LMFDB - Embedded newform 4030.2.a.q.1.5

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			1.5
Root			$0.161390$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +0.161390 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.161390 q^{6} +0.164045 q^{7} +1.00000 q^{8} -2.97395 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.161390 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.161390 q^{6} +0.164045 q^{7} +1.00000 q^{8} -2.97395 q^{9} -1.00000 q^{10} +2.35029 q^{11} +0.161390 q^{12} +1.00000 q^{13} +0.164045 q^{14} -0.161390 q^{15} +1.00000 q^{16} -3.98188 q^{17} -2.97395 q^{18} +7.89930 q^{19} -1.00000 q^{20} +0.0264751 q^{21} +2.35029 q^{22} -3.21714 q^{23} +0.161390 q^{24} +1.00000 q^{25} +1.00000 q^{26} -0.964134 q^{27} +0.164045 q^{28} +10.4346 q^{29} -0.161390 q^{30} +1.00000 q^{31} +1.00000 q^{32} +0.379313 q^{33} -3.98188 q^{34} -0.164045 q^{35} -2.97395 q^{36} +0.957283 q^{37} +7.89930 q^{38} +0.161390 q^{39} -1.00000 q^{40} +3.80875 q^{41} +0.0264751 q^{42} -11.7499 q^{43} +2.35029 q^{44} +2.97395 q^{45} -3.21714 q^{46} +3.52210 q^{47} +0.161390 q^{48} -6.97309 q^{49} +1.00000 q^{50} -0.642634 q^{51} +1.00000 q^{52} -5.93869 q^{53} -0.964134 q^{54} -2.35029 q^{55} +0.164045 q^{56} +1.27486 q^{57} +10.4346 q^{58} +4.00308 q^{59} -0.161390 q^{60} +6.23073 q^{61} +1.00000 q^{62} -0.487861 q^{63} +1.00000 q^{64} -1.00000 q^{65} +0.379313 q^{66} -1.88309 q^{67} -3.98188 q^{68} -0.519213 q^{69} -0.164045 q^{70} +8.81736 q^{71} -2.97395 q^{72} +15.5099 q^{73} +0.957283 q^{74} +0.161390 q^{75} +7.89930 q^{76} +0.385553 q^{77} +0.161390 q^{78} +13.6125 q^{79} -1.00000 q^{80} +8.76626 q^{81} +3.80875 q^{82} +13.7656 q^{83} +0.0264751 q^{84} +3.98188 q^{85} -11.7499 q^{86} +1.68404 q^{87} +2.35029 q^{88} +13.9589 q^{89} +2.97395 q^{90} +0.164045 q^{91} -3.21714 q^{92} +0.161390 q^{93} +3.52210 q^{94} -7.89930 q^{95} +0.161390 q^{96} +9.61531 q^{97} -6.97309 q^{98} -6.98966 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.161390	0.0931784	0.0465892	−	0.998914i	$-0.485165\pi$
$3$	0.161390	0.0931784	0.0465892	+	0.998914i	$0.485165\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.161390	0.0658871
$7$	0.164045	0.0620031	0.0310015	−	0.999519i	$-0.490130\pi$
$7$	0.164045	0.0620031	0.0310015	+	0.999519i	$0.490130\pi$
$8$	1.00000	0.353553
$9$	−2.97395	−0.991318
$10$	−1.00000	−0.316228
$11$	2.35029	0.708640	0.354320	−	0.935124i	$-0.384712\pi$
$11$	2.35029	0.708640	0.354320	+	0.935124i	$0.384712\pi$
$12$	0.161390	0.0465892
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0.164045	0.0438428
$15$	−0.161390	−0.0416706
$16$	1.00000	0.250000
$17$	−3.98188	−0.965747	−0.482873	−	0.875690i	$-0.660407\pi$
$17$	−3.98188	−0.965747	−0.482873	+	0.875690i	$0.660407\pi$
$18$	−2.97395	−0.700968
$19$	7.89930	1.81222	0.906111	−	0.423039i	$-0.139037\pi$
$19$	7.89930	1.81222	0.906111	+	0.423039i	$0.139037\pi$
$20$	−1.00000	−0.223607
$21$	0.0264751	0.00577735
$22$	2.35029	0.501084
$23$	−3.21714	−0.670820	−0.335410	−	0.942072i	$-0.608875\pi$
$23$	−3.21714	−0.670820	−0.335410	+	0.942072i	$0.608875\pi$
$24$	0.161390	0.0329435
$25$	1.00000	0.200000
$26$	1.00000	0.196116
$27$	−0.964134	−0.185548
$28$	0.164045	0.0310015
$29$	10.4346	1.93766	0.968828	−	0.247734i	$-0.0796858\pi$
$29$	10.4346	1.93766	0.968828	+	0.247734i	$0.0796858\pi$
$30$	−0.161390	−0.0294656
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	1.00000	0.176777
$33$	0.379313	0.0660299
$34$	−3.98188	−0.682886
$35$	−0.164045	−0.0277286
$36$	−2.97395	−0.495659
$37$	0.957283	0.157376	0.0786882	−	0.996899i	$-0.474927\pi$
$37$	0.957283	0.157376	0.0786882	+	0.996899i	$0.474927\pi$
$38$	7.89930	1.28143
$39$	0.161390	0.0258430
$40$	−1.00000	−0.158114
$41$	3.80875	0.594827	0.297413	−	0.954749i	$-0.403876\pi$
$41$	3.80875	0.594827	0.297413	+	0.954749i	$0.403876\pi$
$42$	0.0264751	0.00408520
$43$	−11.7499	−1.79184	−0.895922	−	0.444210i	$-0.853484\pi$
$43$	−11.7499	−1.79184	−0.895922	+	0.444210i	$0.853484\pi$
$44$	2.35029	0.354320
$45$	2.97395	0.443331
$46$	−3.21714	−0.474342
$47$	3.52210	0.513751	0.256876	−	0.966444i	$-0.417307\pi$
$47$	3.52210	0.513751	0.256876	+	0.966444i	$0.417307\pi$
$48$	0.161390	0.0232946
$49$	−6.97309	−0.996156
$50$	1.00000	0.141421
$51$	−0.642634	−0.0899867
$52$	1.00000	0.138675
$53$	−5.93869	−0.815742	−0.407871	−	0.913040i	$-0.633729\pi$
$53$	−5.93869	−0.815742	−0.407871	+	0.913040i	$0.633729\pi$
$54$	−0.964134	−0.131202
$55$	−2.35029	−0.316913
$56$	0.164045	0.0219214
$57$	1.27486	0.168860
$58$	10.4346	1.37013
$59$	4.00308	0.521157	0.260579	−	0.965453i	$-0.416087\pi$
$59$	4.00308	0.521157	0.260579	+	0.965453i	$0.416087\pi$
$60$	−0.161390	−0.0208353
$61$	6.23073	0.797763	0.398882	−	0.917002i	$-0.369398\pi$
$61$	6.23073	0.797763	0.398882	+	0.917002i	$0.369398\pi$
$62$	1.00000	0.127000
$63$	−0.487861	−0.0614648
$64$	1.00000	0.125000
$65$	−1.00000	−0.124035
$66$	0.379313	0.0466902
$67$	−1.88309	−0.230056	−0.115028	−	0.993362i	$-0.536696\pi$
$67$	−1.88309	−0.230056	−0.115028	+	0.993362i	$0.536696\pi$
$68$	−3.98188	−0.482873
$69$	−0.519213	−0.0625060
$70$	−0.164045	−0.0196071
$71$	8.81736	1.04643	0.523214	−	0.852201i	$-0.324733\pi$
$71$	8.81736	1.04643	0.523214	+	0.852201i	$0.324733\pi$
$72$	−2.97395	−0.350484
$73$	15.5099	1.81530	0.907649	−	0.419731i	$-0.137875\pi$
$73$	15.5099	1.81530	0.907649	+	0.419731i	$0.137875\pi$
$74$	0.957283	0.111282
$75$	0.161390	0.0186357
$76$	7.89930	0.906111
$77$	0.385553	0.0439378
$78$	0.161390	0.0182738
$79$	13.6125	1.53153	0.765764	−	0.643121i	$-0.222361\pi$
$79$	13.6125	1.53153	0.765764	+	0.643121i	$0.222361\pi$
$80$	−1.00000	−0.111803
$81$	8.76626	0.974029
$82$	3.80875	0.420606
$83$	13.7656	1.51097	0.755486	−	0.655165i	$-0.227401\pi$
$83$	13.7656	1.51097	0.755486	+	0.655165i	$0.227401\pi$
$84$	0.0264751	0.00288867
$85$	3.98188	0.431895
$86$	−11.7499	−1.26703
$87$	1.68404	0.180548
$88$	2.35029	0.250542
$89$	13.9589	1.47964	0.739820	−	0.672804i	$-0.234910\pi$
$89$	13.9589	1.47964	0.739820	+	0.672804i	$0.234910\pi$
$90$	2.97395	0.313482
$91$	0.164045	0.0171966
$92$	−3.21714	−0.335410
$93$	0.161390	0.0167353
$94$	3.52210	0.363277
$95$	−7.89930	−0.810451
$96$	0.161390	0.0164718
$97$	9.61531	0.976287	0.488144	−	0.872763i	$-0.337674\pi$
$97$	9.61531	0.976287	0.488144	+	0.872763i	$0.337674\pi$
$98$	−6.97309	−0.704388
$99$	−6.98966	−0.702487
$100$	1.00000	0.100000
$101$	−3.34791	−0.333130	−0.166565	−	0.986030i	$-0.553268\pi$
$101$	−3.34791	−0.333130	−0.166565	+	0.986030i	$0.553268\pi$
$102$	−0.642634	−0.0636302
$103$	−0.175650	−0.0173073	−0.00865364	−	0.999963i	$-0.502755\pi$
$103$	−0.175650	−0.0173073	−0.00865364	+	0.999963i	$0.502755\pi$
$104$	1.00000	0.0980581
$105$	−0.0264751	−0.00258371
$106$	−5.93869	−0.576817
$107$	−14.1672	−1.36960	−0.684798	−	0.728733i	$-0.740109\pi$
$107$	−14.1672	−1.36960	−0.684798	+	0.728733i	$0.740109\pi$
$108$	−0.964134	−0.0927739
$109$	−1.55793	−0.149222	−0.0746112	−	0.997213i	$-0.523772\pi$
$109$	−1.55793	−0.149222	−0.0746112	+	0.997213i	$0.523772\pi$
$110$	−2.35029	−0.224092
$111$	0.154496	0.0146641
$112$	0.164045	0.0155008
$113$	−0.280702	−0.0264063	−0.0132031	−	0.999913i	$-0.504203\pi$
$113$	−0.280702	−0.0264063	−0.0132031	+	0.999913i	$0.504203\pi$
$114$	1.27486	0.119402
$115$	3.21714	0.300000
$116$	10.4346	0.968828
$117$	−2.97395	−0.274942
$118$	4.00308	0.368514
$119$	−0.653206	−0.0598793
$120$	−0.161390	−0.0147328
$121$	−5.47613	−0.497830
$122$	6.23073	0.564104
$123$	0.614693	0.0554250
$124$	1.00000	0.0898027
$125$	−1.00000	−0.0894427
$126$	−0.487861	−0.0434621
$127$	−8.42930	−0.747979	−0.373990	−	0.927433i	$-0.622010\pi$
$127$	−8.42930	−0.747979	−0.373990	+	0.927433i	$0.622010\pi$
$128$	1.00000	0.0883883
$129$	−1.89631	−0.166961
$130$	−1.00000	−0.0877058
$131$	12.4500	1.08776	0.543880	−	0.839163i	$-0.316955\pi$
$131$	12.4500	1.08776	0.543880	+	0.839163i	$0.316955\pi$
$132$	0.379313	0.0330149
$133$	1.29584	0.112363
$134$	−1.88309	−0.162674
$135$	0.964134	0.0829795
$136$	−3.98188	−0.341443
$137$	13.8030	1.17927	0.589636	−	0.807669i	$-0.299271\pi$
$137$	13.8030	1.17927	0.589636	+	0.807669i	$0.299271\pi$
$138$	−0.519213	−0.0441984
$139$	−2.57664	−0.218548	−0.109274	−	0.994012i	$-0.534853\pi$
$139$	−2.57664	−0.218548	−0.109274	+	0.994012i	$0.534853\pi$
$140$	−0.164045	−0.0138643
$141$	0.568431	0.0478705
$142$	8.81736	0.739937
$143$	2.35029	0.196541
$144$	−2.97395	−0.247829
$145$	−10.4346	−0.866546
$146$	15.5099	1.28361
$147$	−1.12538	−0.0928202
$148$	0.957283	0.0786882
$149$	−2.13236	−0.174690	−0.0873450	−	0.996178i	$-0.527838\pi$
$149$	−2.13236	−0.174690	−0.0873450	+	0.996178i	$0.527838\pi$
$150$	0.161390	0.0131774
$151$	−5.61008	−0.456541	−0.228271	−	0.973598i	$-0.573307\pi$
$151$	−5.61008	−0.456541	−0.228271	+	0.973598i	$0.573307\pi$
$152$	7.89930	0.640717
$153$	11.8419	0.957362
$154$	0.385553	0.0310687
$155$	−1.00000	−0.0803219
$156$	0.161390	0.0129215
$157$	−5.75864	−0.459590	−0.229795	−	0.973239i	$-0.573806\pi$
$157$	−5.75864	−0.459590	−0.229795	+	0.973239i	$0.573806\pi$
$158$	13.6125	1.08295
$159$	−0.958444	−0.0760095
$160$	−1.00000	−0.0790569
$161$	−0.527755	−0.0415929
$162$	8.76626	0.688742
$163$	8.12147	0.636123	0.318062	−	0.948070i	$-0.396968\pi$
$163$	8.12147	0.636123	0.318062	+	0.948070i	$0.396968\pi$
$164$	3.80875	0.297413
$165$	−0.379313	−0.0295295
$166$	13.7656	1.06842
$167$	−20.2284	−1.56532	−0.782661	−	0.622448i	$-0.786138\pi$
$167$	−20.2284	−1.56532	−0.782661	+	0.622448i	$0.786138\pi$
$168$	0.0264751	0.00204260
$169$	1.00000	0.0769231
$170$	3.98188	0.305396
$171$	−23.4921	−1.79649
$172$	−11.7499	−0.895922
$173$	20.7891	1.58057	0.790285	−	0.612740i	$-0.209933\pi$
$173$	20.7891	1.58057	0.790285	+	0.612740i	$0.209933\pi$
$174$	1.68404	0.127666
$175$	0.164045	0.0124006
$176$	2.35029	0.177160
$177$	0.646056	0.0485606
$178$	13.9589	1.04626
$179$	15.8230	1.18267	0.591334	−	0.806427i	$-0.298601\pi$
$179$	15.8230	1.18267	0.591334	+	0.806427i	$0.298601\pi$
$180$	2.97395	0.221665
$181$	−3.89260	−0.289335	−0.144667	−	0.989480i	$-0.546211\pi$
$181$	−3.89260	−0.289335	−0.144667	+	0.989480i	$0.546211\pi$
$182$	0.164045	0.0121598
$183$	1.00558	0.0743343
$184$	−3.21714	−0.237171
$185$	−0.957283	−0.0703809
$186$	0.161390	0.0118337
$187$	−9.35857	−0.684366
$188$	3.52210	0.256876
$189$	−0.158161	−0.0115045
$190$	−7.89930	−0.573075
$191$	−8.19707	−0.593119	−0.296559	−	0.955014i	$-0.595839\pi$
$191$	−8.19707	−0.593119	−0.296559	+	0.955014i	$0.595839\pi$
$192$	0.161390	0.0116473
$193$	−11.8904	−0.855890	−0.427945	−	0.903805i	$-0.640762\pi$
$193$	−11.8904	−0.855890	−0.427945	+	0.903805i	$0.640762\pi$
$194$	9.61531	0.690339
$195$	−0.161390	−0.0115574
$196$	−6.97309	−0.498078
$197$	19.3699	1.38005	0.690023	−	0.723787i	$-0.257600\pi$
$197$	19.3699	1.38005	0.690023	+	0.723787i	$0.257600\pi$
$198$	−6.98966	−0.496733
$199$	1.14692	0.0813028	0.0406514	−	0.999173i	$-0.487057\pi$
$199$	1.14692	0.0813028	0.0406514	+	0.999173i	$0.487057\pi$
$200$	1.00000	0.0707107
$201$	−0.303912	−0.0214363
$202$	−3.34791	−0.235558
$203$	1.71174	0.120141
$204$	−0.642634	−0.0449933
$205$	−3.80875	−0.266015
$206$	−0.175650	−0.0122381
$207$	9.56763	0.664996
$208$	1.00000	0.0693375
$209$	18.5656	1.28421
$210$	−0.0264751	−0.00182696
$211$	−16.9607	−1.16763	−0.583813	−	0.811888i	$-0.698440\pi$
$211$	−16.9607	−1.16763	−0.583813	+	0.811888i	$0.698440\pi$
$212$	−5.93869	−0.407871
$213$	1.42303	0.0975045
$214$	−14.1672	−0.968450
$215$	11.7499	0.801337
$216$	−0.964134	−0.0656010
$217$	0.164045	0.0111361
$218$	−1.55793	−0.105516
$219$	2.50314	0.169146
$220$	−2.35029	−0.158457
$221$	−3.98188	−0.267850
$222$	0.154496	0.0103691
$223$	4.65058	0.311426	0.155713	−	0.987802i	$-0.450233\pi$
$223$	4.65058	0.311426	0.155713	+	0.987802i	$0.450233\pi$
$224$	0.164045	0.0109607
$225$	−2.97395	−0.198264
$226$	−0.280702	−0.0186720
$227$	−4.05275	−0.268990	−0.134495	−	0.990914i	$-0.542941\pi$
$227$	−4.05275	−0.268990	−0.134495	+	0.990914i	$0.542941\pi$
$228$	1.27486	0.0844300
$229$	−7.43011	−0.490995	−0.245498	−	0.969397i	$-0.578951\pi$
$229$	−7.43011	−0.490995	−0.245498	+	0.969397i	$0.578951\pi$
$230$	3.21714	0.212132
$231$	0.0622243	0.00409406
$232$	10.4346	0.685065
$233$	23.9633	1.56989	0.784943	−	0.619567i	$-0.212692\pi$
$233$	23.9633	1.56989	0.784943	+	0.619567i	$0.212692\pi$
$234$	−2.97395	−0.194413
$235$	−3.52210	−0.229756
$236$	4.00308	0.260579
$237$	2.19692	0.142705
$238$	−0.653206	−0.0423410
$239$	9.76777	0.631824	0.315912	−	0.948788i	$-0.397689\pi$
$239$	9.76777	0.631824	0.315912	+	0.948788i	$0.397689\pi$
$240$	−0.161390	−0.0104177
$241$	10.7270	0.690984	0.345492	−	0.938422i	$-0.387712\pi$
$241$	10.7270	0.690984	0.345492	+	0.938422i	$0.387712\pi$
$242$	−5.47613	−0.352019
$243$	4.30719	0.276306
$244$	6.23073	0.398882
$245$	6.97309	0.445494
$246$	0.614693	0.0391914
$247$	7.89930	0.502620
$248$	1.00000	0.0635001
$249$	2.22163	0.140790
$250$	−1.00000	−0.0632456
$251$	−19.4310	−1.22648	−0.613238	−	0.789898i	$-0.710133\pi$
$251$	−19.4310	−1.22648	−0.613238	+	0.789898i	$0.710133\pi$
$252$	−0.487861	−0.0307324
$253$	−7.56122	−0.475370
$254$	−8.42930	−0.528901
$255$	0.642634	0.0402433
$256$	1.00000	0.0625000
$257$	−5.69369	−0.355162	−0.177581	−	0.984106i	$-0.556827\pi$
$257$	−5.69369	−0.355162	−0.177581	+	0.984106i	$0.556827\pi$
$258$	−1.89631	−0.118059
$259$	0.157037	0.00975782
$260$	−1.00000	−0.0620174
$261$	−31.0320	−1.92083
$262$	12.4500	0.769162
$263$	24.4715	1.50898	0.754488	−	0.656314i	$-0.227885\pi$
$263$	24.4715	1.50898	0.754488	+	0.656314i	$0.227885\pi$
$264$	0.379313	0.0233451
$265$	5.93869	0.364811
$266$	1.29584	0.0794529
$267$	2.25282	0.137871
$268$	−1.88309	−0.115028
$269$	−13.7069	−0.835724	−0.417862	−	0.908511i	$-0.637220\pi$
$269$	−13.7069	−0.835724	−0.417862	+	0.908511i	$0.637220\pi$
$270$	0.964134	0.0586753
$271$	−24.3012	−1.47619	−0.738097	−	0.674694i	$-0.764275\pi$
$271$	−24.3012	−1.47619	−0.738097	+	0.674694i	$0.764275\pi$
$272$	−3.98188	−0.241437
$273$	0.0264751	0.00160235
$274$	13.8030	0.833871
$275$	2.35029	0.141728
$276$	−0.519213	−0.0312530
$277$	−19.4836	−1.17065	−0.585327	−	0.810798i	$-0.699034\pi$
$277$	−19.4836	−1.17065	−0.585327	+	0.810798i	$0.699034\pi$
$278$	−2.57664	−0.154537
$279$	−2.97395	−0.178046
$280$	−0.164045	−0.00980355
$281$	15.0577	0.898269	0.449134	−	0.893464i	$-0.351732\pi$
$281$	15.0577	0.898269	0.449134	+	0.893464i	$0.351732\pi$
$282$	0.568431	0.0338495
$283$	−10.6584	−0.633573	−0.316787	−	0.948497i	$-0.602604\pi$
$283$	−10.6584	−0.633573	−0.316787	+	0.948497i	$0.602604\pi$
$284$	8.81736	0.523214
$285$	−1.27486	−0.0755165
$286$	2.35029	0.138976
$287$	0.624805	0.0368811
$288$	−2.97395	−0.175242
$289$	−1.14467	−0.0673334
$290$	−10.4346	−0.612741
$291$	1.55181	0.0909688
$292$	15.5099	0.907649
$293$	−25.7356	−1.50349	−0.751745	−	0.659453i	$-0.770788\pi$
$293$	−25.7356	−1.50349	−0.751745	+	0.659453i	$0.770788\pi$
$294$	−1.12538	−0.0656338
$295$	−4.00308	−0.233069
$296$	0.957283	0.0556410
$297$	−2.26600	−0.131486
$298$	−2.13236	−0.123525
$299$	−3.21714	−0.186052
$300$	0.161390	0.00931784
$301$	−1.92751	−0.111100
$302$	−5.61008	−0.322824
$303$	−0.540319	−0.0310405
$304$	7.89930	0.453056
$305$	−6.23073	−0.356770
$306$	11.8419	0.676957
$307$	5.41592	0.309103	0.154552	−	0.987985i	$-0.450607\pi$
$307$	5.41592	0.309103	0.154552	+	0.987985i	$0.450607\pi$
$308$	0.385553	0.0219689
$309$	−0.0283481	−0.00161266
$310$	−1.00000	−0.0567962
$311$	−26.8169	−1.52064	−0.760322	−	0.649546i	$-0.774959\pi$
$311$	−26.8169	−1.52064	−0.760322	+	0.649546i	$0.774959\pi$
$312$	0.161390	0.00913689
$313$	−30.5542	−1.72703	−0.863513	−	0.504327i	$-0.831741\pi$
$313$	−30.5542	−1.72703	−0.863513	+	0.504327i	$0.831741\pi$
$314$	−5.75864	−0.324979
$315$	0.487861	0.0274879
$316$	13.6125	0.765764
$317$	20.6021	1.15713	0.578565	−	0.815636i	$-0.303613\pi$
$317$	20.6021	1.15713	0.578565	+	0.815636i	$0.303613\pi$
$318$	−0.958444	−0.0537468
$319$	24.5244	1.37310
$320$	−1.00000	−0.0559017
$321$	−2.28644	−0.127617
$322$	−0.527755	−0.0294106
$323$	−31.4540	−1.75015
$324$	8.76626	0.487014
$325$	1.00000	0.0554700
$326$	8.12147	0.449807
$327$	−0.251433	−0.0139043
$328$	3.80875	0.210303
$329$	0.577782	0.0318541
$330$	−0.379313	−0.0208805
$331$	−1.36971	−0.0752859	−0.0376429	−	0.999291i	$-0.511985\pi$
$331$	−1.36971	−0.0752859	−0.0376429	+	0.999291i	$0.511985\pi$
$332$	13.7656	0.755486
$333$	−2.84692	−0.156010
$334$	−20.2284	−1.10685
$335$	1.88309	0.102884
$336$	0.0264751	0.00144434
$337$	17.7784	0.968452	0.484226	−	0.874943i	$-0.339101\pi$
$337$	17.7784	0.968452	0.484226	+	0.874943i	$0.339101\pi$
$338$	1.00000	0.0543928
$339$	−0.0453025	−0.00246049
$340$	3.98188	0.215948
$341$	2.35029	0.127275
$342$	−23.4921	−1.27031
$343$	−2.29221	−0.123768
$344$	−11.7499	−0.633513
$345$	0.519213	0.0279535
$346$	20.7891	1.11763
$347$	16.3148	0.875823	0.437911	−	0.899018i	$-0.355718\pi$
$347$	16.3148	0.875823	0.437911	+	0.899018i	$0.355718\pi$
$348$	1.68404	0.0902738
$349$	−4.89341	−0.261938	−0.130969	−	0.991386i	$-0.541809\pi$
$349$	−4.89341	−0.261938	−0.130969	+	0.991386i	$0.541809\pi$
$350$	0.164045	0.00876856
$351$	−0.964134	−0.0514617
$352$	2.35029	0.125271
$353$	−17.3087	−0.921248	−0.460624	−	0.887595i	$-0.652374\pi$
$353$	−17.3087	−0.921248	−0.460624	+	0.887595i	$0.652374\pi$
$354$	0.646056	0.0343375
$355$	−8.81736	−0.467977
$356$	13.9589	0.739820
$357$	−0.105421	−0.00557945
$358$	15.8230	0.836273
$359$	6.18508	0.326436	0.163218	−	0.986590i	$-0.447813\pi$
$359$	6.18508	0.326436	0.163218	+	0.986590i	$0.447813\pi$
$360$	2.97395	0.156741
$361$	43.3989	2.28415
$362$	−3.89260	−0.204590
$363$	−0.883791	−0.0463870
$364$	0.164045	0.00859828
$365$	−15.5099	−0.811826
$366$	1.00558	0.0525623
$367$	−34.9399	−1.82385	−0.911924	−	0.410359i	$-0.865403\pi$
$367$	−34.9399	−1.82385	−0.911924	+	0.410359i	$0.865403\pi$
$368$	−3.21714	−0.167705
$369$	−11.3270	−0.589662
$370$	−0.957283	−0.0497668
$371$	−0.974211	−0.0505785
$372$	0.161390	0.00836766
$373$	15.5298	0.804104	0.402052	−	0.915617i	$-0.368297\pi$
$373$	15.5298	0.804104	0.402052	+	0.915617i	$0.368297\pi$
$374$	−9.35857	−0.483920
$375$	−0.161390	−0.00833413
$376$	3.52210	0.181638
$377$	10.4346	0.537409
$378$	−0.158161	−0.00813493
$379$	3.18149	0.163422	0.0817110	−	0.996656i	$-0.473962\pi$
$379$	3.18149	0.163422	0.0817110	+	0.996656i	$0.473962\pi$
$380$	−7.89930	−0.405225
$381$	−1.36040	−0.0696955
$382$	−8.19707	−0.419398
$383$	12.9166	0.660005	0.330003	−	0.943980i	$-0.392950\pi$
$383$	12.9166	0.660005	0.330003	+	0.943980i	$0.392950\pi$
$384$	0.161390	0.00823588
$385$	−0.385553	−0.0196496
$386$	−11.8904	−0.605205
$387$	34.9437	1.77629
$388$	9.61531	0.488144
$389$	−4.20221	−0.213061	−0.106530	−	0.994309i	$-0.533974\pi$
$389$	−4.20221	−0.213061	−0.106530	+	0.994309i	$0.533974\pi$
$390$	−0.161390	−0.00817228
$391$	12.8103	0.647843
$392$	−6.97309	−0.352194
$393$	2.00930	0.101356
$394$	19.3699	0.975840
$395$	−13.6125	−0.684921
$396$	−6.98966	−0.351244
$397$	−7.41505	−0.372151	−0.186075	−	0.982535i	$-0.559577\pi$
$397$	−7.41505	−0.372151	−0.186075	+	0.982535i	$0.559577\pi$
$398$	1.14692	0.0574898
$399$	0.209135	0.0104698
$400$	1.00000	0.0500000
$401$	−35.1352	−1.75457	−0.877284	−	0.479971i	$-0.840647\pi$
$401$	−35.1352	−1.75457	−0.877284	+	0.479971i	$0.840647\pi$
$402$	−0.303912	−0.0151577
$403$	1.00000	0.0498135
$404$	−3.34791	−0.166565
$405$	−8.76626	−0.435599
$406$	1.71174	0.0849523
$407$	2.24990	0.111523
$408$	−0.642634	−0.0318151
$409$	−10.9834	−0.543094	−0.271547	−	0.962425i	$-0.587535\pi$
$409$	−10.9834	−0.543094	−0.271547	+	0.962425i	$0.587535\pi$
$410$	−3.80875	−0.188101
$411$	2.22766	0.109883
$412$	−0.175650	−0.00865364
$413$	0.656685	0.0323133
$414$	9.56763	0.470223
$415$	−13.7656	−0.675727
$416$	1.00000	0.0490290
$417$	−0.415843	−0.0203639
$418$	18.5656	0.908076
$419$	−12.9208	−0.631222	−0.315611	−	0.948889i	$-0.602210\pi$
$419$	−12.9208	−0.631222	−0.315611	+	0.948889i	$0.602210\pi$
$420$	−0.0264751	−0.00129185
$421$	−22.3718	−1.09033	−0.545167	−	0.838328i	$-0.683534\pi$
$421$	−22.3718	−1.09033	−0.545167	+	0.838328i	$0.683534\pi$
$422$	−16.9607	−0.825636
$423$	−10.4746	−0.509291
$424$	−5.93869	−0.288408
$425$	−3.98188	−0.193149
$426$	1.42303	0.0689461
$427$	1.02212	0.0494638
$428$	−14.1672	−0.684798
$429$	0.379313	0.0183134
$430$	11.7499	0.566631
$431$	30.3537	1.46208	0.731042	−	0.682332i	$-0.239034\pi$
$431$	30.3537	1.46208	0.731042	+	0.682332i	$0.239034\pi$
$432$	−0.964134	−0.0463869
$433$	−12.2160	−0.587066	−0.293533	−	0.955949i	$-0.594831\pi$
$433$	−12.2160	−0.587066	−0.293533	+	0.955949i	$0.594831\pi$
$434$	0.164045	0.00787440
$435$	−1.68404	−0.0807434
$436$	−1.55793	−0.0746112
$437$	−25.4132	−1.21568
$438$	2.50314	0.119605
$439$	41.7062	1.99053	0.995264	−	0.0972104i	$-0.0309920\pi$
$439$	41.7062	1.99053	0.995264	+	0.0972104i	$0.0309920\pi$
$440$	−2.35029	−0.112046
$441$	20.7376	0.987507
$442$	−3.98188	−0.189398
$443$	−36.5964	−1.73875	−0.869373	−	0.494156i	$-0.835477\pi$
$443$	−36.5964	−1.73875	−0.869373	+	0.494156i	$0.835477\pi$
$444$	0.154496	0.00733204
$445$	−13.9589	−0.661715
$446$	4.65058	0.220211
$447$	−0.344142	−0.0162773
$448$	0.164045	0.00775038
$449$	27.1663	1.28206	0.641028	−	0.767517i	$-0.278508\pi$
$449$	27.1663	1.28206	0.641028	+	0.767517i	$0.278508\pi$
$450$	−2.97395	−0.140194
$451$	8.95167	0.421518
$452$	−0.280702	−0.0132031
$453$	−0.905408	−0.0425398
$454$	−4.05275	−0.190205
$455$	−0.164045	−0.00769054
$456$	1.27486	0.0597010
$457$	−20.6435	−0.965663	−0.482831	−	0.875713i	$-0.660392\pi$
$457$	−20.6435	−0.965663	−0.482831	+	0.875713i	$0.660392\pi$
$458$	−7.43011	−0.347186
$459$	3.83906	0.179192
$460$	3.21714	0.150000
$461$	−38.5338	−1.79470	−0.897349	−	0.441321i	$-0.854510\pi$
$461$	−38.5338	−1.79470	−0.897349	+	0.441321i	$0.854510\pi$
$462$	0.0622243	0.00289493
$463$	27.5212	1.27902	0.639510	−	0.768783i	$-0.279137\pi$
$463$	27.5212	1.27902	0.639510	+	0.768783i	$0.279137\pi$
$464$	10.4346	0.484414
$465$	−0.161390	−0.00748427
$466$	23.9633	1.11008
$467$	−6.30800	−0.291899	−0.145950	−	0.989292i	$-0.546624\pi$
$467$	−6.30800	−0.291899	−0.145950	+	0.989292i	$0.546624\pi$
$468$	−2.97395	−0.137471
$469$	−0.308911	−0.0142642
$470$	−3.52210	−0.162462
$471$	−0.929385	−0.0428238
$472$	4.00308	0.184257
$473$	−27.6157	−1.26977
$474$	2.19692	0.100908
$475$	7.89930	0.362445
$476$	−0.653206	−0.0299396
$477$	17.6614	0.808660
$478$	9.76777	0.446767
$479$	40.8995	1.86874	0.934372	−	0.356298i	$-0.115961\pi$
$479$	40.8995	1.86874	0.934372	+	0.356298i	$0.115961\pi$
$480$	−0.161390	−0.00736640
$481$	0.957283	0.0436484
$482$	10.7270	0.488599
$483$	−0.0851742	−0.00387556
$484$	−5.47613	−0.248915
$485$	−9.61531	−0.436609
$486$	4.30719	0.195378
$487$	12.9703	0.587741	0.293871	−	0.955845i	$-0.405056\pi$
$487$	12.9703	0.587741	0.293871	+	0.955845i	$0.405056\pi$
$488$	6.23073	0.282052
$489$	1.31072	0.0592729
$490$	6.97309	0.315012
$491$	−32.7317	−1.47716	−0.738581	−	0.674165i	$-0.764504\pi$
$491$	−32.7317	−1.47716	−0.738581	+	0.674165i	$0.764504\pi$
$492$	0.614693	0.0277125
$493$	−41.5493	−1.87129
$494$	7.89930	0.355406
$495$	6.98966	0.314162
$496$	1.00000	0.0449013
$497$	1.44644	0.0648818
$498$	2.22163	0.0995535
$499$	30.4654	1.36382	0.681910	−	0.731436i	$-0.261150\pi$
$499$	30.4654	1.36382	0.681910	+	0.731436i	$0.261150\pi$
$500$	−1.00000	−0.0447214
$501$	−3.26466	−0.145854
$502$	−19.4310	−0.867250
$503$	−3.73047	−0.166334	−0.0831668	−	0.996536i	$-0.526503\pi$
$503$	−3.73047	−0.166334	−0.0831668	+	0.996536i	$0.526503\pi$
$504$	−0.487861	−0.0217311
$505$	3.34791	0.148980
$506$	−7.56122	−0.336137
$507$	0.161390	0.00716757
$508$	−8.42930	−0.373990
$509$	27.0022	1.19685	0.598425	−	0.801179i	$-0.295793\pi$
$509$	27.0022	1.19685	0.598425	+	0.801179i	$0.295793\pi$
$510$	0.642634	0.0284563
$511$	2.54432	0.112554
$512$	1.00000	0.0441942
$513$	−7.61598	−0.336254
$514$	−5.69369	−0.251138
$515$	0.175650	0.00774006
$516$	−1.89631	−0.0834806
$517$	8.27796	0.364064
$518$	0.157037	0.00689982
$519$	3.35515	0.147275
$520$	−1.00000	−0.0438529
$521$	−12.7648	−0.559234	−0.279617	−	0.960112i	$-0.590208\pi$
$521$	−12.7648	−0.559234	−0.279617	+	0.960112i	$0.590208\pi$
$522$	−31.0320	−1.35823
$523$	7.03315	0.307538	0.153769	−	0.988107i	$-0.450859\pi$
$523$	7.03315	0.307538	0.153769	+	0.988107i	$0.450859\pi$
$524$	12.4500	0.543880
$525$	0.0264751	0.00115547
$526$	24.4715	1.06701
$527$	−3.98188	−0.173453
$528$	0.379313	0.0165075
$529$	−12.6500	−0.550000
$530$	5.93869	0.257960
$531$	−11.9050	−0.516632
$532$	1.29584	0.0561817
$533$	3.80875	0.164975
$534$	2.25282	0.0974892
$535$	14.1672	0.612502
$536$	−1.88309	−0.0813372
$537$	2.55367	0.110199
$538$	−13.7069	−0.590946
$539$	−16.3888	−0.705915
$540$	0.964134	0.0414897
$541$	−6.04848	−0.260045	−0.130022	−	0.991511i	$-0.541505\pi$
$541$	−6.04848	−0.260045	−0.130022	+	0.991511i	$0.541505\pi$
$542$	−24.3012	−1.04383
$543$	−0.628225	−0.0269597
$544$	−3.98188	−0.170721
$545$	1.55793	0.0667343
$546$	0.0264751	0.00113303
$547$	26.0761	1.11493	0.557467	−	0.830199i	$-0.311773\pi$
$547$	26.0761	1.11493	0.557467	+	0.830199i	$0.311773\pi$
$548$	13.8030	0.589636
$549$	−18.5299	−0.790837
$550$	2.35029	0.100217
$551$	82.4260	3.51146
$552$	−0.519213	−0.0220992
$553$	2.23306	0.0949595
$554$	−19.4836	−0.827777
$555$	−0.154496	−0.00655797
$556$	−2.57664	−0.109274
$557$	−4.68504	−0.198512	−0.0992558	−	0.995062i	$-0.531646\pi$
$557$	−4.68504	−0.198512	−0.0992558	+	0.995062i	$0.531646\pi$
$558$	−2.97395	−0.125897
$559$	−11.7499	−0.496968
$560$	−0.164045	−0.00693215
$561$	−1.51038	−0.0637681
$562$	15.0577	0.635172
$563$	−39.6968	−1.67302	−0.836511	−	0.547950i	$-0.815409\pi$
$563$	−39.6968	−1.67302	−0.836511	+	0.547950i	$0.815409\pi$
$564$	0.568431	0.0239352
$565$	0.280702	0.0118092
$566$	−10.6584	−0.448004
$567$	1.43806	0.0603928
$568$	8.81736	0.369968
$569$	−28.0771	−1.17706	−0.588528	−	0.808477i	$-0.700292\pi$
$569$	−28.0771	−1.17706	−0.588528	+	0.808477i	$0.700292\pi$
$570$	−1.27486	−0.0533982
$571$	−5.29214	−0.221469	−0.110735	−	0.993850i	$-0.535320\pi$
$571$	−5.29214	−0.221469	−0.110735	+	0.993850i	$0.535320\pi$
$572$	2.35029	0.0982706
$573$	−1.32292	−0.0552658
$574$	0.624805	0.0260789
$575$	−3.21714	−0.134164
$576$	−2.97395	−0.123915
$577$	−0.303675	−0.0126422	−0.00632109	−	0.999980i	$-0.502012\pi$
$577$	−0.303675	−0.0126422	−0.00632109	+	0.999980i	$0.502012\pi$
$578$	−1.14467	−0.0476119
$579$	−1.91899	−0.0797504
$580$	−10.4346	−0.433273
$581$	2.25818	0.0936849
$582$	1.55181	0.0643247
$583$	−13.9577	−0.578067
$584$	15.5099	0.641805
$585$	2.97395	0.122958
$586$	−25.7356	−1.06313
$587$	−24.6242	−1.01635	−0.508175	−	0.861254i	$-0.669680\pi$
$587$	−24.6242	−1.01635	−0.508175	+	0.861254i	$0.669680\pi$
$588$	−1.12538	−0.0464101
$589$	7.89930	0.325485
$590$	−4.00308	−0.164804
$591$	3.12610	0.128590
$592$	0.957283	0.0393441
$593$	−11.2385	−0.461510	−0.230755	−	0.973012i	$-0.574120\pi$
$593$	−11.2385	−0.461510	−0.230755	+	0.973012i	$0.574120\pi$
$594$	−2.26600	−0.0929750
$595$	0.653206	0.0267788
$596$	−2.13236	−0.0873450
$597$	0.185101	0.00757566
$598$	−3.21714	−0.131559
$599$	17.9143	0.731959	0.365979	−	0.930623i	$-0.380734\pi$
$599$	17.9143	0.731959	0.365979	+	0.930623i	$0.380734\pi$
$600$	0.161390	0.00658871
$601$	−15.8206	−0.645335	−0.322667	−	0.946512i	$-0.604580\pi$
$601$	−15.8206	−0.645335	−0.322667	+	0.946512i	$0.604580\pi$
$602$	−1.92751	−0.0785595
$603$	5.60023	0.228059
$604$	−5.61008	−0.228271
$605$	5.47613	0.222636
$606$	−0.540319	−0.0219489
$607$	−21.2441	−0.862270	−0.431135	−	0.902287i	$-0.641887\pi$
$607$	−21.2441	−0.862270	−0.431135	+	0.902287i	$0.641887\pi$
$608$	7.89930	0.320359
$609$	0.276257	0.0111945
$610$	−6.23073	−0.252275
$611$	3.52210	0.142489
$612$	11.8419	0.478681
$613$	−24.4275	−0.986616	−0.493308	−	0.869855i	$-0.664212\pi$
$613$	−24.4275	−0.986616	−0.493308	+	0.869855i	$0.664212\pi$
$614$	5.41592	0.218569
$615$	−0.614693	−0.0247868
$616$	0.385553	0.0155344
$617$	−21.3128	−0.858019	−0.429010	−	0.903300i	$-0.641137\pi$
$617$	−21.3128	−0.858019	−0.429010	+	0.903300i	$0.641137\pi$
$618$	−0.0283481	−0.00114033
$619$	20.4062	0.820195	0.410098	−	0.912042i	$-0.365495\pi$
$619$	20.4062	0.820195	0.410098	+	0.912042i	$0.365495\pi$
$620$	−1.00000	−0.0401610
$621$	3.10176	0.124469
$622$	−26.8169	−1.07526
$623$	2.28988	0.0917423
$624$	0.161390	0.00646076
$625$	1.00000	0.0400000
$626$	−30.5542	−1.22119
$627$	2.99630	0.119661
$628$	−5.75864	−0.229795
$629$	−3.81178	−0.151986
$630$	0.487861	0.0194369
$631$	−6.56216	−0.261235	−0.130618	−	0.991433i	$-0.541696\pi$
$631$	−6.56216	−0.261235	−0.130618	+	0.991433i	$0.541696\pi$
$632$	13.6125	0.541477
$633$	−2.73729	−0.108797
$634$	20.6021	0.818215
$635$	8.42930	0.334506
$636$	−0.958444	−0.0380048
$637$	−6.97309	−0.276284
$638$	24.5244	0.970928
$639$	−26.2224	−1.03734
$640$	−1.00000	−0.0395285
$641$	8.32016	0.328627	0.164313	−	0.986408i	$-0.447459\pi$
$641$	8.32016	0.328627	0.164313	+	0.986408i	$0.447459\pi$
$642$	−2.28644	−0.0902386
$643$	2.96381	0.116881	0.0584407	−	0.998291i	$-0.481387\pi$
$643$	2.96381	0.116881	0.0584407	+	0.998291i	$0.481387\pi$
$644$	−0.527755	−0.0207965
$645$	1.89631	0.0746673
$646$	−31.4540	−1.23754
$647$	40.0786	1.57565	0.787826	−	0.615899i	$-0.211207\pi$
$647$	40.0786	1.57565	0.787826	+	0.615899i	$0.211207\pi$
$648$	8.76626	0.344371
$649$	9.40841	0.369313
$650$	1.00000	0.0392232
$651$	0.0264751	0.00103764
$652$	8.12147	0.318062
$653$	35.8583	1.40324	0.701621	−	0.712550i	$-0.252460\pi$
$653$	35.8583	1.40324	0.701621	+	0.712550i	$0.252460\pi$
$654$	−0.251433	−0.00983182
$655$	−12.4500	−0.486461
$656$	3.80875	0.148707
$657$	−46.1257	−1.79954
$658$	0.577782	0.0225243
$659$	2.84094	0.110667	0.0553337	−	0.998468i	$-0.482378\pi$
$659$	2.84094	0.110667	0.0553337	+	0.998468i	$0.482378\pi$
$660$	−0.379313	−0.0147647
$661$	−15.0391	−0.584954	−0.292477	−	0.956273i	$-0.594479\pi$
$661$	−15.0391	−0.584954	−0.292477	+	0.956273i	$0.594479\pi$
$662$	−1.36971	−0.0532351
$663$	−0.642634	−0.0249578
$664$	13.7656	0.534209
$665$	−1.29584	−0.0502504
$666$	−2.84692	−0.110316
$667$	−33.5696	−1.29982
$668$	−20.2284	−0.782661
$669$	0.750555	0.0290181
$670$	1.88309	0.0727502
$671$	14.6440	0.565326
$672$	0.0264751	0.00102130
$673$	−11.0146	−0.424582	−0.212291	−	0.977207i	$-0.568092\pi$
$673$	−11.0146	−0.424582	−0.212291	+	0.977207i	$0.568092\pi$
$674$	17.7784	0.684799
$675$	−0.964134	−0.0371095
$676$	1.00000	0.0384615
$677$	22.7790	0.875467	0.437734	−	0.899105i	$-0.355781\pi$
$677$	22.7790	0.875467	0.437734	+	0.899105i	$0.355781\pi$
$678$	−0.0453025	−0.00173983
$679$	1.57734	0.0605328
$680$	3.98188	0.152698
$681$	−0.654072	−0.0250641
$682$	2.35029	0.0899973
$683$	0.525781	0.0201185	0.0100592	−	0.999949i	$-0.496798\pi$
$683$	0.525781	0.0201185	0.0100592	+	0.999949i	$0.496798\pi$
$684$	−23.4921	−0.898244
$685$	−13.8030	−0.527386
$686$	−2.29221	−0.0875170
$687$	−1.19914	−0.0457502
$688$	−11.7499	−0.447961
$689$	−5.93869	−0.226246
$690$	0.519213	0.0197661
$691$	4.47719	0.170320	0.0851602	−	0.996367i	$-0.472860\pi$
$691$	4.47719	0.170320	0.0851602	+	0.996367i	$0.472860\pi$
$692$	20.7891	0.790285
$693$	−1.14662	−0.0435564
$694$	16.3148	0.619300
$695$	2.57664	0.0977375
$696$	1.68404	0.0638332
$697$	−15.1660	−0.574452
$698$	−4.89341	−0.185218
$699$	3.86743	0.146280
$700$	0.164045	0.00620031
$701$	−28.2170	−1.06574	−0.532871	−	0.846197i	$-0.678887\pi$
$701$	−28.2170	−1.06574	−0.532871	+	0.846197i	$0.678887\pi$
$702$	−0.964134	−0.0363889
$703$	7.56186	0.285201
$704$	2.35029	0.0885800
$705$	−0.568431	−0.0214083
$706$	−17.3087	−0.651421
$707$	−0.549208	−0.0206551
$708$	0.646056	0.0242803
$709$	42.6946	1.60343	0.801716	−	0.597706i	$-0.203921\pi$
$709$	42.6946	1.60343	0.801716	+	0.597706i	$0.203921\pi$
$710$	−8.81736	−0.330910
$711$	−40.4830	−1.51823
$712$	13.9589	0.523132
$713$	−3.21714	−0.120483
$714$	−0.105421	−0.00394527
$715$	−2.35029	−0.0878959
$716$	15.8230	0.591334
$717$	1.57642	0.0588724
$718$	6.18508	0.230825
$719$	17.8622	0.666149	0.333074	−	0.942901i	$-0.391914\pi$
$719$	17.8622	0.666149	0.333074	+	0.942901i	$0.391914\pi$
$720$	2.97395	0.110833
$721$	−0.0288144	−0.00107311
$722$	43.3989	1.61514
$723$	1.73122	0.0643847
$724$	−3.89260	−0.144667
$725$	10.4346	0.387531
$726$	−0.883791	−0.0328005
$727$	−23.9593	−0.888601	−0.444300	−	0.895878i	$-0.646548\pi$
$727$	−23.9593	−0.888601	−0.444300	+	0.895878i	$0.646548\pi$
$728$	0.164045	0.00607990
$729$	−25.6036	−0.948283
$730$	−15.5099	−0.574047
$731$	46.7867	1.73047
$732$	1.00558	0.0371671
$733$	42.1696	1.55757	0.778784	−	0.627292i	$-0.215837\pi$
$733$	42.1696	1.55757	0.778784	+	0.627292i	$0.215837\pi$
$734$	−34.9399	−1.28966
$735$	1.12538	0.0415104
$736$	−3.21714	−0.118585
$737$	−4.42582	−0.163027
$738$	−11.3270	−0.416954
$739$	3.13480	0.115315	0.0576577	−	0.998336i	$-0.481637\pi$
$739$	3.13480	0.115315	0.0576577	+	0.998336i	$0.481637\pi$
$740$	−0.957283	−0.0351904
$741$	1.27486	0.0468333
$742$	−0.974211	−0.0357644
$743$	−14.9292	−0.547700	−0.273850	−	0.961772i	$-0.588297\pi$
$743$	−14.9292	−0.547700	−0.273850	+	0.961772i	$0.588297\pi$
$744$	0.161390	0.00591683
$745$	2.13236	0.0781238
$746$	15.5298	0.568587
$747$	−40.9383	−1.49785
$748$	−9.35857	−0.342183
$749$	−2.32405	−0.0849191
$750$	−0.161390	−0.00589312
$751$	−37.2298	−1.35854	−0.679268	−	0.733890i	$-0.737703\pi$
$751$	−37.2298	−1.35854	−0.679268	+	0.733890i	$0.737703\pi$
$752$	3.52210	0.128438
$753$	−3.13597	−0.114281
$754$	10.4346	0.380006
$755$	5.61008	0.204172
$756$	−0.158161	−0.00575227
$757$	17.2813	0.628098	0.314049	−	0.949407i	$-0.398314\pi$
$757$	17.2813	0.628098	0.314049	+	0.949407i	$0.398314\pi$
$758$	3.18149	0.115557
$759$	−1.22030	−0.0442942
$760$	−7.89930	−0.286538
$761$	−9.05145	−0.328115	−0.164057	−	0.986451i	$-0.552458\pi$
$761$	−9.05145	−0.328115	−0.164057	+	0.986451i	$0.552458\pi$
$762$	−1.36040	−0.0492821
$763$	−0.255570	−0.00925225
$764$	−8.19707	−0.296559
$765$	−11.8419	−0.428145
$766$	12.9166	0.466694
$767$	4.00308	0.144543
$768$	0.161390	0.00582365
$769$	1.51663	0.0546910	0.0273455	−	0.999626i	$-0.491295\pi$
$769$	1.51663	0.0546910	0.0273455	+	0.999626i	$0.491295\pi$
$770$	−0.385553	−0.0138944
$771$	−0.918902	−0.0330934
$772$	−11.8904	−0.427945
$773$	38.9073	1.39940	0.699699	−	0.714438i	$-0.253318\pi$
$773$	38.9073	1.39940	0.699699	+	0.714438i	$0.253318\pi$
$774$	34.9437	1.25603
$775$	1.00000	0.0359211
$776$	9.61531	0.345170
$777$	0.0253442	0.000909218 0
$778$	−4.20221	−0.150657
$779$	30.0864	1.07796
$780$	−0.161390	−0.00577868
$781$	20.7234	0.741541
$782$	12.8103	0.458094
$783$	−10.0604	−0.359528
$784$	−6.97309	−0.249039
$785$	5.75864	0.205535
$786$	2.00930	0.0716693
$787$	−25.9872	−0.926343	−0.463172	−	0.886269i	$-0.653289\pi$
$787$	−25.9872	−0.926343	−0.463172	+	0.886269i	$0.653289\pi$
$788$	19.3699	0.690023
$789$	3.94944	0.140604
$790$	−13.6125	−0.484312
$791$	−0.0460477	−0.00163727
$792$	−6.98966	−0.248367
$793$	6.23073	0.221260
$794$	−7.41505	−0.263150
$795$	0.958444	0.0339925
$796$	1.14692	0.0406514
$797$	−40.7744	−1.44430	−0.722152	−	0.691735i	$-0.756847\pi$
$797$	−40.7744	−1.44430	−0.722152	+	0.691735i	$0.756847\pi$
$798$	0.209135	0.00740329
$799$	−14.0246	−0.496153
$800$	1.00000	0.0353553
$801$	−41.5131	−1.46679
$802$	−35.1352	−1.24067
$803$	36.4528	1.28639
$804$	−0.303912	−0.0107181
$805$	0.527755	0.0186009
$806$	1.00000	0.0352235
$807$	−2.21215	−0.0778714
$808$	−3.34791	−0.117779
$809$	−32.1220	−1.12935	−0.564674	−	0.825314i	$-0.690998\pi$
$809$	−32.1220	−1.12935	−0.564674	+	0.825314i	$0.690998\pi$
$810$	−8.76626	−0.308015
$811$	−22.5538	−0.791970	−0.395985	−	0.918257i	$-0.629597\pi$
$811$	−22.5538	−0.791970	−0.395985	+	0.918257i	$0.629597\pi$
$812$	1.71174	0.0600703
$813$	−3.92197	−0.137549
$814$	2.24990	0.0788588
$815$	−8.12147	−0.284483
$816$	−0.642634	−0.0224967
$817$	−92.8160	−3.24722
$818$	−10.9834	−0.384026
$819$	−0.487861	−0.0170473
$820$	−3.80875	−0.133007
$821$	−23.0109	−0.803088	−0.401544	−	0.915840i	$-0.631526\pi$
$821$	−23.0109	−0.803088	−0.401544	+	0.915840i	$0.631526\pi$
$822$	2.22766	0.0776987
$823$	3.74567	0.130566	0.0652829	−	0.997867i	$-0.479205\pi$
$823$	3.74567	0.130566	0.0652829	+	0.997867i	$0.479205\pi$
$824$	−0.175650	−0.00611905
$825$	0.379313	0.0132060
$826$	0.656685	0.0228490
$827$	−4.28996	−0.149177	−0.0745883	−	0.997214i	$-0.523764\pi$
$827$	−4.28996	−0.149177	−0.0745883	+	0.997214i	$0.523764\pi$
$828$	9.56763	0.332498
$829$	14.5788	0.506342	0.253171	−	0.967422i	$-0.418526\pi$
$829$	14.5788	0.506342	0.253171	+	0.967422i	$0.418526\pi$
$830$	−13.7656	−0.477811
$831$	−3.14444	−0.109080
$832$	1.00000	0.0346688
$833$	27.7660	0.962034
$834$	−0.415843	−0.0143995
$835$	20.2284	0.700033
$836$	18.5656	0.642106
$837$	−0.964134	−0.0333254
$838$	−12.9208	−0.446342
$839$	−43.2766	−1.49407	−0.747037	−	0.664782i	$-0.768524\pi$
$839$	−43.2766	−1.49407	−0.747037	+	0.664782i	$0.768524\pi$
$840$	−0.0264751	−0.000913479 0
$841$	79.8808	2.75451
$842$	−22.3718	−0.770982
$843$	2.43016	0.0836992
$844$	−16.9607	−0.583813
$845$	−1.00000	−0.0344010
$846$	−10.4746	−0.360123
$847$	−0.898330	−0.0308670
$848$	−5.93869	−0.203936
$849$	−1.72015	−0.0590353
$850$	−3.98188	−0.136577
$851$	−3.07972	−0.105571
$852$	1.42303	0.0487523
$853$	5.39246	0.184634	0.0923171	−	0.995730i	$-0.470573\pi$
$853$	5.39246	0.184634	0.0923171	+	0.995730i	$0.470573\pi$
$854$	1.02212	0.0349762
$855$	23.4921	0.803414
$856$	−14.1672	−0.484225
$857$	−8.91952	−0.304685	−0.152342	−	0.988328i	$-0.548682\pi$
$857$	−8.91952	−0.304685	−0.152342	+	0.988328i	$0.548682\pi$
$858$	0.379313	0.0129495
$859$	−35.5230	−1.21203	−0.606015	−	0.795453i	$-0.707233\pi$
$859$	−35.5230	−1.21203	−0.606015	+	0.795453i	$0.707233\pi$
$860$	11.7499	0.400669
$861$	0.100837	0.00343652
$862$	30.3537	1.03385
$863$	−25.1968	−0.857708	−0.428854	−	0.903374i	$-0.641083\pi$
$863$	−25.1968	−0.857708	−0.428854	+	0.903374i	$0.641083\pi$
$864$	−0.964134	−0.0328005
$865$	−20.7891	−0.706852
$866$	−12.2160	−0.415118
$867$	−0.184738	−0.00627402
$868$	0.164045	0.00556804
$869$	31.9934	1.08530
$870$	−1.68404	−0.0570942
$871$	−1.88309	−0.0638061
$872$	−1.55793	−0.0527581
$873$	−28.5955	−0.967811
$874$	−25.4132	−0.859613
$875$	−0.164045	−0.00554572
$876$	2.50314	0.0845732
$877$	−32.1682	−1.08624	−0.543122	−	0.839654i	$-0.682758\pi$
$877$	−32.1682	−1.08624	−0.543122	+	0.839654i	$0.682758\pi$
$878$	41.7062	1.40752
$879$	−4.15346	−0.140093
$880$	−2.35029	−0.0792283
$881$	22.1859	0.747462	0.373731	−	0.927537i	$-0.378078\pi$
$881$	22.1859	0.747462	0.373731	+	0.927537i	$0.378078\pi$
$882$	20.7376	0.698273
$883$	43.6665	1.46949	0.734747	−	0.678341i	$-0.237301\pi$
$883$	43.6665	1.46949	0.734747	+	0.678341i	$0.237301\pi$
$884$	−3.98188	−0.133925
$885$	−0.646056	−0.0217169
$886$	−36.5964	−1.22948
$887$	−10.6129	−0.356347	−0.178174	−	0.983999i	$-0.557019\pi$
$887$	−10.6129	−0.356347	−0.178174	+	0.983999i	$0.557019\pi$
$888$	0.154496	0.00518453
$889$	−1.38278	−0.0463770
$890$	−13.9589	−0.467903
$891$	20.6033	0.690235
$892$	4.65058	0.155713
$893$	27.8221	0.931031
$894$	−0.344142	−0.0115098
$895$	−15.8230	−0.528905
$896$	0.164045	0.00548035
$897$	−0.519213	−0.0173360
$898$	27.1663	0.906551
$899$	10.4346	0.348013
$900$	−2.97395	−0.0991318
$901$	23.6471	0.787800
$902$	8.95167	0.298058
$903$	−0.311080	−0.0103521
$904$	−0.280702	−0.00933602
$905$	3.89260	0.129394
$906$	−0.905408	−0.0300802
$907$	−30.8264	−1.02357	−0.511786	−	0.859113i	$-0.671016\pi$
$907$	−30.8264	−1.02357	−0.511786	+	0.859113i	$0.671016\pi$
$908$	−4.05275	−0.134495
$909$	9.95654	0.330238
$910$	−0.164045	−0.00543803
$911$	44.3854	1.47055	0.735277	−	0.677767i	$-0.237052\pi$
$911$	44.3854	1.47055	0.735277	+	0.677767i	$0.237052\pi$
$912$	1.27486	0.0422150
$913$	32.3532	1.07073
$914$	−20.6435	−0.682827
$915$	−1.00558	−0.0332433
$916$	−7.43011	−0.245498
$917$	2.04235	0.0674444
$918$	3.83906	0.126708
$919$	12.4438	0.410484	0.205242	−	0.978711i	$-0.434202\pi$
$919$	12.4438	0.410484	0.205242	+	0.978711i	$0.434202\pi$
$920$	3.21714	0.106066
$921$	0.874074	0.0288017
$922$	−38.5338	−1.26904
$923$	8.81736	0.290227
$924$	0.0622243	0.00204703
$925$	0.957283	0.0314753
$926$	27.5212	0.904403
$927$	0.522374	0.0171570
$928$	10.4346	0.342532
$929$	−4.08534	−0.134036	−0.0670178	−	0.997752i	$-0.521348\pi$
$929$	−4.08534	−0.134036	−0.0670178	+	0.997752i	$0.521348\pi$
$930$	−0.161390	−0.00529218
$931$	−55.0825	−1.80526
$932$	23.9633	0.784943
$933$	−4.32796	−0.141691
$934$	−6.30800	−0.206404
$935$	9.35857	0.306058
$936$	−2.97395	−0.0972067
$937$	−21.0578	−0.687929	−0.343964	−	0.938983i	$-0.611770\pi$
$937$	−21.0578	−0.687929	−0.343964	+	0.938983i	$0.611770\pi$
$938$	−0.308911	−0.0100863
$939$	−4.93113	−0.160921
$940$	−3.52210	−0.114878
$941$	−22.1589	−0.722359	−0.361180	−	0.932496i	$-0.617626\pi$
$941$	−22.1589	−0.722359	−0.361180	+	0.932496i	$0.617626\pi$
$942$	−0.929385	−0.0302810
$943$	−12.2533	−0.399022
$944$	4.00308	0.130289
$945$	0.158161	0.00514498
$946$	−27.6157	−0.897865
$947$	32.5934	1.05914	0.529571	−	0.848266i	$-0.322353\pi$
$947$	32.5934	1.05914	0.529571	+	0.848266i	$0.322353\pi$
$948$	2.19692	0.0713527
$949$	15.5099	0.503473
$950$	7.89930	0.256287
$951$	3.32497	0.107820
$952$	−0.653206	−0.0211705
$953$	−51.2414	−1.65987	−0.829936	−	0.557858i	$-0.811623\pi$
$953$	−51.2414	−1.65987	−0.829936	+	0.557858i	$0.811623\pi$
$954$	17.6614	0.571809
$955$	8.19707	0.265251
$956$	9.76777	0.315912
$957$	3.95798	0.127943
$958$	40.8995	1.32140
$959$	2.26431	0.0731184
$960$	−0.161390	−0.00520883
$961$	1.00000	0.0322581
$962$	0.957283	0.0308641
$963$	42.1326	1.35770
$964$	10.7270	0.345492
$965$	11.8904	0.382765
$966$	−0.0851742	−0.00274044
$967$	17.6935	0.568986	0.284493	−	0.958678i	$-0.408175\pi$
$967$	17.6935	0.568986	0.284493	+	0.958678i	$0.408175\pi$
$968$	−5.47613	−0.176009
$969$	−5.07635	−0.163076
$970$	−9.61531	−0.308729
$971$	31.3443	1.00589	0.502944	−	0.864319i	$-0.332250\pi$
$971$	31.3443	1.00589	0.502944	+	0.864319i	$0.332250\pi$
$972$	4.30719	0.138153
$973$	−0.422684	−0.0135506
$974$	12.9703	0.415596
$975$	0.161390	0.00516861
$976$	6.23073	0.199441
$977$	11.2254	0.359134	0.179567	−	0.983746i	$-0.442530\pi$
$977$	11.2254	0.359134	0.179567	+	0.983746i	$0.442530\pi$
$978$	1.31072	0.0419123
$979$	32.8075	1.04853
$980$	6.97309	0.222747
$981$	4.63320	0.147927
$982$	−32.7317	−1.04451
$983$	50.9298	1.62441	0.812204	−	0.583374i	$-0.198268\pi$
$983$	50.9298	1.62441	0.812204	+	0.583374i	$0.198268\pi$
$984$	0.614693	0.0195957
$985$	−19.3699	−0.617176
$986$	−41.5493	−1.32320
$987$	0.0932480	0.00296812
$988$	7.89930	0.251310
$989$	37.8011	1.20201
$990$	6.98966	0.222146
$991$	21.4150	0.680269	0.340134	−	0.940377i	$-0.389527\pi$
$991$	21.4150	0.680269	0.340134	+	0.940377i	$0.389527\pi$
$992$	1.00000	0.0317500
$993$	−0.221056	−0.00701501
$994$	1.44644	0.0458784
$995$	−1.14692	−0.0363597
$996$	2.22163	0.0703950
$997$	−10.6713	−0.337964	−0.168982	−	0.985619i	$-0.554048\pi$
$997$	−10.6713	−0.337964	−0.168982	+	0.985619i	$0.554048\pi$
$998$	30.4654	0.964366
$999$	−0.922950	−0.0292008

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4030.2.a.q.1.5	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4030.2.a.q.1.5	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.161390 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.161390 q^{6} +0.164045 q^{7} +1.00000 q^{8} -2.97395 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.161390 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.161390 q^{6} +0.164045 q^{7} +1.00000 q^{8} -2.97395 q^{9} -1.00000 q^{10} +2.35029 q^{11} +0.161390 q^{12} +1.00000 q^{13} +0.164045 q^{14} -0.161390 q^{15} +1.00000 q^{16} -3.98188 q^{17} -2.97395 q^{18} +7.89930 q^{19} -1.00000 q^{20} +0.0264751 q^{21} +2.35029 q^{22} -3.21714 q^{23} +0.161390 q^{24} +1.00000 q^{25} +1.00000 q^{26} -0.964134 q^{27} +0.164045 q^{28} +10.4346 q^{29} -0.161390 q^{30} +1.00000 q^{31} +1.00000 q^{32} +0.379313 q^{33} -3.98188 q^{34} -0.164045 q^{35} -2.97395 q^{36} +0.957283 q^{37} +7.89930 q^{38} +0.161390 q^{39} -1.00000 q^{40} +3.80875 q^{41} +0.0264751 q^{42} -11.7499 q^{43} +2.35029 q^{44} +2.97395 q^{45} -3.21714 q^{46} +3.52210 q^{47} +0.161390 q^{48} -6.97309 q^{49} +1.00000 q^{50} -0.642634 q^{51} +1.00000 q^{52} -5.93869 q^{53} -0.964134 q^{54} -2.35029 q^{55} +0.164045 q^{56} +1.27486 q^{57} +10.4346 q^{58} +4.00308 q^{59} -0.161390 q^{60} +6.23073 q^{61} +1.00000 q^{62} -0.487861 q^{63} +1.00000 q^{64} -1.00000 q^{65} +0.379313 q^{66} -1.88309 q^{67} -3.98188 q^{68} -0.519213 q^{69} -0.164045 q^{70} +8.81736 q^{71} -2.97395 q^{72} +15.5099 q^{73} +0.957283 q^{74} +0.161390 q^{75} +7.89930 q^{76} +0.385553 q^{77} +0.161390 q^{78} +13.6125 q^{79} -1.00000 q^{80} +8.76626 q^{81} +3.80875 q^{82} +13.7656 q^{83} +0.0264751 q^{84} +3.98188 q^{85} -11.7499 q^{86} +1.68404 q^{87} +2.35029 q^{88} +13.9589 q^{89} +2.97395 q^{90} +0.164045 q^{91} -3.21714 q^{92} +0.161390 q^{93} +3.52210 q^{94} -7.89930 q^{95} +0.161390 q^{96} +9.61531 q^{97} -6.97309 q^{98} -6.98966 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} + 3 q^{3} + 9 q^{4} - 9 q^{5} + 3 q^{6} + 3 q^{7} + 9 q^{8} + 14 q^{9}+O(q^{10}) \) 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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