LMFDB - Embedded newform 4006.2.a.h.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4006,2,Mod(1,4006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4006, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4006 = 2 \cdot 2003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4006.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:	$31.9880710497$
Analytic rank:	$0$
Dimension:	$42$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	4006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.83249 q^{3} +1.00000 q^{4} -3.27043 q^{5} +2.83249 q^{6} -1.58563 q^{7} -1.00000 q^{8} +5.02302 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.83249 q^{3} +1.00000 q^{4} -3.27043 q^{5} +2.83249 q^{6} -1.58563 q^{7} -1.00000 q^{8} +5.02302 q^{9} +3.27043 q^{10} +2.07103 q^{11} -2.83249 q^{12} -0.763482 q^{13} +1.58563 q^{14} +9.26348 q^{15} +1.00000 q^{16} +4.68604 q^{17} -5.02302 q^{18} +6.23401 q^{19} -3.27043 q^{20} +4.49130 q^{21} -2.07103 q^{22} -5.02605 q^{23} +2.83249 q^{24} +5.69572 q^{25} +0.763482 q^{26} -5.73020 q^{27} -1.58563 q^{28} +7.85516 q^{29} -9.26348 q^{30} -2.22751 q^{31} -1.00000 q^{32} -5.86619 q^{33} -4.68604 q^{34} +5.18571 q^{35} +5.02302 q^{36} -3.70338 q^{37} -6.23401 q^{38} +2.16256 q^{39} +3.27043 q^{40} -5.08000 q^{41} -4.49130 q^{42} -6.46356 q^{43} +2.07103 q^{44} -16.4275 q^{45} +5.02605 q^{46} +5.88006 q^{47} -2.83249 q^{48} -4.48576 q^{49} -5.69572 q^{50} -13.2732 q^{51} -0.763482 q^{52} -1.72299 q^{53} +5.73020 q^{54} -6.77317 q^{55} +1.58563 q^{56} -17.6578 q^{57} -7.85516 q^{58} -7.20880 q^{59} +9.26348 q^{60} +8.63544 q^{61} +2.22751 q^{62} -7.96468 q^{63} +1.00000 q^{64} +2.49691 q^{65} +5.86619 q^{66} -7.02847 q^{67} +4.68604 q^{68} +14.2363 q^{69} -5.18571 q^{70} +11.9510 q^{71} -5.02302 q^{72} -4.45320 q^{73} +3.70338 q^{74} -16.1331 q^{75} +6.23401 q^{76} -3.28390 q^{77} -2.16256 q^{78} -0.488301 q^{79} -3.27043 q^{80} +1.16170 q^{81} +5.08000 q^{82} -1.42747 q^{83} +4.49130 q^{84} -15.3254 q^{85} +6.46356 q^{86} -22.2497 q^{87} -2.07103 q^{88} +3.62801 q^{89} +16.4275 q^{90} +1.21060 q^{91} -5.02605 q^{92} +6.30941 q^{93} -5.88006 q^{94} -20.3879 q^{95} +2.83249 q^{96} +1.21114 q^{97} +4.48576 q^{98} +10.4029 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q - 42 q^{2} + 42 q^{4} + 27 q^{5} - 10 q^{7} - 42 q^{8} + 56 q^{9}+O(q^{10}) $ 42 * q - 42 * q^2 + 42 * q^4 + 27 * q^5 - 10 * q^7 - 42 * q^8 + 56 * q^9	\( 42 q - 42 q^{2} + 42 q^{4} + 27 q^{5} - 10 q^{7} - 42 q^{8} + 56 q^{9} - 27 q^{10} + 23 q^{11} + 15 q^{13} + 10 q^{14} + 6 q^{15} + 42 q^{16} + 14 q^{17} - 56 q^{18} - 4 q^{19} + 27 q^{20} + 26 q^{21} - 23 q^{22} + 12 q^{23} + 45 q^{25} - 15 q^{26} - 3 q^{27} - 10 q^{28} + 41 q^{29} - 6 q^{30} + 18 q^{31} - 42 q^{32} + 25 q^{33} - 14 q^{34} + 8 q^{35} + 56 q^{36} + 33 q^{37} + 4 q^{38} + 10 q^{39} - 27 q^{40} + 84 q^{41} - 26 q^{42} - 36 q^{43} + 23 q^{44} + 66 q^{45} - 12 q^{46} + 28 q^{47} + 58 q^{49} - 45 q^{50} + 17 q^{51} + 15 q^{52} + 68 q^{53} + 3 q^{54} - 28 q^{55} + 10 q^{56} - 9 q^{57} - 41 q^{58} + 59 q^{59} + 6 q^{60} + 41 q^{61} - 18 q^{62} - 28 q^{63} + 42 q^{64} + 44 q^{65} - 25 q^{66} + 14 q^{68} + 67 q^{69} - 8 q^{70} + 69 q^{71} - 56 q^{72} - 27 q^{73} - 33 q^{74} + 14 q^{75} - 4 q^{76} + 43 q^{77} - 10 q^{78} - 19 q^{79} + 27 q^{80} + 74 q^{81} - 84 q^{82} + 20 q^{83} + 26 q^{84} + 16 q^{85} + 36 q^{86} - 28 q^{87} - 23 q^{88} + 123 q^{89} - 66 q^{90} - 9 q^{91} + 12 q^{92} + 48 q^{93} - 28 q^{94} + 28 q^{95} + 10 q^{97} - 58 q^{98} + 75 q^{99}+O(q^{100}) \) 42 * q - 42 * q^2 + 42 * q^4 + 27 * q^5 - 10 * q^7 - 42 * q^8 + 56 * q^9 - 27 * q^10 + 23 * q^11 + 15 * q^13 + 10 * q^14 + 6 * q^15 + 42 * q^16 + 14 * q^17 - 56 * q^18 - 4 * q^19 + 27 * q^20 + 26 * q^21 - 23 * q^22 + 12 * q^23 + 45 * q^25 - 15 * q^26 - 3 * q^27 - 10 * q^28 + 41 * q^29 - 6 * q^30 + 18 * q^31 - 42 * q^32 + 25 * q^33 - 14 * q^34 + 8 * q^35 + 56 * q^36 + 33 * q^37 + 4 * q^38 + 10 * q^39 - 27 * q^40 + 84 * q^41 - 26 * q^42 - 36 * q^43 + 23 * q^44 + 66 * q^45 - 12 * q^46 + 28 * q^47 + 58 * q^49 - 45 * q^50 + 17 * q^51 + 15 * q^52 + 68 * q^53 + 3 * q^54 - 28 * q^55 + 10 * q^56 - 9 * q^57 - 41 * q^58 + 59 * q^59 + 6 * q^60 + 41 * q^61 - 18 * q^62 - 28 * q^63 + 42 * q^64 + 44 * q^65 - 25 * q^66 + 14 * q^68 + 67 * q^69 - 8 * q^70 + 69 * q^71 - 56 * q^72 - 27 * q^73 - 33 * q^74 + 14 * q^75 - 4 * q^76 + 43 * q^77 - 10 * q^78 - 19 * q^79 + 27 * q^80 + 74 * q^81 - 84 * q^82 + 20 * q^83 + 26 * q^84 + 16 * q^85 + 36 * q^86 - 28 * q^87 - 23 * q^88 + 123 * q^89 - 66 * q^90 - 9 * q^91 + 12 * q^92 + 48 * q^93 - 28 * q^94 + 28 * q^95 + 10 * q^97 - 58 * q^98 + 75 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.83249	−1.63534	−0.817671	−	0.575686i	$-0.804735\pi$
$3$	−2.83249	−1.63534	−0.817671	+	0.575686i	$0.804735\pi$
$4$	1.00000	0.500000
$5$	−3.27043	−1.46258	−0.731291	−	0.682066i	$-0.761082\pi$
$5$	−3.27043	−1.46258	−0.731291	+	0.682066i	$0.761082\pi$
$6$	2.83249	1.15636
$7$	−1.58563	−0.599313	−0.299657	−	0.954047i	$-0.596872\pi$
$7$	−1.58563	−0.599313	−0.299657	+	0.954047i	$0.596872\pi$
$8$	−1.00000	−0.353553
$9$	5.02302	1.67434
$10$	3.27043	1.03420
$11$	2.07103	0.624440	0.312220	−	0.950010i	$-0.398927\pi$
$11$	2.07103	0.624440	0.312220	+	0.950010i	$0.398927\pi$
$12$	−2.83249	−0.817671
$13$	−0.763482	−0.211752	−0.105876	−	0.994379i	$-0.533765\pi$
$13$	−0.763482	−0.211752	−0.105876	+	0.994379i	$0.533765\pi$
$14$	1.58563	0.423779
$15$	9.26348	2.39182
$16$	1.00000	0.250000
$17$	4.68604	1.13653	0.568265	−	0.822845i	$-0.307615\pi$
$17$	4.68604	1.13653	0.568265	+	0.822845i	$0.307615\pi$
$18$	−5.02302	−1.18394
$19$	6.23401	1.43018	0.715090	−	0.699032i	$-0.246386\pi$
$19$	6.23401	1.43018	0.715090	+	0.699032i	$0.246386\pi$
$20$	−3.27043	−0.731291
$21$	4.49130	0.980082
$22$	−2.07103	−0.441546
$23$	−5.02605	−1.04800	−0.524002	−	0.851717i	$-0.675562\pi$
$23$	−5.02605	−1.04800	−0.524002	+	0.851717i	$0.675562\pi$
$24$	2.83249	0.578180
$25$	5.69572	1.13914
$26$	0.763482	0.149731
$27$	−5.73020	−1.10278
$28$	−1.58563	−0.299657
$29$	7.85516	1.45867	0.729333	−	0.684159i	$-0.239830\pi$
$29$	7.85516	1.45867	0.729333	+	0.684159i	$0.239830\pi$
$30$	−9.26348	−1.69127
$31$	−2.22751	−0.400072	−0.200036	−	0.979789i	$-0.564106\pi$
$31$	−2.22751	−0.400072	−0.200036	+	0.979789i	$0.564106\pi$
$32$	−1.00000	−0.176777
$33$	−5.86619	−1.02117
$34$	−4.68604	−0.803649
$35$	5.18571	0.876544
$36$	5.02302	0.837171
$37$	−3.70338	−0.608831	−0.304416	−	0.952539i	$-0.598461\pi$
$37$	−3.70338	−0.608831	−0.304416	+	0.952539i	$0.598461\pi$
$38$	−6.23401	−1.01129
$39$	2.16256	0.346286
$40$	3.27043	0.517101
$41$	−5.08000	−0.793363	−0.396682	−	0.917956i	$-0.629838\pi$
$41$	−5.08000	−0.793363	−0.396682	+	0.917956i	$0.629838\pi$
$42$	−4.49130	−0.693023
$43$	−6.46356	−0.985683	−0.492842	−	0.870119i	$-0.664042\pi$
$43$	−6.46356	−0.985683	−0.492842	+	0.870119i	$0.664042\pi$
$44$	2.07103	0.312220
$45$	−16.4275	−2.44886
$46$	5.02605	0.741051
$47$	5.88006	0.857694	0.428847	−	0.903377i	$-0.358920\pi$
$47$	5.88006	0.857694	0.428847	+	0.903377i	$0.358920\pi$
$48$	−2.83249	−0.408835
$49$	−4.48576	−0.640823
$50$	−5.69572	−0.805496
$51$	−13.2732	−1.85862
$52$	−0.763482	−0.105876
$53$	−1.72299	−0.236671	−0.118336	−	0.992974i	$-0.537756\pi$
$53$	−1.72299	−0.236671	−0.118336	+	0.992974i	$0.537756\pi$
$54$	5.73020	0.779782
$55$	−6.77317	−0.913295
$56$	1.58563	0.211889
$57$	−17.6578	−2.33883
$58$	−7.85516	−1.03143
$59$	−7.20880	−0.938506	−0.469253	−	0.883064i	$-0.655477\pi$
$59$	−7.20880	−0.938506	−0.469253	+	0.883064i	$0.655477\pi$
$60$	9.26348	1.19591
$61$	8.63544	1.10566	0.552828	−	0.833296i	$-0.313549\pi$
$61$	8.63544	1.10566	0.552828	+	0.833296i	$0.313549\pi$
$62$	2.22751	0.282894
$63$	−7.96468	−1.00346
$64$	1.00000	0.125000
$65$	2.49691	0.309704
$66$	5.86619	0.722078
$67$	−7.02847	−0.858665	−0.429332	−	0.903147i	$-0.641251\pi$
$67$	−7.02847	−0.858665	−0.429332	+	0.903147i	$0.641251\pi$
$68$	4.68604	0.568265
$69$	14.2363	1.71384
$70$	−5.18571	−0.619811
$71$	11.9510	1.41832	0.709162	−	0.705046i	$-0.249073\pi$
$71$	11.9510	1.41832	0.709162	+	0.705046i	$0.249073\pi$
$72$	−5.02302	−0.591969
$73$	−4.45320	−0.521207	−0.260604	−	0.965446i	$-0.583922\pi$
$73$	−4.45320	−0.521207	−0.260604	+	0.965446i	$0.583922\pi$
$74$	3.70338	0.430509
$75$	−16.1331	−1.86289
$76$	6.23401	0.715090
$77$	−3.28390	−0.374235
$78$	−2.16256	−0.244861
$79$	−0.488301	−0.0549382	−0.0274691	−	0.999623i	$-0.508745\pi$
$79$	−0.488301	−0.0549382	−0.0274691	+	0.999623i	$0.508745\pi$
$80$	−3.27043	−0.365645
$81$	1.16170	0.129077
$82$	5.08000	0.560992
$83$	−1.42747	−0.156685	−0.0783425	−	0.996927i	$-0.524963\pi$
$83$	−1.42747	−0.156685	−0.0783425	+	0.996927i	$0.524963\pi$
$84$	4.49130	0.490041
$85$	−15.3254	−1.66227
$86$	6.46356	0.696983
$87$	−22.2497	−2.38542
$88$	−2.07103	−0.220773
$89$	3.62801	0.384568	0.192284	−	0.981339i	$-0.438411\pi$
$89$	3.62801	0.384568	0.192284	+	0.981339i	$0.438411\pi$
$90$	16.4275	1.73161
$91$	1.21060	0.126906
$92$	−5.02605	−0.524002
$93$	6.30941	0.654255
$94$	−5.88006	−0.606481
$95$	−20.3879	−2.09175
$96$	2.83249	0.289090
$97$	1.21114	0.122973	0.0614865	−	0.998108i	$-0.480416\pi$
$97$	1.21114	0.122973	0.0614865	+	0.998108i	$0.480416\pi$
$98$	4.48576	0.453131
$99$	10.4029	1.04553
$100$	5.69572	0.569572
$101$	7.91433	0.787505	0.393753	−	0.919216i	$-0.371177\pi$
$101$	7.91433	0.787505	0.393753	+	0.919216i	$0.371177\pi$
$102$	13.2732	1.31424
$103$	−6.37361	−0.628010	−0.314005	−	0.949421i	$-0.601671\pi$
$103$	−6.37361	−0.628010	−0.314005	+	0.949421i	$0.601671\pi$
$104$	0.763482	0.0748656
$105$	−14.6885	−1.43345
$106$	1.72299	0.167352
$107$	7.30835	0.706525	0.353263	−	0.935524i	$-0.385072\pi$
$107$	7.30835	0.706525	0.353263	+	0.935524i	$0.385072\pi$
$108$	−5.73020	−0.551389
$109$	−0.112473	−0.0107729	−0.00538646	−	0.999985i	$-0.501715\pi$
$109$	−0.112473	−0.0107729	−0.00538646	+	0.999985i	$0.501715\pi$
$110$	6.77317	0.645797
$111$	10.4898	0.995647
$112$	−1.58563	−0.149828
$113$	−10.8758	−1.02311	−0.511554	−	0.859251i	$-0.670930\pi$
$113$	−10.8758	−1.02311	−0.511554	+	0.859251i	$0.670930\pi$
$114$	17.6578	1.65380
$115$	16.4374	1.53279
$116$	7.85516	0.729333
$117$	−3.83499	−0.354545
$118$	7.20880	0.663624
$119$	−7.43034	−0.681138
$120$	−9.26348	−0.845636
$121$	−6.71082	−0.610074
$122$	−8.63544	−0.781816
$123$	14.3891	1.29742
$124$	−2.22751	−0.200036
$125$	−2.27530	−0.203509
$126$	7.96468	0.709550
$127$	−9.23004	−0.819034	−0.409517	−	0.912302i	$-0.634303\pi$
$127$	−9.23004	−0.819034	−0.409517	+	0.912302i	$0.634303\pi$
$128$	−1.00000	−0.0883883
$129$	18.3080	1.61193
$130$	−2.49691	−0.218994
$131$	−15.1154	−1.32064	−0.660318	−	0.750987i	$-0.729578\pi$
$131$	−15.1154	−1.32064	−0.660318	+	0.750987i	$0.729578\pi$
$132$	−5.86619	−0.510587
$133$	−9.88486	−0.857126
$134$	7.02847	0.607168
$135$	18.7402	1.61290
$136$	−4.68604	−0.401824
$137$	16.0029	1.36722	0.683611	−	0.729847i	$-0.260409\pi$
$137$	16.0029	1.36722	0.683611	+	0.729847i	$0.260409\pi$
$138$	−14.2363	−1.21187
$139$	−0.466422	−0.0395614	−0.0197807	−	0.999804i	$-0.506297\pi$
$139$	−0.466422	−0.0395614	−0.0197807	+	0.999804i	$0.506297\pi$
$140$	5.18571	0.438272
$141$	−16.6552	−1.40262
$142$	−11.9510	−1.00291
$143$	−1.58120	−0.132226
$144$	5.02302	0.418585
$145$	−25.6898	−2.13342
$146$	4.45320	0.368549
$147$	12.7059	1.04797
$148$	−3.70338	−0.304416
$149$	−3.53195	−0.289349	−0.144674	−	0.989479i	$-0.546213\pi$
$149$	−3.53195	−0.289349	−0.144674	+	0.989479i	$0.546213\pi$
$150$	16.1331	1.31726
$151$	−1.54227	−0.125508	−0.0627540	−	0.998029i	$-0.519988\pi$
$151$	−1.54227	−0.125508	−0.0627540	+	0.998029i	$0.519988\pi$
$152$	−6.23401	−0.505645
$153$	23.5381	1.90294
$154$	3.28390	0.264624
$155$	7.28491	0.585138
$156$	2.16256	0.173143
$157$	2.42508	0.193543	0.0967714	−	0.995307i	$-0.469148\pi$
$157$	2.42508	0.193543	0.0967714	+	0.995307i	$0.469148\pi$
$158$	0.488301	0.0388472
$159$	4.88036	0.387038
$160$	3.27043	0.258550
$161$	7.96948	0.628083
$162$	−1.16170	−0.0912715
$163$	−4.59512	−0.359918	−0.179959	−	0.983674i	$-0.557596\pi$
$163$	−4.59512	−0.359918	−0.179959	+	0.983674i	$0.557596\pi$
$164$	−5.08000	−0.396682
$165$	19.1850	1.49355
$166$	1.42747	0.110793
$167$	10.2467	0.792910	0.396455	−	0.918054i	$-0.370240\pi$
$167$	10.2467	0.792910	0.396455	+	0.918054i	$0.370240\pi$
$168$	−4.49130	−0.346511
$169$	−12.4171	−0.955161
$170$	15.3254	1.17540
$171$	31.3136	2.39461
$172$	−6.46356	−0.492842
$173$	3.05336	0.232143	0.116071	−	0.993241i	$-0.462970\pi$
$173$	3.05336	0.232143	0.116071	+	0.993241i	$0.462970\pi$
$174$	22.2497	1.68674
$175$	−9.03132	−0.682704
$176$	2.07103	0.156110
$177$	20.4189	1.53478
$178$	−3.62801	−0.271931
$179$	15.5719	1.16390	0.581951	−	0.813224i	$-0.302290\pi$
$179$	15.5719	1.16390	0.581951	+	0.813224i	$0.302290\pi$
$180$	−16.4275	−1.22443
$181$	15.0167	1.11618	0.558091	−	0.829780i	$-0.311534\pi$
$181$	15.0167	1.11618	0.558091	+	0.829780i	$0.311534\pi$
$182$	−1.21060	−0.0897359
$183$	−24.4598	−1.80812
$184$	5.02605	0.370525
$185$	12.1116	0.890465
$186$	−6.30941	−0.462628
$187$	9.70494	0.709696
$188$	5.88006	0.428847
$189$	9.08601	0.660910
$190$	20.3879	1.47909
$191$	−15.3858	−1.11327	−0.556637	−	0.830756i	$-0.687909\pi$
$191$	−15.3858	−1.11327	−0.556637	+	0.830756i	$0.687909\pi$
$192$	−2.83249	−0.204418
$193$	10.2801	0.739977	0.369989	−	0.929036i	$-0.379362\pi$
$193$	10.2801	0.739977	0.369989	+	0.929036i	$0.379362\pi$
$194$	−1.21114	−0.0869550
$195$	−7.07250	−0.506472
$196$	−4.48576	−0.320412
$197$	13.3140	0.948586	0.474293	−	0.880367i	$-0.342704\pi$
$197$	13.3140	0.948586	0.474293	+	0.880367i	$0.342704\pi$
$198$	−10.4029	−0.739299
$199$	17.1547	1.21606	0.608032	−	0.793913i	$-0.291959\pi$
$199$	17.1547	1.21606	0.608032	+	0.793913i	$0.291959\pi$
$200$	−5.69572	−0.402748
$201$	19.9081	1.40421
$202$	−7.91433	−0.556850
$203$	−12.4554	−0.874198
$204$	−13.2732	−0.929308
$205$	16.6138	1.16036
$206$	6.37361	0.444070
$207$	−25.2460	−1.75472
$208$	−0.763482	−0.0529379
$209$	12.9108	0.893062
$210$	14.6885	1.01360
$211$	−25.5062	−1.75592	−0.877960	−	0.478735i	$-0.841096\pi$
$211$	−25.5062	−1.75592	−0.877960	+	0.478735i	$0.841096\pi$
$212$	−1.72299	−0.118336
$213$	−33.8512	−2.31944
$214$	−7.30835	−0.499589
$215$	21.1386	1.44164
$216$	5.73020	0.389891
$217$	3.53201	0.239769
$218$	0.112473	0.00761760
$219$	12.6137	0.852352
$220$	−6.77317	−0.456647
$221$	−3.57770	−0.240662
$222$	−10.4898	−0.704029
$223$	−12.8115	−0.857923	−0.428962	−	0.903323i	$-0.641120\pi$
$223$	−12.8115	−0.857923	−0.428962	+	0.903323i	$0.641120\pi$
$224$	1.58563	0.105945
$225$	28.6097	1.90731
$226$	10.8758	0.723447
$227$	8.71645	0.578531	0.289266	−	0.957249i	$-0.406589\pi$
$227$	8.71645	0.578531	0.289266	+	0.957249i	$0.406589\pi$
$228$	−17.6578	−1.16942
$229$	1.93862	0.128107	0.0640537	−	0.997946i	$-0.479597\pi$
$229$	1.93862	0.128107	0.0640537	+	0.997946i	$0.479597\pi$
$230$	−16.4374	−1.08385
$231$	9.30164	0.612003
$232$	−7.85516	−0.515716
$233$	−0.191782	−0.0125641	−0.00628204	−	0.999980i	$-0.502000\pi$
$233$	−0.191782	−0.0125641	−0.00628204	+	0.999980i	$0.502000\pi$
$234$	3.83499	0.250701
$235$	−19.2303	−1.25445
$236$	−7.20880	−0.469253
$237$	1.38311	0.0898427
$238$	7.43034	0.481637
$239$	−12.1948	−0.788817	−0.394408	−	0.918935i	$-0.629050\pi$
$239$	−12.1948	−0.788817	−0.394408	+	0.918935i	$0.629050\pi$
$240$	9.26348	0.597955
$241$	−9.14348	−0.588983	−0.294492	−	0.955654i	$-0.595150\pi$
$241$	−9.14348	−0.588983	−0.294492	+	0.955654i	$0.595150\pi$
$242$	6.71082	0.431388
$243$	13.9001	0.891693
$244$	8.63544	0.552828
$245$	14.6704	0.937256
$246$	−14.3891	−0.917414
$247$	−4.75955	−0.302843
$248$	2.22751	0.141447
$249$	4.04330	0.256234
$250$	2.27530	0.143902
$251$	−8.31274	−0.524696	−0.262348	−	0.964973i	$-0.584497\pi$
$251$	−8.31274	−0.524696	−0.262348	+	0.964973i	$0.584497\pi$
$252$	−7.96468	−0.501728
$253$	−10.4091	−0.654416
$254$	9.23004	0.579145
$255$	43.4090	2.71838
$256$	1.00000	0.0625000
$257$	7.21973	0.450354	0.225177	−	0.974318i	$-0.427704\pi$
$257$	7.21973	0.450354	0.225177	+	0.974318i	$0.427704\pi$
$258$	−18.3080	−1.13981
$259$	5.87220	0.364881
$260$	2.49691	0.154852
$261$	39.4566	2.44231
$262$	15.1154	0.933830
$263$	−23.1468	−1.42730	−0.713648	−	0.700505i	$-0.752958\pi$
$263$	−23.1468	−1.42730	−0.713648	+	0.700505i	$0.752958\pi$
$264$	5.86619	0.361039
$265$	5.63492	0.346151
$266$	9.88486	0.606080
$267$	−10.2763	−0.628900
$268$	−7.02847	−0.429332
$269$	19.0889	1.16387	0.581935	−	0.813235i	$-0.302296\pi$
$269$	19.0889	1.16387	0.581935	+	0.813235i	$0.302296\pi$
$270$	−18.7402	−1.14049
$271$	−14.7778	−0.897686	−0.448843	−	0.893611i	$-0.648164\pi$
$271$	−14.7778	−0.897686	−0.448843	+	0.893611i	$0.648164\pi$
$272$	4.68604	0.284133
$273$	−3.42903	−0.207534
$274$	−16.0029	−0.966772
$275$	11.7960	0.711327
$276$	14.2363	0.856922
$277$	−6.48841	−0.389851	−0.194925	−	0.980818i	$-0.562446\pi$
$277$	−6.48841	−0.389851	−0.194925	+	0.980818i	$0.562446\pi$
$278$	0.466422	0.0279741
$279$	−11.1888	−0.669858
$280$	−5.18571	−0.309905
$281$	−24.5796	−1.46629	−0.733147	−	0.680071i	$-0.761949\pi$
$281$	−24.5796	−1.46629	−0.733147	+	0.680071i	$0.761949\pi$
$282$	16.6552	0.991804
$283$	18.7048	1.11189	0.555944	−	0.831220i	$-0.312357\pi$
$283$	18.7048	1.11189	0.555944	+	0.831220i	$0.312357\pi$
$284$	11.9510	0.709162
$285$	57.7486	3.42073
$286$	1.58120	0.0934981
$287$	8.05503	0.475473
$288$	−5.02302	−0.295985
$289$	4.95893	0.291702
$290$	25.6898	1.50855
$291$	−3.43056	−0.201103
$292$	−4.45320	−0.260604
$293$	14.7103	0.859386	0.429693	−	0.902975i	$-0.358622\pi$
$293$	14.7103	0.859386	0.429693	+	0.902975i	$0.358622\pi$
$294$	−12.7059	−0.741023
$295$	23.5759	1.37264
$296$	3.70338	0.215254
$297$	−11.8674	−0.688619
$298$	3.53195	0.204601
$299$	3.83730	0.221917
$300$	−16.1331	−0.931444
$301$	10.2488	0.590733
$302$	1.54227	0.0887476
$303$	−22.4173	−1.28784
$304$	6.23401	0.357545
$305$	−28.2416	−1.61711
$306$	−23.5381	−1.34558
$307$	12.6186	0.720184	0.360092	−	0.932917i	$-0.382745\pi$
$307$	12.6186	0.720184	0.360092	+	0.932917i	$0.382745\pi$
$308$	−3.28390	−0.187118
$309$	18.0532	1.02701
$310$	−7.28491	−0.413755
$311$	24.4649	1.38727	0.693637	−	0.720324i	$-0.256007\pi$
$311$	24.4649	1.38727	0.693637	+	0.720324i	$0.256007\pi$
$312$	−2.16256	−0.122431
$313$	4.84117	0.273639	0.136820	−	0.990596i	$-0.456312\pi$
$313$	4.84117	0.273639	0.136820	+	0.990596i	$0.456312\pi$
$314$	−2.42508	−0.136855
$315$	26.0479	1.46763
$316$	−0.488301	−0.0274691
$317$	10.6666	0.599094	0.299547	−	0.954082i	$-0.403164\pi$
$317$	10.6666	0.599094	0.299547	+	0.954082i	$0.403164\pi$
$318$	−4.88036	−0.273677
$319$	16.2683	0.910850
$320$	−3.27043	−0.182823
$321$	−20.7009	−1.15541
$322$	−7.96948	−0.444122
$323$	29.2128	1.62544
$324$	1.16170	0.0645387
$325$	−4.34858	−0.241216
$326$	4.59512	0.254500
$327$	0.318578	0.0176174
$328$	5.08000	0.280496
$329$	−9.32362	−0.514028
$330$	−19.1850	−1.05610
$331$	17.4040	0.956608	0.478304	−	0.878194i	$-0.341252\pi$
$331$	17.4040	0.956608	0.478304	+	0.878194i	$0.341252\pi$
$332$	−1.42747	−0.0783425
$333$	−18.6022	−1.01939
$334$	−10.2467	−0.560672
$335$	22.9861	1.25587
$336$	4.49130	0.245020
$337$	17.2199	0.938028	0.469014	−	0.883191i	$-0.344609\pi$
$337$	17.2199	0.938028	0.469014	+	0.883191i	$0.344609\pi$
$338$	12.4171	0.675401
$339$	30.8056	1.67313
$340$	−15.3254	−0.831134
$341$	−4.61325	−0.249821
$342$	−31.3136	−1.69324
$343$	18.2122	0.983367
$344$	6.46356	0.348492
$345$	−46.5587	−2.50664
$346$	−3.05336	−0.164150
$347$	2.59857	0.139499	0.0697494	−	0.997565i	$-0.477780\pi$
$347$	2.59857	0.139499	0.0697494	+	0.997565i	$0.477780\pi$
$348$	−22.2497	−1.19271
$349$	30.1167	1.61211	0.806054	−	0.591842i	$-0.201599\pi$
$349$	30.1167	1.61211	0.806054	+	0.591842i	$0.201599\pi$
$350$	9.03132	0.482745
$351$	4.37491	0.233515
$352$	−2.07103	−0.110387
$353$	−33.2920	−1.77195	−0.885977	−	0.463729i	$-0.846511\pi$
$353$	−33.2920	−1.77195	−0.885977	+	0.463729i	$0.846511\pi$
$354$	−20.4189	−1.08525
$355$	−39.0850	−2.07441
$356$	3.62801	0.192284
$357$	21.0464	1.11389
$358$	−15.5719	−0.823003
$359$	21.9179	1.15678	0.578392	−	0.815759i	$-0.303680\pi$
$359$	21.9179	1.15678	0.578392	+	0.815759i	$0.303680\pi$
$360$	16.4275	0.865803
$361$	19.8629	1.04541
$362$	−15.0167	−0.789260
$363$	19.0083	0.997680
$364$	1.21060	0.0634528
$365$	14.5639	0.762308
$366$	24.4598	1.27854
$367$	19.2664	1.00570	0.502848	−	0.864375i	$-0.332285\pi$
$367$	19.2664	1.00570	0.502848	+	0.864375i	$0.332285\pi$
$368$	−5.02605	−0.262001
$369$	−25.5170	−1.32836
$370$	−12.1116	−0.629654
$371$	2.73203	0.141840
$372$	6.30941	0.327128
$373$	10.7883	0.558598	0.279299	−	0.960204i	$-0.409898\pi$
$373$	10.7883	0.558598	0.279299	+	0.960204i	$0.409898\pi$
$374$	−9.70494	−0.501831
$375$	6.44476	0.332806
$376$	−5.88006	−0.303241
$377$	−5.99727	−0.308875
$378$	−9.08601	−0.467334
$379$	−32.6288	−1.67603	−0.838014	−	0.545649i	$-0.816283\pi$
$379$	−32.6288	−1.67603	−0.838014	+	0.545649i	$0.816283\pi$
$380$	−20.3879	−1.04588
$381$	26.1440	1.33940
$382$	15.3858	0.787204
$383$	−25.0216	−1.27854	−0.639272	−	0.768981i	$-0.720764\pi$
$383$	−25.0216	−1.27854	−0.639272	+	0.768981i	$0.720764\pi$
$384$	2.83249	0.144545
$385$	10.7398	0.547350
$386$	−10.2801	−0.523243
$387$	−32.4666	−1.65037
$388$	1.21114	0.0614865
$389$	−0.209913	−0.0106430	−0.00532150	−	0.999986i	$-0.501694\pi$
$389$	−0.209913	−0.0106430	−0.00532150	+	0.999986i	$0.501694\pi$
$390$	7.07250	0.358130
$391$	−23.5523	−1.19109
$392$	4.48576	0.226565
$393$	42.8142	2.15969
$394$	−13.3140	−0.670751
$395$	1.59696	0.0803515
$396$	10.4029	0.522763
$397$	18.0222	0.904508	0.452254	−	0.891889i	$-0.350620\pi$
$397$	18.0222	0.904508	0.452254	+	0.891889i	$0.350620\pi$
$398$	−17.1547	−0.859887
$399$	27.9988	1.40169
$400$	5.69572	0.284786
$401$	−10.9500	−0.546818	−0.273409	−	0.961898i	$-0.588151\pi$
$401$	−10.9500	−0.546818	−0.273409	+	0.961898i	$0.588151\pi$
$402$	−19.9081	−0.992926
$403$	1.70066	0.0847160
$404$	7.91433	0.393753
$405$	−3.79925	−0.188786
$406$	12.4554	0.618151
$407$	−7.66982	−0.380179
$408$	13.2732	0.657120
$409$	−16.0885	−0.795525	−0.397763	−	0.917488i	$-0.630213\pi$
$409$	−16.0885	−0.795525	−0.397763	+	0.917488i	$0.630213\pi$
$410$	−16.6138	−0.820497
$411$	−45.3282	−2.23587
$412$	−6.37361	−0.314005
$413$	11.4305	0.562459
$414$	25.2460	1.24077
$415$	4.66844	0.229165
$416$	0.763482	0.0374328
$417$	1.32114	0.0646964
$418$	−12.9108	−0.631490
$419$	−23.4622	−1.14620	−0.573101	−	0.819484i	$-0.694260\pi$
$419$	−23.4622	−1.14620	−0.573101	+	0.819484i	$0.694260\pi$
$420$	−14.6885	−0.716725
$421$	−19.0266	−0.927298	−0.463649	−	0.886019i	$-0.653460\pi$
$421$	−19.0266	−0.927298	−0.463649	+	0.886019i	$0.653460\pi$
$422$	25.5062	1.24162
$423$	29.5357	1.43607
$424$	1.72299	0.0836759
$425$	26.6903	1.29467
$426$	33.8512	1.64009
$427$	−13.6927	−0.662634
$428$	7.30835	0.353263
$429$	4.47873	0.216235
$430$	−21.1386	−1.01939
$431$	29.2423	1.40855	0.704276	−	0.709926i	$-0.251272\pi$
$431$	29.2423	1.40855	0.704276	+	0.709926i	$0.251272\pi$
$432$	−5.73020	−0.275695
$433$	6.73881	0.323847	0.161923	−	0.986803i	$-0.448230\pi$
$433$	6.73881	0.323847	0.161923	+	0.986803i	$0.448230\pi$
$434$	−3.53201	−0.169542
$435$	72.7661	3.48887
$436$	−0.112473	−0.00538646
$437$	−31.3325	−1.49883
$438$	−12.6137	−0.602704
$439$	−26.4575	−1.26275	−0.631374	−	0.775478i	$-0.717509\pi$
$439$	−26.4575	−1.26275	−0.631374	+	0.775478i	$0.717509\pi$
$440$	6.77317	0.322898
$441$	−22.5321	−1.07296
$442$	3.57770	0.170174
$443$	9.29324	0.441535	0.220768	−	0.975326i	$-0.429144\pi$
$443$	9.29324	0.441535	0.220768	+	0.975326i	$0.429144\pi$
$444$	10.4898	0.497824
$445$	−11.8651	−0.562462
$446$	12.8115	0.606643
$447$	10.0042	0.473184
$448$	−1.58563	−0.0749142
$449$	11.9721	0.564999	0.282499	−	0.959267i	$-0.408836\pi$
$449$	11.9721	0.564999	0.282499	+	0.959267i	$0.408836\pi$
$450$	−28.6097	−1.34868
$451$	−10.5209	−0.495408
$452$	−10.8758	−0.511554
$453$	4.36847	0.205249
$454$	−8.71645	−0.409083
$455$	−3.95919	−0.185610
$456$	17.6578	0.826902
$457$	−6.94158	−0.324713	−0.162357	−	0.986732i	$-0.551909\pi$
$457$	−6.94158	−0.324713	−0.162357	+	0.986732i	$0.551909\pi$
$458$	−1.93862	−0.0905856
$459$	−26.8519	−1.25334
$460$	16.4374	0.766396
$461$	32.9987	1.53690	0.768451	−	0.639908i	$-0.221028\pi$
$461$	32.9987	1.53690	0.768451	+	0.639908i	$0.221028\pi$
$462$	−9.30164	−0.432751
$463$	−14.7379	−0.684928	−0.342464	−	0.939531i	$-0.611261\pi$
$463$	−14.7379	−0.684928	−0.342464	+	0.939531i	$0.611261\pi$
$464$	7.85516	0.364667
$465$	−20.6345	−0.956901
$466$	0.191782	0.00888415
$467$	−11.6496	−0.539081	−0.269541	−	0.962989i	$-0.586872\pi$
$467$	−11.6496	−0.539081	−0.269541	+	0.962989i	$0.586872\pi$
$468$	−3.83499	−0.177272
$469$	11.1446	0.514609
$470$	19.2303	0.887028
$471$	−6.86904	−0.316509
$472$	7.20880	0.331812
$473$	−13.3863	−0.615500
$474$	−1.38311	−0.0635284
$475$	35.5072	1.62918
$476$	−7.43034	−0.340569
$477$	−8.65463	−0.396268
$478$	12.1948	0.557778
$479$	29.9613	1.36897	0.684484	−	0.729027i	$-0.260027\pi$
$479$	29.9613	1.36897	0.684484	+	0.729027i	$0.260027\pi$
$480$	−9.26348	−0.422818
$481$	2.82746	0.128921
$482$	9.14348	0.416474
$483$	−22.5735	−1.02713
$484$	−6.71082	−0.305037
$485$	−3.96096	−0.179858
$486$	−13.9001	−0.630522
$487$	−13.7369	−0.622476	−0.311238	−	0.950332i	$-0.600744\pi$
$487$	−13.7369	−0.622476	−0.311238	+	0.950332i	$0.600744\pi$
$488$	−8.63544	−0.390908
$489$	13.0157	0.588588
$490$	−14.6704	−0.662740
$491$	16.9989	0.767150	0.383575	−	0.923510i	$-0.374693\pi$
$491$	16.9989	0.767150	0.383575	+	0.923510i	$0.374693\pi$
$492$	14.3891	0.648710
$493$	36.8096	1.65782
$494$	4.75955	0.214142
$495$	−34.0218	−1.52917
$496$	−2.22751	−0.100018
$497$	−18.9499	−0.850021
$498$	−4.04330	−0.181184
$499$	−29.4009	−1.31616	−0.658082	−	0.752947i	$-0.728632\pi$
$499$	−29.4009	−1.31616	−0.658082	+	0.752947i	$0.728632\pi$
$500$	−2.27530	−0.101754
$501$	−29.0236	−1.29668
$502$	8.31274	0.371016
$503$	−6.33963	−0.282670	−0.141335	−	0.989962i	$-0.545140\pi$
$503$	−6.33963	−0.282670	−0.141335	+	0.989962i	$0.545140\pi$
$504$	7.96468	0.354775
$505$	−25.8833	−1.15179
$506$	10.4091	0.462742
$507$	35.1714	1.56201
$508$	−9.23004	−0.409517
$509$	43.0044	1.90614	0.953068	−	0.302755i	$-0.0979064\pi$
$509$	43.0044	1.90614	0.953068	+	0.302755i	$0.0979064\pi$
$510$	−43.4090	−1.92218
$511$	7.06114	0.312366
$512$	−1.00000	−0.0441942
$513$	−35.7221	−1.57717
$514$	−7.21973	−0.318449
$515$	20.8444	0.918516
$516$	18.3080	0.805964
$517$	12.1778	0.535579
$518$	−5.87220	−0.258010
$519$	−8.64862	−0.379632
$520$	−2.49691	−0.109497
$521$	25.3540	1.11078	0.555389	−	0.831591i	$-0.312570\pi$
$521$	25.3540	1.11078	0.555389	+	0.831591i	$0.312570\pi$
$522$	−39.4566	−1.72697
$523$	−13.0492	−0.570603	−0.285302	−	0.958438i	$-0.592094\pi$
$523$	−13.0492	−0.570603	−0.285302	+	0.958438i	$0.592094\pi$
$524$	−15.1154	−0.660318
$525$	25.5812	1.11645
$526$	23.1468	1.00925
$527$	−10.4382	−0.454695
$528$	−5.86619	−0.255293
$529$	2.26119	0.0983127
$530$	−5.63492	−0.244765
$531$	−36.2100	−1.57138
$532$	−9.88486	−0.428563
$533$	3.87849	0.167996
$534$	10.2763	0.444699
$535$	−23.9015	−1.03335
$536$	7.02847	0.303584
$537$	−44.1074	−1.90338
$538$	−19.0889	−0.822980
$539$	−9.29017	−0.400156
$540$	18.7402	0.806451
$541$	7.32738	0.315029	0.157514	−	0.987517i	$-0.449652\pi$
$541$	7.32738	0.315029	0.157514	+	0.987517i	$0.449652\pi$
$542$	14.7778	0.634760
$543$	−42.5347	−1.82534
$544$	−4.68604	−0.200912
$545$	0.367834	0.0157563
$546$	3.42903	0.146749
$547$	−17.0328	−0.728270	−0.364135	−	0.931346i	$-0.618635\pi$
$547$	−17.0328	−0.728270	−0.364135	+	0.931346i	$0.618635\pi$
$548$	16.0029	0.683611
$549$	43.3760	1.85124
$550$	−11.7960	−0.502984
$551$	48.9691	2.08616
$552$	−14.2363	−0.605936
$553$	0.774267	0.0329252
$554$	6.48841	0.275666
$555$	−34.3061	−1.45621
$556$	−0.466422	−0.0197807
$557$	28.7211	1.21695	0.608476	−	0.793572i	$-0.291781\pi$
$557$	28.7211	1.21695	0.608476	+	0.793572i	$0.291781\pi$
$558$	11.1888	0.473661
$559$	4.93481	0.208720
$560$	5.18571	0.219136
$561$	−27.4892	−1.16059
$562$	24.5796	1.03683
$563$	17.6289	0.742971	0.371485	−	0.928439i	$-0.378849\pi$
$563$	17.6289	0.742971	0.371485	+	0.928439i	$0.378849\pi$
$564$	−16.6552	−0.701311
$565$	35.5685	1.49638
$566$	−18.7048	−0.786223
$567$	−1.84203	−0.0773578
$568$	−11.9510	−0.501453
$569$	30.8221	1.29213	0.646064	−	0.763283i	$-0.276414\pi$
$569$	30.8221	1.29213	0.646064	+	0.763283i	$0.276414\pi$
$570$	−57.7486	−2.41882
$571$	11.1256	0.465591	0.232795	−	0.972526i	$-0.425213\pi$
$571$	11.1256	0.465591	0.232795	+	0.972526i	$0.425213\pi$
$572$	−1.58120	−0.0661132
$573$	43.5801	1.82058
$574$	−8.05503	−0.336210
$575$	−28.6270	−1.19383
$576$	5.02302	0.209293
$577$	4.81486	0.200445	0.100223	−	0.994965i	$-0.468044\pi$
$577$	4.81486	0.200445	0.100223	+	0.994965i	$0.468044\pi$
$578$	−4.95893	−0.206264
$579$	−29.1183	−1.21012
$580$	−25.6898	−1.06671
$581$	2.26344	0.0939035
$582$	3.43056	0.142201
$583$	−3.56837	−0.147787
$584$	4.45320	0.184275
$585$	12.5421	0.518550
$586$	−14.7103	−0.607677
$587$	−28.3912	−1.17183	−0.585914	−	0.810373i	$-0.699264\pi$
$587$	−28.3912	−1.17183	−0.585914	+	0.810373i	$0.699264\pi$
$588$	12.7059	0.523983
$589$	−13.8863	−0.572176
$590$	−23.5759	−0.970604
$591$	−37.7119	−1.55126
$592$	−3.70338	−0.152208
$593$	−3.53322	−0.145092	−0.0725459	−	0.997365i	$-0.523112\pi$
$593$	−3.53322	−0.145092	−0.0725459	+	0.997365i	$0.523112\pi$
$594$	11.8674	0.486927
$595$	24.3004	0.996220
$596$	−3.53195	−0.144674
$597$	−48.5905	−1.98868
$598$	−3.83730	−0.156919
$599$	8.29699	0.339006	0.169503	−	0.985530i	$-0.445784\pi$
$599$	8.29699	0.339006	0.169503	+	0.985530i	$0.445784\pi$
$600$	16.1331	0.658631
$601$	15.6336	0.637709	0.318855	−	0.947804i	$-0.396702\pi$
$601$	15.6336	0.637709	0.318855	+	0.947804i	$0.396702\pi$
$602$	−10.2488	−0.417711
$603$	−35.3042	−1.43770
$604$	−1.54227	−0.0627540
$605$	21.9473	0.892283
$606$	22.4173	0.910640
$607$	28.9765	1.17612	0.588061	−	0.808817i	$-0.299892\pi$
$607$	28.9765	1.17612	0.588061	+	0.808817i	$0.299892\pi$
$608$	−6.23401	−0.252822
$609$	35.2799	1.42961
$610$	28.2416	1.14347
$611$	−4.48932	−0.181618
$612$	23.5381	0.951470
$613$	37.6051	1.51886	0.759428	−	0.650591i	$-0.225479\pi$
$613$	37.6051	1.51886	0.759428	+	0.650591i	$0.225479\pi$
$614$	−12.6186	−0.509247
$615$	−47.0585	−1.89758
$616$	3.28390	0.132312
$617$	27.2420	1.09672	0.548362	−	0.836241i	$-0.315252\pi$
$617$	27.2420	1.09672	0.548362	+	0.836241i	$0.315252\pi$
$618$	−18.0532	−0.726206
$619$	−14.2146	−0.571332	−0.285666	−	0.958329i	$-0.592215\pi$
$619$	−14.2146	−0.571332	−0.285666	+	0.958329i	$0.592215\pi$
$620$	7.28491	0.292569
$621$	28.8003	1.15572
$622$	−24.4649	−0.980951
$623$	−5.75269	−0.230477
$624$	2.16256	0.0865716
$625$	−21.0374	−0.841496
$626$	−4.84117	−0.193492
$627$	−36.5699	−1.46046
$628$	2.42508	0.0967714
$629$	−17.3542	−0.691956
$630$	−26.0479	−1.03777
$631$	−34.7315	−1.38264	−0.691320	−	0.722548i	$-0.742971\pi$
$631$	−34.7315	−1.38264	−0.691320	+	0.722548i	$0.742971\pi$
$632$	0.488301	0.0194236
$633$	72.2462	2.87153
$634$	−10.6666	−0.423624
$635$	30.1862	1.19790
$636$	4.88036	0.193519
$637$	3.42480	0.135696
$638$	−16.2683	−0.644068
$639$	60.0302	2.37476
$640$	3.27043	0.129275
$641$	23.5167	0.928853	0.464427	−	0.885612i	$-0.346260\pi$
$641$	23.5167	0.928853	0.464427	+	0.885612i	$0.346260\pi$
$642$	20.7009	0.816998
$643$	−19.8646	−0.783384	−0.391692	−	0.920096i	$-0.628110\pi$
$643$	−19.8646	−0.783384	−0.391692	+	0.920096i	$0.628110\pi$
$644$	7.96948	0.314041
$645$	−59.8750	−2.35758
$646$	−29.2128	−1.14936
$647$	−38.7769	−1.52448	−0.762239	−	0.647295i	$-0.775900\pi$
$647$	−38.7769	−1.52448	−0.762239	+	0.647295i	$0.775900\pi$
$648$	−1.16170	−0.0456357
$649$	−14.9297	−0.586041
$650$	4.34858	0.170565
$651$	−10.0044	−0.392104
$652$	−4.59512	−0.179959
$653$	−36.1183	−1.41342	−0.706709	−	0.707505i	$-0.749821\pi$
$653$	−36.1183	−1.41342	−0.706709	+	0.707505i	$0.749821\pi$
$654$	−0.318578	−0.0124574
$655$	49.4337	1.93154
$656$	−5.08000	−0.198341
$657$	−22.3685	−0.872679
$658$	9.32362	0.363472
$659$	8.18695	0.318918	0.159459	−	0.987205i	$-0.449025\pi$
$659$	8.18695	0.318918	0.159459	+	0.987205i	$0.449025\pi$
$660$	19.1850	0.746774
$661$	43.6100	1.69623	0.848115	−	0.529812i	$-0.177737\pi$
$661$	43.6100	1.69623	0.848115	+	0.529812i	$0.177737\pi$
$662$	−17.4040	−0.676424
$663$	10.1338	0.393565
$664$	1.42747	0.0553965
$665$	32.3277	1.25362
$666$	18.6022	0.720819
$667$	−39.4804	−1.52869
$668$	10.2467	0.396455
$669$	36.2886	1.40300
$670$	−22.9861	−0.888032
$671$	17.8843	0.690416
$672$	−4.49130	−0.173256
$673$	13.2398	0.510358	0.255179	−	0.966894i	$-0.417866\pi$
$673$	13.2398	0.510358	0.255179	+	0.966894i	$0.417866\pi$
$674$	−17.2199	−0.663286
$675$	−32.6376	−1.25622
$676$	−12.4171	−0.477581
$677$	−20.5148	−0.788446	−0.394223	−	0.919015i	$-0.628986\pi$
$677$	−20.5148	−0.788446	−0.394223	+	0.919015i	$0.628986\pi$
$678$	−30.8056	−1.18308
$679$	−1.92043	−0.0736993
$680$	15.3254	0.587701
$681$	−24.6893	−0.946096
$682$	4.61325	0.176650
$683$	−23.4404	−0.896923	−0.448462	−	0.893802i	$-0.648028\pi$
$683$	−23.4404	−0.896923	−0.448462	+	0.893802i	$0.648028\pi$
$684$	31.3136	1.19730
$685$	−52.3364	−1.99967
$686$	−18.2122	−0.695346
$687$	−5.49112	−0.209499
$688$	−6.46356	−0.246421
$689$	1.31547	0.0501155
$690$	46.5587	1.77246
$691$	43.6349	1.65995	0.829975	−	0.557800i	$-0.188354\pi$
$691$	43.6349	1.65995	0.829975	+	0.557800i	$0.188354\pi$
$692$	3.05336	0.116071
$693$	−16.4951	−0.626598
$694$	−2.59857	−0.0986405
$695$	1.52540	0.0578617
$696$	22.2497	0.843372
$697$	−23.8051	−0.901681
$698$	−30.1167	−1.13993
$699$	0.543223	0.0205466
$700$	−9.03132	−0.341352
$701$	−20.5755	−0.777127	−0.388563	−	0.921422i	$-0.627029\pi$
$701$	−20.5755	−0.777127	−0.388563	+	0.921422i	$0.627029\pi$
$702$	−4.37491	−0.165120
$703$	−23.0869	−0.870739
$704$	2.07103	0.0780550
$705$	54.4698	2.05145
$706$	33.2920	1.25296
$707$	−12.5492	−0.471962
$708$	20.4189	0.767389
$709$	−38.8954	−1.46075	−0.730374	−	0.683048i	$-0.760654\pi$
$709$	−38.8954	−1.46075	−0.730374	+	0.683048i	$0.760654\pi$
$710$	39.0850	1.46683
$711$	−2.45275	−0.0919853
$712$	−3.62801	−0.135965
$713$	11.1956	0.419278
$714$	−21.0464	−0.787641
$715$	5.17120	0.193392
$716$	15.5719	0.581951
$717$	34.5417	1.28998
$718$	−21.9179	−0.817970
$719$	7.69773	0.287077	0.143538	−	0.989645i	$-0.454152\pi$
$719$	7.69773	0.287077	0.143538	+	0.989645i	$0.454152\pi$
$720$	−16.4275	−0.612215
$721$	10.1062	0.376375
$722$	−19.8629	−0.739220
$723$	25.8989	0.963189
$724$	15.0167	0.558091
$725$	44.7408	1.66163
$726$	−19.0083	−0.705466
$727$	9.75954	0.361961	0.180981	−	0.983487i	$-0.442073\pi$
$727$	9.75954	0.361961	0.180981	+	0.983487i	$0.442073\pi$
$728$	−1.21060	−0.0448679
$729$	−42.8571	−1.58730
$730$	−14.5639	−0.539033
$731$	−30.2885	−1.12026
$732$	−24.4598	−0.904062
$733$	4.14282	0.153019	0.0765093	−	0.997069i	$-0.475623\pi$
$733$	4.14282	0.153019	0.0765093	+	0.997069i	$0.475623\pi$
$734$	−19.2664	−0.711135
$735$	−41.5538	−1.53273
$736$	5.02605	0.185263
$737$	−14.5562	−0.536185
$738$	25.5170	0.939293
$739$	32.7330	1.20410	0.602052	−	0.798457i	$-0.294350\pi$
$739$	32.7330	1.20410	0.602052	+	0.798457i	$0.294350\pi$
$740$	12.1116	0.445233
$741$	13.4814	0.495252
$742$	−2.73203	−0.100296
$743$	−1.01405	−0.0372019	−0.0186009	−	0.999827i	$-0.505921\pi$
$743$	−1.01405	−0.0372019	−0.0186009	+	0.999827i	$0.505921\pi$
$744$	−6.30941	−0.231314
$745$	11.5510	0.423196
$746$	−10.7883	−0.394989
$747$	−7.17021	−0.262344
$748$	9.70494	0.354848
$749$	−11.5884	−0.423430
$750$	−6.44476	−0.235329
$751$	−20.2892	−0.740363	−0.370182	−	0.928959i	$-0.620705\pi$
$751$	−20.2892	−0.740363	−0.370182	+	0.928959i	$0.620705\pi$
$752$	5.88006	0.214424
$753$	23.5458	0.858056
$754$	5.99727	0.218408
$755$	5.04388	0.183566
$756$	9.08601	0.330455
$757$	−20.0860	−0.730037	−0.365018	−	0.931000i	$-0.618937\pi$
$757$	−20.0860	−0.730037	−0.365018	+	0.931000i	$0.618937\pi$
$758$	32.6288	1.18513
$759$	29.4838	1.07019
$760$	20.3879	0.739547
$761$	−20.7869	−0.753523	−0.376761	−	0.926310i	$-0.622962\pi$
$761$	−20.7869	−0.753523	−0.376761	+	0.926310i	$0.622962\pi$
$762$	−26.1440	−0.947099
$763$	0.178340	0.00645635
$764$	−15.3858	−0.556637
$765$	−76.9796	−2.78320
$766$	25.0216	0.904067
$767$	5.50379	0.198730
$768$	−2.83249	−0.102209
$769$	7.24557	0.261282	0.130641	−	0.991430i	$-0.458296\pi$
$769$	7.24557	0.261282	0.130641	+	0.991430i	$0.458296\pi$
$770$	−10.7398	−0.387035
$771$	−20.4498	−0.736483
$772$	10.2801	0.369989
$773$	−9.26515	−0.333244	−0.166622	−	0.986021i	$-0.553286\pi$
$773$	−9.26515	−0.333244	−0.166622	+	0.986021i	$0.553286\pi$
$774$	32.4666	1.16699
$775$	−12.6873	−0.455740
$776$	−1.21114	−0.0434775
$777$	−16.6330	−0.596705
$778$	0.209913	0.00752574
$779$	−31.6688	−1.13465
$780$	−7.07250	−0.253236
$781$	24.7510	0.885659
$782$	23.5523	0.842227
$783$	−45.0117	−1.60859
$784$	−4.48576	−0.160206
$785$	−7.93107	−0.283072
$786$	−42.8142	−1.52713
$787$	−18.1365	−0.646495	−0.323248	−	0.946314i	$-0.604775\pi$
$787$	−18.1365	−0.646495	−0.323248	+	0.946314i	$0.604775\pi$
$788$	13.3140	0.474293
$789$	65.5633	2.33412
$790$	−1.59696	−0.0568171
$791$	17.2450	0.613163
$792$	−10.4029	−0.369649
$793$	−6.59300	−0.234124
$794$	−18.0222	−0.639584
$795$	−15.9609	−0.566074
$796$	17.1547	0.608032
$797$	34.1001	1.20789	0.603944	−	0.797026i	$-0.293595\pi$
$797$	34.1001	1.20789	0.603944	+	0.797026i	$0.293595\pi$
$798$	−27.9988	−0.991147
$799$	27.5542	0.974796
$800$	−5.69572	−0.201374
$801$	18.2236	0.643898
$802$	10.9500	0.386658
$803$	−9.22272	−0.325463
$804$	19.9081	0.702105
$805$	−26.0636	−0.918622
$806$	−1.70066	−0.0599033
$807$	−54.0692	−1.90332
$808$	−7.91433	−0.278425
$809$	24.6684	0.867294	0.433647	−	0.901083i	$-0.357227\pi$
$809$	24.6684	0.867294	0.433647	+	0.901083i	$0.357227\pi$
$810$	3.79925	0.133492
$811$	−19.2193	−0.674880	−0.337440	−	0.941347i	$-0.609561\pi$
$811$	−19.2193	−0.674880	−0.337440	+	0.941347i	$0.609561\pi$
$812$	−12.4554	−0.437099
$813$	41.8579	1.46802
$814$	7.66982	0.268827
$815$	15.0280	0.526409
$816$	−13.2732	−0.464654
$817$	−40.2939	−1.40970
$818$	16.0885	0.562521
$819$	6.08089	0.212483
$820$	16.6138	0.580179
$821$	46.2983	1.61582	0.807912	−	0.589304i	$-0.200598\pi$
$821$	46.2983	1.61582	0.807912	+	0.589304i	$0.200598\pi$
$822$	45.3282	1.58100
$823$	3.25388	0.113423	0.0567116	−	0.998391i	$-0.481938\pi$
$823$	3.25388	0.113423	0.0567116	+	0.998391i	$0.481938\pi$
$824$	6.37361	0.222035
$825$	−33.4122	−1.16326
$826$	−11.4305	−0.397719
$827$	31.5695	1.09778	0.548890	−	0.835894i	$-0.315050\pi$
$827$	31.5695	1.09778	0.548890	+	0.835894i	$0.315050\pi$
$828$	−25.2460	−0.877358
$829$	27.6082	0.958872	0.479436	−	0.877577i	$-0.340841\pi$
$829$	27.6082	0.958872	0.479436	+	0.877577i	$0.340841\pi$
$830$	−4.66844	−0.162044
$831$	18.3784	0.637539
$832$	−0.763482	−0.0264690
$833$	−21.0205	−0.728316
$834$	−1.32114	−0.0457472
$835$	−33.5110	−1.15970
$836$	12.9108	0.446531
$837$	12.7641	0.441191
$838$	23.4622	0.810488
$839$	−11.1344	−0.384403	−0.192201	−	0.981356i	$-0.561563\pi$
$839$	−11.1344	−0.384403	−0.192201	+	0.981356i	$0.561563\pi$
$840$	14.6885	0.506801
$841$	32.7035	1.12771
$842$	19.0266	0.655699
$843$	69.6214	2.39789
$844$	−25.5062	−0.877960
$845$	40.6093	1.39700
$846$	−29.5357	−1.01546
$847$	10.6409	0.365626
$848$	−1.72299	−0.0591678
$849$	−52.9814	−1.81832
$850$	−26.6903	−0.915471
$851$	18.6134	0.638058
$852$	−33.8512	−1.15972
$853$	10.4933	0.359284	0.179642	−	0.983732i	$-0.442506\pi$
$853$	10.4933	0.359284	0.179642	+	0.983732i	$0.442506\pi$
$854$	13.6927	0.468553
$855$	−102.409	−3.50231
$856$	−7.30835	−0.249794
$857$	−1.92314	−0.0656933	−0.0328467	−	0.999460i	$-0.510457\pi$
$857$	−1.92314	−0.0656933	−0.0328467	+	0.999460i	$0.510457\pi$
$858$	−4.47873	−0.152901
$859$	−4.49958	−0.153524	−0.0767618	−	0.997049i	$-0.524458\pi$
$859$	−4.49958	−0.153524	−0.0767618	+	0.997049i	$0.524458\pi$
$860$	21.1386	0.720821
$861$	−22.8158	−0.777561
$862$	−29.2423	−0.995997
$863$	−21.4486	−0.730119	−0.365059	−	0.930984i	$-0.618951\pi$
$863$	−21.4486	−0.730119	−0.365059	+	0.930984i	$0.618951\pi$
$864$	5.73020	0.194945
$865$	−9.98580	−0.339527
$866$	−6.73881	−0.228994
$867$	−14.0461	−0.477032
$868$	3.53201	0.119884
$869$	−1.01129	−0.0343056
$870$	−72.7661	−2.46700
$871$	5.36611	0.181824
$872$	0.112473	0.00380880
$873$	6.08360	0.205899
$874$	31.3325	1.05984
$875$	3.60779	0.121965
$876$	12.6137	0.426176
$877$	40.8691	1.38005	0.690025	−	0.723785i	$-0.257599\pi$
$877$	40.8691	1.38005	0.690025	+	0.723785i	$0.257599\pi$
$878$	26.4575	0.892898
$879$	−41.6669	−1.40539
$880$	−6.77317	−0.228324
$881$	−28.9637	−0.975811	−0.487906	−	0.872896i	$-0.662239\pi$
$881$	−28.9637	−0.975811	−0.487906	+	0.872896i	$0.662239\pi$
$882$	22.5321	0.758695
$883$	−55.1407	−1.85563	−0.927816	−	0.373037i	$-0.878316\pi$
$883$	−55.1407	−1.85563	−0.927816	+	0.373037i	$0.878316\pi$
$884$	−3.57770	−0.120331
$885$	−66.7786	−2.24474
$886$	−9.29324	−0.312213
$887$	14.5151	0.487369	0.243685	−	0.969855i	$-0.421644\pi$
$887$	14.5151	0.487369	0.243685	+	0.969855i	$0.421644\pi$
$888$	−10.4898	−0.352014
$889$	14.6355	0.490858
$890$	11.8651	0.397720
$891$	2.40591	0.0806011
$892$	−12.8115	−0.428962
$893$	36.6563	1.22666
$894$	−10.0042	−0.334592
$895$	−50.9270	−1.70230
$896$	1.58563	0.0529723
$897$	−10.8691	−0.362910
$898$	−11.9721	−0.399514
$899$	−17.4974	−0.583572
$900$	28.6097	0.953657
$901$	−8.07400	−0.268984
$902$	10.5209	0.350306
$903$	−29.0298	−0.966050
$904$	10.8758	0.361724
$905$	−49.1111	−1.63251
$906$	−4.36847	−0.145133
$907$	−56.5518	−1.87777	−0.938886	−	0.344227i	$-0.888141\pi$
$907$	−56.5518	−1.87777	−0.938886	+	0.344227i	$0.888141\pi$
$908$	8.71645	0.289266
$909$	39.7539	1.31855
$910$	3.95919	0.131246
$911$	−12.0977	−0.400814	−0.200407	−	0.979713i	$-0.564226\pi$
$911$	−12.0977	−0.400814	−0.200407	+	0.979713i	$0.564226\pi$
$912$	−17.6578	−0.584708
$913$	−2.95634	−0.0978405
$914$	6.94158	0.229607
$915$	79.9942	2.64453
$916$	1.93862	0.0640537
$917$	23.9674	0.791474
$918$	26.8519	0.886246
$919$	25.7876	0.850656	0.425328	−	0.905039i	$-0.360159\pi$
$919$	25.7876	0.850656	0.425328	+	0.905039i	$0.360159\pi$
$920$	−16.4374	−0.541923
$921$	−35.7422	−1.17775
$922$	−32.9987	−1.08675
$923$	−9.12438	−0.300333
$924$	9.30164	0.306001
$925$	−21.0934	−0.693546
$926$	14.7379	0.484317
$927$	−32.0148	−1.05150
$928$	−7.85516	−0.257858
$929$	−28.6757	−0.940821	−0.470410	−	0.882448i	$-0.655894\pi$
$929$	−28.6757	−0.940821	−0.470410	+	0.882448i	$0.655894\pi$
$930$	20.6345	0.676631
$931$	−27.9643	−0.916493
$932$	−0.191782	−0.00628204
$933$	−69.2966	−2.26867
$934$	11.6496	0.381188
$935$	−31.7393	−1.03799
$936$	3.83499	0.125350
$937$	−6.87808	−0.224697	−0.112349	−	0.993669i	$-0.535837\pi$
$937$	−6.87808	−0.224697	−0.112349	+	0.993669i	$0.535837\pi$
$938$	−11.1446	−0.363884
$939$	−13.7126	−0.447494
$940$	−19.2303	−0.627224
$941$	19.2472	0.627440	0.313720	−	0.949515i	$-0.398425\pi$
$941$	19.2472	0.627440	0.313720	+	0.949515i	$0.398425\pi$
$942$	6.86904	0.223805
$943$	25.5324	0.831448
$944$	−7.20880	−0.234627
$945$	−29.7152	−0.966634
$946$	13.3863	0.435225
$947$	55.2085	1.79403	0.897017	−	0.441996i	$-0.145730\pi$
$947$	55.2085	1.79403	0.897017	+	0.441996i	$0.145730\pi$
$948$	1.38311	0.0449213
$949$	3.39993	0.110367
$950$	−35.5072	−1.15200
$951$	−30.2130	−0.979724
$952$	7.43034	0.240819
$953$	−11.0025	−0.356407	−0.178204	−	0.983994i	$-0.557029\pi$
$953$	−11.0025	−0.356407	−0.178204	+	0.983994i	$0.557029\pi$
$954$	8.65463	0.280204
$955$	50.3180	1.62825
$956$	−12.1948	−0.394408
$957$	−46.0799	−1.48955
$958$	−29.9613	−0.968007
$959$	−25.3748	−0.819394
$960$	9.26348	0.298977
$961$	−26.0382	−0.839942
$962$	−2.82746	−0.0911610
$963$	36.7100	1.18296
$964$	−9.14348	−0.294492
$965$	−33.6203	−1.08228
$966$	22.5735	0.726291
$967$	−3.80274	−0.122288	−0.0611439	−	0.998129i	$-0.519475\pi$
$967$	−3.80274	−0.122288	−0.0611439	+	0.998129i	$0.519475\pi$
$968$	6.71082	0.215694
$969$	−82.7451	−2.65815
$970$	3.96096	0.127179
$971$	34.0042	1.09125	0.545623	−	0.838031i	$-0.316293\pi$
$971$	34.0042	1.09125	0.545623	+	0.838031i	$0.316293\pi$
$972$	13.9001	0.445846
$973$	0.739574	0.0237097
$974$	13.7369	0.440157
$975$	12.3173	0.394470
$976$	8.63544	0.276414
$977$	21.8562	0.699240	0.349620	−	0.936892i	$-0.386311\pi$
$977$	21.8562	0.699240	0.349620	+	0.936892i	$0.386311\pi$
$978$	−13.0157	−0.416195
$979$	7.51372	0.240140
$980$	14.6704	0.468628
$981$	−0.564952	−0.0180375
$982$	−16.9989	−0.542457
$983$	−41.3247	−1.31805	−0.659027	−	0.752119i	$-0.729032\pi$
$983$	−41.3247	−1.31805	−0.659027	+	0.752119i	$0.729032\pi$
$984$	−14.3891	−0.458707
$985$	−43.5426	−1.38738
$986$	−36.8096	−1.17226
$987$	26.4091	0.840611
$988$	−4.75955	−0.151422
$989$	32.4862	1.03300
$990$	34.0218	1.08128
$991$	−53.0001	−1.68360	−0.841802	−	0.539787i	$-0.818505\pi$
$991$	−53.0001	−1.68360	−0.841802	+	0.539787i	$0.818505\pi$
$992$	2.22751	0.0707235
$993$	−49.2966	−1.56438
$994$	18.9499	0.601055
$995$	−56.1032	−1.77859
$996$	4.04330	0.128117
$997$	−17.4218	−0.551755	−0.275877	−	0.961193i	$-0.588968\pi$
$997$	−17.4218	−0.551755	−0.275877	+	0.961193i	$0.588968\pi$
$998$	29.4009	0.930668
$999$	21.2211	0.671406

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4006.2.a.h.1.5	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4006.2.a.h.1.5	✓	42	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:	\( N \)	\(=\)	\( 4006 = 2 \cdot 2003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4006.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.83249 q^{3} +1.00000 q^{4} -3.27043 q^{5} +2.83249 q^{6} -1.58563 q^{7} -1.00000 q^{8} +5.02302 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.83249 q^{3} +1.00000 q^{4} -3.27043 q^{5} +2.83249 q^{6} -1.58563 q^{7} -1.00000 q^{8} +5.02302 q^{9} +3.27043 q^{10} +2.07103 q^{11} -2.83249 q^{12} -0.763482 q^{13} +1.58563 q^{14} +9.26348 q^{15} +1.00000 q^{16} +4.68604 q^{17} -5.02302 q^{18} +6.23401 q^{19} -3.27043 q^{20} +4.49130 q^{21} -2.07103 q^{22} -5.02605 q^{23} +2.83249 q^{24} +5.69572 q^{25} +0.763482 q^{26} -5.73020 q^{27} -1.58563 q^{28} +7.85516 q^{29} -9.26348 q^{30} -2.22751 q^{31} -1.00000 q^{32} -5.86619 q^{33} -4.68604 q^{34} +5.18571 q^{35} +5.02302 q^{36} -3.70338 q^{37} -6.23401 q^{38} +2.16256 q^{39} +3.27043 q^{40} -5.08000 q^{41} -4.49130 q^{42} -6.46356 q^{43} +2.07103 q^{44} -16.4275 q^{45} +5.02605 q^{46} +5.88006 q^{47} -2.83249 q^{48} -4.48576 q^{49} -5.69572 q^{50} -13.2732 q^{51} -0.763482 q^{52} -1.72299 q^{53} +5.73020 q^{54} -6.77317 q^{55} +1.58563 q^{56} -17.6578 q^{57} -7.85516 q^{58} -7.20880 q^{59} +9.26348 q^{60} +8.63544 q^{61} +2.22751 q^{62} -7.96468 q^{63} +1.00000 q^{64} +2.49691 q^{65} +5.86619 q^{66} -7.02847 q^{67} +4.68604 q^{68} +14.2363 q^{69} -5.18571 q^{70} +11.9510 q^{71} -5.02302 q^{72} -4.45320 q^{73} +3.70338 q^{74} -16.1331 q^{75} +6.23401 q^{76} -3.28390 q^{77} -2.16256 q^{78} -0.488301 q^{79} -3.27043 q^{80} +1.16170 q^{81} +5.08000 q^{82} -1.42747 q^{83} +4.49130 q^{84} -15.3254 q^{85} +6.46356 q^{86} -22.2497 q^{87} -2.07103 q^{88} +3.62801 q^{89} +16.4275 q^{90} +1.21060 q^{91} -5.02605 q^{92} +6.30941 q^{93} -5.88006 q^{94} -20.3879 q^{95} +2.83249 q^{96} +1.21114 q^{97} +4.48576 q^{98} +10.4029 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q - 42 q^{2} + 42 q^{4} + 27 q^{5} - 10 q^{7} - 42 q^{8} + 56 q^{9}+O(q^{10}) \) 42 * q - 42 * q^2 + 42 * q^4 + 27 * q^5 - 10 * q^7 - 42 * q^8 + 56 * q^9	\( 42 q - 42 q^{2} + 42 q^{4} + 27 q^{5} - 10 q^{7} - 42 q^{8} + 56 q^{9} - 27 q^{10} + 23 q^{11} + 15 q^{13} + 10 q^{14} + 6 q^{15} + 42 q^{16} + 14 q^{17} - 56 q^{18} - 4 q^{19} + 27 q^{20} + 26 q^{21} - 23 q^{22} + 12 q^{23} + 45 q^{25} - 15 q^{26} - 3 q^{27} - 10 q^{28} + 41 q^{29} - 6 q^{30} + 18 q^{31} - 42 q^{32} + 25 q^{33} - 14 q^{34} + 8 q^{35} + 56 q^{36} + 33 q^{37} + 4 q^{38} + 10 q^{39} - 27 q^{40} + 84 q^{41} - 26 q^{42} - 36 q^{43} + 23 q^{44} + 66 q^{45} - 12 q^{46} + 28 q^{47} + 58 q^{49} - 45 q^{50} + 17 q^{51} + 15 q^{52} + 68 q^{53} + 3 q^{54} - 28 q^{55} + 10 q^{56} - 9 q^{57} - 41 q^{58} + 59 q^{59} + 6 q^{60} + 41 q^{61} - 18 q^{62} - 28 q^{63} + 42 q^{64} + 44 q^{65} - 25 q^{66} + 14 q^{68} + 67 q^{69} - 8 q^{70} + 69 q^{71} - 56 q^{72} - 27 q^{73} - 33 q^{74} + 14 q^{75} - 4 q^{76} + 43 q^{77} - 10 q^{78} - 19 q^{79} + 27 q^{80} + 74 q^{81} - 84 q^{82} + 20 q^{83} + 26 q^{84} + 16 q^{85} + 36 q^{86} - 28 q^{87} - 23 q^{88} + 123 q^{89} - 66 q^{90} - 9 q^{91} + 12 q^{92} + 48 q^{93} - 28 q^{94} + 28 q^{95} + 10 q^{97} - 58 q^{98} + 75 q^{99}+O(q^{100}) \) 42 * q - 42 * q^2 + 42 * q^4 + 27 * q^5 - 10 * q^7 - 42 * q^8 + 56 * q^9 - 27 * q^10 + 23 * q^11 + 15 * q^13 + 10 * q^14 + 6 * q^15 + 42 * q^16 + 14 * q^17 - 56 * q^18 - 4 * q^19 + 27 * q^20 + 26 * q^21 - 23 * q^22 + 12 * q^23 + 45 * q^25 - 15 * q^26 - 3 * q^27 - 10 * q^28 + 41 * q^29 - 6 * q^30 + 18 * q^31 - 42 * q^32 + 25 * q^33 - 14 * q^34 + 8 * q^35 + 56 * q^36 + 33 * q^37 + 4 * q^38 + 10 * q^39 - 27 * q^40 + 84 * q^41 - 26 * q^42 - 36 * q^43 + 23 * q^44 + 66 * q^45 - 12 * q^46 + 28 * q^47 + 58 * q^49 - 45 * q^50 + 17 * q^51 + 15 * q^52 + 68 * q^53 + 3 * q^54 - 28 * q^55 + 10 * q^56 - 9 * q^57 - 41 * q^58 + 59 * q^59 + 6 * q^60 + 41 * q^61 - 18 * q^62 - 28 * q^63 + 42 * q^64 + 44 * q^65 - 25 * q^66 + 14 * q^68 + 67 * q^69 - 8 * q^70 + 69 * q^71 - 56 * q^72 - 27 * q^73 - 33 * q^74 + 14 * q^75 - 4 * q^76 + 43 * q^77 - 10 * q^78 - 19 * q^79 + 27 * q^80 + 74 * q^81 - 84 * q^82 + 20 * q^83 + 26 * q^84 + 16 * q^85 + 36 * q^86 - 28 * q^87 - 23 * q^88 + 123 * q^89 - 66 * q^90 - 9 * q^91 + 12 * q^92 + 48 * q^93 - 28 * q^94 + 28 * q^95 + 10 * q^97 - 58 * q^98 + 75 * q^99

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