LMFDB - Embedded newform 8030.2.a.bd.1.6

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			1.6
Root			$0.0877386$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +0.0877386 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.0877386 q^{6} -3.09806 q^{7} +1.00000 q^{8} -2.99230 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.0877386 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.0877386 q^{6} -3.09806 q^{7} +1.00000 q^{8} -2.99230 q^{9} -1.00000 q^{10} +1.00000 q^{11} +0.0877386 q^{12} -0.428506 q^{13} -3.09806 q^{14} -0.0877386 q^{15} +1.00000 q^{16} -5.47172 q^{17} -2.99230 q^{18} -5.33482 q^{19} -1.00000 q^{20} -0.271820 q^{21} +1.00000 q^{22} -4.57145 q^{23} +0.0877386 q^{24} +1.00000 q^{25} -0.428506 q^{26} -0.525756 q^{27} -3.09806 q^{28} +6.93370 q^{29} -0.0877386 q^{30} -0.798883 q^{31} +1.00000 q^{32} +0.0877386 q^{33} -5.47172 q^{34} +3.09806 q^{35} -2.99230 q^{36} +0.856267 q^{37} -5.33482 q^{38} -0.0375965 q^{39} -1.00000 q^{40} +2.42193 q^{41} -0.271820 q^{42} -1.85455 q^{43} +1.00000 q^{44} +2.99230 q^{45} -4.57145 q^{46} +7.90423 q^{47} +0.0877386 q^{48} +2.59798 q^{49} +1.00000 q^{50} -0.480082 q^{51} -0.428506 q^{52} -1.80556 q^{53} -0.525756 q^{54} -1.00000 q^{55} -3.09806 q^{56} -0.468070 q^{57} +6.93370 q^{58} +13.7711 q^{59} -0.0877386 q^{60} +11.3201 q^{61} -0.798883 q^{62} +9.27034 q^{63} +1.00000 q^{64} +0.428506 q^{65} +0.0877386 q^{66} -7.60376 q^{67} -5.47172 q^{68} -0.401093 q^{69} +3.09806 q^{70} -3.31813 q^{71} -2.99230 q^{72} +1.00000 q^{73} +0.856267 q^{74} +0.0877386 q^{75} -5.33482 q^{76} -3.09806 q^{77} -0.0375965 q^{78} +14.9119 q^{79} -1.00000 q^{80} +8.93078 q^{81} +2.42193 q^{82} +15.7352 q^{83} -0.271820 q^{84} +5.47172 q^{85} -1.85455 q^{86} +0.608353 q^{87} +1.00000 q^{88} +13.5221 q^{89} +2.99230 q^{90} +1.32754 q^{91} -4.57145 q^{92} -0.0700929 q^{93} +7.90423 q^{94} +5.33482 q^{95} +0.0877386 q^{96} -11.8372 q^{97} +2.59798 q^{98} -2.99230 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.0877386	0.0506559	0.0253280	−	0.999679i	$-0.491937\pi$
$3$	0.0877386	0.0506559	0.0253280	+	0.999679i	$0.491937\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.0877386	0.0358191
$7$	−3.09806	−1.17096	−0.585479	−	0.810688i	$-0.699093\pi$
$7$	−3.09806	−1.17096	−0.585479	+	0.810688i	$0.699093\pi$
$8$	1.00000	0.353553
$9$	−2.99230	−0.997434
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.0877386	0.0253280
$13$	−0.428506	−0.118846	−0.0594230	−	0.998233i	$-0.518926\pi$
$13$	−0.428506	−0.118846	−0.0594230	+	0.998233i	$0.518926\pi$
$14$	−3.09806	−0.827992
$15$	−0.0877386	−0.0226540
$16$	1.00000	0.250000
$17$	−5.47172	−1.32709	−0.663544	−	0.748137i	$-0.730948\pi$
$17$	−5.47172	−1.32709	−0.663544	+	0.748137i	$0.730948\pi$
$18$	−2.99230	−0.705292
$19$	−5.33482	−1.22389	−0.611946	−	0.790899i	$-0.709613\pi$
$19$	−5.33482	−1.22389	−0.611946	+	0.790899i	$0.709613\pi$
$20$	−1.00000	−0.223607
$21$	−0.271820	−0.0593159
$22$	1.00000	0.213201
$23$	−4.57145	−0.953213	−0.476607	−	0.879117i	$-0.658133\pi$
$23$	−4.57145	−0.953213	−0.476607	+	0.879117i	$0.658133\pi$
$24$	0.0877386	0.0179096
$25$	1.00000	0.200000
$26$	−0.428506	−0.0840368
$27$	−0.525756	−0.101182
$28$	−3.09806	−0.585479
$29$	6.93370	1.28756	0.643778	−	0.765212i	$-0.277366\pi$
$29$	6.93370	1.28756	0.643778	+	0.765212i	$0.277366\pi$
$30$	−0.0877386	−0.0160188
$31$	−0.798883	−0.143484	−0.0717418	−	0.997423i	$-0.522856\pi$
$31$	−0.798883	−0.143484	−0.0717418	+	0.997423i	$0.522856\pi$
$32$	1.00000	0.176777
$33$	0.0877386	0.0152733
$34$	−5.47172	−0.938393
$35$	3.09806	0.523668
$36$	−2.99230	−0.498717
$37$	0.856267	0.140769	0.0703847	−	0.997520i	$-0.477577\pi$
$37$	0.856267	0.140769	0.0703847	+	0.997520i	$0.477577\pi$
$38$	−5.33482	−0.865423
$39$	−0.0375965	−0.00602026
$40$	−1.00000	−0.158114
$41$	2.42193	0.378243	0.189121	−	0.981954i	$-0.439436\pi$
$41$	2.42193	0.378243	0.189121	+	0.981954i	$0.439436\pi$
$42$	−0.271820	−0.0419427
$43$	−1.85455	−0.282816	−0.141408	−	0.989951i	$-0.545163\pi$
$43$	−1.85455	−0.282816	−0.141408	+	0.989951i	$0.545163\pi$
$44$	1.00000	0.150756
$45$	2.99230	0.446066
$46$	−4.57145	−0.674024
$47$	7.90423	1.15295	0.576475	−	0.817115i	$-0.304428\pi$
$47$	7.90423	1.15295	0.576475	+	0.817115i	$0.304428\pi$
$48$	0.0877386	0.0126640
$49$	2.59798	0.371141
$50$	1.00000	0.141421
$51$	−0.480082	−0.0672249
$52$	−0.428506	−0.0594230
$53$	−1.80556	−0.248012	−0.124006	−	0.992281i	$-0.539574\pi$
$53$	−1.80556	−0.248012	−0.124006	+	0.992281i	$0.539574\pi$
$54$	−0.525756	−0.0715464
$55$	−1.00000	−0.134840
$56$	−3.09806	−0.413996
$57$	−0.468070	−0.0619974
$58$	6.93370	0.910439
$59$	13.7711	1.79284	0.896420	−	0.443206i	$-0.146159\pi$
$59$	13.7711	1.79284	0.896420	+	0.443206i	$0.146159\pi$
$60$	−0.0877386	−0.0113270
$61$	11.3201	1.44939	0.724697	−	0.689068i	$-0.241980\pi$
$61$	11.3201	1.44939	0.724697	+	0.689068i	$0.241980\pi$
$62$	−0.798883	−0.101458
$63$	9.27034	1.16795
$64$	1.00000	0.125000
$65$	0.428506	0.0531496
$66$	0.0877386	0.0107999
$67$	−7.60376	−0.928947	−0.464474	−	0.885587i	$-0.653756\pi$
$67$	−7.60376	−0.928947	−0.464474	+	0.885587i	$0.653756\pi$
$68$	−5.47172	−0.663544
$69$	−0.401093	−0.0482859
$70$	3.09806	0.370289
$71$	−3.31813	−0.393789	−0.196895	−	0.980425i	$-0.563086\pi$
$71$	−3.31813	−0.393789	−0.196895	+	0.980425i	$0.563086\pi$
$72$	−2.99230	−0.352646
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	0.856267	0.0995390
$75$	0.0877386	0.0101312
$76$	−5.33482	−0.611946
$77$	−3.09806	−0.353057
$78$	−0.0375965	−0.00425696
$79$	14.9119	1.67772	0.838859	−	0.544349i	$-0.183223\pi$
$79$	14.9119	1.67772	0.838859	+	0.544349i	$0.183223\pi$
$80$	−1.00000	−0.111803
$81$	8.93078	0.992309
$82$	2.42193	0.267458
$83$	15.7352	1.72717	0.863584	−	0.504205i	$-0.168215\pi$
$83$	15.7352	1.72717	0.863584	+	0.504205i	$0.168215\pi$
$84$	−0.271820	−0.0296580
$85$	5.47172	0.593492
$86$	−1.85455	−0.199981
$87$	0.608353	0.0652223
$88$	1.00000	0.106600
$89$	13.5221	1.43334	0.716668	−	0.697414i	$-0.245666\pi$
$89$	13.5221	1.43334	0.716668	+	0.697414i	$0.245666\pi$
$90$	2.99230	0.315416
$91$	1.32754	0.139164
$92$	−4.57145	−0.476607
$93$	−0.0700929	−0.00726830
$94$	7.90423	0.815259
$95$	5.33482	0.547341
$96$	0.0877386	0.00895479
$97$	−11.8372	−1.20189	−0.600943	−	0.799292i	$-0.705208\pi$
$97$	−11.8372	−1.20189	−0.600943	+	0.799292i	$0.705208\pi$
$98$	2.59798	0.262436
$99$	−2.99230	−0.300738
$100$	1.00000	0.100000
$101$	−16.0857	−1.60059	−0.800295	−	0.599607i	$-0.795324\pi$
$101$	−16.0857	−1.60059	−0.800295	+	0.599607i	$0.795324\pi$
$102$	−0.480082	−0.0475352
$103$	3.73627	0.368146	0.184073	−	0.982913i	$-0.441072\pi$
$103$	3.73627	0.368146	0.184073	+	0.982913i	$0.441072\pi$
$104$	−0.428506	−0.0420184
$105$	0.271820	0.0265269
$106$	−1.80556	−0.175371
$107$	8.99520	0.869598	0.434799	−	0.900527i	$-0.356819\pi$
$107$	8.99520	0.869598	0.434799	+	0.900527i	$0.356819\pi$
$108$	−0.525756	−0.0505909
$109$	−4.70416	−0.450577	−0.225289	−	0.974292i	$-0.572333\pi$
$109$	−4.70416	−0.450577	−0.225289	+	0.974292i	$0.572333\pi$
$110$	−1.00000	−0.0953463
$111$	0.0751277	0.00713080
$112$	−3.09806	−0.292739
$113$	−7.39319	−0.695493	−0.347747	−	0.937589i	$-0.613053\pi$
$113$	−7.39319	−0.695493	−0.347747	+	0.937589i	$0.613053\pi$
$114$	−0.468070	−0.0438388
$115$	4.57145	0.426290
$116$	6.93370	0.643778
$117$	1.28222	0.118541
$118$	13.7711	1.26773
$119$	16.9517	1.55396
$120$	−0.0877386	−0.00800940
$121$	1.00000	0.0909091
$122$	11.3201	1.02488
$123$	0.212497	0.0191602
$124$	−0.798883	−0.0717418
$125$	−1.00000	−0.0894427
$126$	9.27034	0.825867
$127$	−8.89083	−0.788934	−0.394467	−	0.918910i	$-0.629071\pi$
$127$	−8.89083	−0.788934	−0.394467	+	0.918910i	$0.629071\pi$
$128$	1.00000	0.0883883
$129$	−0.162716	−0.0143263
$130$	0.428506	0.0375824
$131$	−18.4381	−1.61095	−0.805473	−	0.592632i	$-0.798089\pi$
$131$	−18.4381	−1.61095	−0.805473	+	0.592632i	$0.798089\pi$
$132$	0.0877386	0.00763667
$133$	16.5276	1.43313
$134$	−7.60376	−0.656865
$135$	0.525756	0.0452499
$136$	−5.47172	−0.469196
$137$	11.0378	0.943021	0.471511	−	0.881860i	$-0.343709\pi$
$137$	11.0378	0.943021	0.471511	+	0.881860i	$0.343709\pi$
$138$	−0.401093	−0.0341433
$139$	−5.14265	−0.436194	−0.218097	−	0.975927i	$-0.569985\pi$
$139$	−5.14265	−0.436194	−0.218097	+	0.975927i	$0.569985\pi$
$140$	3.09806	0.261834
$141$	0.693506	0.0584038
$142$	−3.31813	−0.278451
$143$	−0.428506	−0.0358334
$144$	−2.99230	−0.249358
$145$	−6.93370	−0.575812
$146$	1.00000	0.0827606
$147$	0.227944	0.0188005
$148$	0.856267	0.0703847
$149$	13.0899	1.07236	0.536182	−	0.844103i	$-0.319866\pi$
$149$	13.0899	1.07236	0.536182	+	0.844103i	$0.319866\pi$
$150$	0.0877386	0.00716383
$151$	9.13916	0.743735	0.371867	−	0.928286i	$-0.378718\pi$
$151$	9.13916	0.743735	0.371867	+	0.928286i	$0.378718\pi$
$152$	−5.33482	−0.432711
$153$	16.3730	1.32368
$154$	−3.09806	−0.249649
$155$	0.798883	0.0641678
$156$	−0.0375965	−0.00301013
$157$	−12.5910	−1.00487	−0.502437	−	0.864614i	$-0.667563\pi$
$157$	−12.5910	−1.00487	−0.502437	+	0.864614i	$0.667563\pi$
$158$	14.9119	1.18633
$159$	−0.158417	−0.0125633
$160$	−1.00000	−0.0790569
$161$	14.1626	1.11617
$162$	8.93078	0.701668
$163$	19.9368	1.56157	0.780785	−	0.624800i	$-0.214820\pi$
$163$	19.9368	1.56157	0.780785	+	0.624800i	$0.214820\pi$
$164$	2.42193	0.189121
$165$	−0.0877386	−0.00683044
$166$	15.7352	1.22129
$167$	−3.51487	−0.271989	−0.135995	−	0.990710i	$-0.543423\pi$
$167$	−3.51487	−0.271989	−0.135995	+	0.990710i	$0.543423\pi$
$168$	−0.271820	−0.0209713
$169$	−12.8164	−0.985876
$170$	5.47172	0.419662
$171$	15.9634	1.22075
$172$	−1.85455	−0.141408
$173$	−4.53972	−0.345149	−0.172574	−	0.984996i	$-0.555209\pi$
$173$	−4.53972	−0.345149	−0.172574	+	0.984996i	$0.555209\pi$
$174$	0.608353	0.0461192
$175$	−3.09806	−0.234191
$176$	1.00000	0.0753778
$177$	1.20825	0.0908179
$178$	13.5221	1.01352
$179$	4.51099	0.337168	0.168584	−	0.985687i	$-0.446081\pi$
$179$	4.51099	0.337168	0.168584	+	0.985687i	$0.446081\pi$
$180$	2.99230	0.223033
$181$	−3.45967	−0.257155	−0.128578	−	0.991699i	$-0.541041\pi$
$181$	−3.45967	−0.257155	−0.128578	+	0.991699i	$0.541041\pi$
$182$	1.32754	0.0984035
$183$	0.993212	0.0734203
$184$	−4.57145	−0.337012
$185$	−0.856267	−0.0629540
$186$	−0.0700929	−0.00513946
$187$	−5.47172	−0.400132
$188$	7.90423	0.576475
$189$	1.62883	0.118480
$190$	5.33482	0.387029
$191$	−23.0514	−1.66794	−0.833969	−	0.551812i	$-0.813937\pi$
$191$	−23.0514	−1.66794	−0.833969	+	0.551812i	$0.813937\pi$
$192$	0.0877386	0.00633199
$193$	−8.44209	−0.607675	−0.303838	−	0.952724i	$-0.598268\pi$
$193$	−8.44209	−0.607675	−0.303838	+	0.952724i	$0.598268\pi$
$194$	−11.8372	−0.849861
$195$	0.0375965	0.00269234
$196$	2.59798	0.185570
$197$	−9.53237	−0.679153	−0.339577	−	0.940578i	$-0.610284\pi$
$197$	−9.53237	−0.679153	−0.339577	+	0.940578i	$0.610284\pi$
$198$	−2.99230	−0.212654
$199$	12.7045	0.900600	0.450300	−	0.892877i	$-0.351317\pi$
$199$	12.7045	0.900600	0.450300	+	0.892877i	$0.351317\pi$
$200$	1.00000	0.0707107
$201$	−0.667144	−0.0470567
$202$	−16.0857	−1.13179
$203$	−21.4810	−1.50767
$204$	−0.480082	−0.0336124
$205$	−2.42193	−0.169155
$206$	3.73627	0.260318
$207$	13.6792	0.950768
$208$	−0.428506	−0.0297115
$209$	−5.33482	−0.369018
$210$	0.271820	0.0187573
$211$	18.9710	1.30602	0.653008	−	0.757351i	$-0.273507\pi$
$211$	18.9710	1.30602	0.653008	+	0.757351i	$0.273507\pi$
$212$	−1.80556	−0.124006
$213$	−0.291128	−0.0199478
$214$	8.99520	0.614899
$215$	1.85455	0.126479
$216$	−0.525756	−0.0357732
$217$	2.47499	0.168013
$218$	−4.70416	−0.318606
$219$	0.0877386	0.00592883
$220$	−1.00000	−0.0674200
$221$	2.34466	0.157719
$222$	0.0751277	0.00504224
$223$	0.238686	0.0159836	0.00799178	−	0.999968i	$-0.497456\pi$
$223$	0.238686	0.0159836	0.00799178	+	0.999968i	$0.497456\pi$
$224$	−3.09806	−0.206998
$225$	−2.99230	−0.199487
$226$	−7.39319	−0.491788
$227$	16.2769	1.08034	0.540168	−	0.841557i	$-0.318361\pi$
$227$	16.2769	1.08034	0.540168	+	0.841557i	$0.318361\pi$
$228$	−0.468070	−0.0309987
$229$	−3.12255	−0.206344	−0.103172	−	0.994664i	$-0.532899\pi$
$229$	−3.12255	−0.206344	−0.103172	+	0.994664i	$0.532899\pi$
$230$	4.57145	0.301433
$231$	−0.271820	−0.0178844
$232$	6.93370	0.455220
$233$	9.46801	0.620270	0.310135	−	0.950692i	$-0.399626\pi$
$233$	9.46801	0.620270	0.310135	+	0.950692i	$0.399626\pi$
$234$	1.28222	0.0838212
$235$	−7.90423	−0.515615
$236$	13.7711	0.896420
$237$	1.30835	0.0849863
$238$	16.9517	1.09882
$239$	−6.69936	−0.433346	−0.216673	−	0.976244i	$-0.569521\pi$
$239$	−6.69936	−0.433346	−0.216673	+	0.976244i	$0.569521\pi$
$240$	−0.0877386	−0.00566350
$241$	18.5243	1.19325	0.596626	−	0.802519i	$-0.296507\pi$
$241$	18.5243	1.19325	0.596626	+	0.802519i	$0.296507\pi$
$242$	1.00000	0.0642824
$243$	2.36084	0.151448
$244$	11.3201	0.724697
$245$	−2.59798	−0.165979
$246$	0.212497	0.0135483
$247$	2.28600	0.145455
$248$	−0.798883	−0.0507291
$249$	1.38059	0.0874913
$250$	−1.00000	−0.0632456
$251$	29.8313	1.88294	0.941469	−	0.337100i	$-0.109446\pi$
$251$	29.8313	1.88294	0.941469	+	0.337100i	$0.109446\pi$
$252$	9.27034	0.583976
$253$	−4.57145	−0.287405
$254$	−8.89083	−0.557860
$255$	0.480082	0.0300639
$256$	1.00000	0.0625000
$257$	3.70908	0.231366	0.115683	−	0.993286i	$-0.463094\pi$
$257$	3.70908	0.231366	0.115683	+	0.993286i	$0.463094\pi$
$258$	−0.162716	−0.0101302
$259$	−2.65277	−0.164835
$260$	0.428506	0.0265748
$261$	−20.7477	−1.28425
$262$	−18.4381	−1.13911
$263$	−4.91692	−0.303191	−0.151595	−	0.988443i	$-0.548441\pi$
$263$	−4.91692	−0.303191	−0.151595	+	0.988443i	$0.548441\pi$
$264$	0.0877386	0.00539994
$265$	1.80556	0.110914
$266$	16.5276	1.01337
$267$	1.18641	0.0726070
$268$	−7.60376	−0.464474
$269$	18.1661	1.10761	0.553804	−	0.832647i	$-0.313176\pi$
$269$	18.1661	1.10761	0.553804	+	0.832647i	$0.313176\pi$
$270$	0.525756	0.0319965
$271$	−23.9240	−1.45328	−0.726638	−	0.687020i	$-0.758918\pi$
$271$	−23.9240	−1.45328	−0.726638	+	0.687020i	$0.758918\pi$
$272$	−5.47172	−0.331772
$273$	0.116476	0.00704946
$274$	11.0378	0.666817
$275$	1.00000	0.0603023
$276$	−0.401093	−0.0241430
$277$	−9.63697	−0.579029	−0.289515	−	0.957174i	$-0.593494\pi$
$277$	−9.63697	−0.579029	−0.289515	+	0.957174i	$0.593494\pi$
$278$	−5.14265	−0.308436
$279$	2.39050	0.143115
$280$	3.09806	0.185145
$281$	20.6921	1.23439	0.617194	−	0.786811i	$-0.288270\pi$
$281$	20.6921	1.23439	0.617194	+	0.786811i	$0.288270\pi$
$282$	0.693506	0.0412977
$283$	−6.07567	−0.361161	−0.180581	−	0.983560i	$-0.557798\pi$
$283$	−6.07567	−0.361161	−0.180581	+	0.983560i	$0.557798\pi$
$284$	−3.31813	−0.196895
$285$	0.468070	0.0277261
$286$	−0.428506	−0.0253381
$287$	−7.50330	−0.442906
$288$	−2.99230	−0.176323
$289$	12.9398	0.761162
$290$	−6.93370	−0.407161
$291$	−1.03858	−0.0608826
$292$	1.00000	0.0585206
$293$	−5.34389	−0.312193	−0.156097	−	0.987742i	$-0.549891\pi$
$293$	−5.34389	−0.312193	−0.156097	+	0.987742i	$0.549891\pi$
$294$	0.227944	0.0132939
$295$	−13.7711	−0.801782
$296$	0.856267	0.0497695
$297$	−0.525756	−0.0305075
$298$	13.0899	0.758276
$299$	1.95889	0.113286
$300$	0.0877386	0.00506559
$301$	5.74551	0.331166
$302$	9.13916	0.525900
$303$	−1.41134	−0.0810793
$304$	−5.33482	−0.305973
$305$	−11.3201	−0.648188
$306$	16.3730	0.935985
$307$	−14.6883	−0.838308	−0.419154	−	0.907915i	$-0.637673\pi$
$307$	−14.6883	−0.838308	−0.419154	+	0.907915i	$0.637673\pi$
$308$	−3.09806	−0.176528
$309$	0.327815	0.0186488
$310$	0.798883	0.0453735
$311$	−13.5129	−0.766247	−0.383124	−	0.923697i	$-0.625152\pi$
$311$	−13.5129	−0.766247	−0.383124	+	0.923697i	$0.625152\pi$
$312$	−0.0375965	−0.00212848
$313$	13.1851	0.745265	0.372632	−	0.927979i	$-0.378455\pi$
$313$	13.1851	0.745265	0.372632	+	0.927979i	$0.378455\pi$
$314$	−12.5910	−0.710554
$315$	−9.27034	−0.522324
$316$	14.9119	0.838859
$317$	−24.2307	−1.36093	−0.680466	−	0.732780i	$-0.738223\pi$
$317$	−24.2307	−1.36093	−0.680466	+	0.732780i	$0.738223\pi$
$318$	−0.158417	−0.00888359
$319$	6.93370	0.388213
$320$	−1.00000	−0.0559017
$321$	0.789226	0.0440503
$322$	14.1626	0.789253
$323$	29.1907	1.62421
$324$	8.93078	0.496154
$325$	−0.428506	−0.0237692
$326$	19.9368	1.10420
$327$	−0.412737	−0.0228244
$328$	2.42193	0.133729
$329$	−24.4878	−1.35006
$330$	−0.0877386	−0.00482985
$331$	−21.7213	−1.19391	−0.596956	−	0.802274i	$-0.703623\pi$
$331$	−21.7213	−1.19391	−0.596956	+	0.802274i	$0.703623\pi$
$332$	15.7352	0.863584
$333$	−2.56221	−0.140408
$334$	−3.51487	−0.192325
$335$	7.60376	0.415438
$336$	−0.271820	−0.0148290
$337$	−19.8815	−1.08301	−0.541507	−	0.840696i	$-0.682146\pi$
$337$	−19.8815	−1.08301	−0.541507	+	0.840696i	$0.682146\pi$
$338$	−12.8164	−0.697119
$339$	−0.648669	−0.0352308
$340$	5.47172	0.296746
$341$	−0.798883	−0.0432619
$342$	15.9634	0.863202
$343$	13.6377	0.736367
$344$	−1.85455	−0.0999907
$345$	0.401093	0.0215941
$346$	−4.53972	−0.244057
$347$	−5.34425	−0.286894	−0.143447	−	0.989658i	$-0.545819\pi$
$347$	−5.34425	−0.286894	−0.143447	+	0.989658i	$0.545819\pi$
$348$	0.608353	0.0326112
$349$	18.6016	0.995722	0.497861	−	0.867257i	$-0.334119\pi$
$349$	18.6016	0.995722	0.497861	+	0.867257i	$0.334119\pi$
$350$	−3.09806	−0.165598
$351$	0.225290	0.0120251
$352$	1.00000	0.0533002
$353$	33.0069	1.75678	0.878391	−	0.477942i	$-0.158617\pi$
$353$	33.0069	1.75678	0.878391	+	0.477942i	$0.158617\pi$
$354$	1.20825	0.0642180
$355$	3.31813	0.176108
$356$	13.5221	0.716668
$357$	1.48732	0.0787174
$358$	4.51099	0.238413
$359$	−24.3854	−1.28701	−0.643507	−	0.765441i	$-0.722521\pi$
$359$	−24.3854	−1.28701	−0.643507	+	0.765441i	$0.722521\pi$
$360$	2.99230	0.157708
$361$	9.46035	0.497913
$362$	−3.45967	−0.181836
$363$	0.0877386	0.00460508
$364$	1.32754	0.0695818
$365$	−1.00000	−0.0523424
$366$	0.993212	0.0519160
$367$	18.6679	0.974457	0.487229	−	0.873274i	$-0.338008\pi$
$367$	18.6679	0.974457	0.487229	+	0.873274i	$0.338008\pi$
$368$	−4.57145	−0.238303
$369$	−7.24716	−0.377272
$370$	−0.856267	−0.0445152
$371$	5.59373	0.290412
$372$	−0.0700929	−0.00363415
$373$	25.5042	1.32056	0.660278	−	0.751021i	$-0.270438\pi$
$373$	25.5042	1.32056	0.660278	+	0.751021i	$0.270438\pi$
$374$	−5.47172	−0.282936
$375$	−0.0877386	−0.00453080
$376$	7.90423	0.407629
$377$	−2.97113	−0.153021
$378$	1.62883	0.0837777
$379$	−7.42784	−0.381543	−0.190771	−	0.981634i	$-0.561099\pi$
$379$	−7.42784	−0.381543	−0.190771	+	0.981634i	$0.561099\pi$
$380$	5.33482	0.273671
$381$	−0.780069	−0.0399642
$382$	−23.0514	−1.17941
$383$	24.2506	1.23915	0.619575	−	0.784937i	$-0.287305\pi$
$383$	24.2506	1.23915	0.619575	+	0.784937i	$0.287305\pi$
$384$	0.0877386	0.00447739
$385$	3.09806	0.157892
$386$	−8.44209	−0.429691
$387$	5.54937	0.282091
$388$	−11.8372	−0.600943
$389$	13.5678	0.687914	0.343957	−	0.938985i	$-0.388233\pi$
$389$	13.5678	0.687914	0.343957	+	0.938985i	$0.388233\pi$
$390$	0.0375965	0.00190377
$391$	25.0137	1.26500
$392$	2.59798	0.131218
$393$	−1.61774	−0.0816040
$394$	−9.53237	−0.480234
$395$	−14.9119	−0.750298
$396$	−2.99230	−0.150369
$397$	31.5646	1.58418	0.792090	−	0.610405i	$-0.208993\pi$
$397$	31.5646	1.58418	0.792090	+	0.610405i	$0.208993\pi$
$398$	12.7045	0.636820
$399$	1.45011	0.0725963
$400$	1.00000	0.0500000
$401$	−7.25783	−0.362439	−0.181219	−	0.983443i	$-0.558004\pi$
$401$	−7.25783	−0.362439	−0.181219	+	0.983443i	$0.558004\pi$
$402$	−0.667144	−0.0332741
$403$	0.342326	0.0170525
$404$	−16.0857	−0.800295
$405$	−8.93078	−0.443774
$406$	−21.4810	−1.06609
$407$	0.856267	0.0424436
$408$	−0.480082	−0.0237676
$409$	21.6122	1.06866	0.534328	−	0.845277i	$-0.320565\pi$
$409$	21.6122	1.06866	0.534328	+	0.845277i	$0.320565\pi$
$410$	−2.42193	−0.119611
$411$	0.968440	0.0477696
$412$	3.73627	0.184073
$413$	−42.6636	−2.09934
$414$	13.6792	0.672294
$415$	−15.7352	−0.772413
$416$	−0.428506	−0.0210092
$417$	−0.451209	−0.0220958
$418$	−5.33482	−0.260935
$419$	2.68800	0.131318	0.0656588	−	0.997842i	$-0.479085\pi$
$419$	2.68800	0.131318	0.0656588	+	0.997842i	$0.479085\pi$
$420$	0.271820	0.0132634
$421$	15.6260	0.761566	0.380783	−	0.924665i	$-0.375655\pi$
$421$	15.6260	0.761566	0.380783	+	0.924665i	$0.375655\pi$
$422$	18.9710	0.923493
$423$	−23.6518	−1.14999
$424$	−1.80556	−0.0876856
$425$	−5.47172	−0.265418
$426$	−0.291128	−0.0141052
$427$	−35.0704	−1.69718
$428$	8.99520	0.434799
$429$	−0.0375965	−0.00181518
$430$	1.85455	0.0894344
$431$	13.8133	0.665361	0.332681	−	0.943040i	$-0.392047\pi$
$431$	13.8133	0.665361	0.332681	+	0.943040i	$0.392047\pi$
$432$	−0.525756	−0.0252955
$433$	32.7883	1.57570	0.787851	−	0.615865i	$-0.211193\pi$
$433$	32.7883	1.57570	0.787851	+	0.615865i	$0.211193\pi$
$434$	2.47499	0.118803
$435$	−0.608353	−0.0291683
$436$	−4.70416	−0.225289
$437$	24.3879	1.16663
$438$	0.0877386	0.00419231
$439$	0.778763	0.0371683	0.0185842	−	0.999827i	$-0.494084\pi$
$439$	0.778763	0.0371683	0.0185842	+	0.999827i	$0.494084\pi$
$440$	−1.00000	−0.0476731
$441$	−7.77395	−0.370188
$442$	2.34466	0.111524
$443$	−13.6465	−0.648364	−0.324182	−	0.945995i	$-0.605089\pi$
$443$	−13.6465	−0.648364	−0.324182	+	0.945995i	$0.605089\pi$
$444$	0.0751277	0.00356540
$445$	−13.5221	−0.641008
$446$	0.238686	0.0113021
$447$	1.14849	0.0543216
$448$	−3.09806	−0.146370
$449$	33.5335	1.58255	0.791273	−	0.611463i	$-0.209419\pi$
$449$	33.5335	1.58255	0.791273	+	0.611463i	$0.209419\pi$
$450$	−2.99230	−0.141058
$451$	2.42193	0.114044
$452$	−7.39319	−0.347747
$453$	0.801858	0.0376746
$454$	16.2769	0.763914
$455$	−1.32754	−0.0622359
$456$	−0.468070	−0.0219194
$457$	4.03016	0.188523	0.0942615	−	0.995547i	$-0.469951\pi$
$457$	4.03016	0.188523	0.0942615	+	0.995547i	$0.469951\pi$
$458$	−3.12255	−0.145907
$459$	2.87679	0.134277
$460$	4.57145	0.213145
$461$	−19.5599	−0.910994	−0.455497	−	0.890237i	$-0.650538\pi$
$461$	−19.5599	−0.910994	−0.455497	+	0.890237i	$0.650538\pi$
$462$	−0.271820	−0.0126462
$463$	19.2020	0.892393	0.446197	−	0.894935i	$-0.352778\pi$
$463$	19.2020	0.892393	0.446197	+	0.894935i	$0.352778\pi$
$464$	6.93370	0.321889
$465$	0.0700929	0.00325048
$466$	9.46801	0.438597
$467$	22.4067	1.03686	0.518430	−	0.855120i	$-0.326517\pi$
$467$	22.4067	1.03686	0.518430	+	0.855120i	$0.326517\pi$
$468$	1.28222	0.0592705
$469$	23.5569	1.08776
$470$	−7.90423	−0.364595
$471$	−1.10472	−0.0509029
$472$	13.7711	0.633864
$473$	−1.85455	−0.0852723
$474$	1.30835	0.0600944
$475$	−5.33482	−0.244779
$476$	16.9517	0.776981
$477$	5.40277	0.247376
$478$	−6.69936	−0.306422
$479$	17.6062	0.804446	0.402223	−	0.915542i	$-0.368238\pi$
$479$	17.6062	0.804446	0.402223	+	0.915542i	$0.368238\pi$
$480$	−0.0877386	−0.00400470
$481$	−0.366915	−0.0167299
$482$	18.5243	0.843757
$483$	1.24261	0.0565407
$484$	1.00000	0.0454545
$485$	11.8372	0.537499
$486$	2.36084	0.107090
$487$	−8.06567	−0.365491	−0.182745	−	0.983160i	$-0.558498\pi$
$487$	−8.06567	−0.365491	−0.182745	+	0.983160i	$0.558498\pi$
$488$	11.3201	0.512438
$489$	1.74923	0.0791027
$490$	−2.59798	−0.117365
$491$	−9.39828	−0.424138	−0.212069	−	0.977255i	$-0.568020\pi$
$491$	−9.39828	−0.424138	−0.212069	+	0.977255i	$0.568020\pi$
$492$	0.212497	0.00958012
$493$	−37.9393	−1.70870
$494$	2.28600	0.102852
$495$	2.99230	0.134494
$496$	−0.798883	−0.0358709
$497$	10.2798	0.461110
$498$	1.38059	0.0618657
$499$	−9.43000	−0.422145	−0.211072	−	0.977470i	$-0.567696\pi$
$499$	−9.43000	−0.422145	−0.211072	+	0.977470i	$0.567696\pi$
$500$	−1.00000	−0.0447214
$501$	−0.308390	−0.0137779
$502$	29.8313	1.33144
$503$	23.7198	1.05761	0.528806	−	0.848743i	$-0.322640\pi$
$503$	23.7198	1.05761	0.528806	+	0.848743i	$0.322640\pi$
$504$	9.27034	0.412934
$505$	16.0857	0.715805
$506$	−4.57145	−0.203226
$507$	−1.12449	−0.0499404
$508$	−8.89083	−0.394467
$509$	−2.14836	−0.0952245	−0.0476122	−	0.998866i	$-0.515161\pi$
$509$	−2.14836	−0.0952245	−0.0476122	+	0.998866i	$0.515161\pi$
$510$	0.480082	0.0212584
$511$	−3.09806	−0.137050
$512$	1.00000	0.0441942
$513$	2.80482	0.123836
$514$	3.70908	0.163600
$515$	−3.73627	−0.164640
$516$	−0.162716	−0.00716316
$517$	7.90423	0.347628
$518$	−2.65277	−0.116556
$519$	−0.398309	−0.0174838
$520$	0.428506	0.0187912
$521$	−22.4315	−0.982740	−0.491370	−	0.870951i	$-0.663504\pi$
$521$	−22.4315	−0.982740	−0.491370	+	0.870951i	$0.663504\pi$
$522$	−20.7477	−0.908103
$523$	−16.8265	−0.735773	−0.367886	−	0.929871i	$-0.619918\pi$
$523$	−16.8265	−0.735773	−0.367886	+	0.929871i	$0.619918\pi$
$524$	−18.4381	−0.805473
$525$	−0.271820	−0.0118632
$526$	−4.91692	−0.214388
$527$	4.37127	0.190415
$528$	0.0877386	0.00381833
$529$	−2.10183	−0.0913840
$530$	1.80556	0.0784284
$531$	−41.2072	−1.78824
$532$	16.5276	0.716563
$533$	−1.03781	−0.0449527
$534$	1.18641	0.0513409
$535$	−8.99520	−0.388896
$536$	−7.60376	−0.328432
$537$	0.395788	0.0170795
$538$	18.1661	0.783197
$539$	2.59798	0.111903
$540$	0.525756	0.0226250
$541$	16.9425	0.728414	0.364207	−	0.931318i	$-0.381340\pi$
$541$	16.9425	0.728414	0.364207	+	0.931318i	$0.381340\pi$
$542$	−23.9240	−1.02762
$543$	−0.303547	−0.0130264
$544$	−5.47172	−0.234598
$545$	4.70416	0.201504
$546$	0.116476	0.00498472
$547$	26.9805	1.15360	0.576802	−	0.816884i	$-0.304300\pi$
$547$	26.9805	1.15360	0.576802	+	0.816884i	$0.304300\pi$
$548$	11.0378	0.471511
$549$	−33.8732	−1.44567
$550$	1.00000	0.0426401
$551$	−36.9901	−1.57583
$552$	−0.401093	−0.0170716
$553$	−46.1979	−1.96453
$554$	−9.63697	−0.409435
$555$	−0.0751277	−0.00318899
$556$	−5.14265	−0.218097
$557$	−30.6364	−1.29811	−0.649054	−	0.760742i	$-0.724835\pi$
$557$	−30.6364	−1.29811	−0.649054	+	0.760742i	$0.724835\pi$
$558$	2.39050	0.101198
$559$	0.794685	0.0336116
$560$	3.09806	0.130917
$561$	−0.480082	−0.0202691
$562$	20.6921	0.872844
$563$	−25.0984	−1.05777	−0.528885	−	0.848694i	$-0.677390\pi$
$563$	−25.0984	−1.05777	−0.528885	+	0.848694i	$0.677390\pi$
$564$	0.693506	0.0292019
$565$	7.39319	0.311034
$566$	−6.07567	−0.255380
$567$	−27.6681	−1.16195
$568$	−3.31813	−0.139225
$569$	2.09418	0.0877927	0.0438963	−	0.999036i	$-0.486023\pi$
$569$	2.09418	0.0877927	0.0438963	+	0.999036i	$0.486023\pi$
$570$	0.468070	0.0196053
$571$	−22.8838	−0.957657	−0.478829	−	0.877908i	$-0.658938\pi$
$571$	−22.8838	−0.957657	−0.478829	+	0.877908i	$0.658938\pi$
$572$	−0.428506	−0.0179167
$573$	−2.02249	−0.0844909
$574$	−7.50330	−0.313182
$575$	−4.57145	−0.190643
$576$	−2.99230	−0.124679
$577$	32.0979	1.33625	0.668127	−	0.744047i	$-0.267096\pi$
$577$	32.0979	1.33625	0.668127	+	0.744047i	$0.267096\pi$
$578$	12.9398	0.538223
$579$	−0.740698	−0.0307823
$580$	−6.93370	−0.287906
$581$	−48.7488	−2.02244
$582$	−1.03858	−0.0430505
$583$	−1.80556	−0.0747785
$584$	1.00000	0.0413803
$585$	−1.28222	−0.0530132
$586$	−5.34389	−0.220754
$587$	−41.5024	−1.71299	−0.856493	−	0.516159i	$-0.827361\pi$
$587$	−41.5024	−1.71299	−0.856493	+	0.516159i	$0.827361\pi$
$588$	0.227944	0.00940024
$589$	4.26190	0.175609
$590$	−13.7711	−0.566946
$591$	−0.836357	−0.0344031
$592$	0.856267	0.0351924
$593$	−40.0572	−1.64495	−0.822475	−	0.568801i	$-0.807408\pi$
$593$	−40.0572	−1.64495	−0.822475	+	0.568801i	$0.807408\pi$
$594$	−0.525756	−0.0215720
$595$	−16.9517	−0.694953
$596$	13.0899	0.536182
$597$	1.11468	0.0456207
$598$	1.95889	0.0801051
$599$	16.9685	0.693315	0.346657	−	0.937992i	$-0.387317\pi$
$599$	16.9685	0.693315	0.346657	+	0.937992i	$0.387317\pi$
$600$	0.0877386	0.00358191
$601$	−19.4517	−0.793451	−0.396725	−	0.917937i	$-0.629854\pi$
$601$	−19.4517	−0.793451	−0.396725	+	0.917937i	$0.629854\pi$
$602$	5.74551	0.234170
$603$	22.7527	0.926563
$604$	9.13916	0.371867
$605$	−1.00000	−0.0406558
$606$	−1.41134	−0.0573317
$607$	20.2428	0.821631	0.410815	−	0.911719i	$-0.365244\pi$
$607$	20.2428	0.821631	0.410815	+	0.911719i	$0.365244\pi$
$608$	−5.33482	−0.216356
$609$	−1.88472	−0.0763726
$610$	−11.3201	−0.458338
$611$	−3.38701	−0.137024
$612$	16.3730	0.661841
$613$	−17.4207	−0.703615	−0.351807	−	0.936072i	$-0.614433\pi$
$613$	−17.4207	−0.703615	−0.351807	+	0.936072i	$0.614433\pi$
$614$	−14.6883	−0.592774
$615$	−0.212497	−0.00856872
$616$	−3.09806	−0.124824
$617$	−32.3686	−1.30311	−0.651555	−	0.758601i	$-0.725883\pi$
$617$	−32.3686	−1.30311	−0.651555	+	0.758601i	$0.725883\pi$
$618$	0.327815	0.0131867
$619$	−24.3679	−0.979429	−0.489714	−	0.871883i	$-0.662899\pi$
$619$	−24.3679	−0.979429	−0.489714	+	0.871883i	$0.662899\pi$
$620$	0.798883	0.0320839
$621$	2.40347	0.0964479
$622$	−13.5129	−0.541819
$623$	−41.8922	−1.67838
$624$	−0.0375965	−0.00150506
$625$	1.00000	0.0400000
$626$	13.1851	0.526982
$627$	−0.468070	−0.0186929
$628$	−12.5910	−0.502437
$629$	−4.68526	−0.186813
$630$	−9.27034	−0.369339
$631$	43.7497	1.74165	0.870825	−	0.491594i	$-0.163585\pi$
$631$	43.7497	1.74165	0.870825	+	0.491594i	$0.163585\pi$
$632$	14.9119	0.593163
$633$	1.66449	0.0661575
$634$	−24.2307	−0.962324
$635$	8.89083	0.352822
$636$	−0.158417	−0.00628165
$637$	−1.11325	−0.0441086
$638$	6.93370	0.274508
$639$	9.92883	0.392779
$640$	−1.00000	−0.0395285
$641$	15.1559	0.598622	0.299311	−	0.954156i	$-0.403243\pi$
$641$	15.1559	0.598622	0.299311	+	0.954156i	$0.403243\pi$
$642$	0.789226	0.0311483
$643$	−37.6108	−1.48322	−0.741612	−	0.670829i	$-0.765938\pi$
$643$	−37.6108	−1.48322	−0.741612	+	0.670829i	$0.765938\pi$
$644$	14.1626	0.558086
$645$	0.162716	0.00640693
$646$	29.1907	1.14849
$647$	17.3463	0.681954	0.340977	−	0.940072i	$-0.389242\pi$
$647$	17.3463	0.681954	0.340977	+	0.940072i	$0.389242\pi$
$648$	8.93078	0.350834
$649$	13.7711	0.540561
$650$	−0.428506	−0.0168074
$651$	0.217152	0.00851086
$652$	19.9368	0.780785
$653$	−23.8340	−0.932696	−0.466348	−	0.884601i	$-0.654431\pi$
$653$	−23.8340	−0.932696	−0.466348	+	0.884601i	$0.654431\pi$
$654$	−0.412737	−0.0161393
$655$	18.4381	0.720437
$656$	2.42193	0.0945607
$657$	−2.99230	−0.116741
$658$	−24.4878	−0.954633
$659$	27.3585	1.06574	0.532868	−	0.846198i	$-0.321114\pi$
$659$	27.3585	1.06574	0.532868	+	0.846198i	$0.321114\pi$
$660$	−0.0877386	−0.00341522
$661$	−1.03157	−0.0401236	−0.0200618	−	0.999799i	$-0.506386\pi$
$661$	−1.03157	−0.0401236	−0.0200618	+	0.999799i	$0.506386\pi$
$662$	−21.7213	−0.844223
$663$	0.205718	0.00798941
$664$	15.7352	0.610646
$665$	−16.5276	−0.640913
$666$	−2.56221	−0.0992836
$667$	−31.6971	−1.22732
$668$	−3.51487	−0.135995
$669$	0.0209419	0.000809662 0
$670$	7.60376	0.293759
$671$	11.3201	0.437008
$672$	−0.271820	−0.0104857
$673$	−18.8908	−0.728188	−0.364094	−	0.931362i	$-0.618621\pi$
$673$	−18.8908	−0.728188	−0.364094	+	0.931362i	$0.618621\pi$
$674$	−19.8815	−0.765806
$675$	−0.525756	−0.0202364
$676$	−12.8164	−0.492938
$677$	−9.05335	−0.347948	−0.173974	−	0.984750i	$-0.555661\pi$
$677$	−9.05335	−0.347948	−0.173974	+	0.984750i	$0.555661\pi$
$678$	−0.648669	−0.0249120
$679$	36.6724	1.40736
$680$	5.47172	0.209831
$681$	1.42811	0.0547255
$682$	−0.798883	−0.0305908
$683$	39.2707	1.50265	0.751325	−	0.659932i	$-0.229415\pi$
$683$	39.2707	1.50265	0.751325	+	0.659932i	$0.229415\pi$
$684$	15.9634	0.610376
$685$	−11.0378	−0.421732
$686$	13.6377	0.520690
$687$	−0.273969	−0.0104526
$688$	−1.85455	−0.0707041
$689$	0.773691	0.0294753
$690$	0.401093	0.0152693
$691$	25.9553	0.987386	0.493693	−	0.869636i	$-0.335647\pi$
$691$	25.9553	0.987386	0.493693	+	0.869636i	$0.335647\pi$
$692$	−4.53972	−0.172574
$693$	9.27034	0.352151
$694$	−5.34425	−0.202865
$695$	5.14265	0.195072
$696$	0.608353	0.0230596
$697$	−13.2522	−0.501961
$698$	18.6016	0.704082
$699$	0.830711	0.0314204
$700$	−3.09806	−0.117096
$701$	−9.75218	−0.368335	−0.184167	−	0.982895i	$-0.558959\pi$
$701$	−9.75218	−0.368335	−0.184167	+	0.982895i	$0.558959\pi$
$702$	0.225290	0.00850301
$703$	−4.56803	−0.172287
$704$	1.00000	0.0376889
$705$	−0.693506	−0.0261190
$706$	33.0069	1.24223
$707$	49.8346	1.87422
$708$	1.20825	0.0454090
$709$	28.0060	1.05179	0.525894	−	0.850550i	$-0.323731\pi$
$709$	28.0060	1.05179	0.525894	+	0.850550i	$0.323731\pi$
$710$	3.31813	0.124527
$711$	−44.6208	−1.67341
$712$	13.5221	0.506761
$713$	3.65206	0.136771
$714$	1.48732	0.0556616
$715$	0.428506	0.0160252
$716$	4.51099	0.168584
$717$	−0.587793	−0.0219515
$718$	−24.3854	−0.910056
$719$	42.2236	1.57467	0.787337	−	0.616523i	$-0.211459\pi$
$719$	42.2236	1.57467	0.787337	+	0.616523i	$0.211459\pi$
$720$	2.99230	0.111517
$721$	−11.5752	−0.431083
$722$	9.46035	0.352078
$723$	1.62529	0.0604453
$724$	−3.45967	−0.128578
$725$	6.93370	0.257511
$726$	0.0877386	0.00325629
$727$	−31.1489	−1.15525	−0.577624	−	0.816303i	$-0.696020\pi$
$727$	−31.1489	−1.15525	−0.577624	+	0.816303i	$0.696020\pi$
$728$	1.32754	0.0492018
$729$	−26.5852	−0.984637
$730$	−1.00000	−0.0370117
$731$	10.1476	0.375322
$732$	0.993212	0.0367102
$733$	−9.71948	−0.358997	−0.179499	−	0.983758i	$-0.557448\pi$
$733$	−9.71948	−0.358997	−0.179499	+	0.983758i	$0.557448\pi$
$734$	18.6679	0.689045
$735$	−0.227944	−0.00840783
$736$	−4.57145	−0.168506
$737$	−7.60376	−0.280088
$738$	−7.24716	−0.266772
$739$	−19.6147	−0.721538	−0.360769	−	0.932655i	$-0.617486\pi$
$739$	−19.6147	−0.721538	−0.360769	+	0.932655i	$0.617486\pi$
$740$	−0.856267	−0.0314770
$741$	0.200571	0.00736815
$742$	5.59373	0.205352
$743$	17.4785	0.641223	0.320612	−	0.947211i	$-0.396112\pi$
$743$	17.4785	0.641223	0.320612	+	0.947211i	$0.396112\pi$
$744$	−0.0700929	−0.00256973
$745$	−13.0899	−0.479576
$746$	25.5042	0.933774
$747$	−47.0846	−1.72274
$748$	−5.47172	−0.200066
$749$	−27.8677	−1.01826
$750$	−0.0877386	−0.00320376
$751$	−46.8771	−1.71057	−0.855285	−	0.518158i	$-0.826618\pi$
$751$	−46.8771	−1.71057	−0.855285	+	0.518158i	$0.826618\pi$
$752$	7.90423	0.288238
$753$	2.61736	0.0953819
$754$	−2.97113	−0.108202
$755$	−9.13916	−0.332608
$756$	1.62883	0.0592398
$757$	34.5595	1.25609	0.628043	−	0.778178i	$-0.283856\pi$
$757$	34.5595	1.25609	0.628043	+	0.778178i	$0.283856\pi$
$758$	−7.42784	−0.269791
$759$	−0.401093	−0.0145587
$760$	5.33482	0.193514
$761$	31.1360	1.12868	0.564340	−	0.825542i	$-0.309131\pi$
$761$	31.1360	1.12868	0.564340	+	0.825542i	$0.309131\pi$
$762$	−0.780069	−0.0282589
$763$	14.5738	0.527607
$764$	−23.0514	−0.833969
$765$	−16.3730	−0.591969
$766$	24.2506	0.876212
$767$	−5.90098	−0.213072
$768$	0.0877386	0.00316600
$769$	−3.50785	−0.126496	−0.0632481	−	0.997998i	$-0.520146\pi$
$769$	−3.50785	−0.126496	−0.0632481	+	0.997998i	$0.520146\pi$
$770$	3.09806	0.111646
$771$	0.325429	0.0117200
$772$	−8.44209	−0.303838
$773$	8.42142	0.302898	0.151449	−	0.988465i	$-0.451606\pi$
$773$	8.42142	0.302898	0.151449	+	0.988465i	$0.451606\pi$
$774$	5.54937	0.199468
$775$	−0.798883	−0.0286967
$776$	−11.8372	−0.424931
$777$	−0.232750	−0.00834987
$778$	13.5678	0.486429
$779$	−12.9206	−0.462928
$780$	0.0375965	0.00134617
$781$	−3.31813	−0.118732
$782$	25.0137	0.894489
$783$	−3.64544	−0.130277
$784$	2.59798	0.0927852
$785$	12.5910	0.449394
$786$	−1.61774	−0.0577027
$787$	−27.7217	−0.988172	−0.494086	−	0.869413i	$-0.664497\pi$
$787$	−27.7217	−0.988172	−0.494086	+	0.869413i	$0.664497\pi$
$788$	−9.53237	−0.339577
$789$	−0.431404	−0.0153584
$790$	−14.9119	−0.530541
$791$	22.9046	0.814393
$792$	−2.99230	−0.106327
$793$	−4.85073	−0.172255
$794$	31.5646	1.12018
$795$	0.158417	0.00561847
$796$	12.7045	0.450300
$797$	−39.8328	−1.41095	−0.705475	−	0.708735i	$-0.749266\pi$
$797$	−39.8328	−1.41095	−0.705475	+	0.708735i	$0.749266\pi$
$798$	1.45011	0.0513333
$799$	−43.2498	−1.53007
$800$	1.00000	0.0353553
$801$	−40.4621	−1.42966
$802$	−7.25783	−0.256283
$803$	1.00000	0.0352892
$804$	−0.667144	−0.0235283
$805$	−14.1626	−0.499167
$806$	0.342326	0.0120579
$807$	1.59387	0.0561069
$808$	−16.0857	−0.565894
$809$	8.07514	0.283907	0.141953	−	0.989873i	$-0.454662\pi$
$809$	8.07514	0.283907	0.141953	+	0.989873i	$0.454662\pi$
$810$	−8.93078	−0.313796
$811$	6.65359	0.233639	0.116820	−	0.993153i	$-0.462730\pi$
$811$	6.65359	0.233639	0.116820	+	0.993153i	$0.462730\pi$
$812$	−21.4810	−0.753836
$813$	−2.09906	−0.0736171
$814$	0.856267	0.0300121
$815$	−19.9368	−0.698355
$816$	−0.480082	−0.0168062
$817$	9.89370	0.346137
$818$	21.6122	0.755654
$819$	−3.97239	−0.138807
$820$	−2.42193	−0.0845776
$821$	−6.59148	−0.230044	−0.115022	−	0.993363i	$-0.536694\pi$
$821$	−6.59148	−0.230044	−0.115022	+	0.993363i	$0.536694\pi$
$822$	0.968440	0.0337782
$823$	−34.0833	−1.18807	−0.594034	−	0.804440i	$-0.702466\pi$
$823$	−34.0833	−1.18807	−0.594034	+	0.804440i	$0.702466\pi$
$824$	3.73627	0.130159
$825$	0.0877386	0.00305467
$826$	−42.6636	−1.48446
$827$	20.9964	0.730115	0.365057	−	0.930985i	$-0.381049\pi$
$827$	20.9964	0.730115	0.365057	+	0.930985i	$0.381049\pi$
$828$	13.6792	0.475384
$829$	−42.0360	−1.45997	−0.729986	−	0.683463i	$-0.760473\pi$
$829$	−42.0360	−1.45997	−0.729986	+	0.683463i	$0.760473\pi$
$830$	−15.7352	−0.546178
$831$	−0.845534	−0.0293313
$832$	−0.428506	−0.0148558
$833$	−14.2155	−0.492536
$834$	−0.451209	−0.0156241
$835$	3.51487	0.121637
$836$	−5.33482	−0.184509
$837$	0.420018	0.0145179
$838$	2.68800	0.0928555
$839$	42.4018	1.46387	0.731936	−	0.681374i	$-0.238617\pi$
$839$	42.4018	1.46387	0.731936	+	0.681374i	$0.238617\pi$
$840$	0.271820	0.00937867
$841$	19.0762	0.657800
$842$	15.6260	0.538508
$843$	1.81550	0.0625290
$844$	18.9710	0.653008
$845$	12.8164	0.440897
$846$	−23.6518	−0.813167
$847$	−3.09806	−0.106451
$848$	−1.80556	−0.0620031
$849$	−0.533071	−0.0182950
$850$	−5.47172	−0.187679
$851$	−3.91438	−0.134183
$852$	−0.291128	−0.00997388
$853$	−6.61533	−0.226505	−0.113252	−	0.993566i	$-0.536127\pi$
$853$	−6.61533	−0.226505	−0.113252	+	0.993566i	$0.536127\pi$
$854$	−35.0704	−1.20009
$855$	−15.9634	−0.545937
$856$	8.99520	0.307449
$857$	−13.4896	−0.460796	−0.230398	−	0.973096i	$-0.574003\pi$
$857$	−13.4896	−0.460796	−0.230398	+	0.973096i	$0.574003\pi$
$858$	−0.0375965	−0.00128352
$859$	46.2184	1.57695	0.788476	−	0.615066i	$-0.210871\pi$
$859$	46.2184	1.57695	0.788476	+	0.615066i	$0.210871\pi$
$860$	1.85455	0.0632396
$861$	−0.658330	−0.0224358
$862$	13.8133	0.470481
$863$	12.1126	0.412317	0.206159	−	0.978519i	$-0.433904\pi$
$863$	12.1126	0.412317	0.206159	+	0.978519i	$0.433904\pi$
$864$	−0.525756	−0.0178866
$865$	4.53972	0.154355
$866$	32.7883	1.11419
$867$	1.13532	0.0385574
$868$	2.47499	0.0840066
$869$	14.9119	0.505851
$870$	−0.608353	−0.0206251
$871$	3.25825	0.110402
$872$	−4.70416	−0.159303
$873$	35.4205	1.19880
$874$	24.3879	0.824933
$875$	3.09806	0.104734
$876$	0.0877386	0.00296441
$877$	−51.7693	−1.74812	−0.874062	−	0.485814i	$-0.838523\pi$
$877$	−51.7693	−1.74812	−0.874062	+	0.485814i	$0.838523\pi$
$878$	0.778763	0.0262820
$879$	−0.468866	−0.0158144
$880$	−1.00000	−0.0337100
$881$	−29.8558	−1.00587	−0.502934	−	0.864325i	$-0.667746\pi$
$881$	−29.8558	−1.00587	−0.502934	+	0.864325i	$0.667746\pi$
$882$	−7.77395	−0.261763
$883$	−5.45583	−0.183603	−0.0918016	−	0.995777i	$-0.529263\pi$
$883$	−5.45583	−0.183603	−0.0918016	+	0.995777i	$0.529263\pi$
$884$	2.34466	0.0788596
$885$	−1.20825	−0.0406150
$886$	−13.6465	−0.458462
$887$	19.0645	0.640125	0.320062	−	0.947396i	$-0.396296\pi$
$887$	19.0645	0.640125	0.320062	+	0.947396i	$0.396296\pi$
$888$	0.0751277	0.00252112
$889$	27.5443	0.923807
$890$	−13.5221	−0.453261
$891$	8.93078	0.299192
$892$	0.238686	0.00799178
$893$	−42.1677	−1.41109
$894$	1.14849	0.0384111
$895$	−4.51099	−0.150786
$896$	−3.09806	−0.103499
$897$	0.171871	0.00573859
$898$	33.5335	1.11903
$899$	−5.53922	−0.184743
$900$	−2.99230	−0.0997434
$901$	9.87951	0.329134
$902$	2.42193	0.0806416
$903$	0.504103	0.0167755
$904$	−7.39319	−0.245894
$905$	3.45967	0.115003
$906$	0.801858	0.0266399
$907$	−25.9653	−0.862164	−0.431082	−	0.902313i	$-0.641868\pi$
$907$	−25.9653	−0.862164	−0.431082	+	0.902313i	$0.641868\pi$
$908$	16.2769	0.540168
$909$	48.1333	1.59648
$910$	−1.32754	−0.0440074
$911$	34.9420	1.15768	0.578841	−	0.815441i	$-0.303505\pi$
$911$	34.9420	1.15768	0.578841	+	0.815441i	$0.303505\pi$
$912$	−0.468070	−0.0154994
$913$	15.7352	0.520761
$914$	4.03016	0.133306
$915$	−0.993212	−0.0328346
$916$	−3.12255	−0.103172
$917$	57.1224	1.88635
$918$	2.87679	0.0949483
$919$	18.9996	0.626741	0.313370	−	0.949631i	$-0.398542\pi$
$919$	18.9996	0.626741	0.313370	+	0.949631i	$0.398542\pi$
$920$	4.57145	0.150716
$921$	−1.28874	−0.0424653
$922$	−19.5599	−0.644170
$923$	1.42184	0.0468003
$924$	−0.271820	−0.00894221
$925$	0.856267	0.0281539
$926$	19.2020	0.631017
$927$	−11.1801	−0.367201
$928$	6.93370	0.227610
$929$	−6.18642	−0.202970	−0.101485	−	0.994837i	$-0.532359\pi$
$929$	−6.18642	−0.202970	−0.101485	+	0.994837i	$0.532359\pi$
$930$	0.0700929	0.00229844
$931$	−13.8598	−0.454236
$932$	9.46801	0.310135
$933$	−1.18560	−0.0388150
$934$	22.4067	0.733171
$935$	5.47172	0.178944
$936$	1.28222	0.0419106
$937$	49.1516	1.60571	0.802856	−	0.596173i	$-0.203313\pi$
$937$	49.1516	1.60571	0.802856	+	0.596173i	$0.203313\pi$
$938$	23.5569	0.769161
$939$	1.15684	0.0377521
$940$	−7.90423	−0.257808
$941$	−5.95847	−0.194241	−0.0971203	−	0.995273i	$-0.530963\pi$
$941$	−5.95847	−0.194241	−0.0971203	+	0.995273i	$0.530963\pi$
$942$	−1.10472	−0.0359938
$943$	−11.0718	−0.360546
$944$	13.7711	0.448210
$945$	−1.62883	−0.0529857
$946$	−1.85455	−0.0602966
$947$	14.6508	0.476086	0.238043	−	0.971255i	$-0.423494\pi$
$947$	14.6508	0.476086	0.238043	+	0.971255i	$0.423494\pi$
$948$	1.30835	0.0424932
$949$	−0.428506	−0.0139099
$950$	−5.33482	−0.173085
$951$	−2.12597	−0.0689392
$952$	16.9517	0.549409
$953$	−42.3939	−1.37327	−0.686636	−	0.727001i	$-0.740913\pi$
$953$	−42.3939	−1.37327	−0.686636	+	0.727001i	$0.740913\pi$
$954$	5.40277	0.174921
$955$	23.0514	0.745924
$956$	−6.69936	−0.216673
$957$	0.608353	0.0196653
$958$	17.6062	0.568829
$959$	−34.1957	−1.10424
$960$	−0.0877386	−0.00283175
$961$	−30.3618	−0.979412
$962$	−0.366915	−0.0118298
$963$	−26.9163	−0.867367
$964$	18.5243	0.596626
$965$	8.44209	0.271761
$966$	1.24261	0.0399803
$967$	−6.14161	−0.197501	−0.0987504	−	0.995112i	$-0.531485\pi$
$967$	−6.14161	−0.197501	−0.0987504	+	0.995112i	$0.531485\pi$
$968$	1.00000	0.0321412
$969$	2.56115	0.0822760
$970$	11.8372	0.380069
$971$	50.0058	1.60476	0.802381	−	0.596812i	$-0.203566\pi$
$971$	50.0058	1.60476	0.802381	+	0.596812i	$0.203566\pi$
$972$	2.36084	0.0757241
$973$	15.9323	0.510765
$974$	−8.06567	−0.258441
$975$	−0.0375965	−0.00120405
$976$	11.3201	0.362348
$977$	36.4683	1.16672	0.583362	−	0.812213i	$-0.301737\pi$
$977$	36.4683	1.16672	0.583362	+	0.812213i	$0.301737\pi$
$978$	1.74923	0.0559341
$979$	13.5221	0.432167
$980$	−2.59798	−0.0829896
$981$	14.0763	0.449421
$982$	−9.39828	−0.299911
$983$	46.4605	1.48186	0.740930	−	0.671582i	$-0.234385\pi$
$983$	46.4605	1.48186	0.740930	+	0.671582i	$0.234385\pi$
$984$	0.212497	0.00677417
$985$	9.53237	0.303727
$986$	−37.9393	−1.20823
$987$	−2.14852	−0.0683883
$988$	2.28600	0.0727274
$989$	8.47799	0.269584
$990$	2.99230	0.0951016
$991$	−14.4909	−0.460320	−0.230160	−	0.973153i	$-0.573925\pi$
$991$	−14.4909	−0.460320	−0.230160	+	0.973153i	$0.573925\pi$
$992$	−0.798883	−0.0253646
$993$	−1.90580	−0.0604787
$994$	10.2798	0.326054
$995$	−12.7045	−0.402761
$996$	1.38059	0.0437456
$997$	42.8852	1.35819	0.679093	−	0.734052i	$-0.262373\pi$
$997$	42.8852	1.35819	0.679093	+	0.734052i	$0.262373\pi$
$998$	−9.43000	−0.298501
$999$	−0.450188	−0.0142433

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8030.2.a.bd.1.6	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8030.2.a.bd.1.6	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.0877386 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.0877386 q^{6} -3.09806 q^{7} +1.00000 q^{8} -2.99230 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.0877386 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.0877386 q^{6} -3.09806 q^{7} +1.00000 q^{8} -2.99230 q^{9} -1.00000 q^{10} +1.00000 q^{11} +0.0877386 q^{12} -0.428506 q^{13} -3.09806 q^{14} -0.0877386 q^{15} +1.00000 q^{16} -5.47172 q^{17} -2.99230 q^{18} -5.33482 q^{19} -1.00000 q^{20} -0.271820 q^{21} +1.00000 q^{22} -4.57145 q^{23} +0.0877386 q^{24} +1.00000 q^{25} -0.428506 q^{26} -0.525756 q^{27} -3.09806 q^{28} +6.93370 q^{29} -0.0877386 q^{30} -0.798883 q^{31} +1.00000 q^{32} +0.0877386 q^{33} -5.47172 q^{34} +3.09806 q^{35} -2.99230 q^{36} +0.856267 q^{37} -5.33482 q^{38} -0.0375965 q^{39} -1.00000 q^{40} +2.42193 q^{41} -0.271820 q^{42} -1.85455 q^{43} +1.00000 q^{44} +2.99230 q^{45} -4.57145 q^{46} +7.90423 q^{47} +0.0877386 q^{48} +2.59798 q^{49} +1.00000 q^{50} -0.480082 q^{51} -0.428506 q^{52} -1.80556 q^{53} -0.525756 q^{54} -1.00000 q^{55} -3.09806 q^{56} -0.468070 q^{57} +6.93370 q^{58} +13.7711 q^{59} -0.0877386 q^{60} +11.3201 q^{61} -0.798883 q^{62} +9.27034 q^{63} +1.00000 q^{64} +0.428506 q^{65} +0.0877386 q^{66} -7.60376 q^{67} -5.47172 q^{68} -0.401093 q^{69} +3.09806 q^{70} -3.31813 q^{71} -2.99230 q^{72} +1.00000 q^{73} +0.856267 q^{74} +0.0877386 q^{75} -5.33482 q^{76} -3.09806 q^{77} -0.0375965 q^{78} +14.9119 q^{79} -1.00000 q^{80} +8.93078 q^{81} +2.42193 q^{82} +15.7352 q^{83} -0.271820 q^{84} +5.47172 q^{85} -1.85455 q^{86} +0.608353 q^{87} +1.00000 q^{88} +13.5221 q^{89} +2.99230 q^{90} +1.32754 q^{91} -4.57145 q^{92} -0.0700929 q^{93} +7.90423 q^{94} +5.33482 q^{95} +0.0877386 q^{96} -11.8372 q^{97} +2.59798 q^{98} -2.99230 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 14 q^{2} + 6 q^{3} + 14 q^{4} - 14 q^{5} + 6 q^{6} + 4 q^{7} + 14 q^{8} + 24 q^{9}+O(q^{10}) \) 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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