LMFDB - Embedded newform 8034.2.a.u.1.2

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:	$1$
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} - 4x^{10} - 18x^{9} + 64x^{8} + 85x^{7} - 249x^{6} - 109x^{5} + 230x^{4} + 97x^{3} - 53x^{2} - 32x - 4 $ x^11 - 4x^10 - 18x^9 + 64x^8 + 85x^7 - 249x^6 - 109x^5 + 230x^4 + 97x^3 - 53x^2 - 32x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.403660$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.98995 q^{5} -1.00000 q^{6} +3.36753 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.98995 q^{5} -1.00000 q^{6} +3.36753 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.98995 q^{10} +3.96145 q^{11} -1.00000 q^{12} -1.00000 q^{13} +3.36753 q^{14} +2.98995 q^{15} +1.00000 q^{16} +1.88527 q^{17} +1.00000 q^{18} -7.32220 q^{19} -2.98995 q^{20} -3.36753 q^{21} +3.96145 q^{22} -3.99496 q^{23} -1.00000 q^{24} +3.93978 q^{25} -1.00000 q^{26} -1.00000 q^{27} +3.36753 q^{28} -8.71741 q^{29} +2.98995 q^{30} +1.96556 q^{31} +1.00000 q^{32} -3.96145 q^{33} +1.88527 q^{34} -10.0687 q^{35} +1.00000 q^{36} -2.32599 q^{37} -7.32220 q^{38} +1.00000 q^{39} -2.98995 q^{40} +6.61752 q^{41} -3.36753 q^{42} -4.18343 q^{43} +3.96145 q^{44} -2.98995 q^{45} -3.99496 q^{46} +8.39320 q^{47} -1.00000 q^{48} +4.34029 q^{49} +3.93978 q^{50} -1.88527 q^{51} -1.00000 q^{52} -11.6304 q^{53} -1.00000 q^{54} -11.8445 q^{55} +3.36753 q^{56} +7.32220 q^{57} -8.71741 q^{58} -0.371710 q^{59} +2.98995 q^{60} -11.3295 q^{61} +1.96556 q^{62} +3.36753 q^{63} +1.00000 q^{64} +2.98995 q^{65} -3.96145 q^{66} +3.43944 q^{67} +1.88527 q^{68} +3.99496 q^{69} -10.0687 q^{70} +3.20633 q^{71} +1.00000 q^{72} +0.938618 q^{73} -2.32599 q^{74} -3.93978 q^{75} -7.32220 q^{76} +13.3403 q^{77} +1.00000 q^{78} -4.29557 q^{79} -2.98995 q^{80} +1.00000 q^{81} +6.61752 q^{82} -12.1900 q^{83} -3.36753 q^{84} -5.63686 q^{85} -4.18343 q^{86} +8.71741 q^{87} +3.96145 q^{88} +18.2704 q^{89} -2.98995 q^{90} -3.36753 q^{91} -3.99496 q^{92} -1.96556 q^{93} +8.39320 q^{94} +21.8930 q^{95} -1.00000 q^{96} +1.18993 q^{97} +4.34029 q^{98} +3.96145 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} - 2 q^{5} - 11 q^{6} - 2 q^{7} + 11 q^{8} + 11 q^{9}+O(q^{10}) $ 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 - 2 * q^5 - 11 * q^6 - 2 * q^7 + 11 * q^8 + 11 * q^9	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} - 2 q^{5} - 11 q^{6} - 2 q^{7} + 11 q^{8} + 11 q^{9} - 2 q^{10} - 10 q^{11} - 11 q^{12} - 11 q^{13} - 2 q^{14} + 2 q^{15} + 11 q^{16} + 6 q^{17} + 11 q^{18} - 3 q^{19} - 2 q^{20} + 2 q^{21} - 10 q^{22} + 3 q^{23} - 11 q^{24} - q^{25} - 11 q^{26} - 11 q^{27} - 2 q^{28} - 22 q^{29} + 2 q^{30} - 5 q^{31} + 11 q^{32} + 10 q^{33} + 6 q^{34} - 20 q^{35} + 11 q^{36} - 26 q^{37} - 3 q^{38} + 11 q^{39} - 2 q^{40} - 6 q^{41} + 2 q^{42} - 8 q^{43} - 10 q^{44} - 2 q^{45} + 3 q^{46} + 6 q^{47} - 11 q^{48} - 5 q^{49} - q^{50} - 6 q^{51} - 11 q^{52} - 25 q^{53} - 11 q^{54} - 2 q^{56} + 3 q^{57} - 22 q^{58} + 7 q^{59} + 2 q^{60} - 36 q^{61} - 5 q^{62} - 2 q^{63} + 11 q^{64} + 2 q^{65} + 10 q^{66} - 12 q^{67} + 6 q^{68} - 3 q^{69} - 20 q^{70} - 15 q^{71} + 11 q^{72} - 12 q^{73} - 26 q^{74} + q^{75} - 3 q^{76} - q^{77} + 11 q^{78} - 15 q^{79} - 2 q^{80} + 11 q^{81} - 6 q^{82} - 16 q^{83} + 2 q^{84} - 25 q^{85} - 8 q^{86} + 22 q^{87} - 10 q^{88} - 2 q^{89} - 2 q^{90} + 2 q^{91} + 3 q^{92} + 5 q^{93} + 6 q^{94} + 16 q^{95} - 11 q^{96} - 10 q^{97} - 5 q^{98} - 10 q^{99}+O(q^{100}) \) 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 - 2 * q^5 - 11 * q^6 - 2 * q^7 + 11 * q^8 + 11 * q^9 - 2 * q^10 - 10 * q^11 - 11 * q^12 - 11 * q^13 - 2 * q^14 + 2 * q^15 + 11 * q^16 + 6 * q^17 + 11 * q^18 - 3 * q^19 - 2 * q^20 + 2 * q^21 - 10 * q^22 + 3 * q^23 - 11 * q^24 - q^25 - 11 * q^26 - 11 * q^27 - 2 * q^28 - 22 * q^29 + 2 * q^30 - 5 * q^31 + 11 * q^32 + 10 * q^33 + 6 * q^34 - 20 * q^35 + 11 * q^36 - 26 * q^37 - 3 * q^38 + 11 * q^39 - 2 * q^40 - 6 * q^41 + 2 * q^42 - 8 * q^43 - 10 * q^44 - 2 * q^45 + 3 * q^46 + 6 * q^47 - 11 * q^48 - 5 * q^49 - q^50 - 6 * q^51 - 11 * q^52 - 25 * q^53 - 11 * q^54 - 2 * q^56 + 3 * q^57 - 22 * q^58 + 7 * q^59 + 2 * q^60 - 36 * q^61 - 5 * q^62 - 2 * q^63 + 11 * q^64 + 2 * q^65 + 10 * q^66 - 12 * q^67 + 6 * q^68 - 3 * q^69 - 20 * q^70 - 15 * q^71 + 11 * q^72 - 12 * q^73 - 26 * q^74 + q^75 - 3 * q^76 - q^77 + 11 * q^78 - 15 * q^79 - 2 * q^80 + 11 * q^81 - 6 * q^82 - 16 * q^83 + 2 * q^84 - 25 * q^85 - 8 * q^86 + 22 * q^87 - 10 * q^88 - 2 * q^89 - 2 * q^90 + 2 * q^91 + 3 * q^92 + 5 * q^93 + 6 * q^94 + 16 * q^95 - 11 * q^96 - 10 * q^97 - 5 * q^98 - 10 * 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
$5$	−2.98995	−1.33714	−0.668572	−	0.743647i	$-0.733094\pi$
$5$	−2.98995	−1.33714	−0.668572	+	0.743647i	$0.733094\pi$
$6$	−1.00000	−0.408248
$7$	3.36753	1.27281	0.636404	−	0.771356i	$-0.280421\pi$
$7$	3.36753	1.27281	0.636404	+	0.771356i	$0.280421\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−2.98995	−0.945504
$11$	3.96145	1.19442	0.597211	−	0.802084i	$-0.296275\pi$
$11$	3.96145	1.19442	0.597211	+	0.802084i	$0.296275\pi$
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	3.36753	0.900011
$15$	2.98995	0.772001
$16$	1.00000	0.250000
$17$	1.88527	0.457246	0.228623	−	0.973515i	$-0.426578\pi$
$17$	1.88527	0.457246	0.228623	+	0.973515i	$0.426578\pi$
$18$	1.00000	0.235702
$19$	−7.32220	−1.67983	−0.839914	−	0.542720i	$-0.817395\pi$
$19$	−7.32220	−1.67983	−0.839914	+	0.542720i	$0.817395\pi$
$20$	−2.98995	−0.668572
$21$	−3.36753	−0.734856
$22$	3.96145	0.844585
$23$	−3.99496	−0.833006	−0.416503	−	0.909134i	$-0.636745\pi$
$23$	−3.99496	−0.833006	−0.416503	+	0.909134i	$0.636745\pi$
$24$	−1.00000	−0.204124
$25$	3.93978	0.787955
$26$	−1.00000	−0.196116
$27$	−1.00000	−0.192450
$28$	3.36753	0.636404
$29$	−8.71741	−1.61878	−0.809391	−	0.587270i	$-0.800203\pi$
$29$	−8.71741	−1.61878	−0.809391	+	0.587270i	$0.800203\pi$
$30$	2.98995	0.545887
$31$	1.96556	0.353025	0.176512	−	0.984298i	$-0.443518\pi$
$31$	1.96556	0.353025	0.176512	+	0.984298i	$0.443518\pi$
$32$	1.00000	0.176777
$33$	−3.96145	−0.689600
$34$	1.88527	0.323322
$35$	−10.0687	−1.70193
$36$	1.00000	0.166667
$37$	−2.32599	−0.382391	−0.191195	−	0.981552i	$-0.561236\pi$
$37$	−2.32599	−0.382391	−0.191195	+	0.981552i	$0.561236\pi$
$38$	−7.32220	−1.18782
$39$	1.00000	0.160128
$40$	−2.98995	−0.472752
$41$	6.61752	1.03348	0.516742	−	0.856141i	$-0.327145\pi$
$41$	6.61752	1.03348	0.516742	+	0.856141i	$0.327145\pi$
$42$	−3.36753	−0.519622
$43$	−4.18343	−0.637967	−0.318983	−	0.947760i	$-0.603341\pi$
$43$	−4.18343	−0.637967	−0.318983	+	0.947760i	$0.603341\pi$
$44$	3.96145	0.597211
$45$	−2.98995	−0.445715
$46$	−3.99496	−0.589024
$47$	8.39320	1.22427	0.612137	−	0.790752i	$-0.290310\pi$
$47$	8.39320	1.22427	0.612137	+	0.790752i	$0.290310\pi$
$48$	−1.00000	−0.144338
$49$	4.34029	0.620041
$50$	3.93978	0.557169
$51$	−1.88527	−0.263991
$52$	−1.00000	−0.138675
$53$	−11.6304	−1.59756	−0.798779	−	0.601625i	$-0.794520\pi$
$53$	−11.6304	−1.59756	−0.798779	+	0.601625i	$0.794520\pi$
$54$	−1.00000	−0.136083
$55$	−11.8445	−1.59712
$56$	3.36753	0.450006
$57$	7.32220	0.969849
$58$	−8.71741	−1.14465
$59$	−0.371710	−0.0483926	−0.0241963	−	0.999707i	$-0.507703\pi$
$59$	−0.371710	−0.0483926	−0.0241963	+	0.999707i	$0.507703\pi$
$60$	2.98995	0.386000
$61$	−11.3295	−1.45059	−0.725297	−	0.688436i	$-0.758298\pi$
$61$	−11.3295	−1.45059	−0.725297	+	0.688436i	$0.758298\pi$
$62$	1.96556	0.249626
$63$	3.36753	0.424269
$64$	1.00000	0.125000
$65$	2.98995	0.370857
$66$	−3.96145	−0.487621
$67$	3.43944	0.420194	0.210097	−	0.977680i	$-0.432622\pi$
$67$	3.43944	0.420194	0.210097	+	0.977680i	$0.432622\pi$
$68$	1.88527	0.228623
$69$	3.99496	0.480936
$70$	−10.0687	−1.20345
$71$	3.20633	0.380521	0.190261	−	0.981734i	$-0.439067\pi$
$71$	3.20633	0.380521	0.190261	+	0.981734i	$0.439067\pi$
$72$	1.00000	0.117851
$73$	0.938618	0.109857	0.0549284	−	0.998490i	$-0.482507\pi$
$73$	0.938618	0.109857	0.0549284	+	0.998490i	$0.482507\pi$
$74$	−2.32599	−0.270391
$75$	−3.93978	−0.454926
$76$	−7.32220	−0.839914
$77$	13.3403	1.52027
$78$	1.00000	0.113228
$79$	−4.29557	−0.483289	−0.241645	−	0.970365i	$-0.577687\pi$
$79$	−4.29557	−0.483289	−0.241645	+	0.970365i	$0.577687\pi$
$80$	−2.98995	−0.334286
$81$	1.00000	0.111111
$82$	6.61752	0.730783
$83$	−12.1900	−1.33803	−0.669013	−	0.743251i	$-0.733283\pi$
$83$	−12.1900	−1.33803	−0.669013	+	0.743251i	$0.733283\pi$
$84$	−3.36753	−0.367428
$85$	−5.63686	−0.611404
$86$	−4.18343	−0.451111
$87$	8.71741	0.934604
$88$	3.96145	0.422292
$89$	18.2704	1.93666	0.968329	−	0.249679i	$-0.0803251\pi$
$89$	18.2704	1.93666	0.968329	+	0.249679i	$0.0803251\pi$
$90$	−2.98995	−0.315168
$91$	−3.36753	−0.353013
$92$	−3.99496	−0.416503
$93$	−1.96556	−0.203819
$94$	8.39320	0.865692
$95$	21.8930	2.24617
$96$	−1.00000	−0.102062
$97$	1.18993	0.120819	0.0604094	−	0.998174i	$-0.480759\pi$
$97$	1.18993	0.120819	0.0604094	+	0.998174i	$0.480759\pi$
$98$	4.34029	0.438435
$99$	3.96145	0.398141
$100$	3.93978	0.393978
$101$	4.25536	0.423424	0.211712	−	0.977332i	$-0.432096\pi$
$101$	4.25536	0.423424	0.211712	+	0.977332i	$0.432096\pi$
$102$	−1.88527	−0.186670
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−1.00000	−0.0980581
$105$	10.0687	0.982609
$106$	−11.6304	−1.12964
$107$	−3.43481	−0.332056	−0.166028	−	0.986121i	$-0.553094\pi$
$107$	−3.43481	−0.332056	−0.166028	+	0.986121i	$0.553094\pi$
$108$	−1.00000	−0.0962250
$109$	−11.8754	−1.13746	−0.568729	−	0.822525i	$-0.692565\pi$
$109$	−11.8754	−1.13746	−0.568729	+	0.822525i	$0.692565\pi$
$110$	−11.8445	−1.12933
$111$	2.32599	0.220773
$112$	3.36753	0.318202
$113$	−16.0040	−1.50553	−0.752765	−	0.658289i	$-0.771280\pi$
$113$	−16.0040	−1.50553	−0.752765	+	0.658289i	$0.771280\pi$
$114$	7.32220	0.685787
$115$	11.9447	1.11385
$116$	−8.71741	−0.809391
$117$	−1.00000	−0.0924500
$118$	−0.371710	−0.0342187
$119$	6.34872	0.581986
$120$	2.98995	0.272943
$121$	4.69311	0.426646
$122$	−11.3295	−1.02572
$123$	−6.61752	−0.596682
$124$	1.96556	0.176512
$125$	3.17001	0.283534
$126$	3.36753	0.300004
$127$	1.19167	0.105743	0.0528717	−	0.998601i	$-0.483163\pi$
$127$	1.19167	0.105743	0.0528717	+	0.998601i	$0.483163\pi$
$128$	1.00000	0.0883883
$129$	4.18343	0.368330
$130$	2.98995	0.262236
$131$	−7.75154	−0.677255	−0.338627	−	0.940921i	$-0.609963\pi$
$131$	−7.75154	−0.677255	−0.338627	+	0.940921i	$0.609963\pi$
$132$	−3.96145	−0.344800
$133$	−24.6578	−2.13810
$134$	3.43944	0.297122
$135$	2.98995	0.257334
$136$	1.88527	0.161661
$137$	−7.21052	−0.616036	−0.308018	−	0.951380i	$-0.599666\pi$
$137$	−7.21052	−0.616036	−0.308018	+	0.951380i	$0.599666\pi$
$138$	3.99496	0.340073
$139$	3.22021	0.273134	0.136567	−	0.990631i	$-0.456393\pi$
$139$	3.22021	0.273134	0.136567	+	0.990631i	$0.456393\pi$
$140$	−10.0687	−0.850964
$141$	−8.39320	−0.706835
$142$	3.20633	0.269069
$143$	−3.96145	−0.331273
$144$	1.00000	0.0833333
$145$	26.0646	2.16455
$146$	0.938618	0.0776805
$147$	−4.34029	−0.357981
$148$	−2.32599	−0.191195
$149$	14.6144	1.19725	0.598627	−	0.801028i	$-0.295713\pi$
$149$	14.6144	1.19725	0.598627	+	0.801028i	$0.295713\pi$
$150$	−3.93978	−0.321681
$151$	−21.9812	−1.78880	−0.894402	−	0.447264i	$-0.852398\pi$
$151$	−21.9812	−1.78880	−0.894402	+	0.447264i	$0.852398\pi$
$152$	−7.32220	−0.593909
$153$	1.88527	0.152415
$154$	13.3403	1.07499
$155$	−5.87691	−0.472045
$156$	1.00000	0.0800641
$157$	4.35685	0.347715	0.173857	−	0.984771i	$-0.444377\pi$
$157$	4.35685	0.347715	0.173857	+	0.984771i	$0.444377\pi$
$158$	−4.29557	−0.341737
$159$	11.6304	0.922350
$160$	−2.98995	−0.236376
$161$	−13.4532	−1.06026
$162$	1.00000	0.0785674
$163$	−3.22333	−0.252471	−0.126235	−	0.992000i	$-0.540289\pi$
$163$	−3.22333	−0.252471	−0.126235	+	0.992000i	$0.540289\pi$
$164$	6.61752	0.516742
$165$	11.8445	0.922095
$166$	−12.1900	−0.946127
$167$	11.2600	0.871327	0.435663	−	0.900110i	$-0.356514\pi$
$167$	11.2600	0.871327	0.435663	+	0.900110i	$0.356514\pi$
$168$	−3.36753	−0.259811
$169$	1.00000	0.0769231
$170$	−5.63686	−0.432328
$171$	−7.32220	−0.559943
$172$	−4.18343	−0.318983
$173$	13.6284	1.03615	0.518074	−	0.855336i	$-0.326649\pi$
$173$	13.6284	1.03615	0.518074	+	0.855336i	$0.326649\pi$
$174$	8.71741	0.660865
$175$	13.2673	1.00292
$176$	3.96145	0.298606
$177$	0.371710	0.0279395
$178$	18.2704	1.36942
$179$	−19.3986	−1.44992	−0.724959	−	0.688792i	$-0.758142\pi$
$179$	−19.3986	−1.44992	−0.724959	+	0.688792i	$0.758142\pi$
$180$	−2.98995	−0.222857
$181$	0.359727	0.0267383	0.0133691	−	0.999911i	$-0.495744\pi$
$181$	0.359727	0.0267383	0.0133691	+	0.999911i	$0.495744\pi$
$182$	−3.36753	−0.249618
$183$	11.3295	0.837501
$184$	−3.99496	−0.294512
$185$	6.95459	0.511312
$186$	−1.96556	−0.144122
$187$	7.46842	0.546145
$188$	8.39320	0.612137
$189$	−3.36753	−0.244952
$190$	21.8930	1.58828
$191$	−8.40888	−0.608445	−0.304222	−	0.952601i	$-0.598397\pi$
$191$	−8.40888	−0.608445	−0.304222	+	0.952601i	$0.598397\pi$
$192$	−1.00000	−0.0721688
$193$	−7.29565	−0.525153	−0.262576	−	0.964911i	$-0.584572\pi$
$193$	−7.29565	−0.525153	−0.262576	+	0.964911i	$0.584572\pi$
$194$	1.18993	0.0854318
$195$	−2.98995	−0.214114
$196$	4.34029	0.310020
$197$	22.6951	1.61696	0.808478	−	0.588527i	$-0.200292\pi$
$197$	22.6951	1.61696	0.808478	+	0.588527i	$0.200292\pi$
$198$	3.96145	0.281528
$199$	−13.2639	−0.940251	−0.470126	−	0.882599i	$-0.655791\pi$
$199$	−13.2639	−0.940251	−0.470126	+	0.882599i	$0.655791\pi$
$200$	3.93978	0.278584
$201$	−3.43944	−0.242599
$202$	4.25536	0.299406
$203$	−29.3562	−2.06040
$204$	−1.88527	−0.131995
$205$	−19.7860	−1.38192
$206$	1.00000	0.0696733
$207$	−3.99496	−0.277669
$208$	−1.00000	−0.0693375
$209$	−29.0065	−2.00642
$210$	10.0687	0.694809
$211$	8.46427	0.582704	0.291352	−	0.956616i	$-0.405895\pi$
$211$	8.46427	0.582704	0.291352	+	0.956616i	$0.405895\pi$
$212$	−11.6304	−0.798779
$213$	−3.20633	−0.219694
$214$	−3.43481	−0.234799
$215$	12.5082	0.853054
$216$	−1.00000	−0.0680414
$217$	6.61908	0.449333
$218$	−11.8754	−0.804304
$219$	−0.938618	−0.0634259
$220$	−11.8445	−0.798558
$221$	−1.88527	−0.126817
$222$	2.32599	0.156110
$223$	25.4971	1.70741	0.853706	−	0.520756i	$-0.174350\pi$
$223$	25.4971	1.70741	0.853706	+	0.520756i	$0.174350\pi$
$224$	3.36753	0.225003
$225$	3.93978	0.262652
$226$	−16.0040	−1.06457
$227$	−17.5112	−1.16226	−0.581131	−	0.813810i	$-0.697389\pi$
$227$	−17.5112	−1.16226	−0.581131	+	0.813810i	$0.697389\pi$
$228$	7.32220	0.484924
$229$	12.7544	0.842831	0.421416	−	0.906868i	$-0.361533\pi$
$229$	12.7544	0.842831	0.421416	+	0.906868i	$0.361533\pi$
$230$	11.9447	0.787611
$231$	−13.3403	−0.877729
$232$	−8.71741	−0.572326
$233$	−4.94049	−0.323662	−0.161831	−	0.986818i	$-0.551740\pi$
$233$	−4.94049	−0.323662	−0.161831	+	0.986818i	$0.551740\pi$
$234$	−1.00000	−0.0653720
$235$	−25.0952	−1.63703
$236$	−0.371710	−0.0241963
$237$	4.29557	0.279027
$238$	6.34872	0.411526
$239$	7.50420	0.485406	0.242703	−	0.970101i	$-0.421966\pi$
$239$	7.50420	0.485406	0.242703	+	0.970101i	$0.421966\pi$
$240$	2.98995	0.193000
$241$	−7.65535	−0.493124	−0.246562	−	0.969127i	$-0.579301\pi$
$241$	−7.65535	−0.493124	−0.246562	+	0.969127i	$0.579301\pi$
$242$	4.69311	0.301684
$243$	−1.00000	−0.0641500
$244$	−11.3295	−0.725297
$245$	−12.9772	−0.829084
$246$	−6.61752	−0.421918
$247$	7.32220	0.465900
$248$	1.96556	0.124813
$249$	12.1900	0.772510
$250$	3.17001	0.200489
$251$	−15.8698	−1.00169	−0.500847	−	0.865536i	$-0.666978\pi$
$251$	−15.8698	−1.00169	−0.500847	+	0.865536i	$0.666978\pi$
$252$	3.36753	0.212135
$253$	−15.8258	−0.994962
$254$	1.19167	0.0747719
$255$	5.63686	0.352994
$256$	1.00000	0.0625000
$257$	−27.6097	−1.72225	−0.861123	−	0.508396i	$-0.830239\pi$
$257$	−27.6097	−1.72225	−0.861123	+	0.508396i	$0.830239\pi$
$258$	4.18343	0.260449
$259$	−7.83286	−0.486710
$260$	2.98995	0.185429
$261$	−8.71741	−0.539594
$262$	−7.75154	−0.478892
$263$	0.0484908	0.00299007	0.00149504	−	0.999999i	$-0.499524\pi$
$263$	0.0484908	0.00299007	0.00149504	+	0.999999i	$0.499524\pi$
$264$	−3.96145	−0.243811
$265$	34.7743	2.13617
$266$	−24.6578	−1.51186
$267$	−18.2704	−1.11813
$268$	3.43944	0.210097
$269$	0.0448286	0.00273325	0.00136662	−	0.999999i	$-0.499565\pi$
$269$	0.0448286	0.00273325	0.00136662	+	0.999999i	$0.499565\pi$
$270$	2.98995	0.181962
$271$	−31.9180	−1.93888	−0.969439	−	0.245333i	$-0.921103\pi$
$271$	−31.9180	−1.93888	−0.969439	+	0.245333i	$0.921103\pi$
$272$	1.88527	0.114311
$273$	3.36753	0.203812
$274$	−7.21052	−0.435603
$275$	15.6072	0.941152
$276$	3.99496	0.240468
$277$	−3.87624	−0.232900	−0.116450	−	0.993197i	$-0.537152\pi$
$277$	−3.87624	−0.232900	−0.116450	+	0.993197i	$0.537152\pi$
$278$	3.22021	0.193135
$279$	1.96556	0.117675
$280$	−10.0687	−0.601723
$281$	13.8117	0.823935	0.411968	−	0.911198i	$-0.364842\pi$
$281$	13.8117	0.823935	0.411968	+	0.911198i	$0.364842\pi$
$282$	−8.39320	−0.499808
$283$	−1.89656	−0.112739	−0.0563693	−	0.998410i	$-0.517952\pi$
$283$	−1.89656	−0.112739	−0.0563693	+	0.998410i	$0.517952\pi$
$284$	3.20633	0.190261
$285$	−21.8930	−1.29683
$286$	−3.96145	−0.234246
$287$	22.2847	1.31543
$288$	1.00000	0.0589256
$289$	−13.4457	−0.790926
$290$	26.0646	1.53056
$291$	−1.18993	−0.0697548
$292$	0.938618	0.0549284
$293$	11.1381	0.650693	0.325347	−	0.945595i	$-0.394519\pi$
$293$	11.1381	0.650693	0.325347	+	0.945595i	$0.394519\pi$
$294$	−4.34029	−0.253131
$295$	1.11139	0.0647079
$296$	−2.32599	−0.135196
$297$	−3.96145	−0.229867
$298$	14.6144	0.846587
$299$	3.99496	0.231034
$300$	−3.93978	−0.227463
$301$	−14.0878	−0.812009
$302$	−21.9812	−1.26488
$303$	−4.25536	−0.244464
$304$	−7.32220	−0.419957
$305$	33.8746	1.93965
$306$	1.88527	0.107774
$307$	−19.2222	−1.09707	−0.548534	−	0.836128i	$-0.684814\pi$
$307$	−19.2222	−1.09707	−0.548534	+	0.836128i	$0.684814\pi$
$308$	13.3403	0.760136
$309$	−1.00000	−0.0568880
$310$	−5.87691	−0.333786
$311$	−13.8049	−0.782802	−0.391401	−	0.920220i	$-0.628009\pi$
$311$	−13.8049	−0.782802	−0.391401	+	0.920220i	$0.628009\pi$
$312$	1.00000	0.0566139
$313$	−17.9113	−1.01241	−0.506203	−	0.862414i	$-0.668951\pi$
$313$	−17.9113	−1.01241	−0.506203	+	0.862414i	$0.668951\pi$
$314$	4.35685	0.245871
$315$	−10.0687	−0.567310
$316$	−4.29557	−0.241645
$317$	17.3801	0.976165	0.488083	−	0.872797i	$-0.337696\pi$
$317$	17.3801	0.976165	0.488083	+	0.872797i	$0.337696\pi$
$318$	11.6304	0.652200
$319$	−34.5336	−1.93351
$320$	−2.98995	−0.167143
$321$	3.43481	0.191712
$322$	−13.4532	−0.749715
$323$	−13.8043	−0.768094
$324$	1.00000	0.0555556
$325$	−3.93978	−0.218540
$326$	−3.22333	−0.178524
$327$	11.8754	0.656711
$328$	6.61752	0.365392
$329$	28.2644	1.55827
$330$	11.8445	0.652020
$331$	−18.0574	−0.992526	−0.496263	−	0.868172i	$-0.665295\pi$
$331$	−18.0574	−0.992526	−0.496263	+	0.868172i	$0.665295\pi$
$332$	−12.1900	−0.669013
$333$	−2.32599	−0.127464
$334$	11.2600	0.616121
$335$	−10.2837	−0.561861
$336$	−3.36753	−0.183714
$337$	−32.7236	−1.78257	−0.891284	−	0.453446i	$-0.850195\pi$
$337$	−32.7236	−1.78257	−0.891284	+	0.453446i	$0.850195\pi$
$338$	1.00000	0.0543928
$339$	16.0040	0.869218
$340$	−5.63686	−0.305702
$341$	7.78646	0.421661
$342$	−7.32220	−0.395939
$343$	−8.95668	−0.483615
$344$	−4.18343	−0.225555
$345$	−11.9447	−0.643081
$346$	13.6284	0.732667
$347$	−15.2856	−0.820572	−0.410286	−	0.911957i	$-0.634571\pi$
$347$	−15.2856	−0.820572	−0.410286	+	0.911957i	$0.634571\pi$
$348$	8.71741	0.467302
$349$	−9.53771	−0.510542	−0.255271	−	0.966870i	$-0.582165\pi$
$349$	−9.53771	−0.510542	−0.255271	+	0.966870i	$0.582165\pi$
$350$	13.2673	0.709169
$351$	1.00000	0.0533761
$352$	3.96145	0.211146
$353$	−13.9522	−0.742603	−0.371301	−	0.928512i	$-0.621088\pi$
$353$	−13.9522	−0.742603	−0.371301	+	0.928512i	$0.621088\pi$
$354$	0.371710	0.0197562
$355$	−9.58676	−0.508812
$356$	18.2704	0.968329
$357$	−6.34872	−0.336010
$358$	−19.3986	−1.02525
$359$	23.0761	1.21791	0.608954	−	0.793206i	$-0.291589\pi$
$359$	23.0761	1.21791	0.608954	+	0.793206i	$0.291589\pi$
$360$	−2.98995	−0.157584
$361$	34.6146	1.82182
$362$	0.359727	0.0189068
$363$	−4.69311	−0.246324
$364$	−3.36753	−0.176507
$365$	−2.80642	−0.146895
$366$	11.3295	0.592202
$367$	9.02794	0.471255	0.235627	−	0.971843i	$-0.424286\pi$
$367$	9.02794	0.471255	0.235627	+	0.971843i	$0.424286\pi$
$368$	−3.99496	−0.208252
$369$	6.61752	0.344494
$370$	6.95459	0.361552
$371$	−39.1658	−2.03338
$372$	−1.96556	−0.101909
$373$	−18.9151	−0.979385	−0.489692	−	0.871895i	$-0.662891\pi$
$373$	−18.9151	−0.979385	−0.489692	+	0.871895i	$0.662891\pi$
$374$	7.46842	0.386183
$375$	−3.17001	−0.163699
$376$	8.39320	0.432846
$377$	8.71741	0.448969
$378$	−3.36753	−0.173207
$379$	−27.6929	−1.42249	−0.711243	−	0.702946i	$-0.751867\pi$
$379$	−27.6929	−1.42249	−0.711243	+	0.702946i	$0.751867\pi$
$380$	21.8930	1.12309
$381$	−1.19167	−0.0610510
$382$	−8.40888	−0.430236
$383$	−4.43191	−0.226460	−0.113230	−	0.993569i	$-0.536120\pi$
$383$	−4.43191	−0.226460	−0.113230	+	0.993569i	$0.536120\pi$
$384$	−1.00000	−0.0510310
$385$	−39.8869	−2.03282
$386$	−7.29565	−0.371339
$387$	−4.18343	−0.212656
$388$	1.18993	0.0604094
$389$	−5.10864	−0.259018	−0.129509	−	0.991578i	$-0.541340\pi$
$389$	−5.10864	−0.259018	−0.129509	+	0.991578i	$0.541340\pi$
$390$	−2.98995	−0.151402
$391$	−7.53158	−0.380889
$392$	4.34029	0.219218
$393$	7.75154	0.391013
$394$	22.6951	1.14336
$395$	12.8435	0.646227
$396$	3.96145	0.199070
$397$	−25.6823	−1.28896	−0.644479	−	0.764622i	$-0.722926\pi$
$397$	−25.6823	−1.28896	−0.644479	+	0.764622i	$0.722926\pi$
$398$	−13.2639	−0.664858
$399$	24.6578	1.23443
$400$	3.93978	0.196989
$401$	−3.28901	−0.164245	−0.0821227	−	0.996622i	$-0.526170\pi$
$401$	−3.28901	−0.164245	−0.0821227	+	0.996622i	$0.526170\pi$
$402$	−3.43944	−0.171544
$403$	−1.96556	−0.0979114
$404$	4.25536	0.211712
$405$	−2.98995	−0.148572
$406$	−29.3562	−1.45692
$407$	−9.21431	−0.456736
$408$	−1.88527	−0.0933349
$409$	−19.2759	−0.953131	−0.476566	−	0.879139i	$-0.658119\pi$
$409$	−19.2759	−0.953131	−0.476566	+	0.879139i	$0.658119\pi$
$410$	−19.7860	−0.977163
$411$	7.21052	0.355669
$412$	1.00000	0.0492665
$413$	−1.25175	−0.0615945
$414$	−3.99496	−0.196341
$415$	36.4474	1.78913
$416$	−1.00000	−0.0490290
$417$	−3.22021	−0.157694
$418$	−29.0065	−1.41876
$419$	1.46668	0.0716522	0.0358261	−	0.999358i	$-0.488594\pi$
$419$	1.46668	0.0716522	0.0358261	+	0.999358i	$0.488594\pi$
$420$	10.0687	0.491304
$421$	−9.37200	−0.456764	−0.228382	−	0.973572i	$-0.573343\pi$
$421$	−9.37200	−0.456764	−0.228382	+	0.973572i	$0.573343\pi$
$422$	8.46427	0.412034
$423$	8.39320	0.408091
$424$	−11.6304	−0.564822
$425$	7.42755	0.360289
$426$	−3.20633	−0.155347
$427$	−38.1525	−1.84633
$428$	−3.43481	−0.166028
$429$	3.96145	0.191261
$430$	12.5082	0.603200
$431$	6.40339	0.308440	0.154220	−	0.988037i	$-0.450713\pi$
$431$	6.40339	0.308440	0.154220	+	0.988037i	$0.450713\pi$
$432$	−1.00000	−0.0481125
$433$	18.0095	0.865483	0.432741	−	0.901518i	$-0.357546\pi$
$433$	18.0095	0.865483	0.432741	+	0.901518i	$0.357546\pi$
$434$	6.61908	0.317726
$435$	−26.0646	−1.24970
$436$	−11.8754	−0.568729
$437$	29.2519	1.39931
$438$	−0.938618	−0.0448489
$439$	6.68092	0.318863	0.159432	−	0.987209i	$-0.449034\pi$
$439$	6.68092	0.318863	0.159432	+	0.987209i	$0.449034\pi$
$440$	−11.8445	−0.564666
$441$	4.34029	0.206680
$442$	−1.88527	−0.0896733
$443$	−32.1795	−1.52890	−0.764448	−	0.644686i	$-0.776988\pi$
$443$	−32.1795	−1.52890	−0.764448	+	0.644686i	$0.776988\pi$
$444$	2.32599	0.110387
$445$	−54.6275	−2.58959
$446$	25.4971	1.20732
$447$	−14.6144	−0.691235
$448$	3.36753	0.159101
$449$	41.6136	1.96387	0.981935	−	0.189220i	$-0.0605960\pi$
$449$	41.6136	1.96387	0.981935	+	0.189220i	$0.0605960\pi$
$450$	3.93978	0.185723
$451$	26.2150	1.23442
$452$	−16.0040	−0.752765
$453$	21.9812	1.03277
$454$	−17.5112	−0.821843
$455$	10.0687	0.472030
$456$	7.32220	0.342893
$457$	−16.0133	−0.749070	−0.374535	−	0.927213i	$-0.622198\pi$
$457$	−16.0133	−0.749070	−0.374535	+	0.927213i	$0.622198\pi$
$458$	12.7544	0.595972
$459$	−1.88527	−0.0879970
$460$	11.9447	0.556925
$461$	−11.6384	−0.542052	−0.271026	−	0.962572i	$-0.587363\pi$
$461$	−11.6384	−0.542052	−0.271026	+	0.962572i	$0.587363\pi$
$462$	−13.3403	−0.620648
$463$	12.2693	0.570202	0.285101	−	0.958497i	$-0.407973\pi$
$463$	12.2693	0.570202	0.285101	+	0.958497i	$0.407973\pi$
$464$	−8.71741	−0.404695
$465$	5.87691	0.272535
$466$	−4.94049	−0.228864
$467$	16.4922	0.763168	0.381584	−	0.924334i	$-0.375379\pi$
$467$	16.4922	0.763168	0.381584	+	0.924334i	$0.375379\pi$
$468$	−1.00000	−0.0462250
$469$	11.5824	0.534827
$470$	−25.0952	−1.15756
$471$	−4.35685	−0.200753
$472$	−0.371710	−0.0171094
$473$	−16.5724	−0.762002
$474$	4.29557	0.197302
$475$	−28.8478	−1.32363
$476$	6.34872	0.290993
$477$	−11.6304	−0.532519
$478$	7.50420	0.343234
$479$	−36.5476	−1.66990	−0.834950	−	0.550325i	$-0.814504\pi$
$479$	−36.5476	−1.66990	−0.834950	+	0.550325i	$0.814504\pi$
$480$	2.98995	0.136472
$481$	2.32599	0.106056
$482$	−7.65535	−0.348691
$483$	13.4532	0.612140
$484$	4.69311	0.213323
$485$	−3.55782	−0.161552
$486$	−1.00000	−0.0453609
$487$	−27.5989	−1.25063	−0.625314	−	0.780374i	$-0.715029\pi$
$487$	−27.5989	−1.25063	−0.625314	+	0.780374i	$0.715029\pi$
$488$	−11.3295	−0.512862
$489$	3.22333	0.145764
$490$	−12.9772	−0.586251
$491$	7.02874	0.317203	0.158601	−	0.987343i	$-0.449302\pi$
$491$	7.02874	0.317203	0.158601	+	0.987343i	$0.449302\pi$
$492$	−6.61752	−0.298341
$493$	−16.4347	−0.740181
$494$	7.32220	0.329441
$495$	−11.8445	−0.532372
$496$	1.96556	0.0882561
$497$	10.7974	0.484331
$498$	12.1900	0.546247
$499$	−0.497425	−0.0222678	−0.0111339	−	0.999938i	$-0.503544\pi$
$499$	−0.497425	−0.0222678	−0.0111339	+	0.999938i	$0.503544\pi$
$500$	3.17001	0.141767
$501$	−11.2600	−0.503061
$502$	−15.8698	−0.708305
$503$	40.8967	1.82350	0.911748	−	0.410751i	$-0.134733\pi$
$503$	40.8967	1.82350	0.911748	+	0.410751i	$0.134733\pi$
$504$	3.36753	0.150002
$505$	−12.7233	−0.566179
$506$	−15.8258	−0.703544
$507$	−1.00000	−0.0444116
$508$	1.19167	0.0528717
$509$	42.3634	1.87772	0.938861	−	0.344295i	$-0.111882\pi$
$509$	42.3634	1.87772	0.938861	+	0.344295i	$0.111882\pi$
$510$	5.63686	0.249605
$511$	3.16083	0.139827
$512$	1.00000	0.0441942
$513$	7.32220	0.323283
$514$	−27.6097	−1.21781
$515$	−2.98995	−0.131753
$516$	4.18343	0.184165
$517$	33.2493	1.46230
$518$	−7.83286	−0.344156
$519$	−13.6284	−0.598220
$520$	2.98995	0.131118
$521$	29.3941	1.28778	0.643889	−	0.765119i	$-0.277320\pi$
$521$	29.3941	1.28778	0.643889	+	0.765119i	$0.277320\pi$
$522$	−8.71741	−0.381551
$523$	3.33102	0.145655	0.0728276	−	0.997345i	$-0.476798\pi$
$523$	3.33102	0.145655	0.0728276	+	0.997345i	$0.476798\pi$
$524$	−7.75154	−0.338627
$525$	−13.2673	−0.579034
$526$	0.0484908	0.00211430
$527$	3.70561	0.161419
$528$	−3.96145	−0.172400
$529$	−7.04031	−0.306101
$530$	34.7743	1.51050
$531$	−0.371710	−0.0161309
$532$	−24.6578	−1.06905
$533$	−6.61752	−0.286637
$534$	−18.2704	−0.790637
$535$	10.2699	0.444006
$536$	3.43944	0.148561
$537$	19.3986	0.837111
$538$	0.0448286	0.00193270
$539$	17.1938	0.740591
$540$	2.98995	0.128667
$541$	12.2627	0.527214	0.263607	−	0.964630i	$-0.415088\pi$
$541$	12.2627	0.527214	0.263607	+	0.964630i	$0.415088\pi$
$542$	−31.9180	−1.37099
$543$	−0.359727	−0.0154373
$544$	1.88527	0.0808304
$545$	35.5068	1.52094
$546$	3.36753	0.144117
$547$	19.9837	0.854442	0.427221	−	0.904147i	$-0.359493\pi$
$547$	19.9837	0.854442	0.427221	+	0.904147i	$0.359493\pi$
$548$	−7.21052	−0.308018
$549$	−11.3295	−0.483531
$550$	15.6072	0.665495
$551$	63.8306	2.71927
$552$	3.99496	0.170037
$553$	−14.4655	−0.615134
$554$	−3.87624	−0.164685
$555$	−6.95459	−0.295206
$556$	3.22021	0.136567
$557$	13.5984	0.576182	0.288091	−	0.957603i	$-0.406979\pi$
$557$	13.5984	0.576182	0.288091	+	0.957603i	$0.406979\pi$
$558$	1.96556	0.0832087
$559$	4.18343	0.176940
$560$	−10.0687	−0.425482
$561$	−7.46842	−0.315317
$562$	13.8117	0.582610
$563$	17.7752	0.749136	0.374568	−	0.927199i	$-0.377791\pi$
$563$	17.7752	0.749136	0.374568	+	0.927199i	$0.377791\pi$
$564$	−8.39320	−0.353417
$565$	47.8511	2.01311
$566$	−1.89656	−0.0797183
$567$	3.36753	0.141423
$568$	3.20633	0.134535
$569$	−26.5730	−1.11400	−0.556999	−	0.830513i	$-0.688047\pi$
$569$	−26.5730	−1.11400	−0.556999	+	0.830513i	$0.688047\pi$
$570$	−21.8930	−0.916996
$571$	−11.5670	−0.484066	−0.242033	−	0.970268i	$-0.577814\pi$
$571$	−11.5670	−0.484066	−0.242033	+	0.970268i	$0.577814\pi$
$572$	−3.96145	−0.165637
$573$	8.40888	0.351286
$574$	22.2847	0.930147
$575$	−15.7392	−0.656372
$576$	1.00000	0.0416667
$577$	−9.79760	−0.407880	−0.203940	−	0.978983i	$-0.565375\pi$
$577$	−9.79760	−0.407880	−0.203940	+	0.978983i	$0.565375\pi$
$578$	−13.4457	−0.559269
$579$	7.29565	0.303197
$580$	26.0646	1.08227
$581$	−41.0502	−1.70305
$582$	−1.18993	−0.0493241
$583$	−46.0733	−1.90816
$584$	0.938618	0.0388403
$585$	2.98995	0.123619
$586$	11.1381	0.460110
$587$	1.40763	0.0580990	0.0290495	−	0.999578i	$-0.490752\pi$
$587$	1.40763	0.0580990	0.0290495	+	0.999578i	$0.490752\pi$
$588$	−4.34029	−0.178990
$589$	−14.3922	−0.593020
$590$	1.11139	0.0457554
$591$	−22.6951	−0.933550
$592$	−2.32599	−0.0955977
$593$	−28.7339	−1.17996	−0.589980	−	0.807418i	$-0.700864\pi$
$593$	−28.7339	−1.17996	−0.589980	+	0.807418i	$0.700864\pi$
$594$	−3.96145	−0.162540
$595$	−18.9823	−0.778200
$596$	14.6144	0.598627
$597$	13.2639	0.542854
$598$	3.99496	0.163366
$599$	21.3086	0.870646	0.435323	−	0.900274i	$-0.356634\pi$
$599$	21.3086	0.870646	0.435323	+	0.900274i	$0.356634\pi$
$600$	−3.93978	−0.160841
$601$	−33.3921	−1.36209	−0.681045	−	0.732241i	$-0.738474\pi$
$601$	−33.3921	−1.36209	−0.681045	+	0.732241i	$0.738474\pi$
$602$	−14.0878	−0.574177
$603$	3.43944	0.140065
$604$	−21.9812	−0.894402
$605$	−14.0321	−0.570488
$606$	−4.25536	−0.172862
$607$	−4.80223	−0.194917	−0.0974583	−	0.995240i	$-0.531071\pi$
$607$	−4.80223	−0.194917	−0.0974583	+	0.995240i	$0.531071\pi$
$608$	−7.32220	−0.296954
$609$	29.3562	1.18957
$610$	33.8746	1.37154
$611$	−8.39320	−0.339552
$612$	1.88527	0.0762076
$613$	11.4718	0.463340	0.231670	−	0.972794i	$-0.425581\pi$
$613$	11.4718	0.463340	0.231670	+	0.972794i	$0.425581\pi$
$614$	−19.2222	−0.775745
$615$	19.7860	0.797850
$616$	13.3403	0.537497
$617$	−28.9082	−1.16380	−0.581901	−	0.813260i	$-0.697691\pi$
$617$	−28.9082	−1.16380	−0.581901	+	0.813260i	$0.697691\pi$
$618$	−1.00000	−0.0402259
$619$	40.4238	1.62477	0.812385	−	0.583122i	$-0.198169\pi$
$619$	40.4238	1.62477	0.812385	+	0.583122i	$0.198169\pi$
$620$	−5.87691	−0.236022
$621$	3.99496	0.160312
$622$	−13.8049	−0.553525
$623$	61.5262	2.46499
$624$	1.00000	0.0400320
$625$	−29.1770	−1.16708
$626$	−17.9113	−0.715879
$627$	29.0065	1.15841
$628$	4.35685	0.173857
$629$	−4.38513	−0.174847
$630$	−10.0687	−0.401148
$631$	−14.3541	−0.571430	−0.285715	−	0.958315i	$-0.592231\pi$
$631$	−14.3541	−0.571430	−0.285715	+	0.958315i	$0.592231\pi$
$632$	−4.29557	−0.170869
$633$	−8.46427	−0.336424
$634$	17.3801	0.690253
$635$	−3.56302	−0.141394
$636$	11.6304	0.461175
$637$	−4.34029	−0.171968
$638$	−34.5336	−1.36720
$639$	3.20633	0.126840
$640$	−2.98995	−0.118188
$641$	19.8536	0.784169	0.392084	−	0.919929i	$-0.371754\pi$
$641$	19.8536	0.784169	0.392084	+	0.919929i	$0.371754\pi$
$642$	3.43481	0.135561
$643$	28.0440	1.10595	0.552974	−	0.833199i	$-0.313493\pi$
$643$	28.0440	1.10595	0.552974	+	0.833199i	$0.313493\pi$
$644$	−13.4532	−0.530129
$645$	−12.5082	−0.492511
$646$	−13.8043	−0.543125
$647$	−29.4151	−1.15643	−0.578213	−	0.815886i	$-0.696250\pi$
$647$	−29.4151	−1.15643	−0.578213	+	0.815886i	$0.696250\pi$
$648$	1.00000	0.0392837
$649$	−1.47251	−0.0578012
$650$	−3.93978	−0.154531
$651$	−6.61908	−0.259422
$652$	−3.22333	−0.126235
$653$	9.86329	0.385980	0.192990	−	0.981201i	$-0.438181\pi$
$653$	9.86329	0.385980	0.192990	+	0.981201i	$0.438181\pi$
$654$	11.8754	0.464365
$655$	23.1767	0.905588
$656$	6.61752	0.258371
$657$	0.938618	0.0366190
$658$	28.2644	1.10186
$659$	26.7818	1.04327	0.521636	−	0.853168i	$-0.325322\pi$
$659$	26.7818	1.04327	0.521636	+	0.853168i	$0.325322\pi$
$660$	11.8445	0.461048
$661$	−42.5690	−1.65574	−0.827871	−	0.560919i	$-0.810448\pi$
$661$	−42.5690	−1.65574	−0.827871	+	0.560919i	$0.810448\pi$
$662$	−18.0574	−0.701822
$663$	1.88527	0.0732179
$664$	−12.1900	−0.473064
$665$	73.7254	2.85895
$666$	−2.32599	−0.0901304
$667$	34.8257	1.34846
$668$	11.2600	0.435663
$669$	−25.4971	−0.985774
$670$	−10.2837	−0.397296
$671$	−44.8813	−1.73262
$672$	−3.36753	−0.129905
$673$	32.1094	1.23773	0.618863	−	0.785499i	$-0.287594\pi$
$673$	32.1094	1.23773	0.618863	+	0.785499i	$0.287594\pi$
$674$	−32.7236	−1.26047
$675$	−3.93978	−0.151642
$676$	1.00000	0.0384615
$677$	15.4786	0.594889	0.297445	−	0.954739i	$-0.403866\pi$
$677$	15.4786	0.594889	0.297445	+	0.954739i	$0.403866\pi$
$678$	16.0040	0.614630
$679$	4.00712	0.153779
$680$	−5.63686	−0.216164
$681$	17.5112	0.671032
$682$	7.78646	0.298159
$683$	−17.5947	−0.673243	−0.336622	−	0.941640i	$-0.609284\pi$
$683$	−17.5947	−0.673243	−0.336622	+	0.941640i	$0.609284\pi$
$684$	−7.32220	−0.279971
$685$	21.5591	0.823729
$686$	−8.95668	−0.341968
$687$	−12.7544	−0.486609
$688$	−4.18343	−0.159492
$689$	11.6304	0.443083
$690$	−11.9447	−0.454727
$691$	8.74227	0.332571	0.166286	−	0.986078i	$-0.446823\pi$
$691$	8.74227	0.332571	0.166286	+	0.986078i	$0.446823\pi$
$692$	13.6284	0.518074
$693$	13.3403	0.506757
$694$	−15.2856	−0.580232
$695$	−9.62824	−0.365220
$696$	8.71741	0.330432
$697$	12.4758	0.472556
$698$	−9.53771	−0.361008
$699$	4.94049	0.186866
$700$	13.2673	0.501458
$701$	39.7969	1.50311	0.751555	−	0.659671i	$-0.229304\pi$
$701$	39.7969	1.50311	0.751555	+	0.659671i	$0.229304\pi$
$702$	1.00000	0.0377426
$703$	17.0314	0.642351
$704$	3.96145	0.149303
$705$	25.0952	0.945140
$706$	−13.9522	−0.525100
$707$	14.3301	0.538937
$708$	0.371710	0.0139697
$709$	29.5019	1.10797	0.553983	−	0.832528i	$-0.313107\pi$
$709$	29.5019	1.10797	0.553983	+	0.832528i	$0.313107\pi$
$710$	−9.58676	−0.359785
$711$	−4.29557	−0.161096
$712$	18.2704	0.684712
$713$	−7.85232	−0.294072
$714$	−6.34872	−0.237595
$715$	11.8445	0.442960
$716$	−19.3986	−0.724959
$717$	−7.50420	−0.280250
$718$	23.0761	0.861191
$719$	30.3057	1.13021	0.565106	−	0.825019i	$-0.308835\pi$
$719$	30.3057	1.13021	0.565106	+	0.825019i	$0.308835\pi$
$720$	−2.98995	−0.111429
$721$	3.36753	0.125414
$722$	34.6146	1.28822
$723$	7.65535	0.284705
$724$	0.359727	0.0133691
$725$	−34.3446	−1.27553
$726$	−4.69311	−0.174178
$727$	22.1684	0.822181	0.411090	−	0.911595i	$-0.365148\pi$
$727$	22.1684	0.822181	0.411090	+	0.911595i	$0.365148\pi$
$728$	−3.36753	−0.124809
$729$	1.00000	0.0370370
$730$	−2.80642	−0.103870
$731$	−7.88690	−0.291708
$732$	11.3295	0.418750
$733$	53.4431	1.97397	0.986983	−	0.160824i	$-0.0514152\pi$
$733$	53.4431	1.97397	0.986983	+	0.160824i	$0.0514152\pi$
$734$	9.02794	0.333227
$735$	12.9772	0.478672
$736$	−3.99496	−0.147256
$737$	13.6252	0.501890
$738$	6.61752	0.243594
$739$	−42.2998	−1.55602	−0.778012	−	0.628250i	$-0.783772\pi$
$739$	−42.2998	−1.55602	−0.778012	+	0.628250i	$0.783772\pi$
$740$	6.95459	0.255656
$741$	−7.32220	−0.268988
$742$	−39.1658	−1.43782
$743$	−43.1487	−1.58297	−0.791486	−	0.611188i	$-0.790692\pi$
$743$	−43.1487	−1.58297	−0.791486	+	0.611188i	$0.790692\pi$
$744$	−1.96556	−0.0720608
$745$	−43.6961	−1.60090
$746$	−18.9151	−0.692530
$747$	−12.1900	−0.446009
$748$	7.46842	0.273072
$749$	−11.5668	−0.422643
$750$	−3.17001	−0.115752
$751$	4.11708	0.150234	0.0751171	−	0.997175i	$-0.476067\pi$
$751$	4.11708	0.150234	0.0751171	+	0.997175i	$0.476067\pi$
$752$	8.39320	0.306068
$753$	15.8698	0.578328
$754$	8.71741	0.317469
$755$	65.7226	2.39189
$756$	−3.36753	−0.122476
$757$	23.2886	0.846437	0.423219	−	0.906028i	$-0.360900\pi$
$757$	23.2886	0.846437	0.423219	+	0.906028i	$0.360900\pi$
$758$	−27.6929	−1.00585
$759$	15.8258	0.574441
$760$	21.8930	0.794142
$761$	−11.3353	−0.410903	−0.205452	−	0.978667i	$-0.565866\pi$
$761$	−11.3353	−0.410903	−0.205452	+	0.978667i	$0.565866\pi$
$762$	−1.19167	−0.0431696
$763$	−39.9908	−1.44777
$764$	−8.40888	−0.304222
$765$	−5.63686	−0.203801
$766$	−4.43191	−0.160131
$767$	0.371710	0.0134217
$768$	−1.00000	−0.0360844
$769$	44.4540	1.60305	0.801527	−	0.597959i	$-0.204022\pi$
$769$	44.4540	1.60305	0.801527	+	0.597959i	$0.204022\pi$
$770$	−39.8869	−1.43742
$771$	27.6097	0.994340
$772$	−7.29565	−0.262576
$773$	−26.8309	−0.965040	−0.482520	−	0.875885i	$-0.660278\pi$
$773$	−26.8309	−0.965040	−0.482520	+	0.875885i	$0.660278\pi$
$774$	−4.18343	−0.150370
$775$	7.74386	0.278168
$776$	1.18993	0.0427159
$777$	7.83286	0.281002
$778$	−5.10864	−0.183153
$779$	−48.4548	−1.73607
$780$	−2.98995	−0.107057
$781$	12.7017	0.454504
$782$	−7.53158	−0.269329
$783$	8.71741	0.311535
$784$	4.34029	0.155010
$785$	−13.0267	−0.464945
$786$	7.75154	0.276488
$787$	6.13664	0.218747	0.109374	−	0.994001i	$-0.465115\pi$
$787$	6.13664	0.218747	0.109374	+	0.994001i	$0.465115\pi$
$788$	22.6951	0.808478
$789$	−0.0484908	−0.00172632
$790$	12.8435	0.456952
$791$	−53.8940	−1.91625
$792$	3.96145	0.140764
$793$	11.3295	0.402322
$794$	−25.6823	−0.911431
$795$	−34.7743	−1.23332
$796$	−13.2639	−0.470126
$797$	11.2523	0.398576	0.199288	−	0.979941i	$-0.436137\pi$
$797$	11.2523	0.398576	0.199288	+	0.979941i	$0.436137\pi$
$798$	24.6578	0.872875
$799$	15.8235	0.559794
$800$	3.93978	0.139292
$801$	18.2704	0.645552
$802$	−3.28901	−0.116139
$803$	3.71829	0.131216
$804$	−3.43944	−0.121300
$805$	40.2242	1.41772
$806$	−1.96556	−0.0692338
$807$	−0.0448286	−0.00157804
$808$	4.25536	0.149703
$809$	−47.3200	−1.66368	−0.831841	−	0.555014i	$-0.812713\pi$
$809$	−47.3200	−1.66368	−0.831841	+	0.555014i	$0.812713\pi$
$810$	−2.98995	−0.105056
$811$	39.8628	1.39977	0.699886	−	0.714255i	$-0.253234\pi$
$811$	39.8628	1.39977	0.699886	+	0.714255i	$0.253234\pi$
$812$	−29.3562	−1.03020
$813$	31.9180	1.11941
$814$	−9.21431	−0.322961
$815$	9.63758	0.337590
$816$	−1.88527	−0.0659977
$817$	30.6319	1.07167
$818$	−19.2759	−0.673966
$819$	−3.36753	−0.117671
$820$	−19.7860	−0.690958
$821$	18.2811	0.638016	0.319008	−	0.947752i	$-0.396650\pi$
$821$	18.2811	0.638016	0.319008	+	0.947752i	$0.396650\pi$
$822$	7.21052	0.251496
$823$	−42.5308	−1.48253	−0.741265	−	0.671212i	$-0.765774\pi$
$823$	−42.5308	−1.48253	−0.741265	+	0.671212i	$0.765774\pi$
$824$	1.00000	0.0348367
$825$	−15.6072	−0.543374
$826$	−1.25175	−0.0435539
$827$	−21.4092	−0.744471	−0.372236	−	0.928138i	$-0.621409\pi$
$827$	−21.4092	−0.744471	−0.372236	+	0.928138i	$0.621409\pi$
$828$	−3.99496	−0.138834
$829$	5.95323	0.206764	0.103382	−	0.994642i	$-0.467034\pi$
$829$	5.95323	0.206764	0.103382	+	0.994642i	$0.467034\pi$
$830$	36.4474	1.26511
$831$	3.87624	0.134465
$832$	−1.00000	−0.0346688
$833$	8.18262	0.283511
$834$	−3.22021	−0.111507
$835$	−33.6669	−1.16509
$836$	−29.0065	−1.00321
$837$	−1.96556	−0.0679396
$838$	1.46668	0.0506657
$839$	−18.1862	−0.627857	−0.313929	−	0.949447i	$-0.601645\pi$
$839$	−18.1862	−0.627857	−0.313929	+	0.949447i	$0.601645\pi$
$840$	10.0687	0.347405
$841$	46.9932	1.62045
$842$	−9.37200	−0.322981
$843$	−13.8117	−0.475699
$844$	8.46427	0.291352
$845$	−2.98995	−0.102857
$846$	8.39320	0.288564
$847$	15.8042	0.543039
$848$	−11.6304	−0.399389
$849$	1.89656	0.0650897
$850$	7.42755	0.254763
$851$	9.29224	0.318534
$852$	−3.20633	−0.109847
$853$	−5.31961	−0.182140	−0.0910700	−	0.995844i	$-0.529029\pi$
$853$	−5.31961	−0.182140	−0.0910700	+	0.995844i	$0.529029\pi$
$854$	−38.1525	−1.30555
$855$	21.8930	0.748724
$856$	−3.43481	−0.117399
$857$	−20.9234	−0.714729	−0.357365	−	0.933965i	$-0.616325\pi$
$857$	−20.9234	−0.714729	−0.357365	+	0.933965i	$0.616325\pi$
$858$	3.96145	0.135242
$859$	−8.50182	−0.290078	−0.145039	−	0.989426i	$-0.546331\pi$
$859$	−8.50182	−0.290078	−0.145039	+	0.989426i	$0.546331\pi$
$860$	12.5082	0.426527
$861$	−22.2847	−0.759462
$862$	6.40339	0.218100
$863$	−17.0303	−0.579720	−0.289860	−	0.957069i	$-0.593609\pi$
$863$	−17.0303	−0.579720	−0.289860	+	0.957069i	$0.593609\pi$
$864$	−1.00000	−0.0340207
$865$	−40.7482	−1.38548
$866$	18.0095	0.611989
$867$	13.4457	0.456641
$868$	6.61908	0.224666
$869$	−17.0167	−0.577252
$870$	−26.0646	−0.883672
$871$	−3.43944	−0.116541
$872$	−11.8754	−0.402152
$873$	1.18993	0.0402729
$874$	29.2519	0.989459
$875$	10.6751	0.360885
$876$	−0.938618	−0.0317129
$877$	−30.7544	−1.03850	−0.519251	−	0.854622i	$-0.673789\pi$
$877$	−30.7544	−1.03850	−0.519251	+	0.854622i	$0.673789\pi$
$878$	6.68092	0.225470
$879$	−11.1381	−0.375678
$880$	−11.8445	−0.399279
$881$	46.4661	1.56548	0.782741	−	0.622347i	$-0.213821\pi$
$881$	46.4661	1.56548	0.782741	+	0.622347i	$0.213821\pi$
$882$	4.34029	0.146145
$883$	−31.5818	−1.06281	−0.531406	−	0.847117i	$-0.678336\pi$
$883$	−31.5818	−1.06281	−0.531406	+	0.847117i	$0.678336\pi$
$884$	−1.88527	−0.0634086
$885$	−1.11139	−0.0373591
$886$	−32.1795	−1.08109
$887$	44.6676	1.49979	0.749896	−	0.661556i	$-0.230104\pi$
$887$	44.6676	1.49979	0.749896	+	0.661556i	$0.230104\pi$
$888$	2.32599	0.0780552
$889$	4.01298	0.134591
$890$	−54.6275	−1.83112
$891$	3.96145	0.132714
$892$	25.4971	0.853706
$893$	−61.4567	−2.05657
$894$	−14.6144	−0.488777
$895$	58.0007	1.93875
$896$	3.36753	0.112501
$897$	−3.99496	−0.133388
$898$	41.6136	1.38867
$899$	−17.1346	−0.571470
$900$	3.93978	0.131326
$901$	−21.9265	−0.730476
$902$	26.2150	0.872864
$903$	14.0878	0.468814
$904$	−16.0040	−0.532285
$905$	−1.07556	−0.0357529
$906$	21.9812	0.730276
$907$	6.43700	0.213737	0.106869	−	0.994273i	$-0.465918\pi$
$907$	6.43700	0.213737	0.106869	+	0.994273i	$0.465918\pi$
$908$	−17.5112	−0.581131
$909$	4.25536	0.141141
$910$	10.0687	0.333776
$911$	−53.3685	−1.76818	−0.884088	−	0.467320i	$-0.845220\pi$
$911$	−53.3685	−1.76818	−0.884088	+	0.467320i	$0.845220\pi$
$912$	7.32220	0.242462
$913$	−48.2901	−1.59817
$914$	−16.0133	−0.529672
$915$	−33.8746	−1.11986
$916$	12.7544	0.421416
$917$	−26.1036	−0.862016
$918$	−1.88527	−0.0622233
$919$	10.9239	0.360346	0.180173	−	0.983635i	$-0.442334\pi$
$919$	10.9239	0.360346	0.180173	+	0.983635i	$0.442334\pi$
$920$	11.9447	0.393805
$921$	19.2222	0.633393
$922$	−11.6384	−0.383289
$923$	−3.20633	−0.105538
$924$	−13.3403	−0.438865
$925$	−9.16389	−0.301307
$926$	12.2693	0.403194
$927$	1.00000	0.0328443
$928$	−8.71741	−0.286163
$929$	54.3605	1.78351	0.891755	−	0.452519i	$-0.149475\pi$
$929$	54.3605	1.78351	0.891755	+	0.452519i	$0.149475\pi$
$930$	5.87691	0.192711
$931$	−31.7804	−1.04156
$932$	−4.94049	−0.161831
$933$	13.8049	0.451951
$934$	16.4922	0.539641
$935$	−22.3302	−0.730275
$936$	−1.00000	−0.0326860
$937$	47.1115	1.53907	0.769533	−	0.638607i	$-0.220489\pi$
$937$	47.1115	1.53907	0.769533	+	0.638607i	$0.220489\pi$
$938$	11.5824	0.378180
$939$	17.9113	0.584513
$940$	−25.0952	−0.818515
$941$	−6.37632	−0.207862	−0.103931	−	0.994585i	$-0.533142\pi$
$941$	−6.37632	−0.207862	−0.103931	+	0.994585i	$0.533142\pi$
$942$	−4.35685	−0.141954
$943$	−26.4367	−0.860898
$944$	−0.371710	−0.0120981
$945$	10.0687	0.327536
$946$	−16.5724	−0.538817
$947$	56.1804	1.82562	0.912809	−	0.408387i	$-0.133909\pi$
$947$	56.1804	1.82562	0.912809	+	0.408387i	$0.133909\pi$
$948$	4.29557	0.139514
$949$	−0.938618	−0.0304688
$950$	−28.8478	−0.935947
$951$	−17.3801	−0.563589
$952$	6.34872	0.205763
$953$	36.3008	1.17590	0.587949	−	0.808898i	$-0.299935\pi$
$953$	36.3008	1.17590	0.587949	+	0.808898i	$0.299935\pi$
$954$	−11.6304	−0.376548
$955$	25.1421	0.813579
$956$	7.50420	0.242703
$957$	34.5336	1.11631
$958$	−36.5476	−1.18080
$959$	−24.2817	−0.784096
$960$	2.98995	0.0965001
$961$	−27.1366	−0.875374
$962$	2.32599	0.0749930
$963$	−3.43481	−0.110685
$964$	−7.65535	−0.246562
$965$	21.8136	0.702205
$966$	13.4532	0.432848
$967$	−0.556441	−0.0178939	−0.00894697	−	0.999960i	$-0.502848\pi$
$967$	−0.556441	−0.0178939	−0.00894697	+	0.999960i	$0.502848\pi$
$968$	4.69311	0.150842
$969$	13.8043	0.443459
$970$	−3.55782	−0.114235
$971$	19.7572	0.634038	0.317019	−	0.948419i	$-0.397318\pi$
$971$	19.7572	0.634038	0.317019	+	0.948419i	$0.397318\pi$
$972$	−1.00000	−0.0320750
$973$	10.8442	0.347648
$974$	−27.5989	−0.884327
$975$	3.93978	0.126174
$976$	−11.3295	−0.362648
$977$	−11.6126	−0.371520	−0.185760	−	0.982595i	$-0.559475\pi$
$977$	−11.6126	−0.371520	−0.185760	+	0.982595i	$0.559475\pi$
$978$	3.22333	0.103071
$979$	72.3773	2.31319
$980$	−12.9772	−0.414542
$981$	−11.8754	−0.379152
$982$	7.02874	0.224296
$983$	44.1417	1.40790	0.703951	−	0.710249i	$-0.251418\pi$
$983$	44.1417	1.40790	0.703951	+	0.710249i	$0.251418\pi$
$984$	−6.61752	−0.210959
$985$	−67.8570	−2.16210
$986$	−16.4347	−0.523387
$987$	−28.2644	−0.899665
$988$	7.32220	0.232950
$989$	16.7126	0.531430
$990$	−11.8445	−0.376444
$991$	32.7778	1.04122	0.520610	−	0.853794i	$-0.325704\pi$
$991$	32.7778	1.04122	0.520610	+	0.853794i	$0.325704\pi$
$992$	1.96556	0.0624065
$993$	18.0574	0.573035
$994$	10.7974	0.342474
$995$	39.6583	1.25725
$996$	12.1900	0.386255
$997$	−42.6152	−1.34964	−0.674819	−	0.737983i	$-0.735778\pi$
$997$	−42.6152	−1.34964	−0.674819	+	0.737983i	$0.735778\pi$
$998$	−0.497425	−0.0157457
$999$	2.32599	0.0735912

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.u.1.2	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.u.1.2	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.98995 q^{5} -1.00000 q^{6} +3.36753 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.98995 q^{5} -1.00000 q^{6} +3.36753 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.98995 q^{10} +3.96145 q^{11} -1.00000 q^{12} -1.00000 q^{13} +3.36753 q^{14} +2.98995 q^{15} +1.00000 q^{16} +1.88527 q^{17} +1.00000 q^{18} -7.32220 q^{19} -2.98995 q^{20} -3.36753 q^{21} +3.96145 q^{22} -3.99496 q^{23} -1.00000 q^{24} +3.93978 q^{25} -1.00000 q^{26} -1.00000 q^{27} +3.36753 q^{28} -8.71741 q^{29} +2.98995 q^{30} +1.96556 q^{31} +1.00000 q^{32} -3.96145 q^{33} +1.88527 q^{34} -10.0687 q^{35} +1.00000 q^{36} -2.32599 q^{37} -7.32220 q^{38} +1.00000 q^{39} -2.98995 q^{40} +6.61752 q^{41} -3.36753 q^{42} -4.18343 q^{43} +3.96145 q^{44} -2.98995 q^{45} -3.99496 q^{46} +8.39320 q^{47} -1.00000 q^{48} +4.34029 q^{49} +3.93978 q^{50} -1.88527 q^{51} -1.00000 q^{52} -11.6304 q^{53} -1.00000 q^{54} -11.8445 q^{55} +3.36753 q^{56} +7.32220 q^{57} -8.71741 q^{58} -0.371710 q^{59} +2.98995 q^{60} -11.3295 q^{61} +1.96556 q^{62} +3.36753 q^{63} +1.00000 q^{64} +2.98995 q^{65} -3.96145 q^{66} +3.43944 q^{67} +1.88527 q^{68} +3.99496 q^{69} -10.0687 q^{70} +3.20633 q^{71} +1.00000 q^{72} +0.938618 q^{73} -2.32599 q^{74} -3.93978 q^{75} -7.32220 q^{76} +13.3403 q^{77} +1.00000 q^{78} -4.29557 q^{79} -2.98995 q^{80} +1.00000 q^{81} +6.61752 q^{82} -12.1900 q^{83} -3.36753 q^{84} -5.63686 q^{85} -4.18343 q^{86} +8.71741 q^{87} +3.96145 q^{88} +18.2704 q^{89} -2.98995 q^{90} -3.36753 q^{91} -3.99496 q^{92} -1.96556 q^{93} +8.39320 q^{94} +21.8930 q^{95} -1.00000 q^{96} +1.18993 q^{97} +4.34029 q^{98} +3.96145 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} - 2 q^{5} - 11 q^{6} - 2 q^{7} + 11 q^{8} + 11 q^{9}+O(q^{10}) \) 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 - 2 * q^5 - 11 * q^6 - 2 * q^7 + 11 * q^8 + 11 * q^9	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} - 2 q^{5} - 11 q^{6} - 2 q^{7} + 11 q^{8} + 11 q^{9} - 2 q^{10} - 10 q^{11} - 11 q^{12} - 11 q^{13} - 2 q^{14} + 2 q^{15} + 11 q^{16} + 6 q^{17} + 11 q^{18} - 3 q^{19} - 2 q^{20} + 2 q^{21} - 10 q^{22} + 3 q^{23} - 11 q^{24} - q^{25} - 11 q^{26} - 11 q^{27} - 2 q^{28} - 22 q^{29} + 2 q^{30} - 5 q^{31} + 11 q^{32} + 10 q^{33} + 6 q^{34} - 20 q^{35} + 11 q^{36} - 26 q^{37} - 3 q^{38} + 11 q^{39} - 2 q^{40} - 6 q^{41} + 2 q^{42} - 8 q^{43} - 10 q^{44} - 2 q^{45} + 3 q^{46} + 6 q^{47} - 11 q^{48} - 5 q^{49} - q^{50} - 6 q^{51} - 11 q^{52} - 25 q^{53} - 11 q^{54} - 2 q^{56} + 3 q^{57} - 22 q^{58} + 7 q^{59} + 2 q^{60} - 36 q^{61} - 5 q^{62} - 2 q^{63} + 11 q^{64} + 2 q^{65} + 10 q^{66} - 12 q^{67} + 6 q^{68} - 3 q^{69} - 20 q^{70} - 15 q^{71} + 11 q^{72} - 12 q^{73} - 26 q^{74} + q^{75} - 3 q^{76} - q^{77} + 11 q^{78} - 15 q^{79} - 2 q^{80} + 11 q^{81} - 6 q^{82} - 16 q^{83} + 2 q^{84} - 25 q^{85} - 8 q^{86} + 22 q^{87} - 10 q^{88} - 2 q^{89} - 2 q^{90} + 2 q^{91} + 3 q^{92} + 5 q^{93} + 6 q^{94} + 16 q^{95} - 11 q^{96} - 10 q^{97} - 5 q^{98} - 10 q^{99}+O(q^{100}) \) 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 - 2 * q^5 - 11 * q^6 - 2 * q^7 + 11 * q^8 + 11 * q^9 - 2 * q^10 - 10 * q^11 - 11 * q^12 - 11 * q^13 - 2 * q^14 + 2 * q^15 + 11 * q^16 + 6 * q^17 + 11 * q^18 - 3 * q^19 - 2 * q^20 + 2 * q^21 - 10 * q^22 + 3 * q^23 - 11 * q^24 - q^25 - 11 * q^26 - 11 * q^27 - 2 * q^28 - 22 * q^29 + 2 * q^30 - 5 * q^31 + 11 * q^32 + 10 * q^33 + 6 * q^34 - 20 * q^35 + 11 * q^36 - 26 * q^37 - 3 * q^38 + 11 * q^39 - 2 * q^40 - 6 * q^41 + 2 * q^42 - 8 * q^43 - 10 * q^44 - 2 * q^45 + 3 * q^46 + 6 * q^47 - 11 * q^48 - 5 * q^49 - q^50 - 6 * q^51 - 11 * q^52 - 25 * q^53 - 11 * q^54 - 2 * q^56 + 3 * q^57 - 22 * q^58 + 7 * q^59 + 2 * q^60 - 36 * q^61 - 5 * q^62 - 2 * q^63 + 11 * q^64 + 2 * q^65 + 10 * q^66 - 12 * q^67 + 6 * q^68 - 3 * q^69 - 20 * q^70 - 15 * q^71 + 11 * q^72 - 12 * q^73 - 26 * q^74 + q^75 - 3 * q^76 - q^77 + 11 * q^78 - 15 * q^79 - 2 * q^80 + 11 * q^81 - 6 * q^82 - 16 * q^83 + 2 * q^84 - 25 * q^85 - 8 * q^86 + 22 * q^87 - 10 * q^88 - 2 * q^89 - 2 * q^90 + 2 * q^91 + 3 * q^92 + 5 * q^93 + 6 * q^94 + 16 * q^95 - 11 * q^96 - 10 * q^97 - 5 * q^98 - 10 * q^99

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