LMFDB - Embedded newform 4030.2.a.q.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4030,2,Mod(1,4030)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4030, 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("4030.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4030 = 2 \cdot 5 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4030.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:	$32.1797120146$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 3x^{8} - 16x^{7} + 48x^{6} + 66x^{5} - 202x^{4} - 75x^{3} + 210x^{2} + 68x - 16 $ x^9 - 3x^8 - 16x^7 + 48x^6 + 66x^5 - 202x^4 - 75x^3 + 210x^2 + 68x - 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$3.41400$ of defining polynomial
Character	$\chi$	$=$	4030.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +3.41400 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.41400 q^{6} +0.254978 q^{7} +1.00000 q^{8} +8.65540 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +3.41400 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.41400 q^{6} +0.254978 q^{7} +1.00000 q^{8} +8.65540 q^{9} -1.00000 q^{10} +0.408580 q^{11} +3.41400 q^{12} +1.00000 q^{13} +0.254978 q^{14} -3.41400 q^{15} +1.00000 q^{16} -4.76009 q^{17} +8.65540 q^{18} +2.53780 q^{19} -1.00000 q^{20} +0.870496 q^{21} +0.408580 q^{22} +0.818634 q^{23} +3.41400 q^{24} +1.00000 q^{25} +1.00000 q^{26} +19.3075 q^{27} +0.254978 q^{28} -2.14816 q^{29} -3.41400 q^{30} +1.00000 q^{31} +1.00000 q^{32} +1.39489 q^{33} -4.76009 q^{34} -0.254978 q^{35} +8.65540 q^{36} -6.80066 q^{37} +2.53780 q^{38} +3.41400 q^{39} -1.00000 q^{40} +10.3853 q^{41} +0.870496 q^{42} -2.30648 q^{43} +0.408580 q^{44} -8.65540 q^{45} +0.818634 q^{46} +10.0436 q^{47} +3.41400 q^{48} -6.93499 q^{49} +1.00000 q^{50} -16.2509 q^{51} +1.00000 q^{52} +7.35099 q^{53} +19.3075 q^{54} -0.408580 q^{55} +0.254978 q^{56} +8.66405 q^{57} -2.14816 q^{58} -9.94392 q^{59} -3.41400 q^{60} +12.2706 q^{61} +1.00000 q^{62} +2.20694 q^{63} +1.00000 q^{64} -1.00000 q^{65} +1.39489 q^{66} -6.70295 q^{67} -4.76009 q^{68} +2.79482 q^{69} -0.254978 q^{70} +3.19469 q^{71} +8.65540 q^{72} +1.60291 q^{73} -6.80066 q^{74} +3.41400 q^{75} +2.53780 q^{76} +0.104179 q^{77} +3.41400 q^{78} +4.49076 q^{79} -1.00000 q^{80} +39.9497 q^{81} +10.3853 q^{82} -16.6175 q^{83} +0.870496 q^{84} +4.76009 q^{85} -2.30648 q^{86} -7.33382 q^{87} +0.408580 q^{88} -15.7653 q^{89} -8.65540 q^{90} +0.254978 q^{91} +0.818634 q^{92} +3.41400 q^{93} +10.0436 q^{94} -2.53780 q^{95} +3.41400 q^{96} -6.74792 q^{97} -6.93499 q^{98} +3.53642 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 9 q^{2} + 3 q^{3} + 9 q^{4} - 9 q^{5} + 3 q^{6} + 3 q^{7} + 9 q^{8} + 14 q^{9}+O(q^{10}) $ 9 * q + 9 * q^2 + 3 * q^3 + 9 * q^4 - 9 * q^5 + 3 * q^6 + 3 * q^7 + 9 * q^8 + 14 * q^9	\( 9 q + 9 q^{2} + 3 q^{3} + 9 q^{4} - 9 q^{5} + 3 q^{6} + 3 q^{7} + 9 q^{8} + 14 q^{9} - 9 q^{10} + 6 q^{11} + 3 q^{12} + 9 q^{13} + 3 q^{14} - 3 q^{15} + 9 q^{16} + 3 q^{17} + 14 q^{18} + 6 q^{19} - 9 q^{20} - q^{21} + 6 q^{22} + 14 q^{23} + 3 q^{24} + 9 q^{25} + 9 q^{26} + 9 q^{27} + 3 q^{28} + 17 q^{29} - 3 q^{30} + 9 q^{31} + 9 q^{32} - 8 q^{33} + 3 q^{34} - 3 q^{35} + 14 q^{36} - 3 q^{37} + 6 q^{38} + 3 q^{39} - 9 q^{40} + 4 q^{41} - q^{42} + 5 q^{43} + 6 q^{44} - 14 q^{45} + 14 q^{46} + 25 q^{47} + 3 q^{48} + 8 q^{49} + 9 q^{50} + 15 q^{51} + 9 q^{52} + 18 q^{53} + 9 q^{54} - 6 q^{55} + 3 q^{56} + 13 q^{57} + 17 q^{58} - 6 q^{59} - 3 q^{60} + 26 q^{61} + 9 q^{62} + 8 q^{63} + 9 q^{64} - 9 q^{65} - 8 q^{66} - 2 q^{67} + 3 q^{68} + 8 q^{69} - 3 q^{70} + 18 q^{71} + 14 q^{72} - 5 q^{73} - 3 q^{74} + 3 q^{75} + 6 q^{76} + 19 q^{77} + 3 q^{78} + 18 q^{79} - 9 q^{80} + 41 q^{81} + 4 q^{82} + 13 q^{83} - q^{84} - 3 q^{85} + 5 q^{86} + 19 q^{87} + 6 q^{88} + 9 q^{89} - 14 q^{90} + 3 q^{91} + 14 q^{92} + 3 q^{93} + 25 q^{94} - 6 q^{95} + 3 q^{96} - 18 q^{97} + 8 q^{98} + 21 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 3 * q^3 + 9 * q^4 - 9 * q^5 + 3 * q^6 + 3 * q^7 + 9 * q^8 + 14 * q^9 - 9 * q^10 + 6 * q^11 + 3 * q^12 + 9 * q^13 + 3 * q^14 - 3 * q^15 + 9 * q^16 + 3 * q^17 + 14 * q^18 + 6 * q^19 - 9 * q^20 - q^21 + 6 * q^22 + 14 * q^23 + 3 * q^24 + 9 * q^25 + 9 * q^26 + 9 * q^27 + 3 * q^28 + 17 * q^29 - 3 * q^30 + 9 * q^31 + 9 * q^32 - 8 * q^33 + 3 * q^34 - 3 * q^35 + 14 * q^36 - 3 * q^37 + 6 * q^38 + 3 * q^39 - 9 * q^40 + 4 * q^41 - q^42 + 5 * q^43 + 6 * q^44 - 14 * q^45 + 14 * q^46 + 25 * q^47 + 3 * q^48 + 8 * q^49 + 9 * q^50 + 15 * q^51 + 9 * q^52 + 18 * q^53 + 9 * q^54 - 6 * q^55 + 3 * q^56 + 13 * q^57 + 17 * q^58 - 6 * q^59 - 3 * q^60 + 26 * q^61 + 9 * q^62 + 8 * q^63 + 9 * q^64 - 9 * q^65 - 8 * q^66 - 2 * q^67 + 3 * q^68 + 8 * q^69 - 3 * q^70 + 18 * q^71 + 14 * q^72 - 5 * q^73 - 3 * q^74 + 3 * q^75 + 6 * q^76 + 19 * q^77 + 3 * q^78 + 18 * q^79 - 9 * q^80 + 41 * q^81 + 4 * q^82 + 13 * q^83 - q^84 - 3 * q^85 + 5 * q^86 + 19 * q^87 + 6 * q^88 + 9 * q^89 - 14 * q^90 + 3 * q^91 + 14 * q^92 + 3 * q^93 + 25 * q^94 - 6 * q^95 + 3 * q^96 - 18 * q^97 + 8 * q^98 + 21 * 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
$3$	3.41400	1.97107	0.985537	−	0.169461i	$-0.0542027\pi$
$3$	3.41400	1.97107	0.985537	+	0.169461i	$0.0542027\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	3.41400	1.39376
$7$	0.254978	0.0963727	0.0481864	−	0.998838i	$-0.484656\pi$
$7$	0.254978	0.0963727	0.0481864	+	0.998838i	$0.484656\pi$
$8$	1.00000	0.353553
$9$	8.65540	2.88513
$10$	−1.00000	−0.316228
$11$	0.408580	0.123192	0.0615958	−	0.998101i	$-0.480381\pi$
$11$	0.408580	0.123192	0.0615958	+	0.998101i	$0.480381\pi$
$12$	3.41400	0.985537
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0.254978	0.0681458
$15$	−3.41400	−0.881491
$16$	1.00000	0.250000
$17$	−4.76009	−1.15449	−0.577246	−	0.816571i	$-0.695872\pi$
$17$	−4.76009	−1.15449	−0.577246	+	0.816571i	$0.695872\pi$
$18$	8.65540	2.04010
$19$	2.53780	0.582211	0.291106	−	0.956691i	$-0.405977\pi$
$19$	2.53780	0.582211	0.291106	+	0.956691i	$0.405977\pi$
$20$	−1.00000	−0.223607
$21$	0.870496	0.189958
$22$	0.408580	0.0871096
$23$	0.818634	0.170697	0.0853485	−	0.996351i	$-0.472800\pi$
$23$	0.818634	0.170697	0.0853485	+	0.996351i	$0.472800\pi$
$24$	3.41400	0.696880
$25$	1.00000	0.200000
$26$	1.00000	0.196116
$27$	19.3075	3.71573
$28$	0.254978	0.0481864
$29$	−2.14816	−0.398904	−0.199452	−	0.979908i	$-0.563916\pi$
$29$	−2.14816	−0.398904	−0.199452	+	0.979908i	$0.563916\pi$
$30$	−3.41400	−0.623308
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	1.00000	0.176777
$33$	1.39489	0.242820
$34$	−4.76009	−0.816349
$35$	−0.254978	−0.0430992
$36$	8.65540	1.44257
$37$	−6.80066	−1.11802	−0.559011	−	0.829160i	$-0.688819\pi$
$37$	−6.80066	−1.11802	−0.559011	+	0.829160i	$0.688819\pi$
$38$	2.53780	0.411686
$39$	3.41400	0.546677
$40$	−1.00000	−0.158114
$41$	10.3853	1.62190	0.810952	−	0.585112i	$-0.198950\pi$
$41$	10.3853	1.62190	0.810952	+	0.585112i	$0.198950\pi$
$42$	0.870496	0.134320
$43$	−2.30648	−0.351735	−0.175868	−	0.984414i	$-0.556273\pi$
$43$	−2.30648	−0.351735	−0.175868	+	0.984414i	$0.556273\pi$
$44$	0.408580	0.0615958
$45$	−8.65540	−1.29027
$46$	0.818634	0.120701
$47$	10.0436	1.46501	0.732507	−	0.680760i	$-0.238350\pi$
$47$	10.0436	1.46501	0.732507	+	0.680760i	$0.238350\pi$
$48$	3.41400	0.492768
$49$	−6.93499	−0.990712
$50$	1.00000	0.141421
$51$	−16.2509	−2.27559
$52$	1.00000	0.138675
$53$	7.35099	1.00974	0.504868	−	0.863196i	$-0.331541\pi$
$53$	7.35099	1.00974	0.504868	+	0.863196i	$0.331541\pi$
$54$	19.3075	2.62742
$55$	−0.408580	−0.0550929
$56$	0.254978	0.0340729
$57$	8.66405	1.14758
$58$	−2.14816	−0.282067
$59$	−9.94392	−1.29459	−0.647294	−	0.762240i	$-0.724099\pi$
$59$	−9.94392	−1.29459	−0.647294	+	0.762240i	$0.724099\pi$
$60$	−3.41400	−0.440745
$61$	12.2706	1.57108	0.785542	−	0.618809i	$-0.212384\pi$
$61$	12.2706	1.57108	0.785542	+	0.618809i	$0.212384\pi$
$62$	1.00000	0.127000
$63$	2.20694	0.278048
$64$	1.00000	0.125000
$65$	−1.00000	−0.124035
$66$	1.39489	0.171699
$67$	−6.70295	−0.818896	−0.409448	−	0.912333i	$-0.634279\pi$
$67$	−6.70295	−0.818896	−0.409448	+	0.912333i	$0.634279\pi$
$68$	−4.76009	−0.577246
$69$	2.79482	0.336456
$70$	−0.254978	−0.0304757
$71$	3.19469	0.379140	0.189570	−	0.981867i	$-0.439291\pi$
$71$	3.19469	0.379140	0.189570	+	0.981867i	$0.439291\pi$
$72$	8.65540	1.02005
$73$	1.60291	0.187607	0.0938034	−	0.995591i	$-0.470097\pi$
$73$	1.60291	0.187607	0.0938034	+	0.995591i	$0.470097\pi$
$74$	−6.80066	−0.790561
$75$	3.41400	0.394215
$76$	2.53780	0.291106
$77$	0.104179	0.0118723
$78$	3.41400	0.386559
$79$	4.49076	0.505250	0.252625	−	0.967564i	$-0.418706\pi$
$79$	4.49076	0.505250	0.252625	+	0.967564i	$0.418706\pi$
$80$	−1.00000	−0.111803
$81$	39.9497	4.43885
$82$	10.3853	1.14686
$83$	−16.6175	−1.82401	−0.912006	−	0.410176i	$-0.865467\pi$
$83$	−16.6175	−1.82401	−0.912006	+	0.410176i	$0.865467\pi$
$84$	0.870496	0.0949789
$85$	4.76009	0.516304
$86$	−2.30648	−0.248714
$87$	−7.33382	−0.786268
$88$	0.408580	0.0435548
$89$	−15.7653	−1.67112	−0.835559	−	0.549401i	$-0.814856\pi$
$89$	−15.7653	−1.67112	−0.835559	+	0.549401i	$0.814856\pi$
$90$	−8.65540	−0.912359
$91$	0.254978	0.0267290
$92$	0.818634	0.0853485
$93$	3.41400	0.354015
$94$	10.0436	1.03592
$95$	−2.53780	−0.260373
$96$	3.41400	0.348440
$97$	−6.74792	−0.685147	−0.342573	−	0.939491i	$-0.611299\pi$
$97$	−6.74792	−0.685147	−0.342573	+	0.939491i	$0.611299\pi$
$98$	−6.93499	−0.700539
$99$	3.53642	0.355424
$100$	1.00000	0.100000
$101$	17.0386	1.69541	0.847703	−	0.530472i	$-0.177985\pi$
$101$	17.0386	1.69541	0.847703	+	0.530472i	$0.177985\pi$
$102$	−16.2509	−1.60908
$103$	4.70454	0.463552	0.231776	−	0.972769i	$-0.425546\pi$
$103$	4.70454	0.463552	0.231776	+	0.972769i	$0.425546\pi$
$104$	1.00000	0.0980581
$105$	−0.870496	−0.0849517
$106$	7.35099	0.713992
$107$	−4.21975	−0.407938	−0.203969	−	0.978977i	$-0.565384\pi$
$107$	−4.21975	−0.407938	−0.203969	+	0.978977i	$0.565384\pi$
$108$	19.3075	1.85787
$109$	−11.2558	−1.07811	−0.539056	−	0.842270i	$-0.681219\pi$
$109$	−11.2558	−1.07811	−0.539056	+	0.842270i	$0.681219\pi$
$110$	−0.408580	−0.0389566
$111$	−23.2175	−2.20370
$112$	0.254978	0.0240932
$113$	−7.63822	−0.718544	−0.359272	−	0.933233i	$-0.616975\pi$
$113$	−7.63822	−0.718544	−0.359272	+	0.933233i	$0.616975\pi$
$114$	8.66405	0.811463
$115$	−0.818634	−0.0763380
$116$	−2.14816	−0.199452
$117$	8.65540	0.800192
$118$	−9.94392	−0.915412
$119$	−1.21372	−0.111261
$120$	−3.41400	−0.311654
$121$	−10.8331	−0.984824
$122$	12.2706	1.11092
$123$	35.4553	3.19689
$124$	1.00000	0.0898027
$125$	−1.00000	−0.0894427
$126$	2.20694	0.196610
$127$	−7.09595	−0.629663	−0.314832	−	0.949148i	$-0.601948\pi$
$127$	−7.09595	−0.629663	−0.314832	+	0.949148i	$0.601948\pi$
$128$	1.00000	0.0883883
$129$	−7.87433	−0.693296
$130$	−1.00000	−0.0877058
$131$	−4.66978	−0.408000	−0.204000	−	0.978971i	$-0.565394\pi$
$131$	−4.66978	−0.408000	−0.204000	+	0.978971i	$0.565394\pi$
$132$	1.39489	0.121410
$133$	0.647084	0.0561093
$134$	−6.70295	−0.579047
$135$	−19.3075	−1.66173
$136$	−4.76009	−0.408174
$137$	−16.8841	−1.44250	−0.721252	−	0.692673i	$-0.756433\pi$
$137$	−16.8841	−1.44250	−0.721252	+	0.692673i	$0.756433\pi$
$138$	2.79482	0.237911
$139$	−4.74625	−0.402572	−0.201286	−	0.979533i	$-0.564512\pi$
$139$	−4.74625	−0.402572	−0.201286	+	0.979533i	$0.564512\pi$
$140$	−0.254978	−0.0215496
$141$	34.2889	2.88765
$142$	3.19469	0.268093
$143$	0.408580	0.0341672
$144$	8.65540	0.721283
$145$	2.14816	0.178395
$146$	1.60291	0.132658
$147$	−23.6760	−1.95277
$148$	−6.80066	−0.559011
$149$	3.49754	0.286530	0.143265	−	0.989684i	$-0.454240\pi$
$149$	3.49754	0.286530	0.143265	+	0.989684i	$0.454240\pi$
$150$	3.41400	0.278752
$151$	−8.88900	−0.723377	−0.361688	−	0.932299i	$-0.617800\pi$
$151$	−8.88900	−0.723377	−0.361688	+	0.932299i	$0.617800\pi$
$152$	2.53780	0.205843
$153$	−41.2005	−3.33086
$154$	0.104179	0.00839499
$155$	−1.00000	−0.0803219
$156$	3.41400	0.273339
$157$	−15.0972	−1.20489	−0.602445	−	0.798160i	$-0.705807\pi$
$157$	−15.0972	−1.20489	−0.602445	+	0.798160i	$0.705807\pi$
$158$	4.49076	0.357266
$159$	25.0963	1.99027
$160$	−1.00000	−0.0790569
$161$	0.208734	0.0164505
$162$	39.9497	3.13874
$163$	−5.36029	−0.419850	−0.209925	−	0.977717i	$-0.567322\pi$
$163$	−5.36029	−0.419850	−0.209925	+	0.977717i	$0.567322\pi$
$164$	10.3853	0.810952
$165$	−1.39489	−0.108592
$166$	−16.6175	−1.28977
$167$	11.8772	0.919089	0.459544	−	0.888155i	$-0.348013\pi$
$167$	11.8772	0.919089	0.459544	+	0.888155i	$0.348013\pi$
$168$	0.870496	0.0671602
$169$	1.00000	0.0769231
$170$	4.76009	0.365082
$171$	21.9657	1.67976
$172$	−2.30648	−0.175868
$173$	−10.5971	−0.805686	−0.402843	−	0.915269i	$-0.631978\pi$
$173$	−10.5971	−0.805686	−0.402843	+	0.915269i	$0.631978\pi$
$174$	−7.33382	−0.555976
$175$	0.254978	0.0192745
$176$	0.408580	0.0307979
$177$	−33.9485	−2.55173
$178$	−15.7653	−1.18166
$179$	18.1936	1.35985	0.679927	−	0.733280i	$-0.262011\pi$
$179$	18.1936	1.35985	0.679927	+	0.733280i	$0.262011\pi$
$180$	−8.65540	−0.645135
$181$	6.96292	0.517550	0.258775	−	0.965938i	$-0.416681\pi$
$181$	6.96292	0.517550	0.258775	+	0.965938i	$0.416681\pi$
$182$	0.254978	0.0189002
$183$	41.8917	3.09672
$184$	0.818634	0.0603505
$185$	6.80066	0.499995
$186$	3.41400	0.250327
$187$	−1.94488	−0.142224
$188$	10.0436	0.732507
$189$	4.92300	0.358095
$190$	−2.53780	−0.184111
$191$	11.5795	0.837864	0.418932	−	0.908018i	$-0.362405\pi$
$191$	11.5795	0.837864	0.418932	+	0.908018i	$0.362405\pi$
$192$	3.41400	0.246384
$193$	−23.6987	−1.70587	−0.852934	−	0.522020i	$-0.825179\pi$
$193$	−23.6987	−1.70587	−0.852934	+	0.522020i	$0.825179\pi$
$194$	−6.74792	−0.484472
$195$	−3.41400	−0.244482
$196$	−6.93499	−0.495356
$197$	12.3060	0.876765	0.438382	−	0.898789i	$-0.355552\pi$
$197$	12.3060	0.876765	0.438382	+	0.898789i	$0.355552\pi$
$198$	3.53642	0.251323
$199$	−19.3168	−1.36933	−0.684666	−	0.728857i	$-0.740052\pi$
$199$	−19.3168	−1.36933	−0.684666	+	0.728857i	$0.740052\pi$
$200$	1.00000	0.0707107
$201$	−22.8839	−1.61410
$202$	17.0386	1.19883
$203$	−0.547734	−0.0384434
$204$	−16.2509	−1.13779
$205$	−10.3853	−0.725338
$206$	4.70454	0.327781
$207$	7.08560	0.492483
$208$	1.00000	0.0693375
$209$	1.03690	0.0717236
$210$	−0.870496	−0.0600699
$211$	−9.09477	−0.626110	−0.313055	−	0.949735i	$-0.601352\pi$
$211$	−9.09477	−0.626110	−0.313055	+	0.949735i	$0.601352\pi$
$212$	7.35099	0.504868
$213$	10.9067	0.747313
$214$	−4.21975	−0.288456
$215$	2.30648	0.157301
$216$	19.3075	1.31371
$217$	0.254978	0.0173090
$218$	−11.2558	−0.762341
$219$	5.47235	0.369787
$220$	−0.408580	−0.0275465
$221$	−4.76009	−0.320198
$222$	−23.2175	−1.55825
$223$	−15.7142	−1.05230	−0.526149	−	0.850392i	$-0.676365\pi$
$223$	−15.7142	−1.05230	−0.526149	+	0.850392i	$0.676365\pi$
$224$	0.254978	0.0170364
$225$	8.65540	0.577026
$226$	−7.63822	−0.508087
$227$	23.4330	1.55530	0.777651	−	0.628696i	$-0.216411\pi$
$227$	23.4330	1.55530	0.777651	+	0.628696i	$0.216411\pi$
$228$	8.66405	0.573791
$229$	26.5167	1.75227	0.876135	−	0.482066i	$-0.160114\pi$
$229$	26.5167	1.75227	0.876135	+	0.482066i	$0.160114\pi$
$230$	−0.818634	−0.0539791
$231$	0.355667	0.0234012
$232$	−2.14816	−0.141034
$233$	24.6168	1.61270	0.806351	−	0.591437i	$-0.201439\pi$
$233$	24.6168	1.61270	0.806351	+	0.591437i	$0.201439\pi$
$234$	8.65540	0.565821
$235$	−10.0436	−0.655174
$236$	−9.94392	−0.647294
$237$	15.3314	0.995884
$238$	−1.21372	−0.0786737
$239$	−8.67546	−0.561169	−0.280584	−	0.959829i	$-0.590528\pi$
$239$	−8.67546	−0.561169	−0.280584	+	0.959829i	$0.590528\pi$
$240$	−3.41400	−0.220373
$241$	7.90914	0.509473	0.254736	−	0.967011i	$-0.418011\pi$
$241$	7.90914	0.509473	0.254736	+	0.967011i	$0.418011\pi$
$242$	−10.8331	−0.696376
$243$	78.4657	5.03357
$244$	12.2706	0.785542
$245$	6.93499	0.443060
$246$	35.4553	2.26055
$247$	2.53780	0.161476
$248$	1.00000	0.0635001
$249$	−56.7323	−3.59526
$250$	−1.00000	−0.0632456
$251$	11.8752	0.749558	0.374779	−	0.927114i	$-0.377719\pi$
$251$	11.8752	0.749558	0.374779	+	0.927114i	$0.377719\pi$
$252$	2.20694	0.139024
$253$	0.334478	0.0210284
$254$	−7.09595	−0.445239
$255$	16.2509	1.01767
$256$	1.00000	0.0625000
$257$	7.69737	0.480149	0.240074	−	0.970755i	$-0.422828\pi$
$257$	7.69737	0.480149	0.240074	+	0.970755i	$0.422828\pi$
$258$	−7.87433	−0.490234
$259$	−1.73402	−0.107747
$260$	−1.00000	−0.0620174
$261$	−18.5932	−1.15089
$262$	−4.66978	−0.288500
$263$	4.77495	0.294436	0.147218	−	0.989104i	$-0.452968\pi$
$263$	4.77495	0.294436	0.147218	+	0.989104i	$0.452968\pi$
$264$	1.39489	0.0858497
$265$	−7.35099	−0.451568
$266$	0.647084	0.0396753
$267$	−53.8227	−3.29390
$268$	−6.70295	−0.409448
$269$	29.8105	1.81758	0.908790	−	0.417255i	$-0.137008\pi$
$269$	29.8105	1.81758	0.908790	+	0.417255i	$0.137008\pi$
$270$	−19.3075	−1.17502
$271$	27.7938	1.68835	0.844177	−	0.536064i	$-0.180090\pi$
$271$	27.7938	1.68835	0.844177	+	0.536064i	$0.180090\pi$
$272$	−4.76009	−0.288623
$273$	0.870496	0.0526848
$274$	−16.8841	−1.02000
$275$	0.408580	0.0246383
$276$	2.79482	0.168228
$277$	10.1985	0.612770	0.306385	−	0.951908i	$-0.400880\pi$
$277$	10.1985	0.612770	0.306385	+	0.951908i	$0.400880\pi$
$278$	−4.74625	−0.284661
$279$	8.65540	0.518185
$280$	−0.254978	−0.0152379
$281$	−21.9154	−1.30736	−0.653681	−	0.756771i	$-0.726776\pi$
$281$	−21.9154	−1.30736	−0.653681	+	0.756771i	$0.726776\pi$
$282$	34.2889	2.04188
$283$	−17.9772	−1.06863	−0.534317	−	0.845284i	$-0.679431\pi$
$283$	−17.9772	−1.06863	−0.534317	+	0.845284i	$0.679431\pi$
$284$	3.19469	0.189570
$285$	−8.66405	−0.513214
$286$	0.408580	0.0241599
$287$	2.64801	0.156307
$288$	8.65540	0.510024
$289$	5.65845	0.332850
$290$	2.14816	0.126144
$291$	−23.0374	−1.35048
$292$	1.60291	0.0938034
$293$	−16.9191	−0.988426	−0.494213	−	0.869341i	$-0.664544\pi$
$293$	−16.9191	−0.988426	−0.494213	+	0.869341i	$0.664544\pi$
$294$	−23.6760	−1.38081
$295$	9.94392	0.578957
$296$	−6.80066	−0.395281
$297$	7.88867	0.457747
$298$	3.49754	0.202607
$299$	0.818634	0.0473428
$300$	3.41400	0.197107
$301$	−0.588103	−0.0338977
$302$	−8.88900	−0.511505
$303$	58.1698	3.34177
$304$	2.53780	0.145553
$305$	−12.2706	−0.702610
$306$	−41.2005	−2.35527
$307$	−9.63962	−0.550162	−0.275081	−	0.961421i	$-0.588705\pi$
$307$	−9.63962	−0.550162	−0.275081	+	0.961421i	$0.588705\pi$
$308$	0.104179	0.00593615
$309$	16.0613	0.913695
$310$	−1.00000	−0.0567962
$311$	−13.0402	−0.739444	−0.369722	−	0.929142i	$-0.620547\pi$
$311$	−13.0402	−0.739444	−0.369722	+	0.929142i	$0.620547\pi$
$312$	3.41400	0.193280
$313$	17.6463	0.997425	0.498713	−	0.866767i	$-0.333806\pi$
$313$	17.6463	0.997425	0.498713	+	0.866767i	$0.333806\pi$
$314$	−15.0972	−0.851987
$315$	−2.20694	−0.124347
$316$	4.49076	0.252625
$317$	−18.5074	−1.03948	−0.519740	−	0.854325i	$-0.673971\pi$
$317$	−18.5074	−1.03948	−0.519740	+	0.854325i	$0.673971\pi$
$318$	25.0963	1.40733
$319$	−0.877696	−0.0491416
$320$	−1.00000	−0.0559017
$321$	−14.4062	−0.804076
$322$	0.208734	0.0116323
$323$	−12.0802	−0.672158
$324$	39.9497	2.21943
$325$	1.00000	0.0554700
$326$	−5.36029	−0.296879
$327$	−38.4274	−2.12504
$328$	10.3853	0.573430
$329$	2.56091	0.141187
$330$	−1.39489	−0.0767863
$331$	−10.2077	−0.561067	−0.280534	−	0.959844i	$-0.590511\pi$
$331$	−10.2077	−0.561067	−0.280534	+	0.959844i	$0.590511\pi$
$332$	−16.6175	−0.912006
$333$	−58.8624	−3.22564
$334$	11.8772	0.649894
$335$	6.70295	0.366221
$336$	0.870496	0.0474894
$337$	−13.8709	−0.755595	−0.377797	−	0.925888i	$-0.623318\pi$
$337$	−13.8709	−0.755595	−0.377797	+	0.925888i	$0.623318\pi$
$338$	1.00000	0.0543928
$339$	−26.0769	−1.41630
$340$	4.76009	0.258152
$341$	0.408580	0.0221259
$342$	21.9657	1.18777
$343$	−3.55312	−0.191850
$344$	−2.30648	−0.124357
$345$	−2.79482	−0.150468
$346$	−10.5971	−0.569706
$347$	−25.0355	−1.34397	−0.671987	−	0.740563i	$-0.734559\pi$
$347$	−25.0355	−1.34397	−0.671987	+	0.740563i	$0.734559\pi$
$348$	−7.33382	−0.393134
$349$	−19.3382	−1.03515	−0.517574	−	0.855638i	$-0.673165\pi$
$349$	−19.3382	−1.03515	−0.517574	+	0.855638i	$0.673165\pi$
$350$	0.254978	0.0136292
$351$	19.3075	1.03056
$352$	0.408580	0.0217774
$353$	31.7916	1.69210	0.846049	−	0.533105i	$-0.178975\pi$
$353$	31.7916	1.69210	0.846049	+	0.533105i	$0.178975\pi$
$354$	−33.9485	−1.80434
$355$	−3.19469	−0.169557
$356$	−15.7653	−0.835559
$357$	−4.14364	−0.219305
$358$	18.1936	0.961562
$359$	7.80062	0.411701	0.205851	−	0.978583i	$-0.434004\pi$
$359$	7.80062	0.411701	0.205851	+	0.978583i	$0.434004\pi$
$360$	−8.65540	−0.456179
$361$	−12.5596	−0.661030
$362$	6.96292	0.365963
$363$	−36.9841	−1.94116
$364$	0.254978	0.0133645
$365$	−1.60291	−0.0839003
$366$	41.8917	2.18971
$367$	−19.3865	−1.01197	−0.505983	−	0.862543i	$-0.668870\pi$
$367$	−19.3865	−1.01197	−0.505983	+	0.862543i	$0.668870\pi$
$368$	0.818634	0.0426742
$369$	89.8885	4.67941
$370$	6.80066	0.353550
$371$	1.87434	0.0973111
$372$	3.41400	0.177008
$373$	21.5533	1.11599	0.557993	−	0.829846i	$-0.311572\pi$
$373$	21.5533	1.11599	0.557993	+	0.829846i	$0.311572\pi$
$374$	−1.94488	−0.100567
$375$	−3.41400	−0.176298
$376$	10.0436	0.517960
$377$	−2.14816	−0.110636
$378$	4.92300	0.253212
$379$	−14.9922	−0.770099	−0.385050	−	0.922896i	$-0.625816\pi$
$379$	−14.9922	−0.770099	−0.385050	+	0.922896i	$0.625816\pi$
$380$	−2.53780	−0.130186
$381$	−24.2256	−1.24111
$382$	11.5795	0.592459
$383$	−17.9523	−0.917321	−0.458661	−	0.888612i	$-0.651671\pi$
$383$	−17.9523	−0.917321	−0.458661	+	0.888612i	$0.651671\pi$
$384$	3.41400	0.174220
$385$	−0.104179	−0.00530946
$386$	−23.6987	−1.20623
$387$	−19.9635	−1.01480
$388$	−6.74792	−0.342573
$389$	0.223357	0.0113247	0.00566233	−	0.999984i	$-0.498198\pi$
$389$	0.223357	0.0113247	0.00566233	+	0.999984i	$0.498198\pi$
$390$	−3.41400	−0.172875
$391$	−3.89677	−0.197068
$392$	−6.93499	−0.350270
$393$	−15.9426	−0.804199
$394$	12.3060	0.619966
$395$	−4.49076	−0.225955
$396$	3.53642	0.177712
$397$	−31.7829	−1.59514	−0.797569	−	0.603228i	$-0.793881\pi$
$397$	−31.7829	−1.59514	−0.797569	+	0.603228i	$0.793881\pi$
$398$	−19.3168	−0.968264
$399$	2.20914	0.110596
$400$	1.00000	0.0500000
$401$	9.90413	0.494589	0.247294	−	0.968940i	$-0.420459\pi$
$401$	9.90413	0.494589	0.247294	+	0.968940i	$0.420459\pi$
$402$	−22.8839	−1.14134
$403$	1.00000	0.0498135
$404$	17.0386	0.847703
$405$	−39.9497	−1.98512
$406$	−0.547734	−0.0271836
$407$	−2.77862	−0.137731
$408$	−16.2509	−0.804542
$409$	10.8960	0.538772	0.269386	−	0.963032i	$-0.413179\pi$
$409$	10.8960	0.538772	0.269386	+	0.963032i	$0.413179\pi$
$410$	−10.3853	−0.512891
$411$	−57.6422	−2.84328
$412$	4.70454	0.231776
$413$	−2.53548	−0.124763
$414$	7.08560	0.348238
$415$	16.6175	0.815723
$416$	1.00000	0.0490290
$417$	−16.2037	−0.793499
$418$	1.03690	0.0507162
$419$	−4.24675	−0.207467	−0.103734	−	0.994605i	$-0.533079\pi$
$419$	−4.24675	−0.207467	−0.103734	+	0.994605i	$0.533079\pi$
$420$	−0.870496	−0.0424758
$421$	17.1635	0.836498	0.418249	−	0.908332i	$-0.362644\pi$
$421$	17.1635	0.836498	0.418249	+	0.908332i	$0.362644\pi$
$422$	−9.09477	−0.442727
$423$	86.9315	4.22676
$424$	7.35099	0.356996
$425$	−4.76009	−0.230898
$426$	10.9067	0.528430
$427$	3.12872	0.151410
$428$	−4.21975	−0.203969
$429$	1.39489	0.0673461
$430$	2.30648	0.111228
$431$	−28.0157	−1.34947	−0.674735	−	0.738060i	$-0.735742\pi$
$431$	−28.0157	−1.34947	−0.674735	+	0.738060i	$0.735742\pi$
$432$	19.3075	0.928933
$433$	33.8984	1.62906	0.814528	−	0.580125i	$-0.196996\pi$
$433$	33.8984	1.62906	0.814528	+	0.580125i	$0.196996\pi$
$434$	0.254978	0.0122393
$435$	7.33382	0.351630
$436$	−11.2558	−0.539056
$437$	2.07753	0.0993817
$438$	5.47235	0.261479
$439$	−26.8620	−1.28205	−0.641026	−	0.767519i	$-0.721491\pi$
$439$	−26.8620	−1.28205	−0.641026	+	0.767519i	$0.721491\pi$
$440$	−0.408580	−0.0194783
$441$	−60.0250	−2.85834
$442$	−4.76009	−0.226414
$443$	23.3086	1.10743	0.553713	−	0.832707i	$-0.313210\pi$
$443$	23.3086	1.10743	0.553713	+	0.832707i	$0.313210\pi$
$444$	−23.2175	−1.10185
$445$	15.7653	0.747346
$446$	−15.7142	−0.744087
$447$	11.9406	0.564772
$448$	0.254978	0.0120466
$449$	−13.7087	−0.646956	−0.323478	−	0.946236i	$-0.604852\pi$
$449$	−13.7087	−0.646956	−0.323478	+	0.946236i	$0.604852\pi$
$450$	8.65540	0.408019
$451$	4.24321	0.199805
$452$	−7.63822	−0.359272
$453$	−30.3470	−1.42583
$454$	23.4330	1.09976
$455$	−0.254978	−0.0119536
$456$	8.66405	0.405731
$457$	−12.9520	−0.605870	−0.302935	−	0.953011i	$-0.597966\pi$
$457$	−12.9520	−0.605870	−0.302935	+	0.953011i	$0.597966\pi$
$458$	26.5167	1.23904
$459$	−91.9055	−4.28978
$460$	−0.818634	−0.0381690
$461$	−16.5287	−0.769820	−0.384910	−	0.922954i	$-0.625768\pi$
$461$	−16.5287	−0.769820	−0.384910	+	0.922954i	$0.625768\pi$
$462$	0.355667	0.0165471
$463$	5.36923	0.249529	0.124765	−	0.992186i	$-0.460182\pi$
$463$	5.36923	0.249529	0.124765	+	0.992186i	$0.460182\pi$
$464$	−2.14816	−0.0997259
$465$	−3.41400	−0.158320
$466$	24.6168	1.14035
$467$	−7.99331	−0.369886	−0.184943	−	0.982749i	$-0.559210\pi$
$467$	−7.99331	−0.369886	−0.184943	+	0.982749i	$0.559210\pi$
$468$	8.65540	0.400096
$469$	−1.70911	−0.0789192
$470$	−10.0436	−0.463278
$471$	−51.5420	−2.37493
$472$	−9.94392	−0.457706
$473$	−0.942383	−0.0433308
$474$	15.3314	0.704197
$475$	2.53780	0.116442
$476$	−1.21372	−0.0556307
$477$	63.6258	2.91322
$478$	−8.67546	−0.396806
$479$	−36.4198	−1.66406	−0.832031	−	0.554729i	$-0.812822\pi$
$479$	−36.4198	−1.66406	−0.832031	+	0.554729i	$0.812822\pi$
$480$	−3.41400	−0.155827
$481$	−6.80066	−0.310084
$482$	7.90914	0.360251
$483$	0.712617	0.0324252
$484$	−10.8331	−0.492412
$485$	6.74792	0.306407
$486$	78.4657	3.55927
$487$	39.4871	1.78933	0.894665	−	0.446738i	$-0.147415\pi$
$487$	39.4871	1.78933	0.894665	+	0.446738i	$0.147415\pi$
$488$	12.2706	0.555462
$489$	−18.3000	−0.827556
$490$	6.93499	0.313291
$491$	−0.336368	−0.0151801	−0.00759005	−	0.999971i	$-0.502416\pi$
$491$	−0.336368	−0.0151801	−0.00759005	+	0.999971i	$0.502416\pi$
$492$	35.4553	1.59845
$493$	10.2254	0.460531
$494$	2.53780	0.114181
$495$	−3.53642	−0.158950
$496$	1.00000	0.0449013
$497$	0.814577	0.0365388
$498$	−56.7323	−2.54223
$499$	−17.9413	−0.803162	−0.401581	−	0.915824i	$-0.631539\pi$
$499$	−17.9413	−0.803162	−0.401581	+	0.915824i	$0.631539\pi$
$500$	−1.00000	−0.0447214
$501$	40.5489	1.81159
$502$	11.8752	0.530017
$503$	6.97265	0.310895	0.155447	−	0.987844i	$-0.450318\pi$
$503$	6.97265	0.310895	0.155447	+	0.987844i	$0.450318\pi$
$504$	2.20694	0.0983048
$505$	−17.0386	−0.758208
$506$	0.334478	0.0148693
$507$	3.41400	0.151621
$508$	−7.09595	−0.314832
$509$	−9.08267	−0.402582	−0.201291	−	0.979531i	$-0.564514\pi$
$509$	−9.08267	−0.402582	−0.201291	+	0.979531i	$0.564514\pi$
$510$	16.2509	0.719604
$511$	0.408708	0.0180802
$512$	1.00000	0.0441942
$513$	48.9986	2.16334
$514$	7.69737	0.339516
$515$	−4.70454	−0.207307
$516$	−7.87433	−0.346648
$517$	4.10363	0.180477
$518$	−1.73402	−0.0761885
$519$	−36.1787	−1.58807
$520$	−1.00000	−0.0438529
$521$	18.2180	0.798147	0.399073	−	0.916919i	$-0.369332\pi$
$521$	18.2180	0.798147	0.399073	+	0.916919i	$0.369332\pi$
$522$	−18.5932	−0.813802
$523$	−15.9837	−0.698921	−0.349460	−	0.936951i	$-0.613635\pi$
$523$	−15.9837	−0.698921	−0.349460	+	0.936951i	$0.613635\pi$
$524$	−4.66978	−0.204000
$525$	0.870496	0.0379915
$526$	4.77495	0.208198
$527$	−4.76009	−0.207353
$528$	1.39489	0.0607049
$529$	−22.3298	−0.970863
$530$	−7.35099	−0.319307
$531$	−86.0686	−3.73506
$532$	0.647084	0.0280546
$533$	10.3853	0.449835
$534$	−53.8227	−2.32914
$535$	4.21975	0.182436
$536$	−6.70295	−0.289523
$537$	62.1130	2.68037
$538$	29.8105	1.28522
$539$	−2.83350	−0.122047
$540$	−19.3075	−0.830863
$541$	31.3724	1.34881	0.674403	−	0.738364i	$-0.264401\pi$
$541$	31.3724	1.34881	0.674403	+	0.738364i	$0.264401\pi$
$542$	27.7938	1.19385
$543$	23.7714	1.02013
$544$	−4.76009	−0.204087
$545$	11.2558	0.482147
$546$	0.870496	0.0372538
$547$	13.1778	0.563442	0.281721	−	0.959496i	$-0.409095\pi$
$547$	13.1778	0.563442	0.281721	+	0.959496i	$0.409095\pi$
$548$	−16.8841	−0.721252
$549$	106.207	4.53278
$550$	0.408580	0.0174219
$551$	−5.45161	−0.232246
$552$	2.79482	0.118955
$553$	1.14505	0.0486923
$554$	10.1985	0.433294
$555$	23.2175	0.985526
$556$	−4.74625	−0.201286
$557$	11.4136	0.483609	0.241805	−	0.970325i	$-0.422261\pi$
$557$	11.4136	0.483609	0.241805	+	0.970325i	$0.422261\pi$
$558$	8.65540	0.366412
$559$	−2.30648	−0.0975538
$560$	−0.254978	−0.0107748
$561$	−6.63981	−0.280333
$562$	−21.9154	−0.924444
$563$	9.57743	0.403641	0.201820	−	0.979423i	$-0.435314\pi$
$563$	9.57743	0.403641	0.201820	+	0.979423i	$0.435314\pi$
$564$	34.2889	1.44382
$565$	7.63822	0.321342
$566$	−17.9772	−0.755638
$567$	10.1863	0.427784
$568$	3.19469	0.134046
$569$	7.53080	0.315707	0.157854	−	0.987463i	$-0.449543\pi$
$569$	7.53080	0.315707	0.157854	+	0.987463i	$0.449543\pi$
$570$	−8.66405	−0.362897
$571$	36.1618	1.51332	0.756662	−	0.653807i	$-0.226829\pi$
$571$	36.1618	1.51332	0.756662	+	0.653807i	$0.226829\pi$
$572$	0.408580	0.0170836
$573$	39.5324	1.65149
$574$	2.64801	0.110526
$575$	0.818634	0.0341394
$576$	8.65540	0.360641
$577$	−19.1150	−0.795768	−0.397884	−	0.917436i	$-0.630255\pi$
$577$	−19.1150	−0.795768	−0.397884	+	0.917436i	$0.630255\pi$
$578$	5.65845	0.235361
$579$	−80.9072	−3.36239
$580$	2.14816	0.0891975
$581$	−4.23711	−0.175785
$582$	−23.0374	−0.954930
$583$	3.00347	0.124391
$584$	1.60291	0.0663290
$585$	−8.65540	−0.357857
$586$	−16.9191	−0.698923
$587$	−27.2589	−1.12509	−0.562547	−	0.826765i	$-0.690178\pi$
$587$	−27.2589	−1.12509	−0.562547	+	0.826765i	$0.690178\pi$
$588$	−23.6760	−0.976384
$589$	2.53780	0.104568
$590$	9.94392	0.409385
$591$	42.0126	1.72817
$592$	−6.80066	−0.279506
$593$	−25.5212	−1.04803	−0.524016	−	0.851709i	$-0.675567\pi$
$593$	−25.5212	−1.04803	−0.524016	+	0.851709i	$0.675567\pi$
$594$	7.88867	0.323676
$595$	1.21372	0.0497576
$596$	3.49754	0.143265
$597$	−65.9476	−2.69906
$598$	0.818634	0.0334764
$599$	−9.48979	−0.387742	−0.193871	−	0.981027i	$-0.562104\pi$
$599$	−9.48979	−0.387742	−0.193871	+	0.981027i	$0.562104\pi$
$600$	3.41400	0.139376
$601$	−30.2241	−1.23287	−0.616433	−	0.787407i	$-0.711423\pi$
$601$	−30.2241	−1.23287	−0.616433	+	0.787407i	$0.711423\pi$
$602$	−0.588103	−0.0239693
$603$	−58.0167	−2.36262
$604$	−8.88900	−0.361688
$605$	10.8331	0.440427
$606$	58.1698	2.36299
$607$	32.4546	1.31729	0.658646	−	0.752453i	$-0.271130\pi$
$607$	32.4546	1.31729	0.658646	+	0.752453i	$0.271130\pi$
$608$	2.53780	0.102921
$609$	−1.86996	−0.0757748
$610$	−12.2706	−0.496820
$611$	10.0436	0.406322
$612$	−41.2005	−1.66543
$613$	−6.15743	−0.248696	−0.124348	−	0.992239i	$-0.539684\pi$
$613$	−6.15743	−0.248696	−0.124348	+	0.992239i	$0.539684\pi$
$614$	−9.63962	−0.389024
$615$	−35.4553	−1.42969
$616$	0.104179	0.00419749
$617$	13.0641	0.525943	0.262971	−	0.964804i	$-0.415298\pi$
$617$	13.0641	0.525943	0.262971	+	0.964804i	$0.415298\pi$
$618$	16.0613	0.646080
$619$	−25.8162	−1.03764	−0.518820	−	0.854883i	$-0.673629\pi$
$619$	−25.8162	−1.03764	−0.518820	+	0.854883i	$0.673629\pi$
$620$	−1.00000	−0.0401610
$621$	15.8058	0.634264
$622$	−13.0402	−0.522866
$623$	−4.01981	−0.161050
$624$	3.41400	0.136669
$625$	1.00000	0.0400000
$626$	17.6463	0.705286
$627$	3.53996	0.141372
$628$	−15.0972	−0.602445
$629$	32.3718	1.29075
$630$	−2.20694	−0.0879265
$631$	−8.91827	−0.355031	−0.177515	−	0.984118i	$-0.556806\pi$
$631$	−8.91827	−0.355031	−0.177515	+	0.984118i	$0.556806\pi$
$632$	4.49076	0.178633
$633$	−31.0496	−1.23411
$634$	−18.5074	−0.735023
$635$	7.09595	0.281594
$636$	25.0963	0.995133
$637$	−6.93499	−0.274774
$638$	−0.877696	−0.0347483
$639$	27.6513	1.09387
$640$	−1.00000	−0.0395285
$641$	10.5261	0.415758	0.207879	−	0.978155i	$-0.433344\pi$
$641$	10.5261	0.415758	0.207879	+	0.978155i	$0.433344\pi$
$642$	−14.4062	−0.568568
$643$	23.3734	0.921758	0.460879	−	0.887463i	$-0.347534\pi$
$643$	23.3734	0.921758	0.460879	+	0.887463i	$0.347534\pi$
$644$	0.208734	0.00822526
$645$	7.87433	0.310051
$646$	−12.0802	−0.475288
$647$	−17.8055	−0.700006	−0.350003	−	0.936749i	$-0.613819\pi$
$647$	−17.8055	−0.700006	−0.350003	+	0.936749i	$0.613819\pi$
$648$	39.9497	1.56937
$649$	−4.06289	−0.159482
$650$	1.00000	0.0392232
$651$	0.870496	0.0341174
$652$	−5.36029	−0.209925
$653$	13.7236	0.537046	0.268523	−	0.963273i	$-0.413464\pi$
$653$	13.7236	0.537046	0.268523	+	0.963273i	$0.413464\pi$
$654$	−38.4274	−1.50263
$655$	4.66978	0.182463
$656$	10.3853	0.405476
$657$	13.8739	0.541271
$658$	2.56091	0.0998345
$659$	35.8716	1.39736	0.698679	−	0.715436i	$-0.253772\pi$
$659$	35.8716	1.39736	0.698679	+	0.715436i	$0.253772\pi$
$660$	−1.39489	−0.0542961
$661$	−28.2189	−1.09759	−0.548795	−	0.835957i	$-0.684913\pi$
$661$	−28.2189	−1.09759	−0.548795	+	0.835957i	$0.684913\pi$
$662$	−10.2077	−0.396734
$663$	−16.2509	−0.631134
$664$	−16.6175	−0.644886
$665$	−0.647084	−0.0250928
$666$	−58.8624	−2.28087
$667$	−1.75856	−0.0680916
$668$	11.8772	0.459544
$669$	−53.6482	−2.07416
$670$	6.70295	0.258958
$671$	5.01351	0.193544
$672$	0.870496	0.0335801
$673$	35.4331	1.36584	0.682922	−	0.730491i	$-0.260709\pi$
$673$	35.4331	1.36584	0.682922	+	0.730491i	$0.260709\pi$
$674$	−13.8709	−0.534286
$675$	19.3075	0.743147
$676$	1.00000	0.0384615
$677$	50.4007	1.93705	0.968527	−	0.248907i	$-0.0800715\pi$
$677$	50.4007	1.93705	0.968527	+	0.248907i	$0.0800715\pi$
$678$	−26.0769	−1.00148
$679$	−1.72057	−0.0660295
$680$	4.76009	0.182541
$681$	80.0002	3.06561
$682$	0.408580	0.0156453
$683$	28.4748	1.08956	0.544780	−	0.838579i	$-0.316613\pi$
$683$	28.4748	1.08956	0.544780	+	0.838579i	$0.316613\pi$
$684$	21.9657	0.839878
$685$	16.8841	0.645107
$686$	−3.55312	−0.135659
$687$	90.5278	3.45385
$688$	−2.30648	−0.0879338
$689$	7.35099	0.280051
$690$	−2.79482	−0.106397
$691$	−26.0959	−0.992735	−0.496368	−	0.868112i	$-0.665333\pi$
$691$	−26.0959	−0.992735	−0.496368	+	0.868112i	$0.665333\pi$
$692$	−10.5971	−0.402843
$693$	0.901711	0.0342532
$694$	−25.0355	−0.950333
$695$	4.74625	0.180036
$696$	−7.33382	−0.277988
$697$	−49.4347	−1.87247
$698$	−19.3382	−0.731961
$699$	84.0419	3.17876
$700$	0.254978	0.00963727
$701$	−15.3529	−0.579870	−0.289935	−	0.957046i	$-0.593634\pi$
$701$	−15.3529	−0.579870	−0.289935	+	0.957046i	$0.593634\pi$
$702$	19.3075	0.728715
$703$	−17.2587	−0.650925
$704$	0.408580	0.0153989
$705$	−34.2889	−1.29140
$706$	31.7916	1.19649
$707$	4.34447	0.163391
$708$	−33.9485	−1.27586
$709$	21.4270	0.804707	0.402354	−	0.915484i	$-0.368192\pi$
$709$	21.4270	0.804707	0.402354	+	0.915484i	$0.368192\pi$
$710$	−3.19469	−0.119895
$711$	38.8693	1.45771
$712$	−15.7653	−0.590829
$713$	0.818634	0.0306581
$714$	−4.14364	−0.155072
$715$	−0.408580	−0.0152800
$716$	18.1936	0.679927
$717$	−29.6180	−1.10610
$718$	7.80062	0.291117
$719$	9.54254	0.355877	0.177938	−	0.984042i	$-0.443057\pi$
$719$	9.54254	0.355877	0.177938	+	0.984042i	$0.443057\pi$
$720$	−8.65540	−0.322568
$721$	1.19955	0.0446737
$722$	−12.5596	−0.467419
$723$	27.0018	1.00421
$724$	6.96292	0.258775
$725$	−2.14816	−0.0797807
$726$	−36.9841	−1.37261
$727$	16.8234	0.623946	0.311973	−	0.950091i	$-0.399010\pi$
$727$	16.8234	0.623946	0.311973	+	0.950091i	$0.399010\pi$
$728$	0.254978	0.00945012
$729$	148.033	5.48269
$730$	−1.60291	−0.0593265
$731$	10.9791	0.406075
$732$	41.8917	1.54836
$733$	−18.4233	−0.680481	−0.340240	−	0.940338i	$-0.610508\pi$
$733$	−18.4233	−0.680481	−0.340240	+	0.940338i	$0.610508\pi$
$734$	−19.3865	−0.715569
$735$	23.6760	0.873304
$736$	0.818634	0.0301752
$737$	−2.73869	−0.100881
$738$	89.8885	3.30884
$739$	37.2352	1.36972	0.684860	−	0.728674i	$-0.259863\pi$
$739$	37.2352	1.36972	0.684860	+	0.728674i	$0.259863\pi$
$740$	6.80066	0.249997
$741$	8.66405	0.318282
$742$	1.87434	0.0688093
$743$	13.6396	0.500390	0.250195	−	0.968195i	$-0.419505\pi$
$743$	13.6396	0.500390	0.250195	+	0.968195i	$0.419505\pi$
$744$	3.41400	0.125163
$745$	−3.49754	−0.128140
$746$	21.5533	0.789121
$747$	−143.831	−5.26252
$748$	−1.94488	−0.0711118
$749$	−1.07594	−0.0393141
$750$	−3.41400	−0.124662
$751$	−20.1305	−0.734574	−0.367287	−	0.930108i	$-0.619713\pi$
$751$	−20.1305	−0.734574	−0.367287	+	0.930108i	$0.619713\pi$
$752$	10.0436	0.366253
$753$	40.5420	1.47743
$754$	−2.14816	−0.0782314
$755$	8.88900	0.323504
$756$	4.92300	0.179048
$757$	−26.4825	−0.962522	−0.481261	−	0.876577i	$-0.659821\pi$
$757$	−26.4825	−0.962522	−0.481261	+	0.876577i	$0.659821\pi$
$758$	−14.9922	−0.544543
$759$	1.14191	0.0414486
$760$	−2.53780	−0.0920557
$761$	33.6100	1.21836	0.609180	−	0.793032i	$-0.291499\pi$
$761$	33.6100	1.21836	0.609180	+	0.793032i	$0.291499\pi$
$762$	−24.2256	−0.877599
$763$	−2.86999	−0.103901
$764$	11.5795	0.418932
$765$	41.2005	1.48961
$766$	−17.9523	−0.648644
$767$	−9.94392	−0.359054
$768$	3.41400	0.123192
$769$	30.9825	1.11726	0.558629	−	0.829418i	$-0.311328\pi$
$769$	30.9825	1.11726	0.558629	+	0.829418i	$0.311328\pi$
$770$	−0.104179	−0.00375435
$771$	26.2788	0.946408
$772$	−23.6987	−0.852934
$773$	3.56214	0.128121	0.0640606	−	0.997946i	$-0.479595\pi$
$773$	3.56214	0.128121	0.0640606	+	0.997946i	$0.479595\pi$
$774$	−19.9635	−0.717574
$775$	1.00000	0.0359211
$776$	−6.74792	−0.242236
$777$	−5.91995	−0.212377
$778$	0.223357	0.00800774
$779$	26.3557	0.944291
$780$	−3.41400	−0.122241
$781$	1.30529	0.0467069
$782$	−3.89677	−0.139348
$783$	−41.4757	−1.48222
$784$	−6.93499	−0.247678
$785$	15.0972	0.538844
$786$	−15.9426	−0.568655
$787$	21.9080	0.780936	0.390468	−	0.920617i	$-0.372313\pi$
$787$	21.9080	0.780936	0.390468	+	0.920617i	$0.372313\pi$
$788$	12.3060	0.438382
$789$	16.3017	0.580356
$790$	−4.49076	−0.159774
$791$	−1.94758	−0.0692480
$792$	3.53642	0.125661
$793$	12.2706	0.435740
$794$	−31.7829	−1.12793
$795$	−25.0963	−0.890074
$796$	−19.3168	−0.684666
$797$	−42.8225	−1.51685	−0.758426	−	0.651759i	$-0.774031\pi$
$797$	−42.8225	−1.51685	−0.758426	+	0.651759i	$0.774031\pi$
$798$	2.20914	0.0782029
$799$	−47.8086	−1.69134
$800$	1.00000	0.0353553
$801$	−136.455	−4.82139
$802$	9.90413	0.349727
$803$	0.654919	0.0231116
$804$	−22.8839	−0.807052
$805$	−0.208734	−0.00735690
$806$	1.00000	0.0352235
$807$	101.773	3.58258
$808$	17.0386	0.599416
$809$	31.0363	1.09118	0.545589	−	0.838053i	$-0.316306\pi$
$809$	31.0363	1.09118	0.545589	+	0.838053i	$0.316306\pi$
$810$	−39.9497	−1.40369
$811$	−14.1179	−0.495747	−0.247873	−	0.968792i	$-0.579732\pi$
$811$	−14.1179	−0.495747	−0.247873	+	0.968792i	$0.579732\pi$
$812$	−0.547734	−0.0192217
$813$	94.8881	3.32787
$814$	−2.77862	−0.0973905
$815$	5.36029	0.187763
$816$	−16.2509	−0.568897
$817$	−5.85339	−0.204784
$818$	10.8960	0.380969
$819$	2.20694	0.0771166
$820$	−10.3853	−0.362669
$821$	−2.54013	−0.0886512	−0.0443256	−	0.999017i	$-0.514114\pi$
$821$	−2.54013	−0.0886512	−0.0443256	+	0.999017i	$0.514114\pi$
$822$	−57.6422	−2.01050
$823$	−17.7954	−0.620309	−0.310155	−	0.950686i	$-0.600381\pi$
$823$	−17.7954	−0.620309	−0.310155	+	0.950686i	$0.600381\pi$
$824$	4.70454	0.163890
$825$	1.39489	0.0485639
$826$	−2.53548	−0.0882207
$827$	−25.5676	−0.889071	−0.444536	−	0.895761i	$-0.646631\pi$
$827$	−25.5676	−0.889071	−0.444536	+	0.895761i	$0.646631\pi$
$828$	7.08560	0.246242
$829$	−37.5876	−1.30547	−0.652736	−	0.757586i	$-0.726379\pi$
$829$	−37.5876	−1.30547	−0.652736	+	0.757586i	$0.726379\pi$
$830$	16.6175	0.576803
$831$	34.8178	1.20782
$832$	1.00000	0.0346688
$833$	33.0112	1.14377
$834$	−16.2037	−0.561088
$835$	−11.8772	−0.411029
$836$	1.03690	0.0358618
$837$	19.3075	0.667365
$838$	−4.24675	−0.146702
$839$	1.80642	0.0623646	0.0311823	−	0.999514i	$-0.490073\pi$
$839$	1.80642	0.0623646	0.0311823	+	0.999514i	$0.490073\pi$
$840$	−0.870496	−0.0300349
$841$	−24.3854	−0.840876
$842$	17.1635	0.591493
$843$	−74.8191	−2.57691
$844$	−9.09477	−0.313055
$845$	−1.00000	−0.0344010
$846$	86.9315	2.98877
$847$	−2.76219	−0.0949101
$848$	7.35099	0.252434
$849$	−61.3741	−2.10635
$850$	−4.76009	−0.163270
$851$	−5.56725	−0.190843
$852$	10.9067	0.373657
$853$	−16.8441	−0.576730	−0.288365	−	0.957521i	$-0.593112\pi$
$853$	−16.8441	−0.576730	−0.288365	+	0.957521i	$0.593112\pi$
$854$	3.12872	0.107063
$855$	−21.9657	−0.751210
$856$	−4.21975	−0.144228
$857$	−23.8794	−0.815704	−0.407852	−	0.913048i	$-0.633722\pi$
$857$	−23.8794	−0.815704	−0.407852	+	0.913048i	$0.633722\pi$
$858$	1.39489	0.0476209
$859$	8.54352	0.291501	0.145751	−	0.989321i	$-0.453440\pi$
$859$	8.54352	0.291501	0.145751	+	0.989321i	$0.453440\pi$
$860$	2.30648	0.0786504
$861$	9.04032	0.308093
$862$	−28.0157	−0.954220
$863$	−4.08009	−0.138888	−0.0694439	−	0.997586i	$-0.522122\pi$
$863$	−4.08009	−0.138888	−0.0694439	+	0.997586i	$0.522122\pi$
$864$	19.3075	0.656855
$865$	10.5971	0.360314
$866$	33.8984	1.15192
$867$	19.3180	0.656072
$868$	0.254978	0.00865452
$869$	1.83483	0.0622425
$870$	7.33382	0.248640
$871$	−6.70295	−0.227121
$872$	−11.2558	−0.381170
$873$	−58.4059	−1.97674
$874$	2.07753	0.0702735
$875$	−0.254978	−0.00861984
$876$	5.47235	0.184893
$877$	33.9936	1.14788	0.573940	−	0.818897i	$-0.305414\pi$
$877$	33.9936	1.14788	0.573940	+	0.818897i	$0.305414\pi$
$878$	−26.8620	−0.906547
$879$	−57.7619	−1.94826
$880$	−0.408580	−0.0137732
$881$	9.35850	0.315296	0.157648	−	0.987495i	$-0.449609\pi$
$881$	9.35850	0.315296	0.157648	+	0.987495i	$0.449609\pi$
$882$	−60.0250	−2.02115
$883$	30.5835	1.02922	0.514608	−	0.857425i	$-0.327937\pi$
$883$	30.5835	1.02922	0.514608	+	0.857425i	$0.327937\pi$
$884$	−4.76009	−0.160099
$885$	33.9485	1.14117
$886$	23.3086	0.783069
$887$	−16.6070	−0.557609	−0.278805	−	0.960348i	$-0.589938\pi$
$887$	−16.6070	−0.557609	−0.278805	+	0.960348i	$0.589938\pi$
$888$	−23.2175	−0.779127
$889$	−1.80931	−0.0606824
$890$	15.7653	0.528454
$891$	16.3227	0.546829
$892$	−15.7142	−0.526149
$893$	25.4887	0.852948
$894$	11.9406	0.399354
$895$	−18.1936	−0.608145
$896$	0.254978	0.00851822
$897$	2.79482	0.0933162
$898$	−13.7087	−0.457467
$899$	−2.14816	−0.0716452
$900$	8.65540	0.288513
$901$	−34.9914	−1.16573
$902$	4.24321	0.141283
$903$	−2.00778	−0.0668148
$904$	−7.63822	−0.254044
$905$	−6.96292	−0.231455
$906$	−30.3470	−1.00821
$907$	−22.3574	−0.742365	−0.371182	−	0.928560i	$-0.621048\pi$
$907$	−22.3574	−0.742365	−0.371182	+	0.928560i	$0.621048\pi$
$908$	23.4330	0.777651
$909$	147.476	4.89147
$910$	−0.254978	−0.00845245
$911$	−29.6866	−0.983561	−0.491780	−	0.870719i	$-0.663654\pi$
$911$	−29.6866	−0.983561	−0.491780	+	0.870719i	$0.663654\pi$
$912$	8.66405	0.286895
$913$	−6.78960	−0.224703
$914$	−12.9520	−0.428415
$915$	−41.8917	−1.38490
$916$	26.5167	0.876135
$917$	−1.19069	−0.0393201
$918$	−91.9055	−3.03333
$919$	47.9736	1.58250	0.791251	−	0.611492i	$-0.209430\pi$
$919$	47.9736	1.58250	0.791251	+	0.611492i	$0.209430\pi$
$920$	−0.818634	−0.0269896
$921$	−32.9097	−1.08441
$922$	−16.5287	−0.544345
$923$	3.19469	0.105155
$924$	0.355667	0.0117006
$925$	−6.80066	−0.223604
$926$	5.36923	0.176444
$927$	40.7196	1.33741
$928$	−2.14816	−0.0705168
$929$	−27.6229	−0.906279	−0.453139	−	0.891440i	$-0.649696\pi$
$929$	−27.6229	−0.906279	−0.453139	+	0.891440i	$0.649696\pi$
$930$	−3.41400	−0.111949
$931$	−17.5996	−0.576804
$932$	24.6168	0.806351
$933$	−44.5194	−1.45750
$934$	−7.99331	−0.261549
$935$	1.94488	0.0636043
$936$	8.65540	0.282910
$937$	21.1957	0.692434	0.346217	−	0.938154i	$-0.387466\pi$
$937$	21.1957	0.692434	0.346217	+	0.938154i	$0.387466\pi$
$938$	−1.70911	−0.0558043
$939$	60.2443	1.96600
$940$	−10.0436	−0.327587
$941$	19.7911	0.645172	0.322586	−	0.946540i	$-0.395448\pi$
$941$	19.7911	0.645172	0.322586	+	0.946540i	$0.395448\pi$
$942$	−51.5420	−1.67933
$943$	8.50172	0.276854
$944$	−9.94392	−0.323647
$945$	−4.92300	−0.160145
$946$	−0.942383	−0.0306395
$947$	22.8256	0.741731	0.370866	−	0.928687i	$-0.379061\pi$
$947$	22.8256	0.741731	0.370866	+	0.928687i	$0.379061\pi$
$948$	15.3314	0.497942
$949$	1.60291	0.0520328
$950$	2.53780	0.0823371
$951$	−63.1843	−2.04889
$952$	−1.21372	−0.0393369
$953$	−12.8758	−0.417089	−0.208544	−	0.978013i	$-0.566873\pi$
$953$	−12.8758	−0.417089	−0.208544	+	0.978013i	$0.566873\pi$
$954$	63.6258	2.05996
$955$	−11.5795	−0.374704
$956$	−8.67546	−0.280584
$957$	−2.99645	−0.0968616
$958$	−36.4198	−1.17667
$959$	−4.30507	−0.139018
$960$	−3.41400	−0.110186
$961$	1.00000	0.0322581
$962$	−6.80066	−0.219262
$963$	−36.5236	−1.17696
$964$	7.90914	0.254736
$965$	23.6987	0.762887
$966$	0.712617	0.0229281
$967$	46.2358	1.48684	0.743421	−	0.668824i	$-0.233202\pi$
$967$	46.2358	1.48684	0.743421	+	0.668824i	$0.233202\pi$
$968$	−10.8331	−0.348188
$969$	−41.2417	−1.32487
$970$	6.74792	0.216662
$971$	−2.74406	−0.0880612	−0.0440306	−	0.999030i	$-0.514020\pi$
$971$	−2.74406	−0.0880612	−0.0440306	+	0.999030i	$0.514020\pi$
$972$	78.4657	2.51679
$973$	−1.21019	−0.0387969
$974$	39.4871	1.26525
$975$	3.41400	0.109335
$976$	12.2706	0.392771
$977$	18.6071	0.595293	0.297647	−	0.954676i	$-0.403798\pi$
$977$	18.6071	0.595293	0.297647	+	0.954676i	$0.403798\pi$
$978$	−18.3000	−0.585170
$979$	−6.44139	−0.205868
$980$	6.93499	0.221530
$981$	−97.4236	−3.11050
$982$	−0.336368	−0.0107339
$983$	−53.9844	−1.72184	−0.860918	−	0.508744i	$-0.830110\pi$
$983$	−53.9844	−1.72184	−0.860918	+	0.508744i	$0.830110\pi$
$984$	35.4553	1.13027
$985$	−12.3060	−0.392101
$986$	10.2254	0.325644
$987$	8.74293	0.278291
$988$	2.53780	0.0807382
$989$	−1.88816	−0.0600402
$990$	−3.53642	−0.112395
$991$	44.6702	1.41899	0.709497	−	0.704708i	$-0.248922\pi$
$991$	44.6702	1.41899	0.709497	+	0.704708i	$0.248922\pi$
$992$	1.00000	0.0317500
$993$	−34.8492	−1.10591
$994$	0.814577	0.0258368
$995$	19.3168	0.612384
$996$	−56.7323	−1.79763
$997$	−5.51723	−0.174732	−0.0873662	−	0.996176i	$-0.527845\pi$
$997$	−5.51723	−0.174732	−0.0873662	+	0.996176i	$0.527845\pi$
$998$	−17.9413	−0.567921
$999$	−131.304	−4.15427

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4030.2.a.q.1.9	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4030.2.a.q.1.9	✓	9	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:	\( N \)	\(=\)	\( 4030 = 2 \cdot 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4030.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +3.41400 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.41400 q^{6} +0.254978 q^{7} +1.00000 q^{8} +8.65540 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +3.41400 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.41400 q^{6} +0.254978 q^{7} +1.00000 q^{8} +8.65540 q^{9} -1.00000 q^{10} +0.408580 q^{11} +3.41400 q^{12} +1.00000 q^{13} +0.254978 q^{14} -3.41400 q^{15} +1.00000 q^{16} -4.76009 q^{17} +8.65540 q^{18} +2.53780 q^{19} -1.00000 q^{20} +0.870496 q^{21} +0.408580 q^{22} +0.818634 q^{23} +3.41400 q^{24} +1.00000 q^{25} +1.00000 q^{26} +19.3075 q^{27} +0.254978 q^{28} -2.14816 q^{29} -3.41400 q^{30} +1.00000 q^{31} +1.00000 q^{32} +1.39489 q^{33} -4.76009 q^{34} -0.254978 q^{35} +8.65540 q^{36} -6.80066 q^{37} +2.53780 q^{38} +3.41400 q^{39} -1.00000 q^{40} +10.3853 q^{41} +0.870496 q^{42} -2.30648 q^{43} +0.408580 q^{44} -8.65540 q^{45} +0.818634 q^{46} +10.0436 q^{47} +3.41400 q^{48} -6.93499 q^{49} +1.00000 q^{50} -16.2509 q^{51} +1.00000 q^{52} +7.35099 q^{53} +19.3075 q^{54} -0.408580 q^{55} +0.254978 q^{56} +8.66405 q^{57} -2.14816 q^{58} -9.94392 q^{59} -3.41400 q^{60} +12.2706 q^{61} +1.00000 q^{62} +2.20694 q^{63} +1.00000 q^{64} -1.00000 q^{65} +1.39489 q^{66} -6.70295 q^{67} -4.76009 q^{68} +2.79482 q^{69} -0.254978 q^{70} +3.19469 q^{71} +8.65540 q^{72} +1.60291 q^{73} -6.80066 q^{74} +3.41400 q^{75} +2.53780 q^{76} +0.104179 q^{77} +3.41400 q^{78} +4.49076 q^{79} -1.00000 q^{80} +39.9497 q^{81} +10.3853 q^{82} -16.6175 q^{83} +0.870496 q^{84} +4.76009 q^{85} -2.30648 q^{86} -7.33382 q^{87} +0.408580 q^{88} -15.7653 q^{89} -8.65540 q^{90} +0.254978 q^{91} +0.818634 q^{92} +3.41400 q^{93} +10.0436 q^{94} -2.53780 q^{95} +3.41400 q^{96} -6.74792 q^{97} -6.93499 q^{98} +3.53642 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} + 3 q^{3} + 9 q^{4} - 9 q^{5} + 3 q^{6} + 3 q^{7} + 9 q^{8} + 14 q^{9}+O(q^{10}) \) 9 * q + 9 * q^2 + 3 * q^3 + 9 * q^4 - 9 * q^5 + 3 * q^6 + 3 * q^7 + 9 * q^8 + 14 * q^9	\( 9 q + 9 q^{2} + 3 q^{3} + 9 q^{4} - 9 q^{5} + 3 q^{6} + 3 q^{7} + 9 q^{8} + 14 q^{9} - 9 q^{10} + 6 q^{11} + 3 q^{12} + 9 q^{13} + 3 q^{14} - 3 q^{15} + 9 q^{16} + 3 q^{17} + 14 q^{18} + 6 q^{19} - 9 q^{20} - q^{21} + 6 q^{22} + 14 q^{23} + 3 q^{24} + 9 q^{25} + 9 q^{26} + 9 q^{27} + 3 q^{28} + 17 q^{29} - 3 q^{30} + 9 q^{31} + 9 q^{32} - 8 q^{33} + 3 q^{34} - 3 q^{35} + 14 q^{36} - 3 q^{37} + 6 q^{38} + 3 q^{39} - 9 q^{40} + 4 q^{41} - q^{42} + 5 q^{43} + 6 q^{44} - 14 q^{45} + 14 q^{46} + 25 q^{47} + 3 q^{48} + 8 q^{49} + 9 q^{50} + 15 q^{51} + 9 q^{52} + 18 q^{53} + 9 q^{54} - 6 q^{55} + 3 q^{56} + 13 q^{57} + 17 q^{58} - 6 q^{59} - 3 q^{60} + 26 q^{61} + 9 q^{62} + 8 q^{63} + 9 q^{64} - 9 q^{65} - 8 q^{66} - 2 q^{67} + 3 q^{68} + 8 q^{69} - 3 q^{70} + 18 q^{71} + 14 q^{72} - 5 q^{73} - 3 q^{74} + 3 q^{75} + 6 q^{76} + 19 q^{77} + 3 q^{78} + 18 q^{79} - 9 q^{80} + 41 q^{81} + 4 q^{82} + 13 q^{83} - q^{84} - 3 q^{85} + 5 q^{86} + 19 q^{87} + 6 q^{88} + 9 q^{89} - 14 q^{90} + 3 q^{91} + 14 q^{92} + 3 q^{93} + 25 q^{94} - 6 q^{95} + 3 q^{96} - 18 q^{97} + 8 q^{98} + 21 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 3 * q^3 + 9 * q^4 - 9 * q^5 + 3 * q^6 + 3 * q^7 + 9 * q^8 + 14 * q^9 - 9 * q^10 + 6 * q^11 + 3 * q^12 + 9 * q^13 + 3 * q^14 - 3 * q^15 + 9 * q^16 + 3 * q^17 + 14 * q^18 + 6 * q^19 - 9 * q^20 - q^21 + 6 * q^22 + 14 * q^23 + 3 * q^24 + 9 * q^25 + 9 * q^26 + 9 * q^27 + 3 * q^28 + 17 * q^29 - 3 * q^30 + 9 * q^31 + 9 * q^32 - 8 * q^33 + 3 * q^34 - 3 * q^35 + 14 * q^36 - 3 * q^37 + 6 * q^38 + 3 * q^39 - 9 * q^40 + 4 * q^41 - q^42 + 5 * q^43 + 6 * q^44 - 14 * q^45 + 14 * q^46 + 25 * q^47 + 3 * q^48 + 8 * q^49 + 9 * q^50 + 15 * q^51 + 9 * q^52 + 18 * q^53 + 9 * q^54 - 6 * q^55 + 3 * q^56 + 13 * q^57 + 17 * q^58 - 6 * q^59 - 3 * q^60 + 26 * q^61 + 9 * q^62 + 8 * q^63 + 9 * q^64 - 9 * q^65 - 8 * q^66 - 2 * q^67 + 3 * q^68 + 8 * q^69 - 3 * q^70 + 18 * q^71 + 14 * q^72 - 5 * q^73 - 3 * q^74 + 3 * q^75 + 6 * q^76 + 19 * q^77 + 3 * q^78 + 18 * q^79 - 9 * q^80 + 41 * q^81 + 4 * q^82 + 13 * q^83 - q^84 - 3 * q^85 + 5 * q^86 + 19 * q^87 + 6 * q^88 + 9 * q^89 - 14 * q^90 + 3 * q^91 + 14 * q^92 + 3 * q^93 + 25 * q^94 - 6 * q^95 + 3 * q^96 - 18 * q^97 + 8 * q^98 + 21 * q^99

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