LMFDB - Embedded newform 8018.2.a.e.1.1

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:	$32$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
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)

$f(q)$	$=$	$q+1.00000 q^{2} -3.42265 q^{3} +1.00000 q^{4} -0.619065 q^{5} -3.42265 q^{6} +1.32007 q^{7} +1.00000 q^{8} +8.71451 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.42265 q^{3} +1.00000 q^{4} -0.619065 q^{5} -3.42265 q^{6} +1.32007 q^{7} +1.00000 q^{8} +8.71451 q^{9} -0.619065 q^{10} +0.161662 q^{11} -3.42265 q^{12} +3.16351 q^{13} +1.32007 q^{14} +2.11884 q^{15} +1.00000 q^{16} +2.28106 q^{17} +8.71451 q^{18} -1.00000 q^{19} -0.619065 q^{20} -4.51812 q^{21} +0.161662 q^{22} +2.92655 q^{23} -3.42265 q^{24} -4.61676 q^{25} +3.16351 q^{26} -19.5587 q^{27} +1.32007 q^{28} -10.3080 q^{29} +2.11884 q^{30} -3.84968 q^{31} +1.00000 q^{32} -0.553313 q^{33} +2.28106 q^{34} -0.817207 q^{35} +8.71451 q^{36} -5.99206 q^{37} -1.00000 q^{38} -10.8276 q^{39} -0.619065 q^{40} -8.59575 q^{41} -4.51812 q^{42} +8.29898 q^{43} +0.161662 q^{44} -5.39484 q^{45} +2.92655 q^{46} +5.98679 q^{47} -3.42265 q^{48} -5.25742 q^{49} -4.61676 q^{50} -7.80725 q^{51} +3.16351 q^{52} -0.490156 q^{53} -19.5587 q^{54} -0.100079 q^{55} +1.32007 q^{56} +3.42265 q^{57} -10.3080 q^{58} +2.84777 q^{59} +2.11884 q^{60} +2.87823 q^{61} -3.84968 q^{62} +11.5037 q^{63} +1.00000 q^{64} -1.95842 q^{65} -0.553313 q^{66} -15.8212 q^{67} +2.28106 q^{68} -10.0165 q^{69} -0.817207 q^{70} -1.60089 q^{71} +8.71451 q^{72} +12.4595 q^{73} -5.99206 q^{74} +15.8015 q^{75} -1.00000 q^{76} +0.213405 q^{77} -10.8276 q^{78} -6.24352 q^{79} -0.619065 q^{80} +40.7991 q^{81} -8.59575 q^{82} +13.7245 q^{83} -4.51812 q^{84} -1.41212 q^{85} +8.29898 q^{86} +35.2807 q^{87} +0.161662 q^{88} -5.35892 q^{89} -5.39484 q^{90} +4.17605 q^{91} +2.92655 q^{92} +13.1761 q^{93} +5.98679 q^{94} +0.619065 q^{95} -3.42265 q^{96} +3.14636 q^{97} -5.25742 q^{98} +1.40881 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{2} - 7 q^{3} + 32 q^{4} - 6 q^{5} - 7 q^{6} - 5 q^{7} + 32 q^{8} + 15 q^{9}+O(q^{10}) $ 32 * q + 32 * q^2 - 7 * q^3 + 32 * q^4 - 6 * q^5 - 7 * q^6 - 5 * q^7 + 32 * q^8 + 15 * q^9	\( 32 q + 32 q^{2} - 7 q^{3} + 32 q^{4} - 6 q^{5} - 7 q^{6} - 5 q^{7} + 32 q^{8} + 15 q^{9} - 6 q^{10} - 21 q^{11} - 7 q^{12} - 19 q^{13} - 5 q^{14} - 14 q^{15} + 32 q^{16} - 14 q^{17} + 15 q^{18} - 32 q^{19} - 6 q^{20} - 26 q^{21} - 21 q^{22} - 13 q^{23} - 7 q^{24} - 10 q^{25} - 19 q^{26} - 25 q^{27} - 5 q^{28} - 42 q^{29} - 14 q^{30} - 15 q^{31} + 32 q^{32} - 32 q^{33} - 14 q^{34} - 22 q^{35} + 15 q^{36} - 54 q^{37} - 32 q^{38} - 32 q^{39} - 6 q^{40} - 16 q^{41} - 26 q^{42} - 37 q^{43} - 21 q^{44} - 46 q^{45} - 13 q^{46} - 9 q^{47} - 7 q^{48} - 7 q^{49} - 10 q^{50} - 32 q^{51} - 19 q^{52} - 53 q^{53} - 25 q^{54} - 17 q^{55} - 5 q^{56} + 7 q^{57} - 42 q^{58} - 34 q^{59} - 14 q^{60} - 33 q^{61} - 15 q^{62} + 18 q^{63} + 32 q^{64} - 50 q^{65} - 32 q^{66} - 53 q^{67} - 14 q^{68} - 40 q^{69} - 22 q^{70} - 27 q^{71} + 15 q^{72} - 43 q^{73} - 54 q^{74} + 5 q^{75} - 32 q^{76} - 56 q^{77} - 32 q^{78} - 11 q^{79} - 6 q^{80} - 8 q^{81} - 16 q^{82} - 17 q^{83} - 26 q^{84} - 30 q^{85} - 37 q^{86} + 3 q^{87} - 21 q^{88} - 21 q^{89} - 46 q^{90} - 67 q^{91} - 13 q^{92} - 31 q^{93} - 9 q^{94} + 6 q^{95} - 7 q^{96} - 51 q^{97} - 7 q^{98} - 32 q^{99}+O(q^{100}) \) 32 * q + 32 * q^2 - 7 * q^3 + 32 * q^4 - 6 * q^5 - 7 * q^6 - 5 * q^7 + 32 * q^8 + 15 * q^9 - 6 * q^10 - 21 * q^11 - 7 * q^12 - 19 * q^13 - 5 * q^14 - 14 * q^15 + 32 * q^16 - 14 * q^17 + 15 * q^18 - 32 * q^19 - 6 * q^20 - 26 * q^21 - 21 * q^22 - 13 * q^23 - 7 * q^24 - 10 * q^25 - 19 * q^26 - 25 * q^27 - 5 * q^28 - 42 * q^29 - 14 * q^30 - 15 * q^31 + 32 * q^32 - 32 * q^33 - 14 * q^34 - 22 * q^35 + 15 * q^36 - 54 * q^37 - 32 * q^38 - 32 * q^39 - 6 * q^40 - 16 * q^41 - 26 * q^42 - 37 * q^43 - 21 * q^44 - 46 * q^45 - 13 * q^46 - 9 * q^47 - 7 * q^48 - 7 * q^49 - 10 * q^50 - 32 * q^51 - 19 * q^52 - 53 * q^53 - 25 * q^54 - 17 * q^55 - 5 * q^56 + 7 * q^57 - 42 * q^58 - 34 * q^59 - 14 * q^60 - 33 * q^61 - 15 * q^62 + 18 * q^63 + 32 * q^64 - 50 * q^65 - 32 * q^66 - 53 * q^67 - 14 * q^68 - 40 * q^69 - 22 * q^70 - 27 * q^71 + 15 * q^72 - 43 * q^73 - 54 * q^74 + 5 * q^75 - 32 * q^76 - 56 * q^77 - 32 * q^78 - 11 * q^79 - 6 * q^80 - 8 * q^81 - 16 * q^82 - 17 * q^83 - 26 * q^84 - 30 * q^85 - 37 * q^86 + 3 * q^87 - 21 * q^88 - 21 * q^89 - 46 * q^90 - 67 * q^91 - 13 * q^92 - 31 * q^93 - 9 * q^94 + 6 * q^95 - 7 * q^96 - 51 * q^97 - 7 * q^98 - 32 * 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
$3$	−3.42265	−1.97607	−0.988033	−	0.154244i	$-0.950706\pi$
$3$	−3.42265	−1.97607	−0.988033	+	0.154244i	$0.950706\pi$
$4$	1.00000	0.500000
$5$	−0.619065	−0.276854	−0.138427	−	0.990373i	$-0.544205\pi$
$5$	−0.619065	−0.276854	−0.138427	+	0.990373i	$0.544205\pi$
$6$	−3.42265	−1.39729
$7$	1.32007	0.498939	0.249469	−	0.968383i	$-0.419744\pi$
$7$	1.32007	0.498939	0.249469	+	0.968383i	$0.419744\pi$
$8$	1.00000	0.353553
$9$	8.71451	2.90484
$10$	−0.619065	−0.195765
$11$	0.161662	0.0487430	0.0243715	−	0.999703i	$-0.492242\pi$
$11$	0.161662	0.0487430	0.0243715	+	0.999703i	$0.492242\pi$
$12$	−3.42265	−0.988033
$13$	3.16351	0.877400	0.438700	−	0.898633i	$-0.355439\pi$
$13$	3.16351	0.877400	0.438700	+	0.898633i	$0.355439\pi$
$14$	1.32007	0.352803
$15$	2.11884	0.547082
$16$	1.00000	0.250000
$17$	2.28106	0.553238	0.276619	−	0.960980i	$-0.410786\pi$
$17$	2.28106	0.553238	0.276619	+	0.960980i	$0.410786\pi$
$18$	8.71451	2.05403
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−0.619065	−0.138427
$21$	−4.51812	−0.985935
$22$	0.161662	0.0344665
$23$	2.92655	0.610228	0.305114	−	0.952316i	$-0.401306\pi$
$23$	2.92655	0.610228	0.305114	+	0.952316i	$0.401306\pi$
$24$	−3.42265	−0.698645
$25$	−4.61676	−0.923352
$26$	3.16351	0.620416
$27$	−19.5587	−3.76408
$28$	1.32007	0.249469
$29$	−10.3080	−1.91415	−0.957076	−	0.289838i	$-0.906399\pi$
$29$	−10.3080	−1.91415	−0.957076	+	0.289838i	$0.906399\pi$
$30$	2.11884	0.386845
$31$	−3.84968	−0.691423	−0.345711	−	0.938341i	$-0.612362\pi$
$31$	−3.84968	−0.691423	−0.345711	+	0.938341i	$0.612362\pi$
$32$	1.00000	0.176777
$33$	−0.553313	−0.0963193
$34$	2.28106	0.391198
$35$	−0.817207	−0.138133
$36$	8.71451	1.45242
$37$	−5.99206	−0.985088	−0.492544	−	0.870287i	$-0.663933\pi$
$37$	−5.99206	−0.985088	−0.492544	+	0.870287i	$0.663933\pi$
$38$	−1.00000	−0.162221
$39$	−10.8276	−1.73380
$40$	−0.619065	−0.0978827
$41$	−8.59575	−1.34243	−0.671216	−	0.741262i	$-0.734228\pi$
$41$	−8.59575	−1.34243	−0.671216	+	0.741262i	$0.734228\pi$
$42$	−4.51812	−0.697162
$43$	8.29898	1.26558	0.632791	−	0.774322i	$-0.281909\pi$
$43$	8.29898	1.26558	0.632791	+	0.774322i	$0.281909\pi$
$44$	0.161662	0.0243715
$45$	−5.39484	−0.804216
$46$	2.92655	0.431496
$47$	5.98679	0.873262	0.436631	−	0.899641i	$-0.356171\pi$
$47$	5.98679	0.873262	0.436631	+	0.899641i	$0.356171\pi$
$48$	−3.42265	−0.494016
$49$	−5.25742	−0.751060
$50$	−4.61676	−0.652908
$51$	−7.80725	−1.09323
$52$	3.16351	0.438700
$53$	−0.490156	−0.0673282	−0.0336641	−	0.999433i	$-0.510718\pi$
$53$	−0.490156	−0.0673282	−0.0336641	+	0.999433i	$0.510718\pi$
$54$	−19.5587	−2.66161
$55$	−0.100079	−0.0134947
$56$	1.32007	0.176401
$57$	3.42265	0.453341
$58$	−10.3080	−1.35351
$59$	2.84777	0.370748	0.185374	−	0.982668i	$-0.440650\pi$
$59$	2.84777	0.370748	0.185374	+	0.982668i	$0.440650\pi$
$60$	2.11884	0.273541
$61$	2.87823	0.368520	0.184260	−	0.982878i	$-0.441011\pi$
$61$	2.87823	0.368520	0.184260	+	0.982878i	$0.441011\pi$
$62$	−3.84968	−0.488910
$63$	11.5037	1.44933
$64$	1.00000	0.125000
$65$	−1.95842	−0.242912
$66$	−0.553313	−0.0681081
$67$	−15.8212	−1.93287	−0.966435	−	0.256910i	$-0.917296\pi$
$67$	−15.8212	−1.93287	−0.966435	+	0.256910i	$0.917296\pi$
$68$	2.28106	0.276619
$69$	−10.0165	−1.20585
$70$	−0.817207	−0.0976749
$71$	−1.60089	−0.189990	−0.0949951	−	0.995478i	$-0.530284\pi$
$71$	−1.60089	−0.189990	−0.0949951	+	0.995478i	$0.530284\pi$
$72$	8.71451	1.02701
$73$	12.4595	1.45827	0.729135	−	0.684370i	$-0.239923\pi$
$73$	12.4595	1.45827	0.729135	+	0.684370i	$0.239923\pi$
$74$	−5.99206	−0.696563
$75$	15.8015	1.82460
$76$	−1.00000	−0.114708
$77$	0.213405	0.0243198
$78$	−10.8276	−1.22598
$79$	−6.24352	−0.702451	−0.351225	−	0.936291i	$-0.614235\pi$
$79$	−6.24352	−0.702451	−0.351225	+	0.936291i	$0.614235\pi$
$80$	−0.619065	−0.0692135
$81$	40.7991	4.53323
$82$	−8.59575	−0.949242
$83$	13.7245	1.50646	0.753230	−	0.657758i	$-0.228495\pi$
$83$	13.7245	1.50646	0.753230	+	0.657758i	$0.228495\pi$
$84$	−4.51812	−0.492968
$85$	−1.41212	−0.153166
$86$	8.29898	0.894902
$87$	35.2807	3.78249
$88$	0.161662	0.0172332
$89$	−5.35892	−0.568044	−0.284022	−	0.958818i	$-0.591669\pi$
$89$	−5.35892	−0.568044	−0.284022	+	0.958818i	$0.591669\pi$
$90$	−5.39484	−0.568666
$91$	4.17605	0.437769
$92$	2.92655	0.305114
$93$	13.1761	1.36630
$94$	5.98679	0.617490
$95$	0.619065	0.0635147
$96$	−3.42265	−0.349322
$97$	3.14636	0.319465	0.159732	−	0.987160i	$-0.448937\pi$
$97$	3.14636	0.319465	0.159732	+	0.987160i	$0.448937\pi$
$98$	−5.25742	−0.531080
$99$	1.40881	0.141590
$100$	−4.61676	−0.461676
$101$	−10.3594	−1.03080	−0.515400	−	0.856949i	$-0.672357\pi$
$101$	−10.3594	−1.03080	−0.515400	+	0.856949i	$0.672357\pi$
$102$	−7.80725	−0.773033
$103$	−1.20248	−0.118484	−0.0592420	−	0.998244i	$-0.518868\pi$
$103$	−1.20248	−0.118484	−0.0592420	+	0.998244i	$0.518868\pi$
$104$	3.16351	0.310208
$105$	2.79701	0.272960
$106$	−0.490156	−0.0476082
$107$	0.239441	0.0231477	0.0115738	−	0.999933i	$-0.496316\pi$
$107$	0.239441	0.0231477	0.0115738	+	0.999933i	$0.496316\pi$
$108$	−19.5587	−1.88204
$109$	13.9533	1.33648	0.668242	−	0.743944i	$-0.267047\pi$
$109$	13.9533	1.33648	0.668242	+	0.743944i	$0.267047\pi$
$110$	−0.100079	−0.00954219
$111$	20.5087	1.94660
$112$	1.32007	0.124735
$113$	−5.56885	−0.523873	−0.261937	−	0.965085i	$-0.584361\pi$
$113$	−5.56885	−0.523873	−0.261937	+	0.965085i	$0.584361\pi$
$114$	3.42265	0.320560
$115$	−1.81172	−0.168944
$116$	−10.3080	−0.957076
$117$	27.5684	2.54870
$118$	2.84777	0.262159
$119$	3.01115	0.276032
$120$	2.11884	0.193423
$121$	−10.9739	−0.997624
$122$	2.87823	0.260583
$123$	29.4202	2.65273
$124$	−3.84968	−0.345711
$125$	5.95340	0.532488
$126$	11.5037	1.02483
$127$	−2.90650	−0.257910	−0.128955	−	0.991650i	$-0.541162\pi$
$127$	−2.90650	−0.257910	−0.128955	+	0.991650i	$0.541162\pi$
$128$	1.00000	0.0883883
$129$	−28.4045	−2.50087
$130$	−1.95842	−0.171765
$131$	3.80304	0.332273	0.166136	−	0.986103i	$-0.446871\pi$
$131$	3.80304	0.332273	0.166136	+	0.986103i	$0.446871\pi$
$132$	−0.553313	−0.0481597
$133$	−1.32007	−0.114464
$134$	−15.8212	−1.36675
$135$	12.1081	1.04210
$136$	2.28106	0.195599
$137$	−4.61953	−0.394673	−0.197337	−	0.980336i	$-0.563229\pi$
$137$	−4.61953	−0.394673	−0.197337	+	0.980336i	$0.563229\pi$
$138$	−10.0165	−0.852665
$139$	−9.66020	−0.819367	−0.409684	−	0.912228i	$-0.634361\pi$
$139$	−9.66020	−0.819367	−0.409684	+	0.912228i	$0.634361\pi$
$140$	−0.817207	−0.0690666
$141$	−20.4906	−1.72562
$142$	−1.60089	−0.134343
$143$	0.511420	0.0427671
$144$	8.71451	0.726209
$145$	6.38133	0.529941
$146$	12.4595	1.03115
$147$	17.9943	1.48414
$148$	−5.99206	−0.492544
$149$	−22.8681	−1.87342	−0.936712	−	0.350101i	$-0.886147\pi$
$149$	−22.8681	−1.87342	−0.936712	+	0.350101i	$0.886147\pi$
$150$	15.8015	1.29019
$151$	18.0275	1.46705	0.733527	−	0.679660i	$-0.237873\pi$
$151$	18.0275	1.46705	0.733527	+	0.679660i	$0.237873\pi$
$152$	−1.00000	−0.0811107
$153$	19.8783	1.60706
$154$	0.213405	0.0171967
$155$	2.38320	0.191423
$156$	−10.8276	−0.866900
$157$	−21.2324	−1.69453	−0.847267	−	0.531168i	$-0.821753\pi$
$157$	−21.2324	−1.69453	−0.847267	+	0.531168i	$0.821753\pi$
$158$	−6.24352	−0.496708
$159$	1.67763	0.133045
$160$	−0.619065	−0.0489414
$161$	3.86324	0.304466
$162$	40.7991	3.20548
$163$	−13.7863	−1.07982	−0.539912	−	0.841722i	$-0.681542\pi$
$163$	−13.7863	−1.07982	−0.539912	+	0.841722i	$0.681542\pi$
$164$	−8.59575	−0.671216
$165$	0.342536	0.0266664
$166$	13.7245	1.06523
$167$	8.81437	0.682077	0.341038	−	0.940049i	$-0.389221\pi$
$167$	8.81437	0.682077	0.341038	+	0.940049i	$0.389221\pi$
$168$	−4.51812	−0.348581
$169$	−2.99219	−0.230168
$170$	−1.41212	−0.108305
$171$	−8.71451	−0.666415
$172$	8.29898	0.632791
$173$	−0.600476	−0.0456534	−0.0228267	−	0.999739i	$-0.507267\pi$
$173$	−0.600476	−0.0456534	−0.0228267	+	0.999739i	$0.507267\pi$
$174$	35.2807	2.67462
$175$	−6.09443	−0.460696
$176$	0.161662	0.0121857
$177$	−9.74691	−0.732623
$178$	−5.35892	−0.401668
$179$	−0.691555	−0.0516893	−0.0258446	−	0.999666i	$-0.508228\pi$
$179$	−0.691555	−0.0516893	−0.0258446	+	0.999666i	$0.508228\pi$
$180$	−5.39484	−0.402108
$181$	−19.0535	−1.41624	−0.708120	−	0.706093i	$-0.750456\pi$
$181$	−19.0535	−1.41624	−0.708120	+	0.706093i	$0.750456\pi$
$182$	4.17605	0.309549
$183$	−9.85117	−0.728219
$184$	2.92655	0.215748
$185$	3.70947	0.272726
$186$	13.1761	0.966118
$187$	0.368761	0.0269665
$188$	5.98679	0.436631
$189$	−25.8188	−1.87804
$190$	0.619065	0.0449117
$191$	−3.79863	−0.274859	−0.137430	−	0.990512i	$-0.543884\pi$
$191$	−3.79863	−0.274859	−0.137430	+	0.990512i	$0.543884\pi$
$192$	−3.42265	−0.247008
$193$	−3.18507	−0.229266	−0.114633	−	0.993408i	$-0.536569\pi$
$193$	−3.18507	−0.229266	−0.114633	+	0.993408i	$0.536569\pi$
$194$	3.14636	0.225896
$195$	6.70297	0.480010
$196$	−5.25742	−0.375530
$197$	−13.1219	−0.934898	−0.467449	−	0.884020i	$-0.654827\pi$
$197$	−13.1219	−0.934898	−0.467449	+	0.884020i	$0.654827\pi$
$198$	1.40881	0.100120
$199$	11.6164	0.823468	0.411734	−	0.911304i	$-0.364923\pi$
$199$	11.6164	0.823468	0.411734	+	0.911304i	$0.364923\pi$
$200$	−4.61676	−0.326454
$201$	54.1505	3.81948
$202$	−10.3594	−0.728886
$203$	−13.6073	−0.955044
$204$	−7.80725	−0.546617
$205$	5.32133	0.371658
$206$	−1.20248	−0.0837809
$207$	25.5034	1.77261
$208$	3.16351	0.219350
$209$	−0.161662	−0.0111824
$210$	2.79701	0.193012
$211$	1.00000	0.0688428
$211$	1.00000	0.0688428
$212$	−0.490156	−0.0336641
$213$	5.47926	0.375433
$214$	0.239441	0.0163679
$215$	−5.13761	−0.350382
$216$	−19.5587	−1.33080
$217$	−5.08184	−0.344977
$218$	13.9533	0.945038
$219$	−42.6443	−2.88164
$220$	−0.100079	−0.00674735
$221$	7.21615	0.485411
$222$	20.5087	1.37645
$223$	−1.47092	−0.0985004	−0.0492502	−	0.998786i	$-0.515683\pi$
$223$	−1.47092	−0.0985004	−0.0492502	+	0.998786i	$0.515683\pi$
$224$	1.32007	0.0882007
$225$	−40.2328	−2.68218
$226$	−5.56885	−0.370434
$227$	9.83492	0.652766	0.326383	−	0.945238i	$-0.394170\pi$
$227$	9.83492	0.652766	0.326383	+	0.945238i	$0.394170\pi$
$228$	3.42265	0.226670
$229$	19.1619	1.26625	0.633126	−	0.774049i	$-0.281772\pi$
$229$	19.1619	1.26625	0.633126	+	0.774049i	$0.281772\pi$
$230$	−1.81172	−0.119461
$231$	−0.730410	−0.0480574
$232$	−10.3080	−0.676755
$233$	4.49161	0.294255	0.147128	−	0.989118i	$-0.452997\pi$
$233$	4.49161	0.294255	0.147128	+	0.989118i	$0.452997\pi$
$234$	27.5684	1.80221
$235$	−3.70621	−0.241766
$236$	2.84777	0.185374
$237$	21.3694	1.38809
$238$	3.01115	0.195184
$239$	29.2944	1.89490	0.947449	−	0.319907i	$-0.103652\pi$
$239$	29.2944	1.89490	0.947449	+	0.319907i	$0.103652\pi$
$240$	2.11884	0.136770
$241$	15.3424	0.988290	0.494145	−	0.869379i	$-0.335481\pi$
$241$	15.3424	0.988290	0.494145	+	0.869379i	$0.335481\pi$
$242$	−10.9739	−0.705427
$243$	−80.9647	−5.19389
$244$	2.87823	0.184260
$245$	3.25468	0.207934
$246$	29.4202	1.87576
$247$	−3.16351	−0.201289
$248$	−3.84968	−0.244455
$249$	−46.9741	−2.97686
$250$	5.95340	0.376526
$251$	−3.34371	−0.211053	−0.105526	−	0.994416i	$-0.533653\pi$
$251$	−3.34371	−0.211053	−0.105526	+	0.994416i	$0.533653\pi$
$252$	11.5037	0.724667
$253$	0.473112	0.0297443
$254$	−2.90650	−0.182370
$255$	4.83319	0.302666
$256$	1.00000	0.0625000
$257$	16.1547	1.00770	0.503850	−	0.863791i	$-0.331916\pi$
$257$	16.1547	1.00770	0.503850	+	0.863791i	$0.331916\pi$
$258$	−28.4045	−1.76839
$259$	−7.90992	−0.491499
$260$	−1.95842	−0.121456
$261$	−89.8293	−5.56029
$262$	3.80304	0.234952
$263$	−9.74045	−0.600622	−0.300311	−	0.953841i	$-0.597090\pi$
$263$	−9.74045	−0.600622	−0.300311	+	0.953841i	$0.597090\pi$
$264$	−0.553313	−0.0340540
$265$	0.303438	0.0186401
$266$	−1.32007	−0.0809385
$267$	18.3417	1.12249
$268$	−15.8212	−0.966435
$269$	−32.3438	−1.97204	−0.986018	−	0.166636i	$-0.946710\pi$
$269$	−32.3438	−1.97204	−0.986018	+	0.166636i	$0.946710\pi$
$270$	12.1081	0.736877
$271$	−7.26269	−0.441177	−0.220589	−	0.975367i	$-0.570798\pi$
$271$	−7.26269	−0.441177	−0.220589	+	0.975367i	$0.570798\pi$
$272$	2.28106	0.138309
$273$	−14.2931	−0.865060
$274$	−4.61953	−0.279076
$275$	−0.746355	−0.0450069
$276$	−10.0165	−0.602925
$277$	2.15934	0.129742	0.0648712	−	0.997894i	$-0.479336\pi$
$277$	2.15934	0.129742	0.0648712	+	0.997894i	$0.479336\pi$
$278$	−9.66020	−0.579380
$279$	−33.5480	−2.00847
$280$	−0.817207	−0.0488375
$281$	−0.211029	−0.0125889	−0.00629446	−	0.999980i	$-0.502004\pi$
$281$	−0.211029	−0.0125889	−0.00629446	+	0.999980i	$0.502004\pi$
$282$	−20.4906	−1.22020
$283$	−9.00981	−0.535578	−0.267789	−	0.963478i	$-0.586293\pi$
$283$	−9.00981	−0.535578	−0.267789	+	0.963478i	$0.586293\pi$
$284$	−1.60089	−0.0949951
$285$	−2.11884	−0.125509
$286$	0.511420	0.0302409
$287$	−11.3470	−0.669791
$288$	8.71451	0.513507
$289$	−11.7968	−0.693928
$290$	6.38133	0.374725
$291$	−10.7689	−0.631284
$292$	12.4595	0.729135
$293$	−9.34231	−0.545783	−0.272892	−	0.962045i	$-0.587980\pi$
$293$	−9.34231	−0.545783	−0.272892	+	0.962045i	$0.587980\pi$
$294$	17.9943	1.04945
$295$	−1.76295	−0.102643
$296$	−5.99206	−0.348281
$297$	−3.16191	−0.183472
$298$	−22.8681	−1.32471
$299$	9.25817	0.535414
$300$	15.8015	0.912302
$301$	10.9552	0.631448
$302$	18.0275	1.03736
$303$	35.4566	2.03693
$304$	−1.00000	−0.0573539
$305$	−1.78181	−0.102026
$306$	19.8783	1.13637
$307$	−28.6760	−1.63663	−0.818313	−	0.574773i	$-0.805090\pi$
$307$	−28.6760	−1.63663	−0.818313	+	0.574773i	$0.805090\pi$
$308$	0.213405	0.0121599
$309$	4.11567	0.234132
$310$	2.38320	0.135357
$311$	7.61045	0.431549	0.215774	−	0.976443i	$-0.430772\pi$
$311$	7.61045	0.431549	0.215774	+	0.976443i	$0.430772\pi$
$312$	−10.8276	−0.612991
$313$	−26.9199	−1.52160	−0.760801	−	0.648985i	$-0.775194\pi$
$313$	−26.9199	−1.52160	−0.760801	+	0.648985i	$0.775194\pi$
$314$	−21.2324	−1.19822
$315$	−7.12156	−0.401254
$316$	−6.24352	−0.351225
$317$	−21.9199	−1.23115	−0.615573	−	0.788080i	$-0.711075\pi$
$317$	−21.9199	−1.23115	−0.615573	+	0.788080i	$0.711075\pi$
$318$	1.67763	0.0940769
$319$	−1.66642	−0.0933015
$320$	−0.619065	−0.0346068
$321$	−0.819523	−0.0457413
$322$	3.86324	0.215290
$323$	−2.28106	−0.126921
$324$	40.7991	2.26662
$325$	−14.6052	−0.810149
$326$	−13.7863	−0.763551
$327$	−47.7572	−2.64098
$328$	−8.59575	−0.474621
$329$	7.90296	0.435704
$330$	0.342536	0.0188560
$331$	12.3206	0.677202	0.338601	−	0.940930i	$-0.390046\pi$
$331$	12.3206	0.677202	0.338601	+	0.940930i	$0.390046\pi$
$332$	13.7245	0.753230
$333$	−52.2178	−2.86152
$334$	8.81437	0.482301
$335$	9.79436	0.535123
$336$	−4.51812	−0.246484
$337$	−11.2097	−0.610630	−0.305315	−	0.952251i	$-0.598762\pi$
$337$	−11.2097	−0.610630	−0.305315	+	0.952251i	$0.598762\pi$
$338$	−2.99219	−0.162754
$339$	19.0602	1.03521
$340$	−1.41212	−0.0765831
$341$	−0.622348	−0.0337020
$342$	−8.71451	−0.471227
$343$	−16.1806	−0.873671
$344$	8.29898	0.447451
$345$	6.20089	0.333844
$346$	−0.600476	−0.0322818
$347$	26.0730	1.39967	0.699837	−	0.714303i	$-0.253256\pi$
$347$	26.0730	1.39967	0.699837	+	0.714303i	$0.253256\pi$
$348$	35.2807	1.89124
$349$	19.3113	1.03371	0.516856	−	0.856072i	$-0.327102\pi$
$349$	19.3113	1.03371	0.516856	+	0.856072i	$0.327102\pi$
$350$	−6.09443	−0.325761
$351$	−61.8743	−3.30261
$352$	0.161662	0.00861662
$353$	−16.5840	−0.882676	−0.441338	−	0.897341i	$-0.645496\pi$
$353$	−16.5840	−0.882676	−0.441338	+	0.897341i	$0.645496\pi$
$354$	−9.74691	−0.518043
$355$	0.991052	0.0525996
$356$	−5.35892	−0.284022
$357$	−10.3061	−0.545457
$358$	−0.691555	−0.0365498
$359$	5.17866	0.273319	0.136660	−	0.990618i	$-0.456363\pi$
$359$	5.17866	0.273319	0.136660	+	0.990618i	$0.456363\pi$
$360$	−5.39484	−0.284333
$361$	1.00000	0.0526316
$362$	−19.0535	−1.00143
$363$	37.5597	1.97137
$364$	4.17605	0.218884
$365$	−7.71321	−0.403728
$366$	−9.85117	−0.514929
$367$	−0.348973	−0.0182163	−0.00910813	−	0.999959i	$-0.502899\pi$
$367$	−0.348973	−0.0182163	−0.00910813	+	0.999959i	$0.502899\pi$
$368$	2.92655	0.152557
$369$	−74.9077	−3.89954
$370$	3.70947	0.192846
$371$	−0.647039	−0.0335926
$372$	13.1761	0.683148
$373$	3.83432	0.198533	0.0992667	−	0.995061i	$-0.468350\pi$
$373$	3.83432	0.198533	0.0992667	+	0.995061i	$0.468350\pi$
$374$	0.368761	0.0190682
$375$	−20.3764	−1.05223
$376$	5.98679	0.308745
$377$	−32.6095	−1.67948
$378$	−25.8188	−1.32798
$379$	15.7436	0.808694	0.404347	−	0.914606i	$-0.367499\pi$
$379$	15.7436	0.808694	0.404347	+	0.914606i	$0.367499\pi$
$380$	0.619065	0.0317573
$381$	9.94792	0.509647
$382$	−3.79863	−0.194355
$383$	−5.30104	−0.270870	−0.135435	−	0.990786i	$-0.543243\pi$
$383$	−5.30104	−0.270870	−0.135435	+	0.990786i	$0.543243\pi$
$384$	−3.42265	−0.174661
$385$	−0.132111	−0.00673303
$386$	−3.18507	−0.162116
$387$	72.3215	3.67631
$388$	3.14636	0.159732
$389$	27.5208	1.39536	0.697680	−	0.716409i	$-0.254216\pi$
$389$	27.5208	1.39536	0.697680	+	0.716409i	$0.254216\pi$
$390$	6.70297	0.339418
$391$	6.67563	0.337601
$392$	−5.25742	−0.265540
$393$	−13.0165	−0.656593
$394$	−13.1219	−0.661073
$395$	3.86514	0.194476
$396$	1.40881	0.0707952
$397$	−15.1454	−0.760127	−0.380064	−	0.924960i	$-0.624098\pi$
$397$	−15.1454	−0.760127	−0.380064	+	0.924960i	$0.624098\pi$
$398$	11.6164	0.582280
$399$	4.51812	0.226189
$400$	−4.61676	−0.230838
$401$	7.43686	0.371379	0.185689	−	0.982608i	$-0.440548\pi$
$401$	7.43686	0.371379	0.185689	+	0.982608i	$0.440548\pi$
$402$	54.1505	2.70078
$403$	−12.1785	−0.606655
$404$	−10.3594	−0.515400
$405$	−25.2573	−1.25504
$406$	−13.6073	−0.675318
$407$	−0.968689	−0.0480162
$408$	−7.80725	−0.386517
$409$	25.8033	1.27589	0.637947	−	0.770081i	$-0.279784\pi$
$409$	25.8033	1.27589	0.637947	+	0.770081i	$0.279784\pi$
$410$	5.32133	0.262802
$411$	15.8110	0.779900
$412$	−1.20248	−0.0592420
$413$	3.75925	0.184981
$414$	25.5034	1.25343
$415$	−8.49635	−0.417070
$416$	3.16351	0.155104
$417$	33.0634	1.61912
$418$	−0.161662	−0.00790716
$419$	13.7166	0.670098	0.335049	−	0.942201i	$-0.391247\pi$
$419$	13.7166	0.670098	0.335049	+	0.942201i	$0.391247\pi$
$420$	2.79701	0.136480
$421$	13.0946	0.638192	0.319096	−	0.947722i	$-0.396621\pi$
$421$	13.0946	0.638192	0.319096	+	0.947722i	$0.396621\pi$
$422$	1.00000	0.0486792
$423$	52.1719	2.53668
$424$	−0.490156	−0.0238041
$425$	−10.5311	−0.510833
$426$	5.47926	0.265471
$427$	3.79946	0.183869
$428$	0.239441	0.0115738
$429$	−1.75041	−0.0845106
$430$	−5.13761	−0.247757
$431$	−9.59760	−0.462300	−0.231150	−	0.972918i	$-0.574249\pi$
$431$	−9.59760	−0.462300	−0.231150	+	0.972918i	$0.574249\pi$
$432$	−19.5587	−0.941020
$433$	17.3387	0.833246	0.416623	−	0.909079i	$-0.363213\pi$
$433$	17.3387	0.833246	0.416623	+	0.909079i	$0.363213\pi$
$434$	−5.08184	−0.243936
$435$	−21.8410	−1.04720
$436$	13.9533	0.668242
$437$	−2.92655	−0.139996
$438$	−42.6443	−2.03763
$439$	−4.21784	−0.201306	−0.100653	−	0.994922i	$-0.532093\pi$
$439$	−4.21784	−0.201306	−0.100653	+	0.994922i	$0.532093\pi$
$440$	−0.100079	−0.00477110
$441$	−45.8158	−2.18171
$442$	7.21615	0.343237
$443$	−10.2230	−0.485707	−0.242854	−	0.970063i	$-0.578083\pi$
$443$	−10.2230	−0.485707	−0.242854	+	0.970063i	$0.578083\pi$
$444$	20.5087	0.973300
$445$	3.31752	0.157265
$446$	−1.47092	−0.0696503
$447$	78.2692	3.70201
$448$	1.32007	0.0623673
$449$	−14.3702	−0.678172	−0.339086	−	0.940755i	$-0.610118\pi$
$449$	−14.3702	−0.678172	−0.339086	+	0.940755i	$0.610118\pi$
$450$	−40.2328	−1.89659
$451$	−1.38961	−0.0654341
$452$	−5.56885	−0.261937
$453$	−61.7016	−2.89899
$454$	9.83492	0.461575
$455$	−2.58524	−0.121198
$456$	3.42265	0.160280
$457$	−34.2824	−1.60366	−0.801831	−	0.597551i	$-0.796141\pi$
$457$	−34.2824	−1.60366	−0.801831	+	0.597551i	$0.796141\pi$
$458$	19.1619	0.895375
$459$	−44.6146	−2.08243
$460$	−1.81172	−0.0844720
$461$	6.07671	0.283021	0.141510	−	0.989937i	$-0.454804\pi$
$461$	6.07671	0.283021	0.141510	+	0.989937i	$0.454804\pi$
$462$	−0.730410	−0.0339817
$463$	5.80221	0.269652	0.134826	−	0.990869i	$-0.456953\pi$
$463$	5.80221	0.269652	0.134826	+	0.990869i	$0.456953\pi$
$464$	−10.3080	−0.478538
$465$	−8.15685	−0.378265
$466$	4.49161	0.208070
$467$	−35.1197	−1.62514	−0.812572	−	0.582860i	$-0.801933\pi$
$467$	−35.1197	−1.62514	−0.812572	+	0.582860i	$0.801933\pi$
$468$	27.5684	1.27435
$469$	−20.8851	−0.964384
$470$	−3.70621	−0.170955
$471$	72.6711	3.34851
$472$	2.84777	0.131079
$473$	1.34163	0.0616883
$474$	21.3694	0.981527
$475$	4.61676	0.211831
$476$	3.01115	0.138016
$477$	−4.27147	−0.195577
$478$	29.2944	1.33989
$479$	14.8383	0.677980	0.338990	−	0.940790i	$-0.389915\pi$
$479$	14.8383	0.677980	0.338990	+	0.940790i	$0.389915\pi$
$480$	2.11884	0.0967113
$481$	−18.9560	−0.864317
$482$	15.3424	0.698827
$483$	−13.2225	−0.601645
$484$	−10.9739	−0.498812
$485$	−1.94780	−0.0884452
$486$	−80.9647	−3.67263
$487$	−27.7323	−1.25667	−0.628335	−	0.777943i	$-0.716263\pi$
$487$	−27.7323	−1.25667	−0.628335	+	0.777943i	$0.716263\pi$
$488$	2.87823	0.130291
$489$	47.1855	2.13380
$490$	3.25468	0.147032
$491$	−27.4811	−1.24020	−0.620101	−	0.784522i	$-0.712909\pi$
$491$	−27.4811	−1.24020	−0.620101	+	0.784522i	$0.712909\pi$
$492$	29.4202	1.32637
$493$	−23.5132	−1.05898
$494$	−3.16351	−0.142333
$495$	−0.872142	−0.0391999
$496$	−3.84968	−0.172856
$497$	−2.11328	−0.0947934
$498$	−46.9741	−2.10496
$499$	−33.5213	−1.50062	−0.750309	−	0.661087i	$-0.770095\pi$
$499$	−33.5213	−1.50062	−0.750309	+	0.661087i	$0.770095\pi$
$500$	5.95340	0.266244
$501$	−30.1685	−1.34783
$502$	−3.34371	−0.149237
$503$	2.25541	0.100564	0.0502818	−	0.998735i	$-0.483988\pi$
$503$	2.25541	0.100564	0.0502818	+	0.998735i	$0.483988\pi$
$504$	11.5037	0.512417
$505$	6.41315	0.285381
$506$	0.473112	0.0210324
$507$	10.2412	0.454828
$508$	−2.90650	−0.128955
$509$	40.1809	1.78099	0.890493	−	0.454997i	$-0.150360\pi$
$509$	40.1809	1.78099	0.890493	+	0.454997i	$0.150360\pi$
$510$	4.83319	0.214017
$511$	16.4473	0.727587
$512$	1.00000	0.0441942
$513$	19.5587	0.863539
$514$	16.1547	0.712552
$515$	0.744414	0.0328028
$516$	−28.4045	−1.25044
$517$	0.967837	0.0425654
$518$	−7.90992	−0.347542
$519$	2.05522	0.0902140
$520$	−1.95842	−0.0858823
$521$	8.53265	0.373822	0.186911	−	0.982377i	$-0.440152\pi$
$521$	8.53265	0.373822	0.186911	+	0.982377i	$0.440152\pi$
$522$	−89.8293	−3.93172
$523$	−3.44362	−0.150579	−0.0752895	−	0.997162i	$-0.523988\pi$
$523$	−3.44362	−0.150579	−0.0752895	+	0.997162i	$0.523988\pi$
$524$	3.80304	0.166136
$525$	20.8591	0.910365
$526$	−9.74045	−0.424704
$527$	−8.78134	−0.382521
$528$	−0.553313	−0.0240798
$529$	−14.4353	−0.627622
$530$	0.303438	0.0131805
$531$	24.8169	1.07696
$532$	−1.32007	−0.0572322
$533$	−27.1928	−1.17785
$534$	18.3417	0.793722
$535$	−0.148230	−0.00640853
$536$	−15.8212	−0.683373
$537$	2.36695	0.102141
$538$	−32.3438	−1.39444
$539$	−0.849926	−0.0366089
$540$	12.1081	0.521050
$541$	14.7611	0.634629	0.317314	−	0.948320i	$-0.397219\pi$
$541$	14.7611	0.634629	0.317314	+	0.948320i	$0.397219\pi$
$542$	−7.26269	−0.311959
$543$	65.2136	2.79858
$544$	2.28106	0.0977995
$545$	−8.63800	−0.370011
$546$	−14.2931	−0.611690
$547$	−26.4651	−1.13156	−0.565782	−	0.824555i	$-0.691426\pi$
$547$	−26.4651	−1.13156	−0.565782	+	0.824555i	$0.691426\pi$
$548$	−4.61953	−0.197337
$549$	25.0824	1.07049
$550$	−0.746355	−0.0318247
$551$	10.3080	0.439136
$552$	−10.0165	−0.426332
$553$	−8.24186	−0.350480
$554$	2.15934	0.0917418
$555$	−12.6962	−0.538924
$556$	−9.66020	−0.409684
$557$	−23.7829	−1.00771	−0.503857	−	0.863787i	$-0.668086\pi$
$557$	−23.7829	−1.00771	−0.503857	+	0.863787i	$0.668086\pi$
$558$	−33.5480	−1.42020
$559$	26.2539	1.11042
$560$	−0.817207	−0.0345333
$561$	−1.26214	−0.0532875
$562$	−0.211029	−0.00890171
$563$	−2.65238	−0.111785	−0.0558923	−	0.998437i	$-0.517800\pi$
$563$	−2.65238	−0.111785	−0.0558923	+	0.998437i	$0.517800\pi$
$564$	−20.4906	−0.862812
$565$	3.44748	0.145036
$566$	−9.00981	−0.378711
$567$	53.8576	2.26180
$568$	−1.60089	−0.0671717
$569$	−28.8447	−1.20923	−0.604617	−	0.796517i	$-0.706674\pi$
$569$	−28.8447	−1.20923	−0.604617	+	0.796517i	$0.706674\pi$
$570$	−2.11884	−0.0887484
$571$	18.8404	0.788447	0.394224	−	0.919015i	$-0.371014\pi$
$571$	18.8404	0.788447	0.394224	+	0.919015i	$0.371014\pi$
$572$	0.511420	0.0213836
$573$	13.0014	0.543140
$574$	−11.3470	−0.473614
$575$	−13.5112	−0.563455
$576$	8.71451	0.363104
$577$	27.3433	1.13832	0.569159	−	0.822228i	$-0.307269\pi$
$577$	27.3433	1.13832	0.569159	+	0.822228i	$0.307269\pi$
$578$	−11.7968	−0.490681
$579$	10.9014	0.453046
$580$	6.38133	0.264970
$581$	18.1173	0.751631
$582$	−10.7689	−0.446385
$583$	−0.0792398	−0.00328178
$584$	12.4595	0.515576
$585$	−17.0667	−0.705619
$586$	−9.34231	−0.385927
$587$	22.9665	0.947927	0.473964	−	0.880544i	$-0.342823\pi$
$587$	22.9665	0.947927	0.473964	+	0.880544i	$0.342823\pi$
$588$	17.9943	0.742072
$589$	3.84968	0.158623
$590$	−1.76295	−0.0725797
$591$	44.9117	1.84742
$592$	−5.99206	−0.246272
$593$	41.3640	1.69862	0.849309	−	0.527896i	$-0.177019\pi$
$593$	41.3640	1.69862	0.849309	+	0.527896i	$0.177019\pi$
$594$	−3.16191	−0.129735
$595$	−1.86410	−0.0764205
$596$	−22.8681	−0.936712
$597$	−39.7590	−1.62723
$598$	9.25817	0.378595
$599$	33.3896	1.36426	0.682131	−	0.731230i	$-0.261054\pi$
$599$	33.3896	1.36426	0.682131	+	0.731230i	$0.261054\pi$
$600$	15.8015	0.645095
$601$	35.3656	1.44259	0.721296	−	0.692627i	$-0.243547\pi$
$601$	35.3656	1.44259	0.721296	+	0.692627i	$0.243547\pi$
$602$	10.9552	0.446501
$603$	−137.874	−5.61467
$604$	18.0275	0.733527
$605$	6.79353	0.276196
$606$	35.4566	1.44033
$607$	−6.80149	−0.276064	−0.138032	−	0.990428i	$-0.544078\pi$
$607$	−6.80149	−0.276064	−0.138032	+	0.990428i	$0.544078\pi$
$608$	−1.00000	−0.0405554
$609$	46.5729	1.88723
$610$	−1.78181	−0.0721434
$611$	18.9393	0.766201
$612$	19.8783	0.803532
$613$	−28.2381	−1.14053	−0.570263	−	0.821462i	$-0.693159\pi$
$613$	−28.2381	−1.14053	−0.570263	+	0.821462i	$0.693159\pi$
$614$	−28.6760	−1.15727
$615$	−18.2130	−0.734420
$616$	0.213405	0.00859833
$617$	11.5652	0.465597	0.232799	−	0.972525i	$-0.425212\pi$
$617$	11.5652	0.465597	0.232799	+	0.972525i	$0.425212\pi$
$618$	4.11567	0.165557
$619$	−46.3229	−1.86188	−0.930938	−	0.365177i	$-0.881009\pi$
$619$	−46.3229	−1.86188	−0.930938	+	0.365177i	$0.881009\pi$
$620$	2.38320	0.0957116
$621$	−57.2396	−2.29695
$622$	7.61045	0.305151
$623$	−7.07413	−0.283419
$624$	−10.8276	−0.433450
$625$	19.3983	0.775930
$626$	−26.9199	−1.07593
$627$	0.553313	0.0220972
$628$	−21.2324	−0.847267
$629$	−13.6682	−0.544988
$630$	−7.12156	−0.283730
$631$	−25.9115	−1.03152	−0.515759	−	0.856734i	$-0.672490\pi$
$631$	−25.9115	−1.03152	−0.515759	+	0.856734i	$0.672490\pi$
$632$	−6.24352	−0.248354
$633$	−3.42265	−0.136038
$634$	−21.9199	−0.870552
$635$	1.79931	0.0714035
$636$	1.67763	0.0665224
$637$	−16.6319	−0.658981
$638$	−1.66642	−0.0659741
$639$	−13.9509	−0.551890
$640$	−0.619065	−0.0244707
$641$	−8.14330	−0.321641	−0.160821	−	0.986984i	$-0.551414\pi$
$641$	−8.14330	−0.321641	−0.160821	+	0.986984i	$0.551414\pi$
$642$	−0.819523	−0.0323440
$643$	7.67038	0.302490	0.151245	−	0.988496i	$-0.451672\pi$
$643$	7.67038	0.302490	0.151245	+	0.988496i	$0.451672\pi$
$644$	3.86324	0.152233
$645$	17.5842	0.692378
$646$	−2.28106	−0.0897470
$647$	0.410869	0.0161529	0.00807646	−	0.999967i	$-0.497429\pi$
$647$	0.410869	0.0161529	0.00807646	+	0.999967i	$0.497429\pi$
$648$	40.7991	1.60274
$649$	0.460377	0.0180714
$650$	−14.6052	−0.572862
$651$	17.3933	0.681698
$652$	−13.7863	−0.539912
$653$	−45.0442	−1.76271	−0.881357	−	0.472451i	$-0.843369\pi$
$653$	−45.0442	−1.76271	−0.881357	+	0.472451i	$0.843369\pi$
$654$	−47.7572	−1.86746
$655$	−2.35433	−0.0919911
$656$	−8.59575	−0.335608
$657$	108.578	4.23603
$658$	7.90296	0.308089
$659$	29.3045	1.14154	0.570770	−	0.821110i	$-0.306645\pi$
$659$	29.3045	1.14154	0.570770	+	0.821110i	$0.306645\pi$
$660$	0.342536	0.0133332
$661$	−2.58248	−0.100447	−0.0502234	−	0.998738i	$-0.515993\pi$
$661$	−2.58248	−0.100447	−0.0502234	+	0.998738i	$0.515993\pi$
$662$	12.3206	0.478854
$663$	−24.6983	−0.959204
$664$	13.7245	0.532614
$665$	0.817207	0.0316899
$666$	−52.2178	−2.02340
$667$	−30.1669	−1.16807
$668$	8.81437	0.341038
$669$	5.03445	0.194643
$670$	9.79436	0.378389
$671$	0.465301	0.0179628
$672$	−4.51812	−0.174290
$673$	−3.30520	−0.127406	−0.0637030	−	0.997969i	$-0.520291\pi$
$673$	−3.30520	−0.127406	−0.0637030	+	0.997969i	$0.520291\pi$
$674$	−11.2097	−0.431781
$675$	90.2979	3.47557
$676$	−2.99219	−0.115084
$677$	−2.56451	−0.0985621	−0.0492810	−	0.998785i	$-0.515693\pi$
$677$	−2.56451	−0.0985621	−0.0492810	+	0.998785i	$0.515693\pi$
$678$	19.0602	0.732002
$679$	4.15341	0.159393
$680$	−1.41212	−0.0541524
$681$	−33.6614	−1.28991
$682$	−0.622348	−0.0238309
$683$	−38.0205	−1.45481	−0.727407	−	0.686207i	$-0.759275\pi$
$683$	−38.0205	−1.45481	−0.727407	+	0.686207i	$0.759275\pi$
$684$	−8.71451	−0.333207
$685$	2.85979	0.109267
$686$	−16.1806	−0.617779
$687$	−65.5842	−2.50220
$688$	8.29898	0.316396
$689$	−1.55062	−0.0590737
$690$	6.20089	0.236064
$691$	30.4958	1.16011	0.580057	−	0.814576i	$-0.303030\pi$
$691$	30.4958	1.16011	0.580057	+	0.814576i	$0.303030\pi$
$692$	−0.600476	−0.0228267
$693$	1.85972	0.0706449
$694$	26.0730	0.989718
$695$	5.98029	0.226845
$696$	35.2807	1.33731
$697$	−19.6074	−0.742684
$698$	19.3113	0.730945
$699$	−15.3732	−0.581467
$700$	−6.09443	−0.230348
$701$	−42.3557	−1.59975	−0.799876	−	0.600165i	$-0.795101\pi$
$701$	−42.3557	−1.59975	−0.799876	+	0.600165i	$0.795101\pi$
$702$	−61.8743	−2.33529
$703$	5.99206	0.225995
$704$	0.161662	0.00609287
$705$	12.6850	0.477746
$706$	−16.5840	−0.624146
$707$	−13.6751	−0.514306
$708$	−9.74691	−0.366311
$709$	−23.2297	−0.872410	−0.436205	−	0.899847i	$-0.643678\pi$
$709$	−23.2297	−0.872410	−0.436205	+	0.899847i	$0.643678\pi$
$710$	0.991052	0.0371935
$711$	−54.4092	−2.04050
$712$	−5.35892	−0.200834
$713$	−11.2663	−0.421925
$714$	−10.3061	−0.385696
$715$	−0.316602	−0.0118403
$716$	−0.691555	−0.0258446
$717$	−100.264	−3.74444
$718$	5.17866	0.193266
$719$	−27.7059	−1.03326	−0.516629	−	0.856210i	$-0.672813\pi$
$719$	−27.7059	−1.03326	−0.516629	+	0.856210i	$0.672813\pi$
$720$	−5.39484	−0.201054
$721$	−1.58736	−0.0591163
$722$	1.00000	0.0372161
$723$	−52.5116	−1.95293
$724$	−19.0535	−0.708120
$725$	47.5896	1.76744
$726$	37.5597	1.39397
$727$	29.6637	1.10017	0.550083	−	0.835110i	$-0.314596\pi$
$727$	29.6637	1.10017	0.550083	+	0.835110i	$0.314596\pi$
$728$	4.17605	0.154775
$729$	154.716	5.73023
$730$	−7.71321	−0.285479
$731$	18.9305	0.700168
$732$	−9.85117	−0.364110
$733$	−30.4043	−1.12301	−0.561505	−	0.827474i	$-0.689777\pi$
$733$	−30.4043	−1.12301	−0.561505	+	0.827474i	$0.689777\pi$
$734$	−0.348973	−0.0128808
$735$	−11.1396	−0.410892
$736$	2.92655	0.107874
$737$	−2.55769	−0.0942139
$738$	−74.9077	−2.75739
$739$	−35.1641	−1.29353	−0.646766	−	0.762688i	$-0.723879\pi$
$739$	−35.1641	−1.29353	−0.646766	+	0.762688i	$0.723879\pi$
$740$	3.70947	0.136363
$741$	10.8276	0.397761
$742$	−0.647039	−0.0237536
$743$	−30.2626	−1.11023	−0.555114	−	0.831775i	$-0.687325\pi$
$743$	−30.2626	−1.11023	−0.555114	+	0.831775i	$0.687325\pi$
$744$	13.1761	0.483059
$745$	14.1568	0.518665
$746$	3.83432	0.140384
$747$	119.602	4.37602
$748$	0.368761	0.0134832
$749$	0.316079	0.0115493
$750$	−20.3764	−0.744040
$751$	−53.8665	−1.96562	−0.982808	−	0.184629i	$-0.940892\pi$
$751$	−53.8665	−1.96562	−0.982808	+	0.184629i	$0.940892\pi$
$752$	5.98679	0.218316
$753$	11.4443	0.417054
$754$	−32.6095	−1.18757
$755$	−11.1602	−0.406160
$756$	−25.8188	−0.939022
$757$	−34.9278	−1.26947	−0.634736	−	0.772729i	$-0.718891\pi$
$757$	−34.9278	−1.26947	−0.634736	+	0.772729i	$0.718891\pi$
$758$	15.7436	0.571833
$759$	−1.61930	−0.0587767
$760$	0.619065	0.0224558
$761$	−29.3266	−1.06309	−0.531543	−	0.847031i	$-0.678388\pi$
$761$	−29.3266	−1.06309	−0.531543	+	0.847031i	$0.678388\pi$
$762$	9.94792	0.360375
$763$	18.4193	0.666824
$764$	−3.79863	−0.137430
$765$	−12.3059	−0.444922
$766$	−5.30104	−0.191534
$767$	9.00896	0.325295
$768$	−3.42265	−0.123504
$769$	−27.4069	−0.988319	−0.494159	−	0.869371i	$-0.664524\pi$
$769$	−27.4069	−0.988319	−0.494159	+	0.869371i	$0.664524\pi$
$770$	−0.132111	−0.00476097
$771$	−55.2917	−1.99128
$772$	−3.18507	−0.114633
$773$	−8.10807	−0.291627	−0.145813	−	0.989312i	$-0.546580\pi$
$773$	−8.10807	−0.291627	−0.145813	+	0.989312i	$0.546580\pi$
$774$	72.3215	2.59954
$775$	17.7730	0.638426
$776$	3.14636	0.112948
$777$	27.0729	0.971233
$778$	27.5208	0.986669
$779$	8.59575	0.307975
$780$	6.70297	0.240005
$781$	−0.258803	−0.00926069
$782$	6.67563	0.238720
$783$	201.612	7.20502
$784$	−5.25742	−0.187765
$785$	13.1443	0.469138
$786$	−13.0165	−0.464281
$787$	7.78991	0.277680	0.138840	−	0.990315i	$-0.455663\pi$
$787$	7.78991	0.277680	0.138840	+	0.990315i	$0.455663\pi$
$788$	−13.1219	−0.467449
$789$	33.3381	1.18687
$790$	3.86514	0.137516
$791$	−7.35125	−0.261381
$792$	1.40881	0.0500598
$793$	9.10532	0.323339
$794$	−15.1454	−0.537491
$795$	−1.03856	−0.0368340
$796$	11.6164	0.411734
$797$	48.1942	1.70713	0.853564	−	0.520988i	$-0.174436\pi$
$797$	48.1942	1.70713	0.853564	+	0.520988i	$0.174436\pi$
$798$	4.51812	0.159940
$799$	13.6562	0.483122
$800$	−4.61676	−0.163227
$801$	−46.7003	−1.65007
$802$	7.43686	0.262605
$803$	2.01422	0.0710804
$804$	54.1505	1.90974
$805$	−2.39160	−0.0842927
$806$	−12.1785	−0.428970
$807$	110.701	3.89687
$808$	−10.3594	−0.364443
$809$	−3.60412	−0.126714	−0.0633570	−	0.997991i	$-0.520181\pi$
$809$	−3.60412	−0.126714	−0.0633570	+	0.997991i	$0.520181\pi$
$810$	−25.2573	−0.887450
$811$	−55.4774	−1.94807	−0.974037	−	0.226389i	$-0.927308\pi$
$811$	−55.4774	−1.94807	−0.974037	+	0.226389i	$0.927308\pi$
$812$	−13.6073	−0.477522
$813$	24.8576	0.871795
$814$	−0.968689	−0.0339525
$815$	8.53459	0.298954
$816$	−7.80725	−0.273309
$817$	−8.29898	−0.290345
$818$	25.8033	0.902193
$819$	36.3922	1.27165
$820$	5.32133	0.185829
$821$	19.6657	0.686339	0.343169	−	0.939274i	$-0.388500\pi$
$821$	19.6657	0.686339	0.343169	+	0.939274i	$0.388500\pi$
$822$	15.8110	0.551473
$823$	−10.5552	−0.367930	−0.183965	−	0.982933i	$-0.558893\pi$
$823$	−10.5552	−0.367930	−0.183965	+	0.982933i	$0.558893\pi$
$824$	−1.20248	−0.0418904
$825$	2.55451	0.0889366
$826$	3.75925	0.130801
$827$	18.0043	0.626069	0.313035	−	0.949742i	$-0.398654\pi$
$827$	18.0043	0.626069	0.313035	+	0.949742i	$0.398654\pi$
$828$	25.5034	0.886305
$829$	29.3950	1.02093	0.510466	−	0.859898i	$-0.329473\pi$
$829$	29.3950	1.02093	0.510466	+	0.859898i	$0.329473\pi$
$830$	−8.49635	−0.294913
$831$	−7.39067	−0.256380
$832$	3.16351	0.109675
$833$	−11.9925	−0.415515
$834$	33.0634	1.14489
$835$	−5.45667	−0.188836
$836$	−0.161662	−0.00559120
$837$	75.2948	2.60257
$838$	13.7166	0.473831
$839$	4.73643	0.163520	0.0817599	−	0.996652i	$-0.473946\pi$
$839$	4.73643	0.163520	0.0817599	+	0.996652i	$0.473946\pi$
$840$	2.79701	0.0965060
$841$	77.2553	2.66398
$842$	13.0946	0.451270
$843$	0.722276	0.0248765
$844$	1.00000	0.0344214
$845$	1.85236	0.0637231
$846$	52.1719	1.79371
$847$	−14.4862	−0.497753
$848$	−0.490156	−0.0168320
$849$	30.8374	1.05834
$850$	−10.5311	−0.361214
$851$	−17.5361	−0.601128
$852$	5.47926	0.187717
$853$	−34.6665	−1.18696	−0.593479	−	0.804850i	$-0.702246\pi$
$853$	−34.6665	−1.18696	−0.593479	+	0.804850i	$0.702246\pi$
$854$	3.79946	0.130015
$855$	5.39484	0.184500
$856$	0.239441	0.00818394
$857$	37.7996	1.29121	0.645604	−	0.763672i	$-0.276606\pi$
$857$	37.7996	1.29121	0.645604	+	0.763672i	$0.276606\pi$
$858$	−1.75041	−0.0597580
$859$	20.2548	0.691086	0.345543	−	0.938403i	$-0.387695\pi$
$859$	20.2548	0.691086	0.345543	+	0.938403i	$0.387695\pi$
$860$	−5.13761	−0.175191
$861$	38.8367	1.32355
$862$	−9.59760	−0.326896
$863$	18.1868	0.619085	0.309543	−	0.950886i	$-0.399824\pi$
$863$	18.1868	0.619085	0.309543	+	0.950886i	$0.399824\pi$
$864$	−19.5587	−0.665402
$865$	0.371734	0.0126393
$866$	17.3387	0.589194
$867$	40.3762	1.37125
$868$	−5.08184	−0.172489
$869$	−1.00934	−0.0342395
$870$	−21.8410	−0.740481
$871$	−50.0506	−1.69590
$872$	13.9533	0.472519
$873$	27.4190	0.927993
$874$	−2.92655	−0.0989920
$875$	7.85888	0.265679
$876$	−42.6443	−1.44082
$877$	−53.1518	−1.79481	−0.897404	−	0.441210i	$-0.854549\pi$
$877$	−53.1518	−1.79481	−0.897404	+	0.441210i	$0.854549\pi$
$878$	−4.21784	−0.142345
$879$	31.9754	1.07850
$880$	−0.100079	−0.00337367
$881$	3.00996	0.101408	0.0507041	−	0.998714i	$-0.483853\pi$
$881$	3.00996	0.101408	0.0507041	+	0.998714i	$0.483853\pi$
$882$	−45.8158	−1.54270
$883$	−13.5427	−0.455749	−0.227875	−	0.973690i	$-0.573178\pi$
$883$	−13.5427	−0.455749	−0.227875	+	0.973690i	$0.573178\pi$
$884$	7.21615	0.242706
$885$	6.03397	0.202830
$886$	−10.2230	−0.343447
$887$	18.8906	0.634284	0.317142	−	0.948378i	$-0.397277\pi$
$887$	18.8906	0.634284	0.317142	+	0.948378i	$0.397277\pi$
$888$	20.5087	0.688227
$889$	−3.83677	−0.128681
$890$	3.31752	0.111203
$891$	6.59567	0.220963
$892$	−1.47092	−0.0492502
$893$	−5.98679	−0.200340
$894$	78.2692	2.61772
$895$	0.428117	0.0143104
$896$	1.32007	0.0441004
$897$	−31.6874	−1.05801
$898$	−14.3702	−0.479540
$899$	39.6826	1.32349
$900$	−40.2328	−1.34109
$901$	−1.11807	−0.0372485
$902$	−1.38961	−0.0462689
$903$	−37.4958	−1.24778
$904$	−5.56885	−0.185217
$905$	11.7954	0.392092
$906$	−61.7016	−2.04990
$907$	−15.5154	−0.515182	−0.257591	−	0.966254i	$-0.582929\pi$
$907$	−15.5154	−0.515182	−0.257591	+	0.966254i	$0.582929\pi$
$908$	9.83492	0.326383
$909$	−90.2772	−2.99431
$910$	−2.58524	−0.0857000
$911$	−12.6684	−0.419722	−0.209861	−	0.977731i	$-0.567301\pi$
$911$	−12.6684	−0.419722	−0.209861	+	0.977731i	$0.567301\pi$
$912$	3.42265	0.113335
$913$	2.21873	0.0734293
$914$	−34.2824	−1.13396
$915$	6.09851	0.201611
$916$	19.1619	0.633126
$917$	5.02027	0.165784
$918$	−44.6146	−1.47250
$919$	38.3271	1.26429	0.632147	−	0.774848i	$-0.282174\pi$
$919$	38.3271	1.26429	0.632147	+	0.774848i	$0.282174\pi$
$920$	−1.81172	−0.0597307
$921$	98.1478	3.23408
$922$	6.07671	0.200126
$923$	−5.06442	−0.166697
$924$	−0.730410	−0.0240287
$925$	27.6639	0.909583
$926$	5.80221	0.190672
$927$	−10.4790	−0.344177
$928$	−10.3080	−0.338377
$929$	−56.5284	−1.85464	−0.927318	−	0.374275i	$-0.877892\pi$
$929$	−56.5284	−1.85464	−0.927318	+	0.374275i	$0.877892\pi$
$930$	−8.15685	−0.267474
$931$	5.25742	0.172305
$932$	4.49161	0.147128
$933$	−26.0479	−0.852769
$934$	−35.1197	−1.14915
$935$	−0.228287	−0.00746578
$936$	27.5684	0.901103
$937$	−56.0882	−1.83232	−0.916161	−	0.400811i	$-0.868728\pi$
$937$	−56.0882	−1.83232	−0.916161	+	0.400811i	$0.868728\pi$
$938$	−20.8851	−0.681922
$939$	92.1372	3.00678
$940$	−3.70621	−0.120883
$941$	−35.1801	−1.14684	−0.573419	−	0.819262i	$-0.694383\pi$
$941$	−35.1801	−1.14684	−0.573419	+	0.819262i	$0.694383\pi$
$942$	72.6711	2.36775
$943$	−25.1559	−0.819189
$944$	2.84777	0.0926871
$945$	15.9835	0.519944
$946$	1.34163	0.0436202
$947$	15.9595	0.518613	0.259307	−	0.965795i	$-0.416506\pi$
$947$	15.9595	0.518613	0.259307	+	0.965795i	$0.416506\pi$
$948$	21.3694	0.694044
$949$	39.4157	1.27949
$950$	4.61676	0.149787
$951$	75.0242	2.43283
$952$	3.01115	0.0975919
$953$	30.5077	0.988243	0.494121	−	0.869393i	$-0.335490\pi$
$953$	30.5077	0.988243	0.494121	+	0.869393i	$0.335490\pi$
$954$	−4.27147	−0.138294
$955$	2.35160	0.0760960
$956$	29.2944	0.947449
$957$	5.70356	0.184370
$958$	14.8383	0.479404
$959$	−6.09809	−0.196918
$960$	2.11884	0.0683852
$961$	−16.1800	−0.521935
$962$	−18.9560	−0.611164
$963$	2.08661	0.0672402
$964$	15.3424	0.494145
$965$	1.97177	0.0634734
$966$	−13.2225	−0.425427
$967$	−20.7378	−0.666884	−0.333442	−	0.942771i	$-0.608210\pi$
$967$	−20.7378	−0.666884	−0.333442	+	0.942771i	$0.608210\pi$
$968$	−10.9739	−0.352713
$969$	7.80725	0.250805
$970$	−1.94780	−0.0625402
$971$	56.5838	1.81586	0.907930	−	0.419123i	$-0.137662\pi$
$971$	56.5838	1.81586	0.907930	+	0.419123i	$0.137662\pi$
$972$	−80.9647	−2.59694
$973$	−12.7521	−0.408814
$974$	−27.7323	−0.888600
$975$	49.9883	1.60091
$976$	2.87823	0.0921299
$977$	30.9278	0.989468	0.494734	−	0.869044i	$-0.335265\pi$
$977$	30.9278	0.989468	0.494734	+	0.869044i	$0.335265\pi$
$978$	47.1855	1.50883
$979$	−0.866334	−0.0276882
$980$	3.25468	0.103967
$981$	121.596	3.88227
$982$	−27.4811	−0.876956
$983$	3.35647	0.107055	0.0535274	−	0.998566i	$-0.482954\pi$
$983$	3.35647	0.107055	0.0535274	+	0.998566i	$0.482954\pi$
$984$	29.4202	0.937882
$985$	8.12332	0.258830
$986$	−23.5132	−0.748813
$987$	−27.0490	−0.860980
$988$	−3.16351	−0.100645
$989$	24.2874	0.772294
$990$	−0.872142	−0.0277185
$991$	21.3953	0.679643	0.339821	−	0.940490i	$-0.389633\pi$
$991$	21.3953	0.679643	0.339821	+	0.940490i	$0.389633\pi$
$992$	−3.84968	−0.122227
$993$	−42.1691	−1.33819
$994$	−2.11328	−0.0670291
$995$	−7.19133	−0.227980
$996$	−46.9741	−1.48843
$997$	−15.1562	−0.480002	−0.240001	−	0.970773i	$-0.577148\pi$
$997$	−15.1562	−0.480002	−0.240001	+	0.970773i	$0.577148\pi$
$998$	−33.5213	−1.06110
$999$	117.197	3.70795

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.e.1.1	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.e.1.1	✓	32	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.42265 q^{3} +1.00000 q^{4} -0.619065 q^{5} -3.42265 q^{6} +1.32007 q^{7} +1.00000 q^{8} +8.71451 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.42265 q^{3} +1.00000 q^{4} -0.619065 q^{5} -3.42265 q^{6} +1.32007 q^{7} +1.00000 q^{8} +8.71451 q^{9} -0.619065 q^{10} +0.161662 q^{11} -3.42265 q^{12} +3.16351 q^{13} +1.32007 q^{14} +2.11884 q^{15} +1.00000 q^{16} +2.28106 q^{17} +8.71451 q^{18} -1.00000 q^{19} -0.619065 q^{20} -4.51812 q^{21} +0.161662 q^{22} +2.92655 q^{23} -3.42265 q^{24} -4.61676 q^{25} +3.16351 q^{26} -19.5587 q^{27} +1.32007 q^{28} -10.3080 q^{29} +2.11884 q^{30} -3.84968 q^{31} +1.00000 q^{32} -0.553313 q^{33} +2.28106 q^{34} -0.817207 q^{35} +8.71451 q^{36} -5.99206 q^{37} -1.00000 q^{38} -10.8276 q^{39} -0.619065 q^{40} -8.59575 q^{41} -4.51812 q^{42} +8.29898 q^{43} +0.161662 q^{44} -5.39484 q^{45} +2.92655 q^{46} +5.98679 q^{47} -3.42265 q^{48} -5.25742 q^{49} -4.61676 q^{50} -7.80725 q^{51} +3.16351 q^{52} -0.490156 q^{53} -19.5587 q^{54} -0.100079 q^{55} +1.32007 q^{56} +3.42265 q^{57} -10.3080 q^{58} +2.84777 q^{59} +2.11884 q^{60} +2.87823 q^{61} -3.84968 q^{62} +11.5037 q^{63} +1.00000 q^{64} -1.95842 q^{65} -0.553313 q^{66} -15.8212 q^{67} +2.28106 q^{68} -10.0165 q^{69} -0.817207 q^{70} -1.60089 q^{71} +8.71451 q^{72} +12.4595 q^{73} -5.99206 q^{74} +15.8015 q^{75} -1.00000 q^{76} +0.213405 q^{77} -10.8276 q^{78} -6.24352 q^{79} -0.619065 q^{80} +40.7991 q^{81} -8.59575 q^{82} +13.7245 q^{83} -4.51812 q^{84} -1.41212 q^{85} +8.29898 q^{86} +35.2807 q^{87} +0.161662 q^{88} -5.35892 q^{89} -5.39484 q^{90} +4.17605 q^{91} +2.92655 q^{92} +13.1761 q^{93} +5.98679 q^{94} +0.619065 q^{95} -3.42265 q^{96} +3.14636 q^{97} -5.25742 q^{98} +1.40881 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{2} - 7 q^{3} + 32 q^{4} - 6 q^{5} - 7 q^{6} - 5 q^{7} + 32 q^{8} + 15 q^{9}+O(q^{10}) \) 32 * q + 32 * q^2 - 7 * q^3 + 32 * q^4 - 6 * q^5 - 7 * q^6 - 5 * q^7 + 32 * q^8 + 15 * q^9	\( 32 q + 32 q^{2} - 7 q^{3} + 32 q^{4} - 6 q^{5} - 7 q^{6} - 5 q^{7} + 32 q^{8} + 15 q^{9} - 6 q^{10} - 21 q^{11} - 7 q^{12} - 19 q^{13} - 5 q^{14} - 14 q^{15} + 32 q^{16} - 14 q^{17} + 15 q^{18} - 32 q^{19} - 6 q^{20} - 26 q^{21} - 21 q^{22} - 13 q^{23} - 7 q^{24} - 10 q^{25} - 19 q^{26} - 25 q^{27} - 5 q^{28} - 42 q^{29} - 14 q^{30} - 15 q^{31} + 32 q^{32} - 32 q^{33} - 14 q^{34} - 22 q^{35} + 15 q^{36} - 54 q^{37} - 32 q^{38} - 32 q^{39} - 6 q^{40} - 16 q^{41} - 26 q^{42} - 37 q^{43} - 21 q^{44} - 46 q^{45} - 13 q^{46} - 9 q^{47} - 7 q^{48} - 7 q^{49} - 10 q^{50} - 32 q^{51} - 19 q^{52} - 53 q^{53} - 25 q^{54} - 17 q^{55} - 5 q^{56} + 7 q^{57} - 42 q^{58} - 34 q^{59} - 14 q^{60} - 33 q^{61} - 15 q^{62} + 18 q^{63} + 32 q^{64} - 50 q^{65} - 32 q^{66} - 53 q^{67} - 14 q^{68} - 40 q^{69} - 22 q^{70} - 27 q^{71} + 15 q^{72} - 43 q^{73} - 54 q^{74} + 5 q^{75} - 32 q^{76} - 56 q^{77} - 32 q^{78} - 11 q^{79} - 6 q^{80} - 8 q^{81} - 16 q^{82} - 17 q^{83} - 26 q^{84} - 30 q^{85} - 37 q^{86} + 3 q^{87} - 21 q^{88} - 21 q^{89} - 46 q^{90} - 67 q^{91} - 13 q^{92} - 31 q^{93} - 9 q^{94} + 6 q^{95} - 7 q^{96} - 51 q^{97} - 7 q^{98} - 32 q^{99}+O(q^{100}) \) 32 * q + 32 * q^2 - 7 * q^3 + 32 * q^4 - 6 * q^5 - 7 * q^6 - 5 * q^7 + 32 * q^8 + 15 * q^9 - 6 * q^10 - 21 * q^11 - 7 * q^12 - 19 * q^13 - 5 * q^14 - 14 * q^15 + 32 * q^16 - 14 * q^17 + 15 * q^18 - 32 * q^19 - 6 * q^20 - 26 * q^21 - 21 * q^22 - 13 * q^23 - 7 * q^24 - 10 * q^25 - 19 * q^26 - 25 * q^27 - 5 * q^28 - 42 * q^29 - 14 * q^30 - 15 * q^31 + 32 * q^32 - 32 * q^33 - 14 * q^34 - 22 * q^35 + 15 * q^36 - 54 * q^37 - 32 * q^38 - 32 * q^39 - 6 * q^40 - 16 * q^41 - 26 * q^42 - 37 * q^43 - 21 * q^44 - 46 * q^45 - 13 * q^46 - 9 * q^47 - 7 * q^48 - 7 * q^49 - 10 * q^50 - 32 * q^51 - 19 * q^52 - 53 * q^53 - 25 * q^54 - 17 * q^55 - 5 * q^56 + 7 * q^57 - 42 * q^58 - 34 * q^59 - 14 * q^60 - 33 * q^61 - 15 * q^62 + 18 * q^63 + 32 * q^64 - 50 * q^65 - 32 * q^66 - 53 * q^67 - 14 * q^68 - 40 * q^69 - 22 * q^70 - 27 * q^71 + 15 * q^72 - 43 * q^73 - 54 * q^74 + 5 * q^75 - 32 * q^76 - 56 * q^77 - 32 * q^78 - 11 * q^79 - 6 * q^80 - 8 * q^81 - 16 * q^82 - 17 * q^83 - 26 * q^84 - 30 * q^85 - 37 * q^86 + 3 * q^87 - 21 * q^88 - 21 * q^89 - 46 * q^90 - 67 * q^91 - 13 * q^92 - 31 * q^93 - 9 * q^94 + 6 * q^95 - 7 * q^96 - 51 * q^97 - 7 * q^98 - 32 * q^99

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