LMFDB - Embedded newform 8034.2.a.u.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:	$1$
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			1.1
Root			$-0.740393$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.99294 q^{5} -1.00000 q^{6} -2.56934 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.99294 q^{5} -1.00000 q^{6} -2.56934 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.99294 q^{10} -2.60174 q^{11} -1.00000 q^{12} -1.00000 q^{13} -2.56934 q^{14} +3.99294 q^{15} +1.00000 q^{16} +2.12859 q^{17} +1.00000 q^{18} +0.868075 q^{19} -3.99294 q^{20} +2.56934 q^{21} -2.60174 q^{22} +5.16856 q^{23} -1.00000 q^{24} +10.9436 q^{25} -1.00000 q^{26} -1.00000 q^{27} -2.56934 q^{28} -0.693615 q^{29} +3.99294 q^{30} +4.86980 q^{31} +1.00000 q^{32} +2.60174 q^{33} +2.12859 q^{34} +10.2592 q^{35} +1.00000 q^{36} +4.94544 q^{37} +0.868075 q^{38} +1.00000 q^{39} -3.99294 q^{40} +6.68086 q^{41} +2.56934 q^{42} -10.4261 q^{43} -2.60174 q^{44} -3.99294 q^{45} +5.16856 q^{46} +0.0582968 q^{47} -1.00000 q^{48} -0.398475 q^{49} +10.9436 q^{50} -2.12859 q^{51} -1.00000 q^{52} -0.983603 q^{53} -1.00000 q^{54} +10.3886 q^{55} -2.56934 q^{56} -0.868075 q^{57} -0.693615 q^{58} +5.02274 q^{59} +3.99294 q^{60} +2.12798 q^{61} +4.86980 q^{62} -2.56934 q^{63} +1.00000 q^{64} +3.99294 q^{65} +2.60174 q^{66} +3.67387 q^{67} +2.12859 q^{68} -5.16856 q^{69} +10.2592 q^{70} -12.7794 q^{71} +1.00000 q^{72} -14.6741 q^{73} +4.94544 q^{74} -10.9436 q^{75} +0.868075 q^{76} +6.68477 q^{77} +1.00000 q^{78} +11.4341 q^{79} -3.99294 q^{80} +1.00000 q^{81} +6.68086 q^{82} +10.8428 q^{83} +2.56934 q^{84} -8.49932 q^{85} -10.4261 q^{86} +0.693615 q^{87} -2.60174 q^{88} +4.29246 q^{89} -3.99294 q^{90} +2.56934 q^{91} +5.16856 q^{92} -4.86980 q^{93} +0.0582968 q^{94} -3.46618 q^{95} -1.00000 q^{96} -4.60864 q^{97} -0.398475 q^{98} -2.60174 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−3.99294	−1.78570	−0.892850	−	0.450355i	$-0.851297\pi$
$5$	−3.99294	−1.78570	−0.892850	+	0.450355i	$0.851297\pi$
$6$	−1.00000	−0.408248
$7$	−2.56934	−0.971121	−0.485560	−	0.874203i	$-0.661384\pi$
$7$	−2.56934	−0.971121	−0.485560	+	0.874203i	$0.661384\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−3.99294	−1.26268
$11$	−2.60174	−0.784455	−0.392227	−	0.919868i	$-0.628295\pi$
$11$	−2.60174	−0.784455	−0.392227	+	0.919868i	$0.628295\pi$
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−2.56934	−0.686686
$15$	3.99294	1.03097
$16$	1.00000	0.250000
$17$	2.12859	0.516258	0.258129	−	0.966110i	$-0.416894\pi$
$17$	2.12859	0.516258	0.258129	+	0.966110i	$0.416894\pi$
$18$	1.00000	0.235702
$19$	0.868075	0.199150	0.0995751	−	0.995030i	$-0.468252\pi$
$19$	0.868075	0.199150	0.0995751	+	0.995030i	$0.468252\pi$
$20$	−3.99294	−0.892850
$21$	2.56934	0.560677
$22$	−2.60174	−0.554693
$23$	5.16856	1.07772	0.538859	−	0.842396i	$-0.318855\pi$
$23$	5.16856	1.07772	0.538859	+	0.842396i	$0.318855\pi$
$24$	−1.00000	−0.204124
$25$	10.9436	2.18872
$26$	−1.00000	−0.196116
$27$	−1.00000	−0.192450
$28$	−2.56934	−0.485560
$29$	−0.693615	−0.128801	−0.0644006	−	0.997924i	$-0.520514\pi$
$29$	−0.693615	−0.128801	−0.0644006	+	0.997924i	$0.520514\pi$
$30$	3.99294	0.729009
$31$	4.86980	0.874641	0.437321	−	0.899306i	$-0.355927\pi$
$31$	4.86980	0.874641	0.437321	+	0.899306i	$0.355927\pi$
$32$	1.00000	0.176777
$33$	2.60174	0.452905
$34$	2.12859	0.365049
$35$	10.2592	1.73413
$36$	1.00000	0.166667
$37$	4.94544	0.813025	0.406513	−	0.913645i	$-0.366745\pi$
$37$	4.94544	0.813025	0.406513	+	0.913645i	$0.366745\pi$
$38$	0.868075	0.140820
$39$	1.00000	0.160128
$40$	−3.99294	−0.631340
$41$	6.68086	1.04337	0.521687	−	0.853137i	$-0.325303\pi$
$41$	6.68086	1.04337	0.521687	+	0.853137i	$0.325303\pi$
$42$	2.56934	0.396458
$43$	−10.4261	−1.58996	−0.794982	−	0.606633i	$-0.792520\pi$
$43$	−10.4261	−1.58996	−0.794982	+	0.606633i	$0.792520\pi$
$44$	−2.60174	−0.392227
$45$	−3.99294	−0.595233
$46$	5.16856	0.762062
$47$	0.0582968	0.00850347	0.00425173	−	0.999991i	$-0.498647\pi$
$47$	0.0582968	0.00850347	0.00425173	+	0.999991i	$0.498647\pi$
$48$	−1.00000	−0.144338
$49$	−0.398475	−0.0569249
$50$	10.9436	1.54766
$51$	−2.12859	−0.298062
$52$	−1.00000	−0.138675
$53$	−0.983603	−0.135108	−0.0675541	−	0.997716i	$-0.521520\pi$
$53$	−0.983603	−0.135108	−0.0675541	+	0.997716i	$0.521520\pi$
$54$	−1.00000	−0.136083
$55$	10.3886	1.40080
$56$	−2.56934	−0.343343
$57$	−0.868075	−0.114979
$58$	−0.693615	−0.0910761
$59$	5.02274	0.653906	0.326953	−	0.945041i	$-0.393978\pi$
$59$	5.02274	0.653906	0.326953	+	0.945041i	$0.393978\pi$
$60$	3.99294	0.515487
$61$	2.12798	0.272460	0.136230	−	0.990677i	$-0.456501\pi$
$61$	2.12798	0.272460	0.136230	+	0.990677i	$0.456501\pi$
$62$	4.86980	0.618465
$63$	−2.56934	−0.323707
$64$	1.00000	0.125000
$65$	3.99294	0.495264
$66$	2.60174	0.320252
$67$	3.67387	0.448835	0.224418	−	0.974493i	$-0.427952\pi$
$67$	3.67387	0.448835	0.224418	+	0.974493i	$0.427952\pi$
$68$	2.12859	0.258129
$69$	−5.16856	−0.622221
$70$	10.2592	1.22621
$71$	−12.7794	−1.51664	−0.758318	−	0.651885i	$-0.773978\pi$
$71$	−12.7794	−1.51664	−0.758318	+	0.651885i	$0.773978\pi$
$72$	1.00000	0.117851
$73$	−14.6741	−1.71747	−0.858737	−	0.512417i	$-0.828750\pi$
$73$	−14.6741	−1.71747	−0.858737	+	0.512417i	$0.828750\pi$
$74$	4.94544	0.574896
$75$	−10.9436	−1.26366
$76$	0.868075	0.0995751
$77$	6.68477	0.761800
$78$	1.00000	0.113228
$79$	11.4341	1.28643	0.643217	−	0.765684i	$-0.277599\pi$
$79$	11.4341	1.28643	0.643217	+	0.765684i	$0.277599\pi$
$80$	−3.99294	−0.446425
$81$	1.00000	0.111111
$82$	6.68086	0.737777
$83$	10.8428	1.19015	0.595074	−	0.803671i	$-0.297123\pi$
$83$	10.8428	1.19015	0.595074	+	0.803671i	$0.297123\pi$
$84$	2.56934	0.280338
$85$	−8.49932	−0.921881
$86$	−10.4261	−1.12427
$87$	0.693615	0.0743634
$88$	−2.60174	−0.277347
$89$	4.29246	0.455000	0.227500	−	0.973778i	$-0.426945\pi$
$89$	4.29246	0.455000	0.227500	+	0.973778i	$0.426945\pi$
$90$	−3.99294	−0.420893
$91$	2.56934	0.269340
$92$	5.16856	0.538859
$93$	−4.86980	−0.504974
$94$	0.0582968	0.00601286
$95$	−3.46618	−0.355622
$96$	−1.00000	−0.102062
$97$	−4.60864	−0.467936	−0.233968	−	0.972244i	$-0.575171\pi$
$97$	−4.60864	−0.467936	−0.233968	+	0.972244i	$0.575171\pi$
$98$	−0.398475	−0.0402520
$99$	−2.60174	−0.261485
$100$	10.9436	1.09436
$101$	9.54533	0.949796	0.474898	−	0.880041i	$-0.342485\pi$
$101$	9.54533	0.949796	0.474898	+	0.880041i	$0.342485\pi$
$102$	−2.12859	−0.210761
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−1.00000	−0.0980581
$105$	−10.2592	−1.00120
$106$	−0.983603	−0.0955359
$107$	16.5615	1.60106	0.800528	−	0.599295i	$-0.204552\pi$
$107$	16.5615	1.60106	0.800528	+	0.599295i	$0.204552\pi$
$108$	−1.00000	−0.0962250
$109$	−17.3830	−1.66499	−0.832493	−	0.554036i	$-0.813087\pi$
$109$	−17.3830	−1.66499	−0.832493	+	0.554036i	$0.813087\pi$
$110$	10.3886	0.990515
$111$	−4.94544	−0.469400
$112$	−2.56934	−0.242780
$113$	−7.45583	−0.701385	−0.350693	−	0.936491i	$-0.614054\pi$
$113$	−7.45583	−0.701385	−0.350693	+	0.936491i	$0.614054\pi$
$114$	−0.868075	−0.0813027
$115$	−20.6378	−1.92448
$116$	−0.693615	−0.0644006
$117$	−1.00000	−0.0924500
$118$	5.02274	0.462381
$119$	−5.46907	−0.501348
$120$	3.99294	0.364504
$121$	−4.23094	−0.384631
$122$	2.12798	0.192659
$123$	−6.68086	−0.602393
$124$	4.86980	0.437321
$125$	−23.7325	−2.12270
$126$	−2.56934	−0.228895
$127$	−7.71404	−0.684511	−0.342255	−	0.939607i	$-0.611191\pi$
$127$	−7.71404	−0.684511	−0.342255	+	0.939607i	$0.611191\pi$
$128$	1.00000	0.0883883
$129$	10.4261	0.917966
$130$	3.99294	0.350204
$131$	−19.0357	−1.66316	−0.831580	−	0.555405i	$-0.812563\pi$
$131$	−19.0357	−1.66316	−0.831580	+	0.555405i	$0.812563\pi$
$132$	2.60174	0.226453
$133$	−2.23038	−0.193399
$134$	3.67387	0.317374
$135$	3.99294	0.343658
$136$	2.12859	0.182525
$137$	10.7685	0.920013	0.460006	−	0.887916i	$-0.347847\pi$
$137$	10.7685	0.920013	0.460006	+	0.887916i	$0.347847\pi$
$138$	−5.16856	−0.439977
$139$	−0.0497599	−0.00422058	−0.00211029	−	0.999998i	$-0.500672\pi$
$139$	−0.0497599	−0.00422058	−0.00211029	+	0.999998i	$0.500672\pi$
$140$	10.2592	0.867064
$141$	−0.0582968	−0.00490948
$142$	−12.7794	−1.07242
$143$	2.60174	0.217569
$144$	1.00000	0.0833333
$145$	2.76957	0.230000
$146$	−14.6741	−1.21444
$147$	0.398475	0.0328656
$148$	4.94544	0.406513
$149$	−16.2978	−1.33517	−0.667583	−	0.744535i	$-0.732671\pi$
$149$	−16.2978	−1.33517	−0.667583	+	0.744535i	$0.732671\pi$
$150$	−10.9436	−0.893542
$151$	6.10676	0.496961	0.248480	−	0.968637i	$-0.420069\pi$
$151$	6.10676	0.496961	0.248480	+	0.968637i	$0.420069\pi$
$152$	0.868075	0.0704102
$153$	2.12859	0.172086
$154$	6.68477	0.538674
$155$	−19.4448	−1.56185
$156$	1.00000	0.0800641
$157$	−0.366268	−0.0292313	−0.0146157	−	0.999893i	$-0.504652\pi$
$157$	−0.366268	−0.0292313	−0.0146157	+	0.999893i	$0.504652\pi$
$158$	11.4341	0.909647
$159$	0.983603	0.0780048
$160$	−3.99294	−0.315670
$161$	−13.2798	−1.04659
$162$	1.00000	0.0785674
$163$	−18.2292	−1.42782	−0.713910	−	0.700237i	$-0.753078\pi$
$163$	−18.2292	−1.42782	−0.713910	+	0.700237i	$0.753078\pi$
$164$	6.68086	0.521687
$165$	−10.3886	−0.808752
$166$	10.8428	0.841562
$167$	−0.659040	−0.0509980	−0.0254990	−	0.999675i	$-0.508117\pi$
$167$	−0.659040	−0.0509980	−0.0254990	+	0.999675i	$0.508117\pi$
$168$	2.56934	0.198229
$169$	1.00000	0.0769231
$170$	−8.49932	−0.651868
$171$	0.868075	0.0663834
$172$	−10.4261	−0.794982
$173$	6.27169	0.476828	0.238414	−	0.971164i	$-0.423372\pi$
$173$	6.27169	0.476828	0.238414	+	0.971164i	$0.423372\pi$
$174$	0.693615	0.0525828
$175$	−28.1179	−2.12551
$176$	−2.60174	−0.196114
$177$	−5.02274	−0.377533
$178$	4.29246	0.321734
$179$	−7.95567	−0.594635	−0.297317	−	0.954779i	$-0.596092\pi$
$179$	−7.95567	−0.594635	−0.297317	+	0.954779i	$0.596092\pi$
$180$	−3.99294	−0.297617
$181$	−22.3853	−1.66388	−0.831942	−	0.554862i	$-0.812771\pi$
$181$	−22.3853	−1.66388	−0.831942	+	0.554862i	$0.812771\pi$
$182$	2.56934	0.190452
$183$	−2.12798	−0.157305
$184$	5.16856	0.381031
$185$	−19.7469	−1.45182
$186$	−4.86980	−0.357071
$187$	−5.53803	−0.404981
$188$	0.0582968	0.00425173
$189$	2.56934	0.186892
$190$	−3.46618	−0.251463
$191$	−0.114963	−0.00831841	−0.00415921	−	0.999991i	$-0.501324\pi$
$191$	−0.114963	−0.00831841	−0.00415921	+	0.999991i	$0.501324\pi$
$192$	−1.00000	−0.0721688
$193$	−9.48769	−0.682939	−0.341470	−	0.939893i	$-0.610925\pi$
$193$	−9.48769	−0.682939	−0.341470	+	0.939893i	$0.610925\pi$
$194$	−4.60864	−0.330881
$195$	−3.99294	−0.285941
$196$	−0.398475	−0.0284625
$197$	6.92277	0.493227	0.246614	−	0.969114i	$-0.420682\pi$
$197$	6.92277	0.493227	0.246614	+	0.969114i	$0.420682\pi$
$198$	−2.60174	−0.184898
$199$	28.0215	1.98639	0.993195	−	0.116461i	$-0.0371548\pi$
$199$	28.0215	1.98639	0.993195	+	0.116461i	$0.0371548\pi$
$200$	10.9436	0.773830
$201$	−3.67387	−0.259135
$202$	9.54533	0.671607
$203$	1.78214	0.125081
$204$	−2.12859	−0.149031
$205$	−26.6763	−1.86315
$206$	1.00000	0.0696733
$207$	5.16856	0.359240
$208$	−1.00000	−0.0693375
$209$	−2.25851	−0.156224
$210$	−10.2592	−0.707955
$211$	−19.4194	−1.33689	−0.668444	−	0.743763i	$-0.733039\pi$
$211$	−19.4194	−1.33689	−0.668444	+	0.743763i	$0.733039\pi$
$212$	−0.983603	−0.0675541
$213$	12.7794	0.875630
$214$	16.5615	1.13212
$215$	41.6308	2.83920
$216$	−1.00000	−0.0680414
$217$	−12.5122	−0.849382
$218$	−17.3830	−1.17732
$219$	14.6741	0.991584
$220$	10.3886	0.700400
$221$	−2.12859	−0.143184
$222$	−4.94544	−0.331916
$223$	−0.829123	−0.0555222	−0.0277611	−	0.999615i	$-0.508838\pi$
$223$	−0.829123	−0.0555222	−0.0277611	+	0.999615i	$0.508838\pi$
$224$	−2.56934	−0.171671
$225$	10.9436	0.729574
$226$	−7.45583	−0.495954
$227$	−20.8962	−1.38693	−0.693464	−	0.720491i	$-0.743916\pi$
$227$	−20.8962	−1.38693	−0.693464	+	0.720491i	$0.743916\pi$
$228$	−0.868075	−0.0574897
$229$	14.9686	0.989150	0.494575	−	0.869135i	$-0.335324\pi$
$229$	14.9686	0.989150	0.494575	+	0.869135i	$0.335324\pi$
$230$	−20.6378	−1.36081
$231$	−6.68477	−0.439825
$232$	−0.693615	−0.0455381
$233$	12.2295	0.801183	0.400592	−	0.916257i	$-0.368805\pi$
$233$	12.2295	0.801183	0.400592	+	0.916257i	$0.368805\pi$
$234$	−1.00000	−0.0653720
$235$	−0.232776	−0.0151846
$236$	5.02274	0.326953
$237$	−11.4341	−0.742724
$238$	−5.46907	−0.354507
$239$	−22.5228	−1.45688	−0.728438	−	0.685112i	$-0.759753\pi$
$239$	−22.5228	−1.45688	−0.728438	+	0.685112i	$0.759753\pi$
$240$	3.99294	0.257743
$241$	−8.37912	−0.539746	−0.269873	−	0.962896i	$-0.586982\pi$
$241$	−8.37912	−0.539746	−0.269873	+	0.962896i	$0.586982\pi$
$242$	−4.23094	−0.271975
$243$	−1.00000	−0.0641500
$244$	2.12798	0.136230
$245$	1.59109	0.101651
$246$	−6.68086	−0.425956
$247$	−0.868075	−0.0552343
$248$	4.86980	0.309232
$249$	−10.8428	−0.687132
$250$	−23.7325	−1.50097
$251$	26.2666	1.65793	0.828965	−	0.559300i	$-0.188930\pi$
$251$	26.2666	1.65793	0.828965	+	0.559300i	$0.188930\pi$
$252$	−2.56934	−0.161853
$253$	−13.4472	−0.845421
$254$	−7.71404	−0.484022
$255$	8.49932	0.532248
$256$	1.00000	0.0625000
$257$	9.91895	0.618727	0.309364	−	0.950944i	$-0.399884\pi$
$257$	9.91895	0.618727	0.309364	+	0.950944i	$0.399884\pi$
$258$	10.4261	0.649100
$259$	−12.7065	−0.789545
$260$	3.99294	0.247632
$261$	−0.693615	−0.0429337
$262$	−19.0357	−1.17603
$263$	10.5006	0.647493	0.323746	−	0.946144i	$-0.395058\pi$
$263$	10.5006	0.647493	0.323746	+	0.946144i	$0.395058\pi$
$264$	2.60174	0.160126
$265$	3.92747	0.241263
$266$	−2.23038	−0.136754
$267$	−4.29246	−0.262695
$268$	3.67387	0.224418
$269$	−7.22816	−0.440709	−0.220354	−	0.975420i	$-0.570721\pi$
$269$	−7.22816	−0.440709	−0.220354	+	0.975420i	$0.570721\pi$
$270$	3.99294	0.243003
$271$	25.3063	1.53725	0.768625	−	0.639699i	$-0.220941\pi$
$271$	25.3063	1.53725	0.768625	+	0.639699i	$0.220941\pi$
$272$	2.12859	0.129064
$273$	−2.56934	−0.155504
$274$	10.7685	0.650547
$275$	−28.4724	−1.71695
$276$	−5.16856	−0.311111
$277$	−2.65876	−0.159749	−0.0798746	−	0.996805i	$-0.525452\pi$
$277$	−2.65876	−0.159749	−0.0798746	+	0.996805i	$0.525452\pi$
$278$	−0.0497599	−0.00298440
$279$	4.86980	0.291547
$280$	10.2592	0.613107
$281$	−18.6038	−1.10981	−0.554905	−	0.831914i	$-0.687245\pi$
$281$	−18.6038	−1.10981	−0.554905	+	0.831914i	$0.687245\pi$
$282$	−0.0582968	−0.00347153
$283$	−0.839448	−0.0499000	−0.0249500	−	0.999689i	$-0.507943\pi$
$283$	−0.839448	−0.0499000	−0.0249500	+	0.999689i	$0.507943\pi$
$284$	−12.7794	−0.758318
$285$	3.46618	0.205319
$286$	2.60174	0.153844
$287$	−17.1654	−1.01324
$288$	1.00000	0.0589256
$289$	−12.4691	−0.733478
$290$	2.76957	0.162635
$291$	4.60864	0.270163
$292$	−14.6741	−0.858737
$293$	2.83894	0.165853	0.0829264	−	0.996556i	$-0.473573\pi$
$293$	2.83894	0.165853	0.0829264	+	0.996556i	$0.473573\pi$
$294$	0.398475	0.0232395
$295$	−20.0555	−1.16768
$296$	4.94544	0.287448
$297$	2.60174	0.150968
$298$	−16.2978	−0.944105
$299$	−5.16856	−0.298905
$300$	−10.9436	−0.631829
$301$	26.7882	1.54405
$302$	6.10676	0.351404
$303$	−9.54533	−0.548365
$304$	0.868075	0.0497875
$305$	−8.49692	−0.486532
$306$	2.12859	0.121683
$307$	0.0966486	0.00551603	0.00275801	−	0.999996i	$-0.499122\pi$
$307$	0.0966486	0.00551603	0.00275801	+	0.999996i	$0.499122\pi$
$308$	6.68477	0.380900
$309$	−1.00000	−0.0568880
$310$	−19.4448	−1.10439
$311$	5.12763	0.290761	0.145381	−	0.989376i	$-0.453559\pi$
$311$	5.12763	0.290761	0.145381	+	0.989376i	$0.453559\pi$
$312$	1.00000	0.0566139
$313$	30.6614	1.73308	0.866542	−	0.499105i	$-0.166338\pi$
$313$	30.6614	1.73308	0.866542	+	0.499105i	$0.166338\pi$
$314$	−0.366268	−0.0206697
$315$	10.2592	0.578043
$316$	11.4341	0.643217
$317$	2.12477	0.119339	0.0596695	−	0.998218i	$-0.480995\pi$
$317$	2.12477	0.119339	0.0596695	+	0.998218i	$0.480995\pi$
$318$	0.983603	0.0551577
$319$	1.80461	0.101039
$320$	−3.99294	−0.223212
$321$	−16.5615	−0.924370
$322$	−13.2798	−0.740054
$323$	1.84777	0.102813
$324$	1.00000	0.0555556
$325$	−10.9436	−0.607042
$326$	−18.2292	−1.00962
$327$	17.3830	0.961280
$328$	6.68086	0.368889
$329$	−0.149785	−0.00825789
$330$	−10.3886	−0.571874
$331$	−14.7383	−0.810092	−0.405046	−	0.914296i	$-0.632744\pi$
$331$	−14.7383	−0.810092	−0.405046	+	0.914296i	$0.632744\pi$
$332$	10.8428	0.595074
$333$	4.94544	0.271008
$334$	−0.659040	−0.0360611
$335$	−14.6696	−0.801485
$336$	2.56934	0.140169
$337$	−8.10845	−0.441695	−0.220848	−	0.975308i	$-0.570882\pi$
$337$	−8.10845	−0.441695	−0.220848	+	0.975308i	$0.570882\pi$
$338$	1.00000	0.0543928
$339$	7.45583	0.404945
$340$	−8.49932	−0.460940
$341$	−12.6700	−0.686117
$342$	0.868075	0.0469401
$343$	19.0092	1.02640
$344$	−10.4261	−0.562137
$345$	20.6378	1.11110
$346$	6.27169	0.337168
$347$	10.6754	0.573088	0.286544	−	0.958067i	$-0.407494\pi$
$347$	10.6754	0.573088	0.286544	+	0.958067i	$0.407494\pi$
$348$	0.693615	0.0371817
$349$	11.1505	0.596875	0.298438	−	0.954429i	$-0.403535\pi$
$349$	11.1505	0.596875	0.298438	+	0.954429i	$0.403535\pi$
$350$	−28.1179	−1.50296
$351$	1.00000	0.0533761
$352$	−2.60174	−0.138673
$353$	15.1570	0.806725	0.403363	−	0.915040i	$-0.367841\pi$
$353$	15.1570	0.806725	0.403363	+	0.915040i	$0.367841\pi$
$354$	−5.02274	−0.266956
$355$	51.0274	2.70825
$356$	4.29246	0.227500
$357$	5.46907	0.289454
$358$	−7.95567	−0.420470
$359$	−27.0061	−1.42533	−0.712664	−	0.701505i	$-0.752512\pi$
$359$	−27.0061	−1.42533	−0.712664	+	0.701505i	$0.752512\pi$
$360$	−3.99294	−0.210447
$361$	−18.2464	−0.960339
$362$	−22.3853	−1.17654
$363$	4.23094	0.222067
$364$	2.56934	0.134670
$365$	58.5929	3.06689
$366$	−2.12798	−0.111231
$367$	−5.41239	−0.282524	−0.141262	−	0.989972i	$-0.545116\pi$
$367$	−5.41239	−0.282524	−0.141262	+	0.989972i	$0.545116\pi$
$368$	5.16856	0.269430
$369$	6.68086	0.347792
$370$	−19.7469	−1.02659
$371$	2.52721	0.131206
$372$	−4.86980	−0.252487
$373$	−20.3470	−1.05353	−0.526765	−	0.850011i	$-0.676595\pi$
$373$	−20.3470	−1.05353	−0.526765	+	0.850011i	$0.676595\pi$
$374$	−5.53803	−0.286365
$375$	23.7325	1.22554
$376$	0.0582968	0.00300643
$377$	0.693615	0.0357230
$378$	2.56934	0.132153
$379$	−32.6260	−1.67589	−0.837943	−	0.545757i	$-0.816242\pi$
$379$	−32.6260	−1.67589	−0.837943	+	0.545757i	$0.816242\pi$
$380$	−3.46618	−0.177811
$381$	7.71404	0.395202
$382$	−0.114963	−0.00588201
$383$	−27.6385	−1.41226	−0.706132	−	0.708081i	$-0.749561\pi$
$383$	−27.6385	−1.41226	−0.706132	+	0.708081i	$0.749561\pi$
$384$	−1.00000	−0.0510310
$385$	−26.6919	−1.36035
$386$	−9.48769	−0.482911
$387$	−10.4261	−0.529988
$388$	−4.60864	−0.233968
$389$	−9.22011	−0.467478	−0.233739	−	0.972299i	$-0.575096\pi$
$389$	−9.22011	−0.467478	−0.233739	+	0.972299i	$0.575096\pi$
$390$	−3.99294	−0.202191
$391$	11.0017	0.556381
$392$	−0.398475	−0.0201260
$393$	19.0357	0.960226
$394$	6.92277	0.348764
$395$	−45.6557	−2.29719
$396$	−2.60174	−0.130742
$397$	−12.8295	−0.643897	−0.321948	−	0.946757i	$-0.604338\pi$
$397$	−12.8295	−0.643897	−0.321948	+	0.946757i	$0.604338\pi$
$398$	28.0215	1.40459
$399$	2.23038	0.111659
$400$	10.9436	0.547180
$401$	−10.8805	−0.543347	−0.271673	−	0.962390i	$-0.587577\pi$
$401$	−10.8805	−0.543347	−0.271673	+	0.962390i	$0.587577\pi$
$402$	−3.67387	−0.183236
$403$	−4.86980	−0.242582
$404$	9.54533	0.474898
$405$	−3.99294	−0.198411
$406$	1.78214	0.0884459
$407$	−12.8668	−0.637781
$408$	−2.12859	−0.105381
$409$	−30.7660	−1.52128	−0.760642	−	0.649172i	$-0.775116\pi$
$409$	−30.7660	−1.52128	−0.760642	+	0.649172i	$0.775116\pi$
$410$	−26.6763	−1.31745
$411$	−10.7685	−0.531170
$412$	1.00000	0.0492665
$413$	−12.9052	−0.635021
$414$	5.16856	0.254021
$415$	−43.2945	−2.12525
$416$	−1.00000	−0.0490290
$417$	0.0497599	0.00243675
$418$	−2.25851	−0.110467
$419$	23.9414	1.16961	0.584807	−	0.811173i	$-0.301170\pi$
$419$	23.9414	1.16961	0.584807	+	0.811173i	$0.301170\pi$
$420$	−10.2592	−0.500600
$421$	−11.8804	−0.579014	−0.289507	−	0.957176i	$-0.593491\pi$
$421$	−11.8804	−0.579014	−0.289507	+	0.957176i	$0.593491\pi$
$422$	−19.4194	−0.945322
$423$	0.0582968	0.00283449
$424$	−0.983603	−0.0477680
$425$	23.2944	1.12994
$426$	12.7794	0.619164
$427$	−5.46752	−0.264592
$428$	16.5615	0.800528
$429$	−2.60174	−0.125613
$430$	41.6308	2.00762
$431$	13.4438	0.647566	0.323783	−	0.946131i	$-0.395045\pi$
$431$	13.4438	0.647566	0.323783	+	0.946131i	$0.395045\pi$
$432$	−1.00000	−0.0481125
$433$	−6.25872	−0.300775	−0.150387	−	0.988627i	$-0.548052\pi$
$433$	−6.25872	−0.300775	−0.150387	+	0.988627i	$0.548052\pi$
$434$	−12.5122	−0.600604
$435$	−2.76957	−0.132791
$436$	−17.3830	−0.832493
$437$	4.48670	0.214628
$438$	14.6741	0.701156
$439$	−4.55812	−0.217547	−0.108774	−	0.994067i	$-0.534692\pi$
$439$	−4.55812	−0.217547	−0.108774	+	0.994067i	$0.534692\pi$
$440$	10.3886	0.495258
$441$	−0.398475	−0.0189750
$442$	−2.12859	−0.101246
$443$	12.7154	0.604128	0.302064	−	0.953288i	$-0.402324\pi$
$443$	12.7154	0.604128	0.302064	+	0.953288i	$0.402324\pi$
$444$	−4.94544	−0.234700
$445$	−17.1396	−0.812494
$446$	−0.829123	−0.0392601
$447$	16.2978	0.770858
$448$	−2.56934	−0.121390
$449$	−4.29412	−0.202652	−0.101326	−	0.994853i	$-0.532309\pi$
$449$	−4.29412	−0.202652	−0.101326	+	0.994853i	$0.532309\pi$
$450$	10.9436	0.515887
$451$	−17.3819	−0.818480
$452$	−7.45583	−0.350693
$453$	−6.10676	−0.286920
$454$	−20.8962	−0.980706
$455$	−10.2592	−0.480961
$456$	−0.868075	−0.0406514
$457$	27.8952	1.30488	0.652442	−	0.757839i	$-0.273745\pi$
$457$	27.8952	1.30488	0.652442	+	0.757839i	$0.273745\pi$
$458$	14.9686	0.699435
$459$	−2.12859	−0.0993538
$460$	−20.6378	−0.962240
$461$	36.3652	1.69370	0.846849	−	0.531834i	$-0.178497\pi$
$461$	36.3652	1.69370	0.846849	+	0.531834i	$0.178497\pi$
$462$	−6.68477	−0.311004
$463$	34.6581	1.61070	0.805350	−	0.592800i	$-0.201978\pi$
$463$	34.6581	1.61070	0.805350	+	0.592800i	$0.201978\pi$
$464$	−0.693615	−0.0322003
$465$	19.4448	0.901732
$466$	12.2295	0.566522
$467$	16.6871	0.772186	0.386093	−	0.922460i	$-0.373824\pi$
$467$	16.6871	0.772186	0.386093	+	0.922460i	$0.373824\pi$
$468$	−1.00000	−0.0462250
$469$	−9.43945	−0.435873
$470$	−0.232776	−0.0107372
$471$	0.366268	0.0168767
$472$	5.02274	0.231191
$473$	27.1260	1.24725
$474$	−11.4341	−0.525185
$475$	9.49987	0.435884
$476$	−5.46907	−0.250674
$477$	−0.983603	−0.0450361
$478$	−22.5228	−1.03017
$479$	−22.9844	−1.05018	−0.525091	−	0.851046i	$-0.675969\pi$
$479$	−22.9844	−1.05018	−0.525091	+	0.851046i	$0.675969\pi$
$480$	3.99294	0.182252
$481$	−4.94544	−0.225493
$482$	−8.37912	−0.381658
$483$	13.2798	0.604252
$484$	−4.23094	−0.192315
$485$	18.4020	0.835593
$486$	−1.00000	−0.0453609
$487$	15.5009	0.702413	0.351207	−	0.936298i	$-0.385771\pi$
$487$	15.5009	0.702413	0.351207	+	0.936298i	$0.385771\pi$
$488$	2.12798	0.0963293
$489$	18.2292	0.824353
$490$	1.59109	0.0718780
$491$	22.1141	0.997996	0.498998	−	0.866603i	$-0.333701\pi$
$491$	22.1141	0.997996	0.498998	+	0.866603i	$0.333701\pi$
$492$	−6.68086	−0.301196
$493$	−1.47642	−0.0664946
$494$	−0.868075	−0.0390566
$495$	10.3886	0.466933
$496$	4.86980	0.218660
$497$	32.8347	1.47284
$498$	−10.8428	−0.485876
$499$	−26.7737	−1.19855	−0.599277	−	0.800542i	$-0.704545\pi$
$499$	−26.7737	−1.19855	−0.599277	+	0.800542i	$0.704545\pi$
$500$	−23.7325	−1.06135
$501$	0.659040	0.0294437
$502$	26.2666	1.17233
$503$	25.2140	1.12424	0.562119	−	0.827056i	$-0.309986\pi$
$503$	25.2140	1.12424	0.562119	+	0.827056i	$0.309986\pi$
$504$	−2.56934	−0.114448
$505$	−38.1140	−1.69605
$506$	−13.4472	−0.597803
$507$	−1.00000	−0.0444116
$508$	−7.71404	−0.342255
$509$	3.77260	0.167217	0.0836087	−	0.996499i	$-0.473355\pi$
$509$	3.77260	0.167217	0.0836087	+	0.996499i	$0.473355\pi$
$510$	8.49932	0.376356
$511$	37.7028	1.66787
$512$	1.00000	0.0441942
$513$	−0.868075	−0.0383265
$514$	9.91895	0.437506
$515$	−3.99294	−0.175950
$516$	10.4261	0.458983
$517$	−0.151673	−0.00667058
$518$	−12.7065	−0.558293
$519$	−6.27169	−0.275297
$520$	3.99294	0.175102
$521$	2.69176	0.117928	0.0589641	−	0.998260i	$-0.481220\pi$
$521$	2.69176	0.117928	0.0589641	+	0.998260i	$0.481220\pi$
$522$	−0.693615	−0.0303587
$523$	−39.3404	−1.72024	−0.860118	−	0.510095i	$-0.829610\pi$
$523$	−39.3404	−1.72024	−0.860118	+	0.510095i	$0.829610\pi$
$524$	−19.0357	−0.831580
$525$	28.1179	1.22716
$526$	10.5006	0.457847
$527$	10.3658	0.451540
$528$	2.60174	0.113226
$529$	3.71398	0.161477
$530$	3.92747	0.170598
$531$	5.02274	0.217969
$532$	−2.23038	−0.0966994
$533$	−6.68086	−0.289380
$534$	−4.29246	−0.185753
$535$	−66.1290	−2.85900
$536$	3.67387	0.158687
$537$	7.95567	0.343313
$538$	−7.22816	−0.311628
$539$	1.03673	0.0446550
$540$	3.99294	0.171829
$541$	−32.4857	−1.39667	−0.698334	−	0.715772i	$-0.746075\pi$
$541$	−32.4857	−1.39667	−0.698334	+	0.715772i	$0.746075\pi$
$542$	25.3063	1.08700
$543$	22.3853	0.960644
$544$	2.12859	0.0912623
$545$	69.4092	2.97316
$546$	−2.56934	−0.109958
$547$	22.2758	0.952446	0.476223	−	0.879325i	$-0.342005\pi$
$547$	22.2758	0.952446	0.476223	+	0.879325i	$0.342005\pi$
$548$	10.7685	0.460006
$549$	2.12798	0.0908201
$550$	−28.4724	−1.21407
$551$	−0.602110	−0.0256508
$552$	−5.16856	−0.219988
$553$	−29.3781	−1.24928
$554$	−2.65876	−0.112960
$555$	19.7469	0.838208
$556$	−0.0497599	−0.00211029
$557$	−13.8034	−0.584867	−0.292434	−	0.956286i	$-0.594465\pi$
$557$	−13.8034	−0.584867	−0.292434	+	0.956286i	$0.594465\pi$
$558$	4.86980	0.206155
$559$	10.4261	0.440977
$560$	10.2592	0.433532
$561$	5.53803	0.233816
$562$	−18.6038	−0.784754
$563$	−8.48593	−0.357639	−0.178820	−	0.983882i	$-0.557228\pi$
$563$	−8.48593	−0.357639	−0.178820	+	0.983882i	$0.557228\pi$
$564$	−0.0582968	−0.00245474
$565$	29.7707	1.25246
$566$	−0.839448	−0.0352846
$567$	−2.56934	−0.107902
$568$	−12.7794	−0.536211
$569$	25.2067	1.05672	0.528361	−	0.849020i	$-0.322807\pi$
$569$	25.2067	1.05672	0.528361	+	0.849020i	$0.322807\pi$
$570$	3.46618	0.145182
$571$	−12.6196	−0.528112	−0.264056	−	0.964507i	$-0.585060\pi$
$571$	−12.6196	−0.528112	−0.264056	+	0.964507i	$0.585060\pi$
$572$	2.60174	0.108784
$573$	0.114963	0.00480264
$574$	−17.1654	−0.716471
$575$	56.5626	2.35883
$576$	1.00000	0.0416667
$577$	−2.30550	−0.0959794	−0.0479897	−	0.998848i	$-0.515281\pi$
$577$	−2.30550	−0.0959794	−0.0479897	+	0.998848i	$0.515281\pi$
$578$	−12.4691	−0.518647
$579$	9.48769	0.394295
$580$	2.76957	0.115000
$581$	−27.8588	−1.15578
$582$	4.60864	0.191034
$583$	2.55908	0.105986
$584$	−14.6741	−0.607219
$585$	3.99294	0.165088
$586$	2.83894	0.117276
$587$	−36.7651	−1.51746	−0.758729	−	0.651406i	$-0.774179\pi$
$587$	−36.7651	−1.51746	−0.758729	+	0.651406i	$0.774179\pi$
$588$	0.398475	0.0164328
$589$	4.22735	0.174185
$590$	−20.0555	−0.825673
$591$	−6.92277	−0.284765
$592$	4.94544	0.203256
$593$	−11.5682	−0.475048	−0.237524	−	0.971382i	$-0.576336\pi$
$593$	−11.5682	−0.475048	−0.237524	+	0.971382i	$0.576336\pi$
$594$	2.60174	0.106751
$595$	21.8377	0.895258
$596$	−16.2978	−0.667583
$597$	−28.0215	−1.14684
$598$	−5.16856	−0.211358
$599$	−21.6737	−0.885564	−0.442782	−	0.896629i	$-0.646008\pi$
$599$	−21.6737	−0.885564	−0.442782	+	0.896629i	$0.646008\pi$
$600$	−10.9436	−0.446771
$601$	−26.1812	−1.06795	−0.533976	−	0.845500i	$-0.679303\pi$
$601$	−26.1812	−1.06795	−0.533976	+	0.845500i	$0.679303\pi$
$602$	26.7882	1.09181
$603$	3.67387	0.149612
$604$	6.10676	0.248480
$605$	16.8939	0.686835
$606$	−9.54533	−0.387753
$607$	40.5029	1.64396	0.821981	−	0.569515i	$-0.192869\pi$
$607$	40.5029	1.64396	0.821981	+	0.569515i	$0.192869\pi$
$608$	0.868075	0.0352051
$609$	−1.78214	−0.0722158
$610$	−8.49692	−0.344030
$611$	−0.0582968	−0.00235844
$612$	2.12859	0.0860430
$613$	−2.67226	−0.107931	−0.0539657	−	0.998543i	$-0.517186\pi$
$613$	−2.67226	−0.107931	−0.0539657	+	0.998543i	$0.517186\pi$
$614$	0.0966486	0.00390042
$615$	26.6763	1.07569
$616$	6.68477	0.269337
$617$	−33.8934	−1.36450	−0.682248	−	0.731121i	$-0.738998\pi$
$617$	−33.8934	−1.36450	−0.682248	+	0.731121i	$0.738998\pi$
$618$	−1.00000	−0.0402259
$619$	2.74644	0.110389	0.0551944	−	0.998476i	$-0.482422\pi$
$619$	2.74644	0.110389	0.0551944	+	0.998476i	$0.482422\pi$
$620$	−19.4448	−0.780923
$621$	−5.16856	−0.207407
$622$	5.12763	0.205599
$623$	−11.0288	−0.441860
$624$	1.00000	0.0400320
$625$	40.0445	1.60178
$626$	30.6614	1.22547
$627$	2.25851	0.0901961
$628$	−0.366268	−0.0146157
$629$	10.5268	0.419731
$630$	10.2592	0.408738
$631$	27.0527	1.07695	0.538476	−	0.842641i	$-0.319000\pi$
$631$	27.0527	1.07695	0.538476	+	0.842641i	$0.319000\pi$
$632$	11.4341	0.454823
$633$	19.4194	0.771852
$634$	2.12477	0.0843854
$635$	30.8018	1.22233
$636$	0.983603	0.0390024
$637$	0.398475	0.0157881
$638$	1.80461	0.0714451
$639$	−12.7794	−0.505545
$640$	−3.99294	−0.157835
$641$	11.2769	0.445412	0.222706	−	0.974886i	$-0.428511\pi$
$641$	11.2769	0.445412	0.222706	+	0.974886i	$0.428511\pi$
$642$	−16.5615	−0.653629
$643$	−37.7429	−1.48843	−0.744217	−	0.667937i	$-0.767177\pi$
$643$	−37.7429	−1.48843	−0.744217	+	0.667937i	$0.767177\pi$
$644$	−13.2798	−0.523297
$645$	−41.6308	−1.63921
$646$	1.84777	0.0726996
$647$	−33.9233	−1.33366	−0.666830	−	0.745210i	$-0.732349\pi$
$647$	−33.9233	−1.33366	−0.666830	+	0.745210i	$0.732349\pi$
$648$	1.00000	0.0392837
$649$	−13.0679	−0.512959
$650$	−10.9436	−0.429244
$651$	12.5122	0.490391
$652$	−18.2292	−0.713910
$653$	−30.1596	−1.18024	−0.590118	−	0.807317i	$-0.700919\pi$
$653$	−30.1596	−1.18024	−0.590118	+	0.807317i	$0.700919\pi$
$654$	17.3830	0.679728
$655$	76.0087	2.96990
$656$	6.68086	0.260844
$657$	−14.6741	−0.572491
$658$	−0.149785	−0.00583921
$659$	3.42450	0.133400	0.0666998	−	0.997773i	$-0.478753\pi$
$659$	3.42450	0.133400	0.0666998	+	0.997773i	$0.478753\pi$
$660$	−10.3886	−0.404376
$661$	−43.7128	−1.70023	−0.850116	−	0.526596i	$-0.823468\pi$
$661$	−43.7128	−1.70023	−0.850116	+	0.526596i	$0.823468\pi$
$662$	−14.7383	−0.572822
$663$	2.12859	0.0826674
$664$	10.8428	0.420781
$665$	8.90580	0.345352
$666$	4.94544	0.191632
$667$	−3.58499	−0.138811
$668$	−0.659040	−0.0254990
$669$	0.829123	0.0320558
$670$	−14.6696	−0.566735
$671$	−5.53646	−0.213733
$672$	2.56934	0.0991146
$673$	−40.9084	−1.57690	−0.788451	−	0.615098i	$-0.789116\pi$
$673$	−40.9084	−1.57690	−0.788451	+	0.615098i	$0.789116\pi$
$674$	−8.10845	−0.312326
$675$	−10.9436	−0.421220
$676$	1.00000	0.0384615
$677$	−31.5828	−1.21383	−0.606913	−	0.794768i	$-0.707592\pi$
$677$	−31.5828	−1.21383	−0.606913	+	0.794768i	$0.707592\pi$
$678$	7.45583	0.286339
$679$	11.8412	0.454422
$680$	−8.49932	−0.325934
$681$	20.8962	0.800743
$682$	−12.6700	−0.485158
$683$	−22.8340	−0.873720	−0.436860	−	0.899530i	$-0.643909\pi$
$683$	−22.8340	−0.873720	−0.436860	+	0.899530i	$0.643909\pi$
$684$	0.868075	0.0331917
$685$	−42.9979	−1.64287
$686$	19.0092	0.725775
$687$	−14.9686	−0.571086
$688$	−10.4261	−0.397491
$689$	0.983603	0.0374723
$690$	20.6378	0.785666
$691$	3.91733	0.149022	0.0745111	−	0.997220i	$-0.476260\pi$
$691$	3.91733	0.149022	0.0745111	+	0.997220i	$0.476260\pi$
$692$	6.27169	0.238414
$693$	6.68477	0.253933
$694$	10.6754	0.405234
$695$	0.198689	0.00753669
$696$	0.693615	0.0262914
$697$	14.2208	0.538650
$698$	11.1505	0.422054
$699$	−12.2295	−0.462563
$700$	−28.1179	−1.06276
$701$	13.3208	0.503121	0.251561	−	0.967842i	$-0.419056\pi$
$701$	13.3208	0.503121	0.251561	+	0.967842i	$0.419056\pi$
$702$	1.00000	0.0377426
$703$	4.29301	0.161914
$704$	−2.60174	−0.0980568
$705$	0.232776	0.00876685
$706$	15.1570	0.570441
$707$	−24.5252	−0.922367
$708$	−5.02274	−0.188766
$709$	2.59946	0.0976246	0.0488123	−	0.998808i	$-0.484456\pi$
$709$	2.59946	0.0976246	0.0488123	+	0.998808i	$0.484456\pi$
$710$	51.0274	1.91502
$711$	11.4341	0.428812
$712$	4.29246	0.160867
$713$	25.1698	0.942617
$714$	5.46907	0.204675
$715$	−10.3886	−0.388512
$716$	−7.95567	−0.297317
$717$	22.5228	0.841128
$718$	−27.0061	−1.00786
$719$	20.1641	0.751994	0.375997	−	0.926621i	$-0.377300\pi$
$719$	20.1641	0.751994	0.375997	+	0.926621i	$0.377300\pi$
$720$	−3.99294	−0.148808
$721$	−2.56934	−0.0956873
$722$	−18.2464	−0.679062
$723$	8.37912	0.311623
$724$	−22.3853	−0.831942
$725$	−7.59065	−0.281910
$726$	4.23094	0.157025
$727$	−37.9251	−1.40656	−0.703281	−	0.710912i	$-0.748283\pi$
$727$	−37.9251	−1.40656	−0.703281	+	0.710912i	$0.748283\pi$
$728$	2.56934	0.0952262
$729$	1.00000	0.0370370
$730$	58.5929	2.16862
$731$	−22.1928	−0.820831
$732$	−2.12798	−0.0786525
$733$	−22.3684	−0.826197	−0.413098	−	0.910686i	$-0.635553\pi$
$733$	−22.3684	−0.826197	−0.413098	+	0.910686i	$0.635553\pi$
$734$	−5.41239	−0.199775
$735$	−1.59109	−0.0586881
$736$	5.16856	0.190516
$737$	−9.55847	−0.352091
$738$	6.68086	0.245926
$739$	−9.15790	−0.336879	−0.168439	−	0.985712i	$-0.553873\pi$
$739$	−9.15790	−0.336879	−0.168439	+	0.985712i	$0.553873\pi$
$740$	−19.7469	−0.725909
$741$	0.868075	0.0318895
$742$	2.52721	0.0927769
$743$	33.1614	1.21657	0.608286	−	0.793718i	$-0.291857\pi$
$743$	33.1614	1.21657	0.608286	+	0.793718i	$0.291857\pi$
$744$	−4.86980	−0.178535
$745$	65.0761	2.38420
$746$	−20.3470	−0.744958
$747$	10.8428	0.396716
$748$	−5.53803	−0.202490
$749$	−42.5521	−1.55482
$750$	23.7325	0.866588
$751$	2.50178	0.0912914	0.0456457	−	0.998958i	$-0.485465\pi$
$751$	2.50178	0.0912914	0.0456457	+	0.998958i	$0.485465\pi$
$752$	0.0582968	0.00212587
$753$	−26.2666	−0.957207
$754$	0.693615	0.0252600
$755$	−24.3839	−0.887422
$756$	2.56934	0.0934461
$757$	13.8483	0.503324	0.251662	−	0.967815i	$-0.419023\pi$
$757$	13.8483	0.503324	0.251662	+	0.967815i	$0.419023\pi$
$758$	−32.6260	−1.18503
$759$	13.4472	0.488104
$760$	−3.46618	−0.125731
$761$	−9.29927	−0.337098	−0.168549	−	0.985693i	$-0.553908\pi$
$761$	−9.29927	−0.337098	−0.168549	+	0.985693i	$0.553908\pi$
$762$	7.71404	0.279450
$763$	44.6628	1.61690
$764$	−0.114963	−0.00415921
$765$	−8.49932	−0.307294
$766$	−27.6385	−0.998621
$767$	−5.02274	−0.181361
$768$	−1.00000	−0.0360844
$769$	32.4683	1.17084	0.585419	−	0.810731i	$-0.300930\pi$
$769$	32.4683	1.17084	0.585419	+	0.810731i	$0.300930\pi$
$770$	−26.6919	−0.961910
$771$	−9.91895	−0.357222
$772$	−9.48769	−0.341470
$773$	45.9727	1.65352	0.826762	−	0.562552i	$-0.190180\pi$
$773$	45.9727	1.65352	0.826762	+	0.562552i	$0.190180\pi$
$774$	−10.4261	−0.374758
$775$	53.2931	1.91435
$776$	−4.60864	−0.165440
$777$	12.7065	0.455844
$778$	−9.22011	−0.330557
$779$	5.79949	0.207788
$780$	−3.99294	−0.142970
$781$	33.2487	1.18973
$782$	11.0017	0.393420
$783$	0.693615	0.0247878
$784$	−0.398475	−0.0142312
$785$	1.46249	0.0521984
$786$	19.0357	0.678982
$787$	−47.8978	−1.70737	−0.853686	−	0.520788i	$-0.825638\pi$
$787$	−47.8978	−1.70737	−0.853686	+	0.520788i	$0.825638\pi$
$788$	6.92277	0.246614
$789$	−10.5006	−0.373830
$790$	−45.6557	−1.62436
$791$	19.1566	0.681130
$792$	−2.60174	−0.0924489
$793$	−2.12798	−0.0755669
$794$	−12.8295	−0.455304
$795$	−3.92747	−0.139293
$796$	28.0215	0.993195
$797$	31.1030	1.10172	0.550862	−	0.834597i	$-0.314299\pi$
$797$	31.1030	1.10172	0.550862	+	0.834597i	$0.314299\pi$
$798$	2.23038	0.0789547
$799$	0.124090	0.00438998
$800$	10.9436	0.386915
$801$	4.29246	0.151667
$802$	−10.8805	−0.384204
$803$	38.1782	1.34728
$804$	−3.67387	−0.129568
$805$	53.0255	1.86890
$806$	−4.86980	−0.171531
$807$	7.22816	0.254443
$808$	9.54533	0.335804
$809$	26.5752	0.934335	0.467168	−	0.884169i	$-0.345274\pi$
$809$	26.5752	0.934335	0.467168	+	0.884169i	$0.345274\pi$
$810$	−3.99294	−0.140298
$811$	2.78173	0.0976799	0.0488400	−	0.998807i	$-0.484448\pi$
$811$	2.78173	0.0976799	0.0488400	+	0.998807i	$0.484448\pi$
$812$	1.78214	0.0625407
$813$	−25.3063	−0.887532
$814$	−12.8668	−0.450980
$815$	72.7882	2.54966
$816$	−2.12859	−0.0745154
$817$	−9.05063	−0.316642
$818$	−30.7660	−1.07571
$819$	2.56934	0.0897801
$820$	−26.6763	−0.931577
$821$	14.0393	0.489976	0.244988	−	0.969526i	$-0.421216\pi$
$821$	14.0393	0.489976	0.244988	+	0.969526i	$0.421216\pi$
$822$	−10.7685	−0.375594
$823$	24.5764	0.856678	0.428339	−	0.903618i	$-0.359099\pi$
$823$	24.5764	0.856678	0.428339	+	0.903618i	$0.359099\pi$
$824$	1.00000	0.0348367
$825$	28.4724	0.991283
$826$	−12.9052	−0.449028
$827$	−3.93984	−0.137002	−0.0685009	−	0.997651i	$-0.521822\pi$
$827$	−3.93984	−0.137002	−0.0685009	+	0.997651i	$0.521822\pi$
$828$	5.16856	0.179620
$829$	−5.81683	−0.202027	−0.101013	−	0.994885i	$-0.532209\pi$
$829$	−5.81683	−0.202027	−0.101013	+	0.994885i	$0.532209\pi$
$830$	−43.2945	−1.50278
$831$	2.65876	0.0922312
$832$	−1.00000	−0.0346688
$833$	−0.848187	−0.0293879
$834$	0.0497599	0.00172304
$835$	2.63151	0.0910671
$836$	−2.25851	−0.0781121
$837$	−4.86980	−0.168325
$838$	23.9414	0.827041
$839$	−50.8579	−1.75581	−0.877905	−	0.478835i	$-0.841059\pi$
$839$	−50.8579	−1.75581	−0.877905	+	0.478835i	$0.841059\pi$
$840$	−10.2592	−0.353978
$841$	−28.5189	−0.983410
$842$	−11.8804	−0.409425
$843$	18.6038	0.640749
$844$	−19.4194	−0.668444
$845$	−3.99294	−0.137361
$846$	0.0582968	0.00200429
$847$	10.8707	0.373523
$848$	−0.983603	−0.0337771
$849$	0.839448	0.0288098
$850$	23.2944	0.798991
$851$	25.5608	0.876212
$852$	12.7794	0.437815
$853$	−9.23135	−0.316075	−0.158038	−	0.987433i	$-0.550517\pi$
$853$	−9.23135	−0.316075	−0.158038	+	0.987433i	$0.550517\pi$
$854$	−5.46752	−0.187095
$855$	−3.46618	−0.118541
$856$	16.5615	0.566059
$857$	5.90669	0.201769	0.100884	−	0.994898i	$-0.467833\pi$
$857$	5.90669	0.201769	0.100884	+	0.994898i	$0.467833\pi$
$858$	−2.60174	−0.0888220
$859$	−33.0654	−1.12818	−0.564089	−	0.825714i	$-0.690773\pi$
$859$	−33.0654	−1.12818	−0.564089	+	0.825714i	$0.690773\pi$
$860$	41.6308	1.41960
$861$	17.1654	0.584996
$862$	13.4438	0.457898
$863$	−7.42065	−0.252602	−0.126301	−	0.991992i	$-0.540311\pi$
$863$	−7.42065	−0.252602	−0.126301	+	0.991992i	$0.540311\pi$
$864$	−1.00000	−0.0340207
$865$	−25.0425	−0.851471
$866$	−6.25872	−0.212680
$867$	12.4691	0.423474
$868$	−12.5122	−0.424691
$869$	−29.7485	−1.00915
$870$	−2.76957	−0.0938971
$871$	−3.67387	−0.124485
$872$	−17.3830	−0.588661
$873$	−4.60864	−0.155979
$874$	4.48670	0.151765
$875$	60.9769	2.06140
$876$	14.6741	0.495792
$877$	−37.8310	−1.27746	−0.638731	−	0.769430i	$-0.720541\pi$
$877$	−37.8310	−1.27746	−0.638731	+	0.769430i	$0.720541\pi$
$878$	−4.55812	−0.153829
$879$	−2.83894	−0.0957551
$880$	10.3886	0.350200
$881$	−0.914126	−0.0307977	−0.0153988	−	0.999881i	$-0.504902\pi$
$881$	−0.914126	−0.0307977	−0.0153988	+	0.999881i	$0.504902\pi$
$882$	−0.398475	−0.0134173
$883$	36.3165	1.22215	0.611074	−	0.791573i	$-0.290738\pi$
$883$	36.3165	1.22215	0.611074	+	0.791573i	$0.290738\pi$
$884$	−2.12859	−0.0715921
$885$	20.0555	0.674160
$886$	12.7154	0.427183
$887$	−0.437810	−0.0147002	−0.00735012	−	0.999973i	$-0.502340\pi$
$887$	−0.437810	−0.0147002	−0.00735012	+	0.999973i	$0.502340\pi$
$888$	−4.94544	−0.165958
$889$	19.8200	0.664742
$890$	−17.1396	−0.574520
$891$	−2.60174	−0.0871616
$892$	−0.829123	−0.0277611
$893$	0.0506060	0.00169347
$894$	16.2978	0.545079
$895$	31.7666	1.06184
$896$	−2.56934	−0.0858357
$897$	5.16856	0.172573
$898$	−4.29412	−0.143297
$899$	−3.37777	−0.112655
$900$	10.9436	0.364787
$901$	−2.09368	−0.0697507
$902$	−17.3819	−0.578753
$903$	−26.7882	−0.891456
$904$	−7.45583	−0.247977
$905$	89.3832	2.97120
$906$	−6.10676	−0.202883
$907$	−11.4955	−0.381701	−0.190851	−	0.981619i	$-0.561125\pi$
$907$	−11.4955	−0.381701	−0.190851	+	0.981619i	$0.561125\pi$
$908$	−20.8962	−0.693464
$909$	9.54533	0.316599
$910$	−10.2592	−0.340091
$911$	43.1850	1.43078	0.715392	−	0.698723i	$-0.246248\pi$
$911$	43.1850	1.43078	0.715392	+	0.698723i	$0.246248\pi$
$912$	−0.868075	−0.0287448
$913$	−28.2101	−0.933617
$914$	27.8952	0.922692
$915$	8.49692	0.280899
$916$	14.9686	0.494575
$917$	48.9094	1.61513
$918$	−2.12859	−0.0702538
$919$	3.31270	0.109276	0.0546379	−	0.998506i	$-0.482600\pi$
$919$	3.31270	0.109276	0.0546379	+	0.998506i	$0.482600\pi$
$920$	−20.6378	−0.680407
$921$	−0.0966486	−0.00318468
$922$	36.3652	1.19763
$923$	12.7794	0.420639
$924$	−6.68477	−0.219913
$925$	54.1209	1.77949
$926$	34.6581	1.13894
$927$	1.00000	0.0328443
$928$	−0.693615	−0.0227690
$929$	7.88991	0.258860	0.129430	−	0.991589i	$-0.458685\pi$
$929$	7.88991	0.258860	0.129430	+	0.991589i	$0.458685\pi$
$930$	19.4448	0.637621
$931$	−0.345906	−0.0113366
$932$	12.2295	0.400592
$933$	−5.12763	−0.167871
$934$	16.6871	0.546018
$935$	22.1130	0.723174
$936$	−1.00000	−0.0326860
$937$	48.9424	1.59888	0.799440	−	0.600747i	$-0.205130\pi$
$937$	48.9424	1.59888	0.799440	+	0.600747i	$0.205130\pi$
$938$	−9.43945	−0.308209
$939$	−30.6614	−1.00060
$940$	−0.232776	−0.00759232
$941$	8.03996	0.262095	0.131048	−	0.991376i	$-0.458166\pi$
$941$	8.03996	0.262095	0.131048	+	0.991376i	$0.458166\pi$
$942$	0.366268	0.0119336
$943$	34.5304	1.12446
$944$	5.02274	0.163476
$945$	−10.2592	−0.333733
$946$	27.1260	0.881942
$947$	17.2090	0.559216	0.279608	−	0.960114i	$-0.409795\pi$
$947$	17.2090	0.559216	0.279608	+	0.960114i	$0.409795\pi$
$948$	−11.4341	−0.371362
$949$	14.6741	0.476341
$950$	9.49987	0.308217
$951$	−2.12477	−0.0689004
$952$	−5.46907	−0.177253
$953$	−39.7511	−1.28766	−0.643832	−	0.765167i	$-0.722656\pi$
$953$	−39.7511	−1.28766	−0.643832	+	0.765167i	$0.722656\pi$
$954$	−0.983603	−0.0318453
$955$	0.459040	0.0148542
$956$	−22.5228	−0.728438
$957$	−1.80461	−0.0583347
$958$	−22.9844	−0.742591
$959$	−27.6679	−0.893443
$960$	3.99294	0.128872
$961$	−7.28507	−0.235002
$962$	−4.94544	−0.159447
$963$	16.5615	0.533685
$964$	−8.37912	−0.269873
$965$	37.8838	1.21952
$966$	13.2798	0.427270
$967$	10.1415	0.326129	0.163064	−	0.986615i	$-0.447862\pi$
$967$	10.1415	0.326129	0.163064	+	0.986615i	$0.447862\pi$
$968$	−4.23094	−0.135988
$969$	−1.84777	−0.0593590
$970$	18.4020	0.590854
$971$	−56.6702	−1.81863	−0.909316	−	0.416107i	$-0.863394\pi$
$971$	−56.6702	−1.81863	−0.909316	+	0.416107i	$0.863394\pi$
$972$	−1.00000	−0.0320750
$973$	0.127850	0.00409869
$974$	15.5009	0.496681
$975$	10.9436	0.350476
$976$	2.12798	0.0681151
$977$	−19.1925	−0.614023	−0.307012	−	0.951706i	$-0.599329\pi$
$977$	−19.1925	−0.614023	−0.307012	+	0.951706i	$0.599329\pi$
$978$	18.2292	0.582905
$979$	−11.1679	−0.356927
$980$	1.59109	0.0508254
$981$	−17.3830	−0.554995
$982$	22.1141	0.705690
$983$	−8.40875	−0.268198	−0.134099	−	0.990968i	$-0.542814\pi$
$983$	−8.40875	−0.268198	−0.134099	+	0.990968i	$0.542814\pi$
$984$	−6.68086	−0.212978
$985$	−27.6422	−0.880755
$986$	−1.47642	−0.0470188
$987$	0.149785	0.00476770
$988$	−0.868075	−0.0276172
$989$	−53.8878	−1.71353
$990$	10.3886	0.330172
$991$	35.2342	1.11925	0.559625	−	0.828746i	$-0.310945\pi$
$991$	35.2342	1.11925	0.559625	+	0.828746i	$0.310945\pi$
$992$	4.86980	0.154616
$993$	14.7383	0.467707
$994$	32.8347	1.04145
$995$	−111.888	−3.54710
$996$	−10.8428	−0.343566
$997$	19.0727	0.604038	0.302019	−	0.953302i	$-0.402339\pi$
$997$	19.0727	0.604038	0.302019	+	0.953302i	$0.402339\pi$
$998$	−26.7737	−0.847505
$999$	−4.94544	−0.156467

Twists

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.99294 q^{5} -1.00000 q^{6} -2.56934 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.99294 q^{5} -1.00000 q^{6} -2.56934 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.99294 q^{10} -2.60174 q^{11} -1.00000 q^{12} -1.00000 q^{13} -2.56934 q^{14} +3.99294 q^{15} +1.00000 q^{16} +2.12859 q^{17} +1.00000 q^{18} +0.868075 q^{19} -3.99294 q^{20} +2.56934 q^{21} -2.60174 q^{22} +5.16856 q^{23} -1.00000 q^{24} +10.9436 q^{25} -1.00000 q^{26} -1.00000 q^{27} -2.56934 q^{28} -0.693615 q^{29} +3.99294 q^{30} +4.86980 q^{31} +1.00000 q^{32} +2.60174 q^{33} +2.12859 q^{34} +10.2592 q^{35} +1.00000 q^{36} +4.94544 q^{37} +0.868075 q^{38} +1.00000 q^{39} -3.99294 q^{40} +6.68086 q^{41} +2.56934 q^{42} -10.4261 q^{43} -2.60174 q^{44} -3.99294 q^{45} +5.16856 q^{46} +0.0582968 q^{47} -1.00000 q^{48} -0.398475 q^{49} +10.9436 q^{50} -2.12859 q^{51} -1.00000 q^{52} -0.983603 q^{53} -1.00000 q^{54} +10.3886 q^{55} -2.56934 q^{56} -0.868075 q^{57} -0.693615 q^{58} +5.02274 q^{59} +3.99294 q^{60} +2.12798 q^{61} +4.86980 q^{62} -2.56934 q^{63} +1.00000 q^{64} +3.99294 q^{65} +2.60174 q^{66} +3.67387 q^{67} +2.12859 q^{68} -5.16856 q^{69} +10.2592 q^{70} -12.7794 q^{71} +1.00000 q^{72} -14.6741 q^{73} +4.94544 q^{74} -10.9436 q^{75} +0.868075 q^{76} +6.68477 q^{77} +1.00000 q^{78} +11.4341 q^{79} -3.99294 q^{80} +1.00000 q^{81} +6.68086 q^{82} +10.8428 q^{83} +2.56934 q^{84} -8.49932 q^{85} -10.4261 q^{86} +0.693615 q^{87} -2.60174 q^{88} +4.29246 q^{89} -3.99294 q^{90} +2.56934 q^{91} +5.16856 q^{92} -4.86980 q^{93} +0.0582968 q^{94} -3.46618 q^{95} -1.00000 q^{96} -4.60864 q^{97} -0.398475 q^{98} -2.60174 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} - 2 q^{5} - 11 q^{6} - 2 q^{7} + 11 q^{8} + 11 q^{9}+O(q^{10}) \) 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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