LMFDB - Embedded newform 8034.2.a.u.1.11

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			1.11
Root			$0.722678$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.07315 q^{5} -1.00000 q^{6} +1.35002 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.07315 q^{5} -1.00000 q^{6} +1.35002 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.07315 q^{10} -4.89632 q^{11} -1.00000 q^{12} -1.00000 q^{13} +1.35002 q^{14} -3.07315 q^{15} +1.00000 q^{16} -1.97318 q^{17} +1.00000 q^{18} +2.41746 q^{19} +3.07315 q^{20} -1.35002 q^{21} -4.89632 q^{22} -6.79256 q^{23} -1.00000 q^{24} +4.44424 q^{25} -1.00000 q^{26} -1.00000 q^{27} +1.35002 q^{28} -8.43275 q^{29} -3.07315 q^{30} -4.76941 q^{31} +1.00000 q^{32} +4.89632 q^{33} -1.97318 q^{34} +4.14881 q^{35} +1.00000 q^{36} -7.88412 q^{37} +2.41746 q^{38} +1.00000 q^{39} +3.07315 q^{40} +0.626941 q^{41} -1.35002 q^{42} +6.69991 q^{43} -4.89632 q^{44} +3.07315 q^{45} -6.79256 q^{46} +4.68192 q^{47} -1.00000 q^{48} -5.17745 q^{49} +4.44424 q^{50} +1.97318 q^{51} -1.00000 q^{52} -7.22179 q^{53} -1.00000 q^{54} -15.0471 q^{55} +1.35002 q^{56} -2.41746 q^{57} -8.43275 q^{58} +4.90327 q^{59} -3.07315 q^{60} -13.1327 q^{61} -4.76941 q^{62} +1.35002 q^{63} +1.00000 q^{64} -3.07315 q^{65} +4.89632 q^{66} -8.10929 q^{67} -1.97318 q^{68} +6.79256 q^{69} +4.14881 q^{70} +2.60694 q^{71} +1.00000 q^{72} +3.29388 q^{73} -7.88412 q^{74} -4.44424 q^{75} +2.41746 q^{76} -6.61012 q^{77} +1.00000 q^{78} -9.82114 q^{79} +3.07315 q^{80} +1.00000 q^{81} +0.626941 q^{82} +3.34211 q^{83} -1.35002 q^{84} -6.06389 q^{85} +6.69991 q^{86} +8.43275 q^{87} -4.89632 q^{88} +1.83284 q^{89} +3.07315 q^{90} -1.35002 q^{91} -6.79256 q^{92} +4.76941 q^{93} +4.68192 q^{94} +7.42922 q^{95} -1.00000 q^{96} -14.2035 q^{97} -5.17745 q^{98} -4.89632 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	3.07315	1.37435	0.687177	−	0.726490i	$-0.258850\pi$
$5$	3.07315	1.37435	0.687177	+	0.726490i	$0.258850\pi$
$6$	−1.00000	−0.408248
$7$	1.35002	0.510260	0.255130	−	0.966907i	$-0.417882\pi$
$7$	1.35002	0.510260	0.255130	+	0.966907i	$0.417882\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	3.07315	0.971815
$11$	−4.89632	−1.47629	−0.738147	−	0.674640i	$-0.764299\pi$
$11$	−4.89632	−1.47629	−0.738147	+	0.674640i	$0.764299\pi$
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	1.35002	0.360808
$15$	−3.07315	−0.793484
$16$	1.00000	0.250000
$17$	−1.97318	−0.478567	−0.239284	−	0.970950i	$-0.576913\pi$
$17$	−1.97318	−0.478567	−0.239284	+	0.970950i	$0.576913\pi$
$18$	1.00000	0.235702
$19$	2.41746	0.554604	0.277302	−	0.960783i	$-0.410560\pi$
$19$	2.41746	0.554604	0.277302	+	0.960783i	$0.410560\pi$
$20$	3.07315	0.687177
$21$	−1.35002	−0.294599
$22$	−4.89632	−1.04390
$23$	−6.79256	−1.41635	−0.708173	−	0.706039i	$-0.750480\pi$
$23$	−6.79256	−1.41635	−0.708173	+	0.706039i	$0.750480\pi$
$24$	−1.00000	−0.204124
$25$	4.44424	0.888849
$26$	−1.00000	−0.196116
$27$	−1.00000	−0.192450
$28$	1.35002	0.255130
$29$	−8.43275	−1.56592	−0.782961	−	0.622070i	$-0.786292\pi$
$29$	−8.43275	−1.56592	−0.782961	+	0.622070i	$0.786292\pi$
$30$	−3.07315	−0.561078
$31$	−4.76941	−0.856611	−0.428305	−	0.903634i	$-0.640889\pi$
$31$	−4.76941	−0.856611	−0.428305	+	0.903634i	$0.640889\pi$
$32$	1.00000	0.176777
$33$	4.89632	0.852339
$34$	−1.97318	−0.338398
$35$	4.14881	0.701277
$36$	1.00000	0.166667
$37$	−7.88412	−1.29614	−0.648071	−	0.761580i	$-0.724424\pi$
$37$	−7.88412	−1.29614	−0.648071	+	0.761580i	$0.724424\pi$
$38$	2.41746	0.392164
$39$	1.00000	0.160128
$40$	3.07315	0.485907
$41$	0.626941	0.0979118	0.0489559	−	0.998801i	$-0.484411\pi$
$41$	0.626941	0.0979118	0.0489559	+	0.998801i	$0.484411\pi$
$42$	−1.35002	−0.208313
$43$	6.69991	1.02173	0.510864	−	0.859662i	$-0.329326\pi$
$43$	6.69991	1.02173	0.510864	+	0.859662i	$0.329326\pi$
$44$	−4.89632	−0.738147
$45$	3.07315	0.458118
$46$	−6.79256	−1.00151
$47$	4.68192	0.682928	0.341464	−	0.939895i	$-0.389077\pi$
$47$	4.68192	0.682928	0.341464	+	0.939895i	$0.389077\pi$
$48$	−1.00000	−0.144338
$49$	−5.17745	−0.739635
$50$	4.44424	0.628511
$51$	1.97318	0.276301
$52$	−1.00000	−0.138675
$53$	−7.22179	−0.991990	−0.495995	−	0.868325i	$-0.665197\pi$
$53$	−7.22179	−0.991990	−0.495995	+	0.868325i	$0.665197\pi$
$54$	−1.00000	−0.136083
$55$	−15.0471	−2.02895
$56$	1.35002	0.180404
$57$	−2.41746	−0.320201
$58$	−8.43275	−1.10727
$59$	4.90327	0.638351	0.319176	−	0.947696i	$-0.396594\pi$
$59$	4.90327	0.638351	0.319176	+	0.947696i	$0.396594\pi$
$60$	−3.07315	−0.396742
$61$	−13.1327	−1.68148	−0.840738	−	0.541443i	$-0.817878\pi$
$61$	−13.1327	−1.68148	−0.840738	+	0.541443i	$0.817878\pi$
$62$	−4.76941	−0.605715
$63$	1.35002	0.170087
$64$	1.00000	0.125000
$65$	−3.07315	−0.381177
$66$	4.89632	0.602695
$67$	−8.10929	−0.990708	−0.495354	−	0.868691i	$-0.664962\pi$
$67$	−8.10929	−0.990708	−0.495354	+	0.868691i	$0.664962\pi$
$68$	−1.97318	−0.239284
$69$	6.79256	0.817728
$70$	4.14881	0.495878
$71$	2.60694	0.309387	0.154693	−	0.987963i	$-0.450561\pi$
$71$	2.60694	0.309387	0.154693	+	0.987963i	$0.450561\pi$
$72$	1.00000	0.117851
$73$	3.29388	0.385519	0.192760	−	0.981246i	$-0.438256\pi$
$73$	3.29388	0.385519	0.192760	+	0.981246i	$0.438256\pi$
$74$	−7.88412	−0.916511
$75$	−4.44424	−0.513177
$76$	2.41746	0.277302
$77$	−6.61012	−0.753293
$78$	1.00000	0.113228
$79$	−9.82114	−1.10496	−0.552482	−	0.833525i	$-0.686319\pi$
$79$	−9.82114	−1.10496	−0.552482	+	0.833525i	$0.686319\pi$
$80$	3.07315	0.343588
$81$	1.00000	0.111111
$82$	0.626941	0.0692341
$83$	3.34211	0.366844	0.183422	−	0.983034i	$-0.441283\pi$
$83$	3.34211	0.366844	0.183422	+	0.983034i	$0.441283\pi$
$84$	−1.35002	−0.147299
$85$	−6.06389	−0.657721
$86$	6.69991	0.722470
$87$	8.43275	0.904086
$88$	−4.89632	−0.521949
$89$	1.83284	0.194281	0.0971403	−	0.995271i	$-0.469030\pi$
$89$	1.83284	0.194281	0.0971403	+	0.995271i	$0.469030\pi$
$90$	3.07315	0.323938
$91$	−1.35002	−0.141521
$92$	−6.79256	−0.708173
$93$	4.76941	0.494564
$94$	4.68192	0.482903
$95$	7.42922	0.762222
$96$	−1.00000	−0.102062
$97$	−14.2035	−1.44215	−0.721073	−	0.692859i	$-0.756351\pi$
$97$	−14.2035	−1.44215	−0.721073	+	0.692859i	$0.756351\pi$
$98$	−5.17745	−0.523001
$99$	−4.89632	−0.492098
$100$	4.44424	0.444424
$101$	13.0222	1.29576	0.647879	−	0.761743i	$-0.275656\pi$
$101$	13.0222	1.29576	0.647879	+	0.761743i	$0.275656\pi$
$102$	1.97318	0.195374
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−1.00000	−0.0980581
$105$	−4.14881	−0.404883
$106$	−7.22179	−0.701443
$107$	9.65559	0.933441	0.466720	−	0.884405i	$-0.345435\pi$
$107$	9.65559	0.933441	0.466720	+	0.884405i	$0.345435\pi$
$108$	−1.00000	−0.0962250
$109$	−7.78555	−0.745720	−0.372860	−	0.927888i	$-0.621623\pi$
$109$	−7.78555	−0.745720	−0.372860	+	0.927888i	$0.621623\pi$
$110$	−15.0471	−1.43469
$111$	7.88412	0.748328
$112$	1.35002	0.127565
$113$	−9.42707	−0.886825	−0.443412	−	0.896318i	$-0.646232\pi$
$113$	−9.42707	−0.886825	−0.443412	+	0.896318i	$0.646232\pi$
$114$	−2.41746	−0.226416
$115$	−20.8745	−1.94656
$116$	−8.43275	−0.782961
$117$	−1.00000	−0.0924500
$118$	4.90327	0.451383
$119$	−2.66384	−0.244194
$120$	−3.07315	−0.280539
$121$	12.9739	1.17945
$122$	−13.1327	−1.18898
$123$	−0.626941	−0.0565294
$124$	−4.76941	−0.428305
$125$	−1.70792	−0.152761
$126$	1.35002	0.120269
$127$	−10.0323	−0.890221	−0.445111	−	0.895476i	$-0.646836\pi$
$127$	−10.0323	−0.890221	−0.445111	+	0.895476i	$0.646836\pi$
$128$	1.00000	0.0883883
$129$	−6.69991	−0.589895
$130$	−3.07315	−0.269533
$131$	−17.6810	−1.54480	−0.772398	−	0.635139i	$-0.780943\pi$
$131$	−17.6810	−1.54480	−0.772398	+	0.635139i	$0.780943\pi$
$132$	4.89632	0.426170
$133$	3.26362	0.282992
$134$	−8.10929	−0.700536
$135$	−3.07315	−0.264495
$136$	−1.97318	−0.169199
$137$	16.9650	1.44942	0.724708	−	0.689057i	$-0.241975\pi$
$137$	16.9650	1.44942	0.724708	+	0.689057i	$0.241975\pi$
$138$	6.79256	0.578221
$139$	6.93587	0.588293	0.294146	−	0.955760i	$-0.404965\pi$
$139$	6.93587	0.588293	0.294146	+	0.955760i	$0.404965\pi$
$140$	4.14881	0.350639
$141$	−4.68192	−0.394289
$142$	2.60694	0.218770
$143$	4.89632	0.409450
$144$	1.00000	0.0833333
$145$	−25.9151	−2.15213
$146$	3.29388	0.272603
$147$	5.17745	0.427029
$148$	−7.88412	−0.648071
$149$	20.3264	1.66521	0.832603	−	0.553870i	$-0.186850\pi$
$149$	20.3264	1.66521	0.832603	+	0.553870i	$0.186850\pi$
$150$	−4.44424	−0.362871
$151$	14.3020	1.16388	0.581942	−	0.813231i	$-0.302293\pi$
$151$	14.3020	1.16388	0.581942	+	0.813231i	$0.302293\pi$
$152$	2.41746	0.196082
$153$	−1.97318	−0.159522
$154$	−6.61012	−0.532659
$155$	−14.6571	−1.17729
$156$	1.00000	0.0800641
$157$	−20.9174	−1.66939	−0.834695	−	0.550713i	$-0.814356\pi$
$157$	−20.9174	−1.66939	−0.834695	+	0.550713i	$0.814356\pi$
$158$	−9.82114	−0.781328
$159$	7.22179	0.572726
$160$	3.07315	0.242954
$161$	−9.17009	−0.722704
$162$	1.00000	0.0785674
$163$	14.0778	1.10266	0.551329	−	0.834288i	$-0.314121\pi$
$163$	14.0778	1.10266	0.551329	+	0.834288i	$0.314121\pi$
$164$	0.626941	0.0489559
$165$	15.0471	1.17142
$166$	3.34211	0.259398
$167$	−5.51429	−0.426708	−0.213354	−	0.976975i	$-0.568439\pi$
$167$	−5.51429	−0.426708	−0.213354	+	0.976975i	$0.568439\pi$
$168$	−1.35002	−0.104156
$169$	1.00000	0.0769231
$170$	−6.06389	−0.465079
$171$	2.41746	0.184868
$172$	6.69991	0.510864
$173$	−2.86976	−0.218184	−0.109092	−	0.994032i	$-0.534794\pi$
$173$	−2.86976	−0.218184	−0.109092	+	0.994032i	$0.534794\pi$
$174$	8.43275	0.639285
$175$	5.99982	0.453544
$176$	−4.89632	−0.369074
$177$	−4.90327	−0.368552
$178$	1.83284	0.137377
$179$	−13.2036	−0.986883	−0.493441	−	0.869779i	$-0.664261\pi$
$179$	−13.2036	−0.986883	−0.493441	+	0.869779i	$0.664261\pi$
$180$	3.07315	0.229059
$181$	−1.40259	−0.104253	−0.0521267	−	0.998640i	$-0.516600\pi$
$181$	−1.40259	−0.104253	−0.0521267	+	0.998640i	$0.516600\pi$
$182$	−1.35002	−0.100070
$183$	13.1327	0.970800
$184$	−6.79256	−0.500754
$185$	−24.2291	−1.78136
$186$	4.76941	0.349710
$187$	9.66133	0.706506
$188$	4.68192	0.341464
$189$	−1.35002	−0.0981995
$190$	7.42922	0.538972
$191$	25.5624	1.84963	0.924816	−	0.380414i	$-0.124219\pi$
$191$	25.5624	1.84963	0.924816	+	0.380414i	$0.124219\pi$
$192$	−1.00000	−0.0721688
$193$	16.3227	1.17493	0.587465	−	0.809249i	$-0.300126\pi$
$193$	16.3227	1.17493	0.587465	+	0.809249i	$0.300126\pi$
$194$	−14.2035	−1.01975
$195$	3.07315	0.220073
$196$	−5.17745	−0.369818
$197$	21.0353	1.49871	0.749353	−	0.662170i	$-0.230365\pi$
$197$	21.0353	1.49871	0.749353	+	0.662170i	$0.230365\pi$
$198$	−4.89632	−0.347966
$199$	6.03109	0.427532	0.213766	−	0.976885i	$-0.431427\pi$
$199$	6.03109	0.427532	0.213766	+	0.976885i	$0.431427\pi$
$200$	4.44424	0.314255
$201$	8.10929	0.571985
$202$	13.0222	0.916239
$203$	−11.3844	−0.799027
$204$	1.97318	0.138150
$205$	1.92668	0.134565
$206$	1.00000	0.0696733
$207$	−6.79256	−0.472115
$208$	−1.00000	−0.0693375
$209$	−11.8367	−0.818759
$210$	−4.14881	−0.286295
$211$	18.0834	1.24491	0.622457	−	0.782654i	$-0.286134\pi$
$211$	18.0834	1.24491	0.622457	+	0.782654i	$0.286134\pi$
$212$	−7.22179	−0.495995
$213$	−2.60694	−0.178625
$214$	9.65559	0.660042
$215$	20.5898	1.40421
$216$	−1.00000	−0.0680414
$217$	−6.43879	−0.437094
$218$	−7.78555	−0.527304
$219$	−3.29388	−0.222580
$220$	−15.0471	−1.01448
$221$	1.97318	0.132731
$222$	7.88412	0.529148
$223$	−12.7237	−0.852040	−0.426020	−	0.904714i	$-0.640085\pi$
$223$	−12.7237	−0.852040	−0.426020	+	0.904714i	$0.640085\pi$
$224$	1.35002	0.0902020
$225$	4.44424	0.296283
$226$	−9.42707	−0.627080
$227$	19.6837	1.30645	0.653227	−	0.757162i	$-0.273415\pi$
$227$	19.6837	1.30645	0.653227	+	0.757162i	$0.273415\pi$
$228$	−2.41746	−0.160100
$229$	3.08303	0.203732	0.101866	−	0.994798i	$-0.467519\pi$
$229$	3.08303	0.203732	0.101866	+	0.994798i	$0.467519\pi$
$230$	−20.8745	−1.37643
$231$	6.61012	0.434914
$232$	−8.43275	−0.553637
$233$	15.9538	1.04517	0.522583	−	0.852589i	$-0.324969\pi$
$233$	15.9538	1.04517	0.522583	+	0.852589i	$0.324969\pi$
$234$	−1.00000	−0.0653720
$235$	14.3882	0.938585
$236$	4.90327	0.319176
$237$	9.82114	0.637951
$238$	−2.66384	−0.172671
$239$	25.3598	1.64039	0.820193	−	0.572087i	$-0.193866\pi$
$239$	25.3598	1.64039	0.820193	+	0.572087i	$0.193866\pi$
$240$	−3.07315	−0.198371
$241$	−21.8863	−1.40982	−0.704911	−	0.709296i	$-0.749013\pi$
$241$	−21.8863	−1.40982	−0.704911	+	0.709296i	$0.749013\pi$
$242$	12.9739	0.833994
$243$	−1.00000	−0.0641500
$244$	−13.1327	−0.840738
$245$	−15.9111	−1.01652
$246$	−0.626941	−0.0399723
$247$	−2.41746	−0.153819
$248$	−4.76941	−0.302858
$249$	−3.34211	−0.211797
$250$	−1.70792	−0.108019
$251$	−11.9365	−0.753425	−0.376713	−	0.926330i	$-0.622946\pi$
$251$	−11.9365	−0.753425	−0.376713	+	0.926330i	$0.622946\pi$
$252$	1.35002	0.0850433
$253$	33.2585	2.09094
$254$	−10.0323	−0.629482
$255$	6.06389	0.379735
$256$	1.00000	0.0625000
$257$	−12.6936	−0.791803	−0.395902	−	0.918293i	$-0.629568\pi$
$257$	−12.6936	−0.791803	−0.395902	+	0.918293i	$0.629568\pi$
$258$	−6.69991	−0.417118
$259$	−10.6437	−0.661369
$260$	−3.07315	−0.190589
$261$	−8.43275	−0.521974
$262$	−17.6810	−1.09234
$263$	−3.48488	−0.214887	−0.107443	−	0.994211i	$-0.534266\pi$
$263$	−3.48488	−0.214887	−0.107443	+	0.994211i	$0.534266\pi$
$264$	4.89632	0.301347
$265$	−22.1936	−1.36334
$266$	3.26362	0.200106
$267$	−1.83284	−0.112168
$268$	−8.10929	−0.495354
$269$	−16.0869	−0.980835	−0.490417	−	0.871488i	$-0.663156\pi$
$269$	−16.0869	−0.980835	−0.490417	+	0.871488i	$0.663156\pi$
$270$	−3.07315	−0.187026
$271$	28.7340	1.74547	0.872733	−	0.488198i	$-0.162345\pi$
$271$	28.7340	1.74547	0.872733	+	0.488198i	$0.162345\pi$
$272$	−1.97318	−0.119642
$273$	1.35002	0.0817069
$274$	16.9650	1.02489
$275$	−21.7604	−1.31220
$276$	6.79256	0.408864
$277$	−7.30668	−0.439016	−0.219508	−	0.975611i	$-0.570445\pi$
$277$	−7.30668	−0.439016	−0.219508	+	0.975611i	$0.570445\pi$
$278$	6.93587	0.415986
$279$	−4.76941	−0.285537
$280$	4.14881	0.247939
$281$	−14.1025	−0.841283	−0.420641	−	0.907227i	$-0.638195\pi$
$281$	−14.1025	−0.841283	−0.420641	+	0.907227i	$0.638195\pi$
$282$	−4.68192	−0.278804
$283$	−8.34705	−0.496181	−0.248090	−	0.968737i	$-0.579803\pi$
$283$	−8.34705	−0.496181	−0.248090	+	0.968737i	$0.579803\pi$
$284$	2.60694	0.154693
$285$	−7.42922	−0.440069
$286$	4.89632	0.289525
$287$	0.846383	0.0499604
$288$	1.00000	0.0589256
$289$	−13.1065	−0.770973
$290$	−25.9151	−1.52179
$291$	14.2035	0.832623
$292$	3.29388	0.192760
$293$	−20.6107	−1.20409	−0.602044	−	0.798463i	$-0.705647\pi$
$293$	−20.6107	−1.20409	−0.602044	+	0.798463i	$0.705647\pi$
$294$	5.17745	0.301955
$295$	15.0685	0.877321
$296$	−7.88412	−0.458255
$297$	4.89632	0.284113
$298$	20.3264	1.17748
$299$	6.79256	0.392824
$300$	−4.44424	−0.256588
$301$	9.04502	0.521346
$302$	14.3020	0.822990
$303$	−13.0222	−0.748106
$304$	2.41746	0.138651
$305$	−40.3589	−2.31094
$306$	−1.97318	−0.112799
$307$	8.08441	0.461402	0.230701	−	0.973025i	$-0.425898\pi$
$307$	8.08441	0.461402	0.230701	+	0.973025i	$0.425898\pi$
$308$	−6.61012	−0.376647
$309$	−1.00000	−0.0568880
$310$	−14.6571	−0.832467
$311$	7.33377	0.415860	0.207930	−	0.978144i	$-0.433327\pi$
$311$	7.33377	0.415860	0.207930	+	0.978144i	$0.433327\pi$
$312$	1.00000	0.0566139
$313$	−8.77279	−0.495868	−0.247934	−	0.968777i	$-0.579752\pi$
$313$	−8.77279	−0.495868	−0.247934	+	0.968777i	$0.579752\pi$
$314$	−20.9174	−1.18044
$315$	4.14881	0.233759
$316$	−9.82114	−0.552482
$317$	−3.29083	−0.184831	−0.0924157	−	0.995721i	$-0.529459\pi$
$317$	−3.29083	−0.184831	−0.0924157	+	0.995721i	$0.529459\pi$
$318$	7.22179	0.404978
$319$	41.2894	2.31176
$320$	3.07315	0.171794
$321$	−9.65559	−0.538922
$322$	−9.17009	−0.511029
$323$	−4.77010	−0.265415
$324$	1.00000	0.0555556
$325$	−4.44424	−0.246522
$326$	14.0778	0.779697
$327$	7.78555	0.430542
$328$	0.626941	0.0346170
$329$	6.32069	0.348471
$330$	15.0471	0.828316
$331$	−0.439269	−0.0241444	−0.0120722	−	0.999927i	$-0.503843\pi$
$331$	−0.439269	−0.0241444	−0.0120722	+	0.999927i	$0.503843\pi$
$332$	3.34211	0.183422
$333$	−7.88412	−0.432047
$334$	−5.51429	−0.301728
$335$	−24.9211	−1.36158
$336$	−1.35002	−0.0736496
$337$	18.3538	0.999794	0.499897	−	0.866085i	$-0.333371\pi$
$337$	18.3538	0.999794	0.499897	+	0.866085i	$0.333371\pi$
$338$	1.00000	0.0543928
$339$	9.42707	0.512008
$340$	−6.06389	−0.328860
$341$	23.3525	1.26461
$342$	2.41746	0.130721
$343$	−16.4398	−0.887666
$344$	6.69991	0.361235
$345$	20.8745	1.12385
$346$	−2.86976	−0.154279
$347$	−11.0058	−0.590820	−0.295410	−	0.955371i	$-0.595456\pi$
$347$	−11.0058	−0.590820	−0.295410	+	0.955371i	$0.595456\pi$
$348$	8.43275	0.452043
$349$	−4.10456	−0.219712	−0.109856	−	0.993948i	$-0.535039\pi$
$349$	−4.10456	−0.219712	−0.109856	+	0.993948i	$0.535039\pi$
$350$	5.99982	0.320704
$351$	1.00000	0.0533761
$352$	−4.89632	−0.260974
$353$	−3.04904	−0.162284	−0.0811420	−	0.996703i	$-0.525857\pi$
$353$	−3.04904	−0.162284	−0.0811420	+	0.996703i	$0.525857\pi$
$354$	−4.90327	−0.260606
$355$	8.01151	0.425207
$356$	1.83284	0.0971403
$357$	2.66384	0.140985
$358$	−13.2036	−0.697832
$359$	21.8129	1.15124	0.575620	−	0.817717i	$-0.304761\pi$
$359$	21.8129	1.15124	0.575620	+	0.817717i	$0.304761\pi$
$360$	3.07315	0.161969
$361$	−13.1559	−0.692414
$362$	−1.40259	−0.0737183
$363$	−12.9739	−0.680953
$364$	−1.35002	−0.0707603
$365$	10.1226	0.529840
$366$	13.1327	0.686459
$367$	11.0750	0.578109	0.289054	−	0.957313i	$-0.406659\pi$
$367$	11.0750	0.578109	0.289054	+	0.957313i	$0.406659\pi$
$368$	−6.79256	−0.354086
$369$	0.626941	0.0326373
$370$	−24.2291	−1.25961
$371$	−9.74957	−0.506172
$372$	4.76941	0.247282
$373$	9.54656	0.494302	0.247151	−	0.968977i	$-0.420506\pi$
$373$	9.54656	0.494302	0.247151	+	0.968977i	$0.420506\pi$
$374$	9.66133	0.499575
$375$	1.70792	0.0881968
$376$	4.68192	0.241452
$377$	8.43275	0.434309
$378$	−1.35002	−0.0694375
$379$	−34.1909	−1.75627	−0.878133	−	0.478416i	$-0.841211\pi$
$379$	−34.1909	−1.75627	−0.878133	+	0.478416i	$0.841211\pi$
$380$	7.42922	0.381111
$381$	10.0323	0.513969
$382$	25.5624	1.30789
$383$	7.10974	0.363291	0.181645	−	0.983364i	$-0.441858\pi$
$383$	7.10974	0.363291	0.181645	+	0.983364i	$0.441858\pi$
$384$	−1.00000	−0.0510310
$385$	−20.3139	−1.03529
$386$	16.3227	0.830802
$387$	6.69991	0.340576
$388$	−14.2035	−0.721073
$389$	−1.00258	−0.0508326	−0.0254163	−	0.999677i	$-0.508091\pi$
$389$	−1.00258	−0.0508326	−0.0254163	+	0.999677i	$0.508091\pi$
$390$	3.07315	0.155615
$391$	13.4030	0.677817
$392$	−5.17745	−0.261501
$393$	17.6810	0.891888
$394$	21.0353	1.05975
$395$	−30.1818	−1.51861
$396$	−4.89632	−0.246049
$397$	4.93346	0.247603	0.123802	−	0.992307i	$-0.460491\pi$
$397$	4.93346	0.247603	0.123802	+	0.992307i	$0.460491\pi$
$398$	6.03109	0.302311
$399$	−3.26362	−0.163386
$400$	4.44424	0.222212
$401$	−36.2600	−1.81074	−0.905370	−	0.424623i	$-0.860407\pi$
$401$	−36.2600	−1.81074	−0.905370	+	0.424623i	$0.860407\pi$
$402$	8.10929	0.404455
$403$	4.76941	0.237581
$404$	13.0222	0.647879
$405$	3.07315	0.152706
$406$	−11.3844	−0.564997
$407$	38.6031	1.91349
$408$	1.97318	0.0976871
$409$	3.24497	0.160453	0.0802266	−	0.996777i	$-0.474436\pi$
$409$	3.24497	0.160453	0.0802266	+	0.996777i	$0.474436\pi$
$410$	1.92668	0.0951521
$411$	−16.9650	−0.836820
$412$	1.00000	0.0492665
$413$	6.61951	0.325725
$414$	−6.79256	−0.333836
$415$	10.2708	0.504173
$416$	−1.00000	−0.0490290
$417$	−6.93587	−0.339651
$418$	−11.8367	−0.578950
$419$	4.82254	0.235597	0.117798	−	0.993038i	$-0.462416\pi$
$419$	4.82254	0.235597	0.117798	+	0.993038i	$0.462416\pi$
$420$	−4.14881	−0.202441
$421$	−24.3014	−1.18438	−0.592190	−	0.805798i	$-0.701737\pi$
$421$	−24.3014	−1.18438	−0.592190	+	0.805798i	$0.701737\pi$
$422$	18.0834	0.880288
$423$	4.68192	0.227643
$424$	−7.22179	−0.350721
$425$	−8.76931	−0.425374
$426$	−2.60694	−0.126307
$427$	−17.7295	−0.857989
$428$	9.65559	0.466720
$429$	−4.89632	−0.236396
$430$	20.5898	0.992930
$431$	26.3229	1.26793	0.633964	−	0.773363i	$-0.281427\pi$
$431$	26.3229	1.26793	0.633964	+	0.773363i	$0.281427\pi$
$432$	−1.00000	−0.0481125
$433$	−0.480737	−0.0231028	−0.0115514	−	0.999933i	$-0.503677\pi$
$433$	−0.480737	−0.0231028	−0.0115514	+	0.999933i	$0.503677\pi$
$434$	−6.43879	−0.309072
$435$	25.9151	1.24253
$436$	−7.78555	−0.372860
$437$	−16.4208	−0.785511
$438$	−3.29388	−0.157387
$439$	−35.0168	−1.67126	−0.835630	−	0.549293i	$-0.814897\pi$
$439$	−35.0168	−1.67126	−0.835630	+	0.549293i	$0.814897\pi$
$440$	−15.0471	−0.717343
$441$	−5.17745	−0.246545
$442$	1.97318	0.0938548
$443$	24.9626	1.18601	0.593004	−	0.805199i	$-0.297942\pi$
$443$	24.9626	1.18601	0.593004	+	0.805199i	$0.297942\pi$
$444$	7.88412	0.374164
$445$	5.63259	0.267010
$446$	−12.7237	−0.602483
$447$	−20.3264	−0.961407
$448$	1.35002	0.0637825
$449$	−13.5575	−0.639818	−0.319909	−	0.947448i	$-0.603652\pi$
$449$	−13.5575	−0.639818	−0.319909	+	0.947448i	$0.603652\pi$
$450$	4.44424	0.209504
$451$	−3.06970	−0.144547
$452$	−9.42707	−0.443412
$453$	−14.3020	−0.671968
$454$	19.6837	0.923802
$455$	−4.14881	−0.194499
$456$	−2.41746	−0.113208
$457$	30.2262	1.41392	0.706960	−	0.707253i	$-0.250066\pi$
$457$	30.2262	1.41392	0.706960	+	0.707253i	$0.250066\pi$
$458$	3.08303	0.144060
$459$	1.97318	0.0921003
$460$	−20.8745	−0.973280
$461$	34.4796	1.60587	0.802937	−	0.596064i	$-0.203269\pi$
$461$	34.4796	1.60587	0.802937	+	0.596064i	$0.203269\pi$
$462$	6.61012	0.307531
$463$	−21.0228	−0.977011	−0.488506	−	0.872561i	$-0.662458\pi$
$463$	−21.0228	−0.977011	−0.488506	+	0.872561i	$0.662458\pi$
$464$	−8.43275	−0.391481
$465$	14.6571	0.679706
$466$	15.9538	0.739044
$467$	21.1114	0.976921	0.488461	−	0.872586i	$-0.337559\pi$
$467$	21.1114	0.976921	0.488461	+	0.872586i	$0.337559\pi$
$468$	−1.00000	−0.0462250
$469$	−10.9477	−0.505518
$470$	14.3882	0.663680
$471$	20.9174	0.963823
$472$	4.90327	0.225691
$473$	−32.8049	−1.50837
$474$	9.82114	0.451100
$475$	10.7438	0.492959
$476$	−2.66384	−0.122097
$477$	−7.22179	−0.330663
$478$	25.3598	1.15993
$479$	14.5628	0.665390	0.332695	−	0.943034i	$-0.392042\pi$
$479$	14.5628	0.665390	0.332695	+	0.943034i	$0.392042\pi$
$480$	−3.07315	−0.140269
$481$	7.88412	0.359485
$482$	−21.8863	−0.996895
$483$	9.17009	0.417253
$484$	12.9739	0.589723
$485$	−43.6494	−1.98202
$486$	−1.00000	−0.0453609
$487$	−17.1711	−0.778095	−0.389048	−	0.921218i	$-0.627196\pi$
$487$	−17.1711	−0.778095	−0.389048	+	0.921218i	$0.627196\pi$
$488$	−13.1327	−0.594491
$489$	−14.0778	−0.636620
$490$	−15.9111	−0.718788
$491$	4.69389	0.211832	0.105916	−	0.994375i	$-0.466223\pi$
$491$	4.69389	0.211832	0.105916	+	0.994375i	$0.466223\pi$
$492$	−0.626941	−0.0282647
$493$	16.6394	0.749399
$494$	−2.41746	−0.108767
$495$	−15.0471	−0.676317
$496$	−4.76941	−0.214153
$497$	3.51942	0.157868
$498$	−3.34211	−0.149763
$499$	6.16254	0.275873	0.137937	−	0.990441i	$-0.455953\pi$
$499$	6.16254	0.275873	0.137937	+	0.990441i	$0.455953\pi$
$500$	−1.70792	−0.0763807
$501$	5.51429	0.246360
$502$	−11.9365	−0.532752
$503$	−23.7574	−1.05929	−0.529645	−	0.848220i	$-0.677675\pi$
$503$	−23.7574	−1.05929	−0.529645	+	0.848220i	$0.677675\pi$
$504$	1.35002	0.0601347
$505$	40.0192	1.78083
$506$	33.2585	1.47852
$507$	−1.00000	−0.0444116
$508$	−10.0323	−0.445111
$509$	−5.84723	−0.259174	−0.129587	−	0.991568i	$-0.541365\pi$
$509$	−5.84723	−0.259174	−0.129587	+	0.991568i	$0.541365\pi$
$510$	6.06389	0.268513
$511$	4.44680	0.196715
$512$	1.00000	0.0441942
$513$	−2.41746	−0.106734
$514$	−12.6936	−0.559889
$515$	3.07315	0.135419
$516$	−6.69991	−0.294947
$517$	−22.9242	−1.00820
$518$	−10.6437	−0.467658
$519$	2.86976	0.125968
$520$	−3.07315	−0.134766
$521$	8.52329	0.373412	0.186706	−	0.982416i	$-0.440219\pi$
$521$	8.52329	0.373412	0.186706	+	0.982416i	$0.440219\pi$
$522$	−8.43275	−0.369091
$523$	1.34567	0.0588421	0.0294210	−	0.999567i	$-0.490634\pi$
$523$	1.34567	0.0588421	0.0294210	+	0.999567i	$0.490634\pi$
$524$	−17.6810	−0.772398
$525$	−5.99982	−0.261853
$526$	−3.48488	−0.151948
$527$	9.41091	0.409946
$528$	4.89632	0.213085
$529$	23.1388	1.00604
$530$	−22.1936	−0.964030
$531$	4.90327	0.212784
$532$	3.26362	0.141496
$533$	−0.626941	−0.0271558
$534$	−1.83284	−0.0793147
$535$	29.6731	1.28288
$536$	−8.10929	−0.350268
$537$	13.2036	0.569777
$538$	−16.0869	−0.693555
$539$	25.3504	1.09192
$540$	−3.07315	−0.132247
$541$	27.9305	1.20083	0.600414	−	0.799689i	$-0.295003\pi$
$541$	27.9305	1.20083	0.600414	+	0.799689i	$0.295003\pi$
$542$	28.7340	1.23423
$543$	1.40259	0.0601908
$544$	−1.97318	−0.0845996
$545$	−23.9261	−1.02488
$546$	1.35002	0.0577755
$547$	−29.4819	−1.26055	−0.630277	−	0.776370i	$-0.717059\pi$
$547$	−29.4819	−1.26055	−0.630277	+	0.776370i	$0.717059\pi$
$548$	16.9650	0.724708
$549$	−13.1327	−0.560492
$550$	−21.7604	−0.927867
$551$	−20.3859	−0.868467
$552$	6.79256	0.289110
$553$	−13.2587	−0.563819
$554$	−7.30668	−0.310431
$555$	24.2291	1.02847
$556$	6.93587	0.294146
$557$	−20.6614	−0.875453	−0.437727	−	0.899108i	$-0.644216\pi$
$557$	−20.6614	−0.875453	−0.437727	+	0.899108i	$0.644216\pi$
$558$	−4.76941	−0.201905
$559$	−6.69991	−0.283376
$560$	4.14881	0.175319
$561$	−9.66133	−0.407902
$562$	−14.1025	−0.594877
$563$	−13.2928	−0.560225	−0.280112	−	0.959967i	$-0.590372\pi$
$563$	−13.2928	−0.560225	−0.280112	+	0.959967i	$0.590372\pi$
$564$	−4.68192	−0.197144
$565$	−28.9708	−1.21881
$566$	−8.34705	−0.350853
$567$	1.35002	0.0566955
$568$	2.60694	0.109385
$569$	−0.471312	−0.0197584	−0.00987921	−	0.999951i	$-0.503145\pi$
$569$	−0.471312	−0.0197584	−0.00987921	+	0.999951i	$0.503145\pi$
$570$	−7.42922	−0.311176
$571$	−32.6674	−1.36709	−0.683545	−	0.729909i	$-0.739563\pi$
$571$	−32.6674	−1.36709	−0.683545	+	0.729909i	$0.739563\pi$
$572$	4.89632	0.204725
$573$	−25.5624	−1.06789
$574$	0.846383	0.0353274
$575$	−30.1878	−1.25892
$576$	1.00000	0.0416667
$577$	−35.3994	−1.47370	−0.736848	−	0.676058i	$-0.763687\pi$
$577$	−35.3994	−1.47370	−0.736848	+	0.676058i	$0.763687\pi$
$578$	−13.1065	−0.545160
$579$	−16.3227	−0.678347
$580$	−25.9151	−1.07607
$581$	4.51191	0.187186
$582$	14.2035	0.588753
$583$	35.3602	1.46447
$584$	3.29388	0.136302
$585$	−3.07315	−0.127059
$586$	−20.6107	−0.851419
$587$	−2.67102	−0.110245	−0.0551224	−	0.998480i	$-0.517555\pi$
$587$	−2.67102	−0.110245	−0.0551224	+	0.998480i	$0.517555\pi$
$588$	5.17745	0.213514
$589$	−11.5299	−0.475080
$590$	15.0685	0.620359
$591$	−21.0353	−0.865279
$592$	−7.88412	−0.324035
$593$	−10.8027	−0.443613	−0.221807	−	0.975091i	$-0.571195\pi$
$593$	−10.8027	−0.443613	−0.221807	+	0.975091i	$0.571195\pi$
$594$	4.89632	0.200898
$595$	−8.18637	−0.335608
$596$	20.3264	0.832603
$597$	−6.03109	−0.246836
$598$	6.79256	0.277768
$599$	−4.75007	−0.194083	−0.0970414	−	0.995280i	$-0.530938\pi$
$599$	−4.75007	−0.194083	−0.0970414	+	0.995280i	$0.530938\pi$
$600$	−4.44424	−0.181435
$601$	41.4605	1.69121	0.845604	−	0.533811i	$-0.179241\pi$
$601$	41.4605	1.69121	0.845604	+	0.533811i	$0.179241\pi$
$602$	9.04502	0.368647
$603$	−8.10929	−0.330236
$604$	14.3020	0.581942
$605$	39.8707	1.62098
$606$	−13.0222	−0.528991
$607$	−24.0343	−0.975524	−0.487762	−	0.872977i	$-0.662187\pi$
$607$	−24.0343	−0.975524	−0.487762	+	0.872977i	$0.662187\pi$
$608$	2.41746	0.0980411
$609$	11.3844	0.461318
$610$	−40.3589	−1.63408
$611$	−4.68192	−0.189410
$612$	−1.97318	−0.0797612
$613$	15.2342	0.615305	0.307653	−	0.951499i	$-0.400456\pi$
$613$	15.2342	0.615305	0.307653	+	0.951499i	$0.400456\pi$
$614$	8.08441	0.326260
$615$	−1.92668	−0.0776914
$616$	−6.61012	−0.266329
$617$	−27.4380	−1.10461	−0.552306	−	0.833641i	$-0.686252\pi$
$617$	−27.4380	−1.10461	−0.552306	+	0.833641i	$0.686252\pi$
$618$	−1.00000	−0.0402259
$619$	−9.85637	−0.396161	−0.198081	−	0.980186i	$-0.563471\pi$
$619$	−9.85637	−0.396161	−0.198081	+	0.980186i	$0.563471\pi$
$620$	−14.6571	−0.588643
$621$	6.79256	0.272576
$622$	7.33377	0.294058
$623$	2.47437	0.0991336
$624$	1.00000	0.0400320
$625$	−27.4699	−1.09880
$626$	−8.77279	−0.350631
$627$	11.8367	0.472711
$628$	−20.9174	−0.834695
$629$	15.5568	0.620291
$630$	4.14881	0.165293
$631$	−7.60267	−0.302657	−0.151329	−	0.988483i	$-0.548355\pi$
$631$	−7.60267	−0.302657	−0.151329	+	0.988483i	$0.548355\pi$
$632$	−9.82114	−0.390664
$633$	−18.0834	−0.718752
$634$	−3.29083	−0.130696
$635$	−30.8307	−1.22348
$636$	7.22179	0.286363
$637$	5.17745	0.205138
$638$	41.2894	1.63466
$639$	2.60694	0.103129
$640$	3.07315	0.121477
$641$	−26.1965	−1.03470	−0.517351	−	0.855773i	$-0.673082\pi$
$641$	−26.1965	−1.03470	−0.517351	+	0.855773i	$0.673082\pi$
$642$	−9.65559	−0.381076
$643$	−1.29627	−0.0511199	−0.0255599	−	0.999673i	$-0.508137\pi$
$643$	−1.29627	−0.0511199	−0.0255599	+	0.999673i	$0.508137\pi$
$644$	−9.17009	−0.361352
$645$	−20.5898	−0.810724
$646$	−4.77010	−0.187677
$647$	21.3117	0.837850	0.418925	−	0.908021i	$-0.362407\pi$
$647$	21.3117	0.837850	0.418925	+	0.908021i	$0.362407\pi$
$648$	1.00000	0.0392837
$649$	−24.0080	−0.942395
$650$	−4.44424	−0.174318
$651$	6.43879	0.252356
$652$	14.0778	0.551329
$653$	−6.81676	−0.266760	−0.133380	−	0.991065i	$-0.542583\pi$
$653$	−6.81676	−0.266760	−0.133380	+	0.991065i	$0.542583\pi$
$654$	7.78555	0.304439
$655$	−54.3363	−2.12310
$656$	0.626941	0.0244779
$657$	3.29388	0.128506
$658$	6.32069	0.246406
$659$	−17.8696	−0.696101	−0.348051	−	0.937476i	$-0.613156\pi$
$659$	−17.8696	−0.696101	−0.348051	+	0.937476i	$0.613156\pi$
$660$	15.0471	0.585708
$661$	25.0087	0.972726	0.486363	−	0.873757i	$-0.338323\pi$
$661$	25.0087	0.972726	0.486363	+	0.873757i	$0.338323\pi$
$662$	−0.439269	−0.0170727
$663$	−1.97318	−0.0766321
$664$	3.34211	0.129699
$665$	10.0296	0.388931
$666$	−7.88412	−0.305504
$667$	57.2799	2.21789
$668$	−5.51429	−0.213354
$669$	12.7237	0.491926
$670$	−24.9211	−0.962785
$671$	64.3020	2.48235
$672$	−1.35002	−0.0520782
$673$	−44.3981	−1.71142	−0.855711	−	0.517454i	$-0.826880\pi$
$673$	−44.3981	−1.71142	−0.855711	+	0.517454i	$0.826880\pi$
$674$	18.3538	0.706961
$675$	−4.44424	−0.171059
$676$	1.00000	0.0384615
$677$	32.4537	1.24730	0.623648	−	0.781705i	$-0.285650\pi$
$677$	32.4537	1.24730	0.623648	+	0.781705i	$0.285650\pi$
$678$	9.42707	0.362045
$679$	−19.1750	−0.735869
$680$	−6.06389	−0.232539
$681$	−19.6837	−0.754282
$682$	23.3525	0.894214
$683$	−8.43711	−0.322837	−0.161419	−	0.986886i	$-0.551607\pi$
$683$	−8.43711	−0.322837	−0.161419	+	0.986886i	$0.551607\pi$
$684$	2.41746	0.0924340
$685$	52.1359	1.99201
$686$	−16.4398	−0.627674
$687$	−3.08303	−0.117625
$688$	6.69991	0.255432
$689$	7.22179	0.275128
$690$	20.8745	0.794680
$691$	−14.5137	−0.552126	−0.276063	−	0.961140i	$-0.589030\pi$
$691$	−14.5137	−0.552126	−0.276063	+	0.961140i	$0.589030\pi$
$692$	−2.86976	−0.109092
$693$	−6.61012	−0.251098
$694$	−11.0058	−0.417773
$695$	21.3150	0.808522
$696$	8.43275	0.319643
$697$	−1.23707	−0.0468574
$698$	−4.10456	−0.155360
$699$	−15.9538	−0.603427
$700$	5.99982	0.226772
$701$	−34.8785	−1.31734	−0.658671	−	0.752431i	$-0.728881\pi$
$701$	−34.8785	−1.31734	−0.658671	+	0.752431i	$0.728881\pi$
$702$	1.00000	0.0377426
$703$	−19.0596	−0.718845
$704$	−4.89632	−0.184537
$705$	−14.3882	−0.541892
$706$	−3.04904	−0.114752
$707$	17.5802	0.661173
$708$	−4.90327	−0.184276
$709$	39.8900	1.49810	0.749051	−	0.662512i	$-0.230510\pi$
$709$	39.8900	1.49810	0.749051	+	0.662512i	$0.230510\pi$
$710$	8.01151	0.300667
$711$	−9.82114	−0.368321
$712$	1.83284	0.0686886
$713$	32.3965	1.21326
$714$	2.66384	0.0996916
$715$	15.0471	0.562730
$716$	−13.2036	−0.493441
$717$	−25.3598	−0.947077
$718$	21.8129	0.814050
$719$	−41.4992	−1.54766	−0.773829	−	0.633394i	$-0.781661\pi$
$719$	−41.4992	−1.54766	−0.773829	+	0.633394i	$0.781661\pi$
$720$	3.07315	0.114529
$721$	1.35002	0.0502774
$722$	−13.1559	−0.489611
$723$	21.8863	0.813961
$724$	−1.40259	−0.0521267
$725$	−37.4772	−1.39187
$726$	−12.9739	−0.481507
$727$	22.4748	0.833545	0.416772	−	0.909011i	$-0.363161\pi$
$727$	22.4748	0.833545	0.416772	+	0.909011i	$0.363161\pi$
$728$	−1.35002	−0.0500351
$729$	1.00000	0.0370370
$730$	10.1226	0.374653
$731$	−13.2202	−0.488965
$732$	13.1327	0.485400
$733$	−12.6918	−0.468783	−0.234391	−	0.972142i	$-0.575310\pi$
$733$	−12.6918	−0.468783	−0.234391	+	0.972142i	$0.575310\pi$
$734$	11.0750	0.408784
$735$	15.9111	0.586888
$736$	−6.79256	−0.250377
$737$	39.7057	1.46258
$738$	0.626941	0.0230780
$739$	−28.9186	−1.06379	−0.531894	−	0.846811i	$-0.678520\pi$
$739$	−28.9186	−1.06379	−0.531894	+	0.846811i	$0.678520\pi$
$740$	−24.2291	−0.890679
$741$	2.41746	0.0888077
$742$	−9.74957	−0.357918
$743$	−19.0167	−0.697656	−0.348828	−	0.937187i	$-0.613420\pi$
$743$	−19.0167	−0.697656	−0.348828	+	0.937187i	$0.613420\pi$
$744$	4.76941	0.174855
$745$	62.4661	2.28858
$746$	9.54656	0.349524
$747$	3.34211	0.122281
$748$	9.66133	0.353253
$749$	13.0352	0.476297
$750$	1.70792	0.0623646
$751$	41.4827	1.51373	0.756863	−	0.653574i	$-0.226731\pi$
$751$	41.4827	1.51373	0.756863	+	0.653574i	$0.226731\pi$
$752$	4.68192	0.170732
$753$	11.9365	0.434990
$754$	8.43275	0.307103
$755$	43.9523	1.59959
$756$	−1.35002	−0.0490998
$757$	17.5960	0.639538	0.319769	−	0.947496i	$-0.396395\pi$
$757$	17.5960	0.639538	0.319769	+	0.947496i	$0.396395\pi$
$758$	−34.1909	−1.24187
$759$	−33.2585	−1.20721
$760$	7.42922	0.269486
$761$	−44.0550	−1.59699	−0.798495	−	0.602001i	$-0.794370\pi$
$761$	−44.0550	−1.59699	−0.798495	+	0.602001i	$0.794370\pi$
$762$	10.0323	0.363431
$763$	−10.5106	−0.380511
$764$	25.5624	0.924816
$765$	−6.06389	−0.219240
$766$	7.10974	0.256886
$767$	−4.90327	−0.177047
$768$	−1.00000	−0.0360844
$769$	3.43769	0.123966	0.0619832	−	0.998077i	$-0.480257\pi$
$769$	3.43769	0.123966	0.0619832	+	0.998077i	$0.480257\pi$
$770$	−20.3139	−0.732062
$771$	12.6936	0.457148
$772$	16.3227	0.587465
$773$	−30.5916	−1.10030	−0.550152	−	0.835065i	$-0.685430\pi$
$773$	−30.5916	−1.10030	−0.550152	+	0.835065i	$0.685430\pi$
$774$	6.69991	0.240823
$775$	−21.1964	−0.761397
$776$	−14.2035	−0.509875
$777$	10.6437	0.381841
$778$	−1.00258	−0.0359441
$779$	1.51561	0.0543023
$780$	3.07315	0.110036
$781$	−12.7644	−0.456746
$782$	13.4030	0.479289
$783$	8.43275	0.301362
$784$	−5.17745	−0.184909
$785$	−64.2823	−2.29433
$786$	17.6810	0.630660
$787$	−36.4355	−1.29878	−0.649392	−	0.760453i	$-0.724977\pi$
$787$	−36.4355	−1.29878	−0.649392	+	0.760453i	$0.724977\pi$
$788$	21.0353	0.749353
$789$	3.48488	0.124065
$790$	−30.1818	−1.07382
$791$	−12.7267	−0.452511
$792$	−4.89632	−0.173983
$793$	13.1327	0.466357
$794$	4.93346	0.175082
$795$	22.1936	0.787128
$796$	6.03109	0.213766
$797$	−42.2924	−1.49808	−0.749038	−	0.662527i	$-0.769484\pi$
$797$	−42.2924	−1.49808	−0.749038	+	0.662527i	$0.769484\pi$
$798$	−3.26362	−0.115531
$799$	−9.23829	−0.326827
$800$	4.44424	0.157128
$801$	1.83284	0.0647602
$802$	−36.2600	−1.28039
$803$	−16.1279	−0.569140
$804$	8.10929	0.285993
$805$	−28.1810	−0.993251
$806$	4.76941	0.167995
$807$	16.0869	0.566285
$808$	13.0222	0.458120
$809$	−8.92073	−0.313636	−0.156818	−	0.987628i	$-0.550124\pi$
$809$	−8.92073	−0.313636	−0.156818	+	0.987628i	$0.550124\pi$
$810$	3.07315	0.107979
$811$	−22.5576	−0.792106	−0.396053	−	0.918228i	$-0.629620\pi$
$811$	−22.5576	−0.792106	−0.396053	+	0.918228i	$0.629620\pi$
$812$	−11.3844	−0.399514
$813$	−28.7340	−1.00775
$814$	38.6031	1.35304
$815$	43.2632	1.51544
$816$	1.97318	0.0690752
$817$	16.1968	0.566654
$818$	3.24497	0.113458
$819$	−1.35002	−0.0471735
$820$	1.92668	0.0672827
$821$	−22.4196	−0.782450	−0.391225	−	0.920295i	$-0.627949\pi$
$821$	−22.4196	−0.782450	−0.391225	+	0.920295i	$0.627949\pi$
$822$	−16.9650	−0.591721
$823$	16.1128	0.561658	0.280829	−	0.959758i	$-0.409391\pi$
$823$	16.1128	0.561658	0.280829	+	0.959758i	$0.409391\pi$
$824$	1.00000	0.0348367
$825$	21.7604	0.757600
$826$	6.61951	0.230322
$827$	21.4637	0.746365	0.373183	−	0.927758i	$-0.378266\pi$
$827$	21.4637	0.746365	0.373183	+	0.927758i	$0.378266\pi$
$828$	−6.79256	−0.236058
$829$	−24.9710	−0.867278	−0.433639	−	0.901087i	$-0.642771\pi$
$829$	−24.9710	−0.867278	−0.433639	+	0.901087i	$0.642771\pi$
$830$	10.2708	0.356504
$831$	7.30668	0.253466
$832$	−1.00000	−0.0346688
$833$	10.2161	0.353965
$834$	−6.93587	−0.240169
$835$	−16.9462	−0.586448
$836$	−11.8367	−0.409379
$837$	4.76941	0.164855
$838$	4.82254	0.166592
$839$	44.0031	1.51916	0.759578	−	0.650416i	$-0.225406\pi$
$839$	44.0031	1.51916	0.759578	+	0.650416i	$0.225406\pi$
$840$	−4.14881	−0.143148
$841$	42.1113	1.45211
$842$	−24.3014	−0.837483
$843$	14.1025	0.485715
$844$	18.0834	0.622457
$845$	3.07315	0.105720
$846$	4.68192	0.160968
$847$	17.5150	0.601823
$848$	−7.22179	−0.247997
$849$	8.34705	0.286470
$850$	−8.76931	−0.300785
$851$	53.5533	1.83578
$852$	−2.60694	−0.0893123
$853$	4.47516	0.153226	0.0766132	−	0.997061i	$-0.475589\pi$
$853$	4.47516	0.153226	0.0766132	+	0.997061i	$0.475589\pi$
$854$	−17.7295	−0.606690
$855$	7.42922	0.254074
$856$	9.65559	0.330021
$857$	46.1599	1.57679	0.788395	−	0.615169i	$-0.210912\pi$
$857$	46.1599	1.57679	0.788395	+	0.615169i	$0.210912\pi$
$858$	−4.89632	−0.167157
$859$	−8.97082	−0.306081	−0.153040	−	0.988220i	$-0.548906\pi$
$859$	−8.97082	−0.306081	−0.153040	+	0.988220i	$0.548906\pi$
$860$	20.5898	0.702107
$861$	−0.846383	−0.0288447
$862$	26.3229	0.896560
$863$	−22.3419	−0.760527	−0.380264	−	0.924878i	$-0.624167\pi$
$863$	−22.3419	−0.760527	−0.380264	+	0.924878i	$0.624167\pi$
$864$	−1.00000	−0.0340207
$865$	−8.81919	−0.299862
$866$	−0.480737	−0.0163361
$867$	13.1065	0.445122
$868$	−6.43879	−0.218547
$869$	48.0874	1.63125
$870$	25.9151	0.878604
$871$	8.10929	0.274773
$872$	−7.78555	−0.263652
$873$	−14.2035	−0.480715
$874$	−16.4208	−0.555440
$875$	−2.30573	−0.0779480
$876$	−3.29388	−0.111290
$877$	−29.1329	−0.983748	−0.491874	−	0.870666i	$-0.663688\pi$
$877$	−29.1329	−0.983748	−0.491874	+	0.870666i	$0.663688\pi$
$878$	−35.0168	−1.18176
$879$	20.6107	0.695181
$880$	−15.0471	−0.507238
$881$	−13.8652	−0.467130	−0.233565	−	0.972341i	$-0.575039\pi$
$881$	−13.8652	−0.467130	−0.233565	+	0.972341i	$0.575039\pi$
$882$	−5.17745	−0.174334
$883$	−56.6663	−1.90697	−0.953487	−	0.301436i	$-0.902534\pi$
$883$	−56.6663	−1.90697	−0.953487	+	0.301436i	$0.902534\pi$
$884$	1.97318	0.0663653
$885$	−15.0685	−0.506521
$886$	24.9626	0.838635
$887$	−28.8895	−0.970015	−0.485008	−	0.874510i	$-0.661183\pi$
$887$	−28.8895	−0.970015	−0.485008	+	0.874510i	$0.661183\pi$
$888$	7.88412	0.264574
$889$	−13.5438	−0.454244
$890$	5.63259	0.188805
$891$	−4.89632	−0.164033
$892$	−12.7237	−0.426020
$893$	11.3184	0.378755
$894$	−20.3264	−0.679818
$895$	−40.5766	−1.35633
$896$	1.35002	0.0451010
$897$	−6.79256	−0.226797
$898$	−13.5575	−0.452420
$899$	40.2192	1.34139
$900$	4.44424	0.148141
$901$	14.2499	0.474734
$902$	−3.06970	−0.102210
$903$	−9.04502	−0.300999
$904$	−9.42707	−0.313540
$905$	−4.31036	−0.143281
$906$	−14.3020	−0.475153
$907$	−32.9629	−1.09451	−0.547257	−	0.836965i	$-0.684328\pi$
$907$	−32.9629	−1.09451	−0.547257	+	0.836965i	$0.684328\pi$
$908$	19.6837	0.653227
$909$	13.0222	0.431919
$910$	−4.14881	−0.137532
$911$	−4.01723	−0.133097	−0.0665483	−	0.997783i	$-0.521199\pi$
$911$	−4.01723	−0.133097	−0.0665483	+	0.997783i	$0.521199\pi$
$912$	−2.41746	−0.0800502
$913$	−16.3640	−0.541569
$914$	30.2262	0.999793
$915$	40.3589	1.33422
$916$	3.08303	0.101866
$917$	−23.8697	−0.788247
$918$	1.97318	0.0651248
$919$	−25.1519	−0.829685	−0.414843	−	0.909893i	$-0.636163\pi$
$919$	−25.1519	−0.829685	−0.414843	+	0.909893i	$0.636163\pi$
$920$	−20.8745	−0.688213
$921$	−8.08441	−0.266390
$922$	34.4796	1.13552
$923$	−2.60694	−0.0858085
$924$	6.61012	0.217457
$925$	−35.0390	−1.15207
$926$	−21.0228	−0.690851
$927$	1.00000	0.0328443
$928$	−8.43275	−0.276819
$929$	−13.9612	−0.458053	−0.229027	−	0.973420i	$-0.573554\pi$
$929$	−13.9612	−0.458053	−0.229027	+	0.973420i	$0.573554\pi$
$930$	14.6571	0.480625
$931$	−12.5163	−0.410205
$932$	15.9538	0.522583
$933$	−7.33377	−0.240097
$934$	21.1114	0.690787
$935$	29.6907	0.970990
$936$	−1.00000	−0.0326860
$937$	−7.97669	−0.260587	−0.130294	−	0.991475i	$-0.541592\pi$
$937$	−7.97669	−0.260587	−0.130294	+	0.991475i	$0.541592\pi$
$938$	−10.9477	−0.357455
$939$	8.77279	0.286289
$940$	14.3882	0.469293
$941$	47.0555	1.53396	0.766982	−	0.641668i	$-0.221757\pi$
$941$	47.0555	1.53396	0.766982	+	0.641668i	$0.221757\pi$
$942$	20.9174	0.681526
$943$	−4.25853	−0.138677
$944$	4.90327	0.159588
$945$	−4.14881	−0.134961
$946$	−32.8049	−1.06658
$947$	36.6078	1.18959	0.594797	−	0.803876i	$-0.297232\pi$
$947$	36.6078	1.18959	0.594797	+	0.803876i	$0.297232\pi$
$948$	9.82114	0.318976
$949$	−3.29388	−0.106924
$950$	10.7438	0.348575
$951$	3.29083	0.106712
$952$	−2.66384	−0.0863355
$953$	−17.5883	−0.569740	−0.284870	−	0.958566i	$-0.591950\pi$
$953$	−17.5883	−0.569740	−0.284870	+	0.958566i	$0.591950\pi$
$954$	−7.22179	−0.233814
$955$	78.5571	2.54205
$956$	25.3598	0.820193
$957$	−41.2894	−1.33470
$958$	14.5628	0.470502
$959$	22.9030	0.739578
$960$	−3.07315	−0.0991854
$961$	−8.25276	−0.266218
$962$	7.88412	0.254194
$963$	9.65559	0.311147
$964$	−21.8863	−0.704911
$965$	50.1620	1.61477
$966$	9.17009	0.295043
$967$	60.0395	1.93074	0.965370	−	0.260883i	$-0.0840138\pi$
$967$	60.0395	1.93074	0.965370	+	0.260883i	$0.0840138\pi$
$968$	12.9739	0.416997
$969$	4.77010	0.153238
$970$	−43.6494	−1.40150
$971$	−2.95884	−0.0949536	−0.0474768	−	0.998872i	$-0.515118\pi$
$971$	−2.95884	−0.0949536	−0.0474768	+	0.998872i	$0.515118\pi$
$972$	−1.00000	−0.0320750
$973$	9.36356	0.300182
$974$	−17.1711	−0.550196
$975$	4.44424	0.142330
$976$	−13.1327	−0.420369
$977$	61.7228	1.97469	0.987343	−	0.158598i	$-0.0506974\pi$
$977$	61.7228	1.97469	0.987343	+	0.158598i	$0.0506974\pi$
$978$	−14.0778	−0.450158
$979$	−8.97416	−0.286815
$980$	−15.9111	−0.508260
$981$	−7.78555	−0.248573
$982$	4.69389	0.149788
$983$	27.4391	0.875172	0.437586	−	0.899176i	$-0.355833\pi$
$983$	27.4391	0.875172	0.437586	+	0.899176i	$0.355833\pi$
$984$	−0.626941	−0.0199862
$985$	64.6448	2.05975
$986$	16.6394	0.529905
$987$	−6.32069	−0.201190
$988$	−2.41746	−0.0769097
$989$	−45.5095	−1.44712
$990$	−15.0471	−0.478228
$991$	−24.9068	−0.791189	−0.395595	−	0.918425i	$-0.629461\pi$
$991$	−24.9068	−0.791189	−0.395595	+	0.918425i	$0.629461\pi$
$992$	−4.76941	−0.151429
$993$	0.439269	0.0139398
$994$	3.51942	0.111629
$995$	18.5344	0.587581
$996$	−3.34211	−0.105899
$997$	0.574159	0.0181838	0.00909190	−	0.999959i	$-0.497106\pi$
$997$	0.574159	0.0181838	0.00909190	+	0.999959i	$0.497106\pi$
$998$	6.16254	0.195072
$999$	7.88412	0.249443

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.u.1.11	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.u.1.11	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.07315 q^{5} -1.00000 q^{6} +1.35002 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.07315 q^{5} -1.00000 q^{6} +1.35002 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.07315 q^{10} -4.89632 q^{11} -1.00000 q^{12} -1.00000 q^{13} +1.35002 q^{14} -3.07315 q^{15} +1.00000 q^{16} -1.97318 q^{17} +1.00000 q^{18} +2.41746 q^{19} +3.07315 q^{20} -1.35002 q^{21} -4.89632 q^{22} -6.79256 q^{23} -1.00000 q^{24} +4.44424 q^{25} -1.00000 q^{26} -1.00000 q^{27} +1.35002 q^{28} -8.43275 q^{29} -3.07315 q^{30} -4.76941 q^{31} +1.00000 q^{32} +4.89632 q^{33} -1.97318 q^{34} +4.14881 q^{35} +1.00000 q^{36} -7.88412 q^{37} +2.41746 q^{38} +1.00000 q^{39} +3.07315 q^{40} +0.626941 q^{41} -1.35002 q^{42} +6.69991 q^{43} -4.89632 q^{44} +3.07315 q^{45} -6.79256 q^{46} +4.68192 q^{47} -1.00000 q^{48} -5.17745 q^{49} +4.44424 q^{50} +1.97318 q^{51} -1.00000 q^{52} -7.22179 q^{53} -1.00000 q^{54} -15.0471 q^{55} +1.35002 q^{56} -2.41746 q^{57} -8.43275 q^{58} +4.90327 q^{59} -3.07315 q^{60} -13.1327 q^{61} -4.76941 q^{62} +1.35002 q^{63} +1.00000 q^{64} -3.07315 q^{65} +4.89632 q^{66} -8.10929 q^{67} -1.97318 q^{68} +6.79256 q^{69} +4.14881 q^{70} +2.60694 q^{71} +1.00000 q^{72} +3.29388 q^{73} -7.88412 q^{74} -4.44424 q^{75} +2.41746 q^{76} -6.61012 q^{77} +1.00000 q^{78} -9.82114 q^{79} +3.07315 q^{80} +1.00000 q^{81} +0.626941 q^{82} +3.34211 q^{83} -1.35002 q^{84} -6.06389 q^{85} +6.69991 q^{86} +8.43275 q^{87} -4.89632 q^{88} +1.83284 q^{89} +3.07315 q^{90} -1.35002 q^{91} -6.79256 q^{92} +4.76941 q^{93} +4.68192 q^{94} +7.42922 q^{95} -1.00000 q^{96} -14.2035 q^{97} -5.17745 q^{98} -4.89632 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} - 2 q^{5} - 11 q^{6} - 2 q^{7} + 11 q^{8} + 11 q^{9}+O(q^{10}) \) 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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