LMFDB - Embedded newform 8007.2.a.f.1.2

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:	$48$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
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)

$f(q)$	$=$	$q-2.66751 q^{2} -1.00000 q^{3} +5.11563 q^{4} -0.759881 q^{5} +2.66751 q^{6} -3.14723 q^{7} -8.31098 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.66751 q^{2} -1.00000 q^{3} +5.11563 q^{4} -0.759881 q^{5} +2.66751 q^{6} -3.14723 q^{7} -8.31098 q^{8} +1.00000 q^{9} +2.02699 q^{10} +2.82913 q^{11} -5.11563 q^{12} -3.24759 q^{13} +8.39529 q^{14} +0.759881 q^{15} +11.9384 q^{16} -1.00000 q^{17} -2.66751 q^{18} +6.68456 q^{19} -3.88727 q^{20} +3.14723 q^{21} -7.54675 q^{22} +3.37760 q^{23} +8.31098 q^{24} -4.42258 q^{25} +8.66298 q^{26} -1.00000 q^{27} -16.1001 q^{28} +3.85637 q^{29} -2.02699 q^{30} +2.88443 q^{31} -15.2239 q^{32} -2.82913 q^{33} +2.66751 q^{34} +2.39153 q^{35} +5.11563 q^{36} -4.84157 q^{37} -17.8312 q^{38} +3.24759 q^{39} +6.31536 q^{40} -2.20878 q^{41} -8.39529 q^{42} -7.84352 q^{43} +14.4728 q^{44} -0.759881 q^{45} -9.00979 q^{46} -8.89782 q^{47} -11.9384 q^{48} +2.90509 q^{49} +11.7973 q^{50} +1.00000 q^{51} -16.6134 q^{52} +6.46681 q^{53} +2.66751 q^{54} -2.14981 q^{55} +26.1566 q^{56} -6.68456 q^{57} -10.2869 q^{58} -2.68202 q^{59} +3.88727 q^{60} +0.513119 q^{61} -7.69425 q^{62} -3.14723 q^{63} +16.7331 q^{64} +2.46778 q^{65} +7.54675 q^{66} +0.811036 q^{67} -5.11563 q^{68} -3.37760 q^{69} -6.37943 q^{70} -2.81349 q^{71} -8.31098 q^{72} +9.87519 q^{73} +12.9149 q^{74} +4.42258 q^{75} +34.1957 q^{76} -8.90395 q^{77} -8.66298 q^{78} -11.0802 q^{79} -9.07177 q^{80} +1.00000 q^{81} +5.89195 q^{82} -2.15464 q^{83} +16.1001 q^{84} +0.759881 q^{85} +20.9227 q^{86} -3.85637 q^{87} -23.5129 q^{88} +1.54344 q^{89} +2.02699 q^{90} +10.2209 q^{91} +17.2785 q^{92} -2.88443 q^{93} +23.7350 q^{94} -5.07947 q^{95} +15.2239 q^{96} -1.93782 q^{97} -7.74936 q^{98} +2.82913 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - q^{2} - 48 q^{3} + 45 q^{4} + q^{5} + q^{6} - 13 q^{7} - 6 q^{8} + 48 q^{9}+O(q^{10}) $ 48 * q - q^2 - 48 * q^3 + 45 * q^4 + q^5 + q^6 - 13 * q^7 - 6 * q^8 + 48 * q^9	\( 48 q - q^{2} - 48 q^{3} + 45 q^{4} + q^{5} + q^{6} - 13 q^{7} - 6 q^{8} + 48 q^{9} - 20 q^{10} + 5 q^{11} - 45 q^{12} - 8 q^{13} + 4 q^{14} - q^{15} + 39 q^{16} - 48 q^{17} - q^{18} - 6 q^{19} + 6 q^{20} + 13 q^{21} - 35 q^{22} - 8 q^{23} + 6 q^{24} + 13 q^{25} + 17 q^{26} - 48 q^{27} - 38 q^{28} + q^{29} + 20 q^{30} - 21 q^{31} - 3 q^{32} - 5 q^{33} + q^{34} + 19 q^{35} + 45 q^{36} - 58 q^{37} - 14 q^{38} + 8 q^{39} - 54 q^{40} - 3 q^{41} - 4 q^{42} - 33 q^{43} + 2 q^{44} + q^{45} - 26 q^{46} + 9 q^{47} - 39 q^{48} + 11 q^{49} + 4 q^{50} + 48 q^{51} - 31 q^{52} - 33 q^{53} + q^{54} - 21 q^{55} + 6 q^{57} - 55 q^{58} + 77 q^{59} - 6 q^{60} - 29 q^{61} - 46 q^{62} - 13 q^{63} + 24 q^{64} - 49 q^{65} + 35 q^{66} - 44 q^{67} - 45 q^{68} + 8 q^{69} + 4 q^{70} + 22 q^{71} - 6 q^{72} - 63 q^{73} - 16 q^{74} - 13 q^{75} - 46 q^{76} - 30 q^{77} - 17 q^{78} - 46 q^{79} - 14 q^{80} + 48 q^{81} - 75 q^{82} + 11 q^{83} + 38 q^{84} - q^{85} + 8 q^{86} - q^{87} - 116 q^{88} + 10 q^{89} - 20 q^{90} - 67 q^{91} - 64 q^{92} + 21 q^{93} - 16 q^{94} - 8 q^{95} + 3 q^{96} - 96 q^{97} - 46 q^{98} + 5 q^{99}+O(q^{100}) \) 48 * q - q^2 - 48 * q^3 + 45 * q^4 + q^5 + q^6 - 13 * q^7 - 6 * q^8 + 48 * q^9 - 20 * q^10 + 5 * q^11 - 45 * q^12 - 8 * q^13 + 4 * q^14 - q^15 + 39 * q^16 - 48 * q^17 - q^18 - 6 * q^19 + 6 * q^20 + 13 * q^21 - 35 * q^22 - 8 * q^23 + 6 * q^24 + 13 * q^25 + 17 * q^26 - 48 * q^27 - 38 * q^28 + q^29 + 20 * q^30 - 21 * q^31 - 3 * q^32 - 5 * q^33 + q^34 + 19 * q^35 + 45 * q^36 - 58 * q^37 - 14 * q^38 + 8 * q^39 - 54 * q^40 - 3 * q^41 - 4 * q^42 - 33 * q^43 + 2 * q^44 + q^45 - 26 * q^46 + 9 * q^47 - 39 * q^48 + 11 * q^49 + 4 * q^50 + 48 * q^51 - 31 * q^52 - 33 * q^53 + q^54 - 21 * q^55 + 6 * q^57 - 55 * q^58 + 77 * q^59 - 6 * q^60 - 29 * q^61 - 46 * q^62 - 13 * q^63 + 24 * q^64 - 49 * q^65 + 35 * q^66 - 44 * q^67 - 45 * q^68 + 8 * q^69 + 4 * q^70 + 22 * q^71 - 6 * q^72 - 63 * q^73 - 16 * q^74 - 13 * q^75 - 46 * q^76 - 30 * q^77 - 17 * q^78 - 46 * q^79 - 14 * q^80 + 48 * q^81 - 75 * q^82 + 11 * q^83 + 38 * q^84 - q^85 + 8 * q^86 - q^87 - 116 * q^88 + 10 * q^89 - 20 * q^90 - 67 * q^91 - 64 * q^92 + 21 * q^93 - 16 * q^94 - 8 * q^95 + 3 * q^96 - 96 * q^97 - 46 * q^98 + 5 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.66751	−1.88622	−0.943108	−	0.332485i	$-0.892113\pi$
$2$	−2.66751	−1.88622	−0.943108	+	0.332485i	$0.892113\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.11563	2.55781
$5$	−0.759881	−0.339829	−0.169915	−	0.985459i	$-0.554349\pi$
$5$	−0.759881	−0.339829	−0.169915	+	0.985459i	$0.554349\pi$
$6$	2.66751	1.08901
$7$	−3.14723	−1.18954	−0.594771	−	0.803895i	$-0.702757\pi$
$7$	−3.14723	−1.18954	−0.594771	+	0.803895i	$0.702757\pi$
$8$	−8.31098	−2.93838
$9$	1.00000	0.333333
$10$	2.02699	0.640992
$11$	2.82913	0.853016	0.426508	−	0.904484i	$-0.359744\pi$
$11$	2.82913	0.853016	0.426508	+	0.904484i	$0.359744\pi$
$12$	−5.11563	−1.47675
$13$	−3.24759	−0.900718	−0.450359	−	0.892848i	$-0.648704\pi$
$13$	−3.24759	−0.900718	−0.450359	+	0.892848i	$0.648704\pi$
$14$	8.39529	2.24374
$15$	0.759881	0.196201
$16$	11.9384	2.98460
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−2.66751	−0.628739
$19$	6.68456	1.53354	0.766772	−	0.641920i	$-0.221862\pi$
$19$	6.68456	1.53354	0.766772	+	0.641920i	$0.221862\pi$
$20$	−3.88727	−0.869220
$21$	3.14723	0.686783
$22$	−7.54675	−1.60897
$23$	3.37760	0.704278	0.352139	−	0.935948i	$-0.385454\pi$
$23$	3.37760	0.704278	0.352139	+	0.935948i	$0.385454\pi$
$24$	8.31098	1.69647
$25$	−4.42258	−0.884516
$26$	8.66298	1.69895
$27$	−1.00000	−0.192450
$28$	−16.1001	−3.04263
$29$	3.85637	0.716109	0.358055	−	0.933701i	$-0.383440\pi$
$29$	3.85637	0.716109	0.358055	+	0.933701i	$0.383440\pi$
$30$	−2.02699	−0.370077
$31$	2.88443	0.518058	0.259029	−	0.965870i	$-0.416597\pi$
$31$	2.88443	0.518058	0.259029	+	0.965870i	$0.416597\pi$
$32$	−15.2239	−2.69123
$33$	−2.82913	−0.492489
$34$	2.66751	0.457475
$35$	2.39153	0.404242
$36$	5.11563	0.852605
$37$	−4.84157	−0.795949	−0.397974	−	0.917397i	$-0.630287\pi$
$37$	−4.84157	−0.795949	−0.397974	+	0.917397i	$0.630287\pi$
$38$	−17.8312	−2.89260
$39$	3.24759	0.520030
$40$	6.31536	0.998546
$41$	−2.20878	−0.344954	−0.172477	−	0.985014i	$-0.555177\pi$
$41$	−2.20878	−0.344954	−0.172477	+	0.985014i	$0.555177\pi$
$42$	−8.39529	−1.29542
$43$	−7.84352	−1.19612	−0.598062	−	0.801450i	$-0.704063\pi$
$43$	−7.84352	−1.19612	−0.598062	+	0.801450i	$0.704063\pi$
$44$	14.4728	2.18186
$45$	−0.759881	−0.113276
$46$	−9.00979	−1.32842
$47$	−8.89782	−1.29788	−0.648940	−	0.760840i	$-0.724787\pi$
$47$	−8.89782	−1.29788	−0.648940	+	0.760840i	$0.724787\pi$
$48$	−11.9384	−1.72316
$49$	2.90509	0.415013
$50$	11.7973	1.66839
$51$	1.00000	0.140028
$52$	−16.6134	−2.30387
$53$	6.46681	0.888284	0.444142	−	0.895956i	$-0.353508\pi$
$53$	6.46681	0.888284	0.444142	+	0.895956i	$0.353508\pi$
$54$	2.66751	0.363003
$55$	−2.14981	−0.289880
$56$	26.1566	3.49532
$57$	−6.68456	−0.885392
$58$	−10.2869	−1.35074
$59$	−2.68202	−0.349169	−0.174585	−	0.984642i	$-0.555858\pi$
$59$	−2.68202	−0.349169	−0.174585	+	0.984642i	$0.555858\pi$
$60$	3.88727	0.501844
$61$	0.513119	0.0656981	0.0328491	−	0.999460i	$-0.489542\pi$
$61$	0.513119	0.0656981	0.0328491	+	0.999460i	$0.489542\pi$
$62$	−7.69425	−0.977170
$63$	−3.14723	−0.396514
$64$	16.7331	2.09164
$65$	2.46778	0.306090
$66$	7.54675	0.928941
$67$	0.811036	0.0990839	0.0495419	−	0.998772i	$-0.484224\pi$
$67$	0.811036	0.0990839	0.0495419	+	0.998772i	$0.484224\pi$
$68$	−5.11563	−0.620361
$69$	−3.37760	−0.406615
$70$	−6.37943	−0.762487
$71$	−2.81349	−0.333900	−0.166950	−	0.985965i	$-0.553392\pi$
$71$	−2.81349	−0.333900	−0.166950	+	0.985965i	$0.553392\pi$
$72$	−8.31098	−0.979458
$73$	9.87519	1.15580	0.577902	−	0.816106i	$-0.303872\pi$
$73$	9.87519	1.15580	0.577902	+	0.816106i	$0.303872\pi$
$74$	12.9149	1.50133
$75$	4.42258	0.510676
$76$	34.1957	3.92252
$77$	−8.90395	−1.01470
$78$	−8.66298	−0.980889
$79$	−11.0802	−1.24662	−0.623310	−	0.781975i	$-0.714213\pi$
$79$	−11.0802	−1.24662	−0.623310	+	0.781975i	$0.714213\pi$
$80$	−9.07177	−1.01425
$81$	1.00000	0.111111
$82$	5.89195	0.650657
$83$	−2.15464	−0.236503	−0.118251	−	0.992984i	$-0.537729\pi$
$83$	−2.15464	−0.236503	−0.118251	+	0.992984i	$0.537729\pi$
$84$	16.1001	1.75666
$85$	0.759881	0.0824207
$86$	20.9227	2.25615
$87$	−3.85637	−0.413446
$88$	−23.5129	−2.50648
$89$	1.54344	0.163604	0.0818019	−	0.996649i	$-0.473933\pi$
$89$	1.54344	0.163604	0.0818019	+	0.996649i	$0.473933\pi$
$90$	2.02699	0.213664
$91$	10.2209	1.07144
$92$	17.2785	1.80141
$93$	−2.88443	−0.299101
$94$	23.7350	2.44808
$95$	−5.07947	−0.521143
$96$	15.2239	1.55378
$97$	−1.93782	−0.196756	−0.0983778	−	0.995149i	$-0.531365\pi$
$97$	−1.93782	−0.196756	−0.0983778	+	0.995149i	$0.531365\pi$
$98$	−7.74936	−0.782804
$99$	2.82913	0.284339
$100$	−22.6243	−2.26243
$101$	12.3656	1.23042	0.615212	−	0.788361i	$-0.289070\pi$
$101$	12.3656	1.23042	0.615212	+	0.788361i	$0.289070\pi$
$102$	−2.66751	−0.264123
$103$	2.43192	0.239624	0.119812	−	0.992797i	$-0.461771\pi$
$103$	2.43192	0.239624	0.119812	+	0.992797i	$0.461771\pi$
$104$	26.9906	2.64665
$105$	−2.39153	−0.233389
$106$	−17.2503	−1.67550
$107$	15.3997	1.48874	0.744370	−	0.667767i	$-0.232750\pi$
$107$	15.3997	1.48874	0.744370	+	0.667767i	$0.232750\pi$
$108$	−5.11563	−0.492252
$109$	−6.96117	−0.666759	−0.333380	−	0.942793i	$-0.608189\pi$
$109$	−6.96117	−0.666759	−0.333380	+	0.942793i	$0.608189\pi$
$110$	5.73464	0.546776
$111$	4.84157	0.459541
$112$	−37.5729	−3.55031
$113$	13.1260	1.23479	0.617393	−	0.786655i	$-0.288189\pi$
$113$	13.1260	1.23479	0.617393	+	0.786655i	$0.288189\pi$
$114$	17.8312	1.67004
$115$	−2.56657	−0.239334
$116$	19.7277	1.83167
$117$	−3.24759	−0.300239
$118$	7.15432	0.658609
$119$	3.14723	0.288507
$120$	−6.31536	−0.576511
$121$	−2.99600	−0.272364
$122$	−1.36875	−0.123921
$123$	2.20878	0.199159
$124$	14.7557	1.32510
$125$	7.16004	0.640414
$126$	8.39529	0.747912
$127$	−2.80815	−0.249183	−0.124591	−	0.992208i	$-0.539762\pi$
$127$	−2.80815	−0.249183	−0.124591	+	0.992208i	$0.539762\pi$
$128$	−14.1880	−1.25405
$129$	7.84352	0.690583
$130$	−6.58284	−0.577353
$131$	−7.57495	−0.661826	−0.330913	−	0.943661i	$-0.607357\pi$
$131$	−7.57495	−0.661826	−0.330913	+	0.943661i	$0.607357\pi$
$132$	−14.4728	−1.25970
$133$	−21.0379	−1.82422
$134$	−2.16345	−0.186894
$135$	0.759881	0.0654002
$136$	8.31098	0.712661
$137$	14.2870	1.22062	0.610311	−	0.792162i	$-0.291045\pi$
$137$	14.2870	1.22062	0.610311	+	0.792162i	$0.291045\pi$
$138$	9.00979	0.766964
$139$	−9.78869	−0.830266	−0.415133	−	0.909761i	$-0.636265\pi$
$139$	−9.78869	−0.830266	−0.415133	+	0.909761i	$0.636265\pi$
$140$	12.2342	1.03397
$141$	8.89782	0.749331
$142$	7.50503	0.629808
$143$	−9.18785	−0.768327
$144$	11.9384	0.994866
$145$	−2.93038	−0.243355
$146$	−26.3422	−2.18010
$147$	−2.90509	−0.239608
$148$	−24.7677	−2.03589
$149$	19.6890	1.61299	0.806495	−	0.591241i	$-0.201362\pi$
$149$	19.6890	1.61299	0.806495	+	0.591241i	$0.201362\pi$
$150$	−11.7973	−0.963245
$151$	17.7580	1.44513	0.722564	−	0.691304i	$-0.242964\pi$
$151$	17.7580	1.44513	0.722564	+	0.691304i	$0.242964\pi$
$152$	−55.5553	−4.50613
$153$	−1.00000	−0.0808452
$154$	23.7514	1.91394
$155$	−2.19182	−0.176051
$156$	16.6134	1.33014
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	29.5566	2.35140
$159$	−6.46681	−0.512851
$160$	11.5683	0.914557
$161$	−10.6301	−0.837769
$162$	−2.66751	−0.209580
$163$	−5.38266	−0.421602	−0.210801	−	0.977529i	$-0.567607\pi$
$163$	−5.38266	−0.421602	−0.210801	+	0.977529i	$0.567607\pi$
$164$	−11.2993	−0.882327
$165$	2.14981	0.167362
$166$	5.74754	0.446096
$167$	7.00409	0.541993	0.270997	−	0.962580i	$-0.412647\pi$
$167$	7.00409	0.541993	0.270997	+	0.962580i	$0.412647\pi$
$168$	−26.1566	−2.01803
$169$	−2.45319	−0.188707
$170$	−2.02699	−0.155463
$171$	6.68456	0.511181
$172$	−40.1245	−3.05947
$173$	15.4732	1.17640	0.588202	−	0.808714i	$-0.299836\pi$
$173$	15.4732	1.17640	0.588202	+	0.808714i	$0.299836\pi$
$174$	10.2869	0.779848
$175$	13.9189	1.05217
$176$	33.7753	2.54591
$177$	2.68202	0.201593
$178$	−4.11714	−0.308592
$179$	−4.49026	−0.335618	−0.167809	−	0.985820i	$-0.553669\pi$
$179$	−4.49026	−0.335618	−0.167809	+	0.985820i	$0.553669\pi$
$180$	−3.88727	−0.289740
$181$	−12.5814	−0.935165	−0.467583	−	0.883949i	$-0.654875\pi$
$181$	−12.5814	−0.935165	−0.467583	+	0.883949i	$0.654875\pi$
$182$	−27.2644	−2.02097
$183$	−0.513119	−0.0379308
$184$	−28.0711	−2.06943
$185$	3.67902	0.270487
$186$	7.69425	0.564169
$187$	−2.82913	−0.206887
$188$	−45.5179	−3.31974
$189$	3.14723	0.228928
$190$	13.5496	0.982989
$191$	10.5539	0.763653	0.381826	−	0.924234i	$-0.375295\pi$
$191$	10.5539	0.763653	0.381826	+	0.924234i	$0.375295\pi$
$192$	−16.7331	−1.20761
$193$	−6.12973	−0.441228	−0.220614	−	0.975361i	$-0.570806\pi$
$193$	−6.12973	−0.441228	−0.220614	+	0.975361i	$0.570806\pi$
$194$	5.16915	0.371124
$195$	−2.46778	−0.176721
$196$	14.8613	1.06152
$197$	−0.641410	−0.0456985	−0.0228493	−	0.999739i	$-0.507274\pi$
$197$	−0.641410	−0.0456985	−0.0228493	+	0.999739i	$0.507274\pi$
$198$	−7.54675	−0.536324
$199$	0.0117886	0.000835670 0	0.000417835	−	1.00000i	$-0.499867\pi$
$199$	0.0117886	0.000835670 0	0.000417835		1.00000i	$0.499867\pi$
$200$	36.7560	2.59904
$201$	−0.811036	−0.0572061
$202$	−32.9854	−2.32085
$203$	−12.1369	−0.851843
$204$	5.11563	0.358166
$205$	1.67841	0.117225
$206$	−6.48718	−0.451983
$207$	3.37760	0.234759
$208$	−38.7710	−2.68828
$209$	18.9115	1.30814
$210$	6.37943	0.440222
$211$	−15.8802	−1.09324	−0.546618	−	0.837382i	$-0.684085\pi$
$211$	−15.8802	−1.09324	−0.546618	+	0.837382i	$0.684085\pi$
$212$	33.0818	2.27207
$213$	2.81349	0.192777
$214$	−41.0788	−2.80809
$215$	5.96014	0.406478
$216$	8.31098	0.565491
$217$	−9.07797	−0.616253
$218$	18.5690	1.25765
$219$	−9.87519	−0.667303
$220$	−10.9976	−0.741459
$221$	3.24759	0.218456
$222$	−12.9149	−0.866794
$223$	5.26595	0.352634	0.176317	−	0.984333i	$-0.443582\pi$
$223$	5.26595	0.352634	0.176317	+	0.984333i	$0.443582\pi$
$224$	47.9131	3.20133
$225$	−4.42258	−0.294839
$226$	−35.0137	−2.32908
$227$	1.83842	0.122021	0.0610103	−	0.998137i	$-0.480568\pi$
$227$	1.83842	0.122021	0.0610103	+	0.998137i	$0.480568\pi$
$228$	−34.1957	−2.26467
$229$	6.83685	0.451792	0.225896	−	0.974151i	$-0.427469\pi$
$229$	6.83685	0.451792	0.225896	+	0.974151i	$0.427469\pi$
$230$	6.84637	0.451436
$231$	8.90395	0.585837
$232$	−32.0502	−2.10420
$233$	8.06025	0.528044	0.264022	−	0.964517i	$-0.414951\pi$
$233$	8.06025	0.528044	0.264022	+	0.964517i	$0.414951\pi$
$234$	8.66298	0.566317
$235$	6.76129	0.441058
$236$	−13.7202	−0.893110
$237$	11.0802	0.719737
$238$	−8.39529	−0.544186
$239$	−12.4804	−0.807292	−0.403646	−	0.914915i	$-0.632257\pi$
$239$	−12.4804	−0.807292	−0.403646	+	0.914915i	$0.632257\pi$
$240$	9.07177	0.585580
$241$	−0.772995	−0.0497930	−0.0248965	−	0.999690i	$-0.507926\pi$
$241$	−0.772995	−0.0497930	−0.0248965	+	0.999690i	$0.507926\pi$
$242$	7.99188	0.513738
$243$	−1.00000	−0.0641500
$244$	2.62492	0.168044
$245$	−2.20752	−0.141033
$246$	−5.89195	−0.375657
$247$	−21.7087	−1.38129
$248$	−23.9724	−1.52225
$249$	2.15464	0.136545
$250$	−19.0995	−1.20796
$251$	5.60340	0.353684	0.176842	−	0.984239i	$-0.443412\pi$
$251$	5.60340	0.353684	0.176842	+	0.984239i	$0.443412\pi$
$252$	−16.1001	−1.01421
$253$	9.55567	0.600760
$254$	7.49077	0.470013
$255$	−0.759881	−0.0475856
$256$	4.38052	0.273782
$257$	−12.4898	−0.779093	−0.389546	−	0.921007i	$-0.627368\pi$
$257$	−12.4898	−0.779093	−0.389546	+	0.921007i	$0.627368\pi$
$258$	−20.9227	−1.30259
$259$	15.2375	0.946815
$260$	12.6242	0.782922
$261$	3.85637	0.238703
$262$	20.2063	1.24835
$263$	−24.6807	−1.52188	−0.760939	−	0.648824i	$-0.775261\pi$
$263$	−24.6807	−1.52188	−0.760939	+	0.648824i	$0.775261\pi$
$264$	23.5129	1.44712
$265$	−4.91401	−0.301865
$266$	56.1188	3.44087
$267$	−1.54344	−0.0944567
$268$	4.14896	0.253438
$269$	−22.8330	−1.39215	−0.696077	−	0.717967i	$-0.745073\pi$
$269$	−22.8330	−1.39215	−0.696077	+	0.717967i	$0.745073\pi$
$270$	−2.02699	−0.123359
$271$	32.3091	1.96264	0.981318	−	0.192393i	$-0.0616249\pi$
$271$	32.3091	1.96264	0.981318	+	0.192393i	$0.0616249\pi$
$272$	−11.9384	−0.723872
$273$	−10.2209	−0.618598
$274$	−38.1108	−2.30236
$275$	−12.5121	−0.754506
$276$	−17.2785	−1.04005
$277$	−6.19453	−0.372193	−0.186096	−	0.982531i	$-0.559584\pi$
$277$	−6.19453	−0.372193	−0.186096	+	0.982531i	$0.559584\pi$
$278$	26.1115	1.56606
$279$	2.88443	0.172686
$280$	−19.8759	−1.18781
$281$	−9.37561	−0.559302	−0.279651	−	0.960102i	$-0.590219\pi$
$281$	−9.37561	−0.559302	−0.279651	+	0.960102i	$0.590219\pi$
$282$	−23.7350	−1.41340
$283$	−4.59361	−0.273062	−0.136531	−	0.990636i	$-0.543595\pi$
$283$	−4.59361	−0.273062	−0.136531	+	0.990636i	$0.543595\pi$
$284$	−14.3928	−0.854055
$285$	5.07947	0.300882
$286$	24.5087	1.44923
$287$	6.95155	0.410337
$288$	−15.2239	−0.897075
$289$	1.00000	0.0588235
$290$	7.81683	0.459020
$291$	1.93782	0.113597
$292$	50.5178	2.95633
$293$	12.3861	0.723605	0.361802	−	0.932255i	$-0.382162\pi$
$293$	12.3861	0.723605	0.361802	+	0.932255i	$0.382162\pi$
$294$	7.74936	0.451952
$295$	2.03802	0.118658
$296$	40.2382	2.33880
$297$	−2.82913	−0.164163
$298$	−52.5208	−3.04245
$299$	−10.9690	−0.634356
$300$	22.6243	1.30621
$301$	24.6854	1.42284
$302$	−47.3698	−2.72582
$303$	−12.3656	−0.710386
$304$	79.8029	4.57701
$305$	−0.389909	−0.0223261
$306$	2.66751	0.152492
$307$	−5.33559	−0.304518	−0.152259	−	0.988341i	$-0.548655\pi$
$307$	−5.33559	−0.304518	−0.152259	+	0.988341i	$0.548655\pi$
$308$	−45.5493	−2.59541
$309$	−2.43192	−0.138347
$310$	5.84671	0.332071
$311$	12.3195	0.698576	0.349288	−	0.937015i	$-0.386424\pi$
$311$	12.3195	0.698576	0.349288	+	0.937015i	$0.386424\pi$
$312$	−26.9906	−1.52804
$313$	22.9268	1.29590	0.647948	−	0.761684i	$-0.275627\pi$
$313$	22.9268	1.29590	0.647948	+	0.761684i	$0.275627\pi$
$314$	2.66751	0.150536
$315$	2.39153	0.134747
$316$	−56.6822	−3.18862
$317$	−9.94107	−0.558346	−0.279173	−	0.960241i	$-0.590060\pi$
$317$	−9.94107	−0.558346	−0.279173	+	0.960241i	$0.590060\pi$
$318$	17.2503	0.967349
$319$	10.9102	0.610852
$320$	−12.7152	−0.710799
$321$	−15.3997	−0.859525
$322$	28.3559	1.58021
$323$	−6.68456	−0.371939
$324$	5.11563	0.284202
$325$	14.3627	0.796700
$326$	14.3583	0.795233
$327$	6.96117	0.384954
$328$	18.3571	1.01360
$329$	28.0035	1.54388
$330$	−5.73464	−0.315681
$331$	−6.48028	−0.356188	−0.178094	−	0.984013i	$-0.556993\pi$
$331$	−6.48028	−0.356188	−0.178094	+	0.984013i	$0.556993\pi$
$332$	−11.0224	−0.604930
$333$	−4.84157	−0.265316
$334$	−18.6835	−1.02232
$335$	−0.616291	−0.0336716
$336$	37.5729	2.04977
$337$	28.1226	1.53194	0.765968	−	0.642878i	$-0.222260\pi$
$337$	28.1226	1.53194	0.765968	+	0.642878i	$0.222260\pi$
$338$	6.54392	0.355942
$339$	−13.1260	−0.712904
$340$	3.88727	0.210817
$341$	8.16043	0.441912
$342$	−17.8312	−0.964198
$343$	12.8877	0.695868
$344$	65.1873	3.51466
$345$	2.56657	0.138180
$346$	−41.2749	−2.21895
$347$	8.85764	0.475503	0.237751	−	0.971326i	$-0.423590\pi$
$347$	8.85764	0.475503	0.237751	+	0.971326i	$0.423590\pi$
$348$	−19.7277	−1.05752
$349$	−35.0088	−1.87398	−0.936988	−	0.349361i	$-0.886399\pi$
$349$	−35.0088	−1.87398	−0.936988	+	0.349361i	$0.886399\pi$
$350$	−37.1289	−1.98462
$351$	3.24759	0.173343
$352$	−43.0704	−2.29566
$353$	−14.7136	−0.783127	−0.391564	−	0.920151i	$-0.628066\pi$
$353$	−14.7136	−0.783127	−0.391564	+	0.920151i	$0.628066\pi$
$354$	−7.15432	−0.380248
$355$	2.13792	0.113469
$356$	7.89564	0.418468
$357$	−3.14723	−0.166569
$358$	11.9778	0.633048
$359$	24.9632	1.31751	0.658754	−	0.752358i	$-0.271084\pi$
$359$	24.9632	1.31751	0.658754	+	0.752358i	$0.271084\pi$
$360$	6.31536	0.332849
$361$	25.6833	1.35176
$362$	33.5610	1.76392
$363$	2.99600	0.157249
$364$	52.2864	2.74055
$365$	−7.50397	−0.392776
$366$	1.36875	0.0715458
$367$	−4.99446	−0.260709	−0.130354	−	0.991467i	$-0.541612\pi$
$367$	−4.99446	−0.260709	−0.130354	+	0.991467i	$0.541612\pi$
$368$	40.3231	2.10199
$369$	−2.20878	−0.114985
$370$	−9.81382	−0.510196
$371$	−20.3526	−1.05665
$372$	−14.7557	−0.765045
$373$	34.4089	1.78162	0.890812	−	0.454372i	$-0.150136\pi$
$373$	34.4089	1.78162	0.890812	+	0.454372i	$0.150136\pi$
$374$	7.54675	0.390233
$375$	−7.16004	−0.369743
$376$	73.9496	3.81366
$377$	−12.5239	−0.645012
$378$	−8.39529	−0.431807
$379$	−24.9110	−1.27959	−0.639796	−	0.768545i	$-0.720981\pi$
$379$	−24.9110	−1.27959	−0.639796	+	0.768545i	$0.720981\pi$
$380$	−25.9847	−1.33299
$381$	2.80815	0.143866
$382$	−28.1527	−1.44041
$383$	−21.9404	−1.12110	−0.560551	−	0.828120i	$-0.689411\pi$
$383$	−21.9404	−1.12110	−0.560551	+	0.828120i	$0.689411\pi$
$384$	14.1880	0.724029
$385$	6.76594	0.344824
$386$	16.3511	0.832251
$387$	−7.84352	−0.398708
$388$	−9.91315	−0.503264
$389$	−29.5598	−1.49874	−0.749370	−	0.662152i	$-0.769643\pi$
$389$	−29.5598	−1.49874	−0.749370	+	0.662152i	$0.769643\pi$
$390$	6.58284	0.333335
$391$	−3.37760	−0.170812
$392$	−24.1441	−1.21946
$393$	7.57495	0.382105
$394$	1.71097	0.0861974
$395$	8.41964	0.423638
$396$	14.4728	0.727285
$397$	13.6910	0.687132	0.343566	−	0.939128i	$-0.388365\pi$
$397$	13.6910	0.687132	0.343566	+	0.939128i	$0.388365\pi$
$398$	−0.0314462	−0.00157626
$399$	21.0379	1.05321
$400$	−52.7985	−2.63993
$401$	−12.4462	−0.621535	−0.310767	−	0.950486i	$-0.600586\pi$
$401$	−12.4462	−0.621535	−0.310767	+	0.950486i	$0.600586\pi$
$402$	2.16345	0.107903
$403$	−9.36742	−0.466624
$404$	63.2579	3.14720
$405$	−0.759881	−0.0377588
$406$	32.3753	1.60676
$407$	−13.6974	−0.678957
$408$	−8.31098	−0.411455
$409$	−6.29135	−0.311087	−0.155544	−	0.987829i	$-0.549713\pi$
$409$	−6.29135	−0.311087	−0.155544	+	0.987829i	$0.549713\pi$
$410$	−4.47718	−0.221112
$411$	−14.2870	−0.704726
$412$	12.4408	0.612914
$413$	8.44094	0.415352
$414$	−9.00979	−0.442807
$415$	1.63727	0.0803706
$416$	49.4408	2.42404
$417$	9.78869	0.479354
$418$	−50.4467	−2.46743
$419$	17.2067	0.840602	0.420301	−	0.907385i	$-0.361925\pi$
$419$	17.2067	0.840602	0.420301	+	0.907385i	$0.361925\pi$
$420$	−12.2342	−0.596966
$421$	−0.690778	−0.0336664	−0.0168332	−	0.999858i	$-0.505358\pi$
$421$	−0.690778	−0.0336664	−0.0168332	+	0.999858i	$0.505358\pi$
$422$	42.3606	2.06208
$423$	−8.89782	−0.432627
$424$	−53.7455	−2.61011
$425$	4.42258	0.214527
$426$	−7.50503	−0.363620
$427$	−1.61491	−0.0781507
$428$	78.7789	3.80792
$429$	9.18785	0.443594
$430$	−15.8988	−0.766706
$431$	38.5781	1.85824	0.929120	−	0.369778i	$-0.120566\pi$
$431$	38.5781	1.85824	0.929120	+	0.369778i	$0.120566\pi$
$432$	−11.9384	−0.574386
$433$	13.0955	0.629328	0.314664	−	0.949203i	$-0.398108\pi$
$433$	13.0955	0.629328	0.314664	+	0.949203i	$0.398108\pi$
$434$	24.2156	1.16239
$435$	2.93038	0.140501
$436$	−35.6108	−1.70545
$437$	22.5778	1.08004
$438$	26.3422	1.25868
$439$	13.1677	0.628459	0.314230	−	0.949347i	$-0.398254\pi$
$439$	13.1677	0.628459	0.314230	+	0.949347i	$0.398254\pi$
$440$	17.8670	0.851776
$441$	2.90509	0.138338
$442$	−8.66298	−0.412056
$443$	−4.89848	−0.232734	−0.116367	−	0.993206i	$-0.537125\pi$
$443$	−4.89848	−0.232734	−0.116367	+	0.993206i	$0.537125\pi$
$444$	24.7677	1.17542
$445$	−1.17283	−0.0555974
$446$	−14.0470	−0.665145
$447$	−19.6890	−0.931260
$448$	−52.6630	−2.48809
$449$	−23.1431	−1.09219	−0.546095	−	0.837723i	$-0.683886\pi$
$449$	−23.1431	−1.09219	−0.546095	+	0.837723i	$0.683886\pi$
$450$	11.7973	0.556130
$451$	−6.24893	−0.294251
$452$	67.1475	3.15835
$453$	−17.7580	−0.834345
$454$	−4.90402	−0.230157
$455$	−7.76668	−0.364108
$456$	55.5553	2.60161
$457$	−25.7840	−1.20612	−0.603062	−	0.797694i	$-0.706053\pi$
$457$	−25.7840	−1.20612	−0.603062	+	0.797694i	$0.706053\pi$
$458$	−18.2374	−0.852177
$459$	1.00000	0.0466760
$460$	−13.1296	−0.612172
$461$	13.4365	0.625799	0.312899	−	0.949786i	$-0.398700\pi$
$461$	13.4365	0.625799	0.312899	+	0.949786i	$0.398700\pi$
$462$	−23.7514	−1.10502
$463$	0.619263	0.0287796	0.0143898	−	0.999896i	$-0.495419\pi$
$463$	0.619263	0.0287796	0.0143898	+	0.999896i	$0.495419\pi$
$464$	46.0388	2.13730
$465$	2.19182	0.101643
$466$	−21.5008	−0.996006
$467$	24.8542	1.15011	0.575057	−	0.818113i	$-0.304980\pi$
$467$	24.8542	1.15011	0.575057	+	0.818113i	$0.304980\pi$
$468$	−16.6134	−0.767956
$469$	−2.55252	−0.117865
$470$	−18.0358	−0.831930
$471$	1.00000	0.0460776
$472$	22.2902	1.02599
$473$	−22.1903	−1.02031
$474$	−29.5566	−1.35758
$475$	−29.5630	−1.35644
$476$	16.1001	0.737946
$477$	6.46681	0.296095
$478$	33.2917	1.52273
$479$	9.89026	0.451897	0.225949	−	0.974139i	$-0.427452\pi$
$479$	9.89026	0.451897	0.225949	+	0.974139i	$0.427452\pi$
$480$	−11.5683	−0.528020
$481$	15.7234	0.716925
$482$	2.06197	0.0939203
$483$	10.6301	0.483686
$484$	−15.3264	−0.696657
$485$	1.47251	0.0668633
$486$	2.66751	0.121001
$487$	24.4457	1.10774	0.553869	−	0.832604i	$-0.313151\pi$
$487$	24.4457	1.10774	0.553869	+	0.832604i	$0.313151\pi$
$488$	−4.26452	−0.193046
$489$	5.38266	0.243412
$490$	5.88860	0.266020
$491$	−8.26575	−0.373028	−0.186514	−	0.982452i	$-0.559719\pi$
$491$	−8.26575	−0.373028	−0.186514	+	0.982452i	$0.559719\pi$
$492$	11.2993	0.509412
$493$	−3.85637	−0.173682
$494$	57.9082	2.60541
$495$	−2.14981	−0.0966266
$496$	34.4354	1.54620
$497$	8.85473	0.397189
$498$	−5.74754	−0.257553
$499$	−7.59437	−0.339971	−0.169985	−	0.985447i	$-0.554372\pi$
$499$	−7.59437	−0.339971	−0.169985	+	0.985447i	$0.554372\pi$
$500$	36.6281	1.63806
$501$	−7.00409	−0.312920
$502$	−14.9472	−0.667124
$503$	−1.76162	−0.0785466	−0.0392733	−	0.999229i	$-0.512504\pi$
$503$	−1.76162	−0.0785466	−0.0392733	+	0.999229i	$0.512504\pi$
$504$	26.1566	1.16511
$505$	−9.39640	−0.418134
$506$	−25.4899	−1.13316
$507$	2.45319	0.108950
$508$	−14.3654	−0.637363
$509$	−8.11323	−0.359613	−0.179806	−	0.983702i	$-0.557547\pi$
$509$	−8.11323	−0.359613	−0.179806	+	0.983702i	$0.557547\pi$
$510$	2.02699	0.0897568
$511$	−31.0795	−1.37488
$512$	16.6909	0.737642
$513$	−6.68456	−0.295131
$514$	33.3167	1.46954
$515$	−1.84797	−0.0814313
$516$	40.1245	1.76638
$517$	−25.1731	−1.10711
$518$	−40.6464	−1.78590
$519$	−15.4732	−0.679198
$520$	−20.5097	−0.899408
$521$	−4.52635	−0.198303	−0.0991515	−	0.995072i	$-0.531613\pi$
$521$	−4.52635	−0.198303	−0.0991515	+	0.995072i	$0.531613\pi$
$522$	−10.2869	−0.450246
$523$	−10.0719	−0.440412	−0.220206	−	0.975453i	$-0.570673\pi$
$523$	−10.0719	−0.440412	−0.220206	+	0.975453i	$0.570673\pi$
$524$	−38.7506	−1.69283
$525$	−13.9189	−0.607471
$526$	65.8361	2.87059
$527$	−2.88443	−0.125648
$528$	−33.7753	−1.46988
$529$	−11.5918	−0.503993
$530$	13.1082	0.569383
$531$	−2.68202	−0.116390
$532$	−107.622	−4.66600
$533$	7.17320	0.310706
$534$	4.11714	0.178166
$535$	−11.7019	−0.505918
$536$	−6.74051	−0.291146
$537$	4.49026	0.193769
$538$	60.9074	2.62590
$539$	8.21888	0.354012
$540$	3.88727	0.167281
$541$	9.80129	0.421390	0.210695	−	0.977552i	$-0.432427\pi$
$541$	9.80129	0.421390	0.210695	+	0.977552i	$0.432427\pi$
$542$	−86.1849	−3.70196
$543$	12.5814	0.539918
$544$	15.2239	0.652718
$545$	5.28966	0.226584
$546$	27.2644	1.16681
$547$	29.0640	1.24269	0.621344	−	0.783538i	$-0.286587\pi$
$547$	29.0640	1.24269	0.621344	+	0.783538i	$0.286587\pi$
$548$	73.0870	3.12212
$549$	0.513119	0.0218994
$550$	33.3761	1.42316
$551$	25.7781	1.09818
$552$	28.0711	1.19479
$553$	34.8720	1.48291
$554$	16.5240	0.702037
$555$	−3.67902	−0.156166
$556$	−50.0753	−2.12367
$557$	−9.33729	−0.395634	−0.197817	−	0.980239i	$-0.563385\pi$
$557$	−9.33729	−0.395634	−0.197817	+	0.980239i	$0.563385\pi$
$558$	−7.69425	−0.325723
$559$	25.4725	1.07737
$560$	28.5510	1.20650
$561$	2.82913	0.119446
$562$	25.0096	1.05497
$563$	−15.9171	−0.670826	−0.335413	−	0.942071i	$-0.608876\pi$
$563$	−15.9171	−0.670826	−0.335413	+	0.942071i	$0.608876\pi$
$564$	45.5179	1.91665
$565$	−9.97417	−0.419617
$566$	12.2535	0.515053
$567$	−3.14723	−0.132171
$568$	23.3829	0.981124
$569$	−12.6052	−0.528437	−0.264218	−	0.964463i	$-0.585114\pi$
$569$	−12.6052	−0.528437	−0.264218	+	0.964463i	$0.585114\pi$
$570$	−13.5496	−0.567529
$571$	−26.5004	−1.10901	−0.554504	−	0.832181i	$-0.687092\pi$
$571$	−26.5004	−1.10901	−0.554504	+	0.832181i	$0.687092\pi$
$572$	−47.0016	−1.96524
$573$	−10.5539	−0.440895
$574$	−18.5434	−0.773985
$575$	−14.9377	−0.622945
$576$	16.7331	0.697212
$577$	13.4575	0.560244	0.280122	−	0.959964i	$-0.409625\pi$
$577$	13.4575	0.560244	0.280122	+	0.959964i	$0.409625\pi$
$578$	−2.66751	−0.110954
$579$	6.12973	0.254743
$580$	−14.9907	−0.622456
$581$	6.78117	0.281330
$582$	−5.16915	−0.214268
$583$	18.2955	0.757721
$584$	−82.0725	−3.39618
$585$	2.46778	0.102030
$586$	−33.0401	−1.36488
$587$	−1.73388	−0.0715648	−0.0357824	−	0.999360i	$-0.511392\pi$
$587$	−1.73388	−0.0715648	−0.0357824	+	0.999360i	$0.511392\pi$
$588$	−14.8613	−0.612872
$589$	19.2811	0.794465
$590$	−5.43644	−0.223815
$591$	0.641410	0.0263841
$592$	−57.8005	−2.37559
$593$	−31.5011	−1.29360	−0.646798	−	0.762661i	$-0.723892\pi$
$593$	−31.5011	−1.29360	−0.646798	+	0.762661i	$0.723892\pi$
$594$	7.54675	0.309647
$595$	−2.39153	−0.0980430
$596$	100.722	4.12573
$597$	−0.0117886	−0.000482474 0
$598$	29.2601	1.19653
$599$	10.1964	0.416612	0.208306	−	0.978064i	$-0.433205\pi$
$599$	10.1964	0.416612	0.208306	+	0.978064i	$0.433205\pi$
$600$	−36.7560	−1.50056
$601$	−37.4615	−1.52809	−0.764043	−	0.645165i	$-0.776788\pi$
$601$	−37.4615	−1.52809	−0.764043	+	0.645165i	$0.776788\pi$
$602$	−65.8486	−2.68379
$603$	0.811036	0.0330280
$604$	90.8435	3.69637
$605$	2.27661	0.0925573
$606$	32.9854	1.33994
$607$	34.0661	1.38270	0.691351	−	0.722519i	$-0.257016\pi$
$607$	34.0661	1.38270	0.691351	+	0.722519i	$0.257016\pi$
$608$	−101.765	−4.12711
$609$	12.1369	0.491812
$610$	1.04009	0.0421120
$611$	28.8964	1.16902
$612$	−5.11563	−0.206787
$613$	13.1212	0.529962	0.264981	−	0.964254i	$-0.414634\pi$
$613$	13.1212	0.529962	0.264981	+	0.964254i	$0.414634\pi$
$614$	14.2328	0.574387
$615$	−1.67841	−0.0676801
$616$	74.0005	2.98157
$617$	24.5517	0.988415	0.494208	−	0.869344i	$-0.335458\pi$
$617$	24.5517	0.988415	0.494208	+	0.869344i	$0.335458\pi$
$618$	6.48718	0.260952
$619$	−45.6370	−1.83431	−0.917154	−	0.398534i	$-0.869519\pi$
$619$	−45.6370	−1.83431	−0.917154	+	0.398534i	$0.869519\pi$
$620$	−11.2125	−0.450307
$621$	−3.37760	−0.135538
$622$	−32.8625	−1.31767
$623$	−4.85755	−0.194614
$624$	38.7710	1.55208
$625$	16.6721	0.666885
$626$	−61.1574	−2.44434
$627$	−18.9115	−0.755253
$628$	−5.11563	−0.204136
$629$	4.84157	0.193046
$630$	−6.37943	−0.254162
$631$	−35.7625	−1.42368	−0.711841	−	0.702340i	$-0.752139\pi$
$631$	−35.7625	−1.42368	−0.711841	+	0.702340i	$0.752139\pi$
$632$	92.0874	3.66304
$633$	15.8802	0.631180
$634$	26.5179	1.05316
$635$	2.13386	0.0846796
$636$	−33.0818	−1.31178
$637$	−9.43452	−0.373809
$638$	−29.1030	−1.15220
$639$	−2.81349	−0.111300
$640$	10.7812	0.426165
$641$	−44.2584	−1.74810	−0.874051	−	0.485834i	$-0.838516\pi$
$641$	−44.2584	−1.74810	−0.874051	+	0.485834i	$0.838516\pi$
$642$	41.0788	1.62125
$643$	−1.36480	−0.0538225	−0.0269112	−	0.999638i	$-0.508567\pi$
$643$	−1.36480	−0.0538225	−0.0269112	+	0.999638i	$0.508567\pi$
$644$	−54.3796	−2.14286
$645$	−5.96014	−0.234680
$646$	17.8312	0.701557
$647$	−14.8379	−0.583340	−0.291670	−	0.956519i	$-0.594211\pi$
$647$	−14.8379	−0.583340	−0.291670	+	0.956519i	$0.594211\pi$
$648$	−8.31098	−0.326486
$649$	−7.58779	−0.297847
$650$	−38.3127	−1.50275
$651$	9.07797	0.355794
$652$	−27.5357	−1.07838
$653$	−29.1855	−1.14212	−0.571059	−	0.820909i	$-0.693467\pi$
$653$	−29.1855	−1.14212	−0.571059	+	0.820909i	$0.693467\pi$
$654$	−18.5690	−0.726106
$655$	5.75606	0.224908
$656$	−26.3693	−1.02955
$657$	9.87519	0.385268
$658$	−74.6998	−2.91210
$659$	−33.3257	−1.29819	−0.649093	−	0.760709i	$-0.724851\pi$
$659$	−33.3257	−1.29819	−0.649093	+	0.760709i	$0.724851\pi$
$660$	10.9976	0.428081
$661$	32.2325	1.25370	0.626849	−	0.779141i	$-0.284344\pi$
$661$	32.2325	1.25370	0.626849	+	0.779141i	$0.284344\pi$
$662$	17.2862	0.671848
$663$	−3.24759	−0.126126
$664$	17.9072	0.694934
$665$	15.9863	0.619922
$666$	12.9149	0.500444
$667$	13.0253	0.504340
$668$	35.8303	1.38632
$669$	−5.26595	−0.203594
$670$	1.64397	0.0635119
$671$	1.45168	0.0560415
$672$	−47.9131	−1.84829
$673$	−19.6485	−0.757394	−0.378697	−	0.925521i	$-0.623628\pi$
$673$	−19.6485	−0.757394	−0.378697	+	0.925521i	$0.623628\pi$
$674$	−75.0175	−2.88956
$675$	4.42258	0.170225
$676$	−12.5496	−0.482677
$677$	−18.9303	−0.727549	−0.363775	−	0.931487i	$-0.618512\pi$
$677$	−18.9303	−0.727549	−0.363775	+	0.931487i	$0.618512\pi$
$678$	35.0137	1.34469
$679$	6.09877	0.234049
$680$	−6.31536	−0.242183
$681$	−1.83842	−0.0704486
$682$	−21.7680	−0.833542
$683$	14.8209	0.567107	0.283554	−	0.958956i	$-0.408487\pi$
$683$	14.8209	0.567107	0.283554	+	0.958956i	$0.408487\pi$
$684$	34.1957	1.30751
$685$	−10.8564	−0.414803
$686$	−34.3780	−1.31256
$687$	−6.83685	−0.260842
$688$	−93.6390	−3.56995
$689$	−21.0015	−0.800094
$690$	−6.84637	−0.260637
$691$	−22.7929	−0.867083	−0.433542	−	0.901134i	$-0.642736\pi$
$691$	−22.7929	−0.867083	−0.433542	+	0.901134i	$0.642736\pi$
$692$	79.1551	3.00902
$693$	−8.90395	−0.338233
$694$	−23.6279	−0.896902
$695$	7.43825	0.282149
$696$	32.0502	1.21486
$697$	2.20878	0.0836635
$698$	93.3864	3.53473
$699$	−8.06025	−0.304867
$700$	71.2039	2.69126
$701$	1.59758	0.0603396	0.0301698	−	0.999545i	$-0.490395\pi$
$701$	1.59758	0.0603396	0.0301698	+	0.999545i	$0.490395\pi$
$702$	−8.66298	−0.326963
$703$	−32.3637	−1.22062
$704$	47.3402	1.78420
$705$	−6.76129	−0.254645
$706$	39.2488	1.47715
$707$	−38.9175	−1.46364
$708$	13.7202	0.515637
$709$	−46.1682	−1.73388	−0.866941	−	0.498411i	$-0.833917\pi$
$709$	−46.1682	−1.73388	−0.866941	+	0.498411i	$0.833917\pi$
$710$	−5.70293	−0.214027
$711$	−11.0802	−0.415540
$712$	−12.8275	−0.480730
$713$	9.74243	0.364857
$714$	8.39529	0.314186
$715$	6.98168	0.261100
$716$	−22.9705	−0.858448
$717$	12.4804	0.466090
$718$	−66.5897	−2.48511
$719$	10.1788	0.379605	0.189803	−	0.981822i	$-0.439215\pi$
$719$	10.1788	0.379605	0.189803	+	0.981822i	$0.439215\pi$
$720$	−9.07177	−0.338085
$721$	−7.65382	−0.285043
$722$	−68.5107	−2.54970
$723$	0.772995	0.0287480
$724$	−64.3616	−2.39198
$725$	−17.0551	−0.633410
$726$	−7.99188	−0.296607
$727$	19.1832	0.711466	0.355733	−	0.934588i	$-0.384231\pi$
$727$	19.1832	0.711466	0.355733	+	0.934588i	$0.384231\pi$
$728$	−84.9458	−3.14830
$729$	1.00000	0.0370370
$730$	20.0169	0.740861
$731$	7.84352	0.290103
$732$	−2.62492	−0.0970200
$733$	52.3403	1.93323	0.966617	−	0.256225i	$-0.0824789\pi$
$733$	52.3403	1.93323	0.966617	+	0.256225i	$0.0824789\pi$
$734$	13.3228	0.491754
$735$	2.20752	0.0814257
$736$	−51.4201	−1.89537
$737$	2.29453	0.0845201
$738$	5.89195	0.216886
$739$	−1.11122	−0.0408767	−0.0204384	−	0.999791i	$-0.506506\pi$
$739$	−1.11122	−0.0408767	−0.0204384	+	0.999791i	$0.506506\pi$
$740$	18.8205	0.691855
$741$	21.7087	0.797488
$742$	54.2907	1.99308
$743$	−36.5068	−1.33930	−0.669652	−	0.742675i	$-0.733557\pi$
$743$	−36.5068	−1.33930	−0.669652	+	0.742675i	$0.733557\pi$
$744$	23.9724	0.878871
$745$	−14.9613	−0.548141
$746$	−91.7861	−3.36053
$747$	−2.15464	−0.0788343
$748$	−14.4728	−0.529178
$749$	−48.4663	−1.77092
$750$	19.0995	0.697416
$751$	0.573211	0.0209168	0.0104584	−	0.999945i	$-0.496671\pi$
$751$	0.573211	0.0209168	0.0104584	+	0.999945i	$0.496671\pi$
$752$	−106.226	−3.87365
$753$	−5.60340	−0.204199
$754$	33.4076	1.21663
$755$	−13.4940	−0.491097
$756$	16.1001	0.585554
$757$	−37.0281	−1.34581	−0.672905	−	0.739729i	$-0.734954\pi$
$757$	−37.0281	−1.34581	−0.672905	+	0.739729i	$0.734954\pi$
$758$	66.4505	2.41359
$759$	−9.55567	−0.346849
$760$	42.2154	1.53131
$761$	−32.2101	−1.16762	−0.583808	−	0.811892i	$-0.698438\pi$
$761$	−32.2101	−1.16762	−0.583808	+	0.811892i	$0.698438\pi$
$762$	−7.49077	−0.271362
$763$	21.9084	0.793139
$764$	53.9898	1.95328
$765$	0.759881	0.0274736
$766$	58.5263	2.11464
$767$	8.71008	0.314503
$768$	−4.38052	−0.158068
$769$	−32.9179	−1.18705	−0.593525	−	0.804815i	$-0.702264\pi$
$769$	−32.9179	−1.18705	−0.593525	+	0.804815i	$0.702264\pi$
$770$	−18.0482	−0.650414
$771$	12.4898	0.449809
$772$	−31.3574	−1.12858
$773$	20.2927	0.729876	0.364938	−	0.931032i	$-0.381090\pi$
$773$	20.2927	0.729876	0.364938	+	0.931032i	$0.381090\pi$
$774$	20.9227	0.752050
$775$	−12.7566	−0.458231
$776$	16.1052	0.578142
$777$	−15.2375	−0.546644
$778$	78.8511	2.82695
$779$	−14.7647	−0.529001
$780$	−12.6242	−0.452020
$781$	−7.95975	−0.284822
$782$	9.00979	0.322189
$783$	−3.85637	−0.137815
$784$	34.6821	1.23865
$785$	0.759881	0.0271213
$786$	−20.2063	−0.720734
$787$	−21.3572	−0.761300	−0.380650	−	0.924719i	$-0.624300\pi$
$787$	−21.3572	−0.761300	−0.380650	+	0.924719i	$0.624300\pi$
$788$	−3.28121	−0.116888
$789$	24.6807	0.878656
$790$	−22.4595	−0.799073
$791$	−41.3105	−1.46883
$792$	−23.5129	−0.835494
$793$	−1.66640	−0.0591755
$794$	−36.5210	−1.29608
$795$	4.91401	0.174282
$796$	0.0603060	0.00213749
$797$	−30.8470	−1.09266	−0.546329	−	0.837571i	$-0.683975\pi$
$797$	−30.8470	−1.09266	−0.546329	+	0.837571i	$0.683975\pi$
$798$	−56.1188	−1.98659
$799$	8.89782	0.314782
$800$	67.3288	2.38043
$801$	1.54344	0.0545346
$802$	33.2005	1.17235
$803$	27.9382	0.985919
$804$	−4.14896	−0.146323
$805$	8.07761	0.284698
$806$	24.9877	0.880155
$807$	22.8330	0.803760
$808$	−102.770	−3.61545
$809$	−22.5476	−0.792731	−0.396365	−	0.918093i	$-0.629729\pi$
$809$	−22.5476	−0.792731	−0.396365	+	0.918093i	$0.629729\pi$
$810$	2.02699	0.0712213
$811$	10.1874	0.357728	0.178864	−	0.983874i	$-0.442758\pi$
$811$	10.1874	0.357728	0.178864	+	0.983874i	$0.442758\pi$
$812$	−62.0878	−2.17886
$813$	−32.3091	−1.13313
$814$	36.5381	1.28066
$815$	4.09018	0.143273
$816$	11.9384	0.417927
$817$	−52.4304	−1.83431
$818$	16.7823	0.586778
$819$	10.2209	0.357148
$820$	8.58613	0.299841
$821$	16.8083	0.586613	0.293306	−	0.956018i	$-0.405244\pi$
$821$	16.8083	0.586613	0.293306	+	0.956018i	$0.405244\pi$
$822$	38.1108	1.32927
$823$	−31.5932	−1.10127	−0.550634	−	0.834746i	$-0.685614\pi$
$823$	−31.5932	−1.10127	−0.550634	+	0.834746i	$0.685614\pi$
$824$	−20.2116	−0.704105
$825$	12.5121	0.435614
$826$	−22.5163	−0.783443
$827$	16.1401	0.561246	0.280623	−	0.959818i	$-0.409459\pi$
$827$	16.1401	0.561246	0.280623	+	0.959818i	$0.409459\pi$
$828$	17.2785	0.600471
$829$	9.65887	0.335467	0.167733	−	0.985832i	$-0.446355\pi$
$829$	9.65887	0.335467	0.167733	+	0.985832i	$0.446355\pi$
$830$	−4.36745	−0.151596
$831$	6.19453	0.214886
$832$	−54.3422	−1.88398
$833$	−2.90509	−0.100655
$834$	−26.1115	−0.904166
$835$	−5.32228	−0.184185
$836$	96.7443	3.34597
$837$	−2.88443	−0.0997004
$838$	−45.8991	−1.58556
$839$	3.22548	0.111356	0.0556779	−	0.998449i	$-0.482268\pi$
$839$	3.22548	0.111356	0.0556779	+	0.998449i	$0.482268\pi$
$840$	19.8759	0.685784
$841$	−14.1284	−0.487188
$842$	1.84266	0.0635022
$843$	9.37561	0.322913
$844$	−81.2370	−2.79629
$845$	1.86413	0.0641281
$846$	23.7350	0.816028
$847$	9.42913	0.323989
$848$	77.2033	2.65117
$849$	4.59361	0.157652
$850$	−11.7973	−0.404644
$851$	−16.3529	−0.560569
$852$	14.3928	0.493089
$853$	−3.62450	−0.124100	−0.0620502	−	0.998073i	$-0.519764\pi$
$853$	−3.62450	−0.124100	−0.0620502	+	0.998073i	$0.519764\pi$
$854$	4.30778	0.147409
$855$	−5.07947	−0.173714
$856$	−127.986	−4.37448
$857$	−1.86891	−0.0638408	−0.0319204	−	0.999490i	$-0.510162\pi$
$857$	−1.86891	−0.0638408	−0.0319204	+	0.999490i	$0.510162\pi$
$858$	−24.5087	−0.836714
$859$	−3.90668	−0.133294	−0.0666471	−	0.997777i	$-0.521230\pi$
$859$	−3.90668	−0.133294	−0.0666471	+	0.997777i	$0.521230\pi$
$860$	30.4899	1.03970
$861$	−6.95155	−0.236908
$862$	−102.908	−3.50504
$863$	−17.9763	−0.611921	−0.305961	−	0.952044i	$-0.598978\pi$
$863$	−17.9763	−0.611921	−0.305961	+	0.952044i	$0.598978\pi$
$864$	15.2239	0.517927
$865$	−11.7578	−0.399777
$866$	−34.9323	−1.18705
$867$	−1.00000	−0.0339618
$868$	−46.4395	−1.57626
$869$	−31.3474	−1.06339
$870$	−7.81683	−0.265015
$871$	−2.63391	−0.0892466
$872$	57.8542	1.95919
$873$	−1.93782	−0.0655852
$874$	−60.2265	−2.03719
$875$	−22.5343	−0.761800
$876$	−50.5178	−1.70684
$877$	−2.79679	−0.0944408	−0.0472204	−	0.998884i	$-0.515036\pi$
$877$	−2.79679	−0.0944408	−0.0472204	+	0.998884i	$0.515036\pi$
$878$	−35.1250	−1.18541
$879$	−12.3861	−0.417773
$880$	−25.6652	−0.865175
$881$	37.1342	1.25108	0.625542	−	0.780190i	$-0.284878\pi$
$881$	37.1342	1.25108	0.625542	+	0.780190i	$0.284878\pi$
$882$	−7.74936	−0.260935
$883$	−7.30786	−0.245929	−0.122965	−	0.992411i	$-0.539240\pi$
$883$	−7.30786	−0.245929	−0.122965	+	0.992411i	$0.539240\pi$
$884$	16.6134	0.558770
$885$	−2.03802	−0.0685072
$886$	13.0668	0.438987
$887$	−58.8423	−1.97573	−0.987866	−	0.155309i	$-0.950363\pi$
$887$	−58.8423	−1.97573	−0.987866	+	0.155309i	$0.950363\pi$
$888$	−40.2382	−1.35030
$889$	8.83790	0.296414
$890$	3.12853	0.104869
$891$	2.82913	0.0947795
$892$	26.9387	0.901973
$893$	−59.4780	−1.99036
$894$	52.5208	1.75656
$895$	3.41206	0.114053
$896$	44.6530	1.49175
$897$	10.9690	0.366245
$898$	61.7345	2.06011
$899$	11.1234	0.370986
$900$	−22.6243	−0.754143
$901$	−6.46681	−0.215441
$902$	16.6691	0.555021
$903$	−24.6854	−0.821478
$904$	−109.090	−3.62827
$905$	9.56034	0.317797
$906$	47.3698	1.57376
$907$	1.07045	0.0355438	0.0177719	−	0.999842i	$-0.494343\pi$
$907$	1.07045	0.0355438	0.0177719	+	0.999842i	$0.494343\pi$
$908$	9.40470	0.312106
$909$	12.3656	0.410142
$910$	20.7177	0.686786
$911$	−14.1314	−0.468193	−0.234097	−	0.972213i	$-0.575213\pi$
$911$	−14.1314	−0.468193	−0.234097	+	0.972213i	$0.575213\pi$
$912$	−79.8029	−2.64254
$913$	−6.09577	−0.201741
$914$	68.7791	2.27501
$915$	0.389909	0.0128900
$916$	34.9748	1.15560
$917$	23.8401	0.787271
$918$	−2.66751	−0.0880411
$919$	44.3813	1.46401	0.732003	−	0.681302i	$-0.238586\pi$
$919$	44.3813	1.46401	0.732003	+	0.681302i	$0.238586\pi$
$920$	21.3307	0.703254
$921$	5.33559	0.175814
$922$	−35.8420	−1.18039
$923$	9.13706	0.300750
$924$	45.5493	1.49846
$925$	21.4122	0.704029
$926$	−1.65189	−0.0542845
$927$	2.43192	0.0798747
$928$	−58.7088	−1.92721
$929$	0.674930	0.0221437	0.0110719	−	0.999939i	$-0.496476\pi$
$929$	0.674930	0.0221437	0.0110719	+	0.999939i	$0.496476\pi$
$930$	−5.84671	−0.191721
$931$	19.4192	0.636440
$932$	41.2332	1.35064
$933$	−12.3195	−0.403323
$934$	−66.2989	−2.16936
$935$	2.14981	0.0703062
$936$	26.9906	0.882216
$937$	−12.7371	−0.416103	−0.208052	−	0.978118i	$-0.566712\pi$
$937$	−12.7371	−0.416103	−0.208052	+	0.978118i	$0.566712\pi$
$938$	6.80889	0.222318
$939$	−22.9268	−0.748186
$940$	34.5882	1.12814
$941$	−48.5758	−1.58352	−0.791762	−	0.610829i	$-0.790836\pi$
$941$	−48.5758	−1.58352	−0.791762	+	0.610829i	$0.790836\pi$
$942$	−2.66751	−0.0869123
$943$	−7.46037	−0.242943
$944$	−32.0190	−1.04213
$945$	−2.39153	−0.0777963
$946$	59.1931	1.92453
$947$	−3.47933	−0.113063	−0.0565315	−	0.998401i	$-0.518004\pi$
$947$	−3.47933	−0.113063	−0.0565315	+	0.998401i	$0.518004\pi$
$948$	56.6822	1.84095
$949$	−32.0705	−1.04105
$950$	78.8597	2.55855
$951$	9.94107	0.322361
$952$	−26.1566	−0.847741
$953$	−44.1556	−1.43034	−0.715171	−	0.698950i	$-0.753651\pi$
$953$	−44.1556	−1.43034	−0.715171	+	0.698950i	$0.753651\pi$
$954$	−17.2503	−0.558499
$955$	−8.01971	−0.259512
$956$	−63.8453	−2.06490
$957$	−10.9102	−0.352676
$958$	−26.3824	−0.852376
$959$	−44.9646	−1.45198
$960$	12.7152	0.410380
$961$	−22.6801	−0.731616
$962$	−41.9424	−1.35228
$963$	15.3997	0.496247
$964$	−3.95435	−0.127361
$965$	4.65787	0.149942
$966$	−28.3559	−0.912337
$967$	26.8292	0.862768	0.431384	−	0.902169i	$-0.358026\pi$
$967$	26.8292	0.862768	0.431384	+	0.902169i	$0.358026\pi$
$968$	24.8997	0.800308
$969$	6.68456	0.214739
$970$	−3.92794	−0.126119
$971$	−4.26089	−0.136738	−0.0683692	−	0.997660i	$-0.521780\pi$
$971$	−4.26089	−0.136738	−0.0683692	+	0.997660i	$0.521780\pi$
$972$	−5.11563	−0.164084
$973$	30.8073	0.987637
$974$	−65.2091	−2.08943
$975$	−14.3627	−0.459975
$976$	6.12582	0.196083
$977$	−40.5153	−1.29620	−0.648100	−	0.761555i	$-0.724436\pi$
$977$	−40.5153	−1.29620	−0.648100	+	0.761555i	$0.724436\pi$
$978$	−14.3583	−0.459128
$979$	4.36659	0.139557
$980$	−11.2929	−0.360737
$981$	−6.96117	−0.222253
$982$	22.0490	0.703612
$983$	22.5853	0.720358	0.360179	−	0.932883i	$-0.382716\pi$
$983$	22.5853	0.720358	0.360179	+	0.932883i	$0.382716\pi$
$984$	−18.3571	−0.585204
$985$	0.487395	0.0155297
$986$	10.2869	0.327602
$987$	−28.0035	−0.891362
$988$	−111.054	−3.53308
$989$	−26.4922	−0.842404
$990$	5.73464	0.182259
$991$	−49.4913	−1.57214	−0.786072	−	0.618135i	$-0.787889\pi$
$991$	−49.4913	−1.57214	−0.786072	+	0.618135i	$0.787889\pi$
$992$	−43.9121	−1.39421
$993$	6.48028	0.205645
$994$	−23.6201	−0.749184
$995$	−0.00895792	−0.000283985 0
$996$	11.0224	0.349257
$997$	−45.5599	−1.44290	−0.721448	−	0.692468i	$-0.756523\pi$
$997$	−45.5599	−1.44290	−0.721448	+	0.692468i	$0.756523\pi$
$998$	20.2581	0.641259
$999$	4.84157	0.153180

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.f.1.2	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.f.1.2	✓	48	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)

\(f(q)\)	\(=\)	\(q-2.66751 q^{2} -1.00000 q^{3} +5.11563 q^{4} -0.759881 q^{5} +2.66751 q^{6} -3.14723 q^{7} -8.31098 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.66751 q^{2} -1.00000 q^{3} +5.11563 q^{4} -0.759881 q^{5} +2.66751 q^{6} -3.14723 q^{7} -8.31098 q^{8} +1.00000 q^{9} +2.02699 q^{10} +2.82913 q^{11} -5.11563 q^{12} -3.24759 q^{13} +8.39529 q^{14} +0.759881 q^{15} +11.9384 q^{16} -1.00000 q^{17} -2.66751 q^{18} +6.68456 q^{19} -3.88727 q^{20} +3.14723 q^{21} -7.54675 q^{22} +3.37760 q^{23} +8.31098 q^{24} -4.42258 q^{25} +8.66298 q^{26} -1.00000 q^{27} -16.1001 q^{28} +3.85637 q^{29} -2.02699 q^{30} +2.88443 q^{31} -15.2239 q^{32} -2.82913 q^{33} +2.66751 q^{34} +2.39153 q^{35} +5.11563 q^{36} -4.84157 q^{37} -17.8312 q^{38} +3.24759 q^{39} +6.31536 q^{40} -2.20878 q^{41} -8.39529 q^{42} -7.84352 q^{43} +14.4728 q^{44} -0.759881 q^{45} -9.00979 q^{46} -8.89782 q^{47} -11.9384 q^{48} +2.90509 q^{49} +11.7973 q^{50} +1.00000 q^{51} -16.6134 q^{52} +6.46681 q^{53} +2.66751 q^{54} -2.14981 q^{55} +26.1566 q^{56} -6.68456 q^{57} -10.2869 q^{58} -2.68202 q^{59} +3.88727 q^{60} +0.513119 q^{61} -7.69425 q^{62} -3.14723 q^{63} +16.7331 q^{64} +2.46778 q^{65} +7.54675 q^{66} +0.811036 q^{67} -5.11563 q^{68} -3.37760 q^{69} -6.37943 q^{70} -2.81349 q^{71} -8.31098 q^{72} +9.87519 q^{73} +12.9149 q^{74} +4.42258 q^{75} +34.1957 q^{76} -8.90395 q^{77} -8.66298 q^{78} -11.0802 q^{79} -9.07177 q^{80} +1.00000 q^{81} +5.89195 q^{82} -2.15464 q^{83} +16.1001 q^{84} +0.759881 q^{85} +20.9227 q^{86} -3.85637 q^{87} -23.5129 q^{88} +1.54344 q^{89} +2.02699 q^{90} +10.2209 q^{91} +17.2785 q^{92} -2.88443 q^{93} +23.7350 q^{94} -5.07947 q^{95} +15.2239 q^{96} -1.93782 q^{97} -7.74936 q^{98} +2.82913 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - q^{2} - 48 q^{3} + 45 q^{4} + q^{5} + q^{6} - 13 q^{7} - 6 q^{8} + 48 q^{9}+O(q^{10}) \) 48 * q - q^2 - 48 * q^3 + 45 * q^4 + q^5 + q^6 - 13 * q^7 - 6 * q^8 + 48 * q^9	\( 48 q - q^{2} - 48 q^{3} + 45 q^{4} + q^{5} + q^{6} - 13 q^{7} - 6 q^{8} + 48 q^{9} - 20 q^{10} + 5 q^{11} - 45 q^{12} - 8 q^{13} + 4 q^{14} - q^{15} + 39 q^{16} - 48 q^{17} - q^{18} - 6 q^{19} + 6 q^{20} + 13 q^{21} - 35 q^{22} - 8 q^{23} + 6 q^{24} + 13 q^{25} + 17 q^{26} - 48 q^{27} - 38 q^{28} + q^{29} + 20 q^{30} - 21 q^{31} - 3 q^{32} - 5 q^{33} + q^{34} + 19 q^{35} + 45 q^{36} - 58 q^{37} - 14 q^{38} + 8 q^{39} - 54 q^{40} - 3 q^{41} - 4 q^{42} - 33 q^{43} + 2 q^{44} + q^{45} - 26 q^{46} + 9 q^{47} - 39 q^{48} + 11 q^{49} + 4 q^{50} + 48 q^{51} - 31 q^{52} - 33 q^{53} + q^{54} - 21 q^{55} + 6 q^{57} - 55 q^{58} + 77 q^{59} - 6 q^{60} - 29 q^{61} - 46 q^{62} - 13 q^{63} + 24 q^{64} - 49 q^{65} + 35 q^{66} - 44 q^{67} - 45 q^{68} + 8 q^{69} + 4 q^{70} + 22 q^{71} - 6 q^{72} - 63 q^{73} - 16 q^{74} - 13 q^{75} - 46 q^{76} - 30 q^{77} - 17 q^{78} - 46 q^{79} - 14 q^{80} + 48 q^{81} - 75 q^{82} + 11 q^{83} + 38 q^{84} - q^{85} + 8 q^{86} - q^{87} - 116 q^{88} + 10 q^{89} - 20 q^{90} - 67 q^{91} - 64 q^{92} + 21 q^{93} - 16 q^{94} - 8 q^{95} + 3 q^{96} - 96 q^{97} - 46 q^{98} + 5 q^{99}+O(q^{100}) \) 48 * q - q^2 - 48 * q^3 + 45 * q^4 + q^5 + q^6 - 13 * q^7 - 6 * q^8 + 48 * q^9 - 20 * q^10 + 5 * q^11 - 45 * q^12 - 8 * q^13 + 4 * q^14 - q^15 + 39 * q^16 - 48 * q^17 - q^18 - 6 * q^19 + 6 * q^20 + 13 * q^21 - 35 * q^22 - 8 * q^23 + 6 * q^24 + 13 * q^25 + 17 * q^26 - 48 * q^27 - 38 * q^28 + q^29 + 20 * q^30 - 21 * q^31 - 3 * q^32 - 5 * q^33 + q^34 + 19 * q^35 + 45 * q^36 - 58 * q^37 - 14 * q^38 + 8 * q^39 - 54 * q^40 - 3 * q^41 - 4 * q^42 - 33 * q^43 + 2 * q^44 + q^45 - 26 * q^46 + 9 * q^47 - 39 * q^48 + 11 * q^49 + 4 * q^50 + 48 * q^51 - 31 * q^52 - 33 * q^53 + q^54 - 21 * q^55 + 6 * q^57 - 55 * q^58 + 77 * q^59 - 6 * q^60 - 29 * q^61 - 46 * q^62 - 13 * q^63 + 24 * q^64 - 49 * q^65 + 35 * q^66 - 44 * q^67 - 45 * q^68 + 8 * q^69 + 4 * q^70 + 22 * q^71 - 6 * q^72 - 63 * q^73 - 16 * q^74 - 13 * q^75 - 46 * q^76 - 30 * q^77 - 17 * q^78 - 46 * q^79 - 14 * q^80 + 48 * q^81 - 75 * q^82 + 11 * q^83 + 38 * q^84 - q^85 + 8 * q^86 - q^87 - 116 * q^88 + 10 * q^89 - 20 * q^90 - 67 * q^91 - 64 * q^92 + 21 * q^93 - 16 * q^94 - 8 * q^95 + 3 * q^96 - 96 * q^97 - 46 * q^98 + 5 * q^99

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