LMFDB - Embedded newform 8007.2.a.d.1.11

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:	$40$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.72962 q^{2} +1.00000 q^{3} +0.991576 q^{4} +0.136397 q^{5} -1.72962 q^{6} -2.36016 q^{7} +1.74419 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.72962 q^{2} +1.00000 q^{3} +0.991576 q^{4} +0.136397 q^{5} -1.72962 q^{6} -2.36016 q^{7} +1.74419 q^{8} +1.00000 q^{9} -0.235915 q^{10} +2.70133 q^{11} +0.991576 q^{12} -6.10946 q^{13} +4.08217 q^{14} +0.136397 q^{15} -4.99993 q^{16} +1.00000 q^{17} -1.72962 q^{18} -0.719030 q^{19} +0.135249 q^{20} -2.36016 q^{21} -4.67227 q^{22} +4.34049 q^{23} +1.74419 q^{24} -4.98140 q^{25} +10.5670 q^{26} +1.00000 q^{27} -2.34028 q^{28} +9.14692 q^{29} -0.235915 q^{30} -5.92398 q^{31} +5.15959 q^{32} +2.70133 q^{33} -1.72962 q^{34} -0.321920 q^{35} +0.991576 q^{36} +0.0402388 q^{37} +1.24365 q^{38} -6.10946 q^{39} +0.237903 q^{40} -0.431344 q^{41} +4.08217 q^{42} +6.80049 q^{43} +2.67858 q^{44} +0.136397 q^{45} -7.50738 q^{46} -4.70353 q^{47} -4.99993 q^{48} -1.42965 q^{49} +8.61591 q^{50} +1.00000 q^{51} -6.05800 q^{52} -0.843402 q^{53} -1.72962 q^{54} +0.368455 q^{55} -4.11656 q^{56} -0.719030 q^{57} -15.8207 q^{58} +7.90026 q^{59} +0.135249 q^{60} +6.28519 q^{61} +10.2462 q^{62} -2.36016 q^{63} +1.07574 q^{64} -0.833315 q^{65} -4.67227 q^{66} +4.65327 q^{67} +0.991576 q^{68} +4.34049 q^{69} +0.556798 q^{70} +11.3792 q^{71} +1.74419 q^{72} -1.61514 q^{73} -0.0695977 q^{74} -4.98140 q^{75} -0.712973 q^{76} -6.37557 q^{77} +10.5670 q^{78} -16.0844 q^{79} -0.681978 q^{80} +1.00000 q^{81} +0.746060 q^{82} -16.8047 q^{83} -2.34028 q^{84} +0.136397 q^{85} -11.7622 q^{86} +9.14692 q^{87} +4.71163 q^{88} +10.3432 q^{89} -0.235915 q^{90} +14.4193 q^{91} +4.30393 q^{92} -5.92398 q^{93} +8.13532 q^{94} -0.0980739 q^{95} +5.15959 q^{96} -5.91157 q^{97} +2.47275 q^{98} +2.70133 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 7 q^{2} + 40 q^{3} + 29 q^{4} - 15 q^{5} - 7 q^{6} - 13 q^{7} - 18 q^{8} + 40 q^{9}+O(q^{10}) $ 40 * q - 7 * q^2 + 40 * q^3 + 29 * q^4 - 15 * q^5 - 7 * q^6 - 13 * q^7 - 18 * q^8 + 40 * q^9	\( 40 q - 7 q^{2} + 40 q^{3} + 29 q^{4} - 15 q^{5} - 7 q^{6} - 13 q^{7} - 18 q^{8} + 40 q^{9} - 6 q^{10} - 25 q^{11} + 29 q^{12} - 24 q^{13} - 22 q^{14} - 15 q^{15} + 7 q^{16} + 40 q^{17} - 7 q^{18} - 18 q^{19} - 20 q^{20} - 13 q^{21} - 25 q^{22} - 28 q^{23} - 18 q^{24} - 11 q^{25} - 13 q^{26} + 40 q^{27} - 8 q^{28} - 23 q^{29} - 6 q^{30} - 11 q^{31} - 23 q^{32} - 25 q^{33} - 7 q^{34} - 45 q^{35} + 29 q^{36} - 38 q^{37} - 30 q^{38} - 24 q^{39} - 12 q^{40} - 33 q^{41} - 22 q^{42} - 25 q^{43} - 14 q^{44} - 15 q^{45} + 8 q^{46} - 55 q^{47} + 7 q^{48} - 21 q^{49} + 2 q^{50} + 40 q^{51} - 39 q^{52} - 39 q^{53} - 7 q^{54} - 9 q^{55} - 48 q^{56} - 18 q^{57} - 13 q^{58} - 81 q^{59} - 20 q^{60} - 9 q^{61} - 16 q^{62} - 13 q^{63} - 4 q^{64} - 43 q^{65} - 25 q^{66} - 24 q^{67} + 29 q^{68} - 28 q^{69} + 48 q^{70} - 32 q^{71} - 18 q^{72} - 43 q^{73} - 20 q^{74} - 11 q^{75} - 58 q^{76} - 32 q^{77} - 13 q^{78} - 22 q^{79} - 48 q^{80} + 40 q^{81} - 11 q^{82} - 45 q^{83} - 8 q^{84} - 15 q^{85} - 30 q^{86} - 23 q^{87} - 48 q^{88} - 94 q^{89} - 6 q^{90} - 7 q^{91} - 98 q^{92} - 11 q^{93} + 32 q^{94} - 23 q^{96} - 28 q^{97} - 46 q^{98} - 25 q^{99}+O(q^{100}) \) 40 * q - 7 * q^2 + 40 * q^3 + 29 * q^4 - 15 * q^5 - 7 * q^6 - 13 * q^7 - 18 * q^8 + 40 * q^9 - 6 * q^10 - 25 * q^11 + 29 * q^12 - 24 * q^13 - 22 * q^14 - 15 * q^15 + 7 * q^16 + 40 * q^17 - 7 * q^18 - 18 * q^19 - 20 * q^20 - 13 * q^21 - 25 * q^22 - 28 * q^23 - 18 * q^24 - 11 * q^25 - 13 * q^26 + 40 * q^27 - 8 * q^28 - 23 * q^29 - 6 * q^30 - 11 * q^31 - 23 * q^32 - 25 * q^33 - 7 * q^34 - 45 * q^35 + 29 * q^36 - 38 * q^37 - 30 * q^38 - 24 * q^39 - 12 * q^40 - 33 * q^41 - 22 * q^42 - 25 * q^43 - 14 * q^44 - 15 * q^45 + 8 * q^46 - 55 * q^47 + 7 * q^48 - 21 * q^49 + 2 * q^50 + 40 * q^51 - 39 * q^52 - 39 * q^53 - 7 * q^54 - 9 * q^55 - 48 * q^56 - 18 * q^57 - 13 * q^58 - 81 * q^59 - 20 * q^60 - 9 * q^61 - 16 * q^62 - 13 * q^63 - 4 * q^64 - 43 * q^65 - 25 * q^66 - 24 * q^67 + 29 * q^68 - 28 * q^69 + 48 * q^70 - 32 * q^71 - 18 * q^72 - 43 * q^73 - 20 * q^74 - 11 * q^75 - 58 * q^76 - 32 * q^77 - 13 * q^78 - 22 * q^79 - 48 * q^80 + 40 * q^81 - 11 * q^82 - 45 * q^83 - 8 * q^84 - 15 * q^85 - 30 * q^86 - 23 * q^87 - 48 * q^88 - 94 * q^89 - 6 * q^90 - 7 * q^91 - 98 * q^92 - 11 * q^93 + 32 * q^94 - 23 * q^96 - 28 * q^97 - 46 * q^98 - 25 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.72962	−1.22302	−0.611512	−	0.791235i	$-0.709438\pi$
$2$	−1.72962	−1.22302	−0.611512	+	0.791235i	$0.709438\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.991576	0.495788
$5$	0.136397	0.0609988	0.0304994	−	0.999535i	$-0.490290\pi$
$5$	0.136397	0.0609988	0.0304994	+	0.999535i	$0.490290\pi$
$6$	−1.72962	−0.706113
$7$	−2.36016	−0.892056	−0.446028	−	0.895019i	$-0.647162\pi$
$7$	−2.36016	−0.892056	−0.446028	+	0.895019i	$0.647162\pi$
$8$	1.74419	0.616663
$9$	1.00000	0.333333
$10$	−0.235915	−0.0746030
$11$	2.70133	0.814482	0.407241	−	0.913321i	$-0.366491\pi$
$11$	2.70133	0.814482	0.407241	+	0.913321i	$0.366491\pi$
$12$	0.991576	0.286243
$13$	−6.10946	−1.69446	−0.847230	−	0.531226i	$-0.821731\pi$
$13$	−6.10946	−1.69446	−0.847230	+	0.531226i	$0.821731\pi$
$14$	4.08217	1.09101
$15$	0.136397	0.0352177
$16$	−4.99993	−1.24998
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.72962	−0.407675
$19$	−0.719030	−0.164957	−0.0824784	−	0.996593i	$-0.526284\pi$
$19$	−0.719030	−0.164957	−0.0824784	+	0.996593i	$0.526284\pi$
$20$	0.135249	0.0302425
$21$	−2.36016	−0.515029
$22$	−4.67227	−0.996132
$23$	4.34049	0.905054	0.452527	−	0.891751i	$-0.350523\pi$
$23$	4.34049	0.905054	0.452527	+	0.891751i	$0.350523\pi$
$24$	1.74419	0.356031
$25$	−4.98140	−0.996279
$26$	10.5670	2.07237
$27$	1.00000	0.192450
$28$	−2.34028	−0.442271
$29$	9.14692	1.69854	0.849270	−	0.527958i	$-0.177042\pi$
$29$	9.14692	1.69854	0.849270	+	0.527958i	$0.177042\pi$
$30$	−0.235915	−0.0430721
$31$	−5.92398	−1.06398	−0.531989	−	0.846751i	$-0.678555\pi$
$31$	−5.92398	−1.06398	−0.531989	+	0.846751i	$0.678555\pi$
$32$	5.15959	0.912095
$33$	2.70133	0.470242
$34$	−1.72962	−0.296627
$35$	−0.321920	−0.0544144
$36$	0.991576	0.165263
$37$	0.0402388	0.00661521	0.00330761	−	0.999995i	$-0.498947\pi$
$37$	0.0402388	0.00661521	0.00330761	+	0.999995i	$0.498947\pi$
$38$	1.24365	0.201746
$39$	−6.10946	−0.978297
$40$	0.237903	0.0376157
$41$	−0.431344	−0.0673646	−0.0336823	−	0.999433i	$-0.510723\pi$
$41$	−0.431344	−0.0673646	−0.0336823	+	0.999433i	$0.510723\pi$
$42$	4.08217	0.629893
$43$	6.80049	1.03706	0.518532	−	0.855058i	$-0.326479\pi$
$43$	6.80049	1.03706	0.518532	+	0.855058i	$0.326479\pi$
$44$	2.67858	0.403811
$45$	0.136397	0.0203329
$46$	−7.50738	−1.10690
$47$	−4.70353	−0.686081	−0.343041	−	0.939321i	$-0.611457\pi$
$47$	−4.70353	−0.686081	−0.343041	+	0.939321i	$0.611457\pi$
$48$	−4.99993	−0.721678
$49$	−1.42965	−0.204236
$50$	8.61591	1.21847
$51$	1.00000	0.140028
$52$	−6.05800	−0.840093
$53$	−0.843402	−0.115850	−0.0579251	−	0.998321i	$-0.518448\pi$
$53$	−0.843402	−0.115850	−0.0579251	+	0.998321i	$0.518448\pi$
$54$	−1.72962	−0.235371
$55$	0.368455	0.0496825
$56$	−4.11656	−0.550098
$57$	−0.719030	−0.0952379
$58$	−15.8207	−2.07736
$59$	7.90026	1.02853	0.514263	−	0.857632i	$-0.328065\pi$
$59$	7.90026	1.02853	0.514263	+	0.857632i	$0.328065\pi$
$60$	0.135249	0.0174605
$61$	6.28519	0.804736	0.402368	−	0.915478i	$-0.368187\pi$
$61$	6.28519	0.804736	0.402368	+	0.915478i	$0.368187\pi$
$62$	10.2462	1.30127
$63$	−2.36016	−0.297352
$64$	1.07574	0.134467
$65$	−0.833315	−0.103360
$66$	−4.67227	−0.575117
$67$	4.65327	0.568487	0.284243	−	0.958752i	$-0.408258\pi$
$67$	4.65327	0.568487	0.284243	+	0.958752i	$0.408258\pi$
$68$	0.991576	0.120246
$69$	4.34049	0.522533
$70$	0.556798	0.0665501
$71$	11.3792	1.35047	0.675234	−	0.737604i	$-0.264043\pi$
$71$	11.3792	1.35047	0.675234	+	0.737604i	$0.264043\pi$
$72$	1.74419	0.205554
$73$	−1.61514	−0.189038	−0.0945188	−	0.995523i	$-0.530131\pi$
$73$	−1.61514	−0.189038	−0.0945188	+	0.995523i	$0.530131\pi$
$74$	−0.0695977	−0.00809057
$75$	−4.98140	−0.575202
$76$	−0.712973	−0.0817836
$77$	−6.37557	−0.726564
$78$	10.5670	1.19648
$79$	−16.0844	−1.80964	−0.904819	−	0.425797i	$-0.859994\pi$
$79$	−16.0844	−1.80964	−0.904819	+	0.425797i	$0.859994\pi$
$80$	−0.681978	−0.0762474
$81$	1.00000	0.111111
$82$	0.746060	0.0823886
$83$	−16.8047	−1.84455	−0.922276	−	0.386533i	$-0.873673\pi$
$83$	−16.8047	−1.84455	−0.922276	+	0.386533i	$0.873673\pi$
$84$	−2.34028	−0.255345
$85$	0.136397	0.0147944
$86$	−11.7622	−1.26836
$87$	9.14692	0.980653
$88$	4.71163	0.502261
$89$	10.3432	1.09638	0.548190	−	0.836354i	$-0.315317\pi$
$89$	10.3432	1.09638	0.548190	+	0.836354i	$0.315317\pi$
$90$	−0.235915	−0.0248677
$91$	14.4193	1.51155
$92$	4.30393	0.448715
$93$	−5.92398	−0.614289
$94$	8.13532	0.839094
$95$	−0.0980739	−0.0100622
$96$	5.15959	0.526599
$97$	−5.91157	−0.600229	−0.300114	−	0.953903i	$-0.597025\pi$
$97$	−5.91157	−0.600229	−0.300114	+	0.953903i	$0.597025\pi$
$98$	2.47275	0.249785
$99$	2.70133	0.271494
$100$	−4.93943	−0.493943
$101$	15.2467	1.51710	0.758550	−	0.651615i	$-0.225908\pi$
$101$	15.2467	1.51710	0.758550	+	0.651615i	$0.225908\pi$
$102$	−1.72962	−0.171258
$103$	3.61622	0.356317	0.178158	−	0.984002i	$-0.442986\pi$
$103$	3.61622	0.356317	0.178158	+	0.984002i	$0.442986\pi$
$104$	−10.6560	−1.04491
$105$	−0.321920	−0.0314162
$106$	1.45876	0.141688
$107$	−5.58060	−0.539497	−0.269749	−	0.962931i	$-0.586941\pi$
$107$	−5.58060	−0.539497	−0.269749	+	0.962931i	$0.586941\pi$
$108$	0.991576	0.0954145
$109$	−9.32871	−0.893528	−0.446764	−	0.894652i	$-0.647424\pi$
$109$	−9.32871	−0.893528	−0.446764	+	0.894652i	$0.647424\pi$
$110$	−0.637286	−0.0607629
$111$	0.0402388	0.00381930
$112$	11.8006	1.11505
$113$	−14.6904	−1.38196	−0.690979	−	0.722875i	$-0.742820\pi$
$113$	−14.6904	−1.38196	−0.690979	+	0.722875i	$0.742820\pi$
$114$	1.24365	0.116478
$115$	0.592032	0.0552072
$116$	9.06987	0.842117
$117$	−6.10946	−0.564820
$118$	−13.6644	−1.25791
$119$	−2.36016	−0.216355
$120$	0.237903	0.0217174
$121$	−3.70280	−0.336618
$122$	−10.8710	−0.984212
$123$	−0.431344	−0.0388930
$124$	−5.87408	−0.527508
$125$	−1.36144	−0.121771
$126$	4.08217	0.363669
$127$	9.59367	0.851300	0.425650	−	0.904888i	$-0.360045\pi$
$127$	9.59367	0.851300	0.425650	+	0.904888i	$0.360045\pi$
$128$	−12.1798	−1.07655
$129$	6.80049	0.598750
$130$	1.44132	0.126412
$131$	4.19546	0.366559	0.183280	−	0.983061i	$-0.441329\pi$
$131$	4.19546	0.366559	0.183280	+	0.983061i	$0.441329\pi$
$132$	2.67858	0.233140
$133$	1.69703	0.147151
$134$	−8.04837	−0.695273
$135$	0.136397	0.0117392
$136$	1.74419	0.149563
$137$	−8.88336	−0.758956	−0.379478	−	0.925201i	$-0.623896\pi$
$137$	−8.88336	−0.758956	−0.379478	+	0.925201i	$0.623896\pi$
$138$	−7.50738	−0.639071
$139$	−11.2201	−0.951680	−0.475840	−	0.879532i	$-0.657856\pi$
$139$	−11.2201	−0.951680	−0.475840	+	0.879532i	$0.657856\pi$
$140$	−0.319208	−0.0269780
$141$	−4.70353	−0.396109
$142$	−19.6817	−1.65165
$143$	−16.5037	−1.38011
$144$	−4.99993	−0.416661
$145$	1.24762	0.103609
$146$	2.79357	0.231198
$147$	−1.42965	−0.117916
$148$	0.0398998	0.00327975
$149$	−2.32932	−0.190825	−0.0954125	−	0.995438i	$-0.530417\pi$
$149$	−2.32932	−0.190825	−0.0954125	+	0.995438i	$0.530417\pi$
$150$	8.61591	0.703486
$151$	−16.8198	−1.36878	−0.684389	−	0.729117i	$-0.739931\pi$
$151$	−16.8198	−1.36878	−0.684389	+	0.729117i	$0.739931\pi$
$152$	−1.25412	−0.101723
$153$	1.00000	0.0808452
$154$	11.0273	0.888606
$155$	−0.808017	−0.0649015
$156$	−6.05800	−0.485028
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	27.8199	2.21323
$159$	−0.843402	−0.0668861
$160$	0.703755	0.0556367
$161$	−10.2442	−0.807359
$162$	−1.72962	−0.135892
$163$	6.15323	0.481958	0.240979	−	0.970530i	$-0.422531\pi$
$163$	6.15323	0.481958	0.240979	+	0.970530i	$0.422531\pi$
$164$	−0.427711	−0.0333986
$165$	0.368455	0.0286842
$166$	29.0656	2.25593
$167$	6.87944	0.532347	0.266174	−	0.963925i	$-0.414241\pi$
$167$	6.87944	0.532347	0.266174	+	0.963925i	$0.414241\pi$
$168$	−4.11656	−0.317599
$169$	24.3255	1.87119
$170$	−0.235915	−0.0180939
$171$	−0.719030	−0.0549856
$172$	6.74321	0.514165
$173$	0.960427	0.0730199	0.0365099	−	0.999333i	$-0.488376\pi$
$173$	0.960427	0.0730199	0.0365099	+	0.999333i	$0.488376\pi$
$174$	−15.8207	−1.19936
$175$	11.7569	0.888737
$176$	−13.5065	−1.01809
$177$	7.90026	0.593820
$178$	−17.8898	−1.34090
$179$	−11.5405	−0.862580	−0.431290	−	0.902213i	$-0.641941\pi$
$179$	−11.5405	−0.862580	−0.431290	+	0.902213i	$0.641941\pi$
$180$	0.135249	0.0100808
$181$	17.3120	1.28679	0.643395	−	0.765534i	$-0.277525\pi$
$181$	17.3120	1.28679	0.643395	+	0.765534i	$0.277525\pi$
$182$	−24.9399	−1.84867
$183$	6.28519	0.464615
$184$	7.57062	0.558114
$185$	0.00548847	0.000403520 0
$186$	10.2462	0.751290
$187$	2.70133	0.197541
$188$	−4.66391	−0.340151
$189$	−2.36016	−0.171676
$190$	0.169630	0.0123063
$191$	−5.39627	−0.390460	−0.195230	−	0.980757i	$-0.562545\pi$
$191$	−5.39627	−0.390460	−0.195230	+	0.980757i	$0.562545\pi$
$192$	1.07574	0.0776348
$193$	8.48203	0.610550	0.305275	−	0.952264i	$-0.401252\pi$
$193$	8.48203	0.610550	0.305275	+	0.952264i	$0.401252\pi$
$194$	10.2248	0.734094
$195$	−0.833315	−0.0596749
$196$	−1.41761	−0.101258
$197$	14.1223	1.00617	0.503087	−	0.864236i	$-0.332197\pi$
$197$	14.1223	1.00617	0.503087	+	0.864236i	$0.332197\pi$
$198$	−4.67227	−0.332044
$199$	3.17895	0.225350	0.112675	−	0.993632i	$-0.464058\pi$
$199$	3.17895	0.225350	0.112675	+	0.993632i	$0.464058\pi$
$200$	−8.68849	−0.614369
$201$	4.65327	0.328216
$202$	−26.3709	−1.85545
$203$	−21.5882	−1.51519
$204$	0.991576	0.0694242
$205$	−0.0588342	−0.00410916
$206$	−6.25467	−0.435784
$207$	4.34049	0.301685
$208$	30.5469	2.11804
$209$	−1.94234	−0.134354
$210$	0.556798	0.0384227
$211$	−26.7798	−1.84360	−0.921799	−	0.387667i	$-0.873281\pi$
$211$	−26.7798	−1.84360	−0.921799	+	0.387667i	$0.873281\pi$
$212$	−0.836297	−0.0574371
$213$	11.3792	0.779693
$214$	9.65231	0.659818
$215$	0.927570	0.0632597
$216$	1.74419	0.118677
$217$	13.9815	0.949129
$218$	16.1351	1.09281
$219$	−1.61514	−0.109141
$220$	0.365351	0.0246320
$221$	−6.10946	−0.410967
$222$	−0.0695977	−0.00467109
$223$	−14.9703	−1.00249	−0.501244	−	0.865306i	$-0.667124\pi$
$223$	−14.9703	−1.00249	−0.501244	+	0.865306i	$0.667124\pi$
$224$	−12.1775	−0.813640
$225$	−4.98140	−0.332093
$226$	25.4088	1.69017
$227$	20.4763	1.35906	0.679530	−	0.733648i	$-0.262184\pi$
$227$	20.4763	1.35906	0.679530	+	0.733648i	$0.262184\pi$
$228$	−0.712973	−0.0472178
$229$	−21.3762	−1.41258	−0.706290	−	0.707923i	$-0.749632\pi$
$229$	−21.3762	−1.41258	−0.706290	+	0.707923i	$0.749632\pi$
$230$	−1.02399	−0.0675198
$231$	−6.37557	−0.419482
$232$	15.9539	1.04743
$233$	−12.6137	−0.826351	−0.413176	−	0.910651i	$-0.635580\pi$
$233$	−12.6137	−0.826351	−0.413176	+	0.910651i	$0.635580\pi$
$234$	10.5670	0.690788
$235$	−0.641550	−0.0418501
$236$	7.83372	0.509931
$237$	−16.0844	−1.04479
$238$	4.08217	0.264608
$239$	7.50667	0.485566	0.242783	−	0.970081i	$-0.421940\pi$
$239$	7.50667	0.485566	0.242783	+	0.970081i	$0.421940\pi$
$240$	−0.681978	−0.0440215
$241$	15.0146	0.967178	0.483589	−	0.875295i	$-0.339333\pi$
$241$	15.0146	0.967178	0.483589	+	0.875295i	$0.339333\pi$
$242$	6.40443	0.411692
$243$	1.00000	0.0641500
$244$	6.23225	0.398979
$245$	−0.195001	−0.0124581
$246$	0.746060	0.0475671
$247$	4.39289	0.279513
$248$	−10.3325	−0.656117
$249$	−16.8047	−1.06495
$250$	2.35477	0.148928
$251$	−9.86897	−0.622924	−0.311462	−	0.950259i	$-0.600819\pi$
$251$	−9.86897	−0.622924	−0.311462	+	0.950259i	$0.600819\pi$
$252$	−2.34028	−0.147424
$253$	11.7251	0.737151
$254$	−16.5934	−1.04116
$255$	0.136397	0.00854154
$256$	18.9149	1.18218
$257$	−26.0094	−1.62242	−0.811212	−	0.584753i	$-0.801192\pi$
$257$	−26.0094	−1.62242	−0.811212	+	0.584753i	$0.801192\pi$
$258$	−11.7622	−0.732285
$259$	−0.0949699	−0.00590114
$260$	−0.826296	−0.0512447
$261$	9.14692	0.566180
$262$	−7.25655	−0.448311
$263$	13.7524	0.848009	0.424005	−	0.905660i	$-0.360624\pi$
$263$	13.7524	0.848009	0.424005	+	0.905660i	$0.360624\pi$
$264$	4.71163	0.289981
$265$	−0.115038	−0.00706672
$266$	−2.93520	−0.179969
$267$	10.3432	0.632995
$268$	4.61407	0.281849
$269$	−19.9320	−1.21528	−0.607638	−	0.794214i	$-0.707883\pi$
$269$	−19.9320	−1.21528	−0.607638	+	0.794214i	$0.707883\pi$
$270$	−0.235915	−0.0143574
$271$	−13.5841	−0.825178	−0.412589	−	0.910917i	$-0.635375\pi$
$271$	−13.5841	−0.825178	−0.412589	+	0.910917i	$0.635375\pi$
$272$	−4.99993	−0.303165
$273$	14.4193	0.872696
$274$	15.3648	0.928222
$275$	−13.4564	−0.811452
$276$	4.30393	0.259066
$277$	−13.8920	−0.834687	−0.417344	−	0.908749i	$-0.637039\pi$
$277$	−13.8920	−0.834687	−0.417344	+	0.908749i	$0.637039\pi$
$278$	19.4066	1.16393
$279$	−5.92398	−0.354660
$280$	−0.561488	−0.0335553
$281$	5.72051	0.341257	0.170629	−	0.985335i	$-0.445420\pi$
$281$	5.72051	0.341257	0.170629	+	0.985335i	$0.445420\pi$
$282$	8.13532	0.484451
$283$	−12.0908	−0.718724	−0.359362	−	0.933198i	$-0.617006\pi$
$283$	−12.0908	−0.718724	−0.359362	+	0.933198i	$0.617006\pi$
$284$	11.2834	0.669546
$285$	−0.0980739	−0.00580940
$286$	28.5451	1.68791
$287$	1.01804	0.0600930
$288$	5.15959	0.304032
$289$	1.00000	0.0588235
$290$	−2.15790	−0.126716
$291$	−5.91157	−0.346542
$292$	−1.60153	−0.0937227
$293$	7.25675	0.423944	0.211972	−	0.977276i	$-0.432011\pi$
$293$	7.25675	0.423944	0.211972	+	0.977276i	$0.432011\pi$
$294$	2.47275	0.144214
$295$	1.07758	0.0627389
$296$	0.0701839	0.00407936
$297$	2.70133	0.156747
$298$	4.02883	0.233384
$299$	−26.5180	−1.53358
$300$	−4.93943	−0.285178
$301$	−16.0502	−0.925120
$302$	29.0919	1.67405
$303$	15.2467	0.875898
$304$	3.59510	0.206193
$305$	0.857284	0.0490880
$306$	−1.72962	−0.0988756
$307$	−3.25442	−0.185740	−0.0928698	−	0.995678i	$-0.529604\pi$
$307$	−3.25442	−0.185740	−0.0928698	+	0.995678i	$0.529604\pi$
$308$	−6.32187	−0.360222
$309$	3.61622	0.205719
$310$	1.39756	0.0793760
$311$	31.0893	1.76291	0.881455	−	0.472268i	$-0.156564\pi$
$311$	31.0893	1.76291	0.881455	+	0.472268i	$0.156564\pi$
$312$	−10.6560	−0.603280
$313$	10.3781	0.586604	0.293302	−	0.956020i	$-0.405246\pi$
$313$	10.3781	0.586604	0.293302	+	0.956020i	$0.405246\pi$
$314$	1.72962	0.0976080
$315$	−0.321920	−0.0181381
$316$	−15.9489	−0.897197
$317$	−26.0339	−1.46221	−0.731105	−	0.682265i	$-0.760995\pi$
$317$	−26.0339	−1.46221	−0.731105	+	0.682265i	$0.760995\pi$
$318$	1.45876	0.0818033
$319$	24.7089	1.38343
$320$	0.146728	0.00820236
$321$	−5.58060	−0.311479
$322$	17.7186	0.987420
$323$	−0.719030	−0.0400079
$324$	0.991576	0.0550876
$325$	30.4336	1.68816
$326$	−10.6427	−0.589447
$327$	−9.32871	−0.515879
$328$	−0.752345	−0.0415413
$329$	11.1011	0.612023
$330$	−0.637286	−0.0350815
$331$	12.6099	0.693104	0.346552	−	0.938031i	$-0.387352\pi$
$331$	12.6099	0.693104	0.346552	+	0.938031i	$0.387352\pi$
$332$	−16.6631	−0.914507
$333$	0.0402388	0.00220507
$334$	−11.8988	−0.651074
$335$	0.634694	0.0346770
$336$	11.8006	0.643777
$337$	−18.0358	−0.982475	−0.491238	−	0.871026i	$-0.663455\pi$
$337$	−18.0358	−0.982475	−0.491238	+	0.871026i	$0.663455\pi$
$338$	−42.0739	−2.28852
$339$	−14.6904	−0.797874
$340$	0.135249	0.00733488
$341$	−16.0027	−0.866592
$342$	1.24365	0.0672487
$343$	19.8953	1.07425
$344$	11.8613	0.639520
$345$	0.592032	0.0318739
$346$	−1.66117	−0.0893051
$347$	−22.7079	−1.21902	−0.609512	−	0.792777i	$-0.708635\pi$
$347$	−22.7079	−1.21902	−0.609512	+	0.792777i	$0.708635\pi$
$348$	9.06987	0.486196
$349$	−2.64345	−0.141501	−0.0707503	−	0.997494i	$-0.522539\pi$
$349$	−2.64345	−0.141501	−0.0707503	+	0.997494i	$0.522539\pi$
$350$	−20.3349	−1.08695
$351$	−6.10946	−0.326099
$352$	13.9378	0.742886
$353$	−34.3821	−1.82998	−0.914988	−	0.403480i	$-0.867800\pi$
$353$	−34.3821	−1.82998	−0.914988	+	0.403480i	$0.867800\pi$
$354$	−13.6644	−0.726256
$355$	1.55210	0.0823769
$356$	10.2561	0.543572
$357$	−2.36016	−0.124913
$358$	19.9607	1.05496
$359$	1.28002	0.0675566	0.0337783	−	0.999429i	$-0.489246\pi$
$359$	1.28002	0.0675566	0.0337783	+	0.999429i	$0.489246\pi$
$360$	0.237903	0.0125386
$361$	−18.4830	−0.972789
$362$	−29.9431	−1.57378
$363$	−3.70280	−0.194347
$364$	14.2978	0.749410
$365$	−0.220301	−0.0115311
$366$	−10.8710	−0.568235
$367$	−26.6074	−1.38890	−0.694448	−	0.719543i	$-0.744351\pi$
$367$	−26.6074	−1.38890	−0.694448	+	0.719543i	$0.744351\pi$
$368$	−21.7021	−1.13130
$369$	−0.431344	−0.0224549
$370$	−0.00949295	−0.000493515 0
$371$	1.99056	0.103345
$372$	−5.87408	−0.304557
$373$	−14.7068	−0.761489	−0.380744	−	0.924680i	$-0.624332\pi$
$373$	−14.7068	−0.761489	−0.380744	+	0.924680i	$0.624332\pi$
$374$	−4.67227	−0.241597
$375$	−1.36144	−0.0703043
$376$	−8.20384	−0.423081
$377$	−55.8828	−2.87811
$378$	4.08217	0.209964
$379$	−24.0468	−1.23520	−0.617601	−	0.786492i	$-0.711895\pi$
$379$	−24.0468	−1.23520	−0.617601	+	0.786492i	$0.711895\pi$
$380$	−0.0972478	−0.00498871
$381$	9.59367	0.491498
$382$	9.33347	0.477542
$383$	33.5084	1.71220	0.856099	−	0.516812i	$-0.172881\pi$
$383$	33.5084	1.71220	0.856099	+	0.516812i	$0.172881\pi$
$384$	−12.1798	−0.621548
$385$	−0.869612	−0.0443196
$386$	−14.6707	−0.746717
$387$	6.80049	0.345688
$388$	−5.86177	−0.297586
$389$	9.94305	0.504133	0.252066	−	0.967710i	$-0.418890\pi$
$389$	9.94305	0.504133	0.252066	+	0.967710i	$0.418890\pi$
$390$	1.44132	0.0729839
$391$	4.34049	0.219508
$392$	−2.49358	−0.125945
$393$	4.19546	0.211633
$394$	−24.4262	−1.23058
$395$	−2.19387	−0.110386
$396$	2.67858	0.134604
$397$	−5.66391	−0.284264	−0.142132	−	0.989848i	$-0.545396\pi$
$397$	−5.66391	−0.284264	−0.142132	+	0.989848i	$0.545396\pi$
$398$	−5.49837	−0.275608
$399$	1.69703	0.0849575
$400$	24.9066	1.24533
$401$	19.7528	0.986409	0.493204	−	0.869913i	$-0.335825\pi$
$401$	19.7528	0.986409	0.493204	+	0.869913i	$0.335825\pi$
$402$	−8.04837	−0.401416
$403$	36.1924	1.80287
$404$	15.1182	0.752160
$405$	0.136397	0.00677765
$406$	37.3393	1.85312
$407$	0.108698	0.00538798
$408$	1.74419	0.0863501
$409$	18.2655	0.903171	0.451586	−	0.892228i	$-0.350859\pi$
$409$	18.2655	0.903171	0.451586	+	0.892228i	$0.350859\pi$
$410$	0.101761	0.00502560
$411$	−8.88336	−0.438184
$412$	3.58576	0.176658
$413$	−18.6459	−0.917504
$414$	−7.50738	−0.368968
$415$	−2.29211	−0.112515
$416$	−31.5223	−1.54551
$417$	−11.2201	−0.549453
$418$	3.35950	0.164319
$419$	−7.76327	−0.379260	−0.189630	−	0.981856i	$-0.560729\pi$
$419$	−7.76327	−0.379260	−0.189630	+	0.981856i	$0.560729\pi$
$420$	−0.319208	−0.0155758
$421$	−20.6374	−1.00581	−0.502904	−	0.864343i	$-0.667735\pi$
$421$	−20.6374	−1.00581	−0.502904	+	0.864343i	$0.667735\pi$
$422$	46.3188	2.25477
$423$	−4.70353	−0.228694
$424$	−1.47105	−0.0714405
$425$	−4.98140	−0.241633
$426$	−19.6817	−0.953583
$427$	−14.8340	−0.717870
$428$	−5.53360	−0.267476
$429$	−16.5037	−0.796806
$430$	−1.60434	−0.0773682
$431$	13.5053	0.650529	0.325265	−	0.945623i	$-0.394547\pi$
$431$	13.5053	0.650529	0.325265	+	0.945623i	$0.394547\pi$
$432$	−4.99993	−0.240559
$433$	−18.1629	−0.872853	−0.436426	−	0.899740i	$-0.643756\pi$
$433$	−18.1629	−0.872853	−0.436426	+	0.899740i	$0.643756\pi$
$434$	−24.1827	−1.16081
$435$	1.24762	0.0598187
$436$	−9.25013	−0.443001
$437$	−3.12094	−0.149295
$438$	2.79357	0.133482
$439$	27.5719	1.31594	0.657968	−	0.753046i	$-0.271416\pi$
$439$	27.5719	1.31594	0.657968	+	0.753046i	$0.271416\pi$
$440$	0.642654	0.0306373
$441$	−1.42965	−0.0680786
$442$	10.5670	0.502622
$443$	−12.8692	−0.611434	−0.305717	−	0.952122i	$-0.598896\pi$
$443$	−12.8692	−0.611434	−0.305717	+	0.952122i	$0.598896\pi$
$444$	0.0398998	0.00189356
$445$	1.41079	0.0668778
$446$	25.8929	1.22607
$447$	−2.32932	−0.110173
$448$	−2.53892	−0.119953
$449$	24.8605	1.17324	0.586620	−	0.809862i	$-0.300458\pi$
$449$	24.8605	1.17324	0.586620	+	0.809862i	$0.300458\pi$
$450$	8.61591	0.406158
$451$	−1.16520	−0.0548673
$452$	−14.5667	−0.685159
$453$	−16.8198	−0.790264
$454$	−35.4162	−1.66216
$455$	1.96676	0.0922030
$456$	−1.25412	−0.0587297
$457$	32.7702	1.53292	0.766462	−	0.642289i	$-0.222015\pi$
$457$	32.7702	1.53292	0.766462	+	0.642289i	$0.222015\pi$
$458$	36.9727	1.72762
$459$	1.00000	0.0466760
$460$	0.587045	0.0273711
$461$	31.3399	1.45965	0.729823	−	0.683637i	$-0.239603\pi$
$461$	31.3399	1.45965	0.729823	+	0.683637i	$0.239603\pi$
$462$	11.0273	0.513037
$463$	−20.2375	−0.940516	−0.470258	−	0.882529i	$-0.655839\pi$
$463$	−20.2375	−0.940516	−0.470258	+	0.882529i	$0.655839\pi$
$464$	−45.7340	−2.12315
$465$	−0.808017	−0.0374709
$466$	21.8169	1.01065
$467$	−14.8305	−0.686273	−0.343136	−	0.939286i	$-0.611489\pi$
$467$	−14.8305	−0.686273	−0.343136	+	0.939286i	$0.611489\pi$
$468$	−6.05800	−0.280031
$469$	−10.9824	−0.507122
$470$	1.10964	0.0511837
$471$	−1.00000	−0.0460776
$472$	13.7795	0.634255
$473$	18.3704	0.844671
$474$	27.8199	1.27781
$475$	3.58177	0.164343
$476$	−2.34028	−0.107266
$477$	−0.843402	−0.0386167
$478$	−12.9837	−0.593859
$479$	−30.0857	−1.37465	−0.687324	−	0.726351i	$-0.741215\pi$
$479$	−30.0857	−1.37465	−0.687324	+	0.726351i	$0.741215\pi$
$480$	0.703755	0.0321219
$481$	−0.245837	−0.0112092
$482$	−25.9696	−1.18288
$483$	−10.2442	−0.466129
$484$	−3.67161	−0.166891
$485$	−0.806323	−0.0366132
$486$	−1.72962	−0.0784570
$487$	−2.38365	−0.108014	−0.0540068	−	0.998541i	$-0.517199\pi$
$487$	−2.38365	−0.108014	−0.0540068	+	0.998541i	$0.517199\pi$
$488$	10.9625	0.496251
$489$	6.15323	0.278259
$490$	0.337277	0.0152366
$491$	−39.0663	−1.76304	−0.881520	−	0.472147i	$-0.843479\pi$
$491$	−39.0663	−1.76304	−0.881520	+	0.472147i	$0.843479\pi$
$492$	−0.427711	−0.0192827
$493$	9.14692	0.411957
$494$	−7.59801	−0.341851
$495$	0.368455	0.0165608
$496$	29.6195	1.32995
$497$	−26.8568	−1.20469
$498$	29.0656	1.30246
$499$	−33.0538	−1.47969	−0.739846	−	0.672776i	$-0.765102\pi$
$499$	−33.0538	−1.47969	−0.739846	+	0.672776i	$0.765102\pi$
$500$	−1.34997	−0.0603725
$501$	6.87944	0.307351
$502$	17.0696	0.761851
$503$	8.61373	0.384067	0.192034	−	0.981388i	$-0.438492\pi$
$503$	8.61373	0.384067	0.192034	+	0.981388i	$0.438492\pi$
$504$	−4.11656	−0.183366
$505$	2.07961	0.0925413
$506$	−20.2799	−0.901553
$507$	24.3255	1.08033
$508$	9.51285	0.422065
$509$	24.9905	1.10768	0.553842	−	0.832621i	$-0.313161\pi$
$509$	24.9905	1.10768	0.553842	+	0.832621i	$0.313161\pi$
$510$	−0.235915	−0.0104465
$511$	3.81198	0.168632
$512$	−8.35597	−0.369285
$513$	−0.719030	−0.0317460
$514$	44.9864	1.98426
$515$	0.493243	0.0217349
$516$	6.74321	0.296853
$517$	−12.7058	−0.558801
$518$	0.164262	0.00721724
$519$	0.960427	0.0421581
$520$	−1.45346	−0.0637383
$521$	10.8164	0.473874	0.236937	−	0.971525i	$-0.423857\pi$
$521$	10.8164	0.473874	0.236937	+	0.971525i	$0.423857\pi$
$522$	−15.8207	−0.692452
$523$	−29.7309	−1.30004	−0.650022	−	0.759916i	$-0.725240\pi$
$523$	−29.7309	−1.30004	−0.650022	+	0.759916i	$0.725240\pi$
$524$	4.16012	0.181736
$525$	11.7569	0.513113
$526$	−23.7864	−1.03714
$527$	−5.92398	−0.258053
$528$	−13.5065	−0.587794
$529$	−4.16017	−0.180877
$530$	0.198972	0.00864277
$531$	7.90026	0.342842
$532$	1.68273	0.0729556
$533$	2.63528	0.114147
$534$	−17.8898	−0.774168
$535$	−0.761180	−0.0329087
$536$	8.11617	0.350565
$537$	−11.5405	−0.498011
$538$	34.4747	1.48631
$539$	−3.86196	−0.166346
$540$	0.135249	0.00582017
$541$	7.24244	0.311377	0.155688	−	0.987806i	$-0.450240\pi$
$541$	7.24244	0.311377	0.155688	+	0.987806i	$0.450240\pi$
$542$	23.4954	1.00921
$543$	17.3120	0.742929
$544$	5.15959	0.221216
$545$	−1.27241	−0.0545042
$546$	−24.9399	−1.06733
$547$	−35.2370	−1.50663	−0.753313	−	0.657662i	$-0.771546\pi$
$547$	−35.2370	−1.50663	−0.753313	+	0.657662i	$0.771546\pi$
$548$	−8.80853	−0.376282
$549$	6.28519	0.268245
$550$	23.2744	0.992425
$551$	−6.57691	−0.280186
$552$	7.57062	0.322227
$553$	37.9618	1.61430
$554$	24.0278	1.02084
$555$	0.00548847	0.000232972 0
$556$	−11.1256	−0.471832
$557$	−6.84082	−0.289855	−0.144927	−	0.989442i	$-0.546295\pi$
$557$	−6.84082	−0.289855	−0.144927	+	0.989442i	$0.546295\pi$
$558$	10.2462	0.433757
$559$	−41.5473	−1.75726
$560$	1.60958	0.0680170
$561$	2.70133	0.114050
$562$	−9.89429	−0.417366
$563$	−3.90168	−0.164436	−0.0822180	−	0.996614i	$-0.526200\pi$
$563$	−3.90168	−0.164436	−0.0822180	+	0.996614i	$0.526200\pi$
$564$	−4.66391	−0.196386
$565$	−2.00374	−0.0842978
$566$	20.9125	0.879016
$567$	−2.36016	−0.0991174
$568$	19.8475	0.832784
$569$	9.62197	0.403374	0.201687	−	0.979450i	$-0.435358\pi$
$569$	9.62197	0.403374	0.201687	+	0.979450i	$0.435358\pi$
$570$	0.169630	0.00710503
$571$	−41.5778	−1.73998	−0.869989	−	0.493071i	$-0.835874\pi$
$571$	−41.5778	−1.73998	−0.869989	+	0.493071i	$0.835874\pi$
$572$	−16.3647	−0.684241
$573$	−5.39627	−0.225432
$574$	−1.76082	−0.0734952
$575$	−21.6217	−0.901687
$576$	1.07574	0.0448225
$577$	−29.0663	−1.21005	−0.605023	−	0.796208i	$-0.706836\pi$
$577$	−29.0663	−1.21005	−0.605023	+	0.796208i	$0.706836\pi$
$578$	−1.72962	−0.0719426
$579$	8.48203	0.352501
$580$	1.23711	0.0513681
$581$	39.6617	1.64544
$582$	10.2248	0.423830
$583$	−2.27831	−0.0943579
$584$	−2.81710	−0.116573
$585$	−0.833315	−0.0344533
$586$	−12.5514	−0.518493
$587$	34.3811	1.41906	0.709530	−	0.704676i	$-0.248907\pi$
$587$	34.3811	1.41906	0.709530	+	0.704676i	$0.248907\pi$
$588$	−1.41761	−0.0584611
$589$	4.25952	0.175511
$590$	−1.86379	−0.0767312
$591$	14.1223	0.580915
$592$	−0.201191	−0.00826890
$593$	26.3631	1.08260	0.541302	−	0.840828i	$-0.317931\pi$
$593$	26.3631	1.08260	0.541302	+	0.840828i	$0.317931\pi$
$594$	−4.67227	−0.191706
$595$	−0.321920	−0.0131974
$596$	−2.30969	−0.0946088
$597$	3.17895	0.130106
$598$	45.8661	1.87560
$599$	−10.2993	−0.420818	−0.210409	−	0.977613i	$-0.567480\pi$
$599$	−10.2993	−0.420818	−0.210409	+	0.977613i	$0.567480\pi$
$600$	−8.68849	−0.354706
$601$	15.1699	0.618794	0.309397	−	0.950933i	$-0.399873\pi$
$601$	15.1699	0.618794	0.309397	+	0.950933i	$0.399873\pi$
$602$	27.7608	1.13144
$603$	4.65327	0.189496
$604$	−16.6781	−0.678624
$605$	−0.505053	−0.0205333
$606$	−26.3709	−1.07124
$607$	15.5679	0.631882	0.315941	−	0.948779i	$-0.397680\pi$
$607$	15.5679	0.631882	0.315941	+	0.948779i	$0.397680\pi$
$608$	−3.70990	−0.150456
$609$	−21.5882	−0.874798
$610$	−1.48277	−0.0600358
$611$	28.7361	1.16254
$612$	0.991576	0.0400821
$613$	11.9783	0.483800	0.241900	−	0.970301i	$-0.422229\pi$
$613$	11.9783	0.483800	0.241900	+	0.970301i	$0.422229\pi$
$614$	5.62890	0.227164
$615$	−0.0588342	−0.00237243
$616$	−11.1202	−0.448045
$617$	−3.19937	−0.128802	−0.0644009	−	0.997924i	$-0.520514\pi$
$617$	−3.19937	−0.128802	−0.0644009	+	0.997924i	$0.520514\pi$
$618$	−6.25467	−0.251600
$619$	−38.9000	−1.56352	−0.781762	−	0.623576i	$-0.785679\pi$
$619$	−38.9000	−1.56352	−0.781762	+	0.623576i	$0.785679\pi$
$620$	−0.801210	−0.0321774
$621$	4.34049	0.174178
$622$	−53.7725	−2.15608
$623$	−24.4116	−0.978032
$624$	30.5469	1.22285
$625$	24.7213	0.988851
$626$	−17.9501	−0.717431
$627$	−1.94234	−0.0775696
$628$	−0.991576	−0.0395682
$629$	0.0402388	0.00160442
$630$	0.556798	0.0221834
$631$	−15.6101	−0.621430	−0.310715	−	0.950503i	$-0.600568\pi$
$631$	−15.6101	−0.621430	−0.310715	+	0.950503i	$0.600568\pi$
$632$	−28.0542	−1.11594
$633$	−26.7798	−1.06440
$634$	45.0287	1.78832
$635$	1.30855	0.0519283
$636$	−0.836297	−0.0331613
$637$	8.73439	0.346069
$638$	−42.7369	−1.69197
$639$	11.3792	0.450156
$640$	−1.66129	−0.0656684
$641$	−15.2032	−0.600490	−0.300245	−	0.953862i	$-0.597068\pi$
$641$	−15.2032	−0.600490	−0.300245	+	0.953862i	$0.597068\pi$
$642$	9.65231	0.380946
$643$	23.8468	0.940427	0.470214	−	0.882553i	$-0.344177\pi$
$643$	23.8468	0.940427	0.470214	+	0.882553i	$0.344177\pi$
$644$	−10.1579	−0.400279
$645$	0.927570	0.0365230
$646$	1.24365	0.0489306
$647$	17.8004	0.699805	0.349903	−	0.936786i	$-0.386215\pi$
$647$	17.8004	0.699805	0.349903	+	0.936786i	$0.386215\pi$
$648$	1.74419	0.0685181
$649$	21.3412	0.837717
$650$	−52.6386	−2.06465
$651$	13.9815	0.547980
$652$	6.10140	0.238949
$653$	0.851338	0.0333154	0.0166577	−	0.999861i	$-0.494697\pi$
$653$	0.851338	0.0333154	0.0166577	+	0.999861i	$0.494697\pi$
$654$	16.1351	0.630932
$655$	0.572251	0.0223597
$656$	2.15669	0.0842046
$657$	−1.61514	−0.0630126
$658$	−19.2006	−0.748519
$659$	−37.8408	−1.47407	−0.737035	−	0.675855i	$-0.763775\pi$
$659$	−37.8408	−1.47407	−0.737035	+	0.675855i	$0.763775\pi$
$660$	0.365351	0.0142213
$661$	1.73347	0.0674243	0.0337122	−	0.999432i	$-0.489267\pi$
$661$	1.73347	0.0674243	0.0337122	+	0.999432i	$0.489267\pi$
$662$	−21.8103	−0.847683
$663$	−6.10946	−0.237272
$664$	−29.3105	−1.13747
$665$	0.231470	0.00897602
$666$	−0.0695977	−0.00269686
$667$	39.7021	1.53727
$668$	6.82149	0.263932
$669$	−14.9703	−0.578786
$670$	−1.09778	−0.0424108
$671$	16.9784	0.655444
$672$	−12.1775	−0.469755
$673$	−5.57194	−0.214783	−0.107391	−	0.994217i	$-0.534250\pi$
$673$	−5.57194	−0.214783	−0.107391	+	0.994217i	$0.534250\pi$
$674$	31.1951	1.20159
$675$	−4.98140	−0.191734
$676$	24.1206	0.927716
$677$	−26.0038	−0.999405	−0.499703	−	0.866197i	$-0.666557\pi$
$677$	−26.0038	−0.999405	−0.499703	+	0.866197i	$0.666557\pi$
$678$	25.4088	0.975819
$679$	13.9522	0.535438
$680$	0.237903	0.00912315
$681$	20.4763	0.784654
$682$	27.6785	1.05986
$683$	−1.72951	−0.0661779	−0.0330889	−	0.999452i	$-0.510534\pi$
$683$	−1.72951	−0.0661779	−0.0330889	+	0.999452i	$0.510534\pi$
$684$	−0.712973	−0.0272612
$685$	−1.21167	−0.0462954
$686$	−34.4113	−1.31383
$687$	−21.3762	−0.815553
$688$	−34.0020	−1.29631
$689$	5.15273	0.196303
$690$	−1.02399	−0.0389826
$691$	12.0370	0.457910	0.228955	−	0.973437i	$-0.426469\pi$
$691$	12.0370	0.457910	0.228955	+	0.973437i	$0.426469\pi$
$692$	0.952337	0.0362024
$693$	−6.37557	−0.242188
$694$	39.2760	1.49090
$695$	−1.53040	−0.0580514
$696$	15.9539	0.604733
$697$	−0.431344	−0.0163383
$698$	4.57216	0.173059
$699$	−12.6137	−0.477094
$700$	11.6579	0.440625
$701$	12.3017	0.464631	0.232315	−	0.972641i	$-0.425370\pi$
$701$	12.3017	0.464631	0.232315	+	0.972641i	$0.425370\pi$
$702$	10.5670	0.398827
$703$	−0.0289329	−0.00109122
$704$	2.90593	0.109521
$705$	−0.641550	−0.0241622
$706$	59.4680	2.23811
$707$	−35.9845	−1.35334
$708$	7.83372	0.294409
$709$	−31.3177	−1.17616	−0.588080	−	0.808803i	$-0.700116\pi$
$709$	−31.3177	−1.17616	−0.588080	+	0.808803i	$0.700116\pi$
$710$	−2.68454	−0.100749
$711$	−16.0844	−0.603213
$712$	18.0405	0.676097
$713$	−25.7130	−0.962959
$714$	4.08217	0.152771
$715$	−2.25106	−0.0841849
$716$	−11.4433	−0.427657
$717$	7.50667	0.280342
$718$	−2.21394	−0.0826234
$719$	30.3782	1.13291	0.566457	−	0.824091i	$-0.308314\pi$
$719$	30.3782	1.13291	0.566457	+	0.824091i	$0.308314\pi$
$720$	−0.681978	−0.0254158
$721$	−8.53485	−0.317854
$722$	31.9685	1.18974
$723$	15.0146	0.558401
$724$	17.1662	0.637976
$725$	−45.5644	−1.69222
$726$	6.40443	0.237691
$727$	42.1432	1.56301	0.781503	−	0.623902i	$-0.214454\pi$
$727$	42.1432	1.56301	0.781503	+	0.623902i	$0.214454\pi$
$728$	25.1500	0.932119
$729$	1.00000	0.0370370
$730$	0.381036	0.0141028
$731$	6.80049	0.251525
$732$	6.23225	0.230350
$733$	−40.9718	−1.51333	−0.756664	−	0.653804i	$-0.773172\pi$
$733$	−40.9718	−1.51333	−0.756664	+	0.653804i	$0.773172\pi$
$734$	46.0206	1.69865
$735$	−0.195001	−0.00719271
$736$	22.3951	0.825496
$737$	12.5700	0.463023
$738$	0.746060	0.0274629
$739$	36.4675	1.34148	0.670739	−	0.741693i	$-0.265977\pi$
$739$	36.4675	1.34148	0.670739	+	0.741693i	$0.265977\pi$
$740$	0.00544224	0.000200061 0
$741$	4.39289	0.161377
$742$	−3.44291	−0.126393
$743$	−27.4519	−1.00711	−0.503557	−	0.863962i	$-0.667976\pi$
$743$	−27.4519	−1.00711	−0.503557	+	0.863962i	$0.667976\pi$
$744$	−10.3325	−0.378809
$745$	−0.317713	−0.0116401
$746$	25.4371	0.931319
$747$	−16.8047	−0.614850
$748$	2.67858	0.0979385
$749$	13.1711	0.481262
$750$	2.35477	0.0859839
$751$	−29.9009	−1.09110	−0.545549	−	0.838079i	$-0.683679\pi$
$751$	−29.9009	−1.09110	−0.545549	+	0.838079i	$0.683679\pi$
$752$	23.5173	0.857589
$753$	−9.86897	−0.359645
$754$	96.6558	3.52000
$755$	−2.29418	−0.0834938
$756$	−2.34028	−0.0851151
$757$	12.4222	0.451493	0.225747	−	0.974186i	$-0.427518\pi$
$757$	12.4222	0.451493	0.225747	+	0.974186i	$0.427518\pi$
$758$	41.5918	1.51068
$759$	11.7251	0.425594
$760$	−0.171059	−0.00620497
$761$	8.43757	0.305862	0.152931	−	0.988237i	$-0.451129\pi$
$761$	8.43757	0.305862	0.152931	+	0.988237i	$0.451129\pi$
$762$	−16.5934	−0.601115
$763$	22.0172	0.797077
$764$	−5.35081	−0.193586
$765$	0.136397	0.00493146
$766$	−57.9567	−2.09406
$767$	−48.2664	−1.74280
$768$	18.9149	0.682533
$769$	22.9779	0.828606	0.414303	−	0.910139i	$-0.364025\pi$
$769$	22.9779	0.828606	0.414303	+	0.910139i	$0.364025\pi$
$770$	1.50410	0.0542039
$771$	−26.0094	−0.936707
$772$	8.41058	0.302703
$773$	25.6236	0.921616	0.460808	−	0.887500i	$-0.347560\pi$
$773$	25.6236	0.921616	0.460808	+	0.887500i	$0.347560\pi$
$774$	−11.7622	−0.422785
$775$	29.5097	1.06002
$776$	−10.3109	−0.370139
$777$	−0.0949699	−0.00340703
$778$	−17.1977	−0.616566
$779$	0.310149	0.0111123
$780$	−0.826296	−0.0295861
$781$	30.7391	1.09993
$782$	−7.50738	−0.268463
$783$	9.14692	0.326884
$784$	7.14815	0.255291
$785$	−0.136397	−0.00486824
$786$	−7.25655	−0.258832
$787$	−49.4878	−1.76405	−0.882024	−	0.471204i	$-0.843820\pi$
$787$	−49.4878	−1.76405	−0.882024	+	0.471204i	$0.843820\pi$
$788$	14.0034	0.498849
$789$	13.7524	0.489598
$790$	3.79456	0.135004
$791$	34.6717	1.23278
$792$	4.71163	0.167420
$793$	−38.3991	−1.36359
$794$	9.79640	0.347661
$795$	−0.115038	−0.00407997
$796$	3.15217	0.111726
$797$	−29.0070	−1.02748	−0.513741	−	0.857946i	$-0.671741\pi$
$797$	−29.0070	−1.02748	−0.513741	+	0.857946i	$0.671741\pi$
$798$	−2.93520	−0.103905
$799$	−4.70353	−0.166399
$800$	−25.7020	−0.908702
$801$	10.3432	0.365460
$802$	−34.1648	−1.20640
$803$	−4.36303	−0.153968
$804$	4.61407	0.162726
$805$	−1.39729	−0.0492480
$806$	−62.5989	−2.20495
$807$	−19.9320	−0.701640
$808$	26.5930	0.935540
$809$	−35.7259	−1.25606	−0.628028	−	0.778191i	$-0.716137\pi$
$809$	−35.7259	−1.25606	−0.628028	+	0.778191i	$0.716137\pi$
$810$	−0.235915	−0.00828923
$811$	10.3687	0.364094	0.182047	−	0.983290i	$-0.441728\pi$
$811$	10.3687	0.364094	0.182047	+	0.983290i	$0.441728\pi$
$812$	−21.4063	−0.751215
$813$	−13.5841	−0.476416
$814$	−0.188006	−0.00658962
$815$	0.839285	0.0293989
$816$	−4.99993	−0.175033
$817$	−4.88976	−0.171071
$818$	−31.5923	−1.10460
$819$	14.4193	0.503851
$820$	−0.0583387	−0.00203727
$821$	34.1787	1.19284	0.596422	−	0.802671i	$-0.296588\pi$
$821$	34.1787	1.19284	0.596422	+	0.802671i	$0.296588\pi$
$822$	15.3648	0.535909
$823$	1.65651	0.0577424	0.0288712	−	0.999583i	$-0.490809\pi$
$823$	1.65651	0.0577424	0.0288712	+	0.999583i	$0.490809\pi$
$824$	6.30736	0.219727
$825$	−13.4564	−0.468492
$826$	32.2502	1.12213
$827$	−42.4814	−1.47722	−0.738612	−	0.674131i	$-0.764518\pi$
$827$	−42.4814	−1.47722	−0.738612	+	0.674131i	$0.764518\pi$
$828$	4.30393	0.149572
$829$	−26.6369	−0.925136	−0.462568	−	0.886584i	$-0.653072\pi$
$829$	−26.6369	−0.925136	−0.462568	+	0.886584i	$0.653072\pi$
$830$	3.96448	0.137609
$831$	−13.8920	−0.481907
$832$	−6.57219	−0.227850
$833$	−1.42965	−0.0495344
$834$	19.4066	0.671994
$835$	0.938339	0.0324726
$836$	−1.92598	−0.0666113
$837$	−5.92398	−0.204763
$838$	13.4275	0.463845
$839$	3.54404	0.122354	0.0611770	−	0.998127i	$-0.480515\pi$
$839$	3.54404	0.122354	0.0611770	+	0.998127i	$0.480515\pi$
$840$	−0.561488	−0.0193732
$841$	54.6662	1.88504
$842$	35.6949	1.23013
$843$	5.72051	0.197025
$844$	−26.5542	−0.914035
$845$	3.31794	0.114141
$846$	8.13532	0.279698
$847$	8.73920	0.300282
$848$	4.21695	0.144811
$849$	−12.0908	−0.414955
$850$	8.61591	0.295523
$851$	0.174656	0.00598713
$852$	11.2834	0.386563
$853$	−31.6134	−1.08242	−0.541211	−	0.840887i	$-0.682034\pi$
$853$	−31.6134	−1.08242	−0.541211	+	0.840887i	$0.682034\pi$
$854$	25.6572	0.877972
$855$	−0.0980739	−0.00335406
$856$	−9.73362	−0.332688
$857$	−38.0375	−1.29934	−0.649669	−	0.760218i	$-0.725092\pi$
$857$	−38.0375	−1.29934	−0.649669	+	0.760218i	$0.725092\pi$
$858$	28.5451	0.974513
$859$	−51.0625	−1.74223	−0.871116	−	0.491078i	$-0.836603\pi$
$859$	−51.0625	−1.74223	−0.871116	+	0.491078i	$0.836603\pi$
$860$	0.919756	0.0313634
$861$	1.01804	0.0346947
$862$	−23.3591	−0.795613
$863$	−44.0267	−1.49869	−0.749343	−	0.662182i	$-0.769631\pi$
$863$	−44.0267	−1.49869	−0.749343	+	0.662182i	$0.769631\pi$
$864$	5.15959	0.175533
$865$	0.131000	0.00445413
$866$	31.4148	1.06752
$867$	1.00000	0.0339618
$868$	13.8638	0.470567
$869$	−43.4494	−1.47392
$870$	−2.15790	−0.0731597
$871$	−28.4290	−0.963278
$872$	−16.2710	−0.551006
$873$	−5.91157	−0.200076
$874$	5.39803	0.182591
$875$	3.21321	0.108626
$876$	−1.60153	−0.0541108
$877$	−53.4754	−1.80574	−0.902868	−	0.429918i	$-0.858543\pi$
$877$	−53.4754	−1.80574	−0.902868	+	0.429918i	$0.858543\pi$
$878$	−47.6888	−1.60942
$879$	7.25675	0.244764
$880$	−1.84225	−0.0621022
$881$	−27.9333	−0.941098	−0.470549	−	0.882374i	$-0.655944\pi$
$881$	−27.9333	−0.941098	−0.470549	+	0.882374i	$0.655944\pi$
$882$	2.47275	0.0832617
$883$	18.7815	0.632048	0.316024	−	0.948751i	$-0.397652\pi$
$883$	18.7815	0.632048	0.316024	+	0.948751i	$0.397652\pi$
$884$	−6.05800	−0.203753
$885$	1.07758	0.0362223
$886$	22.2588	0.747798
$887$	−40.4945	−1.35967	−0.679836	−	0.733364i	$-0.737949\pi$
$887$	−40.4945	−1.35967	−0.679836	+	0.733364i	$0.737949\pi$
$888$	0.0701839	0.00235522
$889$	−22.6426	−0.759408
$890$	−2.44013	−0.0817932
$891$	2.70133	0.0904981
$892$	−14.8442	−0.497021
$893$	3.38198	0.113174
$894$	4.02883	0.134744
$895$	−1.57410	−0.0526164
$896$	28.7463	0.960345
$897$	−26.5180	−0.885412
$898$	−42.9992	−1.43490
$899$	−54.1862	−1.80721
$900$	−4.93943	−0.164648
$901$	−0.843402	−0.0280978
$902$	2.01536	0.0671040
$903$	−16.0502	−0.534118
$904$	−25.6228	−0.852203
$905$	2.36131	0.0784927
$906$	29.0919	0.966512
$907$	−6.83519	−0.226959	−0.113479	−	0.993540i	$-0.536200\pi$
$907$	−6.83519	−0.226959	−0.113479	+	0.993540i	$0.536200\pi$
$908$	20.3038	0.673806
$909$	15.2467	0.505700
$910$	−3.40174	−0.112766
$911$	−13.1624	−0.436091	−0.218045	−	0.975939i	$-0.569968\pi$
$911$	−13.1624	−0.436091	−0.218045	+	0.975939i	$0.569968\pi$
$912$	3.59510	0.119046
$913$	−45.3950	−1.50235
$914$	−56.6799	−1.87480
$915$	0.857284	0.0283409
$916$	−21.1961	−0.700340
$917$	−9.90196	−0.326992
$918$	−1.72962	−0.0570859
$919$	13.3956	0.441882	0.220941	−	0.975287i	$-0.429087\pi$
$919$	13.3956	0.441882	0.220941	+	0.975287i	$0.429087\pi$
$920$	1.03261	0.0340443
$921$	−3.25442	−0.107237
$922$	−54.2061	−1.78518
$923$	−69.5210	−2.28831
$924$	−6.32187	−0.207974
$925$	−0.200445	−0.00659060
$926$	35.0031	1.15027
$927$	3.61622	0.118772
$928$	47.1944	1.54923
$929$	−10.4813	−0.343879	−0.171939	−	0.985108i	$-0.555003\pi$
$929$	−10.4813	−0.343879	−0.171939	+	0.985108i	$0.555003\pi$
$930$	1.39756	0.0458278
$931$	1.02796	0.0336901
$932$	−12.5075	−0.409695
$933$	31.0893	1.01782
$934$	25.6511	0.839328
$935$	0.368455	0.0120498
$936$	−10.6560	−0.348304
$937$	−0.369810	−0.0120812	−0.00604058	−	0.999982i	$-0.501923\pi$
$937$	−0.369810	−0.0120812	−0.00604058	+	0.999982i	$0.501923\pi$
$938$	18.9954	0.620223
$939$	10.3781	0.338676
$940$	−0.636146	−0.0207488
$941$	−13.4718	−0.439168	−0.219584	−	0.975594i	$-0.570470\pi$
$941$	−13.4718	−0.439168	−0.219584	+	0.975594i	$0.570470\pi$
$942$	1.72962	0.0563540
$943$	−1.87224	−0.0609686
$944$	−39.5008	−1.28564
$945$	−0.321920	−0.0104721
$946$	−31.7737	−1.03305
$947$	−11.5159	−0.374216	−0.187108	−	0.982339i	$-0.559911\pi$
$947$	−11.5159	−0.374216	−0.187108	+	0.982339i	$0.559911\pi$
$948$	−15.9489	−0.517997
$949$	9.86763	0.320317
$950$	−6.19510	−0.200995
$951$	−26.0339	−0.844207
$952$	−4.11656	−0.133418
$953$	−32.9674	−1.06792	−0.533960	−	0.845510i	$-0.679297\pi$
$953$	−32.9674	−1.06792	−0.533960	+	0.845510i	$0.679297\pi$
$954$	1.45876	0.0472292
$955$	−0.736037	−0.0238176
$956$	7.44344	0.240738
$957$	24.7089	0.798725
$958$	52.0367	1.68123
$959$	20.9661	0.677032
$960$	0.146728	0.00473563
$961$	4.09358	0.132051
$962$	0.425204	0.0137091
$963$	−5.58060	−0.179832
$964$	14.8882	0.479516
$965$	1.15693	0.0372428
$966$	17.7186	0.570087
$967$	46.5551	1.49711	0.748555	−	0.663073i	$-0.230748\pi$
$967$	46.5551	1.49711	0.748555	+	0.663073i	$0.230748\pi$
$968$	−6.45838	−0.207580
$969$	−0.719030	−0.0230986
$970$	1.39463	0.0447789
$971$	15.1232	0.485327	0.242663	−	0.970111i	$-0.421979\pi$
$971$	15.1232	0.485327	0.242663	+	0.970111i	$0.421979\pi$
$972$	0.991576	0.0318048
$973$	26.4813	0.848952
$974$	4.12281	0.132103
$975$	30.4336	0.974657
$976$	−31.4255	−1.00591
$977$	−2.40369	−0.0769008	−0.0384504	−	0.999261i	$-0.512242\pi$
$977$	−2.40369	−0.0769008	−0.0384504	+	0.999261i	$0.512242\pi$
$978$	−10.6427	−0.340317
$979$	27.9405	0.892982
$980$	−0.193358	−0.00617660
$981$	−9.32871	−0.297843
$982$	67.5698	2.15624
$983$	−47.4498	−1.51341	−0.756707	−	0.653755i	$-0.773193\pi$
$983$	−47.4498	−1.51341	−0.756707	+	0.653755i	$0.773193\pi$
$984$	−0.752345	−0.0239839
$985$	1.92625	0.0613754
$986$	−15.8207	−0.503833
$987$	11.1011	0.353352
$988$	4.35588	0.138579
$989$	29.5174	0.938600
$990$	−0.637286	−0.0202543
$991$	16.8518	0.535316	0.267658	−	0.963514i	$-0.413750\pi$
$991$	16.8518	0.535316	0.267658	+	0.963514i	$0.413750\pi$
$992$	−30.5653	−0.970450
$993$	12.6099	0.400164
$994$	46.4520	1.47337
$995$	0.433601	0.0137461
$996$	−16.6631	−0.527991
$997$	30.6989	0.972245	0.486122	−	0.873891i	$-0.338411\pi$
$997$	30.6989	0.972245	0.486122	+	0.873891i	$0.338411\pi$
$998$	57.1704	1.80970
$999$	0.0402388	0.00127310

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.d.1.11	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.d.1.11	✓	40	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q-1.72962 q^{2} +1.00000 q^{3} +0.991576 q^{4} +0.136397 q^{5} -1.72962 q^{6} -2.36016 q^{7} +1.74419 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.72962 q^{2} +1.00000 q^{3} +0.991576 q^{4} +0.136397 q^{5} -1.72962 q^{6} -2.36016 q^{7} +1.74419 q^{8} +1.00000 q^{9} -0.235915 q^{10} +2.70133 q^{11} +0.991576 q^{12} -6.10946 q^{13} +4.08217 q^{14} +0.136397 q^{15} -4.99993 q^{16} +1.00000 q^{17} -1.72962 q^{18} -0.719030 q^{19} +0.135249 q^{20} -2.36016 q^{21} -4.67227 q^{22} +4.34049 q^{23} +1.74419 q^{24} -4.98140 q^{25} +10.5670 q^{26} +1.00000 q^{27} -2.34028 q^{28} +9.14692 q^{29} -0.235915 q^{30} -5.92398 q^{31} +5.15959 q^{32} +2.70133 q^{33} -1.72962 q^{34} -0.321920 q^{35} +0.991576 q^{36} +0.0402388 q^{37} +1.24365 q^{38} -6.10946 q^{39} +0.237903 q^{40} -0.431344 q^{41} +4.08217 q^{42} +6.80049 q^{43} +2.67858 q^{44} +0.136397 q^{45} -7.50738 q^{46} -4.70353 q^{47} -4.99993 q^{48} -1.42965 q^{49} +8.61591 q^{50} +1.00000 q^{51} -6.05800 q^{52} -0.843402 q^{53} -1.72962 q^{54} +0.368455 q^{55} -4.11656 q^{56} -0.719030 q^{57} -15.8207 q^{58} +7.90026 q^{59} +0.135249 q^{60} +6.28519 q^{61} +10.2462 q^{62} -2.36016 q^{63} +1.07574 q^{64} -0.833315 q^{65} -4.67227 q^{66} +4.65327 q^{67} +0.991576 q^{68} +4.34049 q^{69} +0.556798 q^{70} +11.3792 q^{71} +1.74419 q^{72} -1.61514 q^{73} -0.0695977 q^{74} -4.98140 q^{75} -0.712973 q^{76} -6.37557 q^{77} +10.5670 q^{78} -16.0844 q^{79} -0.681978 q^{80} +1.00000 q^{81} +0.746060 q^{82} -16.8047 q^{83} -2.34028 q^{84} +0.136397 q^{85} -11.7622 q^{86} +9.14692 q^{87} +4.71163 q^{88} +10.3432 q^{89} -0.235915 q^{90} +14.4193 q^{91} +4.30393 q^{92} -5.92398 q^{93} +8.13532 q^{94} -0.0980739 q^{95} +5.15959 q^{96} -5.91157 q^{97} +2.47275 q^{98} +2.70133 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 7 q^{2} + 40 q^{3} + 29 q^{4} - 15 q^{5} - 7 q^{6} - 13 q^{7} - 18 q^{8} + 40 q^{9}+O(q^{10}) \) 40 * q - 7 * q^2 + 40 * q^3 + 29 * q^4 - 15 * q^5 - 7 * q^6 - 13 * q^7 - 18 * q^8 + 40 * q^9	\( 40 q - 7 q^{2} + 40 q^{3} + 29 q^{4} - 15 q^{5} - 7 q^{6} - 13 q^{7} - 18 q^{8} + 40 q^{9} - 6 q^{10} - 25 q^{11} + 29 q^{12} - 24 q^{13} - 22 q^{14} - 15 q^{15} + 7 q^{16} + 40 q^{17} - 7 q^{18} - 18 q^{19} - 20 q^{20} - 13 q^{21} - 25 q^{22} - 28 q^{23} - 18 q^{24} - 11 q^{25} - 13 q^{26} + 40 q^{27} - 8 q^{28} - 23 q^{29} - 6 q^{30} - 11 q^{31} - 23 q^{32} - 25 q^{33} - 7 q^{34} - 45 q^{35} + 29 q^{36} - 38 q^{37} - 30 q^{38} - 24 q^{39} - 12 q^{40} - 33 q^{41} - 22 q^{42} - 25 q^{43} - 14 q^{44} - 15 q^{45} + 8 q^{46} - 55 q^{47} + 7 q^{48} - 21 q^{49} + 2 q^{50} + 40 q^{51} - 39 q^{52} - 39 q^{53} - 7 q^{54} - 9 q^{55} - 48 q^{56} - 18 q^{57} - 13 q^{58} - 81 q^{59} - 20 q^{60} - 9 q^{61} - 16 q^{62} - 13 q^{63} - 4 q^{64} - 43 q^{65} - 25 q^{66} - 24 q^{67} + 29 q^{68} - 28 q^{69} + 48 q^{70} - 32 q^{71} - 18 q^{72} - 43 q^{73} - 20 q^{74} - 11 q^{75} - 58 q^{76} - 32 q^{77} - 13 q^{78} - 22 q^{79} - 48 q^{80} + 40 q^{81} - 11 q^{82} - 45 q^{83} - 8 q^{84} - 15 q^{85} - 30 q^{86} - 23 q^{87} - 48 q^{88} - 94 q^{89} - 6 q^{90} - 7 q^{91} - 98 q^{92} - 11 q^{93} + 32 q^{94} - 23 q^{96} - 28 q^{97} - 46 q^{98} - 25 q^{99}+O(q^{100}) \) 40 * q - 7 * q^2 + 40 * q^3 + 29 * q^4 - 15 * q^5 - 7 * q^6 - 13 * q^7 - 18 * q^8 + 40 * q^9 - 6 * q^10 - 25 * q^11 + 29 * q^12 - 24 * q^13 - 22 * q^14 - 15 * q^15 + 7 * q^16 + 40 * q^17 - 7 * q^18 - 18 * q^19 - 20 * q^20 - 13 * q^21 - 25 * q^22 - 28 * q^23 - 18 * q^24 - 11 * q^25 - 13 * q^26 + 40 * q^27 - 8 * q^28 - 23 * q^29 - 6 * q^30 - 11 * q^31 - 23 * q^32 - 25 * q^33 - 7 * q^34 - 45 * q^35 + 29 * q^36 - 38 * q^37 - 30 * q^38 - 24 * q^39 - 12 * q^40 - 33 * q^41 - 22 * q^42 - 25 * q^43 - 14 * q^44 - 15 * q^45 + 8 * q^46 - 55 * q^47 + 7 * q^48 - 21 * q^49 + 2 * q^50 + 40 * q^51 - 39 * q^52 - 39 * q^53 - 7 * q^54 - 9 * q^55 - 48 * q^56 - 18 * q^57 - 13 * q^58 - 81 * q^59 - 20 * q^60 - 9 * q^61 - 16 * q^62 - 13 * q^63 - 4 * q^64 - 43 * q^65 - 25 * q^66 - 24 * q^67 + 29 * q^68 - 28 * q^69 + 48 * q^70 - 32 * q^71 - 18 * q^72 - 43 * q^73 - 20 * q^74 - 11 * q^75 - 58 * q^76 - 32 * q^77 - 13 * q^78 - 22 * q^79 - 48 * q^80 + 40 * q^81 - 11 * q^82 - 45 * q^83 - 8 * q^84 - 15 * q^85 - 30 * q^86 - 23 * q^87 - 48 * q^88 - 94 * q^89 - 6 * q^90 - 7 * q^91 - 98 * q^92 - 11 * q^93 + 32 * q^94 - 23 * q^96 - 28 * q^97 - 46 * q^98 - 25 * q^99

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