LMFDB - Embedded newform 4730.2.a.v.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4730,2,Mod(1,4730)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4730, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4730.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4730 = 2 \cdot 5 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4730.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:	$37.7692401561$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.220036.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 5x^{3} + 11x^{2} - 2x - 1 $ x^5 - 2x^4 - 5x^3 + 11x^2 - 2x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.217250$ of defining polynomial
Character	$\chi$	$=$	4730.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.217250 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.217250 q^{6} -0.574201 q^{7} +1.00000 q^{8} -2.95280 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.217250 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.217250 q^{6} -0.574201 q^{7} +1.00000 q^{8} -2.95280 q^{9} -1.00000 q^{10} +1.00000 q^{11} -0.217250 q^{12} +0.293244 q^{13} -0.574201 q^{14} +0.217250 q^{15} +1.00000 q^{16} -3.05078 q^{17} -2.95280 q^{18} +7.65701 q^{19} -1.00000 q^{20} +0.124745 q^{21} +1.00000 q^{22} -1.42425 q^{23} -0.217250 q^{24} +1.00000 q^{25} +0.293244 q^{26} +1.29324 q^{27} -0.574201 q^{28} -2.90750 q^{29} +0.217250 q^{30} -7.89469 q^{31} +1.00000 q^{32} -0.217250 q^{33} -3.05078 q^{34} +0.574201 q^{35} -2.95280 q^{36} +3.05948 q^{37} +7.65701 q^{38} -0.0637073 q^{39} -1.00000 q^{40} +0.956727 q^{41} +0.124745 q^{42} -1.00000 q^{43} +1.00000 q^{44} +2.95280 q^{45} -1.42425 q^{46} -0.211773 q^{47} -0.217250 q^{48} -6.67029 q^{49} +1.00000 q^{50} +0.662782 q^{51} +0.293244 q^{52} +1.64627 q^{53} +1.29324 q^{54} -1.00000 q^{55} -0.574201 q^{56} -1.66348 q^{57} -2.90750 q^{58} +1.84938 q^{59} +0.217250 q^{60} -6.14651 q^{61} -7.89469 q^{62} +1.69550 q^{63} +1.00000 q^{64} -0.293244 q^{65} -0.217250 q^{66} -16.1351 q^{67} -3.05078 q^{68} +0.309417 q^{69} +0.574201 q^{70} -3.35136 q^{71} -2.95280 q^{72} +2.43139 q^{73} +3.05948 q^{74} -0.217250 q^{75} +7.65701 q^{76} -0.574201 q^{77} -0.0637073 q^{78} -11.5086 q^{79} -1.00000 q^{80} +8.57745 q^{81} +0.956727 q^{82} -15.2765 q^{83} +0.124745 q^{84} +3.05078 q^{85} -1.00000 q^{86} +0.631652 q^{87} +1.00000 q^{88} -0.829948 q^{89} +2.95280 q^{90} -0.168381 q^{91} -1.42425 q^{92} +1.71512 q^{93} -0.211773 q^{94} -7.65701 q^{95} -0.217250 q^{96} +15.1085 q^{97} -6.67029 q^{98} -2.95280 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 5 q^{2} + 2 q^{3} + 5 q^{4} - 5 q^{5} + 2 q^{6} - 6 q^{7} + 5 q^{8} - q^{9}+O(q^{10}) $ 5 * q + 5 * q^2 + 2 * q^3 + 5 * q^4 - 5 * q^5 + 2 * q^6 - 6 * q^7 + 5 * q^8 - q^9	\( 5 q + 5 q^{2} + 2 q^{3} + 5 q^{4} - 5 q^{5} + 2 q^{6} - 6 q^{7} + 5 q^{8} - q^{9} - 5 q^{10} + 5 q^{11} + 2 q^{12} - 12 q^{13} - 6 q^{14} - 2 q^{15} + 5 q^{16} - 2 q^{17} - q^{18} - 4 q^{19} - 5 q^{20} + 2 q^{21} + 5 q^{22} - 6 q^{23} + 2 q^{24} + 5 q^{25} - 12 q^{26} - 7 q^{27} - 6 q^{28} - 19 q^{29} - 2 q^{30} - 7 q^{31} + 5 q^{32} + 2 q^{33} - 2 q^{34} + 6 q^{35} - q^{36} - q^{37} - 4 q^{38} - 20 q^{39} - 5 q^{40} - 2 q^{41} + 2 q^{42} - 5 q^{43} + 5 q^{44} + q^{45} - 6 q^{46} + 7 q^{47} + 2 q^{48} - 5 q^{49} + 5 q^{50} - 5 q^{51} - 12 q^{52} - 6 q^{53} - 7 q^{54} - 5 q^{55} - 6 q^{56} - 15 q^{57} - 19 q^{58} - 5 q^{59} - 2 q^{60} - 5 q^{61} - 7 q^{62} - 17 q^{63} + 5 q^{64} + 12 q^{65} + 2 q^{66} - 20 q^{67} - 2 q^{68} - 40 q^{69} + 6 q^{70} - 22 q^{71} - q^{72} + 10 q^{73} - q^{74} + 2 q^{75} - 4 q^{76} - 6 q^{77} - 20 q^{78} - 9 q^{79} - 5 q^{80} - 15 q^{81} - 2 q^{82} - 19 q^{83} + 2 q^{84} + 2 q^{85} - 5 q^{86} + 15 q^{87} + 5 q^{88} - 21 q^{89} + q^{90} + 10 q^{91} - 6 q^{92} - 15 q^{93} + 7 q^{94} + 4 q^{95} + 2 q^{96} + 10 q^{97} - 5 q^{98} - q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 + 2 * q^3 + 5 * q^4 - 5 * q^5 + 2 * q^6 - 6 * q^7 + 5 * q^8 - q^9 - 5 * q^10 + 5 * q^11 + 2 * q^12 - 12 * q^13 - 6 * q^14 - 2 * q^15 + 5 * q^16 - 2 * q^17 - q^18 - 4 * q^19 - 5 * q^20 + 2 * q^21 + 5 * q^22 - 6 * q^23 + 2 * q^24 + 5 * q^25 - 12 * q^26 - 7 * q^27 - 6 * q^28 - 19 * q^29 - 2 * q^30 - 7 * q^31 + 5 * q^32 + 2 * q^33 - 2 * q^34 + 6 * q^35 - q^36 - q^37 - 4 * q^38 - 20 * q^39 - 5 * q^40 - 2 * q^41 + 2 * q^42 - 5 * q^43 + 5 * q^44 + q^45 - 6 * q^46 + 7 * q^47 + 2 * q^48 - 5 * q^49 + 5 * q^50 - 5 * q^51 - 12 * q^52 - 6 * q^53 - 7 * q^54 - 5 * q^55 - 6 * q^56 - 15 * q^57 - 19 * q^58 - 5 * q^59 - 2 * q^60 - 5 * q^61 - 7 * q^62 - 17 * q^63 + 5 * q^64 + 12 * q^65 + 2 * q^66 - 20 * q^67 - 2 * q^68 - 40 * q^69 + 6 * q^70 - 22 * q^71 - q^72 + 10 * q^73 - q^74 + 2 * q^75 - 4 * q^76 - 6 * q^77 - 20 * q^78 - 9 * q^79 - 5 * q^80 - 15 * q^81 - 2 * q^82 - 19 * q^83 + 2 * q^84 + 2 * q^85 - 5 * q^86 + 15 * q^87 + 5 * q^88 - 21 * q^89 + q^90 + 10 * q^91 - 6 * q^92 - 15 * q^93 + 7 * q^94 + 4 * q^95 + 2 * q^96 + 10 * q^97 - 5 * q^98 - 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
$3$	−0.217250	−0.125429	−0.0627146	−	0.998032i	$-0.519976\pi$
$3$	−0.217250	−0.125429	−0.0627146	+	0.998032i	$0.519976\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.217250	−0.0886918
$7$	−0.574201	−0.217028	−0.108514	−	0.994095i	$-0.534609\pi$
$7$	−0.574201	−0.217028	−0.108514	+	0.994095i	$0.534609\pi$
$8$	1.00000	0.353553
$9$	−2.95280	−0.984268
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.217250	−0.0627146
$13$	0.293244	0.0813314	0.0406657	−	0.999173i	$-0.487052\pi$
$13$	0.293244	0.0813314	0.0406657	+	0.999173i	$0.487052\pi$
$14$	−0.574201	−0.153462
$15$	0.217250	0.0560936
$16$	1.00000	0.250000
$17$	−3.05078	−0.739924	−0.369962	−	0.929047i	$-0.620629\pi$
$17$	−3.05078	−0.739924	−0.369962	+	0.929047i	$0.620629\pi$
$18$	−2.95280	−0.695982
$19$	7.65701	1.75664	0.878319	−	0.478075i	$-0.158665\pi$
$19$	7.65701	1.75664	0.878319	+	0.478075i	$0.158665\pi$
$20$	−1.00000	−0.223607
$21$	0.124745	0.0272216
$22$	1.00000	0.213201
$23$	−1.42425	−0.296976	−0.148488	−	0.988914i	$-0.547441\pi$
$23$	−1.42425	−0.296976	−0.148488	+	0.988914i	$0.547441\pi$
$24$	−0.217250	−0.0443459
$25$	1.00000	0.200000
$26$	0.293244	0.0575100
$27$	1.29324	0.248885
$28$	−0.574201	−0.108514
$29$	−2.90750	−0.539908	−0.269954	−	0.962873i	$-0.587009\pi$
$29$	−2.90750	−0.539908	−0.269954	+	0.962873i	$0.587009\pi$
$30$	0.217250	0.0396642
$31$	−7.89469	−1.41793	−0.708964	−	0.705245i	$-0.750837\pi$
$31$	−7.89469	−1.41793	−0.708964	+	0.705245i	$0.750837\pi$
$32$	1.00000	0.176777
$33$	−0.217250	−0.0378183
$34$	−3.05078	−0.523205
$35$	0.574201	0.0970577
$36$	−2.95280	−0.492134
$37$	3.05948	0.502976	0.251488	−	0.967860i	$-0.419080\pi$
$37$	3.05948	0.502976	0.251488	+	0.967860i	$0.419080\pi$
$38$	7.65701	1.24213
$39$	−0.0637073	−0.0102013
$40$	−1.00000	−0.158114
$41$	0.956727	0.149416	0.0747078	−	0.997205i	$-0.476198\pi$
$41$	0.956727	0.149416	0.0747078	+	0.997205i	$0.476198\pi$
$42$	0.124745	0.0192486
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	1.00000	0.150756
$45$	2.95280	0.440178
$46$	−1.42425	−0.209994
$47$	−0.211773	−0.0308902	−0.0154451	−	0.999881i	$-0.504917\pi$
$47$	−0.211773	−0.0308902	−0.0154451	+	0.999881i	$0.504917\pi$
$48$	−0.217250	−0.0313573
$49$	−6.67029	−0.952899
$50$	1.00000	0.141421
$51$	0.662782	0.0928080
$52$	0.293244	0.0406657
$53$	1.64627	0.226133	0.113066	−	0.993587i	$-0.463933\pi$
$53$	1.64627	0.226133	0.113066	+	0.993587i	$0.463933\pi$
$54$	1.29324	0.175988
$55$	−1.00000	−0.134840
$56$	−0.574201	−0.0767309
$57$	−1.66348	−0.220334
$58$	−2.90750	−0.381773
$59$	1.84938	0.240769	0.120385	−	0.992727i	$-0.461587\pi$
$59$	1.84938	0.240769	0.120385	+	0.992727i	$0.461587\pi$
$60$	0.217250	0.0280468
$61$	−6.14651	−0.786980	−0.393490	−	0.919329i	$-0.628732\pi$
$61$	−6.14651	−0.786980	−0.393490	+	0.919329i	$0.628732\pi$
$62$	−7.89469	−1.00263
$63$	1.69550	0.213613
$64$	1.00000	0.125000
$65$	−0.293244	−0.0363725
$66$	−0.217250	−0.0267416
$67$	−16.1351	−1.97122	−0.985611	−	0.169031i	$-0.945936\pi$
$67$	−16.1351	−1.97122	−0.985611	+	0.169031i	$0.945936\pi$
$68$	−3.05078	−0.369962
$69$	0.309417	0.0372494
$70$	0.574201	0.0686302
$71$	−3.35136	−0.397733	−0.198866	−	0.980027i	$-0.563726\pi$
$71$	−3.35136	−0.397733	−0.198866	+	0.980027i	$0.563726\pi$
$72$	−2.95280	−0.347991
$73$	2.43139	0.284573	0.142287	−	0.989826i	$-0.454555\pi$
$73$	2.43139	0.284573	0.142287	+	0.989826i	$0.454555\pi$
$74$	3.05948	0.355658
$75$	−0.217250	−0.0250858
$76$	7.65701	0.878319
$77$	−0.574201	−0.0654363
$78$	−0.0637073	−0.00721343
$79$	−11.5086	−1.29482	−0.647410	−	0.762142i	$-0.724148\pi$
$79$	−11.5086	−1.29482	−0.647410	+	0.762142i	$0.724148\pi$
$80$	−1.00000	−0.111803
$81$	8.57745	0.953050
$82$	0.956727	0.105653
$83$	−15.2765	−1.67682	−0.838408	−	0.545044i	$-0.816513\pi$
$83$	−15.2765	−1.67682	−0.838408	+	0.545044i	$0.816513\pi$
$84$	0.124745	0.0136108
$85$	3.05078	0.330904
$86$	−1.00000	−0.107833
$87$	0.631652	0.0677202
$88$	1.00000	0.106600
$89$	−0.829948	−0.0879743	−0.0439871	−	0.999032i	$-0.514006\pi$
$89$	−0.829948	−0.0879743	−0.0439871	+	0.999032i	$0.514006\pi$
$90$	2.95280	0.311253
$91$	−0.168381	−0.0176512
$92$	−1.42425	−0.148488
$93$	1.71512	0.177850
$94$	−0.211773	−0.0218427
$95$	−7.65701	−0.785592
$96$	−0.217250	−0.0221730
$97$	15.1085	1.53404	0.767018	−	0.641626i	$-0.221740\pi$
$97$	15.1085	1.53404	0.767018	+	0.641626i	$0.221740\pi$
$98$	−6.67029	−0.673801
$99$	−2.95280	−0.296768
$100$	1.00000	0.100000
$101$	−2.77898	−0.276519	−0.138260	−	0.990396i	$-0.544151\pi$
$101$	−2.77898	−0.276519	−0.138260	+	0.990396i	$0.544151\pi$
$102$	0.662782	0.0656252
$103$	−12.7766	−1.25892	−0.629460	−	0.777033i	$-0.716724\pi$
$103$	−12.7766	−1.25892	−0.629460	+	0.777033i	$0.716724\pi$
$104$	0.293244	0.0287550
$105$	−0.124745	−0.0121739
$106$	1.64627	0.159900
$107$	4.76302	0.460458	0.230229	−	0.973136i	$-0.426052\pi$
$107$	4.76302	0.460458	0.230229	+	0.973136i	$0.426052\pi$
$108$	1.29324	0.124443
$109$	−11.4665	−1.09829	−0.549147	−	0.835726i	$-0.685047\pi$
$109$	−11.4665	−1.09829	−0.549147	+	0.835726i	$0.685047\pi$
$110$	−1.00000	−0.0953463
$111$	−0.664672	−0.0630879
$112$	−0.574201	−0.0542569
$113$	2.42224	0.227865	0.113932	−	0.993488i	$-0.463655\pi$
$113$	2.42224	0.227865	0.113932	+	0.993488i	$0.463655\pi$
$114$	−1.66348	−0.155799
$115$	1.42425	0.132812
$116$	−2.90750	−0.269954
$117$	−0.865893	−0.0800518
$118$	1.84938	0.170250
$119$	1.75176	0.160584
$120$	0.217250	0.0198321
$121$	1.00000	0.0909091
$122$	−6.14651	−0.556479
$123$	−0.207849	−0.0187411
$124$	−7.89469	−0.708964
$125$	−1.00000	−0.0894427
$126$	1.69550	0.151047
$127$	4.22643	0.375035	0.187518	−	0.982261i	$-0.439956\pi$
$127$	4.22643	0.375035	0.187518	+	0.982261i	$0.439956\pi$
$128$	1.00000	0.0883883
$129$	0.217250	0.0191278
$130$	−0.293244	−0.0257192
$131$	−13.4541	−1.17549	−0.587744	−	0.809047i	$-0.699984\pi$
$131$	−13.4541	−1.17549	−0.587744	+	0.809047i	$0.699984\pi$
$132$	−0.217250	−0.0189092
$133$	−4.39666	−0.381239
$134$	−16.1351	−1.39386
$135$	−1.29324	−0.111305
$136$	−3.05078	−0.261603
$137$	9.79482	0.836828	0.418414	−	0.908256i	$-0.362586\pi$
$137$	9.79482	0.836828	0.418414	+	0.908256i	$0.362586\pi$
$138$	0.309417	0.0263393
$139$	−12.6027	−1.06894	−0.534472	−	0.845186i	$-0.679489\pi$
$139$	−12.6027	−1.06894	−0.534472	+	0.845186i	$0.679489\pi$
$140$	0.574201	0.0485289
$141$	0.0460075	0.00387453
$142$	−3.35136	−0.281240
$143$	0.293244	0.0245223
$144$	−2.95280	−0.246067
$145$	2.90750	0.241454
$146$	2.43139	0.201224
$147$	1.44912	0.119521
$148$	3.05948	0.251488
$149$	−17.7630	−1.45520	−0.727600	−	0.686001i	$-0.759364\pi$
$149$	−17.7630	−1.45520	−0.727600	+	0.686001i	$0.759364\pi$
$150$	−0.217250	−0.0177384
$151$	−2.27707	−0.185305	−0.0926527	−	0.995698i	$-0.529535\pi$
$151$	−2.27707	−0.185305	−0.0926527	+	0.995698i	$0.529535\pi$
$152$	7.65701	0.621065
$153$	9.00836	0.728283
$154$	−0.574201	−0.0462705
$155$	7.89469	0.634117
$156$	−0.0637073	−0.00510066
$157$	−16.3592	−1.30561	−0.652803	−	0.757528i	$-0.726407\pi$
$157$	−16.3592	−1.30561	−0.652803	+	0.757528i	$0.726407\pi$
$158$	−11.5086	−0.915575
$159$	−0.357652	−0.0283637
$160$	−1.00000	−0.0790569
$161$	0.817804	0.0644520
$162$	8.57745	0.673908
$163$	−10.1498	−0.794992	−0.397496	−	0.917604i	$-0.630121\pi$
$163$	−10.1498	−0.794992	−0.397496	+	0.917604i	$0.630121\pi$
$164$	0.956727	0.0747078
$165$	0.217250	0.0169129
$166$	−15.2765	−1.18569
$167$	−5.80285	−0.449038	−0.224519	−	0.974470i	$-0.572081\pi$
$167$	−5.80285	−0.449038	−0.224519	+	0.974470i	$0.572081\pi$
$168$	0.124745	0.00962429
$169$	−12.9140	−0.993385
$170$	3.05078	0.233984
$171$	−22.6096	−1.72900
$172$	−1.00000	−0.0762493
$173$	6.31864	0.480397	0.240198	−	0.970724i	$-0.422787\pi$
$173$	6.31864	0.480397	0.240198	+	0.970724i	$0.422787\pi$
$174$	0.631652	0.0478854
$175$	−0.574201	−0.0434055
$176$	1.00000	0.0753778
$177$	−0.401778	−0.0301995
$178$	−0.829948	−0.0622072
$179$	12.1482	0.908000	0.454000	−	0.891002i	$-0.349997\pi$
$179$	12.1482	0.908000	0.454000	+	0.891002i	$0.349997\pi$
$180$	2.95280	0.220089
$181$	−9.73179	−0.723358	−0.361679	−	0.932303i	$-0.617796\pi$
$181$	−9.73179	−0.723358	−0.361679	+	0.932303i	$0.617796\pi$
$182$	−0.168381	−0.0124813
$183$	1.33533	0.0987103
$184$	−1.42425	−0.104997
$185$	−3.05948	−0.224938
$186$	1.71512	0.125759
$187$	−3.05078	−0.223095
$188$	−0.211773	−0.0154451
$189$	−0.742583	−0.0540149
$190$	−7.65701	−0.555498
$191$	16.7270	1.21032	0.605162	−	0.796102i	$-0.293108\pi$
$191$	16.7270	1.21032	0.605162	+	0.796102i	$0.293108\pi$
$192$	−0.217250	−0.0156786
$193$	−12.2772	−0.883730	−0.441865	−	0.897081i	$-0.645683\pi$
$193$	−12.2772	−0.883730	−0.441865	+	0.897081i	$0.645683\pi$
$194$	15.1085	1.08473
$195$	0.0637073	0.00456217
$196$	−6.67029	−0.476449
$197$	10.4314	0.743206	0.371603	−	0.928392i	$-0.378808\pi$
$197$	10.4314	0.743206	0.371603	+	0.928392i	$0.378808\pi$
$198$	−2.95280	−0.209847
$199$	14.3812	1.01946	0.509728	−	0.860336i	$-0.329746\pi$
$199$	14.3812	1.01946	0.509728	+	0.860336i	$0.329746\pi$
$200$	1.00000	0.0707107
$201$	3.50535	0.247249
$202$	−2.77898	−0.195529
$203$	1.66949	0.117175
$204$	0.662782	0.0464040
$205$	−0.956727	−0.0668207
$206$	−12.7766	−0.890191
$207$	4.20552	0.292304
$208$	0.293244	0.0203328
$209$	7.65701	0.529646
$210$	−0.124745	−0.00860823
$211$	0.779718	0.0536780	0.0268390	−	0.999640i	$-0.491456\pi$
$211$	0.779718	0.0536780	0.0268390	+	0.999640i	$0.491456\pi$
$212$	1.64627	0.113066
$213$	0.728081	0.0498873
$214$	4.76302	0.325593
$215$	1.00000	0.0681994
$216$	1.29324	0.0879941
$217$	4.53314	0.307730
$218$	−11.4665	−0.776611
$219$	−0.528219	−0.0356938
$220$	−1.00000	−0.0674200
$221$	−0.894626	−0.0601790
$222$	−0.664672	−0.0446099
$223$	2.88873	0.193444	0.0967219	−	0.995311i	$-0.469164\pi$
$223$	2.88873	0.193444	0.0967219	+	0.995311i	$0.469164\pi$
$224$	−0.574201	−0.0383654
$225$	−2.95280	−0.196854
$226$	2.42224	0.161125
$227$	16.5363	1.09755	0.548777	−	0.835969i	$-0.315094\pi$
$227$	16.5363	1.09755	0.548777	+	0.835969i	$0.315094\pi$
$228$	−1.66348	−0.110167
$229$	−7.43809	−0.491523	−0.245761	−	0.969330i	$-0.579038\pi$
$229$	−7.43809	−0.491523	−0.245761	+	0.969330i	$0.579038\pi$
$230$	1.42425	0.0939120
$231$	0.124745	0.00820762
$232$	−2.90750	−0.190886
$233$	7.63502	0.500187	0.250093	−	0.968222i	$-0.419539\pi$
$233$	7.63502	0.500187	0.250093	+	0.968222i	$0.419539\pi$
$234$	−0.865893	−0.0566052
$235$	0.211773	0.0138145
$236$	1.84938	0.120385
$237$	2.50024	0.162408
$238$	1.75176	0.113550
$239$	−7.66193	−0.495609	−0.247805	−	0.968810i	$-0.579709\pi$
$239$	−7.66193	−0.495609	−0.247805	+	0.968810i	$0.579709\pi$
$240$	0.217250	0.0140234
$241$	13.4628	0.867212	0.433606	−	0.901103i	$-0.357241\pi$
$241$	13.4628	0.867212	0.433606	+	0.901103i	$0.357241\pi$
$242$	1.00000	0.0642824
$243$	−5.74318	−0.368425
$244$	−6.14651	−0.393490
$245$	6.67029	0.426149
$246$	−0.207849	−0.0132519
$247$	2.24537	0.142870
$248$	−7.89469	−0.501313
$249$	3.31882	0.210322
$250$	−1.00000	−0.0632456
$251$	7.56708	0.477630	0.238815	−	0.971065i	$-0.423241\pi$
$251$	7.56708	0.477630	0.238815	+	0.971065i	$0.423241\pi$
$252$	1.69550	0.106807
$253$	−1.42425	−0.0895416
$254$	4.22643	0.265190
$255$	−0.662782	−0.0415050
$256$	1.00000	0.0625000
$257$	−12.3923	−0.773012	−0.386506	−	0.922287i	$-0.626318\pi$
$257$	−12.3923	−0.773012	−0.386506	+	0.922287i	$0.626318\pi$
$258$	0.217250	0.0135254
$259$	−1.75676	−0.109160
$260$	−0.293244	−0.0181862
$261$	8.58526	0.531414
$262$	−13.4541	−0.831196
$263$	12.0994	0.746078	0.373039	−	0.927816i	$-0.378316\pi$
$263$	12.0994	0.746078	0.373039	+	0.927816i	$0.378316\pi$
$264$	−0.217250	−0.0133708
$265$	−1.64627	−0.101130
$266$	−4.39666	−0.269577
$267$	0.180306	0.0110345
$268$	−16.1351	−0.985611
$269$	−2.55392	−0.155716	−0.0778578	−	0.996964i	$-0.524808\pi$
$269$	−2.55392	−0.155716	−0.0778578	+	0.996964i	$0.524808\pi$
$270$	−1.29324	−0.0787044
$271$	−2.07211	−0.125872	−0.0629359	−	0.998018i	$-0.520046\pi$
$271$	−2.07211	−0.125872	−0.0629359	+	0.998018i	$0.520046\pi$
$272$	−3.05078	−0.184981
$273$	0.0365808	0.00221397
$274$	9.79482	0.591727
$275$	1.00000	0.0603023
$276$	0.309417	0.0186247
$277$	−4.44982	−0.267364	−0.133682	−	0.991024i	$-0.542680\pi$
$277$	−4.44982	−0.267364	−0.133682	+	0.991024i	$0.542680\pi$
$278$	−12.6027	−0.755857
$279$	23.3115	1.39562
$280$	0.574201	0.0343151
$281$	17.1728	1.02444	0.512220	−	0.858854i	$-0.328823\pi$
$281$	17.1728	1.02444	0.512220	+	0.858854i	$0.328823\pi$
$282$	0.0460075	0.00273971
$283$	6.20755	0.369001	0.184500	−	0.982832i	$-0.440933\pi$
$283$	6.20755	0.369001	0.184500	+	0.982832i	$0.440933\pi$
$284$	−3.35136	−0.198866
$285$	1.66348	0.0985362
$286$	0.293244	0.0173399
$287$	−0.549354	−0.0324273
$288$	−2.95280	−0.173996
$289$	−7.69272	−0.452513
$290$	2.90750	0.170734
$291$	−3.28232	−0.192413
$292$	2.43139	0.142287
$293$	−21.6182	−1.26295	−0.631475	−	0.775396i	$-0.717550\pi$
$293$	−21.6182	−1.26295	−0.631475	+	0.775396i	$0.717550\pi$
$294$	1.44912	0.0845143
$295$	−1.84938	−0.107675
$296$	3.05948	0.177829
$297$	1.29324	0.0750417
$298$	−17.7630	−1.02898
$299$	−0.417652	−0.0241534
$300$	−0.217250	−0.0125429
$301$	0.574201	0.0330964
$302$	−2.27707	−0.131031
$303$	0.603733	0.0346836
$304$	7.65701	0.439159
$305$	6.14651	0.351948
$306$	9.00836	0.514974
$307$	−27.2975	−1.55795	−0.778976	−	0.627054i	$-0.784261\pi$
$307$	−27.2975	−1.55795	−0.778976	+	0.627054i	$0.784261\pi$
$308$	−0.574201	−0.0327182
$309$	2.77572	0.157905
$310$	7.89469	0.448388
$311$	27.2215	1.54359	0.771796	−	0.635870i	$-0.219359\pi$
$311$	27.2215	1.54359	0.771796	+	0.635870i	$0.219359\pi$
$312$	−0.0637073	−0.00360671
$313$	−1.21648	−0.0687593	−0.0343796	−	0.999409i	$-0.510946\pi$
$313$	−1.21648	−0.0687593	−0.0343796	+	0.999409i	$0.510946\pi$
$314$	−16.3592	−0.923203
$315$	−1.69550	−0.0955308
$316$	−11.5086	−0.647410
$317$	4.14259	0.232671	0.116335	−	0.993210i	$-0.462885\pi$
$317$	4.14259	0.232671	0.116335	+	0.993210i	$0.462885\pi$
$318$	−0.357652	−0.0200561
$319$	−2.90750	−0.162788
$320$	−1.00000	−0.0559017
$321$	−1.03476	−0.0577549
$322$	0.817804	0.0455744
$323$	−23.3599	−1.29978
$324$	8.57745	0.476525
$325$	0.293244	0.0162663
$326$	−10.1498	−0.562144
$327$	2.49110	0.137758
$328$	0.956727	0.0528264
$329$	0.121600	0.00670403
$330$	0.217250	0.0119592
$331$	25.6858	1.41182	0.705910	−	0.708301i	$-0.250538\pi$
$331$	25.6858	1.41182	0.705910	+	0.708301i	$0.250538\pi$
$332$	−15.2765	−0.838408
$333$	−9.03405	−0.495063
$334$	−5.80285	−0.317518
$335$	16.1351	0.881557
$336$	0.124745	0.00680540
$337$	−8.33811	−0.454206	−0.227103	−	0.973871i	$-0.572925\pi$
$337$	−8.33811	−0.454206	−0.227103	+	0.973871i	$0.572925\pi$
$338$	−12.9140	−0.702429
$339$	−0.526230	−0.0285809
$340$	3.05078	0.165452
$341$	−7.89469	−0.427521
$342$	−22.6096	−1.22259
$343$	7.84950	0.423833
$344$	−1.00000	−0.0539164
$345$	−0.309417	−0.0166584
$346$	6.31864	0.339692
$347$	12.3104	0.660858	0.330429	−	0.943831i	$-0.392807\pi$
$347$	12.3104	0.660858	0.330429	+	0.943831i	$0.392807\pi$
$348$	0.631652	0.0338601
$349$	−13.3147	−0.712719	−0.356359	−	0.934349i	$-0.615982\pi$
$349$	−13.3147	−0.712719	−0.356359	+	0.934349i	$0.615982\pi$
$350$	−0.574201	−0.0306924
$351$	0.379237	0.0202422
$352$	1.00000	0.0533002
$353$	20.5921	1.09601	0.548004	−	0.836476i	$-0.315388\pi$
$353$	20.5921	1.09601	0.548004	+	0.836476i	$0.315388\pi$
$354$	−0.401778	−0.0213543
$355$	3.35136	0.177872
$356$	−0.829948	−0.0439871
$357$	−0.380570	−0.0201419
$358$	12.1482	0.642053
$359$	−25.0741	−1.32336	−0.661680	−	0.749787i	$-0.730156\pi$
$359$	−25.0741	−1.32336	−0.661680	+	0.749787i	$0.730156\pi$
$360$	2.95280	0.155626
$361$	39.6298	2.08578
$362$	−9.73179	−0.511491
$363$	−0.217250	−0.0114027
$364$	−0.168381	−0.00882558
$365$	−2.43139	−0.127265
$366$	1.33533	0.0697987
$367$	−17.4540	−0.911089	−0.455545	−	0.890213i	$-0.650555\pi$
$367$	−17.4540	−0.911089	−0.455545	+	0.890213i	$0.650555\pi$
$368$	−1.42425	−0.0742439
$369$	−2.82503	−0.147065
$370$	−3.05948	−0.159055
$371$	−0.945292	−0.0490771
$372$	1.71512	0.0889248
$373$	34.4152	1.78195	0.890977	−	0.454049i	$-0.150021\pi$
$373$	34.4152	1.78195	0.890977	+	0.454049i	$0.150021\pi$
$374$	−3.05078	−0.157752
$375$	0.217250	0.0112187
$376$	−0.211773	−0.0109213
$377$	−0.852607	−0.0439115
$378$	−0.742583	−0.0381943
$379$	−18.4999	−0.950277	−0.475138	−	0.879911i	$-0.657602\pi$
$379$	−18.4999	−0.950277	−0.475138	+	0.879911i	$0.657602\pi$
$380$	−7.65701	−0.392796
$381$	−0.918191	−0.0470403
$382$	16.7270	0.855828
$383$	10.8455	0.554178	0.277089	−	0.960844i	$-0.410630\pi$
$383$	10.8455	0.554178	0.277089	+	0.960844i	$0.410630\pi$
$384$	−0.217250	−0.0110865
$385$	0.574201	0.0292640
$386$	−12.2772	−0.624892
$387$	2.95280	0.150099
$388$	15.1085	0.767018
$389$	−29.3101	−1.48608	−0.743040	−	0.669247i	$-0.766617\pi$
$389$	−29.3101	−1.48608	−0.743040	+	0.669247i	$0.766617\pi$
$390$	0.0637073	0.00322594
$391$	4.34507	0.219739
$392$	−6.67029	−0.336901
$393$	2.92289	0.147441
$394$	10.4314	0.525526
$395$	11.5086	0.579061
$396$	−2.95280	−0.148384
$397$	6.31522	0.316952	0.158476	−	0.987363i	$-0.449342\pi$
$397$	6.31522	0.316952	0.158476	+	0.987363i	$0.449342\pi$
$398$	14.3812	0.720864
$399$	0.955174	0.0478185
$400$	1.00000	0.0500000
$401$	−6.82435	−0.340792	−0.170396	−	0.985376i	$-0.554505\pi$
$401$	−6.82435	−0.340792	−0.170396	+	0.985376i	$0.554505\pi$
$402$	3.50535	0.174831
$403$	−2.31507	−0.115322
$404$	−2.77898	−0.138260
$405$	−8.57745	−0.426217
$406$	1.66949	0.0828553
$407$	3.05948	0.151653
$408$	0.662782	0.0328126
$409$	10.7347	0.530795	0.265397	−	0.964139i	$-0.414497\pi$
$409$	10.7347	0.530795	0.265397	+	0.964139i	$0.414497\pi$
$410$	−0.956727	−0.0472494
$411$	−2.12792	−0.104963
$412$	−12.7766	−0.629460
$413$	−1.06192	−0.0522536
$414$	4.20552	0.206690
$415$	15.2765	0.749895
$416$	0.293244	0.0143775
$417$	2.73792	0.134077
$418$	7.65701	0.374516
$419$	5.10987	0.249633	0.124817	−	0.992180i	$-0.460166\pi$
$419$	5.10987	0.249633	0.124817	+	0.992180i	$0.460166\pi$
$420$	−0.124745	−0.00608694
$421$	−2.92145	−0.142383	−0.0711915	−	0.997463i	$-0.522680\pi$
$421$	−2.92145	−0.142383	−0.0711915	+	0.997463i	$0.522680\pi$
$422$	0.779718	0.0379561
$423$	0.625323	0.0304042
$424$	1.64627	0.0799500
$425$	−3.05078	−0.147985
$426$	0.728081	0.0352756
$427$	3.52934	0.170797
$428$	4.76302	0.230229
$429$	−0.0637073	−0.00307582
$430$	1.00000	0.0482243
$431$	−10.1391	−0.488382	−0.244191	−	0.969727i	$-0.578522\pi$
$431$	−10.1391	−0.488382	−0.244191	+	0.969727i	$0.578522\pi$
$432$	1.29324	0.0622213
$433$	1.65655	0.0796089	0.0398044	−	0.999207i	$-0.487327\pi$
$433$	1.65655	0.0796089	0.0398044	+	0.999207i	$0.487327\pi$
$434$	4.53314	0.217598
$435$	−0.631652	−0.0302854
$436$	−11.4665	−0.549147
$437$	−10.9055	−0.521679
$438$	−0.528219	−0.0252393
$439$	−12.0056	−0.572998	−0.286499	−	0.958081i	$-0.592492\pi$
$439$	−12.0056	−0.572998	−0.286499	+	0.958081i	$0.592492\pi$
$440$	−1.00000	−0.0476731
$441$	19.6961	0.937908
$442$	−0.894626	−0.0425530
$443$	−33.8444	−1.60800	−0.803999	−	0.594631i	$-0.797298\pi$
$443$	−33.8444	−1.60800	−0.803999	+	0.594631i	$0.797298\pi$
$444$	−0.664672	−0.0315439
$445$	0.829948	0.0393433
$446$	2.88873	0.136785
$447$	3.85900	0.182525
$448$	−0.574201	−0.0271285
$449$	−21.2449	−1.00261	−0.501304	−	0.865271i	$-0.667146\pi$
$449$	−21.2449	−1.00261	−0.501304	+	0.865271i	$0.667146\pi$
$450$	−2.95280	−0.139196
$451$	0.956727	0.0450505
$452$	2.42224	0.113932
$453$	0.494693	0.0232427
$454$	16.5363	0.776087
$455$	0.168381	0.00789384
$456$	−1.66348	−0.0778997
$457$	−19.3029	−0.902951	−0.451475	−	0.892284i	$-0.649102\pi$
$457$	−19.3029	−0.902951	−0.451475	+	0.892284i	$0.649102\pi$
$458$	−7.43809	−0.347559
$459$	−3.94541	−0.184156
$460$	1.42425	0.0664058
$461$	24.8744	1.15852	0.579258	−	0.815144i	$-0.303342\pi$
$461$	24.8744	1.15852	0.579258	+	0.815144i	$0.303342\pi$
$462$	0.124745	0.00580367
$463$	7.46911	0.347119	0.173559	−	0.984823i	$-0.444473\pi$
$463$	7.46911	0.347119	0.173559	+	0.984823i	$0.444473\pi$
$464$	−2.90750	−0.134977
$465$	−1.71512	−0.0795367
$466$	7.63502	0.353685
$467$	36.2796	1.67882	0.839410	−	0.543498i	$-0.182901\pi$
$467$	36.2796	1.67882	0.839410	+	0.543498i	$0.182901\pi$
$468$	−0.865893	−0.0400259
$469$	9.26482	0.427810
$470$	0.211773	0.00976835
$471$	3.55403	0.163761
$472$	1.84938	0.0851248
$473$	−1.00000	−0.0459800
$474$	2.50024	0.114840
$475$	7.65701	0.351328
$476$	1.75176	0.0802920
$477$	−4.86112	−0.222575
$478$	−7.66193	−0.350448
$479$	21.6211	0.987893	0.493947	−	0.869492i	$-0.335554\pi$
$479$	21.6211	0.987893	0.493947	+	0.869492i	$0.335554\pi$
$480$	0.217250	0.00991605
$481$	0.897177	0.0409077
$482$	13.4628	0.613212
$483$	−0.177668	−0.00808416
$484$	1.00000	0.0454545
$485$	−15.1085	−0.686042
$486$	−5.74318	−0.260516
$487$	26.5006	1.20086	0.600429	−	0.799678i	$-0.294996\pi$
$487$	26.5006	1.20086	0.600429	+	0.799678i	$0.294996\pi$
$488$	−6.14651	−0.278240
$489$	2.20504	0.0997152
$490$	6.67029	0.301333
$491$	6.31809	0.285132	0.142566	−	0.989785i	$-0.454465\pi$
$491$	6.31809	0.285132	0.142566	+	0.989785i	$0.454465\pi$
$492$	−0.207849	−0.00937054
$493$	8.87014	0.399491
$494$	2.24537	0.101024
$495$	2.95280	0.132719
$496$	−7.89469	−0.354482
$497$	1.92435	0.0863191
$498$	3.31882	0.148720
$499$	24.6045	1.10145	0.550725	−	0.834687i	$-0.314351\pi$
$499$	24.6045	1.10145	0.550725	+	0.834687i	$0.314351\pi$
$500$	−1.00000	−0.0447214
$501$	1.26067	0.0563224
$502$	7.56708	0.337735
$503$	1.11431	0.0496847	0.0248423	−	0.999691i	$-0.492092\pi$
$503$	1.11431	0.0496847	0.0248423	+	0.999691i	$0.492092\pi$
$504$	1.69550	0.0755237
$505$	2.77898	0.123663
$506$	−1.42425	−0.0633154
$507$	2.80556	0.124599
$508$	4.22643	0.187518
$509$	−41.9819	−1.86082	−0.930409	−	0.366524i	$-0.880548\pi$
$509$	−41.9819	−1.86082	−0.930409	+	0.366524i	$0.880548\pi$
$510$	−0.662782	−0.0293485
$511$	−1.39611	−0.0617603
$512$	1.00000	0.0441942
$513$	9.90238	0.437201
$514$	−12.3923	−0.546602
$515$	12.7766	0.563006
$516$	0.217250	0.00956388
$517$	−0.211773	−0.00931375
$518$	−1.75676	−0.0771876
$519$	−1.37272	−0.0602558
$520$	−0.293244	−0.0128596
$521$	−18.9739	−0.831262	−0.415631	−	0.909533i	$-0.636439\pi$
$521$	−18.9739	−0.831262	−0.415631	+	0.909533i	$0.636439\pi$
$522$	8.58526	0.375767
$523$	22.1796	0.969847	0.484924	−	0.874557i	$-0.338847\pi$
$523$	22.1796	0.969847	0.484924	+	0.874557i	$0.338847\pi$
$524$	−13.4541	−0.587744
$525$	0.124745	0.00544432
$526$	12.0994	0.527557
$527$	24.0850	1.04916
$528$	−0.217250	−0.00945458
$529$	−20.9715	−0.911805
$530$	−1.64627	−0.0715095
$531$	−5.46086	−0.236981
$532$	−4.39666	−0.190620
$533$	0.280555	0.0121522
$534$	0.180306	0.00780260
$535$	−4.76302	−0.205923
$536$	−16.1351	−0.696932
$537$	−2.63919	−0.113890
$538$	−2.55392	−0.110108
$539$	−6.67029	−0.287310
$540$	−1.29324	−0.0556524
$541$	15.0577	0.647380	0.323690	−	0.946163i	$-0.395077\pi$
$541$	15.0577	0.647380	0.323690	+	0.946163i	$0.395077\pi$
$542$	−2.07211	−0.0890047
$543$	2.11423	0.0907302
$544$	−3.05078	−0.130801
$545$	11.4665	0.491172
$546$	0.0365808	0.00156551
$547$	−32.3123	−1.38157	−0.690787	−	0.723058i	$-0.742736\pi$
$547$	−32.3123	−1.38157	−0.690787	+	0.723058i	$0.742736\pi$
$548$	9.79482	0.418414
$549$	18.1494	0.774599
$550$	1.00000	0.0426401
$551$	−22.2627	−0.948423
$552$	0.309417	0.0131697
$553$	6.60826	0.281012
$554$	−4.44982	−0.189055
$555$	0.664672	0.0282138
$556$	−12.6027	−0.534472
$557$	15.5137	0.657336	0.328668	−	0.944446i	$-0.393400\pi$
$557$	15.5137	0.657336	0.328668	+	0.944446i	$0.393400\pi$
$558$	23.3115	0.986853
$559$	−0.293244	−0.0124029
$560$	0.574201	0.0242644
$561$	0.662782	0.0279827
$562$	17.1728	0.724389
$563$	25.5070	1.07499	0.537496	−	0.843266i	$-0.319370\pi$
$563$	25.5070	1.07499	0.537496	+	0.843266i	$0.319370\pi$
$564$	0.0460075	0.00193727
$565$	−2.42224	−0.101904
$566$	6.20755	0.260923
$567$	−4.92518	−0.206838
$568$	−3.35136	−0.140620
$569$	−18.3283	−0.768364	−0.384182	−	0.923257i	$-0.625516\pi$
$569$	−18.3283	−0.768364	−0.384182	+	0.923257i	$0.625516\pi$
$570$	1.66348	0.0696756
$571$	−37.7376	−1.57927	−0.789634	−	0.613578i	$-0.789730\pi$
$571$	−37.7376	−1.57927	−0.789634	+	0.613578i	$0.789730\pi$
$572$	0.293244	0.0122612
$573$	−3.63394	−0.151810
$574$	−0.549354	−0.0229296
$575$	−1.42425	−0.0593952
$576$	−2.95280	−0.123033
$577$	−12.0301	−0.500820	−0.250410	−	0.968140i	$-0.580565\pi$
$577$	−12.0301	−0.500820	−0.250410	+	0.968140i	$0.580565\pi$
$578$	−7.69272	−0.319975
$579$	2.66721	0.110846
$580$	2.90750	0.120727
$581$	8.77180	0.363915
$582$	−3.28232	−0.136056
$583$	1.64627	0.0681816
$584$	2.43139	0.100612
$585$	0.865893	0.0358003
$586$	−21.6182	−0.893040
$587$	13.6970	0.565335	0.282668	−	0.959218i	$-0.408781\pi$
$587$	13.6970	0.565335	0.282668	+	0.959218i	$0.408781\pi$
$588$	1.44912	0.0597607
$589$	−60.4497	−2.49079
$590$	−1.84938	−0.0761379
$591$	−2.26622	−0.0932197
$592$	3.05948	0.125744
$593$	1.72259	0.0707384	0.0353692	−	0.999374i	$-0.488739\pi$
$593$	1.72259	0.0707384	0.0353692	+	0.999374i	$0.488739\pi$
$594$	1.29324	0.0530625
$595$	−1.75176	−0.0718153
$596$	−17.7630	−0.727600
$597$	−3.12431	−0.127869
$598$	−0.417652	−0.0170791
$599$	8.31800	0.339864	0.169932	−	0.985456i	$-0.445645\pi$
$599$	8.31800	0.339864	0.169932	+	0.985456i	$0.445645\pi$
$600$	−0.217250	−0.00886918
$601$	32.4143	1.32221	0.661103	−	0.750295i	$-0.270089\pi$
$601$	32.4143	1.32221	0.661103	+	0.750295i	$0.270089\pi$
$602$	0.574201	0.0234027
$603$	47.6439	1.94021
$604$	−2.27707	−0.0926527
$605$	−1.00000	−0.0406558
$606$	0.603733	0.0245250
$607$	−32.5605	−1.32159	−0.660796	−	0.750566i	$-0.729781\pi$
$607$	−32.5605	−1.32159	−0.660796	+	0.750566i	$0.729781\pi$
$608$	7.65701	0.310533
$609$	−0.362696	−0.0146972
$610$	6.14651	0.248865
$611$	−0.0621012	−0.00251234
$612$	9.00836	0.364142
$613$	6.70902	0.270975	0.135487	−	0.990779i	$-0.456740\pi$
$613$	6.70902	0.270975	0.135487	+	0.990779i	$0.456740\pi$
$614$	−27.2975	−1.10164
$615$	0.207849	0.00838126
$616$	−0.574201	−0.0231352
$617$	−4.69807	−0.189137	−0.0945685	−	0.995518i	$-0.530147\pi$
$617$	−4.69807	−0.189137	−0.0945685	+	0.995518i	$0.530147\pi$
$618$	2.77572	0.111656
$619$	42.4652	1.70682	0.853410	−	0.521240i	$-0.174530\pi$
$619$	42.4652	1.70682	0.853410	+	0.521240i	$0.174530\pi$
$620$	7.89469	0.317058
$621$	−1.84190	−0.0739128
$622$	27.2215	1.09148
$623$	0.476557	0.0190929
$624$	−0.0637073	−0.00255033
$625$	1.00000	0.0400000
$626$	−1.21648	−0.0486202
$627$	−1.66348	−0.0664331
$628$	−16.3592	−0.652803
$629$	−9.33383	−0.372164
$630$	−1.69550	−0.0675505
$631$	−6.73830	−0.268247	−0.134124	−	0.990965i	$-0.542822\pi$
$631$	−6.73830	−0.268247	−0.134124	+	0.990965i	$0.542822\pi$
$632$	−11.5086	−0.457788
$633$	−0.169393	−0.00673279
$634$	4.14259	0.164523
$635$	−4.22643	−0.167721
$636$	−0.357652	−0.0141818
$637$	−1.95603	−0.0775006
$638$	−2.90750	−0.115109
$639$	9.89589	0.391476
$640$	−1.00000	−0.0395285
$641$	1.55208	0.0613036	0.0306518	−	0.999530i	$-0.490242\pi$
$641$	1.55208	0.0613036	0.0306518	+	0.999530i	$0.490242\pi$
$642$	−1.03476	−0.0408389
$643$	42.0280	1.65742	0.828711	−	0.559676i	$-0.189074\pi$
$643$	42.0280	1.65742	0.828711	+	0.559676i	$0.189074\pi$
$644$	0.817804	0.0322260
$645$	−0.217250	−0.00855420
$646$	−23.3599	−0.919082
$647$	−3.69193	−0.145145	−0.0725723	−	0.997363i	$-0.523121\pi$
$647$	−3.69193	−0.145145	−0.0725723	+	0.997363i	$0.523121\pi$
$648$	8.57745	0.336954
$649$	1.84938	0.0725946
$650$	0.293244	0.0115020
$651$	−0.984824	−0.0385983
$652$	−10.1498	−0.397496
$653$	−14.7046	−0.575434	−0.287717	−	0.957716i	$-0.592896\pi$
$653$	−14.7046	−0.575434	−0.287717	+	0.957716i	$0.592896\pi$
$654$	2.49110	0.0974096
$655$	13.4541	0.525694
$656$	0.956727	0.0373539
$657$	−7.17943	−0.280096
$658$	0.121600	0.00474047
$659$	4.58451	0.178587	0.0892936	−	0.996005i	$-0.471539\pi$
$659$	4.58451	0.178587	0.0892936	+	0.996005i	$0.471539\pi$
$660$	0.217250	0.00845643
$661$	−30.6586	−1.19248	−0.596241	−	0.802806i	$-0.703340\pi$
$661$	−30.6586	−1.19248	−0.596241	+	0.802806i	$0.703340\pi$
$662$	25.6858	0.998308
$663$	0.194357	0.00754820
$664$	−15.2765	−0.592844
$665$	4.39666	0.170495
$666$	−9.03405	−0.350063
$667$	4.14099	0.160340
$668$	−5.80285	−0.224519
$669$	−0.627576	−0.0242635
$670$	16.1351	0.623355
$671$	−6.14651	−0.237283
$672$	0.124745	0.00481215
$673$	−12.1795	−0.469486	−0.234743	−	0.972057i	$-0.575425\pi$
$673$	−12.1795	−0.469486	−0.234743	+	0.972057i	$0.575425\pi$
$674$	−8.33811	−0.321172
$675$	1.29324	0.0497770
$676$	−12.9140	−0.496693
$677$	9.41854	0.361984	0.180992	−	0.983485i	$-0.442069\pi$
$677$	9.41854	0.361984	0.180992	+	0.983485i	$0.442069\pi$
$678$	−0.526230	−0.0202098
$679$	−8.67532	−0.332928
$680$	3.05078	0.116992
$681$	−3.59251	−0.137665
$682$	−7.89469	−0.302303
$683$	14.0544	0.537777	0.268888	−	0.963171i	$-0.413344\pi$
$683$	14.0544	0.537777	0.268888	+	0.963171i	$0.413344\pi$
$684$	−22.6096	−0.864501
$685$	−9.79482	−0.374241
$686$	7.84950	0.299695
$687$	1.61592	0.0616513
$688$	−1.00000	−0.0381246
$689$	0.482760	0.0183917
$690$	−0.309417	−0.0117793
$691$	33.9216	1.29044	0.645220	−	0.763997i	$-0.276766\pi$
$691$	33.9216	1.29044	0.645220	+	0.763997i	$0.276766\pi$
$692$	6.31864	0.240198
$693$	1.69550	0.0644068
$694$	12.3104	0.467297
$695$	12.6027	0.478046
$696$	0.631652	0.0239427
$697$	−2.91877	−0.110556
$698$	−13.3147	−0.503968
$699$	−1.65871	−0.0627380
$700$	−0.574201	−0.0217028
$701$	−18.8245	−0.710993	−0.355497	−	0.934678i	$-0.615688\pi$
$701$	−18.8245	−0.710993	−0.355497	+	0.934678i	$0.615688\pi$
$702$	0.379237	0.0143134
$703$	23.4265	0.883547
$704$	1.00000	0.0376889
$705$	−0.0460075	−0.00173274
$706$	20.5921	0.774995
$707$	1.59570	0.0600123
$708$	−0.401778	−0.0150997
$709$	−13.9255	−0.522984	−0.261492	−	0.965206i	$-0.584214\pi$
$709$	−13.9255	−0.522984	−0.261492	+	0.965206i	$0.584214\pi$
$710$	3.35136	0.125774
$711$	33.9826	1.27445
$712$	−0.829948	−0.0311036
$713$	11.2440	0.421090
$714$	−0.380570	−0.0142425
$715$	−0.293244	−0.0109667
$716$	12.1482	0.454000
$717$	1.66455	0.0621638
$718$	−25.0741	−0.935756
$719$	−49.6812	−1.85280	−0.926398	−	0.376545i	$-0.877112\pi$
$719$	−49.6812	−1.85280	−0.926398	+	0.376545i	$0.877112\pi$
$720$	2.95280	0.110044
$721$	7.33636	0.273220
$722$	39.6298	1.47487
$723$	−2.92478	−0.108774
$724$	−9.73179	−0.361679
$725$	−2.90750	−0.107982
$726$	−0.217250	−0.00806289
$727$	17.1067	0.634453	0.317226	−	0.948350i	$-0.397248\pi$
$727$	17.1067	0.634453	0.317226	+	0.948350i	$0.397248\pi$
$728$	−0.168381	−0.00624063
$729$	−24.4846	−0.906839
$730$	−2.43139	−0.0899899
$731$	3.05078	0.112837
$732$	1.33533	0.0493551
$733$	19.5116	0.720678	0.360339	−	0.932821i	$-0.382661\pi$
$733$	19.5116	0.720678	0.360339	+	0.932821i	$0.382661\pi$
$734$	−17.4540	−0.644237
$735$	−1.44912	−0.0534516
$736$	−1.42425	−0.0524984
$737$	−16.1351	−0.594346
$738$	−2.82503	−0.103991
$739$	35.4068	1.30246	0.651230	−	0.758881i	$-0.274253\pi$
$739$	35.4068	1.30246	0.651230	+	0.758881i	$0.274253\pi$
$740$	−3.05948	−0.112469
$741$	−0.487807	−0.0179200
$742$	−0.945292	−0.0347028
$743$	20.5694	0.754619	0.377309	−	0.926087i	$-0.376849\pi$
$743$	20.5694	0.754619	0.377309	+	0.926087i	$0.376849\pi$
$744$	1.71512	0.0628793
$745$	17.7630	0.650786
$746$	34.4152	1.26003
$747$	45.1085	1.65043
$748$	−3.05078	−0.111548
$749$	−2.73493	−0.0999322
$750$	0.217250	0.00793284
$751$	30.6167	1.11722	0.558610	−	0.829431i	$-0.311335\pi$
$751$	30.6167	1.11722	0.558610	+	0.829431i	$0.311335\pi$
$752$	−0.211773	−0.00772256
$753$	−1.64395	−0.0599087
$754$	−0.852607	−0.0310501
$755$	2.27707	0.0828711
$756$	−0.742583	−0.0270075
$757$	31.1804	1.13327	0.566635	−	0.823969i	$-0.308245\pi$
$757$	31.1804	1.13327	0.566635	+	0.823969i	$0.308245\pi$
$758$	−18.4999	−0.671947
$759$	0.309417	0.0112311
$760$	−7.65701	−0.277749
$761$	−14.4873	−0.525162	−0.262581	−	0.964910i	$-0.584574\pi$
$761$	−14.4873	−0.525162	−0.262581	+	0.964910i	$0.584574\pi$
$762$	−0.918191	−0.0332625
$763$	6.58409	0.238360
$764$	16.7270	0.605162
$765$	−9.00836	−0.325698
$766$	10.8455	0.391863
$767$	0.542321	0.0195821
$768$	−0.217250	−0.00783932
$769$	7.78536	0.280747	0.140374	−	0.990099i	$-0.455170\pi$
$769$	7.78536	0.280747	0.140374	+	0.990099i	$0.455170\pi$
$770$	0.574201	0.0206928
$771$	2.69223	0.0969582
$772$	−12.2772	−0.441865
$773$	17.4105	0.626214	0.313107	−	0.949718i	$-0.398630\pi$
$773$	17.4105	0.626214	0.313107	+	0.949718i	$0.398630\pi$
$774$	2.95280	0.106136
$775$	−7.89469	−0.283586
$776$	15.1085	0.542363
$777$	0.381656	0.0136918
$778$	−29.3101	−1.05082
$779$	7.32566	0.262469
$780$	0.0637073	0.00228109
$781$	−3.35136	−0.119921
$782$	4.34507	0.155379
$783$	−3.76010	−0.134375
$784$	−6.67029	−0.238225
$785$	16.3592	0.583885
$786$	2.92289	0.104256
$787$	−9.62174	−0.342978	−0.171489	−	0.985186i	$-0.554858\pi$
$787$	−9.62174	−0.342978	−0.171489	+	0.985186i	$0.554858\pi$
$788$	10.4314	0.371603
$789$	−2.62858	−0.0935800
$790$	11.5086	0.409458
$791$	−1.39085	−0.0494530
$792$	−2.95280	−0.104923
$793$	−1.80243	−0.0640062
$794$	6.31522	0.224119
$795$	0.357652	0.0126846
$796$	14.3812	0.509728
$797$	49.0605	1.73781	0.868906	−	0.494977i	$-0.164823\pi$
$797$	49.0605	1.73781	0.868906	+	0.494977i	$0.164823\pi$
$798$	0.955174	0.0338128
$799$	0.646073	0.0228564
$800$	1.00000	0.0353553
$801$	2.45067	0.0865902
$802$	−6.82435	−0.240976
$803$	2.43139	0.0858020
$804$	3.50535	0.123624
$805$	−0.817804	−0.0288238
$806$	−2.31507	−0.0815450
$807$	0.554839	0.0195313
$808$	−2.77898	−0.0977643
$809$	−3.38314	−0.118945	−0.0594725	−	0.998230i	$-0.518942\pi$
$809$	−3.38314	−0.118945	−0.0594725	+	0.998230i	$0.518942\pi$
$810$	−8.57745	−0.301381
$811$	42.6286	1.49689	0.748447	−	0.663194i	$-0.230800\pi$
$811$	42.6286	1.49689	0.748447	+	0.663194i	$0.230800\pi$
$812$	1.66949	0.0585875
$813$	0.450165	0.0157880
$814$	3.05948	0.107235
$815$	10.1498	0.355531
$816$	0.662782	0.0232020
$817$	−7.65701	−0.267885
$818$	10.7347	0.375329
$819$	0.497197	0.0173735
$820$	−0.956727	−0.0334103
$821$	13.1402	0.458596	0.229298	−	0.973356i	$-0.426357\pi$
$821$	13.1402	0.458596	0.229298	+	0.973356i	$0.426357\pi$
$822$	−2.12792	−0.0742198
$823$	−23.3397	−0.813571	−0.406786	−	0.913524i	$-0.633350\pi$
$823$	−23.3397	−0.813571	−0.406786	+	0.913524i	$0.633350\pi$
$824$	−12.7766	−0.445095
$825$	−0.217250	−0.00756366
$826$	−1.06192	−0.0369489
$827$	6.20930	0.215918	0.107959	−	0.994155i	$-0.465568\pi$
$827$	6.20930	0.215918	0.107959	+	0.994155i	$0.465568\pi$
$828$	4.20552	0.146152
$829$	−34.4906	−1.19791	−0.598955	−	0.800783i	$-0.704417\pi$
$829$	−34.4906	−1.19791	−0.598955	+	0.800783i	$0.704417\pi$
$830$	15.2765	0.530256
$831$	0.966722	0.0335352
$832$	0.293244	0.0101664
$833$	20.3496	0.705073
$834$	2.73792	0.0948066
$835$	5.80285	0.200816
$836$	7.65701	0.264823
$837$	−10.2098	−0.352901
$838$	5.10987	0.176517
$839$	2.98168	0.102939	0.0514695	−	0.998675i	$-0.483610\pi$
$839$	2.98168	0.102939	0.0514695	+	0.998675i	$0.483610\pi$
$840$	−0.124745	−0.00430411
$841$	−20.5465	−0.708499
$842$	−2.92145	−0.100680
$843$	−3.73078	−0.128495
$844$	0.779718	0.0268390
$845$	12.9140	0.444255
$846$	0.625323	0.0214990
$847$	−0.574201	−0.0197298
$848$	1.64627	0.0565332
$849$	−1.34859	−0.0462834
$850$	−3.05078	−0.104641
$851$	−4.35746	−0.149372
$852$	0.728081	0.0249436
$853$	1.48451	0.0508286	0.0254143	−	0.999677i	$-0.491910\pi$
$853$	1.48451	0.0508286	0.0254143	+	0.999677i	$0.491910\pi$
$854$	3.52934	0.120771
$855$	22.6096	0.773233
$856$	4.76302	0.162797
$857$	15.0982	0.515746	0.257873	−	0.966179i	$-0.416978\pi$
$857$	15.0982	0.515746	0.257873	+	0.966179i	$0.416978\pi$
$858$	−0.0637073	−0.00217493
$859$	−47.3730	−1.61634	−0.808172	−	0.588946i	$-0.799543\pi$
$859$	−47.3730	−1.61634	−0.808172	+	0.588946i	$0.799543\pi$
$860$	1.00000	0.0340997
$861$	0.119347	0.00406733
$862$	−10.1391	−0.345338
$863$	−4.23745	−0.144244	−0.0721222	−	0.997396i	$-0.522977\pi$
$863$	−4.23745	−0.144244	−0.0721222	+	0.997396i	$0.522977\pi$
$864$	1.29324	0.0439971
$865$	−6.31864	−0.214840
$866$	1.65655	0.0562920
$867$	1.67124	0.0567583
$868$	4.53314	0.153865
$869$	−11.5086	−0.390403
$870$	−0.631652	−0.0214150
$871$	−4.73154	−0.160322
$872$	−11.4665	−0.388305
$873$	−44.6124	−1.50990
$874$	−10.9055	−0.368883
$875$	0.574201	0.0194115
$876$	−0.528219	−0.0178469
$877$	15.3613	0.518715	0.259358	−	0.965781i	$-0.416489\pi$
$877$	15.3613	0.518715	0.259358	+	0.965781i	$0.416489\pi$
$878$	−12.0056	−0.405171
$879$	4.69655	0.158411
$880$	−1.00000	−0.0337100
$881$	20.4703	0.689661	0.344830	−	0.938665i	$-0.387936\pi$
$881$	20.4703	0.689661	0.344830	+	0.938665i	$0.387936\pi$
$882$	19.6961	0.663201
$883$	−51.0066	−1.71651	−0.858254	−	0.513225i	$-0.828451\pi$
$883$	−51.0066	−1.71651	−0.858254	+	0.513225i	$0.828451\pi$
$884$	−0.894626	−0.0300895
$885$	0.401778	0.0135056
$886$	−33.8444	−1.13703
$887$	−15.6508	−0.525501	−0.262751	−	0.964864i	$-0.584630\pi$
$887$	−15.6508	−0.525501	−0.262751	+	0.964864i	$0.584630\pi$
$888$	−0.664672	−0.0223049
$889$	−2.42682	−0.0813930
$890$	0.829948	0.0278199
$891$	8.57745	0.287355
$892$	2.88873	0.0967219
$893$	−1.62154	−0.0542629
$894$	3.85900	0.129064
$895$	−12.1482	−0.406070
$896$	−0.574201	−0.0191827
$897$	0.0907348	0.00302955
$898$	−21.2449	−0.708950
$899$	22.9538	0.765551
$900$	−2.95280	−0.0984268
$901$	−5.02242	−0.167321
$902$	0.956727	0.0318555
$903$	−0.124745	−0.00415126
$904$	2.42224	0.0805624
$905$	9.73179	0.323496
$906$	0.494693	0.0164351
$907$	4.15884	0.138092	0.0690460	−	0.997613i	$-0.478004\pi$
$907$	4.15884	0.138092	0.0690460	+	0.997613i	$0.478004\pi$
$908$	16.5363	0.548777
$909$	8.20579	0.272169
$910$	0.168381	0.00558179
$911$	−0.529347	−0.0175381	−0.00876903	−	0.999962i	$-0.502791\pi$
$911$	−0.529347	−0.0175381	−0.00876903	+	0.999962i	$0.502791\pi$
$912$	−1.66348	−0.0550834
$913$	−15.2765	−0.505579
$914$	−19.3029	−0.638482
$915$	−1.33533	−0.0441446
$916$	−7.43809	−0.245761
$917$	7.72535	0.255114
$918$	−3.94541	−0.130218
$919$	−17.4049	−0.574134	−0.287067	−	0.957911i	$-0.592680\pi$
$919$	−17.4049	−0.574134	−0.287067	+	0.957911i	$0.592680\pi$
$920$	1.42425	0.0469560
$921$	5.93038	0.195413
$922$	24.8744	0.819195
$923$	−0.982767	−0.0323482
$924$	0.124745	0.00410381
$925$	3.05948	0.100595
$926$	7.46911	0.245450
$927$	37.7269	1.23911
$928$	−2.90750	−0.0954432
$929$	15.4660	0.507423	0.253711	−	0.967280i	$-0.418349\pi$
$929$	15.4660	0.507423	0.253711	+	0.967280i	$0.418349\pi$
$930$	−1.71512	−0.0562410
$931$	−51.0745	−1.67390
$932$	7.63502	0.250093
$933$	−5.91387	−0.193611
$934$	36.2796	1.18711
$935$	3.05078	0.0997713
$936$	−0.865893	−0.0283026
$937$	14.0772	0.459882	0.229941	−	0.973205i	$-0.426147\pi$
$937$	14.0772	0.459882	0.229941	+	0.973205i	$0.426147\pi$
$938$	9.26482	0.302507
$939$	0.264279	0.00862442
$940$	0.211773	0.00690726
$941$	−18.0215	−0.587484	−0.293742	−	0.955885i	$-0.594901\pi$
$941$	−18.0215	−0.587484	−0.293742	+	0.955885i	$0.594901\pi$
$942$	3.55403	0.115797
$943$	−1.36261	−0.0443728
$944$	1.84938	0.0601923
$945$	0.742583	0.0241562
$946$	−1.00000	−0.0325128
$947$	33.1308	1.07661	0.538304	−	0.842751i	$-0.319065\pi$
$947$	33.1308	1.07661	0.538304	+	0.842751i	$0.319065\pi$
$948$	2.50024	0.0812040
$949$	0.712993	0.0231447
$950$	7.65701	0.248426
$951$	−0.899976	−0.0291837
$952$	1.75176	0.0567750
$953$	−38.9642	−1.26217	−0.631087	−	0.775712i	$-0.717391\pi$
$953$	−38.9642	−1.26217	−0.631087	+	0.775712i	$0.717391\pi$
$954$	−4.86112	−0.157384
$955$	−16.7270	−0.541273
$956$	−7.66193	−0.247805
$957$	0.631652	0.0204184
$958$	21.6211	0.698546
$959$	−5.62420	−0.181615
$960$	0.217250	0.00701170
$961$	31.3261	1.01052
$962$	0.897177	0.0289261
$963$	−14.0642	−0.453214
$964$	13.4628	0.433606
$965$	12.2772	0.395216
$966$	−0.177668	−0.00571636
$967$	−6.59365	−0.212037	−0.106019	−	0.994364i	$-0.533810\pi$
$967$	−6.59365	−0.212037	−0.106019	+	0.994364i	$0.533810\pi$
$968$	1.00000	0.0321412
$969$	5.07493	0.163030
$970$	−15.1085	−0.485105
$971$	−28.7862	−0.923794	−0.461897	−	0.886933i	$-0.652831\pi$
$971$	−28.7862	−0.923794	−0.461897	+	0.886933i	$0.652831\pi$
$972$	−5.74318	−0.184213
$973$	7.23647	0.231990
$974$	26.5006	0.849135
$975$	−0.0637073	−0.00204027
$976$	−6.14651	−0.196745
$977$	7.47563	0.239167	0.119583	−	0.992824i	$-0.461844\pi$
$977$	7.47563	0.239167	0.119583	+	0.992824i	$0.461844\pi$
$978$	2.20504	0.0705093
$979$	−0.829948	−0.0265252
$980$	6.67029	0.213075
$981$	33.8584	1.08101
$982$	6.31809	0.201618
$983$	6.08688	0.194141	0.0970707	−	0.995277i	$-0.469053\pi$
$983$	6.08688	0.194141	0.0970707	+	0.995277i	$0.469053\pi$
$984$	−0.207849	−0.00662597
$985$	−10.4314	−0.332372
$986$	8.87014	0.282483
$987$	−0.0264176	−0.000840881 0
$988$	2.24537	0.0714349
$989$	1.42425	0.0452884
$990$	2.95280	0.0938462
$991$	2.22301	0.0706162	0.0353081	−	0.999376i	$-0.488759\pi$
$991$	2.22301	0.0706162	0.0353081	+	0.999376i	$0.488759\pi$
$992$	−7.89469	−0.250657
$993$	−5.58024	−0.177083
$994$	1.92435	0.0610368
$995$	−14.3812	−0.455914
$996$	3.31882	0.105161
$997$	−9.58064	−0.303422	−0.151711	−	0.988425i	$-0.548478\pi$
$997$	−9.58064	−0.303422	−0.151711	+	0.988425i	$0.548478\pi$
$998$	24.6045	0.778842
$999$	3.95666	0.125183

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.v.1.2	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.v.1.2	✓	5	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:	\( N \)	\(=\)	\( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4730.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.217250 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.217250 q^{6} -0.574201 q^{7} +1.00000 q^{8} -2.95280 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.217250 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.217250 q^{6} -0.574201 q^{7} +1.00000 q^{8} -2.95280 q^{9} -1.00000 q^{10} +1.00000 q^{11} -0.217250 q^{12} +0.293244 q^{13} -0.574201 q^{14} +0.217250 q^{15} +1.00000 q^{16} -3.05078 q^{17} -2.95280 q^{18} +7.65701 q^{19} -1.00000 q^{20} +0.124745 q^{21} +1.00000 q^{22} -1.42425 q^{23} -0.217250 q^{24} +1.00000 q^{25} +0.293244 q^{26} +1.29324 q^{27} -0.574201 q^{28} -2.90750 q^{29} +0.217250 q^{30} -7.89469 q^{31} +1.00000 q^{32} -0.217250 q^{33} -3.05078 q^{34} +0.574201 q^{35} -2.95280 q^{36} +3.05948 q^{37} +7.65701 q^{38} -0.0637073 q^{39} -1.00000 q^{40} +0.956727 q^{41} +0.124745 q^{42} -1.00000 q^{43} +1.00000 q^{44} +2.95280 q^{45} -1.42425 q^{46} -0.211773 q^{47} -0.217250 q^{48} -6.67029 q^{49} +1.00000 q^{50} +0.662782 q^{51} +0.293244 q^{52} +1.64627 q^{53} +1.29324 q^{54} -1.00000 q^{55} -0.574201 q^{56} -1.66348 q^{57} -2.90750 q^{58} +1.84938 q^{59} +0.217250 q^{60} -6.14651 q^{61} -7.89469 q^{62} +1.69550 q^{63} +1.00000 q^{64} -0.293244 q^{65} -0.217250 q^{66} -16.1351 q^{67} -3.05078 q^{68} +0.309417 q^{69} +0.574201 q^{70} -3.35136 q^{71} -2.95280 q^{72} +2.43139 q^{73} +3.05948 q^{74} -0.217250 q^{75} +7.65701 q^{76} -0.574201 q^{77} -0.0637073 q^{78} -11.5086 q^{79} -1.00000 q^{80} +8.57745 q^{81} +0.956727 q^{82} -15.2765 q^{83} +0.124745 q^{84} +3.05078 q^{85} -1.00000 q^{86} +0.631652 q^{87} +1.00000 q^{88} -0.829948 q^{89} +2.95280 q^{90} -0.168381 q^{91} -1.42425 q^{92} +1.71512 q^{93} -0.211773 q^{94} -7.65701 q^{95} -0.217250 q^{96} +15.1085 q^{97} -6.67029 q^{98} -2.95280 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} + 2 q^{3} + 5 q^{4} - 5 q^{5} + 2 q^{6} - 6 q^{7} + 5 q^{8} - q^{9}+O(q^{10}) \) 5 * q + 5 * q^2 + 2 * q^3 + 5 * q^4 - 5 * q^5 + 2 * q^6 - 6 * q^7 + 5 * q^8 - q^9	\( 5 q + 5 q^{2} + 2 q^{3} + 5 q^{4} - 5 q^{5} + 2 q^{6} - 6 q^{7} + 5 q^{8} - q^{9} - 5 q^{10} + 5 q^{11} + 2 q^{12} - 12 q^{13} - 6 q^{14} - 2 q^{15} + 5 q^{16} - 2 q^{17} - q^{18} - 4 q^{19} - 5 q^{20} + 2 q^{21} + 5 q^{22} - 6 q^{23} + 2 q^{24} + 5 q^{25} - 12 q^{26} - 7 q^{27} - 6 q^{28} - 19 q^{29} - 2 q^{30} - 7 q^{31} + 5 q^{32} + 2 q^{33} - 2 q^{34} + 6 q^{35} - q^{36} - q^{37} - 4 q^{38} - 20 q^{39} - 5 q^{40} - 2 q^{41} + 2 q^{42} - 5 q^{43} + 5 q^{44} + q^{45} - 6 q^{46} + 7 q^{47} + 2 q^{48} - 5 q^{49} + 5 q^{50} - 5 q^{51} - 12 q^{52} - 6 q^{53} - 7 q^{54} - 5 q^{55} - 6 q^{56} - 15 q^{57} - 19 q^{58} - 5 q^{59} - 2 q^{60} - 5 q^{61} - 7 q^{62} - 17 q^{63} + 5 q^{64} + 12 q^{65} + 2 q^{66} - 20 q^{67} - 2 q^{68} - 40 q^{69} + 6 q^{70} - 22 q^{71} - q^{72} + 10 q^{73} - q^{74} + 2 q^{75} - 4 q^{76} - 6 q^{77} - 20 q^{78} - 9 q^{79} - 5 q^{80} - 15 q^{81} - 2 q^{82} - 19 q^{83} + 2 q^{84} + 2 q^{85} - 5 q^{86} + 15 q^{87} + 5 q^{88} - 21 q^{89} + q^{90} + 10 q^{91} - 6 q^{92} - 15 q^{93} + 7 q^{94} + 4 q^{95} + 2 q^{96} + 10 q^{97} - 5 q^{98} - q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 + 2 * q^3 + 5 * q^4 - 5 * q^5 + 2 * q^6 - 6 * q^7 + 5 * q^8 - q^9 - 5 * q^10 + 5 * q^11 + 2 * q^12 - 12 * q^13 - 6 * q^14 - 2 * q^15 + 5 * q^16 - 2 * q^17 - q^18 - 4 * q^19 - 5 * q^20 + 2 * q^21 + 5 * q^22 - 6 * q^23 + 2 * q^24 + 5 * q^25 - 12 * q^26 - 7 * q^27 - 6 * q^28 - 19 * q^29 - 2 * q^30 - 7 * q^31 + 5 * q^32 + 2 * q^33 - 2 * q^34 + 6 * q^35 - q^36 - q^37 - 4 * q^38 - 20 * q^39 - 5 * q^40 - 2 * q^41 + 2 * q^42 - 5 * q^43 + 5 * q^44 + q^45 - 6 * q^46 + 7 * q^47 + 2 * q^48 - 5 * q^49 + 5 * q^50 - 5 * q^51 - 12 * q^52 - 6 * q^53 - 7 * q^54 - 5 * q^55 - 6 * q^56 - 15 * q^57 - 19 * q^58 - 5 * q^59 - 2 * q^60 - 5 * q^61 - 7 * q^62 - 17 * q^63 + 5 * q^64 + 12 * q^65 + 2 * q^66 - 20 * q^67 - 2 * q^68 - 40 * q^69 + 6 * q^70 - 22 * q^71 - q^72 + 10 * q^73 - q^74 + 2 * q^75 - 4 * q^76 - 6 * q^77 - 20 * q^78 - 9 * q^79 - 5 * q^80 - 15 * q^81 - 2 * q^82 - 19 * q^83 + 2 * q^84 + 2 * q^85 - 5 * q^86 + 15 * q^87 + 5 * q^88 - 21 * q^89 + q^90 + 10 * q^91 - 6 * q^92 - 15 * q^93 + 7 * q^94 + 4 * q^95 + 2 * q^96 + 10 * q^97 - 5 * q^98 - q^99

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