LMFDB - Embedded newform 1334.2.a.i.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1334,2,Mod(1,1334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1334, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1334 = 2 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1334.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:	$10.6520436296$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 22x^{6} + 151x^{4} - 332x^{2} + 6 $ x^8 - 22x^6 + 151x^4 - 332*x^2 + 6
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$2.39983$ of defining polynomial
Character	$\chi$	$=$	1334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.90642 q^{3} +1.00000 q^{4} -2.39983 q^{5} +2.90642 q^{6} +0.548309 q^{7} +1.00000 q^{8} +5.44730 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.90642 q^{3} +1.00000 q^{4} -2.39983 q^{5} +2.90642 q^{6} +0.548309 q^{7} +1.00000 q^{8} +5.44730 q^{9} -2.39983 q^{10} +4.89367 q^{11} +2.90642 q^{12} -5.66121 q^{13} +0.548309 q^{14} -6.97492 q^{15} +1.00000 q^{16} +7.46691 q^{17} +5.44730 q^{18} +0.237786 q^{19} -2.39983 q^{20} +1.59362 q^{21} +4.89367 q^{22} -1.00000 q^{23} +2.90642 q^{24} +0.759171 q^{25} -5.66121 q^{26} +7.11290 q^{27} +0.548309 q^{28} -1.00000 q^{29} -6.97492 q^{30} +7.69664 q^{31} +1.00000 q^{32} +14.2231 q^{33} +7.46691 q^{34} -1.31585 q^{35} +5.44730 q^{36} -2.97612 q^{37} +0.237786 q^{38} -16.4539 q^{39} -2.39983 q^{40} -5.61419 q^{41} +1.59362 q^{42} -3.80313 q^{43} +4.89367 q^{44} -13.0726 q^{45} -1.00000 q^{46} +5.88047 q^{47} +2.90642 q^{48} -6.69936 q^{49} +0.759171 q^{50} +21.7020 q^{51} -5.66121 q^{52} -0.959699 q^{53} +7.11290 q^{54} -11.7440 q^{55} +0.548309 q^{56} +0.691108 q^{57} -1.00000 q^{58} -12.2728 q^{59} -6.97492 q^{60} +8.70749 q^{61} +7.69664 q^{62} +2.98681 q^{63} +1.00000 q^{64} +13.5859 q^{65} +14.2231 q^{66} -0.366509 q^{67} +7.46691 q^{68} -2.90642 q^{69} -1.31585 q^{70} -9.03164 q^{71} +5.44730 q^{72} +12.1849 q^{73} -2.97612 q^{74} +2.20647 q^{75} +0.237786 q^{76} +2.68324 q^{77} -16.4539 q^{78} -2.47130 q^{79} -2.39983 q^{80} +4.33119 q^{81} -5.61419 q^{82} -5.49155 q^{83} +1.59362 q^{84} -17.9193 q^{85} -3.80313 q^{86} -2.90642 q^{87} +4.89367 q^{88} +11.3699 q^{89} -13.0726 q^{90} -3.10409 q^{91} -1.00000 q^{92} +22.3697 q^{93} +5.88047 q^{94} -0.570646 q^{95} +2.90642 q^{96} -10.4615 q^{97} -6.69936 q^{98} +26.6573 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 4 q^{3} + 8 q^{4} + 4 q^{6} + 8 q^{7} + 8 q^{8} + 12 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 + 4 * q^3 + 8 * q^4 + 4 * q^6 + 8 * q^7 + 8 * q^8 + 12 * q^9	$ 8 q + 8 q^{2} + 4 q^{3} + 8 q^{4} + 4 q^{6} + 8 q^{7} + 8 q^{8} + 12 q^{9} + 8 q^{11} + 4 q^{12} + 4 q^{13} + 8 q^{14} + 8 q^{16} + 8 q^{17} + 12 q^{18} + 16 q^{19} - 4 q^{21} + 8 q^{22} - 8 q^{23} + 4 q^{24} + 4 q^{25} + 4 q^{26} + 4 q^{27} + 8 q^{28} - 8 q^{29} + 8 q^{31} + 8 q^{32} + 12 q^{33} + 8 q^{34} + 4 q^{35} + 12 q^{36} + 8 q^{37} + 16 q^{38} - 16 q^{39} + 8 q^{41} - 4 q^{42} + 32 q^{43} + 8 q^{44} - 8 q^{46} + 16 q^{47} + 4 q^{48} + 4 q^{49} + 4 q^{50} + 12 q^{51} + 4 q^{52} + 4 q^{54} + 8 q^{56} + 8 q^{57} - 8 q^{58} - 4 q^{59} + 8 q^{61} + 8 q^{62} + 24 q^{63} + 8 q^{64} - 4 q^{65} + 12 q^{66} + 20 q^{67} + 8 q^{68} - 4 q^{69} + 4 q^{70} - 24 q^{71} + 12 q^{72} - 4 q^{73} + 8 q^{74} - 16 q^{75} + 16 q^{76} - 16 q^{77} - 16 q^{78} + 4 q^{79} - 8 q^{81} + 8 q^{82} - 4 q^{83} - 4 q^{84} - 44 q^{85} + 32 q^{86} - 4 q^{87} + 8 q^{88} + 20 q^{89} - 8 q^{92} - 4 q^{93} + 16 q^{94} - 8 q^{95} + 4 q^{96} + 4 q^{97} + 4 q^{98}+O(q^{100}) $ 8 * q + 8 * q^2 + 4 * q^3 + 8 * q^4 + 4 * q^6 + 8 * q^7 + 8 * q^8 + 12 * q^9 + 8 * q^11 + 4 * q^12 + 4 * q^13 + 8 * q^14 + 8 * q^16 + 8 * q^17 + 12 * q^18 + 16 * q^19 - 4 * q^21 + 8 * q^22 - 8 * q^23 + 4 * q^24 + 4 * q^25 + 4 * q^26 + 4 * q^27 + 8 * q^28 - 8 * q^29 + 8 * q^31 + 8 * q^32 + 12 * q^33 + 8 * q^34 + 4 * q^35 + 12 * q^36 + 8 * q^37 + 16 * q^38 - 16 * q^39 + 8 * q^41 - 4 * q^42 + 32 * q^43 + 8 * q^44 - 8 * q^46 + 16 * q^47 + 4 * q^48 + 4 * q^49 + 4 * q^50 + 12 * q^51 + 4 * q^52 + 4 * q^54 + 8 * q^56 + 8 * q^57 - 8 * q^58 - 4 * q^59 + 8 * q^61 + 8 * q^62 + 24 * q^63 + 8 * q^64 - 4 * q^65 + 12 * q^66 + 20 * q^67 + 8 * q^68 - 4 * q^69 + 4 * q^70 - 24 * q^71 + 12 * q^72 - 4 * q^73 + 8 * q^74 - 16 * q^75 + 16 * q^76 - 16 * q^77 - 16 * q^78 + 4 * q^79 - 8 * q^81 + 8 * q^82 - 4 * q^83 - 4 * q^84 - 44 * q^85 + 32 * q^86 - 4 * q^87 + 8 * q^88 + 20 * q^89 - 8 * q^92 - 4 * q^93 + 16 * q^94 - 8 * q^95 + 4 * q^96 + 4 * q^97 + 4 * q^98

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
$3$	2.90642	1.67802	0.839012	−	0.544112i	$-0.183133\pi$
$3$	2.90642	1.67802	0.839012	+	0.544112i	$0.183133\pi$
$4$	1.00000	0.500000
$5$	−2.39983	−1.07324	−0.536618	−	0.843825i	$-0.680298\pi$
$5$	−2.39983	−1.07324	−0.536618	+	0.843825i	$0.680298\pi$
$6$	2.90642	1.18654
$7$	0.548309	0.207241	0.103621	−	0.994617i	$-0.466957\pi$
$7$	0.548309	0.207241	0.103621	+	0.994617i	$0.466957\pi$
$8$	1.00000	0.353553
$9$	5.44730	1.81577
$10$	−2.39983	−0.758892
$11$	4.89367	1.47550	0.737748	−	0.675076i	$-0.235889\pi$
$11$	4.89367	1.47550	0.737748	+	0.675076i	$0.235889\pi$
$12$	2.90642	0.839012
$13$	−5.66121	−1.57014	−0.785068	−	0.619410i	$-0.787372\pi$
$13$	−5.66121	−1.57014	−0.785068	+	0.619410i	$0.787372\pi$
$14$	0.548309	0.146542
$15$	−6.97492	−1.80092
$16$	1.00000	0.250000
$17$	7.46691	1.81099	0.905496	−	0.424356i	$-0.139499\pi$
$17$	7.46691	1.81099	0.905496	+	0.424356i	$0.139499\pi$
$18$	5.44730	1.28394
$19$	0.237786	0.0545519	0.0272760	−	0.999628i	$-0.491317\pi$
$19$	0.237786	0.0545519	0.0272760	+	0.999628i	$0.491317\pi$
$20$	−2.39983	−0.536618
$21$	1.59362	0.347756
$22$	4.89367	1.04333
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	2.90642	0.593271
$25$	0.759171	0.151834
$26$	−5.66121	−1.11025
$27$	7.11290	1.36888
$28$	0.548309	0.103621
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−6.97492	−1.27344
$31$	7.69664	1.38236	0.691178	−	0.722684i	$-0.257092\pi$
$31$	7.69664	1.38236	0.691178	+	0.722684i	$0.257092\pi$
$32$	1.00000	0.176777
$33$	14.2231	2.47592
$34$	7.46691	1.28056
$35$	−1.31585	−0.222419
$36$	5.44730	0.907884
$37$	−2.97612	−0.489271	−0.244635	−	0.969615i	$-0.578668\pi$
$37$	−2.97612	−0.489271	−0.244635	+	0.969615i	$0.578668\pi$
$38$	0.237786	0.0385740
$39$	−16.4539	−2.63473
$40$	−2.39983	−0.379446
$41$	−5.61419	−0.876789	−0.438394	−	0.898783i	$-0.644453\pi$
$41$	−5.61419	−0.876789	−0.438394	+	0.898783i	$0.644453\pi$
$42$	1.59362	0.245901
$43$	−3.80313	−0.579973	−0.289986	−	0.957031i	$-0.593651\pi$
$43$	−3.80313	−0.579973	−0.289986	+	0.957031i	$0.593651\pi$
$44$	4.89367	0.737748
$45$	−13.0726	−1.94875
$46$	−1.00000	−0.147442
$47$	5.88047	0.857755	0.428878	−	0.903363i	$-0.358909\pi$
$47$	5.88047	0.857755	0.428878	+	0.903363i	$0.358909\pi$
$48$	2.90642	0.419506
$49$	−6.69936	−0.957051
$50$	0.759171	0.107363
$51$	21.7020	3.03889
$52$	−5.66121	−0.785068
$53$	−0.959699	−0.131825	−0.0659124	−	0.997825i	$-0.520996\pi$
$53$	−0.959699	−0.131825	−0.0659124	+	0.997825i	$0.520996\pi$
$54$	7.11290	0.967943
$55$	−11.7440	−1.58355
$56$	0.548309	0.0732709
$57$	0.691108	0.0915395
$58$	−1.00000	−0.131306
$59$	−12.2728	−1.59778	−0.798889	−	0.601478i	$-0.794579\pi$
$59$	−12.2728	−1.59778	−0.798889	+	0.601478i	$0.794579\pi$
$60$	−6.97492	−0.900458
$61$	8.70749	1.11488	0.557440	−	0.830217i	$-0.311784\pi$
$61$	8.70749	1.11488	0.557440	+	0.830217i	$0.311784\pi$
$62$	7.69664	0.977474
$63$	2.98681	0.376302
$64$	1.00000	0.125000
$65$	13.5859	1.68513
$66$	14.2231	1.75074
$67$	−0.366509	−0.0447762	−0.0223881	−	0.999749i	$-0.507127\pi$
$67$	−0.366509	−0.0447762	−0.0223881	+	0.999749i	$0.507127\pi$
$68$	7.46691	0.905496
$69$	−2.90642	−0.349892
$70$	−1.31585	−0.157274
$71$	−9.03164	−1.07186	−0.535929	−	0.844263i	$-0.680039\pi$
$71$	−9.03164	−1.07186	−0.535929	+	0.844263i	$0.680039\pi$
$72$	5.44730	0.641971
$73$	12.1849	1.42614	0.713070	−	0.701093i	$-0.247304\pi$
$73$	12.1849	1.42614	0.713070	+	0.701093i	$0.247304\pi$
$74$	−2.97612	−0.345967
$75$	2.20647	0.254781
$76$	0.237786	0.0272760
$77$	2.68324	0.305784
$78$	−16.4539	−1.86303
$79$	−2.47130	−0.278043	−0.139021	−	0.990289i	$-0.544396\pi$
$79$	−2.47130	−0.278043	−0.139021	+	0.990289i	$0.544396\pi$
$80$	−2.39983	−0.268309
$81$	4.33119	0.481243
$82$	−5.61419	−0.619983
$83$	−5.49155	−0.602776	−0.301388	−	0.953502i	$-0.597450\pi$
$83$	−5.49155	−0.602776	−0.301388	+	0.953502i	$0.597450\pi$
$84$	1.59362	0.173878
$85$	−17.9193	−1.94362
$86$	−3.80313	−0.410103
$87$	−2.90642	−0.311601
$88$	4.89367	0.521667
$89$	11.3699	1.20521	0.602605	−	0.798040i	$-0.294130\pi$
$89$	11.3699	1.20521	0.602605	+	0.798040i	$0.294130\pi$
$90$	−13.0726	−1.37797
$91$	−3.10409	−0.325397
$92$	−1.00000	−0.104257
$93$	22.3697	2.31963
$94$	5.88047	0.606525
$95$	−0.570646	−0.0585471
$96$	2.90642	0.296636
$97$	−10.4615	−1.06221	−0.531104	−	0.847306i	$-0.678223\pi$
$97$	−10.4615	−1.06221	−0.531104	+	0.847306i	$0.678223\pi$
$98$	−6.69936	−0.676737
$99$	26.6573	2.67916
$100$	0.759171	0.0759171
$101$	−15.9889	−1.59096	−0.795478	−	0.605983i	$-0.792780\pi$
$101$	−15.9889	−1.59096	−0.795478	+	0.605983i	$0.792780\pi$
$102$	21.7020	2.14882
$103$	−5.01980	−0.494615	−0.247308	−	0.968937i	$-0.579546\pi$
$103$	−5.01980	−0.494615	−0.247308	+	0.968937i	$0.579546\pi$
$104$	−5.66121	−0.555127
$105$	−3.82441	−0.373224
$106$	−0.959699	−0.0932142
$107$	8.06585	0.779755	0.389878	−	0.920867i	$-0.372517\pi$
$107$	8.06585	0.779755	0.389878	+	0.920867i	$0.372517\pi$
$108$	7.11290	0.684439
$109$	−7.19580	−0.689233	−0.344616	−	0.938744i	$-0.611991\pi$
$109$	−7.19580	−0.689233	−0.344616	+	0.938744i	$0.611991\pi$
$110$	−11.7440	−1.11974
$111$	−8.64986	−0.821008
$112$	0.548309	0.0518104
$113$	9.05685	0.851997	0.425998	−	0.904724i	$-0.359923\pi$
$113$	9.05685	0.851997	0.425998	+	0.904724i	$0.359923\pi$
$114$	0.691108	0.0647282
$115$	2.39983	0.223785
$116$	−1.00000	−0.0928477
$117$	−30.8383	−2.85100
$118$	−12.2728	−1.12980
$119$	4.09417	0.375312
$120$	−6.97492	−0.636720
$121$	12.9480	1.17709
$122$	8.70749	0.788339
$123$	−16.3172	−1.47127
$124$	7.69664	0.691178
$125$	10.1773	0.910282
$126$	2.98681	0.266086
$127$	−11.0659	−0.981938	−0.490969	−	0.871177i	$-0.663357\pi$
$127$	−11.0659	−0.981938	−0.490969	+	0.871177i	$0.663357\pi$
$128$	1.00000	0.0883883
$129$	−11.0535	−0.973208
$130$	13.5859	1.19156
$131$	−10.1810	−0.889519	−0.444760	−	0.895650i	$-0.646711\pi$
$131$	−10.1810	−0.889519	−0.444760	+	0.895650i	$0.646711\pi$
$132$	14.2231	1.23796
$133$	0.130380	0.0113054
$134$	−0.366509	−0.0316616
$135$	−17.0697	−1.46913
$136$	7.46691	0.640282
$137$	−3.66689	−0.313283	−0.156642	−	0.987655i	$-0.550067\pi$
$137$	−3.66689	−0.313283	−0.156642	+	0.987655i	$0.550067\pi$
$138$	−2.90642	−0.247411
$139$	−13.3722	−1.13421	−0.567107	−	0.823644i	$-0.691937\pi$
$139$	−13.3722	−1.13421	−0.567107	+	0.823644i	$0.691937\pi$
$140$	−1.31585	−0.111209
$141$	17.0912	1.43933
$142$	−9.03164	−0.757918
$143$	−27.7041	−2.31673
$144$	5.44730	0.453942
$145$	2.39983	0.199295
$146$	12.1849	1.00843
$147$	−19.4712	−1.60596
$148$	−2.97612	−0.244635
$149$	−11.2967	−0.925466	−0.462733	−	0.886498i	$-0.653131\pi$
$149$	−11.2967	−0.925466	−0.462733	+	0.886498i	$0.653131\pi$
$150$	2.20647	0.180158
$151$	−3.14026	−0.255551	−0.127775	−	0.991803i	$-0.540784\pi$
$151$	−3.14026	−0.255551	−0.127775	+	0.991803i	$0.540784\pi$
$152$	0.237786	0.0192870
$153$	40.6745	3.28834
$154$	2.68324	0.216222
$155$	−18.4706	−1.48359
$156$	−16.4539	−1.31736
$157$	−11.3109	−0.902708	−0.451354	−	0.892345i	$-0.649059\pi$
$157$	−11.3109	−0.902708	−0.451354	+	0.892345i	$0.649059\pi$
$158$	−2.47130	−0.196606
$159$	−2.78929	−0.221205
$160$	−2.39983	−0.189723
$161$	−0.548309	−0.0432128
$162$	4.33119	0.340290
$163$	−17.1887	−1.34632	−0.673160	−	0.739497i	$-0.735063\pi$
$163$	−17.1887	−1.34632	−0.673160	+	0.739497i	$0.735063\pi$
$164$	−5.61419	−0.438394
$165$	−34.1329	−2.65724
$166$	−5.49155	−0.426227
$167$	−10.2105	−0.790111	−0.395056	−	0.918657i	$-0.629275\pi$
$167$	−10.2105	−0.790111	−0.395056	+	0.918657i	$0.629275\pi$
$168$	1.59362	0.122950
$169$	19.0493	1.46533
$170$	−17.9193	−1.37435
$171$	1.29529	0.0990536
$172$	−3.80313	−0.289986
$173$	−4.51123	−0.342983	−0.171491	−	0.985186i	$-0.554859\pi$
$173$	−4.51123	−0.342983	−0.171491	+	0.985186i	$0.554859\pi$
$174$	−2.90642	−0.220335
$175$	0.416260	0.0314663
$176$	4.89367	0.368874
$177$	−35.6699	−2.68111
$178$	11.3699	0.852212
$179$	−13.3463	−0.997548	−0.498774	−	0.866732i	$-0.666216\pi$
$179$	−13.3463	−0.997548	−0.498774	+	0.866732i	$0.666216\pi$
$180$	−13.0726	−0.974373
$181$	20.3057	1.50931	0.754656	−	0.656121i	$-0.227804\pi$
$181$	20.3057	1.50931	0.754656	+	0.656121i	$0.227804\pi$
$182$	−3.10409	−0.230091
$183$	25.3077	1.87080
$184$	−1.00000	−0.0737210
$185$	7.14217	0.525103
$186$	22.3697	1.64023
$187$	36.5406	2.67211
$188$	5.88047	0.428878
$189$	3.90007	0.283688
$190$	−0.570646	−0.0413990
$191$	−4.17798	−0.302308	−0.151154	−	0.988510i	$-0.548299\pi$
$191$	−4.17798	−0.302308	−0.151154	+	0.988510i	$0.548299\pi$
$192$	2.90642	0.209753
$193$	26.6927	1.92138	0.960692	−	0.277617i	$-0.0895446\pi$
$193$	26.6927	1.92138	0.960692	+	0.277617i	$0.0895446\pi$
$194$	−10.4615	−0.751095
$195$	39.4864	2.82768
$196$	−6.69936	−0.478525
$197$	6.85653	0.488507	0.244254	−	0.969711i	$-0.421457\pi$
$197$	6.85653	0.488507	0.244254	+	0.969711i	$0.421457\pi$
$198$	26.6573	1.89445
$199$	16.7592	1.18803	0.594015	−	0.804454i	$-0.297542\pi$
$199$	16.7592	1.18803	0.594015	+	0.804454i	$0.297542\pi$
$200$	0.759171	0.0536815
$201$	−1.06523	−0.0751356
$202$	−15.9889	−1.12498
$203$	−0.548309	−0.0384838
$204$	21.7020	1.51944
$205$	13.4731	0.941001
$206$	−5.01980	−0.349746
$207$	−5.44730	−0.378614
$208$	−5.66121	−0.392534
$209$	1.16365	0.0804912
$210$	−3.82441	−0.263909
$211$	24.9187	1.71547	0.857736	−	0.514090i	$-0.171870\pi$
$211$	24.9187	1.71547	0.857736	+	0.514090i	$0.171870\pi$
$212$	−0.959699	−0.0659124
$213$	−26.2498	−1.79861
$214$	8.06585	0.551370
$215$	9.12687	0.622447
$216$	7.11290	0.483971
$217$	4.22014	0.286482
$218$	−7.19580	−0.487361
$219$	35.4146	2.39310
$220$	−11.7440	−0.791777
$221$	−42.2717	−2.84350
$222$	−8.64986	−0.580541
$223$	16.0399	1.07411	0.537055	−	0.843547i	$-0.319537\pi$
$223$	16.0399	1.07411	0.537055	+	0.843547i	$0.319537\pi$
$224$	0.548309	0.0366355
$225$	4.13543	0.275695
$226$	9.05685	0.602453
$227$	18.7851	1.24681	0.623406	−	0.781898i	$-0.285748\pi$
$227$	18.7851	1.24681	0.623406	+	0.781898i	$0.285748\pi$
$228$	0.691108	0.0457698
$229$	8.68794	0.574115	0.287057	−	0.957913i	$-0.407323\pi$
$229$	8.68794	0.574115	0.287057	+	0.957913i	$0.407323\pi$
$230$	2.39983	0.158240
$231$	7.79864	0.513113
$232$	−1.00000	−0.0656532
$233$	−28.6026	−1.87382	−0.936909	−	0.349573i	$-0.886327\pi$
$233$	−28.6026	−1.87382	−0.936909	+	0.349573i	$0.886327\pi$
$234$	−30.8383	−2.01596
$235$	−14.1121	−0.920573
$236$	−12.2728	−0.798889
$237$	−7.18264	−0.466562
$238$	4.09417	0.265386
$239$	−8.32984	−0.538813	−0.269406	−	0.963027i	$-0.586827\pi$
$239$	−8.32984	−0.538813	−0.269406	+	0.963027i	$0.586827\pi$
$240$	−6.97492	−0.450229
$241$	25.9375	1.67078	0.835392	−	0.549655i	$-0.185241\pi$
$241$	25.9375	1.67078	0.835392	+	0.549655i	$0.185241\pi$
$242$	12.9480	0.832328
$243$	−8.75041	−0.561339
$244$	8.70749	0.557440
$245$	16.0773	1.02714
$246$	−16.3172	−1.04035
$247$	−1.34616	−0.0856540
$248$	7.69664	0.488737
$249$	−15.9608	−1.01147
$250$	10.1773	0.643666
$251$	−4.85573	−0.306491	−0.153246	−	0.988188i	$-0.548973\pi$
$251$	−4.85573	−0.306491	−0.153246	+	0.988188i	$0.548973\pi$
$252$	2.98681	0.188151
$253$	−4.89367	−0.307662
$254$	−11.0659	−0.694335
$255$	−52.0811	−3.26144
$256$	1.00000	0.0625000
$257$	−2.65252	−0.165460	−0.0827299	−	0.996572i	$-0.526364\pi$
$257$	−2.65252	−0.165460	−0.0827299	+	0.996572i	$0.526364\pi$
$258$	−11.0535	−0.688162
$259$	−1.63183	−0.101397
$260$	13.5859	0.842563
$261$	−5.44730	−0.337180
$262$	−10.1810	−0.628985
$263$	−14.9852	−0.924025	−0.462012	−	0.886874i	$-0.652872\pi$
$263$	−14.9852	−0.924025	−0.462012	+	0.886874i	$0.652872\pi$
$264$	14.2231	0.875370
$265$	2.30311	0.141479
$266$	0.130380	0.00799414
$267$	33.0458	2.02237
$268$	−0.366509	−0.0223881
$269$	13.8803	0.846296	0.423148	−	0.906061i	$-0.360925\pi$
$269$	13.8803	0.846296	0.423148	+	0.906061i	$0.360925\pi$
$270$	−17.0697	−1.03883
$271$	9.05531	0.550071	0.275035	−	0.961434i	$-0.411310\pi$
$271$	9.05531	0.550071	0.275035	+	0.961434i	$0.411310\pi$
$272$	7.46691	0.452748
$273$	−9.02181	−0.546025
$274$	−3.66689	−0.221525
$275$	3.71513	0.224031
$276$	−2.90642	−0.174946
$277$	15.8407	0.951778	0.475889	−	0.879505i	$-0.342126\pi$
$277$	15.8407	0.951778	0.475889	+	0.879505i	$0.342126\pi$
$278$	−13.3722	−0.802010
$279$	41.9259	2.51004
$280$	−1.31585	−0.0786369
$281$	11.9704	0.714096	0.357048	−	0.934086i	$-0.383783\pi$
$281$	11.9704	0.714096	0.357048	+	0.934086i	$0.383783\pi$
$282$	17.0912	1.01776
$283$	−8.20413	−0.487685	−0.243842	−	0.969815i	$-0.578408\pi$
$283$	−8.20413	−0.487685	−0.243842	+	0.969815i	$0.578408\pi$
$284$	−9.03164	−0.535929
$285$	−1.65854	−0.0982434
$286$	−27.7041	−1.63818
$287$	−3.07831	−0.181707
$288$	5.44730	0.320985
$289$	38.7547	2.27969
$290$	2.39983	0.140923
$291$	−30.4057	−1.78241
$292$	12.1849	0.713070
$293$	−16.6064	−0.970155	−0.485077	−	0.874471i	$-0.661209\pi$
$293$	−16.6064	−0.970155	−0.485077	+	0.874471i	$0.661209\pi$
$294$	−19.4712	−1.13558
$295$	29.4525	1.71479
$296$	−2.97612	−0.172983
$297$	34.8082	2.01977
$298$	−11.2967	−0.654403
$299$	5.66121	0.327396
$300$	2.20647	0.127391
$301$	−2.08529	−0.120194
$302$	−3.14026	−0.180702
$303$	−46.4705	−2.66966
$304$	0.237786	0.0136380
$305$	−20.8965	−1.19653
$306$	40.6745	2.32521
$307$	7.96636	0.454664	0.227332	−	0.973817i	$-0.427000\pi$
$307$	7.96636	0.454664	0.227332	+	0.973817i	$0.427000\pi$
$308$	2.68324	0.152892
$309$	−14.5897	−0.829977
$310$	−18.4706	−1.04906
$311$	13.7216	0.778079	0.389040	−	0.921221i	$-0.372807\pi$
$311$	13.7216	0.778079	0.389040	+	0.921221i	$0.372807\pi$
$312$	−16.4539	−0.931517
$313$	−22.6312	−1.27919	−0.639595	−	0.768712i	$-0.720898\pi$
$313$	−22.6312	−1.27919	−0.639595	+	0.768712i	$0.720898\pi$
$314$	−11.3109	−0.638311
$315$	−7.16782	−0.403861
$316$	−2.47130	−0.139021
$317$	19.7203	1.10760	0.553801	−	0.832649i	$-0.313177\pi$
$317$	19.7203	1.10760	0.553801	+	0.832649i	$0.313177\pi$
$318$	−2.78929	−0.156416
$319$	−4.89367	−0.273993
$320$	−2.39983	−0.134154
$321$	23.4428	1.30845
$322$	−0.548309	−0.0305561
$323$	1.77553	0.0987931
$324$	4.33119	0.240622
$325$	−4.29782	−0.238400
$326$	−17.1887	−0.951991
$327$	−20.9141	−1.15655
$328$	−5.61419	−0.309992
$329$	3.22432	0.177762
$330$	−34.1329	−1.87896
$331$	13.9168	0.764935	0.382468	−	0.923969i	$-0.375074\pi$
$331$	13.9168	0.764935	0.382468	+	0.923969i	$0.375074\pi$
$332$	−5.49155	−0.301388
$333$	−16.2118	−0.888402
$334$	−10.2105	−0.558693
$335$	0.879559	0.0480554
$336$	1.59362	0.0869391
$337$	−4.75575	−0.259062	−0.129531	−	0.991575i	$-0.541347\pi$
$337$	−4.75575	−0.259062	−0.129531	+	0.991575i	$0.541347\pi$
$338$	19.0493	1.03614
$339$	26.3230	1.42967
$340$	−17.9193	−0.971810
$341$	37.6648	2.03966
$342$	1.29529	0.0700415
$343$	−7.51148	−0.405582
$344$	−3.80313	−0.205051
$345$	6.97492	0.375517
$346$	−4.51123	−0.242525
$347$	−20.5204	−1.10159	−0.550797	−	0.834639i	$-0.685676\pi$
$347$	−20.5204	−1.10159	−0.550797	+	0.834639i	$0.685676\pi$
$348$	−2.90642	−0.155801
$349$	−17.7179	−0.948419	−0.474209	−	0.880412i	$-0.657266\pi$
$349$	−17.7179	−0.948419	−0.474209	+	0.880412i	$0.657266\pi$
$350$	0.416260	0.0222501
$351$	−40.2676	−2.14932
$352$	4.89367	0.260833
$353$	−5.65854	−0.301174	−0.150587	−	0.988597i	$-0.548116\pi$
$353$	−5.65854	−0.301174	−0.150587	+	0.988597i	$0.548116\pi$
$354$	−35.6699	−1.89583
$355$	21.6744	1.15036
$356$	11.3699	0.602605
$357$	11.8994	0.629783
$358$	−13.3463	−0.705373
$359$	32.5299	1.71686	0.858431	−	0.512930i	$-0.171440\pi$
$359$	32.5299	1.71686	0.858431	+	0.512930i	$0.171440\pi$
$360$	−13.0726	−0.688986
$361$	−18.9435	−0.997024
$362$	20.3057	1.06724
$363$	37.6323	1.97519
$364$	−3.10409	−0.162699
$365$	−29.2417	−1.53058
$366$	25.3077	1.32285
$367$	7.97195	0.416133	0.208066	−	0.978115i	$-0.433283\pi$
$367$	7.97195	0.416133	0.208066	+	0.978115i	$0.433283\pi$
$368$	−1.00000	−0.0521286
$369$	−30.5822	−1.59204
$370$	7.14217	0.371304
$371$	−0.526212	−0.0273196
$372$	22.3697	1.15981
$373$	−16.1446	−0.835937	−0.417968	−	0.908462i	$-0.637258\pi$
$373$	−16.1446	−0.835937	−0.417968	+	0.908462i	$0.637258\pi$
$374$	36.5406	1.88947
$375$	29.5794	1.52748
$376$	5.88047	0.303262
$377$	5.66121	0.291567
$378$	3.90007	0.200598
$379$	−24.5485	−1.26097	−0.630486	−	0.776201i	$-0.717144\pi$
$379$	−24.5485	−1.26097	−0.630486	+	0.776201i	$0.717144\pi$
$380$	−0.570646	−0.0292735
$381$	−32.1621	−1.64772
$382$	−4.17798	−0.213764
$383$	0.365721	0.0186875	0.00934375	−	0.999956i	$-0.497026\pi$
$383$	0.365721	0.0186875	0.00934375	+	0.999956i	$0.497026\pi$
$384$	2.90642	0.148318
$385$	−6.43932	−0.328178
$386$	26.6927	1.35862
$387$	−20.7168	−1.05310
$388$	−10.4615	−0.531104
$389$	−9.13785	−0.463308	−0.231654	−	0.972798i	$-0.574414\pi$
$389$	−9.13785	−0.463308	−0.231654	+	0.972798i	$0.574414\pi$
$390$	39.4864	1.99947
$391$	−7.46691	−0.377618
$392$	−6.69936	−0.338369
$393$	−29.5903	−1.49264
$394$	6.85653	0.345427
$395$	5.93068	0.298405
$396$	26.6573	1.33958
$397$	26.3442	1.32218	0.661088	−	0.750309i	$-0.270095\pi$
$397$	26.3442	1.32218	0.661088	+	0.750309i	$0.270095\pi$
$398$	16.7592	0.840064
$399$	0.378941	0.0189708
$400$	0.759171	0.0379585
$401$	6.55378	0.327280	0.163640	−	0.986520i	$-0.447676\pi$
$401$	6.55378	0.327280	0.163640	+	0.986520i	$0.447676\pi$
$402$	−1.06523	−0.0531289
$403$	−43.5723	−2.17049
$404$	−15.9889	−0.795478
$405$	−10.3941	−0.516487
$406$	−0.548309	−0.0272121
$407$	−14.5641	−0.721917
$408$	21.7020	1.07441
$409$	34.9888	1.73009	0.865043	−	0.501698i	$-0.167291\pi$
$409$	34.9888	1.73009	0.865043	+	0.501698i	$0.167291\pi$
$410$	13.4731	0.665388
$411$	−10.6575	−0.525697
$412$	−5.01980	−0.247308
$413$	−6.72928	−0.331126
$414$	−5.44730	−0.267720
$415$	13.1788	0.646920
$416$	−5.66121	−0.277563
$417$	−38.8652	−1.90324
$418$	1.16365	0.0569159
$419$	19.5638	0.955756	0.477878	−	0.878426i	$-0.341406\pi$
$419$	19.5638	0.955756	0.477878	+	0.878426i	$0.341406\pi$
$420$	−3.82441	−0.186612
$421$	−17.3764	−0.846873	−0.423437	−	0.905926i	$-0.639176\pi$
$421$	−17.3764	−0.846873	−0.423437	+	0.905926i	$0.639176\pi$
$422$	24.9187	1.21302
$423$	32.0327	1.55748
$424$	−0.959699	−0.0466071
$425$	5.66866	0.274970
$426$	−26.2498	−1.27181
$427$	4.77440	0.231049
$428$	8.06585	0.389878
$429$	−80.5198	−3.88753
$430$	9.12687	0.440137
$431$	−24.7832	−1.19376	−0.596881	−	0.802330i	$-0.703594\pi$
$431$	−24.7832	−1.19376	−0.596881	+	0.802330i	$0.703594\pi$
$432$	7.11290	0.342219
$433$	−31.7819	−1.52734	−0.763670	−	0.645607i	$-0.776604\pi$
$433$	−31.7819	−1.52734	−0.763670	+	0.645607i	$0.776604\pi$
$434$	4.22014	0.202573
$435$	6.97492	0.334422
$436$	−7.19580	−0.344616
$437$	−0.237786	−0.0113749
$438$	35.4146	1.69217
$439$	31.7272	1.51426	0.757129	−	0.653266i	$-0.226602\pi$
$439$	31.7272	1.51426	0.757129	+	0.653266i	$0.226602\pi$
$440$	−11.7440	−0.559871
$441$	−36.4934	−1.73778
$442$	−42.2717	−2.01066
$443$	−30.2446	−1.43696	−0.718482	−	0.695546i	$-0.755163\pi$
$443$	−30.2446	−1.43696	−0.718482	+	0.695546i	$0.755163\pi$
$444$	−8.64986	−0.410504
$445$	−27.2859	−1.29347
$446$	16.0399	0.759511
$447$	−32.8331	−1.55295
$448$	0.548309	0.0259052
$449$	15.8848	0.749650	0.374825	−	0.927096i	$-0.377703\pi$
$449$	15.8848	0.749650	0.374825	+	0.927096i	$0.377703\pi$
$450$	4.13543	0.194946
$451$	−27.4740	−1.29370
$452$	9.05685	0.425998
$453$	−9.12692	−0.428820
$454$	18.7851	0.881629
$455$	7.44928	0.349228
$456$	0.691108	0.0323641
$457$	33.2629	1.55597	0.777987	−	0.628280i	$-0.216241\pi$
$457$	33.2629	1.55597	0.777987	+	0.628280i	$0.216241\pi$
$458$	8.68794	0.405961
$459$	53.1113	2.47903
$460$	2.39983	0.111893
$461$	25.1703	1.17230	0.586148	−	0.810204i	$-0.300644\pi$
$461$	25.1703	1.17230	0.586148	+	0.810204i	$0.300644\pi$
$462$	7.79864	0.362826
$463$	14.1216	0.656285	0.328143	−	0.944628i	$-0.393577\pi$
$463$	14.1216	0.656285	0.328143	+	0.944628i	$0.393577\pi$
$464$	−1.00000	−0.0464238
$465$	−53.6834	−2.48951
$466$	−28.6026	−1.32499
$467$	15.8875	0.735187	0.367593	−	0.929987i	$-0.380182\pi$
$467$	15.8875	0.735187	0.367593	+	0.929987i	$0.380182\pi$
$468$	−30.8383	−1.42550
$469$	−0.200960	−0.00927949
$470$	−14.1121	−0.650944
$471$	−32.8743	−1.51477
$472$	−12.2728	−0.564900
$473$	−18.6113	−0.855747
$474$	−7.18264	−0.329909
$475$	0.180520	0.00828285
$476$	4.09417	0.187656
$477$	−5.22777	−0.239363
$478$	−8.32984	−0.380998
$479$	29.3659	1.34176	0.670881	−	0.741565i	$-0.265916\pi$
$479$	29.3659	1.34176	0.670881	+	0.741565i	$0.265916\pi$
$480$	−6.97492	−0.318360
$481$	16.8484	0.768222
$482$	25.9375	1.18142
$483$	−1.59362	−0.0725122
$484$	12.9480	0.588545
$485$	25.1059	1.14000
$486$	−8.75041	−0.396927
$487$	−13.3797	−0.606290	−0.303145	−	0.952944i	$-0.598037\pi$
$487$	−13.3797	−0.606290	−0.303145	+	0.952944i	$0.598037\pi$
$488$	8.70749	0.394170
$489$	−49.9575	−2.25916
$490$	16.0773	0.726298
$491$	−31.3778	−1.41606	−0.708031	−	0.706181i	$-0.750416\pi$
$491$	−31.3778	−1.41606	−0.708031	+	0.706181i	$0.750416\pi$
$492$	−16.3172	−0.735637
$493$	−7.46691	−0.336293
$494$	−1.34616	−0.0605665
$495$	−63.9729	−2.87537
$496$	7.69664	0.345589
$497$	−4.95213	−0.222133
$498$	−15.9608	−0.715219
$499$	−11.0204	−0.493342	−0.246671	−	0.969099i	$-0.579337\pi$
$499$	−11.0204	−0.493342	−0.246671	+	0.969099i	$0.579337\pi$
$500$	10.1773	0.455141
$501$	−29.6760	−1.32583
$502$	−4.85573	−0.216722
$503$	16.2002	0.722333	0.361166	−	0.932501i	$-0.382379\pi$
$503$	16.2002	0.722333	0.361166	+	0.932501i	$0.382379\pi$
$504$	2.98681	0.133043
$505$	38.3706	1.70747
$506$	−4.89367	−0.217550
$507$	55.3652	2.45886
$508$	−11.0659	−0.490969
$509$	−14.7366	−0.653188	−0.326594	−	0.945165i	$-0.605901\pi$
$509$	−14.7366	−0.653188	−0.326594	+	0.945165i	$0.605901\pi$
$510$	−52.0811	−2.30619
$511$	6.68111	0.295555
$512$	1.00000	0.0441942
$513$	1.69135	0.0746749
$514$	−2.65252	−0.116998
$515$	12.0466	0.530839
$516$	−11.0535	−0.486604
$517$	28.7771	1.26561
$518$	−1.63183	−0.0716986
$519$	−13.1116	−0.575534
$520$	13.5859	0.595782
$521$	6.77906	0.296996	0.148498	−	0.988913i	$-0.452556\pi$
$521$	6.77906	0.296996	0.148498	+	0.988913i	$0.452556\pi$
$522$	−5.44730	−0.238422
$523$	37.4306	1.63672	0.818362	−	0.574703i	$-0.194882\pi$
$523$	37.4306	1.63672	0.818362	+	0.574703i	$0.194882\pi$
$524$	−10.1810	−0.444760
$525$	1.20983	0.0528013
$526$	−14.9852	−0.653384
$527$	57.4701	2.50344
$528$	14.2231	0.618980
$529$	1.00000	0.0434783
$530$	2.30311	0.100041
$531$	−66.8535	−2.90119
$532$	0.130380	0.00565271
$533$	31.7831	1.37668
$534$	33.0458	1.43003
$535$	−19.3566	−0.836861
$536$	−0.366509	−0.0158308
$537$	−38.7900	−1.67391
$538$	13.8803	0.598422
$539$	−32.7844	−1.41213
$540$	−17.0697	−0.734564
$541$	31.2539	1.34371	0.671854	−	0.740683i	$-0.265498\pi$
$541$	31.2539	1.34371	0.671854	+	0.740683i	$0.265498\pi$
$542$	9.05531	0.388959
$543$	59.0170	2.53266
$544$	7.46691	0.320141
$545$	17.2687	0.739709
$546$	−9.02181	−0.386098
$547$	39.6265	1.69431	0.847153	−	0.531349i	$-0.178315\pi$
$547$	39.6265	1.69431	0.847153	+	0.531349i	$0.178315\pi$
$548$	−3.66689	−0.156642
$549$	47.4323	2.02436
$550$	3.71513	0.158414
$551$	−0.237786	−0.0101300
$552$	−2.90642	−0.123706
$553$	−1.35503	−0.0576219
$554$	15.8407	0.673009
$555$	20.7582	0.881135
$556$	−13.3722	−0.567107
$557$	−37.4552	−1.58703	−0.793513	−	0.608553i	$-0.791750\pi$
$557$	−37.4552	−1.58703	−0.793513	+	0.608553i	$0.791750\pi$
$558$	41.9259	1.77487
$559$	21.5303	0.910636
$560$	−1.31585	−0.0556047
$561$	106.202	4.48387
$562$	11.9704	0.504942
$563$	35.9038	1.51316	0.756582	−	0.653899i	$-0.226868\pi$
$563$	35.9038	1.51316	0.756582	+	0.653899i	$0.226868\pi$
$564$	17.0912	0.719667
$565$	−21.7349	−0.914393
$566$	−8.20413	−0.344845
$567$	2.37483	0.0997336
$568$	−9.03164	−0.378959
$569$	−14.0402	−0.588596	−0.294298	−	0.955714i	$-0.595086\pi$
$569$	−14.0402	−0.588596	−0.294298	+	0.955714i	$0.595086\pi$
$570$	−1.65854	−0.0694686
$571$	29.0290	1.21483	0.607413	−	0.794386i	$-0.292207\pi$
$571$	29.0290	1.21483	0.607413	+	0.794386i	$0.292207\pi$
$572$	−27.7041	−1.15836
$573$	−12.1430	−0.507280
$574$	−3.07831	−0.128486
$575$	−0.759171	−0.0316596
$576$	5.44730	0.226971
$577$	−18.7668	−0.781270	−0.390635	−	0.920546i	$-0.627745\pi$
$577$	−18.7668	−0.781270	−0.390635	+	0.920546i	$0.627745\pi$
$578$	38.7547	1.61198
$579$	77.5804	3.22413
$580$	2.39983	0.0996474
$581$	−3.01107	−0.124920
$582$	−30.4057	−1.26036
$583$	−4.69645	−0.194507
$584$	12.1849	0.504216
$585$	74.0066	3.05980
$586$	−16.6064	−0.686003
$587$	15.3335	0.632880	0.316440	−	0.948612i	$-0.397512\pi$
$587$	15.3335	0.632880	0.316440	+	0.948612i	$0.397512\pi$
$588$	−19.4712	−0.802978
$589$	1.83016	0.0754103
$590$	29.4525	1.21254
$591$	19.9280	0.819728
$592$	−2.97612	−0.122318
$593$	−17.6515	−0.724861	−0.362431	−	0.932011i	$-0.618053\pi$
$593$	−17.6515	−0.724861	−0.362431	+	0.932011i	$0.618053\pi$
$594$	34.8082	1.42820
$595$	−9.82531	−0.402799
$596$	−11.2967	−0.462733
$597$	48.7094	1.99354
$598$	5.66121	0.231504
$599$	−8.34131	−0.340817	−0.170408	−	0.985374i	$-0.554509\pi$
$599$	−8.34131	−0.340817	−0.170408	+	0.985374i	$0.554509\pi$
$600$	2.20647	0.0900789
$601$	−47.4432	−1.93525	−0.967625	−	0.252394i	$-0.918782\pi$
$601$	−47.4432	−1.93525	−0.967625	+	0.252394i	$0.918782\pi$
$602$	−2.08529	−0.0849902
$603$	−1.99649	−0.0813032
$604$	−3.14026	−0.127775
$605$	−31.0729	−1.26329
$606$	−46.4705	−1.88774
$607$	−24.2096	−0.982639	−0.491319	−	0.870979i	$-0.663485\pi$
$607$	−24.2096	−0.982639	−0.491319	+	0.870979i	$0.663485\pi$
$608$	0.237786	0.00964351
$609$	−1.59362	−0.0645767
$610$	−20.8965	−0.846073
$611$	−33.2906	−1.34679
$612$	40.6745	1.64417
$613$	45.7282	1.84694	0.923472	−	0.383665i	$-0.125338\pi$
$613$	45.7282	1.84694	0.923472	+	0.383665i	$0.125338\pi$
$614$	7.96636	0.321496
$615$	39.1585	1.57902
$616$	2.68324	0.108111
$617$	−7.81415	−0.314586	−0.157293	−	0.987552i	$-0.550277\pi$
$617$	−7.81415	−0.314586	−0.157293	+	0.987552i	$0.550277\pi$
$618$	−14.5897	−0.586882
$619$	27.0074	1.08552	0.542759	−	0.839889i	$-0.317380\pi$
$619$	27.0074	1.08552	0.542759	+	0.839889i	$0.317380\pi$
$620$	−18.4706	−0.741797
$621$	−7.11290	−0.285431
$622$	13.7216	0.550185
$623$	6.23424	0.249769
$624$	−16.4539	−0.658682
$625$	−28.2195	−1.12878
$626$	−22.6312	−0.904524
$627$	3.38205	0.135066
$628$	−11.3109	−0.451354
$629$	−22.2224	−0.886065
$630$	−7.16782	−0.285573
$631$	−36.4282	−1.45018	−0.725092	−	0.688652i	$-0.758203\pi$
$631$	−36.4282	−1.45018	−0.725092	+	0.688652i	$0.758203\pi$
$632$	−2.47130	−0.0983029
$633$	72.4242	2.87861
$634$	19.7203	0.783193
$635$	26.5562	1.05385
$636$	−2.78929	−0.110603
$637$	37.9264	1.50270
$638$	−4.89367	−0.193742
$639$	−49.1981	−1.94625
$640$	−2.39983	−0.0948615
$641$	−10.3389	−0.408362	−0.204181	−	0.978933i	$-0.565453\pi$
$641$	−10.3389	−0.408362	−0.204181	+	0.978933i	$0.565453\pi$
$642$	23.4428	0.925213
$643$	−32.3884	−1.27727	−0.638637	−	0.769508i	$-0.720502\pi$
$643$	−32.3884	−1.27727	−0.638637	+	0.769508i	$0.720502\pi$
$644$	−0.548309	−0.0216064
$645$	26.5265	1.04448
$646$	1.77553	0.0698573
$647$	28.1048	1.10491	0.552456	−	0.833542i	$-0.313691\pi$
$647$	28.1048	1.10491	0.552456	+	0.833542i	$0.313691\pi$
$648$	4.33119	0.170145
$649$	−60.0589	−2.35752
$650$	−4.29782	−0.168574
$651$	12.2655	0.480723
$652$	−17.1887	−0.673160
$653$	−37.1160	−1.45246	−0.726231	−	0.687450i	$-0.758730\pi$
$653$	−37.1160	−1.45246	−0.726231	+	0.687450i	$0.758730\pi$
$654$	−20.9141	−0.817804
$655$	24.4327	0.954664
$656$	−5.61419	−0.219197
$657$	66.3750	2.58954
$658$	3.22432	0.125697
$659$	−10.0331	−0.390835	−0.195417	−	0.980720i	$-0.562606\pi$
$659$	−10.0331	−0.390835	−0.195417	+	0.980720i	$0.562606\pi$
$660$	−34.1329	−1.32862
$661$	13.6246	0.529936	0.264968	−	0.964257i	$-0.414639\pi$
$661$	13.6246	0.529936	0.264968	+	0.964257i	$0.414639\pi$
$662$	13.9168	0.540891
$663$	−122.859	−4.77147
$664$	−5.49155	−0.213113
$665$	−0.312891	−0.0121334
$666$	−16.2118	−0.628195
$667$	1.00000	0.0387202
$668$	−10.2105	−0.395056
$669$	46.6187	1.80238
$670$	0.879559	0.0339803
$671$	42.6116	1.64500
$672$	1.59362	0.0614752
$673$	46.7799	1.80323	0.901616	−	0.432538i	$-0.142382\pi$
$673$	46.7799	1.80323	0.901616	+	0.432538i	$0.142382\pi$
$674$	−4.75575	−0.183185
$675$	5.39990	0.207842
$676$	19.0493	0.732664
$677$	19.9003	0.764832	0.382416	−	0.923990i	$-0.375092\pi$
$677$	19.9003	0.764832	0.382416	+	0.923990i	$0.375092\pi$
$678$	26.3230	1.01093
$679$	−5.73616	−0.220134
$680$	−17.9193	−0.687173
$681$	54.5975	2.09218
$682$	37.6648	1.44226
$683$	35.6280	1.36327	0.681633	−	0.731694i	$-0.261270\pi$
$683$	35.6280	1.36327	0.681633	+	0.731694i	$0.261270\pi$
$684$	1.29529	0.0495268
$685$	8.79990	0.336227
$686$	−7.51148	−0.286790
$687$	25.2508	0.963379
$688$	−3.80313	−0.144993
$689$	5.43306	0.206983
$690$	6.97492	0.265531
$691$	19.2458	0.732144	0.366072	−	0.930587i	$-0.380702\pi$
$691$	19.2458	0.732144	0.366072	+	0.930587i	$0.380702\pi$
$692$	−4.51123	−0.171491
$693$	14.6164	0.555233
$694$	−20.5204	−0.778945
$695$	32.0909	1.21728
$696$	−2.90642	−0.110168
$697$	−41.9206	−1.58786
$698$	−17.7179	−0.670633
$699$	−83.1313	−3.14431
$700$	0.416260	0.0157332
$701$	33.0618	1.24873	0.624363	−	0.781135i	$-0.285359\pi$
$701$	33.0618	1.24873	0.624363	+	0.781135i	$0.285359\pi$
$702$	−40.2676	−1.51980
$703$	−0.707680	−0.0266907
$704$	4.89367	0.184437
$705$	−41.0158	−1.54474
$706$	−5.65854	−0.212962
$707$	−8.76686	−0.329712
$708$	−35.6699	−1.34056
$709$	−27.0916	−1.01745	−0.508724	−	0.860930i	$-0.669882\pi$
$709$	−27.0916	−1.01745	−0.508724	+	0.860930i	$0.669882\pi$
$710$	21.6744	0.813425
$711$	−13.4619	−0.504861
$712$	11.3699	0.426106
$713$	−7.69664	−0.288241
$714$	11.8994	0.445324
$715$	66.4850	2.48640
$716$	−13.3463	−0.498774
$717$	−24.2101	−0.904141
$718$	32.5299	1.21400
$719$	11.1284	0.415019	0.207509	−	0.978233i	$-0.433464\pi$
$719$	11.1284	0.415019	0.207509	+	0.978233i	$0.433464\pi$
$720$	−13.0726	−0.487186
$721$	−2.75240	−0.102505
$722$	−18.9435	−0.705002
$723$	75.3855	2.80362
$724$	20.3057	0.754656
$725$	−0.759171	−0.0281949
$726$	37.6323	1.39667
$727$	21.5355	0.798709	0.399354	−	0.916797i	$-0.369234\pi$
$727$	21.5355	0.798709	0.399354	+	0.916797i	$0.369234\pi$
$728$	−3.10409	−0.115045
$729$	−38.4260	−1.42318
$730$	−29.2417	−1.08229
$731$	−28.3977	−1.05033
$732$	25.3077	0.935398
$733$	−29.7640	−1.09936	−0.549680	−	0.835375i	$-0.685250\pi$
$733$	−29.7640	−1.09936	−0.549680	+	0.835375i	$0.685250\pi$
$734$	7.97195	0.294250
$735$	46.7275	1.72357
$736$	−1.00000	−0.0368605
$737$	−1.79357	−0.0660671
$738$	−30.5822	−1.12575
$739$	−42.0491	−1.54680	−0.773400	−	0.633918i	$-0.781446\pi$
$739$	−42.0491	−1.54680	−0.773400	+	0.633918i	$0.781446\pi$
$740$	7.14217	0.262551
$741$	−3.91251	−0.143729
$742$	−0.526212	−0.0193179
$743$	−7.77987	−0.285416	−0.142708	−	0.989765i	$-0.545581\pi$
$743$	−7.77987	−0.285416	−0.142708	+	0.989765i	$0.545581\pi$
$744$	22.3697	0.820113
$745$	27.1102	0.993242
$746$	−16.1446	−0.591097
$747$	−29.9141	−1.09450
$748$	36.5406	1.33606
$749$	4.42258	0.161598
$750$	29.5794	1.08009
$751$	38.8690	1.41835	0.709175	−	0.705032i	$-0.249067\pi$
$751$	38.8690	1.41835	0.709175	+	0.705032i	$0.249067\pi$
$752$	5.88047	0.214439
$753$	−14.1128	−0.514300
$754$	5.66121	0.206169
$755$	7.53608	0.274266
$756$	3.90007	0.141844
$757$	−17.9935	−0.653986	−0.326993	−	0.945027i	$-0.606035\pi$
$757$	−17.9935	−0.653986	−0.326993	+	0.945027i	$0.606035\pi$
$758$	−24.5485	−0.891642
$759$	−14.2231	−0.516265
$760$	−0.570646	−0.0206995
$761$	−14.3301	−0.519466	−0.259733	−	0.965681i	$-0.583634\pi$
$761$	−14.3301	−0.519466	−0.259733	+	0.965681i	$0.583634\pi$
$762$	−32.1621	−1.16511
$763$	−3.94553	−0.142838
$764$	−4.17798	−0.151154
$765$	−97.6118	−3.52916
$766$	0.365721	0.0132141
$767$	69.4787	2.50873
$768$	2.90642	0.104877
$769$	37.5875	1.35544	0.677719	−	0.735321i	$-0.262969\pi$
$769$	37.5875	1.35544	0.677719	+	0.735321i	$0.262969\pi$
$770$	−6.43932	−0.232057
$771$	−7.70936	−0.277646
$772$	26.6927	0.960692
$773$	−17.9837	−0.646828	−0.323414	−	0.946258i	$-0.604831\pi$
$773$	−17.9837	−0.646828	−0.323414	+	0.946258i	$0.604831\pi$
$774$	−20.7168	−0.744651
$775$	5.84306	0.209889
$776$	−10.4615	−0.375548
$777$	−4.74280	−0.170147
$778$	−9.13785	−0.327608
$779$	−1.33498	−0.0478305
$780$	39.4864	1.41384
$781$	−44.1978	−1.58152
$782$	−7.46691	−0.267016
$783$	−7.11290	−0.254194
$784$	−6.69936	−0.239263
$785$	27.1442	0.968818
$786$	−29.5903	−1.05545
$787$	−34.2952	−1.22249	−0.611246	−	0.791441i	$-0.709331\pi$
$787$	−34.2952	−1.22249	−0.611246	+	0.791441i	$0.709331\pi$
$788$	6.85653	0.244254
$789$	−43.5532	−1.55054
$790$	5.93068	0.211004
$791$	4.96595	0.176569
$792$	26.6573	0.947225
$793$	−49.2949	−1.75051
$794$	26.3442	0.934919
$795$	6.69382	0.237405
$796$	16.7592	0.594015
$797$	−24.5548	−0.869776	−0.434888	−	0.900485i	$-0.643212\pi$
$797$	−24.5548	−0.869776	−0.434888	+	0.900485i	$0.643212\pi$
$798$	0.378941	0.0134144
$799$	43.9090	1.55339
$800$	0.759171	0.0268407
$801$	61.9354	2.18838
$802$	6.55378	0.231422
$803$	59.6290	2.10426
$804$	−1.06523	−0.0375678
$805$	1.31585	0.0463775
$806$	−43.5723	−1.53477
$807$	40.3420	1.42011
$808$	−15.9889	−0.562488
$809$	−18.1336	−0.637545	−0.318772	−	0.947831i	$-0.603271\pi$
$809$	−18.1336	−0.637545	−0.318772	+	0.947831i	$0.603271\pi$
$810$	−10.3941	−0.365212
$811$	−5.91416	−0.207674	−0.103837	−	0.994594i	$-0.533112\pi$
$811$	−5.91416	−0.207674	−0.103837	+	0.994594i	$0.533112\pi$
$812$	−0.548309	−0.0192419
$813$	26.3186	0.923032
$814$	−14.5641	−0.510473
$815$	41.2498	1.44492
$816$	21.7020	0.759722
$817$	−0.904334	−0.0316386
$818$	34.9888	1.22336
$819$	−16.9089	−0.590846
$820$	13.4731	0.470500
$821$	13.1621	0.459361	0.229681	−	0.973266i	$-0.426232\pi$
$821$	13.1621	0.459361	0.229681	+	0.973266i	$0.426232\pi$
$822$	−10.6575	−0.371724
$823$	−5.53223	−0.192841	−0.0964207	−	0.995341i	$-0.530739\pi$
$823$	−5.53223	−0.192841	−0.0964207	+	0.995341i	$0.530739\pi$
$824$	−5.01980	−0.174873
$825$	10.7977	0.375929
$826$	−6.72928	−0.234141
$827$	−49.1010	−1.70741	−0.853704	−	0.520758i	$-0.825649\pi$
$827$	−49.1010	−1.70741	−0.853704	+	0.520758i	$0.825649\pi$
$828$	−5.44730	−0.189307
$829$	49.1485	1.70700	0.853500	−	0.521093i	$-0.174476\pi$
$829$	49.1485	1.70700	0.853500	+	0.521093i	$0.174476\pi$
$830$	13.1788	0.457442
$831$	46.0399	1.59711
$832$	−5.66121	−0.196267
$833$	−50.0235	−1.73321
$834$	−38.8652	−1.34579
$835$	24.5034	0.847976
$836$	1.16365	0.0402456
$837$	54.7454	1.89228
$838$	19.5638	0.675821
$839$	19.0241	0.656784	0.328392	−	0.944542i	$-0.393493\pi$
$839$	19.0241	0.656784	0.328392	+	0.944542i	$0.393493\pi$
$840$	−3.82441	−0.131955
$841$	1.00000	0.0344828
$842$	−17.3764	−0.598830
$843$	34.7911	1.19827
$844$	24.9187	0.857736
$845$	−45.7149	−1.57264
$846$	32.0327	1.10131
$847$	7.09950	0.243942
$848$	−0.959699	−0.0329562
$849$	−23.8447	−0.818347
$850$	5.66866	0.194433
$851$	2.97612	0.102020
$852$	−26.2498	−0.899303
$853$	−21.2354	−0.727087	−0.363543	−	0.931577i	$-0.618433\pi$
$853$	−21.2354	−0.727087	−0.363543	+	0.931577i	$0.618433\pi$
$854$	4.77440	0.163377
$855$	−3.10848	−0.106308
$856$	8.06585	0.275685
$857$	−24.7521	−0.845516	−0.422758	−	0.906243i	$-0.638938\pi$
$857$	−24.7521	−0.845516	−0.422758	+	0.906243i	$0.638938\pi$
$858$	−80.5198	−2.74890
$859$	−10.2969	−0.351324	−0.175662	−	0.984451i	$-0.556207\pi$
$859$	−10.2969	−0.351324	−0.175662	+	0.984451i	$0.556207\pi$
$860$	9.12687	0.311224
$861$	−8.94688	−0.304909
$862$	−24.7832	−0.844118
$863$	14.8031	0.503902	0.251951	−	0.967740i	$-0.418928\pi$
$863$	14.8031	0.503902	0.251951	+	0.967740i	$0.418928\pi$
$864$	7.11290	0.241986
$865$	10.8262	0.368101
$866$	−31.7819	−1.07999
$867$	112.638	3.82537
$868$	4.22014	0.143241
$869$	−12.0937	−0.410251
$870$	6.97492	0.236472
$871$	2.07488	0.0703047
$872$	−7.19580	−0.243681
$873$	−56.9872	−1.92872
$874$	−0.237786	−0.00804324
$875$	5.58028	0.188648
$876$	35.4146	1.19655
$877$	12.0171	0.405789	0.202895	−	0.979201i	$-0.434965\pi$
$877$	12.0171	0.405789	0.202895	+	0.979201i	$0.434965\pi$
$878$	31.7272	1.07074
$879$	−48.2652	−1.62794
$880$	−11.7440	−0.395889
$881$	−44.7613	−1.50805	−0.754024	−	0.656847i	$-0.771890\pi$
$881$	−44.7613	−1.50805	−0.754024	+	0.656847i	$0.771890\pi$
$882$	−36.4934	−1.22880
$883$	20.1375	0.677680	0.338840	−	0.940844i	$-0.389965\pi$
$883$	20.1375	0.677680	0.338840	+	0.940844i	$0.389965\pi$
$884$	−42.2717	−1.42175
$885$	85.6016	2.87747
$886$	−30.2446	−1.01609
$887$	50.2160	1.68609	0.843044	−	0.537845i	$-0.180761\pi$
$887$	50.2160	1.68609	0.843044	+	0.537845i	$0.180761\pi$
$888$	−8.64986	−0.290270
$889$	−6.06752	−0.203498
$890$	−27.2859	−0.914624
$891$	21.1954	0.710073
$892$	16.0399	0.537055
$893$	1.39830	0.0467922
$894$	−32.8331	−1.09810
$895$	32.0288	1.07060
$896$	0.548309	0.0183177
$897$	16.4539	0.549379
$898$	15.8848	0.530083
$899$	−7.69664	−0.256697
$900$	4.13543	0.137848
$901$	−7.16599	−0.238734
$902$	−27.4740	−0.914783
$903$	−6.06075	−0.201689
$904$	9.05685	0.301226
$905$	−48.7302	−1.61985
$906$	−9.12692	−0.303222
$907$	26.8252	0.890716	0.445358	−	0.895353i	$-0.353076\pi$
$907$	26.8252	0.890716	0.445358	+	0.895353i	$0.353076\pi$
$908$	18.7851	0.623406
$909$	−87.0964	−2.88880
$910$	7.44928	0.246941
$911$	−31.2306	−1.03472	−0.517358	−	0.855769i	$-0.673084\pi$
$911$	−31.2306	−1.03472	−0.517358	+	0.855769i	$0.673084\pi$
$912$	0.691108	0.0228849
$913$	−26.8738	−0.889394
$914$	33.2629	1.10024
$915$	−60.7340	−2.00780
$916$	8.68794	0.287057
$917$	−5.58235	−0.184345
$918$	53.1113	1.75294
$919$	25.2815	0.833960	0.416980	−	0.908916i	$-0.363088\pi$
$919$	25.2815	0.833960	0.416980	+	0.908916i	$0.363088\pi$
$920$	2.39983	0.0791200
$921$	23.1536	0.762938
$922$	25.1703	0.828939
$923$	51.1300	1.68296
$924$	7.79864	0.256557
$925$	−2.25938	−0.0742880
$926$	14.1216	0.464064
$927$	−27.3443	−0.898106
$928$	−1.00000	−0.0328266
$929$	−23.1386	−0.759152	−0.379576	−	0.925161i	$-0.623930\pi$
$929$	−23.1386	−0.759152	−0.379576	+	0.925161i	$0.623930\pi$
$930$	−53.6834	−1.76035
$931$	−1.59302	−0.0522090
$932$	−28.6026	−0.936909
$933$	39.8807	1.30564
$934$	15.8875	0.519855
$935$	−87.6910	−2.86780
$936$	−30.8383	−1.00798
$937$	5.96576	0.194893	0.0974464	−	0.995241i	$-0.468933\pi$
$937$	5.96576	0.194893	0.0974464	+	0.995241i	$0.468933\pi$
$938$	−0.200960	−0.00656159
$939$	−65.7758	−2.14651
$940$	−14.1121	−0.460287
$941$	12.7560	0.415834	0.207917	−	0.978146i	$-0.433332\pi$
$941$	12.7560	0.415834	0.207917	+	0.978146i	$0.433332\pi$
$942$	−32.8743	−1.07110
$943$	5.61419	0.182823
$944$	−12.2728	−0.399445
$945$	−9.35949	−0.304464
$946$	−18.6113	−0.605105
$947$	−3.93945	−0.128015	−0.0640074	−	0.997949i	$-0.520388\pi$
$947$	−3.93945	−0.128015	−0.0640074	+	0.997949i	$0.520388\pi$
$948$	−7.18264	−0.233281
$949$	−68.9814	−2.23923
$950$	0.180520	0.00585686
$951$	57.3155	1.85858
$952$	4.09417	0.132693
$953$	−46.7186	−1.51336	−0.756682	−	0.653783i	$-0.773181\pi$
$953$	−46.7186	−1.51336	−0.756682	+	0.653783i	$0.773181\pi$
$954$	−5.22777	−0.169255
$955$	10.0264	0.324448
$956$	−8.32984	−0.269406
$957$	−14.2231	−0.459767
$958$	29.3659	0.948769
$959$	−2.01059	−0.0649253
$960$	−6.97492	−0.225114
$961$	28.2382	0.910911
$962$	16.8484	0.543215
$963$	43.9371	1.41585
$964$	25.9375	0.835392
$965$	−64.0579	−2.06210
$966$	−1.59362	−0.0512739
$967$	−12.5614	−0.403947	−0.201973	−	0.979391i	$-0.564735\pi$
$967$	−12.5614	−0.403947	−0.201973	+	0.979391i	$0.564735\pi$
$968$	12.9480	0.416164
$969$	5.16044	0.165777
$970$	25.1059	0.806102
$971$	0.798208	0.0256157	0.0128079	−	0.999918i	$-0.495923\pi$
$971$	0.798208	0.0256157	0.0128079	+	0.999918i	$0.495923\pi$
$972$	−8.75041	−0.280670
$973$	−7.33209	−0.235056
$974$	−13.3797	−0.428712
$975$	−12.4913	−0.400042
$976$	8.70749	0.278720
$977$	18.1341	0.580160	0.290080	−	0.957002i	$-0.406318\pi$
$977$	18.1341	0.580160	0.290080	+	0.957002i	$0.406318\pi$
$978$	−49.9575	−1.59747
$979$	55.6406	1.77828
$980$	16.0773	0.513570
$981$	−39.1977	−1.25149
$982$	−31.3778	−1.00131
$983$	12.2310	0.390109	0.195055	−	0.980792i	$-0.437512\pi$
$983$	12.2310	0.390109	0.195055	+	0.980792i	$0.437512\pi$
$984$	−16.3172	−0.520174
$985$	−16.4545	−0.524283
$986$	−7.46691	−0.237795
$987$	9.37124	0.298290
$988$	−1.34616	−0.0428270
$989$	3.80313	0.120933
$990$	−63.9729	−2.03319
$991$	−38.4204	−1.22046	−0.610232	−	0.792223i	$-0.708924\pi$
$991$	−38.4204	−1.22046	−0.610232	+	0.792223i	$0.708924\pi$
$992$	7.69664	0.244368
$993$	40.4481	1.28358
$994$	−4.95213	−0.157072
$995$	−40.2192	−1.27504
$996$	−15.9608	−0.505736
$997$	41.7216	1.32134	0.660668	−	0.750678i	$-0.270273\pi$
$997$	41.7216	1.32134	0.660668	+	0.750678i	$0.270273\pi$
$998$	−11.0204	−0.348845
$999$	−21.1688	−0.669752

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1334.2.a.i.1.7	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1334.2.a.i.1.7	✓	8	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:	\( N \)	\(=\)	\( 1334 = 2 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1334.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.90642 q^{3} +1.00000 q^{4} -2.39983 q^{5} +2.90642 q^{6} +0.548309 q^{7} +1.00000 q^{8} +5.44730 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.90642 q^{3} +1.00000 q^{4} -2.39983 q^{5} +2.90642 q^{6} +0.548309 q^{7} +1.00000 q^{8} +5.44730 q^{9} -2.39983 q^{10} +4.89367 q^{11} +2.90642 q^{12} -5.66121 q^{13} +0.548309 q^{14} -6.97492 q^{15} +1.00000 q^{16} +7.46691 q^{17} +5.44730 q^{18} +0.237786 q^{19} -2.39983 q^{20} +1.59362 q^{21} +4.89367 q^{22} -1.00000 q^{23} +2.90642 q^{24} +0.759171 q^{25} -5.66121 q^{26} +7.11290 q^{27} +0.548309 q^{28} -1.00000 q^{29} -6.97492 q^{30} +7.69664 q^{31} +1.00000 q^{32} +14.2231 q^{33} +7.46691 q^{34} -1.31585 q^{35} +5.44730 q^{36} -2.97612 q^{37} +0.237786 q^{38} -16.4539 q^{39} -2.39983 q^{40} -5.61419 q^{41} +1.59362 q^{42} -3.80313 q^{43} +4.89367 q^{44} -13.0726 q^{45} -1.00000 q^{46} +5.88047 q^{47} +2.90642 q^{48} -6.69936 q^{49} +0.759171 q^{50} +21.7020 q^{51} -5.66121 q^{52} -0.959699 q^{53} +7.11290 q^{54} -11.7440 q^{55} +0.548309 q^{56} +0.691108 q^{57} -1.00000 q^{58} -12.2728 q^{59} -6.97492 q^{60} +8.70749 q^{61} +7.69664 q^{62} +2.98681 q^{63} +1.00000 q^{64} +13.5859 q^{65} +14.2231 q^{66} -0.366509 q^{67} +7.46691 q^{68} -2.90642 q^{69} -1.31585 q^{70} -9.03164 q^{71} +5.44730 q^{72} +12.1849 q^{73} -2.97612 q^{74} +2.20647 q^{75} +0.237786 q^{76} +2.68324 q^{77} -16.4539 q^{78} -2.47130 q^{79} -2.39983 q^{80} +4.33119 q^{81} -5.61419 q^{82} -5.49155 q^{83} +1.59362 q^{84} -17.9193 q^{85} -3.80313 q^{86} -2.90642 q^{87} +4.89367 q^{88} +11.3699 q^{89} -13.0726 q^{90} -3.10409 q^{91} -1.00000 q^{92} +22.3697 q^{93} +5.88047 q^{94} -0.570646 q^{95} +2.90642 q^{96} -10.4615 q^{97} -6.69936 q^{98} +26.6573 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 4 q^{3} + 8 q^{4} + 4 q^{6} + 8 q^{7} + 8 q^{8} + 12 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 + 4 * q^3 + 8 * q^4 + 4 * q^6 + 8 * q^7 + 8 * q^8 + 12 * q^9	\( 8 q + 8 q^{2} + 4 q^{3} + 8 q^{4} + 4 q^{6} + 8 q^{7} + 8 q^{8} + 12 q^{9} + 8 q^{11} + 4 q^{12} + 4 q^{13} + 8 q^{14} + 8 q^{16} + 8 q^{17} + 12 q^{18} + 16 q^{19} - 4 q^{21} + 8 q^{22} - 8 q^{23} + 4 q^{24} + 4 q^{25} + 4 q^{26} + 4 q^{27} + 8 q^{28} - 8 q^{29} + 8 q^{31} + 8 q^{32} + 12 q^{33} + 8 q^{34} + 4 q^{35} + 12 q^{36} + 8 q^{37} + 16 q^{38} - 16 q^{39} + 8 q^{41} - 4 q^{42} + 32 q^{43} + 8 q^{44} - 8 q^{46} + 16 q^{47} + 4 q^{48} + 4 q^{49} + 4 q^{50} + 12 q^{51} + 4 q^{52} + 4 q^{54} + 8 q^{56} + 8 q^{57} - 8 q^{58} - 4 q^{59} + 8 q^{61} + 8 q^{62} + 24 q^{63} + 8 q^{64} - 4 q^{65} + 12 q^{66} + 20 q^{67} + 8 q^{68} - 4 q^{69} + 4 q^{70} - 24 q^{71} + 12 q^{72} - 4 q^{73} + 8 q^{74} - 16 q^{75} + 16 q^{76} - 16 q^{77} - 16 q^{78} + 4 q^{79} - 8 q^{81} + 8 q^{82} - 4 q^{83} - 4 q^{84} - 44 q^{85} + 32 q^{86} - 4 q^{87} + 8 q^{88} + 20 q^{89} - 8 q^{92} - 4 q^{93} + 16 q^{94} - 8 q^{95} + 4 q^{96} + 4 q^{97} + 4 q^{98}+O(q^{100}) \) 8 * q + 8 * q^2 + 4 * q^3 + 8 * q^4 + 4 * q^6 + 8 * q^7 + 8 * q^8 + 12 * q^9 + 8 * q^11 + 4 * q^12 + 4 * q^13 + 8 * q^14 + 8 * q^16 + 8 * q^17 + 12 * q^18 + 16 * q^19 - 4 * q^21 + 8 * q^22 - 8 * q^23 + 4 * q^24 + 4 * q^25 + 4 * q^26 + 4 * q^27 + 8 * q^28 - 8 * q^29 + 8 * q^31 + 8 * q^32 + 12 * q^33 + 8 * q^34 + 4 * q^35 + 12 * q^36 + 8 * q^37 + 16 * q^38 - 16 * q^39 + 8 * q^41 - 4 * q^42 + 32 * q^43 + 8 * q^44 - 8 * q^46 + 16 * q^47 + 4 * q^48 + 4 * q^49 + 4 * q^50 + 12 * q^51 + 4 * q^52 + 4 * q^54 + 8 * q^56 + 8 * q^57 - 8 * q^58 - 4 * q^59 + 8 * q^61 + 8 * q^62 + 24 * q^63 + 8 * q^64 - 4 * q^65 + 12 * q^66 + 20 * q^67 + 8 * q^68 - 4 * q^69 + 4 * q^70 - 24 * q^71 + 12 * q^72 - 4 * q^73 + 8 * q^74 - 16 * q^75 + 16 * q^76 - 16 * q^77 - 16 * q^78 + 4 * q^79 - 8 * q^81 + 8 * q^82 - 4 * q^83 - 4 * q^84 - 44 * q^85 + 32 * q^86 - 4 * q^87 + 8 * q^88 + 20 * q^89 - 8 * q^92 - 4 * q^93 + 16 * q^94 - 8 * q^95 + 4 * q^96 + 4 * q^97 + 4 * q^98

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