LMFDB - Embedded newform 8034.2.a.w.1.11

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:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} - 8 x^{10} + 94 x^{9} - 7 x^{8} - 580 x^{7} + 180 x^{6} + 1787 x^{5} - 308 x^{4} + \cdots + 768 $ x^12 - 6x^11 - 8x^10 + 94x^9 - 7x^8 - 580x^7 + 180x^6 + 1787x^5 - 308x^4 - 2790x^3 - 352x^2 + 1768*x + 768
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$2.65870$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.30797 q^{5} -1.00000 q^{6} +4.49849 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.30797 q^{5} -1.00000 q^{6} +4.49849 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.30797 q^{10} -3.07064 q^{11} +1.00000 q^{12} +1.00000 q^{13} -4.49849 q^{14} +2.30797 q^{15} +1.00000 q^{16} -6.42341 q^{17} -1.00000 q^{18} -7.58167 q^{19} +2.30797 q^{20} +4.49849 q^{21} +3.07064 q^{22} -9.27355 q^{23} -1.00000 q^{24} +0.326720 q^{25} -1.00000 q^{26} +1.00000 q^{27} +4.49849 q^{28} -3.29159 q^{29} -2.30797 q^{30} -5.32783 q^{31} -1.00000 q^{32} -3.07064 q^{33} +6.42341 q^{34} +10.3824 q^{35} +1.00000 q^{36} +2.93933 q^{37} +7.58167 q^{38} +1.00000 q^{39} -2.30797 q^{40} +7.89321 q^{41} -4.49849 q^{42} -0.660219 q^{43} -3.07064 q^{44} +2.30797 q^{45} +9.27355 q^{46} -10.3443 q^{47} +1.00000 q^{48} +13.2364 q^{49} -0.326720 q^{50} -6.42341 q^{51} +1.00000 q^{52} +3.71472 q^{53} -1.00000 q^{54} -7.08695 q^{55} -4.49849 q^{56} -7.58167 q^{57} +3.29159 q^{58} -8.12616 q^{59} +2.30797 q^{60} +4.61685 q^{61} +5.32783 q^{62} +4.49849 q^{63} +1.00000 q^{64} +2.30797 q^{65} +3.07064 q^{66} -6.12513 q^{67} -6.42341 q^{68} -9.27355 q^{69} -10.3824 q^{70} -8.35045 q^{71} -1.00000 q^{72} +16.0060 q^{73} -2.93933 q^{74} +0.326720 q^{75} -7.58167 q^{76} -13.8133 q^{77} -1.00000 q^{78} -14.8666 q^{79} +2.30797 q^{80} +1.00000 q^{81} -7.89321 q^{82} -12.9601 q^{83} +4.49849 q^{84} -14.8250 q^{85} +0.660219 q^{86} -3.29159 q^{87} +3.07064 q^{88} +1.15775 q^{89} -2.30797 q^{90} +4.49849 q^{91} -9.27355 q^{92} -5.32783 q^{93} +10.3443 q^{94} -17.4983 q^{95} -1.00000 q^{96} +5.29299 q^{97} -13.2364 q^{98} -3.07064 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} + 12 q^{3} + 12 q^{4} - 4 q^{5} - 12 q^{6} - 12 q^{8} + 12 q^{9}+O(q^{10}) $ 12 * q - 12 * q^2 + 12 * q^3 + 12 * q^4 - 4 * q^5 - 12 * q^6 - 12 * q^8 + 12 * q^9	\( 12 q - 12 q^{2} + 12 q^{3} + 12 q^{4} - 4 q^{5} - 12 q^{6} - 12 q^{8} + 12 q^{9} + 4 q^{10} - 9 q^{11} + 12 q^{12} + 12 q^{13} - 4 q^{15} + 12 q^{16} - 20 q^{17} - 12 q^{18} + 4 q^{19} - 4 q^{20} + 9 q^{22} - 30 q^{23} - 12 q^{24} + 14 q^{25} - 12 q^{26} + 12 q^{27} - 29 q^{29} + 4 q^{30} + 6 q^{31} - 12 q^{32} - 9 q^{33} + 20 q^{34} - 22 q^{35} + 12 q^{36} + 7 q^{37} - 4 q^{38} + 12 q^{39} + 4 q^{40} - 8 q^{41} - 8 q^{43} - 9 q^{44} - 4 q^{45} + 30 q^{46} - 16 q^{47} + 12 q^{48} + 10 q^{49} - 14 q^{50} - 20 q^{51} + 12 q^{52} - 9 q^{53} - 12 q^{54} - 20 q^{55} + 4 q^{57} + 29 q^{58} - 29 q^{59} - 4 q^{60} - 26 q^{61} - 6 q^{62} + 12 q^{64} - 4 q^{65} + 9 q^{66} + 12 q^{67} - 20 q^{68} - 30 q^{69} + 22 q^{70} - 35 q^{71} - 12 q^{72} + 18 q^{73} - 7 q^{74} + 14 q^{75} + 4 q^{76} - 25 q^{77} - 12 q^{78} - 37 q^{79} - 4 q^{80} + 12 q^{81} + 8 q^{82} - 24 q^{83} - 17 q^{85} + 8 q^{86} - 29 q^{87} + 9 q^{88} + 15 q^{89} + 4 q^{90} - 30 q^{92} + 6 q^{93} + 16 q^{94} - 54 q^{95} - 12 q^{96} - 11 q^{97} - 10 q^{98} - 9 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 12 * q^3 + 12 * q^4 - 4 * q^5 - 12 * q^6 - 12 * q^8 + 12 * q^9 + 4 * q^10 - 9 * q^11 + 12 * q^12 + 12 * q^13 - 4 * q^15 + 12 * q^16 - 20 * q^17 - 12 * q^18 + 4 * q^19 - 4 * q^20 + 9 * q^22 - 30 * q^23 - 12 * q^24 + 14 * q^25 - 12 * q^26 + 12 * q^27 - 29 * q^29 + 4 * q^30 + 6 * q^31 - 12 * q^32 - 9 * q^33 + 20 * q^34 - 22 * q^35 + 12 * q^36 + 7 * q^37 - 4 * q^38 + 12 * q^39 + 4 * q^40 - 8 * q^41 - 8 * q^43 - 9 * q^44 - 4 * q^45 + 30 * q^46 - 16 * q^47 + 12 * q^48 + 10 * q^49 - 14 * q^50 - 20 * q^51 + 12 * q^52 - 9 * q^53 - 12 * q^54 - 20 * q^55 + 4 * q^57 + 29 * q^58 - 29 * q^59 - 4 * q^60 - 26 * q^61 - 6 * q^62 + 12 * q^64 - 4 * q^65 + 9 * q^66 + 12 * q^67 - 20 * q^68 - 30 * q^69 + 22 * q^70 - 35 * q^71 - 12 * q^72 + 18 * q^73 - 7 * q^74 + 14 * q^75 + 4 * q^76 - 25 * q^77 - 12 * q^78 - 37 * q^79 - 4 * q^80 + 12 * q^81 + 8 * q^82 - 24 * q^83 - 17 * q^85 + 8 * q^86 - 29 * q^87 + 9 * q^88 + 15 * q^89 + 4 * q^90 - 30 * q^92 + 6 * q^93 + 16 * q^94 - 54 * q^95 - 12 * q^96 - 11 * q^97 - 10 * 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
$5$	2.30797	1.03216	0.516078	−	0.856542i	$-0.327392\pi$
$5$	2.30797	1.03216	0.516078	+	0.856542i	$0.327392\pi$
$6$	−1.00000	−0.408248
$7$	4.49849	1.70027	0.850134	−	0.526566i	$-0.176521\pi$
$7$	4.49849	1.70027	0.850134	+	0.526566i	$0.176521\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−2.30797	−0.729844
$11$	−3.07064	−0.925834	−0.462917	−	0.886402i	$-0.653197\pi$
$11$	−3.07064	−0.925834	−0.462917	+	0.886402i	$0.653197\pi$
$12$	1.00000	0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−4.49849	−1.20227
$15$	2.30797	0.595915
$16$	1.00000	0.250000
$17$	−6.42341	−1.55791	−0.778953	−	0.627083i	$-0.784249\pi$
$17$	−6.42341	−1.55791	−0.778953	+	0.627083i	$0.784249\pi$
$18$	−1.00000	−0.235702
$19$	−7.58167	−1.73935	−0.869677	−	0.493621i	$-0.835673\pi$
$19$	−7.58167	−1.73935	−0.869677	+	0.493621i	$0.835673\pi$
$20$	2.30797	0.516078
$21$	4.49849	0.981650
$22$	3.07064	0.654664
$23$	−9.27355	−1.93367	−0.966835	−	0.255403i	$-0.917792\pi$
$23$	−9.27355	−1.93367	−0.966835	+	0.255403i	$0.917792\pi$
$24$	−1.00000	−0.204124
$25$	0.326720	0.0653440
$26$	−1.00000	−0.196116
$27$	1.00000	0.192450
$28$	4.49849	0.850134
$29$	−3.29159	−0.611233	−0.305616	−	0.952155i	$-0.598863\pi$
$29$	−3.29159	−0.611233	−0.305616	+	0.952155i	$0.598863\pi$
$30$	−2.30797	−0.421376
$31$	−5.32783	−0.956906	−0.478453	−	0.878113i	$-0.658802\pi$
$31$	−5.32783	−0.956906	−0.478453	+	0.878113i	$0.658802\pi$
$32$	−1.00000	−0.176777
$33$	−3.07064	−0.534531
$34$	6.42341	1.10161
$35$	10.3824	1.75494
$36$	1.00000	0.166667
$37$	2.93933	0.483223	0.241611	−	0.970373i	$-0.422324\pi$
$37$	2.93933	0.483223	0.241611	+	0.970373i	$0.422324\pi$
$38$	7.58167	1.22991
$39$	1.00000	0.160128
$40$	−2.30797	−0.364922
$41$	7.89321	1.23271	0.616356	−	0.787468i	$-0.288608\pi$
$41$	7.89321	1.23271	0.616356	+	0.787468i	$0.288608\pi$
$42$	−4.49849	−0.694131
$43$	−0.660219	−0.100683	−0.0503413	−	0.998732i	$-0.516031\pi$
$43$	−0.660219	−0.100683	−0.0503413	+	0.998732i	$0.516031\pi$
$44$	−3.07064	−0.462917
$45$	2.30797	0.344052
$46$	9.27355	1.36731
$47$	−10.3443	−1.50888	−0.754439	−	0.656371i	$-0.772091\pi$
$47$	−10.3443	−1.50888	−0.754439	+	0.656371i	$0.772091\pi$
$48$	1.00000	0.144338
$49$	13.2364	1.89091
$50$	−0.326720	−0.0462052
$51$	−6.42341	−0.899457
$52$	1.00000	0.138675
$53$	3.71472	0.510256	0.255128	−	0.966907i	$-0.417882\pi$
$53$	3.71472	0.510256	0.255128	+	0.966907i	$0.417882\pi$
$54$	−1.00000	−0.136083
$55$	−7.08695	−0.955604
$56$	−4.49849	−0.601136
$57$	−7.58167	−1.00422
$58$	3.29159	0.432207
$59$	−8.12616	−1.05794	−0.528968	−	0.848642i	$-0.677421\pi$
$59$	−8.12616	−1.05794	−0.528968	+	0.848642i	$0.677421\pi$
$60$	2.30797	0.297957
$61$	4.61685	0.591127	0.295563	−	0.955323i	$-0.404493\pi$
$61$	4.61685	0.591127	0.295563	+	0.955323i	$0.404493\pi$
$62$	5.32783	0.676635
$63$	4.49849	0.566756
$64$	1.00000	0.125000
$65$	2.30797	0.286268
$66$	3.07064	0.377970
$67$	−6.12513	−0.748304	−0.374152	−	0.927367i	$-0.622066\pi$
$67$	−6.12513	−0.748304	−0.374152	+	0.927367i	$0.622066\pi$
$68$	−6.42341	−0.778953
$69$	−9.27355	−1.11640
$70$	−10.3824	−1.24093
$71$	−8.35045	−0.991016	−0.495508	−	0.868603i	$-0.665018\pi$
$71$	−8.35045	−0.991016	−0.495508	+	0.868603i	$0.665018\pi$
$72$	−1.00000	−0.117851
$73$	16.0060	1.87337	0.936683	−	0.350179i	$-0.113879\pi$
$73$	16.0060	1.87337	0.936683	+	0.350179i	$0.113879\pi$
$74$	−2.93933	−0.341690
$75$	0.326720	0.0377264
$76$	−7.58167	−0.869677
$77$	−13.8133	−1.57417
$78$	−1.00000	−0.113228
$79$	−14.8666	−1.67263	−0.836313	−	0.548253i	$-0.815293\pi$
$79$	−14.8666	−1.67263	−0.836313	+	0.548253i	$0.815293\pi$
$80$	2.30797	0.258039
$81$	1.00000	0.111111
$82$	−7.89321	−0.871659
$83$	−12.9601	−1.42255	−0.711276	−	0.702913i	$-0.751883\pi$
$83$	−12.9601	−1.42255	−0.711276	+	0.702913i	$0.751883\pi$
$84$	4.49849	0.490825
$85$	−14.8250	−1.60800
$86$	0.660219	0.0711933
$87$	−3.29159	−0.352895
$88$	3.07064	0.327332
$89$	1.15775	0.122721	0.0613607	−	0.998116i	$-0.480456\pi$
$89$	1.15775	0.122721	0.0613607	+	0.998116i	$0.480456\pi$
$90$	−2.30797	−0.243281
$91$	4.49849	0.471569
$92$	−9.27355	−0.966835
$93$	−5.32783	−0.552470
$94$	10.3443	1.06694
$95$	−17.4983	−1.79528
$96$	−1.00000	−0.102062
$97$	5.29299	0.537421	0.268711	−	0.963221i	$-0.413402\pi$
$97$	5.29299	0.537421	0.268711	+	0.963221i	$0.413402\pi$
$98$	−13.2364	−1.33708
$99$	−3.07064	−0.308611
$100$	0.326720	0.0326720
$101$	2.72101	0.270751	0.135375	−	0.990794i	$-0.456776\pi$
$101$	2.72101	0.270751	0.135375	+	0.990794i	$0.456776\pi$
$102$	6.42341	0.636012
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−1.00000	−0.0980581
$105$	10.3824	1.01322
$106$	−3.71472	−0.360806
$107$	3.60502	0.348511	0.174255	−	0.984700i	$-0.444248\pi$
$107$	3.60502	0.348511	0.174255	+	0.984700i	$0.444248\pi$
$108$	1.00000	0.0962250
$109$	−12.4950	−1.19680	−0.598401	−	0.801196i	$-0.704197\pi$
$109$	−12.4950	−1.19680	−0.598401	+	0.801196i	$0.704197\pi$
$110$	7.08695	0.675714
$111$	2.93933	0.278989
$112$	4.49849	0.425067
$113$	−2.67954	−0.252070	−0.126035	−	0.992026i	$-0.540225\pi$
$113$	−2.67954	−0.252070	−0.126035	+	0.992026i	$0.540225\pi$
$114$	7.58167	0.710089
$115$	−21.4031	−1.99585
$116$	−3.29159	−0.305616
$117$	1.00000	0.0924500
$118$	8.12616	0.748074
$119$	−28.8956	−2.64886
$120$	−2.30797	−0.210688
$121$	−1.57114	−0.142831
$122$	−4.61685	−0.417990
$123$	7.89321	0.711707
$124$	−5.32783	−0.478453
$125$	−10.7858	−0.964710
$126$	−4.49849	−0.400757
$127$	−12.4620	−1.10582	−0.552911	−	0.833240i	$-0.686483\pi$
$127$	−12.4620	−1.10582	−0.552911	+	0.833240i	$0.686483\pi$
$128$	−1.00000	−0.0883883
$129$	−0.660219	−0.0581291
$130$	−2.30797	−0.202422
$131$	16.5343	1.44461	0.722306	−	0.691574i	$-0.243082\pi$
$131$	16.5343	1.44461	0.722306	+	0.691574i	$0.243082\pi$
$132$	−3.07064	−0.267265
$133$	−34.1060	−2.95737
$134$	6.12513	0.529131
$135$	2.30797	0.198638
$136$	6.42341	0.550803
$137$	13.6535	1.16650	0.583248	−	0.812294i	$-0.301782\pi$
$137$	13.6535	1.16650	0.583248	+	0.812294i	$0.301782\pi$
$138$	9.27355	0.789417
$139$	−7.77347	−0.659337	−0.329669	−	0.944097i	$-0.606937\pi$
$139$	−7.77347	−0.659337	−0.329669	+	0.944097i	$0.606937\pi$
$140$	10.3824	0.877470
$141$	−10.3443	−0.871151
$142$	8.35045	0.700754
$143$	−3.07064	−0.256780
$144$	1.00000	0.0833333
$145$	−7.59689	−0.630887
$146$	−16.0060	−1.32467
$147$	13.2364	1.09172
$148$	2.93933	0.241611
$149$	−4.13520	−0.338768	−0.169384	−	0.985550i	$-0.554178\pi$
$149$	−4.13520	−0.338768	−0.169384	+	0.985550i	$0.554178\pi$
$150$	−0.326720	−0.0266766
$151$	16.9804	1.38184	0.690922	−	0.722930i	$-0.257205\pi$
$151$	16.9804	1.38184	0.690922	+	0.722930i	$0.257205\pi$
$152$	7.58167	0.614955
$153$	−6.42341	−0.519302
$154$	13.8133	1.11310
$155$	−12.2965	−0.987676
$156$	1.00000	0.0800641
$157$	11.2088	0.894562	0.447281	−	0.894393i	$-0.352392\pi$
$157$	11.2088	0.894562	0.447281	+	0.894393i	$0.352392\pi$
$158$	14.8666	1.18272
$159$	3.71472	0.294597
$160$	−2.30797	−0.182461
$161$	−41.7170	−3.28776
$162$	−1.00000	−0.0785674
$163$	16.1485	1.26485	0.632425	−	0.774622i	$-0.282060\pi$
$163$	16.1485	1.26485	0.632425	+	0.774622i	$0.282060\pi$
$164$	7.89321	0.616356
$165$	−7.08695	−0.551718
$166$	12.9601	1.00590
$167$	−13.4298	−1.03923	−0.519614	−	0.854401i	$-0.673924\pi$
$167$	−13.4298	−1.03923	−0.519614	+	0.854401i	$0.673924\pi$
$168$	−4.49849	−0.347066
$169$	1.00000	0.0769231
$170$	14.8250	1.13703
$171$	−7.58167	−0.579785
$172$	−0.660219	−0.0503413
$173$	19.5550	1.48674	0.743369	−	0.668881i	$-0.233227\pi$
$173$	19.5550	1.48674	0.743369	+	0.668881i	$0.233227\pi$
$174$	3.29159	0.249535
$175$	1.46975	0.111102
$176$	−3.07064	−0.231459
$177$	−8.12616	−0.610800
$178$	−1.15775	−0.0867771
$179$	20.1020	1.50249	0.751247	−	0.660022i	$-0.229453\pi$
$179$	20.1020	1.50249	0.751247	+	0.660022i	$0.229453\pi$
$180$	2.30797	0.172026
$181$	7.14284	0.530923	0.265462	−	0.964121i	$-0.414476\pi$
$181$	7.14284	0.530923	0.265462	+	0.964121i	$0.414476\pi$
$182$	−4.49849	−0.333450
$183$	4.61685	0.341287
$184$	9.27355	0.683655
$185$	6.78388	0.498761
$186$	5.32783	0.390655
$187$	19.7240	1.44236
$188$	−10.3443	−0.754439
$189$	4.49849	0.327217
$190$	17.4983	1.26946
$191$	−5.32169	−0.385064	−0.192532	−	0.981291i	$-0.561670\pi$
$191$	−5.32169	−0.385064	−0.192532	+	0.981291i	$0.561670\pi$
$192$	1.00000	0.0721688
$193$	0.0650024	0.00467897	0.00233949	−	0.999997i	$-0.499255\pi$
$193$	0.0650024	0.00467897	0.00233949	+	0.999997i	$0.499255\pi$
$194$	−5.29299	−0.380014
$195$	2.30797	0.165277
$196$	13.2364	0.945456
$197$	−14.4690	−1.03087	−0.515436	−	0.856928i	$-0.672370\pi$
$197$	−14.4690	−1.03087	−0.515436	+	0.856928i	$0.672370\pi$
$198$	3.07064	0.218221
$199$	5.34906	0.379185	0.189593	−	0.981863i	$-0.439283\pi$
$199$	5.34906	0.379185	0.189593	+	0.981863i	$0.439283\pi$
$200$	−0.326720	−0.0231026
$201$	−6.12513	−0.432033
$202$	−2.72101	−0.191450
$203$	−14.8072	−1.03926
$204$	−6.42341	−0.449728
$205$	18.2173	1.27235
$206$	1.00000	0.0696733
$207$	−9.27355	−0.644557
$208$	1.00000	0.0693375
$209$	23.2806	1.61035
$210$	−10.3824	−0.716451
$211$	17.0007	1.17038	0.585189	−	0.810897i	$-0.301020\pi$
$211$	17.0007	1.17038	0.585189	+	0.810897i	$0.301020\pi$
$212$	3.71472	0.255128
$213$	−8.35045	−0.572164
$214$	−3.60502	−0.246434
$215$	−1.52377	−0.103920
$216$	−1.00000	−0.0680414
$217$	−23.9672	−1.62700
$218$	12.4950	0.846267
$219$	16.0060	1.08159
$220$	−7.08695	−0.477802
$221$	−6.42341	−0.432085
$222$	−2.93933	−0.197275
$223$	7.92415	0.530640	0.265320	−	0.964160i	$-0.414522\pi$
$223$	7.92415	0.530640	0.265320	+	0.964160i	$0.414522\pi$
$224$	−4.49849	−0.300568
$225$	0.326720	0.0217813
$226$	2.67954	0.178240
$227$	−22.2557	−1.47716	−0.738580	−	0.674166i	$-0.764503\pi$
$227$	−22.2557	−1.47716	−0.738580	+	0.674166i	$0.764503\pi$
$228$	−7.58167	−0.502108
$229$	−11.7515	−0.776559	−0.388280	−	0.921542i	$-0.626931\pi$
$229$	−11.7515	−0.776559	−0.388280	+	0.921542i	$0.626931\pi$
$230$	21.4031	1.41128
$231$	−13.8133	−0.908845
$232$	3.29159	0.216103
$233$	−26.8321	−1.75783	−0.878915	−	0.476978i	$-0.841732\pi$
$233$	−26.8321	−1.75783	−0.878915	+	0.476978i	$0.841732\pi$
$234$	−1.00000	−0.0653720
$235$	−23.8744	−1.55740
$236$	−8.12616	−0.528968
$237$	−14.8666	−0.965691
$238$	28.8956	1.87302
$239$	21.8917	1.41606	0.708029	−	0.706183i	$-0.249585\pi$
$239$	21.8917	1.41606	0.708029	+	0.706183i	$0.249585\pi$
$240$	2.30797	0.148979
$241$	−26.7387	−1.72239	−0.861197	−	0.508271i	$-0.830285\pi$
$241$	−26.7387	−1.72239	−0.861197	+	0.508271i	$0.830285\pi$
$242$	1.57114	0.100997
$243$	1.00000	0.0641500
$244$	4.61685	0.295563
$245$	30.5491	1.95171
$246$	−7.89321	−0.503253
$247$	−7.58167	−0.482410
$248$	5.32783	0.338318
$249$	−12.9601	−0.821311
$250$	10.7858	0.682153
$251$	−15.2561	−0.962957	−0.481479	−	0.876458i	$-0.659900\pi$
$251$	−15.2561	−0.962957	−0.481479	+	0.876458i	$0.659900\pi$
$252$	4.49849	0.283378
$253$	28.4758	1.79026
$254$	12.4620	0.781934
$255$	−14.8250	−0.928379
$256$	1.00000	0.0625000
$257$	16.8820	1.05307	0.526534	−	0.850154i	$-0.323491\pi$
$257$	16.8820	1.05307	0.526534	+	0.850154i	$0.323491\pi$
$258$	0.660219	0.0411035
$259$	13.2225	0.821608
$260$	2.30797	0.143134
$261$	−3.29159	−0.203744
$262$	−16.5343	−1.02150
$263$	16.9537	1.04541	0.522706	−	0.852513i	$-0.324923\pi$
$263$	16.9537	1.04541	0.522706	+	0.852513i	$0.324923\pi$
$264$	3.07064	0.188985
$265$	8.57346	0.526664
$266$	34.1060	2.09118
$267$	1.15775	0.0708532
$268$	−6.12513	−0.374152
$269$	−15.1010	−0.920725	−0.460362	−	0.887731i	$-0.652280\pi$
$269$	−15.1010	−0.920725	−0.460362	+	0.887731i	$0.652280\pi$
$270$	−2.30797	−0.140459
$271$	19.6361	1.19281	0.596405	−	0.802683i	$-0.296595\pi$
$271$	19.6361	1.19281	0.596405	+	0.802683i	$0.296595\pi$
$272$	−6.42341	−0.389476
$273$	4.49849	0.272261
$274$	−13.6535	−0.824837
$275$	−1.00324	−0.0604977
$276$	−9.27355	−0.558202
$277$	−23.0876	−1.38720	−0.693599	−	0.720361i	$-0.743976\pi$
$277$	−23.0876	−1.38720	−0.693599	+	0.720361i	$0.743976\pi$
$278$	7.77347	0.466222
$279$	−5.32783	−0.318969
$280$	−10.3824	−0.620465
$281$	14.6426	0.873502	0.436751	−	0.899582i	$-0.356129\pi$
$281$	14.6426	0.873502	0.436751	+	0.899582i	$0.356129\pi$
$282$	10.3443	0.615997
$283$	7.91544	0.470524	0.235262	−	0.971932i	$-0.424405\pi$
$283$	7.91544	0.470524	0.235262	+	0.971932i	$0.424405\pi$
$284$	−8.35045	−0.495508
$285$	−17.4983	−1.03651
$286$	3.07064	0.181571
$287$	35.5075	2.09594
$288$	−1.00000	−0.0589256
$289$	24.2602	1.42707
$290$	7.59689	0.446105
$291$	5.29299	0.310280
$292$	16.0060	0.936683
$293$	11.8360	0.691467	0.345734	−	0.938333i	$-0.387630\pi$
$293$	11.8360	0.691467	0.345734	+	0.938333i	$0.387630\pi$
$294$	−13.2364	−0.771961
$295$	−18.7549	−1.09195
$296$	−2.93933	−0.170845
$297$	−3.07064	−0.178177
$298$	4.13520	0.239545
$299$	−9.27355	−0.536303
$300$	0.326720	0.0188632
$301$	−2.96999	−0.171187
$302$	−16.9804	−0.977111
$303$	2.72101	0.156318
$304$	−7.58167	−0.434839
$305$	10.6555	0.610135
$306$	6.42341	0.367202
$307$	−19.8623	−1.13360	−0.566802	−	0.823854i	$-0.691820\pi$
$307$	−19.8623	−1.13360	−0.566802	+	0.823854i	$0.691820\pi$
$308$	−13.8133	−0.787083
$309$	−1.00000	−0.0568880
$310$	12.2965	0.698392
$311$	−5.31128	−0.301175	−0.150587	−	0.988597i	$-0.548117\pi$
$311$	−5.31128	−0.301175	−0.150587	+	0.988597i	$0.548117\pi$
$312$	−1.00000	−0.0566139
$313$	−15.0309	−0.849598	−0.424799	−	0.905288i	$-0.639655\pi$
$313$	−15.0309	−0.849598	−0.424799	+	0.905288i	$0.639655\pi$
$314$	−11.2088	−0.632551
$315$	10.3824	0.584980
$316$	−14.8666	−0.836313
$317$	8.94002	0.502122	0.251061	−	0.967971i	$-0.419221\pi$
$317$	8.94002	0.502122	0.251061	+	0.967971i	$0.419221\pi$
$318$	−3.71472	−0.208311
$319$	10.1073	0.565900
$320$	2.30797	0.129019
$321$	3.60502	0.201213
$322$	41.7170	2.32479
$323$	48.7002	2.70975
$324$	1.00000	0.0555556
$325$	0.326720	0.0181232
$326$	−16.1485	−0.894383
$327$	−12.4950	−0.690974
$328$	−7.89321	−0.435830
$329$	−46.5339	−2.56550
$330$	7.08695	0.390124
$331$	−19.7105	−1.08339	−0.541693	−	0.840576i	$-0.682217\pi$
$331$	−19.7105	−1.08339	−0.541693	+	0.840576i	$0.682217\pi$
$332$	−12.9601	−0.711276
$333$	2.93933	0.161074
$334$	13.4298	0.734845
$335$	−14.1366	−0.772365
$336$	4.49849	0.245413
$337$	10.6622	0.580807	0.290404	−	0.956904i	$-0.406210\pi$
$337$	10.6622	0.580807	0.290404	+	0.956904i	$0.406210\pi$
$338$	−1.00000	−0.0543928
$339$	−2.67954	−0.145533
$340$	−14.8250	−0.804000
$341$	16.3599	0.885937
$342$	7.58167	0.409970
$343$	28.0543	1.51479
$344$	0.660219	0.0355966
$345$	−21.4031	−1.15230
$346$	−19.5550	−1.05128
$347$	4.94453	0.265437	0.132718	−	0.991154i	$-0.457629\pi$
$347$	4.94453	0.265437	0.132718	+	0.991154i	$0.457629\pi$
$348$	−3.29159	−0.176448
$349$	13.6533	0.730846	0.365423	−	0.930842i	$-0.380924\pi$
$349$	13.6533	0.730846	0.365423	+	0.930842i	$0.380924\pi$
$350$	−1.46975	−0.0785612
$351$	1.00000	0.0533761
$352$	3.07064	0.163666
$353$	24.1245	1.28401	0.642007	−	0.766698i	$-0.278102\pi$
$353$	24.1245	1.28401	0.642007	+	0.766698i	$0.278102\pi$
$354$	8.12616	0.431901
$355$	−19.2726	−1.02288
$356$	1.15775	0.0613607
$357$	−28.8956	−1.52932
$358$	−20.1020	−1.06242
$359$	32.9593	1.73952	0.869762	−	0.493471i	$-0.164272\pi$
$359$	32.9593	1.73952	0.869762	+	0.493471i	$0.164272\pi$
$360$	−2.30797	−0.121641
$361$	38.4817	2.02535
$362$	−7.14284	−0.375420
$363$	−1.57114	−0.0824636
$364$	4.49849	0.235785
$365$	36.9415	1.93360
$366$	−4.61685	−0.241327
$367$	−19.8490	−1.03611	−0.518054	−	0.855348i	$-0.673344\pi$
$367$	−19.8490	−1.03611	−0.518054	+	0.855348i	$0.673344\pi$
$368$	−9.27355	−0.483417
$369$	7.89321	0.410904
$370$	−6.78388	−0.352677
$371$	16.7106	0.867572
$372$	−5.32783	−0.276235
$373$	16.8027	0.870009	0.435004	−	0.900428i	$-0.356747\pi$
$373$	16.8027	0.870009	0.435004	+	0.900428i	$0.356747\pi$
$374$	−19.7240	−1.01990
$375$	−10.7858	−0.556976
$376$	10.3443	0.533469
$377$	−3.29159	−0.169525
$378$	−4.49849	−0.231377
$379$	15.2413	0.782895	0.391447	−	0.920200i	$-0.371974\pi$
$379$	15.2413	0.782895	0.391447	+	0.920200i	$0.371974\pi$
$380$	−17.4983	−0.897642
$381$	−12.4620	−0.638446
$382$	5.32169	0.272281
$383$	−19.8328	−1.01341	−0.506704	−	0.862120i	$-0.669136\pi$
$383$	−19.8328	−1.01341	−0.506704	+	0.862120i	$0.669136\pi$
$384$	−1.00000	−0.0510310
$385$	−31.8806	−1.62478
$386$	−0.0650024	−0.00330853
$387$	−0.660219	−0.0335608
$388$	5.29299	0.268711
$389$	4.41628	0.223914	0.111957	−	0.993713i	$-0.464288\pi$
$389$	4.41628	0.223914	0.111957	+	0.993713i	$0.464288\pi$
$390$	−2.30797	−0.116869
$391$	59.5678	3.01247
$392$	−13.2364	−0.668538
$393$	16.5343	0.834047
$394$	14.4690	0.728936
$395$	−34.3117	−1.72641
$396$	−3.07064	−0.154306
$397$	12.5999	0.632371	0.316185	−	0.948697i	$-0.397598\pi$
$397$	12.5999	0.632371	0.316185	+	0.948697i	$0.397598\pi$
$398$	−5.34906	−0.268124
$399$	−34.1060	−1.70744
$400$	0.326720	0.0163360
$401$	21.0919	1.05328	0.526641	−	0.850088i	$-0.323451\pi$
$401$	21.0919	1.05328	0.526641	+	0.850088i	$0.323451\pi$
$402$	6.12513	0.305494
$403$	−5.32783	−0.265398
$404$	2.72101	0.135375
$405$	2.30797	0.114684
$406$	14.8072	0.734868
$407$	−9.02564	−0.447384
$408$	6.42341	0.318006
$409$	−28.0566	−1.38731	−0.693655	−	0.720308i	$-0.744001\pi$
$409$	−28.0566	−1.38731	−0.693655	+	0.720308i	$0.744001\pi$
$410$	−18.2173	−0.899688
$411$	13.6535	0.673476
$412$	−1.00000	−0.0492665
$413$	−36.5554	−1.79878
$414$	9.27355	0.455770
$415$	−29.9114	−1.46829
$416$	−1.00000	−0.0490290
$417$	−7.77347	−0.380669
$418$	−23.2806	−1.13869
$419$	−30.0038	−1.46578	−0.732890	−	0.680347i	$-0.761829\pi$
$419$	−30.0038	−1.46578	−0.732890	+	0.680347i	$0.761829\pi$
$420$	10.3824	0.506608
$421$	−16.9752	−0.827319	−0.413660	−	0.910432i	$-0.635750\pi$
$421$	−16.9752	−0.827319	−0.413660	+	0.910432i	$0.635750\pi$
$422$	−17.0007	−0.827582
$423$	−10.3443	−0.502959
$424$	−3.71472	−0.180403
$425$	−2.09866	−0.101800
$426$	8.35045	0.404581
$427$	20.7688	1.00507
$428$	3.60502	0.174255
$429$	−3.07064	−0.148252
$430$	1.52377	0.0734825
$431$	4.12181	0.198540	0.0992702	−	0.995061i	$-0.468349\pi$
$431$	4.12181	0.198540	0.0992702	+	0.995061i	$0.468349\pi$
$432$	1.00000	0.0481125
$433$	10.3207	0.495983	0.247991	−	0.968762i	$-0.420230\pi$
$433$	10.3207	0.495983	0.247991	+	0.968762i	$0.420230\pi$
$434$	23.9672	1.15046
$435$	−7.59689	−0.364243
$436$	−12.4950	−0.598401
$437$	70.3090	3.36334
$438$	−16.0060	−0.764798
$439$	20.6072	0.983528	0.491764	−	0.870728i	$-0.336352\pi$
$439$	20.6072	0.983528	0.491764	+	0.870728i	$0.336352\pi$
$440$	7.08695	0.337857
$441$	13.2364	0.630304
$442$	6.42341	0.305530
$443$	11.9518	0.567845	0.283923	−	0.958847i	$-0.408364\pi$
$443$	11.9518	0.567845	0.283923	+	0.958847i	$0.408364\pi$
$444$	2.93933	0.139494
$445$	2.67205	0.126667
$446$	−7.92415	−0.375219
$447$	−4.13520	−0.195588
$448$	4.49849	0.212533
$449$	−31.7564	−1.49868	−0.749339	−	0.662187i	$-0.769629\pi$
$449$	−31.7564	−1.49868	−0.749339	+	0.662187i	$0.769629\pi$
$450$	−0.326720	−0.0154017
$451$	−24.2372	−1.14129
$452$	−2.67954	−0.126035
$453$	16.9804	0.797807
$454$	22.2557	1.04451
$455$	10.3824	0.486733
$456$	7.58167	0.355044
$457$	17.5169	0.819405	0.409702	−	0.912219i	$-0.365633\pi$
$457$	17.5169	0.819405	0.409702	+	0.912219i	$0.365633\pi$
$458$	11.7515	0.549110
$459$	−6.42341	−0.299819
$460$	−21.4031	−0.997923
$461$	29.9410	1.39449	0.697245	−	0.716832i	$-0.254409\pi$
$461$	29.9410	1.39449	0.697245	+	0.716832i	$0.254409\pi$
$462$	13.8133	0.642651
$463$	2.46778	0.114687	0.0573437	−	0.998354i	$-0.481737\pi$
$463$	2.46778	0.114687	0.0573437	+	0.998354i	$0.481737\pi$
$464$	−3.29159	−0.152808
$465$	−12.2965	−0.570235
$466$	26.8321	1.24297
$467$	−7.56075	−0.349870	−0.174935	−	0.984580i	$-0.555972\pi$
$467$	−7.56075	−0.349870	−0.174935	+	0.984580i	$0.555972\pi$
$468$	1.00000	0.0462250
$469$	−27.5538	−1.27232
$470$	23.8744	1.10124
$471$	11.2088	0.516476
$472$	8.12616	0.374037
$473$	2.02730	0.0932153
$474$	14.8666	0.682846
$475$	−2.47708	−0.113656
$476$	−28.8956	−1.32443
$477$	3.71472	0.170085
$478$	−21.8917	−1.00130
$479$	13.0787	0.597579	0.298789	−	0.954319i	$-0.403417\pi$
$479$	13.0787	0.597579	0.298789	+	0.954319i	$0.403417\pi$
$480$	−2.30797	−0.105344
$481$	2.93933	0.134022
$482$	26.7387	1.21792
$483$	−41.7170	−1.89819
$484$	−1.57114	−0.0714156
$485$	12.2160	0.554702
$486$	−1.00000	−0.0453609
$487$	14.0815	0.638092	0.319046	−	0.947739i	$-0.396638\pi$
$487$	14.0815	0.638092	0.319046	+	0.947739i	$0.396638\pi$
$488$	−4.61685	−0.208995
$489$	16.1485	0.730261
$490$	−30.5491	−1.38007
$491$	25.6762	1.15875	0.579375	−	0.815061i	$-0.303297\pi$
$491$	25.6762	1.15875	0.579375	+	0.815061i	$0.303297\pi$
$492$	7.89321	0.355853
$493$	21.1432	0.952243
$494$	7.58167	0.341115
$495$	−7.08695	−0.318535
$496$	−5.32783	−0.239227
$497$	−37.5644	−1.68499
$498$	12.9601	0.580755
$499$	−11.4674	−0.513349	−0.256675	−	0.966498i	$-0.582627\pi$
$499$	−11.4674	−0.513349	−0.256675	+	0.966498i	$0.582627\pi$
$500$	−10.7858	−0.482355
$501$	−13.4298	−0.599999
$502$	15.2561	0.680913
$503$	−13.5082	−0.602299	−0.301150	−	0.953577i	$-0.597370\pi$
$503$	−13.5082	−0.602299	−0.301150	+	0.953577i	$0.597370\pi$
$504$	−4.49849	−0.200379
$505$	6.28000	0.279457
$506$	−28.4758	−1.26590
$507$	1.00000	0.0444116
$508$	−12.4620	−0.552911
$509$	8.23158	0.364859	0.182429	−	0.983219i	$-0.441604\pi$
$509$	8.23158	0.364859	0.182429	+	0.983219i	$0.441604\pi$
$510$	14.8250	0.656463
$511$	72.0030	3.18522
$512$	−1.00000	−0.0441942
$513$	−7.58167	−0.334739
$514$	−16.8820	−0.744632
$515$	−2.30797	−0.101701
$516$	−0.660219	−0.0290645
$517$	31.7638	1.39697
$518$	−13.2225	−0.580965
$519$	19.5550	0.858369
$520$	−2.30797	−0.101211
$521$	−6.99521	−0.306466	−0.153233	−	0.988190i	$-0.548968\pi$
$521$	−6.99521	−0.306466	−0.153233	+	0.988190i	$0.548968\pi$
$522$	3.29159	0.144069
$523$	−14.8102	−0.647603	−0.323802	−	0.946125i	$-0.604961\pi$
$523$	−14.8102	−0.647603	−0.323802	+	0.946125i	$0.604961\pi$
$524$	16.5343	0.722306
$525$	1.46975	0.0641450
$526$	−16.9537	−0.739218
$527$	34.2228	1.49077
$528$	−3.07064	−0.133633
$529$	62.9988	2.73908
$530$	−8.57346	−0.372407
$531$	−8.12616	−0.352645
$532$	−34.1060	−1.47868
$533$	7.89321	0.341893
$534$	−1.15775	−0.0501008
$535$	8.32028	0.359717
$536$	6.12513	0.264565
$537$	20.1020	0.867465
$538$	15.1010	0.651051
$539$	−40.6442	−1.75067
$540$	2.30797	0.0993192
$541$	−42.2998	−1.81861	−0.909306	−	0.416128i	$-0.863387\pi$
$541$	−42.2998	−1.81861	−0.909306	+	0.416128i	$0.863387\pi$
$542$	−19.6361	−0.843444
$543$	7.14284	0.306529
$544$	6.42341	0.275401
$545$	−28.8380	−1.23529
$546$	−4.49849	−0.192517
$547$	−36.3830	−1.55563	−0.777813	−	0.628496i	$-0.783671\pi$
$547$	−36.3830	−1.55563	−0.777813	+	0.628496i	$0.783671\pi$
$548$	13.6535	0.583248
$549$	4.61685	0.197042
$550$	1.00324	0.0427784
$551$	24.9557	1.06315
$552$	9.27355	0.394709
$553$	−66.8773	−2.84391
$554$	23.0876	0.980897
$555$	6.78388	0.287960
$556$	−7.77347	−0.329669
$557$	−41.6451	−1.76456	−0.882280	−	0.470725i	$-0.843992\pi$
$557$	−41.6451	−1.76456	−0.882280	+	0.470725i	$0.843992\pi$
$558$	5.32783	0.225545
$559$	−0.660219	−0.0279243
$560$	10.3824	0.438735
$561$	19.7240	0.832748
$562$	−14.6426	−0.617659
$563$	1.32087	0.0556680	0.0278340	−	0.999613i	$-0.491139\pi$
$563$	1.32087	0.0556680	0.0278340	+	0.999613i	$0.491139\pi$
$564$	−10.3443	−0.435575
$565$	−6.18430	−0.260175
$566$	−7.91544	−0.332711
$567$	4.49849	0.188919
$568$	8.35045	0.350377
$569$	7.64593	0.320534	0.160267	−	0.987074i	$-0.448764\pi$
$569$	7.64593	0.320534	0.160267	+	0.987074i	$0.448764\pi$
$570$	17.4983	0.732921
$571$	−43.4082	−1.81658	−0.908288	−	0.418345i	$-0.862610\pi$
$571$	−43.4082	−1.81658	−0.908288	+	0.418345i	$0.862610\pi$
$572$	−3.07064	−0.128390
$573$	−5.32169	−0.222317
$574$	−35.5075	−1.48205
$575$	−3.02986	−0.126354
$576$	1.00000	0.0416667
$577$	−16.3677	−0.681395	−0.340698	−	0.940173i	$-0.610663\pi$
$577$	−16.3677	−0.681395	−0.340698	+	0.940173i	$0.610663\pi$
$578$	−24.2602	−1.00909
$579$	0.0650024	0.00270141
$580$	−7.59689	−0.315444
$581$	−58.3007	−2.41872
$582$	−5.29299	−0.219401
$583$	−11.4066	−0.472413
$584$	−16.0060	−0.662335
$585$	2.30797	0.0954228
$586$	−11.8360	−0.488941
$587$	11.4748	0.473614	0.236807	−	0.971557i	$-0.423899\pi$
$587$	11.4748	0.473614	0.236807	+	0.971557i	$0.423899\pi$
$588$	13.2364	0.545859
$589$	40.3939	1.66440
$590$	18.7549	0.772128
$591$	−14.4690	−0.595174
$592$	2.93933	0.120806
$593$	−38.6695	−1.58796	−0.793982	−	0.607941i	$-0.791996\pi$
$593$	−38.6695	−1.58796	−0.793982	+	0.607941i	$0.791996\pi$
$594$	3.07064	0.125990
$595$	−66.6902	−2.73403
$596$	−4.13520	−0.169384
$597$	5.34906	0.218923
$598$	9.27355	0.379224
$599$	−38.0549	−1.55488	−0.777440	−	0.628958i	$-0.783482\pi$
$599$	−38.0549	−1.55488	−0.777440	+	0.628958i	$0.783482\pi$
$600$	−0.326720	−0.0133383
$601$	7.28609	0.297206	0.148603	−	0.988897i	$-0.452522\pi$
$601$	7.28609	0.297206	0.148603	+	0.988897i	$0.452522\pi$
$602$	2.96999	0.121048
$603$	−6.12513	−0.249435
$604$	16.9804	0.690922
$605$	−3.62615	−0.147424
$606$	−2.72101	−0.110533
$607$	24.2090	0.982611	0.491306	−	0.870987i	$-0.336520\pi$
$607$	24.2090	0.982611	0.491306	+	0.870987i	$0.336520\pi$
$608$	7.58167	0.307477
$609$	−14.8072	−0.600017
$610$	−10.6555	−0.431430
$611$	−10.3443	−0.418487
$612$	−6.42341	−0.259651
$613$	−6.72585	−0.271654	−0.135827	−	0.990733i	$-0.543369\pi$
$613$	−6.72585	−0.271654	−0.135827	+	0.990733i	$0.543369\pi$
$614$	19.8623	0.801579
$615$	18.2173	0.734592
$616$	13.8133	0.556552
$617$	−14.2561	−0.573929	−0.286965	−	0.957941i	$-0.592646\pi$
$617$	−14.2561	−0.573929	−0.286965	+	0.957941i	$0.592646\pi$
$618$	1.00000	0.0402259
$619$	14.7719	0.593732	0.296866	−	0.954919i	$-0.404059\pi$
$619$	14.7719	0.593732	0.296866	+	0.954919i	$0.404059\pi$
$620$	−12.2965	−0.493838
$621$	−9.27355	−0.372135
$622$	5.31128	0.212963
$623$	5.20813	0.208659
$624$	1.00000	0.0400320
$625$	−26.5269	−1.06107
$626$	15.0309	0.600756
$627$	23.2806	0.929738
$628$	11.2088	0.447281
$629$	−18.8805	−0.752815
$630$	−10.3824	−0.413643
$631$	5.01834	0.199777	0.0998885	−	0.994999i	$-0.468151\pi$
$631$	5.01834	0.199777	0.0998885	+	0.994999i	$0.468151\pi$
$632$	14.8666	0.591362
$633$	17.0007	0.675718
$634$	−8.94002	−0.355054
$635$	−28.7619	−1.14138
$636$	3.71472	0.147298
$637$	13.2364	0.524444
$638$	−10.1073	−0.400152
$639$	−8.35045	−0.330339
$640$	−2.30797	−0.0912305
$641$	3.33394	0.131683	0.0658414	−	0.997830i	$-0.479027\pi$
$641$	3.33394	0.131683	0.0658414	+	0.997830i	$0.479027\pi$
$642$	−3.60502	−0.142279
$643$	−4.71017	−0.185751	−0.0928756	−	0.995678i	$-0.529606\pi$
$643$	−4.71017	−0.185751	−0.0928756	+	0.995678i	$0.529606\pi$
$644$	−41.7170	−1.64388
$645$	−1.52377	−0.0599982
$646$	−48.7002	−1.91608
$647$	−38.2893	−1.50531	−0.752653	−	0.658417i	$-0.771226\pi$
$647$	−38.2893	−1.50531	−0.752653	+	0.658417i	$0.771226\pi$
$648$	−1.00000	−0.0392837
$649$	24.9526	0.979473
$650$	−0.326720	−0.0128150
$651$	−23.9672	−0.939347
$652$	16.1485	0.632425
$653$	−28.1788	−1.10272	−0.551362	−	0.834266i	$-0.685892\pi$
$653$	−28.1788	−1.10272	−0.551362	+	0.834266i	$0.685892\pi$
$654$	12.4950	0.488593
$655$	38.1607	1.49106
$656$	7.89321	0.308178
$657$	16.0060	0.624455
$658$	46.5339	1.81408
$659$	50.0023	1.94781	0.973906	−	0.226950i	$-0.0728754\pi$
$659$	50.0023	1.94781	0.973906	+	0.226950i	$0.0728754\pi$
$660$	−7.08695	−0.275859
$661$	27.3898	1.06534	0.532670	−	0.846323i	$-0.321189\pi$
$661$	27.3898	1.06534	0.532670	+	0.846323i	$0.321189\pi$
$662$	19.7105	0.766070
$663$	−6.42341	−0.249464
$664$	12.9601	0.502948
$665$	−78.7157	−3.05246
$666$	−2.93933	−0.113897
$667$	30.5247	1.18192
$668$	−13.4298	−0.519614
$669$	7.92415	0.306365
$670$	14.1366	0.546145
$671$	−14.1767	−0.547286
$672$	−4.49849	−0.173533
$673$	19.7615	0.761750	0.380875	−	0.924626i	$-0.375623\pi$
$673$	19.7615	0.761750	0.380875	+	0.924626i	$0.375623\pi$
$674$	−10.6622	−0.410693
$675$	0.326720	0.0125755
$676$	1.00000	0.0384615
$677$	4.08334	0.156935	0.0784677	−	0.996917i	$-0.474997\pi$
$677$	4.08334	0.156935	0.0784677	+	0.996917i	$0.474997\pi$
$678$	2.67954	0.102907
$679$	23.8104	0.913760
$680$	14.8250	0.568514
$681$	−22.2557	−0.852838
$682$	−16.3599	−0.626452
$683$	19.9022	0.761535	0.380768	−	0.924671i	$-0.375660\pi$
$683$	19.9022	0.761535	0.380768	+	0.924671i	$0.375660\pi$
$684$	−7.58167	−0.289892
$685$	31.5118	1.20400
$686$	−28.0543	−1.07112
$687$	−11.7515	−0.448347
$688$	−0.660219	−0.0251706
$689$	3.71472	0.141520
$690$	21.4031	0.814801
$691$	−10.7309	−0.408222	−0.204111	−	0.978948i	$-0.565430\pi$
$691$	−10.7309	−0.408222	−0.204111	+	0.978948i	$0.565430\pi$
$692$	19.5550	0.743369
$693$	−13.8133	−0.524722
$694$	−4.94453	−0.187692
$695$	−17.9409	−0.680538
$696$	3.29159	0.124767
$697$	−50.7013	−1.92045
$698$	−13.6533	−0.516786
$699$	−26.8321	−1.01488
$700$	1.46975	0.0555512
$701$	−42.0313	−1.58750	−0.793750	−	0.608244i	$-0.791874\pi$
$701$	−42.0313	−1.58750	−0.793750	+	0.608244i	$0.791874\pi$
$702$	−1.00000	−0.0377426
$703$	−22.2850	−0.840496
$704$	−3.07064	−0.115729
$705$	−23.8744	−0.899163
$706$	−24.1245	−0.907936
$707$	12.2404	0.460348
$708$	−8.12616	−0.305400
$709$	34.0159	1.27749	0.638747	−	0.769417i	$-0.279453\pi$
$709$	34.0159	1.27749	0.638747	+	0.769417i	$0.279453\pi$
$710$	19.2726	0.723287
$711$	−14.8666	−0.557542
$712$	−1.15775	−0.0433886
$713$	49.4079	1.85034
$714$	28.8956	1.08139
$715$	−7.08695	−0.265037
$716$	20.1020	0.751247
$717$	21.8917	0.817561
$718$	−32.9593	−1.23003
$719$	−26.7071	−0.996007	−0.498003	−	0.867175i	$-0.665933\pi$
$719$	−26.7071	−0.996007	−0.498003	+	0.867175i	$0.665933\pi$
$720$	2.30797	0.0860129
$721$	−4.49849	−0.167532
$722$	−38.4817	−1.43214
$723$	−26.7387	−0.994425
$724$	7.14284	0.265462
$725$	−1.07543	−0.0399404
$726$	1.57114	0.0583106
$727$	41.4609	1.53770	0.768850	−	0.639429i	$-0.220829\pi$
$727$	41.4609	1.53770	0.768850	+	0.639429i	$0.220829\pi$
$728$	−4.49849	−0.166725
$729$	1.00000	0.0370370
$730$	−36.9415	−1.36726
$731$	4.24086	0.156854
$732$	4.61685	0.170644
$733$	45.1082	1.66611	0.833054	−	0.553192i	$-0.186590\pi$
$733$	45.1082	1.66611	0.833054	+	0.553192i	$0.186590\pi$
$734$	19.8490	0.732640
$735$	30.5491	1.12682
$736$	9.27355	0.341828
$737$	18.8081	0.692805
$738$	−7.89321	−0.290553
$739$	7.71378	0.283756	0.141878	−	0.989884i	$-0.454686\pi$
$739$	7.71378	0.283756	0.141878	+	0.989884i	$0.454686\pi$
$740$	6.78388	0.249380
$741$	−7.58167	−0.278520
$742$	−16.7106	−0.613466
$743$	19.7540	0.724705	0.362353	−	0.932041i	$-0.381974\pi$
$743$	19.7540	0.724705	0.362353	+	0.932041i	$0.381974\pi$
$744$	5.32783	0.195328
$745$	−9.54390	−0.349662
$746$	−16.8027	−0.615189
$747$	−12.9601	−0.474184
$748$	19.7240	0.721181
$749$	16.2171	0.592562
$750$	10.7858	0.393841
$751$	−17.9708	−0.655763	−0.327881	−	0.944719i	$-0.606335\pi$
$751$	−17.9708	−0.655763	−0.327881	+	0.944719i	$0.606335\pi$
$752$	−10.3443	−0.377219
$753$	−15.2561	−0.555963
$754$	3.29159	0.119873
$755$	39.1902	1.42628
$756$	4.49849	0.163608
$757$	−21.0114	−0.763672	−0.381836	−	0.924230i	$-0.624708\pi$
$757$	−21.0114	−0.763672	−0.381836	+	0.924230i	$0.624708\pi$
$758$	−15.2413	−0.553590
$759$	28.4758	1.03361
$760$	17.4983	0.634729
$761$	−9.48934	−0.343988	−0.171994	−	0.985098i	$-0.555021\pi$
$761$	−9.48934	−0.343988	−0.171994	+	0.985098i	$0.555021\pi$
$762$	12.4620	0.451450
$763$	−56.2085	−2.03489
$764$	−5.32169	−0.192532
$765$	−14.8250	−0.536000
$766$	19.8328	0.716588
$767$	−8.12616	−0.293419
$768$	1.00000	0.0360844
$769$	47.3283	1.70670	0.853350	−	0.521338i	$-0.174567\pi$
$769$	47.3283	1.70670	0.853350	+	0.521338i	$0.174567\pi$
$770$	31.8806	1.14890
$771$	16.8820	0.607989
$772$	0.0650024	0.00233949
$773$	−46.6715	−1.67866	−0.839328	−	0.543625i	$-0.817051\pi$
$773$	−46.6715	−1.67866	−0.839328	+	0.543625i	$0.817051\pi$
$774$	0.660219	0.0237311
$775$	−1.74071	−0.0625281
$776$	−5.29299	−0.190007
$777$	13.2225	0.474356
$778$	−4.41628	−0.158331
$779$	−59.8437	−2.14412
$780$	2.30797	0.0826385
$781$	25.6413	0.917517
$782$	−59.5678	−2.13014
$783$	−3.29159	−0.117632
$784$	13.2364	0.472728
$785$	25.8696	0.923327
$786$	−16.5343	−0.589760
$787$	−44.3381	−1.58048	−0.790242	−	0.612795i	$-0.790045\pi$
$787$	−44.3381	−1.58048	−0.790242	+	0.612795i	$0.790045\pi$
$788$	−14.4690	−0.515436
$789$	16.9537	0.603569
$790$	34.3117	1.22076
$791$	−12.0539	−0.428587
$792$	3.07064	0.109111
$793$	4.61685	0.163949
$794$	−12.5999	−0.447153
$795$	8.57346	0.304069
$796$	5.34906	0.189593
$797$	27.9432	0.989799	0.494900	−	0.868950i	$-0.335205\pi$
$797$	27.9432	0.989799	0.494900	+	0.868950i	$0.335205\pi$
$798$	34.1060	1.20734
$799$	66.4459	2.35069
$800$	−0.326720	−0.0115513
$801$	1.15775	0.0409071
$802$	−21.0919	−0.744782
$803$	−49.1489	−1.73443
$804$	−6.12513	−0.216017
$805$	−96.2814	−3.39347
$806$	5.32783	0.187665
$807$	−15.1010	−0.531581
$808$	−2.72101	−0.0957248
$809$	−49.8493	−1.75261	−0.876305	−	0.481757i	$-0.839999\pi$
$809$	−49.8493	−1.75261	−0.876305	+	0.481757i	$0.839999\pi$
$810$	−2.30797	−0.0810938
$811$	−4.89957	−0.172047	−0.0860235	−	0.996293i	$-0.527416\pi$
$811$	−4.89957	−0.172047	−0.0860235	+	0.996293i	$0.527416\pi$
$812$	−14.8072	−0.519630
$813$	19.6361	0.688670
$814$	9.02564	0.316348
$815$	37.2703	1.30552
$816$	−6.42341	−0.224864
$817$	5.00557	0.175123
$818$	28.0566	0.980976
$819$	4.49849	0.157190
$820$	18.2173	0.636175
$821$	−22.7975	−0.795637	−0.397818	−	0.917464i	$-0.630233\pi$
$821$	−22.7975	−0.795637	−0.397818	+	0.917464i	$0.630233\pi$
$822$	−13.6535	−0.476220
$823$	−42.6615	−1.48709	−0.743543	−	0.668688i	$-0.766856\pi$
$823$	−42.6615	−1.48709	−0.743543	+	0.668688i	$0.766856\pi$
$824$	1.00000	0.0348367
$825$	−1.00324	−0.0349284
$826$	36.5554	1.27193
$827$	9.16292	0.318626	0.159313	−	0.987228i	$-0.449072\pi$
$827$	9.16292	0.318626	0.159313	+	0.987228i	$0.449072\pi$
$828$	−9.27355	−0.322278
$829$	25.5976	0.889041	0.444520	−	0.895769i	$-0.353374\pi$
$829$	25.5976	0.889041	0.444520	+	0.895769i	$0.353374\pi$
$830$	29.9114	1.03824
$831$	−23.0876	−0.800899
$832$	1.00000	0.0346688
$833$	−85.0226	−2.94586
$834$	7.77347	0.269173
$835$	−30.9955	−1.07264
$836$	23.2806	0.805177
$837$	−5.32783	−0.184157
$838$	30.0038	1.03646
$839$	9.62037	0.332132	0.166066	−	0.986115i	$-0.446894\pi$
$839$	9.62037	0.332132	0.166066	+	0.986115i	$0.446894\pi$
$840$	−10.3824	−0.358226
$841$	−18.1654	−0.626394
$842$	16.9752	0.585003
$843$	14.6426	0.504317
$844$	17.0007	0.585189
$845$	2.30797	0.0793965
$846$	10.3443	0.355646
$847$	−7.06777	−0.242851
$848$	3.71472	0.127564
$849$	7.91544	0.271657
$850$	2.09866	0.0719833
$851$	−27.2580	−0.934393
$852$	−8.35045	−0.286082
$853$	8.42538	0.288479	0.144240	−	0.989543i	$-0.453926\pi$
$853$	8.42538	0.288479	0.144240	+	0.989543i	$0.453926\pi$
$854$	−20.7688	−0.710695
$855$	−17.4983	−0.598428
$856$	−3.60502	−0.123217
$857$	−45.2094	−1.54432	−0.772161	−	0.635427i	$-0.780824\pi$
$857$	−45.2094	−1.54432	−0.772161	+	0.635427i	$0.780824\pi$
$858$	3.07064	0.104830
$859$	57.5928	1.96504	0.982521	−	0.186151i	$-0.0596013\pi$
$859$	57.5928	1.96504	0.982521	+	0.186151i	$0.0596013\pi$
$860$	−1.52377	−0.0519600
$861$	35.5075	1.21009
$862$	−4.12181	−0.140389
$863$	50.1018	1.70548	0.852742	−	0.522332i	$-0.174938\pi$
$863$	50.1018	1.70548	0.852742	+	0.522332i	$0.174938\pi$
$864$	−1.00000	−0.0340207
$865$	45.1323	1.53454
$866$	−10.3207	−0.350713
$867$	24.2602	0.823918
$868$	−23.9672	−0.813499
$869$	45.6501	1.54857
$870$	7.59689	0.257559
$871$	−6.12513	−0.207542
$872$	12.4950	0.423134
$873$	5.29299	0.179140
$874$	−70.3090	−2.37824
$875$	−48.5197	−1.64027
$876$	16.0060	0.540794
$877$	−12.1544	−0.410423	−0.205212	−	0.978718i	$-0.565788\pi$
$877$	−12.1544	−0.410423	−0.205212	+	0.978718i	$0.565788\pi$
$878$	−20.6072	−0.695459
$879$	11.8360	0.399219
$880$	−7.08695	−0.238901
$881$	46.8341	1.57788	0.788940	−	0.614470i	$-0.210630\pi$
$881$	46.8341	1.57788	0.788940	+	0.614470i	$0.210630\pi$
$882$	−13.2364	−0.445692
$883$	8.24979	0.277628	0.138814	−	0.990318i	$-0.455671\pi$
$883$	8.24979	0.277628	0.138814	+	0.990318i	$0.455671\pi$
$884$	−6.42341	−0.216043
$885$	−18.7549	−0.630440
$886$	−11.9518	−0.401527
$887$	−19.1402	−0.642666	−0.321333	−	0.946966i	$-0.604131\pi$
$887$	−19.1402	−0.642666	−0.321333	+	0.946966i	$0.604131\pi$
$888$	−2.93933	−0.0986374
$889$	−56.0600	−1.88019
$890$	−2.67205	−0.0895674
$891$	−3.07064	−0.102870
$892$	7.92415	0.265320
$893$	78.4274	2.62447
$894$	4.13520	0.138302
$895$	46.3948	1.55081
$896$	−4.49849	−0.150284
$897$	−9.27355	−0.309635
$898$	31.7564	1.05973
$899$	17.5370	0.584893
$900$	0.326720	0.0108907
$901$	−23.8612	−0.794931
$902$	24.2372	0.807012
$903$	−2.96999	−0.0988350
$904$	2.67954	0.0891202
$905$	16.4855	0.547995
$906$	−16.9804	−0.564135
$907$	−29.1930	−0.969338	−0.484669	−	0.874698i	$-0.661060\pi$
$907$	−29.1930	−0.969338	−0.484669	+	0.874698i	$0.661060\pi$
$908$	−22.2557	−0.738580
$909$	2.72101	0.0902502
$910$	−10.3824	−0.344172
$911$	−25.1881	−0.834519	−0.417259	−	0.908787i	$-0.637009\pi$
$911$	−25.1881	−0.834519	−0.417259	+	0.908787i	$0.637009\pi$
$912$	−7.58167	−0.251054
$913$	39.7958	1.31705
$914$	−17.5169	−0.579407
$915$	10.6555	0.352261
$916$	−11.7515	−0.388280
$917$	74.3795	2.45623
$918$	6.42341	0.212004
$919$	48.1378	1.58792	0.793960	−	0.607970i	$-0.208016\pi$
$919$	48.1378	1.58792	0.793960	+	0.607970i	$0.208016\pi$
$920$	21.4031	0.705638
$921$	−19.8623	−0.654486
$922$	−29.9410	−0.986054
$923$	−8.35045	−0.274858
$924$	−13.8133	−0.454423
$925$	0.960338	0.0315757
$926$	−2.46778	−0.0810962
$927$	−1.00000	−0.0328443
$928$	3.29159	0.108052
$929$	−51.1981	−1.67975	−0.839877	−	0.542776i	$-0.817373\pi$
$929$	−51.1981	−1.67975	−0.839877	+	0.542776i	$0.817373\pi$
$930$	12.2965	0.403217
$931$	−100.354	−3.28896
$932$	−26.8321	−0.878915
$933$	−5.31128	−0.173883
$934$	7.56075	0.247395
$935$	45.5224	1.48874
$936$	−1.00000	−0.0326860
$937$	1.68937	0.0551894	0.0275947	−	0.999619i	$-0.491215\pi$
$937$	1.68937	0.0551894	0.0275947	+	0.999619i	$0.491215\pi$
$938$	27.5538	0.899664
$939$	−15.0309	−0.490515
$940$	−23.8744	−0.778698
$941$	6.17306	0.201236	0.100618	−	0.994925i	$-0.467918\pi$
$941$	6.17306	0.201236	0.100618	+	0.994925i	$0.467918\pi$
$942$	−11.2088	−0.365204
$943$	−73.1981	−2.38366
$944$	−8.12616	−0.264484
$945$	10.3824	0.337738
$946$	−2.02730	−0.0659132
$947$	−27.0779	−0.879912	−0.439956	−	0.898019i	$-0.645006\pi$
$947$	−27.0779	−0.879912	−0.439956	+	0.898019i	$0.645006\pi$
$948$	−14.8666	−0.482845
$949$	16.0060	0.519578
$950$	2.47708	0.0803672
$951$	8.94002	0.289900
$952$	28.8956	0.936512
$953$	−2.10774	−0.0682765	−0.0341383	−	0.999417i	$-0.510869\pi$
$953$	−2.10774	−0.0682765	−0.0341383	+	0.999417i	$0.510869\pi$
$954$	−3.71472	−0.120269
$955$	−12.2823	−0.397446
$956$	21.8917	0.708029
$957$	10.1073	0.326723
$958$	−13.0787	−0.422552
$959$	61.4200	1.98335
$960$	2.30797	0.0744894
$961$	−2.61423	−0.0843300
$962$	−2.93933	−0.0947678
$963$	3.60502	0.116170
$964$	−26.7387	−0.861197
$965$	0.150023	0.00482943
$966$	41.7170	1.34222
$967$	26.1368	0.840502	0.420251	−	0.907408i	$-0.361942\pi$
$967$	26.1368	0.840502	0.420251	+	0.907408i	$0.361942\pi$
$968$	1.57114	0.0504984
$969$	48.7002	1.56447
$970$	−12.2160	−0.392234
$971$	38.0132	1.21990	0.609951	−	0.792439i	$-0.291189\pi$
$971$	38.0132	1.21990	0.609951	+	0.792439i	$0.291189\pi$
$972$	1.00000	0.0320750
$973$	−34.9689	−1.12105
$974$	−14.0815	−0.451199
$975$	0.326720	0.0104634
$976$	4.61685	0.147782
$977$	23.1277	0.739920	0.369960	−	0.929048i	$-0.379371\pi$
$977$	23.1277	0.739920	0.369960	+	0.929048i	$0.379371\pi$
$978$	−16.1485	−0.516372
$979$	−3.55504	−0.113620
$980$	30.5491	0.975857
$981$	−12.4950	−0.398934
$982$	−25.6762	−0.819360
$983$	−6.20487	−0.197905	−0.0989523	−	0.995092i	$-0.531549\pi$
$983$	−6.20487	−0.197905	−0.0989523	+	0.995092i	$0.531549\pi$
$984$	−7.89321	−0.251626
$985$	−33.3939	−1.06402
$986$	−21.1432	−0.673337
$987$	−46.5339	−1.48119
$988$	−7.58167	−0.241205
$989$	6.12258	0.194687
$990$	7.08695	0.225238
$991$	28.9708	0.920287	0.460143	−	0.887845i	$-0.347798\pi$
$991$	28.9708	0.920287	0.460143	+	0.887845i	$0.347798\pi$
$992$	5.32783	0.169159
$993$	−19.7105	−0.625493
$994$	37.5644	1.19147
$995$	12.3455	0.391378
$996$	−12.9601	−0.410656
$997$	−27.3521	−0.866250	−0.433125	−	0.901334i	$-0.642589\pi$
$997$	−27.3521	−0.866250	−0.433125	+	0.901334i	$0.642589\pi$
$998$	11.4674	0.362993
$999$	2.93933	0.0929963

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.w.1.11	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.w.1.11	✓	12	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.30797 q^{5} -1.00000 q^{6} +4.49849 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.30797 q^{5} -1.00000 q^{6} +4.49849 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.30797 q^{10} -3.07064 q^{11} +1.00000 q^{12} +1.00000 q^{13} -4.49849 q^{14} +2.30797 q^{15} +1.00000 q^{16} -6.42341 q^{17} -1.00000 q^{18} -7.58167 q^{19} +2.30797 q^{20} +4.49849 q^{21} +3.07064 q^{22} -9.27355 q^{23} -1.00000 q^{24} +0.326720 q^{25} -1.00000 q^{26} +1.00000 q^{27} +4.49849 q^{28} -3.29159 q^{29} -2.30797 q^{30} -5.32783 q^{31} -1.00000 q^{32} -3.07064 q^{33} +6.42341 q^{34} +10.3824 q^{35} +1.00000 q^{36} +2.93933 q^{37} +7.58167 q^{38} +1.00000 q^{39} -2.30797 q^{40} +7.89321 q^{41} -4.49849 q^{42} -0.660219 q^{43} -3.07064 q^{44} +2.30797 q^{45} +9.27355 q^{46} -10.3443 q^{47} +1.00000 q^{48} +13.2364 q^{49} -0.326720 q^{50} -6.42341 q^{51} +1.00000 q^{52} +3.71472 q^{53} -1.00000 q^{54} -7.08695 q^{55} -4.49849 q^{56} -7.58167 q^{57} +3.29159 q^{58} -8.12616 q^{59} +2.30797 q^{60} +4.61685 q^{61} +5.32783 q^{62} +4.49849 q^{63} +1.00000 q^{64} +2.30797 q^{65} +3.07064 q^{66} -6.12513 q^{67} -6.42341 q^{68} -9.27355 q^{69} -10.3824 q^{70} -8.35045 q^{71} -1.00000 q^{72} +16.0060 q^{73} -2.93933 q^{74} +0.326720 q^{75} -7.58167 q^{76} -13.8133 q^{77} -1.00000 q^{78} -14.8666 q^{79} +2.30797 q^{80} +1.00000 q^{81} -7.89321 q^{82} -12.9601 q^{83} +4.49849 q^{84} -14.8250 q^{85} +0.660219 q^{86} -3.29159 q^{87} +3.07064 q^{88} +1.15775 q^{89} -2.30797 q^{90} +4.49849 q^{91} -9.27355 q^{92} -5.32783 q^{93} +10.3443 q^{94} -17.4983 q^{95} -1.00000 q^{96} +5.29299 q^{97} -13.2364 q^{98} -3.07064 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} + 12 q^{3} + 12 q^{4} - 4 q^{5} - 12 q^{6} - 12 q^{8} + 12 q^{9}+O(q^{10}) \) 12 * q - 12 * q^2 + 12 * q^3 + 12 * q^4 - 4 * q^5 - 12 * q^6 - 12 * q^8 + 12 * q^9	\( 12 q - 12 q^{2} + 12 q^{3} + 12 q^{4} - 4 q^{5} - 12 q^{6} - 12 q^{8} + 12 q^{9} + 4 q^{10} - 9 q^{11} + 12 q^{12} + 12 q^{13} - 4 q^{15} + 12 q^{16} - 20 q^{17} - 12 q^{18} + 4 q^{19} - 4 q^{20} + 9 q^{22} - 30 q^{23} - 12 q^{24} + 14 q^{25} - 12 q^{26} + 12 q^{27} - 29 q^{29} + 4 q^{30} + 6 q^{31} - 12 q^{32} - 9 q^{33} + 20 q^{34} - 22 q^{35} + 12 q^{36} + 7 q^{37} - 4 q^{38} + 12 q^{39} + 4 q^{40} - 8 q^{41} - 8 q^{43} - 9 q^{44} - 4 q^{45} + 30 q^{46} - 16 q^{47} + 12 q^{48} + 10 q^{49} - 14 q^{50} - 20 q^{51} + 12 q^{52} - 9 q^{53} - 12 q^{54} - 20 q^{55} + 4 q^{57} + 29 q^{58} - 29 q^{59} - 4 q^{60} - 26 q^{61} - 6 q^{62} + 12 q^{64} - 4 q^{65} + 9 q^{66} + 12 q^{67} - 20 q^{68} - 30 q^{69} + 22 q^{70} - 35 q^{71} - 12 q^{72} + 18 q^{73} - 7 q^{74} + 14 q^{75} + 4 q^{76} - 25 q^{77} - 12 q^{78} - 37 q^{79} - 4 q^{80} + 12 q^{81} + 8 q^{82} - 24 q^{83} - 17 q^{85} + 8 q^{86} - 29 q^{87} + 9 q^{88} + 15 q^{89} + 4 q^{90} - 30 q^{92} + 6 q^{93} + 16 q^{94} - 54 q^{95} - 12 q^{96} - 11 q^{97} - 10 q^{98} - 9 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 12 * q^3 + 12 * q^4 - 4 * q^5 - 12 * q^6 - 12 * q^8 + 12 * q^9 + 4 * q^10 - 9 * q^11 + 12 * q^12 + 12 * q^13 - 4 * q^15 + 12 * q^16 - 20 * q^17 - 12 * q^18 + 4 * q^19 - 4 * q^20 + 9 * q^22 - 30 * q^23 - 12 * q^24 + 14 * q^25 - 12 * q^26 + 12 * q^27 - 29 * q^29 + 4 * q^30 + 6 * q^31 - 12 * q^32 - 9 * q^33 + 20 * q^34 - 22 * q^35 + 12 * q^36 + 7 * q^37 - 4 * q^38 + 12 * q^39 + 4 * q^40 - 8 * q^41 - 8 * q^43 - 9 * q^44 - 4 * q^45 + 30 * q^46 - 16 * q^47 + 12 * q^48 + 10 * q^49 - 14 * q^50 - 20 * q^51 + 12 * q^52 - 9 * q^53 - 12 * q^54 - 20 * q^55 + 4 * q^57 + 29 * q^58 - 29 * q^59 - 4 * q^60 - 26 * q^61 - 6 * q^62 + 12 * q^64 - 4 * q^65 + 9 * q^66 + 12 * q^67 - 20 * q^68 - 30 * q^69 + 22 * q^70 - 35 * q^71 - 12 * q^72 + 18 * q^73 - 7 * q^74 + 14 * q^75 + 4 * q^76 - 25 * q^77 - 12 * q^78 - 37 * q^79 - 4 * q^80 + 12 * q^81 + 8 * q^82 - 24 * q^83 - 17 * q^85 + 8 * q^86 - 29 * q^87 + 9 * q^88 + 15 * q^89 + 4 * q^90 - 30 * q^92 + 6 * q^93 + 16 * q^94 - 54 * q^95 - 12 * q^96 - 11 * q^97 - 10 * q^98 - 9 * q^99

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