LMFDB - Embedded newform 4017.2.a.e.1.9

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			1.9
Root			$-0.228474$ 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)

$f(q)$	$=$	$q+0.228474 q^{2} +1.00000 q^{3} -1.94780 q^{4} -1.93998 q^{5} +0.228474 q^{6} +1.64440 q^{7} -0.901970 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.228474 q^{2} +1.00000 q^{3} -1.94780 q^{4} -1.93998 q^{5} +0.228474 q^{6} +1.64440 q^{7} -0.901970 q^{8} +1.00000 q^{9} -0.443234 q^{10} -3.11220 q^{11} -1.94780 q^{12} -1.00000 q^{13} +0.375703 q^{14} -1.93998 q^{15} +3.68952 q^{16} +0.133546 q^{17} +0.228474 q^{18} +1.02069 q^{19} +3.77868 q^{20} +1.64440 q^{21} -0.711056 q^{22} +6.84011 q^{23} -0.901970 q^{24} -1.23649 q^{25} -0.228474 q^{26} +1.00000 q^{27} -3.20296 q^{28} +3.24021 q^{29} -0.443234 q^{30} +3.81098 q^{31} +2.64690 q^{32} -3.11220 q^{33} +0.0305118 q^{34} -3.19010 q^{35} -1.94780 q^{36} +4.03920 q^{37} +0.233201 q^{38} -1.00000 q^{39} +1.74980 q^{40} -7.88323 q^{41} +0.375703 q^{42} -9.84997 q^{43} +6.06193 q^{44} -1.93998 q^{45} +1.56279 q^{46} +6.07643 q^{47} +3.68952 q^{48} -4.29595 q^{49} -0.282507 q^{50} +0.133546 q^{51} +1.94780 q^{52} -0.0869136 q^{53} +0.228474 q^{54} +6.03758 q^{55} -1.48320 q^{56} +1.02069 q^{57} +0.740305 q^{58} -3.11730 q^{59} +3.77868 q^{60} -9.30112 q^{61} +0.870710 q^{62} +1.64440 q^{63} -6.77430 q^{64} +1.93998 q^{65} -0.711056 q^{66} -5.15027 q^{67} -0.260121 q^{68} +6.84011 q^{69} -0.728855 q^{70} +2.32389 q^{71} -0.901970 q^{72} -11.9683 q^{73} +0.922853 q^{74} -1.23649 q^{75} -1.98810 q^{76} -5.11769 q^{77} -0.228474 q^{78} -7.62462 q^{79} -7.15758 q^{80} +1.00000 q^{81} -1.80111 q^{82} +6.31144 q^{83} -3.20296 q^{84} -0.259076 q^{85} -2.25046 q^{86} +3.24021 q^{87} +2.80711 q^{88} -5.62541 q^{89} -0.443234 q^{90} -1.64440 q^{91} -13.3232 q^{92} +3.81098 q^{93} +1.38831 q^{94} -1.98011 q^{95} +2.64690 q^{96} -8.05740 q^{97} -0.981514 q^{98} -3.11220 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.228474	0.161556	0.0807778	−	0.996732i	$-0.474260\pi$
$2$	0.228474	0.161556	0.0807778	+	0.996732i	$0.474260\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.94780	−0.973900
$5$	−1.93998	−0.867584	−0.433792	−	0.901013i	$-0.642825\pi$
$5$	−1.93998	−0.867584	−0.433792	+	0.901013i	$0.642825\pi$
$6$	0.228474	0.0932742
$7$	1.64440	0.621525	0.310762	−	0.950488i	$-0.399416\pi$
$7$	1.64440	0.621525	0.310762	+	0.950488i	$0.399416\pi$
$8$	−0.901970	−0.318895
$9$	1.00000	0.333333
$10$	−0.443234	−0.140163
$11$	−3.11220	−0.938362	−0.469181	−	0.883102i	$-0.655451\pi$
$11$	−3.11220	−0.938362	−0.469181	+	0.883102i	$0.655451\pi$
$12$	−1.94780	−0.562281
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0.375703	0.100411
$15$	−1.93998	−0.500900
$16$	3.68952	0.922381
$17$	0.133546	0.0323897	0.0161948	−	0.999869i	$-0.494845\pi$
$17$	0.133546	0.0323897	0.0161948	+	0.999869i	$0.494845\pi$
$18$	0.228474	0.0538519
$19$	1.02069	0.234162	0.117081	−	0.993122i	$-0.462646\pi$
$19$	1.02069	0.234162	0.117081	+	0.993122i	$0.462646\pi$
$20$	3.77868	0.844940
$21$	1.64440	0.358837
$22$	−0.711056	−0.151598
$23$	6.84011	1.42626	0.713130	−	0.701032i	$-0.247277\pi$
$23$	6.84011	1.42626	0.713130	+	0.701032i	$0.247277\pi$
$24$	−0.901970	−0.184114
$25$	−1.23649	−0.247299
$26$	−0.228474	−0.0448075
$27$	1.00000	0.192450
$28$	−3.20296	−0.605303
$29$	3.24021	0.601692	0.300846	−	0.953673i	$-0.402731\pi$
$29$	3.24021	0.601692	0.300846	+	0.953673i	$0.402731\pi$
$30$	−0.443234	−0.0809232
$31$	3.81098	0.684472	0.342236	−	0.939614i	$-0.388816\pi$
$31$	3.81098	0.684472	0.342236	+	0.939614i	$0.388816\pi$
$32$	2.64690	0.467910
$33$	−3.11220	−0.541764
$34$	0.0305118	0.00523273
$35$	−3.19010	−0.539225
$36$	−1.94780	−0.324633
$37$	4.03920	0.664040	0.332020	−	0.943272i	$-0.392270\pi$
$37$	4.03920	0.664040	0.332020	+	0.943272i	$0.392270\pi$
$38$	0.233201	0.0378302
$39$	−1.00000	−0.160128
$40$	1.74980	0.276668
$41$	−7.88323	−1.23115	−0.615577	−	0.788077i	$-0.711077\pi$
$41$	−7.88323	−1.23115	−0.615577	+	0.788077i	$0.711077\pi$
$42$	0.375703	0.0579722
$43$	−9.84997	−1.50211	−0.751054	−	0.660241i	$-0.770454\pi$
$43$	−9.84997	−1.50211	−0.751054	+	0.660241i	$0.770454\pi$
$44$	6.06193	0.913871
$45$	−1.93998	−0.289195
$46$	1.56279	0.230420
$47$	6.07643	0.886338	0.443169	−	0.896438i	$-0.353854\pi$
$47$	6.07643	0.886338	0.443169	+	0.896438i	$0.353854\pi$
$48$	3.68952	0.532537
$49$	−4.29595	−0.613707
$50$	−0.282507	−0.0399525
$51$	0.133546	0.0187002
$52$	1.94780	0.270111
$53$	−0.0869136	−0.0119385	−0.00596925	−	0.999982i	$-0.501900\pi$
$53$	−0.0869136	−0.0119385	−0.00596925	+	0.999982i	$0.501900\pi$
$54$	0.228474	0.0310914
$55$	6.03758	0.814108
$56$	−1.48320	−0.198201
$57$	1.02069	0.135193
$58$	0.740305	0.0972068
$59$	−3.11730	−0.405838	−0.202919	−	0.979195i	$-0.565043\pi$
$59$	−3.11730	−0.405838	−0.202919	+	0.979195i	$0.565043\pi$
$60$	3.77868	0.487826
$61$	−9.30112	−1.19089	−0.595443	−	0.803397i	$-0.703024\pi$
$61$	−9.30112	−1.19089	−0.595443	+	0.803397i	$0.703024\pi$
$62$	0.870710	0.110580
$63$	1.64440	0.207175
$64$	−6.77430	−0.846787
$65$	1.93998	0.240624
$66$	−0.711056	−0.0875250
$67$	−5.15027	−0.629205	−0.314603	−	0.949223i	$-0.601871\pi$
$67$	−5.15027	−0.629205	−0.314603	+	0.949223i	$0.601871\pi$
$68$	−0.260121	−0.0315443
$69$	6.84011	0.823452
$70$	−0.728855	−0.0871148
$71$	2.32389	0.275795	0.137898	−	0.990446i	$-0.455966\pi$
$71$	2.32389	0.275795	0.137898	+	0.990446i	$0.455966\pi$
$72$	−0.901970	−0.106298
$73$	−11.9683	−1.40079	−0.700393	−	0.713758i	$-0.746992\pi$
$73$	−11.9683	−1.40079	−0.700393	+	0.713758i	$0.746992\pi$
$74$	0.922853	0.107279
$75$	−1.23649	−0.142778
$76$	−1.98810	−0.228050
$77$	−5.11769	−0.583215
$78$	−0.228474	−0.0258696
$79$	−7.62462	−0.857837	−0.428919	−	0.903343i	$-0.641105\pi$
$79$	−7.62462	−0.857837	−0.428919	+	0.903343i	$0.641105\pi$
$80$	−7.15758	−0.800242
$81$	1.00000	0.111111
$82$	−1.80111	−0.198900
$83$	6.31144	0.692771	0.346385	−	0.938092i	$-0.387409\pi$
$83$	6.31144	0.692771	0.346385	+	0.938092i	$0.387409\pi$
$84$	−3.20296	−0.349472
$85$	−0.259076	−0.0281008
$86$	−2.25046	−0.242674
$87$	3.24021	0.347387
$88$	2.80711	0.299239
$89$	−5.62541	−0.596292	−0.298146	−	0.954520i	$-0.596368\pi$
$89$	−5.62541	−0.596292	−0.298146	+	0.954520i	$0.596368\pi$
$90$	−0.443234	−0.0467210
$91$	−1.64440	−0.172380
$92$	−13.3232	−1.38903
$93$	3.81098	0.395180
$94$	1.38831	0.143193
$95$	−1.98011	−0.203155
$96$	2.64690	0.270148
$97$	−8.05740	−0.818105	−0.409053	−	0.912511i	$-0.634141\pi$
$97$	−8.05740	−0.818105	−0.409053	+	0.912511i	$0.634141\pi$
$98$	−0.981514	−0.0991478
$99$	−3.11220	−0.312787
$100$	2.40844	0.240844
$101$	−4.29092	−0.426963	−0.213481	−	0.976947i	$-0.568480\pi$
$101$	−4.29092	−0.426963	−0.213481	+	0.976947i	$0.568480\pi$
$102$	0.0305118	0.00302112
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	0.901970	0.0884455
$105$	−3.19010	−0.311322
$106$	−0.0198575	−0.00192873
$107$	2.64125	0.255339	0.127669	−	0.991817i	$-0.459250\pi$
$107$	2.64125	0.255339	0.127669	+	0.991817i	$0.459250\pi$
$108$	−1.94780	−0.187427
$109$	−11.5581	−1.10707	−0.553535	−	0.832826i	$-0.686721\pi$
$109$	−11.5581	−1.10707	−0.553535	+	0.832826i	$0.686721\pi$
$110$	1.37943	0.131524
$111$	4.03920	0.383384
$112$	6.06705	0.573282
$113$	−1.42880	−0.134410	−0.0672052	−	0.997739i	$-0.521408\pi$
$113$	−1.42880	−0.134410	−0.0672052	+	0.997739i	$0.521408\pi$
$114$	0.233201	0.0218413
$115$	−13.2696	−1.23740
$116$	−6.31129	−0.585988
$117$	−1.00000	−0.0924500
$118$	−0.712223	−0.0655655
$119$	0.219603	0.0201310
$120$	1.74980	0.159734
$121$	−1.31424	−0.119476
$122$	−2.12507	−0.192394
$123$	−7.88323	−0.710807
$124$	−7.42302	−0.666607
$125$	12.0986	1.08214
$126$	0.375703	0.0334703
$127$	−17.0803	−1.51563	−0.757815	−	0.652470i	$-0.773733\pi$
$127$	−17.0803	−1.51563	−0.757815	+	0.652470i	$0.773733\pi$
$128$	−6.84155	−0.604714
$129$	−9.84997	−0.867242
$130$	0.443234	0.0388742
$131$	−1.77719	−0.155274	−0.0776370	−	0.996982i	$-0.524738\pi$
$131$	−1.77719	−0.155274	−0.0776370	+	0.996982i	$0.524738\pi$
$132$	6.06193	0.527624
$133$	1.67842	0.145537
$134$	−1.17670	−0.101652
$135$	−1.93998	−0.166967
$136$	−0.120455	−0.0103289
$137$	−6.59385	−0.563350	−0.281675	−	0.959510i	$-0.590890\pi$
$137$	−6.59385	−0.563350	−0.281675	+	0.959510i	$0.590890\pi$
$138$	1.56279	0.133033
$139$	0.222543	0.0188759	0.00943794	−	0.999955i	$-0.496996\pi$
$139$	0.222543	0.0188759	0.00943794	+	0.999955i	$0.496996\pi$
$140$	6.21367	0.525151
$141$	6.07643	0.511728
$142$	0.530949	0.0445563
$143$	3.11220	0.260255
$144$	3.68952	0.307460
$145$	−6.28594	−0.522019
$146$	−2.73445	−0.226305
$147$	−4.29595	−0.354324
$148$	−7.86755	−0.646709
$149$	11.1411	0.912713	0.456357	−	0.889797i	$-0.349154\pi$
$149$	11.1411	0.912713	0.456357	+	0.889797i	$0.349154\pi$
$150$	−0.282507	−0.0230666
$151$	13.9016	1.13130	0.565649	−	0.824646i	$-0.308626\pi$
$151$	13.9016	1.13130	0.565649	+	0.824646i	$0.308626\pi$
$152$	−0.920630	−0.0746730
$153$	0.133546	0.0107966
$154$	−1.16926	−0.0942217
$155$	−7.39320	−0.593836
$156$	1.94780	0.155949
$157$	13.6634	1.09046	0.545231	−	0.838286i	$-0.316442\pi$
$157$	13.6634	1.09046	0.545231	+	0.838286i	$0.316442\pi$
$158$	−1.74203	−0.138588
$159$	−0.0869136	−0.00689270
$160$	−5.13492	−0.405951
$161$	11.2479	0.886456
$162$	0.228474	0.0179506
$163$	17.0577	1.33606	0.668031	−	0.744133i	$-0.267137\pi$
$163$	17.0577	1.33606	0.668031	+	0.744133i	$0.267137\pi$
$164$	15.3550	1.19902
$165$	6.03758	0.470025
$166$	1.44200	0.111921
$167$	−4.05812	−0.314027	−0.157013	−	0.987596i	$-0.550187\pi$
$167$	−4.05812	−0.314027	−0.157013	+	0.987596i	$0.550187\pi$
$168$	−1.48320	−0.114431
$169$	1.00000	0.0769231
$170$	−0.0591922	−0.00453984
$171$	1.02069	0.0780540
$172$	19.1858	1.46290
$173$	5.92325	0.450336	0.225168	−	0.974320i	$-0.427707\pi$
$173$	5.92325	0.450336	0.225168	+	0.974320i	$0.427707\pi$
$174$	0.740305	0.0561224
$175$	−2.03329	−0.153702
$176$	−11.4825	−0.865527
$177$	−3.11730	−0.234311
$178$	−1.28526	−0.0963344
$179$	−8.01017	−0.598708	−0.299354	−	0.954142i	$-0.596771\pi$
$179$	−8.01017	−0.598708	−0.299354	+	0.954142i	$0.596771\pi$
$180$	3.77868	0.281647
$181$	−23.2459	−1.72785	−0.863927	−	0.503617i	$-0.832002\pi$
$181$	−23.2459	−1.72785	−0.863927	+	0.503617i	$0.832002\pi$
$182$	−0.375703	−0.0278489
$183$	−9.30112	−0.687559
$184$	−6.16957	−0.454827
$185$	−7.83595	−0.576111
$186$	0.870710	0.0638435
$187$	−0.415621	−0.0303932
$188$	−11.8357	−0.863204
$189$	1.64440	0.119612
$190$	−0.452404	−0.0328209
$191$	3.66893	0.265474	0.132737	−	0.991151i	$-0.457623\pi$
$191$	3.66893	0.265474	0.132737	+	0.991151i	$0.457623\pi$
$192$	−6.77430	−0.488893
$193$	−16.7685	−1.20702	−0.603511	−	0.797355i	$-0.706232\pi$
$193$	−16.7685	−1.20702	−0.603511	+	0.797355i	$0.706232\pi$
$194$	−1.84091	−0.132170
$195$	1.93998	0.138925
$196$	8.36765	0.597689
$197$	1.81641	0.129414	0.0647069	−	0.997904i	$-0.479389\pi$
$197$	1.81641	0.129414	0.0647069	+	0.997904i	$0.479389\pi$
$198$	−0.711056	−0.0505326
$199$	−16.9702	−1.20299	−0.601494	−	0.798877i	$-0.705428\pi$
$199$	−16.9702	−1.20299	−0.601494	+	0.798877i	$0.705428\pi$
$200$	1.11528	0.0788622
$201$	−5.15027	−0.363272
$202$	−0.980366	−0.0689783
$203$	5.32821	0.373967
$204$	−0.260121	−0.0182121
$205$	15.2933	1.06813
$206$	0.228474	0.0159186
$207$	6.84011	0.475420
$208$	−3.68952	−0.255822
$209$	−3.17658	−0.219729
$210$	−0.728855	−0.0502957
$211$	−7.07125	−0.486805	−0.243402	−	0.969925i	$-0.578264\pi$
$211$	−7.07125	−0.486805	−0.243402	+	0.969925i	$0.578264\pi$
$212$	0.169290	0.0116269
$213$	2.32389	0.159230
$214$	0.603456	0.0412514
$215$	19.1087	1.30320
$216$	−0.901970	−0.0613713
$217$	6.26677	0.425416
$218$	−2.64074	−0.178853
$219$	−11.9683	−0.808744
$220$	−11.7600	−0.792859
$221$	−0.133546	−0.00898328
$222$	0.922853	0.0619378
$223$	12.8699	0.861835	0.430917	−	0.902391i	$-0.358190\pi$
$223$	12.8699	0.861835	0.430917	+	0.902391i	$0.358190\pi$
$224$	4.35256	0.290818
$225$	−1.23649	−0.0824328
$226$	−0.326444	−0.0217148
$227$	14.6262	0.970772	0.485386	−	0.874300i	$-0.338679\pi$
$227$	14.6262	0.970772	0.485386	+	0.874300i	$0.338679\pi$
$228$	−1.98810	−0.131665
$229$	−13.2156	−0.873309	−0.436655	−	0.899629i	$-0.643837\pi$
$229$	−13.2156	−0.873309	−0.436655	+	0.899629i	$0.643837\pi$
$230$	−3.03177	−0.199909
$231$	−5.11769	−0.336719
$232$	−2.92258	−0.191877
$233$	−13.2976	−0.871152	−0.435576	−	0.900152i	$-0.643455\pi$
$233$	−13.2976	−0.871152	−0.435576	+	0.900152i	$0.643455\pi$
$234$	−0.228474	−0.0149358
$235$	−11.7881	−0.768972
$236$	6.07188	0.395246
$237$	−7.62462	−0.495272
$238$	0.0501736	0.00325227
$239$	−18.1245	−1.17238	−0.586188	−	0.810175i	$-0.699372\pi$
$239$	−18.1245	−1.17238	−0.586188	+	0.810175i	$0.699372\pi$
$240$	−7.15758	−0.462020
$241$	15.8342	1.01997	0.509986	−	0.860183i	$-0.329651\pi$
$241$	15.8342	1.01997	0.509986	+	0.860183i	$0.329651\pi$
$242$	−0.300270	−0.0193021
$243$	1.00000	0.0641500
$244$	18.1167	1.15980
$245$	8.33404	0.532442
$246$	−1.80111	−0.114835
$247$	−1.02069	−0.0649448
$248$	−3.43739	−0.218274
$249$	6.31144	0.399971
$250$	2.76423	0.174825
$251$	−13.9469	−0.880320	−0.440160	−	0.897919i	$-0.645078\pi$
$251$	−13.9469	−0.880320	−0.440160	+	0.897919i	$0.645078\pi$
$252$	−3.20296	−0.201768
$253$	−21.2877	−1.33835
$254$	−3.90240	−0.244859
$255$	−0.259076	−0.0162240
$256$	11.9855	0.749092
$257$	−20.3474	−1.26923	−0.634617	−	0.772827i	$-0.718842\pi$
$257$	−20.3474	−1.26923	−0.634617	+	0.772827i	$0.718842\pi$
$258$	−2.25046	−0.140108
$259$	6.64206	0.412718
$260$	−3.77868	−0.234344
$261$	3.24021	0.200564
$262$	−0.406042	−0.0250854
$263$	−32.0735	−1.97773	−0.988867	−	0.148802i	$-0.952458\pi$
$263$	−32.0735	−1.97773	−0.988867	+	0.148802i	$0.952458\pi$
$264$	2.80711	0.172766
$265$	0.168610	0.0103577
$266$	0.383476	0.0235124
$267$	−5.62541	−0.344270
$268$	10.0317	0.612783
$269$	−0.579509	−0.0353333	−0.0176667	−	0.999844i	$-0.505624\pi$
$269$	−0.579509	−0.0353333	−0.0176667	+	0.999844i	$0.505624\pi$
$270$	−0.443234	−0.0269744
$271$	−3.89097	−0.236360	−0.118180	−	0.992992i	$-0.537706\pi$
$271$	−3.89097	−0.236360	−0.118180	+	0.992992i	$0.537706\pi$
$272$	0.492721	0.0298756
$273$	−1.64440	−0.0995236
$274$	−1.50652	−0.0910124
$275$	3.84821	0.232056
$276$	−13.3232	−0.801960
$277$	28.6893	1.72377	0.861885	−	0.507103i	$-0.169284\pi$
$277$	28.6893	1.72377	0.861885	+	0.507103i	$0.169284\pi$
$278$	0.0508454	0.00304950
$279$	3.81098	0.228157
$280$	2.87737	0.171956
$281$	−7.24188	−0.432014	−0.216007	−	0.976392i	$-0.569303\pi$
$281$	−7.24188	−0.432014	−0.216007	+	0.976392i	$0.569303\pi$
$282$	1.38831	0.0826725
$283$	−12.4699	−0.741260	−0.370630	−	0.928781i	$-0.620858\pi$
$283$	−12.4699	−0.741260	−0.370630	+	0.928781i	$0.620858\pi$
$284$	−4.52647	−0.268597
$285$	−1.98011	−0.117292
$286$	0.711056	0.0420456
$287$	−12.9632	−0.765192
$288$	2.64690	0.155970
$289$	−16.9822	−0.998951
$290$	−1.43617	−0.0843350
$291$	−8.05740	−0.472333
$292$	23.3119	1.36422
$293$	2.47590	0.144644	0.0723219	−	0.997381i	$-0.476959\pi$
$293$	2.47590	0.144644	0.0723219	+	0.997381i	$0.476959\pi$
$294$	−0.981514	−0.0572430
$295$	6.04749	0.352099
$296$	−3.64324	−0.211759
$297$	−3.11220	−0.180588
$298$	2.54545	0.147454
$299$	−6.84011	−0.395573
$300$	2.40844	0.139051
$301$	−16.1973	−0.933597
$302$	3.17616	0.182767
$303$	−4.29092	−0.246507
$304$	3.76585	0.215986
$305$	18.0440	1.03319
$306$	0.0305118	0.00174424
$307$	23.5410	1.34356	0.671778	−	0.740753i	$-0.265531\pi$
$307$	23.5410	1.34356	0.671778	+	0.740753i	$0.265531\pi$
$308$	9.96824	0.567993
$309$	1.00000	0.0568880
$310$	−1.68916	−0.0959376
$311$	−9.98613	−0.566262	−0.283131	−	0.959081i	$-0.591373\pi$
$311$	−9.98613	−0.566262	−0.283131	+	0.959081i	$0.591373\pi$
$312$	0.901970	0.0510640
$313$	−4.32374	−0.244392	−0.122196	−	0.992506i	$-0.538994\pi$
$313$	−4.32374	−0.244392	−0.122196	+	0.992506i	$0.538994\pi$
$314$	3.12174	0.176170
$315$	−3.19010	−0.179742
$316$	14.8512	0.835447
$317$	−15.2227	−0.854993	−0.427496	−	0.904017i	$-0.640604\pi$
$317$	−15.2227	−0.854993	−0.427496	+	0.904017i	$0.640604\pi$
$318$	−0.0198575	−0.00111355
$319$	−10.0842	−0.564605
$320$	13.1420	0.734659
$321$	2.64125	0.147420
$322$	2.56985	0.143212
$323$	0.136309	0.00758443
$324$	−1.94780	−0.108211
$325$	1.23649	0.0685883
$326$	3.89725	0.215848
$327$	−11.5581	−0.639167
$328$	7.11044	0.392608
$329$	9.99208	0.550881
$330$	1.37943	0.0759352
$331$	−6.47626	−0.355968	−0.177984	−	0.984033i	$-0.556957\pi$
$331$	−6.47626	−0.355968	−0.177984	+	0.984033i	$0.556957\pi$
$332$	−12.2934	−0.674689
$333$	4.03920	0.221347
$334$	−0.927176	−0.0507328
$335$	9.99140	0.545888
$336$	6.06705	0.330985
$337$	−24.6208	−1.34118	−0.670590	−	0.741828i	$-0.733959\pi$
$337$	−24.6208	−1.34118	−0.670590	+	0.741828i	$0.733959\pi$
$338$	0.228474	0.0124274
$339$	−1.42880	−0.0776019
$340$	0.504628	0.0273673
$341$	−11.8605	−0.642282
$342$	0.233201	0.0126101
$343$	−18.5751	−1.00296
$344$	8.88438	0.479014
$345$	−13.2696	−0.714413
$346$	1.35331	0.0727544
$347$	−20.6314	−1.10755	−0.553777	−	0.832665i	$-0.686814\pi$
$347$	−20.6314	−1.10755	−0.553777	+	0.832665i	$0.686814\pi$
$348$	−6.31129	−0.338320
$349$	−1.60368	−0.0858430	−0.0429215	−	0.999078i	$-0.513667\pi$
$349$	−1.60368	−0.0858430	−0.0429215	+	0.999078i	$0.513667\pi$
$350$	−0.464554	−0.0248314
$351$	−1.00000	−0.0533761
$352$	−8.23767	−0.439069
$353$	−15.7458	−0.838065	−0.419032	−	0.907971i	$-0.637631\pi$
$353$	−15.7458	−0.838065	−0.419032	+	0.907971i	$0.637631\pi$
$354$	−0.712223	−0.0378542
$355$	−4.50829	−0.239275
$356$	10.9572	0.580729
$357$	0.219603	0.0116226
$358$	−1.83012	−0.0967247
$359$	33.2994	1.75747	0.878737	−	0.477306i	$-0.158387\pi$
$359$	33.2994	1.75747	0.878737	+	0.477306i	$0.158387\pi$
$360$	1.74980	0.0922226
$361$	−17.9582	−0.945168
$362$	−5.31109	−0.279145
$363$	−1.31424	−0.0689797
$364$	3.20296	0.167881
$365$	23.2182	1.21530
$366$	−2.12507	−0.111079
$367$	−4.51983	−0.235933	−0.117966	−	0.993018i	$-0.537638\pi$
$367$	−4.51983	−0.235933	−0.117966	+	0.993018i	$0.537638\pi$
$368$	25.2367	1.31555
$369$	−7.88323	−0.410385
$370$	−1.79031	−0.0930739
$371$	−0.142921	−0.00742008
$372$	−7.42302	−0.384866
$373$	27.6822	1.43333	0.716665	−	0.697418i	$-0.245668\pi$
$373$	27.6822	1.43333	0.716665	+	0.697418i	$0.245668\pi$
$374$	−0.0949588	−0.00491020
$375$	12.0986	0.624771
$376$	−5.48076	−0.282648
$377$	−3.24021	−0.166879
$378$	0.375703	0.0193241
$379$	4.27868	0.219781	0.109890	−	0.993944i	$-0.464950\pi$
$379$	4.27868	0.219781	0.109890	+	0.993944i	$0.464950\pi$
$380$	3.85686	0.197853
$381$	−17.0803	−0.875049
$382$	0.838255	0.0428889
$383$	11.6061	0.593044	0.296522	−	0.955026i	$-0.404173\pi$
$383$	11.6061	0.593044	0.296522	+	0.955026i	$0.404173\pi$
$384$	−6.84155	−0.349132
$385$	9.92820	0.505988
$386$	−3.83116	−0.195001
$387$	−9.84997	−0.500702
$388$	15.6942	0.796753
$389$	20.4813	1.03844	0.519222	−	0.854640i	$-0.326222\pi$
$389$	20.4813	1.03844	0.519222	+	0.854640i	$0.326222\pi$
$390$	0.443234	0.0224440
$391$	0.913469	0.0461961
$392$	3.87482	0.195708
$393$	−1.77719	−0.0896475
$394$	0.415002	0.0209075
$395$	14.7916	0.744245
$396$	6.06193	0.304624
$397$	14.0873	0.707019	0.353509	−	0.935431i	$-0.384988\pi$
$397$	14.0873	0.707019	0.353509	+	0.935431i	$0.384988\pi$
$398$	−3.87726	−0.194349
$399$	1.67842	0.0840261
$400$	−4.56207	−0.228103
$401$	−0.348428	−0.0173996	−0.00869982	−	0.999962i	$-0.502769\pi$
$401$	−0.348428	−0.0173996	−0.00869982	+	0.999962i	$0.502769\pi$
$402$	−1.17670	−0.0586886
$403$	−3.81098	−0.189838
$404$	8.35786	0.415819
$405$	−1.93998	−0.0963982
$406$	1.21736	0.0604164
$407$	−12.5708	−0.623110
$408$	−0.120455	−0.00596339
$409$	−15.2721	−0.755155	−0.377578	−	0.925978i	$-0.623243\pi$
$409$	−15.2721	−0.755155	−0.377578	+	0.925978i	$0.623243\pi$
$410$	3.49412	0.172562
$411$	−6.59385	−0.325251
$412$	−1.94780	−0.0959612
$413$	−5.12609	−0.252239
$414$	1.56279	0.0768068
$415$	−12.2440	−0.601036
$416$	−2.64690	−0.129775
$417$	0.222543	0.0108980
$418$	−0.725767	−0.0354984
$419$	38.3605	1.87403	0.937017	−	0.349285i	$-0.113575\pi$
$419$	38.3605	1.87403	0.937017	+	0.349285i	$0.113575\pi$
$420$	6.21367	0.303196
$421$	−4.13633	−0.201592	−0.100796	−	0.994907i	$-0.532139\pi$
$421$	−4.13633	−0.201592	−0.100796	+	0.994907i	$0.532139\pi$
$422$	−1.61560	−0.0786461
$423$	6.07643	0.295446
$424$	0.0783935	0.00380713
$425$	−0.165129	−0.00800992
$426$	0.530949	0.0257246
$427$	−15.2948	−0.740165
$428$	−5.14462	−0.248674
$429$	3.11220	0.150258
$430$	4.36585	0.210540
$431$	9.13888	0.440204	0.220102	−	0.975477i	$-0.429361\pi$
$431$	9.13888	0.440204	0.220102	+	0.975477i	$0.429361\pi$
$432$	3.68952	0.177512
$433$	−13.5482	−0.651086	−0.325543	−	0.945527i	$-0.605547\pi$
$433$	−13.5482	−0.651086	−0.325543	+	0.945527i	$0.605547\pi$
$434$	1.43179	0.0687284
$435$	−6.28594	−0.301388
$436$	22.5129	1.07817
$437$	6.98162	0.333976
$438$	−2.73445	−0.130657
$439$	21.4302	1.02281	0.511403	−	0.859341i	$-0.329126\pi$
$439$	21.4302	1.02281	0.511403	+	0.859341i	$0.329126\pi$
$440$	−5.44572	−0.259615
$441$	−4.29595	−0.204569
$442$	−0.0305118	−0.00145130
$443$	10.3058	0.489645	0.244822	−	0.969568i	$-0.421270\pi$
$443$	10.3058	0.489645	0.244822	+	0.969568i	$0.421270\pi$
$444$	−7.86755	−0.373378
$445$	10.9132	0.517334
$446$	2.94045	0.139234
$447$	11.1411	0.526955
$448$	−11.1396	−0.526299
$449$	6.84073	0.322834	0.161417	−	0.986886i	$-0.448394\pi$
$449$	6.84073	0.322834	0.161417	+	0.986886i	$0.448394\pi$
$450$	−0.282507	−0.0133175
$451$	24.5342	1.15527
$452$	2.78302	0.130902
$453$	13.9016	0.653155
$454$	3.34170	0.156834
$455$	3.19010	0.149554
$456$	−0.920630	−0.0431125
$457$	13.5915	0.635786	0.317893	−	0.948127i	$-0.397025\pi$
$457$	13.5915	0.635786	0.317893	+	0.948127i	$0.397025\pi$
$458$	−3.01942	−0.141088
$459$	0.133546	0.00623340
$460$	25.8466	1.20510
$461$	−17.4745	−0.813870	−0.406935	−	0.913457i	$-0.633402\pi$
$461$	−17.4745	−0.813870	−0.406935	+	0.913457i	$0.633402\pi$
$462$	−1.16926	−0.0543989
$463$	0.342618	0.0159228	0.00796142	−	0.999968i	$-0.497466\pi$
$463$	0.342618	0.0159228	0.00796142	+	0.999968i	$0.497466\pi$
$464$	11.9548	0.554989
$465$	−7.39320	−0.342852
$466$	−3.03815	−0.140739
$467$	14.4380	0.668111	0.334055	−	0.942553i	$-0.391583\pi$
$467$	14.4380	0.668111	0.334055	+	0.942553i	$0.391583\pi$
$468$	1.94780	0.0900371
$469$	−8.46910	−0.391067
$470$	−2.69328	−0.124232
$471$	13.6634	0.629578
$472$	2.81171	0.129420
$473$	30.6550	1.40952
$474$	−1.74203	−0.0800141
$475$	−1.26207	−0.0579079
$476$	−0.427743	−0.0196056
$477$	−0.0869136	−0.00397950
$478$	−4.14098	−0.189404
$479$	18.6926	0.854087	0.427044	−	0.904231i	$-0.359555\pi$
$479$	18.6926	0.854087	0.427044	+	0.904231i	$0.359555\pi$
$480$	−5.13492	−0.234376
$481$	−4.03920	−0.184172
$482$	3.61771	0.164782
$483$	11.2479	0.511796
$484$	2.55987	0.116358
$485$	15.6312	0.709775
$486$	0.228474	0.0103638
$487$	−20.3255	−0.921035	−0.460518	−	0.887651i	$-0.652336\pi$
$487$	−20.3255	−0.921035	−0.460518	+	0.887651i	$0.652336\pi$
$488$	8.38934	0.379767
$489$	17.0577	0.771376
$490$	1.90411	0.0860191
$491$	26.7805	1.20859	0.604294	−	0.796761i	$-0.293455\pi$
$491$	26.7805	1.20859	0.604294	+	0.796761i	$0.293455\pi$
$492$	15.3550	0.692255
$493$	0.432718	0.0194886
$494$	−0.233201	−0.0104922
$495$	6.03758	0.271369
$496$	14.0607	0.631343
$497$	3.82141	0.171413
$498$	1.44200	0.0646176
$499$	−21.4121	−0.958537	−0.479269	−	0.877668i	$-0.659098\pi$
$499$	−21.4121	−0.958537	−0.479269	+	0.877668i	$0.659098\pi$
$500$	−23.5657	−1.05389
$501$	−4.05812	−0.181303
$502$	−3.18651	−0.142221
$503$	6.71485	0.299400	0.149700	−	0.988731i	$-0.452169\pi$
$503$	6.71485	0.299400	0.149700	+	0.988731i	$0.452169\pi$
$504$	−1.48320	−0.0660670
$505$	8.32429	0.370426
$506$	−4.86370	−0.216218
$507$	1.00000	0.0444116
$508$	33.2690	1.47607
$509$	8.34480	0.369877	0.184938	−	0.982750i	$-0.440791\pi$
$509$	8.34480	0.369877	0.184938	+	0.982750i	$0.440791\pi$
$510$	−0.0591922	−0.00262108
$511$	−19.6807	−0.870623
$512$	16.4215	0.725734
$513$	1.02069	0.0450645
$514$	−4.64885	−0.205052
$515$	−1.93998	−0.0854856
$516$	19.1858	0.844607
$517$	−18.9110	−0.831706
$518$	1.51754	0.0666768
$519$	5.92325	0.260002
$520$	−1.74980	−0.0767338
$521$	−27.0183	−1.18369	−0.591847	−	0.806050i	$-0.701601\pi$
$521$	−27.0183	−1.18369	−0.591847	+	0.806050i	$0.701601\pi$
$522$	0.740305	0.0324023
$523$	26.6858	1.16689	0.583445	−	0.812153i	$-0.301704\pi$
$523$	26.6858	1.16689	0.583445	+	0.812153i	$0.301704\pi$
$524$	3.46161	0.151221
$525$	−2.03329	−0.0887400
$526$	−7.32796	−0.319514
$527$	0.508941	0.0221698
$528$	−11.4825	−0.499712
$529$	23.7870	1.03422
$530$	0.0385231	0.00167334
$531$	−3.11730	−0.135279
$532$	−3.26922	−0.141739
$533$	7.88323	0.341461
$534$	−1.28526	−0.0556187
$535$	−5.12395	−0.221528
$536$	4.64539	0.200650
$537$	−8.01017	−0.345664
$538$	−0.132403	−0.00570830
$539$	13.3698	0.575880
$540$	3.77868	0.162609
$541$	−25.9912	−1.11745	−0.558724	−	0.829354i	$-0.688709\pi$
$541$	−25.9912	−1.11745	−0.558724	+	0.829354i	$0.688709\pi$
$542$	−0.888987	−0.0381853
$543$	−23.2459	−0.997577
$544$	0.353483	0.0151555
$545$	22.4225	0.960475
$546$	−0.375703	−0.0160786
$547$	40.5922	1.73560	0.867799	−	0.496916i	$-0.165534\pi$
$547$	40.5922	1.73560	0.867799	+	0.496916i	$0.165534\pi$
$548$	12.8435	0.548647
$549$	−9.30112	−0.396962
$550$	0.879216	0.0374899
$551$	3.30725	0.140893
$552$	−6.16957	−0.262594
$553$	−12.5379	−0.533167
$554$	6.55476	0.278485
$555$	−7.83595	−0.332618
$556$	−0.433470	−0.0183832
$557$	18.0887	0.766445	0.383222	−	0.923656i	$-0.374814\pi$
$557$	18.0887	0.766445	0.383222	+	0.923656i	$0.374814\pi$
$558$	0.870710	0.0368601
$559$	9.84997	0.416610
$560$	−11.7699	−0.497370
$561$	−0.415621	−0.0175475
$562$	−1.65458	−0.0697943
$563$	−22.7281	−0.957877	−0.478939	−	0.877848i	$-0.658978\pi$
$563$	−22.7281	−0.957877	−0.478939	+	0.877848i	$0.658978\pi$
$564$	−11.8357	−0.498371
$565$	2.77184	0.116612
$566$	−2.84905	−0.119755
$567$	1.64440	0.0690583
$568$	−2.09608	−0.0879496
$569$	23.0295	0.965448	0.482724	−	0.875772i	$-0.339647\pi$
$569$	23.0295	0.965448	0.482724	+	0.875772i	$0.339647\pi$
$570$	−0.452404	−0.0189491
$571$	−17.7419	−0.742476	−0.371238	−	0.928538i	$-0.621067\pi$
$571$	−17.7419	−0.742476	−0.371238	+	0.928538i	$0.621067\pi$
$572$	−6.06193	−0.253462
$573$	3.66893	0.153272
$574$	−2.96175	−0.123621
$575$	−8.45774	−0.352712
$576$	−6.77430	−0.282262
$577$	−7.35528	−0.306204	−0.153102	−	0.988210i	$-0.548926\pi$
$577$	−7.35528	−0.306204	−0.153102	+	0.988210i	$0.548926\pi$
$578$	−3.87999	−0.161386
$579$	−16.7685	−0.696874
$580$	12.2437	0.508394
$581$	10.3785	0.430574
$582$	−1.84091	−0.0763081
$583$	0.270492	0.0112026
$584$	10.7951	0.446703
$585$	1.93998	0.0802081
$586$	0.565680	0.0233680
$587$	41.6688	1.71986	0.859929	−	0.510414i	$-0.170508\pi$
$587$	41.6688	1.71986	0.859929	+	0.510414i	$0.170508\pi$
$588$	8.36765	0.345076
$589$	3.88982	0.160277
$590$	1.38170	0.0568835
$591$	1.81641	0.0747171
$592$	14.9027	0.612498
$593$	28.0778	1.15302	0.576509	−	0.817091i	$-0.304415\pi$
$593$	28.0778	1.15302	0.576509	+	0.817091i	$0.304415\pi$
$594$	−0.711056	−0.0291750
$595$	−0.426025	−0.0174653
$596$	−21.7006	−0.888891
$597$	−16.9702	−0.694545
$598$	−1.56279	−0.0639071
$599$	19.6649	0.803487	0.401743	−	0.915752i	$-0.368404\pi$
$599$	19.6649	0.803487	0.401743	+	0.915752i	$0.368404\pi$
$600$	1.11528	0.0455311
$601$	1.20690	0.0492306	0.0246153	−	0.999697i	$-0.492164\pi$
$601$	1.20690	0.0492306	0.0246153	+	0.999697i	$0.492164\pi$
$602$	−3.70066	−0.150828
$603$	−5.15027	−0.209735
$604$	−27.0776	−1.10177
$605$	2.54959	0.103656
$606$	−0.980366	−0.0398246
$607$	13.8583	0.562490	0.281245	−	0.959636i	$-0.409253\pi$
$607$	13.8583	0.562490	0.281245	+	0.959636i	$0.409253\pi$
$608$	2.70166	0.109567
$609$	5.32821	0.215910
$610$	4.12258	0.166918
$611$	−6.07643	−0.245826
$612$	−0.260121	−0.0105148
$613$	4.95008	0.199932	0.0999659	−	0.994991i	$-0.468127\pi$
$613$	4.95008	0.199932	0.0999659	+	0.994991i	$0.468127\pi$
$614$	5.37851	0.217059
$615$	15.2933	0.616685
$616$	4.61601	0.185984
$617$	−23.1023	−0.930064	−0.465032	−	0.885294i	$-0.653957\pi$
$617$	−23.1023	−0.930064	−0.465032	+	0.885294i	$0.653957\pi$
$618$	0.228474	0.00919058
$619$	−7.62415	−0.306441	−0.153220	−	0.988192i	$-0.548964\pi$
$619$	−7.62415	−0.306441	−0.153220	+	0.988192i	$0.548964\pi$
$620$	14.4005	0.578337
$621$	6.84011	0.274484
$622$	−2.28157	−0.0914828
$623$	−9.25043	−0.370610
$624$	−3.68952	−0.147699
$625$	−17.2886	−0.691545
$626$	−0.987863	−0.0394829
$627$	−3.17658	−0.126860
$628$	−26.6136	−1.06200
$629$	0.539419	0.0215081
$630$	−0.728855	−0.0290383
$631$	−49.0489	−1.95260	−0.976302	−	0.216413i	$-0.930564\pi$
$631$	−49.0489	−1.95260	−0.976302	+	0.216413i	$0.930564\pi$
$632$	6.87718	0.273560
$633$	−7.07125	−0.281057
$634$	−3.47800	−0.138129
$635$	33.1353	1.31494
$636$	0.169290	0.00671280
$637$	4.29595	0.170212
$638$	−2.30397	−0.0912152
$639$	2.32389	0.0919317
$640$	13.2725	0.524640
$641$	−22.3797	−0.883943	−0.441972	−	0.897029i	$-0.645721\pi$
$641$	−22.3797	−0.883943	−0.441972	+	0.897029i	$0.645721\pi$
$642$	0.603456	0.0238165
$643$	−30.7085	−1.21102	−0.605512	−	0.795836i	$-0.707032\pi$
$643$	−30.7085	−1.21102	−0.605512	+	0.795836i	$0.707032\pi$
$644$	−21.9086	−0.863319
$645$	19.1087	0.752405
$646$	0.0311431	0.00122531
$647$	−21.5401	−0.846827	−0.423414	−	0.905937i	$-0.639168\pi$
$647$	−21.5401	−0.846827	−0.423414	+	0.905937i	$0.639168\pi$
$648$	−0.901970	−0.0354327
$649$	9.70166	0.380823
$650$	0.282507	0.0110808
$651$	6.26677	0.245614
$652$	−33.2250	−1.30119
$653$	3.92531	0.153609	0.0768046	−	0.997046i	$-0.475528\pi$
$653$	3.92531	0.153609	0.0768046	+	0.997046i	$0.475528\pi$
$654$	−2.64074	−0.103261
$655$	3.44771	0.134713
$656$	−29.0854	−1.13559
$657$	−11.9683	−0.466928
$658$	2.28293	0.0889979
$659$	10.0870	0.392933	0.196466	−	0.980511i	$-0.437053\pi$
$659$	10.0870	0.392933	0.196466	+	0.980511i	$0.437053\pi$
$660$	−11.7600	−0.457758
$661$	−14.4989	−0.563942	−0.281971	−	0.959423i	$-0.590988\pi$
$661$	−14.4989	−0.563942	−0.281971	+	0.959423i	$0.590988\pi$
$662$	−1.47966	−0.0575086
$663$	−0.133546	−0.00518650
$664$	−5.69273	−0.220921
$665$	−3.25609	−0.126266
$666$	0.922853	0.0357598
$667$	22.1634	0.858170
$668$	7.90441	0.305831
$669$	12.8699	0.497580
$670$	2.28278	0.0881914
$671$	28.9469	1.11748
$672$	4.35256	0.167904
$673$	29.5666	1.13971	0.569855	−	0.821745i	$-0.306999\pi$
$673$	29.5666	1.13971	0.569855	+	0.821745i	$0.306999\pi$
$674$	−5.62522	−0.216675
$675$	−1.23649	−0.0475926
$676$	−1.94780	−0.0749154
$677$	24.1149	0.926809	0.463405	−	0.886147i	$-0.346628\pi$
$677$	24.1149	0.926809	0.463405	+	0.886147i	$0.346628\pi$
$678$	−0.326444	−0.0125370
$679$	−13.2496	−0.508473
$680$	0.233679	0.00896118
$681$	14.6262	0.560476
$682$	−2.70982	−0.103764
$683$	−1.59426	−0.0610027	−0.0305013	−	0.999535i	$-0.509710\pi$
$683$	−1.59426	−0.0610027	−0.0305013	+	0.999535i	$0.509710\pi$
$684$	−1.98810	−0.0760168
$685$	12.7919	0.488754
$686$	−4.24392	−0.162034
$687$	−13.2156	−0.504205
$688$	−36.3417	−1.38551
$689$	0.0869136	0.00331115
$690$	−3.03177	−0.115418
$691$	20.4565	0.778203	0.389102	−	0.921195i	$-0.372785\pi$
$691$	20.4565	0.778203	0.389102	+	0.921195i	$0.372785\pi$
$692$	−11.5373	−0.438582
$693$	−5.11769	−0.194405
$694$	−4.71375	−0.178932
$695$	−0.431729	−0.0163764
$696$	−2.92258	−0.110780
$697$	−1.05277	−0.0398767
$698$	−0.366399	−0.0138684
$699$	−13.2976	−0.502960
$700$	3.96044	0.149690
$701$	19.5735	0.739282	0.369641	−	0.929175i	$-0.379481\pi$
$701$	19.5735	0.739282	0.369641	+	0.929175i	$0.379481\pi$
$702$	−0.228474	−0.00862320
$703$	4.12276	0.155493
$704$	21.0829	0.794593
$705$	−11.7881	−0.443966
$706$	−3.59751	−0.135394
$707$	−7.05600	−0.265368
$708$	6.07188	0.228195
$709$	0.124349	0.00467002	0.00233501	−	0.999997i	$-0.499257\pi$
$709$	0.124349	0.00467002	0.00233501	+	0.999997i	$0.499257\pi$
$710$	−1.03003	−0.0386563
$711$	−7.62462	−0.285946
$712$	5.07395	0.190154
$713$	26.0675	0.976235
$714$	0.0501736	0.00187770
$715$	−6.03758	−0.225793
$716$	15.6022	0.583082
$717$	−18.1245	−0.676871
$718$	7.60805	0.283930
$719$	−8.44984	−0.315126	−0.157563	−	0.987509i	$-0.550364\pi$
$719$	−8.44984	−0.315126	−0.157563	+	0.987509i	$0.550364\pi$
$720$	−7.15758	−0.266747
$721$	1.64440	0.0612406
$722$	−4.10298	−0.152697
$723$	15.8342	0.588881
$724$	45.2783	1.68276
$725$	−4.00650	−0.148798
$726$	−0.300270	−0.0111441
$727$	22.8383	0.847027	0.423514	−	0.905890i	$-0.360797\pi$
$727$	22.8383	0.847027	0.423514	+	0.905890i	$0.360797\pi$
$728$	1.48320	0.0549710
$729$	1.00000	0.0370370
$730$	5.30477	0.196338
$731$	−1.31543	−0.0486528
$732$	18.1167	0.669613
$733$	25.1434	0.928692	0.464346	−	0.885654i	$-0.346289\pi$
$733$	25.1434	0.928692	0.464346	+	0.885654i	$0.346289\pi$
$734$	−1.03266	−0.0381163
$735$	8.33404	0.307406
$736$	18.1051	0.667362
$737$	16.0286	0.590423
$738$	−1.80111	−0.0662999
$739$	−15.8728	−0.583889	−0.291945	−	0.956435i	$-0.594302\pi$
$739$	−15.8728	−0.583889	−0.291945	+	0.956435i	$0.594302\pi$
$740$	15.2629	0.561074
$741$	−1.02069	−0.0374959
$742$	−0.0326537	−0.00119876
$743$	−29.4103	−1.07896	−0.539480	−	0.841998i	$-0.681379\pi$
$743$	−29.4103	−1.07896	−0.539480	+	0.841998i	$0.681379\pi$
$744$	−3.43739	−0.126021
$745$	−21.6134	−0.791855
$746$	6.32467	0.231563
$747$	6.31144	0.230924
$748$	0.809547	0.0296000
$749$	4.34326	0.158699
$750$	2.76423	0.100935
$751$	−37.3070	−1.36135	−0.680676	−	0.732584i	$-0.738314\pi$
$751$	−37.3070	−1.36135	−0.680676	+	0.732584i	$0.738314\pi$
$752$	22.4191	0.817541
$753$	−13.9469	−0.508253
$754$	−0.740305	−0.0269603
$755$	−26.9688	−0.981495
$756$	−3.20296	−0.116491
$757$	−34.0126	−1.23621	−0.618104	−	0.786096i	$-0.712099\pi$
$757$	−34.0126	−1.23621	−0.618104	+	0.786096i	$0.712099\pi$
$758$	0.977567	0.0355068
$759$	−21.2877	−0.772696
$760$	1.78600	0.0647851
$761$	−39.6851	−1.43858	−0.719292	−	0.694708i	$-0.755534\pi$
$761$	−39.6851	−1.43858	−0.719292	+	0.694708i	$0.755534\pi$
$762$	−3.90240	−0.141369
$763$	−19.0062	−0.688071
$764$	−7.14634	−0.258545
$765$	−0.259076	−0.00936692
$766$	2.65169	0.0958096
$767$	3.11730	0.112559
$768$	11.9855	0.432489
$769$	32.8096	1.18314	0.591572	−	0.806252i	$-0.298508\pi$
$769$	32.8096	1.18314	0.591572	+	0.806252i	$0.298508\pi$
$770$	2.26834	0.0817452
$771$	−20.3474	−0.732792
$772$	32.6616	1.17552
$773$	−29.2470	−1.05194	−0.525971	−	0.850503i	$-0.676298\pi$
$773$	−29.2470	−1.05194	−0.525971	+	0.850503i	$0.676298\pi$
$774$	−2.25046	−0.0808913
$775$	−4.71224	−0.169269
$776$	7.26754	0.260889
$777$	6.64206	0.238283
$778$	4.67945	0.167766
$779$	−8.04632	−0.288289
$780$	−3.77868	−0.135299
$781$	−7.23240	−0.258796
$782$	0.208704	0.00746324
$783$	3.24021	0.115796
$784$	−15.8500	−0.566071
$785$	−26.5068	−0.946067
$786$	−0.406042	−0.0144831
$787$	44.3479	1.58083	0.790416	−	0.612570i	$-0.209864\pi$
$787$	44.3479	1.58083	0.790416	+	0.612570i	$0.209864\pi$
$788$	−3.53800	−0.126036
$789$	−32.0735	−1.14185
$790$	3.37950	0.120237
$791$	−2.34952	−0.0835394
$792$	2.80711	0.0997462
$793$	9.30112	0.330293
$794$	3.21857	0.114223
$795$	0.168610	0.00597999
$796$	33.0546	1.17159
$797$	−16.4161	−0.581490	−0.290745	−	0.956801i	$-0.593903\pi$
$797$	−16.4161	−0.581490	−0.290745	+	0.956801i	$0.593903\pi$
$798$	0.383476	0.0135749
$799$	0.811483	0.0287082
$800$	−3.27287	−0.115714
$801$	−5.62541	−0.198764
$802$	−0.0796067	−0.00281101
$803$	37.2477	1.31444
$804$	10.0317	0.353790
$805$	−21.8206	−0.769075
$806$	−0.870710	−0.0306694
$807$	−0.579509	−0.0203997
$808$	3.87029	0.136156
$809$	46.1192	1.62146	0.810732	−	0.585418i	$-0.199069\pi$
$809$	46.1192	1.62146	0.810732	+	0.585418i	$0.199069\pi$
$810$	−0.443234	−0.0155737
$811$	−28.4005	−0.997276	−0.498638	−	0.866810i	$-0.666166\pi$
$811$	−28.4005	−0.997276	−0.498638	+	0.866810i	$0.666166\pi$
$812$	−10.3783	−0.364206
$813$	−3.89097	−0.136462
$814$	−2.87210	−0.100667
$815$	−33.0915	−1.15915
$816$	0.492721	0.0172487
$817$	−10.0538	−0.351736
$818$	−3.48927	−0.122000
$819$	−1.64440	−0.0574600
$820$	−29.7882	−1.04025
$821$	−23.1396	−0.807576	−0.403788	−	0.914853i	$-0.632307\pi$
$821$	−23.1396	−0.807576	−0.403788	+	0.914853i	$0.632307\pi$
$822$	−1.50652	−0.0525461
$823$	3.73387	0.130155	0.0650773	−	0.997880i	$-0.479271\pi$
$823$	3.73387	0.130155	0.0650773	+	0.997880i	$0.479271\pi$
$824$	−0.901970	−0.0314216
$825$	3.84821	0.133977
$826$	−1.17118	−0.0407506
$827$	−27.3907	−0.952468	−0.476234	−	0.879319i	$-0.657998\pi$
$827$	−27.3907	−0.952468	−0.476234	+	0.879319i	$0.657998\pi$
$828$	−13.3232	−0.463012
$829$	−23.9628	−0.832264	−0.416132	−	0.909304i	$-0.636614\pi$
$829$	−23.9628	−0.832264	−0.416132	+	0.909304i	$0.636614\pi$
$830$	−2.79745	−0.0971008
$831$	28.6893	0.995220
$832$	6.77430	0.234856
$833$	−0.573707	−0.0198778
$834$	0.0508454	0.00176063
$835$	7.87266	0.272445
$836$	6.18734	0.213994
$837$	3.81098	0.131727
$838$	8.76438	0.302761
$839$	−8.74924	−0.302057	−0.151029	−	0.988529i	$-0.548259\pi$
$839$	−8.74924	−0.302057	−0.151029	+	0.988529i	$0.548259\pi$
$840$	2.87737	0.0992788
$841$	−18.5010	−0.637966
$842$	−0.945044	−0.0325684
$843$	−7.24188	−0.249424
$844$	13.7734	0.474099
$845$	−1.93998	−0.0667372
$846$	1.38831	0.0477310
$847$	−2.16113	−0.0742575
$848$	−0.320670	−0.0110118
$849$	−12.4699	−0.427966
$850$	−0.0377276	−0.00129405
$851$	27.6286	0.947095
$852$	−4.52647	−0.155074
$853$	42.6828	1.46143	0.730715	−	0.682683i	$-0.239187\pi$
$853$	42.6828	1.46143	0.730715	+	0.682683i	$0.239187\pi$
$854$	−3.49446	−0.119578
$855$	−1.98011	−0.0677184
$856$	−2.38232	−0.0814262
$857$	13.8412	0.472807	0.236403	−	0.971655i	$-0.424031\pi$
$857$	13.8412	0.472807	0.236403	+	0.971655i	$0.424031\pi$
$858$	0.711056	0.0242751
$859$	−36.9115	−1.25941	−0.629703	−	0.776836i	$-0.716823\pi$
$859$	−36.9115	−1.25941	−0.629703	+	0.776836i	$0.716823\pi$
$860$	−37.2199	−1.26919
$861$	−12.9632	−0.441784
$862$	2.08800	0.0711175
$863$	51.1732	1.74195	0.870977	−	0.491323i	$-0.163487\pi$
$863$	51.1732	1.74195	0.870977	+	0.491323i	$0.163487\pi$
$864$	2.64690	0.0900494
$865$	−11.4910	−0.390704
$866$	−3.09542	−0.105187
$867$	−16.9822	−0.576745
$868$	−12.2064	−0.414313
$869$	23.7293	0.804962
$870$	−1.43617	−0.0486909
$871$	5.15027	0.174510
$872$	10.4251	0.353039
$873$	−8.05740	−0.272702
$874$	1.59512	0.0539557
$875$	19.8950	0.672574
$876$	23.3119	0.787635
$877$	−4.47425	−0.151085	−0.0755424	−	0.997143i	$-0.524069\pi$
$877$	−4.47425	−0.151085	−0.0755424	+	0.997143i	$0.524069\pi$
$878$	4.89624	0.165240
$879$	2.47590	0.0835101
$880$	22.2758	0.750917
$881$	−42.5692	−1.43419	−0.717096	−	0.696975i	$-0.754529\pi$
$881$	−42.5692	−1.43419	−0.717096	+	0.696975i	$0.754529\pi$
$882$	−0.981514	−0.0330493
$883$	−4.62915	−0.155783	−0.0778917	−	0.996962i	$-0.524819\pi$
$883$	−4.62915	−0.155783	−0.0778917	+	0.996962i	$0.524819\pi$
$884$	0.260121	0.00874881
$885$	6.04749	0.203284
$886$	2.35462	0.0791049
$887$	−32.6152	−1.09511	−0.547556	−	0.836769i	$-0.684442\pi$
$887$	−32.6152	−1.09511	−0.547556	+	0.836769i	$0.684442\pi$
$888$	−3.64324	−0.122259
$889$	−28.0868	−0.942001
$890$	2.49338	0.0835782
$891$	−3.11220	−0.104262
$892$	−25.0681	−0.839341
$893$	6.20214	0.207547
$894$	2.54545	0.0851326
$895$	15.5395	0.519430
$896$	−11.2502	−0.375844
$897$	−6.84011	−0.228384
$898$	1.56293	0.0521557
$899$	12.3484	0.411841
$900$	2.40844	0.0802813
$901$	−0.0116070	−0.000386684 0
$902$	5.60542	0.186640
$903$	−16.1973	−0.539012
$904$	1.28874	0.0428628
$905$	45.0965	1.49906
$906$	3.17616	0.105521
$907$	27.6990	0.919730	0.459865	−	0.887989i	$-0.347898\pi$
$907$	27.6990	0.919730	0.459865	+	0.887989i	$0.347898\pi$
$908$	−28.4888	−0.945435
$909$	−4.29092	−0.142321
$910$	0.728855	0.0241613
$911$	35.5535	1.17794	0.588971	−	0.808154i	$-0.299533\pi$
$911$	35.5535	1.17794	0.588971	+	0.808154i	$0.299533\pi$
$912$	3.76585	0.124700
$913$	−19.6424	−0.650070
$914$	3.10532	0.102715
$915$	18.0440	0.596515
$916$	25.7413	0.850516
$917$	−2.92241	−0.0965066
$918$	0.0305118	0.00100704
$919$	−28.8023	−0.950100	−0.475050	−	0.879959i	$-0.657570\pi$
$919$	−28.8023	−0.950100	−0.475050	+	0.879959i	$0.657570\pi$
$920$	11.9688	0.394600
$921$	23.5410	0.775702
$922$	−3.99248	−0.131485
$923$	−2.32389	−0.0764918
$924$	9.96824	0.327931
$925$	−4.99444	−0.164216
$926$	0.0782795	0.00257242
$927$	1.00000	0.0328443
$928$	8.57652	0.281538
$929$	−7.94752	−0.260750	−0.130375	−	0.991465i	$-0.541618\pi$
$929$	−7.94752	−0.260750	−0.130375	+	0.991465i	$0.541618\pi$
$930$	−1.68916	−0.0553896
$931$	−4.38483	−0.143707
$932$	25.9010	0.848415
$933$	−9.98613	−0.326931
$934$	3.29871	0.107937
$935$	0.806296	0.0263687
$936$	0.901970	0.0294818
$937$	−3.63476	−0.118742	−0.0593712	−	0.998236i	$-0.518910\pi$
$937$	−3.63476	−0.118742	−0.0593712	+	0.998236i	$0.518910\pi$
$938$	−1.93497	−0.0631790
$939$	−4.32374	−0.141100
$940$	22.9609	0.748902
$941$	−1.51835	−0.0494967	−0.0247483	−	0.999694i	$-0.507878\pi$
$941$	−1.51835	−0.0494967	−0.0247483	+	0.999694i	$0.507878\pi$
$942$	3.12174	0.101712
$943$	−53.9221	−1.75595
$944$	−11.5014	−0.374337
$945$	−3.19010	−0.103774
$946$	7.00389	0.227716
$947$	−34.2958	−1.11446	−0.557232	−	0.830357i	$-0.688136\pi$
$947$	−34.2958	−1.11446	−0.557232	+	0.830357i	$0.688136\pi$
$948$	14.8512	0.482346
$949$	11.9683	0.388508
$950$	−0.288351	−0.00935535
$951$	−15.2227	−0.493630
$952$	−0.198075	−0.00641966
$953$	−19.8864	−0.644184	−0.322092	−	0.946708i	$-0.604386\pi$
$953$	−19.8864	−0.644184	−0.322092	+	0.946708i	$0.604386\pi$
$954$	−0.0198575	−0.000642911 0
$955$	−7.11763	−0.230321
$956$	35.3029	1.14178
$957$	−10.0842	−0.325975
$958$	4.27078	0.137983
$959$	−10.8429	−0.350136
$960$	13.1420	0.424155
$961$	−16.4765	−0.531499
$962$	−0.922853	−0.0297540
$963$	2.64125	0.0851129
$964$	−30.8419	−0.993350
$965$	32.5304	1.04719
$966$	2.56985	0.0826835
$967$	2.90483	0.0934131	0.0467065	−	0.998909i	$-0.485127\pi$
$967$	2.90483	0.0934131	0.0467065	+	0.998909i	$0.485127\pi$
$968$	1.18540	0.0381004
$969$	0.136309	0.00437887
$970$	3.57132	0.114668
$971$	−5.70732	−0.183157	−0.0915783	−	0.995798i	$-0.529191\pi$
$971$	−5.70732	−0.183157	−0.0915783	+	0.995798i	$0.529191\pi$
$972$	−1.94780	−0.0624757
$973$	0.365950	0.0117318
$974$	−4.64385	−0.148798
$975$	1.23649	0.0395995
$976$	−34.3167	−1.09845
$977$	49.7902	1.59293	0.796465	−	0.604684i	$-0.206701\pi$
$977$	49.7902	1.59293	0.796465	+	0.604684i	$0.206701\pi$
$978$	3.89725	0.124620
$979$	17.5074	0.559538
$980$	−16.2330	−0.518545
$981$	−11.5581	−0.369023
$982$	6.11866	0.195254
$983$	60.4587	1.92833	0.964167	−	0.265296i	$-0.0854698\pi$
$983$	60.4587	1.92833	0.964167	+	0.265296i	$0.0854698\pi$
$984$	7.11044	0.226673
$985$	−3.52379	−0.112277
$986$	0.0988648	0.00314850
$987$	9.99208	0.318051
$988$	1.98810	0.0632498
$989$	−67.3749	−2.14240
$990$	1.37943	0.0438412
$991$	7.68174	0.244018	0.122009	−	0.992529i	$-0.461066\pi$
$991$	7.68174	0.244018	0.122009	+	0.992529i	$0.461066\pi$
$992$	10.0873	0.320271
$993$	−6.47626	−0.205518
$994$	0.873092	0.0276928
$995$	32.9218	1.04369
$996$	−12.2934	−0.389532
$997$	34.9066	1.10550	0.552752	−	0.833346i	$-0.313578\pi$
$997$	34.9066	1.10550	0.552752	+	0.833346i	$0.313578\pi$
$998$	−4.89211	−0.154857
$999$	4.03920	0.127795

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.e.1.9	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.e.1.9	✓	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)

\(f(q)\)	\(=\)	\(q+0.228474 q^{2} +1.00000 q^{3} -1.94780 q^{4} -1.93998 q^{5} +0.228474 q^{6} +1.64440 q^{7} -0.901970 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.228474 q^{2} +1.00000 q^{3} -1.94780 q^{4} -1.93998 q^{5} +0.228474 q^{6} +1.64440 q^{7} -0.901970 q^{8} +1.00000 q^{9} -0.443234 q^{10} -3.11220 q^{11} -1.94780 q^{12} -1.00000 q^{13} +0.375703 q^{14} -1.93998 q^{15} +3.68952 q^{16} +0.133546 q^{17} +0.228474 q^{18} +1.02069 q^{19} +3.77868 q^{20} +1.64440 q^{21} -0.711056 q^{22} +6.84011 q^{23} -0.901970 q^{24} -1.23649 q^{25} -0.228474 q^{26} +1.00000 q^{27} -3.20296 q^{28} +3.24021 q^{29} -0.443234 q^{30} +3.81098 q^{31} +2.64690 q^{32} -3.11220 q^{33} +0.0305118 q^{34} -3.19010 q^{35} -1.94780 q^{36} +4.03920 q^{37} +0.233201 q^{38} -1.00000 q^{39} +1.74980 q^{40} -7.88323 q^{41} +0.375703 q^{42} -9.84997 q^{43} +6.06193 q^{44} -1.93998 q^{45} +1.56279 q^{46} +6.07643 q^{47} +3.68952 q^{48} -4.29595 q^{49} -0.282507 q^{50} +0.133546 q^{51} +1.94780 q^{52} -0.0869136 q^{53} +0.228474 q^{54} +6.03758 q^{55} -1.48320 q^{56} +1.02069 q^{57} +0.740305 q^{58} -3.11730 q^{59} +3.77868 q^{60} -9.30112 q^{61} +0.870710 q^{62} +1.64440 q^{63} -6.77430 q^{64} +1.93998 q^{65} -0.711056 q^{66} -5.15027 q^{67} -0.260121 q^{68} +6.84011 q^{69} -0.728855 q^{70} +2.32389 q^{71} -0.901970 q^{72} -11.9683 q^{73} +0.922853 q^{74} -1.23649 q^{75} -1.98810 q^{76} -5.11769 q^{77} -0.228474 q^{78} -7.62462 q^{79} -7.15758 q^{80} +1.00000 q^{81} -1.80111 q^{82} +6.31144 q^{83} -3.20296 q^{84} -0.259076 q^{85} -2.25046 q^{86} +3.24021 q^{87} +2.80711 q^{88} -5.62541 q^{89} -0.443234 q^{90} -1.64440 q^{91} -13.3232 q^{92} +3.81098 q^{93} +1.38831 q^{94} -1.98011 q^{95} +2.64690 q^{96} -8.05740 q^{97} -0.981514 q^{98} -3.11220 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{3} + 10 q^{4} - 6 q^{5} - 13 q^{7} - 9 q^{8} + 16 q^{9}+O(q^{10}) \) 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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