LMFDB - Embedded newform 8045.2.a.b.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8045,2,Mod(1,8045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8045, 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("8045.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8045 = 5 \cdot 1609 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8045.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:	$64.2396484261$
Analytic rank:	$1$
Dimension:	$126$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	8045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.02597 q^{2} -2.39891 q^{3} +2.10454 q^{4} -1.00000 q^{5} +4.86012 q^{6} -3.38637 q^{7} -0.211794 q^{8} +2.75479 q^{9} +O(q^{10})$	\(q-2.02597 q^{2} -2.39891 q^{3} +2.10454 q^{4} -1.00000 q^{5} +4.86012 q^{6} -3.38637 q^{7} -0.211794 q^{8} +2.75479 q^{9} +2.02597 q^{10} -1.46449 q^{11} -5.04861 q^{12} +1.25991 q^{13} +6.86067 q^{14} +2.39891 q^{15} -3.77999 q^{16} +5.15410 q^{17} -5.58111 q^{18} -0.396702 q^{19} -2.10454 q^{20} +8.12361 q^{21} +2.96701 q^{22} -4.48556 q^{23} +0.508075 q^{24} +1.00000 q^{25} -2.55253 q^{26} +0.588236 q^{27} -7.12675 q^{28} +1.44286 q^{29} -4.86012 q^{30} -9.23051 q^{31} +8.08172 q^{32} +3.51318 q^{33} -10.4420 q^{34} +3.38637 q^{35} +5.79757 q^{36} +6.78143 q^{37} +0.803705 q^{38} -3.02241 q^{39} +0.211794 q^{40} -11.5949 q^{41} -16.4582 q^{42} -1.84037 q^{43} -3.08207 q^{44} -2.75479 q^{45} +9.08760 q^{46} -0.822167 q^{47} +9.06788 q^{48} +4.46749 q^{49} -2.02597 q^{50} -12.3642 q^{51} +2.65152 q^{52} +1.19606 q^{53} -1.19175 q^{54} +1.46449 q^{55} +0.717212 q^{56} +0.951655 q^{57} -2.92319 q^{58} -7.78487 q^{59} +5.04861 q^{60} +3.32061 q^{61} +18.7007 q^{62} -9.32874 q^{63} -8.81332 q^{64} -1.25991 q^{65} -7.11759 q^{66} +0.964934 q^{67} +10.8470 q^{68} +10.7605 q^{69} -6.86067 q^{70} +0.994986 q^{71} -0.583448 q^{72} +9.13181 q^{73} -13.7389 q^{74} -2.39891 q^{75} -0.834875 q^{76} +4.95930 q^{77} +6.12330 q^{78} -1.18072 q^{79} +3.77999 q^{80} -9.67550 q^{81} +23.4909 q^{82} -14.2425 q^{83} +17.0965 q^{84} -5.15410 q^{85} +3.72854 q^{86} -3.46130 q^{87} +0.310170 q^{88} +1.82529 q^{89} +5.58111 q^{90} -4.26651 q^{91} -9.44004 q^{92} +22.1432 q^{93} +1.66568 q^{94} +0.396702 q^{95} -19.3874 q^{96} -3.32925 q^{97} -9.05098 q^{98} -4.03436 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 126 q + 5 q^{2} - 9 q^{3} + 109 q^{4} - 126 q^{5} - 21 q^{6} - 23 q^{7} + 12 q^{8} + 109 q^{9}+O(q^{10}) $ 126 * q + 5 * q^2 - 9 * q^3 + 109 * q^4 - 126 * q^5 - 21 * q^6 - 23 * q^7 + 12 * q^8 + 109 * q^9	\( 126 q + 5 q^{2} - 9 q^{3} + 109 q^{4} - 126 q^{5} - 21 q^{6} - 23 q^{7} + 12 q^{8} + 109 q^{9} - 5 q^{10} - 44 q^{11} - 11 q^{12} - 35 q^{13} - 14 q^{14} + 9 q^{15} + 75 q^{16} + 11 q^{17} - 15 q^{18} - 130 q^{19} - 109 q^{20} - 44 q^{21} - 14 q^{22} + 75 q^{23} - 63 q^{24} + 126 q^{25} - 43 q^{26} - 42 q^{27} - 77 q^{28} - 24 q^{29} + 21 q^{30} - 78 q^{31} + 24 q^{32} - 29 q^{33} - 57 q^{34} + 23 q^{35} + 50 q^{36} - 31 q^{37} - 3 q^{38} - 57 q^{39} - 12 q^{40} - 38 q^{41} - 10 q^{42} - 100 q^{43} - 90 q^{44} - 109 q^{45} - 96 q^{46} + 12 q^{47} - 22 q^{48} + 65 q^{49} + 5 q^{50} - 74 q^{51} - 112 q^{52} + 20 q^{53} - 90 q^{54} + 44 q^{55} - 57 q^{56} + 6 q^{57} - 35 q^{58} - 97 q^{59} + 11 q^{60} - 102 q^{61} - 16 q^{62} - 15 q^{63} + 4 q^{64} + 35 q^{65} - 83 q^{66} - 121 q^{67} + 41 q^{68} - 71 q^{69} + 14 q^{70} - 32 q^{71} - 32 q^{72} - 85 q^{73} - 42 q^{74} - 9 q^{75} - 275 q^{76} + 13 q^{77} + 10 q^{78} - 97 q^{79} - 75 q^{80} + 86 q^{81} - 55 q^{82} - 73 q^{83} - 111 q^{84} - 11 q^{85} - 56 q^{86} - q^{87} - 37 q^{88} - 67 q^{89} + 15 q^{90} - 180 q^{91} + 98 q^{92} - 44 q^{93} - 86 q^{94} + 130 q^{95} - 179 q^{96} - 50 q^{97} + 18 q^{98} - 217 q^{99}+O(q^{100}) \) 126 * q + 5 * q^2 - 9 * q^3 + 109 * q^4 - 126 * q^5 - 21 * q^6 - 23 * q^7 + 12 * q^8 + 109 * q^9 - 5 * q^10 - 44 * q^11 - 11 * q^12 - 35 * q^13 - 14 * q^14 + 9 * q^15 + 75 * q^16 + 11 * q^17 - 15 * q^18 - 130 * q^19 - 109 * q^20 - 44 * q^21 - 14 * q^22 + 75 * q^23 - 63 * q^24 + 126 * q^25 - 43 * q^26 - 42 * q^27 - 77 * q^28 - 24 * q^29 + 21 * q^30 - 78 * q^31 + 24 * q^32 - 29 * q^33 - 57 * q^34 + 23 * q^35 + 50 * q^36 - 31 * q^37 - 3 * q^38 - 57 * q^39 - 12 * q^40 - 38 * q^41 - 10 * q^42 - 100 * q^43 - 90 * q^44 - 109 * q^45 - 96 * q^46 + 12 * q^47 - 22 * q^48 + 65 * q^49 + 5 * q^50 - 74 * q^51 - 112 * q^52 + 20 * q^53 - 90 * q^54 + 44 * q^55 - 57 * q^56 + 6 * q^57 - 35 * q^58 - 97 * q^59 + 11 * q^60 - 102 * q^61 - 16 * q^62 - 15 * q^63 + 4 * q^64 + 35 * q^65 - 83 * q^66 - 121 * q^67 + 41 * q^68 - 71 * q^69 + 14 * q^70 - 32 * q^71 - 32 * q^72 - 85 * q^73 - 42 * q^74 - 9 * q^75 - 275 * q^76 + 13 * q^77 + 10 * q^78 - 97 * q^79 - 75 * q^80 + 86 * q^81 - 55 * q^82 - 73 * q^83 - 111 * q^84 - 11 * q^85 - 56 * q^86 - q^87 - 37 * q^88 - 67 * q^89 + 15 * q^90 - 180 * q^91 + 98 * q^92 - 44 * q^93 - 86 * q^94 + 130 * q^95 - 179 * q^96 - 50 * q^97 + 18 * q^98 - 217 * 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 $

$2$	−2.02597	−1.43257	−0.716287	−	0.697806i	$-0.754160\pi$
$2$	−2.02597	−1.43257	−0.716287	+	0.697806i	$0.754160\pi$
$3$	−2.39891	−1.38501	−0.692507	−	0.721411i	$-0.743494\pi$
$3$	−2.39891	−1.38501	−0.692507	+	0.721411i	$0.743494\pi$
$4$	2.10454	1.05227
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	4.86012	1.98414
$7$	−3.38637	−1.27993	−0.639963	−	0.768405i	$-0.721050\pi$
$7$	−3.38637	−1.27993	−0.639963	+	0.768405i	$0.721050\pi$
$8$	−0.211794	−0.0748804
$9$	2.75479	0.918264
$10$	2.02597	0.640667
$11$	−1.46449	−0.441560	−0.220780	−	0.975324i	$-0.570860\pi$
$11$	−1.46449	−0.441560	−0.220780	+	0.975324i	$0.570860\pi$
$12$	−5.04861	−1.45741
$13$	1.25991	0.349435	0.174718	−	0.984619i	$-0.444099\pi$
$13$	1.25991	0.349435	0.174718	+	0.984619i	$0.444099\pi$
$14$	6.86067	1.83359
$15$	2.39891	0.619397
$16$	−3.77999	−0.944998
$17$	5.15410	1.25005	0.625026	−	0.780604i	$-0.285088\pi$
$17$	5.15410	1.25005	0.625026	+	0.780604i	$0.285088\pi$
$18$	−5.58111	−1.31548
$19$	−0.396702	−0.0910097	−0.0455049	−	0.998964i	$-0.514490\pi$
$19$	−0.396702	−0.0910097	−0.0455049	+	0.998964i	$0.514490\pi$
$20$	−2.10454	−0.470589
$21$	8.12361	1.77272
$22$	2.96701	0.632568
$23$	−4.48556	−0.935304	−0.467652	−	0.883913i	$-0.654900\pi$
$23$	−4.48556	−0.935304	−0.467652	+	0.883913i	$0.654900\pi$
$24$	0.508075	0.103710
$25$	1.00000	0.200000
$26$	−2.55253	−0.500592
$27$	0.588236	0.113206
$28$	−7.12675	−1.34683
$29$	1.44286	0.267932	0.133966	−	0.990986i	$-0.457229\pi$
$29$	1.44286	0.267932	0.133966	+	0.990986i	$0.457229\pi$
$30$	−4.86012	−0.887332
$31$	−9.23051	−1.65785	−0.828924	−	0.559361i	$-0.811047\pi$
$31$	−9.23051	−1.65785	−0.828924	+	0.559361i	$0.811047\pi$
$32$	8.08172	1.42866
$33$	3.51318	0.611567
$34$	−10.4420	−1.79079
$35$	3.38637	0.572401
$36$	5.79757	0.966261
$37$	6.78143	1.11486	0.557430	−	0.830224i	$-0.311787\pi$
$37$	6.78143	1.11486	0.557430	+	0.830224i	$0.311787\pi$
$38$	0.803705	0.130378
$39$	−3.02241	−0.483973
$40$	0.211794	0.0334875
$41$	−11.5949	−1.81082	−0.905410	−	0.424539i	$-0.860436\pi$
$41$	−11.5949	−1.81082	−0.905410	+	0.424539i	$0.860436\pi$
$42$	−16.4582	−2.53955
$43$	−1.84037	−0.280654	−0.140327	−	0.990105i	$-0.544815\pi$
$43$	−1.84037	−0.280654	−0.140327	+	0.990105i	$0.544815\pi$
$44$	−3.08207	−0.464640
$45$	−2.75479	−0.410660
$46$	9.08760	1.33989
$47$	−0.822167	−0.119925	−0.0599627	−	0.998201i	$-0.519098\pi$
$47$	−0.822167	−0.119925	−0.0599627	+	0.998201i	$0.519098\pi$
$48$	9.06788	1.30884
$49$	4.46749	0.638213
$50$	−2.02597	−0.286515
$51$	−12.3642	−1.73134
$52$	2.65152	0.367700
$53$	1.19606	0.164291	0.0821457	−	0.996620i	$-0.473823\pi$
$53$	1.19606	0.164291	0.0821457	+	0.996620i	$0.473823\pi$
$54$	−1.19175	−0.162176
$55$	1.46449	0.197472
$56$	0.717212	0.0958414
$57$	0.951655	0.126050
$58$	−2.92319	−0.383833
$59$	−7.78487	−1.01350	−0.506752	−	0.862092i	$-0.669154\pi$
$59$	−7.78487	−1.01350	−0.506752	+	0.862092i	$0.669154\pi$
$60$	5.04861	0.651773
$61$	3.32061	0.425161	0.212580	−	0.977144i	$-0.431813\pi$
$61$	3.32061	0.425161	0.212580	+	0.977144i	$0.431813\pi$
$62$	18.7007	2.37499
$63$	−9.32874	−1.17531
$64$	−8.81332	−1.10166
$65$	−1.25991	−0.156272
$66$	−7.11759	−0.876115
$67$	0.964934	0.117885	0.0589427	−	0.998261i	$-0.481227\pi$
$67$	0.964934	0.117885	0.0589427	+	0.998261i	$0.481227\pi$
$68$	10.8470	1.31539
$69$	10.7605	1.29541
$70$	−6.86067	−0.820007
$71$	0.994986	0.118083	0.0590415	−	0.998256i	$-0.481196\pi$
$71$	0.994986	0.118083	0.0590415	+	0.998256i	$0.481196\pi$
$72$	−0.583448	−0.0687600
$73$	9.13181	1.06880	0.534398	−	0.845233i	$-0.320538\pi$
$73$	9.13181	1.06880	0.534398	+	0.845233i	$0.320538\pi$
$74$	−13.7389	−1.59712
$75$	−2.39891	−0.277003
$76$	−0.834875	−0.0957668
$77$	4.95930	0.565164
$78$	6.12330	0.693327
$79$	−1.18072	−0.132841	−0.0664206	−	0.997792i	$-0.521158\pi$
$79$	−1.18072	−0.132841	−0.0664206	+	0.997792i	$0.521158\pi$
$80$	3.77999	0.422616
$81$	−9.67550	−1.07506
$82$	23.4909	2.59413
$83$	−14.2425	−1.56332	−0.781659	−	0.623705i	$-0.785626\pi$
$83$	−14.2425	−1.56332	−0.781659	+	0.623705i	$0.785626\pi$
$84$	17.0965	1.86538
$85$	−5.15410	−0.559041
$86$	3.72854	0.402058
$87$	−3.46130	−0.371090
$88$	0.310170	0.0330642
$89$	1.82529	0.193480	0.0967399	−	0.995310i	$-0.469158\pi$
$89$	1.82529	0.193480	0.0967399	+	0.995310i	$0.469158\pi$
$90$	5.58111	0.588301
$91$	−4.26651	−0.447252
$92$	−9.44004	−0.984192
$93$	22.1432	2.29614
$94$	1.66568	0.171802
$95$	0.396702	0.0407008
$96$	−19.3874	−1.97871
$97$	−3.32925	−0.338034	−0.169017	−	0.985613i	$-0.554059\pi$
$97$	−3.32925	−0.338034	−0.169017	+	0.985613i	$0.554059\pi$
$98$	−9.05098	−0.914287
$99$	−4.03436	−0.405468
$100$	2.10454	0.210454
$101$	6.66153	0.662847	0.331423	−	0.943482i	$-0.392471\pi$
$101$	6.66153	0.662847	0.331423	+	0.943482i	$0.392471\pi$
$102$	25.0495	2.48027
$103$	4.59165	0.452429	0.226214	−	0.974078i	$-0.427365\pi$
$103$	4.59165	0.452429	0.226214	+	0.974078i	$0.427365\pi$
$104$	−0.266840	−0.0261659
$105$	−8.12361	−0.792783
$106$	−2.42318	−0.235360
$107$	4.47955	0.433054	0.216527	−	0.976277i	$-0.430527\pi$
$107$	4.47955	0.433054	0.216527	+	0.976277i	$0.430527\pi$
$108$	1.23797	0.119123
$109$	10.1108	0.968435	0.484217	−	0.874948i	$-0.339104\pi$
$109$	10.1108	0.968435	0.484217	+	0.874948i	$0.339104\pi$
$110$	−2.96701	−0.282893
$111$	−16.2681	−1.54410
$112$	12.8004	1.20953
$113$	17.1111	1.60967	0.804837	−	0.593497i	$-0.202253\pi$
$113$	17.1111	1.60967	0.804837	+	0.593497i	$0.202253\pi$
$114$	−1.92802	−0.180576
$115$	4.48556	0.418281
$116$	3.03656	0.281937
$117$	3.47078	0.320874
$118$	15.7719	1.45192
$119$	−17.4537	−1.59998
$120$	−0.508075	−0.0463807
$121$	−8.85527	−0.805025
$122$	−6.72745	−0.609075
$123$	27.8152	2.50801
$124$	−19.4260	−1.74450
$125$	−1.00000	−0.0894427
$126$	18.8997	1.68372
$127$	5.74191	0.509512	0.254756	−	0.967005i	$-0.418005\pi$
$127$	5.74191	0.509512	0.254756	+	0.967005i	$0.418005\pi$
$128$	1.69204	0.149556
$129$	4.41490	0.388710
$130$	2.55253	0.223872
$131$	−5.44772	−0.475969	−0.237985	−	0.971269i	$-0.576487\pi$
$131$	−5.44772	−0.475969	−0.237985	+	0.971269i	$0.576487\pi$
$132$	7.39363	0.643533
$133$	1.34338	0.116486
$134$	−1.95492	−0.168880
$135$	−0.588236	−0.0506273
$136$	−1.09161	−0.0936045
$137$	−6.19704	−0.529449	−0.264724	−	0.964324i	$-0.585281\pi$
$137$	−6.19704	−0.529449	−0.264724	+	0.964324i	$0.585281\pi$
$138$	−21.8004	−1.85577
$139$	4.07871	0.345951	0.172976	−	0.984926i	$-0.444662\pi$
$139$	4.07871	0.345951	0.172976	+	0.984926i	$0.444662\pi$
$140$	7.12675	0.602320
$141$	1.97231	0.166098
$142$	−2.01581	−0.169163
$143$	−1.84512	−0.154297
$144$	−10.4131	−0.867757
$145$	−1.44286	−0.119823
$146$	−18.5007	−1.53113
$147$	−10.7171	−0.883933
$148$	14.2718	1.17313
$149$	10.1072	0.828016	0.414008	−	0.910273i	$-0.364129\pi$
$149$	10.1072	0.828016	0.414008	+	0.910273i	$0.364129\pi$
$150$	4.86012	0.396827
$151$	2.43546	0.198195	0.0990976	−	0.995078i	$-0.468404\pi$
$151$	2.43546	0.198195	0.0990976	+	0.995078i	$0.468404\pi$
$152$	0.0840191	0.00681484
$153$	14.1985	1.14788
$154$	−10.0474	−0.809640
$155$	9.23051	0.741412
$156$	−6.36078	−0.509270
$157$	1.74298	0.139105	0.0695525	−	0.997578i	$-0.477843\pi$
$157$	1.74298	0.139105	0.0695525	+	0.997578i	$0.477843\pi$
$158$	2.39210	0.190305
$159$	−2.86925	−0.227546
$160$	−8.08172	−0.638916
$161$	15.1898	1.19712
$162$	19.6022	1.54010
$163$	13.4042	1.04990	0.524949	−	0.851134i	$-0.324084\pi$
$163$	13.4042	1.04990	0.524949	+	0.851134i	$0.324084\pi$
$164$	−24.4019	−1.90547
$165$	−3.51318	−0.273501
$166$	28.8549	2.23957
$167$	−13.7237	−1.06197	−0.530986	−	0.847381i	$-0.678178\pi$
$167$	−13.7237	−1.06197	−0.530986	+	0.847381i	$0.678178\pi$
$168$	−1.72053	−0.132742
$169$	−11.4126	−0.877895
$170$	10.4420	0.800867
$171$	−1.09283	−0.0835709
$172$	−3.87314	−0.295324
$173$	13.5532	1.03043	0.515215	−	0.857061i	$-0.327712\pi$
$173$	13.5532	1.03043	0.515215	+	0.857061i	$0.327712\pi$
$174$	7.01247	0.531614
$175$	−3.38637	−0.255985
$176$	5.53576	0.417273
$177$	18.6752	1.40372
$178$	−3.69797	−0.277174
$179$	−5.23802	−0.391508	−0.195754	−	0.980653i	$-0.562715\pi$
$179$	−5.23802	−0.391508	−0.195754	+	0.980653i	$0.562715\pi$
$180$	−5.79757	−0.432125
$181$	−1.78250	−0.132492	−0.0662461	−	0.997803i	$-0.521102\pi$
$181$	−1.78250	−0.132492	−0.0662461	+	0.997803i	$0.521102\pi$
$182$	8.64380	0.640721
$183$	−7.96587	−0.588854
$184$	0.950014	0.0700360
$185$	−6.78143	−0.498581
$186$	−44.8614	−3.28940
$187$	−7.54812	−0.551973
$188$	−1.73028	−0.126194
$189$	−1.99198	−0.144895
$190$	−0.803705	−0.0583069
$191$	25.3105	1.83140	0.915702	−	0.401857i	$-0.131635\pi$
$191$	25.3105	1.83140	0.915702	+	0.401857i	$0.131635\pi$
$192$	21.1424	1.52582
$193$	−11.9047	−0.856920	−0.428460	−	0.903561i	$-0.640944\pi$
$193$	−11.9047	−0.856920	−0.428460	+	0.903561i	$0.640944\pi$
$194$	6.74495	0.484259
$195$	3.02241	0.216439
$196$	9.40201	0.671572
$197$	14.7761	1.05275	0.526376	−	0.850252i	$-0.323550\pi$
$197$	14.7761	1.05275	0.526376	+	0.850252i	$0.323550\pi$
$198$	8.17348	0.580864
$199$	−9.67733	−0.686008	−0.343004	−	0.939334i	$-0.611444\pi$
$199$	−9.67733	−0.686008	−0.343004	+	0.939334i	$0.611444\pi$
$200$	−0.211794	−0.0149761
$201$	−2.31479	−0.163273
$202$	−13.4960	−0.949578
$203$	−4.88605	−0.342934
$204$	−26.0210	−1.82184
$205$	11.5949	0.809823
$206$	−9.30253	−0.648138
$207$	−12.3568	−0.858856
$208$	−4.76244	−0.330216
$209$	0.580966	0.0401863
$210$	16.4582	1.13572
$211$	20.4504	1.40786	0.703931	−	0.710268i	$-0.251426\pi$
$211$	20.4504	1.40786	0.703931	+	0.710268i	$0.251426\pi$
$212$	2.51716	0.172879
$213$	−2.38689	−0.163547
$214$	−9.07541	−0.620382
$215$	1.84037	0.125512
$216$	−0.124585	−0.00847691
$217$	31.2579	2.12193
$218$	−20.4840	−1.38735
$219$	−21.9064	−1.48030
$220$	3.08207	0.207793
$221$	6.49368	0.436812
$222$	32.9586	2.21203
$223$	−8.34873	−0.559072	−0.279536	−	0.960135i	$-0.590181\pi$
$223$	−8.34873	−0.559072	−0.279536	+	0.960135i	$0.590181\pi$
$224$	−27.3677	−1.82858
$225$	2.75479	0.183653
$226$	−34.6664	−2.30598
$227$	7.90921	0.524952	0.262476	−	0.964938i	$-0.415461\pi$
$227$	7.90921	0.524952	0.262476	+	0.964938i	$0.415461\pi$
$228$	2.00279	0.132638
$229$	−15.2673	−1.00889	−0.504446	−	0.863443i	$-0.668303\pi$
$229$	−15.2673	−1.00889	−0.504446	+	0.863443i	$0.668303\pi$
$230$	−9.08760	−0.599218
$231$	−11.8969	−0.782761
$232$	−0.305589	−0.0200629
$233$	18.4735	1.21024	0.605118	−	0.796136i	$-0.293126\pi$
$233$	18.4735	1.21024	0.605118	+	0.796136i	$0.293126\pi$
$234$	−7.03168	−0.459675
$235$	0.822167	0.0536323
$236$	−16.3836	−1.06648
$237$	2.83244	0.183987
$238$	35.3606	2.29208
$239$	25.3325	1.63863	0.819313	−	0.573347i	$-0.194355\pi$
$239$	25.3325	1.63863	0.819313	+	0.573347i	$0.194355\pi$
$240$	−9.06788	−0.585329
$241$	9.39787	0.605370	0.302685	−	0.953091i	$-0.402117\pi$
$241$	9.39787	0.605370	0.302685	+	0.953091i	$0.402117\pi$
$242$	17.9405	1.15326
$243$	21.4460	1.37576
$244$	6.98836	0.447384
$245$	−4.46749	−0.285417
$246$	−56.3526	−3.59291
$247$	−0.499808	−0.0318020
$248$	1.95496	0.124140
$249$	34.1666	2.16522
$250$	2.02597	0.128133
$251$	12.9685	0.818563	0.409281	−	0.912408i	$-0.365779\pi$
$251$	12.9685	0.818563	0.409281	+	0.912408i	$0.365779\pi$
$252$	−19.6327	−1.23674
$253$	6.56905	0.412993
$254$	−11.6329	−0.729914
$255$	12.3642	0.774279
$256$	14.1986	0.887414
$257$	−15.2080	−0.948650	−0.474325	−	0.880350i	$-0.657308\pi$
$257$	−15.2080	−0.948650	−0.474325	+	0.880350i	$0.657308\pi$
$258$	−8.94444	−0.556856
$259$	−22.9644	−1.42694
$260$	−2.65152	−0.164441
$261$	3.97478	0.246033
$262$	11.0369	0.681861
$263$	−7.80807	−0.481466	−0.240733	−	0.970591i	$-0.577388\pi$
$263$	−7.80807	−0.481466	−0.240733	+	0.970591i	$0.577388\pi$
$264$	−0.744070	−0.0457944
$265$	−1.19606	−0.0734734
$266$	−2.72164	−0.166875
$267$	−4.37870	−0.267972
$268$	2.03074	0.124047
$269$	−9.95890	−0.607205	−0.303602	−	0.952799i	$-0.598189\pi$
$269$	−9.95890	−0.607205	−0.303602	+	0.952799i	$0.598189\pi$
$270$	1.19175	0.0725274
$271$	2.29536	0.139433	0.0697167	−	0.997567i	$-0.477790\pi$
$271$	2.29536	0.139433	0.0697167	+	0.997567i	$0.477790\pi$
$272$	−19.4825	−1.18130
$273$	10.2350	0.619450
$274$	12.5550	0.758475
$275$	−1.46449	−0.0883120
$276$	22.6459	1.36312
$277$	−25.4601	−1.52975	−0.764874	−	0.644180i	$-0.777199\pi$
$277$	−25.4601	−1.52975	−0.764874	+	0.644180i	$0.777199\pi$
$278$	−8.26332	−0.495601
$279$	−25.4281	−1.52234
$280$	−0.717212	−0.0428616
$281$	19.3355	1.15346	0.576730	−	0.816935i	$-0.304329\pi$
$281$	19.3355	1.15346	0.576730	+	0.816935i	$0.304329\pi$
$282$	−3.99583	−0.237948
$283$	−7.86175	−0.467332	−0.233666	−	0.972317i	$-0.575072\pi$
$283$	−7.86175	−0.467332	−0.233666	+	0.972317i	$0.575072\pi$
$284$	2.09399	0.124255
$285$	−0.951655	−0.0563712
$286$	3.73815	0.221041
$287$	39.2646	2.31772
$288$	22.2635	1.31189
$289$	9.56474	0.562632
$290$	2.92319	0.171655
$291$	7.98659	0.468182
$292$	19.2182	1.12466
$293$	−6.15176	−0.359389	−0.179695	−	0.983722i	$-0.557511\pi$
$293$	−6.15176	−0.359389	−0.179695	+	0.983722i	$0.557511\pi$
$294$	21.7125	1.26630
$295$	7.78487	0.453253
$296$	−1.43626	−0.0834812
$297$	−0.861465	−0.0499873
$298$	−20.4769	−1.18619
$299$	−5.65139	−0.326828
$300$	−5.04861	−0.291482
$301$	6.23218	0.359217
$302$	−4.93417	−0.283929
$303$	−15.9804	−0.918052
$304$	1.49953	0.0860040
$305$	−3.32061	−0.190138
$306$	−28.7656	−1.64442
$307$	20.7805	1.18600	0.593002	−	0.805201i	$-0.297942\pi$
$307$	20.7805	1.18600	0.593002	+	0.805201i	$0.297942\pi$
$308$	10.4370	0.594705
$309$	−11.0150	−0.626620
$310$	−18.7007	−1.06213
$311$	17.0819	0.968627	0.484314	−	0.874894i	$-0.339069\pi$
$311$	17.0819	0.968627	0.484314	+	0.874894i	$0.339069\pi$
$312$	0.640127	0.0362401
$313$	28.4942	1.61059	0.805293	−	0.592877i	$-0.202008\pi$
$313$	28.4942	1.61059	0.805293	+	0.592877i	$0.202008\pi$
$314$	−3.53122	−0.199278
$315$	9.32874	0.525615
$316$	−2.48487	−0.139785
$317$	17.8140	1.00053	0.500266	−	0.865872i	$-0.333235\pi$
$317$	17.8140	1.00053	0.500266	+	0.865872i	$0.333235\pi$
$318$	5.81300	0.325977
$319$	−2.11305	−0.118308
$320$	8.81332	0.492679
$321$	−10.7460	−0.599786
$322$	−30.7739	−1.71496
$323$	−2.04464	−0.113767
$324$	−20.3625	−1.13125
$325$	1.25991	0.0698870
$326$	−27.1565	−1.50406
$327$	−24.2548	−1.34130
$328$	2.45573	0.135595
$329$	2.78416	0.153496
$330$	7.11759	0.391811
$331$	1.43329	0.0787807	0.0393903	−	0.999224i	$-0.487458\pi$
$331$	1.43329	0.0787807	0.0393903	+	0.999224i	$0.487458\pi$
$332$	−29.9739	−1.64503
$333$	18.6814	1.02374
$334$	27.8037	1.52135
$335$	−0.964934	−0.0527200
$336$	−30.7072	−1.67521
$337$	15.1899	0.827445	0.413723	−	0.910403i	$-0.364228\pi$
$337$	15.1899	0.827445	0.413723	+	0.910403i	$0.364228\pi$
$338$	23.1216	1.25765
$339$	−41.0480	−2.22942
$340$	−10.8470	−0.588262
$341$	13.5180	0.732040
$342$	2.21404	0.119722
$343$	8.57602	0.463061
$344$	0.389780	0.0210155
$345$	−10.7605	−0.579325
$346$	−27.4583	−1.47617
$347$	19.8663	1.06648	0.533240	−	0.845964i	$-0.320974\pi$
$347$	19.8663	1.06648	0.533240	+	0.845964i	$0.320974\pi$
$348$	−7.28444	−0.390487
$349$	10.4829	0.561135	0.280568	−	0.959834i	$-0.409477\pi$
$349$	10.4829	0.561135	0.280568	+	0.959834i	$0.409477\pi$
$350$	6.86067	0.366718
$351$	0.741122	0.0395582
$352$	−11.8356	−0.630839
$353$	8.49720	0.452260	0.226130	−	0.974097i	$-0.427393\pi$
$353$	8.49720	0.452260	0.226130	+	0.974097i	$0.427393\pi$
$354$	−37.8354	−2.01093
$355$	−0.994986	−0.0528084
$356$	3.84139	0.203593
$357$	41.8699	2.21599
$358$	10.6121	0.560864
$359$	8.08472	0.426695	0.213348	−	0.976976i	$-0.431563\pi$
$359$	8.08472	0.426695	0.213348	+	0.976976i	$0.431563\pi$
$360$	0.583448	0.0307504
$361$	−18.8426	−0.991717
$362$	3.61128	0.189805
$363$	21.2430	1.11497
$364$	−8.97903	−0.470629
$365$	−9.13181	−0.477981
$366$	16.1386	0.843577
$367$	−15.1838	−0.792586	−0.396293	−	0.918124i	$-0.629704\pi$
$367$	−15.1838	−0.792586	−0.396293	+	0.918124i	$0.629704\pi$
$368$	16.9554	0.883861
$369$	−31.9415	−1.66281
$370$	13.7389	0.714254
$371$	−4.05030	−0.210281
$372$	46.6013	2.41616
$373$	−5.12099	−0.265155	−0.132577	−	0.991173i	$-0.542325\pi$
$373$	−5.12099	−0.265155	−0.132577	+	0.991173i	$0.542325\pi$
$374$	15.2922	0.790743
$375$	2.39891	0.123879
$376$	0.174130	0.00898006
$377$	1.81787	0.0936250
$378$	4.03569	0.207574
$379$	−25.2354	−1.29626	−0.648129	−	0.761531i	$-0.724448\pi$
$379$	−25.2354	−1.29626	−0.648129	+	0.761531i	$0.724448\pi$
$380$	0.834875	0.0428282
$381$	−13.7744	−0.705682
$382$	−51.2783	−2.62362
$383$	6.80234	0.347583	0.173792	−	0.984782i	$-0.444398\pi$
$383$	6.80234	0.347583	0.173792	+	0.984782i	$0.444398\pi$
$384$	−4.05905	−0.207137
$385$	−4.95930	−0.252749
$386$	24.1186	1.22760
$387$	−5.06985	−0.257715
$388$	−7.00654	−0.355703
$389$	0.944206	0.0478732	0.0239366	−	0.999713i	$-0.492380\pi$
$389$	0.944206	0.0478732	0.0239366	+	0.999713i	$0.492380\pi$
$390$	−6.12330	−0.310065
$391$	−23.1190	−1.16918
$392$	−0.946186	−0.0477896
$393$	13.0686	0.659224
$394$	−29.9358	−1.50815
$395$	1.18072	0.0594084
$396$	−8.49047	−0.426662
$397$	−17.9026	−0.898504	−0.449252	−	0.893405i	$-0.648309\pi$
$397$	−17.9026	−0.898504	−0.449252	+	0.893405i	$0.648309\pi$
$398$	19.6059	0.982757
$399$	−3.22265	−0.161334
$400$	−3.77999	−0.189000
$401$	−4.74978	−0.237193	−0.118596	−	0.992943i	$-0.537839\pi$
$401$	−4.74978	−0.237193	−0.118596	+	0.992943i	$0.537839\pi$
$402$	4.68970	0.233901
$403$	−11.6296	−0.579311
$404$	14.0195	0.697494
$405$	9.67550	0.480779
$406$	9.89898	0.491278
$407$	−9.93133	−0.492278
$408$	2.61867	0.129643
$409$	−2.41995	−0.119659	−0.0598294	−	0.998209i	$-0.519056\pi$
$409$	−2.41995	−0.119659	−0.0598294	+	0.998209i	$0.519056\pi$
$410$	−23.4909	−1.16013
$411$	14.8662	0.733294
$412$	9.66331	0.476077
$413$	26.3624	1.29721
$414$	25.0344	1.23037
$415$	14.2425	0.699137
$416$	10.1822	0.499224
$417$	−9.78447	−0.479147
$418$	−1.17702	−0.0575698
$419$	28.3667	1.38580	0.692902	−	0.721032i	$-0.256332\pi$
$419$	28.3667	1.38580	0.692902	+	0.721032i	$0.256332\pi$
$420$	−17.0965	−0.834222
$421$	19.3601	0.943555	0.471777	−	0.881718i	$-0.343613\pi$
$421$	19.3601	0.943555	0.471777	+	0.881718i	$0.343613\pi$
$422$	−41.4318	−2.01687
$423$	−2.26490	−0.110123
$424$	−0.253318	−0.0123022
$425$	5.15410	0.250011
$426$	4.83575	0.234293
$427$	−11.2448	−0.544175
$428$	9.42738	0.455690
$429$	4.42628	0.213703
$430$	−3.72854	−0.179806
$431$	−14.7254	−0.709296	−0.354648	−	0.935000i	$-0.615399\pi$
$431$	−14.7254	−0.709296	−0.354648	+	0.935000i	$0.615399\pi$
$432$	−2.22353	−0.106979
$433$	11.1514	0.535903	0.267951	−	0.963432i	$-0.413653\pi$
$433$	11.1514	0.535903	0.267951	+	0.963432i	$0.413653\pi$
$434$	−63.3275	−3.03982
$435$	3.46130	0.165957
$436$	21.2785	1.01905
$437$	1.77943	0.0851218
$438$	44.3817	2.12064
$439$	12.3548	0.589661	0.294831	−	0.955550i	$-0.404737\pi$
$439$	12.3548	0.589661	0.294831	+	0.955550i	$0.404737\pi$
$440$	−0.310170	−0.0147868
$441$	12.3070	0.586047
$442$	−13.1560	−0.625766
$443$	9.64190	0.458100	0.229050	−	0.973415i	$-0.426438\pi$
$443$	9.64190	0.458100	0.229050	+	0.973415i	$0.426438\pi$
$444$	−34.2368	−1.62481
$445$	−1.82529	−0.0865268
$446$	16.9143	0.800913
$447$	−24.2464	−1.14681
$448$	29.8451	1.41005
$449$	5.94473	0.280549	0.140275	−	0.990113i	$-0.455201\pi$
$449$	5.94473	0.280549	0.140275	+	0.990113i	$0.455201\pi$
$450$	−5.58111	−0.263096
$451$	16.9806	0.799585
$452$	36.0109	1.69381
$453$	−5.84247	−0.274503
$454$	−16.0238	−0.752034
$455$	4.26651	0.200017
$456$	−0.201555	−0.00943866
$457$	−28.7055	−1.34279	−0.671393	−	0.741102i	$-0.734304\pi$
$457$	−28.7055	−1.34279	−0.671393	+	0.741102i	$0.734304\pi$
$458$	30.9311	1.44531
$459$	3.03183	0.141514
$460$	9.44004	0.440144
$461$	−0.0365556	−0.00170256	−0.000851282	−	1.00000i	$-0.500271\pi$
$461$	−0.0365556	−0.00170256	−0.000851282		1.00000i	$0.500271\pi$
$462$	24.1028	1.12136
$463$	13.2626	0.616363	0.308182	−	0.951328i	$-0.400280\pi$
$463$	13.2626	0.616363	0.308182	+	0.951328i	$0.400280\pi$
$464$	−5.45400	−0.253196
$465$	−22.1432	−1.02687
$466$	−37.4266	−1.73375
$467$	25.3297	1.17212	0.586059	−	0.810269i	$-0.300679\pi$
$467$	25.3297	1.17212	0.586059	+	0.810269i	$0.300679\pi$
$468$	7.30439	0.337646
$469$	−3.26762	−0.150885
$470$	−1.66568	−0.0768322
$471$	−4.18126	−0.192662
$472$	1.64879	0.0758916
$473$	2.69521	0.123926
$474$	−5.73844	−0.263575
$475$	−0.396702	−0.0182019
$476$	−36.7320	−1.68361
$477$	3.29490	0.150863
$478$	−51.3229	−2.34745
$479$	−24.4082	−1.11524	−0.557620	−	0.830096i	$-0.688285\pi$
$479$	−24.4082	−1.11524	−0.557620	+	0.830096i	$0.688285\pi$
$480$	19.3874	0.884908
$481$	8.54397	0.389571
$482$	−19.0398	−0.867238
$483$	−36.4389	−1.65803
$484$	−18.6363	−0.847103
$485$	3.32925	0.151173
$486$	−43.4489	−1.97088
$487$	−40.1366	−1.81876	−0.909381	−	0.415964i	$-0.863444\pi$
$487$	−40.1366	−1.81876	−0.909381	+	0.415964i	$0.863444\pi$
$488$	−0.703285	−0.0318362
$489$	−32.1555	−1.45412
$490$	9.05098	0.408882
$491$	17.0215	0.768169	0.384084	−	0.923298i	$-0.374517\pi$
$491$	17.0215	0.768169	0.384084	+	0.923298i	$0.374517\pi$
$492$	58.5381	2.63910
$493$	7.43664	0.334930
$494$	1.01259	0.0455587
$495$	4.03436	0.181331
$496$	34.8913	1.56666
$497$	−3.36939	−0.151138
$498$	−69.2203	−3.10184
$499$	8.49308	0.380203	0.190101	−	0.981764i	$-0.439118\pi$
$499$	8.49308	0.380203	0.190101	+	0.981764i	$0.439118\pi$
$500$	−2.10454	−0.0941179
$501$	32.9220	1.47084
$502$	−26.2737	−1.17265
$503$	30.1549	1.34454	0.672269	−	0.740307i	$-0.265320\pi$
$503$	30.1549	1.34454	0.672269	+	0.740307i	$0.265320\pi$
$504$	1.97577	0.0880077
$505$	−6.66153	−0.296434
$506$	−13.3087	−0.591643
$507$	27.3779	1.21590
$508$	12.0841	0.536144
$509$	−18.5260	−0.821152	−0.410576	−	0.911826i	$-0.634672\pi$
$509$	−18.5260	−0.821152	−0.410576	+	0.911826i	$0.634672\pi$
$510$	−25.0495	−1.10921
$511$	−30.9237	−1.36798
$512$	−32.1500	−1.42084
$513$	−0.233354	−0.0103029
$514$	30.8109	1.35901
$515$	−4.59165	−0.202332
$516$	9.29133	0.409028
$517$	1.20405	0.0529543
$518$	46.5251	2.04420
$519$	−32.5129	−1.42716
$520$	0.266840	0.0117017
$521$	5.55358	0.243307	0.121653	−	0.992573i	$-0.461180\pi$
$521$	5.55358	0.243307	0.121653	+	0.992573i	$0.461180\pi$
$522$	−8.05277	−0.352460
$523$	−5.58305	−0.244130	−0.122065	−	0.992522i	$-0.538952\pi$
$523$	−5.58305	−0.244130	−0.122065	+	0.992522i	$0.538952\pi$
$524$	−11.4649	−0.500848
$525$	8.12361	0.354543
$526$	15.8189	0.689736
$527$	−47.5750	−2.07240
$528$	−13.2798	−0.577929
$529$	−2.87974	−0.125206
$530$	2.42318	0.105256
$531$	−21.4457	−0.930664
$532$	2.82720	0.122574
$533$	−14.6085	−0.632764
$534$	8.87111	0.383890
$535$	−4.47955	−0.193668
$536$	−0.204367	−0.00882731
$537$	12.5656	0.542244
$538$	20.1764	0.869866
$539$	−6.54259	−0.281809
$540$	−1.23797	−0.0532736
$541$	−19.5400	−0.840092	−0.420046	−	0.907503i	$-0.637986\pi$
$541$	−19.5400	−0.840092	−0.420046	+	0.907503i	$0.637986\pi$
$542$	−4.65033	−0.199749
$543$	4.27606	0.183503
$544$	41.6540	1.78590
$545$	−10.1108	−0.433097
$546$	−20.7357	−0.887408
$547$	4.76922	0.203917	0.101959	−	0.994789i	$-0.467489\pi$
$547$	4.76922	0.203917	0.101959	+	0.994789i	$0.467489\pi$
$548$	−13.0419	−0.557123
$549$	9.14760	0.390410
$550$	2.96701	0.126514
$551$	−0.572386	−0.0243845
$552$	−2.27900	−0.0970008
$553$	3.99835	0.170027
$554$	51.5813	2.19148
$555$	16.2681	0.690541
$556$	8.58380	0.364034
$557$	−4.27661	−0.181206	−0.0906029	−	0.995887i	$-0.528879\pi$
$557$	−4.27661	−0.181206	−0.0906029	+	0.995887i	$0.528879\pi$
$558$	51.5165	2.18087
$559$	−2.31870	−0.0980706
$560$	−12.8004	−0.540918
$561$	18.1073	0.764491
$562$	−39.1731	−1.65242
$563$	18.5896	0.783458	0.391729	−	0.920081i	$-0.371877\pi$
$563$	18.5896	0.783458	0.391729	+	0.920081i	$0.371877\pi$
$564$	4.15080	0.174780
$565$	−17.1111	−0.719868
$566$	15.9276	0.669488
$567$	32.7648	1.37599
$568$	−0.210732	−0.00884211
$569$	25.7786	1.08069	0.540347	−	0.841442i	$-0.318293\pi$
$569$	25.7786	1.08069	0.540347	+	0.841442i	$0.318293\pi$
$570$	1.92802	0.0807559
$571$	−16.1965	−0.677801	−0.338900	−	0.940822i	$-0.610055\pi$
$571$	−16.1965	−0.677801	−0.338900	+	0.940822i	$0.610055\pi$
$572$	−3.88313	−0.162362
$573$	−60.7178	−2.53652
$574$	−79.5488	−3.32030
$575$	−4.48556	−0.187061
$576$	−24.2788	−1.01162
$577$	−5.10533	−0.212538	−0.106269	−	0.994337i	$-0.533890\pi$
$577$	−5.10533	−0.212538	−0.106269	+	0.994337i	$0.533890\pi$
$578$	−19.3778	−0.806012
$579$	28.5584	1.18685
$580$	−3.03656	−0.126086
$581$	48.2304	2.00093
$582$	−16.1806	−0.670706
$583$	−1.75162	−0.0725446
$584$	−1.93406	−0.0800320
$585$	−3.47078	−0.143499
$586$	12.4633	0.514852
$587$	−7.67924	−0.316956	−0.158478	−	0.987362i	$-0.550659\pi$
$587$	−7.67924	−0.316956	−0.158478	+	0.987362i	$0.550659\pi$
$588$	−22.5546	−0.930136
$589$	3.66176	0.150880
$590$	−15.7719	−0.649318
$591$	−35.4465	−1.45808
$592$	−25.6338	−1.05354
$593$	−25.9791	−1.06683	−0.533416	−	0.845853i	$-0.679092\pi$
$593$	−25.9791	−1.06683	−0.533416	+	0.845853i	$0.679092\pi$
$594$	1.74530	0.0716105
$595$	17.4537	0.715531
$596$	21.2710	0.871296
$597$	23.2151	0.950130
$598$	11.4495	0.468206
$599$	−1.22803	−0.0501760	−0.0250880	−	0.999685i	$-0.507987\pi$
$599$	−1.22803	−0.0501760	−0.0250880	+	0.999685i	$0.507987\pi$
$600$	0.508075	0.0207421
$601$	−10.1233	−0.412938	−0.206469	−	0.978453i	$-0.566197\pi$
$601$	−10.1233	−0.412938	−0.206469	+	0.978453i	$0.566197\pi$
$602$	−12.6262	−0.514605
$603$	2.65819	0.108250
$604$	5.12553	0.208555
$605$	8.85527	0.360018
$606$	32.3758	1.31518
$607$	−31.9963	−1.29869	−0.649345	−	0.760494i	$-0.724957\pi$
$607$	−31.9963	−1.29869	−0.649345	+	0.760494i	$0.724957\pi$
$608$	−3.20604	−0.130022
$609$	11.7212	0.474968
$610$	6.72745	0.272387
$611$	−1.03585	−0.0419062
$612$	29.8812	1.20788
$613$	−10.7757	−0.435228	−0.217614	−	0.976035i	$-0.569827\pi$
$613$	−10.7757	−0.435228	−0.217614	+	0.976035i	$0.569827\pi$
$614$	−42.1006	−1.69904
$615$	−27.8152	−1.12162
$616$	−1.05035	−0.0423197
$617$	32.4535	1.30653	0.653264	−	0.757130i	$-0.273399\pi$
$617$	32.4535	1.30653	0.653264	+	0.757130i	$0.273399\pi$
$618$	22.3160	0.897680
$619$	12.0620	0.484815	0.242407	−	0.970175i	$-0.422063\pi$
$619$	12.0620	0.484815	0.242407	+	0.970175i	$0.422063\pi$
$620$	19.4260	0.780166
$621$	−2.63857	−0.105882
$622$	−34.6074	−1.38763
$623$	−6.18109	−0.247640
$624$	11.4247	0.457353
$625$	1.00000	0.0400000
$626$	−57.7282	−2.30728
$627$	−1.39369	−0.0556585
$628$	3.66817	0.146376
$629$	34.9522	1.39363
$630$	−18.8997	−0.752982
$631$	−7.03090	−0.279896	−0.139948	−	0.990159i	$-0.544694\pi$
$631$	−7.03090	−0.279896	−0.139948	+	0.990159i	$0.544694\pi$
$632$	0.250069	0.00994721
$633$	−49.0587	−1.94991
$634$	−36.0905	−1.43334
$635$	−5.74191	−0.227861
$636$	−6.03844	−0.239440
$637$	5.62862	0.223014
$638$	4.28097	0.169485
$639$	2.74098	0.108431
$640$	−1.69204	−0.0668836
$641$	−36.9475	−1.45934	−0.729668	−	0.683801i	$-0.760326\pi$
$641$	−36.9475	−1.45934	−0.729668	+	0.683801i	$0.760326\pi$
$642$	21.7711	0.859238
$643$	23.8513	0.940604	0.470302	−	0.882505i	$-0.344145\pi$
$643$	23.8513	0.940604	0.470302	+	0.882505i	$0.344145\pi$
$644$	31.9675	1.25969
$645$	−4.41490	−0.173837
$646$	4.14238	0.162980
$647$	−38.4959	−1.51343	−0.756715	−	0.653745i	$-0.773197\pi$
$647$	−38.4959	−1.51343	−0.756715	+	0.653745i	$0.773197\pi$
$648$	2.04921	0.0805006
$649$	11.4009	0.447523
$650$	−2.55253	−0.100118
$651$	−74.9850	−2.93890
$652$	28.2097	1.10478
$653$	−34.8995	−1.36572	−0.682862	−	0.730547i	$-0.739265\pi$
$653$	−34.8995	−1.36572	−0.682862	+	0.730547i	$0.739265\pi$
$654$	49.1395	1.92151
$655$	5.44772	0.212860
$656$	43.8286	1.71122
$657$	25.1562	0.981437
$658$	−5.64062	−0.219894
$659$	−30.9926	−1.20730	−0.603650	−	0.797249i	$-0.706288\pi$
$659$	−30.9926	−1.20730	−0.603650	+	0.797249i	$0.706288\pi$
$660$	−7.39363	−0.287797
$661$	−5.89179	−0.229164	−0.114582	−	0.993414i	$-0.536553\pi$
$661$	−5.89179	−0.229164	−0.114582	+	0.993414i	$0.536553\pi$
$662$	−2.90379	−0.112859
$663$	−15.5778	−0.604991
$664$	3.01648	0.117062
$665$	−1.34338	−0.0520940
$666$	−37.8479	−1.46658
$667$	−6.47204	−0.250598
$668$	−28.8821	−1.11748
$669$	20.0279	0.774323
$670$	1.95492	0.0755253
$671$	−4.86300	−0.187734
$672$	65.6528	2.53261
$673$	13.3293	0.513805	0.256903	−	0.966437i	$-0.417298\pi$
$673$	13.3293	0.513805	0.256903	+	0.966437i	$0.417298\pi$
$674$	−30.7742	−1.18538
$675$	0.588236	0.0226412
$676$	−24.0183	−0.923782
$677$	−1.63247	−0.0627408	−0.0313704	−	0.999508i	$-0.509987\pi$
$677$	−1.63247	−0.0627408	−0.0313704	+	0.999508i	$0.509987\pi$
$678$	83.1618	3.19381
$679$	11.2741	0.432659
$680$	1.09161	0.0418612
$681$	−18.9735	−0.727066
$682$	−27.3870	−1.04870
$683$	−7.46031	−0.285461	−0.142730	−	0.989762i	$-0.545588\pi$
$683$	−7.46031	−0.285461	−0.142730	+	0.989762i	$0.545588\pi$
$684$	−2.29991	−0.0879392
$685$	6.19704	0.236777
$686$	−17.3747	−0.663370
$687$	36.6250	1.39733
$688$	6.95660	0.265218
$689$	1.50692	0.0574092
$690$	21.8004	0.829926
$691$	−29.7902	−1.13327	−0.566637	−	0.823967i	$-0.691756\pi$
$691$	−29.7902	−1.13327	−0.566637	+	0.823967i	$0.691756\pi$
$692$	28.5232	1.08429
$693$	13.6618	0.518970
$694$	−40.2485	−1.52781
$695$	−4.07871	−0.154714
$696$	0.733081	0.0277874
$697$	−59.7613	−2.26362
$698$	−21.2379	−0.803868
$699$	−44.3162	−1.67619
$700$	−7.12675	−0.269366
$701$	−50.4962	−1.90721	−0.953607	−	0.301054i	$-0.902662\pi$
$701$	−50.4962	−1.90721	−0.953607	+	0.301054i	$0.902662\pi$
$702$	−1.50149	−0.0566700
$703$	−2.69021	−0.101463
$704$	12.9070	0.486451
$705$	−1.97231	−0.0742814
$706$	−17.2150	−0.647897
$707$	−22.5584	−0.848396
$708$	39.3028	1.47709
$709$	−13.3812	−0.502542	−0.251271	−	0.967917i	$-0.580849\pi$
$709$	−13.3812	−0.502542	−0.251271	+	0.967917i	$0.580849\pi$
$710$	2.01581	0.0756519
$711$	−3.25263	−0.121983
$712$	−0.386584	−0.0144878
$713$	41.4040	1.55059
$714$	−84.8270	−3.17457
$715$	1.84512	0.0690035
$716$	−11.0236	−0.411972
$717$	−60.7706	−2.26952
$718$	−16.3794	−0.611273
$719$	−13.5039	−0.503611	−0.251806	−	0.967778i	$-0.581024\pi$
$719$	−13.5039	−0.503611	−0.251806	+	0.967778i	$0.581024\pi$
$720$	10.4131	0.388073
$721$	−15.5490	−0.579076
$722$	38.1745	1.42071
$723$	−22.5447	−0.838446
$724$	−3.75134	−0.139418
$725$	1.44286	0.0535865
$726$	−43.0377	−1.59728
$727$	−16.4150	−0.608798	−0.304399	−	0.952545i	$-0.598456\pi$
$727$	−16.4150	−0.608798	−0.304399	+	0.952545i	$0.598456\pi$
$728$	0.903620	0.0334904
$729$	−22.4206	−0.830392
$730$	18.5007	0.684743
$731$	−9.48547	−0.350833
$732$	−16.7645	−0.619633
$733$	3.30497	0.122072	0.0610358	−	0.998136i	$-0.480560\pi$
$733$	3.30497	0.122072	0.0610358	+	0.998136i	$0.480560\pi$
$734$	30.7618	1.13544
$735$	10.7171	0.395307
$736$	−36.2511	−1.33623
$737$	−1.41314	−0.0520535
$738$	64.7125	2.38210
$739$	−8.87583	−0.326503	−0.163251	−	0.986585i	$-0.552198\pi$
$739$	−8.87583	−0.326503	−0.163251	+	0.986585i	$0.552198\pi$
$740$	−14.2718	−0.524641
$741$	1.19900	0.0440462
$742$	8.20577	0.301243
$743$	13.3281	0.488960	0.244480	−	0.969654i	$-0.421383\pi$
$743$	13.3281	0.488960	0.244480	+	0.969654i	$0.421383\pi$
$744$	−4.68979	−0.171936
$745$	−10.1072	−0.370300
$746$	10.3750	0.379854
$747$	−39.2351	−1.43554
$748$	−15.8853	−0.580825
$749$	−15.1694	−0.554277
$750$	−4.86012	−0.177466
$751$	2.29595	0.0837804	0.0418902	−	0.999122i	$-0.486662\pi$
$751$	2.29595	0.0837804	0.0418902	+	0.999122i	$0.486662\pi$
$752$	3.10779	0.113329
$753$	−31.1103	−1.13372
$754$	−3.68294	−0.134125
$755$	−2.43546	−0.0886356
$756$	−4.19221	−0.152469
$757$	−25.2552	−0.917917	−0.458959	−	0.888458i	$-0.651777\pi$
$757$	−25.2552	−0.917917	−0.458959	+	0.888458i	$0.651777\pi$
$758$	51.1261	1.85699
$759$	−15.7586	−0.572001
$760$	−0.0840191	−0.00304769
$761$	34.5465	1.25231	0.626155	−	0.779699i	$-0.284628\pi$
$761$	34.5465	1.25231	0.626155	+	0.779699i	$0.284628\pi$
$762$	27.9064	1.01094
$763$	−34.2387	−1.23953
$764$	53.2670	1.92713
$765$	−14.1985	−0.513347
$766$	−13.7813	−0.497939
$767$	−9.80821	−0.354154
$768$	−34.0613	−1.22908
$769$	−47.0960	−1.69832	−0.849162	−	0.528132i	$-0.822893\pi$
$769$	−47.0960	−1.69832	−0.849162	+	0.528132i	$0.822893\pi$
$770$	10.0474	0.362082
$771$	36.4827	1.31389
$772$	−25.0539	−0.901711
$773$	−14.5281	−0.522538	−0.261269	−	0.965266i	$-0.584141\pi$
$773$	−14.5281	−0.522538	−0.261269	+	0.965266i	$0.584141\pi$
$774$	10.2713	0.369196
$775$	−9.23051	−0.331570
$776$	0.705115	0.0253121
$777$	55.0897	1.97633
$778$	−1.91293	−0.0685819
$779$	4.59972	0.164802
$780$	6.36078	0.227752
$781$	−1.45715	−0.0521408
$782$	46.8384	1.67494
$783$	0.848742	0.0303316
$784$	−16.8871	−0.603110
$785$	−1.74298	−0.0622097
$786$	−26.4766	−0.944387
$787$	−47.5672	−1.69559	−0.847794	−	0.530325i	$-0.822070\pi$
$787$	−47.5672	−1.69559	−0.847794	+	0.530325i	$0.822070\pi$
$788$	31.0968	1.10778
$789$	18.7309	0.666837
$790$	−2.39210	−0.0851070
$791$	−57.9443	−2.06026
$792$	0.854452	0.0303616
$793$	4.18366	0.148566
$794$	36.2700	1.28717
$795$	2.86925	0.101762
$796$	−20.3663	−0.721865
$797$	6.58301	0.233182	0.116591	−	0.993180i	$-0.462803\pi$
$797$	6.58301	0.233182	0.116591	+	0.993180i	$0.462803\pi$
$798$	6.52899	0.231124
$799$	−4.23753	−0.149913
$800$	8.08172	0.285732
$801$	5.02828	0.177666
$802$	9.62290	0.339796
$803$	−13.3734	−0.471938
$804$	−4.87158	−0.171807
$805$	−15.1898	−0.535369
$806$	23.5611	0.829906
$807$	23.8905	0.840987
$808$	−1.41087	−0.0496342
$809$	−19.2376	−0.676357	−0.338179	−	0.941082i	$-0.609811\pi$
$809$	−19.2376	−0.676357	−0.338179	+	0.941082i	$0.609811\pi$
$810$	−19.6022	−0.688752
$811$	54.5150	1.91428	0.957141	−	0.289623i	$-0.0935299\pi$
$811$	54.5150	1.91428	0.957141	+	0.289623i	$0.0935299\pi$
$812$	−10.2829	−0.360859
$813$	−5.50638	−0.193117
$814$	20.1205	0.705224
$815$	−13.4042	−0.469529
$816$	46.7367	1.63611
$817$	0.730080	0.0255423
$818$	4.90274	0.171420
$819$	−11.7533	−0.410695
$820$	24.4019	0.852152
$821$	32.0410	1.11824	0.559120	−	0.829087i	$-0.311139\pi$
$821$	32.0410	1.11824	0.559120	+	0.829087i	$0.311139\pi$
$822$	−30.1184	−1.05050
$823$	−8.12477	−0.283212	−0.141606	−	0.989923i	$-0.545227\pi$
$823$	−8.12477	−0.283212	−0.141606	+	0.989923i	$0.545227\pi$
$824$	−0.972483	−0.0338780
$825$	3.51318	0.122313
$826$	−53.4094	−1.85835
$827$	25.8642	0.899388	0.449694	−	0.893183i	$-0.351533\pi$
$827$	25.8642	0.899388	0.449694	+	0.893183i	$0.351533\pi$
$828$	−26.0053	−0.903748
$829$	51.9317	1.80366	0.901832	−	0.432088i	$-0.142223\pi$
$829$	51.9317	1.80366	0.901832	+	0.432088i	$0.142223\pi$
$830$	−28.8549	−1.00157
$831$	61.0766	2.11872
$832$	−11.1040	−0.384960
$833$	23.0259	0.797799
$834$	19.8230	0.686414
$835$	13.7237	0.474928
$836$	1.22267	0.0422868
$837$	−5.42972	−0.187678
$838$	−57.4700	−1.98527
$839$	22.1858	0.765938	0.382969	−	0.923761i	$-0.374902\pi$
$839$	22.1858	0.765938	0.382969	+	0.923761i	$0.374902\pi$
$840$	1.72053	0.0593639
$841$	−26.9182	−0.928212
$842$	−39.2230	−1.35171
$843$	−46.3842	−1.59756
$844$	43.0386	1.48145
$845$	11.4126	0.392607
$846$	4.58861	0.157760
$847$	29.9872	1.03037
$848$	−4.52110	−0.155255
$849$	18.8597	0.647262
$850$	−10.4420	−0.358159
$851$	−30.4185	−1.04273
$852$	−5.02329	−0.172095
$853$	17.6443	0.604129	0.302065	−	0.953287i	$-0.402324\pi$
$853$	17.6443	0.604129	0.302065	+	0.953287i	$0.402324\pi$
$854$	22.7816	0.779571
$855$	1.09283	0.0373741
$856$	−0.948740	−0.0324273
$857$	55.3924	1.89217	0.946085	−	0.323920i	$-0.105001\pi$
$857$	55.3924	1.89217	0.946085	+	0.323920i	$0.105001\pi$
$858$	−8.96750	−0.306145
$859$	9.54626	0.325714	0.162857	−	0.986650i	$-0.447929\pi$
$859$	9.54626	0.325714	0.162857	+	0.986650i	$0.447929\pi$
$860$	3.87314	0.132073
$861$	−94.1924	−3.21007
$862$	29.8331	1.01612
$863$	−21.8766	−0.744690	−0.372345	−	0.928094i	$-0.621446\pi$
$863$	−21.8766	−0.744690	−0.372345	+	0.928094i	$0.621446\pi$
$864$	4.75396	0.161733
$865$	−13.5532	−0.460822
$866$	−22.5924	−0.767721
$867$	−22.9450	−0.779253
$868$	65.7835	2.23284
$869$	1.72915	0.0586574
$870$	−7.01247	−0.237745
$871$	1.21573	0.0411933
$872$	−2.14139	−0.0725168
$873$	−9.17139	−0.310404
$874$	−3.60507	−0.121943
$875$	3.38637	0.114480
$876$	−46.1029	−1.55767
$877$	−32.2602	−1.08935	−0.544676	−	0.838647i	$-0.683347\pi$
$877$	−32.2602	−1.08935	−0.544676	+	0.838647i	$0.683347\pi$
$878$	−25.0304	−0.844733
$879$	14.7575	0.497759
$880$	−5.53576	−0.186610
$881$	49.4811	1.66706	0.833531	−	0.552473i	$-0.186316\pi$
$881$	49.4811	1.66706	0.833531	+	0.552473i	$0.186316\pi$
$882$	−24.9336	−0.839557
$883$	−46.3233	−1.55890	−0.779451	−	0.626463i	$-0.784502\pi$
$883$	−46.3233	−1.55890	−0.779451	+	0.626463i	$0.784502\pi$
$884$	13.6662	0.459645
$885$	−18.6752	−0.627762
$886$	−19.5342	−0.656263
$887$	0.259273	0.00870552	0.00435276	−	0.999991i	$-0.498614\pi$
$887$	0.259273	0.00870552	0.00435276	+	0.999991i	$0.498614\pi$
$888$	3.44548	0.115623
$889$	−19.4442	−0.652138
$890$	3.69797	0.123956
$891$	14.1697	0.474702
$892$	−17.5702	−0.588295
$893$	0.326155	0.0109144
$894$	49.1223	1.64290
$895$	5.23802	0.175088
$896$	−5.72985	−0.191421
$897$	13.5572	0.452662
$898$	−12.0438	−0.401907
$899$	−13.3183	−0.444191
$900$	5.79757	0.193252
$901$	6.16461	0.205373
$902$	−34.4021	−1.14547
$903$	−14.9505	−0.497521
$904$	−3.62402	−0.120533
$905$	1.78250	0.0592523
$906$	11.8366	0.393246
$907$	1.88166	0.0624795	0.0312397	−	0.999512i	$-0.490054\pi$
$907$	1.88166	0.0624795	0.0312397	+	0.999512i	$0.490054\pi$
$908$	16.6452	0.552392
$909$	18.3511	0.608668
$910$	−8.64380	−0.286539
$911$	−9.88981	−0.327664	−0.163832	−	0.986488i	$-0.552386\pi$
$911$	−9.88981	−0.327664	−0.163832	+	0.986488i	$0.552386\pi$
$912$	−3.59725	−0.119117
$913$	20.8580	0.690299
$914$	58.1563	1.92364
$915$	7.96587	0.263343
$916$	−32.1307	−1.06163
$917$	18.4480	0.609206
$918$	−6.14238	−0.202729
$919$	16.6404	0.548916	0.274458	−	0.961599i	$-0.411502\pi$
$919$	16.6404	0.548916	0.274458	+	0.961599i	$0.411502\pi$
$920$	−0.950014	−0.0313210
$921$	−49.8506	−1.64263
$922$	0.0740604	0.00243905
$923$	1.25359	0.0412624
$924$	−25.0376	−0.823675
$925$	6.78143	0.222972
$926$	−26.8695	−0.882987
$927$	12.6490	0.415449
$928$	11.6608	0.382784
$929$	0.141171	0.00463166	0.00231583	−	0.999997i	$-0.499263\pi$
$929$	0.141171	0.00463166	0.00231583	+	0.999997i	$0.499263\pi$
$930$	44.8614	1.47106
$931$	−1.77226	−0.0580836
$932$	38.8781	1.27349
$933$	−40.9781	−1.34156
$934$	−51.3170	−1.67915
$935$	7.54812	0.246850
$936$	−0.735089	−0.0240272
$937$	−17.0689	−0.557616	−0.278808	−	0.960347i	$-0.589939\pi$
$937$	−17.0689	−0.557616	−0.278808	+	0.960347i	$0.589939\pi$
$938$	6.62009	0.216154
$939$	−68.3551	−2.23068
$940$	1.73028	0.0564356
$941$	−55.0423	−1.79433	−0.897163	−	0.441699i	$-0.854376\pi$
$941$	−55.0423	−1.79433	−0.897163	+	0.441699i	$0.854376\pi$
$942$	8.47110	0.276003
$943$	52.0096	1.69367
$944$	29.4268	0.957759
$945$	1.99198	0.0647992
$946$	−5.46040	−0.177533
$947$	−17.8288	−0.579360	−0.289680	−	0.957124i	$-0.593549\pi$
$947$	−17.8288	−0.579360	−0.289680	+	0.957124i	$0.593549\pi$
$948$	5.96099	0.193604
$949$	11.5052	0.373475
$950$	0.803705	0.0260756
$951$	−42.7342	−1.38575
$952$	3.69658	0.119807
$953$	3.24492	0.105113	0.0525566	−	0.998618i	$-0.483263\pi$
$953$	3.24492	0.105113	0.0525566	+	0.998618i	$0.483263\pi$
$954$	−6.67535	−0.216122
$955$	−25.3105	−0.819029
$956$	53.3133	1.72428
$957$	5.06903	0.163859
$958$	49.4502	1.59766
$959$	20.9855	0.677656
$960$	−21.1424	−0.682368
$961$	54.2023	1.74846
$962$	−17.3098	−0.558090
$963$	12.3402	0.397658
$964$	19.7782	0.637013
$965$	11.9047	0.383226
$966$	73.8241	2.37525
$967$	−49.4567	−1.59042	−0.795210	−	0.606334i	$-0.792640\pi$
$967$	−49.4567	−1.59042	−0.795210	+	0.606334i	$0.792640\pi$
$968$	1.87549	0.0602806
$969$	4.90492	0.157569
$970$	−6.74495	−0.216567
$971$	−12.8333	−0.411840	−0.205920	−	0.978569i	$-0.566019\pi$
$971$	−12.8333	−0.411840	−0.205920	+	0.978569i	$0.566019\pi$
$972$	45.1339	1.44767
$973$	−13.8120	−0.442792
$974$	81.3154	2.60551
$975$	−3.02241	−0.0967945
$976$	−12.5519	−0.401776
$977$	37.7749	1.20853	0.604264	−	0.796784i	$-0.293467\pi$
$977$	37.7749	1.20853	0.604264	+	0.796784i	$0.293467\pi$
$978$	65.1460	2.08314
$979$	−2.67311	−0.0854330
$980$	−9.40201	−0.300336
$981$	27.8530	0.889278
$982$	−34.4850	−1.10046
$983$	5.61583	0.179117	0.0895585	−	0.995982i	$-0.471454\pi$
$983$	5.61583	0.179117	0.0895585	+	0.995982i	$0.471454\pi$
$984$	−5.89108	−0.187801
$985$	−14.7761	−0.470805
$986$	−15.0664	−0.479812
$987$	−6.67896	−0.212594
$988$	−1.05187	−0.0334643
$989$	8.25511	0.262497
$990$	−8.17348	−0.259770
$991$	−38.4942	−1.22281	−0.611404	−	0.791319i	$-0.709395\pi$
$991$	−38.4942	−1.22281	−0.611404	+	0.791319i	$0.709395\pi$
$992$	−74.5984	−2.36850
$993$	−3.43834	−0.109112
$994$	6.82627	0.216516
$995$	9.67733	0.306792
$996$	71.9049	2.27839
$997$	38.1342	1.20772	0.603860	−	0.797090i	$-0.293628\pi$
$997$	38.1342	1.20772	0.603860	+	0.797090i	$0.293628\pi$
$998$	−17.2067	−0.544669
$999$	3.98908	0.126209

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8045.2.a.b.1.20	✓	126

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8045.2.a.b.1.20	✓	126	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:	\( N \)	\(=\)	\( 8045 = 5 \cdot 1609 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8045.a (trivial)

\(f(q)\)	\(=\)	\(q-2.02597 q^{2} -2.39891 q^{3} +2.10454 q^{4} -1.00000 q^{5} +4.86012 q^{6} -3.38637 q^{7} -0.211794 q^{8} +2.75479 q^{9} +O(q^{10})\)	\(q-2.02597 q^{2} -2.39891 q^{3} +2.10454 q^{4} -1.00000 q^{5} +4.86012 q^{6} -3.38637 q^{7} -0.211794 q^{8} +2.75479 q^{9} +2.02597 q^{10} -1.46449 q^{11} -5.04861 q^{12} +1.25991 q^{13} +6.86067 q^{14} +2.39891 q^{15} -3.77999 q^{16} +5.15410 q^{17} -5.58111 q^{18} -0.396702 q^{19} -2.10454 q^{20} +8.12361 q^{21} +2.96701 q^{22} -4.48556 q^{23} +0.508075 q^{24} +1.00000 q^{25} -2.55253 q^{26} +0.588236 q^{27} -7.12675 q^{28} +1.44286 q^{29} -4.86012 q^{30} -9.23051 q^{31} +8.08172 q^{32} +3.51318 q^{33} -10.4420 q^{34} +3.38637 q^{35} +5.79757 q^{36} +6.78143 q^{37} +0.803705 q^{38} -3.02241 q^{39} +0.211794 q^{40} -11.5949 q^{41} -16.4582 q^{42} -1.84037 q^{43} -3.08207 q^{44} -2.75479 q^{45} +9.08760 q^{46} -0.822167 q^{47} +9.06788 q^{48} +4.46749 q^{49} -2.02597 q^{50} -12.3642 q^{51} +2.65152 q^{52} +1.19606 q^{53} -1.19175 q^{54} +1.46449 q^{55} +0.717212 q^{56} +0.951655 q^{57} -2.92319 q^{58} -7.78487 q^{59} +5.04861 q^{60} +3.32061 q^{61} +18.7007 q^{62} -9.32874 q^{63} -8.81332 q^{64} -1.25991 q^{65} -7.11759 q^{66} +0.964934 q^{67} +10.8470 q^{68} +10.7605 q^{69} -6.86067 q^{70} +0.994986 q^{71} -0.583448 q^{72} +9.13181 q^{73} -13.7389 q^{74} -2.39891 q^{75} -0.834875 q^{76} +4.95930 q^{77} +6.12330 q^{78} -1.18072 q^{79} +3.77999 q^{80} -9.67550 q^{81} +23.4909 q^{82} -14.2425 q^{83} +17.0965 q^{84} -5.15410 q^{85} +3.72854 q^{86} -3.46130 q^{87} +0.310170 q^{88} +1.82529 q^{89} +5.58111 q^{90} -4.26651 q^{91} -9.44004 q^{92} +22.1432 q^{93} +1.66568 q^{94} +0.396702 q^{95} -19.3874 q^{96} -3.32925 q^{97} -9.05098 q^{98} -4.03436 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 126 q + 5 q^{2} - 9 q^{3} + 109 q^{4} - 126 q^{5} - 21 q^{6} - 23 q^{7} + 12 q^{8} + 109 q^{9}+O(q^{10}) \) 126 * q + 5 * q^2 - 9 * q^3 + 109 * q^4 - 126 * q^5 - 21 * q^6 - 23 * q^7 + 12 * q^8 + 109 * q^9	\( 126 q + 5 q^{2} - 9 q^{3} + 109 q^{4} - 126 q^{5} - 21 q^{6} - 23 q^{7} + 12 q^{8} + 109 q^{9} - 5 q^{10} - 44 q^{11} - 11 q^{12} - 35 q^{13} - 14 q^{14} + 9 q^{15} + 75 q^{16} + 11 q^{17} - 15 q^{18} - 130 q^{19} - 109 q^{20} - 44 q^{21} - 14 q^{22} + 75 q^{23} - 63 q^{24} + 126 q^{25} - 43 q^{26} - 42 q^{27} - 77 q^{28} - 24 q^{29} + 21 q^{30} - 78 q^{31} + 24 q^{32} - 29 q^{33} - 57 q^{34} + 23 q^{35} + 50 q^{36} - 31 q^{37} - 3 q^{38} - 57 q^{39} - 12 q^{40} - 38 q^{41} - 10 q^{42} - 100 q^{43} - 90 q^{44} - 109 q^{45} - 96 q^{46} + 12 q^{47} - 22 q^{48} + 65 q^{49} + 5 q^{50} - 74 q^{51} - 112 q^{52} + 20 q^{53} - 90 q^{54} + 44 q^{55} - 57 q^{56} + 6 q^{57} - 35 q^{58} - 97 q^{59} + 11 q^{60} - 102 q^{61} - 16 q^{62} - 15 q^{63} + 4 q^{64} + 35 q^{65} - 83 q^{66} - 121 q^{67} + 41 q^{68} - 71 q^{69} + 14 q^{70} - 32 q^{71} - 32 q^{72} - 85 q^{73} - 42 q^{74} - 9 q^{75} - 275 q^{76} + 13 q^{77} + 10 q^{78} - 97 q^{79} - 75 q^{80} + 86 q^{81} - 55 q^{82} - 73 q^{83} - 111 q^{84} - 11 q^{85} - 56 q^{86} - q^{87} - 37 q^{88} - 67 q^{89} + 15 q^{90} - 180 q^{91} + 98 q^{92} - 44 q^{93} - 86 q^{94} + 130 q^{95} - 179 q^{96} - 50 q^{97} + 18 q^{98} - 217 q^{99}+O(q^{100}) \) 126 * q + 5 * q^2 - 9 * q^3 + 109 * q^4 - 126 * q^5 - 21 * q^6 - 23 * q^7 + 12 * q^8 + 109 * q^9 - 5 * q^10 - 44 * q^11 - 11 * q^12 - 35 * q^13 - 14 * q^14 + 9 * q^15 + 75 * q^16 + 11 * q^17 - 15 * q^18 - 130 * q^19 - 109 * q^20 - 44 * q^21 - 14 * q^22 + 75 * q^23 - 63 * q^24 + 126 * q^25 - 43 * q^26 - 42 * q^27 - 77 * q^28 - 24 * q^29 + 21 * q^30 - 78 * q^31 + 24 * q^32 - 29 * q^33 - 57 * q^34 + 23 * q^35 + 50 * q^36 - 31 * q^37 - 3 * q^38 - 57 * q^39 - 12 * q^40 - 38 * q^41 - 10 * q^42 - 100 * q^43 - 90 * q^44 - 109 * q^45 - 96 * q^46 + 12 * q^47 - 22 * q^48 + 65 * q^49 + 5 * q^50 - 74 * q^51 - 112 * q^52 + 20 * q^53 - 90 * q^54 + 44 * q^55 - 57 * q^56 + 6 * q^57 - 35 * q^58 - 97 * q^59 + 11 * q^60 - 102 * q^61 - 16 * q^62 - 15 * q^63 + 4 * q^64 + 35 * q^65 - 83 * q^66 - 121 * q^67 + 41 * q^68 - 71 * q^69 + 14 * q^70 - 32 * q^71 - 32 * q^72 - 85 * q^73 - 42 * q^74 - 9 * q^75 - 275 * q^76 + 13 * q^77 + 10 * q^78 - 97 * q^79 - 75 * q^80 + 86 * q^81 - 55 * q^82 - 73 * q^83 - 111 * q^84 - 11 * q^85 - 56 * q^86 - q^87 - 37 * q^88 - 67 * q^89 + 15 * q^90 - 180 * q^91 + 98 * q^92 - 44 * q^93 - 86 * q^94 + 130 * q^95 - 179 * q^96 - 50 * q^97 + 18 * q^98 - 217 * q^99

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