LMFDB - Embedded newform 731.2.a.d.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(1,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("731.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.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:	$5.83706438776$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 9x^{6} + 9x^{5} + 21x^{4} - 21x^{3} - 8x^{2} + 7x - 1 $ x^8 - x^7 - 9x^6 + 9x^5 + 21x^4 - 21x^3 - 8x^2 + 7x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$0.298156$ of defining polynomial
Character	$\chi$	$=$	731.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.298156 q^{2} +0.0958345 q^{3} -1.91110 q^{4} +0.959960 q^{5} +0.0285736 q^{6} +1.32998 q^{7} -1.16612 q^{8} -2.99082 q^{9} +O(q^{10})$	\(q+0.298156 q^{2} +0.0958345 q^{3} -1.91110 q^{4} +0.959960 q^{5} +0.0285736 q^{6} +1.32998 q^{7} -1.16612 q^{8} -2.99082 q^{9} +0.286218 q^{10} -2.70096 q^{11} -0.183150 q^{12} -2.46427 q^{13} +0.396542 q^{14} +0.0919973 q^{15} +3.47452 q^{16} +1.00000 q^{17} -0.891729 q^{18} -2.75255 q^{19} -1.83458 q^{20} +0.127458 q^{21} -0.805308 q^{22} -1.10970 q^{23} -0.111754 q^{24} -4.07848 q^{25} -0.734738 q^{26} -0.574127 q^{27} -2.54173 q^{28} -7.14525 q^{29} +0.0274295 q^{30} -3.87150 q^{31} +3.36819 q^{32} -0.258845 q^{33} +0.298156 q^{34} +1.27673 q^{35} +5.71576 q^{36} +2.00755 q^{37} -0.820688 q^{38} -0.236162 q^{39} -1.11943 q^{40} +8.57961 q^{41} +0.0380024 q^{42} +1.00000 q^{43} +5.16182 q^{44} -2.87106 q^{45} -0.330864 q^{46} -10.6131 q^{47} +0.332979 q^{48} -5.23115 q^{49} -1.21602 q^{50} +0.0958345 q^{51} +4.70948 q^{52} -6.91942 q^{53} -0.171179 q^{54} -2.59282 q^{55} -1.55092 q^{56} -0.263789 q^{57} -2.13040 q^{58} +0.411022 q^{59} -0.175816 q^{60} +3.33157 q^{61} -1.15431 q^{62} -3.97773 q^{63} -5.94480 q^{64} -2.36560 q^{65} -0.0771763 q^{66} -10.1773 q^{67} -1.91110 q^{68} -0.106348 q^{69} +0.380664 q^{70} +6.68091 q^{71} +3.48765 q^{72} -3.67968 q^{73} +0.598564 q^{74} -0.390859 q^{75} +5.26040 q^{76} -3.59223 q^{77} -0.0704132 q^{78} +10.7249 q^{79} +3.33540 q^{80} +8.91743 q^{81} +2.55806 q^{82} +5.23738 q^{83} -0.243586 q^{84} +0.959960 q^{85} +0.298156 q^{86} -0.684761 q^{87} +3.14964 q^{88} -8.72756 q^{89} -0.856024 q^{90} -3.27744 q^{91} +2.12075 q^{92} -0.371023 q^{93} -3.16435 q^{94} -2.64233 q^{95} +0.322788 q^{96} +1.38021 q^{97} -1.55970 q^{98} +8.07808 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} - 3 q^{3} + 3 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} - 3 q^{8} + 5 q^{9}+O(q^{10}) $ 8 * q + q^2 - 3 * q^3 + 3 * q^4 - 7 * q^5 - q^6 - 5 * q^7 - 3 * q^8 + 5 * q^9	\( 8 q + q^{2} - 3 q^{3} + 3 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} - 3 q^{8} + 5 q^{9} - 12 q^{10} - 4 q^{11} - 13 q^{12} - 12 q^{13} + q^{14} - 9 q^{15} - 3 q^{16} + 8 q^{17} + 5 q^{18} - 5 q^{20} - 20 q^{21} - 14 q^{22} - 9 q^{23} - q^{24} - 7 q^{25} - 17 q^{26} - 12 q^{27} + q^{28} - 27 q^{29} + 10 q^{30} - 12 q^{31} + 5 q^{32} + 10 q^{33} + q^{34} + 15 q^{35} - 4 q^{36} - 24 q^{37} - q^{38} + 3 q^{39} - 9 q^{40} - 8 q^{41} - 9 q^{42} + 8 q^{43} - 16 q^{44} + 10 q^{45} - 14 q^{46} + 15 q^{47} + 10 q^{48} - 7 q^{49} + 21 q^{50} - 3 q^{51} + q^{52} - 23 q^{53} - 19 q^{54} - 14 q^{55} - 20 q^{56} - 13 q^{57} - 7 q^{58} + 16 q^{59} - 3 q^{60} - 34 q^{61} + 15 q^{62} + 9 q^{63} - 25 q^{64} + 10 q^{65} + 15 q^{66} + 3 q^{68} - 19 q^{69} + 11 q^{70} - 3 q^{71} - 19 q^{72} - 3 q^{73} - 4 q^{74} + 27 q^{75} + 13 q^{76} - 3 q^{77} + 4 q^{78} - 24 q^{79} + 20 q^{80} - 8 q^{81} + 33 q^{82} - 8 q^{83} + 17 q^{84} - 7 q^{85} + q^{86} + 48 q^{87} + 16 q^{88} + 23 q^{89} + 11 q^{90} - 16 q^{91} + 49 q^{92} + 17 q^{93} - 11 q^{94} + 3 q^{95} + 37 q^{96} - 10 q^{97} + 29 q^{98} - 15 q^{99}+O(q^{100}) \) 8 * q + q^2 - 3 * q^3 + 3 * q^4 - 7 * q^5 - q^6 - 5 * q^7 - 3 * q^8 + 5 * q^9 - 12 * q^10 - 4 * q^11 - 13 * q^12 - 12 * q^13 + q^14 - 9 * q^15 - 3 * q^16 + 8 * q^17 + 5 * q^18 - 5 * q^20 - 20 * q^21 - 14 * q^22 - 9 * q^23 - q^24 - 7 * q^25 - 17 * q^26 - 12 * q^27 + q^28 - 27 * q^29 + 10 * q^30 - 12 * q^31 + 5 * q^32 + 10 * q^33 + q^34 + 15 * q^35 - 4 * q^36 - 24 * q^37 - q^38 + 3 * q^39 - 9 * q^40 - 8 * q^41 - 9 * q^42 + 8 * q^43 - 16 * q^44 + 10 * q^45 - 14 * q^46 + 15 * q^47 + 10 * q^48 - 7 * q^49 + 21 * q^50 - 3 * q^51 + q^52 - 23 * q^53 - 19 * q^54 - 14 * q^55 - 20 * q^56 - 13 * q^57 - 7 * q^58 + 16 * q^59 - 3 * q^60 - 34 * q^61 + 15 * q^62 + 9 * q^63 - 25 * q^64 + 10 * q^65 + 15 * q^66 + 3 * q^68 - 19 * q^69 + 11 * q^70 - 3 * q^71 - 19 * q^72 - 3 * q^73 - 4 * q^74 + 27 * q^75 + 13 * q^76 - 3 * q^77 + 4 * q^78 - 24 * q^79 + 20 * q^80 - 8 * q^81 + 33 * q^82 - 8 * q^83 + 17 * q^84 - 7 * q^85 + q^86 + 48 * q^87 + 16 * q^88 + 23 * q^89 + 11 * q^90 - 16 * q^91 + 49 * q^92 + 17 * q^93 - 11 * q^94 + 3 * q^95 + 37 * q^96 - 10 * q^97 + 29 * q^98 - 15 * 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 $

$2$	0.298156	0.210828	0.105414	−	0.994428i	$-0.466383\pi$
$2$	0.298156	0.210828	0.105414	+	0.994428i	$0.466383\pi$
$3$	0.0958345	0.0553301	0.0276650	−	0.999617i	$-0.491193\pi$
$3$	0.0958345	0.0553301	0.0276650	+	0.999617i	$0.491193\pi$
$4$	−1.91110	−0.955552
$5$	0.959960	0.429307	0.214654	−	0.976690i	$-0.431138\pi$
$5$	0.959960	0.429307	0.214654	+	0.976690i	$0.431138\pi$
$6$	0.0285736	0.0116651
$7$	1.32998	0.502686	0.251343	−	0.967898i	$-0.419128\pi$
$7$	1.32998	0.502686	0.251343	+	0.967898i	$0.419128\pi$
$8$	−1.16612	−0.412285
$9$	−2.99082	−0.996939
$10$	0.286218	0.0905100
$11$	−2.70096	−0.814371	−0.407185	−	0.913345i	$-0.633490\pi$
$11$	−2.70096	−0.814371	−0.407185	+	0.913345i	$0.633490\pi$
$12$	−0.183150	−0.0528707
$13$	−2.46427	−0.683467	−0.341733	−	0.939797i	$-0.611014\pi$
$13$	−2.46427	−0.683467	−0.341733	+	0.939797i	$0.611014\pi$
$14$	0.396542	0.105980
$15$	0.0919973	0.0237536
$16$	3.47452	0.868630
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−0.891729	−0.210183
$19$	−2.75255	−0.631477	−0.315739	−	0.948846i	$-0.602252\pi$
$19$	−2.75255	−0.631477	−0.315739	+	0.948846i	$0.602252\pi$
$20$	−1.83458	−0.410225
$21$	0.127458	0.0278136
$22$	−0.805308	−0.171692
$23$	−1.10970	−0.231389	−0.115694	−	0.993285i	$-0.536909\pi$
$23$	−1.10970	−0.231389	−0.115694	+	0.993285i	$0.536909\pi$
$24$	−0.111754	−0.0228118
$25$	−4.07848	−0.815695
$26$	−0.734738	−0.144094
$27$	−0.574127	−0.110491
$28$	−2.54173	−0.480342
$29$	−7.14525	−1.32684	−0.663420	−	0.748247i	$-0.730896\pi$
$29$	−7.14525	−1.32684	−0.663420	+	0.748247i	$0.730896\pi$
$30$	0.0274295	0.00500792
$31$	−3.87150	−0.695342	−0.347671	−	0.937617i	$-0.613027\pi$
$31$	−3.87150	−0.695342	−0.347671	+	0.937617i	$0.613027\pi$
$32$	3.36819	0.595417
$33$	−0.258845	−0.0450592
$34$	0.298156	0.0511333
$35$	1.27673	0.215807
$36$	5.71576	0.952626
$37$	2.00755	0.330040	0.165020	−	0.986290i	$-0.447231\pi$
$37$	2.00755	0.330040	0.165020	+	0.986290i	$0.447231\pi$
$38$	−0.820688	−0.133133
$39$	−0.236162	−0.0378163
$40$	−1.11943	−0.176997
$41$	8.57961	1.33991	0.669955	−	0.742401i	$-0.266313\pi$
$41$	8.57961	1.33991	0.669955	+	0.742401i	$0.266313\pi$
$42$	0.0380024	0.00586390
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	5.16182	0.778173
$45$	−2.87106	−0.427993
$46$	−0.330864	−0.0487832
$47$	−10.6131	−1.54808	−0.774038	−	0.633139i	$-0.781766\pi$
$47$	−10.6131	−1.54808	−0.774038	+	0.633139i	$0.781766\pi$
$48$	0.332979	0.0480614
$49$	−5.23115	−0.747307
$50$	−1.21602	−0.171971
$51$	0.0958345	0.0134195
$52$	4.70948	0.653088
$53$	−6.91942	−0.950456	−0.475228	−	0.879863i	$-0.657634\pi$
$53$	−6.91942	−0.950456	−0.475228	+	0.879863i	$0.657634\pi$
$54$	−0.171179	−0.0232946
$55$	−2.59282	−0.349615
$56$	−1.55092	−0.207250
$57$	−0.263789	−0.0349397
$58$	−2.13040	−0.279735
$59$	0.411022	0.0535105	0.0267552	−	0.999642i	$-0.491483\pi$
$59$	0.411022	0.0535105	0.0267552	+	0.999642i	$0.491483\pi$
$60$	−0.175816	−0.0226978
$61$	3.33157	0.426564	0.213282	−	0.976991i	$-0.431585\pi$
$61$	3.33157	0.426564	0.213282	+	0.976991i	$0.431585\pi$
$62$	−1.15431	−0.146598
$63$	−3.97773	−0.501147
$64$	−5.94480	−0.743100
$65$	−2.36560	−0.293417
$66$	−0.0771763	−0.00949974
$67$	−10.1773	−1.24336	−0.621679	−	0.783272i	$-0.713549\pi$
$67$	−10.1773	−1.24336	−0.621679	+	0.783272i	$0.713549\pi$
$68$	−1.91110	−0.231755
$69$	−0.106348	−0.0128027
$70$	0.380664	0.0454981
$71$	6.68091	0.792878	0.396439	−	0.918061i	$-0.370246\pi$
$71$	6.68091	0.792878	0.396439	+	0.918061i	$0.370246\pi$
$72$	3.48765	0.411023
$73$	−3.67968	−0.430674	−0.215337	−	0.976540i	$-0.569085\pi$
$73$	−3.67968	−0.430674	−0.215337	+	0.976540i	$0.569085\pi$
$74$	0.598564	0.0695816
$75$	−0.390859	−0.0451325
$76$	5.26040	0.603409
$77$	−3.59223	−0.409373
$78$	−0.0704132	−0.00797273
$79$	10.7249	1.20664	0.603321	−	0.797498i	$-0.293844\pi$
$79$	10.7249	1.20664	0.603321	+	0.797498i	$0.293844\pi$
$80$	3.33540	0.372909
$81$	8.91743	0.990825
$82$	2.55806	0.282491
$83$	5.23738	0.574877	0.287439	−	0.957799i	$-0.407196\pi$
$83$	5.23738	0.574877	0.287439	+	0.957799i	$0.407196\pi$
$84$	−0.243586	−0.0265774
$85$	0.959960	0.104122
$86$	0.298156	0.0321510
$87$	−0.684761	−0.0734141
$88$	3.14964	0.335753
$89$	−8.72756	−0.925120	−0.462560	−	0.886588i	$-0.653069\pi$
$89$	−8.72756	−0.925120	−0.462560	+	0.886588i	$0.653069\pi$
$90$	−0.856024	−0.0902329
$91$	−3.27744	−0.343569
$92$	2.12075	0.221104
$93$	−0.371023	−0.0384733
$94$	−3.16435	−0.326378
$95$	−2.64233	−0.271098
$96$	0.322788	0.0329445
$97$	1.38021	0.140139	0.0700697	−	0.997542i	$-0.477678\pi$
$97$	1.38021	0.140139	0.0700697	+	0.997542i	$0.477678\pi$
$98$	−1.55970	−0.157553
$99$	8.07808	0.811878
$100$	7.79439	0.779439
$101$	2.31213	0.230066	0.115033	−	0.993362i	$-0.463303\pi$
$101$	2.31213	0.230066	0.115033	+	0.993362i	$0.463303\pi$
$102$	0.0285736	0.00282921
$103$	5.50110	0.542040	0.271020	−	0.962574i	$-0.412639\pi$
$103$	5.50110	0.542040	0.271020	+	0.962574i	$0.412639\pi$
$104$	2.87364	0.281783
$105$	0.122355	0.0119406
$106$	−2.06307	−0.200383
$107$	5.19972	0.502676	0.251338	−	0.967899i	$-0.419129\pi$
$107$	5.19972	0.502676	0.251338	+	0.967899i	$0.419129\pi$
$108$	1.09722	0.105580
$109$	10.3641	0.992701	0.496351	−	0.868122i	$-0.334673\pi$
$109$	10.3641	0.992701	0.496351	+	0.868122i	$0.334673\pi$
$110$	−0.773063	−0.0737087
$111$	0.192393	0.0182611
$112$	4.62105	0.436648
$113$	9.58715	0.901883	0.450942	−	0.892553i	$-0.351088\pi$
$113$	9.58715	0.901883	0.450942	+	0.892553i	$0.351088\pi$
$114$	−0.0786502	−0.00736626
$115$	−1.06527	−0.0993368
$116$	13.6553	1.26786
$117$	7.37019	0.681374
$118$	0.122549	0.0112815
$119$	1.32998	0.121919
$120$	−0.107280	−0.00979325
$121$	−3.70480	−0.336800
$122$	0.993328	0.0899317
$123$	0.822223	0.0741373
$124$	7.39884	0.664435
$125$	−8.71497	−0.779491
$126$	−1.18598	−0.105656
$127$	3.75661	0.333345	0.166672	−	0.986012i	$-0.446698\pi$
$127$	3.75661	0.333345	0.166672	+	0.986012i	$0.446698\pi$
$128$	−8.50885	−0.752083
$129$	0.0958345	0.00843776
$130$	−0.705319	−0.0618606
$131$	−4.02272	−0.351467	−0.175733	−	0.984438i	$-0.556230\pi$
$131$	−4.02272	−0.351467	−0.175733	+	0.984438i	$0.556230\pi$
$132$	0.494680	0.0430564
$133$	−3.66083	−0.317435
$134$	−3.03443	−0.262135
$135$	−0.551139	−0.0474345
$136$	−1.16612	−0.0999938
$137$	8.69484	0.742850	0.371425	−	0.928463i	$-0.378869\pi$
$137$	8.69484	0.742850	0.371425	+	0.928463i	$0.378869\pi$
$138$	−0.0317082	−0.00269918
$139$	3.40559	0.288858	0.144429	−	0.989515i	$-0.453865\pi$
$139$	3.40559	0.288858	0.144429	+	0.989515i	$0.453865\pi$
$140$	−2.43996	−0.206214
$141$	−1.01710	−0.0856551
$142$	1.99195	0.167161
$143$	6.65591	0.556595
$144$	−10.3917	−0.865971
$145$	−6.85915	−0.569622
$146$	−1.09712	−0.0907982
$147$	−0.501325	−0.0413486
$148$	−3.83664	−0.315370
$149$	−0.135778	−0.0111234	−0.00556169	−	0.999985i	$-0.501770\pi$
$149$	−0.135778	−0.0111234	−0.00556169	+	0.999985i	$0.501770\pi$
$150$	−0.116537	−0.00951519
$151$	17.2582	1.40446	0.702228	−	0.711953i	$-0.252189\pi$
$151$	17.2582	1.40446	0.702228	+	0.711953i	$0.252189\pi$
$152$	3.20979	0.260349
$153$	−2.99082	−0.241793
$154$	−1.07104	−0.0863072
$155$	−3.71648	−0.298515
$156$	0.451331	0.0361354
$157$	−8.06577	−0.643719	−0.321859	−	0.946787i	$-0.604308\pi$
$157$	−8.06577	−0.643719	−0.321859	+	0.946787i	$0.604308\pi$
$158$	3.19768	0.254394
$159$	−0.663119	−0.0525888
$160$	3.23332	0.255617
$161$	−1.47588	−0.116316
$162$	2.65878	0.208894
$163$	−3.57087	−0.279692	−0.139846	−	0.990173i	$-0.544661\pi$
$163$	−3.57087	−0.279692	−0.139846	+	0.990173i	$0.544661\pi$
$164$	−16.3965	−1.28035
$165$	−0.248481	−0.0193442
$166$	1.56156	0.121200
$167$	20.1036	1.55567	0.777833	−	0.628471i	$-0.216319\pi$
$167$	20.1036	1.55567	0.777833	+	0.628471i	$0.216319\pi$
$168$	−0.148631	−0.0114671
$169$	−6.92735	−0.532873
$170$	0.286218	0.0219519
$171$	8.23236	0.629544
$172$	−1.91110	−0.145720
$173$	−10.1390	−0.770852	−0.385426	−	0.922739i	$-0.625945\pi$
$173$	−10.1390	−0.770852	−0.385426	+	0.922739i	$0.625945\pi$
$174$	−0.204166	−0.0154778
$175$	−5.42430	−0.410038
$176$	−9.38455	−0.707387
$177$	0.0393900	0.00296074
$178$	−2.60217	−0.195041
$179$	8.98907	0.671875	0.335937	−	0.941884i	$-0.390947\pi$
$179$	8.98907	0.671875	0.335937	+	0.941884i	$0.390947\pi$
$180$	5.48690	0.408969
$181$	11.9183	0.885882	0.442941	−	0.896551i	$-0.353935\pi$
$181$	11.9183	0.885882	0.442941	+	0.896551i	$0.353935\pi$
$182$	−0.977188	−0.0724340
$183$	0.319280	0.0236018
$184$	1.29404	0.0953981
$185$	1.92717	0.141688
$186$	−0.110623	−0.00811126
$187$	−2.70096	−0.197514
$188$	20.2827	1.47927
$189$	−0.763578	−0.0555421
$190$	−0.787827	−0.0571550
$191$	−0.997523	−0.0721782	−0.0360891	−	0.999349i	$-0.511490\pi$
$191$	−0.997523	−0.0721782	−0.0360891	+	0.999349i	$0.511490\pi$
$192$	−0.569717	−0.0411158
$193$	−10.6216	−0.764558	−0.382279	−	0.924047i	$-0.624861\pi$
$193$	−10.6216	−0.764558	−0.382279	+	0.924047i	$0.624861\pi$
$194$	0.411519	0.0295453
$195$	−0.226706	−0.0162348
$196$	9.99727	0.714090
$197$	−1.74780	−0.124526	−0.0622628	−	0.998060i	$-0.519832\pi$
$197$	−1.74780	−0.124526	−0.0622628	+	0.998060i	$0.519832\pi$
$198$	2.40853	0.171167
$199$	−10.1359	−0.718515	−0.359257	−	0.933239i	$-0.616970\pi$
$199$	−10.1359	−0.718515	−0.359257	+	0.933239i	$0.616970\pi$
$200$	4.75599	0.336299
$201$	−0.975338	−0.0687951
$202$	0.689376	0.0485043
$203$	−9.50305	−0.666983
$204$	−0.183150	−0.0128230
$205$	8.23608	0.575233
$206$	1.64019	0.114277
$207$	3.31891	0.230680
$208$	−8.56217	−0.593680
$209$	7.43452	0.514257
$210$	0.0364808	0.00251741
$211$	−23.7242	−1.63324	−0.816620	−	0.577176i	$-0.804155\pi$
$211$	−23.7242	−1.63324	−0.816620	+	0.577176i	$0.804155\pi$
$212$	13.2237	0.908209
$213$	0.640262	0.0438700
$214$	1.55033	0.105978
$215$	0.959960	0.0654687
$216$	0.669500	0.0455537
$217$	−5.14902	−0.349539
$218$	3.09012	0.209289
$219$	−0.352640	−0.0238292
$220$	4.95514	0.334075
$221$	−2.46427	−0.165765
$222$	0.0573631	0.00384996
$223$	−9.46251	−0.633657	−0.316828	−	0.948483i	$-0.602618\pi$
$223$	−9.46251	−0.633657	−0.316828	+	0.948483i	$0.602618\pi$
$224$	4.47962	0.299308
$225$	12.1980	0.813198
$226$	2.85847	0.190142
$227$	−13.7447	−0.912269	−0.456135	−	0.889911i	$-0.650766\pi$
$227$	−13.7447	−0.912269	−0.456135	+	0.889911i	$0.650766\pi$
$228$	0.504128	0.0333867
$229$	1.23192	0.0814077	0.0407039	−	0.999171i	$-0.487040\pi$
$229$	1.23192	0.0814077	0.0407039	+	0.999171i	$0.487040\pi$
$230$	−0.317616	−0.0209430
$231$	−0.344260	−0.0226506
$232$	8.33221	0.547036
$233$	−13.7017	−0.897629	−0.448815	−	0.893625i	$-0.648154\pi$
$233$	−13.7017	−0.897629	−0.448815	+	0.893625i	$0.648154\pi$
$234$	2.19747	0.143653
$235$	−10.1881	−0.664600
$236$	−0.785505	−0.0511320
$237$	1.02781	0.0667636
$238$	0.396542	0.0257040
$239$	7.11256	0.460073	0.230037	−	0.973182i	$-0.426115\pi$
$239$	7.11256	0.460073	0.230037	+	0.973182i	$0.426115\pi$
$240$	0.319646	0.0206331
$241$	−20.4739	−1.31884	−0.659419	−	0.751776i	$-0.729198\pi$
$241$	−20.4739	−1.31884	−0.659419	+	0.751776i	$0.729198\pi$
$242$	−1.10461	−0.0710069
$243$	2.57698	0.165313
$244$	−6.36698	−0.407604
$245$	−5.02169	−0.320824
$246$	0.245151	0.0156302
$247$	6.78303	0.431594
$248$	4.51463	0.286679
$249$	0.501922	0.0318080
$250$	−2.59842	−0.164339
$251$	15.7290	0.992809	0.496404	−	0.868091i	$-0.334653\pi$
$251$	15.7290	0.992809	0.496404	+	0.868091i	$0.334653\pi$
$252$	7.60185	0.478872
$253$	2.99726	0.188436
$254$	1.12005	0.0702784
$255$	0.0919973	0.00576109
$256$	9.35263	0.584540
$257$	−7.45252	−0.464875	−0.232438	−	0.972611i	$-0.574670\pi$
$257$	−7.45252	−0.464875	−0.232438	+	0.972611i	$0.574670\pi$
$258$	0.0285736	0.00177892
$259$	2.67001	0.165906
$260$	4.52091	0.280375
$261$	21.3701	1.32278
$262$	−1.19940	−0.0740991
$263$	11.0353	0.680465	0.340232	−	0.940341i	$-0.389494\pi$
$263$	11.0353	0.680465	0.340232	+	0.940341i	$0.389494\pi$
$264$	0.301844	0.0185772
$265$	−6.64237	−0.408037
$266$	−1.09150	−0.0669241
$267$	−0.836401	−0.0511869
$268$	19.4499	1.18809
$269$	−3.22242	−0.196474	−0.0982372	−	0.995163i	$-0.531320\pi$
$269$	−3.22242	−0.196474	−0.0982372	+	0.995163i	$0.531320\pi$
$270$	−0.164325	−0.0100005
$271$	6.35747	0.386189	0.193094	−	0.981180i	$-0.438148\pi$
$271$	6.35747	0.386189	0.193094	+	0.981180i	$0.438148\pi$
$272$	3.47452	0.210674
$273$	−0.314092	−0.0190097
$274$	2.59242	0.156614
$275$	11.0158	0.664279
$276$	0.203241	0.0122337
$277$	−33.1224	−1.99013	−0.995066	−	0.0992110i	$-0.968368\pi$
$277$	−33.1224	−1.99013	−0.995066	+	0.0992110i	$0.968368\pi$
$278$	1.01540	0.0608994
$279$	11.5789	0.693213
$280$	−1.48882	−0.0889738
$281$	10.6660	0.636280	0.318140	−	0.948044i	$-0.396942\pi$
$281$	10.6660	0.636280	0.318140	+	0.948044i	$0.396942\pi$
$282$	−0.303254	−0.0180585
$283$	4.98600	0.296387	0.148193	−	0.988958i	$-0.452654\pi$
$283$	4.98600	0.296387	0.148193	+	0.988958i	$0.452654\pi$
$284$	−12.7679	−0.757636
$285$	−0.253227	−0.0149999
$286$	1.98450	0.117346
$287$	11.4107	0.673554
$288$	−10.0736	−0.593594
$289$	1.00000	0.0588235
$290$	−2.04510	−0.120092
$291$	0.132272	0.00775393
$292$	7.03225	0.411531
$293$	−28.5392	−1.66728	−0.833638	−	0.552311i	$-0.813746\pi$
$293$	−28.5392	−1.66728	−0.833638	+	0.552311i	$0.813746\pi$
$294$	−0.149473	−0.00871743
$295$	0.394564	0.0229724
$296$	−2.34105	−0.136070
$297$	1.55070	0.0899805
$298$	−0.0404831	−0.00234512
$299$	2.73461	0.158146
$300$	0.746971	0.0431264
$301$	1.32998	0.0766589
$302$	5.14564	0.296099
$303$	0.221582	0.0127296
$304$	−9.56378	−0.548520
$305$	3.19818	0.183127
$306$	−0.891729	−0.0509768
$307$	−2.14596	−0.122476	−0.0612381	−	0.998123i	$-0.519505\pi$
$307$	−2.14596	−0.122476	−0.0612381	+	0.998123i	$0.519505\pi$
$308$	6.86512	0.391177
$309$	0.527195	0.0299911
$310$	−1.10809	−0.0629354
$311$	−4.63915	−0.263062	−0.131531	−	0.991312i	$-0.541989\pi$
$311$	−4.63915	−0.263062	−0.131531	+	0.991312i	$0.541989\pi$
$312$	0.275393	0.0155911
$313$	−32.1567	−1.81760	−0.908801	−	0.417230i	$-0.863001\pi$
$313$	−32.1567	−1.81760	−0.908801	+	0.417230i	$0.863001\pi$
$314$	−2.40486	−0.135714
$315$	−3.81846	−0.215146
$316$	−20.4963	−1.15301
$317$	30.2105	1.69679	0.848395	−	0.529363i	$-0.177569\pi$
$317$	30.2105	1.69679	0.848395	+	0.529363i	$0.177569\pi$
$318$	−0.197713	−0.0110872
$319$	19.2991	1.08054
$320$	−5.70677	−0.319018
$321$	0.498313	0.0278131
$322$	−0.440043	−0.0245226
$323$	−2.75255	−0.153156
$324$	−17.0421	−0.946784
$325$	10.0505	0.557501
$326$	−1.06468	−0.0589669
$327$	0.993239	0.0549262
$328$	−10.0048	−0.552425
$329$	−14.1152	−0.778195
$330$	−0.0740861	−0.00407831
$331$	−33.6752	−1.85095	−0.925477	−	0.378803i	$-0.876336\pi$
$331$	−33.6752	−1.85095	−0.925477	+	0.378803i	$0.876336\pi$
$332$	−10.0092	−0.549325
$333$	−6.00422	−0.329029
$334$	5.99401	0.327978
$335$	−9.76982	−0.533782
$336$	0.442856	0.0241598
$337$	12.5760	0.685057	0.342529	−	0.939507i	$-0.388717\pi$
$337$	12.5760	0.685057	0.342529	+	0.939507i	$0.388717\pi$
$338$	−2.06543	−0.112345
$339$	0.918780	0.0499013
$340$	−1.83458	−0.0994942
$341$	10.4568	0.566266
$342$	2.45453	0.132726
$343$	−16.2672	−0.878346
$344$	−1.16612	−0.0628729
$345$	−0.102089	−0.00549631
$346$	−3.02299	−0.162517
$347$	28.9422	1.55370	0.776848	−	0.629688i	$-0.216817\pi$
$347$	28.9422	1.55370	0.776848	+	0.629688i	$0.216817\pi$
$348$	1.30865	0.0701510
$349$	−25.2498	−1.35159	−0.675794	−	0.737090i	$-0.736199\pi$
$349$	−25.2498	−1.35159	−0.675794	+	0.737090i	$0.736199\pi$
$350$	−1.61729	−0.0864476
$351$	1.41481	0.0755168
$352$	−9.09734	−0.484890
$353$	−28.9597	−1.54137	−0.770684	−	0.637217i	$-0.780085\pi$
$353$	−28.9597	−1.54137	−0.770684	+	0.637217i	$0.780085\pi$
$354$	0.0117444	0.000624206 0
$355$	6.41341	0.340388
$356$	16.6793	0.884000
$357$	0.127458	0.00674580
$358$	2.68014	0.141650
$359$	29.9386	1.58010	0.790048	−	0.613045i	$-0.210055\pi$
$359$	29.9386	1.58010	0.790048	+	0.613045i	$0.210055\pi$
$360$	3.34800	0.176455
$361$	−11.4235	−0.601237
$362$	3.55352	0.186769
$363$	−0.355048	−0.0186352
$364$	6.26352	0.328298
$365$	−3.53234	−0.184891
$366$	0.0951951	0.00497593
$367$	−28.0882	−1.46619	−0.733096	−	0.680126i	$-0.761925\pi$
$367$	−28.0882	−1.46619	−0.733096	+	0.680126i	$0.761925\pi$
$368$	−3.85568	−0.200991
$369$	−25.6600	−1.33581
$370$	0.574597	0.0298719
$371$	−9.20270	−0.477780
$372$	0.709064	0.0367632
$373$	−5.11861	−0.265032	−0.132516	−	0.991181i	$-0.542306\pi$
$373$	−5.11861	−0.265032	−0.132516	+	0.991181i	$0.542306\pi$
$374$	−0.805308	−0.0416415
$375$	−0.835195	−0.0431293
$376$	12.3761	0.638249
$377$	17.6079	0.906851
$378$	−0.227665	−0.0117098
$379$	−30.2042	−1.55148	−0.775742	−	0.631050i	$-0.782624\pi$
$379$	−30.2042	−1.55148	−0.775742	+	0.631050i	$0.782624\pi$
$380$	5.04977	0.259048
$381$	0.360012	0.0184440
$382$	−0.297417	−0.0152172
$383$	9.34056	0.477280	0.238640	−	0.971108i	$-0.423298\pi$
$383$	9.34056	0.477280	0.238640	+	0.971108i	$0.423298\pi$
$384$	−0.815441	−0.0416128
$385$	−3.44840	−0.175747
$386$	−3.16689	−0.161190
$387$	−2.99082	−0.152032
$388$	−2.63773	−0.133910
$389$	−22.9383	−1.16302	−0.581510	−	0.813539i	$-0.697538\pi$
$389$	−22.9383	−1.16302	−0.581510	+	0.813539i	$0.697538\pi$
$390$	−0.0675939	−0.00342275
$391$	−1.10970	−0.0561200
$392$	6.10014	0.308104
$393$	−0.385515	−0.0194467
$394$	−0.521117	−0.0262535
$395$	10.2954	0.518020
$396$	−15.4380	−0.775791
$397$	−14.0212	−0.703706	−0.351853	−	0.936055i	$-0.614448\pi$
$397$	−14.0212	−0.703706	−0.351853	+	0.936055i	$0.614448\pi$
$398$	−3.02208	−0.151483
$399$	−0.350834	−0.0175637
$400$	−14.1708	−0.708538
$401$	27.4931	1.37294	0.686469	−	0.727159i	$-0.259160\pi$
$401$	27.4931	1.37294	0.686469	+	0.727159i	$0.259160\pi$
$402$	−0.290803	−0.0145039
$403$	9.54044	0.475243
$404$	−4.41872	−0.219840
$405$	8.56037	0.425368
$406$	−2.83339	−0.140619
$407$	−5.42233	−0.268775
$408$	−0.111754	−0.00553267
$409$	−21.9406	−1.08490	−0.542448	−	0.840090i	$-0.682502\pi$
$409$	−21.9406	−1.08490	−0.542448	+	0.840090i	$0.682502\pi$
$410$	2.45564	0.121275
$411$	0.833265	0.0411019
$412$	−10.5132	−0.517947
$413$	0.546651	0.0268989
$414$	0.989553	0.0486339
$415$	5.02768	0.246799
$416$	−8.30013	−0.406948
$417$	0.326373	0.0159826
$418$	2.21665	0.108420
$419$	27.3211	1.33472	0.667361	−	0.744735i	$-0.267424\pi$
$419$	27.3211	1.33472	0.667361	+	0.744735i	$0.267424\pi$
$420$	−0.233832	−0.0114099
$421$	6.79433	0.331135	0.165568	−	0.986198i	$-0.447054\pi$
$421$	6.79433	0.331135	0.165568	+	0.986198i	$0.447054\pi$
$422$	−7.07350	−0.344333
$423$	31.7417	1.54334
$424$	8.06886	0.391859
$425$	−4.07848	−0.197835
$426$	0.190898	0.00924903
$427$	4.43093	0.214428
$428$	−9.93720	−0.480333
$429$	0.637866	0.0307965
$430$	0.286218	0.0138026
$431$	5.07429	0.244420	0.122210	−	0.992504i	$-0.461002\pi$
$431$	5.07429	0.244420	0.122210	+	0.992504i	$0.461002\pi$
$432$	−1.99482	−0.0959756
$433$	15.9577	0.766876	0.383438	−	0.923567i	$-0.374740\pi$
$433$	15.9577	0.766876	0.383438	+	0.923567i	$0.374740\pi$
$434$	−1.53521	−0.0736925
$435$	−0.657343	−0.0315172
$436$	−19.8069	−0.948577
$437$	3.05450	0.146117
$438$	−0.105142	−0.00502387
$439$	15.4958	0.739575	0.369787	−	0.929116i	$-0.379431\pi$
$439$	15.4958	0.739575	0.369787	+	0.929116i	$0.379431\pi$
$440$	3.02353	0.144141
$441$	15.6454	0.745019
$442$	−0.734738	−0.0349479
$443$	3.13890	0.149134	0.0745668	−	0.997216i	$-0.476243\pi$
$443$	3.13890	0.149134	0.0745668	+	0.997216i	$0.476243\pi$
$444$	−0.367683	−0.0174494
$445$	−8.37811	−0.397160
$446$	−2.82130	−0.133593
$447$	−0.0130122	−0.000615458 0
$448$	−7.90647	−0.373546
$449$	−11.9193	−0.562507	−0.281254	−	0.959633i	$-0.590750\pi$
$449$	−11.9193	−0.562507	−0.281254	+	0.959633i	$0.590750\pi$
$450$	3.63690	0.171445
$451$	−23.1732	−1.09118
$452$	−18.3220	−0.861796
$453$	1.65393	0.0777086
$454$	−4.09807	−0.192332
$455$	−3.14621	−0.147497
$456$	0.307609	0.0144051
$457$	7.81606	0.365620	0.182810	−	0.983148i	$-0.441481\pi$
$457$	7.81606	0.365620	0.182810	+	0.983148i	$0.441481\pi$
$458$	0.367305	0.0171630
$459$	−0.574127	−0.0267979
$460$	2.03584	0.0949214
$461$	−29.8397	−1.38977	−0.694886	−	0.719120i	$-0.744545\pi$
$461$	−29.8397	−1.38977	−0.694886	+	0.719120i	$0.744545\pi$
$462$	−0.102643	−0.00477539
$463$	−14.5908	−0.678090	−0.339045	−	0.940770i	$-0.610104\pi$
$463$	−14.5908	−0.678090	−0.339045	+	0.940770i	$0.610104\pi$
$464$	−24.8263	−1.15253
$465$	−0.356167	−0.0165169
$466$	−4.08525	−0.189245
$467$	18.3071	0.847152	0.423576	−	0.905861i	$-0.360775\pi$
$467$	18.3071	0.847152	0.423576	+	0.905861i	$0.360775\pi$
$468$	−14.0852	−0.651088
$469$	−13.5356	−0.625018
$470$	−3.03765	−0.140116
$471$	−0.772979	−0.0356170
$472$	−0.479300	−0.0220616
$473$	−2.70096	−0.124190
$474$	0.306448	0.0140756
$475$	11.2262	0.515093
$476$	−2.54173	−0.116500
$477$	20.6947	0.947546
$478$	2.12065	0.0969964
$479$	−20.2172	−0.923746	−0.461873	−	0.886946i	$-0.652822\pi$
$479$	−20.2172	−0.923746	−0.461873	+	0.886946i	$0.652822\pi$
$480$	0.309864	0.0141433
$481$	−4.94716	−0.225571
$482$	−6.10440	−0.278048
$483$	−0.141440	−0.00643576
$484$	7.08025	0.321830
$485$	1.32495	0.0601629
$486$	0.768341	0.0348527
$487$	−5.38727	−0.244121	−0.122060	−	0.992523i	$-0.538950\pi$
$487$	−5.38727	−0.244121	−0.122060	+	0.992523i	$0.538950\pi$
$488$	−3.88501	−0.175866
$489$	−0.342213	−0.0154754
$490$	−1.49725	−0.0676387
$491$	5.35280	0.241569	0.120784	−	0.992679i	$-0.461459\pi$
$491$	5.35280	0.241569	0.120784	+	0.992679i	$0.461459\pi$
$492$	−1.57135	−0.0708421
$493$	−7.14525	−0.321806
$494$	2.02240	0.0909921
$495$	7.75463	0.348545
$496$	−13.4516	−0.603995
$497$	8.88549	0.398569
$498$	0.149651	0.00670602
$499$	1.01919	0.0456252	0.0228126	−	0.999740i	$-0.492738\pi$
$499$	1.01919	0.0456252	0.0228126	+	0.999740i	$0.492738\pi$
$500$	16.6552	0.744844
$501$	1.92662	0.0860751
$502$	4.68971	0.209312
$503$	−8.88795	−0.396294	−0.198147	−	0.980172i	$-0.563492\pi$
$503$	−8.88795	−0.396294	−0.198147	+	0.980172i	$0.563492\pi$
$504$	4.63850	0.206615
$505$	2.21955	0.0987689
$506$	0.893651	0.0397276
$507$	−0.663879	−0.0294839
$508$	−7.17926	−0.318528
$509$	7.26365	0.321956	0.160978	−	0.986958i	$-0.448535\pi$
$509$	7.26365	0.321956	0.160978	+	0.986958i	$0.448535\pi$
$510$	0.0274295	0.00121460
$511$	−4.89391	−0.216494
$512$	19.8062	0.875320
$513$	1.58031	0.0697724
$514$	−2.22201	−0.0980087
$515$	5.28084	0.232701
$516$	−0.183150	−0.00806271
$517$	28.6655	1.26071
$518$	0.796079	0.0349777
$519$	−0.971663	−0.0426513
$520$	2.75857	0.120972
$521$	−0.508687	−0.0222860	−0.0111430	−	0.999938i	$-0.503547\pi$
$521$	−0.508687	−0.0222860	−0.0111430	+	0.999938i	$0.503547\pi$
$522$	6.37163	0.278879
$523$	44.5751	1.94913	0.974567	−	0.224097i	$-0.0719433\pi$
$523$	44.5751	1.94913	0.974567	+	0.224097i	$0.0719433\pi$
$524$	7.68783	0.335845
$525$	−0.519835	−0.0226875
$526$	3.29023	0.143461
$527$	−3.87150	−0.168645
$528$	−0.899364	−0.0391398
$529$	−21.7686	−0.946459
$530$	−1.98046	−0.0860257
$531$	−1.22929	−0.0533466
$532$	6.99623	0.303325
$533$	−21.1425	−0.915784
$534$	−0.249378	−0.0107916
$535$	4.99152	0.215802
$536$	11.8680	0.512618
$537$	0.861463	0.0371749
$538$	−0.960784	−0.0414223
$539$	14.1291	0.608585
$540$	1.05328	0.0453261
$541$	−26.4974	−1.13921	−0.569606	−	0.821918i	$-0.692904\pi$
$541$	−26.4974	−1.13921	−0.569606	+	0.821918i	$0.692904\pi$
$542$	1.89552	0.0814194
$543$	1.14219	0.0490159
$544$	3.36819	0.144410
$545$	9.94912	0.426174
$546$	−0.0936483	−0.00400778
$547$	−21.4578	−0.917470	−0.458735	−	0.888573i	$-0.651697\pi$
$547$	−21.4578	−0.917470	−0.458735	+	0.888573i	$0.651697\pi$
$548$	−16.6167	−0.709832
$549$	−9.96412	−0.425258
$550$	3.28443	0.140049
$551$	19.6676	0.837869
$552$	0.124014	0.00527838
$553$	14.2639	0.606562
$554$	−9.87564	−0.419576
$555$	0.184689	0.00783963
$556$	−6.50843	−0.276019
$557$	−6.37038	−0.269921	−0.134961	−	0.990851i	$-0.543091\pi$
$557$	−6.37038	−0.269921	−0.134961	+	0.990851i	$0.543091\pi$
$558$	3.45233	0.146149
$559$	−2.46427	−0.104228
$560$	4.43602	0.187456
$561$	−0.258845	−0.0109285
$562$	3.18013	0.134146
$563$	−9.24267	−0.389532	−0.194766	−	0.980850i	$-0.562395\pi$
$563$	−9.24267	−0.389532	−0.194766	+	0.980850i	$0.562395\pi$
$564$	1.94378	0.0818479
$565$	9.20328	0.387185
$566$	1.48660	0.0624866
$567$	11.8600	0.498074
$568$	−7.79073	−0.326892
$569$	36.0430	1.51100	0.755500	−	0.655148i	$-0.227394\pi$
$569$	36.0430	1.51100	0.755500	+	0.655148i	$0.227394\pi$
$570$	−0.0755010	−0.00316239
$571$	−9.77412	−0.409034	−0.204517	−	0.978863i	$-0.565562\pi$
$571$	−9.77412	−0.409034	−0.204517	+	0.978863i	$0.565562\pi$
$572$	−12.7201	−0.531856
$573$	−0.0955971	−0.00399363
$574$	3.40218	0.142004
$575$	4.52589	0.188743
$576$	17.7798	0.740825
$577$	35.0739	1.46015	0.730074	−	0.683369i	$-0.239486\pi$
$577$	35.0739	1.46015	0.730074	+	0.683369i	$0.239486\pi$
$578$	0.298156	0.0124017
$579$	−1.01791	−0.0423031
$580$	13.1085	0.544303
$581$	6.96562	0.288983
$582$	0.0394377	0.00163475
$583$	18.6891	0.774023
$584$	4.29094	0.177560
$585$	7.07509	0.292519
$586$	−8.50912	−0.351509
$587$	10.2729	0.424009	0.212005	−	0.977269i	$-0.432001\pi$
$587$	10.2729	0.424009	0.212005	+	0.977269i	$0.432001\pi$
$588$	0.958083	0.0395107
$589$	10.6565	0.439093
$590$	0.117642	0.00484323
$591$	−0.167500	−0.00689001
$592$	6.97529	0.286683
$593$	18.8977	0.776035	0.388017	−	0.921652i	$-0.373160\pi$
$593$	18.8977	0.776035	0.388017	+	0.921652i	$0.373160\pi$
$594$	0.462349	0.0189704
$595$	1.27673	0.0523408
$596$	0.259486	0.0106290
$597$	−0.971368	−0.0397555
$598$	0.815339	0.0333417
$599$	−38.4426	−1.57072	−0.785361	−	0.619038i	$-0.787523\pi$
$599$	−38.4426	−1.57072	−0.785361	+	0.619038i	$0.787523\pi$
$600$	0.455788	0.0186075
$601$	−18.0985	−0.738254	−0.369127	−	0.929379i	$-0.620343\pi$
$601$	−18.0985	−0.738254	−0.369127	+	0.929379i	$0.620343\pi$
$602$	0.396542	0.0161618
$603$	30.4385	1.23955
$604$	−32.9823	−1.34203
$605$	−3.55646	−0.144591
$606$	0.0660660	0.00268375
$607$	−28.2539	−1.14679	−0.573394	−	0.819280i	$-0.694374\pi$
$607$	−28.2539	−1.14679	−0.573394	+	0.819280i	$0.694374\pi$
$608$	−9.27108	−0.375992
$609$	−0.910720	−0.0369042
$610$	0.953555	0.0386083
$611$	26.1535	1.05806
$612$	5.71576	0.231046
$613$	10.6837	0.431510	0.215755	−	0.976447i	$-0.430779\pi$
$613$	10.6837	0.431510	0.215755	+	0.976447i	$0.430779\pi$
$614$	−0.639829	−0.0258214
$615$	0.789301	0.0318277
$616$	4.18897	0.168778
$617$	19.1206	0.769768	0.384884	−	0.922965i	$-0.374242\pi$
$617$	19.1206	0.769768	0.384884	+	0.922965i	$0.374242\pi$
$618$	0.157186	0.00632296
$619$	19.0878	0.767202	0.383601	−	0.923499i	$-0.374684\pi$
$619$	19.0878	0.767202	0.383601	+	0.923499i	$0.374684\pi$
$620$	7.10259	0.285247
$621$	0.637109	0.0255663
$622$	−1.38319	−0.0554609
$623$	−11.6075	−0.465044
$624$	−0.820552	−0.0328484
$625$	12.0264	0.481054
$626$	−9.58770	−0.383201
$627$	0.712484	0.0284539
$628$	15.4145	0.615106
$629$	2.00755	0.0800464
$630$	−1.13850	−0.0453588
$631$	−9.49645	−0.378048	−0.189024	−	0.981972i	$-0.560532\pi$
$631$	−9.49645	−0.378048	−0.189024	+	0.981972i	$0.560532\pi$
$632$	−12.5065	−0.497481
$633$	−2.27359	−0.0903672
$634$	9.00744	0.357731
$635$	3.60619	0.143107
$636$	1.26729	0.0502513
$637$	12.8910	0.510760
$638$	5.75413	0.227808
$639$	−19.9814	−0.790451
$640$	−8.16815	−0.322875
$641$	−45.4539	−1.79532	−0.897660	−	0.440688i	$-0.854734\pi$
$641$	−45.4539	−1.79532	−0.897660	+	0.440688i	$0.854734\pi$
$642$	0.148575	0.00586378
$643$	−10.9240	−0.430802	−0.215401	−	0.976526i	$-0.569106\pi$
$643$	−10.9240	−0.430802	−0.215401	+	0.976526i	$0.569106\pi$
$644$	2.82056	0.111146
$645$	0.0919973	0.00362239
$646$	−0.820688	−0.0322895
$647$	47.0440	1.84949	0.924746	−	0.380585i	$-0.124277\pi$
$647$	47.0440	1.84949	0.924746	+	0.380585i	$0.124277\pi$
$648$	−10.3988	−0.408502
$649$	−1.11015	−0.0435774
$650$	2.99661	0.117537
$651$	−0.493454	−0.0193400
$652$	6.82430	0.267260
$653$	40.0542	1.56744	0.783722	−	0.621112i	$-0.213319\pi$
$653$	40.0542	1.56744	0.783722	+	0.621112i	$0.213319\pi$
$654$	0.296140	0.0115800
$655$	−3.86165	−0.150887
$656$	29.8100	1.16389
$657$	11.0052	0.429355
$658$	−4.20853	−0.164065
$659$	12.6598	0.493154	0.246577	−	0.969123i	$-0.420694\pi$
$659$	12.6598	0.493154	0.246577	+	0.969123i	$0.420694\pi$
$660$	0.474873	0.0184844
$661$	−9.32279	−0.362614	−0.181307	−	0.983427i	$-0.558033\pi$
$661$	−9.32279	−0.362614	−0.181307	+	0.983427i	$0.558033\pi$
$662$	−10.0405	−0.390233
$663$	−0.236162	−0.00917179
$664$	−6.10741	−0.237013
$665$	−3.51425	−0.136277
$666$	−1.79019	−0.0693686
$667$	7.92909	0.307016
$668$	−38.4201	−1.48652
$669$	−0.906835	−0.0350603
$670$	−2.91293	−0.112536
$671$	−8.99845	−0.347381
$672$	0.429303	0.0165607
$673$	24.7774	0.955099	0.477549	−	0.878605i	$-0.341525\pi$
$673$	24.7774	0.955099	0.477549	+	0.878605i	$0.341525\pi$
$674$	3.74960	0.144429
$675$	2.34156	0.0901268
$676$	13.2389	0.509188
$677$	−2.92313	−0.112345	−0.0561725	−	0.998421i	$-0.517890\pi$
$677$	−2.92313	−0.112345	−0.0561725	+	0.998421i	$0.517890\pi$
$678$	0.273940	0.0105206
$679$	1.83566	0.0704461
$680$	−1.11943	−0.0429281
$681$	−1.31722	−0.0504759
$682$	3.11775	0.119385
$683$	−33.0369	−1.26412	−0.632061	−	0.774918i	$-0.717791\pi$
$683$	−33.0369	−1.26412	−0.632061	+	0.774918i	$0.717791\pi$
$684$	−15.7329	−0.601562
$685$	8.34669	0.318911
$686$	−4.85016	−0.185180
$687$	0.118061	0.00450430
$688$	3.47452	0.132465
$689$	17.0514	0.649605
$690$	−0.0304386	−0.00115878
$691$	37.3474	1.42076	0.710382	−	0.703817i	$-0.248522\pi$
$691$	37.3474	1.42076	0.710382	+	0.703817i	$0.248522\pi$
$692$	19.3766	0.736588
$693$	10.7437	0.408119
$694$	8.62928	0.327563
$695$	3.26923	0.124009
$696$	0.798513	0.0302676
$697$	8.57961	0.324976
$698$	−7.52837	−0.284953
$699$	−1.31310	−0.0496659
$700$	10.3664	0.391813
$701$	−6.12044	−0.231166	−0.115583	−	0.993298i	$-0.536874\pi$
$701$	−6.12044	−0.231166	−0.115583	+	0.993298i	$0.536874\pi$
$702$	0.421833	0.0159211
$703$	−5.52588	−0.208413
$704$	16.0567	0.605159
$705$	−0.976373	−0.0367724
$706$	−8.63450	−0.324964
$707$	3.07509	0.115651
$708$	−0.0752784	−0.00282914
$709$	−25.1249	−0.943587	−0.471794	−	0.881709i	$-0.656393\pi$
$709$	−25.1249	−0.943587	−0.471794	+	0.881709i	$0.656393\pi$
$710$	1.91220	0.0717634
$711$	−32.0761	−1.20295
$712$	10.1774	0.381413
$713$	4.29621	0.160894
$714$	0.0380024	0.00142220
$715$	6.38941	0.238950
$716$	−17.1790	−0.642011
$717$	0.681629	0.0254559
$718$	8.92636	0.333129
$719$	−38.4307	−1.43322	−0.716611	−	0.697473i	$-0.754308\pi$
$719$	−38.4307	−1.43322	−0.716611	+	0.697473i	$0.754308\pi$
$720$	−9.97557	−0.371767
$721$	7.31636	0.272476
$722$	−3.40598	−0.126758
$723$	−1.96210	−0.0729714
$724$	−22.7771	−0.846505
$725$	29.1417	1.08230
$726$	−0.105860	−0.00392882
$727$	49.4422	1.83371	0.916855	−	0.399221i	$-0.130719\pi$
$727$	49.4422	1.83371	0.916855	+	0.399221i	$0.130719\pi$
$728$	3.82188	0.141648
$729$	−26.5053	−0.981678
$730$	−1.05319	−0.0389803
$731$	1.00000	0.0369863
$732$	−0.610176	−0.0225528
$733$	40.8293	1.50807	0.754033	−	0.656837i	$-0.228106\pi$
$733$	40.8293	1.50807	0.754033	+	0.656837i	$0.228106\pi$
$734$	−8.37466	−0.309114
$735$	−0.481251	−0.0177512
$736$	−3.73768	−0.137773
$737$	27.4886	1.01255
$738$	−7.65069	−0.281626
$739$	0.637007	0.0234327	0.0117163	−	0.999931i	$-0.496270\pi$
$739$	0.637007	0.0234327	0.0117163	+	0.999931i	$0.496270\pi$
$740$	−3.68302	−0.135391
$741$	0.650048	0.0238801
$742$	−2.74384	−0.100730
$743$	−5.35985	−0.196634	−0.0983170	−	0.995155i	$-0.531346\pi$
$743$	−5.35985	−0.196634	−0.0983170	+	0.995155i	$0.531346\pi$
$744$	0.432657	0.0158620
$745$	−0.130342	−0.00477535
$746$	−1.52614	−0.0558761
$747$	−15.6640	−0.573117
$748$	5.16182	0.188735
$749$	6.91553	0.252688
$750$	−0.249018	−0.00909286
$751$	−24.2548	−0.885072	−0.442536	−	0.896751i	$-0.645921\pi$
$751$	−24.2548	−0.885072	−0.442536	+	0.896751i	$0.645921\pi$
$752$	−36.8753	−1.34471
$753$	1.50739	0.0549322
$754$	5.24989	0.191190
$755$	16.5672	0.602942
$756$	1.45928	0.0530734
$757$	−44.8759	−1.63104	−0.815522	−	0.578726i	$-0.803550\pi$
$757$	−44.8759	−1.63104	−0.815522	+	0.578726i	$0.803550\pi$
$758$	−9.00555	−0.327096
$759$	0.287241	0.0104262
$760$	3.08127	0.111770
$761$	−43.7890	−1.58735	−0.793675	−	0.608343i	$-0.791835\pi$
$761$	−43.7890	−1.58735	−0.793675	+	0.608343i	$0.791835\pi$
$762$	0.107340	0.00388851
$763$	13.7841	0.499017
$764$	1.90637	0.0689700
$765$	−2.87106	−0.103803
$766$	2.78494	0.100624
$767$	−1.01287	−0.0365726
$768$	0.896305	0.0323426
$769$	23.3888	0.843423	0.421711	−	0.906730i	$-0.361430\pi$
$769$	23.3888	0.843423	0.421711	+	0.906730i	$0.361430\pi$
$770$	−1.02816	−0.0370523
$771$	−0.714208	−0.0257216
$772$	20.2989	0.730575
$773$	−11.5643	−0.415939	−0.207969	−	0.978135i	$-0.566685\pi$
$773$	−11.5643	−0.415939	−0.207969	+	0.978135i	$0.566685\pi$
$774$	−0.891729	−0.0320525
$775$	15.7898	0.567187
$776$	−1.60949	−0.0577774
$777$	0.255879	0.00917961
$778$	−6.83920	−0.245197
$779$	−23.6158	−0.846123
$780$	0.433259	0.0155132
$781$	−18.0449	−0.645697
$782$	−0.330864	−0.0118317
$783$	4.10228	0.146604
$784$	−18.1757	−0.649134
$785$	−7.74282	−0.276353
$786$	−0.114944	−0.00409991
$787$	17.7738	0.633569	0.316784	−	0.948498i	$-0.397397\pi$
$787$	17.7738	0.633569	0.316784	+	0.948498i	$0.397397\pi$
$788$	3.34023	0.118991
$789$	1.05756	0.0376502
$790$	3.06965	0.109213
$791$	12.7507	0.453364
$792$	−9.42000	−0.334725
$793$	−8.20991	−0.291542
$794$	−4.18052	−0.148361
$795$	−0.636568	−0.0225767
$796$	19.3707	0.686578
$797$	−39.8700	−1.41227	−0.706134	−	0.708079i	$-0.749562\pi$
$797$	−39.8700	−1.41227	−0.706134	+	0.708079i	$0.749562\pi$
$798$	−0.104603	−0.00370292
$799$	−10.6131	−0.375463
$800$	−13.7371	−0.485679
$801$	26.1025	0.922288
$802$	8.19722	0.289454
$803$	9.93868	0.350728
$804$	1.86397	0.0657372
$805$	−1.41679	−0.0499352
$806$	2.84454	0.100195
$807$	−0.308819	−0.0108709
$808$	−2.69622	−0.0948527
$809$	21.1444	0.743397	0.371698	−	0.928354i	$-0.378776\pi$
$809$	21.1444	0.743397	0.371698	+	0.928354i	$0.378776\pi$
$810$	2.55232	0.0896796
$811$	52.2613	1.83514	0.917572	−	0.397570i	$-0.130146\pi$
$811$	52.2613	1.83514	0.917572	+	0.397570i	$0.130146\pi$
$812$	18.1613	0.637337
$813$	0.609265	0.0213678
$814$	−1.61670	−0.0566653
$815$	−3.42789	−0.120074
$816$	0.332979	0.0116566
$817$	−2.75255	−0.0962994
$818$	−6.54173	−0.228726
$819$	9.80222	0.342517
$820$	−15.7400	−0.549665
$821$	9.49309	0.331311	0.165655	−	0.986184i	$-0.447026\pi$
$821$	9.49309	0.331311	0.165655	+	0.986184i	$0.447026\pi$
$822$	0.248443	0.00866544
$823$	33.2395	1.15866	0.579328	−	0.815095i	$-0.303315\pi$
$823$	33.2395	1.15866	0.579328	+	0.815095i	$0.303315\pi$
$824$	−6.41494	−0.223475
$825$	1.05570	0.0367546
$826$	0.162987	0.00567105
$827$	−3.24514	−0.112845	−0.0564223	−	0.998407i	$-0.517969\pi$
$827$	−3.24514	−0.112845	−0.0564223	+	0.998407i	$0.517969\pi$
$828$	−6.34278	−0.220427
$829$	−16.6144	−0.577043	−0.288521	−	0.957473i	$-0.593164\pi$
$829$	−16.6144	−0.577043	−0.288521	+	0.957473i	$0.593164\pi$
$830$	1.49903	0.0520321
$831$	−3.17427	−0.110114
$832$	14.6496	0.507884
$833$	−5.23115	−0.181249
$834$	0.0973100	0.00336957
$835$	19.2987	0.667858
$836$	−14.2081	−0.491399
$837$	2.22273	0.0768289
$838$	8.14594	0.281397
$839$	16.8944	0.583260	0.291630	−	0.956531i	$-0.405802\pi$
$839$	16.8944	0.583260	0.291630	+	0.956531i	$0.405802\pi$
$840$	−0.142680	−0.00492293
$841$	22.0546	0.760503
$842$	2.02577	0.0698126
$843$	1.02217	0.0352054
$844$	45.3393	1.56064
$845$	−6.64998	−0.228766
$846$	9.46399	0.325379
$847$	−4.92732	−0.169305
$848$	−24.0417	−0.825595
$849$	0.477830	0.0163991
$850$	−1.21602	−0.0417092
$851$	−2.22778	−0.0763675
$852$	−1.22361	−0.0419201
$853$	−9.73997	−0.333490	−0.166745	−	0.986000i	$-0.553326\pi$
$853$	−9.73997	−0.333490	−0.166745	+	0.986000i	$0.553326\pi$
$854$	1.32111	0.0452074
$855$	7.90273	0.270268
$856$	−6.06349	−0.207246
$857$	21.9911	0.751201	0.375600	−	0.926782i	$-0.377436\pi$
$857$	21.9911	0.751201	0.375600	+	0.926782i	$0.377436\pi$
$858$	0.190184	0.00649276
$859$	−40.5626	−1.38398	−0.691990	−	0.721907i	$-0.743266\pi$
$859$	−40.5626	−1.38398	−0.691990	+	0.721907i	$0.743266\pi$
$860$	−1.83458	−0.0625587
$861$	1.09354	0.0372678
$862$	1.51293	0.0515306
$863$	42.9860	1.46326	0.731631	−	0.681701i	$-0.238759\pi$
$863$	42.9860	1.46326	0.731631	+	0.681701i	$0.238759\pi$
$864$	−1.93377	−0.0657880
$865$	−9.73300	−0.330932
$866$	4.75787	0.161679
$867$	0.0958345	0.00325471
$868$	9.84032	0.334002
$869$	−28.9675	−0.982654
$870$	−0.195991	−0.00664471
$871$	25.0797	0.849793
$872$	−12.0858	−0.409276
$873$	−4.12796	−0.139710
$874$	0.910718	0.0308055
$875$	−11.5908	−0.391839
$876$	0.673932	0.0227700
$877$	5.67488	0.191627	0.0958135	−	0.995399i	$-0.469455\pi$
$877$	5.67488	0.191627	0.0958135	+	0.995399i	$0.469455\pi$
$878$	4.62017	0.155923
$879$	−2.73504	−0.0922505
$880$	−9.00879	−0.303686
$881$	39.5749	1.33331	0.666656	−	0.745366i	$-0.267725\pi$
$881$	39.5749	1.33331	0.666656	+	0.745366i	$0.267725\pi$
$882$	4.66477	0.157071
$883$	10.8433	0.364906	0.182453	−	0.983215i	$-0.441596\pi$
$883$	10.8433	0.364906	0.182453	+	0.983215i	$0.441596\pi$
$884$	4.70948	0.158397
$885$	0.0378129	0.00127107
$886$	0.935881	0.0314415
$887$	−19.1495	−0.642977	−0.321488	−	0.946913i	$-0.604183\pi$
$887$	−19.1495	−0.642977	−0.321488	+	0.946913i	$0.604183\pi$
$888$	−0.224353	−0.00752879
$889$	4.99622	0.167568
$890$	−2.49798	−0.0837326
$891$	−24.0856	−0.806899
$892$	18.0838	0.605492
$893$	29.2130	0.977574
$894$	−0.00387967	−0.000129756 0
$895$	8.62915	0.288441
$896$	−11.3166	−0.378061
$897$	0.262070	0.00875025
$898$	−3.55381	−0.118592
$899$	27.6628	0.922607
$900$	−23.3116	−0.777053
$901$	−6.91942	−0.230519
$902$	−6.90923	−0.230052
$903$	0.127458	0.00424154
$904$	−11.1798	−0.371833
$905$	11.4411	0.380315
$906$	0.493130	0.0163832
$907$	0.285554	0.00948166	0.00474083	−	0.999989i	$-0.498491\pi$
$907$	0.285554	0.00948166	0.00474083	+	0.999989i	$0.498491\pi$
$908$	26.2676	0.871720
$909$	−6.91516	−0.229361
$910$	−0.938061	−0.0310964
$911$	40.1680	1.33082	0.665412	−	0.746476i	$-0.268256\pi$
$911$	40.1680	1.33082	0.665412	+	0.746476i	$0.268256\pi$
$912$	−0.916540	−0.0303497
$913$	−14.1460	−0.468163
$914$	2.33040	0.0770829
$915$	0.306496	0.0101324
$916$	−2.35433	−0.0777893
$917$	−5.35014	−0.176677
$918$	−0.171179	−0.00564976
$919$	36.4558	1.20257	0.601283	−	0.799036i	$-0.294656\pi$
$919$	36.4558	1.20257	0.601283	+	0.799036i	$0.294656\pi$
$920$	1.24223	0.0409551
$921$	−0.205657	−0.00677661
$922$	−8.89688	−0.293003
$923$	−16.4636	−0.541906
$924$	0.657916	0.0216438
$925$	−8.18776	−0.269212
$926$	−4.35032	−0.142960
$927$	−16.4528	−0.540380
$928$	−24.0665	−0.790023
$929$	−38.2471	−1.25485	−0.627424	−	0.778678i	$-0.715891\pi$
$929$	−38.2471	−1.25485	−0.627424	+	0.778678i	$0.715891\pi$
$930$	−0.106193	−0.00348222
$931$	14.3990	0.471907
$932$	26.1854	0.857731
$933$	−0.444591	−0.0145553
$934$	5.45837	0.178603
$935$	−2.59282	−0.0847941
$936$	−8.59451	−0.280921
$937$	12.9637	0.423504	0.211752	−	0.977323i	$-0.432083\pi$
$937$	12.9637	0.423504	0.211752	+	0.977323i	$0.432083\pi$
$938$	−4.03573	−0.131771
$939$	−3.08172	−0.100568
$940$	19.4706	0.635059
$941$	−12.6712	−0.413069	−0.206535	−	0.978439i	$-0.566219\pi$
$941$	−12.6712	−0.413069	−0.206535	+	0.978439i	$0.566219\pi$
$942$	−0.230468	−0.00750906
$943$	−9.52080	−0.310040
$944$	1.42810	0.0464808
$945$	−0.733004	−0.0238446
$946$	−0.805308	−0.0261828
$947$	15.5136	0.504125	0.252063	−	0.967711i	$-0.418891\pi$
$947$	15.5136	0.504125	0.252063	+	0.967711i	$0.418891\pi$
$948$	−1.96426	−0.0637960
$949$	9.06774	0.294351
$950$	3.34716	0.108596
$951$	2.89521	0.0938835
$952$	−1.55092	−0.0502655
$953$	15.8733	0.514185	0.257093	−	0.966387i	$-0.417235\pi$
$953$	15.8733	0.514185	0.257093	+	0.966387i	$0.417235\pi$
$954$	6.17025	0.199769
$955$	−0.957582	−0.0309866
$956$	−13.5928	−0.439624
$957$	1.84952	0.0597863
$958$	−6.02787	−0.194752
$959$	11.5640	0.373420
$960$	−0.546905	−0.0176513
$961$	−16.0115	−0.516499
$962$	−1.47503	−0.0475567
$963$	−15.5514	−0.501137
$964$	39.1277	1.26022
$965$	−10.1963	−0.328230
$966$	−0.0421713	−0.00135684
$967$	−30.7382	−0.988474	−0.494237	−	0.869327i	$-0.664552\pi$
$967$	−30.7382	−0.988474	−0.494237	+	0.869327i	$0.664552\pi$
$968$	4.32024	0.138858
$969$	−0.263789	−0.00847412
$970$	0.395042	0.0126840
$971$	12.6101	0.404676	0.202338	−	0.979316i	$-0.435146\pi$
$971$	12.6101	0.404676	0.202338	+	0.979316i	$0.435146\pi$
$972$	−4.92487	−0.157965
$973$	4.52937	0.145205
$974$	−1.60625	−0.0514675
$975$	0.963183	0.0308466
$976$	11.5756	0.370526
$977$	−35.0133	−1.12018	−0.560088	−	0.828433i	$-0.689232\pi$
$977$	−35.0133	−1.12018	−0.560088	+	0.828433i	$0.689232\pi$
$978$	−0.102033	−0.00326265
$979$	23.5728	0.753391
$980$	9.59697	0.306564
$981$	−30.9971	−0.989662
$982$	1.59597	0.0509294
$983$	−9.62559	−0.307009	−0.153504	−	0.988148i	$-0.549056\pi$
$983$	−9.62559	−0.307009	−0.153504	+	0.988148i	$0.549056\pi$
$984$	−0.958809	−0.0305657
$985$	−1.67782	−0.0534597
$986$	−2.13040	−0.0678457
$987$	−1.35272	−0.0430576
$988$	−12.9631	−0.412410
$989$	−1.10970	−0.0352864
$990$	2.31209	0.0734830
$991$	−3.82114	−0.121382	−0.0606912	−	0.998157i	$-0.519330\pi$
$991$	−3.82114	−0.121382	−0.0606912	+	0.998157i	$0.519330\pi$
$992$	−13.0399	−0.414018
$993$	−3.22724	−0.102413
$994$	2.64926	0.0840295
$995$	−9.73005	−0.308463
$996$	−0.959224	−0.0303942
$997$	−15.5663	−0.492989	−0.246494	−	0.969144i	$-0.579279\pi$
$997$	−15.5663	−0.492989	−0.246494	+	0.969144i	$0.579279\pi$
$998$	0.303878	0.00961908
$999$	−1.15259	−0.0364663

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.a.d.1.5	✓	8
3.2	odd	2		6579.2.a.k.1.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.a.d.1.5	✓	8	1.1	even	1	trivial
6579.2.a.k.1.4		8	3.2	odd	2

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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.a (trivial)

\(f(q)\)	\(=\)	\(q+0.298156 q^{2} +0.0958345 q^{3} -1.91110 q^{4} +0.959960 q^{5} +0.0285736 q^{6} +1.32998 q^{7} -1.16612 q^{8} -2.99082 q^{9} +O(q^{10})\)	\(q+0.298156 q^{2} +0.0958345 q^{3} -1.91110 q^{4} +0.959960 q^{5} +0.0285736 q^{6} +1.32998 q^{7} -1.16612 q^{8} -2.99082 q^{9} +0.286218 q^{10} -2.70096 q^{11} -0.183150 q^{12} -2.46427 q^{13} +0.396542 q^{14} +0.0919973 q^{15} +3.47452 q^{16} +1.00000 q^{17} -0.891729 q^{18} -2.75255 q^{19} -1.83458 q^{20} +0.127458 q^{21} -0.805308 q^{22} -1.10970 q^{23} -0.111754 q^{24} -4.07848 q^{25} -0.734738 q^{26} -0.574127 q^{27} -2.54173 q^{28} -7.14525 q^{29} +0.0274295 q^{30} -3.87150 q^{31} +3.36819 q^{32} -0.258845 q^{33} +0.298156 q^{34} +1.27673 q^{35} +5.71576 q^{36} +2.00755 q^{37} -0.820688 q^{38} -0.236162 q^{39} -1.11943 q^{40} +8.57961 q^{41} +0.0380024 q^{42} +1.00000 q^{43} +5.16182 q^{44} -2.87106 q^{45} -0.330864 q^{46} -10.6131 q^{47} +0.332979 q^{48} -5.23115 q^{49} -1.21602 q^{50} +0.0958345 q^{51} +4.70948 q^{52} -6.91942 q^{53} -0.171179 q^{54} -2.59282 q^{55} -1.55092 q^{56} -0.263789 q^{57} -2.13040 q^{58} +0.411022 q^{59} -0.175816 q^{60} +3.33157 q^{61} -1.15431 q^{62} -3.97773 q^{63} -5.94480 q^{64} -2.36560 q^{65} -0.0771763 q^{66} -10.1773 q^{67} -1.91110 q^{68} -0.106348 q^{69} +0.380664 q^{70} +6.68091 q^{71} +3.48765 q^{72} -3.67968 q^{73} +0.598564 q^{74} -0.390859 q^{75} +5.26040 q^{76} -3.59223 q^{77} -0.0704132 q^{78} +10.7249 q^{79} +3.33540 q^{80} +8.91743 q^{81} +2.55806 q^{82} +5.23738 q^{83} -0.243586 q^{84} +0.959960 q^{85} +0.298156 q^{86} -0.684761 q^{87} +3.14964 q^{88} -8.72756 q^{89} -0.856024 q^{90} -3.27744 q^{91} +2.12075 q^{92} -0.371023 q^{93} -3.16435 q^{94} -2.64233 q^{95} +0.322788 q^{96} +1.38021 q^{97} -1.55970 q^{98} +8.07808 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - 3 q^{3} + 3 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} - 3 q^{8} + 5 q^{9}+O(q^{10}) \) 8 * q + q^2 - 3 * q^3 + 3 * q^4 - 7 * q^5 - q^6 - 5 * q^7 - 3 * q^8 + 5 * q^9	\( 8 q + q^{2} - 3 q^{3} + 3 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} - 3 q^{8} + 5 q^{9} - 12 q^{10} - 4 q^{11} - 13 q^{12} - 12 q^{13} + q^{14} - 9 q^{15} - 3 q^{16} + 8 q^{17} + 5 q^{18} - 5 q^{20} - 20 q^{21} - 14 q^{22} - 9 q^{23} - q^{24} - 7 q^{25} - 17 q^{26} - 12 q^{27} + q^{28} - 27 q^{29} + 10 q^{30} - 12 q^{31} + 5 q^{32} + 10 q^{33} + q^{34} + 15 q^{35} - 4 q^{36} - 24 q^{37} - q^{38} + 3 q^{39} - 9 q^{40} - 8 q^{41} - 9 q^{42} + 8 q^{43} - 16 q^{44} + 10 q^{45} - 14 q^{46} + 15 q^{47} + 10 q^{48} - 7 q^{49} + 21 q^{50} - 3 q^{51} + q^{52} - 23 q^{53} - 19 q^{54} - 14 q^{55} - 20 q^{56} - 13 q^{57} - 7 q^{58} + 16 q^{59} - 3 q^{60} - 34 q^{61} + 15 q^{62} + 9 q^{63} - 25 q^{64} + 10 q^{65} + 15 q^{66} + 3 q^{68} - 19 q^{69} + 11 q^{70} - 3 q^{71} - 19 q^{72} - 3 q^{73} - 4 q^{74} + 27 q^{75} + 13 q^{76} - 3 q^{77} + 4 q^{78} - 24 q^{79} + 20 q^{80} - 8 q^{81} + 33 q^{82} - 8 q^{83} + 17 q^{84} - 7 q^{85} + q^{86} + 48 q^{87} + 16 q^{88} + 23 q^{89} + 11 q^{90} - 16 q^{91} + 49 q^{92} + 17 q^{93} - 11 q^{94} + 3 q^{95} + 37 q^{96} - 10 q^{97} + 29 q^{98} - 15 q^{99}+O(q^{100}) \) 8 * q + q^2 - 3 * q^3 + 3 * q^4 - 7 * q^5 - q^6 - 5 * q^7 - 3 * q^8 + 5 * q^9 - 12 * q^10 - 4 * q^11 - 13 * q^12 - 12 * q^13 + q^14 - 9 * q^15 - 3 * q^16 + 8 * q^17 + 5 * q^18 - 5 * q^20 - 20 * q^21 - 14 * q^22 - 9 * q^23 - q^24 - 7 * q^25 - 17 * q^26 - 12 * q^27 + q^28 - 27 * q^29 + 10 * q^30 - 12 * q^31 + 5 * q^32 + 10 * q^33 + q^34 + 15 * q^35 - 4 * q^36 - 24 * q^37 - q^38 + 3 * q^39 - 9 * q^40 - 8 * q^41 - 9 * q^42 + 8 * q^43 - 16 * q^44 + 10 * q^45 - 14 * q^46 + 15 * q^47 + 10 * q^48 - 7 * q^49 + 21 * q^50 - 3 * q^51 + q^52 - 23 * q^53 - 19 * q^54 - 14 * q^55 - 20 * q^56 - 13 * q^57 - 7 * q^58 + 16 * q^59 - 3 * q^60 - 34 * q^61 + 15 * q^62 + 9 * q^63 - 25 * q^64 + 10 * q^65 + 15 * q^66 + 3 * q^68 - 19 * q^69 + 11 * q^70 - 3 * q^71 - 19 * q^72 - 3 * q^73 - 4 * q^74 + 27 * q^75 + 13 * q^76 - 3 * q^77 + 4 * q^78 - 24 * q^79 + 20 * q^80 - 8 * q^81 + 33 * q^82 - 8 * q^83 + 17 * q^84 - 7 * q^85 + q^86 + 48 * q^87 + 16 * q^88 + 23 * q^89 + 11 * q^90 - 16 * q^91 + 49 * q^92 + 17 * q^93 - 11 * q^94 + 3 * q^95 + 37 * q^96 - 10 * q^97 + 29 * q^98 - 15 * q^99

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