LMFDB - Embedded newform 2738.2.a.r.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2738,2,Mod(1,2738)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2738, 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("2738.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2738 = 2 \cdot 37^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2738.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:	$21.8630400734$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{36})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 6x^{4} + 9x^{2} - 3 $ x^6 - 6x^4 + 9x^2 - 3
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 74)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$1.96962$ of defining polynomial
Character	$\chi$	$=$	2738.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.53209 q^{3} +1.00000 q^{4} +3.07935 q^{5} -1.53209 q^{6} +0.199962 q^{7} -1.00000 q^{8} -0.652704 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.53209 q^{3} +1.00000 q^{4} +3.07935 q^{5} -1.53209 q^{6} +0.199962 q^{7} -1.00000 q^{8} -0.652704 q^{9} -3.07935 q^{10} +4.34349 q^{11} +1.53209 q^{12} +4.67033 q^{13} -0.199962 q^{14} +4.71783 q^{15} +1.00000 q^{16} +6.79623 q^{17} +0.652704 q^{18} +4.14257 q^{19} +3.07935 q^{20} +0.306359 q^{21} -4.34349 q^{22} +1.03567 q^{23} -1.53209 q^{24} +4.48238 q^{25} -4.67033 q^{26} -5.59627 q^{27} +0.199962 q^{28} -1.45420 q^{29} -4.71783 q^{30} -5.10852 q^{31} -1.00000 q^{32} +6.65461 q^{33} -6.79623 q^{34} +0.615752 q^{35} -0.652704 q^{36} -4.14257 q^{38} +7.15536 q^{39} -3.07935 q^{40} -4.75161 q^{41} -0.306359 q^{42} -0.399970 q^{43} +4.34349 q^{44} -2.00990 q^{45} -1.03567 q^{46} -8.20949 q^{47} +1.53209 q^{48} -6.96002 q^{49} -4.48238 q^{50} +10.4124 q^{51} +4.67033 q^{52} -11.2997 q^{53} +5.59627 q^{54} +13.3751 q^{55} -0.199962 q^{56} +6.34679 q^{57} +1.45420 q^{58} -4.19601 q^{59} +4.71783 q^{60} -10.5302 q^{61} +5.10852 q^{62} -0.130516 q^{63} +1.00000 q^{64} +14.3816 q^{65} -6.65461 q^{66} -8.71096 q^{67} +6.79623 q^{68} +1.58674 q^{69} -0.615752 q^{70} +14.1639 q^{71} +0.652704 q^{72} -7.27588 q^{73} +6.86740 q^{75} +4.14257 q^{76} +0.868532 q^{77} -7.15536 q^{78} +6.29548 q^{79} +3.07935 q^{80} -6.61587 q^{81} +4.75161 q^{82} +15.4158 q^{83} +0.306359 q^{84} +20.9279 q^{85} +0.399970 q^{86} -2.22796 q^{87} -4.34349 q^{88} -3.21429 q^{89} +2.00990 q^{90} +0.933888 q^{91} +1.03567 q^{92} -7.82671 q^{93} +8.20949 q^{94} +12.7564 q^{95} -1.53209 q^{96} -2.39427 q^{97} +6.96002 q^{98} -2.83501 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 6 q^{4} + 6 q^{5} - 6 q^{8} - 6 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 + 6 * q^4 + 6 * q^5 - 6 * q^8 - 6 * q^9	$ 6 q - 6 q^{2} + 6 q^{4} + 6 q^{5} - 6 q^{8} - 6 q^{9} - 6 q^{10} - 6 q^{11} + 12 q^{13} - 6 q^{15} + 6 q^{16} + 12 q^{17} + 6 q^{18} + 12 q^{19} + 6 q^{20} - 12 q^{21} + 6 q^{22} - 6 q^{23} + 6 q^{25} - 12 q^{26} - 6 q^{27} - 6 q^{29} + 6 q^{30} + 18 q^{31} - 6 q^{32} + 6 q^{33} - 12 q^{34} + 24 q^{35} - 6 q^{36} - 12 q^{38} + 6 q^{39} - 6 q^{40} - 12 q^{41} + 12 q^{42} - 6 q^{44} + 6 q^{45} + 6 q^{46} - 6 q^{47} - 12 q^{49} - 6 q^{50} + 24 q^{51} + 12 q^{52} - 24 q^{53} + 6 q^{54} + 36 q^{55} + 24 q^{57} + 6 q^{58} + 12 q^{59} - 6 q^{60} + 12 q^{61} - 18 q^{62} + 6 q^{63} + 6 q^{64} + 18 q^{65} - 6 q^{66} + 18 q^{67} + 12 q^{68} + 24 q^{69} - 24 q^{70} + 24 q^{71} + 6 q^{72} - 18 q^{75} + 12 q^{76} + 30 q^{77} - 6 q^{78} + 12 q^{79} + 6 q^{80} - 18 q^{81} + 12 q^{82} - 6 q^{83} - 12 q^{84} + 18 q^{85} + 6 q^{87} + 6 q^{88} - 6 q^{90} + 12 q^{91} - 6 q^{92} - 36 q^{93} + 6 q^{94} + 18 q^{95} - 12 q^{97} + 12 q^{98} + 12 q^{99}+O(q^{100}) $ 6 * q - 6 * q^2 + 6 * q^4 + 6 * q^5 - 6 * q^8 - 6 * q^9 - 6 * q^10 - 6 * q^11 + 12 * q^13 - 6 * q^15 + 6 * q^16 + 12 * q^17 + 6 * q^18 + 12 * q^19 + 6 * q^20 - 12 * q^21 + 6 * q^22 - 6 * q^23 + 6 * q^25 - 12 * q^26 - 6 * q^27 - 6 * q^29 + 6 * q^30 + 18 * q^31 - 6 * q^32 + 6 * q^33 - 12 * q^34 + 24 * q^35 - 6 * q^36 - 12 * q^38 + 6 * q^39 - 6 * q^40 - 12 * q^41 + 12 * q^42 - 6 * q^44 + 6 * q^45 + 6 * q^46 - 6 * q^47 - 12 * q^49 - 6 * q^50 + 24 * q^51 + 12 * q^52 - 24 * q^53 + 6 * q^54 + 36 * q^55 + 24 * q^57 + 6 * q^58 + 12 * q^59 - 6 * q^60 + 12 * q^61 - 18 * q^62 + 6 * q^63 + 6 * q^64 + 18 * q^65 - 6 * q^66 + 18 * q^67 + 12 * q^68 + 24 * q^69 - 24 * q^70 + 24 * q^71 + 6 * q^72 - 18 * q^75 + 12 * q^76 + 30 * q^77 - 6 * q^78 + 12 * q^79 + 6 * q^80 - 18 * q^81 + 12 * q^82 - 6 * q^83 - 12 * q^84 + 18 * q^85 + 6 * q^87 + 6 * q^88 - 6 * q^90 + 12 * q^91 - 6 * q^92 - 36 * q^93 + 6 * q^94 + 18 * q^95 - 12 * q^97 + 12 * q^98 + 12 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.53209	0.884552	0.442276	−	0.896879i	$-0.354171\pi$
$3$	1.53209	0.884552	0.442276	+	0.896879i	$0.354171\pi$
$4$	1.00000	0.500000
$5$	3.07935	1.37713	0.688563	−	0.725177i	$-0.258242\pi$
$5$	3.07935	1.37713	0.688563	+	0.725177i	$0.258242\pi$
$6$	−1.53209	−0.625473
$7$	0.199962	0.0755785	0.0377893	−	0.999286i	$-0.487968\pi$
$7$	0.199962	0.0755785	0.0377893	+	0.999286i	$0.487968\pi$
$8$	−1.00000	−0.353553
$9$	−0.652704	−0.217568
$10$	−3.07935	−0.973775
$11$	4.34349	1.30961	0.654805	−	0.755798i	$-0.272751\pi$
$11$	4.34349	1.30961	0.654805	+	0.755798i	$0.272751\pi$
$12$	1.53209	0.442276
$13$	4.67033	1.29532	0.647658	−	0.761931i	$-0.275748\pi$
$13$	4.67033	1.29532	0.647658	+	0.761931i	$0.275748\pi$
$14$	−0.199962	−0.0534421
$15$	4.71783	1.21814
$16$	1.00000	0.250000
$17$	6.79623	1.64833	0.824164	−	0.566352i	$-0.191646\pi$
$17$	6.79623	1.64833	0.824164	+	0.566352i	$0.191646\pi$
$18$	0.652704	0.153844
$19$	4.14257	0.950371	0.475186	−	0.879886i	$-0.342381\pi$
$19$	4.14257	0.950371	0.475186	+	0.879886i	$0.342381\pi$
$20$	3.07935	0.688563
$21$	0.306359	0.0668531
$22$	−4.34349	−0.926035
$23$	1.03567	0.215952	0.107976	−	0.994154i	$-0.465563\pi$
$23$	1.03567	0.215952	0.107976	+	0.994154i	$0.465563\pi$
$24$	−1.53209	−0.312736
$25$	4.48238	0.896476
$26$	−4.67033	−0.915927
$27$	−5.59627	−1.07700
$28$	0.199962	0.0377893
$29$	−1.45420	−0.270038	−0.135019	−	0.990843i	$-0.543110\pi$
$29$	−1.45420	−0.270038	−0.135019	+	0.990843i	$0.543110\pi$
$30$	−4.71783	−0.861355
$31$	−5.10852	−0.917518	−0.458759	−	0.888561i	$-0.651706\pi$
$31$	−5.10852	−0.917518	−0.458759	+	0.888561i	$0.651706\pi$
$32$	−1.00000	−0.176777
$33$	6.65461	1.15842
$34$	−6.79623	−1.16554
$35$	0.615752	0.104081
$36$	−0.652704	−0.108784
$37$	0	0
$37$	0	0
$38$	−4.14257	−0.672014
$39$	7.15536	1.14577
$40$	−3.07935	−0.486888
$41$	−4.75161	−0.742077	−0.371038	−	0.928617i	$-0.620998\pi$
$41$	−4.75161	−0.742077	−0.371038	+	0.928617i	$0.620998\pi$
$42$	−0.306359	−0.0472723
$43$	−0.399970	−0.0609948	−0.0304974	−	0.999535i	$-0.509709\pi$
$43$	−0.399970	−0.0609948	−0.0304974	+	0.999535i	$0.509709\pi$
$44$	4.34349	0.654805
$45$	−2.00990	−0.299618
$46$	−1.03567	−0.152701
$47$	−8.20949	−1.19748	−0.598739	−	0.800944i	$-0.704331\pi$
$47$	−8.20949	−1.19748	−0.598739	+	0.800944i	$0.704331\pi$
$48$	1.53209	0.221138
$49$	−6.96002	−0.994288
$50$	−4.48238	−0.633904
$51$	10.4124	1.45803
$52$	4.67033	0.647658
$53$	−11.2997	−1.55213	−0.776065	−	0.630653i	$-0.782787\pi$
$53$	−11.2997	−1.55213	−0.776065	+	0.630653i	$0.782787\pi$
$54$	5.59627	0.761555
$55$	13.3751	1.80350
$56$	−0.199962	−0.0267210
$57$	6.34679	0.840653
$58$	1.45420	0.190946
$59$	−4.19601	−0.546274	−0.273137	−	0.961975i	$-0.588061\pi$
$59$	−4.19601	−0.546274	−0.273137	+	0.961975i	$0.588061\pi$
$60$	4.71783	0.609070
$61$	−10.5302	−1.34825	−0.674126	−	0.738616i	$-0.735480\pi$
$61$	−10.5302	−1.34825	−0.674126	+	0.738616i	$0.735480\pi$
$62$	5.10852	0.648783
$63$	−0.130516	−0.0164435
$64$	1.00000	0.125000
$65$	14.3816	1.78381
$66$	−6.65461	−0.819126
$67$	−8.71096	−1.06421	−0.532107	−	0.846677i	$-0.678600\pi$
$67$	−8.71096	−1.06421	−0.532107	+	0.846677i	$0.678600\pi$
$68$	6.79623	0.824164
$69$	1.58674	0.191021
$70$	−0.615752	−0.0735965
$71$	14.1639	1.68095	0.840473	−	0.541854i	$-0.182277\pi$
$71$	14.1639	1.68095	0.840473	+	0.541854i	$0.182277\pi$
$72$	0.652704	0.0769219
$73$	−7.27588	−0.851577	−0.425789	−	0.904823i	$-0.640003\pi$
$73$	−7.27588	−0.851577	−0.425789	+	0.904823i	$0.640003\pi$
$74$	0	0
$75$	6.86740	0.792979
$76$	4.14257	0.475186
$77$	0.868532	0.0989784
$78$	−7.15536	−0.810185
$79$	6.29548	0.708296	0.354148	−	0.935189i	$-0.384771\pi$
$79$	6.29548	0.708296	0.354148	+	0.935189i	$0.384771\pi$
$80$	3.07935	0.344281
$81$	−6.61587	−0.735096
$82$	4.75161	0.524728
$83$	15.4158	1.69210	0.846051	−	0.533102i	$-0.178974\pi$
$83$	15.4158	1.69210	0.846051	+	0.533102i	$0.178974\pi$
$84$	0.306359	0.0334266
$85$	20.9279	2.26995
$86$	0.399970	0.0431298
$87$	−2.22796	−0.238863
$88$	−4.34349	−0.463017
$89$	−3.21429	−0.340714	−0.170357	−	0.985382i	$-0.554492\pi$
$89$	−3.21429	−0.340714	−0.170357	+	0.985382i	$0.554492\pi$
$90$	2.00990	0.211862
$91$	0.933888	0.0978981
$92$	1.03567	0.107976
$93$	−7.82671	−0.811592
$94$	8.20949	0.846744
$95$	12.7564	1.30878
$96$	−1.53209	−0.156368
$97$	−2.39427	−0.243101	−0.121551	−	0.992585i	$-0.538787\pi$
$97$	−2.39427	−0.243101	−0.121551	+	0.992585i	$0.538787\pi$
$98$	6.96002	0.703068
$99$	−2.83501	−0.284929
$100$	4.48238	0.448238
$101$	10.9630	1.09086	0.545429	−	0.838157i	$-0.316367\pi$
$101$	10.9630	1.09086	0.545429	+	0.838157i	$0.316367\pi$
$102$	−10.4124	−1.03098
$103$	15.7356	1.55048	0.775238	−	0.631670i	$-0.217630\pi$
$103$	15.7356	1.55048	0.775238	+	0.631670i	$0.217630\pi$
$104$	−4.67033	−0.457964
$105$	0.943387	0.0920652
$106$	11.2997	1.09752
$107$	−18.6160	−1.79968	−0.899838	−	0.436225i	$-0.856315\pi$
$107$	−18.6160	−1.79968	−0.899838	+	0.436225i	$0.856315\pi$
$108$	−5.59627	−0.538501
$109$	−0.00702336	−0.000672715 0	−0.000336358	−	1.00000i	$-0.500107\pi$
$109$	−0.00702336	−0.000672715 0	−0.000336358		1.00000i	$0.500107\pi$
$110$	−13.3751	−1.27527
$111$	0	0
$112$	0.199962	0.0188946
$113$	2.56262	0.241071	0.120535	−	0.992709i	$-0.461539\pi$
$113$	2.56262	0.241071	0.120535	+	0.992709i	$0.461539\pi$
$114$	−6.34679	−0.594431
$115$	3.18918	0.297393
$116$	−1.45420	−0.135019
$117$	−3.04834	−0.281819
$118$	4.19601	0.386274
$119$	1.35899	0.124578
$120$	−4.71783	−0.430677
$121$	7.86588	0.715080
$122$	10.5302	0.953358
$123$	−7.27989	−0.656406
$124$	−5.10852	−0.458759
$125$	−1.59393	−0.142566
$126$	0.130516	0.0116273
$127$	−5.80702	−0.515289	−0.257645	−	0.966240i	$-0.582946\pi$
$127$	−5.80702	−0.515289	−0.257645	+	0.966240i	$0.582946\pi$
$128$	−1.00000	−0.0883883
$129$	−0.612789	−0.0539531
$130$	−14.3816	−1.26135
$131$	8.36959	0.731254	0.365627	−	0.930761i	$-0.380855\pi$
$131$	8.36959	0.731254	0.365627	+	0.930761i	$0.380855\pi$
$132$	6.65461	0.579209
$133$	0.828357	0.0718276
$134$	8.71096	0.752513
$135$	−17.2328	−1.48317
$136$	−6.79623	−0.582772
$137$	−1.57799	−0.134817	−0.0674084	−	0.997725i	$-0.521473\pi$
$137$	−1.57799	−0.134817	−0.0674084	+	0.997725i	$0.521473\pi$
$138$	−1.58674	−0.135072
$139$	−9.92368	−0.841716	−0.420858	−	0.907127i	$-0.638271\pi$
$139$	−9.92368	−0.841716	−0.420858	+	0.907127i	$0.638271\pi$
$140$	0.615752	0.0520406
$141$	−12.5777	−1.05923
$142$	−14.1639	−1.18861
$143$	20.2855	1.69636
$144$	−0.652704	−0.0543920
$145$	−4.47799	−0.371877
$146$	7.27588	0.602156
$147$	−10.6634	−0.879499
$148$	0	0
$149$	12.8504	1.05274	0.526372	−	0.850254i	$-0.323552\pi$
$149$	12.8504	1.05274	0.526372	+	0.850254i	$0.323552\pi$
$150$	−6.86740	−0.560721
$151$	−5.18633	−0.422058	−0.211029	−	0.977480i	$-0.567681\pi$
$151$	−5.18633	−0.422058	−0.211029	+	0.977480i	$0.567681\pi$
$152$	−4.14257	−0.336007
$153$	−4.43592	−0.358623
$154$	−0.868532	−0.0699883
$155$	−15.7309	−1.26354
$156$	7.15536	0.572887
$157$	11.9635	0.954795	0.477398	−	0.878687i	$-0.341580\pi$
$157$	11.9635	0.954795	0.477398	+	0.878687i	$0.341580\pi$
$158$	−6.29548	−0.500841
$159$	−17.3121	−1.37294
$160$	−3.07935	−0.243444
$161$	0.207094	0.0163213
$162$	6.61587	0.519792
$163$	0.706906	0.0553691	0.0276846	−	0.999617i	$-0.491187\pi$
$163$	0.706906	0.0553691	0.0276846	+	0.999617i	$0.491187\pi$
$164$	−4.75161	−0.371038
$165$	20.4918	1.59529
$166$	−15.4158	−1.19650
$167$	−6.60985	−0.511486	−0.255743	−	0.966745i	$-0.582320\pi$
$167$	−6.60985	−0.511486	−0.255743	+	0.966745i	$0.582320\pi$
$168$	−0.306359	−0.0236361
$169$	8.81198	0.677845
$170$	−20.9279	−1.60510
$171$	−2.70387	−0.206770
$172$	−0.399970	−0.0304974
$173$	−15.4016	−1.17096	−0.585482	−	0.810685i	$-0.699095\pi$
$173$	−15.4016	−1.17096	−0.585482	+	0.810685i	$0.699095\pi$
$174$	2.22796	0.168902
$175$	0.896305	0.0677543
$176$	4.34349	0.327403
$177$	−6.42866	−0.483208
$178$	3.21429	0.240922
$179$	−2.55438	−0.190923	−0.0954617	−	0.995433i	$-0.530433\pi$
$179$	−2.55438	−0.190923	−0.0954617	+	0.995433i	$0.530433\pi$
$180$	−2.00990	−0.149809
$181$	8.38797	0.623473	0.311736	−	0.950169i	$-0.399089\pi$
$181$	8.38797	0.623473	0.311736	+	0.950169i	$0.399089\pi$
$182$	−0.933888	−0.0692244
$183$	−16.1332	−1.19260
$184$	−1.03567	−0.0763505
$185$	0	0
$186$	7.82671	0.573882
$187$	29.5193	2.15867
$188$	−8.20949	−0.598739
$189$	−1.11904	−0.0813982
$190$	−12.7564	−0.925448
$191$	−6.48182	−0.469008	−0.234504	−	0.972115i	$-0.575347\pi$
$191$	−6.48182	−0.469008	−0.234504	+	0.972115i	$0.575347\pi$
$192$	1.53209	0.110569
$193$	−20.9828	−1.51037	−0.755186	−	0.655511i	$-0.772453\pi$
$193$	−20.9828	−1.51037	−0.755186	+	0.655511i	$0.772453\pi$
$194$	2.39427	0.171898
$195$	22.0338	1.57788
$196$	−6.96002	−0.497144
$197$	−1.65809	−0.118134	−0.0590672	−	0.998254i	$-0.518813\pi$
$197$	−1.65809	−0.118134	−0.0590672	+	0.998254i	$0.518813\pi$
$198$	2.83501	0.201475
$199$	7.21981	0.511799	0.255900	−	0.966703i	$-0.417628\pi$
$199$	7.21981	0.511799	0.255900	+	0.966703i	$0.417628\pi$
$200$	−4.48238	−0.316952
$201$	−13.3460	−0.941352
$202$	−10.9630	−0.771354
$203$	−0.290785	−0.0204091
$204$	10.4124	0.729016
$205$	−14.6319	−1.02193
$206$	−15.7356	−1.09635
$207$	−0.675985	−0.0469842
$208$	4.67033	0.323829
$209$	17.9932	1.24462
$210$	−0.943387	−0.0650999
$211$	4.50868	0.310390	0.155195	−	0.987884i	$-0.450399\pi$
$211$	4.50868	0.310390	0.155195	+	0.987884i	$0.450399\pi$
$212$	−11.2997	−0.776065
$213$	21.7003	1.48688
$214$	18.6160	1.27256
$215$	−1.23165	−0.0839975
$216$	5.59627	0.380778
$217$	−1.02151	−0.0693446
$218$	0.00702336	0.000475682 0
$219$	−11.1473	−0.753264
$220$	13.3751	0.901749
$221$	31.7406	2.13511
$222$	0	0
$223$	13.6418	0.913526	0.456763	−	0.889588i	$-0.349009\pi$
$223$	13.6418	0.913526	0.456763	+	0.889588i	$0.349009\pi$
$224$	−0.199962	−0.0133605
$225$	−2.92567	−0.195044
$226$	−2.56262	−0.170463
$227$	27.2382	1.80786	0.903931	−	0.427679i	$-0.140669\pi$
$227$	27.2382	1.80786	0.903931	+	0.427679i	$0.140669\pi$
$228$	6.34679	0.420326
$229$	2.03796	0.134672	0.0673362	−	0.997730i	$-0.478550\pi$
$229$	2.03796	0.134672	0.0673362	+	0.997730i	$0.478550\pi$
$230$	−3.18918	−0.210289
$231$	1.33067	0.0875515
$232$	1.45420	0.0954729
$233$	3.88495	0.254511	0.127256	−	0.991870i	$-0.459383\pi$
$233$	3.88495	0.254511	0.127256	+	0.991870i	$0.459383\pi$
$234$	3.04834	0.199276
$235$	−25.2799	−1.64908
$236$	−4.19601	−0.273137
$237$	9.64523	0.626525
$238$	−1.35899	−0.0880900
$239$	−18.5705	−1.20123	−0.600613	−	0.799540i	$-0.705077\pi$
$239$	−18.5705	−1.20123	−0.600613	+	0.799540i	$0.705077\pi$
$240$	4.71783	0.304535
$241$	25.3378	1.63215	0.816074	−	0.577947i	$-0.196146\pi$
$241$	25.3378	1.63215	0.816074	+	0.577947i	$0.196146\pi$
$242$	−7.86588	−0.505638
$243$	6.65270	0.426771
$244$	−10.5302	−0.674126
$245$	−21.4323	−1.36926
$246$	7.27989	0.464149
$247$	19.3472	1.23103
$248$	5.10852	0.324392
$249$	23.6184	1.49675
$250$	1.59393	0.100809
$251$	−12.7123	−0.802394	−0.401197	−	0.915992i	$-0.631406\pi$
$251$	−12.7123	−0.802394	−0.401197	+	0.915992i	$0.631406\pi$
$252$	−0.130516	−0.00822173
$253$	4.49841	0.282813
$254$	5.80702	0.364365
$255$	32.0635	2.00789
$256$	1.00000	0.0625000
$257$	−4.34710	−0.271165	−0.135582	−	0.990766i	$-0.543291\pi$
$257$	−4.34710	−0.271165	−0.135582	+	0.990766i	$0.543291\pi$
$258$	0.612789	0.0381506
$259$	0	0
$260$	14.3816	0.891907
$261$	0.949162	0.0587517
$262$	−8.36959	−0.517075
$263$	6.51139	0.401509	0.200755	−	0.979642i	$-0.435661\pi$
$263$	6.51139	0.401509	0.200755	+	0.979642i	$0.435661\pi$
$264$	−6.65461	−0.409563
$265$	−34.7956	−2.13748
$266$	−0.828357	−0.0507898
$267$	−4.92458	−0.301380
$268$	−8.71096	−0.532107
$269$	−9.90213	−0.603743	−0.301872	−	0.953349i	$-0.597611\pi$
$269$	−9.90213	−0.603743	−0.301872	+	0.953349i	$0.597611\pi$
$270$	17.2328	1.04876
$271$	9.02508	0.548235	0.274117	−	0.961696i	$-0.411614\pi$
$271$	9.02508	0.548235	0.274117	+	0.961696i	$0.411614\pi$
$272$	6.79623	0.412082
$273$	1.43080	0.0865959
$274$	1.57799	0.0953298
$275$	19.4692	1.17403
$276$	1.58674	0.0955103
$277$	0.208088	0.0125028	0.00625138	−	0.999980i	$-0.498010\pi$
$277$	0.208088	0.0125028	0.00625138	+	0.999980i	$0.498010\pi$
$278$	9.92368	0.595183
$279$	3.33435	0.199622
$280$	−0.615752	−0.0367982
$281$	−27.0593	−1.61422	−0.807111	−	0.590400i	$-0.798970\pi$
$281$	−27.0593	−1.61422	−0.807111	+	0.590400i	$0.798970\pi$
$282$	12.5777	0.748989
$283$	0.812894	0.0483215	0.0241608	−	0.999708i	$-0.492309\pi$
$283$	0.812894	0.0483215	0.0241608	+	0.999708i	$0.492309\pi$
$284$	14.1639	0.840473
$285$	19.5440	1.15768
$286$	−20.2855	−1.19951
$287$	−0.950141	−0.0560851
$288$	0.652704	0.0384609
$289$	29.1887	1.71698
$290$	4.47799	0.262957
$291$	−3.66823	−0.215036
$292$	−7.27588	−0.425789
$293$	−8.79957	−0.514076	−0.257038	−	0.966401i	$-0.582747\pi$
$293$	−8.79957	−0.514076	−0.257038	+	0.966401i	$0.582747\pi$
$294$	10.6634	0.621900
$295$	−12.9210	−0.752288
$296$	0	0
$297$	−24.3073	−1.41045
$298$	−12.8504	−0.744403
$299$	4.83691	0.279726
$300$	6.86740	0.396490
$301$	−0.0799787	−0.00460989
$302$	5.18633	0.298440
$303$	16.7963	0.964921
$304$	4.14257	0.237593
$305$	−32.4261	−1.85671
$306$	4.43592	0.253585
$307$	−24.4541	−1.39567	−0.697836	−	0.716258i	$-0.745854\pi$
$307$	−24.4541	−1.39567	−0.697836	+	0.716258i	$0.745854\pi$
$308$	0.868532	0.0494892
$309$	24.1083	1.37148
$310$	15.7309	0.893456
$311$	−0.0126953	−0.000719885 0	−0.000359942	−	1.00000i	$-0.500115\pi$
$311$	−0.0126953	−0.000719885 0	−0.000359942		1.00000i	$0.500115\pi$
$312$	−7.15536	−0.405093
$313$	17.4684	0.987375	0.493687	−	0.869639i	$-0.335649\pi$
$313$	17.4684	0.987375	0.493687	+	0.869639i	$0.335649\pi$
$314$	−11.9635	−0.675142
$315$	−0.401904	−0.0226447
$316$	6.29548	0.354148
$317$	−2.72890	−0.153270	−0.0766352	−	0.997059i	$-0.524418\pi$
$317$	−2.72890	−0.153270	−0.0766352	+	0.997059i	$0.524418\pi$
$318$	17.3121	0.970815
$319$	−6.31630	−0.353645
$320$	3.07935	0.172141
$321$	−28.5213	−1.59191
$322$	−0.207094	−0.0115409
$323$	28.1539	1.56652
$324$	−6.61587	−0.367548
$325$	20.9342	1.16122
$326$	−0.706906	−0.0391519
$327$	−0.0107604	−0.000595052 0
$328$	4.75161	0.262364
$329$	−1.64159	−0.0905036
$330$	−20.4918	−1.12804
$331$	23.6161	1.29806	0.649028	−	0.760765i	$-0.275176\pi$
$331$	23.6161	1.29806	0.649028	+	0.760765i	$0.275176\pi$
$332$	15.4158	0.846051
$333$	0	0
$334$	6.60985	0.361675
$335$	−26.8241	−1.46556
$336$	0.306359	0.0167133
$337$	22.4456	1.22269	0.611345	−	0.791364i	$-0.290629\pi$
$337$	22.4456	1.22269	0.611345	+	0.791364i	$0.290629\pi$
$338$	−8.81198	−0.479308
$339$	3.92616	0.213240
$340$	20.9279	1.13498
$341$	−22.1888	−1.20159
$342$	2.70387	0.146209
$343$	−2.79147	−0.150725
$344$	0.399970	0.0215649
$345$	4.88611	0.263059
$346$	15.4016	0.827997
$347$	−1.21511	−0.0652306	−0.0326153	−	0.999468i	$-0.510384\pi$
$347$	−1.21511	−0.0652306	−0.0326153	+	0.999468i	$0.510384\pi$
$348$	−2.22796	−0.119431
$349$	17.7395	0.949573	0.474786	−	0.880101i	$-0.342525\pi$
$349$	17.7395	0.949573	0.474786	+	0.880101i	$0.342525\pi$
$350$	−0.896305	−0.0479095
$351$	−26.1364	−1.39506
$352$	−4.34349	−0.231509
$353$	−1.60606	−0.0854818	−0.0427409	−	0.999086i	$-0.513609\pi$
$353$	−1.60606	−0.0854818	−0.0427409	+	0.999086i	$0.513609\pi$
$354$	6.42866	0.341680
$355$	43.6156	2.31487
$356$	−3.21429	−0.170357
$357$	2.08209	0.110196
$358$	2.55438	0.135003
$359$	−32.0124	−1.68955	−0.844775	−	0.535121i	$-0.820266\pi$
$359$	−32.0124	−1.68955	−0.844775	+	0.535121i	$0.820266\pi$
$360$	2.00990	0.105931
$361$	−1.83909	−0.0967942
$362$	−8.38797	−0.440862
$363$	12.0512	0.632525
$364$	0.933888	0.0489490
$365$	−22.4050	−1.17273
$366$	16.1332	0.843295
$367$	16.0363	0.837088	0.418544	−	0.908197i	$-0.362541\pi$
$367$	16.0363	0.837088	0.418544	+	0.908197i	$0.362541\pi$
$368$	1.03567	0.0539880
$369$	3.10139	0.161452
$370$	0	0
$371$	−2.25951	−0.117308
$372$	−7.82671	−0.405796
$373$	1.11639	0.0578043	0.0289022	−	0.999582i	$-0.490799\pi$
$373$	1.11639	0.0578043	0.0289022	+	0.999582i	$0.490799\pi$
$374$	−29.5193	−1.52641
$375$	−2.44205	−0.126107
$376$	8.20949	0.423372
$377$	−6.79160	−0.349785
$378$	1.11904	0.0575572
$379$	36.4410	1.87185	0.935924	−	0.352201i	$-0.114567\pi$
$379$	36.4410	1.87185	0.935924	+	0.352201i	$0.114567\pi$
$380$	12.7564	0.654391
$381$	−8.89686	−0.455800
$382$	6.48182	0.331639
$383$	−6.03086	−0.308162	−0.154081	−	0.988058i	$-0.549242\pi$
$383$	−6.03086	−0.308162	−0.154081	+	0.988058i	$0.549242\pi$
$384$	−1.53209	−0.0781841
$385$	2.67451	0.136306
$386$	20.9828	1.06799
$387$	0.261062	0.0132705
$388$	−2.39427	−0.121551
$389$	18.8329	0.954867	0.477434	−	0.878668i	$-0.341567\pi$
$389$	18.8329	0.954867	0.477434	+	0.878668i	$0.341567\pi$
$390$	−22.0338	−1.11573
$391$	7.03864	0.355959
$392$	6.96002	0.351534
$393$	12.8229	0.646832
$394$	1.65809	0.0835336
$395$	19.3860	0.975413
$396$	−2.83501	−0.142465
$397$	−27.5114	−1.38076	−0.690378	−	0.723449i	$-0.742556\pi$
$397$	−27.5114	−1.38076	−0.690378	+	0.723449i	$0.742556\pi$
$398$	−7.21981	−0.361897
$399$	1.26912	0.0635353
$400$	4.48238	0.224119
$401$	−22.0721	−1.10223	−0.551114	−	0.834430i	$-0.685797\pi$
$401$	−22.0721	−1.10223	−0.551114	+	0.834430i	$0.685797\pi$
$402$	13.3460	0.665637
$403$	−23.8585	−1.18848
$404$	10.9630	0.545429
$405$	−20.3726	−1.01232
$406$	0.290785	0.0144314
$407$	0	0
$408$	−10.4124	−0.515492
$409$	−1.42090	−0.0702591	−0.0351296	−	0.999383i	$-0.511184\pi$
$409$	−1.42090	−0.0702591	−0.0351296	+	0.999383i	$0.511184\pi$
$410$	14.6319	0.722616
$411$	−2.41762	−0.119252
$412$	15.7356	0.775238
$413$	−0.839043	−0.0412866
$414$	0.675985	0.0332228
$415$	47.4706	2.33024
$416$	−4.67033	−0.228982
$417$	−15.2040	−0.744541
$418$	−17.9932	−0.880077
$419$	−13.6400	−0.666358	−0.333179	−	0.942864i	$-0.608121\pi$
$419$	−13.6400	−0.666358	−0.333179	+	0.942864i	$0.608121\pi$
$420$	0.943387	0.0460326
$421$	−27.9978	−1.36453	−0.682264	−	0.731106i	$-0.739005\pi$
$421$	−27.9978	−1.36453	−0.682264	+	0.731106i	$0.739005\pi$
$422$	−4.50868	−0.219479
$423$	5.35837	0.260533
$424$	11.2997	0.548761
$425$	30.4633	1.47769
$426$	−21.7003	−1.05139
$427$	−2.10564	−0.101899
$428$	−18.6160	−0.899838
$429$	31.0792	1.50052
$430$	1.23165	0.0593952
$431$	−2.84949	−0.137255	−0.0686275	−	0.997642i	$-0.521862\pi$
$431$	−2.84949	−0.137255	−0.0686275	+	0.997642i	$0.521862\pi$
$432$	−5.59627	−0.269251
$433$	−31.1352	−1.49626	−0.748130	−	0.663552i	$-0.769048\pi$
$433$	−31.1352	−1.49626	−0.748130	+	0.663552i	$0.769048\pi$
$434$	1.02151	0.0490341
$435$	−6.86068	−0.328944
$436$	−0.00702336	−0.000336358 0
$437$	4.29033	0.205234
$438$	11.1473	0.532638
$439$	−28.7800	−1.37359	−0.686796	−	0.726850i	$-0.740984\pi$
$439$	−28.7800	−1.37359	−0.686796	+	0.726850i	$0.740984\pi$
$440$	−13.3751	−0.637633
$441$	4.54283	0.216325
$442$	−31.7406	−1.50975
$443$	19.3903	0.921259	0.460630	−	0.887592i	$-0.347624\pi$
$443$	19.3903	0.921259	0.460630	+	0.887592i	$0.347624\pi$
$444$	0	0
$445$	−9.89793	−0.469207
$446$	−13.6418	−0.645960
$447$	19.6879	0.931208
$448$	0.199962	0.00944731
$449$	−17.0799	−0.806052	−0.403026	−	0.915188i	$-0.632042\pi$
$449$	−17.0799	−0.806052	−0.403026	+	0.915188i	$0.632042\pi$
$450$	2.92567	0.137917
$451$	−20.6386	−0.971832
$452$	2.56262	0.120535
$453$	−7.94592	−0.373332
$454$	−27.2382	−1.27835
$455$	2.87577	0.134818
$456$	−6.34679	−0.297216
$457$	2.41654	0.113041	0.0565206	−	0.998401i	$-0.481999\pi$
$457$	2.41654	0.113041	0.0565206	+	0.998401i	$0.481999\pi$
$458$	−2.03796	−0.0952278
$459$	−38.0335	−1.77525
$460$	3.18918	0.148696
$461$	−18.7400	−0.872808	−0.436404	−	0.899751i	$-0.643748\pi$
$461$	−18.7400	−0.872808	−0.436404	+	0.899751i	$0.643748\pi$
$462$	−1.33067	−0.0619083
$463$	5.15947	0.239781	0.119890	−	0.992787i	$-0.461746\pi$
$463$	5.15947	0.239781	0.119890	+	0.992787i	$0.461746\pi$
$464$	−1.45420	−0.0675096
$465$	−24.1012	−1.11766
$466$	−3.88495	−0.179967
$467$	30.9314	1.43134	0.715668	−	0.698441i	$-0.246122\pi$
$467$	30.9314	1.43134	0.715668	+	0.698441i	$0.246122\pi$
$468$	−3.04834	−0.140910
$469$	−1.74186	−0.0804317
$470$	25.2799	1.16607
$471$	18.3292	0.844566
$472$	4.19601	0.193137
$473$	−1.73726	−0.0798794
$474$	−9.64523	−0.443020
$475$	18.5686	0.851985
$476$	1.35899	0.0622891
$477$	7.37534	0.337694
$478$	18.5705	0.849395
$479$	−12.8783	−0.588425	−0.294212	−	0.955740i	$-0.595057\pi$
$479$	−12.8783	−0.588425	−0.294212	+	0.955740i	$0.595057\pi$
$480$	−4.71783	−0.215339
$481$	0	0
$482$	−25.3378	−1.15410
$483$	0.317287	0.0144371
$484$	7.86588	0.357540
$485$	−7.37278	−0.334781
$486$	−6.65270	−0.301773
$487$	17.2601	0.782130	0.391065	−	0.920363i	$-0.372107\pi$
$487$	17.2601	0.782130	0.391065	+	0.920363i	$0.372107\pi$
$488$	10.5302	0.476679
$489$	1.08304	0.0489769
$490$	21.4323	0.968213
$491$	17.1066	0.772011	0.386005	−	0.922496i	$-0.373855\pi$
$491$	17.1066	0.772011	0.386005	+	0.922496i	$0.373855\pi$
$492$	−7.27989	−0.328203
$493$	−9.88308	−0.445111
$494$	−19.3472	−0.870471
$495$	−8.72998	−0.392383
$496$	−5.10852	−0.229379
$497$	2.83224	0.127043
$498$	−23.6184	−1.05836
$499$	18.5412	0.830020	0.415010	−	0.909817i	$-0.363778\pi$
$499$	18.5412	0.830020	0.415010	+	0.909817i	$0.363778\pi$
$500$	−1.59393	−0.0712829
$501$	−10.1269	−0.452436
$502$	12.7123	0.567378
$503$	3.35590	0.149632	0.0748162	−	0.997197i	$-0.476163\pi$
$503$	3.35590	0.149632	0.0748162	+	0.997197i	$0.476163\pi$
$504$	0.130516	0.00581364
$505$	33.7589	1.50225
$506$	−4.49841	−0.199979
$507$	13.5007	0.599589
$508$	−5.80702	−0.257645
$509$	11.0197	0.488441	0.244221	−	0.969720i	$-0.421468\pi$
$509$	11.0197	0.488441	0.244221	+	0.969720i	$0.421468\pi$
$510$	−32.0635	−1.41979
$511$	−1.45490	−0.0643609
$512$	−1.00000	−0.0441942
$513$	−23.1829	−1.02355
$514$	4.34710	0.191742
$515$	48.4554	2.13520
$516$	−0.612789	−0.0269765
$517$	−35.6578	−1.56823
$518$	0	0
$519$	−23.5967	−1.03578
$520$	−14.3816	−0.630673
$521$	7.83217	0.343134	0.171567	−	0.985172i	$-0.445117\pi$
$521$	7.83217	0.343134	0.171567	+	0.985172i	$0.445117\pi$
$522$	−0.949162	−0.0415437
$523$	−1.81284	−0.0792700	−0.0396350	−	0.999214i	$-0.512620\pi$
$523$	−1.81284	−0.0792700	−0.0396350	+	0.999214i	$0.512620\pi$
$524$	8.36959	0.365627
$525$	1.37322	0.0599322
$526$	−6.51139	−0.283910
$527$	−34.7187	−1.51237
$528$	6.65461	0.289605
$529$	−21.9274	−0.953365
$530$	34.7956	1.51143
$531$	2.73875	0.118852
$532$	0.828357	0.0359138
$533$	−22.1916	−0.961224
$534$	4.92458	0.213108
$535$	−57.3251	−2.47838
$536$	8.71096	0.376256
$537$	−3.91354	−0.168882
$538$	9.90213	0.426911
$539$	−30.2307	−1.30213
$540$	−17.2328	−0.741584
$541$	6.95357	0.298958	0.149479	−	0.988765i	$-0.452240\pi$
$541$	6.95357	0.298958	0.149479	+	0.988765i	$0.452240\pi$
$542$	−9.02508	−0.387660
$543$	12.8511	0.551494
$544$	−6.79623	−0.291386
$545$	−0.0216274	−0.000926414 0
$546$	−1.43080	−0.0612326
$547$	−4.86631	−0.208068	−0.104034	−	0.994574i	$-0.533175\pi$
$547$	−4.86631	−0.208068	−0.104034	+	0.994574i	$0.533175\pi$
$548$	−1.57799	−0.0674084
$549$	6.87309	0.293336
$550$	−19.4692	−0.830168
$551$	−6.02413	−0.256637
$552$	−1.58674	−0.0675360
$553$	1.25886	0.0535320
$554$	−0.208088	−0.00884079
$555$	0	0
$556$	−9.92368	−0.420858
$557$	−7.28236	−0.308563	−0.154282	−	0.988027i	$-0.549306\pi$
$557$	−7.28236	−0.308563	−0.154282	+	0.988027i	$0.549306\pi$
$558$	−3.33435	−0.141154
$559$	−1.86799	−0.0790075
$560$	0.615752	0.0260203
$561$	45.2262	1.90945
$562$	27.0593	1.14143
$563$	27.6116	1.16369	0.581845	−	0.813300i	$-0.302331\pi$
$563$	27.6116	1.16369	0.581845	+	0.813300i	$0.302331\pi$
$564$	−12.5777	−0.529616
$565$	7.89119	0.331985
$566$	−0.812894	−0.0341685
$567$	−1.32292	−0.0555575
$568$	−14.1639	−0.594304
$569$	−5.64776	−0.236766	−0.118383	−	0.992968i	$-0.537771\pi$
$569$	−5.64776	−0.236766	−0.118383	+	0.992968i	$0.537771\pi$
$570$	−19.5440	−0.818607
$571$	13.4951	0.564753	0.282377	−	0.959304i	$-0.408877\pi$
$571$	13.4951	0.564753	0.282377	+	0.959304i	$0.408877\pi$
$572$	20.2855	0.848180
$573$	−9.93073	−0.414862
$574$	0.950141	0.0396581
$575$	4.64226	0.193596
$576$	−0.652704	−0.0271960
$577$	42.1146	1.75326	0.876628	−	0.481169i	$-0.159788\pi$
$577$	42.1146	1.75326	0.876628	+	0.481169i	$0.159788\pi$
$578$	−29.1887	−1.21409
$579$	−32.1475	−1.33600
$580$	−4.47799	−0.185938
$581$	3.08257	0.127887
$582$	3.66823	0.152053
$583$	−49.0800	−2.03269
$584$	7.27588	0.301078
$585$	−9.38690	−0.388101
$586$	8.79957	0.363507
$587$	−41.4835	−1.71221	−0.856104	−	0.516804i	$-0.827121\pi$
$587$	−41.4835	−1.71221	−0.856104	+	0.516804i	$0.827121\pi$
$588$	−10.6634	−0.439750
$589$	−21.1624	−0.871983
$590$	12.9210	0.531948
$591$	−2.54035	−0.104496
$592$	0	0
$593$	−29.6746	−1.21859	−0.609295	−	0.792944i	$-0.708548\pi$
$593$	−29.6746	−1.21859	−0.609295	+	0.792944i	$0.708548\pi$
$594$	24.3073	0.997341
$595$	4.18479	0.171560
$596$	12.8504	0.526372
$597$	11.0614	0.452713
$598$	−4.83691	−0.197796
$599$	−4.48941	−0.183432	−0.0917162	−	0.995785i	$-0.529235\pi$
$599$	−4.48941	−0.183432	−0.0917162	+	0.995785i	$0.529235\pi$
$600$	−6.86740	−0.280361
$601$	−14.2046	−0.579419	−0.289710	−	0.957115i	$-0.593559\pi$
$601$	−14.2046	−0.579419	−0.289710	+	0.957115i	$0.593559\pi$
$602$	0.0799787	0.00325969
$603$	5.68568	0.231539
$604$	−5.18633	−0.211029
$605$	24.2218	0.984755
$606$	−16.7963	−0.682302
$607$	25.2743	1.02585	0.512926	−	0.858433i	$-0.328562\pi$
$607$	25.2743	1.02585	0.512926	+	0.858433i	$0.328562\pi$
$608$	−4.14257	−0.168004
$609$	−0.445508	−0.0180529
$610$	32.4261	1.31289
$611$	−38.3410	−1.55111
$612$	−4.43592	−0.179312
$613$	−1.47148	−0.0594326	−0.0297163	−	0.999558i	$-0.509460\pi$
$613$	−1.47148	−0.0594326	−0.0297163	+	0.999558i	$0.509460\pi$
$614$	24.4541	0.986889
$615$	−22.4173	−0.903953
$616$	−0.868532	−0.0349942
$617$	15.6742	0.631020	0.315510	−	0.948922i	$-0.397824\pi$
$617$	15.6742	0.631020	0.315510	+	0.948922i	$0.397824\pi$
$618$	−24.1083	−0.969780
$619$	−40.3039	−1.61995	−0.809974	−	0.586465i	$-0.800519\pi$
$619$	−40.3039	−1.61995	−0.809974	+	0.586465i	$0.800519\pi$
$620$	−15.7309	−0.631769
$621$	−5.79588	−0.232581
$622$	0.0126953	0.000509035 0
$623$	−0.642736	−0.0257507
$624$	7.15536	0.286444
$625$	−27.3202	−1.09281
$626$	−17.4684	−0.698179
$627$	27.5672	1.10093
$628$	11.9635	0.477398
$629$	0	0
$630$	0.401904	0.0160122
$631$	29.5332	1.17570	0.587848	−	0.808971i	$-0.299975\pi$
$631$	29.5332	1.17570	0.587848	+	0.808971i	$0.299975\pi$
$632$	−6.29548	−0.250421
$633$	6.90770	0.274556
$634$	2.72890	0.108379
$635$	−17.8818	−0.709618
$636$	−17.3121	−0.686470
$637$	−32.5056	−1.28792
$638$	6.31630	0.250065
$639$	−9.24483	−0.365720
$640$	−3.07935	−0.121722
$641$	−23.8544	−0.942191	−0.471096	−	0.882082i	$-0.656141\pi$
$641$	−23.8544	−0.942191	−0.471096	+	0.882082i	$0.656141\pi$
$642$	28.5213	1.12565
$643$	20.1057	0.792891	0.396445	−	0.918058i	$-0.370244\pi$
$643$	20.1057	0.792891	0.396445	+	0.918058i	$0.370244\pi$
$644$	0.207094	0.00816066
$645$	−1.88699	−0.0743002
$646$	−28.1539	−1.10770
$647$	−15.5440	−0.611099	−0.305549	−	0.952176i	$-0.598840\pi$
$647$	−15.5440	−0.611099	−0.305549	+	0.952176i	$0.598840\pi$
$648$	6.61587	0.259896
$649$	−18.2253	−0.715407
$650$	−20.9342	−0.821106
$651$	−1.56504	−0.0613389
$652$	0.706906	0.0276846
$653$	3.24230	0.126881	0.0634404	−	0.997986i	$-0.479793\pi$
$653$	3.24230	0.126881	0.0634404	+	0.997986i	$0.479793\pi$
$654$	0.0107604	0.000420765 0
$655$	25.7729	1.00703
$656$	−4.75161	−0.185519
$657$	4.74899	0.185276
$658$	1.64159	0.0639957
$659$	14.1540	0.551360	0.275680	−	0.961250i	$-0.411097\pi$
$659$	14.1540	0.551360	0.275680	+	0.961250i	$0.411097\pi$
$660$	20.4918	0.797644
$661$	47.1036	1.83212	0.916059	−	0.401044i	$-0.131353\pi$
$661$	47.1036	1.83212	0.916059	+	0.401044i	$0.131353\pi$
$662$	−23.6161	−0.917864
$663$	48.6295	1.88861
$664$	−15.4158	−0.598248
$665$	2.55080	0.0989157
$666$	0	0
$667$	−1.50607	−0.0583153
$668$	−6.60985	−0.255743
$669$	20.9005	0.808061
$670$	26.8241	1.03630
$671$	−45.7377	−1.76568
$672$	−0.306359	−0.0118181
$673$	−4.88924	−0.188466	−0.0942332	−	0.995550i	$-0.530040\pi$
$673$	−4.88924	−0.188466	−0.0942332	+	0.995550i	$0.530040\pi$
$674$	−22.4456	−0.864573
$675$	−25.0846	−0.965506
$676$	8.81198	0.338922
$677$	−5.90249	−0.226851	−0.113426	−	0.993546i	$-0.536182\pi$
$677$	−5.90249	−0.226851	−0.113426	+	0.993546i	$0.536182\pi$
$678$	−3.92616	−0.150783
$679$	−0.478763	−0.0183732
$680$	−20.9279	−0.802550
$681$	41.7313	1.59915
$682$	22.1888	0.849653
$683$	22.6465	0.866544	0.433272	−	0.901263i	$-0.357359\pi$
$683$	22.6465	0.866544	0.433272	+	0.901263i	$0.357359\pi$
$684$	−2.70387	−0.103385
$685$	−4.85918	−0.185660
$686$	2.79147	0.106579
$687$	3.12234	0.119125
$688$	−0.399970	−0.0152487
$689$	−52.7732	−2.01050
$690$	−4.88611	−0.186011
$691$	−41.8846	−1.59336	−0.796682	−	0.604398i	$-0.793414\pi$
$691$	−41.8846	−1.59336	−0.796682	+	0.604398i	$0.793414\pi$
$692$	−15.4016	−0.585482
$693$	−0.566894	−0.0215345
$694$	1.21511	0.0461250
$695$	−30.5585	−1.15915
$696$	2.22796	0.0844508
$697$	−32.2930	−1.22319
$698$	−17.7395	−0.671449
$699$	5.95209	0.225129
$700$	0.896305	0.0338771
$701$	−8.86456	−0.334810	−0.167405	−	0.985888i	$-0.553539\pi$
$701$	−8.86456	−0.334810	−0.167405	+	0.985888i	$0.553539\pi$
$702$	26.1364	0.986455
$703$	0	0
$704$	4.34349	0.163701
$705$	−38.7310	−1.45869
$706$	1.60606	0.0604448
$707$	2.19218	0.0824455
$708$	−6.42866	−0.241604
$709$	45.8415	1.72161	0.860807	−	0.508931i	$-0.169959\pi$
$709$	45.8415	1.72161	0.860807	+	0.508931i	$0.169959\pi$
$710$	−43.6156	−1.63686
$711$	−4.10908	−0.154103
$712$	3.21429	0.120461
$713$	−5.29074	−0.198140
$714$	−2.08209	−0.0779202
$715$	62.4661	2.33610
$716$	−2.55438	−0.0954617
$717$	−28.4517	−1.06255
$718$	32.0124	1.19469
$719$	−6.49120	−0.242081	−0.121040	−	0.992648i	$-0.538623\pi$
$719$	−6.49120	−0.242081	−0.121040	+	0.992648i	$0.538623\pi$
$720$	−2.00990	−0.0749046
$721$	3.14652	0.117183
$722$	1.83909	0.0684439
$723$	38.8197	1.44372
$724$	8.38797	0.311736
$725$	−6.51828	−0.242083
$726$	−12.0512	−0.447263
$727$	26.6650	0.988951	0.494476	−	0.869192i	$-0.335360\pi$
$727$	26.6650	0.988951	0.494476	+	0.869192i	$0.335360\pi$
$728$	−0.933888	−0.0346122
$729$	30.0401	1.11260
$730$	22.4050	0.829245
$731$	−2.71828	−0.100539
$732$	−16.1332	−0.596299
$733$	48.8996	1.80615	0.903075	−	0.429484i	$-0.141304\pi$
$733$	48.8996	1.80615	0.903075	+	0.429484i	$0.141304\pi$
$734$	−16.0363	−0.591910
$735$	−32.8362	−1.21118
$736$	−1.03567	−0.0381753
$737$	−37.8360	−1.39371
$738$	−3.10139	−0.114164
$739$	53.7875	1.97861	0.989303	−	0.145878i	$-0.0466006\pi$
$739$	53.7875	1.97861	0.989303	+	0.145878i	$0.0466006\pi$
$740$	0	0
$741$	29.6416	1.08891
$742$	2.25951	0.0829491
$743$	22.4907	0.825104	0.412552	−	0.910934i	$-0.364637\pi$
$743$	22.4907	0.825104	0.412552	+	0.910934i	$0.364637\pi$
$744$	7.82671	0.286941
$745$	39.5708	1.44976
$746$	−1.11639	−0.0408738
$747$	−10.0619	−0.368147
$748$	29.5193	1.07933
$749$	−3.72249	−0.136017
$750$	2.44205	0.0891711
$751$	−7.12554	−0.260015	−0.130007	−	0.991513i	$-0.541500\pi$
$751$	−7.12554	−0.260015	−0.130007	+	0.991513i	$0.541500\pi$
$752$	−8.20949	−0.299369
$753$	−19.4764	−0.709759
$754$	6.79160	0.247335
$755$	−15.9705	−0.581226
$756$	−1.11904	−0.0406991
$757$	−5.41741	−0.196899	−0.0984495	−	0.995142i	$-0.531388\pi$
$757$	−5.41741	−0.196899	−0.0984495	+	0.995142i	$0.531388\pi$
$758$	−36.4410	−1.32360
$759$	6.89197	0.250163
$760$	−12.7564	−0.462724
$761$	−25.7999	−0.935246	−0.467623	−	0.883928i	$-0.654890\pi$
$761$	−25.7999	−0.935246	−0.467623	+	0.883928i	$0.654890\pi$
$762$	8.89686	0.322299
$763$	−0.00140440	−5.08428e−5 0
$764$	−6.48182	−0.234504
$765$	−13.6597	−0.493869
$766$	6.03086	0.217904
$767$	−19.5968	−0.707598
$768$	1.53209	0.0552845
$769$	1.92534	0.0694296	0.0347148	−	0.999397i	$-0.488948\pi$
$769$	1.92534	0.0694296	0.0347148	+	0.999397i	$0.488948\pi$
$770$	−2.67451	−0.0963827
$771$	−6.66015	−0.239859
$772$	−20.9828	−0.755186
$773$	27.3985	0.985455	0.492727	−	0.870184i	$-0.336000\pi$
$773$	27.3985	0.985455	0.492727	+	0.870184i	$0.336000\pi$
$774$	−0.261062	−0.00938366
$775$	−22.8983	−0.822533
$776$	2.39427	0.0859492
$777$	0	0
$778$	−18.8329	−0.675193
$779$	−19.6839	−0.705249
$780$	22.0338	0.788938
$781$	61.5207	2.20138
$782$	−7.03864	−0.251701
$783$	8.13809	0.290832
$784$	−6.96002	−0.248572
$785$	36.8399	1.31487
$786$	−12.8229	−0.457379
$787$	−35.5331	−1.26662	−0.633309	−	0.773899i	$-0.718304\pi$
$787$	−35.5331	−1.26662	−0.633309	+	0.773899i	$0.718304\pi$
$788$	−1.65809	−0.0590672
$789$	9.97602	0.355156
$790$	−19.3860	−0.689721
$791$	0.512426	0.0182198
$792$	2.83501	0.100738
$793$	−49.1794	−1.74641
$794$	27.5114	0.976342
$795$	−53.3100	−1.89071
$796$	7.21981	0.255900
$797$	−51.3638	−1.81940	−0.909699	−	0.415269i	$-0.863688\pi$
$797$	−51.3638	−1.81940	−0.909699	+	0.415269i	$0.863688\pi$
$798$	−1.26912	−0.0449262
$799$	−55.7936	−1.97384
$800$	−4.48238	−0.158476
$801$	2.09798	0.0741285
$802$	22.0721	0.779392
$803$	−31.6027	−1.11523
$804$	−13.3460	−0.470676
$805$	0.637715	0.0224765
$806$	23.8585	0.840379
$807$	−15.1709	−0.534042
$808$	−10.9630	−0.385677
$809$	16.6586	0.585684	0.292842	−	0.956161i	$-0.405399\pi$
$809$	16.6586	0.585684	0.292842	+	0.956161i	$0.405399\pi$
$810$	20.3726	0.715818
$811$	−34.1029	−1.19751	−0.598757	−	0.800931i	$-0.704339\pi$
$811$	−34.1029	−1.19751	−0.598757	+	0.800931i	$0.704339\pi$
$812$	−0.290785	−0.0102045
$813$	13.8272	0.484942
$814$	0	0
$815$	2.17681	0.0762503
$816$	10.4124	0.364508
$817$	−1.65690	−0.0579677
$818$	1.42090	0.0496807
$819$	−0.609552	−0.0212995
$820$	−14.6319	−0.510967
$821$	21.6278	0.754816	0.377408	−	0.926047i	$-0.376815\pi$
$821$	21.6278	0.754816	0.377408	+	0.926047i	$0.376815\pi$
$822$	2.41762	0.0843242
$823$	22.4604	0.782920	0.391460	−	0.920195i	$-0.371970\pi$
$823$	22.4604	0.782920	0.391460	+	0.920195i	$0.371970\pi$
$824$	−15.7356	−0.548176
$825$	29.8285	1.03849
$826$	0.839043	0.0291940
$827$	32.9258	1.14494	0.572472	−	0.819924i	$-0.305985\pi$
$827$	32.9258	1.14494	0.572472	+	0.819924i	$0.305985\pi$
$828$	−0.675985	−0.0234921
$829$	18.3840	0.638501	0.319251	−	0.947670i	$-0.396569\pi$
$829$	18.3840	0.638501	0.319251	+	0.947670i	$0.396569\pi$
$830$	−47.4706	−1.64773
$831$	0.318809	0.0110593
$832$	4.67033	0.161915
$833$	−47.3019	−1.63891
$834$	15.2040	0.526470
$835$	−20.3540	−0.704380
$836$	17.9932	0.622308
$837$	28.5887	0.988169
$838$	13.6400	0.471186
$839$	−11.2213	−0.387401	−0.193701	−	0.981061i	$-0.562049\pi$
$839$	−11.2213	−0.387401	−0.193701	+	0.981061i	$0.562049\pi$
$840$	−0.943387	−0.0325499
$841$	−26.8853	−0.927079
$842$	27.9978	0.964868
$843$	−41.4572	−1.42786
$844$	4.50868	0.155195
$845$	27.1351	0.933477
$846$	−5.35837	−0.184224
$847$	1.57288	0.0540447
$848$	−11.2997	−0.388033
$849$	1.24543	0.0427429
$850$	−30.4633	−1.04488
$851$	0	0
$852$	21.7003	0.743442
$853$	−0.0974550	−0.00333680	−0.00166840	−	0.999999i	$-0.500531\pi$
$853$	−0.0974550	−0.00333680	−0.00166840	+	0.999999i	$0.500531\pi$
$854$	2.10564	0.0720534
$855$	−8.32616	−0.284749
$856$	18.6160	0.636281
$857$	−27.1799	−0.928447	−0.464223	−	0.885718i	$-0.653667\pi$
$857$	−27.1799	−0.928447	−0.464223	+	0.885718i	$0.653667\pi$
$858$	−31.0792	−1.06103
$859$	16.1327	0.550442	0.275221	−	0.961381i	$-0.411249\pi$
$859$	16.1327	0.550442	0.275221	+	0.961381i	$0.411249\pi$
$860$	−1.23165	−0.0419987
$861$	−1.45570	−0.0496102
$862$	2.84949	0.0970539
$863$	41.7582	1.42146	0.710732	−	0.703463i	$-0.248364\pi$
$863$	41.7582	1.42146	0.710732	+	0.703463i	$0.248364\pi$
$864$	5.59627	0.190389
$865$	−47.4270	−1.61257
$866$	31.1352	1.05802
$867$	44.7197	1.51876
$868$	−1.02151	−0.0346723
$869$	27.3443	0.927592
$870$	6.86068	0.232599
$871$	−40.6831	−1.37849
$872$	0.00702336	0.000237841 0
$873$	1.56275	0.0528910
$874$	−4.29033	−0.145123
$875$	−0.318726	−0.0107749
$876$	−11.1473	−0.376632
$877$	13.0499	0.440665	0.220332	−	0.975425i	$-0.429286\pi$
$877$	13.0499	0.440665	0.220332	+	0.975425i	$0.429286\pi$
$878$	28.7800	0.971277
$879$	−13.4817	−0.454727
$880$	13.3751	0.450875
$881$	10.4442	0.351875	0.175938	−	0.984401i	$-0.443704\pi$
$881$	10.4442	0.351875	0.175938	+	0.984401i	$0.443704\pi$
$882$	−4.54283	−0.152965
$883$	32.3018	1.08704	0.543520	−	0.839396i	$-0.317091\pi$
$883$	32.3018	1.08704	0.543520	+	0.839396i	$0.317091\pi$
$884$	31.7406	1.06755
$885$	−19.7961	−0.665438
$886$	−19.3903	−0.651429
$887$	9.33190	0.313334	0.156667	−	0.987651i	$-0.449925\pi$
$887$	9.33190	0.313334	0.156667	+	0.987651i	$0.449925\pi$
$888$	0	0
$889$	−1.16118	−0.0389448
$890$	9.89793	0.331779
$891$	−28.7359	−0.962690
$892$	13.6418	0.456763
$893$	−34.0084	−1.13805
$894$	−19.6879	−0.658463
$895$	−7.86583	−0.262926
$896$	−0.199962	−0.00668026
$897$	7.41058	0.247432
$898$	17.0799	0.569965
$899$	7.42882	0.247765
$900$	−2.92567	−0.0975222
$901$	−76.7952	−2.55842
$902$	20.6386	0.687189
$903$	−0.122534	−0.00407769
$904$	−2.56262	−0.0852314
$905$	25.8295	0.858601
$906$	7.94592	0.263985
$907$	31.7333	1.05369	0.526843	−	0.849963i	$-0.323376\pi$
$907$	31.7333	1.05369	0.526843	+	0.849963i	$0.323376\pi$
$908$	27.2382	0.903931
$909$	−7.15559	−0.237336
$910$	−2.87577	−0.0953307
$911$	−47.0729	−1.55959	−0.779797	−	0.626033i	$-0.784678\pi$
$911$	−47.0729	−1.55959	−0.779797	+	0.626033i	$0.784678\pi$
$912$	6.34679	0.210163
$913$	66.9583	2.21599
$914$	−2.41654	−0.0799322
$915$	−49.6797	−1.64236
$916$	2.03796	0.0673362
$917$	1.67360	0.0552671
$918$	38.0335	1.25529
$919$	36.4389	1.20201	0.601004	−	0.799246i	$-0.294767\pi$
$919$	36.4389	1.20201	0.601004	+	0.799246i	$0.294767\pi$
$920$	−3.18918	−0.105144
$921$	−37.4659	−1.23454
$922$	18.7400	0.617169
$923$	66.1501	2.17736
$924$	1.33067	0.0437758
$925$	0	0
$926$	−5.15947	−0.169551
$927$	−10.2707	−0.337334
$928$	1.45420	0.0477365
$929$	−34.2969	−1.12524	−0.562622	−	0.826715i	$-0.690207\pi$
$929$	−34.2969	−1.12524	−0.562622	+	0.826715i	$0.690207\pi$
$930$	24.1012	0.790308
$931$	−28.8324	−0.944943
$932$	3.88495	0.127256
$933$	−0.0194503	−0.000636775 0
$934$	−30.9314	−1.01211
$935$	90.9003	2.97276
$936$	3.04834	0.0996381
$937$	−5.44402	−0.177848	−0.0889242	−	0.996038i	$-0.528343\pi$
$937$	−5.44402	−0.177848	−0.0889242	+	0.996038i	$0.528343\pi$
$938$	1.74186	0.0568738
$939$	26.7632	0.873384
$940$	−25.2799	−0.824539
$941$	−40.0282	−1.30488	−0.652441	−	0.757839i	$-0.726255\pi$
$941$	−40.0282	−1.30488	−0.652441	+	0.757839i	$0.726255\pi$
$942$	−18.3292	−0.597198
$943$	−4.92109	−0.160253
$944$	−4.19601	−0.136569
$945$	−3.44591	−0.112096
$946$	1.73726	0.0564833
$947$	−35.1144	−1.14106	−0.570532	−	0.821275i	$-0.693263\pi$
$947$	−35.1144	−1.14106	−0.570532	+	0.821275i	$0.693263\pi$
$948$	9.64523	0.313262
$949$	−33.9808	−1.10306
$950$	−18.5686	−0.602444
$951$	−4.18092	−0.135576
$952$	−1.35899	−0.0440450
$953$	9.02673	0.292405	0.146202	−	0.989255i	$-0.453295\pi$
$953$	9.02673	0.292405	0.146202	+	0.989255i	$0.453295\pi$
$954$	−7.37534	−0.238786
$955$	−19.9598	−0.645883
$956$	−18.5705	−0.600613
$957$	−9.67713	−0.312817
$958$	12.8783	0.416079
$959$	−0.315538	−0.0101892
$960$	4.71783	0.152267
$961$	−4.90299	−0.158161
$962$	0	0
$963$	12.1507	0.391552
$964$	25.3378	0.816074
$965$	−64.6132	−2.07997
$966$	−0.317287	−0.0102085
$967$	−38.8473	−1.24925	−0.624623	−	0.780927i	$-0.714747\pi$
$967$	−38.8473	−1.24925	−0.624623	+	0.780927i	$0.714747\pi$
$968$	−7.86588	−0.252819
$969$	43.1342	1.38567
$970$	7.37278	0.236726
$971$	−26.4600	−0.849142	−0.424571	−	0.905395i	$-0.639575\pi$
$971$	−26.4600	−0.849142	−0.424571	+	0.905395i	$0.639575\pi$
$972$	6.65270	0.213386
$973$	−1.98436	−0.0636156
$974$	−17.2601	−0.553050
$975$	32.0730	1.02716
$976$	−10.5302	−0.337063
$977$	−55.2016	−1.76606	−0.883028	−	0.469320i	$-0.844499\pi$
$977$	−55.2016	−1.76606	−0.883028	+	0.469320i	$0.844499\pi$
$978$	−1.08304	−0.0346319
$979$	−13.9612	−0.446203
$980$	−21.4323	−0.684630
$981$	0.00458417	0.000146361 0
$982$	−17.1066	−0.545894
$983$	29.7000	0.947283	0.473641	−	0.880718i	$-0.342939\pi$
$983$	29.7000	0.947283	0.473641	+	0.880718i	$0.342939\pi$
$984$	7.27989	0.232074
$985$	−5.10585	−0.162686
$986$	9.88308	0.314741
$987$	−2.51506	−0.0800551
$988$	19.3472	0.615516
$989$	−0.414236	−0.0131719
$990$	8.72998	0.277457
$991$	20.1762	0.640917	0.320458	−	0.947263i	$-0.396163\pi$
$991$	20.1762	0.640917	0.320458	+	0.947263i	$0.396163\pi$
$992$	5.10852	0.162196
$993$	36.1819	1.14820
$994$	−2.83224	−0.0898332
$995$	22.2323	0.704812
$996$	23.6184	0.748376
$997$	−36.9911	−1.17152	−0.585759	−	0.810485i	$-0.699204\pi$
$997$	−36.9911	−1.17152	−0.585759	+	0.810485i	$0.699204\pi$
$998$	−18.5412	−0.586913
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2738.2.a.r.1.6		6
37.2	odd	36		74.2.h.a.41.1	✓	12
37.19	odd	36		74.2.h.a.65.1	yes	12
37.36	even	2		2738.2.a.s.1.5		6
111.2	even	36		666.2.bj.c.559.2		12
111.56	even	36		666.2.bj.c.361.2		12
148.19	even	36		592.2.bq.b.65.1		12
148.39	even	36		592.2.bq.b.337.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.h.a.41.1	✓	12	37.2	odd	36
74.2.h.a.65.1	yes	12	37.19	odd	36
592.2.bq.b.65.1		12	148.19	even	36
592.2.bq.b.337.1		12	148.39	even	36
666.2.bj.c.361.2		12	111.56	even	36
666.2.bj.c.559.2		12	111.2	even	36
2738.2.a.r.1.6		6	1.1	even	1	trivial
2738.2.a.s.1.5		6	37.36	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:	\( N \)	\(=\)	\( 2738 = 2 \cdot 37^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2738.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.53209 q^{3} +1.00000 q^{4} +3.07935 q^{5} -1.53209 q^{6} +0.199962 q^{7} -1.00000 q^{8} -0.652704 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.53209 q^{3} +1.00000 q^{4} +3.07935 q^{5} -1.53209 q^{6} +0.199962 q^{7} -1.00000 q^{8} -0.652704 q^{9} -3.07935 q^{10} +4.34349 q^{11} +1.53209 q^{12} +4.67033 q^{13} -0.199962 q^{14} +4.71783 q^{15} +1.00000 q^{16} +6.79623 q^{17} +0.652704 q^{18} +4.14257 q^{19} +3.07935 q^{20} +0.306359 q^{21} -4.34349 q^{22} +1.03567 q^{23} -1.53209 q^{24} +4.48238 q^{25} -4.67033 q^{26} -5.59627 q^{27} +0.199962 q^{28} -1.45420 q^{29} -4.71783 q^{30} -5.10852 q^{31} -1.00000 q^{32} +6.65461 q^{33} -6.79623 q^{34} +0.615752 q^{35} -0.652704 q^{36} -4.14257 q^{38} +7.15536 q^{39} -3.07935 q^{40} -4.75161 q^{41} -0.306359 q^{42} -0.399970 q^{43} +4.34349 q^{44} -2.00990 q^{45} -1.03567 q^{46} -8.20949 q^{47} +1.53209 q^{48} -6.96002 q^{49} -4.48238 q^{50} +10.4124 q^{51} +4.67033 q^{52} -11.2997 q^{53} +5.59627 q^{54} +13.3751 q^{55} -0.199962 q^{56} +6.34679 q^{57} +1.45420 q^{58} -4.19601 q^{59} +4.71783 q^{60} -10.5302 q^{61} +5.10852 q^{62} -0.130516 q^{63} +1.00000 q^{64} +14.3816 q^{65} -6.65461 q^{66} -8.71096 q^{67} +6.79623 q^{68} +1.58674 q^{69} -0.615752 q^{70} +14.1639 q^{71} +0.652704 q^{72} -7.27588 q^{73} +6.86740 q^{75} +4.14257 q^{76} +0.868532 q^{77} -7.15536 q^{78} +6.29548 q^{79} +3.07935 q^{80} -6.61587 q^{81} +4.75161 q^{82} +15.4158 q^{83} +0.306359 q^{84} +20.9279 q^{85} +0.399970 q^{86} -2.22796 q^{87} -4.34349 q^{88} -3.21429 q^{89} +2.00990 q^{90} +0.933888 q^{91} +1.03567 q^{92} -7.82671 q^{93} +8.20949 q^{94} +12.7564 q^{95} -1.53209 q^{96} -2.39427 q^{97} +6.96002 q^{98} -2.83501 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 6 q^{4} + 6 q^{5} - 6 q^{8} - 6 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 + 6 * q^4 + 6 * q^5 - 6 * q^8 - 6 * q^9	\( 6 q - 6 q^{2} + 6 q^{4} + 6 q^{5} - 6 q^{8} - 6 q^{9} - 6 q^{10} - 6 q^{11} + 12 q^{13} - 6 q^{15} + 6 q^{16} + 12 q^{17} + 6 q^{18} + 12 q^{19} + 6 q^{20} - 12 q^{21} + 6 q^{22} - 6 q^{23} + 6 q^{25} - 12 q^{26} - 6 q^{27} - 6 q^{29} + 6 q^{30} + 18 q^{31} - 6 q^{32} + 6 q^{33} - 12 q^{34} + 24 q^{35} - 6 q^{36} - 12 q^{38} + 6 q^{39} - 6 q^{40} - 12 q^{41} + 12 q^{42} - 6 q^{44} + 6 q^{45} + 6 q^{46} - 6 q^{47} - 12 q^{49} - 6 q^{50} + 24 q^{51} + 12 q^{52} - 24 q^{53} + 6 q^{54} + 36 q^{55} + 24 q^{57} + 6 q^{58} + 12 q^{59} - 6 q^{60} + 12 q^{61} - 18 q^{62} + 6 q^{63} + 6 q^{64} + 18 q^{65} - 6 q^{66} + 18 q^{67} + 12 q^{68} + 24 q^{69} - 24 q^{70} + 24 q^{71} + 6 q^{72} - 18 q^{75} + 12 q^{76} + 30 q^{77} - 6 q^{78} + 12 q^{79} + 6 q^{80} - 18 q^{81} + 12 q^{82} - 6 q^{83} - 12 q^{84} + 18 q^{85} + 6 q^{87} + 6 q^{88} - 6 q^{90} + 12 q^{91} - 6 q^{92} - 36 q^{93} + 6 q^{94} + 18 q^{95} - 12 q^{97} + 12 q^{98} + 12 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + 6 * q^4 + 6 * q^5 - 6 * q^8 - 6 * q^9 - 6 * q^10 - 6 * q^11 + 12 * q^13 - 6 * q^15 + 6 * q^16 + 12 * q^17 + 6 * q^18 + 12 * q^19 + 6 * q^20 - 12 * q^21 + 6 * q^22 - 6 * q^23 + 6 * q^25 - 12 * q^26 - 6 * q^27 - 6 * q^29 + 6 * q^30 + 18 * q^31 - 6 * q^32 + 6 * q^33 - 12 * q^34 + 24 * q^35 - 6 * q^36 - 12 * q^38 + 6 * q^39 - 6 * q^40 - 12 * q^41 + 12 * q^42 - 6 * q^44 + 6 * q^45 + 6 * q^46 - 6 * q^47 - 12 * q^49 - 6 * q^50 + 24 * q^51 + 12 * q^52 - 24 * q^53 + 6 * q^54 + 36 * q^55 + 24 * q^57 + 6 * q^58 + 12 * q^59 - 6 * q^60 + 12 * q^61 - 18 * q^62 + 6 * q^63 + 6 * q^64 + 18 * q^65 - 6 * q^66 + 18 * q^67 + 12 * q^68 + 24 * q^69 - 24 * q^70 + 24 * q^71 + 6 * q^72 - 18 * q^75 + 12 * q^76 + 30 * q^77 - 6 * q^78 + 12 * q^79 + 6 * q^80 - 18 * q^81 + 12 * q^82 - 6 * q^83 - 12 * q^84 + 18 * q^85 + 6 * q^87 + 6 * q^88 - 6 * q^90 + 12 * q^91 - 6 * q^92 - 36 * q^93 + 6 * q^94 + 18 * q^95 - 12 * q^97 + 12 * q^98 + 12 * q^99

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