LMFDB - Embedded newform 8007.2.a.e.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.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:	$63.9362168984$
Analytic rank:	$1$
Dimension:	$46$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.42497 q^{2} +1.00000 q^{3} +0.0305258 q^{4} +0.348852 q^{5} -1.42497 q^{6} -0.489415 q^{7} +2.80643 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.42497 q^{2} +1.00000 q^{3} +0.0305258 q^{4} +0.348852 q^{5} -1.42497 q^{6} -0.489415 q^{7} +2.80643 q^{8} +1.00000 q^{9} -0.497102 q^{10} +2.33512 q^{11} +0.0305258 q^{12} +5.30367 q^{13} +0.697399 q^{14} +0.348852 q^{15} -4.06012 q^{16} -1.00000 q^{17} -1.42497 q^{18} -4.47923 q^{19} +0.0106490 q^{20} -0.489415 q^{21} -3.32746 q^{22} +2.78427 q^{23} +2.80643 q^{24} -4.87830 q^{25} -7.55754 q^{26} +1.00000 q^{27} -0.0149398 q^{28} +0.169133 q^{29} -0.497102 q^{30} +2.78442 q^{31} +0.172665 q^{32} +2.33512 q^{33} +1.42497 q^{34} -0.170733 q^{35} +0.0305258 q^{36} -11.1454 q^{37} +6.38275 q^{38} +5.30367 q^{39} +0.979029 q^{40} +0.741898 q^{41} +0.697399 q^{42} -3.38376 q^{43} +0.0712813 q^{44} +0.348852 q^{45} -3.96749 q^{46} -0.461826 q^{47} -4.06012 q^{48} -6.76047 q^{49} +6.95141 q^{50} -1.00000 q^{51} +0.161898 q^{52} -9.58285 q^{53} -1.42497 q^{54} +0.814611 q^{55} -1.37351 q^{56} -4.47923 q^{57} -0.241009 q^{58} -10.0596 q^{59} +0.0106490 q^{60} +1.32822 q^{61} -3.96770 q^{62} -0.489415 q^{63} +7.87420 q^{64} +1.85019 q^{65} -3.32746 q^{66} -2.14227 q^{67} -0.0305258 q^{68} +2.78427 q^{69} +0.243289 q^{70} +8.64535 q^{71} +2.80643 q^{72} +1.89207 q^{73} +15.8818 q^{74} -4.87830 q^{75} -0.136732 q^{76} -1.14284 q^{77} -7.55754 q^{78} -5.45077 q^{79} -1.41638 q^{80} +1.00000 q^{81} -1.05718 q^{82} -14.7039 q^{83} -0.0149398 q^{84} -0.348852 q^{85} +4.82174 q^{86} +0.169133 q^{87} +6.55335 q^{88} -6.89341 q^{89} -0.497102 q^{90} -2.59569 q^{91} +0.0849920 q^{92} +2.78442 q^{93} +0.658086 q^{94} -1.56259 q^{95} +0.172665 q^{96} +7.97411 q^{97} +9.63344 q^{98} +2.33512 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9}+O(q^{10}) $ 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9} - 10 q^{10} - 25 q^{11} + 43 q^{12} - 8 q^{13} - 28 q^{14} - 19 q^{15} + 33 q^{16} - 46 q^{17} - 5 q^{18} - 2 q^{19} - 56 q^{20} + q^{21} - 19 q^{22} - 64 q^{23} - 18 q^{24} + 11 q^{25} - 13 q^{26} + 46 q^{27} - 38 q^{28} - 51 q^{29} - 10 q^{30} - 19 q^{31} - 61 q^{32} - 25 q^{33} + 5 q^{34} - 39 q^{35} + 43 q^{36} - 46 q^{37} - 48 q^{38} - 8 q^{39} - 10 q^{40} - 53 q^{41} - 28 q^{42} - 33 q^{43} - 62 q^{44} - 19 q^{45} + 2 q^{46} - 45 q^{47} + 33 q^{48} + 21 q^{49} - 60 q^{50} - 46 q^{51} - 63 q^{52} - 47 q^{53} - 5 q^{54} + 5 q^{55} - 82 q^{56} - 2 q^{57} - 21 q^{58} - 65 q^{59} - 56 q^{60} - 37 q^{61} - 46 q^{62} + q^{63} + 74 q^{64} - 85 q^{65} - 19 q^{66} - 52 q^{67} - 43 q^{68} - 64 q^{69} - 20 q^{70} - 48 q^{71} - 18 q^{72} - 39 q^{73} - 16 q^{74} + 11 q^{75} + 42 q^{76} - 78 q^{77} - 13 q^{78} - 26 q^{79} - 78 q^{80} + 46 q^{81} + 3 q^{82} - 47 q^{83} - 38 q^{84} + 19 q^{85} - 6 q^{86} - 51 q^{87} - 58 q^{88} - 58 q^{89} - 10 q^{90} - 43 q^{91} - 68 q^{92} - 19 q^{93} - 78 q^{95} - 61 q^{96} - 44 q^{97} - 4 q^{98} - 25 q^{99}+O(q^{100}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9 - 10 * q^10 - 25 * q^11 + 43 * q^12 - 8 * q^13 - 28 * q^14 - 19 * q^15 + 33 * q^16 - 46 * q^17 - 5 * q^18 - 2 * q^19 - 56 * q^20 + q^21 - 19 * q^22 - 64 * q^23 - 18 * q^24 + 11 * q^25 - 13 * q^26 + 46 * q^27 - 38 * q^28 - 51 * q^29 - 10 * q^30 - 19 * q^31 - 61 * q^32 - 25 * q^33 + 5 * q^34 - 39 * q^35 + 43 * q^36 - 46 * q^37 - 48 * q^38 - 8 * q^39 - 10 * q^40 - 53 * q^41 - 28 * q^42 - 33 * q^43 - 62 * q^44 - 19 * q^45 + 2 * q^46 - 45 * q^47 + 33 * q^48 + 21 * q^49 - 60 * q^50 - 46 * q^51 - 63 * q^52 - 47 * q^53 - 5 * q^54 + 5 * q^55 - 82 * q^56 - 2 * q^57 - 21 * q^58 - 65 * q^59 - 56 * q^60 - 37 * q^61 - 46 * q^62 + q^63 + 74 * q^64 - 85 * q^65 - 19 * q^66 - 52 * q^67 - 43 * q^68 - 64 * q^69 - 20 * q^70 - 48 * q^71 - 18 * q^72 - 39 * q^73 - 16 * q^74 + 11 * q^75 + 42 * q^76 - 78 * q^77 - 13 * q^78 - 26 * q^79 - 78 * q^80 + 46 * q^81 + 3 * q^82 - 47 * q^83 - 38 * q^84 + 19 * q^85 - 6 * q^86 - 51 * q^87 - 58 * q^88 - 58 * q^89 - 10 * q^90 - 43 * q^91 - 68 * q^92 - 19 * q^93 - 78 * q^95 - 61 * q^96 - 44 * q^97 - 4 * q^98 - 25 * 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 $

$2$	−1.42497	−1.00760	−0.503801	−	0.863820i	$-0.668066\pi$
$2$	−1.42497	−1.00760	−0.503801	+	0.863820i	$0.668066\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.0305258	0.0152629
$5$	0.348852	0.156011	0.0780057	−	0.996953i	$-0.475145\pi$
$5$	0.348852	0.156011	0.0780057	+	0.996953i	$0.475145\pi$
$6$	−1.42497	−0.581740
$7$	−0.489415	−0.184981	−0.0924907	−	0.995714i	$-0.529483\pi$
$7$	−0.489415	−0.184981	−0.0924907	+	0.995714i	$0.529483\pi$
$8$	2.80643	0.992224
$9$	1.00000	0.333333
$10$	−0.497102	−0.157197
$11$	2.33512	0.704065	0.352033	−	0.935988i	$-0.385491\pi$
$11$	2.33512	0.704065	0.352033	+	0.935988i	$0.385491\pi$
$12$	0.0305258	0.00881203
$13$	5.30367	1.47097	0.735486	−	0.677540i	$-0.236954\pi$
$13$	5.30367	1.47097	0.735486	+	0.677540i	$0.236954\pi$
$14$	0.697399	0.186388
$15$	0.348852	0.0900732
$16$	−4.06012	−1.01503
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.42497	−0.335868
$19$	−4.47923	−1.02761	−0.513803	−	0.857908i	$-0.671764\pi$
$19$	−4.47923	−1.02761	−0.513803	+	0.857908i	$0.671764\pi$
$20$	0.0106490	0.00238118
$21$	−0.489415	−0.106799
$22$	−3.32746	−0.709418
$23$	2.78427	0.580561	0.290280	−	0.956942i	$-0.406251\pi$
$23$	2.78427	0.580561	0.290280	+	0.956942i	$0.406251\pi$
$24$	2.80643	0.572861
$25$	−4.87830	−0.975660
$26$	−7.55754	−1.48216
$27$	1.00000	0.192450
$28$	−0.0149398	−0.00282335
$29$	0.169133	0.0314073	0.0157036	−	0.999877i	$-0.495001\pi$
$29$	0.169133	0.0314073	0.0157036	+	0.999877i	$0.495001\pi$
$30$	−0.497102	−0.0907580
$31$	2.78442	0.500096	0.250048	−	0.968233i	$-0.419554\pi$
$31$	2.78442	0.500096	0.250048	+	0.968233i	$0.419554\pi$
$32$	0.172665	0.0305231
$33$	2.33512	0.406492
$34$	1.42497	0.244380
$35$	−0.170733	−0.0288592
$36$	0.0305258	0.00508763
$37$	−11.1454	−1.83229	−0.916145	−	0.400848i	$-0.868716\pi$
$37$	−11.1454	−1.83229	−0.916145	+	0.400848i	$0.868716\pi$
$38$	6.38275	1.03542
$39$	5.30367	0.849266
$40$	0.979029	0.154798
$41$	0.741898	0.115865	0.0579325	−	0.998321i	$-0.481549\pi$
$41$	0.741898	0.115865	0.0579325	+	0.998321i	$0.481549\pi$
$42$	0.697399	0.107611
$43$	−3.38376	−0.516018	−0.258009	−	0.966142i	$-0.583066\pi$
$43$	−3.38376	−0.516018	−0.258009	+	0.966142i	$0.583066\pi$
$44$	0.0712813	0.0107461
$45$	0.348852	0.0520038
$46$	−3.96749	−0.584974
$47$	−0.461826	−0.0673643	−0.0336821	−	0.999433i	$-0.510723\pi$
$47$	−0.461826	−0.0673643	−0.0336821	+	0.999433i	$0.510723\pi$
$48$	−4.06012	−0.586028
$49$	−6.76047	−0.965782
$50$	6.95141	0.983078
$51$	−1.00000	−0.140028
$52$	0.161898	0.0224513
$53$	−9.58285	−1.31631	−0.658153	−	0.752884i	$-0.728662\pi$
$53$	−9.58285	−1.31631	−0.658153	+	0.752884i	$0.728662\pi$
$54$	−1.42497	−0.193913
$55$	0.814611	0.109842
$56$	−1.37351	−0.183543
$57$	−4.47923	−0.593289
$58$	−0.241009	−0.0316461
$59$	−10.0596	−1.30965	−0.654825	−	0.755780i	$-0.727258\pi$
$59$	−10.0596	−1.30965	−0.654825	+	0.755780i	$0.727258\pi$
$60$	0.0106490	0.00137478
$61$	1.32822	0.170061	0.0850305	−	0.996378i	$-0.472901\pi$
$61$	1.32822	0.170061	0.0850305	+	0.996378i	$0.472901\pi$
$62$	−3.96770	−0.503898
$63$	−0.489415	−0.0616605
$64$	7.87420	0.984275
$65$	1.85019	0.229488
$66$	−3.32746	−0.409583
$67$	−2.14227	−0.261720	−0.130860	−	0.991401i	$-0.541774\pi$
$67$	−2.14227	−0.261720	−0.130860	+	0.991401i	$0.541774\pi$
$68$	−0.0305258	−0.00370179
$69$	2.78427	0.335187
$70$	0.243289	0.0290786
$71$	8.64535	1.02601	0.513007	−	0.858384i	$-0.328531\pi$
$71$	8.64535	1.02601	0.513007	+	0.858384i	$0.328531\pi$
$72$	2.80643	0.330741
$73$	1.89207	0.221450	0.110725	−	0.993851i	$-0.464683\pi$
$73$	1.89207	0.221450	0.110725	+	0.993851i	$0.464683\pi$
$74$	15.8818	1.84622
$75$	−4.87830	−0.563298
$76$	−0.136732	−0.0156842
$77$	−1.14284	−0.130239
$78$	−7.55754	−0.855723
$79$	−5.45077	−0.613259	−0.306630	−	0.951829i	$-0.599201\pi$
$79$	−5.45077	−0.613259	−0.306630	+	0.951829i	$0.599201\pi$
$80$	−1.41638	−0.158356
$81$	1.00000	0.111111
$82$	−1.05718	−0.116746
$83$	−14.7039	−1.61397	−0.806984	−	0.590574i	$-0.798901\pi$
$83$	−14.7039	−1.61397	−0.806984	+	0.590574i	$0.798901\pi$
$84$	−0.0149398	−0.00163006
$85$	−0.348852	−0.0378383
$86$	4.82174	0.519941
$87$	0.169133	0.0181330
$88$	6.55335	0.698590
$89$	−6.89341	−0.730700	−0.365350	−	0.930870i	$-0.619051\pi$
$89$	−6.89341	−0.730700	−0.365350	+	0.930870i	$0.619051\pi$
$90$	−0.497102	−0.0523991
$91$	−2.59569	−0.272103
$92$	0.0849920	0.00886103
$93$	2.78442	0.288731
$94$	0.658086	0.0678764
$95$	−1.56259	−0.160318
$96$	0.172665	0.0176225
$97$	7.97411	0.809648	0.404824	−	0.914395i	$-0.367333\pi$
$97$	7.97411	0.809648	0.404824	+	0.914395i	$0.367333\pi$
$98$	9.63344	0.973124
$99$	2.33512	0.234688
$100$	−0.148914	−0.0148914
$101$	4.19110	0.417030	0.208515	−	0.978019i	$-0.433137\pi$
$101$	4.19110	0.417030	0.208515	+	0.978019i	$0.433137\pi$
$102$	1.42497	0.141093
$103$	−8.44324	−0.831937	−0.415969	−	0.909379i	$-0.636557\pi$
$103$	−8.44324	−0.831937	−0.415969	+	0.909379i	$0.636557\pi$
$104$	14.8844	1.45953
$105$	−0.170733	−0.0166619
$106$	13.6552	1.32631
$107$	−17.0461	−1.64791	−0.823954	−	0.566657i	$-0.808236\pi$
$107$	−17.0461	−1.64791	−0.823954	+	0.566657i	$0.808236\pi$
$108$	0.0305258	0.00293734
$109$	−12.2364	−1.17203	−0.586017	−	0.810299i	$-0.699305\pi$
$109$	−12.2364	−1.17203	−0.586017	+	0.810299i	$0.699305\pi$
$110$	−1.16079	−0.110677
$111$	−11.1454	−1.05787
$112$	1.98708	0.187762
$113$	−11.3345	−1.06626	−0.533131	−	0.846033i	$-0.678985\pi$
$113$	−11.3345	−1.06626	−0.533131	+	0.846033i	$0.678985\pi$
$114$	6.38275	0.597799
$115$	0.971299	0.0905741
$116$	0.00516293	0.000479366 0
$117$	5.30367	0.490324
$118$	14.3346	1.31961
$119$	0.489415	0.0448646
$120$	0.979029	0.0893727
$121$	−5.54722	−0.504292
$122$	−1.89267	−0.171354
$123$	0.741898	0.0668947
$124$	0.0849965	0.00763291
$125$	−3.44607	−0.308225
$126$	0.697399	0.0621293
$127$	−10.7485	−0.953775	−0.476888	−	0.878964i	$-0.658235\pi$
$127$	−10.7485	−0.953775	−0.476888	+	0.878964i	$0.658235\pi$
$128$	−11.5658	−1.02228
$129$	−3.38376	−0.297923
$130$	−2.63646	−0.231233
$131$	0.693525	0.0605936	0.0302968	−	0.999541i	$-0.490355\pi$
$131$	0.693525	0.0605936	0.0302968	+	0.999541i	$0.490355\pi$
$132$	0.0712813	0.00620424
$133$	2.19220	0.190088
$134$	3.05266	0.263710
$135$	0.348852	0.0300244
$136$	−2.80643	−0.240650
$137$	15.8390	1.35322	0.676610	−	0.736341i	$-0.263448\pi$
$137$	15.8390	1.35322	0.676610	+	0.736341i	$0.263448\pi$
$138$	−3.96749	−0.337735
$139$	9.19610	0.780003	0.390001	−	0.920814i	$-0.372475\pi$
$139$	9.19610	0.780003	0.390001	+	0.920814i	$0.372475\pi$
$140$	−0.00521177	−0.000440475 0
$141$	−0.461826	−0.0388928
$142$	−12.3193	−1.03381
$143$	12.3847	1.03566
$144$	−4.06012	−0.338343
$145$	0.0590025	0.00489989
$146$	−2.69613	−0.223134
$147$	−6.76047	−0.557594
$148$	−0.340221	−0.0279660
$149$	−9.54121	−0.781646	−0.390823	−	0.920466i	$-0.627810\pi$
$149$	−9.54121	−0.781646	−0.390823	+	0.920466i	$0.627810\pi$
$150$	6.95141	0.567580
$151$	5.67816	0.462082	0.231041	−	0.972944i	$-0.425787\pi$
$151$	5.67816	0.462082	0.231041	+	0.972944i	$0.425787\pi$
$152$	−12.5707	−1.01962
$153$	−1.00000	−0.0808452
$154$	1.62851	0.131229
$155$	0.971350	0.0780207
$156$	0.161898	0.0129623
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	7.76715	0.617921
$159$	−9.58285	−0.759969
$160$	0.0602345	0.00476195
$161$	−1.36266	−0.107393
$162$	−1.42497	−0.111956
$163$	12.6255	0.988909	0.494455	−	0.869203i	$-0.335368\pi$
$163$	12.6255	0.988909	0.494455	+	0.869203i	$0.335368\pi$
$164$	0.0226470	0.00176843
$165$	0.814611	0.0634174
$166$	20.9526	1.62624
$167$	−2.36517	−0.183022	−0.0915112	−	0.995804i	$-0.529170\pi$
$167$	−2.36517	−0.183022	−0.0915112	+	0.995804i	$0.529170\pi$
$168$	−1.37351	−0.105969
$169$	15.1289	1.16376
$170$	0.497102	0.0381260
$171$	−4.47923	−0.342535
$172$	−0.103292	−0.00787593
$173$	16.5360	1.25721	0.628603	−	0.777726i	$-0.283627\pi$
$173$	16.5360	1.25721	0.628603	+	0.777726i	$0.283627\pi$
$174$	−0.241009	−0.0182709
$175$	2.38751	0.180479
$176$	−9.48086	−0.714647
$177$	−10.0596	−0.756127
$178$	9.82287	0.736255
$179$	17.6710	1.32079	0.660395	−	0.750918i	$-0.270389\pi$
$179$	17.6710	1.32079	0.660395	+	0.750918i	$0.270389\pi$
$180$	0.0106490	0.000793728 0
$181$	2.10984	0.156824	0.0784118	−	0.996921i	$-0.475015\pi$
$181$	2.10984	0.156824	0.0784118	+	0.996921i	$0.475015\pi$
$182$	3.69877	0.274171
$183$	1.32822	0.0981848
$184$	7.81387	0.576046
$185$	−3.88809	−0.285858
$186$	−3.96770	−0.290926
$187$	−2.33512	−0.170761
$188$	−0.0140976	−0.00102817
$189$	−0.489415	−0.0355997
$190$	2.22663	0.161537
$191$	−8.00882	−0.579498	−0.289749	−	0.957103i	$-0.593572\pi$
$191$	−8.00882	−0.579498	−0.289749	+	0.957103i	$0.593572\pi$
$192$	7.87420	0.568271
$193$	7.43250	0.535003	0.267502	−	0.963557i	$-0.413802\pi$
$193$	7.43250	0.535003	0.267502	+	0.963557i	$0.413802\pi$
$194$	−11.3628	−0.815804
$195$	1.85019	0.132495
$196$	−0.206369	−0.0147406
$197$	19.8609	1.41503	0.707517	−	0.706696i	$-0.249815\pi$
$197$	19.8609	1.41503	0.707517	+	0.706696i	$0.249815\pi$
$198$	−3.32746	−0.236473
$199$	−2.82278	−0.200102	−0.100051	−	0.994982i	$-0.531901\pi$
$199$	−2.82278	−0.200102	−0.100051	+	0.994982i	$0.531901\pi$
$200$	−13.6906	−0.968073
$201$	−2.14227	−0.151104
$202$	−5.97217	−0.420201
$203$	−0.0827764	−0.00580977
$204$	−0.0305258	−0.00213723
$205$	0.258813	0.0180763
$206$	12.0313	0.838262
$207$	2.78427	0.193520
$208$	−21.5335	−1.49308
$209$	−10.4595	−0.723502
$210$	0.243289	0.0167885
$211$	25.3175	1.74293	0.871465	−	0.490457i	$-0.163170\pi$
$211$	25.3175	1.74293	0.871465	+	0.490457i	$0.163170\pi$
$212$	−0.292524	−0.0200906
$213$	8.64535	0.592370
$214$	24.2901	1.66044
$215$	−1.18043	−0.0805047
$216$	2.80643	0.190954
$217$	−1.36274	−0.0925085
$218$	17.4364	1.18094
$219$	1.89207	0.127854
$220$	0.0248666	0.00167651
$221$	−5.30367	−0.356763
$222$	15.8818	1.06592
$223$	6.67044	0.446685	0.223343	−	0.974740i	$-0.428303\pi$
$223$	6.67044	0.446685	0.223343	+	0.974740i	$0.428303\pi$
$224$	−0.0845047	−0.00564621
$225$	−4.87830	−0.325220
$226$	16.1513	1.07437
$227$	−16.0647	−1.06625	−0.533125	−	0.846037i	$-0.678982\pi$
$227$	−16.0647	−1.06625	−0.533125	+	0.846037i	$0.678982\pi$
$228$	−0.136732	−0.00905530
$229$	−26.9121	−1.77840	−0.889200	−	0.457519i	$-0.848738\pi$
$229$	−26.9121	−1.77840	−0.889200	+	0.457519i	$0.848738\pi$
$230$	−1.38407	−0.0912626
$231$	−1.14284	−0.0751935
$232$	0.474662	0.0311631
$233$	−2.77499	−0.181796	−0.0908978	−	0.995860i	$-0.528974\pi$
$233$	−2.77499	−0.181796	−0.0908978	+	0.995860i	$0.528974\pi$
$234$	−7.55754	−0.494052
$235$	−0.161109	−0.0105096
$236$	−0.307077	−0.0199890
$237$	−5.45077	−0.354065
$238$	−0.697399	−0.0452057
$239$	−22.6060	−1.46226	−0.731130	−	0.682238i	$-0.761007\pi$
$239$	−22.6060	−1.46226	−0.731130	+	0.682238i	$0.761007\pi$
$240$	−1.41638	−0.0914270
$241$	30.2829	1.95070	0.975348	−	0.220673i	$-0.0708253\pi$
$241$	30.2829	1.95070	0.975348	+	0.220673i	$0.0708253\pi$
$242$	7.90459	0.508126
$243$	1.00000	0.0641500
$244$	0.0405449	0.00259562
$245$	−2.35840	−0.150673
$246$	−1.05718	−0.0674033
$247$	−23.7563	−1.51158
$248$	7.81428	0.496207
$249$	−14.7039	−0.931824
$250$	4.91052	0.310569
$251$	29.1827	1.84199	0.920997	−	0.389570i	$-0.127376\pi$
$251$	29.1827	1.84199	0.920997	+	0.389570i	$0.127376\pi$
$252$	−0.0149398	−0.000941117 0
$253$	6.50161	0.408752
$254$	15.3162	0.961026
$255$	−0.348852	−0.0218460
$256$	0.732449	0.0457780
$257$	8.11579	0.506249	0.253124	−	0.967434i	$-0.418542\pi$
$257$	8.11579	0.506249	0.253124	+	0.967434i	$0.418542\pi$
$258$	4.82174	0.300188
$259$	5.45471	0.338939
$260$	0.0564786	0.00350265
$261$	0.169133	0.0104691
$262$	−0.988250	−0.0610543
$263$	−5.33971	−0.329261	−0.164630	−	0.986355i	$-0.552643\pi$
$263$	−5.33971	−0.329261	−0.164630	+	0.986355i	$0.552643\pi$
$264$	6.55335	0.403331
$265$	−3.34300	−0.205359
$266$	−3.12381	−0.191533
$267$	−6.89341	−0.421870
$268$	−0.0653944	−0.00399460
$269$	−17.1954	−1.04842	−0.524211	−	0.851588i	$-0.675640\pi$
$269$	−17.1954	−1.04842	−0.524211	+	0.851588i	$0.675640\pi$
$270$	−0.497102	−0.0302527
$271$	−28.5092	−1.73181	−0.865904	−	0.500210i	$-0.833256\pi$
$271$	−28.5092	−1.73181	−0.865904	+	0.500210i	$0.833256\pi$
$272$	4.06012	0.246181
$273$	−2.59569	−0.157099
$274$	−22.5701	−1.36351
$275$	−11.3914	−0.686928
$276$	0.0849920	0.00511592
$277$	12.2251	0.734537	0.367268	−	0.930115i	$-0.380293\pi$
$277$	12.2251	0.734537	0.367268	+	0.930115i	$0.380293\pi$
$278$	−13.1041	−0.785933
$279$	2.78442	0.166699
$280$	−0.479152	−0.0286348
$281$	−14.9343	−0.890906	−0.445453	−	0.895305i	$-0.646957\pi$
$281$	−14.9343	−0.890906	−0.445453	+	0.895305i	$0.646957\pi$
$282$	0.658086	0.0391885
$283$	16.2222	0.964308	0.482154	−	0.876087i	$-0.339855\pi$
$283$	16.2222	0.964308	0.482154	+	0.876087i	$0.339855\pi$
$284$	0.263906	0.0156599
$285$	−1.56259	−0.0925598
$286$	−17.6478	−1.04353
$287$	−0.363096	−0.0214329
$288$	0.172665	0.0101744
$289$	1.00000	0.0588235
$290$	−0.0840766	−0.00493715
$291$	7.97411	0.467451
$292$	0.0577569	0.00337997
$293$	3.47252	0.202867	0.101433	−	0.994842i	$-0.467657\pi$
$293$	3.47252	0.202867	0.101433	+	0.994842i	$0.467657\pi$
$294$	9.63344	0.561834
$295$	−3.50932	−0.204320
$296$	−31.2788	−1.81804
$297$	2.33512	0.135497
$298$	13.5959	0.787589
$299$	14.7668	0.853989
$300$	−0.148914	−0.00859755
$301$	1.65606	0.0954538
$302$	−8.09117	−0.465595
$303$	4.19110	0.240773
$304$	18.1862	1.04305
$305$	0.463352	0.0265315
$306$	1.42497	0.0814598
$307$	−30.0799	−1.71675	−0.858377	−	0.513020i	$-0.828527\pi$
$307$	−30.0799	−1.71675	−0.858377	+	0.513020i	$0.828527\pi$
$308$	−0.0348861	−0.00198782
$309$	−8.44324	−0.480319
$310$	−1.38414	−0.0786139
$311$	−22.8202	−1.29402	−0.647009	−	0.762483i	$-0.723980\pi$
$311$	−22.8202	−1.29402	−0.647009	+	0.762483i	$0.723980\pi$
$312$	14.8844	0.842662
$313$	12.6425	0.714595	0.357298	−	0.933991i	$-0.383698\pi$
$313$	12.6425	0.714595	0.357298	+	0.933991i	$0.383698\pi$
$314$	−1.42497	−0.0804154
$315$	−0.170733	−0.00961973
$316$	−0.166389	−0.00936010
$317$	15.0795	0.846947	0.423474	−	0.905908i	$-0.360811\pi$
$317$	15.0795	0.846947	0.423474	+	0.905908i	$0.360811\pi$
$318$	13.6552	0.765747
$319$	0.394947	0.0221128
$320$	2.74693	0.153558
$321$	−17.0461	−0.951420
$322$	1.94175	0.108209
$323$	4.47923	0.249231
$324$	0.0305258	0.00169588
$325$	−25.8729	−1.43517
$326$	−17.9910	−0.996427
$327$	−12.2364	−0.676674
$328$	2.08209	0.114964
$329$	0.226025	0.0124611
$330$	−1.16079	−0.0638995
$331$	−6.17594	−0.339460	−0.169730	−	0.985491i	$-0.554290\pi$
$331$	−6.17594	−0.339460	−0.169730	+	0.985491i	$0.554290\pi$
$332$	−0.448849	−0.0246338
$333$	−11.1454	−0.610763
$334$	3.37029	0.184414
$335$	−0.747335	−0.0408313
$336$	1.98708	0.108404
$337$	−9.67193	−0.526863	−0.263432	−	0.964678i	$-0.584854\pi$
$337$	−9.67193	−0.526863	−0.263432	+	0.964678i	$0.584854\pi$
$338$	−21.5581	−1.17261
$339$	−11.3345	−0.615606
$340$	−0.0106490	−0.000577522 0
$341$	6.50195	0.352100
$342$	6.38275	0.345140
$343$	6.73458	0.363633
$344$	−9.49629	−0.512006
$345$	0.971299	0.0522930
$346$	−23.5632	−1.26676
$347$	−37.1764	−1.99573	−0.997867	−	0.0652755i	$-0.979207\pi$
$347$	−37.1764	−1.99573	−0.997867	+	0.0652755i	$0.979207\pi$
$348$	0.00516293	0.000276762 0
$349$	−7.65529	−0.409778	−0.204889	−	0.978785i	$-0.565683\pi$
$349$	−7.65529	−0.409778	−0.204889	+	0.978785i	$0.565683\pi$
$350$	−3.40212	−0.181851
$351$	5.30367	0.283089
$352$	0.403193	0.0214903
$353$	−5.89078	−0.313535	−0.156767	−	0.987636i	$-0.550107\pi$
$353$	−5.89078	−0.313535	−0.156767	+	0.987636i	$0.550107\pi$
$354$	14.3346	0.761875
$355$	3.01595	0.160070
$356$	−0.210427	−0.0111526
$357$	0.489415	0.0259026
$358$	−25.1805	−1.33083
$359$	−21.6384	−1.14203	−0.571015	−	0.820939i	$-0.693450\pi$
$359$	−21.6384	−1.14203	−0.571015	+	0.820939i	$0.693450\pi$
$360$	0.979029	0.0515994
$361$	1.06351	0.0559744
$362$	−3.00646	−0.158016
$363$	−5.54722	−0.291153
$364$	−0.0792355	−0.00415307
$365$	0.660052	0.0345487
$366$	−1.89267	−0.0989312
$367$	−22.9579	−1.19839	−0.599196	−	0.800602i	$-0.704513\pi$
$367$	−22.9579	−1.19839	−0.599196	+	0.800602i	$0.704513\pi$
$368$	−11.3045	−0.589286
$369$	0.741898	0.0386217
$370$	5.54039	0.288031
$371$	4.68999	0.243492
$372$	0.0849965	0.00440686
$373$	−7.42511	−0.384458	−0.192229	−	0.981350i	$-0.561572\pi$
$373$	−7.42511	−0.384458	−0.192229	+	0.981350i	$0.561572\pi$
$374$	3.32746	0.172059
$375$	−3.44607	−0.177954
$376$	−1.29608	−0.0668404
$377$	0.897027	0.0461993
$378$	0.697399	0.0358703
$379$	8.31064	0.426889	0.213444	−	0.976955i	$-0.431532\pi$
$379$	8.31064	0.426889	0.213444	+	0.976955i	$0.431532\pi$
$380$	−0.0476992	−0.00244692
$381$	−10.7485	−0.550662
$382$	11.4123	0.583904
$383$	−16.3401	−0.834938	−0.417469	−	0.908691i	$-0.637083\pi$
$383$	−16.3401	−0.834938	−0.417469	+	0.908691i	$0.637083\pi$
$384$	−11.5658	−0.590214
$385$	−0.398683	−0.0203188
$386$	−10.5911	−0.539071
$387$	−3.38376	−0.172006
$388$	0.243416	0.0123576
$389$	−2.10522	−0.106739	−0.0533694	−	0.998575i	$-0.516996\pi$
$389$	−2.10522	−0.106739	−0.0533694	+	0.998575i	$0.516996\pi$
$390$	−2.63646	−0.133502
$391$	−2.78427	−0.140807
$392$	−18.9728	−0.958272
$393$	0.693525	0.0349837
$394$	−28.3012	−1.42579
$395$	−1.90151	−0.0956754
$396$	0.0712813	0.00358202
$397$	15.6209	0.783993	0.391996	−	0.919967i	$-0.371785\pi$
$397$	15.6209	0.783993	0.391996	+	0.919967i	$0.371785\pi$
$398$	4.02236	0.201623
$399$	2.19220	0.109747
$400$	19.8065	0.990325
$401$	38.8161	1.93838	0.969191	−	0.246309i	$-0.0792178\pi$
$401$	38.8161	1.93838	0.969191	+	0.246309i	$0.0792178\pi$
$402$	3.05266	0.152253
$403$	14.7676	0.735628
$404$	0.127937	0.00636508
$405$	0.348852	0.0173346
$406$	0.117954	0.00585394
$407$	−26.0258	−1.29005
$408$	−2.80643	−0.138939
$409$	20.1758	0.997630	0.498815	−	0.866708i	$-0.333769\pi$
$409$	20.1758	0.997630	0.498815	+	0.866708i	$0.333769\pi$
$410$	−0.368799	−0.0182137
$411$	15.8390	0.781282
$412$	−0.257736	−0.0126978
$413$	4.92333	0.242261
$414$	−3.96749	−0.194991
$415$	−5.12950	−0.251797
$416$	0.915756	0.0448987
$417$	9.19610	0.450335
$418$	14.9045	0.729002
$419$	25.0095	1.22179	0.610897	−	0.791710i	$-0.290809\pi$
$419$	25.0095	1.22179	0.610897	+	0.791710i	$0.290809\pi$
$420$	−0.00521177	−0.000254308 0
$421$	12.4874	0.608598	0.304299	−	0.952577i	$-0.401578\pi$
$421$	12.4874	0.608598	0.304299	+	0.952577i	$0.401578\pi$
$422$	−36.0766	−1.75618
$423$	−0.461826	−0.0224548
$424$	−26.8936	−1.30607
$425$	4.87830	0.236632
$426$	−12.3193	−0.596873
$427$	−0.650050	−0.0314581
$428$	−0.520345	−0.0251518
$429$	12.3847	0.597939
$430$	1.68207	0.0811168
$431$	−13.8286	−0.666101	−0.333050	−	0.942909i	$-0.608078\pi$
$431$	−13.8286	−0.666101	−0.333050	+	0.942909i	$0.608078\pi$
$432$	−4.06012	−0.195343
$433$	6.15204	0.295648	0.147824	−	0.989014i	$-0.452773\pi$
$433$	6.15204	0.295648	0.147824	+	0.989014i	$0.452773\pi$
$434$	1.94185	0.0932118
$435$	0.0590025	0.00282896
$436$	−0.373525	−0.0178886
$437$	−12.4714	−0.596588
$438$	−2.69613	−0.128826
$439$	−15.1854	−0.724760	−0.362380	−	0.932030i	$-0.618036\pi$
$439$	−15.1854	−0.724760	−0.362380	+	0.932030i	$0.618036\pi$
$440$	2.28615	0.108988
$441$	−6.76047	−0.321927
$442$	7.55754	0.359476
$443$	10.2396	0.486500	0.243250	−	0.969964i	$-0.421786\pi$
$443$	10.2396	0.486500	0.243250	+	0.969964i	$0.421786\pi$
$444$	−0.340221	−0.0161462
$445$	−2.40478	−0.113997
$446$	−9.50514	−0.450081
$447$	−9.54121	−0.451284
$448$	−3.85375	−0.182073
$449$	−35.5269	−1.67662	−0.838309	−	0.545195i	$-0.816455\pi$
$449$	−35.5269	−1.67662	−0.838309	+	0.545195i	$0.816455\pi$
$450$	6.95141	0.327693
$451$	1.73242	0.0815765
$452$	−0.345995	−0.0162742
$453$	5.67816	0.266783
$454$	22.8916	1.07436
$455$	−0.905513	−0.0424511
$456$	−12.5707	−0.588675
$457$	30.1442	1.41008	0.705042	−	0.709166i	$-0.250928\pi$
$457$	30.1442	1.41008	0.705042	+	0.709166i	$0.250928\pi$
$458$	38.3488	1.79192
$459$	−1.00000	−0.0466760
$460$	0.0296496	0.00138242
$461$	−13.0371	−0.607198	−0.303599	−	0.952800i	$-0.598188\pi$
$461$	−13.0371	−0.607198	−0.303599	+	0.952800i	$0.598188\pi$
$462$	1.62851	0.0757652
$463$	14.2463	0.662083	0.331041	−	0.943616i	$-0.392600\pi$
$463$	14.2463	0.662083	0.331041	+	0.943616i	$0.392600\pi$
$464$	−0.686702	−0.0318793
$465$	0.971350	0.0450453
$466$	3.95426	0.183178
$467$	13.3593	0.618196	0.309098	−	0.951030i	$-0.399973\pi$
$467$	13.3593	0.618196	0.309098	+	0.951030i	$0.399973\pi$
$468$	0.161898	0.00748376
$469$	1.04846	0.0484133
$470$	0.229575	0.0105895
$471$	1.00000	0.0460776
$472$	−28.2316	−1.29947
$473$	−7.90148	−0.363310
$474$	7.76715	0.356757
$475$	21.8510	1.00259
$476$	0.0149398	0.000684763 0
$477$	−9.58285	−0.438769
$478$	32.2128	1.47338
$479$	6.22110	0.284249	0.142125	−	0.989849i	$-0.454607\pi$
$479$	6.22110	0.284249	0.142125	+	0.989849i	$0.454607\pi$
$480$	0.0602345	0.00274931
$481$	−59.1114	−2.69525
$482$	−43.1521	−1.96553
$483$	−1.36266	−0.0620034
$484$	−0.169333	−0.00769696
$485$	2.78178	0.126314
$486$	−1.42497	−0.0646377
$487$	23.2152	1.05198	0.525991	−	0.850490i	$-0.323694\pi$
$487$	23.2152	1.05198	0.525991	+	0.850490i	$0.323694\pi$
$488$	3.72756	0.168739
$489$	12.6255	0.570947
$490$	3.36064	0.151818
$491$	24.7210	1.11564	0.557821	−	0.829961i	$-0.311638\pi$
$491$	24.7210	1.11564	0.557821	+	0.829961i	$0.311638\pi$
$492$	0.0226470	0.00102101
$493$	−0.169133	−0.00761739
$494$	33.8520	1.52307
$495$	0.814611	0.0366140
$496$	−11.3051	−0.507613
$497$	−4.23116	−0.189794
$498$	20.9526	0.938909
$499$	22.1365	0.990967	0.495483	−	0.868617i	$-0.334991\pi$
$499$	22.1365	0.990967	0.495483	+	0.868617i	$0.334991\pi$
$500$	−0.105194	−0.00470441
$501$	−2.36517	−0.105668
$502$	−41.5843	−1.85600
$503$	20.4650	0.912490	0.456245	−	0.889854i	$-0.349194\pi$
$503$	20.4650	0.912490	0.456245	+	0.889854i	$0.349194\pi$
$504$	−1.37351	−0.0611810
$505$	1.46207	0.0650615
$506$	−9.26456	−0.411860
$507$	15.1289	0.671897
$508$	−0.328106	−0.0145574
$509$	−39.2385	−1.73922	−0.869608	−	0.493743i	$-0.835629\pi$
$509$	−39.2385	−1.73922	−0.869608	+	0.493743i	$0.835629\pi$
$510$	0.497102	0.0220120
$511$	−0.926007	−0.0409641
$512$	22.0879	0.976155
$513$	−4.47923	−0.197763
$514$	−11.5647	−0.510098
$515$	−2.94544	−0.129792
$516$	−0.103292	−0.00454717
$517$	−1.07842	−0.0474288
$518$	−7.77278	−0.341516
$519$	16.5360	0.725848
$520$	5.19245	0.227704
$521$	−30.3709	−1.33057	−0.665286	−	0.746589i	$-0.731690\pi$
$521$	−30.3709	−1.33057	−0.665286	+	0.746589i	$0.731690\pi$
$522$	−0.241009	−0.0105487
$523$	35.2499	1.54137	0.770686	−	0.637215i	$-0.219914\pi$
$523$	35.2499	1.54137	0.770686	+	0.637215i	$0.219914\pi$
$524$	0.0211704	0.000924833 0
$525$	2.38751	0.104200
$526$	7.60890	0.331764
$527$	−2.78442	−0.121291
$528$	−9.48086	−0.412602
$529$	−15.2478	−0.662949
$530$	4.76365	0.206920
$531$	−10.0596	−0.436550
$532$	0.0669187	0.00290129
$533$	3.93478	0.170434
$534$	9.82287	0.425077
$535$	−5.94656	−0.257092
$536$	−6.01214	−0.259685
$537$	17.6710	0.762559
$538$	24.5029	1.05639
$539$	−15.7865	−0.679973
$540$	0.0106490	0.000458259 0
$541$	−41.6138	−1.78912	−0.894559	−	0.446950i	$-0.852510\pi$
$541$	−41.6138	−1.78912	−0.894559	+	0.446950i	$0.852510\pi$
$542$	40.6246	1.74497
$543$	2.10984	0.0905421
$544$	−0.172665	−0.00740294
$545$	−4.26869	−0.182851
$546$	3.69877	0.158293
$547$	19.8902	0.850444	0.425222	−	0.905089i	$-0.360196\pi$
$547$	19.8902	0.850444	0.425222	+	0.905089i	$0.360196\pi$
$548$	0.483499	0.0206540
$549$	1.32822	0.0566870
$550$	16.2324	0.692151
$551$	−0.757588	−0.0322743
$552$	7.81387	0.332580
$553$	2.66769	0.113442
$554$	−17.4204	−0.740121
$555$	−3.88809	−0.165040
$556$	0.280718	0.0119051
$557$	−23.5130	−0.996276	−0.498138	−	0.867098i	$-0.665983\pi$
$557$	−23.5130	−0.996276	−0.498138	+	0.867098i	$0.665983\pi$
$558$	−3.96770	−0.167966
$559$	−17.9463	−0.759049
$560$	0.693198	0.0292930
$561$	−2.33512	−0.0985888
$562$	21.2809	0.897679
$563$	−24.4768	−1.03158	−0.515788	−	0.856716i	$-0.672501\pi$
$563$	−24.4768	−1.03158	−0.515788	+	0.856716i	$0.672501\pi$
$564$	−0.0140976	−0.000593616 0
$565$	−3.95407	−0.166349
$566$	−23.1160	−0.971639
$567$	−0.489415	−0.0205535
$568$	24.2626	1.01804
$569$	−34.2509	−1.43587	−0.717936	−	0.696109i	$-0.754913\pi$
$569$	−34.2509	−1.43587	−0.717936	+	0.696109i	$0.754913\pi$
$570$	2.22663	0.0932635
$571$	14.6683	0.613847	0.306924	−	0.951734i	$-0.400700\pi$
$571$	14.6683	0.613847	0.306924	+	0.951734i	$0.400700\pi$
$572$	0.378052	0.0158072
$573$	−8.00882	−0.334573
$574$	0.517399	0.0215958
$575$	−13.5825	−0.566430
$576$	7.87420	0.328092
$577$	0.531756	0.0221373	0.0110686	−	0.999939i	$-0.496477\pi$
$577$	0.531756	0.0221373	0.0110686	+	0.999939i	$0.496477\pi$
$578$	−1.42497	−0.0592707
$579$	7.43250	0.308884
$580$	0.00180110	7.47865e−5 0
$581$	7.19633	0.298554
$582$	−11.3628	−0.471005
$583$	−22.3771	−0.926765
$584$	5.30997	0.219728
$585$	1.85019	0.0764961
$586$	−4.94822	−0.204409
$587$	−35.3636	−1.45961	−0.729806	−	0.683655i	$-0.760389\pi$
$587$	−35.3636	−1.45961	−0.729806	+	0.683655i	$0.760389\pi$
$588$	−0.206369	−0.00851050
$589$	−12.4721	−0.513902
$590$	5.00065	0.205874
$591$	19.8609	0.816970
$592$	45.2516	1.85983
$593$	−18.5077	−0.760018	−0.380009	−	0.924983i	$-0.624079\pi$
$593$	−18.5077	−0.760018	−0.380009	+	0.924983i	$0.624079\pi$
$594$	−3.32746	−0.136528
$595$	0.170733	0.00699939
$596$	−0.291253	−0.0119302
$597$	−2.82278	−0.115529
$598$	−21.0422	−0.860481
$599$	0.315731	0.0129004	0.00645021	−	0.999979i	$-0.497947\pi$
$599$	0.315731	0.0129004	0.00645021	+	0.999979i	$0.497947\pi$
$600$	−13.6906	−0.558917
$601$	−39.7301	−1.62063	−0.810313	−	0.585997i	$-0.800703\pi$
$601$	−39.7301	−1.62063	−0.810313	+	0.585997i	$0.800703\pi$
$602$	−2.35983	−0.0961795
$603$	−2.14227	−0.0872400
$604$	0.173330	0.00705270
$605$	−1.93516	−0.0786753
$606$	−5.97217	−0.242603
$607$	35.1286	1.42583	0.712914	−	0.701252i	$-0.247375\pi$
$607$	35.1286	1.42583	0.712914	+	0.701252i	$0.247375\pi$
$608$	−0.773406	−0.0313657
$609$	−0.0827764	−0.00335427
$610$	−0.660260	−0.0267332
$611$	−2.44937	−0.0990910
$612$	−0.0305258	−0.00123393
$613$	38.1985	1.54282	0.771411	−	0.636337i	$-0.219551\pi$
$613$	38.1985	1.54282	0.771411	+	0.636337i	$0.219551\pi$
$614$	42.8629	1.72980
$615$	0.258813	0.0104363
$616$	−3.20731	−0.129226
$617$	−26.9450	−1.08477	−0.542383	−	0.840131i	$-0.682478\pi$
$617$	−26.9450	−1.08477	−0.542383	+	0.840131i	$0.682478\pi$
$618$	12.0313	0.483971
$619$	25.6530	1.03108	0.515541	−	0.856865i	$-0.327591\pi$
$619$	25.6530	1.03108	0.515541	+	0.856865i	$0.327591\pi$
$620$	0.0296512	0.00119082
$621$	2.78427	0.111729
$622$	32.5181	1.30386
$623$	3.37374	0.135166
$624$	−21.5335	−0.862031
$625$	23.1893	0.927574
$626$	−18.0151	−0.720028
$627$	−10.4595	−0.417714
$628$	0.0305258	0.00121811
$629$	11.1454	0.444395
$630$	0.243289	0.00969287
$631$	−3.37801	−0.134476	−0.0672382	−	0.997737i	$-0.521419\pi$
$631$	−3.37801	−0.134476	−0.0672382	+	0.997737i	$0.521419\pi$
$632$	−15.2972	−0.608490
$633$	25.3175	1.00628
$634$	−21.4877	−0.853386
$635$	−3.74963	−0.148800
$636$	−0.292524	−0.0115993
$637$	−35.8553	−1.42064
$638$	−0.562786	−0.0222809
$639$	8.64535	0.342005
$640$	−4.03475	−0.159487
$641$	−0.774988	−0.0306102	−0.0153051	−	0.999883i	$-0.504872\pi$
$641$	−0.774988	−0.0306102	−0.0153051	+	0.999883i	$0.504872\pi$
$642$	24.2901	0.958653
$643$	−11.1018	−0.437813	−0.218907	−	0.975746i	$-0.570249\pi$
$643$	−11.1018	−0.437813	−0.218907	+	0.975746i	$0.570249\pi$
$644$	−0.0415964	−0.00163913
$645$	−1.18043	−0.0464794
$646$	−6.38275	−0.251126
$647$	−22.1721	−0.871676	−0.435838	−	0.900025i	$-0.643548\pi$
$647$	−22.1721	−0.871676	−0.435838	+	0.900025i	$0.643548\pi$
$648$	2.80643	0.110247
$649$	−23.4904	−0.922079
$650$	36.8680	1.44608
$651$	−1.36274	−0.0534098
$652$	0.385404	0.0150936
$653$	−31.2762	−1.22393	−0.611966	−	0.790884i	$-0.709621\pi$
$653$	−31.2762	−1.22393	−0.611966	+	0.790884i	$0.709621\pi$
$654$	17.4364	0.681819
$655$	0.241938	0.00945329
$656$	−3.01220	−0.117606
$657$	1.89207	0.0738167
$658$	−0.322077	−0.0125559
$659$	−25.7084	−1.00146	−0.500729	−	0.865604i	$-0.666935\pi$
$659$	−25.7084	−1.00146	−0.500729	+	0.865604i	$0.666935\pi$
$660$	0.0248666	0.000967932 0
$661$	47.5950	1.85123	0.925616	−	0.378463i	$-0.123547\pi$
$661$	47.5950	1.85123	0.925616	+	0.378463i	$0.123547\pi$
$662$	8.80049	0.342041
$663$	−5.30367	−0.205977
$664$	−41.2656	−1.60142
$665$	0.764754	0.0296559
$666$	15.8818	0.615406
$667$	0.470913	0.0182338
$668$	−0.0721987	−0.00279345
$669$	6.67044	0.257894
$670$	1.06493	0.0411417
$671$	3.10155	0.119734
$672$	−0.0845047	−0.00325984
$673$	15.1214	0.582888	0.291444	−	0.956588i	$-0.405864\pi$
$673$	15.1214	0.582888	0.291444	+	0.956588i	$0.405864\pi$
$674$	13.7822	0.530869
$675$	−4.87830	−0.187766
$676$	0.461821	0.0177623
$677$	10.4928	0.403269	0.201635	−	0.979461i	$-0.435375\pi$
$677$	10.4928	0.403269	0.201635	+	0.979461i	$0.435375\pi$
$678$	16.1513	0.620287
$679$	−3.90265	−0.149770
$680$	−0.979029	−0.0375441
$681$	−16.0647	−0.615599
$682$	−9.26505	−0.354777
$683$	21.8847	0.837395	0.418698	−	0.908126i	$-0.362487\pi$
$683$	21.8847	0.837395	0.418698	+	0.908126i	$0.362487\pi$
$684$	−0.136732	−0.00522808
$685$	5.52548	0.211118
$686$	−9.59654	−0.366398
$687$	−26.9121	−1.02676
$688$	13.7385	0.523774
$689$	−50.8242	−1.93625
$690$	−1.38407	−0.0526905
$691$	−16.2348	−0.617602	−0.308801	−	0.951127i	$-0.599928\pi$
$691$	−16.2348	−0.617602	−0.308801	+	0.951127i	$0.599928\pi$
$692$	0.504773	0.0191886
$693$	−1.14284	−0.0434130
$694$	52.9751	2.01091
$695$	3.20808	0.121689
$696$	0.474662	0.0179920
$697$	−0.741898	−0.0281014
$698$	10.9085	0.412893
$699$	−2.77499	−0.104960
$700$	0.0728807	0.00275463
$701$	12.7919	0.483145	0.241573	−	0.970383i	$-0.422337\pi$
$701$	12.7919	0.483145	0.241573	+	0.970383i	$0.422337\pi$
$702$	−7.55754	−0.285241
$703$	49.9227	1.88287
$704$	18.3872	0.692993
$705$	−0.161109	−0.00606772
$706$	8.39416	0.315918
$707$	−2.05119	−0.0771429
$708$	−0.307077	−0.0115407
$709$	10.0571	0.377703	0.188852	−	0.982006i	$-0.439523\pi$
$709$	10.0571	0.377703	0.188852	+	0.982006i	$0.439523\pi$
$710$	−4.29762	−0.161287
$711$	−5.45077	−0.204420
$712$	−19.3459	−0.725018
$713$	7.75258	0.290336
$714$	−0.697399	−0.0260995
$715$	4.32043	0.161575
$716$	0.539420	0.0201591
$717$	−22.6060	−0.844236
$718$	30.8340	1.15071
$719$	15.1650	0.565558	0.282779	−	0.959185i	$-0.408744\pi$
$719$	15.1650	0.565558	0.282779	+	0.959185i	$0.408744\pi$
$720$	−1.41638	−0.0527854
$721$	4.13225	0.153893
$722$	−1.51547	−0.0564000
$723$	30.2829	1.12623
$724$	0.0644046	0.00239358
$725$	−0.825084	−0.0306429
$726$	7.90459	0.293367
$727$	−3.04565	−0.112957	−0.0564785	−	0.998404i	$-0.517987\pi$
$727$	−3.04565	−0.112957	−0.0564785	+	0.998404i	$0.517987\pi$
$728$	−7.28464	−0.269987
$729$	1.00000	0.0370370
$730$	−0.940551	−0.0348114
$731$	3.38376	0.125153
$732$	0.0405449	0.00149858
$733$	3.09265	0.114230	0.0571149	−	0.998368i	$-0.481810\pi$
$733$	3.09265	0.114230	0.0571149	+	0.998368i	$0.481810\pi$
$734$	32.7142	1.20750
$735$	−2.35840	−0.0869911
$736$	0.480746	0.0177205
$737$	−5.00246	−0.184268
$738$	−1.05718	−0.0389153
$739$	50.0797	1.84221	0.921105	−	0.389314i	$-0.127288\pi$
$739$	50.0797	1.84221	0.921105	+	0.389314i	$0.127288\pi$
$740$	−0.118687	−0.00436302
$741$	−23.7563	−0.872711
$742$	−6.68307	−0.245343
$743$	−8.37497	−0.307248	−0.153624	−	0.988129i	$-0.549094\pi$
$743$	−8.37497	−0.307248	−0.153624	+	0.988129i	$0.549094\pi$
$744$	7.81428	0.286485
$745$	−3.32847	−0.121946
$746$	10.5805	0.387381
$747$	−14.7039	−0.537989
$748$	−0.0712813	−0.00260630
$749$	8.34261	0.304832
$750$	4.91052	0.179307
$751$	17.9225	0.654002	0.327001	−	0.945024i	$-0.393962\pi$
$751$	17.9225	0.654002	0.327001	+	0.945024i	$0.393962\pi$
$752$	1.87507	0.0683768
$753$	29.1827	1.06348
$754$	−1.27823	−0.0465505
$755$	1.98084	0.0720900
$756$	−0.0149398	−0.000543354 0
$757$	−27.2271	−0.989585	−0.494793	−	0.869011i	$-0.664756\pi$
$757$	−27.2271	−0.989585	−0.494793	+	0.869011i	$0.664756\pi$
$758$	−11.8424	−0.430134
$759$	6.50161	0.235993
$760$	−4.38530	−0.159072
$761$	−15.9627	−0.578649	−0.289325	−	0.957231i	$-0.593431\pi$
$761$	−15.9627	−0.578649	−0.289325	+	0.957231i	$0.593431\pi$
$762$	15.3162	0.554849
$763$	5.98868	0.216805
$764$	−0.244475	−0.00884481
$765$	−0.348852	−0.0126128
$766$	23.2840	0.841286
$767$	−53.3528	−1.92646
$768$	0.732449	0.0264300
$769$	−30.0755	−1.08455	−0.542276	−	0.840201i	$-0.682437\pi$
$769$	−30.0755	−1.08455	−0.542276	+	0.840201i	$0.682437\pi$
$770$	0.568109	0.0204732
$771$	8.11579	0.292283
$772$	0.226883	0.00816569
$773$	17.7997	0.640210	0.320105	−	0.947382i	$-0.396282\pi$
$773$	17.7997	0.640210	0.320105	+	0.947382i	$0.396282\pi$
$774$	4.82174	0.173314
$775$	−13.5832	−0.487924
$776$	22.3788	0.803352
$777$	5.45471	0.195687
$778$	2.99986	0.107550
$779$	−3.32313	−0.119064
$780$	0.0564786	0.00202226
$781$	20.1879	0.722381
$782$	3.96749	0.141877
$783$	0.169133	0.00604434
$784$	27.4483	0.980297
$785$	0.348852	0.0124511
$786$	−0.988250	−0.0352497
$787$	−46.2565	−1.64887	−0.824433	−	0.565960i	$-0.808506\pi$
$787$	−46.2565	−1.64887	−0.824433	+	0.565960i	$0.808506\pi$
$788$	0.606271	0.0215975
$789$	−5.33971	−0.190099
$790$	2.70959	0.0964028
$791$	5.54728	0.197239
$792$	6.55335	0.232863
$793$	7.04443	0.250155
$794$	−22.2593	−0.789953
$795$	−3.34300	−0.118564
$796$	−0.0861675	−0.00305413
$797$	4.46866	0.158288	0.0791440	−	0.996863i	$-0.474781\pi$
$797$	4.46866	0.158288	0.0791440	+	0.996863i	$0.474781\pi$
$798$	−3.12381	−0.110582
$799$	0.461826	0.0163382
$800$	−0.842311	−0.0297802
$801$	−6.89341	−0.243567
$802$	−55.3116	−1.95312
$803$	4.41821	0.155915
$804$	−0.0653944	−0.00230628
$805$	−0.475368	−0.0167545
$806$	−21.0434	−0.741221
$807$	−17.1954	−0.605307
$808$	11.7620	0.413787
$809$	29.6131	1.04114	0.520570	−	0.853819i	$-0.325719\pi$
$809$	29.6131	1.04114	0.520570	+	0.853819i	$0.325719\pi$
$810$	−0.497102	−0.0174664
$811$	37.9980	1.33429	0.667144	−	0.744928i	$-0.267516\pi$
$811$	37.9980	1.33429	0.667144	+	0.744928i	$0.267516\pi$
$812$	−0.00252681	−8.86738e−5 0
$813$	−28.5092	−0.999860
$814$	37.0859	1.29986
$815$	4.40445	0.154281
$816$	4.06012	0.142133
$817$	15.1566	0.530264
$818$	−28.7498	−1.00521
$819$	−2.59569	−0.0907009
$820$	0.00790045	0.000275896 0
$821$	−10.6176	−0.370556	−0.185278	−	0.982686i	$-0.559319\pi$
$821$	−10.6176	−0.370556	−0.185278	+	0.982686i	$0.559319\pi$
$822$	−22.5701	−0.787222
$823$	1.67879	0.0585191	0.0292595	−	0.999572i	$-0.490685\pi$
$823$	1.67879	0.0585191	0.0292595	+	0.999572i	$0.490685\pi$
$824$	−23.6954	−0.825468
$825$	−11.3914	−0.396598
$826$	−7.01557	−0.244103
$827$	−4.13727	−0.143867	−0.0719336	−	0.997409i	$-0.522917\pi$
$827$	−4.13727	−0.143867	−0.0719336	+	0.997409i	$0.522917\pi$
$828$	0.0849920	0.00295368
$829$	−38.3100	−1.33056	−0.665281	−	0.746593i	$-0.731688\pi$
$829$	−38.3100	−1.33056	−0.665281	+	0.746593i	$0.731688\pi$
$830$	7.30936	0.253711
$831$	12.2251	0.424085
$832$	41.7621	1.44784
$833$	6.76047	0.234237
$834$	−13.1041	−0.453759
$835$	−0.825095	−0.0285536
$836$	−0.319285	−0.0110427
$837$	2.78442	0.0962436
$838$	−35.6377	−1.23108
$839$	−5.84342	−0.201737	−0.100869	−	0.994900i	$-0.532162\pi$
$839$	−5.84342	−0.201737	−0.100869	+	0.994900i	$0.532162\pi$
$840$	−0.479152	−0.0165323
$841$	−28.9714	−0.999014
$842$	−17.7941	−0.613225
$843$	−14.9343	−0.514365
$844$	0.772837	0.0266021
$845$	5.27774	0.181560
$846$	0.658086	0.0226255
$847$	2.71489	0.0932847
$848$	38.9075	1.33609
$849$	16.2222	0.556743
$850$	−6.95141	−0.238431
$851$	−31.0318	−1.06376
$852$	0.263906	0.00904127
$853$	−49.7842	−1.70458	−0.852289	−	0.523070i	$-0.824786\pi$
$853$	−49.7842	−1.70458	−0.852289	+	0.523070i	$0.824786\pi$
$854$	0.926299	0.0316973
$855$	−1.56259	−0.0534394
$856$	−47.8387	−1.63509
$857$	−18.0709	−0.617292	−0.308646	−	0.951177i	$-0.599876\pi$
$857$	−18.0709	−0.617292	−0.308646	+	0.951177i	$0.599876\pi$
$858$	−17.6478	−0.602485
$859$	−45.4163	−1.54958	−0.774791	−	0.632217i	$-0.782145\pi$
$859$	−45.4163	−1.54958	−0.774791	+	0.632217i	$0.782145\pi$
$860$	−0.0360336	−0.00122873
$861$	−0.363096	−0.0123743
$862$	19.7053	0.671165
$863$	37.7648	1.28553	0.642765	−	0.766064i	$-0.277787\pi$
$863$	37.7648	1.28553	0.642765	+	0.766064i	$0.277787\pi$
$864$	0.172665	0.00587418
$865$	5.76860	0.196138
$866$	−8.76645	−0.297896
$867$	1.00000	0.0339618
$868$	−0.0415986	−0.00141195
$869$	−12.7282	−0.431774
$870$	−0.0840766	−0.00285046
$871$	−11.3619	−0.384983
$872$	−34.3406	−1.16292
$873$	7.97411	0.269883
$874$	17.7713	0.601123
$875$	1.68656	0.0570160
$876$	0.0577569	0.00195142
$877$	−55.5063	−1.87431	−0.937157	−	0.348909i	$-0.886552\pi$
$877$	−55.5063	−1.87431	−0.937157	+	0.348909i	$0.886552\pi$
$878$	21.6387	0.730270
$879$	3.47252	0.117125
$880$	−3.30742	−0.111493
$881$	−37.8148	−1.27401	−0.637007	−	0.770858i	$-0.719828\pi$
$881$	−37.8148	−1.27401	−0.637007	+	0.770858i	$0.719828\pi$
$882$	9.63344	0.324375
$883$	−15.4684	−0.520552	−0.260276	−	0.965534i	$-0.583814\pi$
$883$	−15.4684	−0.520552	−0.260276	+	0.965534i	$0.583814\pi$
$884$	−0.161898	−0.00544523
$885$	−3.50932	−0.117964
$886$	−14.5911	−0.490199
$887$	−31.4518	−1.05605	−0.528024	−	0.849230i	$-0.677067\pi$
$887$	−31.4518	−1.05605	−0.528024	+	0.849230i	$0.677067\pi$
$888$	−31.2788	−1.04965
$889$	5.26048	0.176431
$890$	3.42673	0.114864
$891$	2.33512	0.0782294
$892$	0.203620	0.00681771
$893$	2.06863	0.0692239
$894$	13.5959	0.454715
$895$	6.16455	0.206058
$896$	5.66047	0.189103
$897$	14.7668	0.493051
$898$	50.6246	1.68936
$899$	0.470938	0.0157067
$900$	−0.148914	−0.00496380
$901$	9.58285	0.319251
$902$	−2.46864	−0.0821967
$903$	1.65606	0.0551103
$904$	−31.8096	−1.05797
$905$	0.736023	0.0244662
$906$	−8.09117	−0.268811
$907$	−3.71802	−0.123455	−0.0617274	−	0.998093i	$-0.519661\pi$
$907$	−3.71802	−0.123455	−0.0617274	+	0.998093i	$0.519661\pi$
$908$	−0.490386	−0.0162740
$909$	4.19110	0.139010
$910$	1.29032	0.0427738
$911$	46.3971	1.53721	0.768603	−	0.639726i	$-0.220952\pi$
$911$	46.3971	1.53721	0.768603	+	0.639726i	$0.220952\pi$
$912$	18.1862	0.602206
$913$	−34.3355	−1.13634
$914$	−42.9544	−1.42080
$915$	0.463352	0.0153179
$916$	−0.821511	−0.0271435
$917$	−0.339422	−0.0112087
$918$	1.42497	0.0470309
$919$	−4.45244	−0.146872	−0.0734362	−	0.997300i	$-0.523397\pi$
$919$	−4.45244	−0.146872	−0.0734362	+	0.997300i	$0.523397\pi$
$920$	2.72588	0.0898697
$921$	−30.0799	−0.991168
$922$	18.5774	0.611814
$923$	45.8520	1.50924
$924$	−0.0348861	−0.00114767
$925$	54.3705	1.78769
$926$	−20.3005	−0.667116
$927$	−8.44324	−0.277312
$928$	0.0292034	0.000958648 0
$929$	2.68218	0.0879996	0.0439998	−	0.999032i	$-0.485990\pi$
$929$	2.68218	0.0879996	0.0439998	+	0.999032i	$0.485990\pi$
$930$	−1.38414	−0.0453877
$931$	30.2817	0.992443
$932$	−0.0847087	−0.00277473
$933$	−22.8202	−0.747101
$934$	−19.0366	−0.622896
$935$	−0.814611	−0.0266406
$936$	14.8844	0.486511
$937$	35.8050	1.16970	0.584849	−	0.811142i	$-0.301154\pi$
$937$	35.8050	1.16970	0.584849	+	0.811142i	$0.301154\pi$
$938$	−1.49402	−0.0487814
$939$	12.6425	0.412572
$940$	−0.00491798	−0.000160407 0
$941$	28.7903	0.938537	0.469269	−	0.883056i	$-0.344518\pi$
$941$	28.7903	0.938537	0.469269	+	0.883056i	$0.344518\pi$
$942$	−1.42497	−0.0464279
$943$	2.06565	0.0672667
$944$	40.8432	1.32933
$945$	−0.170733	−0.00555396
$946$	11.2593	0.366073
$947$	2.70980	0.0880566	0.0440283	−	0.999030i	$-0.485981\pi$
$947$	2.70980	0.0880566	0.0440283	+	0.999030i	$0.485981\pi$
$948$	−0.166389	−0.00540406
$949$	10.0349	0.325747
$950$	−31.1370	−1.01022
$951$	15.0795	0.488985
$952$	1.37351	0.0445157
$953$	6.09947	0.197581	0.0987905	−	0.995108i	$-0.468503\pi$
$953$	6.09947	0.197581	0.0987905	+	0.995108i	$0.468503\pi$
$954$	13.6552	0.442104
$955$	−2.79389	−0.0904083
$956$	−0.690065	−0.0223183
$957$	0.394947	0.0127668
$958$	−8.86486	−0.286410
$959$	−7.75186	−0.250321
$960$	2.74693	0.0886568
$961$	−23.2470	−0.749904
$962$	84.2317	2.71574
$963$	−17.0461	−0.549302
$964$	0.924410	0.0297732
$965$	2.59284	0.0834666
$966$	1.94175	0.0624747
$967$	58.5178	1.88181	0.940903	−	0.338676i	$-0.109979\pi$
$967$	58.5178	1.88181	0.940903	+	0.338676i	$0.109979\pi$
$968$	−15.5679	−0.500371
$969$	4.47923	0.143894
$970$	−3.96395	−0.127275
$971$	44.3759	1.42409	0.712044	−	0.702134i	$-0.247769\pi$
$971$	44.3759	1.42409	0.712044	+	0.702134i	$0.247769\pi$
$972$	0.0305258	0.000979114 0
$973$	−4.50071	−0.144286
$974$	−33.0809	−1.05998
$975$	−25.8729	−0.828596
$976$	−5.39273	−0.172617
$977$	−26.3430	−0.842788	−0.421394	−	0.906878i	$-0.638459\pi$
$977$	−26.3430	−0.842788	−0.421394	+	0.906878i	$0.638459\pi$
$978$	−17.9910	−0.575288
$979$	−16.0969	−0.514460
$980$	−0.0719921	−0.00229970
$981$	−12.2364	−0.390678
$982$	−35.2265	−1.12412
$983$	−6.15658	−0.196364	−0.0981821	−	0.995168i	$-0.531303\pi$
$983$	−6.15658	−0.196364	−0.0981821	+	0.995168i	$0.531303\pi$
$984$	2.08209	0.0663745
$985$	6.92853	0.220761
$986$	0.241009	0.00767530
$987$	0.226025	0.00719444
$988$	−0.725181	−0.0230711
$989$	−9.42130	−0.299580
$990$	−1.16079	−0.0368924
$991$	60.2209	1.91298	0.956490	−	0.291765i	$-0.0942426\pi$
$991$	60.2209	1.91298	0.956490	+	0.291765i	$0.0942426\pi$
$992$	0.480771	0.0152645
$993$	−6.17594	−0.195987
$994$	6.02926	0.191236
$995$	−0.984732	−0.0312181
$996$	−0.448849	−0.0142223
$997$	35.5554	1.12605	0.563025	−	0.826440i	$-0.309637\pi$
$997$	35.5554	1.12605	0.563025	+	0.826440i	$0.309637\pi$
$998$	−31.5438	−0.998501
$999$	−11.1454	−0.352624

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.e.1.15	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.e.1.15	✓	46	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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q-1.42497 q^{2} +1.00000 q^{3} +0.0305258 q^{4} +0.348852 q^{5} -1.42497 q^{6} -0.489415 q^{7} +2.80643 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.42497 q^{2} +1.00000 q^{3} +0.0305258 q^{4} +0.348852 q^{5} -1.42497 q^{6} -0.489415 q^{7} +2.80643 q^{8} +1.00000 q^{9} -0.497102 q^{10} +2.33512 q^{11} +0.0305258 q^{12} +5.30367 q^{13} +0.697399 q^{14} +0.348852 q^{15} -4.06012 q^{16} -1.00000 q^{17} -1.42497 q^{18} -4.47923 q^{19} +0.0106490 q^{20} -0.489415 q^{21} -3.32746 q^{22} +2.78427 q^{23} +2.80643 q^{24} -4.87830 q^{25} -7.55754 q^{26} +1.00000 q^{27} -0.0149398 q^{28} +0.169133 q^{29} -0.497102 q^{30} +2.78442 q^{31} +0.172665 q^{32} +2.33512 q^{33} +1.42497 q^{34} -0.170733 q^{35} +0.0305258 q^{36} -11.1454 q^{37} +6.38275 q^{38} +5.30367 q^{39} +0.979029 q^{40} +0.741898 q^{41} +0.697399 q^{42} -3.38376 q^{43} +0.0712813 q^{44} +0.348852 q^{45} -3.96749 q^{46} -0.461826 q^{47} -4.06012 q^{48} -6.76047 q^{49} +6.95141 q^{50} -1.00000 q^{51} +0.161898 q^{52} -9.58285 q^{53} -1.42497 q^{54} +0.814611 q^{55} -1.37351 q^{56} -4.47923 q^{57} -0.241009 q^{58} -10.0596 q^{59} +0.0106490 q^{60} +1.32822 q^{61} -3.96770 q^{62} -0.489415 q^{63} +7.87420 q^{64} +1.85019 q^{65} -3.32746 q^{66} -2.14227 q^{67} -0.0305258 q^{68} +2.78427 q^{69} +0.243289 q^{70} +8.64535 q^{71} +2.80643 q^{72} +1.89207 q^{73} +15.8818 q^{74} -4.87830 q^{75} -0.136732 q^{76} -1.14284 q^{77} -7.55754 q^{78} -5.45077 q^{79} -1.41638 q^{80} +1.00000 q^{81} -1.05718 q^{82} -14.7039 q^{83} -0.0149398 q^{84} -0.348852 q^{85} +4.82174 q^{86} +0.169133 q^{87} +6.55335 q^{88} -6.89341 q^{89} -0.497102 q^{90} -2.59569 q^{91} +0.0849920 q^{92} +2.78442 q^{93} +0.658086 q^{94} -1.56259 q^{95} +0.172665 q^{96} +7.97411 q^{97} +9.63344 q^{98} +2.33512 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9}+O(q^{10}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9} - 10 q^{10} - 25 q^{11} + 43 q^{12} - 8 q^{13} - 28 q^{14} - 19 q^{15} + 33 q^{16} - 46 q^{17} - 5 q^{18} - 2 q^{19} - 56 q^{20} + q^{21} - 19 q^{22} - 64 q^{23} - 18 q^{24} + 11 q^{25} - 13 q^{26} + 46 q^{27} - 38 q^{28} - 51 q^{29} - 10 q^{30} - 19 q^{31} - 61 q^{32} - 25 q^{33} + 5 q^{34} - 39 q^{35} + 43 q^{36} - 46 q^{37} - 48 q^{38} - 8 q^{39} - 10 q^{40} - 53 q^{41} - 28 q^{42} - 33 q^{43} - 62 q^{44} - 19 q^{45} + 2 q^{46} - 45 q^{47} + 33 q^{48} + 21 q^{49} - 60 q^{50} - 46 q^{51} - 63 q^{52} - 47 q^{53} - 5 q^{54} + 5 q^{55} - 82 q^{56} - 2 q^{57} - 21 q^{58} - 65 q^{59} - 56 q^{60} - 37 q^{61} - 46 q^{62} + q^{63} + 74 q^{64} - 85 q^{65} - 19 q^{66} - 52 q^{67} - 43 q^{68} - 64 q^{69} - 20 q^{70} - 48 q^{71} - 18 q^{72} - 39 q^{73} - 16 q^{74} + 11 q^{75} + 42 q^{76} - 78 q^{77} - 13 q^{78} - 26 q^{79} - 78 q^{80} + 46 q^{81} + 3 q^{82} - 47 q^{83} - 38 q^{84} + 19 q^{85} - 6 q^{86} - 51 q^{87} - 58 q^{88} - 58 q^{89} - 10 q^{90} - 43 q^{91} - 68 q^{92} - 19 q^{93} - 78 q^{95} - 61 q^{96} - 44 q^{97} - 4 q^{98} - 25 q^{99}+O(q^{100}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9 - 10 * q^10 - 25 * q^11 + 43 * q^12 - 8 * q^13 - 28 * q^14 - 19 * q^15 + 33 * q^16 - 46 * q^17 - 5 * q^18 - 2 * q^19 - 56 * q^20 + q^21 - 19 * q^22 - 64 * q^23 - 18 * q^24 + 11 * q^25 - 13 * q^26 + 46 * q^27 - 38 * q^28 - 51 * q^29 - 10 * q^30 - 19 * q^31 - 61 * q^32 - 25 * q^33 + 5 * q^34 - 39 * q^35 + 43 * q^36 - 46 * q^37 - 48 * q^38 - 8 * q^39 - 10 * q^40 - 53 * q^41 - 28 * q^42 - 33 * q^43 - 62 * q^44 - 19 * q^45 + 2 * q^46 - 45 * q^47 + 33 * q^48 + 21 * q^49 - 60 * q^50 - 46 * q^51 - 63 * q^52 - 47 * q^53 - 5 * q^54 + 5 * q^55 - 82 * q^56 - 2 * q^57 - 21 * q^58 - 65 * q^59 - 56 * q^60 - 37 * q^61 - 46 * q^62 + q^63 + 74 * q^64 - 85 * q^65 - 19 * q^66 - 52 * q^67 - 43 * q^68 - 64 * q^69 - 20 * q^70 - 48 * q^71 - 18 * q^72 - 39 * q^73 - 16 * q^74 + 11 * q^75 + 42 * q^76 - 78 * q^77 - 13 * q^78 - 26 * q^79 - 78 * q^80 + 46 * q^81 + 3 * q^82 - 47 * q^83 - 38 * q^84 + 19 * q^85 - 6 * q^86 - 51 * q^87 - 58 * q^88 - 58 * q^89 - 10 * q^90 - 43 * q^91 - 68 * q^92 - 19 * q^93 - 78 * q^95 - 61 * q^96 - 44 * q^97 - 4 * q^98 - 25 * q^99

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