LMFDB - Embedded newform 4029.2.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} - 10 x^{16} + 120 x^{15} - 56 x^{14} - 921 x^{13} + 1181 x^{12} + 3316 x^{11} + \cdots + 138 $ x^18 - 6x^17 - 10x^16 + 120x^15 - 56x^14 - 921x^13 + 1181x^12 + 3316x^11 - 6280x^10 - 5249x^9 + 15005x^8 + 1809x^7 - 16711x^6 + 2434x^5 + 8758x^4 - 1858x^3 - 1942x^2 + 318*x + 138
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.77821$ of defining polynomial
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.77821 q^{2} +1.00000 q^{3} +5.71847 q^{4} +1.71746 q^{5} -2.77821 q^{6} -2.08361 q^{7} -10.3307 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.77821 q^{2} +1.00000 q^{3} +5.71847 q^{4} +1.71746 q^{5} -2.77821 q^{6} -2.08361 q^{7} -10.3307 q^{8} +1.00000 q^{9} -4.77148 q^{10} -0.368134 q^{11} +5.71847 q^{12} -1.86242 q^{13} +5.78871 q^{14} +1.71746 q^{15} +17.2640 q^{16} +1.00000 q^{17} -2.77821 q^{18} -4.42091 q^{19} +9.82125 q^{20} -2.08361 q^{21} +1.02275 q^{22} +0.403244 q^{23} -10.3307 q^{24} -2.05032 q^{25} +5.17420 q^{26} +1.00000 q^{27} -11.9151 q^{28} -7.21557 q^{29} -4.77148 q^{30} +6.40933 q^{31} -27.3015 q^{32} -0.368134 q^{33} -2.77821 q^{34} -3.57852 q^{35} +5.71847 q^{36} +8.74409 q^{37} +12.2822 q^{38} -1.86242 q^{39} -17.7426 q^{40} -3.56145 q^{41} +5.78871 q^{42} +6.08766 q^{43} -2.10516 q^{44} +1.71746 q^{45} -1.12030 q^{46} +10.8741 q^{47} +17.2640 q^{48} -2.65857 q^{49} +5.69624 q^{50} +1.00000 q^{51} -10.6502 q^{52} -9.41725 q^{53} -2.77821 q^{54} -0.632256 q^{55} +21.5251 q^{56} -4.42091 q^{57} +20.0464 q^{58} -12.9599 q^{59} +9.82125 q^{60} +11.1366 q^{61} -17.8065 q^{62} -2.08361 q^{63} +41.3216 q^{64} -3.19864 q^{65} +1.02275 q^{66} +14.6010 q^{67} +5.71847 q^{68} +0.403244 q^{69} +9.94189 q^{70} -14.7734 q^{71} -10.3307 q^{72} +10.4730 q^{73} -24.2930 q^{74} -2.05032 q^{75} -25.2808 q^{76} +0.767048 q^{77} +5.17420 q^{78} -1.00000 q^{79} +29.6502 q^{80} +1.00000 q^{81} +9.89447 q^{82} +7.66166 q^{83} -11.9151 q^{84} +1.71746 q^{85} -16.9128 q^{86} -7.21557 q^{87} +3.80308 q^{88} +0.676255 q^{89} -4.77148 q^{90} +3.88056 q^{91} +2.30594 q^{92} +6.40933 q^{93} -30.2106 q^{94} -7.59275 q^{95} -27.3015 q^{96} -13.5348 q^{97} +7.38607 q^{98} -0.368134 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9}+O(q^{10}) $ 18 * q - 6 * q^2 + 18 * q^3 + 20 * q^4 - 5 * q^5 - 6 * q^6 - 13 * q^7 - 12 * q^8 + 18 * q^9	\( 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9} - 15 q^{10} - 27 q^{11} + 20 q^{12} - 4 q^{13} - 5 q^{14} - 5 q^{15} + 16 q^{16} + 18 q^{17} - 6 q^{18} - 30 q^{19} - 16 q^{20} - 13 q^{21} + 13 q^{22} - 21 q^{23} - 12 q^{24} + 13 q^{25} - 20 q^{26} + 18 q^{27} - 33 q^{28} - 47 q^{29} - 15 q^{30} - 18 q^{31} - 45 q^{32} - 27 q^{33} - 6 q^{34} - 17 q^{35} + 20 q^{36} + q^{37} + 5 q^{38} - 4 q^{39} - 12 q^{40} - 18 q^{41} - 5 q^{42} - 39 q^{43} - 34 q^{44} - 5 q^{45} - 7 q^{46} + 16 q^{48} + 15 q^{49} - 23 q^{50} + 18 q^{51} + 5 q^{52} - 9 q^{53} - 6 q^{54} + q^{55} - 24 q^{56} - 30 q^{57} + 41 q^{58} - 42 q^{59} - 16 q^{60} - 43 q^{61} - 54 q^{62} - 13 q^{63} + 22 q^{64} - 25 q^{65} + 13 q^{66} + 20 q^{68} - 21 q^{69} + 17 q^{70} + 9 q^{71} - 12 q^{72} + 19 q^{73} - 30 q^{74} + 13 q^{75} - 17 q^{76} - 14 q^{77} - 20 q^{78} - 18 q^{79} + 36 q^{80} + 18 q^{81} - 3 q^{82} - 61 q^{83} - 33 q^{84} - 5 q^{85} - 24 q^{86} - 47 q^{87} - 25 q^{88} + 10 q^{89} - 15 q^{90} - 52 q^{91} - 74 q^{92} - 18 q^{93} + 31 q^{94} - 37 q^{95} - 45 q^{96} - 9 q^{97} + 27 q^{98} - 27 q^{99}+O(q^{100}) \) 18 * q - 6 * q^2 + 18 * q^3 + 20 * q^4 - 5 * q^5 - 6 * q^6 - 13 * q^7 - 12 * q^8 + 18 * q^9 - 15 * q^10 - 27 * q^11 + 20 * q^12 - 4 * q^13 - 5 * q^14 - 5 * q^15 + 16 * q^16 + 18 * q^17 - 6 * q^18 - 30 * q^19 - 16 * q^20 - 13 * q^21 + 13 * q^22 - 21 * q^23 - 12 * q^24 + 13 * q^25 - 20 * q^26 + 18 * q^27 - 33 * q^28 - 47 * q^29 - 15 * q^30 - 18 * q^31 - 45 * q^32 - 27 * q^33 - 6 * q^34 - 17 * q^35 + 20 * q^36 + q^37 + 5 * q^38 - 4 * q^39 - 12 * q^40 - 18 * q^41 - 5 * q^42 - 39 * q^43 - 34 * q^44 - 5 * q^45 - 7 * q^46 + 16 * q^48 + 15 * q^49 - 23 * q^50 + 18 * q^51 + 5 * q^52 - 9 * q^53 - 6 * q^54 + q^55 - 24 * q^56 - 30 * q^57 + 41 * q^58 - 42 * q^59 - 16 * q^60 - 43 * q^61 - 54 * q^62 - 13 * q^63 + 22 * q^64 - 25 * q^65 + 13 * q^66 + 20 * q^68 - 21 * q^69 + 17 * q^70 + 9 * q^71 - 12 * q^72 + 19 * q^73 - 30 * q^74 + 13 * q^75 - 17 * q^76 - 14 * q^77 - 20 * q^78 - 18 * q^79 + 36 * q^80 + 18 * q^81 - 3 * q^82 - 61 * q^83 - 33 * q^84 - 5 * q^85 - 24 * q^86 - 47 * q^87 - 25 * q^88 + 10 * q^89 - 15 * q^90 - 52 * q^91 - 74 * q^92 - 18 * q^93 + 31 * q^94 - 37 * q^95 - 45 * q^96 - 9 * q^97 + 27 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.77821	−1.96449	−0.982247	−	0.187594i	$-0.939931\pi$
$2$	−2.77821	−1.96449	−0.982247	+	0.187594i	$0.939931\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.71847	2.85923
$5$	1.71746	0.768072	0.384036	−	0.923318i	$-0.374534\pi$
$5$	1.71746	0.768072	0.384036	+	0.923318i	$0.374534\pi$
$6$	−2.77821	−1.13420
$7$	−2.08361	−0.787530	−0.393765	−	0.919211i	$-0.628828\pi$
$7$	−2.08361	−0.787530	−0.393765	+	0.919211i	$0.628828\pi$
$8$	−10.3307	−3.65245
$9$	1.00000	0.333333
$10$	−4.77148	−1.50887
$11$	−0.368134	−0.110997	−0.0554983	−	0.998459i	$-0.517675\pi$
$11$	−0.368134	−0.110997	−0.0554983	+	0.998459i	$0.517675\pi$
$12$	5.71847	1.65078
$13$	−1.86242	−0.516543	−0.258271	−	0.966072i	$-0.583153\pi$
$13$	−1.86242	−0.516543	−0.258271	+	0.966072i	$0.583153\pi$
$14$	5.78871	1.54710
$15$	1.71746	0.443447
$16$	17.2640	4.31599
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.77821	−0.654831
$19$	−4.42091	−1.01423	−0.507113	−	0.861879i	$-0.669287\pi$
$19$	−4.42091	−1.01423	−0.507113	+	0.861879i	$0.669287\pi$
$20$	9.82125	2.19610
$21$	−2.08361	−0.454681
$22$	1.02275	0.218052
$23$	0.403244	0.0840822	0.0420411	−	0.999116i	$-0.486614\pi$
$23$	0.403244	0.0840822	0.0420411	+	0.999116i	$0.486614\pi$
$24$	−10.3307	−2.10875
$25$	−2.05032	−0.410065
$26$	5.17420	1.01474
$27$	1.00000	0.192450
$28$	−11.9151	−2.25173
$29$	−7.21557	−1.33990	−0.669949	−	0.742408i	$-0.733684\pi$
$29$	−7.21557	−1.33990	−0.669949	+	0.742408i	$0.733684\pi$
$30$	−4.77148	−0.871148
$31$	6.40933	1.15115	0.575575	−	0.817749i	$-0.304778\pi$
$31$	6.40933	1.15115	0.575575	+	0.817749i	$0.304778\pi$
$32$	−27.3015	−4.82628
$33$	−0.368134	−0.0640839
$34$	−2.77821	−0.476460
$35$	−3.57852	−0.604880
$36$	5.71847	0.953078
$37$	8.74409	1.43752	0.718760	−	0.695258i	$-0.244710\pi$
$37$	8.74409	1.43752	0.718760	+	0.695258i	$0.244710\pi$
$38$	12.2822	1.99244
$39$	−1.86242	−0.298226
$40$	−17.7426	−2.80535
$41$	−3.56145	−0.556205	−0.278103	−	0.960551i	$-0.589705\pi$
$41$	−3.56145	−0.556205	−0.278103	+	0.960551i	$0.589705\pi$
$42$	5.78871	0.893218
$43$	6.08766	0.928360	0.464180	−	0.885741i	$-0.346349\pi$
$43$	6.08766	0.928360	0.464180	+	0.885741i	$0.346349\pi$
$44$	−2.10516	−0.317365
$45$	1.71746	0.256024
$46$	−1.12030	−0.165179
$47$	10.8741	1.58615	0.793077	−	0.609122i	$-0.208478\pi$
$47$	10.8741	1.58615	0.793077	+	0.609122i	$0.208478\pi$
$48$	17.2640	2.49184
$49$	−2.65857	−0.379796
$50$	5.69624	0.805570
$51$	1.00000	0.140028
$52$	−10.6502	−1.47692
$53$	−9.41725	−1.29356	−0.646779	−	0.762677i	$-0.723884\pi$
$53$	−9.41725	−1.29356	−0.646779	+	0.762677i	$0.723884\pi$
$54$	−2.77821	−0.378067
$55$	−0.632256	−0.0852534
$56$	21.5251	2.87642
$57$	−4.42091	−0.585564
$58$	20.0464	2.63222
$59$	−12.9599	−1.68723	−0.843617	−	0.536946i	$-0.819578\pi$
$59$	−12.9599	−1.68723	−0.843617	+	0.536946i	$0.819578\pi$
$60$	9.82125	1.26792
$61$	11.1366	1.42590	0.712951	−	0.701214i	$-0.247358\pi$
$61$	11.1366	1.42590	0.712951	+	0.701214i	$0.247358\pi$
$62$	−17.8065	−2.26143
$63$	−2.08361	−0.262510
$64$	41.3216	5.16520
$65$	−3.19864	−0.396742
$66$	1.02275	0.125892
$67$	14.6010	1.78380	0.891899	−	0.452235i	$-0.149373\pi$
$67$	14.6010	1.78380	0.891899	+	0.452235i	$0.149373\pi$
$68$	5.71847	0.693466
$69$	0.403244	0.0485449
$70$	9.94189	1.18828
$71$	−14.7734	−1.75328	−0.876642	−	0.481143i	$-0.840222\pi$
$71$	−14.7734	−1.75328	−0.876642	+	0.481143i	$0.840222\pi$
$72$	−10.3307	−1.21748
$73$	10.4730	1.22577	0.612884	−	0.790173i	$-0.290009\pi$
$73$	10.4730	1.22577	0.612884	+	0.790173i	$0.290009\pi$
$74$	−24.2930	−2.82400
$75$	−2.05032	−0.236751
$76$	−25.2808	−2.89991
$77$	0.767048	0.0874132
$78$	5.17420	0.585863
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	29.6502	3.31499
$81$	1.00000	0.111111
$82$	9.89447	1.09266
$83$	7.66166	0.840977	0.420488	−	0.907298i	$-0.361859\pi$
$83$	7.66166	0.840977	0.420488	+	0.907298i	$0.361859\pi$
$84$	−11.9151	−1.30004
$85$	1.71746	0.186285
$86$	−16.9128	−1.82376
$87$	−7.21557	−0.773590
$88$	3.80308	0.405410
$89$	0.676255	0.0716829	0.0358415	−	0.999357i	$-0.488589\pi$
$89$	0.676255	0.0716829	0.0358415	+	0.999357i	$0.488589\pi$
$90$	−4.77148	−0.502958
$91$	3.88056	0.406793
$92$	2.30594	0.240411
$93$	6.40933	0.664617
$94$	−30.2106	−3.11599
$95$	−7.59275	−0.778999
$96$	−27.3015	−2.78645
$97$	−13.5348	−1.37425	−0.687125	−	0.726539i	$-0.741128\pi$
$97$	−13.5348	−1.37425	−0.687125	+	0.726539i	$0.741128\pi$
$98$	7.38607	0.746106
$99$	−0.368134	−0.0369989
$100$	−11.7247	−1.17247
$101$	−9.65451	−0.960660	−0.480330	−	0.877088i	$-0.659483\pi$
$101$	−9.65451	−0.960660	−0.480330	+	0.877088i	$0.659483\pi$
$102$	−2.77821	−0.275084
$103$	−13.4641	−1.32666	−0.663331	−	0.748326i	$-0.730858\pi$
$103$	−13.4641	−1.32666	−0.663331	+	0.748326i	$0.730858\pi$
$104$	19.2401	1.88665
$105$	−3.57852	−0.349228
$106$	26.1631	2.54119
$107$	−12.0411	−1.16406	−0.582029	−	0.813168i	$-0.697741\pi$
$107$	−12.0411	−1.16406	−0.582029	+	0.813168i	$0.697741\pi$
$108$	5.71847	0.550260
$109$	−10.9423	−1.04809	−0.524043	−	0.851692i	$-0.675577\pi$
$109$	−10.9423	−1.04809	−0.524043	+	0.851692i	$0.675577\pi$
$110$	1.75654	0.167480
$111$	8.74409	0.829952
$112$	−35.9713	−3.39897
$113$	−15.3905	−1.44782	−0.723910	−	0.689894i	$-0.757657\pi$
$113$	−15.3905	−1.44782	−0.723910	+	0.689894i	$0.757657\pi$
$114$	12.2822	1.15034
$115$	0.692556	0.0645812
$116$	−41.2620	−3.83108
$117$	−1.86242	−0.172181
$118$	36.0053	3.31456
$119$	−2.08361	−0.191004
$120$	−17.7426	−1.61967
$121$	−10.8645	−0.987680
$122$	−30.9400	−2.80117
$123$	−3.56145	−0.321125
$124$	36.6516	3.29141
$125$	−12.1087	−1.08303
$126$	5.78871	0.515700
$127$	−6.72708	−0.596932	−0.298466	−	0.954420i	$-0.596475\pi$
$127$	−6.72708	−0.596932	−0.298466	+	0.954420i	$0.596475\pi$
$128$	−60.1971	−5.32072
$129$	6.08766	0.535989
$130$	8.88650	0.779397
$131$	3.14767	0.275013	0.137506	−	0.990501i	$-0.456091\pi$
$131$	3.14767	0.275013	0.137506	+	0.990501i	$0.456091\pi$
$132$	−2.10516	−0.183231
$133$	9.21145	0.798734
$134$	−40.5647	−3.50426
$135$	1.71746	0.147816
$136$	−10.3307	−0.885850
$137$	4.64795	0.397101	0.198551	−	0.980091i	$-0.436377\pi$
$137$	4.64795	0.397101	0.198551	+	0.980091i	$0.436377\pi$
$138$	−1.12030	−0.0953661
$139$	−13.3144	−1.12931	−0.564657	−	0.825326i	$-0.690992\pi$
$139$	−13.3144	−1.12931	−0.564657	+	0.825326i	$0.690992\pi$
$140$	−20.4637	−1.72950
$141$	10.8741	0.915766
$142$	41.0438	3.44432
$143$	0.685621	0.0573345
$144$	17.2640	1.43866
$145$	−12.3925	−1.02914
$146$	−29.0961	−2.40801
$147$	−2.65857	−0.219275
$148$	50.0028	4.11021
$149$	−5.46817	−0.447970	−0.223985	−	0.974593i	$-0.571907\pi$
$149$	−5.46817	−0.447970	−0.223985	+	0.974593i	$0.571907\pi$
$150$	5.69624	0.465096
$151$	−19.3545	−1.57504	−0.787522	−	0.616287i	$-0.788636\pi$
$151$	−19.3545	−1.57504	−0.787522	+	0.616287i	$0.788636\pi$
$152$	45.6711	3.70442
$153$	1.00000	0.0808452
$154$	−2.13102	−0.171723
$155$	11.0078	0.884167
$156$	−10.6502	−0.852698
$157$	−7.34983	−0.586581	−0.293290	−	0.956023i	$-0.594750\pi$
$157$	−7.34983	−0.586581	−0.293290	+	0.956023i	$0.594750\pi$
$158$	2.77821	0.221023
$159$	−9.41725	−0.746836
$160$	−46.8894	−3.70693
$161$	−0.840203	−0.0662173
$162$	−2.77821	−0.218277
$163$	7.70622	0.603597	0.301799	−	0.953372i	$-0.402413\pi$
$163$	7.70622	0.603597	0.301799	+	0.953372i	$0.402413\pi$
$164$	−20.3660	−1.59032
$165$	−0.632256	−0.0492211
$166$	−21.2857	−1.65209
$167$	7.38206	0.571241	0.285620	−	0.958343i	$-0.407800\pi$
$167$	7.38206	0.571241	0.285620	+	0.958343i	$0.407800\pi$
$168$	21.5251	1.66070
$169$	−9.53139	−0.733184
$170$	−4.77148	−0.365956
$171$	−4.42091	−0.338076
$172$	34.8121	2.65440
$173$	12.5006	0.950401	0.475201	−	0.879878i	$-0.342376\pi$
$173$	12.5006	0.950401	0.475201	+	0.879878i	$0.342376\pi$
$174$	20.0464	1.51971
$175$	4.27208	0.322939
$176$	−6.35545	−0.479060
$177$	−12.9599	−0.974125
$178$	−1.87878	−0.140821
$179$	−1.08318	−0.0809607	−0.0404804	−	0.999180i	$-0.512889\pi$
$179$	−1.08318	−0.0809607	−0.0404804	+	0.999180i	$0.512889\pi$
$180$	9.82125	0.732033
$181$	7.04972	0.524001	0.262001	−	0.965068i	$-0.415618\pi$
$181$	7.04972	0.524001	0.262001	+	0.965068i	$0.415618\pi$
$182$	−10.7810	−0.799142
$183$	11.1366	0.823245
$184$	−4.16579	−0.307106
$185$	15.0176	1.10412
$186$	−17.8065	−1.30564
$187$	−0.368134	−0.0269206
$188$	62.1833	4.53518
$189$	−2.08361	−0.151560
$190$	21.0943	1.53034
$191$	−3.78964	−0.274209	−0.137104	−	0.990557i	$-0.543780\pi$
$191$	−3.78964	−0.274209	−0.137104	+	0.990557i	$0.543780\pi$
$192$	41.3216	2.98213
$193$	−8.65072	−0.622693	−0.311346	−	0.950297i	$-0.600780\pi$
$193$	−8.65072	−0.622693	−0.311346	+	0.950297i	$0.600780\pi$
$194$	37.6026	2.69971
$195$	−3.19864	−0.229059
$196$	−15.2030	−1.08593
$197$	4.72589	0.336706	0.168353	−	0.985727i	$-0.446155\pi$
$197$	4.72589	0.336706	0.168353	+	0.985727i	$0.446155\pi$
$198$	1.02275	0.0726840
$199$	−16.4603	−1.16684	−0.583419	−	0.812171i	$-0.698286\pi$
$199$	−16.4603	−1.16684	−0.583419	+	0.812171i	$0.698286\pi$
$200$	21.1813	1.49774
$201$	14.6010	1.02988
$202$	26.8223	1.88721
$203$	15.0344	1.05521
$204$	5.71847	0.400373
$205$	−6.11666	−0.427206
$206$	37.4063	2.60622
$207$	0.403244	0.0280274
$208$	−32.1527	−2.22939
$209$	1.62749	0.112576
$210$	9.94189	0.686056
$211$	−21.0295	−1.44773	−0.723865	−	0.689942i	$-0.757636\pi$
$211$	−21.0295	−1.44773	−0.723865	+	0.689942i	$0.757636\pi$
$212$	−53.8522	−3.69859
$213$	−14.7734	−1.01226
$214$	33.4528	2.28678
$215$	10.4553	0.713047
$216$	−10.3307	−0.702915
$217$	−13.3545	−0.906566
$218$	30.4001	2.05896
$219$	10.4730	0.707697
$220$	−3.61554	−0.243760
$221$	−1.86242	−0.125280
$222$	−24.2930	−1.63044
$223$	9.07486	0.607697	0.303849	−	0.952720i	$-0.401728\pi$
$223$	9.07486	0.607697	0.303849	+	0.952720i	$0.401728\pi$
$224$	56.8857	3.80084
$225$	−2.05032	−0.136688
$226$	42.7582	2.84423
$227$	−9.58827	−0.636396	−0.318198	−	0.948024i	$-0.603078\pi$
$227$	−9.58827	−0.636396	−0.318198	+	0.948024i	$0.603078\pi$
$228$	−25.2808	−1.67426
$229$	28.2795	1.86876	0.934381	−	0.356276i	$-0.115954\pi$
$229$	28.2795	1.86876	0.934381	+	0.356276i	$0.115954\pi$
$230$	−1.92407	−0.126869
$231$	0.767048	0.0504680
$232$	74.5419	4.89391
$233$	6.73219	0.441041	0.220520	−	0.975382i	$-0.429224\pi$
$233$	6.73219	0.441041	0.220520	+	0.975382i	$0.429224\pi$
$234$	5.17420	0.338248
$235$	18.6759	1.21828
$236$	−74.1107	−4.82420
$237$	−1.00000	−0.0649570
$238$	5.78871	0.375227
$239$	−11.1289	−0.719870	−0.359935	−	0.932977i	$-0.617201\pi$
$239$	−11.1289	−0.719870	−0.359935	+	0.932977i	$0.617201\pi$
$240$	29.6502	1.91391
$241$	10.8123	0.696480	0.348240	−	0.937405i	$-0.386779\pi$
$241$	10.8123	0.696480	0.348240	+	0.937405i	$0.386779\pi$
$242$	30.1838	1.94029
$243$	1.00000	0.0641500
$244$	63.6846	4.07699
$245$	−4.56599	−0.291711
$246$	9.89447	0.630848
$247$	8.23360	0.523891
$248$	−66.2129	−4.20452
$249$	7.66166	0.485538
$250$	33.6405	2.12761
$251$	11.0835	0.699587	0.349794	−	0.936827i	$-0.386252\pi$
$251$	11.0835	0.699587	0.349794	+	0.936827i	$0.386252\pi$
$252$	−11.9151	−0.750578
$253$	−0.148448	−0.00933283
$254$	18.6893	1.17267
$255$	1.71746	0.107552
$256$	84.5972	5.28733
$257$	24.9568	1.55676	0.778380	−	0.627793i	$-0.216042\pi$
$257$	24.9568	1.55676	0.778380	+	0.627793i	$0.216042\pi$
$258$	−16.9128	−1.05295
$259$	−18.2193	−1.13209
$260$	−18.2913	−1.13438
$261$	−7.21557	−0.446632
$262$	−8.74489	−0.540261
$263$	−28.0200	−1.72778	−0.863892	−	0.503677i	$-0.831980\pi$
$263$	−28.0200	−1.72778	−0.863892	+	0.503677i	$0.831980\pi$
$264$	3.80308	0.234064
$265$	−16.1738	−0.993546
$266$	−25.5914	−1.56911
$267$	0.676255	0.0413861
$268$	83.4955	5.10030
$269$	−16.3145	−0.994710	−0.497355	−	0.867547i	$-0.665695\pi$
$269$	−16.3145	−0.994710	−0.497355	+	0.867547i	$0.665695\pi$
$270$	−4.77148	−0.290383
$271$	−25.2976	−1.53672	−0.768361	−	0.640017i	$-0.778927\pi$
$271$	−25.2976	−1.53672	−0.768361	+	0.640017i	$0.778927\pi$
$272$	17.2640	1.04678
$273$	3.88056	0.234862
$274$	−12.9130	−0.780102
$275$	0.754794	0.0455158
$276$	2.30594	0.138801
$277$	−11.8848	−0.714090	−0.357045	−	0.934087i	$-0.616216\pi$
$277$	−11.8848	−0.714090	−0.357045	+	0.934087i	$0.616216\pi$
$278$	36.9903	2.21853
$279$	6.40933	0.383717
$280$	36.9686	2.20930
$281$	18.4506	1.10067	0.550334	−	0.834945i	$-0.314500\pi$
$281$	18.4506	1.10067	0.550334	+	0.834945i	$0.314500\pi$
$282$	−30.2106	−1.79902
$283$	9.65019	0.573644	0.286822	−	0.957984i	$-0.407401\pi$
$283$	9.65019	0.573644	0.286822	+	0.957984i	$0.407401\pi$
$284$	−84.4814	−5.01305
$285$	−7.59275	−0.449756
$286$	−1.90480	−0.112633
$287$	7.42067	0.438028
$288$	−27.3015	−1.60876
$289$	1.00000	0.0588235
$290$	34.4289	2.02173
$291$	−13.5348	−0.793424
$292$	59.8893	3.50476
$293$	−15.8289	−0.924732	−0.462366	−	0.886689i	$-0.652999\pi$
$293$	−15.8289	−0.924732	−0.462366	+	0.886689i	$0.652999\pi$
$294$	7.38607	0.430765
$295$	−22.2581	−1.29592
$296$	−90.3326	−5.25048
$297$	−0.368134	−0.0213613
$298$	15.1917	0.880034
$299$	−0.751010	−0.0434320
$300$	−11.7247	−0.676927
$301$	−12.6843	−0.731112
$302$	53.7708	3.09416
$303$	−9.65451	−0.554637
$304$	−76.3224	−4.37739
$305$	19.1268	1.09520
$306$	−2.77821	−0.158820
$307$	−28.1829	−1.60848	−0.804242	−	0.594302i	$-0.797428\pi$
$307$	−28.1829	−1.60848	−0.804242	+	0.594302i	$0.797428\pi$
$308$	4.38634	0.249935
$309$	−13.4641	−0.765949
$310$	−30.5820	−1.73694
$311$	−7.27982	−0.412801	−0.206400	−	0.978468i	$-0.566175\pi$
$311$	−7.27982	−0.412801	−0.206400	+	0.978468i	$0.566175\pi$
$312$	19.2401	1.08926
$313$	10.3813	0.586786	0.293393	−	0.955992i	$-0.405216\pi$
$313$	10.3813	0.586786	0.293393	+	0.955992i	$0.405216\pi$
$314$	20.4194	1.15233
$315$	−3.57852	−0.201627
$316$	−5.71847	−0.321689
$317$	−7.01154	−0.393807	−0.196904	−	0.980423i	$-0.563089\pi$
$317$	−7.01154	−0.393807	−0.196904	+	0.980423i	$0.563089\pi$
$318$	26.1631	1.46715
$319$	2.65630	0.148724
$320$	70.9683	3.96725
$321$	−12.0411	−0.672069
$322$	2.33426	0.130083
$323$	−4.42091	−0.245986
$324$	5.71847	0.317693
$325$	3.81857	0.211816
$326$	−21.4095	−1.18576
$327$	−10.9423	−0.605112
$328$	36.7923	2.03151
$329$	−22.6574	−1.24914
$330$	1.75654	0.0966945
$331$	−22.2161	−1.22111	−0.610555	−	0.791974i	$-0.709054\pi$
$331$	−22.2161	−1.22111	−0.610555	+	0.791974i	$0.709054\pi$
$332$	43.8130	2.40455
$333$	8.74409	0.479173
$334$	−20.5089	−1.12220
$335$	25.0767	1.37009
$336$	−35.9713	−1.96240
$337$	3.42440	0.186539	0.0932695	−	0.995641i	$-0.470268\pi$
$337$	3.42440	0.186539	0.0932695	+	0.995641i	$0.470268\pi$
$338$	26.4802	1.44033
$339$	−15.3905	−0.835900
$340$	9.82125	0.532632
$341$	−2.35949	−0.127774
$342$	12.2822	0.664147
$343$	20.1247	1.08663
$344$	−62.8898	−3.39079
$345$	0.692556	0.0372860
$346$	−34.7293	−1.86706
$347$	−5.00098	−0.268466	−0.134233	−	0.990950i	$-0.542857\pi$
$347$	−5.00098	−0.268466	−0.134233	+	0.990950i	$0.542857\pi$
$348$	−41.2620	−2.21188
$349$	11.3614	0.608163	0.304082	−	0.952646i	$-0.401650\pi$
$349$	11.3614	0.608163	0.304082	+	0.952646i	$0.401650\pi$
$350$	−11.8687	−0.634411
$351$	−1.86242	−0.0994087
$352$	10.0506	0.535700
$353$	−16.9512	−0.902220	−0.451110	−	0.892468i	$-0.648972\pi$
$353$	−16.9512	−0.902220	−0.451110	+	0.892468i	$0.648972\pi$
$354$	36.0053	1.91366
$355$	−25.3728	−1.34665
$356$	3.86714	0.204958
$357$	−2.08361	−0.110276
$358$	3.00931	0.159047
$359$	10.4970	0.554010	0.277005	−	0.960868i	$-0.410658\pi$
$359$	10.4970	0.554010	0.277005	+	0.960868i	$0.410658\pi$
$360$	−17.7426	−0.935116
$361$	0.544458	0.0286557
$362$	−19.5856	−1.02940
$363$	−10.8645	−0.570237
$364$	22.1909	1.16312
$365$	17.9869	0.941479
$366$	−30.9400	−1.61726
$367$	4.78109	0.249571	0.124785	−	0.992184i	$-0.460176\pi$
$367$	4.78109	0.249571	0.124785	+	0.992184i	$0.460176\pi$
$368$	6.96158	0.362898
$369$	−3.56145	−0.185402
$370$	−41.7222	−2.16904
$371$	19.6219	1.01872
$372$	36.6516	1.90030
$373$	−6.74198	−0.349086	−0.174543	−	0.984650i	$-0.555845\pi$
$373$	−6.74198	−0.349086	−0.174543	+	0.984650i	$0.555845\pi$
$374$	1.02275	0.0528854
$375$	−12.1087	−0.625289
$376$	−112.337	−5.79335
$377$	13.4384	0.692114
$378$	5.78871	0.297739
$379$	29.0762	1.49354	0.746771	−	0.665081i	$-0.231603\pi$
$379$	29.0762	1.49354	0.746771	+	0.665081i	$0.231603\pi$
$380$	−43.4189	−2.22734
$381$	−6.72708	−0.344639
$382$	10.5284	0.538682
$383$	−29.0208	−1.48289	−0.741447	−	0.671012i	$-0.765860\pi$
$383$	−29.0208	−1.48289	−0.741447	+	0.671012i	$0.765860\pi$
$384$	−60.1971	−3.07192
$385$	1.31738	0.0671397
$386$	24.0335	1.22328
$387$	6.08766	0.309453
$388$	−77.3983	−3.92931
$389$	9.05028	0.458867	0.229434	−	0.973324i	$-0.426313\pi$
$389$	9.05028	0.458867	0.229434	+	0.973324i	$0.426313\pi$
$390$	8.88650	0.449985
$391$	0.403244	0.0203929
$392$	27.4649	1.38719
$393$	3.14767	0.158779
$394$	−13.1295	−0.661457
$395$	−1.71746	−0.0864149
$396$	−2.10516	−0.105788
$397$	21.8294	1.09559	0.547794	−	0.836613i	$-0.315468\pi$
$397$	21.8294	1.09559	0.547794	+	0.836613i	$0.315468\pi$
$398$	45.7302	2.29225
$399$	9.21145	0.461150
$400$	−35.3967	−1.76983
$401$	12.5900	0.628714	0.314357	−	0.949305i	$-0.398211\pi$
$401$	12.5900	0.628714	0.314357	+	0.949305i	$0.398211\pi$
$402$	−40.5647	−2.02319
$403$	−11.9369	−0.594618
$404$	−55.2090	−2.74675
$405$	1.71746	0.0853414
$406$	−41.7688	−2.07295
$407$	−3.21900	−0.159560
$408$	−10.3307	−0.511446
$409$	12.3193	0.609149	0.304574	−	0.952489i	$-0.401486\pi$
$409$	12.3193	0.609149	0.304574	+	0.952489i	$0.401486\pi$
$410$	16.9934	0.839243
$411$	4.64795	0.229266
$412$	−76.9943	−3.79324
$413$	27.0033	1.32875
$414$	−1.12030	−0.0550596
$415$	13.1586	0.645931
$416$	50.8470	2.49298
$417$	−13.3144	−0.652010
$418$	−4.52151	−0.221154
$419$	−25.6478	−1.25298	−0.626489	−	0.779430i	$-0.715509\pi$
$419$	−25.6478	−1.25298	−0.626489	+	0.779430i	$0.715509\pi$
$420$	−20.4637	−0.998524
$421$	−12.1318	−0.591267	−0.295634	−	0.955301i	$-0.595531\pi$
$421$	−12.1318	−0.591267	−0.295634	+	0.955301i	$0.595531\pi$
$422$	58.4244	2.84406
$423$	10.8741	0.528718
$424$	97.2867	4.72466
$425$	−2.05032	−0.0994553
$426$	41.0438	1.98858
$427$	−23.2044	−1.12294
$428$	−68.8567	−3.32831
$429$	0.685621	0.0331021
$430$	−29.0471	−1.40078
$431$	37.5781	1.81007	0.905036	−	0.425336i	$-0.139844\pi$
$431$	37.5781	1.81007	0.905036	+	0.425336i	$0.139844\pi$
$432$	17.2640	0.830612
$433$	25.5611	1.22839	0.614194	−	0.789155i	$-0.289481\pi$
$433$	25.5611	1.22839	0.614194	+	0.789155i	$0.289481\pi$
$434$	37.1018	1.78094
$435$	−12.3925	−0.594173
$436$	−62.5734	−2.99672
$437$	−1.78271	−0.0852784
$438$	−29.0961	−1.39027
$439$	−0.424235	−0.0202477	−0.0101238	−	0.999949i	$-0.503223\pi$
$439$	−0.424235	−0.0202477	−0.0101238	+	0.999949i	$0.503223\pi$
$440$	6.53165	0.311384
$441$	−2.65857	−0.126599
$442$	5.17420	0.246112
$443$	−26.6224	−1.26487	−0.632435	−	0.774613i	$-0.717944\pi$
$443$	−26.6224	−1.26487	−0.632435	+	0.774613i	$0.717944\pi$
$444$	50.0028	2.37303
$445$	1.16144	0.0550577
$446$	−25.2119	−1.19382
$447$	−5.46817	−0.258636
$448$	−86.0981	−4.06775
$449$	31.4052	1.48210	0.741050	−	0.671449i	$-0.234328\pi$
$449$	31.4052	1.48210	0.741050	+	0.671449i	$0.234328\pi$
$450$	5.69624	0.268523
$451$	1.31109	0.0617369
$452$	−88.0104	−4.13966
$453$	−19.3545	−0.909352
$454$	26.6383	1.25020
$455$	6.66471	0.312447
$456$	45.6711	2.13875
$457$	26.6679	1.24747	0.623736	−	0.781635i	$-0.285614\pi$
$457$	26.6679	1.24747	0.623736	+	0.781635i	$0.285614\pi$
$458$	−78.5665	−3.67117
$459$	1.00000	0.0466760
$460$	3.96036	0.184653
$461$	24.0088	1.11820	0.559101	−	0.829100i	$-0.311147\pi$
$461$	24.0088	1.11820	0.559101	+	0.829100i	$0.311147\pi$
$462$	−2.13102	−0.0991441
$463$	−35.9964	−1.67290	−0.836448	−	0.548047i	$-0.815372\pi$
$463$	−35.9964	−1.67290	−0.836448	+	0.548047i	$0.815372\pi$
$464$	−124.569	−5.78298
$465$	11.0078	0.510474
$466$	−18.7035	−0.866422
$467$	−1.00898	−0.0466900	−0.0233450	−	0.999727i	$-0.507432\pi$
$467$	−1.00898	−0.0466900	−0.0233450	+	0.999727i	$0.507432\pi$
$468$	−10.6502	−0.492306
$469$	−30.4228	−1.40480
$470$	−51.8856	−2.39330
$471$	−7.34983	−0.338663
$472$	133.885	6.16254
$473$	−2.24108	−0.103045
$474$	2.77821	0.127608
$475$	9.06430	0.415899
$476$	−11.9151	−0.546126
$477$	−9.41725	−0.431186
$478$	30.9185	1.41418
$479$	−17.0896	−0.780843	−0.390422	−	0.920636i	$-0.627671\pi$
$479$	−17.0896	−0.780843	−0.390422	+	0.920636i	$0.627671\pi$
$480$	−46.8894	−2.14020
$481$	−16.2852	−0.742540
$482$	−30.0388	−1.36823
$483$	−0.840203	−0.0382306
$484$	−62.1282	−2.82401
$485$	−23.2455	−1.05552
$486$	−2.77821	−0.126022
$487$	−38.7268	−1.75488	−0.877438	−	0.479689i	$-0.840749\pi$
$487$	−38.7268	−1.75488	−0.877438	+	0.479689i	$0.840749\pi$
$488$	−115.049	−5.20804
$489$	7.70622	0.348487
$490$	12.6853	0.573064
$491$	−26.5116	−1.19645	−0.598226	−	0.801327i	$-0.704127\pi$
$491$	−26.5116	−1.19645	−0.598226	+	0.801327i	$0.704127\pi$
$492$	−20.3660	−0.918172
$493$	−7.21557	−0.324973
$494$	−22.8747	−1.02918
$495$	−0.632256	−0.0284178
$496$	110.650	4.96835
$497$	30.7821	1.38076
$498$	−21.2857	−0.953837
$499$	−4.91960	−0.220232	−0.110116	−	0.993919i	$-0.535122\pi$
$499$	−4.91960	−0.220232	−0.110116	+	0.993919i	$0.535122\pi$
$500$	−69.2430	−3.09664
$501$	7.38206	0.329806
$502$	−30.7925	−1.37433
$503$	35.6056	1.58758	0.793788	−	0.608194i	$-0.208106\pi$
$503$	35.6056	1.58758	0.793788	+	0.608194i	$0.208106\pi$
$504$	21.5251	0.958806
$505$	−16.5813	−0.737856
$506$	0.412420	0.0183343
$507$	−9.53139	−0.423304
$508$	−38.4686	−1.70677
$509$	−0.712952	−0.0316011	−0.0158005	−	0.999875i	$-0.505030\pi$
$509$	−0.712952	−0.0316011	−0.0158005	+	0.999875i	$0.505030\pi$
$510$	−4.77148	−0.211285
$511$	−21.8216	−0.965330
$512$	−114.635	−5.06620
$513$	−4.42091	−0.195188
$514$	−69.3352	−3.05824
$515$	−23.1242	−1.01897
$516$	34.8121	1.53252
$517$	−4.00313	−0.176058
$518$	50.6170	2.22398
$519$	12.5006	0.548714
$520$	33.0442	1.44908
$521$	12.1022	0.530208	0.265104	−	0.964220i	$-0.414594\pi$
$521$	12.1022	0.530208	0.265104	+	0.964220i	$0.414594\pi$
$522$	20.0464	0.877406
$523$	25.4225	1.11165	0.555825	−	0.831299i	$-0.312402\pi$
$523$	25.4225	1.11165	0.555825	+	0.831299i	$0.312402\pi$
$524$	17.9998	0.786326
$525$	4.27208	0.186449
$526$	77.8454	3.39422
$527$	6.40933	0.279195
$528$	−6.35545	−0.276585
$529$	−22.8374	−0.992930
$530$	44.9342	1.95182
$531$	−12.9599	−0.562411
$532$	52.6754	2.28377
$533$	6.63292	0.287304
$534$	−1.87878	−0.0813028
$535$	−20.6801	−0.894081
$536$	−150.839	−6.51524
$537$	−1.08318	−0.0467427
$538$	45.3251	1.95410
$539$	0.978710	0.0421560
$540$	9.82125	0.422639
$541$	36.6519	1.57579	0.787894	−	0.615811i	$-0.211171\pi$
$541$	36.6519	1.57579	0.787894	+	0.615811i	$0.211171\pi$
$542$	70.2822	3.01888
$543$	7.04972	0.302532
$544$	−27.3015	−1.17054
$545$	−18.7930	−0.805005
$546$	−10.7810	−0.461385
$547$	−3.12374	−0.133561	−0.0667807	−	0.997768i	$-0.521273\pi$
$547$	−3.12374	−0.133561	−0.0667807	+	0.997768i	$0.521273\pi$
$548$	26.5791	1.13540
$549$	11.1366	0.475300
$550$	−2.09698	−0.0894155
$551$	31.8994	1.35896
$552$	−4.16579	−0.177308
$553$	2.08361	0.0886041
$554$	33.0186	1.40282
$555$	15.0176	0.637464
$556$	−76.1381	−3.22897
$557$	−12.4748	−0.528576	−0.264288	−	0.964444i	$-0.585137\pi$
$557$	−12.4748	−0.528576	−0.264288	+	0.964444i	$0.585137\pi$
$558$	−17.8065	−0.753809
$559$	−11.3378	−0.479537
$560$	−61.7794	−2.61066
$561$	−0.368134	−0.0155426
$562$	−51.2596	−2.16225
$563$	−19.6398	−0.827718	−0.413859	−	0.910341i	$-0.635819\pi$
$563$	−19.6398	−0.827718	−0.413859	+	0.910341i	$0.635819\pi$
$564$	62.1833	2.61839
$565$	−26.4327	−1.11203
$566$	−26.8103	−1.12692
$567$	−2.08361	−0.0875034
$568$	152.620	6.40379
$569$	18.6627	0.782379	0.391190	−	0.920310i	$-0.372064\pi$
$569$	18.6627	0.782379	0.391190	+	0.920310i	$0.372064\pi$
$570$	21.0943	0.883542
$571$	0.346166	0.0144866	0.00724330	−	0.999974i	$-0.497694\pi$
$571$	0.346166	0.0144866	0.00724330	+	0.999974i	$0.497694\pi$
$572$	3.92070	0.163933
$573$	−3.78964	−0.158315
$574$	−20.6162	−0.860504
$575$	−0.826781	−0.0344791
$576$	41.3216	1.72173
$577$	17.0469	0.709672	0.354836	−	0.934928i	$-0.384537\pi$
$577$	17.0469	0.709672	0.354836	+	0.934928i	$0.384537\pi$
$578$	−2.77821	−0.115558
$579$	−8.65072	−0.359512
$580$	−70.8659	−2.94255
$581$	−15.9639	−0.662295
$582$	37.6026	1.55868
$583$	3.46681	0.143581
$584$	−108.193	−4.47706
$585$	−3.19864	−0.132247
$586$	43.9759	1.81663
$587$	43.0443	1.77663	0.888313	−	0.459238i	$-0.151878\pi$
$587$	43.0443	1.77663	0.888313	+	0.459238i	$0.151878\pi$
$588$	−15.2030	−0.626959
$589$	−28.3351	−1.16753
$590$	61.8378	2.54582
$591$	4.72589	0.194397
$592$	150.958	6.20432
$593$	−42.0280	−1.72588	−0.862941	−	0.505305i	$-0.831380\pi$
$593$	−42.0280	−1.72588	−0.862941	+	0.505305i	$0.831380\pi$
$594$	1.02275	0.0419641
$595$	−3.57852	−0.146705
$596$	−31.2696	−1.28085
$597$	−16.4603	−0.673675
$598$	2.08647	0.0853219
$599$	−24.7164	−1.00989	−0.504943	−	0.863153i	$-0.668487\pi$
$599$	−24.7164	−1.00989	−0.504943	+	0.863153i	$0.668487\pi$
$600$	21.1813	0.864722
$601$	−18.5227	−0.755555	−0.377778	−	0.925896i	$-0.623312\pi$
$601$	−18.5227	−0.755555	−0.377778	+	0.925896i	$0.623312\pi$
$602$	35.2397	1.43626
$603$	14.6010	0.594599
$604$	−110.678	−4.50342
$605$	−18.6593	−0.758610
$606$	26.8223	1.08958
$607$	18.8766	0.766179	0.383089	−	0.923711i	$-0.374860\pi$
$607$	18.8766	0.766179	0.383089	+	0.923711i	$0.374860\pi$
$608$	120.698	4.89494
$609$	15.0344	0.609226
$610$	−53.1382	−2.15150
$611$	−20.2522	−0.819316
$612$	5.71847	0.231155
$613$	39.5086	1.59574	0.797868	−	0.602832i	$-0.205961\pi$
$613$	39.5086	1.59574	0.797868	+	0.602832i	$0.205961\pi$
$614$	78.2981	3.15986
$615$	−6.11666	−0.246647
$616$	−7.92414	−0.319273
$617$	7.68959	0.309571	0.154786	−	0.987948i	$-0.450531\pi$
$617$	7.68959	0.309571	0.154786	+	0.987948i	$0.450531\pi$
$618$	37.4063	1.50470
$619$	8.09295	0.325283	0.162642	−	0.986685i	$-0.447999\pi$
$619$	8.09295	0.325283	0.162642	+	0.986685i	$0.447999\pi$
$620$	62.9477	2.52804
$621$	0.403244	0.0161816
$622$	20.2249	0.810945
$623$	−1.40905	−0.0564525
$624$	−32.1527	−1.28714
$625$	−10.5446	−0.421782
$626$	−28.8415	−1.15274
$627$	1.62749	0.0649956
$628$	−42.0298	−1.67717
$629$	8.74409	0.348650
$630$	9.94189	0.396095
$631$	−39.3268	−1.56558	−0.782788	−	0.622288i	$-0.786203\pi$
$631$	−39.3268	−1.56558	−0.782788	+	0.622288i	$0.786203\pi$
$632$	10.3307	0.410933
$633$	−21.0295	−0.835847
$634$	19.4795	0.773632
$635$	−11.5535	−0.458487
$636$	−53.8522	−2.13538
$637$	4.95138	0.196181
$638$	−7.37976	−0.292167
$639$	−14.7734	−0.584428
$640$	−103.386	−4.08670
$641$	7.30964	0.288713	0.144357	−	0.989526i	$-0.453889\pi$
$641$	7.30964	0.288713	0.144357	+	0.989526i	$0.453889\pi$
$642$	33.4528	1.32028
$643$	−39.6459	−1.56348	−0.781740	−	0.623605i	$-0.785668\pi$
$643$	−39.6459	−1.56348	−0.781740	+	0.623605i	$0.785668\pi$
$644$	−4.80467	−0.189331
$645$	10.4553	0.411678
$646$	12.2822	0.483238
$647$	22.3629	0.879177	0.439589	−	0.898199i	$-0.355124\pi$
$647$	22.3629	0.879177	0.439589	+	0.898199i	$0.355124\pi$
$648$	−10.3307	−0.405828
$649$	4.77098	0.187277
$650$	−10.6088	−0.416111
$651$	−13.3545	−0.523406
$652$	44.0678	1.72583
$653$	−20.9931	−0.821524	−0.410762	−	0.911743i	$-0.634737\pi$
$653$	−20.9931	−0.821524	−0.410762	+	0.911743i	$0.634737\pi$
$654$	30.4001	1.18874
$655$	5.40600	0.211230
$656$	−61.4847	−2.40057
$657$	10.4730	0.408589
$658$	62.9472	2.45394
$659$	−31.1494	−1.21341	−0.606704	−	0.794928i	$-0.707509\pi$
$659$	−31.1494	−1.21341	−0.606704	+	0.794928i	$0.707509\pi$
$660$	−3.61554	−0.140735
$661$	32.8754	1.27870	0.639352	−	0.768914i	$-0.279203\pi$
$661$	32.8754	1.27870	0.639352	+	0.768914i	$0.279203\pi$
$662$	61.7212	2.39886
$663$	−1.86242	−0.0723304
$664$	−79.1503	−3.07163
$665$	15.8203	0.613486
$666$	−24.2930	−0.941333
$667$	−2.90963	−0.112661
$668$	42.2141	1.63331
$669$	9.07486	0.350854
$670$	−69.6684	−2.69152
$671$	−4.09978	−0.158270
$672$	56.8857	2.19442
$673$	−6.83650	−0.263528	−0.131764	−	0.991281i	$-0.542064\pi$
$673$	−6.83650	−0.263528	−0.131764	+	0.991281i	$0.542064\pi$
$674$	−9.51372	−0.366455
$675$	−2.05032	−0.0789170
$676$	−54.5049	−2.09634
$677$	−39.9789	−1.53651	−0.768257	−	0.640142i	$-0.778876\pi$
$677$	−39.9789	−1.53651	−0.768257	+	0.640142i	$0.778876\pi$
$678$	42.7582	1.64212
$679$	28.2012	1.08226
$680$	−17.7426	−0.680397
$681$	−9.58827	−0.367423
$682$	6.55518	0.251011
$683$	−21.2810	−0.814296	−0.407148	−	0.913362i	$-0.633477\pi$
$683$	−21.2810	−0.814296	−0.407148	+	0.913362i	$0.633477\pi$
$684$	−25.2808	−0.966637
$685$	7.98267	0.305002
$686$	−55.9107	−2.13468
$687$	28.2795	1.07893
$688$	105.097	4.00679
$689$	17.5389	0.668178
$690$	−1.92407	−0.0732480
$691$	−8.27330	−0.314731	−0.157366	−	0.987540i	$-0.550300\pi$
$691$	−8.27330	−0.314731	−0.157366	+	0.987540i	$0.550300\pi$
$692$	71.4842	2.71742
$693$	0.767048	0.0291377
$694$	13.8938	0.527401
$695$	−22.8670	−0.867395
$696$	74.5419	2.82550
$697$	−3.56145	−0.134900
$698$	−31.5645	−1.19473
$699$	6.73219	0.254635
$700$	24.4297	0.923357
$701$	34.8012	1.31442	0.657212	−	0.753706i	$-0.271736\pi$
$701$	34.8012	1.31442	0.657212	+	0.753706i	$0.271736\pi$
$702$	5.17420	0.195288
$703$	−38.6569	−1.45797
$704$	−15.2119	−0.573319
$705$	18.6759	0.703375
$706$	47.0940	1.77240
$707$	20.1162	0.756549
$708$	−74.1107	−2.78525
$709$	8.74507	0.328428	0.164214	−	0.986425i	$-0.447491\pi$
$709$	8.74507	0.328428	0.164214	+	0.986425i	$0.447491\pi$
$710$	70.4911	2.64548
$711$	−1.00000	−0.0375029
$712$	−6.98619	−0.261819
$713$	2.58452	0.0967912
$714$	5.78871	0.216637
$715$	1.17753	0.0440370
$716$	−6.19413	−0.231486
$717$	−11.1289	−0.415617
$718$	−29.1629	−1.08835
$719$	−7.47978	−0.278949	−0.139474	−	0.990226i	$-0.544541\pi$
$719$	−7.47978	−0.278949	−0.139474	+	0.990226i	$0.544541\pi$
$720$	29.6502	1.10500
$721$	28.0540	1.04479
$722$	−1.51262	−0.0562939
$723$	10.8123	0.402113
$724$	40.3136	1.49824
$725$	14.7943	0.549445
$726$	30.1838	1.12023
$727$	18.5920	0.689541	0.344770	−	0.938687i	$-0.387957\pi$
$727$	18.5920	0.689541	0.344770	+	0.938687i	$0.387957\pi$
$728$	−40.0889	−1.48579
$729$	1.00000	0.0370370
$730$	−49.9715	−1.84953
$731$	6.08766	0.225160
$732$	63.6846	2.35385
$733$	−35.7257	−1.31956	−0.659779	−	0.751460i	$-0.729350\pi$
$733$	−35.7257	−1.31956	−0.659779	+	0.751460i	$0.729350\pi$
$734$	−13.2829	−0.490281
$735$	−4.56599	−0.168419
$736$	−11.0092	−0.405804
$737$	−5.37513	−0.197996
$738$	9.89447	0.364220
$739$	−47.0825	−1.73196	−0.865979	−	0.500080i	$-0.833304\pi$
$739$	−47.0825	−1.73196	−0.865979	+	0.500080i	$0.833304\pi$
$740$	85.8779	3.15694
$741$	8.23360	0.302469
$742$	−54.5137	−2.00126
$743$	−22.5497	−0.827267	−0.413634	−	0.910443i	$-0.635741\pi$
$743$	−22.5497	−0.827267	−0.413634	+	0.910443i	$0.635741\pi$
$744$	−66.2129	−2.42748
$745$	−9.39137	−0.344073
$746$	18.7307	0.685778
$747$	7.66166	0.280326
$748$	−2.10516	−0.0769724
$749$	25.0890	0.916731
$750$	33.6405	1.22838
$751$	53.1635	1.93996	0.969982	−	0.243175i	$-0.0781890\pi$
$751$	53.1635	1.93996	0.969982	+	0.243175i	$0.0781890\pi$
$752$	187.730	6.84582
$753$	11.0835	0.403907
$754$	−37.3348	−1.35965
$755$	−33.2406	−1.20975
$756$	−11.9151	−0.433346
$757$	−15.7393	−0.572056	−0.286028	−	0.958221i	$-0.592335\pi$
$757$	−15.7393	−0.572056	−0.286028	+	0.958221i	$0.592335\pi$
$758$	−80.7798	−2.93405
$759$	−0.148448	−0.00538831
$760$	78.4384	2.84526
$761$	−1.71020	−0.0619947	−0.0309974	−	0.999519i	$-0.509868\pi$
$761$	−1.71020	−0.0619947	−0.0309974	+	0.999519i	$0.509868\pi$
$762$	18.6893	0.677041
$763$	22.7995	0.825399
$764$	−21.6710	−0.784028
$765$	1.71746	0.0620950
$766$	80.6260	2.91313
$767$	24.1368	0.871528
$768$	84.5972	3.05264
$769$	3.95837	0.142743	0.0713713	−	0.997450i	$-0.477262\pi$
$769$	3.95837	0.142743	0.0713713	+	0.997450i	$0.477262\pi$
$770$	−3.65995	−0.131895
$771$	24.9568	0.898796
$772$	−49.4689	−1.78042
$773$	23.9172	0.860241	0.430120	−	0.902772i	$-0.358471\pi$
$773$	23.9172	0.860241	0.430120	+	0.902772i	$0.358471\pi$
$774$	−16.9128	−0.607919
$775$	−13.1412	−0.472046
$776$	139.824	5.01939
$777$	−18.2193	−0.653613
$778$	−25.1436	−0.901442
$779$	15.7449	0.564118
$780$	−18.2913	−0.654934
$781$	5.43860	0.194609
$782$	−1.12030	−0.0400618
$783$	−7.21557	−0.257863
$784$	−45.8974	−1.63919
$785$	−12.6231	−0.450536
$786$	−8.74489	−0.311920
$787$	32.7045	1.16579	0.582895	−	0.812547i	$-0.301920\pi$
$787$	32.7045	1.16579	0.582895	+	0.812547i	$0.301920\pi$
$788$	27.0249	0.962722
$789$	−28.0200	−0.997537
$790$	4.77148	0.169761
$791$	32.0679	1.14020
$792$	3.80308	0.135137
$793$	−20.7411	−0.736539
$794$	−60.6469	−2.15228
$795$	−16.1738	−0.573624
$796$	−94.1276	−3.33627
$797$	11.6056	0.411090	0.205545	−	0.978648i	$-0.434103\pi$
$797$	11.6056	0.411090	0.205545	+	0.978648i	$0.434103\pi$
$798$	−25.5914	−0.905925
$799$	10.8741	0.384699
$800$	55.9770	1.97909
$801$	0.676255	0.0238943
$802$	−34.9777	−1.23511
$803$	−3.85546	−0.136056
$804$	83.4955	2.94466
$805$	−1.44302	−0.0508597
$806$	33.1632	1.16812
$807$	−16.3145	−0.574296
$808$	99.7378	3.50876
$809$	19.5369	0.686881	0.343440	−	0.939174i	$-0.388408\pi$
$809$	19.5369	0.686881	0.343440	+	0.939174i	$0.388408\pi$
$810$	−4.77148	−0.167653
$811$	47.4123	1.66487	0.832435	−	0.554123i	$-0.186946\pi$
$811$	47.4123	1.66487	0.832435	+	0.554123i	$0.186946\pi$
$812$	85.9739	3.01709
$813$	−25.2976	−0.887226
$814$	8.94306	0.313454
$815$	13.2351	0.463607
$816$	17.2640	0.604359
$817$	−26.9130	−0.941567
$818$	−34.2256	−1.19667
$819$	3.88056	0.135598
$820$	−34.9779	−1.22148
$821$	−22.6783	−0.791477	−0.395738	−	0.918363i	$-0.629511\pi$
$821$	−22.6783	−0.791477	−0.395738	+	0.918363i	$0.629511\pi$
$822$	−12.9130	−0.450392
$823$	−28.5598	−0.995531	−0.497766	−	0.867312i	$-0.665846\pi$
$823$	−28.5598	−0.995531	−0.497766	+	0.867312i	$0.665846\pi$
$824$	139.094	4.84557
$825$	0.754794	0.0262786
$826$	−75.0211	−2.61032
$827$	−24.6634	−0.857630	−0.428815	−	0.903392i	$-0.641069\pi$
$827$	−24.6634	−0.857630	−0.428815	+	0.903392i	$0.641069\pi$
$828$	2.30594	0.0801369
$829$	−7.17061	−0.249046	−0.124523	−	0.992217i	$-0.539740\pi$
$829$	−7.17061	−0.249046	−0.124523	+	0.992217i	$0.539740\pi$
$830$	−36.5574	−1.26893
$831$	−11.8848	−0.412280
$832$	−76.9582	−2.66805
$833$	−2.65857	−0.0921140
$834$	36.9903	1.28087
$835$	12.6784	0.438754
$836$	9.30674	0.321880
$837$	6.40933	0.221539
$838$	71.2552	2.46147
$839$	50.1469	1.73126	0.865632	−	0.500681i	$-0.166917\pi$
$839$	50.1469	1.73126	0.865632	+	0.500681i	$0.166917\pi$
$840$	36.9686	1.27554
$841$	23.0644	0.795324
$842$	33.7047	1.16154
$843$	18.4506	0.635471
$844$	−120.257	−4.13940
$845$	−16.3698	−0.563138
$846$	−30.2106	−1.03866
$847$	22.6373	0.777828
$848$	−162.579	−5.58298
$849$	9.65019	0.331194
$850$	5.69624	0.195379
$851$	3.52600	0.120870
$852$	−84.4814	−2.89429
$853$	6.59870	0.225935	0.112968	−	0.993599i	$-0.463964\pi$
$853$	6.59870	0.225935	0.112968	+	0.993599i	$0.463964\pi$
$854$	64.4668	2.20601
$855$	−7.59275	−0.259666
$856$	124.393	4.25167
$857$	−33.9573	−1.15996	−0.579980	−	0.814631i	$-0.696940\pi$
$857$	−33.9573	−1.15996	−0.579980	+	0.814631i	$0.696940\pi$
$858$	−1.90480	−0.0650288
$859$	6.87002	0.234402	0.117201	−	0.993108i	$-0.462608\pi$
$859$	6.87002	0.234402	0.117201	+	0.993108i	$0.462608\pi$
$860$	59.7885	2.03877
$861$	7.42067	0.252896
$862$	−104.400	−3.55587
$863$	12.9498	0.440816	0.220408	−	0.975408i	$-0.429261\pi$
$863$	12.9498	0.440816	0.220408	+	0.975408i	$0.429261\pi$
$864$	−27.3015	−0.928817
$865$	21.4693	0.729977
$866$	−71.0142	−2.41316
$867$	1.00000	0.0339618
$868$	−76.3676	−2.59208
$869$	0.368134	0.0124881
$870$	34.4289	1.16725
$871$	−27.1932	−0.921408
$872$	113.042	3.82808
$873$	−13.5348	−0.458084
$874$	4.95274	0.167529
$875$	25.2297	0.852921
$876$	59.8893	2.02347
$877$	7.94684	0.268346	0.134173	−	0.990958i	$-0.457162\pi$
$877$	7.94684	0.268346	0.134173	+	0.990958i	$0.457162\pi$
$878$	1.17862	0.0397764
$879$	−15.8289	−0.533894
$880$	−10.9152	−0.367953
$881$	−15.1253	−0.509583	−0.254791	−	0.966996i	$-0.582007\pi$
$881$	−15.1253	−0.509583	−0.254791	+	0.966996i	$0.582007\pi$
$882$	7.38607	0.248702
$883$	−30.3417	−1.02108	−0.510540	−	0.859854i	$-0.670555\pi$
$883$	−30.3417	−1.02108	−0.510540	+	0.859854i	$0.670555\pi$
$884$	−10.6502	−0.358205
$885$	−22.2581	−0.748198
$886$	73.9628	2.48483
$887$	−12.9892	−0.436134	−0.218067	−	0.975934i	$-0.569975\pi$
$887$	−12.9892	−0.436134	−0.218067	+	0.975934i	$0.569975\pi$
$888$	−90.3326	−3.03136
$889$	14.0166	0.470102
$890$	−3.22674	−0.108160
$891$	−0.368134	−0.0123330
$892$	51.8943	1.73755
$893$	−48.0735	−1.60872
$894$	15.1917	0.508088
$895$	−1.86032	−0.0621837
$896$	125.427	4.19023
$897$	−0.751010	−0.0250755
$898$	−87.2502	−2.91158
$899$	−46.2470	−1.54242
$900$	−11.7247	−0.390824
$901$	−9.41725	−0.313734
$902$	−3.64249	−0.121282
$903$	−12.6843	−0.422107
$904$	158.995	5.28810
$905$	12.1076	0.402471
$906$	53.7708	1.78642
$907$	−16.6269	−0.552088	−0.276044	−	0.961145i	$-0.589024\pi$
$907$	−16.6269	−0.552088	−0.276044	+	0.961145i	$0.589024\pi$
$908$	−54.8302	−1.81961
$909$	−9.65451	−0.320220
$910$	−18.5160	−0.613799
$911$	−5.68676	−0.188411	−0.0942054	−	0.995553i	$-0.530031\pi$
$911$	−5.68676	−0.188411	−0.0942054	+	0.995553i	$0.530031\pi$
$912$	−76.3224	−2.52729
$913$	−2.82052	−0.0933456
$914$	−74.0891	−2.45065
$915$	19.1268	0.632311
$916$	161.715	5.34323
$917$	−6.55851	−0.216581
$918$	−2.77821	−0.0916947
$919$	20.6701	0.681845	0.340922	−	0.940091i	$-0.389261\pi$
$919$	20.6701	0.681845	0.340922	+	0.940091i	$0.389261\pi$
$920$	−7.15459	−0.235880
$921$	−28.1829	−0.928658
$922$	−66.7016	−2.19670
$923$	27.5144	0.905646
$924$	4.38634	0.144300
$925$	−17.9282	−0.589476
$926$	100.006	3.28639
$927$	−13.4641	−0.442221
$928$	196.996	6.46671
$929$	−7.34538	−0.240994	−0.120497	−	0.992714i	$-0.538449\pi$
$929$	−7.34538	−0.240994	−0.120497	+	0.992714i	$0.538449\pi$
$930$	−30.5820	−1.00282
$931$	11.7533	0.385199
$932$	38.4978	1.26104
$933$	−7.27982	−0.238331
$934$	2.80316	0.0917222
$935$	−0.632256	−0.0206770
$936$	19.2401	0.628883
$937$	15.0498	0.491655	0.245827	−	0.969314i	$-0.420940\pi$
$937$	15.0498	0.491655	0.245827	+	0.969314i	$0.420940\pi$
$938$	84.5211	2.75971
$939$	10.3813	0.338781
$940$	106.797	3.48335
$941$	23.4395	0.764105	0.382052	−	0.924141i	$-0.375217\pi$
$941$	23.4395	0.764105	0.382052	+	0.924141i	$0.375217\pi$
$942$	20.4194	0.665300
$943$	−1.43613	−0.0467669
$944$	−223.739	−7.28208
$945$	−3.57852	−0.116409
$946$	6.22619	0.202431
$947$	13.0593	0.424370	0.212185	−	0.977230i	$-0.431942\pi$
$947$	13.0593	0.424370	0.212185	+	0.977230i	$0.431942\pi$
$948$	−5.71847	−0.185727
$949$	−19.5051	−0.633161
$950$	−25.1826	−0.817030
$951$	−7.01154	−0.227365
$952$	21.5251	0.697634
$953$	−0.484111	−0.0156819	−0.00784094	−	0.999969i	$-0.502496\pi$
$953$	−0.484111	−0.0156819	−0.00784094	+	0.999969i	$0.502496\pi$
$954$	26.1631	0.847062
$955$	−6.50857	−0.210612
$956$	−63.6404	−2.05828
$957$	2.65630	0.0858659
$958$	47.4785	1.53396
$959$	−9.68451	−0.312729
$960$	70.9683	2.29049
$961$	10.0795	0.325146
$962$	45.2437	1.45872
$963$	−12.0411	−0.388019
$964$	61.8297	1.99140
$965$	−14.8573	−0.478273
$966$	2.33426	0.0751037
$967$	−5.92654	−0.190585	−0.0952923	−	0.995449i	$-0.530379\pi$
$967$	−5.92654	−0.190585	−0.0952923	+	0.995449i	$0.530379\pi$
$968$	112.238	3.60745
$969$	−4.42091	−0.142020
$970$	64.5810	2.07357
$971$	4.79861	0.153995	0.0769974	−	0.997031i	$-0.475467\pi$
$971$	4.79861	0.153995	0.0769974	+	0.997031i	$0.475467\pi$
$972$	5.71847	0.183420
$973$	27.7420	0.889369
$974$	107.591	3.44744
$975$	3.81857	0.122292
$976$	192.262	6.15417
$977$	12.2620	0.392295	0.196148	−	0.980574i	$-0.437157\pi$
$977$	12.2620	0.392295	0.196148	+	0.980574i	$0.437157\pi$
$978$	−21.4095	−0.684601
$979$	−0.248953	−0.00795656
$980$	−26.1105	−0.834069
$981$	−10.9423	−0.349362
$982$	73.6549	2.35042
$983$	−3.27675	−0.104512	−0.0522561	−	0.998634i	$-0.516641\pi$
$983$	−3.27675	−0.104512	−0.0522561	+	0.998634i	$0.516641\pi$
$984$	36.7923	1.17289
$985$	8.11654	0.258615
$986$	20.0464	0.638407
$987$	−22.6574	−0.721194
$988$	47.0836	1.49793
$989$	2.45481	0.0780585
$990$	1.75654	0.0558266
$991$	−19.1650	−0.608798	−0.304399	−	0.952545i	$-0.598456\pi$
$991$	−19.1650	−0.608798	−0.304399	+	0.952545i	$0.598456\pi$
$992$	−174.985	−5.55577
$993$	−22.2161	−0.705008
$994$	−85.5192	−2.71250
$995$	−28.2699	−0.896217
$996$	43.8130	1.38827
$997$	36.4404	1.15408	0.577040	−	0.816716i	$-0.304208\pi$
$997$	36.4404	1.15408	0.577040	+	0.816716i	$0.304208\pi$
$998$	13.6677	0.432644
$999$	8.74409	0.276651

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.e.1.1	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.e.1.1	✓	18	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q-2.77821 q^{2} +1.00000 q^{3} +5.71847 q^{4} +1.71746 q^{5} -2.77821 q^{6} -2.08361 q^{7} -10.3307 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.77821 q^{2} +1.00000 q^{3} +5.71847 q^{4} +1.71746 q^{5} -2.77821 q^{6} -2.08361 q^{7} -10.3307 q^{8} +1.00000 q^{9} -4.77148 q^{10} -0.368134 q^{11} +5.71847 q^{12} -1.86242 q^{13} +5.78871 q^{14} +1.71746 q^{15} +17.2640 q^{16} +1.00000 q^{17} -2.77821 q^{18} -4.42091 q^{19} +9.82125 q^{20} -2.08361 q^{21} +1.02275 q^{22} +0.403244 q^{23} -10.3307 q^{24} -2.05032 q^{25} +5.17420 q^{26} +1.00000 q^{27} -11.9151 q^{28} -7.21557 q^{29} -4.77148 q^{30} +6.40933 q^{31} -27.3015 q^{32} -0.368134 q^{33} -2.77821 q^{34} -3.57852 q^{35} +5.71847 q^{36} +8.74409 q^{37} +12.2822 q^{38} -1.86242 q^{39} -17.7426 q^{40} -3.56145 q^{41} +5.78871 q^{42} +6.08766 q^{43} -2.10516 q^{44} +1.71746 q^{45} -1.12030 q^{46} +10.8741 q^{47} +17.2640 q^{48} -2.65857 q^{49} +5.69624 q^{50} +1.00000 q^{51} -10.6502 q^{52} -9.41725 q^{53} -2.77821 q^{54} -0.632256 q^{55} +21.5251 q^{56} -4.42091 q^{57} +20.0464 q^{58} -12.9599 q^{59} +9.82125 q^{60} +11.1366 q^{61} -17.8065 q^{62} -2.08361 q^{63} +41.3216 q^{64} -3.19864 q^{65} +1.02275 q^{66} +14.6010 q^{67} +5.71847 q^{68} +0.403244 q^{69} +9.94189 q^{70} -14.7734 q^{71} -10.3307 q^{72} +10.4730 q^{73} -24.2930 q^{74} -2.05032 q^{75} -25.2808 q^{76} +0.767048 q^{77} +5.17420 q^{78} -1.00000 q^{79} +29.6502 q^{80} +1.00000 q^{81} +9.89447 q^{82} +7.66166 q^{83} -11.9151 q^{84} +1.71746 q^{85} -16.9128 q^{86} -7.21557 q^{87} +3.80308 q^{88} +0.676255 q^{89} -4.77148 q^{90} +3.88056 q^{91} +2.30594 q^{92} +6.40933 q^{93} -30.2106 q^{94} -7.59275 q^{95} -27.3015 q^{96} -13.5348 q^{97} +7.38607 q^{98} -0.368134 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9}+O(q^{10}) \) 18 * q - 6 * q^2 + 18 * q^3 + 20 * q^4 - 5 * q^5 - 6 * q^6 - 13 * q^7 - 12 * q^8 + 18 * q^9	\( 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9} - 15 q^{10} - 27 q^{11} + 20 q^{12} - 4 q^{13} - 5 q^{14} - 5 q^{15} + 16 q^{16} + 18 q^{17} - 6 q^{18} - 30 q^{19} - 16 q^{20} - 13 q^{21} + 13 q^{22} - 21 q^{23} - 12 q^{24} + 13 q^{25} - 20 q^{26} + 18 q^{27} - 33 q^{28} - 47 q^{29} - 15 q^{30} - 18 q^{31} - 45 q^{32} - 27 q^{33} - 6 q^{34} - 17 q^{35} + 20 q^{36} + q^{37} + 5 q^{38} - 4 q^{39} - 12 q^{40} - 18 q^{41} - 5 q^{42} - 39 q^{43} - 34 q^{44} - 5 q^{45} - 7 q^{46} + 16 q^{48} + 15 q^{49} - 23 q^{50} + 18 q^{51} + 5 q^{52} - 9 q^{53} - 6 q^{54} + q^{55} - 24 q^{56} - 30 q^{57} + 41 q^{58} - 42 q^{59} - 16 q^{60} - 43 q^{61} - 54 q^{62} - 13 q^{63} + 22 q^{64} - 25 q^{65} + 13 q^{66} + 20 q^{68} - 21 q^{69} + 17 q^{70} + 9 q^{71} - 12 q^{72} + 19 q^{73} - 30 q^{74} + 13 q^{75} - 17 q^{76} - 14 q^{77} - 20 q^{78} - 18 q^{79} + 36 q^{80} + 18 q^{81} - 3 q^{82} - 61 q^{83} - 33 q^{84} - 5 q^{85} - 24 q^{86} - 47 q^{87} - 25 q^{88} + 10 q^{89} - 15 q^{90} - 52 q^{91} - 74 q^{92} - 18 q^{93} + 31 q^{94} - 37 q^{95} - 45 q^{96} - 9 q^{97} + 27 q^{98} - 27 q^{99}+O(q^{100}) \) 18 * q - 6 * q^2 + 18 * q^3 + 20 * q^4 - 5 * q^5 - 6 * q^6 - 13 * q^7 - 12 * q^8 + 18 * q^9 - 15 * q^10 - 27 * q^11 + 20 * q^12 - 4 * q^13 - 5 * q^14 - 5 * q^15 + 16 * q^16 + 18 * q^17 - 6 * q^18 - 30 * q^19 - 16 * q^20 - 13 * q^21 + 13 * q^22 - 21 * q^23 - 12 * q^24 + 13 * q^25 - 20 * q^26 + 18 * q^27 - 33 * q^28 - 47 * q^29 - 15 * q^30 - 18 * q^31 - 45 * q^32 - 27 * q^33 - 6 * q^34 - 17 * q^35 + 20 * q^36 + q^37 + 5 * q^38 - 4 * q^39 - 12 * q^40 - 18 * q^41 - 5 * q^42 - 39 * q^43 - 34 * q^44 - 5 * q^45 - 7 * q^46 + 16 * q^48 + 15 * q^49 - 23 * q^50 + 18 * q^51 + 5 * q^52 - 9 * q^53 - 6 * q^54 + q^55 - 24 * q^56 - 30 * q^57 + 41 * q^58 - 42 * q^59 - 16 * q^60 - 43 * q^61 - 54 * q^62 - 13 * q^63 + 22 * q^64 - 25 * q^65 + 13 * q^66 + 20 * q^68 - 21 * q^69 + 17 * q^70 + 9 * q^71 - 12 * q^72 + 19 * q^73 - 30 * q^74 + 13 * q^75 - 17 * q^76 - 14 * q^77 - 20 * q^78 - 18 * q^79 + 36 * q^80 + 18 * q^81 - 3 * q^82 - 61 * q^83 - 33 * q^84 - 5 * q^85 - 24 * q^86 - 47 * q^87 - 25 * q^88 + 10 * q^89 - 15 * q^90 - 52 * q^91 - 74 * q^92 - 18 * q^93 + 31 * q^94 - 37 * q^95 - 45 * q^96 - 9 * q^97 + 27 * q^98 - 27 * q^99

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