LMFDB - Embedded newform 8043.2.a.q.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8043,2,Mod(1,8043)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8043, 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("8043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8043 = 3 \cdot 7 \cdot 383 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8043.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:	$64.2236783457$
Analytic rank:	$1$
Dimension:	$44$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	8043.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.07517 q^{2} +1.00000 q^{3} -0.844015 q^{4} -3.93529 q^{5} -1.07517 q^{6} -1.00000 q^{7} +3.05779 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.07517 q^{2} +1.00000 q^{3} -0.844015 q^{4} -3.93529 q^{5} -1.07517 q^{6} -1.00000 q^{7} +3.05779 q^{8} +1.00000 q^{9} +4.23110 q^{10} -2.84999 q^{11} -0.844015 q^{12} +3.86785 q^{13} +1.07517 q^{14} -3.93529 q^{15} -1.59961 q^{16} -4.03805 q^{17} -1.07517 q^{18} -1.48814 q^{19} +3.32145 q^{20} -1.00000 q^{21} +3.06421 q^{22} -3.14849 q^{23} +3.05779 q^{24} +10.4865 q^{25} -4.15859 q^{26} +1.00000 q^{27} +0.844015 q^{28} +6.33211 q^{29} +4.23110 q^{30} +3.46326 q^{31} -4.39574 q^{32} -2.84999 q^{33} +4.34158 q^{34} +3.93529 q^{35} -0.844015 q^{36} -1.65105 q^{37} +1.60000 q^{38} +3.86785 q^{39} -12.0333 q^{40} -7.97903 q^{41} +1.07517 q^{42} +0.217870 q^{43} +2.40543 q^{44} -3.93529 q^{45} +3.38516 q^{46} -6.01662 q^{47} -1.59961 q^{48} +1.00000 q^{49} -11.2748 q^{50} -4.03805 q^{51} -3.26453 q^{52} -5.66066 q^{53} -1.07517 q^{54} +11.2155 q^{55} -3.05779 q^{56} -1.48814 q^{57} -6.80808 q^{58} +12.0314 q^{59} +3.32145 q^{60} +1.68685 q^{61} -3.72358 q^{62} -1.00000 q^{63} +7.92537 q^{64} -15.2211 q^{65} +3.06421 q^{66} -3.50257 q^{67} +3.40818 q^{68} -3.14849 q^{69} -4.23110 q^{70} +16.5683 q^{71} +3.05779 q^{72} +15.5142 q^{73} +1.77515 q^{74} +10.4865 q^{75} +1.25601 q^{76} +2.84999 q^{77} -4.15859 q^{78} +12.3196 q^{79} +6.29494 q^{80} +1.00000 q^{81} +8.57879 q^{82} -15.2753 q^{83} +0.844015 q^{84} +15.8909 q^{85} -0.234246 q^{86} +6.33211 q^{87} -8.71467 q^{88} +15.2249 q^{89} +4.23110 q^{90} -3.86785 q^{91} +2.65737 q^{92} +3.46326 q^{93} +6.46888 q^{94} +5.85626 q^{95} -4.39574 q^{96} +3.59265 q^{97} -1.07517 q^{98} -2.84999 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 4 q^{2} + 44 q^{3} + 44 q^{4} - 16 q^{5} - 4 q^{6} - 44 q^{7} - 15 q^{8} + 44 q^{9}+O(q^{10}) $ 44 * q - 4 * q^2 + 44 * q^3 + 44 * q^4 - 16 * q^5 - 4 * q^6 - 44 * q^7 - 15 * q^8 + 44 * q^9	\( 44 q - 4 q^{2} + 44 q^{3} + 44 q^{4} - 16 q^{5} - 4 q^{6} - 44 q^{7} - 15 q^{8} + 44 q^{9} - 16 q^{10} - 2 q^{11} + 44 q^{12} - 34 q^{13} + 4 q^{14} - 16 q^{15} + 24 q^{16} - 4 q^{17} - 4 q^{18} - 22 q^{19} - 39 q^{20} - 44 q^{21} - 23 q^{22} - 56 q^{23} - 15 q^{24} + 32 q^{25} - 17 q^{26} + 44 q^{27} - 44 q^{28} - 33 q^{29} - 16 q^{30} - 32 q^{31} - 34 q^{32} - 2 q^{33} - 25 q^{34} + 16 q^{35} + 44 q^{36} - 47 q^{37} - 40 q^{38} - 34 q^{39} - 50 q^{40} + 2 q^{41} + 4 q^{42} - 12 q^{43} - 22 q^{44} - 16 q^{45} + 8 q^{46} - 27 q^{47} + 24 q^{48} + 44 q^{49} - 21 q^{50} - 4 q^{51} - 82 q^{52} - 114 q^{53} - 4 q^{54} - 29 q^{55} + 15 q^{56} - 22 q^{57} - 26 q^{58} - 40 q^{59} - 39 q^{60} - 47 q^{61} - 37 q^{62} - 44 q^{63} - 5 q^{64} - 20 q^{65} - 23 q^{66} - 14 q^{67} - 72 q^{68} - 56 q^{69} + 16 q^{70} - 65 q^{71} - 15 q^{72} - 21 q^{73} - 26 q^{74} + 32 q^{75} - 15 q^{76} + 2 q^{77} - 17 q^{78} + 6 q^{79} - 77 q^{80} + 44 q^{81} - 51 q^{82} - 30 q^{83} - 44 q^{84} - 26 q^{85} - 65 q^{86} - 33 q^{87} - 84 q^{88} - 32 q^{89} - 16 q^{90} + 34 q^{91} - 140 q^{92} - 32 q^{93} - 35 q^{94} - 50 q^{95} - 34 q^{96} - 83 q^{97} - 4 q^{98} - 2 q^{99}+O(q^{100}) \) 44 * q - 4 * q^2 + 44 * q^3 + 44 * q^4 - 16 * q^5 - 4 * q^6 - 44 * q^7 - 15 * q^8 + 44 * q^9 - 16 * q^10 - 2 * q^11 + 44 * q^12 - 34 * q^13 + 4 * q^14 - 16 * q^15 + 24 * q^16 - 4 * q^17 - 4 * q^18 - 22 * q^19 - 39 * q^20 - 44 * q^21 - 23 * q^22 - 56 * q^23 - 15 * q^24 + 32 * q^25 - 17 * q^26 + 44 * q^27 - 44 * q^28 - 33 * q^29 - 16 * q^30 - 32 * q^31 - 34 * q^32 - 2 * q^33 - 25 * q^34 + 16 * q^35 + 44 * q^36 - 47 * q^37 - 40 * q^38 - 34 * q^39 - 50 * q^40 + 2 * q^41 + 4 * q^42 - 12 * q^43 - 22 * q^44 - 16 * q^45 + 8 * q^46 - 27 * q^47 + 24 * q^48 + 44 * q^49 - 21 * q^50 - 4 * q^51 - 82 * q^52 - 114 * q^53 - 4 * q^54 - 29 * q^55 + 15 * q^56 - 22 * q^57 - 26 * q^58 - 40 * q^59 - 39 * q^60 - 47 * q^61 - 37 * q^62 - 44 * q^63 - 5 * q^64 - 20 * q^65 - 23 * q^66 - 14 * q^67 - 72 * q^68 - 56 * q^69 + 16 * q^70 - 65 * q^71 - 15 * q^72 - 21 * q^73 - 26 * q^74 + 32 * q^75 - 15 * q^76 + 2 * q^77 - 17 * q^78 + 6 * q^79 - 77 * q^80 + 44 * q^81 - 51 * q^82 - 30 * q^83 - 44 * q^84 - 26 * q^85 - 65 * q^86 - 33 * q^87 - 84 * q^88 - 32 * q^89 - 16 * q^90 + 34 * q^91 - 140 * q^92 - 32 * q^93 - 35 * q^94 - 50 * q^95 - 34 * q^96 - 83 * q^97 - 4 * q^98 - 2 * 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 $

$2$	−1.07517	−0.760258	−0.380129	−	0.924933i	$-0.624120\pi$
$2$	−1.07517	−0.760258	−0.380129	+	0.924933i	$0.624120\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.844015	−0.422007
$5$	−3.93529	−1.75992	−0.879959	−	0.475050i	$-0.842430\pi$
$5$	−3.93529	−1.75992	−0.879959	+	0.475050i	$0.842430\pi$
$6$	−1.07517	−0.438935
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	3.05779	1.08109
$9$	1.00000	0.333333
$10$	4.23110	1.33799
$11$	−2.84999	−0.859303	−0.429652	−	0.902995i	$-0.641364\pi$
$11$	−2.84999	−0.859303	−0.429652	+	0.902995i	$0.641364\pi$
$12$	−0.844015	−0.243646
$13$	3.86785	1.07275	0.536375	−	0.843980i	$-0.319793\pi$
$13$	3.86785	1.07275	0.536375	+	0.843980i	$0.319793\pi$
$14$	1.07517	0.287351
$15$	−3.93529	−1.01609
$16$	−1.59961	−0.399903
$17$	−4.03805	−0.979372	−0.489686	−	0.871899i	$-0.662889\pi$
$17$	−4.03805	−0.979372	−0.489686	+	0.871899i	$0.662889\pi$
$18$	−1.07517	−0.253419
$19$	−1.48814	−0.341402	−0.170701	−	0.985323i	$-0.554603\pi$
$19$	−1.48814	−0.341402	−0.170701	+	0.985323i	$0.554603\pi$
$20$	3.32145	0.742698
$21$	−1.00000	−0.218218
$22$	3.06421	0.653293
$23$	−3.14849	−0.656506	−0.328253	−	0.944590i	$-0.606460\pi$
$23$	−3.14849	−0.656506	−0.328253	+	0.944590i	$0.606460\pi$
$24$	3.05779	0.624169
$25$	10.4865	2.09731
$26$	−4.15859	−0.815567
$27$	1.00000	0.192450
$28$	0.844015	0.159504
$29$	6.33211	1.17584	0.587922	−	0.808918i	$-0.299946\pi$
$29$	6.33211	1.17584	0.587922	+	0.808918i	$0.299946\pi$
$30$	4.23110	0.772490
$31$	3.46326	0.622020	0.311010	−	0.950407i	$-0.399333\pi$
$31$	3.46326	0.622020	0.311010	+	0.950407i	$0.399333\pi$
$32$	−4.39574	−0.777064
$33$	−2.84999	−0.496119
$34$	4.34158	0.744576
$35$	3.93529	0.665186
$36$	−0.844015	−0.140669
$37$	−1.65105	−0.271431	−0.135715	−	0.990748i	$-0.543333\pi$
$37$	−1.65105	−0.271431	−0.135715	+	0.990748i	$0.543333\pi$
$38$	1.60000	0.259554
$39$	3.86785	0.619352
$40$	−12.0333	−1.90263
$41$	−7.97903	−1.24611	−0.623057	−	0.782176i	$-0.714110\pi$
$41$	−7.97903	−1.24611	−0.623057	+	0.782176i	$0.714110\pi$
$42$	1.07517	0.165902
$43$	0.217870	0.0332248	0.0166124	−	0.999862i	$-0.494712\pi$
$43$	0.217870	0.0332248	0.0166124	+	0.999862i	$0.494712\pi$
$44$	2.40543	0.362632
$45$	−3.93529	−0.586639
$46$	3.38516	0.499114
$47$	−6.01662	−0.877615	−0.438807	−	0.898581i	$-0.644599\pi$
$47$	−6.01662	−0.877615	−0.438807	+	0.898581i	$0.644599\pi$
$48$	−1.59961	−0.230884
$49$	1.00000	0.142857
$50$	−11.2748	−1.59450
$51$	−4.03805	−0.565441
$52$	−3.26453	−0.452708
$53$	−5.66066	−0.777552	−0.388776	−	0.921332i	$-0.627102\pi$
$53$	−5.66066	−0.777552	−0.388776	+	0.921332i	$0.627102\pi$
$54$	−1.07517	−0.146312
$55$	11.2155	1.51230
$56$	−3.05779	−0.408615
$57$	−1.48814	−0.197109
$58$	−6.80808	−0.893945
$59$	12.0314	1.56636	0.783178	−	0.621798i	$-0.213597\pi$
$59$	12.0314	1.56636	0.783178	+	0.621798i	$0.213597\pi$
$60$	3.32145	0.428797
$61$	1.68685	0.215979	0.107990	−	0.994152i	$-0.465559\pi$
$61$	1.68685	0.215979	0.107990	+	0.994152i	$0.465559\pi$
$62$	−3.72358	−0.472896
$63$	−1.00000	−0.125988
$64$	7.92537	0.990672
$65$	−15.2211	−1.88795
$66$	3.06421	0.377179
$67$	−3.50257	−0.427907	−0.213954	−	0.976844i	$-0.568634\pi$
$67$	−3.50257	−0.427907	−0.213954	+	0.976844i	$0.568634\pi$
$68$	3.40818	0.413302
$69$	−3.14849	−0.379034
$70$	−4.23110	−0.505713
$71$	16.5683	1.96629	0.983145	−	0.182825i	$-0.0585242\pi$
$71$	16.5683	1.96629	0.983145	+	0.182825i	$0.0585242\pi$
$72$	3.05779	0.360364
$73$	15.5142	1.81581	0.907903	−	0.419181i	$-0.137683\pi$
$73$	15.5142	1.81581	0.907903	+	0.419181i	$0.137683\pi$
$74$	1.77515	0.206357
$75$	10.4865	1.21088
$76$	1.25601	0.144074
$77$	2.84999	0.324786
$78$	−4.15859	−0.470868
$79$	12.3196	1.38606	0.693030	−	0.720909i	$-0.256275\pi$
$79$	12.3196	1.38606	0.693030	+	0.720909i	$0.256275\pi$
$80$	6.29494	0.703796
$81$	1.00000	0.111111
$82$	8.57879	0.947369
$83$	−15.2753	−1.67668	−0.838339	−	0.545150i	$-0.816473\pi$
$83$	−15.2753	−1.67668	−0.838339	+	0.545150i	$0.816473\pi$
$84$	0.844015	0.0920895
$85$	15.8909	1.72361
$86$	−0.234246	−0.0252594
$87$	6.33211	0.678873
$88$	−8.71467	−0.928987
$89$	15.2249	1.61384	0.806920	−	0.590661i	$-0.201133\pi$
$89$	15.2249	1.61384	0.806920	+	0.590661i	$0.201133\pi$
$90$	4.23110	0.445997
$91$	−3.86785	−0.405461
$92$	2.65737	0.277050
$93$	3.46326	0.359123
$94$	6.46888	0.667214
$95$	5.85626	0.600840
$96$	−4.39574	−0.448638
$97$	3.59265	0.364778	0.182389	−	0.983226i	$-0.441617\pi$
$97$	3.59265	0.364778	0.182389	+	0.983226i	$0.441617\pi$
$98$	−1.07517	−0.108608
$99$	−2.84999	−0.286434
$100$	−8.85080	−0.885080
$101$	4.55392	0.453132	0.226566	−	0.973996i	$-0.427250\pi$
$101$	4.55392	0.453132	0.226566	+	0.973996i	$0.427250\pi$
$102$	4.34158	0.429881
$103$	−14.3145	−1.41045	−0.705226	−	0.708983i	$-0.749154\pi$
$103$	−14.3145	−1.41045	−0.705226	+	0.708983i	$0.749154\pi$
$104$	11.8271	1.15974
$105$	3.93529	0.384045
$106$	6.08616	0.591140
$107$	−5.09224	−0.492285	−0.246143	−	0.969234i	$-0.579163\pi$
$107$	−5.09224	−0.492285	−0.246143	+	0.969234i	$0.579163\pi$
$108$	−0.844015	−0.0812153
$109$	−3.88944	−0.372540	−0.186270	−	0.982499i	$-0.559640\pi$
$109$	−3.88944	−0.372540	−0.186270	+	0.982499i	$0.559640\pi$
$110$	−12.0586	−1.14974
$111$	−1.65105	−0.156711
$112$	1.59961	0.151149
$113$	12.0390	1.13253	0.566267	−	0.824222i	$-0.308387\pi$
$113$	12.0390	1.13253	0.566267	+	0.824222i	$0.308387\pi$
$114$	1.60000	0.149854
$115$	12.3902	1.15540
$116$	−5.34439	−0.496214
$117$	3.86785	0.357583
$118$	−12.9358	−1.19083
$119$	4.03805	0.370168
$120$	−12.0333	−1.09849
$121$	−2.87757	−0.261598
$122$	−1.81365	−0.164200
$123$	−7.97903	−0.719445
$124$	−2.92304	−0.262497
$125$	−21.5912	−1.93117
$126$	1.07517	0.0957835
$127$	1.15467	0.102460	0.0512301	−	0.998687i	$-0.483686\pi$
$127$	1.15467	0.102460	0.0512301	+	0.998687i	$0.483686\pi$
$128$	0.270366	0.0238972
$129$	0.217870	0.0191823
$130$	16.3653	1.43533
$131$	−15.6348	−1.36602	−0.683010	−	0.730409i	$-0.739329\pi$
$131$	−15.6348	−1.36602	−0.683010	+	0.730409i	$0.739329\pi$
$132$	2.40543	0.209366
$133$	1.48814	0.129038
$134$	3.76585	0.325320
$135$	−3.93529	−0.338696
$136$	−12.3475	−1.05879
$137$	7.71347	0.659006	0.329503	−	0.944155i	$-0.393119\pi$
$137$	7.71347	0.659006	0.329503	+	0.944155i	$0.393119\pi$
$138$	3.38516	0.288164
$139$	14.2351	1.20741	0.603704	−	0.797209i	$-0.293691\pi$
$139$	14.2351	1.20741	0.603704	+	0.797209i	$0.293691\pi$
$140$	−3.32145	−0.280713
$141$	−6.01662	−0.506691
$142$	−17.8137	−1.49489
$143$	−11.0233	−0.921818
$144$	−1.59961	−0.133301
$145$	−24.9187	−2.06939
$146$	−16.6804	−1.38048
$147$	1.00000	0.0824786
$148$	1.39351	0.114546
$149$	7.92162	0.648964	0.324482	−	0.945892i	$-0.394810\pi$
$149$	7.92162	0.648964	0.324482	+	0.945892i	$0.394810\pi$
$150$	−11.2748	−0.920583
$151$	18.4095	1.49814	0.749072	−	0.662489i	$-0.230500\pi$
$151$	18.4095	1.49814	0.749072	+	0.662489i	$0.230500\pi$
$152$	−4.55042	−0.369088
$153$	−4.03805	−0.326457
$154$	−3.06421	−0.246921
$155$	−13.6289	−1.09470
$156$	−3.26453	−0.261371
$157$	−4.64994	−0.371105	−0.185553	−	0.982634i	$-0.559408\pi$
$157$	−4.64994	−0.371105	−0.185553	+	0.982634i	$0.559408\pi$
$158$	−13.2456	−1.05376
$159$	−5.66066	−0.448920
$160$	17.2985	1.36757
$161$	3.14849	0.248136
$162$	−1.07517	−0.0844731
$163$	−3.40606	−0.266784	−0.133392	−	0.991063i	$-0.542587\pi$
$163$	−3.40606	−0.266784	−0.133392	+	0.991063i	$0.542587\pi$
$164$	6.73441	0.525869
$165$	11.2155	0.873128
$166$	16.4235	1.27471
$167$	−5.98540	−0.463164	−0.231582	−	0.972815i	$-0.574390\pi$
$167$	−5.98540	−0.463164	−0.231582	+	0.972815i	$0.574390\pi$
$168$	−3.05779	−0.235914
$169$	1.96030	0.150792
$170$	−17.0854	−1.31039
$171$	−1.48814	−0.113801
$172$	−0.183885	−0.0140211
$173$	7.78574	0.591939	0.295969	−	0.955197i	$-0.404357\pi$
$173$	7.78574	0.591939	0.295969	+	0.955197i	$0.404357\pi$
$174$	−6.80808	−0.516119
$175$	−10.4865	−0.792708
$176$	4.55887	0.343638
$177$	12.0314	0.904336
$178$	−16.3694	−1.22693
$179$	9.65035	0.721301	0.360651	−	0.932701i	$-0.382555\pi$
$179$	9.65035	0.721301	0.360651	+	0.932701i	$0.382555\pi$
$180$	3.32145	0.247566
$181$	−6.73077	−0.500294	−0.250147	−	0.968208i	$-0.580479\pi$
$181$	−6.73077	−0.500294	−0.250147	+	0.968208i	$0.580479\pi$
$182$	4.15859	0.308255
$183$	1.68685	0.124696
$184$	−9.62744	−0.709744
$185$	6.49736	0.477695
$186$	−3.72358	−0.273026
$187$	11.5084	0.841578
$188$	5.07812	0.370360
$189$	−1.00000	−0.0727393
$190$	−6.29646	−0.456793
$191$	−10.6688	−0.771968	−0.385984	−	0.922505i	$-0.626138\pi$
$191$	−10.6688	−0.771968	−0.385984	+	0.922505i	$0.626138\pi$
$192$	7.92537	0.571965
$193$	−15.2497	−1.09770	−0.548848	−	0.835922i	$-0.684933\pi$
$193$	−15.2497	−1.09770	−0.548848	+	0.835922i	$0.684933\pi$
$194$	−3.86270	−0.277326
$195$	−15.2211	−1.09001
$196$	−0.844015	−0.0602868
$197$	−12.9185	−0.920406	−0.460203	−	0.887814i	$-0.652223\pi$
$197$	−12.9185	−0.920406	−0.460203	+	0.887814i	$0.652223\pi$
$198$	3.06421	0.217764
$199$	8.53976	0.605367	0.302684	−	0.953091i	$-0.402117\pi$
$199$	8.53976	0.605367	0.302684	+	0.953091i	$0.402117\pi$
$200$	32.0657	2.26739
$201$	−3.50257	−0.247052
$202$	−4.89623	−0.344498
$203$	−6.33211	−0.444427
$204$	3.40818	0.238620
$205$	31.3998	2.19306
$206$	15.3905	1.07231
$207$	−3.14849	−0.218835
$208$	−6.18706	−0.428995
$209$	4.24117	0.293368
$210$	−4.23110	−0.291974
$211$	17.2974	1.19080	0.595401	−	0.803428i	$-0.296993\pi$
$211$	17.2974	1.19080	0.595401	+	0.803428i	$0.296993\pi$
$212$	4.77768	0.328132
$213$	16.5683	1.13524
$214$	5.47501	0.374264
$215$	−0.857381	−0.0584729
$216$	3.05779	0.208056
$217$	−3.46326	−0.235101
$218$	4.18180	0.283227
$219$	15.5142	1.04836
$220$	−9.46608	−0.638203
$221$	−15.6186	−1.05062
$222$	1.77515	0.119140
$223$	−18.4488	−1.23542	−0.617712	−	0.786405i	$-0.711940\pi$
$223$	−18.4488	−1.23542	−0.617712	+	0.786405i	$0.711940\pi$
$224$	4.39574	0.293702
$225$	10.4865	0.699103
$226$	−12.9439	−0.861019
$227$	−6.24947	−0.414792	−0.207396	−	0.978257i	$-0.566499\pi$
$227$	−6.24947	−0.414792	−0.207396	+	0.978257i	$0.566499\pi$
$228$	1.25601	0.0831813
$229$	−2.46267	−0.162738	−0.0813688	−	0.996684i	$-0.525929\pi$
$229$	−2.46267	−0.162738	−0.0813688	+	0.996684i	$0.525929\pi$
$230$	−13.3216	−0.878400
$231$	2.84999	0.187515
$232$	19.3623	1.27120
$233$	−12.2214	−0.800650	−0.400325	−	0.916373i	$-0.631103\pi$
$233$	−12.2214	−0.800650	−0.400325	+	0.916373i	$0.631103\pi$
$234$	−4.15859	−0.271856
$235$	23.6772	1.54453
$236$	−10.1547	−0.661013
$237$	12.3196	0.800242
$238$	−4.34158	−0.281423
$239$	−2.12224	−0.137276	−0.0686382	−	0.997642i	$-0.521865\pi$
$239$	−2.12224	−0.137276	−0.0686382	+	0.997642i	$0.521865\pi$
$240$	6.29494	0.406337
$241$	−6.89671	−0.444256	−0.222128	−	0.975018i	$-0.571300\pi$
$241$	−6.89671	−0.444256	−0.222128	+	0.975018i	$0.571300\pi$
$242$	3.09388	0.198882
$243$	1.00000	0.0641500
$244$	−1.42373	−0.0911449
$245$	−3.93529	−0.251417
$246$	8.57879	0.546964
$247$	−5.75590	−0.366239
$248$	10.5899	0.672461
$249$	−15.2753	−0.968030
$250$	23.2141	1.46819
$251$	−2.58862	−0.163392	−0.0816962	−	0.996657i	$-0.526034\pi$
$251$	−2.58862	−0.163392	−0.0816962	+	0.996657i	$0.526034\pi$
$252$	0.844015	0.0531679
$253$	8.97316	0.564138
$254$	−1.24146	−0.0778962
$255$	15.8909	0.995129
$256$	−16.1414	−1.00884
$257$	−10.5948	−0.660884	−0.330442	−	0.943826i	$-0.607198\pi$
$257$	−10.5948	−0.660884	−0.330442	+	0.943826i	$0.607198\pi$
$258$	−0.234246	−0.0145835
$259$	1.65105	0.102591
$260$	12.8469	0.796729
$261$	6.33211	0.391948
$262$	16.8100	1.03853
$263$	−4.67767	−0.288437	−0.144219	−	0.989546i	$-0.546067\pi$
$263$	−4.67767	−0.288437	−0.144219	+	0.989546i	$0.546067\pi$
$264$	−8.71467	−0.536351
$265$	22.2764	1.36843
$266$	−1.60000	−0.0981022
$267$	15.2249	0.931751
$268$	2.95622	0.180580
$269$	−11.2727	−0.687309	−0.343655	−	0.939096i	$-0.611665\pi$
$269$	−11.2727	−0.687309	−0.343655	+	0.939096i	$0.611665\pi$
$270$	4.23110	0.257497
$271$	18.8781	1.14676	0.573381	−	0.819289i	$-0.305631\pi$
$271$	18.8781	1.14676	0.573381	+	0.819289i	$0.305631\pi$
$272$	6.45931	0.391653
$273$	−3.86785	−0.234093
$274$	−8.29327	−0.501015
$275$	−29.8865	−1.80222
$276$	2.65737	0.159955
$277$	−20.4812	−1.23059	−0.615297	−	0.788295i	$-0.710964\pi$
$277$	−20.4812	−1.23059	−0.615297	+	0.788295i	$0.710964\pi$
$278$	−15.3051	−0.917941
$279$	3.46326	0.207340
$280$	12.0333	0.719128
$281$	8.58160	0.511935	0.255968	−	0.966685i	$-0.417606\pi$
$281$	8.58160	0.511935	0.255968	+	0.966685i	$0.417606\pi$
$282$	6.46888	0.385216
$283$	11.2413	0.668228	0.334114	−	0.942533i	$-0.391563\pi$
$283$	11.2413	0.668228	0.334114	+	0.942533i	$0.391563\pi$
$284$	−13.9839	−0.829789
$285$	5.85626	0.346895
$286$	11.8519	0.700819
$287$	7.97903	0.470987
$288$	−4.39574	−0.259021
$289$	−0.694124	−0.0408308
$290$	26.7918	1.57327
$291$	3.59265	0.210605
$292$	−13.0942	−0.766283
$293$	−13.0426	−0.761955	−0.380978	−	0.924584i	$-0.624413\pi$
$293$	−13.0426	−0.761955	−0.380978	+	0.924584i	$0.624413\pi$
$294$	−1.07517	−0.0627051
$295$	−47.3471	−2.75666
$296$	−5.04856	−0.293442
$297$	−2.84999	−0.165373
$298$	−8.51707	−0.493381
$299$	−12.1779	−0.704267
$300$	−8.85080	−0.511001
$301$	−0.217870	−0.0125578
$302$	−19.7933	−1.13898
$303$	4.55392	0.261616
$304$	2.38044	0.136528
$305$	−6.63827	−0.380106
$306$	4.34158	0.248192
$307$	25.2102	1.43882	0.719410	−	0.694585i	$-0.244412\pi$
$307$	25.2102	1.43882	0.719410	+	0.694585i	$0.244412\pi$
$308$	−2.40543	−0.137062
$309$	−14.3145	−0.814324
$310$	14.6534	0.832257
$311$	−3.63566	−0.206159	−0.103080	−	0.994673i	$-0.532870\pi$
$311$	−3.63566	−0.206159	−0.103080	+	0.994673i	$0.532870\pi$
$312$	11.8271	0.669577
$313$	−24.3718	−1.37757	−0.688786	−	0.724964i	$-0.741856\pi$
$313$	−24.3718	−1.37757	−0.688786	+	0.724964i	$0.741856\pi$
$314$	4.99946	0.282136
$315$	3.93529	0.221729
$316$	−10.3979	−0.584927
$317$	−10.9978	−0.617698	−0.308849	−	0.951111i	$-0.599944\pi$
$317$	−10.9978	−0.617698	−0.308849	+	0.951111i	$0.599944\pi$
$318$	6.08616	0.341295
$319$	−18.0464	−1.01041
$320$	−31.1887	−1.74350
$321$	−5.09224	−0.284221
$322$	−3.38516	−0.188647
$323$	6.00918	0.334360
$324$	−0.844015	−0.0468897
$325$	40.5604	2.24989
$326$	3.66209	0.202824
$327$	−3.88944	−0.215086
$328$	−24.3982	−1.34717
$329$	6.01662	0.331707
$330$	−12.0586	−0.663803
$331$	−5.45983	−0.300100	−0.150050	−	0.988678i	$-0.547943\pi$
$331$	−5.45983	−0.300100	−0.150050	+	0.988678i	$0.547943\pi$
$332$	12.8925	0.707570
$333$	−1.65105	−0.0904769
$334$	6.43530	0.352124
$335$	13.7836	0.753081
$336$	1.59961	0.0872659
$337$	−29.2566	−1.59371	−0.796853	−	0.604173i	$-0.793504\pi$
$337$	−29.2566	−1.59371	−0.796853	+	0.604173i	$0.793504\pi$
$338$	−2.10765	−0.114641
$339$	12.0390	0.653869
$340$	−13.4122	−0.727377
$341$	−9.87024	−0.534504
$342$	1.60000	0.0865180
$343$	−1.00000	−0.0539949
$344$	0.666200	0.0359191
$345$	12.3902	0.667069
$346$	−8.37097	−0.450026
$347$	−8.54995	−0.458985	−0.229493	−	0.973310i	$-0.573707\pi$
$347$	−8.54995	−0.458985	−0.229493	+	0.973310i	$0.573707\pi$
$348$	−5.34439	−0.286490
$349$	−15.8925	−0.850705	−0.425353	−	0.905028i	$-0.639850\pi$
$349$	−15.8925	−0.850705	−0.425353	+	0.905028i	$0.639850\pi$
$350$	11.2748	0.602663
$351$	3.86785	0.206451
$352$	12.5278	0.667733
$353$	36.2292	1.92829	0.964143	−	0.265382i	$-0.0854981\pi$
$353$	36.2292	1.92829	0.964143	+	0.265382i	$0.0854981\pi$
$354$	−12.9358	−0.687529
$355$	−65.2010	−3.46051
$356$	−12.8501	−0.681052
$357$	4.03805	0.213716
$358$	−10.3757	−0.548375
$359$	32.7692	1.72949	0.864746	−	0.502210i	$-0.167479\pi$
$359$	32.7692	1.72949	0.864746	+	0.502210i	$0.167479\pi$
$360$	−12.0333	−0.634211
$361$	−16.7854	−0.883444
$362$	7.23671	0.380353
$363$	−2.87757	−0.151034
$364$	3.26453	0.171108
$365$	−61.0531	−3.19567
$366$	−1.81365	−0.0948010
$367$	−1.52514	−0.0796116	−0.0398058	−	0.999207i	$-0.512674\pi$
$367$	−1.52514	−0.0796116	−0.0398058	+	0.999207i	$0.512674\pi$
$368$	5.03636	0.262539
$369$	−7.97903	−0.415372
$370$	−6.98575	−0.363172
$371$	5.66066	0.293887
$372$	−2.92304	−0.151553
$373$	−17.1144	−0.886151	−0.443075	−	0.896484i	$-0.646113\pi$
$373$	−17.1144	−0.886151	−0.443075	+	0.896484i	$0.646113\pi$
$374$	−12.3735	−0.639816
$375$	−21.5912	−1.11496
$376$	−18.3976	−0.948783
$377$	24.4917	1.26139
$378$	1.07517	0.0553007
$379$	0.590979	0.0303566	0.0151783	−	0.999885i	$-0.495168\pi$
$379$	0.590979	0.0303566	0.0151783	+	0.999885i	$0.495168\pi$
$380$	−4.94277	−0.253559
$381$	1.15467	0.0591554
$382$	11.4708	0.586895
$383$	1.00000	0.0510976
$383$	1.00000	0.0510976
$384$	0.270366	0.0137970
$385$	−11.2155	−0.571597
$386$	16.3960	0.834532
$387$	0.217870	0.0110749
$388$	−3.03225	−0.153939
$389$	14.8255	0.751683	0.375841	−	0.926684i	$-0.377354\pi$
$389$	14.8255	0.751683	0.375841	+	0.926684i	$0.377354\pi$
$390$	16.3653	0.828688
$391$	12.7138	0.642964
$392$	3.05779	0.154442
$393$	−15.6348	−0.788672
$394$	13.8896	0.699746
$395$	−48.4811	−2.43935
$396$	2.40543	0.120877
$397$	13.1835	0.661660	0.330830	−	0.943690i	$-0.392671\pi$
$397$	13.1835	0.661660	0.330830	+	0.943690i	$0.392671\pi$
$398$	−9.18167	−0.460236
$399$	1.48814	0.0745001
$400$	−16.7744	−0.838719
$401$	12.2581	0.612141	0.306070	−	0.952009i	$-0.400986\pi$
$401$	12.2581	0.612141	0.306070	+	0.952009i	$0.400986\pi$
$402$	3.76585	0.187824
$403$	13.3954	0.667271
$404$	−3.84358	−0.191225
$405$	−3.93529	−0.195546
$406$	6.80808	0.337879
$407$	4.70546	0.233241
$408$	−12.3475	−0.611294
$409$	−38.7125	−1.91421	−0.957104	−	0.289744i	$-0.906430\pi$
$409$	−38.7125	−1.91421	−0.957104	+	0.289744i	$0.906430\pi$
$410$	−33.7601	−1.66729
$411$	7.71347	0.380477
$412$	12.0817	0.595221
$413$	−12.0314	−0.592027
$414$	3.38516	0.166371
$415$	60.1126	2.95081
$416$	−17.0021	−0.833595
$417$	14.2351	0.697097
$418$	−4.55997	−0.223036
$419$	−39.6387	−1.93648	−0.968240	−	0.250024i	$-0.919561\pi$
$419$	−39.6387	−1.93648	−0.968240	+	0.250024i	$0.919561\pi$
$420$	−3.32145	−0.162070
$421$	−16.6600	−0.811957	−0.405979	−	0.913883i	$-0.633069\pi$
$421$	−16.6600	−0.811957	−0.405979	+	0.913883i	$0.633069\pi$
$422$	−18.5976	−0.905318
$423$	−6.01662	−0.292538
$424$	−17.3091	−0.840605
$425$	−42.3452	−2.05405
$426$	−17.8137	−0.863075
$427$	−1.68685	−0.0816326
$428$	4.29792	0.207748
$429$	−11.0233	−0.532212
$430$	0.921828	0.0444545
$431$	−17.6284	−0.849128	−0.424564	−	0.905398i	$-0.639573\pi$
$431$	−17.6284	−0.849128	−0.424564	+	0.905398i	$0.639573\pi$
$432$	−1.59961	−0.0769613
$433$	4.98038	0.239342	0.119671	−	0.992814i	$-0.461816\pi$
$433$	4.98038	0.239342	0.119671	+	0.992814i	$0.461816\pi$
$434$	3.72358	0.178738
$435$	−24.9187	−1.19476
$436$	3.28274	0.157215
$437$	4.68539	0.224133
$438$	−16.6804	−0.797021
$439$	10.1380	0.483859	0.241930	−	0.970294i	$-0.422220\pi$
$439$	10.1380	0.483859	0.241930	+	0.970294i	$0.422220\pi$
$440$	34.2948	1.63494
$441$	1.00000	0.0476190
$442$	16.7926	0.798743
$443$	−15.8765	−0.754315	−0.377158	−	0.926149i	$-0.623099\pi$
$443$	−15.8765	−0.754315	−0.377158	+	0.926149i	$0.623099\pi$
$444$	1.39351	0.0661330
$445$	−59.9146	−2.84022
$446$	19.8356	0.939241
$447$	7.92162	0.374680
$448$	−7.92537	−0.374439
$449$	−10.2947	−0.485836	−0.242918	−	0.970047i	$-0.578105\pi$
$449$	−10.2947	−0.485836	−0.242918	+	0.970047i	$0.578105\pi$
$450$	−11.2748	−0.531499
$451$	22.7401	1.07079
$452$	−10.1611	−0.477938
$453$	18.4095	0.864953
$454$	6.71923	0.315349
$455$	15.2211	0.713578
$456$	−4.55042	−0.213093
$457$	17.6579	0.826004	0.413002	−	0.910730i	$-0.364480\pi$
$457$	17.6579	0.826004	0.413002	+	0.910730i	$0.364480\pi$
$458$	2.64778	0.123723
$459$	−4.03805	−0.188480
$460$	−10.4575	−0.487586
$461$	−0.621330	−0.0289382	−0.0144691	−	0.999895i	$-0.504606\pi$
$461$	−0.621330	−0.0289382	−0.0144691	+	0.999895i	$0.504606\pi$
$462$	−3.06421	−0.142560
$463$	36.2361	1.68404	0.842018	−	0.539449i	$-0.181368\pi$
$463$	36.2361	1.68404	0.842018	+	0.539449i	$0.181368\pi$
$464$	−10.1289	−0.470223
$465$	−13.6289	−0.632027
$466$	13.1400	0.608701
$467$	−37.0916	−1.71639	−0.858196	−	0.513322i	$-0.828415\pi$
$467$	−37.0916	−1.71639	−0.858196	+	0.513322i	$0.828415\pi$
$468$	−3.26453	−0.150903
$469$	3.50257	0.161734
$470$	−25.4569	−1.17424
$471$	−4.64994	−0.214258
$472$	36.7895	1.69338
$473$	−0.620926	−0.0285502
$474$	−13.2456	−0.608391
$475$	−15.6054	−0.716026
$476$	−3.40818	−0.156213
$477$	−5.66066	−0.259184
$478$	2.28176	0.104365
$479$	−12.7390	−0.582060	−0.291030	−	0.956714i	$-0.593998\pi$
$479$	−12.7390	−0.582060	−0.291030	+	0.956714i	$0.593998\pi$
$480$	17.2985	0.789566
$481$	−6.38601	−0.291177
$482$	7.41511	0.337749
$483$	3.14849	0.143261
$484$	2.42871	0.110396
$485$	−14.1381	−0.641980
$486$	−1.07517	−0.0487706
$487$	−34.4636	−1.56169	−0.780847	−	0.624722i	$-0.785212\pi$
$487$	−34.4636	−1.56169	−0.780847	+	0.624722i	$0.785212\pi$
$488$	5.15805	0.233494
$489$	−3.40606	−0.154028
$490$	4.23110	0.191142
$491$	0.951418	0.0429369	0.0214684	−	0.999770i	$-0.493166\pi$
$491$	0.951418	0.0429369	0.0214684	+	0.999770i	$0.493166\pi$
$492$	6.73441	0.303611
$493$	−25.5694	−1.15159
$494$	6.18856	0.278436
$495$	11.2155	0.504101
$496$	−5.53986	−0.248747
$497$	−16.5683	−0.743188
$498$	16.4235	0.735953
$499$	−4.75249	−0.212751	−0.106375	−	0.994326i	$-0.533925\pi$
$499$	−4.75249	−0.212751	−0.106375	+	0.994326i	$0.533925\pi$
$500$	18.2233	0.814969
$501$	−5.98540	−0.267408
$502$	2.78320	0.124220
$503$	−27.1031	−1.20847	−0.604233	−	0.796808i	$-0.706520\pi$
$503$	−27.1031	−1.20847	−0.604233	+	0.796808i	$0.706520\pi$
$504$	−3.05779	−0.136205
$505$	−17.9210	−0.797475
$506$	−9.64766	−0.428891
$507$	1.96030	0.0870599
$508$	−0.974556	−0.0432389
$509$	−5.48140	−0.242959	−0.121479	−	0.992594i	$-0.538764\pi$
$509$	−5.48140	−0.242959	−0.121479	+	0.992594i	$0.538764\pi$
$510$	−17.0854	−0.756555
$511$	−15.5142	−0.686310
$512$	16.8140	0.743082
$513$	−1.48814	−0.0657029
$514$	11.3912	0.502443
$515$	56.3318	2.48228
$516$	−0.183885	−0.00809509
$517$	17.1473	0.754137
$518$	−1.77515	−0.0779958
$519$	7.78574	0.341756
$520$	−46.5431	−2.04105
$521$	−0.315568	−0.0138253	−0.00691264	−	0.999976i	$-0.502200\pi$
$521$	−0.315568	−0.0138253	−0.00691264	+	0.999976i	$0.502200\pi$
$522$	−6.80808	−0.297982
$523$	10.7047	0.468085	0.234043	−	0.972226i	$-0.424804\pi$
$523$	10.7047	0.468085	0.234043	+	0.972226i	$0.424804\pi$
$524$	13.1960	0.576470
$525$	−10.4865	−0.457670
$526$	5.02928	0.219287
$527$	−13.9848	−0.609189
$528$	4.55887	0.198399
$529$	−13.0870	−0.569000
$530$	−23.9508	−1.04036
$531$	12.0314	0.522118
$532$	−1.25601	−0.0544549
$533$	−30.8617	−1.33677
$534$	−16.3694	−0.708371
$535$	20.0395	0.866381
$536$	−10.7101	−0.462607
$537$	9.65035	0.416444
$538$	12.1201	0.522533
$539$	−2.84999	−0.122758
$540$	3.32145	0.142932
$541$	−10.4258	−0.448241	−0.224120	−	0.974561i	$-0.571951\pi$
$541$	−10.4258	−0.448241	−0.224120	+	0.974561i	$0.571951\pi$
$542$	−20.2971	−0.871835
$543$	−6.73077	−0.288845
$544$	17.7502	0.761034
$545$	15.3061	0.655640
$546$	4.15859	0.177971
$547$	39.3496	1.68247	0.841233	−	0.540673i	$-0.181830\pi$
$547$	39.3496	1.68247	0.841233	+	0.540673i	$0.181830\pi$
$548$	−6.51028	−0.278105
$549$	1.68685	0.0719931
$550$	32.1330	1.37016
$551$	−9.42305	−0.401436
$552$	−9.62744	−0.409771
$553$	−12.3196	−0.523881
$554$	22.0207	0.935570
$555$	6.49736	0.275798
$556$	−12.0146	−0.509535
$557$	−2.20654	−0.0934943	−0.0467471	−	0.998907i	$-0.514886\pi$
$557$	−2.20654	−0.0934943	−0.0467471	+	0.998907i	$0.514886\pi$
$558$	−3.72358	−0.157632
$559$	0.842688	0.0356419
$560$	−6.29494	−0.266010
$561$	11.5084	0.485885
$562$	−9.22666	−0.389203
$563$	−27.3963	−1.15462	−0.577309	−	0.816526i	$-0.695897\pi$
$563$	−27.3963	−1.15462	−0.577309	+	0.816526i	$0.695897\pi$
$564$	5.07812	0.213827
$565$	−47.3770	−1.99317
$566$	−12.0863	−0.508026
$567$	−1.00000	−0.0419961
$568$	50.6623	2.12574
$569$	−37.2875	−1.56317	−0.781587	−	0.623797i	$-0.785589\pi$
$569$	−37.2875	−1.56317	−0.781587	+	0.623797i	$0.785589\pi$
$570$	−6.29646	−0.263730
$571$	11.0818	0.463757	0.231879	−	0.972745i	$-0.425513\pi$
$571$	11.0818	0.463757	0.231879	+	0.972745i	$0.425513\pi$
$572$	9.30385	0.389014
$573$	−10.6688	−0.445696
$574$	−8.57879	−0.358072
$575$	−33.0168	−1.37690
$576$	7.92537	0.330224
$577$	10.7652	0.448163	0.224082	−	0.974570i	$-0.428062\pi$
$577$	10.7652	0.448163	0.224082	+	0.974570i	$0.428062\pi$
$578$	0.746300	0.0310420
$579$	−15.2497	−0.633755
$580$	21.0318	0.873296
$581$	15.2753	0.633724
$582$	−3.86270	−0.160114
$583$	16.1328	0.668153
$584$	47.4393	1.96305
$585$	−15.2211	−0.629317
$586$	14.0230	0.579283
$587$	8.46144	0.349241	0.174620	−	0.984636i	$-0.444130\pi$
$587$	8.46144	0.349241	0.174620	+	0.984636i	$0.444130\pi$
$588$	−0.844015	−0.0348066
$589$	−5.15381	−0.212359
$590$	50.9061	2.09577
$591$	−12.9185	−0.531397
$592$	2.64103	0.108546
$593$	−35.8749	−1.47321	−0.736604	−	0.676325i	$-0.763572\pi$
$593$	−35.8749	−1.47321	−0.736604	+	0.676325i	$0.763572\pi$
$594$	3.06421	0.125726
$595$	−15.8909	−0.651465
$596$	−6.68596	−0.273868
$597$	8.53976	0.349509
$598$	13.0933	0.535425
$599$	25.4008	1.03785	0.518924	−	0.854821i	$-0.326333\pi$
$599$	25.4008	1.03785	0.518924	+	0.854821i	$0.326333\pi$
$600$	32.0657	1.30908
$601$	31.8151	1.29776	0.648882	−	0.760889i	$-0.275237\pi$
$601$	31.8151	1.29776	0.648882	+	0.760889i	$0.275237\pi$
$602$	0.234246	0.00954717
$603$	−3.50257	−0.142636
$604$	−15.5379	−0.632227
$605$	11.3241	0.460390
$606$	−4.89623	−0.198896
$607$	32.7109	1.32769	0.663847	−	0.747868i	$-0.268923\pi$
$607$	32.7109	1.32769	0.663847	+	0.747868i	$0.268923\pi$
$608$	6.54146	0.265291
$609$	−6.33211	−0.256590
$610$	7.13725	0.288979
$611$	−23.2714	−0.941461
$612$	3.40818	0.137767
$613$	−2.22363	−0.0898116	−0.0449058	−	0.998991i	$-0.514299\pi$
$613$	−2.22363	−0.0898116	−0.0449058	+	0.998991i	$0.514299\pi$
$614$	−27.1052	−1.09388
$615$	31.3998	1.26616
$616$	8.71467	0.351124
$617$	9.17304	0.369293	0.184646	−	0.982805i	$-0.440886\pi$
$617$	9.17304	0.369293	0.184646	+	0.982805i	$0.440886\pi$
$618$	15.3905	0.619097
$619$	15.0488	0.604861	0.302431	−	0.953171i	$-0.402202\pi$
$619$	15.0488	0.604861	0.302431	+	0.953171i	$0.402202\pi$
$620$	11.5030	0.461973
$621$	−3.14849	−0.126345
$622$	3.90894	0.156734
$623$	−15.2249	−0.609974
$624$	−6.18706	−0.247681
$625$	32.5349	1.30140
$626$	26.2037	1.04731
$627$	4.24117	0.169376
$628$	3.92461	0.156609
$629$	6.66702	0.265831
$630$	−4.23110	−0.168571
$631$	−22.7097	−0.904060	−0.452030	−	0.892003i	$-0.649300\pi$
$631$	−22.7097	−0.904060	−0.452030	+	0.892003i	$0.649300\pi$
$632$	37.6707	1.49846
$633$	17.2974	0.687510
$634$	11.8245	0.469610
$635$	−4.54396	−0.180321
$636$	4.77768	0.189447
$637$	3.86785	0.153250
$638$	19.4029	0.768170
$639$	16.5683	0.655430
$640$	−1.06397	−0.0420571
$641$	−1.41037	−0.0557063	−0.0278532	−	0.999612i	$-0.508867\pi$
$641$	−1.41037	−0.0557063	−0.0278532	+	0.999612i	$0.508867\pi$
$642$	5.47501	0.216081
$643$	4.49295	0.177184	0.0885922	−	0.996068i	$-0.471763\pi$
$643$	4.49295	0.177184	0.0885922	+	0.996068i	$0.471763\pi$
$644$	−2.65737	−0.104715
$645$	−0.857381	−0.0337593
$646$	−6.46088	−0.254200
$647$	−41.4410	−1.62921	−0.814606	−	0.580014i	$-0.803047\pi$
$647$	−41.4410	−1.62921	−0.814606	+	0.580014i	$0.803047\pi$
$648$	3.05779	0.120121
$649$	−34.2893	−1.34597
$650$	−43.6093	−1.71050
$651$	−3.46326	−0.135736
$652$	2.87477	0.112585
$653$	6.28913	0.246113	0.123056	−	0.992400i	$-0.460730\pi$
$653$	6.28913	0.246113	0.123056	+	0.992400i	$0.460730\pi$
$654$	4.18180	0.163521
$655$	61.5276	2.40408
$656$	12.7633	0.498325
$657$	15.5142	0.605268
$658$	−6.46888	−0.252183
$659$	21.7819	0.848501	0.424251	−	0.905545i	$-0.360538\pi$
$659$	21.7819	0.848501	0.424251	+	0.905545i	$0.360538\pi$
$660$	−9.46608	−0.368467
$661$	−8.03922	−0.312689	−0.156345	−	0.987703i	$-0.549971\pi$
$661$	−8.03922	−0.312689	−0.156345	+	0.987703i	$0.549971\pi$
$662$	5.87024	0.228153
$663$	−15.6186	−0.606576
$664$	−46.7086	−1.81264
$665$	−5.85626	−0.227096
$666$	1.77515	0.0687858
$667$	−19.9366	−0.771948
$668$	5.05176	0.195458
$669$	−18.4488	−0.713272
$670$	−14.8197	−0.572536
$671$	−4.80751	−0.185592
$672$	4.39574	0.169569
$673$	−39.9689	−1.54069	−0.770345	−	0.637627i	$-0.779916\pi$
$673$	−39.9689	−1.54069	−0.770345	+	0.637627i	$0.779916\pi$
$674$	31.4557	1.21163
$675$	10.4865	0.403627
$676$	−1.65452	−0.0636354
$677$	−16.4532	−0.632350	−0.316175	−	0.948701i	$-0.602399\pi$
$677$	−16.4532	−0.632350	−0.316175	+	0.948701i	$0.602399\pi$
$678$	−12.9439	−0.497109
$679$	−3.59265	−0.137873
$680$	48.5912	1.86339
$681$	−6.24947	−0.239480
$682$	10.6122	0.406361
$683$	9.14589	0.349958	0.174979	−	0.984572i	$-0.444014\pi$
$683$	9.14589	0.349958	0.174979	+	0.984572i	$0.444014\pi$
$684$	1.25601	0.0480247
$685$	−30.3548	−1.15980
$686$	1.07517	0.0410501
$687$	−2.46267	−0.0939565
$688$	−0.348507	−0.0132867
$689$	−21.8946	−0.834118
$690$	−13.3216	−0.507144
$691$	−10.1755	−0.387095	−0.193547	−	0.981091i	$-0.561999\pi$
$691$	−10.1755	−0.387095	−0.193547	+	0.981091i	$0.561999\pi$
$692$	−6.57127	−0.249802
$693$	2.84999	0.108262
$694$	9.19263	0.348947
$695$	−56.0194	−2.12494
$696$	19.3623	0.733925
$697$	32.2197	1.22041
$698$	17.0871	0.646756
$699$	−12.2214	−0.462256
$700$	8.85080	0.334529
$701$	15.1449	0.572014	0.286007	−	0.958228i	$-0.407672\pi$
$701$	15.1449	0.572014	0.286007	+	0.958228i	$0.407672\pi$
$702$	−4.15859	−0.156956
$703$	2.45699	0.0926670
$704$	−22.5872	−0.851288
$705$	23.6772	0.891734
$706$	−38.9525	−1.46600
$707$	−4.55392	−0.171268
$708$	−10.1547	−0.381636
$709$	3.41590	0.128287	0.0641435	−	0.997941i	$-0.479568\pi$
$709$	3.41590	0.128287	0.0641435	+	0.997941i	$0.479568\pi$
$710$	70.1020	2.63088
$711$	12.3196	0.462020
$712$	46.5547	1.74471
$713$	−10.9040	−0.408360
$714$	−4.34158	−0.162480
$715$	43.3801	1.62232
$716$	−8.14504	−0.304394
$717$	−2.12224	−0.0792565
$718$	−35.2324	−1.31486
$719$	−29.7267	−1.10862	−0.554310	−	0.832310i	$-0.687018\pi$
$719$	−29.7267	−1.10862	−0.554310	+	0.832310i	$0.687018\pi$
$720$	6.29494	0.234599
$721$	14.3145	0.533101
$722$	18.0472	0.671646
$723$	−6.89671	−0.256491
$724$	5.68087	0.211128
$725$	66.4020	2.46611
$726$	3.09388	0.114824
$727$	21.3869	0.793197	0.396599	−	0.917992i	$-0.370190\pi$
$727$	21.3869	0.793197	0.396599	+	0.917992i	$0.370190\pi$
$728$	−11.8271	−0.438341
$729$	1.00000	0.0370370
$730$	65.6424	2.42953
$731$	−0.879769	−0.0325394
$732$	−1.42373	−0.0526225
$733$	−2.94945	−0.108940	−0.0544702	−	0.998515i	$-0.517347\pi$
$733$	−2.94945	−0.108940	−0.0544702	+	0.998515i	$0.517347\pi$
$734$	1.63978	0.0605254
$735$	−3.93529	−0.145156
$736$	13.8399	0.510147
$737$	9.98228	0.367702
$738$	8.57879	0.315790
$739$	28.6940	1.05553	0.527763	−	0.849392i	$-0.323031\pi$
$739$	28.6940	1.05553	0.527763	+	0.849392i	$0.323031\pi$
$740$	−5.48387	−0.201591
$741$	−5.75590	−0.211448
$742$	−6.08616	−0.223430
$743$	38.3699	1.40766	0.703828	−	0.710371i	$-0.251473\pi$
$743$	38.3699	1.40766	0.703828	+	0.710371i	$0.251473\pi$
$744$	10.5899	0.388246
$745$	−31.1739	−1.14212
$746$	18.4009	0.673703
$747$	−15.2753	−0.558892
$748$	−9.71326	−0.355152
$749$	5.09224	0.186066
$750$	23.2141	0.847660
$751$	−4.68787	−0.171063	−0.0855313	−	0.996335i	$-0.527259\pi$
$751$	−4.68787	−0.171063	−0.0855313	+	0.996335i	$0.527259\pi$
$752$	9.62425	0.350960
$753$	−2.58862	−0.0943347
$754$	−26.3327	−0.958979
$755$	−72.4468	−2.63661
$756$	0.844015	0.0306965
$757$	48.0956	1.74806	0.874032	−	0.485868i	$-0.161496\pi$
$757$	48.0956	1.74806	0.874032	+	0.485868i	$0.161496\pi$
$758$	−0.635402	−0.0230788
$759$	8.97316	0.325705
$760$	17.9072	0.649564
$761$	−49.5743	−1.79707	−0.898533	−	0.438906i	$-0.855366\pi$
$761$	−49.5743	−1.79707	−0.898533	+	0.438906i	$0.855366\pi$
$762$	−1.24146	−0.0449734
$763$	3.88944	0.140807
$764$	9.00463	0.325776
$765$	15.8909	0.574538
$766$	−1.07517	−0.0388474
$767$	46.5357	1.68031
$768$	−16.1414	−0.582454
$769$	28.8817	1.04150	0.520751	−	0.853709i	$-0.325652\pi$
$769$	28.8817	1.04150	0.520751	+	0.853709i	$0.325652\pi$
$770$	12.0586	0.434561
$771$	−10.5948	−0.381562
$772$	12.8709	0.463235
$773$	−33.2692	−1.19661	−0.598306	−	0.801268i	$-0.704159\pi$
$773$	−33.2692	−1.19661	−0.598306	+	0.801268i	$0.704159\pi$
$774$	−0.234246	−0.00841981
$775$	36.3176	1.30457
$776$	10.9856	0.394359
$777$	1.65105	0.0592310
$778$	−15.9399	−0.571473
$779$	11.8739	0.425426
$780$	12.8469	0.459992
$781$	−47.2193	−1.68964
$782$	−13.6694	−0.488818
$783$	6.33211	0.226291
$784$	−1.59961	−0.0571289
$785$	18.2989	0.653115
$786$	16.8100	0.599594
$787$	−44.4220	−1.58347	−0.791737	−	0.610862i	$-0.790823\pi$
$787$	−44.4220	−1.58347	−0.791737	+	0.610862i	$0.790823\pi$
$788$	10.9034	0.388418
$789$	−4.67767	−0.166529
$790$	52.1254	1.85454
$791$	−12.0390	−0.428058
$792$	−8.71467	−0.309662
$793$	6.52450	0.231692
$794$	−14.1745	−0.503033
$795$	22.2764	0.790061
$796$	−7.20768	−0.255469
$797$	21.1653	0.749712	0.374856	−	0.927083i	$-0.377692\pi$
$797$	21.1653	0.749712	0.374856	+	0.927083i	$0.377692\pi$
$798$	−1.60000	−0.0566393
$799$	24.2954	0.859511
$800$	−46.0961	−1.62974
$801$	15.2249	0.537946
$802$	−13.1795	−0.465385
$803$	−44.2154	−1.56033
$804$	2.95622	0.104258
$805$	−12.3902	−0.436699
$806$	−14.4023	−0.507299
$807$	−11.2727	−0.396818
$808$	13.9249	0.489878
$809$	20.2337	0.711380	0.355690	−	0.934604i	$-0.384246\pi$
$809$	20.2337	0.711380	0.355690	+	0.934604i	$0.384246\pi$
$810$	4.23110	0.148666
$811$	20.7131	0.727335	0.363668	−	0.931529i	$-0.381524\pi$
$811$	20.7131	0.727335	0.363668	+	0.931529i	$0.381524\pi$
$812$	5.34439	0.187551
$813$	18.8781	0.662083
$814$	−5.05916	−0.177324
$815$	13.4039	0.469517
$816$	6.45931	0.226121
$817$	−0.324220	−0.0113430
$818$	41.6224	1.45529
$819$	−3.86785	−0.135154
$820$	−26.5019	−0.925487
$821$	13.1807	0.460011	0.230005	−	0.973189i	$-0.426126\pi$
$821$	13.1807	0.460011	0.230005	+	0.973189i	$0.426126\pi$
$822$	−8.29327	−0.289261
$823$	−43.8707	−1.52924	−0.764618	−	0.644484i	$-0.777072\pi$
$823$	−43.8707	−1.52924	−0.764618	+	0.644484i	$0.777072\pi$
$824$	−43.7708	−1.52483
$825$	−29.8865	−1.04051
$826$	12.9358	0.450093
$827$	−1.81427	−0.0630884	−0.0315442	−	0.999502i	$-0.510042\pi$
$827$	−1.81427	−0.0630884	−0.0315442	+	0.999502i	$0.510042\pi$
$828$	2.65737	0.0923501
$829$	−13.6897	−0.475462	−0.237731	−	0.971331i	$-0.576404\pi$
$829$	−13.6897	−0.475462	−0.237731	+	0.971331i	$0.576404\pi$
$830$	−64.6312	−2.24338
$831$	−20.4812	−0.710484
$832$	30.6542	1.06274
$833$	−4.03805	−0.139910
$834$	−15.3051	−0.529974
$835$	23.5543	0.815130
$836$	−3.57961	−0.123803
$837$	3.46326	0.119708
$838$	42.6183	1.47222
$839$	8.21528	0.283623	0.141811	−	0.989894i	$-0.454707\pi$
$839$	8.21528	0.283623	0.141811	+	0.989894i	$0.454707\pi$
$840$	12.0333	0.415189
$841$	11.0956	0.382608
$842$	17.9123	0.617297
$843$	8.58160	0.295566
$844$	−14.5993	−0.502527
$845$	−7.71435	−0.265382
$846$	6.46888	0.222405
$847$	2.87757	0.0988746
$848$	9.05485	0.310945
$849$	11.2413	0.385802
$850$	45.5282	1.56161
$851$	5.19831	0.178196
$852$	−13.9839	−0.479079
$853$	25.3475	0.867883	0.433942	−	0.900941i	$-0.357122\pi$
$853$	25.3475	0.867883	0.433942	+	0.900941i	$0.357122\pi$
$854$	1.81365	0.0620618
$855$	5.85626	0.200280
$856$	−15.5710	−0.532206
$857$	32.1553	1.09840	0.549202	−	0.835689i	$-0.314932\pi$
$857$	32.1553	1.09840	0.549202	+	0.835689i	$0.314932\pi$
$858$	11.8519	0.404618
$859$	−26.3611	−0.899430	−0.449715	−	0.893172i	$-0.648474\pi$
$859$	−26.3611	−0.899430	−0.449715	+	0.893172i	$0.648474\pi$
$860$	0.723642	0.0246760
$861$	7.97903	0.271925
$862$	18.9534	0.645557
$863$	51.7589	1.76189	0.880946	−	0.473216i	$-0.156907\pi$
$863$	51.7589	1.76189	0.880946	+	0.473216i	$0.156907\pi$
$864$	−4.39574	−0.149546
$865$	−30.6392	−1.04176
$866$	−5.35475	−0.181962
$867$	−0.694124	−0.0235737
$868$	2.92304	0.0992145
$869$	−35.1106	−1.19105
$870$	26.7918	0.908327
$871$	−13.5474	−0.459037
$872$	−11.8931	−0.402751
$873$	3.59265	0.121593
$874$	−5.03758	−0.170399
$875$	21.5912	0.729915
$876$	−13.0942	−0.442414
$877$	−19.0175	−0.642176	−0.321088	−	0.947049i	$-0.604048\pi$
$877$	−19.0175	−0.642176	−0.321088	+	0.947049i	$0.604048\pi$
$878$	−10.9000	−0.367858
$879$	−13.0426	−0.439915
$880$	−17.9405	−0.604774
$881$	−24.2406	−0.816687	−0.408343	−	0.912828i	$-0.633893\pi$
$881$	−24.2406	−0.816687	−0.408343	+	0.912828i	$0.633893\pi$
$882$	−1.07517	−0.0362028
$883$	41.5672	1.39885	0.699424	−	0.714707i	$-0.253440\pi$
$883$	41.5672	1.39885	0.699424	+	0.714707i	$0.253440\pi$
$884$	13.1823	0.443370
$885$	−47.3471	−1.59156
$886$	17.0699	0.573474
$887$	−49.4970	−1.66195	−0.830973	−	0.556313i	$-0.812216\pi$
$887$	−49.4970	−1.66195	−0.830973	+	0.556313i	$0.812216\pi$
$888$	−5.04856	−0.169419
$889$	−1.15467	−0.0387263
$890$	64.4182	2.15930
$891$	−2.84999	−0.0954782
$892$	15.5711	0.521358
$893$	8.95357	0.299620
$894$	−8.51707	−0.284853
$895$	−37.9770	−1.26943
$896$	−0.270366	−0.00903228
$897$	−12.1779	−0.406609
$898$	11.0685	0.369361
$899$	21.9297	0.731398
$900$	−8.85080	−0.295027
$901$	22.8580	0.761512
$902$	−24.4494	−0.814077
$903$	−0.217870	−0.00725025
$904$	36.8128	1.22437
$905$	26.4876	0.880476
$906$	−19.7933	−0.657588
$907$	−40.0729	−1.33060	−0.665300	−	0.746577i	$-0.731696\pi$
$907$	−40.0729	−1.33060	−0.665300	+	0.746577i	$0.731696\pi$
$908$	5.27464	0.175045
$909$	4.55392	0.151044
$910$	−16.3653	−0.542504
$911$	5.01182	0.166049	0.0830246	−	0.996548i	$-0.473542\pi$
$911$	5.01182	0.166049	0.0830246	+	0.996548i	$0.473542\pi$
$912$	2.38044	0.0788243
$913$	43.5343	1.44077
$914$	−18.9852	−0.627976
$915$	−6.63827	−0.219454
$916$	2.07853	0.0686764
$917$	15.6348	0.516307
$918$	4.34158	0.143294
$919$	−33.2160	−1.09569	−0.547847	−	0.836579i	$-0.684552\pi$
$919$	−33.2160	−1.09569	−0.547847	+	0.836579i	$0.684552\pi$
$920$	37.8868	1.24909
$921$	25.2102	0.830703
$922$	0.668034	0.0220005
$923$	64.0836	2.10934
$924$	−2.40543	−0.0791328
$925$	−17.3138	−0.569274
$926$	−38.9599	−1.28030
$927$	−14.3145	−0.470150
$928$	−27.8343	−0.913705
$929$	35.4090	1.16173	0.580865	−	0.814000i	$-0.302714\pi$
$929$	35.4090	1.16173	0.580865	+	0.814000i	$0.302714\pi$
$930$	14.6534	0.480504
$931$	−1.48814	−0.0487718
$932$	10.3150	0.337880
$933$	−3.63566	−0.119026
$934$	39.8796	1.30490
$935$	−45.2889	−1.48111
$936$	11.8271	0.386581
$937$	−34.0154	−1.11123	−0.555617	−	0.831438i	$-0.687518\pi$
$937$	−34.0154	−1.11123	−0.555617	+	0.831438i	$0.687518\pi$
$938$	−3.76585	−0.122959
$939$	−24.3718	−0.795342
$940$	−19.9839	−0.651803
$941$	−10.7827	−0.351505	−0.175752	−	0.984434i	$-0.556236\pi$
$941$	−10.7827	−0.351505	−0.175752	+	0.984434i	$0.556236\pi$
$942$	4.99946	0.162891
$943$	25.1219	0.818082
$944$	−19.2456	−0.626390
$945$	3.93529	0.128015
$946$	0.667599	0.0217055
$947$	1.24728	0.0405312	0.0202656	−	0.999795i	$-0.493549\pi$
$947$	1.24728	0.0405312	0.0202656	+	0.999795i	$0.493549\pi$
$948$	−10.3979	−0.337708
$949$	60.0068	1.94790
$950$	16.7785	0.544365
$951$	−10.9978	−0.356628
$952$	12.3475	0.400186
$953$	−33.8151	−1.09538	−0.547689	−	0.836682i	$-0.684492\pi$
$953$	−33.8151	−1.09538	−0.547689	+	0.836682i	$0.684492\pi$
$954$	6.08616	0.197047
$955$	41.9849	1.35860
$956$	1.79120	0.0579316
$957$	−18.0464	−0.583358
$958$	13.6966	0.442516
$959$	−7.71347	−0.249081
$960$	−31.1887	−1.00661
$961$	−19.0058	−0.613092
$962$	6.86603	0.221370
$963$	−5.09224	−0.164095
$964$	5.82092	0.187479
$965$	60.0120	1.93185
$966$	−3.38516	−0.108916
$967$	−16.4928	−0.530372	−0.265186	−	0.964197i	$-0.585433\pi$
$967$	−16.4928	−0.530372	−0.265186	+	0.964197i	$0.585433\pi$
$968$	−8.79903	−0.282811
$969$	6.00918	0.193043
$970$	15.2009	0.488071
$971$	27.7160	0.889449	0.444724	−	0.895667i	$-0.353302\pi$
$971$	27.7160	0.889449	0.444724	+	0.895667i	$0.353302\pi$
$972$	−0.844015	−0.0270718
$973$	−14.2351	−0.456357
$974$	37.0541	1.18729
$975$	40.5604	1.29897
$976$	−2.69831	−0.0863707
$977$	26.6664	0.853133	0.426566	−	0.904456i	$-0.359723\pi$
$977$	26.6664	0.853133	0.426566	+	0.904456i	$0.359723\pi$
$978$	3.66209	0.117101
$979$	−43.3909	−1.38678
$980$	3.32145	0.106100
$981$	−3.88944	−0.124180
$982$	−1.02293	−0.0326431
$983$	−47.1423	−1.50361	−0.751803	−	0.659388i	$-0.770815\pi$
$983$	−47.1423	−1.50361	−0.751803	+	0.659388i	$0.770815\pi$
$984$	−24.3982	−0.777786
$985$	50.8382	1.61984
$986$	27.4914	0.875504
$987$	6.01662	0.191511
$988$	4.85806	0.154556
$989$	−0.685961	−0.0218123
$990$	−12.0586	−0.383247
$991$	39.2684	1.24740	0.623701	−	0.781663i	$-0.285628\pi$
$991$	39.2684	1.24740	0.623701	+	0.781663i	$0.285628\pi$
$992$	−15.2236	−0.483349
$993$	−5.45983	−0.173263
$994$	17.8137	0.565015
$995$	−33.6065	−1.06540
$996$	12.8925	0.408516
$997$	55.5622	1.75967	0.879837	−	0.475276i	$-0.157652\pi$
$997$	55.5622	1.75967	0.879837	+	0.475276i	$0.157652\pi$
$998$	5.10973	0.161746
$999$	−1.65105	−0.0522368

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.q.1.17	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.q.1.17	✓	44	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:	\( N \)	\(=\)	\( 8043 = 3 \cdot 7 \cdot 383 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8043.a (trivial)

\(f(q)\)	\(=\)	\(q-1.07517 q^{2} +1.00000 q^{3} -0.844015 q^{4} -3.93529 q^{5} -1.07517 q^{6} -1.00000 q^{7} +3.05779 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.07517 q^{2} +1.00000 q^{3} -0.844015 q^{4} -3.93529 q^{5} -1.07517 q^{6} -1.00000 q^{7} +3.05779 q^{8} +1.00000 q^{9} +4.23110 q^{10} -2.84999 q^{11} -0.844015 q^{12} +3.86785 q^{13} +1.07517 q^{14} -3.93529 q^{15} -1.59961 q^{16} -4.03805 q^{17} -1.07517 q^{18} -1.48814 q^{19} +3.32145 q^{20} -1.00000 q^{21} +3.06421 q^{22} -3.14849 q^{23} +3.05779 q^{24} +10.4865 q^{25} -4.15859 q^{26} +1.00000 q^{27} +0.844015 q^{28} +6.33211 q^{29} +4.23110 q^{30} +3.46326 q^{31} -4.39574 q^{32} -2.84999 q^{33} +4.34158 q^{34} +3.93529 q^{35} -0.844015 q^{36} -1.65105 q^{37} +1.60000 q^{38} +3.86785 q^{39} -12.0333 q^{40} -7.97903 q^{41} +1.07517 q^{42} +0.217870 q^{43} +2.40543 q^{44} -3.93529 q^{45} +3.38516 q^{46} -6.01662 q^{47} -1.59961 q^{48} +1.00000 q^{49} -11.2748 q^{50} -4.03805 q^{51} -3.26453 q^{52} -5.66066 q^{53} -1.07517 q^{54} +11.2155 q^{55} -3.05779 q^{56} -1.48814 q^{57} -6.80808 q^{58} +12.0314 q^{59} +3.32145 q^{60} +1.68685 q^{61} -3.72358 q^{62} -1.00000 q^{63} +7.92537 q^{64} -15.2211 q^{65} +3.06421 q^{66} -3.50257 q^{67} +3.40818 q^{68} -3.14849 q^{69} -4.23110 q^{70} +16.5683 q^{71} +3.05779 q^{72} +15.5142 q^{73} +1.77515 q^{74} +10.4865 q^{75} +1.25601 q^{76} +2.84999 q^{77} -4.15859 q^{78} +12.3196 q^{79} +6.29494 q^{80} +1.00000 q^{81} +8.57879 q^{82} -15.2753 q^{83} +0.844015 q^{84} +15.8909 q^{85} -0.234246 q^{86} +6.33211 q^{87} -8.71467 q^{88} +15.2249 q^{89} +4.23110 q^{90} -3.86785 q^{91} +2.65737 q^{92} +3.46326 q^{93} +6.46888 q^{94} +5.85626 q^{95} -4.39574 q^{96} +3.59265 q^{97} -1.07517 q^{98} -2.84999 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 4 q^{2} + 44 q^{3} + 44 q^{4} - 16 q^{5} - 4 q^{6} - 44 q^{7} - 15 q^{8} + 44 q^{9}+O(q^{10}) \) 44 * q - 4 * q^2 + 44 * q^3 + 44 * q^4 - 16 * q^5 - 4 * q^6 - 44 * q^7 - 15 * q^8 + 44 * q^9	\( 44 q - 4 q^{2} + 44 q^{3} + 44 q^{4} - 16 q^{5} - 4 q^{6} - 44 q^{7} - 15 q^{8} + 44 q^{9} - 16 q^{10} - 2 q^{11} + 44 q^{12} - 34 q^{13} + 4 q^{14} - 16 q^{15} + 24 q^{16} - 4 q^{17} - 4 q^{18} - 22 q^{19} - 39 q^{20} - 44 q^{21} - 23 q^{22} - 56 q^{23} - 15 q^{24} + 32 q^{25} - 17 q^{26} + 44 q^{27} - 44 q^{28} - 33 q^{29} - 16 q^{30} - 32 q^{31} - 34 q^{32} - 2 q^{33} - 25 q^{34} + 16 q^{35} + 44 q^{36} - 47 q^{37} - 40 q^{38} - 34 q^{39} - 50 q^{40} + 2 q^{41} + 4 q^{42} - 12 q^{43} - 22 q^{44} - 16 q^{45} + 8 q^{46} - 27 q^{47} + 24 q^{48} + 44 q^{49} - 21 q^{50} - 4 q^{51} - 82 q^{52} - 114 q^{53} - 4 q^{54} - 29 q^{55} + 15 q^{56} - 22 q^{57} - 26 q^{58} - 40 q^{59} - 39 q^{60} - 47 q^{61} - 37 q^{62} - 44 q^{63} - 5 q^{64} - 20 q^{65} - 23 q^{66} - 14 q^{67} - 72 q^{68} - 56 q^{69} + 16 q^{70} - 65 q^{71} - 15 q^{72} - 21 q^{73} - 26 q^{74} + 32 q^{75} - 15 q^{76} + 2 q^{77} - 17 q^{78} + 6 q^{79} - 77 q^{80} + 44 q^{81} - 51 q^{82} - 30 q^{83} - 44 q^{84} - 26 q^{85} - 65 q^{86} - 33 q^{87} - 84 q^{88} - 32 q^{89} - 16 q^{90} + 34 q^{91} - 140 q^{92} - 32 q^{93} - 35 q^{94} - 50 q^{95} - 34 q^{96} - 83 q^{97} - 4 q^{98} - 2 q^{99}+O(q^{100}) \) 44 * q - 4 * q^2 + 44 * q^3 + 44 * q^4 - 16 * q^5 - 4 * q^6 - 44 * q^7 - 15 * q^8 + 44 * q^9 - 16 * q^10 - 2 * q^11 + 44 * q^12 - 34 * q^13 + 4 * q^14 - 16 * q^15 + 24 * q^16 - 4 * q^17 - 4 * q^18 - 22 * q^19 - 39 * q^20 - 44 * q^21 - 23 * q^22 - 56 * q^23 - 15 * q^24 + 32 * q^25 - 17 * q^26 + 44 * q^27 - 44 * q^28 - 33 * q^29 - 16 * q^30 - 32 * q^31 - 34 * q^32 - 2 * q^33 - 25 * q^34 + 16 * q^35 + 44 * q^36 - 47 * q^37 - 40 * q^38 - 34 * q^39 - 50 * q^40 + 2 * q^41 + 4 * q^42 - 12 * q^43 - 22 * q^44 - 16 * q^45 + 8 * q^46 - 27 * q^47 + 24 * q^48 + 44 * q^49 - 21 * q^50 - 4 * q^51 - 82 * q^52 - 114 * q^53 - 4 * q^54 - 29 * q^55 + 15 * q^56 - 22 * q^57 - 26 * q^58 - 40 * q^59 - 39 * q^60 - 47 * q^61 - 37 * q^62 - 44 * q^63 - 5 * q^64 - 20 * q^65 - 23 * q^66 - 14 * q^67 - 72 * q^68 - 56 * q^69 + 16 * q^70 - 65 * q^71 - 15 * q^72 - 21 * q^73 - 26 * q^74 + 32 * q^75 - 15 * q^76 + 2 * q^77 - 17 * q^78 + 6 * q^79 - 77 * q^80 + 44 * q^81 - 51 * q^82 - 30 * q^83 - 44 * q^84 - 26 * q^85 - 65 * q^86 - 33 * q^87 - 84 * q^88 - 32 * q^89 - 16 * q^90 + 34 * q^91 - 140 * q^92 - 32 * q^93 - 35 * q^94 - 50 * q^95 - 34 * q^96 - 83 * q^97 - 4 * q^98 - 2 * q^99

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