LMFDB - Embedded newform 731.2.a.d.1.4

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			1.4
Root			$0.235409$ 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)

$f(q)$	$=$	$q+0.235409 q^{2} +2.48067 q^{3} -1.94458 q^{4} -0.468153 q^{5} +0.583972 q^{6} -5.07261 q^{7} -0.928590 q^{8} +3.15374 q^{9} +O(q^{10})$	\(q+0.235409 q^{2} +2.48067 q^{3} -1.94458 q^{4} -0.468153 q^{5} +0.583972 q^{6} -5.07261 q^{7} -0.928590 q^{8} +3.15374 q^{9} -0.110207 q^{10} -2.07060 q^{11} -4.82387 q^{12} -2.16400 q^{13} -1.19414 q^{14} -1.16133 q^{15} +3.67057 q^{16} +1.00000 q^{17} +0.742417 q^{18} +0.772556 q^{19} +0.910362 q^{20} -12.5835 q^{21} -0.487438 q^{22} -6.12987 q^{23} -2.30353 q^{24} -4.78083 q^{25} -0.509424 q^{26} +0.381367 q^{27} +9.86411 q^{28} +1.60870 q^{29} -0.273388 q^{30} +0.668713 q^{31} +2.72126 q^{32} -5.13648 q^{33} +0.235409 q^{34} +2.37476 q^{35} -6.13270 q^{36} -0.278077 q^{37} +0.181866 q^{38} -5.36817 q^{39} +0.434722 q^{40} -8.44086 q^{41} -2.96226 q^{42} +1.00000 q^{43} +4.02646 q^{44} -1.47643 q^{45} -1.44303 q^{46} +0.605286 q^{47} +9.10547 q^{48} +18.7314 q^{49} -1.12545 q^{50} +2.48067 q^{51} +4.20807 q^{52} -5.14757 q^{53} +0.0897772 q^{54} +0.969358 q^{55} +4.71037 q^{56} +1.91646 q^{57} +0.378702 q^{58} +7.61136 q^{59} +2.25831 q^{60} -3.15908 q^{61} +0.157421 q^{62} -15.9977 q^{63} -6.70052 q^{64} +1.01308 q^{65} -1.20917 q^{66} +14.6167 q^{67} -1.94458 q^{68} -15.2062 q^{69} +0.559039 q^{70} +1.58612 q^{71} -2.92853 q^{72} -0.0451814 q^{73} -0.0654618 q^{74} -11.8597 q^{75} -1.50230 q^{76} +10.5034 q^{77} -1.26372 q^{78} +0.717817 q^{79} -1.71839 q^{80} -8.51516 q^{81} -1.98705 q^{82} +11.3829 q^{83} +24.4696 q^{84} -0.468153 q^{85} +0.235409 q^{86} +3.99066 q^{87} +1.92274 q^{88} -1.50246 q^{89} -0.347565 q^{90} +10.9771 q^{91} +11.9200 q^{92} +1.65886 q^{93} +0.142490 q^{94} -0.361674 q^{95} +6.75056 q^{96} +7.17798 q^{97} +4.40953 q^{98} -6.53013 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.235409	0.166459	0.0832296	−	0.996530i	$-0.473477\pi$
$2$	0.235409	0.166459	0.0832296	+	0.996530i	$0.473477\pi$
$3$	2.48067	1.43222	0.716108	−	0.697989i	$-0.245922\pi$
$3$	2.48067	1.43222	0.716108	+	0.697989i	$0.245922\pi$
$4$	−1.94458	−0.972291
$5$	−0.468153	−0.209364	−0.104682	−	0.994506i	$-0.533383\pi$
$5$	−0.468153	−0.209364	−0.104682	+	0.994506i	$0.533383\pi$
$6$	0.583972	0.238406
$7$	−5.07261	−1.91727	−0.958633	−	0.284645i	$-0.908124\pi$
$7$	−5.07261	−1.91727	−0.958633	+	0.284645i	$0.908124\pi$
$8$	−0.928590	−0.328306
$9$	3.15374	1.05125
$10$	−0.110207	−0.0348506
$11$	−2.07060	−0.624310	−0.312155	−	0.950031i	$-0.601051\pi$
$11$	−2.07060	−0.624310	−0.312155	+	0.950031i	$0.601051\pi$
$12$	−4.82387	−1.39253
$13$	−2.16400	−0.600185	−0.300093	−	0.953910i	$-0.597018\pi$
$13$	−2.16400	−0.600185	−0.300093	+	0.953910i	$0.597018\pi$
$14$	−1.19414	−0.319147
$15$	−1.16133	−0.299855
$16$	3.67057	0.917642
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	0.742417	0.174989
$19$	0.772556	0.177236	0.0886182	−	0.996066i	$-0.471755\pi$
$19$	0.772556	0.177236	0.0886182	+	0.996066i	$0.471755\pi$
$20$	0.910362	0.203563
$21$	−12.5835	−2.74594
$22$	−0.487438	−0.103922
$23$	−6.12987	−1.27817	−0.639084	−	0.769137i	$-0.720686\pi$
$23$	−6.12987	−1.27817	−0.639084	+	0.769137i	$0.720686\pi$
$24$	−2.30353	−0.470205
$25$	−4.78083	−0.956167
$26$	−0.509424	−0.0999064
$27$	0.381367	0.0733941
$28$	9.86411	1.86414
$29$	1.60870	0.298728	0.149364	−	0.988782i	$-0.452277\pi$
$29$	1.60870	0.298728	0.149364	+	0.988782i	$0.452277\pi$
$30$	−0.273388	−0.0499136
$31$	0.668713	0.120104	0.0600522	−	0.998195i	$-0.480873\pi$
$31$	0.668713	0.120104	0.0600522	+	0.998195i	$0.480873\pi$
$32$	2.72126	0.481056
$33$	−5.13648	−0.894147
$34$	0.235409	0.0403723
$35$	2.37476	0.401407
$36$	−6.13270	−1.02212
$37$	−0.278077	−0.0457156	−0.0228578	−	0.999739i	$-0.507276\pi$
$37$	−0.278077	−0.0457156	−0.0228578	+	0.999739i	$0.507276\pi$
$38$	0.181866	0.0295026
$39$	−5.36817	−0.859595
$40$	0.434722	0.0687356
$41$	−8.44086	−1.31824	−0.659120	−	0.752037i	$-0.729071\pi$
$41$	−8.44086	−1.31824	−0.659120	+	0.752037i	$0.729071\pi$
$42$	−2.96226	−0.457087
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	4.02646	0.607011
$45$	−1.47643	−0.220093
$46$	−1.44303	−0.212763
$47$	0.605286	0.0882901	0.0441450	−	0.999025i	$-0.485944\pi$
$47$	0.605286	0.0882901	0.0441450	+	0.999025i	$0.485944\pi$
$48$	9.10547	1.31426
$49$	18.7314	2.67591
$50$	−1.12545	−0.159163
$51$	2.48067	0.347364
$52$	4.20807	0.583555
$53$	−5.14757	−0.707073	−0.353536	−	0.935421i	$-0.615021\pi$
$53$	−5.14757	−0.707073	−0.353536	+	0.935421i	$0.615021\pi$
$54$	0.0897772	0.0122171
$55$	0.969358	0.130708
$56$	4.71037	0.629450
$57$	1.91646	0.253841
$58$	0.378702	0.0497260
$59$	7.61136	0.990915	0.495458	−	0.868632i	$-0.335000\pi$
$59$	7.61136	0.990915	0.495458	+	0.868632i	$0.335000\pi$
$60$	2.25831	0.291546
$61$	−3.15908	−0.404479	−0.202240	−	0.979336i	$-0.564822\pi$
$61$	−3.15908	−0.404479	−0.202240	+	0.979336i	$0.564822\pi$
$62$	0.157421	0.0199925
$63$	−15.9977	−2.01552
$64$	−6.70052	−0.837566
$65$	1.01308	0.125657
$66$	−1.20917	−0.148839
$67$	14.6167	1.78571	0.892856	−	0.450342i	$-0.148698\pi$
$67$	14.6167	1.78571	0.892856	+	0.450342i	$0.148698\pi$
$68$	−1.94458	−0.235815
$69$	−15.2062	−1.83061
$70$	0.559039	0.0668179
$71$	1.58612	0.188237	0.0941187	−	0.995561i	$-0.469997\pi$
$71$	1.58612	0.188237	0.0941187	+	0.995561i	$0.469997\pi$
$72$	−2.92853	−0.345130
$73$	−0.0451814	−0.00528809	−0.00264404	−	0.999997i	$-0.500842\pi$
$73$	−0.0451814	−0.00528809	−0.00264404	+	0.999997i	$0.500842\pi$
$74$	−0.0654618	−0.00760978
$75$	−11.8597	−1.36944
$76$	−1.50230	−0.172325
$77$	10.5034	1.19697
$78$	−1.26372	−0.143088
$79$	0.717817	0.0807608	0.0403804	−	0.999184i	$-0.487143\pi$
$79$	0.717817	0.0807608	0.0403804	+	0.999184i	$0.487143\pi$
$80$	−1.71839	−0.192121
$81$	−8.51516	−0.946129
$82$	−1.98705	−0.219433
$83$	11.3829	1.24944	0.624718	−	0.780850i	$-0.285214\pi$
$83$	11.3829	1.24944	0.624718	+	0.780850i	$0.285214\pi$
$84$	24.4696	2.66985
$85$	−0.468153	−0.0507783
$86$	0.235409	0.0253848
$87$	3.99066	0.427843
$88$	1.92274	0.204965
$89$	−1.50246	−0.159261	−0.0796304	−	0.996824i	$-0.525374\pi$
$89$	−1.50246	−0.159261	−0.0796304	+	0.996824i	$0.525374\pi$
$90$	−0.347565	−0.0366365
$91$	10.9771	1.15071
$92$	11.9200	1.24275
$93$	1.65886	0.172016
$94$	0.142490	0.0146967
$95$	−0.361674	−0.0371070
$96$	6.75056	0.688976
$97$	7.17798	0.728813	0.364407	−	0.931240i	$-0.381272\pi$
$97$	7.17798	0.728813	0.364407	+	0.931240i	$0.381272\pi$
$98$	4.40953	0.445430
$99$	−6.53013	−0.656303
$100$	9.29672	0.929672
$101$	−13.0207	−1.29561	−0.647804	−	0.761807i	$-0.724312\pi$
$101$	−13.0207	−1.29561	−0.647804	+	0.761807i	$0.724312\pi$
$102$	0.583972	0.0578219
$103$	0.488122	0.0480961	0.0240480	−	0.999711i	$-0.492345\pi$
$103$	0.488122	0.0480961	0.0240480	+	0.999711i	$0.492345\pi$
$104$	2.00947	0.197044
$105$	5.89099	0.574902
$106$	−1.21178	−0.117699
$107$	6.59940	0.637988	0.318994	−	0.947757i	$-0.396655\pi$
$107$	6.59940	0.637988	0.318994	+	0.947757i	$0.396655\pi$
$108$	−0.741600	−0.0713605
$109$	−14.2698	−1.36680	−0.683401	−	0.730043i	$-0.739500\pi$
$109$	−14.2698	−1.36680	−0.683401	+	0.730043i	$0.739500\pi$
$110$	0.228195	0.0217576
$111$	−0.689818	−0.0654746
$112$	−18.6194	−1.75936
$113$	−16.3098	−1.53430	−0.767148	−	0.641470i	$-0.778325\pi$
$113$	−16.3098	−1.53430	−0.767148	+	0.641470i	$0.778325\pi$
$114$	0.451151	0.0422542
$115$	2.86972	0.267603
$116$	−3.12825	−0.290451
$117$	−6.82468	−0.630942
$118$	1.79178	0.164947
$119$	−5.07261	−0.465005
$120$	1.07840	0.0984442
$121$	−6.71261	−0.610237
$122$	−0.743676	−0.0673293
$123$	−20.9390	−1.88801
$124$	−1.30037	−0.116777
$125$	4.57892	0.409551
$126$	−3.76599	−0.335501
$127$	9.75836	0.865915	0.432957	−	0.901414i	$-0.357470\pi$
$127$	9.75836	0.865915	0.432957	+	0.901414i	$0.357470\pi$
$128$	−7.01989	−0.620476
$129$	2.48067	0.218411
$130$	0.238488	0.0209168
$131$	−15.3206	−1.33857	−0.669285	−	0.743006i	$-0.733399\pi$
$131$	−15.3206	−1.33857	−0.669285	+	0.743006i	$0.733399\pi$
$132$	9.98832	0.869372
$133$	−3.91887	−0.339809
$134$	3.44090	0.297248
$135$	−0.178538	−0.0153661
$136$	−0.928590	−0.0796259
$137$	−1.51303	−0.129267	−0.0646336	−	0.997909i	$-0.520588\pi$
$137$	−1.51303	−0.129267	−0.0646336	+	0.997909i	$0.520588\pi$
$138$	−3.57968	−0.304722
$139$	−14.3779	−1.21951	−0.609757	−	0.792588i	$-0.708733\pi$
$139$	−14.3779	−1.21951	−0.609757	+	0.792588i	$0.708733\pi$
$140$	−4.61791	−0.390285
$141$	1.50152	0.126451
$142$	0.373386	0.0313339
$143$	4.48078	0.374702
$144$	11.5760	0.964666
$145$	−0.753117	−0.0625430
$146$	−0.0106361	−0.000880251 0
$147$	46.4664	3.83248
$148$	0.540744	0.0444489
$149$	4.08204	0.334414	0.167207	−	0.985922i	$-0.446525\pi$
$149$	4.08204	0.334414	0.167207	+	0.985922i	$0.446525\pi$
$150$	−2.79187	−0.227956
$151$	−14.0689	−1.14491	−0.572454	−	0.819937i	$-0.694009\pi$
$151$	−14.0689	−1.14491	−0.572454	+	0.819937i	$0.694009\pi$
$152$	−0.717387	−0.0581878
$153$	3.15374	0.254964
$154$	2.47258	0.199246
$155$	−0.313060	−0.0251456
$156$	10.4389	0.835777
$157$	−8.15975	−0.651219	−0.325610	−	0.945504i	$-0.605569\pi$
$157$	−8.15975	−0.651219	−0.325610	+	0.945504i	$0.605569\pi$
$158$	0.168981	0.0134434
$159$	−12.7694	−1.01268
$160$	−1.27397	−0.100716
$161$	31.0945	2.45059
$162$	−2.00454	−0.157492
$163$	10.9725	0.859432	0.429716	−	0.902964i	$-0.358614\pi$
$163$	10.9725	0.859432	0.429716	+	0.902964i	$0.358614\pi$
$164$	16.4140	1.28171
$165$	2.40466	0.187202
$166$	2.67964	0.207980
$167$	−4.62763	−0.358097	−0.179048	−	0.983840i	$-0.557302\pi$
$167$	−4.62763	−0.358097	−0.179048	+	0.983840i	$0.557302\pi$
$168$	11.6849	0.901509
$169$	−8.31711	−0.639778
$170$	−0.110207	−0.00845251
$171$	2.43644	0.186319
$172$	−1.94458	−0.148273
$173$	5.59176	0.425133	0.212567	−	0.977147i	$-0.431818\pi$
$173$	5.59176	0.425133	0.212567	+	0.977147i	$0.431818\pi$
$174$	0.939436	0.0712184
$175$	24.2513	1.83323
$176$	−7.60028	−0.572893
$177$	18.8813	1.41921
$178$	−0.353693	−0.0265104
$179$	13.2831	0.992824	0.496412	−	0.868087i	$-0.334651\pi$
$179$	13.2831	0.992824	0.496412	+	0.868087i	$0.334651\pi$
$180$	2.87104	0.213995
$181$	−3.74581	−0.278424	−0.139212	−	0.990263i	$-0.544457\pi$
$181$	−3.74581	−0.278424	−0.139212	+	0.990263i	$0.544457\pi$
$182$	2.58411	0.191547
$183$	−7.83665	−0.579302
$184$	5.69214	0.419630
$185$	0.130183	0.00957121
$186$	0.390510	0.0286336
$187$	−2.07060	−0.151417
$188$	−1.17703	−0.0858437
$189$	−1.93453	−0.140716
$190$	−0.0851413	−0.00617680
$191$	−12.9252	−0.935236	−0.467618	−	0.883931i	$-0.654888\pi$
$191$	−12.9252	−0.935236	−0.467618	+	0.883931i	$0.654888\pi$
$192$	−16.6218	−1.19958
$193$	−14.0488	−1.01126	−0.505629	−	0.862751i	$-0.668739\pi$
$193$	−14.0488	−1.01126	−0.505629	+	0.862751i	$0.668739\pi$
$194$	1.68976	0.121318
$195$	2.51312	0.179969
$196$	−36.4247	−2.60176
$197$	26.9563	1.92056	0.960279	−	0.279043i	$-0.0900173\pi$
$197$	26.9563	1.92056	0.960279	+	0.279043i	$0.0900173\pi$
$198$	−1.53725	−0.109248
$199$	−1.70350	−0.120758	−0.0603790	−	0.998176i	$-0.519231\pi$
$199$	−1.70350	−0.120758	−0.0603790	+	0.998176i	$0.519231\pi$
$200$	4.43943	0.313915
$201$	36.2592	2.55753
$202$	−3.06519	−0.215666
$203$	−8.16030	−0.572741
$204$	−4.82387	−0.337739
$205$	3.95161	0.275993
$206$	0.114908	0.00800603
$207$	−19.3320	−1.34367
$208$	−7.94310	−0.550755
$209$	−1.59966	−0.110650
$210$	1.38679	0.0956977
$211$	−17.3367	−1.19351	−0.596754	−	0.802424i	$-0.703543\pi$
$211$	−17.3367	−1.19351	−0.596754	+	0.802424i	$0.703543\pi$
$212$	10.0099	0.687480
$213$	3.93464	0.269597
$214$	1.55356	0.106199
$215$	−0.468153	−0.0319278
$216$	−0.354133	−0.0240957
$217$	−3.39212	−0.230272
$218$	−3.35924	−0.227517
$219$	−0.112080	−0.00757369
$220$	−1.88500	−0.127086
$221$	−2.16400	−0.145566
$222$	−0.162389	−0.0108989
$223$	3.08361	0.206494	0.103247	−	0.994656i	$-0.467077\pi$
$223$	3.08361	0.206494	0.103247	+	0.994656i	$0.467077\pi$
$224$	−13.8039	−0.922312
$225$	−15.0775	−1.00517
$226$	−3.83947	−0.255398
$227$	15.9697	1.05994	0.529972	−	0.848015i	$-0.322203\pi$
$227$	15.9697	1.05994	0.529972	+	0.848015i	$0.322203\pi$
$228$	−3.72671	−0.246807
$229$	−9.39496	−0.620836	−0.310418	−	0.950600i	$-0.600469\pi$
$229$	−9.39496	−0.620836	−0.310418	+	0.950600i	$0.600469\pi$
$230$	0.675557	0.0445449
$231$	26.0554	1.71432
$232$	−1.49382	−0.0980742
$233$	23.2938	1.52603	0.763015	−	0.646381i	$-0.223718\pi$
$233$	23.2938	1.52603	0.763015	+	0.646381i	$0.223718\pi$
$234$	−1.60659	−0.105026
$235$	−0.283366	−0.0184848
$236$	−14.8009	−0.963458
$237$	1.78067	0.115667
$238$	−1.19414	−0.0774044
$239$	16.9433	1.09597	0.547987	−	0.836487i	$-0.315394\pi$
$239$	16.9433	1.09597	0.547987	+	0.836487i	$0.315394\pi$
$240$	−4.26275	−0.275160
$241$	15.1915	0.978569	0.489285	−	0.872124i	$-0.337258\pi$
$241$	15.1915	0.978569	0.489285	+	0.872124i	$0.337258\pi$
$242$	−1.58021	−0.101580
$243$	−22.2674	−1.42846
$244$	6.14310	0.393272
$245$	−8.76914	−0.560240
$246$	−4.92923	−0.314276
$247$	−1.67181	−0.106375
$248$	−0.620960	−0.0394310
$249$	28.2373	1.78946
$250$	1.07792	0.0681736
$251$	1.25848	0.0794343	0.0397171	−	0.999211i	$-0.487354\pi$
$251$	1.25848	0.0794343	0.0397171	+	0.999211i	$0.487354\pi$
$252$	31.1088	1.95967
$253$	12.6925	0.797972
$254$	2.29720	0.144139
$255$	−1.16133	−0.0727255
$256$	11.7485	0.734282
$257$	−19.7644	−1.23287	−0.616434	−	0.787407i	$-0.711423\pi$
$257$	−19.7644	−1.23287	−0.616434	+	0.787407i	$0.711423\pi$
$258$	0.583972	0.0363565
$259$	1.41058	0.0876489
$260$	−1.97002	−0.122176
$261$	5.07341	0.314036
$262$	−3.60661	−0.222817
$263$	−23.4523	−1.44613	−0.723065	−	0.690780i	$-0.757267\pi$
$263$	−23.4523	−1.44613	−0.723065	+	0.690780i	$0.757267\pi$
$264$	4.76969	0.293554
$265$	2.40985	0.148036
$266$	−0.922538	−0.0565644
$267$	−3.72712	−0.228096
$268$	−28.4234	−1.73623
$269$	28.1145	1.71417	0.857086	−	0.515174i	$-0.172273\pi$
$269$	28.1145	1.71417	0.857086	+	0.515174i	$0.172273\pi$
$270$	−0.0420294	−0.00255783
$271$	−26.7827	−1.62693	−0.813466	−	0.581613i	$-0.802422\pi$
$271$	−26.7827	−1.62693	−0.813466	+	0.581613i	$0.802422\pi$
$272$	3.67057	0.222561
$273$	27.2306	1.64807
$274$	−0.356182	−0.0215177
$275$	9.89920	0.596944
$276$	29.5697	1.77989
$277$	−18.8797	−1.13437	−0.567187	−	0.823589i	$-0.691968\pi$
$277$	−18.8797	−1.13437	−0.567187	+	0.823589i	$0.691968\pi$
$278$	−3.38468	−0.202999
$279$	2.10894	0.126259
$280$	−2.20517	−0.131784
$281$	−23.9388	−1.42807	−0.714034	−	0.700111i	$-0.753134\pi$
$281$	−23.9388	−1.42807	−0.714034	+	0.700111i	$0.753134\pi$
$282$	0.353470	0.0210489
$283$	−33.2265	−1.97511	−0.987556	−	0.157267i	$-0.949732\pi$
$283$	−33.2265	−1.97511	−0.987556	+	0.157267i	$0.949732\pi$
$284$	−3.08434	−0.183022
$285$	−0.897195	−0.0531452
$286$	1.05482	0.0623725
$287$	42.8172	2.52742
$288$	8.58214	0.505708
$289$	1.00000	0.0588235
$290$	−0.177290	−0.0104109
$291$	17.8062	1.04382
$292$	0.0878590	0.00514156
$293$	−13.1838	−0.770207	−0.385104	−	0.922873i	$-0.625834\pi$
$293$	−13.1838	−0.770207	−0.385104	+	0.922873i	$0.625834\pi$
$294$	10.9386	0.637952
$295$	−3.56328	−0.207462
$296$	0.258219	0.0150087
$297$	−0.789659	−0.0458207
$298$	0.960948	0.0556663
$299$	13.2650	0.767137
$300$	23.0621	1.33149
$301$	−5.07261	−0.292380
$302$	−3.31194	−0.190581
$303$	−32.3001	−1.85559
$304$	2.83572	0.162640
$305$	1.47893	0.0846835
$306$	0.742417	0.0424412
$307$	16.3349	0.932282	0.466141	−	0.884711i	$-0.345644\pi$
$307$	16.3349	0.932282	0.466141	+	0.884711i	$0.345644\pi$
$308$	−20.4246	−1.16380
$309$	1.21087	0.0688840
$310$	−0.0736971	−0.00418571
$311$	16.0033	0.907466	0.453733	−	0.891138i	$-0.350092\pi$
$311$	16.0033	0.907466	0.453733	+	0.891138i	$0.350092\pi$
$312$	4.98483	0.282210
$313$	32.7405	1.85060	0.925300	−	0.379235i	$-0.123813\pi$
$313$	32.7405	1.85060	0.925300	+	0.379235i	$0.123813\pi$
$314$	−1.92088	−0.108401
$315$	7.48935	0.421977
$316$	−1.39586	−0.0785230
$317$	−22.0841	−1.24036	−0.620182	−	0.784458i	$-0.712941\pi$
$317$	−22.0841	−1.24036	−0.620182	+	0.784458i	$0.712941\pi$
$318$	−3.00604	−0.168570
$319$	−3.33098	−0.186499
$320$	3.13687	0.175356
$321$	16.3709	0.913737
$322$	7.31991	0.407923
$323$	0.772556	0.0429862
$324$	16.5584	0.919913
$325$	10.3457	0.573877
$326$	2.58302	0.143060
$327$	−35.3988	−1.95756
$328$	7.83810	0.432786
$329$	−3.07038	−0.169276
$330$	0.566078	0.0311616
$331$	27.9860	1.53825	0.769124	−	0.639099i	$-0.220693\pi$
$331$	27.9860	1.53825	0.769124	+	0.639099i	$0.220693\pi$
$332$	−22.1350	−1.21482
$333$	−0.876981	−0.0480583
$334$	−1.08939	−0.0596085
$335$	−6.84284	−0.373864
$336$	−46.1885	−2.51979
$337$	−8.49924	−0.462983	−0.231491	−	0.972837i	$-0.574361\pi$
$337$	−8.49924	−0.462983	−0.231491	+	0.972837i	$0.574361\pi$
$338$	−1.95792	−0.106497
$339$	−40.4592	−2.19744
$340$	0.910362	0.0493713
$341$	−1.38464	−0.0749824
$342$	0.573559	0.0310145
$343$	−59.5086	−3.21316
$344$	−0.928590	−0.0500662
$345$	7.11883	0.383265
$346$	1.31635	0.0707674
$347$	14.8522	0.797310	0.398655	−	0.917101i	$-0.369477\pi$
$347$	14.8522	0.797310	0.398655	+	0.917101i	$0.369477\pi$
$348$	−7.76016	−0.415988
$349$	−25.9063	−1.38673	−0.693367	−	0.720585i	$-0.743873\pi$
$349$	−25.9063	−1.38673	−0.693367	+	0.720585i	$0.743873\pi$
$350$	5.70897	0.305157
$351$	−0.825278	−0.0440501
$352$	−5.63465	−0.300328
$353$	8.44817	0.449651	0.224825	−	0.974399i	$-0.427819\pi$
$353$	8.44817	0.449651	0.224825	+	0.974399i	$0.427819\pi$
$354$	4.44483	0.236240
$355$	−0.742545	−0.0394102
$356$	2.92166	0.154848
$357$	−12.5835	−0.665988
$358$	3.12696	0.165265
$359$	21.5004	1.13475	0.567375	−	0.823460i	$-0.307959\pi$
$359$	21.5004	1.13475	0.567375	+	0.823460i	$0.307959\pi$
$360$	1.37100	0.0722579
$361$	−18.4032	−0.968587
$362$	−0.881798	−0.0463463
$363$	−16.6518	−0.873992
$364$	−21.3459	−1.11883
$365$	0.0211518	0.00110714
$366$	−1.84482	−0.0964301
$367$	−19.2265	−1.00362	−0.501808	−	0.864979i	$-0.667332\pi$
$367$	−19.2265	−1.00362	−0.501808	+	0.864979i	$0.667332\pi$
$368$	−22.5001	−1.17290
$369$	−26.6202	−1.38579
$370$	0.0306461	0.00159322
$371$	26.1116	1.35565
$372$	−3.22579	−0.167249
$373$	0.324897	0.0168225	0.00841126	−	0.999965i	$-0.497323\pi$
$373$	0.324897	0.0168225	0.00841126	+	0.999965i	$0.497323\pi$
$374$	−0.487438	−0.0252048
$375$	11.3588	0.586566
$376$	−0.562063	−0.0289862
$377$	−3.48122	−0.179292
$378$	−0.455404	−0.0234235
$379$	−13.6995	−0.703696	−0.351848	−	0.936057i	$-0.614447\pi$
$379$	−13.6995	−0.703696	−0.351848	+	0.936057i	$0.614447\pi$
$380$	0.703305	0.0360788
$381$	24.2073	1.24018
$382$	−3.04271	−0.155679
$383$	−20.2418	−1.03431	−0.517154	−	0.855892i	$-0.673009\pi$
$383$	−20.2418	−1.03431	−0.517154	+	0.855892i	$0.673009\pi$
$384$	−17.4140	−0.888657
$385$	−4.91717	−0.250602
$386$	−3.30722	−0.168333
$387$	3.15374	0.160313
$388$	−13.9582	−0.708619
$389$	−7.60992	−0.385838	−0.192919	−	0.981215i	$-0.561796\pi$
$389$	−7.60992	−0.385838	−0.192919	+	0.981215i	$0.561796\pi$
$390$	0.591612	0.0299574
$391$	−6.12987	−0.310001
$392$	−17.3938	−0.878517
$393$	−38.0054	−1.91712
$394$	6.34575	0.319694
$395$	−0.336048	−0.0169084
$396$	12.6984	0.638118
$397$	−17.6924	−0.887955	−0.443978	−	0.896038i	$-0.646433\pi$
$397$	−17.6924	−0.887955	−0.443978	+	0.896038i	$0.646433\pi$
$398$	−0.401019	−0.0201013
$399$	−9.72144	−0.486681
$400$	−17.5484	−0.877418
$401$	9.97667	0.498211	0.249106	−	0.968476i	$-0.419863\pi$
$401$	9.97667	0.498211	0.249106	+	0.968476i	$0.419863\pi$
$402$	8.53574	0.425724
$403$	−1.44709	−0.0720849
$404$	25.3198	1.25971
$405$	3.98640	0.198086
$406$	−1.92101	−0.0953380
$407$	0.575787	0.0285407
$408$	−2.30353	−0.114042
$409$	9.49851	0.469671	0.234836	−	0.972035i	$-0.424545\pi$
$409$	9.49851	0.469671	0.234836	+	0.972035i	$0.424545\pi$
$410$	0.930245	0.0459415
$411$	−3.75334	−0.185139
$412$	−0.949193	−0.0467634
$413$	−38.6095	−1.89985
$414$	−4.55092	−0.223666
$415$	−5.32894	−0.261587
$416$	−5.88881	−0.288723
$417$	−35.6668	−1.74661
$418$	−0.376573	−0.0184188
$419$	−27.3615	−1.33670	−0.668349	−	0.743848i	$-0.732999\pi$
$419$	−27.3615	−1.33670	−0.668349	+	0.743848i	$0.732999\pi$
$420$	−11.4555	−0.558972
$421$	−7.25064	−0.353375	−0.176687	−	0.984267i	$-0.556538\pi$
$421$	−7.25064	−0.353375	−0.176687	+	0.984267i	$0.556538\pi$
$422$	−4.08121	−0.198670
$423$	1.90891	0.0928145
$424$	4.77998	0.232136
$425$	−4.78083	−0.231904
$426$	0.926248	0.0448769
$427$	16.0248	0.775494
$428$	−12.8331	−0.620310
$429$	11.1153	0.536654
$430$	−0.110207	−0.00531467
$431$	−20.4081	−0.983026	−0.491513	−	0.870870i	$-0.663556\pi$
$431$	−20.4081	−0.983026	−0.491513	+	0.870870i	$0.663556\pi$
$432$	1.39983	0.0673495
$433$	−4.95234	−0.237994	−0.118997	−	0.992895i	$-0.537968\pi$
$433$	−4.95234	−0.237994	−0.118997	+	0.992895i	$0.537968\pi$
$434$	−0.798535	−0.0383309
$435$	−1.86824	−0.0895751
$436$	27.7489	1.32893
$437$	−4.73567	−0.226538
$438$	−0.0263847	−0.00126071
$439$	−34.8643	−1.66398	−0.831992	−	0.554787i	$-0.812800\pi$
$439$	−34.8643	−1.66398	−0.831992	+	0.554787i	$0.812800\pi$
$440$	−0.900136	−0.0429123
$441$	59.0738	2.81304
$442$	−0.509424	−0.0242308
$443$	41.8487	1.98829	0.994146	−	0.108045i	$-0.0344589\pi$
$443$	41.8487	1.98829	0.994146	+	0.108045i	$0.0344589\pi$
$444$	1.34141	0.0636604
$445$	0.703382	0.0333435
$446$	0.725909	0.0343728
$447$	10.1262	0.478953
$448$	33.9891	1.60584
$449$	2.48332	0.117195	0.0585975	−	0.998282i	$-0.481337\pi$
$449$	2.48332	0.117195	0.0585975	+	0.998282i	$0.481337\pi$
$450$	−3.54937	−0.167319
$451$	17.4777	0.822991
$452$	31.7157	1.49178
$453$	−34.9003	−1.63976
$454$	3.75940	0.176437
$455$	−5.13897	−0.240919
$456$	−1.77960	−0.0833376
$457$	−10.9755	−0.513410	−0.256705	−	0.966490i	$-0.582637\pi$
$457$	−10.9755	−0.513410	−0.256705	+	0.966490i	$0.582637\pi$
$458$	−2.21166	−0.103344
$459$	0.381367	0.0178007
$460$	−5.58040	−0.260188
$461$	22.1577	1.03199	0.515993	−	0.856593i	$-0.327423\pi$
$461$	22.1577	1.03199	0.515993	+	0.856593i	$0.327423\pi$
$462$	6.13367	0.285364
$463$	28.7824	1.33763	0.668815	−	0.743429i	$-0.266802\pi$
$463$	28.7824	1.33763	0.668815	+	0.743429i	$0.266802\pi$
$464$	5.90484	0.274125
$465$	−0.776599	−0.0360139
$466$	5.48357	0.254022
$467$	−1.42299	−0.0658482	−0.0329241	−	0.999458i	$-0.510482\pi$
$467$	−1.42299	−0.0658482	−0.0329241	+	0.999458i	$0.510482\pi$
$468$	13.2712	0.613459
$469$	−74.1447	−3.42369
$470$	−0.0667070	−0.00307696
$471$	−20.2417	−0.932687
$472$	−7.06783	−0.325323
$473$	−2.07060	−0.0952064
$474$	0.419185	0.0192538
$475$	−3.69346	−0.169468
$476$	9.86411	0.452121
$477$	−16.2341	−0.743307
$478$	3.98861	0.182435
$479$	−31.1607	−1.42377	−0.711883	−	0.702298i	$-0.752158\pi$
$479$	−31.1607	−1.42377	−0.711883	+	0.702298i	$0.752158\pi$
$480$	−3.16029	−0.144247
$481$	0.601758	0.0274378
$482$	3.57621	0.162892
$483$	77.1352	3.50977
$484$	13.0532	0.593328
$485$	−3.36039	−0.152587
$486$	−5.24195	−0.237780
$487$	38.7041	1.75385	0.876924	−	0.480629i	$-0.159592\pi$
$487$	38.7041	1.75385	0.876924	+	0.480629i	$0.159592\pi$
$488$	2.93349	0.132793
$489$	27.2192	1.23089
$490$	−2.06433	−0.0932571
$491$	23.6190	1.06591	0.532955	−	0.846143i	$-0.321081\pi$
$491$	23.6190	1.06591	0.532955	+	0.846143i	$0.321081\pi$
$492$	40.7176	1.83569
$493$	1.60870	0.0724522
$494$	−0.393559	−0.0177070
$495$	3.05710	0.137406
$496$	2.45456	0.110213
$497$	−8.04575	−0.360901
$498$	6.64730	0.297873
$499$	24.5501	1.09902	0.549508	−	0.835489i	$-0.314815\pi$
$499$	24.5501	1.09902	0.549508	+	0.835489i	$0.314815\pi$
$500$	−8.90410	−0.398203
$501$	−11.4796	−0.512873
$502$	0.296256	0.0132226
$503$	−23.9952	−1.06990	−0.534948	−	0.844885i	$-0.679669\pi$
$503$	−23.9952	−1.06990	−0.534948	+	0.844885i	$0.679669\pi$
$504$	14.8553	0.661706
$505$	6.09567	0.271254
$506$	2.98793	0.132830
$507$	−20.6320	−0.916300
$508$	−18.9759	−0.841921
$509$	39.3815	1.74555	0.872777	−	0.488119i	$-0.162317\pi$
$509$	39.3815	1.74555	0.872777	+	0.488119i	$0.162317\pi$
$510$	−0.273388	−0.0121058
$511$	0.229188	0.0101387
$512$	16.8055	0.742704
$513$	0.294627	0.0130081
$514$	−4.65271	−0.205222
$515$	−0.228516	−0.0100696
$516$	−4.82387	−0.212359
$517$	−1.25331	−0.0551204
$518$	0.332062	0.0145900
$519$	13.8713	0.608883
$520$	−0.940737	−0.0412541
$521$	−26.8001	−1.17413	−0.587066	−	0.809539i	$-0.699717\pi$
$521$	−26.8001	−1.17413	−0.587066	+	0.809539i	$0.699717\pi$
$522$	1.19433	0.0522742
$523$	32.9038	1.43878	0.719392	−	0.694605i	$-0.244421\pi$
$523$	32.9038	1.43878	0.719392	+	0.694605i	$0.244421\pi$
$524$	29.7922	1.30148
$525$	60.1595	2.62558
$526$	−5.52088	−0.240722
$527$	0.668713	0.0291296
$528$	−18.8538	−0.820507
$529$	14.5754	0.633711
$530$	0.567299	0.0246419
$531$	24.0042	1.04169
$532$	7.62057	0.330394
$533$	18.2660	0.791189
$534$	−0.877397	−0.0379687
$535$	−3.08953	−0.133572
$536$	−13.5729	−0.586260
$537$	32.9510	1.42194
$538$	6.61840	0.285340
$539$	−38.7852	−1.67060
$540$	0.347182	0.0149403
$541$	7.68418	0.330369	0.165184	−	0.986263i	$-0.447178\pi$
$541$	7.68418	0.330369	0.165184	+	0.986263i	$0.447178\pi$
$542$	−6.30488	−0.270818
$543$	−9.29214	−0.398764
$544$	2.72126	0.116673
$545$	6.68046	0.286159
$546$	6.41033	0.274337
$547$	−18.0466	−0.771617	−0.385809	−	0.922579i	$-0.626077\pi$
$547$	−18.0466	−0.771617	−0.385809	+	0.922579i	$0.626077\pi$
$548$	2.94222	0.125685
$549$	−9.96291	−0.425207
$550$	2.33036	0.0993669
$551$	1.24281	0.0529455
$552$	14.1203	0.601001
$553$	−3.64121	−0.154840
$554$	−4.44446	−0.188827
$555$	0.322940	0.0137080
$556$	27.9589	1.18572
$557$	28.5394	1.20925	0.604627	−	0.796509i	$-0.293322\pi$
$557$	28.5394	1.20925	0.604627	+	0.796509i	$0.293322\pi$
$558$	0.496464	0.0210170
$559$	−2.16400	−0.0915274
$560$	8.71670	0.368348
$561$	−5.13648	−0.216863
$562$	−5.63540	−0.237715
$563$	−32.6313	−1.37524	−0.687622	−	0.726069i	$-0.741346\pi$
$563$	−32.6313	−1.37524	−0.687622	+	0.726069i	$0.741346\pi$
$564$	−2.91982	−0.122947
$565$	7.63547	0.321227
$566$	−7.82182	−0.328776
$567$	43.1941	1.81398
$568$	−1.47285	−0.0617995
$569$	−14.2077	−0.595618	−0.297809	−	0.954625i	$-0.596256\pi$
$569$	−14.2077	−0.595618	−0.297809	+	0.954625i	$0.596256\pi$
$570$	−0.211208	−0.00884652
$571$	−9.41808	−0.394134	−0.197067	−	0.980390i	$-0.563142\pi$
$571$	−9.41808	−0.394134	−0.197067	+	0.980390i	$0.563142\pi$
$572$	−8.71325	−0.364319
$573$	−32.0632	−1.33946
$574$	10.0795	0.420712
$575$	29.3059	1.22214
$576$	−21.1317	−0.880487
$577$	−45.6943	−1.90228	−0.951140	−	0.308761i	$-0.900086\pi$
$577$	−45.6943	−1.90228	−0.951140	+	0.308761i	$0.900086\pi$
$578$	0.235409	0.00979172
$579$	−34.8505	−1.44834
$580$	1.46450	0.0608100
$581$	−57.7410	−2.39550
$582$	4.19174	0.173753
$583$	10.6586	0.441432
$584$	0.0419550	0.00173611
$585$	3.19499	0.132097
$586$	−3.10359	−0.128208
$587$	−2.10079	−0.0867087	−0.0433544	−	0.999060i	$-0.513804\pi$
$587$	−2.10079	−0.0867087	−0.0433544	+	0.999060i	$0.513804\pi$
$588$	−90.3577	−3.72629
$589$	0.516618	0.0212869
$590$	−0.838828	−0.0345340
$591$	66.8698	2.75065
$592$	−1.02070	−0.0419505
$593$	6.82159	0.280129	0.140065	−	0.990142i	$-0.455269\pi$
$593$	6.82159	0.280129	0.140065	+	0.990142i	$0.455269\pi$
$594$	−0.185893	−0.00762727
$595$	2.37476	0.0973555
$596$	−7.93787	−0.325148
$597$	−4.22583	−0.172952
$598$	3.12271	0.127697
$599$	35.5977	1.45448	0.727242	−	0.686382i	$-0.240802\pi$
$599$	35.5977	1.45448	0.727242	+	0.686382i	$0.240802\pi$
$600$	11.0128	0.449595
$601$	−23.4225	−0.955424	−0.477712	−	0.878516i	$-0.658534\pi$
$601$	−23.4225	−0.955424	−0.477712	+	0.878516i	$0.658534\pi$
$602$	−1.19414	−0.0486694
$603$	46.0972	1.87722
$604$	27.3581	1.11318
$605$	3.14253	0.127762
$606$	−7.60373	−0.308880
$607$	35.7010	1.44906	0.724529	−	0.689244i	$-0.242057\pi$
$607$	35.7010	1.44906	0.724529	+	0.689244i	$0.242057\pi$
$608$	2.10233	0.0852607
$609$	−20.2430	−0.820289
$610$	0.348154	0.0140963
$611$	−1.30984	−0.0529904
$612$	−6.13270	−0.247900
$613$	42.4099	1.71292	0.856460	−	0.516213i	$-0.172659\pi$
$613$	42.4099	1.71292	0.856460	+	0.516213i	$0.172659\pi$
$614$	3.84538	0.155187
$615$	9.80266	0.395281
$616$	−9.75331	−0.392972
$617$	−34.9532	−1.40716	−0.703582	−	0.710614i	$-0.748417\pi$
$617$	−34.9532	−1.40716	−0.703582	+	0.710614i	$0.748417\pi$
$618$	0.285050	0.0114664
$619$	43.2058	1.73659	0.868294	−	0.496051i	$-0.165217\pi$
$619$	43.2058	1.73659	0.868294	+	0.496051i	$0.165217\pi$
$620$	0.608771	0.0244488
$621$	−2.33773	−0.0938099
$622$	3.76733	0.151056
$623$	7.62141	0.305345
$624$	−19.7042	−0.788801
$625$	21.7605	0.870421
$626$	7.70740	0.308050
$627$	−3.96822	−0.158475
$628$	15.8673	0.633175
$629$	−0.278077	−0.0110877
$630$	1.76306	0.0702420
$631$	−11.4347	−0.455210	−0.227605	−	0.973754i	$-0.573089\pi$
$631$	−11.4347	−0.455210	−0.227605	+	0.973754i	$0.573089\pi$
$632$	−0.666558	−0.0265142
$633$	−43.0067	−1.70936
$634$	−5.19878	−0.206470
$635$	−4.56840	−0.181292
$636$	24.8312	0.984621
$637$	−40.5346	−1.60604
$638$	−0.784141	−0.0310444
$639$	5.00219	0.197884
$640$	3.28638	0.129906
$641$	18.5864	0.734118	0.367059	−	0.930198i	$-0.380365\pi$
$641$	18.5864	0.734118	0.367059	+	0.930198i	$0.380365\pi$
$642$	3.85386	0.152100
$643$	2.40493	0.0948413	0.0474206	−	0.998875i	$-0.484900\pi$
$643$	2.40493	0.0948413	0.0474206	+	0.998875i	$0.484900\pi$
$644$	−60.4657	−2.38268
$645$	−1.16133	−0.0457275
$646$	0.181866	0.00715544
$647$	30.9406	1.21640	0.608200	−	0.793784i	$-0.291892\pi$
$647$	30.9406	1.21640	0.608200	+	0.793784i	$0.291892\pi$
$648$	7.90709	0.310620
$649$	−15.7601	−0.618638
$650$	2.43547	0.0955271
$651$	−8.41474	−0.329800
$652$	−21.3369	−0.835618
$653$	36.3617	1.42294	0.711471	−	0.702715i	$-0.248029\pi$
$653$	36.3617	1.42294	0.711471	+	0.702715i	$0.248029\pi$
$654$	−8.33318	−0.325853
$655$	7.17239	0.280249
$656$	−30.9827	−1.20967
$657$	−0.142490	−0.00555907
$658$	−0.722795	−0.0281775
$659$	6.54341	0.254895	0.127448	−	0.991845i	$-0.459322\pi$
$659$	6.54341	0.254895	0.127448	+	0.991845i	$0.459322\pi$
$660$	−4.67606	−0.182015
$661$	−31.9924	−1.24436	−0.622181	−	0.782874i	$-0.713753\pi$
$661$	−31.9924	−1.24436	−0.622181	+	0.782874i	$0.713753\pi$
$662$	6.58815	0.256056
$663$	−5.36817	−0.208483
$664$	−10.5700	−0.410197
$665$	1.83463	0.0711440
$666$	−0.206449	−0.00799974
$667$	−9.86112	−0.381824
$668$	8.99882	0.348175
$669$	7.64943	0.295744
$670$	−1.61087	−0.0622332
$671$	6.54120	0.252520
$672$	−34.2430	−1.32095
$673$	−28.4642	−1.09721	−0.548607	−	0.836080i	$-0.684842\pi$
$673$	−28.4642	−1.09721	−0.548607	+	0.836080i	$0.684842\pi$
$674$	−2.00080	−0.0770678
$675$	−1.82325	−0.0701770
$676$	16.1733	0.622050
$677$	−0.228791	−0.00879317	−0.00439659	−	0.999990i	$-0.501399\pi$
$677$	−0.228791	−0.00879317	−0.00439659	+	0.999990i	$0.501399\pi$
$678$	−9.52446	−0.365785
$679$	−36.4111	−1.39733
$680$	0.434722	0.0166708
$681$	39.6155	1.51807
$682$	−0.325956	−0.0124815
$683$	30.1791	1.15477	0.577386	−	0.816472i	$-0.304073\pi$
$683$	30.1791	1.15477	0.577386	+	0.816472i	$0.304073\pi$
$684$	−4.73785	−0.181156
$685$	0.708331	0.0270639
$686$	−14.0089	−0.534861
$687$	−23.3058	−0.889172
$688$	3.67057	0.139939
$689$	11.1393	0.424374
$690$	1.67584	0.0637980
$691$	31.8254	1.21070	0.605349	−	0.795961i	$-0.293034\pi$
$691$	31.8254	1.21070	0.605349	+	0.795961i	$0.293034\pi$
$692$	−10.8736	−0.413353
$693$	33.1248	1.25831
$694$	3.49635	0.132720
$695$	6.73104	0.255323
$696$	−3.70568	−0.140463
$697$	−8.44086	−0.319720
$698$	−6.09858	−0.230834
$699$	57.7844	2.18561
$700$	−47.1587	−1.78243
$701$	24.6098	0.929500	0.464750	−	0.885442i	$-0.346144\pi$
$701$	24.6098	0.929500	0.464750	+	0.885442i	$0.346144\pi$
$702$	−0.194278	−0.00733254
$703$	−0.214830	−0.00810247
$704$	13.8741	0.522901
$705$	−0.702939	−0.0264742
$706$	1.98877	0.0748485
$707$	66.0489	2.48402
$708$	−36.7162	−1.37988
$709$	−43.7360	−1.64254	−0.821269	−	0.570541i	$-0.806734\pi$
$709$	−43.7360	−1.64254	−0.821269	+	0.570541i	$0.806734\pi$
$710$	−0.174802	−0.00656019
$711$	2.26381	0.0848994
$712$	1.39517	0.0522863
$713$	−4.09913	−0.153514
$714$	−2.96226	−0.110860
$715$	−2.09769	−0.0784491
$716$	−25.8301	−0.965314
$717$	42.0309	1.56967
$718$	5.06139	0.188890
$719$	22.3294	0.832747	0.416373	−	0.909194i	$-0.363301\pi$
$719$	22.3294	0.832747	0.416373	+	0.909194i	$0.363301\pi$
$720$	−5.41934	−0.201967
$721$	−2.47605	−0.0922130
$722$	−4.33227	−0.161230
$723$	37.6851	1.40152
$724$	7.28405	0.270709
$725$	−7.69092	−0.285634
$726$	−3.91998	−0.145484
$727$	−29.9447	−1.11059	−0.555295	−	0.831654i	$-0.687395\pi$
$727$	−29.9447	−1.11059	−0.555295	+	0.831654i	$0.687395\pi$
$728$	−10.1932	−0.377787
$729$	−29.6927	−1.09973
$730$	0.00497932	0.000184293 0
$731$	1.00000	0.0369863
$732$	15.2390	0.563250
$733$	35.1366	1.29780	0.648900	−	0.760874i	$-0.275229\pi$
$733$	35.1366	1.29780	0.648900	+	0.760874i	$0.275229\pi$
$734$	−4.52609	−0.167061
$735$	−21.7534	−0.802385
$736$	−16.6810	−0.614870
$737$	−30.2653	−1.11484
$738$	−6.26664	−0.230678
$739$	−17.8196	−0.655505	−0.327752	−	0.944764i	$-0.606291\pi$
$739$	−17.8196	−0.655505	−0.327752	+	0.944764i	$0.606291\pi$
$740$	−0.253151	−0.00930600
$741$	−4.14721	−0.152352
$742$	6.14690	0.225660
$743$	−47.2909	−1.73494	−0.867468	−	0.497493i	$-0.834254\pi$
$743$	−47.2909	−1.73494	−0.867468	+	0.497493i	$0.834254\pi$
$744$	−1.54040	−0.0564738
$745$	−1.91102	−0.0700143
$746$	0.0764835	0.00280026
$747$	35.8987	1.31346
$748$	4.02646	0.147222
$749$	−33.4762	−1.22319
$750$	2.67396	0.0976394
$751$	13.2127	0.482140	0.241070	−	0.970508i	$-0.422502\pi$
$751$	13.2127	0.482140	0.241070	+	0.970508i	$0.422502\pi$
$752$	2.22174	0.0810187
$753$	3.12187	0.113767
$754$	−0.819511	−0.0298448
$755$	6.58638	0.239703
$756$	3.76184	0.136817
$757$	20.2304	0.735286	0.367643	−	0.929967i	$-0.380165\pi$
$757$	20.2304	0.735286	0.367643	+	0.929967i	$0.380165\pi$
$758$	−3.22499	−0.117137
$759$	31.4860	1.14287
$760$	0.335847	0.0121824
$761$	37.8841	1.37330	0.686649	−	0.726989i	$-0.259081\pi$
$761$	37.8841	1.37330	0.686649	+	0.726989i	$0.259081\pi$
$762$	5.69861	0.206439
$763$	72.3853	2.62052
$764$	25.1342	0.909322
$765$	−1.47643	−0.0533804
$766$	−4.76510	−0.172170
$767$	−16.4710	−0.594733
$768$	29.1442	1.05165
$769$	−26.5545	−0.957581	−0.478790	−	0.877929i	$-0.658925\pi$
$769$	−26.5545	−0.957581	−0.478790	+	0.877929i	$0.658925\pi$
$770$	−1.15755	−0.0417151
$771$	−49.0290	−1.76573
$772$	27.3191	0.983236
$773$	−2.03483	−0.0731878	−0.0365939	−	0.999330i	$-0.511651\pi$
$773$	−2.03483	−0.0731878	−0.0365939	+	0.999330i	$0.511651\pi$
$774$	0.742417	0.0266856
$775$	−3.19701	−0.114840
$776$	−6.66540	−0.239274
$777$	3.49918	0.125532
$778$	−1.79144	−0.0642263
$779$	−6.52104	−0.233640
$780$	−4.88698	−0.174982
$781$	−3.28422	−0.117519
$782$	−1.44303	−0.0516025
$783$	0.613505	0.0219249
$784$	68.7547	2.45553
$785$	3.82001	0.136342
$786$	−8.94682	−0.319122
$787$	2.64360	0.0942342	0.0471171	−	0.998889i	$-0.484997\pi$
$787$	2.64360	0.0942342	0.0471171	+	0.998889i	$0.484997\pi$
$788$	−52.4188	−1.86734
$789$	−58.1774	−2.07117
$790$	−0.0791087	−0.00281456
$791$	82.7332	2.94165
$792$	6.06381	0.215468
$793$	6.83625	0.242762
$794$	−4.16494	−0.147808
$795$	5.97804	0.212019
$796$	3.31260	0.117412
$797$	38.7290	1.37185	0.685925	−	0.727672i	$-0.259398\pi$
$797$	38.7290	1.37185	0.685925	+	0.727672i	$0.259398\pi$
$798$	−2.28851	−0.0810125
$799$	0.605286	0.0214135
$800$	−13.0099	−0.459970
$801$	−4.73837	−0.167422
$802$	2.34860	0.0829318
$803$	0.0935527	0.00330140
$804$	−70.5090	−2.48666
$805$	−14.5570	−0.513065
$806$	−0.340659	−0.0119992
$807$	69.7429	2.45507
$808$	12.0909	0.425356
$809$	29.4587	1.03571	0.517856	−	0.855468i	$-0.326730\pi$
$809$	29.4587	1.03571	0.517856	+	0.855468i	$0.326730\pi$
$810$	0.938433	0.0329732
$811$	−14.2407	−0.500057	−0.250029	−	0.968238i	$-0.580440\pi$
$811$	−14.2407	−0.500057	−0.250029	+	0.968238i	$0.580440\pi$
$812$	15.8684	0.556871
$813$	−66.4390	−2.33012
$814$	0.135545	0.00475086
$815$	−5.13680	−0.179934
$816$	9.10547	0.318755
$817$	0.772556	0.0270283
$818$	2.23603	0.0781811
$819$	34.6189	1.20968
$820$	−7.68424	−0.268345
$821$	−15.5622	−0.543124	−0.271562	−	0.962421i	$-0.587540\pi$
$821$	−15.5622	−0.543124	−0.271562	+	0.962421i	$0.587540\pi$
$822$	−0.883570	−0.0308180
$823$	45.6840	1.59244	0.796222	−	0.605005i	$-0.206829\pi$
$823$	45.6840	1.59244	0.796222	+	0.605005i	$0.206829\pi$
$824$	−0.453265	−0.0157902
$825$	24.5567	0.854954
$826$	−9.08901	−0.316247
$827$	1.18192	0.0410993	0.0205497	−	0.999789i	$-0.493458\pi$
$827$	1.18192	0.0410993	0.0205497	+	0.999789i	$0.493458\pi$
$828$	37.5927	1.30644
$829$	−19.3140	−0.670804	−0.335402	−	0.942075i	$-0.608872\pi$
$829$	−19.3140	−0.670804	−0.335402	+	0.942075i	$0.608872\pi$
$830$	−1.25448	−0.0435436
$831$	−46.8345	−1.62467
$832$	14.4999	0.502694
$833$	18.7314	0.649003
$834$	−8.39627	−0.290739
$835$	2.16644	0.0749727
$836$	3.11066	0.107585
$837$	0.255025	0.00881496
$838$	−6.44114	−0.222506
$839$	−20.7988	−0.718056	−0.359028	−	0.933327i	$-0.616892\pi$
$839$	−20.7988	−0.718056	−0.359028	+	0.933327i	$0.616892\pi$
$840$	−5.47031	−0.188744
$841$	−26.4121	−0.910762
$842$	−1.70687	−0.0588225
$843$	−59.3842	−2.04530
$844$	33.7127	1.16044
$845$	3.89368	0.133947
$846$	0.449375	0.0154498
$847$	34.0504	1.16999
$848$	−18.8945	−0.648839
$849$	−82.4241	−2.82879
$850$	−1.12545	−0.0386026
$851$	1.70458	0.0584321
$852$	−7.65123	−0.262127
$853$	12.4245	0.425408	0.212704	−	0.977117i	$-0.431773\pi$
$853$	12.4245	0.425408	0.212704	+	0.977117i	$0.431773\pi$
$854$	3.77238	0.129088
$855$	−1.14062	−0.0390085
$856$	−6.12813	−0.209455
$857$	−47.2053	−1.61250	−0.806250	−	0.591574i	$-0.798507\pi$
$857$	−47.2053	−1.61250	−0.806250	+	0.591574i	$0.798507\pi$
$858$	2.61665	0.0893310
$859$	25.0241	0.853811	0.426905	−	0.904296i	$-0.359604\pi$
$859$	25.0241	0.853811	0.426905	+	0.904296i	$0.359604\pi$
$860$	0.910362	0.0310431
$861$	106.215	3.61981
$862$	−4.80426	−0.163634
$863$	−33.0483	−1.12498	−0.562488	−	0.826805i	$-0.690156\pi$
$863$	−33.0483	−1.12498	−0.562488	+	0.826805i	$0.690156\pi$
$864$	1.03780	0.0353067
$865$	−2.61780	−0.0890077
$866$	−1.16583	−0.0396164
$867$	2.48067	0.0842481
$868$	6.59626	0.223892
$869$	−1.48631	−0.0504198
$870$	−0.439799	−0.0149106
$871$	−31.6305	−1.07176
$872$	13.2508	0.448729
$873$	22.6374	0.766161
$874$	−1.11482	−0.0377093
$875$	−23.2271	−0.785219
$876$	0.217949	0.00736383
$877$	32.9203	1.11164	0.555820	−	0.831303i	$-0.312404\pi$
$877$	32.9203	1.11164	0.555820	+	0.831303i	$0.312404\pi$
$878$	−8.20738	−0.276985
$879$	−32.7048	−1.10310
$880$	3.55809	0.119943
$881$	−8.04137	−0.270921	−0.135460	−	0.990783i	$-0.543251\pi$
$881$	−8.04137	−0.270921	−0.135460	+	0.990783i	$0.543251\pi$
$882$	13.9065	0.468256
$883$	−14.2749	−0.480387	−0.240194	−	0.970725i	$-0.577211\pi$
$883$	−14.2749	−0.480387	−0.240194	+	0.970725i	$0.577211\pi$
$884$	4.20807	0.141533
$885$	−8.83933	−0.297131
$886$	9.85156	0.330970
$887$	−33.7632	−1.13366	−0.566828	−	0.823836i	$-0.691830\pi$
$887$	−33.7632	−1.13366	−0.566828	+	0.823836i	$0.691830\pi$
$888$	0.640558	0.0214957
$889$	−49.5004	−1.66019
$890$	0.165582	0.00555033
$891$	17.6315	0.590678
$892$	−5.99634	−0.200772
$893$	0.467617	0.0156482
$894$	2.38380	0.0797261
$895$	−6.21851	−0.207862
$896$	35.6092	1.18962
$897$	32.9062	1.09871
$898$	0.584595	0.0195082
$899$	1.07576	0.0358786
$900$	29.3194	0.977314
$901$	−5.14757	−0.171490
$902$	4.11440	0.136994
$903$	−12.5835	−0.418752
$904$	15.1451	0.503718
$905$	1.75361	0.0582921
$906$	−8.21583	−0.272953
$907$	8.23935	0.273583	0.136792	−	0.990600i	$-0.456321\pi$
$907$	8.23935	0.273583	0.136792	+	0.990600i	$0.456321\pi$
$908$	−31.0543	−1.03057
$909$	−41.0638	−1.36200
$910$	−1.20976	−0.0401031
$911$	35.0952	1.16276	0.581378	−	0.813634i	$-0.302514\pi$
$911$	35.0952	1.16276	0.581378	+	0.813634i	$0.302514\pi$
$912$	7.03449	0.232935
$913$	−23.5695	−0.780035
$914$	−2.58372	−0.0854619
$915$	3.66875	0.121285
$916$	18.2693	0.603634
$917$	77.7155	2.56639
$918$	0.0897772	0.00296309
$919$	−32.6491	−1.07700	−0.538498	−	0.842627i	$-0.681008\pi$
$919$	−32.6491	−1.07700	−0.538498	+	0.842627i	$0.681008\pi$
$920$	−2.66479	−0.0878555
$921$	40.5215	1.33523
$922$	5.21612	0.171784
$923$	−3.43235	−0.112977
$924$	−50.6668	−1.66682
$925$	1.32944	0.0437117
$926$	6.77562	0.222661
$927$	1.53941	0.0505608
$928$	4.37769	0.143705
$929$	−6.67053	−0.218853	−0.109427	−	0.993995i	$-0.534901\pi$
$929$	−6.67053	−0.218853	−0.109427	+	0.993995i	$0.534901\pi$
$930$	−0.182818	−0.00599485
$931$	14.4710	0.474269
$932$	−45.2968	−1.48375
$933$	39.6990	1.29969
$934$	−0.334985	−0.0109610
$935$	0.969358	0.0317014
$936$	6.33733	0.207142
$937$	−8.42680	−0.275292	−0.137646	−	0.990482i	$-0.543954\pi$
$937$	−8.42680	−0.275292	−0.137646	+	0.990482i	$0.543954\pi$
$938$	−17.4543	−0.569904
$939$	81.2184	2.65046
$940$	0.551029	0.0179726
$941$	−40.2106	−1.31083	−0.655414	−	0.755270i	$-0.727506\pi$
$941$	−40.2106	−1.31083	−0.655414	+	0.755270i	$0.727506\pi$
$942$	−4.76507	−0.155254
$943$	51.7414	1.68493
$944$	27.9380	0.909305
$945$	0.905654	0.0294609
$946$	−0.487438	−0.0158480
$947$	31.3540	1.01887	0.509434	−	0.860510i	$-0.329855\pi$
$947$	31.3540	1.01887	0.509434	+	0.860510i	$0.329855\pi$
$948$	−3.46266	−0.112462
$949$	0.0977725	0.00317383
$950$	−0.869473	−0.0282094
$951$	−54.7833	−1.77647
$952$	4.71037	0.152664
$953$	44.4185	1.43886	0.719429	−	0.694566i	$-0.244404\pi$
$953$	44.4185	1.43886	0.719429	+	0.694566i	$0.244404\pi$
$954$	−3.82164	−0.123730
$955$	6.05098	0.195805
$956$	−32.9477	−1.06561
$957$	−8.26306	−0.267107
$958$	−7.33550	−0.236999
$959$	7.67503	0.247840
$960$	7.78154	0.251148
$961$	−30.5528	−0.985575
$962$	0.141659	0.00456728
$963$	20.8127	0.670681
$964$	−29.5411	−0.951455
$965$	6.57700	0.211721
$966$	18.1583	0.584234
$967$	−41.4672	−1.33349	−0.666747	−	0.745284i	$-0.732314\pi$
$967$	−41.4672	−1.33349	−0.666747	+	0.745284i	$0.732314\pi$
$968$	6.23326	0.200345
$969$	1.91646	0.0615655
$970$	−0.791066	−0.0253996
$971$	−26.8077	−0.860301	−0.430150	−	0.902757i	$-0.641539\pi$
$971$	−26.8077	−0.860301	−0.430150	+	0.902757i	$0.641539\pi$
$972$	43.3008	1.38888
$973$	72.9333	2.33813
$974$	9.11128	0.291944
$975$	25.6643	0.821916
$976$	−11.5956	−0.371167
$977$	−42.4967	−1.35959	−0.679795	−	0.733402i	$-0.737931\pi$
$977$	−42.4967	−1.35959	−0.679795	+	0.733402i	$0.737931\pi$
$978$	6.40763	0.204894
$979$	3.11100	0.0994281
$980$	17.0523	0.544716
$981$	−45.0033	−1.43684
$982$	5.56012	0.177431
$983$	53.9099	1.71946	0.859730	−	0.510749i	$-0.170632\pi$
$983$	53.9099	1.71946	0.859730	+	0.510749i	$0.170632\pi$
$984$	19.4437	0.619844
$985$	−12.6197	−0.402096
$986$	0.378702	0.0120603
$987$	−7.61661	−0.242439
$988$	3.25097	0.103427
$989$	−6.12987	−0.194919
$990$	0.719668	0.0228726
$991$	10.5395	0.334799	0.167399	−	0.985889i	$-0.446463\pi$
$991$	10.5395	0.334799	0.167399	+	0.985889i	$0.446463\pi$
$992$	1.81975	0.0577770
$993$	69.4240	2.20310
$994$	−1.89404	−0.0600753
$995$	0.797498	0.0252824
$996$	−54.9097	−1.73988
$997$	−56.9012	−1.80208	−0.901039	−	0.433738i	$-0.857194\pi$
$997$	−56.9012	−1.80208	−0.901039	+	0.433738i	$0.857194\pi$
$998$	5.77932	0.182941
$999$	−0.106049	−0.00335525

Twists

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

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

\(f(q)\)	\(=\)	\(q+0.235409 q^{2} +2.48067 q^{3} -1.94458 q^{4} -0.468153 q^{5} +0.583972 q^{6} -5.07261 q^{7} -0.928590 q^{8} +3.15374 q^{9} +O(q^{10})\)	\(q+0.235409 q^{2} +2.48067 q^{3} -1.94458 q^{4} -0.468153 q^{5} +0.583972 q^{6} -5.07261 q^{7} -0.928590 q^{8} +3.15374 q^{9} -0.110207 q^{10} -2.07060 q^{11} -4.82387 q^{12} -2.16400 q^{13} -1.19414 q^{14} -1.16133 q^{15} +3.67057 q^{16} +1.00000 q^{17} +0.742417 q^{18} +0.772556 q^{19} +0.910362 q^{20} -12.5835 q^{21} -0.487438 q^{22} -6.12987 q^{23} -2.30353 q^{24} -4.78083 q^{25} -0.509424 q^{26} +0.381367 q^{27} +9.86411 q^{28} +1.60870 q^{29} -0.273388 q^{30} +0.668713 q^{31} +2.72126 q^{32} -5.13648 q^{33} +0.235409 q^{34} +2.37476 q^{35} -6.13270 q^{36} -0.278077 q^{37} +0.181866 q^{38} -5.36817 q^{39} +0.434722 q^{40} -8.44086 q^{41} -2.96226 q^{42} +1.00000 q^{43} +4.02646 q^{44} -1.47643 q^{45} -1.44303 q^{46} +0.605286 q^{47} +9.10547 q^{48} +18.7314 q^{49} -1.12545 q^{50} +2.48067 q^{51} +4.20807 q^{52} -5.14757 q^{53} +0.0897772 q^{54} +0.969358 q^{55} +4.71037 q^{56} +1.91646 q^{57} +0.378702 q^{58} +7.61136 q^{59} +2.25831 q^{60} -3.15908 q^{61} +0.157421 q^{62} -15.9977 q^{63} -6.70052 q^{64} +1.01308 q^{65} -1.20917 q^{66} +14.6167 q^{67} -1.94458 q^{68} -15.2062 q^{69} +0.559039 q^{70} +1.58612 q^{71} -2.92853 q^{72} -0.0451814 q^{73} -0.0654618 q^{74} -11.8597 q^{75} -1.50230 q^{76} +10.5034 q^{77} -1.26372 q^{78} +0.717817 q^{79} -1.71839 q^{80} -8.51516 q^{81} -1.98705 q^{82} +11.3829 q^{83} +24.4696 q^{84} -0.468153 q^{85} +0.235409 q^{86} +3.99066 q^{87} +1.92274 q^{88} -1.50246 q^{89} -0.347565 q^{90} +10.9771 q^{91} +11.9200 q^{92} +1.65886 q^{93} +0.142490 q^{94} -0.361674 q^{95} +6.75056 q^{96} +7.17798 q^{97} +4.40953 q^{98} -6.53013 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - 3 q^{3} + 3 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} - 3 q^{8} + 5 q^{9}+O(q^{10}) \) 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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