LMFDB - Embedded newform 87.2.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [87,2,Mod(1,87)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(87, 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("87.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 87 = 3 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	87.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:	$0.694698497585$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.229.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 4x - 1 $ x^3 - 4*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.254102$ of defining polynomial
Character	$\chi$	$=$	87.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.93543 q^{2} -1.00000 q^{3} +1.74590 q^{4} +0.508203 q^{5} +1.93543 q^{6} +3.68133 q^{7} +0.491797 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.93543 q^{2} -1.00000 q^{3} +1.74590 q^{4} +0.508203 q^{5} +1.93543 q^{6} +3.68133 q^{7} +0.491797 q^{8} +1.00000 q^{9} -0.983593 q^{10} -0.318669 q^{11} -1.74590 q^{12} +4.18953 q^{13} -7.12497 q^{14} -0.508203 q^{15} -4.44364 q^{16} +3.17313 q^{17} -1.93543 q^{18} -5.87086 q^{19} +0.887271 q^{20} -3.68133 q^{21} +0.616763 q^{22} +2.50820 q^{23} -0.491797 q^{24} -4.74173 q^{25} -8.10856 q^{26} -1.00000 q^{27} +6.42723 q^{28} +1.00000 q^{29} +0.983593 q^{30} +2.50820 q^{31} +7.61676 q^{32} +0.318669 q^{33} -6.14137 q^{34} +1.87086 q^{35} +1.74590 q^{36} +7.87086 q^{37} +11.3627 q^{38} -4.18953 q^{39} +0.249933 q^{40} +8.72532 q^{41} +7.12497 q^{42} -10.7253 q^{43} -0.556364 q^{44} +0.508203 q^{45} -4.85446 q^{46} -11.0440 q^{47} +4.44364 q^{48} +6.55220 q^{49} +9.17730 q^{50} -3.17313 q^{51} +7.31450 q^{52} -8.24993 q^{53} +1.93543 q^{54} -0.161949 q^{55} +1.81047 q^{56} +5.87086 q^{57} -1.93543 q^{58} -11.3627 q^{59} -0.887271 q^{60} -3.87086 q^{61} -4.85446 q^{62} +3.68133 q^{63} -5.85446 q^{64} +2.12914 q^{65} -0.616763 q^{66} +7.04399 q^{67} +5.53996 q^{68} -2.50820 q^{69} -3.62093 q^{70} +6.24993 q^{71} +0.491797 q^{72} -7.87086 q^{73} -15.2335 q^{74} +4.74173 q^{75} -10.2499 q^{76} -1.17313 q^{77} +8.10856 q^{78} -4.85446 q^{79} -2.25827 q^{80} +1.00000 q^{81} -16.8873 q^{82} -8.37907 q^{83} -6.42723 q^{84} +1.61259 q^{85} +20.7581 q^{86} -1.00000 q^{87} -0.156721 q^{88} -15.9313 q^{89} -0.983593 q^{90} +15.4231 q^{91} +4.37907 q^{92} -2.50820 q^{93} +21.3749 q^{94} -2.98359 q^{95} -7.61676 q^{96} +11.2335 q^{97} -12.6813 q^{98} -0.318669 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 2 q^{2} - 3 q^{3} + 6 q^{4} - 2 q^{6} + 4 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 2 * q^2 - 3 * q^3 + 6 * q^4 - 2 * q^6 + 4 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + 2 q^{2} - 3 q^{3} + 6 q^{4} - 2 q^{6} + 4 q^{7} + 3 q^{8} + 3 q^{9} - 6 q^{10} - 8 q^{11} - 6 q^{12} + 4 q^{13} - 5 q^{14} - 4 q^{16} + 4 q^{17} + 2 q^{18} - 2 q^{19} - 16 q^{20} - 4 q^{21} - 13 q^{22} + 6 q^{23} - 3 q^{24} + 17 q^{25} - 11 q^{26} - 3 q^{27} + 13 q^{28} + 3 q^{29} + 6 q^{30} + 6 q^{31} + 8 q^{32} + 8 q^{33} + q^{34} - 10 q^{35} + 6 q^{36} + 8 q^{37} + 20 q^{38} - 4 q^{39} - 32 q^{40} - 2 q^{41} + 5 q^{42} - 4 q^{43} - 11 q^{44} - 2 q^{46} - 12 q^{47} + 4 q^{48} - 3 q^{49} + 54 q^{50} - 4 q^{51} - 3 q^{52} + 8 q^{53} - 2 q^{54} - 10 q^{55} + 14 q^{56} + 2 q^{57} + 2 q^{58} - 20 q^{59} + 16 q^{60} + 4 q^{61} - 2 q^{62} + 4 q^{63} - 5 q^{64} + 22 q^{65} + 13 q^{66} + 29 q^{68} - 6 q^{69} - 28 q^{70} - 14 q^{71} + 3 q^{72} - 8 q^{73} - 16 q^{74} - 17 q^{75} + 2 q^{76} + 2 q^{77} + 11 q^{78} - 2 q^{79} - 38 q^{80} + 3 q^{81} - 32 q^{82} - 8 q^{83} - 13 q^{84} - 42 q^{85} + 28 q^{86} - 3 q^{87} + 2 q^{88} - 8 q^{89} - 6 q^{90} + 8 q^{91} - 4 q^{92} - 6 q^{93} + 15 q^{94} - 12 q^{95} - 8 q^{96} + 4 q^{97} - 31 q^{98} - 8 q^{99}+O(q^{100}) \) 3 * q + 2 * q^2 - 3 * q^3 + 6 * q^4 - 2 * q^6 + 4 * q^7 + 3 * q^8 + 3 * q^9 - 6 * q^10 - 8 * q^11 - 6 * q^12 + 4 * q^13 - 5 * q^14 - 4 * q^16 + 4 * q^17 + 2 * q^18 - 2 * q^19 - 16 * q^20 - 4 * q^21 - 13 * q^22 + 6 * q^23 - 3 * q^24 + 17 * q^25 - 11 * q^26 - 3 * q^27 + 13 * q^28 + 3 * q^29 + 6 * q^30 + 6 * q^31 + 8 * q^32 + 8 * q^33 + q^34 - 10 * q^35 + 6 * q^36 + 8 * q^37 + 20 * q^38 - 4 * q^39 - 32 * q^40 - 2 * q^41 + 5 * q^42 - 4 * q^43 - 11 * q^44 - 2 * q^46 - 12 * q^47 + 4 * q^48 - 3 * q^49 + 54 * q^50 - 4 * q^51 - 3 * q^52 + 8 * q^53 - 2 * q^54 - 10 * q^55 + 14 * q^56 + 2 * q^57 + 2 * q^58 - 20 * q^59 + 16 * q^60 + 4 * q^61 - 2 * q^62 + 4 * q^63 - 5 * q^64 + 22 * q^65 + 13 * q^66 + 29 * q^68 - 6 * q^69 - 28 * q^70 - 14 * q^71 + 3 * q^72 - 8 * q^73 - 16 * q^74 - 17 * q^75 + 2 * q^76 + 2 * q^77 + 11 * q^78 - 2 * q^79 - 38 * q^80 + 3 * q^81 - 32 * q^82 - 8 * q^83 - 13 * q^84 - 42 * q^85 + 28 * q^86 - 3 * q^87 + 2 * q^88 - 8 * q^89 - 6 * q^90 + 8 * q^91 - 4 * q^92 - 6 * q^93 + 15 * q^94 - 12 * q^95 - 8 * q^96 + 4 * q^97 - 31 * q^98 - 8 * 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 $

$2$	−1.93543	−1.36856	−0.684279	−	0.729221i	$-0.739883\pi$
$2$	−1.93543	−1.36856	−0.684279	+	0.729221i	$0.739883\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.74590	0.872949
$5$	0.508203	0.227275	0.113638	−	0.993522i	$-0.463750\pi$
$5$	0.508203	0.227275	0.113638	+	0.993522i	$0.463750\pi$
$6$	1.93543	0.790137
$7$	3.68133	1.39141	0.695706	−	0.718327i	$-0.255092\pi$
$7$	3.68133	1.39141	0.695706	+	0.718327i	$0.255092\pi$
$8$	0.491797	0.173876
$9$	1.00000	0.333333
$10$	−0.983593	−0.311039
$11$	−0.318669	−0.0960824	−0.0480412	−	0.998845i	$-0.515298\pi$
$11$	−0.318669	−0.0960824	−0.0480412	+	0.998845i	$0.515298\pi$
$12$	−1.74590	−0.503997
$13$	4.18953	1.16197	0.580984	−	0.813915i	$-0.302668\pi$
$13$	4.18953	1.16197	0.580984	+	0.813915i	$0.302668\pi$
$14$	−7.12497	−1.90423
$15$	−0.508203	−0.131218
$16$	−4.44364	−1.11091
$17$	3.17313	0.769596	0.384798	−	0.923001i	$-0.374271\pi$
$17$	3.17313	0.769596	0.384798	+	0.923001i	$0.374271\pi$
$18$	−1.93543	−0.456186
$19$	−5.87086	−1.34687	−0.673434	−	0.739247i	$-0.735182\pi$
$19$	−5.87086	−1.34687	−0.673434	+	0.739247i	$0.735182\pi$
$20$	0.887271	0.198400
$21$	−3.68133	−0.803332
$22$	0.616763	0.131494
$23$	2.50820	0.522997	0.261498	−	0.965204i	$-0.415783\pi$
$23$	2.50820	0.522997	0.261498	+	0.965204i	$0.415783\pi$
$24$	−0.491797	−0.100388
$25$	−4.74173	−0.948346
$26$	−8.10856	−1.59022
$27$	−1.00000	−0.192450
$28$	6.42723	1.21463
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	0.983593	0.179579
$31$	2.50820	0.450487	0.225243	−	0.974303i	$-0.427682\pi$
$31$	2.50820	0.450487	0.225243	+	0.974303i	$0.427682\pi$
$32$	7.61676	1.34647
$33$	0.318669	0.0554732
$34$	−6.14137	−1.05324
$35$	1.87086	0.316234
$36$	1.74590	0.290983
$37$	7.87086	1.29396	0.646981	−	0.762506i	$-0.276031\pi$
$37$	7.87086	1.29396	0.646981	+	0.762506i	$0.276031\pi$
$38$	11.3627	1.84327
$39$	−4.18953	−0.670862
$40$	0.249933	0.0395178
$41$	8.72532	1.36267	0.681333	−	0.731973i	$-0.261400\pi$
$41$	8.72532	1.36267	0.681333	+	0.731973i	$0.261400\pi$
$42$	7.12497	1.09941
$43$	−10.7253	−1.63560	−0.817798	−	0.575505i	$-0.804805\pi$
$43$	−10.7253	−1.63560	−0.817798	+	0.575505i	$0.804805\pi$
$44$	−0.556364	−0.0838751
$45$	0.508203	0.0757585
$46$	−4.85446	−0.715751
$47$	−11.0440	−1.61093	−0.805466	−	0.592642i	$-0.798085\pi$
$47$	−11.0440	−1.61093	−0.805466	+	0.592642i	$0.798085\pi$
$48$	4.44364	0.641384
$49$	6.55220	0.936028
$50$	9.17730	1.29787
$51$	−3.17313	−0.444327
$52$	7.31450	1.01434
$53$	−8.24993	−1.13322	−0.566608	−	0.823988i	$-0.691744\pi$
$53$	−8.24993	−1.13322	−0.566608	+	0.823988i	$0.691744\pi$
$54$	1.93543	0.263379
$55$	−0.161949	−0.0218372
$56$	1.81047	0.241934
$57$	5.87086	0.777615
$58$	−1.93543	−0.254135
$59$	−11.3627	−1.47929	−0.739646	−	0.672996i	$-0.765007\pi$
$59$	−11.3627	−1.47929	−0.739646	+	0.672996i	$0.765007\pi$
$60$	−0.887271	−0.114546
$61$	−3.87086	−0.495613	−0.247807	−	0.968809i	$-0.579710\pi$
$61$	−3.87086	−0.495613	−0.247807	+	0.968809i	$0.579710\pi$
$62$	−4.85446	−0.616517
$63$	3.68133	0.463804
$64$	−5.85446	−0.731807
$65$	2.12914	0.264087
$66$	−0.616763	−0.0759183
$67$	7.04399	0.860561	0.430280	−	0.902695i	$-0.358415\pi$
$67$	7.04399	0.860561	0.430280	+	0.902695i	$0.358415\pi$
$68$	5.53996	0.671819
$69$	−2.50820	−0.301952
$70$	−3.62093	−0.432784
$71$	6.24993	0.741731	0.370865	−	0.928687i	$-0.379061\pi$
$71$	6.24993	0.741731	0.370865	+	0.928687i	$0.379061\pi$
$72$	0.491797	0.0579588
$73$	−7.87086	−0.921215	−0.460608	−	0.887604i	$-0.652368\pi$
$73$	−7.87086	−0.921215	−0.460608	+	0.887604i	$0.652368\pi$
$74$	−15.2335	−1.77086
$75$	4.74173	0.547528
$76$	−10.2499	−1.17575
$77$	−1.17313	−0.133690
$78$	8.10856	0.918114
$79$	−4.85446	−0.546169	−0.273085	−	0.961990i	$-0.588044\pi$
$79$	−4.85446	−0.546169	−0.273085	+	0.961990i	$0.588044\pi$
$80$	−2.25827	−0.252482
$81$	1.00000	0.111111
$82$	−16.8873	−1.86489
$83$	−8.37907	−0.919722	−0.459861	−	0.887991i	$-0.652101\pi$
$83$	−8.37907	−0.919722	−0.459861	+	0.887991i	$0.652101\pi$
$84$	−6.42723	−0.701268
$85$	1.61259	0.174910
$86$	20.7581	2.23841
$87$	−1.00000	−0.107211
$88$	−0.156721	−0.0167065
$89$	−15.9313	−1.68871	−0.844355	−	0.535784i	$-0.820016\pi$
$89$	−15.9313	−1.68871	−0.844355	+	0.535784i	$0.820016\pi$
$90$	−0.983593	−0.103680
$91$	15.4231	1.61678
$92$	4.37907	0.456549
$93$	−2.50820	−0.260089
$94$	21.3749	2.20465
$95$	−2.98359	−0.306110
$96$	−7.61676	−0.777383
$97$	11.2335	1.14059	0.570296	−	0.821439i	$-0.306829\pi$
$97$	11.2335	1.14059	0.570296	+	0.821439i	$0.306829\pi$
$98$	−12.6813	−1.28101
$99$	−0.318669	−0.0320275
$100$	−8.27858	−0.827858
$101$	10.9149	1.08607	0.543034	−	0.839710i	$-0.317275\pi$
$101$	10.9149	1.08607	0.543034	+	0.839710i	$0.317275\pi$
$102$	6.14137	0.608087
$103$	8.00000	0.788263	0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000	0.788263	0.394132	+	0.919054i	$0.371045\pi$
$104$	2.06040	0.202039
$105$	−1.87086	−0.182578
$106$	15.9672	1.55087
$107$	3.83805	0.371038	0.185519	−	0.982641i	$-0.440603\pi$
$107$	3.83805	0.371038	0.185519	+	0.982641i	$0.440603\pi$
$108$	−1.74590	−0.167999
$109$	−8.18953	−0.784415	−0.392208	−	0.919877i	$-0.628288\pi$
$109$	−8.18953	−0.784415	−0.392208	+	0.919877i	$0.628288\pi$
$110$	0.313441	0.0298854
$111$	−7.87086	−0.747069
$112$	−16.3585	−1.54573
$113$	13.2059	1.24231	0.621155	−	0.783688i	$-0.286664\pi$
$113$	13.2059	1.24231	0.621155	+	0.783688i	$0.286664\pi$
$114$	−11.3627	−1.06421
$115$	1.27468	0.118864
$116$	1.74590	0.162103
$117$	4.18953	0.387323
$118$	21.9917	2.02450
$119$	11.6813	1.07083
$120$	−0.249933	−0.0228156
$121$	−10.8984	−0.990768
$122$	7.49180	0.678275
$123$	−8.72532	−0.786736
$124$	4.37907	0.393252
$125$	−4.95078	−0.442811
$126$	−7.12497	−0.634742
$127$	9.39547	0.833714	0.416857	−	0.908972i	$-0.363132\pi$
$127$	9.39547	0.833714	0.416857	+	0.908972i	$0.363132\pi$
$128$	−3.90262	−0.344946
$129$	10.7253	0.944312
$130$	−4.12080	−0.361418
$131$	−17.0768	−1.49201	−0.746004	−	0.665942i	$-0.768030\pi$
$131$	−17.0768	−1.49201	−0.746004	+	0.665942i	$0.768030\pi$
$132$	0.556364	0.0484253
$133$	−21.6126	−1.87405
$134$	−13.6332	−1.17773
$135$	−0.508203	−0.0437392
$136$	1.56053	0.133815
$137$	15.0164	1.28294	0.641469	−	0.767149i	$-0.278325\pi$
$137$	15.0164	1.28294	0.641469	+	0.767149i	$0.278325\pi$
$138$	4.85446	0.413239
$139$	7.68133	0.651522	0.325761	−	0.945452i	$-0.394380\pi$
$139$	7.68133	0.651522	0.325761	+	0.945452i	$0.394380\pi$
$140$	3.26634	0.276056
$141$	11.0440	0.930072
$142$	−12.0963	−1.01510
$143$	−1.33508	−0.111645
$144$	−4.44364	−0.370303
$145$	0.508203	0.0422040
$146$	15.2335	1.26074
$147$	−6.55220	−0.540416
$148$	13.7417	1.12956
$149$	−11.3955	−0.933554	−0.466777	−	0.884375i	$-0.654585\pi$
$149$	−11.3955	−0.933554	−0.466777	+	0.884375i	$0.654585\pi$
$150$	−9.17730	−0.749323
$151$	−2.03281	−0.165428	−0.0827140	−	0.996573i	$-0.526359\pi$
$151$	−2.03281	−0.165428	−0.0827140	+	0.996573i	$0.526359\pi$
$152$	−2.88727	−0.234189
$153$	3.17313	0.256532
$154$	2.27051	0.182963
$155$	1.27468	0.102385
$156$	−7.31450	−0.585629
$157$	−10.7581	−0.858593	−0.429296	−	0.903164i	$-0.641238\pi$
$157$	−10.7581	−0.858593	−0.429296	+	0.903164i	$0.641238\pi$
$158$	9.39547	0.747464
$159$	8.24993	0.654262
$160$	3.87086	0.306019
$161$	9.23353	0.727704
$162$	−1.93543	−0.152062
$163$	21.8297	1.70984	0.854918	−	0.518764i	$-0.173608\pi$
$163$	21.8297	1.70984	0.854918	+	0.518764i	$0.173608\pi$
$164$	15.2335	1.18954
$165$	0.161949	0.0126077
$166$	16.2171	1.25869
$167$	−20.4999	−1.58633	−0.793164	−	0.609009i	$-0.791567\pi$
$167$	−20.4999	−1.58633	−0.793164	+	0.609009i	$0.791567\pi$
$168$	−1.81047	−0.139680
$169$	4.55220	0.350169
$170$	−3.12107	−0.239375
$171$	−5.87086	−0.448956
$172$	−18.7253	−1.42779
$173$	1.62093	0.123237	0.0616186	−	0.998100i	$-0.480374\pi$
$173$	1.62093	0.123237	0.0616186	+	0.998100i	$0.480374\pi$
$174$	1.93543	0.146725
$175$	−17.4559	−1.31954
$176$	1.41605	0.106739
$177$	11.3627	0.854070
$178$	30.8339	2.31110
$179$	4.47539	0.334506	0.167253	−	0.985914i	$-0.446510\pi$
$179$	4.47539	0.334506	0.167253	+	0.985914i	$0.446510\pi$
$180$	0.887271	0.0661333
$181$	1.20594	0.0896369	0.0448184	−	0.998995i	$-0.485729\pi$
$181$	1.20594	0.0896369	0.0448184	+	0.998995i	$0.485729\pi$
$182$	−29.8503	−2.21265
$183$	3.87086	0.286143
$184$	1.23353	0.0909367
$185$	4.00000	0.294086
$186$	4.85446	0.355946
$187$	−1.01118	−0.0739447
$188$	−19.2817	−1.40626
$189$	−3.68133	−0.267777
$190$	5.77454	0.418929
$191$	0.758136	0.0548568	0.0274284	−	0.999624i	$-0.491268\pi$
$191$	0.758136	0.0548568	0.0274284	+	0.999624i	$0.491268\pi$
$192$	5.85446	0.422509
$193$	−16.4671	−1.18532	−0.592662	−	0.805451i	$-0.701923\pi$
$193$	−16.4671	−1.18532	−0.592662	+	0.805451i	$0.701923\pi$
$194$	−21.7417	−1.56097
$195$	−2.12914	−0.152471
$196$	11.4395	0.817105
$197$	−17.9588	−1.27951	−0.639757	−	0.768577i	$-0.720965\pi$
$197$	−17.9588	−1.27951	−0.639757	+	0.768577i	$0.720965\pi$
$198$	0.616763	0.0438314
$199$	1.33508	0.0946410	0.0473205	−	0.998880i	$-0.484932\pi$
$199$	1.33508	0.0946410	0.0473205	+	0.998880i	$0.484932\pi$
$200$	−2.33197	−0.164895
$201$	−7.04399	−0.496845
$202$	−21.1250	−1.48635
$203$	3.68133	0.258379
$204$	−5.53996	−0.387875
$205$	4.43424	0.309701
$206$	−15.4835	−1.07878
$207$	2.50820	0.174332
$208$	−18.6168	−1.29084
$209$	1.87086	0.129410
$210$	3.62093	0.249868
$211$	8.37907	0.576839	0.288419	−	0.957504i	$-0.406870\pi$
$211$	8.37907	0.576839	0.288419	+	0.957504i	$0.406870\pi$
$212$	−14.4035	−0.989239
$213$	−6.24993	−0.428238
$214$	−7.42829	−0.507787
$215$	−5.45065	−0.371731
$216$	−0.491797	−0.0334625
$217$	9.23353	0.626813
$218$	15.8503	1.07352
$219$	7.87086	0.531864
$220$	−0.282746	−0.0190627
$221$	13.2939	0.894246
$222$	15.2335	1.02241
$223$	−6.66492	−0.446316	−0.223158	−	0.974782i	$-0.571637\pi$
$223$	−6.66492	−0.446316	−0.223158	+	0.974782i	$0.571637\pi$
$224$	28.0398	1.87349
$225$	−4.74173	−0.316115
$226$	−25.5592	−1.70017
$227$	0.379068	0.0251596	0.0125798	−	0.999921i	$-0.495996\pi$
$227$	0.379068	0.0251596	0.0125798	+	0.999921i	$0.495996\pi$
$228$	10.2499	0.678818
$229$	9.26634	0.612337	0.306168	−	0.951977i	$-0.400953\pi$
$229$	9.26634	0.612337	0.306168	+	0.951977i	$0.400953\pi$
$230$	−2.46705	−0.162673
$231$	1.17313	0.0771861
$232$	0.491797	0.0322880
$233$	13.7417	0.900251	0.450125	−	0.892965i	$-0.351379\pi$
$233$	13.7417	0.900251	0.450125	+	0.892965i	$0.351379\pi$
$234$	−8.10856	−0.530073
$235$	−5.61259	−0.366125
$236$	−19.8381	−1.29135
$237$	4.85446	0.315331
$238$	−22.6084	−1.46549
$239$	17.8709	1.15597	0.577985	−	0.816047i	$-0.303839\pi$
$239$	17.8709	1.15597	0.577985	+	0.816047i	$0.303839\pi$
$240$	2.25827	0.145771
$241$	−14.2223	−0.916142	−0.458071	−	0.888916i	$-0.651459\pi$
$241$	−14.2223	−0.916142	−0.458071	+	0.888916i	$0.651459\pi$
$242$	21.0932	1.35592
$243$	−1.00000	−0.0641500
$244$	−6.75814	−0.432645
$245$	3.32985	0.212736
$246$	16.8873	1.07669
$247$	−24.5962	−1.56502
$248$	1.23353	0.0783290
$249$	8.37907	0.531002
$250$	9.58190	0.606013
$251$	8.43947	0.532694	0.266347	−	0.963877i	$-0.414183\pi$
$251$	8.43947	0.532694	0.266347	+	0.963877i	$0.414183\pi$
$252$	6.42723	0.404877
$253$	−0.799288	−0.0502508
$254$	−18.1843	−1.14098
$255$	−1.61259	−0.100985
$256$	19.2622	1.20389
$257$	25.3627	1.58208	0.791040	−	0.611765i	$-0.209540\pi$
$257$	25.3627	1.58208	0.791040	+	0.611765i	$0.209540\pi$
$258$	−20.7581	−1.29235
$259$	28.9753	1.80043
$260$	3.71725	0.230534
$261$	1.00000	0.0618984
$262$	33.0510	2.04190
$263$	23.4835	1.44805	0.724026	−	0.689773i	$-0.242290\pi$
$263$	23.4835	1.44805	0.724026	+	0.689773i	$0.242290\pi$
$264$	0.156721	0.00964548
$265$	−4.19264	−0.257552
$266$	41.8297	2.56474
$267$	15.9313	0.974977
$268$	12.2981	0.751226
$269$	−2.10155	−0.128134	−0.0640669	−	0.997946i	$-0.520407\pi$
$269$	−2.10155	−0.128134	−0.0640669	+	0.997946i	$0.520407\pi$
$270$	0.983593	0.0598596
$271$	3.10439	0.188578	0.0942892	−	0.995545i	$-0.469942\pi$
$271$	3.10439	0.188578	0.0942892	+	0.995545i	$0.469942\pi$
$272$	−14.1002	−0.854952
$273$	−15.4231	−0.933446
$274$	−29.0632	−1.75577
$275$	1.51104	0.0911194
$276$	−4.37907	−0.263589
$277$	−13.9641	−0.839020	−0.419510	−	0.907751i	$-0.637798\pi$
$277$	−13.9641	−0.839020	−0.419510	+	0.907751i	$0.637798\pi$
$278$	−14.8667	−0.891645
$279$	2.50820	0.150162
$280$	0.920085	0.0549856
$281$	−14.4342	−0.861074	−0.430537	−	0.902573i	$-0.641676\pi$
$281$	−14.4342	−0.861074	−0.430537	+	0.902573i	$0.641676\pi$
$282$	−21.3749	−1.27286
$283$	8.25827	0.490903	0.245452	−	0.969409i	$-0.421064\pi$
$283$	8.25827	0.490903	0.245452	+	0.969409i	$0.421064\pi$
$284$	10.9117	0.647493
$285$	2.98359	0.176733
$286$	2.58395	0.152792
$287$	32.1208	1.89603
$288$	7.61676	0.448822
$289$	−6.93126	−0.407721
$290$	−0.983593	−0.0577586
$291$	−11.2335	−0.658521
$292$	−13.7417	−0.804174
$293$	−12.4478	−0.727209	−0.363604	−	0.931554i	$-0.618454\pi$
$293$	−12.4478	−0.727209	−0.363604	+	0.931554i	$0.618454\pi$
$294$	12.6813	0.739590
$295$	−5.77454	−0.336207
$296$	3.87086	0.224989
$297$	0.318669	0.0184911
$298$	22.0552	1.27762
$299$	10.5082	0.607705
$300$	8.27858	0.477964
$301$	−39.4835	−2.27579
$302$	3.93437	0.226398
$303$	−10.9149	−0.627042
$304$	26.0880	1.49625
$305$	−1.96719	−0.112641
$306$	−6.14137	−0.351079
$307$	−21.9917	−1.25513	−0.627565	−	0.778564i	$-0.715948\pi$
$307$	−21.9917	−1.25513	−0.627565	+	0.778564i	$0.715948\pi$
$308$	−2.04816	−0.116705
$309$	−8.00000	−0.455104
$310$	−2.46705	−0.140119
$311$	−19.0440	−1.07989	−0.539943	−	0.841702i	$-0.681554\pi$
$311$	−19.0440	−1.07989	−0.539943	+	0.841702i	$0.681554\pi$
$312$	−2.06040	−0.116647
$313$	9.89845	0.559493	0.279747	−	0.960074i	$-0.409750\pi$
$313$	9.89845	0.559493	0.279747	+	0.960074i	$0.409750\pi$
$314$	20.8216	1.17503
$315$	1.87086	0.105411
$316$	−8.47539	−0.476778
$317$	0.568602	0.0319359	0.0159679	−	0.999873i	$-0.494917\pi$
$317$	0.568602	0.0319359	0.0159679	+	0.999873i	$0.494917\pi$
$318$	−15.9672	−0.895395
$319$	−0.318669	−0.0178421
$320$	−2.97526	−0.166322
$321$	−3.83805	−0.214219
$322$	−17.8709	−0.995904
$323$	−18.6290	−1.03655
$324$	1.74590	0.0969944
$325$	−19.8656	−1.10195
$326$	−42.2499	−2.34001
$327$	8.18953	0.452882
$328$	4.29108	0.236935
$329$	−40.6566	−2.24147
$330$	−0.313441	−0.0172544
$331$	1.17836	0.0647683	0.0323841	−	0.999475i	$-0.489690\pi$
$331$	1.17836	0.0647683	0.0323841	+	0.999475i	$0.489690\pi$
$332$	−14.6290	−0.802871
$333$	7.87086	0.431321
$334$	39.6761	2.17098
$335$	3.57978	0.195584
$336$	16.3585	0.892429
$337$	17.2007	0.936983	0.468491	−	0.883468i	$-0.344798\pi$
$337$	17.2007	0.936983	0.468491	+	0.883468i	$0.344798\pi$
$338$	−8.81047	−0.479226
$339$	−13.2059	−0.717248
$340$	2.81543	0.152688
$341$	−0.799288	−0.0432838
$342$	11.3627	0.614422
$343$	−1.64852	−0.0890116
$344$	−5.27468	−0.284392
$345$	−1.27468	−0.0686263
$346$	−3.13720	−0.168657
$347$	15.2663	0.819540	0.409770	−	0.912189i	$-0.365609\pi$
$347$	15.2663	0.819540	0.409770	+	0.912189i	$0.365609\pi$
$348$	−1.74590	−0.0935900
$349$	−27.7089	−1.48322	−0.741612	−	0.670829i	$-0.765938\pi$
$349$	−27.7089	−1.48322	−0.741612	+	0.670829i	$0.765938\pi$
$350$	33.7847	1.80587
$351$	−4.18953	−0.223621
$352$	−2.42723	−0.129372
$353$	2.79929	0.148991	0.0744955	−	0.997221i	$-0.476265\pi$
$353$	2.79929	0.148991	0.0744955	+	0.997221i	$0.476265\pi$
$354$	−21.9917	−1.16884
$355$	3.17624	0.168577
$356$	−27.8144	−1.47416
$357$	−11.6813	−0.618242
$358$	−8.66181	−0.457791
$359$	12.2583	0.646967	0.323483	−	0.946234i	$-0.395146\pi$
$359$	12.2583	0.646967	0.323483	+	0.946234i	$0.395146\pi$
$360$	0.249933	0.0131726
$361$	15.4671	0.814055
$362$	−2.33402	−0.122673
$363$	10.8984	0.572020
$364$	26.9271	1.41136
$365$	−4.00000	−0.209370
$366$	−7.49180	−0.391602
$367$	−4.25827	−0.222280	−0.111140	−	0.993805i	$-0.535450\pi$
$367$	−4.25827	−0.222280	−0.111140	+	0.993805i	$0.535450\pi$
$368$	−11.1455	−0.581002
$369$	8.72532	0.454222
$370$	−7.74173	−0.402473
$371$	−30.3707	−1.57677
$372$	−4.37907	−0.227044
$373$	25.7417	1.33286	0.666428	−	0.745569i	$-0.267822\pi$
$373$	25.7417	1.33286	0.666428	+	0.745569i	$0.267822\pi$
$374$	1.95707	0.101198
$375$	4.95078	0.255657
$376$	−5.43140	−0.280103
$377$	4.18953	0.215772
$378$	7.12497	0.366469
$379$	19.6454	1.00912	0.504558	−	0.863378i	$-0.331655\pi$
$379$	19.6454	1.00912	0.504558	+	0.863378i	$0.331655\pi$
$380$	−5.20905	−0.267219
$381$	−9.39547	−0.481345
$382$	−1.46732	−0.0750747
$383$	−22.5634	−1.15293	−0.576467	−	0.817120i	$-0.695569\pi$
$383$	−22.5634	−1.15293	−0.576467	+	0.817120i	$0.695569\pi$
$384$	3.90262	0.199155
$385$	−0.596187	−0.0303845
$386$	31.8709	1.62218
$387$	−10.7253	−0.545199
$388$	19.6126	0.995679
$389$	15.8105	0.801622	0.400811	−	0.916161i	$-0.368728\pi$
$389$	15.8105	0.801622	0.400811	+	0.916161i	$0.368728\pi$
$390$	4.12080	0.208665
$391$	7.95885	0.402496
$392$	3.22235	0.162753
$393$	17.0768	0.861411
$394$	34.7581	1.75109
$395$	−2.46705	−0.124131
$396$	−0.556364	−0.0279584
$397$	−3.27468	−0.164351	−0.0821757	−	0.996618i	$-0.526187\pi$
$397$	−3.27468	−0.164351	−0.0821757	+	0.996618i	$0.526187\pi$
$398$	−2.58395	−0.129522
$399$	21.6126	1.08198
$400$	21.0705	1.05353
$401$	2.47539	0.123615	0.0618075	−	0.998088i	$-0.480314\pi$
$401$	2.47539	0.123615	0.0618075	+	0.998088i	$0.480314\pi$
$402$	13.6332	0.679961
$403$	10.5082	0.523451
$404$	19.0562	0.948083
$405$	0.508203	0.0252528
$406$	−7.12497	−0.353606
$407$	−2.50820	−0.124327
$408$	−1.56053	−0.0772579
$409$	15.0164	0.742514	0.371257	−	0.928530i	$-0.378927\pi$
$409$	15.0164	0.742514	0.371257	+	0.928530i	$0.378927\pi$
$410$	−8.58217	−0.423843
$411$	−15.0164	−0.740705
$412$	13.9672	0.688114
$413$	−41.8297	−2.05831
$414$	−4.85446	−0.238584
$415$	−4.25827	−0.209030
$416$	31.9107	1.56455
$417$	−7.68133	−0.376156
$418$	−3.62093	−0.177106
$419$	−13.8709	−0.677636	−0.338818	−	0.940852i	$-0.610027\pi$
$419$	−13.8709	−0.677636	−0.338818	+	0.940852i	$0.610027\pi$
$420$	−3.26634	−0.159381
$421$	−7.45065	−0.363122	−0.181561	−	0.983380i	$-0.558115\pi$
$421$	−7.45065	−0.363122	−0.181561	+	0.983380i	$0.558115\pi$
$422$	−16.2171	−0.789437
$423$	−11.0440	−0.536977
$424$	−4.05729	−0.197039
$425$	−15.0461	−0.729844
$426$	12.0963	0.586069
$427$	−14.2499	−0.689603
$428$	6.70085	0.323898
$429$	1.33508	0.0644581
$430$	10.5494	0.508735
$431$	14.7253	0.709294	0.354647	−	0.935000i	$-0.384601\pi$
$431$	14.7253	0.709294	0.354647	+	0.935000i	$0.384601\pi$
$432$	4.44364	0.213795
$433$	1.52461	0.0732681	0.0366340	−	0.999329i	$-0.488336\pi$
$433$	1.52461	0.0732681	0.0366340	+	0.999329i	$0.488336\pi$
$434$	−17.8709	−0.857829
$435$	−0.508203	−0.0243665
$436$	−14.2981	−0.684754
$437$	−14.7253	−0.704408
$438$	−15.2335	−0.727886
$439$	23.3023	1.11216	0.556078	−	0.831130i	$-0.312306\pi$
$439$	23.3023	1.11216	0.556078	+	0.831130i	$0.312306\pi$
$440$	−0.0796459	−0.00379697
$441$	6.55220	0.312009
$442$	−25.7295	−1.22383
$443$	23.0440	1.09485	0.547427	−	0.836854i	$-0.315608\pi$
$443$	23.0440	1.09485	0.547427	+	0.836854i	$0.315608\pi$
$444$	−13.7417	−0.652154
$445$	−8.09632	−0.383802
$446$	12.8995	0.610809
$447$	11.3955	0.538987
$448$	−21.5522	−1.01825
$449$	−6.53579	−0.308443	−0.154221	−	0.988036i	$-0.549287\pi$
$449$	−6.53579	−0.308443	−0.154221	+	0.988036i	$0.549287\pi$
$450$	9.17730	0.432622
$451$	−2.78049	−0.130928
$452$	23.0562	1.08447
$453$	2.03281	0.0955099
$454$	−0.733661	−0.0344324
$455$	7.83805	0.367454
$456$	2.88727	0.135209
$457$	10.2223	0.478181	0.239091	−	0.970997i	$-0.423151\pi$
$457$	10.2223	0.478181	0.239091	+	0.970997i	$0.423151\pi$
$458$	−17.9344	−0.838018
$459$	−3.17313	−0.148109
$460$	2.22546	0.103762
$461$	14.0000	0.652045	0.326023	−	0.945362i	$-0.394291\pi$
$461$	14.0000	0.652045	0.326023	+	0.945362i	$0.394291\pi$
$462$	−2.27051	−0.105634
$463$	−24.1812	−1.12380	−0.561898	−	0.827207i	$-0.689929\pi$
$463$	−24.1812	−1.12380	−0.561898	+	0.827207i	$0.689929\pi$
$464$	−4.44364	−0.206291
$465$	−1.27468	−0.0591118
$466$	−26.5962	−1.23204
$467$	−9.96719	−0.461226	−0.230613	−	0.973046i	$-0.574073\pi$
$467$	−9.96719	−0.461226	−0.230613	+	0.973046i	$0.574073\pi$
$468$	7.31450	0.338113
$469$	25.9313	1.19739
$470$	10.8628	0.501063
$471$	10.7581	0.495709
$472$	−5.58812	−0.257214
$473$	3.41783	0.157152
$474$	−9.39547	−0.431548
$475$	27.8381	1.27730
$476$	20.3944	0.934776
$477$	−8.24993	−0.377738
$478$	−34.5878	−1.58201
$479$	−21.7745	−0.994904	−0.497452	−	0.867491i	$-0.665731\pi$
$479$	−21.7745	−0.994904	−0.497452	+	0.867491i	$0.665731\pi$
$480$	−3.87086	−0.176680
$481$	32.9753	1.50354
$482$	27.5264	1.25379
$483$	−9.23353	−0.420140
$484$	−19.0276	−0.864890
$485$	5.70892	0.259229
$486$	1.93543	0.0877930
$487$	37.4506	1.69705	0.848525	−	0.529155i	$-0.177491\pi$
$487$	37.4506	1.69705	0.848525	+	0.529155i	$0.177491\pi$
$488$	−1.90368	−0.0861755
$489$	−21.8297	−0.987174
$490$	−6.44470	−0.291142
$491$	−16.6925	−0.753322	−0.376661	−	0.926351i	$-0.622928\pi$
$491$	−16.6925	−0.753322	−0.376661	+	0.926351i	$0.622928\pi$
$492$	−15.2335	−0.686780
$493$	3.17313	0.142910
$494$	47.6043	2.14182
$495$	−0.161949	−0.00727906
$496$	−11.1455	−0.500450
$497$	23.0081	1.03205
$498$	−16.2171	−0.726706
$499$	43.8573	1.96332	0.981661	−	0.190634i	$-0.0610544\pi$
$499$	43.8573	1.96332	0.981661	+	0.190634i	$0.0610544\pi$
$500$	−8.64356	−0.386552
$501$	20.4999	0.915866
$502$	−16.3340	−0.729023
$503$	26.4067	1.17741	0.588707	−	0.808346i	$-0.299637\pi$
$503$	26.4067	1.17741	0.588707	+	0.808346i	$0.299637\pi$
$504$	1.81047	0.0806446
$505$	5.54697	0.246837
$506$	1.54697	0.0687711
$507$	−4.55220	−0.202170
$508$	16.4035	0.727790
$509$	−36.1432	−1.60202	−0.801009	−	0.598653i	$-0.795703\pi$
$509$	−36.1432	−1.60202	−0.801009	+	0.598653i	$0.795703\pi$
$510$	3.12107	0.138203
$511$	−28.9753	−1.28179
$512$	−29.4754	−1.30264
$513$	5.87086	0.259205
$514$	−49.0877	−2.16517
$515$	4.06563	0.179153
$516$	18.7253	0.824336
$517$	3.51938	0.154782
$518$	−56.0796	−2.46400
$519$	−1.62093	−0.0711510
$520$	1.04710	0.0459184
$521$	26.1208	1.14437	0.572186	−	0.820124i	$-0.306095\pi$
$521$	26.1208	1.14437	0.572186	+	0.820124i	$0.306095\pi$
$522$	−1.93543	−0.0847116
$523$	−2.35148	−0.102823	−0.0514116	−	0.998678i	$-0.516372\pi$
$523$	−2.35148	−0.102823	−0.0514116	+	0.998678i	$0.516372\pi$
$524$	−29.8144	−1.30245
$525$	17.4559	0.761837
$526$	−45.4506	−1.98174
$527$	7.95885	0.346693
$528$	−1.41605	−0.0616257
$529$	−16.7089	−0.726475
$530$	8.11458	0.352475
$531$	−11.3627	−0.493097
$532$	−37.7334	−1.63595
$533$	36.5550	1.58337
$534$	−30.8339	−1.33431
$535$	1.95051	0.0843279
$536$	3.46421	0.149631
$537$	−4.47539	−0.193127
$538$	4.06741	0.175358
$539$	−2.08798	−0.0899358
$540$	−0.887271	−0.0381821
$541$	12.2499	0.526666	0.263333	−	0.964705i	$-0.415178\pi$
$541$	12.2499	0.526666	0.263333	+	0.964705i	$0.415178\pi$
$542$	−6.00834	−0.258080
$543$	−1.20594	−0.0517519
$544$	24.1690	1.03624
$545$	−4.16195	−0.178278
$546$	29.8503	1.27747
$547$	−11.3023	−0.483250	−0.241625	−	0.970370i	$-0.577680\pi$
$547$	−11.3023	−0.483250	−0.241625	+	0.970370i	$0.577680\pi$
$548$	26.2171	1.11994
$549$	−3.87086	−0.165204
$550$	−2.92452	−0.124702
$551$	−5.87086	−0.250107
$552$	−1.23353	−0.0525024
$553$	−17.8709	−0.759946
$554$	27.0265	1.14825
$555$	−4.00000	−0.169791
$556$	13.4108	0.568746
$557$	32.4671	1.37567	0.687837	−	0.725866i	$-0.258561\pi$
$557$	32.4671	1.37567	0.687837	+	0.725866i	$0.258561\pi$
$558$	−4.85446	−0.205506
$559$	−44.9341	−1.90051
$560$	−8.31344	−0.351307
$561$	1.01118	0.0426920
$562$	27.9365	1.17843
$563$	11.5439	0.486516	0.243258	−	0.969962i	$-0.421784\pi$
$563$	11.5439	0.486516	0.243258	+	0.969962i	$0.421784\pi$
$564$	19.2817	0.811905
$565$	6.71130	0.282347
$566$	−15.9833	−0.671829
$567$	3.68133	0.154601
$568$	3.07370	0.128969
$569$	34.5358	1.44782	0.723908	−	0.689897i	$-0.242344\pi$
$569$	34.5358	1.44782	0.723908	+	0.689897i	$0.242344\pi$
$570$	−5.77454	−0.241869
$571$	21.7089	0.908490	0.454245	−	0.890877i	$-0.349909\pi$
$571$	21.7089	0.908490	0.454245	+	0.890877i	$0.349909\pi$
$572$	−2.33091	−0.0974601
$573$	−0.758136	−0.0316716
$574$	−62.1676	−2.59483
$575$	−11.8932	−0.495982
$576$	−5.85446	−0.243936
$577$	−3.13720	−0.130604	−0.0653018	−	0.997866i	$-0.520801\pi$
$577$	−3.13720	−0.130604	−0.0653018	+	0.997866i	$0.520801\pi$
$578$	13.4150	0.557990
$579$	16.4671	0.684347
$580$	0.887271	0.0368419
$581$	−30.8461	−1.27971
$582$	21.7417	0.901224
$583$	2.62900	0.108882
$584$	−3.87086	−0.160178
$585$	2.12914	0.0880289
$586$	24.0919	0.995227
$587$	31.5386	1.30174	0.650869	−	0.759190i	$-0.274405\pi$
$587$	31.5386	1.30174	0.650869	+	0.759190i	$0.274405\pi$
$588$	−11.4395	−0.471756
$589$	−14.7253	−0.606746
$590$	11.1762	0.460118
$591$	17.9588	0.738728
$592$	−34.9753	−1.43747
$593$	−26.9753	−1.10774	−0.553870	−	0.832603i	$-0.686850\pi$
$593$	−26.9753	−1.10774	−0.553870	+	0.832603i	$0.686850\pi$
$594$	−0.616763	−0.0253061
$595$	5.93649	0.243372
$596$	−19.8953	−0.814945
$597$	−1.33508	−0.0546410
$598$	−20.3379	−0.831679
$599$	−20.2364	−0.826836	−0.413418	−	0.910541i	$-0.635665\pi$
$599$	−20.2364	−0.826836	−0.413418	+	0.910541i	$0.635665\pi$
$600$	2.33197	0.0952021
$601$	−42.7826	−1.74514	−0.872570	−	0.488490i	$-0.837548\pi$
$601$	−42.7826	−1.74514	−0.872570	+	0.488490i	$0.837548\pi$
$602$	76.4176	3.11455
$603$	7.04399	0.286854
$604$	−3.54909	−0.144410
$605$	−5.53863	−0.225177
$606$	21.1250	0.858143
$607$	3.42829	0.139150	0.0695750	−	0.997577i	$-0.477836\pi$
$607$	3.42829	0.139150	0.0695750	+	0.997577i	$0.477836\pi$
$608$	−44.7170	−1.81351
$609$	−3.68133	−0.149175
$610$	3.80736	0.154155
$611$	−46.2692	−1.87185
$612$	5.53996	0.223940
$613$	−21.3267	−0.861379	−0.430689	−	0.902500i	$-0.641730\pi$
$613$	−21.3267	−0.861379	−0.430689	+	0.902500i	$0.641730\pi$
$614$	42.5634	1.71772
$615$	−4.43424	−0.178806
$616$	−0.576940	−0.0232456
$617$	−29.8074	−1.20000	−0.599999	−	0.800000i	$-0.704833\pi$
$617$	−29.8074	−1.20000	−0.599999	+	0.800000i	$0.704833\pi$
$618$	15.4835	0.622836
$619$	5.87086	0.235970	0.117985	−	0.993015i	$-0.462357\pi$
$619$	5.87086	0.235970	0.117985	+	0.993015i	$0.462357\pi$
$620$	2.22546	0.0893765
$621$	−2.50820	−0.100651
$622$	36.8584	1.47789
$623$	−58.6482	−2.34969
$624$	18.6168	0.745267
$625$	21.1926	0.847706
$626$	−19.1578	−0.765699
$627$	−1.87086	−0.0747151
$628$	−18.7826	−0.749508
$629$	24.9753	0.995829
$630$	−3.62093	−0.144261
$631$	20.7529	0.826160	0.413080	−	0.910695i	$-0.364453\pi$
$631$	20.7529	0.826160	0.413080	+	0.910695i	$0.364453\pi$
$632$	−2.38741	−0.0949659
$633$	−8.37907	−0.333038
$634$	−1.10049	−0.0437061
$635$	4.77481	0.189483
$636$	14.4035	0.571138
$637$	27.4506	1.08763
$638$	0.616763	0.0244179
$639$	6.24993	0.247244
$640$	−1.98332	−0.0783978
$641$	−18.9149	−0.747092	−0.373546	−	0.927612i	$-0.621858\pi$
$641$	−18.9149	−0.747092	−0.373546	+	0.927612i	$0.621858\pi$
$642$	7.42829	0.293171
$643$	−47.1648	−1.86000	−0.929999	−	0.367562i	$-0.880192\pi$
$643$	−47.1648	−1.86000	−0.929999	+	0.367562i	$0.880192\pi$
$644$	16.1208	0.635248
$645$	5.45065	0.214619
$646$	36.0552	1.41857
$647$	7.20071	0.283089	0.141545	−	0.989932i	$-0.454793\pi$
$647$	7.20071	0.283089	0.141545	+	0.989932i	$0.454793\pi$
$648$	0.491797	0.0193196
$649$	3.62093	0.142134
$650$	38.4486	1.50808
$651$	−9.23353	−0.361890
$652$	38.1125	1.49260
$653$	42.5191	1.66390	0.831951	−	0.554850i	$-0.187224\pi$
$653$	42.5191	1.66390	0.831951	+	0.554850i	$0.187224\pi$
$654$	−15.8503	−0.619795
$655$	−8.67849	−0.339097
$656$	−38.7722	−1.51380
$657$	−7.87086	−0.307072
$658$	78.6881	3.06758
$659$	−1.90679	−0.0742779	−0.0371390	−	0.999310i	$-0.511824\pi$
$659$	−1.90679	−0.0742779	−0.0371390	+	0.999310i	$0.511824\pi$
$660$	0.282746	0.0110059
$661$	35.9969	1.40012	0.700058	−	0.714086i	$-0.253157\pi$
$661$	35.9969	1.40012	0.700058	+	0.714086i	$0.253157\pi$
$662$	−2.28063	−0.0886391
$663$	−13.2939	−0.516293
$664$	−4.12080	−0.159918
$665$	−10.9836	−0.425925
$666$	−15.2335	−0.590287
$667$	2.50820	0.0971180
$668$	−35.7907	−1.38478
$669$	6.66492	0.257681
$670$	−6.92842	−0.267668
$671$	1.23353	0.0476197
$672$	−28.0398	−1.08166
$673$	9.46421	0.364819	0.182409	−	0.983223i	$-0.441610\pi$
$673$	9.46421	0.364819	0.182409	+	0.983223i	$0.441610\pi$
$674$	−33.2908	−1.28231
$675$	4.74173	0.182509
$676$	7.94767	0.305680
$677$	−3.81047	−0.146448	−0.0732241	−	0.997316i	$-0.523329\pi$
$677$	−3.81047	−0.146448	−0.0732241	+	0.997316i	$0.523329\pi$
$678$	25.5592	0.981595
$679$	41.3543	1.58703
$680$	0.793068	0.0304128
$681$	−0.379068	−0.0145259
$682$	1.54697	0.0592364
$683$	32.9341	1.26019	0.630094	−	0.776519i	$-0.283016\pi$
$683$	32.9341	1.26019	0.630094	+	0.776519i	$0.283016\pi$
$684$	−10.2499	−0.391916
$685$	7.63139	0.291580
$686$	3.19059	0.121817
$687$	−9.26634	−0.353533
$688$	47.6594	1.81700
$689$	−34.5634	−1.31676
$690$	2.46705	0.0939191
$691$	0.752908	0.0286420	0.0143210	−	0.999897i	$-0.495441\pi$
$691$	0.752908	0.0286420	0.0143210	+	0.999897i	$0.495441\pi$
$692$	2.82998	0.107580
$693$	−1.17313	−0.0445634
$694$	−29.5470	−1.12159
$695$	3.90368	0.148075
$696$	−0.491797	−0.0186415
$697$	27.6866	1.04870
$698$	53.6287	2.02988
$699$	−13.7417	−0.519760
$700$	−30.4762	−1.15189
$701$	−27.3543	−1.03316	−0.516579	−	0.856239i	$-0.672795\pi$
$701$	−27.3543	−1.03316	−0.516579	+	0.856239i	$0.672795\pi$
$702$	8.10856	0.306038
$703$	−46.2088	−1.74280
$704$	1.86564	0.0703138
$705$	5.61259	0.211383
$706$	−5.41783	−0.203903
$707$	40.1812	1.51117
$708$	19.8381	0.745560
$709$	50.1760	1.88440	0.942199	−	0.335054i	$-0.108754\pi$
$709$	50.1760	1.88440	0.942199	+	0.335054i	$0.108754\pi$
$710$	−6.14739	−0.230707
$711$	−4.85446	−0.182056
$712$	−7.83494	−0.293627
$713$	6.29108	0.235603
$714$	22.6084	0.846099
$715$	−0.678490	−0.0253741
$716$	7.81358	0.292007
$717$	−17.8709	−0.667400
$718$	−23.7251	−0.885411
$719$	30.4014	1.13378	0.566891	−	0.823793i	$-0.308146\pi$
$719$	30.4014	1.13378	0.566891	+	0.823793i	$0.308146\pi$
$720$	−2.25827	−0.0841608
$721$	29.4506	1.09680
$722$	−29.9354	−1.11408
$723$	14.2223	0.528935
$724$	2.10545	0.0782484
$725$	−4.74173	−0.176103
$726$	−21.0932	−0.782843
$727$	−46.1676	−1.71226	−0.856131	−	0.516758i	$-0.827139\pi$
$727$	−46.1676	−1.71226	−0.856131	+	0.516758i	$0.827139\pi$
$728$	7.58501	0.281119
$729$	1.00000	0.0370370
$730$	7.74173	0.286534
$731$	−34.0328	−1.25875
$732$	6.75814	0.249788
$733$	−34.1208	−1.26028	−0.630140	−	0.776481i	$-0.717003\pi$
$733$	−34.1208	−1.26028	−0.630140	+	0.776481i	$0.717003\pi$
$734$	8.24159	0.304203
$735$	−3.32985	−0.122823
$736$	19.1044	0.704197
$737$	−2.24470	−0.0826847
$738$	−16.8873	−0.621629
$739$	−40.7826	−1.50021	−0.750106	−	0.661317i	$-0.769998\pi$
$739$	−40.7826	−1.50021	−0.750106	+	0.661317i	$0.769998\pi$
$740$	6.98359	0.256722
$741$	24.5962	0.903564
$742$	58.7805	2.15790
$743$	−14.3515	−0.526505	−0.263252	−	0.964727i	$-0.584795\pi$
$743$	−14.3515	−0.526505	−0.263252	+	0.964727i	$0.584795\pi$
$744$	−1.23353	−0.0452233
$745$	−5.79122	−0.212174
$746$	−49.8214	−1.82409
$747$	−8.37907	−0.306574
$748$	−1.76541	−0.0645500
$749$	14.1291	0.516267
$750$	−9.58190	−0.349881
$751$	−21.4506	−0.782745	−0.391373	−	0.920232i	$-0.628000\pi$
$751$	−21.4506	−0.782745	−0.391373	+	0.920232i	$0.628000\pi$
$752$	49.0755	1.78960
$753$	−8.43947	−0.307551
$754$	−8.10856	−0.295296
$755$	−1.03308	−0.0375977
$756$	−6.42723	−0.233756
$757$	0.862796	0.0313588	0.0156794	−	0.999877i	$-0.495009\pi$
$757$	0.862796	0.0313588	0.0156794	+	0.999877i	$0.495009\pi$
$758$	−38.0224	−1.38103
$759$	0.799288	0.0290123
$760$	−1.46732	−0.0532253
$761$	25.4423	0.922283	0.461141	−	0.887327i	$-0.347440\pi$
$761$	25.4423	0.922283	0.461141	+	0.887327i	$0.347440\pi$
$762$	18.1843	0.658748
$763$	−30.1484	−1.09144
$764$	1.32363	0.0478872
$765$	1.61259	0.0583035
$766$	43.6699	1.57786
$767$	−47.6043	−1.71889
$768$	−19.2622	−0.695064
$769$	−0.194762	−0.00702331	−0.00351165	−	0.999994i	$-0.501118\pi$
$769$	−0.194762	−0.00702331	−0.00351165	+	0.999994i	$0.501118\pi$
$770$	1.15388	0.0415830
$771$	−25.3627	−0.913414
$772$	−28.7498	−1.03473
$773$	44.5327	1.60173	0.800865	−	0.598846i	$-0.204374\pi$
$773$	44.5327	1.60173	0.800865	+	0.598846i	$0.204374\pi$
$774$	20.7581	0.746136
$775$	−11.8932	−0.427217
$776$	5.52461	0.198322
$777$	−28.9753	−1.03948
$778$	−30.6001	−1.09707
$779$	−51.2252	−1.83533
$780$	−3.71725	−0.133099
$781$	−1.99166	−0.0712673
$782$	−15.4038	−0.550839
$783$	−1.00000	−0.0357371
$784$	−29.1156	−1.03984
$785$	−5.46732	−0.195137
$786$	−33.0510	−1.17889
$787$	−24.4999	−0.873326	−0.436663	−	0.899625i	$-0.643840\pi$
$787$	−24.4999	−0.873326	−0.436663	+	0.899625i	$0.643840\pi$
$788$	−31.3543	−1.11695
$789$	−23.4835	−0.836033
$790$	4.77481	0.169880
$791$	48.6154	1.72857
$792$	−0.156721	−0.00556882
$793$	−16.2171	−0.575887
$794$	6.33792	0.224924
$795$	4.19264	0.148698
$796$	2.33091	0.0826168
$797$	12.7253	0.450754	0.225377	−	0.974272i	$-0.427639\pi$
$797$	12.7253	0.450754	0.225377	+	0.974272i	$0.427639\pi$
$798$	−41.8297	−1.48076
$799$	−35.0440	−1.23977
$800$	−36.1166	−1.27692
$801$	−15.9313	−0.562904
$802$	−4.79095	−0.169174
$803$	2.50820	0.0885126
$804$	−12.2981	−0.433720
$805$	4.69251	0.165389
$806$	−20.3379	−0.716373
$807$	2.10155	0.0739781
$808$	5.36789	0.188842
$809$	13.6402	0.479563	0.239782	−	0.970827i	$-0.422924\pi$
$809$	13.6402	0.479563	0.239782	+	0.970827i	$0.422924\pi$
$810$	−0.983593	−0.0345599
$811$	15.9948	0.561652	0.280826	−	0.959759i	$-0.409392\pi$
$811$	15.9948	0.561652	0.280826	+	0.959759i	$0.409392\pi$
$812$	6.42723	0.225552
$813$	−3.10439	−0.108876
$814$	4.85446	0.170149
$815$	11.0939	0.388604
$816$	14.1002	0.493606
$817$	62.9669	2.20293
$818$	−29.0632	−1.01617
$819$	15.4231	0.538925
$820$	7.74173	0.270353
$821$	−3.70892	−0.129442	−0.0647210	−	0.997903i	$-0.520616\pi$
$821$	−3.70892	−0.129442	−0.0647210	+	0.997903i	$0.520616\pi$
$822$	29.0632	1.01370
$823$	−48.8685	−1.70345	−0.851724	−	0.523991i	$-0.824443\pi$
$823$	−48.8685	−1.70345	−0.851724	+	0.523991i	$0.824443\pi$
$824$	3.93437	0.137060
$825$	−1.51104	−0.0526078
$826$	80.9586	2.81691
$827$	1.20905	0.0420428	0.0210214	−	0.999779i	$-0.493308\pi$
$827$	1.20905	0.0420428	0.0210214	+	0.999779i	$0.493308\pi$
$828$	4.37907	0.152183
$829$	−4.67015	−0.162201	−0.0811005	−	0.996706i	$-0.525843\pi$
$829$	−4.67015	−0.162201	−0.0811005	+	0.996706i	$0.525843\pi$
$830$	8.24159	0.286070
$831$	13.9641	0.484408
$832$	−24.5275	−0.850336
$833$	20.7909	0.720364
$834$	14.8667	0.514792
$835$	−10.4181	−0.360533
$836$	3.26634	0.112969
$837$	−2.50820	−0.0866962
$838$	26.8461	0.927384
$839$	−10.8513	−0.374630	−0.187315	−	0.982300i	$-0.559979\pi$
$839$	−10.8513	−0.374630	−0.187315	+	0.982300i	$0.559979\pi$
$840$	−0.920085	−0.0317459
$841$	1.00000	0.0344828
$842$	14.4202	0.496954
$843$	14.4342	0.497142
$844$	14.6290	0.503551
$845$	2.31344	0.0795848
$846$	21.3749	0.734884
$847$	−40.1208	−1.37857
$848$	36.6597	1.25890
$849$	−8.25827	−0.283423
$850$	29.1207	0.998833
$851$	19.7417	0.676738
$852$	−10.9117	−0.373830
$853$	44.3296	1.51782	0.758908	−	0.651198i	$-0.225733\pi$
$853$	44.3296	1.51782	0.758908	+	0.651198i	$0.225733\pi$
$854$	27.5798	0.943761
$855$	−2.98359	−0.102037
$856$	1.88754	0.0645148
$857$	3.23353	0.110455	0.0552276	−	0.998474i	$-0.482412\pi$
$857$	3.23353	0.110455	0.0552276	+	0.998474i	$0.482412\pi$
$858$	−2.58395	−0.0882146
$859$	38.3463	1.30836	0.654179	−	0.756340i	$-0.273014\pi$
$859$	38.3463	1.30836	0.654179	+	0.756340i	$0.273014\pi$
$860$	−9.51627	−0.324502
$861$	−32.1208	−1.09467
$862$	−28.4999	−0.970709
$863$	41.4751	1.41183	0.705915	−	0.708297i	$-0.250536\pi$
$863$	41.4751	1.41183	0.705915	+	0.708297i	$0.250536\pi$
$864$	−7.61676	−0.259128
$865$	0.823763	0.0280088
$866$	−2.95078	−0.100272
$867$	6.93126	0.235398
$868$	16.1208	0.547176
$869$	1.54697	0.0524773
$870$	0.983593	0.0333469
$871$	29.5110	0.999944
$872$	−4.02759	−0.136391
$873$	11.2335	0.380197
$874$	28.4999	0.964022
$875$	−18.2255	−0.616133
$876$	13.7417	0.464290
$877$	13.0492	0.440641	0.220320	−	0.975428i	$-0.429290\pi$
$877$	13.0492	0.440641	0.220320	+	0.975428i	$0.429290\pi$
$878$	−45.1000	−1.52205
$879$	12.4478	0.419854
$880$	0.719642	0.0242591
$881$	−39.6074	−1.33441	−0.667203	−	0.744876i	$-0.732509\pi$
$881$	−39.6074	−1.33441	−0.667203	+	0.744876i	$0.732509\pi$
$882$	−12.6813	−0.427003
$883$	29.9505	1.00791	0.503957	−	0.863728i	$-0.331877\pi$
$883$	29.9505	1.00791	0.503957	+	0.863728i	$0.331877\pi$
$884$	23.2098	0.780631
$885$	5.77454	0.194109
$886$	−44.6001	−1.49837
$887$	47.5439	1.59637	0.798183	−	0.602415i	$-0.205795\pi$
$887$	47.5439	1.59637	0.798183	+	0.602415i	$0.205795\pi$
$888$	−3.87086	−0.129898
$889$	34.5878	1.16004
$890$	15.6699	0.525256
$891$	−0.318669	−0.0106758
$892$	−11.6363	−0.389611
$893$	64.8378	2.16971
$894$	−22.0552	−0.737635
$895$	2.27441	0.0760251
$896$	−14.3668	−0.479962
$897$	−10.5082	−0.350859
$898$	12.6496	0.422122
$899$	2.50820	0.0836533
$900$	−8.27858	−0.275953
$901$	−26.1781	−0.872119
$902$	5.38146	0.179183
$903$	39.4835	1.31393
$904$	6.49464	0.216008
$905$	0.612863	0.0203723
$906$	−3.93437	−0.130711
$907$	14.8628	0.493511	0.246756	−	0.969078i	$-0.420636\pi$
$907$	14.8628	0.493511	0.246756	+	0.969078i	$0.420636\pi$
$908$	0.661814	0.0219631
$909$	10.9149	0.362023
$910$	−15.1700	−0.502881
$911$	−28.5603	−0.946244	−0.473122	−	0.880997i	$-0.656873\pi$
$911$	−28.5603	−0.946244	−0.473122	+	0.880997i	$0.656873\pi$
$912$	−26.0880	−0.863859
$913$	2.67015	0.0883691
$914$	−19.7847	−0.654418
$915$	1.96719	0.0650332
$916$	16.1781	0.534539
$917$	−62.8654	−2.07600
$918$	6.14137	0.202696
$919$	−9.32462	−0.307591	−0.153795	−	0.988103i	$-0.549150\pi$
$919$	−9.32462	−0.307591	−0.153795	+	0.988103i	$0.549150\pi$
$920$	0.626882	0.0206677
$921$	21.9917	0.724650
$922$	−27.0961	−0.892361
$923$	26.1843	0.861867
$924$	2.04816	0.0673795
$925$	−37.3215	−1.22712
$926$	46.8011	1.53798
$927$	8.00000	0.262754
$928$	7.61676	0.250032
$929$	−4.29108	−0.140786	−0.0703930	−	0.997519i	$-0.522425\pi$
$929$	−4.29108	−0.140786	−0.0703930	+	0.997519i	$0.522425\pi$
$930$	2.46705	0.0808978
$931$	−38.4671	−1.26071
$932$	23.9917	0.785873
$933$	19.0440	0.623472
$934$	19.2908	0.631215
$935$	−0.513884	−0.0168058
$936$	2.06040	0.0673462
$937$	−4.94767	−0.161633	−0.0808167	−	0.996729i	$-0.525753\pi$
$937$	−4.94767	−0.161633	−0.0808167	+	0.996729i	$0.525753\pi$
$938$	−50.1882	−1.63870
$939$	−9.89845	−0.323024
$940$	−9.79902	−0.319609
$941$	−17.7969	−0.580162	−0.290081	−	0.957002i	$-0.593682\pi$
$941$	−17.7969	−0.580162	−0.290081	+	0.957002i	$0.593682\pi$
$942$	−20.8216	−0.678406
$943$	21.8849	0.712670
$944$	50.4915	1.64336
$945$	−1.87086	−0.0608592
$946$	−6.61498	−0.215072
$947$	−53.7693	−1.74727	−0.873634	−	0.486584i	$-0.838243\pi$
$947$	−53.7693	−1.74727	−0.873634	+	0.486584i	$0.838243\pi$
$948$	8.47539	0.275268
$949$	−32.9753	−1.07042
$950$	−53.8787	−1.74805
$951$	−0.568602	−0.0184382
$952$	5.74484	0.186191
$953$	50.5550	1.63764	0.818819	−	0.574052i	$-0.194629\pi$
$953$	50.5550	1.63764	0.818819	+	0.574052i	$0.194629\pi$
$954$	15.9672	0.516957
$955$	0.385287	0.0124676
$956$	31.2007	1.00910
$957$	0.318669	0.0103011
$958$	42.1432	1.36158
$959$	55.2804	1.78510
$960$	2.97526	0.0960260
$961$	−24.7089	−0.797062
$962$	−63.8214	−2.05768
$963$	3.83805	0.123679
$964$	−24.8308	−0.799745
$965$	−8.36861	−0.269395
$966$	17.8709	0.574986
$967$	−13.1784	−0.423787	−0.211894	−	0.977293i	$-0.567963\pi$
$967$	−13.1784	−0.423787	−0.211894	+	0.977293i	$0.567963\pi$
$968$	−5.35982	−0.172271
$969$	18.6290	0.598450
$970$	−11.0492	−0.354769
$971$	−16.3686	−0.525294	−0.262647	−	0.964892i	$-0.584595\pi$
$971$	−16.3686	−0.525294	−0.262647	+	0.964892i	$0.584595\pi$
$972$	−1.74590	−0.0559997
$973$	28.2775	0.906536
$974$	−72.4832	−2.32251
$975$	19.8656	0.636210
$976$	17.2007	0.550581
$977$	−59.7229	−1.91071	−0.955353	−	0.295467i	$-0.904525\pi$
$977$	−59.7229	−1.91071	−0.955353	+	0.295467i	$0.904525\pi$
$978$	42.2499	1.35100
$979$	5.07681	0.162255
$980$	5.81358	0.185708
$981$	−8.18953	−0.261472
$982$	32.3072	1.03096
$983$	55.4835	1.76965	0.884824	−	0.465926i	$-0.154279\pi$
$983$	55.4835	1.76965	0.884824	+	0.465926i	$0.154279\pi$
$984$	−4.29108	−0.136795
$985$	−9.12675	−0.290802
$986$	−6.14137	−0.195581
$987$	40.6566	1.29411
$988$	−42.9424	−1.36618
$989$	−26.9013	−0.855411
$990$	0.313441	0.00996181
$991$	12.8737	0.408947	0.204473	−	0.978872i	$-0.434452\pi$
$991$	12.8737	0.408947	0.204473	+	0.978872i	$0.434452\pi$
$992$	19.1044	0.606565
$993$	−1.17836	−0.0373940
$994$	−44.5306	−1.41242
$995$	0.678490	0.0215096
$996$	14.6290	0.463538
$997$	−16.0880	−0.509512	−0.254756	−	0.967005i	$-0.581995\pi$
$997$	−16.0880	−0.509512	−0.254756	+	0.967005i	$0.581995\pi$
$998$	−84.8828	−2.68692
$999$	−7.87086	−0.249023

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	87.2.a.b.1.1	✓	3
3.2	odd	2		261.2.a.e.1.3		3
4.3	odd	2		1392.2.a.u.1.2		3
5.2	odd	4		2175.2.c.l.349.2		6
5.3	odd	4		2175.2.c.l.349.5		6
5.4	even	2		2175.2.a.t.1.3		3
7.6	odd	2		4263.2.a.m.1.1		3
8.3	odd	2		5568.2.a.bx.1.2		3
8.5	even	2		5568.2.a.cb.1.2		3
12.11	even	2		4176.2.a.bx.1.2		3
15.14	odd	2		6525.2.a.bg.1.1		3
29.28	even	2		2523.2.a.h.1.3		3
87.86	odd	2		7569.2.a.t.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.2.a.b.1.1	✓	3	1.1	even	1	trivial
261.2.a.e.1.3		3	3.2	odd	2
1392.2.a.u.1.2		3	4.3	odd	2
2175.2.a.t.1.3		3	5.4	even	2
2175.2.c.l.349.2		6	5.2	odd	4
2175.2.c.l.349.5		6	5.3	odd	4
2523.2.a.h.1.3		3	29.28	even	2
4176.2.a.bx.1.2		3	12.11	even	2
4263.2.a.m.1.1		3	7.6	odd	2
5568.2.a.bx.1.2		3	8.3	odd	2
5568.2.a.cb.1.2		3	8.5	even	2
6525.2.a.bg.1.1		3	15.14	odd	2
7569.2.a.t.1.1		3	87.86	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 87 = 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	87.a (trivial)

\(f(q)\)	\(=\)	\(q-1.93543 q^{2} -1.00000 q^{3} +1.74590 q^{4} +0.508203 q^{5} +1.93543 q^{6} +3.68133 q^{7} +0.491797 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.93543 q^{2} -1.00000 q^{3} +1.74590 q^{4} +0.508203 q^{5} +1.93543 q^{6} +3.68133 q^{7} +0.491797 q^{8} +1.00000 q^{9} -0.983593 q^{10} -0.318669 q^{11} -1.74590 q^{12} +4.18953 q^{13} -7.12497 q^{14} -0.508203 q^{15} -4.44364 q^{16} +3.17313 q^{17} -1.93543 q^{18} -5.87086 q^{19} +0.887271 q^{20} -3.68133 q^{21} +0.616763 q^{22} +2.50820 q^{23} -0.491797 q^{24} -4.74173 q^{25} -8.10856 q^{26} -1.00000 q^{27} +6.42723 q^{28} +1.00000 q^{29} +0.983593 q^{30} +2.50820 q^{31} +7.61676 q^{32} +0.318669 q^{33} -6.14137 q^{34} +1.87086 q^{35} +1.74590 q^{36} +7.87086 q^{37} +11.3627 q^{38} -4.18953 q^{39} +0.249933 q^{40} +8.72532 q^{41} +7.12497 q^{42} -10.7253 q^{43} -0.556364 q^{44} +0.508203 q^{45} -4.85446 q^{46} -11.0440 q^{47} +4.44364 q^{48} +6.55220 q^{49} +9.17730 q^{50} -3.17313 q^{51} +7.31450 q^{52} -8.24993 q^{53} +1.93543 q^{54} -0.161949 q^{55} +1.81047 q^{56} +5.87086 q^{57} -1.93543 q^{58} -11.3627 q^{59} -0.887271 q^{60} -3.87086 q^{61} -4.85446 q^{62} +3.68133 q^{63} -5.85446 q^{64} +2.12914 q^{65} -0.616763 q^{66} +7.04399 q^{67} +5.53996 q^{68} -2.50820 q^{69} -3.62093 q^{70} +6.24993 q^{71} +0.491797 q^{72} -7.87086 q^{73} -15.2335 q^{74} +4.74173 q^{75} -10.2499 q^{76} -1.17313 q^{77} +8.10856 q^{78} -4.85446 q^{79} -2.25827 q^{80} +1.00000 q^{81} -16.8873 q^{82} -8.37907 q^{83} -6.42723 q^{84} +1.61259 q^{85} +20.7581 q^{86} -1.00000 q^{87} -0.156721 q^{88} -15.9313 q^{89} -0.983593 q^{90} +15.4231 q^{91} +4.37907 q^{92} -2.50820 q^{93} +21.3749 q^{94} -2.98359 q^{95} -7.61676 q^{96} +11.2335 q^{97} -12.6813 q^{98} -0.318669 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 2 q^{2} - 3 q^{3} + 6 q^{4} - 2 q^{6} + 4 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 2 * q^2 - 3 * q^3 + 6 * q^4 - 2 * q^6 + 4 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + 2 q^{2} - 3 q^{3} + 6 q^{4} - 2 q^{6} + 4 q^{7} + 3 q^{8} + 3 q^{9} - 6 q^{10} - 8 q^{11} - 6 q^{12} + 4 q^{13} - 5 q^{14} - 4 q^{16} + 4 q^{17} + 2 q^{18} - 2 q^{19} - 16 q^{20} - 4 q^{21} - 13 q^{22} + 6 q^{23} - 3 q^{24} + 17 q^{25} - 11 q^{26} - 3 q^{27} + 13 q^{28} + 3 q^{29} + 6 q^{30} + 6 q^{31} + 8 q^{32} + 8 q^{33} + q^{34} - 10 q^{35} + 6 q^{36} + 8 q^{37} + 20 q^{38} - 4 q^{39} - 32 q^{40} - 2 q^{41} + 5 q^{42} - 4 q^{43} - 11 q^{44} - 2 q^{46} - 12 q^{47} + 4 q^{48} - 3 q^{49} + 54 q^{50} - 4 q^{51} - 3 q^{52} + 8 q^{53} - 2 q^{54} - 10 q^{55} + 14 q^{56} + 2 q^{57} + 2 q^{58} - 20 q^{59} + 16 q^{60} + 4 q^{61} - 2 q^{62} + 4 q^{63} - 5 q^{64} + 22 q^{65} + 13 q^{66} + 29 q^{68} - 6 q^{69} - 28 q^{70} - 14 q^{71} + 3 q^{72} - 8 q^{73} - 16 q^{74} - 17 q^{75} + 2 q^{76} + 2 q^{77} + 11 q^{78} - 2 q^{79} - 38 q^{80} + 3 q^{81} - 32 q^{82} - 8 q^{83} - 13 q^{84} - 42 q^{85} + 28 q^{86} - 3 q^{87} + 2 q^{88} - 8 q^{89} - 6 q^{90} + 8 q^{91} - 4 q^{92} - 6 q^{93} + 15 q^{94} - 12 q^{95} - 8 q^{96} + 4 q^{97} - 31 q^{98} - 8 q^{99}+O(q^{100}) \) 3 * q + 2 * q^2 - 3 * q^3 + 6 * q^4 - 2 * q^6 + 4 * q^7 + 3 * q^8 + 3 * q^9 - 6 * q^10 - 8 * q^11 - 6 * q^12 + 4 * q^13 - 5 * q^14 - 4 * q^16 + 4 * q^17 + 2 * q^18 - 2 * q^19 - 16 * q^20 - 4 * q^21 - 13 * q^22 + 6 * q^23 - 3 * q^24 + 17 * q^25 - 11 * q^26 - 3 * q^27 + 13 * q^28 + 3 * q^29 + 6 * q^30 + 6 * q^31 + 8 * q^32 + 8 * q^33 + q^34 - 10 * q^35 + 6 * q^36 + 8 * q^37 + 20 * q^38 - 4 * q^39 - 32 * q^40 - 2 * q^41 + 5 * q^42 - 4 * q^43 - 11 * q^44 - 2 * q^46 - 12 * q^47 + 4 * q^48 - 3 * q^49 + 54 * q^50 - 4 * q^51 - 3 * q^52 + 8 * q^53 - 2 * q^54 - 10 * q^55 + 14 * q^56 + 2 * q^57 + 2 * q^58 - 20 * q^59 + 16 * q^60 + 4 * q^61 - 2 * q^62 + 4 * q^63 - 5 * q^64 + 22 * q^65 + 13 * q^66 + 29 * q^68 - 6 * q^69 - 28 * q^70 - 14 * q^71 + 3 * q^72 - 8 * q^73 - 16 * q^74 - 17 * q^75 + 2 * q^76 + 2 * q^77 + 11 * q^78 - 2 * q^79 - 38 * q^80 + 3 * q^81 - 32 * q^82 - 8 * q^83 - 13 * q^84 - 42 * q^85 + 28 * q^86 - 3 * q^87 + 2 * q^88 - 8 * q^89 - 6 * q^90 + 8 * q^91 - 4 * q^92 - 6 * q^93 + 15 * q^94 - 12 * q^95 - 8 * q^96 + 4 * q^97 - 31 * q^98 - 8 * q^99

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