LMFDB - Embedded newform 8030.2.a.be.1.7

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:	$15$
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} - 3 x^{14} - 24 x^{13} + 64 x^{12} + 237 x^{11} - 524 x^{10} - 1225 x^{9} + 2074 x^{8} + \cdots - 52 $ x^15 - 3x^14 - 24x^13 + 64x^12 + 237x^11 - 524x^10 - 1225x^9 + 2074x^8 + 3463x^7 - 4142x^6 - 5157x^5 + 3892x^4 + 3622x^3 - 1239x^2 - 907x - 52
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			1.7
Root			$-0.424375$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -0.424375 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.424375 q^{6} -2.28477 q^{7} -1.00000 q^{8} -2.81991 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.424375 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.424375 q^{6} -2.28477 q^{7} -1.00000 q^{8} -2.81991 q^{9} -1.00000 q^{10} -1.00000 q^{11} -0.424375 q^{12} +2.89252 q^{13} +2.28477 q^{14} -0.424375 q^{15} +1.00000 q^{16} -5.96673 q^{17} +2.81991 q^{18} +5.16794 q^{19} +1.00000 q^{20} +0.969600 q^{21} +1.00000 q^{22} +0.280767 q^{23} +0.424375 q^{24} +1.00000 q^{25} -2.89252 q^{26} +2.46982 q^{27} -2.28477 q^{28} -4.77848 q^{29} +0.424375 q^{30} -1.28904 q^{31} -1.00000 q^{32} +0.424375 q^{33} +5.96673 q^{34} -2.28477 q^{35} -2.81991 q^{36} +1.07462 q^{37} -5.16794 q^{38} -1.22751 q^{39} -1.00000 q^{40} +3.62581 q^{41} -0.969600 q^{42} +8.78880 q^{43} -1.00000 q^{44} -2.81991 q^{45} -0.280767 q^{46} +4.59021 q^{47} -0.424375 q^{48} -1.77983 q^{49} -1.00000 q^{50} +2.53213 q^{51} +2.89252 q^{52} -10.5405 q^{53} -2.46982 q^{54} -1.00000 q^{55} +2.28477 q^{56} -2.19315 q^{57} +4.77848 q^{58} -2.27511 q^{59} -0.424375 q^{60} -10.2729 q^{61} +1.28904 q^{62} +6.44283 q^{63} +1.00000 q^{64} +2.89252 q^{65} -0.424375 q^{66} +4.41447 q^{67} -5.96673 q^{68} -0.119150 q^{69} +2.28477 q^{70} -15.6267 q^{71} +2.81991 q^{72} -1.00000 q^{73} -1.07462 q^{74} -0.424375 q^{75} +5.16794 q^{76} +2.28477 q^{77} +1.22751 q^{78} -1.58984 q^{79} +1.00000 q^{80} +7.41158 q^{81} -3.62581 q^{82} -2.44843 q^{83} +0.969600 q^{84} -5.96673 q^{85} -8.78880 q^{86} +2.02787 q^{87} +1.00000 q^{88} +1.57853 q^{89} +2.81991 q^{90} -6.60874 q^{91} +0.280767 q^{92} +0.547038 q^{93} -4.59021 q^{94} +5.16794 q^{95} +0.424375 q^{96} +15.9243 q^{97} +1.77983 q^{98} +2.81991 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 15 q^{2} + 3 q^{3} + 15 q^{4} + 15 q^{5} - 3 q^{6} + 7 q^{7} - 15 q^{8} + 12 q^{9}+O(q^{10}) $ 15 * q - 15 * q^2 + 3 * q^3 + 15 * q^4 + 15 * q^5 - 3 * q^6 + 7 * q^7 - 15 * q^8 + 12 * q^9	\( 15 q - 15 q^{2} + 3 q^{3} + 15 q^{4} + 15 q^{5} - 3 q^{6} + 7 q^{7} - 15 q^{8} + 12 q^{9} - 15 q^{10} - 15 q^{11} + 3 q^{12} + 13 q^{13} - 7 q^{14} + 3 q^{15} + 15 q^{16} + 20 q^{17} - 12 q^{18} + 3 q^{19} + 15 q^{20} + 22 q^{21} + 15 q^{22} + 2 q^{23} - 3 q^{24} + 15 q^{25} - 13 q^{26} + 33 q^{27} + 7 q^{28} + 11 q^{29} - 3 q^{30} - 3 q^{31} - 15 q^{32} - 3 q^{33} - 20 q^{34} + 7 q^{35} + 12 q^{36} + 9 q^{37} - 3 q^{38} + 11 q^{39} - 15 q^{40} + 17 q^{41} - 22 q^{42} + 29 q^{43} - 15 q^{44} + 12 q^{45} - 2 q^{46} - 2 q^{47} + 3 q^{48} + 20 q^{49} - 15 q^{50} + 7 q^{51} + 13 q^{52} + 3 q^{53} - 33 q^{54} - 15 q^{55} - 7 q^{56} + 13 q^{57} - 11 q^{58} - 32 q^{59} + 3 q^{60} + 61 q^{61} + 3 q^{62} + 20 q^{63} + 15 q^{64} + 13 q^{65} + 3 q^{66} + 7 q^{67} + 20 q^{68} - 23 q^{69} - 7 q^{70} - 6 q^{71} - 12 q^{72} - 15 q^{73} - 9 q^{74} + 3 q^{75} + 3 q^{76} - 7 q^{77} - 11 q^{78} + 12 q^{79} + 15 q^{80} + 3 q^{81} - 17 q^{82} + 17 q^{83} + 22 q^{84} + 20 q^{85} - 29 q^{86} + 23 q^{87} + 15 q^{88} - 18 q^{89} - 12 q^{90} - 15 q^{91} + 2 q^{92} + 32 q^{93} + 2 q^{94} + 3 q^{95} - 3 q^{96} + 36 q^{97} - 20 q^{98} - 12 q^{99}+O(q^{100}) \) 15 * q - 15 * q^2 + 3 * q^3 + 15 * q^4 + 15 * q^5 - 3 * q^6 + 7 * q^7 - 15 * q^8 + 12 * q^9 - 15 * q^10 - 15 * q^11 + 3 * q^12 + 13 * q^13 - 7 * q^14 + 3 * q^15 + 15 * q^16 + 20 * q^17 - 12 * q^18 + 3 * q^19 + 15 * q^20 + 22 * q^21 + 15 * q^22 + 2 * q^23 - 3 * q^24 + 15 * q^25 - 13 * q^26 + 33 * q^27 + 7 * q^28 + 11 * q^29 - 3 * q^30 - 3 * q^31 - 15 * q^32 - 3 * q^33 - 20 * q^34 + 7 * q^35 + 12 * q^36 + 9 * q^37 - 3 * q^38 + 11 * q^39 - 15 * q^40 + 17 * q^41 - 22 * q^42 + 29 * q^43 - 15 * q^44 + 12 * q^45 - 2 * q^46 - 2 * q^47 + 3 * q^48 + 20 * q^49 - 15 * q^50 + 7 * q^51 + 13 * q^52 + 3 * q^53 - 33 * q^54 - 15 * q^55 - 7 * q^56 + 13 * q^57 - 11 * q^58 - 32 * q^59 + 3 * q^60 + 61 * q^61 + 3 * q^62 + 20 * q^63 + 15 * q^64 + 13 * q^65 + 3 * q^66 + 7 * q^67 + 20 * q^68 - 23 * q^69 - 7 * q^70 - 6 * q^71 - 12 * q^72 - 15 * q^73 - 9 * q^74 + 3 * q^75 + 3 * q^76 - 7 * q^77 - 11 * q^78 + 12 * q^79 + 15 * q^80 + 3 * q^81 - 17 * q^82 + 17 * q^83 + 22 * q^84 + 20 * q^85 - 29 * q^86 + 23 * q^87 + 15 * q^88 - 18 * q^89 - 12 * q^90 - 15 * q^91 + 2 * q^92 + 32 * q^93 + 2 * q^94 + 3 * q^95 - 3 * q^96 + 36 * q^97 - 20 * q^98 - 12 * 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
$3$	−0.424375	−0.245013	−0.122507	−	0.992468i	$-0.539093\pi$
$3$	−0.424375	−0.245013	−0.122507	+	0.992468i	$0.539093\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.424375	0.173251
$7$	−2.28477	−0.863562	−0.431781	−	0.901979i	$-0.642115\pi$
$7$	−2.28477	−0.863562	−0.431781	+	0.901979i	$0.642115\pi$
$8$	−1.00000	−0.353553
$9$	−2.81991	−0.939969
$10$	−1.00000	−0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.424375	−0.122507
$13$	2.89252	0.802241	0.401120	−	0.916025i	$-0.368621\pi$
$13$	2.89252	0.802241	0.401120	+	0.916025i	$0.368621\pi$
$14$	2.28477	0.610630
$15$	−0.424375	−0.109573
$16$	1.00000	0.250000
$17$	−5.96673	−1.44714	−0.723572	−	0.690249i	$-0.757501\pi$
$17$	−5.96673	−1.44714	−0.723572	+	0.690249i	$0.757501\pi$
$18$	2.81991	0.664658
$19$	5.16794	1.18561	0.592803	−	0.805347i	$-0.298021\pi$
$19$	5.16794	1.18561	0.592803	+	0.805347i	$0.298021\pi$
$20$	1.00000	0.223607
$21$	0.969600	0.211584
$22$	1.00000	0.213201
$23$	0.280767	0.0585439	0.0292719	−	0.999571i	$-0.490681\pi$
$23$	0.280767	0.0585439	0.0292719	+	0.999571i	$0.490681\pi$
$24$	0.424375	0.0866253
$25$	1.00000	0.200000
$26$	−2.89252	−0.567270
$27$	2.46982	0.475318
$28$	−2.28477	−0.431781
$29$	−4.77848	−0.887341	−0.443670	−	0.896190i	$-0.646324\pi$
$29$	−4.77848	−0.887341	−0.443670	+	0.896190i	$0.646324\pi$
$30$	0.424375	0.0774800
$31$	−1.28904	−0.231519	−0.115759	−	0.993277i	$-0.536930\pi$
$31$	−1.28904	−0.231519	−0.115759	+	0.993277i	$0.536930\pi$
$32$	−1.00000	−0.176777
$33$	0.424375	0.0738743
$34$	5.96673	1.02329
$35$	−2.28477	−0.386197
$36$	−2.81991	−0.469984
$37$	1.07462	0.176666	0.0883332	−	0.996091i	$-0.471846\pi$
$37$	1.07462	0.176666	0.0883332	+	0.996091i	$0.471846\pi$
$38$	−5.16794	−0.838350
$39$	−1.22751	−0.196560
$40$	−1.00000	−0.158114
$41$	3.62581	0.566256	0.283128	−	0.959082i	$-0.408628\pi$
$41$	3.62581	0.566256	0.283128	+	0.959082i	$0.408628\pi$
$42$	−0.969600	−0.149613
$43$	8.78880	1.34028	0.670140	−	0.742235i	$-0.266234\pi$
$43$	8.78880	1.34028	0.670140	+	0.742235i	$0.266234\pi$
$44$	−1.00000	−0.150756
$45$	−2.81991	−0.420367
$46$	−0.280767	−0.0413968
$47$	4.59021	0.669551	0.334775	−	0.942298i	$-0.391340\pi$
$47$	4.59021	0.669551	0.334775	+	0.942298i	$0.391340\pi$
$48$	−0.424375	−0.0612533
$49$	−1.77983	−0.254261
$50$	−1.00000	−0.141421
$51$	2.53213	0.354569
$52$	2.89252	0.401120
$53$	−10.5405	−1.44785	−0.723924	−	0.689880i	$-0.757663\pi$
$53$	−10.5405	−1.44785	−0.723924	+	0.689880i	$0.757663\pi$
$54$	−2.46982	−0.336101
$55$	−1.00000	−0.134840
$56$	2.28477	0.305315
$57$	−2.19315	−0.290489
$58$	4.77848	0.627445
$59$	−2.27511	−0.296194	−0.148097	−	0.988973i	$-0.547315\pi$
$59$	−2.27511	−0.296194	−0.148097	+	0.988973i	$0.547315\pi$
$60$	−0.424375	−0.0547866
$61$	−10.2729	−1.31531	−0.657654	−	0.753320i	$-0.728451\pi$
$61$	−10.2729	−1.31531	−0.657654	+	0.753320i	$0.728451\pi$
$62$	1.28904	0.163709
$63$	6.44283	0.811721
$64$	1.00000	0.125000
$65$	2.89252	0.358773
$66$	−0.424375	−0.0522370
$67$	4.41447	0.539314	0.269657	−	0.962956i	$-0.413090\pi$
$67$	4.41447	0.539314	0.269657	+	0.962956i	$0.413090\pi$
$68$	−5.96673	−0.723572
$69$	−0.119150	−0.0143440
$70$	2.28477	0.273082
$71$	−15.6267	−1.85455	−0.927273	−	0.374385i	$-0.877854\pi$
$71$	−15.6267	−1.85455	−0.927273	+	0.374385i	$0.877854\pi$
$72$	2.81991	0.332329
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	−1.07462	−0.124922
$75$	−0.424375	−0.0490026
$76$	5.16794	0.592803
$77$	2.28477	0.260374
$78$	1.22751	0.138989
$79$	−1.58984	−0.178871	−0.0894353	−	0.995993i	$-0.528506\pi$
$79$	−1.58984	−0.178871	−0.0894353	+	0.995993i	$0.528506\pi$
$80$	1.00000	0.111803
$81$	7.41158	0.823509
$82$	−3.62581	−0.400404
$83$	−2.44843	−0.268750	−0.134375	−	0.990931i	$-0.542903\pi$
$83$	−2.44843	−0.268750	−0.134375	+	0.990931i	$0.542903\pi$
$84$	0.969600	0.105792
$85$	−5.96673	−0.647183
$86$	−8.78880	−0.947720
$87$	2.02787	0.217410
$88$	1.00000	0.106600
$89$	1.57853	0.167324	0.0836618	−	0.996494i	$-0.473338\pi$
$89$	1.57853	0.167324	0.0836618	+	0.996494i	$0.473338\pi$
$90$	2.81991	0.297244
$91$	−6.60874	−0.692784
$92$	0.280767	0.0292719
$93$	0.547038	0.0567252
$94$	−4.59021	−0.473444
$95$	5.16794	0.530219
$96$	0.424375	0.0433126
$97$	15.9243	1.61687	0.808436	−	0.588584i	$-0.200314\pi$
$97$	15.9243	1.61687	0.808436	+	0.588584i	$0.200314\pi$
$98$	1.77983	0.179790
$99$	2.81991	0.283411
$100$	1.00000	0.100000
$101$	−18.3021	−1.82112	−0.910562	−	0.413373i	$-0.864351\pi$
$101$	−18.3021	−1.82112	−0.910562	+	0.413373i	$0.864351\pi$
$102$	−2.53213	−0.250718
$103$	−6.20376	−0.611274	−0.305637	−	0.952148i	$-0.598869\pi$
$103$	−6.20376	−0.611274	−0.305637	+	0.952148i	$0.598869\pi$
$104$	−2.89252	−0.283635
$105$	0.969600	0.0946233
$106$	10.5405	1.02378
$107$	−4.04329	−0.390879	−0.195440	−	0.980716i	$-0.562613\pi$
$107$	−4.04329	−0.390879	−0.195440	+	0.980716i	$0.562613\pi$
$108$	2.46982	0.237659
$109$	11.1122	1.06436	0.532178	−	0.846632i	$-0.321374\pi$
$109$	11.1122	1.06436	0.532178	+	0.846632i	$0.321374\pi$
$110$	1.00000	0.0953463
$111$	−0.456042	−0.0432856
$112$	−2.28477	−0.215890
$113$	−3.56750	−0.335602	−0.167801	−	0.985821i	$-0.553667\pi$
$113$	−3.56750	−0.335602	−0.167801	+	0.985821i	$0.553667\pi$
$114$	2.19315	0.205407
$115$	0.280767	0.0261816
$116$	−4.77848	−0.443670
$117$	−8.15663	−0.754081
$118$	2.27511	0.209441
$119$	13.6326	1.24970
$120$	0.424375	0.0387400
$121$	1.00000	0.0909091
$122$	10.2729	0.930064
$123$	−1.53870	−0.138740
$124$	−1.28904	−0.115759
$125$	1.00000	0.0894427
$126$	−6.44283	−0.573973
$127$	17.8367	1.58275	0.791374	−	0.611332i	$-0.209366\pi$
$127$	17.8367	1.58275	0.791374	+	0.611332i	$0.209366\pi$
$128$	−1.00000	−0.0883883
$129$	−3.72975	−0.328386
$130$	−2.89252	−0.253691
$131$	3.17792	0.277656	0.138828	−	0.990316i	$-0.455666\pi$
$131$	3.17792	0.277656	0.138828	+	0.990316i	$0.455666\pi$
$132$	0.424375	0.0369371
$133$	−11.8075	−1.02384
$134$	−4.41447	−0.381352
$135$	2.46982	0.212569
$136$	5.96673	0.511643
$137$	−6.22981	−0.532248	−0.266124	−	0.963939i	$-0.585743\pi$
$137$	−6.22981	−0.532248	−0.266124	+	0.963939i	$0.585743\pi$
$138$	0.119150	0.0101428
$139$	−0.850907	−0.0721730	−0.0360865	−	0.999349i	$-0.511489\pi$
$139$	−0.850907	−0.0721730	−0.0360865	+	0.999349i	$0.511489\pi$
$140$	−2.28477	−0.193098
$141$	−1.94797	−0.164049
$142$	15.6267	1.31136
$143$	−2.89252	−0.241885
$144$	−2.81991	−0.234992
$145$	−4.77848	−0.396831
$146$	1.00000	0.0827606
$147$	0.755315	0.0622973
$148$	1.07462	0.0883332
$149$	17.7306	1.45254	0.726272	−	0.687407i	$-0.241251\pi$
$149$	17.7306	1.45254	0.726272	+	0.687407i	$0.241251\pi$
$150$	0.424375	0.0346501
$151$	−23.5452	−1.91608	−0.958040	−	0.286634i	$-0.907464\pi$
$151$	−23.5452	−1.91608	−0.958040	+	0.286634i	$0.907464\pi$
$152$	−5.16794	−0.419175
$153$	16.8256	1.36027
$154$	−2.28477	−0.184112
$155$	−1.28904	−0.103538
$156$	−1.22751	−0.0982798
$157$	−4.68555	−0.373947	−0.186974	−	0.982365i	$-0.559868\pi$
$157$	−4.68555	−0.373947	−0.186974	+	0.982365i	$0.559868\pi$
$158$	1.58984	0.126481
$159$	4.47312	0.354742
$160$	−1.00000	−0.0790569
$161$	−0.641487	−0.0505562
$162$	−7.41158	−0.582309
$163$	14.4805	1.13420	0.567100	−	0.823649i	$-0.308065\pi$
$163$	14.4805	1.13420	0.567100	+	0.823649i	$0.308065\pi$
$164$	3.62581	0.283128
$165$	0.424375	0.0330376
$166$	2.44843	0.190035
$167$	−4.33397	−0.335372	−0.167686	−	0.985840i	$-0.553630\pi$
$167$	−4.33397	−0.335372	−0.167686	+	0.985840i	$0.553630\pi$
$168$	−0.969600	−0.0748063
$169$	−4.63333	−0.356410
$170$	5.96673	0.457627
$171$	−14.5731	−1.11443
$172$	8.78880	0.670140
$173$	15.1585	1.15248	0.576238	−	0.817282i	$-0.304520\pi$
$173$	15.1585	1.15248	0.576238	+	0.817282i	$0.304520\pi$
$174$	−2.02787	−0.153732
$175$	−2.28477	−0.172712
$176$	−1.00000	−0.0753778
$177$	0.965502	0.0725715
$178$	−1.57853	−0.118316
$179$	12.8544	0.960782	0.480391	−	0.877054i	$-0.340495\pi$
$179$	12.8544	0.960782	0.480391	+	0.877054i	$0.340495\pi$
$180$	−2.81991	−0.210183
$181$	18.1191	1.34678	0.673392	−	0.739285i	$-0.264837\pi$
$181$	18.1191	1.34678	0.673392	+	0.739285i	$0.264837\pi$
$182$	6.60874	0.489873
$183$	4.35956	0.322268
$184$	−0.280767	−0.0206984
$185$	1.07462	0.0790076
$186$	−0.547038	−0.0401108
$187$	5.96673	0.436330
$188$	4.59021	0.334775
$189$	−5.64298	−0.410466
$190$	−5.16794	−0.374922
$191$	−15.2365	−1.10247	−0.551237	−	0.834349i	$-0.685844\pi$
$191$	−15.2365	−1.10247	−0.551237	+	0.834349i	$0.685844\pi$
$192$	−0.424375	−0.0306267
$193$	8.00094	0.575920	0.287960	−	0.957642i	$-0.407023\pi$
$193$	8.00094	0.575920	0.287960	+	0.957642i	$0.407023\pi$
$194$	−15.9243	−1.14330
$195$	−1.22751	−0.0879041
$196$	−1.77983	−0.127131
$197$	12.5400	0.893439	0.446720	−	0.894674i	$-0.352592\pi$
$197$	12.5400	0.893439	0.446720	+	0.894674i	$0.352592\pi$
$198$	−2.81991	−0.200402
$199$	2.01593	0.142905	0.0714526	−	0.997444i	$-0.477237\pi$
$199$	2.01593	0.142905	0.0714526	+	0.997444i	$0.477237\pi$
$200$	−1.00000	−0.0707107
$201$	−1.87339	−0.132139
$202$	18.3021	1.28773
$203$	10.9177	0.766273
$204$	2.53213	0.177285
$205$	3.62581	0.253237
$206$	6.20376	0.432236
$207$	−0.791735	−0.0550294
$208$	2.89252	0.200560
$209$	−5.16794	−0.357474
$210$	−0.969600	−0.0669087
$211$	5.88236	0.404958	0.202479	−	0.979287i	$-0.435100\pi$
$211$	5.88236	0.404958	0.202479	+	0.979287i	$0.435100\pi$
$212$	−10.5405	−0.723924
$213$	6.63158	0.454389
$214$	4.04329	0.276393
$215$	8.78880	0.599391
$216$	−2.46982	−0.168050
$217$	2.94516	0.199931
$218$	−11.1122	−0.752614
$219$	0.424375	0.0286766
$220$	−1.00000	−0.0674200
$221$	−17.2589	−1.16096
$222$	0.456042	0.0306076
$223$	0.663088	0.0444037	0.0222018	−	0.999754i	$-0.492932\pi$
$223$	0.663088	0.0444037	0.0222018	+	0.999754i	$0.492932\pi$
$224$	2.28477	0.152658
$225$	−2.81991	−0.187994
$226$	3.56750	0.237306
$227$	20.9640	1.39143	0.695715	−	0.718318i	$-0.255088\pi$
$227$	20.9640	1.39143	0.695715	+	0.718318i	$0.255088\pi$
$228$	−2.19315	−0.145245
$229$	18.8367	1.24477	0.622383	−	0.782713i	$-0.286164\pi$
$229$	18.8367	1.24477	0.622383	+	0.782713i	$0.286164\pi$
$230$	−0.280767	−0.0185132
$231$	−0.969600	−0.0637950
$232$	4.77848	0.313722
$233$	20.3461	1.33292	0.666460	−	0.745541i	$-0.267809\pi$
$233$	20.3461	1.33292	0.666460	+	0.745541i	$0.267809\pi$
$234$	8.15663	0.533216
$235$	4.59021	0.299432
$236$	−2.27511	−0.148097
$237$	0.674688	0.0438257
$238$	−13.6326	−0.883670
$239$	−1.47103	−0.0951532	−0.0475766	−	0.998868i	$-0.515150\pi$
$239$	−1.47103	−0.0951532	−0.0475766	+	0.998868i	$0.515150\pi$
$240$	−0.424375	−0.0273933
$241$	19.4117	1.25042	0.625210	−	0.780457i	$-0.285013\pi$
$241$	19.4117	1.25042	0.625210	+	0.780457i	$0.285013\pi$
$242$	−1.00000	−0.0642824
$243$	−10.5548	−0.677089
$244$	−10.2729	−0.657654
$245$	−1.77983	−0.113709
$246$	1.53870	0.0981042
$247$	14.9484	0.951142
$248$	1.28904	0.0818543
$249$	1.03905	0.0658473
$250$	−1.00000	−0.0632456
$251$	13.7709	0.869213	0.434607	−	0.900620i	$-0.356887\pi$
$251$	13.7709	0.869213	0.434607	+	0.900620i	$0.356887\pi$
$252$	6.44283	0.405860
$253$	−0.280767	−0.0176516
$254$	−17.8367	−1.11917
$255$	2.53213	0.158568
$256$	1.00000	0.0625000
$257$	4.74225	0.295813	0.147907	−	0.989001i	$-0.452747\pi$
$257$	4.74225	0.295813	0.147907	+	0.989001i	$0.452747\pi$
$258$	3.72975	0.232204
$259$	−2.45526	−0.152562
$260$	2.89252	0.179386
$261$	13.4748	0.834072
$262$	−3.17792	−0.196333
$263$	−19.6772	−1.21335	−0.606673	−	0.794952i	$-0.707496\pi$
$263$	−19.6772	−1.21335	−0.606673	+	0.794952i	$0.707496\pi$
$264$	−0.424375	−0.0261185
$265$	−10.5405	−0.647497
$266$	11.8075	0.723967
$267$	−0.669888	−0.0409965
$268$	4.41447	0.269657
$269$	2.94252	0.179409	0.0897043	−	0.995968i	$-0.471408\pi$
$269$	2.94252	0.179409	0.0897043	+	0.995968i	$0.471408\pi$
$270$	−2.46982	−0.150309
$271$	−19.8849	−1.20792	−0.603960	−	0.797015i	$-0.706411\pi$
$271$	−19.8849	−1.20792	−0.603960	+	0.797015i	$0.706411\pi$
$272$	−5.96673	−0.361786
$273$	2.80459	0.169741
$274$	6.22981	0.376356
$275$	−1.00000	−0.0603023
$276$	−0.119150	−0.00717201
$277$	−10.4428	−0.627444	−0.313722	−	0.949515i	$-0.601576\pi$
$277$	−10.4428	−0.627444	−0.313722	+	0.949515i	$0.601576\pi$
$278$	0.850907	0.0510340
$279$	3.63498	0.217620
$280$	2.28477	0.136541
$281$	33.3628	1.99026	0.995129	−	0.0985793i	$-0.0314298\pi$
$281$	33.3628	1.99026	0.995129	+	0.0985793i	$0.0314298\pi$
$282$	1.94797	0.116000
$283$	16.0249	0.952579	0.476289	−	0.879289i	$-0.341981\pi$
$283$	16.0249	0.952579	0.476289	+	0.879289i	$0.341981\pi$
$284$	−15.6267	−0.927273
$285$	−2.19315	−0.129911
$286$	2.89252	0.171038
$287$	−8.28414	−0.488997
$288$	2.81991	0.166165
$289$	18.6019	1.09423
$290$	4.77848	0.280602
$291$	−6.75790	−0.396155
$292$	−1.00000	−0.0585206
$293$	7.22197	0.421912	0.210956	−	0.977496i	$-0.432342\pi$
$293$	7.22197	0.421912	0.210956	+	0.977496i	$0.432342\pi$
$294$	−0.755315	−0.0440509
$295$	−2.27511	−0.132462
$296$	−1.07462	−0.0624610
$297$	−2.46982	−0.143314
$298$	−17.7306	−1.02710
$299$	0.812123	0.0469663
$300$	−0.424375	−0.0245013
$301$	−20.0804	−1.15741
$302$	23.5452	1.35487
$303$	7.76695	0.446199
$304$	5.16794	0.296402
$305$	−10.2729	−0.588224
$306$	−16.8256	−0.961856
$307$	9.84365	0.561807	0.280903	−	0.959736i	$-0.409366\pi$
$307$	9.84365	0.561807	0.280903	+	0.959736i	$0.409366\pi$
$308$	2.28477	0.130187
$309$	2.63272	0.149770
$310$	1.28904	0.0732127
$311$	17.9322	1.01684	0.508421	−	0.861109i	$-0.330229\pi$
$311$	17.9322	1.01684	0.508421	+	0.861109i	$0.330229\pi$
$312$	1.22751	0.0694943
$313$	−23.1208	−1.30686	−0.653432	−	0.756985i	$-0.726672\pi$
$313$	−23.1208	−1.30686	−0.653432	+	0.756985i	$0.726672\pi$
$314$	4.68555	0.264421
$315$	6.44283	0.363013
$316$	−1.58984	−0.0894353
$317$	15.7946	0.887114	0.443557	−	0.896246i	$-0.353716\pi$
$317$	15.7946	0.887114	0.443557	+	0.896246i	$0.353716\pi$
$318$	−4.47312	−0.250840
$319$	4.77848	0.267543
$320$	1.00000	0.0559017
$321$	1.71587	0.0957706
$322$	0.641487	0.0357487
$323$	−30.8357	−1.71574
$324$	7.41158	0.411755
$325$	2.89252	0.160448
$326$	−14.4805	−0.802001
$327$	−4.71575	−0.260781
$328$	−3.62581	−0.200202
$329$	−10.4876	−0.578198
$330$	−0.424375	−0.0233611
$331$	−13.6907	−0.752511	−0.376255	−	0.926516i	$-0.622789\pi$
$331$	−13.6907	−0.752511	−0.376255	+	0.926516i	$0.622789\pi$
$332$	−2.44843	−0.134375
$333$	−3.03033	−0.166061
$334$	4.33397	0.237144
$335$	4.41447	0.241188
$336$	0.969600	0.0528960
$337$	16.8047	0.915411	0.457705	−	0.889104i	$-0.348671\pi$
$337$	16.8047	0.915411	0.457705	+	0.889104i	$0.348671\pi$
$338$	4.63333	0.252020
$339$	1.51396	0.0822269
$340$	−5.96673	−0.323591
$341$	1.28904	0.0698056
$342$	14.5731	0.788023
$343$	20.0599	1.08313
$344$	−8.78880	−0.473860
$345$	−0.119150	−0.00641484
$346$	−15.1585	−0.814924
$347$	−6.46071	−0.346829	−0.173414	−	0.984849i	$-0.555480\pi$
$347$	−6.46071	−0.346829	−0.173414	+	0.984849i	$0.555480\pi$
$348$	2.02787	0.108705
$349$	23.7713	1.27245	0.636225	−	0.771504i	$-0.280495\pi$
$349$	23.7713	1.27245	0.636225	+	0.771504i	$0.280495\pi$
$350$	2.28477	0.122126
$351$	7.14402	0.381319
$352$	1.00000	0.0533002
$353$	29.0297	1.54509	0.772547	−	0.634958i	$-0.218983\pi$
$353$	29.0297	1.54509	0.772547	+	0.634958i	$0.218983\pi$
$354$	−0.965502	−0.0513158
$355$	−15.6267	−0.829379
$356$	1.57853	0.0836618
$357$	−5.78534	−0.306193
$358$	−12.8544	−0.679375
$359$	9.35363	0.493666	0.246833	−	0.969058i	$-0.420610\pi$
$359$	9.35363	0.493666	0.246833	+	0.969058i	$0.420610\pi$
$360$	2.81991	0.148622
$361$	7.70758	0.405662
$362$	−18.1191	−0.952320
$363$	−0.424375	−0.0222739
$364$	−6.60874	−0.346392
$365$	−1.00000	−0.0523424
$366$	−4.35956	−0.227878
$367$	−20.0430	−1.04624	−0.523118	−	0.852260i	$-0.675231\pi$
$367$	−20.0430	−1.04624	−0.523118	+	0.852260i	$0.675231\pi$
$368$	0.280767	0.0146360
$369$	−10.2244	−0.532263
$370$	−1.07462	−0.0558668
$371$	24.0826	1.25031
$372$	0.547038	0.0283626
$373$	−15.8575	−0.821071	−0.410535	−	0.911845i	$-0.634658\pi$
$373$	−15.8575	−0.821071	−0.410535	+	0.911845i	$0.634658\pi$
$374$	−5.96673	−0.308532
$375$	−0.424375	−0.0219146
$376$	−4.59021	−0.236722
$377$	−13.8218	−0.711861
$378$	5.64298	0.290244
$379$	−18.2862	−0.939298	−0.469649	−	0.882853i	$-0.655619\pi$
$379$	−18.2862	−0.939298	−0.469649	+	0.882853i	$0.655619\pi$
$380$	5.16794	0.265110
$381$	−7.56944	−0.387794
$382$	15.2365	0.779567
$383$	−29.9917	−1.53250	−0.766252	−	0.642540i	$-0.777880\pi$
$383$	−29.9917	−1.53250	−0.766252	+	0.642540i	$0.777880\pi$
$384$	0.424375	0.0216563
$385$	2.28477	0.116443
$386$	−8.00094	−0.407237
$387$	−24.7836	−1.25982
$388$	15.9243	0.808436
$389$	8.71552	0.441894	0.220947	−	0.975286i	$-0.429085\pi$
$389$	8.71552	0.441894	0.220947	+	0.975286i	$0.429085\pi$
$390$	1.22751	0.0621576
$391$	−1.67526	−0.0847214
$392$	1.77983	0.0898949
$393$	−1.34863	−0.0680295
$394$	−12.5400	−0.631757
$395$	−1.58984	−0.0799934
$396$	2.81991	0.141706
$397$	33.1037	1.66142	0.830712	−	0.556702i	$-0.187933\pi$
$397$	33.1037	1.66142	0.830712	+	0.556702i	$0.187933\pi$
$398$	−2.01593	−0.101049
$399$	5.01083	0.250855
$400$	1.00000	0.0500000
$401$	6.49606	0.324398	0.162199	−	0.986758i	$-0.448141\pi$
$401$	6.49606	0.324398	0.162199	+	0.986758i	$0.448141\pi$
$402$	1.87339	0.0934364
$403$	−3.72858	−0.185734
$404$	−18.3021	−0.910562
$405$	7.41158	0.368285
$406$	−10.9177	−0.541837
$407$	−1.07462	−0.0532669
$408$	−2.53213	−0.125359
$409$	−7.98965	−0.395063	−0.197531	−	0.980297i	$-0.563292\pi$
$409$	−7.98965	−0.395063	−0.197531	+	0.980297i	$0.563292\pi$
$410$	−3.62581	−0.179066
$411$	2.64378	0.130408
$412$	−6.20376	−0.305637
$413$	5.19811	0.255782
$414$	0.791735	0.0389117
$415$	−2.44843	−0.120189
$416$	−2.89252	−0.141817
$417$	0.361104	0.0176833
$418$	5.16794	0.252772
$419$	−30.1347	−1.47218	−0.736089	−	0.676885i	$-0.763329\pi$
$419$	−30.1347	−1.47218	−0.736089	+	0.676885i	$0.763329\pi$
$420$	0.969600	0.0473116
$421$	−16.6583	−0.811877	−0.405938	−	0.913900i	$-0.633055\pi$
$421$	−16.6583	−0.811877	−0.405938	+	0.913900i	$0.633055\pi$
$422$	−5.88236	−0.286349
$423$	−12.9440	−0.629357
$424$	10.5405	0.511892
$425$	−5.96673	−0.289429
$426$	−6.63158	−0.321301
$427$	23.4712	1.13585
$428$	−4.04329	−0.195440
$429$	1.22751	0.0592649
$430$	−8.78880	−0.423833
$431$	−12.0419	−0.580036	−0.290018	−	0.957021i	$-0.593661\pi$
$431$	−12.0419	−0.580036	−0.290018	+	0.957021i	$0.593661\pi$
$432$	2.46982	0.118829
$433$	−9.35962	−0.449794	−0.224897	−	0.974382i	$-0.572205\pi$
$433$	−9.35962	−0.449794	−0.224897	+	0.974382i	$0.572205\pi$
$434$	−2.94516	−0.141372
$435$	2.02787	0.0972288
$436$	11.1122	0.532178
$437$	1.45098	0.0694100
$438$	−0.424375	−0.0202774
$439$	5.04284	0.240682	0.120341	−	0.992733i	$-0.461601\pi$
$439$	5.04284	0.240682	0.120341	+	0.992733i	$0.461601\pi$
$440$	1.00000	0.0476731
$441$	5.01895	0.238997
$442$	17.2589	0.820921
$443$	8.85119	0.420533	0.210266	−	0.977644i	$-0.432567\pi$
$443$	8.85119	0.420533	0.210266	+	0.977644i	$0.432567\pi$
$444$	−0.456042	−0.0216428
$445$	1.57853	0.0748294
$446$	−0.663088	−0.0313981
$447$	−7.52441	−0.355893
$448$	−2.28477	−0.107945
$449$	−0.163476	−0.00771492	−0.00385746	−	0.999993i	$-0.501228\pi$
$449$	−0.163476	−0.00771492	−0.00385746	+	0.999993i	$0.501228\pi$
$450$	2.81991	0.132932
$451$	−3.62581	−0.170733
$452$	−3.56750	−0.167801
$453$	9.99200	0.469465
$454$	−20.9640	−0.983890
$455$	−6.60874	−0.309823
$456$	2.19315	0.102703
$457$	−9.38179	−0.438862	−0.219431	−	0.975628i	$-0.570420\pi$
$457$	−9.38179	−0.438862	−0.219431	+	0.975628i	$0.570420\pi$
$458$	−18.8367	−0.880183
$459$	−14.7368	−0.687854
$460$	0.280767	0.0130908
$461$	21.4120	0.997257	0.498629	−	0.866816i	$-0.333837\pi$
$461$	21.4120	0.997257	0.498629	+	0.866816i	$0.333837\pi$
$462$	0.969600	0.0451099
$463$	−10.5800	−0.491696	−0.245848	−	0.969308i	$-0.579066\pi$
$463$	−10.5800	−0.491696	−0.245848	+	0.969308i	$0.579066\pi$
$464$	−4.77848	−0.221835
$465$	0.547038	0.0253683
$466$	−20.3461	−0.942517
$467$	25.0705	1.16013	0.580063	−	0.814572i	$-0.303028\pi$
$467$	25.0705	1.16013	0.580063	+	0.814572i	$0.303028\pi$
$468$	−8.15663	−0.377041
$469$	−10.0861	−0.465731
$470$	−4.59021	−0.211731
$471$	1.98843	0.0916221
$472$	2.27511	0.104721
$473$	−8.78880	−0.404109
$474$	−0.674688	−0.0309894
$475$	5.16794	0.237121
$476$	13.6326	0.624849
$477$	29.7232	1.36093
$478$	1.47103	0.0672835
$479$	−16.8507	−0.769929	−0.384965	−	0.922931i	$-0.625786\pi$
$479$	−16.8507	−0.769929	−0.384965	+	0.922931i	$0.625786\pi$
$480$	0.424375	0.0193700
$481$	3.10836	0.141729
$482$	−19.4117	−0.884180
$483$	0.272231	0.0123869
$484$	1.00000	0.0454545
$485$	15.9243	0.723087
$486$	10.5548	0.478774
$487$	24.7210	1.12022	0.560108	−	0.828420i	$-0.310760\pi$
$487$	24.7210	1.12022	0.560108	+	0.828420i	$0.310760\pi$
$488$	10.2729	0.465032
$489$	−6.14517	−0.277894
$490$	1.77983	0.0804044
$491$	18.8463	0.850522	0.425261	−	0.905071i	$-0.360182\pi$
$491$	18.8463	0.850522	0.425261	+	0.905071i	$0.360182\pi$
$492$	−1.53870	−0.0693701
$493$	28.5119	1.28411
$494$	−14.9484	−0.672559
$495$	2.81991	0.126745
$496$	−1.28904	−0.0578797
$497$	35.7034	1.60152
$498$	−1.03905	−0.0465611
$499$	−8.07162	−0.361335	−0.180668	−	0.983544i	$-0.557826\pi$
$499$	−8.07162	−0.361335	−0.180668	+	0.983544i	$0.557826\pi$
$500$	1.00000	0.0447214
$501$	1.83923	0.0821707
$502$	−13.7709	−0.614627
$503$	−14.8285	−0.661171	−0.330585	−	0.943776i	$-0.607246\pi$
$503$	−14.8285	−0.661171	−0.330585	+	0.943776i	$0.607246\pi$
$504$	−6.44283	−0.286987
$505$	−18.3021	−0.814431
$506$	0.280767	0.0124816
$507$	1.96627	0.0873251
$508$	17.8367	0.791374
$509$	−23.7578	−1.05305	−0.526523	−	0.850161i	$-0.676505\pi$
$509$	−23.7578	−1.05305	−0.526523	+	0.850161i	$0.676505\pi$
$510$	−2.53213	−0.112125
$511$	2.28477	0.101072
$512$	−1.00000	−0.0441942
$513$	12.7639	0.563540
$514$	−4.74225	−0.209171
$515$	−6.20376	−0.273370
$516$	−3.72975	−0.164193
$517$	−4.59021	−0.201877
$518$	2.45526	0.107878
$519$	−6.43288	−0.282372
$520$	−2.89252	−0.126845
$521$	−27.0572	−1.18540	−0.592699	−	0.805424i	$-0.701938\pi$
$521$	−27.0572	−1.18540	−0.592699	+	0.805424i	$0.701938\pi$
$522$	−13.4748	−0.589778
$523$	42.5869	1.86220	0.931099	−	0.364768i	$-0.118852\pi$
$523$	42.5869	1.86220	0.931099	+	0.364768i	$0.118852\pi$
$524$	3.17792	0.138828
$525$	0.969600	0.0423168
$526$	19.6772	0.857965
$527$	7.69137	0.335041
$528$	0.424375	0.0184686
$529$	−22.9212	−0.996573
$530$	10.5405	0.457850
$531$	6.41560	0.278413
$532$	−11.8075	−0.511922
$533$	10.4877	0.454274
$534$	0.669888	0.0289889
$535$	−4.04329	−0.174806
$536$	−4.41447	−0.190676
$537$	−5.45508	−0.235404
$538$	−2.94252	−0.126861
$539$	1.77983	0.0766626
$540$	2.46982	0.106284
$541$	29.8526	1.28346	0.641732	−	0.766929i	$-0.278216\pi$
$541$	29.8526	1.28346	0.641732	+	0.766929i	$0.278216\pi$
$542$	19.8849	0.854128
$543$	−7.68931	−0.329980
$544$	5.96673	0.255821
$545$	11.1122	0.475995
$546$	−2.80459	−0.120025
$547$	−10.1758	−0.435086	−0.217543	−	0.976051i	$-0.569804\pi$
$547$	−10.1758	−0.435086	−0.217543	+	0.976051i	$0.569804\pi$
$548$	−6.22981	−0.266124
$549$	28.9686	1.23635
$550$	1.00000	0.0426401
$551$	−24.6949	−1.05204
$552$	0.119150	0.00507138
$553$	3.63241	0.154466
$554$	10.4428	0.443670
$555$	−0.456042	−0.0193579
$556$	−0.850907	−0.0360865
$557$	20.2641	0.858616	0.429308	−	0.903158i	$-0.358757\pi$
$557$	20.2641	0.858616	0.429308	+	0.903158i	$0.358757\pi$
$558$	−3.63498	−0.153881
$559$	25.4218	1.07523
$560$	−2.28477	−0.0965491
$561$	−2.53213	−0.106907
$562$	−33.3628	−1.40733
$563$	−34.5346	−1.45546	−0.727729	−	0.685864i	$-0.759424\pi$
$563$	−34.5346	−1.45546	−0.727729	+	0.685864i	$0.759424\pi$
$564$	−1.94797	−0.0820244
$565$	−3.56750	−0.150086
$566$	−16.0249	−0.673575
$567$	−16.9338	−0.711151
$568$	15.6267	0.655681
$569$	12.5688	0.526913	0.263456	−	0.964671i	$-0.415138\pi$
$569$	12.5688	0.526913	0.263456	+	0.964671i	$0.415138\pi$
$570$	2.19315	0.0918607
$571$	−13.3540	−0.558849	−0.279424	−	0.960168i	$-0.590144\pi$
$571$	−13.3540	−0.558849	−0.279424	+	0.960168i	$0.590144\pi$
$572$	−2.89252	−0.120942
$573$	6.46600	0.270121
$574$	8.28414	0.345773
$575$	0.280767	0.0117088
$576$	−2.81991	−0.117496
$577$	11.7050	0.487284	0.243642	−	0.969865i	$-0.421658\pi$
$577$	11.7050	0.487284	0.243642	+	0.969865i	$0.421658\pi$
$578$	−18.6019	−0.773735
$579$	−3.39540	−0.141108
$580$	−4.77848	−0.198415
$581$	5.59410	0.232082
$582$	6.75790	0.280124
$583$	10.5405	0.436543
$584$	1.00000	0.0413803
$585$	−8.15663	−0.337235
$586$	−7.22197	−0.298337
$587$	35.3341	1.45840	0.729198	−	0.684303i	$-0.239893\pi$
$587$	35.3341	1.45840	0.729198	+	0.684303i	$0.239893\pi$
$588$	0.755315	0.0311487
$589$	−6.66169	−0.274490
$590$	2.27511	0.0936649
$591$	−5.32167	−0.218904
$592$	1.07462	0.0441666
$593$	25.6903	1.05498	0.527488	−	0.849563i	$-0.323134\pi$
$593$	25.6903	1.05498	0.527488	+	0.849563i	$0.323134\pi$
$594$	2.46982	0.101338
$595$	13.6326	0.558882
$596$	17.7306	0.726272
$597$	−0.855510	−0.0350137
$598$	−0.812123	−0.0332102
$599$	−22.7148	−0.928101	−0.464050	−	0.885809i	$-0.653604\pi$
$599$	−22.7148	−0.928101	−0.464050	+	0.885809i	$0.653604\pi$
$600$	0.424375	0.0173251
$601$	28.7049	1.17090	0.585449	−	0.810709i	$-0.300918\pi$
$601$	28.7049	1.17090	0.585449	+	0.810709i	$0.300918\pi$
$602$	20.0804	0.818415
$603$	−12.4484	−0.506938
$604$	−23.5452	−0.958040
$605$	1.00000	0.0406558
$606$	−7.76695	−0.315511
$607$	−22.0116	−0.893422	−0.446711	−	0.894678i	$-0.647405\pi$
$607$	−22.0116	−0.893422	−0.446711	+	0.894678i	$0.647405\pi$
$608$	−5.16794	−0.209588
$609$	−4.63321	−0.187747
$610$	10.2729	0.415937
$611$	13.2773	0.537141
$612$	16.8256	0.680135
$613$	39.8854	1.61096	0.805479	−	0.592624i	$-0.201908\pi$
$613$	39.8854	1.61096	0.805479	+	0.592624i	$0.201908\pi$
$614$	−9.84365	−0.397257
$615$	−1.53870	−0.0620465
$616$	−2.28477	−0.0920560
$617$	0.925386	0.0372546	0.0186273	−	0.999826i	$-0.494070\pi$
$617$	0.925386	0.0372546	0.0186273	+	0.999826i	$0.494070\pi$
$618$	−2.63272	−0.105904
$619$	8.47675	0.340709	0.170355	−	0.985383i	$-0.445509\pi$
$619$	8.47675	0.340709	0.170355	+	0.985383i	$0.445509\pi$
$620$	−1.28904	−0.0517692
$621$	0.693444	0.0278270
$622$	−17.9322	−0.719016
$623$	−3.60657	−0.144494
$624$	−1.22751	−0.0491399
$625$	1.00000	0.0400000
$626$	23.1208	0.924093
$627$	2.19315	0.0875858
$628$	−4.68555	−0.186974
$629$	−6.41197	−0.255662
$630$	−6.44283	−0.256689
$631$	−39.9444	−1.59016	−0.795081	−	0.606504i	$-0.792572\pi$
$631$	−39.9444	−1.59016	−0.795081	+	0.606504i	$0.792572\pi$
$632$	1.58984	0.0632403
$633$	−2.49633	−0.0992201
$634$	−15.7946	−0.627284
$635$	17.8367	0.707826
$636$	4.47312	0.177371
$637$	−5.14819	−0.203979
$638$	−4.77848	−0.189182
$639$	44.0658	1.74322
$640$	−1.00000	−0.0395285
$641$	35.0875	1.38587	0.692937	−	0.720998i	$-0.256316\pi$
$641$	35.0875	1.38587	0.692937	+	0.720998i	$0.256316\pi$
$642$	−1.71587	−0.0677200
$643$	26.2736	1.03613	0.518065	−	0.855341i	$-0.326652\pi$
$643$	26.2736	1.03613	0.518065	+	0.855341i	$0.326652\pi$
$644$	−0.641487	−0.0252781
$645$	−3.72975	−0.146859
$646$	30.8357	1.21321
$647$	1.67582	0.0658834	0.0329417	−	0.999457i	$-0.489512\pi$
$647$	1.67582	0.0658834	0.0329417	+	0.999457i	$0.489512\pi$
$648$	−7.41158	−0.291155
$649$	2.27511	0.0893060
$650$	−2.89252	−0.113454
$651$	−1.24986	−0.0489857
$652$	14.4805	0.567100
$653$	−27.2141	−1.06497	−0.532485	−	0.846439i	$-0.678742\pi$
$653$	−27.2141	−1.06497	−0.532485	+	0.846439i	$0.678742\pi$
$654$	4.71575	0.184400
$655$	3.17792	0.124172
$656$	3.62581	0.141564
$657$	2.81991	0.110015
$658$	10.4876	0.408848
$659$	48.9646	1.90739	0.953695	−	0.300775i	$-0.0972452\pi$
$659$	48.9646	1.90739	0.953695	+	0.300775i	$0.0972452\pi$
$660$	0.424375	0.0165188
$661$	−5.93871	−0.230989	−0.115495	−	0.993308i	$-0.536845\pi$
$661$	−5.93871	−0.230989	−0.115495	+	0.993308i	$0.536845\pi$
$662$	13.6907	0.532106
$663$	7.32424	0.284450
$664$	2.44843	0.0950175
$665$	−11.8075	−0.457877
$666$	3.03033	0.117423
$667$	−1.34164	−0.0519484
$668$	−4.33397	−0.167686
$669$	−0.281398	−0.0108795
$670$	−4.41447	−0.170546
$671$	10.2729	0.396581
$672$	−0.969600	−0.0374031
$673$	−12.0162	−0.463190	−0.231595	−	0.972812i	$-0.574394\pi$
$673$	−12.0162	−0.463190	−0.231595	+	0.972812i	$0.574394\pi$
$674$	−16.8047	−0.647293
$675$	2.46982	0.0950636
$676$	−4.63333	−0.178205
$677$	−8.69101	−0.334023	−0.167011	−	0.985955i	$-0.553412\pi$
$677$	−8.69101	−0.334023	−0.167011	+	0.985955i	$0.553412\pi$
$678$	−1.51396	−0.0581432
$679$	−36.3835	−1.39627
$680$	5.96673	0.228814
$681$	−8.89661	−0.340919
$682$	−1.28904	−0.0493600
$683$	46.0065	1.76039	0.880196	−	0.474611i	$-0.157411\pi$
$683$	46.0065	1.76039	0.880196	+	0.474611i	$0.157411\pi$
$684$	−14.5731	−0.557216
$685$	−6.22981	−0.238029
$686$	−20.0599	−0.765890
$687$	−7.99385	−0.304984
$688$	8.78880	0.335070
$689$	−30.4886	−1.16152
$690$	0.119150	0.00453598
$691$	−6.11498	−0.232625	−0.116312	−	0.993213i	$-0.537107\pi$
$691$	−6.11498	−0.232625	−0.116312	+	0.993213i	$0.537107\pi$
$692$	15.1585	0.576238
$693$	−6.44283	−0.244743
$694$	6.46071	0.245245
$695$	−0.850907	−0.0322767
$696$	−2.02787	−0.0768661
$697$	−21.6342	−0.819454
$698$	−23.7713	−0.899758
$699$	−8.63440	−0.326583
$700$	−2.28477	−0.0863562
$701$	25.9048	0.978410	0.489205	−	0.872169i	$-0.337287\pi$
$701$	25.9048	0.978410	0.489205	+	0.872169i	$0.337287\pi$
$702$	−7.14402	−0.269634
$703$	5.55357	0.209457
$704$	−1.00000	−0.0376889
$705$	−1.94797	−0.0733649
$706$	−29.0297	−1.09255
$707$	41.8160	1.57265
$708$	0.965502	0.0362858
$709$	12.0280	0.451722	0.225861	−	0.974160i	$-0.427480\pi$
$709$	12.0280	0.451722	0.225861	+	0.974160i	$0.427480\pi$
$710$	15.6267	0.586459
$711$	4.48319	0.168133
$712$	−1.57853	−0.0591578
$713$	−0.361920	−0.0135540
$714$	5.78534	0.216511
$715$	−2.89252	−0.108174
$716$	12.8544	0.480391
$717$	0.624270	0.0233138
$718$	−9.35363	−0.349074
$719$	0.821978	0.0306546	0.0153273	−	0.999883i	$-0.495121\pi$
$719$	0.821978	0.0306546	0.0153273	+	0.999883i	$0.495121\pi$
$720$	−2.81991	−0.105092
$721$	14.1742	0.527873
$722$	−7.70758	−0.286846
$723$	−8.23786	−0.306369
$724$	18.1191	0.673392
$725$	−4.77848	−0.177468
$726$	0.424375	0.0157500
$727$	7.34898	0.272559	0.136279	−	0.990670i	$-0.456486\pi$
$727$	7.34898	0.272559	0.136279	+	0.990670i	$0.456486\pi$
$728$	6.60874	0.244936
$729$	−17.7556	−0.657614
$730$	1.00000	0.0370117
$731$	−52.4404	−1.93958
$732$	4.35956	0.161134
$733$	5.95851	0.220083	0.110041	−	0.993927i	$-0.464902\pi$
$733$	5.95851	0.220083	0.110041	+	0.993927i	$0.464902\pi$
$734$	20.0430	0.739801
$735$	0.755315	0.0278602
$736$	−0.280767	−0.0103492
$737$	−4.41447	−0.162609
$738$	10.2244	0.376367
$739$	47.9272	1.76303	0.881516	−	0.472154i	$-0.156523\pi$
$739$	47.9272	1.76303	0.881516	+	0.472154i	$0.156523\pi$
$740$	1.07462	0.0395038
$741$	−6.34372	−0.233042
$742$	−24.0826	−0.884100
$743$	48.7272	1.78763	0.893813	−	0.448439i	$-0.148020\pi$
$743$	48.7272	1.78763	0.893813	+	0.448439i	$0.148020\pi$
$744$	−0.547038	−0.0200554
$745$	17.7306	0.649598
$746$	15.8575	0.580585
$747$	6.90434	0.252617
$748$	5.96673	0.218165
$749$	9.23798	0.337548
$750$	0.424375	0.0154960
$751$	−9.11360	−0.332560	−0.166280	−	0.986079i	$-0.553176\pi$
$751$	−9.11360	−0.332560	−0.166280	+	0.986079i	$0.553176\pi$
$752$	4.59021	0.167388
$753$	−5.84404	−0.212969
$754$	13.8218	0.503362
$755$	−23.5452	−0.856897
$756$	−5.64298	−0.205233
$757$	28.0645	1.02002	0.510010	−	0.860168i	$-0.329642\pi$
$757$	28.0645	1.02002	0.510010	+	0.860168i	$0.329642\pi$
$758$	18.2862	0.664184
$759$	0.119150	0.00432489
$760$	−5.16794	−0.187461
$761$	−41.4684	−1.50323	−0.751614	−	0.659603i	$-0.770725\pi$
$761$	−41.4684	−1.50323	−0.751614	+	0.659603i	$0.770725\pi$
$762$	7.56944	0.274212
$763$	−25.3888	−0.919137
$764$	−15.2365	−0.551237
$765$	16.8256	0.608331
$766$	29.9917	1.08364
$767$	−6.58081	−0.237619
$768$	−0.424375	−0.0153133
$769$	12.7446	0.459581	0.229791	−	0.973240i	$-0.426196\pi$
$769$	12.7446	0.459581	0.229791	+	0.973240i	$0.426196\pi$
$770$	−2.28477	−0.0823374
$771$	−2.01249	−0.0724781
$772$	8.00094	0.287960
$773$	22.2150	0.799018	0.399509	−	0.916729i	$-0.369181\pi$
$773$	22.2150	0.799018	0.399509	+	0.916729i	$0.369181\pi$
$774$	24.7836	0.890827
$775$	−1.28904	−0.0463038
$776$	−15.9243	−0.571651
$777$	1.04195	0.0373798
$778$	−8.71552	−0.312466
$779$	18.7380	0.671357
$780$	−1.22751	−0.0439521
$781$	15.6267	0.559167
$782$	1.67526	0.0599071
$783$	−11.8020	−0.421769
$784$	−1.77983	−0.0635653
$785$	−4.68555	−0.167234
$786$	1.34863	0.0481041
$787$	−23.6495	−0.843013	−0.421506	−	0.906825i	$-0.638498\pi$
$787$	−23.6495	−0.843013	−0.421506	+	0.906825i	$0.638498\pi$
$788$	12.5400	0.446720
$789$	8.35050	0.297286
$790$	1.58984	0.0565639
$791$	8.15091	0.289813
$792$	−2.81991	−0.100201
$793$	−29.7145	−1.05519
$794$	−33.1037	−1.17480
$795$	4.47312	0.158645
$796$	2.01593	0.0714526
$797$	50.9108	1.80335	0.901676	−	0.432412i	$-0.142337\pi$
$797$	50.9108	1.80335	0.901676	+	0.432412i	$0.142337\pi$
$798$	−5.01083	−0.177382
$799$	−27.3885	−0.968937
$800$	−1.00000	−0.0353553
$801$	−4.45130	−0.157279
$802$	−6.49606	−0.229384
$803$	1.00000	0.0352892
$804$	−1.87339	−0.0660695
$805$	−0.641487	−0.0226094
$806$	3.72858	0.131334
$807$	−1.24873	−0.0439575
$808$	18.3021	0.643865
$809$	−43.2398	−1.52023	−0.760115	−	0.649789i	$-0.774857\pi$
$809$	−43.2398	−1.52023	−0.760115	+	0.649789i	$0.774857\pi$
$810$	−7.41158	−0.260417
$811$	−47.6318	−1.67258	−0.836289	−	0.548290i	$-0.815279\pi$
$811$	−47.6318	−1.67258	−0.836289	+	0.548290i	$0.815279\pi$
$812$	10.9177	0.383137
$813$	8.43864	0.295956
$814$	1.07462	0.0376654
$815$	14.4805	0.507230
$816$	2.53213	0.0886424
$817$	45.4200	1.58904
$818$	7.98965	0.279352
$819$	18.6360	0.651196
$820$	3.62581	0.126619
$821$	28.5818	0.997511	0.498756	−	0.866743i	$-0.333791\pi$
$821$	28.5818	0.997511	0.498756	+	0.866743i	$0.333791\pi$
$822$	−2.64378	−0.0922123
$823$	−54.6391	−1.90460	−0.952299	−	0.305167i	$-0.901288\pi$
$823$	−54.6391	−1.90460	−0.952299	+	0.305167i	$0.901288\pi$
$824$	6.20376	0.216118
$825$	0.424375	0.0147749
$826$	−5.19811	−0.180865
$827$	42.0720	1.46299	0.731493	−	0.681849i	$-0.238824\pi$
$827$	42.0720	1.46299	0.731493	+	0.681849i	$0.238824\pi$
$828$	−0.791735	−0.0275147
$829$	0.195435	0.00678775	0.00339388	−	0.999994i	$-0.498920\pi$
$829$	0.195435	0.00678775	0.00339388	+	0.999994i	$0.498920\pi$
$830$	2.44843	0.0849862
$831$	4.43165	0.153732
$832$	2.89252	0.100280
$833$	10.6198	0.367953
$834$	−0.361104	−0.0125040
$835$	−4.33397	−0.149983
$836$	−5.16794	−0.178737
$837$	−3.18371	−0.110045
$838$	30.1347	1.04099
$839$	−4.68159	−0.161626	−0.0808132	−	0.996729i	$-0.525752\pi$
$839$	−4.68159	−0.161626	−0.0808132	+	0.996729i	$0.525752\pi$
$840$	−0.969600	−0.0334544
$841$	−6.16617	−0.212627
$842$	16.6583	0.574084
$843$	−14.1584	−0.487640
$844$	5.88236	0.202479
$845$	−4.63333	−0.159391
$846$	12.9440	0.445022
$847$	−2.28477	−0.0785056
$848$	−10.5405	−0.361962
$849$	−6.80055	−0.233394
$850$	5.96673	0.204657
$851$	0.301717	0.0103427
$852$	6.63158	0.227194
$853$	33.3457	1.14173	0.570867	−	0.821042i	$-0.306607\pi$
$853$	33.3457	1.14173	0.570867	+	0.821042i	$0.306607\pi$
$854$	−23.4712	−0.803168
$855$	−14.5731	−0.498389
$856$	4.04329	0.138197
$857$	−57.7445	−1.97251	−0.986257	−	0.165220i	$-0.947166\pi$
$857$	−57.7445	−1.97251	−0.986257	+	0.165220i	$0.947166\pi$
$858$	−1.22751	−0.0419066
$859$	14.2348	0.485686	0.242843	−	0.970066i	$-0.421920\pi$
$859$	14.2348	0.485686	0.242843	+	0.970066i	$0.421920\pi$
$860$	8.78880	0.299696
$861$	3.51558	0.119811
$862$	12.0419	0.410147
$863$	44.3945	1.51121	0.755603	−	0.655030i	$-0.227344\pi$
$863$	44.3945	1.51121	0.755603	+	0.655030i	$0.227344\pi$
$864$	−2.46982	−0.0840251
$865$	15.1585	0.515403
$866$	9.35962	0.318053
$867$	−7.89417	−0.268100
$868$	2.94516	0.0999654
$869$	1.58984	0.0539315
$870$	−2.02787	−0.0687511
$871$	12.7690	0.432659
$872$	−11.1122	−0.376307
$873$	−44.9052	−1.51981
$874$	−1.45098	−0.0490803
$875$	−2.28477	−0.0772393
$876$	0.424375	0.0143383
$877$	35.7208	1.20620	0.603102	−	0.797664i	$-0.293931\pi$
$877$	35.7208	1.20620	0.603102	+	0.797664i	$0.293931\pi$
$878$	−5.04284	−0.170188
$879$	−3.06483	−0.103374
$880$	−1.00000	−0.0337100
$881$	14.9360	0.503208	0.251604	−	0.967830i	$-0.419042\pi$
$881$	14.9360	0.503208	0.251604	+	0.967830i	$0.419042\pi$
$882$	−5.01895	−0.168997
$883$	42.1888	1.41977	0.709884	−	0.704319i	$-0.248747\pi$
$883$	42.1888	1.41977	0.709884	+	0.704319i	$0.248747\pi$
$884$	−17.2589	−0.580479
$885$	0.965502	0.0324550
$886$	−8.85119	−0.297362
$887$	−38.0769	−1.27850	−0.639248	−	0.769001i	$-0.720754\pi$
$887$	−38.0769	−1.27850	−0.639248	+	0.769001i	$0.720754\pi$
$888$	0.456042	0.0153038
$889$	−40.7527	−1.36680
$890$	−1.57853	−0.0529123
$891$	−7.41158	−0.248297
$892$	0.663088	0.0222018
$893$	23.7219	0.793824
$894$	7.52441	0.251654
$895$	12.8544	0.429675
$896$	2.28477	0.0763288
$897$	−0.344645	−0.0115074
$898$	0.163476	0.00545527
$899$	6.15966	0.205436
$900$	−2.81991	−0.0939969
$901$	62.8923	2.09524
$902$	3.62581	0.120726
$903$	8.52162	0.283582
$904$	3.56750	0.118653
$905$	18.1191	0.602300
$906$	−9.99200	−0.331962
$907$	15.2845	0.507515	0.253757	−	0.967268i	$-0.418334\pi$
$907$	15.2845	0.507515	0.253757	+	0.967268i	$0.418334\pi$
$908$	20.9640	0.695715
$909$	51.6101	1.71180
$910$	6.60874	0.219078
$911$	2.72224	0.0901918	0.0450959	−	0.998983i	$-0.485641\pi$
$911$	2.72224	0.0901918	0.0450959	+	0.998983i	$0.485641\pi$
$912$	−2.19315	−0.0726223
$913$	2.44843	0.0810312
$914$	9.38179	0.310322
$915$	4.35956	0.144123
$916$	18.8367	0.622383
$917$	−7.26082	−0.239773
$918$	14.7368	0.486386
$919$	50.8849	1.67854	0.839269	−	0.543716i	$-0.182983\pi$
$919$	50.8849	1.67854	0.839269	+	0.543716i	$0.182983\pi$
$920$	−0.280767	−0.00925660
$921$	−4.17740	−0.137650
$922$	−21.4120	−0.705167
$923$	−45.2005	−1.48779
$924$	−0.969600	−0.0318975
$925$	1.07462	0.0353333
$926$	10.5800	0.347681
$927$	17.4940	0.574579
$928$	4.77848	0.156861
$929$	−43.7131	−1.43418	−0.717090	−	0.696981i	$-0.754526\pi$
$929$	−43.7131	−1.43418	−0.717090	+	0.696981i	$0.754526\pi$
$930$	−0.547038	−0.0179381
$931$	−9.19804	−0.301454
$932$	20.3461	0.666460
$933$	−7.60999	−0.249140
$934$	−25.0705	−0.820332
$935$	5.96673	0.195133
$936$	8.15663	0.266608
$937$	10.0645	0.328792	0.164396	−	0.986394i	$-0.447432\pi$
$937$	10.0645	0.328792	0.164396	+	0.986394i	$0.447432\pi$
$938$	10.0861	0.329321
$939$	9.81190	0.320199
$940$	4.59021	0.149716
$941$	23.5846	0.768836	0.384418	−	0.923159i	$-0.374402\pi$
$941$	23.5846	0.768836	0.384418	+	0.923159i	$0.374402\pi$
$942$	−1.98843	−0.0647866
$943$	1.01801	0.0331508
$944$	−2.27511	−0.0740486
$945$	−5.64298	−0.183566
$946$	8.78880	0.285748
$947$	−25.9174	−0.842201	−0.421100	−	0.907014i	$-0.638356\pi$
$947$	−25.9174	−0.842201	−0.421100	+	0.907014i	$0.638356\pi$
$948$	0.674688	0.0219128
$949$	−2.89252	−0.0938952
$950$	−5.16794	−0.167670
$951$	−6.70285	−0.217355
$952$	−13.6326	−0.441835
$953$	31.5958	1.02349	0.511744	−	0.859138i	$-0.329000\pi$
$953$	31.5958	1.02349	0.511744	+	0.859138i	$0.329000\pi$
$954$	−29.7232	−0.962324
$955$	−15.2365	−0.493042
$956$	−1.47103	−0.0475766
$957$	−2.02787	−0.0655516
$958$	16.8507	0.544422
$959$	14.2337	0.459629
$960$	−0.424375	−0.0136967
$961$	−29.3384	−0.946399
$962$	−3.10836	−0.100218
$963$	11.4017	0.367414
$964$	19.4117	0.625210
$965$	8.00094	0.257559
$966$	−0.272231	−0.00875890
$967$	32.5765	1.04759	0.523795	−	0.851844i	$-0.324516\pi$
$967$	32.5765	1.04759	0.523795	+	0.851844i	$0.324516\pi$
$968$	−1.00000	−0.0321412
$969$	13.0859	0.420380
$970$	−15.9243	−0.511300
$971$	−2.99746	−0.0961929	−0.0480965	−	0.998843i	$-0.515315\pi$
$971$	−2.99746	−0.0961929	−0.0480965	+	0.998843i	$0.515315\pi$
$972$	−10.5548	−0.338544
$973$	1.94413	0.0623258
$974$	−24.7210	−0.792112
$975$	−1.22751	−0.0393119
$976$	−10.2729	−0.328827
$977$	4.61428	0.147624	0.0738119	−	0.997272i	$-0.476484\pi$
$977$	4.61428	0.147624	0.0738119	+	0.997272i	$0.476484\pi$
$978$	6.14517	0.196501
$979$	−1.57853	−0.0504499
$980$	−1.77983	−0.0568545
$981$	−31.3354	−1.00046
$982$	−18.8463	−0.601410
$983$	15.6011	0.497598	0.248799	−	0.968555i	$-0.419964\pi$
$983$	15.6011	0.497598	0.248799	+	0.968555i	$0.419964\pi$
$984$	1.53870	0.0490521
$985$	12.5400	0.399558
$986$	−28.5119	−0.908003
$987$	4.45067	0.141666
$988$	14.9484	0.475571
$989$	2.46760	0.0784651
$990$	−2.81991	−0.0896225
$991$	50.8672	1.61585	0.807924	−	0.589286i	$-0.200591\pi$
$991$	50.8672	1.61585	0.807924	+	0.589286i	$0.200591\pi$
$992$	1.28904	0.0409271
$993$	5.81001	0.184375
$994$	−35.7034	−1.13244
$995$	2.01593	0.0639092
$996$	1.03905	0.0329237
$997$	36.5477	1.15748	0.578738	−	0.815513i	$-0.303545\pi$
$997$	36.5477	1.15748	0.578738	+	0.815513i	$0.303545\pi$
$998$	8.07162	0.255503
$999$	2.65412	0.0839727

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8030.2.a.be.1.7	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8030.2.a.be.1.7	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.424375 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.424375 q^{6} -2.28477 q^{7} -1.00000 q^{8} -2.81991 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.424375 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.424375 q^{6} -2.28477 q^{7} -1.00000 q^{8} -2.81991 q^{9} -1.00000 q^{10} -1.00000 q^{11} -0.424375 q^{12} +2.89252 q^{13} +2.28477 q^{14} -0.424375 q^{15} +1.00000 q^{16} -5.96673 q^{17} +2.81991 q^{18} +5.16794 q^{19} +1.00000 q^{20} +0.969600 q^{21} +1.00000 q^{22} +0.280767 q^{23} +0.424375 q^{24} +1.00000 q^{25} -2.89252 q^{26} +2.46982 q^{27} -2.28477 q^{28} -4.77848 q^{29} +0.424375 q^{30} -1.28904 q^{31} -1.00000 q^{32} +0.424375 q^{33} +5.96673 q^{34} -2.28477 q^{35} -2.81991 q^{36} +1.07462 q^{37} -5.16794 q^{38} -1.22751 q^{39} -1.00000 q^{40} +3.62581 q^{41} -0.969600 q^{42} +8.78880 q^{43} -1.00000 q^{44} -2.81991 q^{45} -0.280767 q^{46} +4.59021 q^{47} -0.424375 q^{48} -1.77983 q^{49} -1.00000 q^{50} +2.53213 q^{51} +2.89252 q^{52} -10.5405 q^{53} -2.46982 q^{54} -1.00000 q^{55} +2.28477 q^{56} -2.19315 q^{57} +4.77848 q^{58} -2.27511 q^{59} -0.424375 q^{60} -10.2729 q^{61} +1.28904 q^{62} +6.44283 q^{63} +1.00000 q^{64} +2.89252 q^{65} -0.424375 q^{66} +4.41447 q^{67} -5.96673 q^{68} -0.119150 q^{69} +2.28477 q^{70} -15.6267 q^{71} +2.81991 q^{72} -1.00000 q^{73} -1.07462 q^{74} -0.424375 q^{75} +5.16794 q^{76} +2.28477 q^{77} +1.22751 q^{78} -1.58984 q^{79} +1.00000 q^{80} +7.41158 q^{81} -3.62581 q^{82} -2.44843 q^{83} +0.969600 q^{84} -5.96673 q^{85} -8.78880 q^{86} +2.02787 q^{87} +1.00000 q^{88} +1.57853 q^{89} +2.81991 q^{90} -6.60874 q^{91} +0.280767 q^{92} +0.547038 q^{93} -4.59021 q^{94} +5.16794 q^{95} +0.424375 q^{96} +15.9243 q^{97} +1.77983 q^{98} +2.81991 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 15 q^{2} + 3 q^{3} + 15 q^{4} + 15 q^{5} - 3 q^{6} + 7 q^{7} - 15 q^{8} + 12 q^{9}+O(q^{10}) \) 15 * q - 15 * q^2 + 3 * q^3 + 15 * q^4 + 15 * q^5 - 3 * q^6 + 7 * q^7 - 15 * q^8 + 12 * q^9	\( 15 q - 15 q^{2} + 3 q^{3} + 15 q^{4} + 15 q^{5} - 3 q^{6} + 7 q^{7} - 15 q^{8} + 12 q^{9} - 15 q^{10} - 15 q^{11} + 3 q^{12} + 13 q^{13} - 7 q^{14} + 3 q^{15} + 15 q^{16} + 20 q^{17} - 12 q^{18} + 3 q^{19} + 15 q^{20} + 22 q^{21} + 15 q^{22} + 2 q^{23} - 3 q^{24} + 15 q^{25} - 13 q^{26} + 33 q^{27} + 7 q^{28} + 11 q^{29} - 3 q^{30} - 3 q^{31} - 15 q^{32} - 3 q^{33} - 20 q^{34} + 7 q^{35} + 12 q^{36} + 9 q^{37} - 3 q^{38} + 11 q^{39} - 15 q^{40} + 17 q^{41} - 22 q^{42} + 29 q^{43} - 15 q^{44} + 12 q^{45} - 2 q^{46} - 2 q^{47} + 3 q^{48} + 20 q^{49} - 15 q^{50} + 7 q^{51} + 13 q^{52} + 3 q^{53} - 33 q^{54} - 15 q^{55} - 7 q^{56} + 13 q^{57} - 11 q^{58} - 32 q^{59} + 3 q^{60} + 61 q^{61} + 3 q^{62} + 20 q^{63} + 15 q^{64} + 13 q^{65} + 3 q^{66} + 7 q^{67} + 20 q^{68} - 23 q^{69} - 7 q^{70} - 6 q^{71} - 12 q^{72} - 15 q^{73} - 9 q^{74} + 3 q^{75} + 3 q^{76} - 7 q^{77} - 11 q^{78} + 12 q^{79} + 15 q^{80} + 3 q^{81} - 17 q^{82} + 17 q^{83} + 22 q^{84} + 20 q^{85} - 29 q^{86} + 23 q^{87} + 15 q^{88} - 18 q^{89} - 12 q^{90} - 15 q^{91} + 2 q^{92} + 32 q^{93} + 2 q^{94} + 3 q^{95} - 3 q^{96} + 36 q^{97} - 20 q^{98} - 12 q^{99}+O(q^{100}) \) 15 * q - 15 * q^2 + 3 * q^3 + 15 * q^4 + 15 * q^5 - 3 * q^6 + 7 * q^7 - 15 * q^8 + 12 * q^9 - 15 * q^10 - 15 * q^11 + 3 * q^12 + 13 * q^13 - 7 * q^14 + 3 * q^15 + 15 * q^16 + 20 * q^17 - 12 * q^18 + 3 * q^19 + 15 * q^20 + 22 * q^21 + 15 * q^22 + 2 * q^23 - 3 * q^24 + 15 * q^25 - 13 * q^26 + 33 * q^27 + 7 * q^28 + 11 * q^29 - 3 * q^30 - 3 * q^31 - 15 * q^32 - 3 * q^33 - 20 * q^34 + 7 * q^35 + 12 * q^36 + 9 * q^37 - 3 * q^38 + 11 * q^39 - 15 * q^40 + 17 * q^41 - 22 * q^42 + 29 * q^43 - 15 * q^44 + 12 * q^45 - 2 * q^46 - 2 * q^47 + 3 * q^48 + 20 * q^49 - 15 * q^50 + 7 * q^51 + 13 * q^52 + 3 * q^53 - 33 * q^54 - 15 * q^55 - 7 * q^56 + 13 * q^57 - 11 * q^58 - 32 * q^59 + 3 * q^60 + 61 * q^61 + 3 * q^62 + 20 * q^63 + 15 * q^64 + 13 * q^65 + 3 * q^66 + 7 * q^67 + 20 * q^68 - 23 * q^69 - 7 * q^70 - 6 * q^71 - 12 * q^72 - 15 * q^73 - 9 * q^74 + 3 * q^75 + 3 * q^76 - 7 * q^77 - 11 * q^78 + 12 * q^79 + 15 * q^80 + 3 * q^81 - 17 * q^82 + 17 * q^83 + 22 * q^84 + 20 * q^85 - 29 * q^86 + 23 * q^87 + 15 * q^88 - 18 * q^89 - 12 * q^90 - 15 * q^91 + 2 * q^92 + 32 * q^93 + 2 * q^94 + 3 * q^95 - 3 * q^96 + 36 * q^97 - 20 * q^98 - 12 * q^99

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