LMFDB - Embedded newform 4017.2.a.e.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, 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("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 21 x^{14} - 3 x^{13} + 177 x^{12} + 45 x^{11} - 763 x^{10} - 251 x^{9} + 1771 x^{8} + 639 x^{7} + \cdots + 7 $ x^16 - 21x^14 - 3x^13 + 177x^12 + 45x^11 - 763x^10 - 251x^9 + 1771x^8 + 639x^7 - 2118x^6 - 710x^5 + 1113x^4 + 243x^3 - 183x^2 - 10x + 7
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$-1.68093$ of defining polynomial
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.68093 q^{2} +1.00000 q^{3} +0.825530 q^{4} +3.10294 q^{5} +1.68093 q^{6} -2.88861 q^{7} -1.97420 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.68093 q^{2} +1.00000 q^{3} +0.825530 q^{4} +3.10294 q^{5} +1.68093 q^{6} -2.88861 q^{7} -1.97420 q^{8} +1.00000 q^{9} +5.21583 q^{10} -6.33881 q^{11} +0.825530 q^{12} -1.00000 q^{13} -4.85556 q^{14} +3.10294 q^{15} -4.96956 q^{16} +2.51078 q^{17} +1.68093 q^{18} -3.30114 q^{19} +2.56157 q^{20} -2.88861 q^{21} -10.6551 q^{22} -8.10901 q^{23} -1.97420 q^{24} +4.62823 q^{25} -1.68093 q^{26} +1.00000 q^{27} -2.38464 q^{28} -5.38671 q^{29} +5.21583 q^{30} +4.15203 q^{31} -4.40508 q^{32} -6.33881 q^{33} +4.22045 q^{34} -8.96319 q^{35} +0.825530 q^{36} -2.47083 q^{37} -5.54899 q^{38} -1.00000 q^{39} -6.12583 q^{40} +10.5456 q^{41} -4.85556 q^{42} -7.60188 q^{43} -5.23288 q^{44} +3.10294 q^{45} -13.6307 q^{46} +0.133876 q^{47} -4.96956 q^{48} +1.34408 q^{49} +7.77973 q^{50} +2.51078 q^{51} -0.825530 q^{52} +9.74524 q^{53} +1.68093 q^{54} -19.6689 q^{55} +5.70271 q^{56} -3.30114 q^{57} -9.05470 q^{58} +2.12828 q^{59} +2.56157 q^{60} -5.40280 q^{61} +6.97928 q^{62} -2.88861 q^{63} +2.53448 q^{64} -3.10294 q^{65} -10.6551 q^{66} -3.99871 q^{67} +2.07272 q^{68} -8.10901 q^{69} -15.0665 q^{70} -8.14246 q^{71} -1.97420 q^{72} +1.35362 q^{73} -4.15330 q^{74} +4.62823 q^{75} -2.72519 q^{76} +18.3104 q^{77} -1.68093 q^{78} -1.64215 q^{79} -15.4202 q^{80} +1.00000 q^{81} +17.7264 q^{82} -10.0548 q^{83} -2.38464 q^{84} +7.79080 q^{85} -12.7782 q^{86} -5.38671 q^{87} +12.5141 q^{88} +2.13059 q^{89} +5.21583 q^{90} +2.88861 q^{91} -6.69423 q^{92} +4.15203 q^{93} +0.225037 q^{94} -10.2432 q^{95} -4.40508 q^{96} +13.5640 q^{97} +2.25931 q^{98} -6.33881 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{3} + 10 q^{4} - 6 q^{5} - 13 q^{7} - 9 q^{8} + 16 q^{9}+O(q^{10}) $ 16 * q + 16 * q^3 + 10 * q^4 - 6 * q^5 - 13 * q^7 - 9 * q^8 + 16 * q^9	\( 16 q + 16 q^{3} + 10 q^{4} - 6 q^{5} - 13 q^{7} - 9 q^{8} + 16 q^{9} - 8 q^{10} - 5 q^{11} + 10 q^{12} - 16 q^{13} - 8 q^{14} - 6 q^{15} - 14 q^{16} - q^{17} + 6 q^{19} - 4 q^{20} - 13 q^{21} - 11 q^{22} - 21 q^{23} - 9 q^{24} - 10 q^{25} + 16 q^{27} - 10 q^{28} - 17 q^{29} - 8 q^{30} - 33 q^{31} - 18 q^{32} - 5 q^{33} - 5 q^{34} - 4 q^{35} + 10 q^{36} - 23 q^{37} - 28 q^{38} - 16 q^{39} - 12 q^{40} + 7 q^{41} - 8 q^{42} - 33 q^{43} + 11 q^{44} - 6 q^{45} - 15 q^{46} - 13 q^{47} - 14 q^{48} - 17 q^{49} + 35 q^{50} - q^{51} - 10 q^{52} - 20 q^{53} - 54 q^{55} + 12 q^{56} + 6 q^{57} - 33 q^{58} + 6 q^{59} - 4 q^{60} - 49 q^{61} - 13 q^{62} - 13 q^{63} - 35 q^{64} + 6 q^{65} - 11 q^{66} - 4 q^{67} - 14 q^{68} - 21 q^{69} - 33 q^{70} - 29 q^{71} - 9 q^{72} - 21 q^{73} + 22 q^{74} - 10 q^{75} + 10 q^{76} - 21 q^{77} - 70 q^{79} - 8 q^{80} + 16 q^{81} - 10 q^{82} + 5 q^{83} - 10 q^{84} + 14 q^{85} + 29 q^{86} - 17 q^{87} - 45 q^{88} - 8 q^{89} - 8 q^{90} + 13 q^{91} - 29 q^{92} - 33 q^{93} + 12 q^{94} - 45 q^{95} - 18 q^{96} - 30 q^{97} + 15 q^{98} - 5 q^{99}+O(q^{100}) \) 16 * q + 16 * q^3 + 10 * q^4 - 6 * q^5 - 13 * q^7 - 9 * q^8 + 16 * q^9 - 8 * q^10 - 5 * q^11 + 10 * q^12 - 16 * q^13 - 8 * q^14 - 6 * q^15 - 14 * q^16 - q^17 + 6 * q^19 - 4 * q^20 - 13 * q^21 - 11 * q^22 - 21 * q^23 - 9 * q^24 - 10 * q^25 + 16 * q^27 - 10 * q^28 - 17 * q^29 - 8 * q^30 - 33 * q^31 - 18 * q^32 - 5 * q^33 - 5 * q^34 - 4 * q^35 + 10 * q^36 - 23 * q^37 - 28 * q^38 - 16 * q^39 - 12 * q^40 + 7 * q^41 - 8 * q^42 - 33 * q^43 + 11 * q^44 - 6 * q^45 - 15 * q^46 - 13 * q^47 - 14 * q^48 - 17 * q^49 + 35 * q^50 - q^51 - 10 * q^52 - 20 * q^53 - 54 * q^55 + 12 * q^56 + 6 * q^57 - 33 * q^58 + 6 * q^59 - 4 * q^60 - 49 * q^61 - 13 * q^62 - 13 * q^63 - 35 * q^64 + 6 * q^65 - 11 * q^66 - 4 * q^67 - 14 * q^68 - 21 * q^69 - 33 * q^70 - 29 * q^71 - 9 * q^72 - 21 * q^73 + 22 * q^74 - 10 * q^75 + 10 * q^76 - 21 * q^77 - 70 * q^79 - 8 * q^80 + 16 * q^81 - 10 * q^82 + 5 * q^83 - 10 * q^84 + 14 * q^85 + 29 * q^86 - 17 * q^87 - 45 * q^88 - 8 * q^89 - 8 * q^90 + 13 * q^91 - 29 * q^92 - 33 * q^93 + 12 * q^94 - 45 * q^95 - 18 * q^96 - 30 * q^97 + 15 * q^98 - 5 * 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 $

$2$	1.68093	1.18860	0.594299	−	0.804244i	$-0.297430\pi$
$2$	1.68093	1.18860	0.594299	+	0.804244i	$0.297430\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.825530	0.412765
$5$	3.10294	1.38768	0.693838	−	0.720131i	$-0.255918\pi$
$5$	3.10294	1.38768	0.693838	+	0.720131i	$0.255918\pi$
$6$	1.68093	0.686237
$7$	−2.88861	−1.09179	−0.545896	−	0.837853i	$-0.683811\pi$
$7$	−2.88861	−1.09179	−0.545896	+	0.837853i	$0.683811\pi$
$8$	−1.97420	−0.697986
$9$	1.00000	0.333333
$10$	5.21583	1.64939
$11$	−6.33881	−1.91122	−0.955611	−	0.294632i	$-0.904803\pi$
$11$	−6.33881	−1.91122	−0.955611	+	0.294632i	$0.904803\pi$
$12$	0.825530	0.238310
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−4.85556	−1.29770
$15$	3.10294	0.801175
$16$	−4.96956	−1.24239
$17$	2.51078	0.608954	0.304477	−	0.952520i	$-0.401518\pi$
$17$	2.51078	0.608954	0.304477	+	0.952520i	$0.401518\pi$
$18$	1.68093	0.396199
$19$	−3.30114	−0.757334	−0.378667	−	0.925533i	$-0.623617\pi$
$19$	−3.30114	−0.757334	−0.378667	+	0.925533i	$0.623617\pi$
$20$	2.56157	0.572784
$21$	−2.88861	−0.630347
$22$	−10.6551	−2.27167
$23$	−8.10901	−1.69084	−0.845422	−	0.534098i	$-0.820651\pi$
$23$	−8.10901	−1.69084	−0.845422	+	0.534098i	$0.820651\pi$
$24$	−1.97420	−0.402982
$25$	4.62823	0.925646
$26$	−1.68093	−0.329658
$27$	1.00000	0.192450
$28$	−2.38464	−0.450654
$29$	−5.38671	−1.00029	−0.500144	−	0.865942i	$-0.666720\pi$
$29$	−5.38671	−1.00029	−0.500144	+	0.865942i	$0.666720\pi$
$30$	5.21583	0.952275
$31$	4.15203	0.745727	0.372863	−	0.927886i	$-0.378376\pi$
$31$	4.15203	0.745727	0.372863	+	0.927886i	$0.378376\pi$
$32$	−4.40508	−0.778716
$33$	−6.33881	−1.10344
$34$	4.22045	0.723801
$35$	−8.96319	−1.51505
$36$	0.825530	0.137588
$37$	−2.47083	−0.406202	−0.203101	−	0.979158i	$-0.565102\pi$
$37$	−2.47083	−0.406202	−0.203101	+	0.979158i	$0.565102\pi$
$38$	−5.54899	−0.900165
$39$	−1.00000	−0.160128
$40$	−6.12583	−0.968579
$41$	10.5456	1.64694	0.823471	−	0.567359i	$-0.192035\pi$
$41$	10.5456	1.64694	0.823471	+	0.567359i	$0.192035\pi$
$42$	−4.85556	−0.749229
$43$	−7.60188	−1.15928	−0.579638	−	0.814874i	$-0.696806\pi$
$43$	−7.60188	−1.15928	−0.579638	+	0.814874i	$0.696806\pi$
$44$	−5.23288	−0.788886
$45$	3.10294	0.462559
$46$	−13.6307	−2.00973
$47$	0.133876	0.0195279	0.00976393	−	0.999952i	$-0.496892\pi$
$47$	0.133876	0.0195279	0.00976393	+	0.999952i	$0.496892\pi$
$48$	−4.96956	−0.717294
$49$	1.34408	0.192011
$50$	7.77973	1.10022
$51$	2.51078	0.351579
$52$	−0.825530	−0.114480
$53$	9.74524	1.33861	0.669306	−	0.742987i	$-0.266592\pi$
$53$	9.74524	1.33861	0.669306	+	0.742987i	$0.266592\pi$
$54$	1.68093	0.228746
$55$	−19.6689	−2.65216
$56$	5.70271	0.762056
$57$	−3.30114	−0.437247
$58$	−9.05470	−1.18894
$59$	2.12828	0.277078	0.138539	−	0.990357i	$-0.455759\pi$
$59$	2.12828	0.277078	0.138539	+	0.990357i	$0.455759\pi$
$60$	2.56157	0.330697
$61$	−5.40280	−0.691758	−0.345879	−	0.938279i	$-0.612419\pi$
$61$	−5.40280	−0.691758	−0.345879	+	0.938279i	$0.612419\pi$
$62$	6.97928	0.886369
$63$	−2.88861	−0.363931
$64$	2.53448	0.316810
$65$	−3.10294	−0.384872
$66$	−10.6551	−1.31155
$67$	−3.99871	−0.488520	−0.244260	−	0.969710i	$-0.578545\pi$
$67$	−3.99871	−0.488520	−0.244260	+	0.969710i	$0.578545\pi$
$68$	2.07272	0.251355
$69$	−8.10901	−0.976210
$70$	−15.0665	−1.80079
$71$	−8.14246	−0.966333	−0.483166	−	0.875529i	$-0.660513\pi$
$71$	−8.14246	−0.966333	−0.483166	+	0.875529i	$0.660513\pi$
$72$	−1.97420	−0.232662
$73$	1.35362	0.158429	0.0792146	−	0.996858i	$-0.474759\pi$
$73$	1.35362	0.158429	0.0792146	+	0.996858i	$0.474759\pi$
$74$	−4.15330	−0.482811
$75$	4.62823	0.534422
$76$	−2.72519	−0.312601
$77$	18.3104	2.08666
$78$	−1.68093	−0.190328
$79$	−1.64215	−0.184756	−0.0923780	−	0.995724i	$-0.529447\pi$
$79$	−1.64215	−0.184756	−0.0923780	+	0.995724i	$0.529447\pi$
$80$	−15.4202	−1.72404
$81$	1.00000	0.111111
$82$	17.7264	1.95755
$83$	−10.0548	−1.10366	−0.551829	−	0.833957i	$-0.686070\pi$
$83$	−10.0548	−1.10366	−0.551829	+	0.833957i	$0.686070\pi$
$84$	−2.38464	−0.260185
$85$	7.79080	0.845030
$86$	−12.7782	−1.37791
$87$	−5.38671	−0.577516
$88$	12.5141	1.33401
$89$	2.13059	0.225842	0.112921	−	0.993604i	$-0.463979\pi$
$89$	2.13059	0.225842	0.112921	+	0.993604i	$0.463979\pi$
$90$	5.21583	0.549796
$91$	2.88861	0.302809
$92$	−6.69423	−0.697922
$93$	4.15203	0.430546
$94$	0.225037	0.0232108
$95$	−10.2432	−1.05093
$96$	−4.40508	−0.449592
$97$	13.5640	1.37722	0.688609	−	0.725133i	$-0.258222\pi$
$97$	13.5640	1.37722	0.688609	+	0.725133i	$0.258222\pi$
$98$	2.25931	0.228224
$99$	−6.33881	−0.637074
$100$	3.82074	0.382074
$101$	4.48138	0.445914	0.222957	−	0.974828i	$-0.428429\pi$
$101$	4.48138	0.445914	0.222957	+	0.974828i	$0.428429\pi$
$102$	4.22045	0.417887
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	1.97420	0.193587
$105$	−8.96319	−0.874717
$106$	16.3811	1.59107
$107$	7.61288	0.735965	0.367982	−	0.929833i	$-0.380049\pi$
$107$	7.61288	0.735965	0.367982	+	0.929833i	$0.380049\pi$
$108$	0.825530	0.0794367
$109$	−4.03943	−0.386908	−0.193454	−	0.981109i	$-0.561969\pi$
$109$	−4.03943	−0.386908	−0.193454	+	0.981109i	$0.561969\pi$
$110$	−33.0621	−3.15235
$111$	−2.47083	−0.234521
$112$	14.3551	1.35643
$113$	−17.3917	−1.63607	−0.818036	−	0.575168i	$-0.804937\pi$
$113$	−17.3917	−1.63607	−0.818036	+	0.575168i	$0.804937\pi$
$114$	−5.54899	−0.519711
$115$	−25.1617	−2.34634
$116$	−4.44690	−0.412884
$117$	−1.00000	−0.0924500
$118$	3.57749	0.329334
$119$	−7.25267	−0.664851
$120$	−6.12583	−0.559209
$121$	29.1805	2.65277
$122$	−9.08174	−0.822222
$123$	10.5456	0.950862
$124$	3.42763	0.307810
$125$	−1.15359	−0.103180
$126$	−4.85556	−0.432568
$127$	13.0239	1.15568	0.577841	−	0.816149i	$-0.303895\pi$
$127$	13.0239	1.15568	0.577841	+	0.816149i	$0.303895\pi$
$128$	13.0704	1.15528
$129$	−7.60188	−0.669308
$130$	−5.21583	−0.457458
$131$	9.00844	0.787071	0.393536	−	0.919309i	$-0.371252\pi$
$131$	9.00844	0.787071	0.393536	+	0.919309i	$0.371252\pi$
$132$	−5.23288	−0.455463
$133$	9.53571	0.826851
$134$	−6.72156	−0.580654
$135$	3.10294	0.267058
$136$	−4.95679	−0.425041
$137$	−12.6192	−1.07813	−0.539064	−	0.842265i	$-0.681222\pi$
$137$	−12.6192	−1.07813	−0.539064	+	0.842265i	$0.681222\pi$
$138$	−13.6307	−1.16032
$139$	−7.15961	−0.607270	−0.303635	−	0.952788i	$-0.598200\pi$
$139$	−7.15961	−0.607270	−0.303635	+	0.952788i	$0.598200\pi$
$140$	−7.39938	−0.625362
$141$	0.133876	0.0112744
$142$	−13.6869	−1.14858
$143$	6.33881	0.530078
$144$	−4.96956	−0.414130
$145$	−16.7146	−1.38808
$146$	2.27534	0.188309
$147$	1.34408	0.110858
$148$	−2.03975	−0.167666
$149$	1.37190	0.112390	0.0561951	−	0.998420i	$-0.482103\pi$
$149$	1.37190	0.112390	0.0561951	+	0.998420i	$0.482103\pi$
$150$	7.77973	0.635213
$151$	14.3968	1.17160	0.585799	−	0.810457i	$-0.300781\pi$
$151$	14.3968	1.17160	0.585799	+	0.810457i	$0.300781\pi$
$152$	6.51712	0.528608
$153$	2.51078	0.202985
$154$	30.7784	2.48020
$155$	12.8835	1.03483
$156$	−0.825530	−0.0660953
$157$	0.163215	0.0130260	0.00651301	−	0.999979i	$-0.497927\pi$
$157$	0.163215	0.0130260	0.00651301	+	0.999979i	$0.497927\pi$
$158$	−2.76034	−0.219601
$159$	9.74524	0.772848
$160$	−13.6687	−1.08061
$161$	23.4238	1.84605
$162$	1.68093	0.132066
$163$	−3.18739	−0.249656	−0.124828	−	0.992178i	$-0.539838\pi$
$163$	−3.18739	−0.249656	−0.124828	+	0.992178i	$0.539838\pi$
$164$	8.70569	0.679800
$165$	−19.6689	−1.53122
$166$	−16.9014	−1.31181
$167$	−7.13151	−0.551853	−0.275926	−	0.961179i	$-0.588985\pi$
$167$	−7.13151	−0.551853	−0.275926	+	0.961179i	$0.588985\pi$
$168$	5.70271	0.439973
$169$	1.00000	0.0769231
$170$	13.0958	1.00440
$171$	−3.30114	−0.252445
$172$	−6.27558	−0.478509
$173$	−1.49915	−0.113978	−0.0569892	−	0.998375i	$-0.518150\pi$
$173$	−1.49915	−0.113978	−0.0569892	+	0.998375i	$0.518150\pi$
$174$	−9.05470	−0.686435
$175$	−13.3692	−1.01061
$176$	31.5011	2.37448
$177$	2.12828	0.159971
$178$	3.58137	0.268435
$179$	−0.789368	−0.0590002	−0.0295001	−	0.999565i	$-0.509392\pi$
$179$	−0.789368	−0.0590002	−0.0295001	+	0.999565i	$0.509392\pi$
$180$	2.56157	0.190928
$181$	−16.0588	−1.19364	−0.596821	−	0.802374i	$-0.703570\pi$
$181$	−16.0588	−1.19364	−0.596821	+	0.802374i	$0.703570\pi$
$182$	4.85556	0.359918
$183$	−5.40280	−0.399386
$184$	16.0088	1.18019
$185$	−7.66684	−0.563677
$186$	6.97928	0.511746
$187$	−15.9153	−1.16385
$188$	0.110519	0.00806042
$189$	−2.88861	−0.210116
$190$	−17.2182	−1.24914
$191$	0.971495	0.0702949	0.0351475	−	0.999382i	$-0.488810\pi$
$191$	0.971495	0.0702949	0.0351475	+	0.999382i	$0.488810\pi$
$192$	2.53448	0.182910
$193$	14.8698	1.07035	0.535175	−	0.844741i	$-0.320246\pi$
$193$	14.8698	1.07035	0.535175	+	0.844741i	$0.320246\pi$
$194$	22.8002	1.63696
$195$	−3.10294	−0.222206
$196$	1.10958	0.0792556
$197$	−23.7237	−1.69024	−0.845120	−	0.534576i	$-0.820471\pi$
$197$	−23.7237	−1.69024	−0.845120	+	0.534576i	$0.820471\pi$
$198$	−10.6551	−0.757225
$199$	1.73854	0.123242	0.0616211	−	0.998100i	$-0.480373\pi$
$199$	1.73854	0.123242	0.0616211	+	0.998100i	$0.480373\pi$
$200$	−9.13706	−0.646088
$201$	−3.99871	−0.282047
$202$	7.53289	0.530013
$203$	15.5601	1.09211
$204$	2.07272	0.145120
$205$	32.7223	2.28542
$206$	1.68093	0.117116
$207$	−8.10901	−0.563615
$208$	4.96956	0.344577
$209$	20.9253	1.44743
$210$	−15.0665	−1.03969
$211$	−10.4953	−0.722528	−0.361264	−	0.932464i	$-0.617655\pi$
$211$	−10.4953	−0.722528	−0.361264	+	0.932464i	$0.617655\pi$
$212$	8.04499	0.552532
$213$	−8.14246	−0.557912
$214$	12.7967	0.874766
$215$	−23.5882	−1.60870
$216$	−1.97420	−0.134327
$217$	−11.9936	−0.814179
$218$	−6.79001	−0.459878
$219$	1.35362	0.0914692
$220$	−16.2373	−1.09472
$221$	−2.51078	−0.168893
$222$	−4.15330	−0.278751
$223$	−6.23793	−0.417722	−0.208861	−	0.977945i	$-0.566976\pi$
$223$	−6.23793	−0.417722	−0.208861	+	0.977945i	$0.566976\pi$
$224$	12.7246	0.850197
$225$	4.62823	0.308549
$226$	−29.2342	−1.94463
$227$	18.5572	1.23169	0.615843	−	0.787869i	$-0.288816\pi$
$227$	18.5572	1.23169	0.615843	+	0.787869i	$0.288816\pi$
$228$	−2.72519	−0.180480
$229$	−8.45592	−0.558783	−0.279391	−	0.960177i	$-0.590133\pi$
$229$	−8.45592	−0.558783	−0.279391	+	0.960177i	$0.590133\pi$
$230$	−42.2952	−2.78886
$231$	18.3104	1.20473
$232$	10.6345	0.698187
$233$	−12.9047	−0.845414	−0.422707	−	0.906266i	$-0.638920\pi$
$233$	−12.9047	−0.845414	−0.422707	+	0.906266i	$0.638920\pi$
$234$	−1.68093	−0.109886
$235$	0.415410	0.0270984
$236$	1.75696	0.114368
$237$	−1.64215	−0.106669
$238$	−12.1912	−0.790241
$239$	−8.68039	−0.561487	−0.280744	−	0.959783i	$-0.590581\pi$
$239$	−8.68039	−0.561487	−0.280744	+	0.959783i	$0.590581\pi$
$240$	−15.4202	−0.995372
$241$	12.2041	0.786138	0.393069	−	0.919509i	$-0.371413\pi$
$241$	12.2041	0.786138	0.393069	+	0.919509i	$0.371413\pi$
$242$	49.0503	3.15308
$243$	1.00000	0.0641500
$244$	−4.46018	−0.285533
$245$	4.17060	0.266450
$246$	17.7264	1.13019
$247$	3.30114	0.210047
$248$	−8.19695	−0.520507
$249$	−10.0548	−0.637198
$250$	−1.93910	−0.122639
$251$	16.8203	1.06169	0.530845	−	0.847469i	$-0.321875\pi$
$251$	16.8203	1.06169	0.530845	+	0.847469i	$0.321875\pi$
$252$	−2.38464	−0.150218
$253$	51.4014	3.23158
$254$	21.8922	1.37364
$255$	7.79080	0.487879
$256$	16.9016	1.05635
$257$	−29.3034	−1.82790	−0.913948	−	0.405832i	$-0.866982\pi$
$257$	−29.3034	−1.82790	−0.913948	+	0.405832i	$0.866982\pi$
$258$	−12.7782	−0.795538
$259$	7.13727	0.443489
$260$	−2.56157	−0.158862
$261$	−5.38671	−0.333429
$262$	15.1426	0.935511
$263$	0.0275597	0.00169940	0.000849702	−	1.00000i	$-0.499730\pi$
$263$	0.0275597	0.00169940	0.000849702		1.00000i	$0.499730\pi$
$264$	12.5141	0.770189
$265$	30.2389	1.85756
$266$	16.0289	0.982794
$267$	2.13059	0.130390
$268$	−3.30106	−0.201644
$269$	−4.35764	−0.265690	−0.132845	−	0.991137i	$-0.542411\pi$
$269$	−4.35764	−0.265690	−0.132845	+	0.991137i	$0.542411\pi$
$270$	5.21583	0.317425
$271$	−18.9317	−1.15002	−0.575010	−	0.818146i	$-0.695002\pi$
$271$	−18.9317	−1.15002	−0.575010	+	0.818146i	$0.695002\pi$
$272$	−12.4775	−0.756558
$273$	2.88861	0.174827
$274$	−21.2120	−1.28146
$275$	−29.3374	−1.76911
$276$	−6.69423	−0.402945
$277$	−1.14646	−0.0688841	−0.0344421	−	0.999407i	$-0.510965\pi$
$277$	−1.14646	−0.0688841	−0.0344421	+	0.999407i	$0.510965\pi$
$278$	−12.0348	−0.721800
$279$	4.15203	0.248576
$280$	17.6951	1.05749
$281$	31.0649	1.85318	0.926590	−	0.376074i	$-0.122726\pi$
$281$	31.0649	1.85318	0.926590	+	0.376074i	$0.122726\pi$
$282$	0.225037	0.0134007
$283$	22.3233	1.32698	0.663492	−	0.748184i	$-0.269074\pi$
$283$	22.3233	1.32698	0.663492	+	0.748184i	$0.269074\pi$
$284$	−6.72185	−0.398868
$285$	−10.2432	−0.606757
$286$	10.6551	0.630049
$287$	−30.4621	−1.79812
$288$	−4.40508	−0.259572
$289$	−10.6960	−0.629176
$290$	−28.0962	−1.64986
$291$	13.5640	0.795137
$292$	1.11745	0.0653941
$293$	12.0618	0.704657	0.352328	−	0.935876i	$-0.385390\pi$
$293$	12.0618	0.704657	0.352328	+	0.935876i	$0.385390\pi$
$294$	2.25931	0.131765
$295$	6.60391	0.384495
$296$	4.87792	0.283524
$297$	−6.33881	−0.367815
$298$	2.30606	0.133587
$299$	8.10901	0.468956
$300$	3.82074	0.220591
$301$	21.9589	1.26569
$302$	24.2001	1.39256
$303$	4.48138	0.257449
$304$	16.4052	0.940904
$305$	−16.7646	−0.959936
$306$	4.22045	0.241267
$307$	−5.39287	−0.307787	−0.153894	−	0.988087i	$-0.549181\pi$
$307$	−5.39287	−0.307787	−0.153894	+	0.988087i	$0.549181\pi$
$308$	15.1157	0.861300
$309$	1.00000	0.0568880
$310$	21.6563	1.22999
$311$	5.89432	0.334237	0.167118	−	0.985937i	$-0.446554\pi$
$311$	5.89432	0.334237	0.167118	+	0.985937i	$0.446554\pi$
$312$	1.97420	0.111767
$313$	−17.3864	−0.982735	−0.491367	−	0.870952i	$-0.663503\pi$
$313$	−17.3864	−0.982735	−0.491367	+	0.870952i	$0.663503\pi$
$314$	0.274354	0.0154827
$315$	−8.96319	−0.505018
$316$	−1.35564	−0.0762609
$317$	14.6317	0.821799	0.410899	−	0.911681i	$-0.365215\pi$
$317$	14.6317	0.821799	0.410899	+	0.911681i	$0.365215\pi$
$318$	16.3811	0.918605
$319$	34.1453	1.91177
$320$	7.86433	0.439629
$321$	7.61288	0.424910
$322$	39.3738	2.19421
$323$	−8.28844	−0.461181
$324$	0.825530	0.0458628
$325$	−4.62823	−0.256728
$326$	−5.35779	−0.296741
$327$	−4.03943	−0.223381
$328$	−20.8191	−1.14954
$329$	−0.386717	−0.0213204
$330$	−33.0621	−1.82001
$331$	−17.0163	−0.935298	−0.467649	−	0.883914i	$-0.654899\pi$
$331$	−17.0163	−0.935298	−0.467649	+	0.883914i	$0.654899\pi$
$332$	−8.30055	−0.455552
$333$	−2.47083	−0.135401
$334$	−11.9876	−0.655931
$335$	−12.4078	−0.677908
$336$	14.3551	0.783137
$337$	2.54973	0.138893	0.0694464	−	0.997586i	$-0.477877\pi$
$337$	2.54973	0.138893	0.0694464	+	0.997586i	$0.477877\pi$
$338$	1.68093	0.0914306
$339$	−17.3917	−0.944586
$340$	6.43154	0.348799
$341$	−26.3189	−1.42525
$342$	−5.54899	−0.300055
$343$	16.3378	0.882156
$344$	15.0077	0.809158
$345$	−25.1617	−1.35466
$346$	−2.51997	−0.135474
$347$	−28.9612	−1.55472	−0.777359	−	0.629057i	$-0.783441\pi$
$347$	−28.9612	−1.55472	−0.777359	+	0.629057i	$0.783441\pi$
$348$	−4.44690	−0.238379
$349$	1.83638	0.0982989	0.0491495	−	0.998791i	$-0.484349\pi$
$349$	1.83638	0.0982989	0.0491495	+	0.998791i	$0.484349\pi$
$350$	−22.4726	−1.20121
$351$	−1.00000	−0.0533761
$352$	27.9230	1.48830
$353$	−28.7296	−1.52912	−0.764562	−	0.644550i	$-0.777045\pi$
$353$	−28.7296	−1.52912	−0.764562	+	0.644550i	$0.777045\pi$
$354$	3.57749	0.190141
$355$	−25.2656	−1.34096
$356$	1.75886	0.0932196
$357$	−7.25267	−0.383852
$358$	−1.32687	−0.0701275
$359$	−14.7337	−0.777613	−0.388806	−	0.921319i	$-0.627113\pi$
$359$	−14.7337	−0.777613	−0.388806	+	0.921319i	$0.627113\pi$
$360$	−6.12583	−0.322860
$361$	−8.10247	−0.426446
$362$	−26.9938	−1.41876
$363$	29.1805	1.53158
$364$	2.38464	0.124989
$365$	4.20020	0.219849
$366$	−9.08174	−0.474710
$367$	−37.8105	−1.97369	−0.986847	−	0.161656i	$-0.948316\pi$
$367$	−37.8105	−1.97369	−0.986847	+	0.161656i	$0.948316\pi$
$368$	40.2982	2.10069
$369$	10.5456	0.548980
$370$	−12.8874	−0.669986
$371$	−28.1502	−1.46149
$372$	3.42763	0.177714
$373$	24.8546	1.28692	0.643461	−	0.765479i	$-0.277498\pi$
$373$	24.8546	1.28692	0.643461	+	0.765479i	$0.277498\pi$
$374$	−26.7526	−1.38334
$375$	−1.15359	−0.0595709
$376$	−0.264299	−0.0136302
$377$	5.38671	0.277430
$378$	−4.85556	−0.249743
$379$	32.1232	1.65006	0.825029	−	0.565090i	$-0.191158\pi$
$379$	32.1232	1.65006	0.825029	+	0.565090i	$0.191158\pi$
$380$	−8.45610	−0.433789
$381$	13.0239	0.667233
$382$	1.63302	0.0835524
$383$	3.19113	0.163059	0.0815296	−	0.996671i	$-0.474019\pi$
$383$	3.19113	0.163059	0.0815296	+	0.996671i	$0.474019\pi$
$384$	13.0704	0.666999
$385$	56.8159	2.89561
$386$	24.9951	1.27222
$387$	−7.60188	−0.386425
$388$	11.1975	0.568467
$389$	10.7161	0.543326	0.271663	−	0.962393i	$-0.412426\pi$
$389$	10.7161	0.543326	0.271663	+	0.962393i	$0.412426\pi$
$390$	−5.21583	−0.264114
$391$	−20.3599	−1.02965
$392$	−2.65349	−0.134021
$393$	9.00844	0.454416
$394$	−39.8778	−2.00902
$395$	−5.09548	−0.256382
$396$	−5.23288	−0.262962
$397$	−8.91433	−0.447397	−0.223699	−	0.974658i	$-0.571813\pi$
$397$	−8.91433	−0.447397	−0.223699	+	0.974658i	$0.571813\pi$
$398$	2.92237	0.146485
$399$	9.53571	0.477383
$400$	−23.0003	−1.15001
$401$	−22.6795	−1.13256	−0.566279	−	0.824214i	$-0.691618\pi$
$401$	−22.6795	−1.13256	−0.566279	+	0.824214i	$0.691618\pi$
$402$	−6.72156	−0.335241
$403$	−4.15203	−0.206827
$404$	3.69952	0.184058
$405$	3.10294	0.154186
$406$	26.1555	1.29808
$407$	15.6621	0.776343
$408$	−4.95679	−0.245398
$409$	27.7219	1.37076	0.685380	−	0.728185i	$-0.259636\pi$
$409$	27.7219	1.37076	0.685380	+	0.728185i	$0.259636\pi$
$410$	55.0039	2.71645
$411$	−12.6192	−0.622458
$412$	0.825530	0.0406710
$413$	−6.14776	−0.302512
$414$	−13.6307	−0.669911
$415$	−31.1995	−1.53152
$416$	4.40508	0.215977
$417$	−7.15961	−0.350607
$418$	35.1740	1.72042
$419$	23.3936	1.14285	0.571425	−	0.820654i	$-0.306391\pi$
$419$	23.3936	1.14285	0.571425	+	0.820654i	$0.306391\pi$
$420$	−7.39938	−0.361053
$421$	−2.92877	−0.142739	−0.0713697	−	0.997450i	$-0.522737\pi$
$421$	−2.92877	−0.142739	−0.0713697	+	0.997450i	$0.522737\pi$
$422$	−17.6419	−0.858795
$423$	0.133876	0.00650929
$424$	−19.2391	−0.934332
$425$	11.6205	0.563675
$426$	−13.6869	−0.663134
$427$	15.6066	0.755256
$428$	6.28466	0.303781
$429$	6.33881	0.306040
$430$	−39.6501	−1.91210
$431$	−18.6661	−0.899116	−0.449558	−	0.893251i	$-0.648419\pi$
$431$	−18.6661	−0.899116	−0.449558	+	0.893251i	$0.648419\pi$
$432$	−4.96956	−0.239098
$433$	−29.3753	−1.41168	−0.705842	−	0.708369i	$-0.749431\pi$
$433$	−29.3753	−1.41168	−0.705842	+	0.708369i	$0.749431\pi$
$434$	−20.1604	−0.967732
$435$	−16.7146	−0.801406
$436$	−3.33467	−0.159702
$437$	26.7690	1.28053
$438$	2.27534	0.108720
$439$	−34.2663	−1.63544	−0.817720	−	0.575616i	$-0.804762\pi$
$439$	−34.2663	−1.63544	−0.817720	+	0.575616i	$0.804762\pi$
$440$	38.8305	1.85117
$441$	1.34408	0.0640038
$442$	−4.22045	−0.200746
$443$	−4.94881	−0.235125	−0.117562	−	0.993065i	$-0.537508\pi$
$443$	−4.94881	−0.235125	−0.117562	+	0.993065i	$0.537508\pi$
$444$	−2.03975	−0.0968021
$445$	6.61108	0.313395
$446$	−10.4855	−0.496504
$447$	1.37190	0.0648885
$448$	−7.32112	−0.345890
$449$	−27.6563	−1.30518	−0.652590	−	0.757711i	$-0.726318\pi$
$449$	−27.6563	−1.30518	−0.652590	+	0.757711i	$0.726318\pi$
$450$	7.77973	0.366740
$451$	−66.8463	−3.14767
$452$	−14.3574	−0.675313
$453$	14.3968	0.676422
$454$	31.1934	1.46398
$455$	8.96319	0.420201
$456$	6.51712	0.305192
$457$	11.9850	0.560636	0.280318	−	0.959907i	$-0.409560\pi$
$457$	11.9850	0.560636	0.280318	+	0.959907i	$0.409560\pi$
$458$	−14.2138	−0.664168
$459$	2.51078	0.117193
$460$	−20.7718	−0.968489
$461$	5.59649	0.260655	0.130327	−	0.991471i	$-0.458397\pi$
$461$	5.59649	0.260655	0.130327	+	0.991471i	$0.458397\pi$
$462$	30.7784	1.43194
$463$	15.8037	0.734462	0.367231	−	0.930130i	$-0.380306\pi$
$463$	15.8037	0.734462	0.367231	+	0.930130i	$0.380306\pi$
$464$	26.7696	1.24275
$465$	12.8835	0.597458
$466$	−21.6919	−1.00486
$467$	37.8545	1.75170	0.875848	−	0.482587i	$-0.160303\pi$
$467$	37.8545	1.75170	0.875848	+	0.482587i	$0.160303\pi$
$468$	−0.825530	−0.0381602
$469$	11.5507	0.533363
$470$	0.698276	0.0322090
$471$	0.163215	0.00752057
$472$	−4.20165	−0.193397
$473$	48.1868	2.21563
$474$	−2.76034	−0.126786
$475$	−15.2784	−0.701022
$476$	−5.98730	−0.274427
$477$	9.74524	0.446204
$478$	−14.5911	−0.667383
$479$	27.3818	1.25111	0.625553	−	0.780182i	$-0.284874\pi$
$479$	27.3818	1.25111	0.625553	+	0.780182i	$0.284874\pi$
$480$	−13.6687	−0.623888
$481$	2.47083	0.112660
$482$	20.5143	0.934401
$483$	23.4238	1.06582
$484$	24.0894	1.09497
$485$	42.0883	1.91113
$486$	1.68093	0.0762486
$487$	−22.8992	−1.03766	−0.518832	−	0.854876i	$-0.673633\pi$
$487$	−22.8992	−1.03766	−0.518832	+	0.854876i	$0.673633\pi$
$488$	10.6662	0.482837
$489$	−3.18739	−0.144139
$490$	7.01049	0.316701
$491$	4.41164	0.199094	0.0995472	−	0.995033i	$-0.468261\pi$
$491$	4.41164	0.199094	0.0995472	+	0.995033i	$0.468261\pi$
$492$	8.70569	0.392483
$493$	−13.5249	−0.609129
$494$	5.54899	0.249661
$495$	−19.6689	−0.884052
$496$	−20.6338	−0.926484
$497$	23.5204	1.05503
$498$	−16.9014	−0.757372
$499$	−21.4321	−0.959431	−0.479715	−	0.877424i	$-0.659260\pi$
$499$	−21.4321	−0.959431	−0.479715	+	0.877424i	$0.659260\pi$
$500$	−0.952320	−0.0425891
$501$	−7.13151	−0.318612
$502$	28.2738	1.26192
$503$	−35.6426	−1.58922	−0.794612	−	0.607117i	$-0.792326\pi$
$503$	−35.6426	−1.58922	−0.794612	+	0.607117i	$0.792326\pi$
$504$	5.70271	0.254019
$505$	13.9055	0.618784
$506$	86.4022	3.84105
$507$	1.00000	0.0444116
$508$	10.7516	0.477025
$509$	−42.9677	−1.90451	−0.952256	−	0.305302i	$-0.901243\pi$
$509$	−42.9677	−1.90451	−0.952256	+	0.305302i	$0.901243\pi$
$510$	13.0958	0.579891
$511$	−3.91008	−0.172972
$512$	2.26949	0.100298
$513$	−3.30114	−0.145749
$514$	−49.2570	−2.17263
$515$	3.10294	0.136732
$516$	−6.27558	−0.276267
$517$	−0.848616	−0.0373221
$518$	11.9973	0.527130
$519$	−1.49915	−0.0658054
$520$	6.12583	0.268635
$521$	−13.3828	−0.586313	−0.293156	−	0.956065i	$-0.594706\pi$
$521$	−13.3828	−0.586313	−0.293156	+	0.956065i	$0.594706\pi$
$522$	−9.05470	−0.396313
$523$	−12.8927	−0.563756	−0.281878	−	0.959450i	$-0.590957\pi$
$523$	−12.8927	−0.563756	−0.281878	+	0.959450i	$0.590957\pi$
$524$	7.43674	0.324876
$525$	−13.3692	−0.583478
$526$	0.0463260	0.00201991
$527$	10.4248	0.454113
$528$	31.5011	1.37091
$529$	42.7560	1.85896
$530$	50.8295	2.20789
$531$	2.12828	0.0923593
$532$	7.87202	0.341295
$533$	−10.5456	−0.456779
$534$	3.58137	0.154981
$535$	23.6223	1.02128
$536$	7.89427	0.340980
$537$	−0.789368	−0.0340638
$538$	−7.32489	−0.315799
$539$	−8.51986	−0.366976
$540$	2.56157	0.110232
$541$	−45.7215	−1.96572	−0.982860	−	0.184355i	$-0.940980\pi$
$541$	−45.7215	−1.96572	−0.982860	+	0.184355i	$0.940980\pi$
$542$	−31.8229	−1.36691
$543$	−16.0588	−0.689150
$544$	−11.0602	−0.474202
$545$	−12.5341	−0.536902
$546$	4.85556	0.207799
$547$	33.5943	1.43639	0.718194	−	0.695843i	$-0.244969\pi$
$547$	33.5943	1.43639	0.718194	+	0.695843i	$0.244969\pi$
$548$	−10.4175	−0.445014
$549$	−5.40280	−0.230586
$550$	−49.3142	−2.10277
$551$	17.7823	0.757551
$552$	16.0088	0.681381
$553$	4.74353	0.201715
$554$	−1.92712	−0.0818755
$555$	−7.66684	−0.325439
$556$	−5.91047	−0.250660
$557$	8.05010	0.341094	0.170547	−	0.985350i	$-0.445447\pi$
$557$	8.05010	0.341094	0.170547	+	0.985350i	$0.445447\pi$
$558$	6.97928	0.295456
$559$	7.60188	0.321525
$560$	44.5431	1.88229
$561$	−15.9153	−0.671946
$562$	52.2180	2.20268
$563$	−44.6365	−1.88121	−0.940603	−	0.339509i	$-0.889739\pi$
$563$	−44.6365	−1.88121	−0.940603	+	0.339509i	$0.889739\pi$
$564$	0.110519	0.00465369
$565$	−53.9653	−2.27034
$566$	37.5240	1.57725
$567$	−2.88861	−0.121310
$568$	16.0749	0.674487
$569$	−42.1549	−1.76723	−0.883613	−	0.468218i	$-0.844896\pi$
$569$	−42.1549	−1.76723	−0.883613	+	0.468218i	$0.844896\pi$
$570$	−17.2182	−0.721190
$571$	30.4914	1.27602	0.638012	−	0.770026i	$-0.279757\pi$
$571$	30.4914	1.27602	0.638012	+	0.770026i	$0.279757\pi$
$572$	5.23288	0.218798
$573$	0.971495	0.0405848
$574$	−51.2046	−2.13724
$575$	−37.5303	−1.56512
$576$	2.53448	0.105603
$577$	−36.2024	−1.50713	−0.753564	−	0.657375i	$-0.771667\pi$
$577$	−36.2024	−1.50713	−0.753564	+	0.657375i	$0.771667\pi$
$578$	−17.9792	−0.747837
$579$	14.8698	0.617967
$580$	−13.7984	−0.572949
$581$	29.0444	1.20497
$582$	22.8002	0.945098
$583$	−61.7732	−2.55838
$584$	−2.67232	−0.110581
$585$	−3.10294	−0.128291
$586$	20.2750	0.837554
$587$	29.7081	1.22618	0.613091	−	0.790012i	$-0.289926\pi$
$587$	29.7081	1.22618	0.613091	+	0.790012i	$0.289926\pi$
$588$	1.10958	0.0457582
$589$	−13.7064	−0.564764
$590$	11.1007	0.457009
$591$	−23.7237	−0.975861
$592$	12.2789	0.504662
$593$	23.9081	0.981788	0.490894	−	0.871219i	$-0.336670\pi$
$593$	23.9081	0.981788	0.490894	+	0.871219i	$0.336670\pi$
$594$	−10.6551	−0.437184
$595$	−22.5046	−0.922598
$596$	1.13254	0.0463907
$597$	1.73854	0.0711539
$598$	13.6307	0.557400
$599$	24.1624	0.987248	0.493624	−	0.869675i	$-0.335672\pi$
$599$	24.1624	0.987248	0.493624	+	0.869675i	$0.335672\pi$
$600$	−9.13706	−0.373019
$601$	−36.2331	−1.47798	−0.738990	−	0.673716i	$-0.764697\pi$
$601$	−36.2331	−1.47798	−0.738990	+	0.673716i	$0.764697\pi$
$602$	36.9114	1.50440
$603$	−3.99871	−0.162840
$604$	11.8850	0.483595
$605$	90.5452	3.68118
$606$	7.53289	0.306003
$607$	−6.71439	−0.272529	−0.136264	−	0.990673i	$-0.543510\pi$
$607$	−6.71439	−0.272529	−0.136264	+	0.990673i	$0.543510\pi$
$608$	14.5418	0.589748
$609$	15.5601	0.630528
$610$	−28.1801	−1.14098
$611$	−0.133876	−0.00541605
$612$	2.07272	0.0837849
$613$	37.5932	1.51838	0.759188	−	0.650872i	$-0.225596\pi$
$613$	37.5932	1.51838	0.759188	+	0.650872i	$0.225596\pi$
$614$	−9.06504	−0.365835
$615$	32.7223	1.31949
$616$	−36.1483	−1.45646
$617$	−28.8766	−1.16253	−0.581264	−	0.813715i	$-0.697442\pi$
$617$	−28.8766	−1.16253	−0.581264	+	0.813715i	$0.697442\pi$
$618$	1.68093	0.0676170
$619$	−24.1474	−0.970568	−0.485284	−	0.874357i	$-0.661284\pi$
$619$	−24.1474	−0.970568	−0.485284	+	0.874357i	$0.661284\pi$
$620$	10.6357	0.427141
$621$	−8.10901	−0.325403
$622$	9.90796	0.397273
$623$	−6.15444	−0.246572
$624$	4.96956	0.198942
$625$	−26.7206	−1.06883
$626$	−29.2253	−1.16808
$627$	20.9253	0.835676
$628$	0.134739	0.00537668
$629$	−6.20371	−0.247358
$630$	−15.0665	−0.600264
$631$	−4.97005	−0.197855	−0.0989273	−	0.995095i	$-0.531541\pi$
$631$	−4.97005	−0.197855	−0.0989273	+	0.995095i	$0.531541\pi$
$632$	3.24193	0.128957
$633$	−10.4953	−0.417152
$634$	24.5949	0.976788
$635$	40.4123	1.60371
$636$	8.04499	0.319005
$637$	−1.34408	−0.0532544
$638$	57.3960	2.27233
$639$	−8.14246	−0.322111
$640$	40.5568	1.60315
$641$	17.2507	0.681360	0.340680	−	0.940179i	$-0.389343\pi$
$641$	17.2507	0.681360	0.340680	+	0.940179i	$0.389343\pi$
$642$	12.7967	0.505047
$643$	14.1980	0.559916	0.279958	−	0.960012i	$-0.409680\pi$
$643$	14.1980	0.559916	0.279958	+	0.960012i	$0.409680\pi$
$644$	19.3370	0.761986
$645$	−23.5882	−0.928783
$646$	−13.9323	−0.548159
$647$	−16.0424	−0.630693	−0.315346	−	0.948977i	$-0.602121\pi$
$647$	−16.0424	−0.630693	−0.315346	+	0.948977i	$0.602121\pi$
$648$	−1.97420	−0.0775540
$649$	−13.4907	−0.529557
$650$	−7.77973	−0.305146
$651$	−11.9936	−0.470067
$652$	−2.63129	−0.103049
$653$	38.3731	1.50166	0.750828	−	0.660498i	$-0.229655\pi$
$653$	38.3731	1.50166	0.750828	+	0.660498i	$0.229655\pi$
$654$	−6.79001	−0.265510
$655$	27.9526	1.09220
$656$	−52.4068	−2.04614
$657$	1.35362	0.0528098
$658$	−0.650044	−0.0253414
$659$	−15.5861	−0.607150	−0.303575	−	0.952808i	$-0.598180\pi$
$659$	−15.5861	−0.607150	−0.303575	+	0.952808i	$0.598180\pi$
$660$	−16.2373	−0.632036
$661$	1.73594	0.0675201	0.0337600	−	0.999430i	$-0.489252\pi$
$661$	1.73594	0.0675201	0.0337600	+	0.999430i	$0.489252\pi$
$662$	−28.6032	−1.11169
$663$	−2.51078	−0.0975106
$664$	19.8502	0.770339
$665$	29.5887	1.14740
$666$	−4.15330	−0.160937
$667$	43.6809	1.69133
$668$	−5.88728	−0.227786
$669$	−6.23793	−0.241172
$670$	−20.8566	−0.805760
$671$	34.2473	1.32210
$672$	12.7246	0.490861
$673$	−14.2711	−0.550109	−0.275054	−	0.961429i	$-0.588696\pi$
$673$	−14.2711	−0.550109	−0.275054	+	0.961429i	$0.588696\pi$
$674$	4.28593	0.165088
$675$	4.62823	0.178141
$676$	0.825530	0.0317512
$677$	25.7105	0.988133	0.494067	−	0.869424i	$-0.335510\pi$
$677$	25.7105	0.988133	0.494067	+	0.869424i	$0.335510\pi$
$678$	−29.2342	−1.12273
$679$	−39.1812	−1.50364
$680$	−15.3806	−0.589820
$681$	18.5572	0.711114
$682$	−44.2403	−1.69405
$683$	22.2794	0.852496	0.426248	−	0.904606i	$-0.359835\pi$
$683$	22.2794	0.852496	0.426248	+	0.904606i	$0.359835\pi$
$684$	−2.72519	−0.104200
$685$	−39.1565	−1.49609
$686$	27.4627	1.04853
$687$	−8.45592	−0.322613
$688$	37.7780	1.44027
$689$	−9.74524	−0.371264
$690$	−42.2952	−1.61015
$691$	32.8512	1.24972	0.624860	−	0.780737i	$-0.285156\pi$
$691$	32.8512	1.24972	0.624860	+	0.780737i	$0.285156\pi$
$692$	−1.23759	−0.0470463
$693$	18.3104	0.695553
$694$	−48.6818	−1.84794
$695$	−22.2158	−0.842694
$696$	10.6345	0.403098
$697$	26.4776	1.00291
$698$	3.08682	0.116838
$699$	−12.9047	−0.488100
$700$	−11.0366	−0.417146
$701$	28.3100	1.06925	0.534626	−	0.845089i	$-0.320452\pi$
$701$	28.3100	1.06925	0.534626	+	0.845089i	$0.320452\pi$
$702$	−1.68093	−0.0634427
$703$	8.15656	0.307631
$704$	−16.0656	−0.605493
$705$	0.415410	0.0156452
$706$	−48.2925	−1.81751
$707$	−12.9450	−0.486846
$708$	1.75696	0.0660305
$709$	26.6267	0.999987	0.499993	−	0.866029i	$-0.333336\pi$
$709$	26.6267	0.999987	0.499993	+	0.866029i	$0.333336\pi$
$710$	−42.4697	−1.59386
$711$	−1.64215	−0.0615853
$712$	−4.20621	−0.157634
$713$	−33.6688	−1.26091
$714$	−12.1912	−0.456246
$715$	19.6689	0.735576
$716$	−0.651647	−0.0243532
$717$	−8.68039	−0.324175
$718$	−24.7663	−0.924269
$719$	−37.5654	−1.40095	−0.700477	−	0.713675i	$-0.747029\pi$
$719$	−37.5654	−1.40095	−0.700477	+	0.713675i	$0.747029\pi$
$720$	−15.4202	−0.574678
$721$	−2.88861	−0.107578
$722$	−13.6197	−0.506873
$723$	12.2041	0.453877
$724$	−13.2570	−0.492694
$725$	−24.9309	−0.925912
$726$	49.0503	1.82043
$727$	−9.70797	−0.360049	−0.180024	−	0.983662i	$-0.557618\pi$
$727$	−9.70797	−0.360049	−0.180024	+	0.983662i	$0.557618\pi$
$728$	−5.70271	−0.211356
$729$	1.00000	0.0370370
$730$	7.06025	0.261312
$731$	−19.0866	−0.705945
$732$	−4.46018	−0.164853
$733$	−19.0879	−0.705026	−0.352513	−	0.935807i	$-0.614673\pi$
$733$	−19.0879	−0.705026	−0.352513	+	0.935807i	$0.614673\pi$
$734$	−63.5569	−2.34593
$735$	4.17060	0.153835
$736$	35.7209	1.31669
$737$	25.3471	0.933671
$738$	17.7264	0.652517
$739$	−20.3101	−0.747119	−0.373559	−	0.927606i	$-0.621863\pi$
$739$	−20.3101	−0.747119	−0.373559	+	0.927606i	$0.621863\pi$
$740$	−6.32921	−0.232666
$741$	3.30114	0.121270
$742$	−47.3186	−1.73712
$743$	36.5749	1.34180	0.670901	−	0.741547i	$-0.265908\pi$
$743$	36.5749	1.34180	0.670901	+	0.741547i	$0.265908\pi$
$744$	−8.19695	−0.300515
$745$	4.25691	0.155961
$746$	41.7789	1.52963
$747$	−10.0548	−0.367886
$748$	−13.1386	−0.480395
$749$	−21.9907	−0.803521
$750$	−1.93910	−0.0708059
$751$	−33.8043	−1.23354	−0.616768	−	0.787145i	$-0.711558\pi$
$751$	−33.8043	−1.23354	−0.616768	+	0.787145i	$0.711558\pi$
$752$	−0.665306	−0.0242612
$753$	16.8203	0.612967
$754$	9.05470	0.329753
$755$	44.6725	1.62580
$756$	−2.38464	−0.0867284
$757$	−39.0652	−1.41985	−0.709925	−	0.704278i	$-0.751271\pi$
$757$	−39.0652	−1.41985	−0.709925	+	0.704278i	$0.751271\pi$
$758$	53.9969	1.96126
$759$	51.4014	1.86575
$760$	20.2222	0.733537
$761$	16.8747	0.611707	0.305854	−	0.952079i	$-0.401058\pi$
$761$	16.8747	0.611707	0.305854	+	0.952079i	$0.401058\pi$
$762$	21.8922	0.793072
$763$	11.6684	0.422423
$764$	0.801999	0.0290153
$765$	7.79080	0.281677
$766$	5.36407	0.193812
$767$	−2.12828	−0.0768476
$768$	16.9016	0.609883
$769$	49.4920	1.78473	0.892364	−	0.451316i	$-0.149045\pi$
$769$	49.4920	1.78473	0.892364	+	0.451316i	$0.149045\pi$
$770$	95.5036	3.44171
$771$	−29.3034	−1.05534
$772$	12.2754	0.441803
$773$	−15.9650	−0.574222	−0.287111	−	0.957897i	$-0.592695\pi$
$773$	−15.9650	−0.574222	−0.287111	+	0.957897i	$0.592695\pi$
$774$	−12.7782	−0.459304
$775$	19.2165	0.690279
$776$	−26.7781	−0.961279
$777$	7.13727	0.256048
$778$	18.0130	0.645796
$779$	−34.8124	−1.24728
$780$	−2.56157	−0.0917189
$781$	51.6135	1.84688
$782$	−34.2236	−1.22383
$783$	−5.38671	−0.192505
$784$	−6.67948	−0.238553
$785$	0.506448	0.0180759
$786$	15.1426	0.540118
$787$	37.8719	1.34999	0.674994	−	0.737823i	$-0.264146\pi$
$787$	37.8719	1.34999	0.674994	+	0.737823i	$0.264146\pi$
$788$	−19.5846	−0.697672
$789$	0.0275597	0.000981151 0
$790$	−8.56516	−0.304735
$791$	50.2378	1.78625
$792$	12.5141	0.444669
$793$	5.40280	0.191859
$794$	−14.9844	−0.531775
$795$	30.2389	1.07246
$796$	1.43522	0.0508701
$797$	47.7760	1.69231	0.846157	−	0.532933i	$-0.178910\pi$
$797$	47.7760	1.69231	0.846157	+	0.532933i	$0.178910\pi$
$798$	16.0289	0.567416
$799$	0.336134	0.0118916
$800$	−20.3877	−0.720815
$801$	2.13059	0.0752806
$802$	−38.1226	−1.34616
$803$	−8.58034	−0.302793
$804$	−3.30106	−0.116419
$805$	72.6825	2.56172
$806$	−6.97928	−0.245835
$807$	−4.35764	−0.153396
$808$	−8.84716	−0.311242
$809$	9.73836	0.342383	0.171191	−	0.985238i	$-0.445238\pi$
$809$	9.73836	0.342383	0.171191	+	0.985238i	$0.445238\pi$
$810$	5.21583	0.183265
$811$	34.2714	1.20343	0.601715	−	0.798711i	$-0.294484\pi$
$811$	34.2714	1.20343	0.601715	+	0.798711i	$0.294484\pi$
$812$	12.8454	0.450784
$813$	−18.9317	−0.663965
$814$	26.3270	0.922759
$815$	−9.89029	−0.346442
$816$	−12.4775	−0.436799
$817$	25.0949	0.877959
$818$	46.5986	1.62928
$819$	2.88861	0.100936
$820$	27.0132	0.943342
$821$	26.6241	0.929187	0.464594	−	0.885524i	$-0.346200\pi$
$821$	26.6241	0.929187	0.464594	+	0.885524i	$0.346200\pi$
$822$	−21.2120	−0.739852
$823$	31.2881	1.09064	0.545318	−	0.838230i	$-0.316409\pi$
$823$	31.2881	1.09064	0.545318	+	0.838230i	$0.316409\pi$
$824$	−1.97420	−0.0687746
$825$	−29.3374	−1.02140
$826$	−10.3340	−0.359565
$827$	43.5330	1.51379	0.756895	−	0.653536i	$-0.226715\pi$
$827$	43.5330	1.51379	0.756895	+	0.653536i	$0.226715\pi$
$828$	−6.69423	−0.232641
$829$	−12.1419	−0.421706	−0.210853	−	0.977518i	$-0.567624\pi$
$829$	−12.1419	−0.421706	−0.210853	+	0.977518i	$0.567624\pi$
$830$	−52.4441	−1.82036
$831$	−1.14646	−0.0397703
$832$	−2.53448	−0.0878672
$833$	3.37469	0.116926
$834$	−12.0348	−0.416731
$835$	−22.1286	−0.765793
$836$	17.2745	0.597450
$837$	4.15203	0.143515
$838$	39.3230	1.35839
$839$	6.44270	0.222427	0.111213	−	0.993797i	$-0.464526\pi$
$839$	6.44270	0.222427	0.111213	+	0.993797i	$0.464526\pi$
$840$	17.6951	0.610541
$841$	0.0166831	0.000575279 0
$842$	−4.92306	−0.169660
$843$	31.0649	1.06993
$844$	−8.66421	−0.298234
$845$	3.10294	0.106744
$846$	0.225037	0.00773693
$847$	−84.2910	−2.89627
$848$	−48.4296	−1.66308
$849$	22.3233	0.766134
$850$	19.5332	0.669983
$851$	20.0360	0.686825
$852$	−6.72185	−0.230287
$853$	4.08210	0.139768	0.0698842	−	0.997555i	$-0.477737\pi$
$853$	4.08210	0.139768	0.0698842	+	0.997555i	$0.477737\pi$
$854$	26.2336	0.897696
$855$	−10.2432	−0.350311
$856$	−15.0294	−0.513693
$857$	−40.0341	−1.36754	−0.683769	−	0.729698i	$-0.739660\pi$
$857$	−40.0341	−1.36754	−0.683769	+	0.729698i	$0.739660\pi$
$858$	10.6551	0.363759
$859$	50.2496	1.71449	0.857247	−	0.514906i	$-0.172173\pi$
$859$	50.2496	1.71449	0.857247	+	0.514906i	$0.172173\pi$
$860$	−19.4727	−0.664015
$861$	−30.4621	−1.03814
$862$	−31.3765	−1.06869
$863$	22.2654	0.757924	0.378962	−	0.925412i	$-0.376281\pi$
$863$	22.2654	0.757924	0.378962	+	0.925412i	$0.376281\pi$
$864$	−4.40508	−0.149864
$865$	−4.65177	−0.158165
$866$	−49.3778	−1.67793
$867$	−10.6960	−0.363255
$868$	−9.90109	−0.336065
$869$	10.4093	0.353110
$870$	−28.0962	−0.952549
$871$	3.99871	0.135491
$872$	7.97466	0.270056
$873$	13.5640	0.459072
$874$	44.9968	1.52204
$875$	3.33226	0.112651
$876$	1.11745	0.0377553
$877$	32.1232	1.08472	0.542362	−	0.840145i	$-0.317530\pi$
$877$	32.1232	1.08472	0.542362	+	0.840145i	$0.317530\pi$
$878$	−57.5993	−1.94388
$879$	12.0618	0.406834
$880$	97.7459	3.29501
$881$	43.6668	1.47117	0.735586	−	0.677431i	$-0.236907\pi$
$881$	43.6668	1.47117	0.735586	+	0.677431i	$0.236907\pi$
$882$	2.25931	0.0760748
$883$	−48.2470	−1.62364	−0.811820	−	0.583907i	$-0.801523\pi$
$883$	−48.2470	−1.62364	−0.811820	+	0.583907i	$0.801523\pi$
$884$	−2.07272	−0.0697133
$885$	6.60391	0.221988
$886$	−8.31861	−0.279469
$887$	16.7696	0.563069	0.281535	−	0.959551i	$-0.409157\pi$
$887$	16.7696	0.563069	0.281535	+	0.959551i	$0.409157\pi$
$888$	4.87792	0.163692
$889$	−37.6209	−1.26177
$890$	11.1128	0.372501
$891$	−6.33881	−0.212358
$892$	−5.14960	−0.172421
$893$	−0.441944	−0.0147891
$894$	2.30606	0.0771263
$895$	−2.44936	−0.0818731
$896$	−37.7555	−1.26132
$897$	8.10901	0.270752
$898$	−46.4883	−1.55133
$899$	−22.3658	−0.745941
$900$	3.82074	0.127358
$901$	24.4682	0.815152
$902$	−112.364	−3.74131
$903$	21.9589	0.730746
$904$	34.3347	1.14196
$905$	−49.8295	−1.65639
$906$	24.2001	0.803994
$907$	38.1465	1.26663	0.633316	−	0.773893i	$-0.281693\pi$
$907$	38.1465	1.26663	0.633316	+	0.773893i	$0.281693\pi$
$908$	15.3195	0.508397
$909$	4.48138	0.148638
$910$	15.0665	0.499450
$911$	50.0815	1.65927	0.829637	−	0.558304i	$-0.188548\pi$
$911$	50.0815	1.65927	0.829637	+	0.558304i	$0.188548\pi$
$912$	16.4052	0.543231
$913$	63.7355	2.10934
$914$	20.1460	0.666371
$915$	−16.7646	−0.554219
$916$	−6.98061	−0.230646
$917$	−26.0219	−0.859319
$918$	4.22045	0.139296
$919$	−4.26891	−0.140818	−0.0704091	−	0.997518i	$-0.522430\pi$
$919$	−4.26891	−0.140818	−0.0704091	+	0.997518i	$0.522430\pi$
$920$	49.6744	1.63772
$921$	−5.39287	−0.177701
$922$	9.40732	0.309814
$923$	8.14246	0.268012
$924$	15.1157	0.497272
$925$	−11.4356	−0.375999
$926$	26.5650	0.872980
$927$	1.00000	0.0328443
$928$	23.7289	0.778940
$929$	−8.97559	−0.294479	−0.147240	−	0.989101i	$-0.547039\pi$
$929$	−8.97559	−0.294479	−0.147240	+	0.989101i	$0.547039\pi$
$930$	21.6563	0.710137
$931$	−4.43699	−0.145417
$932$	−10.6532	−0.348958
$933$	5.89432	0.192972
$934$	63.6308	2.08206
$935$	−49.3843	−1.61504
$936$	1.97420	0.0645288
$937$	46.1776	1.50856	0.754278	−	0.656555i	$-0.227987\pi$
$937$	46.1776	1.50856	0.754278	+	0.656555i	$0.227987\pi$
$938$	19.4160	0.633954
$939$	−17.3864	−0.567382
$940$	0.342933	0.0111853
$941$	36.4393	1.18789	0.593944	−	0.804506i	$-0.297570\pi$
$941$	36.4393	1.18789	0.593944	+	0.804506i	$0.297570\pi$
$942$	0.274354	0.00893894
$943$	−85.5141	−2.78472
$944$	−10.5766	−0.344239
$945$	−8.96319	−0.291572
$946$	80.9988	2.63350
$947$	32.1205	1.04378	0.521888	−	0.853014i	$-0.325228\pi$
$947$	32.1205	1.04378	0.521888	+	0.853014i	$0.325228\pi$
$948$	−1.35564	−0.0440292
$949$	−1.35362	−0.0439404
$950$	−25.6820	−0.833234
$951$	14.6317	0.474466
$952$	14.3182	0.464057
$953$	−33.9750	−1.10056	−0.550279	−	0.834981i	$-0.685479\pi$
$953$	−33.9750	−1.10056	−0.550279	+	0.834981i	$0.685479\pi$
$954$	16.3811	0.530357
$955$	3.01449	0.0975466
$956$	−7.16592	−0.231762
$957$	34.1453	1.10376
$958$	46.0269	1.48706
$959$	36.4519	1.17709
$960$	7.86433	0.253820
$961$	−13.7606	−0.443892
$962$	4.15330	0.133908
$963$	7.61288	0.245322
$964$	10.0749	0.324490
$965$	46.1400	1.48530
$966$	39.3738	1.26683
$967$	9.24477	0.297292	0.148646	−	0.988890i	$-0.452509\pi$
$967$	9.24477	0.297292	0.148646	+	0.988890i	$0.452509\pi$
$968$	−57.6081	−1.85160
$969$	−8.28844	−0.266263
$970$	70.7476	2.27157
$971$	45.9022	1.47307	0.736535	−	0.676399i	$-0.236461\pi$
$971$	45.9022	1.47307	0.736535	+	0.676399i	$0.236461\pi$
$972$	0.825530	0.0264789
$973$	20.6813	0.663013
$974$	−38.4920	−1.23336
$975$	−4.62823	−0.148222
$976$	26.8495	0.859433
$977$	0.447249	0.0143087	0.00715437	−	0.999974i	$-0.497723\pi$
$977$	0.447249	0.0143087	0.00715437	+	0.999974i	$0.497723\pi$
$978$	−5.35779	−0.171323
$979$	−13.5054	−0.431634
$980$	3.44295	0.109981
$981$	−4.03943	−0.128969
$982$	7.41566	0.236643
$983$	−33.4509	−1.06692	−0.533459	−	0.845826i	$-0.679108\pi$
$983$	−33.4509	−1.06692	−0.533459	+	0.845826i	$0.679108\pi$
$984$	−20.8191	−0.663689
$985$	−73.6130	−2.34551
$986$	−22.7343	−0.724009
$987$	−0.386717	−0.0123093
$988$	2.72519	0.0866999
$989$	61.6437	1.96016
$990$	−33.0621	−1.05078
$991$	−55.3693	−1.75886	−0.879432	−	0.476024i	$-0.842077\pi$
$991$	−55.3693	−1.75886	−0.879432	+	0.476024i	$0.842077\pi$
$992$	−18.2900	−0.580710
$993$	−17.0163	−0.539995
$994$	39.5362	1.25401
$995$	5.39460	0.171020
$996$	−8.30055	−0.263013
$997$	−25.3976	−0.804351	−0.402176	−	0.915563i	$-0.631746\pi$
$997$	−25.3976	−0.804351	−0.402176	+	0.915563i	$0.631746\pi$
$998$	−36.0258	−1.14038
$999$	−2.47083	−0.0781737

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.e.1.13	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.e.1.13	✓	16	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q+1.68093 q^{2} +1.00000 q^{3} +0.825530 q^{4} +3.10294 q^{5} +1.68093 q^{6} -2.88861 q^{7} -1.97420 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.68093 q^{2} +1.00000 q^{3} +0.825530 q^{4} +3.10294 q^{5} +1.68093 q^{6} -2.88861 q^{7} -1.97420 q^{8} +1.00000 q^{9} +5.21583 q^{10} -6.33881 q^{11} +0.825530 q^{12} -1.00000 q^{13} -4.85556 q^{14} +3.10294 q^{15} -4.96956 q^{16} +2.51078 q^{17} +1.68093 q^{18} -3.30114 q^{19} +2.56157 q^{20} -2.88861 q^{21} -10.6551 q^{22} -8.10901 q^{23} -1.97420 q^{24} +4.62823 q^{25} -1.68093 q^{26} +1.00000 q^{27} -2.38464 q^{28} -5.38671 q^{29} +5.21583 q^{30} +4.15203 q^{31} -4.40508 q^{32} -6.33881 q^{33} +4.22045 q^{34} -8.96319 q^{35} +0.825530 q^{36} -2.47083 q^{37} -5.54899 q^{38} -1.00000 q^{39} -6.12583 q^{40} +10.5456 q^{41} -4.85556 q^{42} -7.60188 q^{43} -5.23288 q^{44} +3.10294 q^{45} -13.6307 q^{46} +0.133876 q^{47} -4.96956 q^{48} +1.34408 q^{49} +7.77973 q^{50} +2.51078 q^{51} -0.825530 q^{52} +9.74524 q^{53} +1.68093 q^{54} -19.6689 q^{55} +5.70271 q^{56} -3.30114 q^{57} -9.05470 q^{58} +2.12828 q^{59} +2.56157 q^{60} -5.40280 q^{61} +6.97928 q^{62} -2.88861 q^{63} +2.53448 q^{64} -3.10294 q^{65} -10.6551 q^{66} -3.99871 q^{67} +2.07272 q^{68} -8.10901 q^{69} -15.0665 q^{70} -8.14246 q^{71} -1.97420 q^{72} +1.35362 q^{73} -4.15330 q^{74} +4.62823 q^{75} -2.72519 q^{76} +18.3104 q^{77} -1.68093 q^{78} -1.64215 q^{79} -15.4202 q^{80} +1.00000 q^{81} +17.7264 q^{82} -10.0548 q^{83} -2.38464 q^{84} +7.79080 q^{85} -12.7782 q^{86} -5.38671 q^{87} +12.5141 q^{88} +2.13059 q^{89} +5.21583 q^{90} +2.88861 q^{91} -6.69423 q^{92} +4.15203 q^{93} +0.225037 q^{94} -10.2432 q^{95} -4.40508 q^{96} +13.5640 q^{97} +2.25931 q^{98} -6.33881 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{3} + 10 q^{4} - 6 q^{5} - 13 q^{7} - 9 q^{8} + 16 q^{9}+O(q^{10}) \) 16 * q + 16 * q^3 + 10 * q^4 - 6 * q^5 - 13 * q^7 - 9 * q^8 + 16 * q^9	\( 16 q + 16 q^{3} + 10 q^{4} - 6 q^{5} - 13 q^{7} - 9 q^{8} + 16 q^{9} - 8 q^{10} - 5 q^{11} + 10 q^{12} - 16 q^{13} - 8 q^{14} - 6 q^{15} - 14 q^{16} - q^{17} + 6 q^{19} - 4 q^{20} - 13 q^{21} - 11 q^{22} - 21 q^{23} - 9 q^{24} - 10 q^{25} + 16 q^{27} - 10 q^{28} - 17 q^{29} - 8 q^{30} - 33 q^{31} - 18 q^{32} - 5 q^{33} - 5 q^{34} - 4 q^{35} + 10 q^{36} - 23 q^{37} - 28 q^{38} - 16 q^{39} - 12 q^{40} + 7 q^{41} - 8 q^{42} - 33 q^{43} + 11 q^{44} - 6 q^{45} - 15 q^{46} - 13 q^{47} - 14 q^{48} - 17 q^{49} + 35 q^{50} - q^{51} - 10 q^{52} - 20 q^{53} - 54 q^{55} + 12 q^{56} + 6 q^{57} - 33 q^{58} + 6 q^{59} - 4 q^{60} - 49 q^{61} - 13 q^{62} - 13 q^{63} - 35 q^{64} + 6 q^{65} - 11 q^{66} - 4 q^{67} - 14 q^{68} - 21 q^{69} - 33 q^{70} - 29 q^{71} - 9 q^{72} - 21 q^{73} + 22 q^{74} - 10 q^{75} + 10 q^{76} - 21 q^{77} - 70 q^{79} - 8 q^{80} + 16 q^{81} - 10 q^{82} + 5 q^{83} - 10 q^{84} + 14 q^{85} + 29 q^{86} - 17 q^{87} - 45 q^{88} - 8 q^{89} - 8 q^{90} + 13 q^{91} - 29 q^{92} - 33 q^{93} + 12 q^{94} - 45 q^{95} - 18 q^{96} - 30 q^{97} + 15 q^{98} - 5 q^{99}+O(q^{100}) \) 16 * q + 16 * q^3 + 10 * q^4 - 6 * q^5 - 13 * q^7 - 9 * q^8 + 16 * q^9 - 8 * q^10 - 5 * q^11 + 10 * q^12 - 16 * q^13 - 8 * q^14 - 6 * q^15 - 14 * q^16 - q^17 + 6 * q^19 - 4 * q^20 - 13 * q^21 - 11 * q^22 - 21 * q^23 - 9 * q^24 - 10 * q^25 + 16 * q^27 - 10 * q^28 - 17 * q^29 - 8 * q^30 - 33 * q^31 - 18 * q^32 - 5 * q^33 - 5 * q^34 - 4 * q^35 + 10 * q^36 - 23 * q^37 - 28 * q^38 - 16 * q^39 - 12 * q^40 + 7 * q^41 - 8 * q^42 - 33 * q^43 + 11 * q^44 - 6 * q^45 - 15 * q^46 - 13 * q^47 - 14 * q^48 - 17 * q^49 + 35 * q^50 - q^51 - 10 * q^52 - 20 * q^53 - 54 * q^55 + 12 * q^56 + 6 * q^57 - 33 * q^58 + 6 * q^59 - 4 * q^60 - 49 * q^61 - 13 * q^62 - 13 * q^63 - 35 * q^64 + 6 * q^65 - 11 * q^66 - 4 * q^67 - 14 * q^68 - 21 * q^69 - 33 * q^70 - 29 * q^71 - 9 * q^72 - 21 * q^73 + 22 * q^74 - 10 * q^75 + 10 * q^76 - 21 * q^77 - 70 * q^79 - 8 * q^80 + 16 * q^81 - 10 * q^82 + 5 * q^83 - 10 * q^84 + 14 * q^85 + 29 * q^86 - 17 * q^87 - 45 * q^88 - 8 * q^89 - 8 * q^90 + 13 * q^91 - 29 * q^92 - 33 * q^93 + 12 * q^94 - 45 * q^95 - 18 * q^96 - 30 * q^97 + 15 * q^98 - 5 * q^99

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