LMFDB - Embedded newform 8030.2.a.bf.1.4

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:	$1$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 4 x^{14} - 23 x^{13} + 99 x^{12} + 191 x^{11} - 922 x^{10} - 702 x^{9} + 4108 x^{8} + 957 x^{7} + \cdots + 8 $ x^15 - 4x^14 - 23x^13 + 99x^12 + 191x^11 - 922x^10 - 702x^9 + 4108x^8 + 957x^7 - 8875x^6 + 479x^5 + 7698x^4 - 1731x^3 - 626x^2 + 46x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$2.39402$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.39402 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.39402 q^{6} -0.390362 q^{7} +1.00000 q^{8} +2.73133 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.39402 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.39402 q^{6} -0.390362 q^{7} +1.00000 q^{8} +2.73133 q^{9} -1.00000 q^{10} -1.00000 q^{11} -2.39402 q^{12} +2.13825 q^{13} -0.390362 q^{14} +2.39402 q^{15} +1.00000 q^{16} -6.00087 q^{17} +2.73133 q^{18} +4.60230 q^{19} -1.00000 q^{20} +0.934535 q^{21} -1.00000 q^{22} -3.04125 q^{23} -2.39402 q^{24} +1.00000 q^{25} +2.13825 q^{26} +0.643201 q^{27} -0.390362 q^{28} +7.98624 q^{29} +2.39402 q^{30} -9.73058 q^{31} +1.00000 q^{32} +2.39402 q^{33} -6.00087 q^{34} +0.390362 q^{35} +2.73133 q^{36} +8.76032 q^{37} +4.60230 q^{38} -5.11901 q^{39} -1.00000 q^{40} -4.78343 q^{41} +0.934535 q^{42} -3.21354 q^{43} -1.00000 q^{44} -2.73133 q^{45} -3.04125 q^{46} +6.38474 q^{47} -2.39402 q^{48} -6.84762 q^{49} +1.00000 q^{50} +14.3662 q^{51} +2.13825 q^{52} -3.09818 q^{53} +0.643201 q^{54} +1.00000 q^{55} -0.390362 q^{56} -11.0180 q^{57} +7.98624 q^{58} +4.39505 q^{59} +2.39402 q^{60} -1.48139 q^{61} -9.73058 q^{62} -1.06621 q^{63} +1.00000 q^{64} -2.13825 q^{65} +2.39402 q^{66} +12.1439 q^{67} -6.00087 q^{68} +7.28082 q^{69} +0.390362 q^{70} -4.34448 q^{71} +2.73133 q^{72} +1.00000 q^{73} +8.76032 q^{74} -2.39402 q^{75} +4.60230 q^{76} +0.390362 q^{77} -5.11901 q^{78} -10.9514 q^{79} -1.00000 q^{80} -9.73383 q^{81} -4.78343 q^{82} +14.4006 q^{83} +0.934535 q^{84} +6.00087 q^{85} -3.21354 q^{86} -19.1192 q^{87} -1.00000 q^{88} +6.37070 q^{89} -2.73133 q^{90} -0.834691 q^{91} -3.04125 q^{92} +23.2952 q^{93} +6.38474 q^{94} -4.60230 q^{95} -2.39402 q^{96} +10.0956 q^{97} -6.84762 q^{98} -2.73133 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q + 15 q^{2} - 4 q^{3} + 15 q^{4} - 15 q^{5} - 4 q^{6} - 6 q^{7} + 15 q^{8} + 17 q^{9}+O(q^{10}) $ 15 * q + 15 * q^2 - 4 * q^3 + 15 * q^4 - 15 * q^5 - 4 * q^6 - 6 * q^7 + 15 * q^8 + 17 * q^9	\( 15 q + 15 q^{2} - 4 q^{3} + 15 q^{4} - 15 q^{5} - 4 q^{6} - 6 q^{7} + 15 q^{8} + 17 q^{9} - 15 q^{10} - 15 q^{11} - 4 q^{12} - 6 q^{13} - 6 q^{14} + 4 q^{15} + 15 q^{16} + 2 q^{17} + 17 q^{18} - 8 q^{19} - 15 q^{20} - 17 q^{21} - 15 q^{22} - 4 q^{23} - 4 q^{24} + 15 q^{25} - 6 q^{26} - 19 q^{27} - 6 q^{28} - 13 q^{29} + 4 q^{30} - 20 q^{31} + 15 q^{32} + 4 q^{33} + 2 q^{34} + 6 q^{35} + 17 q^{36} - 15 q^{37} - 8 q^{38} - 11 q^{39} - 15 q^{40} + 2 q^{41} - 17 q^{42} - 26 q^{43} - 15 q^{44} - 17 q^{45} - 4 q^{46} - 14 q^{47} - 4 q^{48} + 11 q^{49} + 15 q^{50} - 39 q^{51} - 6 q^{52} - 21 q^{53} - 19 q^{54} + 15 q^{55} - 6 q^{56} + q^{57} - 13 q^{58} - 14 q^{59} + 4 q^{60} - 45 q^{61} - 20 q^{62} - 17 q^{63} + 15 q^{64} + 6 q^{65} + 4 q^{66} - 10 q^{67} + 2 q^{68} - 23 q^{69} + 6 q^{70} - 9 q^{71} + 17 q^{72} + 15 q^{73} - 15 q^{74} - 4 q^{75} - 8 q^{76} + 6 q^{77} - 11 q^{78} - 26 q^{79} - 15 q^{80} + 15 q^{81} + 2 q^{82} - 30 q^{83} - 17 q^{84} - 2 q^{85} - 26 q^{86} - 14 q^{87} - 15 q^{88} + 10 q^{89} - 17 q^{90} - 17 q^{91} - 4 q^{92} - 8 q^{93} - 14 q^{94} + 8 q^{95} - 4 q^{96} - 27 q^{97} + 11 q^{98} - 17 q^{99}+O(q^{100}) \) 15 * q + 15 * q^2 - 4 * q^3 + 15 * q^4 - 15 * q^5 - 4 * q^6 - 6 * q^7 + 15 * q^8 + 17 * q^9 - 15 * q^10 - 15 * q^11 - 4 * q^12 - 6 * q^13 - 6 * q^14 + 4 * q^15 + 15 * q^16 + 2 * q^17 + 17 * q^18 - 8 * q^19 - 15 * q^20 - 17 * q^21 - 15 * q^22 - 4 * q^23 - 4 * q^24 + 15 * q^25 - 6 * q^26 - 19 * q^27 - 6 * q^28 - 13 * q^29 + 4 * q^30 - 20 * q^31 + 15 * q^32 + 4 * q^33 + 2 * q^34 + 6 * q^35 + 17 * q^36 - 15 * q^37 - 8 * q^38 - 11 * q^39 - 15 * q^40 + 2 * q^41 - 17 * q^42 - 26 * q^43 - 15 * q^44 - 17 * q^45 - 4 * q^46 - 14 * q^47 - 4 * q^48 + 11 * q^49 + 15 * q^50 - 39 * q^51 - 6 * q^52 - 21 * q^53 - 19 * q^54 + 15 * q^55 - 6 * q^56 + q^57 - 13 * q^58 - 14 * q^59 + 4 * q^60 - 45 * q^61 - 20 * q^62 - 17 * q^63 + 15 * q^64 + 6 * q^65 + 4 * q^66 - 10 * q^67 + 2 * q^68 - 23 * q^69 + 6 * q^70 - 9 * q^71 + 17 * q^72 + 15 * q^73 - 15 * q^74 - 4 * q^75 - 8 * q^76 + 6 * q^77 - 11 * q^78 - 26 * q^79 - 15 * q^80 + 15 * q^81 + 2 * q^82 - 30 * q^83 - 17 * q^84 - 2 * q^85 - 26 * q^86 - 14 * q^87 - 15 * q^88 + 10 * q^89 - 17 * q^90 - 17 * q^91 - 4 * q^92 - 8 * q^93 - 14 * q^94 + 8 * q^95 - 4 * q^96 - 27 * q^97 + 11 * q^98 - 17 * 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
$3$	−2.39402	−1.38219	−0.691094	−	0.722765i	$-0.742871\pi$
$3$	−2.39402	−1.38219	−0.691094	+	0.722765i	$0.742871\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.39402	−0.977354
$7$	−0.390362	−0.147543	−0.0737715	−	0.997275i	$-0.523504\pi$
$7$	−0.390362	−0.147543	−0.0737715	+	0.997275i	$0.523504\pi$
$8$	1.00000	0.353553
$9$	2.73133	0.910443
$10$	−1.00000	−0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−2.39402	−0.691094
$13$	2.13825	0.593043	0.296522	−	0.955026i	$-0.404173\pi$
$13$	2.13825	0.593043	0.296522	+	0.955026i	$0.404173\pi$
$14$	−0.390362	−0.104329
$15$	2.39402	0.618133
$16$	1.00000	0.250000
$17$	−6.00087	−1.45543	−0.727713	−	0.685882i	$-0.759417\pi$
$17$	−6.00087	−1.45543	−0.727713	+	0.685882i	$0.759417\pi$
$18$	2.73133	0.643781
$19$	4.60230	1.05584	0.527920	−	0.849294i	$-0.322972\pi$
$19$	4.60230	1.05584	0.527920	+	0.849294i	$0.322972\pi$
$20$	−1.00000	−0.223607
$21$	0.934535	0.203932
$22$	−1.00000	−0.213201
$23$	−3.04125	−0.634145	−0.317073	−	0.948401i	$-0.602700\pi$
$23$	−3.04125	−0.634145	−0.317073	+	0.948401i	$0.602700\pi$
$24$	−2.39402	−0.488677
$25$	1.00000	0.200000
$26$	2.13825	0.419345
$27$	0.643201	0.123784
$28$	−0.390362	−0.0737715
$29$	7.98624	1.48301	0.741504	−	0.670949i	$-0.234113\pi$
$29$	7.98624	1.48301	0.741504	+	0.670949i	$0.234113\pi$
$30$	2.39402	0.437086
$31$	−9.73058	−1.74766	−0.873831	−	0.486229i	$-0.838372\pi$
$31$	−9.73058	−1.74766	−0.873831	+	0.486229i	$0.838372\pi$
$32$	1.00000	0.176777
$33$	2.39402	0.416745
$34$	−6.00087	−1.02914
$35$	0.390362	0.0659833
$36$	2.73133	0.455222
$37$	8.76032	1.44019	0.720094	−	0.693876i	$-0.244099\pi$
$37$	8.76032	1.44019	0.720094	+	0.693876i	$0.244099\pi$
$38$	4.60230	0.746591
$39$	−5.11901	−0.819697
$40$	−1.00000	−0.158114
$41$	−4.78343	−0.747046	−0.373523	−	0.927621i	$-0.621850\pi$
$41$	−4.78343	−0.747046	−0.373523	+	0.927621i	$0.621850\pi$
$42$	0.934535	0.144202
$43$	−3.21354	−0.490061	−0.245030	−	0.969515i	$-0.578798\pi$
$43$	−3.21354	−0.490061	−0.245030	+	0.969515i	$0.578798\pi$
$44$	−1.00000	−0.150756
$45$	−2.73133	−0.407163
$46$	−3.04125	−0.448408
$47$	6.38474	0.931310	0.465655	−	0.884966i	$-0.345819\pi$
$47$	6.38474	0.931310	0.465655	+	0.884966i	$0.345819\pi$
$48$	−2.39402	−0.345547
$49$	−6.84762	−0.978231
$50$	1.00000	0.141421
$51$	14.3662	2.01167
$52$	2.13825	0.296522
$53$	−3.09818	−0.425568	−0.212784	−	0.977099i	$-0.568253\pi$
$53$	−3.09818	−0.425568	−0.212784	+	0.977099i	$0.568253\pi$
$54$	0.643201	0.0875286
$55$	1.00000	0.134840
$56$	−0.390362	−0.0521643
$57$	−11.0180	−1.45937
$58$	7.98624	1.04864
$59$	4.39505	0.572187	0.286093	−	0.958202i	$-0.407643\pi$
$59$	4.39505	0.572187	0.286093	+	0.958202i	$0.407643\pi$
$60$	2.39402	0.309067
$61$	−1.48139	−0.189672	−0.0948362	−	0.995493i	$-0.530233\pi$
$61$	−1.48139	−0.189672	−0.0948362	+	0.995493i	$0.530233\pi$
$62$	−9.73058	−1.23578
$63$	−1.06621	−0.134330
$64$	1.00000	0.125000
$65$	−2.13825	−0.265217
$66$	2.39402	0.294683
$67$	12.1439	1.48361	0.741806	−	0.670614i	$-0.233969\pi$
$67$	12.1439	1.48361	0.741806	+	0.670614i	$0.233969\pi$
$68$	−6.00087	−0.727713
$69$	7.28082	0.876508
$70$	0.390362	0.0466572
$71$	−4.34448	−0.515595	−0.257797	−	0.966199i	$-0.582997\pi$
$71$	−4.34448	−0.515595	−0.257797	+	0.966199i	$0.582997\pi$
$72$	2.73133	0.321890
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	8.76032	1.01837
$75$	−2.39402	−0.276438
$76$	4.60230	0.527920
$77$	0.390362	0.0444859
$78$	−5.11901	−0.579613
$79$	−10.9514	−1.23213	−0.616063	−	0.787697i	$-0.711273\pi$
$79$	−10.9514	−1.23213	−0.616063	+	0.787697i	$0.711273\pi$
$80$	−1.00000	−0.111803
$81$	−9.73383	−1.08154
$82$	−4.78343	−0.528241
$83$	14.4006	1.58067	0.790334	−	0.612677i	$-0.209907\pi$
$83$	14.4006	1.58067	0.790334	+	0.612677i	$0.209907\pi$
$84$	0.934535	0.101966
$85$	6.00087	0.650886
$86$	−3.21354	−0.346525
$87$	−19.1192	−2.04979
$88$	−1.00000	−0.106600
$89$	6.37070	0.675293	0.337647	−	0.941273i	$-0.390369\pi$
$89$	6.37070	0.675293	0.337647	+	0.941273i	$0.390369\pi$
$90$	−2.73133	−0.287907
$91$	−0.834691	−0.0874994
$92$	−3.04125	−0.317073
$93$	23.2952	2.41560
$94$	6.38474	0.658535
$95$	−4.60230	−0.472186
$96$	−2.39402	−0.244339
$97$	10.0956	1.02505	0.512525	−	0.858673i	$-0.328710\pi$
$97$	10.0956	1.02505	0.512525	+	0.858673i	$0.328710\pi$
$98$	−6.84762	−0.691714
$99$	−2.73133	−0.274509
$100$	1.00000	0.100000
$101$	11.2773	1.12214	0.561069	−	0.827769i	$-0.310390\pi$
$101$	11.2773	1.12214	0.561069	+	0.827769i	$0.310390\pi$
$102$	14.3662	1.42247
$103$	−8.99111	−0.885920	−0.442960	−	0.896541i	$-0.646072\pi$
$103$	−8.99111	−0.885920	−0.442960	+	0.896541i	$0.646072\pi$
$104$	2.13825	0.209672
$105$	−0.934535	−0.0912013
$106$	−3.09818	−0.300922
$107$	−14.4501	−1.39694	−0.698472	−	0.715637i	$-0.746136\pi$
$107$	−14.4501	−1.39694	−0.698472	+	0.715637i	$0.746136\pi$
$108$	0.643201	0.0618921
$109$	−16.9926	−1.62759	−0.813797	−	0.581150i	$-0.802603\pi$
$109$	−16.9926	−1.62759	−0.813797	+	0.581150i	$0.802603\pi$
$110$	1.00000	0.0953463
$111$	−20.9724	−1.99061
$112$	−0.390362	−0.0368858
$113$	7.31591	0.688223	0.344111	−	0.938929i	$-0.388180\pi$
$113$	7.31591	0.688223	0.344111	+	0.938929i	$0.388180\pi$
$114$	−11.0180	−1.03193
$115$	3.04125	0.283598
$116$	7.98624	0.741504
$117$	5.84026	0.539932
$118$	4.39505	0.404597
$119$	2.34251	0.214738
$120$	2.39402	0.218543
$121$	1.00000	0.0909091
$122$	−1.48139	−0.134119
$123$	11.4516	1.03256
$124$	−9.73058	−0.873831
$125$	−1.00000	−0.0894427
$126$	−1.06621	−0.0949854
$127$	13.8500	1.22899	0.614496	−	0.788920i	$-0.289360\pi$
$127$	13.8500	1.22899	0.614496	+	0.788920i	$0.289360\pi$
$128$	1.00000	0.0883883
$129$	7.69329	0.677356
$130$	−2.13825	−0.187537
$131$	−9.09972	−0.795046	−0.397523	−	0.917592i	$-0.630130\pi$
$131$	−9.09972	−0.795046	−0.397523	+	0.917592i	$0.630130\pi$
$132$	2.39402	0.208373
$133$	−1.79656	−0.155782
$134$	12.1439	1.04907
$135$	−0.643201	−0.0553580
$136$	−6.00087	−0.514571
$137$	0.553777	0.0473123	0.0236562	−	0.999720i	$-0.492469\pi$
$137$	0.553777	0.0473123	0.0236562	+	0.999720i	$0.492469\pi$
$138$	7.28082	0.619785
$139$	−9.86204	−0.836487	−0.418244	−	0.908335i	$-0.637354\pi$
$139$	−9.86204	−0.836487	−0.418244	+	0.908335i	$0.637354\pi$
$140$	0.390362	0.0329916
$141$	−15.2852	−1.28724
$142$	−4.34448	−0.364580
$143$	−2.13825	−0.178809
$144$	2.73133	0.227611
$145$	−7.98624	−0.663221
$146$	1.00000	0.0827606
$147$	16.3933	1.35210
$148$	8.76032	0.720094
$149$	14.6134	1.19717	0.598587	−	0.801058i	$-0.295729\pi$
$149$	14.6134	1.19717	0.598587	+	0.801058i	$0.295729\pi$
$150$	−2.39402	−0.195471
$151$	−7.22010	−0.587563	−0.293782	−	0.955873i	$-0.594914\pi$
$151$	−7.22010	−0.587563	−0.293782	+	0.955873i	$0.594914\pi$
$152$	4.60230	0.373296
$153$	−16.3904	−1.32508
$154$	0.390362	0.0314563
$155$	9.73058	0.781579
$156$	−5.11901	−0.409848
$157$	−14.6572	−1.16977	−0.584887	−	0.811115i	$-0.698861\pi$
$157$	−14.6572	−1.16977	−0.584887	+	0.811115i	$0.698861\pi$
$158$	−10.9514	−0.871245
$159$	7.41710	0.588214
$160$	−1.00000	−0.0790569
$161$	1.18719	0.0935637
$162$	−9.73383	−0.764762
$163$	−2.99847	−0.234858	−0.117429	−	0.993081i	$-0.537465\pi$
$163$	−2.99847	−0.234858	−0.117429	+	0.993081i	$0.537465\pi$
$164$	−4.78343	−0.373523
$165$	−2.39402	−0.186374
$166$	14.4006	1.11770
$167$	−23.4853	−1.81735	−0.908673	−	0.417508i	$-0.862904\pi$
$167$	−23.4853	−1.81735	−0.908673	+	0.417508i	$0.862904\pi$
$168$	0.934535	0.0721009
$169$	−8.42790	−0.648300
$170$	6.00087	0.460246
$171$	12.5704	0.961282
$172$	−3.21354	−0.245030
$173$	−10.4333	−0.793228	−0.396614	−	0.917985i	$-0.629815\pi$
$173$	−10.4333	−0.793228	−0.396614	+	0.917985i	$0.629815\pi$
$174$	−19.1192	−1.44942
$175$	−0.390362	−0.0295086
$176$	−1.00000	−0.0753778
$177$	−10.5218	−0.790869
$178$	6.37070	0.477505
$179$	23.0214	1.72070	0.860351	−	0.509701i	$-0.170244\pi$
$179$	23.0214	1.72070	0.860351	+	0.509701i	$0.170244\pi$
$180$	−2.73133	−0.203581
$181$	−3.59862	−0.267484	−0.133742	−	0.991016i	$-0.542699\pi$
$181$	−3.59862	−0.267484	−0.133742	+	0.991016i	$0.542699\pi$
$182$	−0.834691	−0.0618714
$183$	3.54648	0.262163
$184$	−3.04125	−0.224204
$185$	−8.76032	−0.644072
$186$	23.2952	1.70809
$187$	6.00087	0.438827
$188$	6.38474	0.465655
$189$	−0.251081	−0.0182635
$190$	−4.60230	−0.333886
$191$	−13.7250	−0.993108	−0.496554	−	0.868006i	$-0.665401\pi$
$191$	−13.7250	−0.993108	−0.496554	+	0.868006i	$0.665401\pi$
$192$	−2.39402	−0.172773
$193$	14.5551	1.04770	0.523850	−	0.851810i	$-0.324495\pi$
$193$	14.5551	1.04770	0.523850	+	0.851810i	$0.324495\pi$
$194$	10.0956	0.724819
$195$	5.11901	0.366580
$196$	−6.84762	−0.489116
$197$	−10.3620	−0.738259	−0.369129	−	0.929378i	$-0.620344\pi$
$197$	−10.3620	−0.738259	−0.369129	+	0.929378i	$0.620344\pi$
$198$	−2.73133	−0.194107
$199$	−4.35445	−0.308679	−0.154339	−	0.988018i	$-0.549325\pi$
$199$	−4.35445	−0.308679	−0.154339	+	0.988018i	$0.549325\pi$
$200$	1.00000	0.0707107
$201$	−29.0727	−2.05063
$202$	11.2773	0.793471
$203$	−3.11753	−0.218807
$204$	14.3662	1.00584
$205$	4.78343	0.334089
$206$	−8.99111	−0.626440
$207$	−8.30667	−0.577353
$208$	2.13825	0.148261
$209$	−4.60230	−0.318348
$210$	−0.934535	−0.0644890
$211$	0.234813	0.0161652	0.00808261	−	0.999967i	$-0.497427\pi$
$211$	0.234813	0.0161652	0.00808261	+	0.999967i	$0.497427\pi$
$212$	−3.09818	−0.212784
$213$	10.4008	0.712649
$214$	−14.4501	−0.987788
$215$	3.21354	0.219162
$216$	0.643201	0.0437643
$217$	3.79845	0.257856
$218$	−16.9926	−1.15088
$219$	−2.39402	−0.161773
$220$	1.00000	0.0674200
$221$	−12.8313	−0.863130
$222$	−20.9724	−1.40757
$223$	−22.5133	−1.50760	−0.753800	−	0.657104i	$-0.771781\pi$
$223$	−22.5133	−1.50760	−0.753800	+	0.657104i	$0.771781\pi$
$224$	−0.390362	−0.0260822
$225$	2.73133	0.182089
$226$	7.31591	0.486647
$227$	8.96335	0.594918	0.297459	−	0.954735i	$-0.403861\pi$
$227$	8.96335	0.594918	0.297459	+	0.954735i	$0.403861\pi$
$228$	−11.0180	−0.729684
$229$	−3.74258	−0.247317	−0.123658	−	0.992325i	$-0.539463\pi$
$229$	−3.74258	−0.247317	−0.123658	+	0.992325i	$0.539463\pi$
$230$	3.04125	0.200534
$231$	−0.934535	−0.0614879
$232$	7.98624	0.524322
$233$	23.3858	1.53205	0.766026	−	0.642809i	$-0.222231\pi$
$233$	23.3858	1.53205	0.766026	+	0.642809i	$0.222231\pi$
$234$	5.84026	0.381790
$235$	−6.38474	−0.416494
$236$	4.39505	0.286093
$237$	26.2178	1.70303
$238$	2.34251	0.151843
$239$	−3.85948	−0.249649	−0.124825	−	0.992179i	$-0.539837\pi$
$239$	−3.85948	−0.249649	−0.124825	+	0.992179i	$0.539837\pi$
$240$	2.39402	0.154533
$241$	−29.5226	−1.90172	−0.950858	−	0.309627i	$-0.899796\pi$
$241$	−29.5226	−1.90172	−0.950858	+	0.309627i	$0.899796\pi$
$242$	1.00000	0.0642824
$243$	21.3734	1.37110
$244$	−1.48139	−0.0948362
$245$	6.84762	0.437478
$246$	11.4516	0.730128
$247$	9.84085	0.626158
$248$	−9.73058	−0.617892
$249$	−34.4752	−2.18478
$250$	−1.00000	−0.0632456
$251$	−25.5975	−1.61570	−0.807852	−	0.589386i	$-0.799370\pi$
$251$	−25.5975	−1.61570	−0.807852	+	0.589386i	$0.799370\pi$
$252$	−1.06621	−0.0671648
$253$	3.04125	0.191202
$254$	13.8500	0.869028
$255$	−14.3662	−0.899647
$256$	1.00000	0.0625000
$257$	7.94437	0.495556	0.247778	−	0.968817i	$-0.420300\pi$
$257$	7.94437	0.495556	0.247778	+	0.968817i	$0.420300\pi$
$258$	7.69329	0.478963
$259$	−3.41970	−0.212490
$260$	−2.13825	−0.132608
$261$	21.8131	1.35019
$262$	−9.09972	−0.562183
$263$	17.3583	1.07036	0.535179	−	0.844739i	$-0.320244\pi$
$263$	17.3583	1.07036	0.535179	+	0.844739i	$0.320244\pi$
$264$	2.39402	0.147342
$265$	3.09818	0.190320
$266$	−1.79656	−0.110154
$267$	−15.2516	−0.933382
$268$	12.1439	0.741806
$269$	1.57963	0.0963119	0.0481559	−	0.998840i	$-0.484666\pi$
$269$	1.57963	0.0963119	0.0481559	+	0.998840i	$0.484666\pi$
$270$	−0.643201	−0.0391440
$271$	−10.4765	−0.636405	−0.318203	−	0.948023i	$-0.603079\pi$
$271$	−10.4765	−0.636405	−0.318203	+	0.948023i	$0.603079\pi$
$272$	−6.00087	−0.363856
$273$	1.99827	0.120941
$274$	0.553777	0.0334549
$275$	−1.00000	−0.0603023
$276$	7.28082	0.438254
$277$	−7.93126	−0.476543	−0.238272	−	0.971199i	$-0.576581\pi$
$277$	−7.93126	−0.476543	−0.238272	+	0.971199i	$0.576581\pi$
$278$	−9.86204	−0.591486
$279$	−26.5774	−1.59115
$280$	0.390362	0.0233286
$281$	−5.52571	−0.329636	−0.164818	−	0.986324i	$-0.552704\pi$
$281$	−5.52571	−0.329636	−0.164818	+	0.986324i	$0.552704\pi$
$282$	−15.2852	−0.910220
$283$	−28.0362	−1.66658	−0.833289	−	0.552838i	$-0.813545\pi$
$283$	−28.0362	−1.66658	−0.833289	+	0.552838i	$0.813545\pi$
$284$	−4.34448	−0.257797
$285$	11.0180	0.652649
$286$	−2.13825	−0.126437
$287$	1.86727	0.110221
$288$	2.73133	0.160945
$289$	19.0105	1.11826
$290$	−7.98624	−0.468968
$291$	−24.1690	−1.41681
$292$	1.00000	0.0585206
$293$	26.8280	1.56731	0.783655	−	0.621197i	$-0.213353\pi$
$293$	26.8280	1.56731	0.783655	+	0.621197i	$0.213353\pi$
$294$	16.3933	0.956078
$295$	−4.39505	−0.255890
$296$	8.76032	0.509183
$297$	−0.643201	−0.0373223
$298$	14.6134	0.846530
$299$	−6.50295	−0.376075
$300$	−2.39402	−0.138219
$301$	1.25445	0.0723051
$302$	−7.22010	−0.415470
$303$	−26.9982	−1.55100
$304$	4.60230	0.263960
$305$	1.48139	0.0848241
$306$	−16.3904	−0.936975
$307$	−12.2059	−0.696630	−0.348315	−	0.937378i	$-0.613246\pi$
$307$	−12.2059	−0.696630	−0.348315	+	0.937378i	$0.613246\pi$
$308$	0.390362	0.0222430
$309$	21.5249	1.22451
$310$	9.73058	0.552660
$311$	0.0110162	0.000624673 0	0.000312336	−	1.00000i	$-0.499901\pi$
$311$	0.0110162	0.000624673 0	0.000312336		1.00000i	$0.499901\pi$
$312$	−5.11901	−0.289807
$313$	−13.1816	−0.745067	−0.372533	−	0.928019i	$-0.621511\pi$
$313$	−13.1816	−0.745067	−0.372533	+	0.928019i	$0.621511\pi$
$314$	−14.6572	−0.827155
$315$	1.06621	0.0600740
$316$	−10.9514	−0.616063
$317$	−7.70001	−0.432476	−0.216238	−	0.976341i	$-0.569379\pi$
$317$	−7.70001	−0.432476	−0.216238	+	0.976341i	$0.569379\pi$
$318$	7.41710	0.415930
$319$	−7.98624	−0.447143
$320$	−1.00000	−0.0559017
$321$	34.5938	1.93084
$322$	1.18719	0.0661595
$323$	−27.6178	−1.53670
$324$	−9.73383	−0.540768
$325$	2.13825	0.118609
$326$	−2.99847	−0.166070
$327$	40.6806	2.24964
$328$	−4.78343	−0.264121
$329$	−2.49236	−0.137408
$330$	−2.39402	−0.131786
$331$	−23.5349	−1.29360	−0.646799	−	0.762661i	$-0.723893\pi$
$331$	−23.5349	−1.29360	−0.646799	+	0.762661i	$0.723893\pi$
$332$	14.4006	0.790334
$333$	23.9273	1.31121
$334$	−23.4853	−1.28506
$335$	−12.1439	−0.663492
$336$	0.934535	0.0509831
$337$	7.94195	0.432626	0.216313	−	0.976324i	$-0.430597\pi$
$337$	7.94195	0.432626	0.216313	+	0.976324i	$0.430597\pi$
$338$	−8.42790	−0.458417
$339$	−17.5144	−0.951253
$340$	6.00087	0.325443
$341$	9.73058	0.526940
$342$	12.5704	0.679729
$343$	5.40559	0.291874
$344$	−3.21354	−0.173263
$345$	−7.28082	−0.391986
$346$	−10.4333	−0.560897
$347$	−11.3392	−0.608721	−0.304361	−	0.952557i	$-0.598443\pi$
$347$	−11.3392	−0.608721	−0.304361	+	0.952557i	$0.598443\pi$
$348$	−19.1192	−1.02490
$349$	−21.4622	−1.14885	−0.574424	−	0.818558i	$-0.694774\pi$
$349$	−21.4622	−1.14885	−0.574424	+	0.818558i	$0.694774\pi$
$350$	−0.390362	−0.0208657
$351$	1.37532	0.0734093
$352$	−1.00000	−0.0533002
$353$	−1.39522	−0.0742598	−0.0371299	−	0.999310i	$-0.511822\pi$
$353$	−1.39522	−0.0742598	−0.0371299	+	0.999310i	$0.511822\pi$
$354$	−10.5218	−0.559229
$355$	4.34448	0.230581
$356$	6.37070	0.337647
$357$	−5.60802	−0.296808
$358$	23.0214	1.21672
$359$	−21.5720	−1.13853	−0.569264	−	0.822155i	$-0.692772\pi$
$359$	−21.5720	−1.13853	−0.569264	+	0.822155i	$0.692772\pi$
$360$	−2.73133	−0.143954
$361$	2.18115	0.114797
$362$	−3.59862	−0.189139
$363$	−2.39402	−0.125653
$364$	−0.834691	−0.0437497
$365$	−1.00000	−0.0523424
$366$	3.54648	0.185377
$367$	−17.9978	−0.939477	−0.469738	−	0.882806i	$-0.655652\pi$
$367$	−17.9978	−0.939477	−0.469738	+	0.882806i	$0.655652\pi$
$368$	−3.04125	−0.158536
$369$	−13.0651	−0.680143
$370$	−8.76032	−0.455428
$371$	1.20941	0.0627895
$372$	23.2952	1.20780
$373$	12.5794	0.651336	0.325668	−	0.945484i	$-0.394411\pi$
$373$	12.5794	0.651336	0.325668	+	0.945484i	$0.394411\pi$
$374$	6.00087	0.310298
$375$	2.39402	0.123627
$376$	6.38474	0.329268
$377$	17.0766	0.879487
$378$	−0.251081	−0.0129142
$379$	−13.5226	−0.694610	−0.347305	−	0.937752i	$-0.612903\pi$
$379$	−13.5226	−0.694610	−0.347305	+	0.937752i	$0.612903\pi$
$380$	−4.60230	−0.236093
$381$	−33.1572	−1.69870
$382$	−13.7250	−0.702233
$383$	18.1975	0.929850	0.464925	−	0.885350i	$-0.346081\pi$
$383$	18.1975	0.929850	0.464925	+	0.885350i	$0.346081\pi$
$384$	−2.39402	−0.122169
$385$	−0.390362	−0.0198947
$386$	14.5551	0.740836
$387$	−8.77725	−0.446173
$388$	10.0956	0.512525
$389$	−17.5979	−0.892248	−0.446124	−	0.894971i	$-0.647196\pi$
$389$	−17.5979	−0.892248	−0.446124	+	0.894971i	$0.647196\pi$
$390$	5.11901	0.259211
$391$	18.2502	0.922951
$392$	−6.84762	−0.345857
$393$	21.7849	1.09890
$394$	−10.3620	−0.522028
$395$	10.9514	0.551024
$396$	−2.73133	−0.137254
$397$	1.66020	0.0833230	0.0416615	−	0.999132i	$-0.486735\pi$
$397$	1.66020	0.0833230	0.0416615	+	0.999132i	$0.486735\pi$
$398$	−4.35445	−0.218269
$399$	4.30101	0.215320
$400$	1.00000	0.0500000
$401$	23.2184	1.15947	0.579736	−	0.814804i	$-0.303156\pi$
$401$	23.2184	1.15947	0.579736	+	0.814804i	$0.303156\pi$
$402$	−29.0727	−1.45002
$403$	−20.8064	−1.03644
$404$	11.2773	0.561069
$405$	9.73383	0.483678
$406$	−3.11753	−0.154720
$407$	−8.76032	−0.434233
$408$	14.3662	0.711233
$409$	−11.2615	−0.556844	−0.278422	−	0.960459i	$-0.589811\pi$
$409$	−11.2615	−0.556844	−0.278422	+	0.960459i	$0.589811\pi$
$410$	4.78343	0.236237
$411$	−1.32575	−0.0653946
$412$	−8.99111	−0.442960
$413$	−1.71566	−0.0844222
$414$	−8.30667	−0.408250
$415$	−14.4006	−0.706896
$416$	2.13825	0.104836
$417$	23.6099	1.15618
$418$	−4.60230	−0.225106
$419$	−32.2066	−1.57339	−0.786697	−	0.617339i	$-0.788211\pi$
$419$	−32.2066	−1.57339	−0.786697	+	0.617339i	$0.788211\pi$
$420$	−0.934535	−0.0456006
$421$	1.94497	0.0947921	0.0473960	−	0.998876i	$-0.484908\pi$
$421$	1.94497	0.0947921	0.0473960	+	0.998876i	$0.484908\pi$
$422$	0.234813	0.0114305
$423$	17.4388	0.847905
$424$	−3.09818	−0.150461
$425$	−6.00087	−0.291085
$426$	10.4008	0.503919
$427$	0.578278	0.0279849
$428$	−14.4501	−0.698472
$429$	5.11901	0.247148
$430$	3.21354	0.154971
$431$	20.3610	0.980753	0.490376	−	0.871511i	$-0.336859\pi$
$431$	20.3610	0.980753	0.490376	+	0.871511i	$0.336859\pi$
$432$	0.643201	0.0309460
$433$	−38.5994	−1.85497	−0.927485	−	0.373861i	$-0.878034\pi$
$433$	−38.5994	−1.85497	−0.927485	+	0.373861i	$0.878034\pi$
$434$	3.79845	0.182331
$435$	19.1192	0.916696
$436$	−16.9926	−0.813797
$437$	−13.9968	−0.669555
$438$	−2.39402	−0.114391
$439$	−25.6016	−1.22190	−0.610950	−	0.791669i	$-0.709212\pi$
$439$	−25.6016	−1.22190	−0.610950	+	0.791669i	$0.709212\pi$
$440$	1.00000	0.0476731
$441$	−18.7031	−0.890624
$442$	−12.8313	−0.610325
$443$	6.65295	0.316091	0.158046	−	0.987432i	$-0.449481\pi$
$443$	6.65295	0.316091	0.158046	+	0.987432i	$0.449481\pi$
$444$	−20.9724	−0.995305
$445$	−6.37070	−0.302000
$446$	−22.5133	−1.06603
$447$	−34.9847	−1.65472
$448$	−0.390362	−0.0184429
$449$	−30.9257	−1.45947	−0.729737	−	0.683728i	$-0.760357\pi$
$449$	−30.9257	−1.45947	−0.729737	+	0.683728i	$0.760357\pi$
$450$	2.73133	0.128756
$451$	4.78343	0.225243
$452$	7.31591	0.344111
$453$	17.2851	0.812123
$454$	8.96335	0.420671
$455$	0.834691	0.0391309
$456$	−11.0180	−0.515965
$457$	−36.6322	−1.71358	−0.856791	−	0.515663i	$-0.827546\pi$
$457$	−36.6322	−1.71358	−0.856791	+	0.515663i	$0.827546\pi$
$458$	−3.74258	−0.174879
$459$	−3.85977	−0.180159
$460$	3.04125	0.141799
$461$	−8.47525	−0.394732	−0.197366	−	0.980330i	$-0.563239\pi$
$461$	−8.47525	−0.394732	−0.197366	+	0.980330i	$0.563239\pi$
$462$	−0.934535	−0.0434785
$463$	11.5243	0.535580	0.267790	−	0.963477i	$-0.413707\pi$
$463$	11.5243	0.535580	0.267790	+	0.963477i	$0.413707\pi$
$464$	7.98624	0.370752
$465$	−23.2952	−1.08029
$466$	23.3858	1.08332
$467$	15.8089	0.731549	0.365774	−	0.930704i	$-0.380804\pi$
$467$	15.8089	0.731549	0.365774	+	0.930704i	$0.380804\pi$
$468$	5.84026	0.269966
$469$	−4.74052	−0.218897
$470$	−6.38474	−0.294506
$471$	35.0897	1.61685
$472$	4.39505	0.202299
$473$	3.21354	0.147759
$474$	26.2178	1.20422
$475$	4.60230	0.211168
$476$	2.34251	0.107369
$477$	−8.46215	−0.387455
$478$	−3.85948	−0.176529
$479$	−11.8087	−0.539555	−0.269778	−	0.962923i	$-0.586950\pi$
$479$	−11.8087	−0.539555	−0.269778	+	0.962923i	$0.586950\pi$
$480$	2.39402	0.109272
$481$	18.7317	0.854094
$482$	−29.5226	−1.34472
$483$	−2.84216	−0.129323
$484$	1.00000	0.0454545
$485$	−10.0956	−0.458416
$486$	21.3734	0.969516
$487$	−16.1420	−0.731464	−0.365732	−	0.930720i	$-0.619181\pi$
$487$	−16.1420	−0.731464	−0.365732	+	0.930720i	$0.619181\pi$
$488$	−1.48139	−0.0670593
$489$	7.17839	0.324618
$490$	6.84762	0.309344
$491$	28.2549	1.27513	0.637563	−	0.770398i	$-0.279943\pi$
$491$	28.2549	1.27513	0.637563	+	0.770398i	$0.279943\pi$
$492$	11.4516	0.516279
$493$	−47.9244	−2.15841
$494$	9.84085	0.442761
$495$	2.73133	0.122764
$496$	−9.73058	−0.436916
$497$	1.69592	0.0760724
$498$	−34.4752	−1.54487
$499$	26.1825	1.17209	0.586046	−	0.810278i	$-0.300684\pi$
$499$	26.1825	1.17209	0.586046	+	0.810278i	$0.300684\pi$
$500$	−1.00000	−0.0447214
$501$	56.2242	2.51191
$502$	−25.5975	−1.14247
$503$	−40.2352	−1.79400	−0.896998	−	0.442034i	$-0.854257\pi$
$503$	−40.2352	−1.79400	−0.896998	+	0.442034i	$0.854257\pi$
$504$	−1.06621	−0.0474927
$505$	−11.2773	−0.501835
$506$	3.04125	0.135200
$507$	20.1766	0.896072
$508$	13.8500	0.614496
$509$	24.5080	1.08630	0.543149	−	0.839636i	$-0.317232\pi$
$509$	24.5080	1.08630	0.543149	+	0.839636i	$0.317232\pi$
$510$	−14.3662	−0.636146
$511$	−0.390362	−0.0172686
$512$	1.00000	0.0441942
$513$	2.96020	0.130696
$514$	7.94437	0.350411
$515$	8.99111	0.396196
$516$	7.69329	0.338678
$517$	−6.38474	−0.280800
$518$	−3.41970	−0.150253
$519$	24.9775	1.09639
$520$	−2.13825	−0.0937683
$521$	31.8785	1.39662	0.698312	−	0.715793i	$-0.253935\pi$
$521$	31.8785	1.39662	0.698312	+	0.715793i	$0.253935\pi$
$522$	21.8131	0.954731
$523$	−28.9694	−1.26674	−0.633371	−	0.773848i	$-0.718329\pi$
$523$	−28.9694	−1.26674	−0.633371	+	0.773848i	$0.718329\pi$
$524$	−9.09972	−0.397523
$525$	0.934535	0.0407864
$526$	17.3583	0.756858
$527$	58.3919	2.54359
$528$	2.39402	0.104186
$529$	−13.7508	−0.597860
$530$	3.09818	0.134576
$531$	12.0043	0.520944
$532$	−1.79656	−0.0778909
$533$	−10.2281	−0.443030
$534$	−15.2516	−0.660001
$535$	14.4501	0.624732
$536$	12.1439	0.524536
$537$	−55.1138	−2.37833
$538$	1.57963	0.0681028
$539$	6.84762	0.294948
$540$	−0.643201	−0.0276790
$541$	19.6457	0.844636	0.422318	−	0.906448i	$-0.361217\pi$
$541$	19.6457	0.844636	0.422318	+	0.906448i	$0.361217\pi$
$542$	−10.4765	−0.450006
$543$	8.61518	0.369713
$544$	−6.00087	−0.257285
$545$	16.9926	0.727882
$546$	1.99827	0.0855179
$547$	−35.0610	−1.49910	−0.749549	−	0.661949i	$-0.769730\pi$
$547$	−35.0610	−1.49910	−0.749549	+	0.661949i	$0.769730\pi$
$548$	0.553777	0.0236562
$549$	−4.04616	−0.172686
$550$	−1.00000	−0.0426401
$551$	36.7550	1.56582
$552$	7.28082	0.309892
$553$	4.27501	0.181792
$554$	−7.93126	−0.336967
$555$	20.9724	0.890228
$556$	−9.86204	−0.418244
$557$	8.94467	0.378998	0.189499	−	0.981881i	$-0.439314\pi$
$557$	8.94467	0.378998	0.189499	+	0.981881i	$0.439314\pi$
$558$	−26.5774	−1.12511
$559$	−6.87135	−0.290627
$560$	0.390362	0.0164958
$561$	−14.3662	−0.606542
$562$	−5.52571	−0.233088
$563$	−36.5050	−1.53850	−0.769251	−	0.638947i	$-0.779370\pi$
$563$	−36.5050	−1.53850	−0.769251	+	0.638947i	$0.779370\pi$
$564$	−15.2852	−0.643622
$565$	−7.31591	−0.307782
$566$	−28.0362	−1.17845
$567$	3.79972	0.159573
$568$	−4.34448	−0.182290
$569$	−19.1937	−0.804644	−0.402322	−	0.915498i	$-0.631797\pi$
$569$	−19.1937	−0.804644	−0.402322	+	0.915498i	$0.631797\pi$
$570$	11.0180	0.461493
$571$	26.1798	1.09559	0.547794	−	0.836613i	$-0.315468\pi$
$571$	26.1798	1.09559	0.547794	+	0.836613i	$0.315468\pi$
$572$	−2.13825	−0.0894046
$573$	32.8580	1.37266
$574$	1.86727	0.0779383
$575$	−3.04125	−0.126829
$576$	2.73133	0.113805
$577$	−38.4267	−1.59972	−0.799862	−	0.600184i	$-0.795094\pi$
$577$	−38.4267	−1.59972	−0.799862	+	0.600184i	$0.795094\pi$
$578$	19.0105	0.790731
$579$	−34.8452	−1.44812
$580$	−7.98624	−0.331610
$581$	−5.62144	−0.233216
$582$	−24.1690	−1.00184
$583$	3.09818	0.128313
$584$	1.00000	0.0413803
$585$	−5.84026	−0.241465
$586$	26.8280	1.10825
$587$	−3.43699	−0.141860	−0.0709298	−	0.997481i	$-0.522597\pi$
$587$	−3.43699	−0.141860	−0.0709298	+	0.997481i	$0.522597\pi$
$588$	16.3933	0.676050
$589$	−44.7830	−1.84525
$590$	−4.39505	−0.180941
$591$	24.8067	1.02041
$592$	8.76032	0.360047
$593$	42.8383	1.75916	0.879578	−	0.475754i	$-0.157825\pi$
$593$	42.8383	1.75916	0.879578	+	0.475754i	$0.157825\pi$
$594$	−0.643201	−0.0263909
$595$	−2.34251	−0.0960337
$596$	14.6134	0.598587
$597$	10.4246	0.426652
$598$	−6.50295	−0.265925
$599$	−23.4793	−0.959340	−0.479670	−	0.877449i	$-0.659244\pi$
$599$	−23.4793	−0.959340	−0.479670	+	0.877449i	$0.659244\pi$
$600$	−2.39402	−0.0977354
$601$	−11.5281	−0.470239	−0.235120	−	0.971966i	$-0.575548\pi$
$601$	−11.5281	−0.470239	−0.235120	+	0.971966i	$0.575548\pi$
$602$	1.25445	0.0511274
$603$	33.1690	1.35075
$604$	−7.22010	−0.293782
$605$	−1.00000	−0.0406558
$606$	−26.9982	−1.09673
$607$	31.1001	1.26231	0.631157	−	0.775655i	$-0.282580\pi$
$607$	31.1001	1.26231	0.631157	+	0.775655i	$0.282580\pi$
$608$	4.60230	0.186648
$609$	7.46342	0.302433
$610$	1.48139	0.0599797
$611$	13.6521	0.552307
$612$	−16.3904	−0.662541
$613$	−24.7112	−0.998075	−0.499037	−	0.866580i	$-0.666313\pi$
$613$	−24.7112	−0.998075	−0.499037	+	0.866580i	$0.666313\pi$
$614$	−12.2059	−0.492592
$615$	−11.4516	−0.461774
$616$	0.390362	0.0157281
$617$	−16.5354	−0.665691	−0.332846	−	0.942981i	$-0.608009\pi$
$617$	−16.5354	−0.665691	−0.332846	+	0.942981i	$0.608009\pi$
$618$	21.5249	0.865858
$619$	7.18170	0.288657	0.144329	−	0.989530i	$-0.453898\pi$
$619$	7.18170	0.288657	0.144329	+	0.989530i	$0.453898\pi$
$620$	9.73058	0.390789
$621$	−1.95614	−0.0784971
$622$	0.0110162	0.000441710 0
$623$	−2.48688	−0.0996348
$624$	−5.11901	−0.204924
$625$	1.00000	0.0400000
$626$	−13.1816	−0.526842
$627$	11.0180	0.440016
$628$	−14.6572	−0.584887
$629$	−52.5696	−2.09609
$630$	1.06621	0.0424787
$631$	−12.4501	−0.495632	−0.247816	−	0.968807i	$-0.579713\pi$
$631$	−12.4501	−0.495632	−0.247816	+	0.968807i	$0.579713\pi$
$632$	−10.9514	−0.435623
$633$	−0.562148	−0.0223434
$634$	−7.70001	−0.305807
$635$	−13.8500	−0.549622
$636$	7.41710	0.294107
$637$	−14.6419	−0.580133
$638$	−7.98624	−0.316178
$639$	−11.8662	−0.469420
$640$	−1.00000	−0.0395285
$641$	3.47346	0.137193	0.0685966	−	0.997644i	$-0.478148\pi$
$641$	3.47346	0.137193	0.0685966	+	0.997644i	$0.478148\pi$
$642$	34.5938	1.36531
$643$	6.77910	0.267342	0.133671	−	0.991026i	$-0.457324\pi$
$643$	6.77910	0.267342	0.133671	+	0.991026i	$0.457324\pi$
$644$	1.18719	0.0467818
$645$	−7.69329	−0.302923
$646$	−27.6178	−1.08661
$647$	3.46607	0.136265	0.0681326	−	0.997676i	$-0.478296\pi$
$647$	3.46607	0.136265	0.0681326	+	0.997676i	$0.478296\pi$
$648$	−9.73383	−0.382381
$649$	−4.39505	−0.172521
$650$	2.13825	0.0838690
$651$	−9.09356	−0.356405
$652$	−2.99847	−0.117429
$653$	10.4887	0.410455	0.205227	−	0.978714i	$-0.434207\pi$
$653$	10.4887	0.410455	0.205227	+	0.978714i	$0.434207\pi$
$654$	40.6806	1.59074
$655$	9.09972	0.355555
$656$	−4.78343	−0.186761
$657$	2.73133	0.106559
$658$	−2.49236	−0.0971623
$659$	33.9969	1.32433	0.662165	−	0.749358i	$-0.269638\pi$
$659$	33.9969	1.32433	0.662165	+	0.749358i	$0.269638\pi$
$660$	−2.39402	−0.0931871
$661$	7.94597	0.309062	0.154531	−	0.987988i	$-0.450613\pi$
$661$	7.94597	0.309062	0.154531	+	0.987988i	$0.450613\pi$
$662$	−23.5349	−0.914712
$663$	30.7185	1.19301
$664$	14.4006	0.558850
$665$	1.79656	0.0696677
$666$	23.9273	0.927165
$667$	−24.2882	−0.940442
$668$	−23.4853	−0.908673
$669$	53.8972	2.08379
$670$	−12.1439	−0.469160
$671$	1.48139	0.0571884
$672$	0.934535	0.0360505
$673$	23.8684	0.920058	0.460029	−	0.887904i	$-0.347839\pi$
$673$	23.8684	0.920058	0.460029	+	0.887904i	$0.347839\pi$
$674$	7.94195	0.305912
$675$	0.643201	0.0247568
$676$	−8.42790	−0.324150
$677$	40.6956	1.56406	0.782030	−	0.623241i	$-0.214185\pi$
$677$	40.6956	1.56406	0.782030	+	0.623241i	$0.214185\pi$
$678$	−17.5144	−0.672637
$679$	−3.94093	−0.151239
$680$	6.00087	0.230123
$681$	−21.4584	−0.822289
$682$	9.73058	0.372603
$683$	−38.3051	−1.46570	−0.732851	−	0.680389i	$-0.761811\pi$
$683$	−38.3051	−1.46570	−0.732851	+	0.680389i	$0.761811\pi$
$684$	12.5704	0.480641
$685$	−0.553777	−0.0211587
$686$	5.40559	0.206386
$687$	8.95982	0.341838
$688$	−3.21354	−0.122515
$689$	−6.62467	−0.252380
$690$	−7.28082	−0.277176
$691$	−6.57093	−0.249970	−0.124985	−	0.992159i	$-0.539888\pi$
$691$	−6.57093	−0.249970	−0.124985	+	0.992159i	$0.539888\pi$
$692$	−10.4333	−0.396614
$693$	1.06621	0.0405019
$694$	−11.3392	−0.430431
$695$	9.86204	0.374089
$696$	−19.1192	−0.724712
$697$	28.7047	1.08727
$698$	−21.4622	−0.812358
$699$	−55.9860	−2.11758
$700$	−0.390362	−0.0147543
$701$	−14.2253	−0.537281	−0.268640	−	0.963241i	$-0.586574\pi$
$701$	−14.2253	−0.537281	−0.268640	+	0.963241i	$0.586574\pi$
$702$	1.37532	0.0519082
$703$	40.3176	1.52061
$704$	−1.00000	−0.0376889
$705$	15.2852	0.575673
$706$	−1.39522	−0.0525096
$707$	−4.40225	−0.165564
$708$	−10.5218	−0.395435
$709$	18.1124	0.680225	0.340113	−	0.940385i	$-0.389535\pi$
$709$	18.1124	0.680225	0.340113	+	0.940385i	$0.389535\pi$
$710$	4.34448	0.163045
$711$	−29.9118	−1.12178
$712$	6.37070	0.238752
$713$	29.5931	1.10827
$714$	−5.60802	−0.209875
$715$	2.13825	0.0799659
$716$	23.0214	0.860351
$717$	9.23968	0.345062
$718$	−21.5720	−0.805061
$719$	1.03373	0.0385517	0.0192758	−	0.999814i	$-0.493864\pi$
$719$	1.03373	0.0385517	0.0192758	+	0.999814i	$0.493864\pi$
$720$	−2.73133	−0.101791
$721$	3.50979	0.130711
$722$	2.18115	0.0811739
$723$	70.6776	2.62853
$724$	−3.59862	−0.133742
$725$	7.98624	0.296601
$726$	−2.39402	−0.0888504
$727$	−10.8749	−0.403328	−0.201664	−	0.979455i	$-0.564635\pi$
$727$	−10.8749	−0.403328	−0.201664	+	0.979455i	$0.564635\pi$
$728$	−0.834691	−0.0309357
$729$	−21.9668	−0.813585
$730$	−1.00000	−0.0370117
$731$	19.2841	0.713247
$732$	3.54648	0.131082
$733$	6.88075	0.254146	0.127073	−	0.991893i	$-0.459442\pi$
$733$	6.88075	0.254146	0.127073	+	0.991893i	$0.459442\pi$
$734$	−17.9978	−0.664310
$735$	−16.3933	−0.604677
$736$	−3.04125	−0.112102
$737$	−12.1439	−0.447326
$738$	−13.0651	−0.480934
$739$	−13.8820	−0.510658	−0.255329	−	0.966854i	$-0.582184\pi$
$739$	−13.8820	−0.510658	−0.255329	+	0.966854i	$0.582184\pi$
$740$	−8.76032	−0.322036
$741$	−23.5592	−0.865468
$742$	1.20941	0.0443989
$743$	−39.3282	−1.44281	−0.721405	−	0.692513i	$-0.756504\pi$
$743$	−39.3282	−1.44281	−0.721405	+	0.692513i	$0.756504\pi$
$744$	23.2952	0.854043
$745$	−14.6134	−0.535393
$746$	12.5794	0.460564
$747$	39.3327	1.43911
$748$	6.00087	0.219414
$749$	5.64077	0.206109
$750$	2.39402	0.0874172
$751$	21.6309	0.789324	0.394662	−	0.918826i	$-0.370862\pi$
$751$	21.6309	0.789324	0.394662	+	0.918826i	$0.370862\pi$
$752$	6.38474	0.232827
$753$	61.2810	2.23321
$754$	17.0766	0.621891
$755$	7.22010	0.262766
$756$	−0.251081	−0.00913175
$757$	1.97181	0.0716667	0.0358334	−	0.999358i	$-0.488591\pi$
$757$	1.97181	0.0716667	0.0358334	+	0.999358i	$0.488591\pi$
$758$	−13.5226	−0.491164
$759$	−7.28082	−0.264277
$760$	−4.60230	−0.166943
$761$	−11.8213	−0.428522	−0.214261	−	0.976776i	$-0.568734\pi$
$761$	−11.8213	−0.428522	−0.214261	+	0.976776i	$0.568734\pi$
$762$	−33.1572	−1.20116
$763$	6.63326	0.240140
$764$	−13.7250	−0.496554
$765$	16.3904	0.592595
$766$	18.1975	0.657503
$767$	9.39770	0.339331
$768$	−2.39402	−0.0863867
$769$	29.8104	1.07499	0.537495	−	0.843267i	$-0.319371\pi$
$769$	29.8104	1.07499	0.537495	+	0.843267i	$0.319371\pi$
$770$	−0.390362	−0.0140677
$771$	−19.0190	−0.684952
$772$	14.5551	0.523850
$773$	−1.57193	−0.0565385	−0.0282693	−	0.999600i	$-0.509000\pi$
$773$	−1.57193	−0.0565385	−0.0282693	+	0.999600i	$0.509000\pi$
$774$	−8.77725	−0.315492
$775$	−9.73058	−0.349533
$776$	10.0956	0.362410
$777$	8.18683	0.293701
$778$	−17.5979	−0.630914
$779$	−22.0148	−0.788760
$780$	5.11901	0.183290
$781$	4.34448	0.155458
$782$	18.2502	0.652625
$783$	5.13676	0.183573
$784$	−6.84762	−0.244558
$785$	14.6572	0.523139
$786$	21.7849	0.777042
$787$	8.97084	0.319776	0.159888	−	0.987135i	$-0.448887\pi$
$787$	8.97084	0.319776	0.159888	+	0.987135i	$0.448887\pi$
$788$	−10.3620	−0.369129
$789$	−41.5561	−1.47944
$790$	10.9514	0.389633
$791$	−2.85585	−0.101542
$792$	−2.73133	−0.0970536
$793$	−3.16758	−0.112484
$794$	1.66020	0.0589183
$795$	−7.41710	−0.263057
$796$	−4.35445	−0.154339
$797$	−8.21141	−0.290863	−0.145431	−	0.989368i	$-0.546457\pi$
$797$	−8.21141	−0.290863	−0.145431	+	0.989368i	$0.546457\pi$
$798$	4.30101	0.152254
$799$	−38.3140	−1.35545
$800$	1.00000	0.0353553
$801$	17.4005	0.614816
$802$	23.2184	0.819871
$803$	−1.00000	−0.0352892
$804$	−29.0727	−1.02532
$805$	−1.18719	−0.0418430
$806$	−20.8064	−0.732873
$807$	−3.78167	−0.133121
$808$	11.2773	0.396735
$809$	10.3813	0.364986	0.182493	−	0.983207i	$-0.441583\pi$
$809$	10.3813	0.364986	0.182493	+	0.983207i	$0.441583\pi$
$810$	9.73383	0.342012
$811$	−10.5020	−0.368776	−0.184388	−	0.982854i	$-0.559030\pi$
$811$	−10.5020	−0.368776	−0.184388	+	0.982854i	$0.559030\pi$
$812$	−3.11753	−0.109404
$813$	25.0811	0.879631
$814$	−8.76032	−0.307049
$815$	2.99847	0.105032
$816$	14.3662	0.502918
$817$	−14.7897	−0.517426
$818$	−11.2615	−0.393748
$819$	−2.27982	−0.0796632
$820$	4.78343	0.167045
$821$	−16.0717	−0.560905	−0.280453	−	0.959868i	$-0.590485\pi$
$821$	−16.0717	−0.560905	−0.280453	+	0.959868i	$0.590485\pi$
$822$	−1.32575	−0.0462409
$823$	32.8784	1.14607	0.573034	−	0.819531i	$-0.305766\pi$
$823$	32.8784	1.14607	0.573034	+	0.819531i	$0.305766\pi$
$824$	−8.99111	−0.313220
$825$	2.39402	0.0833491
$826$	−1.71566	−0.0596955
$827$	−13.3727	−0.465013	−0.232507	−	0.972595i	$-0.574693\pi$
$827$	−13.3727	−0.465013	−0.232507	+	0.972595i	$0.574693\pi$
$828$	−8.30667	−0.288677
$829$	−28.1903	−0.979088	−0.489544	−	0.871978i	$-0.662837\pi$
$829$	−28.1903	−0.979088	−0.489544	+	0.871978i	$0.662837\pi$
$830$	−14.4006	−0.499851
$831$	18.9876	0.658672
$832$	2.13825	0.0741304
$833$	41.0917	1.42374
$834$	23.6099	0.817545
$835$	23.4853	0.812742
$836$	−4.60230	−0.159174
$837$	−6.25872	−0.216333
$838$	−32.2066	−1.11256
$839$	−13.7102	−0.473328	−0.236664	−	0.971592i	$-0.576054\pi$
$839$	−13.7102	−0.473328	−0.236664	+	0.971592i	$0.576054\pi$
$840$	−0.934535	−0.0322445
$841$	34.7800	1.19931
$842$	1.94497	0.0670281
$843$	13.2287	0.455619
$844$	0.234813	0.00808261
$845$	8.42790	0.289929
$846$	17.4388	0.599559
$847$	−0.390362	−0.0134130
$848$	−3.09818	−0.106392
$849$	67.1191	2.30352
$850$	−6.00087	−0.205828
$851$	−26.6424	−0.913288
$852$	10.4008	0.356324
$853$	38.2515	1.30971	0.654853	−	0.755757i	$-0.272731\pi$
$853$	38.2515	1.30971	0.654853	+	0.755757i	$0.272731\pi$
$854$	0.578278	0.0197883
$855$	−12.5704	−0.429898
$856$	−14.4501	−0.493894
$857$	−38.5755	−1.31772	−0.658858	−	0.752268i	$-0.728960\pi$
$857$	−38.5755	−1.31772	−0.658858	+	0.752268i	$0.728960\pi$
$858$	5.11901	0.174760
$859$	37.6815	1.28568	0.642839	−	0.766002i	$-0.277757\pi$
$859$	37.6815	1.28568	0.642839	+	0.766002i	$0.277757\pi$
$860$	3.21354	0.109581
$861$	−4.47028	−0.152347
$862$	20.3610	0.693497
$863$	49.5315	1.68607	0.843036	−	0.537856i	$-0.180766\pi$
$863$	49.5315	1.68607	0.843036	+	0.537856i	$0.180766\pi$
$864$	0.643201	0.0218822
$865$	10.4333	0.354742
$866$	−38.5994	−1.31166
$867$	−45.5114	−1.54565
$868$	3.79845	0.128928
$869$	10.9514	0.371500
$870$	19.1192	0.648202
$871$	25.9666	0.879846
$872$	−16.9926	−0.575441
$873$	27.5743	0.933249
$874$	−13.9968	−0.473447
$875$	0.390362	0.0131967
$876$	−2.39402	−0.0808864
$877$	21.7002	0.732762	0.366381	−	0.930465i	$-0.380597\pi$
$877$	21.7002	0.732762	0.366381	+	0.930465i	$0.380597\pi$
$878$	−25.6016	−0.864014
$879$	−64.2268	−2.16632
$880$	1.00000	0.0337100
$881$	28.8770	0.972890	0.486445	−	0.873711i	$-0.338293\pi$
$881$	28.8770	0.972890	0.486445	+	0.873711i	$0.338293\pi$
$882$	−18.7031	−0.629766
$883$	14.7340	0.495839	0.247919	−	0.968781i	$-0.420253\pi$
$883$	14.7340	0.495839	0.247919	+	0.968781i	$0.420253\pi$
$884$	−12.8313	−0.431565
$885$	10.5218	0.353688
$886$	6.65295	0.223510
$887$	−4.71255	−0.158232	−0.0791160	−	0.996865i	$-0.525210\pi$
$887$	−4.71255	−0.158232	−0.0791160	+	0.996865i	$0.525210\pi$
$888$	−20.9724	−0.703787
$889$	−5.40653	−0.181329
$890$	−6.37070	−0.213547
$891$	9.73383	0.326095
$892$	−22.5133	−0.753800
$893$	29.3845	0.983314
$894$	−34.9847	−1.17006
$895$	−23.0214	−0.769522
$896$	−0.390362	−0.0130411
$897$	15.5682	0.519807
$898$	−30.9257	−1.03200
$899$	−77.7107	−2.59180
$900$	2.73133	0.0910443
$901$	18.5918	0.619382
$902$	4.78343	0.159271
$903$	−3.00317	−0.0999392
$904$	7.31591	0.243323
$905$	3.59862	0.119622
$906$	17.2851	0.574257
$907$	27.8502	0.924749	0.462375	−	0.886685i	$-0.346998\pi$
$907$	27.8502	0.924749	0.462375	+	0.886685i	$0.346998\pi$
$908$	8.96335	0.297459
$909$	30.8021	1.02164
$910$	0.834691	0.0276697
$911$	−50.9055	−1.68657	−0.843286	−	0.537464i	$-0.819382\pi$
$911$	−50.9055	−1.68657	−0.843286	+	0.537464i	$0.819382\pi$
$912$	−11.0180	−0.364842
$913$	−14.4006	−0.476589
$914$	−36.6322	−1.21169
$915$	−3.54648	−0.117243
$916$	−3.74258	−0.123658
$917$	3.55219	0.117304
$918$	−3.85977	−0.127391
$919$	−1.75148	−0.0577759	−0.0288880	−	0.999583i	$-0.509197\pi$
$919$	−1.75148	−0.0577759	−0.0288880	+	0.999583i	$0.509197\pi$
$920$	3.04125	0.100267
$921$	29.2213	0.962873
$922$	−8.47525	−0.279117
$923$	−9.28957	−0.305770
$924$	−0.934535	−0.0307439
$925$	8.76032	0.288038
$926$	11.5243	0.378712
$927$	−24.5577	−0.806580
$928$	7.98624	0.262161
$929$	6.85188	0.224803	0.112401	−	0.993663i	$-0.464146\pi$
$929$	6.85188	0.224803	0.112401	+	0.993663i	$0.464146\pi$
$930$	−23.2952	−0.763879
$931$	−31.5148	−1.03286
$932$	23.3858	0.766026
$933$	−0.0263731	−0.000863415 0
$934$	15.8089	0.517283
$935$	−6.00087	−0.196250
$936$	5.84026	0.190895
$937$	14.6061	0.477162	0.238581	−	0.971123i	$-0.423318\pi$
$937$	14.6061	0.477162	0.238581	+	0.971123i	$0.423318\pi$
$938$	−4.74052	−0.154783
$939$	31.5569	1.02982
$940$	−6.38474	−0.208247
$941$	45.7672	1.49197	0.745984	−	0.665964i	$-0.231980\pi$
$941$	45.7672	1.49197	0.745984	+	0.665964i	$0.231980\pi$
$942$	35.0897	1.14328
$943$	14.5476	0.473735
$944$	4.39505	0.143047
$945$	0.251081	0.00816768
$946$	3.21354	0.104481
$947$	−10.6113	−0.344819	−0.172410	−	0.985025i	$-0.555155\pi$
$947$	−10.6113	−0.344819	−0.172410	+	0.985025i	$0.555155\pi$
$948$	26.2178	0.851515
$949$	2.13825	0.0694104
$950$	4.60230	0.149318
$951$	18.4340	0.597763
$952$	2.34251	0.0759213
$953$	−6.14596	−0.199087	−0.0995437	−	0.995033i	$-0.531738\pi$
$953$	−6.14596	−0.199087	−0.0995437	+	0.995033i	$0.531738\pi$
$954$	−8.46215	−0.273972
$955$	13.7250	0.444131
$956$	−3.85948	−0.124825
$957$	19.1192	0.618036
$958$	−11.8087	−0.381523
$959$	−0.216174	−0.00698061
$960$	2.39402	0.0772667
$961$	63.6841	2.05433
$962$	18.7317	0.603935
$963$	−39.4680	−1.27184
$964$	−29.5226	−0.950858
$965$	−14.5551	−0.468546
$966$	−2.84216	−0.0914449
$967$	1.29617	0.0416819	0.0208410	−	0.999783i	$-0.493366\pi$
$967$	1.29617	0.0416819	0.0208410	+	0.999783i	$0.493366\pi$
$968$	1.00000	0.0321412
$969$	66.1176	2.12400
$970$	−10.0956	−0.324149
$971$	57.7649	1.85377	0.926883	−	0.375351i	$-0.122478\pi$
$971$	57.7649	1.85377	0.926883	+	0.375351i	$0.122478\pi$
$972$	21.3734	0.685551
$973$	3.84977	0.123418
$974$	−16.1420	−0.517223
$975$	−5.11901	−0.163939
$976$	−1.48139	−0.0474181
$977$	14.6867	0.469869	0.234934	−	0.972011i	$-0.424512\pi$
$977$	14.6867	0.469869	0.234934	+	0.972011i	$0.424512\pi$
$978$	7.17839	0.229540
$979$	−6.37070	−0.203609
$980$	6.84762	0.218739
$981$	−46.4123	−1.48183
$982$	28.2549	0.901650
$983$	−57.9985	−1.84986	−0.924932	−	0.380132i	$-0.875879\pi$
$983$	−57.9985	−1.84986	−0.924932	+	0.380132i	$0.875879\pi$
$984$	11.4516	0.365064
$985$	10.3620	0.330159
$986$	−47.9244	−1.52622
$987$	5.96676	0.189924
$988$	9.84085	0.313079
$989$	9.77320	0.310770
$990$	2.73133	0.0868074
$991$	45.5905	1.44823	0.724116	−	0.689678i	$-0.242248\pi$
$991$	45.5905	1.44823	0.724116	+	0.689678i	$0.242248\pi$
$992$	−9.73058	−0.308946
$993$	56.3431	1.78800
$994$	1.69592	0.0537913
$995$	4.35445	0.138045
$996$	−34.4752	−1.09239
$997$	20.8346	0.659839	0.329920	−	0.944009i	$-0.392978\pi$
$997$	20.8346	0.659839	0.329920	+	0.944009i	$0.392978\pi$
$998$	26.1825	0.828794
$999$	5.63465	0.178272

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8030.2.a.bf.1.4	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8030.2.a.bf.1.4	✓	15	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.39402 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.39402 q^{6} -0.390362 q^{7} +1.00000 q^{8} +2.73133 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.39402 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.39402 q^{6} -0.390362 q^{7} +1.00000 q^{8} +2.73133 q^{9} -1.00000 q^{10} -1.00000 q^{11} -2.39402 q^{12} +2.13825 q^{13} -0.390362 q^{14} +2.39402 q^{15} +1.00000 q^{16} -6.00087 q^{17} +2.73133 q^{18} +4.60230 q^{19} -1.00000 q^{20} +0.934535 q^{21} -1.00000 q^{22} -3.04125 q^{23} -2.39402 q^{24} +1.00000 q^{25} +2.13825 q^{26} +0.643201 q^{27} -0.390362 q^{28} +7.98624 q^{29} +2.39402 q^{30} -9.73058 q^{31} +1.00000 q^{32} +2.39402 q^{33} -6.00087 q^{34} +0.390362 q^{35} +2.73133 q^{36} +8.76032 q^{37} +4.60230 q^{38} -5.11901 q^{39} -1.00000 q^{40} -4.78343 q^{41} +0.934535 q^{42} -3.21354 q^{43} -1.00000 q^{44} -2.73133 q^{45} -3.04125 q^{46} +6.38474 q^{47} -2.39402 q^{48} -6.84762 q^{49} +1.00000 q^{50} +14.3662 q^{51} +2.13825 q^{52} -3.09818 q^{53} +0.643201 q^{54} +1.00000 q^{55} -0.390362 q^{56} -11.0180 q^{57} +7.98624 q^{58} +4.39505 q^{59} +2.39402 q^{60} -1.48139 q^{61} -9.73058 q^{62} -1.06621 q^{63} +1.00000 q^{64} -2.13825 q^{65} +2.39402 q^{66} +12.1439 q^{67} -6.00087 q^{68} +7.28082 q^{69} +0.390362 q^{70} -4.34448 q^{71} +2.73133 q^{72} +1.00000 q^{73} +8.76032 q^{74} -2.39402 q^{75} +4.60230 q^{76} +0.390362 q^{77} -5.11901 q^{78} -10.9514 q^{79} -1.00000 q^{80} -9.73383 q^{81} -4.78343 q^{82} +14.4006 q^{83} +0.934535 q^{84} +6.00087 q^{85} -3.21354 q^{86} -19.1192 q^{87} -1.00000 q^{88} +6.37070 q^{89} -2.73133 q^{90} -0.834691 q^{91} -3.04125 q^{92} +23.2952 q^{93} +6.38474 q^{94} -4.60230 q^{95} -2.39402 q^{96} +10.0956 q^{97} -6.84762 q^{98} -2.73133 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 15 q^{2} - 4 q^{3} + 15 q^{4} - 15 q^{5} - 4 q^{6} - 6 q^{7} + 15 q^{8} + 17 q^{9}+O(q^{10}) \) 15 * q + 15 * q^2 - 4 * q^3 + 15 * q^4 - 15 * q^5 - 4 * q^6 - 6 * q^7 + 15 * q^8 + 17 * q^9	\( 15 q + 15 q^{2} - 4 q^{3} + 15 q^{4} - 15 q^{5} - 4 q^{6} - 6 q^{7} + 15 q^{8} + 17 q^{9} - 15 q^{10} - 15 q^{11} - 4 q^{12} - 6 q^{13} - 6 q^{14} + 4 q^{15} + 15 q^{16} + 2 q^{17} + 17 q^{18} - 8 q^{19} - 15 q^{20} - 17 q^{21} - 15 q^{22} - 4 q^{23} - 4 q^{24} + 15 q^{25} - 6 q^{26} - 19 q^{27} - 6 q^{28} - 13 q^{29} + 4 q^{30} - 20 q^{31} + 15 q^{32} + 4 q^{33} + 2 q^{34} + 6 q^{35} + 17 q^{36} - 15 q^{37} - 8 q^{38} - 11 q^{39} - 15 q^{40} + 2 q^{41} - 17 q^{42} - 26 q^{43} - 15 q^{44} - 17 q^{45} - 4 q^{46} - 14 q^{47} - 4 q^{48} + 11 q^{49} + 15 q^{50} - 39 q^{51} - 6 q^{52} - 21 q^{53} - 19 q^{54} + 15 q^{55} - 6 q^{56} + q^{57} - 13 q^{58} - 14 q^{59} + 4 q^{60} - 45 q^{61} - 20 q^{62} - 17 q^{63} + 15 q^{64} + 6 q^{65} + 4 q^{66} - 10 q^{67} + 2 q^{68} - 23 q^{69} + 6 q^{70} - 9 q^{71} + 17 q^{72} + 15 q^{73} - 15 q^{74} - 4 q^{75} - 8 q^{76} + 6 q^{77} - 11 q^{78} - 26 q^{79} - 15 q^{80} + 15 q^{81} + 2 q^{82} - 30 q^{83} - 17 q^{84} - 2 q^{85} - 26 q^{86} - 14 q^{87} - 15 q^{88} + 10 q^{89} - 17 q^{90} - 17 q^{91} - 4 q^{92} - 8 q^{93} - 14 q^{94} + 8 q^{95} - 4 q^{96} - 27 q^{97} + 11 q^{98} - 17 q^{99}+O(q^{100}) \) 15 * q + 15 * q^2 - 4 * q^3 + 15 * q^4 - 15 * q^5 - 4 * q^6 - 6 * q^7 + 15 * q^8 + 17 * q^9 - 15 * q^10 - 15 * q^11 - 4 * q^12 - 6 * q^13 - 6 * q^14 + 4 * q^15 + 15 * q^16 + 2 * q^17 + 17 * q^18 - 8 * q^19 - 15 * q^20 - 17 * q^21 - 15 * q^22 - 4 * q^23 - 4 * q^24 + 15 * q^25 - 6 * q^26 - 19 * q^27 - 6 * q^28 - 13 * q^29 + 4 * q^30 - 20 * q^31 + 15 * q^32 + 4 * q^33 + 2 * q^34 + 6 * q^35 + 17 * q^36 - 15 * q^37 - 8 * q^38 - 11 * q^39 - 15 * q^40 + 2 * q^41 - 17 * q^42 - 26 * q^43 - 15 * q^44 - 17 * q^45 - 4 * q^46 - 14 * q^47 - 4 * q^48 + 11 * q^49 + 15 * q^50 - 39 * q^51 - 6 * q^52 - 21 * q^53 - 19 * q^54 + 15 * q^55 - 6 * q^56 + q^57 - 13 * q^58 - 14 * q^59 + 4 * q^60 - 45 * q^61 - 20 * q^62 - 17 * q^63 + 15 * q^64 + 6 * q^65 + 4 * q^66 - 10 * q^67 + 2 * q^68 - 23 * q^69 + 6 * q^70 - 9 * q^71 + 17 * q^72 + 15 * q^73 - 15 * q^74 - 4 * q^75 - 8 * q^76 + 6 * q^77 - 11 * q^78 - 26 * q^79 - 15 * q^80 + 15 * q^81 + 2 * q^82 - 30 * q^83 - 17 * q^84 - 2 * q^85 - 26 * q^86 - 14 * q^87 - 15 * q^88 + 10 * q^89 - 17 * q^90 - 17 * q^91 - 4 * q^92 - 8 * q^93 - 14 * q^94 + 8 * q^95 - 4 * q^96 - 27 * q^97 + 11 * q^98 - 17 * q^99

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