LMFDB - Embedded newform 6031.2.a.d.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6031,2,Mod(1,6031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6031, 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("6031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6031 = 37 \cdot 163 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6031.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:	$48.1577774590$
Analytic rank:	$0$
Dimension:	$133$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	6031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.20408 q^{2} +0.816725 q^{3} +2.85795 q^{4} -2.28441 q^{5} -1.80012 q^{6} +0.445697 q^{7} -1.89098 q^{8} -2.33296 q^{9} +O(q^{10})$	\(q-2.20408 q^{2} +0.816725 q^{3} +2.85795 q^{4} -2.28441 q^{5} -1.80012 q^{6} +0.445697 q^{7} -1.89098 q^{8} -2.33296 q^{9} +5.03501 q^{10} +1.90035 q^{11} +2.33416 q^{12} -5.49904 q^{13} -0.982349 q^{14} -1.86573 q^{15} -1.54803 q^{16} -0.603781 q^{17} +5.14202 q^{18} -1.58401 q^{19} -6.52872 q^{20} +0.364012 q^{21} -4.18852 q^{22} -8.24076 q^{23} -1.54441 q^{24} +0.218517 q^{25} +12.1203 q^{26} -4.35556 q^{27} +1.27378 q^{28} +3.91209 q^{29} +4.11222 q^{30} +2.93225 q^{31} +7.19394 q^{32} +1.55206 q^{33} +1.33078 q^{34} -1.01815 q^{35} -6.66748 q^{36} -1.00000 q^{37} +3.49127 q^{38} -4.49120 q^{39} +4.31977 q^{40} -12.5315 q^{41} -0.802309 q^{42} -2.64931 q^{43} +5.43110 q^{44} +5.32943 q^{45} +18.1632 q^{46} -8.63493 q^{47} -1.26432 q^{48} -6.80135 q^{49} -0.481628 q^{50} -0.493123 q^{51} -15.7160 q^{52} +4.44385 q^{53} +9.59999 q^{54} -4.34118 q^{55} -0.842803 q^{56} -1.29370 q^{57} -8.62254 q^{58} +2.42060 q^{59} -5.33217 q^{60} +10.9813 q^{61} -6.46290 q^{62} -1.03979 q^{63} -12.7599 q^{64} +12.5620 q^{65} -3.42087 q^{66} -1.54894 q^{67} -1.72557 q^{68} -6.73043 q^{69} +2.24408 q^{70} +1.55694 q^{71} +4.41158 q^{72} -3.52989 q^{73} +2.20408 q^{74} +0.178469 q^{75} -4.52701 q^{76} +0.846980 q^{77} +9.89895 q^{78} -4.36923 q^{79} +3.53634 q^{80} +3.44158 q^{81} +27.6204 q^{82} +2.44261 q^{83} +1.04033 q^{84} +1.37928 q^{85} +5.83928 q^{86} +3.19510 q^{87} -3.59352 q^{88} +17.8509 q^{89} -11.7465 q^{90} -2.45090 q^{91} -23.5516 q^{92} +2.39484 q^{93} +19.0320 q^{94} +3.61852 q^{95} +5.87547 q^{96} -0.226435 q^{97} +14.9907 q^{98} -4.43344 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 133 q + 14 q^{2} + 8 q^{3} + 142 q^{4} + 34 q^{5} + 20 q^{6} + 8 q^{7} + 42 q^{8} + 177 q^{9}+O(q^{10}) $ 133 * q + 14 * q^2 + 8 * q^3 + 142 * q^4 + 34 * q^5 + 20 * q^6 + 8 * q^7 + 42 * q^8 + 177 * q^9	\( 133 q + 14 q^{2} + 8 q^{3} + 142 q^{4} + 34 q^{5} + 20 q^{6} + 8 q^{7} + 42 q^{8} + 177 q^{9} + 9 q^{10} + 23 q^{11} + 24 q^{12} + 23 q^{13} + 31 q^{14} + 9 q^{15} + 168 q^{16} + 98 q^{17} + 38 q^{18} + 29 q^{19} + 83 q^{20} + 26 q^{21} + 2 q^{22} + 34 q^{23} + 75 q^{24} + 177 q^{25} + 67 q^{26} + 32 q^{27} + 32 q^{28} + 91 q^{29} + 12 q^{30} + 24 q^{31} + 88 q^{32} + 27 q^{33} + 23 q^{34} + 66 q^{35} + 232 q^{36} - 133 q^{37} + 26 q^{38} + 28 q^{39} + 41 q^{40} + 132 q^{41} + 13 q^{42} + 11 q^{43} + 65 q^{44} + 107 q^{45} + 20 q^{46} + 10 q^{47} + 27 q^{48} + 229 q^{49} + 78 q^{50} + 19 q^{51} + 71 q^{52} + 7 q^{53} + 43 q^{54} + 41 q^{55} + 67 q^{56} + 45 q^{57} + 25 q^{58} + 97 q^{59} - 42 q^{60} + 65 q^{61} + 24 q^{62} + 39 q^{63} + 200 q^{64} + 60 q^{65} + 35 q^{66} + 25 q^{67} + 227 q^{68} + 120 q^{69} + 37 q^{70} + 26 q^{71} + 93 q^{72} + 55 q^{73} - 14 q^{74} + 5 q^{75} + 34 q^{76} + 21 q^{77} - 2 q^{78} + 50 q^{79} + 162 q^{80} + 341 q^{81} + 66 q^{82} + 30 q^{83} - 89 q^{84} + 30 q^{85} - 12 q^{86} + 80 q^{87} - 85 q^{88} + 225 q^{89} - 86 q^{90} + q^{91} + 82 q^{92} + 42 q^{93} - 17 q^{94} + 70 q^{95} + 55 q^{96} + 12 q^{97} + 90 q^{98} + 17 q^{99}+O(q^{100}) \) 133 * q + 14 * q^2 + 8 * q^3 + 142 * q^4 + 34 * q^5 + 20 * q^6 + 8 * q^7 + 42 * q^8 + 177 * q^9 + 9 * q^10 + 23 * q^11 + 24 * q^12 + 23 * q^13 + 31 * q^14 + 9 * q^15 + 168 * q^16 + 98 * q^17 + 38 * q^18 + 29 * q^19 + 83 * q^20 + 26 * q^21 + 2 * q^22 + 34 * q^23 + 75 * q^24 + 177 * q^25 + 67 * q^26 + 32 * q^27 + 32 * q^28 + 91 * q^29 + 12 * q^30 + 24 * q^31 + 88 * q^32 + 27 * q^33 + 23 * q^34 + 66 * q^35 + 232 * q^36 - 133 * q^37 + 26 * q^38 + 28 * q^39 + 41 * q^40 + 132 * q^41 + 13 * q^42 + 11 * q^43 + 65 * q^44 + 107 * q^45 + 20 * q^46 + 10 * q^47 + 27 * q^48 + 229 * q^49 + 78 * q^50 + 19 * q^51 + 71 * q^52 + 7 * q^53 + 43 * q^54 + 41 * q^55 + 67 * q^56 + 45 * q^57 + 25 * q^58 + 97 * q^59 - 42 * q^60 + 65 * q^61 + 24 * q^62 + 39 * q^63 + 200 * q^64 + 60 * q^65 + 35 * q^66 + 25 * q^67 + 227 * q^68 + 120 * q^69 + 37 * q^70 + 26 * q^71 + 93 * q^72 + 55 * q^73 - 14 * q^74 + 5 * q^75 + 34 * q^76 + 21 * q^77 - 2 * q^78 + 50 * q^79 + 162 * q^80 + 341 * q^81 + 66 * q^82 + 30 * q^83 - 89 * q^84 + 30 * q^85 - 12 * q^86 + 80 * q^87 - 85 * q^88 + 225 * q^89 - 86 * q^90 + q^91 + 82 * q^92 + 42 * q^93 - 17 * q^94 + 70 * q^95 + 55 * q^96 + 12 * q^97 + 90 * q^98 + 17 * 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 $

$2$	−2.20408	−1.55852	−0.779258	−	0.626703i	$-0.784404\pi$
$2$	−2.20408	−1.55852	−0.779258	+	0.626703i	$0.784404\pi$
$3$	0.816725	0.471537	0.235768	−	0.971809i	$-0.424239\pi$
$3$	0.816725	0.471537	0.235768	+	0.971809i	$0.424239\pi$
$4$	2.85795	1.42897
$5$	−2.28441	−1.02162	−0.510809	−	0.859694i	$-0.670654\pi$
$5$	−2.28441	−1.02162	−0.510809	+	0.859694i	$0.670654\pi$
$6$	−1.80012	−0.734898
$7$	0.445697	0.168457	0.0842287	−	0.996446i	$-0.473157\pi$
$7$	0.445697	0.168457	0.0842287	+	0.996446i	$0.473157\pi$
$8$	−1.89098	−0.668562
$9$	−2.33296	−0.777653
$10$	5.03501	1.59221
$11$	1.90035	0.572977	0.286489	−	0.958084i	$-0.407512\pi$
$11$	1.90035	0.572977	0.286489	+	0.958084i	$0.407512\pi$
$12$	2.33416	0.673813
$13$	−5.49904	−1.52516	−0.762579	−	0.646895i	$-0.776067\pi$
$13$	−5.49904	−1.52516	−0.762579	+	0.646895i	$0.776067\pi$
$14$	−0.982349	−0.262544
$15$	−1.86573	−0.481730
$16$	−1.54803	−0.387008
$17$	−0.603781	−0.146438	−0.0732192	−	0.997316i	$-0.523327\pi$
$17$	−0.603781	−0.146438	−0.0732192	+	0.997316i	$0.523327\pi$
$18$	5.14202	1.21199
$19$	−1.58401	−0.363396	−0.181698	−	0.983354i	$-0.558159\pi$
$19$	−1.58401	−0.363396	−0.181698	+	0.983354i	$0.558159\pi$
$20$	−6.52872	−1.45987
$21$	0.364012	0.0794339
$22$	−4.18852	−0.892995
$23$	−8.24076	−1.71832	−0.859158	−	0.511710i	$-0.829012\pi$
$23$	−8.24076	−1.71832	−0.859158	+	0.511710i	$0.829012\pi$
$24$	−1.54441	−0.315252
$25$	0.218517	0.0437034
$26$	12.1203	2.37698
$27$	−4.35556	−0.838229
$28$	1.27378	0.240721
$29$	3.91209	0.726457	0.363229	−	0.931700i	$-0.381674\pi$
$29$	3.91209	0.726457	0.363229	+	0.931700i	$0.381674\pi$
$30$	4.11222	0.750785
$31$	2.93225	0.526648	0.263324	−	0.964707i	$-0.415181\pi$
$31$	2.93225	0.526648	0.263324	+	0.964707i	$0.415181\pi$
$32$	7.19394	1.27172
$33$	1.55206	0.270180
$34$	1.33078	0.228227
$35$	−1.01815	−0.172099
$36$	−6.66748	−1.11125
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	3.49127	0.566359
$39$	−4.49120	−0.719168
$40$	4.31977	0.683015
$41$	−12.5315	−1.95710	−0.978548	−	0.206017i	$-0.933950\pi$
$41$	−12.5315	−1.95710	−0.978548	+	0.206017i	$0.933950\pi$
$42$	−0.802309	−0.123799
$43$	−2.64931	−0.404016	−0.202008	−	0.979384i	$-0.564747\pi$
$43$	−2.64931	−0.404016	−0.202008	+	0.979384i	$0.564747\pi$
$44$	5.43110	0.818769
$45$	5.32943	0.794465
$46$	18.1632	2.67802
$47$	−8.63493	−1.25953	−0.629767	−	0.776784i	$-0.716850\pi$
$47$	−8.63493	−1.25953	−0.629767	+	0.776784i	$0.716850\pi$
$48$	−1.26432	−0.182489
$49$	−6.80135	−0.971622
$50$	−0.481628	−0.0681125
$51$	−0.493123	−0.0690511
$52$	−15.7160	−2.17941
$53$	4.44385	0.610410	0.305205	−	0.952287i	$-0.401275\pi$
$53$	4.44385	0.610410	0.305205	+	0.952287i	$0.401275\pi$
$54$	9.59999	1.30639
$55$	−4.34118	−0.585364
$56$	−0.842803	−0.112624
$57$	−1.29370	−0.171355
$58$	−8.62254	−1.13220
$59$	2.42060	0.315136	0.157568	−	0.987508i	$-0.449635\pi$
$59$	2.42060	0.315136	0.157568	+	0.987508i	$0.449635\pi$
$60$	−5.33217	−0.688380
$61$	10.9813	1.40601	0.703004	−	0.711186i	$-0.251841\pi$
$61$	10.9813	1.40601	0.703004	+	0.711186i	$0.251841\pi$
$62$	−6.46290	−0.820789
$63$	−1.03979	−0.131002
$64$	−12.7599	−1.59499
$65$	12.5620	1.55813
$66$	−3.42087	−0.421080
$67$	−1.54894	−0.189234	−0.0946168	−	0.995514i	$-0.530163\pi$
$67$	−1.54894	−0.189234	−0.0946168	+	0.995514i	$0.530163\pi$
$68$	−1.72557	−0.209257
$69$	−6.73043	−0.810249
$70$	2.24408	0.268219
$71$	1.55694	0.184775	0.0923875	−	0.995723i	$-0.470550\pi$
$71$	1.55694	0.184775	0.0923875	+	0.995723i	$0.470550\pi$
$72$	4.41158	0.519910
$73$	−3.52989	−0.413143	−0.206571	−	0.978432i	$-0.566231\pi$
$73$	−3.52989	−0.413143	−0.206571	+	0.978432i	$0.566231\pi$
$74$	2.20408	0.256219
$75$	0.178469	0.0206078
$76$	−4.52701	−0.519283
$77$	0.846980	0.0965223
$78$	9.89895	1.12084
$79$	−4.36923	−0.491577	−0.245788	−	0.969323i	$-0.579047\pi$
$79$	−4.36923	−0.491577	−0.245788	+	0.969323i	$0.579047\pi$
$80$	3.53634	0.395375
$81$	3.44158	0.382398
$82$	27.6204	3.05017
$83$	2.44261	0.268111	0.134055	−	0.990974i	$-0.457200\pi$
$83$	2.44261	0.268111	0.134055	+	0.990974i	$0.457200\pi$
$84$	1.04033	0.113509
$85$	1.37928	0.149604
$86$	5.83928	0.629666
$87$	3.19510	0.342551
$88$	−3.59352	−0.383071
$89$	17.8509	1.89219	0.946097	−	0.323884i	$-0.104989\pi$
$89$	17.8509	1.89219	0.946097	+	0.323884i	$0.104989\pi$
$90$	−11.7465	−1.23819
$91$	−2.45090	−0.256924
$92$	−23.5516	−2.45543
$93$	2.39484	0.248334
$94$	19.0320	1.96300
$95$	3.61852	0.371252
$96$	5.87547	0.599663
$97$	−0.226435	−0.0229910	−0.0114955	−	0.999934i	$-0.503659\pi$
$97$	−0.226435	−0.0229910	−0.0114955	+	0.999934i	$0.503659\pi$
$98$	14.9907	1.51429
$99$	−4.43344	−0.445578
$100$	0.624510	0.0624510
$101$	0.257477	0.0256199	0.0128100	−	0.999918i	$-0.495922\pi$
$101$	0.257477	0.0256199	0.0128100	+	0.999918i	$0.495922\pi$
$102$	1.08688	0.107617
$103$	−3.45099	−0.340036	−0.170018	−	0.985441i	$-0.554383\pi$
$103$	−3.45099	−0.340036	−0.170018	+	0.985441i	$0.554383\pi$
$104$	10.3986	1.01966
$105$	−0.831551	−0.0811511
$106$	−9.79458	−0.951333
$107$	−9.68495	−0.936279	−0.468140	−	0.883654i	$-0.655076\pi$
$107$	−9.68495	−0.936279	−0.468140	+	0.883654i	$0.655076\pi$
$108$	−12.4480	−1.19781
$109$	−11.1132	−1.06446	−0.532228	−	0.846601i	$-0.678645\pi$
$109$	−11.1132	−1.06446	−0.532228	+	0.846601i	$0.678645\pi$
$110$	9.56828	0.912299
$111$	−0.816725	−0.0775201
$112$	−0.689953	−0.0651944
$113$	0.226062	0.0212662	0.0106331	−	0.999943i	$-0.496615\pi$
$113$	0.226062	0.0212662	0.0106331	+	0.999943i	$0.496615\pi$
$114$	2.85141	0.267059
$115$	18.8252	1.75546
$116$	11.1806	1.03809
$117$	12.8290	1.18604
$118$	−5.33519	−0.491144
$119$	−0.269103	−0.0246687
$120$	3.52806	0.322067
$121$	−7.38867	−0.671697
$122$	−24.2036	−2.19129
$123$	−10.2348	−0.922843
$124$	8.38022	0.752566
$125$	10.9229	0.976970
$126$	2.29178	0.204168
$127$	−11.6747	−1.03596	−0.517979	−	0.855393i	$-0.673316\pi$
$127$	−11.6747	−1.03596	−0.517979	+	0.855393i	$0.673316\pi$
$128$	13.7359	1.21410
$129$	−2.16376	−0.190508
$130$	−27.6877	−2.42837
$131$	11.6477	1.01767	0.508833	−	0.860865i	$-0.330077\pi$
$131$	11.6477	1.01767	0.508833	+	0.860865i	$0.330077\pi$
$132$	4.43572	0.386080
$133$	−0.705986	−0.0612168
$134$	3.41399	0.294924
$135$	9.94988	0.856349
$136$	1.14174	0.0979032
$137$	−4.66991	−0.398977	−0.199489	−	0.979900i	$-0.563928\pi$
$137$	−4.66991	−0.398977	−0.199489	+	0.979900i	$0.563928\pi$
$138$	14.8344	1.26279
$139$	9.33242	0.791565	0.395783	−	0.918344i	$-0.370473\pi$
$139$	9.33242	0.791565	0.395783	+	0.918344i	$0.370473\pi$
$140$	−2.90983	−0.245925
$141$	−7.05237	−0.593916
$142$	−3.43162	−0.287975
$143$	−10.4501	−0.873881
$144$	3.61150	0.300958
$145$	−8.93681	−0.742162
$146$	7.78015	0.643890
$147$	−5.55484	−0.458155
$148$	−2.85795	−0.234922
$149$	−6.46280	−0.529453	−0.264727	−	0.964323i	$-0.585282\pi$
$149$	−6.46280	−0.529453	−0.264727	+	0.964323i	$0.585282\pi$
$150$	−0.393358	−0.0321175
$151$	3.93113	0.319911	0.159955	−	0.987124i	$-0.448865\pi$
$151$	3.93113	0.319911	0.159955	+	0.987124i	$0.448865\pi$
$152$	2.99532	0.242953
$153$	1.40860	0.113878
$154$	−1.86681	−0.150432
$155$	−6.69846	−0.538033
$156$	−12.8356	−1.02767
$157$	−9.44227	−0.753575	−0.376788	−	0.926300i	$-0.622971\pi$
$157$	−9.44227	−0.753575	−0.376788	+	0.926300i	$0.622971\pi$
$158$	9.63011	0.766131
$159$	3.62940	0.287830
$160$	−16.4339	−1.29921
$161$	−3.67288	−0.289463
$162$	−7.58550	−0.595973
$163$	1.00000	0.0783260
$163$	1.00000	0.0783260
$164$	−35.8145	−2.79664
$165$	−3.54555	−0.276021
$166$	−5.38369	−0.417855
$167$	11.1572	0.863369	0.431684	−	0.902025i	$-0.357919\pi$
$167$	11.1572	0.863369	0.431684	+	0.902025i	$0.357919\pi$
$168$	−0.688339	−0.0531065
$169$	17.2394	1.32611
$170$	−3.04004	−0.233161
$171$	3.69542	0.282596
$172$	−7.57159	−0.577328
$173$	10.5406	0.801389	0.400695	−	0.916212i	$-0.368769\pi$
$173$	10.5406	0.801389	0.400695	+	0.916212i	$0.368769\pi$
$174$	−7.04225	−0.533872
$175$	0.0973924	0.00736217
$176$	−2.94181	−0.221747
$177$	1.97697	0.148598
$178$	−39.3448	−2.94901
$179$	−9.28539	−0.694023	−0.347011	−	0.937861i	$-0.612804\pi$
$179$	−9.28539	−0.694023	−0.347011	+	0.937861i	$0.612804\pi$
$180$	15.2312	1.13527
$181$	9.00997	0.669706	0.334853	−	0.942270i	$-0.391313\pi$
$181$	9.00997	0.669706	0.334853	+	0.942270i	$0.391313\pi$
$182$	5.40197	0.400421
$183$	8.96869	0.662985
$184$	15.5831	1.14880
$185$	2.28441	0.167953
$186$	−5.27842	−0.387032
$187$	−1.14740	−0.0839059
$188$	−24.6782	−1.79984
$189$	−1.94126	−0.141206
$190$	−7.97548	−0.578602
$191$	24.6405	1.78292	0.891461	−	0.453097i	$-0.149681\pi$
$191$	24.6405	1.78292	0.891461	+	0.453097i	$0.149681\pi$
$192$	−10.4213	−0.752096
$193$	6.01508	0.432975	0.216487	−	0.976285i	$-0.430540\pi$
$193$	6.01508	0.432975	0.216487	+	0.976285i	$0.430540\pi$
$194$	0.499081	0.0358319
$195$	10.2597	0.734715
$196$	−19.4379	−1.38842
$197$	−8.89228	−0.633549	−0.316775	−	0.948501i	$-0.602600\pi$
$197$	−8.89228	−0.633549	−0.316775	+	0.948501i	$0.602600\pi$
$198$	9.77164	0.694440
$199$	−18.7013	−1.32570	−0.662852	−	0.748751i	$-0.730654\pi$
$199$	−18.7013	−1.32570	−0.662852	+	0.748751i	$0.730654\pi$
$200$	−0.413211	−0.0292185
$201$	−1.26506	−0.0892305
$202$	−0.567499	−0.0399291
$203$	1.74361	0.122377
$204$	−1.40932	−0.0986722
$205$	28.6271	1.99941
$206$	7.60624	0.529952
$207$	19.2254	1.33625
$208$	8.51269	0.590249
$209$	−3.01017	−0.208218
$210$	1.83280	0.126475
$211$	−12.8333	−0.883478	−0.441739	−	0.897144i	$-0.645638\pi$
$211$	−12.8333	−0.883478	−0.441739	+	0.897144i	$0.645638\pi$
$212$	12.7003	0.872259
$213$	1.27159	0.0871282
$214$	21.3464	1.45921
$215$	6.05210	0.412750
$216$	8.23628	0.560408
$217$	1.30689	0.0887178
$218$	24.4944	1.65897
$219$	−2.88295	−0.194812
$220$	−12.4068	−0.836470
$221$	3.32022	0.223342
$222$	1.80012	0.120816
$223$	−6.11012	−0.409164	−0.204582	−	0.978849i	$-0.565583\pi$
$223$	−6.11012	−0.409164	−0.204582	+	0.978849i	$0.565583\pi$
$224$	3.20631	0.214231
$225$	−0.509792	−0.0339861
$226$	−0.498258	−0.0331437
$227$	−3.38117	−0.224416	−0.112208	−	0.993685i	$-0.535792\pi$
$227$	−3.38117	−0.224416	−0.112208	+	0.993685i	$0.535792\pi$
$228$	−3.69732	−0.244861
$229$	−3.22465	−0.213091	−0.106545	−	0.994308i	$-0.533979\pi$
$229$	−3.22465	−0.213091	−0.106545	+	0.994308i	$0.533979\pi$
$230$	−41.4922	−2.73592
$231$	0.691750	0.0455138
$232$	−7.39769	−0.485682
$233$	8.59175	0.562864	0.281432	−	0.959581i	$-0.409191\pi$
$233$	8.59175	0.562864	0.281432	+	0.959581i	$0.409191\pi$
$234$	−28.2762	−1.84847
$235$	19.7257	1.28676
$236$	6.91796	0.450321
$237$	−3.56846	−0.231797
$238$	0.593124	0.0384465
$239$	18.7022	1.20975	0.604874	−	0.796322i	$-0.293224\pi$
$239$	18.7022	1.20975	0.604874	+	0.796322i	$0.293224\pi$
$240$	2.88822	0.186434
$241$	−24.4714	−1.57634	−0.788171	−	0.615456i	$-0.788972\pi$
$241$	−24.4714	−1.57634	−0.788171	+	0.615456i	$0.788972\pi$
$242$	16.2852	1.04685
$243$	15.8775	1.01854
$244$	31.3839	2.00915
$245$	15.5371	0.992627
$246$	22.5583	1.43827
$247$	8.71051	0.554237
$248$	−5.54483	−0.352097
$249$	1.99494	0.126424
$250$	−24.0748	−1.52262
$251$	17.7578	1.12086	0.560431	−	0.828201i	$-0.310635\pi$
$251$	17.7578	1.12086	0.560431	+	0.828201i	$0.310635\pi$
$252$	−2.97167	−0.187198
$253$	−15.6603	−0.984556
$254$	25.7318	1.61456
$255$	1.12649	0.0705438
$256$	−4.75520	−0.297200
$257$	−13.4275	−0.837584	−0.418792	−	0.908082i	$-0.637546\pi$
$257$	−13.4275	−0.837584	−0.418792	+	0.908082i	$0.637546\pi$
$258$	4.76909	0.296910
$259$	−0.445697	−0.0276942
$260$	35.9017	2.22653
$261$	−9.12675	−0.564932
$262$	−25.6725	−1.58605
$263$	10.6129	0.654417	0.327209	−	0.944952i	$-0.393892\pi$
$263$	10.6129	0.654417	0.327209	+	0.944952i	$0.393892\pi$
$264$	−2.93492	−0.180632
$265$	−10.1516	−0.623605
$266$	1.55605	0.0954074
$267$	14.5793	0.892239
$268$	−4.42680	−0.270410
$269$	−9.94649	−0.606448	−0.303224	−	0.952919i	$-0.598063\pi$
$269$	−9.94649	−0.606448	−0.303224	+	0.952919i	$0.598063\pi$
$270$	−21.9303	−1.33463
$271$	−5.56343	−0.337954	−0.168977	−	0.985620i	$-0.554046\pi$
$271$	−5.56343	−0.337954	−0.168977	+	0.985620i	$0.554046\pi$
$272$	0.934673	0.0566729
$273$	−2.00171	−0.121149
$274$	10.2928	0.621813
$275$	0.415259	0.0250411
$276$	−19.2352	−1.15782
$277$	23.8490	1.43295	0.716474	−	0.697613i	$-0.245755\pi$
$277$	23.8490	1.43295	0.716474	+	0.697613i	$0.245755\pi$
$278$	−20.5694	−1.23367
$279$	−6.84082	−0.409549
$280$	1.92531	0.115059
$281$	12.9091	0.770093	0.385046	−	0.922897i	$-0.374185\pi$
$281$	12.9091	0.770093	0.385046	+	0.922897i	$0.374185\pi$
$282$	15.5439	0.925628
$283$	−9.55461	−0.567963	−0.283981	−	0.958830i	$-0.591655\pi$
$283$	−9.55461	−0.567963	−0.283981	+	0.958830i	$0.591655\pi$
$284$	4.44966	0.264039
$285$	2.95533	0.175059
$286$	23.0328	1.36196
$287$	−5.58526	−0.329688
$288$	−16.7832	−0.988958
$289$	−16.6354	−0.978556
$290$	19.6974	1.15667
$291$	−0.184936	−0.0108411
$292$	−10.0883	−0.590370
$293$	−21.3437	−1.24691	−0.623456	−	0.781858i	$-0.714272\pi$
$293$	−21.3437	−1.24691	−0.623456	+	0.781858i	$0.714272\pi$
$294$	12.2433	0.714043
$295$	−5.52965	−0.321949
$296$	1.89098	0.109911
$297$	−8.27710	−0.480286
$298$	14.2445	0.825162
$299$	45.3162	2.62071
$300$	0.510054	0.0294480
$301$	−1.18079	−0.0680595
$302$	−8.66450	−0.498586
$303$	0.210288	0.0120807
$304$	2.45210	0.140637
$305$	−25.0857	−1.43640
$306$	−3.10465	−0.177481
$307$	1.18990	0.0679113	0.0339556	−	0.999423i	$-0.489190\pi$
$307$	1.18990	0.0679113	0.0339556	+	0.999423i	$0.489190\pi$
$308$	2.42062	0.137928
$309$	−2.81851	−0.160339
$310$	14.7639	0.838533
$311$	−30.2069	−1.71288	−0.856439	−	0.516249i	$-0.827328\pi$
$311$	−30.2069	−1.71288	−0.856439	+	0.516249i	$0.827328\pi$
$312$	8.49277	0.480809
$313$	29.9911	1.69520	0.847598	−	0.530638i	$-0.178048\pi$
$313$	29.9911	1.69520	0.847598	+	0.530638i	$0.178048\pi$
$314$	20.8115	1.17446
$315$	2.37531	0.133834
$316$	−12.4870	−0.702450
$317$	22.1743	1.24544	0.622718	−	0.782447i	$-0.286028\pi$
$317$	22.1743	1.24544	0.622718	+	0.782447i	$0.286028\pi$
$318$	−7.99948	−0.448588
$319$	7.43435	0.416244
$320$	29.1489	1.62947
$321$	−7.90994	−0.441490
$322$	8.09530	0.451133
$323$	0.956394	0.0532152
$324$	9.83585	0.546436
$325$	−1.20163	−0.0666547
$326$	−2.20408	−0.122072
$327$	−9.07646	−0.501929
$328$	23.6969	1.30844
$329$	−3.84856	−0.212178
$330$	7.81465	0.430183
$331$	31.3166	1.72132	0.860659	−	0.509182i	$-0.170052\pi$
$331$	31.3166	1.72132	0.860659	+	0.509182i	$0.170052\pi$
$332$	6.98084	0.383123
$333$	2.33296	0.127845
$334$	−24.5913	−1.34557
$335$	3.53842	0.193324
$336$	−0.563502	−0.0307416
$337$	4.82329	0.262741	0.131371	−	0.991333i	$-0.458062\pi$
$337$	4.82329	0.262741	0.131371	+	0.991333i	$0.458062\pi$
$338$	−37.9970	−2.06676
$339$	0.184631	0.0100278
$340$	3.94192	0.213780
$341$	5.57231	0.301757
$342$	−8.14499	−0.440431
$343$	−6.15122	−0.332134
$344$	5.00979	0.270110
$345$	15.3751	0.827765
$346$	−23.2323	−1.24898
$347$	−9.78758	−0.525425	−0.262713	−	0.964874i	$-0.584617\pi$
$347$	−9.78758	−0.525425	−0.262713	+	0.964874i	$0.584617\pi$
$348$	9.13144	0.489497
$349$	−11.8254	−0.633000	−0.316500	−	0.948593i	$-0.602508\pi$
$349$	−11.8254	−0.633000	−0.316500	+	0.948593i	$0.602508\pi$
$350$	−0.214660	−0.0114741
$351$	23.9514	1.27843
$352$	13.6710	0.728667
$353$	14.9527	0.795854	0.397927	−	0.917417i	$-0.369730\pi$
$353$	14.9527	0.795854	0.397927	+	0.917417i	$0.369730\pi$
$354$	−4.35739	−0.231593
$355$	−3.55669	−0.188769
$356$	51.0170	2.70389
$357$	−0.219783	−0.0116322
$358$	20.4657	1.08165
$359$	21.1690	1.11726	0.558628	−	0.829418i	$-0.311328\pi$
$359$	21.1690	1.11726	0.558628	+	0.829418i	$0.311328\pi$
$360$	−10.0778	−0.531149
$361$	−16.4909	−0.867943
$362$	−19.8587	−1.04375
$363$	−6.03451	−0.316730
$364$	−7.00455	−0.367138
$365$	8.06372	0.422074
$366$	−19.7677	−1.03327
$367$	−30.2005	−1.57645	−0.788226	−	0.615386i	$-0.789000\pi$
$367$	−30.2005	−1.57645	−0.788226	+	0.615386i	$0.789000\pi$
$368$	12.7570	0.665003
$369$	29.2356	1.52194
$370$	−5.03501	−0.261757
$371$	1.98061	0.102828
$372$	6.84434	0.354862
$373$	−19.3311	−1.00093	−0.500463	−	0.865758i	$-0.666837\pi$
$373$	−19.3311	−1.00093	−0.500463	+	0.865758i	$0.666837\pi$
$374$	2.52895	0.130769
$375$	8.92097	0.460677
$376$	16.3285	0.842077
$377$	−21.5127	−1.10796
$378$	4.27868	0.220072
$379$	−13.1342	−0.674656	−0.337328	−	0.941387i	$-0.609523\pi$
$379$	−13.1342	−0.674656	−0.337328	+	0.941387i	$0.609523\pi$
$380$	10.3415	0.530509
$381$	−9.53499	−0.488492
$382$	−54.3095	−2.77871
$383$	−6.88978	−0.352051	−0.176026	−	0.984386i	$-0.556324\pi$
$383$	−6.88978	−0.352051	−0.176026	+	0.984386i	$0.556324\pi$
$384$	11.2185	0.572491
$385$	−1.93485	−0.0986089
$386$	−13.2577	−0.674799
$387$	6.18073	0.314184
$388$	−0.647140	−0.0328536
$389$	−28.8684	−1.46369	−0.731843	−	0.681474i	$-0.761339\pi$
$389$	−28.8684	−1.46369	−0.731843	+	0.681474i	$0.761339\pi$
$390$	−22.6132	−1.14507
$391$	4.97561	0.251628
$392$	12.8612	0.649590
$393$	9.51299	0.479867
$394$	19.5993	0.987397
$395$	9.98110	0.502204
$396$	−12.6705	−0.636719
$397$	27.7136	1.39091	0.695453	−	0.718572i	$-0.255204\pi$
$397$	27.7136	1.39091	0.695453	+	0.718572i	$0.255204\pi$
$398$	41.2192	2.06613
$399$	−0.576597	−0.0288660
$400$	−0.338272	−0.0169136
$401$	9.94045	0.496403	0.248201	−	0.968708i	$-0.420161\pi$
$401$	9.94045	0.496403	0.248201	+	0.968708i	$0.420161\pi$
$402$	2.78829	0.139067
$403$	−16.1246	−0.803221
$404$	0.735855	0.0366102
$405$	−7.86197	−0.390664
$406$	−3.84304	−0.190727
$407$	−1.90035	−0.0941969
$408$	0.932486	0.0461650
$409$	−0.399186	−0.0197385	−0.00986923	−	0.999951i	$-0.503142\pi$
$409$	−0.399186	−0.0197385	−0.00986923	+	0.999951i	$0.503142\pi$
$410$	−63.0963	−3.11611
$411$	−3.81403	−0.188132
$412$	−9.86275	−0.485903
$413$	1.07886	0.0530870
$414$	−42.3741	−2.08257
$415$	−5.57991	−0.273907
$416$	−39.5597	−1.93958
$417$	7.62202	0.373252
$418$	6.63464	0.324511
$419$	20.7688	1.01462	0.507311	−	0.861763i	$-0.330639\pi$
$419$	20.7688	1.01462	0.507311	+	0.861763i	$0.330639\pi$
$420$	−2.37653	−0.115963
$421$	37.5606	1.83059	0.915296	−	0.402783i	$-0.131957\pi$
$421$	37.5606	1.83059	0.915296	+	0.402783i	$0.131957\pi$
$422$	28.2855	1.37691
$423$	20.1449	0.979481
$424$	−8.40323	−0.408097
$425$	−0.131937	−0.00639986
$426$	−2.80269	−0.135791
$427$	4.89432	0.236853
$428$	−27.6791	−1.33792
$429$	−8.53486	−0.412067
$430$	−13.3393	−0.643278
$431$	12.5739	0.605662	0.302831	−	0.953044i	$-0.402068\pi$
$431$	12.5739	0.605662	0.302831	+	0.953044i	$0.402068\pi$
$432$	6.74256	0.324401
$433$	−29.9926	−1.44135	−0.720677	−	0.693271i	$-0.756169\pi$
$433$	−29.9926	−1.44135	−0.720677	+	0.693271i	$0.756169\pi$
$434$	−2.88049	−0.138268
$435$	−7.29892	−0.349956
$436$	−31.7610	−1.52108
$437$	13.0534	0.624429
$438$	6.35425	0.303618
$439$	−14.0538	−0.670751	−0.335376	−	0.942084i	$-0.608863\pi$
$439$	−14.0538	−0.670751	−0.335376	+	0.942084i	$0.608863\pi$
$440$	8.20907	0.391352
$441$	15.8673	0.755585
$442$	−7.31801	−0.348082
$443$	24.5587	1.16682	0.583411	−	0.812177i	$-0.301718\pi$
$443$	24.5587	1.16682	0.583411	+	0.812177i	$0.301718\pi$
$444$	−2.33416	−0.110774
$445$	−40.7788	−1.93310
$446$	13.4672	0.637688
$447$	−5.27833	−0.249657
$448$	−5.68705	−0.268688
$449$	−1.92119	−0.0906666	−0.0453333	−	0.998972i	$-0.514435\pi$
$449$	−1.92119	−0.0906666	−0.0453333	+	0.998972i	$0.514435\pi$
$450$	1.12362	0.0529679
$451$	−23.8143	−1.12137
$452$	0.646074	0.0303888
$453$	3.21065	0.150850
$454$	7.45235	0.349756
$455$	5.59886	0.262479
$456$	2.44636	0.114561
$457$	−31.1260	−1.45601	−0.728007	−	0.685570i	$-0.759553\pi$
$457$	−31.1260	−1.45601	−0.728007	+	0.685570i	$0.759553\pi$
$458$	7.10737	0.332106
$459$	2.62981	0.122749
$460$	53.8015	2.50851
$461$	−21.3956	−0.996494	−0.498247	−	0.867035i	$-0.666023\pi$
$461$	−21.3956	−0.996494	−0.498247	+	0.867035i	$0.666023\pi$
$462$	−1.52467	−0.0709340
$463$	−29.6637	−1.37859	−0.689295	−	0.724481i	$-0.742080\pi$
$463$	−29.6637	−1.37859	−0.689295	+	0.724481i	$0.742080\pi$
$464$	−6.05605	−0.281145
$465$	−5.47080	−0.253702
$466$	−18.9369	−0.877233
$467$	19.0236	0.880307	0.440154	−	0.897923i	$-0.354924\pi$
$467$	19.0236	0.880307	0.440154	+	0.897923i	$0.354924\pi$
$468$	36.6647	1.69483
$469$	−0.690359	−0.0318778
$470$	−43.4769	−2.00544
$471$	−7.71174	−0.355338
$472$	−4.57731	−0.210688
$473$	−5.03462	−0.231492
$474$	7.86516	0.361259
$475$	−0.346133	−0.0158817
$476$	−0.769083	−0.0352509
$477$	−10.3673	−0.474687
$478$	−41.2211	−1.88541
$479$	9.11920	0.416667	0.208333	−	0.978058i	$-0.433196\pi$
$479$	9.11920	0.416667	0.208333	+	0.978058i	$0.433196\pi$
$480$	−13.4220	−0.612627
$481$	5.49904	0.250735
$482$	53.9368	2.45676
$483$	−2.99973	−0.136493
$484$	−21.1164	−0.959837
$485$	0.517271	0.0234881
$486$	−34.9952	−1.58742
$487$	35.7069	1.61803	0.809016	−	0.587786i	$-0.200000\pi$
$487$	35.7069	1.61803	0.809016	+	0.587786i	$0.200000\pi$
$488$	−20.7654	−0.940004
$489$	0.816725	0.0369336
$490$	−34.2449	−1.54702
$491$	15.5186	0.700343	0.350171	−	0.936686i	$-0.386123\pi$
$491$	15.5186	0.700343	0.350171	+	0.936686i	$0.386123\pi$
$492$	−29.2506	−1.31872
$493$	−2.36205	−0.106381
$494$	−19.1986	−0.863787
$495$	10.1278	0.455210
$496$	−4.53922	−0.203817
$497$	0.693924	0.0311267
$498$	−4.39699	−0.197034
$499$	39.0985	1.75029	0.875144	−	0.483863i	$-0.160767\pi$
$499$	39.0985	1.75029	0.875144	+	0.483863i	$0.160767\pi$
$500$	31.2169	1.39606
$501$	9.11235	0.407110
$502$	−39.1395	−1.74688
$503$	−16.4722	−0.734458	−0.367229	−	0.930130i	$-0.619694\pi$
$503$	−16.4722	−0.734458	−0.367229	+	0.930130i	$0.619694\pi$
$504$	1.96623	0.0875827
$505$	−0.588182	−0.0261738
$506$	34.5165	1.53445
$507$	14.0799	0.625309
$508$	−33.3656	−1.48036
$509$	10.0349	0.444790	0.222395	−	0.974957i	$-0.428613\pi$
$509$	10.0349	0.444790	0.222395	+	0.974957i	$0.428613\pi$
$510$	−2.48288	−0.109944
$511$	−1.57326	−0.0695970
$512$	−16.9911	−0.750906
$513$	6.89924	0.304609
$514$	29.5952	1.30539
$515$	7.88347	0.347387
$516$	−6.18391	−0.272231
$517$	−16.4094	−0.721684
$518$	0.982349	0.0431619
$519$	8.60880	0.377884
$520$	−23.7546	−1.04171
$521$	−24.6983	−1.08205	−0.541026	−	0.841006i	$-0.681964\pi$
$521$	−24.6983	−1.08205	−0.541026	+	0.841006i	$0.681964\pi$
$522$	20.1160	0.880456
$523$	18.9352	0.827980	0.413990	−	0.910281i	$-0.364135\pi$
$523$	18.9352	0.827980	0.413990	+	0.910281i	$0.364135\pi$
$524$	33.2886	1.45422
$525$	0.0795428	0.00347153
$526$	−23.3916	−1.01992
$527$	−1.77044	−0.0771215
$528$	−2.40265	−0.104562
$529$	44.9101	1.95261
$530$	22.3748	0.971899
$531$	−5.64717	−0.245066
$532$	−2.01767	−0.0874772
$533$	68.9114	2.98488
$534$	−32.1339	−1.39057
$535$	22.1244	0.956520
$536$	2.92902	0.126514
$537$	−7.58362	−0.327257
$538$	21.9228	0.945159
$539$	−12.9250	−0.556717
$540$	28.4362	1.22370
$541$	−25.0267	−1.07598	−0.537991	−	0.842951i	$-0.680817\pi$
$541$	−25.0267	−1.07598	−0.537991	+	0.842951i	$0.680817\pi$
$542$	12.2622	0.526707
$543$	7.35867	0.315791
$544$	−4.34357	−0.186229
$545$	25.3872	1.08747
$546$	4.41193	0.188813
$547$	−29.3464	−1.25476	−0.627381	−	0.778712i	$-0.715873\pi$
$547$	−29.3464	−1.25476	−0.627381	+	0.778712i	$0.715873\pi$
$548$	−13.3464	−0.570128
$549$	−25.6189	−1.09339
$550$	−0.915263	−0.0390269
$551$	−6.19678	−0.263992
$552$	12.7271	0.541702
$553$	−1.94735	−0.0828098
$554$	−52.5650	−2.23327
$555$	1.86573	0.0791960
$556$	26.6716	1.13113
$557$	−5.80905	−0.246137	−0.123069	−	0.992398i	$-0.539274\pi$
$557$	−5.80905	−0.246137	−0.123069	+	0.992398i	$0.539274\pi$
$558$	15.0777	0.638289
$559$	14.5687	0.616189
$560$	1.57613	0.0666038
$561$	−0.937108	−0.0395647
$562$	−28.4526	−1.20020
$563$	27.3919	1.15443	0.577216	−	0.816592i	$-0.304139\pi$
$563$	27.3919	1.15443	0.577216	+	0.816592i	$0.304139\pi$
$564$	−20.1553	−0.848691
$565$	−0.516418	−0.0217259
$566$	21.0591	0.885179
$567$	1.53390	0.0644178
$568$	−2.94415	−0.123534
$569$	−32.3325	−1.35545	−0.677725	−	0.735316i	$-0.737034\pi$
$569$	−32.3325	−1.35545	−0.677725	+	0.735316i	$0.737034\pi$
$570$	−6.51378	−0.272832
$571$	24.9440	1.04387	0.521936	−	0.852985i	$-0.325210\pi$
$571$	24.9440	1.04387	0.521936	+	0.852985i	$0.325210\pi$
$572$	−29.8658	−1.24875
$573$	20.1245	0.840713
$574$	12.3103	0.513823
$575$	−1.80075	−0.0750963
$576$	29.7684	1.24035
$577$	10.0915	0.420115	0.210058	−	0.977689i	$-0.432635\pi$
$577$	10.0915	0.420115	0.210058	+	0.977689i	$0.432635\pi$
$578$	36.6658	1.52510
$579$	4.91267	0.204164
$580$	−25.5409	−1.06053
$581$	1.08866	0.0451653
$582$	0.407612	0.0168961
$583$	8.44487	0.349751
$584$	6.67496	0.276212
$585$	−29.3067	−1.21168
$586$	47.0431	1.94333
$587$	1.89723	0.0783069	0.0391535	−	0.999233i	$-0.487534\pi$
$587$	1.89723	0.0783069	0.0391535	+	0.999233i	$0.487534\pi$
$588$	−15.8754	−0.654692
$589$	−4.64471	−0.191382
$590$	12.1878	0.501762
$591$	−7.26255	−0.298742
$592$	1.54803	0.0636238
$593$	8.17141	0.335560	0.167780	−	0.985824i	$-0.446340\pi$
$593$	8.17141	0.335560	0.167780	+	0.985824i	$0.446340\pi$
$594$	18.2433	0.748534
$595$	0.614741	0.0252019
$596$	−18.4703	−0.756575
$597$	−15.2739	−0.625118
$598$	−99.8804	−4.08441
$599$	20.5350	0.839039	0.419519	−	0.907746i	$-0.362199\pi$
$599$	20.5350	0.839039	0.419519	+	0.907746i	$0.362199\pi$
$600$	−0.337480	−0.0137776
$601$	36.6534	1.49512	0.747562	−	0.664193i	$-0.231224\pi$
$601$	36.6534	1.49512	0.747562	+	0.664193i	$0.231224\pi$
$602$	2.60255	0.106072
$603$	3.61362	0.147158
$604$	11.2350	0.457144
$605$	16.8787	0.686218
$606$	−0.463490	−0.0188280
$607$	17.4917	0.709967	0.354984	−	0.934873i	$-0.384486\pi$
$607$	17.4917	0.709967	0.354984	+	0.934873i	$0.384486\pi$
$608$	−11.3953	−0.462138
$609$	1.42405	0.0577053
$610$	55.2908	2.23866
$611$	47.4838	1.92099
$612$	4.02570	0.162729
$613$	−16.0044	−0.646412	−0.323206	−	0.946329i	$-0.604761\pi$
$613$	−16.0044	−0.646412	−0.323206	+	0.946329i	$0.604761\pi$
$614$	−2.62263	−0.105841
$615$	23.3805	0.942793
$616$	−1.60162	−0.0645312
$617$	19.3258	0.778028	0.389014	−	0.921232i	$-0.372816\pi$
$617$	19.3258	0.778028	0.389014	+	0.921232i	$0.372816\pi$
$618$	6.21221	0.249892
$619$	5.76292	0.231631	0.115816	−	0.993271i	$-0.463052\pi$
$619$	5.76292	0.231631	0.115816	+	0.993271i	$0.463052\pi$
$620$	−19.1438	−0.768835
$621$	35.8931	1.44034
$622$	66.5783	2.66955
$623$	7.95609	0.318754
$624$	6.95253	0.278324
$625$	−26.0448	−1.04179
$626$	−66.1026	−2.64199
$627$	−2.45848	−0.0981823
$628$	−26.9855	−1.07684
$629$	0.603781	0.0240743
$630$	−5.23536	−0.208582
$631$	−20.6591	−0.822425	−0.411212	−	0.911540i	$-0.634895\pi$
$631$	−20.6591	−0.822425	−0.411212	+	0.911540i	$0.634895\pi$
$632$	8.26213	0.328650
$633$	−10.4812	−0.416592
$634$	−48.8739	−1.94103
$635$	26.6697	1.05835
$636$	10.3726	0.411302
$637$	37.4009	1.48188
$638$	−16.3859	−0.648722
$639$	−3.63228	−0.143691
$640$	−31.3785	−1.24034
$641$	29.0229	1.14633	0.573167	−	0.819438i	$-0.305715\pi$
$641$	29.0229	1.14633	0.573167	+	0.819438i	$0.305715\pi$
$642$	17.4341	0.688069
$643$	24.9863	0.985365	0.492683	−	0.870209i	$-0.336016\pi$
$643$	24.9863	0.985365	0.492683	+	0.870209i	$0.336016\pi$
$644$	−10.4969	−0.413635
$645$	4.94291	0.194627
$646$	−2.10796	−0.0829367
$647$	42.0460	1.65300	0.826500	−	0.562937i	$-0.190329\pi$
$647$	42.0460	1.65300	0.826500	+	0.562937i	$0.190329\pi$
$648$	−6.50796	−0.255657
$649$	4.60000	0.180566
$650$	2.64849	0.103882
$651$	1.06737	0.0418337
$652$	2.85795	0.111926
$653$	−25.8959	−1.01339	−0.506693	−	0.862127i	$-0.669132\pi$
$653$	−25.8959	−1.01339	−0.506693	+	0.862127i	$0.669132\pi$
$654$	20.0052	0.782265
$655$	−26.6081	−1.03967
$656$	19.3992	0.757413
$657$	8.23510	0.321282
$658$	8.48251	0.330683
$659$	35.3809	1.37825	0.689123	−	0.724645i	$-0.257996\pi$
$659$	35.3809	1.37825	0.689123	+	0.724645i	$0.257996\pi$
$660$	−10.1330	−0.394426
$661$	24.8868	0.967984	0.483992	−	0.875072i	$-0.339186\pi$
$661$	24.8868	0.967984	0.483992	+	0.875072i	$0.339186\pi$
$662$	−69.0242	−2.68270
$663$	2.71170	0.105314
$664$	−4.61892	−0.179249
$665$	1.61276	0.0625402
$666$	−5.14202	−0.199249
$667$	−32.2386	−1.24828
$668$	31.8866	1.23373
$669$	−4.99029	−0.192936
$670$	−7.79894	−0.301299
$671$	20.8683	0.805611
$672$	2.61868	0.101018
$673$	16.8938	0.651209	0.325604	−	0.945506i	$-0.394432\pi$
$673$	16.8938	0.651209	0.325604	+	0.945506i	$0.394432\pi$
$674$	−10.6309	−0.409487
$675$	−0.951765	−0.0366335
$676$	49.2693	1.89497
$677$	45.5724	1.75149	0.875746	−	0.482773i	$-0.160370\pi$
$677$	45.5724	1.75149	0.875746	+	0.482773i	$0.160370\pi$
$678$	−0.406940	−0.0156284
$679$	−0.100921	−0.00387301
$680$	−2.60819	−0.100020
$681$	−2.76149	−0.105820
$682$	−12.2818	−0.470294
$683$	30.9548	1.18445	0.592226	−	0.805772i	$-0.298249\pi$
$683$	30.9548	1.18445	0.592226	+	0.805772i	$0.298249\pi$
$684$	10.5613	0.403822
$685$	10.6680	0.407602
$686$	13.5577	0.517637
$687$	−2.63365	−0.100480
$688$	4.10122	0.156358
$689$	−24.4369	−0.930971
$690$	−33.8878	−1.29009
$691$	−14.1380	−0.537836	−0.268918	−	0.963163i	$-0.586666\pi$
$691$	−14.1380	−0.537836	−0.268918	+	0.963163i	$0.586666\pi$
$692$	30.1246	1.14516
$693$	−1.97597	−0.0750609
$694$	21.5726	0.818884
$695$	−21.3190	−0.808677
$696$	−6.04188	−0.229017
$697$	7.56631	0.286594
$698$	26.0641	0.986541
$699$	7.01710	0.265411
$700$	0.278342	0.0105203
$701$	−24.7111	−0.933327	−0.466664	−	0.884435i	$-0.654544\pi$
$701$	−24.7111	−0.933327	−0.466664	+	0.884435i	$0.654544\pi$
$702$	−52.7907	−1.99246
$703$	1.58401	0.0597419
$704$	−24.2483	−0.913893
$705$	16.1105	0.606756
$706$	−32.9569	−1.24035
$707$	0.114757	0.00431587
$708$	5.65007	0.212343
$709$	13.2905	0.499133	0.249567	−	0.968358i	$-0.419712\pi$
$709$	13.2905	0.499133	0.249567	+	0.968358i	$0.419712\pi$
$710$	7.83921	0.294200
$711$	10.1932	0.382276
$712$	−33.7557	−1.26505
$713$	−24.1640	−0.904948
$714$	0.484419	0.0181289
$715$	23.8723	0.892773
$716$	−26.5372	−0.991740
$717$	15.2746	0.570440
$718$	−46.6580	−1.74126
$719$	16.4692	0.614199	0.307099	−	0.951677i	$-0.400642\pi$
$719$	16.4692	0.614199	0.307099	+	0.951677i	$0.400642\pi$
$720$	−8.25014	−0.307464
$721$	−1.53809	−0.0572816
$722$	36.3472	1.35270
$723$	−19.9864	−0.743303
$724$	25.7500	0.956992
$725$	0.854859	0.0317487
$726$	13.3005	0.493628
$727$	−35.5789	−1.31955	−0.659774	−	0.751464i	$-0.729348\pi$
$727$	−35.5789	−1.31955	−0.659774	+	0.751464i	$0.729348\pi$
$728$	4.63461	0.171770
$729$	2.64283	0.0978825
$730$	−17.7730	−0.657810
$731$	1.59960	0.0591635
$732$	25.6320	0.947387
$733$	−19.5617	−0.722526	−0.361263	−	0.932464i	$-0.617654\pi$
$733$	−19.5617	−0.722526	−0.361263	+	0.932464i	$0.617654\pi$
$734$	66.5641	2.45693
$735$	12.6895	0.468060
$736$	−59.2835	−2.18522
$737$	−2.94354	−0.108427
$738$	−64.4374	−2.37197
$739$	−9.25261	−0.340363	−0.170181	−	0.985413i	$-0.554435\pi$
$739$	−9.25261	−0.340363	−0.170181	+	0.985413i	$0.554435\pi$
$740$	6.52872	0.240000
$741$	7.11410	0.261343
$742$	−4.36541	−0.160259
$743$	−34.7417	−1.27455	−0.637275	−	0.770636i	$-0.719938\pi$
$743$	−34.7417	−1.27455	−0.637275	+	0.770636i	$0.719938\pi$
$744$	−4.52860	−0.166027
$745$	14.7637	0.540899
$746$	42.6072	1.55996
$747$	−5.69850	−0.208497
$748$	−3.27920	−0.119899
$749$	−4.31655	−0.157723
$750$	−19.6625	−0.717973
$751$	8.34143	0.304383	0.152192	−	0.988351i	$-0.451367\pi$
$751$	8.34143	0.304383	0.152192	+	0.988351i	$0.451367\pi$
$752$	13.3672	0.487450
$753$	14.5033	0.528528
$754$	47.4157	1.72678
$755$	−8.98030	−0.326827
$756$	−5.54802	−0.201779
$757$	−11.0139	−0.400305	−0.200153	−	0.979765i	$-0.564144\pi$
$757$	−11.0139	−0.400305	−0.200153	+	0.979765i	$0.564144\pi$
$758$	28.9487	1.05146
$759$	−12.7902	−0.464254
$760$	−6.84254	−0.248205
$761$	27.4780	0.996079	0.498039	−	0.867154i	$-0.334054\pi$
$761$	27.4780	0.996079	0.498039	+	0.867154i	$0.334054\pi$
$762$	21.0158	0.761323
$763$	−4.95313	−0.179315
$764$	70.4212	2.54775
$765$	−3.21781	−0.116340
$766$	15.1856	0.548678
$767$	−13.3110	−0.480632
$768$	−3.88369	−0.140141
$769$	32.8463	1.18447	0.592233	−	0.805767i	$-0.298246\pi$
$769$	32.8463	1.18447	0.592233	+	0.805767i	$0.298246\pi$
$770$	4.26455	0.153684
$771$	−10.9666	−0.394951
$772$	17.1908	0.618710
$773$	29.7408	1.06970	0.534851	−	0.844947i	$-0.320368\pi$
$773$	29.7408	1.06970	0.534851	+	0.844947i	$0.320368\pi$
$774$	−13.6228	−0.489662
$775$	0.640747	0.0230163
$776$	0.428185	0.0153709
$777$	−0.364012	−0.0130588
$778$	63.6281	2.28118
$779$	19.8500	0.711201
$780$	29.3218	1.04989
$781$	2.95874	0.105872
$782$	−10.9666	−0.392166
$783$	−17.0394	−0.608937
$784$	10.5287	0.376026
$785$	21.5700	0.769866
$786$	−20.9673	−0.747880
$787$	19.8225	0.706596	0.353298	−	0.935511i	$-0.385060\pi$
$787$	19.8225	0.706596	0.353298	+	0.935511i	$0.385060\pi$
$788$	−25.4137	−0.905325
$789$	8.66780	0.308582
$790$	−21.9991	−0.782693
$791$	0.100755	0.00358244
$792$	8.38355	0.297896
$793$	−60.3865	−2.14439
$794$	−61.0828	−2.16775
$795$	−8.29104	−0.294053
$796$	−53.4475	−1.89440
$797$	−17.5479	−0.621580	−0.310790	−	0.950479i	$-0.600594\pi$
$797$	−17.5479	−0.621580	−0.310790	+	0.950479i	$0.600594\pi$
$798$	1.27086	0.0449881
$799$	5.21361	0.184444
$800$	1.57200	0.0555786
$801$	−41.6455	−1.47147
$802$	−21.9095	−0.773652
$803$	−6.70804	−0.236722
$804$	−3.61548	−0.127508
$805$	8.39035	0.295721
$806$	35.5397	1.25183
$807$	−8.12355	−0.285962
$808$	−0.486884	−0.0171285
$809$	2.33933	0.0822465	0.0411232	−	0.999154i	$-0.486906\pi$
$809$	2.33933	0.0822465	0.0411232	+	0.999154i	$0.486906\pi$
$810$	17.3284	0.608857
$811$	17.1523	0.602299	0.301149	−	0.953577i	$-0.402630\pi$
$811$	17.1523	0.602299	0.301149	+	0.953577i	$0.402630\pi$
$812$	4.98313	0.174874
$813$	−4.54379	−0.159358
$814$	4.18852	0.146807
$815$	−2.28441	−0.0800193
$816$	0.763371	0.0267233
$817$	4.19653	0.146818
$818$	0.879835	0.0307627
$819$	5.71786	0.199798
$820$	81.8148	2.85710
$821$	16.7759	0.585483	0.292742	−	0.956192i	$-0.405432\pi$
$821$	16.7759	0.585483	0.292742	+	0.956192i	$0.405432\pi$
$822$	8.40642	0.293207
$823$	−20.5994	−0.718051	−0.359025	−	0.933328i	$-0.616891\pi$
$823$	−20.5994	−0.718051	−0.359025	+	0.933328i	$0.616891\pi$
$824$	6.52575	0.227335
$825$	0.339153	0.0118078
$826$	−2.37788	−0.0827370
$827$	22.5252	0.783278	0.391639	−	0.920119i	$-0.371908\pi$
$827$	22.5252	0.783278	0.391639	+	0.920119i	$0.371908\pi$
$828$	54.9450	1.90947
$829$	−18.5801	−0.645314	−0.322657	−	0.946516i	$-0.604576\pi$
$829$	−18.5801	−0.645314	−0.322657	+	0.946516i	$0.604576\pi$
$830$	12.2985	0.426888
$831$	19.4781	0.675688
$832$	70.1673	2.43261
$833$	4.10653	0.142283
$834$	−16.7995	−0.581719
$835$	−25.4875	−0.882033
$836$	−8.60290	−0.297538
$837$	−12.7716	−0.441451
$838$	−45.7760	−1.58131
$839$	−29.1431	−1.00613	−0.503066	−	0.864248i	$-0.667795\pi$
$839$	−29.1431	−1.00613	−0.503066	+	0.864248i	$0.667795\pi$
$840$	1.57245	0.0542545
$841$	−13.6955	−0.472260
$842$	−82.7864	−2.85301
$843$	10.5432	0.363127
$844$	−36.6768	−1.26247
$845$	−39.3819	−1.35478
$846$	−44.4010	−1.52654
$847$	−3.29310	−0.113152
$848$	−6.87922	−0.236234
$849$	−7.80350	−0.267815
$850$	0.290798	0.00997429
$851$	8.24076	0.282489
$852$	3.63415	0.124504
$853$	−38.9680	−1.33424	−0.667119	−	0.744951i	$-0.732473\pi$
$853$	−38.9680	−1.33424	−0.667119	+	0.744951i	$0.732473\pi$
$854$	−10.7874	−0.369139
$855$	−8.44185	−0.288705
$856$	18.3140	0.625961
$857$	−11.8808	−0.405840	−0.202920	−	0.979195i	$-0.565043\pi$
$857$	−11.8808	−0.405840	−0.202920	+	0.979195i	$0.565043\pi$
$858$	18.8115	0.642213
$859$	16.7466	0.571385	0.285693	−	0.958321i	$-0.407776\pi$
$859$	16.7466	0.571385	0.285693	+	0.958321i	$0.407776\pi$
$860$	17.2966	0.589809
$861$	−4.56162	−0.155460
$862$	−27.7137	−0.943934
$863$	58.3383	1.98586	0.992930	−	0.118700i	$-0.0378726\pi$
$863$	58.3383	1.98586	0.992930	+	0.118700i	$0.0378726\pi$
$864$	−31.3337	−1.06599
$865$	−24.0791	−0.818714
$866$	66.1060	2.24637
$867$	−13.5866	−0.461425
$868$	3.73503	0.126775
$869$	−8.30307	−0.281662
$870$	16.0874	0.545413
$871$	8.51770	0.288611
$872$	21.0149	0.711654
$873$	0.528265	0.0178791
$874$	−28.7707	−0.973184
$875$	4.86828	0.164578
$876$	−8.23933	−0.278381
$877$	29.5691	0.998479	0.499240	−	0.866464i	$-0.333613\pi$
$877$	29.5691	0.998479	0.499240	+	0.866464i	$0.333613\pi$
$878$	30.9756	1.04538
$879$	−17.4319	−0.587965
$880$	6.72028	0.226541
$881$	12.6450	0.426020	0.213010	−	0.977050i	$-0.431673\pi$
$881$	12.6450	0.426020	0.213010	+	0.977050i	$0.431673\pi$
$882$	−34.9727	−1.17759
$883$	−53.1536	−1.78876	−0.894381	−	0.447306i	$-0.852384\pi$
$883$	−53.1536	−1.78876	−0.894381	+	0.447306i	$0.852384\pi$
$884$	9.48900	0.319150
$885$	−4.51620	−0.151811
$886$	−54.1293	−1.81851
$887$	−10.2077	−0.342742	−0.171371	−	0.985207i	$-0.554820\pi$
$887$	−10.2077	−0.342742	−0.171371	+	0.985207i	$0.554820\pi$
$888$	1.54441	0.0518270
$889$	−5.20336	−0.174515
$890$	89.8795	3.01277
$891$	6.54021	0.219105
$892$	−17.4624	−0.584684
$893$	13.6778	0.457710
$894$	11.6338	0.389094
$895$	21.2116	0.709026
$896$	6.12206	0.204524
$897$	37.0109	1.23576
$898$	4.23445	0.141305
$899$	11.4712	0.382587
$900$	−1.45696	−0.0485653
$901$	−2.68311	−0.0893874
$902$	52.4885	1.74768
$903$	−0.964380	−0.0320926
$904$	−0.427479	−0.0142177
$905$	−20.5824	−0.684184
$906$	−7.07652	−0.235102
$907$	−16.3856	−0.544074	−0.272037	−	0.962287i	$-0.587697\pi$
$907$	−16.3856	−0.544074	−0.272037	+	0.962287i	$0.587697\pi$
$908$	−9.66320	−0.320685
$909$	−0.600683	−0.0199234
$910$	−12.3403	−0.409077
$911$	−10.5940	−0.350994	−0.175497	−	0.984480i	$-0.556153\pi$
$911$	−10.5940	−0.350994	−0.175497	+	0.984480i	$0.556153\pi$
$912$	2.00269	0.0663156
$913$	4.64181	0.153621
$914$	68.6041	2.26922
$915$	−20.4881	−0.677317
$916$	−9.21588	−0.304501
$917$	5.19135	0.171433
$918$	−5.79629	−0.191306
$919$	14.8831	0.490948	0.245474	−	0.969403i	$-0.421056\pi$
$919$	14.8831	0.490948	0.245474	+	0.969403i	$0.421056\pi$
$920$	−35.5981	−1.17364
$921$	0.971823	0.0320227
$922$	47.1576	1.55305
$923$	−8.56168	−0.281811
$924$	1.97698	0.0650380
$925$	−0.218517	−0.00718480
$926$	65.3811	2.14856
$927$	8.05102	0.264430
$928$	28.1434	0.923851
$929$	−49.2484	−1.61579	−0.807893	−	0.589329i	$-0.799392\pi$
$929$	−49.2484	−1.61579	−0.807893	+	0.589329i	$0.799392\pi$
$930$	12.0581	0.395399
$931$	10.7734	0.353084
$932$	24.5548	0.804318
$933$	−24.6708	−0.807684
$934$	−41.9294	−1.37197
$935$	2.62112	0.0857198
$936$	−24.2594	−0.792945
$937$	12.1158	0.395805	0.197903	−	0.980222i	$-0.436587\pi$
$937$	12.1158	0.395805	0.197903	+	0.980222i	$0.436587\pi$
$938$	1.52160	0.0496821
$939$	24.4945	0.799347
$940$	56.3750	1.83875
$941$	43.1577	1.40690	0.703450	−	0.710744i	$-0.251642\pi$
$941$	43.1577	1.40690	0.703450	+	0.710744i	$0.251642\pi$
$942$	16.9973	0.553800
$943$	103.269	3.36291
$944$	−3.74718	−0.121960
$945$	4.43463	0.144258
$946$	11.0967	0.360784
$947$	33.4199	1.08600	0.543000	−	0.839733i	$-0.317288\pi$
$947$	33.4199	1.08600	0.543000	+	0.839733i	$0.317288\pi$
$948$	−10.1985	−0.331231
$949$	19.4110	0.630109
$950$	0.762902	0.0247518
$951$	18.1104	0.587268
$952$	0.508869	0.0164925
$953$	18.5849	0.602024	0.301012	−	0.953620i	$-0.402676\pi$
$953$	18.5849	0.602024	0.301012	+	0.953620i	$0.402676\pi$
$954$	22.8504	0.739807
$955$	−56.2889	−1.82147
$956$	53.4500	1.72870
$957$	6.07182	0.196274
$958$	−20.0994	−0.649382
$959$	−2.08136	−0.0672107
$960$	23.8066	0.768355
$961$	−22.4019	−0.722642
$962$	−12.1203	−0.390774
$963$	22.5946	0.728101
$964$	−69.9380	−2.25255
$965$	−13.7409	−0.442335
$966$	6.61163	0.212726
$967$	−31.3047	−1.00669	−0.503345	−	0.864086i	$-0.667897\pi$
$967$	−31.3047	−1.00669	−0.503345	+	0.864086i	$0.667897\pi$
$968$	13.9718	0.449071
$969$	0.781111	0.0250929
$970$	−1.14010	−0.0366065
$971$	−4.31861	−0.138591	−0.0692954	−	0.997596i	$-0.522075\pi$
$971$	−4.31861	−0.138591	−0.0692954	+	0.997596i	$0.522075\pi$
$972$	45.3771	1.45547
$973$	4.15943	0.133345
$974$	−78.7006	−2.52173
$975$	−0.981405	−0.0314301
$976$	−16.9994	−0.544137
$977$	33.7334	1.07923	0.539614	−	0.841913i	$-0.318570\pi$
$977$	33.7334	1.07923	0.539614	+	0.841913i	$0.318570\pi$
$978$	−1.80012	−0.0575616
$979$	33.9230	1.08418
$980$	44.4041	1.41844
$981$	25.9267	0.827777
$982$	−34.2041	−1.09150
$983$	−13.6886	−0.436598	−0.218299	−	0.975882i	$-0.570051\pi$
$983$	−13.6886	−0.436598	−0.218299	+	0.975882i	$0.570051\pi$
$984$	19.3538	0.616978
$985$	20.3136	0.647245
$986$	5.20613	0.165797
$987$	−3.14322	−0.100050
$988$	24.8942	0.791990
$989$	21.8323	0.694227
$990$	−22.3224	−0.709453
$991$	12.3553	0.392480	0.196240	−	0.980556i	$-0.437127\pi$
$991$	12.3553	0.392480	0.196240	+	0.980556i	$0.437127\pi$
$992$	21.0944	0.669749
$993$	25.5771	0.811664
$994$	−1.52946	−0.0485115
$995$	42.7215	1.35436
$996$	5.70143	0.180657
$997$	40.3275	1.27718	0.638592	−	0.769546i	$-0.279517\pi$
$997$	40.3275	1.27718	0.638592	+	0.769546i	$0.279517\pi$
$998$	−86.1759	−2.72785
$999$	4.35556	0.137804

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6031.2.a.d.1.19	✓	133

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6031.2.a.d.1.19	✓	133	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6031 = 37 \cdot 163 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.20408 q^{2} +0.816725 q^{3} +2.85795 q^{4} -2.28441 q^{5} -1.80012 q^{6} +0.445697 q^{7} -1.89098 q^{8} -2.33296 q^{9} +O(q^{10})\)	\(q-2.20408 q^{2} +0.816725 q^{3} +2.85795 q^{4} -2.28441 q^{5} -1.80012 q^{6} +0.445697 q^{7} -1.89098 q^{8} -2.33296 q^{9} +5.03501 q^{10} +1.90035 q^{11} +2.33416 q^{12} -5.49904 q^{13} -0.982349 q^{14} -1.86573 q^{15} -1.54803 q^{16} -0.603781 q^{17} +5.14202 q^{18} -1.58401 q^{19} -6.52872 q^{20} +0.364012 q^{21} -4.18852 q^{22} -8.24076 q^{23} -1.54441 q^{24} +0.218517 q^{25} +12.1203 q^{26} -4.35556 q^{27} +1.27378 q^{28} +3.91209 q^{29} +4.11222 q^{30} +2.93225 q^{31} +7.19394 q^{32} +1.55206 q^{33} +1.33078 q^{34} -1.01815 q^{35} -6.66748 q^{36} -1.00000 q^{37} +3.49127 q^{38} -4.49120 q^{39} +4.31977 q^{40} -12.5315 q^{41} -0.802309 q^{42} -2.64931 q^{43} +5.43110 q^{44} +5.32943 q^{45} +18.1632 q^{46} -8.63493 q^{47} -1.26432 q^{48} -6.80135 q^{49} -0.481628 q^{50} -0.493123 q^{51} -15.7160 q^{52} +4.44385 q^{53} +9.59999 q^{54} -4.34118 q^{55} -0.842803 q^{56} -1.29370 q^{57} -8.62254 q^{58} +2.42060 q^{59} -5.33217 q^{60} +10.9813 q^{61} -6.46290 q^{62} -1.03979 q^{63} -12.7599 q^{64} +12.5620 q^{65} -3.42087 q^{66} -1.54894 q^{67} -1.72557 q^{68} -6.73043 q^{69} +2.24408 q^{70} +1.55694 q^{71} +4.41158 q^{72} -3.52989 q^{73} +2.20408 q^{74} +0.178469 q^{75} -4.52701 q^{76} +0.846980 q^{77} +9.89895 q^{78} -4.36923 q^{79} +3.53634 q^{80} +3.44158 q^{81} +27.6204 q^{82} +2.44261 q^{83} +1.04033 q^{84} +1.37928 q^{85} +5.83928 q^{86} +3.19510 q^{87} -3.59352 q^{88} +17.8509 q^{89} -11.7465 q^{90} -2.45090 q^{91} -23.5516 q^{92} +2.39484 q^{93} +19.0320 q^{94} +3.61852 q^{95} +5.87547 q^{96} -0.226435 q^{97} +14.9907 q^{98} -4.43344 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 133 q + 14 q^{2} + 8 q^{3} + 142 q^{4} + 34 q^{5} + 20 q^{6} + 8 q^{7} + 42 q^{8} + 177 q^{9}+O(q^{10}) \) 133 * q + 14 * q^2 + 8 * q^3 + 142 * q^4 + 34 * q^5 + 20 * q^6 + 8 * q^7 + 42 * q^8 + 177 * q^9	\( 133 q + 14 q^{2} + 8 q^{3} + 142 q^{4} + 34 q^{5} + 20 q^{6} + 8 q^{7} + 42 q^{8} + 177 q^{9} + 9 q^{10} + 23 q^{11} + 24 q^{12} + 23 q^{13} + 31 q^{14} + 9 q^{15} + 168 q^{16} + 98 q^{17} + 38 q^{18} + 29 q^{19} + 83 q^{20} + 26 q^{21} + 2 q^{22} + 34 q^{23} + 75 q^{24} + 177 q^{25} + 67 q^{26} + 32 q^{27} + 32 q^{28} + 91 q^{29} + 12 q^{30} + 24 q^{31} + 88 q^{32} + 27 q^{33} + 23 q^{34} + 66 q^{35} + 232 q^{36} - 133 q^{37} + 26 q^{38} + 28 q^{39} + 41 q^{40} + 132 q^{41} + 13 q^{42} + 11 q^{43} + 65 q^{44} + 107 q^{45} + 20 q^{46} + 10 q^{47} + 27 q^{48} + 229 q^{49} + 78 q^{50} + 19 q^{51} + 71 q^{52} + 7 q^{53} + 43 q^{54} + 41 q^{55} + 67 q^{56} + 45 q^{57} + 25 q^{58} + 97 q^{59} - 42 q^{60} + 65 q^{61} + 24 q^{62} + 39 q^{63} + 200 q^{64} + 60 q^{65} + 35 q^{66} + 25 q^{67} + 227 q^{68} + 120 q^{69} + 37 q^{70} + 26 q^{71} + 93 q^{72} + 55 q^{73} - 14 q^{74} + 5 q^{75} + 34 q^{76} + 21 q^{77} - 2 q^{78} + 50 q^{79} + 162 q^{80} + 341 q^{81} + 66 q^{82} + 30 q^{83} - 89 q^{84} + 30 q^{85} - 12 q^{86} + 80 q^{87} - 85 q^{88} + 225 q^{89} - 86 q^{90} + q^{91} + 82 q^{92} + 42 q^{93} - 17 q^{94} + 70 q^{95} + 55 q^{96} + 12 q^{97} + 90 q^{98} + 17 q^{99}+O(q^{100}) \) 133 * q + 14 * q^2 + 8 * q^3 + 142 * q^4 + 34 * q^5 + 20 * q^6 + 8 * q^7 + 42 * q^8 + 177 * q^9 + 9 * q^10 + 23 * q^11 + 24 * q^12 + 23 * q^13 + 31 * q^14 + 9 * q^15 + 168 * q^16 + 98 * q^17 + 38 * q^18 + 29 * q^19 + 83 * q^20 + 26 * q^21 + 2 * q^22 + 34 * q^23 + 75 * q^24 + 177 * q^25 + 67 * q^26 + 32 * q^27 + 32 * q^28 + 91 * q^29 + 12 * q^30 + 24 * q^31 + 88 * q^32 + 27 * q^33 + 23 * q^34 + 66 * q^35 + 232 * q^36 - 133 * q^37 + 26 * q^38 + 28 * q^39 + 41 * q^40 + 132 * q^41 + 13 * q^42 + 11 * q^43 + 65 * q^44 + 107 * q^45 + 20 * q^46 + 10 * q^47 + 27 * q^48 + 229 * q^49 + 78 * q^50 + 19 * q^51 + 71 * q^52 + 7 * q^53 + 43 * q^54 + 41 * q^55 + 67 * q^56 + 45 * q^57 + 25 * q^58 + 97 * q^59 - 42 * q^60 + 65 * q^61 + 24 * q^62 + 39 * q^63 + 200 * q^64 + 60 * q^65 + 35 * q^66 + 25 * q^67 + 227 * q^68 + 120 * q^69 + 37 * q^70 + 26 * q^71 + 93 * q^72 + 55 * q^73 - 14 * q^74 + 5 * q^75 + 34 * q^76 + 21 * q^77 - 2 * q^78 + 50 * q^79 + 162 * q^80 + 341 * q^81 + 66 * q^82 + 30 * q^83 - 89 * q^84 + 30 * q^85 - 12 * q^86 + 80 * q^87 - 85 * q^88 + 225 * q^89 - 86 * q^90 + q^91 + 82 * q^92 + 42 * q^93 - 17 * q^94 + 70 * q^95 + 55 * q^96 + 12 * q^97 + 90 * q^98 + 17 * q^99

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