LMFDB - Embedded newform 8018.2.a.g.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, 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("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$1$
Dimension:	$34$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.00067 q^{3} +1.00000 q^{4} -2.58515 q^{5} +3.00067 q^{6} -5.14244 q^{7} -1.00000 q^{8} +6.00401 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.00067 q^{3} +1.00000 q^{4} -2.58515 q^{5} +3.00067 q^{6} -5.14244 q^{7} -1.00000 q^{8} +6.00401 q^{9} +2.58515 q^{10} +0.908404 q^{11} -3.00067 q^{12} -2.31713 q^{13} +5.14244 q^{14} +7.75719 q^{15} +1.00000 q^{16} -0.446378 q^{17} -6.00401 q^{18} +1.00000 q^{19} -2.58515 q^{20} +15.4307 q^{21} -0.908404 q^{22} -6.32474 q^{23} +3.00067 q^{24} +1.68302 q^{25} +2.31713 q^{26} -9.01404 q^{27} -5.14244 q^{28} -5.00947 q^{29} -7.75719 q^{30} -3.57419 q^{31} -1.00000 q^{32} -2.72582 q^{33} +0.446378 q^{34} +13.2940 q^{35} +6.00401 q^{36} -4.33521 q^{37} -1.00000 q^{38} +6.95295 q^{39} +2.58515 q^{40} -0.259380 q^{41} -15.4307 q^{42} -7.06499 q^{43} +0.908404 q^{44} -15.5213 q^{45} +6.32474 q^{46} -6.65002 q^{47} -3.00067 q^{48} +19.4447 q^{49} -1.68302 q^{50} +1.33943 q^{51} -2.31713 q^{52} +1.48898 q^{53} +9.01404 q^{54} -2.34836 q^{55} +5.14244 q^{56} -3.00067 q^{57} +5.00947 q^{58} -5.22340 q^{59} +7.75719 q^{60} +1.07770 q^{61} +3.57419 q^{62} -30.8752 q^{63} +1.00000 q^{64} +5.99015 q^{65} +2.72582 q^{66} +4.83054 q^{67} -0.446378 q^{68} +18.9784 q^{69} -13.2940 q^{70} -0.367378 q^{71} -6.00401 q^{72} +5.00877 q^{73} +4.33521 q^{74} -5.05019 q^{75} +1.00000 q^{76} -4.67141 q^{77} -6.95295 q^{78} -5.38936 q^{79} -2.58515 q^{80} +9.03611 q^{81} +0.259380 q^{82} +5.97953 q^{83} +15.4307 q^{84} +1.15396 q^{85} +7.06499 q^{86} +15.0317 q^{87} -0.908404 q^{88} +12.3960 q^{89} +15.5213 q^{90} +11.9157 q^{91} -6.32474 q^{92} +10.7250 q^{93} +6.65002 q^{94} -2.58515 q^{95} +3.00067 q^{96} +2.41517 q^{97} -19.4447 q^{98} +5.45407 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 34 q^{2} - 6 q^{3} + 34 q^{4} + q^{5} + 6 q^{6} - 22 q^{7} - 34 q^{8} + 30 q^{9}+O(q^{10}) $ 34 * q - 34 * q^2 - 6 * q^3 + 34 * q^4 + q^5 + 6 * q^6 - 22 * q^7 - 34 * q^8 + 30 * q^9	\( 34 q - 34 q^{2} - 6 q^{3} + 34 q^{4} + q^{5} + 6 q^{6} - 22 q^{7} - 34 q^{8} + 30 q^{9} - q^{10} + 7 q^{11} - 6 q^{12} - 11 q^{13} + 22 q^{14} - 18 q^{15} + 34 q^{16} - 10 q^{17} - 30 q^{18} + 34 q^{19} + q^{20} + 14 q^{21} - 7 q^{22} - 30 q^{23} + 6 q^{24} + 11 q^{25} + 11 q^{26} - 21 q^{27} - 22 q^{28} + 12 q^{29} + 18 q^{30} - 13 q^{31} - 34 q^{32} - 4 q^{33} + 10 q^{34} - 16 q^{35} + 30 q^{36} - 46 q^{37} - 34 q^{38} - 36 q^{39} - q^{40} + 25 q^{41} - 14 q^{42} - 51 q^{43} + 7 q^{44} - 17 q^{45} + 30 q^{46} - 20 q^{47} - 6 q^{48} - 2 q^{49} - 11 q^{50} + 4 q^{51} - 11 q^{52} - 7 q^{53} + 21 q^{54} - 39 q^{55} + 22 q^{56} - 6 q^{57} - 12 q^{58} + 19 q^{59} - 18 q^{60} - 26 q^{61} + 13 q^{62} - 57 q^{63} + 34 q^{64} + 20 q^{65} + 4 q^{66} - 54 q^{67} - 10 q^{68} + 16 q^{70} + 9 q^{71} - 30 q^{72} - 57 q^{73} + 46 q^{74} + 26 q^{75} + 34 q^{76} + 2 q^{77} + 36 q^{78} - 7 q^{79} + q^{80} + 22 q^{81} - 25 q^{82} - 15 q^{83} + 14 q^{84} - 30 q^{85} + 51 q^{86} - 37 q^{87} - 7 q^{88} + 78 q^{89} + 17 q^{90} - 31 q^{91} - 30 q^{92} - 43 q^{93} + 20 q^{94} + q^{95} + 6 q^{96} - 38 q^{97} + 2 q^{98} + 2 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 6 * q^3 + 34 * q^4 + q^5 + 6 * q^6 - 22 * q^7 - 34 * q^8 + 30 * q^9 - q^10 + 7 * q^11 - 6 * q^12 - 11 * q^13 + 22 * q^14 - 18 * q^15 + 34 * q^16 - 10 * q^17 - 30 * q^18 + 34 * q^19 + q^20 + 14 * q^21 - 7 * q^22 - 30 * q^23 + 6 * q^24 + 11 * q^25 + 11 * q^26 - 21 * q^27 - 22 * q^28 + 12 * q^29 + 18 * q^30 - 13 * q^31 - 34 * q^32 - 4 * q^33 + 10 * q^34 - 16 * q^35 + 30 * q^36 - 46 * q^37 - 34 * q^38 - 36 * q^39 - q^40 + 25 * q^41 - 14 * q^42 - 51 * q^43 + 7 * q^44 - 17 * q^45 + 30 * q^46 - 20 * q^47 - 6 * q^48 - 2 * q^49 - 11 * q^50 + 4 * q^51 - 11 * q^52 - 7 * q^53 + 21 * q^54 - 39 * q^55 + 22 * q^56 - 6 * q^57 - 12 * q^58 + 19 * q^59 - 18 * q^60 - 26 * q^61 + 13 * q^62 - 57 * q^63 + 34 * q^64 + 20 * q^65 + 4 * q^66 - 54 * q^67 - 10 * q^68 + 16 * q^70 + 9 * q^71 - 30 * q^72 - 57 * q^73 + 46 * q^74 + 26 * q^75 + 34 * q^76 + 2 * q^77 + 36 * q^78 - 7 * q^79 + q^80 + 22 * q^81 - 25 * q^82 - 15 * q^83 + 14 * q^84 - 30 * q^85 + 51 * q^86 - 37 * q^87 - 7 * q^88 + 78 * q^89 + 17 * q^90 - 31 * q^91 - 30 * q^92 - 43 * q^93 + 20 * q^94 + q^95 + 6 * q^96 - 38 * q^97 + 2 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−3.00067	−1.73244	−0.866218	−	0.499666i	$-0.833456\pi$
$3$	−3.00067	−1.73244	−0.866218	+	0.499666i	$0.833456\pi$
$4$	1.00000	0.500000
$5$	−2.58515	−1.15612	−0.578058	−	0.815996i	$-0.696189\pi$
$5$	−2.58515	−1.15612	−0.578058	+	0.815996i	$0.696189\pi$
$6$	3.00067	1.22502
$7$	−5.14244	−1.94366	−0.971829	−	0.235686i	$-0.924266\pi$
$7$	−5.14244	−1.94366	−0.971829	+	0.235686i	$0.924266\pi$
$8$	−1.00000	−0.353553
$9$	6.00401	2.00134
$10$	2.58515	0.817497
$11$	0.908404	0.273894	0.136947	−	0.990578i	$-0.456271\pi$
$11$	0.908404	0.273894	0.136947	+	0.990578i	$0.456271\pi$
$12$	−3.00067	−0.866218
$13$	−2.31713	−0.642657	−0.321329	−	0.946968i	$-0.604129\pi$
$13$	−2.31713	−0.642657	−0.321329	+	0.946968i	$0.604129\pi$
$14$	5.14244	1.37437
$15$	7.75719	2.00290
$16$	1.00000	0.250000
$17$	−0.446378	−0.108263	−0.0541313	−	0.998534i	$-0.517239\pi$
$17$	−0.446378	−0.108263	−0.0541313	+	0.998534i	$0.517239\pi$
$18$	−6.00401	−1.41516
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−2.58515	−0.578058
$21$	15.4307	3.36727
$22$	−0.908404	−0.193672
$23$	−6.32474	−1.31880	−0.659400	−	0.751793i	$-0.729189\pi$
$23$	−6.32474	−1.31880	−0.659400	+	0.751793i	$0.729189\pi$
$24$	3.00067	0.612509
$25$	1.68302	0.336604
$26$	2.31713	0.454427
$27$	−9.01404	−1.73475
$28$	−5.14244	−0.971829
$29$	−5.00947	−0.930234	−0.465117	−	0.885249i	$-0.653988\pi$
$29$	−5.00947	−0.930234	−0.465117	+	0.885249i	$0.653988\pi$
$30$	−7.75719	−1.41626
$31$	−3.57419	−0.641944	−0.320972	−	0.947089i	$-0.604009\pi$
$31$	−3.57419	−0.641944	−0.320972	+	0.947089i	$0.604009\pi$
$32$	−1.00000	−0.176777
$33$	−2.72582	−0.474504
$34$	0.446378	0.0765532
$35$	13.2940	2.24709
$36$	6.00401	1.00067
$37$	−4.33521	−0.712704	−0.356352	−	0.934352i	$-0.615980\pi$
$37$	−4.33521	−0.712704	−0.356352	+	0.934352i	$0.615980\pi$
$38$	−1.00000	−0.162221
$39$	6.95295	1.11336
$40$	2.58515	0.408749
$41$	−0.259380	−0.0405084	−0.0202542	−	0.999795i	$-0.506448\pi$
$41$	−0.259380	−0.0405084	−0.0202542	+	0.999795i	$0.506448\pi$
$42$	−15.4307	−2.38102
$43$	−7.06499	−1.07740	−0.538701	−	0.842497i	$-0.681085\pi$
$43$	−7.06499	−1.07740	−0.538701	+	0.842497i	$0.681085\pi$
$44$	0.908404	0.136947
$45$	−15.5213	−2.31378
$46$	6.32474	0.932532
$47$	−6.65002	−0.970005	−0.485002	−	0.874513i	$-0.661181\pi$
$47$	−6.65002	−0.970005	−0.485002	+	0.874513i	$0.661181\pi$
$48$	−3.00067	−0.433109
$49$	19.4447	2.77781
$50$	−1.68302	−0.238015
$51$	1.33943	0.187558
$52$	−2.31713	−0.321329
$53$	1.48898	0.204527	0.102263	−	0.994757i	$-0.467392\pi$
$53$	1.48898	0.204527	0.102263	+	0.994757i	$0.467392\pi$
$54$	9.01404	1.22666
$55$	−2.34836	−0.316653
$56$	5.14244	0.687187
$57$	−3.00067	−0.397448
$58$	5.00947	0.657775
$59$	−5.22340	−0.680029	−0.340014	−	0.940420i	$-0.610432\pi$
$59$	−5.22340	−0.680029	−0.340014	+	0.940420i	$0.610432\pi$
$60$	7.75719	1.00145
$61$	1.07770	0.137986	0.0689929	−	0.997617i	$-0.478021\pi$
$61$	1.07770	0.137986	0.0689929	+	0.997617i	$0.478021\pi$
$62$	3.57419	0.453923
$63$	−30.8752	−3.88992
$64$	1.00000	0.125000
$65$	5.99015	0.742987
$66$	2.72582	0.335525
$67$	4.83054	0.590144	0.295072	−	0.955475i	$-0.404656\pi$
$67$	4.83054	0.590144	0.295072	+	0.955475i	$0.404656\pi$
$68$	−0.446378	−0.0541313
$69$	18.9784	2.28474
$70$	−13.2940	−1.58894
$71$	−0.367378	−0.0435997	−0.0217999	−	0.999762i	$-0.506940\pi$
$71$	−0.367378	−0.0435997	−0.0217999	+	0.999762i	$0.506940\pi$
$72$	−6.00401	−0.707579
$73$	5.00877	0.586233	0.293116	−	0.956077i	$-0.405308\pi$
$73$	5.00877	0.586233	0.293116	+	0.956077i	$0.405308\pi$
$74$	4.33521	0.503958
$75$	−5.05019	−0.583146
$76$	1.00000	0.114708
$77$	−4.67141	−0.532357
$78$	−6.95295	−0.787267
$79$	−5.38936	−0.606350	−0.303175	−	0.952935i	$-0.598047\pi$
$79$	−5.38936	−0.606350	−0.303175	+	0.952935i	$0.598047\pi$
$80$	−2.58515	−0.289029
$81$	9.03611	1.00401
$82$	0.259380	0.0286438
$83$	5.97953	0.656339	0.328170	−	0.944619i	$-0.393568\pi$
$83$	5.97953	0.656339	0.328170	+	0.944619i	$0.393568\pi$
$84$	15.4307	1.68363
$85$	1.15396	0.125164
$86$	7.06499	0.761838
$87$	15.0317	1.61157
$88$	−0.908404	−0.0968362
$89$	12.3960	1.31398	0.656988	−	0.753901i	$-0.271830\pi$
$89$	12.3960	1.31398	0.656988	+	0.753901i	$0.271830\pi$
$90$	15.5213	1.63609
$91$	11.9157	1.24911
$92$	−6.32474	−0.659400
$93$	10.7250	1.11213
$94$	6.65002	0.685897
$95$	−2.58515	−0.265231
$96$	3.00067	0.306254
$97$	2.41517	0.245223	0.122611	−	0.992455i	$-0.460873\pi$
$97$	2.41517	0.245223	0.122611	+	0.992455i	$0.460873\pi$
$98$	−19.4447	−1.96421
$99$	5.45407	0.548154
$100$	1.68302	0.168302
$101$	15.2851	1.52093	0.760463	−	0.649381i	$-0.224972\pi$
$101$	15.2851	1.52093	0.760463	+	0.649381i	$0.224972\pi$
$102$	−1.33943	−0.132624
$103$	4.15550	0.409454	0.204727	−	0.978819i	$-0.434369\pi$
$103$	4.15550	0.409454	0.204727	+	0.978819i	$0.434369\pi$
$104$	2.31713	0.227214
$105$	−39.8909	−3.89295
$106$	−1.48898	−0.144622
$107$	7.74176	0.748424	0.374212	−	0.927343i	$-0.377913\pi$
$107$	7.74176	0.748424	0.374212	+	0.927343i	$0.377913\pi$
$108$	−9.01404	−0.867376
$109$	−8.04958	−0.771010	−0.385505	−	0.922706i	$-0.625973\pi$
$109$	−8.04958	−0.771010	−0.385505	+	0.922706i	$0.625973\pi$
$110$	2.34836	0.223908
$111$	13.0085	1.23471
$112$	−5.14244	−0.485915
$113$	8.08126	0.760221	0.380110	−	0.924941i	$-0.375886\pi$
$113$	8.08126	0.760221	0.380110	+	0.924941i	$0.375886\pi$
$114$	3.00067	0.281038
$115$	16.3504	1.52468
$116$	−5.00947	−0.465117
$117$	−13.9121	−1.28617
$118$	5.22340	0.480853
$119$	2.29547	0.210426
$120$	−7.75719	−0.708131
$121$	−10.1748	−0.924982
$122$	−1.07770	−0.0975707
$123$	0.778315	0.0701783
$124$	−3.57419	−0.320972
$125$	8.57490	0.766962
$126$	30.8752	2.75059
$127$	17.9613	1.59381	0.796904	−	0.604106i	$-0.206470\pi$
$127$	17.9613	1.59381	0.796904	+	0.604106i	$0.206470\pi$
$128$	−1.00000	−0.0883883
$129$	21.1997	1.86653
$130$	−5.99015	−0.525371
$131$	−0.578127	−0.0505112	−0.0252556	−	0.999681i	$-0.508040\pi$
$131$	−0.578127	−0.0505112	−0.0252556	+	0.999681i	$0.508040\pi$
$132$	−2.72582	−0.237252
$133$	−5.14244	−0.445906
$134$	−4.83054	−0.417295
$135$	23.3027	2.00558
$136$	0.446378	0.0382766
$137$	9.40589	0.803599	0.401800	−	0.915728i	$-0.368385\pi$
$137$	9.40589	0.803599	0.401800	+	0.915728i	$0.368385\pi$
$138$	−18.9784	−1.61555
$139$	−2.70650	−0.229562	−0.114781	−	0.993391i	$-0.536617\pi$
$139$	−2.70650	−0.229562	−0.114781	+	0.993391i	$0.536617\pi$
$140$	13.2940	1.12355
$141$	19.9545	1.68047
$142$	0.367378	0.0308297
$143$	−2.10489	−0.176020
$144$	6.00401	0.500334
$145$	12.9502	1.07546
$146$	−5.00877	−0.414529
$147$	−58.3470	−4.81238
$148$	−4.33521	−0.356352
$149$	6.25140	0.512135	0.256067	−	0.966659i	$-0.417573\pi$
$149$	6.25140	0.512135	0.256067	+	0.966659i	$0.417573\pi$
$150$	5.05019	0.412346
$151$	0.701861	0.0571166	0.0285583	−	0.999592i	$-0.490908\pi$
$151$	0.701861	0.0571166	0.0285583	+	0.999592i	$0.490908\pi$
$152$	−1.00000	−0.0811107
$153$	−2.68006	−0.216670
$154$	4.67141	0.376433
$155$	9.23984	0.742161
$156$	6.95295	0.556682
$157$	2.95538	0.235865	0.117932	−	0.993022i	$-0.462373\pi$
$157$	2.95538	0.235865	0.117932	+	0.993022i	$0.462373\pi$
$158$	5.38936	0.428754
$159$	−4.46793	−0.354330
$160$	2.58515	0.204374
$161$	32.5246	2.56330
$162$	−9.03611	−0.709944
$163$	16.1770	1.26708	0.633542	−	0.773709i	$-0.281600\pi$
$163$	16.1770	1.26708	0.633542	+	0.773709i	$0.281600\pi$
$164$	−0.259380	−0.0202542
$165$	7.04666	0.548582
$166$	−5.97953	−0.464102
$167$	−6.98841	−0.540779	−0.270390	−	0.962751i	$-0.587152\pi$
$167$	−6.98841	−0.540779	−0.270390	+	0.962751i	$0.587152\pi$
$168$	−15.4307	−1.19051
$169$	−7.63089	−0.586991
$170$	−1.15396	−0.0885044
$171$	6.00401	0.459138
$172$	−7.06499	−0.538701
$173$	−1.44390	−0.109778	−0.0548888	−	0.998492i	$-0.517480\pi$
$173$	−1.44390	−0.109778	−0.0548888	+	0.998492i	$0.517480\pi$
$174$	−15.0317	−1.13955
$175$	−8.65483	−0.654244
$176$	0.908404	0.0684735
$177$	15.6737	1.17811
$178$	−12.3960	−0.929122
$179$	11.7831	0.880712	0.440356	−	0.897823i	$-0.354852\pi$
$179$	11.7831	0.880712	0.440356	+	0.897823i	$0.354852\pi$
$180$	−15.5213	−1.15689
$181$	4.51905	0.335898	0.167949	−	0.985796i	$-0.446286\pi$
$181$	4.51905	0.335898	0.167949	+	0.985796i	$0.446286\pi$
$182$	−11.9157	−0.883252
$183$	−3.23383	−0.239052
$184$	6.32474	0.466266
$185$	11.2072	0.823968
$186$	−10.7250	−0.786392
$187$	−0.405492	−0.0296525
$188$	−6.65002	−0.485002
$189$	46.3541	3.37177
$190$	2.58515	0.187547
$191$	−20.2954	−1.46852	−0.734262	−	0.678866i	$-0.762472\pi$
$191$	−20.2954	−1.46852	−0.734262	+	0.678866i	$0.762472\pi$
$192$	−3.00067	−0.216555
$193$	4.57495	0.329312	0.164656	−	0.986351i	$-0.447349\pi$
$193$	4.57495	0.329312	0.164656	+	0.986351i	$0.447349\pi$
$194$	−2.41517	−0.173399
$195$	−17.9745	−1.28718
$196$	19.4447	1.38890
$197$	−17.9582	−1.27947	−0.639736	−	0.768595i	$-0.720956\pi$
$197$	−17.9582	−1.27947	−0.639736	+	0.768595i	$0.720956\pi$
$198$	−5.45407	−0.387604
$199$	2.14584	0.152115	0.0760573	−	0.997103i	$-0.475767\pi$
$199$	2.14584	0.152115	0.0760573	+	0.997103i	$0.475767\pi$
$200$	−1.68302	−0.119008
$201$	−14.4948	−1.02239
$202$	−15.2851	−1.07546
$203$	25.7609	1.80806
$204$	1.33943	0.0937790
$205$	0.670539	0.0468324
$206$	−4.15550	−0.289528
$207$	−37.9738	−2.63936
$208$	−2.31713	−0.160664
$209$	0.908404	0.0628356
$210$	39.8909	2.75273
$211$	1.00000	0.0688428
$211$	1.00000	0.0688428
$212$	1.48898	0.102263
$213$	1.10238	0.0755338
$214$	−7.74176	−0.529216
$215$	18.2641	1.24560
$216$	9.01404	0.613328
$217$	18.3801	1.24772
$218$	8.04958	0.545186
$219$	−15.0297	−1.01561
$220$	−2.34836	−0.158327
$221$	1.03432	0.0695758
$222$	−13.0085	−0.873075
$223$	−24.2574	−1.62440	−0.812199	−	0.583381i	$-0.801729\pi$
$223$	−24.2574	−1.62440	−0.812199	+	0.583381i	$0.801729\pi$
$224$	5.14244	0.343594
$225$	10.1049	0.673659
$226$	−8.08126	−0.537557
$227$	9.07856	0.602565	0.301282	−	0.953535i	$-0.402585\pi$
$227$	9.07856	0.602565	0.301282	+	0.953535i	$0.402585\pi$
$228$	−3.00067	−0.198724
$229$	25.6262	1.69343	0.846714	−	0.532049i	$-0.178578\pi$
$229$	25.6262	1.69343	0.846714	+	0.532049i	$0.178578\pi$
$230$	−16.3504	−1.07812
$231$	14.0174	0.922274
$232$	5.00947	0.328888
$233$	2.04783	0.134158	0.0670788	−	0.997748i	$-0.478632\pi$
$233$	2.04783	0.134158	0.0670788	+	0.997748i	$0.478632\pi$
$234$	13.9121	0.909462
$235$	17.1913	1.12144
$236$	−5.22340	−0.340014
$237$	16.1717	1.05046
$238$	−2.29547	−0.148793
$239$	9.00416	0.582431	0.291215	−	0.956658i	$-0.405940\pi$
$239$	9.00416	0.582431	0.291215	+	0.956658i	$0.405940\pi$
$240$	7.75719	0.500724
$241$	−3.58951	−0.231221	−0.115610	−	0.993295i	$-0.536882\pi$
$241$	−3.58951	−0.231221	−0.115610	+	0.993295i	$0.536882\pi$
$242$	10.1748	0.654061
$243$	−0.0722613	−0.00463556
$244$	1.07770	0.0689929
$245$	−50.2674	−3.21147
$246$	−0.778315	−0.0496235
$247$	−2.31713	−0.147436
$248$	3.57419	0.226961
$249$	−17.9426	−1.13707
$250$	−8.57490	−0.542324
$251$	−24.3355	−1.53605	−0.768023	−	0.640422i	$-0.778759\pi$
$251$	−24.3355	−1.53605	−0.768023	+	0.640422i	$0.778759\pi$
$252$	−30.8752	−1.94496
$253$	−5.74542	−0.361211
$254$	−17.9613	−1.12699
$255$	−3.46264	−0.216839
$256$	1.00000	0.0625000
$257$	−5.13080	−0.320051	−0.160025	−	0.987113i	$-0.551158\pi$
$257$	−5.13080	−0.320051	−0.160025	+	0.987113i	$0.551158\pi$
$258$	−21.1997	−1.31984
$259$	22.2935	1.38525
$260$	5.99015	0.371493
$261$	−30.0769	−1.86171
$262$	0.578127	0.0357168
$263$	−19.4161	−1.19725	−0.598624	−	0.801030i	$-0.704286\pi$
$263$	−19.4161	−1.19725	−0.598624	+	0.801030i	$0.704286\pi$
$264$	2.72582	0.167763
$265$	−3.84924	−0.236457
$266$	5.14244	0.315303
$267$	−37.1964	−2.27638
$268$	4.83054	0.295072
$269$	0.784757	0.0478475	0.0239237	−	0.999714i	$-0.492384\pi$
$269$	0.784757	0.0478475	0.0239237	+	0.999714i	$0.492384\pi$
$270$	−23.3027	−1.41816
$271$	27.9215	1.69611	0.848056	−	0.529907i	$-0.177773\pi$
$271$	27.9215	1.69611	0.848056	+	0.529907i	$0.177773\pi$
$272$	−0.446378	−0.0270656
$273$	−35.7551	−2.16400
$274$	−9.40589	−0.568231
$275$	1.52886	0.0921939
$276$	18.9784	1.14237
$277$	−18.4050	−1.10585	−0.552926	−	0.833230i	$-0.686489\pi$
$277$	−18.4050	−1.10585	−0.552926	+	0.833230i	$0.686489\pi$
$278$	2.70650	0.162325
$279$	−21.4595	−1.28475
$280$	−13.2940	−0.794468
$281$	−2.86125	−0.170688	−0.0853440	−	0.996352i	$-0.527199\pi$
$281$	−2.86125	−0.170688	−0.0853440	+	0.996352i	$0.527199\pi$
$282$	−19.9545	−1.18827
$283$	−8.49639	−0.505058	−0.252529	−	0.967589i	$-0.581262\pi$
$283$	−8.49639	−0.505058	−0.252529	+	0.967589i	$0.581262\pi$
$284$	−0.367378	−0.0217999
$285$	7.75719	0.459496
$286$	2.10489	0.124465
$287$	1.33385	0.0787345
$288$	−6.00401	−0.353790
$289$	−16.8007	−0.988279
$290$	−12.9502	−0.760464
$291$	−7.24711	−0.424833
$292$	5.00877	0.293116
$293$	−9.20606	−0.537824	−0.268912	−	0.963165i	$-0.586664\pi$
$293$	−9.20606	−0.537824	−0.268912	+	0.963165i	$0.586664\pi$
$294$	58.3470	3.40286
$295$	13.5033	0.786192
$296$	4.33521	0.251979
$297$	−8.18839	−0.475139
$298$	−6.25140	−0.362134
$299$	14.6553	0.847536
$300$	−5.05019	−0.291573
$301$	36.3313	2.09410
$302$	−0.701861	−0.0403876
$303$	−45.8656	−2.63491
$304$	1.00000	0.0573539
$305$	−2.78603	−0.159528
$306$	2.68006	0.153209
$307$	−14.2482	−0.813186	−0.406593	−	0.913610i	$-0.633283\pi$
$307$	−14.2482	−0.813186	−0.406593	+	0.913610i	$0.633283\pi$
$308$	−4.67141	−0.266178
$309$	−12.4693	−0.709353
$310$	−9.23984	−0.524787
$311$	30.0187	1.70221	0.851103	−	0.524999i	$-0.175934\pi$
$311$	30.0187	1.70221	0.851103	+	0.524999i	$0.175934\pi$
$312$	−6.95295	−0.393633
$313$	20.6065	1.16475	0.582374	−	0.812921i	$-0.302124\pi$
$313$	20.6065	1.16475	0.582374	+	0.812921i	$0.302124\pi$
$314$	−2.95538	−0.166782
$315$	79.8173	4.49719
$316$	−5.38936	−0.303175
$317$	−17.8230	−1.00104	−0.500520	−	0.865725i	$-0.666858\pi$
$317$	−17.8230	−1.00104	−0.500520	+	0.865725i	$0.666858\pi$
$318$	4.46793	0.250549
$319$	−4.55062	−0.254786
$320$	−2.58515	−0.144515
$321$	−23.2304	−1.29660
$322$	−32.5246	−1.81252
$323$	−0.446378	−0.0248371
$324$	9.03611	0.502006
$325$	−3.89979	−0.216321
$326$	−16.1770	−0.895963
$327$	24.1541	1.33573
$328$	0.259380	0.0143219
$329$	34.1973	1.88536
$330$	−7.04666	−0.387906
$331$	22.1842	1.21935	0.609676	−	0.792650i	$-0.291299\pi$
$331$	22.1842	1.21935	0.609676	+	0.792650i	$0.291299\pi$
$332$	5.97953	0.328170
$333$	−26.0286	−1.42636
$334$	6.98841	0.382389
$335$	−12.4877	−0.682275
$336$	15.4307	0.841816
$337$	0.733003	0.0399292	0.0199646	−	0.999801i	$-0.493645\pi$
$337$	0.733003	0.0399292	0.0199646	+	0.999801i	$0.493645\pi$
$338$	7.63089	0.415066
$339$	−24.2492	−1.31703
$340$	1.15396	0.0625821
$341$	−3.24681	−0.175825
$342$	−6.00401	−0.324660
$343$	−63.9959	−3.45545
$344$	7.06499	0.380919
$345$	−49.0622	−2.64142
$346$	1.44390	0.0776244
$347$	25.7102	1.38019	0.690097	−	0.723717i	$-0.257568\pi$
$347$	25.7102	1.38019	0.690097	+	0.723717i	$0.257568\pi$
$348$	15.0317	0.805786
$349$	33.2208	1.77827	0.889135	−	0.457646i	$-0.151307\pi$
$349$	33.2208	1.77827	0.889135	+	0.457646i	$0.151307\pi$
$350$	8.65483	0.462620
$351$	20.8867	1.11485
$352$	−0.908404	−0.0484181
$353$	6.34342	0.337626	0.168813	−	0.985648i	$-0.446007\pi$
$353$	6.34342	0.337626	0.168813	+	0.985648i	$0.446007\pi$
$354$	−15.6737	−0.833047
$355$	0.949728	0.0504063
$356$	12.3960	0.656988
$357$	−6.88795	−0.364549
$358$	−11.7831	−0.622758
$359$	−10.0933	−0.532706	−0.266353	−	0.963876i	$-0.585819\pi$
$359$	−10.0933	−0.532706	−0.266353	+	0.963876i	$0.585819\pi$
$360$	15.5213	0.818044
$361$	1.00000	0.0526316
$362$	−4.51905	−0.237516
$363$	30.5312	1.60247
$364$	11.9157	0.624553
$365$	−12.9485	−0.677753
$366$	3.23383	0.169035
$367$	−3.16419	−0.165169	−0.0825846	−	0.996584i	$-0.526317\pi$
$367$	−3.16419	−0.165169	−0.0825846	+	0.996584i	$0.526317\pi$
$368$	−6.32474	−0.329700
$369$	−1.55732	−0.0810710
$370$	−11.2072	−0.582633
$371$	−7.65697	−0.397530
$372$	10.7250	0.556063
$373$	18.8641	0.976746	0.488373	−	0.872635i	$-0.337591\pi$
$373$	18.8641	0.976746	0.488373	+	0.872635i	$0.337591\pi$
$374$	0.405492	0.0209675
$375$	−25.7304	−1.32871
$376$	6.65002	0.342948
$377$	11.6076	0.597822
$378$	−46.3541	−2.38420
$379$	−8.24781	−0.423661	−0.211831	−	0.977306i	$-0.567943\pi$
$379$	−8.24781	−0.423661	−0.211831	+	0.977306i	$0.567943\pi$
$380$	−2.58515	−0.132616
$381$	−53.8959	−2.76117
$382$	20.2954	1.03840
$383$	24.7066	1.26245	0.631224	−	0.775600i	$-0.282553\pi$
$383$	24.7066	1.26245	0.631224	+	0.775600i	$0.282553\pi$
$384$	3.00067	0.153127
$385$	12.0763	0.615466
$386$	−4.57495	−0.232859
$387$	−42.4183	−2.15624
$388$	2.41517	0.122611
$389$	6.67423	0.338397	0.169199	−	0.985582i	$-0.445882\pi$
$389$	6.67423	0.338397	0.169199	+	0.985582i	$0.445882\pi$
$390$	17.9745	0.910172
$391$	2.82323	0.142777
$392$	−19.4447	−0.982103
$393$	1.73477	0.0875075
$394$	17.9582	0.904723
$395$	13.9323	0.701011
$396$	5.45407	0.274077
$397$	−18.4171	−0.924327	−0.462164	−	0.886795i	$-0.652927\pi$
$397$	−18.4171	−0.924327	−0.462164	+	0.886795i	$0.652927\pi$
$398$	−2.14584	−0.107561
$399$	15.4307	0.772504
$400$	1.68302	0.0841511
$401$	12.5338	0.625909	0.312954	−	0.949768i	$-0.398681\pi$
$401$	12.5338	0.625909	0.312954	+	0.949768i	$0.398681\pi$
$402$	14.4948	0.722937
$403$	8.28188	0.412550
$404$	15.2851	0.760463
$405$	−23.3597	−1.16076
$406$	−25.7609	−1.27849
$407$	−3.93812	−0.195205
$408$	−1.33943	−0.0663118
$409$	26.7773	1.32405	0.662026	−	0.749480i	$-0.269697\pi$
$409$	26.7773	1.32405	0.662026	+	0.749480i	$0.269697\pi$
$410$	−0.670539	−0.0331155
$411$	−28.2240	−1.39218
$412$	4.15550	0.204727
$413$	26.8610	1.32174
$414$	37.9738	1.86631
$415$	−15.4580	−0.758804
$416$	2.31713	0.113607
$417$	8.12131	0.397702
$418$	−0.908404	−0.0444315
$419$	−10.3385	−0.505067	−0.252534	−	0.967588i	$-0.581264\pi$
$419$	−10.3385	−0.505067	−0.252534	+	0.967588i	$0.581264\pi$
$420$	−39.8909	−1.94647
$421$	−20.9904	−1.02301	−0.511505	−	0.859280i	$-0.670912\pi$
$421$	−20.9904	−1.02301	−0.511505	+	0.859280i	$0.670912\pi$
$422$	−1.00000	−0.0486792
$423$	−39.9268	−1.94131
$424$	−1.48898	−0.0723111
$425$	−0.751264	−0.0364417
$426$	−1.10238	−0.0534104
$427$	−5.54202	−0.268197
$428$	7.74176	0.374212
$429$	6.31609	0.304944
$430$	−18.2641	−0.880773
$431$	−8.35912	−0.402645	−0.201322	−	0.979525i	$-0.564524\pi$
$431$	−8.35912	−0.402645	−0.201322	+	0.979525i	$0.564524\pi$
$432$	−9.01404	−0.433688
$433$	3.59017	0.172532	0.0862662	−	0.996272i	$-0.472506\pi$
$433$	3.59017	0.172532	0.0862662	+	0.996272i	$0.472506\pi$
$434$	−18.3801	−0.882271
$435$	−38.8594	−1.86316
$436$	−8.04958	−0.385505
$437$	−6.32474	−0.302553
$438$	15.0297	0.718145
$439$	−29.5333	−1.40955	−0.704774	−	0.709432i	$-0.748952\pi$
$439$	−29.5333	−1.40955	−0.704774	+	0.709432i	$0.748952\pi$
$440$	2.34836	0.111954
$441$	116.746	5.55933
$442$	−1.03432	−0.0491975
$443$	13.6373	0.647929	0.323965	−	0.946069i	$-0.394984\pi$
$443$	13.6373	0.647929	0.323965	+	0.946069i	$0.394984\pi$
$444$	13.0085	0.617357
$445$	−32.0457	−1.51911
$446$	24.2574	1.14862
$447$	−18.7584	−0.887241
$448$	−5.14244	−0.242957
$449$	24.8116	1.17093	0.585465	−	0.810698i	$-0.300912\pi$
$449$	24.8116	1.17093	0.585465	+	0.810698i	$0.300912\pi$
$450$	−10.1049	−0.476349
$451$	−0.235622	−0.0110950
$452$	8.08126	0.380110
$453$	−2.10605	−0.0989510
$454$	−9.07856	−0.426078
$455$	−30.8040	−1.44411
$456$	3.00067	0.140519
$457$	19.2085	0.898538	0.449269	−	0.893397i	$-0.351685\pi$
$457$	19.2085	0.898538	0.449269	+	0.893397i	$0.351685\pi$
$458$	−25.6262	−1.19743
$459$	4.02367	0.187809
$460$	16.3504	0.762342
$461$	33.5103	1.56073	0.780365	−	0.625324i	$-0.215033\pi$
$461$	33.5103	1.56073	0.780365	+	0.625324i	$0.215033\pi$
$462$	−14.0174	−0.652146
$463$	−20.2233	−0.939858	−0.469929	−	0.882704i	$-0.655720\pi$
$463$	−20.2233	−0.939858	−0.469929	+	0.882704i	$0.655720\pi$
$464$	−5.00947	−0.232559
$465$	−27.7257	−1.28575
$466$	−2.04783	−0.0948638
$467$	8.00387	0.370375	0.185188	−	0.982703i	$-0.440711\pi$
$467$	8.00387	0.370375	0.185188	+	0.982703i	$0.440711\pi$
$468$	−13.9121	−0.643087
$469$	−24.8407	−1.14704
$470$	−17.1913	−0.792976
$471$	−8.86811	−0.408621
$472$	5.22340	0.240426
$473$	−6.41787	−0.295094
$474$	−16.1717	−0.742789
$475$	1.68302	0.0772223
$476$	2.29547	0.105213
$477$	8.93984	0.409327
$478$	−9.00416	−0.411841
$479$	−34.9026	−1.59474	−0.797369	−	0.603492i	$-0.793776\pi$
$479$	−34.9026	−1.59474	−0.797369	+	0.603492i	$0.793776\pi$
$480$	−7.75719	−0.354066
$481$	10.0453	0.458024
$482$	3.58951	0.163498
$483$	−97.5955	−4.44075
$484$	−10.1748	−0.462491
$485$	−6.24357	−0.283506
$486$	0.0722613	0.00327784
$487$	−29.9596	−1.35760	−0.678800	−	0.734323i	$-0.737500\pi$
$487$	−29.9596	−1.35760	−0.678800	+	0.734323i	$0.737500\pi$
$488$	−1.07770	−0.0487854
$489$	−48.5419	−2.19514
$490$	50.2674	2.27085
$491$	−2.57311	−0.116123	−0.0580614	−	0.998313i	$-0.518492\pi$
$491$	−2.57311	−0.116123	−0.0580614	+	0.998313i	$0.518492\pi$
$492$	0.778315	0.0350891
$493$	2.23612	0.100710
$494$	2.31713	0.104253
$495$	−14.0996	−0.633730
$496$	−3.57419	−0.160486
$497$	1.88922	0.0847430
$498$	17.9426	0.804027
$499$	−15.8497	−0.709528	−0.354764	−	0.934956i	$-0.615439\pi$
$499$	−15.8497	−0.709528	−0.354764	+	0.934956i	$0.615439\pi$
$500$	8.57490	0.383481
$501$	20.9699	0.936865
$502$	24.3355	1.08615
$503$	19.6851	0.877715	0.438857	−	0.898557i	$-0.355383\pi$
$503$	19.6851	0.877715	0.438857	+	0.898557i	$0.355383\pi$
$504$	30.8752	1.37529
$505$	−39.5144	−1.75837
$506$	5.74542	0.255415
$507$	22.8978	1.01693
$508$	17.9613	0.796904
$509$	33.5257	1.48600	0.743001	−	0.669291i	$-0.233402\pi$
$509$	33.5257	1.48600	0.743001	+	0.669291i	$0.233402\pi$
$510$	3.46264	0.153328
$511$	−25.7573	−1.13944
$512$	−1.00000	−0.0441942
$513$	−9.01404	−0.397980
$514$	5.13080	0.226310
$515$	−10.7426	−0.473376
$516$	21.1997	0.933265
$517$	−6.04090	−0.265679
$518$	−22.2935	−0.979521
$519$	4.33266	0.190183
$520$	−5.99015	−0.262685
$521$	3.30740	0.144900	0.0724500	−	0.997372i	$-0.476918\pi$
$521$	3.30740	0.144900	0.0724500	+	0.997372i	$0.476918\pi$
$522$	30.0769	1.31643
$523$	5.10494	0.223224	0.111612	−	0.993752i	$-0.464399\pi$
$523$	5.10494	0.223224	0.111612	+	0.993752i	$0.464399\pi$
$524$	−0.578127	−0.0252556
$525$	25.9703	1.13344
$526$	19.4161	0.846583
$527$	1.59544	0.0694985
$528$	−2.72582	−0.118626
$529$	17.0023	0.739231
$530$	3.84924	0.167200
$531$	−31.3613	−1.36097
$532$	−5.14244	−0.222953
$533$	0.601019	0.0260330
$534$	37.1964	1.60964
$535$	−20.0136	−0.865265
$536$	−4.83054	−0.208647
$537$	−35.3573	−1.52578
$538$	−0.784757	−0.0338333
$539$	17.6636	0.760825
$540$	23.3027	1.00279
$541$	15.9783	0.686960	0.343480	−	0.939160i	$-0.388394\pi$
$541$	15.9783	0.686960	0.343480	+	0.939160i	$0.388394\pi$
$542$	−27.9215	−1.19933
$543$	−13.5602	−0.581922
$544$	0.446378	0.0191383
$545$	20.8094	0.891377
$546$	35.7551	1.53018
$547$	36.0104	1.53970	0.769848	−	0.638228i	$-0.220332\pi$
$547$	36.0104	1.53970	0.769848	+	0.638228i	$0.220332\pi$
$548$	9.40589	0.401800
$549$	6.47055	0.276156
$550$	−1.52886	−0.0651910
$551$	−5.00947	−0.213410
$552$	−18.9784	−0.807776
$553$	27.7144	1.17854
$554$	18.4050	0.781955
$555$	−33.6290	−1.42747
$556$	−2.70650	−0.114781
$557$	40.4753	1.71499	0.857497	−	0.514489i	$-0.172018\pi$
$557$	40.4753	1.71499	0.857497	+	0.514489i	$0.172018\pi$
$558$	21.4595	0.908452
$559$	16.3705	0.692400
$560$	13.2940	0.561774
$561$	1.21675	0.0513711
$562$	2.86125	0.120695
$563$	−35.1628	−1.48194	−0.740968	−	0.671540i	$-0.765633\pi$
$563$	−35.1628	−1.48194	−0.740968	+	0.671540i	$0.765633\pi$
$564$	19.9545	0.840236
$565$	−20.8913	−0.878904
$566$	8.49639	0.357130
$567$	−46.4676	−1.95146
$568$	0.367378	0.0154148
$569$	−23.7108	−0.994009	−0.497005	−	0.867748i	$-0.665567\pi$
$569$	−23.7108	−0.994009	−0.497005	+	0.867748i	$0.665567\pi$
$570$	−7.75719	−0.324913
$571$	−8.00209	−0.334877	−0.167438	−	0.985883i	$-0.553550\pi$
$571$	−8.00209	−0.334877	−0.167438	+	0.985883i	$0.553550\pi$
$572$	−2.10489	−0.0880101
$573$	60.8998	2.54413
$574$	−1.33385	−0.0556737
$575$	−10.6447	−0.443913
$576$	6.00401	0.250167
$577$	−21.1568	−0.880771	−0.440385	−	0.897809i	$-0.645158\pi$
$577$	−21.1568	−0.880771	−0.440385	+	0.897809i	$0.645158\pi$
$578$	16.8007	0.698819
$579$	−13.7279	−0.570512
$580$	12.9502	0.537729
$581$	−30.7494	−1.27570
$582$	7.24711	0.300402
$583$	1.35259	0.0560187
$584$	−5.00877	−0.207265
$585$	35.9649	1.48697
$586$	9.20606	0.380299
$587$	16.0508	0.662486	0.331243	−	0.943546i	$-0.392532\pi$
$587$	16.0508	0.662486	0.331243	+	0.943546i	$0.392532\pi$
$588$	−58.3470	−2.40619
$589$	−3.57419	−0.147272
$590$	−13.5033	−0.555922
$591$	53.8867	2.21660
$592$	−4.33521	−0.178176
$593$	−27.0488	−1.11076	−0.555381	−	0.831596i	$-0.687427\pi$
$593$	−27.0488	−1.11076	−0.555381	+	0.831596i	$0.687427\pi$
$594$	8.18839	0.335974
$595$	−5.93415	−0.243276
$596$	6.25140	0.256067
$597$	−6.43896	−0.263529
$598$	−14.6553	−0.599299
$599$	−6.07674	−0.248289	−0.124144	−	0.992264i	$-0.539619\pi$
$599$	−6.07674	−0.248289	−0.124144	+	0.992264i	$0.539619\pi$
$600$	5.05019	0.206173
$601$	−0.872820	−0.0356031	−0.0178015	−	0.999842i	$-0.505667\pi$
$601$	−0.872820	−0.0356031	−0.0178015	+	0.999842i	$0.505667\pi$
$602$	−36.3313	−1.48075
$603$	29.0026	1.18108
$604$	0.701861	0.0285583
$605$	26.3034	1.06939
$606$	45.8656	1.86316
$607$	2.67370	0.108522	0.0542611	−	0.998527i	$-0.482720\pi$
$607$	2.67370	0.108522	0.0542611	+	0.998527i	$0.482720\pi$
$608$	−1.00000	−0.0405554
$609$	−77.2998	−3.13235
$610$	2.78603	0.112803
$611$	15.4090	0.623381
$612$	−2.68006	−0.108335
$613$	−38.5827	−1.55834	−0.779170	−	0.626813i	$-0.784359\pi$
$613$	−38.5827	−1.55834	−0.779170	+	0.626813i	$0.784359\pi$
$614$	14.2482	0.575009
$615$	−2.01206	−0.0811342
$616$	4.67141	0.188216
$617$	−22.8591	−0.920273	−0.460137	−	0.887848i	$-0.652200\pi$
$617$	−22.8591	−0.920273	−0.460137	+	0.887848i	$0.652200\pi$
$618$	12.4693	0.501588
$619$	−46.4373	−1.86647	−0.933236	−	0.359263i	$-0.883028\pi$
$619$	−46.4373	−1.86647	−0.933236	+	0.359263i	$0.883028\pi$
$620$	9.23984	0.371081
$621$	57.0115	2.28779
$622$	−30.0187	−1.20364
$623$	−63.7458	−2.55392
$624$	6.95295	0.278341
$625$	−30.5825	−1.22330
$626$	−20.6065	−0.823602
$627$	−2.72582	−0.108859
$628$	2.95538	0.117932
$629$	1.93514	0.0771591
$630$	−79.8173	−3.18000
$631$	−9.95338	−0.396238	−0.198119	−	0.980178i	$-0.563483\pi$
$631$	−9.95338	−0.396238	−0.198119	+	0.980178i	$0.563483\pi$
$632$	5.38936	0.214377
$633$	−3.00067	−0.119266
$634$	17.8230	0.707843
$635$	−46.4327	−1.84263
$636$	−4.46793	−0.177165
$637$	−45.0559	−1.78518
$638$	4.55062	0.180161
$639$	−2.20574	−0.0872577
$640$	2.58515	0.102187
$641$	−23.2209	−0.917172	−0.458586	−	0.888650i	$-0.651644\pi$
$641$	−23.2209	−0.917172	−0.458586	+	0.888650i	$0.651644\pi$
$642$	23.2304	0.916833
$643$	−16.7751	−0.661547	−0.330773	−	0.943710i	$-0.607310\pi$
$643$	−16.7751	−0.661547	−0.330773	+	0.943710i	$0.607310\pi$
$644$	32.5246	1.28165
$645$	−54.8045	−2.15792
$646$	0.446378	0.0175625
$647$	26.0141	1.02272	0.511360	−	0.859367i	$-0.329142\pi$
$647$	26.0141	1.02272	0.511360	+	0.859367i	$0.329142\pi$
$648$	−9.03611	−0.354972
$649$	−4.74496	−0.186256
$650$	3.89979	0.152962
$651$	−55.1524	−2.16159
$652$	16.1770	0.633542
$653$	−1.56240	−0.0611413	−0.0305706	−	0.999533i	$-0.509732\pi$
$653$	−1.56240	−0.0611413	−0.0305706	+	0.999533i	$0.509732\pi$
$654$	−24.1541	−0.944501
$655$	1.49455	0.0583968
$656$	−0.259380	−0.0101271
$657$	30.0727	1.17325
$658$	−34.1973	−1.33315
$659$	−33.2421	−1.29493	−0.647465	−	0.762095i	$-0.724171\pi$
$659$	−33.2421	−1.29493	−0.647465	+	0.762095i	$0.724171\pi$
$660$	7.04666	0.274291
$661$	−9.68468	−0.376690	−0.188345	−	0.982103i	$-0.560312\pi$
$661$	−9.68468	−0.376690	−0.188345	+	0.982103i	$0.560312\pi$
$662$	−22.1842	−0.862213
$663$	−3.10365	−0.120536
$664$	−5.97953	−0.232051
$665$	13.2940	0.515519
$666$	26.0286	1.00859
$667$	31.6836	1.22679
$668$	−6.98841	−0.270390
$669$	72.7885	2.81417
$670$	12.4877	0.482441
$671$	0.978991	0.0377935
$672$	−15.4307	−0.595254
$673$	40.7718	1.57164	0.785818	−	0.618457i	$-0.212242\pi$
$673$	40.7718	1.57164	0.785818	+	0.618457i	$0.212242\pi$
$674$	−0.733003	−0.0282342
$675$	−15.1708	−0.583925
$676$	−7.63089	−0.293496
$677$	31.4914	1.21031	0.605157	−	0.796106i	$-0.293110\pi$
$677$	31.4914	1.21031	0.605157	+	0.796106i	$0.293110\pi$
$678$	24.2492	0.931284
$679$	−12.4198	−0.476629
$680$	−1.15396	−0.0442522
$681$	−27.2417	−1.04391
$682$	3.24681	0.124327
$683$	−15.1346	−0.579109	−0.289555	−	0.957161i	$-0.593507\pi$
$683$	−15.1346	−0.579109	−0.289555	+	0.957161i	$0.593507\pi$
$684$	6.00401	0.229569
$685$	−24.3157	−0.929054
$686$	63.9959	2.44337
$687$	−76.8958	−2.93376
$688$	−7.06499	−0.269350
$689$	−3.45016	−0.131441
$690$	49.0622	1.86777
$691$	−17.0222	−0.647556	−0.323778	−	0.946133i	$-0.604953\pi$
$691$	−17.0222	−0.647556	−0.323778	+	0.946133i	$0.604953\pi$
$692$	−1.44390	−0.0548888
$693$	−28.0472	−1.06543
$694$	−25.7102	−0.975944
$695$	6.99672	0.265401
$696$	−15.0317	−0.569777
$697$	0.115782	0.00438555
$698$	−33.2208	−1.25743
$699$	−6.14485	−0.232420
$700$	−8.65483	−0.327122
$701$	37.8567	1.42983	0.714914	−	0.699212i	$-0.246466\pi$
$701$	37.8567	1.42983	0.714914	+	0.699212i	$0.246466\pi$
$702$	−20.8867	−0.788319
$703$	−4.33521	−0.163505
$704$	0.908404	0.0342368
$705$	−51.5854	−1.94282
$706$	−6.34342	−0.238738
$707$	−78.6027	−2.95616
$708$	15.6737	0.589053
$709$	−27.4911	−1.03245	−0.516225	−	0.856453i	$-0.672663\pi$
$709$	−27.4911	−1.03245	−0.516225	+	0.856453i	$0.672663\pi$
$710$	−0.949728	−0.0356427
$711$	−32.3578	−1.21351
$712$	−12.3960	−0.464561
$713$	22.6058	0.846595
$714$	6.88795	0.257775
$715$	5.44148	0.203500
$716$	11.7831	0.440356
$717$	−27.0185	−1.00902
$718$	10.0933	0.376680
$719$	−1.97197	−0.0735420	−0.0367710	−	0.999324i	$-0.511707\pi$
$719$	−1.97197	−0.0735420	−0.0367710	+	0.999324i	$0.511707\pi$
$720$	−15.5213	−0.578444
$721$	−21.3694	−0.795839
$722$	−1.00000	−0.0372161
$723$	10.7709	0.400576
$724$	4.51905	0.167949
$725$	−8.43104	−0.313121
$726$	−30.5312	−1.13312
$727$	−30.7478	−1.14037	−0.570187	−	0.821515i	$-0.693129\pi$
$727$	−30.7478	−1.14037	−0.570187	+	0.821515i	$0.693129\pi$
$728$	−11.9157	−0.441626
$729$	−26.8915	−0.995982
$730$	12.9485	0.479244
$731$	3.15366	0.116642
$732$	−3.23383	−0.119526
$733$	1.85771	0.0686161	0.0343080	−	0.999411i	$-0.489077\pi$
$733$	1.85771	0.0686161	0.0343080	+	0.999411i	$0.489077\pi$
$734$	3.16419	0.116792
$735$	150.836	5.56367
$736$	6.32474	0.233133
$737$	4.38808	0.161637
$738$	1.55732	0.0573259
$739$	−5.01730	−0.184564	−0.0922821	−	0.995733i	$-0.529416\pi$
$739$	−5.01730	−0.184564	−0.0922821	+	0.995733i	$0.529416\pi$
$740$	11.2072	0.411984
$741$	6.95295	0.255423
$742$	7.65697	0.281096
$743$	34.6420	1.27089	0.635445	−	0.772146i	$-0.280817\pi$
$743$	34.6420	1.27089	0.635445	+	0.772146i	$0.280817\pi$
$744$	−10.7250	−0.393196
$745$	−16.1608	−0.592087
$746$	−18.8641	−0.690663
$747$	35.9012	1.31356
$748$	−0.405492	−0.0148262
$749$	−39.8115	−1.45468
$750$	25.7304	0.939543
$751$	−10.8473	−0.395822	−0.197911	−	0.980220i	$-0.563416\pi$
$751$	−10.8473	−0.395822	−0.197911	+	0.980220i	$0.563416\pi$
$752$	−6.65002	−0.242501
$753$	73.0229	2.66110
$754$	−11.6076	−0.422724
$755$	−1.81442	−0.0660335
$756$	46.3541	1.68588
$757$	1.15076	0.0418252	0.0209126	−	0.999781i	$-0.493343\pi$
$757$	1.15076	0.0418252	0.0209126	+	0.999781i	$0.493343\pi$
$758$	8.24781	0.299574
$759$	17.2401	0.625776
$760$	2.58515	0.0937734
$761$	−10.1822	−0.369106	−0.184553	−	0.982823i	$-0.559084\pi$
$761$	−10.1822	−0.369106	−0.184553	+	0.982823i	$0.559084\pi$
$762$	53.8959	1.95244
$763$	41.3945	1.49858
$764$	−20.2954	−0.734262
$765$	6.92837	0.250496
$766$	−24.7066	−0.892686
$767$	12.1033	0.437026
$768$	−3.00067	−0.108277
$769$	23.8580	0.860343	0.430171	−	0.902747i	$-0.358453\pi$
$769$	23.8580	0.860343	0.430171	+	0.902747i	$0.358453\pi$
$770$	−12.0763	−0.435200
$771$	15.3958	0.554468
$772$	4.57495	0.164656
$773$	40.5287	1.45772	0.728858	−	0.684665i	$-0.240051\pi$
$773$	40.5287	1.45772	0.728858	+	0.684665i	$0.240051\pi$
$774$	42.4183	1.52469
$775$	−6.01544	−0.216081
$776$	−2.41517	−0.0866994
$777$	−66.8955	−2.39986
$778$	−6.67423	−0.239283
$779$	−0.259380	−0.00929327
$780$	−17.9745	−0.643589
$781$	−0.333728	−0.0119417
$782$	−2.82323	−0.100958
$783$	45.1555	1.61373
$784$	19.4447	0.694452
$785$	−7.64011	−0.272687
$786$	−1.73477	−0.0618771
$787$	11.3354	0.404063	0.202031	−	0.979379i	$-0.435246\pi$
$787$	11.3354	0.404063	0.202031	+	0.979379i	$0.435246\pi$
$788$	−17.9582	−0.639736
$789$	58.2613	2.07416
$790$	−13.9323	−0.495690
$791$	−41.5574	−1.47761
$792$	−5.45407	−0.193802
$793$	−2.49718	−0.0886776
$794$	18.4171	0.653598
$795$	11.5503	0.409646
$796$	2.14584	0.0760573
$797$	7.57948	0.268479	0.134240	−	0.990949i	$-0.457141\pi$
$797$	7.57948	0.268479	0.134240	+	0.990949i	$0.457141\pi$
$798$	−15.4307	−0.546243
$799$	2.96842	0.105015
$800$	−1.68302	−0.0595038
$801$	74.4259	2.62971
$802$	−12.5338	−0.442584
$803$	4.54999	0.160566
$804$	−14.4948	−0.511194
$805$	−84.0810	−2.96347
$806$	−8.28188	−0.291717
$807$	−2.35479	−0.0828927
$808$	−15.2851	−0.537728
$809$	−38.6062	−1.35732	−0.678660	−	0.734452i	$-0.737439\pi$
$809$	−38.6062	−1.35732	−0.678660	+	0.734452i	$0.737439\pi$
$810$	23.3597	0.820778
$811$	54.4575	1.91226	0.956131	−	0.292939i	$-0.0946333\pi$
$811$	54.4575	1.91226	0.956131	+	0.292939i	$0.0946333\pi$
$812$	25.7609	0.904029
$813$	−83.7832	−2.93841
$814$	3.93812	0.138031
$815$	−41.8201	−1.46490
$816$	1.33943	0.0468895
$817$	−7.06499	−0.247173
$818$	−26.7773	−0.936247
$819$	71.5421	2.49988
$820$	0.670539	0.0234162
$821$	−7.58653	−0.264772	−0.132386	−	0.991198i	$-0.542264\pi$
$821$	−7.58653	−0.264772	−0.132386	+	0.991198i	$0.542264\pi$
$822$	28.2240	0.984423
$823$	−22.3197	−0.778015	−0.389008	−	0.921235i	$-0.627182\pi$
$823$	−22.3197	−0.778015	−0.389008	+	0.921235i	$0.627182\pi$
$824$	−4.15550	−0.144764
$825$	−4.58761	−0.159720
$826$	−26.8610	−0.934614
$827$	39.3701	1.36903	0.684517	−	0.728997i	$-0.260013\pi$
$827$	39.3701	1.36903	0.684517	+	0.728997i	$0.260013\pi$
$828$	−37.9738	−1.31968
$829$	12.3130	0.427647	0.213823	−	0.976872i	$-0.431408\pi$
$829$	12.3130	0.427647	0.213823	+	0.976872i	$0.431408\pi$
$830$	15.4580	0.536556
$831$	55.2274	1.91582
$832$	−2.31713	−0.0803322
$833$	−8.67967	−0.300733
$834$	−8.12131	−0.281218
$835$	18.0661	0.625203
$836$	0.908404	0.0314178
$837$	32.2179	1.11361
$838$	10.3385	0.357136
$839$	19.5046	0.673373	0.336686	−	0.941617i	$-0.390694\pi$
$839$	19.5046	0.673373	0.336686	+	0.941617i	$0.390694\pi$
$840$	39.8909	1.37637
$841$	−3.90525	−0.134664
$842$	20.9904	0.723377
$843$	8.58567	0.295706
$844$	1.00000	0.0344214
$845$	19.7270	0.678630
$846$	39.9268	1.37271
$847$	52.3233	1.79785
$848$	1.48898	0.0511317
$849$	25.4949	0.874981
$850$	0.751264	0.0257681
$851$	27.4190	0.939913
$852$	1.10238	0.0377669
$853$	−25.3750	−0.868822	−0.434411	−	0.900715i	$-0.643044\pi$
$853$	−25.3750	−0.868822	−0.434411	+	0.900715i	$0.643044\pi$
$854$	5.54202	0.189644
$855$	−15.5213	−0.530817
$856$	−7.74176	−0.264608
$857$	34.9708	1.19458	0.597291	−	0.802025i	$-0.296244\pi$
$857$	34.9708	1.19458	0.597291	+	0.802025i	$0.296244\pi$
$858$	−6.31609	−0.215628
$859$	−15.2852	−0.521526	−0.260763	−	0.965403i	$-0.583974\pi$
$859$	−15.2852	−0.521526	−0.260763	+	0.965403i	$0.583974\pi$
$860$	18.2641	0.622800
$861$	−4.00244	−0.136403
$862$	8.35912	0.284713
$863$	39.7184	1.35203	0.676015	−	0.736888i	$-0.263705\pi$
$863$	39.7184	1.35203	0.676015	+	0.736888i	$0.263705\pi$
$864$	9.01404	0.306664
$865$	3.73270	0.126916
$866$	−3.59017	−0.121999
$867$	50.4135	1.71213
$868$	18.3801	0.623860
$869$	−4.89571	−0.166076
$870$	38.8594	1.31746
$871$	−11.1930	−0.379260
$872$	8.04958	0.272593
$873$	14.5007	0.490774
$874$	6.32474	0.213937
$875$	−44.0959	−1.49071
$876$	−15.0297	−0.507805
$877$	14.3742	0.485383	0.242691	−	0.970104i	$-0.421970\pi$
$877$	14.3742	0.485383	0.242691	+	0.970104i	$0.421970\pi$
$878$	29.5333	0.996701
$879$	27.6243	0.931746
$880$	−2.34836	−0.0791634
$881$	29.2395	0.985104	0.492552	−	0.870283i	$-0.336064\pi$
$881$	29.2395	0.985104	0.492552	+	0.870283i	$0.336064\pi$
$882$	−116.746	−3.93104
$883$	3.73408	0.125662	0.0628310	−	0.998024i	$-0.479987\pi$
$883$	3.73408	0.125662	0.0628310	+	0.998024i	$0.479987\pi$
$884$	1.03432	0.0347879
$885$	−40.5189	−1.36203
$886$	−13.6373	−0.458155
$887$	−12.1814	−0.409012	−0.204506	−	0.978865i	$-0.565559\pi$
$887$	−12.1814	−0.409012	−0.204506	+	0.978865i	$0.565559\pi$
$888$	−13.0085	−0.436537
$889$	−92.3648	−3.09782
$890$	32.0457	1.07417
$891$	8.20844	0.274993
$892$	−24.2574	−0.812199
$893$	−6.65002	−0.222534
$894$	18.7584	0.627374
$895$	−30.4612	−1.01821
$896$	5.14244	0.171797
$897$	−43.9756	−1.46830
$898$	−24.8116	−0.827973
$899$	17.9048	0.597158
$900$	10.1049	0.336829
$901$	−0.664647	−0.0221426
$902$	0.235622	0.00784536
$903$	−109.018	−3.62790
$904$	−8.08126	−0.268779
$905$	−11.6824	−0.388337
$906$	2.10605	0.0699689
$907$	20.0683	0.666356	0.333178	−	0.942864i	$-0.391879\pi$
$907$	20.0683	0.666356	0.333178	+	0.942864i	$0.391879\pi$
$908$	9.07856	0.301282
$909$	91.7720	3.04389
$910$	30.8040	1.02114
$911$	−32.7705	−1.08573	−0.542867	−	0.839819i	$-0.682661\pi$
$911$	−32.7705	−1.08573	−0.542867	+	0.839819i	$0.682661\pi$
$912$	−3.00067	−0.0993621
$913$	5.43183	0.179767
$914$	−19.2085	−0.635362
$915$	8.35995	0.276372
$916$	25.6262	0.846714
$917$	2.97298	0.0981765
$918$	−4.02367	−0.132801
$919$	−24.9758	−0.823874	−0.411937	−	0.911212i	$-0.635148\pi$
$919$	−24.9758	−0.823874	−0.411937	+	0.911212i	$0.635148\pi$
$920$	−16.3504	−0.539058
$921$	42.7540	1.40879
$922$	−33.5103	−1.10360
$923$	0.851264	0.0280197
$924$	14.0174	0.461137
$925$	−7.29625	−0.239899
$926$	20.2233	0.664580
$927$	24.9497	0.819455
$928$	5.00947	0.164444
$929$	−41.3440	−1.35645	−0.678226	−	0.734853i	$-0.737251\pi$
$929$	−41.3440	−1.35645	−0.678226	+	0.734853i	$0.737251\pi$
$930$	27.7257	0.909161
$931$	19.4447	0.637273
$932$	2.04783	0.0670788
$933$	−90.0762	−2.94896
$934$	−8.00387	−0.261895
$935$	1.04826	0.0342817
$936$	13.9121	0.454731
$937$	−42.2223	−1.37934	−0.689671	−	0.724123i	$-0.742245\pi$
$937$	−42.2223	−1.37934	−0.689671	+	0.724123i	$0.742245\pi$
$938$	24.8407	0.811079
$939$	−61.8333	−2.01785
$940$	17.1913	0.560719
$941$	7.50051	0.244510	0.122255	−	0.992499i	$-0.460987\pi$
$941$	7.50051	0.244510	0.122255	+	0.992499i	$0.460987\pi$
$942$	8.86811	0.288939
$943$	1.64051	0.0534225
$944$	−5.22340	−0.170007
$945$	−119.833	−3.89815
$946$	6.41787	0.208663
$947$	−3.43805	−0.111721	−0.0558607	−	0.998439i	$-0.517790\pi$
$947$	−3.43805	−0.111721	−0.0558607	+	0.998439i	$0.517790\pi$
$948$	16.1717	0.525231
$949$	−11.6060	−0.376747
$950$	−1.68302	−0.0546044
$951$	53.4810	1.73424
$952$	−2.29547	−0.0743967
$953$	59.9784	1.94289	0.971445	−	0.237263i	$-0.0762503\pi$
$953$	59.9784	1.94289	0.971445	+	0.237263i	$0.0762503\pi$
$954$	−8.93984	−0.289438
$955$	52.4668	1.69778
$956$	9.00416	0.291215
$957$	13.6549	0.441400
$958$	34.9026	1.12765
$959$	−48.3692	−1.56192
$960$	7.75719	0.250362
$961$	−18.2252	−0.587908
$962$	−10.0453	−0.323872
$963$	46.4816	1.49785
$964$	−3.58951	−0.115610
$965$	−11.8269	−0.380723
$966$	97.5955	3.14008
$967$	−15.3510	−0.493654	−0.246827	−	0.969060i	$-0.579388\pi$
$967$	−15.3510	−0.493654	−0.246827	+	0.969060i	$0.579388\pi$
$968$	10.1748	0.327031
$969$	1.33943	0.0430288
$970$	6.24357	0.200469
$971$	−5.89801	−0.189276	−0.0946380	−	0.995512i	$-0.530169\pi$
$971$	−5.89801	−0.189276	−0.0946380	+	0.995512i	$0.530169\pi$
$972$	−0.0722613	−0.00231778
$973$	13.9180	0.446191
$974$	29.9596	0.959968
$975$	11.7020	0.374763
$976$	1.07770	0.0344965
$977$	−40.4603	−1.29444	−0.647219	−	0.762304i	$-0.724068\pi$
$977$	−40.4603	−1.29444	−0.647219	+	0.762304i	$0.724068\pi$
$978$	48.5419	1.55220
$979$	11.2606	0.359891
$980$	−50.2674	−1.60573
$981$	−48.3298	−1.54305
$982$	2.57311	0.0821113
$983$	50.3551	1.60608	0.803039	−	0.595926i	$-0.203215\pi$
$983$	50.3551	1.60608	0.803039	+	0.595926i	$0.203215\pi$
$984$	−0.778315	−0.0248118
$985$	46.4248	1.47922
$986$	−2.23612	−0.0712124
$987$	−102.615	−3.26626
$988$	−2.31713	−0.0737179
$989$	44.6842	1.42088
$990$	14.0996	0.448115
$991$	−18.1236	−0.575717	−0.287858	−	0.957673i	$-0.592943\pi$
$991$	−18.1236	−0.575717	−0.287858	+	0.957673i	$0.592943\pi$
$992$	3.57419	0.113481
$993$	−66.5674	−2.11245
$994$	−1.88922	−0.0599223
$995$	−5.54733	−0.175862
$996$	−17.9426	−0.568533
$997$	−40.2704	−1.27537	−0.637687	−	0.770295i	$-0.720109\pi$
$997$	−40.2704	−1.27537	−0.637687	+	0.770295i	$0.720109\pi$
$998$	15.8497	0.501712
$999$	39.0777	1.23636

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.g.1.3	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.g.1.3	✓	34	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.00067 q^{3} +1.00000 q^{4} -2.58515 q^{5} +3.00067 q^{6} -5.14244 q^{7} -1.00000 q^{8} +6.00401 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.00067 q^{3} +1.00000 q^{4} -2.58515 q^{5} +3.00067 q^{6} -5.14244 q^{7} -1.00000 q^{8} +6.00401 q^{9} +2.58515 q^{10} +0.908404 q^{11} -3.00067 q^{12} -2.31713 q^{13} +5.14244 q^{14} +7.75719 q^{15} +1.00000 q^{16} -0.446378 q^{17} -6.00401 q^{18} +1.00000 q^{19} -2.58515 q^{20} +15.4307 q^{21} -0.908404 q^{22} -6.32474 q^{23} +3.00067 q^{24} +1.68302 q^{25} +2.31713 q^{26} -9.01404 q^{27} -5.14244 q^{28} -5.00947 q^{29} -7.75719 q^{30} -3.57419 q^{31} -1.00000 q^{32} -2.72582 q^{33} +0.446378 q^{34} +13.2940 q^{35} +6.00401 q^{36} -4.33521 q^{37} -1.00000 q^{38} +6.95295 q^{39} +2.58515 q^{40} -0.259380 q^{41} -15.4307 q^{42} -7.06499 q^{43} +0.908404 q^{44} -15.5213 q^{45} +6.32474 q^{46} -6.65002 q^{47} -3.00067 q^{48} +19.4447 q^{49} -1.68302 q^{50} +1.33943 q^{51} -2.31713 q^{52} +1.48898 q^{53} +9.01404 q^{54} -2.34836 q^{55} +5.14244 q^{56} -3.00067 q^{57} +5.00947 q^{58} -5.22340 q^{59} +7.75719 q^{60} +1.07770 q^{61} +3.57419 q^{62} -30.8752 q^{63} +1.00000 q^{64} +5.99015 q^{65} +2.72582 q^{66} +4.83054 q^{67} -0.446378 q^{68} +18.9784 q^{69} -13.2940 q^{70} -0.367378 q^{71} -6.00401 q^{72} +5.00877 q^{73} +4.33521 q^{74} -5.05019 q^{75} +1.00000 q^{76} -4.67141 q^{77} -6.95295 q^{78} -5.38936 q^{79} -2.58515 q^{80} +9.03611 q^{81} +0.259380 q^{82} +5.97953 q^{83} +15.4307 q^{84} +1.15396 q^{85} +7.06499 q^{86} +15.0317 q^{87} -0.908404 q^{88} +12.3960 q^{89} +15.5213 q^{90} +11.9157 q^{91} -6.32474 q^{92} +10.7250 q^{93} +6.65002 q^{94} -2.58515 q^{95} +3.00067 q^{96} +2.41517 q^{97} -19.4447 q^{98} +5.45407 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{2} - 6 q^{3} + 34 q^{4} + q^{5} + 6 q^{6} - 22 q^{7} - 34 q^{8} + 30 q^{9}+O(q^{10}) \) 34 * q - 34 * q^2 - 6 * q^3 + 34 * q^4 + q^5 + 6 * q^6 - 22 * q^7 - 34 * q^8 + 30 * q^9	\( 34 q - 34 q^{2} - 6 q^{3} + 34 q^{4} + q^{5} + 6 q^{6} - 22 q^{7} - 34 q^{8} + 30 q^{9} - q^{10} + 7 q^{11} - 6 q^{12} - 11 q^{13} + 22 q^{14} - 18 q^{15} + 34 q^{16} - 10 q^{17} - 30 q^{18} + 34 q^{19} + q^{20} + 14 q^{21} - 7 q^{22} - 30 q^{23} + 6 q^{24} + 11 q^{25} + 11 q^{26} - 21 q^{27} - 22 q^{28} + 12 q^{29} + 18 q^{30} - 13 q^{31} - 34 q^{32} - 4 q^{33} + 10 q^{34} - 16 q^{35} + 30 q^{36} - 46 q^{37} - 34 q^{38} - 36 q^{39} - q^{40} + 25 q^{41} - 14 q^{42} - 51 q^{43} + 7 q^{44} - 17 q^{45} + 30 q^{46} - 20 q^{47} - 6 q^{48} - 2 q^{49} - 11 q^{50} + 4 q^{51} - 11 q^{52} - 7 q^{53} + 21 q^{54} - 39 q^{55} + 22 q^{56} - 6 q^{57} - 12 q^{58} + 19 q^{59} - 18 q^{60} - 26 q^{61} + 13 q^{62} - 57 q^{63} + 34 q^{64} + 20 q^{65} + 4 q^{66} - 54 q^{67} - 10 q^{68} + 16 q^{70} + 9 q^{71} - 30 q^{72} - 57 q^{73} + 46 q^{74} + 26 q^{75} + 34 q^{76} + 2 q^{77} + 36 q^{78} - 7 q^{79} + q^{80} + 22 q^{81} - 25 q^{82} - 15 q^{83} + 14 q^{84} - 30 q^{85} + 51 q^{86} - 37 q^{87} - 7 q^{88} + 78 q^{89} + 17 q^{90} - 31 q^{91} - 30 q^{92} - 43 q^{93} + 20 q^{94} + q^{95} + 6 q^{96} - 38 q^{97} + 2 q^{98} + 2 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 6 * q^3 + 34 * q^4 + q^5 + 6 * q^6 - 22 * q^7 - 34 * q^8 + 30 * q^9 - q^10 + 7 * q^11 - 6 * q^12 - 11 * q^13 + 22 * q^14 - 18 * q^15 + 34 * q^16 - 10 * q^17 - 30 * q^18 + 34 * q^19 + q^20 + 14 * q^21 - 7 * q^22 - 30 * q^23 + 6 * q^24 + 11 * q^25 + 11 * q^26 - 21 * q^27 - 22 * q^28 + 12 * q^29 + 18 * q^30 - 13 * q^31 - 34 * q^32 - 4 * q^33 + 10 * q^34 - 16 * q^35 + 30 * q^36 - 46 * q^37 - 34 * q^38 - 36 * q^39 - q^40 + 25 * q^41 - 14 * q^42 - 51 * q^43 + 7 * q^44 - 17 * q^45 + 30 * q^46 - 20 * q^47 - 6 * q^48 - 2 * q^49 - 11 * q^50 + 4 * q^51 - 11 * q^52 - 7 * q^53 + 21 * q^54 - 39 * q^55 + 22 * q^56 - 6 * q^57 - 12 * q^58 + 19 * q^59 - 18 * q^60 - 26 * q^61 + 13 * q^62 - 57 * q^63 + 34 * q^64 + 20 * q^65 + 4 * q^66 - 54 * q^67 - 10 * q^68 + 16 * q^70 + 9 * q^71 - 30 * q^72 - 57 * q^73 + 46 * q^74 + 26 * q^75 + 34 * q^76 + 2 * q^77 + 36 * q^78 - 7 * q^79 + q^80 + 22 * q^81 - 25 * q^82 - 15 * q^83 + 14 * q^84 - 30 * q^85 + 51 * q^86 - 37 * q^87 - 7 * q^88 + 78 * q^89 + 17 * q^90 - 31 * q^91 - 30 * q^92 - 43 * q^93 + 20 * q^94 + q^95 + 6 * q^96 - 38 * q^97 + 2 * q^98 + 2 * q^99

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