LMFDB - Embedded newform 2738.2.a.u.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:	$1$
Dimension:	$9$
Coefficient field:	$\Q(\zeta_{38})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - x^{8} - 8x^{7} + 7x^{6} + 21x^{5} - 15x^{4} - 20x^{3} + 10x^{2} + 5x - 1 $ x^9 - x^8 - 8x^7 + 7x^6 + 21x^5 - 15x^4 - 20x^3 + 10x^2 + 5*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$1.97272$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -0.605558 q^{3} +1.00000 q^{4} -2.32729 q^{5} +0.605558 q^{6} +0.184773 q^{7} -1.00000 q^{8} -2.63330 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.605558 q^{3} +1.00000 q^{4} -2.32729 q^{5} +0.605558 q^{6} +0.184773 q^{7} -1.00000 q^{8} -2.63330 q^{9} +2.32729 q^{10} -3.42659 q^{11} -0.605558 q^{12} -0.254348 q^{13} -0.184773 q^{14} +1.40931 q^{15} +1.00000 q^{16} +5.79927 q^{17} +2.63330 q^{18} +1.20251 q^{19} -2.32729 q^{20} -0.111891 q^{21} +3.42659 q^{22} +8.62984 q^{23} +0.605558 q^{24} +0.416259 q^{25} +0.254348 q^{26} +3.41129 q^{27} +0.184773 q^{28} +5.85911 q^{29} -1.40931 q^{30} +2.37990 q^{31} -1.00000 q^{32} +2.07500 q^{33} -5.79927 q^{34} -0.430020 q^{35} -2.63330 q^{36} -1.20251 q^{38} +0.154022 q^{39} +2.32729 q^{40} -8.31493 q^{41} +0.111891 q^{42} -1.32703 q^{43} -3.42659 q^{44} +6.12844 q^{45} -8.62984 q^{46} +8.89664 q^{47} -0.605558 q^{48} -6.96586 q^{49} -0.416259 q^{50} -3.51179 q^{51} -0.254348 q^{52} +12.0093 q^{53} -3.41129 q^{54} +7.97466 q^{55} -0.184773 q^{56} -0.728191 q^{57} -5.85911 q^{58} -11.9163 q^{59} +1.40931 q^{60} -4.60897 q^{61} -2.37990 q^{62} -0.486563 q^{63} +1.00000 q^{64} +0.591940 q^{65} -2.07500 q^{66} -12.9078 q^{67} +5.79927 q^{68} -5.22587 q^{69} +0.430020 q^{70} -7.10570 q^{71} +2.63330 q^{72} -15.1625 q^{73} -0.252069 q^{75} +1.20251 q^{76} -0.633141 q^{77} -0.154022 q^{78} -11.5695 q^{79} -2.32729 q^{80} +5.83416 q^{81} +8.31493 q^{82} +8.49365 q^{83} -0.111891 q^{84} -13.4965 q^{85} +1.32703 q^{86} -3.54803 q^{87} +3.42659 q^{88} -5.98605 q^{89} -6.12844 q^{90} -0.0469966 q^{91} +8.62984 q^{92} -1.44117 q^{93} -8.89664 q^{94} -2.79859 q^{95} +0.605558 q^{96} -1.35210 q^{97} +6.96586 q^{98} +9.02324 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 9 q^{2} - 7 q^{3} + 9 q^{4} + 7 q^{5} + 7 q^{6} - 14 q^{7} - 9 q^{8} + 8 q^{9}+O(q^{10}) $ 9 * q - 9 * q^2 - 7 * q^3 + 9 * q^4 + 7 * q^5 + 7 * q^6 - 14 * q^7 - 9 * q^8 + 8 * q^9	\( 9 q - 9 q^{2} - 7 q^{3} + 9 q^{4} + 7 q^{5} + 7 q^{6} - 14 q^{7} - 9 q^{8} + 8 q^{9} - 7 q^{10} - q^{11} - 7 q^{12} + 3 q^{13} + 14 q^{14} - 16 q^{15} + 9 q^{16} + 10 q^{17} - 8 q^{18} + 9 q^{19} + 7 q^{20} - 6 q^{21} + q^{22} - 3 q^{23} + 7 q^{24} - 10 q^{25} - 3 q^{26} - 19 q^{27} - 14 q^{28} + 12 q^{29} + 16 q^{30} + 2 q^{31} - 9 q^{32} - 14 q^{33} - 10 q^{34} - 13 q^{35} + 8 q^{36} - 9 q^{38} + 23 q^{39} - 7 q^{40} - 16 q^{41} + 6 q^{42} - 6 q^{43} - q^{44} + 40 q^{45} + 3 q^{46} - 15 q^{47} - 7 q^{48} + q^{49} + 10 q^{50} - 12 q^{51} + 3 q^{52} - 7 q^{53} + 19 q^{54} + 14 q^{55} + 14 q^{56} - 26 q^{57} - 12 q^{58} + q^{59} - 16 q^{60} + 7 q^{61} - 2 q^{62} - 4 q^{63} + 9 q^{64} - 4 q^{65} + 14 q^{66} - 66 q^{67} + 10 q^{68} + 34 q^{69} + 13 q^{70} - 15 q^{71} - 8 q^{72} - 50 q^{73} - 26 q^{75} + 9 q^{76} - 28 q^{77} - 23 q^{78} - 29 q^{79} + 7 q^{80} + 33 q^{81} + 16 q^{82} - 43 q^{83} - 6 q^{84} - 26 q^{85} + 6 q^{86} - 3 q^{87} + q^{88} + 6 q^{89} - 40 q^{90} - 30 q^{91} - 3 q^{92} + 28 q^{93} + 15 q^{94} - 12 q^{95} + 7 q^{96} + 50 q^{97} - q^{98} - 22 q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - 7 * q^3 + 9 * q^4 + 7 * q^5 + 7 * q^6 - 14 * q^7 - 9 * q^8 + 8 * q^9 - 7 * q^10 - q^11 - 7 * q^12 + 3 * q^13 + 14 * q^14 - 16 * q^15 + 9 * q^16 + 10 * q^17 - 8 * q^18 + 9 * q^19 + 7 * q^20 - 6 * q^21 + q^22 - 3 * q^23 + 7 * q^24 - 10 * q^25 - 3 * q^26 - 19 * q^27 - 14 * q^28 + 12 * q^29 + 16 * q^30 + 2 * q^31 - 9 * q^32 - 14 * q^33 - 10 * q^34 - 13 * q^35 + 8 * q^36 - 9 * q^38 + 23 * q^39 - 7 * q^40 - 16 * q^41 + 6 * q^42 - 6 * q^43 - q^44 + 40 * q^45 + 3 * q^46 - 15 * q^47 - 7 * q^48 + q^49 + 10 * q^50 - 12 * q^51 + 3 * q^52 - 7 * q^53 + 19 * q^54 + 14 * q^55 + 14 * q^56 - 26 * q^57 - 12 * q^58 + q^59 - 16 * q^60 + 7 * q^61 - 2 * q^62 - 4 * q^63 + 9 * q^64 - 4 * q^65 + 14 * q^66 - 66 * q^67 + 10 * q^68 + 34 * q^69 + 13 * q^70 - 15 * q^71 - 8 * q^72 - 50 * q^73 - 26 * q^75 + 9 * q^76 - 28 * q^77 - 23 * q^78 - 29 * q^79 + 7 * q^80 + 33 * q^81 + 16 * q^82 - 43 * q^83 - 6 * q^84 - 26 * q^85 + 6 * q^86 - 3 * q^87 + q^88 + 6 * q^89 - 40 * q^90 - 30 * q^91 - 3 * q^92 + 28 * q^93 + 15 * q^94 - 12 * q^95 + 7 * q^96 + 50 * q^97 - q^98 - 22 * 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
$3$	−0.605558	−0.349619	−0.174810	−	0.984602i	$-0.555931\pi$
$3$	−0.605558	−0.349619	−0.174810	+	0.984602i	$0.555931\pi$
$4$	1.00000	0.500000
$5$	−2.32729	−1.04079	−0.520397	−	0.853925i	$-0.674216\pi$
$5$	−2.32729	−1.04079	−0.520397	+	0.853925i	$0.674216\pi$
$6$	0.605558	0.247218
$7$	0.184773	0.0698376	0.0349188	−	0.999390i	$-0.488883\pi$
$7$	0.184773	0.0698376	0.0349188	+	0.999390i	$0.488883\pi$
$8$	−1.00000	−0.353553
$9$	−2.63330	−0.877766
$10$	2.32729	0.735952
$11$	−3.42659	−1.03316	−0.516578	−	0.856240i	$-0.672794\pi$
$11$	−3.42659	−1.03316	−0.516578	+	0.856240i	$0.672794\pi$
$12$	−0.605558	−0.174810
$13$	−0.254348	−0.0705434	−0.0352717	−	0.999378i	$-0.511230\pi$
$13$	−0.254348	−0.0705434	−0.0352717	+	0.999378i	$0.511230\pi$
$14$	−0.184773	−0.0493827
$15$	1.40931	0.363882
$16$	1.00000	0.250000
$17$	5.79927	1.40653	0.703264	−	0.710929i	$-0.251725\pi$
$17$	5.79927	1.40653	0.703264	+	0.710929i	$0.251725\pi$
$18$	2.63330	0.620675
$19$	1.20251	0.275875	0.137938	−	0.990441i	$-0.455953\pi$
$19$	1.20251	0.275875	0.137938	+	0.990441i	$0.455953\pi$
$20$	−2.32729	−0.520397
$21$	−0.111891	−0.0244166
$22$	3.42659	0.730552
$23$	8.62984	1.79945	0.899723	−	0.436461i	$-0.143768\pi$
$23$	8.62984	1.79945	0.899723	+	0.436461i	$0.143768\pi$
$24$	0.605558	0.123609
$25$	0.416259	0.0832518
$26$	0.254348	0.0498817
$27$	3.41129	0.656503
$28$	0.184773	0.0349188
$29$	5.85911	1.08801	0.544005	−	0.839082i	$-0.316907\pi$
$29$	5.85911	1.08801	0.544005	+	0.839082i	$0.316907\pi$
$30$	−1.40931	−0.257303
$31$	2.37990	0.427442	0.213721	−	0.976895i	$-0.431442\pi$
$31$	2.37990	0.427442	0.213721	+	0.976895i	$0.431442\pi$
$32$	−1.00000	−0.176777
$33$	2.07500	0.361211
$34$	−5.79927	−0.994566
$35$	−0.430020	−0.0726866
$36$	−2.63330	−0.438883
$37$	0	0
$37$	0	0
$38$	−1.20251	−0.195073
$39$	0.154022	0.0246633
$40$	2.32729	0.367976
$41$	−8.31493	−1.29857	−0.649287	−	0.760544i	$-0.724932\pi$
$41$	−8.31493	−1.29857	−0.649287	+	0.760544i	$0.724932\pi$
$42$	0.111891	0.0172651
$43$	−1.32703	−0.202370	−0.101185	−	0.994868i	$-0.532263\pi$
$43$	−1.32703	−0.202370	−0.101185	+	0.994868i	$0.532263\pi$
$44$	−3.42659	−0.516578
$45$	6.12844	0.913574
$46$	−8.62984	−1.27240
$47$	8.89664	1.29771	0.648854	−	0.760913i	$-0.275248\pi$
$47$	8.89664	1.29771	0.648854	+	0.760913i	$0.275248\pi$
$48$	−0.605558	−0.0874048
$49$	−6.96586	−0.995123
$50$	−0.416259	−0.0588679
$51$	−3.51179	−0.491749
$52$	−0.254348	−0.0352717
$53$	12.0093	1.64960	0.824799	−	0.565426i	$-0.191288\pi$
$53$	12.0093	1.64960	0.824799	+	0.565426i	$0.191288\pi$
$54$	−3.41129	−0.464218
$55$	7.97466	1.07530
$56$	−0.184773	−0.0246913
$57$	−0.728191	−0.0964513
$58$	−5.85911	−0.769339
$59$	−11.9163	−1.55137	−0.775683	−	0.631122i	$-0.782595\pi$
$59$	−11.9163	−1.55137	−0.775683	+	0.631122i	$0.782595\pi$
$60$	1.40931	0.181941
$61$	−4.60897	−0.590119	−0.295059	−	0.955479i	$-0.595339\pi$
$61$	−4.60897	−0.590119	−0.295059	+	0.955479i	$0.595339\pi$
$62$	−2.37990	−0.302247
$63$	−0.486563	−0.0613011
$64$	1.00000	0.125000
$65$	0.591940	0.0734211
$66$	−2.07500	−0.255415
$67$	−12.9078	−1.57694	−0.788470	−	0.615073i	$-0.789127\pi$
$67$	−12.9078	−1.57694	−0.788470	+	0.615073i	$0.789127\pi$
$68$	5.79927	0.703264
$69$	−5.22587	−0.629121
$70$	0.430020	0.0513972
$71$	−7.10570	−0.843291	−0.421645	−	0.906761i	$-0.638547\pi$
$71$	−7.10570	−0.843291	−0.421645	+	0.906761i	$0.638547\pi$
$72$	2.63330	0.310337
$73$	−15.1625	−1.77464	−0.887319	−	0.461157i	$-0.847435\pi$
$73$	−15.1625	−1.77464	−0.887319	+	0.461157i	$0.847435\pi$
$74$	0	0
$75$	−0.252069	−0.0291064
$76$	1.20251	0.137938
$77$	−0.633141	−0.0721532
$78$	−0.154022	−0.0174396
$79$	−11.5695	−1.30167	−0.650835	−	0.759220i	$-0.725581\pi$
$79$	−11.5695	−1.30167	−0.650835	+	0.759220i	$0.725581\pi$
$80$	−2.32729	−0.260198
$81$	5.83416	0.648240
$82$	8.31493	0.918230
$83$	8.49365	0.932300	0.466150	−	0.884706i	$-0.345641\pi$
$83$	8.49365	0.932300	0.466150	+	0.884706i	$0.345641\pi$
$84$	−0.111891	−0.0122083
$85$	−13.4965	−1.46391
$86$	1.32703	0.143097
$87$	−3.54803	−0.380389
$88$	3.42659	0.365276
$89$	−5.98605	−0.634520	−0.317260	−	0.948339i	$-0.602763\pi$
$89$	−5.98605	−0.634520	−0.317260	+	0.948339i	$0.602763\pi$
$90$	−6.12844	−0.645994
$91$	−0.0469966	−0.00492658
$92$	8.62984	0.899723
$93$	−1.44117	−0.149442
$94$	−8.89664	−0.917619
$95$	−2.79859	−0.287129
$96$	0.605558	0.0618045
$97$	−1.35210	−0.137285	−0.0686427	−	0.997641i	$-0.521867\pi$
$97$	−1.35210	−0.137285	−0.0686427	+	0.997641i	$0.521867\pi$
$98$	6.96586	0.703658
$99$	9.02324	0.906869
$100$	0.416259	0.0416259
$101$	7.66464	0.762660	0.381330	−	0.924439i	$-0.375466\pi$
$101$	7.66464	0.762660	0.381330	+	0.924439i	$0.375466\pi$
$102$	3.51179	0.347719
$103$	1.14991	0.113304	0.0566521	−	0.998394i	$-0.481957\pi$
$103$	1.14991	0.113304	0.0566521	+	0.998394i	$0.481957\pi$
$104$	0.254348	0.0249409
$105$	0.260402	0.0254126
$106$	−12.0093	−1.16644
$107$	14.8926	1.43972	0.719862	−	0.694117i	$-0.244205\pi$
$107$	14.8926	1.43972	0.719862	+	0.694117i	$0.244205\pi$
$108$	3.41129	0.328252
$109$	14.1828	1.35846	0.679231	−	0.733925i	$-0.262313\pi$
$109$	14.1828	1.35846	0.679231	+	0.733925i	$0.262313\pi$
$110$	−7.97466	−0.760354
$111$	0	0
$112$	0.184773	0.0174594
$113$	−7.82951	−0.736538	−0.368269	−	0.929719i	$-0.620050\pi$
$113$	−7.82951	−0.736538	−0.368269	+	0.929719i	$0.620050\pi$
$114$	0.728191	0.0682014
$115$	−20.0841	−1.87285
$116$	5.85911	0.544005
$117$	0.669774	0.0619206
$118$	11.9163	1.09698
$119$	1.07155	0.0982286
$120$	−1.40931	−0.128652
$121$	0.741522	0.0674111
$122$	4.60897	0.417277
$123$	5.03517	0.454006
$124$	2.37990	0.213721
$125$	10.6677	0.954146
$126$	0.486563	0.0433464
$127$	−5.27050	−0.467681	−0.233841	−	0.972275i	$-0.575129\pi$
$127$	−5.27050	−0.467681	−0.233841	+	0.972275i	$0.575129\pi$
$128$	−1.00000	−0.0883883
$129$	0.803594	0.0707525
$130$	−0.591940	−0.0519166
$131$	−10.6978	−0.934671	−0.467335	−	0.884080i	$-0.654786\pi$
$131$	−10.6978	−0.934671	−0.467335	+	0.884080i	$0.654786\pi$
$132$	2.07500	0.180606
$133$	0.222192	0.0192665
$134$	12.9078	1.11507
$135$	−7.93905	−0.683285
$136$	−5.79927	−0.497283
$137$	−19.4007	−1.65751	−0.828757	−	0.559609i	$-0.810951\pi$
$137$	−19.4007	−1.65751	−0.828757	+	0.559609i	$0.810951\pi$
$138$	5.22587	0.444856
$139$	10.1980	0.864984	0.432492	−	0.901638i	$-0.357634\pi$
$139$	10.1980	0.864984	0.432492	+	0.901638i	$0.357634\pi$
$140$	−0.430020	−0.0363433
$141$	−5.38744	−0.453704
$142$	7.10570	0.596297
$143$	0.871546	0.0728823
$144$	−2.63330	−0.219442
$145$	−13.6358	−1.13239
$146$	15.1625	1.25486
$147$	4.21823	0.347914
$148$	0	0
$149$	1.34665	0.110322	0.0551611	−	0.998477i	$-0.482433\pi$
$149$	1.34665	0.110322	0.0551611	+	0.998477i	$0.482433\pi$
$150$	0.252069	0.0205814
$151$	−14.5370	−1.18300	−0.591501	−	0.806305i	$-0.701464\pi$
$151$	−14.5370	−1.18300	−0.591501	+	0.806305i	$0.701464\pi$
$152$	−1.20251	−0.0975366
$153$	−15.2712	−1.23460
$154$	0.633141	0.0510200
$155$	−5.53870	−0.444879
$156$	0.154022	0.0123317
$157$	6.18465	0.493589	0.246794	−	0.969068i	$-0.420623\pi$
$157$	6.18465	0.493589	0.246794	+	0.969068i	$0.420623\pi$
$158$	11.5695	0.920419
$159$	−7.27230	−0.576731
$160$	2.32729	0.183988
$161$	1.59456	0.125669
$162$	−5.83416	−0.458375
$163$	−10.7680	−0.843418	−0.421709	−	0.906731i	$-0.638570\pi$
$163$	−10.7680	−0.843418	−0.421709	+	0.906731i	$0.638570\pi$
$164$	−8.31493	−0.649287
$165$	−4.82912	−0.375946
$166$	−8.49365	−0.659235
$167$	−18.0672	−1.39808	−0.699041	−	0.715082i	$-0.746390\pi$
$167$	−18.0672	−1.39808	−0.699041	+	0.715082i	$0.746390\pi$
$168$	0.111891	0.00863257
$169$	−12.9353	−0.995024
$170$	13.4965	1.03514
$171$	−3.16657	−0.242154
$172$	−1.32703	−0.101185
$173$	−2.70163	−0.205401	−0.102701	−	0.994712i	$-0.532748\pi$
$173$	−2.70163	−0.205401	−0.102701	+	0.994712i	$0.532748\pi$
$174$	3.54803	0.268976
$175$	0.0769134	0.00581411
$176$	−3.42659	−0.258289
$177$	7.21600	0.542388
$178$	5.98605	0.448674
$179$	17.7785	1.32883	0.664414	−	0.747365i	$-0.268681\pi$
$179$	17.7785	1.32883	0.664414	+	0.747365i	$0.268681\pi$
$180$	6.12844	0.456787
$181$	17.2072	1.27900	0.639501	−	0.768790i	$-0.279141\pi$
$181$	17.2072	1.27900	0.639501	+	0.768790i	$0.279141\pi$
$182$	0.0469966	0.00348362
$183$	2.79100	0.206317
$184$	−8.62984	−0.636200
$185$	0	0
$186$	1.44117	0.105671
$187$	−19.8717	−1.45316
$188$	8.89664	0.648854
$189$	0.630315	0.0458486
$190$	2.79859	0.203031
$191$	3.19925	0.231490	0.115745	−	0.993279i	$-0.463074\pi$
$191$	3.19925	0.231490	0.115745	+	0.993279i	$0.463074\pi$
$192$	−0.605558	−0.0437024
$193$	−10.6153	−0.764108	−0.382054	−	0.924140i	$-0.624783\pi$
$193$	−10.6153	−0.764108	−0.382054	+	0.924140i	$0.624783\pi$
$194$	1.35210	0.0970754
$195$	−0.358454	−0.0256694
$196$	−6.96586	−0.497561
$197$	−13.6068	−0.969441	−0.484721	−	0.874669i	$-0.661079\pi$
$197$	−13.6068	−0.969441	−0.484721	+	0.874669i	$0.661079\pi$
$198$	−9.02324	−0.641254
$199$	6.19346	0.439043	0.219521	−	0.975608i	$-0.429550\pi$
$199$	6.19346	0.439043	0.219521	+	0.975608i	$0.429550\pi$
$200$	−0.416259	−0.0294340
$201$	7.81644	0.551329
$202$	−7.66464	−0.539282
$203$	1.08261	0.0759840
$204$	−3.51179	−0.245875
$205$	19.3512	1.35155
$206$	−1.14991	−0.0801181
$207$	−22.7250	−1.57949
$208$	−0.254348	−0.0176359
$209$	−4.12052	−0.285022
$210$	−0.260402	−0.0179694
$211$	6.74870	0.464600	0.232300	−	0.972644i	$-0.425375\pi$
$211$	6.74870	0.464600	0.232300	+	0.972644i	$0.425375\pi$
$212$	12.0093	0.824799
$213$	4.30291	0.294831
$214$	−14.8926	−1.01804
$215$	3.08838	0.210626
$216$	−3.41129	−0.232109
$217$	0.439741	0.0298515
$218$	−14.1828	−0.960578
$219$	9.18178	0.620447
$220$	7.97466	0.537651
$221$	−1.47503	−0.0992213
$222$	0	0
$223$	−21.3936	−1.43262	−0.716312	−	0.697780i	$-0.754171\pi$
$223$	−21.3936	−1.43262	−0.716312	+	0.697780i	$0.754171\pi$
$224$	−0.184773	−0.0123457
$225$	−1.09613	−0.0730756
$226$	7.82951	0.520811
$227$	17.4592	1.15881	0.579403	−	0.815041i	$-0.303286\pi$
$227$	17.4592	1.15881	0.579403	+	0.815041i	$0.303286\pi$
$228$	−0.728191	−0.0482256
$229$	−10.7382	−0.709599	−0.354800	−	0.934942i	$-0.615451\pi$
$229$	−10.7382	−0.709599	−0.354800	+	0.934942i	$0.615451\pi$
$230$	20.0841	1.32431
$231$	0.383404	0.0252261
$232$	−5.85911	−0.384669
$233$	−7.60442	−0.498182	−0.249091	−	0.968480i	$-0.580132\pi$
$233$	−7.60442	−0.498182	−0.249091	+	0.968480i	$0.580132\pi$
$234$	−0.669774	−0.0437845
$235$	−20.7050	−1.35065
$236$	−11.9163	−0.775683
$237$	7.00600	0.455089
$238$	−1.07155	−0.0694581
$239$	16.0914	1.04087	0.520433	−	0.853902i	$-0.325770\pi$
$239$	16.0914	1.04087	0.520433	+	0.853902i	$0.325770\pi$
$240$	1.40931	0.0909704
$241$	30.2107	1.94604	0.973022	−	0.230714i	$-0.0741060\pi$
$241$	30.2107	1.94604	0.973022	+	0.230714i	$0.0741060\pi$
$242$	−0.741522	−0.0476668
$243$	−13.7668	−0.883141
$244$	−4.60897	−0.295059
$245$	16.2115	1.03572
$246$	−5.03517	−0.321031
$247$	−0.305856	−0.0194612
$248$	−2.37990	−0.151124
$249$	−5.14340	−0.325950
$250$	−10.6677	−0.674683
$251$	−3.09322	−0.195242	−0.0976212	−	0.995224i	$-0.531123\pi$
$251$	−3.09322	−0.195242	−0.0976212	+	0.995224i	$0.531123\pi$
$252$	−0.486563	−0.0306506
$253$	−29.5709	−1.85911
$254$	5.27050	0.330700
$255$	8.17295	0.511810
$256$	1.00000	0.0625000
$257$	−10.7991	−0.673627	−0.336813	−	0.941571i	$-0.609349\pi$
$257$	−10.7991	−0.673627	−0.336813	+	0.941571i	$0.609349\pi$
$258$	−0.803594	−0.0500296
$259$	0	0
$260$	0.591940	0.0367106
$261$	−15.4288	−0.955018
$262$	10.6978	0.660912
$263$	7.87050	0.485316	0.242658	−	0.970112i	$-0.421981\pi$
$263$	7.87050	0.485316	0.242658	+	0.970112i	$0.421981\pi$
$264$	−2.07500	−0.127707
$265$	−27.9490	−1.71689
$266$	−0.222192	−0.0136235
$267$	3.62491	0.221841
$268$	−12.9078	−0.788470
$269$	−15.6752	−0.955737	−0.477868	−	0.878432i	$-0.658590\pi$
$269$	−15.6752	−0.955737	−0.477868	+	0.878432i	$0.658590\pi$
$270$	7.93905	0.483155
$271$	−30.7408	−1.86737	−0.933686	−	0.358093i	$-0.883427\pi$
$271$	−30.7408	−1.86737	−0.933686	+	0.358093i	$0.883427\pi$
$272$	5.79927	0.351632
$273$	0.0284592	0.00172243
$274$	19.4007	1.17204
$275$	−1.42635	−0.0860121
$276$	−5.22587	−0.314561
$277$	−4.94272	−0.296980	−0.148490	−	0.988914i	$-0.547441\pi$
$277$	−4.94272	−0.296980	−0.148490	+	0.988914i	$0.547441\pi$
$278$	−10.1980	−0.611636
$279$	−6.26698	−0.375194
$280$	0.430020	0.0256986
$281$	12.3461	0.736509	0.368255	−	0.929725i	$-0.379955\pi$
$281$	12.3461	0.736509	0.368255	+	0.929725i	$0.379955\pi$
$282$	5.38744	0.320817
$283$	−2.13533	−0.126932	−0.0634662	−	0.997984i	$-0.520216\pi$
$283$	−2.13533	−0.126932	−0.0634662	+	0.997984i	$0.520216\pi$
$284$	−7.10570	−0.421645
$285$	1.69471	0.100386
$286$	−0.871546	−0.0515356
$287$	−1.53637	−0.0906893
$288$	2.63330	0.155169
$289$	16.6315	0.978322
$290$	13.6358	0.800723
$291$	0.818778	0.0479976
$292$	−15.1625	−0.887319
$293$	8.70583	0.508600	0.254300	−	0.967125i	$-0.418155\pi$
$293$	8.70583	0.508600	0.254300	+	0.967125i	$0.418155\pi$
$294$	−4.21823	−0.246012
$295$	27.7326	1.61465
$296$	0	0
$297$	−11.6891	−0.678270
$298$	−1.34665	−0.0780095
$299$	−2.19498	−0.126939
$300$	−0.252069	−0.0145532
$301$	−0.245199	−0.0141331
$302$	14.5370	0.836508
$303$	−4.64139	−0.266641
$304$	1.20251	0.0689688
$305$	10.7264	0.614192
$306$	15.2712	0.872996
$307$	0.307165	0.0175308	0.00876540	−	0.999962i	$-0.497210\pi$
$307$	0.307165	0.0175308	0.00876540	+	0.999962i	$0.497210\pi$
$308$	−0.633141	−0.0360766
$309$	−0.696339	−0.0396133
$310$	5.53870	0.314577
$311$	−17.7256	−1.00512	−0.502562	−	0.864541i	$-0.667609\pi$
$311$	−17.7256	−1.00512	−0.502562	+	0.864541i	$0.667609\pi$
$312$	−0.154022	−0.00871981
$313$	3.88513	0.219600	0.109800	−	0.993954i	$-0.464979\pi$
$313$	3.88513	0.219600	0.109800	+	0.993954i	$0.464979\pi$
$314$	−6.18465	−0.349020
$315$	1.13237	0.0638018
$316$	−11.5695	−0.650835
$317$	−12.9286	−0.726143	−0.363071	−	0.931761i	$-0.618272\pi$
$317$	−12.9286	−0.726143	−0.363071	+	0.931761i	$0.618272\pi$
$318$	7.27230	0.407811
$319$	−20.0768	−1.12408
$320$	−2.32729	−0.130099
$321$	−9.01836	−0.503356
$322$	−1.59456	−0.0888615
$323$	6.97369	0.388026
$324$	5.83416	0.324120
$325$	−0.105875	−0.00587287
$326$	10.7680	0.596387
$327$	−8.58849	−0.474945
$328$	8.31493	0.459115
$329$	1.64386	0.0906289
$330$	4.82912	0.265834
$331$	−5.21827	−0.286822	−0.143411	−	0.989663i	$-0.545807\pi$
$331$	−5.21827	−0.286822	−0.143411	+	0.989663i	$0.545807\pi$
$332$	8.49365	0.466150
$333$	0	0
$334$	18.0672	0.988593
$335$	30.0402	1.64127
$336$	−0.111891	−0.00610415
$337$	−0.132927	−0.00724101	−0.00362051	−	0.999993i	$-0.501152\pi$
$337$	−0.132927	−0.00724101	−0.00362051	+	0.999993i	$0.501152\pi$
$338$	12.9353	0.703588
$339$	4.74123	0.257508
$340$	−13.4965	−0.731953
$341$	−8.15493	−0.441614
$342$	3.16657	0.171229
$343$	−2.58051	−0.139335
$344$	1.32703	0.0715487
$345$	12.1621	0.654785
$346$	2.70163	0.145241
$347$	−19.2645	−1.03417	−0.517087	−	0.855933i	$-0.672984\pi$
$347$	−19.2645	−1.03417	−0.517087	+	0.855933i	$0.672984\pi$
$348$	−3.54803	−0.190195
$349$	15.2909	0.818505	0.409253	−	0.912421i	$-0.365789\pi$
$349$	15.2909	0.818505	0.409253	+	0.912421i	$0.365789\pi$
$350$	−0.0769134	−0.00411120
$351$	−0.867655	−0.0463120
$352$	3.42659	0.182638
$353$	7.42366	0.395122	0.197561	−	0.980291i	$-0.436698\pi$
$353$	7.42366	0.395122	0.197561	+	0.980291i	$0.436698\pi$
$354$	−7.21600	−0.383526
$355$	16.5370	0.877692
$356$	−5.98605	−0.317260
$357$	−0.648885	−0.0343426
$358$	−17.7785	−0.939623
$359$	−20.7204	−1.09358	−0.546790	−	0.837270i	$-0.684150\pi$
$359$	−20.7204	−1.09358	−0.546790	+	0.837270i	$0.684150\pi$
$360$	−6.12844	−0.322997
$361$	−17.5540	−0.923893
$362$	−17.2072	−0.904392
$363$	−0.449035	−0.0235682
$364$	−0.0469966	−0.00246329
$365$	35.2875	1.84703
$366$	−2.79100	−0.145888
$367$	−0.118556	−0.00618858	−0.00309429	−	0.999995i	$-0.500985\pi$
$367$	−0.118556	−0.00618858	−0.00309429	+	0.999995i	$0.500985\pi$
$368$	8.62984	0.449862
$369$	21.8957	1.13984
$370$	0	0
$371$	2.21899	0.115204
$372$	−1.44117	−0.0747210
$373$	−10.8673	−0.562688	−0.281344	−	0.959607i	$-0.590780\pi$
$373$	−10.8673	−0.562688	−0.281344	+	0.959607i	$0.590780\pi$
$374$	19.8717	1.02754
$375$	−6.45990	−0.333588
$376$	−8.89664	−0.458809
$377$	−1.49025	−0.0767519
$378$	−0.630315	−0.0324199
$379$	−2.07760	−0.106719	−0.0533595	−	0.998575i	$-0.516993\pi$
$379$	−2.07760	−0.106719	−0.0533595	+	0.998575i	$0.516993\pi$
$380$	−2.79859	−0.143565
$381$	3.19159	0.163510
$382$	−3.19925	−0.163688
$383$	8.43195	0.430853	0.215426	−	0.976520i	$-0.430886\pi$
$383$	8.43195	0.430853	0.215426	+	0.976520i	$0.430886\pi$
$384$	0.605558	0.0309023
$385$	1.47350	0.0750966
$386$	10.6153	0.540306
$387$	3.49447	0.177634
$388$	−1.35210	−0.0686427
$389$	−22.7257	−1.15224	−0.576119	−	0.817366i	$-0.695434\pi$
$389$	−22.7257	−1.15224	−0.576119	+	0.817366i	$0.695434\pi$
$390$	0.358454	0.0181510
$391$	50.0467	2.53097
$392$	6.96586	0.351829
$393$	6.47814	0.326779
$394$	13.6068	0.685499
$395$	26.9255	1.35477
$396$	9.02324	0.453435
$397$	−28.5749	−1.43413	−0.717066	−	0.697005i	$-0.754515\pi$
$397$	−28.5749	−1.43413	−0.717066	+	0.697005i	$0.754515\pi$
$398$	−6.19346	−0.310450
$399$	−0.134550	−0.00673593
$400$	0.416259	0.0208129
$401$	−7.12911	−0.356011	−0.178005	−	0.984030i	$-0.556964\pi$
$401$	−7.12911	−0.356011	−0.178005	+	0.984030i	$0.556964\pi$
$402$	−7.81644	−0.389848
$403$	−0.605322	−0.0301532
$404$	7.66464	0.381330
$405$	−13.5778	−0.674684
$406$	−1.08261	−0.0537288
$407$	0	0
$408$	3.51179	0.173860
$409$	−9.53620	−0.471535	−0.235767	−	0.971810i	$-0.575760\pi$
$409$	−9.53620	−0.471535	−0.235767	+	0.971810i	$0.575760\pi$
$410$	−19.3512	−0.955688
$411$	11.7483	0.579499
$412$	1.14991	0.0566521
$413$	−2.20181	−0.108344
$414$	22.7250	1.11687
$415$	−19.7672	−0.970332
$416$	0.254348	0.0124704
$417$	−6.17549	−0.302415
$418$	4.12052	0.201541
$419$	15.3107	0.747978	0.373989	−	0.927433i	$-0.377990\pi$
$419$	15.3107	0.747978	0.373989	+	0.927433i	$0.377990\pi$
$420$	0.260402	0.0127063
$421$	26.8043	1.30636	0.653182	−	0.757201i	$-0.273434\pi$
$421$	26.8043	1.30636	0.653182	+	0.757201i	$0.273434\pi$
$422$	−6.74870	−0.328522
$423$	−23.4275	−1.13908
$424$	−12.0093	−0.583221
$425$	2.41400	0.117096
$426$	−4.30291	−0.208477
$427$	−0.851614	−0.0412125
$428$	14.8926	0.719862
$429$	−0.527772	−0.0254811
$430$	−3.08838	−0.148935
$431$	−16.1088	−0.775935	−0.387968	−	0.921673i	$-0.626823\pi$
$431$	−16.1088	−0.775935	−0.387968	+	0.921673i	$0.626823\pi$
$432$	3.41129	0.164126
$433$	13.4957	0.648564	0.324282	−	0.945960i	$-0.394877\pi$
$433$	13.4957	0.648564	0.324282	+	0.945960i	$0.394877\pi$
$434$	−0.439741	−0.0211082
$435$	8.25729	0.395907
$436$	14.1828	0.679231
$437$	10.3775	0.496423
$438$	−9.18178	−0.438723
$439$	−32.2530	−1.53935	−0.769675	−	0.638436i	$-0.779582\pi$
$439$	−32.2530	−1.53935	−0.769675	+	0.638436i	$0.779582\pi$
$440$	−7.97466	−0.380177
$441$	18.3432	0.873485
$442$	1.47503	0.0701601
$443$	16.6757	0.792288	0.396144	−	0.918188i	$-0.370348\pi$
$443$	16.6757	0.792288	0.396144	+	0.918188i	$0.370348\pi$
$444$	0	0
$445$	13.9313	0.660405
$446$	21.3936	1.01302
$447$	−0.815477	−0.0385708
$448$	0.184773	0.00872970
$449$	−11.1346	−0.525475	−0.262737	−	0.964867i	$-0.584625\pi$
$449$	−11.1346	−0.525475	−0.262737	+	0.964867i	$0.584625\pi$
$450$	1.09613	0.0516723
$451$	28.4918	1.34163
$452$	−7.82951	−0.368269
$453$	8.80298	0.413600
$454$	−17.4592	−0.819399
$455$	0.109375	0.00512756
$456$	0.728191	0.0341007
$457$	8.50711	0.397946	0.198973	−	0.980005i	$-0.436239\pi$
$457$	8.50711	0.397946	0.198973	+	0.980005i	$0.436239\pi$
$458$	10.7382	0.501762
$459$	19.7830	0.923391
$460$	−20.0841	−0.936426
$461$	3.96942	0.184875	0.0924373	−	0.995719i	$-0.470534\pi$
$461$	3.96942	0.184875	0.0924373	+	0.995719i	$0.470534\pi$
$462$	−0.383404	−0.0178376
$463$	21.2249	0.986407	0.493203	−	0.869914i	$-0.335826\pi$
$463$	21.2249	0.986407	0.493203	+	0.869914i	$0.335826\pi$
$464$	5.85911	0.272002
$465$	3.35401	0.155538
$466$	7.60442	0.352268
$467$	−28.5845	−1.32273	−0.661367	−	0.750062i	$-0.730024\pi$
$467$	−28.5845	−1.32273	−0.661367	+	0.750062i	$0.730024\pi$
$468$	0.669774	0.0309603
$469$	−2.38502	−0.110130
$470$	20.7050	0.955052
$471$	−3.74517	−0.172568
$472$	11.9163	0.548491
$473$	4.54719	0.209080
$474$	−7.00600	−0.321796
$475$	0.500556	0.0229671
$476$	1.07155	0.0491143
$477$	−31.6240	−1.44796
$478$	−16.0914	−0.736004
$479$	−30.7377	−1.40444	−0.702221	−	0.711959i	$-0.747808\pi$
$479$	−30.7377	−1.40444	−0.702221	+	0.711959i	$0.747808\pi$
$480$	−1.40931	−0.0643258
$481$	0	0
$482$	−30.2107	−1.37606
$483$	−0.965600	−0.0439363
$484$	0.741522	0.0337055
$485$	3.14673	0.142886
$486$	13.7668	0.624475
$487$	19.4211	0.880053	0.440026	−	0.897985i	$-0.354969\pi$
$487$	19.4211	0.880053	0.440026	+	0.897985i	$0.354969\pi$
$488$	4.60897	0.208638
$489$	6.52068	0.294875
$490$	−16.2115	−0.732363
$491$	−41.2649	−1.86226	−0.931129	−	0.364690i	$-0.881175\pi$
$491$	−41.2649	−1.86226	−0.931129	+	0.364690i	$0.881175\pi$
$492$	5.03517	0.227003
$493$	33.9785	1.53032
$494$	0.305856	0.0137611
$495$	−20.9997	−0.943864
$496$	2.37990	0.106861
$497$	−1.31294	−0.0588934
$498$	5.14340	0.230481
$499$	−32.1976	−1.44136	−0.720681	−	0.693267i	$-0.756171\pi$
$499$	−32.1976	−1.44136	−0.720681	+	0.693267i	$0.756171\pi$
$500$	10.6677	0.477073
$501$	10.9407	0.488796
$502$	3.09322	0.138057
$503$	−41.9943	−1.87243	−0.936217	−	0.351422i	$-0.885698\pi$
$503$	−41.9943	−1.87243	−0.936217	+	0.351422i	$0.885698\pi$
$504$	0.486563	0.0216732
$505$	−17.8378	−0.793772
$506$	29.5709	1.31459
$507$	7.83308	0.347879
$508$	−5.27050	−0.233841
$509$	−6.35122	−0.281513	−0.140756	−	0.990044i	$-0.544953\pi$
$509$	−6.35122	−0.281513	−0.140756	+	0.990044i	$0.544953\pi$
$510$	−8.17295	−0.361904
$511$	−2.80162	−0.123936
$512$	−1.00000	−0.0441942
$513$	4.10212	0.181113
$514$	10.7991	0.476326
$515$	−2.67617	−0.117926
$516$	0.803594	0.0353763
$517$	−30.4851	−1.34074
$518$	0	0
$519$	1.63600	0.0718122
$520$	−0.591940	−0.0259583
$521$	29.8419	1.30740	0.653700	−	0.756754i	$-0.273216\pi$
$521$	29.8419	1.30740	0.653700	+	0.756754i	$0.273216\pi$
$522$	15.4288	0.675300
$523$	16.8953	0.738781	0.369390	−	0.929274i	$-0.379567\pi$
$523$	16.8953	0.738781	0.369390	+	0.929274i	$0.379567\pi$
$524$	−10.6978	−0.467335
$525$	−0.0465756	−0.00203272
$526$	−7.87050	−0.343170
$527$	13.8017	0.601209
$528$	2.07500	0.0903028
$529$	51.4742	2.23801
$530$	27.9490	1.21403
$531$	31.3791	1.36174
$532$	0.222192	0.00963324
$533$	2.11488	0.0916058
$534$	−3.62491	−0.156865
$535$	−34.6594	−1.49846
$536$	12.9078	0.557533
$537$	−10.7659	−0.464584
$538$	15.6752	0.675808
$539$	23.8691	1.02812
$540$	−7.93905	−0.341642
$541$	−19.5375	−0.839981	−0.419990	−	0.907529i	$-0.637967\pi$
$541$	−19.5375	−0.839981	−0.419990	+	0.907529i	$0.637967\pi$
$542$	30.7408	1.32043
$543$	−10.4200	−0.447164
$544$	−5.79927	−0.248641
$545$	−33.0073	−1.41388
$546$	−0.0284592	−0.00121794
$547$	−16.8309	−0.719639	−0.359820	−	0.933022i	$-0.617162\pi$
$547$	−16.8309	−0.719639	−0.359820	+	0.933022i	$0.617162\pi$
$548$	−19.4007	−0.828757
$549$	12.1368	0.517986
$550$	1.42635	0.0608197
$551$	7.04565	0.300155
$552$	5.22587	0.222428
$553$	−2.13773	−0.0909055
$554$	4.94272	0.209996
$555$	0	0
$556$	10.1980	0.432492
$557$	38.5019	1.63138	0.815689	−	0.578491i	$-0.196358\pi$
$557$	38.5019	1.63138	0.815689	+	0.578491i	$0.196358\pi$
$558$	6.26698	0.265302
$559$	0.337527	0.0142759
$560$	−0.430020	−0.0181716
$561$	12.0335	0.508054
$562$	−12.3461	−0.520791
$563$	−34.0446	−1.43481	−0.717405	−	0.696656i	$-0.754670\pi$
$563$	−34.0446	−1.43481	−0.717405	+	0.696656i	$0.754670\pi$
$564$	−5.38744	−0.226852
$565$	18.2215	0.766585
$566$	2.13533	0.0897548
$567$	1.07800	0.0452716
$568$	7.10570	0.298148
$569$	9.35427	0.392152	0.196076	−	0.980589i	$-0.437180\pi$
$569$	9.35427	0.392152	0.196076	+	0.980589i	$0.437180\pi$
$570$	−1.69471	−0.0709836
$571$	37.3975	1.56504	0.782518	−	0.622628i	$-0.213935\pi$
$571$	37.3975	1.56504	0.782518	+	0.622628i	$0.213935\pi$
$572$	0.871546	0.0364412
$573$	−1.93733	−0.0809333
$574$	1.53637	0.0641270
$575$	3.59225	0.149807
$576$	−2.63330	−0.109721
$577$	16.1995	0.674392	0.337196	−	0.941434i	$-0.390521\pi$
$577$	16.1995	0.674392	0.337196	+	0.941434i	$0.390521\pi$
$578$	−16.6315	−0.691778
$579$	6.42820	0.267147
$580$	−13.6358	−0.566197
$581$	1.56940	0.0651096
$582$	−0.818778	−0.0339394
$583$	−41.1508	−1.70429
$584$	15.1625	0.627429
$585$	−1.55876	−0.0644466
$586$	−8.70583	−0.359635
$587$	4.81330	0.198666	0.0993332	−	0.995054i	$-0.468329\pi$
$587$	4.81330	0.198666	0.0993332	+	0.995054i	$0.468329\pi$
$588$	4.21823	0.173957
$589$	2.86185	0.117921
$590$	−27.7326	−1.14173
$591$	8.23969	0.338935
$592$	0	0
$593$	4.16487	0.171031	0.0855153	−	0.996337i	$-0.472746\pi$
$593$	4.16487	0.171031	0.0855153	+	0.996337i	$0.472746\pi$
$594$	11.6891	0.479610
$595$	−2.49380	−0.102236
$596$	1.34665	0.0551611
$597$	−3.75050	−0.153498
$598$	2.19498	0.0897595
$599$	−16.2239	−0.662889	−0.331444	−	0.943475i	$-0.607536\pi$
$599$	−16.2239	−0.662889	−0.331444	+	0.943475i	$0.607536\pi$
$600$	0.252069	0.0102907
$601$	−10.9283	−0.445775	−0.222888	−	0.974844i	$-0.571548\pi$
$601$	−10.9283	−0.445775	−0.222888	+	0.974844i	$0.571548\pi$
$602$	0.245199	0.00999358
$603$	33.9901	1.38419
$604$	−14.5370	−0.591501
$605$	−1.72573	−0.0701611
$606$	4.64139	0.188543
$607$	−11.3288	−0.459820	−0.229910	−	0.973212i	$-0.573843\pi$
$607$	−11.3288	−0.459820	−0.229910	+	0.973212i	$0.573843\pi$
$608$	−1.20251	−0.0487683
$609$	−0.655581	−0.0265655
$610$	−10.7264	−0.434299
$611$	−2.26284	−0.0915448
$612$	−15.2712	−0.617302
$613$	14.6307	0.590929	0.295464	−	0.955354i	$-0.404526\pi$
$613$	14.6307	0.590929	0.295464	+	0.955354i	$0.404526\pi$
$614$	−0.307165	−0.0123962
$615$	−11.7183	−0.472527
$616$	0.633141	0.0255100
$617$	15.1467	0.609782	0.304891	−	0.952387i	$-0.401380\pi$
$617$	15.1467	0.609782	0.304891	+	0.952387i	$0.401380\pi$
$618$	0.696339	0.0280108
$619$	20.3056	0.816151	0.408075	−	0.912948i	$-0.366200\pi$
$619$	20.3056	0.816151	0.408075	+	0.912948i	$0.366200\pi$
$620$	−5.53870	−0.222440
$621$	29.4389	1.18134
$622$	17.7256	0.710730
$623$	−1.10606	−0.0443134
$624$	0.154022	0.00616583
$625$	−26.9080	−1.07632
$626$	−3.88513	−0.155281
$627$	2.49521	0.0996492
$628$	6.18465	0.246794
$629$	0	0
$630$	−1.13237	−0.0451147
$631$	36.2251	1.44210	0.721050	−	0.692883i	$-0.243660\pi$
$631$	36.2251	1.44210	0.721050	+	0.692883i	$0.243660\pi$
$632$	11.5695	0.460210
$633$	−4.08673	−0.162433
$634$	12.9286	0.513460
$635$	12.2660	0.486760
$636$	−7.27230	−0.288366
$637$	1.77175	0.0701993
$638$	20.0768	0.794847
$639$	18.7114	0.740212
$640$	2.32729	0.0919940
$641$	44.5075	1.75794	0.878970	−	0.476877i	$-0.158231\pi$
$641$	44.5075	1.75794	0.878970	+	0.476877i	$0.158231\pi$
$642$	9.01836	0.355926
$643$	−26.5119	−1.04553	−0.522764	−	0.852478i	$-0.675099\pi$
$643$	−26.5119	−1.04553	−0.522764	+	0.852478i	$0.675099\pi$
$644$	1.59456	0.0628345
$645$	−1.87019	−0.0736388
$646$	−6.97369	−0.274376
$647$	−13.0815	−0.514288	−0.257144	−	0.966373i	$-0.582782\pi$
$647$	−13.0815	−0.514288	−0.257144	+	0.966373i	$0.582782\pi$
$648$	−5.83416	−0.229187
$649$	40.8322	1.60280
$650$	0.105875	0.00415274
$651$	−0.266289	−0.0104367
$652$	−10.7680	−0.421709
$653$	46.1461	1.80584	0.902919	−	0.429811i	$-0.141420\pi$
$653$	46.1461	1.80584	0.902919	+	0.429811i	$0.141420\pi$
$654$	8.58849	0.335836
$655$	24.8968	0.972799
$656$	−8.31493	−0.324643
$657$	39.9274	1.55772
$658$	−1.64386	−0.0640843
$659$	−27.8028	−1.08304	−0.541521	−	0.840687i	$-0.682151\pi$
$659$	−27.8028	−1.08304	−0.541521	+	0.840687i	$0.682151\pi$
$660$	−4.82912	−0.187973
$661$	15.1834	0.590567	0.295283	−	0.955410i	$-0.404586\pi$
$661$	15.1834	0.590567	0.295283	+	0.955410i	$0.404586\pi$
$662$	5.21827	0.202814
$663$	0.893217	0.0346897
$664$	−8.49365	−0.329618
$665$	−0.517104	−0.0200524
$666$	0	0
$667$	50.5632	1.95781
$668$	−18.0672	−0.699041
$669$	12.9551	0.500873
$670$	−30.0402	−1.16055
$671$	15.7931	0.609684
$672$	0.111891	0.00431628
$673$	−0.940130	−0.0362394	−0.0181197	−	0.999836i	$-0.505768\pi$
$673$	−0.940130	−0.0362394	−0.0181197	+	0.999836i	$0.505768\pi$
$674$	0.132927	0.00512017
$675$	1.41998	0.0546551
$676$	−12.9353	−0.497512
$677$	2.14615	0.0824834	0.0412417	−	0.999149i	$-0.486869\pi$
$677$	2.14615	0.0824834	0.0412417	+	0.999149i	$0.486869\pi$
$678$	−4.74123	−0.182086
$679$	−0.249832	−0.00958769
$680$	13.4965	0.517569
$681$	−10.5725	−0.405141
$682$	8.15493	0.312268
$683$	31.3174	1.19833	0.599163	−	0.800627i	$-0.295500\pi$
$683$	31.3174	1.19833	0.599163	+	0.800627i	$0.295500\pi$
$684$	−3.16657	−0.121077
$685$	45.1510	1.72513
$686$	2.58051	0.0985245
$687$	6.50260	0.248090
$688$	−1.32703	−0.0505926
$689$	−3.05453	−0.116368
$690$	−12.1621	−0.463003
$691$	−16.2426	−0.617897	−0.308949	−	0.951079i	$-0.599977\pi$
$691$	−16.2426	−0.617897	−0.308949	+	0.951079i	$0.599977\pi$
$692$	−2.70163	−0.102701
$693$	1.66725	0.0633336
$694$	19.2645	0.731272
$695$	−23.7337	−0.900270
$696$	3.54803	0.134488
$697$	−48.2205	−1.82648
$698$	−15.2909	−0.578771
$699$	4.60492	0.174174
$700$	0.0769134	0.00290705
$701$	−42.9787	−1.62328	−0.811642	−	0.584155i	$-0.801426\pi$
$701$	−42.9787	−1.62328	−0.811642	+	0.584155i	$0.801426\pi$
$702$	0.867655	0.0327475
$703$	0	0
$704$	−3.42659	−0.129144
$705$	12.5381	0.472212
$706$	−7.42366	−0.279393
$707$	1.41622	0.0532624
$708$	7.21600	0.271194
$709$	−10.9434	−0.410987	−0.205494	−	0.978658i	$-0.565880\pi$
$709$	−10.9434	−0.410987	−0.205494	+	0.978658i	$0.565880\pi$
$710$	−16.5370	−0.620622
$711$	30.4659	1.14256
$712$	5.98605	0.224337
$713$	20.5381	0.769159
$714$	0.648885	0.0242839
$715$	−2.02834	−0.0758555
$716$	17.7785	0.664414
$717$	−9.74429	−0.363907
$718$	20.7204	0.773278
$719$	−51.0202	−1.90273	−0.951367	−	0.308061i	$-0.900320\pi$
$719$	−51.0202	−1.90273	−0.951367	+	0.308061i	$0.900320\pi$
$720$	6.12844	0.228393
$721$	0.212473	0.00791289
$722$	17.5540	0.653291
$723$	−18.2944	−0.680374
$724$	17.2072	0.639501
$725$	2.43891	0.0905787
$726$	0.449035	0.0166652
$727$	44.8745	1.66430	0.832151	−	0.554550i	$-0.187109\pi$
$727$	44.8745	1.66430	0.832151	+	0.554550i	$0.187109\pi$
$728$	0.0469966	0.00174181
$729$	−9.16588	−0.339477
$730$	−35.2875	−1.30605
$731$	−7.69580	−0.284639
$732$	2.79100	0.103158
$733$	14.1853	0.523947	0.261973	−	0.965075i	$-0.415627\pi$
$733$	14.1853	0.523947	0.261973	+	0.965075i	$0.415627\pi$
$734$	0.118556	0.00437599
$735$	−9.81704	−0.362107
$736$	−8.62984	−0.318100
$737$	44.2298	1.62923
$738$	−21.8957	−0.805991
$739$	−2.45558	−0.0903301	−0.0451650	−	0.998980i	$-0.514381\pi$
$739$	−2.45558	−0.0903301	−0.0451650	+	0.998980i	$0.514381\pi$
$740$	0	0
$741$	0.185214	0.00680400
$742$	−2.21899	−0.0814615
$743$	5.61616	0.206037	0.103019	−	0.994679i	$-0.467150\pi$
$743$	5.61616	0.206037	0.103019	+	0.994679i	$0.467150\pi$
$744$	1.44117	0.0528357
$745$	−3.13405	−0.114823
$746$	10.8673	0.397881
$747$	−22.3663	−0.818341
$748$	−19.8717	−0.726582
$749$	2.75176	0.100547
$750$	6.45990	0.235882
$751$	−20.7964	−0.758872	−0.379436	−	0.925218i	$-0.623882\pi$
$751$	−20.7964	−0.758872	−0.379436	+	0.925218i	$0.623882\pi$
$752$	8.89664	0.324427
$753$	1.87313	0.0682605
$754$	1.49025	0.0542718
$755$	33.8317	1.23126
$756$	0.630315	0.0229243
$757$	15.7283	0.571656	0.285828	−	0.958281i	$-0.407731\pi$
$757$	15.7283	0.571656	0.285828	+	0.958281i	$0.407731\pi$
$758$	2.07760	0.0754618
$759$	17.9069	0.649980
$760$	2.79859	0.101515
$761$	−43.1713	−1.56496	−0.782479	−	0.622676i	$-0.786045\pi$
$761$	−43.1713	−1.56496	−0.782479	+	0.622676i	$0.786045\pi$
$762$	−3.19159	−0.115619
$763$	2.62059	0.0948718
$764$	3.19925	0.115745
$765$	35.5404	1.28497
$766$	−8.43195	−0.304659
$767$	3.03088	0.109439
$768$	−0.605558	−0.0218512
$769$	29.9212	1.07899	0.539494	−	0.841990i	$-0.318616\pi$
$769$	29.9212	1.07899	0.539494	+	0.841990i	$0.318616\pi$
$770$	−1.47350	−0.0531013
$771$	6.53946	0.235513
$772$	−10.6153	−0.382054
$773$	−36.9978	−1.33072	−0.665358	−	0.746524i	$-0.731721\pi$
$773$	−36.9978	−1.33072	−0.665358	+	0.746524i	$0.731721\pi$
$774$	−3.49447	−0.125606
$775$	0.990653	0.0355853
$776$	1.35210	0.0485377
$777$	0	0
$778$	22.7257	0.814755
$779$	−9.99880	−0.358244
$780$	−0.358454	−0.0128347
$781$	24.3483	0.871251
$782$	−50.0467	−1.78967
$783$	19.9871	0.714282
$784$	−6.96586	−0.248781
$785$	−14.3934	−0.513724
$786$	−6.47814	−0.231068
$787$	−41.7465	−1.48810	−0.744052	−	0.668122i	$-0.767098\pi$
$787$	−41.7465	−1.48810	−0.744052	+	0.668122i	$0.767098\pi$
$788$	−13.6068	−0.484721
$789$	−4.76605	−0.169676
$790$	−26.9255	−0.957966
$791$	−1.44668	−0.0514381
$792$	−9.02324	−0.320627
$793$	1.17228	0.0416290
$794$	28.5749	1.01408
$795$	16.9247	0.600258
$796$	6.19346	0.219521
$797$	13.3352	0.472358	0.236179	−	0.971710i	$-0.424105\pi$
$797$	13.3352	0.472358	0.236179	+	0.971710i	$0.424105\pi$
$798$	0.134550	0.00476302
$799$	51.5940	1.82526
$800$	−0.416259	−0.0147170
$801$	15.7631	0.556961
$802$	7.12911	0.251738
$803$	51.9557	1.83348
$804$	7.81644	0.275665
$805$	−3.71100	−0.130796
$806$	0.605322	0.0213215
$807$	9.49228	0.334144
$808$	−7.66464	−0.269641
$809$	7.96418	0.280006	0.140003	−	0.990151i	$-0.455289\pi$
$809$	7.96418	0.280006	0.140003	+	0.990151i	$0.455289\pi$
$810$	13.5778	0.477074
$811$	−20.3473	−0.714489	−0.357245	−	0.934011i	$-0.616284\pi$
$811$	−20.3473	−0.714489	−0.357245	+	0.934011i	$0.616284\pi$
$812$	1.08261	0.0379920
$813$	18.6154	0.652869
$814$	0	0
$815$	25.0603	0.877824
$816$	−3.51179	−0.122937
$817$	−1.59577	−0.0558289
$818$	9.53620	0.333425
$819$	0.123756	0.00432439
$820$	19.3512	0.675773
$821$	38.2417	1.33464	0.667322	−	0.744769i	$-0.267440\pi$
$821$	38.2417	1.33464	0.667322	+	0.744769i	$0.267440\pi$
$822$	−11.7483	−0.409768
$823$	−40.8235	−1.42302	−0.711508	−	0.702678i	$-0.751988\pi$
$823$	−40.8235	−1.42302	−0.711508	+	0.702678i	$0.751988\pi$
$824$	−1.14991	−0.0400591
$825$	0.863738	0.0300715
$826$	2.20181	0.0766106
$827$	−42.5536	−1.47973	−0.739867	−	0.672753i	$-0.765111\pi$
$827$	−42.5536	−1.47973	−0.739867	+	0.672753i	$0.765111\pi$
$828$	−22.7250	−0.789747
$829$	14.8227	0.514813	0.257406	−	0.966303i	$-0.417132\pi$
$829$	14.8227	0.514813	0.257406	+	0.966303i	$0.417132\pi$
$830$	19.7672	0.686128
$831$	2.99311	0.103830
$832$	−0.254348	−0.00881793
$833$	−40.3969	−1.39967
$834$	6.17549	0.213840
$835$	42.0475	1.45512
$836$	−4.12052	−0.142511
$837$	8.11852	0.280617
$838$	−15.3107	−0.528900
$839$	−28.0130	−0.967116	−0.483558	−	0.875312i	$-0.660656\pi$
$839$	−28.0130	−0.967116	−0.483558	+	0.875312i	$0.660656\pi$
$840$	−0.260402	−0.00898472
$841$	5.32916	0.183764
$842$	−26.8043	−0.923738
$843$	−7.47631	−0.257498
$844$	6.74870	0.232300
$845$	30.1042	1.03561
$846$	23.4275	0.805455
$847$	0.137013	0.00470783
$848$	12.0093	0.412399
$849$	1.29307	0.0443780
$850$	−2.41400	−0.0827994
$851$	0	0
$852$	4.30291	0.147415
$853$	−15.3613	−0.525961	−0.262980	−	0.964801i	$-0.584705\pi$
$853$	−15.3613	−0.525961	−0.262980	+	0.964801i	$0.584705\pi$
$854$	0.851614	0.0291416
$855$	7.36952	0.252032
$856$	−14.8926	−0.509020
$857$	22.5764	0.771196	0.385598	−	0.922667i	$-0.373995\pi$
$857$	22.5764	0.771196	0.385598	+	0.922667i	$0.373995\pi$
$858$	0.527772	0.0180178
$859$	−28.8318	−0.983727	−0.491863	−	0.870672i	$-0.663684\pi$
$859$	−28.8318	−0.983727	−0.491863	+	0.870672i	$0.663684\pi$
$860$	3.08838	0.105313
$861$	0.930364	0.0317067
$862$	16.1088	0.548669
$863$	−17.5920	−0.598837	−0.299419	−	0.954122i	$-0.596793\pi$
$863$	−17.5920	−0.598837	−0.299419	+	0.954122i	$0.596793\pi$
$864$	−3.41129	−0.116054
$865$	6.28747	0.213780
$866$	−13.4957	−0.458604
$867$	−10.0713	−0.342040
$868$	0.439741	0.0149258
$869$	39.6439	1.34483
$870$	−8.25729	−0.279948
$871$	3.28308	0.111243
$872$	−14.1828	−0.480289
$873$	3.56050	0.120505
$874$	−10.3775	−0.351024
$875$	1.97110	0.0666353
$876$	9.18178	0.310224
$877$	−30.9202	−1.04410	−0.522051	−	0.852914i	$-0.674833\pi$
$877$	−30.9202	−1.04410	−0.522051	+	0.852914i	$0.674833\pi$
$878$	32.2530	1.08848
$879$	−5.27189	−0.177816
$880$	7.97466	0.268826
$881$	21.4333	0.722106	0.361053	−	0.932545i	$-0.382417\pi$
$881$	21.4333	0.722106	0.361053	+	0.932545i	$0.382417\pi$
$882$	−18.3432	−0.617647
$883$	−32.3684	−1.08928	−0.544642	−	0.838669i	$-0.683334\pi$
$883$	−32.3684	−1.08928	−0.544642	+	0.838669i	$0.683334\pi$
$884$	−1.47503	−0.0496107
$885$	−16.7937	−0.564514
$886$	−16.6757	−0.560232
$887$	−38.6283	−1.29701	−0.648506	−	0.761210i	$-0.724606\pi$
$887$	−38.6283	−1.29701	−0.648506	+	0.761210i	$0.724606\pi$
$888$	0	0
$889$	−0.973846	−0.0326617
$890$	−13.9313	−0.466977
$891$	−19.9913	−0.669733
$892$	−21.3936	−0.716312
$893$	10.6983	0.358006
$894$	0.815477	0.0272736
$895$	−41.3756	−1.38304
$896$	−0.184773	−0.00617283
$897$	1.32919	0.0443804
$898$	11.1346	0.371567
$899$	13.9441	0.465061
$900$	−1.09613	−0.0365378
$901$	69.6448	2.32021
$902$	−28.4918	−0.948675
$903$	0.148483	0.00494119
$904$	7.82951	0.260406
$905$	−40.0461	−1.33118
$906$	−8.80298	−0.292459
$907$	14.7717	0.490486	0.245243	−	0.969462i	$-0.421132\pi$
$907$	14.7717	0.490486	0.245243	+	0.969462i	$0.421132\pi$
$908$	17.4592	0.579403
$909$	−20.1833	−0.669437
$910$	−0.109375	−0.00362573
$911$	16.0891	0.533055	0.266527	−	0.963827i	$-0.414124\pi$
$911$	16.0891	0.533055	0.266527	+	0.963827i	$0.414124\pi$
$912$	−0.728191	−0.0241128
$913$	−29.1043	−0.963211
$914$	−8.50711	−0.281390
$915$	−6.49546	−0.214733
$916$	−10.7382	−0.354800
$917$	−1.97666	−0.0652752
$918$	−19.7830	−0.652936
$919$	6.30883	0.208109	0.104055	−	0.994572i	$-0.466818\pi$
$919$	6.30883	0.208109	0.104055	+	0.994572i	$0.466818\pi$
$920$	20.0841	0.662153
$921$	−0.186006	−0.00612911
$922$	−3.96942	−0.130726
$923$	1.80732	0.0594886
$924$	0.383404	0.0126131
$925$	0	0
$926$	−21.2249	−0.697495
$927$	−3.02806	−0.0994546
$928$	−5.85911	−0.192335
$929$	50.3539	1.65206	0.826029	−	0.563627i	$-0.190595\pi$
$929$	50.3539	1.65206	0.826029	+	0.563627i	$0.190595\pi$
$930$	−3.35401	−0.109982
$931$	−8.37653	−0.274530
$932$	−7.60442	−0.249091
$933$	10.7339	0.351411
$934$	28.5845	0.935315
$935$	46.2471	1.51244
$936$	−0.669774	−0.0218922
$937$	−40.2293	−1.31423	−0.657116	−	0.753789i	$-0.728224\pi$
$937$	−40.2293	−1.31423	−0.657116	+	0.753789i	$0.728224\pi$
$938$	2.38502	0.0778735
$939$	−2.35267	−0.0767765
$940$	−20.7050	−0.675324
$941$	8.21312	0.267740	0.133870	−	0.990999i	$-0.457260\pi$
$941$	8.21312	0.267740	0.133870	+	0.990999i	$0.457260\pi$
$942$	3.74517	0.122024
$943$	−71.7565	−2.33671
$944$	−11.9163	−0.387842
$945$	−1.46692	−0.0477190
$946$	−4.54719	−0.147842
$947$	−8.94025	−0.290519	−0.145260	−	0.989394i	$-0.546402\pi$
$947$	−8.94025	−0.290519	−0.145260	+	0.989394i	$0.546402\pi$
$948$	7.00600	0.227544
$949$	3.85655	0.125189
$950$	−0.500556	−0.0162402
$951$	7.82902	0.253873
$952$	−1.07155	−0.0347291
$953$	37.6011	1.21802	0.609010	−	0.793163i	$-0.291567\pi$
$953$	37.6011	1.21802	0.609010	+	0.793163i	$0.291567\pi$
$954$	31.6240	1.02386
$955$	−7.44558	−0.240933
$956$	16.0914	0.520433
$957$	12.1577	0.393001
$958$	30.7377	0.993090
$959$	−3.58473	−0.115757
$960$	1.40931	0.0454852
$961$	−25.3361	−0.817293
$962$	0	0
$963$	−39.2167	−1.26374
$964$	30.2107	0.973022
$965$	24.7049	0.795279
$966$	0.965600	0.0310677
$967$	17.1713	0.552191	0.276096	−	0.961130i	$-0.410959\pi$
$967$	17.1713	0.552191	0.276096	+	0.961130i	$0.410959\pi$
$968$	−0.741522	−0.0238334
$969$	−4.22297	−0.135661
$970$	−3.14673	−0.101036
$971$	−46.0084	−1.47648	−0.738239	−	0.674539i	$-0.764342\pi$
$971$	−46.0084	−1.47648	−0.738239	+	0.674539i	$0.764342\pi$
$972$	−13.7668	−0.441570
$973$	1.88432	0.0604084
$974$	−19.4211	−0.622291
$975$	0.0641132	0.00205327
$976$	−4.60897	−0.147530
$977$	51.2139	1.63848	0.819239	−	0.573452i	$-0.194396\pi$
$977$	51.2139	1.63848	0.819239	+	0.573452i	$0.194396\pi$
$978$	−6.52068	−0.208508
$979$	20.5118	0.655559
$980$	16.2115	0.517859
$981$	−37.3474	−1.19241
$982$	41.2649	1.31682
$983$	14.6596	0.467569	0.233784	−	0.972288i	$-0.424889\pi$
$983$	14.6596	0.467569	0.233784	+	0.972288i	$0.424889\pi$
$984$	−5.03517	−0.160515
$985$	31.6668	1.00899
$986$	−33.9785	−1.08210
$987$	−0.995453	−0.0316856
$988$	−0.305856	−0.00973059
$989$	−11.4521	−0.364154
$990$	20.9997	0.667413
$991$	5.59117	0.177609	0.0888047	−	0.996049i	$-0.471695\pi$
$991$	5.59117	0.177609	0.0888047	+	0.996049i	$0.471695\pi$
$992$	−2.37990	−0.0755618
$993$	3.15997	0.100279
$994$	1.31294	0.0416440
$995$	−14.4140	−0.456953
$996$	−5.14340	−0.162975
$997$	55.0584	1.74372	0.871858	−	0.489758i	$-0.162915\pi$
$997$	55.0584	1.74372	0.871858	+	0.489758i	$0.162915\pi$
$998$	32.1976	1.01920
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2738.2.a.u.1.6	✓	9
37.36	even	2		2738.2.a.v.1.6	yes	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2738.2.a.u.1.6	✓	9	1.1	even	1	trivial
2738.2.a.v.1.6	yes	9	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.605558 q^{3} +1.00000 q^{4} -2.32729 q^{5} +0.605558 q^{6} +0.184773 q^{7} -1.00000 q^{8} -2.63330 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.605558 q^{3} +1.00000 q^{4} -2.32729 q^{5} +0.605558 q^{6} +0.184773 q^{7} -1.00000 q^{8} -2.63330 q^{9} +2.32729 q^{10} -3.42659 q^{11} -0.605558 q^{12} -0.254348 q^{13} -0.184773 q^{14} +1.40931 q^{15} +1.00000 q^{16} +5.79927 q^{17} +2.63330 q^{18} +1.20251 q^{19} -2.32729 q^{20} -0.111891 q^{21} +3.42659 q^{22} +8.62984 q^{23} +0.605558 q^{24} +0.416259 q^{25} +0.254348 q^{26} +3.41129 q^{27} +0.184773 q^{28} +5.85911 q^{29} -1.40931 q^{30} +2.37990 q^{31} -1.00000 q^{32} +2.07500 q^{33} -5.79927 q^{34} -0.430020 q^{35} -2.63330 q^{36} -1.20251 q^{38} +0.154022 q^{39} +2.32729 q^{40} -8.31493 q^{41} +0.111891 q^{42} -1.32703 q^{43} -3.42659 q^{44} +6.12844 q^{45} -8.62984 q^{46} +8.89664 q^{47} -0.605558 q^{48} -6.96586 q^{49} -0.416259 q^{50} -3.51179 q^{51} -0.254348 q^{52} +12.0093 q^{53} -3.41129 q^{54} +7.97466 q^{55} -0.184773 q^{56} -0.728191 q^{57} -5.85911 q^{58} -11.9163 q^{59} +1.40931 q^{60} -4.60897 q^{61} -2.37990 q^{62} -0.486563 q^{63} +1.00000 q^{64} +0.591940 q^{65} -2.07500 q^{66} -12.9078 q^{67} +5.79927 q^{68} -5.22587 q^{69} +0.430020 q^{70} -7.10570 q^{71} +2.63330 q^{72} -15.1625 q^{73} -0.252069 q^{75} +1.20251 q^{76} -0.633141 q^{77} -0.154022 q^{78} -11.5695 q^{79} -2.32729 q^{80} +5.83416 q^{81} +8.31493 q^{82} +8.49365 q^{83} -0.111891 q^{84} -13.4965 q^{85} +1.32703 q^{86} -3.54803 q^{87} +3.42659 q^{88} -5.98605 q^{89} -6.12844 q^{90} -0.0469966 q^{91} +8.62984 q^{92} -1.44117 q^{93} -8.89664 q^{94} -2.79859 q^{95} +0.605558 q^{96} -1.35210 q^{97} +6.96586 q^{98} +9.02324 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 9 q^{2} - 7 q^{3} + 9 q^{4} + 7 q^{5} + 7 q^{6} - 14 q^{7} - 9 q^{8} + 8 q^{9}+O(q^{10}) \) 9 * q - 9 * q^2 - 7 * q^3 + 9 * q^4 + 7 * q^5 + 7 * q^6 - 14 * q^7 - 9 * q^8 + 8 * q^9	\( 9 q - 9 q^{2} - 7 q^{3} + 9 q^{4} + 7 q^{5} + 7 q^{6} - 14 q^{7} - 9 q^{8} + 8 q^{9} - 7 q^{10} - q^{11} - 7 q^{12} + 3 q^{13} + 14 q^{14} - 16 q^{15} + 9 q^{16} + 10 q^{17} - 8 q^{18} + 9 q^{19} + 7 q^{20} - 6 q^{21} + q^{22} - 3 q^{23} + 7 q^{24} - 10 q^{25} - 3 q^{26} - 19 q^{27} - 14 q^{28} + 12 q^{29} + 16 q^{30} + 2 q^{31} - 9 q^{32} - 14 q^{33} - 10 q^{34} - 13 q^{35} + 8 q^{36} - 9 q^{38} + 23 q^{39} - 7 q^{40} - 16 q^{41} + 6 q^{42} - 6 q^{43} - q^{44} + 40 q^{45} + 3 q^{46} - 15 q^{47} - 7 q^{48} + q^{49} + 10 q^{50} - 12 q^{51} + 3 q^{52} - 7 q^{53} + 19 q^{54} + 14 q^{55} + 14 q^{56} - 26 q^{57} - 12 q^{58} + q^{59} - 16 q^{60} + 7 q^{61} - 2 q^{62} - 4 q^{63} + 9 q^{64} - 4 q^{65} + 14 q^{66} - 66 q^{67} + 10 q^{68} + 34 q^{69} + 13 q^{70} - 15 q^{71} - 8 q^{72} - 50 q^{73} - 26 q^{75} + 9 q^{76} - 28 q^{77} - 23 q^{78} - 29 q^{79} + 7 q^{80} + 33 q^{81} + 16 q^{82} - 43 q^{83} - 6 q^{84} - 26 q^{85} + 6 q^{86} - 3 q^{87} + q^{88} + 6 q^{89} - 40 q^{90} - 30 q^{91} - 3 q^{92} + 28 q^{93} + 15 q^{94} - 12 q^{95} + 7 q^{96} + 50 q^{97} - q^{98} - 22 q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - 7 * q^3 + 9 * q^4 + 7 * q^5 + 7 * q^6 - 14 * q^7 - 9 * q^8 + 8 * q^9 - 7 * q^10 - q^11 - 7 * q^12 + 3 * q^13 + 14 * q^14 - 16 * q^15 + 9 * q^16 + 10 * q^17 - 8 * q^18 + 9 * q^19 + 7 * q^20 - 6 * q^21 + q^22 - 3 * q^23 + 7 * q^24 - 10 * q^25 - 3 * q^26 - 19 * q^27 - 14 * q^28 + 12 * q^29 + 16 * q^30 + 2 * q^31 - 9 * q^32 - 14 * q^33 - 10 * q^34 - 13 * q^35 + 8 * q^36 - 9 * q^38 + 23 * q^39 - 7 * q^40 - 16 * q^41 + 6 * q^42 - 6 * q^43 - q^44 + 40 * q^45 + 3 * q^46 - 15 * q^47 - 7 * q^48 + q^49 + 10 * q^50 - 12 * q^51 + 3 * q^52 - 7 * q^53 + 19 * q^54 + 14 * q^55 + 14 * q^56 - 26 * q^57 - 12 * q^58 + q^59 - 16 * q^60 + 7 * q^61 - 2 * q^62 - 4 * q^63 + 9 * q^64 - 4 * q^65 + 14 * q^66 - 66 * q^67 + 10 * q^68 + 34 * q^69 + 13 * q^70 - 15 * q^71 - 8 * q^72 - 50 * q^73 - 26 * q^75 + 9 * q^76 - 28 * q^77 - 23 * q^78 - 29 * q^79 + 7 * q^80 + 33 * q^81 + 16 * q^82 - 43 * q^83 - 6 * q^84 - 26 * q^85 + 6 * q^86 - 3 * q^87 + q^88 + 6 * q^89 - 40 * q^90 - 30 * q^91 - 3 * q^92 + 28 * q^93 + 15 * q^94 - 12 * q^95 + 7 * q^96 + 50 * q^97 - q^98 - 22 * q^99

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