LMFDB - Embedded newform 4026.2.a.bc.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4026,2,Mod(1,4026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4026, 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("4026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4026 = 2 \cdot 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4026.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:	$32.1477718538$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - x^{8} - 30x^{7} + 7x^{6} + 284x^{5} + 100x^{4} - 777x^{3} - 250x^{2} + 574x - 68 $ x^9 - x^8 - 30x^7 + 7x^6 + 284x^5 + 100x^4 - 777x^3 - 250x^2 + 574*x - 68
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$0.731055$ of defining polynomial
Character	$\chi$	$=$	4026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.268945 q^{5} +1.00000 q^{6} +3.42672 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.268945 q^{5} +1.00000 q^{6} +3.42672 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.268945 q^{10} +1.00000 q^{11} +1.00000 q^{12} +1.26655 q^{13} +3.42672 q^{14} +0.268945 q^{15} +1.00000 q^{16} +0.867540 q^{17} +1.00000 q^{18} +6.18750 q^{19} +0.268945 q^{20} +3.42672 q^{21} +1.00000 q^{22} -8.86224 q^{23} +1.00000 q^{24} -4.92767 q^{25} +1.26655 q^{26} +1.00000 q^{27} +3.42672 q^{28} +1.57247 q^{29} +0.268945 q^{30} -6.59330 q^{31} +1.00000 q^{32} +1.00000 q^{33} +0.867540 q^{34} +0.921599 q^{35} +1.00000 q^{36} +8.55030 q^{37} +6.18750 q^{38} +1.26655 q^{39} +0.268945 q^{40} +3.44241 q^{41} +3.42672 q^{42} +12.3719 q^{43} +1.00000 q^{44} +0.268945 q^{45} -8.86224 q^{46} +5.99112 q^{47} +1.00000 q^{48} +4.74240 q^{49} -4.92767 q^{50} +0.867540 q^{51} +1.26655 q^{52} +4.13724 q^{53} +1.00000 q^{54} +0.268945 q^{55} +3.42672 q^{56} +6.18750 q^{57} +1.57247 q^{58} -13.3632 q^{59} +0.268945 q^{60} -1.00000 q^{61} -6.59330 q^{62} +3.42672 q^{63} +1.00000 q^{64} +0.340633 q^{65} +1.00000 q^{66} -0.380487 q^{67} +0.867540 q^{68} -8.86224 q^{69} +0.921599 q^{70} -10.4281 q^{71} +1.00000 q^{72} -2.36638 q^{73} +8.55030 q^{74} -4.92767 q^{75} +6.18750 q^{76} +3.42672 q^{77} +1.26655 q^{78} -8.37132 q^{79} +0.268945 q^{80} +1.00000 q^{81} +3.44241 q^{82} +2.32547 q^{83} +3.42672 q^{84} +0.233320 q^{85} +12.3719 q^{86} +1.57247 q^{87} +1.00000 q^{88} -11.6165 q^{89} +0.268945 q^{90} +4.34011 q^{91} -8.86224 q^{92} -6.59330 q^{93} +5.99112 q^{94} +1.66410 q^{95} +1.00000 q^{96} -11.5077 q^{97} +4.74240 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 9 q^{2} + 9 q^{3} + 9 q^{4} + 8 q^{5} + 9 q^{6} + 9 q^{7} + 9 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q + 9 * q^2 + 9 * q^3 + 9 * q^4 + 8 * q^5 + 9 * q^6 + 9 * q^7 + 9 * q^8 + 9 * q^9	\( 9 q + 9 q^{2} + 9 q^{3} + 9 q^{4} + 8 q^{5} + 9 q^{6} + 9 q^{7} + 9 q^{8} + 9 q^{9} + 8 q^{10} + 9 q^{11} + 9 q^{12} + 8 q^{13} + 9 q^{14} + 8 q^{15} + 9 q^{16} + q^{17} + 9 q^{18} + 5 q^{19} + 8 q^{20} + 9 q^{21} + 9 q^{22} - q^{23} + 9 q^{24} + 23 q^{25} + 8 q^{26} + 9 q^{27} + 9 q^{28} - 14 q^{29} + 8 q^{30} + 25 q^{31} + 9 q^{32} + 9 q^{33} + q^{34} + 5 q^{35} + 9 q^{36} + 16 q^{37} + 5 q^{38} + 8 q^{39} + 8 q^{40} + 5 q^{41} + 9 q^{42} + 5 q^{43} + 9 q^{44} + 8 q^{45} - q^{46} + 8 q^{47} + 9 q^{48} + 30 q^{49} + 23 q^{50} + q^{51} + 8 q^{52} + q^{53} + 9 q^{54} + 8 q^{55} + 9 q^{56} + 5 q^{57} - 14 q^{58} + 4 q^{59} + 8 q^{60} - 9 q^{61} + 25 q^{62} + 9 q^{63} + 9 q^{64} - 14 q^{65} + 9 q^{66} - 4 q^{67} + q^{68} - q^{69} + 5 q^{70} + 20 q^{71} + 9 q^{72} + 15 q^{73} + 16 q^{74} + 23 q^{75} + 5 q^{76} + 9 q^{77} + 8 q^{78} - 2 q^{79} + 8 q^{80} + 9 q^{81} + 5 q^{82} + 21 q^{83} + 9 q^{84} - 16 q^{85} + 5 q^{86} - 14 q^{87} + 9 q^{88} + 10 q^{89} + 8 q^{90} - 19 q^{91} - q^{92} + 25 q^{93} + 8 q^{94} - 7 q^{95} + 9 q^{96} + 3 q^{97} + 30 q^{98} + 9 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 9 * q^3 + 9 * q^4 + 8 * q^5 + 9 * q^6 + 9 * q^7 + 9 * q^8 + 9 * q^9 + 8 * q^10 + 9 * q^11 + 9 * q^12 + 8 * q^13 + 9 * q^14 + 8 * q^15 + 9 * q^16 + q^17 + 9 * q^18 + 5 * q^19 + 8 * q^20 + 9 * q^21 + 9 * q^22 - q^23 + 9 * q^24 + 23 * q^25 + 8 * q^26 + 9 * q^27 + 9 * q^28 - 14 * q^29 + 8 * q^30 + 25 * q^31 + 9 * q^32 + 9 * q^33 + q^34 + 5 * q^35 + 9 * q^36 + 16 * q^37 + 5 * q^38 + 8 * q^39 + 8 * q^40 + 5 * q^41 + 9 * q^42 + 5 * q^43 + 9 * q^44 + 8 * q^45 - q^46 + 8 * q^47 + 9 * q^48 + 30 * q^49 + 23 * q^50 + q^51 + 8 * q^52 + q^53 + 9 * q^54 + 8 * q^55 + 9 * q^56 + 5 * q^57 - 14 * q^58 + 4 * q^59 + 8 * q^60 - 9 * q^61 + 25 * q^62 + 9 * q^63 + 9 * q^64 - 14 * q^65 + 9 * q^66 - 4 * q^67 + q^68 - q^69 + 5 * q^70 + 20 * q^71 + 9 * q^72 + 15 * q^73 + 16 * q^74 + 23 * q^75 + 5 * q^76 + 9 * q^77 + 8 * q^78 - 2 * q^79 + 8 * q^80 + 9 * q^81 + 5 * q^82 + 21 * q^83 + 9 * q^84 - 16 * q^85 + 5 * q^86 - 14 * q^87 + 9 * q^88 + 10 * q^89 + 8 * q^90 - 19 * q^91 - q^92 + 25 * q^93 + 8 * q^94 - 7 * q^95 + 9 * q^96 + 3 * q^97 + 30 * q^98 + 9 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	0.268945	0.120276	0.0601379	−	0.998190i	$-0.480846\pi$
$5$	0.268945	0.120276	0.0601379	+	0.998190i	$0.480846\pi$
$6$	1.00000	0.408248
$7$	3.42672	1.29518	0.647589	−	0.761990i	$-0.275777\pi$
$7$	3.42672	1.29518	0.647589	+	0.761990i	$0.275777\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0.268945	0.0850479
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.00000	0.288675
$13$	1.26655	0.351278	0.175639	−	0.984455i	$-0.443801\pi$
$13$	1.26655	0.351278	0.175639	+	0.984455i	$0.443801\pi$
$14$	3.42672	0.915829
$15$	0.268945	0.0694413
$16$	1.00000	0.250000
$17$	0.867540	0.210409	0.105205	−	0.994451i	$-0.466450\pi$
$17$	0.867540	0.210409	0.105205	+	0.994451i	$0.466450\pi$
$18$	1.00000	0.235702
$19$	6.18750	1.41951	0.709755	−	0.704449i	$-0.248806\pi$
$19$	6.18750	1.41951	0.709755	+	0.704449i	$0.248806\pi$
$20$	0.268945	0.0601379
$21$	3.42672	0.747771
$22$	1.00000	0.213201
$23$	−8.86224	−1.84791	−0.923953	−	0.382506i	$-0.875061\pi$
$23$	−8.86224	−1.84791	−0.923953	+	0.382506i	$0.875061\pi$
$24$	1.00000	0.204124
$25$	−4.92767	−0.985534
$26$	1.26655	0.248391
$27$	1.00000	0.192450
$28$	3.42672	0.647589
$29$	1.57247	0.292001	0.146001	−	0.989285i	$-0.453360\pi$
$29$	1.57247	0.292001	0.146001	+	0.989285i	$0.453360\pi$
$30$	0.268945	0.0491024
$31$	−6.59330	−1.18419	−0.592096	−	0.805868i	$-0.701699\pi$
$31$	−6.59330	−1.18419	−0.592096	+	0.805868i	$0.701699\pi$
$32$	1.00000	0.176777
$33$	1.00000	0.174078
$34$	0.867540	0.148782
$35$	0.921599	0.155779
$36$	1.00000	0.166667
$37$	8.55030	1.40566	0.702830	−	0.711358i	$-0.251919\pi$
$37$	8.55030	1.40566	0.702830	+	0.711358i	$0.251919\pi$
$38$	6.18750	1.00374
$39$	1.26655	0.202811
$40$	0.268945	0.0425239
$41$	3.44241	0.537614	0.268807	−	0.963194i	$-0.413371\pi$
$41$	3.44241	0.537614	0.268807	+	0.963194i	$0.413371\pi$
$42$	3.42672	0.528754
$43$	12.3719	1.88669	0.943345	−	0.331813i	$-0.107660\pi$
$43$	12.3719	1.88669	0.943345	+	0.331813i	$0.107660\pi$
$44$	1.00000	0.150756
$45$	0.268945	0.0400920
$46$	−8.86224	−1.30667
$47$	5.99112	0.873894	0.436947	−	0.899487i	$-0.356060\pi$
$47$	5.99112	0.873894	0.436947	+	0.899487i	$0.356060\pi$
$48$	1.00000	0.144338
$49$	4.74240	0.677485
$50$	−4.92767	−0.696878
$51$	0.867540	0.121480
$52$	1.26655	0.175639
$53$	4.13724	0.568293	0.284147	−	0.958781i	$-0.408290\pi$
$53$	4.13724	0.568293	0.284147	+	0.958781i	$0.408290\pi$
$54$	1.00000	0.136083
$55$	0.268945	0.0362645
$56$	3.42672	0.457914
$57$	6.18750	0.819554
$58$	1.57247	0.206476
$59$	−13.3632	−1.73974	−0.869870	−	0.493281i	$-0.835797\pi$
$59$	−13.3632	−1.73974	−0.869870	+	0.493281i	$0.835797\pi$
$60$	0.268945	0.0347207
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	−6.59330	−0.837350
$63$	3.42672	0.431726
$64$	1.00000	0.125000
$65$	0.340633	0.0422503
$66$	1.00000	0.123091
$67$	−0.380487	−0.0464839	−0.0232420	−	0.999730i	$-0.507399\pi$
$67$	−0.380487	−0.0464839	−0.0232420	+	0.999730i	$0.507399\pi$
$68$	0.867540	0.105205
$69$	−8.86224	−1.06689
$70$	0.921599	0.110152
$71$	−10.4281	−1.23759	−0.618796	−	0.785551i	$-0.712379\pi$
$71$	−10.4281	−1.23759	−0.618796	+	0.785551i	$0.712379\pi$
$72$	1.00000	0.117851
$73$	−2.36638	−0.276964	−0.138482	−	0.990365i	$-0.544222\pi$
$73$	−2.36638	−0.276964	−0.138482	+	0.990365i	$0.544222\pi$
$74$	8.55030	0.993952
$75$	−4.92767	−0.568998
$76$	6.18750	0.709755
$77$	3.42672	0.390511
$78$	1.26655	0.143409
$79$	−8.37132	−0.941847	−0.470924	−	0.882174i	$-0.656079\pi$
$79$	−8.37132	−0.941847	−0.470924	+	0.882174i	$0.656079\pi$
$80$	0.268945	0.0300690
$81$	1.00000	0.111111
$82$	3.44241	0.380150
$83$	2.32547	0.255254	0.127627	−	0.991822i	$-0.459264\pi$
$83$	2.32547	0.255254	0.127627	+	0.991822i	$0.459264\pi$
$84$	3.42672	0.373886
$85$	0.233320	0.0253072
$86$	12.3719	1.33409
$87$	1.57247	0.168587
$88$	1.00000	0.106600
$89$	−11.6165	−1.23134	−0.615671	−	0.788004i	$-0.711115\pi$
$89$	−11.6165	−1.23134	−0.615671	+	0.788004i	$0.711115\pi$
$90$	0.268945	0.0283493
$91$	4.34011	0.454968
$92$	−8.86224	−0.923953
$93$	−6.59330	−0.683693
$94$	5.99112	0.617937
$95$	1.66410	0.170733
$96$	1.00000	0.102062
$97$	−11.5077	−1.16843	−0.584215	−	0.811599i	$-0.698597\pi$
$97$	−11.5077	−1.16843	−0.584215	+	0.811599i	$0.698597\pi$
$98$	4.74240	0.479054
$99$	1.00000	0.100504
$100$	−4.92767	−0.492767
$101$	−10.6426	−1.05898	−0.529489	−	0.848317i	$-0.677616\pi$
$101$	−10.6426	−1.05898	−0.529489	+	0.848317i	$0.677616\pi$
$102$	0.867540	0.0858992
$103$	1.00764	0.0992852	0.0496426	−	0.998767i	$-0.484192\pi$
$103$	1.00764	0.0992852	0.0496426	+	0.998767i	$0.484192\pi$
$104$	1.26655	0.124196
$105$	0.921599	0.0899388
$106$	4.13724	0.401844
$107$	−6.78676	−0.656101	−0.328051	−	0.944660i	$-0.606392\pi$
$107$	−6.78676	−0.656101	−0.328051	+	0.944660i	$0.606392\pi$
$108$	1.00000	0.0962250
$109$	−10.9790	−1.05160	−0.525800	−	0.850608i	$-0.676234\pi$
$109$	−10.9790	−1.05160	−0.525800	+	0.850608i	$0.676234\pi$
$110$	0.268945	0.0256429
$111$	8.55030	0.811558
$112$	3.42672	0.323794
$113$	−0.304968	−0.0286890	−0.0143445	−	0.999897i	$-0.504566\pi$
$113$	−0.304968	−0.0286890	−0.0143445	+	0.999897i	$0.504566\pi$
$114$	6.18750	0.579512
$115$	−2.38346	−0.222258
$116$	1.57247	0.146001
$117$	1.26655	0.117093
$118$	−13.3632	−1.23018
$119$	2.97281	0.272517
$120$	0.268945	0.0245512
$121$	1.00000	0.0909091
$122$	−1.00000	−0.0905357
$123$	3.44241	0.310391
$124$	−6.59330	−0.592096
$125$	−2.67000	−0.238812
$126$	3.42672	0.305276
$127$	18.8689	1.67435	0.837174	−	0.546936i	$-0.184206\pi$
$127$	18.8689	1.67435	0.837174	+	0.546936i	$0.184206\pi$
$128$	1.00000	0.0883883
$129$	12.3719	1.08928
$130$	0.340633	0.0298755
$131$	3.68893	0.322304	0.161152	−	0.986930i	$-0.448479\pi$
$131$	3.68893	0.322304	0.161152	+	0.986930i	$0.448479\pi$
$132$	1.00000	0.0870388
$133$	21.2028	1.83852
$134$	−0.380487	−0.0328691
$135$	0.268945	0.0231471
$136$	0.867540	0.0743909
$137$	8.47305	0.723901	0.361951	−	0.932197i	$-0.382111\pi$
$137$	8.47305	0.723901	0.361951	+	0.932197i	$0.382111\pi$
$138$	−8.86224	−0.754404
$139$	14.3911	1.22064	0.610320	−	0.792155i	$-0.291041\pi$
$139$	14.3911	1.22064	0.610320	+	0.792155i	$0.291041\pi$
$140$	0.921599	0.0778893
$141$	5.99112	0.504543
$142$	−10.4281	−0.875110
$143$	1.26655	0.105914
$144$	1.00000	0.0833333
$145$	0.422909	0.0351207
$146$	−2.36638	−0.195843
$147$	4.74240	0.391146
$148$	8.55030	0.702830
$149$	19.6765	1.61196	0.805980	−	0.591943i	$-0.201639\pi$
$149$	19.6765	1.61196	0.805980	+	0.591943i	$0.201639\pi$
$150$	−4.92767	−0.402342
$151$	8.71508	0.709223	0.354611	−	0.935014i	$-0.384613\pi$
$151$	8.71508	0.709223	0.354611	+	0.935014i	$0.384613\pi$
$152$	6.18750	0.501872
$153$	0.867540	0.0701364
$154$	3.42672	0.276133
$155$	−1.77324	−0.142430
$156$	1.26655	0.101405
$157$	22.7483	1.81551	0.907755	−	0.419501i	$-0.137795\pi$
$157$	22.7483	1.81551	0.907755	+	0.419501i	$0.137795\pi$
$158$	−8.37132	−0.665986
$159$	4.13724	0.328104
$160$	0.268945	0.0212620
$161$	−30.3684	−2.39337
$162$	1.00000	0.0785674
$163$	−16.9197	−1.32526	−0.662628	−	0.748948i	$-0.730559\pi$
$163$	−16.9197	−1.32526	−0.662628	+	0.748948i	$0.730559\pi$
$164$	3.44241	0.268807
$165$	0.268945	0.0209373
$166$	2.32547	0.180492
$167$	24.5798	1.90204	0.951021	−	0.309125i	$-0.100036\pi$
$167$	24.5798	1.90204	0.951021	+	0.309125i	$0.100036\pi$
$168$	3.42672	0.264377
$169$	−11.3958	−0.876604
$170$	0.233320	0.0178949
$171$	6.18750	0.473170
$172$	12.3719	0.943345
$173$	16.0917	1.22343	0.611715	−	0.791078i	$-0.290480\pi$
$173$	16.0917	1.22343	0.611715	+	0.791078i	$0.290480\pi$
$174$	1.57247	0.119209
$175$	−16.8857	−1.27644
$176$	1.00000	0.0753778
$177$	−13.3632	−1.00444
$178$	−11.6165	−0.870690
$179$	−20.5271	−1.53427	−0.767133	−	0.641488i	$-0.778317\pi$
$179$	−20.5271	−1.53427	−0.767133	+	0.641488i	$0.778317\pi$
$180$	0.268945	0.0200460
$181$	−14.6239	−1.08699	−0.543494	−	0.839413i	$-0.682899\pi$
$181$	−14.6239	−1.08699	−0.543494	+	0.839413i	$0.682899\pi$
$182$	4.34011	0.321711
$183$	−1.00000	−0.0739221
$184$	−8.86224	−0.653333
$185$	2.29956	0.169067
$186$	−6.59330	−0.483444
$187$	0.867540	0.0634408
$188$	5.99112	0.436947
$189$	3.42672	0.249257
$190$	1.66410	0.120726
$191$	−5.11491	−0.370102	−0.185051	−	0.982729i	$-0.559245\pi$
$191$	−5.11491	−0.370102	−0.185051	+	0.982729i	$0.559245\pi$
$192$	1.00000	0.0721688
$193$	−18.9293	−1.36256	−0.681281	−	0.732022i	$-0.738577\pi$
$193$	−18.9293	−1.36256	−0.681281	+	0.732022i	$0.738577\pi$
$194$	−11.5077	−0.826204
$195$	0.340633	0.0243932
$196$	4.74240	0.338743
$197$	8.98440	0.640112	0.320056	−	0.947399i	$-0.396298\pi$
$197$	8.98440	0.640112	0.320056	+	0.947399i	$0.396298\pi$
$198$	1.00000	0.0710669
$199$	15.1438	1.07352	0.536758	−	0.843736i	$-0.319649\pi$
$199$	15.1438	1.07352	0.536758	+	0.843736i	$0.319649\pi$
$200$	−4.92767	−0.348439
$201$	−0.380487	−0.0268375
$202$	−10.6426	−0.748810
$203$	5.38842	0.378193
$204$	0.867540	0.0607399
$205$	0.925818	0.0646620
$206$	1.00764	0.0702053
$207$	−8.86224	−0.615969
$208$	1.26655	0.0878196
$209$	6.18750	0.427998
$210$	0.921599	0.0635964
$211$	25.8348	1.77854	0.889271	−	0.457381i	$-0.151212\pi$
$211$	25.8348	1.77854	0.889271	+	0.457381i	$0.151212\pi$
$212$	4.13724	0.284147
$213$	−10.4281	−0.714525
$214$	−6.78676	−0.463934
$215$	3.32735	0.226923
$216$	1.00000	0.0680414
$217$	−22.5934	−1.53374
$218$	−10.9790	−0.743594
$219$	−2.36638	−0.159905
$220$	0.268945	0.0181323
$221$	1.09878	0.0739122
$222$	8.55030	0.573858
$223$	9.89572	0.662666	0.331333	−	0.943514i	$-0.392502\pi$
$223$	9.89572	0.662666	0.331333	+	0.943514i	$0.392502\pi$
$224$	3.42672	0.228957
$225$	−4.92767	−0.328511
$226$	−0.304968	−0.0202862
$227$	1.05470	0.0700032	0.0350016	−	0.999387i	$-0.488856\pi$
$227$	1.05470	0.0700032	0.0350016	+	0.999387i	$0.488856\pi$
$228$	6.18750	0.409777
$229$	−6.19110	−0.409119	−0.204560	−	0.978854i	$-0.565576\pi$
$229$	−6.19110	−0.409119	−0.204560	+	0.978854i	$0.565576\pi$
$230$	−2.38346	−0.157160
$231$	3.42672	0.225461
$232$	1.57247	0.103238
$233$	−28.9847	−1.89885	−0.949426	−	0.313990i	$-0.898334\pi$
$233$	−28.9847	−1.89885	−0.949426	+	0.313990i	$0.898334\pi$
$234$	1.26655	0.0827971
$235$	1.61128	0.105108
$236$	−13.3632	−0.869870
$237$	−8.37132	−0.543776
$238$	2.97281	0.192699
$239$	−4.63720	−0.299955	−0.149978	−	0.988689i	$-0.547920\pi$
$239$	−4.63720	−0.299955	−0.149978	+	0.988689i	$0.547920\pi$
$240$	0.268945	0.0173603
$241$	13.8531	0.892354	0.446177	−	0.894945i	$-0.352785\pi$
$241$	13.8531	0.892354	0.446177	+	0.894945i	$0.352785\pi$
$242$	1.00000	0.0642824
$243$	1.00000	0.0641500
$244$	−1.00000	−0.0640184
$245$	1.27544	0.0814851
$246$	3.44241	0.219480
$247$	7.83679	0.498643
$248$	−6.59330	−0.418675
$249$	2.32547	0.147371
$250$	−2.67000	−0.168865
$251$	−8.63040	−0.544746	−0.272373	−	0.962192i	$-0.587808\pi$
$251$	−8.63040	−0.544746	−0.272373	+	0.962192i	$0.587808\pi$
$252$	3.42672	0.215863
$253$	−8.86224	−0.557165
$254$	18.8689	1.18394
$255$	0.233320	0.0146111
$256$	1.00000	0.0625000
$257$	1.33011	0.0829700	0.0414850	−	0.999139i	$-0.486791\pi$
$257$	1.33011	0.0829700	0.0414850	+	0.999139i	$0.486791\pi$
$258$	12.3719	0.770238
$259$	29.2995	1.82058
$260$	0.340633	0.0211251
$261$	1.57247	0.0973337
$262$	3.68893	0.227903
$263$	−29.1042	−1.79464	−0.897321	−	0.441378i	$-0.854490\pi$
$263$	−29.1042	−1.79464	−0.897321	+	0.441378i	$0.854490\pi$
$264$	1.00000	0.0615457
$265$	1.11269	0.0683520
$266$	21.2028	1.30003
$267$	−11.6165	−0.710915
$268$	−0.380487	−0.0232420
$269$	−2.29032	−0.139643	−0.0698215	−	0.997560i	$-0.522243\pi$
$269$	−2.29032	−0.139643	−0.0698215	+	0.997560i	$0.522243\pi$
$270$	0.268945	0.0163675
$271$	−23.4290	−1.42321	−0.711604	−	0.702580i	$-0.752031\pi$
$271$	−23.4290	−1.42321	−0.711604	+	0.702580i	$0.752031\pi$
$272$	0.867540	0.0526023
$273$	4.34011	0.262676
$274$	8.47305	0.511875
$275$	−4.92767	−0.297150
$276$	−8.86224	−0.533444
$277$	18.8839	1.13463	0.567313	−	0.823502i	$-0.307983\pi$
$277$	18.8839	1.13463	0.567313	+	0.823502i	$0.307983\pi$
$278$	14.3911	0.863123
$279$	−6.59330	−0.394730
$280$	0.921599	0.0550761
$281$	−10.0216	−0.597840	−0.298920	−	0.954278i	$-0.596626\pi$
$281$	−10.0216	−0.597840	−0.298920	+	0.954278i	$0.596626\pi$
$282$	5.99112	0.356766
$283$	2.41609	0.143622	0.0718108	−	0.997418i	$-0.477122\pi$
$283$	2.41609	0.143622	0.0718108	+	0.997418i	$0.477122\pi$
$284$	−10.4281	−0.618796
$285$	1.66410	0.0985726
$286$	1.26655	0.0748928
$287$	11.7962	0.696305
$288$	1.00000	0.0589256
$289$	−16.2474	−0.955728
$290$	0.422909	0.0248341
$291$	−11.5077	−0.674593
$292$	−2.36638	−0.138482
$293$	4.40067	0.257090	0.128545	−	0.991704i	$-0.458969\pi$
$293$	4.40067	0.257090	0.128545	+	0.991704i	$0.458969\pi$
$294$	4.74240	0.276582
$295$	−3.59396	−0.209249
$296$	8.55030	0.496976
$297$	1.00000	0.0580259
$298$	19.6765	1.13983
$299$	−11.2245	−0.649129
$300$	−4.92767	−0.284499
$301$	42.3949	2.44360
$302$	8.71508	0.501496
$303$	−10.6426	−0.611401
$304$	6.18750	0.354877
$305$	−0.268945	−0.0153997
$306$	0.867540	0.0495939
$307$	−17.0682	−0.974136	−0.487068	−	0.873364i	$-0.661934\pi$
$307$	−17.0682	−0.974136	−0.487068	+	0.873364i	$0.661934\pi$
$308$	3.42672	0.195255
$309$	1.00764	0.0573224
$310$	−1.77324	−0.100713
$311$	−28.3715	−1.60880	−0.804400	−	0.594088i	$-0.797513\pi$
$311$	−28.3715	−1.60880	−0.804400	+	0.594088i	$0.797513\pi$
$312$	1.26655	0.0717044
$313$	−9.88599	−0.558789	−0.279395	−	0.960176i	$-0.590134\pi$
$313$	−9.88599	−0.558789	−0.279395	+	0.960176i	$0.590134\pi$
$314$	22.7483	1.28376
$315$	0.921599	0.0519262
$316$	−8.37132	−0.470924
$317$	5.91378	0.332151	0.166075	−	0.986113i	$-0.446890\pi$
$317$	5.91378	0.332151	0.166075	+	0.986113i	$0.446890\pi$
$318$	4.13724	0.232005
$319$	1.57247	0.0880416
$320$	0.268945	0.0150345
$321$	−6.78676	−0.378800
$322$	−30.3684	−1.69237
$323$	5.36790	0.298678
$324$	1.00000	0.0555556
$325$	−6.24115	−0.346197
$326$	−16.9197	−0.937098
$327$	−10.9790	−0.607142
$328$	3.44241	0.190075
$329$	20.5299	1.13185
$330$	0.268945	0.0148049
$331$	18.4377	1.01343	0.506714	−	0.862114i	$-0.330860\pi$
$331$	18.4377	1.01343	0.506714	+	0.862114i	$0.330860\pi$
$332$	2.32547	0.127627
$333$	8.55030	0.468553
$334$	24.5798	1.34495
$335$	−0.102330	−0.00559090
$336$	3.42672	0.186943
$337$	35.4326	1.93014	0.965069	−	0.261998i	$-0.0843813\pi$
$337$	35.4326	1.93014	0.965069	+	0.261998i	$0.0843813\pi$
$338$	−11.3958	−0.619852
$339$	−0.304968	−0.0165636
$340$	0.233320	0.0126536
$341$	−6.59330	−0.357047
$342$	6.18750	0.334582
$343$	−7.73617	−0.417714
$344$	12.3719	0.667046
$345$	−2.38346	−0.128321
$346$	16.0917	0.865096
$347$	32.0180	1.71881	0.859407	−	0.511292i	$-0.170833\pi$
$347$	32.0180	1.71881	0.859407	+	0.511292i	$0.170833\pi$
$348$	1.57247	0.0842935
$349$	0.763609	0.0408751	0.0204375	−	0.999791i	$-0.493494\pi$
$349$	0.763609	0.0408751	0.0204375	+	0.999791i	$0.493494\pi$
$350$	−16.8857	−0.902580
$351$	1.26655	0.0676035
$352$	1.00000	0.0533002
$353$	16.4468	0.875376	0.437688	−	0.899127i	$-0.355798\pi$
$353$	16.4468	0.875376	0.437688	+	0.899127i	$0.355798\pi$
$354$	−13.3632	−0.710246
$355$	−2.80460	−0.148853
$356$	−11.6165	−0.615671
$357$	2.97281	0.157338
$358$	−20.5271	−1.08489
$359$	19.7050	1.03999	0.519995	−	0.854169i	$-0.325934\pi$
$359$	19.7050	1.03999	0.519995	+	0.854169i	$0.325934\pi$
$360$	0.268945	0.0141746
$361$	19.2851	1.01501
$362$	−14.6239	−0.768616
$363$	1.00000	0.0524864
$364$	4.34011	0.227484
$365$	−0.636427	−0.0333121
$366$	−1.00000	−0.0522708
$367$	−20.4095	−1.06537	−0.532684	−	0.846314i	$-0.678817\pi$
$367$	−20.4095	−1.06537	−0.532684	+	0.846314i	$0.678817\pi$
$368$	−8.86224	−0.461976
$369$	3.44241	0.179205
$370$	2.29956	0.119548
$371$	14.1772	0.736041
$372$	−6.59330	−0.341847
$373$	−35.9190	−1.85982	−0.929908	−	0.367793i	$-0.880114\pi$
$373$	−35.9190	−1.85982	−0.929908	+	0.367793i	$0.880114\pi$
$374$	0.867540	0.0448594
$375$	−2.67000	−0.137878
$376$	5.99112	0.308968
$377$	1.99162	0.102574
$378$	3.42672	0.176251
$379$	29.2039	1.50010	0.750051	−	0.661380i	$-0.230029\pi$
$379$	29.2039	1.50010	0.750051	+	0.661380i	$0.230029\pi$
$380$	1.66410	0.0853664
$381$	18.8689	0.966686
$382$	−5.11491	−0.261702
$383$	−30.2591	−1.54617	−0.773083	−	0.634305i	$-0.781286\pi$
$383$	−30.2591	−1.54617	−0.773083	+	0.634305i	$0.781286\pi$
$384$	1.00000	0.0510310
$385$	0.921599	0.0469690
$386$	−18.9293	−0.963477
$387$	12.3719	0.628897
$388$	−11.5077	−0.584215
$389$	−6.13420	−0.311016	−0.155508	−	0.987835i	$-0.549702\pi$
$389$	−6.13420	−0.311016	−0.155508	+	0.987835i	$0.549702\pi$
$390$	0.340633	0.0172486
$391$	−7.68835	−0.388816
$392$	4.74240	0.239527
$393$	3.68893	0.186082
$394$	8.98440	0.452628
$395$	−2.25142	−0.113281
$396$	1.00000	0.0502519
$397$	7.09173	0.355924	0.177962	−	0.984037i	$-0.443050\pi$
$397$	7.09173	0.355924	0.177962	+	0.984037i	$0.443050\pi$
$398$	15.1438	0.759091
$399$	21.2028	1.06147
$400$	−4.92767	−0.246383
$401$	−29.9023	−1.49325	−0.746626	−	0.665244i	$-0.768328\pi$
$401$	−29.9023	−1.49325	−0.746626	+	0.665244i	$0.768328\pi$
$402$	−0.380487	−0.0189770
$403$	−8.35075	−0.415981
$404$	−10.6426	−0.529489
$405$	0.268945	0.0133640
$406$	5.38842	0.267423
$407$	8.55030	0.423822
$408$	0.867540	0.0429496
$409$	−31.4377	−1.55449	−0.777246	−	0.629197i	$-0.783384\pi$
$409$	−31.4377	−1.55449	−0.777246	+	0.629197i	$0.783384\pi$
$410$	0.925818	0.0457229
$411$	8.47305	0.417945
$412$	1.00764	0.0496426
$413$	−45.7919	−2.25327
$414$	−8.86224	−0.435556
$415$	0.625425	0.0307009
$416$	1.26655	0.0620978
$417$	14.3911	0.704737
$418$	6.18750	0.302640
$419$	−6.06492	−0.296291	−0.148145	−	0.988966i	$-0.547330\pi$
$419$	−6.06492	−0.296291	−0.148145	+	0.988966i	$0.547330\pi$
$420$	0.921599	0.0449694
$421$	−11.9703	−0.583397	−0.291698	−	0.956510i	$-0.594220\pi$
$421$	−11.9703	−0.583397	−0.291698	+	0.956510i	$0.594220\pi$
$422$	25.8348	1.25762
$423$	5.99112	0.291298
$424$	4.13724	0.200922
$425$	−4.27495	−0.207365
$426$	−10.4281	−0.505245
$427$	−3.42672	−0.165831
$428$	−6.78676	−0.328051
$429$	1.26655	0.0611497
$430$	3.32735	0.160459
$431$	4.23679	0.204079	0.102039	−	0.994780i	$-0.467463\pi$
$431$	4.23679	0.204079	0.102039	+	0.994780i	$0.467463\pi$
$432$	1.00000	0.0481125
$433$	−12.6590	−0.608352	−0.304176	−	0.952616i	$-0.598381\pi$
$433$	−12.6590	−0.608352	−0.304176	+	0.952616i	$0.598381\pi$
$434$	−22.5934	−1.08452
$435$	0.422909	0.0202769
$436$	−10.9790	−0.525800
$437$	−54.8351	−2.62312
$438$	−2.36638	−0.113070
$439$	−26.5844	−1.26881	−0.634403	−	0.773003i	$-0.718754\pi$
$439$	−26.5844	−1.26881	−0.634403	+	0.773003i	$0.718754\pi$
$440$	0.268945	0.0128215
$441$	4.74240	0.225828
$442$	1.09878	0.0522638
$443$	26.5443	1.26116	0.630579	−	0.776125i	$-0.282817\pi$
$443$	26.5443	1.26116	0.630579	+	0.776125i	$0.282817\pi$
$444$	8.55030	0.405779
$445$	−3.12419	−0.148101
$446$	9.89572	0.468576
$447$	19.6765	0.930665
$448$	3.42672	0.161897
$449$	33.4432	1.57828	0.789140	−	0.614213i	$-0.210526\pi$
$449$	33.4432	1.57828	0.789140	+	0.614213i	$0.210526\pi$
$450$	−4.92767	−0.232293
$451$	3.44241	0.162097
$452$	−0.304968	−0.0143445
$453$	8.71508	0.409470
$454$	1.05470	0.0494997
$455$	1.16725	0.0547216
$456$	6.18750	0.289756
$457$	−39.3979	−1.84296	−0.921479	−	0.388428i	$-0.873018\pi$
$457$	−39.3979	−1.84296	−0.921479	+	0.388428i	$0.873018\pi$
$458$	−6.19110	−0.289291
$459$	0.867540	0.0404933
$460$	−2.38346	−0.111129
$461$	2.36247	0.110031	0.0550155	−	0.998485i	$-0.482479\pi$
$461$	2.36247	0.110031	0.0550155	+	0.998485i	$0.482479\pi$
$462$	3.42672	0.159425
$463$	29.4582	1.36904	0.684520	−	0.728994i	$-0.260012\pi$
$463$	29.4582	1.36904	0.684520	+	0.728994i	$0.260012\pi$
$464$	1.57247	0.0730003
$465$	−1.77324	−0.0822318
$466$	−28.9847	−1.34269
$467$	−1.97701	−0.0914850	−0.0457425	−	0.998953i	$-0.514565\pi$
$467$	−1.97701	−0.0914850	−0.0457425	+	0.998953i	$0.514565\pi$
$468$	1.26655	0.0585464
$469$	−1.30382	−0.0602050
$470$	1.61128	0.0743229
$471$	22.7483	1.04818
$472$	−13.3632	−0.615091
$473$	12.3719	0.568859
$474$	−8.37132	−0.384507
$475$	−30.4899	−1.39897
$476$	2.97281	0.136259
$477$	4.13724	0.189431
$478$	−4.63720	−0.212100
$479$	−26.1584	−1.19521	−0.597604	−	0.801791i	$-0.703880\pi$
$479$	−26.1584	−1.19521	−0.597604	+	0.801791i	$0.703880\pi$
$480$	0.268945	0.0122756
$481$	10.8294	0.493778
$482$	13.8531	0.630990
$483$	−30.3684	−1.38181
$484$	1.00000	0.0454545
$485$	−3.09494	−0.140534
$486$	1.00000	0.0453609
$487$	−28.6097	−1.29643	−0.648215	−	0.761457i	$-0.724484\pi$
$487$	−28.6097	−1.29643	−0.648215	+	0.761457i	$0.724484\pi$
$488$	−1.00000	−0.0452679
$489$	−16.9197	−0.765137
$490$	1.27544	0.0576187
$491$	−12.1722	−0.549322	−0.274661	−	0.961541i	$-0.588566\pi$
$491$	−12.1722	−0.549322	−0.274661	+	0.961541i	$0.588566\pi$
$492$	3.44241	0.155196
$493$	1.36418	0.0614397
$494$	7.83679	0.352594
$495$	0.268945	0.0120882
$496$	−6.59330	−0.296048
$497$	−35.7343	−1.60290
$498$	2.32547	0.104207
$499$	−18.9089	−0.846481	−0.423240	−	0.906017i	$-0.639107\pi$
$499$	−18.9089	−0.846481	−0.423240	+	0.906017i	$0.639107\pi$
$500$	−2.67000	−0.119406
$501$	24.5798	1.09814
$502$	−8.63040	−0.385194
$503$	−16.0313	−0.714800	−0.357400	−	0.933951i	$-0.616337\pi$
$503$	−16.0313	−0.714800	−0.357400	+	0.933951i	$0.616337\pi$
$504$	3.42672	0.152638
$505$	−2.86227	−0.127369
$506$	−8.86224	−0.393975
$507$	−11.3958	−0.506107
$508$	18.8689	0.837174
$509$	41.6067	1.84418	0.922092	−	0.386971i	$-0.126479\pi$
$509$	41.6067	1.84418	0.922092	+	0.386971i	$0.126479\pi$
$510$	0.233320	0.0103316
$511$	−8.10893	−0.358718
$512$	1.00000	0.0441942
$513$	6.18750	0.273185
$514$	1.33011	0.0586687
$515$	0.270998	0.0119416
$516$	12.3719	0.544641
$517$	5.99112	0.263489
$518$	29.2995	1.28734
$519$	16.0917	0.706348
$520$	0.340633	0.0149377
$521$	28.9241	1.26719	0.633593	−	0.773667i	$-0.281579\pi$
$521$	28.9241	1.26719	0.633593	+	0.773667i	$0.281579\pi$
$522$	1.57247	0.0688253
$523$	18.7161	0.818400	0.409200	−	0.912445i	$-0.365808\pi$
$523$	18.7161	0.818400	0.409200	+	0.912445i	$0.365808\pi$
$524$	3.68893	0.161152
$525$	−16.8857	−0.736954
$526$	−29.1042	−1.26900
$527$	−5.71995	−0.249165
$528$	1.00000	0.0435194
$529$	55.5394	2.41476
$530$	1.11269	0.0483322
$531$	−13.3632	−0.579913
$532$	21.2028	0.919259
$533$	4.35999	0.188852
$534$	−11.6165	−0.502693
$535$	−1.82527	−0.0789131
$536$	−0.380487	−0.0164346
$537$	−20.5271	−0.885809
$538$	−2.29032	−0.0987425
$539$	4.74240	0.204269
$540$	0.268945	0.0115736
$541$	−6.77164	−0.291136	−0.145568	−	0.989348i	$-0.546501\pi$
$541$	−6.77164	−0.291136	−0.145568	+	0.989348i	$0.546501\pi$
$542$	−23.4290	−1.00636
$543$	−14.6239	−0.627573
$544$	0.867540	0.0371955
$545$	−2.95276	−0.126482
$546$	4.34011	0.185740
$547$	11.8955	0.508616	0.254308	−	0.967123i	$-0.418152\pi$
$547$	11.8955	0.508616	0.254308	+	0.967123i	$0.418152\pi$
$548$	8.47305	0.361951
$549$	−1.00000	−0.0426790
$550$	−4.92767	−0.210116
$551$	9.72968	0.414498
$552$	−8.86224	−0.377202
$553$	−28.6861	−1.21986
$554$	18.8839	0.802301
$555$	2.29956	0.0976109
$556$	14.3911	0.610320
$557$	−28.9513	−1.22671	−0.613354	−	0.789808i	$-0.710180\pi$
$557$	−28.9513	−1.22671	−0.613354	+	0.789808i	$0.710180\pi$
$558$	−6.59330	−0.279117
$559$	15.6696	0.662753
$560$	0.921599	0.0389447
$561$	0.867540	0.0366276
$562$	−10.0216	−0.422737
$563$	−41.4776	−1.74807	−0.874036	−	0.485861i	$-0.838506\pi$
$563$	−41.4776	−1.74807	−0.874036	+	0.485861i	$0.838506\pi$
$564$	5.99112	0.252272
$565$	−0.0820196	−0.00345059
$566$	2.41609	0.101556
$567$	3.42672	0.143909
$568$	−10.4281	−0.437555
$569$	−8.47596	−0.355331	−0.177665	−	0.984091i	$-0.556854\pi$
$569$	−8.47596	−0.355331	−0.177665	+	0.984091i	$0.556854\pi$
$570$	1.66410	0.0697014
$571$	−14.6693	−0.613892	−0.306946	−	0.951727i	$-0.599307\pi$
$571$	−14.6693	−0.613892	−0.306946	+	0.951727i	$0.599307\pi$
$572$	1.26655	0.0529572
$573$	−5.11491	−0.213679
$574$	11.7962	0.492362
$575$	43.6702	1.82117
$576$	1.00000	0.0416667
$577$	−34.5189	−1.43704	−0.718520	−	0.695506i	$-0.755180\pi$
$577$	−34.5189	−1.43704	−0.718520	+	0.695506i	$0.755180\pi$
$578$	−16.2474	−0.675802
$579$	−18.9293	−0.786676
$580$	0.422909	0.0175603
$581$	7.96874	0.330599
$582$	−11.5077	−0.477009
$583$	4.13724	0.171347
$584$	−2.36638	−0.0979216
$585$	0.340633	0.0140834
$586$	4.40067	0.181790
$587$	−38.5034	−1.58920	−0.794602	−	0.607131i	$-0.792320\pi$
$587$	−38.5034	−1.58920	−0.794602	+	0.607131i	$0.792320\pi$
$588$	4.74240	0.195573
$589$	−40.7960	−1.68097
$590$	−3.59396	−0.147961
$591$	8.98440	0.369569
$592$	8.55030	0.351415
$593$	−13.1113	−0.538416	−0.269208	−	0.963082i	$-0.586762\pi$
$593$	−13.1113	−0.538416	−0.269208	+	0.963082i	$0.586762\pi$
$594$	1.00000	0.0410305
$595$	0.799523	0.0327773
$596$	19.6765	0.805980
$597$	15.1438	0.619795
$598$	−11.2245	−0.459004
$599$	−34.2308	−1.39863	−0.699316	−	0.714813i	$-0.746512\pi$
$599$	−34.2308	−1.39863	−0.699316	+	0.714813i	$0.746512\pi$
$600$	−4.92767	−0.201171
$601$	−2.51772	−0.102700	−0.0513499	−	0.998681i	$-0.516352\pi$
$601$	−2.51772	−0.102700	−0.0513499	+	0.998681i	$0.516352\pi$
$602$	42.3949	1.72789
$603$	−0.380487	−0.0154946
$604$	8.71508	0.354611
$605$	0.268945	0.0109342
$606$	−10.6426	−0.432326
$607$	−24.5474	−0.996349	−0.498174	−	0.867077i	$-0.665996\pi$
$607$	−24.5474	−0.996349	−0.498174	+	0.867077i	$0.665996\pi$
$608$	6.18750	0.250936
$609$	5.38842	0.218350
$610$	−0.268945	−0.0108893
$611$	7.58806	0.306980
$612$	0.867540	0.0350682
$613$	25.2944	1.02163	0.510816	−	0.859690i	$-0.329343\pi$
$613$	25.2944	1.02163	0.510816	+	0.859690i	$0.329343\pi$
$614$	−17.0682	−0.688818
$615$	0.925818	0.0373326
$616$	3.42672	0.138066
$617$	7.83562	0.315450	0.157725	−	0.987483i	$-0.449584\pi$
$617$	7.83562	0.315450	0.157725	+	0.987483i	$0.449584\pi$
$618$	1.00764	0.0405330
$619$	28.4337	1.14285	0.571424	−	0.820655i	$-0.306391\pi$
$619$	28.4337	1.14285	0.571424	+	0.820655i	$0.306391\pi$
$620$	−1.77324	−0.0712148
$621$	−8.86224	−0.355630
$622$	−28.3715	−1.13759
$623$	−39.8063	−1.59481
$624$	1.26655	0.0507026
$625$	23.9203	0.956810
$626$	−9.88599	−0.395124
$627$	6.18750	0.247105
$628$	22.7483	0.907755
$629$	7.41772	0.295764
$630$	0.921599	0.0367174
$631$	13.6904	0.545006	0.272503	−	0.962155i	$-0.412149\pi$
$631$	13.6904	0.545006	0.272503	+	0.962155i	$0.412149\pi$
$632$	−8.37132	−0.332993
$633$	25.8348	1.02684
$634$	5.91378	0.234866
$635$	5.07471	0.201384
$636$	4.13724	0.164052
$637$	6.00649	0.237986
$638$	1.57247	0.0622548
$639$	−10.4281	−0.412531
$640$	0.268945	0.0106310
$641$	−16.9952	−0.671271	−0.335636	−	0.941992i	$-0.608951\pi$
$641$	−16.9952	−0.671271	−0.335636	+	0.941992i	$0.608951\pi$
$642$	−6.78676	−0.267852
$643$	−25.4697	−1.00443	−0.502214	−	0.864743i	$-0.667481\pi$
$643$	−25.4697	−1.00443	−0.502214	+	0.864743i	$0.667481\pi$
$644$	−30.3684	−1.19668
$645$	3.32735	0.131014
$646$	5.36790	0.211197
$647$	−23.3764	−0.919021	−0.459510	−	0.888172i	$-0.651975\pi$
$647$	−23.3764	−0.919021	−0.459510	+	0.888172i	$0.651975\pi$
$648$	1.00000	0.0392837
$649$	−13.3632	−0.524551
$650$	−6.24115	−0.244798
$651$	−22.5934	−0.885504
$652$	−16.9197	−0.662628
$653$	−14.5309	−0.568638	−0.284319	−	0.958730i	$-0.591767\pi$
$653$	−14.5309	−0.568638	−0.284319	+	0.958730i	$0.591767\pi$
$654$	−10.9790	−0.429314
$655$	0.992120	0.0387654
$656$	3.44241	0.134403
$657$	−2.36638	−0.0923214
$658$	20.5299	0.800338
$659$	−1.83670	−0.0715475	−0.0357738	−	0.999360i	$-0.511390\pi$
$659$	−1.83670	−0.0715475	−0.0357738	+	0.999360i	$0.511390\pi$
$660$	0.268945	0.0104687
$661$	27.0191	1.05092	0.525460	−	0.850818i	$-0.323893\pi$
$661$	27.0191	1.05092	0.525460	+	0.850818i	$0.323893\pi$
$662$	18.4377	0.716602
$663$	1.09878	0.0426732
$664$	2.32547	0.0902459
$665$	5.70239	0.221129
$666$	8.55030	0.331317
$667$	−13.9356	−0.539590
$668$	24.5798	0.951021
$669$	9.89572	0.382591
$670$	−0.102330	−0.00395336
$671$	−1.00000	−0.0386046
$672$	3.42672	0.132189
$673$	31.5860	1.21755	0.608775	−	0.793343i	$-0.291661\pi$
$673$	31.5860	1.21755	0.608775	+	0.793343i	$0.291661\pi$
$674$	35.4326	1.36481
$675$	−4.92767	−0.189666
$676$	−11.3958	−0.438302
$677$	33.9490	1.30477	0.652384	−	0.757889i	$-0.273769\pi$
$677$	33.9490	1.30477	0.652384	+	0.757889i	$0.273769\pi$
$678$	−0.304968	−0.0117122
$679$	−39.4336	−1.51332
$680$	0.233320	0.00894743
$681$	1.05470	0.0404164
$682$	−6.59330	−0.252470
$683$	−5.96961	−0.228421	−0.114210	−	0.993457i	$-0.536434\pi$
$683$	−5.96961	−0.228421	−0.114210	+	0.993457i	$0.536434\pi$
$684$	6.18750	0.236585
$685$	2.27878	0.0870679
$686$	−7.73617	−0.295368
$687$	−6.19110	−0.236205
$688$	12.3719	0.471673
$689$	5.24003	0.199629
$690$	−2.38346	−0.0907366
$691$	−17.1589	−0.652757	−0.326378	−	0.945239i	$-0.605828\pi$
$691$	−17.1589	−0.652757	−0.326378	+	0.945239i	$0.605828\pi$
$692$	16.0917	0.611715
$693$	3.42672	0.130170
$694$	32.0180	1.21538
$695$	3.87043	0.146814
$696$	1.57247	0.0596045
$697$	2.98642	0.113119
$698$	0.763609	0.0289030
$699$	−28.9847	−1.09630
$700$	−16.8857	−0.638221
$701$	−23.4422	−0.885399	−0.442699	−	0.896670i	$-0.645979\pi$
$701$	−23.4422	−0.885399	−0.442699	+	0.896670i	$0.645979\pi$
$702$	1.26655	0.0478029
$703$	52.9049	1.99535
$704$	1.00000	0.0376889
$705$	1.61128	0.0606844
$706$	16.4468	0.618984
$707$	−36.4692	−1.37156
$708$	−13.3632	−0.502220
$709$	−12.4098	−0.466061	−0.233030	−	0.972469i	$-0.574864\pi$
$709$	−12.4098	−0.466061	−0.233030	+	0.972469i	$0.574864\pi$
$710$	−2.80460	−0.105255
$711$	−8.37132	−0.313949
$712$	−11.6165	−0.435345
$713$	58.4314	2.18827
$714$	2.97281	0.111255
$715$	0.340633	0.0127389
$716$	−20.5271	−0.767133
$717$	−4.63720	−0.173179
$718$	19.7050	0.735385
$719$	5.73145	0.213747	0.106874	−	0.994273i	$-0.465916\pi$
$719$	5.73145	0.213747	0.106874	+	0.994273i	$0.465916\pi$
$720$	0.268945	0.0100230
$721$	3.45288	0.128592
$722$	19.2851	0.717719
$723$	13.8531	0.515201
$724$	−14.6239	−0.543494
$725$	−7.74863	−0.287777
$726$	1.00000	0.0371135
$727$	−38.7317	−1.43648	−0.718240	−	0.695795i	$-0.755052\pi$
$727$	−38.7317	−1.43648	−0.718240	+	0.695795i	$0.755052\pi$
$728$	4.34011	0.160855
$729$	1.00000	0.0370370
$730$	−0.636427	−0.0235552
$731$	10.7331	0.396977
$732$	−1.00000	−0.0369611
$733$	30.5487	1.12834	0.564171	−	0.825658i	$-0.309196\pi$
$733$	30.5487	1.12834	0.564171	+	0.825658i	$0.309196\pi$
$734$	−20.4095	−0.753329
$735$	1.27544	0.0470454
$736$	−8.86224	−0.326667
$737$	−0.380487	−0.0140154
$738$	3.44241	0.126717
$739$	13.3787	0.492142	0.246071	−	0.969252i	$-0.420860\pi$
$739$	13.3787	0.492142	0.246071	+	0.969252i	$0.420860\pi$
$740$	2.29956	0.0845335
$741$	7.83679	0.287892
$742$	14.1772	0.520460
$743$	41.2178	1.51213	0.756067	−	0.654494i	$-0.227118\pi$
$743$	41.2178	1.51213	0.756067	+	0.654494i	$0.227118\pi$
$744$	−6.59330	−0.241722
$745$	5.29189	0.193880
$746$	−35.9190	−1.31509
$747$	2.32547	0.0850846
$748$	0.867540	0.0317204
$749$	−23.2563	−0.849768
$750$	−2.67000	−0.0974945
$751$	17.5229	0.639420	0.319710	−	0.947515i	$-0.396414\pi$
$751$	17.5229	0.639420	0.319710	+	0.947515i	$0.396414\pi$
$752$	5.99112	0.218474
$753$	−8.63040	−0.314509
$754$	1.99162	0.0725305
$755$	2.34388	0.0853024
$756$	3.42672	0.124629
$757$	−17.5737	−0.638726	−0.319363	−	0.947632i	$-0.603469\pi$
$757$	−17.5737	−0.638726	−0.319363	+	0.947632i	$0.603469\pi$
$758$	29.2039	1.06073
$759$	−8.86224	−0.321679
$760$	1.66410	0.0603631
$761$	−41.5905	−1.50765	−0.753827	−	0.657073i	$-0.771794\pi$
$761$	−41.5905	−1.50765	−0.753827	+	0.657073i	$0.771794\pi$
$762$	18.8689	0.683550
$763$	−37.6220	−1.36201
$764$	−5.11491	−0.185051
$765$	0.233320	0.00843572
$766$	−30.2591	−1.09330
$767$	−16.9252	−0.611133
$768$	1.00000	0.0360844
$769$	22.8539	0.824132	0.412066	−	0.911154i	$-0.364807\pi$
$769$	22.8539	0.824132	0.412066	+	0.911154i	$0.364807\pi$
$770$	0.921599	0.0332121
$771$	1.33011	0.0479028
$772$	−18.9293	−0.681281
$773$	−47.8479	−1.72097	−0.860485	−	0.509476i	$-0.829839\pi$
$773$	−47.8479	−1.72097	−0.860485	+	0.509476i	$0.829839\pi$
$774$	12.3719	0.444697
$775$	32.4896	1.16706
$776$	−11.5077	−0.413102
$777$	29.2995	1.05111
$778$	−6.13420	−0.219922
$779$	21.2999	0.763148
$780$	0.340633	0.0121966
$781$	−10.4281	−0.373148
$782$	−7.68835	−0.274935
$783$	1.57247	0.0561956
$784$	4.74240	0.169371
$785$	6.11803	0.218362
$786$	3.68893	0.131580
$787$	6.39840	0.228078	0.114039	−	0.993476i	$-0.463621\pi$
$787$	6.39840	0.228078	0.114039	+	0.993476i	$0.463621\pi$
$788$	8.98440	0.320056
$789$	−29.1042	−1.03614
$790$	−2.25142	−0.0801021
$791$	−1.04504	−0.0371573
$792$	1.00000	0.0355335
$793$	−1.26655	−0.0449766
$794$	7.09173	0.251676
$795$	1.11269	0.0394630
$796$	15.1438	0.536758
$797$	23.0083	0.814996	0.407498	−	0.913206i	$-0.366401\pi$
$797$	23.0083	0.814996	0.407498	+	0.913206i	$0.366401\pi$
$798$	21.2028	0.750571
$799$	5.19753	0.183875
$800$	−4.92767	−0.174219
$801$	−11.6165	−0.410447
$802$	−29.9023	−1.05589
$803$	−2.36638	−0.0835079
$804$	−0.380487	−0.0134188
$805$	−8.16743	−0.287864
$806$	−8.35075	−0.294143
$807$	−2.29032	−0.0806229
$808$	−10.6426	−0.374405
$809$	23.5409	0.827653	0.413827	−	0.910356i	$-0.364192\pi$
$809$	23.5409	0.827653	0.413827	+	0.910356i	$0.364192\pi$
$810$	0.268945	0.00944976
$811$	13.2119	0.463932	0.231966	−	0.972724i	$-0.425484\pi$
$811$	13.2119	0.463932	0.231966	+	0.972724i	$0.425484\pi$
$812$	5.38842	0.189097
$813$	−23.4290	−0.821690
$814$	8.55030	0.299688
$815$	−4.55048	−0.159396
$816$	0.867540	0.0303700
$817$	76.5509	2.67818
$818$	−31.4377	−1.09919
$819$	4.34011	0.151656
$820$	0.925818	0.0323310
$821$	17.7547	0.619643	0.309821	−	0.950795i	$-0.399731\pi$
$821$	17.7547	0.619643	0.309821	+	0.950795i	$0.399731\pi$
$822$	8.47305	0.295531
$823$	32.3631	1.12811	0.564054	−	0.825738i	$-0.309241\pi$
$823$	32.3631	1.12811	0.564054	+	0.825738i	$0.309241\pi$
$824$	1.00764	0.0351026
$825$	−4.92767	−0.171559
$826$	−45.7919	−1.59330
$827$	−40.4152	−1.40537	−0.702686	−	0.711500i	$-0.748016\pi$
$827$	−40.4152	−1.40537	−0.702686	+	0.711500i	$0.748016\pi$
$828$	−8.86224	−0.307984
$829$	22.9984	0.798767	0.399384	−	0.916784i	$-0.369224\pi$
$829$	22.9984	0.798767	0.399384	+	0.916784i	$0.369224\pi$
$830$	0.625425	0.0217088
$831$	18.8839	0.655076
$832$	1.26655	0.0439098
$833$	4.11422	0.142549
$834$	14.3911	0.498325
$835$	6.61062	0.228770
$836$	6.18750	0.213999
$837$	−6.59330	−0.227898
$838$	−6.06492	−0.209509
$839$	−1.45169	−0.0501179	−0.0250589	−	0.999686i	$-0.507977\pi$
$839$	−1.45169	−0.0501179	−0.0250589	+	0.999686i	$0.507977\pi$
$840$	0.921599	0.0317982
$841$	−26.5273	−0.914735
$842$	−11.9703	−0.412524
$843$	−10.0216	−0.345163
$844$	25.8348	0.889271
$845$	−3.06486	−0.105434
$846$	5.99112	0.205979
$847$	3.42672	0.117743
$848$	4.13724	0.142073
$849$	2.41609	0.0829200
$850$	−4.27495	−0.146629
$851$	−75.7748	−2.59753
$852$	−10.4281	−0.357262
$853$	42.6983	1.46196	0.730981	−	0.682398i	$-0.239063\pi$
$853$	42.6983	1.46196	0.730981	+	0.682398i	$0.239063\pi$
$854$	−3.42672	−0.117260
$855$	1.66410	0.0569109
$856$	−6.78676	−0.231967
$857$	−4.02296	−0.137422	−0.0687108	−	0.997637i	$-0.521889\pi$
$857$	−4.02296	−0.137422	−0.0687108	+	0.997637i	$0.521889\pi$
$858$	1.26655	0.0432394
$859$	−11.2054	−0.382323	−0.191162	−	0.981559i	$-0.561225\pi$
$859$	−11.2054	−0.382323	−0.191162	+	0.981559i	$0.561225\pi$
$860$	3.32735	0.113462
$861$	11.7962	0.402012
$862$	4.23679	0.144306
$863$	−38.2809	−1.30310	−0.651548	−	0.758607i	$-0.725880\pi$
$863$	−38.2809	−1.30310	−0.651548	+	0.758607i	$0.725880\pi$
$864$	1.00000	0.0340207
$865$	4.32779	0.147149
$866$	−12.6590	−0.430170
$867$	−16.2474	−0.551790
$868$	−22.5934	−0.766869
$869$	−8.37132	−0.283978
$870$	0.422909	0.0143380
$871$	−0.481907	−0.0163288
$872$	−10.9790	−0.371797
$873$	−11.5077	−0.389476
$874$	−54.8351	−1.85483
$875$	−9.14933	−0.309304
$876$	−2.36638	−0.0799527
$877$	14.9533	0.504937	0.252468	−	0.967605i	$-0.418758\pi$
$877$	14.9533	0.504937	0.252468	+	0.967605i	$0.418758\pi$
$878$	−26.5844	−0.897181
$879$	4.40067	0.148431
$880$	0.268945	0.00906613
$881$	−13.4894	−0.454469	−0.227234	−	0.973840i	$-0.572968\pi$
$881$	−13.4894	−0.454469	−0.227234	+	0.973840i	$0.572968\pi$
$882$	4.74240	0.159685
$883$	−53.1259	−1.78783	−0.893915	−	0.448236i	$-0.852052\pi$
$883$	−53.1259	−1.78783	−0.893915	+	0.448236i	$0.852052\pi$
$884$	1.09878	0.0369561
$885$	−3.59396	−0.120810
$886$	26.5443	0.891773
$887$	33.1287	1.11235	0.556176	−	0.831065i	$-0.312268\pi$
$887$	33.1287	1.11235	0.556176	+	0.831065i	$0.312268\pi$
$888$	8.55030	0.286929
$889$	64.6586	2.16858
$890$	−3.12419	−0.104723
$891$	1.00000	0.0335013
$892$	9.89572	0.331333
$893$	37.0700	1.24050
$894$	19.6765	0.658080
$895$	−5.52066	−0.184535
$896$	3.42672	0.114479
$897$	−11.2245	−0.374775
$898$	33.4432	1.11601
$899$	−10.3678	−0.345785
$900$	−4.92767	−0.164256
$901$	3.58922	0.119574
$902$	3.44241	0.114620
$903$	42.3949	1.41081
$904$	−0.304968	−0.0101431
$905$	−3.93303	−0.130738
$906$	8.71508	0.289539
$907$	35.6391	1.18338	0.591688	−	0.806167i	$-0.298462\pi$
$907$	35.6391	1.18338	0.591688	+	0.806167i	$0.298462\pi$
$908$	1.05470	0.0350016
$909$	−10.6426	−0.352993
$910$	1.16725	0.0386940
$911$	−40.8527	−1.35351	−0.676755	−	0.736208i	$-0.736614\pi$
$911$	−40.8527	−1.35351	−0.676755	+	0.736208i	$0.736614\pi$
$912$	6.18750	0.204889
$913$	2.32547	0.0769619
$914$	−39.3979	−1.30317
$915$	−0.268945	−0.00889105
$916$	−6.19110	−0.204560
$917$	12.6409	0.417440
$918$	0.867540	0.0286331
$919$	−6.75599	−0.222860	−0.111430	−	0.993772i	$-0.535543\pi$
$919$	−6.75599	−0.222860	−0.111430	+	0.993772i	$0.535543\pi$
$920$	−2.38346	−0.0785802
$921$	−17.0682	−0.562418
$922$	2.36247	0.0778037
$923$	−13.2078	−0.434739
$924$	3.42672	0.112731
$925$	−42.1330	−1.38533
$926$	29.4582	0.968057
$927$	1.00764	0.0330951
$928$	1.57247	0.0516190
$929$	−30.3584	−0.996026	−0.498013	−	0.867170i	$-0.665937\pi$
$929$	−30.3584	−0.996026	−0.498013	+	0.867170i	$0.665937\pi$
$930$	−1.77324	−0.0581467
$931$	29.3436	0.961697
$932$	−28.9847	−0.949426
$933$	−28.3715	−0.928841
$934$	−1.97701	−0.0646896
$935$	0.233320	0.00763040
$936$	1.26655	0.0413985
$937$	−7.42112	−0.242437	−0.121219	−	0.992626i	$-0.538680\pi$
$937$	−7.42112	−0.242437	−0.121219	+	0.992626i	$0.538680\pi$
$938$	−1.30382	−0.0425713
$939$	−9.88599	−0.322617
$940$	1.61128	0.0525542
$941$	−36.7139	−1.19684	−0.598419	−	0.801183i	$-0.704204\pi$
$941$	−36.7139	−1.19684	−0.598419	+	0.801183i	$0.704204\pi$
$942$	22.7483	0.741179
$943$	−30.5075	−0.993459
$944$	−13.3632	−0.434935
$945$	0.921599	0.0299796
$946$	12.3719	0.402244
$947$	27.1926	0.883641	0.441821	−	0.897103i	$-0.354333\pi$
$947$	27.1926	0.883641	0.441821	+	0.897103i	$0.354333\pi$
$948$	−8.37132	−0.271888
$949$	−2.99715	−0.0972915
$950$	−30.4899	−0.989224
$951$	5.91378	0.191767
$952$	2.97281	0.0963494
$953$	−11.2829	−0.365488	−0.182744	−	0.983161i	$-0.558498\pi$
$953$	−11.2829	−0.365488	−0.182744	+	0.983161i	$0.558498\pi$
$954$	4.13724	0.133948
$955$	−1.37563	−0.0445144
$956$	−4.63720	−0.149978
$957$	1.57247	0.0508309
$958$	−26.1584	−0.845140
$959$	29.0347	0.937581
$960$	0.268945	0.00868016
$961$	12.4716	0.402309
$962$	10.8294	0.349154
$963$	−6.78676	−0.218700
$964$	13.8531	0.446177
$965$	−5.09095	−0.163883
$966$	−30.3684	−0.977088
$967$	47.9113	1.54072	0.770361	−	0.637608i	$-0.220076\pi$
$967$	47.9113	1.54072	0.770361	+	0.637608i	$0.220076\pi$
$968$	1.00000	0.0321412
$969$	5.36790	0.172442
$970$	−3.09494	−0.0993724
$971$	27.4932	0.882298	0.441149	−	0.897434i	$-0.354571\pi$
$971$	27.4932	0.882298	0.441149	+	0.897434i	$0.354571\pi$
$972$	1.00000	0.0320750
$973$	49.3144	1.58095
$974$	−28.6097	−0.916715
$975$	−6.24115	−0.199877
$976$	−1.00000	−0.0320092
$977$	7.09610	0.227024	0.113512	−	0.993537i	$-0.463790\pi$
$977$	7.09610	0.227024	0.113512	+	0.993537i	$0.463790\pi$
$978$	−16.9197	−0.541034
$979$	−11.6165	−0.371263
$980$	1.27544	0.0407426
$981$	−10.9790	−0.350533
$982$	−12.1722	−0.388429
$983$	49.9351	1.59268	0.796342	−	0.604847i	$-0.206766\pi$
$983$	49.9351	1.59268	0.796342	+	0.604847i	$0.206766\pi$
$984$	3.44241	0.109740
$985$	2.41631	0.0769901
$986$	1.36418	0.0434445
$987$	20.5299	0.653473
$988$	7.83679	0.249321
$989$	−109.642	−3.48643
$990$	0.268945	0.00854763
$991$	25.0878	0.796942	0.398471	−	0.917181i	$-0.369541\pi$
$991$	25.0878	0.796942	0.398471	+	0.917181i	$0.369541\pi$
$992$	−6.59330	−0.209337
$993$	18.4377	0.585103
$994$	−35.7343	−1.13342
$995$	4.07286	0.129118
$996$	2.32547	0.0736855
$997$	55.0312	1.74285	0.871427	−	0.490525i	$-0.163195\pi$
$997$	55.0312	1.74285	0.871427	+	0.490525i	$0.163195\pi$
$998$	−18.9089	−0.598552
$999$	8.55030	0.270519

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.bc.1.4	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.bc.1.4	✓	9	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.268945 q^{5} +1.00000 q^{6} +3.42672 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.268945 q^{5} +1.00000 q^{6} +3.42672 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.268945 q^{10} +1.00000 q^{11} +1.00000 q^{12} +1.26655 q^{13} +3.42672 q^{14} +0.268945 q^{15} +1.00000 q^{16} +0.867540 q^{17} +1.00000 q^{18} +6.18750 q^{19} +0.268945 q^{20} +3.42672 q^{21} +1.00000 q^{22} -8.86224 q^{23} +1.00000 q^{24} -4.92767 q^{25} +1.26655 q^{26} +1.00000 q^{27} +3.42672 q^{28} +1.57247 q^{29} +0.268945 q^{30} -6.59330 q^{31} +1.00000 q^{32} +1.00000 q^{33} +0.867540 q^{34} +0.921599 q^{35} +1.00000 q^{36} +8.55030 q^{37} +6.18750 q^{38} +1.26655 q^{39} +0.268945 q^{40} +3.44241 q^{41} +3.42672 q^{42} +12.3719 q^{43} +1.00000 q^{44} +0.268945 q^{45} -8.86224 q^{46} +5.99112 q^{47} +1.00000 q^{48} +4.74240 q^{49} -4.92767 q^{50} +0.867540 q^{51} +1.26655 q^{52} +4.13724 q^{53} +1.00000 q^{54} +0.268945 q^{55} +3.42672 q^{56} +6.18750 q^{57} +1.57247 q^{58} -13.3632 q^{59} +0.268945 q^{60} -1.00000 q^{61} -6.59330 q^{62} +3.42672 q^{63} +1.00000 q^{64} +0.340633 q^{65} +1.00000 q^{66} -0.380487 q^{67} +0.867540 q^{68} -8.86224 q^{69} +0.921599 q^{70} -10.4281 q^{71} +1.00000 q^{72} -2.36638 q^{73} +8.55030 q^{74} -4.92767 q^{75} +6.18750 q^{76} +3.42672 q^{77} +1.26655 q^{78} -8.37132 q^{79} +0.268945 q^{80} +1.00000 q^{81} +3.44241 q^{82} +2.32547 q^{83} +3.42672 q^{84} +0.233320 q^{85} +12.3719 q^{86} +1.57247 q^{87} +1.00000 q^{88} -11.6165 q^{89} +0.268945 q^{90} +4.34011 q^{91} -8.86224 q^{92} -6.59330 q^{93} +5.99112 q^{94} +1.66410 q^{95} +1.00000 q^{96} -11.5077 q^{97} +4.74240 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} + 9 q^{3} + 9 q^{4} + 8 q^{5} + 9 q^{6} + 9 q^{7} + 9 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q + 9 * q^2 + 9 * q^3 + 9 * q^4 + 8 * q^5 + 9 * q^6 + 9 * q^7 + 9 * q^8 + 9 * q^9	\( 9 q + 9 q^{2} + 9 q^{3} + 9 q^{4} + 8 q^{5} + 9 q^{6} + 9 q^{7} + 9 q^{8} + 9 q^{9} + 8 q^{10} + 9 q^{11} + 9 q^{12} + 8 q^{13} + 9 q^{14} + 8 q^{15} + 9 q^{16} + q^{17} + 9 q^{18} + 5 q^{19} + 8 q^{20} + 9 q^{21} + 9 q^{22} - q^{23} + 9 q^{24} + 23 q^{25} + 8 q^{26} + 9 q^{27} + 9 q^{28} - 14 q^{29} + 8 q^{30} + 25 q^{31} + 9 q^{32} + 9 q^{33} + q^{34} + 5 q^{35} + 9 q^{36} + 16 q^{37} + 5 q^{38} + 8 q^{39} + 8 q^{40} + 5 q^{41} + 9 q^{42} + 5 q^{43} + 9 q^{44} + 8 q^{45} - q^{46} + 8 q^{47} + 9 q^{48} + 30 q^{49} + 23 q^{50} + q^{51} + 8 q^{52} + q^{53} + 9 q^{54} + 8 q^{55} + 9 q^{56} + 5 q^{57} - 14 q^{58} + 4 q^{59} + 8 q^{60} - 9 q^{61} + 25 q^{62} + 9 q^{63} + 9 q^{64} - 14 q^{65} + 9 q^{66} - 4 q^{67} + q^{68} - q^{69} + 5 q^{70} + 20 q^{71} + 9 q^{72} + 15 q^{73} + 16 q^{74} + 23 q^{75} + 5 q^{76} + 9 q^{77} + 8 q^{78} - 2 q^{79} + 8 q^{80} + 9 q^{81} + 5 q^{82} + 21 q^{83} + 9 q^{84} - 16 q^{85} + 5 q^{86} - 14 q^{87} + 9 q^{88} + 10 q^{89} + 8 q^{90} - 19 q^{91} - q^{92} + 25 q^{93} + 8 q^{94} - 7 q^{95} + 9 q^{96} + 3 q^{97} + 30 q^{98} + 9 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 9 * q^3 + 9 * q^4 + 8 * q^5 + 9 * q^6 + 9 * q^7 + 9 * q^8 + 9 * q^9 + 8 * q^10 + 9 * q^11 + 9 * q^12 + 8 * q^13 + 9 * q^14 + 8 * q^15 + 9 * q^16 + q^17 + 9 * q^18 + 5 * q^19 + 8 * q^20 + 9 * q^21 + 9 * q^22 - q^23 + 9 * q^24 + 23 * q^25 + 8 * q^26 + 9 * q^27 + 9 * q^28 - 14 * q^29 + 8 * q^30 + 25 * q^31 + 9 * q^32 + 9 * q^33 + q^34 + 5 * q^35 + 9 * q^36 + 16 * q^37 + 5 * q^38 + 8 * q^39 + 8 * q^40 + 5 * q^41 + 9 * q^42 + 5 * q^43 + 9 * q^44 + 8 * q^45 - q^46 + 8 * q^47 + 9 * q^48 + 30 * q^49 + 23 * q^50 + q^51 + 8 * q^52 + q^53 + 9 * q^54 + 8 * q^55 + 9 * q^56 + 5 * q^57 - 14 * q^58 + 4 * q^59 + 8 * q^60 - 9 * q^61 + 25 * q^62 + 9 * q^63 + 9 * q^64 - 14 * q^65 + 9 * q^66 - 4 * q^67 + q^68 - q^69 + 5 * q^70 + 20 * q^71 + 9 * q^72 + 15 * q^73 + 16 * q^74 + 23 * q^75 + 5 * q^76 + 9 * q^77 + 8 * q^78 - 2 * q^79 + 8 * q^80 + 9 * q^81 + 5 * q^82 + 21 * q^83 + 9 * q^84 - 16 * q^85 + 5 * q^86 - 14 * q^87 + 9 * q^88 + 10 * q^89 + 8 * q^90 - 19 * q^91 - q^92 + 25 * q^93 + 8 * q^94 - 7 * q^95 + 9 * q^96 + 3 * q^97 + 30 * q^98 + 9 * q^99

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