LMFDB - Embedded newform 7942.2.a.bm.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7942,2,Mod(1,7942)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7942, 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("7942.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7942 = 2 \cdot 11 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7942.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$63.4171892853$
Analytic rank:	$1$
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} - 14x^{6} - 4x^{5} + 38x^{4} + 3x^{3} - 29x^{2} + 2x + 4 $ x^8 - 14x^6 - 4x^5 + 38x^4 + 3x^3 - 29x^2 + 2x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$0.517227$ of defining polynomial
Character	$\chi$	$=$	7942.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.13526 q^{3} +1.00000 q^{4} -1.11348 q^{5} -1.13526 q^{6} +0.931861 q^{7} -1.00000 q^{8} -1.71118 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.13526 q^{3} +1.00000 q^{4} -1.11348 q^{5} -1.13526 q^{6} +0.931861 q^{7} -1.00000 q^{8} -1.71118 q^{9} +1.11348 q^{10} +1.00000 q^{11} +1.13526 q^{12} +5.94597 q^{13} -0.931861 q^{14} -1.26409 q^{15} +1.00000 q^{16} +1.38883 q^{17} +1.71118 q^{18} -1.11348 q^{20} +1.05790 q^{21} -1.00000 q^{22} -2.81882 q^{23} -1.13526 q^{24} -3.76016 q^{25} -5.94597 q^{26} -5.34842 q^{27} +0.931861 q^{28} -4.33121 q^{29} +1.26409 q^{30} +4.05960 q^{31} -1.00000 q^{32} +1.13526 q^{33} -1.38883 q^{34} -1.03761 q^{35} -1.71118 q^{36} -4.07824 q^{37} +6.75023 q^{39} +1.11348 q^{40} -3.36957 q^{41} -1.05790 q^{42} +3.79886 q^{43} +1.00000 q^{44} +1.90537 q^{45} +2.81882 q^{46} -11.1842 q^{47} +1.13526 q^{48} -6.13164 q^{49} +3.76016 q^{50} +1.57669 q^{51} +5.94597 q^{52} +0.924992 q^{53} +5.34842 q^{54} -1.11348 q^{55} -0.931861 q^{56} +4.33121 q^{58} -9.51903 q^{59} -1.26409 q^{60} +0.339887 q^{61} -4.05960 q^{62} -1.59458 q^{63} +1.00000 q^{64} -6.62072 q^{65} -1.13526 q^{66} -5.51528 q^{67} +1.38883 q^{68} -3.20010 q^{69} +1.03761 q^{70} +3.01645 q^{71} +1.71118 q^{72} +11.6220 q^{73} +4.07824 q^{74} -4.26877 q^{75} +0.931861 q^{77} -6.75023 q^{78} -8.25932 q^{79} -1.11348 q^{80} -0.938307 q^{81} +3.36957 q^{82} +1.25952 q^{83} +1.05790 q^{84} -1.54644 q^{85} -3.79886 q^{86} -4.91706 q^{87} -1.00000 q^{88} -12.0048 q^{89} -1.90537 q^{90} +5.54082 q^{91} -2.81882 q^{92} +4.60871 q^{93} +11.1842 q^{94} -1.13526 q^{96} -16.4195 q^{97} +6.13164 q^{98} -1.71118 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} - 4 q^{3} + 8 q^{4} + q^{5} + 4 q^{6} + 4 q^{7} - 8 q^{8} + 6 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 - 4 * q^3 + 8 * q^4 + q^5 + 4 * q^6 + 4 * q^7 - 8 * q^8 + 6 * q^9	\( 8 q - 8 q^{2} - 4 q^{3} + 8 q^{4} + q^{5} + 4 q^{6} + 4 q^{7} - 8 q^{8} + 6 q^{9} - q^{10} + 8 q^{11} - 4 q^{12} - 12 q^{13} - 4 q^{14} + 9 q^{15} + 8 q^{16} + 7 q^{17} - 6 q^{18} + q^{20} - 13 q^{21} - 8 q^{22} - 6 q^{23} + 4 q^{24} + 5 q^{25} + 12 q^{26} - 22 q^{27} + 4 q^{28} + q^{29} - 9 q^{30} - 8 q^{31} - 8 q^{32} - 4 q^{33} - 7 q^{34} + 5 q^{35} + 6 q^{36} - 12 q^{37} + 10 q^{39} - q^{40} - 18 q^{41} + 13 q^{42} - 4 q^{43} + 8 q^{44} - 19 q^{45} + 6 q^{46} + 13 q^{47} - 4 q^{48} + 4 q^{49} - 5 q^{50} - 14 q^{51} - 12 q^{52} + 17 q^{53} + 22 q^{54} + q^{55} - 4 q^{56} - q^{58} - 26 q^{59} + 9 q^{60} - 7 q^{61} + 8 q^{62} + 13 q^{63} + 8 q^{64} - 36 q^{65} + 4 q^{66} - 6 q^{67} + 7 q^{68} - 19 q^{69} - 5 q^{70} + 3 q^{71} - 6 q^{72} + 5 q^{73} + 12 q^{74} - 30 q^{75} + 4 q^{77} - 10 q^{78} - 16 q^{79} + q^{80} + 8 q^{81} + 18 q^{82} - 21 q^{83} - 13 q^{84} - 10 q^{85} + 4 q^{86} - 29 q^{87} - 8 q^{88} - 16 q^{89} + 19 q^{90} - 31 q^{91} - 6 q^{92} + 20 q^{93} - 13 q^{94} + 4 q^{96} + 15 q^{97} - 4 q^{98} + 6 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 - 4 * q^3 + 8 * q^4 + q^5 + 4 * q^6 + 4 * q^7 - 8 * q^8 + 6 * q^9 - q^10 + 8 * q^11 - 4 * q^12 - 12 * q^13 - 4 * q^14 + 9 * q^15 + 8 * q^16 + 7 * q^17 - 6 * q^18 + q^20 - 13 * q^21 - 8 * q^22 - 6 * q^23 + 4 * q^24 + 5 * q^25 + 12 * q^26 - 22 * q^27 + 4 * q^28 + q^29 - 9 * q^30 - 8 * q^31 - 8 * q^32 - 4 * q^33 - 7 * q^34 + 5 * q^35 + 6 * q^36 - 12 * q^37 + 10 * q^39 - q^40 - 18 * q^41 + 13 * q^42 - 4 * q^43 + 8 * q^44 - 19 * q^45 + 6 * q^46 + 13 * q^47 - 4 * q^48 + 4 * q^49 - 5 * q^50 - 14 * q^51 - 12 * q^52 + 17 * q^53 + 22 * q^54 + q^55 - 4 * q^56 - q^58 - 26 * q^59 + 9 * q^60 - 7 * q^61 + 8 * q^62 + 13 * q^63 + 8 * q^64 - 36 * q^65 + 4 * q^66 - 6 * q^67 + 7 * q^68 - 19 * q^69 - 5 * q^70 + 3 * q^71 - 6 * q^72 + 5 * q^73 + 12 * q^74 - 30 * q^75 + 4 * q^77 - 10 * q^78 - 16 * q^79 + q^80 + 8 * q^81 + 18 * q^82 - 21 * q^83 - 13 * q^84 - 10 * q^85 + 4 * q^86 - 29 * q^87 - 8 * q^88 - 16 * q^89 + 19 * q^90 - 31 * q^91 - 6 * q^92 + 20 * q^93 - 13 * q^94 + 4 * q^96 + 15 * q^97 - 4 * q^98 + 6 * 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
$3$	1.13526	0.655443	0.327722	−	0.944774i	$-0.393719\pi$
$3$	1.13526	0.655443	0.327722	+	0.944774i	$0.393719\pi$
$4$	1.00000	0.500000
$5$	−1.11348	−0.497963	−0.248982	−	0.968508i	$-0.580096\pi$
$5$	−1.11348	−0.497963	−0.248982	+	0.968508i	$0.580096\pi$
$6$	−1.13526	−0.463468
$7$	0.931861	0.352210	0.176105	−	0.984371i	$-0.443650\pi$
$7$	0.931861	0.352210	0.176105	+	0.984371i	$0.443650\pi$
$8$	−1.00000	−0.353553
$9$	−1.71118	−0.570394
$10$	1.11348	0.352113
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.13526	0.327722
$13$	5.94597	1.64912	0.824558	−	0.565777i	$-0.191424\pi$
$13$	5.94597	1.64912	0.824558	+	0.565777i	$0.191424\pi$
$14$	−0.931861	−0.249050
$15$	−1.26409	−0.326387
$16$	1.00000	0.250000
$17$	1.38883	0.336842	0.168421	−	0.985715i	$-0.446133\pi$
$17$	1.38883	0.336842	0.168421	+	0.985715i	$0.446133\pi$
$18$	1.71118	0.403330
$19$	0	0
$19$	0	0
$20$	−1.11348	−0.248982
$21$	1.05790	0.230854
$22$	−1.00000	−0.213201
$23$	−2.81882	−0.587766	−0.293883	−	0.955841i	$-0.594948\pi$
$23$	−2.81882	−0.587766	−0.293883	+	0.955841i	$0.594948\pi$
$24$	−1.13526	−0.231734
$25$	−3.76016	−0.752033
$26$	−5.94597	−1.16610
$27$	−5.34842	−1.02930
$28$	0.931861	0.176105
$29$	−4.33121	−0.804286	−0.402143	−	0.915577i	$-0.631734\pi$
$29$	−4.33121	−0.804286	−0.402143	+	0.915577i	$0.631734\pi$
$30$	1.26409	0.230790
$31$	4.05960	0.729126	0.364563	−	0.931179i	$-0.381218\pi$
$31$	4.05960	0.729126	0.364563	+	0.931179i	$0.381218\pi$
$32$	−1.00000	−0.176777
$33$	1.13526	0.197624
$34$	−1.38883	−0.238183
$35$	−1.03761	−0.175388
$36$	−1.71118	−0.285197
$37$	−4.07824	−0.670458	−0.335229	−	0.942137i	$-0.608814\pi$
$37$	−4.07824	−0.670458	−0.335229	+	0.942137i	$0.608814\pi$
$38$	0	0
$39$	6.75023	1.08090
$40$	1.11348	0.176057
$41$	−3.36957	−0.526239	−0.263120	−	0.964763i	$-0.584751\pi$
$41$	−3.36957	−0.526239	−0.263120	+	0.964763i	$0.584751\pi$
$42$	−1.05790	−0.163238
$43$	3.79886	0.579321	0.289661	−	0.957129i	$-0.406458\pi$
$43$	3.79886	0.579321	0.289661	+	0.957129i	$0.406458\pi$
$44$	1.00000	0.150756
$45$	1.90537	0.284035
$46$	2.81882	0.415613
$47$	−11.1842	−1.63138	−0.815690	−	0.578489i	$-0.803642\pi$
$47$	−11.1842	−1.63138	−0.815690	+	0.578489i	$0.803642\pi$
$48$	1.13526	0.163861
$49$	−6.13164	−0.875948
$50$	3.76016	0.531767
$51$	1.57669	0.220781
$52$	5.94597	0.824558
$53$	0.924992	0.127057	0.0635287	−	0.997980i	$-0.479765\pi$
$53$	0.924992	0.127057	0.0635287	+	0.997980i	$0.479765\pi$
$54$	5.34842	0.727828
$55$	−1.11348	−0.150142
$56$	−0.931861	−0.124525
$57$	0	0
$58$	4.33121	0.568716
$59$	−9.51903	−1.23927	−0.619636	−	0.784889i	$-0.712720\pi$
$59$	−9.51903	−1.23927	−0.619636	+	0.784889i	$0.712720\pi$
$60$	−1.26409	−0.163193
$61$	0.339887	0.0435181	0.0217591	−	0.999763i	$-0.493073\pi$
$61$	0.339887	0.0435181	0.0217591	+	0.999763i	$0.493073\pi$
$62$	−4.05960	−0.515570
$63$	−1.59458	−0.200899
$64$	1.00000	0.125000
$65$	−6.62072	−0.821199
$66$	−1.13526	−0.139741
$67$	−5.51528	−0.673799	−0.336899	−	0.941541i	$-0.609378\pi$
$67$	−5.51528	−0.673799	−0.336899	+	0.941541i	$0.609378\pi$
$68$	1.38883	0.168421
$69$	−3.20010	−0.385247
$70$	1.03761	0.124018
$71$	3.01645	0.357987	0.178994	−	0.983850i	$-0.442716\pi$
$71$	3.01645	0.357987	0.178994	+	0.983850i	$0.442716\pi$
$72$	1.71118	0.201665
$73$	11.6220	1.36025	0.680123	−	0.733098i	$-0.261926\pi$
$73$	11.6220	1.36025	0.680123	+	0.733098i	$0.261926\pi$
$74$	4.07824	0.474085
$75$	−4.26877	−0.492915
$76$	0	0
$77$	0.931861	0.106195
$78$	−6.75023	−0.764313
$79$	−8.25932	−0.929246	−0.464623	−	0.885509i	$-0.653810\pi$
$79$	−8.25932	−0.929246	−0.464623	+	0.885509i	$0.653810\pi$
$80$	−1.11348	−0.124491
$81$	−0.938307	−0.104256
$82$	3.36957	0.372107
$83$	1.25952	0.138250	0.0691251	−	0.997608i	$-0.477979\pi$
$83$	1.25952	0.138250	0.0691251	+	0.997608i	$0.477979\pi$
$84$	1.05790	0.115427
$85$	−1.54644	−0.167735
$86$	−3.79886	−0.409642
$87$	−4.91706	−0.527164
$88$	−1.00000	−0.106600
$89$	−12.0048	−1.27251	−0.636254	−	0.771480i	$-0.719517\pi$
$89$	−12.0048	−1.27251	−0.636254	+	0.771480i	$0.719517\pi$
$90$	−1.90537	−0.200843
$91$	5.54082	0.580836
$92$	−2.81882	−0.293883
$93$	4.60871	0.477901
$94$	11.1842	1.15356
$95$	0	0
$96$	−1.13526	−0.115867
$97$	−16.4195	−1.66715	−0.833576	−	0.552404i	$-0.813710\pi$
$97$	−16.4195	−1.66715	−0.833576	+	0.552404i	$0.813710\pi$
$98$	6.13164	0.619389
$99$	−1.71118	−0.171980
$100$	−3.76016	−0.376016
$101$	−9.65673	−0.960880	−0.480440	−	0.877028i	$-0.659523\pi$
$101$	−9.65673	−0.960880	−0.480440	+	0.877028i	$0.659523\pi$
$102$	−1.57669	−0.156116
$103$	4.19494	0.413340	0.206670	−	0.978411i	$-0.433737\pi$
$103$	4.19494	0.413340	0.206670	+	0.978411i	$0.433737\pi$
$104$	−5.94597	−0.583051
$105$	−1.17796	−0.114957
$106$	−0.924992	−0.0898431
$107$	10.7839	1.04252	0.521261	−	0.853397i	$-0.325462\pi$
$107$	10.7839	1.04252	0.521261	+	0.853397i	$0.325462\pi$
$108$	−5.34842	−0.514652
$109$	13.9391	1.33512	0.667561	−	0.744555i	$-0.267338\pi$
$109$	13.9391	1.33512	0.667561	+	0.744555i	$0.267338\pi$
$110$	1.11348	0.106166
$111$	−4.62986	−0.439447
$112$	0.931861	0.0880526
$113$	12.1316	1.14125	0.570623	−	0.821212i	$-0.306702\pi$
$113$	12.1316	1.14125	0.570623	+	0.821212i	$0.306702\pi$
$114$	0	0
$115$	3.13870	0.292686
$116$	−4.33121	−0.402143
$117$	−10.1746	−0.940646
$118$	9.51903	0.876298
$119$	1.29420	0.118639
$120$	1.26409	0.115395
$121$	1.00000	0.0909091
$122$	−0.339887	−0.0307720
$123$	−3.82535	−0.344920
$124$	4.05960	0.364563
$125$	9.75426	0.872448
$126$	1.59458	0.142057
$127$	−6.10820	−0.542015	−0.271008	−	0.962577i	$-0.587357\pi$
$127$	−6.10820	−0.542015	−0.271008	+	0.962577i	$0.587357\pi$
$128$	−1.00000	−0.0883883
$129$	4.31270	0.379712
$130$	6.62072	0.580675
$131$	2.69184	0.235187	0.117593	−	0.993062i	$-0.462482\pi$
$131$	2.69184	0.235187	0.117593	+	0.993062i	$0.462482\pi$
$132$	1.13526	0.0988118
$133$	0	0
$134$	5.51528	0.476448
$135$	5.95536	0.512555
$136$	−1.38883	−0.119092
$137$	19.1142	1.63303	0.816517	−	0.577321i	$-0.195902\pi$
$137$	19.1142	1.63303	0.816517	+	0.577321i	$0.195902\pi$
$138$	3.20010	0.272411
$139$	17.4146	1.47708	0.738542	−	0.674207i	$-0.235515\pi$
$139$	17.4146	1.47708	0.738542	+	0.674207i	$0.235515\pi$
$140$	−1.03761	−0.0876938
$141$	−12.6970	−1.06928
$142$	−3.01645	−0.253135
$143$	5.94597	0.497227
$144$	−1.71118	−0.142599
$145$	4.82271	0.400505
$146$	−11.6220	−0.961840
$147$	−6.96101	−0.574134
$148$	−4.07824	−0.335229
$149$	−9.98497	−0.818000	−0.409000	−	0.912534i	$-0.634122\pi$
$149$	−9.98497	−0.818000	−0.409000	+	0.912534i	$0.634122\pi$
$150$	4.26877	0.348543
$151$	4.32460	0.351931	0.175966	−	0.984396i	$-0.443695\pi$
$151$	4.32460	0.351931	0.175966	+	0.984396i	$0.443695\pi$
$152$	0	0
$153$	−2.37655	−0.192133
$154$	−0.931861	−0.0750915
$155$	−4.52029	−0.363078
$156$	6.75023	0.540451
$157$	15.4045	1.22941	0.614707	−	0.788755i	$-0.289274\pi$
$157$	15.4045	1.22941	0.614707	+	0.788755i	$0.289274\pi$
$158$	8.25932	0.657076
$159$	1.05011	0.0832789
$160$	1.11348	0.0880283
$161$	−2.62675	−0.207017
$162$	0.938307	0.0737204
$163$	−1.79505	−0.140599	−0.0702997	−	0.997526i	$-0.522396\pi$
$163$	−1.79505	−0.140599	−0.0702997	+	0.997526i	$0.522396\pi$
$164$	−3.36957	−0.263120
$165$	−1.26409	−0.0984092
$166$	−1.25952	−0.0977576
$167$	−2.41700	−0.187033	−0.0935167	−	0.995618i	$-0.529811\pi$
$167$	−2.41700	−0.187033	−0.0935167	+	0.995618i	$0.529811\pi$
$168$	−1.05790	−0.0816191
$169$	22.3546	1.71958
$170$	1.54644	0.118606
$171$	0	0
$172$	3.79886	0.289661
$173$	−10.2505	−0.779330	−0.389665	−	0.920957i	$-0.627409\pi$
$173$	−10.2505	−0.779330	−0.389665	+	0.920957i	$0.627409\pi$
$174$	4.91706	0.372761
$175$	−3.50395	−0.264874
$176$	1.00000	0.0753778
$177$	−10.8066	−0.812273
$178$	12.0048	0.899798
$179$	−18.4545	−1.37935	−0.689677	−	0.724117i	$-0.742247\pi$
$179$	−18.4545	−1.37935	−0.689677	+	0.724117i	$0.742247\pi$
$180$	1.90537	0.142018
$181$	−16.6902	−1.24057	−0.620286	−	0.784376i	$-0.712983\pi$
$181$	−16.6902	−1.24057	−0.620286	+	0.784376i	$0.712983\pi$
$182$	−5.54082	−0.410713
$183$	0.385861	0.0285237
$184$	2.81882	0.207807
$185$	4.54103	0.333863
$186$	−4.60871	−0.337927
$187$	1.38883	0.101562
$188$	−11.1842	−0.815690
$189$	−4.98398	−0.362531
$190$	0	0
$191$	−1.38734	−0.100384	−0.0501921	−	0.998740i	$-0.515983\pi$
$191$	−1.38734	−0.100384	−0.0501921	+	0.998740i	$0.515983\pi$
$192$	1.13526	0.0819304
$193$	−6.04410	−0.435064	−0.217532	−	0.976053i	$-0.569801\pi$
$193$	−6.04410	−0.435064	−0.217532	+	0.976053i	$0.569801\pi$
$194$	16.4195	1.17885
$195$	−7.51624	−0.538249
$196$	−6.13164	−0.437974
$197$	−10.0416	−0.715431	−0.357716	−	0.933831i	$-0.616444\pi$
$197$	−10.0416	−0.715431	−0.357716	+	0.933831i	$0.616444\pi$
$198$	1.71118	0.121608
$199$	−14.8759	−1.05453	−0.527263	−	0.849702i	$-0.676782\pi$
$199$	−14.8759	−1.05453	−0.527263	+	0.849702i	$0.676782\pi$
$200$	3.76016	0.265884
$201$	−6.26128	−0.441637
$202$	9.65673	0.679445
$203$	−4.03609	−0.283278
$204$	1.57669	0.110390
$205$	3.75195	0.262048
$206$	−4.19494	−0.292275
$207$	4.82352	0.335258
$208$	5.94597	0.412279
$209$	0	0
$210$	1.17796	0.0812866
$211$	7.02101	0.483346	0.241673	−	0.970358i	$-0.422304\pi$
$211$	7.02101	0.483346	0.241673	+	0.970358i	$0.422304\pi$
$212$	0.924992	0.0635287
$213$	3.42446	0.234640
$214$	−10.7839	−0.737175
$215$	−4.22996	−0.288481
$216$	5.34842	0.363914
$217$	3.78299	0.256806
$218$	−13.9391	−0.944075
$219$	13.1940	0.891565
$220$	−1.11348	−0.0750708
$221$	8.25798	0.555492
$222$	4.62986	0.310736
$223$	−3.07501	−0.205918	−0.102959	−	0.994686i	$-0.532831\pi$
$223$	−3.07501	−0.205918	−0.102959	+	0.994686i	$0.532831\pi$
$224$	−0.931861	−0.0622626
$225$	6.43433	0.428955
$226$	−12.1316	−0.806983
$227$	−12.0169	−0.797590	−0.398795	−	0.917040i	$-0.630572\pi$
$227$	−12.0169	−0.797590	−0.398795	+	0.917040i	$0.630572\pi$
$228$	0	0
$229$	15.0971	0.997646	0.498823	−	0.866704i	$-0.333766\pi$
$229$	15.0971	0.997646	0.498823	+	0.866704i	$0.333766\pi$
$230$	−3.13870	−0.206960
$231$	1.05790	0.0696050
$232$	4.33121	0.284358
$233$	−25.4941	−1.67017	−0.835086	−	0.550120i	$-0.814582\pi$
$233$	−25.4941	−1.67017	−0.835086	+	0.550120i	$0.814582\pi$
$234$	10.1746	0.665137
$235$	12.4533	0.812367
$236$	−9.51903	−0.619636
$237$	−9.37649	−0.609068
$238$	−1.29420	−0.0838906
$239$	11.1287	0.719853	0.359926	−	0.932981i	$-0.382802\pi$
$239$	11.1287	0.719853	0.359926	+	0.932981i	$0.382802\pi$
$240$	−1.26409	−0.0815966
$241$	−23.1531	−1.49142	−0.745711	−	0.666270i	$-0.767890\pi$
$241$	−23.1531	−1.49142	−0.745711	+	0.666270i	$0.767890\pi$
$242$	−1.00000	−0.0642824
$243$	14.9800	0.960970
$244$	0.339887	0.0217591
$245$	6.82745	0.436190
$246$	3.82535	0.243895
$247$	0	0
$248$	−4.05960	−0.257785
$249$	1.42988	0.0906151
$250$	−9.75426	−0.616914
$251$	−28.1374	−1.77602	−0.888009	−	0.459827i	$-0.847911\pi$
$251$	−28.1374	−1.77602	−0.888009	+	0.459827i	$0.847911\pi$
$252$	−1.59458	−0.100449
$253$	−2.81882	−0.177218
$254$	6.10820	0.383263
$255$	−1.75561	−0.109941
$256$	1.00000	0.0625000
$257$	−25.7895	−1.60870	−0.804352	−	0.594153i	$-0.797487\pi$
$257$	−25.7895	−1.60870	−0.804352	+	0.594153i	$0.797487\pi$
$258$	−4.31270	−0.268497
$259$	−3.80035	−0.236142
$260$	−6.62072	−0.410599
$261$	7.41149	0.458760
$262$	−2.69184	−0.166302
$263$	5.31269	0.327595	0.163797	−	0.986494i	$-0.447626\pi$
$263$	5.31269	0.327595	0.163797	+	0.986494i	$0.447626\pi$
$264$	−1.13526	−0.0698705
$265$	−1.02996	−0.0632699
$266$	0	0
$267$	−13.6286	−0.834056
$268$	−5.51528	−0.336899
$269$	3.94833	0.240734	0.120367	−	0.992729i	$-0.461593\pi$
$269$	3.94833	0.240734	0.120367	+	0.992729i	$0.461593\pi$
$270$	−5.95536	−0.362431
$271$	−31.2541	−1.89855	−0.949276	−	0.314443i	$-0.898182\pi$
$271$	−31.2541	−1.89855	−0.949276	+	0.314443i	$0.898182\pi$
$272$	1.38883	0.0842105
$273$	6.29027	0.380705
$274$	−19.1142	−1.15473
$275$	−3.76016	−0.226746
$276$	−3.20010	−0.192623
$277$	−6.34603	−0.381296	−0.190648	−	0.981658i	$-0.561059\pi$
$277$	−6.34603	−0.381296	−0.190648	+	0.981658i	$0.561059\pi$
$278$	−17.4146	−1.04446
$279$	−6.94672	−0.415889
$280$	1.03761	0.0620089
$281$	−9.24922	−0.551762	−0.275881	−	0.961192i	$-0.588970\pi$
$281$	−9.24922	−0.551762	−0.275881	+	0.961192i	$0.588970\pi$
$282$	12.6970	0.756093
$283$	26.8550	1.59636	0.798182	−	0.602416i	$-0.205795\pi$
$283$	26.8550	1.59636	0.798182	+	0.602416i	$0.205795\pi$
$284$	3.01645	0.178994
$285$	0	0
$286$	−5.94597	−0.351593
$287$	−3.13997	−0.185347
$288$	1.71118	0.100832
$289$	−15.0711	−0.886538
$290$	−4.82271	−0.283200
$291$	−18.6405	−1.09272
$292$	11.6220	0.680123
$293$	7.79147	0.455183	0.227591	−	0.973757i	$-0.426915\pi$
$293$	7.79147	0.455183	0.227591	+	0.973757i	$0.426915\pi$
$294$	6.96101	0.405974
$295$	10.5992	0.617112
$296$	4.07824	0.237043
$297$	−5.34842	−0.310347
$298$	9.98497	0.578414
$299$	−16.7607	−0.969294
$300$	−4.26877	−0.246457
$301$	3.54001	0.204043
$302$	−4.32460	−0.248853
$303$	−10.9629	−0.629802
$304$	0	0
$305$	−0.378458	−0.0216704
$306$	2.37655	0.135858
$307$	−12.4501	−0.710567	−0.355283	−	0.934759i	$-0.615616\pi$
$307$	−12.4501	−0.710567	−0.355283	+	0.934759i	$0.615616\pi$
$308$	0.931861	0.0530977
$309$	4.76235	0.270921
$310$	4.52029	0.256735
$311$	19.5424	1.10815	0.554073	−	0.832468i	$-0.313073\pi$
$311$	19.5424	1.10815	0.554073	+	0.832468i	$0.313073\pi$
$312$	−6.75023	−0.382157
$313$	−8.08404	−0.456937	−0.228468	−	0.973551i	$-0.573372\pi$
$313$	−8.08404	−0.456937	−0.228468	+	0.973551i	$0.573372\pi$
$314$	−15.4045	−0.869327
$315$	1.77554	0.100040
$316$	−8.25932	−0.464623
$317$	−2.73433	−0.153576	−0.0767878	−	0.997047i	$-0.524466\pi$
$317$	−2.73433	−0.153576	−0.0767878	+	0.997047i	$0.524466\pi$
$318$	−1.05011	−0.0588871
$319$	−4.33121	−0.242501
$320$	−1.11348	−0.0622454
$321$	12.2426	0.683314
$322$	2.62675	0.146383
$323$	0	0
$324$	−0.938307	−0.0521282
$325$	−22.3578	−1.24019
$326$	1.79505	0.0994188
$327$	15.8245	0.875097
$328$	3.36957	0.186054
$329$	−10.4221	−0.574589
$330$	1.26409	0.0695858
$331$	−23.5477	−1.29430	−0.647149	−	0.762364i	$-0.724039\pi$
$331$	−23.5477	−1.29430	−0.647149	+	0.762364i	$0.724039\pi$
$332$	1.25952	0.0691251
$333$	6.97861	0.382425
$334$	2.41700	0.132253
$335$	6.14115	0.335527
$336$	1.05790	0.0577134
$337$	−25.5101	−1.38963	−0.694813	−	0.719190i	$-0.744513\pi$
$337$	−25.5101	−1.38963	−0.694813	+	0.719190i	$0.744513\pi$
$338$	−22.3546	−1.21593
$339$	13.7725	0.748022
$340$	−1.54644	−0.0838674
$341$	4.05960	0.219840
$342$	0	0
$343$	−12.2369	−0.660728
$344$	−3.79886	−0.204821
$345$	3.56325	0.191839
$346$	10.2505	0.551069
$347$	−14.3705	−0.771447	−0.385724	−	0.922614i	$-0.626048\pi$
$347$	−14.3705	−0.771447	−0.385724	+	0.922614i	$0.626048\pi$
$348$	−4.91706	−0.263582
$349$	3.64353	0.195034	0.0975168	−	0.995234i	$-0.468910\pi$
$349$	3.64353	0.195034	0.0975168	+	0.995234i	$0.468910\pi$
$350$	3.50395	0.187294
$351$	−31.8016	−1.69744
$352$	−1.00000	−0.0533002
$353$	24.6628	1.31267	0.656334	−	0.754471i	$-0.272106\pi$
$353$	24.6628	1.31267	0.656334	+	0.754471i	$0.272106\pi$
$354$	10.8066	0.574364
$355$	−3.35876	−0.178264
$356$	−12.0048	−0.636254
$357$	1.46926	0.0777612
$358$	18.4545	0.975350
$359$	19.9019	1.05038	0.525192	−	0.850984i	$-0.323994\pi$
$359$	19.9019	1.05038	0.525192	+	0.850984i	$0.323994\pi$
$360$	−1.90537	−0.100422
$361$	0	0
$362$	16.6902	0.877216
$363$	1.13526	0.0595857
$364$	5.54082	0.290418
$365$	−12.9408	−0.677353
$366$	−0.385861	−0.0201693
$367$	−22.8591	−1.19323	−0.596617	−	0.802526i	$-0.703489\pi$
$367$	−22.8591	−1.19323	−0.596617	+	0.802526i	$0.703489\pi$
$368$	−2.81882	−0.146941
$369$	5.76596	0.300164
$370$	−4.54103	−0.236077
$371$	0.861963	0.0447509
$372$	4.60871	0.238950
$373$	−6.09152	−0.315407	−0.157703	−	0.987487i	$-0.550409\pi$
$373$	−6.09152	−0.315407	−0.157703	+	0.987487i	$0.550409\pi$
$374$	−1.38883	−0.0718149
$375$	11.0736	0.571840
$376$	11.1842	0.576780
$377$	−25.7533	−1.32636
$378$	4.98398	0.256348
$379$	−3.03073	−0.155678	−0.0778390	−	0.996966i	$-0.524802\pi$
$379$	−3.03073	−0.155678	−0.0778390	+	0.996966i	$0.524802\pi$
$380$	0	0
$381$	−6.93440	−0.355260
$382$	1.38734	0.0709823
$383$	−13.4997	−0.689805	−0.344902	−	0.938639i	$-0.612088\pi$
$383$	−13.4997	−0.689805	−0.344902	+	0.938639i	$0.612088\pi$
$384$	−1.13526	−0.0579335
$385$	−1.03761	−0.0528814
$386$	6.04410	0.307637
$387$	−6.50055	−0.330441
$388$	−16.4195	−0.833576
$389$	−2.24410	−0.113780	−0.0568902	−	0.998380i	$-0.518118\pi$
$389$	−2.24410	−0.113780	−0.0568902	+	0.998380i	$0.518118\pi$
$390$	7.51624	0.380600
$391$	−3.91488	−0.197984
$392$	6.13164	0.309694
$393$	3.05594	0.154152
$394$	10.0416	0.505886
$395$	9.19658	0.462730
$396$	−1.71118	−0.0859902
$397$	8.18711	0.410899	0.205450	−	0.978668i	$-0.434134\pi$
$397$	8.18711	0.410899	0.205450	+	0.978668i	$0.434134\pi$
$398$	14.8759	0.745662
$399$	0	0
$400$	−3.76016	−0.188008
$401$	−10.5442	−0.526554	−0.263277	−	0.964720i	$-0.584803\pi$
$401$	−10.5442	−0.526554	−0.263277	+	0.964720i	$0.584803\pi$
$402$	6.26128	0.312284
$403$	24.1383	1.20241
$404$	−9.65673	−0.480440
$405$	1.04479	0.0519158
$406$	4.03609	0.200308
$407$	−4.07824	−0.202151
$408$	−1.57669	−0.0780578
$409$	−13.3130	−0.658287	−0.329144	−	0.944280i	$-0.606760\pi$
$409$	−13.3130	−0.658287	−0.329144	+	0.944280i	$0.606760\pi$
$410$	−3.75195	−0.185296
$411$	21.6996	1.07036
$412$	4.19494	0.206670
$413$	−8.87041	−0.436484
$414$	−4.82352	−0.237063
$415$	−1.40245	−0.0688435
$416$	−5.94597	−0.291525
$417$	19.7701	0.968145
$418$	0	0
$419$	24.5749	1.20056	0.600281	−	0.799789i	$-0.295055\pi$
$419$	24.5749	1.20056	0.600281	+	0.799789i	$0.295055\pi$
$420$	−1.17796	−0.0574783
$421$	37.0808	1.80721	0.903604	−	0.428368i	$-0.140911\pi$
$421$	37.0808	1.80721	0.903604	+	0.428368i	$0.140911\pi$
$422$	−7.02101	−0.341778
$423$	19.1382	0.930530
$424$	−0.924992	−0.0449216
$425$	−5.22225	−0.253316
$426$	−3.42446	−0.165916
$427$	0.316728	0.0153275
$428$	10.7839	0.521261
$429$	6.75023	0.325904
$430$	4.22996	0.203987
$431$	−1.02908	−0.0495693	−0.0247846	−	0.999693i	$-0.507890\pi$
$431$	−1.02908	−0.0495693	−0.0247846	+	0.999693i	$0.507890\pi$
$432$	−5.34842	−0.257326
$433$	6.26952	0.301294	0.150647	−	0.988588i	$-0.451864\pi$
$433$	6.26952	0.301294	0.150647	+	0.988588i	$0.451864\pi$
$434$	−3.78299	−0.181589
$435$	5.47504	0.262508
$436$	13.9391	0.667561
$437$	0	0
$438$	−13.1940	−0.630431
$439$	5.41464	0.258427	0.129213	−	0.991617i	$-0.458755\pi$
$439$	5.41464	0.258427	0.129213	+	0.991617i	$0.458755\pi$
$440$	1.11348	0.0530830
$441$	10.4923	0.499636
$442$	−8.25798	−0.392792
$443$	1.46362	0.0695387	0.0347694	−	0.999395i	$-0.488930\pi$
$443$	1.46362	0.0695387	0.0347694	+	0.999395i	$0.488930\pi$
$444$	−4.62986	−0.219724
$445$	13.3671	0.633662
$446$	3.07501	0.145606
$447$	−11.3355	−0.536153
$448$	0.931861	0.0440263
$449$	−32.6981	−1.54312	−0.771560	−	0.636157i	$-0.780523\pi$
$449$	−32.6981	−1.54312	−0.771560	+	0.636157i	$0.780523\pi$
$450$	−6.43433	−0.303317
$451$	−3.36957	−0.158667
$452$	12.1316	0.570623
$453$	4.90955	0.230671
$454$	12.0169	0.563981
$455$	−6.16959	−0.289235
$456$	0	0
$457$	17.0277	0.796523	0.398262	−	0.917272i	$-0.369614\pi$
$457$	17.0277	0.796523	0.398262	+	0.917272i	$0.369614\pi$
$458$	−15.0971	−0.705442
$459$	−7.42807	−0.346713
$460$	3.13870	0.146343
$461$	13.9254	0.648569	0.324284	−	0.945960i	$-0.394877\pi$
$461$	13.9254	0.648569	0.324284	+	0.945960i	$0.394877\pi$
$462$	−1.05790	−0.0492182
$463$	25.0656	1.16490	0.582449	−	0.812868i	$-0.302095\pi$
$463$	25.0656	1.16490	0.582449	+	0.812868i	$0.302095\pi$
$464$	−4.33121	−0.201071
$465$	−5.13170	−0.237977
$466$	25.4941	1.18099
$467$	1.50756	0.0697616	0.0348808	−	0.999391i	$-0.488895\pi$
$467$	1.50756	0.0697616	0.0348808	+	0.999391i	$0.488895\pi$
$468$	−10.1746	−0.470323
$469$	−5.13947	−0.237319
$470$	−12.4533	−0.574430
$471$	17.4881	0.805811
$472$	9.51903	0.438149
$473$	3.79886	0.174672
$474$	9.37649	0.430676
$475$	0	0
$476$	1.29420	0.0593196
$477$	−1.58283	−0.0724728
$478$	−11.1287	−0.509013
$479$	−19.6977	−0.900013	−0.450007	−	0.893025i	$-0.648578\pi$
$479$	−19.6977	−0.900013	−0.450007	+	0.893025i	$0.648578\pi$
$480$	1.26409	0.0576975
$481$	−24.2491	−1.10566
$482$	23.1531	1.05459
$483$	−2.98205	−0.135688
$484$	1.00000	0.0454545
$485$	18.2828	0.830180
$486$	−14.9800	−0.679508
$487$	−23.5836	−1.06868	−0.534338	−	0.845271i	$-0.679439\pi$
$487$	−23.5836	−1.06868	−0.534338	+	0.845271i	$0.679439\pi$
$488$	−0.339887	−0.0153860
$489$	−2.03785	−0.0921549
$490$	−6.82745	−0.308433
$491$	−35.2172	−1.58933	−0.794666	−	0.607047i	$-0.792354\pi$
$491$	−35.2172	−1.58933	−0.794666	+	0.607047i	$0.792354\pi$
$492$	−3.82535	−0.172460
$493$	−6.01534	−0.270917
$494$	0	0
$495$	1.90537	0.0856398
$496$	4.05960	0.182282
$497$	2.81091	0.126087
$498$	−1.42988	−0.0640746
$499$	−38.6900	−1.73200	−0.866002	−	0.500041i	$-0.833318\pi$
$499$	−38.6900	−1.73200	−0.866002	+	0.500041i	$0.833318\pi$
$500$	9.75426	0.436224
$501$	−2.74393	−0.122590
$502$	28.1374	1.25583
$503$	17.5437	0.782234	0.391117	−	0.920341i	$-0.372089\pi$
$503$	17.5437	0.782234	0.391117	+	0.920341i	$0.372089\pi$
$504$	1.59458	0.0710284
$505$	10.7526	0.478483
$506$	2.81882	0.125312
$507$	25.3783	1.12709
$508$	−6.10820	−0.271008
$509$	6.27273	0.278034	0.139017	−	0.990290i	$-0.455606\pi$
$509$	6.27273	0.278034	0.139017	+	0.990290i	$0.455606\pi$
$510$	1.75561	0.0777398
$511$	10.8300	0.479093
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	25.7895	1.13753
$515$	−4.67098	−0.205828
$516$	4.31270	0.189856
$517$	−11.1842	−0.491880
$518$	3.80035	0.166978
$519$	−11.6370	−0.510806
$520$	6.62072	0.290338
$521$	−4.48006	−0.196275	−0.0981374	−	0.995173i	$-0.531288\pi$
$521$	−4.48006	−0.196275	−0.0981374	+	0.995173i	$0.531288\pi$
$522$	−7.41149	−0.324392
$523$	−20.7000	−0.905150	−0.452575	−	0.891726i	$-0.649495\pi$
$523$	−20.7000	−0.905150	−0.452575	+	0.891726i	$0.649495\pi$
$524$	2.69184	0.117593
$525$	−3.97790	−0.173610
$526$	−5.31269	−0.231645
$527$	5.63812	0.245600
$528$	1.13526	0.0494059
$529$	−15.0542	−0.654532
$530$	1.02996	0.0447386
$531$	16.2888	0.706874
$532$	0	0
$533$	−20.0354	−0.867829
$534$	13.6286	0.589767
$535$	−12.0077	−0.519138
$536$	5.51528	0.238224
$537$	−20.9507	−0.904088
$538$	−3.94833	−0.170225
$539$	−6.13164	−0.264108
$540$	5.95536	0.256278
$541$	34.2124	1.47091	0.735454	−	0.677575i	$-0.236969\pi$
$541$	34.2124	1.47091	0.735454	+	0.677575i	$0.236969\pi$
$542$	31.2541	1.34248
$543$	−18.9477	−0.813124
$544$	−1.38883	−0.0595458
$545$	−15.5209	−0.664842
$546$	−6.29027	−0.269199
$547$	41.3325	1.76725	0.883625	−	0.468194i	$-0.155095\pi$
$547$	41.3325	1.76725	0.883625	+	0.468194i	$0.155095\pi$
$548$	19.1142	0.816517
$549$	−0.581609	−0.0248225
$550$	3.76016	0.160334
$551$	0	0
$552$	3.20010	0.136205
$553$	−7.69654	−0.327290
$554$	6.34603	0.269617
$555$	5.15526	0.218828
$556$	17.4146	0.738542
$557$	−7.87234	−0.333562	−0.166781	−	0.985994i	$-0.553337\pi$
$557$	−7.87234	−0.333562	−0.166781	+	0.985994i	$0.553337\pi$
$558$	6.94672	0.294078
$559$	22.5879	0.955368
$560$	−1.03761	−0.0438469
$561$	1.57669	0.0665679
$562$	9.24922	0.390155
$563$	−43.8922	−1.84984	−0.924918	−	0.380168i	$-0.875866\pi$
$563$	−43.8922	−1.84984	−0.924918	+	0.380168i	$0.875866\pi$
$564$	−12.6970	−0.534638
$565$	−13.5083	−0.568298
$566$	−26.8550	−1.12880
$567$	−0.874371	−0.0367201
$568$	−3.01645	−0.126568
$569$	24.3450	1.02059	0.510297	−	0.859998i	$-0.329535\pi$
$569$	24.3450	1.02059	0.510297	+	0.859998i	$0.329535\pi$
$570$	0	0
$571$	27.2763	1.14148	0.570740	−	0.821131i	$-0.306657\pi$
$571$	27.2763	1.14148	0.570740	+	0.821131i	$0.306657\pi$
$572$	5.94597	0.248614
$573$	−1.57499	−0.0657961
$574$	3.13997	0.131060
$575$	10.5992	0.442019
$576$	−1.71118	−0.0712993
$577$	19.5181	0.812551	0.406275	−	0.913751i	$-0.366827\pi$
$577$	19.5181	0.812551	0.406275	+	0.913751i	$0.366827\pi$
$578$	15.0711	0.626877
$579$	−6.86163	−0.285160
$580$	4.82271	0.200252
$581$	1.17370	0.0486931
$582$	18.6405	0.772672
$583$	0.924992	0.0383092
$584$	−11.6220	−0.480920
$585$	11.3293	0.468407
$586$	−7.79147	−0.321863
$587$	16.2385	0.670234	0.335117	−	0.942177i	$-0.391224\pi$
$587$	16.2385	0.670234	0.335117	+	0.942177i	$0.391224\pi$
$588$	−6.96101	−0.287067
$589$	0	0
$590$	−10.5992	−0.436364
$591$	−11.3998	−0.468925
$592$	−4.07824	−0.167614
$593$	−9.94748	−0.408494	−0.204247	−	0.978919i	$-0.565475\pi$
$593$	−9.94748	−0.408494	−0.204247	+	0.978919i	$0.565475\pi$
$594$	5.34842	0.219448
$595$	−1.44107	−0.0590779
$596$	−9.98497	−0.409000
$597$	−16.8880	−0.691181
$598$	16.7607	0.685394
$599$	7.31621	0.298932	0.149466	−	0.988767i	$-0.452245\pi$
$599$	7.31621	0.298932	0.149466	+	0.988767i	$0.452245\pi$
$600$	4.26877	0.174272
$601$	0.306838	0.0125162	0.00625810	−	0.999980i	$-0.498008\pi$
$601$	0.306838	0.0125162	0.00625810	+	0.999980i	$0.498008\pi$
$602$	−3.54001	−0.144280
$603$	9.43765	0.384331
$604$	4.32460	0.175966
$605$	−1.11348	−0.0452694
$606$	10.9629	0.445338
$607$	25.3641	1.02950	0.514749	−	0.857341i	$-0.327885\pi$
$607$	25.3641	1.02950	0.514749	+	0.857341i	$0.327885\pi$
$608$	0	0
$609$	−4.58201	−0.185672
$610$	0.378458	0.0153233
$611$	−66.5008	−2.69033
$612$	−2.37655	−0.0960663
$613$	14.5197	0.586444	0.293222	−	0.956044i	$-0.405272\pi$
$613$	14.5197	0.586444	0.293222	+	0.956044i	$0.405272\pi$
$614$	12.4501	0.502447
$615$	4.25944	0.171757
$616$	−0.931861	−0.0375457
$617$	−40.8657	−1.64519	−0.822596	−	0.568627i	$-0.807475\pi$
$617$	−40.8657	−1.64519	−0.822596	+	0.568627i	$0.807475\pi$
$618$	−4.76235	−0.191570
$619$	−13.8735	−0.557623	−0.278811	−	0.960346i	$-0.589940\pi$
$619$	−13.8735	−0.557623	−0.278811	+	0.960346i	$0.589940\pi$
$620$	−4.52029	−0.181539
$621$	15.0763	0.604990
$622$	−19.5424	−0.783578
$623$	−11.1868	−0.448190
$624$	6.75023	0.270226
$625$	7.93965	0.317586
$626$	8.08404	0.323103
$627$	0	0
$628$	15.4045	0.614707
$629$	−5.66400	−0.225838
$630$	−1.77554	−0.0707390
$631$	−11.3059	−0.450083	−0.225041	−	0.974349i	$-0.572252\pi$
$631$	−11.3059	−0.450083	−0.225041	+	0.974349i	$0.572252\pi$
$632$	8.25932	0.328538
$633$	7.97068	0.316806
$634$	2.73433	0.108594
$635$	6.80136	0.269904
$636$	1.05011	0.0416394
$637$	−36.4585	−1.44454
$638$	4.33121	0.171474
$639$	−5.16170	−0.204194
$640$	1.11348	0.0440141
$641$	18.2790	0.721978	0.360989	−	0.932570i	$-0.382439\pi$
$641$	18.2790	0.721978	0.360989	+	0.932570i	$0.382439\pi$
$642$	−12.2426	−0.483176
$643$	−7.60018	−0.299722	−0.149861	−	0.988707i	$-0.547883\pi$
$643$	−7.60018	−0.299722	−0.149861	+	0.988707i	$0.547883\pi$
$644$	−2.62675	−0.103509
$645$	−4.80210	−0.189083
$646$	0	0
$647$	41.9084	1.64759	0.823795	−	0.566888i	$-0.191853\pi$
$647$	41.9084	1.64759	0.823795	+	0.566888i	$0.191853\pi$
$648$	0.938307	0.0368602
$649$	−9.51903	−0.373655
$650$	22.3578	0.876946
$651$	4.29468	0.168322
$652$	−1.79505	−0.0702997
$653$	−6.91779	−0.270714	−0.135357	−	0.990797i	$-0.543218\pi$
$653$	−6.91779	−0.270714	−0.135357	+	0.990797i	$0.543218\pi$
$654$	−15.8245	−0.618787
$655$	−2.99730	−0.117114
$656$	−3.36957	−0.131560
$657$	−19.8873	−0.775877
$658$	10.4221	0.406296
$659$	−33.2006	−1.29331	−0.646655	−	0.762783i	$-0.723833\pi$
$659$	−33.2006	−1.29331	−0.646655	+	0.762783i	$0.723833\pi$
$660$	−1.26409	−0.0492046
$661$	1.54320	0.0600233	0.0300117	−	0.999550i	$-0.490446\pi$
$661$	1.54320	0.0600233	0.0300117	+	0.999550i	$0.490446\pi$
$662$	23.5477	0.915206
$663$	9.37496	0.364093
$664$	−1.25952	−0.0488788
$665$	0	0
$666$	−6.97861	−0.270415
$667$	12.2089	0.472731
$668$	−2.41700	−0.0935167
$669$	−3.49094	−0.134968
$670$	−6.14115	−0.237253
$671$	0.339887	0.0131212
$672$	−1.05790	−0.0408096
$673$	43.4172	1.67361	0.836806	−	0.547500i	$-0.184420\pi$
$673$	43.4172	1.67361	0.836806	+	0.547500i	$0.184420\pi$
$674$	25.5101	0.982614
$675$	20.1109	0.774071
$676$	22.3546	0.859792
$677$	−40.6082	−1.56070	−0.780350	−	0.625343i	$-0.784959\pi$
$677$	−40.6082	−1.56070	−0.780350	+	0.625343i	$0.784959\pi$
$678$	−13.7725	−0.528931
$679$	−15.3007	−0.587188
$680$	1.54644	0.0593032
$681$	−13.6423	−0.522775
$682$	−4.05960	−0.155450
$683$	−14.7330	−0.563742	−0.281871	−	0.959452i	$-0.590955\pi$
$683$	−14.7330	−0.563742	−0.281871	+	0.959452i	$0.590955\pi$
$684$	0	0
$685$	−21.2832	−0.813191
$686$	12.2369	0.467205
$687$	17.1392	0.653900
$688$	3.79886	0.144830
$689$	5.49998	0.209532
$690$	−3.56325	−0.135650
$691$	−5.26591	−0.200325	−0.100162	−	0.994971i	$-0.531936\pi$
$691$	−5.26591	−0.200325	−0.100162	+	0.994971i	$0.531936\pi$
$692$	−10.2505	−0.389665
$693$	−1.59458	−0.0605732
$694$	14.3705	0.545495
$695$	−19.3908	−0.735533
$696$	4.91706	0.186380
$697$	−4.67978	−0.177259
$698$	−3.64353	−0.137910
$699$	−28.9424	−1.09470
$700$	−3.50395	−0.132437
$701$	−7.47926	−0.282488	−0.141244	−	0.989975i	$-0.545110\pi$
$701$	−7.47926	−0.282488	−0.141244	+	0.989975i	$0.545110\pi$
$702$	31.8016	1.20027
$703$	0	0
$704$	1.00000	0.0376889
$705$	14.1378	0.532460
$706$	−24.6628	−0.928196
$707$	−8.99872	−0.338432
$708$	−10.8066	−0.406136
$709$	−14.0723	−0.528496	−0.264248	−	0.964455i	$-0.585124\pi$
$709$	−14.0723	−0.528496	−0.264248	+	0.964455i	$0.585124\pi$
$710$	3.35876	0.126052
$711$	14.1332	0.530037
$712$	12.0048	0.449899
$713$	−11.4433	−0.428555
$714$	−1.46926	−0.0549855
$715$	−6.62072	−0.247601
$716$	−18.4545	−0.689677
$717$	12.6339	0.471823
$718$	−19.9019	−0.742733
$719$	−3.03404	−0.113151	−0.0565753	−	0.998398i	$-0.518018\pi$
$719$	−3.03404	−0.113151	−0.0565753	+	0.998398i	$0.518018\pi$
$720$	1.90537	0.0710088
$721$	3.90910	0.145583
$722$	0	0
$723$	−26.2848	−0.977542
$724$	−16.6902	−0.620286
$725$	16.2861	0.604849
$726$	−1.13526	−0.0421335
$727$	−23.8928	−0.886133	−0.443067	−	0.896489i	$-0.646110\pi$
$727$	−23.8928	−0.886133	−0.443067	+	0.896489i	$0.646110\pi$
$728$	−5.54082	−0.205356
$729$	19.8212	0.734118
$730$	12.9408	0.478961
$731$	5.27599	0.195140
$732$	0.385861	0.0142618
$733$	15.2965	0.564990	0.282495	−	0.959269i	$-0.408838\pi$
$733$	15.2965	0.564990	0.282495	+	0.959269i	$0.408838\pi$
$734$	22.8591	0.843743
$735$	7.75094	0.285898
$736$	2.81882	0.103903
$737$	−5.51528	−0.203158
$738$	−5.76596	−0.212248
$739$	−9.76003	−0.359029	−0.179514	−	0.983755i	$-0.557453\pi$
$739$	−9.76003	−0.359029	−0.179514	+	0.983755i	$0.557453\pi$
$740$	4.54103	0.166932
$741$	0	0
$742$	−0.861963	−0.0316437
$743$	−20.4106	−0.748792	−0.374396	−	0.927269i	$-0.622150\pi$
$743$	−20.4106	−0.748792	−0.374396	+	0.927269i	$0.622150\pi$
$744$	−4.60871	−0.168964
$745$	11.1181	0.407334
$746$	6.09152	0.223026
$747$	−2.15527	−0.0788571
$748$	1.38883	0.0507808
$749$	10.0491	0.367187
$750$	−11.0736	−0.404352
$751$	−43.7845	−1.59772	−0.798859	−	0.601518i	$-0.794563\pi$
$751$	−43.7845	−1.59772	−0.798859	+	0.601518i	$0.794563\pi$
$752$	−11.1842	−0.407845
$753$	−31.9433	−1.16408
$754$	25.7533	0.937879
$755$	−4.81535	−0.175249
$756$	−4.98398	−0.181266
$757$	3.15362	0.114620	0.0573102	−	0.998356i	$-0.481748\pi$
$757$	3.15362	0.114620	0.0573102	+	0.998356i	$0.481748\pi$
$758$	3.03073	0.110081
$759$	−3.20010	−0.116156
$760$	0	0
$761$	18.1905	0.659407	0.329703	−	0.944085i	$-0.393051\pi$
$761$	18.1905	0.659407	0.329703	+	0.944085i	$0.393051\pi$
$762$	6.93440	0.251207
$763$	12.9893	0.470244
$764$	−1.38734	−0.0501921
$765$	2.64624	0.0956750
$766$	13.4997	0.487766
$767$	−56.5999	−2.04370
$768$	1.13526	0.0409652
$769$	16.5803	0.597902	0.298951	−	0.954269i	$-0.403363\pi$
$769$	16.5803	0.597902	0.298951	+	0.954269i	$0.403363\pi$
$770$	1.03761	0.0373928
$771$	−29.2778	−1.05441
$772$	−6.04410	−0.217532
$773$	50.6835	1.82296	0.911480	−	0.411344i	$-0.134941\pi$
$773$	50.6835	1.82296	0.911480	+	0.411344i	$0.134941\pi$
$774$	6.50055	0.233657
$775$	−15.2648	−0.548327
$776$	16.4195	0.589427
$777$	−4.31439	−0.154778
$778$	2.24410	0.0804548
$779$	0	0
$780$	−7.51624	−0.269125
$781$	3.01645	0.107937
$782$	3.91488	0.139996
$783$	23.1651	0.827855
$784$	−6.13164	−0.218987
$785$	−17.1526	−0.612203
$786$	−3.05594	−0.109002
$787$	−11.1466	−0.397332	−0.198666	−	0.980067i	$-0.563661\pi$
$787$	−11.1466	−0.397332	−0.198666	+	0.980067i	$0.563661\pi$
$788$	−10.0416	−0.357716
$789$	6.03130	0.214720
$790$	−9.19658	−0.327200
$791$	11.3050	0.401959
$792$	1.71118	0.0608042
$793$	2.02096	0.0717664
$794$	−8.18711	−0.290550
$795$	−1.16927	−0.0414698
$796$	−14.8759	−0.527263
$797$	−13.4427	−0.476163	−0.238082	−	0.971245i	$-0.576519\pi$
$797$	−13.4427	−0.476163	−0.238082	+	0.971245i	$0.576519\pi$
$798$	0	0
$799$	−15.5330	−0.549517
$800$	3.76016	0.132942
$801$	20.5424	0.725831
$802$	10.5442	0.372330
$803$	11.6220	0.410130
$804$	−6.26128	−0.220818
$805$	2.92483	0.103087
$806$	−24.1383	−0.850235
$807$	4.48239	0.157788
$808$	9.65673	0.339722
$809$	−5.35315	−0.188207	−0.0941033	−	0.995562i	$-0.529998\pi$
$809$	−5.35315	−0.188207	−0.0941033	+	0.995562i	$0.529998\pi$
$810$	−1.04479	−0.0367100
$811$	22.7548	0.799030	0.399515	−	0.916727i	$-0.369179\pi$
$811$	22.7548	0.799030	0.399515	+	0.916727i	$0.369179\pi$
$812$	−4.03609	−0.141639
$813$	−35.4816	−1.24439
$814$	4.07824	0.142942
$815$	1.99875	0.0700133
$816$	1.57669	0.0551952
$817$	0	0
$818$	13.3130	0.465479
$819$	−9.48135	−0.331305
$820$	3.75195	0.131024
$821$	−11.6953	−0.408167	−0.204084	−	0.978953i	$-0.565421\pi$
$821$	−11.6953	−0.408167	−0.204084	+	0.978953i	$0.565421\pi$
$822$	−21.6996	−0.756860
$823$	44.9378	1.56643	0.783216	−	0.621749i	$-0.213578\pi$
$823$	44.9378	1.56643	0.783216	+	0.621749i	$0.213578\pi$
$824$	−4.19494	−0.146138
$825$	−4.26877	−0.148619
$826$	8.87041	0.308641
$827$	45.7453	1.59072	0.795361	−	0.606137i	$-0.207281\pi$
$827$	45.7453	1.59072	0.795361	+	0.606137i	$0.207281\pi$
$828$	4.82352	0.167629
$829$	31.1103	1.08051	0.540253	−	0.841502i	$-0.318328\pi$
$829$	31.1103	1.08051	0.540253	+	0.841502i	$0.318328\pi$
$830$	1.40245	0.0486797
$831$	−7.20440	−0.249918
$832$	5.94597	0.206140
$833$	−8.51583	−0.295056
$834$	−19.7701	−0.684582
$835$	2.69128	0.0931357
$836$	0	0
$837$	−21.7125	−0.750493
$838$	−24.5749	−0.848925
$839$	−53.5250	−1.84789	−0.923945	−	0.382526i	$-0.875054\pi$
$839$	−53.5250	−1.84789	−0.923945	+	0.382526i	$0.875054\pi$
$840$	1.17796	0.0406433
$841$	−10.2406	−0.353124
$842$	−37.0808	−1.27789
$843$	−10.5003	−0.361649
$844$	7.02101	0.241673
$845$	−24.8914	−0.856289
$846$	−19.1382	−0.657984
$847$	0.931861	0.0320191
$848$	0.924992	0.0317643
$849$	30.4874	1.04633
$850$	5.22225	0.179122
$851$	11.4958	0.394072
$852$	3.42446	0.117320
$853$	−20.3401	−0.696433	−0.348216	−	0.937414i	$-0.613213\pi$
$853$	−20.3401	−0.696433	−0.348216	+	0.937414i	$0.613213\pi$
$854$	−0.316728	−0.0108382
$855$	0	0
$856$	−10.7839	−0.368587
$857$	56.4620	1.92870	0.964352	−	0.264623i	$-0.0852476\pi$
$857$	56.4620	1.92870	0.964352	+	0.264623i	$0.0852476\pi$
$858$	−6.75023	−0.230449
$859$	−26.0628	−0.889252	−0.444626	−	0.895716i	$-0.646663\pi$
$859$	−26.0628	−0.889252	−0.444626	+	0.895716i	$0.646663\pi$
$860$	−4.22996	−0.144240
$861$	−3.56469	−0.121484
$862$	1.02908	0.0350508
$863$	−50.1301	−1.70645	−0.853224	−	0.521545i	$-0.825356\pi$
$863$	−50.1301	−1.70645	−0.853224	+	0.521545i	$0.825356\pi$
$864$	5.34842	0.181957
$865$	11.4137	0.388078
$866$	−6.26952	−0.213047
$867$	−17.1097	−0.581075
$868$	3.78299	0.128403
$869$	−8.25932	−0.280178
$870$	−5.47504	−0.185621
$871$	−32.7937	−1.11117
$872$	−13.9391	−0.472037
$873$	28.0968	0.950934
$874$	0	0
$875$	9.08961	0.307285
$876$	13.1940	0.445782
$877$	34.6996	1.17172	0.585861	−	0.810412i	$-0.300757\pi$
$877$	34.6996	1.17172	0.585861	+	0.810412i	$0.300757\pi$
$878$	−5.41464	−0.182735
$879$	8.84536	0.298346
$880$	−1.11348	−0.0375354
$881$	23.5494	0.793400	0.396700	−	0.917948i	$-0.370155\pi$
$881$	23.5494	0.793400	0.396700	+	0.917948i	$0.370155\pi$
$882$	−10.4923	−0.353296
$883$	51.6608	1.73852	0.869262	−	0.494352i	$-0.164595\pi$
$883$	51.6608	1.73852	0.869262	+	0.494352i	$0.164595\pi$
$884$	8.25798	0.277746
$885$	12.0329	0.404482
$886$	−1.46362	−0.0491713
$887$	−8.02954	−0.269606	−0.134803	−	0.990872i	$-0.543040\pi$
$887$	−8.02954	−0.269606	−0.134803	+	0.990872i	$0.543040\pi$
$888$	4.62986	0.155368
$889$	−5.69199	−0.190903
$890$	−13.3671	−0.448066
$891$	−0.938307	−0.0314345
$892$	−3.07501	−0.102959
$893$	0	0
$894$	11.3355	0.379117
$895$	20.5487	0.686867
$896$	−0.931861	−0.0311313
$897$	−19.0277	−0.635317
$898$	32.6981	1.09115
$899$	−17.5830	−0.586426
$900$	6.43433	0.214478
$901$	1.28466	0.0427983
$902$	3.36957	0.112195
$903$	4.01884	0.133738
$904$	−12.1316	−0.403491
$905$	18.5842	0.617759
$906$	−4.90955	−0.163109
$907$	37.7029	1.25190	0.625952	−	0.779862i	$-0.284711\pi$
$907$	37.7029	1.25190	0.625952	+	0.779862i	$0.284711\pi$
$908$	−12.0169	−0.398795
$909$	16.5244	0.548080
$910$	6.16959	0.204520
$911$	−32.8241	−1.08751	−0.543755	−	0.839244i	$-0.682998\pi$
$911$	−32.8241	−1.08751	−0.543755	+	0.839244i	$0.682998\pi$
$912$	0	0
$913$	1.25952	0.0416840
$914$	−17.0277	−0.563227
$915$	−0.429648	−0.0142037
$916$	15.0971	0.498823
$917$	2.50842	0.0828352
$918$	7.42807	0.245163
$919$	−45.9052	−1.51427	−0.757136	−	0.653257i	$-0.773402\pi$
$919$	−45.9052	−1.51427	−0.757136	+	0.653257i	$0.773402\pi$
$920$	−3.13870	−0.103480
$921$	−14.1342	−0.465736
$922$	−13.9254	−0.458607
$923$	17.9358	0.590362
$924$	1.05790	0.0348025
$925$	15.3348	0.504206
$926$	−25.0656	−0.823707
$927$	−7.17831	−0.235767
$928$	4.33121	0.142179
$929$	58.2254	1.91031	0.955157	−	0.296098i	$-0.0956856\pi$
$929$	58.2254	1.91031	0.955157	+	0.296098i	$0.0956856\pi$
$930$	5.13170	0.168275
$931$	0	0
$932$	−25.4941	−0.835086
$933$	22.1857	0.726327
$934$	−1.50756	−0.0493289
$935$	−1.54644	−0.0505740
$936$	10.1746	0.332569
$937$	−22.5676	−0.737251	−0.368625	−	0.929578i	$-0.620171\pi$
$937$	−22.5676	−0.737251	−0.368625	+	0.929578i	$0.620171\pi$
$938$	5.13947	0.167810
$939$	−9.17749	−0.299496
$940$	12.4533	0.406183
$941$	−2.58111	−0.0841418	−0.0420709	−	0.999115i	$-0.513396\pi$
$941$	−2.58111	−0.0841418	−0.0420709	+	0.999115i	$0.513396\pi$
$942$	−17.4881	−0.569795
$943$	9.49824	0.309305
$944$	−9.51903	−0.309818
$945$	5.54956	0.180527
$946$	−3.79886	−0.123512
$947$	46.3665	1.50671	0.753354	−	0.657615i	$-0.228434\pi$
$947$	46.3665	1.50671	0.753354	+	0.657615i	$0.228434\pi$
$948$	−9.37649	−0.304534
$949$	69.1038	2.24320
$950$	0	0
$951$	−3.10418	−0.100660
$952$	−1.29420	−0.0419453
$953$	−11.4226	−0.370014	−0.185007	−	0.982737i	$-0.559231\pi$
$953$	−11.4226	−0.370014	−0.185007	+	0.982737i	$0.559231\pi$
$954$	1.58283	0.0512460
$955$	1.54477	0.0499876
$956$	11.1287	0.359926
$957$	−4.91706	−0.158946
$958$	19.6977	0.636405
$959$	17.8117	0.575171
$960$	−1.26409	−0.0407983
$961$	−14.5196	−0.468375
$962$	24.2491	0.781822
$963$	−18.4533	−0.594649
$964$	−23.1531	−0.745711
$965$	6.72998	0.216646
$966$	2.98205	0.0959458
$967$	16.3979	0.527321	0.263661	−	0.964615i	$-0.415070\pi$
$967$	16.3979	0.527321	0.263661	+	0.964615i	$0.415070\pi$
$968$	−1.00000	−0.0321412
$969$	0	0
$970$	−18.2828	−0.587026
$971$	41.1271	1.31983	0.659915	−	0.751340i	$-0.270592\pi$
$971$	41.1271	1.31983	0.659915	+	0.751340i	$0.270592\pi$
$972$	14.9800	0.480485
$973$	16.2280	0.520244
$974$	23.5836	0.755668
$975$	−25.3820	−0.812874
$976$	0.339887	0.0108795
$977$	−0.0876286	−0.00280349	−0.00140174	−	0.999999i	$-0.500446\pi$
$977$	−0.0876286	−0.00280349	−0.00140174	+	0.999999i	$0.500446\pi$
$978$	2.03785	0.0651634
$979$	−12.0048	−0.383675
$980$	6.82745	0.218095
$981$	−23.8523	−0.761546
$982$	35.2172	1.12383
$983$	15.3665	0.490117	0.245058	−	0.969508i	$-0.421193\pi$
$983$	15.3665	0.490117	0.245058	+	0.969508i	$0.421193\pi$
$984$	3.82535	0.121948
$985$	11.1811	0.356258
$986$	6.01534	0.191567
$987$	−11.8318	−0.376610
$988$	0	0
$989$	−10.7083	−0.340505
$990$	−1.90537	−0.0605565
$991$	17.6223	0.559790	0.279895	−	0.960031i	$-0.409700\pi$
$991$	17.6223	0.559790	0.279895	+	0.960031i	$0.409700\pi$
$992$	−4.05960	−0.128893
$993$	−26.7328	−0.848338
$994$	−2.81091	−0.0891568
$995$	16.5640	0.525115
$996$	1.42988	0.0453076
$997$	−46.5580	−1.47451	−0.737254	−	0.675616i	$-0.763878\pi$
$997$	−46.5580	−1.47451	−0.737254	+	0.675616i	$0.763878\pi$
$998$	38.6900	1.22471
$999$	21.8121	0.690105

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7942.2.a.bm.1.6	✓	8
19.18	odd	2		7942.2.a.br.1.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7942.2.a.bm.1.6	✓	8	1.1	even	1	trivial
7942.2.a.br.1.3	yes	8	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:	\( N \)	\(=\)	\( 7942 = 2 \cdot 11 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7942.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.13526 q^{3} +1.00000 q^{4} -1.11348 q^{5} -1.13526 q^{6} +0.931861 q^{7} -1.00000 q^{8} -1.71118 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.13526 q^{3} +1.00000 q^{4} -1.11348 q^{5} -1.13526 q^{6} +0.931861 q^{7} -1.00000 q^{8} -1.71118 q^{9} +1.11348 q^{10} +1.00000 q^{11} +1.13526 q^{12} +5.94597 q^{13} -0.931861 q^{14} -1.26409 q^{15} +1.00000 q^{16} +1.38883 q^{17} +1.71118 q^{18} -1.11348 q^{20} +1.05790 q^{21} -1.00000 q^{22} -2.81882 q^{23} -1.13526 q^{24} -3.76016 q^{25} -5.94597 q^{26} -5.34842 q^{27} +0.931861 q^{28} -4.33121 q^{29} +1.26409 q^{30} +4.05960 q^{31} -1.00000 q^{32} +1.13526 q^{33} -1.38883 q^{34} -1.03761 q^{35} -1.71118 q^{36} -4.07824 q^{37} +6.75023 q^{39} +1.11348 q^{40} -3.36957 q^{41} -1.05790 q^{42} +3.79886 q^{43} +1.00000 q^{44} +1.90537 q^{45} +2.81882 q^{46} -11.1842 q^{47} +1.13526 q^{48} -6.13164 q^{49} +3.76016 q^{50} +1.57669 q^{51} +5.94597 q^{52} +0.924992 q^{53} +5.34842 q^{54} -1.11348 q^{55} -0.931861 q^{56} +4.33121 q^{58} -9.51903 q^{59} -1.26409 q^{60} +0.339887 q^{61} -4.05960 q^{62} -1.59458 q^{63} +1.00000 q^{64} -6.62072 q^{65} -1.13526 q^{66} -5.51528 q^{67} +1.38883 q^{68} -3.20010 q^{69} +1.03761 q^{70} +3.01645 q^{71} +1.71118 q^{72} +11.6220 q^{73} +4.07824 q^{74} -4.26877 q^{75} +0.931861 q^{77} -6.75023 q^{78} -8.25932 q^{79} -1.11348 q^{80} -0.938307 q^{81} +3.36957 q^{82} +1.25952 q^{83} +1.05790 q^{84} -1.54644 q^{85} -3.79886 q^{86} -4.91706 q^{87} -1.00000 q^{88} -12.0048 q^{89} -1.90537 q^{90} +5.54082 q^{91} -2.81882 q^{92} +4.60871 q^{93} +11.1842 q^{94} -1.13526 q^{96} -16.4195 q^{97} +6.13164 q^{98} -1.71118 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} - 4 q^{3} + 8 q^{4} + q^{5} + 4 q^{6} + 4 q^{7} - 8 q^{8} + 6 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 - 4 * q^3 + 8 * q^4 + q^5 + 4 * q^6 + 4 * q^7 - 8 * q^8 + 6 * q^9	\( 8 q - 8 q^{2} - 4 q^{3} + 8 q^{4} + q^{5} + 4 q^{6} + 4 q^{7} - 8 q^{8} + 6 q^{9} - q^{10} + 8 q^{11} - 4 q^{12} - 12 q^{13} - 4 q^{14} + 9 q^{15} + 8 q^{16} + 7 q^{17} - 6 q^{18} + q^{20} - 13 q^{21} - 8 q^{22} - 6 q^{23} + 4 q^{24} + 5 q^{25} + 12 q^{26} - 22 q^{27} + 4 q^{28} + q^{29} - 9 q^{30} - 8 q^{31} - 8 q^{32} - 4 q^{33} - 7 q^{34} + 5 q^{35} + 6 q^{36} - 12 q^{37} + 10 q^{39} - q^{40} - 18 q^{41} + 13 q^{42} - 4 q^{43} + 8 q^{44} - 19 q^{45} + 6 q^{46} + 13 q^{47} - 4 q^{48} + 4 q^{49} - 5 q^{50} - 14 q^{51} - 12 q^{52} + 17 q^{53} + 22 q^{54} + q^{55} - 4 q^{56} - q^{58} - 26 q^{59} + 9 q^{60} - 7 q^{61} + 8 q^{62} + 13 q^{63} + 8 q^{64} - 36 q^{65} + 4 q^{66} - 6 q^{67} + 7 q^{68} - 19 q^{69} - 5 q^{70} + 3 q^{71} - 6 q^{72} + 5 q^{73} + 12 q^{74} - 30 q^{75} + 4 q^{77} - 10 q^{78} - 16 q^{79} + q^{80} + 8 q^{81} + 18 q^{82} - 21 q^{83} - 13 q^{84} - 10 q^{85} + 4 q^{86} - 29 q^{87} - 8 q^{88} - 16 q^{89} + 19 q^{90} - 31 q^{91} - 6 q^{92} + 20 q^{93} - 13 q^{94} + 4 q^{96} + 15 q^{97} - 4 q^{98} + 6 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 - 4 * q^3 + 8 * q^4 + q^5 + 4 * q^6 + 4 * q^7 - 8 * q^8 + 6 * q^9 - q^10 + 8 * q^11 - 4 * q^12 - 12 * q^13 - 4 * q^14 + 9 * q^15 + 8 * q^16 + 7 * q^17 - 6 * q^18 + q^20 - 13 * q^21 - 8 * q^22 - 6 * q^23 + 4 * q^24 + 5 * q^25 + 12 * q^26 - 22 * q^27 + 4 * q^28 + q^29 - 9 * q^30 - 8 * q^31 - 8 * q^32 - 4 * q^33 - 7 * q^34 + 5 * q^35 + 6 * q^36 - 12 * q^37 + 10 * q^39 - q^40 - 18 * q^41 + 13 * q^42 - 4 * q^43 + 8 * q^44 - 19 * q^45 + 6 * q^46 + 13 * q^47 - 4 * q^48 + 4 * q^49 - 5 * q^50 - 14 * q^51 - 12 * q^52 + 17 * q^53 + 22 * q^54 + q^55 - 4 * q^56 - q^58 - 26 * q^59 + 9 * q^60 - 7 * q^61 + 8 * q^62 + 13 * q^63 + 8 * q^64 - 36 * q^65 + 4 * q^66 - 6 * q^67 + 7 * q^68 - 19 * q^69 - 5 * q^70 + 3 * q^71 - 6 * q^72 + 5 * q^73 + 12 * q^74 - 30 * q^75 + 4 * q^77 - 10 * q^78 - 16 * q^79 + q^80 + 8 * q^81 + 18 * q^82 - 21 * q^83 - 13 * q^84 - 10 * q^85 + 4 * q^86 - 29 * q^87 - 8 * q^88 - 16 * q^89 + 19 * q^90 - 31 * q^91 - 6 * q^92 + 20 * q^93 - 13 * q^94 + 4 * q^96 + 15 * q^97 - 4 * q^98 + 6 * q^99

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