LMFDB - Embedded newform 8034.2.a.t.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8034,2,Mod(1,8034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8034, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8034 = 2 \cdot 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8034.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:	$64.1518129839$
Analytic rank:	$0$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 4 x^{10} - 24 x^{9} + 88 x^{8} + 220 x^{7} - 637 x^{6} - 977 x^{5} + 1739 x^{4} + 1872 x^{3} + \cdots - 162 $ x^11 - 4x^10 - 24x^9 + 88x^8 + 220x^7 - 637x^6 - 977x^5 + 1739x^4 + 1872x^3 - 1494x^2 - 1161x - 162
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$3.71131$ of defining polynomial
Character	$\chi$	$=$	8034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.71131 q^{5} -1.00000 q^{6} +1.88167 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.71131 q^{5} -1.00000 q^{6} +1.88167 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.71131 q^{10} -0.931326 q^{11} +1.00000 q^{12} -1.00000 q^{13} -1.88167 q^{14} +3.71131 q^{15} +1.00000 q^{16} +0.978382 q^{17} -1.00000 q^{18} -4.18743 q^{19} +3.71131 q^{20} +1.88167 q^{21} +0.931326 q^{22} +3.17382 q^{23} -1.00000 q^{24} +8.77385 q^{25} +1.00000 q^{26} +1.00000 q^{27} +1.88167 q^{28} -7.70158 q^{29} -3.71131 q^{30} +0.646278 q^{31} -1.00000 q^{32} -0.931326 q^{33} -0.978382 q^{34} +6.98345 q^{35} +1.00000 q^{36} +0.528740 q^{37} +4.18743 q^{38} -1.00000 q^{39} -3.71131 q^{40} +9.05411 q^{41} -1.88167 q^{42} +9.80555 q^{43} -0.931326 q^{44} +3.71131 q^{45} -3.17382 q^{46} +5.18235 q^{47} +1.00000 q^{48} -3.45934 q^{49} -8.77385 q^{50} +0.978382 q^{51} -1.00000 q^{52} +1.64496 q^{53} -1.00000 q^{54} -3.45644 q^{55} -1.88167 q^{56} -4.18743 q^{57} +7.70158 q^{58} -10.0717 q^{59} +3.71131 q^{60} -8.72574 q^{61} -0.646278 q^{62} +1.88167 q^{63} +1.00000 q^{64} -3.71131 q^{65} +0.931326 q^{66} +6.40426 q^{67} +0.978382 q^{68} +3.17382 q^{69} -6.98345 q^{70} -4.44981 q^{71} -1.00000 q^{72} +5.43840 q^{73} -0.528740 q^{74} +8.77385 q^{75} -4.18743 q^{76} -1.75244 q^{77} +1.00000 q^{78} +14.1564 q^{79} +3.71131 q^{80} +1.00000 q^{81} -9.05411 q^{82} -0.0537224 q^{83} +1.88167 q^{84} +3.63108 q^{85} -9.80555 q^{86} -7.70158 q^{87} +0.931326 q^{88} +1.73023 q^{89} -3.71131 q^{90} -1.88167 q^{91} +3.17382 q^{92} +0.646278 q^{93} -5.18235 q^{94} -15.5409 q^{95} -1.00000 q^{96} +9.80952 q^{97} +3.45934 q^{98} -0.931326 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 11 q^{2} + 11 q^{3} + 11 q^{4} + 4 q^{5} - 11 q^{6} + 4 q^{7} - 11 q^{8} + 11 q^{9}+O(q^{10}) $ 11 * q - 11 * q^2 + 11 * q^3 + 11 * q^4 + 4 * q^5 - 11 * q^6 + 4 * q^7 - 11 * q^8 + 11 * q^9	\( 11 q - 11 q^{2} + 11 q^{3} + 11 q^{4} + 4 q^{5} - 11 q^{6} + 4 q^{7} - 11 q^{8} + 11 q^{9} - 4 q^{10} + 5 q^{11} + 11 q^{12} - 11 q^{13} - 4 q^{14} + 4 q^{15} + 11 q^{16} + 8 q^{17} - 11 q^{18} - 2 q^{19} + 4 q^{20} + 4 q^{21} - 5 q^{22} + 3 q^{23} - 11 q^{24} + 9 q^{25} + 11 q^{26} + 11 q^{27} + 4 q^{28} + 7 q^{29} - 4 q^{30} + 20 q^{31} - 11 q^{32} + 5 q^{33} - 8 q^{34} + 9 q^{35} + 11 q^{36} + q^{37} + 2 q^{38} - 11 q^{39} - 4 q^{40} + 37 q^{41} - 4 q^{42} - 16 q^{43} + 5 q^{44} + 4 q^{45} - 3 q^{46} + 28 q^{47} + 11 q^{48} + 17 q^{49} - 9 q^{50} + 8 q^{51} - 11 q^{52} - 5 q^{53} - 11 q^{54} - 28 q^{55} - 4 q^{56} - 2 q^{57} - 7 q^{58} + 31 q^{59} + 4 q^{60} + 8 q^{61} - 20 q^{62} + 4 q^{63} + 11 q^{64} - 4 q^{65} - 5 q^{66} - 22 q^{67} + 8 q^{68} + 3 q^{69} - 9 q^{70} + 42 q^{71} - 11 q^{72} - 4 q^{73} - q^{74} + 9 q^{75} - 2 q^{76} - 21 q^{77} + 11 q^{78} + 33 q^{79} + 4 q^{80} + 11 q^{81} - 37 q^{82} + 18 q^{83} + 4 q^{84} + 17 q^{85} + 16 q^{86} + 7 q^{87} - 5 q^{88} + 67 q^{89} - 4 q^{90} - 4 q^{91} + 3 q^{92} + 20 q^{93} - 28 q^{94} + 32 q^{95} - 11 q^{96} - 15 q^{97} - 17 q^{98} + 5 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 + 11 * q^3 + 11 * q^4 + 4 * q^5 - 11 * q^6 + 4 * q^7 - 11 * q^8 + 11 * q^9 - 4 * q^10 + 5 * q^11 + 11 * q^12 - 11 * q^13 - 4 * q^14 + 4 * q^15 + 11 * q^16 + 8 * q^17 - 11 * q^18 - 2 * q^19 + 4 * q^20 + 4 * q^21 - 5 * q^22 + 3 * q^23 - 11 * q^24 + 9 * q^25 + 11 * q^26 + 11 * q^27 + 4 * q^28 + 7 * q^29 - 4 * q^30 + 20 * q^31 - 11 * q^32 + 5 * q^33 - 8 * q^34 + 9 * q^35 + 11 * q^36 + q^37 + 2 * q^38 - 11 * q^39 - 4 * q^40 + 37 * q^41 - 4 * q^42 - 16 * q^43 + 5 * q^44 + 4 * q^45 - 3 * q^46 + 28 * q^47 + 11 * q^48 + 17 * q^49 - 9 * q^50 + 8 * q^51 - 11 * q^52 - 5 * q^53 - 11 * q^54 - 28 * q^55 - 4 * q^56 - 2 * q^57 - 7 * q^58 + 31 * q^59 + 4 * q^60 + 8 * q^61 - 20 * q^62 + 4 * q^63 + 11 * q^64 - 4 * q^65 - 5 * q^66 - 22 * q^67 + 8 * q^68 + 3 * q^69 - 9 * q^70 + 42 * q^71 - 11 * q^72 - 4 * q^73 - q^74 + 9 * q^75 - 2 * q^76 - 21 * q^77 + 11 * q^78 + 33 * q^79 + 4 * q^80 + 11 * q^81 - 37 * q^82 + 18 * q^83 + 4 * q^84 + 17 * q^85 + 16 * q^86 + 7 * q^87 - 5 * q^88 + 67 * q^89 - 4 * q^90 - 4 * q^91 + 3 * q^92 + 20 * q^93 - 28 * q^94 + 32 * q^95 - 11 * q^96 - 15 * q^97 - 17 * q^98 + 5 * 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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	3.71131	1.65975	0.829875	−	0.557949i	$-0.188412\pi$
$5$	3.71131	1.65975	0.829875	+	0.557949i	$0.188412\pi$
$6$	−1.00000	−0.408248
$7$	1.88167	0.711203	0.355601	−	0.934638i	$-0.384276\pi$
$7$	1.88167	0.711203	0.355601	+	0.934638i	$0.384276\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−3.71131	−1.17362
$11$	−0.931326	−0.280805	−0.140403	−	0.990094i	$-0.544840\pi$
$11$	−0.931326	−0.280805	−0.140403	+	0.990094i	$0.544840\pi$
$12$	1.00000	0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−1.88167	−0.502896
$15$	3.71131	0.958257
$16$	1.00000	0.250000
$17$	0.978382	0.237292	0.118646	−	0.992937i	$-0.462145\pi$
$17$	0.978382	0.237292	0.118646	+	0.992937i	$0.462145\pi$
$18$	−1.00000	−0.235702
$19$	−4.18743	−0.960663	−0.480331	−	0.877087i	$-0.659484\pi$
$19$	−4.18743	−0.960663	−0.480331	+	0.877087i	$0.659484\pi$
$20$	3.71131	0.829875
$21$	1.88167	0.410613
$22$	0.931326	0.198559
$23$	3.17382	0.661787	0.330893	−	0.943668i	$-0.392650\pi$
$23$	3.17382	0.661787	0.330893	+	0.943668i	$0.392650\pi$
$24$	−1.00000	−0.204124
$25$	8.77385	1.75477
$26$	1.00000	0.196116
$27$	1.00000	0.192450
$28$	1.88167	0.355601
$29$	−7.70158	−1.43015	−0.715074	−	0.699049i	$-0.753607\pi$
$29$	−7.70158	−1.43015	−0.715074	+	0.699049i	$0.753607\pi$
$30$	−3.71131	−0.677590
$31$	0.646278	0.116075	0.0580375	−	0.998314i	$-0.481516\pi$
$31$	0.646278	0.116075	0.0580375	+	0.998314i	$0.481516\pi$
$32$	−1.00000	−0.176777
$33$	−0.931326	−0.162123
$34$	−0.978382	−0.167791
$35$	6.98345	1.18042
$36$	1.00000	0.166667
$37$	0.528740	0.0869243	0.0434621	−	0.999055i	$-0.486161\pi$
$37$	0.528740	0.0869243	0.0434621	+	0.999055i	$0.486161\pi$
$38$	4.18743	0.679291
$39$	−1.00000	−0.160128
$40$	−3.71131	−0.586810
$41$	9.05411	1.41401	0.707007	−	0.707206i	$-0.250045\pi$
$41$	9.05411	1.41401	0.707007	+	0.707206i	$0.250045\pi$
$42$	−1.88167	−0.290347
$43$	9.80555	1.49533	0.747666	−	0.664075i	$-0.231174\pi$
$43$	9.80555	1.49533	0.747666	+	0.664075i	$0.231174\pi$
$44$	−0.931326	−0.140403
$45$	3.71131	0.553250
$46$	−3.17382	−0.467954
$47$	5.18235	0.755923	0.377962	−	0.925821i	$-0.376625\pi$
$47$	5.18235	0.755923	0.377962	+	0.925821i	$0.376625\pi$
$48$	1.00000	0.144338
$49$	−3.45934	−0.494191
$50$	−8.77385	−1.24081
$51$	0.978382	0.137001
$52$	−1.00000	−0.138675
$53$	1.64496	0.225952	0.112976	−	0.993598i	$-0.463962\pi$
$53$	1.64496	0.225952	0.112976	+	0.993598i	$0.463962\pi$
$54$	−1.00000	−0.136083
$55$	−3.45644	−0.466067
$56$	−1.88167	−0.251448
$57$	−4.18743	−0.554639
$58$	7.70158	1.01127
$59$	−10.0717	−1.31122	−0.655612	−	0.755098i	$-0.727589\pi$
$59$	−10.0717	−1.31122	−0.655612	+	0.755098i	$0.727589\pi$
$60$	3.71131	0.479129
$61$	−8.72574	−1.11722	−0.558608	−	0.829432i	$-0.688664\pi$
$61$	−8.72574	−1.11722	−0.558608	+	0.829432i	$0.688664\pi$
$62$	−0.646278	−0.0820774
$63$	1.88167	0.237068
$64$	1.00000	0.125000
$65$	−3.71131	−0.460332
$66$	0.931326	0.114638
$67$	6.40426	0.782405	0.391203	−	0.920305i	$-0.372059\pi$
$67$	6.40426	0.782405	0.391203	+	0.920305i	$0.372059\pi$
$68$	0.978382	0.118646
$69$	3.17382	0.382083
$70$	−6.98345	−0.834682
$71$	−4.44981	−0.528095	−0.264047	−	0.964510i	$-0.585058\pi$
$71$	−4.44981	−0.528095	−0.264047	+	0.964510i	$0.585058\pi$
$72$	−1.00000	−0.117851
$73$	5.43840	0.636516	0.318258	−	0.948004i	$-0.396902\pi$
$73$	5.43840	0.636516	0.318258	+	0.948004i	$0.396902\pi$
$74$	−0.528740	−0.0614647
$75$	8.77385	1.01312
$76$	−4.18743	−0.480331
$77$	−1.75244	−0.199709
$78$	1.00000	0.113228
$79$	14.1564	1.59272	0.796362	−	0.604820i	$-0.206755\pi$
$79$	14.1564	1.59272	0.796362	+	0.604820i	$0.206755\pi$
$80$	3.71131	0.414938
$81$	1.00000	0.111111
$82$	−9.05411	−0.999859
$83$	−0.0537224	−0.00589680	−0.00294840	−	0.999996i	$-0.500939\pi$
$83$	−0.0537224	−0.00589680	−0.00294840	+	0.999996i	$0.500939\pi$
$84$	1.88167	0.205306
$85$	3.63108	0.393846
$86$	−9.80555	−1.05736
$87$	−7.70158	−0.825697
$88$	0.931326	0.0992797
$89$	1.73023	0.183404	0.0917022	−	0.995786i	$-0.470769\pi$
$89$	1.73023	0.183404	0.0917022	+	0.995786i	$0.470769\pi$
$90$	−3.71131	−0.391207
$91$	−1.88167	−0.197252
$92$	3.17382	0.330893
$93$	0.646278	0.0670159
$94$	−5.18235	−0.534518
$95$	−15.5409	−1.59446
$96$	−1.00000	−0.102062
$97$	9.80952	0.996006	0.498003	−	0.867175i	$-0.334067\pi$
$97$	9.80952	0.996006	0.498003	+	0.867175i	$0.334067\pi$
$98$	3.45934	0.349446
$99$	−0.931326	−0.0936018
$100$	8.77385	0.877385
$101$	14.9081	1.48341	0.741704	−	0.670727i	$-0.234018\pi$
$101$	14.9081	1.48341	0.741704	+	0.670727i	$0.234018\pi$
$102$	−0.978382	−0.0968742
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	1.00000	0.0980581
$105$	6.98345	0.681515
$106$	−1.64496	−0.159772
$107$	17.1405	1.65703	0.828515	−	0.559967i	$-0.189186\pi$
$107$	17.1405	1.65703	0.828515	+	0.559967i	$0.189186\pi$
$108$	1.00000	0.0962250
$109$	16.9529	1.62379	0.811895	−	0.583803i	$-0.198436\pi$
$109$	16.9529	1.62379	0.811895	+	0.583803i	$0.198436\pi$
$110$	3.45644	0.329559
$111$	0.528740	0.0501857
$112$	1.88167	0.177801
$113$	6.21794	0.584934	0.292467	−	0.956276i	$-0.405524\pi$
$113$	6.21794	0.584934	0.292467	+	0.956276i	$0.405524\pi$
$114$	4.18743	0.392189
$115$	11.7790	1.09840
$116$	−7.70158	−0.715074
$117$	−1.00000	−0.0924500
$118$	10.0717	0.927175
$119$	1.84099	0.168763
$120$	−3.71131	−0.338795
$121$	−10.1326	−0.921148
$122$	8.72574	0.789991
$123$	9.05411	0.816382
$124$	0.646278	0.0580375
$125$	14.0059	1.25273
$126$	−1.88167	−0.167632
$127$	12.2050	1.08302	0.541508	−	0.840696i	$-0.317854\pi$
$127$	12.2050	1.08302	0.541508	+	0.840696i	$0.317854\pi$
$128$	−1.00000	−0.0883883
$129$	9.80555	0.863330
$130$	3.71131	0.325504
$131$	−2.18190	−0.190634	−0.0953169	−	0.995447i	$-0.530386\pi$
$131$	−2.18190	−0.190634	−0.0953169	+	0.995447i	$0.530386\pi$
$132$	−0.931326	−0.0810615
$133$	−7.87934	−0.683226
$134$	−6.40426	−0.553244
$135$	3.71131	0.319419
$136$	−0.978382	−0.0838956
$137$	−3.04683	−0.260309	−0.130154	−	0.991494i	$-0.541547\pi$
$137$	−3.04683	−0.260309	−0.130154	+	0.991494i	$0.541547\pi$
$138$	−3.17382	−0.270173
$139$	−16.4086	−1.39176	−0.695878	−	0.718160i	$-0.744985\pi$
$139$	−16.4086	−1.39176	−0.695878	+	0.718160i	$0.744985\pi$
$140$	6.98345	0.590209
$141$	5.18235	0.436433
$142$	4.44981	0.373419
$143$	0.931326	0.0778814
$144$	1.00000	0.0833333
$145$	−28.5830	−2.37369
$146$	−5.43840	−0.450085
$147$	−3.45934	−0.285321
$148$	0.528740	0.0434621
$149$	23.5210	1.92692	0.963460	−	0.267853i	$-0.0863143\pi$
$149$	23.5210	1.92692	0.963460	+	0.267853i	$0.0863143\pi$
$150$	−8.77385	−0.716382
$151$	−14.7433	−1.19979	−0.599895	−	0.800078i	$-0.704791\pi$
$151$	−14.7433	−1.19979	−0.599895	+	0.800078i	$0.704791\pi$
$152$	4.18743	0.339646
$153$	0.978382	0.0790975
$154$	1.75244	0.141216
$155$	2.39854	0.192655
$156$	−1.00000	−0.0800641
$157$	1.35050	0.107781	0.0538907	−	0.998547i	$-0.482838\pi$
$157$	1.35050	0.107781	0.0538907	+	0.998547i	$0.482838\pi$
$158$	−14.1564	−1.12623
$159$	1.64496	0.130454
$160$	−3.71131	−0.293405
$161$	5.97206	0.470665
$162$	−1.00000	−0.0785674
$163$	−12.3415	−0.966657	−0.483329	−	0.875439i	$-0.660572\pi$
$163$	−12.3415	−0.966657	−0.483329	+	0.875439i	$0.660572\pi$
$164$	9.05411	0.707007
$165$	−3.45644	−0.269084
$166$	0.0537224	0.00416967
$167$	16.0020	1.23827	0.619137	−	0.785283i	$-0.287483\pi$
$167$	16.0020	1.23827	0.619137	+	0.785283i	$0.287483\pi$
$168$	−1.88167	−0.145174
$169$	1.00000	0.0769231
$170$	−3.63108	−0.278491
$171$	−4.18743	−0.320221
$172$	9.80555	0.747666
$173$	−14.9827	−1.13911	−0.569556	−	0.821953i	$-0.692885\pi$
$173$	−14.9827	−1.13911	−0.569556	+	0.821953i	$0.692885\pi$
$174$	7.70158	0.583856
$175$	16.5094	1.24800
$176$	−0.931326	−0.0702013
$177$	−10.0717	−0.757035
$178$	−1.73023	−0.129686
$179$	16.7055	1.24863	0.624314	−	0.781174i	$-0.285379\pi$
$179$	16.7055	1.24863	0.624314	+	0.781174i	$0.285379\pi$
$180$	3.71131	0.276625
$181$	−12.1779	−0.905180	−0.452590	−	0.891719i	$-0.649500\pi$
$181$	−12.1779	−0.905180	−0.452590	+	0.891719i	$0.649500\pi$
$182$	1.88167	0.139478
$183$	−8.72574	−0.645025
$184$	−3.17382	−0.233977
$185$	1.96232	0.144273
$186$	−0.646278	−0.0473874
$187$	−0.911192	−0.0666330
$188$	5.18235	0.377962
$189$	1.88167	0.136871
$190$	15.5409	1.12745
$191$	10.2973	0.745089	0.372544	−	0.928014i	$-0.378485\pi$
$191$	10.2973	0.745089	0.372544	+	0.928014i	$0.378485\pi$
$192$	1.00000	0.0721688
$193$	12.9274	0.930537	0.465269	−	0.885170i	$-0.345958\pi$
$193$	12.9274	0.930537	0.465269	+	0.885170i	$0.345958\pi$
$194$	−9.80952	−0.704282
$195$	−3.71131	−0.265773
$196$	−3.45934	−0.247095
$197$	10.7818	0.768168	0.384084	−	0.923298i	$-0.374517\pi$
$197$	10.7818	0.768168	0.384084	+	0.923298i	$0.374517\pi$
$198$	0.931326	0.0661864
$199$	4.92857	0.349377	0.174689	−	0.984624i	$-0.444108\pi$
$199$	4.92857	0.349377	0.174689	+	0.984624i	$0.444108\pi$
$200$	−8.77385	−0.620405
$201$	6.40426	0.451722
$202$	−14.9081	−1.04893
$203$	−14.4918	−1.01713
$204$	0.978382	0.0685004
$205$	33.6026	2.34691
$206$	1.00000	0.0696733
$207$	3.17382	0.220596
$208$	−1.00000	−0.0693375
$209$	3.89986	0.269759
$210$	−6.98345	−0.481904
$211$	14.6532	1.00877	0.504386	−	0.863479i	$-0.331719\pi$
$211$	14.6532	1.00877	0.504386	+	0.863479i	$0.331719\pi$
$212$	1.64496	0.112976
$213$	−4.44981	−0.304896
$214$	−17.1405	−1.17170
$215$	36.3915	2.48188
$216$	−1.00000	−0.0680414
$217$	1.21608	0.0825528
$218$	−16.9529	−1.14819
$219$	5.43840	0.367493
$220$	−3.45644	−0.233033
$221$	−0.978382	−0.0658131
$222$	−0.528740	−0.0354867
$223$	17.7404	1.18799	0.593993	−	0.804470i	$-0.297551\pi$
$223$	17.7404	1.18799	0.593993	+	0.804470i	$0.297551\pi$
$224$	−1.88167	−0.125724
$225$	8.77385	0.584923
$226$	−6.21794	−0.413611
$227$	13.7904	0.915302	0.457651	−	0.889132i	$-0.348691\pi$
$227$	13.7904	0.915302	0.457651	+	0.889132i	$0.348691\pi$
$228$	−4.18743	−0.277319
$229$	−18.2583	−1.20655	−0.603273	−	0.797535i	$-0.706137\pi$
$229$	−18.2583	−1.20655	−0.603273	+	0.797535i	$0.706137\pi$
$230$	−11.7790	−0.776687
$231$	−1.75244	−0.115302
$232$	7.70158	0.505634
$233$	−1.96381	−0.128653	−0.0643267	−	0.997929i	$-0.520490\pi$
$233$	−1.96381	−0.128653	−0.0643267	+	0.997929i	$0.520490\pi$
$234$	1.00000	0.0653720
$235$	19.2333	1.25464
$236$	−10.0717	−0.655612
$237$	14.1564	0.919560
$238$	−1.84099	−0.119333
$239$	−8.18873	−0.529685	−0.264843	−	0.964292i	$-0.585320\pi$
$239$	−8.18873	−0.529685	−0.264843	+	0.964292i	$0.585320\pi$
$240$	3.71131	0.239564
$241$	−14.0753	−0.906670	−0.453335	−	0.891340i	$-0.649766\pi$
$241$	−14.0753	−0.906670	−0.453335	+	0.891340i	$0.649766\pi$
$242$	10.1326	0.651350
$243$	1.00000	0.0641500
$244$	−8.72574	−0.558608
$245$	−12.8387	−0.820233
$246$	−9.05411	−0.577269
$247$	4.18743	0.266440
$248$	−0.646278	−0.0410387
$249$	−0.0537224	−0.00340452
$250$	−14.0059	−0.885814
$251$	−26.7651	−1.68940	−0.844700	−	0.535239i	$-0.820221\pi$
$251$	−26.7651	−1.68940	−0.844700	+	0.535239i	$0.820221\pi$
$252$	1.88167	0.118534
$253$	−2.95586	−0.185833
$254$	−12.2050	−0.765808
$255$	3.63108	0.227387
$256$	1.00000	0.0625000
$257$	11.1397	0.694878	0.347439	−	0.937703i	$-0.387051\pi$
$257$	11.1397	0.694878	0.347439	+	0.937703i	$0.387051\pi$
$258$	−9.80555	−0.610467
$259$	0.994911	0.0618208
$260$	−3.71131	−0.230166
$261$	−7.70158	−0.476716
$262$	2.18190	0.134798
$263$	8.73132	0.538396	0.269198	−	0.963085i	$-0.413241\pi$
$263$	8.73132	0.538396	0.269198	+	0.963085i	$0.413241\pi$
$264$	0.931326	0.0573191
$265$	6.10495	0.375024
$266$	7.87934	0.483113
$267$	1.73023	0.105889
$268$	6.40426	0.391203
$269$	−17.4596	−1.06453	−0.532264	−	0.846579i	$-0.678659\pi$
$269$	−17.4596	−1.06453	−0.532264	+	0.846579i	$0.678659\pi$
$270$	−3.71131	−0.225863
$271$	5.32841	0.323678	0.161839	−	0.986817i	$-0.448258\pi$
$271$	5.32841	0.323678	0.161839	+	0.986817i	$0.448258\pi$
$272$	0.978382	0.0593231
$273$	−1.88167	−0.113884
$274$	3.04683	0.184066
$275$	−8.17132	−0.492749
$276$	3.17382	0.191041
$277$	21.0101	1.26237	0.631186	−	0.775631i	$-0.282568\pi$
$277$	21.0101	1.26237	0.631186	+	0.775631i	$0.282568\pi$
$278$	16.4086	0.984121
$279$	0.646278	0.0386916
$280$	−6.98345	−0.417341
$281$	−20.3166	−1.21199	−0.605995	−	0.795469i	$-0.707225\pi$
$281$	−20.3166	−1.21199	−0.605995	+	0.795469i	$0.707225\pi$
$282$	−5.18235	−0.308604
$283$	−24.3194	−1.44564	−0.722819	−	0.691038i	$-0.757154\pi$
$283$	−24.3194	−1.44564	−0.722819	+	0.691038i	$0.757154\pi$
$284$	−4.44981	−0.264047
$285$	−15.5409	−0.920562
$286$	−0.931326	−0.0550705
$287$	17.0368	1.00565
$288$	−1.00000	−0.0589256
$289$	−16.0428	−0.943692
$290$	28.5830	1.67845
$291$	9.80952	0.575044
$292$	5.43840	0.318258
$293$	12.6449	0.738722	0.369361	−	0.929286i	$-0.379577\pi$
$293$	12.6449	0.738722	0.369361	+	0.929286i	$0.379577\pi$
$294$	3.45934	0.201753
$295$	−37.3792	−2.17630
$296$	−0.528740	−0.0307324
$297$	−0.931326	−0.0540410
$298$	−23.5210	−1.36254
$299$	−3.17382	−0.183547
$300$	8.77385	0.506559
$301$	18.4508	1.06348
$302$	14.7433	0.848380
$303$	14.9081	0.856446
$304$	−4.18743	−0.240166
$305$	−32.3840	−1.85430
$306$	−0.978382	−0.0559304
$307$	5.28965	0.301897	0.150948	−	0.988542i	$-0.451767\pi$
$307$	5.28965	0.301897	0.150948	+	0.988542i	$0.451767\pi$
$308$	−1.75244	−0.0998547
$309$	−1.00000	−0.0568880
$310$	−2.39854	−0.136228
$311$	−12.9610	−0.734951	−0.367476	−	0.930033i	$-0.619778\pi$
$311$	−12.9610	−0.734951	−0.367476	+	0.930033i	$0.619778\pi$
$312$	1.00000	0.0566139
$313$	11.7845	0.666102	0.333051	−	0.942909i	$-0.391922\pi$
$313$	11.7845	0.666102	0.333051	+	0.942909i	$0.391922\pi$
$314$	−1.35050	−0.0762130
$315$	6.98345	0.393473
$316$	14.1564	0.796362
$317$	−31.8044	−1.78632	−0.893158	−	0.449744i	$-0.851515\pi$
$317$	−31.8044	−1.78632	−0.893158	+	0.449744i	$0.851515\pi$
$318$	−1.64496	−0.0922446
$319$	7.17268	0.401593
$320$	3.71131	0.207469
$321$	17.1405	0.956687
$322$	−5.97206	−0.332810
$323$	−4.09691	−0.227958
$324$	1.00000	0.0555556
$325$	−8.77385	−0.486686
$326$	12.3415	0.683530
$327$	16.9529	0.937496
$328$	−9.05411	−0.499930
$329$	9.75144	0.537615
$330$	3.45644	0.190271
$331$	15.7206	0.864081	0.432040	−	0.901854i	$-0.357794\pi$
$331$	15.7206	0.864081	0.432040	+	0.901854i	$0.357794\pi$
$332$	−0.0537224	−0.00294840
$333$	0.528740	0.0289748
$334$	−16.0020	−0.875592
$335$	23.7682	1.29860
$336$	1.88167	0.102653
$337$	3.06433	0.166925	0.0834625	−	0.996511i	$-0.473402\pi$
$337$	3.06433	0.166925	0.0834625	+	0.996511i	$0.473402\pi$
$338$	−1.00000	−0.0543928
$339$	6.21794	0.337712
$340$	3.63108	0.196923
$341$	−0.601895	−0.0325945
$342$	4.18743	0.226430
$343$	−19.6810	−1.06267
$344$	−9.80555	−0.528680
$345$	11.7790	0.634162
$346$	14.9827	0.805473
$347$	7.63559	0.409900	0.204950	−	0.978772i	$-0.434297\pi$
$347$	7.63559	0.409900	0.204950	+	0.978772i	$0.434297\pi$
$348$	−7.70158	−0.412848
$349$	−29.8723	−1.59903	−0.799513	−	0.600648i	$-0.794909\pi$
$349$	−29.8723	−1.59903	−0.799513	+	0.600648i	$0.794909\pi$
$350$	−16.5094	−0.882467
$351$	−1.00000	−0.0533761
$352$	0.931326	0.0496398
$353$	−30.0555	−1.59969	−0.799847	−	0.600204i	$-0.795086\pi$
$353$	−30.0555	−1.59969	−0.799847	+	0.600204i	$0.795086\pi$
$354$	10.0717	0.535305
$355$	−16.5146	−0.876505
$356$	1.73023	0.0917022
$357$	1.84099	0.0974354
$358$	−16.7055	−0.882913
$359$	20.7629	1.09583	0.547913	−	0.836535i	$-0.315423\pi$
$359$	20.7629	1.09583	0.547913	+	0.836535i	$0.315423\pi$
$360$	−3.71131	−0.195603
$361$	−1.46542	−0.0771274
$362$	12.1779	0.640059
$363$	−10.1326	−0.531825
$364$	−1.88167	−0.0986260
$365$	20.1836	1.05646
$366$	8.72574	0.456102
$367$	−4.89582	−0.255560	−0.127780	−	0.991803i	$-0.540785\pi$
$367$	−4.89582	−0.255560	−0.127780	+	0.991803i	$0.540785\pi$
$368$	3.17382	0.165447
$369$	9.05411	0.471338
$370$	−1.96232	−0.102016
$371$	3.09526	0.160698
$372$	0.646278	0.0335080
$373$	−12.9373	−0.669867	−0.334934	−	0.942242i	$-0.608714\pi$
$373$	−12.9373	−0.669867	−0.334934	+	0.942242i	$0.608714\pi$
$374$	0.911192	0.0471166
$375$	14.0059	0.723264
$376$	−5.18235	−0.267259
$377$	7.70158	0.396652
$378$	−1.88167	−0.0967824
$379$	−27.7962	−1.42780	−0.713898	−	0.700249i	$-0.753072\pi$
$379$	−27.7962	−1.42780	−0.713898	+	0.700249i	$0.753072\pi$
$380$	−15.5409	−0.797230
$381$	12.2050	0.625280
$382$	−10.2973	−0.526857
$383$	−27.7407	−1.41748	−0.708742	−	0.705468i	$-0.750737\pi$
$383$	−27.7407	−1.41748	−0.708742	+	0.705468i	$0.750737\pi$
$384$	−1.00000	−0.0510310
$385$	−6.50387	−0.331468
$386$	−12.9274	−0.657989
$387$	9.80555	0.498444
$388$	9.80952	0.498003
$389$	−25.4153	−1.28860	−0.644302	−	0.764771i	$-0.722852\pi$
$389$	−25.4153	−1.28860	−0.644302	+	0.764771i	$0.722852\pi$
$390$	3.71131	0.187930
$391$	3.10521	0.157037
$392$	3.45934	0.174723
$393$	−2.18190	−0.110062
$394$	−10.7818	−0.543177
$395$	52.5390	2.64352
$396$	−0.931326	−0.0468009
$397$	−17.9005	−0.898401	−0.449200	−	0.893431i	$-0.648291\pi$
$397$	−17.9005	−0.898401	−0.449200	+	0.893431i	$0.648291\pi$
$398$	−4.92857	−0.247047
$399$	−7.87934	−0.394461
$400$	8.77385	0.438693
$401$	−10.9480	−0.546718	−0.273359	−	0.961912i	$-0.588135\pi$
$401$	−10.9480	−0.546718	−0.273359	+	0.961912i	$0.588135\pi$
$402$	−6.40426	−0.319416
$403$	−0.646278	−0.0321934
$404$	14.9081	0.741704
$405$	3.71131	0.184417
$406$	14.4918	0.719216
$407$	−0.492429	−0.0244088
$408$	−0.978382	−0.0484371
$409$	−25.1669	−1.24442	−0.622212	−	0.782848i	$-0.713766\pi$
$409$	−25.1669	−1.24442	−0.622212	+	0.782848i	$0.713766\pi$
$410$	−33.6026	−1.65952
$411$	−3.04683	−0.150289
$412$	−1.00000	−0.0492665
$413$	−18.9516	−0.932546
$414$	−3.17382	−0.155985
$415$	−0.199381	−0.00978721
$416$	1.00000	0.0490290
$417$	−16.4086	−0.803531
$418$	−3.89986	−0.190749
$419$	−24.3758	−1.19084	−0.595418	−	0.803416i	$-0.703014\pi$
$419$	−24.3758	−1.19084	−0.595418	+	0.803416i	$0.703014\pi$
$420$	6.98345	0.340757
$421$	−9.19360	−0.448069	−0.224034	−	0.974581i	$-0.571923\pi$
$421$	−9.19360	−0.448069	−0.224034	+	0.974581i	$0.571923\pi$
$422$	−14.6532	−0.713309
$423$	5.18235	0.251974
$424$	−1.64496	−0.0798862
$425$	8.58418	0.416394
$426$	4.44981	0.215594
$427$	−16.4189	−0.794567
$428$	17.1405	0.828515
$429$	0.931326	0.0449648
$430$	−36.3915	−1.75495
$431$	−5.70542	−0.274821	−0.137410	−	0.990514i	$-0.543878\pi$
$431$	−5.70542	−0.274821	−0.137410	+	0.990514i	$0.543878\pi$
$432$	1.00000	0.0481125
$433$	3.17770	0.152711	0.0763553	−	0.997081i	$-0.475672\pi$
$433$	3.17770	0.152711	0.0763553	+	0.997081i	$0.475672\pi$
$434$	−1.21608	−0.0583736
$435$	−28.5830	−1.37045
$436$	16.9529	0.811895
$437$	−13.2901	−0.635754
$438$	−5.43840	−0.259857
$439$	−19.3202	−0.922103	−0.461051	−	0.887373i	$-0.652528\pi$
$439$	−19.3202	−0.922103	−0.461051	+	0.887373i	$0.652528\pi$
$440$	3.45644	0.164779
$441$	−3.45934	−0.164730
$442$	0.978382	0.0465369
$443$	−15.8704	−0.754028	−0.377014	−	0.926208i	$-0.623049\pi$
$443$	−15.8704	−0.754028	−0.377014	+	0.926208i	$0.623049\pi$
$444$	0.528740	0.0250929
$445$	6.42144	0.304405
$446$	−17.7404	−0.840032
$447$	23.5210	1.11251
$448$	1.88167	0.0889003
$449$	37.5278	1.77105	0.885524	−	0.464594i	$-0.153800\pi$
$449$	37.5278	1.77105	0.885524	+	0.464594i	$0.153800\pi$
$450$	−8.77385	−0.413603
$451$	−8.43233	−0.397063
$452$	6.21794	0.292467
$453$	−14.7433	−0.692699
$454$	−13.7904	−0.647216
$455$	−6.98345	−0.327389
$456$	4.18743	0.196094
$457$	−23.2955	−1.08972	−0.544859	−	0.838528i	$-0.683417\pi$
$457$	−23.2955	−1.08972	−0.544859	+	0.838528i	$0.683417\pi$
$458$	18.2583	0.853156
$459$	0.978382	0.0456670
$460$	11.7790	0.549200
$461$	−30.6516	−1.42759	−0.713794	−	0.700355i	$-0.753025\pi$
$461$	−30.6516	−1.42759	−0.713794	+	0.700355i	$0.753025\pi$
$462$	1.75244	0.0815310
$463$	29.9474	1.39177	0.695887	−	0.718151i	$-0.255011\pi$
$463$	29.9474	1.39177	0.695887	+	0.718151i	$0.255011\pi$
$464$	−7.70158	−0.357537
$465$	2.39854	0.111230
$466$	1.96381	0.0909717
$467$	23.4968	1.08730	0.543650	−	0.839312i	$-0.317042\pi$
$467$	23.4968	1.08730	0.543650	+	0.839312i	$0.317042\pi$
$468$	−1.00000	−0.0462250
$469$	12.0507	0.556449
$470$	−19.2333	−0.887167
$471$	1.35050	0.0622277
$472$	10.0717	0.463588
$473$	−9.13216	−0.419897
$474$	−14.1564	−0.650227
$475$	−36.7399	−1.68574
$476$	1.84099	0.0843815
$477$	1.64496	0.0753174
$478$	8.18873	0.374544
$479$	40.7926	1.86386	0.931931	−	0.362636i	$-0.118123\pi$
$479$	40.7926	1.86386	0.931931	+	0.362636i	$0.118123\pi$
$480$	−3.71131	−0.169398
$481$	−0.528740	−0.0241085
$482$	14.0753	0.641112
$483$	5.97206	0.271738
$484$	−10.1326	−0.460574
$485$	36.4062	1.65312
$486$	−1.00000	−0.0453609
$487$	−38.7236	−1.75474	−0.877368	−	0.479819i	$-0.840702\pi$
$487$	−38.7236	−1.75474	−0.877368	+	0.479819i	$0.840702\pi$
$488$	8.72574	0.394996
$489$	−12.3415	−0.558100
$490$	12.8387	0.579993
$491$	−0.411054	−0.0185506	−0.00927530	−	0.999957i	$-0.502952\pi$
$491$	−0.411054	−0.0185506	−0.00927530	+	0.999957i	$0.502952\pi$
$492$	9.05411	0.408191
$493$	−7.53509	−0.339363
$494$	−4.18743	−0.188401
$495$	−3.45644	−0.155356
$496$	0.646278	0.0290187
$497$	−8.37304	−0.375582
$498$	0.0537224	0.00240736
$499$	−9.78288	−0.437942	−0.218971	−	0.975731i	$-0.570270\pi$
$499$	−9.78288	−0.437942	−0.218971	+	0.975731i	$0.570270\pi$
$500$	14.0059	0.626365
$501$	16.0020	0.714918
$502$	26.7651	1.19459
$503$	0.686577	0.0306129	0.0153065	−	0.999883i	$-0.495128\pi$
$503$	0.686577	0.0306129	0.0153065	+	0.999883i	$0.495128\pi$
$504$	−1.88167	−0.0838160
$505$	55.3285	2.46209
$506$	2.95586	0.131404
$507$	1.00000	0.0444116
$508$	12.2050	0.541508
$509$	32.6715	1.44814	0.724069	−	0.689727i	$-0.242269\pi$
$509$	32.6715	1.44814	0.724069	+	0.689727i	$0.242269\pi$
$510$	−3.63108	−0.160787
$511$	10.2332	0.452692
$512$	−1.00000	−0.0441942
$513$	−4.18743	−0.184880
$514$	−11.1397	−0.491353
$515$	−3.71131	−0.163540
$516$	9.80555	0.431665
$517$	−4.82646	−0.212267
$518$	−0.994911	−0.0437139
$519$	−14.9827	−0.657666
$520$	3.71131	0.162752
$521$	7.66587	0.335848	0.167924	−	0.985800i	$-0.446294\pi$
$521$	7.66587	0.335848	0.167924	+	0.985800i	$0.446294\pi$
$522$	7.70158	0.337089
$523$	−17.2634	−0.754875	−0.377438	−	0.926035i	$-0.623195\pi$
$523$	−17.2634	−0.754875	−0.377438	+	0.926035i	$0.623195\pi$
$524$	−2.18190	−0.0953169
$525$	16.5094	0.720531
$526$	−8.73132	−0.380704
$527$	0.632307	0.0275437
$528$	−0.931326	−0.0405308
$529$	−12.9269	−0.562038
$530$	−6.10495	−0.265182
$531$	−10.0717	−0.437075
$532$	−7.87934	−0.341613
$533$	−9.05411	−0.392177
$534$	−1.73023	−0.0748745
$535$	63.6136	2.75026
$536$	−6.40426	−0.276622
$537$	16.7055	0.720895
$538$	17.4596	0.752735
$539$	3.22177	0.138771
$540$	3.71131	0.159710
$541$	−38.2299	−1.64363	−0.821815	−	0.569754i	$-0.807038\pi$
$541$	−38.2299	−1.64363	−0.821815	+	0.569754i	$0.807038\pi$
$542$	−5.32841	−0.228875
$543$	−12.1779	−0.522606
$544$	−0.978382	−0.0419478
$545$	62.9174	2.69509
$546$	1.88167	0.0805278
$547$	36.0131	1.53981	0.769904	−	0.638160i	$-0.220304\pi$
$547$	36.0131	1.53981	0.769904	+	0.638160i	$0.220304\pi$
$548$	−3.04683	−0.130154
$549$	−8.72574	−0.372406
$550$	8.17132	0.348426
$551$	32.2499	1.37389
$552$	−3.17382	−0.135087
$553$	26.6377	1.13275
$554$	−21.0101	−0.892632
$555$	1.96232	0.0832958
$556$	−16.4086	−0.695878
$557$	29.2777	1.24053	0.620267	−	0.784391i	$-0.287024\pi$
$557$	29.2777	1.24053	0.620267	+	0.784391i	$0.287024\pi$
$558$	−0.646278	−0.0273591
$559$	−9.80555	−0.414730
$560$	6.98345	0.295105
$561$	−0.911192	−0.0384706
$562$	20.3166	0.857006
$563$	0.805499	0.0339477	0.0169739	−	0.999856i	$-0.494597\pi$
$563$	0.805499	0.0339477	0.0169739	+	0.999856i	$0.494597\pi$
$564$	5.18235	0.218216
$565$	23.0767	0.970845
$566$	24.3194	1.02222
$567$	1.88167	0.0790225
$568$	4.44981	0.186710
$569$	38.8851	1.63015	0.815075	−	0.579356i	$-0.196696\pi$
$569$	38.8851	1.63015	0.815075	+	0.579356i	$0.196696\pi$
$570$	15.5409	0.650935
$571$	11.4911	0.480888	0.240444	−	0.970663i	$-0.422707\pi$
$571$	11.4911	0.480888	0.240444	+	0.970663i	$0.422707\pi$
$572$	0.931326	0.0389407
$573$	10.2973	0.430177
$574$	−17.0368	−0.711102
$575$	27.8466	1.16128
$576$	1.00000	0.0416667
$577$	−32.5380	−1.35457	−0.677287	−	0.735719i	$-0.736844\pi$
$577$	−32.5380	−1.35457	−0.677287	+	0.735719i	$0.736844\pi$
$578$	16.0428	0.667291
$579$	12.9274	0.537246
$580$	−28.5830	−1.18684
$581$	−0.101088	−0.00419382
$582$	−9.80952	−0.406618
$583$	−1.53199	−0.0634486
$584$	−5.43840	−0.225043
$585$	−3.71131	−0.153444
$586$	−12.6449	−0.522355
$587$	−42.5329	−1.75552	−0.877759	−	0.479102i	$-0.840962\pi$
$587$	−42.5329	−1.75552	−0.877759	+	0.479102i	$0.840962\pi$
$588$	−3.45934	−0.142661
$589$	−2.70624	−0.111509
$590$	37.3792	1.53888
$591$	10.7818	0.443502
$592$	0.528740	0.0217311
$593$	25.4644	1.04570	0.522848	−	0.852426i	$-0.324869\pi$
$593$	25.4644	1.04570	0.522848	+	0.852426i	$0.324869\pi$
$594$	0.931326	0.0382128
$595$	6.83248	0.280104
$596$	23.5210	0.963460
$597$	4.92857	0.201713
$598$	3.17382	0.129787
$599$	−21.9340	−0.896200	−0.448100	−	0.893983i	$-0.647899\pi$
$599$	−21.9340	−0.896200	−0.448100	+	0.893983i	$0.647899\pi$
$600$	−8.77385	−0.358191
$601$	−35.9805	−1.46767	−0.733837	−	0.679326i	$-0.762272\pi$
$601$	−35.9805	−1.46767	−0.733837	+	0.679326i	$0.762272\pi$
$602$	−18.4508	−0.751997
$603$	6.40426	0.260802
$604$	−14.7433	−0.599895
$605$	−37.6054	−1.52888
$606$	−14.9081	−0.605599
$607$	−45.9299	−1.86424	−0.932119	−	0.362152i	$-0.882042\pi$
$607$	−45.9299	−1.86424	−0.932119	+	0.362152i	$0.882042\pi$
$608$	4.18743	0.169823
$609$	−14.4918	−0.587237
$610$	32.3840	1.31119
$611$	−5.18235	−0.209655
$612$	0.978382	0.0395487
$613$	−44.3293	−1.79044	−0.895222	−	0.445621i	$-0.852983\pi$
$613$	−44.3293	−1.79044	−0.895222	+	0.445621i	$0.852983\pi$
$614$	−5.28965	−0.213473
$615$	33.6026	1.35499
$616$	1.75244	0.0706080
$617$	−3.97224	−0.159916	−0.0799582	−	0.996798i	$-0.525479\pi$
$617$	−3.97224	−0.159916	−0.0799582	+	0.996798i	$0.525479\pi$
$618$	1.00000	0.0402259
$619$	−7.59646	−0.305328	−0.152664	−	0.988278i	$-0.548785\pi$
$619$	−7.59646	−0.305328	−0.152664	+	0.988278i	$0.548785\pi$
$620$	2.39854	0.0963277
$621$	3.17382	0.127361
$622$	12.9610	0.519689
$623$	3.25572	0.130438
$624$	−1.00000	−0.0400320
$625$	8.11121	0.324449
$626$	−11.7845	−0.471005
$627$	3.89986	0.155746
$628$	1.35050	0.0538907
$629$	0.517309	0.0206265
$630$	−6.98345	−0.278227
$631$	24.0090	0.955783	0.477892	−	0.878419i	$-0.341401\pi$
$631$	24.0090	0.955783	0.477892	+	0.878419i	$0.341401\pi$
$632$	−14.1564	−0.563113
$633$	14.6532	0.582414
$634$	31.8044	1.26312
$635$	45.2965	1.79754
$636$	1.64496	0.0652268
$637$	3.45934	0.137064
$638$	−7.17268	−0.283969
$639$	−4.44981	−0.176032
$640$	−3.71131	−0.146703
$641$	26.7093	1.05495	0.527476	−	0.849570i	$-0.323138\pi$
$641$	26.7093	1.05495	0.527476	+	0.849570i	$0.323138\pi$
$642$	−17.1405	−0.676480
$643$	25.1380	0.991348	0.495674	−	0.868509i	$-0.334921\pi$
$643$	25.1380	0.991348	0.495674	+	0.868509i	$0.334921\pi$
$644$	5.97206	0.235332
$645$	36.3915	1.43291
$646$	4.09691	0.161191
$647$	47.5498	1.86938	0.934689	−	0.355467i	$-0.115678\pi$
$647$	47.5498	1.86938	0.934689	+	0.355467i	$0.115678\pi$
$648$	−1.00000	−0.0392837
$649$	9.38004	0.368199
$650$	8.77385	0.344139
$651$	1.21608	0.0476619
$652$	−12.3415	−0.483329
$653$	−16.4606	−0.644154	−0.322077	−	0.946713i	$-0.604381\pi$
$653$	−16.4606	−0.644154	−0.322077	+	0.946713i	$0.604381\pi$
$654$	−16.9529	−0.662910
$655$	−8.09773	−0.316405
$656$	9.05411	0.353504
$657$	5.43840	0.212172
$658$	−9.75144	−0.380151
$659$	−9.27997	−0.361496	−0.180748	−	0.983529i	$-0.557852\pi$
$659$	−9.27997	−0.361496	−0.180748	+	0.983529i	$0.557852\pi$
$660$	−3.45644	−0.134542
$661$	−6.58624	−0.256175	−0.128088	−	0.991763i	$-0.540884\pi$
$661$	−6.58624	−0.256175	−0.128088	+	0.991763i	$0.540884\pi$
$662$	−15.7206	−0.610997
$663$	−0.978382	−0.0379972
$664$	0.0537224	0.00208483
$665$	−29.2427	−1.13398
$666$	−0.528740	−0.0204882
$667$	−24.4434	−0.946453
$668$	16.0020	0.619137
$669$	17.7404	0.685884
$670$	−23.7682	−0.918247
$671$	8.12651	0.313720
$672$	−1.88167	−0.0725868
$673$	8.45911	0.326075	0.163037	−	0.986620i	$-0.447871\pi$
$673$	8.45911	0.326075	0.163037	+	0.986620i	$0.447871\pi$
$674$	−3.06433	−0.118034
$675$	8.77385	0.337706
$676$	1.00000	0.0384615
$677$	−2.01452	−0.0774241	−0.0387121	−	0.999250i	$-0.512326\pi$
$677$	−2.01452	−0.0774241	−0.0387121	+	0.999250i	$0.512326\pi$
$678$	−6.21794	−0.238798
$679$	18.4582	0.708362
$680$	−3.63108	−0.139246
$681$	13.7904	0.528450
$682$	0.601895	0.0230478
$683$	11.9810	0.458442	0.229221	−	0.973374i	$-0.426382\pi$
$683$	11.9810	0.458442	0.229221	+	0.973374i	$0.426382\pi$
$684$	−4.18743	−0.160110
$685$	−11.3078	−0.432047
$686$	19.6810	0.751423
$687$	−18.2583	−0.696599
$688$	9.80555	0.373833
$689$	−1.64496	−0.0626679
$690$	−11.7790	−0.448420
$691$	−28.1162	−1.06959	−0.534795	−	0.844982i	$-0.679611\pi$
$691$	−28.1162	−1.06959	−0.534795	+	0.844982i	$0.679611\pi$
$692$	−14.9827	−0.569556
$693$	−1.75244	−0.0665698
$694$	−7.63559	−0.289843
$695$	−60.8974	−2.30997
$696$	7.70158	0.291928
$697$	8.85838	0.335535
$698$	29.8723	1.13068
$699$	−1.96381	−0.0742781
$700$	16.5094	0.623999
$701$	−33.9520	−1.28235	−0.641175	−	0.767394i	$-0.721553\pi$
$701$	−33.9520	−1.28235	−0.641175	+	0.767394i	$0.721553\pi$
$702$	1.00000	0.0377426
$703$	−2.21406	−0.0835049
$704$	−0.931326	−0.0351007
$705$	19.2333	0.724369
$706$	30.0555	1.13115
$707$	28.0520	1.05500
$708$	−10.0717	−0.378518
$709$	13.4219	0.504070	0.252035	−	0.967718i	$-0.418900\pi$
$709$	13.4219	0.504070	0.252035	+	0.967718i	$0.418900\pi$
$710$	16.5146	0.619783
$711$	14.1564	0.530908
$712$	−1.73023	−0.0648432
$713$	2.05117	0.0768169
$714$	−1.84099	−0.0688972
$715$	3.45644	0.129264
$716$	16.7055	0.624314
$717$	−8.18873	−0.305814
$718$	−20.7629	−0.774866
$719$	−0.765607	−0.0285523	−0.0142762	−	0.999898i	$-0.504544\pi$
$719$	−0.765607	−0.0285523	−0.0142762	+	0.999898i	$0.504544\pi$
$720$	3.71131	0.138313
$721$	−1.88167	−0.0700769
$722$	1.46542	0.0545373
$723$	−14.0753	−0.523466
$724$	−12.1779	−0.452590
$725$	−67.5726	−2.50958
$726$	10.1326	0.376057
$727$	−34.7825	−1.29001	−0.645007	−	0.764177i	$-0.723145\pi$
$727$	−34.7825	−1.29001	−0.645007	+	0.764177i	$0.723145\pi$
$728$	1.88167	0.0697391
$729$	1.00000	0.0370370
$730$	−20.1836	−0.747029
$731$	9.59357	0.354831
$732$	−8.72574	−0.322513
$733$	−30.6791	−1.13316	−0.566579	−	0.824008i	$-0.691733\pi$
$733$	−30.6791	−1.13316	−0.566579	+	0.824008i	$0.691733\pi$
$734$	4.89582	0.180708
$735$	−12.8387	−0.473562
$736$	−3.17382	−0.116989
$737$	−5.96446	−0.219704
$738$	−9.05411	−0.333286
$739$	26.6283	0.979540	0.489770	−	0.871852i	$-0.337081\pi$
$739$	26.6283	0.979540	0.489770	+	0.871852i	$0.337081\pi$
$740$	1.96232	0.0721363
$741$	4.18743	0.153829
$742$	−3.09526	−0.113631
$743$	27.5232	1.00973	0.504864	−	0.863199i	$-0.331543\pi$
$743$	27.5232	1.00973	0.504864	+	0.863199i	$0.331543\pi$
$744$	−0.646278	−0.0236937
$745$	87.2940	3.19820
$746$	12.9373	0.473668
$747$	−0.0537224	−0.00196560
$748$	−0.911192	−0.0333165
$749$	32.2526	1.17848
$750$	−14.0059	−0.511425
$751$	−15.9210	−0.580964	−0.290482	−	0.956880i	$-0.593816\pi$
$751$	−15.9210	−0.580964	−0.290482	+	0.956880i	$0.593816\pi$
$752$	5.18235	0.188981
$753$	−26.7651	−0.975376
$754$	−7.70158	−0.280475
$755$	−54.7169	−1.99135
$756$	1.88167	0.0684355
$757$	−27.3671	−0.994676	−0.497338	−	0.867557i	$-0.665689\pi$
$757$	−27.3671	−0.994676	−0.497338	+	0.867557i	$0.665689\pi$
$758$	27.7962	1.00960
$759$	−2.95586	−0.107291
$760$	15.5409	0.563727
$761$	45.4877	1.64893	0.824464	−	0.565914i	$-0.191477\pi$
$761$	45.4877	1.64893	0.824464	+	0.565914i	$0.191477\pi$
$762$	−12.2050	−0.442140
$763$	31.8996	1.15484
$764$	10.2973	0.372544
$765$	3.63108	0.131282
$766$	27.7407	1.00231
$767$	10.0717	0.363668
$768$	1.00000	0.0360844
$769$	29.3257	1.05751	0.528755	−	0.848774i	$-0.322659\pi$
$769$	29.3257	1.05751	0.528755	+	0.848774i	$0.322659\pi$
$770$	6.50387	0.234383
$771$	11.1397	0.401188
$772$	12.9274	0.465269
$773$	−47.7073	−1.71591	−0.857956	−	0.513723i	$-0.828266\pi$
$773$	−47.7073	−1.71591	−0.857956	+	0.513723i	$0.828266\pi$
$774$	−9.80555	−0.352453
$775$	5.67035	0.203685
$776$	−9.80952	−0.352141
$777$	0.994911	0.0356922
$778$	25.4153	0.911181
$779$	−37.9135	−1.35839
$780$	−3.71131	−0.132886
$781$	4.14422	0.148292
$782$	−3.10521	−0.111042
$783$	−7.70158	−0.275232
$784$	−3.45934	−0.123548
$785$	5.01212	0.178890
$786$	2.18190	0.0778259
$787$	−0.324112	−0.0115533	−0.00577667	−	0.999983i	$-0.501839\pi$
$787$	−0.324112	−0.0115533	−0.00577667	+	0.999983i	$0.501839\pi$
$788$	10.7818	0.384084
$789$	8.73132	0.310843
$790$	−52.5390	−1.86925
$791$	11.7001	0.416007
$792$	0.931326	0.0330932
$793$	8.72574	0.309860
$794$	17.9005	0.635265
$795$	6.10495	0.216520
$796$	4.92857	0.174689
$797$	−48.6054	−1.72169	−0.860845	−	0.508867i	$-0.830065\pi$
$797$	−48.6054	−1.72169	−0.860845	+	0.508867i	$0.830065\pi$
$798$	7.87934	0.278926
$799$	5.07032	0.179375
$800$	−8.77385	−0.310202
$801$	1.73023	0.0611348
$802$	10.9480	0.386588
$803$	−5.06492	−0.178737
$804$	6.40426	0.225861
$805$	22.1642	0.781185
$806$	0.646278	0.0227642
$807$	−17.4596	−0.614605
$808$	−14.9081	−0.524464
$809$	28.4190	0.999161	0.499580	−	0.866268i	$-0.333488\pi$
$809$	28.4190	0.999161	0.499580	+	0.866268i	$0.333488\pi$
$810$	−3.71131	−0.130402
$811$	10.1975	0.358082	0.179041	−	0.983842i	$-0.442701\pi$
$811$	10.1975	0.358082	0.179041	+	0.983842i	$0.442701\pi$
$812$	−14.4918	−0.508563
$813$	5.32841	0.186875
$814$	0.492429	0.0172596
$815$	−45.8030	−1.60441
$816$	0.978382	0.0342502
$817$	−41.0601	−1.43651
$818$	25.1669	0.879941
$819$	−1.88167	−0.0657507
$820$	33.6026	1.17346
$821$	50.2616	1.75414	0.877072	−	0.480359i	$-0.159494\pi$
$821$	50.2616	1.75414	0.877072	+	0.480359i	$0.159494\pi$
$822$	3.04683	0.106271
$823$	−19.1102	−0.666140	−0.333070	−	0.942902i	$-0.608085\pi$
$823$	−19.1102	−0.666140	−0.333070	+	0.942902i	$0.608085\pi$
$824$	1.00000	0.0348367
$825$	−8.17132	−0.284489
$826$	18.9516	0.659409
$827$	50.9810	1.77278	0.886391	−	0.462937i	$-0.153204\pi$
$827$	50.9810	1.77278	0.886391	+	0.462937i	$0.153204\pi$
$828$	3.17382	0.110298
$829$	32.5229	1.12957	0.564784	−	0.825239i	$-0.308959\pi$
$829$	32.5229	1.12957	0.564784	+	0.825239i	$0.308959\pi$
$830$	0.199381	0.00692060
$831$	21.0101	0.728831
$832$	−1.00000	−0.0346688
$833$	−3.38455	−0.117268
$834$	16.4086	0.568182
$835$	59.3885	2.05523
$836$	3.89986	0.134880
$837$	0.646278	0.0223386
$838$	24.3758	0.842048
$839$	14.8859	0.513918	0.256959	−	0.966422i	$-0.417279\pi$
$839$	14.8859	0.513918	0.256959	+	0.966422i	$0.417279\pi$
$840$	−6.98345	−0.240952
$841$	30.3144	1.04532
$842$	9.19360	0.316832
$843$	−20.3166	−0.699742
$844$	14.6532	0.504386
$845$	3.71131	0.127673
$846$	−5.18235	−0.178173
$847$	−19.0662	−0.655123
$848$	1.64496	0.0564881
$849$	−24.3194	−0.834639
$850$	−8.58418	−0.294435
$851$	1.67812	0.0575253
$852$	−4.44981	−0.152448
$853$	−52.1160	−1.78442	−0.892208	−	0.451624i	$-0.850845\pi$
$853$	−52.1160	−1.78442	−0.892208	+	0.451624i	$0.850845\pi$
$854$	16.4189	0.561844
$855$	−15.5409	−0.531487
$856$	−17.1405	−0.585849
$857$	−8.73329	−0.298324	−0.149162	−	0.988813i	$-0.547658\pi$
$857$	−8.73329	−0.298324	−0.149162	+	0.988813i	$0.547658\pi$
$858$	−0.931326	−0.0317949
$859$	−27.8165	−0.949086	−0.474543	−	0.880232i	$-0.657387\pi$
$859$	−27.8165	−0.949086	−0.474543	+	0.880232i	$0.657387\pi$
$860$	36.3915	1.24094
$861$	17.0368	0.580613
$862$	5.70542	0.194327
$863$	20.4021	0.694497	0.347249	−	0.937773i	$-0.387116\pi$
$863$	20.4021	0.694497	0.347249	+	0.937773i	$0.387116\pi$
$864$	−1.00000	−0.0340207
$865$	−55.6054	−1.89064
$866$	−3.17770	−0.107983
$867$	−16.0428	−0.544841
$868$	1.21608	0.0412764
$869$	−13.1843	−0.447245
$870$	28.5830	0.969054
$871$	−6.40426	−0.217000
$872$	−16.9529	−0.574097
$873$	9.80952	0.332002
$874$	13.2901	0.449546
$875$	26.3545	0.890945
$876$	5.43840	0.183746
$877$	7.27922	0.245802	0.122901	−	0.992419i	$-0.460780\pi$
$877$	7.27922	0.245802	0.122901	+	0.992419i	$0.460780\pi$
$878$	19.3202	0.652025
$879$	12.6449	0.426501
$880$	−3.45644	−0.116517
$881$	−10.6316	−0.358188	−0.179094	−	0.983832i	$-0.557317\pi$
$881$	−10.6316	−0.358188	−0.179094	+	0.983832i	$0.557317\pi$
$882$	3.45934	0.116482
$883$	−11.5657	−0.389217	−0.194609	−	0.980881i	$-0.562344\pi$
$883$	−11.5657	−0.389217	−0.194609	+	0.980881i	$0.562344\pi$
$884$	−0.978382	−0.0329065
$885$	−37.3792	−1.25649
$886$	15.8704	0.533178
$887$	−13.6926	−0.459753	−0.229876	−	0.973220i	$-0.573832\pi$
$887$	−13.6926	−0.459753	−0.229876	+	0.973220i	$0.573832\pi$
$888$	−0.528740	−0.0177433
$889$	22.9657	0.770244
$890$	−6.42144	−0.215247
$891$	−0.931326	−0.0312006
$892$	17.7404	0.593993
$893$	−21.7007	−0.726187
$894$	−23.5210	−0.786662
$895$	61.9993	2.07241
$896$	−1.88167	−0.0628620
$897$	−3.17382	−0.105971
$898$	−37.5278	−1.25232
$899$	−4.97736	−0.166004
$900$	8.77385	0.292462
$901$	1.60940	0.0536168
$902$	8.43233	0.280766
$903$	18.4508	0.614003
$904$	−6.21794	−0.206805
$905$	−45.1962	−1.50237
$906$	14.7433	0.489813
$907$	22.8278	0.757984	0.378992	−	0.925400i	$-0.376271\pi$
$907$	22.8278	0.757984	0.378992	+	0.925400i	$0.376271\pi$
$908$	13.7904	0.457651
$909$	14.9081	0.494469
$910$	6.98345	0.231499
$911$	−42.1640	−1.39695	−0.698477	−	0.715632i	$-0.746139\pi$
$911$	−42.1640	−1.39695	−0.698477	+	0.715632i	$0.746139\pi$
$912$	−4.18743	−0.138660
$913$	0.0500330	0.00165585
$914$	23.2955	0.770546
$915$	−32.3840	−1.07058
$916$	−18.2583	−0.603273
$917$	−4.10561	−0.135579
$918$	−0.978382	−0.0322914
$919$	28.8872	0.952901	0.476450	−	0.879201i	$-0.341923\pi$
$919$	28.8872	0.952901	0.476450	+	0.879201i	$0.341923\pi$
$920$	−11.7790	−0.388343
$921$	5.28965	0.174300
$922$	30.6516	1.00946
$923$	4.44981	0.146467
$924$	−1.75244	−0.0576512
$925$	4.63908	0.152532
$926$	−29.9474	−0.984133
$927$	−1.00000	−0.0328443
$928$	7.70158	0.252817
$929$	−26.4047	−0.866311	−0.433155	−	0.901319i	$-0.642600\pi$
$929$	−26.4047	−0.866311	−0.433155	+	0.901319i	$0.642600\pi$
$930$	−2.39854	−0.0786512
$931$	14.4857	0.474751
$932$	−1.96381	−0.0643267
$933$	−12.9610	−0.424324
$934$	−23.4968	−0.768837
$935$	−3.38172	−0.110594
$936$	1.00000	0.0326860
$937$	26.1932	0.855696	0.427848	−	0.903851i	$-0.359272\pi$
$937$	26.1932	0.855696	0.427848	+	0.903851i	$0.359272\pi$
$938$	−12.0507	−0.393469
$939$	11.7845	0.384574
$940$	19.2333	0.627322
$941$	17.0346	0.555313	0.277656	−	0.960680i	$-0.410442\pi$
$941$	17.0346	0.555313	0.277656	+	0.960680i	$0.410442\pi$
$942$	−1.35050	−0.0440016
$943$	28.7361	0.935776
$944$	−10.0717	−0.327806
$945$	6.98345	0.227172
$946$	9.13216	0.296912
$947$	38.6543	1.25610	0.628048	−	0.778174i	$-0.283854\pi$
$947$	38.6543	1.25610	0.628048	+	0.778174i	$0.283854\pi$
$948$	14.1564	0.459780
$949$	−5.43840	−0.176538
$950$	36.7399	1.19200
$951$	−31.8044	−1.03133
$952$	−1.84099	−0.0596667
$953$	50.0997	1.62289	0.811445	−	0.584429i	$-0.198682\pi$
$953$	50.0997	1.62289	0.811445	+	0.584429i	$0.198682\pi$
$954$	−1.64496	−0.0532575
$955$	38.2166	1.23666
$956$	−8.18873	−0.264843
$957$	7.17268	0.231860
$958$	−40.7926	−1.31795
$959$	−5.73312	−0.185132
$960$	3.71131	0.119782
$961$	−30.5823	−0.986527
$962$	0.528740	0.0170473
$963$	17.1405	0.552343
$964$	−14.0753	−0.453335
$965$	47.9778	1.54446
$966$	−5.97206	−0.192148
$967$	33.5399	1.07857	0.539285	−	0.842123i	$-0.318694\pi$
$967$	33.5399	1.07857	0.539285	+	0.842123i	$0.318694\pi$
$968$	10.1326	0.325675
$969$	−4.09691	−0.131612
$970$	−36.4062	−1.16893
$971$	5.84747	0.187654	0.0938271	−	0.995589i	$-0.470090\pi$
$971$	5.84747	0.187654	0.0938271	+	0.995589i	$0.470090\pi$
$972$	1.00000	0.0320750
$973$	−30.8754	−0.989821
$974$	38.7236	1.24079
$975$	−8.77385	−0.280988
$976$	−8.72574	−0.279304
$977$	−7.56980	−0.242179	−0.121090	−	0.992642i	$-0.538639\pi$
$977$	−7.56980	−0.242179	−0.121090	+	0.992642i	$0.538639\pi$
$978$	12.3415	0.394636
$979$	−1.61141	−0.0515009
$980$	−12.8387	−0.410117
$981$	16.9529	0.541264
$982$	0.411054	0.0131173
$983$	45.0848	1.43798	0.718991	−	0.695019i	$-0.244604\pi$
$983$	45.0848	1.43798	0.718991	+	0.695019i	$0.244604\pi$
$984$	−9.05411	−0.288634
$985$	40.0145	1.27497
$986$	7.53509	0.239966
$987$	9.75144	0.310392
$988$	4.18743	0.133220
$989$	31.1210	0.989591
$990$	3.45644	0.109853
$991$	16.3128	0.518192	0.259096	−	0.965852i	$-0.416575\pi$
$991$	16.3128	0.518192	0.259096	+	0.965852i	$0.416575\pi$
$992$	−0.646278	−0.0205193
$993$	15.7206	0.498877
$994$	8.37304	0.265577
$995$	18.2915	0.579879
$996$	−0.0537224	−0.00170226
$997$	−54.4734	−1.72519	−0.862595	−	0.505894i	$-0.831163\pi$
$997$	−54.4734	−1.72519	−0.862595	+	0.505894i	$0.831163\pi$
$998$	9.78288	0.309672
$999$	0.528740	0.0167286

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.t.1.10	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.t.1.10	✓	11	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.71131 q^{5} -1.00000 q^{6} +1.88167 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.71131 q^{5} -1.00000 q^{6} +1.88167 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.71131 q^{10} -0.931326 q^{11} +1.00000 q^{12} -1.00000 q^{13} -1.88167 q^{14} +3.71131 q^{15} +1.00000 q^{16} +0.978382 q^{17} -1.00000 q^{18} -4.18743 q^{19} +3.71131 q^{20} +1.88167 q^{21} +0.931326 q^{22} +3.17382 q^{23} -1.00000 q^{24} +8.77385 q^{25} +1.00000 q^{26} +1.00000 q^{27} +1.88167 q^{28} -7.70158 q^{29} -3.71131 q^{30} +0.646278 q^{31} -1.00000 q^{32} -0.931326 q^{33} -0.978382 q^{34} +6.98345 q^{35} +1.00000 q^{36} +0.528740 q^{37} +4.18743 q^{38} -1.00000 q^{39} -3.71131 q^{40} +9.05411 q^{41} -1.88167 q^{42} +9.80555 q^{43} -0.931326 q^{44} +3.71131 q^{45} -3.17382 q^{46} +5.18235 q^{47} +1.00000 q^{48} -3.45934 q^{49} -8.77385 q^{50} +0.978382 q^{51} -1.00000 q^{52} +1.64496 q^{53} -1.00000 q^{54} -3.45644 q^{55} -1.88167 q^{56} -4.18743 q^{57} +7.70158 q^{58} -10.0717 q^{59} +3.71131 q^{60} -8.72574 q^{61} -0.646278 q^{62} +1.88167 q^{63} +1.00000 q^{64} -3.71131 q^{65} +0.931326 q^{66} +6.40426 q^{67} +0.978382 q^{68} +3.17382 q^{69} -6.98345 q^{70} -4.44981 q^{71} -1.00000 q^{72} +5.43840 q^{73} -0.528740 q^{74} +8.77385 q^{75} -4.18743 q^{76} -1.75244 q^{77} +1.00000 q^{78} +14.1564 q^{79} +3.71131 q^{80} +1.00000 q^{81} -9.05411 q^{82} -0.0537224 q^{83} +1.88167 q^{84} +3.63108 q^{85} -9.80555 q^{86} -7.70158 q^{87} +0.931326 q^{88} +1.73023 q^{89} -3.71131 q^{90} -1.88167 q^{91} +3.17382 q^{92} +0.646278 q^{93} -5.18235 q^{94} -15.5409 q^{95} -1.00000 q^{96} +9.80952 q^{97} +3.45934 q^{98} -0.931326 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 11 q^{2} + 11 q^{3} + 11 q^{4} + 4 q^{5} - 11 q^{6} + 4 q^{7} - 11 q^{8} + 11 q^{9}+O(q^{10}) \) 11 * q - 11 * q^2 + 11 * q^3 + 11 * q^4 + 4 * q^5 - 11 * q^6 + 4 * q^7 - 11 * q^8 + 11 * q^9	\( 11 q - 11 q^{2} + 11 q^{3} + 11 q^{4} + 4 q^{5} - 11 q^{6} + 4 q^{7} - 11 q^{8} + 11 q^{9} - 4 q^{10} + 5 q^{11} + 11 q^{12} - 11 q^{13} - 4 q^{14} + 4 q^{15} + 11 q^{16} + 8 q^{17} - 11 q^{18} - 2 q^{19} + 4 q^{20} + 4 q^{21} - 5 q^{22} + 3 q^{23} - 11 q^{24} + 9 q^{25} + 11 q^{26} + 11 q^{27} + 4 q^{28} + 7 q^{29} - 4 q^{30} + 20 q^{31} - 11 q^{32} + 5 q^{33} - 8 q^{34} + 9 q^{35} + 11 q^{36} + q^{37} + 2 q^{38} - 11 q^{39} - 4 q^{40} + 37 q^{41} - 4 q^{42} - 16 q^{43} + 5 q^{44} + 4 q^{45} - 3 q^{46} + 28 q^{47} + 11 q^{48} + 17 q^{49} - 9 q^{50} + 8 q^{51} - 11 q^{52} - 5 q^{53} - 11 q^{54} - 28 q^{55} - 4 q^{56} - 2 q^{57} - 7 q^{58} + 31 q^{59} + 4 q^{60} + 8 q^{61} - 20 q^{62} + 4 q^{63} + 11 q^{64} - 4 q^{65} - 5 q^{66} - 22 q^{67} + 8 q^{68} + 3 q^{69} - 9 q^{70} + 42 q^{71} - 11 q^{72} - 4 q^{73} - q^{74} + 9 q^{75} - 2 q^{76} - 21 q^{77} + 11 q^{78} + 33 q^{79} + 4 q^{80} + 11 q^{81} - 37 q^{82} + 18 q^{83} + 4 q^{84} + 17 q^{85} + 16 q^{86} + 7 q^{87} - 5 q^{88} + 67 q^{89} - 4 q^{90} - 4 q^{91} + 3 q^{92} + 20 q^{93} - 28 q^{94} + 32 q^{95} - 11 q^{96} - 15 q^{97} - 17 q^{98} + 5 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 + 11 * q^3 + 11 * q^4 + 4 * q^5 - 11 * q^6 + 4 * q^7 - 11 * q^8 + 11 * q^9 - 4 * q^10 + 5 * q^11 + 11 * q^12 - 11 * q^13 - 4 * q^14 + 4 * q^15 + 11 * q^16 + 8 * q^17 - 11 * q^18 - 2 * q^19 + 4 * q^20 + 4 * q^21 - 5 * q^22 + 3 * q^23 - 11 * q^24 + 9 * q^25 + 11 * q^26 + 11 * q^27 + 4 * q^28 + 7 * q^29 - 4 * q^30 + 20 * q^31 - 11 * q^32 + 5 * q^33 - 8 * q^34 + 9 * q^35 + 11 * q^36 + q^37 + 2 * q^38 - 11 * q^39 - 4 * q^40 + 37 * q^41 - 4 * q^42 - 16 * q^43 + 5 * q^44 + 4 * q^45 - 3 * q^46 + 28 * q^47 + 11 * q^48 + 17 * q^49 - 9 * q^50 + 8 * q^51 - 11 * q^52 - 5 * q^53 - 11 * q^54 - 28 * q^55 - 4 * q^56 - 2 * q^57 - 7 * q^58 + 31 * q^59 + 4 * q^60 + 8 * q^61 - 20 * q^62 + 4 * q^63 + 11 * q^64 - 4 * q^65 - 5 * q^66 - 22 * q^67 + 8 * q^68 + 3 * q^69 - 9 * q^70 + 42 * q^71 - 11 * q^72 - 4 * q^73 - q^74 + 9 * q^75 - 2 * q^76 - 21 * q^77 + 11 * q^78 + 33 * q^79 + 4 * q^80 + 11 * q^81 - 37 * q^82 + 18 * q^83 + 4 * q^84 + 17 * q^85 + 16 * q^86 + 7 * q^87 - 5 * q^88 + 67 * q^89 - 4 * q^90 - 4 * q^91 + 3 * q^92 + 20 * q^93 - 28 * q^94 + 32 * q^95 - 11 * q^96 - 15 * q^97 - 17 * q^98 + 5 * q^99

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