LMFDB - Embedded newform 8030.2.a.bd.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8030,2,Mod(1,8030)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8030, 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("8030.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8030 = 2 \cdot 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8030.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:	$64.1198728231$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 6 x^{13} - 15 x^{12} + 143 x^{11} - 13 x^{10} - 1176 x^{9} + 1018 x^{8} + 4076 x^{7} + \cdots - 54 $ x^14 - 6x^13 - 15x^12 + 143x^11 - 13x^10 - 1176x^9 + 1018x^8 + 4076x^7 - 4865x^6 - 5483x^5 + 7607x^4 + 1210x^3 - 3153x^2 + 878*x - 54
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-2.47616$ of defining polynomial
Character	$\chi$	$=$	8030.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.47616 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.47616 q^{6} -1.89245 q^{7} +1.00000 q^{8} +3.13135 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.47616 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.47616 q^{6} -1.89245 q^{7} +1.00000 q^{8} +3.13135 q^{9} -1.00000 q^{10} +1.00000 q^{11} -2.47616 q^{12} +0.376331 q^{13} -1.89245 q^{14} +2.47616 q^{15} +1.00000 q^{16} +4.34771 q^{17} +3.13135 q^{18} -1.68016 q^{19} -1.00000 q^{20} +4.68601 q^{21} +1.00000 q^{22} +9.43433 q^{23} -2.47616 q^{24} +1.00000 q^{25} +0.376331 q^{26} -0.325247 q^{27} -1.89245 q^{28} +0.679883 q^{29} +2.47616 q^{30} -3.70796 q^{31} +1.00000 q^{32} -2.47616 q^{33} +4.34771 q^{34} +1.89245 q^{35} +3.13135 q^{36} -7.05205 q^{37} -1.68016 q^{38} -0.931855 q^{39} -1.00000 q^{40} +1.15990 q^{41} +4.68601 q^{42} -0.475968 q^{43} +1.00000 q^{44} -3.13135 q^{45} +9.43433 q^{46} -4.40545 q^{47} -2.47616 q^{48} -3.41861 q^{49} +1.00000 q^{50} -10.7656 q^{51} +0.376331 q^{52} -11.2265 q^{53} -0.325247 q^{54} -1.00000 q^{55} -1.89245 q^{56} +4.16034 q^{57} +0.679883 q^{58} +7.86618 q^{59} +2.47616 q^{60} -1.19088 q^{61} -3.70796 q^{62} -5.92594 q^{63} +1.00000 q^{64} -0.376331 q^{65} -2.47616 q^{66} -11.3769 q^{67} +4.34771 q^{68} -23.3609 q^{69} +1.89245 q^{70} -4.41026 q^{71} +3.13135 q^{72} +1.00000 q^{73} -7.05205 q^{74} -2.47616 q^{75} -1.68016 q^{76} -1.89245 q^{77} -0.931855 q^{78} -0.437734 q^{79} -1.00000 q^{80} -8.58869 q^{81} +1.15990 q^{82} +12.7283 q^{83} +4.68601 q^{84} -4.34771 q^{85} -0.475968 q^{86} -1.68350 q^{87} +1.00000 q^{88} +5.89707 q^{89} -3.13135 q^{90} -0.712190 q^{91} +9.43433 q^{92} +9.18150 q^{93} -4.40545 q^{94} +1.68016 q^{95} -2.47616 q^{96} -10.4060 q^{97} -3.41861 q^{98} +3.13135 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 14 q^{2} + 6 q^{3} + 14 q^{4} - 14 q^{5} + 6 q^{6} + 4 q^{7} + 14 q^{8} + 24 q^{9}+O(q^{10}) $ 14 * q + 14 * q^2 + 6 * q^3 + 14 * q^4 - 14 * q^5 + 6 * q^6 + 4 * q^7 + 14 * q^8 + 24 * q^9	\( 14 q + 14 q^{2} + 6 q^{3} + 14 q^{4} - 14 q^{5} + 6 q^{6} + 4 q^{7} + 14 q^{8} + 24 q^{9} - 14 q^{10} + 14 q^{11} + 6 q^{12} + 4 q^{13} + 4 q^{14} - 6 q^{15} + 14 q^{16} + 20 q^{17} + 24 q^{18} - 14 q^{20} + 25 q^{21} + 14 q^{22} - 4 q^{23} + 6 q^{24} + 14 q^{25} + 4 q^{26} + 21 q^{27} + 4 q^{28} + 7 q^{29} - 6 q^{30} + 8 q^{31} + 14 q^{32} + 6 q^{33} + 20 q^{34} - 4 q^{35} + 24 q^{36} + 17 q^{37} + 7 q^{39} - 14 q^{40} - 14 q^{41} + 25 q^{42} + 12 q^{43} + 14 q^{44} - 24 q^{45} - 4 q^{46} + 28 q^{47} + 6 q^{48} + 20 q^{49} + 14 q^{50} - 13 q^{51} + 4 q^{52} + 13 q^{53} + 21 q^{54} - 14 q^{55} + 4 q^{56} - 23 q^{57} + 7 q^{58} + 36 q^{59} - 6 q^{60} + 25 q^{61} + 8 q^{62} + 45 q^{63} + 14 q^{64} - 4 q^{65} + 6 q^{66} + 20 q^{68} - 7 q^{69} - 4 q^{70} + 17 q^{71} + 24 q^{72} + 14 q^{73} + 17 q^{74} + 6 q^{75} + 4 q^{77} + 7 q^{78} + 10 q^{79} - 14 q^{80} + 58 q^{81} - 14 q^{82} - 6 q^{83} + 25 q^{84} - 20 q^{85} + 12 q^{86} + 44 q^{87} + 14 q^{88} + 36 q^{89} - 24 q^{90} - 15 q^{91} - 4 q^{92} - 2 q^{93} + 28 q^{94} + 6 q^{96} - 19 q^{97} + 20 q^{98} + 24 q^{99}+O(q^{100}) \) 14 * q + 14 * q^2 + 6 * q^3 + 14 * q^4 - 14 * q^5 + 6 * q^6 + 4 * q^7 + 14 * q^8 + 24 * q^9 - 14 * q^10 + 14 * q^11 + 6 * q^12 + 4 * q^13 + 4 * q^14 - 6 * q^15 + 14 * q^16 + 20 * q^17 + 24 * q^18 - 14 * q^20 + 25 * q^21 + 14 * q^22 - 4 * q^23 + 6 * q^24 + 14 * q^25 + 4 * q^26 + 21 * q^27 + 4 * q^28 + 7 * q^29 - 6 * q^30 + 8 * q^31 + 14 * q^32 + 6 * q^33 + 20 * q^34 - 4 * q^35 + 24 * q^36 + 17 * q^37 + 7 * q^39 - 14 * q^40 - 14 * q^41 + 25 * q^42 + 12 * q^43 + 14 * q^44 - 24 * q^45 - 4 * q^46 + 28 * q^47 + 6 * q^48 + 20 * q^49 + 14 * q^50 - 13 * q^51 + 4 * q^52 + 13 * q^53 + 21 * q^54 - 14 * q^55 + 4 * q^56 - 23 * q^57 + 7 * q^58 + 36 * q^59 - 6 * q^60 + 25 * q^61 + 8 * q^62 + 45 * q^63 + 14 * q^64 - 4 * q^65 + 6 * q^66 + 20 * q^68 - 7 * q^69 - 4 * q^70 + 17 * q^71 + 24 * q^72 + 14 * q^73 + 17 * q^74 + 6 * q^75 + 4 * q^77 + 7 * q^78 + 10 * q^79 - 14 * q^80 + 58 * q^81 - 14 * q^82 - 6 * q^83 + 25 * q^84 - 20 * q^85 + 12 * q^86 + 44 * q^87 + 14 * q^88 + 36 * q^89 - 24 * q^90 - 15 * q^91 - 4 * q^92 - 2 * q^93 + 28 * q^94 + 6 * q^96 - 19 * q^97 + 20 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.47616	−1.42961	−0.714805	−	0.699324i	$-0.753484\pi$
$3$	−2.47616	−1.42961	−0.714805	+	0.699324i	$0.753484\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.47616	−1.01089
$7$	−1.89245	−0.715281	−0.357640	−	0.933859i	$-0.616419\pi$
$7$	−1.89245	−0.715281	−0.357640	+	0.933859i	$0.616419\pi$
$8$	1.00000	0.353553
$9$	3.13135	1.04378
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−2.47616	−0.714805
$13$	0.376331	0.104376	0.0521878	−	0.998637i	$-0.483381\pi$
$13$	0.376331	0.104376	0.0521878	+	0.998637i	$0.483381\pi$
$14$	−1.89245	−0.505780
$15$	2.47616	0.639341
$16$	1.00000	0.250000
$17$	4.34771	1.05447	0.527237	−	0.849718i	$-0.323228\pi$
$17$	4.34771	1.05447	0.527237	+	0.849718i	$0.323228\pi$
$18$	3.13135	0.738067
$19$	−1.68016	−0.385455	−0.192728	−	0.981252i	$-0.561733\pi$
$19$	−1.68016	−0.385455	−0.192728	+	0.981252i	$0.561733\pi$
$20$	−1.00000	−0.223607
$21$	4.68601	1.02257
$22$	1.00000	0.213201
$23$	9.43433	1.96719	0.983597	−	0.180378i	$-0.0577322\pi$
$23$	9.43433	1.96719	0.983597	+	0.180378i	$0.0577322\pi$
$24$	−2.47616	−0.505443
$25$	1.00000	0.200000
$26$	0.376331	0.0738047
$27$	−0.325247	−0.0625938
$28$	−1.89245	−0.357640
$29$	0.679883	0.126251	0.0631256	−	0.998006i	$-0.479893\pi$
$29$	0.679883	0.126251	0.0631256	+	0.998006i	$0.479893\pi$
$30$	2.47616	0.452082
$31$	−3.70796	−0.665970	−0.332985	−	0.942932i	$-0.608056\pi$
$31$	−3.70796	−0.665970	−0.332985	+	0.942932i	$0.608056\pi$
$32$	1.00000	0.176777
$33$	−2.47616	−0.431044
$34$	4.34771	0.745626
$35$	1.89245	0.319883
$36$	3.13135	0.521892
$37$	−7.05205	−1.15935	−0.579675	−	0.814848i	$-0.696820\pi$
$37$	−7.05205	−1.15935	−0.579675	+	0.814848i	$0.696820\pi$
$38$	−1.68016	−0.272558
$39$	−0.931855	−0.149216
$40$	−1.00000	−0.158114
$41$	1.15990	0.181146	0.0905730	−	0.995890i	$-0.471130\pi$
$41$	1.15990	0.181146	0.0905730	+	0.995890i	$0.471130\pi$
$42$	4.68601	0.723068
$43$	−0.475968	−0.0725844	−0.0362922	−	0.999341i	$-0.511555\pi$
$43$	−0.475968	−0.0725844	−0.0362922	+	0.999341i	$0.511555\pi$
$44$	1.00000	0.150756
$45$	−3.13135	−0.466794
$46$	9.43433	1.39102
$47$	−4.40545	−0.642601	−0.321300	−	0.946977i	$-0.604120\pi$
$47$	−4.40545	−0.642601	−0.321300	+	0.946977i	$0.604120\pi$
$48$	−2.47616	−0.357402
$49$	−3.41861	−0.488374
$50$	1.00000	0.141421
$51$	−10.7656	−1.50749
$52$	0.376331	0.0521878
$53$	−11.2265	−1.54207	−0.771036	−	0.636792i	$-0.780261\pi$
$53$	−11.2265	−1.54207	−0.771036	+	0.636792i	$0.780261\pi$
$54$	−0.325247	−0.0442605
$55$	−1.00000	−0.134840
$56$	−1.89245	−0.252890
$57$	4.16034	0.551051
$58$	0.679883	0.0892730
$59$	7.86618	1.02409	0.512045	−	0.858959i	$-0.328888\pi$
$59$	7.86618	1.02409	0.512045	+	0.858959i	$0.328888\pi$
$60$	2.47616	0.319670
$61$	−1.19088	−0.152477	−0.0762383	−	0.997090i	$-0.524291\pi$
$61$	−1.19088	−0.152477	−0.0762383	+	0.997090i	$0.524291\pi$
$62$	−3.70796	−0.470912
$63$	−5.92594	−0.746598
$64$	1.00000	0.125000
$65$	−0.376331	−0.0466782
$66$	−2.47616	−0.304794
$67$	−11.3769	−1.38991	−0.694954	−	0.719054i	$-0.744575\pi$
$67$	−11.3769	−1.38991	−0.694954	+	0.719054i	$0.744575\pi$
$68$	4.34771	0.527237
$69$	−23.3609	−2.81232
$70$	1.89245	0.226192
$71$	−4.41026	−0.523401	−0.261701	−	0.965149i	$-0.584283\pi$
$71$	−4.41026	−0.523401	−0.261701	+	0.965149i	$0.584283\pi$
$72$	3.13135	0.369033
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	−7.05205	−0.819784
$75$	−2.47616	−0.285922
$76$	−1.68016	−0.192728
$77$	−1.89245	−0.215665
$78$	−0.931855	−0.105512
$79$	−0.437734	−0.0492489	−0.0246244	−	0.999697i	$-0.507839\pi$
$79$	−0.437734	−0.0492489	−0.0246244	+	0.999697i	$0.507839\pi$
$80$	−1.00000	−0.111803
$81$	−8.58869	−0.954299
$82$	1.15990	0.128090
$83$	12.7283	1.39712	0.698558	−	0.715553i	$-0.253825\pi$
$83$	12.7283	1.39712	0.698558	+	0.715553i	$0.253825\pi$
$84$	4.68601	0.511286
$85$	−4.34771	−0.471575
$86$	−0.475968	−0.0513249
$87$	−1.68350	−0.180490
$88$	1.00000	0.106600
$89$	5.89707	0.625088	0.312544	−	0.949903i	$-0.398819\pi$
$89$	5.89707	0.625088	0.312544	+	0.949903i	$0.398819\pi$
$90$	−3.13135	−0.330073
$91$	−0.712190	−0.0746578
$92$	9.43433	0.983597
$93$	9.18150	0.952077
$94$	−4.40545	−0.454387
$95$	1.68016	0.172381
$96$	−2.47616	−0.252722
$97$	−10.4060	−1.05657	−0.528285	−	0.849067i	$-0.677165\pi$
$97$	−10.4060	−1.05657	−0.528285	+	0.849067i	$0.677165\pi$
$98$	−3.41861	−0.345332
$99$	3.13135	0.314713
$100$	1.00000	0.100000
$101$	13.9770	1.39077	0.695383	−	0.718639i	$-0.255235\pi$
$101$	13.9770	1.39077	0.695383	+	0.718639i	$0.255235\pi$
$102$	−10.7656	−1.06595
$103$	−10.0818	−0.993393	−0.496697	−	0.867924i	$-0.665454\pi$
$103$	−10.0818	−0.993393	−0.496697	+	0.867924i	$0.665454\pi$
$104$	0.376331	0.0369023
$105$	−4.68601	−0.457308
$106$	−11.2265	−1.09041
$107$	9.67316	0.935140	0.467570	−	0.883956i	$-0.345130\pi$
$107$	9.67316	0.935140	0.467570	+	0.883956i	$0.345130\pi$
$108$	−0.325247	−0.0312969
$109$	7.85264	0.752146	0.376073	−	0.926590i	$-0.377274\pi$
$109$	7.85264	0.752146	0.376073	+	0.926590i	$0.377274\pi$
$110$	−1.00000	−0.0953463
$111$	17.4620	1.65742
$112$	−1.89245	−0.178820
$113$	−1.23372	−0.116059	−0.0580293	−	0.998315i	$-0.518482\pi$
$113$	−1.23372	−0.116059	−0.0580293	+	0.998315i	$0.518482\pi$
$114$	4.16034	0.389652
$115$	−9.43433	−0.879756
$116$	0.679883	0.0631256
$117$	1.17843	0.108946
$118$	7.86618	0.724140
$119$	−8.22785	−0.754245
$120$	2.47616	0.226041
$121$	1.00000	0.0909091
$122$	−1.19088	−0.107817
$123$	−2.87210	−0.258968
$124$	−3.70796	−0.332985
$125$	−1.00000	−0.0894427
$126$	−5.92594	−0.527925
$127$	15.0828	1.33838	0.669192	−	0.743090i	$-0.266640\pi$
$127$	15.0828	1.33838	0.669192	+	0.743090i	$0.266640\pi$
$128$	1.00000	0.0883883
$129$	1.17857	0.103767
$130$	−0.376331	−0.0330064
$131$	17.4573	1.52526	0.762628	−	0.646838i	$-0.223909\pi$
$131$	17.4573	1.52526	0.762628	+	0.646838i	$0.223909\pi$
$132$	−2.47616	−0.215522
$133$	3.17963	0.275709
$134$	−11.3769	−0.982814
$135$	0.325247	0.0279928
$136$	4.34771	0.372813
$137$	−7.26045	−0.620302	−0.310151	−	0.950687i	$-0.600380\pi$
$137$	−7.26045	−0.620302	−0.310151	+	0.950687i	$0.600380\pi$
$138$	−23.3609	−1.98861
$139$	12.3277	1.04563	0.522813	−	0.852448i	$-0.324883\pi$
$139$	12.3277	1.04563	0.522813	+	0.852448i	$0.324883\pi$
$140$	1.89245	0.159942
$141$	10.9086	0.918668
$142$	−4.41026	−0.370101
$143$	0.376331	0.0314704
$144$	3.13135	0.260946
$145$	−0.679883	−0.0564612
$146$	1.00000	0.0827606
$147$	8.46502	0.698183
$148$	−7.05205	−0.579675
$149$	19.1876	1.57191	0.785955	−	0.618284i	$-0.212172\pi$
$149$	19.1876	1.57191	0.785955	+	0.618284i	$0.212172\pi$
$150$	−2.47616	−0.202177
$151$	−8.19139	−0.666606	−0.333303	−	0.942820i	$-0.608163\pi$
$151$	−8.19139	−0.666606	−0.333303	+	0.942820i	$0.608163\pi$
$152$	−1.68016	−0.136279
$153$	13.6142	1.10064
$154$	−1.89245	−0.152498
$155$	3.70796	0.297831
$156$	−0.931855	−0.0746081
$157$	16.6605	1.32965	0.664825	−	0.746999i	$-0.268506\pi$
$157$	16.6605	1.32965	0.664825	+	0.746999i	$0.268506\pi$
$158$	−0.437734	−0.0348242
$159$	27.7985	2.20456
$160$	−1.00000	−0.0790569
$161$	−17.8541	−1.40710
$162$	−8.58869	−0.674791
$163$	−9.17440	−0.718594	−0.359297	−	0.933223i	$-0.616984\pi$
$163$	−9.17440	−0.718594	−0.359297	+	0.933223i	$0.616984\pi$
$164$	1.15990	0.0905730
$165$	2.47616	0.192769
$166$	12.7283	0.987910
$167$	9.23459	0.714594	0.357297	−	0.933991i	$-0.383698\pi$
$167$	9.23459	0.714594	0.357297	+	0.933991i	$0.383698\pi$
$168$	4.68601	0.361534
$169$	−12.8584	−0.989106
$170$	−4.34771	−0.333454
$171$	−5.26117	−0.402332
$172$	−0.475968	−0.0362922
$173$	−12.3939	−0.942288	−0.471144	−	0.882056i	$-0.656159\pi$
$173$	−12.3939	−0.942288	−0.471144	+	0.882056i	$0.656159\pi$
$174$	−1.68350	−0.127626
$175$	−1.89245	−0.143056
$176$	1.00000	0.0753778
$177$	−19.4779	−1.46405
$178$	5.89707	0.442004
$179$	17.3314	1.29541	0.647704	−	0.761892i	$-0.275729\pi$
$179$	17.3314	1.29541	0.647704	+	0.761892i	$0.275729\pi$
$180$	−3.13135	−0.233397
$181$	16.9105	1.25695	0.628474	−	0.777831i	$-0.283680\pi$
$181$	16.9105	1.25695	0.628474	+	0.777831i	$0.283680\pi$
$182$	−0.712190	−0.0527910
$183$	2.94881	0.217982
$184$	9.43433	0.695508
$185$	7.05205	0.518477
$186$	9.18150	0.673220
$187$	4.34771	0.317936
$188$	−4.40545	−0.321300
$189$	0.615515	0.0447721
$190$	1.68016	0.121892
$191$	−8.92014	−0.645438	−0.322719	−	0.946495i	$-0.604597\pi$
$191$	−8.92014	−0.645438	−0.322719	+	0.946495i	$0.604597\pi$
$192$	−2.47616	−0.178701
$193$	13.1223	0.944567	0.472283	−	0.881447i	$-0.343430\pi$
$193$	13.1223	0.944567	0.472283	+	0.881447i	$0.343430\pi$
$194$	−10.4060	−0.747107
$195$	0.931855	0.0667316
$196$	−3.41861	−0.244187
$197$	−20.9393	−1.49186	−0.745932	−	0.666022i	$-0.767996\pi$
$197$	−20.9393	−1.49186	−0.745932	+	0.666022i	$0.767996\pi$
$198$	3.13135	0.222535
$199$	−15.5621	−1.10316	−0.551582	−	0.834120i	$-0.685976\pi$
$199$	−15.5621	−1.10316	−0.551582	+	0.834120i	$0.685976\pi$
$200$	1.00000	0.0707107
$201$	28.1710	1.98703
$202$	13.9770	0.983420
$203$	−1.28665	−0.0903050
$204$	−10.7656	−0.753744
$205$	−1.15990	−0.0810110
$206$	−10.0818	−0.702435
$207$	29.5422	2.05333
$208$	0.376331	0.0260939
$209$	−1.68016	−0.116219
$210$	−4.68601	−0.323366
$211$	−3.42188	−0.235572	−0.117786	−	0.993039i	$-0.537580\pi$
$211$	−3.42188	−0.235572	−0.117786	+	0.993039i	$0.537580\pi$
$212$	−11.2265	−0.771036
$213$	10.9205	0.748260
$214$	9.67316	0.661244
$215$	0.475968	0.0324607
$216$	−0.325247	−0.0221303
$217$	7.01716	0.476356
$218$	7.85264	0.531848
$219$	−2.47616	−0.167323
$220$	−1.00000	−0.0674200
$221$	1.63618	0.110061
$222$	17.4620	1.17197
$223$	19.2354	1.28810	0.644048	−	0.764985i	$-0.277254\pi$
$223$	19.2354	1.28810	0.644048	+	0.764985i	$0.277254\pi$
$224$	−1.89245	−0.126445
$225$	3.13135	0.208757
$226$	−1.23372	−0.0820659
$227$	15.6015	1.03551	0.517753	−	0.855530i	$-0.326769\pi$
$227$	15.6015	1.03551	0.517753	+	0.855530i	$0.326769\pi$
$228$	4.16034	0.275525
$229$	−4.12825	−0.272803	−0.136401	−	0.990654i	$-0.543554\pi$
$229$	−4.12825	−0.272803	−0.136401	+	0.990654i	$0.543554\pi$
$230$	−9.43433	−0.622082
$231$	4.68601	0.308317
$232$	0.679883	0.0446365
$233$	−23.2775	−1.52496	−0.762481	−	0.647011i	$-0.776019\pi$
$233$	−23.2775	−1.52496	−0.762481	+	0.647011i	$0.776019\pi$
$234$	1.17843	0.0770361
$235$	4.40545	0.287380
$236$	7.86618	0.512045
$237$	1.08390	0.0704067
$238$	−8.22785	−0.533332
$239$	17.6003	1.13847	0.569233	−	0.822176i	$-0.307240\pi$
$239$	17.6003	1.13847	0.569233	+	0.822176i	$0.307240\pi$
$240$	2.47616	0.159835
$241$	−12.0692	−0.777446	−0.388723	−	0.921355i	$-0.627084\pi$
$241$	−12.0692	−0.777446	−0.388723	+	0.921355i	$0.627084\pi$
$242$	1.00000	0.0642824
$243$	22.2427	1.42687
$244$	−1.19088	−0.0762383
$245$	3.41861	0.218407
$246$	−2.87210	−0.183118
$247$	−0.632297	−0.0402321
$248$	−3.70796	−0.235456
$249$	−31.5173	−1.99733
$250$	−1.00000	−0.0632456
$251$	17.0109	1.07372	0.536859	−	0.843672i	$-0.319611\pi$
$251$	17.0109	1.07372	0.536859	+	0.843672i	$0.319611\pi$
$252$	−5.92594	−0.373299
$253$	9.43433	0.593131
$254$	15.0828	0.946380
$255$	10.7656	0.674169
$256$	1.00000	0.0625000
$257$	6.97056	0.434811	0.217406	−	0.976081i	$-0.430241\pi$
$257$	6.97056	0.434811	0.217406	+	0.976081i	$0.430241\pi$
$258$	1.17857	0.0733746
$259$	13.3457	0.829260
$260$	−0.376331	−0.0233391
$261$	2.12895	0.131779
$262$	17.4573	1.07852
$263$	6.12800	0.377869	0.188934	−	0.981990i	$-0.439497\pi$
$263$	6.12800	0.377869	0.188934	+	0.981990i	$0.439497\pi$
$264$	−2.47616	−0.152397
$265$	11.2265	0.689636
$266$	3.17963	0.194956
$267$	−14.6021	−0.893632
$268$	−11.3769	−0.694954
$269$	18.7745	1.14470	0.572352	−	0.820008i	$-0.306031\pi$
$269$	18.7745	1.14470	0.572352	+	0.820008i	$0.306031\pi$
$270$	0.325247	0.0197939
$271$	10.2634	0.623454	0.311727	−	0.950172i	$-0.399093\pi$
$271$	10.2634	0.623454	0.311727	+	0.950172i	$0.399093\pi$
$272$	4.34771	0.263619
$273$	1.76349	0.106732
$274$	−7.26045	−0.438620
$275$	1.00000	0.0603023
$276$	−23.3609	−1.40616
$277$	10.1674	0.610902	0.305451	−	0.952208i	$-0.401193\pi$
$277$	10.1674	0.610902	0.305451	+	0.952208i	$0.401193\pi$
$278$	12.3277	0.739369
$279$	−11.6109	−0.695129
$280$	1.89245	0.113096
$281$	14.9775	0.893485	0.446742	−	0.894663i	$-0.352584\pi$
$281$	14.9775	0.893485	0.446742	+	0.894663i	$0.352584\pi$
$282$	10.9086	0.649596
$283$	−30.3852	−1.80621	−0.903107	−	0.429417i	$-0.858719\pi$
$283$	−30.3852	−1.80621	−0.903107	+	0.429417i	$0.858719\pi$
$284$	−4.41026	−0.261701
$285$	−4.16034	−0.246437
$286$	0.376331	0.0222529
$287$	−2.19506	−0.129570
$288$	3.13135	0.184517
$289$	1.90259	0.111917
$290$	−0.679883	−0.0399241
$291$	25.7669	1.51048
$292$	1.00000	0.0585206
$293$	30.4444	1.77858	0.889292	−	0.457340i	$-0.151198\pi$
$293$	30.4444	1.77858	0.889292	+	0.457340i	$0.151198\pi$
$294$	8.46502	0.493690
$295$	−7.86618	−0.457987
$296$	−7.05205	−0.409892
$297$	−0.325247	−0.0188727
$298$	19.1876	1.11151
$299$	3.55044	0.205327
$300$	−2.47616	−0.142961
$301$	0.900747	0.0519182
$302$	−8.19139	−0.471362
$303$	−34.6093	−1.98825
$304$	−1.68016	−0.0963638
$305$	1.19088	0.0681896
$306$	13.6142	0.778273
$307$	23.5568	1.34446	0.672228	−	0.740344i	$-0.265338\pi$
$307$	23.5568	1.34446	0.672228	+	0.740344i	$0.265338\pi$
$308$	−1.89245	−0.107833
$309$	24.9642	1.42016
$310$	3.70796	0.210598
$311$	13.6272	0.772729	0.386365	−	0.922346i	$-0.373731\pi$
$311$	13.6272	0.772729	0.386365	+	0.922346i	$0.373731\pi$
$312$	−0.931855	−0.0527559
$313$	−28.3488	−1.60237	−0.801184	−	0.598418i	$-0.795796\pi$
$313$	−28.3488	−1.60237	−0.801184	+	0.598418i	$0.795796\pi$
$314$	16.6605	0.940205
$315$	5.92594	0.333889
$316$	−0.437734	−0.0246244
$317$	−9.79107	−0.549921	−0.274961	−	0.961456i	$-0.588665\pi$
$317$	−9.79107	−0.549921	−0.274961	+	0.961456i	$0.588665\pi$
$318$	27.7985	1.55886
$319$	0.679883	0.0380661
$320$	−1.00000	−0.0559017
$321$	−23.9523	−1.33689
$322$	−17.8541	−0.994967
$323$	−7.30485	−0.406453
$324$	−8.58869	−0.477150
$325$	0.376331	0.0208751
$326$	−9.17440	−0.508123
$327$	−19.4444	−1.07528
$328$	1.15990	0.0640448
$329$	8.33711	0.459640
$330$	2.47616	0.136308
$331$	−31.8940	−1.75306	−0.876528	−	0.481352i	$-0.840146\pi$
$331$	−31.8940	−1.75306	−0.876528	+	0.481352i	$0.840146\pi$
$332$	12.7283	0.698558
$333$	−22.0824	−1.21011
$334$	9.23459	0.505294
$335$	11.3769	0.621586
$336$	4.68601	0.255643
$337$	−31.4621	−1.71385	−0.856924	−	0.515443i	$-0.827627\pi$
$337$	−31.4621	−1.71385	−0.856924	+	0.515443i	$0.827627\pi$
$338$	−12.8584	−0.699403
$339$	3.05489	0.165919
$340$	−4.34771	−0.235788
$341$	−3.70796	−0.200798
$342$	−5.26117	−0.284492
$343$	19.7168	1.06460
$344$	−0.475968	−0.0256624
$345$	23.3609	1.25771
$346$	−12.3939	−0.666298
$347$	31.0748	1.66818	0.834092	−	0.551625i	$-0.185992\pi$
$347$	31.0748	1.66818	0.834092	+	0.551625i	$0.185992\pi$
$348$	−1.68350	−0.0902449
$349$	−10.2592	−0.549161	−0.274580	−	0.961564i	$-0.588539\pi$
$349$	−10.2592	−0.549161	−0.274580	+	0.961564i	$0.588539\pi$
$350$	−1.89245	−0.101156
$351$	−0.122401	−0.00653326
$352$	1.00000	0.0533002
$353$	−35.8171	−1.90635	−0.953176	−	0.302416i	$-0.902207\pi$
$353$	−35.8171	−1.90635	−0.953176	+	0.302416i	$0.902207\pi$
$354$	−19.4779	−1.03524
$355$	4.41026	0.234072
$356$	5.89707	0.312544
$357$	20.3734	1.07828
$358$	17.3314	0.915992
$359$	34.6644	1.82952	0.914758	−	0.404001i	$-0.132381\pi$
$359$	34.6644	1.82952	0.914758	+	0.404001i	$0.132381\pi$
$360$	−3.13135	−0.165037
$361$	−16.1771	−0.851424
$362$	16.9105	0.888796
$363$	−2.47616	−0.129965
$364$	−0.712190	−0.0373289
$365$	−1.00000	−0.0523424
$366$	2.94881	0.154137
$367$	26.2836	1.37199	0.685995	−	0.727606i	$-0.259367\pi$
$367$	26.2836	1.37199	0.685995	+	0.727606i	$0.259367\pi$
$368$	9.43433	0.491799
$369$	3.63206	0.189077
$370$	7.05205	0.366619
$371$	21.2456	1.10301
$372$	9.18150	0.476039
$373$	−6.60649	−0.342071	−0.171035	−	0.985265i	$-0.554711\pi$
$373$	−6.60649	−0.342071	−0.171035	+	0.985265i	$0.554711\pi$
$374$	4.34771	0.224815
$375$	2.47616	0.127868
$376$	−4.40545	−0.227194
$377$	0.255861	0.0131775
$378$	0.615515	0.0316587
$379$	−23.5208	−1.20818	−0.604092	−	0.796915i	$-0.706464\pi$
$379$	−23.5208	−1.20818	−0.604092	+	0.796915i	$0.706464\pi$
$380$	1.68016	0.0861904
$381$	−37.3474	−1.91337
$382$	−8.92014	−0.456394
$383$	−30.0703	−1.53652	−0.768259	−	0.640139i	$-0.778877\pi$
$383$	−30.0703	−1.53652	−0.768259	+	0.640139i	$0.778877\pi$
$384$	−2.47616	−0.126361
$385$	1.89245	0.0964484
$386$	13.1223	0.667910
$387$	−1.49042	−0.0757624
$388$	−10.4060	−0.528285
$389$	15.2053	0.770939	0.385470	−	0.922721i	$-0.374039\pi$
$389$	15.2053	0.770939	0.385470	+	0.922721i	$0.374039\pi$
$390$	0.931855	0.0471863
$391$	41.0178	2.07436
$392$	−3.41861	−0.172666
$393$	−43.2271	−2.18052
$394$	−20.9393	−1.05491
$395$	0.437734	0.0220248
$396$	3.13135	0.157356
$397$	25.8340	1.29657	0.648285	−	0.761398i	$-0.275487\pi$
$397$	25.8340	1.29657	0.648285	+	0.761398i	$0.275487\pi$
$398$	−15.5621	−0.780055
$399$	−7.87326	−0.394156
$400$	1.00000	0.0500000
$401$	23.1572	1.15641	0.578207	−	0.815890i	$-0.303753\pi$
$401$	23.1572	1.15641	0.578207	+	0.815890i	$0.303753\pi$
$402$	28.1710	1.40504
$403$	−1.39542	−0.0695110
$404$	13.9770	0.695383
$405$	8.58869	0.426776
$406$	−1.28665	−0.0638553
$407$	−7.05205	−0.349557
$408$	−10.7656	−0.532977
$409$	22.6090	1.11794	0.558970	−	0.829188i	$-0.311197\pi$
$409$	22.6090	1.11794	0.558970	+	0.829188i	$0.311197\pi$
$410$	−1.15990	−0.0572834
$411$	17.9780	0.886790
$412$	−10.0818	−0.496697
$413$	−14.8864	−0.732511
$414$	29.5422	1.45192
$415$	−12.7283	−0.624809
$416$	0.376331	0.0184512
$417$	−30.5254	−1.49484
$418$	−1.68016	−0.0821794
$419$	27.5395	1.34539	0.672696	−	0.739919i	$-0.265136\pi$
$419$	27.5395	1.34539	0.672696	+	0.739919i	$0.265136\pi$
$420$	−4.68601	−0.228654
$421$	34.8997	1.70091	0.850453	−	0.526051i	$-0.176328\pi$
$421$	34.8997	1.70091	0.850453	+	0.526051i	$0.176328\pi$
$422$	−3.42188	−0.166575
$423$	−13.7950	−0.670736
$424$	−11.2265	−0.545205
$425$	4.34771	0.210895
$426$	10.9205	0.529099
$427$	2.25369	0.109064
$428$	9.67316	0.467570
$429$	−0.931855	−0.0449904
$430$	0.475968	0.0229532
$431$	−3.53108	−0.170086	−0.0850430	−	0.996377i	$-0.527103\pi$
$431$	−3.53108	−0.170086	−0.0850430	+	0.996377i	$0.527103\pi$
$432$	−0.325247	−0.0156485
$433$	−1.86849	−0.0897938	−0.0448969	−	0.998992i	$-0.514296\pi$
$433$	−1.86849	−0.0897938	−0.0448969	+	0.998992i	$0.514296\pi$
$434$	7.01716	0.336834
$435$	1.68350	0.0807175
$436$	7.85264	0.376073
$437$	−15.8512	−0.758266
$438$	−2.47616	−0.118315
$439$	39.5401	1.88715	0.943573	−	0.331164i	$-0.107441\pi$
$439$	39.5401	1.88715	0.943573	+	0.331164i	$0.107441\pi$
$440$	−1.00000	−0.0476731
$441$	−10.7049	−0.509756
$442$	1.63618	0.0778251
$443$	−28.9281	−1.37442	−0.687209	−	0.726460i	$-0.741164\pi$
$443$	−28.9281	−1.37442	−0.687209	+	0.726460i	$0.741164\pi$
$444$	17.4620	0.828709
$445$	−5.89707	−0.279548
$446$	19.2354	0.910822
$447$	−47.5115	−2.24722
$448$	−1.89245	−0.0894101
$449$	24.9468	1.17731	0.588655	−	0.808384i	$-0.299658\pi$
$449$	24.9468	1.17731	0.588655	+	0.808384i	$0.299658\pi$
$450$	3.13135	0.147613
$451$	1.15990	0.0546176
$452$	−1.23372	−0.0580293
$453$	20.2832	0.952986
$454$	15.6015	0.732213
$455$	0.712190	0.0333880
$456$	4.16034	0.194826
$457$	1.31662	0.0615890	0.0307945	−	0.999526i	$-0.490196\pi$
$457$	1.31662	0.0615890	0.0307945	+	0.999526i	$0.490196\pi$
$458$	−4.12825	−0.192901
$459$	−1.41408	−0.0660036
$460$	−9.43433	−0.439878
$461$	2.91839	0.135923	0.0679614	−	0.997688i	$-0.478351\pi$
$461$	2.91839	0.135923	0.0679614	+	0.997688i	$0.478351\pi$
$462$	4.68601	0.218013
$463$	−27.2696	−1.26732	−0.633662	−	0.773610i	$-0.718449\pi$
$463$	−27.2696	−1.26732	−0.633662	+	0.773610i	$0.718449\pi$
$464$	0.679883	0.0315628
$465$	−9.18150	−0.425782
$466$	−23.2775	−1.07831
$467$	34.3389	1.58901	0.794507	−	0.607255i	$-0.207729\pi$
$467$	34.3389	1.58901	0.794507	+	0.607255i	$0.207729\pi$
$468$	1.17843	0.0544728
$469$	21.5303	0.994175
$470$	4.40545	0.203208
$471$	−41.2539	−1.90088
$472$	7.86618	0.362070
$473$	−0.475968	−0.0218850
$474$	1.08390	0.0497851
$475$	−1.68016	−0.0770911
$476$	−8.22785	−0.377123
$477$	−35.1540	−1.60959
$478$	17.6003	0.805017
$479$	−3.57685	−0.163430	−0.0817152	−	0.996656i	$-0.526040\pi$
$479$	−3.57685	−0.163430	−0.0817152	+	0.996656i	$0.526040\pi$
$480$	2.47616	0.113021
$481$	−2.65391	−0.121008
$482$	−12.0692	−0.549737
$483$	44.2094	2.01160
$484$	1.00000	0.0454545
$485$	10.4060	0.472512
$486$	22.2427	1.00895
$487$	40.1019	1.81719	0.908595	−	0.417678i	$-0.137156\pi$
$487$	40.1019	1.81719	0.908595	+	0.417678i	$0.137156\pi$
$488$	−1.19088	−0.0539086
$489$	22.7172	1.02731
$490$	3.41861	0.154437
$491$	−39.4409	−1.77994	−0.889972	−	0.456015i	$-0.849276\pi$
$491$	−39.4409	−1.77994	−0.889972	+	0.456015i	$0.849276\pi$
$492$	−2.87210	−0.129484
$493$	2.95593	0.133129
$494$	−0.632297	−0.0284484
$495$	−3.13135	−0.140744
$496$	−3.70796	−0.166493
$497$	8.34621	0.374379
$498$	−31.5173	−1.41233
$499$	5.38879	0.241235	0.120618	−	0.992699i	$-0.461512\pi$
$499$	5.38879	0.241235	0.120618	+	0.992699i	$0.461512\pi$
$500$	−1.00000	−0.0447214
$501$	−22.8663	−1.02159
$502$	17.0109	0.759233
$503$	−5.60873	−0.250081	−0.125040	−	0.992152i	$-0.539906\pi$
$503$	−5.60873	−0.250081	−0.125040	+	0.992152i	$0.539906\pi$
$504$	−5.92594	−0.263962
$505$	−13.9770	−0.621970
$506$	9.43433	0.419407
$507$	31.8393	1.41404
$508$	15.0828	0.669192
$509$	−1.78067	−0.0789266	−0.0394633	−	0.999221i	$-0.512565\pi$
$509$	−1.78067	−0.0789266	−0.0394633	+	0.999221i	$0.512565\pi$
$510$	10.7656	0.476709
$511$	−1.89245	−0.0837173
$512$	1.00000	0.0441942
$513$	0.546467	0.0241271
$514$	6.97056	0.307458
$515$	10.0818	0.444259
$516$	1.17857	0.0518837
$517$	−4.40545	−0.193751
$518$	13.3457	0.586376
$519$	30.6891	1.34710
$520$	−0.376331	−0.0165032
$521$	−10.9429	−0.479418	−0.239709	−	0.970845i	$-0.577052\pi$
$521$	−10.9429	−0.479418	−0.239709	+	0.970845i	$0.577052\pi$
$522$	2.12895	0.0931817
$523$	−2.75054	−0.120273	−0.0601364	−	0.998190i	$-0.519154\pi$
$523$	−2.75054	−0.120273	−0.0601364	+	0.998190i	$0.519154\pi$
$524$	17.4573	0.762628
$525$	4.68601	0.204514
$526$	6.12800	0.267194
$527$	−16.1212	−0.702249
$528$	−2.47616	−0.107761
$529$	66.0067	2.86985
$530$	11.2265	0.487646
$531$	24.6318	1.06893
$532$	3.17963	0.137854
$533$	0.436507	0.0189072
$534$	−14.6021	−0.631893
$535$	−9.67316	−0.418207
$536$	−11.3769	−0.491407
$537$	−42.9152	−1.85193
$538$	18.7745	0.809427
$539$	−3.41861	−0.147250
$540$	0.325247	0.0139964
$541$	−19.6480	−0.844732	−0.422366	−	0.906425i	$-0.638800\pi$
$541$	−19.6480	−0.844732	−0.422366	+	0.906425i	$0.638800\pi$
$542$	10.2634	0.440849
$543$	−41.8730	−1.79694
$544$	4.34771	0.186407
$545$	−7.85264	−0.336370
$546$	1.76349	0.0754706
$547$	−5.87215	−0.251075	−0.125537	−	0.992089i	$-0.540066\pi$
$547$	−5.87215	−0.251075	−0.125537	+	0.992089i	$0.540066\pi$
$548$	−7.26045	−0.310151
$549$	−3.72907	−0.159153
$550$	1.00000	0.0426401
$551$	−1.14231	−0.0486642
$552$	−23.3609	−0.994305
$553$	0.828391	0.0352268
$554$	10.1674	0.431973
$555$	−17.4620	−0.741220
$556$	12.3277	0.522813
$557$	−31.9953	−1.35569	−0.677843	−	0.735207i	$-0.737085\pi$
$557$	−31.9953	−1.35569	−0.677843	+	0.735207i	$0.737085\pi$
$558$	−11.6109	−0.491530
$559$	−0.179122	−0.00757603
$560$	1.89245	0.0799708
$561$	−10.7656	−0.454524
$562$	14.9775	0.631789
$563$	2.62989	0.110837	0.0554184	−	0.998463i	$-0.482351\pi$
$563$	2.62989	0.110837	0.0554184	+	0.998463i	$0.482351\pi$
$564$	10.9086	0.459334
$565$	1.23372	0.0519030
$566$	−30.3852	−1.27719
$567$	16.2537	0.682592
$568$	−4.41026	−0.185050
$569$	−4.01807	−0.168446	−0.0842230	−	0.996447i	$-0.526841\pi$
$569$	−4.01807	−0.168446	−0.0842230	+	0.996447i	$0.526841\pi$
$570$	−4.16034	−0.174258
$571$	36.5584	1.52992	0.764961	−	0.644076i	$-0.222758\pi$
$571$	36.5584	1.52992	0.764961	+	0.644076i	$0.222758\pi$
$572$	0.376331	0.0157352
$573$	22.0877	0.922725
$574$	−2.19506	−0.0916200
$575$	9.43433	0.393439
$576$	3.13135	0.130473
$577$	−43.2624	−1.80104	−0.900518	−	0.434818i	$-0.856813\pi$
$577$	−43.2624	−1.80104	−0.900518	+	0.434818i	$0.856813\pi$
$578$	1.90259	0.0791371
$579$	−32.4930	−1.35036
$580$	−0.679883	−0.0282306
$581$	−24.0878	−0.999330
$582$	25.7669	1.06807
$583$	−11.2265	−0.464952
$584$	1.00000	0.0413803
$585$	−1.17843	−0.0487219
$586$	30.4444	1.25765
$587$	34.8399	1.43800	0.718998	−	0.695012i	$-0.244601\pi$
$587$	34.8399	1.43800	0.718998	+	0.695012i	$0.244601\pi$
$588$	8.46502	0.349092
$589$	6.22998	0.256702
$590$	−7.86618	−0.323845
$591$	51.8490	2.13278
$592$	−7.05205	−0.289837
$593$	−11.5221	−0.473155	−0.236577	−	0.971613i	$-0.576026\pi$
$593$	−11.5221	−0.473155	−0.236577	+	0.971613i	$0.576026\pi$
$594$	−0.325247	−0.0133450
$595$	8.22785	0.337309
$596$	19.1876	0.785955
$597$	38.5341	1.57710
$598$	3.55044	0.145188
$599$	−9.75401	−0.398538	−0.199269	−	0.979945i	$-0.563857\pi$
$599$	−9.75401	−0.398538	−0.199269	+	0.979945i	$0.563857\pi$
$600$	−2.47616	−0.101089
$601$	8.07524	0.329396	0.164698	−	0.986344i	$-0.447335\pi$
$601$	8.07524	0.329396	0.164698	+	0.986344i	$0.447335\pi$
$602$	0.900747	0.0367117
$603$	−35.6251	−1.45076
$604$	−8.19139	−0.333303
$605$	−1.00000	−0.0406558
$606$	−34.6093	−1.40591
$607$	7.79014	0.316192	0.158096	−	0.987424i	$-0.449464\pi$
$607$	7.79014	0.316192	0.158096	+	0.987424i	$0.449464\pi$
$608$	−1.68016	−0.0681395
$609$	3.18594	0.129101
$610$	1.19088	0.0482174
$611$	−1.65791	−0.0670718
$612$	13.6142	0.550322
$613$	1.14062	0.0460692	0.0230346	−	0.999735i	$-0.492667\pi$
$613$	1.14062	0.0460692	0.0230346	+	0.999735i	$0.492667\pi$
$614$	23.5568	0.950674
$615$	2.87210	0.115814
$616$	−1.89245	−0.0762492
$617$	16.4938	0.664015	0.332008	−	0.943277i	$-0.392274\pi$
$617$	16.4938	0.664015	0.332008	+	0.943277i	$0.392274\pi$
$618$	24.9642	1.00421
$619$	10.8262	0.435143	0.217572	−	0.976044i	$-0.430186\pi$
$619$	10.8262	0.435143	0.217572	+	0.976044i	$0.430186\pi$
$620$	3.70796	0.148915
$621$	−3.06849	−0.123134
$622$	13.6272	0.546402
$623$	−11.1599	−0.447113
$624$	−0.931855	−0.0373041
$625$	1.00000	0.0400000
$626$	−28.3488	−1.13305
$627$	4.16034	0.166148
$628$	16.6605	0.664825
$629$	−30.6603	−1.22250
$630$	5.92594	0.236095
$631$	14.2206	0.566115	0.283057	−	0.959103i	$-0.408651\pi$
$631$	14.2206	0.566115	0.283057	+	0.959103i	$0.408651\pi$
$632$	−0.437734	−0.0174121
$633$	8.47312	0.336776
$634$	−9.79107	−0.388853
$635$	−15.0828	−0.598543
$636$	27.7985	1.10228
$637$	−1.28653	−0.0509742
$638$	0.679883	0.0269168
$639$	−13.8101	−0.546318
$640$	−1.00000	−0.0395285
$641$	23.2242	0.917301	0.458650	−	0.888617i	$-0.348333\pi$
$641$	23.2242	0.917301	0.458650	+	0.888617i	$0.348333\pi$
$642$	−23.9523	−0.945321
$643$	−4.98109	−0.196435	−0.0982175	−	0.995165i	$-0.531314\pi$
$643$	−4.98109	−0.196435	−0.0982175	+	0.995165i	$0.531314\pi$
$644$	−17.8541	−0.703548
$645$	−1.17857	−0.0464062
$646$	−7.30485	−0.287406
$647$	0.756789	0.0297525	0.0148762	−	0.999889i	$-0.495265\pi$
$647$	0.756789	0.0297525	0.0148762	+	0.999889i	$0.495265\pi$
$648$	−8.58869	−0.337396
$649$	7.86618	0.308775
$650$	0.376331	0.0147609
$651$	−17.3756	−0.681003
$652$	−9.17440	−0.359297
$653$	27.2897	1.06793	0.533964	−	0.845507i	$-0.320702\pi$
$653$	27.2897	1.06793	0.533964	+	0.845507i	$0.320702\pi$
$654$	−19.4444	−0.760335
$655$	−17.4573	−0.682115
$656$	1.15990	0.0452865
$657$	3.13135	0.122166
$658$	8.33711	0.325014
$659$	32.1120	1.25091	0.625454	−	0.780261i	$-0.284914\pi$
$659$	32.1120	1.25091	0.625454	+	0.780261i	$0.284914\pi$
$660$	2.47616	0.0963843
$661$	43.0996	1.67638	0.838191	−	0.545377i	$-0.183613\pi$
$661$	43.0996	1.67638	0.838191	+	0.545377i	$0.183613\pi$
$662$	−31.8940	−1.23960
$663$	−4.05144	−0.157345
$664$	12.7283	0.493955
$665$	−3.17963	−0.123301
$666$	−22.0824	−0.855677
$667$	6.41424	0.248360
$668$	9.23459	0.357297
$669$	−47.6298	−1.84148
$670$	11.3769	0.439528
$671$	−1.19088	−0.0459734
$672$	4.68601	0.180767
$673$	−15.1220	−0.582910	−0.291455	−	0.956585i	$-0.594139\pi$
$673$	−15.1220	−0.582910	−0.291455	+	0.956585i	$0.594139\pi$
$674$	−31.4621	−1.21187
$675$	−0.325247	−0.0125188
$676$	−12.8584	−0.494553
$677$	18.3878	0.706702	0.353351	−	0.935491i	$-0.385042\pi$
$677$	18.3878	0.706702	0.353351	+	0.935491i	$0.385042\pi$
$678$	3.05489	0.117322
$679$	19.6929	0.755744
$680$	−4.34771	−0.166727
$681$	−38.6317	−1.48037
$682$	−3.70796	−0.141985
$683$	31.4322	1.20272	0.601360	−	0.798978i	$-0.294626\pi$
$683$	31.4322	1.20272	0.601360	+	0.798978i	$0.294626\pi$
$684$	−5.26117	−0.201166
$685$	7.26045	0.277408
$686$	19.7168	0.752789
$687$	10.2222	0.390001
$688$	−0.475968	−0.0181461
$689$	−4.22487	−0.160955
$690$	23.3609	0.889334
$691$	5.81972	0.221393	0.110696	−	0.993854i	$-0.464692\pi$
$691$	5.81972	0.221393	0.110696	+	0.993854i	$0.464692\pi$
$692$	−12.3939	−0.471144
$693$	−5.92594	−0.225108
$694$	31.0748	1.17958
$695$	−12.3277	−0.467618
$696$	−1.68350	−0.0638128
$697$	5.04291	0.191014
$698$	−10.2592	−0.388315
$699$	57.6388	2.18010
$700$	−1.89245	−0.0715281
$701$	28.7379	1.08542	0.542708	−	0.839921i	$-0.317399\pi$
$701$	28.7379	1.08542	0.542708	+	0.839921i	$0.317399\pi$
$702$	−0.122401	−0.00461971
$703$	11.8486	0.446877
$704$	1.00000	0.0376889
$705$	−10.9086	−0.410841
$706$	−35.8171	−1.34799
$707$	−26.4509	−0.994788
$708$	−19.4779	−0.732024
$709$	37.9621	1.42569	0.712847	−	0.701319i	$-0.247405\pi$
$709$	37.9621	1.42569	0.712847	+	0.701319i	$0.247405\pi$
$710$	4.41026	0.165514
$711$	−1.37070	−0.0514052
$712$	5.89707	0.221002
$713$	−34.9822	−1.31009
$714$	20.3734	0.762457
$715$	−0.376331	−0.0140740
$716$	17.3314	0.647704
$717$	−43.5810	−1.62756
$718$	34.6644	1.29366
$719$	26.9629	1.00555	0.502773	−	0.864418i	$-0.332313\pi$
$719$	26.9629	1.00555	0.502773	+	0.864418i	$0.332313\pi$
$720$	−3.13135	−0.116699
$721$	19.0794	0.710555
$722$	−16.1771	−0.602048
$723$	29.8852	1.11144
$724$	16.9105	0.628474
$725$	0.679883	0.0252502
$726$	−2.47616	−0.0918988
$727$	−17.2048	−0.638090	−0.319045	−	0.947740i	$-0.603362\pi$
$727$	−17.2048	−0.638090	−0.319045	+	0.947740i	$0.603362\pi$
$728$	−0.712190	−0.0263955
$729$	−29.3103	−1.08557
$730$	−1.00000	−0.0370117
$731$	−2.06937	−0.0765384
$732$	2.94881	0.108991
$733$	−14.1923	−0.524206	−0.262103	−	0.965040i	$-0.584416\pi$
$733$	−14.1923	−0.524206	−0.262103	+	0.965040i	$0.584416\pi$
$734$	26.2836	0.970144
$735$	−8.46502	−0.312237
$736$	9.43433	0.347754
$737$	−11.3769	−0.419073
$738$	3.63206	0.133698
$739$	−5.71070	−0.210072	−0.105036	−	0.994468i	$-0.533496\pi$
$739$	−5.71070	−0.210072	−0.105036	+	0.994468i	$0.533496\pi$
$740$	7.05205	0.259238
$741$	1.56567	0.0575162
$742$	21.2456	0.779949
$743$	−11.9717	−0.439201	−0.219600	−	0.975590i	$-0.570475\pi$
$743$	−11.9717	−0.439201	−0.219600	+	0.975590i	$0.570475\pi$
$744$	9.18150	0.336610
$745$	−19.1876	−0.702979
$746$	−6.60649	−0.241881
$747$	39.8569	1.45829
$748$	4.34771	0.158968
$749$	−18.3060	−0.668888
$750$	2.47616	0.0904165
$751$	15.5270	0.566587	0.283294	−	0.959033i	$-0.408573\pi$
$751$	15.5270	0.566587	0.283294	+	0.959033i	$0.408573\pi$
$752$	−4.40545	−0.160650
$753$	−42.1216	−1.53500
$754$	0.255861	0.00931792
$755$	8.19139	0.298115
$756$	0.615515	0.0223861
$757$	−14.3901	−0.523018	−0.261509	−	0.965201i	$-0.584220\pi$
$757$	−14.3901	−0.523018	−0.261509	+	0.965201i	$0.584220\pi$
$758$	−23.5208	−0.854315
$759$	−23.3609	−0.847947
$760$	1.68016	0.0609458
$761$	8.41179	0.304927	0.152464	−	0.988309i	$-0.451279\pi$
$761$	8.41179	0.304927	0.152464	+	0.988309i	$0.451279\pi$
$762$	−37.3474	−1.35295
$763$	−14.8608	−0.537996
$764$	−8.92014	−0.322719
$765$	−13.6142	−0.492223
$766$	−30.0703	−1.08648
$767$	2.96029	0.106890
$768$	−2.47616	−0.0893506
$769$	−8.60492	−0.310301	−0.155151	−	0.987891i	$-0.549586\pi$
$769$	−8.60492	−0.310301	−0.155151	+	0.987891i	$0.549586\pi$
$770$	1.89245	0.0681993
$771$	−17.2602	−0.621610
$772$	13.1223	0.472283
$773$	3.89369	0.140046	0.0700232	−	0.997545i	$-0.477693\pi$
$773$	3.89369	0.140046	0.0700232	+	0.997545i	$0.477693\pi$
$774$	−1.49042	−0.0535721
$775$	−3.70796	−0.133194
$776$	−10.4060	−0.373554
$777$	−33.0460	−1.18552
$778$	15.2053	0.545136
$779$	−1.94882	−0.0698237
$780$	0.931855	0.0333658
$781$	−4.41026	−0.157811
$782$	41.0178	1.46679
$783$	−0.221130	−0.00790254
$784$	−3.41861	−0.122093
$785$	−16.6605	−0.594638
$786$	−43.2271	−1.54186
$787$	38.0284	1.35556	0.677782	−	0.735263i	$-0.262941\pi$
$787$	38.0284	1.35556	0.677782	+	0.735263i	$0.262941\pi$
$788$	−20.9393	−0.745932
$789$	−15.1739	−0.540205
$790$	0.437734	0.0155739
$791$	2.33476	0.0830145
$792$	3.13135	0.111268
$793$	−0.448166	−0.0159148
$794$	25.8340	0.916813
$795$	−27.7985	−0.985910
$796$	−15.5621	−0.551582
$797$	−25.9641	−0.919695	−0.459847	−	0.887998i	$-0.652096\pi$
$797$	−25.9641	−0.919695	−0.459847	+	0.887998i	$0.652096\pi$
$798$	−7.87326	−0.278710
$799$	−19.1536	−0.677606
$800$	1.00000	0.0353553
$801$	18.4658	0.652457
$802$	23.1572	0.817709
$803$	1.00000	0.0352892
$804$	28.1710	0.993514
$805$	17.8541	0.629273
$806$	−1.39542	−0.0491517
$807$	−46.4887	−1.63648
$808$	13.9770	0.491710
$809$	−20.3568	−0.715709	−0.357854	−	0.933777i	$-0.616492\pi$
$809$	−20.3568	−0.715709	−0.357854	+	0.933777i	$0.616492\pi$
$810$	8.58869	0.301776
$811$	−50.9058	−1.78754	−0.893771	−	0.448523i	$-0.851950\pi$
$811$	−50.9058	−1.78754	−0.893771	+	0.448523i	$0.851950\pi$
$812$	−1.28665	−0.0451525
$813$	−25.4137	−0.891296
$814$	−7.05205	−0.247174
$815$	9.17440	0.321365
$816$	−10.7656	−0.376872
$817$	0.799702	0.0279780
$818$	22.6090	0.790504
$819$	−2.23012	−0.0779266
$820$	−1.15990	−0.0405055
$821$	−28.2981	−0.987610	−0.493805	−	0.869573i	$-0.664394\pi$
$821$	−28.2981	−0.987610	−0.493805	+	0.869573i	$0.664394\pi$
$822$	17.9780	0.627055
$823$	34.1861	1.19165	0.595827	−	0.803113i	$-0.296824\pi$
$823$	34.1861	1.19165	0.595827	+	0.803113i	$0.296824\pi$
$824$	−10.0818	−0.351217
$825$	−2.47616	−0.0862087
$826$	−14.8864	−0.517964
$827$	−46.8776	−1.63010	−0.815048	−	0.579394i	$-0.803289\pi$
$827$	−46.8776	−1.63010	−0.815048	+	0.579394i	$0.803289\pi$
$828$	29.5422	1.02666
$829$	−49.3836	−1.71516	−0.857581	−	0.514348i	$-0.828034\pi$
$829$	−49.3836	−1.71516	−0.857581	+	0.514348i	$0.828034\pi$
$830$	−12.7283	−0.441807
$831$	−25.1762	−0.873351
$832$	0.376331	0.0130469
$833$	−14.8631	−0.514977
$834$	−30.5254	−1.05701
$835$	−9.23459	−0.319576
$836$	−1.68016	−0.0581096
$837$	1.20600	0.0416856
$838$	27.5395	0.951335
$839$	−46.4153	−1.60243	−0.801217	−	0.598374i	$-0.795814\pi$
$839$	−46.4153	−1.60243	−0.801217	+	0.598374i	$0.795814\pi$
$840$	−4.68601	−0.161683
$841$	−28.5378	−0.984061
$842$	34.8997	1.20272
$843$	−37.0867	−1.27733
$844$	−3.42188	−0.117786
$845$	12.8584	0.442342
$846$	−13.7950	−0.474282
$847$	−1.89245	−0.0650255
$848$	−11.2265	−0.385518
$849$	75.2385	2.58218
$850$	4.34771	0.149125
$851$	−66.5314	−2.28067
$852$	10.9205	0.374130
$853$	10.2752	0.351815	0.175908	−	0.984407i	$-0.443714\pi$
$853$	10.2752	0.351815	0.175908	+	0.984407i	$0.443714\pi$
$854$	2.25369	0.0771196
$855$	5.26117	0.179928
$856$	9.67316	0.330622
$857$	44.5511	1.52184	0.760918	−	0.648848i	$-0.224749\pi$
$857$	44.5511	1.52184	0.760918	+	0.648848i	$0.224749\pi$
$858$	−0.931855	−0.0318130
$859$	1.63761	0.0558744	0.0279372	−	0.999610i	$-0.491106\pi$
$859$	1.63761	0.0558744	0.0279372	+	0.999610i	$0.491106\pi$
$860$	0.475968	0.0162304
$861$	5.43531	0.185235
$862$	−3.53108	−0.120269
$863$	19.4841	0.663248	0.331624	−	0.943412i	$-0.392403\pi$
$863$	19.4841	0.663248	0.331624	+	0.943412i	$0.392403\pi$
$864$	−0.325247	−0.0110651
$865$	12.3939	0.421404
$866$	−1.86849	−0.0634938
$867$	−4.71110	−0.159997
$868$	7.01716	0.238178
$869$	−0.437734	−0.0148491
$870$	1.68350	0.0570759
$871$	−4.28148	−0.145072
$872$	7.85264	0.265924
$873$	−32.5848	−1.10283
$874$	−15.8512	−0.536175
$875$	1.89245	0.0639767
$876$	−2.47616	−0.0836616
$877$	29.7151	1.00341	0.501704	−	0.865040i	$-0.332707\pi$
$877$	29.7151	1.00341	0.501704	+	0.865040i	$0.332707\pi$
$878$	39.5401	1.33441
$879$	−75.3852	−2.54268
$880$	−1.00000	−0.0337100
$881$	33.2612	1.12060	0.560299	−	0.828290i	$-0.310686\pi$
$881$	33.2612	1.12060	0.560299	+	0.828290i	$0.310686\pi$
$882$	−10.7049	−0.360452
$883$	12.6430	0.425471	0.212736	−	0.977110i	$-0.431763\pi$
$883$	12.6430	0.425471	0.212736	+	0.977110i	$0.431763\pi$
$884$	1.63618	0.0550307
$885$	19.4779	0.654742
$886$	−28.9281	−0.971860
$887$	7.19524	0.241593	0.120796	−	0.992677i	$-0.461455\pi$
$887$	7.19524	0.241593	0.120796	+	0.992677i	$0.461455\pi$
$888$	17.4620	0.585986
$889$	−28.5436	−0.957320
$890$	−5.89707	−0.197670
$891$	−8.58869	−0.287732
$892$	19.2354	0.644048
$893$	7.40186	0.247694
$894$	−47.5115	−1.58902
$895$	−17.3314	−0.579324
$896$	−1.89245	−0.0632225
$897$	−8.79144	−0.293537
$898$	24.9468	0.832484
$899$	−2.52098	−0.0840795
$900$	3.13135	0.104378
$901$	−48.8094	−1.62608
$902$	1.15990	0.0386205
$903$	−2.23039	−0.0742228
$904$	−1.23372	−0.0410329
$905$	−16.9105	−0.562124
$906$	20.2832	0.673863
$907$	−6.45060	−0.214189	−0.107094	−	0.994249i	$-0.534155\pi$
$907$	−6.45060	−0.214189	−0.107094	+	0.994249i	$0.534155\pi$
$908$	15.6015	0.517753
$909$	43.7670	1.45166
$910$	0.712190	0.0236089
$911$	−24.1601	−0.800461	−0.400231	−	0.916414i	$-0.631070\pi$
$911$	−24.1601	−0.800461	−0.400231	+	0.916414i	$0.631070\pi$
$912$	4.16034	0.137763
$913$	12.7283	0.421246
$914$	1.31662	0.0435500
$915$	−2.94881	−0.0974846
$916$	−4.12825	−0.136401
$917$	−33.0372	−1.09099
$918$	−1.41408	−0.0466716
$919$	19.3953	0.639793	0.319896	−	0.947453i	$-0.396352\pi$
$919$	19.3953	0.639793	0.319896	+	0.947453i	$0.396352\pi$
$920$	−9.43433	−0.311041
$921$	−58.3302	−1.92205
$922$	2.91839	0.0961120
$923$	−1.65972	−0.0546303
$924$	4.68601	0.154159
$925$	−7.05205	−0.231870
$926$	−27.2696	−0.896133
$927$	−31.5698	−1.03689
$928$	0.679883	0.0223183
$929$	42.8726	1.40660	0.703302	−	0.710891i	$-0.251708\pi$
$929$	42.8726	1.40660	0.703302	+	0.710891i	$0.251708\pi$
$930$	−9.18150	−0.301073
$931$	5.74382	0.188246
$932$	−23.2775	−0.762481
$933$	−33.7432	−1.10470
$934$	34.3389	1.12360
$935$	−4.34771	−0.142185
$936$	1.17843	0.0385181
$937$	40.5478	1.32464	0.662320	−	0.749221i	$-0.269572\pi$
$937$	40.5478	1.32464	0.662320	+	0.749221i	$0.269572\pi$
$938$	21.5303	0.702988
$939$	70.1960	2.29076
$940$	4.40545	0.143690
$941$	32.0293	1.04412	0.522062	−	0.852907i	$-0.325163\pi$
$941$	32.0293	1.04412	0.522062	+	0.852907i	$0.325163\pi$
$942$	−41.2539	−1.34413
$943$	10.9429	0.356349
$944$	7.86618	0.256022
$945$	−0.615515	−0.0200227
$946$	−0.475968	−0.0154750
$947$	−7.55688	−0.245566	−0.122783	−	0.992434i	$-0.539182\pi$
$947$	−7.55688	−0.245566	−0.122783	+	0.992434i	$0.539182\pi$
$948$	1.08390	0.0352033
$949$	0.376331	0.0122162
$950$	−1.68016	−0.0545116
$951$	24.2442	0.786173
$952$	−8.22785	−0.266666
$953$	−39.2383	−1.27105	−0.635526	−	0.772080i	$-0.719217\pi$
$953$	−39.2383	−1.27105	−0.635526	+	0.772080i	$0.719217\pi$
$954$	−35.1540	−1.13815
$955$	8.92014	0.288649
$956$	17.6003	0.569233
$957$	−1.68350	−0.0544197
$958$	−3.57685	−0.115563
$959$	13.7401	0.443690
$960$	2.47616	0.0799176
$961$	−17.2510	−0.556484
$962$	−2.65391	−0.0855654
$963$	30.2901	0.976084
$964$	−12.0692	−0.388723
$965$	−13.1223	−0.422423
$966$	44.2094	1.42242
$967$	−37.1700	−1.19531	−0.597654	−	0.801754i	$-0.703900\pi$
$967$	−37.1700	−1.19531	−0.597654	+	0.801754i	$0.703900\pi$
$968$	1.00000	0.0321412
$969$	18.0880	0.581069
$970$	10.4060	0.334117
$971$	−28.5687	−0.916812	−0.458406	−	0.888743i	$-0.651579\pi$
$971$	−28.5687	−0.916812	−0.458406	+	0.888743i	$0.651579\pi$
$972$	22.2427	0.713435
$973$	−23.3297	−0.747916
$974$	40.1019	1.28495
$975$	−0.931855	−0.0298433
$976$	−1.19088	−0.0381192
$977$	−51.1092	−1.63513	−0.817564	−	0.575838i	$-0.804676\pi$
$977$	−51.1092	−1.63513	−0.817564	+	0.575838i	$0.804676\pi$
$978$	22.7172	0.726417
$979$	5.89707	0.188471
$980$	3.41861	0.109204
$981$	24.5894	0.785078
$982$	−39.4409	−1.25861
$983$	−5.57432	−0.177793	−0.0888966	−	0.996041i	$-0.528334\pi$
$983$	−5.57432	−0.177793	−0.0888966	+	0.996041i	$0.528334\pi$
$984$	−2.87210	−0.0915591
$985$	20.9393	0.667182
$986$	2.95593	0.0941361
$987$	−20.6440	−0.657106
$988$	−0.632297	−0.0201161
$989$	−4.49044	−0.142788
$990$	−3.13135	−0.0995209
$991$	36.0753	1.14597	0.572984	−	0.819566i	$-0.305786\pi$
$991$	36.0753	1.14597	0.572984	+	0.819566i	$0.305786\pi$
$992$	−3.70796	−0.117728
$993$	78.9746	2.50618
$994$	8.34621	0.264726
$995$	15.5621	0.493350
$996$	−31.5173	−0.998665
$997$	2.99206	0.0947595	0.0473797	−	0.998877i	$-0.484913\pi$
$997$	2.99206	0.0947595	0.0473797	+	0.998877i	$0.484913\pi$
$998$	5.38879	0.170579
$999$	2.29366	0.0725681

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8030.2.a.bd.1.2	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8030.2.a.bd.1.2	✓	14	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:	\( N \)	\(=\)	\( 8030 = 2 \cdot 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8030.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.47616 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.47616 q^{6} -1.89245 q^{7} +1.00000 q^{8} +3.13135 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.47616 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.47616 q^{6} -1.89245 q^{7} +1.00000 q^{8} +3.13135 q^{9} -1.00000 q^{10} +1.00000 q^{11} -2.47616 q^{12} +0.376331 q^{13} -1.89245 q^{14} +2.47616 q^{15} +1.00000 q^{16} +4.34771 q^{17} +3.13135 q^{18} -1.68016 q^{19} -1.00000 q^{20} +4.68601 q^{21} +1.00000 q^{22} +9.43433 q^{23} -2.47616 q^{24} +1.00000 q^{25} +0.376331 q^{26} -0.325247 q^{27} -1.89245 q^{28} +0.679883 q^{29} +2.47616 q^{30} -3.70796 q^{31} +1.00000 q^{32} -2.47616 q^{33} +4.34771 q^{34} +1.89245 q^{35} +3.13135 q^{36} -7.05205 q^{37} -1.68016 q^{38} -0.931855 q^{39} -1.00000 q^{40} +1.15990 q^{41} +4.68601 q^{42} -0.475968 q^{43} +1.00000 q^{44} -3.13135 q^{45} +9.43433 q^{46} -4.40545 q^{47} -2.47616 q^{48} -3.41861 q^{49} +1.00000 q^{50} -10.7656 q^{51} +0.376331 q^{52} -11.2265 q^{53} -0.325247 q^{54} -1.00000 q^{55} -1.89245 q^{56} +4.16034 q^{57} +0.679883 q^{58} +7.86618 q^{59} +2.47616 q^{60} -1.19088 q^{61} -3.70796 q^{62} -5.92594 q^{63} +1.00000 q^{64} -0.376331 q^{65} -2.47616 q^{66} -11.3769 q^{67} +4.34771 q^{68} -23.3609 q^{69} +1.89245 q^{70} -4.41026 q^{71} +3.13135 q^{72} +1.00000 q^{73} -7.05205 q^{74} -2.47616 q^{75} -1.68016 q^{76} -1.89245 q^{77} -0.931855 q^{78} -0.437734 q^{79} -1.00000 q^{80} -8.58869 q^{81} +1.15990 q^{82} +12.7283 q^{83} +4.68601 q^{84} -4.34771 q^{85} -0.475968 q^{86} -1.68350 q^{87} +1.00000 q^{88} +5.89707 q^{89} -3.13135 q^{90} -0.712190 q^{91} +9.43433 q^{92} +9.18150 q^{93} -4.40545 q^{94} +1.68016 q^{95} -2.47616 q^{96} -10.4060 q^{97} -3.41861 q^{98} +3.13135 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 14 q^{2} + 6 q^{3} + 14 q^{4} - 14 q^{5} + 6 q^{6} + 4 q^{7} + 14 q^{8} + 24 q^{9}+O(q^{10}) \) 14 * q + 14 * q^2 + 6 * q^3 + 14 * q^4 - 14 * q^5 + 6 * q^6 + 4 * q^7 + 14 * q^8 + 24 * q^9	\( 14 q + 14 q^{2} + 6 q^{3} + 14 q^{4} - 14 q^{5} + 6 q^{6} + 4 q^{7} + 14 q^{8} + 24 q^{9} - 14 q^{10} + 14 q^{11} + 6 q^{12} + 4 q^{13} + 4 q^{14} - 6 q^{15} + 14 q^{16} + 20 q^{17} + 24 q^{18} - 14 q^{20} + 25 q^{21} + 14 q^{22} - 4 q^{23} + 6 q^{24} + 14 q^{25} + 4 q^{26} + 21 q^{27} + 4 q^{28} + 7 q^{29} - 6 q^{30} + 8 q^{31} + 14 q^{32} + 6 q^{33} + 20 q^{34} - 4 q^{35} + 24 q^{36} + 17 q^{37} + 7 q^{39} - 14 q^{40} - 14 q^{41} + 25 q^{42} + 12 q^{43} + 14 q^{44} - 24 q^{45} - 4 q^{46} + 28 q^{47} + 6 q^{48} + 20 q^{49} + 14 q^{50} - 13 q^{51} + 4 q^{52} + 13 q^{53} + 21 q^{54} - 14 q^{55} + 4 q^{56} - 23 q^{57} + 7 q^{58} + 36 q^{59} - 6 q^{60} + 25 q^{61} + 8 q^{62} + 45 q^{63} + 14 q^{64} - 4 q^{65} + 6 q^{66} + 20 q^{68} - 7 q^{69} - 4 q^{70} + 17 q^{71} + 24 q^{72} + 14 q^{73} + 17 q^{74} + 6 q^{75} + 4 q^{77} + 7 q^{78} + 10 q^{79} - 14 q^{80} + 58 q^{81} - 14 q^{82} - 6 q^{83} + 25 q^{84} - 20 q^{85} + 12 q^{86} + 44 q^{87} + 14 q^{88} + 36 q^{89} - 24 q^{90} - 15 q^{91} - 4 q^{92} - 2 q^{93} + 28 q^{94} + 6 q^{96} - 19 q^{97} + 20 q^{98} + 24 q^{99}+O(q^{100}) \) 14 * q + 14 * q^2 + 6 * q^3 + 14 * q^4 - 14 * q^5 + 6 * q^6 + 4 * q^7 + 14 * q^8 + 24 * q^9 - 14 * q^10 + 14 * q^11 + 6 * q^12 + 4 * q^13 + 4 * q^14 - 6 * q^15 + 14 * q^16 + 20 * q^17 + 24 * q^18 - 14 * q^20 + 25 * q^21 + 14 * q^22 - 4 * q^23 + 6 * q^24 + 14 * q^25 + 4 * q^26 + 21 * q^27 + 4 * q^28 + 7 * q^29 - 6 * q^30 + 8 * q^31 + 14 * q^32 + 6 * q^33 + 20 * q^34 - 4 * q^35 + 24 * q^36 + 17 * q^37 + 7 * q^39 - 14 * q^40 - 14 * q^41 + 25 * q^42 + 12 * q^43 + 14 * q^44 - 24 * q^45 - 4 * q^46 + 28 * q^47 + 6 * q^48 + 20 * q^49 + 14 * q^50 - 13 * q^51 + 4 * q^52 + 13 * q^53 + 21 * q^54 - 14 * q^55 + 4 * q^56 - 23 * q^57 + 7 * q^58 + 36 * q^59 - 6 * q^60 + 25 * q^61 + 8 * q^62 + 45 * q^63 + 14 * q^64 - 4 * q^65 + 6 * q^66 + 20 * q^68 - 7 * q^69 - 4 * q^70 + 17 * q^71 + 24 * q^72 + 14 * q^73 + 17 * q^74 + 6 * q^75 + 4 * q^77 + 7 * q^78 + 10 * q^79 - 14 * q^80 + 58 * q^81 - 14 * q^82 - 6 * q^83 + 25 * q^84 - 20 * q^85 + 12 * q^86 + 44 * q^87 + 14 * q^88 + 36 * q^89 - 24 * q^90 - 15 * q^91 - 4 * q^92 - 2 * q^93 + 28 * q^94 + 6 * q^96 - 19 * q^97 + 20 * q^98 + 24 * q^99

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