LMFDB - Embedded newform 151.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [151,2,Mod(1,151)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(151, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("151.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 151 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	151.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:	$1.20574107052$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 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			1.1
Root			$1.80194$ of defining polynomial
Character	$\chi$	$=$	151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.24698 q^{2} +1.24698 q^{3} +3.04892 q^{4} -3.80194 q^{5} -2.80194 q^{6} -1.00000 q^{7} -2.35690 q^{8} -1.44504 q^{9} +O(q^{10})$	\(q-2.24698 q^{2} +1.24698 q^{3} +3.04892 q^{4} -3.80194 q^{5} -2.80194 q^{6} -1.00000 q^{7} -2.35690 q^{8} -1.44504 q^{9} +8.54288 q^{10} -1.89008 q^{11} +3.80194 q^{12} +0.911854 q^{13} +2.24698 q^{14} -4.74094 q^{15} -0.801938 q^{16} -3.91185 q^{17} +3.24698 q^{18} -6.76271 q^{19} -11.5918 q^{20} -1.24698 q^{21} +4.24698 q^{22} -0.335126 q^{23} -2.93900 q^{24} +9.45473 q^{25} -2.04892 q^{26} -5.54288 q^{27} -3.04892 q^{28} +7.67994 q^{29} +10.6528 q^{30} -1.46681 q^{31} +6.51573 q^{32} -2.35690 q^{33} +8.78986 q^{34} +3.80194 q^{35} -4.40581 q^{36} +3.08815 q^{37} +15.1957 q^{38} +1.13706 q^{39} +8.96077 q^{40} -10.3840 q^{41} +2.80194 q^{42} +9.51573 q^{43} -5.76271 q^{44} +5.49396 q^{45} +0.753020 q^{46} +7.76809 q^{47} -1.00000 q^{48} -6.00000 q^{49} -21.2446 q^{50} -4.87800 q^{51} +2.78017 q^{52} +4.89977 q^{53} +12.4547 q^{54} +7.18598 q^{55} +2.35690 q^{56} -8.43296 q^{57} -17.2567 q^{58} +8.36658 q^{59} -14.4547 q^{60} -8.23490 q^{61} +3.29590 q^{62} +1.44504 q^{63} -13.0368 q^{64} -3.46681 q^{65} +5.29590 q^{66} -13.6625 q^{67} -11.9269 q^{68} -0.417895 q^{69} -8.54288 q^{70} -9.96615 q^{71} +3.40581 q^{72} +8.70171 q^{73} -6.93900 q^{74} +11.7899 q^{75} -20.6189 q^{76} +1.89008 q^{77} -2.55496 q^{78} +9.50365 q^{79} +3.04892 q^{80} -2.57673 q^{81} +23.3327 q^{82} -3.71379 q^{83} -3.80194 q^{84} +14.8726 q^{85} -21.3817 q^{86} +9.57673 q^{87} +4.45473 q^{88} -12.0000 q^{89} -12.3448 q^{90} -0.911854 q^{91} -1.02177 q^{92} -1.82908 q^{93} -17.4547 q^{94} +25.7114 q^{95} +8.12498 q^{96} +4.07069 q^{97} +13.4819 q^{98} +2.73125 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 2 q^{2} - q^{3} - 7 q^{5} - 4 q^{6} - 3 q^{7} - 3 q^{8} - 4 q^{9}+O(q^{10}) $ 3 * q - 2 * q^2 - q^3 - 7 * q^5 - 4 * q^6 - 3 * q^7 - 3 * q^8 - 4 * q^9	$ 3 q - 2 q^{2} - q^{3} - 7 q^{5} - 4 q^{6} - 3 q^{7} - 3 q^{8} - 4 q^{9} + 7 q^{10} - 5 q^{11} + 7 q^{12} - q^{13} + 2 q^{14} + 2 q^{16} - 8 q^{17} + 5 q^{18} - 3 q^{19} - 7 q^{20} + q^{21} + 8 q^{22} + q^{24} + 6 q^{25} + 3 q^{26} + 2 q^{27} - q^{29} + 14 q^{30} - q^{31} + 7 q^{32} - 3 q^{33} + 3 q^{34} + 7 q^{35} + 13 q^{37} + 9 q^{38} - 2 q^{39} + 14 q^{40} - 21 q^{41} + 4 q^{42} + 16 q^{43} + 7 q^{45} + 7 q^{46} + 3 q^{47} - 3 q^{48} - 18 q^{49} - 18 q^{50} + 5 q^{51} + 7 q^{52} - 8 q^{53} + 15 q^{54} + 7 q^{55} + 3 q^{56} - 6 q^{57} - 25 q^{58} - q^{59} - 21 q^{60} - q^{61} - 4 q^{62} + 4 q^{63} - 11 q^{64} - 7 q^{65} + 2 q^{66} - q^{67} - 7 q^{68} - 7 q^{69} - 7 q^{70} - 14 q^{71} - 3 q^{72} - q^{73} - 11 q^{74} + 12 q^{75} - 28 q^{76} + 5 q^{77} - 8 q^{78} - 3 q^{79} - 5 q^{81} + 28 q^{82} - 3 q^{83} - 7 q^{84} + 28 q^{85} - 13 q^{86} + 26 q^{87} - 9 q^{88} - 36 q^{89} - 14 q^{90} + q^{91} + 5 q^{93} - 30 q^{94} + 28 q^{95} + 12 q^{98} + 16 q^{99}+O(q^{100}) $ 3 * q - 2 * q^2 - q^3 - 7 * q^5 - 4 * q^6 - 3 * q^7 - 3 * q^8 - 4 * q^9 + 7 * q^10 - 5 * q^11 + 7 * q^12 - q^13 + 2 * q^14 + 2 * q^16 - 8 * q^17 + 5 * q^18 - 3 * q^19 - 7 * q^20 + q^21 + 8 * q^22 + q^24 + 6 * q^25 + 3 * q^26 + 2 * q^27 - q^29 + 14 * q^30 - q^31 + 7 * q^32 - 3 * q^33 + 3 * q^34 + 7 * q^35 + 13 * q^37 + 9 * q^38 - 2 * q^39 + 14 * q^40 - 21 * q^41 + 4 * q^42 + 16 * q^43 + 7 * q^45 + 7 * q^46 + 3 * q^47 - 3 * q^48 - 18 * q^49 - 18 * q^50 + 5 * q^51 + 7 * q^52 - 8 * q^53 + 15 * q^54 + 7 * q^55 + 3 * q^56 - 6 * q^57 - 25 * q^58 - q^59 - 21 * q^60 - q^61 - 4 * q^62 + 4 * q^63 - 11 * q^64 - 7 * q^65 + 2 * q^66 - q^67 - 7 * q^68 - 7 * q^69 - 7 * q^70 - 14 * q^71 - 3 * q^72 - q^73 - 11 * q^74 + 12 * q^75 - 28 * q^76 + 5 * q^77 - 8 * q^78 - 3 * q^79 - 5 * q^81 + 28 * q^82 - 3 * q^83 - 7 * q^84 + 28 * q^85 - 13 * q^86 + 26 * q^87 - 9 * q^88 - 36 * q^89 - 14 * q^90 + q^91 + 5 * q^93 - 30 * q^94 + 28 * q^95 + 12 * q^98 + 16 * 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 $

$2$	−2.24698	−1.58885	−0.794427	−	0.607359i	$-0.792229\pi$
$2$	−2.24698	−1.58885	−0.794427	+	0.607359i	$0.792229\pi$
$3$	1.24698	0.719944	0.359972	−	0.932963i	$-0.382786\pi$
$3$	1.24698	0.719944	0.359972	+	0.932963i	$0.382786\pi$
$4$	3.04892	1.52446
$5$	−3.80194	−1.70028	−0.850139	−	0.526558i	$-0.823482\pi$
$5$	−3.80194	−1.70028	−0.850139	+	0.526558i	$0.823482\pi$
$6$	−2.80194	−1.14389
$7$	−1.00000	−0.377964	−0.188982	−	0.981981i	$-0.560519\pi$
$7$	−1.00000	−0.377964	−0.188982	+	0.981981i	$0.560519\pi$
$8$	−2.35690	−0.833289
$9$	−1.44504	−0.481681
$10$	8.54288	2.70149
$11$	−1.89008	−0.569882	−0.284941	−	0.958545i	$-0.591974\pi$
$11$	−1.89008	−0.569882	−0.284941	+	0.958545i	$0.591974\pi$
$12$	3.80194	1.09752
$13$	0.911854	0.252903	0.126451	−	0.991973i	$-0.459641\pi$
$13$	0.911854	0.252903	0.126451	+	0.991973i	$0.459641\pi$
$14$	2.24698	0.600531
$15$	−4.74094	−1.22411
$16$	−0.801938	−0.200484
$17$	−3.91185	−0.948764	−0.474382	−	0.880319i	$-0.657328\pi$
$17$	−3.91185	−0.948764	−0.474382	+	0.880319i	$0.657328\pi$
$18$	3.24698	0.765320
$19$	−6.76271	−1.55147	−0.775736	−	0.631058i	$-0.782621\pi$
$19$	−6.76271	−1.55147	−0.775736	+	0.631058i	$0.782621\pi$
$20$	−11.5918	−2.59200
$21$	−1.24698	−0.272113
$22$	4.24698	0.905459
$23$	−0.335126	−0.0698785	−0.0349393	−	0.999389i	$-0.511124\pi$
$23$	−0.335126	−0.0698785	−0.0349393	+	0.999389i	$0.511124\pi$
$24$	−2.93900	−0.599921
$25$	9.45473	1.89095
$26$	−2.04892	−0.401826
$27$	−5.54288	−1.06673
$28$	−3.04892	−0.576191
$29$	7.67994	1.42613	0.713065	−	0.701098i	$-0.247307\pi$
$29$	7.67994	1.42613	0.713065	+	0.701098i	$0.247307\pi$
$30$	10.6528	1.94492
$31$	−1.46681	−0.263447	−0.131724	−	0.991286i	$-0.542051\pi$
$31$	−1.46681	−0.263447	−0.131724	+	0.991286i	$0.542051\pi$
$32$	6.51573	1.15183
$33$	−2.35690	−0.410283
$34$	8.78986	1.50745
$35$	3.80194	0.642645
$36$	−4.40581	−0.734302
$37$	3.08815	0.507688	0.253844	−	0.967245i	$-0.418305\pi$
$37$	3.08815	0.507688	0.253844	+	0.967245i	$0.418305\pi$
$38$	15.1957	2.46506
$39$	1.13706	0.182076
$40$	8.96077	1.41682
$41$	−10.3840	−1.62172	−0.810858	−	0.585244i	$-0.800999\pi$
$41$	−10.3840	−1.62172	−0.810858	+	0.585244i	$0.800999\pi$
$42$	2.80194	0.432348
$43$	9.51573	1.45114	0.725568	−	0.688151i	$-0.241577\pi$
$43$	9.51573	1.45114	0.725568	+	0.688151i	$0.241577\pi$
$44$	−5.76271	−0.868761
$45$	5.49396	0.818991
$46$	0.753020	0.111027
$47$	7.76809	1.13309	0.566546	−	0.824030i	$-0.308279\pi$
$47$	7.76809	1.13309	0.566546	+	0.824030i	$0.308279\pi$
$48$	−1.00000	−0.144338
$49$	−6.00000	−0.857143
$50$	−21.2446	−3.00444
$51$	−4.87800	−0.683057
$52$	2.78017	0.385540
$53$	4.89977	0.673036	0.336518	−	0.941677i	$-0.390751\pi$
$53$	4.89977	0.673036	0.336518	+	0.941677i	$0.390751\pi$
$54$	12.4547	1.69487
$55$	7.18598	0.968957
$56$	2.35690	0.314953
$57$	−8.43296	−1.11697
$58$	−17.2567	−2.26591
$59$	8.36658	1.08924	0.544618	−	0.838684i	$-0.316675\pi$
$59$	8.36658	1.08924	0.544618	+	0.838684i	$0.316675\pi$
$60$	−14.4547	−1.86610
$61$	−8.23490	−1.05437	−0.527185	−	0.849750i	$-0.676753\pi$
$61$	−8.23490	−1.05437	−0.527185	+	0.849750i	$0.676753\pi$
$62$	3.29590	0.418579
$63$	1.44504	0.182058
$64$	−13.0368	−1.62960
$65$	−3.46681	−0.430005
$66$	5.29590	0.651880
$67$	−13.6625	−1.66914	−0.834569	−	0.550904i	$-0.814283\pi$
$67$	−13.6625	−1.66914	−0.834569	+	0.550904i	$0.814283\pi$
$68$	−11.9269	−1.44635
$69$	−0.417895	−0.0503086
$70$	−8.54288	−1.02107
$71$	−9.96615	−1.18276	−0.591382	−	0.806391i	$-0.701417\pi$
$71$	−9.96615	−1.18276	−0.591382	+	0.806391i	$0.701417\pi$
$72$	3.40581	0.401379
$73$	8.70171	1.01846	0.509229	−	0.860631i	$-0.329931\pi$
$73$	8.70171	1.01846	0.509229	+	0.860631i	$0.329931\pi$
$74$	−6.93900	−0.806642
$75$	11.7899	1.36138
$76$	−20.6189	−2.36515
$77$	1.89008	0.215395
$78$	−2.55496	−0.289292
$79$	9.50365	1.06924	0.534622	−	0.845091i	$-0.320454\pi$
$79$	9.50365	1.06924	0.534622	+	0.845091i	$0.320454\pi$
$80$	3.04892	0.340879
$81$	−2.57673	−0.286303
$82$	23.3327	2.57667
$83$	−3.71379	−0.407642	−0.203821	−	0.979008i	$-0.565336\pi$
$83$	−3.71379	−0.407642	−0.203821	+	0.979008i	$0.565336\pi$
$84$	−3.80194	−0.414825
$85$	14.8726	1.61316
$86$	−21.3817	−2.30564
$87$	9.57673	1.02673
$88$	4.45473	0.474876
$89$	−12.0000	−1.27200	−0.635999	−	0.771690i	$-0.719412\pi$
$89$	−12.0000	−1.27200	−0.635999	+	0.771690i	$0.719412\pi$
$90$	−12.3448	−1.30126
$91$	−0.911854	−0.0955883
$92$	−1.02177	−0.106527
$93$	−1.82908	−0.189667
$94$	−17.4547	−1.80032
$95$	25.7114	2.63793
$96$	8.12498	0.829252
$97$	4.07069	0.413316	0.206658	−	0.978413i	$-0.433741\pi$
$97$	4.07069	0.413316	0.206658	+	0.978413i	$0.433741\pi$
$98$	13.4819	1.36188
$99$	2.73125	0.274501
$100$	28.8267	2.88267
$101$	−0.963164	−0.0958384	−0.0479192	−	0.998851i	$-0.515259\pi$
$101$	−0.963164	−0.0958384	−0.0479192	+	0.998851i	$0.515259\pi$
$102$	10.9608	1.08528
$103$	−14.9584	−1.47389	−0.736946	−	0.675951i	$-0.763733\pi$
$103$	−14.9584	−1.47389	−0.736946	+	0.675951i	$0.763733\pi$
$104$	−2.14914	−0.210741
$105$	4.74094	0.462668
$106$	−11.0097	−1.06936
$107$	10.7409	1.03837	0.519183	−	0.854663i	$-0.326236\pi$
$107$	10.7409	1.03837	0.519183	+	0.854663i	$0.326236\pi$
$108$	−16.8998	−1.62618
$109$	−14.6679	−1.40493	−0.702463	−	0.711720i	$-0.747916\pi$
$109$	−14.6679	−1.40493	−0.702463	+	0.711720i	$0.747916\pi$
$110$	−16.1468	−1.53953
$111$	3.85086	0.365507
$112$	0.801938	0.0757760
$113$	−18.4644	−1.73699	−0.868493	−	0.495701i	$-0.834911\pi$
$113$	−18.4644	−1.73699	−0.868493	+	0.495701i	$0.834911\pi$
$114$	18.9487	1.77471
$115$	1.27413	0.118813
$116$	23.4155	2.17407
$117$	−1.31767	−0.121818
$118$	−18.7995	−1.73064
$119$	3.91185	0.358599
$120$	11.1739	1.02003
$121$	−7.42758	−0.675235
$122$	18.5036	1.67524
$123$	−12.9487	−1.16754
$124$	−4.47219	−0.401614
$125$	−16.9366	−1.51486
$126$	−3.24698	−0.289264
$127$	0.500664	0.0444267	0.0222134	−	0.999753i	$-0.492929\pi$
$127$	0.500664	0.0444267	0.0222134	+	0.999753i	$0.492929\pi$
$128$	16.2620	1.43738
$129$	11.8659	1.04474
$130$	7.78986	0.683216
$131$	7.93900	0.693634	0.346817	−	0.937933i	$-0.387263\pi$
$131$	7.93900	0.693634	0.346817	+	0.937933i	$0.387263\pi$
$132$	−7.18598	−0.625459
$133$	6.76271	0.586401
$134$	30.6993	2.65202
$135$	21.0737	1.81373
$136$	9.21983	0.790594
$137$	−17.1468	−1.46495	−0.732473	−	0.680796i	$-0.761634\pi$
$137$	−17.1468	−1.46495	−0.732473	+	0.680796i	$0.761634\pi$
$138$	0.939001	0.0799331
$139$	−0.493959	−0.0418971	−0.0209485	−	0.999781i	$-0.506669\pi$
$139$	−0.493959	−0.0418971	−0.0209485	+	0.999781i	$0.506669\pi$
$140$	11.5918	0.979685
$141$	9.68664	0.815763
$142$	22.3937	1.87924
$143$	−1.72348	−0.144125
$144$	1.15883	0.0965695
$145$	−29.1987	−2.42482
$146$	−19.5526	−1.61818
$147$	−7.48188	−0.617095
$148$	9.41550	0.773949
$149$	11.7899	0.965863	0.482931	−	0.875658i	$-0.339572\pi$
$149$	11.7899	0.965863	0.482931	+	0.875658i	$0.339572\pi$
$150$	−26.4916	−2.16303
$151$	−1.00000	−0.0813788
$151$	−1.00000	−0.0813788
$152$	15.9390	1.29282
$153$	5.65279	0.457001
$154$	−4.24698	−0.342231
$155$	5.57673	0.447934
$156$	3.46681	0.277567
$157$	−12.8170	−1.02291	−0.511454	−	0.859311i	$-0.670893\pi$
$157$	−12.8170	−1.02291	−0.511454	+	0.859311i	$0.670893\pi$
$158$	−21.3545	−1.69887
$159$	6.10992	0.484548
$160$	−24.7724	−1.95843
$161$	0.335126	0.0264116
$162$	5.78986	0.454894
$163$	4.23191	0.331469	0.165735	−	0.986170i	$-0.447001\pi$
$163$	4.23191	0.331469	0.165735	+	0.986170i	$0.447001\pi$
$164$	−31.6601	−2.47224
$165$	8.96077	0.697595
$166$	8.34481	0.647683
$167$	0.164210	0.0127070	0.00635349	−	0.999980i	$-0.497978\pi$
$167$	0.164210	0.0127070	0.00635349	+	0.999980i	$0.497978\pi$
$168$	2.93900	0.226749
$169$	−12.1685	−0.936040
$170$	−33.4185	−2.56308
$171$	9.77240	0.747314
$172$	29.0127	2.21220
$173$	2.82371	0.214683	0.107341	−	0.994222i	$-0.465766\pi$
$173$	2.82371	0.214683	0.107341	+	0.994222i	$0.465766\pi$
$174$	−21.5187	−1.63133
$175$	−9.45473	−0.714710
$176$	1.51573	0.114252
$177$	10.4330	0.784189
$178$	26.9638	2.02102
$179$	−15.9608	−1.19296	−0.596482	−	0.802626i	$-0.703435\pi$
$179$	−15.9608	−1.19296	−0.596482	+	0.802626i	$0.703435\pi$
$180$	16.7506	1.24852
$181$	0.203439	0.0151215	0.00756075	−	0.999971i	$-0.497593\pi$
$181$	0.203439	0.0151215	0.00756075	+	0.999971i	$0.497593\pi$
$182$	2.04892	0.151876
$183$	−10.2687	−0.759088
$184$	0.789856	0.0582290
$185$	−11.7409	−0.863211
$186$	4.10992	0.301354
$187$	7.39373	0.540683
$188$	23.6843	1.72735
$189$	5.54288	0.403185
$190$	−57.7730	−4.19129
$191$	1.76510	0.127718	0.0638591	−	0.997959i	$-0.479659\pi$
$191$	1.76510	0.127718	0.0638591	+	0.997959i	$0.479659\pi$
$192$	−16.2567	−1.17322
$193$	16.6383	1.19765	0.598826	−	0.800879i	$-0.295634\pi$
$193$	16.6383	1.19765	0.598826	+	0.800879i	$0.295634\pi$
$194$	−9.14675	−0.656699
$195$	−4.32304	−0.309580
$196$	−18.2935	−1.30668
$197$	18.6649	1.32982	0.664909	−	0.746925i	$-0.268470\pi$
$197$	18.6649	1.32982	0.664909	+	0.746925i	$0.268470\pi$
$198$	−6.13706	−0.436142
$199$	21.9909	1.55889	0.779447	−	0.626468i	$-0.215500\pi$
$199$	21.9909	1.55889	0.779447	+	0.626468i	$0.215500\pi$
$200$	−22.2838	−1.57570
$201$	−17.0368	−1.20169
$202$	2.16421	0.152273
$203$	−7.67994	−0.539026
$204$	−14.8726	−1.04129
$205$	39.4795	2.75737
$206$	33.6112	2.34180
$207$	0.484271	0.0336591
$208$	−0.731250	−0.0507031
$209$	12.7821	0.884155
$210$	−10.6528	−0.735113
$211$	6.99761	0.481735	0.240868	−	0.970558i	$-0.422568\pi$
$211$	6.99761	0.481735	0.240868	+	0.970558i	$0.422568\pi$
$212$	14.9390	1.02601
$213$	−12.4276	−0.851524
$214$	−24.1347	−1.64981
$215$	−36.1782	−2.46733
$216$	13.0640	0.888891
$217$	1.46681	0.0995737
$218$	32.9584	2.23222
$219$	10.8509	0.733233
$220$	21.9095	1.47714
$221$	−3.56704	−0.239945
$222$	−8.65279	−0.580737
$223$	4.93661	0.330580	0.165290	−	0.986245i	$-0.447144\pi$
$223$	4.93661	0.330580	0.165290	+	0.986245i	$0.447144\pi$
$224$	−6.51573	−0.435350
$225$	−13.6625	−0.910832
$226$	41.4892	2.75982
$227$	13.5187	0.897269	0.448634	−	0.893715i	$-0.351911\pi$
$227$	13.5187	0.897269	0.448634	+	0.893715i	$0.351911\pi$
$228$	−25.7114	−1.70278
$229$	−8.63102	−0.570354	−0.285177	−	0.958475i	$-0.592052\pi$
$229$	−8.63102	−0.570354	−0.285177	+	0.958475i	$0.592052\pi$
$230$	−2.86294	−0.188776
$231$	2.35690	0.155072
$232$	−18.1008	−1.18838
$233$	−12.1739	−0.797539	−0.398769	−	0.917051i	$-0.630563\pi$
$233$	−12.1739	−0.797539	−0.398769	+	0.917051i	$0.630563\pi$
$234$	2.96077	0.193552
$235$	−29.5338	−1.92657
$236$	25.5090	1.66050
$237$	11.8509	0.769796
$238$	−8.78986	−0.569762
$239$	10.2306	0.661762	0.330881	−	0.943673i	$-0.392654\pi$
$239$	10.2306	0.661762	0.330881	+	0.943673i	$0.392654\pi$
$240$	3.80194	0.245414
$241$	−12.6692	−0.816094	−0.408047	−	0.912961i	$-0.633790\pi$
$241$	−12.6692	−0.816094	−0.408047	+	0.912961i	$0.633790\pi$
$242$	16.6896	1.07285
$243$	13.4155	0.860605
$244$	−25.1075	−1.60734
$245$	22.8116	1.45738
$246$	29.0954	1.85506
$247$	−6.16660	−0.392372
$248$	3.45712	0.219528
$249$	−4.63102	−0.293479
$250$	38.0562	2.40689
$251$	18.8146	1.18757	0.593784	−	0.804625i	$-0.297633\pi$
$251$	18.8146	1.18757	0.593784	+	0.804625i	$0.297633\pi$
$252$	4.40581	0.277540
$253$	0.633415	0.0398225
$254$	−1.12498	−0.0705876
$255$	18.5459	1.16139
$256$	−10.4668	−0.654176
$257$	−13.7735	−0.859165	−0.429582	−	0.903028i	$-0.641339\pi$
$257$	−13.7735	−0.859165	−0.429582	+	0.903028i	$0.641339\pi$
$258$	−26.6625	−1.65993
$259$	−3.08815	−0.191888
$260$	−10.5700	−0.655525
$261$	−11.0978	−0.686939
$262$	−17.8388	−1.10208
$263$	−10.2295	−0.630779	−0.315390	−	0.948962i	$-0.602135\pi$
$263$	−10.2295	−0.630779	−0.315390	+	0.948962i	$0.602135\pi$
$264$	5.55496	0.341884
$265$	−18.6286	−1.14435
$266$	−15.1957	−0.931706
$267$	−14.9638	−0.915767
$268$	−41.6558	−2.54453
$269$	−16.2989	−0.993760	−0.496880	−	0.867819i	$-0.665521\pi$
$269$	−16.2989	−0.993760	−0.496880	+	0.867819i	$0.665521\pi$
$270$	−47.3521	−2.88176
$271$	−19.9323	−1.21080	−0.605400	−	0.795921i	$-0.706987\pi$
$271$	−19.9323	−1.21080	−0.605400	+	0.795921i	$0.706987\pi$
$272$	3.13706	0.190212
$273$	−1.13706	−0.0688182
$274$	38.5284	2.32759
$275$	−17.8702	−1.07762
$276$	−1.27413	−0.0766934
$277$	1.98361	0.119183	0.0595917	−	0.998223i	$-0.481020\pi$
$277$	1.98361	0.119183	0.0595917	+	0.998223i	$0.481020\pi$
$278$	1.10992	0.0665684
$279$	2.11960	0.126897
$280$	−8.96077	−0.535509
$281$	19.6383	1.17152	0.585762	−	0.810483i	$-0.300795\pi$
$281$	19.6383	1.17152	0.585762	+	0.810483i	$0.300795\pi$
$282$	−21.7657	−1.29613
$283$	−0.231914	−0.0137859	−0.00689293	−	0.999976i	$-0.502194\pi$
$283$	−0.231914	−0.0137859	−0.00689293	+	0.999976i	$0.502194\pi$
$284$	−30.3860	−1.80308
$285$	32.0616	1.89916
$286$	3.87263	0.228993
$287$	10.3840	0.612951
$288$	−9.41550	−0.554814
$289$	−1.69740	−0.0998470
$290$	65.6088	3.85268
$291$	5.07606	0.297564
$292$	26.5308	1.55260
$293$	−26.3424	−1.53894	−0.769470	−	0.638683i	$-0.779480\pi$
$293$	−26.3424	−1.53894	−0.769470	+	0.638683i	$0.779480\pi$
$294$	16.8116	0.980474
$295$	−31.8092	−1.85201
$296$	−7.27844	−0.423051
$297$	10.4765	0.607908
$298$	−26.4916	−1.53462
$299$	−0.305586	−0.0176725
$300$	35.9463	2.07536
$301$	−9.51573	−0.548478
$302$	2.24698	0.129299
$303$	−1.20105	−0.0689983
$304$	5.42327	0.311046
$305$	31.3086	1.79272
$306$	−12.7017	−0.726108
$307$	−7.29590	−0.416399	−0.208199	−	0.978086i	$-0.566760\pi$
$307$	−7.29590	−0.416399	−0.208199	+	0.978086i	$0.566760\pi$
$308$	5.76271	0.328361
$309$	−18.6528	−1.06112
$310$	−12.5308	−0.711701
$311$	−6.15213	−0.348855	−0.174428	−	0.984670i	$-0.555808\pi$
$311$	−6.15213	−0.348855	−0.174428	+	0.984670i	$0.555808\pi$
$312$	−2.67994	−0.151722
$313$	31.2965	1.76898	0.884491	−	0.466557i	$-0.154506\pi$
$313$	31.2965	1.76898	0.884491	+	0.466557i	$0.154506\pi$
$314$	28.7995	1.62525
$315$	−5.49396	−0.309550
$316$	28.9758	1.63002
$317$	1.46788	0.0824442	0.0412221	−	0.999150i	$-0.486875\pi$
$317$	1.46788	0.0824442	0.0412221	+	0.999150i	$0.486875\pi$
$318$	−13.7289	−0.769876
$319$	−14.5157	−0.812725
$320$	49.5652	2.77078
$321$	13.3937	0.747565
$322$	−0.753020	−0.0419642
$323$	26.4547	1.47198
$324$	−7.85623	−0.436457
$325$	8.62133	0.478226
$326$	−9.50902	−0.526656
$327$	−18.2905	−1.01147
$328$	24.4741	1.35136
$329$	−7.76809	−0.428268
$330$	−20.1347	−1.10838
$331$	−14.3297	−0.787634	−0.393817	−	0.919189i	$-0.628846\pi$
$331$	−14.3297	−0.787634	−0.393817	+	0.919189i	$0.628846\pi$
$332$	−11.3230	−0.621433
$333$	−4.46250	−0.244544
$334$	−0.368977	−0.0201895
$335$	51.9439	2.83800
$336$	1.00000	0.0545545
$337$	−2.47948	−0.135066	−0.0675331	−	0.997717i	$-0.521513\pi$
$337$	−2.47948	−0.135066	−0.0675331	+	0.997717i	$0.521513\pi$
$338$	27.3424	1.48723
$339$	−23.0248	−1.25053
$340$	45.3454	2.45920
$341$	2.77240	0.150134
$342$	−21.9584	−1.18737
$343$	13.0000	0.701934
$344$	−22.4276	−1.20921
$345$	1.58881	0.0855387
$346$	−6.34481	−0.341099
$347$	−19.4752	−1.04548	−0.522741	−	0.852492i	$-0.675091\pi$
$347$	−19.4752	−1.04548	−0.522741	+	0.852492i	$0.675091\pi$
$348$	29.1987	1.56521
$349$	17.5810	0.941092	0.470546	−	0.882376i	$-0.344057\pi$
$349$	17.5810	0.941092	0.470546	+	0.882376i	$0.344057\pi$
$350$	21.2446	1.13557
$351$	−5.05429	−0.269778
$352$	−12.3153	−0.656406
$353$	−7.43834	−0.395903	−0.197951	−	0.980212i	$-0.563429\pi$
$353$	−7.43834	−0.395903	−0.197951	+	0.980212i	$0.563429\pi$
$354$	−23.4426	−1.24596
$355$	37.8907	2.01103
$356$	−36.5870	−1.93911
$357$	4.87800	0.258171
$358$	35.8635	1.89545
$359$	−7.86294	−0.414990	−0.207495	−	0.978236i	$-0.566531\pi$
$359$	−7.86294	−0.414990	−0.207495	+	0.978236i	$0.566531\pi$
$360$	−12.9487	−0.682456
$361$	26.7342	1.40706
$362$	−0.457123	−0.0240259
$363$	−9.26205	−0.486131
$364$	−2.78017	−0.145720
$365$	−33.0834	−1.73166
$366$	23.0737	1.20608
$367$	−28.8907	−1.50808	−0.754040	−	0.656828i	$-0.771898\pi$
$367$	−28.8907	−1.50808	−0.754040	+	0.656828i	$0.771898\pi$
$368$	0.268750	0.0140096
$369$	15.0054	0.781149
$370$	26.3817	1.37152
$371$	−4.89977	−0.254384
$372$	−5.57673	−0.289140
$373$	−18.5810	−0.962090	−0.481045	−	0.876696i	$-0.659743\pi$
$373$	−18.5810	−0.962090	−0.481045	+	0.876696i	$0.659743\pi$
$374$	−16.6136	−0.859067
$375$	−21.1196	−1.09061
$376$	−18.3086	−0.944192
$377$	7.00298	0.360672
$378$	−12.4547	−0.640602
$379$	20.5579	1.05599	0.527995	−	0.849247i	$-0.322944\pi$
$379$	20.5579	1.05599	0.527995	+	0.849247i	$0.322944\pi$
$380$	78.3919	4.02142
$381$	0.624318	0.0319848
$382$	−3.96615	−0.202926
$383$	27.6093	1.41077	0.705383	−	0.708826i	$-0.250775\pi$
$383$	27.6093	1.41077	0.705383	+	0.708826i	$0.250775\pi$
$384$	20.2784	1.03483
$385$	−7.18598	−0.366231
$386$	−37.3860	−1.90290
$387$	−13.7506	−0.698984
$388$	12.4112	0.630083
$389$	8.29829	0.420740	0.210370	−	0.977622i	$-0.432533\pi$
$389$	8.29829	0.420740	0.210370	+	0.977622i	$0.432533\pi$
$390$	9.71379	0.491877
$391$	1.31096	0.0662982
$392$	14.1414	0.714247
$393$	9.89977	0.499377
$394$	−41.9396	−2.11289
$395$	−36.1323	−1.81801
$396$	8.32736	0.418465
$397$	−5.30021	−0.266010	−0.133005	−	0.991115i	$-0.542463\pi$
$397$	−5.30021	−0.266010	−0.133005	+	0.991115i	$0.542463\pi$
$398$	−49.4131	−2.47686
$399$	8.43296	0.422176
$400$	−7.58211	−0.379105
$401$	0.647416	0.0323304	0.0161652	−	0.999869i	$-0.494854\pi$
$401$	0.647416	0.0323304	0.0161652	+	0.999869i	$0.494854\pi$
$402$	38.2814	1.90930
$403$	−1.33752	−0.0666265
$404$	−2.93661	−0.146102
$405$	9.79656	0.486795
$406$	17.2567	0.856434
$407$	−5.83685	−0.289322
$408$	11.4969	0.569183
$409$	7.82802	0.387071	0.193535	−	0.981093i	$-0.438005\pi$
$409$	7.82802	0.387071	0.193535	+	0.981093i	$0.438005\pi$
$410$	−88.7096	−4.38105
$411$	−21.3817	−1.05468
$412$	−45.6069	−2.24689
$413$	−8.36658	−0.411693
$414$	−1.08815	−0.0534795
$415$	14.1196	0.693104
$416$	5.94139	0.291301
$417$	−0.615957	−0.0301635
$418$	−28.7211	−1.40479
$419$	−3.02284	−0.147675	−0.0738376	−	0.997270i	$-0.523525\pi$
$419$	−3.02284	−0.147675	−0.0738376	+	0.997270i	$0.523525\pi$
$420$	14.4547	0.705319
$421$	34.9801	1.70483	0.852414	−	0.522867i	$-0.175138\pi$
$421$	34.9801	1.70483	0.852414	+	0.522867i	$0.175138\pi$
$422$	−15.7235	−0.765407
$423$	−11.2252	−0.545788
$424$	−11.5483	−0.560833
$425$	−36.9855	−1.79406
$426$	27.9245	1.35295
$427$	8.23490	0.398515
$428$	32.7482	1.58295
$429$	−2.14914	−0.103762
$430$	81.2917	3.92023
$431$	−9.93469	−0.478537	−0.239269	−	0.970953i	$-0.576908\pi$
$431$	−9.93469	−0.478537	−0.239269	+	0.970953i	$0.576908\pi$
$432$	4.44504	0.213862
$433$	−0.588810	−0.0282964	−0.0141482	−	0.999900i	$-0.504504\pi$
$433$	−0.588810	−0.0282964	−0.0141482	+	0.999900i	$0.504504\pi$
$434$	−3.29590	−0.158208
$435$	−36.4101	−1.74573
$436$	−44.7211	−2.14175
$437$	2.26636	0.108415
$438$	−24.3817	−1.16500
$439$	30.0954	1.43638	0.718189	−	0.695849i	$-0.244972\pi$
$439$	30.0954	1.43638	0.718189	+	0.695849i	$0.244972\pi$
$440$	−16.9366	−0.807421
$441$	8.67025	0.412869
$442$	8.01507	0.381238
$443$	15.0204	0.713643	0.356821	−	0.934173i	$-0.383860\pi$
$443$	15.0204	0.713643	0.356821	+	0.934173i	$0.383860\pi$
$444$	11.7409	0.557200
$445$	45.6233	2.16275
$446$	−11.0925	−0.525243
$447$	14.7017	0.695367
$448$	13.0368	0.615933
$449$	−2.54766	−0.120232	−0.0601158	−	0.998191i	$-0.519147\pi$
$449$	−2.54766	−0.120232	−0.0601158	+	0.998191i	$0.519147\pi$
$450$	30.6993	1.44718
$451$	19.6267	0.924186
$452$	−56.2965	−2.64796
$453$	−1.24698	−0.0585882
$454$	−30.3763	−1.42563
$455$	3.46681	0.162527
$456$	19.8756	0.930761
$457$	−35.1390	−1.64373	−0.821866	−	0.569681i	$-0.807067\pi$
$457$	−35.1390	−1.64373	−0.821866	+	0.569681i	$0.807067\pi$
$458$	19.3937	0.906210
$459$	21.6829	1.01207
$460$	3.88471	0.181125
$461$	−28.1148	−1.30944	−0.654719	−	0.755873i	$-0.727213\pi$
$461$	−28.1148	−1.30944	−0.654719	+	0.755873i	$0.727213\pi$
$462$	−5.29590	−0.246387
$463$	24.3370	1.13104	0.565519	−	0.824735i	$-0.308676\pi$
$463$	24.3370	1.13104	0.565519	+	0.824735i	$0.308676\pi$
$464$	−6.15883	−0.285917
$465$	6.95407	0.322487
$466$	27.3545	1.26717
$467$	−23.9444	−1.10801	−0.554007	−	0.832512i	$-0.686902\pi$
$467$	−23.9444	−1.10801	−0.554007	+	0.832512i	$0.686902\pi$
$468$	−4.01746	−0.185707
$469$	13.6625	0.630875
$470$	66.3618	3.06104
$471$	−15.9825	−0.736437
$472$	−19.7192	−0.907648
$473$	−17.9855	−0.826975
$474$	−26.6286	−1.22309
$475$	−63.9396	−2.93375
$476$	11.9269	0.546669
$477$	−7.08038	−0.324188
$478$	−22.9879	−1.05144
$479$	−28.1172	−1.28471	−0.642354	−	0.766408i	$-0.722042\pi$
$479$	−28.1172	−1.28471	−0.642354	+	0.766408i	$0.722042\pi$
$480$	−30.8907	−1.40996
$481$	2.81594	0.128396
$482$	28.4674	1.29665
$483$	0.417895	0.0190149
$484$	−22.6461	−1.02937
$485$	−15.4765	−0.702752
$486$	−30.1444	−1.36738
$487$	−20.3894	−0.923933	−0.461966	−	0.886897i	$-0.652856\pi$
$487$	−20.3894	−0.923933	−0.461966	+	0.886897i	$0.652856\pi$
$488$	19.4088	0.878595
$489$	5.27711	0.238639
$490$	−51.2573	−2.31557
$491$	31.6340	1.42762	0.713811	−	0.700338i	$-0.246967\pi$
$491$	31.6340	1.42762	0.713811	+	0.700338i	$0.246967\pi$
$492$	−39.4795	−1.77987
$493$	−30.0428	−1.35306
$494$	13.8562	0.623421
$495$	−10.3840	−0.466728
$496$	1.17629	0.0528171
$497$	9.96615	0.447043
$498$	10.4058	0.466296
$499$	39.4330	1.76526	0.882631	−	0.470067i	$-0.155770\pi$
$499$	39.4330	1.76526	0.882631	+	0.470067i	$0.155770\pi$
$500$	−51.6383	−2.30934
$501$	0.204767	0.00914832
$502$	−42.2760	−1.88687
$503$	−20.8689	−0.930498	−0.465249	−	0.885180i	$-0.654035\pi$
$503$	−20.8689	−0.930498	−0.465249	+	0.885180i	$0.654035\pi$
$504$	−3.40581	−0.151707
$505$	3.66189	0.162952
$506$	−1.42327	−0.0632721
$507$	−15.1739	−0.673897
$508$	1.52648	0.0677267
$509$	−21.6286	−0.958672	−0.479336	−	0.877631i	$-0.659122\pi$
$509$	−21.6286	−0.958672	−0.479336	+	0.877631i	$0.659122\pi$
$510$	−41.6722	−1.84527
$511$	−8.70171	−0.384941
$512$	−9.00538	−0.397985
$513$	37.4849	1.65500
$514$	30.9487	1.36509
$515$	56.8708	2.50603
$516$	36.1782	1.59266
$517$	−14.6823	−0.645728
$518$	6.93900	0.304882
$519$	3.52111	0.154559
$520$	8.17092	0.358318
$521$	−35.3008	−1.54656	−0.773278	−	0.634067i	$-0.781384\pi$
$521$	−35.3008	−1.54656	−0.773278	+	0.634067i	$0.781384\pi$
$522$	24.9366	1.09145
$523$	30.8025	1.34690	0.673450	−	0.739233i	$-0.264812\pi$
$523$	30.8025	1.34690	0.673450	+	0.739233i	$0.264812\pi$
$524$	24.2054	1.05742
$525$	−11.7899	−0.514552
$526$	22.9855	1.00222
$527$	5.73795	0.249949
$528$	1.89008	0.0822553
$529$	−22.8877	−0.995117
$530$	41.8582	1.81820
$531$	−12.0901	−0.524664
$532$	20.6189	0.893944
$533$	−9.46873	−0.410136
$534$	33.6233	1.45502
$535$	−40.8364	−1.76551
$536$	32.2010	1.39087
$537$	−19.9028	−0.858867
$538$	36.6233	1.57894
$539$	11.3405	0.488470
$540$	64.2519	2.76496
$541$	27.9801	1.20296	0.601480	−	0.798888i	$-0.294578\pi$
$541$	27.9801	1.20296	0.601480	+	0.798888i	$0.294578\pi$
$542$	44.7875	1.92379
$543$	0.253684	0.0108866
$544$	−25.4886	−1.09281
$545$	55.7663	2.38877
$546$	2.55496	0.109342
$547$	−10.4644	−0.447426	−0.223713	−	0.974655i	$-0.571818\pi$
$547$	−10.4644	−0.447426	−0.223713	+	0.974655i	$0.571818\pi$
$548$	−52.2790	−2.23325
$549$	11.8998	0.507870
$550$	40.1540	1.71217
$551$	−51.9372	−2.21260
$552$	0.984935	0.0419216
$553$	−9.50365	−0.404136
$554$	−4.45712	−0.189365
$555$	−14.6407	−0.621464
$556$	−1.50604	−0.0638704
$557$	25.1672	1.06637	0.533184	−	0.845999i	$-0.320995\pi$
$557$	25.1672	1.06637	0.533184	+	0.845999i	$0.320995\pi$
$558$	−4.76271	−0.201622
$559$	8.67696	0.366996
$560$	−3.04892	−0.128840
$561$	9.21983	0.389262
$562$	−44.1269	−1.86138
$563$	−3.45580	−0.145644	−0.0728222	−	0.997345i	$-0.523201\pi$
$563$	−3.45580	−0.145644	−0.0728222	+	0.997345i	$0.523201\pi$
$564$	29.5338	1.24360
$565$	70.2006	2.95336
$566$	0.521106	0.0219037
$567$	2.57673	0.108212
$568$	23.4892	0.985584
$569$	12.5657	0.526782	0.263391	−	0.964689i	$-0.415159\pi$
$569$	12.5657	0.526782	0.263391	+	0.964689i	$0.415159\pi$
$570$	−72.0417	−3.01750
$571$	18.7138	0.783148	0.391574	−	0.920147i	$-0.371931\pi$
$571$	18.7138	0.783148	0.391574	+	0.920147i	$0.371931\pi$
$572$	−5.25475	−0.219712
$573$	2.20105	0.0919500
$574$	−23.3327	−0.973889
$575$	−3.16852	−0.132137
$576$	18.8388	0.784949
$577$	46.5816	1.93922	0.969609	−	0.244658i	$-0.0786758\pi$
$577$	46.5816	1.93922	0.969609	+	0.244658i	$0.0786758\pi$
$578$	3.81402	0.158642
$579$	20.7476	0.862243
$580$	−89.0243	−3.69653
$581$	3.71379	0.154074
$582$	−11.4058	−0.472786
$583$	−9.26098	−0.383551
$584$	−20.5090	−0.848669
$585$	5.00969	0.207125
$586$	59.1909	2.44515
$587$	6.12259	0.252706	0.126353	−	0.991985i	$-0.459673\pi$
$587$	6.12259	0.252706	0.126353	+	0.991985i	$0.459673\pi$
$588$	−22.8116	−0.940736
$589$	9.91962	0.408731
$590$	71.4747	2.94257
$591$	23.2747	0.957394
$592$	−2.47650	−0.101784
$593$	−16.9812	−0.697335	−0.348667	−	0.937247i	$-0.613366\pi$
$593$	−16.9812	−0.697335	−0.348667	+	0.937247i	$0.613366\pi$
$594$	−23.5405	−0.965878
$595$	−14.8726	−0.609718
$596$	35.9463	1.47242
$597$	27.4222	1.12232
$598$	0.686645	0.0280790
$599$	−18.7942	−0.767909	−0.383954	−	0.923352i	$-0.625438\pi$
$599$	−18.7942	−0.767909	−0.383954	+	0.923352i	$0.625438\pi$
$600$	−27.7875	−1.13442
$601$	−5.38298	−0.219576	−0.109788	−	0.993955i	$-0.535017\pi$
$601$	−5.38298	−0.219576	−0.109788	+	0.993955i	$0.535017\pi$
$602$	21.3817	0.871451
$603$	19.7429	0.803991
$604$	−3.04892	−0.124059
$605$	28.2392	1.14809
$606$	2.69873	0.109628
$607$	40.7603	1.65441	0.827205	−	0.561900i	$-0.189929\pi$
$607$	40.7603	1.65441	0.827205	+	0.561900i	$0.189929\pi$
$608$	−44.0640	−1.78703
$609$	−9.57673	−0.388069
$610$	−70.3497	−2.84838
$611$	7.08336	0.286562
$612$	17.2349	0.696679
$613$	22.4776	0.907860	0.453930	−	0.891037i	$-0.350022\pi$
$613$	22.4776	0.907860	0.453930	+	0.891037i	$0.350022\pi$
$614$	16.3937	0.661597
$615$	49.2301	1.98515
$616$	−4.45473	−0.179486
$617$	−19.8810	−0.800378	−0.400189	−	0.916433i	$-0.631056\pi$
$617$	−19.8810	−0.800378	−0.400189	+	0.916433i	$0.631056\pi$
$618$	41.9124	1.68597
$619$	16.6504	0.669236	0.334618	−	0.942354i	$-0.391393\pi$
$619$	16.6504	0.669236	0.334618	+	0.942354i	$0.391393\pi$
$620$	17.0030	0.682856
$621$	1.85756	0.0745413
$622$	13.8237	0.554280
$623$	12.0000	0.480770
$624$	−0.911854	−0.0365034
$625$	17.1183	0.684731
$626$	−70.3226	−2.81066
$627$	15.9390	0.636542
$628$	−39.0780	−1.55938
$629$	−12.0804	−0.481676
$630$	12.3448	0.491829
$631$	−2.16959	−0.0863699	−0.0431850	−	0.999067i	$-0.513750\pi$
$631$	−2.16959	−0.0863699	−0.0431850	+	0.999067i	$0.513750\pi$
$632$	−22.3991	−0.890989
$633$	8.72587	0.346822
$634$	−3.29829	−0.130992
$635$	−1.90349	−0.0755378
$636$	18.6286	0.738673
$637$	−5.47112	−0.216774
$638$	32.6165	1.29130
$639$	14.4015	0.569715
$640$	−61.8273	−2.44394
$641$	−7.54825	−0.298138	−0.149069	−	0.988827i	$-0.547628\pi$
$641$	−7.54825	−0.298138	−0.149069	+	0.988827i	$0.547628\pi$
$642$	−30.0954	−1.18777
$643$	−1.15452	−0.0455299	−0.0227649	−	0.999741i	$-0.507247\pi$
$643$	−1.15452	−0.0455299	−0.0227649	+	0.999741i	$0.507247\pi$
$644$	1.02177	0.0402634
$645$	−45.1135	−1.77634
$646$	−59.4432	−2.33876
$647$	−21.1196	−0.830297	−0.415149	−	0.909754i	$-0.636270\pi$
$647$	−21.1196	−0.830297	−0.415149	+	0.909754i	$0.636270\pi$
$648$	6.07308	0.238573
$649$	−15.8135	−0.620736
$650$	−19.3720	−0.759831
$651$	1.82908	0.0716875
$652$	12.9028	0.505311
$653$	11.8866	0.465160	0.232580	−	0.972577i	$-0.425283\pi$
$653$	11.8866	0.465160	0.232580	+	0.972577i	$0.425283\pi$
$654$	41.0984	1.60708
$655$	−30.1836	−1.17937
$656$	8.32736	0.325129
$657$	−12.5743	−0.490572
$658$	17.4547	0.680456
$659$	26.3545	1.02663	0.513313	−	0.858202i	$-0.328418\pi$
$659$	26.3545	1.02663	0.513313	+	0.858202i	$0.328418\pi$
$660$	27.3207	1.06345
$661$	−13.7788	−0.535935	−0.267967	−	0.963428i	$-0.586352\pi$
$661$	−13.7788	−0.535935	−0.267967	+	0.963428i	$0.586352\pi$
$662$	32.1987	1.25144
$663$	−4.44803	−0.172747
$664$	8.75302	0.339683
$665$	−25.7114	−0.997045
$666$	10.0271	0.388544
$667$	−2.57374	−0.0996558
$668$	0.500664	0.0193713
$669$	6.15585	0.237999
$670$	−116.717	−4.50917
$671$	15.5646	0.600867
$672$	−8.12498	−0.313428
$673$	−34.4825	−1.32920	−0.664601	−	0.747199i	$-0.731398\pi$
$673$	−34.4825	−1.32920	−0.664601	+	0.747199i	$0.731398\pi$
$674$	5.57135	0.214600
$675$	−52.4064	−2.01712
$676$	−37.1008	−1.42695
$677$	6.65710	0.255853	0.127927	−	0.991784i	$-0.459168\pi$
$677$	6.65710	0.255853	0.127927	+	0.991784i	$0.459168\pi$
$678$	51.7362	1.98691
$679$	−4.07069	−0.156219
$680$	−35.0532	−1.34423
$681$	16.8576	0.645983
$682$	−6.22952	−0.238541
$683$	−20.5875	−0.787758	−0.393879	−	0.919162i	$-0.628867\pi$
$683$	−20.5875	−0.787758	−0.393879	+	0.919162i	$0.628867\pi$
$684$	29.7952	1.13925
$685$	65.1909	2.49082
$686$	−29.2107	−1.11527
$687$	−10.7627	−0.410623
$688$	−7.63102	−0.290930
$689$	4.46788	0.170213
$690$	−3.57002	−0.135908
$691$	−4.05861	−0.154397	−0.0771983	−	0.997016i	$-0.524597\pi$
$691$	−4.05861	−0.154397	−0.0771983	+	0.997016i	$0.524597\pi$
$692$	8.60925	0.327275
$693$	−2.73125	−0.103752
$694$	43.7603	1.66112
$695$	1.87800	0.0712367
$696$	−22.5714	−0.855565
$697$	40.6209	1.53862
$698$	−39.5042	−1.49526
$699$	−15.1806	−0.574183
$700$	−28.8267	−1.08955
$701$	−34.4808	−1.30232	−0.651161	−	0.758939i	$-0.725718\pi$
$701$	−34.4808	−1.30232	−0.651161	+	0.758939i	$0.725718\pi$
$702$	11.3569	0.428638
$703$	−20.8842	−0.787664
$704$	24.6407	0.928682
$705$	−36.8280	−1.38702
$706$	16.7138	0.629032
$707$	0.963164	0.0362235
$708$	31.8092	1.19546
$709$	−11.6998	−0.439395	−0.219697	−	0.975568i	$-0.570507\pi$
$709$	−11.6998	−0.439395	−0.219697	+	0.975568i	$0.570507\pi$
$710$	−85.1396	−3.19523
$711$	−13.7332	−0.515034
$712$	28.2828	1.05994
$713$	0.491566	0.0184093
$714$	−10.9608	−0.410197
$715$	6.55257	0.245052
$716$	−48.6631	−1.81862
$717$	12.7573	0.476431
$718$	17.6679	0.659359
$719$	−38.5036	−1.43594	−0.717972	−	0.696072i	$-0.754929\pi$
$719$	−38.5036	−1.43594	−0.717972	+	0.696072i	$0.754929\pi$
$720$	−4.40581	−0.164195
$721$	14.9584	0.557079
$722$	−60.0713	−2.23562
$723$	−15.7982	−0.587542
$724$	0.620269	0.0230521
$725$	72.6118	2.69673
$726$	20.8116	0.772392
$727$	15.2790	0.566668	0.283334	−	0.959021i	$-0.408560\pi$
$727$	15.2790	0.566668	0.283334	+	0.959021i	$0.408560\pi$
$728$	2.14914	0.0796526
$729$	24.4590	0.905890
$730$	74.3376	2.75136
$731$	−37.2241	−1.37678
$732$	−31.3086	−1.15720
$733$	20.3653	0.752208	0.376104	−	0.926577i	$-0.377264\pi$
$733$	20.3653	0.752208	0.376104	+	0.926577i	$0.377264\pi$
$734$	64.9168	2.39612
$735$	28.4456	1.04923
$736$	−2.18359	−0.0804881
$737$	25.8232	0.951211
$738$	−33.7168	−1.24113
$739$	−5.88710	−0.216560	−0.108280	−	0.994120i	$-0.534534\pi$
$739$	−5.88710	−0.216560	−0.108280	+	0.994120i	$0.534534\pi$
$740$	−35.7972	−1.31593
$741$	−7.68963	−0.282486
$742$	11.0097	0.404178
$743$	23.5730	0.864810	0.432405	−	0.901680i	$-0.357665\pi$
$743$	23.5730	0.864810	0.432405	+	0.901680i	$0.357665\pi$
$744$	4.31096	0.158048
$745$	−44.8243	−1.64224
$746$	41.7512	1.52862
$747$	5.36658	0.196353
$748$	22.5429	0.824249
$749$	−10.7409	−0.392465
$750$	47.4553	1.73282
$751$	−29.1927	−1.06526	−0.532628	−	0.846349i	$-0.678796\pi$
$751$	−29.1927	−1.06526	−0.532628	+	0.846349i	$0.678796\pi$
$752$	−6.22952	−0.227167
$753$	23.4614	0.854982
$754$	−15.7356	−0.573055
$755$	3.80194	0.138367
$756$	16.8998	0.614639
$757$	5.22819	0.190022	0.0950110	−	0.995476i	$-0.469711\pi$
$757$	5.22819	0.190022	0.0950110	+	0.995476i	$0.469711\pi$
$758$	−46.1933	−1.67782
$759$	0.789856	0.0286700
$760$	−60.5991	−2.19816
$761$	−28.4843	−1.03255	−0.516277	−	0.856422i	$-0.672682\pi$
$761$	−28.4843	−1.03255	−0.516277	+	0.856422i	$0.672682\pi$
$762$	−1.40283	−0.0508191
$763$	14.6679	0.531012
$764$	5.38165	0.194701
$765$	−21.4916	−0.777029
$766$	−62.0374	−2.24150
$767$	7.62910	0.275471
$768$	−13.0519	−0.470970
$769$	−45.9941	−1.65859	−0.829296	−	0.558810i	$-0.811258\pi$
$769$	−45.9941	−1.65859	−0.829296	+	0.558810i	$0.811258\pi$
$770$	16.1468	0.581889
$771$	−17.1752	−0.618551
$772$	50.7289	1.82577
$773$	13.3787	0.481197	0.240599	−	0.970625i	$-0.422656\pi$
$773$	13.3787	0.481197	0.240599	+	0.970625i	$0.422656\pi$
$774$	30.8974	1.11058
$775$	−13.8683	−0.498165
$776$	−9.59419	−0.344411
$777$	−3.85086	−0.138149
$778$	−18.6461	−0.668495
$779$	70.2243	2.51605
$780$	−13.1806	−0.471941
$781$	18.8369	0.674036
$782$	−2.94571	−0.105338
$783$	−42.5690	−1.52129
$784$	4.81163	0.171844
$785$	48.7294	1.73923
$786$	−22.2446	−0.793438
$787$	−2.32783	−0.0829782	−0.0414891	−	0.999139i	$-0.513210\pi$
$787$	−2.32783	−0.0829782	−0.0414891	+	0.999139i	$0.513210\pi$
$788$	56.9077	2.02725
$789$	−12.7560	−0.454126
$790$	81.1885	2.88856
$791$	18.4644	0.656519
$792$	−6.43727	−0.228739
$793$	−7.50902	−0.266653
$794$	11.9095	0.422651
$795$	−23.2295	−0.823866
$796$	67.0484	2.37647
$797$	−16.3569	−0.579391	−0.289695	−	0.957119i	$-0.593554\pi$
$797$	−16.3569	−0.579391	−0.289695	+	0.957119i	$0.593554\pi$
$798$	−18.9487	−0.670776
$799$	−30.3876	−1.07504
$800$	61.6045	2.17805
$801$	17.3405	0.612697
$802$	−1.45473	−0.0513683
$803$	−16.4470	−0.580401
$804$	−51.9439	−1.83192
$805$	−1.27413	−0.0449071
$806$	3.00538	0.105860
$807$	−20.3244	−0.715452
$808$	2.27008	0.0798611
$809$	13.0610	0.459200	0.229600	−	0.973285i	$-0.426258\pi$
$809$	13.0610	0.459200	0.229600	+	0.973285i	$0.426258\pi$
$810$	−22.0127	−0.773446
$811$	3.19508	0.112194	0.0560972	−	0.998425i	$-0.482134\pi$
$811$	3.19508	0.112194	0.0560972	+	0.998425i	$0.482134\pi$
$812$	−23.4155	−0.821723
$813$	−24.8552	−0.871709
$814$	13.1153	0.459691
$815$	−16.0895	−0.563590
$816$	3.91185	0.136942
$817$	−64.3521	−2.25140
$818$	−17.5894	−0.614999
$819$	1.31767	0.0460430
$820$	120.370	4.20349
$821$	24.0320	0.838724	0.419362	−	0.907819i	$-0.362254\pi$
$821$	24.0320	0.838724	0.419362	+	0.907819i	$0.362254\pi$
$822$	48.0441	1.67573
$823$	7.14914	0.249204	0.124602	−	0.992207i	$-0.460235\pi$
$823$	7.14914	0.249204	0.124602	+	0.992207i	$0.460235\pi$
$824$	35.2553	1.22818
$825$	−22.2838	−0.775823
$826$	18.7995	0.654120
$827$	−21.4983	−0.747568	−0.373784	−	0.927516i	$-0.621940\pi$
$827$	−21.4983	−0.747568	−0.373784	+	0.927516i	$0.621940\pi$
$828$	1.47650	0.0513120
$829$	−37.7144	−1.30987	−0.654937	−	0.755683i	$-0.727305\pi$
$829$	−37.7144	−1.30987	−0.654937	+	0.755683i	$0.727305\pi$
$830$	−31.7265	−1.10124
$831$	2.47352	0.0858054
$832$	−11.8877	−0.412132
$833$	23.4711	0.813226
$834$	1.38404	0.0479255
$835$	−0.624318	−0.0216054
$836$	38.9715	1.34786
$837$	8.13036	0.281026
$838$	6.79225	0.234634
$839$	55.6252	1.92039	0.960197	−	0.279323i	$-0.0901101\pi$
$839$	55.6252	1.92039	0.960197	+	0.279323i	$0.0901101\pi$
$840$	−11.1739	−0.385536
$841$	29.9815	1.03384
$842$	−78.5997	−2.70872
$843$	24.4886	0.843432
$844$	21.3351	0.734385
$845$	46.2640	1.59153
$846$	25.2228	0.867178
$847$	7.42758	0.255215
$848$	−3.92931	−0.134933
$849$	−0.289192	−0.00992505
$850$	83.1057	2.85050
$851$	−1.03492	−0.0354765
$852$	−37.8907	−1.29811
$853$	41.8592	1.43323	0.716616	−	0.697468i	$-0.245690\pi$
$853$	41.8592	1.43323	0.716616	+	0.697468i	$0.245690\pi$
$854$	−18.5036	−0.633182
$855$	−37.1540	−1.27064
$856$	−25.3153	−0.865258
$857$	26.1269	0.892478	0.446239	−	0.894914i	$-0.352763\pi$
$857$	26.1269	0.892478	0.446239	+	0.894914i	$0.352763\pi$
$858$	4.82908	0.164862
$859$	−12.6732	−0.432405	−0.216203	−	0.976349i	$-0.569367\pi$
$859$	−12.6732	−0.432405	−0.216203	+	0.976349i	$0.569367\pi$
$860$	−110.304	−3.76135
$861$	12.9487	0.441290
$862$	22.3230	0.760326
$863$	41.4577	1.41124	0.705619	−	0.708592i	$-0.250669\pi$
$863$	41.4577	1.41124	0.705619	+	0.708592i	$0.250669\pi$
$864$	−36.1159	−1.22869
$865$	−10.7356	−0.365020
$866$	1.32304	0.0449589
$867$	−2.11662	−0.0718842
$868$	4.47219	0.151796
$869$	−17.9627	−0.609343
$870$	81.8128	2.77371
$871$	−12.4582	−0.422130
$872$	34.5706	1.17071
$873$	−5.88231	−0.199086
$874$	−5.09246	−0.172255
$875$	16.9366	0.572562
$876$	33.0834	1.11778
$877$	−49.2978	−1.66467	−0.832334	−	0.554274i	$-0.812996\pi$
$877$	−49.2978	−1.66467	−0.832334	+	0.554274i	$0.812996\pi$
$878$	−67.6238	−2.28219
$879$	−32.8485	−1.10795
$880$	−5.76271	−0.194261
$881$	−27.8062	−0.936816	−0.468408	−	0.883512i	$-0.655172\pi$
$881$	−27.8062	−0.936816	−0.468408	+	0.883512i	$0.655172\pi$
$882$	−19.4819	−0.655989
$883$	−34.2465	−1.15249	−0.576243	−	0.817278i	$-0.695482\pi$
$883$	−34.2465	−1.15249	−0.576243	+	0.817278i	$0.695482\pi$
$884$	−10.8756	−0.365786
$885$	−39.6655	−1.33334
$886$	−33.7506	−1.13387
$887$	29.6866	0.996780	0.498390	−	0.866953i	$-0.333925\pi$
$887$	29.6866	0.996780	0.498390	+	0.866953i	$0.333925\pi$
$888$	−9.07606	−0.304573
$889$	−0.500664	−0.0167917
$890$	−102.515	−3.43629
$891$	4.87023	0.163159
$892$	15.0513	0.503955
$893$	−52.5333	−1.75796
$894$	−33.0344	−1.10484
$895$	60.6819	2.02837
$896$	−16.2620	−0.543277
$897$	−0.381059	−0.0127232
$898$	5.72455	0.191031
$899$	−11.2650	−0.375710
$900$	−41.6558	−1.38853
$901$	−19.1672	−0.638552
$902$	−44.1008	−1.46840
$903$	−11.8659	−0.394873
$904$	43.5187	1.44741
$905$	−0.773463	−0.0257108
$906$	2.80194	0.0930881
$907$	−21.6668	−0.719434	−0.359717	−	0.933061i	$-0.617127\pi$
$907$	−21.6668	−0.719434	−0.359717	+	0.933061i	$0.617127\pi$
$908$	41.2174	1.36785
$909$	1.39181	0.0461635
$910$	−7.78986	−0.258231
$911$	−34.3357	−1.13759	−0.568797	−	0.822478i	$-0.692591\pi$
$911$	−34.3357	−1.13759	−0.568797	+	0.822478i	$0.692591\pi$
$912$	6.76271	0.223936
$913$	7.01938	0.232307
$914$	78.9566	2.61165
$915$	39.0411	1.29066
$916$	−26.3153	−0.869481
$917$	−7.93900	−0.262169
$918$	−48.7211	−1.60804
$919$	5.55496	0.183241	0.0916206	−	0.995794i	$-0.470795\pi$
$919$	5.55496	0.183241	0.0916206	+	0.995794i	$0.470795\pi$
$920$	−3.00298	−0.0990054
$921$	−9.09783	−0.299784
$922$	63.1734	2.08051
$923$	−9.08767	−0.299124
$924$	7.18598	0.236401
$925$	29.1976	0.960011
$926$	−54.6848	−1.79706
$927$	21.6155	0.709946
$928$	50.0404	1.64266
$929$	−30.4504	−0.999046	−0.499523	−	0.866301i	$-0.666491\pi$
$929$	−30.4504	−0.999046	−0.499523	+	0.866301i	$0.666491\pi$
$930$	−15.6256	−0.512385
$931$	40.5763	1.32983
$932$	−37.1172	−1.21581
$933$	−7.67158	−0.251156
$934$	53.8025	1.76047
$935$	−28.1105	−0.919312
$936$	3.10560	0.101510
$937$	−30.2959	−0.989724	−0.494862	−	0.868972i	$-0.664781\pi$
$937$	−30.2959	−0.989724	−0.494862	+	0.868972i	$0.664781\pi$
$938$	−30.6993	−1.00237
$939$	39.0261	1.27357
$940$	−90.0461	−2.93698
$941$	−26.9004	−0.876927	−0.438463	−	0.898749i	$-0.644477\pi$
$941$	−26.9004	−0.876927	−0.438463	+	0.898749i	$0.644477\pi$
$942$	35.9124	1.17009
$943$	3.47996	0.113323
$944$	−6.70948	−0.218375
$945$	−21.0737	−0.685527
$946$	40.4131	1.31394
$947$	29.4064	0.955580	0.477790	−	0.878474i	$-0.341438\pi$
$947$	29.4064	0.955580	0.477790	+	0.878474i	$0.341438\pi$
$948$	36.1323	1.17352
$949$	7.93469	0.257571
$950$	143.671	4.66130
$951$	1.83041	0.0593552
$952$	−9.21983	−0.298816
$953$	31.3586	1.01580	0.507902	−	0.861415i	$-0.330421\pi$
$953$	31.3586	1.01580	0.507902	+	0.861415i	$0.330421\pi$
$954$	15.9095	0.515088
$955$	−6.71081	−0.217157
$956$	31.1922	1.00883
$957$	−18.1008	−0.585116
$958$	63.1788	2.04121
$959$	17.1468	0.553698
$960$	61.8068	1.99481
$961$	−28.8485	−0.930596
$962$	−6.32736	−0.204002
$963$	−15.5211	−0.500161
$964$	−38.6273	−1.24410
$965$	−63.2579	−2.03634
$966$	−0.939001	−0.0302119
$967$	6.46681	0.207959	0.103979	−	0.994579i	$-0.466842\pi$
$967$	6.46681	0.207959	0.103979	+	0.994579i	$0.466842\pi$
$968$	17.5060	0.562665
$969$	32.9885	1.05974
$970$	34.7754	1.11657
$971$	−50.2156	−1.61150	−0.805748	−	0.592258i	$-0.798237\pi$
$971$	−50.2156	−1.61150	−0.805748	+	0.592258i	$0.798237\pi$
$972$	40.9028	1.31196
$973$	0.493959	0.0158356
$974$	45.8146	1.46799
$975$	10.7506	0.344296
$976$	6.60388	0.211385
$977$	−9.08085	−0.290522	−0.145261	−	0.989393i	$-0.546402\pi$
$977$	−9.08085	−0.290522	−0.145261	+	0.989393i	$0.546402\pi$
$978$	−11.8576	−0.379163
$979$	22.6810	0.724888
$980$	69.5508	2.22172
$981$	21.1957	0.676726
$982$	−71.0810	−2.26828
$983$	54.8092	1.74814	0.874072	−	0.485797i	$-0.161471\pi$
$983$	54.8092	1.74814	0.874072	+	0.485797i	$0.161471\pi$
$984$	30.5187	0.972901
$985$	−70.9627	−2.26106
$986$	67.5056	2.14982
$987$	−9.68664	−0.308329
$988$	−18.8015	−0.598154
$989$	−3.18896	−0.101403
$990$	23.3327	0.741563
$991$	35.5235	1.12844	0.564221	−	0.825624i	$-0.309177\pi$
$991$	35.5235	1.12844	0.564221	+	0.825624i	$0.309177\pi$
$992$	−9.55735	−0.303446
$993$	−17.8689	−0.567053
$994$	−22.3937	−0.710286
$995$	−83.6080	−2.65055
$996$	−14.1196	−0.447397
$997$	15.3763	0.486971	0.243486	−	0.969904i	$-0.421709\pi$
$997$	15.3763	0.486971	0.243486	+	0.969904i	$0.421709\pi$
$998$	−88.6051	−2.80474
$999$	−17.1172	−0.541565

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	151.2.a.a.1.1	✓	3
3.2	odd	2		1359.2.a.g.1.3		3
4.3	odd	2		2416.2.a.h.1.1		3
5.4	even	2		3775.2.a.k.1.3		3
7.6	odd	2		7399.2.a.b.1.1		3
8.3	odd	2		9664.2.a.p.1.3		3
8.5	even	2		9664.2.a.t.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
151.2.a.a.1.1	✓	3	1.1	even	1	trivial
1359.2.a.g.1.3		3	3.2	odd	2
2416.2.a.h.1.1		3	4.3	odd	2
3775.2.a.k.1.3		3	5.4	even	2
7399.2.a.b.1.1		3	7.6	odd	2
9664.2.a.p.1.3		3	8.3	odd	2
9664.2.a.t.1.1		3	8.5	even	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:	\( N \)	\(=\)	\( 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	151.a (trivial)

\(f(q)\)	\(=\)	\(q-2.24698 q^{2} +1.24698 q^{3} +3.04892 q^{4} -3.80194 q^{5} -2.80194 q^{6} -1.00000 q^{7} -2.35690 q^{8} -1.44504 q^{9} +O(q^{10})\)	\(q-2.24698 q^{2} +1.24698 q^{3} +3.04892 q^{4} -3.80194 q^{5} -2.80194 q^{6} -1.00000 q^{7} -2.35690 q^{8} -1.44504 q^{9} +8.54288 q^{10} -1.89008 q^{11} +3.80194 q^{12} +0.911854 q^{13} +2.24698 q^{14} -4.74094 q^{15} -0.801938 q^{16} -3.91185 q^{17} +3.24698 q^{18} -6.76271 q^{19} -11.5918 q^{20} -1.24698 q^{21} +4.24698 q^{22} -0.335126 q^{23} -2.93900 q^{24} +9.45473 q^{25} -2.04892 q^{26} -5.54288 q^{27} -3.04892 q^{28} +7.67994 q^{29} +10.6528 q^{30} -1.46681 q^{31} +6.51573 q^{32} -2.35690 q^{33} +8.78986 q^{34} +3.80194 q^{35} -4.40581 q^{36} +3.08815 q^{37} +15.1957 q^{38} +1.13706 q^{39} +8.96077 q^{40} -10.3840 q^{41} +2.80194 q^{42} +9.51573 q^{43} -5.76271 q^{44} +5.49396 q^{45} +0.753020 q^{46} +7.76809 q^{47} -1.00000 q^{48} -6.00000 q^{49} -21.2446 q^{50} -4.87800 q^{51} +2.78017 q^{52} +4.89977 q^{53} +12.4547 q^{54} +7.18598 q^{55} +2.35690 q^{56} -8.43296 q^{57} -17.2567 q^{58} +8.36658 q^{59} -14.4547 q^{60} -8.23490 q^{61} +3.29590 q^{62} +1.44504 q^{63} -13.0368 q^{64} -3.46681 q^{65} +5.29590 q^{66} -13.6625 q^{67} -11.9269 q^{68} -0.417895 q^{69} -8.54288 q^{70} -9.96615 q^{71} +3.40581 q^{72} +8.70171 q^{73} -6.93900 q^{74} +11.7899 q^{75} -20.6189 q^{76} +1.89008 q^{77} -2.55496 q^{78} +9.50365 q^{79} +3.04892 q^{80} -2.57673 q^{81} +23.3327 q^{82} -3.71379 q^{83} -3.80194 q^{84} +14.8726 q^{85} -21.3817 q^{86} +9.57673 q^{87} +4.45473 q^{88} -12.0000 q^{89} -12.3448 q^{90} -0.911854 q^{91} -1.02177 q^{92} -1.82908 q^{93} -17.4547 q^{94} +25.7114 q^{95} +8.12498 q^{96} +4.07069 q^{97} +13.4819 q^{98} +2.73125 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 2 q^{2} - q^{3} - 7 q^{5} - 4 q^{6} - 3 q^{7} - 3 q^{8} - 4 q^{9}+O(q^{10}) \) 3 * q - 2 * q^2 - q^3 - 7 * q^5 - 4 * q^6 - 3 * q^7 - 3 * q^8 - 4 * q^9	\( 3 q - 2 q^{2} - q^{3} - 7 q^{5} - 4 q^{6} - 3 q^{7} - 3 q^{8} - 4 q^{9} + 7 q^{10} - 5 q^{11} + 7 q^{12} - q^{13} + 2 q^{14} + 2 q^{16} - 8 q^{17} + 5 q^{18} - 3 q^{19} - 7 q^{20} + q^{21} + 8 q^{22} + q^{24} + 6 q^{25} + 3 q^{26} + 2 q^{27} - q^{29} + 14 q^{30} - q^{31} + 7 q^{32} - 3 q^{33} + 3 q^{34} + 7 q^{35} + 13 q^{37} + 9 q^{38} - 2 q^{39} + 14 q^{40} - 21 q^{41} + 4 q^{42} + 16 q^{43} + 7 q^{45} + 7 q^{46} + 3 q^{47} - 3 q^{48} - 18 q^{49} - 18 q^{50} + 5 q^{51} + 7 q^{52} - 8 q^{53} + 15 q^{54} + 7 q^{55} + 3 q^{56} - 6 q^{57} - 25 q^{58} - q^{59} - 21 q^{60} - q^{61} - 4 q^{62} + 4 q^{63} - 11 q^{64} - 7 q^{65} + 2 q^{66} - q^{67} - 7 q^{68} - 7 q^{69} - 7 q^{70} - 14 q^{71} - 3 q^{72} - q^{73} - 11 q^{74} + 12 q^{75} - 28 q^{76} + 5 q^{77} - 8 q^{78} - 3 q^{79} - 5 q^{81} + 28 q^{82} - 3 q^{83} - 7 q^{84} + 28 q^{85} - 13 q^{86} + 26 q^{87} - 9 q^{88} - 36 q^{89} - 14 q^{90} + q^{91} + 5 q^{93} - 30 q^{94} + 28 q^{95} + 12 q^{98} + 16 q^{99}+O(q^{100}) \) 3 * q - 2 * q^2 - q^3 - 7 * q^5 - 4 * q^6 - 3 * q^7 - 3 * q^8 - 4 * q^9 + 7 * q^10 - 5 * q^11 + 7 * q^12 - q^13 + 2 * q^14 + 2 * q^16 - 8 * q^17 + 5 * q^18 - 3 * q^19 - 7 * q^20 + q^21 + 8 * q^22 + q^24 + 6 * q^25 + 3 * q^26 + 2 * q^27 - q^29 + 14 * q^30 - q^31 + 7 * q^32 - 3 * q^33 + 3 * q^34 + 7 * q^35 + 13 * q^37 + 9 * q^38 - 2 * q^39 + 14 * q^40 - 21 * q^41 + 4 * q^42 + 16 * q^43 + 7 * q^45 + 7 * q^46 + 3 * q^47 - 3 * q^48 - 18 * q^49 - 18 * q^50 + 5 * q^51 + 7 * q^52 - 8 * q^53 + 15 * q^54 + 7 * q^55 + 3 * q^56 - 6 * q^57 - 25 * q^58 - q^59 - 21 * q^60 - q^61 - 4 * q^62 + 4 * q^63 - 11 * q^64 - 7 * q^65 + 2 * q^66 - q^67 - 7 * q^68 - 7 * q^69 - 7 * q^70 - 14 * q^71 - 3 * q^72 - q^73 - 11 * q^74 + 12 * q^75 - 28 * q^76 + 5 * q^77 - 8 * q^78 - 3 * q^79 - 5 * q^81 + 28 * q^82 - 3 * q^83 - 7 * q^84 + 28 * q^85 - 13 * q^86 + 26 * q^87 - 9 * q^88 - 36 * q^89 - 14 * q^90 + q^91 + 5 * q^93 - 30 * q^94 + 28 * q^95 + 12 * q^98 + 16 * q^99

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