LMFDB - Embedded newform 8018.2.a.i.1.17

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:	$0$
Dimension:	$43$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00471 q^{3} +1.00000 q^{4} -1.06211 q^{5} +1.00471 q^{6} +0.645369 q^{7} -1.00000 q^{8} -1.99055 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00471 q^{3} +1.00000 q^{4} -1.06211 q^{5} +1.00471 q^{6} +0.645369 q^{7} -1.00000 q^{8} -1.99055 q^{9} +1.06211 q^{10} -0.354807 q^{11} -1.00471 q^{12} -2.49871 q^{13} -0.645369 q^{14} +1.06712 q^{15} +1.00000 q^{16} -3.08200 q^{17} +1.99055 q^{18} +1.00000 q^{19} -1.06211 q^{20} -0.648411 q^{21} +0.354807 q^{22} -6.41811 q^{23} +1.00471 q^{24} -3.87192 q^{25} +2.49871 q^{26} +5.01407 q^{27} +0.645369 q^{28} +5.86500 q^{29} -1.06712 q^{30} +2.29899 q^{31} -1.00000 q^{32} +0.356480 q^{33} +3.08200 q^{34} -0.685453 q^{35} -1.99055 q^{36} -1.64673 q^{37} -1.00000 q^{38} +2.51049 q^{39} +1.06211 q^{40} +2.04852 q^{41} +0.648411 q^{42} -6.64431 q^{43} -0.354807 q^{44} +2.11418 q^{45} +6.41811 q^{46} -2.89900 q^{47} -1.00471 q^{48} -6.58350 q^{49} +3.87192 q^{50} +3.09652 q^{51} -2.49871 q^{52} -3.29494 q^{53} -5.01407 q^{54} +0.376844 q^{55} -0.645369 q^{56} -1.00471 q^{57} -5.86500 q^{58} -8.68320 q^{59} +1.06712 q^{60} -3.05627 q^{61} -2.29899 q^{62} -1.28464 q^{63} +1.00000 q^{64} +2.65391 q^{65} -0.356480 q^{66} -0.563043 q^{67} -3.08200 q^{68} +6.44837 q^{69} +0.685453 q^{70} -9.10031 q^{71} +1.99055 q^{72} +5.14500 q^{73} +1.64673 q^{74} +3.89018 q^{75} +1.00000 q^{76} -0.228982 q^{77} -2.51049 q^{78} -10.2970 q^{79} -1.06211 q^{80} +0.933943 q^{81} -2.04852 q^{82} +2.17444 q^{83} -0.648411 q^{84} +3.27342 q^{85} +6.64431 q^{86} -5.89265 q^{87} +0.354807 q^{88} -8.89991 q^{89} -2.11418 q^{90} -1.61259 q^{91} -6.41811 q^{92} -2.30983 q^{93} +2.89900 q^{94} -1.06211 q^{95} +1.00471 q^{96} +14.6540 q^{97} +6.58350 q^{98} +0.706262 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 43 q - 43 q^{2} + 43 q^{4} + 19 q^{7} - 43 q^{8} + 53 q^{9}+O(q^{10}) $ 43 * q - 43 * q^2 + 43 * q^4 + 19 * q^7 - 43 * q^8 + 53 * q^9	$ 43 q - 43 q^{2} + 43 q^{4} + 19 q^{7} - 43 q^{8} + 53 q^{9} + 14 q^{11} + 3 q^{13} - 19 q^{14} + q^{15} + 43 q^{16} + 8 q^{17} - 53 q^{18} + 43 q^{19} - 14 q^{22} + 43 q^{23} + 97 q^{25} - 3 q^{26} + 15 q^{27} + 19 q^{28} - 25 q^{29} - q^{30} + 22 q^{31} - 43 q^{32} + 22 q^{33} - 8 q^{34} - 6 q^{35} + 53 q^{36} + 42 q^{37} - 43 q^{38} + 9 q^{39} - 40 q^{41} + 72 q^{43} + 14 q^{44} - q^{45} - 43 q^{46} + 27 q^{47} + 86 q^{49} - 97 q^{50} - 3 q^{51} + 3 q^{52} - 5 q^{53} - 15 q^{54} + 86 q^{55} - 19 q^{56} + 25 q^{58} - 43 q^{59} + q^{60} + 31 q^{61} - 22 q^{62} + 38 q^{63} + 43 q^{64} - 32 q^{65} - 22 q^{66} + 15 q^{67} + 8 q^{68} - 7 q^{69} + 6 q^{70} + 14 q^{71} - 53 q^{72} + 93 q^{73} - 42 q^{74} - 13 q^{75} + 43 q^{76} + 38 q^{77} - 9 q^{78} + 15 q^{79} + 43 q^{81} + 40 q^{82} + 34 q^{83} + 16 q^{85} - 72 q^{86} + 60 q^{87} - 14 q^{88} - 37 q^{89} + q^{90} - 3 q^{91} + 43 q^{92} + 19 q^{93} - 27 q^{94} + 27 q^{97} - 86 q^{98} - 24 q^{99}+O(q^{100}) $ 43 * q - 43 * q^2 + 43 * q^4 + 19 * q^7 - 43 * q^8 + 53 * q^9 + 14 * q^11 + 3 * q^13 - 19 * q^14 + q^15 + 43 * q^16 + 8 * q^17 - 53 * q^18 + 43 * q^19 - 14 * q^22 + 43 * q^23 + 97 * q^25 - 3 * q^26 + 15 * q^27 + 19 * q^28 - 25 * q^29 - q^30 + 22 * q^31 - 43 * q^32 + 22 * q^33 - 8 * q^34 - 6 * q^35 + 53 * q^36 + 42 * q^37 - 43 * q^38 + 9 * q^39 - 40 * q^41 + 72 * q^43 + 14 * q^44 - q^45 - 43 * q^46 + 27 * q^47 + 86 * q^49 - 97 * q^50 - 3 * q^51 + 3 * q^52 - 5 * q^53 - 15 * q^54 + 86 * q^55 - 19 * q^56 + 25 * q^58 - 43 * q^59 + q^60 + 31 * q^61 - 22 * q^62 + 38 * q^63 + 43 * q^64 - 32 * q^65 - 22 * q^66 + 15 * q^67 + 8 * q^68 - 7 * q^69 + 6 * q^70 + 14 * q^71 - 53 * q^72 + 93 * q^73 - 42 * q^74 - 13 * q^75 + 43 * q^76 + 38 * q^77 - 9 * q^78 + 15 * q^79 + 43 * q^81 + 40 * q^82 + 34 * q^83 + 16 * q^85 - 72 * q^86 + 60 * q^87 - 14 * q^88 - 37 * q^89 + q^90 - 3 * q^91 + 43 * q^92 + 19 * q^93 - 27 * q^94 + 27 * q^97 - 86 * q^98 - 24 * 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
$3$	−1.00471	−0.580072	−0.290036	−	0.957016i	$-0.593667\pi$
$3$	−1.00471	−0.580072	−0.290036	+	0.957016i	$0.593667\pi$
$4$	1.00000	0.500000
$5$	−1.06211	−0.474990	−0.237495	−	0.971389i	$-0.576326\pi$
$5$	−1.06211	−0.474990	−0.237495	+	0.971389i	$0.576326\pi$
$6$	1.00471	0.410173
$7$	0.645369	0.243927	0.121963	−	0.992535i	$-0.461081\pi$
$7$	0.645369	0.243927	0.121963	+	0.992535i	$0.461081\pi$
$8$	−1.00000	−0.353553
$9$	−1.99055	−0.663517
$10$	1.06211	0.335868
$11$	−0.354807	−0.106978	−0.0534892	−	0.998568i	$-0.517034\pi$
$11$	−0.354807	−0.106978	−0.0534892	+	0.998568i	$0.517034\pi$
$12$	−1.00471	−0.290036
$13$	−2.49871	−0.693018	−0.346509	−	0.938047i	$-0.612633\pi$
$13$	−2.49871	−0.693018	−0.346509	+	0.938047i	$0.612633\pi$
$14$	−0.645369	−0.172482
$15$	1.06712	0.275528
$16$	1.00000	0.250000
$17$	−3.08200	−0.747494	−0.373747	−	0.927531i	$-0.621927\pi$
$17$	−3.08200	−0.747494	−0.373747	+	0.927531i	$0.621927\pi$
$18$	1.99055	0.469177
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−1.06211	−0.237495
$21$	−0.648411	−0.141495
$22$	0.354807	0.0756452
$23$	−6.41811	−1.33827	−0.669135	−	0.743141i	$-0.733335\pi$
$23$	−6.41811	−1.33827	−0.669135	+	0.743141i	$0.733335\pi$
$24$	1.00471	0.205086
$25$	−3.87192	−0.774385
$26$	2.49871	0.490038
$27$	5.01407	0.964959
$28$	0.645369	0.121963
$29$	5.86500	1.08910	0.544552	−	0.838727i	$-0.316700\pi$
$29$	5.86500	1.08910	0.544552	+	0.838727i	$0.316700\pi$
$30$	−1.06712	−0.194828
$31$	2.29899	0.412911	0.206456	−	0.978456i	$-0.433807\pi$
$31$	2.29899	0.412911	0.206456	+	0.978456i	$0.433807\pi$
$32$	−1.00000	−0.176777
$33$	0.356480	0.0620552
$34$	3.08200	0.528558
$35$	−0.685453	−0.115863
$36$	−1.99055	−0.331758
$37$	−1.64673	−0.270720	−0.135360	−	0.990796i	$-0.543219\pi$
$37$	−1.64673	−0.270720	−0.135360	+	0.990796i	$0.543219\pi$
$38$	−1.00000	−0.162221
$39$	2.51049	0.402000
$40$	1.06211	0.167934
$41$	2.04852	0.319925	0.159962	−	0.987123i	$-0.448863\pi$
$41$	2.04852	0.319925	0.159962	+	0.987123i	$0.448863\pi$
$42$	0.648411	0.100052
$43$	−6.64431	−1.01325	−0.506624	−	0.862167i	$-0.669107\pi$
$43$	−6.64431	−1.01325	−0.506624	+	0.862167i	$0.669107\pi$
$44$	−0.354807	−0.0534892
$45$	2.11418	0.315164
$46$	6.41811	0.946299
$47$	−2.89900	−0.422862	−0.211431	−	0.977393i	$-0.567812\pi$
$47$	−2.89900	−0.422862	−0.211431	+	0.977393i	$0.567812\pi$
$48$	−1.00471	−0.145018
$49$	−6.58350	−0.940500
$50$	3.87192	0.547573
$51$	3.09652	0.433600
$52$	−2.49871	−0.346509
$53$	−3.29494	−0.452595	−0.226297	−	0.974058i	$-0.572662\pi$
$53$	−3.29494	−0.452595	−0.226297	+	0.974058i	$0.572662\pi$
$54$	−5.01407	−0.682329
$55$	0.376844	0.0508136
$56$	−0.645369	−0.0862411
$57$	−1.00471	−0.133078
$58$	−5.86500	−0.770113
$59$	−8.68320	−1.13046	−0.565228	−	0.824935i	$-0.691212\pi$
$59$	−8.68320	−1.13046	−0.565228	+	0.824935i	$0.691212\pi$
$60$	1.06712	0.137764
$61$	−3.05627	−0.391315	−0.195658	−	0.980672i	$-0.562684\pi$
$61$	−3.05627	−0.391315	−0.195658	+	0.980672i	$0.562684\pi$
$62$	−2.29899	−0.291972
$63$	−1.28464	−0.161849
$64$	1.00000	0.125000
$65$	2.65391	0.329176
$66$	−0.356480	−0.0438796
$67$	−0.563043	−0.0687867	−0.0343933	−	0.999408i	$-0.510950\pi$
$67$	−0.563043	−0.0687867	−0.0343933	+	0.999408i	$0.510950\pi$
$68$	−3.08200	−0.373747
$69$	6.44837	0.776292
$70$	0.685453	0.0819273
$71$	−9.10031	−1.08001	−0.540004	−	0.841663i	$-0.681577\pi$
$71$	−9.10031	−1.08001	−0.540004	+	0.841663i	$0.681577\pi$
$72$	1.99055	0.234589
$73$	5.14500	0.602177	0.301089	−	0.953596i	$-0.402650\pi$
$73$	5.14500	0.602177	0.301089	+	0.953596i	$0.402650\pi$
$74$	1.64673	0.191428
$75$	3.89018	0.449199
$76$	1.00000	0.114708
$77$	−0.228982	−0.0260949
$78$	−2.51049	−0.284257
$79$	−10.2970	−1.15850	−0.579249	−	0.815151i	$-0.696654\pi$
$79$	−10.2970	−1.15850	−0.579249	+	0.815151i	$0.696654\pi$
$80$	−1.06211	−0.118747
$81$	0.933943	0.103771
$82$	−2.04852	−0.226221
$83$	2.17444	0.238676	0.119338	−	0.992854i	$-0.461923\pi$
$83$	2.17444	0.238676	0.119338	+	0.992854i	$0.461923\pi$
$84$	−0.648411	−0.0707475
$85$	3.27342	0.355052
$86$	6.64431	0.716474
$87$	−5.89265	−0.631758
$88$	0.354807	0.0378226
$89$	−8.89991	−0.943388	−0.471694	−	0.881762i	$-0.656357\pi$
$89$	−8.89991	−0.943388	−0.471694	+	0.881762i	$0.656357\pi$
$90$	−2.11418	−0.222854
$91$	−1.61259	−0.169046
$92$	−6.41811	−0.669135
$93$	−2.30983	−0.239518
$94$	2.89900	0.299009
$95$	−1.06211	−0.108970
$96$	1.00471	0.102543
$97$	14.6540	1.48788	0.743942	−	0.668244i	$-0.232954\pi$
$97$	14.6540	1.48788	0.743942	+	0.668244i	$0.232954\pi$
$98$	6.58350	0.665034
$99$	0.706262	0.0709820
$100$	−3.87192	−0.387192
$101$	−5.03686	−0.501186	−0.250593	−	0.968092i	$-0.580626\pi$
$101$	−5.03686	−0.501186	−0.250593	+	0.968092i	$0.580626\pi$
$102$	−3.09652	−0.306602
$103$	17.0674	1.68170	0.840851	−	0.541267i	$-0.182055\pi$
$103$	17.0674	1.68170	0.840851	+	0.541267i	$0.182055\pi$
$104$	2.49871	0.245019
$105$	0.688684	0.0672086
$106$	3.29494	0.320033
$107$	16.5695	1.60184	0.800918	−	0.598774i	$-0.204345\pi$
$107$	16.5695	1.60184	0.800918	+	0.598774i	$0.204345\pi$
$108$	5.01407	0.482480
$109$	7.03581	0.673908	0.336954	−	0.941521i	$-0.390603\pi$
$109$	7.03581	0.673908	0.336954	+	0.941521i	$0.390603\pi$
$110$	−0.376844	−0.0359307
$111$	1.65449	0.157037
$112$	0.645369	0.0609817
$113$	−11.7608	−1.10636	−0.553181	−	0.833061i	$-0.686586\pi$
$113$	−11.7608	−1.10636	−0.553181	+	0.833061i	$0.686586\pi$
$114$	1.00471	0.0941001
$115$	6.81674	0.635664
$116$	5.86500	0.544552
$117$	4.97381	0.459829
$118$	8.68320	0.799354
$119$	−1.98903	−0.182334
$120$	−1.06712	−0.0974138
$121$	−10.8741	−0.988556
$122$	3.05627	0.276702
$123$	−2.05817	−0.185579
$124$	2.29899	0.206456
$125$	9.42295	0.842814
$126$	1.28464	0.114445
$127$	−1.62483	−0.144180	−0.0720901	−	0.997398i	$-0.522967\pi$
$127$	−1.62483	−0.144180	−0.0720901	+	0.997398i	$0.522967\pi$
$128$	−1.00000	−0.0883883
$129$	6.67563	0.587756
$130$	−2.65391	−0.232763
$131$	−14.7336	−1.28728	−0.643639	−	0.765329i	$-0.722576\pi$
$131$	−14.7336	−1.28728	−0.643639	+	0.765329i	$0.722576\pi$
$132$	0.356480	0.0310276
$133$	0.645369	0.0559606
$134$	0.563043	0.0486395
$135$	−5.32549	−0.458345
$136$	3.08200	0.264279
$137$	22.7730	1.94562	0.972812	−	0.231595i	$-0.0743945\pi$
$137$	22.7730	1.94562	0.972812	+	0.231595i	$0.0743945\pi$
$138$	−6.44837	−0.548921
$139$	10.7974	0.915828	0.457914	−	0.888997i	$-0.348597\pi$
$139$	10.7974	0.915828	0.457914	+	0.888997i	$0.348597\pi$
$140$	−0.685453	−0.0579313
$141$	2.91266	0.245290
$142$	9.10031	0.763681
$143$	0.886562	0.0741380
$144$	−1.99055	−0.165879
$145$	−6.22927	−0.517313
$146$	−5.14500	−0.425804
$147$	6.61453	0.545557
$148$	−1.64673	−0.135360
$149$	−12.6481	−1.03617	−0.518086	−	0.855328i	$-0.673355\pi$
$149$	−12.6481	−1.03617	−0.518086	+	0.855328i	$0.673355\pi$
$150$	−3.89018	−0.317632
$151$	−18.4667	−1.50280	−0.751399	−	0.659848i	$-0.770621\pi$
$151$	−18.4667	−1.50280	−0.751399	+	0.659848i	$0.770621\pi$
$152$	−1.00000	−0.0811107
$153$	6.13487	0.495975
$154$	0.228982	0.0184519
$155$	−2.44178	−0.196129
$156$	2.51049	0.201000
$157$	−12.6615	−1.01050	−0.505250	−	0.862973i	$-0.668600\pi$
$157$	−12.6615	−1.01050	−0.505250	+	0.862973i	$0.668600\pi$
$158$	10.2970	0.819182
$159$	3.31047	0.262537
$160$	1.06211	0.0839671
$161$	−4.14205	−0.326440
$162$	−0.933943	−0.0733775
$163$	0.368311	0.0288483	0.0144242	−	0.999896i	$-0.495408\pi$
$163$	0.368311	0.0288483	0.0144242	+	0.999896i	$0.495408\pi$
$164$	2.04852	0.159962
$165$	−0.378620	−0.0294756
$166$	−2.17444	−0.168769
$167$	11.3985	0.882044	0.441022	−	0.897496i	$-0.354616\pi$
$167$	11.3985	0.882044	0.441022	+	0.897496i	$0.354616\pi$
$168$	0.648411	0.0500260
$169$	−6.75643	−0.519726
$170$	−3.27342	−0.251060
$171$	−1.99055	−0.152221
$172$	−6.64431	−0.506624
$173$	8.17479	0.621518	0.310759	−	0.950489i	$-0.399417\pi$
$173$	8.17479	0.621518	0.310759	+	0.950489i	$0.399417\pi$
$174$	5.89265	0.446720
$175$	−2.49882	−0.188893
$176$	−0.354807	−0.0267446
$177$	8.72413	0.655746
$178$	8.89991	0.667076
$179$	−23.3069	−1.74204	−0.871020	−	0.491248i	$-0.836541\pi$
$179$	−23.3069	−1.74204	−0.871020	+	0.491248i	$0.836541\pi$
$180$	2.11418	0.157582
$181$	6.44675	0.479183	0.239592	−	0.970874i	$-0.422986\pi$
$181$	6.44675	0.479183	0.239592	+	0.970874i	$0.422986\pi$
$182$	1.61259	0.119533
$183$	3.07068	0.226991
$184$	6.41811	0.473150
$185$	1.74900	0.128589
$186$	2.30983	0.169365
$187$	1.09352	0.0799658
$188$	−2.89900	−0.211431
$189$	3.23593	0.235379
$190$	1.06211	0.0770535
$191$	−5.32556	−0.385344	−0.192672	−	0.981263i	$-0.561715\pi$
$191$	−5.32556	−0.385344	−0.192672	+	0.981263i	$0.561715\pi$
$192$	−1.00471	−0.0725090
$193$	3.23371	0.232767	0.116384	−	0.993204i	$-0.462870\pi$
$193$	3.23371	0.232767	0.116384	+	0.993204i	$0.462870\pi$
$194$	−14.6540	−1.05209
$195$	−2.66641	−0.190946
$196$	−6.58350	−0.470250
$197$	−3.22052	−0.229452	−0.114726	−	0.993397i	$-0.536599\pi$
$197$	−3.22052	−0.229452	−0.114726	+	0.993397i	$0.536599\pi$
$198$	−0.706262	−0.0501919
$199$	7.41815	0.525859	0.262929	−	0.964815i	$-0.415311\pi$
$199$	7.41815	0.525859	0.262929	+	0.964815i	$0.415311\pi$
$200$	3.87192	0.273786
$201$	0.565697	0.0399012
$202$	5.03686	0.354392
$203$	3.78509	0.265661
$204$	3.09652	0.216800
$205$	−2.17575	−0.151961
$206$	−17.0674	−1.18914
$207$	12.7756	0.887964
$208$	−2.49871	−0.173255
$209$	−0.354807	−0.0245425
$210$	−0.688684	−0.0475237
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	−3.29494	−0.226297
$213$	9.14320	0.626482
$214$	−16.5695	−1.13267
$215$	7.05698	0.481282
$216$	−5.01407	−0.341165
$217$	1.48370	0.100720
$218$	−7.03581	−0.476525
$219$	−5.16926	−0.349306
$220$	0.376844	0.0254068
$221$	7.70103	0.518027
$222$	−1.65449	−0.111042
$223$	4.67792	0.313257	0.156628	−	0.987658i	$-0.449938\pi$
$223$	4.67792	0.313257	0.156628	+	0.987658i	$0.449938\pi$
$224$	−0.645369	−0.0431206
$225$	7.70726	0.513817
$226$	11.7608	0.782317
$227$	−6.63785	−0.440570	−0.220285	−	0.975436i	$-0.570699\pi$
$227$	−6.63785	−0.440570	−0.220285	+	0.975436i	$0.570699\pi$
$228$	−1.00471	−0.0665388
$229$	24.6994	1.63218	0.816091	−	0.577924i	$-0.196137\pi$
$229$	24.6994	1.63218	0.816091	+	0.577924i	$0.196137\pi$
$230$	−6.81674	−0.449482
$231$	0.230061	0.0151369
$232$	−5.86500	−0.385056
$233$	−9.23107	−0.604748	−0.302374	−	0.953189i	$-0.597779\pi$
$233$	−9.23107	−0.604748	−0.302374	+	0.953189i	$0.597779\pi$
$234$	−4.97381	−0.325148
$235$	3.07905	0.200855
$236$	−8.68320	−0.565228
$237$	10.3455	0.672012
$238$	1.98903	0.128929
$239$	3.46528	0.224150	0.112075	−	0.993700i	$-0.464250\pi$
$239$	3.46528	0.224150	0.112075	+	0.993700i	$0.464250\pi$
$240$	1.06712	0.0688820
$241$	5.53320	0.356425	0.178212	−	0.983992i	$-0.442969\pi$
$241$	5.53320	0.356425	0.178212	+	0.983992i	$0.442969\pi$
$242$	10.8741	0.699014
$243$	−15.9806	−1.02515
$244$	−3.05627	−0.195658
$245$	6.99239	0.446728
$246$	2.05817	0.131224
$247$	−2.49871	−0.158989
$248$	−2.29899	−0.145986
$249$	−2.18469	−0.138449
$250$	−9.42295	−0.595960
$251$	−0.442578	−0.0279353	−0.0139676	−	0.999902i	$-0.504446\pi$
$251$	−0.442578	−0.0279353	−0.0139676	+	0.999902i	$0.504446\pi$
$252$	−1.28464	−0.0809247
$253$	2.27719	0.143166
$254$	1.62483	0.101951
$255$	−3.28885	−0.205956
$256$	1.00000	0.0625000
$257$	−25.0201	−1.56071	−0.780355	−	0.625337i	$-0.784962\pi$
$257$	−25.0201	−1.56071	−0.780355	+	0.625337i	$0.784962\pi$
$258$	−6.67563	−0.415607
$259$	−1.06275	−0.0660359
$260$	2.65391	0.164588
$261$	−11.6746	−0.722639
$262$	14.7336	0.910243
$263$	−20.4880	−1.26335	−0.631673	−	0.775235i	$-0.717631\pi$
$263$	−20.4880	−1.26335	−0.631673	+	0.775235i	$0.717631\pi$
$264$	−0.356480	−0.0219398
$265$	3.49959	0.214978
$266$	−0.645369	−0.0395701
$267$	8.94186	0.547233
$268$	−0.563043	−0.0343933
$269$	4.62519	0.282003	0.141001	−	0.990009i	$-0.454968\pi$
$269$	4.62519	0.282003	0.141001	+	0.990009i	$0.454968\pi$
$270$	5.32549	0.324099
$271$	8.80886	0.535100	0.267550	−	0.963544i	$-0.413786\pi$
$271$	8.80886	0.535100	0.267550	+	0.963544i	$0.413786\pi$
$272$	−3.08200	−0.186874
$273$	1.62019	0.0980586
$274$	−22.7730	−1.37576
$275$	1.37379	0.0828425
$276$	6.44837	0.388146
$277$	0.608186	0.0365423	0.0182712	−	0.999833i	$-0.494184\pi$
$277$	0.608186	0.0365423	0.0182712	+	0.999833i	$0.494184\pi$
$278$	−10.7974	−0.647588
$279$	−4.57626	−0.273974
$280$	0.685453	0.0409636
$281$	23.6664	1.41182	0.705909	−	0.708303i	$-0.250539\pi$
$281$	23.6664	1.41182	0.705909	+	0.708303i	$0.250539\pi$
$282$	−2.91266	−0.173447
$283$	−11.9199	−0.708563	−0.354281	−	0.935139i	$-0.615275\pi$
$283$	−11.9199	−0.708563	−0.354281	+	0.935139i	$0.615275\pi$
$284$	−9.10031	−0.540004
$285$	1.06712	0.0632105
$286$	−0.886562	−0.0524235
$287$	1.32205	0.0780382
$288$	1.99055	0.117294
$289$	−7.50129	−0.441252
$290$	6.22927	0.365795
$291$	−14.7230	−0.863080
$292$	5.14500	0.301089
$293$	20.0946	1.17394	0.586970	−	0.809609i	$-0.300321\pi$
$293$	20.0946	1.17394	0.586970	+	0.809609i	$0.300321\pi$
$294$	−6.61453	−0.385767
$295$	9.22251	0.536955
$296$	1.64673	0.0957140
$297$	−1.77903	−0.103230
$298$	12.6481	0.732685
$299$	16.0370	0.927445
$300$	3.89018	0.224599
$301$	−4.28804	−0.247158
$302$	18.4667	1.06264
$303$	5.06060	0.290724
$304$	1.00000	0.0573539
$305$	3.24609	0.185871
$306$	−6.13487	−0.350707
$307$	26.6836	1.52291	0.761457	−	0.648215i	$-0.224484\pi$
$307$	26.6836	1.52291	0.761457	+	0.648215i	$0.224484\pi$
$308$	−0.228982	−0.0130475
$309$	−17.1479	−0.975508
$310$	2.44178	0.138684
$311$	−27.0525	−1.53400	−0.767002	−	0.641644i	$-0.778253\pi$
$311$	−27.0525	−1.53400	−0.767002	+	0.641644i	$0.778253\pi$
$312$	−2.51049	−0.142129
$313$	2.69259	0.152194	0.0760971	−	0.997100i	$-0.475754\pi$
$313$	2.69259	0.152194	0.0760971	+	0.997100i	$0.475754\pi$
$314$	12.6615	0.714532
$315$	1.36443	0.0768768
$316$	−10.2970	−0.579249
$317$	−6.21226	−0.348916	−0.174458	−	0.984665i	$-0.555817\pi$
$317$	−6.21226	−0.348916	−0.174458	+	0.984665i	$0.555817\pi$
$318$	−3.31047	−0.185642
$319$	−2.08095	−0.116511
$320$	−1.06211	−0.0593737
$321$	−16.6476	−0.929180
$322$	4.14205	0.230828
$323$	−3.08200	−0.171487
$324$	0.933943	0.0518857
$325$	9.67483	0.536663
$326$	−0.368311	−0.0203989
$327$	−7.06897	−0.390915
$328$	−2.04852	−0.113110
$329$	−1.87092	−0.103147
$330$	0.378620	0.0208424
$331$	23.5265	1.29313	0.646565	−	0.762859i	$-0.276205\pi$
$331$	23.5265	1.29313	0.646565	+	0.762859i	$0.276205\pi$
$332$	2.17444	0.119338
$333$	3.27789	0.179627
$334$	−11.3985	−0.623700
$335$	0.598013	0.0326729
$336$	−0.648411	−0.0353737
$337$	19.0408	1.03722	0.518609	−	0.855012i	$-0.326450\pi$
$337$	19.0408	1.03722	0.518609	+	0.855012i	$0.326450\pi$
$338$	6.75643	0.367502
$339$	11.8162	0.641770
$340$	3.27342	0.177526
$341$	−0.815700	−0.0441726
$342$	1.99055	0.107637
$343$	−8.76637	−0.473340
$344$	6.64431	0.358237
$345$	−6.84887	−0.368731
$346$	−8.17479	−0.439479
$347$	−4.25617	−0.228483	−0.114242	−	0.993453i	$-0.536444\pi$
$347$	−4.25617	−0.228483	−0.114242	+	0.993453i	$0.536444\pi$
$348$	−5.89265	−0.315879
$349$	13.8186	0.739694	0.369847	−	0.929093i	$-0.379410\pi$
$349$	13.8186	0.739694	0.369847	+	0.929093i	$0.379410\pi$
$350$	2.49882	0.133568
$351$	−12.5287	−0.668734
$352$	0.354807	0.0189113
$353$	28.2807	1.50523	0.752615	−	0.658461i	$-0.228792\pi$
$353$	28.2807	1.50523	0.752615	+	0.658461i	$0.228792\pi$
$354$	−8.72413	−0.463682
$355$	9.66552	0.512992
$356$	−8.89991	−0.471694
$357$	1.99840	0.105767
$358$	23.3069	1.23181
$359$	27.0487	1.42758	0.713789	−	0.700361i	$-0.246978\pi$
$359$	27.0487	1.42758	0.713789	+	0.700361i	$0.246978\pi$
$360$	−2.11418	−0.111427
$361$	1.00000	0.0526316
$362$	−6.44675	−0.338834
$363$	10.9254	0.573433
$364$	−1.61259	−0.0845228
$365$	−5.46455	−0.286028
$366$	−3.07068	−0.160507
$367$	12.7653	0.666344	0.333172	−	0.942866i	$-0.391881\pi$
$367$	12.7653	0.666344	0.333172	+	0.942866i	$0.391881\pi$
$368$	−6.41811	−0.334567
$369$	−4.07768	−0.212275
$370$	−1.74900	−0.0909263
$371$	−2.12645	−0.110400
$372$	−2.30983	−0.119759
$373$	19.8524	1.02792	0.513959	−	0.857815i	$-0.328178\pi$
$373$	19.8524	1.02792	0.513959	+	0.857815i	$0.328178\pi$
$374$	−1.09352	−0.0565443
$375$	−9.46737	−0.488893
$376$	2.89900	0.149504
$377$	−14.6550	−0.754769
$378$	−3.23593	−0.166438
$379$	10.5076	0.539737	0.269868	−	0.962897i	$-0.413020\pi$
$379$	10.5076	0.539737	0.269868	+	0.962897i	$0.413020\pi$
$380$	−1.06211	−0.0544850
$381$	1.63249	0.0836349
$382$	5.32556	0.272479
$383$	−20.2752	−1.03601	−0.518007	−	0.855377i	$-0.673326\pi$
$383$	−20.2752	−1.03601	−0.518007	+	0.855377i	$0.673326\pi$
$384$	1.00471	0.0512716
$385$	0.243204	0.0123948
$386$	−3.23371	−0.164591
$387$	13.2258	0.672307
$388$	14.6540	0.743942
$389$	−1.35263	−0.0685813	−0.0342906	−	0.999412i	$-0.510917\pi$
$389$	−1.35263	−0.0685813	−0.0342906	+	0.999412i	$0.510917\pi$
$390$	2.66641	0.135019
$391$	19.7806	1.00035
$392$	6.58350	0.332517
$393$	14.8030	0.746714
$394$	3.22052	0.162247
$395$	10.9365	0.550274
$396$	0.706262	0.0354910
$397$	25.8486	1.29730	0.648651	−	0.761086i	$-0.275333\pi$
$397$	25.8486	1.29730	0.648651	+	0.761086i	$0.275333\pi$
$398$	−7.41815	−0.371838
$399$	−0.648411	−0.0324612
$400$	−3.87192	−0.193596
$401$	7.23410	0.361253	0.180627	−	0.983552i	$-0.442187\pi$
$401$	7.23410	0.361253	0.180627	+	0.983552i	$0.442187\pi$
$402$	−0.565697	−0.0282144
$403$	−5.74453	−0.286155
$404$	−5.03686	−0.250593
$405$	−0.991949	−0.0492903
$406$	−3.78509	−0.187851
$407$	0.584270	0.0289612
$408$	−3.09652	−0.153301
$409$	−21.6887	−1.07244	−0.536218	−	0.844080i	$-0.680147\pi$
$409$	−21.6887	−1.07244	−0.536218	+	0.844080i	$0.680147\pi$
$410$	2.17575	0.107453
$411$	−22.8803	−1.12860
$412$	17.0674	0.840851
$413$	−5.60387	−0.275749
$414$	−12.7756	−0.627886
$415$	−2.30949	−0.113369
$416$	2.49871	0.122509
$417$	−10.8483	−0.531246
$418$	0.354807	0.0173542
$419$	−8.05129	−0.393331	−0.196666	−	0.980471i	$-0.563011\pi$
$419$	−8.05129	−0.393331	−0.196666	+	0.980471i	$0.563011\pi$
$420$	0.688684	0.0336043
$421$	−31.3804	−1.52939	−0.764694	−	0.644393i	$-0.777110\pi$
$421$	−31.3804	−1.52939	−0.764694	+	0.644393i	$0.777110\pi$
$422$	1.00000	0.0486792
$423$	5.77060	0.280576
$424$	3.29494	0.160016
$425$	11.9333	0.578848
$426$	−9.14320	−0.442990
$427$	−1.97242	−0.0954523
$428$	16.5695	0.800918
$429$	−0.890741	−0.0430054
$430$	−7.05698	−0.340318
$431$	−27.2829	−1.31417	−0.657086	−	0.753815i	$-0.728211\pi$
$431$	−27.2829	−1.31417	−0.657086	+	0.753815i	$0.728211\pi$
$432$	5.01407	0.241240
$433$	−22.2429	−1.06893	−0.534464	−	0.845191i	$-0.679486\pi$
$433$	−22.2429	−1.06893	−0.534464	+	0.845191i	$0.679486\pi$
$434$	−1.48370	−0.0712199
$435$	6.25863	0.300078
$436$	7.03581	0.336954
$437$	−6.41811	−0.307020
$438$	5.16926	0.246997
$439$	−17.4693	−0.833766	−0.416883	−	0.908960i	$-0.636877\pi$
$439$	−17.4693	−0.833766	−0.416883	+	0.908960i	$0.636877\pi$
$440$	−0.376844	−0.0179653
$441$	13.1048	0.624037
$442$	−7.70103	−0.366301
$443$	2.33512	0.110945	0.0554725	−	0.998460i	$-0.482333\pi$
$443$	2.33512	0.110945	0.0554725	+	0.998460i	$0.482333\pi$
$444$	1.65449	0.0785185
$445$	9.45267	0.448100
$446$	−4.67792	−0.221506
$447$	12.7077	0.601054
$448$	0.645369	0.0304908
$449$	−30.3765	−1.43356	−0.716778	−	0.697302i	$-0.754384\pi$
$449$	−30.3765	−1.43356	−0.716778	+	0.697302i	$0.754384\pi$
$450$	−7.70726	−0.363324
$451$	−0.726829	−0.0342251
$452$	−11.7608	−0.553181
$453$	18.5537	0.871731
$454$	6.63785	0.311530
$455$	1.71275	0.0802949
$456$	1.00471	0.0470500
$457$	28.3620	1.32672	0.663359	−	0.748302i	$-0.269130\pi$
$457$	28.3620	1.32672	0.663359	+	0.748302i	$0.269130\pi$
$458$	−24.6994	−1.15413
$459$	−15.4534	−0.721301
$460$	6.81674	0.317832
$461$	−4.05873	−0.189034	−0.0945170	−	0.995523i	$-0.530131\pi$
$461$	−4.05873	−0.189034	−0.0945170	+	0.995523i	$0.530131\pi$
$462$	−0.230061	−0.0107034
$463$	28.5580	1.32720	0.663601	−	0.748086i	$-0.269027\pi$
$463$	28.5580	1.32720	0.663601	+	0.748086i	$0.269027\pi$
$464$	5.86500	0.272276
$465$	2.45329	0.113769
$466$	9.23107	0.427621
$467$	36.9862	1.71152	0.855759	−	0.517375i	$-0.173091\pi$
$467$	36.9862	1.71152	0.855759	+	0.517375i	$0.173091\pi$
$468$	4.97381	0.229915
$469$	−0.363371	−0.0167789
$470$	−3.07905	−0.142026
$471$	12.7212	0.586163
$472$	8.68320	0.399677
$473$	2.35745	0.108396
$474$	−10.3455	−0.475184
$475$	−3.87192	−0.177656
$476$	−1.98903	−0.0911669
$477$	6.55874	0.300304
$478$	−3.46528	−0.158498
$479$	6.08335	0.277955	0.138978	−	0.990296i	$-0.455618\pi$
$479$	6.08335	0.277955	0.138978	+	0.990296i	$0.455618\pi$
$480$	−1.06712	−0.0487069
$481$	4.11470	0.187614
$482$	−5.53320	−0.252030
$483$	4.16158	0.189358
$484$	−10.8741	−0.494278
$485$	−15.5641	−0.706730
$486$	15.9806	0.724893
$487$	32.5413	1.47459	0.737293	−	0.675573i	$-0.236104\pi$
$487$	32.5413	1.47459	0.737293	+	0.675573i	$0.236104\pi$
$488$	3.05627	0.138351
$489$	−0.370047	−0.0167341
$490$	−6.99239	−0.315884
$491$	5.50001	0.248212	0.124106	−	0.992269i	$-0.460394\pi$
$491$	5.50001	0.248212	0.124106	+	0.992269i	$0.460394\pi$
$492$	−2.05817	−0.0927896
$493$	−18.0759	−0.814099
$494$	2.49871	0.112422
$495$	−0.750127	−0.0337157
$496$	2.29899	0.103228
$497$	−5.87306	−0.263443
$498$	2.18469	0.0978984
$499$	6.16152	0.275828	0.137914	−	0.990444i	$-0.455960\pi$
$499$	6.16152	0.275828	0.137914	+	0.990444i	$0.455960\pi$
$500$	9.42295	0.421407
$501$	−11.4523	−0.511649
$502$	0.442578	0.0197532
$503$	−7.33108	−0.326877	−0.163438	−	0.986554i	$-0.552258\pi$
$503$	−7.33108	−0.326877	−0.163438	+	0.986554i	$0.552258\pi$
$504$	1.28464	0.0572224
$505$	5.34970	0.238058
$506$	−2.27719	−0.101234
$507$	6.78828	0.301478
$508$	−1.62483	−0.0720901
$509$	−23.6803	−1.04961	−0.524805	−	0.851222i	$-0.675862\pi$
$509$	−23.6803	−1.04961	−0.524805	+	0.851222i	$0.675862\pi$
$510$	3.28885	0.145633
$511$	3.32043	0.146887
$512$	−1.00000	−0.0441942
$513$	5.01407	0.221377
$514$	25.0201	1.10359
$515$	−18.1274	−0.798791
$516$	6.67563	0.293878
$517$	1.02859	0.0452371
$518$	1.06275	0.0466944
$519$	−8.21332	−0.360525
$520$	−2.65391	−0.116381
$521$	−37.6252	−1.64839	−0.824194	−	0.566308i	$-0.808371\pi$
$521$	−37.6252	−1.64839	−0.824194	+	0.566308i	$0.808371\pi$
$522$	11.6746	0.510983
$523$	27.6317	1.20825	0.604126	−	0.796889i	$-0.293522\pi$
$523$	27.6317	1.20825	0.604126	+	0.796889i	$0.293522\pi$
$524$	−14.7336	−0.643639
$525$	2.51060	0.109572
$526$	20.4880	0.893320
$527$	−7.08549	−0.308649
$528$	0.356480	0.0155138
$529$	18.1922	0.790965
$530$	−3.49959	−0.152012
$531$	17.2844	0.750077
$532$	0.645369	0.0279803
$533$	−5.11866	−0.221714
$534$	−8.94186	−0.386952
$535$	−17.5986	−0.760855
$536$	0.563043	0.0243198
$537$	23.4168	1.01051
$538$	−4.62519	−0.199406
$539$	2.33587	0.100613
$540$	−5.32549	−0.229173
$541$	−27.2753	−1.17265	−0.586327	−	0.810074i	$-0.699427\pi$
$541$	−27.2753	−1.17265	−0.586327	+	0.810074i	$0.699427\pi$
$542$	−8.80886	−0.378373
$543$	−6.47714	−0.277961
$544$	3.08200	0.132140
$545$	−7.47279	−0.320099
$546$	−1.62019	−0.0693379
$547$	−6.59513	−0.281988	−0.140994	−	0.990010i	$-0.545030\pi$
$547$	−6.59513	−0.281988	−0.140994	+	0.990010i	$0.545030\pi$
$548$	22.7730	0.972812
$549$	6.08366	0.259644
$550$	−1.37379	−0.0585785
$551$	5.86500	0.249857
$552$	−6.44837	−0.274461
$553$	−6.64534	−0.282589
$554$	−0.608186	−0.0258393
$555$	−1.75725	−0.0745910
$556$	10.7974	0.457914
$557$	22.6873	0.961292	0.480646	−	0.876915i	$-0.340402\pi$
$557$	22.6873	0.961292	0.480646	+	0.876915i	$0.340402\pi$
$558$	4.57626	0.193729
$559$	16.6022	0.702199
$560$	−0.685453	−0.0289657
$561$	−1.09867	−0.0463859
$562$	−23.6664	−0.998306
$563$	15.5514	0.655414	0.327707	−	0.944779i	$-0.393724\pi$
$563$	15.5514	0.655414	0.327707	+	0.944779i	$0.393724\pi$
$564$	2.91266	0.122645
$565$	12.4912	0.525511
$566$	11.9199	0.501030
$567$	0.602738	0.0253126
$568$	9.10031	0.381840
$569$	23.2610	0.975152	0.487576	−	0.873081i	$-0.337881\pi$
$569$	23.2610	0.975152	0.487576	+	0.873081i	$0.337881\pi$
$570$	−1.06712	−0.0446965
$571$	39.8690	1.66847	0.834234	−	0.551411i	$-0.185910\pi$
$571$	39.8690	1.66847	0.834234	+	0.551411i	$0.185910\pi$
$572$	0.886562	0.0370690
$573$	5.35066	0.223527
$574$	−1.32205	−0.0551813
$575$	24.8505	1.03634
$576$	−1.99055	−0.0829396
$577$	10.9374	0.455330	0.227665	−	0.973740i	$-0.426891\pi$
$577$	10.9374	0.455330	0.227665	+	0.973740i	$0.426891\pi$
$578$	7.50129	0.312013
$579$	−3.24895	−0.135022
$580$	−6.22927	−0.258656
$581$	1.40332	0.0582195
$582$	14.7230	0.610290
$583$	1.16907	0.0484179
$584$	−5.14500	−0.212902
$585$	−5.28273	−0.218414
$586$	−20.0946	−0.830101
$587$	−34.5274	−1.42510	−0.712549	−	0.701622i	$-0.752459\pi$
$587$	−34.5274	−1.42510	−0.712549	+	0.701622i	$0.752459\pi$
$588$	6.61453	0.272779
$589$	2.29899	0.0947284
$590$	−9.22251	−0.379685
$591$	3.23570	0.133099
$592$	−1.64673	−0.0676800
$593$	19.6911	0.808619	0.404309	−	0.914622i	$-0.367512\pi$
$593$	19.6911	0.808619	0.404309	+	0.914622i	$0.367512\pi$
$594$	1.77903	0.0729945
$595$	2.11256	0.0866066
$596$	−12.6481	−0.518086
$597$	−7.45311	−0.305036
$598$	−16.0370	−0.655803
$599$	27.5399	1.12525	0.562624	−	0.826713i	$-0.309792\pi$
$599$	27.5399	1.12525	0.562624	+	0.826713i	$0.309792\pi$
$600$	−3.89018	−0.158816
$601$	10.8315	0.441825	0.220913	−	0.975294i	$-0.429096\pi$
$601$	10.8315	0.441825	0.220913	+	0.975294i	$0.429096\pi$
$602$	4.28804	0.174767
$603$	1.12077	0.0456411
$604$	−18.4667	−0.751399
$605$	11.5495	0.469554
$606$	−5.06060	−0.205573
$607$	−30.7213	−1.24694	−0.623470	−	0.781847i	$-0.714278\pi$
$607$	−30.7213	−1.24694	−0.623470	+	0.781847i	$0.714278\pi$
$608$	−1.00000	−0.0405554
$609$	−3.80293	−0.154103
$610$	−3.24609	−0.131430
$611$	7.24376	0.293051
$612$	6.13487	0.247987
$613$	−6.74053	−0.272247	−0.136124	−	0.990692i	$-0.543464\pi$
$613$	−6.74053	−0.272247	−0.136124	+	0.990692i	$0.543464\pi$
$614$	−26.6836	−1.07686
$615$	2.18600	0.0881482
$616$	0.228982	0.00922594
$617$	−1.94368	−0.0782495	−0.0391248	−	0.999234i	$-0.512457\pi$
$617$	−1.94368	−0.0782495	−0.0391248	+	0.999234i	$0.512457\pi$
$618$	17.1479	0.689788
$619$	37.3337	1.50057	0.750285	−	0.661115i	$-0.229916\pi$
$619$	37.3337	1.50057	0.750285	+	0.661115i	$0.229916\pi$
$620$	−2.44178	−0.0980643
$621$	−32.1809	−1.29138
$622$	27.0525	1.08471
$623$	−5.74373	−0.230118
$624$	2.51049	0.100500
$625$	9.35143	0.374057
$626$	−2.69259	−0.107618
$627$	0.356480	0.0142364
$628$	−12.6615	−0.505250
$629$	5.07521	0.202362
$630$	−1.36443	−0.0543601
$631$	3.15621	0.125647	0.0628234	−	0.998025i	$-0.479990\pi$
$631$	3.15621	0.125647	0.0628234	+	0.998025i	$0.479990\pi$
$632$	10.2970	0.409591
$633$	1.00471	0.0399338
$634$	6.21226	0.246721
$635$	1.72574	0.0684841
$636$	3.31047	0.131269
$637$	16.4503	0.651784
$638$	2.08095	0.0823854
$639$	18.1146	0.716603
$640$	1.06211	0.0419835
$641$	44.3990	1.75366	0.876828	−	0.480805i	$-0.159655\pi$
$641$	44.3990	1.75366	0.876828	+	0.480805i	$0.159655\pi$
$642$	16.6476	0.657029
$643$	−23.5017	−0.926815	−0.463407	−	0.886145i	$-0.653373\pi$
$643$	−23.5017	−0.926815	−0.463407	+	0.886145i	$0.653373\pi$
$644$	−4.14205	−0.163220
$645$	−7.09025	−0.279178
$646$	3.08200	0.121260
$647$	−4.36415	−0.171572	−0.0857862	−	0.996314i	$-0.527340\pi$
$647$	−4.36415	−0.171572	−0.0857862	+	0.996314i	$0.527340\pi$
$648$	−0.933943	−0.0366887
$649$	3.08086	0.120934
$650$	−9.67483	−0.379478
$651$	−1.49069	−0.0584249
$652$	0.368311	0.0144242
$653$	−13.1892	−0.516131	−0.258066	−	0.966127i	$-0.583085\pi$
$653$	−13.1892	−0.516131	−0.258066	+	0.966127i	$0.583085\pi$
$654$	7.06897	0.276419
$655$	15.6487	0.611444
$656$	2.04852	0.0799812
$657$	−10.2414	−0.399555
$658$	1.87092	0.0729362
$659$	39.8982	1.55421	0.777107	−	0.629369i	$-0.216686\pi$
$659$	39.8982	1.55421	0.777107	+	0.629369i	$0.216686\pi$
$660$	−0.378620	−0.0147378
$661$	22.6084	0.879366	0.439683	−	0.898153i	$-0.355091\pi$
$661$	22.6084	0.879366	0.439683	+	0.898153i	$0.355091\pi$
$662$	−23.5265	−0.914382
$663$	−7.73733	−0.300493
$664$	−2.17444	−0.0843847
$665$	−0.685453	−0.0265807
$666$	−3.27789	−0.127016
$667$	−37.6423	−1.45751
$668$	11.3985	0.441022
$669$	−4.69997	−0.181711
$670$	−0.598013	−0.0231033
$671$	1.08439	0.0418623
$672$	0.648411	0.0250130
$673$	−12.8857	−0.496705	−0.248353	−	0.968670i	$-0.579889\pi$
$673$	−12.8857	−0.496705	−0.248353	+	0.968670i	$0.579889\pi$
$674$	−19.0408	−0.733423
$675$	−19.4141	−0.747250
$676$	−6.75643	−0.259863
$677$	−15.6898	−0.603009	−0.301505	−	0.953465i	$-0.597489\pi$
$677$	−15.6898	−0.603009	−0.301505	+	0.953465i	$0.597489\pi$
$678$	−11.8162	−0.453800
$679$	9.45722	0.362935
$680$	−3.27342	−0.125530
$681$	6.66914	0.255562
$682$	0.815700	0.0312348
$683$	4.19144	0.160381	0.0801905	−	0.996780i	$-0.474447\pi$
$683$	4.19144	0.160381	0.0801905	+	0.996780i	$0.474447\pi$
$684$	−1.99055	−0.0761106
$685$	−24.1874	−0.924151
$686$	8.76637	0.334702
$687$	−24.8158	−0.946782
$688$	−6.64431	−0.253312
$689$	8.23311	0.313657
$690$	6.84887	0.260732
$691$	6.28631	0.239142	0.119571	−	0.992826i	$-0.461848\pi$
$691$	6.28631	0.239142	0.119571	+	0.992826i	$0.461848\pi$
$692$	8.17479	0.310759
$693$	0.455800	0.0173144
$694$	4.25617	0.161562
$695$	−11.4681	−0.435008
$696$	5.89265	0.223360
$697$	−6.31353	−0.239142
$698$	−13.8186	−0.523043
$699$	9.27458	0.350797
$700$	−2.49882	−0.0944466
$701$	37.6366	1.42151	0.710757	−	0.703438i	$-0.248353\pi$
$701$	37.6366	1.42151	0.710757	+	0.703438i	$0.248353\pi$
$702$	12.5287	0.472867
$703$	−1.64673	−0.0621074
$704$	−0.354807	−0.0133723
$705$	−3.09356	−0.116510
$706$	−28.2807	−1.06436
$707$	−3.25064	−0.122253
$708$	8.72413	0.327873
$709$	−38.1738	−1.43365	−0.716823	−	0.697255i	$-0.754404\pi$
$709$	−38.1738	−1.43365	−0.716823	+	0.697255i	$0.754404\pi$
$710$	−9.66552	−0.362740
$711$	20.4966	0.768683
$712$	8.89991	0.333538
$713$	−14.7552	−0.552587
$714$	−1.99840	−0.0747883
$715$	−0.941625	−0.0352148
$716$	−23.3069	−0.871020
$717$	−3.48161	−0.130023
$718$	−27.0487	−1.00945
$719$	0.729160	0.0271931	0.0135965	−	0.999908i	$-0.495672\pi$
$719$	0.729160	0.0271931	0.0135965	+	0.999908i	$0.495672\pi$
$720$	2.11418	0.0787909
$721$	11.0148	0.410212
$722$	−1.00000	−0.0372161
$723$	−5.55928	−0.206752
$724$	6.44675	0.239592
$725$	−22.7088	−0.843385
$726$	−10.9254	−0.405478
$727$	27.8938	1.03452	0.517262	−	0.855827i	$-0.326951\pi$
$727$	27.8938	1.03452	0.517262	+	0.855827i	$0.326951\pi$
$728$	1.61259	0.0597667
$729$	13.2541	0.490891
$730$	5.46455	0.202252
$731$	20.4777	0.757397
$732$	3.07068	0.113495
$733$	8.27331	0.305582	0.152791	−	0.988259i	$-0.451174\pi$
$733$	8.27331	0.305582	0.152791	+	0.988259i	$0.451174\pi$
$734$	−12.7653	−0.471176
$735$	−7.02535	−0.259134
$736$	6.41811	0.236575
$737$	0.199772	0.00735869
$738$	4.07768	0.150101
$739$	20.2344	0.744334	0.372167	−	0.928166i	$-0.378615\pi$
$739$	20.2344	0.744334	0.372167	+	0.928166i	$0.378615\pi$
$740$	1.74900	0.0642946
$741$	2.51049	0.0922252
$742$	2.12645	0.0780646
$743$	48.3747	1.77469	0.887347	−	0.461102i	$-0.152546\pi$
$743$	48.3747	1.77469	0.887347	+	0.461102i	$0.152546\pi$
$744$	2.30983	0.0846825
$745$	13.4337	0.492171
$746$	−19.8524	−0.726847
$747$	−4.32834	−0.158366
$748$	1.09352	0.0399829
$749$	10.6935	0.390731
$750$	9.46737	0.345699
$751$	32.4792	1.18518	0.592591	−	0.805504i	$-0.298105\pi$
$751$	32.4792	1.18518	0.592591	+	0.805504i	$0.298105\pi$
$752$	−2.89900	−0.105716
$753$	0.444664	0.0162045
$754$	14.6550	0.533702
$755$	19.6136	0.713814
$756$	3.23593	0.117690
$757$	1.07227	0.0389724	0.0194862	−	0.999810i	$-0.493797\pi$
$757$	1.07227	0.0389724	0.0194862	+	0.999810i	$0.493797\pi$
$758$	−10.5076	−0.381651
$759$	−2.28793	−0.0830465
$760$	1.06211	0.0385267
$761$	29.6255	1.07393	0.536963	−	0.843606i	$-0.319572\pi$
$761$	29.6255	1.07393	0.536963	+	0.843606i	$0.319572\pi$
$762$	−1.63249	−0.0591388
$763$	4.54069	0.164384
$764$	−5.32556	−0.192672
$765$	−6.51590	−0.235583
$766$	20.2752	0.732572
$767$	21.6968	0.783427
$768$	−1.00471	−0.0362545
$769$	2.55778	0.0922360	0.0461180	−	0.998936i	$-0.485315\pi$
$769$	2.55778	0.0922360	0.0461180	+	0.998936i	$0.485315\pi$
$770$	−0.243204	−0.00876445
$771$	25.1380	0.905324
$772$	3.23371	0.116384
$773$	30.0853	1.08209	0.541047	−	0.840993i	$-0.318028\pi$
$773$	30.0853	1.08209	0.541047	+	0.840993i	$0.318028\pi$
$774$	−13.2258	−0.475393
$775$	−8.90153	−0.319752
$776$	−14.6540	−0.526047
$777$	1.06776	0.0383055
$778$	1.35263	0.0484943
$779$	2.04852	0.0733958
$780$	−2.66641	−0.0954730
$781$	3.22886	0.115538
$782$	−19.7806	−0.707353
$783$	29.4076	1.05094
$784$	−6.58350	−0.235125
$785$	13.4479	0.479977
$786$	−14.8030	−0.528006
$787$	35.4168	1.26247	0.631236	−	0.775591i	$-0.282548\pi$
$787$	35.4168	1.26247	0.631236	+	0.775591i	$0.282548\pi$
$788$	−3.22052	−0.114726
$789$	20.5846	0.732831
$790$	−10.9365	−0.389103
$791$	−7.59006	−0.269871
$792$	−0.706262	−0.0250959
$793$	7.63674	0.271189
$794$	−25.8486	−0.917331
$795$	−3.51608	−0.124703
$796$	7.41815	0.262929
$797$	−0.950549	−0.0336702	−0.0168351	−	0.999858i	$-0.505359\pi$
$797$	−0.950549	−0.0336702	−0.0168351	+	0.999858i	$0.505359\pi$
$798$	0.648411	0.0229535
$799$	8.93470	0.316087
$800$	3.87192	0.136893
$801$	17.7157	0.625954
$802$	−7.23410	−0.255445
$803$	−1.82549	−0.0644200
$804$	0.565697	0.0199506
$805$	4.39931	0.155055
$806$	5.74453	0.202342
$807$	−4.64699	−0.163582
$808$	5.03686	0.177196
$809$	−0.211129	−0.00742290	−0.00371145	−	0.999993i	$-0.501181\pi$
$809$	−0.211129	−0.00742290	−0.00371145	+	0.999993i	$0.501181\pi$
$810$	0.991949	0.0348535
$811$	21.5068	0.755208	0.377604	−	0.925967i	$-0.376748\pi$
$811$	21.5068	0.755208	0.377604	+	0.925967i	$0.376748\pi$
$812$	3.78509	0.132831
$813$	−8.85038	−0.310396
$814$	−0.584270	−0.0204787
$815$	−0.391186	−0.0137027
$816$	3.09652	0.108400
$817$	−6.64431	−0.232455
$818$	21.6887	0.758326
$819$	3.20995	0.112165
$820$	−2.17575	−0.0759805
$821$	28.8459	1.00673	0.503364	−	0.864074i	$-0.332096\pi$
$821$	28.8459	1.00673	0.503364	+	0.864074i	$0.332096\pi$
$822$	22.8803	0.798042
$823$	15.6306	0.544848	0.272424	−	0.962177i	$-0.412175\pi$
$823$	15.6306	0.544848	0.272424	+	0.962177i	$0.412175\pi$
$824$	−17.0674	−0.594571
$825$	−1.38026	−0.0480546
$826$	5.60387	0.194984
$827$	9.86963	0.343201	0.171600	−	0.985167i	$-0.445106\pi$
$827$	9.86963	0.343201	0.171600	+	0.985167i	$0.445106\pi$
$828$	12.7756	0.443982
$829$	−6.77270	−0.235226	−0.117613	−	0.993060i	$-0.537524\pi$
$829$	−6.77270	−0.235226	−0.117613	+	0.993060i	$0.537524\pi$
$830$	2.30949	0.0801637
$831$	−0.611052	−0.0211972
$832$	−2.49871	−0.0866273
$833$	20.2903	0.703018
$834$	10.8483	0.375647
$835$	−12.1065	−0.418962
$836$	−0.354807	−0.0122713
$837$	11.5273	0.398443
$838$	8.05129	0.278127
$839$	10.5864	0.365484	0.182742	−	0.983161i	$-0.441503\pi$
$839$	10.5864	0.365484	0.182742	+	0.983161i	$0.441503\pi$
$840$	−0.688684	−0.0237618
$841$	5.39825	0.186147
$842$	31.3804	1.08144
$843$	−23.7779	−0.818955
$844$	−1.00000	−0.0344214
$845$	7.17607	0.246864
$846$	−5.77060	−0.198397
$847$	−7.01782	−0.241135
$848$	−3.29494	−0.113149
$849$	11.9761	0.411017
$850$	−11.9333	−0.409308
$851$	10.5689	0.362296
$852$	9.14320	0.313241
$853$	−38.2935	−1.31115	−0.655573	−	0.755132i	$-0.727573\pi$
$853$	−38.2935	−1.31115	−0.655573	+	0.755132i	$0.727573\pi$
$854$	1.97242	0.0674949
$855$	2.11418	0.0723035
$856$	−16.5695	−0.566335
$857$	39.4441	1.34739	0.673693	−	0.739011i	$-0.264707\pi$
$857$	39.4441	1.34739	0.673693	+	0.739011i	$0.264707\pi$
$858$	0.890741	0.0304094
$859$	−27.0757	−0.923812	−0.461906	−	0.886929i	$-0.652834\pi$
$859$	−27.0757	−0.923812	−0.461906	+	0.886929i	$0.652834\pi$
$860$	7.05698	0.240641
$861$	−1.32828	−0.0452677
$862$	27.2829	0.929261
$863$	−26.8045	−0.912436	−0.456218	−	0.889868i	$-0.650796\pi$
$863$	−26.8045	−0.912436	−0.456218	+	0.889868i	$0.650796\pi$
$864$	−5.01407	−0.170582
$865$	−8.68252	−0.295214
$866$	22.2429	0.755846
$867$	7.53665	0.255958
$868$	1.48370	0.0503601
$869$	3.65343	0.123934
$870$	−6.25863	−0.212188
$871$	1.40688	0.0476704
$872$	−7.03581	−0.238262
$873$	−29.1695	−0.987237
$874$	6.41811	0.217096
$875$	6.08128	0.205585
$876$	−5.16926	−0.174653
$877$	−11.4718	−0.387374	−0.193687	−	0.981063i	$-0.562045\pi$
$877$	−11.4718	−0.387374	−0.193687	+	0.981063i	$0.562045\pi$
$878$	17.4693	0.589561
$879$	−20.1893	−0.680969
$880$	0.376844	0.0127034
$881$	−27.9653	−0.942176	−0.471088	−	0.882086i	$-0.656139\pi$
$881$	−27.9653	−0.942176	−0.471088	+	0.882086i	$0.656139\pi$
$882$	−13.1048	−0.441261
$883$	24.1898	0.814051	0.407025	−	0.913417i	$-0.366566\pi$
$883$	24.1898	0.814051	0.407025	+	0.913417i	$0.366566\pi$
$884$	7.70103	0.259014
$885$	−9.26598	−0.311472
$886$	−2.33512	−0.0784499
$887$	−30.1407	−1.01202	−0.506012	−	0.862526i	$-0.668881\pi$
$887$	−30.1407	−1.01202	−0.506012	+	0.862526i	$0.668881\pi$
$888$	−1.65449	−0.0555210
$889$	−1.04861	−0.0351694
$890$	−9.45267	−0.316854
$891$	−0.331370	−0.0111013
$892$	4.67792	0.156628
$893$	−2.89900	−0.0970113
$894$	−12.7077	−0.425010
$895$	24.7545	0.827450
$896$	−0.645369	−0.0215603
$897$	−16.1126	−0.537985
$898$	30.3765	1.01368
$899$	13.4836	0.449703
$900$	7.70726	0.256909
$901$	10.1550	0.338312
$902$	0.726829	0.0242008
$903$	4.30825	0.143369
$904$	11.7608	0.391158
$905$	−6.84715	−0.227607
$906$	−18.5537	−0.616407
$907$	−32.5160	−1.07968	−0.539838	−	0.841769i	$-0.681514\pi$
$907$	−32.5160	−1.07968	−0.539838	+	0.841769i	$0.681514\pi$
$908$	−6.63785	−0.220285
$909$	10.0261	0.332546
$910$	−1.71275	−0.0567771
$911$	57.3778	1.90101	0.950506	−	0.310707i	$-0.100566\pi$
$911$	57.3778	1.90101	0.950506	+	0.310707i	$0.100566\pi$
$912$	−1.00471	−0.0332694
$913$	−0.771508	−0.0255332
$914$	−28.3620	−0.938131
$915$	−3.26139	−0.107818
$916$	24.6994	0.816091
$917$	−9.50860	−0.314002
$918$	15.4534	0.510037
$919$	58.5337	1.93085	0.965424	−	0.260683i	$-0.0839478\pi$
$919$	58.5337	1.93085	0.965424	+	0.260683i	$0.0839478\pi$
$920$	−6.81674	−0.224741
$921$	−26.8094	−0.883399
$922$	4.05873	0.133667
$923$	22.7391	0.748465
$924$	0.230061	0.00756846
$925$	6.37600	0.209642
$926$	−28.5580	−0.938474
$927$	−33.9735	−1.11584
$928$	−5.86500	−0.192528
$929$	18.3643	0.602513	0.301257	−	0.953543i	$-0.402594\pi$
$929$	18.3643	0.602513	0.301257	+	0.953543i	$0.402594\pi$
$930$	−2.45329	−0.0804466
$931$	−6.58350	−0.215765
$932$	−9.23107	−0.302374
$933$	27.1800	0.889833
$934$	−36.9862	−1.21023
$935$	−1.16143	−0.0379829
$936$	−4.97381	−0.162574
$937$	34.2148	1.11775	0.558875	−	0.829252i	$-0.311233\pi$
$937$	34.2148	1.11775	0.558875	+	0.829252i	$0.311233\pi$
$938$	0.363371	0.0118645
$939$	−2.70528	−0.0882836
$940$	3.07905	0.100428
$941$	−59.3962	−1.93626	−0.968131	−	0.250444i	$-0.919424\pi$
$941$	−59.3962	−1.93626	−0.968131	+	0.250444i	$0.919424\pi$
$942$	−12.7212	−0.414480
$943$	−13.1476	−0.428145
$944$	−8.68320	−0.282614
$945$	−3.43691	−0.111803
$946$	−2.35745	−0.0766473
$947$	−30.4216	−0.988568	−0.494284	−	0.869300i	$-0.664570\pi$
$947$	−30.4216	−0.988568	−0.494284	+	0.869300i	$0.664570\pi$
$948$	10.3455	0.336006
$949$	−12.8559	−0.417320
$950$	3.87192	0.125622
$951$	6.24155	0.202396
$952$	1.98903	0.0644647
$953$	20.3952	0.660665	0.330332	−	0.943865i	$-0.392839\pi$
$953$	20.3952	0.660665	0.330332	+	0.943865i	$0.392839\pi$
$954$	−6.55874	−0.212347
$955$	5.65632	0.183034
$956$	3.46528	0.112075
$957$	2.09075	0.0675845
$958$	−6.08335	−0.196544
$959$	14.6970	0.474590
$960$	1.06712	0.0344410
$961$	−25.7146	−0.829504
$962$	−4.11470	−0.132663
$963$	−32.9825	−1.06285
$964$	5.53320	0.178212
$965$	−3.43455	−0.110562
$966$	−4.16158	−0.133897
$967$	4.41234	0.141891	0.0709457	−	0.997480i	$-0.477398\pi$
$967$	4.41234	0.141891	0.0709457	+	0.997480i	$0.477398\pi$
$968$	10.8741	0.349507
$969$	3.09652	0.0994747
$970$	15.5641	0.499733
$971$	−16.6320	−0.533745	−0.266872	−	0.963732i	$-0.585990\pi$
$971$	−16.6320	−0.533745	−0.266872	+	0.963732i	$0.585990\pi$
$972$	−15.9806	−0.512577
$973$	6.96834	0.223395
$974$	−32.5413	−1.04269
$975$	−9.72043	−0.311303
$976$	−3.05627	−0.0978288
$977$	−43.4115	−1.38886	−0.694429	−	0.719561i	$-0.744343\pi$
$977$	−43.4115	−1.38886	−0.694429	+	0.719561i	$0.744343\pi$
$978$	0.370047	0.0118328
$979$	3.15775	0.100922
$980$	6.99239	0.223364
$981$	−14.0051	−0.447149
$982$	−5.50001	−0.175512
$983$	−26.6736	−0.850756	−0.425378	−	0.905016i	$-0.639859\pi$
$983$	−26.6736	−0.850756	−0.425378	+	0.905016i	$0.639859\pi$
$984$	2.05817	0.0656122
$985$	3.42054	0.108987
$986$	18.0759	0.575655
$987$	1.87974	0.0598329
$988$	−2.49871	−0.0794947
$989$	42.6439	1.35600
$990$	0.750127	0.0238406
$991$	−59.0473	−1.87570	−0.937849	−	0.347044i	$-0.887185\pi$
$991$	−59.0473	−1.87570	−0.937849	+	0.347044i	$0.887185\pi$
$992$	−2.29899	−0.0729931
$993$	−23.6373	−0.750109
$994$	5.87306	0.186282
$995$	−7.87888	−0.249777
$996$	−2.18469	−0.0692246
$997$	42.1138	1.33376	0.666879	−	0.745166i	$-0.267630\pi$
$997$	42.1138	1.33376	0.666879	+	0.745166i	$0.267630\pi$
$998$	−6.16152	−0.195040
$999$	−8.25681	−0.261234

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.i.1.17	✓	43

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.i.1.17	✓	43	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00471 q^{3} +1.00000 q^{4} -1.06211 q^{5} +1.00471 q^{6} +0.645369 q^{7} -1.00000 q^{8} -1.99055 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00471 q^{3} +1.00000 q^{4} -1.06211 q^{5} +1.00471 q^{6} +0.645369 q^{7} -1.00000 q^{8} -1.99055 q^{9} +1.06211 q^{10} -0.354807 q^{11} -1.00471 q^{12} -2.49871 q^{13} -0.645369 q^{14} +1.06712 q^{15} +1.00000 q^{16} -3.08200 q^{17} +1.99055 q^{18} +1.00000 q^{19} -1.06211 q^{20} -0.648411 q^{21} +0.354807 q^{22} -6.41811 q^{23} +1.00471 q^{24} -3.87192 q^{25} +2.49871 q^{26} +5.01407 q^{27} +0.645369 q^{28} +5.86500 q^{29} -1.06712 q^{30} +2.29899 q^{31} -1.00000 q^{32} +0.356480 q^{33} +3.08200 q^{34} -0.685453 q^{35} -1.99055 q^{36} -1.64673 q^{37} -1.00000 q^{38} +2.51049 q^{39} +1.06211 q^{40} +2.04852 q^{41} +0.648411 q^{42} -6.64431 q^{43} -0.354807 q^{44} +2.11418 q^{45} +6.41811 q^{46} -2.89900 q^{47} -1.00471 q^{48} -6.58350 q^{49} +3.87192 q^{50} +3.09652 q^{51} -2.49871 q^{52} -3.29494 q^{53} -5.01407 q^{54} +0.376844 q^{55} -0.645369 q^{56} -1.00471 q^{57} -5.86500 q^{58} -8.68320 q^{59} +1.06712 q^{60} -3.05627 q^{61} -2.29899 q^{62} -1.28464 q^{63} +1.00000 q^{64} +2.65391 q^{65} -0.356480 q^{66} -0.563043 q^{67} -3.08200 q^{68} +6.44837 q^{69} +0.685453 q^{70} -9.10031 q^{71} +1.99055 q^{72} +5.14500 q^{73} +1.64673 q^{74} +3.89018 q^{75} +1.00000 q^{76} -0.228982 q^{77} -2.51049 q^{78} -10.2970 q^{79} -1.06211 q^{80} +0.933943 q^{81} -2.04852 q^{82} +2.17444 q^{83} -0.648411 q^{84} +3.27342 q^{85} +6.64431 q^{86} -5.89265 q^{87} +0.354807 q^{88} -8.89991 q^{89} -2.11418 q^{90} -1.61259 q^{91} -6.41811 q^{92} -2.30983 q^{93} +2.89900 q^{94} -1.06211 q^{95} +1.00471 q^{96} +14.6540 q^{97} +6.58350 q^{98} +0.706262 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 43 q - 43 q^{2} + 43 q^{4} + 19 q^{7} - 43 q^{8} + 53 q^{9}+O(q^{10}) \) 43 * q - 43 * q^2 + 43 * q^4 + 19 * q^7 - 43 * q^8 + 53 * q^9	\( 43 q - 43 q^{2} + 43 q^{4} + 19 q^{7} - 43 q^{8} + 53 q^{9} + 14 q^{11} + 3 q^{13} - 19 q^{14} + q^{15} + 43 q^{16} + 8 q^{17} - 53 q^{18} + 43 q^{19} - 14 q^{22} + 43 q^{23} + 97 q^{25} - 3 q^{26} + 15 q^{27} + 19 q^{28} - 25 q^{29} - q^{30} + 22 q^{31} - 43 q^{32} + 22 q^{33} - 8 q^{34} - 6 q^{35} + 53 q^{36} + 42 q^{37} - 43 q^{38} + 9 q^{39} - 40 q^{41} + 72 q^{43} + 14 q^{44} - q^{45} - 43 q^{46} + 27 q^{47} + 86 q^{49} - 97 q^{50} - 3 q^{51} + 3 q^{52} - 5 q^{53} - 15 q^{54} + 86 q^{55} - 19 q^{56} + 25 q^{58} - 43 q^{59} + q^{60} + 31 q^{61} - 22 q^{62} + 38 q^{63} + 43 q^{64} - 32 q^{65} - 22 q^{66} + 15 q^{67} + 8 q^{68} - 7 q^{69} + 6 q^{70} + 14 q^{71} - 53 q^{72} + 93 q^{73} - 42 q^{74} - 13 q^{75} + 43 q^{76} + 38 q^{77} - 9 q^{78} + 15 q^{79} + 43 q^{81} + 40 q^{82} + 34 q^{83} + 16 q^{85} - 72 q^{86} + 60 q^{87} - 14 q^{88} - 37 q^{89} + q^{90} - 3 q^{91} + 43 q^{92} + 19 q^{93} - 27 q^{94} + 27 q^{97} - 86 q^{98} - 24 q^{99}+O(q^{100}) \) 43 * q - 43 * q^2 + 43 * q^4 + 19 * q^7 - 43 * q^8 + 53 * q^9 + 14 * q^11 + 3 * q^13 - 19 * q^14 + q^15 + 43 * q^16 + 8 * q^17 - 53 * q^18 + 43 * q^19 - 14 * q^22 + 43 * q^23 + 97 * q^25 - 3 * q^26 + 15 * q^27 + 19 * q^28 - 25 * q^29 - q^30 + 22 * q^31 - 43 * q^32 + 22 * q^33 - 8 * q^34 - 6 * q^35 + 53 * q^36 + 42 * q^37 - 43 * q^38 + 9 * q^39 - 40 * q^41 + 72 * q^43 + 14 * q^44 - q^45 - 43 * q^46 + 27 * q^47 + 86 * q^49 - 97 * q^50 - 3 * q^51 + 3 * q^52 - 5 * q^53 - 15 * q^54 + 86 * q^55 - 19 * q^56 + 25 * q^58 - 43 * q^59 + q^60 + 31 * q^61 - 22 * q^62 + 38 * q^63 + 43 * q^64 - 32 * q^65 - 22 * q^66 + 15 * q^67 + 8 * q^68 - 7 * q^69 + 6 * q^70 + 14 * q^71 - 53 * q^72 + 93 * q^73 - 42 * q^74 - 13 * q^75 + 43 * q^76 + 38 * q^77 - 9 * q^78 + 15 * q^79 + 43 * q^81 + 40 * q^82 + 34 * q^83 + 16 * q^85 - 72 * q^86 + 60 * q^87 - 14 * q^88 - 37 * q^89 + q^90 - 3 * q^91 + 43 * q^92 + 19 * q^93 - 27 * q^94 + 27 * q^97 - 86 * q^98 - 24 * q^99

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