LMFDB - Embedded newform 8034.2.a.bc.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8034,2,Mod(1,8034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8034, 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("8034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8034 = 2 \cdot 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8034.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:	$64.1518129839$
Analytic rank:	$0$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - x^{14} - 48 x^{13} + 44 x^{12} + 872 x^{11} - 707 x^{10} - 7580 x^{9} + 5112 x^{8} + \cdots + 2048 $ x^15 - x^14 - 48x^13 + 44x^12 + 872x^11 - 707x^10 - 7580x^9 + 5112x^8 + 33191x^7 - 16428x^6 - 71361x^5 + 21747x^4 + 65434x^3 - 11840x^2 - 17600*x + 2048
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$4.06882$ of defining polynomial
Character	$\chi$	$=$	8034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.06882 q^{5} -1.00000 q^{6} +4.31915 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.06882 q^{5} -1.00000 q^{6} +4.31915 q^{7} +1.00000 q^{8} +1.00000 q^{9} -4.06882 q^{10} -3.45943 q^{11} -1.00000 q^{12} -1.00000 q^{13} +4.31915 q^{14} +4.06882 q^{15} +1.00000 q^{16} -7.56875 q^{17} +1.00000 q^{18} -1.84870 q^{19} -4.06882 q^{20} -4.31915 q^{21} -3.45943 q^{22} -8.50665 q^{23} -1.00000 q^{24} +11.5553 q^{25} -1.00000 q^{26} -1.00000 q^{27} +4.31915 q^{28} +6.61550 q^{29} +4.06882 q^{30} -5.55957 q^{31} +1.00000 q^{32} +3.45943 q^{33} -7.56875 q^{34} -17.5738 q^{35} +1.00000 q^{36} +10.0080 q^{37} -1.84870 q^{38} +1.00000 q^{39} -4.06882 q^{40} +0.695896 q^{41} -4.31915 q^{42} -3.09807 q^{43} -3.45943 q^{44} -4.06882 q^{45} -8.50665 q^{46} -1.17792 q^{47} -1.00000 q^{48} +11.6551 q^{49} +11.5553 q^{50} +7.56875 q^{51} -1.00000 q^{52} +5.76954 q^{53} -1.00000 q^{54} +14.0758 q^{55} +4.31915 q^{56} +1.84870 q^{57} +6.61550 q^{58} +6.88464 q^{59} +4.06882 q^{60} +12.3520 q^{61} -5.55957 q^{62} +4.31915 q^{63} +1.00000 q^{64} +4.06882 q^{65} +3.45943 q^{66} -14.3536 q^{67} -7.56875 q^{68} +8.50665 q^{69} -17.5738 q^{70} +4.40758 q^{71} +1.00000 q^{72} -8.29562 q^{73} +10.0080 q^{74} -11.5553 q^{75} -1.84870 q^{76} -14.9418 q^{77} +1.00000 q^{78} +6.21617 q^{79} -4.06882 q^{80} +1.00000 q^{81} +0.695896 q^{82} -11.6646 q^{83} -4.31915 q^{84} +30.7958 q^{85} -3.09807 q^{86} -6.61550 q^{87} -3.45943 q^{88} -2.88091 q^{89} -4.06882 q^{90} -4.31915 q^{91} -8.50665 q^{92} +5.55957 q^{93} -1.17792 q^{94} +7.52201 q^{95} -1.00000 q^{96} +4.85929 q^{97} +11.6551 q^{98} -3.45943 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q + 15 q^{2} - 15 q^{3} + 15 q^{4} - q^{5} - 15 q^{6} + 5 q^{7} + 15 q^{8} + 15 q^{9}+O(q^{10}) $ 15 * q + 15 * q^2 - 15 * q^3 + 15 * q^4 - q^5 - 15 * q^6 + 5 * q^7 + 15 * q^8 + 15 * q^9	\( 15 q + 15 q^{2} - 15 q^{3} + 15 q^{4} - q^{5} - 15 q^{6} + 5 q^{7} + 15 q^{8} + 15 q^{9} - q^{10} + 3 q^{11} - 15 q^{12} - 15 q^{13} + 5 q^{14} + q^{15} + 15 q^{16} - 2 q^{17} + 15 q^{18} + 8 q^{19} - q^{20} - 5 q^{21} + 3 q^{22} + 3 q^{23} - 15 q^{24} + 22 q^{25} - 15 q^{26} - 15 q^{27} + 5 q^{28} + 26 q^{29} + q^{30} + 15 q^{32} - 3 q^{33} - 2 q^{34} - 8 q^{35} + 15 q^{36} + 25 q^{37} + 8 q^{38} + 15 q^{39} - q^{40} - q^{41} - 5 q^{42} + 10 q^{43} + 3 q^{44} - q^{45} + 3 q^{46} - 3 q^{47} - 15 q^{48} + 32 q^{49} + 22 q^{50} + 2 q^{51} - 15 q^{52} + 13 q^{53} - 15 q^{54} - 2 q^{55} + 5 q^{56} - 8 q^{57} + 26 q^{58} + 28 q^{59} + q^{60} + 22 q^{61} + 5 q^{63} + 15 q^{64} + q^{65} - 3 q^{66} + 29 q^{67} - 2 q^{68} - 3 q^{69} - 8 q^{70} + 18 q^{71} + 15 q^{72} + 23 q^{73} + 25 q^{74} - 22 q^{75} + 8 q^{76} + 17 q^{77} + 15 q^{78} + 27 q^{79} - q^{80} + 15 q^{81} - q^{82} + 7 q^{83} - 5 q^{84} + 43 q^{85} + 10 q^{86} - 26 q^{87} + 3 q^{88} + 35 q^{89} - q^{90} - 5 q^{91} + 3 q^{92} - 3 q^{94} + 6 q^{95} - 15 q^{96} + 19 q^{97} + 32 q^{98} + 3 q^{99}+O(q^{100}) \) 15 * q + 15 * q^2 - 15 * q^3 + 15 * q^4 - q^5 - 15 * q^6 + 5 * q^7 + 15 * q^8 + 15 * q^9 - q^10 + 3 * q^11 - 15 * q^12 - 15 * q^13 + 5 * q^14 + q^15 + 15 * q^16 - 2 * q^17 + 15 * q^18 + 8 * q^19 - q^20 - 5 * q^21 + 3 * q^22 + 3 * q^23 - 15 * q^24 + 22 * q^25 - 15 * q^26 - 15 * q^27 + 5 * q^28 + 26 * q^29 + q^30 + 15 * q^32 - 3 * q^33 - 2 * q^34 - 8 * q^35 + 15 * q^36 + 25 * q^37 + 8 * q^38 + 15 * q^39 - q^40 - q^41 - 5 * q^42 + 10 * q^43 + 3 * q^44 - q^45 + 3 * q^46 - 3 * q^47 - 15 * q^48 + 32 * q^49 + 22 * q^50 + 2 * q^51 - 15 * q^52 + 13 * q^53 - 15 * q^54 - 2 * q^55 + 5 * q^56 - 8 * q^57 + 26 * q^58 + 28 * q^59 + q^60 + 22 * q^61 + 5 * q^63 + 15 * q^64 + q^65 - 3 * q^66 + 29 * q^67 - 2 * q^68 - 3 * q^69 - 8 * q^70 + 18 * q^71 + 15 * q^72 + 23 * q^73 + 25 * q^74 - 22 * q^75 + 8 * q^76 + 17 * q^77 + 15 * q^78 + 27 * q^79 - q^80 + 15 * q^81 - q^82 + 7 * q^83 - 5 * q^84 + 43 * q^85 + 10 * q^86 - 26 * q^87 + 3 * q^88 + 35 * q^89 - q^90 - 5 * q^91 + 3 * q^92 - 3 * q^94 + 6 * q^95 - 15 * q^96 + 19 * q^97 + 32 * q^98 + 3 * 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
$5$	−4.06882	−1.81963	−0.909815	−	0.415015i	$-0.863776\pi$
$5$	−4.06882	−1.81963	−0.909815	+	0.415015i	$0.863776\pi$
$6$	−1.00000	−0.408248
$7$	4.31915	1.63249	0.816243	−	0.577708i	$-0.196053\pi$
$7$	4.31915	1.63249	0.816243	+	0.577708i	$0.196053\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−4.06882	−1.28667
$11$	−3.45943	−1.04306	−0.521529	−	0.853234i	$-0.674638\pi$
$11$	−3.45943	−1.04306	−0.521529	+	0.853234i	$0.674638\pi$
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	4.31915	1.15434
$15$	4.06882	1.05056
$16$	1.00000	0.250000
$17$	−7.56875	−1.83569	−0.917845	−	0.396938i	$-0.870073\pi$
$17$	−7.56875	−1.83569	−0.917845	+	0.396938i	$0.870073\pi$
$18$	1.00000	0.235702
$19$	−1.84870	−0.424120	−0.212060	−	0.977257i	$-0.568017\pi$
$19$	−1.84870	−0.424120	−0.212060	+	0.977257i	$0.568017\pi$
$20$	−4.06882	−0.909815
$21$	−4.31915	−0.942517
$22$	−3.45943	−0.737553
$23$	−8.50665	−1.77376	−0.886879	−	0.462001i	$-0.847132\pi$
$23$	−8.50665	−1.77376	−0.886879	+	0.462001i	$0.847132\pi$
$24$	−1.00000	−0.204124
$25$	11.5553	2.31105
$26$	−1.00000	−0.196116
$27$	−1.00000	−0.192450
$28$	4.31915	0.816243
$29$	6.61550	1.22847	0.614234	−	0.789124i	$-0.289465\pi$
$29$	6.61550	1.22847	0.614234	+	0.789124i	$0.289465\pi$
$30$	4.06882	0.742861
$31$	−5.55957	−0.998528	−0.499264	−	0.866450i	$-0.666396\pi$
$31$	−5.55957	−0.998528	−0.499264	+	0.866450i	$0.666396\pi$
$32$	1.00000	0.176777
$33$	3.45943	0.602210
$34$	−7.56875	−1.29803
$35$	−17.5738	−2.97052
$36$	1.00000	0.166667
$37$	10.0080	1.64530	0.822652	−	0.568545i	$-0.192493\pi$
$37$	10.0080	1.64530	0.822652	+	0.568545i	$0.192493\pi$
$38$	−1.84870	−0.299898
$39$	1.00000	0.160128
$40$	−4.06882	−0.643336
$41$	0.695896	0.108681	0.0543403	−	0.998522i	$-0.482694\pi$
$41$	0.695896	0.108681	0.0543403	+	0.998522i	$0.482694\pi$
$42$	−4.31915	−0.666460
$43$	−3.09807	−0.472452	−0.236226	−	0.971698i	$-0.575910\pi$
$43$	−3.09807	−0.472452	−0.236226	+	0.971698i	$0.575910\pi$
$44$	−3.45943	−0.521529
$45$	−4.06882	−0.606543
$46$	−8.50665	−1.25424
$47$	−1.17792	−0.171818	−0.0859089	−	0.996303i	$-0.527379\pi$
$47$	−1.17792	−0.171818	−0.0859089	+	0.996303i	$0.527379\pi$
$48$	−1.00000	−0.144338
$49$	11.6551	1.66501
$50$	11.5553	1.63416
$51$	7.56875	1.05984
$52$	−1.00000	−0.138675
$53$	5.76954	0.792507	0.396253	−	0.918141i	$-0.370310\pi$
$53$	5.76954	0.792507	0.396253	+	0.918141i	$0.370310\pi$
$54$	−1.00000	−0.136083
$55$	14.0758	1.89798
$56$	4.31915	0.577171
$57$	1.84870	0.244866
$58$	6.61550	0.868657
$59$	6.88464	0.896303	0.448152	−	0.893958i	$-0.352082\pi$
$59$	6.88464	0.896303	0.448152	+	0.893958i	$0.352082\pi$
$60$	4.06882	0.525282
$61$	12.3520	1.58151	0.790755	−	0.612133i	$-0.209688\pi$
$61$	12.3520	1.58151	0.790755	+	0.612133i	$0.209688\pi$
$62$	−5.55957	−0.706066
$63$	4.31915	0.544162
$64$	1.00000	0.125000
$65$	4.06882	0.504674
$66$	3.45943	0.425827
$67$	−14.3536	−1.75357	−0.876786	−	0.480881i	$-0.840317\pi$
$67$	−14.3536	−1.75357	−0.876786	+	0.480881i	$0.840317\pi$
$68$	−7.56875	−0.917845
$69$	8.50665	1.02408
$70$	−17.5738	−2.10048
$71$	4.40758	0.523083	0.261542	−	0.965192i	$-0.415769\pi$
$71$	4.40758	0.523083	0.261542	+	0.965192i	$0.415769\pi$
$72$	1.00000	0.117851
$73$	−8.29562	−0.970928	−0.485464	−	0.874257i	$-0.661349\pi$
$73$	−8.29562	−0.970928	−0.485464	+	0.874257i	$0.661349\pi$
$74$	10.0080	1.16341
$75$	−11.5553	−1.33429
$76$	−1.84870	−0.212060
$77$	−14.9418	−1.70278
$78$	1.00000	0.113228
$79$	6.21617	0.699373	0.349687	−	0.936867i	$-0.386288\pi$
$79$	6.21617	0.699373	0.349687	+	0.936867i	$0.386288\pi$
$80$	−4.06882	−0.454907
$81$	1.00000	0.111111
$82$	0.695896	0.0768488
$83$	−11.6646	−1.28036	−0.640179	−	0.768226i	$-0.721140\pi$
$83$	−11.6646	−1.28036	−0.640179	+	0.768226i	$0.721140\pi$
$84$	−4.31915	−0.471258
$85$	30.7958	3.34028
$86$	−3.09807	−0.334074
$87$	−6.61550	−0.709256
$88$	−3.45943	−0.368777
$89$	−2.88091	−0.305375	−0.152688	−	0.988274i	$-0.548793\pi$
$89$	−2.88091	−0.305375	−0.152688	+	0.988274i	$0.548793\pi$
$90$	−4.06882	−0.428891
$91$	−4.31915	−0.452770
$92$	−8.50665	−0.886879
$93$	5.55957	0.576501
$94$	−1.17792	−0.121494
$95$	7.52201	0.771742
$96$	−1.00000	−0.102062
$97$	4.85929	0.493386	0.246693	−	0.969094i	$-0.420656\pi$
$97$	4.85929	0.493386	0.246693	+	0.969094i	$0.420656\pi$
$98$	11.6551	1.17734
$99$	−3.45943	−0.347686
$100$	11.5553	1.15553
$101$	9.41575	0.936903	0.468451	−	0.883489i	$-0.344812\pi$
$101$	9.41575	0.936903	0.468451	+	0.883489i	$0.344812\pi$
$102$	7.56875	0.749418
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−1.00000	−0.0980581
$105$	17.5738	1.71503
$106$	5.76954	0.560387
$107$	3.81409	0.368722	0.184361	−	0.982859i	$-0.440978\pi$
$107$	3.81409	0.368722	0.184361	+	0.982859i	$0.440978\pi$
$108$	−1.00000	−0.0962250
$109$	18.7539	1.79630	0.898149	−	0.439691i	$-0.144912\pi$
$109$	18.7539	1.79630	0.898149	+	0.439691i	$0.144912\pi$
$110$	14.0758	1.34207
$111$	−10.0080	−0.949917
$112$	4.31915	0.408122
$113$	−10.5876	−0.995998	−0.497999	−	0.867178i	$-0.665932\pi$
$113$	−10.5876	−0.995998	−0.497999	+	0.867178i	$0.665932\pi$
$114$	1.84870	0.173146
$115$	34.6120	3.22758
$116$	6.61550	0.614234
$117$	−1.00000	−0.0924500
$118$	6.88464	0.633782
$119$	−32.6906	−2.99674
$120$	4.06882	0.371430
$121$	0.967666	0.0879696
$122$	12.3520	1.11830
$123$	−0.695896	−0.0627468
$124$	−5.55957	−0.499264
$125$	−26.6721	−2.38563
$126$	4.31915	0.384781
$127$	−21.5905	−1.91585	−0.957923	−	0.287026i	$-0.907333\pi$
$127$	−21.5905	−1.91585	−0.957923	+	0.287026i	$0.907333\pi$
$128$	1.00000	0.0883883
$129$	3.09807	0.272770
$130$	4.06882	0.356859
$131$	−2.47190	−0.215971	−0.107985	−	0.994152i	$-0.534440\pi$
$131$	−2.47190	−0.215971	−0.107985	+	0.994152i	$0.534440\pi$
$132$	3.45943	0.301105
$133$	−7.98481	−0.692370
$134$	−14.3536	−1.23996
$135$	4.06882	0.350188
$136$	−7.56875	−0.649015
$137$	7.60382	0.649638	0.324819	−	0.945776i	$-0.394697\pi$
$137$	7.60382	0.649638	0.324819	+	0.945776i	$0.394697\pi$
$138$	8.50665	0.724134
$139$	−0.701284	−0.0594821	−0.0297410	−	0.999558i	$-0.509468\pi$
$139$	−0.701284	−0.0594821	−0.0297410	+	0.999558i	$0.509468\pi$
$140$	−17.5738	−1.48526
$141$	1.17792	0.0991990
$142$	4.40758	0.369876
$143$	3.45943	0.289292
$144$	1.00000	0.0833333
$145$	−26.9172	−2.23535
$146$	−8.29562	−0.686550
$147$	−11.6551	−0.961296
$148$	10.0080	0.822652
$149$	18.0995	1.48276	0.741382	−	0.671083i	$-0.234171\pi$
$149$	18.0995	1.48276	0.741382	+	0.671083i	$0.234171\pi$
$150$	−11.5553	−0.943483
$151$	16.5279	1.34502	0.672512	−	0.740086i	$-0.265215\pi$
$151$	16.5279	1.34502	0.672512	+	0.740086i	$0.265215\pi$
$152$	−1.84870	−0.149949
$153$	−7.56875	−0.611897
$154$	−14.9418	−1.20405
$155$	22.6209	1.81695
$156$	1.00000	0.0800641
$157$	−8.57471	−0.684336	−0.342168	−	0.939639i	$-0.611161\pi$
$157$	−8.57471	−0.684336	−0.342168	+	0.939639i	$0.611161\pi$
$158$	6.21617	0.494532
$159$	−5.76954	−0.457554
$160$	−4.06882	−0.321668
$161$	−36.7415	−2.89564
$162$	1.00000	0.0785674
$163$	−9.70287	−0.759987	−0.379994	−	0.924989i	$-0.624074\pi$
$163$	−9.70287	−0.759987	−0.379994	+	0.924989i	$0.624074\pi$
$164$	0.695896	0.0543403
$165$	−14.0758	−1.09580
$166$	−11.6646	−0.905350
$167$	13.4484	1.04067	0.520335	−	0.853962i	$-0.325807\pi$
$167$	13.4484	1.04067	0.520335	+	0.853962i	$0.325807\pi$
$168$	−4.31915	−0.333230
$169$	1.00000	0.0769231
$170$	30.7958	2.36193
$171$	−1.84870	−0.141373
$172$	−3.09807	−0.236226
$173$	0.334934	0.0254646	0.0127323	−	0.999919i	$-0.495947\pi$
$173$	0.334934	0.0254646	0.0127323	+	0.999919i	$0.495947\pi$
$174$	−6.61550	−0.501520
$175$	49.9089	3.77276
$176$	−3.45943	−0.260764
$177$	−6.88464	−0.517481
$178$	−2.88091	−0.215933
$179$	18.9801	1.41864	0.709321	−	0.704886i	$-0.249002\pi$
$179$	18.9801	1.41864	0.709321	+	0.704886i	$0.249002\pi$
$180$	−4.06882	−0.303272
$181$	−4.69449	−0.348938	−0.174469	−	0.984663i	$-0.555821\pi$
$181$	−4.69449	−0.348938	−0.174469	+	0.984663i	$0.555821\pi$
$182$	−4.31915	−0.320157
$183$	−12.3520	−0.913085
$184$	−8.50665	−0.627118
$185$	−40.7207	−2.99385
$186$	5.55957	0.407647
$187$	26.1836	1.91473
$188$	−1.17792	−0.0859089
$189$	−4.31915	−0.314172
$190$	7.52201	0.545704
$191$	12.4462	0.900579	0.450289	−	0.892883i	$-0.351321\pi$
$191$	12.4462	0.900579	0.450289	+	0.892883i	$0.351321\pi$
$192$	−1.00000	−0.0721688
$193$	2.02744	0.145939	0.0729693	−	0.997334i	$-0.476752\pi$
$193$	2.02744	0.145939	0.0729693	+	0.997334i	$0.476752\pi$
$194$	4.85929	0.348877
$195$	−4.06882	−0.291374
$196$	11.6551	0.832507
$197$	16.8314	1.19919	0.599595	−	0.800303i	$-0.295328\pi$
$197$	16.8314	1.19919	0.599595	+	0.800303i	$0.295328\pi$
$198$	−3.45943	−0.245851
$199$	−0.301529	−0.0213748	−0.0106874	−	0.999943i	$-0.503402\pi$
$199$	−0.301529	−0.0213748	−0.0106874	+	0.999943i	$0.503402\pi$
$200$	11.5553	0.817080
$201$	14.3536	1.01243
$202$	9.41575	0.662490
$203$	28.5734	2.00546
$204$	7.56875	0.529918
$205$	−2.83147	−0.197759
$206$	−1.00000	−0.0696733
$207$	−8.50665	−0.591253
$208$	−1.00000	−0.0693375
$209$	6.39544	0.442382
$210$	17.5738	1.21271
$211$	−3.92060	−0.269905	−0.134953	−	0.990852i	$-0.543088\pi$
$211$	−3.92060	−0.269905	−0.134953	+	0.990852i	$0.543088\pi$
$212$	5.76954	0.396253
$213$	−4.40758	−0.302002
$214$	3.81409	0.260726
$215$	12.6055	0.859687
$216$	−1.00000	−0.0680414
$217$	−24.0126	−1.63008
$218$	18.7539	1.27017
$219$	8.29562	0.560566
$220$	14.0758	0.948989
$221$	7.56875	0.509129
$222$	−10.0080	−0.671693
$223$	13.3625	0.894819	0.447410	−	0.894329i	$-0.352347\pi$
$223$	13.3625	0.894819	0.447410	+	0.894329i	$0.352347\pi$
$224$	4.31915	0.288586
$225$	11.5553	0.770351
$226$	−10.5876	−0.704277
$227$	−1.25297	−0.0831623	−0.0415811	−	0.999135i	$-0.513240\pi$
$227$	−1.25297	−0.0831623	−0.0415811	+	0.999135i	$0.513240\pi$
$228$	1.84870	0.122433
$229$	8.24201	0.544647	0.272324	−	0.962206i	$-0.412208\pi$
$229$	8.24201	0.544647	0.272324	+	0.962206i	$0.412208\pi$
$230$	34.6120	2.28225
$231$	14.9418	0.983099
$232$	6.61550	0.434329
$233$	12.8913	0.844538	0.422269	−	0.906471i	$-0.361234\pi$
$233$	12.8913	0.844538	0.422269	+	0.906471i	$0.361234\pi$
$234$	−1.00000	−0.0653720
$235$	4.79275	0.312645
$236$	6.88464	0.448152
$237$	−6.21617	−0.403783
$238$	−32.6906	−2.11902
$239$	20.1551	1.30373	0.651864	−	0.758336i	$-0.273987\pi$
$239$	20.1551	1.30373	0.651864	+	0.758336i	$0.273987\pi$
$240$	4.06882	0.262641
$241$	−2.43963	−0.157150	−0.0785751	−	0.996908i	$-0.525037\pi$
$241$	−2.43963	−0.157150	−0.0785751	+	0.996908i	$0.525037\pi$
$242$	0.967666	0.0622039
$243$	−1.00000	−0.0641500
$244$	12.3520	0.790755
$245$	−47.4224	−3.02971
$246$	−0.695896	−0.0443687
$247$	1.84870	0.117630
$248$	−5.55957	−0.353033
$249$	11.6646	0.739215
$250$	−26.6721	−1.68689
$251$	−7.14154	−0.450770	−0.225385	−	0.974270i	$-0.572364\pi$
$251$	−7.14154	−0.450770	−0.225385	+	0.974270i	$0.572364\pi$
$252$	4.31915	0.272081
$253$	29.4282	1.85013
$254$	−21.5905	−1.35471
$255$	−30.7958	−1.92851
$256$	1.00000	0.0625000
$257$	9.93685	0.619844	0.309922	−	0.950762i	$-0.399697\pi$
$257$	9.93685	0.619844	0.309922	+	0.950762i	$0.399697\pi$
$258$	3.09807	0.192878
$259$	43.2261	2.68594
$260$	4.06882	0.252337
$261$	6.61550	0.409489
$262$	−2.47190	−0.152715
$263$	−24.6988	−1.52299	−0.761497	−	0.648168i	$-0.775535\pi$
$263$	−24.6988	−1.52299	−0.761497	+	0.648168i	$0.775535\pi$
$264$	3.45943	0.212913
$265$	−23.4752	−1.44207
$266$	−7.98481	−0.489580
$267$	2.88091	0.176309
$268$	−14.3536	−0.876786
$269$	25.6107	1.56151	0.780756	−	0.624836i	$-0.214834\pi$
$269$	25.6107	1.56151	0.780756	+	0.624836i	$0.214834\pi$
$270$	4.06882	0.247620
$271$	−6.42255	−0.390142	−0.195071	−	0.980789i	$-0.562494\pi$
$271$	−6.42255	−0.390142	−0.195071	+	0.980789i	$0.562494\pi$
$272$	−7.56875	−0.458923
$273$	4.31915	0.261407
$274$	7.60382	0.459364
$275$	−39.9746	−2.41056
$276$	8.50665	0.512040
$277$	18.0070	1.08194	0.540969	−	0.841043i	$-0.318058\pi$
$277$	18.0070	1.08194	0.540969	+	0.841043i	$0.318058\pi$
$278$	−0.701284	−0.0420602
$279$	−5.55957	−0.332843
$280$	−17.5738	−1.05024
$281$	−12.7632	−0.761386	−0.380693	−	0.924701i	$-0.624315\pi$
$281$	−12.7632	−0.761386	−0.380693	+	0.924701i	$0.624315\pi$
$282$	1.17792	0.0701443
$283$	10.4087	0.618732	0.309366	−	0.950943i	$-0.399883\pi$
$283$	10.4087	0.618732	0.309366	+	0.950943i	$0.399883\pi$
$284$	4.40758	0.261542
$285$	−7.52201	−0.445565
$286$	3.45943	0.204560
$287$	3.00568	0.177420
$288$	1.00000	0.0589256
$289$	40.2859	2.36976
$290$	−26.9172	−1.58063
$291$	−4.85929	−0.284857
$292$	−8.29562	−0.485464
$293$	−13.9122	−0.812758	−0.406379	−	0.913705i	$-0.633209\pi$
$293$	−13.9122	−0.812758	−0.406379	+	0.913705i	$0.633209\pi$
$294$	−11.6551	−0.679739
$295$	−28.0123	−1.63094
$296$	10.0080	0.581703
$297$	3.45943	0.200737
$298$	18.0995	1.04847
$299$	8.50665	0.491952
$300$	−11.5553	−0.667143
$301$	−13.3811	−0.771271
$302$	16.5279	0.951076
$303$	−9.41575	−0.540921
$304$	−1.84870	−0.106030
$305$	−50.2580	−2.87776
$306$	−7.56875	−0.432676
$307$	7.65826	0.437080	0.218540	−	0.975828i	$-0.429871\pi$
$307$	7.65826	0.437080	0.218540	+	0.975828i	$0.429871\pi$
$308$	−14.9418	−0.851389
$309$	1.00000	0.0568880
$310$	22.6209	1.28478
$311$	8.22932	0.466642	0.233321	−	0.972400i	$-0.425041\pi$
$311$	8.22932	0.466642	0.233321	+	0.972400i	$0.425041\pi$
$312$	1.00000	0.0566139
$313$	0.937649	0.0529991	0.0264995	−	0.999649i	$-0.491564\pi$
$313$	0.937649	0.0529991	0.0264995	+	0.999649i	$0.491564\pi$
$314$	−8.57471	−0.483899
$315$	−17.5738	−0.990174
$316$	6.21617	0.349687
$317$	−13.7271	−0.770991	−0.385496	−	0.922710i	$-0.625969\pi$
$317$	−13.7271	−0.770991	−0.385496	+	0.922710i	$0.625969\pi$
$318$	−5.76954	−0.323540
$319$	−22.8859	−1.28136
$320$	−4.06882	−0.227454
$321$	−3.81409	−0.212882
$322$	−36.7415	−2.04752
$323$	13.9923	0.778553
$324$	1.00000	0.0555556
$325$	−11.5553	−0.640970
$326$	−9.70287	−0.537392
$327$	−18.7539	−1.03709
$328$	0.695896	0.0384244
$329$	−5.08763	−0.280490
$330$	−14.0758	−0.774847
$331$	33.3238	1.83164	0.915822	−	0.401585i	$-0.131540\pi$
$331$	33.3238	1.83164	0.915822	+	0.401585i	$0.131540\pi$
$332$	−11.6646	−0.640179
$333$	10.0080	0.548435
$334$	13.4484	0.735865
$335$	58.4022	3.19085
$336$	−4.31915	−0.235629
$337$	−11.5951	−0.631623	−0.315811	−	0.948822i	$-0.602277\pi$
$337$	−11.5951	−0.631623	−0.315811	+	0.948822i	$0.602277\pi$
$338$	1.00000	0.0543928
$339$	10.5876	0.575040
$340$	30.7958	1.67014
$341$	19.2330	1.04152
$342$	−1.84870	−0.0999661
$343$	20.1061	1.08563
$344$	−3.09807	−0.167037
$345$	−34.6120	−1.86345
$346$	0.334934	0.0180062
$347$	−11.6647	−0.626192	−0.313096	−	0.949721i	$-0.601366\pi$
$347$	−11.6647	−0.626192	−0.313096	+	0.949721i	$0.601366\pi$
$348$	−6.61550	−0.354628
$349$	9.80093	0.524632	0.262316	−	0.964982i	$-0.415514\pi$
$349$	9.80093	0.524632	0.262316	+	0.964982i	$0.415514\pi$
$350$	49.9089	2.66775
$351$	1.00000	0.0533761
$352$	−3.45943	−0.184388
$353$	6.38978	0.340094	0.170047	−	0.985436i	$-0.445608\pi$
$353$	6.38978	0.340094	0.170047	+	0.985436i	$0.445608\pi$
$354$	−6.88464	−0.365914
$355$	−17.9336	−0.951817
$356$	−2.88091	−0.152688
$357$	32.6906	1.73017
$358$	18.9801	1.00313
$359$	−14.0791	−0.743064	−0.371532	−	0.928420i	$-0.621167\pi$
$359$	−14.0791	−0.743064	−0.371532	+	0.928420i	$0.621167\pi$
$360$	−4.06882	−0.214445
$361$	−15.5823	−0.820122
$362$	−4.69449	−0.246737
$363$	−0.967666	−0.0507893
$364$	−4.31915	−0.226385
$365$	33.7533	1.76673
$366$	−12.3520	−0.645649
$367$	−25.9658	−1.35540	−0.677701	−	0.735338i	$-0.737023\pi$
$367$	−25.9658	−1.35540	−0.677701	+	0.735338i	$0.737023\pi$
$368$	−8.50665	−0.443440
$369$	0.695896	0.0362269
$370$	−40.7207	−2.11697
$371$	24.9195	1.29376
$372$	5.55957	0.288250
$373$	28.3171	1.46620	0.733101	−	0.680120i	$-0.238072\pi$
$373$	28.3171	1.46620	0.733101	+	0.680120i	$0.238072\pi$
$374$	26.1836	1.35392
$375$	26.6721	1.37734
$376$	−1.17792	−0.0607468
$377$	−6.61550	−0.340715
$378$	−4.31915	−0.222153
$379$	5.80714	0.298293	0.149146	−	0.988815i	$-0.452347\pi$
$379$	5.80714	0.298293	0.149146	+	0.988815i	$0.452347\pi$
$380$	7.52201	0.385871
$381$	21.5905	1.10611
$382$	12.4462	0.636805
$383$	22.5633	1.15293	0.576467	−	0.817121i	$-0.304431\pi$
$383$	22.5633	1.15293	0.576467	+	0.817121i	$0.304431\pi$
$384$	−1.00000	−0.0510310
$385$	60.7955	3.09843
$386$	2.02744	0.103194
$387$	−3.09807	−0.157484
$388$	4.85929	0.246693
$389$	23.6159	1.19737	0.598686	−	0.800984i	$-0.295690\pi$
$389$	23.6159	1.19737	0.598686	+	0.800984i	$0.295690\pi$
$390$	−4.06882	−0.206032
$391$	64.3847	3.25607
$392$	11.6551	0.588671
$393$	2.47190	0.124691
$394$	16.8314	0.847956
$395$	−25.2924	−1.27260
$396$	−3.45943	−0.173843
$397$	18.8538	0.946246	0.473123	−	0.880996i	$-0.343127\pi$
$397$	18.8538	0.946246	0.473123	+	0.880996i	$0.343127\pi$
$398$	−0.301529	−0.0151143
$399$	7.98481	0.399740
$400$	11.5553	0.577763
$401$	10.3423	0.516472	0.258236	−	0.966082i	$-0.416859\pi$
$401$	10.3423	0.516472	0.258236	+	0.966082i	$0.416859\pi$
$402$	14.3536	0.715893
$403$	5.55957	0.276942
$404$	9.41575	0.468451
$405$	−4.06882	−0.202181
$406$	28.5734	1.41807
$407$	−34.6220	−1.71615
$408$	7.56875	0.374709
$409$	−18.2409	−0.901956	−0.450978	−	0.892535i	$-0.648925\pi$
$409$	−18.2409	−0.901956	−0.450978	+	0.892535i	$0.648925\pi$
$410$	−2.83147	−0.139836
$411$	−7.60382	−0.375069
$412$	−1.00000	−0.0492665
$413$	29.7358	1.46320
$414$	−8.50665	−0.418079
$415$	47.4612	2.32978
$416$	−1.00000	−0.0490290
$417$	0.701284	0.0343420
$418$	6.39544	0.312811
$419$	−22.7734	−1.11255	−0.556277	−	0.830997i	$-0.687771\pi$
$419$	−22.7734	−1.11255	−0.556277	+	0.830997i	$0.687771\pi$
$420$	17.5738	0.857516
$421$	19.3529	0.943204	0.471602	−	0.881811i	$-0.343676\pi$
$421$	19.3529	0.943204	0.471602	+	0.881811i	$0.343676\pi$
$422$	−3.92060	−0.190852
$423$	−1.17792	−0.0572726
$424$	5.76954	0.280193
$425$	−87.4588	−4.24238
$426$	−4.40758	−0.213548
$427$	53.3501	2.58179
$428$	3.81409	0.184361
$429$	−3.45943	−0.167023
$430$	12.6055	0.607890
$431$	−23.1867	−1.11687	−0.558433	−	0.829550i	$-0.688597\pi$
$431$	−23.1867	−1.11687	−0.558433	+	0.829550i	$0.688597\pi$
$432$	−1.00000	−0.0481125
$433$	5.73037	0.275384	0.137692	−	0.990475i	$-0.456032\pi$
$433$	5.73037	0.275384	0.137692	+	0.990475i	$0.456032\pi$
$434$	−24.0126	−1.15264
$435$	26.9172	1.29058
$436$	18.7539	0.898149
$437$	15.7262	0.752287
$438$	8.29562	0.396380
$439$	−3.84780	−0.183645	−0.0918226	−	0.995775i	$-0.529269\pi$
$439$	−3.84780	−0.183645	−0.0918226	+	0.995775i	$0.529269\pi$
$440$	14.0758	0.671037
$441$	11.6551	0.555004
$442$	7.56875	0.360009
$443$	31.2358	1.48406	0.742029	−	0.670367i	$-0.233864\pi$
$443$	31.2358	1.48406	0.742029	+	0.670367i	$0.233864\pi$
$444$	−10.0080	−0.474959
$445$	11.7219	0.555670
$446$	13.3625	0.632733
$447$	−18.0995	−0.856075
$448$	4.31915	0.204061
$449$	3.02705	0.142855	0.0714277	−	0.997446i	$-0.477244\pi$
$449$	3.02705	0.142855	0.0714277	+	0.997446i	$0.477244\pi$
$450$	11.5553	0.544720
$451$	−2.40740	−0.113360
$452$	−10.5876	−0.497999
$453$	−16.5279	−0.776550
$454$	−1.25297	−0.0588046
$455$	17.5738	0.823874
$456$	1.84870	0.0865732
$457$	−38.0751	−1.78108	−0.890540	−	0.454905i	$-0.849673\pi$
$457$	−38.0751	−1.78108	−0.890540	+	0.454905i	$0.849673\pi$
$458$	8.24201	0.385124
$459$	7.56875	0.353279
$460$	34.6120	1.61379
$461$	−16.0253	−0.746373	−0.373186	−	0.927756i	$-0.621735\pi$
$461$	−16.0253	−0.746373	−0.373186	+	0.927756i	$0.621735\pi$
$462$	14.9418	0.695156
$463$	−7.54870	−0.350818	−0.175409	−	0.984496i	$-0.556125\pi$
$463$	−7.54870	−0.350818	−0.175409	+	0.984496i	$0.556125\pi$
$464$	6.61550	0.307117
$465$	−22.6209	−1.04902
$466$	12.8913	0.597178
$467$	−32.7890	−1.51729	−0.758646	−	0.651503i	$-0.774139\pi$
$467$	−32.7890	−1.51729	−0.758646	+	0.651503i	$0.774139\pi$
$468$	−1.00000	−0.0462250
$469$	−61.9954	−2.86268
$470$	4.79275	0.221073
$471$	8.57471	0.395102
$472$	6.88464	0.316891
$473$	10.7176	0.492794
$474$	−6.21617	−0.285518
$475$	−21.3622	−0.980164
$476$	−32.6906	−1.49837
$477$	5.76954	0.264169
$478$	20.1551	0.921874
$479$	38.4984	1.75904	0.879519	−	0.475863i	$-0.157864\pi$
$479$	38.4984	1.75904	0.879519	+	0.475863i	$0.157864\pi$
$480$	4.06882	0.185715
$481$	−10.0080	−0.456325
$482$	−2.43963	−0.111122
$483$	36.7415	1.67180
$484$	0.967666	0.0439848
$485$	−19.7716	−0.897781
$486$	−1.00000	−0.0453609
$487$	−6.04136	−0.273760	−0.136880	−	0.990588i	$-0.543707\pi$
$487$	−6.04136	−0.273760	−0.136880	+	0.990588i	$0.543707\pi$
$488$	12.3520	0.559148
$489$	9.70287	0.438779
$490$	−47.4224	−2.14233
$491$	26.8174	1.21025	0.605126	−	0.796130i	$-0.293123\pi$
$491$	26.8174	1.21025	0.605126	+	0.796130i	$0.293123\pi$
$492$	−0.695896	−0.0313734
$493$	−50.0710	−2.25509
$494$	1.84870	0.0831768
$495$	14.0758	0.632660
$496$	−5.55957	−0.249632
$497$	19.0370	0.853926
$498$	11.6646	0.522704
$499$	8.59968	0.384975	0.192487	−	0.981299i	$-0.438345\pi$
$499$	8.59968	0.384975	0.192487	+	0.981299i	$0.438345\pi$
$500$	−26.6721	−1.19281
$501$	−13.4484	−0.600832
$502$	−7.14154	−0.318743
$503$	31.4358	1.40165	0.700827	−	0.713331i	$-0.252814\pi$
$503$	31.4358	1.40165	0.700827	+	0.713331i	$0.252814\pi$
$504$	4.31915	0.192390
$505$	−38.3110	−1.70482
$506$	29.4282	1.30824
$507$	−1.00000	−0.0444116
$508$	−21.5905	−0.957923
$509$	31.8853	1.41329	0.706646	−	0.707567i	$-0.250207\pi$
$509$	31.8853	1.41329	0.706646	+	0.707567i	$0.250207\pi$
$510$	−30.7958	−1.36366
$511$	−35.8300	−1.58503
$512$	1.00000	0.0441942
$513$	1.84870	0.0816220
$514$	9.93685	0.438296
$515$	4.06882	0.179293
$516$	3.09807	0.136385
$517$	4.07494	0.179216
$518$	43.2261	1.89925
$519$	−0.334934	−0.0147020
$520$	4.06882	0.178429
$521$	−10.1483	−0.444606	−0.222303	−	0.974978i	$-0.571357\pi$
$521$	−10.1483	−0.444606	−0.222303	+	0.974978i	$0.571357\pi$
$522$	6.61550	0.289552
$523$	27.9932	1.22406	0.612028	−	0.790836i	$-0.290354\pi$
$523$	27.9932	1.22406	0.612028	+	0.790836i	$0.290354\pi$
$524$	−2.47190	−0.107985
$525$	−49.9089	−2.17820
$526$	−24.6988	−1.07692
$527$	42.0790	1.83299
$528$	3.45943	0.150552
$529$	49.3630	2.14622
$530$	−23.4752	−1.01970
$531$	6.88464	0.298768
$532$	−7.98481	−0.346185
$533$	−0.695896	−0.0301426
$534$	2.88091	0.124669
$535$	−15.5188	−0.670937
$536$	−14.3536	−0.619981
$537$	−18.9801	−0.819053
$538$	25.6107	1.10416
$539$	−40.3200	−1.73670
$540$	4.06882	0.175094
$541$	−31.0959	−1.33692	−0.668459	−	0.743749i	$-0.733046\pi$
$541$	−31.0959	−1.33692	−0.668459	+	0.743749i	$0.733046\pi$
$542$	−6.42255	−0.275872
$543$	4.69449	0.201460
$544$	−7.56875	−0.324507
$545$	−76.3062	−3.26860
$546$	4.31915	0.184843
$547$	−13.9231	−0.595311	−0.297655	−	0.954673i	$-0.596205\pi$
$547$	−13.9231	−0.595311	−0.297655	+	0.954673i	$0.596205\pi$
$548$	7.60382	0.324819
$549$	12.3520	0.527170
$550$	−39.9746	−1.70452
$551$	−12.2300	−0.521018
$552$	8.50665	0.362067
$553$	26.8486	1.14172
$554$	18.0070	0.765045
$555$	40.7207	1.72850
$556$	−0.701284	−0.0297410
$557$	40.1013	1.69915	0.849573	−	0.527471i	$-0.176860\pi$
$557$	40.1013	1.69915	0.849573	+	0.527471i	$0.176860\pi$
$558$	−5.55957	−0.235355
$559$	3.09807	0.131034
$560$	−17.5738	−0.742630
$561$	−26.1836	−1.10547
$562$	−12.7632	−0.538382
$563$	16.0210	0.675204	0.337602	−	0.941289i	$-0.390384\pi$
$563$	16.0210	0.675204	0.337602	+	0.941289i	$0.390384\pi$
$564$	1.17792	0.0495995
$565$	43.0790	1.81235
$566$	10.4087	0.437510
$567$	4.31915	0.181387
$568$	4.40758	0.184938
$569$	−0.0543899	−0.00228014	−0.00114007	−	0.999999i	$-0.500363\pi$
$569$	−0.0543899	−0.00228014	−0.00114007	+	0.999999i	$0.500363\pi$
$570$	−7.52201	−0.315062
$571$	3.23201	0.135256	0.0676278	−	0.997711i	$-0.478457\pi$
$571$	3.23201	0.135256	0.0676278	+	0.997711i	$0.478457\pi$
$572$	3.45943	0.144646
$573$	−12.4462	−0.519949
$574$	3.00568	0.125455
$575$	−98.2965	−4.09925
$576$	1.00000	0.0416667
$577$	−17.2957	−0.720029	−0.360015	−	0.932947i	$-0.617228\pi$
$577$	−17.2957	−0.720029	−0.360015	+	0.932947i	$0.617228\pi$
$578$	40.2859	1.67567
$579$	−2.02744	−0.0842577
$580$	−26.9172	−1.11768
$581$	−50.3813	−2.09017
$582$	−4.85929	−0.201424
$583$	−19.9593	−0.826630
$584$	−8.29562	−0.343275
$585$	4.06882	0.168225
$586$	−13.9122	−0.574707
$587$	−20.0181	−0.826237	−0.413119	−	0.910677i	$-0.635561\pi$
$587$	−20.0181	−0.826237	−0.413119	+	0.910677i	$0.635561\pi$
$588$	−11.6551	−0.480648
$589$	10.2780	0.423496
$590$	−28.0123	−1.15325
$591$	−16.8314	−0.692353
$592$	10.0080	0.411326
$593$	0.139648	0.00573467	0.00286733	−	0.999996i	$-0.499087\pi$
$593$	0.139648	0.00573467	0.00286733	+	0.999996i	$0.499087\pi$
$594$	3.45943	0.141942
$595$	133.012	5.45296
$596$	18.0995	0.741382
$597$	0.301529	0.0123408
$598$	8.50665	0.347863
$599$	−38.6375	−1.57869	−0.789343	−	0.613952i	$-0.789579\pi$
$599$	−38.6375	−1.57869	−0.789343	+	0.613952i	$0.789579\pi$
$600$	−11.5553	−0.471741
$601$	4.72512	0.192742	0.0963708	−	0.995346i	$-0.469277\pi$
$601$	4.72512	0.192742	0.0963708	+	0.995346i	$0.469277\pi$
$602$	−13.3811	−0.545371
$603$	−14.3536	−0.584524
$604$	16.5279	0.672512
$605$	−3.93725	−0.160072
$606$	−9.41575	−0.382489
$607$	13.3446	0.541639	0.270819	−	0.962630i	$-0.412705\pi$
$607$	13.3446	0.541639	0.270819	+	0.962630i	$0.412705\pi$
$608$	−1.84870	−0.0749746
$609$	−28.5734	−1.15785
$610$	−50.2580	−2.03489
$611$	1.17792	0.0476537
$612$	−7.56875	−0.305948
$613$	−20.0161	−0.808442	−0.404221	−	0.914661i	$-0.632457\pi$
$613$	−20.0161	−0.808442	−0.404221	+	0.914661i	$0.632457\pi$
$614$	7.65826	0.309062
$615$	2.83147	0.114176
$616$	−14.9418	−0.602023
$617$	−26.6433	−1.07262	−0.536309	−	0.844021i	$-0.680182\pi$
$617$	−26.6433	−1.07262	−0.536309	+	0.844021i	$0.680182\pi$
$618$	1.00000	0.0402259
$619$	35.7643	1.43749	0.718745	−	0.695274i	$-0.244717\pi$
$619$	35.7643	1.43749	0.718745	+	0.695274i	$0.244717\pi$
$620$	22.6209	0.908476
$621$	8.50665	0.341360
$622$	8.22932	0.329966
$623$	−12.4431	−0.498521
$624$	1.00000	0.0400320
$625$	50.7477	2.02991
$626$	0.937649	0.0374760
$627$	−6.39544	−0.255409
$628$	−8.57471	−0.342168
$629$	−75.7480	−3.02027
$630$	−17.5738	−0.700159
$631$	1.98763	0.0791262	0.0395631	−	0.999217i	$-0.487403\pi$
$631$	1.98763	0.0791262	0.0395631	+	0.999217i	$0.487403\pi$
$632$	6.21617	0.247266
$633$	3.92060	0.155830
$634$	−13.7271	−0.545173
$635$	87.8477	3.48613
$636$	−5.76954	−0.228777
$637$	−11.6551	−0.461792
$638$	−22.8859	−0.906060
$639$	4.40758	0.174361
$640$	−4.06882	−0.160834
$641$	25.8792	1.02217	0.511084	−	0.859531i	$-0.329244\pi$
$641$	25.8792	1.02217	0.511084	+	0.859531i	$0.329244\pi$
$642$	−3.81409	−0.150530
$643$	−14.3720	−0.566778	−0.283389	−	0.959005i	$-0.591459\pi$
$643$	−14.3720	−0.566778	−0.283389	+	0.959005i	$0.591459\pi$
$644$	−36.7415	−1.44782
$645$	−12.6055	−0.496340
$646$	13.9923	0.550520
$647$	42.4147	1.66749	0.833747	−	0.552147i	$-0.186191\pi$
$647$	42.4147	1.66749	0.833747	+	0.552147i	$0.186191\pi$
$648$	1.00000	0.0392837
$649$	−23.8169	−0.934896
$650$	−11.5553	−0.453235
$651$	24.0126	0.941130
$652$	−9.70287	−0.379994
$653$	−9.61493	−0.376261	−0.188131	−	0.982144i	$-0.560243\pi$
$653$	−9.61493	−0.376261	−0.188131	+	0.982144i	$0.560243\pi$
$654$	−18.7539	−0.733336
$655$	10.0577	0.392987
$656$	0.695896	0.0271702
$657$	−8.29562	−0.323643
$658$	−5.08763	−0.198337
$659$	0.623573	0.0242910	0.0121455	−	0.999926i	$-0.496134\pi$
$659$	0.623573	0.0242910	0.0121455	+	0.999926i	$0.496134\pi$
$660$	−14.0758	−0.547899
$661$	−7.46895	−0.290508	−0.145254	−	0.989394i	$-0.546400\pi$
$661$	−7.46895	−0.290508	−0.145254	+	0.989394i	$0.546400\pi$
$662$	33.3238	1.29517
$663$	−7.56875	−0.293946
$664$	−11.6646	−0.452675
$665$	32.4887	1.25986
$666$	10.0080	0.387802
$667$	−56.2757	−2.17900
$668$	13.4484	0.520335
$669$	−13.3625	−0.516624
$670$	58.4022	2.25627
$671$	−42.7309	−1.64961
$672$	−4.31915	−0.166615
$673$	45.3201	1.74696	0.873481	−	0.486858i	$-0.161857\pi$
$673$	45.3201	1.74696	0.873481	+	0.486858i	$0.161857\pi$
$674$	−11.5951	−0.446625
$675$	−11.5553	−0.444762
$676$	1.00000	0.0384615
$677$	41.0621	1.57814	0.789072	−	0.614301i	$-0.210562\pi$
$677$	41.0621	1.57814	0.789072	+	0.614301i	$0.210562\pi$
$678$	10.5876	0.406614
$679$	20.9880	0.805447
$680$	30.7958	1.18097
$681$	1.25297	0.0480138
$682$	19.2330	0.736468
$683$	−1.15076	−0.0440324	−0.0220162	−	0.999758i	$-0.507009\pi$
$683$	−1.15076	−0.0440324	−0.0220162	+	0.999758i	$0.507009\pi$
$684$	−1.84870	−0.0706867
$685$	−30.9385	−1.18210
$686$	20.1061	0.767653
$687$	−8.24201	−0.314452
$688$	−3.09807	−0.118113
$689$	−5.76954	−0.219802
$690$	−34.6120	−1.31766
$691$	28.6259	1.08898	0.544490	−	0.838767i	$-0.316723\pi$
$691$	28.6259	1.08898	0.544490	+	0.838767i	$0.316723\pi$
$692$	0.334934	0.0127323
$693$	−14.9418	−0.567593
$694$	−11.6647	−0.442785
$695$	2.85339	0.108235
$696$	−6.61550	−0.250760
$697$	−5.26706	−0.199504
$698$	9.80093	0.370971
$699$	−12.8913	−0.487594
$700$	49.9089	1.88638
$701$	−40.7619	−1.53955	−0.769777	−	0.638313i	$-0.779633\pi$
$701$	−40.7619	−1.53955	−0.769777	+	0.638313i	$0.779633\pi$
$702$	1.00000	0.0377426
$703$	−18.5018	−0.697807
$704$	−3.45943	−0.130382
$705$	−4.79275	−0.180505
$706$	6.38978	0.240482
$707$	40.6681	1.52948
$708$	−6.88464	−0.258740
$709$	−32.4818	−1.21988	−0.609940	−	0.792448i	$-0.708806\pi$
$709$	−32.4818	−1.21988	−0.609940	+	0.792448i	$0.708806\pi$
$710$	−17.9336	−0.673037
$711$	6.21617	0.233124
$712$	−2.88091	−0.107966
$713$	47.2933	1.77115
$714$	32.6906	1.22341
$715$	−14.0758	−0.526405
$716$	18.9801	0.709321
$717$	−20.1551	−0.752707
$718$	−14.0791	−0.525426
$719$	−36.3983	−1.35743	−0.678714	−	0.734403i	$-0.737462\pi$
$719$	−36.3983	−1.35743	−0.678714	+	0.734403i	$0.737462\pi$
$720$	−4.06882	−0.151636
$721$	−4.31915	−0.160854
$722$	−15.5823	−0.579914
$723$	2.43963	0.0907307
$724$	−4.69449	−0.174469
$725$	76.4438	2.83905
$726$	−0.967666	−0.0359134
$727$	−27.7079	−1.02763	−0.513814	−	0.857902i	$-0.671768\pi$
$727$	−27.7079	−1.02763	−0.513814	+	0.857902i	$0.671768\pi$
$728$	−4.31915	−0.160079
$729$	1.00000	0.0370370
$730$	33.7533	1.24927
$731$	23.4485	0.867275
$732$	−12.3520	−0.456543
$733$	31.1625	1.15101	0.575507	−	0.817797i	$-0.304805\pi$
$733$	31.1625	1.15101	0.575507	+	0.817797i	$0.304805\pi$
$734$	−25.9658	−0.958414
$735$	47.4224	1.74920
$736$	−8.50665	−0.313559
$737$	49.6553	1.82908
$738$	0.695896	0.0256163
$739$	−11.1385	−0.409736	−0.204868	−	0.978790i	$-0.565676\pi$
$739$	−11.1385	−0.409736	−0.204868	+	0.978790i	$0.565676\pi$
$740$	−40.7207	−1.49692
$741$	−1.84870	−0.0679136
$742$	24.9195	0.914824
$743$	−32.7056	−1.19985	−0.599925	−	0.800056i	$-0.704803\pi$
$743$	−32.7056	−1.19985	−0.599925	+	0.800056i	$0.704803\pi$
$744$	5.55957	0.203824
$745$	−73.6433	−2.69808
$746$	28.3171	1.03676
$747$	−11.6646	−0.426786
$748$	26.1836	0.957366
$749$	16.4736	0.601934
$750$	26.6721	0.973929
$751$	5.02809	0.183478	0.0917389	−	0.995783i	$-0.470757\pi$
$751$	5.02809	0.183478	0.0917389	+	0.995783i	$0.470757\pi$
$752$	−1.17792	−0.0429544
$753$	7.14154	0.260252
$754$	−6.61550	−0.240922
$755$	−67.2491	−2.44745
$756$	−4.31915	−0.157086
$757$	49.6215	1.80352	0.901762	−	0.432233i	$-0.142274\pi$
$757$	49.6215	1.80352	0.901762	+	0.432233i	$0.142274\pi$
$758$	5.80714	0.210925
$759$	−29.4282	−1.06817
$760$	7.52201	0.272852
$761$	53.9627	1.95615	0.978074	−	0.208258i	$-0.0667793\pi$
$761$	53.9627	1.95615	0.978074	+	0.208258i	$0.0667793\pi$
$762$	21.5905	0.782141
$763$	81.0010	2.93243
$764$	12.4462	0.450289
$765$	30.7958	1.11343
$766$	22.5633	0.815247
$767$	−6.88464	−0.248590
$768$	−1.00000	−0.0360844
$769$	−26.3748	−0.951098	−0.475549	−	0.879689i	$-0.657751\pi$
$769$	−26.3748	−0.951098	−0.475549	+	0.879689i	$0.657751\pi$
$770$	60.7955	2.19092
$771$	−9.93685	−0.357867
$772$	2.02744	0.0729693
$773$	−13.9060	−0.500165	−0.250083	−	0.968225i	$-0.580458\pi$
$773$	−13.9060	−0.500165	−0.250083	+	0.968225i	$0.580458\pi$
$774$	−3.09807	−0.111358
$775$	−64.2423	−2.30765
$776$	4.85929	0.174438
$777$	−43.2261	−1.55073
$778$	23.6159	0.846670
$779$	−1.28650	−0.0460937
$780$	−4.06882	−0.145687
$781$	−15.2477	−0.545606
$782$	64.3847	2.30239
$783$	−6.61550	−0.236419
$784$	11.6551	0.416253
$785$	34.8889	1.24524
$786$	2.47190	0.0881698
$787$	−29.1344	−1.03853	−0.519265	−	0.854613i	$-0.673794\pi$
$787$	−29.1344	−1.03853	−0.519265	+	0.854613i	$0.673794\pi$
$788$	16.8314	0.599595
$789$	24.6988	0.879301
$790$	−25.2924	−0.899864
$791$	−45.7295	−1.62595
$792$	−3.45943	−0.122926
$793$	−12.3520	−0.438632
$794$	18.8538	0.669097
$795$	23.4752	0.832579
$796$	−0.301529	−0.0106874
$797$	−0.139563	−0.00494358	−0.00247179	−	0.999997i	$-0.500787\pi$
$797$	−0.139563	−0.00494358	−0.00247179	+	0.999997i	$0.500787\pi$
$798$	7.98481	0.282659
$799$	8.91540	0.315404
$800$	11.5553	0.408540
$801$	−2.88091	−0.101792
$802$	10.3423	0.365201
$803$	28.6981	1.01273
$804$	14.3536	0.506213
$805$	149.494	5.26899
$806$	5.55957	0.195828
$807$	−25.6107	−0.901540
$808$	9.41575	0.331245
$809$	−32.0202	−1.12577	−0.562884	−	0.826536i	$-0.690308\pi$
$809$	−32.0202	−1.12577	−0.562884	+	0.826536i	$0.690308\pi$
$810$	−4.06882	−0.142964
$811$	−40.4544	−1.42055	−0.710273	−	0.703926i	$-0.751428\pi$
$811$	−40.4544	−1.42055	−0.710273	+	0.703926i	$0.751428\pi$
$812$	28.5734	1.00273
$813$	6.42255	0.225249
$814$	−34.6220	−1.21350
$815$	39.4792	1.38290
$816$	7.56875	0.264959
$817$	5.72740	0.200376
$818$	−18.2409	−0.637779
$819$	−4.31915	−0.150923
$820$	−2.83147	−0.0988793
$821$	−33.3453	−1.16376	−0.581880	−	0.813274i	$-0.697683\pi$
$821$	−33.3453	−1.16376	−0.581880	+	0.813274i	$0.697683\pi$
$822$	−7.60382	−0.265214
$823$	−49.9130	−1.73986	−0.869928	−	0.493179i	$-0.835835\pi$
$823$	−49.9130	−1.73986	−0.869928	+	0.493179i	$0.835835\pi$
$824$	−1.00000	−0.0348367
$825$	39.9746	1.39174
$826$	29.7358	1.03464
$827$	10.8878	0.378606	0.189303	−	0.981919i	$-0.439377\pi$
$827$	10.8878	0.378606	0.189303	+	0.981919i	$0.439377\pi$
$828$	−8.50665	−0.295626
$829$	32.1946	1.11817	0.559083	−	0.829112i	$-0.311153\pi$
$829$	32.1946	1.11817	0.559083	+	0.829112i	$0.311153\pi$
$830$	47.4612	1.64740
$831$	−18.0070	−0.624657
$832$	−1.00000	−0.0346688
$833$	−88.2144	−3.05645
$834$	0.701284	0.0242835
$835$	−54.7192	−1.89364
$836$	6.39544	0.221191
$837$	5.55957	0.192167
$838$	−22.7734	−0.786695
$839$	19.0612	0.658065	0.329033	−	0.944319i	$-0.393277\pi$
$839$	19.0612	0.658065	0.329033	+	0.944319i	$0.393277\pi$
$840$	17.5738	0.606355
$841$	14.7648	0.509131
$842$	19.3529	0.666946
$843$	12.7632	0.439587
$844$	−3.92060	−0.134953
$845$	−4.06882	−0.139972
$846$	−1.17792	−0.0404978
$847$	4.17950	0.143609
$848$	5.76954	0.198127
$849$	−10.4087	−0.357225
$850$	−87.4588	−2.99981
$851$	−85.1345	−2.91837
$852$	−4.40758	−0.151001
$853$	−6.03350	−0.206583	−0.103292	−	0.994651i	$-0.532937\pi$
$853$	−6.03350	−0.206583	−0.103292	+	0.994651i	$0.532937\pi$
$854$	53.3501	1.82560
$855$	7.52201	0.257247
$856$	3.81409	0.130363
$857$	39.3766	1.34508	0.672540	−	0.740061i	$-0.265203\pi$
$857$	39.3766	1.34508	0.672540	+	0.740061i	$0.265203\pi$
$858$	−3.45943	−0.118103
$859$	−37.2844	−1.27213	−0.636063	−	0.771637i	$-0.719438\pi$
$859$	−37.2844	−1.27213	−0.636063	+	0.771637i	$0.719438\pi$
$860$	12.6055	0.429843
$861$	−3.00568	−0.102433
$862$	−23.1867	−0.789743
$863$	−55.0793	−1.87492	−0.937461	−	0.348090i	$-0.886830\pi$
$863$	−55.0793	−1.87492	−0.937461	+	0.348090i	$0.886830\pi$
$864$	−1.00000	−0.0340207
$865$	−1.36278	−0.0463361
$866$	5.73037	0.194726
$867$	−40.2859	−1.36818
$868$	−24.0126	−0.815042
$869$	−21.5044	−0.729487
$870$	26.9172	0.912580
$871$	14.3536	0.486353
$872$	18.7539	0.635087
$873$	4.85929	0.164462
$874$	15.7262	0.531947
$875$	−115.201	−3.89451
$876$	8.29562	0.280283
$877$	−17.2810	−0.583539	−0.291769	−	0.956489i	$-0.594244\pi$
$877$	−17.2810	−0.583539	−0.291769	+	0.956489i	$0.594244\pi$
$878$	−3.84780	−0.129857
$879$	13.9122	0.469246
$880$	14.0758	0.474495
$881$	2.51424	0.0847068	0.0423534	−	0.999103i	$-0.486514\pi$
$881$	2.51424	0.0847068	0.0423534	+	0.999103i	$0.486514\pi$
$882$	11.6551	0.392447
$883$	−46.5170	−1.56542	−0.782711	−	0.622385i	$-0.786164\pi$
$883$	−46.5170	−1.56542	−0.782711	+	0.622385i	$0.786164\pi$
$884$	7.56875	0.254565
$885$	28.0123	0.941624
$886$	31.2358	1.04939
$887$	50.6035	1.69910	0.849550	−	0.527508i	$-0.176874\pi$
$887$	50.6035	1.69910	0.849550	+	0.527508i	$0.176874\pi$
$888$	−10.0080	−0.335846
$889$	−93.2526	−3.12759
$890$	11.7219	0.392918
$891$	−3.45943	−0.115895
$892$	13.3625	0.447410
$893$	2.17762	0.0728714
$894$	−18.0995	−0.605336
$895$	−77.2267	−2.58140
$896$	4.31915	0.144293
$897$	−8.50665	−0.284029
$898$	3.02705	0.101014
$899$	−36.7793	−1.22666
$900$	11.5553	0.385175
$901$	−43.6682	−1.45480
$902$	−2.40740	−0.0801578
$903$	13.3811	0.445293
$904$	−10.5876	−0.352138
$905$	19.1010	0.634939
$906$	−16.5279	−0.549104
$907$	−31.9748	−1.06171	−0.530853	−	0.847464i	$-0.678128\pi$
$907$	−31.9748	−1.06171	−0.530853	+	0.847464i	$0.678128\pi$
$908$	−1.25297	−0.0415811
$909$	9.41575	0.312301
$910$	17.5738	0.582567
$911$	39.0255	1.29297	0.646486	−	0.762926i	$-0.276238\pi$
$911$	39.0255	1.29297	0.646486	+	0.762926i	$0.276238\pi$
$912$	1.84870	0.0612165
$913$	40.3529	1.33549
$914$	−38.0751	−1.25941
$915$	50.2580	1.66148
$916$	8.24201	0.272324
$917$	−10.6765	−0.352570
$918$	7.56875	0.249806
$919$	31.8283	1.04992	0.524959	−	0.851127i	$-0.324081\pi$
$919$	31.8283	1.04992	0.524959	+	0.851127i	$0.324081\pi$
$920$	34.6120	1.14112
$921$	−7.65826	−0.252348
$922$	−16.0253	−0.527765
$923$	−4.40758	−0.145077
$924$	14.9418	0.491550
$925$	115.645	3.80238
$926$	−7.54870	−0.248066
$927$	−1.00000	−0.0328443
$928$	6.61550	0.217164
$929$	28.7737	0.944033	0.472017	−	0.881590i	$-0.343526\pi$
$929$	28.7737	0.944033	0.472017	+	0.881590i	$0.343526\pi$
$930$	−22.6209	−0.741767
$931$	−21.5467	−0.706166
$932$	12.8913	0.422269
$933$	−8.22932	−0.269416
$934$	−32.7890	−1.07289
$935$	−106.536	−3.48410
$936$	−1.00000	−0.0326860
$937$	−52.1487	−1.70362	−0.851812	−	0.523847i	$-0.824496\pi$
$937$	−52.1487	−1.70362	−0.851812	+	0.523847i	$0.824496\pi$
$938$	−61.9954	−2.02422
$939$	−0.937649	−0.0305990
$940$	4.79275	0.156322
$941$	−46.7160	−1.52290	−0.761449	−	0.648225i	$-0.775512\pi$
$941$	−46.7160	−1.52290	−0.761449	+	0.648225i	$0.775512\pi$
$942$	8.57471	0.279379
$943$	−5.91974	−0.192773
$944$	6.88464	0.224076
$945$	17.5738	0.571677
$946$	10.7176	0.348458
$947$	60.8358	1.97690	0.988450	−	0.151549i	$-0.0484263\pi$
$947$	60.8358	1.97690	0.988450	+	0.151549i	$0.0484263\pi$
$948$	−6.21617	−0.201892
$949$	8.29562	0.269287
$950$	−21.3622	−0.693080
$951$	13.7271	0.445132
$952$	−32.6906	−1.05951
$953$	18.6575	0.604375	0.302187	−	0.953249i	$-0.402283\pi$
$953$	18.6575	0.604375	0.302187	+	0.953249i	$0.402283\pi$
$954$	5.76954	0.186796
$955$	−50.6415	−1.63872
$956$	20.1551	0.651864
$957$	22.8859	0.739795
$958$	38.4984	1.24383
$959$	32.8421	1.06053
$960$	4.06882	0.131320
$961$	−0.0911780	−0.00294123
$962$	−10.0080	−0.322671
$963$	3.81409	0.122907
$964$	−2.43963	−0.0785751
$965$	−8.24930	−0.265554
$966$	36.7415	1.18214
$967$	22.4665	0.722474	0.361237	−	0.932474i	$-0.382355\pi$
$967$	22.4665	0.722474	0.361237	+	0.932474i	$0.382355\pi$
$968$	0.967666	0.0311020
$969$	−13.9923	−0.449498
$970$	−19.7716	−0.634827
$971$	−60.8053	−1.95133	−0.975667	−	0.219258i	$-0.929636\pi$
$971$	−60.8053	−1.95133	−0.975667	+	0.219258i	$0.929636\pi$
$972$	−1.00000	−0.0320750
$973$	−3.02895	−0.0971037
$974$	−6.04136	−0.193578
$975$	11.5553	0.370064
$976$	12.3520	0.395378
$977$	−18.3313	−0.586471	−0.293235	−	0.956040i	$-0.594732\pi$
$977$	−18.3313	−0.586471	−0.293235	+	0.956040i	$0.594732\pi$
$978$	9.70287	0.310263
$979$	9.96629	0.318524
$980$	−47.4224	−1.51485
$981$	18.7539	0.598766
$982$	26.8174	0.855778
$983$	18.8713	0.601902	0.300951	−	0.953640i	$-0.402696\pi$
$983$	18.8713	0.601902	0.300951	+	0.953640i	$0.402696\pi$
$984$	−0.695896	−0.0221843
$985$	−68.4840	−2.18208
$986$	−50.0710	−1.59459
$987$	5.08763	0.161941
$988$	1.84870	0.0588149
$989$	26.3542	0.838015
$990$	14.0758	0.447358
$991$	43.5025	1.38190	0.690951	−	0.722902i	$-0.257192\pi$
$991$	43.5025	1.38190	0.690951	+	0.722902i	$0.257192\pi$
$992$	−5.55957	−0.176517
$993$	−33.3238	−1.05750
$994$	19.0370	0.603817
$995$	1.22687	0.0388943
$996$	11.6646	0.369608
$997$	−46.1647	−1.46205	−0.731025	−	0.682351i	$-0.760958\pi$
$997$	−46.1647	−1.46205	−0.731025	+	0.682351i	$0.760958\pi$
$998$	8.59968	0.272218
$999$	−10.0080	−0.316639

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.bc.1.1	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.bc.1.1	✓	15	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:	\( N \)	\(=\)	\( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.06882 q^{5} -1.00000 q^{6} +4.31915 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.06882 q^{5} -1.00000 q^{6} +4.31915 q^{7} +1.00000 q^{8} +1.00000 q^{9} -4.06882 q^{10} -3.45943 q^{11} -1.00000 q^{12} -1.00000 q^{13} +4.31915 q^{14} +4.06882 q^{15} +1.00000 q^{16} -7.56875 q^{17} +1.00000 q^{18} -1.84870 q^{19} -4.06882 q^{20} -4.31915 q^{21} -3.45943 q^{22} -8.50665 q^{23} -1.00000 q^{24} +11.5553 q^{25} -1.00000 q^{26} -1.00000 q^{27} +4.31915 q^{28} +6.61550 q^{29} +4.06882 q^{30} -5.55957 q^{31} +1.00000 q^{32} +3.45943 q^{33} -7.56875 q^{34} -17.5738 q^{35} +1.00000 q^{36} +10.0080 q^{37} -1.84870 q^{38} +1.00000 q^{39} -4.06882 q^{40} +0.695896 q^{41} -4.31915 q^{42} -3.09807 q^{43} -3.45943 q^{44} -4.06882 q^{45} -8.50665 q^{46} -1.17792 q^{47} -1.00000 q^{48} +11.6551 q^{49} +11.5553 q^{50} +7.56875 q^{51} -1.00000 q^{52} +5.76954 q^{53} -1.00000 q^{54} +14.0758 q^{55} +4.31915 q^{56} +1.84870 q^{57} +6.61550 q^{58} +6.88464 q^{59} +4.06882 q^{60} +12.3520 q^{61} -5.55957 q^{62} +4.31915 q^{63} +1.00000 q^{64} +4.06882 q^{65} +3.45943 q^{66} -14.3536 q^{67} -7.56875 q^{68} +8.50665 q^{69} -17.5738 q^{70} +4.40758 q^{71} +1.00000 q^{72} -8.29562 q^{73} +10.0080 q^{74} -11.5553 q^{75} -1.84870 q^{76} -14.9418 q^{77} +1.00000 q^{78} +6.21617 q^{79} -4.06882 q^{80} +1.00000 q^{81} +0.695896 q^{82} -11.6646 q^{83} -4.31915 q^{84} +30.7958 q^{85} -3.09807 q^{86} -6.61550 q^{87} -3.45943 q^{88} -2.88091 q^{89} -4.06882 q^{90} -4.31915 q^{91} -8.50665 q^{92} +5.55957 q^{93} -1.17792 q^{94} +7.52201 q^{95} -1.00000 q^{96} +4.85929 q^{97} +11.6551 q^{98} -3.45943 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 15 q^{2} - 15 q^{3} + 15 q^{4} - q^{5} - 15 q^{6} + 5 q^{7} + 15 q^{8} + 15 q^{9}+O(q^{10}) \) 15 * q + 15 * q^2 - 15 * q^3 + 15 * q^4 - q^5 - 15 * q^6 + 5 * q^7 + 15 * q^8 + 15 * q^9	\( 15 q + 15 q^{2} - 15 q^{3} + 15 q^{4} - q^{5} - 15 q^{6} + 5 q^{7} + 15 q^{8} + 15 q^{9} - q^{10} + 3 q^{11} - 15 q^{12} - 15 q^{13} + 5 q^{14} + q^{15} + 15 q^{16} - 2 q^{17} + 15 q^{18} + 8 q^{19} - q^{20} - 5 q^{21} + 3 q^{22} + 3 q^{23} - 15 q^{24} + 22 q^{25} - 15 q^{26} - 15 q^{27} + 5 q^{28} + 26 q^{29} + q^{30} + 15 q^{32} - 3 q^{33} - 2 q^{34} - 8 q^{35} + 15 q^{36} + 25 q^{37} + 8 q^{38} + 15 q^{39} - q^{40} - q^{41} - 5 q^{42} + 10 q^{43} + 3 q^{44} - q^{45} + 3 q^{46} - 3 q^{47} - 15 q^{48} + 32 q^{49} + 22 q^{50} + 2 q^{51} - 15 q^{52} + 13 q^{53} - 15 q^{54} - 2 q^{55} + 5 q^{56} - 8 q^{57} + 26 q^{58} + 28 q^{59} + q^{60} + 22 q^{61} + 5 q^{63} + 15 q^{64} + q^{65} - 3 q^{66} + 29 q^{67} - 2 q^{68} - 3 q^{69} - 8 q^{70} + 18 q^{71} + 15 q^{72} + 23 q^{73} + 25 q^{74} - 22 q^{75} + 8 q^{76} + 17 q^{77} + 15 q^{78} + 27 q^{79} - q^{80} + 15 q^{81} - q^{82} + 7 q^{83} - 5 q^{84} + 43 q^{85} + 10 q^{86} - 26 q^{87} + 3 q^{88} + 35 q^{89} - q^{90} - 5 q^{91} + 3 q^{92} - 3 q^{94} + 6 q^{95} - 15 q^{96} + 19 q^{97} + 32 q^{98} + 3 q^{99}+O(q^{100}) \) 15 * q + 15 * q^2 - 15 * q^3 + 15 * q^4 - q^5 - 15 * q^6 + 5 * q^7 + 15 * q^8 + 15 * q^9 - q^10 + 3 * q^11 - 15 * q^12 - 15 * q^13 + 5 * q^14 + q^15 + 15 * q^16 - 2 * q^17 + 15 * q^18 + 8 * q^19 - q^20 - 5 * q^21 + 3 * q^22 + 3 * q^23 - 15 * q^24 + 22 * q^25 - 15 * q^26 - 15 * q^27 + 5 * q^28 + 26 * q^29 + q^30 + 15 * q^32 - 3 * q^33 - 2 * q^34 - 8 * q^35 + 15 * q^36 + 25 * q^37 + 8 * q^38 + 15 * q^39 - q^40 - q^41 - 5 * q^42 + 10 * q^43 + 3 * q^44 - q^45 + 3 * q^46 - 3 * q^47 - 15 * q^48 + 32 * q^49 + 22 * q^50 + 2 * q^51 - 15 * q^52 + 13 * q^53 - 15 * q^54 - 2 * q^55 + 5 * q^56 - 8 * q^57 + 26 * q^58 + 28 * q^59 + q^60 + 22 * q^61 + 5 * q^63 + 15 * q^64 + q^65 - 3 * q^66 + 29 * q^67 - 2 * q^68 - 3 * q^69 - 8 * q^70 + 18 * q^71 + 15 * q^72 + 23 * q^73 + 25 * q^74 - 22 * q^75 + 8 * q^76 + 17 * q^77 + 15 * q^78 + 27 * q^79 - q^80 + 15 * q^81 - q^82 + 7 * q^83 - 5 * q^84 + 43 * q^85 + 10 * q^86 - 26 * q^87 + 3 * q^88 + 35 * q^89 - q^90 - 5 * q^91 + 3 * q^92 - 3 * q^94 + 6 * q^95 - 15 * q^96 + 19 * q^97 + 32 * q^98 + 3 * q^99

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