LMFDB - Embedded newform 8018.2.a.h.1.2

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:	$41$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.99911 q^{3} +1.00000 q^{4} +0.291646 q^{5} +2.99911 q^{6} -2.03701 q^{7} -1.00000 q^{8} +5.99467 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.99911 q^{3} +1.00000 q^{4} +0.291646 q^{5} +2.99911 q^{6} -2.03701 q^{7} -1.00000 q^{8} +5.99467 q^{9} -0.291646 q^{10} -3.90634 q^{11} -2.99911 q^{12} -1.34460 q^{13} +2.03701 q^{14} -0.874680 q^{15} +1.00000 q^{16} -3.03154 q^{17} -5.99467 q^{18} -1.00000 q^{19} +0.291646 q^{20} +6.10921 q^{21} +3.90634 q^{22} +5.41153 q^{23} +2.99911 q^{24} -4.91494 q^{25} +1.34460 q^{26} -8.98134 q^{27} -2.03701 q^{28} +1.23449 q^{29} +0.874680 q^{30} +5.75451 q^{31} -1.00000 q^{32} +11.7156 q^{33} +3.03154 q^{34} -0.594085 q^{35} +5.99467 q^{36} -3.72741 q^{37} +1.00000 q^{38} +4.03261 q^{39} -0.291646 q^{40} -11.9602 q^{41} -6.10921 q^{42} +2.22344 q^{43} -3.90634 q^{44} +1.74832 q^{45} -5.41153 q^{46} -3.25754 q^{47} -2.99911 q^{48} -2.85061 q^{49} +4.91494 q^{50} +9.09192 q^{51} -1.34460 q^{52} -0.676787 q^{53} +8.98134 q^{54} -1.13927 q^{55} +2.03701 q^{56} +2.99911 q^{57} -1.23449 q^{58} -9.79100 q^{59} -0.874680 q^{60} -14.3806 q^{61} -5.75451 q^{62} -12.2112 q^{63} +1.00000 q^{64} -0.392149 q^{65} -11.7156 q^{66} +7.21348 q^{67} -3.03154 q^{68} -16.2298 q^{69} +0.594085 q^{70} -8.70976 q^{71} -5.99467 q^{72} +3.63810 q^{73} +3.72741 q^{74} +14.7405 q^{75} -1.00000 q^{76} +7.95725 q^{77} -4.03261 q^{78} +11.4074 q^{79} +0.291646 q^{80} +8.95204 q^{81} +11.9602 q^{82} +2.81553 q^{83} +6.10921 q^{84} -0.884137 q^{85} -2.22344 q^{86} -3.70236 q^{87} +3.90634 q^{88} -3.00143 q^{89} -1.74832 q^{90} +2.73896 q^{91} +5.41153 q^{92} -17.2584 q^{93} +3.25754 q^{94} -0.291646 q^{95} +2.99911 q^{96} -15.6364 q^{97} +2.85061 q^{98} -23.4172 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 41 q - 41 q^{2} + 8 q^{3} + 41 q^{4} - 9 q^{5} - 8 q^{6} + 7 q^{7} - 41 q^{8} + 43 q^{9}+O(q^{10}) $ 41 * q - 41 * q^2 + 8 * q^3 + 41 * q^4 - 9 * q^5 - 8 * q^6 + 7 * q^7 - 41 * q^8 + 43 * q^9	\( 41 q - 41 q^{2} + 8 q^{3} + 41 q^{4} - 9 q^{5} - 8 q^{6} + 7 q^{7} - 41 q^{8} + 43 q^{9} + 9 q^{10} - 9 q^{11} + 8 q^{12} + 13 q^{13} - 7 q^{14} + 26 q^{15} + 41 q^{16} - 16 q^{17} - 43 q^{18} - 41 q^{19} - 9 q^{20} + 2 q^{21} + 9 q^{22} + 10 q^{23} - 8 q^{24} + 60 q^{25} - 13 q^{26} + 47 q^{27} + 7 q^{28} - 14 q^{29} - 26 q^{30} + 49 q^{31} - 41 q^{32} + 12 q^{33} + 16 q^{34} - 8 q^{35} + 43 q^{36} + 54 q^{37} + 41 q^{38} + 16 q^{39} + 9 q^{40} - 18 q^{41} - 2 q^{42} + 29 q^{43} - 9 q^{44} - 13 q^{45} - 10 q^{46} - 8 q^{47} + 8 q^{48} + 44 q^{49} - 60 q^{50} - 16 q^{51} + 13 q^{52} + 7 q^{53} - 47 q^{54} + 19 q^{55} - 7 q^{56} - 8 q^{57} + 14 q^{58} - 5 q^{59} + 26 q^{60} - 6 q^{61} - 49 q^{62} + 24 q^{63} + 41 q^{64} - 26 q^{65} - 12 q^{66} + 66 q^{67} - 16 q^{68} + 12 q^{69} + 8 q^{70} + 27 q^{71} - 43 q^{72} - q^{73} - 54 q^{74} + 62 q^{75} - 41 q^{76} - 8 q^{77} - 16 q^{78} + 87 q^{79} - 9 q^{80} + 73 q^{81} + 18 q^{82} - 41 q^{83} + 2 q^{84} + 14 q^{85} - 29 q^{86} + 35 q^{87} + 9 q^{88} - 4 q^{89} + 13 q^{90} + 39 q^{91} + 10 q^{92} + 17 q^{93} + 8 q^{94} + 9 q^{95} - 8 q^{96} + 64 q^{97} - 44 q^{98} + 40 q^{99}+O(q^{100}) \) 41 * q - 41 * q^2 + 8 * q^3 + 41 * q^4 - 9 * q^5 - 8 * q^6 + 7 * q^7 - 41 * q^8 + 43 * q^9 + 9 * q^10 - 9 * q^11 + 8 * q^12 + 13 * q^13 - 7 * q^14 + 26 * q^15 + 41 * q^16 - 16 * q^17 - 43 * q^18 - 41 * q^19 - 9 * q^20 + 2 * q^21 + 9 * q^22 + 10 * q^23 - 8 * q^24 + 60 * q^25 - 13 * q^26 + 47 * q^27 + 7 * q^28 - 14 * q^29 - 26 * q^30 + 49 * q^31 - 41 * q^32 + 12 * q^33 + 16 * q^34 - 8 * q^35 + 43 * q^36 + 54 * q^37 + 41 * q^38 + 16 * q^39 + 9 * q^40 - 18 * q^41 - 2 * q^42 + 29 * q^43 - 9 * q^44 - 13 * q^45 - 10 * q^46 - 8 * q^47 + 8 * q^48 + 44 * q^49 - 60 * q^50 - 16 * q^51 + 13 * q^52 + 7 * q^53 - 47 * q^54 + 19 * q^55 - 7 * q^56 - 8 * q^57 + 14 * q^58 - 5 * q^59 + 26 * q^60 - 6 * q^61 - 49 * q^62 + 24 * q^63 + 41 * q^64 - 26 * q^65 - 12 * q^66 + 66 * q^67 - 16 * q^68 + 12 * q^69 + 8 * q^70 + 27 * q^71 - 43 * q^72 - q^73 - 54 * q^74 + 62 * q^75 - 41 * q^76 - 8 * q^77 - 16 * q^78 + 87 * q^79 - 9 * q^80 + 73 * q^81 + 18 * q^82 - 41 * q^83 + 2 * q^84 + 14 * q^85 - 29 * q^86 + 35 * q^87 + 9 * q^88 - 4 * q^89 + 13 * q^90 + 39 * q^91 + 10 * q^92 + 17 * q^93 + 8 * q^94 + 9 * q^95 - 8 * q^96 + 64 * q^97 - 44 * q^98 + 40 * 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
$3$	−2.99911	−1.73154	−0.865769	−	0.500444i	$-0.833170\pi$
$3$	−2.99911	−1.73154	−0.865769	+	0.500444i	$0.833170\pi$
$4$	1.00000	0.500000
$5$	0.291646	0.130428	0.0652141	−	0.997871i	$-0.479227\pi$
$5$	0.291646	0.130428	0.0652141	+	0.997871i	$0.479227\pi$
$6$	2.99911	1.22438
$7$	−2.03701	−0.769916	−0.384958	−	0.922934i	$-0.625784\pi$
$7$	−2.03701	−0.769916	−0.384958	+	0.922934i	$0.625784\pi$
$8$	−1.00000	−0.353553
$9$	5.99467	1.99822
$10$	−0.291646	−0.0922267
$11$	−3.90634	−1.17781	−0.588903	−	0.808203i	$-0.700440\pi$
$11$	−3.90634	−1.17781	−0.588903	+	0.808203i	$0.700440\pi$
$12$	−2.99911	−0.865769
$13$	−1.34460	−0.372926	−0.186463	−	0.982462i	$-0.559702\pi$
$13$	−1.34460	−0.372926	−0.186463	+	0.982462i	$0.559702\pi$
$14$	2.03701	0.544413
$15$	−0.874680	−0.225841
$16$	1.00000	0.250000
$17$	−3.03154	−0.735256	−0.367628	−	0.929973i	$-0.619830\pi$
$17$	−3.03154	−0.735256	−0.367628	+	0.929973i	$0.619830\pi$
$18$	−5.99467	−1.41296
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	0.291646	0.0652141
$21$	6.10921	1.33314
$22$	3.90634	0.832835
$23$	5.41153	1.12838	0.564191	−	0.825644i	$-0.309188\pi$
$23$	5.41153	1.12838	0.564191	+	0.825644i	$0.309188\pi$
$24$	2.99911	0.612191
$25$	−4.91494	−0.982988
$26$	1.34460	0.263698
$27$	−8.98134	−1.72846
$28$	−2.03701	−0.384958
$29$	1.23449	0.229238	0.114619	−	0.993409i	$-0.463435\pi$
$29$	1.23449	0.229238	0.114619	+	0.993409i	$0.463435\pi$
$30$	0.874680	0.159694
$31$	5.75451	1.03354	0.516770	−	0.856124i	$-0.327134\pi$
$31$	5.75451	1.03354	0.516770	+	0.856124i	$0.327134\pi$
$32$	−1.00000	−0.176777
$33$	11.7156	2.03942
$34$	3.03154	0.519904
$35$	−0.594085	−0.100419
$36$	5.99467	0.999111
$37$	−3.72741	−0.612782	−0.306391	−	0.951906i	$-0.599121\pi$
$37$	−3.72741	−0.612782	−0.306391	+	0.951906i	$0.599121\pi$
$38$	1.00000	0.162221
$39$	4.03261	0.645735
$40$	−0.291646	−0.0461133
$41$	−11.9602	−1.86787	−0.933936	−	0.357442i	$-0.883649\pi$
$41$	−11.9602	−1.86787	−0.933936	+	0.357442i	$0.883649\pi$
$42$	−6.10921	−0.942671
$43$	2.22344	0.339071	0.169536	−	0.985524i	$-0.445773\pi$
$43$	2.22344	0.339071	0.169536	+	0.985524i	$0.445773\pi$
$44$	−3.90634	−0.588903
$45$	1.74832	0.260625
$46$	−5.41153	−0.797887
$47$	−3.25754	−0.475161	−0.237580	−	0.971368i	$-0.576354\pi$
$47$	−3.25754	−0.475161	−0.237580	+	0.971368i	$0.576354\pi$
$48$	−2.99911	−0.432884
$49$	−2.85061	−0.407229
$50$	4.91494	0.695078
$51$	9.09192	1.27312
$52$	−1.34460	−0.186463
$53$	−0.676787	−0.0929639	−0.0464819	−	0.998919i	$-0.514801\pi$
$53$	−0.676787	−0.0929639	−0.0464819	+	0.998919i	$0.514801\pi$
$54$	8.98134	1.22221
$55$	−1.13927	−0.153619
$56$	2.03701	0.272206
$57$	2.99911	0.397242
$58$	−1.23449	−0.162096
$59$	−9.79100	−1.27468	−0.637340	−	0.770583i	$-0.719965\pi$
$59$	−9.79100	−1.27468	−0.637340	+	0.770583i	$0.719965\pi$
$60$	−0.874680	−0.112921
$61$	−14.3806	−1.84125	−0.920624	−	0.390450i	$-0.872319\pi$
$61$	−14.3806	−1.84125	−0.920624	+	0.390450i	$0.872319\pi$
$62$	−5.75451	−0.730824
$63$	−12.2112	−1.53846
$64$	1.00000	0.125000
$65$	−0.392149	−0.0486401
$66$	−11.7156	−1.44209
$67$	7.21348	0.881267	0.440633	−	0.897687i	$-0.354754\pi$
$67$	7.21348	0.881267	0.440633	+	0.897687i	$0.354754\pi$
$68$	−3.03154	−0.367628
$69$	−16.2298	−1.95384
$70$	0.594085	0.0710068
$71$	−8.70976	−1.03366	−0.516829	−	0.856088i	$-0.672888\pi$
$71$	−8.70976	−1.03366	−0.516829	+	0.856088i	$0.672888\pi$
$72$	−5.99467	−0.706478
$73$	3.63810	0.425807	0.212904	−	0.977073i	$-0.431708\pi$
$73$	3.63810	0.425807	0.212904	+	0.977073i	$0.431708\pi$
$74$	3.72741	0.433302
$75$	14.7405	1.70208
$76$	−1.00000	−0.114708
$77$	7.95725	0.906812
$78$	−4.03261	−0.456604
$79$	11.4074	1.28343	0.641714	−	0.766944i	$-0.278224\pi$
$79$	11.4074	1.28343	0.641714	+	0.766944i	$0.278224\pi$
$80$	0.291646	0.0326071
$81$	8.95204	0.994671
$82$	11.9602	1.32078
$83$	2.81553	0.309044	0.154522	−	0.987989i	$-0.450616\pi$
$83$	2.81553	0.309044	0.154522	+	0.987989i	$0.450616\pi$
$84$	6.10921	0.666569
$85$	−0.884137	−0.0958981
$86$	−2.22344	−0.239760
$87$	−3.70236	−0.396935
$88$	3.90634	0.416418
$89$	−3.00143	−0.318151	−0.159075	−	0.987266i	$-0.550851\pi$
$89$	−3.00143	−0.318151	−0.159075	+	0.987266i	$0.550851\pi$
$90$	−1.74832	−0.184289
$91$	2.73896	0.287121
$92$	5.41153	0.564191
$93$	−17.2584	−1.78961
$94$	3.25754	0.335989
$95$	−0.291646	−0.0299223
$96$	2.99911	0.306095
$97$	−15.6364	−1.58764	−0.793818	−	0.608156i	$-0.791910\pi$
$97$	−15.6364	−1.58764	−0.793818	+	0.608156i	$0.791910\pi$
$98$	2.85061	0.287955
$99$	−23.4172	−2.35352
$100$	−4.91494	−0.491494
$101$	3.56090	0.354322	0.177161	−	0.984182i	$-0.443309\pi$
$101$	3.56090	0.354322	0.177161	+	0.984182i	$0.443309\pi$
$102$	−9.09192	−0.900234
$103$	5.25175	0.517470	0.258735	−	0.965948i	$-0.416694\pi$
$103$	5.25175	0.517470	0.258735	+	0.965948i	$0.416694\pi$
$104$	1.34460	0.131849
$105$	1.78173	0.173879
$106$	0.676787	0.0657354
$107$	11.3116	1.09354	0.546769	−	0.837284i	$-0.315858\pi$
$107$	11.3116	1.09354	0.546769	+	0.837284i	$0.315858\pi$
$108$	−8.98134	−0.864230
$109$	−8.37936	−0.802597	−0.401298	−	0.915947i	$-0.631441\pi$
$109$	−8.37936	−0.802597	−0.401298	+	0.915947i	$0.631441\pi$
$110$	1.13927	0.108625
$111$	11.1789	1.06105
$112$	−2.03701	−0.192479
$113$	17.3880	1.63573	0.817863	−	0.575413i	$-0.195159\pi$
$113$	17.3880	1.63573	0.817863	+	0.575413i	$0.195159\pi$
$114$	−2.99911	−0.280892
$115$	1.57825	0.147173
$116$	1.23449	0.114619
$117$	−8.06045	−0.745189
$118$	9.79100	0.901334
$119$	6.17526	0.566085
$120$	0.874680	0.0798470
$121$	4.25952	0.387229
$122$	14.3806	1.30196
$123$	35.8700	3.23429
$124$	5.75451	0.516770
$125$	−2.89166	−0.258638
$126$	12.2112	1.08786
$127$	13.7151	1.21702	0.608508	−	0.793548i	$-0.291768\pi$
$127$	13.7151	1.21702	0.608508	+	0.793548i	$0.291768\pi$
$128$	−1.00000	−0.0883883
$129$	−6.66834	−0.587114
$130$	0.392149	0.0343937
$131$	−17.7530	−1.55108	−0.775542	−	0.631295i	$-0.782524\pi$
$131$	−17.7530	−1.55108	−0.775542	+	0.631295i	$0.782524\pi$
$132$	11.7156	1.01971
$133$	2.03701	0.176631
$134$	−7.21348	−0.623150
$135$	−2.61938	−0.225440
$136$	3.03154	0.259952
$137$	−9.30784	−0.795222	−0.397611	−	0.917554i	$-0.630161\pi$
$137$	−9.30784	−0.795222	−0.397611	+	0.917554i	$0.630161\pi$
$138$	16.2298	1.38157
$139$	−12.4300	−1.05430	−0.527150	−	0.849772i	$-0.676739\pi$
$139$	−12.4300	−1.05430	−0.527150	+	0.849772i	$0.676739\pi$
$140$	−0.594085	−0.0502094
$141$	9.76972	0.822758
$142$	8.70976	0.730907
$143$	5.25248	0.439235
$144$	5.99467	0.499556
$145$	0.360034	0.0298992
$146$	−3.63810	−0.301091
$147$	8.54929	0.705133
$148$	−3.72741	−0.306391
$149$	4.02416	0.329672	0.164836	−	0.986321i	$-0.447291\pi$
$149$	4.02416	0.329672	0.164836	+	0.986321i	$0.447291\pi$
$150$	−14.7405	−1.20355
$151$	−21.9818	−1.78885	−0.894426	−	0.447216i	$-0.852416\pi$
$151$	−21.9818	−1.78885	−0.894426	+	0.447216i	$0.852416\pi$
$152$	1.00000	0.0811107
$153$	−18.1731	−1.46920
$154$	−7.95725	−0.641213
$155$	1.67828	0.134803
$156$	4.03261	0.322868
$157$	−6.66293	−0.531759	−0.265880	−	0.964006i	$-0.585662\pi$
$157$	−6.66293	−0.531759	−0.265880	+	0.964006i	$0.585662\pi$
$158$	−11.4074	−0.907521
$159$	2.02976	0.160970
$160$	−0.291646	−0.0230567
$161$	−11.0233	−0.868759
$162$	−8.95204	−0.703338
$163$	6.57510	0.515002	0.257501	−	0.966278i	$-0.417101\pi$
$163$	6.57510	0.515002	0.257501	+	0.966278i	$0.417101\pi$
$164$	−11.9602	−0.933936
$165$	3.41680	0.265998
$166$	−2.81553	−0.218527
$167$	−12.0302	−0.930927	−0.465463	−	0.885067i	$-0.654112\pi$
$167$	−12.0302	−0.930927	−0.465463	+	0.885067i	$0.654112\pi$
$168$	−6.10921	−0.471336
$169$	−11.1920	−0.860926
$170$	0.884137	0.0678102
$171$	−5.99467	−0.458424
$172$	2.22344	0.169536
$173$	−12.1414	−0.923096	−0.461548	−	0.887115i	$-0.652706\pi$
$173$	−12.1414	−0.923096	−0.461548	+	0.887115i	$0.652706\pi$
$174$	3.70236	0.280675
$175$	10.0118	0.756818
$176$	−3.90634	−0.294452
$177$	29.3643	2.20716
$178$	3.00143	0.224967
$179$	−13.3258	−0.996018	−0.498009	−	0.867172i	$-0.665935\pi$
$179$	−13.3258	−0.996018	−0.498009	+	0.867172i	$0.665935\pi$
$180$	1.74832	0.130312
$181$	−23.3705	−1.73712	−0.868559	−	0.495586i	$-0.834953\pi$
$181$	−23.3705	−1.73712	−0.868559	+	0.495586i	$0.834953\pi$
$182$	−2.73896	−0.203026
$183$	43.1290	3.18819
$184$	−5.41153	−0.398943
$185$	−1.08708	−0.0799240
$186$	17.2584	1.26545
$187$	11.8422	0.865989
$188$	−3.25754	−0.237580
$189$	18.2950	1.33077
$190$	0.291646	0.0211583
$191$	−6.15566	−0.445408	−0.222704	−	0.974886i	$-0.571488\pi$
$191$	−6.15566	−0.445408	−0.222704	+	0.974886i	$0.571488\pi$
$192$	−2.99911	−0.216442
$193$	−6.73334	−0.484676	−0.242338	−	0.970192i	$-0.577914\pi$
$193$	−6.73334	−0.484676	−0.242338	+	0.970192i	$0.577914\pi$
$194$	15.6364	1.12263
$195$	1.17610	0.0842221
$196$	−2.85061	−0.203615
$197$	−1.29675	−0.0923895	−0.0461947	−	0.998932i	$-0.514709\pi$
$197$	−1.29675	−0.0923895	−0.0461947	+	0.998932i	$0.514709\pi$
$198$	23.4172	1.66419
$199$	16.8224	1.19251	0.596256	−	0.802795i	$-0.296654\pi$
$199$	16.8224	1.19251	0.596256	+	0.802795i	$0.296654\pi$
$200$	4.91494	0.347539
$201$	−21.6340	−1.52595
$202$	−3.56090	−0.250544
$203$	−2.51466	−0.176494
$204$	9.09192	0.636561
$205$	−3.48815	−0.243623
$206$	−5.25175	−0.365907
$207$	32.4403	2.25476
$208$	−1.34460	−0.0932314
$209$	3.90634	0.270207
$210$	−1.78173	−0.122951
$211$	1.00000	0.0688428
$211$	1.00000	0.0688428
$212$	−0.676787	−0.0464819
$213$	26.1215	1.78982
$214$	−11.3116	−0.773248
$215$	0.648458	0.0442245
$216$	8.98134	0.611103
$217$	−11.7220	−0.795740
$218$	8.37936	0.567522
$219$	−10.9111	−0.737301
$220$	−1.13927	−0.0768096
$221$	4.07621	0.274196
$222$	−11.1789	−0.750279
$223$	3.96825	0.265734	0.132867	−	0.991134i	$-0.457582\pi$
$223$	3.96825	0.265734	0.132867	+	0.991134i	$0.457582\pi$
$224$	2.03701	0.136103
$225$	−29.4634	−1.96423
$226$	−17.3880	−1.15663
$227$	−21.2597	−1.41106	−0.705528	−	0.708682i	$-0.749290\pi$
$227$	−21.2597	−1.41106	−0.705528	+	0.708682i	$0.749290\pi$
$228$	2.99911	0.198621
$229$	−19.8579	−1.31224	−0.656122	−	0.754654i	$-0.727805\pi$
$229$	−19.8579	−1.31224	−0.656122	+	0.754654i	$0.727805\pi$
$230$	−1.57825	−0.104067
$231$	−23.8647	−1.57018
$232$	−1.23449	−0.0810480
$233$	−12.5170	−0.820014	−0.410007	−	0.912082i	$-0.634474\pi$
$233$	−12.5170	−0.820014	−0.410007	+	0.912082i	$0.634474\pi$
$234$	8.06045	0.526928
$235$	−0.950049	−0.0619744
$236$	−9.79100	−0.637340
$237$	−34.2119	−2.22230
$238$	−6.17526	−0.400283
$239$	−11.7648	−0.760999	−0.380499	−	0.924781i	$-0.624248\pi$
$239$	−11.7648	−0.760999	−0.380499	+	0.924781i	$0.624248\pi$
$240$	−0.874680	−0.0564603
$241$	25.0910	1.61625	0.808126	−	0.589010i	$-0.200482\pi$
$241$	25.0910	1.61625	0.808126	+	0.589010i	$0.200482\pi$
$242$	−4.25952	−0.273812
$243$	0.0958720	0.00615019
$244$	−14.3806	−0.920624
$245$	−0.831369	−0.0531142
$246$	−35.8700	−2.28699
$247$	1.34460	0.0855550
$248$	−5.75451	−0.365412
$249$	−8.44407	−0.535121
$250$	2.89166	0.182884
$251$	−6.03081	−0.380661	−0.190331	−	0.981720i	$-0.560956\pi$
$251$	−6.03081	−0.380661	−0.190331	+	0.981720i	$0.560956\pi$
$252$	−12.2112	−0.769232
$253$	−21.1393	−1.32902
$254$	−13.7151	−0.860560
$255$	2.65162	0.166051
$256$	1.00000	0.0625000
$257$	−28.1207	−1.75412	−0.877061	−	0.480379i	$-0.840499\pi$
$257$	−28.1207	−1.75412	−0.877061	+	0.480379i	$0.840499\pi$
$258$	6.66834	0.415153
$259$	7.59275	0.471790
$260$	−0.392149	−0.0243200
$261$	7.40034	0.458070
$262$	17.7530	1.09678
$263$	−15.7667	−0.972218	−0.486109	−	0.873898i	$-0.661584\pi$
$263$	−15.7667	−0.972218	−0.486109	+	0.873898i	$0.661584\pi$
$264$	−11.7156	−0.721043
$265$	−0.197383	−0.0121251
$266$	−2.03701	−0.124897
$267$	9.00161	0.550890
$268$	7.21348	0.440633
$269$	11.5162	0.702153	0.351076	−	0.936347i	$-0.385816\pi$
$269$	11.5162	0.702153	0.351076	+	0.936347i	$0.385816\pi$
$270$	2.61938	0.159410
$271$	−13.5163	−0.821055	−0.410527	−	0.911848i	$-0.634655\pi$
$271$	−13.5163	−0.821055	−0.410527	+	0.911848i	$0.634655\pi$
$272$	−3.03154	−0.183814
$273$	−8.21446	−0.497162
$274$	9.30784	0.562307
$275$	19.1995	1.15777
$276$	−16.2298	−0.976918
$277$	6.45108	0.387608	0.193804	−	0.981040i	$-0.437917\pi$
$277$	6.45108	0.387608	0.193804	+	0.981040i	$0.437917\pi$
$278$	12.4300	0.745502
$279$	34.4964	2.06524
$280$	0.594085	0.0355034
$281$	17.2627	1.02981	0.514903	−	0.857248i	$-0.327828\pi$
$281$	17.2627	1.02981	0.514903	+	0.857248i	$0.327828\pi$
$282$	−9.76972	−0.581778
$283$	19.9418	1.18541	0.592707	−	0.805418i	$-0.298059\pi$
$283$	19.9418	1.18541	0.592707	+	0.805418i	$0.298059\pi$
$284$	−8.70976	−0.516829
$285$	0.874680	0.0518116
$286$	−5.25248	−0.310586
$287$	24.3630	1.43810
$288$	−5.99467	−0.353239
$289$	−7.80978	−0.459399
$290$	−0.360034	−0.0211419
$291$	46.8953	2.74905
$292$	3.63810	0.212904
$293$	7.16239	0.418431	0.209216	−	0.977870i	$-0.432909\pi$
$293$	7.16239	0.418431	0.209216	+	0.977870i	$0.432909\pi$
$294$	−8.54929	−0.498604
$295$	−2.85551	−0.166254
$296$	3.72741	0.216651
$297$	35.0842	2.03579
$298$	−4.02416	−0.233113
$299$	−7.27636	−0.420803
$300$	14.7405	0.851041
$301$	−4.52916	−0.261056
$302$	21.9818	1.26491
$303$	−10.6795	−0.613523
$304$	−1.00000	−0.0573539
$305$	−4.19405	−0.240151
$306$	18.1731	1.03888
$307$	−20.8374	−1.18925	−0.594625	−	0.804003i	$-0.702700\pi$
$307$	−20.8374	−1.18925	−0.594625	+	0.804003i	$0.702700\pi$
$308$	7.95725	0.453406
$309$	−15.7506	−0.896019
$310$	−1.67828	−0.0953201
$311$	28.0527	1.59072	0.795360	−	0.606137i	$-0.207282\pi$
$311$	28.0527	1.59072	0.795360	+	0.606137i	$0.207282\pi$
$312$	−4.03261	−0.228302
$313$	3.19649	0.180676	0.0903382	−	0.995911i	$-0.471205\pi$
$313$	3.19649	0.180676	0.0903382	+	0.995911i	$0.471205\pi$
$314$	6.66293	0.376011
$315$	−3.56134	−0.200659
$316$	11.4074	0.641714
$317$	25.4403	1.42887	0.714435	−	0.699702i	$-0.246684\pi$
$317$	25.4403	1.42887	0.714435	+	0.699702i	$0.246684\pi$
$318$	−2.02976	−0.113823
$319$	−4.82233	−0.269999
$320$	0.291646	0.0163035
$321$	−33.9249	−1.89350
$322$	11.0233	0.614306
$323$	3.03154	0.168679
$324$	8.95204	0.497335
$325$	6.60865	0.366582
$326$	−6.57510	−0.364161
$327$	25.1306	1.38973
$328$	11.9602	0.660392
$329$	6.63562	0.365834
$330$	−3.41680	−0.188089
$331$	3.32624	0.182827	0.0914134	−	0.995813i	$-0.470862\pi$
$331$	3.32624	0.182827	0.0914134	+	0.995813i	$0.470862\pi$
$332$	2.81553	0.154522
$333$	−22.3446	−1.22447
$334$	12.0302	0.658265
$335$	2.10379	0.114942
$336$	6.10921	0.333285
$337$	0.928760	0.0505928	0.0252964	−	0.999680i	$-0.491947\pi$
$337$	0.928760	0.0505928	0.0252964	+	0.999680i	$0.491947\pi$
$338$	11.1920	0.608767
$339$	−52.1485	−2.83232
$340$	−0.884137	−0.0479491
$341$	−22.4791	−1.21731
$342$	5.99467	0.324154
$343$	20.0657	1.08345
$344$	−2.22344	−0.119880
$345$	−4.73336	−0.254835
$346$	12.1414	0.652728
$347$	−30.5770	−1.64146	−0.820730	−	0.571316i	$-0.806433\pi$
$347$	−30.5770	−1.64146	−0.820730	+	0.571316i	$0.806433\pi$
$348$	−3.70236	−0.198468
$349$	−19.1209	−1.02352	−0.511760	−	0.859128i	$-0.671006\pi$
$349$	−19.1209	−1.02352	−0.511760	+	0.859128i	$0.671006\pi$
$350$	−10.0118	−0.535151
$351$	12.0763	0.644587
$352$	3.90634	0.208209
$353$	20.5053	1.09139	0.545693	−	0.837985i	$-0.316266\pi$
$353$	20.5053	1.09139	0.545693	+	0.837985i	$0.316266\pi$
$354$	−29.3643	−1.56069
$355$	−2.54017	−0.134818
$356$	−3.00143	−0.159075
$357$	−18.5203	−0.980198
$358$	13.3258	0.704291
$359$	0.0573992	0.00302941	0.00151471	−	0.999999i	$-0.499518\pi$
$359$	0.0573992	0.00302941	0.00151471	+	0.999999i	$0.499518\pi$
$360$	−1.74832	−0.0921447
$361$	1.00000	0.0526316
$362$	23.3705	1.22833
$363$	−12.7748	−0.670502
$364$	2.73896	0.143561
$365$	1.06104	0.0555373
$366$	−43.1290	−2.25439
$367$	−11.8153	−0.616756	−0.308378	−	0.951264i	$-0.599786\pi$
$367$	−11.8153	−0.616756	−0.308378	+	0.951264i	$0.599786\pi$
$368$	5.41153	0.282096
$369$	−71.6975	−3.73242
$370$	1.08708	0.0565148
$371$	1.37862	0.0715744
$372$	−17.2584	−0.894807
$373$	34.1387	1.76764	0.883818	−	0.467831i	$-0.154965\pi$
$373$	34.1387	1.76764	0.883818	+	0.467831i	$0.154965\pi$
$374$	−11.8422	−0.612347
$375$	8.67240	0.447841
$376$	3.25754	0.167995
$377$	−1.65990	−0.0854889
$378$	−18.2950	−0.940996
$379$	19.7091	1.01239	0.506195	−	0.862419i	$-0.331052\pi$
$379$	19.7091	1.01239	0.506195	+	0.862419i	$0.331052\pi$
$380$	−0.291646	−0.0149611
$381$	−41.1330	−2.10731
$382$	6.15566	0.314951
$383$	20.2069	1.03252	0.516261	−	0.856431i	$-0.327323\pi$
$383$	20.2069	1.03252	0.516261	+	0.856431i	$0.327323\pi$
$384$	2.99911	0.153048
$385$	2.32070	0.118274
$386$	6.73334	0.342718
$387$	13.3288	0.677540
$388$	−15.6364	−0.793818
$389$	−7.92801	−0.401966	−0.200983	−	0.979595i	$-0.564414\pi$
$389$	−7.92801	−0.401966	−0.200983	+	0.979595i	$0.564414\pi$
$390$	−1.17610	−0.0595540
$391$	−16.4053	−0.829650
$392$	2.85061	0.143977
$393$	53.2432	2.68576
$394$	1.29675	0.0653292
$395$	3.32692	0.167395
$396$	−23.4172	−1.17676
$397$	−28.5063	−1.43069	−0.715345	−	0.698771i	$-0.753731\pi$
$397$	−28.5063	−1.43069	−0.715345	+	0.698771i	$0.753731\pi$
$398$	−16.8224	−0.843233
$399$	−6.10921	−0.305843
$400$	−4.91494	−0.245747
$401$	5.23457	0.261402	0.130701	−	0.991422i	$-0.458277\pi$
$401$	5.23457	0.261402	0.130701	+	0.991422i	$0.458277\pi$
$402$	21.6340	1.07901
$403$	−7.73753	−0.385434
$404$	3.56090	0.177161
$405$	2.61083	0.129733
$406$	2.51466	0.124800
$407$	14.5605	0.721738
$408$	−9.09192	−0.450117
$409$	37.5530	1.85688	0.928438	−	0.371487i	$-0.121152\pi$
$409$	37.5530	1.85688	0.928438	+	0.371487i	$0.121152\pi$
$410$	3.48815	0.172268
$411$	27.9152	1.37696
$412$	5.25175	0.258735
$413$	19.9443	0.981396
$414$	−32.4403	−1.59436
$415$	0.821138	0.0403081
$416$	1.34460	0.0659246
$417$	37.2790	1.82556
$418$	−3.90634	−0.191066
$419$	−8.63584	−0.421888	−0.210944	−	0.977498i	$-0.567654\pi$
$419$	−8.63584	−0.421888	−0.210944	+	0.977498i	$0.567654\pi$
$420$	1.78173	0.0869394
$421$	−34.9021	−1.70102	−0.850512	−	0.525955i	$-0.823708\pi$
$421$	−34.9021	−1.70102	−0.850512	+	0.525955i	$0.823708\pi$
$422$	−1.00000	−0.0486792
$423$	−19.5279	−0.949477
$424$	0.676787	0.0328677
$425$	14.8998	0.722748
$426$	−26.1215	−1.26559
$427$	29.2934	1.41761
$428$	11.3116	0.546769
$429$	−15.7528	−0.760551
$430$	−0.648458	−0.0312714
$431$	24.4036	1.17548	0.587741	−	0.809049i	$-0.300017\pi$
$431$	24.4036	1.17548	0.587741	+	0.809049i	$0.300017\pi$
$432$	−8.98134	−0.432115
$433$	40.7323	1.95747	0.978734	−	0.205133i	$-0.0657628\pi$
$433$	40.7323	1.95747	0.978734	+	0.205133i	$0.0657628\pi$
$434$	11.7220	0.562673
$435$	−1.07978	−0.0517715
$436$	−8.37936	−0.401298
$437$	−5.41153	−0.258869
$438$	10.9111	0.521351
$439$	23.2331	1.10886	0.554428	−	0.832232i	$-0.312937\pi$
$439$	23.2331	1.10886	0.554428	+	0.832232i	$0.312937\pi$
$440$	1.13927	0.0543126
$441$	−17.0884	−0.813735
$442$	−4.07621	−0.193886
$443$	10.1592	0.482678	0.241339	−	0.970441i	$-0.422413\pi$
$443$	10.1592	0.482678	0.241339	+	0.970441i	$0.422413\pi$
$444$	11.1789	0.530527
$445$	−0.875356	−0.0414958
$446$	−3.96825	−0.187902
$447$	−12.0689	−0.570839
$448$	−2.03701	−0.0962395
$449$	−35.3306	−1.66735	−0.833676	−	0.552253i	$-0.813768\pi$
$449$	−35.3306	−1.66735	−0.833676	+	0.552253i	$0.813768\pi$
$450$	29.4634	1.38892
$451$	46.7207	2.19999
$452$	17.3880	0.817863
$453$	65.9258	3.09747
$454$	21.2597	0.997767
$455$	0.798809	0.0374487
$456$	−2.99911	−0.140446
$457$	−11.1025	−0.519352	−0.259676	−	0.965696i	$-0.583616\pi$
$457$	−11.1025	−0.519352	−0.259676	+	0.965696i	$0.583616\pi$
$458$	19.8579	0.927897
$459$	27.2273	1.27086
$460$	1.57825	0.0735865
$461$	−29.6574	−1.38128	−0.690642	−	0.723197i	$-0.742672\pi$
$461$	−29.6574	−1.38128	−0.690642	+	0.723197i	$0.742672\pi$
$462$	23.8647	1.11028
$463$	1.03364	0.0480371	0.0240185	−	0.999712i	$-0.492354\pi$
$463$	1.03364	0.0480371	0.0240185	+	0.999712i	$0.492354\pi$
$464$	1.23449	0.0573096
$465$	−5.03336	−0.233416
$466$	12.5170	0.579838
$467$	12.1075	0.560269	0.280134	−	0.959961i	$-0.409621\pi$
$467$	12.1075	0.560269	0.280134	+	0.959961i	$0.409621\pi$
$468$	−8.06045	−0.372594
$469$	−14.6939	−0.678501
$470$	0.950049	0.0438225
$471$	19.9829	0.920761
$472$	9.79100	0.450667
$473$	−8.68551	−0.399360
$474$	34.2119	1.57141
$475$	4.91494	0.225513
$476$	6.17526	0.283043
$477$	−4.05711	−0.185763
$478$	11.7648	0.538107
$479$	−8.52230	−0.389394	−0.194697	−	0.980863i	$-0.562372\pi$
$479$	−8.52230	−0.389394	−0.194697	+	0.980863i	$0.562372\pi$
$480$	0.874680	0.0399235
$481$	5.01188	0.228522
$482$	−25.0910	−1.14286
$483$	33.0602	1.50429
$484$	4.25952	0.193615
$485$	−4.56030	−0.207073
$486$	−0.0958720	−0.00434884
$487$	−37.1844	−1.68499	−0.842493	−	0.538707i	$-0.818913\pi$
$487$	−37.1844	−1.68499	−0.842493	+	0.538707i	$0.818913\pi$
$488$	14.3806	0.650979
$489$	−19.7195	−0.891745
$490$	0.831369	0.0375574
$491$	−25.6239	−1.15639	−0.578195	−	0.815899i	$-0.696243\pi$
$491$	−25.6239	−1.15639	−0.578195	+	0.815899i	$0.696243\pi$
$492$	35.8700	1.61714
$493$	−3.74239	−0.168549
$494$	−1.34460	−0.0604966
$495$	−6.82955	−0.306965
$496$	5.75451	0.258385
$497$	17.7418	0.795830
$498$	8.44407	0.378388
$499$	8.55837	0.383125	0.191563	−	0.981480i	$-0.438644\pi$
$499$	8.55837	0.383125	0.191563	+	0.981480i	$0.438644\pi$
$500$	−2.89166	−0.129319
$501$	36.0800	1.61193
$502$	6.03081	0.269168
$503$	−17.3579	−0.773952	−0.386976	−	0.922090i	$-0.626480\pi$
$503$	−17.3579	−0.773952	−0.386976	+	0.922090i	$0.626480\pi$
$504$	12.2112	0.543929
$505$	1.03852	0.0462136
$506$	21.1393	0.939757
$507$	33.5662	1.49073
$508$	13.7151	0.608508
$509$	21.3720	0.947297	0.473648	−	0.880714i	$-0.342937\pi$
$509$	21.3720	0.947297	0.473648	+	0.880714i	$0.342937\pi$
$510$	−2.65162	−0.117416
$511$	−7.41083	−0.327836
$512$	−1.00000	−0.0441942
$513$	8.98134	0.396536
$514$	28.1207	1.24035
$515$	1.53165	0.0674927
$516$	−6.66834	−0.293557
$517$	12.7251	0.559647
$518$	−7.59275	−0.333606
$519$	36.4135	1.59838
$520$	0.392149	0.0171969
$521$	18.9657	0.830904	0.415452	−	0.909615i	$-0.363623\pi$
$521$	18.9657	0.830904	0.415452	+	0.909615i	$0.363623\pi$
$522$	−7.40034	−0.323904
$523$	25.4418	1.11249	0.556245	−	0.831018i	$-0.312241\pi$
$523$	25.4418	1.11249	0.556245	+	0.831018i	$0.312241\pi$
$524$	−17.7530	−0.775542
$525$	−30.0264	−1.31046
$526$	15.7667	0.687462
$527$	−17.4450	−0.759917
$528$	11.7156	0.509854
$529$	6.28467	0.273247
$530$	0.197383	0.00857375
$531$	−58.6938	−2.54709
$532$	2.03701	0.0883154
$533$	16.0817	0.696577
$534$	−9.00161	−0.389538
$535$	3.29900	0.142628
$536$	−7.21348	−0.311575
$537$	39.9656	1.72464
$538$	−11.5162	−0.496497
$539$	11.1354	0.479638
$540$	−2.61938	−0.112720
$541$	26.0697	1.12082	0.560412	−	0.828214i	$-0.310643\pi$
$541$	26.0697	1.12082	0.560412	+	0.828214i	$0.310643\pi$
$542$	13.5163	0.580573
$543$	70.0908	3.00788
$544$	3.03154	0.129976
$545$	−2.44381	−0.104681
$546$	8.21446	0.351546
$547$	18.0646	0.772385	0.386192	−	0.922418i	$-0.373790\pi$
$547$	18.0646	0.772385	0.386192	+	0.922418i	$0.373790\pi$
$548$	−9.30784	−0.397611
$549$	−86.2069	−3.67922
$550$	−19.1995	−0.818667
$551$	−1.23449	−0.0525909
$552$	16.2298	0.690785
$553$	−23.2369	−0.988132
$554$	−6.45108	−0.274080
$555$	3.26029	0.138391
$556$	−12.4300	−0.527150
$557$	−14.3636	−0.608604	−0.304302	−	0.952576i	$-0.598423\pi$
$557$	−14.3636	−0.608604	−0.304302	+	0.952576i	$0.598423\pi$
$558$	−34.4964	−1.46035
$559$	−2.98964	−0.126448
$560$	−0.594085	−0.0251047
$561$	−35.5161	−1.49949
$562$	−17.2627	−0.728183
$563$	26.1683	1.10286	0.551430	−	0.834221i	$-0.314082\pi$
$563$	26.1683	1.10286	0.551430	+	0.834221i	$0.314082\pi$
$564$	9.76972	0.411379
$565$	5.07115	0.213345
$566$	−19.9418	−0.838215
$567$	−18.2354	−0.765813
$568$	8.70976	0.365454
$569$	21.6657	0.908272	0.454136	−	0.890932i	$-0.349948\pi$
$569$	21.6657	0.908272	0.454136	+	0.890932i	$0.349948\pi$
$570$	−0.874680	−0.0366363
$571$	43.4265	1.81734	0.908672	−	0.417510i	$-0.137097\pi$
$571$	43.4265	1.81734	0.908672	+	0.417510i	$0.137097\pi$
$572$	5.25248	0.219617
$573$	18.4615	0.771241
$574$	−24.3630	−1.01689
$575$	−26.5974	−1.10919
$576$	5.99467	0.249778
$577$	38.5227	1.60372	0.801861	−	0.597510i	$-0.203843\pi$
$577$	38.5227	1.60372	0.801861	+	0.597510i	$0.203843\pi$
$578$	7.80978	0.324844
$579$	20.1940	0.839235
$580$	0.360034	0.0149496
$581$	−5.73524	−0.237938
$582$	−46.8953	−1.94387
$583$	2.64376	0.109494
$584$	−3.63810	−0.150546
$585$	−2.35080	−0.0971936
$586$	−7.16239	−0.295876
$587$	−29.8702	−1.23288	−0.616439	−	0.787403i	$-0.711425\pi$
$587$	−29.8702	−1.23288	−0.616439	+	0.787403i	$0.711425\pi$
$588$	8.54929	0.352567
$589$	−5.75451	−0.237111
$590$	2.85551	0.117559
$591$	3.88909	0.159976
$592$	−3.72741	−0.153195
$593$	−44.3993	−1.82326	−0.911630	−	0.411013i	$-0.865175\pi$
$593$	−44.3993	−1.82326	−0.911630	+	0.411013i	$0.865175\pi$
$594$	−35.0842	−1.43952
$595$	1.80099	0.0738335
$596$	4.02416	0.164836
$597$	−50.4524	−2.06488
$598$	7.27636	0.297553
$599$	27.0833	1.10660	0.553298	−	0.832984i	$-0.313369\pi$
$599$	27.0833	1.10660	0.553298	+	0.832984i	$0.313369\pi$
$600$	−14.7405	−0.601777
$601$	18.9116	0.771418	0.385709	−	0.922620i	$-0.373957\pi$
$601$	18.9116	0.771418	0.385709	+	0.922620i	$0.373957\pi$
$602$	4.52916	0.184595
$603$	43.2424	1.76097
$604$	−21.9818	−0.894426
$605$	1.24227	0.0505056
$606$	10.6795	0.433826
$607$	19.7467	0.801492	0.400746	−	0.916189i	$-0.368751\pi$
$607$	19.7467	0.801492	0.400746	+	0.916189i	$0.368751\pi$
$608$	1.00000	0.0405554
$609$	7.54174	0.305607
$610$	4.19405	0.169812
$611$	4.38009	0.177200
$612$	−18.1731	−0.734602
$613$	16.8115	0.679008	0.339504	−	0.940605i	$-0.389741\pi$
$613$	16.8115	0.679008	0.339504	+	0.940605i	$0.389741\pi$
$614$	20.8374	0.840927
$615$	10.4614	0.421843
$616$	−7.95725	−0.320607
$617$	39.7628	1.60079	0.800396	−	0.599472i	$-0.204623\pi$
$617$	39.7628	1.60079	0.800396	+	0.599472i	$0.204623\pi$
$618$	15.7506	0.633581
$619$	−32.4153	−1.30288	−0.651440	−	0.758700i	$-0.725835\pi$
$619$	−32.4153	−1.30288	−0.651440	+	0.758700i	$0.725835\pi$
$620$	1.67828	0.0674015
$621$	−48.6028	−1.95036
$622$	−28.0527	−1.12481
$623$	6.11393	0.244949
$624$	4.03261	0.161434
$625$	23.7314	0.949255
$626$	−3.19649	−0.127758
$627$	−11.7156	−0.467874
$628$	−6.66293	−0.265880
$629$	11.2998	0.450551
$630$	3.56134	0.141887
$631$	−10.0266	−0.399153	−0.199576	−	0.979882i	$-0.563957\pi$
$631$	−10.0266	−0.399153	−0.199576	+	0.979882i	$0.563957\pi$
$632$	−11.4074	−0.453760
$633$	−2.99911	−0.119204
$634$	−25.4403	−1.01036
$635$	3.99995	0.158733
$636$	2.02976	0.0804852
$637$	3.83293	0.151866
$638$	4.82233	0.190918
$639$	−52.2121	−2.06548
$640$	−0.291646	−0.0115283
$641$	36.9537	1.45958	0.729792	−	0.683669i	$-0.239617\pi$
$641$	36.9537	1.45958	0.729792	+	0.683669i	$0.239617\pi$
$642$	33.9249	1.33891
$643$	20.0730	0.791601	0.395801	−	0.918336i	$-0.370467\pi$
$643$	20.0730	0.791601	0.395801	+	0.918336i	$0.370467\pi$
$644$	−11.0233	−0.434380
$645$	−1.94480	−0.0765763
$646$	−3.03154	−0.119274
$647$	−15.5408	−0.610972	−0.305486	−	0.952197i	$-0.598819\pi$
$647$	−15.5408	−0.610972	−0.305486	+	0.952197i	$0.598819\pi$
$648$	−8.95204	−0.351669
$649$	38.2470	1.50133
$650$	−6.60865	−0.259212
$651$	35.1555	1.37785
$652$	6.57510	0.257501
$653$	−28.1212	−1.10047	−0.550234	−	0.835011i	$-0.685461\pi$
$653$	−28.1212	−1.10047	−0.550234	+	0.835011i	$0.685461\pi$
$654$	−25.1306	−0.982685
$655$	−5.17759	−0.202305
$656$	−11.9602	−0.466968
$657$	21.8092	0.850857
$658$	−6.63562	−0.258683
$659$	6.64716	0.258937	0.129468	−	0.991584i	$-0.458673\pi$
$659$	6.64716	0.258937	0.129468	+	0.991584i	$0.458673\pi$
$660$	3.41680	0.132999
$661$	12.3102	0.478812	0.239406	−	0.970919i	$-0.423047\pi$
$661$	12.3102	0.478812	0.239406	+	0.970919i	$0.423047\pi$
$662$	−3.32624	−0.129278
$663$	−12.2250	−0.474780
$664$	−2.81553	−0.109264
$665$	0.594085	0.0230376
$666$	22.3446	0.865834
$667$	6.68047	0.258669
$668$	−12.0302	−0.465463
$669$	−11.9012	−0.460128
$670$	−2.10379	−0.0812763
$671$	56.1756	2.16863
$672$	−6.10921	−0.235668
$673$	−33.5469	−1.29314	−0.646568	−	0.762856i	$-0.723796\pi$
$673$	−33.5469	−1.29314	−0.646568	+	0.762856i	$0.723796\pi$
$674$	−0.928760	−0.0357745
$675$	44.1428	1.69906
$676$	−11.1920	−0.430463
$677$	−10.1274	−0.389228	−0.194614	−	0.980880i	$-0.562345\pi$
$677$	−10.1274	−0.389228	−0.194614	+	0.980880i	$0.562345\pi$
$678$	52.1485	2.00275
$679$	31.8514	1.22235
$680$	0.884137	0.0339051
$681$	63.7602	2.44330
$682$	22.4791	0.860769
$683$	−44.3305	−1.69626	−0.848130	−	0.529789i	$-0.822271\pi$
$683$	−44.3305	−1.69626	−0.848130	+	0.529789i	$0.822271\pi$
$684$	−5.99467	−0.229212
$685$	−2.71460	−0.103719
$686$	−20.0657	−0.766114
$687$	59.5560	2.27220
$688$	2.22344	0.0847678
$689$	0.910010	0.0346686
$690$	4.73336	0.180196
$691$	42.9198	1.63275	0.816374	−	0.577524i	$-0.195981\pi$
$691$	42.9198	1.63275	0.816374	+	0.577524i	$0.195981\pi$
$692$	−12.1414	−0.461548
$693$	47.7010	1.81201
$694$	30.5770	1.16069
$695$	−3.62517	−0.137510
$696$	3.70236	0.140338
$697$	36.2578	1.37336
$698$	19.1209	0.723738
$699$	37.5398	1.41989
$700$	10.0118	0.378409
$701$	−35.7291	−1.34947	−0.674736	−	0.738060i	$-0.735742\pi$
$701$	−35.7291	−1.34947	−0.674736	+	0.738060i	$0.735742\pi$
$702$	−12.0763	−0.455792
$703$	3.72741	0.140582
$704$	−3.90634	−0.147226
$705$	2.84930	0.107311
$706$	−20.5053	−0.771727
$707$	−7.25357	−0.272798
$708$	29.3643	1.10358
$709$	−3.58160	−0.134510	−0.0672550	−	0.997736i	$-0.521424\pi$
$709$	−3.58160	−0.134510	−0.0672550	+	0.997736i	$0.521424\pi$
$710$	2.54017	0.0953309
$711$	68.3833	2.56457
$712$	3.00143	0.112483
$713$	31.1407	1.16623
$714$	18.5203	0.693104
$715$	1.53187	0.0572886
$716$	−13.3258	−0.498009
$717$	35.2838	1.31770
$718$	−0.0573992	−0.00214212
$719$	−27.8590	−1.03897	−0.519483	−	0.854481i	$-0.673876\pi$
$719$	−27.8590	−1.03897	−0.519483	+	0.854481i	$0.673876\pi$
$720$	1.74832	0.0651562
$721$	−10.6978	−0.398409
$722$	−1.00000	−0.0372161
$723$	−75.2506	−2.79860
$724$	−23.3705	−0.868559
$725$	−6.06743	−0.225339
$726$	12.7748	0.474116
$727$	7.49861	0.278108	0.139054	−	0.990285i	$-0.455594\pi$
$727$	7.49861	0.278108	0.139054	+	0.990285i	$0.455594\pi$
$728$	−2.73896	−0.101513
$729$	−27.1436	−1.00532
$730$	−1.06104	−0.0392708
$731$	−6.74044	−0.249304
$732$	43.1290	1.59409
$733$	1.23372	0.0455687	0.0227843	−	0.999740i	$-0.492747\pi$
$733$	1.23372	0.0455687	0.0227843	+	0.999740i	$0.492747\pi$
$734$	11.8153	0.436113
$735$	2.49337	0.0919693
$736$	−5.41153	−0.199472
$737$	−28.1783	−1.03796
$738$	71.6975	2.63922
$739$	3.32285	0.122233	0.0611164	−	0.998131i	$-0.480534\pi$
$739$	3.32285	0.122233	0.0611164	+	0.998131i	$0.480534\pi$
$740$	−1.08708	−0.0399620
$741$	−4.03261	−0.148142
$742$	−1.37862	−0.0506107
$743$	40.3966	1.48201	0.741004	−	0.671501i	$-0.234350\pi$
$743$	40.3966	1.48201	0.741004	+	0.671501i	$0.234350\pi$
$744$	17.2584	0.632724
$745$	1.17363	0.0429985
$746$	−34.1387	−1.24991
$747$	16.8781	0.617539
$748$	11.8422	0.432995
$749$	−23.0419	−0.841932
$750$	−8.67240	−0.316671
$751$	−21.9486	−0.800917	−0.400459	−	0.916315i	$-0.631149\pi$
$751$	−21.9486	−0.800917	−0.400459	+	0.916315i	$0.631149\pi$
$752$	−3.25754	−0.118790
$753$	18.0871	0.659129
$754$	1.65990	0.0604498
$755$	−6.41091	−0.233317
$756$	18.2950	0.665384
$757$	13.8964	0.505074	0.252537	−	0.967587i	$-0.418735\pi$
$757$	13.8964	0.505074	0.252537	+	0.967587i	$0.418735\pi$
$758$	−19.7091	−0.715867
$759$	63.3991	2.30124
$760$	0.291646	0.0105791
$761$	−13.4019	−0.485820	−0.242910	−	0.970049i	$-0.578102\pi$
$761$	−13.4019	−0.485820	−0.242910	+	0.970049i	$0.578102\pi$
$762$	41.1330	1.49009
$763$	17.0688	0.617932
$764$	−6.15566	−0.222704
$765$	−5.30011	−0.191626
$766$	−20.2069	−0.730103
$767$	13.1650	0.475361
$768$	−2.99911	−0.108221
$769$	16.2536	0.586120	0.293060	−	0.956094i	$-0.405326\pi$
$769$	16.2536	0.586120	0.293060	+	0.956094i	$0.405326\pi$
$770$	−2.32070	−0.0836323
$771$	84.3371	3.03733
$772$	−6.73334	−0.242338
$773$	2.34235	0.0842484	0.0421242	−	0.999112i	$-0.486587\pi$
$773$	2.34235	0.0842484	0.0421242	+	0.999112i	$0.486587\pi$
$774$	−13.3288	−0.479093
$775$	−28.2831	−1.01596
$776$	15.6364	0.561314
$777$	−22.7715	−0.816923
$778$	7.92801	0.284233
$779$	11.9602	0.428519
$780$	1.17610	0.0421110
$781$	34.0233	1.21745
$782$	16.4053	0.586651
$783$	−11.0873	−0.396230
$784$	−2.85061	−0.101807
$785$	−1.94322	−0.0693564
$786$	−53.2432	−1.89912
$787$	−13.5950	−0.484611	−0.242305	−	0.970200i	$-0.577904\pi$
$787$	−13.5950	−0.484611	−0.242305	+	0.970200i	$0.577904\pi$
$788$	−1.29675	−0.0461947
$789$	47.2862	1.68343
$790$	−3.32692	−0.118366
$791$	−35.4195	−1.25937
$792$	23.4172	0.832095
$793$	19.3362	0.686649
$794$	28.5063	1.01165
$795$	0.591972	0.0209951
$796$	16.8224	0.596256
$797$	12.1704	0.431099	0.215549	−	0.976493i	$-0.430846\pi$
$797$	12.1704	0.431099	0.215549	+	0.976493i	$0.430846\pi$
$798$	6.10921	0.216264
$799$	9.87534	0.349365
$800$	4.91494	0.173769
$801$	−17.9926	−0.635736
$802$	−5.23457	−0.184839
$803$	−14.2117	−0.501519
$804$	−21.6340	−0.762973
$805$	−3.21491	−0.113311
$806$	7.73753	0.272543
$807$	−34.5382	−1.21580
$808$	−3.56090	−0.125272
$809$	54.8779	1.92940	0.964702	−	0.263343i	$-0.0848250\pi$
$809$	54.8779	1.92940	0.964702	+	0.263343i	$0.0848250\pi$
$810$	−2.61083	−0.0917352
$811$	−0.158779	−0.00557549	−0.00278775	−	0.999996i	$-0.500887\pi$
$811$	−0.158779	−0.00557549	−0.00278775	+	0.999996i	$0.500887\pi$
$812$	−2.51466	−0.0882472
$813$	40.5368	1.42169
$814$	−14.5605	−0.510346
$815$	1.91761	0.0671708
$816$	9.09192	0.318281
$817$	−2.22344	−0.0777883
$818$	−37.5530	−1.31301
$819$	16.4192	0.573733
$820$	−3.48815	−0.121812
$821$	−29.7224	−1.03732	−0.518659	−	0.854981i	$-0.673568\pi$
$821$	−29.7224	−1.03732	−0.518659	+	0.854981i	$0.673568\pi$
$822$	−27.9152	−0.973656
$823$	−18.0720	−0.629951	−0.314975	−	0.949100i	$-0.601996\pi$
$823$	−18.0720	−0.629951	−0.314975	+	0.949100i	$0.601996\pi$
$824$	−5.25175	−0.182953
$825$	−57.5813	−2.00472
$826$	−19.9443	−0.693952
$827$	−9.26718	−0.322251	−0.161126	−	0.986934i	$-0.551512\pi$
$827$	−9.26718	−0.322251	−0.161126	+	0.986934i	$0.551512\pi$
$828$	32.4403	1.12738
$829$	32.9570	1.14464	0.572322	−	0.820029i	$-0.306043\pi$
$829$	32.9570	1.14464	0.572322	+	0.820029i	$0.306043\pi$
$830$	−0.821138	−0.0285021
$831$	−19.3475	−0.671157
$832$	−1.34460	−0.0466157
$833$	8.64172	0.299418
$834$	−37.2790	−1.29087
$835$	−3.50857	−0.121419
$836$	3.90634	0.135104
$837$	−51.6832	−1.78643
$838$	8.63584	0.298320
$839$	19.6164	0.677233	0.338616	−	0.940924i	$-0.390041\pi$
$839$	19.6164	0.677233	0.338616	+	0.940924i	$0.390041\pi$
$840$	−1.78173	−0.0614755
$841$	−27.4760	−0.947450
$842$	34.9021	1.20281
$843$	−51.7728	−1.78315
$844$	1.00000	0.0344214
$845$	−3.26412	−0.112289
$846$	19.5279	0.671381
$847$	−8.67667	−0.298134
$848$	−0.676787	−0.0232410
$849$	−59.8075	−2.05259
$850$	−14.8998	−0.511060
$851$	−20.1710	−0.691452
$852$	26.1215	0.894909
$853$	52.7086	1.80471	0.902354	−	0.430996i	$-0.141838\pi$
$853$	52.7086	1.80471	0.902354	+	0.430996i	$0.141838\pi$
$854$	−29.2934	−1.00240
$855$	−1.74832	−0.0597914
$856$	−11.3116	−0.386624
$857$	14.8623	0.507685	0.253843	−	0.967246i	$-0.418305\pi$
$857$	14.8623	0.507685	0.253843	+	0.967246i	$0.418305\pi$
$858$	15.7528	0.537791
$859$	26.8493	0.916086	0.458043	−	0.888930i	$-0.348551\pi$
$859$	26.8493	0.916086	0.458043	+	0.888930i	$0.348551\pi$
$860$	0.648458	0.0221122
$861$	−73.0674	−2.49013
$862$	−24.4036	−0.831191
$863$	−39.3941	−1.34099	−0.670496	−	0.741913i	$-0.733919\pi$
$863$	−39.3941	−1.34099	−0.670496	+	0.741913i	$0.733919\pi$
$864$	8.98134	0.305551
$865$	−3.54101	−0.120398
$866$	−40.7323	−1.38414
$867$	23.4224	0.795467
$868$	−11.7220	−0.397870
$869$	−44.5611	−1.51163
$870$	1.07978	0.0366080
$871$	−9.69927	−0.328647
$872$	8.37936	0.283761
$873$	−93.7350	−3.17245
$874$	5.41153	0.183048
$875$	5.89032	0.199129
$876$	−10.9111	−0.368651
$877$	−29.9467	−1.01123	−0.505614	−	0.862760i	$-0.668734\pi$
$877$	−29.9467	−1.01123	−0.505614	+	0.862760i	$0.668734\pi$
$878$	−23.2331	−0.784079
$879$	−21.4808	−0.724530
$880$	−1.13927	−0.0384048
$881$	44.1725	1.48821	0.744105	−	0.668063i	$-0.232876\pi$
$881$	44.1725	1.48821	0.744105	+	0.668063i	$0.232876\pi$
$882$	17.0884	0.575398
$883$	−41.4360	−1.39443	−0.697215	−	0.716862i	$-0.745578\pi$
$883$	−41.4360	−1.39443	−0.697215	+	0.716862i	$0.745578\pi$
$884$	4.07621	0.137098
$885$	8.56399	0.287875
$886$	−10.1592	−0.341305
$887$	−2.40488	−0.0807481	−0.0403740	−	0.999185i	$-0.512855\pi$
$887$	−2.40488	−0.0807481	−0.0403740	+	0.999185i	$0.512855\pi$
$888$	−11.1789	−0.375139
$889$	−27.9377	−0.936999
$890$	0.875356	0.0293420
$891$	−34.9697	−1.17153
$892$	3.96825	0.132867
$893$	3.25754	0.109009
$894$	12.0689	0.403644
$895$	−3.88642	−0.129909
$896$	2.03701	0.0680516
$897$	21.8226	0.728636
$898$	35.3306	1.17900
$899$	7.10387	0.236927
$900$	−29.4634	−0.982115
$901$	2.05171	0.0683522
$902$	−46.7207	−1.55563
$903$	13.5834	0.452029
$904$	−17.3880	−0.578316
$905$	−6.81593	−0.226569
$906$	−65.9258	−2.19024
$907$	14.8108	0.491785	0.245892	−	0.969297i	$-0.420919\pi$
$907$	14.8108	0.491785	0.245892	+	0.969297i	$0.420919\pi$
$908$	−21.2597	−0.705528
$909$	21.3464	0.708015
$910$	−0.798809	−0.0264803
$911$	38.9345	1.28996	0.644979	−	0.764201i	$-0.276866\pi$
$911$	38.9345	1.28996	0.644979	+	0.764201i	$0.276866\pi$
$912$	2.99911	0.0993105
$913$	−10.9984	−0.363994
$914$	11.1025	0.367237
$915$	12.5784	0.415830
$916$	−19.8579	−0.656122
$917$	36.1629	1.19421
$918$	−27.2273	−0.898634
$919$	10.0995	0.333152	0.166576	−	0.986029i	$-0.446729\pi$
$919$	10.0995	0.333152	0.166576	+	0.986029i	$0.446729\pi$
$920$	−1.57825	−0.0520335
$921$	62.4935	2.05923
$922$	29.6574	0.976715
$923$	11.7112	0.385478
$924$	−23.8647	−0.785090
$925$	18.3200	0.602357
$926$	−1.03364	−0.0339674
$927$	31.4825	1.03402
$928$	−1.23449	−0.0405240
$929$	15.8308	0.519392	0.259696	−	0.965690i	$-0.416378\pi$
$929$	15.8308	0.519392	0.259696	+	0.965690i	$0.416378\pi$
$930$	5.03336	0.165050
$931$	2.85061	0.0934249
$932$	−12.5170	−0.410007
$933$	−84.1331	−2.75439
$934$	−12.1075	−0.396170
$935$	3.45374	0.112949
$936$	8.06045	0.263464
$937$	0.525584	0.0171701	0.00858504	−	0.999963i	$-0.497267\pi$
$937$	0.525584	0.0171701	0.00858504	+	0.999963i	$0.497267\pi$
$938$	14.6939	0.479773
$939$	−9.58664	−0.312848
$940$	−0.950049	−0.0309872
$941$	−53.2981	−1.73747	−0.868734	−	0.495278i	$-0.835066\pi$
$941$	−53.2981	−1.73747	−0.868734	+	0.495278i	$0.835066\pi$
$942$	−19.9829	−0.651077
$943$	−64.7231	−2.10767
$944$	−9.79100	−0.318670
$945$	5.33568	0.173570
$946$	8.68551	0.282390
$947$	−6.31121	−0.205087	−0.102543	−	0.994729i	$-0.532698\pi$
$947$	−6.31121	−0.205087	−0.102543	+	0.994729i	$0.532698\pi$
$948$	−34.2119	−1.11115
$949$	−4.89180	−0.158794
$950$	−4.91494	−0.159462
$951$	−76.2983	−2.47414
$952$	−6.17526	−0.200141
$953$	−15.5036	−0.502210	−0.251105	−	0.967960i	$-0.580794\pi$
$953$	−15.5036	−0.502210	−0.251105	+	0.967960i	$0.580794\pi$
$954$	4.05711	0.131354
$955$	−1.79528	−0.0580938
$956$	−11.7648	−0.380499
$957$	14.4627	0.467513
$958$	8.52230	0.275343
$959$	18.9601	0.612254
$960$	−0.874680	−0.0282302
$961$	2.11441	0.0682067
$962$	−5.01188	−0.161590
$963$	67.8095	2.18513
$964$	25.0910	0.808126
$965$	−1.96375	−0.0632155
$966$	−33.0602	−1.06369
$967$	−4.89432	−0.157391	−0.0786953	−	0.996899i	$-0.525075\pi$
$967$	−4.89432	−0.157391	−0.0786953	+	0.996899i	$0.525075\pi$
$968$	−4.25952	−0.136906
$969$	−9.09192	−0.292074
$970$	4.56030	0.146422
$971$	38.8087	1.24543	0.622716	−	0.782448i	$-0.286029\pi$
$971$	38.8087	1.24543	0.622716	+	0.782448i	$0.286029\pi$
$972$	0.0958720	0.00307510
$973$	25.3200	0.811722
$974$	37.1844	1.19147
$975$	−19.8201	−0.634750
$976$	−14.3806	−0.460312
$977$	57.0987	1.82675	0.913375	−	0.407119i	$-0.133467\pi$
$977$	57.0987	1.82675	0.913375	+	0.407119i	$0.133467\pi$
$978$	19.7195	0.630559
$979$	11.7246	0.374720
$980$	−0.831369	−0.0265571
$981$	−50.2315	−1.60377
$982$	25.6239	0.817691
$983$	−29.7081	−0.947543	−0.473771	−	0.880648i	$-0.657108\pi$
$983$	−29.7081	−0.947543	−0.473771	+	0.880648i	$0.657108\pi$
$984$	−35.8700	−1.14349
$985$	−0.378192	−0.0120502
$986$	3.74239	0.119182
$987$	−19.9010	−0.633455
$988$	1.34460	0.0427775
$989$	12.0322	0.382602
$990$	6.82955	0.217057
$991$	29.8105	0.946962	0.473481	−	0.880804i	$-0.342997\pi$
$991$	29.8105	0.946962	0.473481	+	0.880804i	$0.342997\pi$
$992$	−5.75451	−0.182706
$993$	−9.97577	−0.316571
$994$	−17.7418	−0.562737
$995$	4.90621	0.155537
$996$	−8.44407	−0.267561
$997$	53.9801	1.70957	0.854783	−	0.518985i	$-0.173690\pi$
$997$	53.9801	1.70957	0.854783	+	0.518985i	$0.173690\pi$
$998$	−8.55837	−0.270910
$999$	33.4771	1.05917

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.h.1.2	✓	41

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.h.1.2	✓	41	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.99911 q^{3} +1.00000 q^{4} +0.291646 q^{5} +2.99911 q^{6} -2.03701 q^{7} -1.00000 q^{8} +5.99467 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.99911 q^{3} +1.00000 q^{4} +0.291646 q^{5} +2.99911 q^{6} -2.03701 q^{7} -1.00000 q^{8} +5.99467 q^{9} -0.291646 q^{10} -3.90634 q^{11} -2.99911 q^{12} -1.34460 q^{13} +2.03701 q^{14} -0.874680 q^{15} +1.00000 q^{16} -3.03154 q^{17} -5.99467 q^{18} -1.00000 q^{19} +0.291646 q^{20} +6.10921 q^{21} +3.90634 q^{22} +5.41153 q^{23} +2.99911 q^{24} -4.91494 q^{25} +1.34460 q^{26} -8.98134 q^{27} -2.03701 q^{28} +1.23449 q^{29} +0.874680 q^{30} +5.75451 q^{31} -1.00000 q^{32} +11.7156 q^{33} +3.03154 q^{34} -0.594085 q^{35} +5.99467 q^{36} -3.72741 q^{37} +1.00000 q^{38} +4.03261 q^{39} -0.291646 q^{40} -11.9602 q^{41} -6.10921 q^{42} +2.22344 q^{43} -3.90634 q^{44} +1.74832 q^{45} -5.41153 q^{46} -3.25754 q^{47} -2.99911 q^{48} -2.85061 q^{49} +4.91494 q^{50} +9.09192 q^{51} -1.34460 q^{52} -0.676787 q^{53} +8.98134 q^{54} -1.13927 q^{55} +2.03701 q^{56} +2.99911 q^{57} -1.23449 q^{58} -9.79100 q^{59} -0.874680 q^{60} -14.3806 q^{61} -5.75451 q^{62} -12.2112 q^{63} +1.00000 q^{64} -0.392149 q^{65} -11.7156 q^{66} +7.21348 q^{67} -3.03154 q^{68} -16.2298 q^{69} +0.594085 q^{70} -8.70976 q^{71} -5.99467 q^{72} +3.63810 q^{73} +3.72741 q^{74} +14.7405 q^{75} -1.00000 q^{76} +7.95725 q^{77} -4.03261 q^{78} +11.4074 q^{79} +0.291646 q^{80} +8.95204 q^{81} +11.9602 q^{82} +2.81553 q^{83} +6.10921 q^{84} -0.884137 q^{85} -2.22344 q^{86} -3.70236 q^{87} +3.90634 q^{88} -3.00143 q^{89} -1.74832 q^{90} +2.73896 q^{91} +5.41153 q^{92} -17.2584 q^{93} +3.25754 q^{94} -0.291646 q^{95} +2.99911 q^{96} -15.6364 q^{97} +2.85061 q^{98} -23.4172 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 41 q - 41 q^{2} + 8 q^{3} + 41 q^{4} - 9 q^{5} - 8 q^{6} + 7 q^{7} - 41 q^{8} + 43 q^{9}+O(q^{10}) \) 41 * q - 41 * q^2 + 8 * q^3 + 41 * q^4 - 9 * q^5 - 8 * q^6 + 7 * q^7 - 41 * q^8 + 43 * q^9	\( 41 q - 41 q^{2} + 8 q^{3} + 41 q^{4} - 9 q^{5} - 8 q^{6} + 7 q^{7} - 41 q^{8} + 43 q^{9} + 9 q^{10} - 9 q^{11} + 8 q^{12} + 13 q^{13} - 7 q^{14} + 26 q^{15} + 41 q^{16} - 16 q^{17} - 43 q^{18} - 41 q^{19} - 9 q^{20} + 2 q^{21} + 9 q^{22} + 10 q^{23} - 8 q^{24} + 60 q^{25} - 13 q^{26} + 47 q^{27} + 7 q^{28} - 14 q^{29} - 26 q^{30} + 49 q^{31} - 41 q^{32} + 12 q^{33} + 16 q^{34} - 8 q^{35} + 43 q^{36} + 54 q^{37} + 41 q^{38} + 16 q^{39} + 9 q^{40} - 18 q^{41} - 2 q^{42} + 29 q^{43} - 9 q^{44} - 13 q^{45} - 10 q^{46} - 8 q^{47} + 8 q^{48} + 44 q^{49} - 60 q^{50} - 16 q^{51} + 13 q^{52} + 7 q^{53} - 47 q^{54} + 19 q^{55} - 7 q^{56} - 8 q^{57} + 14 q^{58} - 5 q^{59} + 26 q^{60} - 6 q^{61} - 49 q^{62} + 24 q^{63} + 41 q^{64} - 26 q^{65} - 12 q^{66} + 66 q^{67} - 16 q^{68} + 12 q^{69} + 8 q^{70} + 27 q^{71} - 43 q^{72} - q^{73} - 54 q^{74} + 62 q^{75} - 41 q^{76} - 8 q^{77} - 16 q^{78} + 87 q^{79} - 9 q^{80} + 73 q^{81} + 18 q^{82} - 41 q^{83} + 2 q^{84} + 14 q^{85} - 29 q^{86} + 35 q^{87} + 9 q^{88} - 4 q^{89} + 13 q^{90} + 39 q^{91} + 10 q^{92} + 17 q^{93} + 8 q^{94} + 9 q^{95} - 8 q^{96} + 64 q^{97} - 44 q^{98} + 40 q^{99}+O(q^{100}) \) 41 * q - 41 * q^2 + 8 * q^3 + 41 * q^4 - 9 * q^5 - 8 * q^6 + 7 * q^7 - 41 * q^8 + 43 * q^9 + 9 * q^10 - 9 * q^11 + 8 * q^12 + 13 * q^13 - 7 * q^14 + 26 * q^15 + 41 * q^16 - 16 * q^17 - 43 * q^18 - 41 * q^19 - 9 * q^20 + 2 * q^21 + 9 * q^22 + 10 * q^23 - 8 * q^24 + 60 * q^25 - 13 * q^26 + 47 * q^27 + 7 * q^28 - 14 * q^29 - 26 * q^30 + 49 * q^31 - 41 * q^32 + 12 * q^33 + 16 * q^34 - 8 * q^35 + 43 * q^36 + 54 * q^37 + 41 * q^38 + 16 * q^39 + 9 * q^40 - 18 * q^41 - 2 * q^42 + 29 * q^43 - 9 * q^44 - 13 * q^45 - 10 * q^46 - 8 * q^47 + 8 * q^48 + 44 * q^49 - 60 * q^50 - 16 * q^51 + 13 * q^52 + 7 * q^53 - 47 * q^54 + 19 * q^55 - 7 * q^56 - 8 * q^57 + 14 * q^58 - 5 * q^59 + 26 * q^60 - 6 * q^61 - 49 * q^62 + 24 * q^63 + 41 * q^64 - 26 * q^65 - 12 * q^66 + 66 * q^67 - 16 * q^68 + 12 * q^69 + 8 * q^70 + 27 * q^71 - 43 * q^72 - q^73 - 54 * q^74 + 62 * q^75 - 41 * q^76 - 8 * q^77 - 16 * q^78 + 87 * q^79 - 9 * q^80 + 73 * q^81 + 18 * q^82 - 41 * q^83 + 2 * q^84 + 14 * q^85 - 29 * q^86 + 35 * q^87 + 9 * q^88 - 4 * q^89 + 13 * q^90 + 39 * q^91 + 10 * q^92 + 17 * q^93 + 8 * q^94 + 9 * q^95 - 8 * q^96 + 64 * q^97 - 44 * q^98 + 40 * q^99

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