LMFDB - Embedded newform 8031.2.a.b.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8031,2,Mod(1,8031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8031, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("8031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8031 = 3 \cdot 2677 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8031.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:	$64.1278578633$
Analytic rank:	$1$
Dimension:	$102$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	8031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.50066 q^{2} -1.00000 q^{3} +4.25331 q^{4} -3.45059 q^{5} +2.50066 q^{6} -2.37826 q^{7} -5.63477 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.50066 q^{2} -1.00000 q^{3} +4.25331 q^{4} -3.45059 q^{5} +2.50066 q^{6} -2.37826 q^{7} -5.63477 q^{8} +1.00000 q^{9} +8.62875 q^{10} -4.98870 q^{11} -4.25331 q^{12} +0.359505 q^{13} +5.94722 q^{14} +3.45059 q^{15} +5.58404 q^{16} -3.23031 q^{17} -2.50066 q^{18} -2.20865 q^{19} -14.6764 q^{20} +2.37826 q^{21} +12.4751 q^{22} -4.09216 q^{23} +5.63477 q^{24} +6.90654 q^{25} -0.899001 q^{26} -1.00000 q^{27} -10.1155 q^{28} -4.85175 q^{29} -8.62875 q^{30} +2.61573 q^{31} -2.69425 q^{32} +4.98870 q^{33} +8.07791 q^{34} +8.20639 q^{35} +4.25331 q^{36} +3.67502 q^{37} +5.52308 q^{38} -0.359505 q^{39} +19.4433 q^{40} +0.698749 q^{41} -5.94722 q^{42} -11.5616 q^{43} -21.2185 q^{44} -3.45059 q^{45} +10.2331 q^{46} -0.673393 q^{47} -5.58404 q^{48} -1.34388 q^{49} -17.2709 q^{50} +3.23031 q^{51} +1.52909 q^{52} +10.9105 q^{53} +2.50066 q^{54} +17.2139 q^{55} +13.4010 q^{56} +2.20865 q^{57} +12.1326 q^{58} +2.22030 q^{59} +14.6764 q^{60} -1.93090 q^{61} -6.54105 q^{62} -2.37826 q^{63} -4.43066 q^{64} -1.24050 q^{65} -12.4751 q^{66} +11.6498 q^{67} -13.7395 q^{68} +4.09216 q^{69} -20.5214 q^{70} -2.95808 q^{71} -5.63477 q^{72} +6.68869 q^{73} -9.18999 q^{74} -6.90654 q^{75} -9.39406 q^{76} +11.8644 q^{77} +0.899001 q^{78} -0.878179 q^{79} -19.2682 q^{80} +1.00000 q^{81} -1.74734 q^{82} -3.27937 q^{83} +10.1155 q^{84} +11.1465 q^{85} +28.9116 q^{86} +4.85175 q^{87} +28.1102 q^{88} -10.7536 q^{89} +8.62875 q^{90} -0.854996 q^{91} -17.4052 q^{92} -2.61573 q^{93} +1.68393 q^{94} +7.62112 q^{95} +2.69425 q^{96} +0.884628 q^{97} +3.36060 q^{98} -4.98870 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 102 q - 6 q^{2} - 102 q^{3} + 96 q^{4} - 20 q^{5} + 6 q^{6} + 12 q^{7} - 21 q^{8} + 102 q^{9}+O(q^{10}) $ 102 * q - 6 * q^2 - 102 * q^3 + 96 * q^4 - 20 * q^5 + 6 * q^6 + 12 * q^7 - 21 * q^8 + 102 * q^9	\( 102 q - 6 q^{2} - 102 q^{3} + 96 q^{4} - 20 q^{5} + 6 q^{6} + 12 q^{7} - 21 q^{8} + 102 q^{9} - 16 q^{10} - 28 q^{11} - 96 q^{12} - 2 q^{13} - 41 q^{14} + 20 q^{15} + 88 q^{16} - 77 q^{17} - 6 q^{18} + 10 q^{19} - 50 q^{20} - 12 q^{21} + 24 q^{22} - 29 q^{23} + 21 q^{24} + 74 q^{25} - 45 q^{26} - 102 q^{27} + 19 q^{28} - 68 q^{29} + 16 q^{30} - 29 q^{31} - 48 q^{32} + 28 q^{33} - 19 q^{34} - 49 q^{35} + 96 q^{36} + 4 q^{37} - 44 q^{38} + 2 q^{39} - 41 q^{40} - 122 q^{41} + 41 q^{42} + 85 q^{43} - 86 q^{44} - 20 q^{45} - 28 q^{46} - 39 q^{47} - 88 q^{48} + 24 q^{49} - 37 q^{50} + 77 q^{51} + 8 q^{52} - 37 q^{53} + 6 q^{54} - 13 q^{55} - 130 q^{56} - 10 q^{57} + 17 q^{58} - 58 q^{59} + 50 q^{60} - 114 q^{61} - 64 q^{62} + 12 q^{63} + 47 q^{64} - 92 q^{65} - 24 q^{66} + 121 q^{67} - 138 q^{68} + 29 q^{69} - 2 q^{70} - 67 q^{71} - 21 q^{72} - 72 q^{73} - 111 q^{74} - 74 q^{75} - 17 q^{76} - 57 q^{77} + 45 q^{78} - 24 q^{79} - 97 q^{80} + 102 q^{81} - q^{82} - 78 q^{83} - 19 q^{84} - 24 q^{85} - 80 q^{86} + 68 q^{87} + 54 q^{88} - 176 q^{89} - 16 q^{90} - 3 q^{91} - 82 q^{92} + 29 q^{93} - 41 q^{94} - 90 q^{95} + 48 q^{96} - 77 q^{97} - 48 q^{98} - 28 q^{99}+O(q^{100}) \) 102 * q - 6 * q^2 - 102 * q^3 + 96 * q^4 - 20 * q^5 + 6 * q^6 + 12 * q^7 - 21 * q^8 + 102 * q^9 - 16 * q^10 - 28 * q^11 - 96 * q^12 - 2 * q^13 - 41 * q^14 + 20 * q^15 + 88 * q^16 - 77 * q^17 - 6 * q^18 + 10 * q^19 - 50 * q^20 - 12 * q^21 + 24 * q^22 - 29 * q^23 + 21 * q^24 + 74 * q^25 - 45 * q^26 - 102 * q^27 + 19 * q^28 - 68 * q^29 + 16 * q^30 - 29 * q^31 - 48 * q^32 + 28 * q^33 - 19 * q^34 - 49 * q^35 + 96 * q^36 + 4 * q^37 - 44 * q^38 + 2 * q^39 - 41 * q^40 - 122 * q^41 + 41 * q^42 + 85 * q^43 - 86 * q^44 - 20 * q^45 - 28 * q^46 - 39 * q^47 - 88 * q^48 + 24 * q^49 - 37 * q^50 + 77 * q^51 + 8 * q^52 - 37 * q^53 + 6 * q^54 - 13 * q^55 - 130 * q^56 - 10 * q^57 + 17 * q^58 - 58 * q^59 + 50 * q^60 - 114 * q^61 - 64 * q^62 + 12 * q^63 + 47 * q^64 - 92 * q^65 - 24 * q^66 + 121 * q^67 - 138 * q^68 + 29 * q^69 - 2 * q^70 - 67 * q^71 - 21 * q^72 - 72 * q^73 - 111 * q^74 - 74 * q^75 - 17 * q^76 - 57 * q^77 + 45 * q^78 - 24 * q^79 - 97 * q^80 + 102 * q^81 - q^82 - 78 * q^83 - 19 * q^84 - 24 * q^85 - 80 * q^86 + 68 * q^87 + 54 * q^88 - 176 * q^89 - 16 * q^90 - 3 * q^91 - 82 * q^92 + 29 * q^93 - 41 * q^94 - 90 * q^95 + 48 * q^96 - 77 * q^97 - 48 * q^98 - 28 * 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 $

$2$	−2.50066	−1.76824	−0.884118	−	0.467264i	$-0.845240\pi$
$2$	−2.50066	−1.76824	−0.884118	+	0.467264i	$0.845240\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.25331	2.12666
$5$	−3.45059	−1.54315	−0.771574	−	0.636139i	$-0.780530\pi$
$5$	−3.45059	−1.54315	−0.771574	+	0.636139i	$0.780530\pi$
$6$	2.50066	1.02089
$7$	−2.37826	−0.898897	−0.449449	−	0.893306i	$-0.648380\pi$
$7$	−2.37826	−0.898897	−0.449449	+	0.893306i	$0.648380\pi$
$8$	−5.63477	−1.99219
$9$	1.00000	0.333333
$10$	8.62875	2.72865
$11$	−4.98870	−1.50415	−0.752075	−	0.659077i	$-0.770947\pi$
$11$	−4.98870	−1.50415	−0.752075	+	0.659077i	$0.770947\pi$
$12$	−4.25331	−1.22783
$13$	0.359505	0.0997088	0.0498544	−	0.998756i	$-0.484124\pi$
$13$	0.359505	0.0997088	0.0498544	+	0.998756i	$0.484124\pi$
$14$	5.94722	1.58946
$15$	3.45059	0.890937
$16$	5.58404	1.39601
$17$	−3.23031	−0.783465	−0.391733	−	0.920079i	$-0.628124\pi$
$17$	−3.23031	−0.783465	−0.391733	+	0.920079i	$0.628124\pi$
$18$	−2.50066	−0.589412
$19$	−2.20865	−0.506698	−0.253349	−	0.967375i	$-0.581532\pi$
$19$	−2.20865	−0.506698	−0.253349	+	0.967375i	$0.581532\pi$
$20$	−14.6764	−3.28175
$21$	2.37826	0.518979
$22$	12.4751	2.65969
$23$	−4.09216	−0.853275	−0.426637	−	0.904423i	$-0.640302\pi$
$23$	−4.09216	−0.853275	−0.426637	+	0.904423i	$0.640302\pi$
$24$	5.63477	1.15019
$25$	6.90654	1.38131
$26$	−0.899001	−0.176309
$27$	−1.00000	−0.192450
$28$	−10.1155	−1.91165
$29$	−4.85175	−0.900948	−0.450474	−	0.892790i	$-0.648745\pi$
$29$	−4.85175	−0.900948	−0.450474	+	0.892790i	$0.648745\pi$
$30$	−8.62875	−1.57539
$31$	2.61573	0.469799	0.234899	−	0.972020i	$-0.424524\pi$
$31$	2.61573	0.469799	0.234899	+	0.972020i	$0.424524\pi$
$32$	−2.69425	−0.476281
$33$	4.98870	0.868422
$34$	8.07791	1.38535
$35$	8.20639	1.38713
$36$	4.25331	0.708885
$37$	3.67502	0.604170	0.302085	−	0.953281i	$-0.402317\pi$
$37$	3.67502	0.604170	0.302085	+	0.953281i	$0.402317\pi$
$38$	5.52308	0.895961
$39$	−0.359505	−0.0575669
$40$	19.4433	3.07425
$41$	0.698749	0.109126	0.0545631	−	0.998510i	$-0.482623\pi$
$41$	0.698749	0.109126	0.0545631	+	0.998510i	$0.482623\pi$
$42$	−5.94722	−0.917676
$43$	−11.5616	−1.76312	−0.881561	−	0.472070i	$-0.843507\pi$
$43$	−11.5616	−1.76312	−0.881561	+	0.472070i	$0.843507\pi$
$44$	−21.2185	−3.19881
$45$	−3.45059	−0.514383
$46$	10.2331	1.50879
$47$	−0.673393	−0.0982244	−0.0491122	−	0.998793i	$-0.515639\pi$
$47$	−0.673393	−0.0982244	−0.0491122	+	0.998793i	$0.515639\pi$
$48$	−5.58404	−0.805987
$49$	−1.34388	−0.191983
$50$	−17.2709	−2.44248
$51$	3.23031	0.452334
$52$	1.52909	0.212046
$53$	10.9105	1.49867	0.749336	−	0.662190i	$-0.230373\pi$
$53$	10.9105	1.49867	0.749336	+	0.662190i	$0.230373\pi$
$54$	2.50066	0.340297
$55$	17.2139	2.32113
$56$	13.4010	1.79078
$57$	2.20865	0.292542
$58$	12.1326	1.59309
$59$	2.22030	0.289059	0.144529	−	0.989501i	$-0.453833\pi$
$59$	2.22030	0.289059	0.144529	+	0.989501i	$0.453833\pi$
$60$	14.6764	1.89472
$61$	−1.93090	−0.247227	−0.123613	−	0.992330i	$-0.539448\pi$
$61$	−1.93090	−0.247227	−0.123613	+	0.992330i	$0.539448\pi$
$62$	−6.54105	−0.830714
$63$	−2.37826	−0.299632
$64$	−4.43066	−0.553833
$65$	−1.24050	−0.153865
$66$	−12.4751	−1.53557
$67$	11.6498	1.42325	0.711623	−	0.702562i	$-0.247960\pi$
$67$	11.6498	1.42325	0.711623	+	0.702562i	$0.247960\pi$
$68$	−13.7395	−1.66616
$69$	4.09216	0.492638
$70$	−20.5214	−2.45278
$71$	−2.95808	−0.351060	−0.175530	−	0.984474i	$-0.556164\pi$
$71$	−2.95808	−0.351060	−0.175530	+	0.984474i	$0.556164\pi$
$72$	−5.63477	−0.664064
$73$	6.68869	0.782852	0.391426	−	0.920210i	$-0.371982\pi$
$73$	6.68869	0.782852	0.391426	+	0.920210i	$0.371982\pi$
$74$	−9.18999	−1.06831
$75$	−6.90654	−0.797499
$76$	−9.39406	−1.07757
$77$	11.8644	1.35208
$78$	0.899001	0.101792
$79$	−0.878179	−0.0988028	−0.0494014	−	0.998779i	$-0.515731\pi$
$79$	−0.878179	−0.0988028	−0.0494014	+	0.998779i	$0.515731\pi$
$80$	−19.2682	−2.15425
$81$	1.00000	0.111111
$82$	−1.74734	−0.192961
$83$	−3.27937	−0.359957	−0.179979	−	0.983671i	$-0.557603\pi$
$83$	−3.27937	−0.359957	−0.179979	+	0.983671i	$0.557603\pi$
$84$	10.1155	1.10369
$85$	11.1465	1.20900
$86$	28.9116	3.11761
$87$	4.85175	0.520163
$88$	28.1102	2.99656
$89$	−10.7536	−1.13987	−0.569937	−	0.821688i	$-0.693033\pi$
$89$	−10.7536	−1.13987	−0.569937	+	0.821688i	$0.693033\pi$
$90$	8.62875	0.909550
$91$	−0.854996	−0.0896280
$92$	−17.4052	−1.81462
$93$	−2.61573	−0.271238
$94$	1.68393	0.173684
$95$	7.62112	0.781911
$96$	2.69425	0.274981
$97$	0.884628	0.0898204	0.0449102	−	0.998991i	$-0.485700\pi$
$97$	0.884628	0.0898204	0.0449102	+	0.998991i	$0.485700\pi$
$98$	3.36060	0.339472
$99$	−4.98870	−0.501383
$100$	29.3757	2.93757
$101$	−16.9294	−1.68454	−0.842268	−	0.539060i	$-0.818780\pi$
$101$	−16.9294	−1.68454	−0.842268	+	0.539060i	$0.818780\pi$
$102$	−8.07791	−0.799833
$103$	6.14669	0.605652	0.302826	−	0.953046i	$-0.402070\pi$
$103$	6.14669	0.605652	0.302826	+	0.953046i	$0.402070\pi$
$104$	−2.02573	−0.198639
$105$	−8.20639	−0.800861
$106$	−27.2835	−2.65001
$107$	13.0834	1.26482	0.632409	−	0.774634i	$-0.282066\pi$
$107$	13.0834	1.26482	0.632409	+	0.774634i	$0.282066\pi$
$108$	−4.25331	−0.409275
$109$	−4.84240	−0.463818	−0.231909	−	0.972738i	$-0.574497\pi$
$109$	−4.84240	−0.463818	−0.231909	+	0.972738i	$0.574497\pi$
$110$	−43.0463	−4.10430
$111$	−3.67502	−0.348818
$112$	−13.2803	−1.25487
$113$	−3.24158	−0.304942	−0.152471	−	0.988308i	$-0.548723\pi$
$113$	−3.24158	−0.304942	−0.152471	+	0.988308i	$0.548723\pi$
$114$	−5.52308	−0.517284
$115$	14.1204	1.31673
$116$	−20.6360	−1.91601
$117$	0.359505	0.0332363
$118$	−5.55223	−0.511124
$119$	7.68251	0.704255
$120$	−19.4433	−1.77492
$121$	13.8871	1.26247
$122$	4.82853	0.437155
$123$	−0.698749	−0.0630041
$124$	11.1255	0.999100
$125$	−6.57869	−0.588416
$126$	5.94722	0.529821
$127$	18.1451	1.61012	0.805060	−	0.593194i	$-0.202133\pi$
$127$	18.1451	1.61012	0.805060	+	0.593194i	$0.202133\pi$
$128$	16.4681	1.45559
$129$	11.5616	1.01794
$130$	3.10208	0.272070
$131$	9.51165	0.831036	0.415518	−	0.909585i	$-0.363600\pi$
$131$	9.51165	0.831036	0.415518	+	0.909585i	$0.363600\pi$
$132$	21.2185	1.84683
$133$	5.25273	0.455470
$134$	−29.1321	−2.51663
$135$	3.45059	0.296979
$136$	18.2021	1.56081
$137$	8.52107	0.728004	0.364002	−	0.931398i	$-0.381410\pi$
$137$	8.52107	0.728004	0.364002	+	0.931398i	$0.381410\pi$
$138$	−10.2331	−0.871100
$139$	14.8358	1.25836	0.629180	−	0.777260i	$-0.283391\pi$
$139$	14.8358	1.25836	0.629180	+	0.777260i	$0.283391\pi$
$140$	34.9043	2.94995
$141$	0.673393	0.0567099
$142$	7.39716	0.620756
$143$	−1.79346	−0.149977
$144$	5.58404	0.465337
$145$	16.7414	1.39030
$146$	−16.7261	−1.38427
$147$	1.34388	0.110842
$148$	15.6310	1.28486
$149$	13.9799	1.14528	0.572638	−	0.819808i	$-0.305920\pi$
$149$	13.9799	1.14528	0.572638	+	0.819808i	$0.305920\pi$
$150$	17.2709	1.41017
$151$	7.37432	0.600114	0.300057	−	0.953921i	$-0.402994\pi$
$151$	7.37432	0.600114	0.300057	+	0.953921i	$0.402994\pi$
$152$	12.4452	1.00944
$153$	−3.23031	−0.261155
$154$	−29.6689	−2.39079
$155$	−9.02579	−0.724969
$156$	−1.52909	−0.122425
$157$	−8.04106	−0.641747	−0.320873	−	0.947122i	$-0.603976\pi$
$157$	−8.04106	−0.641747	−0.320873	+	0.947122i	$0.603976\pi$
$158$	2.19603	0.174707
$159$	−10.9105	−0.865259
$160$	9.29676	0.734973
$161$	9.73222	0.767006
$162$	−2.50066	−0.196471
$163$	1.28484	0.100637	0.0503183	−	0.998733i	$-0.483976\pi$
$163$	1.28484	0.100637	0.0503183	+	0.998733i	$0.483976\pi$
$164$	2.97200	0.232074
$165$	−17.2139	−1.34010
$166$	8.20059	0.636489
$167$	−11.7521	−0.909403	−0.454701	−	0.890644i	$-0.650254\pi$
$167$	−11.7521	−0.909403	−0.454701	+	0.890644i	$0.650254\pi$
$168$	−13.4010	−1.03391
$169$	−12.8708	−0.990058
$170$	−27.8735	−2.13780
$171$	−2.20865	−0.168899
$172$	−49.1749	−3.74955
$173$	−16.6800	−1.26816	−0.634080	−	0.773267i	$-0.718621\pi$
$173$	−16.6800	−1.26816	−0.634080	+	0.773267i	$0.718621\pi$
$174$	−12.1326	−0.919770
$175$	−16.4255	−1.24165
$176$	−27.8571	−2.09981
$177$	−2.22030	−0.166888
$178$	26.8910	2.01557
$179$	12.5375	0.937094	0.468547	−	0.883439i	$-0.344778\pi$
$179$	12.5375	0.937094	0.468547	+	0.883439i	$0.344778\pi$
$180$	−14.6764	−1.09392
$181$	−14.4422	−1.07348	−0.536741	−	0.843747i	$-0.680345\pi$
$181$	−14.4422	−1.07348	−0.536741	+	0.843747i	$0.680345\pi$
$182$	2.13806	0.158483
$183$	1.93090	0.142736
$184$	23.0584	1.69989
$185$	−12.6810	−0.932324
$186$	6.54105	0.479613
$187$	16.1151	1.17845
$188$	−2.86415	−0.208890
$189$	2.37826	0.172993
$190$	−19.0579	−1.38260
$191$	12.3296	0.892138	0.446069	−	0.894999i	$-0.352824\pi$
$191$	12.3296	0.892138	0.446069	+	0.894999i	$0.352824\pi$
$192$	4.43066	0.319755
$193$	−20.4809	−1.47424	−0.737122	−	0.675759i	$-0.763816\pi$
$193$	−20.4809	−1.47424	−0.737122	+	0.675759i	$0.763816\pi$
$194$	−2.21216	−0.158824
$195$	1.24050	0.0888343
$196$	−5.71596	−0.408283
$197$	17.1678	1.22315	0.611577	−	0.791185i	$-0.290535\pi$
$197$	17.1678	1.22315	0.611577	+	0.791185i	$0.290535\pi$
$198$	12.4751	0.886564
$199$	−0.867235	−0.0614767	−0.0307383	−	0.999527i	$-0.509786\pi$
$199$	−0.867235	−0.0614767	−0.0307383	+	0.999527i	$0.509786\pi$
$200$	−38.9168	−2.75183
$201$	−11.6498	−0.821711
$202$	42.3346	2.97865
$203$	11.5387	0.809860
$204$	13.7395	0.961959
$205$	−2.41109	−0.168398
$206$	−15.3708	−1.07093
$207$	−4.09216	−0.284425
$208$	2.00749	0.139194
$209$	11.0183	0.762150
$210$	20.5214	1.41611
$211$	−8.33004	−0.573464	−0.286732	−	0.958011i	$-0.592569\pi$
$211$	−8.33004	−0.573464	−0.286732	+	0.958011i	$0.592569\pi$
$212$	46.4058	3.18716
$213$	2.95808	0.202684
$214$	−32.7171	−2.23650
$215$	39.8942	2.72076
$216$	5.63477	0.383398
$217$	−6.22088	−0.422301
$218$	12.1092	0.820139
$219$	−6.68869	−0.451980
$220$	73.2163	4.93624
$221$	−1.16131	−0.0781183
$222$	9.18999	0.616792
$223$	9.70064	0.649603	0.324801	−	0.945782i	$-0.394703\pi$
$223$	9.70064	0.649603	0.324801	+	0.945782i	$0.394703\pi$
$224$	6.40763	0.428128
$225$	6.90654	0.460436
$226$	8.10610	0.539209
$227$	21.2909	1.41313	0.706564	−	0.707649i	$-0.250244\pi$
$227$	21.2909	1.41313	0.706564	+	0.707649i	$0.250244\pi$
$228$	9.39406	0.622137
$229$	14.2468	0.941456	0.470728	−	0.882279i	$-0.343991\pi$
$229$	14.2468	0.941456	0.470728	+	0.882279i	$0.343991\pi$
$230$	−35.3102	−2.32829
$231$	−11.8644	−0.780622
$232$	27.3385	1.79486
$233$	−1.02376	−0.0670689	−0.0335344	−	0.999438i	$-0.510676\pi$
$233$	−1.02376	−0.0670689	−0.0335344	+	0.999438i	$0.510676\pi$
$234$	−0.899001	−0.0587695
$235$	2.32360	0.151575
$236$	9.44364	0.614729
$237$	0.878179	0.0570438
$238$	−19.2114	−1.24529
$239$	−19.6098	−1.26845	−0.634225	−	0.773149i	$-0.718681\pi$
$239$	−19.6098	−1.26845	−0.634225	+	0.773149i	$0.718681\pi$
$240$	19.2682	1.24376
$241$	−1.09889	−0.0707858	−0.0353929	−	0.999373i	$-0.511268\pi$
$241$	−1.09889	−0.0707858	−0.0353929	+	0.999373i	$0.511268\pi$
$242$	−34.7271	−2.23234
$243$	−1.00000	−0.0641500
$244$	−8.21273	−0.525766
$245$	4.63719	0.296259
$246$	1.74734	0.111406
$247$	−0.794019	−0.0505222
$248$	−14.7390	−0.935929
$249$	3.27937	0.207821
$250$	16.4511	1.04046
$251$	18.2184	1.14994	0.574968	−	0.818176i	$-0.305014\pi$
$251$	18.2184	1.14994	0.574968	+	0.818176i	$0.305014\pi$
$252$	−10.1155	−0.637215
$253$	20.4146	1.28345
$254$	−45.3748	−2.84707
$255$	−11.1465	−0.698018
$256$	−32.3198	−2.01999
$257$	18.0247	1.12435	0.562175	−	0.827018i	$-0.309965\pi$
$257$	18.0247	1.12435	0.562175	+	0.827018i	$0.309965\pi$
$258$	−28.9116	−1.79996
$259$	−8.74016	−0.543087
$260$	−5.27625	−0.327219
$261$	−4.85175	−0.300316
$262$	−23.7854	−1.46947
$263$	−6.51631	−0.401813	−0.200907	−	0.979610i	$-0.564389\pi$
$263$	−6.51631	−0.401813	−0.200907	+	0.979610i	$0.564389\pi$
$264$	−28.1102	−1.73006
$265$	−37.6476	−2.31268
$266$	−13.1353	−0.805377
$267$	10.7536	0.658107
$268$	49.5501	3.02675
$269$	10.9190	0.665741	0.332870	−	0.942973i	$-0.391983\pi$
$269$	10.9190	0.665741	0.332870	+	0.942973i	$0.391983\pi$
$270$	−8.62875	−0.525129
$271$	5.37007	0.326209	0.163104	−	0.986609i	$-0.447849\pi$
$271$	5.37007	0.326209	0.163104	+	0.986609i	$0.447849\pi$
$272$	−18.0382	−1.09373
$273$	0.854996	0.0517467
$274$	−21.3083	−1.28728
$275$	−34.4547	−2.07770
$276$	17.4052	1.04767
$277$	1.14993	0.0690927	0.0345463	−	0.999403i	$-0.489001\pi$
$277$	1.14993	0.0690927	0.0345463	+	0.999403i	$0.489001\pi$
$278$	−37.0994	−2.22508
$279$	2.61573	0.156600
$280$	−46.2411	−2.76344
$281$	15.4000	0.918686	0.459343	−	0.888259i	$-0.348085\pi$
$281$	15.4000	0.918686	0.459343	+	0.888259i	$0.348085\pi$
$282$	−1.68393	−0.100276
$283$	14.7559	0.877146	0.438573	−	0.898696i	$-0.355484\pi$
$283$	14.7559	0.877146	0.438573	+	0.898696i	$0.355484\pi$
$284$	−12.5816	−0.746583
$285$	−7.62112	−0.451436
$286$	4.48485	0.265195
$287$	−1.66181	−0.0980933
$288$	−2.69425	−0.158760
$289$	−6.56510	−0.386182
$290$	−41.8646	−2.45837
$291$	−0.884628	−0.0518578
$292$	28.4491	1.66486
$293$	2.01358	0.117635	0.0588173	−	0.998269i	$-0.481267\pi$
$293$	2.01358	0.117635	0.0588173	+	0.998269i	$0.481267\pi$
$294$	−3.36060	−0.195994
$295$	−7.66134	−0.446061
$296$	−20.7079	−1.20362
$297$	4.98870	0.289474
$298$	−34.9589	−2.02512
$299$	−1.47115	−0.0850790
$300$	−29.3757	−1.69601
$301$	27.4964	1.58487
$302$	−18.4407	−1.06114
$303$	16.9294	0.972567
$304$	−12.3332	−0.707356
$305$	6.66274	0.381507
$306$	8.07791	0.461784
$307$	3.74229	0.213584	0.106792	−	0.994281i	$-0.465942\pi$
$307$	3.74229	0.213584	0.106792	+	0.994281i	$0.465942\pi$
$308$	50.4631	2.87540
$309$	−6.14669	−0.349673
$310$	22.5705	1.28192
$311$	−21.9175	−1.24283	−0.621414	−	0.783482i	$-0.713442\pi$
$311$	−21.9175	−1.24283	−0.621414	+	0.783482i	$0.713442\pi$
$312$	2.02573	0.114684
$313$	−23.1842	−1.31045	−0.655225	−	0.755434i	$-0.727426\pi$
$313$	−23.1842	−1.31045	−0.655225	+	0.755434i	$0.727426\pi$
$314$	20.1080	1.13476
$315$	8.20639	0.462378
$316$	−3.73517	−0.210120
$317$	10.5215	0.590947	0.295473	−	0.955351i	$-0.404523\pi$
$317$	10.5215	0.590947	0.295473	+	0.955351i	$0.404523\pi$
$318$	27.2835	1.52998
$319$	24.2040	1.35516
$320$	15.2884	0.854646
$321$	−13.0834	−0.730243
$322$	−24.3370	−1.35625
$323$	7.13461	0.396980
$324$	4.25331	0.236295
$325$	2.48294	0.137729
$326$	−3.21296	−0.177949
$327$	4.84240	0.267785
$328$	−3.93729	−0.217401
$329$	1.60150	0.0882937
$330$	43.0463	2.36962
$331$	13.2930	0.730651	0.365326	−	0.930880i	$-0.380958\pi$
$331$	13.2930	0.730651	0.365326	+	0.930880i	$0.380958\pi$
$332$	−13.9482	−0.765506
$333$	3.67502	0.201390
$334$	29.3880	1.60804
$335$	−40.1985	−2.19628
$336$	13.2803	0.724500
$337$	−2.60696	−0.142010	−0.0710052	−	0.997476i	$-0.522621\pi$
$337$	−2.60696	−0.142010	−0.0710052	+	0.997476i	$0.522621\pi$
$338$	32.1854	1.75066
$339$	3.24158	0.176058
$340$	47.4094	2.57113
$341$	−13.0491	−0.706648
$342$	5.52308	0.298654
$343$	19.8439	1.07147
$344$	65.1468	3.51248
$345$	−14.1204	−0.760214
$346$	41.7112	2.24241
$347$	−9.70094	−0.520774	−0.260387	−	0.965504i	$-0.583850\pi$
$347$	−9.70094	−0.520774	−0.260387	+	0.965504i	$0.583850\pi$
$348$	20.6360	1.10621
$349$	−21.6278	−1.15771	−0.578854	−	0.815431i	$-0.696500\pi$
$349$	−21.6278	−1.15771	−0.578854	+	0.815431i	$0.696500\pi$
$350$	41.0748	2.19554
$351$	−0.359505	−0.0191890
$352$	13.4408	0.716399
$353$	−29.0633	−1.54688	−0.773441	−	0.633868i	$-0.781466\pi$
$353$	−29.0633	−1.54688	−0.773441	+	0.633868i	$0.781466\pi$
$354$	5.55223	0.295098
$355$	10.2071	0.541738
$356$	−45.7382	−2.42412
$357$	−7.68251	−0.406602
$358$	−31.3520	−1.65700
$359$	−20.2528	−1.06890	−0.534452	−	0.845199i	$-0.679482\pi$
$359$	−20.2528	−1.06890	−0.534452	+	0.845199i	$0.679482\pi$
$360$	19.4433	1.02475
$361$	−14.1219	−0.743257
$362$	36.1151	1.89817
$363$	−13.8871	−0.728886
$364$	−3.63657	−0.190608
$365$	−23.0799	−1.20806
$366$	−4.82853	−0.252391
$367$	11.8139	0.616682	0.308341	−	0.951276i	$-0.400226\pi$
$367$	11.8139	0.616682	0.308341	+	0.951276i	$0.400226\pi$
$368$	−22.8508	−1.19118
$369$	0.698749	0.0363754
$370$	31.7109	1.64857
$371$	−25.9480	−1.34715
$372$	−11.1255	−0.576831
$373$	2.08296	0.107852	0.0539258	−	0.998545i	$-0.482827\pi$
$373$	2.08296	0.107852	0.0539258	+	0.998545i	$0.482827\pi$
$374$	−40.2983	−2.08378
$375$	6.57869	0.339722
$376$	3.79441	0.195682
$377$	−1.74423	−0.0898324
$378$	−5.94722	−0.305892
$379$	29.4342	1.51193	0.755966	−	0.654611i	$-0.227168\pi$
$379$	29.4342	1.51193	0.755966	+	0.654611i	$0.227168\pi$
$380$	32.4150	1.66285
$381$	−18.1451	−0.929603
$382$	−30.8321	−1.57751
$383$	18.4421	0.942348	0.471174	−	0.882040i	$-0.343830\pi$
$383$	18.4421	0.942348	0.471174	+	0.882040i	$0.343830\pi$
$384$	−16.4681	−0.840384
$385$	−40.9392	−2.08646
$386$	51.2157	2.60681
$387$	−11.5616	−0.587707
$388$	3.76260	0.191017
$389$	11.8884	0.602764	0.301382	−	0.953503i	$-0.402552\pi$
$389$	11.8884	0.602764	0.301382	+	0.953503i	$0.402552\pi$
$390$	−3.10208	−0.157080
$391$	13.2189	0.668511
$392$	7.57248	0.382468
$393$	−9.51165	−0.479799
$394$	−42.9309	−2.16283
$395$	3.03023	0.152467
$396$	−21.2185	−1.06627
$397$	23.6609	1.18751	0.593753	−	0.804648i	$-0.297646\pi$
$397$	23.6609	1.18751	0.593753	+	0.804648i	$0.297646\pi$
$398$	2.16866	0.108705
$399$	−5.25273	−0.262965
$400$	38.5664	1.92832
$401$	−5.76204	−0.287743	−0.143871	−	0.989596i	$-0.545955\pi$
$401$	−5.76204	−0.287743	−0.143871	+	0.989596i	$0.545955\pi$
$402$	29.1321	1.45298
$403$	0.940367	0.0468430
$404$	−72.0059	−3.58243
$405$	−3.45059	−0.171461
$406$	−28.8545	−1.43202
$407$	−18.3336	−0.908763
$408$	−18.2021	−0.901136
$409$	−15.3932	−0.761145	−0.380572	−	0.924751i	$-0.624273\pi$
$409$	−15.3932	−0.761145	−0.380572	+	0.924751i	$0.624273\pi$
$410$	6.02933	0.297767
$411$	−8.52107	−0.420313
$412$	26.1438	1.28801
$413$	−5.28045	−0.259834
$414$	10.2331	0.502930
$415$	11.3157	0.555468
$416$	−0.968598	−0.0474894
$417$	−14.8358	−0.726514
$418$	−27.5530	−1.34766
$419$	4.76284	0.232680	0.116340	−	0.993209i	$-0.462884\pi$
$419$	4.76284	0.232680	0.116340	+	0.993209i	$0.462884\pi$
$420$	−34.9043	−1.70316
$421$	2.83510	0.138175	0.0690873	−	0.997611i	$-0.477991\pi$
$421$	2.83510	0.138175	0.0690873	+	0.997611i	$0.477991\pi$
$422$	20.8306	1.01402
$423$	−0.673393	−0.0327415
$424$	−61.4782	−2.98565
$425$	−22.3103	−1.08221
$426$	−7.39716	−0.358394
$427$	4.59218	0.222231
$428$	55.6477	2.68983
$429$	1.79346	0.0865892
$430$	−99.7619	−4.81094
$431$	−4.83037	−0.232671	−0.116335	−	0.993210i	$-0.537115\pi$
$431$	−4.83037	−0.232671	−0.116335	+	0.993210i	$0.537115\pi$
$432$	−5.58404	−0.268662
$433$	26.7298	1.28455	0.642275	−	0.766474i	$-0.277991\pi$
$433$	26.7298	1.28455	0.642275	+	0.766474i	$0.277991\pi$
$434$	15.5563	0.746727
$435$	−16.7414	−0.802688
$436$	−20.5962	−0.986381
$437$	9.03813	0.432353
$438$	16.7261	0.799206
$439$	−35.5152	−1.69505	−0.847525	−	0.530755i	$-0.821908\pi$
$439$	−35.5152	−1.69505	−0.847525	+	0.530755i	$0.821908\pi$
$440$	−96.9967	−4.62414
$441$	−1.34388	−0.0639945
$442$	2.90405	0.138132
$443$	34.3606	1.63252	0.816262	−	0.577682i	$-0.196043\pi$
$443$	34.3606	1.63252	0.816262	+	0.577682i	$0.196043\pi$
$444$	−15.6310	−0.741815
$445$	37.1061	1.75900
$446$	−24.2580	−1.14865
$447$	−13.9799	−0.661225
$448$	10.5373	0.497839
$449$	−26.5345	−1.25224	−0.626121	−	0.779726i	$-0.715358\pi$
$449$	−26.5345	−1.25224	−0.626121	+	0.779726i	$0.715358\pi$
$450$	−17.2709	−0.814160
$451$	−3.48585	−0.164142
$452$	−13.7875	−0.648507
$453$	−7.37432	−0.346476
$454$	−53.2414	−2.49874
$455$	2.95024	0.138309
$456$	−12.4452	−0.582801
$457$	29.5502	1.38230	0.691150	−	0.722712i	$-0.257104\pi$
$457$	29.5502	1.38230	0.691150	+	0.722712i	$0.257104\pi$
$458$	−35.6265	−1.66471
$459$	3.23031	0.150778
$460$	60.0583	2.80023
$461$	16.9152	0.787817	0.393909	−	0.919150i	$-0.371123\pi$
$461$	16.9152	0.787817	0.393909	+	0.919150i	$0.371123\pi$
$462$	29.6689	1.38032
$463$	34.5237	1.60445	0.802227	−	0.597019i	$-0.203648\pi$
$463$	34.5237	1.60445	0.802227	+	0.597019i	$0.203648\pi$
$464$	−27.0924	−1.25773
$465$	9.02579	0.418561
$466$	2.56008	0.118594
$467$	14.5830	0.674822	0.337411	−	0.941357i	$-0.390449\pi$
$467$	14.5830	0.674822	0.337411	+	0.941357i	$0.390449\pi$
$468$	1.52909	0.0706821
$469$	−27.7062	−1.27935
$470$	−5.81054	−0.268020
$471$	8.04106	0.370513
$472$	−12.5109	−0.575861
$473$	57.6772	2.65200
$474$	−2.19603	−0.100867
$475$	−15.2541	−0.699906
$476$	32.6761	1.49771
$477$	10.9105	0.499558
$478$	49.0374	2.24292
$479$	−3.05604	−0.139634	−0.0698170	−	0.997560i	$-0.522242\pi$
$479$	−3.05604	−0.139634	−0.0698170	+	0.997560i	$0.522242\pi$
$480$	−9.29676	−0.424337
$481$	1.32119	0.0602411
$482$	2.74795	0.125166
$483$	−9.73222	−0.442831
$484$	59.0664	2.68484
$485$	−3.05249	−0.138606
$486$	2.50066	0.113432
$487$	8.88268	0.402513	0.201256	−	0.979539i	$-0.435498\pi$
$487$	8.88268	0.402513	0.201256	+	0.979539i	$0.435498\pi$
$488$	10.8802	0.492523
$489$	−1.28484	−0.0581026
$490$	−11.5960	−0.523856
$491$	−12.5135	−0.564726	−0.282363	−	0.959308i	$-0.591118\pi$
$491$	−12.5135	−0.564726	−0.282363	+	0.959308i	$0.591118\pi$
$492$	−2.97200	−0.133988
$493$	15.6727	0.705861
$494$	1.98557	0.0893352
$495$	17.2139	0.773709
$496$	14.6063	0.655844
$497$	7.03509	0.315567
$498$	−8.20059	−0.367477
$499$	15.5103	0.694337	0.347168	−	0.937803i	$-0.387143\pi$
$499$	15.5103	0.694337	0.347168	+	0.937803i	$0.387143\pi$
$500$	−27.9812	−1.25136
$501$	11.7521	0.525044
$502$	−45.5581	−2.03336
$503$	3.51086	0.156542	0.0782708	−	0.996932i	$-0.475060\pi$
$503$	3.51086	0.156542	0.0782708	+	0.996932i	$0.475060\pi$
$504$	13.4010	0.596926
$505$	58.4162	2.59949
$506$	−51.0500	−2.26945
$507$	12.8708	0.571610
$508$	77.1769	3.42417
$509$	24.3771	1.08050	0.540248	−	0.841506i	$-0.318330\pi$
$509$	24.3771	1.08050	0.540248	+	0.841506i	$0.318330\pi$
$510$	27.8735	1.23426
$511$	−15.9074	−0.703703
$512$	47.8848	2.11623
$513$	2.20865	0.0975141
$514$	−45.0737	−1.98811
$515$	−21.2097	−0.934611
$516$	49.1749	2.16481
$517$	3.35935	0.147744
$518$	21.8562	0.960305
$519$	16.6800	0.732173
$520$	6.98995	0.306530
$521$	−3.73885	−0.163802	−0.0819009	−	0.996640i	$-0.526099\pi$
$521$	−3.73885	−0.163802	−0.0819009	+	0.996640i	$0.526099\pi$
$522$	12.1326	0.531029
$523$	−24.8271	−1.08561	−0.542807	−	0.839857i	$-0.682639\pi$
$523$	−24.8271	−1.08561	−0.542807	+	0.839857i	$0.682639\pi$
$524$	40.4560	1.76733
$525$	16.4255	0.716870
$526$	16.2951	0.710500
$527$	−8.44961	−0.368071
$528$	27.8571	1.21233
$529$	−6.25422	−0.271922
$530$	94.1440	4.08935
$531$	2.22030	0.0963529
$532$	22.3415	0.968627
$533$	0.251204	0.0108808
$534$	−26.8910	−1.16369
$535$	−45.1453	−1.95180
$536$	−65.6438	−2.83538
$537$	−12.5375	−0.541032
$538$	−27.3046	−1.17719
$539$	6.70424	0.288772
$540$	14.6764	0.631573
$541$	11.9906	0.515517	0.257758	−	0.966209i	$-0.417016\pi$
$541$	11.9906	0.515517	0.257758	+	0.966209i	$0.417016\pi$
$542$	−13.4287	−0.576814
$543$	14.4422	0.619775
$544$	8.70328	0.373150
$545$	16.7091	0.715740
$546$	−2.13806	−0.0915004
$547$	5.74068	0.245454	0.122727	−	0.992440i	$-0.460836\pi$
$547$	5.74068	0.245454	0.122727	+	0.992440i	$0.460836\pi$
$548$	36.2428	1.54821
$549$	−1.93090	−0.0824089
$550$	86.1595	3.67386
$551$	10.7158	0.456509
$552$	−23.0584	−0.981431
$553$	2.08854	0.0888136
$554$	−2.87559	−0.122172
$555$	12.6810	0.538278
$556$	63.1015	2.67610
$557$	−17.1156	−0.725212	−0.362606	−	0.931943i	$-0.618113\pi$
$557$	−17.1156	−0.725212	−0.362606	+	0.931943i	$0.618113\pi$
$558$	−6.54105	−0.276905
$559$	−4.15644	−0.175799
$560$	45.8248	1.93645
$561$	−16.1151	−0.680378
$562$	−38.5101	−1.62445
$563$	−32.8920	−1.38623	−0.693115	−	0.720827i	$-0.743762\pi$
$563$	−32.8920	−1.38623	−0.693115	+	0.720827i	$0.743762\pi$
$564$	2.86415	0.120602
$565$	11.1853	0.470571
$566$	−36.8995	−1.55100
$567$	−2.37826	−0.0998775
$568$	16.6681	0.699379
$569$	20.6505	0.865715	0.432858	−	0.901462i	$-0.357505\pi$
$569$	20.6505	0.865715	0.432858	+	0.901462i	$0.357505\pi$
$570$	19.0579	0.798246
$571$	5.18592	0.217024	0.108512	−	0.994095i	$-0.465391\pi$
$571$	5.18592	0.217024	0.108512	+	0.994095i	$0.465391\pi$
$572$	−7.62816	−0.318949
$573$	−12.3296	−0.515076
$574$	4.15562	0.173452
$575$	−28.2627	−1.17864
$576$	−4.43066	−0.184611
$577$	−30.3449	−1.26327	−0.631637	−	0.775264i	$-0.717617\pi$
$577$	−30.3449	−1.26327	−0.631637	+	0.775264i	$0.717617\pi$
$578$	16.4171	0.682861
$579$	20.4809	0.851155
$580$	71.2064	2.95668
$581$	7.79919	0.323565
$582$	2.21216	0.0916968
$583$	−54.4292	−2.25423
$584$	−37.6892	−1.55959
$585$	−1.24050	−0.0512885
$586$	−5.03528	−0.208006
$587$	36.7699	1.51766	0.758829	−	0.651290i	$-0.225772\pi$
$587$	36.7699	1.51766	0.758829	+	0.651290i	$0.225772\pi$
$588$	5.71596	0.235722
$589$	−5.77722	−0.238046
$590$	19.1584	0.788740
$591$	−17.1678	−0.706189
$592$	20.5215	0.843428
$593$	41.1306	1.68903	0.844515	−	0.535532i	$-0.179889\pi$
$593$	41.1306	1.68903	0.844515	+	0.535532i	$0.179889\pi$
$594$	−12.4751	−0.511858
$595$	−26.5092	−1.08677
$596$	59.4608	2.43561
$597$	0.867235	0.0354936
$598$	3.67886	0.150440
$599$	−0.957789	−0.0391342	−0.0195671	−	0.999809i	$-0.506229\pi$
$599$	−0.957789	−0.0391342	−0.0195671	+	0.999809i	$0.506229\pi$
$600$	38.9168	1.58877
$601$	18.2618	0.744914	0.372457	−	0.928049i	$-0.378515\pi$
$601$	18.2618	0.744914	0.372457	+	0.928049i	$0.378515\pi$
$602$	−68.7592	−2.80242
$603$	11.6498	0.474415
$604$	31.3653	1.27624
$605$	−47.9188	−1.94818
$606$	−42.3346	−1.71973
$607$	−31.3394	−1.27203	−0.636014	−	0.771678i	$-0.719418\pi$
$607$	−31.3394	−1.27203	−0.636014	+	0.771678i	$0.719418\pi$
$608$	5.95065	0.241331
$609$	−11.5387	−0.467573
$610$	−16.6613	−0.674595
$611$	−0.242088	−0.00979383
$612$	−13.7395	−0.555387
$613$	8.70190	0.351466	0.175733	−	0.984438i	$-0.443770\pi$
$613$	8.70190	0.351466	0.175733	+	0.984438i	$0.443770\pi$
$614$	−9.35821	−0.377666
$615$	2.41109	0.0972247
$616$	−66.8533	−2.69360
$617$	−26.9402	−1.08457	−0.542286	−	0.840194i	$-0.682441\pi$
$617$	−26.9402	−1.08457	−0.542286	+	0.840194i	$0.682441\pi$
$618$	15.3708	0.618304
$619$	23.8633	0.959148	0.479574	−	0.877502i	$-0.340791\pi$
$619$	23.8633	0.959148	0.479574	+	0.877502i	$0.340791\pi$
$620$	−38.3895	−1.54176
$621$	4.09216	0.164213
$622$	54.8083	2.19761
$623$	25.5747	1.02463
$624$	−2.00749	−0.0803640
$625$	−11.8324	−0.473295
$626$	57.9759	2.31718
$627$	−11.0183	−0.440028
$628$	−34.2011	−1.36477
$629$	−11.8715	−0.473346
$630$	−20.5214	−0.817592
$631$	−27.1918	−1.08249	−0.541245	−	0.840865i	$-0.682047\pi$
$631$	−27.1918	−1.08249	−0.541245	+	0.840865i	$0.682047\pi$
$632$	4.94834	0.196834
$633$	8.33004	0.331089
$634$	−26.3107	−1.04493
$635$	−62.6113	−2.48465
$636$	−46.4058	−1.84011
$637$	−0.483133	−0.0191424
$638$	−60.5259	−2.39624
$639$	−2.95808	−0.117020
$640$	−56.8246	−2.24619
$641$	−30.9955	−1.22425	−0.612124	−	0.790762i	$-0.709684\pi$
$641$	−30.9955	−1.22425	−0.612124	+	0.790762i	$0.709684\pi$
$642$	32.7171	1.29124
$643$	21.0172	0.828836	0.414418	−	0.910087i	$-0.363985\pi$
$643$	21.0172	0.828836	0.414418	+	0.910087i	$0.363985\pi$
$644$	41.3942	1.63116
$645$	−39.8942	−1.57083
$646$	−17.8412	−0.701955
$647$	6.00829	0.236210	0.118105	−	0.993001i	$-0.462318\pi$
$647$	6.00829	0.236210	0.118105	+	0.993001i	$0.462318\pi$
$648$	−5.63477	−0.221355
$649$	−11.0764	−0.434788
$650$	−6.20899	−0.243537
$651$	6.22088	0.243815
$652$	5.46484	0.214020
$653$	2.28426	0.0893900	0.0446950	−	0.999001i	$-0.485768\pi$
$653$	2.28426	0.0893900	0.0446950	+	0.999001i	$0.485768\pi$
$654$	−12.1092	−0.473507
$655$	−32.8207	−1.28241
$656$	3.90184	0.152341
$657$	6.68869	0.260951
$658$	−4.00482	−0.156124
$659$	−32.1201	−1.25122	−0.625611	−	0.780135i	$-0.715150\pi$
$659$	−32.1201	−1.25122	−0.625611	+	0.780135i	$0.715150\pi$
$660$	−73.2163	−2.84994
$661$	−8.95937	−0.348479	−0.174240	−	0.984703i	$-0.555747\pi$
$661$	−8.95937	−0.348479	−0.174240	+	0.984703i	$0.555747\pi$
$662$	−33.2414	−1.29196
$663$	1.16131	0.0451016
$664$	18.4785	0.717105
$665$	−18.1250	−0.702857
$666$	−9.18999	−0.356105
$667$	19.8542	0.768756
$668$	−49.9852	−1.93399
$669$	−9.70064	−0.375048
$670$	100.523	3.88354
$671$	9.63269	0.371866
$672$	−6.40763	−0.247180
$673$	−27.7853	−1.07105	−0.535523	−	0.844521i	$-0.679885\pi$
$673$	−27.7853	−1.07105	−0.535523	+	0.844521i	$0.679885\pi$
$674$	6.51914	0.251108
$675$	−6.90654	−0.265833
$676$	−54.7433	−2.10551
$677$	−32.0062	−1.23010	−0.615049	−	0.788489i	$-0.710864\pi$
$677$	−32.0062	−1.23010	−0.615049	+	0.788489i	$0.710864\pi$
$678$	−8.10610	−0.311313
$679$	−2.10388	−0.0807393
$680$	−62.8078	−2.40857
$681$	−21.2909	−0.815870
$682$	32.6314	1.24952
$683$	25.8643	0.989670	0.494835	−	0.868987i	$-0.335228\pi$
$683$	25.8643	0.989670	0.494835	+	0.868987i	$0.335228\pi$
$684$	−9.39406	−0.359191
$685$	−29.4027	−1.12342
$686$	−49.6229	−1.89461
$687$	−14.2468	−0.543550
$688$	−64.5603	−2.46134
$689$	3.92238	0.149431
$690$	35.3102	1.34424
$691$	26.5626	1.01049	0.505244	−	0.862977i	$-0.331403\pi$
$691$	26.5626	1.01049	0.505244	+	0.862977i	$0.331403\pi$
$692$	−70.9455	−2.69694
$693$	11.8644	0.450692
$694$	24.2588	0.920850
$695$	−51.1923	−1.94184
$696$	−27.3385	−1.03626
$697$	−2.25718	−0.0854966
$698$	54.0837	2.04710
$699$	1.02376	0.0387222
$700$	−69.8630	−2.64057
$701$	−47.0319	−1.77637	−0.888185	−	0.459485i	$-0.848034\pi$
$701$	−47.0319	−1.77637	−0.888185	+	0.459485i	$0.848034\pi$
$702$	0.899001	0.0339306
$703$	−8.11682	−0.306132
$704$	22.1032	0.833048
$705$	−2.32360	−0.0875118
$706$	72.6774	2.73525
$707$	40.2624	1.51422
$708$	−9.44364	−0.354914
$709$	−17.0596	−0.640685	−0.320343	−	0.947302i	$-0.603798\pi$
$709$	−17.0596	−0.640685	−0.320343	+	0.947302i	$0.603798\pi$
$710$	−25.5246	−0.957919
$711$	−0.878179	−0.0329343
$712$	60.5938	2.27085
$713$	−10.7040	−0.400867
$714$	19.2114	0.718968
$715$	6.18850	0.231437
$716$	53.3258	1.99288
$717$	19.6098	0.732340
$718$	50.6455	1.89007
$719$	34.3709	1.28182	0.640908	−	0.767617i	$-0.278558\pi$
$719$	34.3709	1.28182	0.640908	+	0.767617i	$0.278558\pi$
$720$	−19.2682	−0.718084
$721$	−14.6184	−0.544419
$722$	35.3141	1.31425
$723$	1.09889	0.0408682
$724$	−61.4273	−2.28293
$725$	−33.5088	−1.24449
$726$	34.7271	1.28884
$727$	−31.5123	−1.16873	−0.584363	−	0.811492i	$-0.698656\pi$
$727$	−31.5123	−1.16873	−0.584363	+	0.811492i	$0.698656\pi$
$728$	4.81771	0.178556
$729$	1.00000	0.0370370
$730$	57.7150	2.13613
$731$	37.3474	1.38134
$732$	8.21273	0.303551
$733$	−7.48172	−0.276344	−0.138172	−	0.990408i	$-0.544123\pi$
$733$	−7.48172	−0.276344	−0.138172	+	0.990408i	$0.544123\pi$
$734$	−29.5427	−1.09044
$735$	−4.63719	−0.171045
$736$	11.0253	0.406399
$737$	−58.1172	−2.14078
$738$	−1.74734	−0.0643203
$739$	−1.60139	−0.0589079	−0.0294540	−	0.999566i	$-0.509377\pi$
$739$	−1.60139	−0.0589079	−0.0294540	+	0.999566i	$0.509377\pi$
$740$	−53.9362	−1.98273
$741$	0.794019	0.0291690
$742$	64.8872	2.38208
$743$	−2.97799	−0.109252	−0.0546259	−	0.998507i	$-0.517397\pi$
$743$	−2.97799	−0.109252	−0.0546259	+	0.998507i	$0.517397\pi$
$744$	14.7390	0.540359
$745$	−48.2388	−1.76733
$746$	−5.20878	−0.190707
$747$	−3.27937	−0.119986
$748$	68.5424	2.50616
$749$	−31.1157	−1.13694
$750$	−16.4511	−0.600709
$751$	15.0487	0.549134	0.274567	−	0.961568i	$-0.411465\pi$
$751$	15.0487	0.549134	0.274567	+	0.961568i	$0.411465\pi$
$752$	−3.76025	−0.137122
$753$	−18.2184	−0.663916
$754$	4.36173	0.158845
$755$	−25.4457	−0.926065
$756$	10.1155	0.367896
$757$	−48.7164	−1.77063	−0.885314	−	0.464995i	$-0.846056\pi$
$757$	−48.7164	−1.77063	−0.885314	+	0.464995i	$0.846056\pi$
$758$	−73.6049	−2.67345
$759$	−20.4146	−0.741002
$760$	−42.9433	−1.55772
$761$	13.3088	0.482442	0.241221	−	0.970470i	$-0.422452\pi$
$761$	13.3088	0.482442	0.241221	+	0.970470i	$0.422452\pi$
$762$	45.3748	1.64376
$763$	11.5165	0.416924
$764$	52.4416	1.89727
$765$	11.1465	0.403001
$766$	−46.1175	−1.66629
$767$	0.798210	0.0288217
$768$	32.3198	1.16624
$769$	0.824043	0.0297157	0.0148579	−	0.999890i	$-0.495270\pi$
$769$	0.824043	0.0297157	0.0148579	+	0.999890i	$0.495270\pi$
$770$	102.375	3.68934
$771$	−18.0247	−0.649144
$772$	−87.1115	−3.13521
$773$	−15.2493	−0.548480	−0.274240	−	0.961661i	$-0.588426\pi$
$773$	−15.2493	−0.548480	−0.274240	+	0.961661i	$0.588426\pi$
$774$	28.9116	1.03920
$775$	18.0656	0.648937
$776$	−4.98468	−0.178940
$777$	8.74016	0.313551
$778$	−29.7288	−1.06583
$779$	−1.54329	−0.0552941
$780$	5.27625	0.188920
$781$	14.7570	0.528047
$782$	−33.0561	−1.18208
$783$	4.85175	0.173388
$784$	−7.50430	−0.268011
$785$	27.7464	0.990311
$786$	23.7854	0.848398
$787$	−38.3307	−1.36634	−0.683170	−	0.730259i	$-0.739399\pi$
$787$	−38.3307	−1.36634	−0.683170	+	0.730259i	$0.739399\pi$
$788$	73.0200	2.60123
$789$	6.51631	0.231987
$790$	−7.57759	−0.269598
$791$	7.70932	0.274112
$792$	28.1102	0.998853
$793$	−0.694169	−0.0246507
$794$	−59.1679	−2.09979
$795$	37.6476	1.33522
$796$	−3.68862	−0.130740
$797$	1.46399	0.0518571	0.0259285	−	0.999664i	$-0.491746\pi$
$797$	1.46399	0.0518571	0.0259285	+	0.999664i	$0.491746\pi$
$798$	13.1353	0.464985
$799$	2.17527	0.0769554
$800$	−18.6080	−0.657892
$801$	−10.7536	−0.379958
$802$	14.4089	0.508797
$803$	−33.3679	−1.17753
$804$	−49.5501	−1.74750
$805$	−33.5819	−1.18361
$806$	−2.35154	−0.0828295
$807$	−10.9190	−0.384366
$808$	95.3931	3.35592
$809$	20.0872	0.706228	0.353114	−	0.935580i	$-0.385123\pi$
$809$	20.0872	0.706228	0.353114	+	0.935580i	$0.385123\pi$
$810$	8.62875	0.303183
$811$	2.64372	0.0928335	0.0464168	−	0.998922i	$-0.485220\pi$
$811$	2.64372	0.0928335	0.0464168	+	0.998922i	$0.485220\pi$
$812$	49.0778	1.72229
$813$	−5.37007	−0.188337
$814$	45.8461	1.60691
$815$	−4.43346	−0.155297
$816$	18.0382	0.631463
$817$	25.5354	0.893371
$818$	38.4932	1.34588
$819$	−0.854996	−0.0298760
$820$	−10.2551	−0.358125
$821$	−29.7265	−1.03746	−0.518731	−	0.854937i	$-0.673595\pi$
$821$	−29.7265	−1.03746	−0.518731	+	0.854937i	$0.673595\pi$
$822$	21.3083	0.743213
$823$	45.3901	1.58220	0.791101	−	0.611686i	$-0.209508\pi$
$823$	45.3901	1.58220	0.791101	+	0.611686i	$0.209508\pi$
$824$	−34.6352	−1.20658
$825$	34.4547	1.19956
$826$	13.2046	0.459448
$827$	−52.9840	−1.84243	−0.921217	−	0.389050i	$-0.872803\pi$
$827$	−52.9840	−1.84243	−0.921217	+	0.389050i	$0.872803\pi$
$828$	−17.4052	−0.604874
$829$	−9.14211	−0.317518	−0.158759	−	0.987317i	$-0.550749\pi$
$829$	−9.14211	−0.317518	−0.158759	+	0.987317i	$0.550749\pi$
$830$	−28.2968	−0.982198
$831$	−1.14993	−0.0398907
$832$	−1.59285	−0.0552220
$833$	4.34116	0.150412
$834$	37.0994	1.28465
$835$	40.5515	1.40334
$836$	46.8642	1.62083
$837$	−2.61573	−0.0904128
$838$	−11.9103	−0.411433
$839$	13.5817	0.468891	0.234446	−	0.972129i	$-0.424673\pi$
$839$	13.5817	0.468891	0.234446	+	0.972129i	$0.424673\pi$
$840$	46.2411	1.59547
$841$	−5.46049	−0.188293
$842$	−7.08964	−0.244325
$843$	−15.4000	−0.530403
$844$	−35.4303	−1.21956
$845$	44.4117	1.52781
$846$	1.68393	0.0578946
$847$	−33.0272	−1.13483
$848$	60.9247	2.09216
$849$	−14.7559	−0.506421
$850$	55.7905	1.91360
$851$	−15.0388	−0.515523
$852$	12.5816	0.431040
$853$	−43.2345	−1.48032	−0.740161	−	0.672430i	$-0.765251\pi$
$853$	−43.2345	−1.48032	−0.740161	+	0.672430i	$0.765251\pi$
$854$	−11.4835	−0.392957
$855$	7.62112	0.260637
$856$	−73.7219	−2.51976
$857$	−21.5246	−0.735266	−0.367633	−	0.929971i	$-0.619832\pi$
$857$	−21.5246	−0.735266	−0.367633	+	0.929971i	$0.619832\pi$
$858$	−4.48485	−0.153110
$859$	−47.1704	−1.60943	−0.804716	−	0.593660i	$-0.797682\pi$
$859$	−47.1704	−1.60943	−0.804716	+	0.593660i	$0.797682\pi$
$860$	169.682	5.78612
$861$	1.66181	0.0566342
$862$	12.0791	0.411416
$863$	−6.58173	−0.224045	−0.112022	−	0.993706i	$-0.535733\pi$
$863$	−6.58173	−0.224045	−0.112022	+	0.993706i	$0.535733\pi$
$864$	2.69425	0.0916604
$865$	57.5559	1.95696
$866$	−66.8421	−2.27139
$867$	6.56510	0.222962
$868$	−26.4593	−0.898088
$869$	4.38097	0.148614
$870$	41.8646	1.41934
$871$	4.18815	0.141910
$872$	27.2858	0.924014
$873$	0.884628	0.0299401
$874$	−22.6013	−0.764501
$875$	15.6458	0.528926
$876$	−28.4491	−0.961205
$877$	19.4200	0.655766	0.327883	−	0.944718i	$-0.393665\pi$
$877$	19.4200	0.655766	0.327883	+	0.944718i	$0.393665\pi$
$878$	88.8116	2.99725
$879$	−2.01358	−0.0679163
$880$	96.1234	3.24032
$881$	−37.6982	−1.27009	−0.635043	−	0.772477i	$-0.719017\pi$
$881$	−37.6982	−1.27009	−0.635043	+	0.772477i	$0.719017\pi$
$882$	3.36060	0.113157
$883$	−27.2481	−0.916970	−0.458485	−	0.888702i	$-0.651608\pi$
$883$	−27.2481	−0.916970	−0.458485	+	0.888702i	$0.651608\pi$
$884$	−4.93943	−0.166131
$885$	7.66134	0.257533
$886$	−85.9244	−2.88669
$887$	−33.0994	−1.11137	−0.555685	−	0.831393i	$-0.687544\pi$
$887$	−33.0994	−1.11137	−0.555685	+	0.831393i	$0.687544\pi$
$888$	20.7079	0.694912
$889$	−43.1538	−1.44733
$890$	−92.7897	−3.11032
$891$	−4.98870	−0.167128
$892$	41.2598	1.38148
$893$	1.48729	0.0497701
$894$	34.9589	1.16920
$895$	−43.2616	−1.44608
$896$	−39.1654	−1.30842
$897$	1.47115	0.0491204
$898$	66.3539	2.21426
$899$	−12.6909	−0.423264
$900$	29.3757	0.979190
$901$	−35.2443	−1.17416
$902$	8.71694	0.290242
$903$	−27.4964	−0.915023
$904$	18.2656	0.607504
$905$	49.8341	1.65654
$906$	18.4407	0.612651
$907$	33.5125	1.11276	0.556382	−	0.830926i	$-0.312189\pi$
$907$	33.5125	1.11276	0.556382	+	0.830926i	$0.312189\pi$
$908$	90.5570	3.00524
$909$	−16.9294	−0.561512
$910$	−7.37755	−0.244563
$911$	−30.7670	−1.01936	−0.509678	−	0.860365i	$-0.670235\pi$
$911$	−30.7670	−1.01936	−0.509678	+	0.860365i	$0.670235\pi$
$912$	12.3332	0.408392
$913$	16.3598	0.541430
$914$	−73.8950	−2.44423
$915$	−6.66274	−0.220263
$916$	60.5961	2.00215
$917$	−22.6212	−0.747016
$918$	−8.07791	−0.266611
$919$	−15.9526	−0.526229	−0.263114	−	0.964765i	$-0.584750\pi$
$919$	−15.9526	−0.526229	−0.263114	+	0.964765i	$0.584750\pi$
$920$	−79.5650	−2.62318
$921$	−3.74229	−0.123313
$922$	−42.2991	−1.39305
$923$	−1.06345	−0.0350037
$924$	−50.4631	−1.66011
$925$	25.3817	0.834545
$926$	−86.3322	−2.83705
$927$	6.14669	0.201884
$928$	13.0719	0.429105
$929$	−3.49501	−0.114668	−0.0573338	−	0.998355i	$-0.518260\pi$
$929$	−3.49501	−0.114668	−0.0573338	+	0.998355i	$0.518260\pi$
$930$	−22.5705	−0.740115
$931$	2.96816	0.0972776
$932$	−4.35438	−0.142632
$933$	21.9175	0.717547
$934$	−36.4672	−1.19324
$935$	−55.6064	−1.81852
$936$	−2.02573	−0.0662130
$937$	−22.4485	−0.733360	−0.366680	−	0.930347i	$-0.619506\pi$
$937$	−22.4485	−0.733360	−0.366680	+	0.930347i	$0.619506\pi$
$938$	69.2838	2.26220
$939$	23.1842	0.756588
$940$	9.88299	0.322348
$941$	20.5143	0.668748	0.334374	−	0.942440i	$-0.391475\pi$
$941$	20.5143	0.668748	0.334374	+	0.942440i	$0.391475\pi$
$942$	−20.1080	−0.655153
$943$	−2.85939	−0.0931147
$944$	12.3983	0.403529
$945$	−8.20639	−0.266954
$946$	−144.231	−4.68936
$947$	−18.9293	−0.615120	−0.307560	−	0.951529i	$-0.599513\pi$
$947$	−18.9293	−0.615120	−0.307560	+	0.951529i	$0.599513\pi$
$948$	3.73517	0.121313
$949$	2.40462	0.0780572
$950$	38.1454	1.23760
$951$	−10.5215	−0.341183
$952$	−43.2892	−1.40301
$953$	36.6529	1.18730	0.593652	−	0.804722i	$-0.297686\pi$
$953$	36.6529	1.18730	0.593652	+	0.804722i	$0.297686\pi$
$954$	−27.2835	−0.883335
$955$	−42.5443	−1.37670
$956$	−83.4064	−2.69756
$957$	−24.2040	−0.782403
$958$	7.64212	0.246906
$959$	−20.2653	−0.654401
$960$	−15.2884	−0.493430
$961$	−24.1580	−0.779289
$962$	−3.30385	−0.106520
$963$	13.0834	0.421606
$964$	−4.67393	−0.150537
$965$	70.6710	2.27498
$966$	24.3370	0.783030
$967$	52.6409	1.69282	0.846408	−	0.532535i	$-0.178760\pi$
$967$	52.6409	1.69282	0.846408	+	0.532535i	$0.178760\pi$
$968$	−78.2509	−2.51508
$969$	−7.13461	−0.229197
$970$	7.63324	0.245088
$971$	−22.5448	−0.723496	−0.361748	−	0.932276i	$-0.617820\pi$
$971$	−22.5448	−0.723496	−0.361748	+	0.932276i	$0.617820\pi$
$972$	−4.25331	−0.136425
$973$	−35.2835	−1.13114
$974$	−22.2126	−0.711737
$975$	−2.48294	−0.0795176
$976$	−10.7822	−0.345131
$977$	−10.0397	−0.321199	−0.160599	−	0.987020i	$-0.551343\pi$
$977$	−10.0397	−0.321199	−0.160599	+	0.987020i	$0.551343\pi$
$978$	3.21296	0.102739
$979$	53.6463	1.71454
$980$	19.7234	0.630041
$981$	−4.84240	−0.154606
$982$	31.2920	0.998568
$983$	29.7013	0.947326	0.473663	−	0.880706i	$-0.342932\pi$
$983$	29.7013	0.947326	0.473663	+	0.880706i	$0.342932\pi$
$984$	3.93729	0.125516
$985$	−59.2389	−1.88751
$986$	−39.1920	−1.24813
$987$	−1.60150	−0.0509764
$988$	−3.37721	−0.107443
$989$	47.3118	1.50443
$990$	−43.0463	−1.36810
$991$	10.8593	0.344959	0.172479	−	0.985013i	$-0.444822\pi$
$991$	10.8593	0.344959	0.172479	+	0.985013i	$0.444822\pi$
$992$	−7.04744	−0.223756
$993$	−13.2930	−0.421842
$994$	−17.5924	−0.557996
$995$	2.99247	0.0948677
$996$	13.9482	0.441965
$997$	−39.6172	−1.25469	−0.627344	−	0.778742i	$-0.715858\pi$
$997$	−39.6172	−1.25469	−0.627344	+	0.778742i	$0.715858\pi$
$998$	−38.7860	−1.22775
$999$	−3.67502	−0.116273

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8031.2.a.b.1.8	✓	102

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8031.2.a.b.1.8	✓	102	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:	\( N \)	\(=\)	\( 8031 = 3 \cdot 2677 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.50066 q^{2} -1.00000 q^{3} +4.25331 q^{4} -3.45059 q^{5} +2.50066 q^{6} -2.37826 q^{7} -5.63477 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.50066 q^{2} -1.00000 q^{3} +4.25331 q^{4} -3.45059 q^{5} +2.50066 q^{6} -2.37826 q^{7} -5.63477 q^{8} +1.00000 q^{9} +8.62875 q^{10} -4.98870 q^{11} -4.25331 q^{12} +0.359505 q^{13} +5.94722 q^{14} +3.45059 q^{15} +5.58404 q^{16} -3.23031 q^{17} -2.50066 q^{18} -2.20865 q^{19} -14.6764 q^{20} +2.37826 q^{21} +12.4751 q^{22} -4.09216 q^{23} +5.63477 q^{24} +6.90654 q^{25} -0.899001 q^{26} -1.00000 q^{27} -10.1155 q^{28} -4.85175 q^{29} -8.62875 q^{30} +2.61573 q^{31} -2.69425 q^{32} +4.98870 q^{33} +8.07791 q^{34} +8.20639 q^{35} +4.25331 q^{36} +3.67502 q^{37} +5.52308 q^{38} -0.359505 q^{39} +19.4433 q^{40} +0.698749 q^{41} -5.94722 q^{42} -11.5616 q^{43} -21.2185 q^{44} -3.45059 q^{45} +10.2331 q^{46} -0.673393 q^{47} -5.58404 q^{48} -1.34388 q^{49} -17.2709 q^{50} +3.23031 q^{51} +1.52909 q^{52} +10.9105 q^{53} +2.50066 q^{54} +17.2139 q^{55} +13.4010 q^{56} +2.20865 q^{57} +12.1326 q^{58} +2.22030 q^{59} +14.6764 q^{60} -1.93090 q^{61} -6.54105 q^{62} -2.37826 q^{63} -4.43066 q^{64} -1.24050 q^{65} -12.4751 q^{66} +11.6498 q^{67} -13.7395 q^{68} +4.09216 q^{69} -20.5214 q^{70} -2.95808 q^{71} -5.63477 q^{72} +6.68869 q^{73} -9.18999 q^{74} -6.90654 q^{75} -9.39406 q^{76} +11.8644 q^{77} +0.899001 q^{78} -0.878179 q^{79} -19.2682 q^{80} +1.00000 q^{81} -1.74734 q^{82} -3.27937 q^{83} +10.1155 q^{84} +11.1465 q^{85} +28.9116 q^{86} +4.85175 q^{87} +28.1102 q^{88} -10.7536 q^{89} +8.62875 q^{90} -0.854996 q^{91} -17.4052 q^{92} -2.61573 q^{93} +1.68393 q^{94} +7.62112 q^{95} +2.69425 q^{96} +0.884628 q^{97} +3.36060 q^{98} -4.98870 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 102 q - 6 q^{2} - 102 q^{3} + 96 q^{4} - 20 q^{5} + 6 q^{6} + 12 q^{7} - 21 q^{8} + 102 q^{9}+O(q^{10}) \) 102 * q - 6 * q^2 - 102 * q^3 + 96 * q^4 - 20 * q^5 + 6 * q^6 + 12 * q^7 - 21 * q^8 + 102 * q^9	\( 102 q - 6 q^{2} - 102 q^{3} + 96 q^{4} - 20 q^{5} + 6 q^{6} + 12 q^{7} - 21 q^{8} + 102 q^{9} - 16 q^{10} - 28 q^{11} - 96 q^{12} - 2 q^{13} - 41 q^{14} + 20 q^{15} + 88 q^{16} - 77 q^{17} - 6 q^{18} + 10 q^{19} - 50 q^{20} - 12 q^{21} + 24 q^{22} - 29 q^{23} + 21 q^{24} + 74 q^{25} - 45 q^{26} - 102 q^{27} + 19 q^{28} - 68 q^{29} + 16 q^{30} - 29 q^{31} - 48 q^{32} + 28 q^{33} - 19 q^{34} - 49 q^{35} + 96 q^{36} + 4 q^{37} - 44 q^{38} + 2 q^{39} - 41 q^{40} - 122 q^{41} + 41 q^{42} + 85 q^{43} - 86 q^{44} - 20 q^{45} - 28 q^{46} - 39 q^{47} - 88 q^{48} + 24 q^{49} - 37 q^{50} + 77 q^{51} + 8 q^{52} - 37 q^{53} + 6 q^{54} - 13 q^{55} - 130 q^{56} - 10 q^{57} + 17 q^{58} - 58 q^{59} + 50 q^{60} - 114 q^{61} - 64 q^{62} + 12 q^{63} + 47 q^{64} - 92 q^{65} - 24 q^{66} + 121 q^{67} - 138 q^{68} + 29 q^{69} - 2 q^{70} - 67 q^{71} - 21 q^{72} - 72 q^{73} - 111 q^{74} - 74 q^{75} - 17 q^{76} - 57 q^{77} + 45 q^{78} - 24 q^{79} - 97 q^{80} + 102 q^{81} - q^{82} - 78 q^{83} - 19 q^{84} - 24 q^{85} - 80 q^{86} + 68 q^{87} + 54 q^{88} - 176 q^{89} - 16 q^{90} - 3 q^{91} - 82 q^{92} + 29 q^{93} - 41 q^{94} - 90 q^{95} + 48 q^{96} - 77 q^{97} - 48 q^{98} - 28 q^{99}+O(q^{100}) \) 102 * q - 6 * q^2 - 102 * q^3 + 96 * q^4 - 20 * q^5 + 6 * q^6 + 12 * q^7 - 21 * q^8 + 102 * q^9 - 16 * q^10 - 28 * q^11 - 96 * q^12 - 2 * q^13 - 41 * q^14 + 20 * q^15 + 88 * q^16 - 77 * q^17 - 6 * q^18 + 10 * q^19 - 50 * q^20 - 12 * q^21 + 24 * q^22 - 29 * q^23 + 21 * q^24 + 74 * q^25 - 45 * q^26 - 102 * q^27 + 19 * q^28 - 68 * q^29 + 16 * q^30 - 29 * q^31 - 48 * q^32 + 28 * q^33 - 19 * q^34 - 49 * q^35 + 96 * q^36 + 4 * q^37 - 44 * q^38 + 2 * q^39 - 41 * q^40 - 122 * q^41 + 41 * q^42 + 85 * q^43 - 86 * q^44 - 20 * q^45 - 28 * q^46 - 39 * q^47 - 88 * q^48 + 24 * q^49 - 37 * q^50 + 77 * q^51 + 8 * q^52 - 37 * q^53 + 6 * q^54 - 13 * q^55 - 130 * q^56 - 10 * q^57 + 17 * q^58 - 58 * q^59 + 50 * q^60 - 114 * q^61 - 64 * q^62 + 12 * q^63 + 47 * q^64 - 92 * q^65 - 24 * q^66 + 121 * q^67 - 138 * q^68 + 29 * q^69 - 2 * q^70 - 67 * q^71 - 21 * q^72 - 72 * q^73 - 111 * q^74 - 74 * q^75 - 17 * q^76 - 57 * q^77 + 45 * q^78 - 24 * q^79 - 97 * q^80 + 102 * q^81 - q^82 - 78 * q^83 - 19 * q^84 - 24 * q^85 - 80 * q^86 + 68 * q^87 + 54 * q^88 - 176 * q^89 - 16 * q^90 - 3 * q^91 - 82 * q^92 + 29 * q^93 - 41 * q^94 - 90 * q^95 + 48 * q^96 - 77 * q^97 - 48 * q^98 - 28 * q^99

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