LMFDB - Embedded newform 4641.2.a.ba.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4641,2,Mod(1,4641)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4641, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4641.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4641 = 3 \cdot 7 \cdot 13 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4641.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:	$37.0585715781$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - x^{16} - 29 x^{15} + 26 x^{14} + 339 x^{13} - 266 x^{12} - 2047 x^{11} + 1356 x^{10} + \cdots + 18 $ x^17 - x^16 - 29x^15 + 26x^14 + 339x^13 - 266x^12 - 2047x^11 + 1356x^10 + 6792x^9 - 3573x^8 - 12125x^7 + 4456x^6 + 10521x^5 - 1858x^4 - 3551x^3 + 34x^2 + 323*x + 18
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-0.396729$ of defining polynomial
Character	$\chi$	$=$	4641.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.396729 q^{2} -1.00000 q^{3} -1.84261 q^{4} -1.99480 q^{5} +0.396729 q^{6} -1.00000 q^{7} +1.52447 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.396729 q^{2} -1.00000 q^{3} -1.84261 q^{4} -1.99480 q^{5} +0.396729 q^{6} -1.00000 q^{7} +1.52447 q^{8} +1.00000 q^{9} +0.791394 q^{10} -1.63440 q^{11} +1.84261 q^{12} +1.00000 q^{13} +0.396729 q^{14} +1.99480 q^{15} +3.08041 q^{16} -1.00000 q^{17} -0.396729 q^{18} +8.51961 q^{19} +3.67562 q^{20} +1.00000 q^{21} +0.648416 q^{22} -9.24882 q^{23} -1.52447 q^{24} -1.02079 q^{25} -0.396729 q^{26} -1.00000 q^{27} +1.84261 q^{28} -4.83621 q^{29} -0.791394 q^{30} -3.53491 q^{31} -4.27103 q^{32} +1.63440 q^{33} +0.396729 q^{34} +1.99480 q^{35} -1.84261 q^{36} +8.58033 q^{37} -3.37998 q^{38} -1.00000 q^{39} -3.04101 q^{40} -12.0273 q^{41} -0.396729 q^{42} -3.86484 q^{43} +3.01156 q^{44} -1.99480 q^{45} +3.66928 q^{46} +12.6134 q^{47} -3.08041 q^{48} +1.00000 q^{49} +0.404975 q^{50} +1.00000 q^{51} -1.84261 q^{52} -3.61717 q^{53} +0.396729 q^{54} +3.26031 q^{55} -1.52447 q^{56} -8.51961 q^{57} +1.91867 q^{58} -7.74328 q^{59} -3.67562 q^{60} -5.19629 q^{61} +1.40240 q^{62} -1.00000 q^{63} -4.46637 q^{64} -1.99480 q^{65} -0.648416 q^{66} -4.70079 q^{67} +1.84261 q^{68} +9.24882 q^{69} -0.791394 q^{70} +1.02949 q^{71} +1.52447 q^{72} +2.72657 q^{73} -3.40407 q^{74} +1.02079 q^{75} -15.6983 q^{76} +1.63440 q^{77} +0.396729 q^{78} -17.5050 q^{79} -6.14479 q^{80} +1.00000 q^{81} +4.77158 q^{82} -1.19600 q^{83} -1.84261 q^{84} +1.99480 q^{85} +1.53330 q^{86} +4.83621 q^{87} -2.49161 q^{88} -3.23325 q^{89} +0.791394 q^{90} -1.00000 q^{91} +17.0419 q^{92} +3.53491 q^{93} -5.00410 q^{94} -16.9949 q^{95} +4.27103 q^{96} -3.77810 q^{97} -0.396729 q^{98} -1.63440 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + q^{2} - 17 q^{3} + 25 q^{4} - 4 q^{5} - q^{6} - 17 q^{7} + 6 q^{8} + 17 q^{9}+O(q^{10}) $ 17 * q + q^2 - 17 * q^3 + 25 * q^4 - 4 * q^5 - q^6 - 17 * q^7 + 6 * q^8 + 17 * q^9	\( 17 q + q^{2} - 17 q^{3} + 25 q^{4} - 4 q^{5} - q^{6} - 17 q^{7} + 6 q^{8} + 17 q^{9} - q^{10} + 4 q^{11} - 25 q^{12} + 17 q^{13} - q^{14} + 4 q^{15} + 53 q^{16} - 17 q^{17} + q^{18} + 13 q^{19} - 5 q^{20} + 17 q^{21} + 4 q^{22} + 8 q^{23} - 6 q^{24} + 37 q^{25} + q^{26} - 17 q^{27} - 25 q^{28} - 3 q^{29} + q^{30} + 10 q^{31} + 18 q^{32} - 4 q^{33} - q^{34} + 4 q^{35} + 25 q^{36} - 25 q^{38} - 17 q^{39} - 12 q^{41} + q^{42} + 29 q^{43} + 12 q^{44} - 4 q^{45} + 19 q^{46} - 4 q^{47} - 53 q^{48} + 17 q^{49} + 9 q^{50} + 17 q^{51} + 25 q^{52} - 8 q^{53} - q^{54} + 27 q^{55} - 6 q^{56} - 13 q^{57} + 2 q^{58} + 25 q^{59} + 5 q^{60} - 5 q^{61} - 37 q^{62} - 17 q^{63} + 94 q^{64} - 4 q^{65} - 4 q^{66} + 15 q^{67} - 25 q^{68} - 8 q^{69} + q^{70} + 32 q^{71} + 6 q^{72} - 15 q^{73} + 16 q^{74} - 37 q^{75} + 3 q^{76} - 4 q^{77} - q^{78} + 27 q^{79} + 41 q^{80} + 17 q^{81} - 8 q^{82} - 24 q^{83} + 25 q^{84} + 4 q^{85} + 53 q^{86} + 3 q^{87} - 9 q^{88} - 8 q^{89} - q^{90} - 17 q^{91} + 14 q^{92} - 10 q^{93} + 51 q^{94} - 9 q^{95} - 18 q^{96} - 22 q^{97} + q^{98} + 4 q^{99}+O(q^{100}) \) 17 * q + q^2 - 17 * q^3 + 25 * q^4 - 4 * q^5 - q^6 - 17 * q^7 + 6 * q^8 + 17 * q^9 - q^10 + 4 * q^11 - 25 * q^12 + 17 * q^13 - q^14 + 4 * q^15 + 53 * q^16 - 17 * q^17 + q^18 + 13 * q^19 - 5 * q^20 + 17 * q^21 + 4 * q^22 + 8 * q^23 - 6 * q^24 + 37 * q^25 + q^26 - 17 * q^27 - 25 * q^28 - 3 * q^29 + q^30 + 10 * q^31 + 18 * q^32 - 4 * q^33 - q^34 + 4 * q^35 + 25 * q^36 - 25 * q^38 - 17 * q^39 - 12 * q^41 + q^42 + 29 * q^43 + 12 * q^44 - 4 * q^45 + 19 * q^46 - 4 * q^47 - 53 * q^48 + 17 * q^49 + 9 * q^50 + 17 * q^51 + 25 * q^52 - 8 * q^53 - q^54 + 27 * q^55 - 6 * q^56 - 13 * q^57 + 2 * q^58 + 25 * q^59 + 5 * q^60 - 5 * q^61 - 37 * q^62 - 17 * q^63 + 94 * q^64 - 4 * q^65 - 4 * q^66 + 15 * q^67 - 25 * q^68 - 8 * q^69 + q^70 + 32 * q^71 + 6 * q^72 - 15 * q^73 + 16 * q^74 - 37 * q^75 + 3 * q^76 - 4 * q^77 - q^78 + 27 * q^79 + 41 * q^80 + 17 * q^81 - 8 * q^82 - 24 * q^83 + 25 * q^84 + 4 * q^85 + 53 * q^86 + 3 * q^87 - 9 * q^88 - 8 * q^89 - q^90 - 17 * q^91 + 14 * q^92 - 10 * q^93 + 51 * q^94 - 9 * q^95 - 18 * q^96 - 22 * q^97 + q^98 + 4 * 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 $

$2$	−0.396729	−0.280530	−0.140265	−	0.990114i	$-0.544795\pi$
$2$	−0.396729	−0.280530	−0.140265	+	0.990114i	$0.544795\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.84261	−0.921303
$5$	−1.99480	−0.892100	−0.446050	−	0.895008i	$-0.647170\pi$
$5$	−1.99480	−0.892100	−0.446050	+	0.895008i	$0.647170\pi$
$6$	0.396729	0.161964
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.52447	0.538983
$9$	1.00000	0.333333
$10$	0.791394	0.250261
$11$	−1.63440	−0.492792	−0.246396	−	0.969169i	$-0.579246\pi$
$11$	−1.63440	−0.492792	−0.246396	+	0.969169i	$0.579246\pi$
$12$	1.84261	0.531915
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0.396729	0.106030
$15$	1.99480	0.515054
$16$	3.08041	0.770102
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−0.396729	−0.0935099
$19$	8.51961	1.95453	0.977266	−	0.212016i	$-0.0680029\pi$
$19$	8.51961	1.95453	0.977266	+	0.212016i	$0.0680029\pi$
$20$	3.67562	0.821895
$21$	1.00000	0.218218
$22$	0.648416	0.138243
$23$	−9.24882	−1.92851	−0.964257	−	0.264971i	$-0.914638\pi$
$23$	−9.24882	−1.92851	−0.964257	+	0.264971i	$0.914638\pi$
$24$	−1.52447	−0.311182
$25$	−1.02079	−0.204157
$26$	−0.396729	−0.0778050
$27$	−1.00000	−0.192450
$28$	1.84261	0.348220
$29$	−4.83621	−0.898062	−0.449031	−	0.893516i	$-0.648231\pi$
$29$	−4.83621	−0.898062	−0.449031	+	0.893516i	$0.648231\pi$
$30$	−0.791394	−0.144488
$31$	−3.53491	−0.634889	−0.317444	−	0.948277i	$-0.602825\pi$
$31$	−3.53491	−0.634889	−0.317444	+	0.948277i	$0.602825\pi$
$32$	−4.27103	−0.755019
$33$	1.63440	0.284513
$34$	0.396729	0.0680385
$35$	1.99480	0.337182
$36$	−1.84261	−0.307101
$37$	8.58033	1.41060	0.705299	−	0.708910i	$-0.250813\pi$
$37$	8.58033	1.41060	0.705299	+	0.708910i	$0.250813\pi$
$38$	−3.37998	−0.548305
$39$	−1.00000	−0.160128
$40$	−3.04101	−0.480827
$41$	−12.0273	−1.87835	−0.939174	−	0.343442i	$-0.888407\pi$
$41$	−12.0273	−1.87835	−0.939174	+	0.343442i	$0.888407\pi$
$42$	−0.396729	−0.0612166
$43$	−3.86484	−0.589383	−0.294692	−	0.955592i	$-0.595217\pi$
$43$	−3.86484	−0.589383	−0.294692	+	0.955592i	$0.595217\pi$
$44$	3.01156	0.454010
$45$	−1.99480	−0.297367
$46$	3.66928	0.541005
$47$	12.6134	1.83985	0.919927	−	0.392091i	$-0.128248\pi$
$47$	12.6134	1.83985	0.919927	+	0.392091i	$0.128248\pi$
$48$	−3.08041	−0.444619
$49$	1.00000	0.142857
$50$	0.404975	0.0572722
$51$	1.00000	0.140028
$52$	−1.84261	−0.255523
$53$	−3.61717	−0.496857	−0.248429	−	0.968650i	$-0.579914\pi$
$53$	−3.61717	−0.496857	−0.248429	+	0.968650i	$0.579914\pi$
$54$	0.396729	0.0539880
$55$	3.26031	0.439620
$56$	−1.52447	−0.203716
$57$	−8.51961	−1.12845
$58$	1.91867	0.251933
$59$	−7.74328	−1.00809	−0.504045	−	0.863678i	$-0.668155\pi$
$59$	−7.74328	−1.00809	−0.504045	+	0.863678i	$0.668155\pi$
$60$	−3.67562	−0.474521
$61$	−5.19629	−0.665316	−0.332658	−	0.943048i	$-0.607946\pi$
$61$	−5.19629	−0.665316	−0.332658	+	0.943048i	$0.607946\pi$
$62$	1.40240	0.178105
$63$	−1.00000	−0.125988
$64$	−4.46637	−0.558297
$65$	−1.99480	−0.247424
$66$	−0.648416	−0.0798145
$67$	−4.70079	−0.574293	−0.287147	−	0.957887i	$-0.592707\pi$
$67$	−4.70079	−0.574293	−0.287147	+	0.957887i	$0.592707\pi$
$68$	1.84261	0.223449
$69$	9.24882	1.11343
$70$	−0.791394	−0.0945897
$71$	1.02949	0.122178	0.0610891	−	0.998132i	$-0.480543\pi$
$71$	1.02949	0.122178	0.0610891	+	0.998132i	$0.480543\pi$
$72$	1.52447	0.179661
$73$	2.72657	0.319120	0.159560	−	0.987188i	$-0.448992\pi$
$73$	2.72657	0.319120	0.159560	+	0.987188i	$0.448992\pi$
$74$	−3.40407	−0.395715
$75$	1.02079	0.117870
$76$	−15.6983	−1.80072
$77$	1.63440	0.186258
$78$	0.396729	0.0449207
$79$	−17.5050	−1.96946	−0.984731	−	0.174084i	$-0.944304\pi$
$79$	−17.5050	−1.96946	−0.984731	+	0.174084i	$0.944304\pi$
$80$	−6.14479	−0.687008
$81$	1.00000	0.111111
$82$	4.77158	0.526933
$83$	−1.19600	−0.131278	−0.0656389	−	0.997843i	$-0.520909\pi$
$83$	−1.19600	−0.131278	−0.0656389	+	0.997843i	$0.520909\pi$
$84$	−1.84261	−0.201045
$85$	1.99480	0.216366
$86$	1.53330	0.165340
$87$	4.83621	0.518497
$88$	−2.49161	−0.265606
$89$	−3.23325	−0.342724	−0.171362	−	0.985208i	$-0.554817\pi$
$89$	−3.23325	−0.342724	−0.171362	+	0.985208i	$0.554817\pi$
$90$	0.791394	0.0834202
$91$	−1.00000	−0.104828
$92$	17.0419	1.77674
$93$	3.53491	0.366553
$94$	−5.00410	−0.516134
$95$	−16.9949	−1.74364
$96$	4.27103	0.435911
$97$	−3.77810	−0.383608	−0.191804	−	0.981433i	$-0.561434\pi$
$97$	−3.77810	−0.383608	−0.191804	+	0.981433i	$0.561434\pi$
$98$	−0.396729	−0.0400757
$99$	−1.63440	−0.164264
$100$	1.88091	0.188091
$101$	−0.187439	−0.0186509	−0.00932545	−	0.999957i	$-0.502968\pi$
$101$	−0.187439	−0.0186509	−0.00932545	+	0.999957i	$0.502968\pi$
$102$	−0.396729	−0.0392820
$103$	−5.36297	−0.528429	−0.264214	−	0.964464i	$-0.585113\pi$
$103$	−5.36297	−0.528429	−0.264214	+	0.964464i	$0.585113\pi$
$104$	1.52447	0.149487
$105$	−1.99480	−0.194672
$106$	1.43504	0.139383
$107$	3.51688	0.339989	0.169995	−	0.985445i	$-0.445625\pi$
$107$	3.51688	0.339989	0.169995	+	0.985445i	$0.445625\pi$
$108$	1.84261	0.177305
$109$	7.14966	0.684813	0.342407	−	0.939552i	$-0.388758\pi$
$109$	7.14966	0.684813	0.342407	+	0.939552i	$0.388758\pi$
$110$	−1.29346	−0.123326
$111$	−8.58033	−0.814409
$112$	−3.08041	−0.291071
$113$	−10.2165	−0.961087	−0.480544	−	0.876971i	$-0.659561\pi$
$113$	−10.2165	−0.961087	−0.480544	+	0.876971i	$0.659561\pi$
$114$	3.37998	0.316564
$115$	18.4495	1.72043
$116$	8.91124	0.827388
$117$	1.00000	0.0924500
$118$	3.07198	0.282799
$119$	1.00000	0.0916698
$120$	3.04101	0.277605
$121$	−8.32872	−0.757156
$122$	2.06152	0.186641
$123$	12.0273	1.08446
$124$	6.51345	0.584925
$125$	12.0102	1.07423
$126$	0.396729	0.0353434
$127$	−7.78400	−0.690719	−0.345359	−	0.938471i	$-0.612243\pi$
$127$	−7.78400	−0.690719	−0.345359	+	0.938471i	$0.612243\pi$
$128$	10.3140	0.911638
$129$	3.86484	0.340281
$130$	0.791394	0.0694098
$131$	−2.81999	−0.246383	−0.123192	−	0.992383i	$-0.539313\pi$
$131$	−2.81999	−0.246383	−0.123192	+	0.992383i	$0.539313\pi$
$132$	−3.01156	−0.262123
$133$	−8.51961	−0.738744
$134$	1.86494	0.161106
$135$	1.99480	0.171685
$136$	−1.52447	−0.130723
$137$	16.5373	1.41288	0.706439	−	0.707774i	$-0.250301\pi$
$137$	16.5373	1.41288	0.706439	+	0.707774i	$0.250301\pi$
$138$	−3.66928	−0.312350
$139$	17.2550	1.46355	0.731777	−	0.681544i	$-0.238691\pi$
$139$	17.2550	1.46355	0.731777	+	0.681544i	$0.238691\pi$
$140$	−3.67562	−0.310647
$141$	−12.6134	−1.06224
$142$	−0.408429	−0.0342746
$143$	−1.63440	−0.136676
$144$	3.08041	0.256701
$145$	9.64726	0.801162
$146$	−1.08171	−0.0895228
$147$	−1.00000	−0.0824786
$148$	−15.8102	−1.29959
$149$	19.8449	1.62576	0.812880	−	0.582431i	$-0.197898\pi$
$149$	19.8449	1.62576	0.812880	+	0.582431i	$0.197898\pi$
$150$	−0.404975	−0.0330661
$151$	21.8292	1.77644	0.888218	−	0.459423i	$-0.151944\pi$
$151$	21.8292	1.77644	0.888218	+	0.459423i	$0.151944\pi$
$152$	12.9879	1.05346
$153$	−1.00000	−0.0808452
$154$	−0.648416	−0.0522508
$155$	7.05143	0.566384
$156$	1.84261	0.147527
$157$	−7.86239	−0.627487	−0.313743	−	0.949508i	$-0.601583\pi$
$157$	−7.86239	−0.627487	−0.313743	+	0.949508i	$0.601583\pi$
$158$	6.94473	0.552493
$159$	3.61717	0.286861
$160$	8.51985	0.673553
$161$	9.24882	0.728909
$162$	−0.396729	−0.0311700
$163$	−3.15000	−0.246727	−0.123364	−	0.992362i	$-0.539368\pi$
$163$	−3.15000	−0.246727	−0.123364	+	0.992362i	$0.539368\pi$
$164$	22.1616	1.73053
$165$	−3.26031	−0.253814
$166$	0.474487	0.0368273
$167$	−18.1399	−1.40371	−0.701853	−	0.712322i	$-0.747644\pi$
$167$	−18.1399	−1.40371	−0.701853	+	0.712322i	$0.747644\pi$
$168$	1.52447	0.117616
$169$	1.00000	0.0769231
$170$	−0.791394	−0.0606971
$171$	8.51961	0.651511
$172$	7.12139	0.543001
$173$	6.14583	0.467259	0.233629	−	0.972326i	$-0.424940\pi$
$173$	6.14583	0.467259	0.233629	+	0.972326i	$0.424940\pi$
$174$	−1.91867	−0.145454
$175$	1.02079	0.0771641
$176$	−5.03464	−0.379500
$177$	7.74328	0.582021
$178$	1.28273	0.0961443
$179$	7.48188	0.559222	0.279611	−	0.960113i	$-0.409795\pi$
$179$	7.48188	0.559222	0.279611	+	0.960113i	$0.409795\pi$
$180$	3.67562	0.273965
$181$	9.97479	0.741420	0.370710	−	0.928749i	$-0.379114\pi$
$181$	9.97479	0.741420	0.370710	+	0.928749i	$0.379114\pi$
$182$	0.396729	0.0294075
$183$	5.19629	0.384120
$184$	−14.0996	−1.03944
$185$	−17.1160	−1.25839
$186$	−1.40240	−0.102829
$187$	1.63440	0.119520
$188$	−23.2415	−1.69506
$189$	1.00000	0.0727393
$190$	6.74237	0.489143
$191$	17.0658	1.23484	0.617419	−	0.786634i	$-0.288178\pi$
$191$	17.0658	1.23484	0.617419	+	0.786634i	$0.288178\pi$
$192$	4.46637	0.322333
$193$	27.2058	1.95831	0.979157	−	0.203103i	$-0.0651027\pi$
$193$	27.2058	1.95831	0.979157	+	0.203103i	$0.0651027\pi$
$194$	1.49888	0.107613
$195$	1.99480	0.142850
$196$	−1.84261	−0.131615
$197$	−26.8919	−1.91597	−0.957983	−	0.286826i	$-0.907400\pi$
$197$	−26.8919	−1.91597	−0.957983	+	0.286826i	$0.907400\pi$
$198$	0.648416	0.0460809
$199$	11.3915	0.807520	0.403760	−	0.914865i	$-0.367703\pi$
$199$	11.3915	0.807520	0.403760	+	0.914865i	$0.367703\pi$
$200$	−1.55616	−0.110037
$201$	4.70079	0.331568
$202$	0.0743626	0.00523213
$203$	4.83621	0.339436
$204$	−1.84261	−0.129008
$205$	23.9920	1.67567
$206$	2.12764	0.148240
$207$	−9.24882	−0.642838
$208$	3.08041	0.213588
$209$	−13.9245	−0.963177
$210$	0.791394	0.0546114
$211$	−8.23761	−0.567100	−0.283550	−	0.958957i	$-0.591512\pi$
$211$	−8.23761	−0.567100	−0.283550	+	0.958957i	$0.591512\pi$
$212$	6.66503	0.457756
$213$	−1.02949	−0.0705396
$214$	−1.39525	−0.0953771
$215$	7.70958	0.525789
$216$	−1.52447	−0.103727
$217$	3.53491	0.239965
$218$	−2.83648	−0.192111
$219$	−2.72657	−0.184244
$220$	−6.00746	−0.405023
$221$	−1.00000	−0.0672673
$222$	3.40407	0.228466
$223$	16.3159	1.09259	0.546296	−	0.837592i	$-0.316037\pi$
$223$	16.3159	1.09259	0.546296	+	0.837592i	$0.316037\pi$
$224$	4.27103	0.285371
$225$	−1.02079	−0.0680524
$226$	4.05318	0.269614
$227$	−2.97286	−0.197316	−0.0986579	−	0.995121i	$-0.531455\pi$
$227$	−2.97286	−0.197316	−0.0986579	+	0.995121i	$0.531455\pi$
$228$	15.6983	1.03964
$229$	3.06395	0.202471	0.101236	−	0.994862i	$-0.467720\pi$
$229$	3.06395	0.202471	0.101236	+	0.994862i	$0.467720\pi$
$230$	−7.31946	−0.482631
$231$	−1.63440	−0.107536
$232$	−7.37268	−0.484040
$233$	−6.88586	−0.451108	−0.225554	−	0.974231i	$-0.572419\pi$
$233$	−6.88586	−0.451108	−0.225554	+	0.974231i	$0.572419\pi$
$234$	−0.396729	−0.0259350
$235$	−25.1612	−1.64133
$236$	14.2678	0.928756
$237$	17.5050	1.13707
$238$	−0.396729	−0.0257161
$239$	−10.8972	−0.704881	−0.352441	−	0.935834i	$-0.614648\pi$
$239$	−10.8972	−0.704881	−0.352441	+	0.935834i	$0.614648\pi$
$240$	6.14479	0.396645
$241$	−26.5876	−1.71266	−0.856328	−	0.516433i	$-0.827260\pi$
$241$	−26.5876	−1.71266	−0.856328	+	0.516433i	$0.827260\pi$
$242$	3.30425	0.212405
$243$	−1.00000	−0.0641500
$244$	9.57471	0.612958
$245$	−1.99480	−0.127443
$246$	−4.77158	−0.304225
$247$	8.51961	0.542090
$248$	−5.38888	−0.342194
$249$	1.19600	0.0757932
$250$	−4.76481	−0.301353
$251$	0.693930	0.0438005	0.0219002	−	0.999760i	$-0.493028\pi$
$251$	0.693930	0.0438005	0.0219002	+	0.999760i	$0.493028\pi$
$252$	1.84261	0.116073
$253$	15.1163	0.950355
$254$	3.08814	0.193767
$255$	−1.99480	−0.124919
$256$	4.84088	0.302555
$257$	4.47539	0.279167	0.139584	−	0.990210i	$-0.455424\pi$
$257$	4.47539	0.279167	0.139584	+	0.990210i	$0.455424\pi$
$258$	−1.53330	−0.0954589
$259$	−8.58033	−0.533156
$260$	3.67562	0.227953
$261$	−4.83621	−0.299354
$262$	1.11877	0.0691179
$263$	11.5632	0.713020	0.356510	−	0.934292i	$-0.383967\pi$
$263$	11.5632	0.713020	0.356510	+	0.934292i	$0.383967\pi$
$264$	2.49161	0.153348
$265$	7.21553	0.443246
$266$	3.37998	0.207240
$267$	3.23325	0.197872
$268$	8.66171	0.529098
$269$	−4.83635	−0.294877	−0.147439	−	0.989071i	$-0.547103\pi$
$269$	−4.83635	−0.294877	−0.147439	+	0.989071i	$0.547103\pi$
$270$	−0.791394	−0.0481627
$271$	−24.1169	−1.46500	−0.732498	−	0.680769i	$-0.761646\pi$
$271$	−24.1169	−1.46500	−0.732498	+	0.680769i	$0.761646\pi$
$272$	−3.08041	−0.186777
$273$	1.00000	0.0605228
$274$	−6.56083	−0.396354
$275$	1.66838	0.100607
$276$	−17.0419	−1.02580
$277$	17.1894	1.03281	0.516406	−	0.856344i	$-0.327270\pi$
$277$	17.1894	1.03281	0.516406	+	0.856344i	$0.327270\pi$
$278$	−6.84558	−0.410570
$279$	−3.53491	−0.211630
$280$	3.04101	0.181735
$281$	1.68962	0.100794	0.0503971	−	0.998729i	$-0.483951\pi$
$281$	1.68962	0.100794	0.0503971	+	0.998729i	$0.483951\pi$
$282$	5.00410	0.297990
$283$	17.3976	1.03418	0.517090	−	0.855931i	$-0.327015\pi$
$283$	17.3976	1.03418	0.517090	+	0.855931i	$0.327015\pi$
$284$	−1.89695	−0.112563
$285$	16.9949	1.00669
$286$	0.648416	0.0383416
$287$	12.0273	0.709949
$288$	−4.27103	−0.251673
$289$	1.00000	0.0588235
$290$	−3.82735	−0.224750
$291$	3.77810	0.221476
$292$	−5.02399	−0.294007
$293$	11.6209	0.678902	0.339451	−	0.940624i	$-0.389759\pi$
$293$	11.6209	0.678902	0.339451	+	0.940624i	$0.389759\pi$
$294$	0.396729	0.0231377
$295$	15.4463	0.899317
$296$	13.0805	0.760288
$297$	1.63440	0.0948378
$298$	−7.87306	−0.456074
$299$	−9.24882	−0.534873
$300$	−1.88091	−0.108594
$301$	3.86484	0.222766
$302$	−8.66028	−0.498343
$303$	0.187439	0.0107681
$304$	26.2439	1.50519
$305$	10.3655	0.593529
$306$	0.396729	0.0226795
$307$	−9.66428	−0.551570	−0.275785	−	0.961219i	$-0.588938\pi$
$307$	−9.66428	−0.551570	−0.275785	+	0.961219i	$0.588938\pi$
$308$	−3.01156	−0.171600
$309$	5.36297	0.305089
$310$	−2.79751	−0.158888
$311$	17.4777	0.991068	0.495534	−	0.868589i	$-0.334972\pi$
$311$	17.4777	0.991068	0.495534	+	0.868589i	$0.334972\pi$
$312$	−1.52447	−0.0863063
$313$	−25.0911	−1.41823	−0.709117	−	0.705091i	$-0.750906\pi$
$313$	−25.0911	−1.41823	−0.709117	+	0.705091i	$0.750906\pi$
$314$	3.11924	0.176029
$315$	1.99480	0.112394
$316$	32.2547	1.81447
$317$	−15.4696	−0.868862	−0.434431	−	0.900705i	$-0.643051\pi$
$317$	−15.4696	−0.868862	−0.434431	+	0.900705i	$0.643051\pi$
$318$	−1.43504	−0.0804729
$319$	7.90433	0.442558
$320$	8.90951	0.498057
$321$	−3.51688	−0.196293
$322$	−3.66928	−0.204481
$323$	−8.51961	−0.474044
$324$	−1.84261	−0.102367
$325$	−1.02079	−0.0566230
$326$	1.24970	0.0692143
$327$	−7.14966	−0.395377
$328$	−18.3353	−1.01240
$329$	−12.6134	−0.695399
$330$	1.29346	0.0712025
$331$	28.6202	1.57311	0.786555	−	0.617521i	$-0.211863\pi$
$331$	28.6202	1.57311	0.786555	+	0.617521i	$0.211863\pi$
$332$	2.20375	0.120947
$333$	8.58033	0.470199
$334$	7.19662	0.393781
$335$	9.37712	0.512327
$336$	3.08041	0.168050
$337$	26.0626	1.41972	0.709859	−	0.704344i	$-0.248759\pi$
$337$	26.0626	1.41972	0.709859	+	0.704344i	$0.248759\pi$
$338$	−0.396729	−0.0215792
$339$	10.2165	0.554884
$340$	−3.67562	−0.199339
$341$	5.77747	0.312868
$342$	−3.37998	−0.182768
$343$	−1.00000	−0.0539949
$344$	−5.89185	−0.317667
$345$	−18.4495	−0.993289
$346$	−2.43823	−0.131080
$347$	−2.94247	−0.157960	−0.0789800	−	0.996876i	$-0.525166\pi$
$347$	−2.94247	−0.157960	−0.0789800	+	0.996876i	$0.525166\pi$
$348$	−8.91124	−0.477692
$349$	−9.13757	−0.489123	−0.244561	−	0.969634i	$-0.578644\pi$
$349$	−9.13757	−0.489123	−0.244561	+	0.969634i	$0.578644\pi$
$350$	−0.404975	−0.0216468
$351$	−1.00000	−0.0533761
$352$	6.98060	0.372067
$353$	−27.5850	−1.46820	−0.734100	−	0.679042i	$-0.762395\pi$
$353$	−27.5850	−1.46820	−0.734100	+	0.679042i	$0.762395\pi$
$354$	−3.07198	−0.163274
$355$	−2.05363	−0.108995
$356$	5.95761	0.315753
$357$	−1.00000	−0.0529256
$358$	−2.96828	−0.156878
$359$	14.6461	0.772993	0.386496	−	0.922291i	$-0.373685\pi$
$359$	14.6461	0.772993	0.386496	+	0.922291i	$0.373685\pi$
$360$	−3.04101	−0.160276
$361$	53.5837	2.82020
$362$	−3.95729	−0.207990
$363$	8.32872	0.437144
$364$	1.84261	0.0965788
$365$	−5.43894	−0.284687
$366$	−2.06152	−0.107757
$367$	0.571322	0.0298228	0.0149114	−	0.999889i	$-0.495253\pi$
$367$	0.571322	0.0298228	0.0149114	+	0.999889i	$0.495253\pi$
$368$	−28.4902	−1.48515
$369$	−12.0273	−0.626116
$370$	6.79042	0.353017
$371$	3.61717	0.187794
$372$	−6.51345	−0.337706
$373$	10.3817	0.537542	0.268771	−	0.963204i	$-0.413382\pi$
$373$	10.3817	0.537542	0.268771	+	0.963204i	$0.413382\pi$
$374$	−0.648416	−0.0335288
$375$	−12.0102	−0.620206
$376$	19.2288	0.991649
$377$	−4.83621	−0.249078
$378$	−0.396729	−0.0204055
$379$	32.3566	1.66205	0.831024	−	0.556236i	$-0.187755\pi$
$379$	32.3566	1.66205	0.831024	+	0.556236i	$0.187755\pi$
$380$	31.3149	1.60642
$381$	7.78400	0.398787
$382$	−6.77050	−0.346409
$383$	−31.4178	−1.60537	−0.802686	−	0.596401i	$-0.796597\pi$
$383$	−31.4178	−1.60537	−0.802686	+	0.596401i	$0.796597\pi$
$384$	−10.3140	−0.526335
$385$	−3.26031	−0.166161
$386$	−10.7933	−0.549366
$387$	−3.86484	−0.196461
$388$	6.96154	0.353419
$389$	−15.4127	−0.781453	−0.390726	−	0.920507i	$-0.627776\pi$
$389$	−15.4127	−0.781453	−0.390726	+	0.920507i	$0.627776\pi$
$390$	−0.791394	−0.0400738
$391$	9.24882	0.467733
$392$	1.52447	0.0769975
$393$	2.81999	0.142249
$394$	10.6688	0.537485
$395$	34.9188	1.75696
$396$	3.01156	0.151337
$397$	10.8285	0.543467	0.271734	−	0.962373i	$-0.412403\pi$
$397$	10.8285	0.543467	0.271734	+	0.962373i	$0.412403\pi$
$398$	−4.51932	−0.226533
$399$	8.51961	0.426514
$400$	−3.14444	−0.157222
$401$	30.2880	1.51251	0.756255	−	0.654277i	$-0.227027\pi$
$401$	30.2880	1.51251	0.756255	+	0.654277i	$0.227027\pi$
$402$	−1.86494	−0.0930148
$403$	−3.53491	−0.176086
$404$	0.345377	0.0171831
$405$	−1.99480	−0.0991223
$406$	−1.91867	−0.0952218
$407$	−14.0237	−0.695131
$408$	1.52447	0.0754727
$409$	−10.4649	−0.517458	−0.258729	−	0.965950i	$-0.583304\pi$
$409$	−10.4649	−0.517458	−0.258729	+	0.965950i	$0.583304\pi$
$410$	−9.51833	−0.470077
$411$	−16.5373	−0.815725
$412$	9.88184	0.486843
$413$	7.74328	0.381022
$414$	3.66928	0.180335
$415$	2.38577	0.117113
$416$	−4.27103	−0.209405
$417$	−17.2550	−0.844983
$418$	5.52425	0.270200
$419$	38.7874	1.89489	0.947445	−	0.319920i	$-0.103656\pi$
$419$	38.7874	1.89489	0.947445	+	0.319920i	$0.103656\pi$
$420$	3.67562	0.179352
$421$	−0.668914	−0.0326009	−0.0163004	−	0.999867i	$-0.505189\pi$
$421$	−0.668914	−0.0326009	−0.0163004	+	0.999867i	$0.505189\pi$
$422$	3.26810	0.159089
$423$	12.6134	0.613284
$424$	−5.51429	−0.267797
$425$	1.02079	0.0495154
$426$	0.408429	0.0197885
$427$	5.19629	0.251466
$428$	−6.48022	−0.313233
$429$	1.63440	0.0789098
$430$	−3.05861	−0.147499
$431$	20.7640	1.00017	0.500084	−	0.865977i	$-0.333303\pi$
$431$	20.7640	1.00017	0.500084	+	0.865977i	$0.333303\pi$
$432$	−3.08041	−0.148206
$433$	−12.3835	−0.595114	−0.297557	−	0.954704i	$-0.596172\pi$
$433$	−12.3835	−0.595114	−0.297557	+	0.954704i	$0.596172\pi$
$434$	−1.40240	−0.0673174
$435$	−9.64726	−0.462551
$436$	−13.1740	−0.630921
$437$	−78.7964	−3.76934
$438$	1.08171	0.0516860
$439$	22.8547	1.09079	0.545397	−	0.838178i	$-0.316379\pi$
$439$	22.8547	1.09079	0.545397	+	0.838178i	$0.316379\pi$
$440$	4.97025	0.236947
$441$	1.00000	0.0476190
$442$	0.396729	0.0188705
$443$	33.1451	1.57477	0.787385	−	0.616462i	$-0.211434\pi$
$443$	33.1451	1.57477	0.787385	+	0.616462i	$0.211434\pi$
$444$	15.8102	0.750317
$445$	6.44968	0.305744
$446$	−6.47299	−0.306505
$447$	−19.8449	−0.938633
$448$	4.46637	0.211016
$449$	7.29120	0.344093	0.172046	−	0.985089i	$-0.444962\pi$
$449$	7.29120	0.344093	0.172046	+	0.985089i	$0.444962\pi$
$450$	0.404975	0.0190907
$451$	19.6575	0.925634
$452$	18.8250	0.885453
$453$	−21.8292	−1.02563
$454$	1.17942	0.0553529
$455$	1.99480	0.0935175
$456$	−12.9879	−0.608215
$457$	−33.3294	−1.55908	−0.779542	−	0.626350i	$-0.784548\pi$
$457$	−33.3294	−1.55908	−0.779542	+	0.626350i	$0.784548\pi$
$458$	−1.21556	−0.0567992
$459$	1.00000	0.0466760
$460$	−33.9952	−1.58503
$461$	−13.5296	−0.630135	−0.315067	−	0.949069i	$-0.602027\pi$
$461$	−13.5296	−0.630135	−0.315067	+	0.949069i	$0.602027\pi$
$462$	0.648416	0.0301670
$463$	17.0595	0.792824	0.396412	−	0.918073i	$-0.370255\pi$
$463$	17.0595	0.792824	0.396412	+	0.918073i	$0.370255\pi$
$464$	−14.8975	−0.691600
$465$	−7.05143	−0.327002
$466$	2.73182	0.126549
$467$	28.2680	1.30809	0.654043	−	0.756457i	$-0.273071\pi$
$467$	28.2680	1.30809	0.654043	+	0.756457i	$0.273071\pi$
$468$	−1.84261	−0.0851745
$469$	4.70079	0.217062
$470$	9.98217	0.460443
$471$	7.86239	0.362280
$472$	−11.8044	−0.543343
$473$	6.31672	0.290443
$474$	−6.94473	−0.318982
$475$	−8.69669	−0.399032
$476$	−1.84261	−0.0844557
$477$	−3.61717	−0.165619
$478$	4.32323	0.197740
$479$	−32.9674	−1.50632	−0.753158	−	0.657839i	$-0.771471\pi$
$479$	−32.9674	−1.50632	−0.753158	+	0.657839i	$0.771471\pi$
$480$	−8.51985	−0.388876
$481$	8.58033	0.391229
$482$	10.5481	0.480451
$483$	−9.24882	−0.420836
$484$	15.3466	0.697571
$485$	7.53653	0.342216
$486$	0.396729	0.0179960
$487$	26.6185	1.20620	0.603099	−	0.797666i	$-0.293932\pi$
$487$	26.6185	1.20620	0.603099	+	0.797666i	$0.293932\pi$
$488$	−7.92160	−0.358594
$489$	3.15000	0.142448
$490$	0.791394	0.0357515
$491$	−12.3395	−0.556874	−0.278437	−	0.960454i	$-0.589816\pi$
$491$	−12.3395	−0.556874	−0.278437	+	0.960454i	$0.589816\pi$
$492$	−22.1616	−0.999121
$493$	4.83621	0.217812
$494$	−3.37998	−0.152072
$495$	3.26031	0.146540
$496$	−10.8890	−0.488929
$497$	−1.02949	−0.0461790
$498$	−0.474487	−0.0212623
$499$	−26.7736	−1.19855	−0.599276	−	0.800542i	$-0.704545\pi$
$499$	−26.7736	−1.19855	−0.599276	+	0.800542i	$0.704545\pi$
$500$	−22.1301	−0.989690
$501$	18.1399	0.810430
$502$	−0.275302	−0.0122873
$503$	−5.83295	−0.260078	−0.130039	−	0.991509i	$-0.541510\pi$
$503$	−5.83295	−0.260078	−0.130039	+	0.991509i	$0.541510\pi$
$504$	−1.52447	−0.0679054
$505$	0.373903	0.0166385
$506$	−5.99708	−0.266603
$507$	−1.00000	−0.0444116
$508$	14.3429	0.636361
$509$	38.4811	1.70564	0.852822	−	0.522202i	$-0.174889\pi$
$509$	38.4811	1.70564	0.852822	+	0.522202i	$0.174889\pi$
$510$	0.791394	0.0350435
$511$	−2.72657	−0.120616
$512$	−22.5485	−0.996514
$513$	−8.51961	−0.376150
$514$	−1.77552	−0.0783147
$515$	10.6980	0.471412
$516$	−7.12139	−0.313502
$517$	−20.6154	−0.906664
$518$	3.40407	0.149566
$519$	−6.14583	−0.269772
$520$	−3.04101	−0.133357
$521$	7.36455	0.322647	0.161323	−	0.986902i	$-0.448424\pi$
$521$	7.36455	0.322647	0.161323	+	0.986902i	$0.448424\pi$
$522$	1.91867	0.0839778
$523$	−12.9961	−0.568281	−0.284140	−	0.958783i	$-0.591708\pi$
$523$	−12.9961	−0.568281	−0.284140	+	0.958783i	$0.591708\pi$
$524$	5.19612	0.226994
$525$	−1.02079	−0.0445507
$526$	−4.58747	−0.200023
$527$	3.53491	0.153983
$528$	5.03464	0.219104
$529$	62.5407	2.71916
$530$	−2.86261	−0.124344
$531$	−7.74328	−0.336030
$532$	15.6983	0.680607
$533$	−12.0273	−0.520960
$534$	−1.28273	−0.0555090
$535$	−7.01546	−0.303305
$536$	−7.16623	−0.309534
$537$	−7.48188	−0.322867
$538$	1.91872	0.0827219
$539$	−1.63440	−0.0703988
$540$	−3.67562	−0.158174
$541$	11.8763	0.510603	0.255302	−	0.966861i	$-0.417825\pi$
$541$	11.8763	0.510603	0.255302	+	0.966861i	$0.417825\pi$
$542$	9.56787	0.410975
$543$	−9.97479	−0.428059
$544$	4.27103	0.183119
$545$	−14.2621	−0.610922
$546$	−0.396729	−0.0169784
$547$	−32.4663	−1.38816	−0.694080	−	0.719898i	$-0.744189\pi$
$547$	−32.4663	−1.38816	−0.694080	+	0.719898i	$0.744189\pi$
$548$	−30.4717	−1.30169
$549$	−5.19629	−0.221772
$550$	−0.661894	−0.0282232
$551$	−41.2027	−1.75529
$552$	14.0996	0.600118
$553$	17.5050	0.744387
$554$	−6.81954	−0.289734
$555$	17.1160	0.726534
$556$	−31.7942	−1.34838
$557$	−29.1775	−1.23629	−0.618145	−	0.786064i	$-0.712115\pi$
$557$	−29.1775	−1.23629	−0.618145	+	0.786064i	$0.712115\pi$
$558$	1.40240	0.0593684
$559$	−3.86484	−0.163466
$560$	6.14479	0.259665
$561$	−1.63440	−0.0690046
$562$	−0.670321	−0.0282758
$563$	−31.2101	−1.31535	−0.657675	−	0.753302i	$-0.728460\pi$
$563$	−31.2101	−1.31535	−0.657675	+	0.753302i	$0.728460\pi$
$564$	23.2415	0.978645
$565$	20.3798	0.857386
$566$	−6.90213	−0.290118
$567$	−1.00000	−0.0419961
$568$	1.56943	0.0658520
$569$	−5.91724	−0.248064	−0.124032	−	0.992278i	$-0.539582\pi$
$569$	−5.91724	−0.248064	−0.124032	+	0.992278i	$0.539582\pi$
$570$	−6.74237	−0.282407
$571$	−22.2733	−0.932108	−0.466054	−	0.884756i	$-0.654325\pi$
$571$	−22.2733	−0.932108	−0.466054	+	0.884756i	$0.654325\pi$
$572$	3.01156	0.125920
$573$	−17.0658	−0.712934
$574$	−4.77158	−0.199162
$575$	9.44107	0.393720
$576$	−4.46637	−0.186099
$577$	−40.0333	−1.66661	−0.833303	−	0.552816i	$-0.813553\pi$
$577$	−40.0333	−1.66661	−0.833303	+	0.552816i	$0.813553\pi$
$578$	−0.396729	−0.0165018
$579$	−27.2058	−1.13063
$580$	−17.7761	−0.738113
$581$	1.19600	0.0496183
$582$	−1.49888	−0.0621306
$583$	5.91193	0.244847
$584$	4.15658	0.172000
$585$	−1.99480	−0.0824747
$586$	−4.61036	−0.190452
$587$	0.262077	0.0108171	0.00540854	−	0.999985i	$-0.498278\pi$
$587$	0.262077	0.0108171	0.00540854	+	0.999985i	$0.498278\pi$
$588$	1.84261	0.0759878
$589$	−30.1161	−1.24091
$590$	−6.12798	−0.252285
$591$	26.8919	1.10618
$592$	26.4309	1.08630
$593$	22.6354	0.929523	0.464761	−	0.885436i	$-0.346140\pi$
$593$	22.6354	0.929523	0.464761	+	0.885436i	$0.346140\pi$
$594$	−0.648416	−0.0266048
$595$	−1.99480	−0.0817787
$596$	−36.5664	−1.49782
$597$	−11.3915	−0.466222
$598$	3.66928	0.150048
$599$	−20.5096	−0.838002	−0.419001	−	0.907986i	$-0.637620\pi$
$599$	−20.5096	−0.838002	−0.419001	+	0.907986i	$0.637620\pi$
$600$	1.55616	0.0635300
$601$	−14.2180	−0.579964	−0.289982	−	0.957032i	$-0.593649\pi$
$601$	−14.2180	−0.579964	−0.289982	+	0.957032i	$0.593649\pi$
$602$	−1.53330	−0.0624925
$603$	−4.70079	−0.191431
$604$	−40.2226	−1.63664
$605$	16.6141	0.675459
$606$	−0.0743626	−0.00302077
$607$	45.2946	1.83845	0.919226	−	0.393730i	$-0.128816\pi$
$607$	45.2946	1.83845	0.919226	+	0.393730i	$0.128816\pi$
$608$	−36.3875	−1.47571
$609$	−4.83621	−0.195973
$610$	−4.11231	−0.166502
$611$	12.6134	0.510283
$612$	1.84261	0.0744829
$613$	−31.3227	−1.26511	−0.632555	−	0.774515i	$-0.717994\pi$
$613$	−31.3227	−1.26511	−0.632555	+	0.774515i	$0.717994\pi$
$614$	3.83410	0.154732
$615$	−23.9920	−0.967451
$616$	2.49161	0.100390
$617$	20.4629	0.823807	0.411903	−	0.911228i	$-0.364864\pi$
$617$	20.4629	0.823807	0.411903	+	0.911228i	$0.364864\pi$
$618$	−2.12764	−0.0855864
$619$	−6.90812	−0.277661	−0.138830	−	0.990316i	$-0.544334\pi$
$619$	−6.90812	−0.277661	−0.138830	+	0.990316i	$0.544334\pi$
$620$	−12.9930	−0.521812
$621$	9.24882	0.371143
$622$	−6.93390	−0.278024
$623$	3.23325	0.129538
$624$	−3.08041	−0.123315
$625$	−18.8541	−0.754163
$626$	9.95437	0.397857
$627$	13.9245	0.556091
$628$	14.4873	0.578105
$629$	−8.58033	−0.342120
$630$	−0.791394	−0.0315299
$631$	−13.9942	−0.557100	−0.278550	−	0.960422i	$-0.589854\pi$
$631$	−13.9942	−0.557100	−0.278550	+	0.960422i	$0.589854\pi$
$632$	−26.6858	−1.06151
$633$	8.23761	0.327416
$634$	6.13726	0.243742
$635$	15.5275	0.616190
$636$	−6.66503	−0.264285
$637$	1.00000	0.0396214
$638$	−3.13588	−0.124151
$639$	1.02949	0.0407261
$640$	−20.5744	−0.813273
$641$	−32.6691	−1.29035	−0.645175	−	0.764034i	$-0.723216\pi$
$641$	−32.6691	−1.29035	−0.645175	+	0.764034i	$0.723216\pi$
$642$	1.39525	0.0550660
$643$	−10.7763	−0.424975	−0.212488	−	0.977164i	$-0.568157\pi$
$643$	−10.7763	−0.424975	−0.212488	+	0.977164i	$0.568157\pi$
$644$	−17.0419	−0.671546
$645$	−7.70958	−0.303564
$646$	3.37998	0.132983
$647$	15.7081	0.617549	0.308775	−	0.951135i	$-0.400081\pi$
$647$	15.7081	0.617549	0.308775	+	0.951135i	$0.400081\pi$
$648$	1.52447	0.0598870
$649$	12.6557	0.496778
$650$	0.404975	0.0158844
$651$	−3.53491	−0.138544
$652$	5.80421	0.227310
$653$	38.8809	1.52153	0.760763	−	0.649029i	$-0.224825\pi$
$653$	38.8809	1.52153	0.760763	+	0.649029i	$0.224825\pi$
$654$	2.83648	0.110915
$655$	5.62530	0.219799
$656$	−37.0490	−1.44652
$657$	2.72657	0.106373
$658$	5.00410	0.195080
$659$	6.87119	0.267663	0.133832	−	0.991004i	$-0.457272\pi$
$659$	6.87119	0.267663	0.133832	+	0.991004i	$0.457272\pi$
$660$	6.00746	0.233840
$661$	36.8122	1.43183	0.715914	−	0.698189i	$-0.246010\pi$
$661$	36.8122	1.43183	0.715914	+	0.698189i	$0.246010\pi$
$662$	−11.3545	−0.441304
$663$	1.00000	0.0388368
$664$	−1.82327	−0.0707564
$665$	16.9949	0.659034
$666$	−3.40407	−0.131905
$667$	44.7293	1.73193
$668$	33.4247	1.29324
$669$	−16.3159	−0.630809
$670$	−3.72018	−0.143723
$671$	8.49283	0.327862
$672$	−4.27103	−0.164759
$673$	41.9603	1.61745	0.808726	−	0.588185i	$-0.200157\pi$
$673$	41.9603	1.61745	0.808726	+	0.588185i	$0.200157\pi$
$674$	−10.3398	−0.398273
$675$	1.02079	0.0392901
$676$	−1.84261	−0.0708695
$677$	−10.5939	−0.407156	−0.203578	−	0.979059i	$-0.565257\pi$
$677$	−10.5939	−0.407156	−0.203578	+	0.979059i	$0.565257\pi$
$678$	−4.05318	−0.155661
$679$	3.77810	0.144990
$680$	3.04101	0.116618
$681$	2.97286	0.113920
$682$	−2.29209	−0.0877687
$683$	49.5038	1.89421	0.947106	−	0.320921i	$-0.103992\pi$
$683$	49.5038	1.89421	0.947106	+	0.320921i	$0.103992\pi$
$684$	−15.6983	−0.600239
$685$	−32.9886	−1.26043
$686$	0.396729	0.0151472
$687$	−3.06395	−0.116897
$688$	−11.9053	−0.453885
$689$	−3.61717	−0.137803
$690$	7.31946	0.278647
$691$	34.8849	1.32708	0.663541	−	0.748139i	$-0.269053\pi$
$691$	34.8849	1.32708	0.663541	+	0.748139i	$0.269053\pi$
$692$	−11.3243	−0.430487
$693$	1.63440	0.0620859
$694$	1.16736	0.0443125
$695$	−34.4203	−1.30564
$696$	7.37268	0.279461
$697$	12.0273	0.455566
$698$	3.62514	0.137214
$699$	6.88586	0.260447
$700$	−1.88091	−0.0710916
$701$	−19.9254	−0.752572	−0.376286	−	0.926504i	$-0.622799\pi$
$701$	−19.9254	−0.752572	−0.376286	+	0.926504i	$0.622799\pi$
$702$	0.396729	0.0149736
$703$	73.1011	2.75706
$704$	7.29986	0.275124
$705$	25.1612	0.947624
$706$	10.9438	0.411874
$707$	0.187439	0.00704938
$708$	−14.2678	−0.536217
$709$	8.80072	0.330518	0.165259	−	0.986250i	$-0.447154\pi$
$709$	8.80072	0.330518	0.165259	+	0.986250i	$0.447154\pi$
$710$	0.814734	0.0305764
$711$	−17.5050	−0.656487
$712$	−4.92901	−0.184722
$713$	32.6938	1.22439
$714$	0.396729	0.0148472
$715$	3.26031	0.121929
$716$	−13.7862	−0.515213
$717$	10.8972	0.406963
$718$	−5.81054	−0.216847
$719$	37.4819	1.39784	0.698919	−	0.715200i	$-0.253665\pi$
$719$	37.4819	1.39784	0.698919	+	0.715200i	$0.253665\pi$
$720$	−6.14479	−0.229003
$721$	5.36297	0.199727
$722$	−21.2582	−0.791149
$723$	26.5876	0.988802
$724$	−18.3796	−0.683073
$725$	4.93674	0.183346
$726$	−3.30425	−0.122632
$727$	−14.3807	−0.533350	−0.266675	−	0.963787i	$-0.585925\pi$
$727$	−14.3807	−0.533350	−0.266675	+	0.963787i	$0.585925\pi$
$728$	−1.52447	−0.0565007
$729$	1.00000	0.0370370
$730$	2.15779	0.0798633
$731$	3.86484	0.142946
$732$	−9.57471	−0.353891
$733$	26.6035	0.982624	0.491312	−	0.870984i	$-0.336517\pi$
$733$	26.6035	0.982624	0.491312	+	0.870984i	$0.336517\pi$
$734$	−0.226660	−0.00836617
$735$	1.99480	0.0735792
$736$	39.5020	1.45606
$737$	7.68300	0.283007
$738$	4.77158	0.175644
$739$	−15.4087	−0.566818	−0.283409	−	0.958999i	$-0.591465\pi$
$739$	−15.4087	−0.566818	−0.283409	+	0.958999i	$0.591465\pi$
$740$	31.5381	1.15936
$741$	−8.51961	−0.312976
$742$	−1.43504	−0.0526819
$743$	1.48476	0.0544706	0.0272353	−	0.999629i	$-0.491330\pi$
$743$	1.48476	0.0544706	0.0272353	+	0.999629i	$0.491330\pi$
$744$	5.38888	0.197566
$745$	−39.5866	−1.45034
$746$	−4.11871	−0.150797
$747$	−1.19600	−0.0437593
$748$	−3.01156	−0.110114
$749$	−3.51688	−0.128504
$750$	4.76481	0.173986
$751$	−3.94847	−0.144082	−0.0720408	−	0.997402i	$-0.522951\pi$
$751$	−3.94847	−0.144082	−0.0720408	+	0.997402i	$0.522951\pi$
$752$	38.8544	1.41688
$753$	−0.693930	−0.0252882
$754$	1.91867	0.0698737
$755$	−43.5448	−1.58476
$756$	−1.84261	−0.0670149
$757$	15.2757	0.555205	0.277602	−	0.960696i	$-0.410460\pi$
$757$	15.2757	0.555205	0.277602	+	0.960696i	$0.410460\pi$
$758$	−12.8368	−0.466254
$759$	−15.1163	−0.548688
$760$	−25.9083	−0.939791
$761$	31.1838	1.13041	0.565205	−	0.824950i	$-0.308797\pi$
$761$	31.1838	1.13041	0.565205	+	0.824950i	$0.308797\pi$
$762$	−3.08814	−0.111872
$763$	−7.14966	−0.258835
$764$	−31.4456	−1.13766
$765$	1.99480	0.0721220
$766$	12.4643	0.450355
$767$	−7.74328	−0.279594
$768$	−4.84088	−0.174680
$769$	22.4607	0.809952	0.404976	−	0.914327i	$-0.367280\pi$
$769$	22.4607	0.809952	0.404976	+	0.914327i	$0.367280\pi$
$770$	1.29346	0.0466130
$771$	−4.47539	−0.161177
$772$	−50.1295	−1.80420
$773$	−11.4303	−0.411120	−0.205560	−	0.978644i	$-0.565902\pi$
$773$	−11.4303	−0.411120	−0.205560	+	0.978644i	$0.565902\pi$
$774$	1.53330	0.0551132
$775$	3.60839	0.129617
$776$	−5.75961	−0.206758
$777$	8.58033	0.307818
$778$	6.11465	0.219221
$779$	−102.468	−3.67129
$780$	−3.67562	−0.131608
$781$	−1.68261	−0.0602084
$782$	−3.66928	−0.131213
$783$	4.83621	0.172832
$784$	3.08041	0.110015
$785$	15.6839	0.559781
$786$	−1.11877	−0.0399052
$787$	43.8048	1.56147	0.780737	−	0.624860i	$-0.214844\pi$
$787$	43.8048	1.56147	0.780737	+	0.624860i	$0.214844\pi$
$788$	49.5511	1.76518
$789$	−11.5632	−0.411662
$790$	−13.8533	−0.492879
$791$	10.2165	0.363257
$792$	−2.49161	−0.0885354
$793$	−5.19629	−0.184526
$794$	−4.29598	−0.152459
$795$	−7.21553	−0.255908
$796$	−20.9900	−0.743970
$797$	4.78896	0.169634	0.0848168	−	0.996397i	$-0.472969\pi$
$797$	4.78896	0.169634	0.0848168	+	0.996397i	$0.472969\pi$
$798$	−3.37998	−0.119650
$799$	−12.6134	−0.446230
$800$	4.35981	0.154143
$801$	−3.23325	−0.114241
$802$	−12.0161	−0.424304
$803$	−4.45631	−0.157260
$804$	−8.66171	−0.305475
$805$	−18.4495	−0.650260
$806$	1.40240	0.0493975
$807$	4.83635	0.170247
$808$	−0.285746	−0.0100525
$809$	−20.5506	−0.722520	−0.361260	−	0.932465i	$-0.617653\pi$
$809$	−20.5506	−0.722520	−0.361260	+	0.932465i	$0.617653\pi$
$810$	0.791394	0.0278067
$811$	−21.5955	−0.758319	−0.379159	−	0.925331i	$-0.623787\pi$
$811$	−21.5955	−0.758319	−0.379159	+	0.925331i	$0.623787\pi$
$812$	−8.91124	−0.312723
$813$	24.1169	0.845816
$814$	5.56362	0.195005
$815$	6.28361	0.220105
$816$	3.08041	0.107836
$817$	−32.9270	−1.15197
$818$	4.15174	0.145162
$819$	−1.00000	−0.0349428
$820$	−44.2078	−1.54380
$821$	35.6162	1.24301	0.621506	−	0.783409i	$-0.286521\pi$
$821$	35.6162	1.24301	0.621506	+	0.783409i	$0.286521\pi$
$822$	6.56083	0.228835
$823$	6.50325	0.226689	0.113344	−	0.993556i	$-0.463844\pi$
$823$	6.50325	0.226689	0.113344	+	0.993556i	$0.463844\pi$
$824$	−8.17570	−0.284814
$825$	−1.66838	−0.0580854
$826$	−3.07198	−0.106888
$827$	−38.9667	−1.35501	−0.677503	−	0.735520i	$-0.736938\pi$
$827$	−38.9667	−1.35501	−0.677503	+	0.735520i	$0.736938\pi$
$828$	17.0419	0.592248
$829$	−4.71224	−0.163663	−0.0818314	−	0.996646i	$-0.526077\pi$
$829$	−4.71224	−0.163663	−0.0818314	+	0.996646i	$0.526077\pi$
$830$	−0.946505	−0.0328537
$831$	−17.1894	−0.596294
$832$	−4.46637	−0.154844
$833$	−1.00000	−0.0346479
$834$	6.84558	0.237043
$835$	36.1854	1.25225
$836$	25.6574	0.887378
$837$	3.53491	0.122184
$838$	−15.3881	−0.531573
$839$	46.8616	1.61784	0.808920	−	0.587918i	$-0.200052\pi$
$839$	46.8616	1.61784	0.808920	+	0.587918i	$0.200052\pi$
$840$	−3.04101	−0.104925
$841$	−5.61103	−0.193484
$842$	0.265378	0.00914552
$843$	−1.68962	−0.0581936
$844$	15.1787	0.522471
$845$	−1.99480	−0.0686231
$846$	−5.00410	−0.172045
$847$	8.32872	0.286178
$848$	−11.1424	−0.382631
$849$	−17.3976	−0.597084
$850$	−0.404975	−0.0138905
$851$	−79.3580	−2.72036
$852$	1.89695	0.0649884
$853$	7.57680	0.259425	0.129712	−	0.991552i	$-0.458595\pi$
$853$	7.57680	0.259425	0.129712	+	0.991552i	$0.458595\pi$
$854$	−2.06152	−0.0705437
$855$	−16.9949	−0.581213
$856$	5.36139	0.183248
$857$	−47.9143	−1.63672	−0.818361	−	0.574705i	$-0.805117\pi$
$857$	−47.9143	−1.63672	−0.818361	+	0.574705i	$0.805117\pi$
$858$	−0.648416	−0.0221366
$859$	1.77779	0.0606573	0.0303286	−	0.999540i	$-0.490345\pi$
$859$	1.77779	0.0606573	0.0303286	+	0.999540i	$0.490345\pi$
$860$	−14.2057	−0.484411
$861$	−12.0273	−0.409889
$862$	−8.23768	−0.280577
$863$	−9.34642	−0.318156	−0.159078	−	0.987266i	$-0.550852\pi$
$863$	−9.34642	−0.318156	−0.159078	+	0.987266i	$0.550852\pi$
$864$	4.27103	0.145304
$865$	−12.2597	−0.416841
$866$	4.91290	0.166947
$867$	−1.00000	−0.0339618
$868$	−6.51345	−0.221081
$869$	28.6102	0.970534
$870$	3.82735	0.129759
$871$	−4.70079	−0.159280
$872$	10.8995	0.369103
$873$	−3.77810	−0.127869
$874$	31.2608	1.05741
$875$	−12.0102	−0.406020
$876$	5.02399	0.169745
$877$	3.69608	0.124808	0.0624039	−	0.998051i	$-0.480123\pi$
$877$	3.69608	0.124808	0.0624039	+	0.998051i	$0.480123\pi$
$878$	−9.06711	−0.306000
$879$	−11.6209	−0.391964
$880$	10.0431	0.338552
$881$	−19.0882	−0.643099	−0.321550	−	0.946893i	$-0.604204\pi$
$881$	−19.0882	−0.643099	−0.321550	+	0.946893i	$0.604204\pi$
$882$	−0.396729	−0.0133586
$883$	−25.1865	−0.847595	−0.423797	−	0.905757i	$-0.639303\pi$
$883$	−25.1865	−0.847595	−0.423797	+	0.905757i	$0.639303\pi$
$884$	1.84261	0.0619735
$885$	−15.4463	−0.519221
$886$	−13.1496	−0.441770
$887$	−3.37522	−0.113329	−0.0566644	−	0.998393i	$-0.518047\pi$
$887$	−3.37522	−0.113329	−0.0566644	+	0.998393i	$0.518047\pi$
$888$	−13.0805	−0.438952
$889$	7.78400	0.261067
$890$	−2.55878	−0.0857704
$891$	−1.63440	−0.0547546
$892$	−30.0638	−1.00661
$893$	107.461	3.59605
$894$	7.87306	0.263315
$895$	−14.9248	−0.498882
$896$	−10.3140	−0.344567
$897$	9.24882	0.308809
$898$	−2.89263	−0.0965283
$899$	17.0956	0.570170
$900$	1.88091	0.0626969
$901$	3.61717	0.120506
$902$	−7.79869	−0.259668
$903$	−3.86484	−0.128614
$904$	−15.5748	−0.518009
$905$	−19.8977	−0.661421
$906$	8.66028	0.287719
$907$	−17.9664	−0.596566	−0.298283	−	0.954477i	$-0.596414\pi$
$907$	−17.9664	−0.596566	−0.298283	+	0.954477i	$0.596414\pi$
$908$	5.47781	0.181788
$909$	−0.187439	−0.00621697
$910$	−0.791394	−0.0262345
$911$	49.3266	1.63426	0.817131	−	0.576452i	$-0.195563\pi$
$911$	49.3266	1.63426	0.817131	+	0.576452i	$0.195563\pi$
$912$	−26.2439	−0.869022
$913$	1.95474	0.0646926
$914$	13.2228	0.437370
$915$	−10.3655	−0.342674
$916$	−5.64564	−0.186537
$917$	2.81999	0.0931241
$918$	−0.396729	−0.0130940
$919$	−16.6755	−0.550074	−0.275037	−	0.961434i	$-0.588690\pi$
$919$	−16.6755	−0.550074	−0.275037	+	0.961434i	$0.588690\pi$
$920$	28.1258	0.927280
$921$	9.66428	0.318449
$922$	5.36757	0.176772
$923$	1.02949	0.0338861
$924$	3.01156	0.0990732
$925$	−8.75868	−0.287984
$926$	−6.76802	−0.222411
$927$	−5.36297	−0.176143
$928$	20.6556	0.678055
$929$	−15.9056	−0.521847	−0.260923	−	0.965360i	$-0.584027\pi$
$929$	−15.9056	−0.521847	−0.260923	+	0.965360i	$0.584027\pi$
$930$	2.79751	0.0917338
$931$	8.51961	0.279219
$932$	12.6879	0.415607
$933$	−17.4777	−0.572193
$934$	−11.2147	−0.366957
$935$	−3.26031	−0.106623
$936$	1.52447	0.0498290
$937$	−10.9484	−0.357668	−0.178834	−	0.983879i	$-0.557233\pi$
$937$	−10.9484	−0.357668	−0.178834	+	0.983879i	$0.557233\pi$
$938$	−1.86494	−0.0608925
$939$	25.0911	0.818817
$940$	46.3621	1.51217
$941$	9.92911	0.323680	0.161840	−	0.986817i	$-0.448257\pi$
$941$	9.92911	0.323680	0.161840	+	0.986817i	$0.448257\pi$
$942$	−3.11924	−0.101630
$943$	111.238	3.62242
$944$	−23.8525	−0.776332
$945$	−1.99480	−0.0648907
$946$	−2.50603	−0.0814780
$947$	−26.6304	−0.865371	−0.432686	−	0.901545i	$-0.642434\pi$
$947$	−26.6304	−0.865371	−0.432686	+	0.901545i	$0.642434\pi$
$948$	−32.2547	−1.04759
$949$	2.72657	0.0885081
$950$	3.45023	0.111940
$951$	15.4696	0.501638
$952$	1.52447	0.0494085
$953$	43.9568	1.42390	0.711950	−	0.702230i	$-0.247812\pi$
$953$	43.9568	1.42390	0.711950	+	0.702230i	$0.247812\pi$
$954$	1.43504	0.0464611
$955$	−34.0428	−1.10160
$956$	20.0792	0.649409
$957$	−7.90433	−0.255511
$958$	13.0791	0.422567
$959$	−16.5373	−0.534017
$960$	−8.90951	−0.287553
$961$	−18.5044	−0.596916
$962$	−3.40407	−0.109752
$963$	3.51688	0.113330
$964$	48.9904	1.57787
$965$	−54.2700	−1.74701
$966$	3.66928	0.118057
$967$	19.6757	0.632729	0.316365	−	0.948638i	$-0.397538\pi$
$967$	19.6757	0.632729	0.316365	+	0.948638i	$0.397538\pi$
$968$	−12.6969	−0.408094
$969$	8.51961	0.273689
$970$	−2.98996	−0.0960019
$971$	21.8575	0.701439	0.350719	−	0.936481i	$-0.385937\pi$
$971$	21.8575	0.701439	0.350719	+	0.936481i	$0.385937\pi$
$972$	1.84261	0.0591016
$973$	−17.2550	−0.553171
$974$	−10.5603	−0.338374
$975$	1.02079	0.0326913
$976$	−16.0067	−0.512362
$977$	−25.5226	−0.816539	−0.408270	−	0.912861i	$-0.633868\pi$
$977$	−25.5226	−0.816539	−0.408270	+	0.912861i	$0.633868\pi$
$978$	−1.24970	−0.0399609
$979$	5.28444	0.168892
$980$	3.67562	0.117414
$981$	7.14966	0.228271
$982$	4.89544	0.156220
$983$	−9.91921	−0.316374	−0.158187	−	0.987409i	$-0.550565\pi$
$983$	−9.91921	−0.316374	−0.158187	+	0.987409i	$0.550565\pi$
$984$	18.3353	0.584508
$985$	53.6438	1.70923
$986$	−1.91867	−0.0611028
$987$	12.6134	0.401489
$988$	−15.6983	−0.499429
$989$	35.7453	1.13663
$990$	−1.29346	−0.0411088
$991$	25.1115	0.797692	0.398846	−	0.917018i	$-0.369411\pi$
$991$	25.1115	0.797692	0.398846	+	0.917018i	$0.369411\pi$
$992$	15.0977	0.479353
$993$	−28.6202	−0.908235
$994$	0.408429	0.0129546
$995$	−22.7237	−0.720388
$996$	−2.20375	−0.0698285
$997$	−47.3233	−1.49874	−0.749372	−	0.662149i	$-0.769645\pi$
$997$	−47.3233	−1.49874	−0.749372	+	0.662149i	$0.769645\pi$
$998$	10.6219	0.336230
$999$	−8.58033	−0.271470

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4641.2.a.ba.1.8	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4641.2.a.ba.1.8	✓	17	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:	\( N \)	\(=\)	\( 4641 = 3 \cdot 7 \cdot 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4641.a (trivial)

\(f(q)\)	\(=\)	\(q-0.396729 q^{2} -1.00000 q^{3} -1.84261 q^{4} -1.99480 q^{5} +0.396729 q^{6} -1.00000 q^{7} +1.52447 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.396729 q^{2} -1.00000 q^{3} -1.84261 q^{4} -1.99480 q^{5} +0.396729 q^{6} -1.00000 q^{7} +1.52447 q^{8} +1.00000 q^{9} +0.791394 q^{10} -1.63440 q^{11} +1.84261 q^{12} +1.00000 q^{13} +0.396729 q^{14} +1.99480 q^{15} +3.08041 q^{16} -1.00000 q^{17} -0.396729 q^{18} +8.51961 q^{19} +3.67562 q^{20} +1.00000 q^{21} +0.648416 q^{22} -9.24882 q^{23} -1.52447 q^{24} -1.02079 q^{25} -0.396729 q^{26} -1.00000 q^{27} +1.84261 q^{28} -4.83621 q^{29} -0.791394 q^{30} -3.53491 q^{31} -4.27103 q^{32} +1.63440 q^{33} +0.396729 q^{34} +1.99480 q^{35} -1.84261 q^{36} +8.58033 q^{37} -3.37998 q^{38} -1.00000 q^{39} -3.04101 q^{40} -12.0273 q^{41} -0.396729 q^{42} -3.86484 q^{43} +3.01156 q^{44} -1.99480 q^{45} +3.66928 q^{46} +12.6134 q^{47} -3.08041 q^{48} +1.00000 q^{49} +0.404975 q^{50} +1.00000 q^{51} -1.84261 q^{52} -3.61717 q^{53} +0.396729 q^{54} +3.26031 q^{55} -1.52447 q^{56} -8.51961 q^{57} +1.91867 q^{58} -7.74328 q^{59} -3.67562 q^{60} -5.19629 q^{61} +1.40240 q^{62} -1.00000 q^{63} -4.46637 q^{64} -1.99480 q^{65} -0.648416 q^{66} -4.70079 q^{67} +1.84261 q^{68} +9.24882 q^{69} -0.791394 q^{70} +1.02949 q^{71} +1.52447 q^{72} +2.72657 q^{73} -3.40407 q^{74} +1.02079 q^{75} -15.6983 q^{76} +1.63440 q^{77} +0.396729 q^{78} -17.5050 q^{79} -6.14479 q^{80} +1.00000 q^{81} +4.77158 q^{82} -1.19600 q^{83} -1.84261 q^{84} +1.99480 q^{85} +1.53330 q^{86} +4.83621 q^{87} -2.49161 q^{88} -3.23325 q^{89} +0.791394 q^{90} -1.00000 q^{91} +17.0419 q^{92} +3.53491 q^{93} -5.00410 q^{94} -16.9949 q^{95} +4.27103 q^{96} -3.77810 q^{97} -0.396729 q^{98} -1.63440 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + q^{2} - 17 q^{3} + 25 q^{4} - 4 q^{5} - q^{6} - 17 q^{7} + 6 q^{8} + 17 q^{9}+O(q^{10}) \) 17 * q + q^2 - 17 * q^3 + 25 * q^4 - 4 * q^5 - q^6 - 17 * q^7 + 6 * q^8 + 17 * q^9	\( 17 q + q^{2} - 17 q^{3} + 25 q^{4} - 4 q^{5} - q^{6} - 17 q^{7} + 6 q^{8} + 17 q^{9} - q^{10} + 4 q^{11} - 25 q^{12} + 17 q^{13} - q^{14} + 4 q^{15} + 53 q^{16} - 17 q^{17} + q^{18} + 13 q^{19} - 5 q^{20} + 17 q^{21} + 4 q^{22} + 8 q^{23} - 6 q^{24} + 37 q^{25} + q^{26} - 17 q^{27} - 25 q^{28} - 3 q^{29} + q^{30} + 10 q^{31} + 18 q^{32} - 4 q^{33} - q^{34} + 4 q^{35} + 25 q^{36} - 25 q^{38} - 17 q^{39} - 12 q^{41} + q^{42} + 29 q^{43} + 12 q^{44} - 4 q^{45} + 19 q^{46} - 4 q^{47} - 53 q^{48} + 17 q^{49} + 9 q^{50} + 17 q^{51} + 25 q^{52} - 8 q^{53} - q^{54} + 27 q^{55} - 6 q^{56} - 13 q^{57} + 2 q^{58} + 25 q^{59} + 5 q^{60} - 5 q^{61} - 37 q^{62} - 17 q^{63} + 94 q^{64} - 4 q^{65} - 4 q^{66} + 15 q^{67} - 25 q^{68} - 8 q^{69} + q^{70} + 32 q^{71} + 6 q^{72} - 15 q^{73} + 16 q^{74} - 37 q^{75} + 3 q^{76} - 4 q^{77} - q^{78} + 27 q^{79} + 41 q^{80} + 17 q^{81} - 8 q^{82} - 24 q^{83} + 25 q^{84} + 4 q^{85} + 53 q^{86} + 3 q^{87} - 9 q^{88} - 8 q^{89} - q^{90} - 17 q^{91} + 14 q^{92} - 10 q^{93} + 51 q^{94} - 9 q^{95} - 18 q^{96} - 22 q^{97} + q^{98} + 4 q^{99}+O(q^{100}) \) 17 * q + q^2 - 17 * q^3 + 25 * q^4 - 4 * q^5 - q^6 - 17 * q^7 + 6 * q^8 + 17 * q^9 - q^10 + 4 * q^11 - 25 * q^12 + 17 * q^13 - q^14 + 4 * q^15 + 53 * q^16 - 17 * q^17 + q^18 + 13 * q^19 - 5 * q^20 + 17 * q^21 + 4 * q^22 + 8 * q^23 - 6 * q^24 + 37 * q^25 + q^26 - 17 * q^27 - 25 * q^28 - 3 * q^29 + q^30 + 10 * q^31 + 18 * q^32 - 4 * q^33 - q^34 + 4 * q^35 + 25 * q^36 - 25 * q^38 - 17 * q^39 - 12 * q^41 + q^42 + 29 * q^43 + 12 * q^44 - 4 * q^45 + 19 * q^46 - 4 * q^47 - 53 * q^48 + 17 * q^49 + 9 * q^50 + 17 * q^51 + 25 * q^52 - 8 * q^53 - q^54 + 27 * q^55 - 6 * q^56 - 13 * q^57 + 2 * q^58 + 25 * q^59 + 5 * q^60 - 5 * q^61 - 37 * q^62 - 17 * q^63 + 94 * q^64 - 4 * q^65 - 4 * q^66 + 15 * q^67 - 25 * q^68 - 8 * q^69 + q^70 + 32 * q^71 + 6 * q^72 - 15 * q^73 + 16 * q^74 - 37 * q^75 + 3 * q^76 - 4 * q^77 - q^78 + 27 * q^79 + 41 * q^80 + 17 * q^81 - 8 * q^82 - 24 * q^83 + 25 * q^84 + 4 * q^85 + 53 * q^86 + 3 * q^87 - 9 * q^88 - 8 * q^89 - q^90 - 17 * q^91 + 14 * q^92 - 10 * q^93 + 51 * q^94 - 9 * q^95 - 18 * q^96 - 22 * q^97 + q^98 + 4 * q^99

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