LMFDB - Embedded newform 8034.2.a.bd.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("8034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.1518129839$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} - 36 x^{14} + 196 x^{13} + 498 x^{12} - 3101 x^{11} - 3150 x^{10} + 25368 x^{9} + \cdots - 66432 $ x^16 - 5x^15 - 36x^14 + 196x^13 + 498x^12 - 3101x^11 - 3150x^10 + 25368x^9 + 6763x^8 - 113788x^7 + 19731x^6 + 270913x^5 - 122680x^4 - 296326x^3 + 185524x^2 + 94528*x - 66432
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-3.26657$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.26657 q^{5} +1.00000 q^{6} +1.36909 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.26657 q^{5} +1.00000 q^{6} +1.36909 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.26657 q^{10} +0.184267 q^{11} +1.00000 q^{12} -1.00000 q^{13} +1.36909 q^{14} -3.26657 q^{15} +1.00000 q^{16} -2.62852 q^{17} +1.00000 q^{18} +0.790202 q^{19} -3.26657 q^{20} +1.36909 q^{21} +0.184267 q^{22} +5.78217 q^{23} +1.00000 q^{24} +5.67051 q^{25} -1.00000 q^{26} +1.00000 q^{27} +1.36909 q^{28} +4.28921 q^{29} -3.26657 q^{30} -10.9060 q^{31} +1.00000 q^{32} +0.184267 q^{33} -2.62852 q^{34} -4.47223 q^{35} +1.00000 q^{36} +7.71294 q^{37} +0.790202 q^{38} -1.00000 q^{39} -3.26657 q^{40} +5.89101 q^{41} +1.36909 q^{42} -2.05447 q^{43} +0.184267 q^{44} -3.26657 q^{45} +5.78217 q^{46} -0.567798 q^{47} +1.00000 q^{48} -5.12559 q^{49} +5.67051 q^{50} -2.62852 q^{51} -1.00000 q^{52} +5.87157 q^{53} +1.00000 q^{54} -0.601921 q^{55} +1.36909 q^{56} +0.790202 q^{57} +4.28921 q^{58} +0.213940 q^{59} -3.26657 q^{60} +0.462239 q^{61} -10.9060 q^{62} +1.36909 q^{63} +1.00000 q^{64} +3.26657 q^{65} +0.184267 q^{66} +8.44778 q^{67} -2.62852 q^{68} +5.78217 q^{69} -4.47223 q^{70} +1.02238 q^{71} +1.00000 q^{72} +14.4245 q^{73} +7.71294 q^{74} +5.67051 q^{75} +0.790202 q^{76} +0.252278 q^{77} -1.00000 q^{78} -8.60821 q^{79} -3.26657 q^{80} +1.00000 q^{81} +5.89101 q^{82} -7.46392 q^{83} +1.36909 q^{84} +8.58626 q^{85} -2.05447 q^{86} +4.28921 q^{87} +0.184267 q^{88} +14.9339 q^{89} -3.26657 q^{90} -1.36909 q^{91} +5.78217 q^{92} -10.9060 q^{93} -0.567798 q^{94} -2.58125 q^{95} +1.00000 q^{96} +9.07983 q^{97} -5.12559 q^{98} +0.184267 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 5 q^{5} + 16 q^{6} + 4 q^{7} + 16 q^{8} + 16 q^{9}+O(q^{10}) $ 16 * q + 16 * q^2 + 16 * q^3 + 16 * q^4 + 5 * q^5 + 16 * q^6 + 4 * q^7 + 16 * q^8 + 16 * q^9	\( 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 5 q^{5} + 16 q^{6} + 4 q^{7} + 16 q^{8} + 16 q^{9} + 5 q^{10} + 18 q^{11} + 16 q^{12} - 16 q^{13} + 4 q^{14} + 5 q^{15} + 16 q^{16} + 17 q^{17} + 16 q^{18} + 8 q^{19} + 5 q^{20} + 4 q^{21} + 18 q^{22} + 9 q^{23} + 16 q^{24} + 17 q^{25} - 16 q^{26} + 16 q^{27} + 4 q^{28} + 14 q^{29} + 5 q^{30} + 12 q^{31} + 16 q^{32} + 18 q^{33} + 17 q^{34} + 16 q^{35} + 16 q^{36} + 31 q^{37} + 8 q^{38} - 16 q^{39} + 5 q^{40} + 29 q^{41} + 4 q^{42} + 30 q^{43} + 18 q^{44} + 5 q^{45} + 9 q^{46} - q^{47} + 16 q^{48} + 36 q^{49} + 17 q^{50} + 17 q^{51} - 16 q^{52} + 12 q^{53} + 16 q^{54} + 30 q^{55} + 4 q^{56} + 8 q^{57} + 14 q^{58} + 38 q^{59} + 5 q^{60} + 12 q^{62} + 4 q^{63} + 16 q^{64} - 5 q^{65} + 18 q^{66} + 28 q^{67} + 17 q^{68} + 9 q^{69} + 16 q^{70} + 32 q^{71} + 16 q^{72} + 20 q^{73} + 31 q^{74} + 17 q^{75} + 8 q^{76} + 26 q^{77} - 16 q^{78} + 13 q^{79} + 5 q^{80} + 16 q^{81} + 29 q^{82} + 39 q^{83} + 4 q^{84} + 31 q^{85} + 30 q^{86} + 14 q^{87} + 18 q^{88} + 9 q^{89} + 5 q^{90} - 4 q^{91} + 9 q^{92} + 12 q^{93} - q^{94} - 20 q^{95} + 16 q^{96} + 35 q^{97} + 36 q^{98} + 18 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 + 16 * q^3 + 16 * q^4 + 5 * q^5 + 16 * q^6 + 4 * q^7 + 16 * q^8 + 16 * q^9 + 5 * q^10 + 18 * q^11 + 16 * q^12 - 16 * q^13 + 4 * q^14 + 5 * q^15 + 16 * q^16 + 17 * q^17 + 16 * q^18 + 8 * q^19 + 5 * q^20 + 4 * q^21 + 18 * q^22 + 9 * q^23 + 16 * q^24 + 17 * q^25 - 16 * q^26 + 16 * q^27 + 4 * q^28 + 14 * q^29 + 5 * q^30 + 12 * q^31 + 16 * q^32 + 18 * q^33 + 17 * q^34 + 16 * q^35 + 16 * q^36 + 31 * q^37 + 8 * q^38 - 16 * q^39 + 5 * q^40 + 29 * q^41 + 4 * q^42 + 30 * q^43 + 18 * q^44 + 5 * q^45 + 9 * q^46 - q^47 + 16 * q^48 + 36 * q^49 + 17 * q^50 + 17 * q^51 - 16 * q^52 + 12 * q^53 + 16 * q^54 + 30 * q^55 + 4 * q^56 + 8 * q^57 + 14 * q^58 + 38 * q^59 + 5 * q^60 + 12 * q^62 + 4 * q^63 + 16 * q^64 - 5 * q^65 + 18 * q^66 + 28 * q^67 + 17 * q^68 + 9 * q^69 + 16 * q^70 + 32 * q^71 + 16 * q^72 + 20 * q^73 + 31 * q^74 + 17 * q^75 + 8 * q^76 + 26 * q^77 - 16 * q^78 + 13 * q^79 + 5 * q^80 + 16 * q^81 + 29 * q^82 + 39 * q^83 + 4 * q^84 + 31 * q^85 + 30 * q^86 + 14 * q^87 + 18 * q^88 + 9 * q^89 + 5 * q^90 - 4 * q^91 + 9 * q^92 + 12 * q^93 - q^94 - 20 * q^95 + 16 * q^96 + 35 * q^97 + 36 * q^98 + 18 * 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
$5$	−3.26657	−1.46086	−0.730428	−	0.682989i	$-0.760679\pi$
$5$	−3.26657	−1.46086	−0.730428	+	0.682989i	$0.760679\pi$
$6$	1.00000	0.408248
$7$	1.36909	0.517467	0.258734	−	0.965949i	$-0.416695\pi$
$7$	1.36909	0.517467	0.258734	+	0.965949i	$0.416695\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−3.26657	−1.03298
$11$	0.184267	0.0555585	0.0277793	−	0.999614i	$-0.491156\pi$
$11$	0.184267	0.0555585	0.0277793	+	0.999614i	$0.491156\pi$
$12$	1.00000	0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	1.36909	0.365904
$15$	−3.26657	−0.843426
$16$	1.00000	0.250000
$17$	−2.62852	−0.637510	−0.318755	−	0.947837i	$-0.603265\pi$
$17$	−2.62852	−0.637510	−0.318755	+	0.947837i	$0.603265\pi$
$18$	1.00000	0.235702
$19$	0.790202	0.181285	0.0906424	−	0.995884i	$-0.471108\pi$
$19$	0.790202	0.181285	0.0906424	+	0.995884i	$0.471108\pi$
$20$	−3.26657	−0.730428
$21$	1.36909	0.298760
$22$	0.184267	0.0392858
$23$	5.78217	1.20567	0.602833	−	0.797867i	$-0.294039\pi$
$23$	5.78217	1.20567	0.602833	+	0.797867i	$0.294039\pi$
$24$	1.00000	0.204124
$25$	5.67051	1.13410
$26$	−1.00000	−0.196116
$27$	1.00000	0.192450
$28$	1.36909	0.258734
$29$	4.28921	0.796486	0.398243	−	0.917280i	$-0.369620\pi$
$29$	4.28921	0.796486	0.398243	+	0.917280i	$0.369620\pi$
$30$	−3.26657	−0.596392
$31$	−10.9060	−1.95877	−0.979387	−	0.201994i	$-0.935258\pi$
$31$	−10.9060	−1.95877	−0.979387	+	0.201994i	$0.935258\pi$
$32$	1.00000	0.176777
$33$	0.184267	0.0320767
$34$	−2.62852	−0.450788
$35$	−4.47223	−0.755945
$36$	1.00000	0.166667
$37$	7.71294	1.26800	0.634000	−	0.773333i	$-0.281412\pi$
$37$	7.71294	1.26800	0.634000	+	0.773333i	$0.281412\pi$
$38$	0.790202	0.128188
$39$	−1.00000	−0.160128
$40$	−3.26657	−0.516491
$41$	5.89101	0.920021	0.460011	−	0.887913i	$-0.347846\pi$
$41$	5.89101	0.920021	0.460011	+	0.887913i	$0.347846\pi$
$42$	1.36909	0.211255
$43$	−2.05447	−0.313303	−0.156652	−	0.987654i	$-0.550070\pi$
$43$	−2.05447	−0.313303	−0.156652	+	0.987654i	$0.550070\pi$
$44$	0.184267	0.0277793
$45$	−3.26657	−0.486952
$46$	5.78217	0.852535
$47$	−0.567798	−0.0828218	−0.0414109	−	0.999142i	$-0.513185\pi$
$47$	−0.567798	−0.0828218	−0.0414109	+	0.999142i	$0.513185\pi$
$48$	1.00000	0.144338
$49$	−5.12559	−0.732228
$50$	5.67051	0.801931
$51$	−2.62852	−0.368067
$52$	−1.00000	−0.138675
$53$	5.87157	0.806522	0.403261	−	0.915085i	$-0.367877\pi$
$53$	5.87157	0.806522	0.403261	+	0.915085i	$0.367877\pi$
$54$	1.00000	0.136083
$55$	−0.601921	−0.0811630
$56$	1.36909	0.182952
$57$	0.790202	0.104665
$58$	4.28921	0.563201
$59$	0.213940	0.0278526	0.0139263	−	0.999903i	$-0.495567\pi$
$59$	0.213940	0.0278526	0.0139263	+	0.999903i	$0.495567\pi$
$60$	−3.26657	−0.421713
$61$	0.462239	0.0591837	0.0295918	−	0.999562i	$-0.490579\pi$
$61$	0.462239	0.0591837	0.0295918	+	0.999562i	$0.490579\pi$
$62$	−10.9060	−1.38506
$63$	1.36909	0.172489
$64$	1.00000	0.125000
$65$	3.26657	0.405169
$66$	0.184267	0.0226817
$67$	8.44778	1.03206	0.516030	−	0.856570i	$-0.327409\pi$
$67$	8.44778	1.03206	0.516030	+	0.856570i	$0.327409\pi$
$68$	−2.62852	−0.318755
$69$	5.78217	0.696092
$70$	−4.47223	−0.534534
$71$	1.02238	0.121335	0.0606673	−	0.998158i	$-0.480677\pi$
$71$	1.02238	0.121335	0.0606673	+	0.998158i	$0.480677\pi$
$72$	1.00000	0.117851
$73$	14.4245	1.68826	0.844130	−	0.536139i	$-0.180118\pi$
$73$	14.4245	1.68826	0.844130	+	0.536139i	$0.180118\pi$
$74$	7.71294	0.896611
$75$	5.67051	0.654774
$76$	0.790202	0.0906424
$77$	0.252278	0.0287497
$78$	−1.00000	−0.113228
$79$	−8.60821	−0.968499	−0.484250	−	0.874930i	$-0.660907\pi$
$79$	−8.60821	−0.968499	−0.484250	+	0.874930i	$0.660907\pi$
$80$	−3.26657	−0.365214
$81$	1.00000	0.111111
$82$	5.89101	0.650553
$83$	−7.46392	−0.819272	−0.409636	−	0.912249i	$-0.634344\pi$
$83$	−7.46392	−0.819272	−0.409636	+	0.912249i	$0.634344\pi$
$84$	1.36909	0.149380
$85$	8.58626	0.931310
$86$	−2.05447	−0.221539
$87$	4.28921	0.459852
$88$	0.184267	0.0196429
$89$	14.9339	1.58299	0.791495	−	0.611176i	$-0.209303\pi$
$89$	14.9339	1.58299	0.791495	+	0.611176i	$0.209303\pi$
$90$	−3.26657	−0.344327
$91$	−1.36909	−0.143520
$92$	5.78217	0.602833
$93$	−10.9060	−1.13090
$94$	−0.567798	−0.0585639
$95$	−2.58125	−0.264831
$96$	1.00000	0.102062
$97$	9.07983	0.921917	0.460958	−	0.887422i	$-0.347506\pi$
$97$	9.07983	0.921917	0.460958	+	0.887422i	$0.347506\pi$
$98$	−5.12559	−0.517763
$99$	0.184267	0.0185195
$100$	5.67051	0.567051
$101$	−7.17756	−0.714194	−0.357097	−	0.934067i	$-0.616233\pi$
$101$	−7.17756	−0.714194	−0.357097	+	0.934067i	$0.616233\pi$
$102$	−2.62852	−0.260262
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−1.00000	−0.0980581
$105$	−4.47223	−0.436445
$106$	5.87157	0.570298
$107$	−0.372330	−0.0359945	−0.0179972	−	0.999838i	$-0.505729\pi$
$107$	−0.372330	−0.0359945	−0.0179972	+	0.999838i	$0.505729\pi$
$108$	1.00000	0.0962250
$109$	−11.8352	−1.13361	−0.566804	−	0.823852i	$-0.691820\pi$
$109$	−11.8352	−1.13361	−0.566804	+	0.823852i	$0.691820\pi$
$110$	−0.601921	−0.0573909
$111$	7.71294	0.732080
$112$	1.36909	0.129367
$113$	2.97629	0.279986	0.139993	−	0.990152i	$-0.455292\pi$
$113$	2.97629	0.279986	0.139993	+	0.990152i	$0.455292\pi$
$114$	0.790202	0.0740092
$115$	−18.8879	−1.76130
$116$	4.28921	0.398243
$117$	−1.00000	−0.0924500
$118$	0.213940	0.0196947
$119$	−3.59868	−0.329890
$120$	−3.26657	−0.298196
$121$	−10.9660	−0.996913
$122$	0.462239	0.0418492
$123$	5.89101	0.531175
$124$	−10.9060	−0.979387
$125$	−2.19026	−0.195903
$126$	1.36909	0.121968
$127$	14.7205	1.30623	0.653116	−	0.757258i	$-0.273461\pi$
$127$	14.7205	1.30623	0.653116	+	0.757258i	$0.273461\pi$
$128$	1.00000	0.0883883
$129$	−2.05447	−0.180886
$130$	3.26657	0.286498
$131$	18.6622	1.63052	0.815262	−	0.579092i	$-0.196593\pi$
$131$	18.6622	1.63052	0.815262	+	0.579092i	$0.196593\pi$
$132$	0.184267	0.0160384
$133$	1.08186	0.0938089
$134$	8.44778	0.729777
$135$	−3.26657	−0.281142
$136$	−2.62852	−0.225394
$137$	20.3231	1.73632	0.868161	−	0.496283i	$-0.165302\pi$
$137$	20.3231	1.73632	0.868161	+	0.496283i	$0.165302\pi$
$138$	5.78217	0.492211
$139$	−4.66308	−0.395517	−0.197758	−	0.980251i	$-0.563366\pi$
$139$	−4.66308	−0.395517	−0.197758	+	0.980251i	$0.563366\pi$
$140$	−4.47223	−0.377973
$141$	−0.567798	−0.0478172
$142$	1.02238	0.0857966
$143$	−0.184267	−0.0154092
$144$	1.00000	0.0833333
$145$	−14.0110	−1.16355
$146$	14.4245	1.19378
$147$	−5.12559	−0.422752
$148$	7.71294	0.634000
$149$	23.1794	1.89893	0.949463	−	0.313878i	$-0.101628\pi$
$149$	23.1794	1.89893	0.949463	+	0.313878i	$0.101628\pi$
$150$	5.67051	0.462995
$151$	3.95450	0.321813	0.160906	−	0.986970i	$-0.448558\pi$
$151$	3.95450	0.321813	0.160906	+	0.986970i	$0.448558\pi$
$152$	0.790202	0.0640938
$153$	−2.62852	−0.212503
$154$	0.252278	0.0203291
$155$	35.6252	2.86149
$156$	−1.00000	−0.0800641
$157$	1.09528	0.0874128	0.0437064	−	0.999044i	$-0.486083\pi$
$157$	1.09528	0.0874128	0.0437064	+	0.999044i	$0.486083\pi$
$158$	−8.60821	−0.684832
$159$	5.87157	0.465646
$160$	−3.26657	−0.258245
$161$	7.91631	0.623892
$162$	1.00000	0.0785674
$163$	14.3202	1.12165	0.560824	−	0.827935i	$-0.310484\pi$
$163$	14.3202	1.12165	0.560824	+	0.827935i	$0.310484\pi$
$164$	5.89101	0.460011
$165$	−0.601921	−0.0468595
$166$	−7.46392	−0.579312
$167$	−21.4119	−1.65690	−0.828450	−	0.560064i	$-0.810777\pi$
$167$	−21.4119	−1.65690	−0.828450	+	0.560064i	$0.810777\pi$
$168$	1.36909	0.105628
$169$	1.00000	0.0769231
$170$	8.58626	0.658536
$171$	0.790202	0.0604282
$172$	−2.05447	−0.156652
$173$	19.1847	1.45858	0.729292	−	0.684202i	$-0.239849\pi$
$173$	19.1847	1.45858	0.729292	+	0.684202i	$0.239849\pi$
$174$	4.28921	0.325164
$175$	7.76343	0.586860
$176$	0.184267	0.0138896
$177$	0.213940	0.0160807
$178$	14.9339	1.11934
$179$	−16.9886	−1.26979	−0.634893	−	0.772600i	$-0.718956\pi$
$179$	−16.9886	−1.26979	−0.634893	+	0.772600i	$0.718956\pi$
$180$	−3.26657	−0.243476
$181$	−13.6570	−1.01512	−0.507559	−	0.861617i	$-0.669452\pi$
$181$	−13.6570	−1.01512	−0.507559	+	0.861617i	$0.669452\pi$
$182$	−1.36909	−0.101484
$183$	0.462239	0.0341697
$184$	5.78217	0.426267
$185$	−25.1949	−1.85237
$186$	−10.9060	−0.799666
$187$	−0.484349	−0.0354191
$188$	−0.567798	−0.0414109
$189$	1.36909	0.0995866
$190$	−2.58125	−0.187264
$191$	20.2016	1.46173	0.730867	−	0.682520i	$-0.239116\pi$
$191$	20.2016	1.46173	0.730867	+	0.682520i	$0.239116\pi$
$192$	1.00000	0.0721688
$193$	17.9141	1.28948	0.644742	−	0.764400i	$-0.276965\pi$
$193$	17.9141	1.28948	0.644742	+	0.764400i	$0.276965\pi$
$194$	9.07983	0.651894
$195$	3.26657	0.233924
$196$	−5.12559	−0.366114
$197$	1.61552	0.115101	0.0575506	−	0.998343i	$-0.481671\pi$
$197$	1.61552	0.115101	0.0575506	+	0.998343i	$0.481671\pi$
$198$	0.184267	0.0130953
$199$	1.44799	0.102646	0.0513228	−	0.998682i	$-0.483656\pi$
$199$	1.44799	0.102646	0.0513228	+	0.998682i	$0.483656\pi$
$200$	5.67051	0.400965
$201$	8.44778	0.595861
$202$	−7.17756	−0.505011
$203$	5.87231	0.412156
$204$	−2.62852	−0.184033
$205$	−19.2434	−1.34402
$206$	1.00000	0.0696733
$207$	5.78217	0.401889
$208$	−1.00000	−0.0693375
$209$	0.145608	0.0100719
$210$	−4.47223	−0.308613
$211$	9.38947	0.646398	0.323199	−	0.946331i	$-0.395242\pi$
$211$	9.38947	0.646398	0.323199	+	0.946331i	$0.395242\pi$
$212$	5.87157	0.403261
$213$	1.02238	0.0700526
$214$	−0.372330	−0.0254520
$215$	6.71107	0.457691
$216$	1.00000	0.0680414
$217$	−14.9313	−1.01360
$218$	−11.8352	−0.801582
$219$	14.4245	0.974717
$220$	−0.601921	−0.0405815
$221$	2.62852	0.176813
$222$	7.71294	0.517659
$223$	12.0959	0.810001	0.405000	−	0.914317i	$-0.367271\pi$
$223$	12.0959	0.810001	0.405000	+	0.914317i	$0.367271\pi$
$224$	1.36909	0.0914761
$225$	5.67051	0.378034
$226$	2.97629	0.197980
$227$	0.319858	0.0212297	0.0106149	−	0.999944i	$-0.496621\pi$
$227$	0.319858	0.0212297	0.0106149	+	0.999944i	$0.496621\pi$
$228$	0.790202	0.0523324
$229$	4.44947	0.294029	0.147015	−	0.989134i	$-0.453034\pi$
$229$	4.44947	0.294029	0.147015	+	0.989134i	$0.453034\pi$
$230$	−18.8879	−1.24543
$231$	0.252278	0.0165986
$232$	4.28921	0.281600
$233$	−6.70065	−0.438974	−0.219487	−	0.975615i	$-0.570438\pi$
$233$	−6.70065	−0.438974	−0.219487	+	0.975615i	$0.570438\pi$
$234$	−1.00000	−0.0653720
$235$	1.85475	0.120991
$236$	0.213940	0.0139263
$237$	−8.60821	−0.559163
$238$	−3.59868	−0.233268
$239$	−18.1794	−1.17593	−0.587964	−	0.808887i	$-0.700071\pi$
$239$	−18.1794	−1.17593	−0.587964	+	0.808887i	$0.700071\pi$
$240$	−3.26657	−0.210856
$241$	−23.8032	−1.53330	−0.766649	−	0.642066i	$-0.778077\pi$
$241$	−23.8032	−1.53330	−0.766649	+	0.642066i	$0.778077\pi$
$242$	−10.9660	−0.704924
$243$	1.00000	0.0641500
$244$	0.462239	0.0295918
$245$	16.7431	1.06968
$246$	5.89101	0.375597
$247$	−0.790202	−0.0502793
$248$	−10.9060	−0.692531
$249$	−7.46392	−0.473007
$250$	−2.19026	−0.138524
$251$	4.35727	0.275029	0.137514	−	0.990500i	$-0.456089\pi$
$251$	4.35727	0.275029	0.137514	+	0.990500i	$0.456089\pi$
$252$	1.36909	0.0862445
$253$	1.06546	0.0669850
$254$	14.7205	0.923645
$255$	8.58626	0.537692
$256$	1.00000	0.0625000
$257$	15.3608	0.958181	0.479091	−	0.877765i	$-0.340967\pi$
$257$	15.3608	0.958181	0.479091	+	0.877765i	$0.340967\pi$
$258$	−2.05447	−0.127906
$259$	10.5597	0.656148
$260$	3.26657	0.202584
$261$	4.28921	0.265495
$262$	18.6622	1.15296
$263$	5.61007	0.345931	0.172966	−	0.984928i	$-0.444665\pi$
$263$	5.61007	0.345931	0.172966	+	0.984928i	$0.444665\pi$
$264$	0.184267	0.0113408
$265$	−19.1799	−1.17821
$266$	1.08186	0.0663329
$267$	14.9339	0.913940
$268$	8.44778	0.516030
$269$	6.59815	0.402296	0.201148	−	0.979561i	$-0.435533\pi$
$269$	6.59815	0.402296	0.201148	+	0.979561i	$0.435533\pi$
$270$	−3.26657	−0.198797
$271$	2.29770	0.139575	0.0697875	−	0.997562i	$-0.477768\pi$
$271$	2.29770	0.139575	0.0697875	+	0.997562i	$0.477768\pi$
$272$	−2.62852	−0.159377
$273$	−1.36909	−0.0828611
$274$	20.3231	1.22776
$275$	1.04489	0.0630090
$276$	5.78217	0.348046
$277$	2.03396	0.122209	0.0611044	−	0.998131i	$-0.480538\pi$
$277$	2.03396	0.122209	0.0611044	+	0.998131i	$0.480538\pi$
$278$	−4.66308	−0.279673
$279$	−10.9060	−0.652925
$280$	−4.47223	−0.267267
$281$	−11.7912	−0.703405	−0.351702	−	0.936112i	$-0.614397\pi$
$281$	−11.7912	−0.703405	−0.351702	+	0.936112i	$0.614397\pi$
$282$	−0.567798	−0.0338119
$283$	12.8160	0.761833	0.380916	−	0.924609i	$-0.375609\pi$
$283$	12.8160	0.761833	0.380916	+	0.924609i	$0.375609\pi$
$284$	1.02238	0.0606673
$285$	−2.58125	−0.152900
$286$	−0.184267	−0.0108959
$287$	8.06532	0.476081
$288$	1.00000	0.0589256
$289$	−10.0909	−0.593581
$290$	−14.0110	−0.822756
$291$	9.07983	0.532269
$292$	14.4245	0.844130
$293$	4.31500	0.252085	0.126043	−	0.992025i	$-0.459772\pi$
$293$	4.31500	0.252085	0.126043	+	0.992025i	$0.459772\pi$
$294$	−5.12559	−0.298931
$295$	−0.698850	−0.0406886
$296$	7.71294	0.448306
$297$	0.184267	0.0106922
$298$	23.1794	1.34274
$299$	−5.78217	−0.334392
$300$	5.67051	0.327387
$301$	−2.81275	−0.162124
$302$	3.95450	0.227556
$303$	−7.17756	−0.412340
$304$	0.790202	0.0453212
$305$	−1.50994	−0.0864589
$306$	−2.62852	−0.150263
$307$	0.864828	0.0493584	0.0246792	−	0.999695i	$-0.492144\pi$
$307$	0.864828	0.0493584	0.0246792	+	0.999695i	$0.492144\pi$
$308$	0.252278	0.0143749
$309$	1.00000	0.0568880
$310$	35.6252	2.02338
$311$	−24.9475	−1.41464	−0.707321	−	0.706893i	$-0.750096\pi$
$311$	−24.9475	−1.41464	−0.707321	+	0.706893i	$0.750096\pi$
$312$	−1.00000	−0.0566139
$313$	−22.8894	−1.29378	−0.646892	−	0.762581i	$-0.723932\pi$
$313$	−22.8894	−1.29378	−0.646892	+	0.762581i	$0.723932\pi$
$314$	1.09528	0.0618102
$315$	−4.47223	−0.251982
$316$	−8.60821	−0.484250
$317$	−4.50648	−0.253109	−0.126555	−	0.991960i	$-0.540392\pi$
$317$	−4.50648	−0.253109	−0.126555	+	0.991960i	$0.540392\pi$
$318$	5.87157	0.329261
$319$	0.790359	0.0442516
$320$	−3.26657	−0.182607
$321$	−0.372330	−0.0207814
$322$	7.91631	0.441159
$323$	−2.07706	−0.115571
$324$	1.00000	0.0555556
$325$	−5.67051	−0.314543
$326$	14.3202	0.793125
$327$	−11.8352	−0.654489
$328$	5.89101	0.325277
$329$	−0.777366	−0.0428576
$330$	−0.601921	−0.0331347
$331$	−23.7315	−1.30440	−0.652200	−	0.758047i	$-0.726154\pi$
$331$	−23.7315	−1.30440	−0.652200	+	0.758047i	$0.726154\pi$
$332$	−7.46392	−0.409636
$333$	7.71294	0.422667
$334$	−21.4119	−1.17160
$335$	−27.5953	−1.50769
$336$	1.36909	0.0746899
$337$	21.3945	1.16543	0.582716	−	0.812676i	$-0.301990\pi$
$337$	21.3945	1.16543	0.582716	+	0.812676i	$0.301990\pi$
$338$	1.00000	0.0543928
$339$	2.97629	0.161650
$340$	8.58626	0.465655
$341$	−2.00961	−0.108827
$342$	0.790202	0.0427292
$343$	−16.6010	−0.896371
$344$	−2.05447	−0.110769
$345$	−18.8879	−1.01689
$346$	19.1847	1.03137
$347$	16.8120	0.902515	0.451258	−	0.892394i	$-0.350976\pi$
$347$	16.8120	0.902515	0.451258	+	0.892394i	$0.350976\pi$
$348$	4.28921	0.229926
$349$	5.94799	0.318389	0.159194	−	0.987247i	$-0.449110\pi$
$349$	5.94799	0.318389	0.159194	+	0.987247i	$0.449110\pi$
$350$	7.76343	0.414973
$351$	−1.00000	−0.0533761
$352$	0.184267	0.00982145
$353$	32.2255	1.71519	0.857596	−	0.514325i	$-0.171957\pi$
$353$	32.2255	1.71519	0.857596	+	0.514325i	$0.171957\pi$
$354$	0.213940	0.0113708
$355$	−3.33969	−0.177253
$356$	14.9339	0.791495
$357$	−3.59868	−0.190462
$358$	−16.9886	−0.897875
$359$	27.4894	1.45083	0.725417	−	0.688310i	$-0.241647\pi$
$359$	27.4894	1.45083	0.725417	+	0.688310i	$0.241647\pi$
$360$	−3.26657	−0.172164
$361$	−18.3756	−0.967136
$362$	−13.6570	−0.717797
$363$	−10.9660	−0.575568
$364$	−1.36909	−0.0717598
$365$	−47.1187	−2.46630
$366$	0.462239	0.0241616
$367$	−28.6857	−1.49738	−0.748692	−	0.662918i	$-0.769318\pi$
$367$	−28.6857	−1.49738	−0.748692	+	0.662918i	$0.769318\pi$
$368$	5.78217	0.301416
$369$	5.89101	0.306674
$370$	−25.1949	−1.30982
$371$	8.03871	0.417349
$372$	−10.9060	−0.565449
$373$	−33.5547	−1.73740	−0.868699	−	0.495341i	$-0.835043\pi$
$373$	−33.5547	−1.73740	−0.868699	+	0.495341i	$0.835043\pi$
$374$	−0.484349	−0.0250451
$375$	−2.19026	−0.113105
$376$	−0.567798	−0.0292819
$377$	−4.28921	−0.220906
$378$	1.36909	0.0704184
$379$	16.4545	0.845209	0.422605	−	0.906314i	$-0.361116\pi$
$379$	16.4545	0.845209	0.422605	+	0.906314i	$0.361116\pi$
$380$	−2.58125	−0.132415
$381$	14.7205	0.754153
$382$	20.2016	1.03360
$383$	28.8025	1.47174	0.735870	−	0.677123i	$-0.236774\pi$
$383$	28.8025	1.47174	0.735870	+	0.677123i	$0.236774\pi$
$384$	1.00000	0.0510310
$385$	−0.824084	−0.0419992
$386$	17.9141	0.911803
$387$	−2.05447	−0.104434
$388$	9.07983	0.460958
$389$	−5.53078	−0.280421	−0.140211	−	0.990122i	$-0.544778\pi$
$389$	−5.53078	−0.280421	−0.140211	+	0.990122i	$0.544778\pi$
$390$	3.26657	0.165409
$391$	−15.1986	−0.768624
$392$	−5.12559	−0.258882
$393$	18.6622	0.941384
$394$	1.61552	0.0813888
$395$	28.1194	1.41484
$396$	0.184267	0.00925975
$397$	−16.3428	−0.820224	−0.410112	−	0.912035i	$-0.634510\pi$
$397$	−16.3428	−0.820224	−0.410112	+	0.912035i	$0.634510\pi$
$398$	1.44799	0.0725814
$399$	1.08186	0.0541606
$400$	5.67051	0.283525
$401$	18.1285	0.905295	0.452648	−	0.891689i	$-0.350480\pi$
$401$	18.1285	0.905295	0.452648	+	0.891689i	$0.350480\pi$
$402$	8.44778	0.421337
$403$	10.9060	0.543266
$404$	−7.17756	−0.357097
$405$	−3.26657	−0.162317
$406$	5.87231	0.291438
$407$	1.42124	0.0704482
$408$	−2.62852	−0.130131
$409$	−6.69234	−0.330915	−0.165457	−	0.986217i	$-0.552910\pi$
$409$	−6.69234	−0.330915	−0.165457	+	0.986217i	$0.552910\pi$
$410$	−19.2434	−0.950365
$411$	20.3231	1.00247
$412$	1.00000	0.0492665
$413$	0.292902	0.0144128
$414$	5.78217	0.284178
$415$	24.3814	1.19684
$416$	−1.00000	−0.0490290
$417$	−4.66308	−0.228352
$418$	0.145608	0.00712191
$419$	22.6074	1.10444	0.552221	−	0.833698i	$-0.313781\pi$
$419$	22.6074	1.10444	0.552221	+	0.833698i	$0.313781\pi$
$420$	−4.47223	−0.218223
$421$	−12.3304	−0.600947	−0.300474	−	0.953790i	$-0.597145\pi$
$421$	−12.3304	−0.600947	−0.300474	+	0.953790i	$0.597145\pi$
$422$	9.38947	0.457072
$423$	−0.567798	−0.0276073
$424$	5.87157	0.285149
$425$	−14.9050	−0.723001
$426$	1.02238	0.0495347
$427$	0.632847	0.0306256
$428$	−0.372330	−0.0179972
$429$	−0.184267	−0.00889648
$430$	6.71107	0.323636
$431$	−0.764527	−0.0368260	−0.0184130	−	0.999830i	$-0.505861\pi$
$431$	−0.764527	−0.0368260	−0.0184130	+	0.999830i	$0.505861\pi$
$432$	1.00000	0.0481125
$433$	−14.4373	−0.693814	−0.346907	−	0.937899i	$-0.612768\pi$
$433$	−14.4373	−0.693814	−0.346907	+	0.937899i	$0.612768\pi$
$434$	−14.9313	−0.716724
$435$	−14.0110	−0.671777
$436$	−11.8352	−0.566804
$437$	4.56908	0.218569
$438$	14.4245	0.689229
$439$	7.88524	0.376342	0.188171	−	0.982136i	$-0.439744\pi$
$439$	7.88524	0.376342	0.188171	+	0.982136i	$0.439744\pi$
$440$	−0.601921	−0.0286955
$441$	−5.12559	−0.244076
$442$	2.62852	0.125026
$443$	8.57092	0.407217	0.203608	−	0.979052i	$-0.434733\pi$
$443$	8.57092	0.407217	0.203608	+	0.979052i	$0.434733\pi$
$444$	7.71294	0.366040
$445$	−48.7827	−2.31252
$446$	12.0959	0.572757
$447$	23.1794	1.09635
$448$	1.36909	0.0646834
$449$	22.8614	1.07890	0.539449	−	0.842018i	$-0.318632\pi$
$449$	22.8614	1.07890	0.539449	+	0.842018i	$0.318632\pi$
$450$	5.67051	0.267310
$451$	1.08552	0.0511150
$452$	2.97629	0.139993
$453$	3.95450	0.185799
$454$	0.319858	0.0150117
$455$	4.47223	0.209661
$456$	0.790202	0.0370046
$457$	30.1622	1.41093	0.705465	−	0.708745i	$-0.250738\pi$
$457$	30.1622	1.41093	0.705465	+	0.708745i	$0.250738\pi$
$458$	4.44947	0.207910
$459$	−2.62852	−0.122689
$460$	−18.8879	−0.880652
$461$	4.03715	0.188029	0.0940144	−	0.995571i	$-0.470030\pi$
$461$	4.03715	0.188029	0.0940144	+	0.995571i	$0.470030\pi$
$462$	0.252278	0.0117370
$463$	−10.6018	−0.492705	−0.246353	−	0.969180i	$-0.579232\pi$
$463$	−10.6018	−0.492705	−0.246353	+	0.969180i	$0.579232\pi$
$464$	4.28921	0.199122
$465$	35.6252	1.65208
$466$	−6.70065	−0.310402
$467$	−35.1909	−1.62844	−0.814220	−	0.580556i	$-0.802835\pi$
$467$	−35.1909	−1.62844	−0.814220	+	0.580556i	$0.802835\pi$
$468$	−1.00000	−0.0462250
$469$	11.5658	0.534057
$470$	1.85475	0.0855534
$471$	1.09528	0.0504678
$472$	0.213940	0.00984737
$473$	−0.378570	−0.0174067
$474$	−8.60821	−0.395388
$475$	4.48085	0.205595
$476$	−3.59868	−0.164945
$477$	5.87157	0.268841
$478$	−18.1794	−0.831507
$479$	23.2211	1.06100	0.530499	−	0.847686i	$-0.322005\pi$
$479$	23.2211	1.06100	0.530499	+	0.847686i	$0.322005\pi$
$480$	−3.26657	−0.149098
$481$	−7.71294	−0.351680
$482$	−23.8032	−1.08421
$483$	7.91631	0.360204
$484$	−10.9660	−0.498457
$485$	−29.6599	−1.34679
$486$	1.00000	0.0453609
$487$	31.1516	1.41162	0.705808	−	0.708404i	$-0.250584\pi$
$487$	31.1516	1.41162	0.705808	+	0.708404i	$0.250584\pi$
$488$	0.462239	0.0209246
$489$	14.3202	0.647584
$490$	16.7431	0.756378
$491$	−12.9524	−0.584534	−0.292267	−	0.956337i	$-0.594410\pi$
$491$	−12.9524	−0.584534	−0.292267	+	0.956337i	$0.594410\pi$
$492$	5.89101	0.265587
$493$	−11.2743	−0.507768
$494$	−0.790202	−0.0355529
$495$	−0.601921	−0.0270543
$496$	−10.9060	−0.489693
$497$	1.39974	0.0627867
$498$	−7.46392	−0.334466
$499$	−37.8440	−1.69413	−0.847066	−	0.531488i	$-0.821633\pi$
$499$	−37.8440	−1.69413	−0.847066	+	0.531488i	$0.821633\pi$
$500$	−2.19026	−0.0979516
$501$	−21.4119	−0.956611
$502$	4.35727	0.194475
$503$	30.3356	1.35260	0.676299	−	0.736628i	$-0.263583\pi$
$503$	30.3356	1.35260	0.676299	+	0.736628i	$0.263583\pi$
$504$	1.36909	0.0609841
$505$	23.4460	1.04333
$506$	1.06546	0.0473655
$507$	1.00000	0.0444116
$508$	14.7205	0.653116
$509$	1.62812	0.0721651	0.0360825	−	0.999349i	$-0.488512\pi$
$509$	1.62812	0.0721651	0.0360825	+	0.999349i	$0.488512\pi$
$510$	8.58626	0.380206
$511$	19.7484	0.873619
$512$	1.00000	0.0441942
$513$	0.790202	0.0348883
$514$	15.3608	0.677536
$515$	−3.26657	−0.143942
$516$	−2.05447	−0.0904429
$517$	−0.104626	−0.00460146
$518$	10.5597	0.463967
$519$	19.1847	0.842114
$520$	3.26657	0.143249
$521$	−26.0412	−1.14089	−0.570444	−	0.821337i	$-0.693229\pi$
$521$	−26.0412	−1.14089	−0.570444	+	0.821337i	$0.693229\pi$
$522$	4.28921	0.187734
$523$	12.5016	0.546658	0.273329	−	0.961921i	$-0.411875\pi$
$523$	12.5016	0.546658	0.273329	+	0.961921i	$0.411875\pi$
$524$	18.6622	0.815262
$525$	7.76343	0.338824
$526$	5.61007	0.244610
$527$	28.6666	1.24874
$528$	0.184267	0.00801918
$529$	10.4335	0.453630
$530$	−19.1799	−0.833123
$531$	0.213940	0.00928419
$532$	1.08186	0.0469044
$533$	−5.89101	−0.255168
$534$	14.9339	0.646253
$535$	1.21624	0.0525828
$536$	8.44778	0.364889
$537$	−16.9886	−0.733112
$538$	6.59815	0.284467
$539$	−0.944477	−0.0406815
$540$	−3.26657	−0.140571
$541$	22.2027	0.954570	0.477285	−	0.878748i	$-0.341621\pi$
$541$	22.2027	0.954570	0.477285	+	0.878748i	$0.341621\pi$
$542$	2.29770	0.0986945
$543$	−13.6570	−0.586079
$544$	−2.62852	−0.112697
$545$	38.6606	1.65604
$546$	−1.36909	−0.0585916
$547$	15.5434	0.664589	0.332295	−	0.943176i	$-0.392177\pi$
$547$	15.5434	0.664589	0.332295	+	0.943176i	$0.392177\pi$
$548$	20.3231	0.868161
$549$	0.462239	0.0197279
$550$	1.04489	0.0445541
$551$	3.38934	0.144391
$552$	5.78217	0.246106
$553$	−11.7854	−0.501166
$554$	2.03396	0.0864147
$555$	−25.1949	−1.06946
$556$	−4.66308	−0.197758
$557$	22.1050	0.936620	0.468310	−	0.883564i	$-0.344863\pi$
$557$	22.1050	0.936620	0.468310	+	0.883564i	$0.344863\pi$
$558$	−10.9060	−0.461687
$559$	2.05447	0.0868947
$560$	−4.47223	−0.188986
$561$	−0.484349	−0.0204492
$562$	−11.7912	−0.497382
$563$	−36.2294	−1.52689	−0.763444	−	0.645874i	$-0.776493\pi$
$563$	−36.2294	−1.52689	−0.763444	+	0.645874i	$0.776493\pi$
$564$	−0.567798	−0.0239086
$565$	−9.72229	−0.409020
$566$	12.8160	0.538697
$567$	1.36909	0.0574963
$568$	1.02238	0.0428983
$569$	14.8227	0.621398	0.310699	−	0.950508i	$-0.399437\pi$
$569$	14.8227	0.621398	0.310699	+	0.950508i	$0.399437\pi$
$570$	−2.58125	−0.108117
$571$	−34.7987	−1.45628	−0.728140	−	0.685428i	$-0.759615\pi$
$571$	−34.7987	−1.45628	−0.728140	+	0.685428i	$0.759615\pi$
$572$	−0.184267	−0.00770458
$573$	20.2016	0.843932
$574$	8.06532	0.336640
$575$	32.7878	1.36735
$576$	1.00000	0.0416667
$577$	12.3691	0.514931	0.257466	−	0.966287i	$-0.417113\pi$
$577$	12.3691	0.514931	0.257466	+	0.966287i	$0.417113\pi$
$578$	−10.0909	−0.419725
$579$	17.9141	0.744484
$580$	−14.0110	−0.581776
$581$	−10.2188	−0.423946
$582$	9.07983	0.376371
$583$	1.08194	0.0448092
$584$	14.4245	0.596890
$585$	3.26657	0.135056
$586$	4.31500	0.178251
$587$	−39.0099	−1.61011	−0.805056	−	0.593199i	$-0.797865\pi$
$587$	−39.0099	−1.61011	−0.805056	+	0.593199i	$0.797865\pi$
$588$	−5.12559	−0.211376
$589$	−8.61793	−0.355096
$590$	−0.698850	−0.0287712
$591$	1.61552	0.0664537
$592$	7.71294	0.317000
$593$	6.34244	0.260453	0.130226	−	0.991484i	$-0.458430\pi$
$593$	6.34244	0.260453	0.130226	+	0.991484i	$0.458430\pi$
$594$	0.184267	0.00756056
$595$	11.7554	0.481923
$596$	23.1794	0.949463
$597$	1.44799	0.0592625
$598$	−5.78217	−0.236451
$599$	−46.4042	−1.89602	−0.948012	−	0.318233i	$-0.896910\pi$
$599$	−46.4042	−1.89602	−0.948012	+	0.318233i	$0.896910\pi$
$600$	5.67051	0.231498
$601$	−22.4808	−0.917011	−0.458505	−	0.888692i	$-0.651615\pi$
$601$	−22.4808	−0.917011	−0.458505	+	0.888692i	$0.651615\pi$
$602$	−2.81275	−0.114639
$603$	8.44778	0.344020
$604$	3.95450	0.160906
$605$	35.8214	1.45635
$606$	−7.17756	−0.291568
$607$	−2.96819	−0.120475	−0.0602375	−	0.998184i	$-0.519186\pi$
$607$	−2.96819	−0.120475	−0.0602375	+	0.998184i	$0.519186\pi$
$608$	0.790202	0.0320469
$609$	5.87231	0.237958
$610$	−1.50994	−0.0611357
$611$	0.567798	0.0229706
$612$	−2.62852	−0.106252
$613$	−12.2995	−0.496772	−0.248386	−	0.968661i	$-0.579900\pi$
$613$	−12.2995	−0.496772	−0.248386	+	0.968661i	$0.579900\pi$
$614$	0.864828	0.0349016
$615$	−19.2434	−0.775970
$616$	0.252278	0.0101646
$617$	−33.4055	−1.34486	−0.672428	−	0.740162i	$-0.734749\pi$
$617$	−33.4055	−1.34486	−0.672428	+	0.740162i	$0.734749\pi$
$618$	1.00000	0.0402259
$619$	−26.0185	−1.04577	−0.522886	−	0.852403i	$-0.675145\pi$
$619$	−26.0185	−1.04577	−0.522886	+	0.852403i	$0.675145\pi$
$620$	35.6252	1.43074
$621$	5.78217	0.232031
$622$	−24.9475	−1.00030
$623$	20.4458	0.819145
$624$	−1.00000	−0.0400320
$625$	−21.1979	−0.847915
$626$	−22.8894	−0.914844
$627$	0.145608	0.00581502
$628$	1.09528	0.0437064
$629$	−20.2736	−0.808363
$630$	−4.47223	−0.178178
$631$	10.9341	0.435280	0.217640	−	0.976029i	$-0.430164\pi$
$631$	10.9341	0.435280	0.217640	+	0.976029i	$0.430164\pi$
$632$	−8.60821	−0.342416
$633$	9.38947	0.373198
$634$	−4.50648	−0.178975
$635$	−48.0856	−1.90822
$636$	5.87157	0.232823
$637$	5.12559	0.203083
$638$	0.790359	0.0312906
$639$	1.02238	0.0404449
$640$	−3.26657	−0.129123
$641$	−3.44370	−0.136018	−0.0680091	−	0.997685i	$-0.521665\pi$
$641$	−3.44370	−0.136018	−0.0680091	+	0.997685i	$0.521665\pi$
$642$	−0.372330	−0.0146947
$643$	20.5582	0.810734	0.405367	−	0.914154i	$-0.367144\pi$
$643$	20.5582	0.810734	0.405367	+	0.914154i	$0.367144\pi$
$644$	7.91631	0.311946
$645$	6.71107	0.264248
$646$	−2.07706	−0.0817209
$647$	34.0328	1.33797	0.668983	−	0.743277i	$-0.266730\pi$
$647$	34.0328	1.33797	0.668983	+	0.743277i	$0.266730\pi$
$648$	1.00000	0.0392837
$649$	0.0394220	0.00154745
$650$	−5.67051	−0.222416
$651$	−14.9313	−0.585203
$652$	14.3202	0.560824
$653$	7.95602	0.311343	0.155672	−	0.987809i	$-0.450246\pi$
$653$	7.95602	0.311343	0.155672	+	0.987809i	$0.450246\pi$
$654$	−11.8352	−0.462794
$655$	−60.9615	−2.38196
$656$	5.89101	0.230005
$657$	14.4245	0.562753
$658$	−0.777366	−0.0303049
$659$	34.0682	1.32711	0.663554	−	0.748129i	$-0.269047\pi$
$659$	34.0682	1.32711	0.663554	+	0.748129i	$0.269047\pi$
$660$	−0.601921	−0.0234297
$661$	17.1545	0.667233	0.333617	−	0.942709i	$-0.391731\pi$
$661$	17.1545	0.667233	0.333617	+	0.942709i	$0.391731\pi$
$662$	−23.7315	−0.922351
$663$	2.62852	0.102083
$664$	−7.46392	−0.289656
$665$	−3.53397	−0.137041
$666$	7.71294	0.298870
$667$	24.8009	0.960297
$668$	−21.4119	−0.828450
$669$	12.0959	0.467654
$670$	−27.5953	−1.06610
$671$	0.0851753	0.00328816
$672$	1.36909	0.0528138
$673$	−35.1459	−1.35477	−0.677387	−	0.735626i	$-0.736888\pi$
$673$	−35.1459	−1.35477	−0.677387	+	0.735626i	$0.736888\pi$
$674$	21.3945	0.824085
$675$	5.67051	0.218258
$676$	1.00000	0.0384615
$677$	−35.0502	−1.34709	−0.673545	−	0.739146i	$-0.735229\pi$
$677$	−35.0502	−1.34709	−0.673545	+	0.739146i	$0.735229\pi$
$678$	2.97629	0.114304
$679$	12.4311	0.477062
$680$	8.58626	0.329268
$681$	0.319858	0.0122570
$682$	−2.00961	−0.0769520
$683$	12.0174	0.459833	0.229917	−	0.973210i	$-0.426155\pi$
$683$	12.0174	0.459833	0.229917	+	0.973210i	$0.426155\pi$
$684$	0.790202	0.0302141
$685$	−66.3870	−2.53652
$686$	−16.6010	−0.633830
$687$	4.44947	0.169758
$688$	−2.05447	−0.0783258
$689$	−5.87157	−0.223689
$690$	−18.8879	−0.719050
$691$	2.75177	0.104682	0.0523412	−	0.998629i	$-0.483332\pi$
$691$	2.75177	0.104682	0.0523412	+	0.998629i	$0.483332\pi$
$692$	19.1847	0.729292
$693$	0.252278	0.00958323
$694$	16.8120	0.638175
$695$	15.2323	0.577794
$696$	4.28921	0.162582
$697$	−15.4846	−0.586523
$698$	5.94799	0.225135
$699$	−6.70065	−0.253442
$700$	7.76343	0.293430
$701$	35.6587	1.34681	0.673405	−	0.739274i	$-0.264831\pi$
$701$	35.6587	1.34681	0.673405	+	0.739274i	$0.264831\pi$
$702$	−1.00000	−0.0377426
$703$	6.09478	0.229869
$704$	0.184267	0.00694481
$705$	1.85475	0.0698541
$706$	32.2255	1.21282
$707$	−9.82672	−0.369572
$708$	0.213940	0.00804034
$709$	7.94155	0.298251	0.149126	−	0.988818i	$-0.452354\pi$
$709$	7.94155	0.298251	0.149126	+	0.988818i	$0.452354\pi$
$710$	−3.33969	−0.125336
$711$	−8.60821	−0.322833
$712$	14.9339	0.559671
$713$	−63.0603	−2.36163
$714$	−3.59868	−0.134677
$715$	0.601921	0.0225106
$716$	−16.9886	−0.634893
$717$	−18.1794	−0.678923
$718$	27.4894	1.02589
$719$	−40.0720	−1.49443	−0.747217	−	0.664580i	$-0.768610\pi$
$719$	−40.0720	−1.49443	−0.747217	+	0.664580i	$0.768610\pi$
$720$	−3.26657	−0.121738
$721$	1.36909	0.0509875
$722$	−18.3756	−0.683868
$723$	−23.8032	−0.885250
$724$	−13.6570	−0.507559
$725$	24.3220	0.903297
$726$	−10.9660	−0.406988
$727$	−25.4201	−0.942779	−0.471389	−	0.881925i	$-0.656247\pi$
$727$	−25.4201	−0.942779	−0.471389	+	0.881925i	$0.656247\pi$
$728$	−1.36909	−0.0507418
$729$	1.00000	0.0370370
$730$	−47.1187	−1.74394
$731$	5.40021	0.199734
$732$	0.462239	0.0170849
$733$	−15.0995	−0.557714	−0.278857	−	0.960333i	$-0.589956\pi$
$733$	−15.0995	−0.557714	−0.278857	+	0.960333i	$0.589956\pi$
$734$	−28.6857	−1.05881
$735$	16.7431	0.617580
$736$	5.78217	0.213134
$737$	1.55664	0.0573398
$738$	5.89101	0.216851
$739$	44.8234	1.64886	0.824428	−	0.565966i	$-0.191497\pi$
$739$	44.8234	1.64886	0.824428	+	0.565966i	$0.191497\pi$
$740$	−25.1949	−0.926183
$741$	−0.790202	−0.0290288
$742$	8.03871	0.295110
$743$	13.9786	0.512824	0.256412	−	0.966568i	$-0.417460\pi$
$743$	13.9786	0.512824	0.256412	+	0.966568i	$0.417460\pi$
$744$	−10.9060	−0.399833
$745$	−75.7171	−2.77406
$746$	−33.5547	−1.22853
$747$	−7.46392	−0.273091
$748$	−0.484349	−0.0177095
$749$	−0.509753	−0.0186260
$750$	−2.19026	−0.0799771
$751$	−15.1992	−0.554628	−0.277314	−	0.960779i	$-0.589444\pi$
$751$	−15.1992	−0.554628	−0.277314	+	0.960779i	$0.589444\pi$
$752$	−0.567798	−0.0207055
$753$	4.35727	0.158788
$754$	−4.28921	−0.156204
$755$	−12.9177	−0.470123
$756$	1.36909	0.0497933
$757$	15.8889	0.577492	0.288746	−	0.957406i	$-0.406762\pi$
$757$	15.8889	0.577492	0.288746	+	0.957406i	$0.406762\pi$
$758$	16.4545	0.597653
$759$	1.06546	0.0386738
$760$	−2.58125	−0.0936319
$761$	−48.3281	−1.75189	−0.875946	−	0.482409i	$-0.839762\pi$
$761$	−48.3281	−1.75189	−0.875946	+	0.482409i	$0.839762\pi$
$762$	14.7205	0.533267
$763$	−16.2035	−0.586605
$764$	20.2016	0.730867
$765$	8.58626	0.310437
$766$	28.8025	1.04068
$767$	−0.213940	−0.00772491
$768$	1.00000	0.0360844
$769$	−30.6769	−1.10624	−0.553119	−	0.833102i	$-0.686563\pi$
$769$	−30.6769	−1.10624	−0.553119	+	0.833102i	$0.686563\pi$
$770$	−0.824084	−0.0296979
$771$	15.3608	0.553206
$772$	17.9141	0.644742
$773$	17.8019	0.640289	0.320144	−	0.947369i	$-0.396269\pi$
$773$	17.8019	0.640289	0.320144	+	0.947369i	$0.396269\pi$
$774$	−2.05447	−0.0738463
$775$	−61.8425	−2.22145
$776$	9.07983	0.325947
$777$	10.5597	0.378827
$778$	−5.53078	−0.198288
$779$	4.65509	0.166786
$780$	3.26657	0.116962
$781$	0.188391	0.00674117
$782$	−15.1986	−0.543499
$783$	4.28921	0.153284
$784$	−5.12559	−0.183057
$785$	−3.57781	−0.127698
$786$	18.6622	0.665659
$787$	−16.5117	−0.588579	−0.294289	−	0.955716i	$-0.595083\pi$
$787$	−16.5117	−0.588579	−0.294289	+	0.955716i	$0.595083\pi$
$788$	1.61552	0.0575506
$789$	5.61007	0.199724
$790$	28.1194	1.00044
$791$	4.07481	0.144884
$792$	0.184267	0.00654763
$793$	−0.462239	−0.0164146
$794$	−16.3428	−0.579986
$795$	−19.1799	−0.680242
$796$	1.44799	0.0513228
$797$	−5.47698	−0.194005	−0.0970024	−	0.995284i	$-0.530925\pi$
$797$	−5.47698	−0.194005	−0.0970024	+	0.995284i	$0.530925\pi$
$798$	1.08186	0.0382973
$799$	1.49247	0.0527997
$800$	5.67051	0.200483
$801$	14.9339	0.527663
$802$	18.1285	0.640141
$803$	2.65795	0.0937972
$804$	8.44778	0.297930
$805$	−25.8592	−0.911417
$806$	10.9060	0.384147
$807$	6.59815	0.232266
$808$	−7.17756	−0.252506
$809$	8.13466	0.286000	0.143000	−	0.989723i	$-0.454325\pi$
$809$	8.13466	0.286000	0.143000	+	0.989723i	$0.454325\pi$
$810$	−3.26657	−0.114776
$811$	35.4438	1.24460	0.622301	−	0.782778i	$-0.286198\pi$
$811$	35.4438	1.24460	0.622301	+	0.782778i	$0.286198\pi$
$812$	5.87231	0.206078
$813$	2.29770	0.0805837
$814$	1.42124	0.0498144
$815$	−46.7782	−1.63857
$816$	−2.62852	−0.0920166
$817$	−1.62344	−0.0567971
$818$	−6.69234	−0.233992
$819$	−1.36909	−0.0478399
$820$	−19.2434	−0.672010
$821$	−52.2007	−1.82182	−0.910909	−	0.412608i	$-0.864618\pi$
$821$	−52.2007	−1.82182	−0.910909	+	0.412608i	$0.864618\pi$
$822$	20.3231	0.708850
$823$	−53.0115	−1.84786	−0.923932	−	0.382557i	$-0.875044\pi$
$823$	−53.0115	−1.84786	−0.923932	+	0.382557i	$0.875044\pi$
$824$	1.00000	0.0348367
$825$	1.04489	0.0363783
$826$	0.292902	0.0101914
$827$	−14.7398	−0.512553	−0.256277	−	0.966603i	$-0.582496\pi$
$827$	−14.7398	−0.512553	−0.256277	+	0.966603i	$0.582496\pi$
$828$	5.78217	0.200944
$829$	39.9822	1.38864	0.694320	−	0.719667i	$-0.255705\pi$
$829$	39.9822	1.38864	0.694320	+	0.719667i	$0.255705\pi$
$830$	24.3814	0.846292
$831$	2.03396	0.0705573
$832$	−1.00000	−0.0346688
$833$	13.4727	0.466802
$834$	−4.66308	−0.161469
$835$	69.9434	2.42049
$836$	0.145608	0.00503595
$837$	−10.9060	−0.376966
$838$	22.6074	0.780958
$839$	−29.9952	−1.03555	−0.517774	−	0.855517i	$-0.673239\pi$
$839$	−29.9952	−1.03555	−0.517774	+	0.855517i	$0.673239\pi$
$840$	−4.47223	−0.154307
$841$	−10.6027	−0.365609
$842$	−12.3304	−0.424934
$843$	−11.7912	−0.406111
$844$	9.38947	0.323199
$845$	−3.26657	−0.112374
$846$	−0.567798	−0.0195213
$847$	−15.0135	−0.515870
$848$	5.87157	0.201631
$849$	12.8160	0.439844
$850$	−14.9050	−0.511239
$851$	44.5975	1.52878
$852$	1.02238	0.0350263
$853$	−49.5405	−1.69624	−0.848118	−	0.529807i	$-0.822264\pi$
$853$	−49.5405	−1.69624	−0.848118	+	0.529807i	$0.822264\pi$
$854$	0.632847	0.0216556
$855$	−2.58125	−0.0882770
$856$	−0.372330	−0.0127260
$857$	−7.56630	−0.258460	−0.129230	−	0.991615i	$-0.541251\pi$
$857$	−7.56630	−0.258460	−0.129230	+	0.991615i	$0.541251\pi$
$858$	−0.184267	−0.00629076
$859$	39.5297	1.34873	0.674367	−	0.738396i	$-0.264416\pi$
$859$	39.5297	1.34873	0.674367	+	0.738396i	$0.264416\pi$
$860$	6.71107	0.228846
$861$	8.06532	0.274865
$862$	−0.764527	−0.0260399
$863$	−12.1835	−0.414732	−0.207366	−	0.978263i	$-0.566489\pi$
$863$	−12.1835	−0.414732	−0.207366	+	0.978263i	$0.566489\pi$
$864$	1.00000	0.0340207
$865$	−62.6682	−2.13078
$866$	−14.4373	−0.490601
$867$	−10.0909	−0.342704
$868$	−14.9313	−0.506800
$869$	−1.58621	−0.0538084
$870$	−14.0110	−0.475018
$871$	−8.44778	−0.286242
$872$	−11.8352	−0.400791
$873$	9.07983	0.307306
$874$	4.56908	0.154551
$875$	−2.99867	−0.101373
$876$	14.4245	0.487358
$877$	31.3212	1.05764	0.528821	−	0.848733i	$-0.322634\pi$
$877$	31.3212	1.05764	0.528821	+	0.848733i	$0.322634\pi$
$878$	7.88524	0.266114
$879$	4.31500	0.145541
$880$	−0.601921	−0.0202908
$881$	51.5289	1.73605	0.868026	−	0.496519i	$-0.165389\pi$
$881$	51.5289	1.73605	0.868026	+	0.496519i	$0.165389\pi$
$882$	−5.12559	−0.172588
$883$	−13.7865	−0.463952	−0.231976	−	0.972722i	$-0.574519\pi$
$883$	−13.7865	−0.463952	−0.231976	+	0.972722i	$0.574519\pi$
$884$	2.62852	0.0884067
$885$	−0.698850	−0.0234916
$886$	8.57092	0.287946
$887$	−32.1550	−1.07966	−0.539829	−	0.841775i	$-0.681511\pi$
$887$	−32.1550	−1.07966	−0.539829	+	0.841775i	$0.681511\pi$
$888$	7.71294	0.258829
$889$	20.1537	0.675932
$890$	−48.7827	−1.63520
$891$	0.184267	0.00617317
$892$	12.0959	0.405000
$893$	−0.448675	−0.0150143
$894$	23.1794	0.775234
$895$	55.4945	1.85498
$896$	1.36909	0.0457381
$897$	−5.78217	−0.193061
$898$	22.8614	0.762896
$899$	−46.7781	−1.56014
$900$	5.67051	0.189017
$901$	−15.4335	−0.514166
$902$	1.08552	0.0361438
$903$	−2.81275	−0.0936024
$904$	2.97629	0.0989901
$905$	44.6117	1.48294
$906$	3.95450	0.131380
$907$	41.4765	1.37721	0.688603	−	0.725139i	$-0.258224\pi$
$907$	41.4765	1.37721	0.688603	+	0.725139i	$0.258224\pi$
$908$	0.319858	0.0106149
$909$	−7.17756	−0.238065
$910$	4.47223	0.148253
$911$	−27.2631	−0.903266	−0.451633	−	0.892204i	$-0.649158\pi$
$911$	−27.2631	−0.903266	−0.451633	+	0.892204i	$0.649158\pi$
$912$	0.790202	0.0261662
$913$	−1.37535	−0.0455175
$914$	30.1622	0.997678
$915$	−1.50994	−0.0499171
$916$	4.44947	0.147015
$917$	25.5502	0.843743
$918$	−2.62852	−0.0867541
$919$	−50.0722	−1.65173	−0.825865	−	0.563868i	$-0.809313\pi$
$919$	−50.0722	−1.65173	−0.825865	+	0.563868i	$0.809313\pi$
$920$	−18.8879	−0.622715
$921$	0.864828	0.0284971
$922$	4.03715	0.132956
$923$	−1.02238	−0.0336522
$924$	0.252278	0.00829932
$925$	43.7363	1.43804
$926$	−10.6018	−0.348395
$927$	1.00000	0.0328443
$928$	4.28921	0.140800
$929$	−59.3057	−1.94576	−0.972878	−	0.231318i	$-0.925696\pi$
$929$	−59.3057	−1.94576	−0.972878	+	0.231318i	$0.925696\pi$
$930$	35.6252	1.16820
$931$	−4.05025	−0.132742
$932$	−6.70065	−0.219487
$933$	−24.9475	−0.816743
$934$	−35.1909	−1.15148
$935$	1.58216	0.0517422
$936$	−1.00000	−0.0326860
$937$	7.78481	0.254319	0.127159	−	0.991882i	$-0.459414\pi$
$937$	7.78481	0.254319	0.127159	+	0.991882i	$0.459414\pi$
$938$	11.5658	0.377636
$939$	−22.8894	−0.746967
$940$	1.85475	0.0604954
$941$	−25.4486	−0.829601	−0.414800	−	0.909912i	$-0.636149\pi$
$941$	−25.4486	−0.829601	−0.414800	+	0.909912i	$0.636149\pi$
$942$	1.09528	0.0356861
$943$	34.0628	1.10924
$944$	0.213940	0.00696314
$945$	−4.47223	−0.145482
$946$	−0.378570	−0.0123084
$947$	52.4549	1.70456	0.852278	−	0.523090i	$-0.175221\pi$
$947$	52.4549	1.70456	0.852278	+	0.523090i	$0.175221\pi$
$948$	−8.60821	−0.279582
$949$	−14.4245	−0.468239
$950$	4.48085	0.145378
$951$	−4.50648	−0.146133
$952$	−3.59868	−0.116634
$953$	23.7935	0.770747	0.385373	−	0.922761i	$-0.374073\pi$
$953$	23.7935	0.770747	0.385373	+	0.922761i	$0.374073\pi$
$954$	5.87157	0.190099
$955$	−65.9899	−2.13538
$956$	−18.1794	−0.587964
$957$	0.790359	0.0255487
$958$	23.2211	0.750239
$959$	27.8242	0.898489
$960$	−3.26657	−0.105428
$961$	87.9406	2.83679
$962$	−7.71294	−0.248675
$963$	−0.372330	−0.0119982
$964$	−23.8032	−0.766649
$965$	−58.5177	−1.88375
$966$	7.91631	0.254703
$967$	−37.9161	−1.21930	−0.609649	−	0.792671i	$-0.708690\pi$
$967$	−37.9161	−1.21930	−0.609649	+	0.792671i	$0.708690\pi$
$968$	−10.9660	−0.352462
$969$	−2.07706	−0.0667248
$970$	−29.6599	−0.952323
$971$	−41.0752	−1.31816	−0.659082	−	0.752071i	$-0.729055\pi$
$971$	−41.0752	−1.31816	−0.659082	+	0.752071i	$0.729055\pi$
$972$	1.00000	0.0320750
$973$	−6.38417	−0.204667
$974$	31.1516	0.998163
$975$	−5.67051	−0.181602
$976$	0.462239	0.0147959
$977$	−8.31047	−0.265876	−0.132938	−	0.991124i	$-0.542441\pi$
$977$	−8.31047	−0.265876	−0.132938	+	0.991124i	$0.542441\pi$
$978$	14.3202	0.457911
$979$	2.75182	0.0879486
$980$	16.7431	0.534840
$981$	−11.8352	−0.377870
$982$	−12.9524	−0.413328
$983$	−29.7399	−0.948555	−0.474278	−	0.880375i	$-0.657291\pi$
$983$	−29.7399	−0.948555	−0.474278	+	0.880375i	$0.657291\pi$
$984$	5.89101	0.187799
$985$	−5.27722	−0.168146
$986$	−11.2743	−0.359046
$987$	−0.777366	−0.0247438
$988$	−0.790202	−0.0251397
$989$	−11.8793	−0.377739
$990$	−0.601921	−0.0191303
$991$	25.4597	0.808755	0.404377	−	0.914592i	$-0.367488\pi$
$991$	25.4597	0.808755	0.404377	+	0.914592i	$0.367488\pi$
$992$	−10.9060	−0.346266
$993$	−23.7315	−0.753096
$994$	1.39974	0.0443969
$995$	−4.72998	−0.149950
$996$	−7.46392	−0.236503
$997$	28.9631	0.917271	0.458635	−	0.888625i	$-0.348338\pi$
$997$	28.9631	0.917271	0.458635	+	0.888625i	$0.348338\pi$
$998$	−37.8440	−1.19793
$999$	7.71294	0.244027

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.bd.1.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.bd.1.1	✓	16	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.26657 q^{5} +1.00000 q^{6} +1.36909 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.26657 q^{5} +1.00000 q^{6} +1.36909 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.26657 q^{10} +0.184267 q^{11} +1.00000 q^{12} -1.00000 q^{13} +1.36909 q^{14} -3.26657 q^{15} +1.00000 q^{16} -2.62852 q^{17} +1.00000 q^{18} +0.790202 q^{19} -3.26657 q^{20} +1.36909 q^{21} +0.184267 q^{22} +5.78217 q^{23} +1.00000 q^{24} +5.67051 q^{25} -1.00000 q^{26} +1.00000 q^{27} +1.36909 q^{28} +4.28921 q^{29} -3.26657 q^{30} -10.9060 q^{31} +1.00000 q^{32} +0.184267 q^{33} -2.62852 q^{34} -4.47223 q^{35} +1.00000 q^{36} +7.71294 q^{37} +0.790202 q^{38} -1.00000 q^{39} -3.26657 q^{40} +5.89101 q^{41} +1.36909 q^{42} -2.05447 q^{43} +0.184267 q^{44} -3.26657 q^{45} +5.78217 q^{46} -0.567798 q^{47} +1.00000 q^{48} -5.12559 q^{49} +5.67051 q^{50} -2.62852 q^{51} -1.00000 q^{52} +5.87157 q^{53} +1.00000 q^{54} -0.601921 q^{55} +1.36909 q^{56} +0.790202 q^{57} +4.28921 q^{58} +0.213940 q^{59} -3.26657 q^{60} +0.462239 q^{61} -10.9060 q^{62} +1.36909 q^{63} +1.00000 q^{64} +3.26657 q^{65} +0.184267 q^{66} +8.44778 q^{67} -2.62852 q^{68} +5.78217 q^{69} -4.47223 q^{70} +1.02238 q^{71} +1.00000 q^{72} +14.4245 q^{73} +7.71294 q^{74} +5.67051 q^{75} +0.790202 q^{76} +0.252278 q^{77} -1.00000 q^{78} -8.60821 q^{79} -3.26657 q^{80} +1.00000 q^{81} +5.89101 q^{82} -7.46392 q^{83} +1.36909 q^{84} +8.58626 q^{85} -2.05447 q^{86} +4.28921 q^{87} +0.184267 q^{88} +14.9339 q^{89} -3.26657 q^{90} -1.36909 q^{91} +5.78217 q^{92} -10.9060 q^{93} -0.567798 q^{94} -2.58125 q^{95} +1.00000 q^{96} +9.07983 q^{97} -5.12559 q^{98} +0.184267 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 5 q^{5} + 16 q^{6} + 4 q^{7} + 16 q^{8} + 16 q^{9}+O(q^{10}) \) 16 * q + 16 * q^2 + 16 * q^3 + 16 * q^4 + 5 * q^5 + 16 * q^6 + 4 * q^7 + 16 * q^8 + 16 * q^9	\( 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 5 q^{5} + 16 q^{6} + 4 q^{7} + 16 q^{8} + 16 q^{9} + 5 q^{10} + 18 q^{11} + 16 q^{12} - 16 q^{13} + 4 q^{14} + 5 q^{15} + 16 q^{16} + 17 q^{17} + 16 q^{18} + 8 q^{19} + 5 q^{20} + 4 q^{21} + 18 q^{22} + 9 q^{23} + 16 q^{24} + 17 q^{25} - 16 q^{26} + 16 q^{27} + 4 q^{28} + 14 q^{29} + 5 q^{30} + 12 q^{31} + 16 q^{32} + 18 q^{33} + 17 q^{34} + 16 q^{35} + 16 q^{36} + 31 q^{37} + 8 q^{38} - 16 q^{39} + 5 q^{40} + 29 q^{41} + 4 q^{42} + 30 q^{43} + 18 q^{44} + 5 q^{45} + 9 q^{46} - q^{47} + 16 q^{48} + 36 q^{49} + 17 q^{50} + 17 q^{51} - 16 q^{52} + 12 q^{53} + 16 q^{54} + 30 q^{55} + 4 q^{56} + 8 q^{57} + 14 q^{58} + 38 q^{59} + 5 q^{60} + 12 q^{62} + 4 q^{63} + 16 q^{64} - 5 q^{65} + 18 q^{66} + 28 q^{67} + 17 q^{68} + 9 q^{69} + 16 q^{70} + 32 q^{71} + 16 q^{72} + 20 q^{73} + 31 q^{74} + 17 q^{75} + 8 q^{76} + 26 q^{77} - 16 q^{78} + 13 q^{79} + 5 q^{80} + 16 q^{81} + 29 q^{82} + 39 q^{83} + 4 q^{84} + 31 q^{85} + 30 q^{86} + 14 q^{87} + 18 q^{88} + 9 q^{89} + 5 q^{90} - 4 q^{91} + 9 q^{92} + 12 q^{93} - q^{94} - 20 q^{95} + 16 q^{96} + 35 q^{97} + 36 q^{98} + 18 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 + 16 * q^3 + 16 * q^4 + 5 * q^5 + 16 * q^6 + 4 * q^7 + 16 * q^8 + 16 * q^9 + 5 * q^10 + 18 * q^11 + 16 * q^12 - 16 * q^13 + 4 * q^14 + 5 * q^15 + 16 * q^16 + 17 * q^17 + 16 * q^18 + 8 * q^19 + 5 * q^20 + 4 * q^21 + 18 * q^22 + 9 * q^23 + 16 * q^24 + 17 * q^25 - 16 * q^26 + 16 * q^27 + 4 * q^28 + 14 * q^29 + 5 * q^30 + 12 * q^31 + 16 * q^32 + 18 * q^33 + 17 * q^34 + 16 * q^35 + 16 * q^36 + 31 * q^37 + 8 * q^38 - 16 * q^39 + 5 * q^40 + 29 * q^41 + 4 * q^42 + 30 * q^43 + 18 * q^44 + 5 * q^45 + 9 * q^46 - q^47 + 16 * q^48 + 36 * q^49 + 17 * q^50 + 17 * q^51 - 16 * q^52 + 12 * q^53 + 16 * q^54 + 30 * q^55 + 4 * q^56 + 8 * q^57 + 14 * q^58 + 38 * q^59 + 5 * q^60 + 12 * q^62 + 4 * q^63 + 16 * q^64 - 5 * q^65 + 18 * q^66 + 28 * q^67 + 17 * q^68 + 9 * q^69 + 16 * q^70 + 32 * q^71 + 16 * q^72 + 20 * q^73 + 31 * q^74 + 17 * q^75 + 8 * q^76 + 26 * q^77 - 16 * q^78 + 13 * q^79 + 5 * q^80 + 16 * q^81 + 29 * q^82 + 39 * q^83 + 4 * q^84 + 31 * q^85 + 30 * q^86 + 14 * q^87 + 18 * q^88 + 9 * q^89 + 5 * q^90 - 4 * q^91 + 9 * q^92 + 12 * q^93 - q^94 - 20 * q^95 + 16 * q^96 + 35 * q^97 + 36 * q^98 + 18 * q^99

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