LMFDB - Embedded newform 5054.2.a.bl.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5054,2,Mod(1,5054)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5054, 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("5054.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5054 = 2 \cdot 7 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5054.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:	$40.3563931816$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 24 x^{10} + 68 x^{9} + 213 x^{8} - 555 x^{7} - 814 x^{6} + 1911 x^{5} + 1005 x^{4} + \cdots + 1 $ x^12 - 3x^11 - 24x^10 + 68x^9 + 213x^8 - 555x^7 - 814x^6 + 1911x^5 + 1005x^4 - 2326x^3 + 570x^2 + 105*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 266)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$-2.77114$ of defining polynomial
Character	$\chi$	$=$	5054.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.77114 q^{3} +1.00000 q^{4} +1.35329 q^{5} -2.77114 q^{6} +1.00000 q^{7} -1.00000 q^{8} +4.67919 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.77114 q^{3} +1.00000 q^{4} +1.35329 q^{5} -2.77114 q^{6} +1.00000 q^{7} -1.00000 q^{8} +4.67919 q^{9} -1.35329 q^{10} +0.777571 q^{11} +2.77114 q^{12} +4.89563 q^{13} -1.00000 q^{14} +3.75015 q^{15} +1.00000 q^{16} +2.66043 q^{17} -4.67919 q^{18} +1.35329 q^{20} +2.77114 q^{21} -0.777571 q^{22} +4.50585 q^{23} -2.77114 q^{24} -3.16860 q^{25} -4.89563 q^{26} +4.65327 q^{27} +1.00000 q^{28} -0.997230 q^{29} -3.75015 q^{30} +7.02486 q^{31} -1.00000 q^{32} +2.15476 q^{33} -2.66043 q^{34} +1.35329 q^{35} +4.67919 q^{36} -5.59129 q^{37} +13.5664 q^{39} -1.35329 q^{40} -10.7721 q^{41} -2.77114 q^{42} +11.0411 q^{43} +0.777571 q^{44} +6.33231 q^{45} -4.50585 q^{46} -3.93075 q^{47} +2.77114 q^{48} +1.00000 q^{49} +3.16860 q^{50} +7.37240 q^{51} +4.89563 q^{52} +7.53218 q^{53} -4.65327 q^{54} +1.05228 q^{55} -1.00000 q^{56} +0.997230 q^{58} -3.36961 q^{59} +3.75015 q^{60} -3.75523 q^{61} -7.02486 q^{62} +4.67919 q^{63} +1.00000 q^{64} +6.62521 q^{65} -2.15476 q^{66} +1.09883 q^{67} +2.66043 q^{68} +12.4863 q^{69} -1.35329 q^{70} -8.04901 q^{71} -4.67919 q^{72} -14.4128 q^{73} +5.59129 q^{74} -8.78062 q^{75} +0.777571 q^{77} -13.5664 q^{78} -2.44722 q^{79} +1.35329 q^{80} -1.14274 q^{81} +10.7721 q^{82} +13.9733 q^{83} +2.77114 q^{84} +3.60033 q^{85} -11.0411 q^{86} -2.76346 q^{87} -0.777571 q^{88} -14.7170 q^{89} -6.33231 q^{90} +4.89563 q^{91} +4.50585 q^{92} +19.4668 q^{93} +3.93075 q^{94} -2.77114 q^{96} +2.32027 q^{97} -1.00000 q^{98} +3.63841 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} - 3 q^{3} + 12 q^{4} + 3 q^{5} + 3 q^{6} + 12 q^{7} - 12 q^{8} + 21 q^{9}+O(q^{10}) $ 12 * q - 12 * q^2 - 3 * q^3 + 12 * q^4 + 3 * q^5 + 3 * q^6 + 12 * q^7 - 12 * q^8 + 21 * q^9	\( 12 q - 12 q^{2} - 3 q^{3} + 12 q^{4} + 3 q^{5} + 3 q^{6} + 12 q^{7} - 12 q^{8} + 21 q^{9} - 3 q^{10} + 3 q^{11} - 3 q^{12} + 6 q^{13} - 12 q^{14} + 6 q^{15} + 12 q^{16} + 3 q^{17} - 21 q^{18} + 3 q^{20} - 3 q^{21} - 3 q^{22} + 12 q^{23} + 3 q^{24} + 33 q^{25} - 6 q^{26} - 21 q^{27} + 12 q^{28} - 6 q^{29} - 6 q^{30} - 3 q^{31} - 12 q^{32} + 6 q^{33} - 3 q^{34} + 3 q^{35} + 21 q^{36} - 27 q^{37} + 27 q^{39} - 3 q^{40} + 27 q^{41} + 3 q^{42} + 30 q^{43} + 3 q^{44} + 30 q^{45} - 12 q^{46} + 21 q^{47} - 3 q^{48} + 12 q^{49} - 33 q^{50} - 3 q^{51} + 6 q^{52} - 6 q^{53} + 21 q^{54} + 48 q^{55} - 12 q^{56} + 6 q^{58} + 27 q^{59} + 6 q^{60} + 18 q^{61} + 3 q^{62} + 21 q^{63} + 12 q^{64} + 9 q^{65} - 6 q^{66} - 9 q^{67} + 3 q^{68} - 18 q^{69} - 3 q^{70} - 27 q^{71} - 21 q^{72} - 9 q^{73} + 27 q^{74} - 33 q^{75} + 3 q^{77} - 27 q^{78} + 12 q^{79} + 3 q^{80} + 24 q^{81} - 27 q^{82} + 9 q^{83} - 3 q^{84} + 78 q^{85} - 30 q^{86} - 45 q^{87} - 3 q^{88} + 24 q^{89} - 30 q^{90} + 6 q^{91} + 12 q^{92} + 3 q^{93} - 21 q^{94} + 3 q^{96} + 18 q^{97} - 12 q^{98} + 48 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 - 3 * q^3 + 12 * q^4 + 3 * q^5 + 3 * q^6 + 12 * q^7 - 12 * q^8 + 21 * q^9 - 3 * q^10 + 3 * q^11 - 3 * q^12 + 6 * q^13 - 12 * q^14 + 6 * q^15 + 12 * q^16 + 3 * q^17 - 21 * q^18 + 3 * q^20 - 3 * q^21 - 3 * q^22 + 12 * q^23 + 3 * q^24 + 33 * q^25 - 6 * q^26 - 21 * q^27 + 12 * q^28 - 6 * q^29 - 6 * q^30 - 3 * q^31 - 12 * q^32 + 6 * q^33 - 3 * q^34 + 3 * q^35 + 21 * q^36 - 27 * q^37 + 27 * q^39 - 3 * q^40 + 27 * q^41 + 3 * q^42 + 30 * q^43 + 3 * q^44 + 30 * q^45 - 12 * q^46 + 21 * q^47 - 3 * q^48 + 12 * q^49 - 33 * q^50 - 3 * q^51 + 6 * q^52 - 6 * q^53 + 21 * q^54 + 48 * q^55 - 12 * q^56 + 6 * q^58 + 27 * q^59 + 6 * q^60 + 18 * q^61 + 3 * q^62 + 21 * q^63 + 12 * q^64 + 9 * q^65 - 6 * q^66 - 9 * q^67 + 3 * q^68 - 18 * q^69 - 3 * q^70 - 27 * q^71 - 21 * q^72 - 9 * q^73 + 27 * q^74 - 33 * q^75 + 3 * q^77 - 27 * q^78 + 12 * q^79 + 3 * q^80 + 24 * q^81 - 27 * q^82 + 9 * q^83 - 3 * q^84 + 78 * q^85 - 30 * q^86 - 45 * q^87 - 3 * q^88 + 24 * q^89 - 30 * q^90 + 6 * q^91 + 12 * q^92 + 3 * q^93 - 21 * q^94 + 3 * q^96 + 18 * q^97 - 12 * q^98 + 48 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	2.77114	1.59992	0.799958	−	0.600056i	$-0.204855\pi$
$3$	2.77114	1.59992	0.799958	+	0.600056i	$0.204855\pi$
$4$	1.00000	0.500000
$5$	1.35329	0.605211	0.302605	−	0.953116i	$-0.402144\pi$
$5$	1.35329	0.605211	0.302605	+	0.953116i	$0.402144\pi$
$6$	−2.77114	−1.13131
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	4.67919	1.55973
$10$	−1.35329	−0.427948
$11$	0.777571	0.234447	0.117223	−	0.993106i	$-0.462601\pi$
$11$	0.777571	0.234447	0.117223	+	0.993106i	$0.462601\pi$
$12$	2.77114	0.799958
$13$	4.89563	1.35780	0.678901	−	0.734229i	$-0.262456\pi$
$13$	4.89563	1.35780	0.678901	+	0.734229i	$0.262456\pi$
$14$	−1.00000	−0.267261
$15$	3.75015	0.968286
$16$	1.00000	0.250000
$17$	2.66043	0.645248	0.322624	−	0.946527i	$-0.395435\pi$
$17$	2.66043	0.645248	0.322624	+	0.946527i	$0.395435\pi$
$18$	−4.67919	−1.10290
$19$	0	0
$19$	0	0
$20$	1.35329	0.302605
$21$	2.77114	0.604711
$22$	−0.777571	−0.165779
$23$	4.50585	0.939534	0.469767	−	0.882791i	$-0.344338\pi$
$23$	4.50585	0.939534	0.469767	+	0.882791i	$0.344338\pi$
$24$	−2.77114	−0.565656
$25$	−3.16860	−0.633720
$26$	−4.89563	−0.960112
$27$	4.65327	0.895522
$28$	1.00000	0.188982
$29$	−0.997230	−0.185181	−0.0925904	−	0.995704i	$-0.529515\pi$
$29$	−0.997230	−0.185181	−0.0925904	+	0.995704i	$0.529515\pi$
$30$	−3.75015	−0.684681
$31$	7.02486	1.26170	0.630851	−	0.775904i	$-0.282706\pi$
$31$	7.02486	1.26170	0.630851	+	0.775904i	$0.282706\pi$
$32$	−1.00000	−0.176777
$33$	2.15476	0.375095
$34$	−2.66043	−0.456259
$35$	1.35329	0.228748
$36$	4.67919	0.779865
$37$	−5.59129	−0.919203	−0.459601	−	0.888125i	$-0.652008\pi$
$37$	−5.59129	−0.919203	−0.459601	+	0.888125i	$0.652008\pi$
$38$	0	0
$39$	13.5664	2.17237
$40$	−1.35329	−0.213974
$41$	−10.7721	−1.68232	−0.841160	−	0.540786i	$-0.818127\pi$
$41$	−10.7721	−1.68232	−0.841160	+	0.540786i	$0.818127\pi$
$42$	−2.77114	−0.427595
$43$	11.0411	1.68375	0.841875	−	0.539673i	$-0.181452\pi$
$43$	11.0411	1.68375	0.841875	+	0.539673i	$0.181452\pi$
$44$	0.777571	0.117223
$45$	6.33231	0.943965
$46$	−4.50585	−0.664351
$47$	−3.93075	−0.573358	−0.286679	−	0.958027i	$-0.592551\pi$
$47$	−3.93075	−0.573358	−0.286679	+	0.958027i	$0.592551\pi$
$48$	2.77114	0.399979
$49$	1.00000	0.142857
$50$	3.16860	0.448108
$51$	7.37240	1.03234
$52$	4.89563	0.678901
$53$	7.53218	1.03462	0.517312	−	0.855797i	$-0.326933\pi$
$53$	7.53218	1.03462	0.517312	+	0.855797i	$0.326933\pi$
$54$	−4.65327	−0.633229
$55$	1.05228	0.141890
$56$	−1.00000	−0.133631
$57$	0	0
$58$	0.997230	0.130943
$59$	−3.36961	−0.438686	−0.219343	−	0.975648i	$-0.570391\pi$
$59$	−3.36961	−0.438686	−0.219343	+	0.975648i	$0.570391\pi$
$60$	3.75015	0.484143
$61$	−3.75523	−0.480807	−0.240404	−	0.970673i	$-0.577280\pi$
$61$	−3.75523	−0.480807	−0.240404	+	0.970673i	$0.577280\pi$
$62$	−7.02486	−0.892159
$63$	4.67919	0.589523
$64$	1.00000	0.125000
$65$	6.62521	0.821757
$66$	−2.15476	−0.265232
$67$	1.09883	0.134244	0.0671218	−	0.997745i	$-0.478618\pi$
$67$	1.09883	0.134244	0.0671218	+	0.997745i	$0.478618\pi$
$68$	2.66043	0.322624
$69$	12.4863	1.50317
$70$	−1.35329	−0.161749
$71$	−8.04901	−0.955241	−0.477621	−	0.878566i	$-0.658501\pi$
$71$	−8.04901	−0.955241	−0.477621	+	0.878566i	$0.658501\pi$
$72$	−4.67919	−0.551448
$73$	−14.4128	−1.68689	−0.843444	−	0.537217i	$-0.819476\pi$
$73$	−14.4128	−1.68689	−0.843444	+	0.537217i	$0.819476\pi$
$74$	5.59129	0.649974
$75$	−8.78062	−1.01390
$76$	0	0
$77$	0.777571	0.0886125
$78$	−13.5664	−1.53610
$79$	−2.44722	−0.275333	−0.137667	−	0.990479i	$-0.543960\pi$
$79$	−2.44722	−0.275333	−0.137667	+	0.990479i	$0.543960\pi$
$80$	1.35329	0.151303
$81$	−1.14274	−0.126971
$82$	10.7721	1.18958
$83$	13.9733	1.53376	0.766882	−	0.641788i	$-0.221807\pi$
$83$	13.9733	1.53376	0.766882	+	0.641788i	$0.221807\pi$
$84$	2.77114	0.302356
$85$	3.60033	0.390511
$86$	−11.0411	−1.19059
$87$	−2.76346	−0.296274
$88$	−0.777571	−0.0828894
$89$	−14.7170	−1.56000	−0.780000	−	0.625780i	$-0.784781\pi$
$89$	−14.7170	−1.56000	−0.780000	+	0.625780i	$0.784781\pi$
$90$	−6.33231	−0.667484
$91$	4.89563	0.513201
$92$	4.50585	0.469767
$93$	19.4668	2.01862
$94$	3.93075	0.405426
$95$	0	0
$96$	−2.77114	−0.282828
$97$	2.32027	0.235587	0.117794	−	0.993038i	$-0.462418\pi$
$97$	2.32027	0.235587	0.117794	+	0.993038i	$0.462418\pi$
$98$	−1.00000	−0.101015
$99$	3.63841	0.365674
$100$	−3.16860	−0.316860
$101$	−5.26224	−0.523612	−0.261806	−	0.965120i	$-0.584318\pi$
$101$	−5.26224	−0.523612	−0.261806	+	0.965120i	$0.584318\pi$
$102$	−7.37240	−0.729976
$103$	10.9843	1.08232	0.541158	−	0.840921i	$-0.317986\pi$
$103$	10.9843	1.08232	0.541158	+	0.840921i	$0.317986\pi$
$104$	−4.89563	−0.480056
$105$	3.75015	0.365978
$106$	−7.53218	−0.731590
$107$	4.44978	0.430176	0.215088	−	0.976595i	$-0.430996\pi$
$107$	4.44978	0.430176	0.215088	+	0.976595i	$0.430996\pi$
$108$	4.65327	0.447761
$109$	−10.4374	−0.999720	−0.499860	−	0.866106i	$-0.666615\pi$
$109$	−10.4374	−0.999720	−0.499860	+	0.866106i	$0.666615\pi$
$110$	−1.05228	−0.100331
$111$	−15.4942	−1.47065
$112$	1.00000	0.0944911
$113$	1.79945	0.169278	0.0846392	−	0.996412i	$-0.473026\pi$
$113$	1.79945	0.169278	0.0846392	+	0.996412i	$0.473026\pi$
$114$	0	0
$115$	6.09772	0.568616
$116$	−0.997230	−0.0925904
$117$	22.9076	2.11781
$118$	3.36961	0.310198
$119$	2.66043	0.243881
$120$	−3.75015	−0.342341
$121$	−10.3954	−0.945035
$122$	3.75523	0.339982
$123$	−29.8510	−2.69157
$124$	7.02486	0.630851
$125$	−11.0545	−0.988745
$126$	−4.67919	−0.416856
$127$	−9.53273	−0.845893	−0.422947	−	0.906155i	$-0.639004\pi$
$127$	−9.53273	−0.845893	−0.422947	+	0.906155i	$0.639004\pi$
$128$	−1.00000	−0.0883883
$129$	30.5963	2.69386
$130$	−6.62521	−0.581070
$131$	9.06565	0.792070	0.396035	−	0.918235i	$-0.370386\pi$
$131$	9.06565	0.792070	0.396035	+	0.918235i	$0.370386\pi$
$132$	2.15476	0.187547
$133$	0	0
$134$	−1.09883	−0.0949245
$135$	6.29723	0.541979
$136$	−2.66043	−0.228130
$137$	−14.3031	−1.22200	−0.611000	−	0.791630i	$-0.709233\pi$
$137$	−14.3031	−1.22200	−0.611000	+	0.791630i	$0.709233\pi$
$138$	−12.4863	−1.06291
$139$	3.65688	0.310172	0.155086	−	0.987901i	$-0.450434\pi$
$139$	3.65688	0.310172	0.155086	+	0.987901i	$0.450434\pi$
$140$	1.35329	0.114374
$141$	−10.8926	−0.917325
$142$	8.04901	0.675458
$143$	3.80670	0.318332
$144$	4.67919	0.389933
$145$	−1.34954	−0.112073
$146$	14.4128	1.19281
$147$	2.77114	0.228559
$148$	−5.59129	−0.459601
$149$	18.9562	1.55295	0.776477	−	0.630145i	$-0.217005\pi$
$149$	18.9562	1.55295	0.776477	+	0.630145i	$0.217005\pi$
$150$	8.78062	0.716935
$151$	−2.55886	−0.208237	−0.104119	−	0.994565i	$-0.533202\pi$
$151$	−2.55886	−0.208237	−0.104119	+	0.994565i	$0.533202\pi$
$152$	0	0
$153$	12.4486	1.00641
$154$	−0.777571	−0.0626585
$155$	9.50669	0.763596
$156$	13.5664	1.08619
$157$	15.4626	1.23405	0.617027	−	0.786942i	$-0.288337\pi$
$157$	15.4626	1.23405	0.617027	+	0.786942i	$0.288337\pi$
$158$	2.44722	0.194690
$159$	20.8727	1.65531
$160$	−1.35329	−0.106987
$161$	4.50585	0.355110
$162$	1.14274	0.0897823
$163$	21.1462	1.65630	0.828149	−	0.560508i	$-0.189394\pi$
$163$	21.1462	1.65630	0.828149	+	0.560508i	$0.189394\pi$
$164$	−10.7721	−0.841160
$165$	2.91601	0.227011
$166$	−13.9733	−1.08453
$167$	−19.0996	−1.47797	−0.738986	−	0.673720i	$-0.764695\pi$
$167$	−19.0996	−1.47797	−0.738986	+	0.673720i	$0.764695\pi$
$168$	−2.77114	−0.213798
$169$	10.9672	0.843629
$170$	−3.60033	−0.276133
$171$	0	0
$172$	11.0411	0.841875
$173$	1.53344	0.116585	0.0582927	−	0.998300i	$-0.481434\pi$
$173$	1.53344	0.116585	0.0582927	+	0.998300i	$0.481434\pi$
$174$	2.76346	0.209497
$175$	−3.16860	−0.239524
$176$	0.777571	0.0586117
$177$	−9.33765	−0.701861
$178$	14.7170	1.10309
$179$	−25.2144	−1.88461	−0.942307	−	0.334749i	$-0.891349\pi$
$179$	−25.2144	−1.88461	−0.942307	+	0.334749i	$0.891349\pi$
$180$	6.33231	0.471983
$181$	21.6479	1.60907	0.804537	−	0.593902i	$-0.202413\pi$
$181$	21.6479	1.60907	0.804537	+	0.593902i	$0.202413\pi$
$182$	−4.89563	−0.362888
$183$	−10.4062	−0.769251
$184$	−4.50585	−0.332175
$185$	−7.56665	−0.556311
$186$	−19.4668	−1.42738
$187$	2.06867	0.151276
$188$	−3.93075	−0.286679
$189$	4.65327	0.338475
$190$	0	0
$191$	6.26341	0.453204	0.226602	−	0.973987i	$-0.427238\pi$
$191$	6.26341	0.453204	0.226602	+	0.973987i	$0.427238\pi$
$192$	2.77114	0.199989
$193$	13.9007	1.00060	0.500298	−	0.865854i	$-0.333224\pi$
$193$	13.9007	1.00060	0.500298	+	0.865854i	$0.333224\pi$
$194$	−2.32027	−0.166585
$195$	18.3594	1.31474
$196$	1.00000	0.0714286
$197$	4.38830	0.312653	0.156327	−	0.987705i	$-0.450035\pi$
$197$	4.38830	0.312653	0.156327	+	0.987705i	$0.450035\pi$
$198$	−3.63841	−0.258570
$199$	−21.1608	−1.50005	−0.750025	−	0.661409i	$-0.769959\pi$
$199$	−21.1608	−1.50005	−0.750025	+	0.661409i	$0.769959\pi$
$200$	3.16860	0.224054
$201$	3.04501	0.214778
$202$	5.26224	0.370250
$203$	−0.997230	−0.0699918
$204$	7.37240	0.516171
$205$	−14.5778	−1.01816
$206$	−10.9843	−0.765313
$207$	21.0837	1.46542
$208$	4.89563	0.339451
$209$	0	0
$210$	−3.75015	−0.258785
$211$	−5.11585	−0.352190	−0.176095	−	0.984373i	$-0.556347\pi$
$211$	−5.11585	−0.352190	−0.176095	+	0.984373i	$0.556347\pi$
$212$	7.53218	0.517312
$213$	−22.3049	−1.52831
$214$	−4.44978	−0.304180
$215$	14.9418	1.01902
$216$	−4.65327	−0.316615
$217$	7.02486	0.476879
$218$	10.4374	0.706909
$219$	−39.9398	−2.69888
$220$	1.05228	0.0709448
$221$	13.0245	0.876120
$222$	15.4942	1.03990
$223$	−9.49819	−0.636046	−0.318023	−	0.948083i	$-0.603019\pi$
$223$	−9.49819	−0.636046	−0.318023	+	0.948083i	$0.603019\pi$
$224$	−1.00000	−0.0668153
$225$	−14.8265	−0.988433
$226$	−1.79945	−0.119698
$227$	0.0136096	0.000903303 0	0.000451651	−	1.00000i	$-0.499856\pi$
$227$	0.0136096	0.000903303 0	0.000451651		1.00000i	$0.499856\pi$
$228$	0	0
$229$	21.0961	1.39407	0.697033	−	0.717039i	$-0.254503\pi$
$229$	21.0961	1.39407	0.697033	+	0.717039i	$0.254503\pi$
$230$	−6.09772	−0.402072
$231$	2.15476	0.141773
$232$	0.997230	0.0654713
$233$	25.7459	1.68667	0.843334	−	0.537390i	$-0.180590\pi$
$233$	25.7459	1.68667	0.843334	+	0.537390i	$0.180590\pi$
$234$	−22.9076	−1.49752
$235$	−5.31945	−0.347003
$236$	−3.36961	−0.219343
$237$	−6.78157	−0.440510
$238$	−2.66043	−0.172450
$239$	−1.70859	−0.110519	−0.0552597	−	0.998472i	$-0.517599\pi$
$239$	−1.70859	−0.110519	−0.0552597	+	0.998472i	$0.517599\pi$
$240$	3.75015	0.242071
$241$	6.93003	0.446402	0.223201	−	0.974772i	$-0.428349\pi$
$241$	6.93003	0.446402	0.223201	+	0.974772i	$0.428349\pi$
$242$	10.3954	0.668241
$243$	−17.1265	−1.09867
$244$	−3.75523	−0.240404
$245$	1.35329	0.0864586
$246$	29.8510	1.90323
$247$	0	0
$248$	−7.02486	−0.446079
$249$	38.7218	2.45389
$250$	11.0545	0.699148
$251$	25.9231	1.63625	0.818126	−	0.575040i	$-0.195013\pi$
$251$	25.9231	1.63625	0.818126	+	0.575040i	$0.195013\pi$
$252$	4.67919	0.294761
$253$	3.50362	0.220270
$254$	9.53273	0.598137
$255$	9.97701	0.624785
$256$	1.00000	0.0625000
$257$	−26.1704	−1.63246	−0.816231	−	0.577725i	$-0.803940\pi$
$257$	−26.1704	−1.63246	−0.816231	+	0.577725i	$0.803940\pi$
$258$	−30.5963	−1.90484
$259$	−5.59129	−0.347426
$260$	6.62521	0.410878
$261$	−4.66623	−0.288832
$262$	−9.06565	−0.560078
$263$	16.4992	1.01738	0.508692	−	0.860949i	$-0.330129\pi$
$263$	16.4992	1.01738	0.508692	+	0.860949i	$0.330129\pi$
$264$	−2.15476	−0.132616
$265$	10.1932	0.626165
$266$	0	0
$267$	−40.7828	−2.49587
$268$	1.09883	0.0671218
$269$	−15.9629	−0.973275	−0.486637	−	0.873604i	$-0.661777\pi$
$269$	−15.9629	−0.973275	−0.486637	+	0.873604i	$0.661777\pi$
$270$	−6.29723	−0.383237
$271$	−17.8296	−1.08307	−0.541536	−	0.840678i	$-0.682157\pi$
$271$	−17.8296	−1.08307	−0.541536	+	0.840678i	$0.682157\pi$
$272$	2.66043	0.161312
$273$	13.5664	0.821079
$274$	14.3031	0.864085
$275$	−2.46381	−0.148574
$276$	12.4863	0.751587
$277$	24.8573	1.49353	0.746766	−	0.665087i	$-0.231605\pi$
$277$	24.8573	1.49353	0.746766	+	0.665087i	$0.231605\pi$
$278$	−3.65688	−0.219325
$279$	32.8707	1.96792
$280$	−1.35329	−0.0808747
$281$	−12.0488	−0.718772	−0.359386	−	0.933189i	$-0.617014\pi$
$281$	−12.0488	−0.718772	−0.359386	+	0.933189i	$0.617014\pi$
$282$	10.8926	0.648647
$283$	−25.9628	−1.54333	−0.771663	−	0.636031i	$-0.780575\pi$
$283$	−25.9628	−1.54333	−0.771663	+	0.636031i	$0.780575\pi$
$284$	−8.04901	−0.477621
$285$	0	0
$286$	−3.80670	−0.225095
$287$	−10.7721	−0.635857
$288$	−4.67919	−0.275724
$289$	−9.92214	−0.583655
$290$	1.34954	0.0792479
$291$	6.42977	0.376920
$292$	−14.4128	−0.843444
$293$	−6.69334	−0.391029	−0.195515	−	0.980701i	$-0.562638\pi$
$293$	−6.69334	−0.391029	−0.195515	+	0.980701i	$0.562638\pi$
$294$	−2.77114	−0.161616
$295$	−4.56007	−0.265497
$296$	5.59129	0.324987
$297$	3.61825	0.209952
$298$	−18.9562	−1.09810
$299$	22.0589	1.27570
$300$	−8.78062	−0.506950
$301$	11.0411	0.636397
$302$	2.55886	0.147246
$303$	−14.5824	−0.837736
$304$	0	0
$305$	−5.08192	−0.290990
$306$	−12.4486	−0.711641
$307$	3.94665	0.225247	0.112624	−	0.993638i	$-0.464075\pi$
$307$	3.94665	0.225247	0.112624	+	0.993638i	$0.464075\pi$
$308$	0.777571	0.0443062
$309$	30.4390	1.73162
$310$	−9.50669	−0.539944
$311$	14.8167	0.840177	0.420089	−	0.907483i	$-0.361999\pi$
$311$	14.8167	0.840177	0.420089	+	0.907483i	$0.361999\pi$
$312$	−13.5664	−0.768049
$313$	−17.7509	−1.00334	−0.501670	−	0.865059i	$-0.667281\pi$
$313$	−17.7509	−1.00334	−0.501670	+	0.865059i	$0.667281\pi$
$314$	−15.4626	−0.872608
$315$	6.33231	0.356785
$316$	−2.44722	−0.137667
$317$	2.83911	0.159460	0.0797301	−	0.996816i	$-0.474594\pi$
$317$	2.83911	0.159460	0.0797301	+	0.996816i	$0.474594\pi$
$318$	−20.8727	−1.17048
$319$	−0.775417	−0.0434150
$320$	1.35329	0.0756513
$321$	12.3309	0.688246
$322$	−4.50585	−0.251101
$323$	0	0
$324$	−1.14274	−0.0634857
$325$	−15.5123	−0.860467
$326$	−21.1462	−1.17118
$327$	−28.9234	−1.59947
$328$	10.7721	0.594790
$329$	−3.93075	−0.216709
$330$	−2.91601	−0.160521
$331$	−2.76023	−0.151716	−0.0758581	−	0.997119i	$-0.524170\pi$
$331$	−2.76023	−0.151716	−0.0758581	+	0.997119i	$0.524170\pi$
$332$	13.9733	0.766882
$333$	−26.1627	−1.43371
$334$	19.0996	1.04508
$335$	1.48704	0.0812456
$336$	2.77114	0.151178
$337$	24.6577	1.34319	0.671595	−	0.740918i	$-0.265609\pi$
$337$	24.6577	1.34319	0.671595	+	0.740918i	$0.265609\pi$
$338$	−10.9672	−0.596536
$339$	4.98653	0.270831
$340$	3.60033	0.195255
$341$	5.46233	0.295802
$342$	0	0
$343$	1.00000	0.0539949
$344$	−11.0411	−0.595295
$345$	16.8976	0.909737
$346$	−1.53344	−0.0824384
$347$	−28.8696	−1.54980	−0.774901	−	0.632082i	$-0.782200\pi$
$347$	−28.8696	−1.54980	−0.774901	+	0.632082i	$0.782200\pi$
$348$	−2.76346	−0.148137
$349$	36.6608	1.96241	0.981204	−	0.192972i	$-0.0618125\pi$
$349$	36.6608	1.96241	0.981204	+	0.192972i	$0.0618125\pi$
$350$	3.16860	0.169369
$351$	22.7807	1.21594
$352$	−0.777571	−0.0414447
$353$	12.3935	0.659639	0.329820	−	0.944044i	$-0.393012\pi$
$353$	12.3935	0.659639	0.329820	+	0.944044i	$0.393012\pi$
$354$	9.33765	0.496290
$355$	−10.8927	−0.578122
$356$	−14.7170	−0.780000
$357$	7.37240	0.390189
$358$	25.2144	1.33262
$359$	−17.9682	−0.948326	−0.474163	−	0.880437i	$-0.657249\pi$
$359$	−17.9682	−0.948326	−0.474163	+	0.880437i	$0.657249\pi$
$360$	−6.33231	−0.333742
$361$	0	0
$362$	−21.6479	−1.13779
$363$	−28.8070	−1.51198
$364$	4.89563	0.256601
$365$	−19.5047	−1.02092
$366$	10.4062	0.543943
$367$	20.7229	1.08173	0.540864	−	0.841110i	$-0.318097\pi$
$367$	20.7229	1.08173	0.540864	+	0.841110i	$0.318097\pi$
$368$	4.50585	0.234883
$369$	−50.4047	−2.62397
$370$	7.56665	0.393371
$371$	7.53218	0.391051
$372$	19.4668	1.00931
$373$	−0.769222	−0.0398288	−0.0199144	−	0.999802i	$-0.506339\pi$
$373$	−0.769222	−0.0398288	−0.0199144	+	0.999802i	$0.506339\pi$
$374$	−2.06867	−0.106968
$375$	−30.6335	−1.58191
$376$	3.93075	0.202713
$377$	−4.88207	−0.251439
$378$	−4.65327	−0.239338
$379$	−25.0167	−1.28502	−0.642512	−	0.766276i	$-0.722108\pi$
$379$	−25.0167	−1.28502	−0.642512	+	0.766276i	$0.722108\pi$
$380$	0	0
$381$	−26.4165	−1.35336
$382$	−6.26341	−0.320464
$383$	21.8893	1.11849	0.559246	−	0.829002i	$-0.311091\pi$
$383$	21.8893	1.11849	0.559246	+	0.829002i	$0.311091\pi$
$384$	−2.77114	−0.141414
$385$	1.05228	0.0536292
$386$	−13.9007	−0.707528
$387$	51.6633	2.62620
$388$	2.32027	0.117794
$389$	−36.1139	−1.83105	−0.915525	−	0.402262i	$-0.868224\pi$
$389$	−36.1139	−1.83105	−0.915525	+	0.402262i	$0.868224\pi$
$390$	−18.3594	−0.929663
$391$	11.9875	0.606232
$392$	−1.00000	−0.0505076
$393$	25.1222	1.26725
$394$	−4.38830	−0.221079
$395$	−3.31180	−0.166635
$396$	3.63841	0.182837
$397$	−13.6226	−0.683698	−0.341849	−	0.939755i	$-0.611053\pi$
$397$	−13.6226	−0.683698	−0.341849	+	0.939755i	$0.611053\pi$
$398$	21.1608	1.06070
$399$	0	0
$400$	−3.16860	−0.158430
$401$	−28.4546	−1.42096	−0.710478	−	0.703719i	$-0.751521\pi$
$401$	−28.4546	−1.42096	−0.710478	+	0.703719i	$0.751521\pi$
$402$	−3.04501	−0.151871
$403$	34.3911	1.71314
$404$	−5.26224	−0.261806
$405$	−1.54646	−0.0768444
$406$	0.997230	0.0494917
$407$	−4.34763	−0.215504
$408$	−7.37240	−0.364988
$409$	6.17138	0.305155	0.152578	−	0.988291i	$-0.451243\pi$
$409$	6.17138	0.305155	0.152578	+	0.988291i	$0.451243\pi$
$410$	14.5778	0.719946
$411$	−39.6360	−1.95510
$412$	10.9843	0.541158
$413$	−3.36961	−0.165808
$414$	−21.0837	−1.03621
$415$	18.9099	0.928250
$416$	−4.89563	−0.240028
$417$	10.1337	0.496250
$418$	0	0
$419$	3.97201	0.194045	0.0970227	−	0.995282i	$-0.469068\pi$
$419$	3.97201	0.194045	0.0970227	+	0.995282i	$0.469068\pi$
$420$	3.75015	0.182989
$421$	2.21450	0.107928	0.0539640	−	0.998543i	$-0.482814\pi$
$421$	2.21450	0.107928	0.0539640	+	0.998543i	$0.482814\pi$
$422$	5.11585	0.249036
$423$	−18.3927	−0.894285
$424$	−7.53218	−0.365795
$425$	−8.42983	−0.408907
$426$	22.3049	1.08068
$427$	−3.75523	−0.181728
$428$	4.44978	0.215088
$429$	10.5489	0.509305
$430$	−14.9418	−0.720558
$431$	−35.0260	−1.68714	−0.843572	−	0.537016i	$-0.819552\pi$
$431$	−35.0260	−1.68714	−0.843572	+	0.537016i	$0.819552\pi$
$432$	4.65327	0.223880
$433$	25.2504	1.21346	0.606728	−	0.794909i	$-0.292482\pi$
$433$	25.2504	1.21346	0.606728	+	0.794909i	$0.292482\pi$
$434$	−7.02486	−0.337204
$435$	−3.73977	−0.179308
$436$	−10.4374	−0.499860
$437$	0	0
$438$	39.9398	1.90840
$439$	−32.0708	−1.53066	−0.765329	−	0.643639i	$-0.777424\pi$
$439$	−32.0708	−1.53066	−0.765329	+	0.643639i	$0.777424\pi$
$440$	−1.05228	−0.0501655
$441$	4.67919	0.222819
$442$	−13.0245	−0.619510
$443$	20.5097	0.974444	0.487222	−	0.873278i	$-0.338010\pi$
$443$	20.5097	0.974444	0.487222	+	0.873278i	$0.338010\pi$
$444$	−15.4942	−0.735323
$445$	−19.9164	−0.944128
$446$	9.49819	0.449752
$447$	52.5303	2.48460
$448$	1.00000	0.0472456
$449$	14.1242	0.666563	0.333282	−	0.942827i	$-0.391844\pi$
$449$	14.1242	0.666563	0.333282	+	0.942827i	$0.391844\pi$
$450$	14.8265	0.698928
$451$	−8.37608	−0.394414
$452$	1.79945	0.0846392
$453$	−7.09095	−0.333162
$454$	−0.0136096	−0.000638732 0
$455$	6.62521	0.310595
$456$	0	0
$457$	−23.6803	−1.10772	−0.553859	−	0.832610i	$-0.686845\pi$
$457$	−23.6803	−1.10772	−0.553859	+	0.832610i	$0.686845\pi$
$458$	−21.0961	−0.985754
$459$	12.3797	0.577834
$460$	6.09772	0.284308
$461$	16.3005	0.759188	0.379594	−	0.925153i	$-0.376064\pi$
$461$	16.3005	0.759188	0.379594	+	0.925153i	$0.376064\pi$
$462$	−2.15476	−0.100248
$463$	25.4188	1.18131	0.590655	−	0.806924i	$-0.298869\pi$
$463$	25.4188	1.18131	0.590655	+	0.806924i	$0.298869\pi$
$464$	−0.997230	−0.0462952
$465$	26.3443	1.22169
$466$	−25.7459	−1.19265
$467$	−25.3370	−1.17246	−0.586229	−	0.810146i	$-0.699388\pi$
$467$	−25.3370	−1.17246	−0.586229	+	0.810146i	$0.699388\pi$
$468$	22.9076	1.05890
$469$	1.09883	0.0507393
$470$	5.31945	0.245368
$471$	42.8491	1.97438
$472$	3.36961	0.155099
$473$	8.58523	0.394749
$474$	6.78157	0.311488
$475$	0	0
$476$	2.66043	0.121940
$477$	35.2445	1.61374
$478$	1.70859	0.0781491
$479$	−28.2100	−1.28895	−0.644474	−	0.764626i	$-0.722924\pi$
$479$	−28.2100	−1.28895	−0.644474	+	0.764626i	$0.722924\pi$
$480$	−3.75015	−0.171170
$481$	−27.3729	−1.24810
$482$	−6.93003	−0.315654
$483$	12.4863	0.568147
$484$	−10.3954	−0.472517
$485$	3.14000	0.142580
$486$	17.1265	0.776873
$487$	−28.1520	−1.27569	−0.637845	−	0.770164i	$-0.720174\pi$
$487$	−28.1520	−1.27569	−0.637845	+	0.770164i	$0.720174\pi$
$488$	3.75523	0.169991
$489$	58.5990	2.64994
$490$	−1.35329	−0.0611355
$491$	−19.1536	−0.864392	−0.432196	−	0.901780i	$-0.642261\pi$
$491$	−19.1536	−0.864392	−0.432196	+	0.901780i	$0.642261\pi$
$492$	−29.8510	−1.34579
$493$	−2.65306	−0.119488
$494$	0	0
$495$	4.92382	0.221309
$496$	7.02486	0.315426
$497$	−8.04901	−0.361047
$498$	−38.7218	−1.73516
$499$	7.01992	0.314255	0.157127	−	0.987578i	$-0.449777\pi$
$499$	7.01992	0.314255	0.157127	+	0.987578i	$0.449777\pi$
$500$	−11.0545	−0.494372
$501$	−52.9276	−2.36463
$502$	−25.9231	−1.15700
$503$	8.77808	0.391395	0.195698	−	0.980664i	$-0.437303\pi$
$503$	8.77808	0.391395	0.195698	+	0.980664i	$0.437303\pi$
$504$	−4.67919	−0.208428
$505$	−7.12134	−0.316896
$506$	−3.50362	−0.155755
$507$	30.3915	1.34974
$508$	−9.53273	−0.422947
$509$	−31.3906	−1.39137	−0.695683	−	0.718349i	$-0.744898\pi$
$509$	−31.3906	−1.39137	−0.695683	+	0.718349i	$0.744898\pi$
$510$	−9.97701	−0.441789
$511$	−14.4128	−0.637584
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	26.1704	1.15433
$515$	14.8650	0.655029
$516$	30.5963	1.34693
$517$	−3.05644	−0.134422
$518$	5.59129	0.245667
$519$	4.24938	0.186527
$520$	−6.62521	−0.290535
$521$	26.7461	1.17177	0.585884	−	0.810395i	$-0.300747\pi$
$521$	26.7461	1.17177	0.585884	+	0.810395i	$0.300747\pi$
$522$	4.66623	0.204235
$523$	10.4679	0.457729	0.228865	−	0.973458i	$-0.426499\pi$
$523$	10.4679	0.457729	0.228865	+	0.973458i	$0.426499\pi$
$524$	9.06565	0.396035
$525$	−8.78062	−0.383218
$526$	−16.4992	−0.719399
$527$	18.6891	0.814111
$528$	2.15476	0.0937737
$529$	−2.69736	−0.117277
$530$	−10.1932	−0.442766
$531$	−15.7671	−0.684232
$532$	0	0
$533$	−52.7362	−2.28426
$534$	40.7828	1.76484
$535$	6.02185	0.260347
$536$	−1.09883	−0.0474622
$537$	−69.8726	−3.01523
$538$	15.9629	0.688209
$539$	0.777571	0.0334924
$540$	6.29723	0.270990
$541$	1.22831	0.0528094	0.0264047	−	0.999651i	$-0.491594\pi$
$541$	1.22831	0.0528094	0.0264047	+	0.999651i	$0.491594\pi$
$542$	17.8296	0.765848
$543$	59.9892	2.57438
$544$	−2.66043	−0.114065
$545$	−14.1248	−0.605041
$546$	−13.5664	−0.580590
$547$	8.42041	0.360031	0.180015	−	0.983664i	$-0.442385\pi$
$547$	8.42041	0.360031	0.180015	+	0.983664i	$0.442385\pi$
$548$	−14.3031	−0.611000
$549$	−17.5714	−0.749930
$550$	2.46381	0.105057
$551$	0	0
$552$	−12.4863	−0.531453
$553$	−2.44722	−0.104066
$554$	−24.8573	−1.05609
$555$	−20.9682	−0.890051
$556$	3.65688	0.155086
$557$	31.3157	1.32689	0.663445	−	0.748225i	$-0.269094\pi$
$557$	31.3157	1.32689	0.663445	+	0.748225i	$0.269094\pi$
$558$	−32.8707	−1.39153
$559$	54.0530	2.28620
$560$	1.35329	0.0571870
$561$	5.73257	0.242029
$562$	12.0488	0.508248
$563$	32.7400	1.37983	0.689913	−	0.723892i	$-0.257649\pi$
$563$	32.7400	1.37983	0.689913	+	0.723892i	$0.257649\pi$
$564$	−10.8926	−0.458663
$565$	2.43519	0.102449
$566$	25.9628	1.09130
$567$	−1.14274	−0.0479907
$568$	8.04901	0.337729
$569$	24.5608	1.02964	0.514821	−	0.857297i	$-0.327858\pi$
$569$	24.5608	1.02964	0.514821	+	0.857297i	$0.327858\pi$
$570$	0	0
$571$	25.8657	1.08244	0.541222	−	0.840880i	$-0.317962\pi$
$571$	25.8657	1.08244	0.541222	+	0.840880i	$0.317962\pi$
$572$	3.80670	0.159166
$573$	17.3568	0.725089
$574$	10.7721	0.449619
$575$	−14.2772	−0.595401
$576$	4.67919	0.194966
$577$	20.2526	0.843128	0.421564	−	0.906799i	$-0.361481\pi$
$577$	20.2526	0.843128	0.421564	+	0.906799i	$0.361481\pi$
$578$	9.92214	0.412706
$579$	38.5208	1.60087
$580$	−1.34954	−0.0560367
$581$	13.9733	0.579708
$582$	−6.42977	−0.266523
$583$	5.85681	0.242564
$584$	14.4128	0.596405
$585$	31.0006	1.28172
$586$	6.69334	0.276499
$587$	16.2617	0.671194	0.335597	−	0.942006i	$-0.391062\pi$
$587$	16.2617	0.671194	0.335597	+	0.942006i	$0.391062\pi$
$588$	2.77114	0.114280
$589$	0	0
$590$	4.56007	0.187735
$591$	12.1606	0.500219
$592$	−5.59129	−0.229801
$593$	−16.6460	−0.683571	−0.341786	−	0.939778i	$-0.611032\pi$
$593$	−16.6460	−0.683571	−0.341786	+	0.939778i	$0.611032\pi$
$594$	−3.61825	−0.148458
$595$	3.60033	0.147599
$596$	18.9562	0.776477
$597$	−58.6395	−2.39995
$598$	−22.0589	−0.902057
$599$	−23.8542	−0.974656	−0.487328	−	0.873219i	$-0.662028\pi$
$599$	−23.8542	−0.974656	−0.487328	+	0.873219i	$0.662028\pi$
$600$	8.78062	0.358467
$601$	13.4655	0.549271	0.274635	−	0.961548i	$-0.411443\pi$
$601$	13.4655	0.549271	0.274635	+	0.961548i	$0.411443\pi$
$602$	−11.0411	−0.450001
$603$	5.14164	0.209384
$604$	−2.55886	−0.104119
$605$	−14.0680	−0.571945
$606$	14.5824	0.592368
$607$	−4.04138	−0.164035	−0.0820173	−	0.996631i	$-0.526136\pi$
$607$	−4.04138	−0.164035	−0.0820173	+	0.996631i	$0.526136\pi$
$608$	0	0
$609$	−2.76346	−0.111981
$610$	5.08192	0.205761
$611$	−19.2435	−0.778508
$612$	12.4486	0.503206
$613$	17.0804	0.689870	0.344935	−	0.938626i	$-0.387901\pi$
$613$	17.0804	0.689870	0.344935	+	0.938626i	$0.387901\pi$
$614$	−3.94665	−0.159274
$615$	−40.3971	−1.62897
$616$	−0.777571	−0.0313292
$617$	−28.9761	−1.16653	−0.583266	−	0.812281i	$-0.698226\pi$
$617$	−28.9761	−1.16653	−0.583266	+	0.812281i	$0.698226\pi$
$618$	−30.4390	−1.22444
$619$	−22.6036	−0.908515	−0.454258	−	0.890870i	$-0.650095\pi$
$619$	−22.6036	−0.908515	−0.454258	+	0.890870i	$0.650095\pi$
$620$	9.50669	0.381798
$621$	20.9669	0.841373
$622$	−14.8167	−0.594095
$623$	−14.7170	−0.589624
$624$	13.5664	0.543093
$625$	0.883040	0.0353216
$626$	17.7509	0.709468
$627$	0	0
$628$	15.4626	0.617027
$629$	−14.8752	−0.593114
$630$	−6.33231	−0.252285
$631$	19.1450	0.762150	0.381075	−	0.924544i	$-0.375554\pi$
$631$	19.1450	0.762150	0.381075	+	0.924544i	$0.375554\pi$
$632$	2.44722	0.0973451
$633$	−14.1767	−0.563474
$634$	−2.83911	−0.112755
$635$	−12.9006	−0.511943
$636$	20.8727	0.827656
$637$	4.89563	0.193972
$638$	0.775417	0.0306991
$639$	−37.6628	−1.48992
$640$	−1.35329	−0.0534936
$641$	4.21500	0.166483	0.0832413	−	0.996529i	$-0.473473\pi$
$641$	4.21500	0.166483	0.0832413	+	0.996529i	$0.473473\pi$
$642$	−12.3309	−0.486663
$643$	37.5432	1.48056	0.740280	−	0.672299i	$-0.234693\pi$
$643$	37.5432	1.48056	0.740280	+	0.672299i	$0.234693\pi$
$644$	4.50585	0.177555
$645$	41.4058	1.63035
$646$	0	0
$647$	−24.8823	−0.978225	−0.489112	−	0.872221i	$-0.662679\pi$
$647$	−24.8823	−0.978225	−0.489112	+	0.872221i	$0.662679\pi$
$648$	1.14274	0.0448911
$649$	−2.62011	−0.102848
$650$	15.5123	0.608442
$651$	19.4668	0.762966
$652$	21.1462	0.828149
$653$	−18.7262	−0.732815	−0.366407	−	0.930455i	$-0.619412\pi$
$653$	−18.7262	−0.732815	−0.366407	+	0.930455i	$0.619412\pi$
$654$	28.9234	1.13099
$655$	12.2685	0.479369
$656$	−10.7721	−0.420580
$657$	−67.4402	−2.63109
$658$	3.93075	0.153237
$659$	29.3137	1.14190	0.570949	−	0.820985i	$-0.306575\pi$
$659$	29.3137	1.14190	0.570949	+	0.820985i	$0.306575\pi$
$660$	2.91601	0.113506
$661$	16.1369	0.627654	0.313827	−	0.949480i	$-0.398389\pi$
$661$	16.1369	0.627654	0.313827	+	0.949480i	$0.398389\pi$
$662$	2.76023	0.107280
$663$	36.0925	1.40172
$664$	−13.9733	−0.542267
$665$	0	0
$666$	26.1627	1.01378
$667$	−4.49336	−0.173984
$668$	−19.0996	−0.738986
$669$	−26.3208	−1.01762
$670$	−1.48704	−0.0574493
$671$	−2.91996	−0.112724
$672$	−2.77114	−0.106899
$673$	19.0332	0.733677	0.366838	−	0.930285i	$-0.380440\pi$
$673$	19.0332	0.733677	0.366838	+	0.930285i	$0.380440\pi$
$674$	−24.6577	−0.949779
$675$	−14.7443	−0.567510
$676$	10.9672	0.421814
$677$	25.2624	0.970914	0.485457	−	0.874260i	$-0.338653\pi$
$677$	25.2624	0.970914	0.485457	+	0.874260i	$0.338653\pi$
$678$	−4.98653	−0.191507
$679$	2.32027	0.0890437
$680$	−3.60033	−0.138066
$681$	0.0377141	0.00144521
$682$	−5.46233	−0.209164
$683$	−9.66935	−0.369987	−0.184994	−	0.982740i	$-0.559226\pi$
$683$	−9.66935	−0.369987	−0.184994	+	0.982740i	$0.559226\pi$
$684$	0	0
$685$	−19.3563	−0.739568
$686$	−1.00000	−0.0381802
$687$	58.4600	2.23039
$688$	11.0411	0.420937
$689$	36.8747	1.40482
$690$	−16.8976	−0.643281
$691$	−19.4773	−0.740950	−0.370475	−	0.928843i	$-0.620805\pi$
$691$	−19.4773	−0.740950	−0.370475	+	0.928843i	$0.620805\pi$
$692$	1.53344	0.0582927
$693$	3.63841	0.138212
$694$	28.8696	1.09588
$695$	4.94882	0.187720
$696$	2.76346	0.104749
$697$	−28.6584	−1.08551
$698$	−36.6608	−1.38763
$699$	71.3453	2.69853
$700$	−3.16860	−0.119762
$701$	−30.7390	−1.16100	−0.580498	−	0.814262i	$-0.697142\pi$
$701$	−30.7390	−1.16100	−0.580498	+	0.814262i	$0.697142\pi$
$702$	−22.7807	−0.859801
$703$	0	0
$704$	0.777571	0.0293058
$705$	−14.7409	−0.555175
$706$	−12.3935	−0.466436
$707$	−5.26224	−0.197907
$708$	−9.33765	−0.350930
$709$	−1.80008	−0.0676036	−0.0338018	−	0.999429i	$-0.510761\pi$
$709$	−1.80008	−0.0676036	−0.0338018	+	0.999429i	$0.510761\pi$
$710$	10.8927	0.408794
$711$	−11.4510	−0.429446
$712$	14.7170	0.551543
$713$	31.6529	1.18541
$714$	−7.37240	−0.275905
$715$	5.15158	0.192658
$716$	−25.2144	−0.942307
$717$	−4.73473	−0.176822
$718$	17.9682	0.670568
$719$	−7.65913	−0.285637	−0.142819	−	0.989749i	$-0.545617\pi$
$719$	−7.65913	−0.285637	−0.142819	+	0.989749i	$0.545617\pi$
$720$	6.33231	0.235991
$721$	10.9843	0.409077
$722$	0	0
$723$	19.2040	0.714206
$724$	21.6479	0.804537
$725$	3.15982	0.117353
$726$	28.8070	1.06913
$727$	−29.7957	−1.10506	−0.552531	−	0.833492i	$-0.686338\pi$
$727$	−29.7957	−1.10506	−0.552531	+	0.833492i	$0.686338\pi$
$728$	−4.89563	−0.181444
$729$	−44.0316	−1.63080
$730$	19.5047	0.721901
$731$	29.3740	1.08644
$732$	−10.4062	−0.384626
$733$	−26.0986	−0.963975	−0.481988	−	0.876178i	$-0.660085\pi$
$733$	−26.0986	−0.963975	−0.481988	+	0.876178i	$0.660085\pi$
$734$	−20.7229	−0.764898
$735$	3.75015	0.138327
$736$	−4.50585	−0.166088
$737$	0.854419	0.0314729
$738$	50.4047	1.85542
$739$	13.9798	0.514255	0.257128	−	0.966377i	$-0.417224\pi$
$739$	13.9798	0.514255	0.257128	+	0.966377i	$0.417224\pi$
$740$	−7.56665	−0.278156
$741$	0	0
$742$	−7.53218	−0.276515
$743$	−13.7329	−0.503810	−0.251905	−	0.967752i	$-0.581057\pi$
$743$	−13.7329	−0.503810	−0.251905	+	0.967752i	$0.581057\pi$
$744$	−19.4668	−0.713689
$745$	25.6533	0.939864
$746$	0.769222	0.0281632
$747$	65.3835	2.39226
$748$	2.06867	0.0756381
$749$	4.44978	0.162591
$750$	30.6335	1.11858
$751$	34.4342	1.25652	0.628260	−	0.778003i	$-0.283767\pi$
$751$	34.4342	1.25652	0.628260	+	0.778003i	$0.283767\pi$
$752$	−3.93075	−0.143340
$753$	71.8364	2.61786
$754$	4.88207	0.177794
$755$	−3.46289	−0.126027
$756$	4.65327	0.169238
$757$	−38.1734	−1.38743	−0.693717	−	0.720247i	$-0.744028\pi$
$757$	−38.1734	−1.38743	−0.693717	+	0.720247i	$0.744028\pi$
$758$	25.0167	0.908649
$759$	9.70900	0.352414
$760$	0	0
$761$	−7.76087	−0.281331	−0.140666	−	0.990057i	$-0.544924\pi$
$761$	−7.76087	−0.281331	−0.140666	+	0.990057i	$0.544924\pi$
$762$	26.4165	0.956968
$763$	−10.4374	−0.377859
$764$	6.26341	0.226602
$765$	16.8466	0.609092
$766$	−21.8893	−0.790893
$767$	−16.4964	−0.595649
$768$	2.77114	0.0999947
$769$	24.4338	0.881106	0.440553	−	0.897727i	$-0.354782\pi$
$769$	24.4338	0.881106	0.440553	+	0.897727i	$0.354782\pi$
$770$	−1.05228	−0.0379216
$771$	−72.5216	−2.61180
$772$	13.9007	0.500298
$773$	−13.5422	−0.487078	−0.243539	−	0.969891i	$-0.578308\pi$
$773$	−13.5422	−0.487078	−0.243539	+	0.969891i	$0.578308\pi$
$774$	−51.6633	−1.85700
$775$	−22.2590	−0.799567
$776$	−2.32027	−0.0832927
$777$	−15.4942	−0.555852
$778$	36.1139	1.29475
$779$	0	0
$780$	18.3594	0.657371
$781$	−6.25868	−0.223953
$782$	−11.9875	−0.428671
$783$	−4.64038	−0.165833
$784$	1.00000	0.0357143
$785$	20.9255	0.746862
$786$	−25.1222	−0.896078
$787$	40.9894	1.46112	0.730558	−	0.682851i	$-0.239260\pi$
$787$	40.9894	1.46112	0.730558	+	0.682851i	$0.239260\pi$
$788$	4.38830	0.156327
$789$	45.7215	1.62773
$790$	3.31180	0.117829
$791$	1.79945	0.0639812
$792$	−3.63841	−0.129285
$793$	−18.3842	−0.652842
$794$	13.6226	0.483448
$795$	28.2468	1.00181
$796$	−21.1608	−0.750025
$797$	11.7912	0.417665	0.208833	−	0.977951i	$-0.433034\pi$
$797$	11.7912	0.417665	0.208833	+	0.977951i	$0.433034\pi$
$798$	0	0
$799$	−10.4575	−0.369958
$800$	3.16860	0.112027
$801$	−68.8637	−2.43318
$802$	28.4546	1.00477
$803$	−11.2070	−0.395485
$804$	3.04501	0.107389
$805$	6.09772	0.214917
$806$	−34.3911	−1.21138
$807$	−44.2353	−1.55716
$808$	5.26224	0.185125
$809$	−22.7546	−0.800008	−0.400004	−	0.916513i	$-0.630991\pi$
$809$	−22.7546	−0.800008	−0.400004	+	0.916513i	$0.630991\pi$
$810$	1.54646	0.0543372
$811$	27.6974	0.972586	0.486293	−	0.873796i	$-0.338349\pi$
$811$	27.6974	0.972586	0.486293	+	0.873796i	$0.338349\pi$
$812$	−0.997230	−0.0349959
$813$	−49.4083	−1.73282
$814$	4.34763	0.152384
$815$	28.6170	1.00241
$816$	7.37240	0.258086
$817$	0	0
$818$	−6.17138	−0.215777
$819$	22.9076	0.800456
$820$	−14.5778	−0.509079
$821$	17.8867	0.624249	0.312125	−	0.950041i	$-0.398959\pi$
$821$	17.8867	0.624249	0.312125	+	0.950041i	$0.398959\pi$
$822$	39.6360	1.38246
$823$	23.7619	0.828286	0.414143	−	0.910212i	$-0.364081\pi$
$823$	23.7619	0.828286	0.414143	+	0.910212i	$0.364081\pi$
$824$	−10.9843	−0.382657
$825$	−6.82756	−0.237705
$826$	3.36961	0.117244
$827$	4.73016	0.164484	0.0822419	−	0.996612i	$-0.473792\pi$
$827$	4.73016	0.164484	0.0822419	+	0.996612i	$0.473792\pi$
$828$	21.0837	0.732710
$829$	26.5287	0.921378	0.460689	−	0.887562i	$-0.347602\pi$
$829$	26.5287	0.921378	0.460689	+	0.887562i	$0.347602\pi$
$830$	−18.9099	−0.656372
$831$	68.8830	2.38953
$832$	4.89563	0.169725
$833$	2.66043	0.0921783
$834$	−10.1337	−0.350901
$835$	−25.8474	−0.894485
$836$	0	0
$837$	32.6886	1.12988
$838$	−3.97201	−0.137211
$839$	−26.6397	−0.919706	−0.459853	−	0.887995i	$-0.652098\pi$
$839$	−26.6397	−0.919706	−0.459853	+	0.887995i	$0.652098\pi$
$840$	−3.75015	−0.129393
$841$	−28.0055	−0.965708
$842$	−2.21450	−0.0763166
$843$	−33.3889	−1.14997
$844$	−5.11585	−0.176095
$845$	14.8418	0.510573
$846$	18.3927	0.632355
$847$	−10.3954	−0.357190
$848$	7.53218	0.258656
$849$	−71.9464	−2.46919
$850$	8.42983	0.289141
$851$	−25.1935	−0.863622
$852$	−22.3049	−0.764153
$853$	22.1664	0.758964	0.379482	−	0.925199i	$-0.376102\pi$
$853$	22.1664	0.758964	0.379482	+	0.925199i	$0.376102\pi$
$854$	3.75523	0.128501
$855$	0	0
$856$	−4.44978	−0.152090
$857$	21.2045	0.724332	0.362166	−	0.932114i	$-0.382037\pi$
$857$	21.2045	0.724332	0.362166	+	0.932114i	$0.382037\pi$
$858$	−10.5489	−0.360133
$859$	39.3164	1.34146	0.670730	−	0.741702i	$-0.265981\pi$
$859$	39.3164	1.34146	0.670730	+	0.741702i	$0.265981\pi$
$860$	14.9418	0.509511
$861$	−29.8510	−1.01732
$862$	35.0260	1.19299
$863$	−14.6679	−0.499301	−0.249651	−	0.968336i	$-0.580316\pi$
$863$	−14.6679	−0.499301	−0.249651	+	0.968336i	$0.580316\pi$
$864$	−4.65327	−0.158307
$865$	2.07519	0.0705587
$866$	−25.2504	−0.858043
$867$	−27.4956	−0.933799
$868$	7.02486	0.238439
$869$	−1.90289	−0.0645510
$870$	3.73977	0.126790
$871$	5.37947	0.182276
$872$	10.4374	0.353454
$873$	10.8570	0.367453
$874$	0	0
$875$	−11.0545	−0.373710
$876$	−39.9398	−1.34944
$877$	6.23078	0.210398	0.105199	−	0.994451i	$-0.466452\pi$
$877$	6.23078	0.210398	0.105199	+	0.994451i	$0.466452\pi$
$878$	32.0708	1.08234
$879$	−18.5482	−0.625614
$880$	1.05228	0.0354724
$881$	−18.1699	−0.612159	−0.306079	−	0.952006i	$-0.599017\pi$
$881$	−18.1699	−0.612159	−0.306079	+	0.952006i	$0.599017\pi$
$882$	−4.67919	−0.157557
$883$	−53.5155	−1.80094	−0.900471	−	0.434917i	$-0.856778\pi$
$883$	−53.5155	−1.80094	−0.900471	+	0.434917i	$0.856778\pi$
$884$	13.0245	0.438060
$885$	−12.6366	−0.424773
$886$	−20.5097	−0.689036
$887$	7.45643	0.250362	0.125181	−	0.992134i	$-0.460049\pi$
$887$	7.45643	0.250362	0.125181	+	0.992134i	$0.460049\pi$
$888$	15.4942	0.519952
$889$	−9.53273	−0.319718
$890$	19.9164	0.667599
$891$	−0.888563	−0.0297680
$892$	−9.49819	−0.318023
$893$	0	0
$894$	−52.5303	−1.75687
$895$	−34.1225	−1.14059
$896$	−1.00000	−0.0334077
$897$	61.1283	2.04102
$898$	−14.1242	−0.471331
$899$	−7.00540	−0.233643
$900$	−14.8265	−0.494216
$901$	20.0388	0.667589
$902$	8.37608	0.278893
$903$	30.5963	1.01818
$904$	−1.79945	−0.0598489
$905$	29.2959	0.973829
$906$	7.09095	0.235581
$907$	−4.81173	−0.159771	−0.0798854	−	0.996804i	$-0.525455\pi$
$907$	−4.81173	−0.159771	−0.0798854	+	0.996804i	$0.525455\pi$
$908$	0.0136096	0.000451651 0
$909$	−24.6230	−0.816694
$910$	−6.62521	−0.219624
$911$	−22.6397	−0.750086	−0.375043	−	0.927007i	$-0.622372\pi$
$911$	−22.6397	−0.750086	−0.375043	+	0.927007i	$0.622372\pi$
$912$	0	0
$913$	10.8652	0.359586
$914$	23.6803	0.783275
$915$	−14.0827	−0.465559
$916$	21.0961	0.697033
$917$	9.06565	0.299374
$918$	−12.3797	−0.408590
$919$	21.5407	0.710562	0.355281	−	0.934760i	$-0.384385\pi$
$919$	21.5407	0.710562	0.355281	+	0.934760i	$0.384385\pi$
$920$	−6.09772	−0.201036
$921$	10.9367	0.360376
$922$	−16.3005	−0.536827
$923$	−39.4049	−1.29703
$924$	2.15476	0.0708863
$925$	17.7166	0.582517
$926$	−25.4188	−0.835312
$927$	51.3977	1.68812
$928$	0.997230	0.0327357
$929$	9.88080	0.324179	0.162089	−	0.986776i	$-0.448177\pi$
$929$	9.88080	0.324179	0.162089	+	0.986776i	$0.448177\pi$
$930$	−26.3443	−0.863864
$931$	0	0
$932$	25.7459	0.843334
$933$	41.0591	1.34421
$934$	25.3370	0.829052
$935$	2.79952	0.0915539
$936$	−22.9076	−0.748758
$937$	40.4795	1.32241	0.661204	−	0.750206i	$-0.270046\pi$
$937$	40.4795	1.32241	0.661204	+	0.750206i	$0.270046\pi$
$938$	−1.09883	−0.0358781
$939$	−49.1901	−1.60526
$940$	−5.31945	−0.173501
$941$	−39.2993	−1.28112	−0.640560	−	0.767908i	$-0.721298\pi$
$941$	−39.2993	−1.28112	−0.640560	+	0.767908i	$0.721298\pi$
$942$	−42.8491	−1.39610
$943$	−48.5374	−1.58060
$944$	−3.36961	−0.109671
$945$	6.29723	0.204849
$946$	−8.58523	−0.279130
$947$	−29.5011	−0.958657	−0.479329	−	0.877635i	$-0.659120\pi$
$947$	−29.5011	−0.958657	−0.479329	+	0.877635i	$0.659120\pi$
$948$	−6.78157	−0.220255
$949$	−70.5596	−2.29046
$950$	0	0
$951$	7.86755	0.255123
$952$	−2.66043	−0.0862249
$953$	17.1798	0.556509	0.278254	−	0.960507i	$-0.410244\pi$
$953$	17.1798	0.556509	0.278254	+	0.960507i	$0.410244\pi$
$954$	−35.2445	−1.14108
$955$	8.47622	0.274284
$956$	−1.70859	−0.0552597
$957$	−2.14879	−0.0694604
$958$	28.2100	0.911424
$959$	−14.3031	−0.461873
$960$	3.75015	0.121036
$961$	18.3487	0.591894
$962$	27.3729	0.882537
$963$	20.8214	0.670959
$964$	6.93003	0.223201
$965$	18.8117	0.605571
$966$	−12.4863	−0.401740
$967$	−38.1823	−1.22786	−0.613929	−	0.789361i	$-0.710412\pi$
$967$	−38.1823	−1.22786	−0.613929	+	0.789361i	$0.710412\pi$
$968$	10.3954	0.334120
$969$	0	0
$970$	−3.14000	−0.100819
$971$	2.36181	0.0757940	0.0378970	−	0.999282i	$-0.487934\pi$
$971$	2.36181	0.0757940	0.0378970	+	0.999282i	$0.487934\pi$
$972$	−17.1265	−0.549333
$973$	3.65688	0.117234
$974$	28.1520	0.902050
$975$	−42.9867	−1.37668
$976$	−3.75523	−0.120202
$977$	35.2488	1.12771	0.563854	−	0.825874i	$-0.309318\pi$
$977$	35.2488	1.12771	0.563854	+	0.825874i	$0.309318\pi$
$978$	−58.5990	−1.87379
$979$	−11.4435	−0.365737
$980$	1.35329	0.0432293
$981$	−48.8385	−1.55929
$982$	19.1536	0.611217
$983$	−23.1990	−0.739934	−0.369967	−	0.929045i	$-0.620631\pi$
$983$	−23.1990	−0.739934	−0.369967	+	0.929045i	$0.620631\pi$
$984$	29.8510	0.951614
$985$	5.93864	0.189221
$986$	2.65306	0.0844905
$987$	−10.8926	−0.346716
$988$	0	0
$989$	49.7494	1.58194
$990$	−4.92382	−0.156489
$991$	−23.9624	−0.761190	−0.380595	−	0.924742i	$-0.624281\pi$
$991$	−23.9624	−0.761190	−0.380595	+	0.924742i	$0.624281\pi$
$992$	−7.02486	−0.223040
$993$	−7.64898	−0.242733
$994$	8.04901	0.255299
$995$	−28.6368	−0.907846
$996$	38.7218	1.22695
$997$	−9.40995	−0.298016	−0.149008	−	0.988836i	$-0.547608\pi$
$997$	−9.40995	−0.298016	−0.149008	+	0.988836i	$0.547608\pi$
$998$	−7.01992	−0.222212
$999$	−26.0178	−0.823166

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5054.2.a.bl.1.12		12
19.9	even	9		266.2.u.d.43.4	✓	24
19.17	even	9		266.2.u.d.99.4	yes	24
19.18	odd	2		5054.2.a.bm.1.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
266.2.u.d.43.4	✓	24	19.9	even	9
266.2.u.d.99.4	yes	24	19.17	even	9
5054.2.a.bl.1.12		12	1.1	even	1	trivial
5054.2.a.bm.1.1		12	19.18	odd	2

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:	\( N \)	\(=\)	\( 5054 = 2 \cdot 7 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5054.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.77114 q^{3} +1.00000 q^{4} +1.35329 q^{5} -2.77114 q^{6} +1.00000 q^{7} -1.00000 q^{8} +4.67919 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.77114 q^{3} +1.00000 q^{4} +1.35329 q^{5} -2.77114 q^{6} +1.00000 q^{7} -1.00000 q^{8} +4.67919 q^{9} -1.35329 q^{10} +0.777571 q^{11} +2.77114 q^{12} +4.89563 q^{13} -1.00000 q^{14} +3.75015 q^{15} +1.00000 q^{16} +2.66043 q^{17} -4.67919 q^{18} +1.35329 q^{20} +2.77114 q^{21} -0.777571 q^{22} +4.50585 q^{23} -2.77114 q^{24} -3.16860 q^{25} -4.89563 q^{26} +4.65327 q^{27} +1.00000 q^{28} -0.997230 q^{29} -3.75015 q^{30} +7.02486 q^{31} -1.00000 q^{32} +2.15476 q^{33} -2.66043 q^{34} +1.35329 q^{35} +4.67919 q^{36} -5.59129 q^{37} +13.5664 q^{39} -1.35329 q^{40} -10.7721 q^{41} -2.77114 q^{42} +11.0411 q^{43} +0.777571 q^{44} +6.33231 q^{45} -4.50585 q^{46} -3.93075 q^{47} +2.77114 q^{48} +1.00000 q^{49} +3.16860 q^{50} +7.37240 q^{51} +4.89563 q^{52} +7.53218 q^{53} -4.65327 q^{54} +1.05228 q^{55} -1.00000 q^{56} +0.997230 q^{58} -3.36961 q^{59} +3.75015 q^{60} -3.75523 q^{61} -7.02486 q^{62} +4.67919 q^{63} +1.00000 q^{64} +6.62521 q^{65} -2.15476 q^{66} +1.09883 q^{67} +2.66043 q^{68} +12.4863 q^{69} -1.35329 q^{70} -8.04901 q^{71} -4.67919 q^{72} -14.4128 q^{73} +5.59129 q^{74} -8.78062 q^{75} +0.777571 q^{77} -13.5664 q^{78} -2.44722 q^{79} +1.35329 q^{80} -1.14274 q^{81} +10.7721 q^{82} +13.9733 q^{83} +2.77114 q^{84} +3.60033 q^{85} -11.0411 q^{86} -2.76346 q^{87} -0.777571 q^{88} -14.7170 q^{89} -6.33231 q^{90} +4.89563 q^{91} +4.50585 q^{92} +19.4668 q^{93} +3.93075 q^{94} -2.77114 q^{96} +2.32027 q^{97} -1.00000 q^{98} +3.63841 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} - 3 q^{3} + 12 q^{4} + 3 q^{5} + 3 q^{6} + 12 q^{7} - 12 q^{8} + 21 q^{9}+O(q^{10}) \) 12 * q - 12 * q^2 - 3 * q^3 + 12 * q^4 + 3 * q^5 + 3 * q^6 + 12 * q^7 - 12 * q^8 + 21 * q^9	\( 12 q - 12 q^{2} - 3 q^{3} + 12 q^{4} + 3 q^{5} + 3 q^{6} + 12 q^{7} - 12 q^{8} + 21 q^{9} - 3 q^{10} + 3 q^{11} - 3 q^{12} + 6 q^{13} - 12 q^{14} + 6 q^{15} + 12 q^{16} + 3 q^{17} - 21 q^{18} + 3 q^{20} - 3 q^{21} - 3 q^{22} + 12 q^{23} + 3 q^{24} + 33 q^{25} - 6 q^{26} - 21 q^{27} + 12 q^{28} - 6 q^{29} - 6 q^{30} - 3 q^{31} - 12 q^{32} + 6 q^{33} - 3 q^{34} + 3 q^{35} + 21 q^{36} - 27 q^{37} + 27 q^{39} - 3 q^{40} + 27 q^{41} + 3 q^{42} + 30 q^{43} + 3 q^{44} + 30 q^{45} - 12 q^{46} + 21 q^{47} - 3 q^{48} + 12 q^{49} - 33 q^{50} - 3 q^{51} + 6 q^{52} - 6 q^{53} + 21 q^{54} + 48 q^{55} - 12 q^{56} + 6 q^{58} + 27 q^{59} + 6 q^{60} + 18 q^{61} + 3 q^{62} + 21 q^{63} + 12 q^{64} + 9 q^{65} - 6 q^{66} - 9 q^{67} + 3 q^{68} - 18 q^{69} - 3 q^{70} - 27 q^{71} - 21 q^{72} - 9 q^{73} + 27 q^{74} - 33 q^{75} + 3 q^{77} - 27 q^{78} + 12 q^{79} + 3 q^{80} + 24 q^{81} - 27 q^{82} + 9 q^{83} - 3 q^{84} + 78 q^{85} - 30 q^{86} - 45 q^{87} - 3 q^{88} + 24 q^{89} - 30 q^{90} + 6 q^{91} + 12 q^{92} + 3 q^{93} - 21 q^{94} + 3 q^{96} + 18 q^{97} - 12 q^{98} + 48 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 - 3 * q^3 + 12 * q^4 + 3 * q^5 + 3 * q^6 + 12 * q^7 - 12 * q^8 + 21 * q^9 - 3 * q^10 + 3 * q^11 - 3 * q^12 + 6 * q^13 - 12 * q^14 + 6 * q^15 + 12 * q^16 + 3 * q^17 - 21 * q^18 + 3 * q^20 - 3 * q^21 - 3 * q^22 + 12 * q^23 + 3 * q^24 + 33 * q^25 - 6 * q^26 - 21 * q^27 + 12 * q^28 - 6 * q^29 - 6 * q^30 - 3 * q^31 - 12 * q^32 + 6 * q^33 - 3 * q^34 + 3 * q^35 + 21 * q^36 - 27 * q^37 + 27 * q^39 - 3 * q^40 + 27 * q^41 + 3 * q^42 + 30 * q^43 + 3 * q^44 + 30 * q^45 - 12 * q^46 + 21 * q^47 - 3 * q^48 + 12 * q^49 - 33 * q^50 - 3 * q^51 + 6 * q^52 - 6 * q^53 + 21 * q^54 + 48 * q^55 - 12 * q^56 + 6 * q^58 + 27 * q^59 + 6 * q^60 + 18 * q^61 + 3 * q^62 + 21 * q^63 + 12 * q^64 + 9 * q^65 - 6 * q^66 - 9 * q^67 + 3 * q^68 - 18 * q^69 - 3 * q^70 - 27 * q^71 - 21 * q^72 - 9 * q^73 + 27 * q^74 - 33 * q^75 + 3 * q^77 - 27 * q^78 + 12 * q^79 + 3 * q^80 + 24 * q^81 - 27 * q^82 + 9 * q^83 - 3 * q^84 + 78 * q^85 - 30 * q^86 - 45 * q^87 - 3 * q^88 + 24 * q^89 - 30 * q^90 + 6 * q^91 + 12 * q^92 + 3 * q^93 - 21 * q^94 + 3 * q^96 + 18 * q^97 - 12 * q^98 + 48 * q^99

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