LMFDB - Embedded newform 1502.2.a.f.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1502,2,Mod(1,1502)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1502, 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("1502.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1502 = 2 \cdot 751 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1502.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:	$11.9935303836$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 20x^{9} - 7x^{8} + 134x^{7} + 70x^{6} - 354x^{5} - 193x^{4} + 341x^{3} + 163x^{2} - 72x - 16 $ x^11 - 20x^9 - 7x^8 + 134x^7 + 70x^6 - 354x^5 - 193x^4 + 341x^3 + 163x^2 - 72*x - 16
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			1.10
Root			$2.47084$ of defining polynomial
Character	$\chi$	$=$	1502.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.47084 q^{3} +1.00000 q^{4} -3.42444 q^{5} +1.47084 q^{6} -2.00214 q^{7} +1.00000 q^{8} -0.836618 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.47084 q^{3} +1.00000 q^{4} -3.42444 q^{5} +1.47084 q^{6} -2.00214 q^{7} +1.00000 q^{8} -0.836618 q^{9} -3.42444 q^{10} +3.77593 q^{11} +1.47084 q^{12} -4.09239 q^{13} -2.00214 q^{14} -5.03681 q^{15} +1.00000 q^{16} -2.88999 q^{17} -0.836618 q^{18} +1.26241 q^{19} -3.42444 q^{20} -2.94483 q^{21} +3.77593 q^{22} -9.00372 q^{23} +1.47084 q^{24} +6.72676 q^{25} -4.09239 q^{26} -5.64307 q^{27} -2.00214 q^{28} +0.872869 q^{29} -5.03681 q^{30} -5.05279 q^{31} +1.00000 q^{32} +5.55380 q^{33} -2.88999 q^{34} +6.85619 q^{35} -0.836618 q^{36} -4.53769 q^{37} +1.26241 q^{38} -6.01927 q^{39} -3.42444 q^{40} -4.02687 q^{41} -2.94483 q^{42} +10.6850 q^{43} +3.77593 q^{44} +2.86494 q^{45} -9.00372 q^{46} +6.17965 q^{47} +1.47084 q^{48} -2.99144 q^{49} +6.72676 q^{50} -4.25072 q^{51} -4.09239 q^{52} -6.04548 q^{53} -5.64307 q^{54} -12.9304 q^{55} -2.00214 q^{56} +1.85681 q^{57} +0.872869 q^{58} +4.45602 q^{59} -5.03681 q^{60} -12.5273 q^{61} -5.05279 q^{62} +1.67502 q^{63} +1.00000 q^{64} +14.0141 q^{65} +5.55380 q^{66} +6.45697 q^{67} -2.88999 q^{68} -13.2431 q^{69} +6.85619 q^{70} +10.5001 q^{71} -0.836618 q^{72} -8.35210 q^{73} -4.53769 q^{74} +9.89401 q^{75} +1.26241 q^{76} -7.55993 q^{77} -6.01927 q^{78} -3.70159 q^{79} -3.42444 q^{80} -5.79022 q^{81} -4.02687 q^{82} +3.33867 q^{83} -2.94483 q^{84} +9.89657 q^{85} +10.6850 q^{86} +1.28385 q^{87} +3.77593 q^{88} +0.0960082 q^{89} +2.86494 q^{90} +8.19354 q^{91} -9.00372 q^{92} -7.43186 q^{93} +6.17965 q^{94} -4.32304 q^{95} +1.47084 q^{96} -6.21823 q^{97} -2.99144 q^{98} -3.15901 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} - 12 q^{5} - 11 q^{6} - 9 q^{7} + 11 q^{8} + 18 q^{9}+O(q^{10}) $ 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 - 12 * q^5 - 11 * q^6 - 9 * q^7 + 11 * q^8 + 18 * q^9	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} - 12 q^{5} - 11 q^{6} - 9 q^{7} + 11 q^{8} + 18 q^{9} - 12 q^{10} - 7 q^{11} - 11 q^{12} - 21 q^{13} - 9 q^{14} - 3 q^{15} + 11 q^{16} - 16 q^{17} + 18 q^{18} - 22 q^{19} - 12 q^{20} - q^{21} - 7 q^{22} - 2 q^{23} - 11 q^{24} + 19 q^{25} - 21 q^{26} - 44 q^{27} - 9 q^{28} + 4 q^{29} - 3 q^{30} - 28 q^{31} + 11 q^{32} - 13 q^{33} - 16 q^{34} - 11 q^{35} + 18 q^{36} - 22 q^{37} - 22 q^{38} + 9 q^{39} - 12 q^{40} - 5 q^{41} - q^{42} - 7 q^{43} - 7 q^{44} - 23 q^{45} - 2 q^{46} - 31 q^{47} - 11 q^{48} - 2 q^{49} + 19 q^{50} - 6 q^{51} - 21 q^{52} - 17 q^{53} - 44 q^{54} - 18 q^{55} - 9 q^{56} + 7 q^{57} + 4 q^{58} - 18 q^{59} - 3 q^{60} - 18 q^{61} - 28 q^{62} - 27 q^{63} + 11 q^{64} + 22 q^{65} - 13 q^{66} - 11 q^{67} - 16 q^{68} + 9 q^{69} - 11 q^{70} - 16 q^{71} + 18 q^{72} - 33 q^{73} - 22 q^{74} - 21 q^{75} - 22 q^{76} + 9 q^{78} + 9 q^{79} - 12 q^{80} + 71 q^{81} - 5 q^{82} - 18 q^{83} - q^{84} - 8 q^{85} - 7 q^{86} - 17 q^{87} - 7 q^{88} - 23 q^{90} - 22 q^{91} - 2 q^{92} + 8 q^{93} - 31 q^{94} - 23 q^{95} - 11 q^{96} - 66 q^{97} - 2 q^{98} - 5 q^{99}+O(q^{100}) \) 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 - 12 * q^5 - 11 * q^6 - 9 * q^7 + 11 * q^8 + 18 * q^9 - 12 * q^10 - 7 * q^11 - 11 * q^12 - 21 * q^13 - 9 * q^14 - 3 * q^15 + 11 * q^16 - 16 * q^17 + 18 * q^18 - 22 * q^19 - 12 * q^20 - q^21 - 7 * q^22 - 2 * q^23 - 11 * q^24 + 19 * q^25 - 21 * q^26 - 44 * q^27 - 9 * q^28 + 4 * q^29 - 3 * q^30 - 28 * q^31 + 11 * q^32 - 13 * q^33 - 16 * q^34 - 11 * q^35 + 18 * q^36 - 22 * q^37 - 22 * q^38 + 9 * q^39 - 12 * q^40 - 5 * q^41 - q^42 - 7 * q^43 - 7 * q^44 - 23 * q^45 - 2 * q^46 - 31 * q^47 - 11 * q^48 - 2 * q^49 + 19 * q^50 - 6 * q^51 - 21 * q^52 - 17 * q^53 - 44 * q^54 - 18 * q^55 - 9 * q^56 + 7 * q^57 + 4 * q^58 - 18 * q^59 - 3 * q^60 - 18 * q^61 - 28 * q^62 - 27 * q^63 + 11 * q^64 + 22 * q^65 - 13 * q^66 - 11 * q^67 - 16 * q^68 + 9 * q^69 - 11 * q^70 - 16 * q^71 + 18 * q^72 - 33 * q^73 - 22 * q^74 - 21 * q^75 - 22 * q^76 + 9 * q^78 + 9 * q^79 - 12 * q^80 + 71 * q^81 - 5 * q^82 - 18 * q^83 - q^84 - 8 * q^85 - 7 * q^86 - 17 * q^87 - 7 * q^88 - 23 * q^90 - 22 * q^91 - 2 * q^92 + 8 * q^93 - 31 * q^94 - 23 * q^95 - 11 * q^96 - 66 * q^97 - 2 * q^98 - 5 * 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
$3$	1.47084	0.849192	0.424596	−	0.905383i	$-0.360416\pi$
$3$	1.47084	0.849192	0.424596	+	0.905383i	$0.360416\pi$
$4$	1.00000	0.500000
$5$	−3.42444	−1.53145	−0.765727	−	0.643166i	$-0.777621\pi$
$5$	−3.42444	−1.53145	−0.765727	+	0.643166i	$0.777621\pi$
$6$	1.47084	0.600470
$7$	−2.00214	−0.756737	−0.378369	−	0.925655i	$-0.623515\pi$
$7$	−2.00214	−0.756737	−0.378369	+	0.925655i	$0.623515\pi$
$8$	1.00000	0.353553
$9$	−0.836618	−0.278873
$10$	−3.42444	−1.08290
$11$	3.77593	1.13849	0.569243	−	0.822170i	$-0.307237\pi$
$11$	3.77593	1.13849	0.569243	+	0.822170i	$0.307237\pi$
$12$	1.47084	0.424596
$13$	−4.09239	−1.13503	−0.567513	−	0.823364i	$-0.692094\pi$
$13$	−4.09239	−1.13503	−0.567513	+	0.823364i	$0.692094\pi$
$14$	−2.00214	−0.535094
$15$	−5.03681	−1.30050
$16$	1.00000	0.250000
$17$	−2.88999	−0.700925	−0.350462	−	0.936577i	$-0.613976\pi$
$17$	−2.88999	−0.700925	−0.350462	+	0.936577i	$0.613976\pi$
$18$	−0.836618	−0.197193
$19$	1.26241	0.289617	0.144808	−	0.989460i	$-0.453743\pi$
$19$	1.26241	0.289617	0.144808	+	0.989460i	$0.453743\pi$
$20$	−3.42444	−0.765727
$21$	−2.94483	−0.642615
$22$	3.77593	0.805030
$23$	−9.00372	−1.87741	−0.938703	−	0.344727i	$-0.887972\pi$
$23$	−9.00372	−1.87741	−0.938703	+	0.344727i	$0.887972\pi$
$24$	1.47084	0.300235
$25$	6.72676	1.34535
$26$	−4.09239	−0.802584
$27$	−5.64307	−1.08601
$28$	−2.00214	−0.378369
$29$	0.872869	0.162088	0.0810439	−	0.996711i	$-0.474175\pi$
$29$	0.872869	0.162088	0.0810439	+	0.996711i	$0.474175\pi$
$30$	−5.03681	−0.919592
$31$	−5.05279	−0.907507	−0.453754	−	0.891127i	$-0.649915\pi$
$31$	−5.05279	−0.907507	−0.453754	+	0.891127i	$0.649915\pi$
$32$	1.00000	0.176777
$33$	5.55380	0.966793
$34$	−2.88999	−0.495628
$35$	6.85619	1.15891
$36$	−0.836618	−0.139436
$37$	−4.53769	−0.745992	−0.372996	−	0.927833i	$-0.621669\pi$
$37$	−4.53769	−0.745992	−0.372996	+	0.927833i	$0.621669\pi$
$38$	1.26241	0.204790
$39$	−6.01927	−0.963855
$40$	−3.42444	−0.541451
$41$	−4.02687	−0.628892	−0.314446	−	0.949275i	$-0.601819\pi$
$41$	−4.02687	−0.628892	−0.314446	+	0.949275i	$0.601819\pi$
$42$	−2.94483	−0.454398
$43$	10.6850	1.62945	0.814724	−	0.579849i	$-0.196888\pi$
$43$	10.6850	1.62945	0.814724	+	0.579849i	$0.196888\pi$
$44$	3.77593	0.569243
$45$	2.86494	0.427081
$46$	−9.00372	−1.32753
$47$	6.17965	0.901395	0.450697	−	0.892677i	$-0.351175\pi$
$47$	6.17965	0.901395	0.450697	+	0.892677i	$0.351175\pi$
$48$	1.47084	0.212298
$49$	−2.99144	−0.427349
$50$	6.72676	0.951307
$51$	−4.25072	−0.595220
$52$	−4.09239	−0.567513
$53$	−6.04548	−0.830411	−0.415205	−	0.909728i	$-0.636290\pi$
$53$	−6.04548	−0.830411	−0.415205	+	0.909728i	$0.636290\pi$
$54$	−5.64307	−0.767924
$55$	−12.9304	−1.74354
$56$	−2.00214	−0.267547
$57$	1.85681	0.245940
$58$	0.872869	0.114613
$59$	4.45602	0.580124	0.290062	−	0.957008i	$-0.406324\pi$
$59$	4.45602	0.580124	0.290062	+	0.957008i	$0.406324\pi$
$60$	−5.03681	−0.650249
$61$	−12.5273	−1.60396	−0.801978	−	0.597353i	$-0.796219\pi$
$61$	−12.5273	−1.60396	−0.801978	+	0.597353i	$0.796219\pi$
$62$	−5.05279	−0.641704
$63$	1.67502	0.211033
$64$	1.00000	0.125000
$65$	14.0141	1.73824
$66$	5.55380	0.683626
$67$	6.45697	0.788845	0.394422	−	0.918929i	$-0.370945\pi$
$67$	6.45697	0.788845	0.394422	+	0.918929i	$0.370945\pi$
$68$	−2.88999	−0.350462
$69$	−13.2431	−1.59428
$70$	6.85619	0.819472
$71$	10.5001	1.24614	0.623069	−	0.782167i	$-0.285886\pi$
$71$	10.5001	1.24614	0.623069	+	0.782167i	$0.285886\pi$
$72$	−0.836618	−0.0985964
$73$	−8.35210	−0.977540	−0.488770	−	0.872413i	$-0.662554\pi$
$73$	−8.35210	−0.977540	−0.488770	+	0.872413i	$0.662554\pi$
$74$	−4.53769	−0.527496
$75$	9.89401	1.14246
$76$	1.26241	0.144808
$77$	−7.55993	−0.861534
$78$	−6.01927	−0.681548
$79$	−3.70159	−0.416461	−0.208230	−	0.978080i	$-0.566770\pi$
$79$	−3.70159	−0.416461	−0.208230	+	0.978080i	$0.566770\pi$
$80$	−3.42444	−0.382864
$81$	−5.79022	−0.643357
$82$	−4.02687	−0.444694
$83$	3.33867	0.366466	0.183233	−	0.983069i	$-0.441344\pi$
$83$	3.33867	0.366466	0.183233	+	0.983069i	$0.441344\pi$
$84$	−2.94483	−0.321308
$85$	9.89657	1.07343
$86$	10.6850	1.15219
$87$	1.28385	0.137644
$88$	3.77593	0.402515
$89$	0.0960082	0.0101768	0.00508842	−	0.999987i	$-0.498380\pi$
$89$	0.0960082	0.0101768	0.00508842	+	0.999987i	$0.498380\pi$
$90$	2.86494	0.301992
$91$	8.19354	0.858916
$92$	−9.00372	−0.938703
$93$	−7.43186	−0.770648
$94$	6.17965	0.637382
$95$	−4.32304	−0.443535
$96$	1.47084	0.150117
$97$	−6.21823	−0.631366	−0.315683	−	0.948865i	$-0.602234\pi$
$97$	−6.21823	−0.631366	−0.315683	+	0.948865i	$0.602234\pi$
$98$	−2.99144	−0.302181
$99$	−3.15901	−0.317492
$100$	6.72676	0.672676
$101$	4.92476	0.490032	0.245016	−	0.969519i	$-0.421207\pi$
$101$	4.92476	0.490032	0.245016	+	0.969519i	$0.421207\pi$
$102$	−4.25072	−0.420884
$103$	3.16339	0.311698	0.155849	−	0.987781i	$-0.450189\pi$
$103$	3.16339	0.311698	0.155849	+	0.987781i	$0.450189\pi$
$104$	−4.09239	−0.401292
$105$	10.0844	0.984136
$106$	−6.04548	−0.587189
$107$	4.87838	0.471611	0.235805	−	0.971800i	$-0.424227\pi$
$107$	4.87838	0.471611	0.235805	+	0.971800i	$0.424227\pi$
$108$	−5.64307	−0.543004
$109$	−0.949889	−0.0909829	−0.0454914	−	0.998965i	$-0.514485\pi$
$109$	−0.949889	−0.0909829	−0.0454914	+	0.998965i	$0.514485\pi$
$110$	−12.9304	−1.23287
$111$	−6.67424	−0.633491
$112$	−2.00214	−0.189184
$113$	−8.41186	−0.791321	−0.395661	−	0.918397i	$-0.629484\pi$
$113$	−8.41186	−0.791321	−0.395661	+	0.918397i	$0.629484\pi$
$114$	1.85681	0.173906
$115$	30.8327	2.87516
$116$	0.872869	0.0810439
$117$	3.42377	0.316528
$118$	4.45602	0.410210
$119$	5.78615	0.530416
$120$	−5.03681	−0.459796
$121$	3.25763	0.296148
$122$	−12.5273	−1.13417
$123$	−5.92290	−0.534050
$124$	−5.05279	−0.453754
$125$	−5.91317	−0.528890
$126$	1.67502	0.149223
$127$	11.9583	1.06113	0.530563	−	0.847645i	$-0.321980\pi$
$127$	11.9583	1.06113	0.530563	+	0.847645i	$0.321980\pi$
$128$	1.00000	0.0883883
$129$	15.7160	1.38371
$130$	14.0141	1.22912
$131$	−8.83638	−0.772038	−0.386019	−	0.922491i	$-0.626150\pi$
$131$	−8.83638	−0.772038	−0.386019	+	0.922491i	$0.626150\pi$
$132$	5.55380	0.483396
$133$	−2.52752	−0.219164
$134$	6.45697	0.557797
$135$	19.3243	1.66317
$136$	−2.88999	−0.247814
$137$	3.57995	0.305856	0.152928	−	0.988237i	$-0.451130\pi$
$137$	3.57995	0.305856	0.152928	+	0.988237i	$0.451130\pi$
$138$	−13.2431	−1.12733
$139$	22.3255	1.89362	0.946812	−	0.321788i	$-0.104284\pi$
$139$	22.3255	1.89362	0.946812	+	0.321788i	$0.104284\pi$
$140$	6.85619	0.579454
$141$	9.08930	0.765457
$142$	10.5001	0.881153
$143$	−15.4526	−1.29221
$144$	−0.836618	−0.0697181
$145$	−2.98909	−0.248230
$146$	−8.35210	−0.691225
$147$	−4.39994	−0.362901
$148$	−4.53769	−0.372996
$149$	13.3373	1.09263	0.546317	−	0.837578i	$-0.316029\pi$
$149$	13.3373	1.09263	0.546317	+	0.837578i	$0.316029\pi$
$150$	9.89401	0.807843
$151$	8.42647	0.685736	0.342868	−	0.939384i	$-0.388602\pi$
$151$	8.42647	0.685736	0.342868	+	0.939384i	$0.388602\pi$
$152$	1.26241	0.102395
$153$	2.41781	0.195469
$154$	−7.55993	−0.609196
$155$	17.3029	1.38981
$156$	−6.01927	−0.481928
$157$	3.91710	0.312619	0.156309	−	0.987708i	$-0.450040\pi$
$157$	3.91710	0.312619	0.156309	+	0.987708i	$0.450040\pi$
$158$	−3.70159	−0.294482
$159$	−8.89196	−0.705178
$160$	−3.42444	−0.270725
$161$	18.0267	1.42070
$162$	−5.79022	−0.454922
$163$	−8.44402	−0.661387	−0.330693	−	0.943738i	$-0.607283\pi$
$163$	−8.44402	−0.661387	−0.330693	+	0.943738i	$0.607283\pi$
$164$	−4.02687	−0.314446
$165$	−19.0186	−1.48060
$166$	3.33867	0.259131
$167$	−21.3283	−1.65044	−0.825218	−	0.564814i	$-0.808948\pi$
$167$	−21.3283	−1.65044	−0.825218	+	0.564814i	$0.808948\pi$
$168$	−2.94483	−0.227199
$169$	3.74769	0.288284
$170$	9.89657	0.759032
$171$	−1.05615	−0.0807662
$172$	10.6850	0.814724
$173$	15.7132	1.19465	0.597327	−	0.801997i	$-0.296229\pi$
$173$	15.7132	1.19465	0.597327	+	0.801997i	$0.296229\pi$
$174$	1.28385	0.0973288
$175$	−13.4679	−1.01808
$176$	3.77593	0.284621
$177$	6.55411	0.492637
$178$	0.0960082	0.00719612
$179$	17.7812	1.32903	0.664516	−	0.747274i	$-0.268638\pi$
$179$	17.7812	1.32903	0.664516	+	0.747274i	$0.268638\pi$
$180$	2.86494	0.213540
$181$	−17.6347	−1.31078	−0.655389	−	0.755291i	$-0.727495\pi$
$181$	−17.6347	−1.31078	−0.655389	+	0.755291i	$0.727495\pi$
$182$	8.19354	0.607346
$183$	−18.4257	−1.36207
$184$	−9.00372	−0.663763
$185$	15.5390	1.14245
$186$	−7.43186	−0.544930
$187$	−10.9124	−0.797992
$188$	6.17965	0.450697
$189$	11.2982	0.821823
$190$	−4.32304	−0.313626
$191$	14.5768	1.05474	0.527372	−	0.849635i	$-0.323177\pi$
$191$	14.5768	1.05474	0.527372	+	0.849635i	$0.323177\pi$
$192$	1.47084	0.106149
$193$	−16.1131	−1.15985	−0.579923	−	0.814672i	$-0.696917\pi$
$193$	−16.1131	−1.15985	−0.579923	+	0.814672i	$0.696917\pi$
$194$	−6.21823	−0.446443
$195$	20.6126	1.47610
$196$	−2.99144	−0.213674
$197$	−21.2594	−1.51467	−0.757336	−	0.653025i	$-0.773499\pi$
$197$	−21.2594	−1.51467	−0.757336	+	0.653025i	$0.773499\pi$
$198$	−3.15901	−0.224501
$199$	23.3621	1.65610	0.828048	−	0.560658i	$-0.189452\pi$
$199$	23.3621	1.65610	0.828048	+	0.560658i	$0.189452\pi$
$200$	6.72676	0.475654
$201$	9.49720	0.669881
$202$	4.92476	0.346505
$203$	−1.74761	−0.122658
$204$	−4.25072	−0.297610
$205$	13.7898	0.963119
$206$	3.16339	0.220404
$207$	7.53268	0.523557
$208$	−4.09239	−0.283756
$209$	4.76677	0.329724
$210$	10.0844	0.695889
$211$	−14.1102	−0.971387	−0.485694	−	0.874129i	$-0.661433\pi$
$211$	−14.1102	−0.971387	−0.485694	+	0.874129i	$0.661433\pi$
$212$	−6.04548	−0.415205
$213$	15.4441	1.05821
$214$	4.87838	0.333479
$215$	−36.5901	−2.49542
$216$	−5.64307	−0.383962
$217$	10.1164	0.686744
$218$	−0.949889	−0.0643346
$219$	−12.2846	−0.830119
$220$	−12.9304	−0.871769
$221$	11.8270	0.795567
$222$	−6.67424	−0.447945
$223$	−6.29680	−0.421665	−0.210832	−	0.977522i	$-0.567617\pi$
$223$	−6.29680	−0.421665	−0.210832	+	0.977522i	$0.567617\pi$
$224$	−2.00214	−0.133773
$225$	−5.62773	−0.375182
$226$	−8.41186	−0.559549
$227$	−11.0800	−0.735404	−0.367702	−	0.929944i	$-0.619855\pi$
$227$	−11.0800	−0.735404	−0.367702	+	0.929944i	$0.619855\pi$
$228$	1.85681	0.122970
$229$	3.99699	0.264129	0.132064	−	0.991241i	$-0.457839\pi$
$229$	3.99699	0.264129	0.132064	+	0.991241i	$0.457839\pi$
$230$	30.8327	2.03305
$231$	−11.1195	−0.731608
$232$	0.872869	0.0573067
$233$	−27.9738	−1.83263	−0.916314	−	0.400461i	$-0.868850\pi$
$233$	−27.9738	−1.83263	−0.916314	+	0.400461i	$0.868850\pi$
$234$	3.42377	0.223819
$235$	−21.1618	−1.38044
$236$	4.45602	0.290062
$237$	−5.44446	−0.353655
$238$	5.78615	0.375060
$239$	−2.36376	−0.152899	−0.0764495	−	0.997073i	$-0.524358\pi$
$239$	−2.36376	−0.152899	−0.0764495	+	0.997073i	$0.524358\pi$
$240$	−5.03681	−0.325125
$241$	−2.27802	−0.146740	−0.0733702	−	0.997305i	$-0.523375\pi$
$241$	−2.27802	−0.146740	−0.0733702	+	0.997305i	$0.523375\pi$
$242$	3.25763	0.209408
$243$	8.41269	0.539674
$244$	−12.5273	−0.801978
$245$	10.2440	0.654465
$246$	−5.92290	−0.377630
$247$	−5.16628	−0.328723
$248$	−5.05279	−0.320852
$249$	4.91066	0.311200
$250$	−5.91317	−0.373982
$251$	−24.8456	−1.56824	−0.784121	−	0.620608i	$-0.786886\pi$
$251$	−24.8456	−1.56824	−0.784121	+	0.620608i	$0.786886\pi$
$252$	1.67502	0.105517
$253$	−33.9974	−2.13740
$254$	11.9583	0.750330
$255$	14.5563	0.911552
$256$	1.00000	0.0625000
$257$	9.68905	0.604386	0.302193	−	0.953247i	$-0.402281\pi$
$257$	9.68905	0.604386	0.302193	+	0.953247i	$0.402281\pi$
$258$	15.7160	0.978434
$259$	9.08509	0.564520
$260$	14.0141	0.869120
$261$	−0.730258	−0.0452018
$262$	−8.83638	−0.545914
$263$	−6.92838	−0.427222	−0.213611	−	0.976919i	$-0.568523\pi$
$263$	−6.92838	−0.427222	−0.213611	+	0.976919i	$0.568523\pi$
$264$	5.55380	0.341813
$265$	20.7024	1.27174
$266$	−2.52752	−0.154972
$267$	0.141213	0.00864210
$268$	6.45697	0.394422
$269$	20.3441	1.24040	0.620201	−	0.784443i	$-0.287051\pi$
$269$	20.3441	1.24040	0.620201	+	0.784443i	$0.287051\pi$
$270$	19.3243	1.17604
$271$	−13.9573	−0.847843	−0.423921	−	0.905699i	$-0.639347\pi$
$271$	−13.9573	−0.847843	−0.423921	+	0.905699i	$0.639347\pi$
$272$	−2.88999	−0.175231
$273$	12.0514	0.729385
$274$	3.57995	0.216273
$275$	25.3998	1.53166
$276$	−13.2431	−0.797139
$277$	9.83725	0.591063	0.295532	−	0.955333i	$-0.404503\pi$
$277$	9.83725	0.591063	0.295532	+	0.955333i	$0.404503\pi$
$278$	22.3255	1.33899
$279$	4.22725	0.253079
$280$	6.85619	0.409736
$281$	4.06418	0.242448	0.121224	−	0.992625i	$-0.461318\pi$
$281$	4.06418	0.242448	0.121224	+	0.992625i	$0.461318\pi$
$282$	9.08930	0.541260
$283$	−22.4964	−1.33727	−0.668636	−	0.743590i	$-0.733122\pi$
$283$	−22.4964	−1.33727	−0.668636	+	0.743590i	$0.733122\pi$
$284$	10.5001	0.623069
$285$	−6.35852	−0.376646
$286$	−15.4526	−0.913730
$287$	8.06235	0.475906
$288$	−0.836618	−0.0492982
$289$	−8.64798	−0.508705
$290$	−2.98909	−0.175525
$291$	−9.14605	−0.536151
$292$	−8.35210	−0.488770
$293$	−8.88745	−0.519210	−0.259605	−	0.965715i	$-0.583592\pi$
$293$	−8.88745	−0.519210	−0.259605	+	0.965715i	$0.583592\pi$
$294$	−4.39994	−0.256610
$295$	−15.2593	−0.888433
$296$	−4.53769	−0.263748
$297$	−21.3078	−1.23640
$298$	13.3373	0.772609
$299$	36.8468	2.13090
$300$	9.89401	0.571231
$301$	−21.3929	−1.23306
$302$	8.42647	0.484889
$303$	7.24356	0.416132
$304$	1.26241	0.0724042
$305$	42.8989	2.45639
$306$	2.41781	0.138217
$307$	−27.8800	−1.59119	−0.795597	−	0.605827i	$-0.792842\pi$
$307$	−27.8800	−1.59119	−0.795597	+	0.605827i	$0.792842\pi$
$308$	−7.55993	−0.430767
$309$	4.65285	0.264691
$310$	17.3029	0.982741
$311$	−11.4904	−0.651562	−0.325781	−	0.945445i	$-0.605627\pi$
$311$	−11.4904	−0.651562	−0.325781	+	0.945445i	$0.605627\pi$
$312$	−6.01927	−0.340774
$313$	−29.3670	−1.65992	−0.829960	−	0.557823i	$-0.811637\pi$
$313$	−29.3670	−1.65992	−0.829960	+	0.557823i	$0.811637\pi$
$314$	3.91710	0.221055
$315$	−5.73601	−0.323188
$316$	−3.70159	−0.208230
$317$	27.6895	1.55520	0.777598	−	0.628762i	$-0.216438\pi$
$317$	27.6895	1.55520	0.777598	+	0.628762i	$0.216438\pi$
$318$	−8.89196	−0.498636
$319$	3.29589	0.184535
$320$	−3.42444	−0.191432
$321$	7.17534	0.400488
$322$	18.0267	1.00459
$323$	−3.64835	−0.202999
$324$	−5.79022	−0.321679
$325$	−27.5285	−1.52701
$326$	−8.44402	−0.467671
$327$	−1.39714	−0.0772619
$328$	−4.02687	−0.222347
$329$	−12.3725	−0.682119
$330$	−19.0186	−1.04694
$331$	1.77513	0.0975702	0.0487851	−	0.998809i	$-0.484465\pi$
$331$	1.77513	0.0975702	0.0487851	+	0.998809i	$0.484465\pi$
$332$	3.33867	0.183233
$333$	3.79631	0.208037
$334$	−21.3283	−1.16703
$335$	−22.1115	−1.20808
$336$	−2.94483	−0.160654
$337$	−12.4321	−0.677218	−0.338609	−	0.940927i	$-0.609956\pi$
$337$	−12.4321	−0.677218	−0.338609	+	0.940927i	$0.609956\pi$
$338$	3.74769	0.203847
$339$	−12.3725	−0.671984
$340$	9.89657	0.536717
$341$	−19.0790	−1.03318
$342$	−1.05615	−0.0571103
$343$	20.0042	1.08013
$344$	10.6850	0.576097
$345$	45.3501	2.44156
$346$	15.7132	0.844749
$347$	31.3220	1.68145	0.840726	−	0.541461i	$-0.182129\pi$
$347$	31.3220	1.68145	0.840726	+	0.541461i	$0.182129\pi$
$348$	1.28385	0.0688218
$349$	3.44998	0.184673	0.0923365	−	0.995728i	$-0.470566\pi$
$349$	3.44998	0.184673	0.0923365	+	0.995728i	$0.470566\pi$
$350$	−13.4679	−0.719890
$351$	23.0937	1.23265
$352$	3.77593	0.201258
$353$	34.6373	1.84356	0.921779	−	0.387716i	$-0.126736\pi$
$353$	34.6373	1.84356	0.921779	+	0.387716i	$0.126736\pi$
$354$	6.55411	0.348347
$355$	−35.9571	−1.90840
$356$	0.0960082	0.00508842
$357$	8.51053	0.450425
$358$	17.7812	0.939767
$359$	−21.7435	−1.14758	−0.573789	−	0.819003i	$-0.694527\pi$
$359$	−21.7435	−1.14758	−0.573789	+	0.819003i	$0.694527\pi$
$360$	2.86494	0.150996
$361$	−17.4063	−0.916122
$362$	−17.6347	−0.926860
$363$	4.79147	0.251487
$364$	8.19354	0.429458
$365$	28.6012	1.49706
$366$	−18.4257	−0.963127
$367$	−28.7330	−1.49985	−0.749926	−	0.661521i	$-0.769911\pi$
$367$	−28.7330	−1.49985	−0.749926	+	0.661521i	$0.769911\pi$
$368$	−9.00372	−0.469352
$369$	3.36895	0.175381
$370$	15.5390	0.807836
$371$	12.1039	0.628403
$372$	−7.43186	−0.385324
$373$	−4.79859	−0.248462	−0.124231	−	0.992253i	$-0.539646\pi$
$373$	−4.79859	−0.248462	−0.124231	+	0.992253i	$0.539646\pi$
$374$	−10.9124	−0.564266
$375$	−8.69736	−0.449129
$376$	6.17965	0.318691
$377$	−3.57213	−0.183974
$378$	11.2982	0.581117
$379$	−13.5779	−0.697452	−0.348726	−	0.937225i	$-0.613386\pi$
$379$	−13.5779	−0.697452	−0.348726	+	0.937225i	$0.613386\pi$
$380$	−4.32304	−0.221767
$381$	17.5888	0.901100
$382$	14.5768	0.745816
$383$	17.0637	0.871915	0.435957	−	0.899967i	$-0.356410\pi$
$383$	17.0637	0.871915	0.435957	+	0.899967i	$0.356410\pi$
$384$	1.47084	0.0750587
$385$	25.8885	1.31940
$386$	−16.1131	−0.820134
$387$	−8.93927	−0.454408
$388$	−6.21823	−0.315683
$389$	−28.2812	−1.43391	−0.716957	−	0.697117i	$-0.754466\pi$
$389$	−28.2812	−1.43391	−0.716957	+	0.697117i	$0.754466\pi$
$390$	20.6126	1.04376
$391$	26.0206	1.31592
$392$	−2.99144	−0.151091
$393$	−12.9969	−0.655609
$394$	−21.2594	−1.07103
$395$	12.6758	0.637791
$396$	−3.15901	−0.158746
$397$	−20.6804	−1.03792	−0.518960	−	0.854799i	$-0.673681\pi$
$397$	−20.6804	−1.03792	−0.518960	+	0.854799i	$0.673681\pi$
$398$	23.3621	1.17104
$399$	−3.71759	−0.186112
$400$	6.72676	0.336338
$401$	3.78294	0.188911	0.0944554	−	0.995529i	$-0.469889\pi$
$401$	3.78294	0.188911	0.0944554	+	0.995529i	$0.469889\pi$
$402$	9.49720	0.473677
$403$	20.6780	1.03004
$404$	4.92476	0.245016
$405$	19.8282	0.985272
$406$	−1.74761	−0.0867322
$407$	−17.1340	−0.849301
$408$	−4.25072	−0.210442
$409$	−5.47806	−0.270873	−0.135436	−	0.990786i	$-0.543244\pi$
$409$	−5.47806	−0.270873	−0.135436	+	0.990786i	$0.543244\pi$
$410$	13.7898	0.681028
$411$	5.26555	0.259730
$412$	3.16339	0.155849
$413$	−8.92156	−0.439001
$414$	7.53268	0.370211
$415$	−11.4331	−0.561226
$416$	−4.09239	−0.200646
$417$	32.8373	1.60805
$418$	4.76677	0.233150
$419$	0.105619	0.00515981	0.00257990	−	0.999997i	$-0.499179\pi$
$419$	0.105619	0.00515981	0.00257990	+	0.999997i	$0.499179\pi$
$420$	10.0844	0.492068
$421$	0.455310	0.0221905	0.0110952	−	0.999938i	$-0.496468\pi$
$421$	0.455310	0.0221905	0.0110952	+	0.999938i	$0.496468\pi$
$422$	−14.1102	−0.686874
$423$	−5.17001	−0.251374
$424$	−6.04548	−0.293595
$425$	−19.4402	−0.942990
$426$	15.4441	0.748268
$427$	25.0814	1.21377
$428$	4.87838	0.235805
$429$	−22.7283	−1.09733
$430$	−36.5901	−1.76453
$431$	30.7660	1.48195	0.740974	−	0.671534i	$-0.234364\pi$
$431$	30.7660	1.48195	0.740974	+	0.671534i	$0.234364\pi$
$432$	−5.64307	−0.271502
$433$	−5.58574	−0.268433	−0.134217	−	0.990952i	$-0.542852\pi$
$433$	−5.58574	−0.268433	−0.134217	+	0.990952i	$0.542852\pi$
$434$	10.1164	0.485602
$435$	−4.39648	−0.210795
$436$	−0.949889	−0.0454914
$437$	−11.3664	−0.543728
$438$	−12.2846	−0.586983
$439$	−1.79100	−0.0854797	−0.0427398	−	0.999086i	$-0.513609\pi$
$439$	−1.79100	−0.0854797	−0.0427398	+	0.999086i	$0.513609\pi$
$440$	−12.9304	−0.616434
$441$	2.50269	0.119176
$442$	11.8270	0.562551
$443$	24.4289	1.16065	0.580326	−	0.814384i	$-0.302925\pi$
$443$	24.4289	1.16065	0.580326	+	0.814384i	$0.302925\pi$
$444$	−6.67424	−0.316745
$445$	−0.328774	−0.0155854
$446$	−6.29680	−0.298162
$447$	19.6171	0.927856
$448$	−2.00214	−0.0945921
$449$	−6.00251	−0.283276	−0.141638	−	0.989919i	$-0.545237\pi$
$449$	−6.00251	−0.283276	−0.141638	+	0.989919i	$0.545237\pi$
$450$	−5.62773	−0.265294
$451$	−15.2052	−0.715984
$452$	−8.41186	−0.395661
$453$	12.3940	0.582322
$454$	−11.0800	−0.520009
$455$	−28.0582	−1.31539
$456$	1.85681	0.0869530
$457$	4.14640	0.193961	0.0969803	−	0.995286i	$-0.469082\pi$
$457$	4.14640	0.193961	0.0969803	+	0.995286i	$0.469082\pi$
$458$	3.99699	0.186767
$459$	16.3084	0.761210
$460$	30.8327	1.43758
$461$	−35.6738	−1.66149	−0.830746	−	0.556652i	$-0.812086\pi$
$461$	−35.6738	−1.66149	−0.830746	+	0.556652i	$0.812086\pi$
$462$	−11.1195	−0.517325
$463$	2.30170	0.106969	0.0534844	−	0.998569i	$-0.482967\pi$
$463$	2.30170	0.106969	0.0534844	+	0.998569i	$0.482967\pi$
$464$	0.872869	0.0405219
$465$	25.4499	1.18021
$466$	−27.9738	−1.29586
$467$	7.74741	0.358507	0.179254	−	0.983803i	$-0.442632\pi$
$467$	7.74741	0.358507	0.179254	+	0.983803i	$0.442632\pi$
$468$	3.42377	0.158264
$469$	−12.9278	−0.596948
$470$	−21.1618	−0.976122
$471$	5.76145	0.265474
$472$	4.45602	0.205105
$473$	40.3458	1.85510
$474$	−5.44446	−0.250072
$475$	8.49193	0.389636
$476$	5.78615	0.265208
$477$	5.05776	0.231579
$478$	−2.36376	−0.108116
$479$	15.9289	0.727809	0.363905	−	0.931436i	$-0.381443\pi$
$479$	15.9289	0.727809	0.363905	+	0.931436i	$0.381443\pi$
$480$	−5.03681	−0.229898
$481$	18.5700	0.846720
$482$	−2.27802	−0.103761
$483$	26.5145	1.20645
$484$	3.25763	0.148074
$485$	21.2939	0.966908
$486$	8.41269	0.381607
$487$	8.75822	0.396873	0.198436	−	0.980114i	$-0.436414\pi$
$487$	8.75822	0.396873	0.198436	+	0.980114i	$0.436414\pi$
$488$	−12.5273	−0.567084
$489$	−12.4198	−0.561645
$490$	10.2440	0.462777
$491$	−28.6689	−1.29381	−0.646904	−	0.762571i	$-0.723937\pi$
$491$	−28.6689	−1.29381	−0.646904	+	0.762571i	$0.723937\pi$
$492$	−5.92290	−0.267025
$493$	−2.52258	−0.113611
$494$	−5.16628	−0.232442
$495$	10.8178	0.486225
$496$	−5.05279	−0.226877
$497$	−21.0227	−0.942999
$498$	4.91066	0.220052
$499$	22.4882	1.00671	0.503356	−	0.864079i	$-0.332098\pi$
$499$	22.4882	1.00671	0.503356	+	0.864079i	$0.332098\pi$
$500$	−5.91317	−0.264445
$501$	−31.3707	−1.40154
$502$	−24.8456	−1.10891
$503$	34.9312	1.55751	0.778753	−	0.627331i	$-0.215853\pi$
$503$	34.9312	1.55751	0.778753	+	0.627331i	$0.215853\pi$
$504$	1.67502	0.0746115
$505$	−16.8645	−0.750462
$506$	−33.9974	−1.51137
$507$	5.51227	0.244808
$508$	11.9583	0.530563
$509$	17.3400	0.768580	0.384290	−	0.923212i	$-0.374446\pi$
$509$	17.3400	0.768580	0.384290	+	0.923212i	$0.374446\pi$
$510$	14.5563	0.644564
$511$	16.7221	0.739741
$512$	1.00000	0.0441942
$513$	−7.12386	−0.314526
$514$	9.68905	0.427366
$515$	−10.8328	−0.477351
$516$	15.7160	0.691857
$517$	23.3339	1.02622
$518$	9.08509	0.399176
$519$	23.1117	1.01449
$520$	14.0141	0.614561
$521$	27.6791	1.21264	0.606321	−	0.795220i	$-0.292645\pi$
$521$	27.6791	1.21264	0.606321	+	0.795220i	$0.292645\pi$
$522$	−0.730258	−0.0319625
$523$	8.56901	0.374697	0.187348	−	0.982294i	$-0.440011\pi$
$523$	8.56901	0.374697	0.187348	+	0.982294i	$0.440011\pi$
$524$	−8.83638	−0.386019
$525$	−19.8092	−0.864544
$526$	−6.92838	−0.302092
$527$	14.6025	0.636094
$528$	5.55380	0.241698
$529$	58.0670	2.52465
$530$	20.7024	0.899253
$531$	−3.72798	−0.161781
$532$	−2.52752	−0.109582
$533$	16.4795	0.713808
$534$	0.141213	0.00611089
$535$	−16.7057	−0.722250
$536$	6.45697	0.278899
$537$	26.1534	1.12860
$538$	20.3441	0.877097
$539$	−11.2955	−0.486530
$540$	19.3243	0.831586
$541$	−5.60331	−0.240905	−0.120453	−	0.992719i	$-0.538435\pi$
$541$	−5.60331	−0.240905	−0.120453	+	0.992719i	$0.538435\pi$
$542$	−13.9573	−0.599515
$543$	−25.9379	−1.11310
$544$	−2.88999	−0.123907
$545$	3.25283	0.139336
$546$	12.0514	0.515753
$547$	−20.7809	−0.888526	−0.444263	−	0.895896i	$-0.646534\pi$
$547$	−20.7809	−0.888526	−0.444263	+	0.895896i	$0.646534\pi$
$548$	3.57995	0.152928
$549$	10.4806	0.447300
$550$	25.3998	1.08305
$551$	1.10192	0.0469433
$552$	−13.2431	−0.563663
$553$	7.41109	0.315151
$554$	9.83725	0.417945
$555$	22.8555	0.970162
$556$	22.3255	0.946812
$557$	−37.7291	−1.59864	−0.799318	−	0.600909i	$-0.794805\pi$
$557$	−37.7291	−1.59864	−0.799318	+	0.600909i	$0.794805\pi$
$558$	4.22725	0.178954
$559$	−43.7272	−1.84947
$560$	6.85619	0.289727
$561$	−16.0504	−0.677649
$562$	4.06418	0.171437
$563$	−43.8677	−1.84880	−0.924401	−	0.381423i	$-0.875434\pi$
$563$	−43.8677	−1.84880	−0.924401	+	0.381423i	$0.875434\pi$
$564$	9.08930	0.382729
$565$	28.8059	1.21187
$566$	−22.4964	−0.945594
$567$	11.5928	0.486853
$568$	10.5001	0.440576
$569$	−10.2971	−0.431675	−0.215838	−	0.976429i	$-0.569248\pi$
$569$	−10.2971	−0.431675	−0.215838	+	0.976429i	$0.569248\pi$
$570$	−6.35852	−0.266329
$571$	28.4486	1.19054	0.595269	−	0.803527i	$-0.297046\pi$
$571$	28.4486	1.19054	0.595269	+	0.803527i	$0.297046\pi$
$572$	−15.4526	−0.646105
$573$	21.4403	0.895680
$574$	8.06235	0.336516
$575$	−60.5659	−2.52577
$576$	−0.836618	−0.0348591
$577$	−24.3687	−1.01448	−0.507242	−	0.861804i	$-0.669335\pi$
$577$	−24.3687	−1.01448	−0.507242	+	0.861804i	$0.669335\pi$
$578$	−8.64798	−0.359709
$579$	−23.6998	−0.984931
$580$	−2.98909	−0.124115
$581$	−6.68447	−0.277319
$582$	−9.14605	−0.379116
$583$	−22.8273	−0.945410
$584$	−8.35210	−0.345612
$585$	−11.7245	−0.484748
$586$	−8.88745	−0.367137
$587$	−32.4551	−1.33956	−0.669782	−	0.742558i	$-0.733612\pi$
$587$	−32.4551	−1.33956	−0.669782	+	0.742558i	$0.733612\pi$
$588$	−4.39994	−0.181451
$589$	−6.37869	−0.262829
$590$	−15.2593	−0.628217
$591$	−31.2693	−1.28625
$592$	−4.53769	−0.186498
$593$	15.4855	0.635913	0.317957	−	0.948105i	$-0.397003\pi$
$593$	15.4855	0.635913	0.317957	+	0.948105i	$0.397003\pi$
$594$	−21.3078	−0.874270
$595$	−19.8143	−0.812307
$596$	13.3373	0.546317
$597$	34.3620	1.40634
$598$	36.8468	1.50678
$599$	−39.6555	−1.62028	−0.810139	−	0.586238i	$-0.800608\pi$
$599$	−39.6555	−1.62028	−0.810139	+	0.586238i	$0.800608\pi$
$600$	9.89401	0.403921
$601$	−26.1682	−1.06742	−0.533711	−	0.845667i	$-0.679203\pi$
$601$	−26.1682	−1.06742	−0.533711	+	0.845667i	$0.679203\pi$
$602$	−21.3929	−0.871908
$603$	−5.40202	−0.219987
$604$	8.42647	0.342868
$605$	−11.1555	−0.453537
$606$	7.24356	0.294249
$607$	1.36323	0.0553316	0.0276658	−	0.999617i	$-0.491193\pi$
$607$	1.36323	0.0553316	0.0276658	+	0.999617i	$0.491193\pi$
$608$	1.26241	0.0511975
$609$	−2.57045	−0.104160
$610$	42.8989	1.73693
$611$	−25.2896	−1.02311
$612$	2.41781	0.0977343
$613$	−7.32097	−0.295691	−0.147846	−	0.989010i	$-0.547234\pi$
$613$	−7.32097	−0.295691	−0.147846	+	0.989010i	$0.547234\pi$
$614$	−27.8800	−1.12514
$615$	20.2826	0.817873
$616$	−7.55993	−0.304598
$617$	23.8565	0.960426	0.480213	−	0.877152i	$-0.340559\pi$
$617$	23.8565	0.960426	0.480213	+	0.877152i	$0.340559\pi$
$618$	4.65285	0.187165
$619$	−25.9956	−1.04485	−0.522425	−	0.852685i	$-0.674973\pi$
$619$	−25.9956	−1.04485	−0.522425	+	0.852685i	$0.674973\pi$
$620$	17.3029	0.694903
$621$	50.8086	2.03888
$622$	−11.4904	−0.460724
$623$	−0.192222	−0.00770120
$624$	−6.01927	−0.240964
$625$	−13.3845	−0.535381
$626$	−29.3670	−1.17374
$627$	7.01117	0.279999
$628$	3.91710	0.156309
$629$	13.1139	0.522884
$630$	−5.73601	−0.228528
$631$	4.99809	0.198971	0.0994854	−	0.995039i	$-0.468280\pi$
$631$	4.99809	0.198971	0.0994854	+	0.995039i	$0.468280\pi$
$632$	−3.70159	−0.147241
$633$	−20.7539	−0.824894
$634$	27.6895	1.09969
$635$	−40.9504	−1.62507
$636$	−8.89196	−0.352589
$637$	12.2422	0.485052
$638$	3.29589	0.130486
$639$	−8.78461	−0.347514
$640$	−3.42444	−0.135363
$641$	−14.4295	−0.569931	−0.284966	−	0.958538i	$-0.591982\pi$
$641$	−14.4295	−0.569931	−0.284966	+	0.958538i	$0.591982\pi$
$642$	7.17534	0.283188
$643$	−46.2897	−1.82549	−0.912745	−	0.408530i	$-0.866041\pi$
$643$	−46.2897	−1.82549	−0.912745	+	0.408530i	$0.866041\pi$
$644$	18.0267	0.710352
$645$	−53.8183	−2.11910
$646$	−3.64835	−0.143542
$647$	−30.7519	−1.20898	−0.604491	−	0.796612i	$-0.706623\pi$
$647$	−30.7519	−1.20898	−0.604491	+	0.796612i	$0.706623\pi$
$648$	−5.79022	−0.227461
$649$	16.8256	0.660462
$650$	−27.5285	−1.07976
$651$	14.8796	0.583178
$652$	−8.44402	−0.330693
$653$	−27.2529	−1.06649	−0.533243	−	0.845962i	$-0.679027\pi$
$653$	−27.2529	−1.06649	−0.533243	+	0.845962i	$0.679027\pi$
$654$	−1.39714	−0.0546324
$655$	30.2596	1.18234
$656$	−4.02687	−0.157223
$657$	6.98752	0.272609
$658$	−12.3725	−0.482331
$659$	45.7319	1.78146	0.890732	−	0.454529i	$-0.150192\pi$
$659$	45.7319	1.78146	0.890732	+	0.454529i	$0.150192\pi$
$660$	−19.0186	−0.740299
$661$	−5.76438	−0.224208	−0.112104	−	0.993696i	$-0.535759\pi$
$661$	−5.76438	−0.224208	−0.112104	+	0.993696i	$0.535759\pi$
$662$	1.77513	0.0689925
$663$	17.3956	0.675590
$664$	3.33867	0.129565
$665$	8.65533	0.335639
$666$	3.79631	0.147104
$667$	−7.85908	−0.304305
$668$	−21.3283	−0.825218
$669$	−9.26161	−0.358074
$670$	−22.1115	−0.854241
$671$	−47.3022	−1.82608
$672$	−2.94483	−0.113599
$673$	−0.814789	−0.0314078	−0.0157039	−	0.999877i	$-0.504999\pi$
$673$	−0.814789	−0.0314078	−0.0157039	+	0.999877i	$0.504999\pi$
$674$	−12.4321	−0.478866
$675$	−37.9595	−1.46106
$676$	3.74769	0.144142
$677$	2.16695	0.0832827	0.0416413	−	0.999133i	$-0.486741\pi$
$677$	2.16695	0.0832827	0.0416413	+	0.999133i	$0.486741\pi$
$678$	−12.3725	−0.475164
$679$	12.4498	0.477778
$680$	9.89657	0.379516
$681$	−16.2969	−0.624499
$682$	−19.0790	−0.730571
$683$	−5.05977	−0.193607	−0.0968034	−	0.995304i	$-0.530862\pi$
$683$	−5.05977	−0.193607	−0.0968034	+	0.995304i	$0.530862\pi$
$684$	−1.05615	−0.0403831
$685$	−12.2593	−0.468404
$686$	20.0042	0.763766
$687$	5.87896	0.224296
$688$	10.6850	0.407362
$689$	24.7405	0.942538
$690$	45.3501	1.72645
$691$	−22.1809	−0.843801	−0.421900	−	0.906642i	$-0.638637\pi$
$691$	−22.1809	−0.843801	−0.421900	+	0.906642i	$0.638637\pi$
$692$	15.7132	0.597327
$693$	6.32477	0.240258
$694$	31.3220	1.18897
$695$	−76.4522	−2.90000
$696$	1.28385	0.0486644
$697$	11.6376	0.440806
$698$	3.44998	0.130584
$699$	−41.1452	−1.55625
$700$	−13.4679	−0.509039
$701$	37.5489	1.41820	0.709101	−	0.705107i	$-0.249101\pi$
$701$	37.5489	1.41820	0.709101	+	0.705107i	$0.249101\pi$
$702$	23.0937	0.871614
$703$	−5.72843	−0.216052
$704$	3.77593	0.142311
$705$	−31.1257	−1.17226
$706$	34.6373	1.30359
$707$	−9.86006	−0.370826
$708$	6.55411	0.246318
$709$	40.1620	1.50832	0.754158	−	0.656693i	$-0.228045\pi$
$709$	40.1620	1.50832	0.754158	+	0.656693i	$0.228045\pi$
$710$	−35.9571	−1.34944
$711$	3.09681	0.116140
$712$	0.0960082	0.00359806
$713$	45.4939	1.70376
$714$	8.51053	0.318498
$715$	52.9164	1.97896
$716$	17.7812	0.664516
$717$	−3.47672	−0.129841
$718$	−21.7435	−0.811460
$719$	40.8763	1.52443	0.762214	−	0.647326i	$-0.224113\pi$
$719$	40.8763	1.52443	0.762214	+	0.647326i	$0.224113\pi$
$720$	2.86494	0.106770
$721$	−6.33354	−0.235873
$722$	−17.4063	−0.647796
$723$	−3.35062	−0.124611
$724$	−17.6347	−0.655389
$725$	5.87158	0.218065
$726$	4.79147	0.177828
$727$	−13.8055	−0.512017	−0.256009	−	0.966675i	$-0.582408\pi$
$727$	−13.8055	−0.512017	−0.256009	+	0.966675i	$0.582408\pi$
$728$	8.19354	0.303673
$729$	29.7444	1.10164
$730$	28.6012	1.05858
$731$	−30.8795	−1.14212
$732$	−18.4257	−0.681034
$733$	6.84360	0.252774	0.126387	−	0.991981i	$-0.459662\pi$
$733$	6.84360	0.252774	0.126387	+	0.991981i	$0.459662\pi$
$734$	−28.7330	−1.06056
$735$	15.0673	0.555767
$736$	−9.00372	−0.331882
$737$	24.3811	0.898088
$738$	3.36895	0.124013
$739$	15.6687	0.576382	0.288191	−	0.957573i	$-0.406946\pi$
$739$	15.6687	0.576382	0.288191	+	0.957573i	$0.406946\pi$
$740$	15.5390	0.571226
$741$	−7.59879	−0.279149
$742$	12.1039	0.444348
$743$	−12.3497	−0.453065	−0.226532	−	0.974004i	$-0.572739\pi$
$743$	−12.3497	−0.453065	−0.226532	+	0.974004i	$0.572739\pi$
$744$	−7.43186	−0.272465
$745$	−45.6727	−1.67332
$746$	−4.79859	−0.175689
$747$	−2.79319	−0.102197
$748$	−10.9124	−0.398996
$749$	−9.76719	−0.356886
$750$	−8.69736	−0.317583
$751$	1.00000	0.0364905
$751$	1.00000	0.0364905
$752$	6.17965	0.225349
$753$	−36.5440	−1.33174
$754$	−3.57213	−0.130089
$755$	−28.8559	−1.05017
$756$	11.2982	0.410912
$757$	3.04043	0.110506	0.0552532	−	0.998472i	$-0.482403\pi$
$757$	3.04043	0.110506	0.0552532	+	0.998472i	$0.482403\pi$
$758$	−13.5779	−0.493173
$759$	−50.0049	−1.81506
$760$	−4.32304	−0.156813
$761$	20.2980	0.735803	0.367902	−	0.929865i	$-0.380076\pi$
$761$	20.2980	0.735803	0.367902	+	0.929865i	$0.380076\pi$
$762$	17.5888	0.637174
$763$	1.90181	0.0688501
$764$	14.5768	0.527372
$765$	−8.27965	−0.299351
$766$	17.0637	0.616537
$767$	−18.2358	−0.658456
$768$	1.47084	0.0530745
$769$	−9.11177	−0.328579	−0.164289	−	0.986412i	$-0.552533\pi$
$769$	−9.11177	−0.328579	−0.164289	+	0.986412i	$0.552533\pi$
$770$	25.8885	0.932956
$771$	14.2511	0.513240
$772$	−16.1131	−0.579923
$773$	14.1671	0.509556	0.254778	−	0.967000i	$-0.417998\pi$
$773$	14.1671	0.509556	0.254778	+	0.967000i	$0.417998\pi$
$774$	−8.93927	−0.321315
$775$	−33.9889	−1.22092
$776$	−6.21823	−0.223221
$777$	13.3627	0.479386
$778$	−28.2812	−1.01393
$779$	−5.08356	−0.182138
$780$	20.6126	0.738050
$781$	39.6478	1.41871
$782$	26.0206	0.930496
$783$	−4.92566	−0.176029
$784$	−2.99144	−0.106837
$785$	−13.4139	−0.478762
$786$	−12.9969	−0.463586
$787$	−1.91961	−0.0684268	−0.0342134	−	0.999415i	$-0.510893\pi$
$787$	−1.91961	−0.0684268	−0.0342134	+	0.999415i	$0.510893\pi$
$788$	−21.2594	−0.757336
$789$	−10.1906	−0.362794
$790$	12.6758	0.450986
$791$	16.8417	0.598822
$792$	−3.15901	−0.112250
$793$	51.2667	1.82053
$794$	−20.6804	−0.733920
$795$	30.4499	1.07995
$796$	23.3621	0.828048
$797$	−17.8587	−0.632586	−0.316293	−	0.948662i	$-0.602438\pi$
$797$	−17.8587	−0.632586	−0.316293	+	0.948662i	$0.602438\pi$
$798$	−3.71759	−0.131601
$799$	−17.8591	−0.631810
$800$	6.72676	0.237827
$801$	−0.0803222	−0.00283804
$802$	3.78294	0.133580
$803$	−31.5369	−1.11291
$804$	9.49720	0.334940
$805$	−61.7313	−2.17574
$806$	20.6780	0.728351
$807$	29.9230	1.05334
$808$	4.92476	0.173253
$809$	−8.53647	−0.300126	−0.150063	−	0.988676i	$-0.547948\pi$
$809$	−8.53647	−0.300126	−0.150063	+	0.988676i	$0.547948\pi$
$810$	19.8282	0.696693
$811$	−17.5508	−0.616293	−0.308146	−	0.951339i	$-0.599709\pi$
$811$	−17.5508	−0.616293	−0.308146	+	0.951339i	$0.599709\pi$
$812$	−1.74761	−0.0613289
$813$	−20.5289	−0.719981
$814$	−17.1340	−0.600546
$815$	28.9160	1.01288
$816$	−4.25072	−0.148805
$817$	13.4889	0.471915
$818$	−5.47806	−0.191536
$819$	−6.85486	−0.239528
$820$	13.7898	0.481559
$821$	−19.2907	−0.673252	−0.336626	−	0.941639i	$-0.609286\pi$
$821$	−19.2907	−0.673252	−0.336626	+	0.941639i	$0.609286\pi$
$822$	5.26555	0.183657
$823$	−18.6829	−0.651244	−0.325622	−	0.945500i	$-0.605574\pi$
$823$	−18.6829	−0.651244	−0.325622	+	0.945500i	$0.605574\pi$
$824$	3.16339	0.110202
$825$	37.3591	1.30068
$826$	−8.92156	−0.310421
$827$	−1.43379	−0.0498578	−0.0249289	−	0.999689i	$-0.507936\pi$
$827$	−1.43379	−0.0498578	−0.0249289	+	0.999689i	$0.507936\pi$
$828$	7.53268	0.261779
$829$	−6.21067	−0.215706	−0.107853	−	0.994167i	$-0.534398\pi$
$829$	−6.21067	−0.215706	−0.107853	+	0.994167i	$0.534398\pi$
$830$	−11.4331	−0.396847
$831$	14.4691	0.501926
$832$	−4.09239	−0.141878
$833$	8.64523	0.299539
$834$	32.8373	1.13706
$835$	73.0375	2.52757
$836$	4.76677	0.164862
$837$	28.5132	0.985561
$838$	0.105619	0.00364853
$839$	−0.666338	−0.0230045	−0.0115023	−	0.999934i	$-0.503661\pi$
$839$	−0.666338	−0.0230045	−0.0115023	+	0.999934i	$0.503661\pi$
$840$	10.0844	0.347945
$841$	−28.2381	−0.973728
$842$	0.455310	0.0156910
$843$	5.97777	0.205885
$844$	−14.1102	−0.485694
$845$	−12.8337	−0.441493
$846$	−5.17001	−0.177748
$847$	−6.52223	−0.224106
$848$	−6.04548	−0.207603
$849$	−33.0887	−1.13560
$850$	−19.4402	−0.666795
$851$	40.8561	1.40053
$852$	15.4441	0.529105
$853$	−21.5569	−0.738093	−0.369047	−	0.929411i	$-0.620316\pi$
$853$	−21.5569	−0.738093	−0.369047	+	0.929411i	$0.620316\pi$
$854$	25.0814	0.858268
$855$	3.61673	0.123690
$856$	4.87838	0.166740
$857$	28.1724	0.962352	0.481176	−	0.876624i	$-0.340210\pi$
$857$	28.1724	0.962352	0.481176	+	0.876624i	$0.340210\pi$
$858$	−22.7283	−0.775933
$859$	38.4453	1.31174	0.655868	−	0.754876i	$-0.272303\pi$
$859$	38.4453	1.31174	0.655868	+	0.754876i	$0.272303\pi$
$860$	−36.5901	−1.24771
$861$	11.8585	0.404135
$862$	30.7660	1.04790
$863$	21.3358	0.726280	0.363140	−	0.931735i	$-0.381705\pi$
$863$	21.3358	0.726280	0.363140	+	0.931735i	$0.381705\pi$
$864$	−5.64307	−0.191981
$865$	−53.8089	−1.82956
$866$	−5.58574	−0.189811
$867$	−12.7198	−0.431988
$868$	10.1164	0.343372
$869$	−13.9769	−0.474135
$870$	−4.39648	−0.149055
$871$	−26.4245	−0.895359
$872$	−0.949889	−0.0321673
$873$	5.20228	0.176071
$874$	−11.3664	−0.384474
$875$	11.8390	0.400231
$876$	−12.2846	−0.415059
$877$	−41.8064	−1.41170	−0.705852	−	0.708360i	$-0.749436\pi$
$877$	−41.8064	−1.41170	−0.705852	+	0.708360i	$0.749436\pi$
$878$	−1.79100	−0.0604433
$879$	−13.0721	−0.440909
$880$	−12.9304	−0.435884
$881$	42.0806	1.41773	0.708866	−	0.705343i	$-0.249207\pi$
$881$	42.0806	1.41773	0.708866	+	0.705343i	$0.249207\pi$
$882$	2.50269	0.0842701
$883$	−48.2901	−1.62509	−0.812545	−	0.582898i	$-0.801919\pi$
$883$	−48.2901	−1.62509	−0.812545	+	0.582898i	$0.801919\pi$
$884$	11.8270	0.397784
$885$	−22.4441	−0.754451
$886$	24.4289	0.820705
$887$	48.0789	1.61433	0.807166	−	0.590324i	$-0.201000\pi$
$887$	48.0789	1.61433	0.807166	+	0.590324i	$0.201000\pi$
$888$	−6.67424	−0.223973
$889$	−23.9422	−0.802994
$890$	−0.328774	−0.0110205
$891$	−21.8634	−0.732453
$892$	−6.29680	−0.210832
$893$	7.80125	0.261059
$894$	19.6171	0.656094
$895$	−60.8907	−2.03535
$896$	−2.00214	−0.0668867
$897$	54.1959	1.80955
$898$	−6.00251	−0.200306
$899$	−4.41042	−0.147096
$900$	−5.62773	−0.187591
$901$	17.4714	0.582055
$902$	−15.2052	−0.506277
$903$	−31.4656	−1.04711
$904$	−8.41186	−0.279774
$905$	60.3889	2.00740
$906$	12.3940	0.411764
$907$	45.2231	1.50161	0.750805	−	0.660524i	$-0.229666\pi$
$907$	45.2231	1.50161	0.750805	+	0.660524i	$0.229666\pi$
$908$	−11.0800	−0.367702
$909$	−4.12015	−0.136657
$910$	−28.0582	−0.930122
$911$	−17.1661	−0.568738	−0.284369	−	0.958715i	$-0.591784\pi$
$911$	−17.1661	−0.568738	−0.284369	+	0.958715i	$0.591784\pi$
$912$	1.85681	0.0614851
$913$	12.6066	0.417216
$914$	4.14640	0.137151
$915$	63.0976	2.08594
$916$	3.99699	0.132064
$917$	17.6917	0.584230
$918$	16.3084	0.538257
$919$	8.19443	0.270309	0.135155	−	0.990825i	$-0.456847\pi$
$919$	8.19443	0.270309	0.135155	+	0.990825i	$0.456847\pi$
$920$	30.8327	1.01652
$921$	−41.0071	−1.35123
$922$	−35.6738	−1.17485
$923$	−42.9707	−1.41440
$924$	−11.1195	−0.365804
$925$	−30.5240	−1.00362
$926$	2.30170	0.0756384
$927$	−2.64655	−0.0869240
$928$	0.872869	0.0286533
$929$	−27.4523	−0.900682	−0.450341	−	0.892857i	$-0.648698\pi$
$929$	−27.4523	−0.900682	−0.450341	+	0.892857i	$0.648698\pi$
$930$	25.4499	0.834536
$931$	−3.77643	−0.123767
$932$	−27.9738	−0.916314
$933$	−16.9006	−0.553301
$934$	7.74741	0.253503
$935$	37.3687	1.22209
$936$	3.42377	0.111909
$937$	−34.3420	−1.12190	−0.560952	−	0.827848i	$-0.689565\pi$
$937$	−34.3420	−1.12190	−0.560952	+	0.827848i	$0.689565\pi$
$938$	−12.9278	−0.422106
$939$	−43.1943	−1.40959
$940$	−21.1618	−0.690222
$941$	50.7415	1.65412	0.827062	−	0.562110i	$-0.190010\pi$
$941$	50.7415	1.65412	0.827062	+	0.562110i	$0.190010\pi$
$942$	5.76145	0.187718
$943$	36.2568	1.18069
$944$	4.45602	0.145031
$945$	−38.6900	−1.25858
$946$	40.3458	1.31176
$947$	12.1830	0.395894	0.197947	−	0.980213i	$-0.436573\pi$
$947$	12.1830	0.395894	0.197947	+	0.980213i	$0.436573\pi$
$948$	−5.44446	−0.176828
$949$	34.1801	1.10953
$950$	8.49193	0.275515
$951$	40.7269	1.32066
$952$	5.78615	0.187530
$953$	15.0663	0.488046	0.244023	−	0.969769i	$-0.421533\pi$
$953$	15.0663	0.488046	0.244023	+	0.969769i	$0.421533\pi$
$954$	5.05776	0.163751
$955$	−49.9175	−1.61529
$956$	−2.36376	−0.0764495
$957$	4.84774	0.156705
$958$	15.9289	0.514639
$959$	−7.16756	−0.231453
$960$	−5.03681	−0.162562
$961$	−5.46936	−0.176431
$962$	18.5700	0.598722
$963$	−4.08134	−0.131519
$964$	−2.27802	−0.0733702
$965$	55.1782	1.77625
$966$	26.5145	0.853089
$967$	−42.6260	−1.37076	−0.685380	−	0.728185i	$-0.740364\pi$
$967$	−42.6260	−1.37076	−0.685380	+	0.728185i	$0.740364\pi$
$968$	3.25763	0.104704
$969$	−5.36615	−0.172386
$970$	21.2939	0.683707
$971$	26.0137	0.834819	0.417409	−	0.908719i	$-0.362938\pi$
$971$	26.0137	0.834819	0.417409	+	0.908719i	$0.362938\pi$
$972$	8.41269	0.269837
$973$	−44.6987	−1.43298
$974$	8.75822	0.280631
$975$	−40.4902	−1.29672
$976$	−12.5273	−0.400989
$977$	0.918649	0.0293902	0.0146951	−	0.999892i	$-0.495322\pi$
$977$	0.918649	0.0293902	0.0146951	+	0.999892i	$0.495322\pi$
$978$	−12.4198	−0.397143
$979$	0.362520	0.0115862
$980$	10.2440	0.327233
$981$	0.794694	0.0253726
$982$	−28.6689	−0.914861
$983$	9.38732	0.299409	0.149704	−	0.988731i	$-0.452168\pi$
$983$	9.38732	0.299409	0.149704	+	0.988731i	$0.452168\pi$
$984$	−5.92290	−0.188815
$985$	72.8016	2.31965
$986$	−2.52258	−0.0803353
$987$	−18.1980	−0.579250
$988$	−5.16628	−0.164361
$989$	−96.2048	−3.05914
$990$	10.8178	0.343813
$991$	−33.5754	−1.06656	−0.533279	−	0.845939i	$-0.679040\pi$
$991$	−33.5754	−1.06656	−0.533279	+	0.845939i	$0.679040\pi$
$992$	−5.05279	−0.160426
$993$	2.61095	0.0828558
$994$	−21.0227	−0.666801
$995$	−80.0020	−2.53623
$996$	4.91066	0.155600
$997$	27.6505	0.875700	0.437850	−	0.899048i	$-0.355740\pi$
$997$	27.6505	0.875700	0.437850	+	0.899048i	$0.355740\pi$
$998$	22.4882	0.711853
$999$	25.6065	0.810154

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1502.2.a.f.1.10	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1502.2.a.f.1.10	✓	11	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1502 = 2 \cdot 751 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1502.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.47084 q^{3} +1.00000 q^{4} -3.42444 q^{5} +1.47084 q^{6} -2.00214 q^{7} +1.00000 q^{8} -0.836618 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.47084 q^{3} +1.00000 q^{4} -3.42444 q^{5} +1.47084 q^{6} -2.00214 q^{7} +1.00000 q^{8} -0.836618 q^{9} -3.42444 q^{10} +3.77593 q^{11} +1.47084 q^{12} -4.09239 q^{13} -2.00214 q^{14} -5.03681 q^{15} +1.00000 q^{16} -2.88999 q^{17} -0.836618 q^{18} +1.26241 q^{19} -3.42444 q^{20} -2.94483 q^{21} +3.77593 q^{22} -9.00372 q^{23} +1.47084 q^{24} +6.72676 q^{25} -4.09239 q^{26} -5.64307 q^{27} -2.00214 q^{28} +0.872869 q^{29} -5.03681 q^{30} -5.05279 q^{31} +1.00000 q^{32} +5.55380 q^{33} -2.88999 q^{34} +6.85619 q^{35} -0.836618 q^{36} -4.53769 q^{37} +1.26241 q^{38} -6.01927 q^{39} -3.42444 q^{40} -4.02687 q^{41} -2.94483 q^{42} +10.6850 q^{43} +3.77593 q^{44} +2.86494 q^{45} -9.00372 q^{46} +6.17965 q^{47} +1.47084 q^{48} -2.99144 q^{49} +6.72676 q^{50} -4.25072 q^{51} -4.09239 q^{52} -6.04548 q^{53} -5.64307 q^{54} -12.9304 q^{55} -2.00214 q^{56} +1.85681 q^{57} +0.872869 q^{58} +4.45602 q^{59} -5.03681 q^{60} -12.5273 q^{61} -5.05279 q^{62} +1.67502 q^{63} +1.00000 q^{64} +14.0141 q^{65} +5.55380 q^{66} +6.45697 q^{67} -2.88999 q^{68} -13.2431 q^{69} +6.85619 q^{70} +10.5001 q^{71} -0.836618 q^{72} -8.35210 q^{73} -4.53769 q^{74} +9.89401 q^{75} +1.26241 q^{76} -7.55993 q^{77} -6.01927 q^{78} -3.70159 q^{79} -3.42444 q^{80} -5.79022 q^{81} -4.02687 q^{82} +3.33867 q^{83} -2.94483 q^{84} +9.89657 q^{85} +10.6850 q^{86} +1.28385 q^{87} +3.77593 q^{88} +0.0960082 q^{89} +2.86494 q^{90} +8.19354 q^{91} -9.00372 q^{92} -7.43186 q^{93} +6.17965 q^{94} -4.32304 q^{95} +1.47084 q^{96} -6.21823 q^{97} -2.99144 q^{98} -3.15901 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} - 12 q^{5} - 11 q^{6} - 9 q^{7} + 11 q^{8} + 18 q^{9}+O(q^{10}) \) 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 - 12 * q^5 - 11 * q^6 - 9 * q^7 + 11 * q^8 + 18 * q^9	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} - 12 q^{5} - 11 q^{6} - 9 q^{7} + 11 q^{8} + 18 q^{9} - 12 q^{10} - 7 q^{11} - 11 q^{12} - 21 q^{13} - 9 q^{14} - 3 q^{15} + 11 q^{16} - 16 q^{17} + 18 q^{18} - 22 q^{19} - 12 q^{20} - q^{21} - 7 q^{22} - 2 q^{23} - 11 q^{24} + 19 q^{25} - 21 q^{26} - 44 q^{27} - 9 q^{28} + 4 q^{29} - 3 q^{30} - 28 q^{31} + 11 q^{32} - 13 q^{33} - 16 q^{34} - 11 q^{35} + 18 q^{36} - 22 q^{37} - 22 q^{38} + 9 q^{39} - 12 q^{40} - 5 q^{41} - q^{42} - 7 q^{43} - 7 q^{44} - 23 q^{45} - 2 q^{46} - 31 q^{47} - 11 q^{48} - 2 q^{49} + 19 q^{50} - 6 q^{51} - 21 q^{52} - 17 q^{53} - 44 q^{54} - 18 q^{55} - 9 q^{56} + 7 q^{57} + 4 q^{58} - 18 q^{59} - 3 q^{60} - 18 q^{61} - 28 q^{62} - 27 q^{63} + 11 q^{64} + 22 q^{65} - 13 q^{66} - 11 q^{67} - 16 q^{68} + 9 q^{69} - 11 q^{70} - 16 q^{71} + 18 q^{72} - 33 q^{73} - 22 q^{74} - 21 q^{75} - 22 q^{76} + 9 q^{78} + 9 q^{79} - 12 q^{80} + 71 q^{81} - 5 q^{82} - 18 q^{83} - q^{84} - 8 q^{85} - 7 q^{86} - 17 q^{87} - 7 q^{88} - 23 q^{90} - 22 q^{91} - 2 q^{92} + 8 q^{93} - 31 q^{94} - 23 q^{95} - 11 q^{96} - 66 q^{97} - 2 q^{98} - 5 q^{99}+O(q^{100}) \) 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 - 12 * q^5 - 11 * q^6 - 9 * q^7 + 11 * q^8 + 18 * q^9 - 12 * q^10 - 7 * q^11 - 11 * q^12 - 21 * q^13 - 9 * q^14 - 3 * q^15 + 11 * q^16 - 16 * q^17 + 18 * q^18 - 22 * q^19 - 12 * q^20 - q^21 - 7 * q^22 - 2 * q^23 - 11 * q^24 + 19 * q^25 - 21 * q^26 - 44 * q^27 - 9 * q^28 + 4 * q^29 - 3 * q^30 - 28 * q^31 + 11 * q^32 - 13 * q^33 - 16 * q^34 - 11 * q^35 + 18 * q^36 - 22 * q^37 - 22 * q^38 + 9 * q^39 - 12 * q^40 - 5 * q^41 - q^42 - 7 * q^43 - 7 * q^44 - 23 * q^45 - 2 * q^46 - 31 * q^47 - 11 * q^48 - 2 * q^49 + 19 * q^50 - 6 * q^51 - 21 * q^52 - 17 * q^53 - 44 * q^54 - 18 * q^55 - 9 * q^56 + 7 * q^57 + 4 * q^58 - 18 * q^59 - 3 * q^60 - 18 * q^61 - 28 * q^62 - 27 * q^63 + 11 * q^64 + 22 * q^65 - 13 * q^66 - 11 * q^67 - 16 * q^68 + 9 * q^69 - 11 * q^70 - 16 * q^71 + 18 * q^72 - 33 * q^73 - 22 * q^74 - 21 * q^75 - 22 * q^76 + 9 * q^78 + 9 * q^79 - 12 * q^80 + 71 * q^81 - 5 * q^82 - 18 * q^83 - q^84 - 8 * q^85 - 7 * q^86 - 17 * q^87 - 7 * q^88 - 23 * q^90 - 22 * q^91 - 2 * q^92 + 8 * q^93 - 31 * q^94 - 23 * q^95 - 11 * q^96 - 66 * q^97 - 2 * q^98 - 5 * q^99

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