LMFDB - Embedded newform 8007.2.a.c.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, 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("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.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:	$63.9362168984$
Analytic rank:	$1$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.833201 q^{2} -1.00000 q^{3} -1.30578 q^{4} -2.56183 q^{5} +0.833201 q^{6} +1.99624 q^{7} +2.75438 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.833201 q^{2} -1.00000 q^{3} -1.30578 q^{4} -2.56183 q^{5} +0.833201 q^{6} +1.99624 q^{7} +2.75438 q^{8} +1.00000 q^{9} +2.13452 q^{10} +2.12320 q^{11} +1.30578 q^{12} +4.16678 q^{13} -1.66327 q^{14} +2.56183 q^{15} +0.316604 q^{16} +1.00000 q^{17} -0.833201 q^{18} -4.35046 q^{19} +3.34518 q^{20} -1.99624 q^{21} -1.76905 q^{22} +4.76822 q^{23} -2.75438 q^{24} +1.56297 q^{25} -3.47177 q^{26} -1.00000 q^{27} -2.60664 q^{28} +1.37217 q^{29} -2.13452 q^{30} -5.24027 q^{31} -5.77255 q^{32} -2.12320 q^{33} -0.833201 q^{34} -5.11402 q^{35} -1.30578 q^{36} -0.204298 q^{37} +3.62481 q^{38} -4.16678 q^{39} -7.05624 q^{40} -10.3797 q^{41} +1.66327 q^{42} +0.0932029 q^{43} -2.77242 q^{44} -2.56183 q^{45} -3.97288 q^{46} -4.14503 q^{47} -0.316604 q^{48} -3.01503 q^{49} -1.30227 q^{50} -1.00000 q^{51} -5.44088 q^{52} -4.98497 q^{53} +0.833201 q^{54} -5.43928 q^{55} +5.49839 q^{56} +4.35046 q^{57} -1.14329 q^{58} +6.46812 q^{59} -3.34518 q^{60} -5.18805 q^{61} +4.36620 q^{62} +1.99624 q^{63} +4.17648 q^{64} -10.6746 q^{65} +1.76905 q^{66} +4.51304 q^{67} -1.30578 q^{68} -4.76822 q^{69} +4.26101 q^{70} +4.87176 q^{71} +2.75438 q^{72} +15.5110 q^{73} +0.170221 q^{74} -1.56297 q^{75} +5.68073 q^{76} +4.23841 q^{77} +3.47177 q^{78} -9.63925 q^{79} -0.811086 q^{80} +1.00000 q^{81} +8.64841 q^{82} -7.95011 q^{83} +2.60664 q^{84} -2.56183 q^{85} -0.0776568 q^{86} -1.37217 q^{87} +5.84809 q^{88} +9.99979 q^{89} +2.13452 q^{90} +8.31789 q^{91} -6.22623 q^{92} +5.24027 q^{93} +3.45364 q^{94} +11.1451 q^{95} +5.77255 q^{96} -2.78079 q^{97} +2.51213 q^{98} +2.12320 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9}+O(q^{10}) $ 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9	\( 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9} + 4 q^{10} + q^{11} - 30 q^{12} - 26 q^{13} - 4 q^{14} + 3 q^{15} + 8 q^{16} + 39 q^{17} - 4 q^{18} - 14 q^{19} - 14 q^{20} + 5 q^{21} - 17 q^{22} + 2 q^{23} + 3 q^{24} - 6 q^{25} - 17 q^{26} - 39 q^{27} - 14 q^{28} - 7 q^{29} - 4 q^{30} - q^{31} - 30 q^{32} - q^{33} - 4 q^{34} + q^{35} + 30 q^{36} - 24 q^{37} - 20 q^{38} + 26 q^{39} + 12 q^{40} + q^{41} + 4 q^{42} - 41 q^{43} - 2 q^{44} - 3 q^{45} - 6 q^{46} - 9 q^{47} - 8 q^{48} - 10 q^{49} - 9 q^{50} - 39 q^{51} - 37 q^{52} - 47 q^{53} + 4 q^{54} - 39 q^{55} + 8 q^{56} + 14 q^{57} - 27 q^{58} + 41 q^{59} + 14 q^{60} - 41 q^{61} + 36 q^{62} - 5 q^{63} - 47 q^{64} - 39 q^{65} + 17 q^{66} - 36 q^{67} + 30 q^{68} - 2 q^{69} - 52 q^{70} - 2 q^{71} - 3 q^{72} - 63 q^{73} - 6 q^{74} + 6 q^{75} - 34 q^{76} - 64 q^{77} + 17 q^{78} + 20 q^{79} - 28 q^{80} + 39 q^{81} - 37 q^{82} + 45 q^{83} + 14 q^{84} - 3 q^{85} + 32 q^{86} + 7 q^{87} + 6 q^{88} - 32 q^{89} + 4 q^{90} - 11 q^{91} + 28 q^{92} + q^{93} - 44 q^{94} + 22 q^{95} + 30 q^{96} - 20 q^{97} + 63 q^{98} + q^{99}+O(q^{100}) \) 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9 + 4 * q^10 + q^11 - 30 * q^12 - 26 * q^13 - 4 * q^14 + 3 * q^15 + 8 * q^16 + 39 * q^17 - 4 * q^18 - 14 * q^19 - 14 * q^20 + 5 * q^21 - 17 * q^22 + 2 * q^23 + 3 * q^24 - 6 * q^25 - 17 * q^26 - 39 * q^27 - 14 * q^28 - 7 * q^29 - 4 * q^30 - q^31 - 30 * q^32 - q^33 - 4 * q^34 + q^35 + 30 * q^36 - 24 * q^37 - 20 * q^38 + 26 * q^39 + 12 * q^40 + q^41 + 4 * q^42 - 41 * q^43 - 2 * q^44 - 3 * q^45 - 6 * q^46 - 9 * q^47 - 8 * q^48 - 10 * q^49 - 9 * q^50 - 39 * q^51 - 37 * q^52 - 47 * q^53 + 4 * q^54 - 39 * q^55 + 8 * q^56 + 14 * q^57 - 27 * q^58 + 41 * q^59 + 14 * q^60 - 41 * q^61 + 36 * q^62 - 5 * q^63 - 47 * q^64 - 39 * q^65 + 17 * q^66 - 36 * q^67 + 30 * q^68 - 2 * q^69 - 52 * q^70 - 2 * q^71 - 3 * q^72 - 63 * q^73 - 6 * q^74 + 6 * q^75 - 34 * q^76 - 64 * q^77 + 17 * q^78 + 20 * q^79 - 28 * q^80 + 39 * q^81 - 37 * q^82 + 45 * q^83 + 14 * q^84 - 3 * q^85 + 32 * q^86 + 7 * q^87 + 6 * q^88 - 32 * q^89 + 4 * q^90 - 11 * q^91 + 28 * q^92 + q^93 - 44 * q^94 + 22 * q^95 + 30 * q^96 - 20 * q^97 + 63 * q^98 + q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.833201	−0.589162	−0.294581	−	0.955627i	$-0.595180\pi$
$2$	−0.833201	−0.589162	−0.294581	+	0.955627i	$0.595180\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.30578	−0.652888
$5$	−2.56183	−1.14569	−0.572843	−	0.819665i	$-0.694159\pi$
$5$	−2.56183	−1.14569	−0.572843	+	0.819665i	$0.694159\pi$
$6$	0.833201	0.340153
$7$	1.99624	0.754507	0.377254	−	0.926110i	$-0.376868\pi$
$7$	1.99624	0.754507	0.377254	+	0.926110i	$0.376868\pi$
$8$	2.75438	0.973819
$9$	1.00000	0.333333
$10$	2.13452	0.674994
$11$	2.12320	0.640169	0.320084	−	0.947389i	$-0.396289\pi$
$11$	2.12320	0.640169	0.320084	+	0.947389i	$0.396289\pi$
$12$	1.30578	0.376945
$13$	4.16678	1.15566	0.577829	−	0.816158i	$-0.303900\pi$
$13$	4.16678	1.15566	0.577829	+	0.816158i	$0.303900\pi$
$14$	−1.66327	−0.444527
$15$	2.56183	0.661462
$16$	0.316604	0.0791511
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−0.833201	−0.196387
$19$	−4.35046	−0.998064	−0.499032	−	0.866583i	$-0.666311\pi$
$19$	−4.35046	−0.998064	−0.499032	+	0.866583i	$0.666311\pi$
$20$	3.34518	0.748004
$21$	−1.99624	−0.435615
$22$	−1.76905	−0.377163
$23$	4.76822	0.994242	0.497121	−	0.867681i	$-0.334390\pi$
$23$	4.76822	0.994242	0.497121	+	0.867681i	$0.334390\pi$
$24$	−2.75438	−0.562235
$25$	1.56297	0.312594
$26$	−3.47177	−0.680869
$27$	−1.00000	−0.192450
$28$	−2.60664	−0.492609
$29$	1.37217	0.254805	0.127403	−	0.991851i	$-0.459336\pi$
$29$	1.37217	0.254805	0.127403	+	0.991851i	$0.459336\pi$
$30$	−2.13452	−0.389708
$31$	−5.24027	−0.941181	−0.470590	−	0.882352i	$-0.655959\pi$
$31$	−5.24027	−0.941181	−0.470590	+	0.882352i	$0.655959\pi$
$32$	−5.77255	−1.02045
$33$	−2.12320	−0.369602
$34$	−0.833201	−0.142893
$35$	−5.11402	−0.864428
$36$	−1.30578	−0.217629
$37$	−0.204298	−0.0335863	−0.0167932	−	0.999859i	$-0.505346\pi$
$37$	−0.204298	−0.0335863	−0.0167932	+	0.999859i	$0.505346\pi$
$38$	3.62481	0.588022
$39$	−4.16678	−0.667219
$40$	−7.05624	−1.11569
$41$	−10.3797	−1.62104	−0.810522	−	0.585709i	$-0.800816\pi$
$41$	−10.3797	−1.62104	−0.810522	+	0.585709i	$0.800816\pi$
$42$	1.66327	0.256648
$43$	0.0932029	0.0142133	0.00710666	−	0.999975i	$-0.497738\pi$
$43$	0.0932029	0.0142133	0.00710666	+	0.999975i	$0.497738\pi$
$44$	−2.77242	−0.417959
$45$	−2.56183	−0.381895
$46$	−3.97288	−0.585770
$47$	−4.14503	−0.604615	−0.302308	−	0.953210i	$-0.597757\pi$
$47$	−4.14503	−0.604615	−0.302308	+	0.953210i	$0.597757\pi$
$48$	−0.316604	−0.0456979
$49$	−3.01503	−0.430719
$50$	−1.30227	−0.184169
$51$	−1.00000	−0.140028
$52$	−5.44088	−0.754515
$53$	−4.98497	−0.684739	−0.342369	−	0.939565i	$-0.611229\pi$
$53$	−4.98497	−0.684739	−0.342369	+	0.939565i	$0.611229\pi$
$54$	0.833201	0.113384
$55$	−5.43928	−0.733432
$56$	5.49839	0.734754
$57$	4.35046	0.576233
$58$	−1.14329	−0.150121
$59$	6.46812	0.842078	0.421039	−	0.907043i	$-0.361666\pi$
$59$	6.46812	0.842078	0.421039	+	0.907043i	$0.361666\pi$
$60$	−3.34518	−0.431860
$61$	−5.18805	−0.664262	−0.332131	−	0.943233i	$-0.607768\pi$
$61$	−5.18805	−0.664262	−0.332131	+	0.943233i	$0.607768\pi$
$62$	4.36620	0.554508
$63$	1.99624	0.251502
$64$	4.17648	0.522060
$65$	−10.6746	−1.32402
$66$	1.76905	0.217755
$67$	4.51304	0.551355	0.275678	−	0.961250i	$-0.411098\pi$
$67$	4.51304	0.551355	0.275678	+	0.961250i	$0.411098\pi$
$68$	−1.30578	−0.158349
$69$	−4.76822	−0.574026
$70$	4.26101	0.509288
$71$	4.87176	0.578172	0.289086	−	0.957303i	$-0.406649\pi$
$71$	4.87176	0.578172	0.289086	+	0.957303i	$0.406649\pi$
$72$	2.75438	0.324606
$73$	15.5110	1.81543	0.907713	−	0.419591i	$-0.137826\pi$
$73$	15.5110	1.81543	0.907713	+	0.419591i	$0.137826\pi$
$74$	0.170221	0.0197878
$75$	−1.56297	−0.180476
$76$	5.68073	0.651624
$77$	4.23841	0.483012
$78$	3.47177	0.393100
$79$	−9.63925	−1.08450	−0.542250	−	0.840217i	$-0.682427\pi$
$79$	−9.63925	−1.08450	−0.542250	+	0.840217i	$0.682427\pi$
$80$	−0.811086	−0.0906822
$81$	1.00000	0.111111
$82$	8.64841	0.955057
$83$	−7.95011	−0.872638	−0.436319	−	0.899792i	$-0.643718\pi$
$83$	−7.95011	−0.872638	−0.436319	+	0.899792i	$0.643718\pi$
$84$	2.60664	0.284408
$85$	−2.56183	−0.277869
$86$	−0.0776568	−0.00837395
$87$	−1.37217	−0.147112
$88$	5.84809	0.623409
$89$	9.99979	1.05998	0.529988	−	0.848005i	$-0.322197\pi$
$89$	9.99979	1.05998	0.529988	+	0.848005i	$0.322197\pi$
$90$	2.13452	0.224998
$91$	8.31789	0.871952
$92$	−6.22623	−0.649129
$93$	5.24027	0.543391
$94$	3.45364	0.356216
$95$	11.1451	1.14347
$96$	5.77255	0.589158
$97$	−2.78079	−0.282346	−0.141173	−	0.989985i	$-0.545087\pi$
$97$	−2.78079	−0.282346	−0.141173	+	0.989985i	$0.545087\pi$
$98$	2.51213	0.253763
$99$	2.12320	0.213390
$100$	−2.04089	−0.204089
$101$	6.20807	0.617726	0.308863	−	0.951107i	$-0.400052\pi$
$101$	6.20807	0.617726	0.308863	+	0.951107i	$0.400052\pi$
$102$	0.833201	0.0824992
$103$	10.9761	1.08151	0.540755	−	0.841180i	$-0.318139\pi$
$103$	10.9761	1.08151	0.540755	+	0.841180i	$0.318139\pi$
$104$	11.4769	1.12540
$105$	5.11402	0.499078
$106$	4.15348	0.403422
$107$	−1.89237	−0.182942	−0.0914709	−	0.995808i	$-0.529157\pi$
$107$	−1.89237	−0.182942	−0.0914709	+	0.995808i	$0.529157\pi$
$108$	1.30578	0.125648
$109$	0.0914903	0.00876318	0.00438159	−	0.999990i	$-0.498605\pi$
$109$	0.0914903	0.00876318	0.00438159	+	0.999990i	$0.498605\pi$
$110$	4.53201	0.432110
$111$	0.204298	0.0193911
$112$	0.632018	0.0597201
$113$	11.0546	1.03993	0.519965	−	0.854188i	$-0.325945\pi$
$113$	11.0546	1.03993	0.519965	+	0.854188i	$0.325945\pi$
$114$	−3.62481	−0.339494
$115$	−12.2154	−1.13909
$116$	−1.79174	−0.166359
$117$	4.16678	0.385219
$118$	−5.38924	−0.496120
$119$	1.99624	0.182995
$120$	7.05624	0.644144
$121$	−6.49202	−0.590184
$122$	4.32269	0.391358
$123$	10.3797	0.935910
$124$	6.84262	0.614486
$125$	8.80508	0.787550
$126$	−1.66327	−0.148176
$127$	−9.59241	−0.851188	−0.425594	−	0.904914i	$-0.639935\pi$
$127$	−9.59241	−0.851188	−0.425594	+	0.904914i	$0.639935\pi$
$128$	8.06524	0.712874
$129$	−0.0932029	−0.00820606
$130$	8.89407	0.780062
$131$	−7.39332	−0.645957	−0.322979	−	0.946406i	$-0.604684\pi$
$131$	−7.39332	−0.645957	−0.322979	+	0.946406i	$0.604684\pi$
$132$	2.77242	0.241309
$133$	−8.68456	−0.753047
$134$	−3.76027	−0.324838
$135$	2.56183	0.220487
$136$	2.75438	0.236186
$137$	−2.91142	−0.248740	−0.124370	−	0.992236i	$-0.539691\pi$
$137$	−2.91142	−0.248740	−0.124370	+	0.992236i	$0.539691\pi$
$138$	3.97288	0.338194
$139$	−2.89992	−0.245968	−0.122984	−	0.992409i	$-0.539246\pi$
$139$	−2.89992	−0.245968	−0.122984	+	0.992409i	$0.539246\pi$
$140$	6.67777	0.564375
$141$	4.14503	0.349075
$142$	−4.05916	−0.340637
$143$	8.84691	0.739816
$144$	0.316604	0.0263837
$145$	−3.51526	−0.291926
$146$	−12.9238	−1.06958
$147$	3.01503	0.248676
$148$	0.266767	0.0219281
$149$	−14.8698	−1.21818	−0.609089	−	0.793102i	$-0.708465\pi$
$149$	−14.8698	−1.21818	−0.609089	+	0.793102i	$0.708465\pi$
$150$	1.30227	0.106330
$151$	−9.49406	−0.772616	−0.386308	−	0.922370i	$-0.626250\pi$
$151$	−9.49406	−0.772616	−0.386308	+	0.922370i	$0.626250\pi$
$152$	−11.9828	−0.971934
$153$	1.00000	0.0808452
$154$	−3.53145	−0.284572
$155$	13.4247	1.07830
$156$	5.44088	0.435619
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	8.03143	0.638946
$159$	4.98497	0.395334
$160$	14.7883	1.16912
$161$	9.51850	0.750163
$162$	−0.833201	−0.0654624
$163$	−10.0075	−0.783849	−0.391925	−	0.919997i	$-0.628191\pi$
$163$	−10.0075	−0.783849	−0.391925	+	0.919997i	$0.628191\pi$
$164$	13.5536	1.05836
$165$	5.43928	0.423447
$166$	6.62404	0.514125
$167$	1.99736	0.154560	0.0772800	−	0.997009i	$-0.475376\pi$
$167$	1.99736	0.154560	0.0772800	+	0.997009i	$0.475376\pi$
$168$	−5.49839	−0.424210
$169$	4.36207	0.335544
$170$	2.13452	0.163710
$171$	−4.35046	−0.332688
$172$	−0.121702	−0.00927971
$173$	9.55547	0.726489	0.363245	−	0.931694i	$-0.381669\pi$
$173$	9.55547	0.726489	0.363245	+	0.931694i	$0.381669\pi$
$174$	1.14329	0.0866727
$175$	3.12007	0.235855
$176$	0.672214	0.0506701
$177$	−6.46812	−0.486174
$178$	−8.33183	−0.624497
$179$	13.1122	0.980051	0.490026	−	0.871708i	$-0.336987\pi$
$179$	13.1122	0.980051	0.490026	+	0.871708i	$0.336987\pi$
$180$	3.34518	0.249335
$181$	−17.2724	−1.28385	−0.641924	−	0.766768i	$-0.721864\pi$
$181$	−17.2724	−1.28385	−0.641924	+	0.766768i	$0.721864\pi$
$182$	−6.93047	−0.513721
$183$	5.18805	0.383512
$184$	13.1335	0.968212
$185$	0.523375	0.0384793
$186$	−4.36620	−0.320145
$187$	2.12320	0.155264
$188$	5.41249	0.394746
$189$	−1.99624	−0.145205
$190$	−9.28614	−0.673688
$191$	4.53789	0.328350	0.164175	−	0.986431i	$-0.447504\pi$
$191$	4.53789	0.328350	0.164175	+	0.986431i	$0.447504\pi$
$192$	−4.17648	−0.301412
$193$	−20.2819	−1.45992	−0.729961	−	0.683489i	$-0.760462\pi$
$193$	−20.2819	−1.45992	−0.729961	+	0.683489i	$0.760462\pi$
$194$	2.31695	0.166348
$195$	10.6746	0.764423
$196$	3.93696	0.281211
$197$	4.53723	0.323264	0.161632	−	0.986851i	$-0.448324\pi$
$197$	4.53723	0.323264	0.161632	+	0.986851i	$0.448324\pi$
$198$	−1.76905	−0.125721
$199$	2.63423	0.186736	0.0933679	−	0.995632i	$-0.470237\pi$
$199$	2.63423	0.186736	0.0933679	+	0.995632i	$0.470237\pi$
$200$	4.30501	0.304410
$201$	−4.51304	−0.318325
$202$	−5.17257	−0.363941
$203$	2.73917	0.192252
$204$	1.30578	0.0914226
$205$	26.5911	1.85720
$206$	−9.14532	−0.637184
$207$	4.76822	0.331414
$208$	1.31922	0.0914715
$209$	−9.23690	−0.638930
$210$	−4.26101	−0.294038
$211$	−19.8832	−1.36881	−0.684407	−	0.729100i	$-0.739939\pi$
$211$	−19.8832	−1.36881	−0.684407	+	0.729100i	$0.739939\pi$
$212$	6.50926	0.447058
$213$	−4.87176	−0.333808
$214$	1.57672	0.107782
$215$	−0.238770	−0.0162840
$216$	−2.75438	−0.187412
$217$	−10.4608	−0.710128
$218$	−0.0762298	−0.00516293
$219$	−15.5110	−1.04814
$220$	7.10248	0.478849
$221$	4.16678	0.280288
$222$	−0.170221	−0.0114245
$223$	9.07276	0.607557	0.303778	−	0.952743i	$-0.401752\pi$
$223$	9.07276	0.607557	0.303778	+	0.952743i	$0.401752\pi$
$224$	−11.5234	−0.769938
$225$	1.56297	0.104198
$226$	−9.21070	−0.612687
$227$	21.7987	1.44683	0.723415	−	0.690414i	$-0.242572\pi$
$227$	21.7987	1.44683	0.723415	+	0.690414i	$0.242572\pi$
$228$	−5.68073	−0.376216
$229$	−24.7942	−1.63845	−0.819224	−	0.573474i	$-0.805596\pi$
$229$	−24.7942	−1.63845	−0.819224	+	0.573474i	$0.805596\pi$
$230$	10.1779	0.671108
$231$	−4.23841	−0.278867
$232$	3.77946	0.248134
$233$	−15.0772	−0.987739	−0.493869	−	0.869536i	$-0.664418\pi$
$233$	−15.0772	−0.987739	−0.493869	+	0.869536i	$0.664418\pi$
$234$	−3.47177	−0.226956
$235$	10.6189	0.692699
$236$	−8.44592	−0.549783
$237$	9.63925	0.626136
$238$	−1.66327	−0.107814
$239$	−9.30206	−0.601700	−0.300850	−	0.953671i	$-0.597270\pi$
$239$	−9.30206	−0.601700	−0.300850	+	0.953671i	$0.597270\pi$
$240$	0.811086	0.0523554
$241$	−5.91923	−0.381291	−0.190646	−	0.981659i	$-0.561058\pi$
$241$	−5.91923	−0.381291	−0.190646	+	0.981659i	$0.561058\pi$
$242$	5.40916	0.347714
$243$	−1.00000	−0.0641500
$244$	6.77443	0.433689
$245$	7.72400	0.493468
$246$	−8.64841	−0.551402
$247$	−18.1274	−1.15342
$248$	−14.4337	−0.916540
$249$	7.95011	0.503818
$250$	−7.33640	−0.463995
$251$	−12.4824	−0.787885	−0.393943	−	0.919135i	$-0.628889\pi$
$251$	−12.4824	−0.787885	−0.393943	+	0.919135i	$0.628889\pi$
$252$	−2.60664	−0.164203
$253$	10.1239	0.636483
$254$	7.99240	0.501488
$255$	2.56183	0.160428
$256$	−15.0729	−0.942058
$257$	15.8787	0.990488	0.495244	−	0.868754i	$-0.335079\pi$
$257$	15.8787	0.990488	0.495244	+	0.868754i	$0.335079\pi$
$258$	0.0776568	0.00483470
$259$	−0.407827	−0.0253411
$260$	13.9386	0.864436
$261$	1.37217	0.0849350
$262$	6.16012	0.380573
$263$	17.9160	1.10475	0.552373	−	0.833597i	$-0.313722\pi$
$263$	17.9160	1.10475	0.552373	+	0.833597i	$0.313722\pi$
$264$	−5.84809	−0.359925
$265$	12.7707	0.784495
$266$	7.23598	0.443667
$267$	−9.99979	−0.611977
$268$	−5.89302	−0.359973
$269$	−4.84988	−0.295702	−0.147851	−	0.989010i	$-0.547236\pi$
$269$	−4.84988	−0.295702	−0.147851	+	0.989010i	$0.547236\pi$
$270$	−2.13452	−0.129903
$271$	5.46180	0.331781	0.165890	−	0.986144i	$-0.446950\pi$
$271$	5.46180	0.331781	0.165890	+	0.986144i	$0.446950\pi$
$272$	0.316604	0.0191970
$273$	−8.31789	−0.503422
$274$	2.42580	0.146548
$275$	3.31850	0.200113
$276$	6.22623	0.374775
$277$	25.0834	1.50712	0.753558	−	0.657382i	$-0.228336\pi$
$277$	25.0834	1.50712	0.753558	+	0.657382i	$0.228336\pi$
$278$	2.41621	0.144915
$279$	−5.24027	−0.313727
$280$	−14.0859	−0.841796
$281$	−4.02571	−0.240153	−0.120077	−	0.992765i	$-0.538314\pi$
$281$	−4.02571	−0.240153	−0.120077	+	0.992765i	$0.538314\pi$
$282$	−3.45364	−0.205662
$283$	18.9517	1.12656	0.563282	−	0.826265i	$-0.309539\pi$
$283$	18.9517	1.12656	0.563282	+	0.826265i	$0.309539\pi$
$284$	−6.36143	−0.377481
$285$	−11.1451	−0.660181
$286$	−7.37125	−0.435871
$287$	−20.7204	−1.22309
$288$	−5.77255	−0.340151
$289$	1.00000	0.0588235
$290$	2.92892	0.171992
$291$	2.78079	0.163013
$292$	−20.2539	−1.18527
$293$	−1.46707	−0.0857069	−0.0428534	−	0.999081i	$-0.513645\pi$
$293$	−1.46707	−0.0857069	−0.0428534	+	0.999081i	$0.513645\pi$
$294$	−2.51213	−0.146510
$295$	−16.5702	−0.964756
$296$	−0.562712	−0.0327070
$297$	−2.12320	−0.123201
$298$	12.3895	0.717705
$299$	19.8681	1.14900
$300$	2.04089	0.117831
$301$	0.186055	0.0107241
$302$	7.91046	0.455196
$303$	−6.20807	−0.356644
$304$	−1.37737	−0.0789979
$305$	13.2909	0.761035
$306$	−0.833201	−0.0476309
$307$	6.79163	0.387619	0.193809	−	0.981039i	$-0.437916\pi$
$307$	6.79163	0.387619	0.193809	+	0.981039i	$0.437916\pi$
$308$	−5.53442	−0.315353
$309$	−10.9761	−0.624410
$310$	−11.1855	−0.635292
$311$	−25.1771	−1.42766	−0.713832	−	0.700317i	$-0.753042\pi$
$311$	−25.1771	−1.42766	−0.713832	+	0.700317i	$0.753042\pi$
$312$	−11.4769	−0.649750
$313$	16.3911	0.926479	0.463240	−	0.886233i	$-0.346687\pi$
$313$	16.3911	0.926479	0.463240	+	0.886233i	$0.346687\pi$
$314$	−0.833201	−0.0470202
$315$	−5.11402	−0.288143
$316$	12.5867	0.708057
$317$	−0.847851	−0.0476200	−0.0238100	−	0.999717i	$-0.507580\pi$
$317$	−0.847851	−0.0476200	−0.0238100	+	0.999717i	$0.507580\pi$
$318$	−4.15348	−0.232916
$319$	2.91339	0.163118
$320$	−10.6994	−0.598117
$321$	1.89237	0.105622
$322$	−7.93082	−0.441968
$323$	−4.35046	−0.242066
$324$	−1.30578	−0.0725431
$325$	6.51256	0.361252
$326$	8.33827	0.461814
$327$	−0.0914903	−0.00505942
$328$	−28.5897	−1.57860
$329$	−8.27447	−0.456187
$330$	−4.53201	−0.249479
$331$	−5.96331	−0.327773	−0.163887	−	0.986479i	$-0.552403\pi$
$331$	−5.96331	−0.327773	−0.163887	+	0.986479i	$0.552403\pi$
$332$	10.3811	0.569735
$333$	−0.204298	−0.0111954
$334$	−1.66420	−0.0910609
$335$	−11.5616	−0.631680
$336$	−0.632018	−0.0344794
$337$	13.0315	0.709872	0.354936	−	0.934891i	$-0.384503\pi$
$337$	13.0315	0.709872	0.354936	+	0.934891i	$0.384503\pi$
$338$	−3.63448	−0.197690
$339$	−11.0546	−0.600403
$340$	3.34518	0.181418
$341$	−11.1261	−0.602515
$342$	3.62481	0.196007
$343$	−19.9924	−1.07949
$344$	0.256716	0.0138412
$345$	12.2154	0.657653
$346$	−7.96163	−0.428020
$347$	30.2123	1.62188	0.810940	−	0.585130i	$-0.198956\pi$
$347$	30.2123	1.62188	0.810940	+	0.585130i	$0.198956\pi$
$348$	1.79174	0.0960475
$349$	15.7962	0.845549	0.422775	−	0.906235i	$-0.361056\pi$
$349$	15.7962	0.845549	0.422775	+	0.906235i	$0.361056\pi$
$350$	−2.59964	−0.138957
$351$	−4.16678	−0.222406
$352$	−12.2563	−0.653261
$353$	−10.6205	−0.565270	−0.282635	−	0.959228i	$-0.591208\pi$
$353$	−10.6205	−0.565270	−0.282635	+	0.959228i	$0.591208\pi$
$354$	5.38924	0.286435
$355$	−12.4806	−0.662403
$356$	−13.0575	−0.692045
$357$	−1.99624	−0.105652
$358$	−10.9251	−0.577409
$359$	−19.0388	−1.00483	−0.502414	−	0.864627i	$-0.667555\pi$
$359$	−19.0388	−1.00483	−0.502414	+	0.864627i	$0.667555\pi$
$360$	−7.05624	−0.371897
$361$	−0.0734838	−0.00386757
$362$	14.3914	0.756395
$363$	6.49202	0.340743
$364$	−10.8613	−0.569287
$365$	−39.7366	−2.07991
$366$	−4.32269	−0.225951
$367$	−19.8979	−1.03866	−0.519332	−	0.854572i	$-0.673819\pi$
$367$	−19.8979	−1.03866	−0.519332	+	0.854572i	$0.673819\pi$
$368$	1.50964	0.0786953
$369$	−10.3797	−0.540348
$370$	−0.436077	−0.0226706
$371$	−9.95120	−0.516640
$372$	−6.84262	−0.354774
$373$	−25.9719	−1.34477	−0.672386	−	0.740201i	$-0.734730\pi$
$373$	−25.9719	−1.34477	−0.672386	+	0.740201i	$0.734730\pi$
$374$	−1.76905	−0.0914755
$375$	−8.80508	−0.454692
$376$	−11.4170	−0.588786
$377$	5.71752	0.294467
$378$	1.66327	0.0855493
$379$	−4.99528	−0.256590	−0.128295	−	0.991736i	$-0.540950\pi$
$379$	−4.99528	−0.256590	−0.128295	+	0.991736i	$0.540950\pi$
$380$	−14.5531	−0.746556
$381$	9.59241	0.491434
$382$	−3.78098	−0.193452
$383$	30.5687	1.56199	0.780995	−	0.624538i	$-0.214713\pi$
$383$	30.5687	1.56199	0.780995	+	0.624538i	$0.214713\pi$
$384$	−8.06524	−0.411578
$385$	−10.8581	−0.553380
$386$	16.8989	0.860130
$387$	0.0932029	0.00473777
$388$	3.63109	0.184340
$389$	11.9228	0.604511	0.302256	−	0.953227i	$-0.402260\pi$
$389$	11.9228	0.604511	0.302256	+	0.953227i	$0.402260\pi$
$390$	−8.89407	−0.450369
$391$	4.76822	0.241139
$392$	−8.30453	−0.419442
$393$	7.39332	0.372943
$394$	−3.78042	−0.190455
$395$	24.6941	1.24250
$396$	−2.77242	−0.139320
$397$	32.6370	1.63800	0.819002	−	0.573791i	$-0.194528\pi$
$397$	32.6370	1.63800	0.819002	+	0.573791i	$0.194528\pi$
$398$	−2.19485	−0.110018
$399$	8.68456	0.434772
$400$	0.494844	0.0247422
$401$	−23.9546	−1.19624	−0.598119	−	0.801407i	$-0.704085\pi$
$401$	−23.9546	−1.19624	−0.598119	+	0.801407i	$0.704085\pi$
$402$	3.76027	0.187545
$403$	−21.8351	−1.08768
$404$	−8.10635	−0.403306
$405$	−2.56183	−0.127298
$406$	−2.28228	−0.113268
$407$	−0.433764	−0.0215009
$408$	−2.75438	−0.136362
$409$	−31.3295	−1.54915	−0.774573	−	0.632484i	$-0.782035\pi$
$409$	−31.3295	−1.54915	−0.774573	+	0.632484i	$0.782035\pi$
$410$	−22.1558	−1.09419
$411$	2.91142	0.143610
$412$	−14.3324	−0.706105
$413$	12.9119	0.635354
$414$	−3.97288	−0.195257
$415$	20.3668	0.999768
$416$	−24.0529	−1.17929
$417$	2.89992	0.142010
$418$	7.69619	0.376433
$419$	−28.3910	−1.38699	−0.693495	−	0.720462i	$-0.743930\pi$
$419$	−28.3910	−1.38699	−0.693495	+	0.720462i	$0.743930\pi$
$420$	−6.67777	−0.325842
$421$	3.03048	0.147697	0.0738483	−	0.997269i	$-0.476472\pi$
$421$	3.03048	0.147697	0.0738483	+	0.997269i	$0.476472\pi$
$422$	16.5667	0.806454
$423$	−4.14503	−0.201538
$424$	−13.7305	−0.666811
$425$	1.56297	0.0758153
$426$	4.05916	0.196667
$427$	−10.3566	−0.501190
$428$	2.47101	0.119441
$429$	−8.84691	−0.427133
$430$	0.198943	0.00959390
$431$	−3.47689	−0.167476	−0.0837381	−	0.996488i	$-0.526686\pi$
$431$	−3.47689	−0.167476	−0.0837381	+	0.996488i	$0.526686\pi$
$432$	−0.316604	−0.0152326
$433$	−6.59729	−0.317046	−0.158523	−	0.987355i	$-0.550673\pi$
$433$	−6.59729	−0.317046	−0.158523	+	0.987355i	$0.550673\pi$
$434$	8.71598	0.418380
$435$	3.51526	0.168544
$436$	−0.119466	−0.00572137
$437$	−20.7440	−0.992318
$438$	12.9238	0.617523
$439$	−21.9597	−1.04808	−0.524040	−	0.851694i	$-0.675576\pi$
$439$	−21.9597	−1.04808	−0.524040	+	0.851694i	$0.675576\pi$
$440$	−14.9818	−0.714230
$441$	−3.01503	−0.143573
$442$	−3.47177	−0.165135
$443$	24.4296	1.16069	0.580343	−	0.814372i	$-0.302919\pi$
$443$	24.4296	1.16069	0.580343	+	0.814372i	$0.302919\pi$
$444$	−0.266767	−0.0126602
$445$	−25.6178	−1.21440
$446$	−7.55943	−0.357949
$447$	14.8698	0.703316
$448$	8.33726	0.393898
$449$	5.23631	0.247117	0.123558	−	0.992337i	$-0.460569\pi$
$449$	5.23631	0.247117	0.123558	+	0.992337i	$0.460569\pi$
$450$	−1.30227	−0.0613896
$451$	−22.0383	−1.03774
$452$	−14.4348	−0.678957
$453$	9.49406	0.446070
$454$	−18.1627	−0.852417
$455$	−21.3090	−0.998982
$456$	11.9828	0.561146
$457$	−13.6965	−0.640697	−0.320349	−	0.947300i	$-0.603800\pi$
$457$	−13.6965	−0.640697	−0.320349	+	0.947300i	$0.603800\pi$
$458$	20.6586	0.965311
$459$	−1.00000	−0.0466760
$460$	15.9505	0.743697
$461$	7.84106	0.365195	0.182597	−	0.983188i	$-0.441550\pi$
$461$	7.84106	0.365195	0.182597	+	0.983188i	$0.441550\pi$
$462$	3.53145	0.164298
$463$	−32.4551	−1.50832	−0.754159	−	0.656691i	$-0.771955\pi$
$463$	−32.4551	−1.50832	−0.754159	+	0.656691i	$0.771955\pi$
$464$	0.434434	0.0201681
$465$	−13.4247	−0.622555
$466$	12.5623	0.581938
$467$	15.6407	0.723764	0.361882	−	0.932224i	$-0.382134\pi$
$467$	15.6407	0.723764	0.361882	+	0.932224i	$0.382134\pi$
$468$	−5.44088	−0.251505
$469$	9.00910	0.416002
$470$	−8.84765	−0.408112
$471$	−1.00000	−0.0460776
$472$	17.8156	0.820031
$473$	0.197888	0.00909892
$474$	−8.03143	−0.368896
$475$	−6.79965	−0.311989
$476$	−2.60664	−0.119475
$477$	−4.98497	−0.228246
$478$	7.75048	0.354499
$479$	11.2547	0.514239	0.257119	−	0.966380i	$-0.417227\pi$
$479$	11.2547	0.514239	0.257119	+	0.966380i	$0.417227\pi$
$480$	−14.7883	−0.674990
$481$	−0.851263	−0.0388143
$482$	4.93191	0.224642
$483$	−9.51850	−0.433107
$484$	8.47713	0.385324
$485$	7.12390	0.323480
$486$	0.833201	0.0377948
$487$	−4.82154	−0.218485	−0.109242	−	0.994015i	$-0.534842\pi$
$487$	−4.82154	−0.218485	−0.109242	+	0.994015i	$0.534842\pi$
$488$	−14.2898	−0.646871
$489$	10.0075	0.452556
$490$	−6.43564	−0.290733
$491$	−11.3238	−0.511034	−0.255517	−	0.966805i	$-0.582246\pi$
$491$	−11.3238	−0.511034	−0.255517	+	0.966805i	$0.582246\pi$
$492$	−13.5536	−0.611044
$493$	1.37217	0.0617993
$494$	15.1038	0.679551
$495$	−5.43928	−0.244477
$496$	−1.65909	−0.0744955
$497$	9.72520	0.436235
$498$	−6.62404	−0.296830
$499$	−5.38556	−0.241091	−0.120545	−	0.992708i	$-0.538464\pi$
$499$	−5.38556	−0.241091	−0.120545	+	0.992708i	$0.538464\pi$
$500$	−11.4975	−0.514182
$501$	−1.99736	−0.0892352
$502$	10.4004	0.464192
$503$	18.3719	0.819162	0.409581	−	0.912274i	$-0.365675\pi$
$503$	18.3719	0.819162	0.409581	+	0.912274i	$0.365675\pi$
$504$	5.49839	0.244918
$505$	−15.9040	−0.707719
$506$	−8.43523	−0.374992
$507$	−4.36207	−0.193726
$508$	12.5255	0.555731
$509$	21.6093	0.957817	0.478909	−	0.877865i	$-0.341033\pi$
$509$	21.6093	0.957817	0.478909	+	0.877865i	$0.341033\pi$
$510$	−2.13452	−0.0945181
$511$	30.9637	1.36975
$512$	−3.57171	−0.157849
$513$	4.35046	0.192078
$514$	−13.2302	−0.583558
$515$	−28.1190	−1.23907
$516$	0.121702	0.00535764
$517$	−8.80073	−0.387056
$518$	0.339802	0.0149300
$519$	−9.55547	−0.419439
$520$	−29.4018	−1.28935
$521$	2.43629	0.106736	0.0533680	−	0.998575i	$-0.483004\pi$
$521$	2.43629	0.106736	0.0533680	+	0.998575i	$0.483004\pi$
$522$	−1.14329	−0.0500405
$523$	−7.16286	−0.313210	−0.156605	−	0.987661i	$-0.550055\pi$
$523$	−7.16286	−0.313210	−0.156605	+	0.987661i	$0.550055\pi$
$524$	9.65402	0.421738
$525$	−3.12007	−0.136171
$526$	−14.9276	−0.650875
$527$	−5.24027	−0.228270
$528$	−0.672214	−0.0292544
$529$	−0.264093	−0.0114823
$530$	−10.6405	−0.462195
$531$	6.46812	0.280693
$532$	11.3401	0.491655
$533$	−43.2501	−1.87337
$534$	8.33183	0.360554
$535$	4.84792	0.209594
$536$	12.4306	0.536920
$537$	−13.1122	−0.565833
$538$	4.04092	0.174216
$539$	−6.40151	−0.275733
$540$	−3.34518	−0.143953
$541$	2.24752	0.0966285	0.0483142	−	0.998832i	$-0.484615\pi$
$541$	2.24752	0.0966285	0.0483142	+	0.998832i	$0.484615\pi$
$542$	−4.55078	−0.195473
$543$	17.2724	0.741231
$544$	−5.77255	−0.247496
$545$	−0.234382	−0.0100398
$546$	6.93047	0.296597
$547$	−29.7218	−1.27081	−0.635406	−	0.772179i	$-0.719167\pi$
$547$	−29.7218	−1.27081	−0.635406	+	0.772179i	$0.719167\pi$
$548$	3.80167	0.162399
$549$	−5.18805	−0.221421
$550$	−2.76498	−0.117899
$551$	−5.96956	−0.254312
$552$	−13.1335	−0.558997
$553$	−19.2422	−0.818263
$554$	−20.8995	−0.887935
$555$	−0.523375	−0.0222161
$556$	3.78664	0.160589
$557$	6.48067	0.274595	0.137297	−	0.990530i	$-0.456158\pi$
$557$	6.48067	0.274595	0.137297	+	0.990530i	$0.456158\pi$
$558$	4.36620	0.184836
$559$	0.388356	0.0164257
$560$	−1.61912	−0.0684204
$561$	−2.12320	−0.0896416
$562$	3.35422	0.141489
$563$	3.54172	0.149266	0.0746329	−	0.997211i	$-0.476221\pi$
$563$	3.54172	0.149266	0.0746329	+	0.997211i	$0.476221\pi$
$564$	−5.41249	−0.227907
$565$	−28.3200	−1.19143
$566$	−15.7906	−0.663728
$567$	1.99624	0.0838342
$568$	13.4187	0.563035
$569$	−20.6294	−0.864828	−0.432414	−	0.901675i	$-0.642338\pi$
$569$	−20.6294	−0.864828	−0.432414	+	0.901675i	$0.642338\pi$
$570$	9.28614	0.388954
$571$	18.2436	0.763470	0.381735	−	0.924272i	$-0.375327\pi$
$571$	18.2436	0.763470	0.381735	+	0.924272i	$0.375327\pi$
$572$	−11.5521	−0.483017
$573$	−4.53789	−0.189573
$574$	17.2643	0.720598
$575$	7.45259	0.310795
$576$	4.17648	0.174020
$577$	9.52787	0.396650	0.198325	−	0.980136i	$-0.436450\pi$
$577$	9.52787	0.396650	0.198325	+	0.980136i	$0.436450\pi$
$578$	−0.833201	−0.0346566
$579$	20.2819	0.842886
$580$	4.59014	0.190595
$581$	−15.8703	−0.658412
$582$	−2.31695	−0.0960408
$583$	−10.5841	−0.438348
$584$	42.7232	1.76790
$585$	−10.6746	−0.441340
$586$	1.22236	0.0504952
$587$	−9.51270	−0.392631	−0.196316	−	0.980541i	$-0.562898\pi$
$587$	−9.51270	−0.392631	−0.196316	+	0.980541i	$0.562898\pi$
$588$	−3.93696	−0.162357
$589$	22.7976	0.939359
$590$	13.8063	0.568397
$591$	−4.53723	−0.186637
$592$	−0.0646815	−0.00265839
$593$	−24.8135	−1.01897	−0.509484	−	0.860480i	$-0.670164\pi$
$593$	−24.8135	−1.01897	−0.509484	+	0.860480i	$0.670164\pi$
$594$	1.76905	0.0725851
$595$	−5.11402	−0.209655
$596$	19.4166	0.795335
$597$	−2.63423	−0.107812
$598$	−16.5541	−0.676949
$599$	9.75144	0.398433	0.199216	−	0.979956i	$-0.436160\pi$
$599$	9.75144	0.398433	0.199216	+	0.979956i	$0.436160\pi$
$600$	−4.30501	−0.175751
$601$	18.2969	0.746347	0.373174	−	0.927762i	$-0.378270\pi$
$601$	18.2969	0.746347	0.373174	+	0.927762i	$0.378270\pi$
$602$	−0.155021	−0.00631820
$603$	4.51304	0.183785
$604$	12.3971	0.504432
$605$	16.6315	0.676165
$606$	5.17257	0.210121
$607$	−34.4338	−1.39763	−0.698813	−	0.715304i	$-0.746288\pi$
$607$	−34.4338	−1.39763	−0.698813	+	0.715304i	$0.746288\pi$
$608$	25.1132	1.01848
$609$	−2.73917	−0.110997
$610$	−11.0740	−0.448373
$611$	−17.2714	−0.698728
$612$	−1.30578	−0.0527829
$613$	19.1525	0.773564	0.386782	−	0.922171i	$-0.373587\pi$
$613$	19.1525	0.773564	0.386782	+	0.922171i	$0.373587\pi$
$614$	−5.65879	−0.228370
$615$	−26.5911	−1.07226
$616$	11.6742	0.470366
$617$	−23.5553	−0.948300	−0.474150	−	0.880444i	$-0.657244\pi$
$617$	−23.5553	−0.948300	−0.474150	+	0.880444i	$0.657244\pi$
$618$	9.14532	0.367879
$619$	43.5404	1.75004	0.875018	−	0.484091i	$-0.160850\pi$
$619$	43.5404	1.75004	0.875018	+	0.484091i	$0.160850\pi$
$620$	−17.5296	−0.704007
$621$	−4.76822	−0.191342
$622$	20.9776	0.841125
$623$	19.9620	0.799759
$624$	−1.31922	−0.0528111
$625$	−30.3720	−1.21488
$626$	−13.6571	−0.545846
$627$	9.23690	0.368886
$628$	−1.30578	−0.0521061
$629$	−0.204298	−0.00814588
$630$	4.26101	0.169763
$631$	−26.7013	−1.06296	−0.531482	−	0.847070i	$-0.678365\pi$
$631$	−26.7013	−1.06296	−0.531482	+	0.847070i	$0.678365\pi$
$632$	−26.5501	−1.05611
$633$	19.8832	0.790286
$634$	0.706430	0.0280559
$635$	24.5741	0.975194
$636$	−6.50926	−0.258109
$637$	−12.5630	−0.497763
$638$	−2.42744	−0.0961031
$639$	4.87176	0.192724
$640$	−20.6618	−0.816729
$641$	−38.7910	−1.53215	−0.766075	−	0.642751i	$-0.777793\pi$
$641$	−38.7910	−1.53215	−0.766075	+	0.642751i	$0.777793\pi$
$642$	−1.57672	−0.0622282
$643$	−8.71344	−0.343625	−0.171812	−	0.985130i	$-0.554962\pi$
$643$	−8.71344	−0.343625	−0.171812	+	0.985130i	$0.554962\pi$
$644$	−12.4290	−0.489773
$645$	0.238770	0.00940156
$646$	3.62481	0.142616
$647$	−3.63313	−0.142833	−0.0714165	−	0.997447i	$-0.522752\pi$
$647$	−3.63313	−0.142833	−0.0714165	+	0.997447i	$0.522752\pi$
$648$	2.75438	0.108202
$649$	13.7331	0.539072
$650$	−5.42627	−0.212836
$651$	10.4608	0.409993
$652$	13.0676	0.511766
$653$	−15.0545	−0.589127	−0.294564	−	0.955632i	$-0.595174\pi$
$653$	−15.0545	−0.589127	−0.294564	+	0.955632i	$0.595174\pi$
$654$	0.0762298	0.00298082
$655$	18.9404	0.740063
$656$	−3.28627	−0.128307
$657$	15.5110	0.605142
$658$	6.89430	0.268768
$659$	−13.1709	−0.513066	−0.256533	−	0.966535i	$-0.582580\pi$
$659$	−13.1709	−0.513066	−0.256533	+	0.966535i	$0.582580\pi$
$660$	−7.10248	−0.276464
$661$	11.0517	0.429863	0.214932	−	0.976629i	$-0.431047\pi$
$661$	11.0517	0.429863	0.214932	+	0.976629i	$0.431047\pi$
$662$	4.96864	0.193112
$663$	−4.16678	−0.161824
$664$	−21.8976	−0.849791
$665$	22.2484	0.862755
$666$	0.170221	0.00659592
$667$	6.54279	0.253338
$668$	−2.60810	−0.100910
$669$	−9.07276	−0.350773
$670$	9.63316	0.372162
$671$	−11.0153	−0.425240
$672$	11.5234	0.444524
$673$	−3.74177	−0.144235	−0.0721174	−	0.997396i	$-0.522976\pi$
$673$	−3.74177	−0.144235	−0.0721174	+	0.997396i	$0.522976\pi$
$674$	−10.8579	−0.418229
$675$	−1.56297	−0.0601588
$676$	−5.69588	−0.219072
$677$	−14.9430	−0.574306	−0.287153	−	0.957885i	$-0.592709\pi$
$677$	−14.9430	−0.574306	−0.287153	+	0.957885i	$0.592709\pi$
$678$	9.21070	0.353735
$679$	−5.55111	−0.213032
$680$	−7.05624	−0.270595
$681$	−21.7987	−0.835327
$682$	9.27032	0.354979
$683$	10.6902	0.409048	0.204524	−	0.978862i	$-0.434435\pi$
$683$	10.6902	0.409048	0.204524	+	0.978862i	$0.434435\pi$
$684$	5.68073	0.217208
$685$	7.45857	0.284977
$686$	16.6577	0.635993
$687$	24.7942	0.945958
$688$	0.0295085	0.00112500
$689$	−20.7713	−0.791323
$690$	−10.1779	−0.387464
$691$	3.93285	0.149613	0.0748064	−	0.997198i	$-0.476166\pi$
$691$	3.93285	0.149613	0.0748064	+	0.997198i	$0.476166\pi$
$692$	−12.4773	−0.474316
$693$	4.23841	0.161004
$694$	−25.1729	−0.955550
$695$	7.42909	0.281802
$696$	−3.77946	−0.143260
$697$	−10.3797	−0.393161
$698$	−13.1614	−0.498166
$699$	15.0772	0.570271
$700$	−4.07411	−0.153987
$701$	0.243728	0.00920547	0.00460274	−	0.999989i	$-0.498535\pi$
$701$	0.243728	0.00920547	0.00460274	+	0.999989i	$0.498535\pi$
$702$	3.47177	0.131033
$703$	0.888789	0.0335213
$704$	8.86751	0.334207
$705$	−10.6189	−0.399930
$706$	8.84897	0.333035
$707$	12.3928	0.466079
$708$	8.44592	0.317417
$709$	21.8552	0.820789	0.410395	−	0.911908i	$-0.365391\pi$
$709$	21.8552	0.820789	0.410395	+	0.911908i	$0.365391\pi$
$710$	10.3989	0.390263
$711$	−9.63925	−0.361500
$712$	27.5432	1.03222
$713$	−24.9868	−0.935762
$714$	1.66327	0.0622462
$715$	−22.6643	−0.847596
$716$	−17.1216	−0.639864
$717$	9.30206	0.347392
$718$	15.8631	0.592007
$719$	−2.19348	−0.0818028	−0.0409014	−	0.999163i	$-0.513023\pi$
$719$	−2.19348	−0.0818028	−0.0409014	+	0.999163i	$0.513023\pi$
$720$	−0.811086	−0.0302274
$721$	21.9110	0.816007
$722$	0.0612268	0.00227862
$723$	5.91923	0.220139
$724$	22.5539	0.838210
$725$	2.14466	0.0796506
$726$	−5.40916	−0.200753
$727$	32.7731	1.21549	0.607744	−	0.794133i	$-0.292075\pi$
$727$	32.7731	1.21549	0.607744	+	0.794133i	$0.292075\pi$
$728$	22.9106	0.849123
$729$	1.00000	0.0370370
$730$	33.1086	1.22540
$731$	0.0932029	0.00344724
$732$	−6.77443	−0.250390
$733$	−40.4476	−1.49397	−0.746983	−	0.664843i	$-0.768499\pi$
$733$	−40.4476	−1.49397	−0.746983	+	0.664843i	$0.768499\pi$
$734$	16.5790	0.611942
$735$	−7.72400	−0.284904
$736$	−27.5248	−1.01458
$737$	9.58208	0.352961
$738$	8.64841	0.318352
$739$	−16.9320	−0.622855	−0.311428	−	0.950270i	$-0.600807\pi$
$739$	−16.9320	−0.622855	−0.311428	+	0.950270i	$0.600807\pi$
$740$	−0.683411	−0.0251227
$741$	18.1274	0.665927
$742$	8.29135	0.304385
$743$	0.770379	0.0282625	0.0141312	−	0.999900i	$-0.495502\pi$
$743$	0.770379	0.0282625	0.0141312	+	0.999900i	$0.495502\pi$
$744$	14.4337	0.529164
$745$	38.0938	1.39565
$746$	21.6398	0.792288
$747$	−7.95011	−0.290879
$748$	−2.77242	−0.101370
$749$	−3.77761	−0.138031
$750$	7.33640	0.267887
$751$	−37.0529	−1.35208	−0.676040	−	0.736865i	$-0.736305\pi$
$751$	−37.0529	−1.35208	−0.676040	+	0.736865i	$0.736305\pi$
$752$	−1.31234	−0.0478559
$753$	12.4824	0.454886
$754$	−4.76384	−0.173489
$755$	24.3222	0.885175
$756$	2.60664	0.0948026
$757$	−10.0923	−0.366813	−0.183406	−	0.983037i	$-0.558712\pi$
$757$	−10.0923	−0.366813	−0.183406	+	0.983037i	$0.558712\pi$
$758$	4.16207	0.151173
$759$	−10.1239	−0.367474
$760$	30.6979	1.11353
$761$	13.4758	0.488497	0.244248	−	0.969713i	$-0.421459\pi$
$761$	13.4758	0.488497	0.244248	+	0.969713i	$0.421459\pi$
$762$	−7.99240	−0.289534
$763$	0.182636	0.00661188
$764$	−5.92547	−0.214376
$765$	−2.56183	−0.0926232
$766$	−25.4699	−0.920265
$767$	26.9512	0.973153
$768$	15.0729	0.543898
$769$	39.5017	1.42447	0.712234	−	0.701942i	$-0.247683\pi$
$769$	39.5017	1.42447	0.712234	+	0.701942i	$0.247683\pi$
$770$	9.04697	0.326030
$771$	−15.8787	−0.571858
$772$	26.4836	0.953165
$773$	34.7469	1.24976	0.624879	−	0.780721i	$-0.285148\pi$
$773$	34.7469	1.24976	0.624879	+	0.780721i	$0.285148\pi$
$774$	−0.0776568	−0.00279132
$775$	−8.19040	−0.294208
$776$	−7.65933	−0.274954
$777$	0.407827	0.0146307
$778$	−9.93411	−0.356155
$779$	45.1567	1.61791
$780$	−13.9386	−0.499083
$781$	10.3437	0.370128
$782$	−3.97288	−0.142070
$783$	−1.37217	−0.0490373
$784$	−0.954572	−0.0340918
$785$	−2.56183	−0.0914356
$786$	−6.16012	−0.219724
$787$	−29.8211	−1.06301	−0.531503	−	0.847056i	$-0.678373\pi$
$787$	−29.8211	−1.06301	−0.531503	+	0.847056i	$0.678373\pi$
$788$	−5.92460	−0.211055
$789$	−17.9160	−0.637826
$790$	−20.5752	−0.732031
$791$	22.0676	0.784634
$792$	5.84809	0.207803
$793$	−21.6175	−0.767659
$794$	−27.1932	−0.965050
$795$	−12.7707	−0.452928
$796$	−3.43972	−0.121918
$797$	−27.2700	−0.965954	−0.482977	−	0.875633i	$-0.660445\pi$
$797$	−27.2700	−0.965954	−0.482977	+	0.875633i	$0.660445\pi$
$798$	−7.23598	−0.256151
$799$	−4.14503	−0.146641
$800$	−9.02233	−0.318987
$801$	9.99979	0.353325
$802$	19.9590	0.704778
$803$	32.9330	1.16218
$804$	5.89302	0.207831
$805$	−24.3848	−0.859451
$806$	18.1930	0.640821
$807$	4.84988	0.170724
$808$	17.0993	0.601553
$809$	43.5315	1.53049	0.765243	−	0.643741i	$-0.222619\pi$
$809$	43.5315	1.53049	0.765243	+	0.643741i	$0.222619\pi$
$810$	2.13452	0.0749993
$811$	−26.7990	−0.941038	−0.470519	−	0.882390i	$-0.655933\pi$
$811$	−26.7990	−0.941038	−0.470519	+	0.882390i	$0.655933\pi$
$812$	−3.57675	−0.125519
$813$	−5.46180	−0.191554
$814$	0.361413	0.0126675
$815$	25.6376	0.898045
$816$	−0.316604	−0.0110834
$817$	−0.405476	−0.0141858
$818$	26.1038	0.912698
$819$	8.31789	0.290651
$820$	−34.7221	−1.21255
$821$	−45.2578	−1.57951	−0.789753	−	0.613425i	$-0.789791\pi$
$821$	−45.2578	−1.57951	−0.789753	+	0.613425i	$0.789791\pi$
$822$	−2.42580	−0.0846095
$823$	−1.24884	−0.0435318	−0.0217659	−	0.999763i	$-0.506929\pi$
$823$	−1.24884	−0.0435318	−0.0217659	+	0.999763i	$0.506929\pi$
$824$	30.2324	1.05319
$825$	−3.31850	−0.115535
$826$	−10.7582	−0.374326
$827$	−15.2350	−0.529773	−0.264887	−	0.964280i	$-0.585335\pi$
$827$	−15.2350	−0.529773	−0.264887	+	0.964280i	$0.585335\pi$
$828$	−6.22623	−0.216376
$829$	−46.2127	−1.60503	−0.802516	−	0.596631i	$-0.796506\pi$
$829$	−46.2127	−1.60503	−0.802516	+	0.596631i	$0.796506\pi$
$830$	−16.9697	−0.589026
$831$	−25.0834	−0.870134
$832$	17.4025	0.603323
$833$	−3.01503	−0.104465
$834$	−2.41621	−0.0836666
$835$	−5.11688	−0.177077
$836$	12.0613	0.417150
$837$	5.24027	0.181130
$838$	23.6554	0.817162
$839$	23.8860	0.824637	0.412318	−	0.911040i	$-0.364719\pi$
$839$	23.8860	0.824637	0.412318	+	0.911040i	$0.364719\pi$
$840$	14.0859	0.486011
$841$	−27.1172	−0.935074
$842$	−2.52500	−0.0870172
$843$	4.02571	0.138653
$844$	25.9630	0.893683
$845$	−11.1749	−0.384427
$846$	3.45364	0.118739
$847$	−12.9596	−0.445298
$848$	−1.57826	−0.0541978
$849$	−18.9517	−0.650422
$850$	−1.30227	−0.0446675
$851$	−0.974135	−0.0333929
$852$	6.36143	0.217939
$853$	49.6199	1.69895	0.849477	−	0.527626i	$-0.176918\pi$
$853$	49.6199	1.69895	0.849477	+	0.527626i	$0.176918\pi$
$854$	8.62912	0.295282
$855$	11.1451	0.381156
$856$	−5.21229	−0.178152
$857$	32.8275	1.12136	0.560682	−	0.828031i	$-0.310539\pi$
$857$	32.8275	1.12136	0.560682	+	0.828031i	$0.310539\pi$
$858$	7.37125	0.251650
$859$	−33.4834	−1.14244	−0.571219	−	0.820798i	$-0.693529\pi$
$859$	−33.4834	−1.14244	−0.571219	+	0.820798i	$0.693529\pi$
$860$	0.311780	0.0106316
$861$	20.7204	0.706151
$862$	2.89695	0.0986706
$863$	−46.3116	−1.57646	−0.788232	−	0.615378i	$-0.789003\pi$
$863$	−46.3116	−1.57646	−0.788232	+	0.615378i	$0.789003\pi$
$864$	5.77255	0.196386
$865$	−24.4795	−0.832328
$866$	5.49687	0.186791
$867$	−1.00000	−0.0339618
$868$	13.6595	0.463634
$869$	−20.4660	−0.694263
$870$	−2.92892	−0.0992996
$871$	18.8048	0.637178
$872$	0.251999	0.00853375
$873$	−2.78079	−0.0941154
$874$	17.2839	0.584636
$875$	17.5770	0.594213
$876$	20.2539	0.684316
$877$	−12.3368	−0.416584	−0.208292	−	0.978067i	$-0.566790\pi$
$877$	−12.3368	−0.416584	−0.208292	+	0.978067i	$0.566790\pi$
$878$	18.2969	0.617489
$879$	1.46707	0.0494829
$880$	−1.72210	−0.0580519
$881$	−39.2605	−1.32272	−0.661359	−	0.750069i	$-0.730020\pi$
$881$	−39.2605	−1.32272	−0.661359	+	0.750069i	$0.730020\pi$
$882$	2.51213	0.0845877
$883$	−27.9769	−0.941499	−0.470749	−	0.882267i	$-0.656016\pi$
$883$	−27.9769	−0.941499	−0.470749	+	0.882267i	$0.656016\pi$
$884$	−5.44088	−0.182997
$885$	16.5702	0.557002
$886$	−20.3548	−0.683832
$887$	11.1718	0.375112	0.187556	−	0.982254i	$-0.439943\pi$
$887$	11.1718	0.375112	0.187556	+	0.982254i	$0.439943\pi$
$888$	0.562712	0.0188834
$889$	−19.1487	−0.642228
$890$	21.3447	0.715477
$891$	2.12320	0.0711299
$892$	−11.8470	−0.396667
$893$	18.0328	0.603445
$894$	−12.3895	−0.414367
$895$	−33.5912	−1.12283
$896$	16.1002	0.537868
$897$	−19.8681	−0.663377
$898$	−4.36290	−0.145592
$899$	−7.19053	−0.239818
$900$	−2.04089	−0.0680297
$901$	−4.98497	−0.166074
$902$	18.3623	0.611398
$903$	−0.186055	−0.00619153
$904$	30.4485	1.01270
$905$	44.2490	1.47089
$906$	−7.91046	−0.262808
$907$	−42.4614	−1.40991	−0.704954	−	0.709253i	$-0.749032\pi$
$907$	−42.4614	−1.40991	−0.704954	+	0.709253i	$0.749032\pi$
$908$	−28.4642	−0.944618
$909$	6.20807	0.205909
$910$	17.7547	0.588562
$911$	−23.2540	−0.770438	−0.385219	−	0.922825i	$-0.625874\pi$
$911$	−23.2540	−0.770438	−0.385219	+	0.922825i	$0.625874\pi$
$912$	1.37737	0.0456094
$913$	−16.8797	−0.558636
$914$	11.4120	0.377475
$915$	−13.2909	−0.439384
$916$	32.3757	1.06972
$917$	−14.7588	−0.487379
$918$	0.833201	0.0274997
$919$	−2.66044	−0.0877597	−0.0438798	−	0.999037i	$-0.513972\pi$
$919$	−2.66044	−0.0877597	−0.0438798	+	0.999037i	$0.513972\pi$
$920$	−33.6457	−1.10927
$921$	−6.79163	−0.223792
$922$	−6.53318	−0.215159
$923$	20.2996	0.668168
$924$	5.53442	0.182069
$925$	−0.319311	−0.0104989
$926$	27.0417	0.888644
$927$	10.9761	0.360503
$928$	−7.92090	−0.260016
$929$	55.2874	1.81392	0.906960	−	0.421216i	$-0.138397\pi$
$929$	55.2874	1.81392	0.906960	+	0.421216i	$0.138397\pi$
$930$	11.1855	0.366786
$931$	13.1168	0.429885
$932$	19.6874	0.644883
$933$	25.1771	0.824262
$934$	−13.0318	−0.426414
$935$	−5.43928	−0.177883
$936$	11.4769	0.375134
$937$	−0.218833	−0.00714896	−0.00357448	−	0.999994i	$-0.501138\pi$
$937$	−0.218833	−0.00714896	−0.00357448	+	0.999994i	$0.501138\pi$
$938$	−7.50639	−0.245092
$939$	−16.3911	−0.534903
$940$	−13.8659	−0.452255
$941$	14.5409	0.474019	0.237009	−	0.971507i	$-0.423833\pi$
$941$	14.5409	0.474019	0.237009	+	0.971507i	$0.423833\pi$
$942$	0.833201	0.0271472
$943$	−49.4929	−1.61171
$944$	2.04784	0.0666514
$945$	5.11402	0.166359
$946$	−0.164881	−0.00536074
$947$	−32.1323	−1.04416	−0.522079	−	0.852897i	$-0.674843\pi$
$947$	−32.1323	−1.04416	−0.522079	+	0.852897i	$0.674843\pi$
$948$	−12.5867	−0.408797
$949$	64.6310	2.09801
$950$	5.66547	0.183812
$951$	0.847851	0.0274934
$952$	5.49839	0.178204
$953$	1.09088	0.0353371	0.0176685	−	0.999844i	$-0.494376\pi$
$953$	1.09088	0.0353371	0.0176685	+	0.999844i	$0.494376\pi$
$954$	4.15348	0.134474
$955$	−11.6253	−0.376186
$956$	12.1464	0.392843
$957$	−2.91339	−0.0941764
$958$	−9.37740	−0.302970
$959$	−5.81189	−0.187676
$960$	10.6994	0.345323
$961$	−3.53954	−0.114179
$962$	0.709273	0.0228679
$963$	−1.89237	−0.0609806
$964$	7.72920	0.248941
$965$	51.9587	1.67261
$966$	7.93082	0.255170
$967$	15.0487	0.483932	0.241966	−	0.970285i	$-0.422208\pi$
$967$	15.0487	0.483932	0.241966	+	0.970285i	$0.422208\pi$
$968$	−17.8815	−0.574732
$969$	4.35046	0.139757
$970$	−5.93564	−0.190582
$971$	11.1835	0.358895	0.179448	−	0.983768i	$-0.442569\pi$
$971$	11.1835	0.358895	0.179448	+	0.983768i	$0.442569\pi$
$972$	1.30578	0.0418828
$973$	−5.78893	−0.185584
$974$	4.01731	0.128723
$975$	−6.51256	−0.208569
$976$	−1.64256	−0.0525770
$977$	1.59214	0.0509372	0.0254686	−	0.999676i	$-0.491892\pi$
$977$	1.59214	0.0509372	0.0254686	+	0.999676i	$0.491892\pi$
$978$	−8.33827	−0.266629
$979$	21.2315	0.678563
$980$	−10.0858	−0.322179
$981$	0.0914903	0.00292106
$982$	9.43497	0.301082
$983$	0.912072	0.0290906	0.0145453	−	0.999894i	$-0.495370\pi$
$983$	0.912072	0.0290906	0.0145453	+	0.999894i	$0.495370\pi$
$984$	28.5897	0.911406
$985$	−11.6236	−0.370359
$986$	−1.14329	−0.0364098
$987$	8.27447	0.263379
$988$	23.6704	0.753054
$989$	0.444412	0.0141315
$990$	4.53201	0.144037
$991$	40.9014	1.29928	0.649639	−	0.760243i	$-0.274920\pi$
$991$	40.9014	1.29928	0.649639	+	0.760243i	$0.274920\pi$
$992$	30.2497	0.960430
$993$	5.96331	0.189240
$994$	−8.10305	−0.257013
$995$	−6.74846	−0.213940
$996$	−10.3811	−0.328937
$997$	32.2965	1.02284	0.511420	−	0.859331i	$-0.329120\pi$
$997$	32.2965	1.02284	0.511420	+	0.859331i	$0.329120\pi$
$998$	4.48726	0.142042
$999$	0.204298	0.00646369

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.c.1.15	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.c.1.15	✓	39	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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q-0.833201 q^{2} -1.00000 q^{3} -1.30578 q^{4} -2.56183 q^{5} +0.833201 q^{6} +1.99624 q^{7} +2.75438 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.833201 q^{2} -1.00000 q^{3} -1.30578 q^{4} -2.56183 q^{5} +0.833201 q^{6} +1.99624 q^{7} +2.75438 q^{8} +1.00000 q^{9} +2.13452 q^{10} +2.12320 q^{11} +1.30578 q^{12} +4.16678 q^{13} -1.66327 q^{14} +2.56183 q^{15} +0.316604 q^{16} +1.00000 q^{17} -0.833201 q^{18} -4.35046 q^{19} +3.34518 q^{20} -1.99624 q^{21} -1.76905 q^{22} +4.76822 q^{23} -2.75438 q^{24} +1.56297 q^{25} -3.47177 q^{26} -1.00000 q^{27} -2.60664 q^{28} +1.37217 q^{29} -2.13452 q^{30} -5.24027 q^{31} -5.77255 q^{32} -2.12320 q^{33} -0.833201 q^{34} -5.11402 q^{35} -1.30578 q^{36} -0.204298 q^{37} +3.62481 q^{38} -4.16678 q^{39} -7.05624 q^{40} -10.3797 q^{41} +1.66327 q^{42} +0.0932029 q^{43} -2.77242 q^{44} -2.56183 q^{45} -3.97288 q^{46} -4.14503 q^{47} -0.316604 q^{48} -3.01503 q^{49} -1.30227 q^{50} -1.00000 q^{51} -5.44088 q^{52} -4.98497 q^{53} +0.833201 q^{54} -5.43928 q^{55} +5.49839 q^{56} +4.35046 q^{57} -1.14329 q^{58} +6.46812 q^{59} -3.34518 q^{60} -5.18805 q^{61} +4.36620 q^{62} +1.99624 q^{63} +4.17648 q^{64} -10.6746 q^{65} +1.76905 q^{66} +4.51304 q^{67} -1.30578 q^{68} -4.76822 q^{69} +4.26101 q^{70} +4.87176 q^{71} +2.75438 q^{72} +15.5110 q^{73} +0.170221 q^{74} -1.56297 q^{75} +5.68073 q^{76} +4.23841 q^{77} +3.47177 q^{78} -9.63925 q^{79} -0.811086 q^{80} +1.00000 q^{81} +8.64841 q^{82} -7.95011 q^{83} +2.60664 q^{84} -2.56183 q^{85} -0.0776568 q^{86} -1.37217 q^{87} +5.84809 q^{88} +9.99979 q^{89} +2.13452 q^{90} +8.31789 q^{91} -6.22623 q^{92} +5.24027 q^{93} +3.45364 q^{94} +11.1451 q^{95} +5.77255 q^{96} -2.78079 q^{97} +2.51213 q^{98} +2.12320 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9}+O(q^{10}) \) 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9	\( 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9} + 4 q^{10} + q^{11} - 30 q^{12} - 26 q^{13} - 4 q^{14} + 3 q^{15} + 8 q^{16} + 39 q^{17} - 4 q^{18} - 14 q^{19} - 14 q^{20} + 5 q^{21} - 17 q^{22} + 2 q^{23} + 3 q^{24} - 6 q^{25} - 17 q^{26} - 39 q^{27} - 14 q^{28} - 7 q^{29} - 4 q^{30} - q^{31} - 30 q^{32} - q^{33} - 4 q^{34} + q^{35} + 30 q^{36} - 24 q^{37} - 20 q^{38} + 26 q^{39} + 12 q^{40} + q^{41} + 4 q^{42} - 41 q^{43} - 2 q^{44} - 3 q^{45} - 6 q^{46} - 9 q^{47} - 8 q^{48} - 10 q^{49} - 9 q^{50} - 39 q^{51} - 37 q^{52} - 47 q^{53} + 4 q^{54} - 39 q^{55} + 8 q^{56} + 14 q^{57} - 27 q^{58} + 41 q^{59} + 14 q^{60} - 41 q^{61} + 36 q^{62} - 5 q^{63} - 47 q^{64} - 39 q^{65} + 17 q^{66} - 36 q^{67} + 30 q^{68} - 2 q^{69} - 52 q^{70} - 2 q^{71} - 3 q^{72} - 63 q^{73} - 6 q^{74} + 6 q^{75} - 34 q^{76} - 64 q^{77} + 17 q^{78} + 20 q^{79} - 28 q^{80} + 39 q^{81} - 37 q^{82} + 45 q^{83} + 14 q^{84} - 3 q^{85} + 32 q^{86} + 7 q^{87} + 6 q^{88} - 32 q^{89} + 4 q^{90} - 11 q^{91} + 28 q^{92} + q^{93} - 44 q^{94} + 22 q^{95} + 30 q^{96} - 20 q^{97} + 63 q^{98} + q^{99}+O(q^{100}) \) 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9 + 4 * q^10 + q^11 - 30 * q^12 - 26 * q^13 - 4 * q^14 + 3 * q^15 + 8 * q^16 + 39 * q^17 - 4 * q^18 - 14 * q^19 - 14 * q^20 + 5 * q^21 - 17 * q^22 + 2 * q^23 + 3 * q^24 - 6 * q^25 - 17 * q^26 - 39 * q^27 - 14 * q^28 - 7 * q^29 - 4 * q^30 - q^31 - 30 * q^32 - q^33 - 4 * q^34 + q^35 + 30 * q^36 - 24 * q^37 - 20 * q^38 + 26 * q^39 + 12 * q^40 + q^41 + 4 * q^42 - 41 * q^43 - 2 * q^44 - 3 * q^45 - 6 * q^46 - 9 * q^47 - 8 * q^48 - 10 * q^49 - 9 * q^50 - 39 * q^51 - 37 * q^52 - 47 * q^53 + 4 * q^54 - 39 * q^55 + 8 * q^56 + 14 * q^57 - 27 * q^58 + 41 * q^59 + 14 * q^60 - 41 * q^61 + 36 * q^62 - 5 * q^63 - 47 * q^64 - 39 * q^65 + 17 * q^66 - 36 * q^67 + 30 * q^68 - 2 * q^69 - 52 * q^70 - 2 * q^71 - 3 * q^72 - 63 * q^73 - 6 * q^74 + 6 * q^75 - 34 * q^76 - 64 * q^77 + 17 * q^78 + 20 * q^79 - 28 * q^80 + 39 * q^81 - 37 * q^82 + 45 * q^83 + 14 * q^84 - 3 * q^85 + 32 * q^86 + 7 * q^87 + 6 * q^88 - 32 * q^89 + 4 * q^90 - 11 * q^91 + 28 * q^92 + q^93 - 44 * q^94 + 22 * q^95 + 30 * q^96 - 20 * q^97 + 63 * q^98 + q^99

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