LMFDB - Embedded newform 8034.2.a.t.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("8034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			1.5
Root			$-0.387444$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.387444 q^{5} -1.00000 q^{6} +5.18739 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.387444 q^{5} -1.00000 q^{6} +5.18739 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.387444 q^{10} -0.897239 q^{11} +1.00000 q^{12} -1.00000 q^{13} -5.18739 q^{14} -0.387444 q^{15} +1.00000 q^{16} +3.72242 q^{17} -1.00000 q^{18} -4.53286 q^{19} -0.387444 q^{20} +5.18739 q^{21} +0.897239 q^{22} +9.05884 q^{23} -1.00000 q^{24} -4.84989 q^{25} +1.00000 q^{26} +1.00000 q^{27} +5.18739 q^{28} -2.78914 q^{29} +0.387444 q^{30} +7.73159 q^{31} -1.00000 q^{32} -0.897239 q^{33} -3.72242 q^{34} -2.00982 q^{35} +1.00000 q^{36} -10.9141 q^{37} +4.53286 q^{38} -1.00000 q^{39} +0.387444 q^{40} +3.40363 q^{41} -5.18739 q^{42} -11.2013 q^{43} -0.897239 q^{44} -0.387444 q^{45} -9.05884 q^{46} +3.73843 q^{47} +1.00000 q^{48} +19.9091 q^{49} +4.84989 q^{50} +3.72242 q^{51} -1.00000 q^{52} +1.47717 q^{53} -1.00000 q^{54} +0.347630 q^{55} -5.18739 q^{56} -4.53286 q^{57} +2.78914 q^{58} +10.7159 q^{59} -0.387444 q^{60} +13.5340 q^{61} -7.73159 q^{62} +5.18739 q^{63} +1.00000 q^{64} +0.387444 q^{65} +0.897239 q^{66} -5.48474 q^{67} +3.72242 q^{68} +9.05884 q^{69} +2.00982 q^{70} +12.8342 q^{71} -1.00000 q^{72} +10.6385 q^{73} +10.9141 q^{74} -4.84989 q^{75} -4.53286 q^{76} -4.65433 q^{77} +1.00000 q^{78} -16.6059 q^{79} -0.387444 q^{80} +1.00000 q^{81} -3.40363 q^{82} -6.67837 q^{83} +5.18739 q^{84} -1.44223 q^{85} +11.2013 q^{86} -2.78914 q^{87} +0.897239 q^{88} -2.89382 q^{89} +0.387444 q^{90} -5.18739 q^{91} +9.05884 q^{92} +7.73159 q^{93} -3.73843 q^{94} +1.75623 q^{95} -1.00000 q^{96} +5.04587 q^{97} -19.9091 q^{98} -0.897239 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 11 q^{2} + 11 q^{3} + 11 q^{4} + 4 q^{5} - 11 q^{6} + 4 q^{7} - 11 q^{8} + 11 q^{9}+O(q^{10}) $ 11 * q - 11 * q^2 + 11 * q^3 + 11 * q^4 + 4 * q^5 - 11 * q^6 + 4 * q^7 - 11 * q^8 + 11 * q^9	\( 11 q - 11 q^{2} + 11 q^{3} + 11 q^{4} + 4 q^{5} - 11 q^{6} + 4 q^{7} - 11 q^{8} + 11 q^{9} - 4 q^{10} + 5 q^{11} + 11 q^{12} - 11 q^{13} - 4 q^{14} + 4 q^{15} + 11 q^{16} + 8 q^{17} - 11 q^{18} - 2 q^{19} + 4 q^{20} + 4 q^{21} - 5 q^{22} + 3 q^{23} - 11 q^{24} + 9 q^{25} + 11 q^{26} + 11 q^{27} + 4 q^{28} + 7 q^{29} - 4 q^{30} + 20 q^{31} - 11 q^{32} + 5 q^{33} - 8 q^{34} + 9 q^{35} + 11 q^{36} + q^{37} + 2 q^{38} - 11 q^{39} - 4 q^{40} + 37 q^{41} - 4 q^{42} - 16 q^{43} + 5 q^{44} + 4 q^{45} - 3 q^{46} + 28 q^{47} + 11 q^{48} + 17 q^{49} - 9 q^{50} + 8 q^{51} - 11 q^{52} - 5 q^{53} - 11 q^{54} - 28 q^{55} - 4 q^{56} - 2 q^{57} - 7 q^{58} + 31 q^{59} + 4 q^{60} + 8 q^{61} - 20 q^{62} + 4 q^{63} + 11 q^{64} - 4 q^{65} - 5 q^{66} - 22 q^{67} + 8 q^{68} + 3 q^{69} - 9 q^{70} + 42 q^{71} - 11 q^{72} - 4 q^{73} - q^{74} + 9 q^{75} - 2 q^{76} - 21 q^{77} + 11 q^{78} + 33 q^{79} + 4 q^{80} + 11 q^{81} - 37 q^{82} + 18 q^{83} + 4 q^{84} + 17 q^{85} + 16 q^{86} + 7 q^{87} - 5 q^{88} + 67 q^{89} - 4 q^{90} - 4 q^{91} + 3 q^{92} + 20 q^{93} - 28 q^{94} + 32 q^{95} - 11 q^{96} - 15 q^{97} - 17 q^{98} + 5 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 + 11 * q^3 + 11 * q^4 + 4 * q^5 - 11 * q^6 + 4 * q^7 - 11 * q^8 + 11 * q^9 - 4 * q^10 + 5 * q^11 + 11 * q^12 - 11 * q^13 - 4 * q^14 + 4 * q^15 + 11 * q^16 + 8 * q^17 - 11 * q^18 - 2 * q^19 + 4 * q^20 + 4 * q^21 - 5 * q^22 + 3 * q^23 - 11 * q^24 + 9 * q^25 + 11 * q^26 + 11 * q^27 + 4 * q^28 + 7 * q^29 - 4 * q^30 + 20 * q^31 - 11 * q^32 + 5 * q^33 - 8 * q^34 + 9 * q^35 + 11 * q^36 + q^37 + 2 * q^38 - 11 * q^39 - 4 * q^40 + 37 * q^41 - 4 * q^42 - 16 * q^43 + 5 * q^44 + 4 * q^45 - 3 * q^46 + 28 * q^47 + 11 * q^48 + 17 * q^49 - 9 * q^50 + 8 * q^51 - 11 * q^52 - 5 * q^53 - 11 * q^54 - 28 * q^55 - 4 * q^56 - 2 * q^57 - 7 * q^58 + 31 * q^59 + 4 * q^60 + 8 * q^61 - 20 * q^62 + 4 * q^63 + 11 * q^64 - 4 * q^65 - 5 * q^66 - 22 * q^67 + 8 * q^68 + 3 * q^69 - 9 * q^70 + 42 * q^71 - 11 * q^72 - 4 * q^73 - q^74 + 9 * q^75 - 2 * q^76 - 21 * q^77 + 11 * q^78 + 33 * q^79 + 4 * q^80 + 11 * q^81 - 37 * q^82 + 18 * q^83 + 4 * q^84 + 17 * q^85 + 16 * q^86 + 7 * q^87 - 5 * q^88 + 67 * q^89 - 4 * q^90 - 4 * q^91 + 3 * q^92 + 20 * q^93 - 28 * q^94 + 32 * q^95 - 11 * q^96 - 15 * q^97 - 17 * q^98 + 5 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−0.387444	−0.173270	−0.0866351	−	0.996240i	$-0.527611\pi$
$5$	−0.387444	−0.173270	−0.0866351	+	0.996240i	$0.527611\pi$
$6$	−1.00000	−0.408248
$7$	5.18739	1.96065	0.980325	−	0.197388i	$-0.0632459\pi$
$7$	5.18739	1.96065	0.980325	+	0.197388i	$0.0632459\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0.387444	0.122521
$11$	−0.897239	−0.270528	−0.135264	−	0.990810i	$-0.543188\pi$
$11$	−0.897239	−0.270528	−0.135264	+	0.990810i	$0.543188\pi$
$12$	1.00000	0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−5.18739	−1.38639
$15$	−0.387444	−0.100038
$16$	1.00000	0.250000
$17$	3.72242	0.902818	0.451409	−	0.892317i	$-0.350921\pi$
$17$	3.72242	0.902818	0.451409	+	0.892317i	$0.350921\pi$
$18$	−1.00000	−0.235702
$19$	−4.53286	−1.03991	−0.519955	−	0.854194i	$-0.674051\pi$
$19$	−4.53286	−1.03991	−0.519955	+	0.854194i	$0.674051\pi$
$20$	−0.387444	−0.0866351
$21$	5.18739	1.13198
$22$	0.897239	0.191292
$23$	9.05884	1.88890	0.944450	−	0.328656i	$-0.106596\pi$
$23$	9.05884	1.88890	0.944450	+	0.328656i	$0.106596\pi$
$24$	−1.00000	−0.204124
$25$	−4.84989	−0.969977
$26$	1.00000	0.196116
$27$	1.00000	0.192450
$28$	5.18739	0.980325
$29$	−2.78914	−0.517930	−0.258965	−	0.965887i	$-0.583381\pi$
$29$	−2.78914	−0.517930	−0.258965	+	0.965887i	$0.583381\pi$
$30$	0.387444	0.0707373
$31$	7.73159	1.38863	0.694317	−	0.719669i	$-0.255707\pi$
$31$	7.73159	1.38863	0.694317	+	0.719669i	$0.255707\pi$
$32$	−1.00000	−0.176777
$33$	−0.897239	−0.156189
$34$	−3.72242	−0.638389
$35$	−2.00982	−0.339722
$36$	1.00000	0.166667
$37$	−10.9141	−1.79427	−0.897137	−	0.441752i	$-0.854357\pi$
$37$	−10.9141	−1.79427	−0.897137	+	0.441752i	$0.854357\pi$
$38$	4.53286	0.735327
$39$	−1.00000	−0.160128
$40$	0.387444	0.0612603
$41$	3.40363	0.531558	0.265779	−	0.964034i	$-0.414371\pi$
$41$	3.40363	0.531558	0.265779	+	0.964034i	$0.414371\pi$
$42$	−5.18739	−0.800432
$43$	−11.2013	−1.70819	−0.854094	−	0.520119i	$-0.825888\pi$
$43$	−11.2013	−1.70819	−0.854094	+	0.520119i	$0.825888\pi$
$44$	−0.897239	−0.135264
$45$	−0.387444	−0.0577567
$46$	−9.05884	−1.33565
$47$	3.73843	0.545306	0.272653	−	0.962112i	$-0.412099\pi$
$47$	3.73843	0.545306	0.272653	+	0.962112i	$0.412099\pi$
$48$	1.00000	0.144338
$49$	19.9091	2.84415
$50$	4.84989	0.685878
$51$	3.72242	0.521242
$52$	−1.00000	−0.138675
$53$	1.47717	0.202905	0.101453	−	0.994840i	$-0.467651\pi$
$53$	1.47717	0.202905	0.101453	+	0.994840i	$0.467651\pi$
$54$	−1.00000	−0.136083
$55$	0.347630	0.0468744
$56$	−5.18739	−0.693195
$57$	−4.53286	−0.600392
$58$	2.78914	0.366232
$59$	10.7159	1.39509	0.697547	−	0.716539i	$-0.254275\pi$
$59$	10.7159	1.39509	0.697547	+	0.716539i	$0.254275\pi$
$60$	−0.387444	−0.0500188
$61$	13.5340	1.73284	0.866422	−	0.499312i	$-0.166414\pi$
$61$	13.5340	1.73284	0.866422	+	0.499312i	$0.166414\pi$
$62$	−7.73159	−0.981912
$63$	5.18739	0.653550
$64$	1.00000	0.125000
$65$	0.387444	0.0480565
$66$	0.897239	0.110442
$67$	−5.48474	−0.670068	−0.335034	−	0.942206i	$-0.608748\pi$
$67$	−5.48474	−0.670068	−0.335034	+	0.942206i	$0.608748\pi$
$68$	3.72242	0.451409
$69$	9.05884	1.09056
$70$	2.00982	0.240220
$71$	12.8342	1.52314	0.761569	−	0.648084i	$-0.224429\pi$
$71$	12.8342	1.52314	0.761569	+	0.648084i	$0.224429\pi$
$72$	−1.00000	−0.117851
$73$	10.6385	1.24514	0.622572	−	0.782562i	$-0.286088\pi$
$73$	10.6385	1.24514	0.622572	+	0.782562i	$0.286088\pi$
$74$	10.9141	1.26874
$75$	−4.84989	−0.560017
$76$	−4.53286	−0.519955
$77$	−4.65433	−0.530410
$78$	1.00000	0.113228
$79$	−16.6059	−1.86831	−0.934153	−	0.356874i	$-0.883843\pi$
$79$	−16.6059	−1.86831	−0.934153	+	0.356874i	$0.883843\pi$
$80$	−0.387444	−0.0433175
$81$	1.00000	0.111111
$82$	−3.40363	−0.375869
$83$	−6.67837	−0.733046	−0.366523	−	0.930409i	$-0.619452\pi$
$83$	−6.67837	−0.733046	−0.366523	+	0.930409i	$0.619452\pi$
$84$	5.18739	0.565991
$85$	−1.44223	−0.156432
$86$	11.2013	1.20787
$87$	−2.78914	−0.299027
$88$	0.897239	0.0956460
$89$	−2.89382	−0.306745	−0.153372	−	0.988168i	$-0.549013\pi$
$89$	−2.89382	−0.306745	−0.153372	+	0.988168i	$0.549013\pi$
$90$	0.387444	0.0408402
$91$	−5.18739	−0.543787
$92$	9.05884	0.944450
$93$	7.73159	0.801728
$94$	−3.73843	−0.385590
$95$	1.75623	0.180185
$96$	−1.00000	−0.102062
$97$	5.04587	0.512331	0.256165	−	0.966633i	$-0.417541\pi$
$97$	5.04587	0.512331	0.256165	+	0.966633i	$0.417541\pi$
$98$	−19.9091	−2.01112
$99$	−0.897239	−0.0901759
$100$	−4.84989	−0.484989
$101$	−17.7523	−1.76642	−0.883208	−	0.468982i	$-0.844621\pi$
$101$	−17.7523	−1.76642	−0.883208	+	0.468982i	$0.844621\pi$
$102$	−3.72242	−0.368574
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	1.00000	0.0980581
$105$	−2.00982	−0.196139
$106$	−1.47717	−0.143476
$107$	16.5712	1.60200	0.801000	−	0.598664i	$-0.204301\pi$
$107$	16.5712	1.60200	0.801000	+	0.598664i	$0.204301\pi$
$108$	1.00000	0.0962250
$109$	14.9168	1.42877	0.714384	−	0.699754i	$-0.246707\pi$
$109$	14.9168	1.42877	0.714384	+	0.699754i	$0.246707\pi$
$110$	−0.347630	−0.0331452
$111$	−10.9141	−1.03592
$112$	5.18739	0.490163
$113$	5.15101	0.484566	0.242283	−	0.970206i	$-0.422104\pi$
$113$	5.15101	0.484566	0.242283	+	0.970206i	$0.422104\pi$
$114$	4.53286	0.424541
$115$	−3.50979	−0.327290
$116$	−2.78914	−0.258965
$117$	−1.00000	−0.0924500
$118$	−10.7159	−0.986480
$119$	19.3096	1.77011
$120$	0.387444	0.0353686
$121$	−10.1950	−0.926815
$122$	−13.5340	−1.22531
$123$	3.40363	0.306895
$124$	7.73159	0.694317
$125$	3.81628	0.341338
$126$	−5.18739	−0.462130
$127$	−1.24874	−0.110807	−0.0554037	−	0.998464i	$-0.517645\pi$
$127$	−1.24874	−0.110807	−0.0554037	+	0.998464i	$0.517645\pi$
$128$	−1.00000	−0.0883883
$129$	−11.2013	−0.986223
$130$	−0.387444	−0.0339811
$131$	14.9987	1.31045	0.655223	−	0.755436i	$-0.272575\pi$
$131$	14.9987	1.31045	0.655223	+	0.755436i	$0.272575\pi$
$132$	−0.897239	−0.0780946
$133$	−23.5137	−2.03890
$134$	5.48474	0.473810
$135$	−0.387444	−0.0333459
$136$	−3.72242	−0.319194
$137$	0.904010	0.0772348	0.0386174	−	0.999254i	$-0.487705\pi$
$137$	0.904010	0.0772348	0.0386174	+	0.999254i	$0.487705\pi$
$138$	−9.05884	−0.771140
$139$	16.9188	1.43503	0.717517	−	0.696541i	$-0.245279\pi$
$139$	16.9188	1.43503	0.717517	+	0.696541i	$0.245279\pi$
$140$	−2.00982	−0.169861
$141$	3.73843	0.314833
$142$	−12.8342	−1.07702
$143$	0.897239	0.0750309
$144$	1.00000	0.0833333
$145$	1.08063	0.0897418
$146$	−10.6385	−0.880450
$147$	19.9091	1.64207
$148$	−10.9141	−0.897137
$149$	17.1391	1.40409	0.702047	−	0.712131i	$-0.252270\pi$
$149$	17.1391	1.40409	0.702047	+	0.712131i	$0.252270\pi$
$150$	4.84989	0.395992
$151$	−9.88820	−0.804690	−0.402345	−	0.915488i	$-0.631805\pi$
$151$	−9.88820	−0.804690	−0.402345	+	0.915488i	$0.631805\pi$
$152$	4.53286	0.367663
$153$	3.72242	0.300939
$154$	4.65433	0.375057
$155$	−2.99556	−0.240609
$156$	−1.00000	−0.0800641
$157$	−3.20219	−0.255563	−0.127781	−	0.991802i	$-0.540786\pi$
$157$	−3.20219	−0.255563	−0.127781	+	0.991802i	$0.540786\pi$
$158$	16.6059	1.32109
$159$	1.47717	0.117147
$160$	0.387444	0.0306301
$161$	46.9918	3.70347
$162$	−1.00000	−0.0785674
$163$	−10.3840	−0.813340	−0.406670	−	0.913575i	$-0.633310\pi$
$163$	−10.3840	−0.813340	−0.406670	+	0.913575i	$0.633310\pi$
$164$	3.40363	0.265779
$165$	0.347630	0.0270629
$166$	6.67837	0.518342
$167$	23.0269	1.78187	0.890937	−	0.454126i	$-0.150049\pi$
$167$	23.0269	1.78187	0.890937	+	0.454126i	$0.150049\pi$
$168$	−5.18739	−0.400216
$169$	1.00000	0.0769231
$170$	1.44223	0.110614
$171$	−4.53286	−0.346636
$172$	−11.2013	−0.854094
$173$	14.3746	1.09288	0.546442	−	0.837497i	$-0.315982\pi$
$173$	14.3746	1.09288	0.546442	+	0.837497i	$0.315982\pi$
$174$	2.78914	0.211444
$175$	−25.1583	−1.90179
$176$	−0.897239	−0.0676319
$177$	10.7159	0.805458
$178$	2.89382	0.216901
$179$	10.1192	0.756343	0.378171	−	0.925736i	$-0.376553\pi$
$179$	10.1192	0.756343	0.378171	+	0.925736i	$0.376553\pi$
$180$	−0.387444	−0.0288784
$181$	−2.23634	−0.166226	−0.0831130	−	0.996540i	$-0.526486\pi$
$181$	−2.23634	−0.166226	−0.0831130	+	0.996540i	$0.526486\pi$
$182$	5.18739	0.384515
$183$	13.5340	1.00046
$184$	−9.05884	−0.667827
$185$	4.22862	0.310894
$186$	−7.73159	−0.566907
$187$	−3.33990	−0.244237
$188$	3.73843	0.272653
$189$	5.18739	0.377327
$190$	−1.75623	−0.127410
$191$	−12.8464	−0.929532	−0.464766	−	0.885434i	$-0.653862\pi$
$191$	−12.8464	−0.929532	−0.464766	+	0.885434i	$0.653862\pi$
$192$	1.00000	0.0721688
$193$	−8.58419	−0.617904	−0.308952	−	0.951078i	$-0.599978\pi$
$193$	−8.58419	−0.617904	−0.308952	+	0.951078i	$0.599978\pi$
$194$	−5.04587	−0.362273
$195$	0.387444	0.0277454
$196$	19.9091	1.42208
$197$	−11.6199	−0.827885	−0.413943	−	0.910303i	$-0.635849\pi$
$197$	−11.6199	−0.827885	−0.413943	+	0.910303i	$0.635849\pi$
$198$	0.897239	0.0637640
$199$	−15.9048	−1.12746	−0.563732	−	0.825958i	$-0.690635\pi$
$199$	−15.9048	−1.12746	−0.563732	+	0.825958i	$0.690635\pi$
$200$	4.84989	0.342939
$201$	−5.48474	−0.386864
$202$	17.7523	1.24904
$203$	−14.4684	−1.01548
$204$	3.72242	0.260621
$205$	−1.31872	−0.0921032
$206$	1.00000	0.0696733
$207$	9.05884	0.629633
$208$	−1.00000	−0.0693375
$209$	4.06706	0.281324
$210$	2.00982	0.138691
$211$	5.86680	0.403887	0.201944	−	0.979397i	$-0.435274\pi$
$211$	5.86680	0.403887	0.201944	+	0.979397i	$0.435274\pi$
$212$	1.47717	0.101453
$213$	12.8342	0.879384
$214$	−16.5712	−1.13279
$215$	4.33989	0.295978
$216$	−1.00000	−0.0680414
$217$	40.1068	2.72263
$218$	−14.9168	−1.01029
$219$	10.6385	0.718885
$220$	0.347630	0.0234372
$221$	−3.72242	−0.250397
$222$	10.9141	0.732510
$223$	18.1592	1.21603	0.608016	−	0.793925i	$-0.291966\pi$
$223$	18.1592	1.21603	0.608016	+	0.793925i	$0.291966\pi$
$224$	−5.18739	−0.346597
$225$	−4.84989	−0.323326
$226$	−5.15101	−0.342640
$227$	−27.2308	−1.80737	−0.903686	−	0.428196i	$-0.859149\pi$
$227$	−27.2308	−1.80737	−0.903686	+	0.428196i	$0.859149\pi$
$228$	−4.53286	−0.300196
$229$	4.44361	0.293642	0.146821	−	0.989163i	$-0.453096\pi$
$229$	4.44361	0.293642	0.146821	+	0.989163i	$0.453096\pi$
$230$	3.50979	0.231429
$231$	−4.65433	−0.306233
$232$	2.78914	0.183116
$233$	−4.98665	−0.326686	−0.163343	−	0.986569i	$-0.552228\pi$
$233$	−4.98665	−0.326686	−0.163343	+	0.986569i	$0.552228\pi$
$234$	1.00000	0.0653720
$235$	−1.44843	−0.0944854
$236$	10.7159	0.697547
$237$	−16.6059	−1.07867
$238$	−19.3096	−1.25166
$239$	7.01038	0.453464	0.226732	−	0.973957i	$-0.427196\pi$
$239$	7.01038	0.453464	0.226732	+	0.973957i	$0.427196\pi$
$240$	−0.387444	−0.0250094
$241$	22.5245	1.45093	0.725464	−	0.688260i	$-0.241625\pi$
$241$	22.5245	1.45093	0.725464	+	0.688260i	$0.241625\pi$
$242$	10.1950	0.655357
$243$	1.00000	0.0641500
$244$	13.5340	0.866422
$245$	−7.71365	−0.492807
$246$	−3.40363	−0.217008
$247$	4.53286	0.288419
$248$	−7.73159	−0.490956
$249$	−6.67837	−0.423224
$250$	−3.81628	−0.241363
$251$	−15.0333	−0.948893	−0.474447	−	0.880284i	$-0.657352\pi$
$251$	−15.0333	−0.948893	−0.474447	+	0.880284i	$0.657352\pi$
$252$	5.18739	0.326775
$253$	−8.12795	−0.511000
$254$	1.24874	0.0783526
$255$	−1.44223	−0.0903158
$256$	1.00000	0.0625000
$257$	19.2371	1.19998	0.599989	−	0.800008i	$-0.295172\pi$
$257$	19.2371	1.19998	0.599989	+	0.800008i	$0.295172\pi$
$258$	11.2013	0.697365
$259$	−56.6160	−3.51795
$260$	0.387444	0.0240283
$261$	−2.78914	−0.172643
$262$	−14.9987	−0.926625
$263$	−20.5262	−1.26570	−0.632848	−	0.774276i	$-0.718114\pi$
$263$	−20.5262	−1.26570	−0.632848	+	0.774276i	$0.718114\pi$
$264$	0.897239	0.0552212
$265$	−0.572321	−0.0351574
$266$	23.5137	1.44172
$267$	−2.89382	−0.177099
$268$	−5.48474	−0.335034
$269$	−15.3749	−0.937422	−0.468711	−	0.883352i	$-0.655281\pi$
$269$	−15.3749	−0.937422	−0.468711	+	0.883352i	$0.655281\pi$
$270$	0.387444	0.0235791
$271$	−25.4152	−1.54386	−0.771932	−	0.635705i	$-0.780710\pi$
$271$	−25.4152	−1.54386	−0.771932	+	0.635705i	$0.780710\pi$
$272$	3.72242	0.225705
$273$	−5.18739	−0.313955
$274$	−0.904010	−0.0546132
$275$	4.35151	0.262406
$276$	9.05884	0.545278
$277$	14.7762	0.887816	0.443908	−	0.896072i	$-0.353592\pi$
$277$	14.7762	0.887816	0.443908	+	0.896072i	$0.353592\pi$
$278$	−16.9188	−1.01472
$279$	7.73159	0.462878
$280$	2.00982	0.120110
$281$	−6.11157	−0.364586	−0.182293	−	0.983244i	$-0.558352\pi$
$281$	−6.11157	−0.364586	−0.182293	+	0.983244i	$0.558352\pi$
$282$	−3.73843	−0.222620
$283$	1.35678	0.0806523	0.0403261	−	0.999187i	$-0.487160\pi$
$283$	1.35678	0.0806523	0.0403261	+	0.999187i	$0.487160\pi$
$284$	12.8342	0.761569
$285$	1.75623	0.104030
$286$	−0.897239	−0.0530548
$287$	17.6560	1.04220
$288$	−1.00000	−0.0589256
$289$	−3.14362	−0.184919
$290$	−1.08063	−0.0634571
$291$	5.04587	0.295794
$292$	10.6385	0.622572
$293$	12.4111	0.725063	0.362532	−	0.931971i	$-0.381912\pi$
$293$	12.4111	0.725063	0.362532	+	0.931971i	$0.381912\pi$
$294$	−19.9091	−1.16112
$295$	−4.15182	−0.241728
$296$	10.9141	0.634372
$297$	−0.897239	−0.0520631
$298$	−17.1391	−0.992844
$299$	−9.05884	−0.523886
$300$	−4.84989	−0.280008
$301$	−58.1058	−3.34916
$302$	9.88820	0.569002
$303$	−17.7523	−1.01984
$304$	−4.53286	−0.259977
$305$	−5.24365	−0.300250
$306$	−3.72242	−0.212796
$307$	−3.48393	−0.198838	−0.0994192	−	0.995046i	$-0.531698\pi$
$307$	−3.48393	−0.198838	−0.0994192	+	0.995046i	$0.531698\pi$
$308$	−4.65433	−0.265205
$309$	−1.00000	−0.0568880
$310$	2.99556	0.170136
$311$	−32.2188	−1.82696	−0.913481	−	0.406881i	$-0.866616\pi$
$311$	−32.2188	−1.82696	−0.913481	+	0.406881i	$0.866616\pi$
$312$	1.00000	0.0566139
$313$	0.950362	0.0537176	0.0268588	−	0.999639i	$-0.491450\pi$
$313$	0.950362	0.0537176	0.0268588	+	0.999639i	$0.491450\pi$
$314$	3.20219	0.180710
$315$	−2.00982	−0.113241
$316$	−16.6059	−0.934153
$317$	9.44366	0.530409	0.265204	−	0.964192i	$-0.414561\pi$
$317$	9.44366	0.530409	0.265204	+	0.964192i	$0.414561\pi$
$318$	−1.47717	−0.0828357
$319$	2.50252	0.140114
$320$	−0.387444	−0.0216588
$321$	16.5712	0.924916
$322$	−46.9918	−2.61875
$323$	−16.8732	−0.938849
$324$	1.00000	0.0555556
$325$	4.84989	0.269023
$326$	10.3840	0.575119
$327$	14.9168	0.824899
$328$	−3.40363	−0.187934
$329$	19.3927	1.06916
$330$	−0.347630	−0.0191364
$331$	−5.39630	−0.296607	−0.148304	−	0.988942i	$-0.547381\pi$
$331$	−5.39630	−0.296607	−0.148304	+	0.988942i	$0.547381\pi$
$332$	−6.67837	−0.366523
$333$	−10.9141	−0.598092
$334$	−23.0269	−1.25998
$335$	2.12503	0.116103
$336$	5.18739	0.282996
$337$	−15.5963	−0.849582	−0.424791	−	0.905291i	$-0.639652\pi$
$337$	−15.5963	−0.849582	−0.424791	+	0.905291i	$0.639652\pi$
$338$	−1.00000	−0.0543928
$339$	5.15101	0.279765
$340$	−1.44223	−0.0782158
$341$	−6.93708	−0.375664
$342$	4.53286	0.245109
$343$	66.9644	3.61574
$344$	11.2013	0.603936
$345$	−3.50979	−0.188961
$346$	−14.3746	−0.772786
$347$	34.9935	1.87855	0.939274	−	0.343168i	$-0.111500\pi$
$347$	34.9935	1.87855	0.939274	+	0.343168i	$0.111500\pi$
$348$	−2.78914	−0.149514
$349$	5.92772	0.317304	0.158652	−	0.987335i	$-0.449285\pi$
$349$	5.92772	0.317304	0.158652	+	0.987335i	$0.449285\pi$
$350$	25.1583	1.34477
$351$	−1.00000	−0.0533761
$352$	0.897239	0.0478230
$353$	13.6757	0.727886	0.363943	−	0.931421i	$-0.381430\pi$
$353$	13.6757	0.727886	0.363943	+	0.931421i	$0.381430\pi$
$354$	−10.7159	−0.569545
$355$	−4.97253	−0.263914
$356$	−2.89382	−0.153372
$357$	19.3096	1.02197
$358$	−10.1192	−0.534815
$359$	−21.9954	−1.16087	−0.580436	−	0.814306i	$-0.697118\pi$
$359$	−21.9954	−1.16087	−0.580436	+	0.814306i	$0.697118\pi$
$360$	0.387444	0.0204201
$361$	1.54682	0.0814113
$362$	2.23634	0.117539
$363$	−10.1950	−0.535097
$364$	−5.18739	−0.271893
$365$	−4.12183	−0.215746
$366$	−13.5340	−0.707431
$367$	32.7399	1.70901	0.854505	−	0.519444i	$-0.173861\pi$
$367$	32.7399	1.70901	0.854505	+	0.519444i	$0.173861\pi$
$368$	9.05884	0.472225
$369$	3.40363	0.177186
$370$	−4.22862	−0.219835
$371$	7.66267	0.397826
$372$	7.73159	0.400864
$373$	−1.58086	−0.0818541	−0.0409270	−	0.999162i	$-0.513031\pi$
$373$	−1.58086	−0.0818541	−0.0409270	+	0.999162i	$0.513031\pi$
$374$	3.33990	0.172702
$375$	3.81628	0.197072
$376$	−3.73843	−0.192795
$377$	2.78914	0.143648
$378$	−5.18739	−0.266811
$379$	10.6823	0.548714	0.274357	−	0.961628i	$-0.411535\pi$
$379$	10.6823	0.548714	0.274357	+	0.961628i	$0.411535\pi$
$380$	1.75623	0.0900926
$381$	−1.24874	−0.0639746
$382$	12.8464	0.657278
$383$	−21.0913	−1.07772	−0.538859	−	0.842396i	$-0.681144\pi$
$383$	−21.0913	−1.07772	−0.538859	+	0.842396i	$0.681144\pi$
$384$	−1.00000	−0.0510310
$385$	1.80329	0.0919043
$386$	8.58419	0.436924
$387$	−11.2013	−0.569396
$388$	5.04587	0.256165
$389$	−23.2112	−1.17685	−0.588427	−	0.808551i	$-0.700252\pi$
$389$	−23.2112	−1.17685	−0.588427	+	0.808551i	$0.700252\pi$
$390$	−0.387444	−0.0196190
$391$	33.7208	1.70533
$392$	−19.9091	−1.00556
$393$	14.9987	0.756586
$394$	11.6199	0.585403
$395$	6.43384	0.323722
$396$	−0.897239	−0.0450879
$397$	−17.1745	−0.861963	−0.430982	−	0.902361i	$-0.641833\pi$
$397$	−17.1745	−0.861963	−0.430982	+	0.902361i	$0.641833\pi$
$398$	15.9048	0.797238
$399$	−23.5137	−1.17716
$400$	−4.84989	−0.242494
$401$	12.5842	0.628426	0.314213	−	0.949352i	$-0.398259\pi$
$401$	12.5842	0.628426	0.314213	+	0.949352i	$0.398259\pi$
$402$	5.48474	0.273554
$403$	−7.73159	−0.385138
$404$	−17.7523	−0.883208
$405$	−0.387444	−0.0192522
$406$	14.4684	0.718053
$407$	9.79259	0.485401
$408$	−3.72242	−0.184287
$409$	34.0417	1.68325	0.841627	−	0.540060i	$-0.181598\pi$
$409$	34.0417	1.68325	0.841627	+	0.540060i	$0.181598\pi$
$410$	1.31872	0.0651268
$411$	0.904010	0.0445915
$412$	−1.00000	−0.0492665
$413$	55.5877	2.73529
$414$	−9.05884	−0.445218
$415$	2.58749	0.127015
$416$	1.00000	0.0490290
$417$	16.9188	0.828517
$418$	−4.06706	−0.198926
$419$	13.7947	0.673916	0.336958	−	0.941520i	$-0.390602\pi$
$419$	13.7947	0.673916	0.336958	+	0.941520i	$0.390602\pi$
$420$	−2.00982	−0.0980694
$421$	−13.4213	−0.654115	−0.327057	−	0.945005i	$-0.606057\pi$
$421$	−13.4213	−0.654115	−0.327057	+	0.945005i	$0.606057\pi$
$422$	−5.86680	−0.285591
$423$	3.73843	0.181769
$424$	−1.47717	−0.0717378
$425$	−18.0533	−0.875713
$426$	−12.8342	−0.621819
$427$	70.2059	3.39750
$428$	16.5712	0.801000
$429$	0.897239	0.0433191
$430$	−4.33989	−0.209288
$431$	4.41378	0.212604	0.106302	−	0.994334i	$-0.466099\pi$
$431$	4.41378	0.212604	0.106302	+	0.994334i	$0.466099\pi$
$432$	1.00000	0.0481125
$433$	−4.12519	−0.198244	−0.0991219	−	0.995075i	$-0.531603\pi$
$433$	−4.12519	−0.198244	−0.0991219	+	0.995075i	$0.531603\pi$
$434$	−40.1068	−1.92519
$435$	1.08063	0.0518125
$436$	14.9168	0.714384
$437$	−41.0625	−1.96428
$438$	−10.6385	−0.508328
$439$	−2.45402	−0.117124	−0.0585620	−	0.998284i	$-0.518652\pi$
$439$	−2.45402	−0.117124	−0.0585620	+	0.998284i	$0.518652\pi$
$440$	−0.347630	−0.0165726
$441$	19.9091	0.948051
$442$	3.72242	0.177057
$443$	−31.8643	−1.51392	−0.756958	−	0.653463i	$-0.773315\pi$
$443$	−31.8643	−1.51392	−0.756958	+	0.653463i	$0.773315\pi$
$444$	−10.9141	−0.517962
$445$	1.12119	0.0531497
$446$	−18.1592	−0.859865
$447$	17.1391	0.810654
$448$	5.18739	0.245081
$449$	10.3009	0.486127	0.243064	−	0.970010i	$-0.421848\pi$
$449$	10.3009	0.486127	0.243064	+	0.970010i	$0.421848\pi$
$450$	4.84989	0.228626
$451$	−3.05387	−0.143801
$452$	5.15101	0.242283
$453$	−9.88820	−0.464588
$454$	27.2308	1.27800
$455$	2.00982	0.0942220
$456$	4.53286	0.212271
$457$	−24.8913	−1.16437	−0.582183	−	0.813058i	$-0.697801\pi$
$457$	−24.8913	−1.16437	−0.582183	+	0.813058i	$0.697801\pi$
$458$	−4.44361	−0.207636
$459$	3.72242	0.173747
$460$	−3.50979	−0.163645
$461$	−26.2280	−1.22156	−0.610781	−	0.791800i	$-0.709144\pi$
$461$	−26.2280	−1.22156	−0.610781	+	0.791800i	$0.709144\pi$
$462$	4.65433	0.216539
$463$	−26.1687	−1.21616	−0.608080	−	0.793876i	$-0.708060\pi$
$463$	−26.1687	−1.21616	−0.608080	+	0.793876i	$0.708060\pi$
$464$	−2.78914	−0.129482
$465$	−2.99556	−0.138916
$466$	4.98665	0.231002
$467$	11.7239	0.542518	0.271259	−	0.962506i	$-0.412560\pi$
$467$	11.7239	0.542518	0.271259	+	0.962506i	$0.412560\pi$
$468$	−1.00000	−0.0462250
$469$	−28.4515	−1.31377
$470$	1.44843	0.0668112
$471$	−3.20219	−0.147549
$472$	−10.7159	−0.493240
$473$	10.0503	0.462112
$474$	16.6059	0.762732
$475$	21.9839	1.00869
$476$	19.3096	0.885056
$477$	1.47717	0.0676351
$478$	−7.01038	−0.320647
$479$	−7.43646	−0.339781	−0.169890	−	0.985463i	$-0.554341\pi$
$479$	−7.43646	−0.339781	−0.169890	+	0.985463i	$0.554341\pi$
$480$	0.387444	0.0176843
$481$	10.9141	0.497642
$482$	−22.5245	−1.02596
$483$	46.9918	2.13820
$484$	−10.1950	−0.463407
$485$	−1.95499	−0.0887716
$486$	−1.00000	−0.0453609
$487$	28.3722	1.28567	0.642834	−	0.766005i	$-0.277758\pi$
$487$	28.3722	1.28567	0.642834	+	0.766005i	$0.277758\pi$
$488$	−13.5340	−0.612653
$489$	−10.3840	−0.469582
$490$	7.71365	0.348467
$491$	9.65334	0.435649	0.217825	−	0.975988i	$-0.430104\pi$
$491$	9.65334	0.435649	0.217825	+	0.975988i	$0.430104\pi$
$492$	3.40363	0.153448
$493$	−10.3823	−0.467597
$494$	−4.53286	−0.203943
$495$	0.347630	0.0156248
$496$	7.73159	0.347158
$497$	66.5760	2.98634
$498$	6.67837	0.299265
$499$	−11.6884	−0.523246	−0.261623	−	0.965170i	$-0.584258\pi$
$499$	−11.6884	−0.523246	−0.261623	+	0.965170i	$0.584258\pi$
$500$	3.81628	0.170669
$501$	23.0269	1.02877
$502$	15.0333	0.670969
$503$	21.9111	0.976967	0.488484	−	0.872573i	$-0.337550\pi$
$503$	21.9111	0.976967	0.488484	+	0.872573i	$0.337550\pi$
$504$	−5.18739	−0.231065
$505$	6.87800	0.306067
$506$	8.12795	0.361331
$507$	1.00000	0.0444116
$508$	−1.24874	−0.0554037
$509$	−36.1515	−1.60239	−0.801194	−	0.598405i	$-0.795801\pi$
$509$	−36.1515	−1.60239	−0.801194	+	0.598405i	$0.795801\pi$
$510$	1.44223	0.0638629
$511$	55.1862	2.44129
$512$	−1.00000	−0.0441942
$513$	−4.53286	−0.200131
$514$	−19.2371	−0.848512
$515$	0.387444	0.0170728
$516$	−11.2013	−0.493111
$517$	−3.35427	−0.147520
$518$	56.6160	2.48756
$519$	14.3746	0.630977
$520$	−0.387444	−0.0169905
$521$	0.301580	0.0132125	0.00660623	−	0.999978i	$-0.497897\pi$
$521$	0.301580	0.0132125	0.00660623	+	0.999978i	$0.497897\pi$
$522$	2.78914	0.122077
$523$	−5.77917	−0.252705	−0.126353	−	0.991985i	$-0.540327\pi$
$523$	−5.77917	−0.252705	−0.126353	+	0.991985i	$0.540327\pi$
$524$	14.9987	0.655223
$525$	−25.1583	−1.09800
$526$	20.5262	0.894983
$527$	28.7802	1.25368
$528$	−0.897239	−0.0390473
$529$	59.0627	2.56794
$530$	0.572321	0.0248601
$531$	10.7159	0.465031
$532$	−23.5137	−1.01945
$533$	−3.40363	−0.147428
$534$	2.89382	0.125228
$535$	−6.42042	−0.277579
$536$	5.48474	0.236905
$537$	10.1192	0.436675
$538$	15.3749	0.662857
$539$	−17.8632	−0.769422
$540$	−0.387444	−0.0166729
$541$	23.5746	1.01355	0.506776	−	0.862077i	$-0.330837\pi$
$541$	23.5746	1.01355	0.506776	+	0.862077i	$0.330837\pi$
$542$	25.4152	1.09168
$543$	−2.23634	−0.0959706
$544$	−3.72242	−0.159597
$545$	−5.77941	−0.247563
$546$	5.18739	0.222000
$547$	−17.8678	−0.763972	−0.381986	−	0.924168i	$-0.624760\pi$
$547$	−17.8678	−0.763972	−0.381986	+	0.924168i	$0.624760\pi$
$548$	0.904010	0.0386174
$549$	13.5340	0.577615
$550$	−4.35151	−0.185549
$551$	12.6428	0.538600
$552$	−9.05884	−0.385570
$553$	−86.1412	−3.66309
$554$	−14.7762	−0.627781
$555$	4.22862	0.179495
$556$	16.9188	0.717517
$557$	28.8409	1.22203	0.611014	−	0.791619i	$-0.290762\pi$
$557$	28.8409	1.22203	0.611014	+	0.791619i	$0.290762\pi$
$558$	−7.73159	−0.327304
$559$	11.2013	0.473766
$560$	−2.00982	−0.0849306
$561$	−3.33990	−0.141010
$562$	6.11157	0.257801
$563$	9.97454	0.420377	0.210188	−	0.977661i	$-0.432592\pi$
$563$	9.97454	0.420377	0.210188	+	0.977661i	$0.432592\pi$
$564$	3.73843	0.157416
$565$	−1.99573	−0.0839609
$566$	−1.35678	−0.0570298
$567$	5.18739	0.217850
$568$	−12.8342	−0.538511
$569$	−3.80662	−0.159582	−0.0797909	−	0.996812i	$-0.525425\pi$
$569$	−3.80662	−0.159582	−0.0797909	+	0.996812i	$0.525425\pi$
$570$	−1.75623	−0.0735603
$571$	−26.6151	−1.11381	−0.556903	−	0.830578i	$-0.688010\pi$
$571$	−26.6151	−1.11381	−0.556903	+	0.830578i	$0.688010\pi$
$572$	0.897239	0.0375154
$573$	−12.8464	−0.536666
$574$	−17.6560	−0.736947
$575$	−43.9344	−1.83219
$576$	1.00000	0.0416667
$577$	−2.96614	−0.123482	−0.0617410	−	0.998092i	$-0.519665\pi$
$577$	−2.96614	−0.123482	−0.0617410	+	0.998092i	$0.519665\pi$
$578$	3.14362	0.130758
$579$	−8.58419	−0.356747
$580$	1.08063	0.0448709
$581$	−34.6433	−1.43725
$582$	−5.04587	−0.209158
$583$	−1.32538	−0.0548915
$584$	−10.6385	−0.440225
$585$	0.387444	0.0160188
$586$	−12.4111	−0.512697
$587$	−1.12532	−0.0464468	−0.0232234	−	0.999730i	$-0.507393\pi$
$587$	−1.12532	−0.0464468	−0.0232234	+	0.999730i	$0.507393\pi$
$588$	19.9091	0.821036
$589$	−35.0462	−1.44405
$590$	4.15182	0.170928
$591$	−11.6199	−0.477980
$592$	−10.9141	−0.448569
$593$	44.6765	1.83464	0.917321	−	0.398148i	$-0.130347\pi$
$593$	44.6765	1.83464	0.917321	+	0.398148i	$0.130347\pi$
$594$	0.897239	0.0368141
$595$	−7.48140	−0.306708
$596$	17.1391	0.702047
$597$	−15.9048	−0.650942
$598$	9.05884	0.370444
$599$	−25.8269	−1.05526	−0.527629	−	0.849475i	$-0.676919\pi$
$599$	−25.8269	−1.05526	−0.527629	+	0.849475i	$0.676919\pi$
$600$	4.84989	0.197996
$601$	46.3033	1.88875	0.944376	−	0.328866i	$-0.106667\pi$
$601$	46.3033	1.88875	0.944376	+	0.328866i	$0.106667\pi$
$602$	58.1058	2.36821
$603$	−5.48474	−0.223356
$604$	−9.88820	−0.402345
$605$	3.94998	0.160589
$606$	17.7523	0.721136
$607$	11.3280	0.459788	0.229894	−	0.973216i	$-0.426162\pi$
$607$	11.3280	0.459788	0.229894	+	0.973216i	$0.426162\pi$
$608$	4.53286	0.183832
$609$	−14.4684	−0.586288
$610$	5.24365	0.212309
$611$	−3.73843	−0.151241
$612$	3.72242	0.150470
$613$	−9.84236	−0.397529	−0.198765	−	0.980047i	$-0.563693\pi$
$613$	−9.84236	−0.397529	−0.198765	+	0.980047i	$0.563693\pi$
$614$	3.48393	0.140600
$615$	−1.31872	−0.0531758
$616$	4.65433	0.187528
$617$	−8.60501	−0.346425	−0.173212	−	0.984885i	$-0.555415\pi$
$617$	−8.60501	−0.346425	−0.173212	+	0.984885i	$0.555415\pi$
$618$	1.00000	0.0402259
$619$	−37.7284	−1.51643	−0.758216	−	0.652003i	$-0.773929\pi$
$619$	−37.7284	−1.51643	−0.758216	+	0.652003i	$0.773929\pi$
$620$	−2.99556	−0.120304
$621$	9.05884	0.363519
$622$	32.2188	1.29186
$623$	−15.0114	−0.601419
$624$	−1.00000	−0.0400320
$625$	22.7708	0.910834
$626$	−0.950362	−0.0379841
$627$	4.06706	0.162423
$628$	−3.20219	−0.127781
$629$	−40.6270	−1.61990
$630$	2.00982	0.0800733
$631$	−16.1058	−0.641163	−0.320582	−	0.947221i	$-0.603878\pi$
$631$	−16.1058	−0.641163	−0.320582	+	0.947221i	$0.603878\pi$
$632$	16.6059	0.660546
$633$	5.86680	0.233184
$634$	−9.44366	−0.375056
$635$	0.483815	0.0191996
$636$	1.47717	0.0585737
$637$	−19.9091	−0.788826
$638$	−2.50252	−0.0990758
$639$	12.8342	0.507713
$640$	0.387444	0.0153151
$641$	−33.5207	−1.32399	−0.661994	−	0.749509i	$-0.730290\pi$
$641$	−33.5207	−1.32399	−0.661994	+	0.749509i	$0.730290\pi$
$642$	−16.5712	−0.654014
$643$	19.4555	0.767249	0.383625	−	0.923489i	$-0.374676\pi$
$643$	19.4555	0.767249	0.383625	+	0.923489i	$0.374676\pi$
$644$	46.9918	1.85174
$645$	4.33989	0.170883
$646$	16.8732	0.663867
$647$	22.3349	0.878074	0.439037	−	0.898469i	$-0.355320\pi$
$647$	22.3349	0.878074	0.439037	+	0.898469i	$0.355320\pi$
$648$	−1.00000	−0.0392837
$649$	−9.61474	−0.377411
$650$	−4.84989	−0.190228
$651$	40.1068	1.57191
$652$	−10.3840	−0.406670
$653$	5.88580	0.230329	0.115165	−	0.993346i	$-0.463260\pi$
$653$	5.88580	0.230329	0.115165	+	0.993346i	$0.463260\pi$
$654$	−14.9168	−0.583292
$655$	−5.81117	−0.227061
$656$	3.40363	0.132890
$657$	10.6385	0.415048
$658$	−19.3927	−0.756007
$659$	−35.2915	−1.37476	−0.687380	−	0.726298i	$-0.741239\pi$
$659$	−35.2915	−1.37476	−0.687380	+	0.726298i	$0.741239\pi$
$660$	0.347630	0.0135315
$661$	30.9858	1.20521	0.602604	−	0.798040i	$-0.294130\pi$
$661$	30.9858	1.20521	0.602604	+	0.798040i	$0.294130\pi$
$662$	5.39630	0.209733
$663$	−3.72242	−0.144567
$664$	6.67837	0.259171
$665$	9.11025	0.353280
$666$	10.9141	0.422915
$667$	−25.2664	−0.978318
$668$	23.0269	0.890937
$669$	18.1592	0.702077
$670$	−2.12503	−0.0820971
$671$	−12.1432	−0.468782
$672$	−5.18739	−0.200108
$673$	6.65533	0.256544	0.128272	−	0.991739i	$-0.459057\pi$
$673$	6.65533	0.256544	0.128272	+	0.991739i	$0.459057\pi$
$674$	15.5963	0.600745
$675$	−4.84989	−0.186672
$676$	1.00000	0.0384615
$677$	7.96965	0.306298	0.153149	−	0.988203i	$-0.451058\pi$
$677$	7.96965	0.306298	0.153149	+	0.988203i	$0.451058\pi$
$678$	−5.15101	−0.197823
$679$	26.1749	1.00450
$680$	1.44223	0.0553069
$681$	−27.2308	−1.04349
$682$	6.93708	0.265634
$683$	−21.4117	−0.819296	−0.409648	−	0.912244i	$-0.634349\pi$
$683$	−21.4117	−0.819296	−0.409648	+	0.912244i	$0.634349\pi$
$684$	−4.53286	−0.173318
$685$	−0.350253	−0.0133825
$686$	−66.9644	−2.55671
$687$	4.44361	0.169534
$688$	−11.2013	−0.427047
$689$	−1.47717	−0.0562758
$690$	3.50979	0.133616
$691$	31.3785	1.19369	0.596847	−	0.802355i	$-0.296420\pi$
$691$	31.3785	1.19369	0.596847	+	0.802355i	$0.296420\pi$
$692$	14.3746	0.546442
$693$	−4.65433	−0.176803
$694$	−34.9935	−1.32833
$695$	−6.55508	−0.248648
$696$	2.78914	0.105722
$697$	12.6697	0.479901
$698$	−5.92772	−0.224367
$699$	−4.98665	−0.188612
$700$	−25.1583	−0.950894
$701$	0.605757	0.0228791	0.0114396	−	0.999935i	$-0.496359\pi$
$701$	0.605757	0.0228791	0.0114396	+	0.999935i	$0.496359\pi$
$702$	1.00000	0.0377426
$703$	49.4723	1.86588
$704$	−0.897239	−0.0338160
$705$	−1.44843	−0.0545511
$706$	−13.6757	−0.514693
$707$	−92.0879	−3.46332
$708$	10.7159	0.402729
$709$	13.2661	0.498220	0.249110	−	0.968475i	$-0.419862\pi$
$709$	13.2661	0.498220	0.249110	+	0.968475i	$0.419862\pi$
$710$	4.97253	0.186616
$711$	−16.6059	−0.622768
$712$	2.89382	0.108451
$713$	70.0392	2.62299
$714$	−19.3096	−0.722645
$715$	−0.347630	−0.0130006
$716$	10.1192	0.378171
$717$	7.01038	0.261807
$718$	21.9954	0.820860
$719$	5.49430	0.204903	0.102451	−	0.994738i	$-0.467331\pi$
$719$	5.49430	0.204903	0.102451	+	0.994738i	$0.467331\pi$
$720$	−0.387444	−0.0144392
$721$	−5.18739	−0.193189
$722$	−1.54682	−0.0575665
$723$	22.5245	0.837694
$724$	−2.23634	−0.0831130
$725$	13.5270	0.502380
$726$	10.1950	0.378371
$727$	35.2898	1.30883	0.654413	−	0.756138i	$-0.272916\pi$
$727$	35.2898	1.30883	0.654413	+	0.756138i	$0.272916\pi$
$728$	5.18739	0.192258
$729$	1.00000	0.0370370
$730$	4.12183	0.152556
$731$	−41.6960	−1.54218
$732$	13.5340	0.500229
$733$	−31.6771	−1.17002	−0.585010	−	0.811026i	$-0.698909\pi$
$733$	−31.6771	−1.17002	−0.585010	+	0.811026i	$0.698909\pi$
$734$	−32.7399	−1.20845
$735$	−7.71365	−0.284522
$736$	−9.05884	−0.333913
$737$	4.92112	0.181272
$738$	−3.40363	−0.125290
$739$	27.0716	0.995844	0.497922	−	0.867222i	$-0.334097\pi$
$739$	27.0716	0.995844	0.497922	+	0.867222i	$0.334097\pi$
$740$	4.22862	0.155447
$741$	4.53286	0.166519
$742$	−7.66267	−0.281306
$743$	−29.1504	−1.06942	−0.534711	−	0.845035i	$-0.679580\pi$
$743$	−29.1504	−1.06942	−0.534711	+	0.845035i	$0.679580\pi$
$744$	−7.73159	−0.283454
$745$	−6.64046	−0.243288
$746$	1.58086	0.0578796
$747$	−6.67837	−0.244349
$748$	−3.33990	−0.122119
$749$	85.9615	3.14096
$750$	−3.81628	−0.139351
$751$	−13.6746	−0.498995	−0.249497	−	0.968375i	$-0.580265\pi$
$751$	−13.6746	−0.498995	−0.249497	+	0.968375i	$0.580265\pi$
$752$	3.73843	0.136327
$753$	−15.0333	−0.547844
$754$	−2.78914	−0.101574
$755$	3.83112	0.139429
$756$	5.18739	0.188664
$757$	−25.4738	−0.925861	−0.462930	−	0.886395i	$-0.653202\pi$
$757$	−25.4738	−0.925861	−0.462930	+	0.886395i	$0.653202\pi$
$758$	−10.6823	−0.387999
$759$	−8.12795	−0.295026
$760$	−1.75623	−0.0637051
$761$	42.1857	1.52923	0.764616	−	0.644486i	$-0.222929\pi$
$761$	42.1857	1.52923	0.764616	+	0.644486i	$0.222929\pi$
$762$	1.24874	0.0452369
$763$	77.3792	2.80131
$764$	−12.8464	−0.464766
$765$	−1.44223	−0.0521438
$766$	21.0913	0.762061
$767$	−10.7159	−0.386929
$768$	1.00000	0.0360844
$769$	32.7870	1.18233	0.591164	−	0.806551i	$-0.298669\pi$
$769$	32.7870	1.18233	0.591164	+	0.806551i	$0.298669\pi$
$770$	−1.80329	−0.0649861
$771$	19.2371	0.692807
$772$	−8.58419	−0.308952
$773$	46.2298	1.66277	0.831385	−	0.555697i	$-0.187548\pi$
$773$	46.2298	1.66277	0.831385	+	0.555697i	$0.187548\pi$
$774$	11.2013	0.402624
$775$	−37.4973	−1.34694
$776$	−5.04587	−0.181136
$777$	−56.6160	−2.03109
$778$	23.2112	0.832161
$779$	−15.4282	−0.552772
$780$	0.387444	0.0138727
$781$	−11.5153	−0.412051
$782$	−33.7208	−1.20585
$783$	−2.78914	−0.0996757
$784$	19.9091	0.711038
$785$	1.24067	0.0442814
$786$	−14.9987	−0.534987
$787$	12.4927	0.445316	0.222658	−	0.974897i	$-0.428527\pi$
$787$	12.4927	0.445316	0.222658	+	0.974897i	$0.428527\pi$
$788$	−11.6199	−0.413943
$789$	−20.5262	−0.730750
$790$	−6.43384	−0.228906
$791$	26.7203	0.950066
$792$	0.897239	0.0318820
$793$	−13.5340	−0.480605
$794$	17.1745	0.609500
$795$	−0.572321	−0.0202981
$796$	−15.9048	−0.563732
$797$	17.4326	0.617495	0.308748	−	0.951144i	$-0.400090\pi$
$797$	17.4326	0.617495	0.308748	+	0.951144i	$0.400090\pi$
$798$	23.5137	0.832377
$799$	13.9160	0.492313
$800$	4.84989	0.171469
$801$	−2.89382	−0.102248
$802$	−12.5842	−0.444364
$803$	−9.54529	−0.336846
$804$	−5.48474	−0.193432
$805$	−18.2067	−0.641701
$806$	7.73159	0.272334
$807$	−15.3749	−0.541221
$808$	17.7523	0.624522
$809$	−8.52316	−0.299658	−0.149829	−	0.988712i	$-0.547872\pi$
$809$	−8.52316	−0.299658	−0.149829	+	0.988712i	$0.547872\pi$
$810$	0.387444	0.0136134
$811$	47.1290	1.65492	0.827461	−	0.561523i	$-0.189784\pi$
$811$	47.1290	1.65492	0.827461	+	0.561523i	$0.189784\pi$
$812$	−14.4684	−0.507740
$813$	−25.4152	−0.891351
$814$	−9.79259	−0.343230
$815$	4.02323	0.140928
$816$	3.72242	0.130311
$817$	50.7741	1.77636
$818$	−34.0417	−1.19024
$819$	−5.18739	−0.181262
$820$	−1.31872	−0.0460516
$821$	10.1331	0.353648	0.176824	−	0.984242i	$-0.443418\pi$
$821$	10.1331	0.353648	0.176824	+	0.984242i	$0.443418\pi$
$822$	−0.904010	−0.0315310
$823$	−25.2300	−0.879461	−0.439731	−	0.898130i	$-0.644926\pi$
$823$	−25.2300	−0.879461	−0.439731	+	0.898130i	$0.644926\pi$
$824$	1.00000	0.0348367
$825$	4.35151	0.151500
$826$	−55.5877	−1.93414
$827$	−8.61838	−0.299690	−0.149845	−	0.988709i	$-0.547878\pi$
$827$	−8.61838	−0.299690	−0.149845	+	0.988709i	$0.547878\pi$
$828$	9.05884	0.314817
$829$	−29.2434	−1.01566	−0.507832	−	0.861456i	$-0.669553\pi$
$829$	−29.2434	−1.01566	−0.507832	+	0.861456i	$0.669553\pi$
$830$	−2.58749	−0.0898132
$831$	14.7762	0.512581
$832$	−1.00000	−0.0346688
$833$	74.1098	2.56775
$834$	−16.9188	−0.585850
$835$	−8.92163	−0.308746
$836$	4.06706	0.140662
$837$	7.73159	0.267243
$838$	−13.7947	−0.476531
$839$	36.1648	1.24855	0.624273	−	0.781206i	$-0.285395\pi$
$839$	36.1648	1.24855	0.624273	+	0.781206i	$0.285395\pi$
$840$	2.00982	0.0693455
$841$	−21.2207	−0.731749
$842$	13.4213	0.462529
$843$	−6.11157	−0.210494
$844$	5.86680	0.201944
$845$	−0.387444	−0.0133285
$846$	−3.73843	−0.128530
$847$	−52.8853	−1.81716
$848$	1.47717	0.0507263
$849$	1.35678	0.0465646
$850$	18.0533	0.619223
$851$	−98.8695	−3.38920
$852$	12.8342	0.439692
$853$	36.2477	1.24110	0.620549	−	0.784168i	$-0.286910\pi$
$853$	36.2477	1.24110	0.620549	+	0.784168i	$0.286910\pi$
$854$	−70.2059	−2.40240
$855$	1.75623	0.0600618
$856$	−16.5712	−0.566393
$857$	−57.5309	−1.96522	−0.982610	−	0.185683i	$-0.940550\pi$
$857$	−57.5309	−1.96522	−0.982610	+	0.185683i	$0.940550\pi$
$858$	−0.897239	−0.0306312
$859$	−7.37278	−0.251556	−0.125778	−	0.992058i	$-0.540143\pi$
$859$	−7.37278	−0.251556	−0.125778	+	0.992058i	$0.540143\pi$
$860$	4.33989	0.147989
$861$	17.6560	0.601715
$862$	−4.41378	−0.150334
$863$	22.2311	0.756757	0.378378	−	0.925651i	$-0.376482\pi$
$863$	22.2311	0.756757	0.378378	+	0.925651i	$0.376482\pi$
$864$	−1.00000	−0.0340207
$865$	−5.56937	−0.189364
$866$	4.12519	0.140180
$867$	−3.14362	−0.106763
$868$	40.1068	1.36131
$869$	14.8994	0.505428
$870$	−1.08063	−0.0366369
$871$	5.48474	0.185843
$872$	−14.9168	−0.505146
$873$	5.04587	0.170777
$874$	41.0625	1.38896
$875$	19.7965	0.669245
$876$	10.6385	0.359442
$877$	42.8291	1.44624	0.723118	−	0.690725i	$-0.242708\pi$
$877$	42.8291	1.44624	0.723118	+	0.690725i	$0.242708\pi$
$878$	2.45402	0.0828192
$879$	12.4111	0.418615
$880$	0.347630	0.0117186
$881$	37.2190	1.25394	0.626970	−	0.779044i	$-0.284295\pi$
$881$	37.2190	1.25394	0.626970	+	0.779044i	$0.284295\pi$
$882$	−19.9091	−0.670373
$883$	26.5532	0.893587	0.446793	−	0.894637i	$-0.352566\pi$
$883$	26.5532	0.893587	0.446793	+	0.894637i	$0.352566\pi$
$884$	−3.72242	−0.125198
$885$	−4.15182	−0.139562
$886$	31.8643	1.07050
$887$	42.2548	1.41878	0.709389	−	0.704817i	$-0.248971\pi$
$887$	42.2548	1.41878	0.709389	+	0.704817i	$0.248971\pi$
$888$	10.9141	0.366255
$889$	−6.47768	−0.217255
$890$	−1.12119	−0.0375825
$891$	−0.897239	−0.0300586
$892$	18.1592	0.608016
$893$	−16.9458	−0.567069
$894$	−17.1391	−0.573219
$895$	−3.92061	−0.131052
$896$	−5.18739	−0.173299
$897$	−9.05884	−0.302466
$898$	−10.3009	−0.343744
$899$	−21.5645	−0.719215
$900$	−4.84989	−0.161663
$901$	5.49865	0.183187
$902$	3.05387	0.101683
$903$	−58.1058	−1.93364
$904$	−5.15101	−0.171320
$905$	0.866457	0.0288020
$906$	9.88820	0.328514
$907$	−1.05259	−0.0349507	−0.0174753	−	0.999847i	$-0.505563\pi$
$907$	−1.05259	−0.0349507	−0.0174753	+	0.999847i	$0.505563\pi$
$908$	−27.2308	−0.903686
$909$	−17.7523	−0.588805
$910$	−2.00982	−0.0666250
$911$	21.9484	0.727182	0.363591	−	0.931559i	$-0.381551\pi$
$911$	21.9484	0.727182	0.363591	+	0.931559i	$0.381551\pi$
$912$	−4.53286	−0.150098
$913$	5.99209	0.198309
$914$	24.8913	0.823331
$915$	−5.24365	−0.173350
$916$	4.44361	0.146821
$917$	77.8044	2.56933
$918$	−3.72242	−0.122858
$919$	−49.0680	−1.61860	−0.809302	−	0.587393i	$-0.800154\pi$
$919$	−49.0680	−1.61860	−0.809302	+	0.587393i	$0.800154\pi$
$920$	3.50979	0.115714
$921$	−3.48393	−0.114799
$922$	26.2280	0.863775
$923$	−12.8342	−0.422442
$924$	−4.65433	−0.153116
$925$	52.9324	1.74041
$926$	26.1687	0.859955
$927$	−1.00000	−0.0328443
$928$	2.78914	0.0915580
$929$	−16.8058	−0.551380	−0.275690	−	0.961247i	$-0.588906\pi$
$929$	−16.8058	−0.551380	−0.275690	+	0.961247i	$0.588906\pi$
$930$	2.99556	0.0982282
$931$	−90.2450	−2.95766
$932$	−4.98665	−0.163343
$933$	−32.2188	−1.05480
$934$	−11.7239	−0.383618
$935$	1.29402	0.0423190
$936$	1.00000	0.0326860
$937$	5.85743	0.191354	0.0956770	−	0.995412i	$-0.469498\pi$
$937$	5.85743	0.191354	0.0956770	+	0.995412i	$0.469498\pi$
$938$	28.4515	0.928975
$939$	0.950362	0.0310139
$940$	−1.44843	−0.0472427
$941$	−10.0404	−0.327309	−0.163655	−	0.986518i	$-0.552328\pi$
$941$	−10.0404	−0.327309	−0.163655	+	0.986518i	$0.552328\pi$
$942$	3.20219	0.104333
$943$	30.8330	1.00406
$944$	10.7159	0.348773
$945$	−2.00982	−0.0653796
$946$	−10.0503	−0.326763
$947$	10.7958	0.350817	0.175409	−	0.984496i	$-0.443875\pi$
$947$	10.7958	0.350817	0.175409	+	0.984496i	$0.443875\pi$
$948$	−16.6059	−0.539333
$949$	−10.6385	−0.345341
$950$	−21.9839	−0.713251
$951$	9.44366	0.306232
$952$	−19.3096	−0.625829
$953$	−30.2301	−0.979250	−0.489625	−	0.871933i	$-0.662866\pi$
$953$	−30.2301	−0.979250	−0.489625	+	0.871933i	$0.662866\pi$
$954$	−1.47717	−0.0478252
$955$	4.97725	0.161060
$956$	7.01038	0.226732
$957$	2.50252	0.0808951
$958$	7.43646	0.240261
$959$	4.68946	0.151430
$960$	−0.387444	−0.0125047
$961$	28.7774	0.928304
$962$	−10.9141	−0.351886
$963$	16.5712	0.534000
$964$	22.5245	0.725464
$965$	3.32589	0.107064
$966$	−46.9918	−1.51194
$967$	−30.4687	−0.979806	−0.489903	−	0.871777i	$-0.662968\pi$
$967$	−30.4687	−0.979806	−0.489903	+	0.871777i	$0.662968\pi$
$968$	10.1950	0.327679
$969$	−16.8732	−0.542045
$970$	1.95499	0.0627710
$971$	−15.8514	−0.508694	−0.254347	−	0.967113i	$-0.581861\pi$
$971$	−15.8514	−0.508694	−0.254347	+	0.967113i	$0.581861\pi$
$972$	1.00000	0.0320750
$973$	87.7644	2.81360
$974$	−28.3722	−0.909105
$975$	4.84989	0.155321
$976$	13.5340	0.433211
$977$	−55.3517	−1.77086	−0.885429	−	0.464775i	$-0.846135\pi$
$977$	−55.3517	−1.77086	−0.885429	+	0.464775i	$0.846135\pi$
$978$	10.3840	0.332045
$979$	2.59645	0.0829829
$980$	−7.71365	−0.246403
$981$	14.9168	0.476256
$982$	−9.65334	−0.308050
$983$	20.1558	0.642869	0.321435	−	0.946932i	$-0.395835\pi$
$983$	20.1558	0.642869	0.321435	+	0.946932i	$0.395835\pi$
$984$	−3.40363	−0.108504
$985$	4.50207	0.143448
$986$	10.3823	0.330641
$987$	19.3927	0.617277
$988$	4.53286	0.144209
$989$	−101.471	−3.22660
$990$	−0.347630	−0.0110484
$991$	−29.9807	−0.952369	−0.476185	−	0.879345i	$-0.657981\pi$
$991$	−29.9807	−0.952369	−0.476185	+	0.879345i	$0.657981\pi$
$992$	−7.73159	−0.245478
$993$	−5.39630	−0.171246
$994$	−66.5760	−2.11166
$995$	6.16224	0.195356
$996$	−6.67837	−0.211612
$997$	−21.8193	−0.691024	−0.345512	−	0.938414i	$-0.612295\pi$
$997$	−21.8193	−0.691024	−0.345512	+	0.938414i	$0.612295\pi$
$998$	11.6884	0.369991
$999$	−10.9141	−0.345308

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.t.1.5	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.t.1.5	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.387444 q^{5} -1.00000 q^{6} +5.18739 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.387444 q^{5} -1.00000 q^{6} +5.18739 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.387444 q^{10} -0.897239 q^{11} +1.00000 q^{12} -1.00000 q^{13} -5.18739 q^{14} -0.387444 q^{15} +1.00000 q^{16} +3.72242 q^{17} -1.00000 q^{18} -4.53286 q^{19} -0.387444 q^{20} +5.18739 q^{21} +0.897239 q^{22} +9.05884 q^{23} -1.00000 q^{24} -4.84989 q^{25} +1.00000 q^{26} +1.00000 q^{27} +5.18739 q^{28} -2.78914 q^{29} +0.387444 q^{30} +7.73159 q^{31} -1.00000 q^{32} -0.897239 q^{33} -3.72242 q^{34} -2.00982 q^{35} +1.00000 q^{36} -10.9141 q^{37} +4.53286 q^{38} -1.00000 q^{39} +0.387444 q^{40} +3.40363 q^{41} -5.18739 q^{42} -11.2013 q^{43} -0.897239 q^{44} -0.387444 q^{45} -9.05884 q^{46} +3.73843 q^{47} +1.00000 q^{48} +19.9091 q^{49} +4.84989 q^{50} +3.72242 q^{51} -1.00000 q^{52} +1.47717 q^{53} -1.00000 q^{54} +0.347630 q^{55} -5.18739 q^{56} -4.53286 q^{57} +2.78914 q^{58} +10.7159 q^{59} -0.387444 q^{60} +13.5340 q^{61} -7.73159 q^{62} +5.18739 q^{63} +1.00000 q^{64} +0.387444 q^{65} +0.897239 q^{66} -5.48474 q^{67} +3.72242 q^{68} +9.05884 q^{69} +2.00982 q^{70} +12.8342 q^{71} -1.00000 q^{72} +10.6385 q^{73} +10.9141 q^{74} -4.84989 q^{75} -4.53286 q^{76} -4.65433 q^{77} +1.00000 q^{78} -16.6059 q^{79} -0.387444 q^{80} +1.00000 q^{81} -3.40363 q^{82} -6.67837 q^{83} +5.18739 q^{84} -1.44223 q^{85} +11.2013 q^{86} -2.78914 q^{87} +0.897239 q^{88} -2.89382 q^{89} +0.387444 q^{90} -5.18739 q^{91} +9.05884 q^{92} +7.73159 q^{93} -3.73843 q^{94} +1.75623 q^{95} -1.00000 q^{96} +5.04587 q^{97} -19.9091 q^{98} -0.897239 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 11 q^{2} + 11 q^{3} + 11 q^{4} + 4 q^{5} - 11 q^{6} + 4 q^{7} - 11 q^{8} + 11 q^{9}+O(q^{10}) \) 11 * q - 11 * q^2 + 11 * q^3 + 11 * q^4 + 4 * q^5 - 11 * q^6 + 4 * q^7 - 11 * q^8 + 11 * q^9	\( 11 q - 11 q^{2} + 11 q^{3} + 11 q^{4} + 4 q^{5} - 11 q^{6} + 4 q^{7} - 11 q^{8} + 11 q^{9} - 4 q^{10} + 5 q^{11} + 11 q^{12} - 11 q^{13} - 4 q^{14} + 4 q^{15} + 11 q^{16} + 8 q^{17} - 11 q^{18} - 2 q^{19} + 4 q^{20} + 4 q^{21} - 5 q^{22} + 3 q^{23} - 11 q^{24} + 9 q^{25} + 11 q^{26} + 11 q^{27} + 4 q^{28} + 7 q^{29} - 4 q^{30} + 20 q^{31} - 11 q^{32} + 5 q^{33} - 8 q^{34} + 9 q^{35} + 11 q^{36} + q^{37} + 2 q^{38} - 11 q^{39} - 4 q^{40} + 37 q^{41} - 4 q^{42} - 16 q^{43} + 5 q^{44} + 4 q^{45} - 3 q^{46} + 28 q^{47} + 11 q^{48} + 17 q^{49} - 9 q^{50} + 8 q^{51} - 11 q^{52} - 5 q^{53} - 11 q^{54} - 28 q^{55} - 4 q^{56} - 2 q^{57} - 7 q^{58} + 31 q^{59} + 4 q^{60} + 8 q^{61} - 20 q^{62} + 4 q^{63} + 11 q^{64} - 4 q^{65} - 5 q^{66} - 22 q^{67} + 8 q^{68} + 3 q^{69} - 9 q^{70} + 42 q^{71} - 11 q^{72} - 4 q^{73} - q^{74} + 9 q^{75} - 2 q^{76} - 21 q^{77} + 11 q^{78} + 33 q^{79} + 4 q^{80} + 11 q^{81} - 37 q^{82} + 18 q^{83} + 4 q^{84} + 17 q^{85} + 16 q^{86} + 7 q^{87} - 5 q^{88} + 67 q^{89} - 4 q^{90} - 4 q^{91} + 3 q^{92} + 20 q^{93} - 28 q^{94} + 32 q^{95} - 11 q^{96} - 15 q^{97} - 17 q^{98} + 5 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 + 11 * q^3 + 11 * q^4 + 4 * q^5 - 11 * q^6 + 4 * q^7 - 11 * q^8 + 11 * q^9 - 4 * q^10 + 5 * q^11 + 11 * q^12 - 11 * q^13 - 4 * q^14 + 4 * q^15 + 11 * q^16 + 8 * q^17 - 11 * q^18 - 2 * q^19 + 4 * q^20 + 4 * q^21 - 5 * q^22 + 3 * q^23 - 11 * q^24 + 9 * q^25 + 11 * q^26 + 11 * q^27 + 4 * q^28 + 7 * q^29 - 4 * q^30 + 20 * q^31 - 11 * q^32 + 5 * q^33 - 8 * q^34 + 9 * q^35 + 11 * q^36 + q^37 + 2 * q^38 - 11 * q^39 - 4 * q^40 + 37 * q^41 - 4 * q^42 - 16 * q^43 + 5 * q^44 + 4 * q^45 - 3 * q^46 + 28 * q^47 + 11 * q^48 + 17 * q^49 - 9 * q^50 + 8 * q^51 - 11 * q^52 - 5 * q^53 - 11 * q^54 - 28 * q^55 - 4 * q^56 - 2 * q^57 - 7 * q^58 + 31 * q^59 + 4 * q^60 + 8 * q^61 - 20 * q^62 + 4 * q^63 + 11 * q^64 - 4 * q^65 - 5 * q^66 - 22 * q^67 + 8 * q^68 + 3 * q^69 - 9 * q^70 + 42 * q^71 - 11 * q^72 - 4 * q^73 - q^74 + 9 * q^75 - 2 * q^76 - 21 * q^77 + 11 * q^78 + 33 * q^79 + 4 * q^80 + 11 * q^81 - 37 * q^82 + 18 * q^83 + 4 * q^84 + 17 * q^85 + 16 * q^86 + 7 * q^87 - 5 * q^88 + 67 * q^89 - 4 * q^90 - 4 * q^91 + 3 * q^92 + 20 * q^93 - 28 * q^94 + 32 * q^95 - 11 * q^96 - 15 * q^97 - 17 * q^98 + 5 * q^99

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