LMFDB - Embedded newform 8031.2.a.b.1.3

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			1.3
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)

$f(q)$	$=$	$q-2.70545 q^{2} -1.00000 q^{3} +5.31943 q^{4} -1.42429 q^{5} +2.70545 q^{6} -0.675914 q^{7} -8.98054 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.70545 q^{2} -1.00000 q^{3} +5.31943 q^{4} -1.42429 q^{5} +2.70545 q^{6} -0.675914 q^{7} -8.98054 q^{8} +1.00000 q^{9} +3.85333 q^{10} -4.37139 q^{11} -5.31943 q^{12} +1.93022 q^{13} +1.82865 q^{14} +1.42429 q^{15} +13.6575 q^{16} +0.416850 q^{17} -2.70545 q^{18} +5.34685 q^{19} -7.57640 q^{20} +0.675914 q^{21} +11.8266 q^{22} +1.72316 q^{23} +8.98054 q^{24} -2.97141 q^{25} -5.22210 q^{26} -1.00000 q^{27} -3.59548 q^{28} -2.61132 q^{29} -3.85333 q^{30} -7.49797 q^{31} -18.9885 q^{32} +4.37139 q^{33} -1.12776 q^{34} +0.962696 q^{35} +5.31943 q^{36} +6.02747 q^{37} -14.4656 q^{38} -1.93022 q^{39} +12.7909 q^{40} +8.02874 q^{41} -1.82865 q^{42} +7.76021 q^{43} -23.2533 q^{44} -1.42429 q^{45} -4.66191 q^{46} +0.257459 q^{47} -13.6575 q^{48} -6.54314 q^{49} +8.03898 q^{50} -0.416850 q^{51} +10.2677 q^{52} -12.4498 q^{53} +2.70545 q^{54} +6.22612 q^{55} +6.07008 q^{56} -5.34685 q^{57} +7.06479 q^{58} -8.01484 q^{59} +7.57640 q^{60} -4.16731 q^{61} +20.2853 q^{62} -0.675914 q^{63} +24.0574 q^{64} -2.74919 q^{65} -11.8266 q^{66} +2.01613 q^{67} +2.21740 q^{68} -1.72316 q^{69} -2.60452 q^{70} -6.48849 q^{71} -8.98054 q^{72} -2.61635 q^{73} -16.3070 q^{74} +2.97141 q^{75} +28.4422 q^{76} +2.95469 q^{77} +5.22210 q^{78} +7.55884 q^{79} -19.4522 q^{80} +1.00000 q^{81} -21.7213 q^{82} +5.54191 q^{83} +3.59548 q^{84} -0.593713 q^{85} -20.9948 q^{86} +2.61132 q^{87} +39.2575 q^{88} +11.3532 q^{89} +3.85333 q^{90} -1.30466 q^{91} +9.16622 q^{92} +7.49797 q^{93} -0.696540 q^{94} -7.61545 q^{95} +18.9885 q^{96} -3.74307 q^{97} +17.7021 q^{98} -4.37139 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.70545	−1.91304	−0.956519	−	0.291669i	$-0.905789\pi$
$2$	−2.70545	−1.91304	−0.956519	+	0.291669i	$0.905789\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.31943	2.65972
$5$	−1.42429	−0.636961	−0.318480	−	0.947929i	$-0.603172\pi$
$5$	−1.42429	−0.636961	−0.318480	+	0.947929i	$0.603172\pi$
$6$	2.70545	1.10449
$7$	−0.675914	−0.255472	−0.127736	−	0.991808i	$-0.540771\pi$
$7$	−0.675914	−0.255472	−0.127736	+	0.991808i	$0.540771\pi$
$8$	−8.98054	−3.17510
$9$	1.00000	0.333333
$10$	3.85333	1.21853
$11$	−4.37139	−1.31802	−0.659012	−	0.752132i	$-0.729025\pi$
$11$	−4.37139	−1.31802	−0.659012	+	0.752132i	$0.729025\pi$
$12$	−5.31943	−1.53559
$13$	1.93022	0.535346	0.267673	−	0.963510i	$-0.413745\pi$
$13$	1.93022	0.535346	0.267673	+	0.963510i	$0.413745\pi$
$14$	1.82865	0.488727
$15$	1.42429	0.367749
$16$	13.6575	3.41438
$17$	0.416850	0.101101	0.0505504	−	0.998722i	$-0.483902\pi$
$17$	0.416850	0.101101	0.0505504	+	0.998722i	$0.483902\pi$
$18$	−2.70545	−0.637680
$19$	5.34685	1.22665	0.613326	−	0.789830i	$-0.289831\pi$
$19$	5.34685	1.22665	0.613326	+	0.789830i	$0.289831\pi$
$20$	−7.57640	−1.69413
$21$	0.675914	0.147497
$22$	11.8266	2.52143
$23$	1.72316	0.359303	0.179652	−	0.983730i	$-0.442503\pi$
$23$	1.72316	0.359303	0.179652	+	0.983730i	$0.442503\pi$
$24$	8.98054	1.83315
$25$	−2.97141	−0.594281
$26$	−5.22210	−1.02414
$27$	−1.00000	−0.192450
$28$	−3.59548	−0.679482
$29$	−2.61132	−0.484910	−0.242455	−	0.970163i	$-0.577953\pi$
$29$	−2.61132	−0.484910	−0.242455	+	0.970163i	$0.577953\pi$
$30$	−3.85333	−0.703519
$31$	−7.49797	−1.34667	−0.673337	−	0.739335i	$-0.735140\pi$
$31$	−7.49797	−1.34667	−0.673337	+	0.739335i	$0.735140\pi$
$32$	−18.9885	−3.35673
$33$	4.37139	0.760962
$34$	−1.12776	−0.193410
$35$	0.962696	0.162725
$36$	5.31943	0.886572
$37$	6.02747	0.990911	0.495455	−	0.868633i	$-0.335001\pi$
$37$	6.02747	0.990911	0.495455	+	0.868633i	$0.335001\pi$
$38$	−14.4656	−2.34663
$39$	−1.93022	−0.309082
$40$	12.7909	2.02241
$41$	8.02874	1.25388	0.626939	−	0.779068i	$-0.284307\pi$
$41$	8.02874	1.25388	0.626939	+	0.779068i	$0.284307\pi$
$42$	−1.82865	−0.282167
$43$	7.76021	1.18342	0.591710	−	0.806151i	$-0.298453\pi$
$43$	7.76021	1.18342	0.591710	+	0.806151i	$0.298453\pi$
$44$	−23.2533	−3.50557
$45$	−1.42429	−0.212320
$46$	−4.66191	−0.687361
$47$	0.257459	0.0375542	0.0187771	−	0.999824i	$-0.494023\pi$
$47$	0.257459	0.0375542	0.0187771	+	0.999824i	$0.494023\pi$
$48$	−13.6575	−1.97129
$49$	−6.54314	−0.934734
$50$	8.03898	1.13688
$51$	−0.416850	−0.0583706
$52$	10.2677	1.42387
$53$	−12.4498	−1.71011	−0.855057	−	0.518534i	$-0.826478\pi$
$53$	−12.4498	−1.71011	−0.855057	+	0.518534i	$0.826478\pi$
$54$	2.70545	0.368164
$55$	6.22612	0.839530
$56$	6.07008	0.811148
$57$	−5.34685	−0.708207
$58$	7.06479	0.927652
$59$	−8.01484	−1.04344	−0.521722	−	0.853116i	$-0.674710\pi$
$59$	−8.01484	−1.04344	−0.521722	+	0.853116i	$0.674710\pi$
$60$	7.57640	0.978109
$61$	−4.16731	−0.533569	−0.266785	−	0.963756i	$-0.585961\pi$
$61$	−4.16731	−0.533569	−0.266785	+	0.963756i	$0.585961\pi$
$62$	20.2853	2.57624
$63$	−0.675914	−0.0851572
$64$	24.0574	3.00718
$65$	−2.74919	−0.340994
$66$	−11.8266	−1.45575
$67$	2.01613	0.246310	0.123155	−	0.992387i	$-0.460699\pi$
$67$	2.01613	0.246310	0.123155	+	0.992387i	$0.460699\pi$
$68$	2.21740	0.268900
$69$	−1.72316	−0.207444
$70$	−2.60452	−0.311300
$71$	−6.48849	−0.770042	−0.385021	−	0.922908i	$-0.625806\pi$
$71$	−6.48849	−0.770042	−0.385021	+	0.922908i	$0.625806\pi$
$72$	−8.98054	−1.05837
$73$	−2.61635	−0.306221	−0.153110	−	0.988209i	$-0.548929\pi$
$73$	−2.61635	−0.306221	−0.153110	+	0.988209i	$0.548929\pi$
$74$	−16.3070	−1.89565
$75$	2.97141	0.343108
$76$	28.4422	3.26254
$77$	2.95469	0.336718
$78$	5.22210	0.591286
$79$	7.55884	0.850436	0.425218	−	0.905091i	$-0.360197\pi$
$79$	7.55884	0.850436	0.425218	+	0.905091i	$0.360197\pi$
$80$	−19.4522	−2.17482
$81$	1.00000	0.111111
$82$	−21.7213	−2.39872
$83$	5.54191	0.608304	0.304152	−	0.952624i	$-0.401627\pi$
$83$	5.54191	0.608304	0.304152	+	0.952624i	$0.401627\pi$
$84$	3.59548	0.392299
$85$	−0.593713	−0.0643973
$86$	−20.9948	−2.26393
$87$	2.61132	0.279963
$88$	39.2575	4.18486
$89$	11.3532	1.20344	0.601719	−	0.798708i	$-0.294483\pi$
$89$	11.3532	1.20344	0.601719	+	0.798708i	$0.294483\pi$
$90$	3.85333	0.406177
$91$	−1.30466	−0.136766
$92$	9.16622	0.955644
$93$	7.49797	0.777503
$94$	−0.696540	−0.0718427
$95$	−7.61545	−0.781329
$96$	18.9885	1.93801
$97$	−3.74307	−0.380051	−0.190025	−	0.981779i	$-0.560857\pi$
$97$	−3.74307	−0.380051	−0.190025	+	0.981779i	$0.560857\pi$
$98$	17.7021	1.78818
$99$	−4.37139	−0.439341
$100$	−15.8062	−1.58062
$101$	2.99930	0.298441	0.149221	−	0.988804i	$-0.452324\pi$
$101$	2.99930	0.298441	0.149221	+	0.988804i	$0.452324\pi$
$102$	1.12776	0.111665
$103$	−14.4225	−1.42109	−0.710544	−	0.703653i	$-0.751551\pi$
$103$	−14.4225	−1.42109	−0.710544	+	0.703653i	$0.751551\pi$
$104$	−17.3344	−1.69978
$105$	−0.962696	−0.0939495
$106$	33.6823	3.27151
$107$	16.3490	1.58052	0.790260	−	0.612771i	$-0.209945\pi$
$107$	16.3490	1.58052	0.790260	+	0.612771i	$0.209945\pi$
$108$	−5.31943	−0.511863
$109$	18.6087	1.78239	0.891197	−	0.453617i	$-0.149866\pi$
$109$	18.6087	1.78239	0.891197	+	0.453617i	$0.149866\pi$
$110$	−16.8444	−1.60605
$111$	−6.02747	−0.572103
$112$	−9.23130	−0.872276
$113$	12.4503	1.17123	0.585613	−	0.810591i	$-0.300854\pi$
$113$	12.4503	1.17123	0.585613	+	0.810591i	$0.300854\pi$
$114$	14.4656	1.35483
$115$	−2.45427	−0.228862
$116$	−13.8908	−1.28972
$117$	1.93022	0.178449
$118$	21.6837	1.99615
$119$	−0.281755	−0.0258284
$120$	−12.7909	−1.16764
$121$	8.10907	0.737188
$122$	11.2744	1.02074
$123$	−8.02874	−0.723927
$124$	−39.8849	−3.58177
$125$	11.3536	1.01549
$126$	1.82865	0.162909
$127$	13.5862	1.20558	0.602791	−	0.797899i	$-0.294055\pi$
$127$	13.5862	1.20558	0.602791	+	0.797899i	$0.294055\pi$
$128$	−27.1090	−2.39612
$129$	−7.76021	−0.683248
$130$	7.43777	0.652336
$131$	15.9264	1.39150	0.695749	−	0.718285i	$-0.255073\pi$
$131$	15.9264	1.39150	0.695749	+	0.718285i	$0.255073\pi$
$132$	23.2533	2.02394
$133$	−3.61401	−0.313375
$134$	−5.45454	−0.471200
$135$	1.42429	0.122583
$136$	−3.74354	−0.321006
$137$	−7.15072	−0.610927	−0.305464	−	0.952204i	$-0.598811\pi$
$137$	−7.15072	−0.610927	−0.305464	+	0.952204i	$0.598811\pi$
$138$	4.66191	0.396848
$139$	0.0195742	0.00166026	0.000830130	−	1.00000i	$-0.499736\pi$
$139$	0.0195742	0.00166026	0.000830130		1.00000i	$0.499736\pi$
$140$	5.12100	0.432803
$141$	−0.257459	−0.0216819
$142$	17.5543	1.47312
$143$	−8.43774	−0.705599
$144$	13.6575	1.13813
$145$	3.71927	0.308869
$146$	7.07839	0.585812
$147$	6.54314	0.539669
$148$	32.0628	2.63554
$149$	−19.2285	−1.57526	−0.787631	−	0.616147i	$-0.788693\pi$
$149$	−19.2285	−1.57526	−0.787631	+	0.616147i	$0.788693\pi$
$150$	−8.03898	−0.656380
$151$	−19.4076	−1.57937	−0.789683	−	0.613515i	$-0.789755\pi$
$151$	−19.4076	−1.57937	−0.789683	+	0.613515i	$0.789755\pi$
$152$	−48.0176	−3.89474
$153$	0.416850	0.0337003
$154$	−7.99374	−0.644154
$155$	10.6793	0.857779
$156$	−10.2677	−0.822071
$157$	−12.1809	−0.972144	−0.486072	−	0.873919i	$-0.661571\pi$
$157$	−12.1809	−0.972144	−0.486072	+	0.873919i	$0.661571\pi$
$158$	−20.4500	−1.62692
$159$	12.4498	0.987335
$160$	27.0451	2.13811
$161$	−1.16471	−0.0917917
$162$	−2.70545	−0.212560
$163$	6.91106	0.541316	0.270658	−	0.962676i	$-0.412759\pi$
$163$	6.91106	0.541316	0.270658	+	0.962676i	$0.412759\pi$
$164$	42.7083	3.33496
$165$	−6.22612	−0.484703
$166$	−14.9933	−1.16371
$167$	15.4420	1.19494	0.597470	−	0.801891i	$-0.296173\pi$
$167$	15.4420	1.19494	0.597470	+	0.801891i	$0.296173\pi$
$168$	−6.07008	−0.468317
$169$	−9.27426	−0.713404
$170$	1.60626	0.123194
$171$	5.34685	0.408884
$172$	41.2799	3.14756
$173$	−18.4837	−1.40529	−0.702646	−	0.711539i	$-0.747998\pi$
$173$	−18.4837	−1.40529	−0.702646	+	0.711539i	$0.747998\pi$
$174$	−7.06479	−0.535580
$175$	2.00842	0.151822
$176$	−59.7023	−4.50023
$177$	8.01484	0.602432
$178$	−30.7155	−2.30222
$179$	−18.5918	−1.38962	−0.694809	−	0.719194i	$-0.744511\pi$
$179$	−18.5918	−1.38962	−0.694809	+	0.719194i	$0.744511\pi$
$180$	−7.57640	−0.564712
$181$	4.79288	0.356252	0.178126	−	0.984008i	$-0.442997\pi$
$181$	4.79288	0.356252	0.178126	+	0.984008i	$0.442997\pi$
$182$	3.52969	0.261638
$183$	4.16731	0.308056
$184$	−15.4749	−1.14082
$185$	−8.58486	−0.631171
$186$	−20.2853	−1.48739
$187$	−1.82221	−0.133253
$188$	1.36953	0.0998836
$189$	0.675914	0.0491655
$190$	20.6032	1.49471
$191$	2.31999	0.167868	0.0839342	−	0.996471i	$-0.473251\pi$
$191$	2.31999	0.167868	0.0839342	+	0.996471i	$0.473251\pi$
$192$	−24.0574	−1.73620
$193$	14.4753	1.04196	0.520978	−	0.853570i	$-0.325567\pi$
$193$	14.4753	1.04196	0.520978	+	0.853570i	$0.325567\pi$
$194$	10.1267	0.727052
$195$	2.74919	0.196873
$196$	−34.8058	−2.48613
$197$	13.0524	0.929943	0.464971	−	0.885326i	$-0.346065\pi$
$197$	13.0524	0.929943	0.464971	+	0.885326i	$0.346065\pi$
$198$	11.8266	0.840477
$199$	9.72171	0.689154	0.344577	−	0.938758i	$-0.388022\pi$
$199$	9.72171	0.689154	0.344577	+	0.938758i	$0.388022\pi$
$200$	26.6848	1.88690
$201$	−2.01613	−0.142207
$202$	−8.11444	−0.570930
$203$	1.76503	0.123881
$204$	−2.21740	−0.155249
$205$	−11.4352	−0.798671
$206$	39.0192	2.71859
$207$	1.72316	0.119768
$208$	26.3620	1.82787
$209$	−23.3732	−1.61676
$210$	2.60452	0.179729
$211$	−18.7865	−1.29332	−0.646659	−	0.762779i	$-0.723834\pi$
$211$	−18.7865	−1.29332	−0.646659	+	0.762779i	$0.723834\pi$
$212$	−66.2260	−4.54842
$213$	6.48849	0.444584
$214$	−44.2314	−3.02360
$215$	−11.0528	−0.753792
$216$	8.98054	0.611049
$217$	5.06798	0.344037
$218$	−50.3449	−3.40979
$219$	2.61635	0.176797
$220$	33.1194	2.23291
$221$	0.804611	0.0541240
$222$	16.3070	1.09445
$223$	24.3143	1.62820	0.814102	−	0.580722i	$-0.197230\pi$
$223$	24.3143	1.62820	0.814102	+	0.580722i	$0.197230\pi$
$224$	12.8346	0.857549
$225$	−2.97141	−0.198094
$226$	−33.6836	−2.24060
$227$	−25.0049	−1.65963	−0.829816	−	0.558037i	$-0.811555\pi$
$227$	−25.0049	−1.65963	−0.829816	+	0.558037i	$0.811555\pi$
$228$	−28.4422	−1.88363
$229$	11.4045	0.753633	0.376817	−	0.926288i	$-0.377019\pi$
$229$	11.4045	0.753633	0.376817	+	0.926288i	$0.377019\pi$
$230$	6.63989	0.437822
$231$	−2.95469	−0.194404
$232$	23.4511	1.53964
$233$	−20.5931	−1.34910	−0.674550	−	0.738229i	$-0.735662\pi$
$233$	−20.5931	−1.34910	−0.674550	+	0.738229i	$0.735662\pi$
$234$	−5.22210	−0.341379
$235$	−0.366695	−0.0239206
$236$	−42.6344	−2.77526
$237$	−7.55884	−0.490999
$238$	0.762272	0.0494107
$239$	8.45614	0.546982	0.273491	−	0.961875i	$-0.411822\pi$
$239$	8.45614	0.546982	0.273491	+	0.961875i	$0.411822\pi$
$240$	19.4522	1.25563
$241$	−8.72431	−0.561982	−0.280991	−	0.959710i	$-0.590663\pi$
$241$	−8.72431	−0.561982	−0.280991	+	0.959710i	$0.590663\pi$
$242$	−21.9386	−1.41027
$243$	−1.00000	−0.0641500
$244$	−22.1677	−1.41914
$245$	9.31931	0.595389
$246$	21.7213	1.38490
$247$	10.3206	0.656683
$248$	67.3358	4.27583
$249$	−5.54191	−0.351204
$250$	−30.7165	−1.94268
$251$	−5.47743	−0.345732	−0.172866	−	0.984945i	$-0.555303\pi$
$251$	−5.47743	−0.345732	−0.172866	+	0.984945i	$0.555303\pi$
$252$	−3.59548	−0.226494
$253$	−7.53259	−0.473570
$254$	−36.7568	−2.30632
$255$	0.593713	0.0371798
$256$	25.2271	1.57669
$257$	20.4761	1.27726	0.638632	−	0.769512i	$-0.279501\pi$
$257$	20.4761	1.27726	0.638632	+	0.769512i	$0.279501\pi$
$258$	20.9948	1.30708
$259$	−4.07406	−0.253150
$260$	−14.6241	−0.906949
$261$	−2.61132	−0.161637
$262$	−43.0880	−2.66199
$263$	24.3198	1.49962	0.749812	−	0.661651i	$-0.230144\pi$
$263$	24.3198	1.49962	0.749812	+	0.661651i	$0.230144\pi$
$264$	−39.2575	−2.41613
$265$	17.7321	1.08927
$266$	9.77751	0.599498
$267$	−11.3532	−0.694805
$268$	10.7247	0.655114
$269$	−25.8552	−1.57642	−0.788211	−	0.615405i	$-0.788992\pi$
$269$	−25.8552	−1.57642	−0.788211	+	0.615405i	$0.788992\pi$
$270$	−3.85333	−0.234506
$271$	21.6811	1.31704	0.658518	−	0.752565i	$-0.271184\pi$
$271$	21.6811	1.31704	0.658518	+	0.752565i	$0.271184\pi$
$272$	5.69312	0.345196
$273$	1.30466	0.0789618
$274$	19.3459	1.16873
$275$	12.9892	0.783277
$276$	−9.16622	−0.551741
$277$	22.4740	1.35033	0.675165	−	0.737667i	$-0.264073\pi$
$277$	22.4740	1.35033	0.675165	+	0.737667i	$0.264073\pi$
$278$	−0.0529569	−0.00317614
$279$	−7.49797	−0.448892
$280$	−8.64554	−0.516670
$281$	18.1874	1.08497	0.542485	−	0.840065i	$-0.317483\pi$
$281$	18.1874	1.08497	0.542485	+	0.840065i	$0.317483\pi$
$282$	0.696540	0.0414784
$283$	−18.9839	−1.12847	−0.564237	−	0.825613i	$-0.690830\pi$
$283$	−18.9839	−1.12847	−0.564237	+	0.825613i	$0.690830\pi$
$284$	−34.5151	−2.04809
$285$	7.61545	0.451100
$286$	22.8278	1.34984
$287$	−5.42674	−0.320330
$288$	−18.9885	−1.11891
$289$	−16.8262	−0.989779
$290$	−10.0623	−0.590878
$291$	3.74307	0.219423
$292$	−13.9175	−0.814460
$293$	−5.11637	−0.298901	−0.149451	−	0.988769i	$-0.547751\pi$
$293$	−5.11637	−0.298901	−0.149451	+	0.988769i	$0.547751\pi$
$294$	−17.7021	−1.03241
$295$	11.4154	0.664632
$296$	−54.1300	−3.14624
$297$	4.37139	0.253654
$298$	52.0217	3.01354
$299$	3.32607	0.192352
$300$	15.8062	0.912571
$301$	−5.24524	−0.302330
$302$	52.5061	3.02139
$303$	−2.99930	−0.172305
$304$	73.0246	4.18825
$305$	5.93545	0.339863
$306$	−1.12776	−0.0644699
$307$	−17.1215	−0.977176	−0.488588	−	0.872515i	$-0.662488\pi$
$307$	−17.1215	−0.977176	−0.488588	+	0.872515i	$0.662488\pi$
$308$	15.7173	0.895574
$309$	14.4225	0.820465
$310$	−28.8921	−1.64096
$311$	22.6374	1.28365	0.641825	−	0.766851i	$-0.278177\pi$
$311$	22.6374	1.28365	0.641825	+	0.766851i	$0.278177\pi$
$312$	17.3344	0.981368
$313$	−0.0822687	−0.00465010	−0.00232505	−	0.999997i	$-0.500740\pi$
$313$	−0.0822687	−0.00465010	−0.00232505	+	0.999997i	$0.500740\pi$
$314$	32.9548	1.85975
$315$	0.962696	0.0542418
$316$	40.2087	2.26192
$317$	19.5083	1.09569	0.547847	−	0.836578i	$-0.315448\pi$
$317$	19.5083	1.09569	0.547847	+	0.836578i	$0.315448\pi$
$318$	−33.6823	−1.88881
$319$	11.4151	0.639124
$320$	−34.2647	−1.91546
$321$	−16.3490	−0.912514
$322$	3.15105	0.175601
$323$	2.22883	0.124015
$324$	5.31943	0.295524
$325$	−5.73546	−0.318146
$326$	−18.6975	−1.03556
$327$	−18.6087	−1.02907
$328$	−72.1025	−3.98119
$329$	−0.174020	−0.00959403
$330$	16.8444	0.927255
$331$	−24.6727	−1.35614	−0.678068	−	0.734999i	$-0.737182\pi$
$331$	−24.6727	−1.35614	−0.678068	+	0.734999i	$0.737182\pi$
$332$	29.4798	1.61792
$333$	6.02747	0.330304
$334$	−41.7776	−2.28597
$335$	−2.87155	−0.156890
$336$	9.23130	0.503609
$337$	−15.9517	−0.868943	−0.434471	−	0.900686i	$-0.643065\pi$
$337$	−15.9517	−0.868943	−0.434471	+	0.900686i	$0.643065\pi$
$338$	25.0910	1.36477
$339$	−12.4503	−0.676207
$340$	−3.15822	−0.171278
$341$	32.7766	1.77495
$342$	−14.4656	−0.782210
$343$	9.15400	0.494270
$344$	−69.6909	−3.75748
$345$	2.45427	0.132133
$346$	50.0067	2.68838
$347$	35.1430	1.88657	0.943287	−	0.331978i	$-0.107716\pi$
$347$	35.1430	1.88657	0.943287	+	0.331978i	$0.107716\pi$
$348$	13.8908	0.744623
$349$	22.5500	1.20707	0.603537	−	0.797335i	$-0.293758\pi$
$349$	22.5500	1.20707	0.603537	+	0.797335i	$0.293758\pi$
$350$	−5.43366	−0.290441
$351$	−1.93022	−0.103027
$352$	83.0063	4.42425
$353$	24.7850	1.31917	0.659587	−	0.751628i	$-0.270731\pi$
$353$	24.7850	1.31917	0.659587	+	0.751628i	$0.270731\pi$
$354$	−21.6837	−1.15248
$355$	9.24148	0.490487
$356$	60.3926	3.20080
$357$	0.281755	0.0149120
$358$	50.2992	2.65839
$359$	−14.3133	−0.755425	−0.377713	−	0.925923i	$-0.623289\pi$
$359$	−14.3133	−0.755425	−0.377713	+	0.925923i	$0.623289\pi$
$360$	12.7909	0.674138
$361$	9.58879	0.504673
$362$	−12.9669	−0.681523
$363$	−8.10907	−0.425616
$364$	−6.94006	−0.363758
$365$	3.72643	0.195050
$366$	−11.2744	−0.589324
$367$	−15.7273	−0.820961	−0.410480	−	0.911869i	$-0.634639\pi$
$367$	−15.7273	−0.820961	−0.410480	+	0.911869i	$0.634639\pi$
$368$	23.5340	1.22680
$369$	8.02874	0.417959
$370$	23.2259	1.20745
$371$	8.41501	0.436885
$372$	39.8849	2.06794
$373$	24.6358	1.27559	0.637797	−	0.770205i	$-0.279846\pi$
$373$	24.6358	1.27559	0.637797	+	0.770205i	$0.279846\pi$
$374$	4.92990	0.254919
$375$	−11.3536	−0.586296
$376$	−2.31212	−0.119238
$377$	−5.04042	−0.259595
$378$	−1.82865	−0.0940556
$379$	14.2477	0.731855	0.365927	−	0.930643i	$-0.380752\pi$
$379$	14.2477	0.731855	0.365927	+	0.930643i	$0.380752\pi$
$380$	−40.5099	−2.07811
$381$	−13.5862	−0.696043
$382$	−6.27660	−0.321139
$383$	22.4821	1.14878	0.574392	−	0.818580i	$-0.305239\pi$
$383$	22.4821	1.14878	0.574392	+	0.818580i	$0.305239\pi$
$384$	27.1090	1.38340
$385$	−4.20832	−0.214476
$386$	−39.1622	−1.99330
$387$	7.76021	0.394473
$388$	−19.9110	−1.01083
$389$	−26.8382	−1.36075	−0.680375	−	0.732864i	$-0.738183\pi$
$389$	−26.8382	−1.36075	−0.680375	+	0.732864i	$0.738183\pi$
$390$	−7.43777	−0.376626
$391$	0.718297	0.0363258
$392$	58.7610	2.96788
$393$	−15.9264	−0.803381
$394$	−35.3125	−1.77902
$395$	−10.7660	−0.541694
$396$	−23.2533	−1.16852
$397$	11.0813	0.556154	0.278077	−	0.960559i	$-0.410303\pi$
$397$	11.0813	0.556154	0.278077	+	0.960559i	$0.410303\pi$
$398$	−26.3016	−1.31838
$399$	3.61401	0.180927
$400$	−40.5820	−2.02910
$401$	−16.1034	−0.804164	−0.402082	−	0.915604i	$-0.631713\pi$
$401$	−16.1034	−0.804164	−0.402082	+	0.915604i	$0.631713\pi$
$402$	5.45454	0.272047
$403$	−14.4727	−0.720937
$404$	15.9546	0.793769
$405$	−1.42429	−0.0707734
$406$	−4.77519	−0.236989
$407$	−26.3485	−1.30604
$408$	3.74354	0.185333
$409$	−2.71128	−0.134064	−0.0670322	−	0.997751i	$-0.521353\pi$
$409$	−2.71128	−0.134064	−0.0670322	+	0.997751i	$0.521353\pi$
$410$	30.9374	1.52789
$411$	7.15072	0.352719
$412$	−76.7193	−3.77969
$413$	5.41735	0.266570
$414$	−4.66191	−0.229120
$415$	−7.89327	−0.387465
$416$	−36.6520	−1.79701
$417$	−0.0195742	−0.000958552 0
$418$	63.2348	3.09292
$419$	−3.83430	−0.187318	−0.0936590	−	0.995604i	$-0.529856\pi$
$419$	−3.83430	−0.187318	−0.0936590	+	0.995604i	$0.529856\pi$
$420$	−5.12100	−0.249879
$421$	−5.71881	−0.278718	−0.139359	−	0.990242i	$-0.544504\pi$
$421$	−5.71881	−0.278718	−0.139359	+	0.990242i	$0.544504\pi$
$422$	50.8259	2.47417
$423$	0.257459	0.0125181
$424$	111.806	5.42978
$425$	−1.23863	−0.0600823
$426$	−17.5543	−0.850507
$427$	2.81674	0.136312
$428$	86.9676	4.20374
$429$	8.43774	0.407378
$430$	29.9026	1.44203
$431$	37.3493	1.79905	0.899525	−	0.436869i	$-0.143913\pi$
$431$	37.3493	1.79905	0.899525	+	0.436869i	$0.143913\pi$
$432$	−13.6575	−0.657097
$433$	−9.11820	−0.438192	−0.219096	−	0.975703i	$-0.570311\pi$
$433$	−9.11820	−0.438192	−0.219096	+	0.975703i	$0.570311\pi$
$434$	−13.7111	−0.658156
$435$	−3.71927	−0.178325
$436$	98.9879	4.74066
$437$	9.21346	0.440740
$438$	−7.07839	−0.338219
$439$	−33.4411	−1.59606	−0.798029	−	0.602618i	$-0.794124\pi$
$439$	−33.4411	−1.59606	−0.798029	+	0.602618i	$0.794124\pi$
$440$	−55.9139	−2.66559
$441$	−6.54314	−0.311578
$442$	−2.17683	−0.103541
$443$	−3.75378	−0.178347	−0.0891737	−	0.996016i	$-0.528423\pi$
$443$	−3.75378	−0.178347	−0.0891737	+	0.996016i	$0.528423\pi$
$444$	−32.0628	−1.52163
$445$	−16.1702	−0.766542
$446$	−65.7809	−3.11482
$447$	19.2285	0.909478
$448$	−16.2608	−0.768249
$449$	−18.8097	−0.887685	−0.443843	−	0.896105i	$-0.646385\pi$
$449$	−18.8097	−0.887685	−0.443843	+	0.896105i	$0.646385\pi$
$450$	8.03898	0.378961
$451$	−35.0968	−1.65264
$452$	66.2285	3.11513
$453$	19.4076	0.911848
$454$	67.6493	3.17494
$455$	1.85821	0.0871144
$456$	48.0176	2.24863
$457$	−5.05022	−0.236239	−0.118120	−	0.992999i	$-0.537687\pi$
$457$	−5.05022	−0.236239	−0.118120	+	0.992999i	$0.537687\pi$
$458$	−30.8544	−1.44173
$459$	−0.416850	−0.0194569
$460$	−13.0553	−0.608708
$461$	−6.20042	−0.288782	−0.144391	−	0.989521i	$-0.546122\pi$
$461$	−6.20042	−0.288782	−0.144391	+	0.989521i	$0.546122\pi$
$462$	7.99374	0.371903
$463$	−12.2317	−0.568456	−0.284228	−	0.958757i	$-0.591737\pi$
$463$	−12.2317	−0.568456	−0.284228	+	0.958757i	$0.591737\pi$
$464$	−35.6641	−1.65567
$465$	−10.6793	−0.495239
$466$	55.7135	2.58088
$467$	−3.58802	−0.166034	−0.0830170	−	0.996548i	$-0.526456\pi$
$467$	−3.58802	−0.166034	−0.0830170	+	0.996548i	$0.526456\pi$
$468$	10.2677	0.474623
$469$	−1.36273	−0.0629251
$470$	0.992074	0.0457609
$471$	12.1809	0.561267
$472$	71.9776	3.31304
$473$	−33.9229	−1.55978
$474$	20.4500	0.939301
$475$	−15.8877	−0.728976
$476$	−1.49877	−0.0686962
$477$	−12.4498	−0.570038
$478$	−22.8776	−1.04640
$479$	12.1543	0.555345	0.277672	−	0.960676i	$-0.410437\pi$
$479$	12.1543	0.555345	0.277672	+	0.960676i	$0.410437\pi$
$480$	−27.0451	−1.23444
$481$	11.6343	0.530480
$482$	23.6031	1.07509
$483$	1.16471	0.0529960
$484$	43.1357	1.96071
$485$	5.33120	0.242078
$486$	2.70545	0.122721
$487$	37.3293	1.69155	0.845777	−	0.533537i	$-0.179137\pi$
$487$	37.3293	1.69155	0.845777	+	0.533537i	$0.179137\pi$
$488$	37.4247	1.69414
$489$	−6.91106	−0.312529
$490$	−25.2129	−1.13900
$491$	−25.6187	−1.15616	−0.578078	−	0.815982i	$-0.696197\pi$
$491$	−25.6187	−1.15616	−0.578078	+	0.815982i	$0.696197\pi$
$492$	−42.7083	−1.92544
$493$	−1.08853	−0.0490249
$494$	−27.9218	−1.25626
$495$	6.22612	0.279843
$496$	−102.404	−4.59805
$497$	4.38566	0.196724
$498$	14.9933	0.671867
$499$	24.2633	1.08617	0.543087	−	0.839677i	$-0.317255\pi$
$499$	24.2633	1.08617	0.543087	+	0.839677i	$0.317255\pi$
$500$	60.3946	2.70093
$501$	−15.4420	−0.689899
$502$	14.8189	0.661399
$503$	23.7459	1.05878	0.529389	−	0.848379i	$-0.322421\pi$
$503$	23.7459	1.05878	0.529389	+	0.848379i	$0.322421\pi$
$504$	6.07008	0.270383
$505$	−4.27186	−0.190095
$506$	20.3790	0.905958
$507$	9.27426	0.411884
$508$	72.2710	3.20651
$509$	−3.19272	−0.141515	−0.0707574	−	0.997494i	$-0.522542\pi$
$509$	−3.19272	−0.141515	−0.0707574	+	0.997494i	$0.522542\pi$
$510$	−1.60626	−0.0711264
$511$	1.76843	0.0782307
$512$	−14.0324	−0.620150
$513$	−5.34685	−0.236069
$514$	−55.3970	−2.44346
$515$	20.5417	0.905177
$516$	−41.2799	−1.81725
$517$	−1.12545	−0.0494974
$518$	11.0221	0.484285
$519$	18.4837	0.811346
$520$	24.6892	1.08269
$521$	−6.20075	−0.271660	−0.135830	−	0.990732i	$-0.543370\pi$
$521$	−6.20075	−0.271660	−0.135830	+	0.990732i	$0.543370\pi$
$522$	7.06479	0.309217
$523$	35.3684	1.54655	0.773276	−	0.634070i	$-0.218617\pi$
$523$	35.3684	1.54655	0.773276	+	0.634070i	$0.218617\pi$
$524$	84.7195	3.70099
$525$	−2.00842	−0.0876545
$526$	−65.7959	−2.86884
$527$	−3.12552	−0.136150
$528$	59.7023	2.59821
$529$	−20.0307	−0.870901
$530$	−47.9733	−2.08383
$531$	−8.01484	−0.347814
$532$	−19.2245	−0.833488
$533$	15.4972	0.671259
$534$	30.7155	1.32919
$535$	−23.2857	−1.00673
$536$	−18.1060	−0.782059
$537$	18.5918	0.802296
$538$	69.9499	3.01576
$539$	28.6026	1.23200
$540$	7.57640	0.326036
$541$	−1.97339	−0.0848429	−0.0424214	−	0.999100i	$-0.513507\pi$
$541$	−1.97339	−0.0848429	−0.0424214	+	0.999100i	$0.513507\pi$
$542$	−58.6572	−2.51954
$543$	−4.79288	−0.205682
$544$	−7.91536	−0.339368
$545$	−26.5042	−1.13531
$546$	−3.52969	−0.151057
$547$	−22.8587	−0.977366	−0.488683	−	0.872461i	$-0.662523\pi$
$547$	−22.8587	−0.977366	−0.488683	+	0.872461i	$0.662523\pi$
$548$	−38.0378	−1.62489
$549$	−4.16731	−0.177856
$550$	−35.1415	−1.49844
$551$	−13.9623	−0.594816
$552$	15.4749	0.658655
$553$	−5.10913	−0.217262
$554$	−60.8021	−2.58323
$555$	8.58486	0.364407
$556$	0.104124	0.00441582
$557$	−24.7081	−1.04692	−0.523459	−	0.852051i	$-0.675359\pi$
$557$	−24.7081	−1.04692	−0.523459	+	0.852051i	$0.675359\pi$
$558$	20.2853	0.858747
$559$	14.9789	0.633540
$560$	13.1480	0.555606
$561$	1.82221	0.0769339
$562$	−49.2051	−2.07559
$563$	0.535016	0.0225482	0.0112741	−	0.999936i	$-0.496411\pi$
$563$	0.535016	0.0225482	0.0112741	+	0.999936i	$0.496411\pi$
$564$	−1.36953	−0.0576678
$565$	−17.7328	−0.746025
$566$	51.3598	2.15881
$567$	−0.675914	−0.0283857
$568$	58.2702	2.44496
$569$	22.1212	0.927367	0.463684	−	0.886001i	$-0.346527\pi$
$569$	22.1212	0.927367	0.463684	+	0.886001i	$0.346527\pi$
$570$	−20.6032	−0.862972
$571$	−10.1916	−0.426505	−0.213253	−	0.976997i	$-0.568406\pi$
$571$	−10.1916	−0.426505	−0.213253	+	0.976997i	$0.568406\pi$
$572$	−44.8840	−1.87669
$573$	−2.31999	−0.0969188
$574$	14.6817	0.612804
$575$	−5.12020	−0.213527
$576$	24.0574	1.00239
$577$	−1.99068	−0.0828733	−0.0414366	−	0.999141i	$-0.513193\pi$
$577$	−1.99068	−0.0828733	−0.0414366	+	0.999141i	$0.513193\pi$
$578$	45.5225	1.89348
$579$	−14.4753	−0.601574
$580$	19.7844	0.821504
$581$	−3.74586	−0.155404
$582$	−10.1267	−0.419764
$583$	54.4230	2.25397
$584$	23.4962	0.972281
$585$	−2.74919	−0.113665
$586$	13.8421	0.571810
$587$	−20.0097	−0.825889	−0.412944	−	0.910756i	$-0.635500\pi$
$587$	−20.0097	−0.825889	−0.412944	+	0.910756i	$0.635500\pi$
$588$	34.8058	1.43537
$589$	−40.0905	−1.65190
$590$	−30.8838	−1.27147
$591$	−13.0524	−0.536903
$592$	82.3203	3.38334
$593$	−22.8243	−0.937283	−0.468642	−	0.883388i	$-0.655256\pi$
$593$	−22.8243	−0.937283	−0.468642	+	0.883388i	$0.655256\pi$
$594$	−11.8266	−0.485250
$595$	0.401299	0.0164517
$596$	−102.285	−4.18975
$597$	−9.72171	−0.397883
$598$	−8.99850	−0.367976
$599$	−18.8711	−0.771051	−0.385525	−	0.922697i	$-0.625980\pi$
$599$	−18.8711	−0.771051	−0.385525	+	0.922697i	$0.625980\pi$
$600$	−26.6848	−1.08940
$601$	−38.4625	−1.56892	−0.784460	−	0.620180i	$-0.787060\pi$
$601$	−38.4625	−1.56892	−0.784460	+	0.620180i	$0.787060\pi$
$602$	14.1907	0.578370
$603$	2.01613	0.0821033
$604$	−103.237	−4.20067
$605$	−11.5496	−0.469560
$606$	8.11444	0.329626
$607$	−19.6547	−0.797759	−0.398880	−	0.917003i	$-0.630601\pi$
$607$	−19.6547	−0.797759	−0.398880	+	0.917003i	$0.630601\pi$
$608$	−101.529	−4.11754
$609$	−1.76503	−0.0715226
$610$	−16.0580	−0.650170
$611$	0.496951	0.0201045
$612$	2.21740	0.0896332
$613$	−26.8761	−1.08552	−0.542758	−	0.839889i	$-0.682620\pi$
$613$	−26.8761	−1.08552	−0.542758	+	0.839889i	$0.682620\pi$
$614$	46.3213	1.86937
$615$	11.4352	0.461113
$616$	−26.5347	−1.06911
$617$	5.18528	0.208752	0.104376	−	0.994538i	$-0.466716\pi$
$617$	5.18528	0.208752	0.104376	+	0.994538i	$0.466716\pi$
$618$	−39.0192	−1.56958
$619$	−47.3334	−1.90249	−0.951245	−	0.308435i	$-0.900195\pi$
$619$	−47.3334	−1.90249	−0.951245	+	0.308435i	$0.900195\pi$
$620$	56.8076	2.28145
$621$	−1.72316	−0.0691479
$622$	−61.2443	−2.45567
$623$	−7.67379	−0.307444
$624$	−26.3620	−1.05532
$625$	−1.31372	−0.0525487
$626$	0.222574	0.00889583
$627$	23.3732	0.933435
$628$	−64.7956	−2.58563
$629$	2.51255	0.100182
$630$	−2.60452	−0.103767
$631$	16.1803	0.644126	0.322063	−	0.946718i	$-0.395624\pi$
$631$	16.1803	0.644126	0.322063	+	0.946718i	$0.395624\pi$
$632$	−67.8825	−2.70022
$633$	18.7865	0.746697
$634$	−52.7786	−2.09611
$635$	−19.3507	−0.767908
$636$	66.2260	2.62603
$637$	−12.6297	−0.500406
$638$	−30.8830	−1.22267
$639$	−6.48849	−0.256681
$640$	38.6110	1.52623
$641$	−8.25460	−0.326037	−0.163019	−	0.986623i	$-0.552123\pi$
$641$	−8.25460	−0.326037	−0.163019	+	0.986623i	$0.552123\pi$
$642$	44.2314	1.74567
$643$	−10.7645	−0.424509	−0.212254	−	0.977214i	$-0.568081\pi$
$643$	−10.7645	−0.424509	−0.212254	+	0.977214i	$0.568081\pi$
$644$	−6.19558	−0.244140
$645$	11.0528	0.435202
$646$	−6.02998	−0.237246
$647$	−34.4408	−1.35401	−0.677003	−	0.735980i	$-0.736722\pi$
$647$	−34.4408	−1.35401	−0.677003	+	0.735980i	$0.736722\pi$
$648$	−8.98054	−0.352789
$649$	35.0360	1.37528
$650$	15.5170	0.608626
$651$	−5.06798	−0.198630
$652$	36.7629	1.43975
$653$	−33.5554	−1.31312	−0.656562	−	0.754272i	$-0.727990\pi$
$653$	−33.5554	−1.31312	−0.656562	+	0.754272i	$0.727990\pi$
$654$	50.3449	1.96864
$655$	−22.6838	−0.886329
$656$	109.653	4.28121
$657$	−2.61635	−0.102074
$658$	0.470802	0.0183538
$659$	−16.7856	−0.653873	−0.326937	−	0.945046i	$-0.606016\pi$
$659$	−16.7856	−0.653873	−0.326937	+	0.945046i	$0.606016\pi$
$660$	−33.1194	−1.28917
$661$	−9.39126	−0.365278	−0.182639	−	0.983180i	$-0.558464\pi$
$661$	−9.39126	−0.365278	−0.182639	+	0.983180i	$0.558464\pi$
$662$	66.7507	2.59434
$663$	−0.804611	−0.0312485
$664$	−49.7694	−1.93143
$665$	5.14739	0.199607
$666$	−16.3070	−0.631884
$667$	−4.49972	−0.174230
$668$	82.1428	3.17820
$669$	−24.3143	−0.940044
$670$	7.76882	0.300136
$671$	18.2169	0.703257
$672$	−12.8346	−0.495106
$673$	−21.1694	−0.816022	−0.408011	−	0.912977i	$-0.633777\pi$
$673$	−21.1694	−0.816022	−0.408011	+	0.912977i	$0.633777\pi$
$674$	43.1564	1.66232
$675$	2.97141	0.114369
$676$	−49.3338	−1.89745
$677$	−49.0467	−1.88502	−0.942508	−	0.334182i	$-0.891540\pi$
$677$	−49.0467	−1.88502	−0.942508	+	0.334182i	$0.891540\pi$
$678$	33.6836	1.29361
$679$	2.52999	0.0970922
$680$	5.33187	0.204468
$681$	25.0049	0.958189
$682$	−88.6752	−3.39555
$683$	33.9732	1.29995	0.649975	−	0.759956i	$-0.274779\pi$
$683$	33.9732	1.29995	0.649975	+	0.759956i	$0.274779\pi$
$684$	28.4422	1.08751
$685$	10.1847	0.389136
$686$	−24.7657	−0.945557
$687$	−11.4045	−0.435110
$688$	105.985	4.04064
$689$	−24.0309	−0.915503
$690$	−6.63989	−0.252776
$691$	46.4047	1.76532	0.882660	−	0.470013i	$-0.155751\pi$
$691$	46.4047	1.76532	0.882660	+	0.470013i	$0.155751\pi$
$692$	−98.3230	−3.73768
$693$	2.95469	0.112239
$694$	−95.0774	−3.60909
$695$	−0.0278793	−0.00105752
$696$	−23.4511	−0.888911
$697$	3.34678	0.126768
$698$	−61.0078	−2.30918
$699$	20.5931	0.778903
$700$	10.6836	0.403803
$701$	9.62938	0.363697	0.181848	−	0.983327i	$-0.441792\pi$
$701$	9.62938	0.363697	0.181848	+	0.983327i	$0.441792\pi$
$702$	5.22210	0.197095
$703$	32.2280	1.21550
$704$	−105.165	−3.96354
$705$	0.366695	0.0138105
$706$	−67.0545	−2.52363
$707$	−2.02727	−0.0762433
$708$	42.6344	1.60230
$709$	−52.0052	−1.95309	−0.976547	−	0.215303i	$-0.930926\pi$
$709$	−52.0052	−1.95309	−0.976547	+	0.215303i	$0.930926\pi$
$710$	−25.0023	−0.938320
$711$	7.55884	0.283479
$712$	−101.958	−3.82104
$713$	−12.9202	−0.483864
$714$	−0.762272	−0.0285273
$715$	12.0178	0.449439
$716$	−98.8980	−3.69599
$717$	−8.45614	−0.315800
$718$	38.7238	1.44516
$719$	−20.2995	−0.757042	−0.378521	−	0.925593i	$-0.623567\pi$
$719$	−20.2995	−0.757042	−0.378521	+	0.925593i	$0.623567\pi$
$720$	−19.4522	−0.724941
$721$	9.74835	0.363047
$722$	−25.9419	−0.965459
$723$	8.72431	0.324460
$724$	25.4954	0.947529
$725$	7.75930	0.288173
$726$	21.9386	0.814219
$727$	46.0650	1.70846	0.854228	−	0.519898i	$-0.174030\pi$
$727$	46.0650	1.70846	0.854228	+	0.519898i	$0.174030\pi$
$728$	11.7166	0.434245
$729$	1.00000	0.0370370
$730$	−10.0817	−0.373139
$731$	3.23484	0.119645
$732$	22.1677	0.819343
$733$	−9.99284	−0.369094	−0.184547	−	0.982824i	$-0.559082\pi$
$733$	−9.99284	−0.369094	−0.184547	+	0.982824i	$0.559082\pi$
$734$	42.5495	1.57053
$735$	−9.31931	−0.343748
$736$	−32.7202	−1.20608
$737$	−8.81330	−0.324642
$738$	−21.7213	−0.799573
$739$	24.1400	0.888006	0.444003	−	0.896025i	$-0.353558\pi$
$739$	24.1400	0.888006	0.444003	+	0.896025i	$0.353558\pi$
$740$	−45.6666	−1.67874
$741$	−10.3206	−0.379136
$742$	−22.7663	−0.835779
$743$	−16.7972	−0.616229	−0.308114	−	0.951349i	$-0.599698\pi$
$743$	−16.7972	−0.616229	−0.308114	+	0.951349i	$0.599698\pi$
$744$	−67.3358	−2.46865
$745$	27.3870	1.00338
$746$	−66.6508	−2.44026
$747$	5.54191	0.202768
$748$	−9.69314	−0.354416
$749$	−11.0505	−0.403778
$750$	30.7165	1.12161
$751$	−17.0424	−0.621885	−0.310942	−	0.950429i	$-0.600645\pi$
$751$	−17.0424	−0.621885	−0.310942	+	0.950429i	$0.600645\pi$
$752$	3.51624	0.128224
$753$	5.47743	0.199608
$754$	13.6366	0.496615
$755$	27.6420	1.00599
$756$	3.59548	0.130766
$757$	43.6150	1.58521	0.792607	−	0.609733i	$-0.208723\pi$
$757$	43.6150	1.58521	0.792607	+	0.609733i	$0.208723\pi$
$758$	−38.5464	−1.40007
$759$	7.53259	0.273416
$760$	68.3909	2.48080
$761$	−6.57001	−0.238163	−0.119081	−	0.992885i	$-0.537995\pi$
$761$	−6.57001	−0.238163	−0.119081	+	0.992885i	$0.537995\pi$
$762$	36.7568	1.33156
$763$	−12.5779	−0.455351
$764$	12.3410	0.446482
$765$	−0.593713	−0.0214658
$766$	−60.8242	−2.19767
$767$	−15.4704	−0.558603
$768$	−25.2271	−0.910303
$769$	9.54212	0.344098	0.172049	−	0.985088i	$-0.444961\pi$
$769$	9.54212	0.344098	0.172049	+	0.985088i	$0.444961\pi$
$770$	11.3854	0.410301
$771$	−20.4761	−0.737429
$772$	77.0005	2.77131
$773$	52.0010	1.87034	0.935172	−	0.354193i	$-0.115245\pi$
$773$	52.0010	1.87034	0.935172	+	0.354193i	$0.115245\pi$
$774$	−20.9948	−0.754643
$775$	22.2795	0.800303
$776$	33.6148	1.20670
$777$	4.07406	0.146156
$778$	72.6092	2.60317
$779$	42.9285	1.53807
$780$	14.6241	0.523627
$781$	28.3637	1.01493
$782$	−1.94331	−0.0694927
$783$	2.61132	0.0933210
$784$	−89.3630	−3.19153
$785$	17.3491	0.619217
$786$	43.0880	1.53690
$787$	7.60915	0.271237	0.135618	−	0.990761i	$-0.456698\pi$
$787$	7.60915	0.271237	0.135618	+	0.990761i	$0.456698\pi$
$788$	69.4312	2.47338
$789$	−24.3198	−0.865809
$790$	29.1267	1.03628
$791$	−8.41533	−0.299215
$792$	39.2575	1.39495
$793$	−8.04382	−0.285644
$794$	−29.9798	−1.06394
$795$	−17.7321	−0.628893
$796$	51.7140	1.83295
$797$	19.6754	0.696939	0.348469	−	0.937320i	$-0.386701\pi$
$797$	19.6754	0.696939	0.348469	+	0.937320i	$0.386701\pi$
$798$	−9.77751	−0.346120
$799$	0.107322	0.00379676
$800$	56.4227	1.99484
$801$	11.3532	0.401146
$802$	43.5668	1.53840
$803$	11.4371	0.403606
$804$	−10.7247	−0.378230
$805$	1.65888	0.0584677
$806$	39.1551	1.37918
$807$	25.8552	0.910147
$808$	−26.9353	−0.947582
$809$	−43.4287	−1.52687	−0.763436	−	0.645884i	$-0.776489\pi$
$809$	−43.4287	−1.52687	−0.763436	+	0.645884i	$0.776489\pi$
$810$	3.85333	0.135392
$811$	−0.674335	−0.0236791	−0.0118396	−	0.999930i	$-0.503769\pi$
$811$	−0.674335	−0.0236791	−0.0118396	+	0.999930i	$0.503769\pi$
$812$	9.38896	0.329488
$813$	−21.6811	−0.760391
$814$	71.2843	2.49851
$815$	−9.84334	−0.344797
$816$	−5.69312	−0.199299
$817$	41.4927	1.45164
$818$	7.33523	0.256470
$819$	−1.30466	−0.0455886
$820$	−60.8289	−2.12424
$821$	−38.0574	−1.32821	−0.664107	−	0.747638i	$-0.731188\pi$
$821$	−38.0574	−1.32821	−0.664107	+	0.747638i	$0.731188\pi$
$822$	−19.3459	−0.674765
$823$	−31.8463	−1.11009	−0.555046	−	0.831820i	$-0.687299\pi$
$823$	−31.8463	−1.11009	−0.555046	+	0.831820i	$0.687299\pi$
$824$	129.522	4.51210
$825$	−12.9892	−0.452225
$826$	−14.6563	−0.509959
$827$	−16.7354	−0.581946	−0.290973	−	0.956731i	$-0.593979\pi$
$827$	−16.7354	−0.581946	−0.290973	+	0.956731i	$0.593979\pi$
$828$	9.16622	0.318548
$829$	2.47772	0.0860548	0.0430274	−	0.999074i	$-0.486300\pi$
$829$	2.47772	0.0860548	0.0430274	+	0.999074i	$0.486300\pi$
$830$	21.3548	0.741236
$831$	−22.4740	−0.779613
$832$	46.4361	1.60988
$833$	−2.72750	−0.0945024
$834$	0.0529569	0.00183375
$835$	−21.9939	−0.761130
$836$	−124.332	−4.30011
$837$	7.49797	0.259168
$838$	10.3735	0.358346
$839$	12.8406	0.443307	0.221653	−	0.975125i	$-0.428855\pi$
$839$	12.8406	0.443307	0.221653	+	0.975125i	$0.428855\pi$
$840$	8.64554	0.298299
$841$	−22.1810	−0.764862
$842$	15.4719	0.533197
$843$	−18.1874	−0.626408
$844$	−99.9337	−3.43986
$845$	13.2092	0.454411
$846$	−0.696540	−0.0239476
$847$	−5.48104	−0.188331
$848$	−170.033	−5.83897
$849$	18.9839	0.651525
$850$	3.35104	0.114940
$851$	10.3863	0.356037
$852$	34.5151	1.18247
$853$	30.5750	1.04687	0.523434	−	0.852066i	$-0.324651\pi$
$853$	30.5750	1.04687	0.523434	+	0.852066i	$0.324651\pi$
$854$	−7.62055	−0.260770
$855$	−7.61545	−0.260443
$856$	−146.823	−5.01832
$857$	−7.55238	−0.257984	−0.128992	−	0.991646i	$-0.541174\pi$
$857$	−7.55238	−0.257984	−0.128992	+	0.991646i	$0.541174\pi$
$858$	−22.8278	−0.779330
$859$	−6.67088	−0.227608	−0.113804	−	0.993503i	$-0.536304\pi$
$859$	−6.67088	−0.227608	−0.113804	+	0.993503i	$0.536304\pi$
$860$	−58.7944	−2.00487
$861$	5.42674	0.184943
$862$	−101.046	−3.44165
$863$	−50.5750	−1.72159	−0.860797	−	0.508948i	$-0.830034\pi$
$863$	−50.5750	−1.72159	−0.860797	+	0.508948i	$0.830034\pi$
$864$	18.9885	0.646003
$865$	26.3262	0.895116
$866$	24.6688	0.838279
$867$	16.8262	0.571449
$868$	26.9588	0.915041
$869$	−33.0426	−1.12090
$870$	10.0623	0.341144
$871$	3.89158	0.131861
$872$	−167.117	−5.65928
$873$	−3.74307	−0.126684
$874$	−24.9265	−0.843152
$875$	−7.67404	−0.259430
$876$	13.9175	0.470229
$877$	8.92848	0.301493	0.150747	−	0.988572i	$-0.451832\pi$
$877$	8.92848	0.301493	0.150747	+	0.988572i	$0.451832\pi$
$878$	90.4732	3.05332
$879$	5.11637	0.172571
$880$	85.0332	2.86647
$881$	−26.2022	−0.882775	−0.441387	−	0.897317i	$-0.645514\pi$
$881$	−26.2022	−0.882775	−0.441387	+	0.897317i	$0.645514\pi$
$882$	17.7021	0.596061
$883$	31.8962	1.07339	0.536696	−	0.843775i	$-0.319672\pi$
$883$	31.8962	1.07339	0.536696	+	0.843775i	$0.319672\pi$
$884$	4.28007	0.143954
$885$	−11.4154	−0.383726
$886$	10.1556	0.341185
$887$	−21.5569	−0.723811	−0.361906	−	0.932215i	$-0.617874\pi$
$887$	−21.5569	−0.723811	−0.361906	+	0.932215i	$0.617874\pi$
$888$	54.1300	1.81648
$889$	−9.18312	−0.307992
$890$	43.7477	1.46642
$891$	−4.37139	−0.146447
$892$	129.338	4.33056
$893$	1.37659	0.0460659
$894$	−52.0217	−1.73987
$895$	26.4801	0.885132
$896$	18.3234	0.612141
$897$	−3.32607	−0.111054
$898$	50.8886	1.69818
$899$	19.5796	0.653016
$900$	−15.8062	−0.526873
$901$	−5.18970	−0.172894
$902$	94.9524	3.16157
$903$	5.24524	0.174551
$904$	−111.810	−3.71876
$905$	−6.82643	−0.226918
$906$	−52.5061	−1.74440
$907$	−25.4819	−0.846111	−0.423056	−	0.906104i	$-0.639042\pi$
$907$	−25.4819	−0.846111	−0.423056	+	0.906104i	$0.639042\pi$
$908$	−133.012	−4.41415
$909$	2.99930	0.0994804
$910$	−5.02730	−0.166653
$911$	5.29028	0.175275	0.0876374	−	0.996152i	$-0.472068\pi$
$911$	5.29028	0.175275	0.0876374	+	0.996152i	$0.472068\pi$
$912$	−73.0246	−2.41809
$913$	−24.2259	−0.801759
$914$	13.6631	0.451935
$915$	−5.93545	−0.196220
$916$	60.6657	2.00445
$917$	−10.7649	−0.355488
$918$	1.12776	0.0372217
$919$	−20.3797	−0.672265	−0.336132	−	0.941815i	$-0.609119\pi$
$919$	−20.3797	−0.672265	−0.336132	+	0.941815i	$0.609119\pi$
$920$	22.0407	0.726660
$921$	17.1215	0.564173
$922$	16.7749	0.552451
$923$	−12.5242	−0.412239
$924$	−15.7173	−0.517060
$925$	−17.9101	−0.588880
$926$	33.0923	1.08748
$927$	−14.4225	−0.473696
$928$	49.5852	1.62771
$929$	−25.7380	−0.844437	−0.422219	−	0.906494i	$-0.638749\pi$
$929$	−25.7380	−0.844437	−0.422219	+	0.906494i	$0.638749\pi$
$930$	28.8921	0.947411
$931$	−34.9852	−1.14659
$932$	−109.544	−3.58822
$933$	−22.6374	−0.741116
$934$	9.70720	0.317629
$935$	2.59535	0.0848772
$936$	−17.3344	−0.566593
$937$	−34.0015	−1.11078	−0.555391	−	0.831590i	$-0.687431\pi$
$937$	−34.0015	−1.11078	−0.555391	+	0.831590i	$0.687431\pi$
$938$	3.68680	0.120378
$939$	0.0822687	0.00268474
$940$	−1.95061	−0.0636219
$941$	24.4236	0.796186	0.398093	−	0.917345i	$-0.369672\pi$
$941$	24.4236	0.796186	0.398093	+	0.917345i	$0.369672\pi$
$942$	−32.9548	−1.07373
$943$	13.8348	0.450522
$944$	−109.463	−3.56271
$945$	−0.962696	−0.0313165
$946$	91.7766	2.98391
$947$	−16.1753	−0.525625	−0.262813	−	0.964847i	$-0.584650\pi$
$947$	−16.1753	−0.525625	−0.262813	+	0.964847i	$0.584650\pi$
$948$	−40.2087	−1.30592
$949$	−5.05013	−0.163934
$950$	42.9832	1.39456
$951$	−19.5083	−0.632600
$952$	2.53031	0.0820078
$953$	11.3022	0.366115	0.183057	−	0.983102i	$-0.441401\pi$
$953$	11.3022	0.366115	0.183057	+	0.983102i	$0.441401\pi$
$954$	33.6823	1.09050
$955$	−3.30433	−0.106926
$956$	44.9819	1.45482
$957$	−11.4151	−0.368998
$958$	−32.8828	−1.06240
$959$	4.83327	0.156075
$960$	34.2647	1.10589
$961$	25.2195	0.813532
$962$	−31.4761	−1.01483
$963$	16.3490	0.526840
$964$	−46.4084	−1.49471
$965$	−20.6170	−0.663685
$966$	−3.15105	−0.101383
$967$	−13.0709	−0.420332	−0.210166	−	0.977666i	$-0.567400\pi$
$967$	−13.0709	−0.420332	−0.210166	+	0.977666i	$0.567400\pi$
$968$	−72.8239	−2.34065
$969$	−2.22883	−0.0716004
$970$	−14.4233	−0.463104
$971$	59.9235	1.92304	0.961518	−	0.274744i	$-0.0885930\pi$
$971$	59.9235	1.92304	0.961518	+	0.274744i	$0.0885930\pi$
$972$	−5.31943	−0.170621
$973$	−0.0132305	−0.000424149 0
$974$	−100.992	−3.23601
$975$	5.73546	0.183682
$976$	−56.9150	−1.82181
$977$	25.7925	0.825174	0.412587	−	0.910918i	$-0.364625\pi$
$977$	25.7925	0.825174	0.412587	+	0.910918i	$0.364625\pi$
$978$	18.6975	0.597880
$979$	−49.6293	−1.58616
$980$	49.5735	1.58357
$981$	18.6087	0.594131
$982$	69.3100	2.21177
$983$	−14.6487	−0.467222	−0.233611	−	0.972330i	$-0.575054\pi$
$983$	−14.6487	−0.467222	−0.233611	+	0.972330i	$0.575054\pi$
$984$	72.1025	2.29854
$985$	−18.5903	−0.592337
$986$	2.94495	0.0937864
$987$	0.174020	0.00553912
$988$	54.8997	1.74659
$989$	13.3721	0.425207
$990$	−16.8444	−0.535351
$991$	−37.0247	−1.17613	−0.588065	−	0.808814i	$-0.700110\pi$
$991$	−37.0247	−1.17613	−0.588065	+	0.808814i	$0.700110\pi$
$992$	142.375	4.52042
$993$	24.6727	0.782965
$994$	−11.8652	−0.376340
$995$	−13.8465	−0.438964
$996$	−29.4798	−0.934104
$997$	−10.9982	−0.348317	−0.174158	−	0.984718i	$-0.555720\pi$
$997$	−10.9982	−0.348317	−0.174158	+	0.984718i	$0.555720\pi$
$998$	−65.6430	−2.07789
$999$	−6.02747	−0.190701

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8031.2.a.b.1.3	✓	102

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8031.2.a.b.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-2.70545 q^{2} -1.00000 q^{3} +5.31943 q^{4} -1.42429 q^{5} +2.70545 q^{6} -0.675914 q^{7} -8.98054 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.70545 q^{2} -1.00000 q^{3} +5.31943 q^{4} -1.42429 q^{5} +2.70545 q^{6} -0.675914 q^{7} -8.98054 q^{8} +1.00000 q^{9} +3.85333 q^{10} -4.37139 q^{11} -5.31943 q^{12} +1.93022 q^{13} +1.82865 q^{14} +1.42429 q^{15} +13.6575 q^{16} +0.416850 q^{17} -2.70545 q^{18} +5.34685 q^{19} -7.57640 q^{20} +0.675914 q^{21} +11.8266 q^{22} +1.72316 q^{23} +8.98054 q^{24} -2.97141 q^{25} -5.22210 q^{26} -1.00000 q^{27} -3.59548 q^{28} -2.61132 q^{29} -3.85333 q^{30} -7.49797 q^{31} -18.9885 q^{32} +4.37139 q^{33} -1.12776 q^{34} +0.962696 q^{35} +5.31943 q^{36} +6.02747 q^{37} -14.4656 q^{38} -1.93022 q^{39} +12.7909 q^{40} +8.02874 q^{41} -1.82865 q^{42} +7.76021 q^{43} -23.2533 q^{44} -1.42429 q^{45} -4.66191 q^{46} +0.257459 q^{47} -13.6575 q^{48} -6.54314 q^{49} +8.03898 q^{50} -0.416850 q^{51} +10.2677 q^{52} -12.4498 q^{53} +2.70545 q^{54} +6.22612 q^{55} +6.07008 q^{56} -5.34685 q^{57} +7.06479 q^{58} -8.01484 q^{59} +7.57640 q^{60} -4.16731 q^{61} +20.2853 q^{62} -0.675914 q^{63} +24.0574 q^{64} -2.74919 q^{65} -11.8266 q^{66} +2.01613 q^{67} +2.21740 q^{68} -1.72316 q^{69} -2.60452 q^{70} -6.48849 q^{71} -8.98054 q^{72} -2.61635 q^{73} -16.3070 q^{74} +2.97141 q^{75} +28.4422 q^{76} +2.95469 q^{77} +5.22210 q^{78} +7.55884 q^{79} -19.4522 q^{80} +1.00000 q^{81} -21.7213 q^{82} +5.54191 q^{83} +3.59548 q^{84} -0.593713 q^{85} -20.9948 q^{86} +2.61132 q^{87} +39.2575 q^{88} +11.3532 q^{89} +3.85333 q^{90} -1.30466 q^{91} +9.16622 q^{92} +7.49797 q^{93} -0.696540 q^{94} -7.61545 q^{95} +18.9885 q^{96} -3.74307 q^{97} +17.7021 q^{98} -4.37139 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 102 q - 6 q^{2} - 102 q^{3} + 96 q^{4} - 20 q^{5} + 6 q^{6} + 12 q^{7} - 21 q^{8} + 102 q^{9}+O(q^{10}) \) 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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