LMFDB - Embedded newform 731.2.a.d.1.8

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			1.8
Root			$2.33565$ 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)

$f(q)$	$=$	$q+2.33565 q^{2} -0.918667 q^{3} +3.45524 q^{4} -2.98883 q^{5} -2.14568 q^{6} -2.77109 q^{7} +3.39893 q^{8} -2.15605 q^{9} +O(q^{10})$	\(q+2.33565 q^{2} -0.918667 q^{3} +3.45524 q^{4} -2.98883 q^{5} -2.14568 q^{6} -2.77109 q^{7} +3.39893 q^{8} -2.15605 q^{9} -6.98085 q^{10} -3.23020 q^{11} -3.17422 q^{12} +0.0632812 q^{13} -6.47228 q^{14} +2.74574 q^{15} +1.02821 q^{16} +1.00000 q^{17} -5.03577 q^{18} +2.49979 q^{19} -10.3271 q^{20} +2.54571 q^{21} -7.54461 q^{22} +0.421860 q^{23} -3.12248 q^{24} +3.93311 q^{25} +0.147803 q^{26} +4.73669 q^{27} -9.57478 q^{28} +1.30766 q^{29} +6.41308 q^{30} -4.47704 q^{31} -4.39633 q^{32} +2.96748 q^{33} +2.33565 q^{34} +8.28231 q^{35} -7.44967 q^{36} -2.80286 q^{37} +5.83862 q^{38} -0.0581344 q^{39} -10.1588 q^{40} +5.65998 q^{41} +5.94587 q^{42} +1.00000 q^{43} -11.1611 q^{44} +6.44407 q^{45} +0.985315 q^{46} +5.40395 q^{47} -0.944580 q^{48} +0.678928 q^{49} +9.18636 q^{50} -0.918667 q^{51} +0.218652 q^{52} -11.4559 q^{53} +11.0632 q^{54} +9.65453 q^{55} -9.41873 q^{56} -2.29648 q^{57} +3.05423 q^{58} +8.99012 q^{59} +9.48720 q^{60} -11.6534 q^{61} -10.4568 q^{62} +5.97461 q^{63} -12.3247 q^{64} -0.189137 q^{65} +6.93098 q^{66} -2.83321 q^{67} +3.45524 q^{68} -0.387549 q^{69} +19.3446 q^{70} -4.67860 q^{71} -7.32826 q^{72} -7.56593 q^{73} -6.54649 q^{74} -3.61322 q^{75} +8.63738 q^{76} +8.95117 q^{77} -0.135781 q^{78} -6.04405 q^{79} -3.07314 q^{80} +2.11671 q^{81} +13.2197 q^{82} -6.52432 q^{83} +8.79603 q^{84} -2.98883 q^{85} +2.33565 q^{86} -1.20131 q^{87} -10.9792 q^{88} +3.14970 q^{89} +15.0511 q^{90} -0.175358 q^{91} +1.45763 q^{92} +4.11291 q^{93} +12.6217 q^{94} -7.47145 q^{95} +4.03876 q^{96} +14.0855 q^{97} +1.58574 q^{98} +6.96448 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.33565	1.65155	0.825775	−	0.563999i	$-0.190738\pi$
$2$	2.33565	1.65155	0.825775	+	0.563999i	$0.190738\pi$
$3$	−0.918667	−0.530393	−0.265196	−	0.964194i	$-0.585437\pi$
$3$	−0.918667	−0.530393	−0.265196	+	0.964194i	$0.585437\pi$
$4$	3.45524	1.72762
$5$	−2.98883	−1.33665	−0.668323	−	0.743871i	$-0.732988\pi$
$5$	−2.98883	−1.33665	−0.668323	+	0.743871i	$0.732988\pi$
$6$	−2.14568	−0.875971
$7$	−2.77109	−1.04737	−0.523686	−	0.851911i	$-0.675444\pi$
$7$	−2.77109	−1.04737	−0.523686	+	0.851911i	$0.675444\pi$
$8$	3.39893	1.20170
$9$	−2.15605	−0.718684
$10$	−6.98085	−2.20754
$11$	−3.23020	−0.973943	−0.486971	−	0.873418i	$-0.661898\pi$
$11$	−3.23020	−0.973943	−0.486971	+	0.873418i	$0.661898\pi$
$12$	−3.17422	−0.916317
$13$	0.0632812	0.0175511	0.00877553	−	0.999961i	$-0.497207\pi$
$13$	0.0632812	0.0175511	0.00877553	+	0.999961i	$0.497207\pi$
$14$	−6.47228	−1.72979
$15$	2.74574	0.708947
$16$	1.02821	0.257052
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−5.03577	−1.18694
$19$	2.49979	0.573491	0.286746	−	0.958007i	$-0.407427\pi$
$19$	2.49979	0.573491	0.286746	+	0.958007i	$0.407427\pi$
$20$	−10.3271	−2.30922
$21$	2.54571	0.555519
$22$	−7.54461	−1.60852
$23$	0.421860	0.0879639	0.0439819	−	0.999032i	$-0.485996\pi$
$23$	0.421860	0.0879639	0.0439819	+	0.999032i	$0.485996\pi$
$24$	−3.12248	−0.637374
$25$	3.93311	0.786623
$26$	0.147803	0.0289865
$27$	4.73669	0.911577
$28$	−9.57478	−1.80946
$29$	1.30766	0.242827	0.121413	−	0.992602i	$-0.461257\pi$
$29$	1.30766	0.242827	0.121413	+	0.992602i	$0.461257\pi$
$30$	6.41308	1.17086
$31$	−4.47704	−0.804101	−0.402050	−	0.915618i	$-0.631702\pi$
$31$	−4.47704	−0.804101	−0.402050	+	0.915618i	$0.631702\pi$
$32$	−4.39633	−0.777168
$33$	2.96748	0.516572
$34$	2.33565	0.400560
$35$	8.28231	1.39997
$36$	−7.44967	−1.24161
$37$	−2.80286	−0.460788	−0.230394	−	0.973097i	$-0.574001\pi$
$37$	−2.80286	−0.460788	−0.230394	+	0.973097i	$0.574001\pi$
$38$	5.83862	0.947150
$39$	−0.0581344	−0.00930895
$40$	−10.1588	−1.60625
$41$	5.65998	0.883941	0.441970	−	0.897030i	$-0.354280\pi$
$41$	5.65998	0.883941	0.441970	+	0.897030i	$0.354280\pi$
$42$	5.94587	0.917468
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−11.1611	−1.68260
$45$	6.44407	0.960626
$46$	0.985315	0.145277
$47$	5.40395	0.788247	0.394123	−	0.919058i	$-0.371048\pi$
$47$	5.40395	0.788247	0.394123	+	0.919058i	$0.371048\pi$
$48$	−0.944580	−0.136338
$49$	0.678928	0.0969898
$50$	9.18636	1.29915
$51$	−0.918667	−0.128639
$52$	0.218652	0.0303216
$53$	−11.4559	−1.57359	−0.786797	−	0.617212i	$-0.788262\pi$
$53$	−11.4559	−1.57359	−0.786797	+	0.617212i	$0.788262\pi$
$54$	11.0632	1.50552
$55$	9.65453	1.30182
$56$	−9.41873	−1.25863
$57$	−2.29648	−0.304176
$58$	3.05423	0.401041
$59$	8.99012	1.17041	0.585207	−	0.810884i	$-0.301013\pi$
$59$	8.99012	1.17041	0.585207	+	0.810884i	$0.301013\pi$
$60$	9.48720	1.22479
$61$	−11.6534	−1.49206	−0.746030	−	0.665913i	$-0.768042\pi$
$61$	−11.6534	−1.49206	−0.746030	+	0.665913i	$0.768042\pi$
$62$	−10.4568	−1.32801
$63$	5.97461	0.752730
$64$	−12.3247	−1.54058
$65$	−0.189137	−0.0234595
$66$	6.93098	0.853145
$67$	−2.83321	−0.346131	−0.173066	−	0.984910i	$-0.555367\pi$
$67$	−2.83321	−0.346131	−0.173066	+	0.984910i	$0.555367\pi$
$68$	3.45524	0.419009
$69$	−0.387549	−0.0466554
$70$	19.3446	2.31212
$71$	−4.67860	−0.555247	−0.277624	−	0.960690i	$-0.589547\pi$
$71$	−4.67860	−0.555247	−0.277624	+	0.960690i	$0.589547\pi$
$72$	−7.32826	−0.863644
$73$	−7.56593	−0.885525	−0.442763	−	0.896639i	$-0.646002\pi$
$73$	−7.56593	−0.885525	−0.442763	+	0.896639i	$0.646002\pi$
$74$	−6.54649	−0.761014
$75$	−3.61322	−0.417219
$76$	8.63738	0.990775
$77$	8.95117	1.02008
$78$	−0.135781	−0.0153742
$79$	−6.04405	−0.680009	−0.340004	−	0.940424i	$-0.610429\pi$
$79$	−6.04405	−0.680009	−0.340004	+	0.940424i	$0.610429\pi$
$80$	−3.07314	−0.343587
$81$	2.11671	0.235190
$82$	13.2197	1.45987
$83$	−6.52432	−0.716137	−0.358068	−	0.933695i	$-0.616565\pi$
$83$	−6.52432	−0.716137	−0.358068	+	0.933695i	$0.616565\pi$
$84$	8.79603	0.959726
$85$	−2.98883	−0.324184
$86$	2.33565	0.251859
$87$	−1.20131	−0.128793
$88$	−10.9792	−1.17039
$89$	3.14970	0.333867	0.166934	−	0.985968i	$-0.446613\pi$
$89$	3.14970	0.333867	0.166934	+	0.985968i	$0.446613\pi$
$90$	15.0511	1.58652
$91$	−0.175358	−0.0183825
$92$	1.45763	0.151968
$93$	4.11291	0.426489
$94$	12.6217	1.30183
$95$	−7.47145	−0.766555
$96$	4.03876	0.412204
$97$	14.0855	1.43017	0.715084	−	0.699039i	$-0.246389\pi$
$97$	14.0855	1.43017	0.715084	+	0.699039i	$0.246389\pi$
$98$	1.58574	0.160184
$99$	6.96448	0.699957
$100$	13.5899	1.35899
$101$	−1.34417	−0.133750	−0.0668749	−	0.997761i	$-0.521303\pi$
$101$	−1.34417	−0.133750	−0.0668749	+	0.997761i	$0.521303\pi$
$102$	−2.14568	−0.212454
$103$	−0.0836191	−0.00823924	−0.00411962	−	0.999992i	$-0.501311\pi$
$103$	−0.0836191	−0.00823924	−0.00411962	+	0.999992i	$0.501311\pi$
$104$	0.215088	0.0210911
$105$	−7.60869	−0.742532
$106$	−26.7570	−2.59887
$107$	−14.0738	−1.36057	−0.680283	−	0.732950i	$-0.738143\pi$
$107$	−14.0738	−1.36057	−0.680283	+	0.732950i	$0.738143\pi$
$108$	16.3664	1.57486
$109$	−5.71135	−0.547048	−0.273524	−	0.961865i	$-0.588189\pi$
$109$	−5.71135	−0.547048	−0.273524	+	0.961865i	$0.588189\pi$
$110$	22.5496	2.15002
$111$	2.57490	0.244398
$112$	−2.84925	−0.269229
$113$	5.29356	0.497976	0.248988	−	0.968507i	$-0.419902\pi$
$113$	5.29356	0.497976	0.248988	+	0.968507i	$0.419902\pi$
$114$	−5.36375	−0.502361
$115$	−1.26087	−0.117577
$116$	4.51829	0.419512
$117$	−0.136438	−0.0126137
$118$	20.9977	1.93300
$119$	−2.77109	−0.254025
$120$	9.33257	0.851944
$121$	−0.565794	−0.0514358
$122$	−27.2181	−2.46421
$123$	−5.19964	−0.468836
$124$	−15.4693	−1.38918
$125$	3.18874	0.285210
$126$	13.9546	1.24317
$127$	0.574257	0.0509570	0.0254785	−	0.999675i	$-0.491889\pi$
$127$	0.574257	0.0509570	0.0254785	+	0.999675i	$0.491889\pi$
$128$	−19.9934	−1.76719
$129$	−0.918667	−0.0808841
$130$	−0.441757	−0.0387446
$131$	16.5127	1.44272	0.721362	−	0.692558i	$-0.243516\pi$
$131$	16.5127	1.44272	0.721362	+	0.692558i	$0.243516\pi$
$132$	10.2534	0.892440
$133$	−6.92714	−0.600659
$134$	−6.61737	−0.571653
$135$	−14.1572	−1.21846
$136$	3.39893	0.291456
$137$	−6.55576	−0.560096	−0.280048	−	0.959986i	$-0.590350\pi$
$137$	−6.55576	−0.560096	−0.280048	+	0.959986i	$0.590350\pi$
$138$	−0.905177	−0.0770538
$139$	−19.6430	−1.66610	−0.833050	−	0.553198i	$-0.813407\pi$
$139$	−19.6430	−1.66610	−0.833050	+	0.553198i	$0.813407\pi$
$140$	28.6174	2.41861
$141$	−4.96443	−0.418080
$142$	−10.9275	−0.917019
$143$	−0.204411	−0.0170937
$144$	−2.21687	−0.184739
$145$	−3.90838	−0.324573
$146$	−17.6713	−1.46249
$147$	−0.623709	−0.0514427
$148$	−9.68456	−0.796066
$149$	12.6366	1.03523	0.517617	−	0.855613i	$-0.326819\pi$
$149$	12.6366	1.03523	0.517617	+	0.855613i	$0.326819\pi$
$150$	−8.43921	−0.689058
$151$	−6.66491	−0.542382	−0.271191	−	0.962526i	$-0.587418\pi$
$151$	−6.66491	−0.542382	−0.271191	+	0.962526i	$0.587418\pi$
$152$	8.49660	0.689166
$153$	−2.15605	−0.174306
$154$	20.9068	1.68472
$155$	13.3811	1.07480
$156$	−0.200868	−0.0160823
$157$	−16.3638	−1.30597	−0.652987	−	0.757369i	$-0.726484\pi$
$157$	−16.3638	−1.30597	−0.652987	+	0.757369i	$0.726484\pi$
$158$	−14.1168	−1.12307
$159$	10.5242	0.834623
$160$	13.1399	1.03880
$161$	−1.16901	−0.0921310
$162$	4.94388	0.388428
$163$	22.8344	1.78853	0.894264	−	0.447540i	$-0.147700\pi$
$163$	22.8344	1.78853	0.894264	+	0.447540i	$0.147700\pi$
$164$	19.5566	1.52711
$165$	−8.86930	−0.690474
$166$	−15.2385	−1.18274
$167$	9.29697	0.719421	0.359711	−	0.933064i	$-0.382875\pi$
$167$	9.29697	0.719421	0.359711	+	0.933064i	$0.382875\pi$
$168$	8.65267	0.667568
$169$	−12.9960	−0.999692
$170$	−6.98085	−0.535407
$171$	−5.38967	−0.412159
$172$	3.45524	0.263460
$173$	17.8635	1.35814	0.679070	−	0.734074i	$-0.262383\pi$
$173$	17.8635	1.35814	0.679070	+	0.734074i	$0.262383\pi$
$174$	−2.80582	−0.212709
$175$	−10.8990	−0.823887
$176$	−3.32132	−0.250354
$177$	−8.25893	−0.620779
$178$	7.35658	0.551399
$179$	11.7073	0.875046	0.437523	−	0.899207i	$-0.355856\pi$
$179$	11.7073	0.875046	0.437523	+	0.899207i	$0.355856\pi$
$180$	22.2658	1.65960
$181$	14.0445	1.04392	0.521959	−	0.852971i	$-0.325201\pi$
$181$	14.0445	1.04392	0.521959	+	0.852971i	$0.325201\pi$
$182$	−0.409574	−0.0303596
$183$	10.7056	0.791377
$184$	1.43387	0.105706
$185$	8.37728	0.615910
$186$	9.60631	0.704369
$187$	−3.23020	−0.236216
$188$	18.6719	1.36179
$189$	−13.1258	−0.954761
$190$	−17.4507	−1.26600
$191$	−0.723573	−0.0523559	−0.0261780	−	0.999657i	$-0.508334\pi$
$191$	−0.723573	−0.0523559	−0.0261780	+	0.999657i	$0.508334\pi$
$192$	11.3223	0.817115
$193$	−17.5538	−1.26355	−0.631776	−	0.775151i	$-0.717674\pi$
$193$	−17.5538	−1.26355	−0.631776	+	0.775151i	$0.717674\pi$
$194$	32.8988	2.36199
$195$	0.173754	0.0124428
$196$	2.34586	0.167562
$197$	−11.2039	−0.798244	−0.399122	−	0.916898i	$-0.630685\pi$
$197$	−11.2039	−0.798244	−0.399122	+	0.916898i	$0.630685\pi$
$198$	16.2666	1.15601
$199$	10.5925	0.750879	0.375440	−	0.926847i	$-0.377492\pi$
$199$	10.5925	0.750879	0.375440	+	0.926847i	$0.377492\pi$
$200$	13.3684	0.945286
$201$	2.60277	0.183586
$202$	−3.13950	−0.220895
$203$	−3.62365	−0.254330
$204$	−3.17422	−0.222240
$205$	−16.9167	−1.18152
$206$	−0.195305	−0.0136075
$207$	−0.909551	−0.0632182
$208$	0.0650662	0.00451153
$209$	−8.07483	−0.558548
$210$	−17.7712	−1.22633
$211$	14.5977	1.00495	0.502475	−	0.864592i	$-0.332423\pi$
$211$	14.5977	1.00495	0.502475	+	0.864592i	$0.332423\pi$
$212$	−39.5830	−2.71857
$213$	4.29807	0.294499
$214$	−32.8714	−2.24704
$215$	−2.98883	−0.203837
$216$	16.0997	1.09544
$217$	12.4063	0.842193
$218$	−13.3397	−0.903478
$219$	6.95057	0.469676
$220$	33.3587	2.24904
$221$	0.0632812	0.00425676
$222$	6.01405	0.403637
$223$	2.32613	0.155769	0.0778847	−	0.996962i	$-0.475183\pi$
$223$	2.32613	0.155769	0.0778847	+	0.996962i	$0.475183\pi$
$224$	12.1826	0.813985
$225$	−8.47999	−0.565333
$226$	12.3639	0.822433
$227$	−23.5975	−1.56622	−0.783110	−	0.621883i	$-0.786368\pi$
$227$	−23.5975	−1.56622	−0.783110	+	0.621883i	$0.786368\pi$
$228$	−7.93487	−0.525500
$229$	−28.1424	−1.85970	−0.929852	−	0.367934i	$-0.880065\pi$
$229$	−28.1424	−1.85970	−0.929852	+	0.367934i	$0.880065\pi$
$230$	−2.94494	−0.194184
$231$	−8.22315	−0.541044
$232$	4.44465	0.291805
$233$	12.6786	0.830603	0.415302	−	0.909684i	$-0.363676\pi$
$233$	12.6786	0.830603	0.415302	+	0.909684i	$0.363676\pi$
$234$	−0.318670	−0.0208321
$235$	−16.1515	−1.05361
$236$	31.0630	2.02203
$237$	5.55247	0.360672
$238$	−6.47228	−0.419536
$239$	−0.854129	−0.0552490	−0.0276245	−	0.999618i	$-0.508794\pi$
$239$	−0.854129	−0.0552490	−0.0276245	+	0.999618i	$0.508794\pi$
$240$	2.82319	0.182236
$241$	−18.7188	−1.20579	−0.602893	−	0.797822i	$-0.705986\pi$
$241$	−18.7188	−1.20579	−0.602893	+	0.797822i	$0.705986\pi$
$242$	−1.32149	−0.0849489
$243$	−16.1546	−1.03632
$244$	−40.2651	−2.57771
$245$	−2.02920	−0.129641
$246$	−12.1445	−0.774306
$247$	0.158190	0.0100654
$248$	−15.2171	−0.966290
$249$	5.99367	0.379834
$250$	7.44778	0.471039
$251$	−5.47267	−0.345432	−0.172716	−	0.984972i	$-0.555254\pi$
$251$	−5.47267	−0.345432	−0.172716	+	0.984972i	$0.555254\pi$
$252$	20.6437	1.30043
$253$	−1.36269	−0.0856718
$254$	1.34126	0.0841582
$255$	2.74574	0.171945
$256$	−22.0482	−1.37801
$257$	−29.6793	−1.85134	−0.925671	−	0.378330i	$-0.876499\pi$
$257$	−29.6793	−1.85134	−0.925671	+	0.378330i	$0.876499\pi$
$258$	−2.14568	−0.133584
$259$	7.76698	0.482617
$260$	−0.653514	−0.0405292
$261$	−2.81938	−0.174516
$262$	38.5679	2.38273
$263$	25.6669	1.58269	0.791346	−	0.611369i	$-0.209381\pi$
$263$	25.6669	1.58269	0.791346	+	0.611369i	$0.209381\pi$
$264$	10.0862	0.620766
$265$	34.2399	2.10334
$266$	−16.1793	−0.992019
$267$	−2.89352	−0.177081
$268$	−9.78941	−0.597983
$269$	−11.5443	−0.703871	−0.351936	−	0.936024i	$-0.614476\pi$
$269$	−11.5443	−0.703871	−0.351936	+	0.936024i	$0.614476\pi$
$270$	−33.0662	−2.01234
$271$	20.2337	1.22911	0.614555	−	0.788874i	$-0.289335\pi$
$271$	20.2337	1.22911	0.614555	+	0.788874i	$0.289335\pi$
$272$	1.02821	0.0623442
$273$	0.161095	0.00974994
$274$	−15.3119	−0.925027
$275$	−12.7048	−0.766125
$276$	−1.33907	−0.0806028
$277$	−4.13639	−0.248532	−0.124266	−	0.992249i	$-0.539658\pi$
$277$	−4.13639	−0.248532	−0.124266	+	0.992249i	$0.539658\pi$
$278$	−45.8792	−2.75165
$279$	9.65274	0.577894
$280$	28.1510	1.68234
$281$	−7.81685	−0.466314	−0.233157	−	0.972439i	$-0.574906\pi$
$281$	−7.81685	−0.466314	−0.233157	+	0.972439i	$0.574906\pi$
$282$	−11.5951	−0.690481
$283$	3.28718	0.195402	0.0977012	−	0.995216i	$-0.468851\pi$
$283$	3.28718	0.195402	0.0977012	+	0.995216i	$0.468851\pi$
$284$	−16.1657	−0.959256
$285$	6.86378	0.406575
$286$	−0.477432	−0.0282311
$287$	−15.6843	−0.925816
$288$	9.47870	0.558538
$289$	1.00000	0.0588235
$290$	−9.12859	−0.536049
$291$	−12.9399	−0.758550
$292$	−26.1421	−1.52985
$293$	0.925251	0.0540537	0.0270269	−	0.999635i	$-0.491396\pi$
$293$	0.925251	0.0540537	0.0270269	+	0.999635i	$0.491396\pi$
$294$	−1.45676	−0.0849602
$295$	−26.8700	−1.56443
$296$	−9.52672	−0.553730
$297$	−15.3005	−0.887824
$298$	29.5147	1.70974
$299$	0.0266958	0.00154386
$300$	−12.4846	−0.720796
$301$	−2.77109	−0.159723
$302$	−15.5669	−0.895772
$303$	1.23484	0.0709399
$304$	2.57030	0.147417
$305$	34.8299	1.99435
$306$	−5.03577	−0.287876
$307$	3.87609	0.221220	0.110610	−	0.993864i	$-0.464720\pi$
$307$	3.87609	0.221220	0.110610	+	0.993864i	$0.464720\pi$
$308$	30.9285	1.76231
$309$	0.0768181	0.00437003
$310$	31.2536	1.77508
$311$	−7.02623	−0.398421	−0.199211	−	0.979957i	$-0.563838\pi$
$311$	−7.02623	−0.398421	−0.199211	+	0.979957i	$0.563838\pi$
$312$	−0.197595	−0.0111866
$313$	10.0308	0.566974	0.283487	−	0.958976i	$-0.408509\pi$
$313$	10.0308	0.566974	0.283487	+	0.958976i	$0.408509\pi$
$314$	−38.2201	−2.15688
$315$	−17.8571	−1.00613
$316$	−20.8836	−1.17480
$317$	−17.8636	−1.00332	−0.501660	−	0.865065i	$-0.667277\pi$
$317$	−17.8636	−1.00332	−0.501660	+	0.865065i	$0.667277\pi$
$318$	24.5808	1.37842
$319$	−4.22401	−0.236499
$320$	36.8364	2.05922
$321$	12.9291	0.721634
$322$	−2.73040	−0.152159
$323$	2.49979	0.139092
$324$	7.31373	0.406318
$325$	0.248892	0.0138061
$326$	53.3330	2.95384
$327$	5.24683	0.290150
$328$	19.2379	1.06223
$329$	−14.9748	−0.825588
$330$	−20.7155	−1.14035
$331$	−2.41881	−0.132950	−0.0664750	−	0.997788i	$-0.521175\pi$
$331$	−2.41881	−0.132950	−0.0664750	+	0.997788i	$0.521175\pi$
$332$	−22.5431	−1.23721
$333$	6.04311	0.331161
$334$	21.7144	1.18816
$335$	8.46798	0.462655
$336$	2.61752	0.142797
$337$	5.10856	0.278281	0.139140	−	0.990273i	$-0.455566\pi$
$337$	5.10856	0.278281	0.139140	+	0.990273i	$0.455566\pi$
$338$	−30.3540	−1.65104
$339$	−4.86302	−0.264123
$340$	−10.3271	−0.560067
$341$	14.4618	0.783148
$342$	−12.5884	−0.680701
$343$	17.5162	0.945788
$344$	3.39893	0.183258
$345$	1.15832	0.0623617
$346$	41.7229	2.24304
$347$	−9.21121	−0.494484	−0.247242	−	0.968954i	$-0.579524\pi$
$347$	−9.21121	−0.494484	−0.247242	+	0.968954i	$0.579524\pi$
$348$	−4.15080	−0.222506
$349$	−17.7733	−0.951381	−0.475690	−	0.879613i	$-0.657802\pi$
$349$	−17.7733	−0.951381	−0.475690	+	0.879613i	$0.657802\pi$
$350$	−25.4562	−1.36069
$351$	0.299744	0.0159991
$352$	14.2010	0.756917
$353$	17.5617	0.934717	0.467358	−	0.884068i	$-0.345206\pi$
$353$	17.5617	0.934717	0.467358	+	0.884068i	$0.345206\pi$
$354$	−19.2899	−1.02525
$355$	13.9835	0.742169
$356$	10.8830	0.576796
$357$	2.54571	0.134733
$358$	27.3442	1.44518
$359$	−18.8445	−0.994576	−0.497288	−	0.867585i	$-0.665671\pi$
$359$	−18.8445	−0.994576	−0.497288	+	0.867585i	$0.665671\pi$
$360$	21.9029	1.15439
$361$	−12.7510	−0.671108
$362$	32.8029	1.72408
$363$	0.519776	0.0272812
$364$	−0.605904	−0.0317580
$365$	22.6133	1.18363
$366$	25.0044	1.30700
$367$	34.1090	1.78048	0.890238	−	0.455497i	$-0.150538\pi$
$367$	34.1090	1.78048	0.890238	+	0.455497i	$0.150538\pi$
$368$	0.433759	0.0226113
$369$	−12.2032	−0.635274
$370$	19.5664	1.01721
$371$	31.7454	1.64814
$372$	14.2111	0.736812
$373$	5.60082	0.289999	0.145000	−	0.989432i	$-0.453682\pi$
$373$	5.60082	0.289999	0.145000	+	0.989432i	$0.453682\pi$
$374$	−7.54461	−0.390122
$375$	−2.92939	−0.151273
$376$	18.3676	0.947238
$377$	0.0827504	0.00426186
$378$	−30.6572	−1.57684
$379$	−11.7887	−0.605543	−0.302771	−	0.953063i	$-0.597912\pi$
$379$	−11.7887	−0.605543	−0.302771	+	0.953063i	$0.597912\pi$
$380$	−25.8157	−1.32432
$381$	−0.527551	−0.0270272
$382$	−1.69001	−0.0864685
$383$	36.8729	1.88412	0.942058	−	0.335451i	$-0.108889\pi$
$383$	36.8729	1.88412	0.942058	+	0.335451i	$0.108889\pi$
$384$	18.3673	0.937302
$385$	−26.7536	−1.36349
$386$	−40.9995	−2.08682
$387$	−2.15605	−0.109598
$388$	48.6688	2.47079
$389$	−29.2324	−1.48214	−0.741070	−	0.671428i	$-0.765681\pi$
$389$	−29.2324	−1.48214	−0.741070	+	0.671428i	$0.765681\pi$
$390$	0.405827	0.0205499
$391$	0.421860	0.0213344
$392$	2.30763	0.116553
$393$	−15.1697	−0.765211
$394$	−26.1683	−1.31834
$395$	18.0646	0.908931
$396$	24.0640	1.20926
$397$	24.3197	1.22057	0.610285	−	0.792182i	$-0.291055\pi$
$397$	24.3197	1.22057	0.610285	+	0.792182i	$0.291055\pi$
$398$	24.7402	1.24012
$399$	6.36373	0.318585
$400$	4.04406	0.202203
$401$	26.1337	1.30505	0.652527	−	0.757765i	$-0.273709\pi$
$401$	26.1337	1.30505	0.652527	+	0.757765i	$0.273709\pi$
$402$	6.07916	0.303201
$403$	−0.283313	−0.0141128
$404$	−4.64442	−0.231069
$405$	−6.32648	−0.314365
$406$	−8.46355	−0.420039
$407$	9.05381	0.448781
$408$	−3.12248	−0.154586
$409$	−1.25503	−0.0620572	−0.0310286	−	0.999518i	$-0.509878\pi$
$409$	−1.25503	−0.0620572	−0.0310286	+	0.999518i	$0.509878\pi$
$410$	−39.5115	−1.95133
$411$	6.02256	0.297071
$412$	−0.288924	−0.0142343
$413$	−24.9124	−1.22586
$414$	−2.12439	−0.104408
$415$	19.5001	0.957221
$416$	−0.278205	−0.0136401
$417$	18.0454	0.883687
$418$	−18.8599	−0.922470
$419$	−21.0555	−1.02863	−0.514313	−	0.857602i	$-0.671953\pi$
$419$	−21.0555	−1.02863	−0.514313	+	0.857602i	$0.671953\pi$
$420$	−26.2899	−1.28281
$421$	−29.6219	−1.44368	−0.721841	−	0.692059i	$-0.756704\pi$
$421$	−29.6219	−1.44368	−0.721841	+	0.692059i	$0.756704\pi$
$422$	34.0951	1.65972
$423$	−11.6512	−0.566500
$424$	−38.9379	−1.89099
$425$	3.93311	0.190784
$426$	10.0388	0.486380
$427$	32.2925	1.56274
$428$	−48.6284	−2.35054
$429$	0.187786	0.00906638
$430$	−6.98085	−0.336647
$431$	−3.74309	−0.180298	−0.0901492	−	0.995928i	$-0.528734\pi$
$431$	−3.74309	−0.180298	−0.0901492	+	0.995928i	$0.528734\pi$
$432$	4.87030	0.234323
$433$	−16.1727	−0.777210	−0.388605	−	0.921404i	$-0.627043\pi$
$433$	−16.1727	−0.777210	−0.388605	+	0.921404i	$0.627043\pi$
$434$	28.9767	1.39093
$435$	3.59050	0.172151
$436$	−19.7341	−0.945092
$437$	1.05456	0.0504465
$438$	16.2341	0.775694
$439$	−6.68299	−0.318962	−0.159481	−	0.987201i	$-0.550982\pi$
$439$	−6.68299	−0.318962	−0.159481	+	0.987201i	$0.550982\pi$
$440$	32.8150	1.56440
$441$	−1.46380	−0.0697050
$442$	0.147803	0.00703025
$443$	24.1615	1.14795	0.573973	−	0.818874i	$-0.305401\pi$
$443$	24.1615	1.14795	0.573973	+	0.818874i	$0.305401\pi$
$444$	8.89689	0.422228
$445$	−9.41392	−0.446262
$446$	5.43303	0.257261
$447$	−11.6089	−0.549080
$448$	34.1528	1.61357
$449$	6.64066	0.313392	0.156696	−	0.987647i	$-0.449916\pi$
$449$	6.64066	0.313392	0.156696	+	0.987647i	$0.449916\pi$
$450$	−19.8063	−0.933676
$451$	−18.2829	−0.860908
$452$	18.2905	0.860314
$453$	6.12283	0.287676
$454$	−55.1154	−2.58669
$455$	0.524115	0.0245709
$456$	−7.80555	−0.365528
$457$	3.09739	0.144890	0.0724449	−	0.997372i	$-0.476920\pi$
$457$	3.09739	0.144890	0.0724449	+	0.997372i	$0.476920\pi$
$458$	−65.7307	−3.07140
$459$	4.73669	0.221090
$460$	−4.35660	−0.203128
$461$	−32.0213	−1.49138	−0.745691	−	0.666292i	$-0.767881\pi$
$461$	−32.0213	−1.49138	−0.745691	+	0.666292i	$0.767881\pi$
$462$	−19.2064	−0.893561
$463$	24.1973	1.12454	0.562272	−	0.826953i	$-0.309928\pi$
$463$	24.1973	1.12454	0.562272	+	0.826953i	$0.309928\pi$
$464$	1.34455	0.0624190
$465$	−12.2928	−0.570065
$466$	29.6127	1.37178
$467$	−31.0981	−1.43905	−0.719524	−	0.694468i	$-0.755640\pi$
$467$	−31.0981	−1.43905	−0.719524	+	0.694468i	$0.755640\pi$
$468$	−0.471425	−0.0217916
$469$	7.85107	0.362529
$470$	−37.7242	−1.74009
$471$	15.0329	0.692679
$472$	30.5568	1.40649
$473$	−3.23020	−0.148525
$474$	12.9686	0.595668
$475$	9.83196	0.451121
$476$	−9.57478	−0.438859
$477$	24.6996	1.13092
$478$	−1.99494	−0.0912466
$479$	5.15811	0.235680	0.117840	−	0.993033i	$-0.462403\pi$
$479$	5.15811	0.235680	0.117840	+	0.993033i	$0.462403\pi$
$480$	−12.0712	−0.550971
$481$	−0.177369	−0.00808731
$482$	−43.7206	−1.99142
$483$	1.07393	0.0488656
$484$	−1.95495	−0.0888616
$485$	−42.0992	−1.91163
$486$	−37.7315	−1.71154
$487$	−32.6373	−1.47894	−0.739468	−	0.673191i	$-0.764923\pi$
$487$	−32.6373	−1.47894	−0.739468	+	0.673191i	$0.764923\pi$
$488$	−39.6089	−1.79301
$489$	−20.9772	−0.948622
$490$	−4.73950	−0.214109
$491$	26.3522	1.18926	0.594630	−	0.804000i	$-0.297299\pi$
$491$	26.3522	1.18926	0.594630	+	0.804000i	$0.297299\pi$
$492$	−17.9660	−0.809970
$493$	1.30766	0.0588941
$494$	0.369475	0.0166235
$495$	−20.8157	−0.935594
$496$	−4.60333	−0.206696
$497$	12.9648	0.581551
$498$	13.9991	0.627315
$499$	12.6072	0.564377	0.282188	−	0.959359i	$-0.408940\pi$
$499$	12.6072	0.564377	0.282188	+	0.959359i	$0.408940\pi$
$500$	11.0179	0.492735
$501$	−8.54082	−0.381576
$502$	−12.7822	−0.570498
$503$	3.53384	0.157566	0.0787831	−	0.996892i	$-0.474897\pi$
$503$	3.53384	0.157566	0.0787831	+	0.996892i	$0.474897\pi$
$504$	20.3072	0.904557
$505$	4.01749	0.178776
$506$	−3.18277	−0.141491
$507$	11.9390	0.530229
$508$	1.98420	0.0880344
$509$	−33.0259	−1.46385	−0.731923	−	0.681387i	$-0.761377\pi$
$509$	−33.0259	−1.46385	−0.731923	+	0.681387i	$0.761377\pi$
$510$	6.41308	0.283976
$511$	20.9659	0.927475
$512$	−11.5099	−0.508672
$513$	11.8407	0.522782
$514$	−69.3203	−3.05759
$515$	0.249923	0.0110129
$516$	−3.17422	−0.139737
$517$	−17.4558	−0.767707
$518$	18.1409	0.797066
$519$	−16.4106	−0.720347
$520$	−0.642863	−0.0281914
$521$	32.0906	1.40591	0.702957	−	0.711233i	$-0.251863\pi$
$521$	32.0906	1.40591	0.702957	+	0.711233i	$0.251863\pi$
$522$	−6.58508	−0.288221
$523$	−16.6935	−0.729956	−0.364978	−	0.931016i	$-0.618923\pi$
$523$	−16.6935	−0.729956	−0.364978	+	0.931016i	$0.618923\pi$
$524$	57.0555	2.49248
$525$	10.0126	0.436984
$526$	59.9489	2.61390
$527$	−4.47704	−0.195023
$528$	3.05119	0.132786
$529$	−22.8220	−0.992262
$530$	79.9722	3.47377
$531$	−19.3832	−0.841157
$532$	−23.9349	−1.03771
$533$	0.358171	0.0155141
$534$	−6.75825	−0.292458
$535$	42.0642	1.81859
$536$	−9.62986	−0.415947
$537$	−10.7551	−0.464118
$538$	−26.9635	−1.16248
$539$	−2.19308	−0.0944625
$540$	−48.9165	−2.10503
$541$	−13.3378	−0.573436	−0.286718	−	0.958015i	$-0.592564\pi$
$541$	−13.3378	−0.573436	−0.286718	+	0.958015i	$0.592564\pi$
$542$	47.2588	2.02994
$543$	−12.9022	−0.553686
$544$	−4.39633	−0.188491
$545$	17.0703	0.731210
$546$	0.376262	0.0161025
$547$	−23.5595	−1.00733	−0.503667	−	0.863898i	$-0.668016\pi$
$547$	−23.5595	−1.00733	−0.503667	+	0.863898i	$0.668016\pi$
$548$	−22.6517	−0.967633
$549$	25.1252	1.07232
$550$	−29.6738	−1.26530
$551$	3.26888	0.139259
$552$	−1.31725	−0.0560659
$553$	16.7486	0.712223
$554$	−9.66115	−0.410463
$555$	−7.69593	−0.326674
$556$	−67.8714	−2.87839
$557$	15.9391	0.675362	0.337681	−	0.941261i	$-0.390357\pi$
$557$	15.9391	0.675362	0.337681	+	0.941261i	$0.390357\pi$
$558$	22.5454	0.954422
$559$	0.0632812	0.00267651
$560$	8.51594	0.359864
$561$	2.96748	0.125287
$562$	−18.2574	−0.770142
$563$	17.6547	0.744058	0.372029	−	0.928221i	$-0.378662\pi$
$563$	17.6547	0.744058	0.372029	+	0.928221i	$0.378662\pi$
$564$	−17.1533	−0.722284
$565$	−15.8216	−0.665618
$566$	7.67768	0.322717
$567$	−5.86558	−0.246331
$568$	−15.9022	−0.667242
$569$	−5.68347	−0.238264	−0.119132	−	0.992878i	$-0.538011\pi$
$569$	−5.68347	−0.238264	−0.119132	+	0.992878i	$0.538011\pi$
$570$	16.0314	0.671479
$571$	24.8249	1.03889	0.519444	−	0.854504i	$-0.326139\pi$
$571$	24.8249	1.03889	0.519444	+	0.854504i	$0.326139\pi$
$572$	−0.706290	−0.0295315
$573$	0.664723	0.0277692
$574$	−36.6330	−1.52903
$575$	1.65922	0.0691944
$576$	26.5726	1.10719
$577$	35.4081	1.47406	0.737029	−	0.675861i	$-0.236228\pi$
$577$	35.4081	1.47406	0.737029	+	0.675861i	$0.236228\pi$
$578$	2.33565	0.0971501
$579$	16.1261	0.670179
$580$	−13.5044	−0.560739
$581$	18.0795	0.750062
$582$	−30.2230	−1.25278
$583$	37.0050	1.53259
$584$	−25.7161	−1.06414
$585$	0.407789	0.0168600
$586$	2.16106	0.0892725
$587$	−16.3789	−0.676030	−0.338015	−	0.941141i	$-0.609755\pi$
$587$	−16.3789	−0.676030	−0.338015	+	0.941141i	$0.609755\pi$
$588$	−2.15507	−0.0888734
$589$	−11.1917	−0.461145
$590$	−62.7587	−2.58373
$591$	10.2926	0.423383
$592$	−2.88192	−0.118446
$593$	21.5577	0.885271	0.442635	−	0.896702i	$-0.354044\pi$
$593$	21.5577	0.885271	0.442635	+	0.896702i	$0.354044\pi$
$594$	−35.7365	−1.46629
$595$	8.28231	0.339542
$596$	43.6626	1.78849
$597$	−9.73094	−0.398261
$598$	0.0623520	0.00254976
$599$	0.925667	0.0378217	0.0189109	−	0.999821i	$-0.493980\pi$
$599$	0.925667	0.0378217	0.0189109	+	0.999821i	$0.493980\pi$
$600$	−12.2811	−0.501373
$601$	31.8875	1.30072	0.650359	−	0.759627i	$-0.274618\pi$
$601$	31.8875	1.30072	0.650359	+	0.759627i	$0.274618\pi$
$602$	−6.47228	−0.263790
$603$	6.10854	0.248759
$604$	−23.0289	−0.937031
$605$	1.69106	0.0687515
$606$	2.88416	0.117161
$607$	−24.5216	−0.995300	−0.497650	−	0.867378i	$-0.665804\pi$
$607$	−24.5216	−0.995300	−0.497650	+	0.867378i	$0.665804\pi$
$608$	−10.9899	−0.445699
$609$	3.32892	0.134895
$610$	81.3503	3.29378
$611$	0.341968	0.0138346
$612$	−7.44967	−0.301135
$613$	−41.5585	−1.67853	−0.839265	−	0.543722i	$-0.817014\pi$
$613$	−41.5585	−1.67853	−0.839265	+	0.543722i	$0.817014\pi$
$614$	9.05317	0.365356
$615$	15.5408	0.626667
$616$	30.4244	1.22583
$617$	44.4156	1.78810	0.894052	−	0.447963i	$-0.147850\pi$
$617$	44.4156	1.78810	0.894052	+	0.447963i	$0.147850\pi$
$618$	0.179420	0.00721733
$619$	−33.2139	−1.33498	−0.667489	−	0.744620i	$-0.732631\pi$
$619$	−33.2139	−1.33498	−0.667489	+	0.744620i	$0.732631\pi$
$620$	46.2350	1.85684
$621$	1.99822	0.0801859
$622$	−16.4108	−0.658013
$623$	−8.72809	−0.349684
$624$	−0.0597742	−0.00239288
$625$	−29.1962	−1.16785
$626$	23.4284	0.936386
$627$	7.41808	0.296250
$628$	−56.5409	−2.25623
$629$	−2.80286	−0.111757
$630$	−41.7078	−1.66168
$631$	−33.9227	−1.35044	−0.675221	−	0.737615i	$-0.735952\pi$
$631$	−33.9227	−1.35044	−0.675221	+	0.737615i	$0.735952\pi$
$632$	−20.5433	−0.817168
$633$	−13.4105	−0.533018
$634$	−41.7230	−1.65703
$635$	−1.71636	−0.0681115
$636$	36.3636	1.44191
$637$	0.0429634	0.00170227
$638$	−9.86579	−0.390591
$639$	10.0873	0.399047
$640$	59.7570	2.36210
$641$	−35.7537	−1.41218	−0.706092	−	0.708120i	$-0.749544\pi$
$641$	−35.7537	−1.41218	−0.706092	+	0.708120i	$0.749544\pi$
$642$	30.1979	1.19182
$643$	1.33912	0.0528097	0.0264048	−	0.999651i	$-0.491594\pi$
$643$	1.33912	0.0528097	0.0264048	+	0.999651i	$0.491594\pi$
$644$	−4.03921	−0.159167
$645$	2.74574	0.108113
$646$	5.83862	0.229718
$647$	30.3291	1.19236	0.596179	−	0.802851i	$-0.296685\pi$
$647$	30.3291	1.19236	0.596179	+	0.802851i	$0.296685\pi$
$648$	7.19453	0.282628
$649$	−29.0399	−1.13992
$650$	0.581324	0.0228014
$651$	−11.3972	−0.446693
$652$	78.8983	3.08990
$653$	−11.7372	−0.459313	−0.229657	−	0.973272i	$-0.573760\pi$
$653$	−11.7372	−0.459313	−0.229657	+	0.973272i	$0.573760\pi$
$654$	12.2547	0.479198
$655$	−49.3538	−1.92841
$656$	5.81964	0.227219
$657$	16.3125	0.636413
$658$	−34.9759	−1.36350
$659$	33.0856	1.28883	0.644415	−	0.764676i	$-0.277101\pi$
$659$	33.0856	1.28883	0.644415	+	0.764676i	$0.277101\pi$
$660$	−30.6456	−1.19288
$661$	−17.7766	−0.691430	−0.345715	−	0.938340i	$-0.612364\pi$
$661$	−17.7766	−0.691430	−0.345715	+	0.938340i	$0.612364\pi$
$662$	−5.64949	−0.219574
$663$	−0.0581344	−0.00225775
$664$	−22.1757	−0.860583
$665$	20.7041	0.802869
$666$	14.1146	0.546929
$667$	0.551650	0.0213600
$668$	32.1233	1.24289
$669$	−2.13694	−0.0826190
$670$	19.7782	0.764098
$671$	37.6427	1.45318
$672$	−11.1918	−0.431731
$673$	−5.70389	−0.219869	−0.109934	−	0.993939i	$-0.535064\pi$
$673$	−5.70389	−0.219869	−0.109934	+	0.993939i	$0.535064\pi$
$674$	11.9318	0.459595
$675$	18.6300	0.717067
$676$	−44.9043	−1.72709
$677$	−19.3819	−0.744906	−0.372453	−	0.928051i	$-0.621483\pi$
$677$	−19.3819	−0.744906	−0.372453	+	0.928051i	$0.621483\pi$
$678$	−11.3583	−0.436213
$679$	−39.0322	−1.49792
$680$	−10.1588	−0.389573
$681$	21.6782	0.830712
$682$	33.7775	1.29341
$683$	43.2535	1.65505	0.827524	−	0.561430i	$-0.189749\pi$
$683$	43.2535	1.65505	0.827524	+	0.561430i	$0.189749\pi$
$684$	−18.6226	−0.712054
$685$	19.5940	0.748650
$686$	40.9117	1.56202
$687$	25.8535	0.986373
$688$	1.02821	0.0392000
$689$	−0.724946	−0.0276182
$690$	2.70542	0.102994
$691$	42.2513	1.60731	0.803657	−	0.595093i	$-0.202885\pi$
$691$	42.2513	1.60731	0.803657	+	0.595093i	$0.202885\pi$
$692$	61.7228	2.34635
$693$	−19.2992	−0.733115
$694$	−21.5141	−0.816665
$695$	58.7097	2.22699
$696$	−4.08315	−0.154771
$697$	5.65998	0.214387
$698$	−41.5120	−1.57125
$699$	−11.6474	−0.440546
$700$	−37.6587	−1.42336
$701$	33.0323	1.24761	0.623807	−	0.781578i	$-0.285585\pi$
$701$	33.0323	1.24761	0.623807	+	0.781578i	$0.285585\pi$
$702$	0.700095	0.0264234
$703$	−7.00657	−0.264258
$704$	39.8112	1.50044
$705$	14.8378	0.558826
$706$	41.0180	1.54373
$707$	3.72481	0.140086
$708$	−28.5366	−1.07247
$709$	−46.0114	−1.72800	−0.863998	−	0.503495i	$-0.832047\pi$
$709$	−46.0114	−1.72800	−0.863998	+	0.503495i	$0.832047\pi$
$710$	32.6606	1.22573
$711$	13.0313	0.488711
$712$	10.7056	0.401209
$713$	−1.88869	−0.0707318
$714$	5.94587	0.222519
$715$	0.610950	0.0228483
$716$	40.4516	1.51175
$717$	0.784661	0.0293037
$718$	−44.0142	−1.64259
$719$	−22.9474	−0.855794	−0.427897	−	0.903827i	$-0.640745\pi$
$719$	−22.9474	−0.855794	−0.427897	+	0.903827i	$0.640745\pi$
$720$	6.62584	0.246931
$721$	0.231716	0.00862955
$722$	−29.7819	−1.10837
$723$	17.1964	0.639540
$724$	48.5270	1.80349
$725$	5.14318	0.191013
$726$	1.21401	0.0450563
$727$	−3.95656	−0.146741	−0.0733704	−	0.997305i	$-0.523376\pi$
$727$	−3.95656	−0.146741	−0.0733704	+	0.997305i	$0.523376\pi$
$728$	−0.596028	−0.0220903
$729$	8.49061	0.314467
$730$	52.8166	1.95483
$731$	1.00000	0.0369863
$732$	36.9903	1.36720
$733$	4.24145	0.156661	0.0783307	−	0.996927i	$-0.475041\pi$
$733$	4.24145	0.156661	0.0783307	+	0.996927i	$0.475041\pi$
$734$	79.6665	2.94055
$735$	1.86416	0.0687606
$736$	−1.85463	−0.0683627
$737$	9.15183	0.337112
$738$	−28.5024	−1.04919
$739$	53.7183	1.97606	0.988029	−	0.154265i	$-0.0493011\pi$
$739$	53.7183	1.97606	0.988029	+	0.154265i	$0.0493011\pi$
$740$	28.9455	1.06406
$741$	−0.145324	−0.00533860
$742$	74.1460	2.72199
$743$	45.0777	1.65374	0.826870	−	0.562394i	$-0.190119\pi$
$743$	45.0777	1.65374	0.826870	+	0.562394i	$0.190119\pi$
$744$	13.9795	0.512513
$745$	−37.7688	−1.38374
$746$	13.0815	0.478949
$747$	14.0668	0.514676
$748$	−11.1611	−0.408091
$749$	38.9997	1.42502
$750$	−6.84203	−0.249836
$751$	−15.5178	−0.566254	−0.283127	−	0.959082i	$-0.591372\pi$
$751$	−15.5178	−0.566254	−0.283127	+	0.959082i	$0.591372\pi$
$752$	5.55638	0.202620
$753$	5.02756	0.183215
$754$	0.193276	0.00703869
$755$	19.9203	0.724973
$756$	−45.3528	−1.64946
$757$	5.69269	0.206904	0.103452	−	0.994634i	$-0.467011\pi$
$757$	5.69269	0.206904	0.103452	+	0.994634i	$0.467011\pi$
$758$	−27.5341	−1.00008
$759$	1.25186	0.0454397
$760$	−25.3949	−0.921171
$761$	37.7152	1.36718	0.683588	−	0.729868i	$-0.260418\pi$
$761$	37.7152	1.36718	0.683588	+	0.729868i	$0.260418\pi$
$762$	−1.23217	−0.0446369
$763$	15.8267	0.572963
$764$	−2.50012	−0.0904512
$765$	6.44407	0.232986
$766$	86.1219	3.11171
$767$	0.568906	0.0205420
$768$	20.2550	0.730888
$769$	42.0210	1.51532	0.757658	−	0.652652i	$-0.226344\pi$
$769$	42.0210	1.51532	0.757658	+	0.652652i	$0.226344\pi$
$770$	−62.4868	−2.25187
$771$	27.2654	0.981938
$772$	−60.6527	−2.18294
$773$	−7.65728	−0.275413	−0.137707	−	0.990473i	$-0.543973\pi$
$773$	−7.65728	−0.275413	−0.137707	+	0.990473i	$0.543973\pi$
$774$	−5.03577	−0.181007
$775$	−17.6087	−0.632524
$776$	47.8756	1.71863
$777$	−7.13527	−0.255976
$778$	−68.2765	−2.44783
$779$	14.1488	0.506932
$780$	0.600361	0.0214964
$781$	15.1128	0.540779
$782$	0.985315	0.0352348
$783$	6.19399	0.221355
$784$	0.698079	0.0249314
$785$	48.9087	1.74563
$786$	−35.4311	−1.26378
$787$	25.5062	0.909197	0.454599	−	0.890696i	$-0.349783\pi$
$787$	25.5062	0.909197	0.454599	+	0.890696i	$0.349783\pi$
$788$	−38.7121	−1.37906
$789$	−23.5794	−0.839448
$790$	42.1926	1.50115
$791$	−14.6689	−0.521567
$792$	23.6718	0.841139
$793$	−0.737438	−0.0261872
$794$	56.8022	2.01583
$795$	−31.4550	−1.11560
$796$	36.5995	1.29723
$797$	7.52073	0.266398	0.133199	−	0.991089i	$-0.457475\pi$
$797$	7.52073	0.266398	0.133199	+	0.991089i	$0.457475\pi$
$798$	14.8634	0.526160
$799$	5.40395	0.191178
$800$	−17.2912	−0.611338
$801$	−6.79091	−0.239945
$802$	61.0390	2.15536
$803$	24.4395	0.862451
$804$	8.99321	0.317166
$805$	3.49398	0.123146
$806$	−0.661718	−0.0233080
$807$	10.6054	0.373328
$808$	−4.56873	−0.160727
$809$	−13.0561	−0.459029	−0.229514	−	0.973305i	$-0.573714\pi$
$809$	−13.0561	−0.459029	−0.229514	+	0.973305i	$0.573714\pi$
$810$	−14.7764	−0.519190
$811$	−10.4730	−0.367756	−0.183878	−	0.982949i	$-0.558865\pi$
$811$	−10.4730	−0.367756	−0.183878	+	0.982949i	$0.558865\pi$
$812$	−12.5206	−0.439386
$813$	−18.5881	−0.651911
$814$	21.1465	0.741184
$815$	−68.2481	−2.39063
$816$	−0.944580	−0.0330669
$817$	2.49979	0.0874566
$818$	−2.93130	−0.102491
$819$	0.378080	0.0132112
$820$	−58.4514	−2.04121
$821$	−36.4282	−1.27135	−0.635676	−	0.771956i	$-0.719279\pi$
$821$	−36.4282	−1.27135	−0.635676	+	0.771956i	$0.719279\pi$
$822$	14.0666	0.490628
$823$	−0.706875	−0.0246401	−0.0123201	−	0.999924i	$-0.503922\pi$
$823$	−0.706875	−0.0246401	−0.0123201	+	0.999924i	$0.503922\pi$
$824$	−0.284215	−0.00990111
$825$	11.6714	0.406347
$826$	−58.1866	−2.02457
$827$	−0.698597	−0.0242926	−0.0121463	−	0.999926i	$-0.503866\pi$
$827$	−0.698597	−0.0242926	−0.0121463	+	0.999926i	$0.503866\pi$
$828$	−3.14272	−0.109217
$829$	6.76510	0.234962	0.117481	−	0.993075i	$-0.462518\pi$
$829$	6.76510	0.234962	0.117481	+	0.993075i	$0.462518\pi$
$830$	45.5453	1.58090
$831$	3.79997	0.131819
$832$	−0.779920	−0.0270389
$833$	0.678928	0.0235235
$834$	42.1477	1.45945
$835$	−27.7871	−0.961611
$836$	−27.9005	−0.964958
$837$	−21.2064	−0.733000
$838$	−49.1781	−1.69883
$839$	46.5371	1.60664	0.803319	−	0.595549i	$-0.203065\pi$
$839$	46.5371	1.60664	0.803319	+	0.595549i	$0.203065\pi$
$840$	−25.8614	−0.892302
$841$	−27.2900	−0.941035
$842$	−69.1862	−2.38431
$843$	7.18108	0.247330
$844$	50.4387	1.73617
$845$	38.8428	1.33623
$846$	−27.2130	−0.935604
$847$	1.56786	0.0538725
$848$	−11.7791	−0.404495
$849$	−3.01982	−0.103640
$850$	9.18636	0.315090
$851$	−1.18242	−0.0405327
$852$	14.8509	0.508783
$853$	−36.3179	−1.24350	−0.621751	−	0.783215i	$-0.713579\pi$
$853$	−36.3179	−1.24350	−0.621751	+	0.783215i	$0.713579\pi$
$854$	75.4238	2.58095
$855$	16.1088	0.550910
$856$	−47.8358	−1.63499
$857$	40.2640	1.37539	0.687695	−	0.725999i	$-0.258622\pi$
$857$	40.2640	1.37539	0.687695	+	0.725999i	$0.258622\pi$
$858$	0.438601	0.0149736
$859$	32.2219	1.09940	0.549699	−	0.835363i	$-0.314742\pi$
$859$	32.2219	1.09940	0.549699	+	0.835363i	$0.314742\pi$
$860$	−10.3271	−0.352152
$861$	14.4087	0.491046
$862$	−8.74254	−0.297772
$863$	4.95481	0.168664	0.0843318	−	0.996438i	$-0.473124\pi$
$863$	4.95481	0.168664	0.0843318	+	0.996438i	$0.473124\pi$
$864$	−20.8241	−0.708449
$865$	−53.3911	−1.81535
$866$	−37.7737	−1.28360
$867$	−0.918667	−0.0311996
$868$	42.8667	1.45499
$869$	19.5235	0.662289
$870$	8.38614	0.284317
$871$	−0.179289	−0.00607497
$872$	−19.4125	−0.657389
$873$	−30.3691	−1.02784
$874$	2.46308	0.0833150
$875$	−8.83629	−0.298721
$876$	24.0159	0.811422
$877$	−15.3526	−0.518422	−0.259211	−	0.965821i	$-0.583463\pi$
$877$	−15.3526	−0.518422	−0.259211	+	0.965821i	$0.583463\pi$
$878$	−15.6091	−0.526782
$879$	−0.849998	−0.0286697
$880$	9.92686	0.334634
$881$	−19.4675	−0.655875	−0.327938	−	0.944699i	$-0.606354\pi$
$881$	−19.4675	−0.655875	−0.327938	+	0.944699i	$0.606354\pi$
$882$	−3.41893	−0.115121
$883$	40.4970	1.36283	0.681416	−	0.731896i	$-0.261365\pi$
$883$	40.4970	1.36283	0.681416	+	0.731896i	$0.261365\pi$
$884$	0.218652	0.00735406
$885$	24.6845	0.829762
$886$	56.4327	1.89589
$887$	13.5478	0.454891	0.227446	−	0.973791i	$-0.426963\pi$
$887$	13.5478	0.454891	0.227446	+	0.973791i	$0.426963\pi$
$888$	8.75189	0.293694
$889$	−1.59132	−0.0533710
$890$	−21.9876	−0.737025
$891$	−6.83739	−0.229061
$892$	8.03735	0.269110
$893$	13.5087	0.452053
$894$	−27.1142	−0.906834
$895$	−34.9912	−1.16963
$896$	55.4035	1.85090
$897$	−0.0245246	−0.000818851 0
$898$	15.5102	0.517583
$899$	−5.85446	−0.195257
$900$	−29.3004	−0.976680
$901$	−11.4559	−0.381653
$902$	−42.7023	−1.42183
$903$	2.54571	0.0847158
$904$	17.9924	0.598419
$905$	−41.9766	−1.39535
$906$	14.3008	0.475111
$907$	−51.3733	−1.70582	−0.852911	−	0.522057i	$-0.825165\pi$
$907$	−51.3733	−1.70582	−0.852911	+	0.522057i	$0.825165\pi$
$908$	−81.5350	−2.70583
$909$	2.89809	0.0961237
$910$	1.22415	0.0405801
$911$	−39.5021	−1.30876	−0.654382	−	0.756164i	$-0.727071\pi$
$911$	−39.5021	−1.30876	−0.654382	+	0.756164i	$0.727071\pi$
$912$	−2.36125	−0.0781889
$913$	21.0749	0.697476
$914$	7.23441	0.239293
$915$	−31.9971	−1.05779
$916$	−97.2389	−3.21286
$917$	−45.7582	−1.51107
$918$	11.0632	0.365141
$919$	−42.9502	−1.41680	−0.708398	−	0.705814i	$-0.750582\pi$
$919$	−42.9502	−1.41680	−0.708398	+	0.705814i	$0.750582\pi$
$920$	−4.28560	−0.141292
$921$	−3.56083	−0.117333
$922$	−74.7905	−2.46309
$923$	−0.296067	−0.00974517
$924$	−28.4130	−0.934718
$925$	−11.0240	−0.362466
$926$	56.5163	1.85724
$927$	0.180287	0.00592140
$928$	−5.74891	−0.188717
$929$	−32.3739	−1.06215	−0.531076	−	0.847324i	$-0.678212\pi$
$929$	−32.3739	−1.06215	−0.531076	+	0.847324i	$0.678212\pi$
$930$	−28.7116	−0.941492
$931$	1.69718	0.0556228
$932$	43.8077	1.43497
$933$	6.45477	0.211320
$934$	−72.6341	−2.37666
$935$	9.65453	0.315737
$936$	−0.463741	−0.0151579
$937$	36.1375	1.18056	0.590281	−	0.807198i	$-0.299017\pi$
$937$	36.1375	1.18056	0.590281	+	0.807198i	$0.299017\pi$
$938$	18.3373	0.598734
$939$	−9.21496	−0.300719
$940$	−55.8073	−1.82023
$941$	−33.9157	−1.10562	−0.552810	−	0.833307i	$-0.686445\pi$
$941$	−33.9157	−1.10562	−0.552810	+	0.833307i	$0.686445\pi$
$942$	35.1115	1.14400
$943$	2.38772	0.0777548
$944$	9.24371	0.300857
$945$	39.2308	1.27618
$946$	−7.54461	−0.245296
$947$	16.6580	0.541312	0.270656	−	0.962676i	$-0.412759\pi$
$947$	16.6580	0.541312	0.270656	+	0.962676i	$0.412759\pi$
$948$	19.1851	0.623104
$949$	−0.478781	−0.0155419
$950$	22.9640	0.745050
$951$	16.4107	0.532153
$952$	−9.41873	−0.305263
$953$	48.5470	1.57259	0.786296	−	0.617850i	$-0.211996\pi$
$953$	48.5470	1.57259	0.786296	+	0.617850i	$0.211996\pi$
$954$	57.6895	1.86777
$955$	2.16264	0.0699813
$956$	−2.95122	−0.0954494
$957$	3.88046	0.125437
$958$	12.0475	0.389238
$959$	18.1666	0.586629
$960$	−33.8404	−1.09219
$961$	−10.9561	−0.353422
$962$	−0.414270	−0.0133566
$963$	30.3438	0.977816
$964$	−64.6781	−2.08314
$965$	52.4654	1.68892
$966$	2.50832	0.0807040
$967$	−40.7639	−1.31088	−0.655440	−	0.755247i	$-0.727517\pi$
$967$	−40.7639	−1.31088	−0.655440	+	0.755247i	$0.727517\pi$
$968$	−1.92309	−0.0618105
$969$	−2.29648	−0.0737734
$970$	−98.3289	−3.15715
$971$	−43.5631	−1.39801	−0.699003	−	0.715119i	$-0.746372\pi$
$971$	−43.5631	−1.39801	−0.699003	+	0.715119i	$0.746372\pi$
$972$	−55.8181	−1.79037
$973$	54.4326	1.74503
$974$	−76.2291	−2.44254
$975$	−0.228649	−0.00732263
$976$	−11.9821	−0.383537
$977$	−18.8813	−0.604066	−0.302033	−	0.953298i	$-0.597665\pi$
$977$	−18.8813	−0.604066	−0.302033	+	0.953298i	$0.597665\pi$
$978$	−48.9953	−1.56670
$979$	−10.1742	−0.325168
$980$	−7.01138	−0.223970
$981$	12.3140	0.393155
$982$	61.5495	1.96412
$983$	−22.8741	−0.729571	−0.364785	−	0.931092i	$-0.618858\pi$
$983$	−22.8741	−0.729571	−0.364785	+	0.931092i	$0.618858\pi$
$984$	−17.6732	−0.563401
$985$	33.4865	1.06697
$986$	3.05423	0.0972666
$987$	13.7569	0.437886
$988$	0.546584	0.0173891
$989$	0.421860	0.0134144
$990$	−48.6180	−1.54518
$991$	−19.5360	−0.620583	−0.310291	−	0.950642i	$-0.600427\pi$
$991$	−19.5360	−0.620583	−0.310291	+	0.950642i	$0.600427\pi$
$992$	19.6825	0.624921
$993$	2.22209	0.0705157
$994$	30.2812	0.960461
$995$	−31.6591	−1.00366
$996$	20.7096	0.656208
$997$	−27.2631	−0.863432	−0.431716	−	0.902010i	$-0.642092\pi$
$997$	−27.2631	−0.863432	−0.431716	+	0.902010i	$0.642092\pi$
$998$	29.4460	0.932097
$999$	−13.2763	−0.420044

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.a.d.1.8	✓	8
3.2	odd	2		6579.2.a.k.1.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.a.d.1.8	✓	8	1.1	even	1	trivial
6579.2.a.k.1.1		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)

\(f(q)\)	\(=\)	\(q+2.33565 q^{2} -0.918667 q^{3} +3.45524 q^{4} -2.98883 q^{5} -2.14568 q^{6} -2.77109 q^{7} +3.39893 q^{8} -2.15605 q^{9} +O(q^{10})\)	\(q+2.33565 q^{2} -0.918667 q^{3} +3.45524 q^{4} -2.98883 q^{5} -2.14568 q^{6} -2.77109 q^{7} +3.39893 q^{8} -2.15605 q^{9} -6.98085 q^{10} -3.23020 q^{11} -3.17422 q^{12} +0.0632812 q^{13} -6.47228 q^{14} +2.74574 q^{15} +1.02821 q^{16} +1.00000 q^{17} -5.03577 q^{18} +2.49979 q^{19} -10.3271 q^{20} +2.54571 q^{21} -7.54461 q^{22} +0.421860 q^{23} -3.12248 q^{24} +3.93311 q^{25} +0.147803 q^{26} +4.73669 q^{27} -9.57478 q^{28} +1.30766 q^{29} +6.41308 q^{30} -4.47704 q^{31} -4.39633 q^{32} +2.96748 q^{33} +2.33565 q^{34} +8.28231 q^{35} -7.44967 q^{36} -2.80286 q^{37} +5.83862 q^{38} -0.0581344 q^{39} -10.1588 q^{40} +5.65998 q^{41} +5.94587 q^{42} +1.00000 q^{43} -11.1611 q^{44} +6.44407 q^{45} +0.985315 q^{46} +5.40395 q^{47} -0.944580 q^{48} +0.678928 q^{49} +9.18636 q^{50} -0.918667 q^{51} +0.218652 q^{52} -11.4559 q^{53} +11.0632 q^{54} +9.65453 q^{55} -9.41873 q^{56} -2.29648 q^{57} +3.05423 q^{58} +8.99012 q^{59} +9.48720 q^{60} -11.6534 q^{61} -10.4568 q^{62} +5.97461 q^{63} -12.3247 q^{64} -0.189137 q^{65} +6.93098 q^{66} -2.83321 q^{67} +3.45524 q^{68} -0.387549 q^{69} +19.3446 q^{70} -4.67860 q^{71} -7.32826 q^{72} -7.56593 q^{73} -6.54649 q^{74} -3.61322 q^{75} +8.63738 q^{76} +8.95117 q^{77} -0.135781 q^{78} -6.04405 q^{79} -3.07314 q^{80} +2.11671 q^{81} +13.2197 q^{82} -6.52432 q^{83} +8.79603 q^{84} -2.98883 q^{85} +2.33565 q^{86} -1.20131 q^{87} -10.9792 q^{88} +3.14970 q^{89} +15.0511 q^{90} -0.175358 q^{91} +1.45763 q^{92} +4.11291 q^{93} +12.6217 q^{94} -7.47145 q^{95} +4.03876 q^{96} +14.0855 q^{97} +1.58574 q^{98} +6.96448 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - 3 q^{3} + 3 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} - 3 q^{8} + 5 q^{9}+O(q^{10}) \) 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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