284
$291$	20.0971	1.17811
$292$	7.58850	0.444084
$293$	8.87948	0.518745	0.259373	−	0.965777i	$-0.416484\pi$
$293$	8.87948	0.518745	0.259373	+	0.965777i	$0.416484\pi$
$294$	28.1958	1.64442
$295$	17.9468	1.04490
$296$	7.84885	0.456205
$297$	−3.91393	−0.227109
$298$	7.61531	0.441143
$299$	−10.5343	−0.609215
$300$	−3.40778	−0.196748
$301$	0.654780	0.0377409
$302$	−19.6573	−1.13115
$303$	−18.2276	−1.04715
$304$	0.428446	0.0245731
$305$	23.4451	1.34246
$306$	9.10965	0.520764
$307$	−26.0237	−1.48525	−0.742625	−	0.669707i	$-0.766420\pi$
$307$	−26.0237	−1.48525	−0.742625	+	0.669707i	$0.766420\pi$
$308$	−9.98468	−0.568930
$309$	−2.09381	−0.119113
$310$	14.0285	0.796767
$311$	−3.85001	−0.218314	−0.109157	−	0.994025i	$-0.534815\pi$
$311$	−3.85001	−0.218314	−0.109157	+	0.994025i	$0.534815\pi$
$312$	9.89324	0.560095
$313$	8.87962	0.501906	0.250953	−	0.967999i	$-0.419256\pi$
$313$	8.87962	0.501906	0.250953	+	0.967999i	$0.419256\pi$
$314$	2.40883	0.135938
$315$	25.1610	1.41766
$316$	16.2556	0.914449
$317$	−17.8569	−1.00294	−0.501470	−	0.865175i	$-0.667207\pi$
$317$	−17.8569	−1.00294	−0.501470	+	0.865175i	$0.667207\pi$
$318$	−1.34462	−0.0754024
$319$	14.4067	0.806620
$320$	2.54707	0.142385
$321$	0.736317	0.0410972
$322$	10.7186	0.597322
$323$	−1.73611	−0.0965997
$324$	−10.6903	−0.593906
$325$	6.42400	0.356339
$326$	12.4717	0.690746
$327$	−38.1269	−2.10842
$328$	−0.720227	−0.0397679
$329$	27.3640	1.50863
$330$	−13.2589	−0.729881
$331$	−18.2337	−1.00222	−0.501109	−	0.865384i	$-0.667074\pi$
$331$	−18.2337	−1.00222	−0.501109	+	0.865384i	$0.667074\pi$
$332$	−8.28928	−0.454933
$333$	−17.6452	−0.966952
$334$	−6.40112	−0.350254
$335$	11.4081	0.623291
$336$	−10.0663	−0.549161
$337$	19.1399	1.04262	0.521310	−	0.853368i	$-0.325444\pi$
$337$	19.1399	1.04262	0.521310	+	0.853368i	$0.325444\pi$
$338$	−5.64976	−0.307306
$339$	−1.09060	−0.0592335
$340$	−10.3210	−0.559733
$341$	12.5152	0.677738
$342$	−0.963201	−0.0520840
$343$	23.3232	1.25933
$344$	−0.149014	−0.00803432
$345$	14.2335	0.766306
$346$	3.93812	0.211715
$347$	32.2277	1.73007	0.865037	−	0.501708i	$-0.167295\pi$
$347$	32.2277	1.73007	0.865037	+	0.501708i	$0.167295\pi$
$348$	14.5244	0.778592
$349$	16.1106	0.862379	0.431189	−	0.902261i	$-0.358094\pi$
$349$	16.1106	0.862379	0.431189	+	0.902261i	$0.358094\pi$
$350$	−6.53636	−0.349383
$351$	7.43846	0.397036
$352$	2.27231	0.121114
$353$	7.60828	0.404948	0.202474	−	0.979288i	$-0.435102\pi$
$353$	7.60828	0.404948	0.202474	+	0.979288i	$0.435102\pi$
$354$	16.1417	0.857921
$355$	3.53015	0.187361
$356$	11.0556	0.585948
$357$	40.7897	2.15882
$358$	−15.8322	−0.836760
$359$	11.6200	0.613278	0.306639	−	0.951826i	$-0.400796\pi$
$359$	11.6200	0.613278	0.306639	+	0.951826i	$0.400796\pi$
$360$	−5.72613	−0.301793
$361$	−18.8164	−0.990339
$362$	−18.9224	−0.994539
$363$	13.3710	0.701796
$364$	18.9760	0.994611
$365$	19.3284	1.01170
$366$	21.0869	1.10223
$367$	11.5682	0.603853	0.301927	−	0.953331i	$-0.402370\pi$
$367$	11.5682	0.603853	0.301927	+	0.953331i	$0.402370\pi$
$368$	−2.43932	−0.127159
$369$	1.61916	0.0842902
$370$	19.9915	1.03931
$371$	−2.57907	−0.133899
$372$	12.6175	0.654188
$373$	16.0669	0.831914	0.415957	−	0.909384i	$-0.363447\pi$
$373$	16.0669	0.831914	0.415957	+	0.909384i	$0.363447\pi$
$374$	−9.20762	−0.476115
$375$	20.4953	1.05837
$376$	−6.22749	−0.321158
$377$	−27.3800	−1.41014
$378$	−7.56857	−0.389285
$379$	6.18546	0.317726	0.158863	−	0.987301i	$-0.449217\pi$
$379$	6.18546	0.317726	0.158863	+	0.987301i	$0.449217\pi$
$380$	1.09128	0.0559815
$381$	−42.7127	−2.18824
$382$	20.5247	1.05013
$383$	23.0468	1.17764	0.588818	−	0.808265i	$-0.299593\pi$
$383$	23.0468	1.17764	0.588818	+	0.808265i	$0.299593\pi$
$384$	2.29088	0.116906
$385$	−25.4316	−1.29612
$386$	−4.64688	−0.236520
$387$	0.335003	0.0170292
$388$	−8.77266	−0.445364
$389$	−22.4014	−1.13580	−0.567898	−	0.823099i	$-0.692243\pi$
$389$	−22.4014	−1.13580	−0.567898	+	0.823099i	$0.692243\pi$
$390$	25.1987	1.27599
$391$	9.88439	0.499875
$392$	−12.3079	−0.621641
$393$	−27.7188	−1.39823
$394$	8.47829	0.427130
$395$	41.4041	2.08327
$396$	−5.10843	−0.256708
$397$	31.3904	1.57544	0.787718	−	0.616036i	$-0.211262\pi$
$397$	31.3904	1.57544	0.787718	+	0.616036i	$0.211262\pi$
$398$	−23.9297	−1.19949
$399$	−4.31286	−0.215913
$400$	1.48754	0.0743770
$401$	−24.8739	−1.24214	−0.621071	−	0.783754i	$-0.713302\pi$
$401$	−24.8739	−1.24214	−0.621071	+	0.783754i	$0.713302\pi$
$402$	10.2607	0.511755
$403$	−23.7853	−1.18483
$404$	7.95661	0.395856
$405$	−27.2289	−1.35302
$406$	27.8589	1.38262
$407$	17.8350	0.884048
$408$	−9.28288	−0.459571
$409$	−21.4035	−1.05833	−0.529167	−	0.848518i	$-0.677495\pi$
$409$	−21.4035	−1.05833	−0.529167	+	0.848518i	$0.677495\pi$
$410$	−1.83447	−0.0905978
$411$	−34.2903	−1.69141
$412$	0.913978	0.0450285
$413$	30.9609	1.52349
$414$	5.48391	0.269519
$415$	−21.1133	−1.03641
$416$	−4.31854	−0.211734
$417$	−26.3707	−1.29138
$418$	0.973561	0.0476184
$419$	−3.49115	−0.170554	−0.0852768	−	0.996357i	$-0.527177\pi$
$419$	−3.49115	−0.170554	−0.0852768	+	0.996357i	$0.527177\pi$
$420$	−25.6395	−1.25108
$421$	−25.2167	−1.22899	−0.614493	−	0.788922i	$-0.710640\pi$
$421$	−25.2167	−1.22899	−0.614493	+	0.788922i	$0.710640\pi$
$422$	26.7814	1.30370
$423$	14.0002	0.680712
$424$	0.586944	0.0285045
$425$	−6.02767	−0.292385
$426$	3.17508	0.153833
$427$	40.4463	1.95733
$428$	−0.321413	−0.0155361
$429$	22.4805	1.08537
$430$	−0.379549	−0.0183035
$431$	27.2174	1.31102	0.655508	−	0.755188i	$-0.272454\pi$
$431$	27.2174	1.31102	0.655508	+	0.755188i	$0.272454\pi$
$432$	1.72245	0.0828714
$433$	20.1085	0.966353	0.483177	−	0.875523i	$-0.339483\pi$
$433$	20.1085	0.966353	0.483177	+	0.875523i	$0.339483\pi$
$434$	24.2013	1.16170
$435$	36.9947	1.77376
$436$	16.6429	0.797050
$437$	−1.04512	−0.0499948
$438$	17.3843	0.830656
$439$	15.4115	0.735553	0.367776	−	0.929914i	$-0.380119\pi$
$439$	15.4115	0.735553	0.367776	+	0.929914i	$0.380119\pi$
$440$	5.78771	0.275918
$441$	27.6697	1.31760
$442$	17.4992	0.832350
$443$	−25.9297	−1.23196	−0.615978	−	0.787764i	$-0.711239\pi$
$443$	−25.9297	−1.23196	−0.615978	+	0.787764i	$0.711239\pi$
$444$	17.9808	0.853330
$445$	28.1594	1.33489
$446$	−3.89073	−0.184232
$447$	17.4458	0.825156
$448$	4.39407	0.207600
$449$	−31.9282	−1.50678	−0.753392	−	0.657572i	$-0.771584\pi$
$449$	−31.9282	−1.50678	−0.753392	+	0.657572i	$0.771584\pi$
$450$	−3.34418	−0.157646
$451$	−1.63658	−0.0770634
$452$	0.476063	0.0223921
$453$	−45.0324	−2.11581
$454$	−20.2891	−0.952216
$455$	48.3330	2.26589
$456$	0.981518	0.0459638
$457$	−5.91536	−0.276709	−0.138354	−	0.990383i	$-0.544181\pi$
$457$	−5.91536	−0.276709	−0.138354	+	0.990383i	$0.544181\pi$
$458$	4.05636	0.189541
$459$	−6.97955	−0.325777
$460$	−6.21312	−0.289688
$461$	17.0935	0.796124	0.398062	−	0.917359i	$-0.369683\pi$
$461$	17.0935	0.796124	0.398062	+	0.917359i	$0.369683\pi$
$462$	−22.8737	−1.06418
$463$	7.13732	0.331699	0.165850	−	0.986151i	$-0.446963\pi$
$463$	7.13732	0.331699	0.165850	+	0.986151i	$0.446963\pi$
$464$	−6.34012	−0.294333
$465$	32.1377	1.49035
$466$	21.2947	0.986459
$467$	0.164316	0.00760364	0.00380182	−	0.999993i	$-0.498790\pi$
$467$	0.164316	0.00760364	0.00380182	+	0.999993i	$0.498790\pi$
$468$	9.70862	0.448781
$469$	19.6807	0.908769
$470$	−15.8618	−0.731651
$471$	5.51833	0.254271
$472$	−7.04607	−0.324322
$473$	−0.338606	−0.0155691
$474$	37.2396	1.71047
$475$	0.637331	0.0292428
$476$	−17.8052	−0.816102
$477$	−1.31952	−0.0604169
$478$	18.7033	0.855469
$479$	−9.22389	−0.421450	−0.210725	−	0.977545i	$-0.567582\pi$
$479$	−9.22389	−0.421450	−0.210725	+	0.977545i	$0.567582\pi$
$480$	5.83502	0.266331
$481$	−33.8956	−1.54550
$482$	11.5431	0.525775
$483$	24.5549	1.11729
$484$	−5.83663	−0.265301
$485$	−22.3445	−1.01461
$486$	−19.3228	−0.876502
$487$	11.1941	0.507252	0.253626	−	0.967302i	$-0.418377\pi$
$487$	11.1941	0.507252	0.253626	+	0.967302i	$0.418377\pi$
$488$	−9.20473	−0.416679
$489$	28.5713	1.29204
$490$	−31.3489	−1.41620
$491$	4.66356	0.210464	0.105232	−	0.994448i	$-0.466442\pi$
$491$	4.66356	0.210464	0.105232	+	0.994448i	$0.466442\pi$
$492$	−1.64995	−0.0743856
$493$	25.6908	1.15706
$494$	−1.85026	−0.0832471
$495$	−13.0115	−0.584824
$496$	−5.50772	−0.247304
$497$	6.09004	0.273176
$498$	−18.9897	−0.850950
$499$	12.8820	0.576678	0.288339	−	0.957528i	$-0.406897\pi$
$499$	12.8820	0.576678	0.288339	+	0.957528i	$0.406897\pi$
$500$	−8.94646	−0.400098
$501$	−14.6642	−0.655148
$502$	−19.0291	−0.849309
$503$	27.5246	1.22726	0.613632	−	0.789592i	$-0.289708\pi$
$503$	27.5246	1.22726	0.613632	+	0.789592i	$0.289708\pi$
$504$	−9.87843	−0.440020
$505$	20.2660	0.901826
$506$	−5.54289	−0.246411
$507$	−12.9429	−0.574815
$508$	18.6447	0.827224
$509$	26.1343	1.15838	0.579192	−	0.815191i	$-0.303368\pi$
$509$	26.1343	1.15838	0.579192	+	0.815191i	$0.303368\pi$
$510$	−23.6441	−1.04698
$511$	33.3444	1.47507
$512$	−1.00000	−0.0441942
$513$	0.737977	0.0325825
$514$	−15.4163	−0.679983
$515$	2.32796	0.102582
$516$	−0.341374	−0.0150282
$517$	−14.1508	−0.622350
$518$	34.4884	1.51533
$519$	9.02177	0.396012
$520$	−10.9996	−0.482364
$521$	3.67934	0.161195	0.0805974	−	0.996747i	$-0.474317\pi$
$521$	3.67934	0.161195	0.0805974	+	0.996747i	$0.474317\pi$
$522$	14.2534	0.623854
$523$	14.2991	0.625254	0.312627	−	0.949876i	$-0.398791\pi$
$523$	14.2991	0.625254	0.312627	+	0.949876i	$0.398791\pi$
$524$	12.0996	0.528575
$525$	−14.9740	−0.653520
$526$	−15.0898	−0.657946
$527$	22.3179	0.972181
$528$	5.20558	0.226544
$529$	−17.0497	−0.741291
$530$	1.49498	0.0649380
$531$	15.8405	0.687418
$532$	1.88262	0.0816221
$533$	3.11033	0.134723
$534$	25.3271	1.09601
$535$	−0.818659	−0.0353937
$536$	−4.47892	−0.193460
$537$	−36.2697	−1.56515
$538$	9.55736	0.412047
$539$	−27.9672	−1.20463
$540$	4.38719	0.188795
$541$	−9.86918	−0.424309	−0.212155	−	0.977236i	$-0.568048\pi$
$541$	−9.86918	−0.424309	−0.212155	+	0.977236i	$0.568048\pi$
$542$	−1.75076	−0.0752017
$543$	−43.3489	−1.86028
$544$	4.05210	0.173733
$545$	42.3906	1.81581
$546$	43.4716	1.86041
$547$	43.9225	1.87799	0.938995	−	0.343931i	$-0.111759\pi$
$547$	43.9225	1.87799	0.938995	+	0.343931i	$0.111759\pi$
$548$	14.9682	0.639409
$549$	20.6934	0.883173
$550$	3.38015	0.144130
$551$	−2.71640	−0.115723
$552$	−5.58819	−0.237849
$553$	71.4283	3.03744
$554$	−23.2596	−0.988207
$555$	45.7982	1.94403
$556$	11.5112	0.488183
$557$	−17.5602	−0.744051	−0.372026	−	0.928222i	$-0.621337\pi$
$557$	−17.5602	−0.744051	−0.372026	+	0.928222i	$0.621337\pi$
$558$	12.3821	0.524174
$559$	0.643524	0.0272182
$560$	11.1920	0.472948
$561$	−21.0935	−0.890570
$562$	16.2462	0.685306
$563$	33.0527	1.39301	0.696503	−	0.717554i	$-0.254738\pi$
$563$	33.0527	1.39301	0.696503	+	0.717554i	$0.254738\pi$
$564$	−14.2664	−0.600725
$565$	1.21256	0.0510130
$566$	−16.2194	−0.681753
$567$	−46.9740	−1.97272
$568$	−1.38597	−0.0581539
$569$	28.7470	1.20514	0.602569	−	0.798067i	$-0.294144\pi$
$569$	28.7470	1.20514	0.602569	+	0.798067i	$0.294144\pi$
$570$	2.49999	0.104713
$571$	−30.3667	−1.27081	−0.635403	−	0.772180i	$-0.719166\pi$
$571$	−30.3667	−1.27081	−0.635403	+	0.772180i	$0.719166\pi$
$572$	−9.81304	−0.410304
$573$	47.0196	1.96427
$574$	−3.16473	−0.132093
$575$	−3.62859	−0.151323
$576$	2.24813	0.0936720
$577$	11.1304	0.463364	0.231682	−	0.972792i	$-0.425577\pi$
$577$	11.1304	0.463364	0.231682	+	0.972792i	$0.425577\pi$
$578$	0.580450	0.0241435
$579$	−10.6454	−0.442409
$580$	−16.1487	−0.670538
$581$	−36.4237	−1.51111
$582$	−20.0971	−0.833052
$583$	1.33372	0.0552369
$584$	−7.58850	−0.314014
$585$	24.7285	1.02240
$586$	−8.87948	−0.366808
$587$	15.7215	0.648896	0.324448	−	0.945904i	$-0.394822\pi$
$587$	15.7215	0.648896	0.324448	+	0.945904i	$0.394822\pi$
$588$	−28.1958	−1.16278
$589$	−2.35976	−0.0972323
$590$	−17.9468	−0.738858
$591$	19.4227	0.798944
$592$	−7.84885	−0.322586
$593$	1.09536	0.0449809	0.0224905	−	0.999747i	$-0.492840\pi$
$593$	1.09536	0.0449809	0.0224905	+	0.999747i	$0.492840\pi$
$594$	3.91393	0.160591
$595$	−45.3511	−1.85921
$596$	−7.61531	−0.311935
$597$	−54.8201	−2.24364
$598$	10.5343	0.430780
$599$	21.3277	0.871426	0.435713	−	0.900086i	$-0.356496\pi$
$599$	21.3277	0.871426	0.435713	+	0.900086i	$0.356496\pi$
$600$	3.40778	0.139122
$601$	8.77795	0.358060	0.179030	−	0.983844i	$-0.442704\pi$
$601$	8.77795	0.358060	0.179030	+	0.983844i	$0.442704\pi$
$602$	−0.654780	−0.0266868
$603$	10.0692	0.410048
$604$	19.6573	0.799843
$605$	−14.8663	−0.604400
$606$	18.2276	0.740447
$607$	−40.6370	−1.64940	−0.824702	−	0.565568i	$-0.808657\pi$
$607$	−40.6370	−1.64940	−0.824702	+	0.565568i	$0.808657\pi$
$608$	−0.428446	−0.0173758
$609$	63.8215	2.58618
$610$	−23.4451	−0.949262
$611$	26.8936	1.08800
$612$	−9.10965	−0.368236
$613$	−41.7616	−1.68673	−0.843367	−	0.537338i	$-0.819430\pi$
$613$	−41.7616	−1.68673	−0.843367	+	0.537338i	$0.819430\pi$
$614$	26.0237	1.05023
$615$	−4.20254	−0.169463
$616$	9.98468	0.402294
$617$	17.8391	0.718173	0.359087	−	0.933304i	$-0.383088\pi$
$617$	17.8391	0.718173	0.359087	+	0.933304i	$0.383088\pi$
$618$	2.09381	0.0842255
$619$	−26.8349	−1.07859	−0.539293	−	0.842118i	$-0.681308\pi$
$619$	−26.8349	−1.07859	−0.539293	+	0.842118i	$0.681308\pi$
$620$	−14.0285	−0.563399
$621$	−4.20161	−0.168605
$622$	3.85001	0.154372
$623$	48.5793	1.94629
$624$	−9.89324	−0.396047
$625$	−30.2249	−1.20900
$626$	−8.87962	−0.354901
$627$	2.23031	0.0890700
$628$	−2.40883	−0.0961226
$629$	31.8044	1.26812
$630$	−25.1610	−1.00244
$631$	−24.1034	−0.959542	−0.479771	−	0.877394i	$-0.659280\pi$
$631$	−24.1034	−0.959542	−0.479771	+	0.877394i	$0.659280\pi$
$632$	−16.2556	−0.646613
$633$	61.3530	2.43856
$634$	17.8569	0.709186
$635$	47.4892	1.88455
$636$	1.34462	0.0533176
$637$	53.1520	2.10596
$638$	−14.4067	−0.570366
$639$	3.11583	0.123260
$640$	−2.54707	−0.100682
$641$	41.4525	1.63728	0.818638	−	0.574309i	$-0.194729\pi$
$641$	41.4525	1.63728	0.818638	+	0.574309i	$0.194729\pi$
$642$	−0.736317	−0.0290601
$643$	22.6785	0.894352	0.447176	−	0.894446i	$-0.352430\pi$
$643$	22.6785	0.894352	0.447176	+	0.894446i	$0.352430\pi$
$644$	−10.7186	−0.422371
$645$	−0.869502	−0.0342366
$646$	1.73611	0.0683063
$647$	−1.41795	−0.0557452	−0.0278726	−	0.999611i	$-0.508873\pi$
$647$	−1.41795	−0.0557452	−0.0278726	+	0.999611i	$0.508873\pi$
$648$	10.6903	0.419955
$649$	−16.0108	−0.628480
$650$	−6.42400	−0.251970
$651$	55.4423	2.17296
$652$	−12.4717	−0.488431
$653$	−33.3800	−1.30626	−0.653129	−	0.757246i	$-0.726544\pi$
$653$	−33.3800	−1.30626	−0.653129	+	0.757246i	$0.726544\pi$
$654$	38.1269	1.49088
$655$	30.8185	1.20418
$656$	0.720227	0.0281201
$657$	17.0599	0.665571
$658$	−27.3640	−1.06676
$659$	−12.9710	−0.505277	−0.252639	−	0.967561i	$-0.581298\pi$
$659$	−12.9710	−0.505277	−0.252639	+	0.967561i	$0.581298\pi$
$660$	13.2589	0.516104
$661$	−1.35552	−0.0527236	−0.0263618	−	0.999652i	$-0.508392\pi$
$661$	−1.35552	−0.0527236	−0.0263618	+	0.999652i	$0.508392\pi$
$662$	18.2337	0.708674
$663$	40.0885	1.55691
$664$	8.28928	0.321686
$665$	4.79516	0.185948
$666$	17.6452	0.683738
$667$	15.4656	0.598831
$668$	6.40112	0.247667
$669$	−8.91320	−0.344604
$670$	−11.4081	−0.440733
$671$	−20.9160	−0.807452
$672$	10.0663	0.388316
$673$	−3.64359	−0.140450	−0.0702250	−	0.997531i	$-0.522372\pi$
$673$	−3.64359	−0.140450	−0.0702250	+	0.997531i	$0.522372\pi$
$674$	−19.1399	−0.737243
$675$	2.56221	0.0986197
$676$	5.64976	0.217298
$677$	−24.6646	−0.947938	−0.473969	−	0.880542i	$-0.657179\pi$
$677$	−24.6646	−0.947938	−0.473969	+	0.880542i	$0.657179\pi$
$678$	1.09060	0.0418844
$679$	−38.5477	−1.47932
$680$	10.3210	0.395791
$681$	−46.4800	−1.78112
$682$	−12.5152	−0.479233
$683$	−31.2933	−1.19740	−0.598702	−	0.800972i	$-0.704317\pi$
$683$	−31.2933	−1.19740	−0.598702	+	0.800972i	$0.704317\pi$
$684$	0.963201	0.0368289
$685$	38.1249	1.45668
$686$	−23.3232	−0.890483
$687$	9.29264	0.354536
$688$	0.149014	0.00568112
$689$	−2.53474	−0.0965659
$690$	−14.2335	−0.541860
$691$	18.4574	0.702152	0.351076	−	0.936347i	$-0.385816\pi$
$691$	18.4574	0.702152	0.351076	+	0.936347i	$0.385816\pi$
$692$	−3.93812	−0.149705
$693$	−22.4468	−0.852684
$694$	−32.2277	−1.22335
$695$	29.3197	1.11216
$696$	−14.5244	−0.550548
$697$	−2.91844	−0.110544
$698$	−16.1106	−0.609794
$699$	48.7836	1.84517
$700$	6.53636	0.247051
$701$	−11.1645	−0.421677	−0.210838	−	0.977521i	$-0.567619\pi$
$701$	−11.1645	−0.421677	−0.210838	+	0.977521i	$0.567619\pi$
$702$	−7.43846	−0.280747
$703$	−3.36281	−0.126831
$704$	−2.27231	−0.0856407
$705$	−36.3375	−1.36855
$706$	−7.60828	−0.286341
$707$	34.9619	1.31488
$708$	−16.1417	−0.606642
$709$	5.59539	0.210139	0.105070	−	0.994465i	$-0.466493\pi$
$709$	5.59539	0.210139	0.105070	+	0.994465i	$0.466493\pi$
$710$	−3.53015	−0.132484
$711$	36.5447	1.37053
$712$	−11.0556	−0.414328
$713$	13.4351	0.503149
$714$	−40.7897	−1.52651
$715$	−24.9944	−0.934739
$716$	15.8322	0.591678
$717$	42.8470	1.60015
$718$	−11.6200	−0.433653
$719$	−34.6241	−1.29126	−0.645630	−	0.763651i	$-0.723405\pi$
$719$	−34.6241	−1.29126	−0.645630	+	0.763651i	$0.723405\pi$
$720$	5.72613	0.213400
$721$	4.01609	0.149567
$722$	18.8164	0.700275
$723$	26.4439	0.983460
$724$	18.9224	0.703245
$725$	−9.43119	−0.350265
$726$	−13.3710	−0.496245
$727$	−32.2095	−1.19458	−0.597292	−	0.802024i	$-0.703757\pi$
$727$	−32.2095	−1.19458	−0.597292	+	0.802024i	$0.703757\pi$
$728$	−18.9760	−0.703296
$729$	−12.1954	−0.451681
$730$	−19.3284	−0.715377
$731$	−0.603822	−0.0223332
$732$	−21.0869	−0.779395
$733$	33.2258	1.22722	0.613611	−	0.789609i	$-0.289716\pi$
$733$	33.2258	1.22722	0.613611	+	0.789609i	$0.289716\pi$
$734$	−11.5682	−0.426989
$735$	−71.8167	−2.64900
$736$	2.43932	0.0899146
$737$	−10.1775	−0.374892
$738$	−1.61916	−0.0596022
$739$	−38.7344	−1.42487	−0.712434	−	0.701739i	$-0.752407\pi$
$739$	−38.7344	−1.42487	−0.712434	+	0.701739i	$0.752407\pi$
$740$	−19.9915	−0.734904
$741$	−4.23872	−0.155713
$742$	2.57907	0.0946808
$743$	9.13539	0.335145	0.167572	−	0.985860i	$-0.446407\pi$
$743$	9.13539	0.335145	0.167572	+	0.985860i	$0.446407\pi$
$744$	−12.6175	−0.462581
$745$	−19.3967	−0.710640
$746$	−16.0669	−0.588252
$747$	−18.6354	−0.681832
$748$	9.20762	0.336664
$749$	−1.41231	−0.0516047
$750$	−20.4953	−0.748381
$751$	−4.35111	−0.158774	−0.0793872	−	0.996844i	$-0.525296\pi$
$751$	−4.35111	−0.158774	−0.0793872	+	0.996844i	$0.525296\pi$
$752$	6.22749	0.227093
$753$	−43.5933	−1.58863
$754$	27.3800	0.997122
$755$	50.0684	1.82217
$756$	7.56857	0.275266
$757$	−16.4158	−0.596644	−0.298322	−	0.954465i	$-0.596427\pi$
$757$	−16.4158	−0.596644	−0.298322	+	0.954465i	$0.596427\pi$
$758$	−6.18546	−0.224666
$759$	−12.6981	−0.460911
$760$	−1.09128	−0.0395849
$761$	32.3684	1.17335	0.586677	−	0.809821i	$-0.300436\pi$
$761$	32.3684	1.17335	0.586677	+	0.809821i	$0.300436\pi$
$762$	42.7127	1.54732
$763$	73.1301	2.64749
$764$	−20.5247	−0.742557
$765$	−23.2029	−0.838901
$766$	−23.0468	−0.832715
$767$	30.4287	1.09872
$768$	−2.29088	−0.0826650
$769$	−44.7044	−1.61208	−0.806041	−	0.591860i	$-0.798394\pi$
$769$	−44.7044	−1.61208	−0.806041	+	0.591860i	$0.798394\pi$
$770$	25.4316	0.916492
$771$	−35.3168	−1.27190
$772$	4.64688	0.167245
$773$	−16.4781	−0.592675	−0.296337	−	0.955083i	$-0.595765\pi$
$773$	−16.4781	−0.592675	−0.296337	+	0.955083i	$0.595765\pi$
$774$	−0.335003	−0.0120414
$775$	−8.19296	−0.294300
$776$	8.77266	0.314920
$777$	79.0088	2.83443
$778$	22.4014	0.803129
$779$	0.308579	0.0110560
$780$	−25.1987	−0.902260
$781$	−3.14934	−0.112692
$782$	−9.88439	−0.353465
$783$	−10.9205	−0.390268
$784$	12.3079	0.439567
$785$	−6.13544	−0.218983
$786$	27.7188	0.988696
$787$	−9.81667	−0.349926	−0.174963	−	0.984575i	$-0.555981\pi$
$787$	−9.81667	−0.349926	−0.174963	+	0.984575i	$0.555981\pi$
$788$	−8.47829	−0.302026
$789$	−34.5689	−1.23069
$790$	−41.4041	−1.47309
$791$	2.09186	0.0743779
$792$	5.10843	0.181520
$793$	39.7510	1.41160
$794$	−31.3904	−1.11400
$795$	3.42483	0.121466
$796$	23.9297	0.848167
$797$	0.895907	0.0317347	0.0158673	−	0.999874i	$-0.494949\pi$
$797$	0.895907	0.0317347	0.0158673	+	0.999874i	$0.494949\pi$
$798$	4.31286	0.152674
$799$	−25.2344	−0.892730
$800$	−1.48754	−0.0525925
$801$	24.8545	0.878190
$802$	24.8739	0.878327
$803$	−17.2434	−0.608506
$804$	−10.2607	−0.361865
$805$	−27.3009	−0.962229
$806$	23.7853	0.837801
$807$	21.8948	0.770732
$808$	−7.95661	−0.279913
$809$	−0.613069	−0.0215544	−0.0107772	−	0.999942i	$-0.503431\pi$
$809$	−0.613069	−0.0215544	−0.0107772	+	0.999942i	$0.503431\pi$
$810$	27.2289	0.956726
$811$	−8.19600	−0.287800	−0.143900	−	0.989592i	$-0.545964\pi$
$811$	−8.19600	−0.287800	−0.143900	+	0.989592i	$0.545964\pi$
$812$	−27.8589	−0.977657
$813$	−4.01079	−0.140664
$814$	−17.8350	−0.625116
$815$	−31.7664	−1.11273
$816$	9.28288	0.324966
$817$	0.0638446	0.00223364
$818$	21.4035	0.748355
$819$	42.6604	1.49067
$820$	1.83447	0.0640623
$821$	−36.6899	−1.28049	−0.640244	−	0.768172i	$-0.721167\pi$
$821$	−36.6899	−1.28049	−0.640244	+	0.768172i	$0.721167\pi$
$822$	34.2903	1.19601
$823$	−6.28960	−0.219242	−0.109621	−	0.993973i	$-0.534964\pi$
$823$	−6.28960	−0.219242	−0.109621	+	0.993973i	$0.534964\pi$
$824$	−0.913978	−0.0318399
$825$	7.74351	0.269594
$826$	−30.9609	−1.07727
$827$	−10.8339	−0.376731	−0.188365	−	0.982099i	$-0.560319\pi$
$827$	−10.8339	−0.376731	−0.188365	+	0.982099i	$0.560319\pi$
$828$	−5.48391	−0.190579
$829$	1.32791	0.0461204	0.0230602	−	0.999734i	$-0.492659\pi$
$829$	1.32791	0.0461204	0.0230602	+	0.999734i	$0.492659\pi$
$830$	21.1133	0.732854
$831$	−53.2850	−1.84844
$832$	4.31854	0.149718
$833$	−49.8728	−1.72799
$834$	26.3707	0.913144
$835$	16.3041	0.564226
$836$	−0.973561	−0.0336713
$837$	−9.48677	−0.327911
$838$	3.49115	0.120600
$839$	−31.4678	−1.08639	−0.543194	−	0.839607i	$-0.682785\pi$
$839$	−31.4678	−1.08639	−0.543194	+	0.839607i	$0.682785\pi$
$840$	25.6395	0.884647
$841$	11.1971	0.386108
$842$	25.2167	0.869025
$843$	37.2182	1.28186
$844$	−26.7814	−0.921855
$845$	14.3903	0.495041
$846$	−14.0002	−0.481336
$847$	−25.6466	−0.881226
$848$	−0.586944	−0.0201557
$849$	−37.1567	−1.27522
$850$	6.02767	0.206747
$851$	19.1459	0.656313
$852$	−3.17508	−0.108777
$853$	10.1849	0.348723	0.174361	−	0.984682i	$-0.444214\pi$
$853$	10.1849	0.348723	0.174361	+	0.984682i	$0.444214\pi$
$854$	−40.4463	−1.38404
$855$	2.45334	0.0839023
$856$	0.321413	0.0109857
$857$	15.2246	0.520063	0.260032	−	0.965600i	$-0.416267\pi$
$857$	15.2246	0.520063	0.260032	+	0.965600i	$0.416267\pi$
$858$	−22.4805	−0.767471
$859$	−35.6025	−1.21474	−0.607371	−	0.794418i	$-0.707776\pi$
$859$	−35.6025	−1.21474	−0.607371	+	0.794418i	$0.707776\pi$
$860$	0.379549	0.0129425
$861$	−7.25001	−0.247080
$862$	−27.2174	−0.927029
$863$	−52.8636	−1.79950	−0.899749	−	0.436407i	$-0.856251\pi$
$863$	−52.8636	−1.79950	−0.899749	+	0.436407i	$0.856251\pi$
$864$	−1.72245	−0.0585989
$865$	−10.0307	−0.341053
$866$	−20.1085	−0.683315
$867$	1.32974	0.0451604
$868$	−24.2013	−0.821446
$869$	−36.9377	−1.25303
$870$	−36.9947	−1.25424
$871$	19.3424	0.655391
$872$	−16.6429	−0.563600
$873$	−19.7221	−0.667490
$874$	1.04512	0.0353517
$875$	−39.3114	−1.32897
$876$	−17.3843	−0.587362
$877$	−49.1960	−1.66123	−0.830616	−	0.556846i	$-0.812011\pi$
$877$	−49.1960	−1.66123	−0.830616	+	0.556846i	$0.812011\pi$
$878$	−15.4115	−0.520114
$879$	−20.3418	−0.686113
$880$	−5.78771	−0.195104
$881$	−14.0863	−0.474581	−0.237291	−	0.971439i	$-0.576259\pi$
$881$	−14.0863	−0.474581	−0.237291	+	0.971439i	$0.576259\pi$
$882$	−27.6697	−0.931686
$883$	1.80903	0.0608787	0.0304393	−	0.999537i	$-0.490309\pi$
$883$	1.80903	0.0608787	0.0304393	+	0.999537i	$0.490309\pi$
$884$	−17.4992	−0.588560
$885$	−41.1140	−1.38203
$886$	25.9297	0.871124
$887$	−21.0118	−0.705507	−0.352753	−	0.935716i	$-0.614755\pi$
$887$	−21.0118	−0.705507	−0.352753	+	0.935716i	$0.614755\pi$
$888$	−17.9808	−0.603395
$889$	81.9261	2.74771
$890$	−28.1594	−0.943907
$891$	24.2916	0.813801
$892$	3.89073	0.130271
$893$	2.66814	0.0892860
$894$	−17.4458	−0.583473
$895$	40.3257	1.34794
$896$	−4.39407	−0.146796
$897$	24.1328	0.805771
$898$	31.9282	1.06546
$899$	34.9196	1.16463
$900$	3.34418	0.111473
$901$	2.37836	0.0792346
$902$	1.63658	0.0544920
$903$	−1.50002	−0.0499176
$904$	−0.476063	−0.0158336
$905$	48.1966	1.60211
$906$	45.0324	1.49610
$907$	0.726823	0.0241338	0.0120669	−	0.999927i	$-0.496159\pi$
$907$	0.726823	0.0241338	0.0120669	+	0.999927i	$0.496159\pi$
$908$	20.2891	0.673319
$909$	17.8875	0.593290
$910$	−48.3330	−1.60222
$911$	−19.5991	−0.649347	−0.324674	−	0.945826i	$-0.605254\pi$
$911$	−19.5991	−0.649347	−0.324674	+	0.945826i	$0.605254\pi$
$912$	−0.981518	−0.0325013
$913$	18.8358	0.623373
$914$	5.91536	0.195663
$915$	−53.7098	−1.77559
$916$	−4.05636	−0.134026
$917$	53.1666	1.75572
$918$	6.97955	0.230359
$919$	9.02726	0.297782	0.148891	−	0.988854i	$-0.452430\pi$
$919$	9.02726	0.297782	0.148891	+	0.988854i	$0.452430\pi$
$920$	6.21312	0.204840
$921$	59.6171	1.96445
$922$	−17.0935	−0.562944
$923$	5.98535	0.197010
$924$	22.8737	0.752489
$925$	−11.6755	−0.383888
$926$	−7.13732	−0.234547
$927$	2.05474	0.0674865
$928$	6.34012	0.208125
$929$	−38.3484	−1.25817	−0.629085	−	0.777337i	$-0.716570\pi$
$929$	−38.3484	−1.25817	−0.629085	+	0.777337i	$0.716570\pi$
$930$	−32.1377	−1.05384
$931$	5.27326	0.172824
$932$	−21.2947	−0.697532
$933$	8.81992	0.288751
$934$	−0.164316	−0.00537658
$935$	23.4524	0.766976
$936$	−9.70862	−0.317336
$937$	16.1214	0.526663	0.263332	−	0.964705i	$-0.415179\pi$
$937$	16.1214	0.526663	0.263332	+	0.964705i	$0.415179\pi$
$938$	−19.6807	−0.642597
$939$	−20.3421	−0.663840
$940$	15.8618	0.517355
$941$	28.1018	0.916093	0.458046	−	0.888928i	$-0.348549\pi$
$941$	28.1018	0.916093	0.458046	+	0.888928i	$0.348549\pi$
$942$	−5.51833	−0.179797
$943$	−1.75687	−0.0572115
$944$	7.04607	0.229330
$945$	19.2776	0.627102
$946$	0.338606	0.0110090
$947$	−47.7350	−1.55118	−0.775590	−	0.631237i	$-0.782548\pi$
$947$	−47.7350	−1.55118	−0.775590	+	0.631237i	$0.782548\pi$
$948$	−37.2396	−1.20949
$949$	32.7712	1.06380
$950$	−0.637331	−0.0206778
$951$	40.9079	1.32653
$952$	17.8052	0.577071
$953$	5.59553	0.181257	0.0906285	−	0.995885i	$-0.471112\pi$
$953$	5.59553	0.181257	0.0906285	+	0.995885i	$0.471112\pi$
$954$	1.31952	0.0427212
$955$	−52.2777	−1.69167
$956$	−18.7033	−0.604908
$957$	−33.0040	−1.06687
$958$	9.22389	0.298010
$959$	65.7712	2.12386
$960$	−5.83502	−0.188324
$961$	−0.665010	−0.0214519
$962$	33.8956	1.09284
$963$	−0.722576	−0.0232847
$964$	−11.5431	−0.371779
$965$	11.8359	0.381011
$966$	−24.5549	−0.790042
$967$	−39.9293	−1.28404	−0.642020	−	0.766688i	$-0.721903\pi$
$967$	−39.9293	−1.28404	−0.642020	+	0.766688i	$0.721903\pi$
$968$	5.83663	0.187596
$969$	3.97721	0.127767
$970$	22.3445	0.717440
$971$	29.8901	0.959221	0.479610	−	0.877482i	$-0.340778\pi$
$971$	29.8901	0.959221	0.479610	+	0.877482i	$0.340778\pi$
$972$	19.3228	0.619781
$973$	50.5810	1.62155
$974$	−11.1941	−0.358681
$975$	−14.7166	−0.471309
$976$	9.20473	0.294636
$977$	46.8847	1.49998	0.749988	−	0.661452i	$-0.230059\pi$
$977$	46.8847	1.49998	0.749988	+	0.661452i	$0.230059\pi$
$978$	−28.5713	−0.913608
$979$	−25.1218	−0.802896
$980$	31.3489	1.00141
$981$	37.4154	1.19458
$982$	−4.66356	−0.148820
$983$	46.1933	1.47334	0.736669	−	0.676253i	$-0.236397\pi$
$983$	46.1933	1.47334	0.736669	+	0.676253i	$0.236397\pi$
$984$	1.64995	0.0525986
$985$	−21.5947	−0.688066
$986$	−25.6908	−0.818163
$987$	−62.6877	−1.99537
$988$	1.85026	0.0588646
$989$	−0.363494	−0.0115584
$990$	13.0115	0.413533
$991$	48.2334	1.53218	0.766092	−	0.642731i	$-0.222199\pi$
$991$	48.2334	1.53218	0.766092	+	0.642731i	$0.222199\pi$
$992$	5.50772	0.174870
$993$	41.7713	1.32557
$994$	−6.09004	−0.193164
$995$	60.9506	1.93226
$996$	18.9897	0.601713
$997$	−27.6135	−0.874528	−0.437264	−	0.899333i	$-0.644052\pi$
$997$	−27.6135	−0.874528	−0.437264	+	0.899333i	$0.644052\pi$
$998$	−12.8820	−0.407773
$999$	−13.5193	−0.427730

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6002.2.a.c.1.13	✓	69

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6002.2.a.c.1.13	✓	69	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:	\( N \)	\(=\)	\( 6002 = 2 \cdot 3001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6002.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.29088 q^{3} +1.00000 q^{4} +2.54707 q^{5} +2.29088 q^{6} +4.39407 q^{7} -1.00000 q^{8} +2.24813 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.29088 q^{3} +1.00000 q^{4} +2.54707 q^{5} +2.29088 q^{6} +4.39407 q^{7} -1.00000 q^{8} +2.24813 q^{9} -2.54707 q^{10} -2.27231 q^{11} -2.29088 q^{12} +4.31854 q^{13} -4.39407 q^{14} -5.83502 q^{15} +1.00000 q^{16} -4.05210 q^{17} -2.24813 q^{18} +0.428446 q^{19} +2.54707 q^{20} -10.0663 q^{21} +2.27231 q^{22} -2.43932 q^{23} +2.29088 q^{24} +1.48754 q^{25} -4.31854 q^{26} +1.72245 q^{27} +4.39407 q^{28} -6.34012 q^{29} +5.83502 q^{30} -5.50772 q^{31} -1.00000 q^{32} +5.20558 q^{33} +4.05210 q^{34} +11.1920 q^{35} +2.24813 q^{36} -7.84885 q^{37} -0.428446 q^{38} -9.89324 q^{39} -2.54707 q^{40} +0.720227 q^{41} +10.0663 q^{42} +0.149014 q^{43} -2.27231 q^{44} +5.72613 q^{45} +2.43932 q^{46} +6.22749 q^{47} -2.29088 q^{48} +12.3079 q^{49} -1.48754 q^{50} +9.28288 q^{51} +4.31854 q^{52} -0.586944 q^{53} -1.72245 q^{54} -5.78771 q^{55} -4.39407 q^{56} -0.981518 q^{57} +6.34012 q^{58} +7.04607 q^{59} -5.83502 q^{60} +9.20473 q^{61} +5.50772 q^{62} +9.87843 q^{63} +1.00000 q^{64} +10.9996 q^{65} -5.20558 q^{66} +4.47892 q^{67} -4.05210 q^{68} +5.58819 q^{69} -11.1920 q^{70} +1.38597 q^{71} -2.24813 q^{72} +7.58850 q^{73} +7.84885 q^{74} -3.40778 q^{75} +0.428446 q^{76} -9.98468 q^{77} +9.89324 q^{78} +16.2556 q^{79} +2.54707 q^{80} -10.6903 q^{81} -0.720227 q^{82} -8.28928 q^{83} -10.0663 q^{84} -10.3210 q^{85} -0.149014 q^{86} +14.5244 q^{87} +2.27231 q^{88} +11.0556 q^{89} -5.72613 q^{90} +18.9760 q^{91} -2.43932 q^{92} +12.6175 q^{93} -6.22749 q^{94} +1.09128 q^{95} +2.29088 q^{96} -8.77266 q^{97} -12.3079 q^{98} -5.10843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 69 q - 69 q^{2} + 11 q^{3} + 69 q^{4} - 2 q^{5} - 11 q^{6} + 23 q^{7} - 69 q^{8} + 72 q^{9}+O(q^{10}) \) 69 * q - 69 * q^2 + 11 * q^3 + 69 * q^4 - 2 * q^5 - 11 * q^6 + 23 * q^7 - 69 * q^8 + 72 * q^9	\( 69 q - 69 q^{2} + 11 q^{3} + 69 q^{4} - 2 q^{5} - 11 q^{6} + 23 q^{7} - 69 q^{8} + 72 q^{9} + 2 q^{10} - 14 q^{11} + 11 q^{12} + 31 q^{13} - 23 q^{14} + 34 q^{15} + 69 q^{16} - 4 q^{17} - 72 q^{18} + 17 q^{19} - 2 q^{20} - 11 q^{21} + 14 q^{22} + 33 q^{23} - 11 q^{24} + 119 q^{25} - 31 q^{26} + 44 q^{27} + 23 q^{28} - 25 q^{29} - 34 q^{30} + 49 q^{31} - 69 q^{32} + 10 q^{33} + 4 q^{34} - 11 q^{35} + 72 q^{36} + 73 q^{37} - 17 q^{38} + 31 q^{39} + 2 q^{40} - 46 q^{41} + 11 q^{42} + 76 q^{43} - 14 q^{44} + 9 q^{45} - 33 q^{46} + 23 q^{47} + 11 q^{48} + 100 q^{49} - 119 q^{50} + 25 q^{51} + 31 q^{52} + 30 q^{53} - 44 q^{54} + 81 q^{55} - 23 q^{56} + 12 q^{57} + 25 q^{58} - 3 q^{59} + 34 q^{60} + 13 q^{61} - 49 q^{62} + 65 q^{63} + 69 q^{64} - 27 q^{65} - 10 q^{66} + 105 q^{67} - 4 q^{68} + 19 q^{69} + 11 q^{70} + 51 q^{71} - 72 q^{72} + 43 q^{73} - 73 q^{74} + 77 q^{75} + 17 q^{76} - 19 q^{77} - 31 q^{78} + 89 q^{79} - 2 q^{80} + 73 q^{81} + 46 q^{82} - 10 q^{83} - 11 q^{84} + 44 q^{85} - 76 q^{86} + 57 q^{87} + 14 q^{88} - 28 q^{89} - 9 q^{90} + 76 q^{91} + 33 q^{92} + 59 q^{93} - 23 q^{94} + 72 q^{95} - 11 q^{96} + 89 q^{97} - 100 q^{98} - 17 q^{99}+O(q^{100}) \) 69 * q - 69 * q^2 + 11 * q^3 + 69 * q^4 - 2 * q^5 - 11 * q^6 + 23 * q^7 - 69 * q^8 + 72 * q^9 + 2 * q^10 - 14 * q^11 + 11 * q^12 + 31 * q^13 - 23 * q^14 + 34 * q^15 + 69 * q^16 - 4 * q^17 - 72 * q^18 + 17 * q^19 - 2 * q^20 - 11 * q^21 + 14 * q^22 + 33 * q^23 - 11 * q^24 + 119 * q^25 - 31 * q^26 + 44 * q^27 + 23 * q^28 - 25 * q^29 - 34 * q^30 + 49 * q^31 - 69 * q^32 + 10 * q^33 + 4 * q^34 - 11 * q^35 + 72 * q^36 + 73 * q^37 - 17 * q^38 + 31 * q^39 + 2 * q^40 - 46 * q^41 + 11 * q^42 + 76 * q^43 - 14 * q^44 + 9 * q^45 - 33 * q^46 + 23 * q^47 + 11 * q^48 + 100 * q^49 - 119 * q^50 + 25 * q^51 + 31 * q^52 + 30 * q^53 - 44 * q^54 + 81 * q^55 - 23 * q^56 + 12 * q^57 + 25 * q^58 - 3 * q^59 + 34 * q^60 + 13 * q^61 - 49 * q^62 + 65 * q^63 + 69 * q^64 - 27 * q^65 - 10 * q^66 + 105 * q^67 - 4 * q^68 + 19 * q^69 + 11 * q^70 + 51 * q^71 - 72 * q^72 + 43 * q^73 - 73 * q^74 + 77 * q^75 + 17 * q^76 - 19 * q^77 - 31 * q^78 + 89 * q^79 - 2 * q^80 + 73 * q^81 + 46 * q^82 - 10 * q^83 - 11 * q^84 + 44 * q^85 - 76 * q^86 + 57 * q^87 + 14 * q^88 - 28 * q^89 - 9 * q^90 + 76 * q^91 + 33 * q^92 + 59 * q^93 - 23 * q^94 + 72 * q^95 - 11 * q^96 + 89 * q^97 - 100 * q^98 - 17 * q^99

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