LMFDB - Embedded newform 8042.2.a.d.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8042,2,Mod(1,8042)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8042, 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("8042.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8042 = 2 \cdot 4021 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8042.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:	$64.2156933055$
Analytic rank:	$0$
Dimension:	$101$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	8042.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.05772 q^{3} +1.00000 q^{4} +1.21871 q^{5} -3.05772 q^{6} -4.97978 q^{7} +1.00000 q^{8} +6.34964 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.05772 q^{3} +1.00000 q^{4} +1.21871 q^{5} -3.05772 q^{6} -4.97978 q^{7} +1.00000 q^{8} +6.34964 q^{9} +1.21871 q^{10} -0.827268 q^{11} -3.05772 q^{12} -0.294479 q^{13} -4.97978 q^{14} -3.72647 q^{15} +1.00000 q^{16} -3.77163 q^{17} +6.34964 q^{18} -6.36496 q^{19} +1.21871 q^{20} +15.2268 q^{21} -0.827268 q^{22} -5.27997 q^{23} -3.05772 q^{24} -3.51475 q^{25} -0.294479 q^{26} -10.2422 q^{27} -4.97978 q^{28} +0.954562 q^{29} -3.72647 q^{30} -9.08194 q^{31} +1.00000 q^{32} +2.52955 q^{33} -3.77163 q^{34} -6.06890 q^{35} +6.34964 q^{36} +8.27313 q^{37} -6.36496 q^{38} +0.900432 q^{39} +1.21871 q^{40} -10.1894 q^{41} +15.2268 q^{42} +1.40206 q^{43} -0.827268 q^{44} +7.73835 q^{45} -5.27997 q^{46} +2.78729 q^{47} -3.05772 q^{48} +17.7982 q^{49} -3.51475 q^{50} +11.5326 q^{51} -0.294479 q^{52} +13.6740 q^{53} -10.2422 q^{54} -1.00820 q^{55} -4.97978 q^{56} +19.4622 q^{57} +0.954562 q^{58} -5.78093 q^{59} -3.72647 q^{60} -1.78730 q^{61} -9.08194 q^{62} -31.6198 q^{63} +1.00000 q^{64} -0.358883 q^{65} +2.52955 q^{66} +12.3285 q^{67} -3.77163 q^{68} +16.1446 q^{69} -6.06890 q^{70} -2.67071 q^{71} +6.34964 q^{72} -9.43466 q^{73} +8.27313 q^{74} +10.7471 q^{75} -6.36496 q^{76} +4.11961 q^{77} +0.900432 q^{78} -3.47393 q^{79} +1.21871 q^{80} +12.2690 q^{81} -10.1894 q^{82} -1.62106 q^{83} +15.2268 q^{84} -4.59652 q^{85} +1.40206 q^{86} -2.91878 q^{87} -0.827268 q^{88} -2.04457 q^{89} +7.73835 q^{90} +1.46644 q^{91} -5.27997 q^{92} +27.7700 q^{93} +2.78729 q^{94} -7.75703 q^{95} -3.05772 q^{96} -12.9651 q^{97} +17.7982 q^{98} -5.25285 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 101 q + 101 q^{2} + 10 q^{3} + 101 q^{4} + 19 q^{5} + 10 q^{6} + 42 q^{7} + 101 q^{8} + 147 q^{9}+O(q^{10}) $ 101 * q + 101 * q^2 + 10 * q^3 + 101 * q^4 + 19 * q^5 + 10 * q^6 + 42 * q^7 + 101 * q^8 + 147 * q^9	\( 101 q + 101 q^{2} + 10 q^{3} + 101 q^{4} + 19 q^{5} + 10 q^{6} + 42 q^{7} + 101 q^{8} + 147 q^{9} + 19 q^{10} + 4 q^{11} + 10 q^{12} + 58 q^{13} + 42 q^{14} + 27 q^{15} + 101 q^{16} + 34 q^{17} + 147 q^{18} + 36 q^{19} + 19 q^{20} + 45 q^{21} + 4 q^{22} + 47 q^{23} + 10 q^{24} + 174 q^{25} + 58 q^{26} + 31 q^{27} + 42 q^{28} + 62 q^{29} + 27 q^{30} + 47 q^{31} + 101 q^{32} + 55 q^{33} + 34 q^{34} + 16 q^{35} + 147 q^{36} + 90 q^{37} + 36 q^{38} + 50 q^{39} + 19 q^{40} + 54 q^{41} + 45 q^{42} + 65 q^{43} + 4 q^{44} + 47 q^{45} + 47 q^{46} + 54 q^{47} + 10 q^{48} + 189 q^{49} + 174 q^{50} + 36 q^{51} + 58 q^{52} + 94 q^{53} + 31 q^{54} + 68 q^{55} + 42 q^{56} + 79 q^{57} + 62 q^{58} - 6 q^{59} + 27 q^{60} + 58 q^{61} + 47 q^{62} + 117 q^{63} + 101 q^{64} + 89 q^{65} + 55 q^{66} + 127 q^{67} + 34 q^{68} + 45 q^{69} + 16 q^{70} + 87 q^{71} + 147 q^{72} + 83 q^{73} + 90 q^{74} - 4 q^{75} + 36 q^{76} + 53 q^{77} + 50 q^{78} + 74 q^{79} + 19 q^{80} + 241 q^{81} + 54 q^{82} + 11 q^{83} + 45 q^{84} + 120 q^{85} + 65 q^{86} + 37 q^{87} + 4 q^{88} + 89 q^{89} + 47 q^{90} + 31 q^{91} + 47 q^{92} + 123 q^{93} + 54 q^{94} + 61 q^{95} + 10 q^{96} + 85 q^{97} + 189 q^{98} - 55 q^{99}+O(q^{100}) \) 101 * q + 101 * q^2 + 10 * q^3 + 101 * q^4 + 19 * q^5 + 10 * q^6 + 42 * q^7 + 101 * q^8 + 147 * q^9 + 19 * q^10 + 4 * q^11 + 10 * q^12 + 58 * q^13 + 42 * q^14 + 27 * q^15 + 101 * q^16 + 34 * q^17 + 147 * q^18 + 36 * q^19 + 19 * q^20 + 45 * q^21 + 4 * q^22 + 47 * q^23 + 10 * q^24 + 174 * q^25 + 58 * q^26 + 31 * q^27 + 42 * q^28 + 62 * q^29 + 27 * q^30 + 47 * q^31 + 101 * q^32 + 55 * q^33 + 34 * q^34 + 16 * q^35 + 147 * q^36 + 90 * q^37 + 36 * q^38 + 50 * q^39 + 19 * q^40 + 54 * q^41 + 45 * q^42 + 65 * q^43 + 4 * q^44 + 47 * q^45 + 47 * q^46 + 54 * q^47 + 10 * q^48 + 189 * q^49 + 174 * q^50 + 36 * q^51 + 58 * q^52 + 94 * q^53 + 31 * q^54 + 68 * q^55 + 42 * q^56 + 79 * q^57 + 62 * q^58 - 6 * q^59 + 27 * q^60 + 58 * q^61 + 47 * q^62 + 117 * q^63 + 101 * q^64 + 89 * q^65 + 55 * q^66 + 127 * q^67 + 34 * q^68 + 45 * q^69 + 16 * q^70 + 87 * q^71 + 147 * q^72 + 83 * q^73 + 90 * q^74 - 4 * q^75 + 36 * q^76 + 53 * q^77 + 50 * q^78 + 74 * q^79 + 19 * q^80 + 241 * q^81 + 54 * q^82 + 11 * q^83 + 45 * q^84 + 120 * q^85 + 65 * q^86 + 37 * q^87 + 4 * q^88 + 89 * q^89 + 47 * q^90 + 31 * q^91 + 47 * q^92 + 123 * q^93 + 54 * q^94 + 61 * q^95 + 10 * q^96 + 85 * q^97 + 189 * q^98 - 55 * 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
$3$	−3.05772	−1.76537	−0.882687	−	0.469961i	$-0.844268\pi$
$3$	−3.05772	−1.76537	−0.882687	+	0.469961i	$0.844268\pi$
$4$	1.00000	0.500000
$5$	1.21871	0.545023	0.272511	−	0.962153i	$-0.412146\pi$
$5$	1.21871	0.545023	0.272511	+	0.962153i	$0.412146\pi$
$6$	−3.05772	−1.24831
$7$	−4.97978	−1.88218	−0.941090	−	0.338156i	$-0.890197\pi$
$7$	−4.97978	−1.88218	−0.941090	+	0.338156i	$0.890197\pi$
$8$	1.00000	0.353553
$9$	6.34964	2.11655
$10$	1.21871	0.385389
$11$	−0.827268	−0.249431	−0.124715	−	0.992193i	$-0.539802\pi$
$11$	−0.827268	−0.249431	−0.124715	+	0.992193i	$0.539802\pi$
$12$	−3.05772	−0.882687
$13$	−0.294479	−0.0816737	−0.0408368	−	0.999166i	$-0.513002\pi$
$13$	−0.294479	−0.0816737	−0.0408368	+	0.999166i	$0.513002\pi$
$14$	−4.97978	−1.33090
$15$	−3.72647	−0.962169
$16$	1.00000	0.250000
$17$	−3.77163	−0.914755	−0.457377	−	0.889273i	$-0.651211\pi$
$17$	−3.77163	−0.914755	−0.457377	+	0.889273i	$0.651211\pi$
$18$	6.34964	1.49662
$19$	−6.36496	−1.46022	−0.730111	−	0.683329i	$-0.760531\pi$
$19$	−6.36496	−1.46022	−0.730111	+	0.683329i	$0.760531\pi$
$20$	1.21871	0.272511
$21$	15.2268	3.32275
$22$	−0.827268	−0.176374
$23$	−5.27997	−1.10095	−0.550475	−	0.834852i	$-0.685553\pi$
$23$	−5.27997	−1.10095	−0.550475	+	0.834852i	$0.685553\pi$
$24$	−3.05772	−0.624154
$25$	−3.51475	−0.702950
$26$	−0.294479	−0.0577520
$27$	−10.2422	−1.97112
$28$	−4.97978	−0.941090
$29$	0.954562	0.177258	0.0886288	−	0.996065i	$-0.471752\pi$
$29$	0.954562	0.177258	0.0886288	+	0.996065i	$0.471752\pi$
$30$	−3.72647	−0.680356
$31$	−9.08194	−1.63116	−0.815582	−	0.578641i	$-0.803583\pi$
$31$	−9.08194	−1.63116	−0.815582	+	0.578641i	$0.803583\pi$
$32$	1.00000	0.176777
$33$	2.52955	0.440338
$34$	−3.77163	−0.646829
$35$	−6.06890	−1.02583
$36$	6.34964	1.05827
$37$	8.27313	1.36009	0.680047	−	0.733168i	$-0.261959\pi$
$37$	8.27313	1.36009	0.680047	+	0.733168i	$0.261959\pi$
$38$	−6.36496	−1.03253
$39$	0.900432	0.144185
$40$	1.21871	0.192695
$41$	−10.1894	−1.59132	−0.795658	−	0.605746i	$-0.792875\pi$
$41$	−10.1894	−1.59132	−0.795658	+	0.605746i	$0.792875\pi$
$42$	15.2268	2.34954
$43$	1.40206	0.213812	0.106906	−	0.994269i	$-0.465906\pi$
$43$	1.40206	0.213812	0.106906	+	0.994269i	$0.465906\pi$
$44$	−0.827268	−0.124715
$45$	7.73835	1.15357
$46$	−5.27997	−0.778489
$47$	2.78729	0.406567	0.203284	−	0.979120i	$-0.434839\pi$
$47$	2.78729	0.406567	0.203284	+	0.979120i	$0.434839\pi$
$48$	−3.05772	−0.441344
$49$	17.7982	2.54260
$50$	−3.51475	−0.497061
$51$	11.5326	1.61488
$52$	−0.294479	−0.0408368
$53$	13.6740	1.87827	0.939134	−	0.343552i	$-0.111630\pi$
$53$	13.6740	1.87827	0.939134	+	0.343552i	$0.111630\pi$
$54$	−10.2422	−1.39379
$55$	−1.00820	−0.135945
$56$	−4.97978	−0.665451
$57$	19.4622	2.57784
$58$	0.954562	0.125340
$59$	−5.78093	−0.752612	−0.376306	−	0.926495i	$-0.622806\pi$
$59$	−5.78093	−0.752612	−0.376306	+	0.926495i	$0.622806\pi$
$60$	−3.72647	−0.481085
$61$	−1.78730	−0.228840	−0.114420	−	0.993432i	$-0.536501\pi$
$61$	−1.78730	−0.228840	−0.114420	+	0.993432i	$0.536501\pi$
$62$	−9.08194	−1.15341
$63$	−31.6198	−3.98372
$64$	1.00000	0.125000
$65$	−0.358883	−0.0445140
$66$	2.52955	0.311366
$67$	12.3285	1.50617	0.753085	−	0.657924i	$-0.228565\pi$
$67$	12.3285	1.50617	0.753085	+	0.657924i	$0.228565\pi$
$68$	−3.77163	−0.457377
$69$	16.1446	1.94359
$70$	−6.06890	−0.725372
$71$	−2.67071	−0.316955	−0.158477	−	0.987363i	$-0.550659\pi$
$71$	−2.67071	−0.316955	−0.158477	+	0.987363i	$0.550659\pi$
$72$	6.34964	0.748312
$73$	−9.43466	−1.10424	−0.552121	−	0.833764i	$-0.686182\pi$
$73$	−9.43466	−1.10424	−0.552121	+	0.833764i	$0.686182\pi$
$74$	8.27313	0.961732
$75$	10.7471	1.24097
$76$	−6.36496	−0.730111
$77$	4.11961	0.469473
$78$	0.900432	0.101954
$79$	−3.47393	−0.390848	−0.195424	−	0.980719i	$-0.562608\pi$
$79$	−3.47393	−0.390848	−0.195424	+	0.980719i	$0.562608\pi$
$80$	1.21871	0.136256
$81$	12.2690	1.36322
$82$	−10.1894	−1.12523
$83$	−1.62106	−0.177934	−0.0889671	−	0.996035i	$-0.528357\pi$
$83$	−1.62106	−0.177934	−0.0889671	+	0.996035i	$0.528357\pi$
$84$	15.2268	1.66138
$85$	−4.59652	−0.498562
$86$	1.40206	0.151188
$87$	−2.91878	−0.312926
$88$	−0.827268	−0.0881870
$89$	−2.04457	−0.216724	−0.108362	−	0.994111i	$-0.534561\pi$
$89$	−2.04457	−0.216724	−0.108362	+	0.994111i	$0.534561\pi$
$90$	7.73835	0.815694
$91$	1.46644	0.153725
$92$	−5.27997	−0.550475
$93$	27.7700	2.87961
$94$	2.78729	0.287487
$95$	−7.75703	−0.795854
$96$	−3.05772	−0.312077
$97$	−12.9651	−1.31640	−0.658202	−	0.752842i	$-0.728683\pi$
$97$	−12.9651	−1.31640	−0.658202	+	0.752842i	$0.728683\pi$
$98$	17.7982	1.79789
$99$	−5.25285	−0.527931
$100$	−3.51475	−0.351475
$101$	−4.56241	−0.453976	−0.226988	−	0.973897i	$-0.572888\pi$
$101$	−4.56241	−0.453976	−0.226988	+	0.973897i	$0.572888\pi$
$102$	11.5326	1.14190
$103$	−16.4782	−1.62364	−0.811821	−	0.583907i	$-0.801523\pi$
$103$	−16.4782	−1.62364	−0.811821	+	0.583907i	$0.801523\pi$
$104$	−0.294479	−0.0288760
$105$	18.5570	1.81098
$106$	13.6740	1.32814
$107$	5.29275	0.511670	0.255835	−	0.966720i	$-0.417650\pi$
$107$	5.29275	0.511670	0.255835	+	0.966720i	$0.417650\pi$
$108$	−10.2422	−0.985560
$109$	−1.40508	−0.134583	−0.0672913	−	0.997733i	$-0.521436\pi$
$109$	−1.40508	−0.134583	−0.0672913	+	0.997733i	$0.521436\pi$
$110$	−1.00820	−0.0961279
$111$	−25.2969	−2.40107
$112$	−4.97978	−0.470545
$113$	−18.5187	−1.74209	−0.871045	−	0.491202i	$-0.836558\pi$
$113$	−18.5187	−1.74209	−0.871045	+	0.491202i	$0.836558\pi$
$114$	19.4622	1.82281
$115$	−6.43474	−0.600042
$116$	0.954562	0.0886288
$117$	−1.86983	−0.172866
$118$	−5.78093	−0.532177
$119$	18.7819	1.72173
$120$	−3.72647	−0.340178
$121$	−10.3156	−0.937784
$122$	−1.78730	−0.161814
$123$	31.1563	2.80927
$124$	−9.08194	−0.815582
$125$	−10.3770	−0.928147
$126$	−31.6198	−2.81692
$127$	12.3683	1.09751	0.548755	−	0.835983i	$-0.315102\pi$
$127$	12.3683	1.09751	0.548755	+	0.835983i	$0.315102\pi$
$128$	1.00000	0.0883883
$129$	−4.28710	−0.377458
$130$	−0.358883	−0.0314762
$131$	11.3013	0.987397	0.493699	−	0.869633i	$-0.335645\pi$
$131$	11.3013	0.987397	0.493699	+	0.869633i	$0.335645\pi$
$132$	2.52955	0.220169
$133$	31.6961	2.74840
$134$	12.3285	1.06502
$135$	−12.4823	−1.07431
$136$	−3.77163	−0.323415
$137$	16.1280	1.37791	0.688956	−	0.724804i	$-0.258069\pi$
$137$	16.1280	1.37791	0.688956	+	0.724804i	$0.258069\pi$
$138$	16.1446	1.37432
$139$	6.64865	0.563932	0.281966	−	0.959424i	$-0.409014\pi$
$139$	6.64865	0.563932	0.281966	+	0.959424i	$0.409014\pi$
$140$	−6.06890	−0.512916
$141$	−8.52273	−0.717744
$142$	−2.67071	−0.224121
$143$	0.243613	0.0203719
$144$	6.34964	0.529136
$145$	1.16333	0.0966095
$146$	−9.43466	−0.780818
$147$	−54.4219	−4.48865
$148$	8.27313	0.680047
$149$	7.99822	0.655239	0.327620	−	0.944810i	$-0.393754\pi$
$149$	7.99822	0.655239	0.327620	+	0.944810i	$0.393754\pi$
$150$	10.7471	0.877498
$151$	2.82585	0.229964	0.114982	−	0.993368i	$-0.463319\pi$
$151$	2.82585	0.229964	0.114982	+	0.993368i	$0.463319\pi$
$152$	−6.36496	−0.516266
$153$	−23.9485	−1.93612
$154$	4.11961	0.331968
$155$	−11.0682	−0.889022
$156$	0.900432	0.0720923
$157$	3.58700	0.286273	0.143137	−	0.989703i	$-0.454281\pi$
$157$	3.58700	0.286273	0.143137	+	0.989703i	$0.454281\pi$
$158$	−3.47393	−0.276371
$159$	−41.8112	−3.31584
$160$	1.21871	0.0963474
$161$	26.2931	2.07218
$162$	12.2690	0.963942
$163$	1.42393	0.111530	0.0557652	−	0.998444i	$-0.482240\pi$
$163$	1.42393	0.111530	0.0557652	+	0.998444i	$0.482240\pi$
$164$	−10.1894	−0.795658
$165$	3.08279	0.239994
$166$	−1.62106	−0.125819
$167$	−22.6588	−1.75339	−0.876697	−	0.481043i	$-0.840258\pi$
$167$	−22.6588	−1.75339	−0.876697	+	0.481043i	$0.840258\pi$
$168$	15.2268	1.17477
$169$	−12.9133	−0.993329
$170$	−4.59652	−0.352537
$171$	−40.4152	−3.09062
$172$	1.40206	0.106906
$173$	8.67980	0.659913	0.329956	−	0.943996i	$-0.392966\pi$
$173$	8.67980	0.659913	0.329956	+	0.943996i	$0.392966\pi$
$174$	−2.91878	−0.221272
$175$	17.5027	1.32308
$176$	−0.827268	−0.0623577
$177$	17.6764	1.32864
$178$	−2.04457	−0.153247
$179$	−19.1876	−1.43415	−0.717075	−	0.696996i	$-0.754519\pi$
$179$	−19.1876	−1.43415	−0.717075	+	0.696996i	$0.754519\pi$
$180$	7.73835	0.576783
$181$	−1.93407	−0.143758	−0.0718792	−	0.997413i	$-0.522900\pi$
$181$	−1.93407	−0.143758	−0.0718792	+	0.997413i	$0.522900\pi$
$182$	1.46644	0.108700
$183$	5.46505	0.403988
$184$	−5.27997	−0.389244
$185$	10.0825	0.741283
$186$	27.7700	2.03620
$187$	3.12015	0.228168
$188$	2.78729	0.203284
$189$	51.0041	3.71000
$190$	−7.75703	−0.562754
$191$	−11.9403	−0.863973	−0.431986	−	0.901880i	$-0.642187\pi$
$191$	−11.9403	−0.863973	−0.431986	+	0.901880i	$0.642187\pi$
$192$	−3.05772	−0.220672
$193$	19.0193	1.36904	0.684518	−	0.728996i	$-0.260013\pi$
$193$	19.0193	1.36904	0.684518	+	0.728996i	$0.260013\pi$
$194$	−12.9651	−0.930838
$195$	1.09736	0.0785839
$196$	17.7982	1.27130
$197$	1.45951	0.103986	0.0519928	−	0.998647i	$-0.483443\pi$
$197$	1.45951	0.103986	0.0519928	+	0.998647i	$0.483443\pi$
$198$	−5.25285	−0.373304
$199$	0.0793401	0.00562427	0.00281214	−	0.999996i	$-0.499105\pi$
$199$	0.0793401	0.00562427	0.00281214	+	0.999996i	$0.499105\pi$
$200$	−3.51475	−0.248530
$201$	−37.6972	−2.65895
$202$	−4.56241	−0.321010
$203$	−4.75351	−0.333631
$204$	11.5326	0.807442
$205$	−12.4179	−0.867304
$206$	−16.4782	−1.14809
$207$	−33.5259	−2.33021
$208$	−0.294479	−0.0204184
$209$	5.26552	0.364224
$210$	18.5570	1.28055
$211$	15.5437	1.07007	0.535035	−	0.844830i	$-0.320298\pi$
$211$	15.5437	1.07007	0.535035	+	0.844830i	$0.320298\pi$
$212$	13.6740	0.939134
$213$	8.16627	0.559544
$214$	5.29275	0.361805
$215$	1.70870	0.116532
$216$	−10.2422	−0.696896
$217$	45.2261	3.07015
$218$	−1.40508	−0.0951643
$219$	28.8485	1.94940
$220$	−1.00820	−0.0679727
$221$	1.11066	0.0747114
$222$	−25.2969	−1.69782
$223$	18.8801	1.26431	0.632153	−	0.774843i	$-0.282171\pi$
$223$	18.8801	1.26431	0.632153	+	0.774843i	$0.282171\pi$
$224$	−4.97978	−0.332726
$225$	−22.3174	−1.48783
$226$	−18.5187	−1.23184
$227$	15.9786	1.06054	0.530268	−	0.847830i	$-0.322091\pi$
$227$	15.9786	1.06054	0.530268	+	0.847830i	$0.322091\pi$
$228$	19.4622	1.28892
$229$	−0.00221362	−0.000146280 0	−7.31400e−5	−	1.00000i	$-0.500023\pi$
$229$	−0.00221362	−0.000146280 0	−7.31400e−5		1.00000i	$0.500023\pi$
$230$	−6.43474	−0.424294
$231$	−12.5966	−0.828796
$232$	0.954562	0.0626701
$233$	−13.0908	−0.857608	−0.428804	−	0.903397i	$-0.641065\pi$
$233$	−13.0908	−0.857608	−0.428804	+	0.903397i	$0.641065\pi$
$234$	−1.86983	−0.122235
$235$	3.39689	0.221589
$236$	−5.78093	−0.376306
$237$	10.6223	0.689993
$238$	18.7819	1.21745
$239$	15.3930	0.995690	0.497845	−	0.867266i	$-0.334125\pi$
$239$	15.3930	0.995690	0.497845	+	0.867266i	$0.334125\pi$
$240$	−3.72647	−0.240542
$241$	4.84292	0.311960	0.155980	−	0.987760i	$-0.450146\pi$
$241$	4.84292	0.311960	0.155980	+	0.987760i	$0.450146\pi$
$242$	−10.3156	−0.663114
$243$	−6.78833	−0.435471
$244$	−1.78730	−0.114420
$245$	21.6908	1.38578
$246$	31.1563	1.98645
$247$	1.87434	0.119262
$248$	−9.08194	−0.576704
$249$	4.95674	0.314121
$250$	−10.3770	−0.656299
$251$	21.0715	1.33002	0.665010	−	0.746834i	$-0.268427\pi$
$251$	21.0715	1.33002	0.665010	+	0.746834i	$0.268427\pi$
$252$	−31.6198	−1.99186
$253$	4.36795	0.274610
$254$	12.3683	0.776057
$255$	14.0548	0.880149
$256$	1.00000	0.0625000
$257$	18.5085	1.15453	0.577265	−	0.816557i	$-0.304120\pi$
$257$	18.5085	1.15453	0.577265	+	0.816557i	$0.304120\pi$
$258$	−4.28710	−0.266903
$259$	−41.1984	−2.55994
$260$	−0.358883	−0.0222570
$261$	6.06112	0.375174
$262$	11.3013	0.698195
$263$	31.4836	1.94136	0.970682	−	0.240366i	$-0.0772675\pi$
$263$	31.4836	1.94136	0.970682	+	0.240366i	$0.0772675\pi$
$264$	2.52955	0.155683
$265$	16.6646	1.02370
$266$	31.6961	1.94341
$267$	6.25172	0.382599
$268$	12.3285	0.753085
$269$	−23.8148	−1.45202	−0.726008	−	0.687686i	$-0.758627\pi$
$269$	−23.8148	−1.45202	−0.726008	+	0.687686i	$0.758627\pi$
$270$	−12.4823	−0.759649
$271$	12.1279	0.736717	0.368358	−	0.929684i	$-0.379920\pi$
$271$	12.1279	0.736717	0.368358	+	0.929684i	$0.379920\pi$
$272$	−3.77163	−0.228689
$273$	−4.48396	−0.271381
$274$	16.1280	0.974330
$275$	2.90764	0.175337
$276$	16.1446	0.971793
$277$	−13.3010	−0.799178	−0.399589	−	0.916694i	$-0.630847\pi$
$277$	−13.3010	−0.799178	−0.399589	+	0.916694i	$0.630847\pi$
$278$	6.64865	0.398760
$279$	−57.6670	−3.45243
$280$	−6.06890	−0.362686
$281$	24.3260	1.45117	0.725583	−	0.688135i	$-0.241570\pi$
$281$	24.3260	1.45117	0.725583	+	0.688135i	$0.241570\pi$
$282$	−8.52273	−0.507521
$283$	9.45570	0.562083	0.281041	−	0.959696i	$-0.409320\pi$
$283$	9.45570	0.562083	0.281041	+	0.959696i	$0.409320\pi$
$284$	−2.67071	−0.158477
$285$	23.7188	1.40498
$286$	0.243613	0.0144051
$287$	50.7410	2.99514
$288$	6.34964	0.374156
$289$	−2.77481	−0.163224
$290$	1.16333	0.0683132
$291$	39.6435	2.32394
$292$	−9.43466	−0.552121
$293$	31.6794	1.85073	0.925364	−	0.379079i	$-0.123759\pi$
$293$	31.6794	1.85073	0.925364	+	0.379079i	$0.123759\pi$
$294$	−54.4219	−3.17395
$295$	−7.04526	−0.410191
$296$	8.27313	0.480866
$297$	8.47308	0.491658
$298$	7.99822	0.463324
$299$	1.55484	0.0899185
$300$	10.7471	0.620485
$301$	−6.98195	−0.402433
$302$	2.82585	0.162609
$303$	13.9506	0.801438
$304$	−6.36496	−0.365055
$305$	−2.17819	−0.124723
$306$	−23.9485	−1.36904
$307$	29.1356	1.66286	0.831428	−	0.555632i	$-0.187524\pi$
$307$	29.1356	1.66286	0.831428	+	0.555632i	$0.187524\pi$
$308$	4.11961	0.234737
$309$	50.3856	2.86633
$310$	−11.0682	−0.628633
$311$	26.3882	1.49634	0.748168	−	0.663509i	$-0.230933\pi$
$311$	26.3882	1.49634	0.748168	+	0.663509i	$0.230933\pi$
$312$	0.900432	0.0509769
$313$	0.704636	0.0398284	0.0199142	−	0.999802i	$-0.493661\pi$
$313$	0.704636	0.0398284	0.0199142	+	0.999802i	$0.493661\pi$
$314$	3.58700	0.202426
$315$	−38.5353	−2.17122
$316$	−3.47393	−0.195424
$317$	−14.1160	−0.792833	−0.396416	−	0.918071i	$-0.629746\pi$
$317$	−14.1160	−0.792833	−0.396416	+	0.918071i	$0.629746\pi$
$318$	−41.8112	−2.34466
$319$	−0.789678	−0.0442135
$320$	1.21871	0.0681279
$321$	−16.1837	−0.903289
$322$	26.2931	1.46526
$323$	24.0063	1.33574
$324$	12.2690	0.681610
$325$	1.03502	0.0574125
$326$	1.42393	0.0788640
$327$	4.29635	0.237589
$328$	−10.1894	−0.562615
$329$	−13.8801	−0.765233
$330$	3.08279	0.169702
$331$	−19.3491	−1.06352	−0.531761	−	0.846895i	$-0.678469\pi$
$331$	−19.3491	−1.06352	−0.531761	+	0.846895i	$0.678469\pi$
$332$	−1.62106	−0.0889671
$333$	52.5314	2.87870
$334$	−22.6588	−1.23984
$335$	15.0249	0.820897
$336$	15.2268	0.830688
$337$	−8.44590	−0.460078	−0.230039	−	0.973181i	$-0.573885\pi$
$337$	−8.44590	−0.460078	−0.230039	+	0.973181i	$0.573885\pi$
$338$	−12.9133	−0.702390
$339$	56.6249	3.07544
$340$	−4.59652	−0.249281
$341$	7.51319	0.406862
$342$	−40.4152	−2.18540
$343$	−53.7728	−2.90346
$344$	1.40206	0.0755939
$345$	19.6756	1.05930
$346$	8.67980	0.466629
$347$	−14.6008	−0.783812	−0.391906	−	0.920005i	$-0.628184\pi$
$347$	−14.6008	−0.783812	−0.391906	+	0.920005i	$0.628184\pi$
$348$	−2.91878	−0.156463
$349$	−33.8053	−1.80956	−0.904778	−	0.425883i	$-0.859963\pi$
$349$	−33.8053	−1.80956	−0.904778	+	0.425883i	$0.859963\pi$
$350$	17.5027	0.935558
$351$	3.01612	0.160989
$352$	−0.827268	−0.0440935
$353$	−10.4862	−0.558124	−0.279062	−	0.960273i	$-0.590024\pi$
$353$	−10.4862	−0.558124	−0.279062	+	0.960273i	$0.590024\pi$
$354$	17.6764	0.939492
$355$	−3.25481	−0.172748
$356$	−2.04457	−0.108362
$357$	−57.4297	−3.03950
$358$	−19.1876	−1.01410
$359$	−29.4725	−1.55550	−0.777748	−	0.628576i	$-0.783638\pi$
$359$	−29.4725	−1.55550	−0.777748	+	0.628576i	$0.783638\pi$
$360$	7.73835	0.407847
$361$	21.5127	1.13225
$362$	−1.93407	−0.101652
$363$	31.5423	1.65554
$364$	1.46644	0.0768623
$365$	−11.4981	−0.601838
$366$	5.46505	0.285663
$367$	−22.2205	−1.15990	−0.579949	−	0.814653i	$-0.696928\pi$
$367$	−22.2205	−1.15990	−0.579949	+	0.814653i	$0.696928\pi$
$368$	−5.27997	−0.275237
$369$	−64.6989	−3.36809
$370$	10.0825	0.524166
$371$	−68.0935	−3.53524
$372$	27.7700	1.43981
$373$	−33.7318	−1.74657	−0.873284	−	0.487212i	$-0.838014\pi$
$373$	−33.7318	−1.74657	−0.873284	+	0.487212i	$0.838014\pi$
$374$	3.12015	0.161339
$375$	31.7299	1.63853
$376$	2.78729	0.143743
$377$	−0.281098	−0.0144773
$378$	51.0041	2.62337
$379$	3.20136	0.164443	0.0822214	−	0.996614i	$-0.473799\pi$
$379$	3.20136	0.164443	0.0822214	+	0.996614i	$0.473799\pi$
$380$	−7.75703	−0.397927
$381$	−37.8188	−1.93752
$382$	−11.9403	−0.610921
$383$	15.6181	0.798047	0.399024	−	0.916941i	$-0.369349\pi$
$383$	15.6181	0.798047	0.399024	+	0.916941i	$0.369349\pi$
$384$	−3.05772	−0.156038
$385$	5.02061	0.255874
$386$	19.0193	0.968055
$387$	8.90256	0.452543
$388$	−12.9651	−0.658202
$389$	24.1416	1.22403	0.612014	−	0.790847i	$-0.290359\pi$
$389$	24.1416	1.22403	0.612014	+	0.790847i	$0.290359\pi$
$390$	1.09736	0.0555672
$391$	19.9141	1.00710
$392$	17.7982	0.898946
$393$	−34.5561	−1.74313
$394$	1.45951	0.0735289
$395$	−4.23371	−0.213021
$396$	−5.25285	−0.263966
$397$	28.0833	1.40946	0.704731	−	0.709474i	$-0.251068\pi$
$397$	28.0833	1.40946	0.704731	+	0.709474i	$0.251068\pi$
$398$	0.0793401	0.00397696
$399$	−96.9177	−4.85195
$400$	−3.51475	−0.175738
$401$	3.00975	0.150300	0.0751498	−	0.997172i	$-0.476056\pi$
$401$	3.00975	0.150300	0.0751498	+	0.997172i	$0.476056\pi$
$402$	−37.6972	−1.88016
$403$	2.67444	0.133223
$404$	−4.56241	−0.226988
$405$	14.9523	0.742986
$406$	−4.75351	−0.235913
$407$	−6.84409	−0.339249
$408$	11.5326	0.570948
$409$	37.3000	1.84437	0.922183	−	0.386754i	$-0.126404\pi$
$409$	37.3000	1.84437	0.922183	+	0.386754i	$0.126404\pi$
$410$	−12.4179	−0.613276
$411$	−49.3150	−2.43253
$412$	−16.4782	−0.811821
$413$	28.7877	1.41655
$414$	−33.5259	−1.64771
$415$	−1.97560	−0.0969782
$416$	−0.294479	−0.0144380
$417$	−20.3297	−0.995550
$418$	5.26552	0.257545
$419$	13.8925	0.678694	0.339347	−	0.940661i	$-0.389794\pi$
$419$	13.8925	0.678694	0.339347	+	0.940661i	$0.389794\pi$
$420$	18.5570	0.905488
$421$	−18.9815	−0.925102	−0.462551	−	0.886593i	$-0.653066\pi$
$421$	−18.9815	−0.925102	−0.462551	+	0.886593i	$0.653066\pi$
$422$	15.5437	0.756654
$423$	17.6983	0.860519
$424$	13.6740	0.664068
$425$	13.2563	0.643027
$426$	8.16627	0.395657
$427$	8.90034	0.430718
$428$	5.29275	0.255835
$429$	−0.744899	−0.0359640
$430$	1.70870	0.0824009
$431$	5.93884	0.286064	0.143032	−	0.989718i	$-0.454315\pi$
$431$	5.93884	0.286064	0.143032	+	0.989718i	$0.454315\pi$
$432$	−10.2422	−0.492780
$433$	−26.8946	−1.29247	−0.646235	−	0.763138i	$-0.723657\pi$
$433$	−26.8946	−1.29247	−0.646235	+	0.763138i	$0.723657\pi$
$434$	45.2261	2.17092
$435$	−3.55714	−0.170552
$436$	−1.40508	−0.0672913
$437$	33.6068	1.60763
$438$	28.8485	1.37844
$439$	20.5396	0.980302	0.490151	−	0.871638i	$-0.336942\pi$
$439$	20.5396	0.980302	0.490151	+	0.871638i	$0.336942\pi$
$440$	−1.00820	−0.0480640
$441$	113.012	5.38153
$442$	1.11066	0.0528289
$443$	20.0214	0.951247	0.475623	−	0.879649i	$-0.342223\pi$
$443$	20.0214	0.951247	0.475623	+	0.879649i	$0.342223\pi$
$444$	−25.2969	−1.20054
$445$	−2.49174	−0.118120
$446$	18.8801	0.894000
$447$	−24.4563	−1.15674
$448$	−4.97978	−0.235273
$449$	−10.6932	−0.504645	−0.252322	−	0.967643i	$-0.581194\pi$
$449$	−10.6932	−0.504645	−0.252322	+	0.967643i	$0.581194\pi$
$450$	−22.3174	−1.05205
$451$	8.42936	0.396923
$452$	−18.5187	−0.871045
$453$	−8.64065	−0.405973
$454$	15.9786	0.749913
$455$	1.78716	0.0837834
$456$	19.4622	0.911403
$457$	9.24484	0.432456	0.216228	−	0.976343i	$-0.430625\pi$
$457$	9.24484	0.432456	0.216228	+	0.976343i	$0.430625\pi$
$458$	−0.00221362	−0.000103436 0
$459$	38.6299	1.80309
$460$	−6.43474	−0.300021
$461$	10.9448	0.509752	0.254876	−	0.966974i	$-0.417965\pi$
$461$	10.9448	0.509752	0.254876	+	0.966974i	$0.417965\pi$
$462$	−12.5966	−0.586047
$463$	−9.54662	−0.443669	−0.221834	−	0.975084i	$-0.571204\pi$
$463$	−9.54662	−0.443669	−0.221834	+	0.975084i	$0.571204\pi$
$464$	0.954562	0.0443144
$465$	33.8435	1.56946
$466$	−13.0908	−0.606421
$467$	25.3312	1.17219	0.586095	−	0.810242i	$-0.300665\pi$
$467$	25.3312	1.17219	0.586095	+	0.810242i	$0.300665\pi$
$468$	−1.86983	−0.0864330
$469$	−61.3934	−2.83488
$470$	3.39689	0.156687
$471$	−10.9680	−0.505380
$472$	−5.78093	−0.266089
$473$	−1.15988	−0.0533313
$474$	10.6223	0.487899
$475$	22.3712	1.02646
$476$	18.7819	0.860867
$477$	86.8249	3.97544
$478$	15.3930	0.704059
$479$	24.6355	1.12563	0.562813	−	0.826584i	$-0.309719\pi$
$479$	24.6355	1.12563	0.562813	+	0.826584i	$0.309719\pi$
$480$	−3.72647	−0.170089
$481$	−2.43626	−0.111084
$482$	4.84292	0.220589
$483$	−80.3968	−3.65818
$484$	−10.3156	−0.468892
$485$	−15.8006	−0.717470
$486$	−6.78833	−0.307925
$487$	−28.3770	−1.28588	−0.642942	−	0.765914i	$-0.722287\pi$
$487$	−28.3770	−1.28588	−0.642942	+	0.765914i	$0.722287\pi$
$488$	−1.78730	−0.0809071
$489$	−4.35396	−0.196893
$490$	21.6908	0.979892
$491$	−23.1951	−1.04678	−0.523390	−	0.852093i	$-0.675333\pi$
$491$	−23.1951	−1.04678	−0.523390	+	0.852093i	$0.675333\pi$
$492$	31.1563	1.40463
$493$	−3.60025	−0.162147
$494$	1.87434	0.0843307
$495$	−6.40169	−0.287735
$496$	−9.08194	−0.407791
$497$	13.2995	0.596566
$498$	4.95674	0.222117
$499$	13.2584	0.593527	0.296764	−	0.954951i	$-0.404093\pi$
$499$	13.2584	0.593527	0.296764	+	0.954951i	$0.404093\pi$
$500$	−10.3770	−0.464073
$501$	69.2843	3.09540
$502$	21.0715	0.940466
$503$	−14.1749	−0.632029	−0.316015	−	0.948754i	$-0.602345\pi$
$503$	−14.1749	−0.632029	−0.316015	+	0.948754i	$0.602345\pi$
$504$	−31.6198	−1.40846
$505$	−5.56024	−0.247428
$506$	4.36795	0.194179
$507$	39.4852	1.75360
$508$	12.3683	0.548755
$509$	−19.6120	−0.869285	−0.434642	−	0.900603i	$-0.643125\pi$
$509$	−19.6120	−0.869285	−0.434642	+	0.900603i	$0.643125\pi$
$510$	14.0548	0.622359
$511$	46.9825	2.07838
$512$	1.00000	0.0441942
$513$	65.1914	2.87827
$514$	18.5085	0.816376
$515$	−20.0821	−0.884922
$516$	−4.28710	−0.188729
$517$	−2.30583	−0.101410
$518$	−41.1984	−1.81015
$519$	−26.5404	−1.16499
$520$	−0.358883	−0.0157381
$521$	−20.3082	−0.889717	−0.444858	−	0.895601i	$-0.646746\pi$
$521$	−20.3082	−0.889717	−0.444858	+	0.895601i	$0.646746\pi$
$522$	6.06112	0.265288
$523$	27.0842	1.18431	0.592154	−	0.805825i	$-0.298278\pi$
$523$	27.0842	1.18431	0.592154	+	0.805825i	$0.298278\pi$
$524$	11.3013	0.493699
$525$	−53.5183	−2.33573
$526$	31.4836	1.37275
$527$	34.2537	1.49212
$528$	2.52955	0.110085
$529$	4.87804	0.212089
$530$	16.6646	0.723864
$531$	−36.7068	−1.59294
$532$	31.6961	1.37420
$533$	3.00056	0.129969
$534$	6.25172	0.270538
$535$	6.45032	0.278872
$536$	12.3285	0.532511
$537$	58.6703	2.53181
$538$	−23.8148	−1.02673
$539$	−14.7239	−0.634203
$540$	−12.4823	−0.537153
$541$	−40.6133	−1.74610	−0.873051	−	0.487629i	$-0.837862\pi$
$541$	−40.6133	−1.74610	−0.873051	+	0.487629i	$0.837862\pi$
$542$	12.1279	0.520937
$543$	5.91384	0.253787
$544$	−3.77163	−0.161707
$545$	−1.71239	−0.0733506
$546$	−4.48396	−0.191896
$547$	−37.7969	−1.61608	−0.808039	−	0.589129i	$-0.799471\pi$
$547$	−37.7969	−1.61608	−0.808039	+	0.589129i	$0.799471\pi$
$548$	16.1280	0.688956
$549$	−11.3487	−0.484350
$550$	2.90764	0.123982
$551$	−6.07574	−0.258835
$552$	16.1446	0.687162
$553$	17.2994	0.735647
$554$	−13.3010	−0.565104
$555$	−30.8295	−1.30864
$556$	6.64865	0.281966
$557$	−0.480098	−0.0203424	−0.0101712	−	0.999948i	$-0.503238\pi$
$557$	−0.480098	−0.0203424	−0.0101712	+	0.999948i	$0.503238\pi$
$558$	−57.6670	−2.44124
$559$	−0.412876	−0.0174628
$560$	−6.06890	−0.256458
$561$	−9.54053	−0.402802
$562$	24.3260	1.02613
$563$	−21.8939	−0.922717	−0.461359	−	0.887214i	$-0.652638\pi$
$563$	−21.8939	−0.922717	−0.461359	+	0.887214i	$0.652638\pi$
$564$	−8.52273	−0.358872
$565$	−22.5689	−0.949479
$566$	9.45570	0.397453
$567$	−61.0968	−2.56582
$568$	−2.67071	−0.112060
$569$	27.8910	1.16925	0.584625	−	0.811304i	$-0.301242\pi$
$569$	27.8910	1.16925	0.584625	+	0.811304i	$0.301242\pi$
$570$	23.7188	0.993471
$571$	27.5530	1.15306	0.576528	−	0.817077i	$-0.304407\pi$
$571$	27.5530	1.15306	0.576528	+	0.817077i	$0.304407\pi$
$572$	0.243613	0.0101860
$573$	36.5102	1.52524
$574$	50.7410	2.11789
$575$	18.5578	0.773912
$576$	6.34964	0.264568
$577$	33.9731	1.41432	0.707160	−	0.707053i	$-0.249976\pi$
$577$	33.9731	1.41432	0.707160	+	0.707053i	$0.249976\pi$
$578$	−2.77481	−0.115417
$579$	−58.1555	−2.41686
$580$	1.16333	0.0483047
$581$	8.07252	0.334904
$582$	39.6435	1.64328
$583$	−11.3121	−0.468497
$584$	−9.43466	−0.390409
$585$	−2.27878	−0.0942159
$586$	31.6794	1.30866
$587$	27.0401	1.11606	0.558032	−	0.829819i	$-0.311557\pi$
$587$	27.0401	1.11606	0.558032	+	0.829819i	$0.311557\pi$
$588$	−54.4219	−2.24432
$589$	57.8061	2.38186
$590$	−7.04526	−0.290049
$591$	−4.46276	−0.183573
$592$	8.27313	0.340024
$593$	−25.3838	−1.04239	−0.521194	−	0.853438i	$-0.674513\pi$
$593$	−25.3838	−1.04239	−0.521194	+	0.853438i	$0.674513\pi$
$594$	8.47308	0.347655
$595$	22.8896	0.938384
$596$	7.99822	0.327620
$597$	−0.242600	−0.00992894
$598$	1.55484	0.0635820
$599$	−26.6094	−1.08723	−0.543615	−	0.839335i	$-0.682945\pi$
$599$	−26.6094	−1.08723	−0.543615	+	0.839335i	$0.682945\pi$
$600$	10.7471	0.438749
$601$	15.0596	0.614296	0.307148	−	0.951662i	$-0.400625\pi$
$601$	15.0596	0.614296	0.307148	+	0.951662i	$0.400625\pi$
$602$	−6.98195	−0.284563
$603$	78.2817	3.18788
$604$	2.82585	0.114982
$605$	−12.5717	−0.511114
$606$	13.9506	0.566702
$607$	−1.76724	−0.0717299	−0.0358650	−	0.999357i	$-0.511419\pi$
$607$	−1.76724	−0.0717299	−0.0358650	+	0.999357i	$0.511419\pi$
$608$	−6.36496	−0.258133
$609$	14.5349	0.588983
$610$	−2.17819	−0.0881925
$611$	−0.820796	−0.0332059
$612$	−23.9485	−0.968060
$613$	−2.87424	−0.116089	−0.0580447	−	0.998314i	$-0.518487\pi$
$613$	−2.87424	−0.116089	−0.0580447	+	0.998314i	$0.518487\pi$
$614$	29.1356	1.17582
$615$	37.9704	1.53112
$616$	4.11961	0.165984
$617$	24.9683	1.00519	0.502594	−	0.864523i	$-0.332379\pi$
$617$	24.9683	1.00519	0.502594	+	0.864523i	$0.332379\pi$
$618$	50.3856	2.02680
$619$	39.4383	1.58516	0.792579	−	0.609769i	$-0.208738\pi$
$619$	39.4383	1.58516	0.792579	+	0.609769i	$0.208738\pi$
$620$	−11.0682	−0.444511
$621$	54.0787	2.17010
$622$	26.3882	1.05807
$623$	10.1815	0.407914
$624$	0.900432	0.0360461
$625$	4.92722	0.197089
$626$	0.704636	0.0281629
$627$	−16.1005	−0.642991
$628$	3.58700	0.143137
$629$	−31.2032	−1.24415
$630$	−38.5353	−1.53528
$631$	−40.6512	−1.61830	−0.809149	−	0.587603i	$-0.800072\pi$
$631$	−40.6512	−1.61830	−0.809149	+	0.587603i	$0.800072\pi$
$632$	−3.47393	−0.138186
$633$	−47.5282	−1.88908
$634$	−14.1160	−0.560618
$635$	15.0734	0.598168
$636$	−41.8112	−1.65792
$637$	−5.24119	−0.207664
$638$	−0.789678	−0.0312637
$639$	−16.9580	−0.670849
$640$	1.21871	0.0481737
$641$	46.0708	1.81969	0.909844	−	0.414951i	$-0.136201\pi$
$641$	46.0708	1.81969	0.909844	+	0.414951i	$0.136201\pi$
$642$	−16.1837	−0.638721
$643$	10.4559	0.412340	0.206170	−	0.978516i	$-0.433900\pi$
$643$	10.4559	0.412340	0.206170	+	0.978516i	$0.433900\pi$
$644$	26.2931	1.03609
$645$	−5.22472	−0.205723
$646$	24.0063	0.944514
$647$	−39.0462	−1.53506	−0.767532	−	0.641011i	$-0.778515\pi$
$647$	−39.0462	−1.53506	−0.767532	+	0.641011i	$0.778515\pi$
$648$	12.2690	0.481971
$649$	4.78237	0.187725
$650$	1.03502	0.0405968
$651$	−138.289	−5.41995
$652$	1.42393	0.0557652
$653$	−0.791613	−0.0309782	−0.0154891	−	0.999880i	$-0.504931\pi$
$653$	−0.791613	−0.0309782	−0.0154891	+	0.999880i	$0.504931\pi$
$654$	4.29635	0.168001
$655$	13.7730	0.538154
$656$	−10.1894	−0.397829
$657$	−59.9066	−2.33718
$658$	−13.8801	−0.541102
$659$	−11.5017	−0.448044	−0.224022	−	0.974584i	$-0.571919\pi$
$659$	−11.5017	−0.448044	−0.224022	+	0.974584i	$0.571919\pi$
$660$	3.08279	0.119997
$661$	−11.4191	−0.444152	−0.222076	−	0.975029i	$-0.571283\pi$
$661$	−11.4191	−0.444152	−0.222076	+	0.975029i	$0.571283\pi$
$662$	−19.3491	−0.752023
$663$	−3.39610	−0.131893
$664$	−1.62106	−0.0629093
$665$	38.6283	1.49794
$666$	52.5314	2.03555
$667$	−5.04005	−0.195152
$668$	−22.6588	−0.876697
$669$	−57.7301	−2.23197
$670$	15.0249	0.580462
$671$	1.47857	0.0570797
$672$	15.2268	0.587385
$673$	−24.7963	−0.955826	−0.477913	−	0.878407i	$-0.658607\pi$
$673$	−24.7963	−0.955826	−0.477913	+	0.878407i	$0.658607\pi$
$674$	−8.44590	−0.325324
$675$	35.9989	1.38560
$676$	−12.9133	−0.496665
$677$	25.2864	0.971837	0.485919	−	0.874004i	$-0.338485\pi$
$677$	25.2864	0.971837	0.485919	+	0.874004i	$0.338485\pi$
$678$	56.6249	2.17467
$679$	64.5632	2.47771
$680$	−4.59652	−0.176268
$681$	−48.8580	−1.87224
$682$	7.51319	0.287695
$683$	−6.47600	−0.247797	−0.123899	−	0.992295i	$-0.539540\pi$
$683$	−6.47600	−0.247797	−0.123899	+	0.992295i	$0.539540\pi$
$684$	−40.4152	−1.54531
$685$	19.6554	0.750993
$686$	−53.7728	−2.05305
$687$	0.00676862	0.000258239 0
$688$	1.40206	0.0534530
$689$	−4.02670	−0.153405
$690$	19.6756	0.749038
$691$	−19.1295	−0.727719	−0.363859	−	0.931454i	$-0.618541\pi$
$691$	−19.1295	−0.727719	−0.363859	+	0.931454i	$0.618541\pi$
$692$	8.67980	0.329956
$693$	26.1580	0.993662
$694$	−14.6008	−0.554239
$695$	8.10277	0.307356
$696$	−2.91878	−0.110636
$697$	38.4306	1.45566
$698$	−33.8053	−1.27955
$699$	40.0280	1.51400
$700$	17.5027	0.661539
$701$	−9.14106	−0.345253	−0.172627	−	0.984987i	$-0.555225\pi$
$701$	−9.14106	−0.345253	−0.172627	+	0.984987i	$0.555225\pi$
$702$	3.01612	0.113836
$703$	−52.6581	−1.98604
$704$	−0.827268	−0.0311788
$705$	−10.3867	−0.391187
$706$	−10.4862	−0.394653
$707$	22.7198	0.854466
$708$	17.6764	0.664321
$709$	−2.98377	−0.112058	−0.0560289	−	0.998429i	$-0.517844\pi$
$709$	−2.98377	−0.112058	−0.0560289	+	0.998429i	$0.517844\pi$
$710$	−3.25481	−0.122151
$711$	−22.0582	−0.827248
$712$	−2.04457	−0.0766235
$713$	47.9523	1.79583
$714$	−57.4297	−2.14925
$715$	0.296893	0.0111032
$716$	−19.1876	−0.717075
$717$	−47.0674	−1.75777
$718$	−29.4725	−1.09990
$719$	45.3759	1.69224	0.846119	−	0.532995i	$-0.178933\pi$
$719$	45.3759	1.69224	0.846119	+	0.532995i	$0.178933\pi$
$720$	7.73835	0.288391
$721$	82.0576	3.05599
$722$	21.5127	0.800619
$723$	−14.8083	−0.550726
$724$	−1.93407	−0.0718792
$725$	−3.35505	−0.124603
$726$	31.5423	1.17064
$727$	−28.9919	−1.07525	−0.537625	−	0.843184i	$-0.680678\pi$
$727$	−28.9919	−1.07525	−0.537625	+	0.843184i	$0.680678\pi$
$728$	1.46644	0.0543498
$729$	−16.0501	−0.594449
$730$	−11.4981	−0.425563
$731$	−5.28805	−0.195585
$732$	5.46505	0.201994
$733$	−33.6672	−1.24353	−0.621763	−	0.783206i	$-0.713583\pi$
$733$	−33.6672	−1.24353	−0.621763	+	0.783206i	$0.713583\pi$
$734$	−22.2205	−0.820172
$735$	−66.3245	−2.44641
$736$	−5.27997	−0.194622
$737$	−10.1990	−0.375685
$738$	−64.6989	−2.38160
$739$	−20.9256	−0.769761	−0.384881	−	0.922966i	$-0.625757\pi$
$739$	−20.9256	−0.769761	−0.384881	+	0.922966i	$0.625757\pi$
$740$	10.0825	0.370641
$741$	−5.73121	−0.210541
$742$	−68.0935	−2.49979
$743$	−15.4838	−0.568047	−0.284023	−	0.958817i	$-0.591669\pi$
$743$	−15.4838	−0.568047	−0.284023	+	0.958817i	$0.591669\pi$
$744$	27.7700	1.01810
$745$	9.74749	0.357120
$746$	−33.7318	−1.23501
$747$	−10.2931	−0.376606
$748$	3.12015	0.114084
$749$	−26.3568	−0.963055
$750$	31.7299	1.15861
$751$	44.2919	1.61624	0.808118	−	0.589021i	$-0.200486\pi$
$751$	44.2919	1.61624	0.808118	+	0.589021i	$0.200486\pi$
$752$	2.78729	0.101642
$753$	−64.4306	−2.34798
$754$	−0.281098	−0.0102370
$755$	3.44389	0.125336
$756$	51.0041	1.85500
$757$	−41.9119	−1.52331	−0.761657	−	0.647981i	$-0.775614\pi$
$757$	−41.9119	−1.52331	−0.761657	+	0.647981i	$0.775614\pi$
$758$	3.20136	0.116279
$759$	−13.3559	−0.484790
$760$	−7.75703	−0.281377
$761$	2.63597	0.0955540	0.0477770	−	0.998858i	$-0.484786\pi$
$761$	2.63597	0.0955540	0.0477770	+	0.998858i	$0.484786\pi$
$762$	−37.8188	−1.37003
$763$	6.99701	0.253309
$764$	−11.9403	−0.431986
$765$	−29.1862	−1.05523
$766$	15.6181	0.564305
$767$	1.70236	0.0614686
$768$	−3.05772	−0.110336
$769$	−47.3617	−1.70791	−0.853954	−	0.520348i	$-0.825802\pi$
$769$	−47.3617	−1.70791	−0.853954	+	0.520348i	$0.825802\pi$
$770$	5.02061	0.180930
$771$	−56.5938	−2.03818
$772$	19.0193	0.684518
$773$	38.4408	1.38262	0.691310	−	0.722559i	$-0.257034\pi$
$773$	38.4408	1.38262	0.691310	+	0.722559i	$0.257034\pi$
$774$	8.90256	0.319996
$775$	31.9207	1.14663
$776$	−12.9651	−0.465419
$777$	125.973	4.51926
$778$	24.1416	0.865519
$779$	64.8550	2.32367
$780$	1.09736	0.0392919
$781$	2.20939	0.0790582
$782$	19.9141	0.712126
$783$	−9.77685	−0.349396
$784$	17.7982	0.635651
$785$	4.37150	0.156026
$786$	−34.5561	−1.23258
$787$	20.0436	0.714477	0.357239	−	0.934013i	$-0.383718\pi$
$787$	20.0436	0.714477	0.357239	+	0.934013i	$0.383718\pi$
$788$	1.45951	0.0519928
$789$	−96.2681	−3.42723
$790$	−4.23371	−0.150629
$791$	92.2190	3.27893
$792$	−5.25285	−0.186652
$793$	0.526320	0.0186902
$794$	28.0833	0.996640
$795$	−50.9557	−1.80721
$796$	0.0793401	0.00281214
$797$	30.9043	1.09469	0.547344	−	0.836908i	$-0.315639\pi$
$797$	30.9043	1.09469	0.547344	+	0.836908i	$0.315639\pi$
$798$	−96.9177	−3.43085
$799$	−10.5126	−0.371909
$800$	−3.51475	−0.124265
$801$	−12.9823	−0.458706
$802$	3.00975	0.106278
$803$	7.80499	0.275432
$804$	−37.6972	−1.32948
$805$	32.0436	1.12939
$806$	2.67444	0.0942030
$807$	72.8191	2.56335
$808$	−4.56241	−0.160505
$809$	25.4049	0.893190	0.446595	−	0.894736i	$-0.352636\pi$
$809$	25.4049	0.893190	0.446595	+	0.894736i	$0.352636\pi$
$810$	14.9523	0.525370
$811$	32.3855	1.13721	0.568603	−	0.822612i	$-0.307484\pi$
$811$	32.3855	1.13721	0.568603	+	0.822612i	$0.307484\pi$
$812$	−4.75351	−0.166815
$813$	−37.0837	−1.30058
$814$	−6.84409	−0.239885
$815$	1.73535	0.0607867
$816$	11.5326	0.403721
$817$	−8.92404	−0.312213
$818$	37.3000	1.30416
$819$	9.31135	0.325365
$820$	−12.4179	−0.433652
$821$	−5.90183	−0.205975	−0.102988	−	0.994683i	$-0.532840\pi$
$821$	−5.90183	−0.205975	−0.102988	+	0.994683i	$0.532840\pi$
$822$	−49.3150	−1.72006
$823$	0.602489	0.0210015	0.0105007	−	0.999945i	$-0.496657\pi$
$823$	0.602489	0.0210015	0.0105007	+	0.999945i	$0.496657\pi$
$824$	−16.4782	−0.574044
$825$	−8.89074	−0.309536
$826$	28.7877	1.00165
$827$	40.9711	1.42470	0.712352	−	0.701822i	$-0.247630\pi$
$827$	40.9711	1.42470	0.712352	+	0.701822i	$0.247630\pi$
$828$	−33.5259	−1.16510
$829$	33.1994	1.15306	0.576531	−	0.817075i	$-0.304406\pi$
$829$	33.1994	1.15306	0.576531	+	0.817075i	$0.304406\pi$
$830$	−1.97560	−0.0685740
$831$	40.6706	1.41085
$832$	−0.294479	−0.0102092
$833$	−67.1283	−2.32586
$834$	−20.3297	−0.703960
$835$	−27.6145	−0.955640
$836$	5.26552	0.182112
$837$	93.0194	3.21522
$838$	13.8925	0.479909
$839$	−46.8093	−1.61604	−0.808019	−	0.589157i	$-0.799460\pi$
$839$	−46.8093	−1.61604	−0.808019	+	0.589157i	$0.799460\pi$
$840$	18.5570	0.640277
$841$	−28.0888	−0.968580
$842$	−18.9815	−0.654146
$843$	−74.3819	−2.56185
$844$	15.5437	0.535035
$845$	−15.7375	−0.541387
$846$	17.6983	0.608478
$847$	51.3696	1.76508
$848$	13.6740	0.469567
$849$	−28.9129	−0.992287
$850$	13.2563	0.454689
$851$	−43.6818	−1.49739
$852$	8.16627	0.279772
$853$	−7.73953	−0.264996	−0.132498	−	0.991183i	$-0.542300\pi$
$853$	−7.73953	−0.264996	−0.132498	+	0.991183i	$0.542300\pi$
$854$	8.90034	0.304564
$855$	−49.2543	−1.68446
$856$	5.29275	0.180903
$857$	48.0234	1.64045	0.820224	−	0.572042i	$-0.193849\pi$
$857$	48.0234	1.64045	0.820224	+	0.572042i	$0.193849\pi$
$858$	−0.744899	−0.0254304
$859$	−57.2697	−1.95402	−0.977008	−	0.213201i	$-0.931611\pi$
$859$	−57.2697	−1.95402	−0.977008	+	0.213201i	$0.931611\pi$
$860$	1.70870	0.0582662
$861$	−155.152	−5.28755
$862$	5.93884	0.202278
$863$	−23.5875	−0.802929	−0.401465	−	0.915875i	$-0.631499\pi$
$863$	−23.5875	−0.802929	−0.401465	+	0.915875i	$0.631499\pi$
$864$	−10.2422	−0.348448
$865$	10.5781	0.359668
$866$	−26.8946	−0.913914
$867$	8.48458	0.288151
$868$	45.2261	1.53507
$869$	2.87387	0.0974895
$870$	−3.55714	−0.120598
$871$	−3.63049	−0.123014
$872$	−1.40508	−0.0475821
$873$	−82.3235	−2.78623
$874$	33.6068	1.13677
$875$	51.6752	1.74694
$876$	28.8485	0.974701
$877$	10.9674	0.370343	0.185172	−	0.982706i	$-0.440716\pi$
$877$	10.9674	0.370343	0.185172	+	0.982706i	$0.440716\pi$
$878$	20.5396	0.693178
$879$	−96.8666	−3.26723
$880$	−1.00820	−0.0339864
$881$	−33.6925	−1.13513	−0.567565	−	0.823328i	$-0.692115\pi$
$881$	−33.6925	−1.13513	−0.567565	+	0.823328i	$0.692115\pi$
$882$	113.012	3.80532
$883$	16.4576	0.553844	0.276922	−	0.960892i	$-0.410686\pi$
$883$	16.4576	0.553844	0.276922	+	0.960892i	$0.410686\pi$
$884$	1.11066	0.0373557
$885$	21.5424	0.724141
$886$	20.0214	0.672633
$887$	−24.7648	−0.831521	−0.415761	−	0.909474i	$-0.636485\pi$
$887$	−24.7648	−0.831521	−0.415761	+	0.909474i	$0.636485\pi$
$888$	−25.2969	−0.848908
$889$	−61.5915	−2.06571
$890$	−2.49174	−0.0835232
$891$	−10.1497	−0.340029
$892$	18.8801	0.632153
$893$	−17.7410	−0.593678
$894$	−24.4563	−0.817941
$895$	−23.3841	−0.781644
$896$	−4.97978	−0.166363
$897$	−4.75425	−0.158740
$898$	−10.6932	−0.356838
$899$	−8.66927	−0.289136
$900$	−22.3174	−0.743913
$901$	−51.5732	−1.71815
$902$	8.42936	0.280667
$903$	21.3488	0.710444
$904$	−18.5187	−0.615922
$905$	−2.35707	−0.0783516
$906$	−8.64065	−0.287066
$907$	13.6393	0.452885	0.226443	−	0.974025i	$-0.427290\pi$
$907$	13.6393	0.452885	0.226443	+	0.974025i	$0.427290\pi$
$908$	15.9786	0.530268
$909$	−28.9696	−0.960862
$910$	1.78716	0.0592438
$911$	34.7132	1.15010	0.575050	−	0.818118i	$-0.304982\pi$
$911$	34.7132	1.15010	0.575050	+	0.818118i	$0.304982\pi$
$912$	19.4622	0.644459
$913$	1.34105	0.0443823
$914$	9.24484	0.305792
$915$	6.66030	0.220183
$916$	−0.00221362	−7.31400e−5 0
$917$	−56.2779	−1.85846
$918$	38.6299	1.27498
$919$	21.1853	0.698839	0.349420	−	0.936966i	$-0.386379\pi$
$919$	21.1853	0.698839	0.349420	+	0.936966i	$0.386379\pi$
$920$	−6.43474	−0.212147
$921$	−89.0884	−2.93556
$922$	10.9448	0.360449
$923$	0.786466	0.0258869
$924$	−12.5966	−0.414398
$925$	−29.0780	−0.956078
$926$	−9.54662	−0.313721
$927$	−104.630	−3.43651
$928$	0.954562	0.0313350
$929$	7.65195	0.251052	0.125526	−	0.992090i	$-0.459938\pi$
$929$	7.65195	0.251052	0.125526	+	0.992090i	$0.459938\pi$
$930$	33.8435	1.10977
$931$	−113.285	−3.71276
$932$	−13.0908	−0.428804
$933$	−80.6876	−2.64159
$934$	25.3312	0.828863
$935$	3.80255	0.124357
$936$	−1.86983	−0.0611174
$937$	15.7559	0.514721	0.257361	−	0.966315i	$-0.417147\pi$
$937$	15.7559	0.514721	0.257361	+	0.966315i	$0.417147\pi$
$938$	−61.3934	−2.00456
$939$	−2.15458	−0.0703119
$940$	3.39689	0.110794
$941$	25.8206	0.841727	0.420863	−	0.907124i	$-0.361727\pi$
$941$	25.8206	0.841727	0.420863	+	0.907124i	$0.361727\pi$
$942$	−10.9680	−0.357357
$943$	53.7997	1.75196
$944$	−5.78093	−0.188153
$945$	62.1591	2.02204
$946$	−1.15988	−0.0377109
$947$	−50.0154	−1.62528	−0.812642	−	0.582764i	$-0.801971\pi$
$947$	−50.0154	−1.62528	−0.812642	+	0.582764i	$0.801971\pi$
$948$	10.6223	0.344997
$949$	2.77830	0.0901876
$950$	22.3712	0.725819
$951$	43.1627	1.39965
$952$	18.7819	0.608725
$953$	52.4370	1.69860	0.849301	−	0.527910i	$-0.177024\pi$
$953$	52.4370	1.69860	0.849301	+	0.527910i	$0.177024\pi$
$954$	86.8249	2.81106
$955$	−14.5518	−0.470885
$956$	15.3930	0.497845
$957$	2.41461	0.0780534
$958$	24.6355	0.795938
$959$	−80.3141	−2.59348
$960$	−3.72647	−0.120271
$961$	51.4816	1.66070
$962$	−2.43626	−0.0785482
$963$	33.6071	1.08297
$964$	4.84292	0.155980
$965$	23.1789	0.746156
$966$	−80.3968	−2.58672
$967$	1.92933	0.0620429	0.0310215	−	0.999519i	$-0.490124\pi$
$967$	1.92933	0.0620429	0.0310215	+	0.999519i	$0.490124\pi$
$968$	−10.3156	−0.331557
$969$	−73.4044	−2.35809
$970$	−15.8006	−0.507328
$971$	−18.9854	−0.609271	−0.304635	−	0.952469i	$-0.598535\pi$
$971$	−18.9854	−0.609271	−0.304635	+	0.952469i	$0.598535\pi$
$972$	−6.78833	−0.217736
$973$	−33.1088	−1.06142
$974$	−28.3770	−0.909258
$975$	−3.16479	−0.101355
$976$	−1.78730	−0.0572100
$977$	21.5235	0.688597	0.344298	−	0.938860i	$-0.388117\pi$
$977$	21.5235	0.688597	0.344298	+	0.938860i	$0.388117\pi$
$978$	−4.35396	−0.139224
$979$	1.69141	0.0540576
$980$	21.6908	0.692888
$981$	−8.92177	−0.284850
$982$	−23.1951	−0.740185
$983$	−54.9203	−1.75169	−0.875843	−	0.482595i	$-0.839694\pi$
$983$	−54.9203	−1.75169	−0.875843	+	0.482595i	$0.839694\pi$
$984$	31.1563	0.993226
$985$	1.77871	0.0566745
$986$	−3.60025	−0.114655
$987$	42.4413	1.35092
$988$	1.87434	0.0596308
$989$	−7.40282	−0.235396
$990$	−6.40169	−0.203459
$991$	5.70933	0.181363	0.0906815	−	0.995880i	$-0.471095\pi$
$991$	5.70933	0.181363	0.0906815	+	0.995880i	$0.471095\pi$
$992$	−9.08194	−0.288352
$993$	59.1640	1.87751
$994$	13.2995	0.421836
$995$	0.0966924	0.00306536
$996$	4.95674	0.157060
$997$	27.8745	0.882795	0.441397	−	0.897312i	$-0.354483\pi$
$997$	27.8745	0.882795	0.441397	+	0.897312i	$0.354483\pi$
$998$	13.2584	0.419687
$999$	−84.7354	−2.68091

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8042.2.a.d.1.7	✓	101

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8042.2.a.d.1.7	✓	101	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:	\( N \)	\(=\)	\( 8042 = 2 \cdot 4021 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8042.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.05772 q^{3} +1.00000 q^{4} +1.21871 q^{5} -3.05772 q^{6} -4.97978 q^{7} +1.00000 q^{8} +6.34964 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.05772 q^{3} +1.00000 q^{4} +1.21871 q^{5} -3.05772 q^{6} -4.97978 q^{7} +1.00000 q^{8} +6.34964 q^{9} +1.21871 q^{10} -0.827268 q^{11} -3.05772 q^{12} -0.294479 q^{13} -4.97978 q^{14} -3.72647 q^{15} +1.00000 q^{16} -3.77163 q^{17} +6.34964 q^{18} -6.36496 q^{19} +1.21871 q^{20} +15.2268 q^{21} -0.827268 q^{22} -5.27997 q^{23} -3.05772 q^{24} -3.51475 q^{25} -0.294479 q^{26} -10.2422 q^{27} -4.97978 q^{28} +0.954562 q^{29} -3.72647 q^{30} -9.08194 q^{31} +1.00000 q^{32} +2.52955 q^{33} -3.77163 q^{34} -6.06890 q^{35} +6.34964 q^{36} +8.27313 q^{37} -6.36496 q^{38} +0.900432 q^{39} +1.21871 q^{40} -10.1894 q^{41} +15.2268 q^{42} +1.40206 q^{43} -0.827268 q^{44} +7.73835 q^{45} -5.27997 q^{46} +2.78729 q^{47} -3.05772 q^{48} +17.7982 q^{49} -3.51475 q^{50} +11.5326 q^{51} -0.294479 q^{52} +13.6740 q^{53} -10.2422 q^{54} -1.00820 q^{55} -4.97978 q^{56} +19.4622 q^{57} +0.954562 q^{58} -5.78093 q^{59} -3.72647 q^{60} -1.78730 q^{61} -9.08194 q^{62} -31.6198 q^{63} +1.00000 q^{64} -0.358883 q^{65} +2.52955 q^{66} +12.3285 q^{67} -3.77163 q^{68} +16.1446 q^{69} -6.06890 q^{70} -2.67071 q^{71} +6.34964 q^{72} -9.43466 q^{73} +8.27313 q^{74} +10.7471 q^{75} -6.36496 q^{76} +4.11961 q^{77} +0.900432 q^{78} -3.47393 q^{79} +1.21871 q^{80} +12.2690 q^{81} -10.1894 q^{82} -1.62106 q^{83} +15.2268 q^{84} -4.59652 q^{85} +1.40206 q^{86} -2.91878 q^{87} -0.827268 q^{88} -2.04457 q^{89} +7.73835 q^{90} +1.46644 q^{91} -5.27997 q^{92} +27.7700 q^{93} +2.78729 q^{94} -7.75703 q^{95} -3.05772 q^{96} -12.9651 q^{97} +17.7982 q^{98} -5.25285 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 101 q + 101 q^{2} + 10 q^{3} + 101 q^{4} + 19 q^{5} + 10 q^{6} + 42 q^{7} + 101 q^{8} + 147 q^{9}+O(q^{10}) \) 101 * q + 101 * q^2 + 10 * q^3 + 101 * q^4 + 19 * q^5 + 10 * q^6 + 42 * q^7 + 101 * q^8 + 147 * q^9	\( 101 q + 101 q^{2} + 10 q^{3} + 101 q^{4} + 19 q^{5} + 10 q^{6} + 42 q^{7} + 101 q^{8} + 147 q^{9} + 19 q^{10} + 4 q^{11} + 10 q^{12} + 58 q^{13} + 42 q^{14} + 27 q^{15} + 101 q^{16} + 34 q^{17} + 147 q^{18} + 36 q^{19} + 19 q^{20} + 45 q^{21} + 4 q^{22} + 47 q^{23} + 10 q^{24} + 174 q^{25} + 58 q^{26} + 31 q^{27} + 42 q^{28} + 62 q^{29} + 27 q^{30} + 47 q^{31} + 101 q^{32} + 55 q^{33} + 34 q^{34} + 16 q^{35} + 147 q^{36} + 90 q^{37} + 36 q^{38} + 50 q^{39} + 19 q^{40} + 54 q^{41} + 45 q^{42} + 65 q^{43} + 4 q^{44} + 47 q^{45} + 47 q^{46} + 54 q^{47} + 10 q^{48} + 189 q^{49} + 174 q^{50} + 36 q^{51} + 58 q^{52} + 94 q^{53} + 31 q^{54} + 68 q^{55} + 42 q^{56} + 79 q^{57} + 62 q^{58} - 6 q^{59} + 27 q^{60} + 58 q^{61} + 47 q^{62} + 117 q^{63} + 101 q^{64} + 89 q^{65} + 55 q^{66} + 127 q^{67} + 34 q^{68} + 45 q^{69} + 16 q^{70} + 87 q^{71} + 147 q^{72} + 83 q^{73} + 90 q^{74} - 4 q^{75} + 36 q^{76} + 53 q^{77} + 50 q^{78} + 74 q^{79} + 19 q^{80} + 241 q^{81} + 54 q^{82} + 11 q^{83} + 45 q^{84} + 120 q^{85} + 65 q^{86} + 37 q^{87} + 4 q^{88} + 89 q^{89} + 47 q^{90} + 31 q^{91} + 47 q^{92} + 123 q^{93} + 54 q^{94} + 61 q^{95} + 10 q^{96} + 85 q^{97} + 189 q^{98} - 55 q^{99}+O(q^{100}) \) 101 * q + 101 * q^2 + 10 * q^3 + 101 * q^4 + 19 * q^5 + 10 * q^6 + 42 * q^7 + 101 * q^8 + 147 * q^9 + 19 * q^10 + 4 * q^11 + 10 * q^12 + 58 * q^13 + 42 * q^14 + 27 * q^15 + 101 * q^16 + 34 * q^17 + 147 * q^18 + 36 * q^19 + 19 * q^20 + 45 * q^21 + 4 * q^22 + 47 * q^23 + 10 * q^24 + 174 * q^25 + 58 * q^26 + 31 * q^27 + 42 * q^28 + 62 * q^29 + 27 * q^30 + 47 * q^31 + 101 * q^32 + 55 * q^33 + 34 * q^34 + 16 * q^35 + 147 * q^36 + 90 * q^37 + 36 * q^38 + 50 * q^39 + 19 * q^40 + 54 * q^41 + 45 * q^42 + 65 * q^43 + 4 * q^44 + 47 * q^45 + 47 * q^46 + 54 * q^47 + 10 * q^48 + 189 * q^49 + 174 * q^50 + 36 * q^51 + 58 * q^52 + 94 * q^53 + 31 * q^54 + 68 * q^55 + 42 * q^56 + 79 * q^57 + 62 * q^58 - 6 * q^59 + 27 * q^60 + 58 * q^61 + 47 * q^62 + 117 * q^63 + 101 * q^64 + 89 * q^65 + 55 * q^66 + 127 * q^67 + 34 * q^68 + 45 * q^69 + 16 * q^70 + 87 * q^71 + 147 * q^72 + 83 * q^73 + 90 * q^74 - 4 * q^75 + 36 * q^76 + 53 * q^77 + 50 * q^78 + 74 * q^79 + 19 * q^80 + 241 * q^81 + 54 * q^82 + 11 * q^83 + 45 * q^84 + 120 * q^85 + 65 * q^86 + 37 * q^87 + 4 * q^88 + 89 * q^89 + 47 * q^90 + 31 * q^91 + 47 * q^92 + 123 * q^93 + 54 * q^94 + 61 * q^95 + 10 * q^96 + 85 * q^97 + 189 * q^98 - 55 * q^99

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