LMFDB - Embedded newform 8015.2.a.o.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, 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("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$0$
Dimension:	$73$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.69749 q^{2} -3.25136 q^{3} +5.27643 q^{4} +1.00000 q^{5} +8.77051 q^{6} +1.00000 q^{7} -8.83812 q^{8} +7.57137 q^{9} +O(q^{10})$	\(q-2.69749 q^{2} -3.25136 q^{3} +5.27643 q^{4} +1.00000 q^{5} +8.77051 q^{6} +1.00000 q^{7} -8.83812 q^{8} +7.57137 q^{9} -2.69749 q^{10} -3.77948 q^{11} -17.1556 q^{12} +4.48451 q^{13} -2.69749 q^{14} -3.25136 q^{15} +13.2879 q^{16} +2.97617 q^{17} -20.4237 q^{18} +1.62997 q^{19} +5.27643 q^{20} -3.25136 q^{21} +10.1951 q^{22} -5.98612 q^{23} +28.7360 q^{24} +1.00000 q^{25} -12.0969 q^{26} -14.8632 q^{27} +5.27643 q^{28} +3.78481 q^{29} +8.77051 q^{30} +10.1034 q^{31} -18.1675 q^{32} +12.2885 q^{33} -8.02819 q^{34} +1.00000 q^{35} +39.9498 q^{36} -3.22855 q^{37} -4.39682 q^{38} -14.5808 q^{39} -8.83812 q^{40} +2.24766 q^{41} +8.77051 q^{42} -9.76674 q^{43} -19.9422 q^{44} +7.57137 q^{45} +16.1475 q^{46} +10.6078 q^{47} -43.2036 q^{48} +1.00000 q^{49} -2.69749 q^{50} -9.67662 q^{51} +23.6622 q^{52} -3.80658 q^{53} +40.0932 q^{54} -3.77948 q^{55} -8.83812 q^{56} -5.29962 q^{57} -10.2095 q^{58} -9.28006 q^{59} -17.1556 q^{60} -0.974217 q^{61} -27.2539 q^{62} +7.57137 q^{63} +22.4310 q^{64} +4.48451 q^{65} -33.1479 q^{66} -12.5647 q^{67} +15.7036 q^{68} +19.4631 q^{69} -2.69749 q^{70} -7.66492 q^{71} -66.9167 q^{72} +11.6843 q^{73} +8.70898 q^{74} -3.25136 q^{75} +8.60042 q^{76} -3.77948 q^{77} +39.3315 q^{78} +14.0778 q^{79} +13.2879 q^{80} +25.6115 q^{81} -6.06303 q^{82} -1.67573 q^{83} -17.1556 q^{84} +2.97617 q^{85} +26.3456 q^{86} -12.3058 q^{87} +33.4035 q^{88} +14.9382 q^{89} -20.4237 q^{90} +4.48451 q^{91} -31.5853 q^{92} -32.8499 q^{93} -28.6143 q^{94} +1.62997 q^{95} +59.0693 q^{96} -4.39806 q^{97} -2.69749 q^{98} -28.6158 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 73 q + 7 q^{2} + 14 q^{3} + 95 q^{4} + 73 q^{5} - q^{6} + 73 q^{7} + 18 q^{8} + 111 q^{9}+O(q^{10}) $ 73 * q + 7 * q^2 + 14 * q^3 + 95 * q^4 + 73 * q^5 - q^6 + 73 * q^7 + 18 * q^8 + 111 * q^9	\( 73 q + 7 q^{2} + 14 q^{3} + 95 q^{4} + 73 q^{5} - q^{6} + 73 q^{7} + 18 q^{8} + 111 q^{9} + 7 q^{10} + 27 q^{11} + 21 q^{12} + 21 q^{13} + 7 q^{14} + 14 q^{15} + 135 q^{16} + 23 q^{17} + 41 q^{18} + 26 q^{19} + 95 q^{20} + 14 q^{21} + 48 q^{22} + 16 q^{23} - q^{24} + 73 q^{25} + 7 q^{26} + 44 q^{27} + 95 q^{28} + 66 q^{29} - q^{30} + 23 q^{31} + 3 q^{32} + 77 q^{33} + 29 q^{34} + 73 q^{35} + 142 q^{36} + 66 q^{37} - 12 q^{38} + 53 q^{39} + 18 q^{40} + 50 q^{41} - q^{42} + 43 q^{43} + 37 q^{44} + 111 q^{45} + 65 q^{46} + 28 q^{47} - 20 q^{48} + 73 q^{49} + 7 q^{50} + 71 q^{51} + 29 q^{52} - 7 q^{53} - 16 q^{54} + 27 q^{55} + 18 q^{56} + 33 q^{57} + 48 q^{58} + 16 q^{59} + 21 q^{60} + 42 q^{61} - 3 q^{62} + 111 q^{63} + 216 q^{64} + 21 q^{65} - 53 q^{66} + 48 q^{67} + 13 q^{68} + 73 q^{69} + 7 q^{70} + 68 q^{71} + 18 q^{72} + 65 q^{73} + 4 q^{74} + 14 q^{75} + 37 q^{76} + 27 q^{77} + 60 q^{78} + 116 q^{79} + 135 q^{80} + 177 q^{81} + 20 q^{82} + 40 q^{83} + 21 q^{84} + 23 q^{85} + 35 q^{86} - 14 q^{87} + 47 q^{88} + 59 q^{89} + 41 q^{90} + 21 q^{91} + 3 q^{92} + 37 q^{93} - 11 q^{94} + 26 q^{95} - 23 q^{96} + 70 q^{97} + 7 q^{98} + 49 q^{99}+O(q^{100}) \) 73 * q + 7 * q^2 + 14 * q^3 + 95 * q^4 + 73 * q^5 - q^6 + 73 * q^7 + 18 * q^8 + 111 * q^9 + 7 * q^10 + 27 * q^11 + 21 * q^12 + 21 * q^13 + 7 * q^14 + 14 * q^15 + 135 * q^16 + 23 * q^17 + 41 * q^18 + 26 * q^19 + 95 * q^20 + 14 * q^21 + 48 * q^22 + 16 * q^23 - q^24 + 73 * q^25 + 7 * q^26 + 44 * q^27 + 95 * q^28 + 66 * q^29 - q^30 + 23 * q^31 + 3 * q^32 + 77 * q^33 + 29 * q^34 + 73 * q^35 + 142 * q^36 + 66 * q^37 - 12 * q^38 + 53 * q^39 + 18 * q^40 + 50 * q^41 - q^42 + 43 * q^43 + 37 * q^44 + 111 * q^45 + 65 * q^46 + 28 * q^47 - 20 * q^48 + 73 * q^49 + 7 * q^50 + 71 * q^51 + 29 * q^52 - 7 * q^53 - 16 * q^54 + 27 * q^55 + 18 * q^56 + 33 * q^57 + 48 * q^58 + 16 * q^59 + 21 * q^60 + 42 * q^61 - 3 * q^62 + 111 * q^63 + 216 * q^64 + 21 * q^65 - 53 * q^66 + 48 * q^67 + 13 * q^68 + 73 * q^69 + 7 * q^70 + 68 * q^71 + 18 * q^72 + 65 * q^73 + 4 * q^74 + 14 * q^75 + 37 * q^76 + 27 * q^77 + 60 * q^78 + 116 * q^79 + 135 * q^80 + 177 * q^81 + 20 * q^82 + 40 * q^83 + 21 * q^84 + 23 * q^85 + 35 * q^86 - 14 * q^87 + 47 * q^88 + 59 * q^89 + 41 * q^90 + 21 * q^91 + 3 * q^92 + 37 * q^93 - 11 * q^94 + 26 * q^95 - 23 * q^96 + 70 * q^97 + 7 * q^98 + 49 * 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 $

$2$	−2.69749	−1.90741	−0.953705	−	0.300743i	$-0.902765\pi$
$2$	−2.69749	−1.90741	−0.953705	+	0.300743i	$0.902765\pi$
$3$	−3.25136	−1.87718	−0.938588	−	0.345040i	$-0.887865\pi$
$3$	−3.25136	−1.87718	−0.938588	+	0.345040i	$0.887865\pi$
$4$	5.27643	2.63821
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	8.77051	3.58054
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−8.83812	−3.12475
$9$	7.57137	2.52379
$10$	−2.69749	−0.853020
$11$	−3.77948	−1.13956	−0.569778	−	0.821799i	$-0.692971\pi$
$11$	−3.77948	−1.13956	−0.569778	+	0.821799i	$0.692971\pi$
$12$	−17.1556	−4.95239
$13$	4.48451	1.24378	0.621890	−	0.783104i	$-0.286365\pi$
$13$	4.48451	1.24378	0.621890	+	0.783104i	$0.286365\pi$
$14$	−2.69749	−0.720933
$15$	−3.25136	−0.839499
$16$	13.2879	3.32196
$17$	2.97617	0.721828	0.360914	−	0.932599i	$-0.382465\pi$
$17$	2.97617	0.721828	0.360914	+	0.932599i	$0.382465\pi$
$18$	−20.4237	−4.81390
$19$	1.62997	0.373941	0.186970	−	0.982366i	$-0.440133\pi$
$19$	1.62997	0.373941	0.186970	+	0.982366i	$0.440133\pi$
$20$	5.27643	1.17985
$21$	−3.25136	−0.709506
$22$	10.1951	2.17360
$23$	−5.98612	−1.24819	−0.624096	−	0.781347i	$-0.714533\pi$
$23$	−5.98612	−1.24819	−0.624096	+	0.781347i	$0.714533\pi$
$24$	28.7360	5.86570
$25$	1.00000	0.200000
$26$	−12.0969	−2.37240
$27$	−14.8632	−2.86042
$28$	5.27643	0.997151
$29$	3.78481	0.702822	0.351411	−	0.936221i	$-0.385702\pi$
$29$	3.78481	0.702822	0.351411	+	0.936221i	$0.385702\pi$
$30$	8.77051	1.60127
$31$	10.1034	1.81463	0.907315	−	0.420451i	$-0.138128\pi$
$31$	10.1034	1.81463	0.907315	+	0.420451i	$0.138128\pi$
$32$	−18.1675	−3.21160
$33$	12.2885	2.13915
$34$	−8.02819	−1.37682
$35$	1.00000	0.169031
$36$	39.9498	6.65830
$37$	−3.22855	−0.530771	−0.265385	−	0.964142i	$-0.585499\pi$
$37$	−3.22855	−0.530771	−0.265385	+	0.964142i	$0.585499\pi$
$38$	−4.39682	−0.713258
$39$	−14.5808	−2.33479
$40$	−8.83812	−1.39743
$41$	2.24766	0.351025	0.175513	−	0.984477i	$-0.443842\pi$
$41$	2.24766	0.351025	0.175513	+	0.984477i	$0.443842\pi$
$42$	8.77051	1.35332
$43$	−9.76674	−1.48941	−0.744707	−	0.667391i	$-0.767411\pi$
$43$	−9.76674	−1.48941	−0.744707	+	0.667391i	$0.767411\pi$
$44$	−19.9422	−3.00639
$45$	7.57137	1.12867
$46$	16.1475	2.38082
$47$	10.6078	1.54730	0.773652	−	0.633610i	$-0.218428\pi$
$47$	10.6078	1.54730	0.773652	+	0.633610i	$0.218428\pi$
$48$	−43.2036	−6.23591
$49$	1.00000	0.142857
$50$	−2.69749	−0.381482
$51$	−9.67662	−1.35500
$52$	23.6622	3.28136
$53$	−3.80658	−0.522874	−0.261437	−	0.965221i	$-0.584196\pi$
$53$	−3.80658	−0.522874	−0.261437	+	0.965221i	$0.584196\pi$
$54$	40.0932	5.45599
$55$	−3.77948	−0.509625
$56$	−8.83812	−1.18104
$57$	−5.29962	−0.701952
$58$	−10.2095	−1.34057
$59$	−9.28006	−1.20816	−0.604080	−	0.796923i	$-0.706459\pi$
$59$	−9.28006	−1.20816	−0.604080	+	0.796923i	$0.706459\pi$
$60$	−17.1556	−2.21478
$61$	−0.974217	−0.124736	−0.0623679	−	0.998053i	$-0.519865\pi$
$61$	−0.974217	−0.124736	−0.0623679	+	0.998053i	$0.519865\pi$
$62$	−27.2539	−3.46125
$63$	7.57137	0.953902
$64$	22.4310	2.80387
$65$	4.48451	0.556236
$66$	−33.1479	−4.08023
$67$	−12.5647	−1.53502	−0.767510	−	0.641037i	$-0.778504\pi$
$67$	−12.5647	−1.53502	−0.767510	+	0.641037i	$0.778504\pi$
$68$	15.7036	1.90434
$69$	19.4631	2.34308
$70$	−2.69749	−0.322411
$71$	−7.66492	−0.909658	−0.454829	−	0.890579i	$-0.650300\pi$
$71$	−7.66492	−0.909658	−0.454829	+	0.890579i	$0.650300\pi$
$72$	−66.9167	−7.88620
$73$	11.6843	1.36754	0.683769	−	0.729698i	$-0.260340\pi$
$73$	11.6843	1.36754	0.683769	+	0.729698i	$0.260340\pi$
$74$	8.70898	1.01240
$75$	−3.25136	−0.375435
$76$	8.60042	0.986536
$77$	−3.77948	−0.430712
$78$	39.3315	4.45341
$79$	14.0778	1.58387	0.791936	−	0.610604i	$-0.209073\pi$
$79$	14.0778	1.58387	0.791936	+	0.610604i	$0.209073\pi$
$80$	13.2879	1.48563
$81$	25.6115	2.84572
$82$	−6.06303	−0.669550
$83$	−1.67573	−0.183936	−0.0919679	−	0.995762i	$-0.529316\pi$
$83$	−1.67573	−0.183936	−0.0919679	+	0.995762i	$0.529316\pi$
$84$	−17.1556	−1.87183
$85$	2.97617	0.322811
$86$	26.3456	2.84092
$87$	−12.3058	−1.31932
$88$	33.4035	3.56083
$89$	14.9382	1.58345	0.791724	−	0.610878i	$-0.209184\pi$
$89$	14.9382	1.58345	0.791724	+	0.610878i	$0.209184\pi$
$90$	−20.4237	−2.15284
$91$	4.48451	0.470105
$92$	−31.5853	−3.29300
$93$	−32.8499	−3.40638
$94$	−28.6143	−2.95134
$95$	1.62997	0.167231
$96$	59.0693	6.02873
$97$	−4.39806	−0.446555	−0.223278	−	0.974755i	$-0.571676\pi$
$97$	−4.39806	−0.446555	−0.223278	+	0.974755i	$0.571676\pi$
$98$	−2.69749	−0.272487
$99$	−28.6158	−2.87600
$100$	5.27643	0.527643
$101$	−0.589738	−0.0586812	−0.0293406	−	0.999569i	$-0.509341\pi$
$101$	−0.589738	−0.0586812	−0.0293406	+	0.999569i	$0.509341\pi$
$102$	26.1026	2.58454
$103$	10.8173	1.06586	0.532928	−	0.846161i	$-0.321092\pi$
$103$	10.8173	1.06586	0.532928	+	0.846161i	$0.321092\pi$
$104$	−39.6347	−3.88650
$105$	−3.25136	−0.317301
$106$	10.2682	0.997336
$107$	−2.09854	−0.202873	−0.101437	−	0.994842i	$-0.532344\pi$
$107$	−2.09854	−0.202873	−0.101437	+	0.994842i	$0.532344\pi$
$108$	−78.4245	−7.54640
$109$	13.3678	1.28041	0.640203	−	0.768206i	$-0.278850\pi$
$109$	13.3678	1.28041	0.640203	+	0.768206i	$0.278850\pi$
$110$	10.1951	0.972064
$111$	10.4972	0.996350
$112$	13.2879	1.25558
$113$	15.5968	1.46723	0.733613	−	0.679567i	$-0.237832\pi$
$113$	15.5968	1.46723	0.733613	+	0.679567i	$0.237832\pi$
$114$	14.2957	1.33891
$115$	−5.98612	−0.558209
$116$	19.9703	1.85420
$117$	33.9539	3.13904
$118$	25.0328	2.30446
$119$	2.97617	0.272825
$120$	28.7360	2.62322
$121$	3.28446	0.298587
$122$	2.62794	0.237922
$123$	−7.30796	−0.658936
$124$	53.3101	4.78739
$125$	1.00000	0.0894427
$126$	−20.4237	−1.81948
$127$	−5.11964	−0.454295	−0.227147	−	0.973860i	$-0.572940\pi$
$127$	−5.11964	−0.454295	−0.227147	+	0.973860i	$0.572940\pi$
$128$	−24.1722	−2.13654
$129$	31.7552	2.79589
$130$	−12.0969	−1.06097
$131$	8.64928	0.755691	0.377846	−	0.925869i	$-0.376665\pi$
$131$	8.64928	0.755691	0.377846	+	0.925869i	$0.376665\pi$
$132$	64.8392	5.64353
$133$	1.62997	0.141336
$134$	33.8930	2.92791
$135$	−14.8632	−1.27922
$136$	−26.3038	−2.25553
$137$	−10.5948	−0.905174	−0.452587	−	0.891720i	$-0.649499\pi$
$137$	−10.5948	−0.905174	−0.452587	+	0.891720i	$0.649499\pi$
$138$	−52.5013	−4.46921
$139$	8.73458	0.740857	0.370429	−	0.928861i	$-0.379211\pi$
$139$	8.73458	0.740857	0.370429	+	0.928861i	$0.379211\pi$
$140$	5.27643	0.445940
$141$	−34.4898	−2.90456
$142$	20.6760	1.73509
$143$	−16.9491	−1.41736
$144$	100.607	8.38393
$145$	3.78481	0.314312
$146$	−31.5181	−2.60846
$147$	−3.25136	−0.268168
$148$	−17.0352	−1.40029
$149$	−9.74499	−0.798341	−0.399170	−	0.916877i	$-0.630702\pi$
$149$	−9.74499	−0.798341	−0.399170	+	0.916877i	$0.630702\pi$
$150$	8.77051	0.716109
$151$	15.8918	1.29326	0.646629	−	0.762804i	$-0.276178\pi$
$151$	15.8918	1.29326	0.646629	+	0.762804i	$0.276178\pi$
$152$	−14.4059	−1.16847
$153$	22.5337	1.82174
$154$	10.1951	0.821544
$155$	10.1034	0.811528
$156$	−76.9345	−6.15969
$157$	19.2937	1.53980	0.769902	−	0.638162i	$-0.220305\pi$
$157$	19.2937	1.53980	0.769902	+	0.638162i	$0.220305\pi$
$158$	−37.9746	−3.02109
$159$	12.3766	0.981527
$160$	−18.1675	−1.43627
$161$	−5.98612	−0.471772
$162$	−69.0866	−5.42796
$163$	14.0794	1.10278	0.551391	−	0.834247i	$-0.314097\pi$
$163$	14.0794	1.10278	0.551391	+	0.834247i	$0.314097\pi$
$164$	11.8596	0.926081
$165$	12.2885	0.956655
$166$	4.52027	0.350841
$167$	6.79440	0.525766	0.262883	−	0.964828i	$-0.415327\pi$
$167$	6.79440	0.525766	0.262883	+	0.964828i	$0.415327\pi$
$168$	28.7360	2.21703
$169$	7.11087	0.546990
$170$	−8.02819	−0.615734
$171$	12.3411	0.943747
$172$	−51.5335	−3.92939
$173$	−12.1614	−0.924615	−0.462307	−	0.886720i	$-0.652978\pi$
$173$	−12.1614	−0.924615	−0.462307	+	0.886720i	$0.652978\pi$
$174$	33.1947	2.51649
$175$	1.00000	0.0755929
$176$	−50.2212	−3.78556
$177$	30.1728	2.26793
$178$	−40.2957	−3.02029
$179$	−3.86928	−0.289204	−0.144602	−	0.989490i	$-0.546190\pi$
$179$	−3.86928	−0.289204	−0.144602	+	0.989490i	$0.546190\pi$
$180$	39.9498	2.97768
$181$	−14.2606	−1.05998	−0.529990	−	0.848004i	$-0.677804\pi$
$181$	−14.2606	−1.05998	−0.529990	+	0.848004i	$0.677804\pi$
$182$	−12.0969	−0.896683
$183$	3.16754	0.234151
$184$	52.9061	3.90029
$185$	−3.22855	−0.237368
$186$	88.6123	6.49737
$187$	−11.2484	−0.822563
$188$	55.9712	4.08212
$189$	−14.8632	−1.08114
$190$	−4.39682	−0.318979
$191$	3.98989	0.288698	0.144349	−	0.989527i	$-0.453891\pi$
$191$	3.98989	0.288698	0.144349	+	0.989527i	$0.453891\pi$
$192$	−72.9313	−5.26336
$193$	26.9823	1.94223	0.971113	−	0.238621i	$-0.0766952\pi$
$193$	26.9823	1.94223	0.971113	+	0.238621i	$0.0766952\pi$
$194$	11.8637	0.851764
$195$	−14.5808	−1.04415
$196$	5.27643	0.376888
$197$	−24.1802	−1.72277	−0.861383	−	0.507955i	$-0.830402\pi$
$197$	−24.1802	−1.72277	−0.861383	+	0.507955i	$0.830402\pi$
$198$	77.1908	5.48571
$199$	−20.0348	−1.42023	−0.710113	−	0.704087i	$-0.751356\pi$
$199$	−20.0348	−1.42023	−0.710113	+	0.704087i	$0.751356\pi$
$200$	−8.83812	−0.624950
$201$	40.8523	2.88150
$202$	1.59081	0.111929
$203$	3.78481	0.265642
$204$	−51.0580	−3.57478
$205$	2.24766	0.156983
$206$	−29.1794	−2.03302
$207$	−45.3231	−3.15017
$208$	59.5896	4.13179
$209$	−6.16043	−0.426126
$210$	8.77051	0.605223
$211$	20.7625	1.42935	0.714675	−	0.699457i	$-0.246575\pi$
$211$	20.7625	1.42935	0.714675	+	0.699457i	$0.246575\pi$
$212$	−20.0852	−1.37945
$213$	24.9214	1.70759
$214$	5.66078	0.386963
$215$	−9.76674	−0.666086
$216$	131.363	8.93809
$217$	10.1034	0.685866
$218$	−36.0595	−2.44226
$219$	−37.9898	−2.56711
$220$	−19.9422	−1.34450
$221$	13.3467	0.897796
$222$	−28.3161	−1.90045
$223$	−13.6881	−0.916623	−0.458312	−	0.888792i	$-0.651546\pi$
$223$	−13.6881	−0.916623	−0.458312	+	0.888792i	$0.651546\pi$
$224$	−18.1675	−1.21387
$225$	7.57137	0.504758
$226$	−42.0722	−2.79860
$227$	14.0909	0.935245	0.467622	−	0.883928i	$-0.345111\pi$
$227$	14.0909	0.935245	0.467622	+	0.883928i	$0.345111\pi$
$228$	−27.9631	−1.85190
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	16.1475	1.06473
$231$	12.2885	0.808521
$232$	−33.4506	−2.19614
$233$	11.5820	0.758765	0.379382	−	0.925240i	$-0.376137\pi$
$233$	11.5820	0.758765	0.379382	+	0.925240i	$0.376137\pi$
$234$	−91.5902	−5.98744
$235$	10.6078	0.691976
$236$	−48.9656	−3.18739
$237$	−45.7719	−2.97321
$238$	−8.02819	−0.520390
$239$	4.74371	0.306845	0.153423	−	0.988161i	$-0.450970\pi$
$239$	4.74371	0.306845	0.153423	+	0.988161i	$0.450970\pi$
$240$	−43.2036	−2.78878
$241$	−28.1715	−1.81469	−0.907344	−	0.420390i	$-0.861893\pi$
$241$	−28.1715	−1.81469	−0.907344	+	0.420390i	$0.861893\pi$
$242$	−8.85979	−0.569529
$243$	−38.6827	−2.48150
$244$	−5.14039	−0.329080
$245$	1.00000	0.0638877
$246$	19.7131	1.25686
$247$	7.30962	0.465100
$248$	−89.2954	−5.67026
$249$	5.44842	0.345280
$250$	−2.69749	−0.170604
$251$	2.52733	0.159524	0.0797620	−	0.996814i	$-0.474584\pi$
$251$	2.52733	0.159524	0.0797620	+	0.996814i	$0.474584\pi$
$252$	39.9498	2.51660
$253$	22.6244	1.42239
$254$	13.8102	0.866527
$255$	−9.67662	−0.605974
$256$	20.3422	1.27139
$257$	14.2129	0.886577	0.443288	−	0.896379i	$-0.353812\pi$
$257$	14.2129	0.886577	0.443288	+	0.896379i	$0.353812\pi$
$258$	−85.6593	−5.33291
$259$	−3.22855	−0.200613
$260$	23.6622	1.46747
$261$	28.6562	1.77377
$262$	−23.3313	−1.44141
$263$	2.86165	0.176457	0.0882285	−	0.996100i	$-0.471879\pi$
$263$	2.86165	0.176457	0.0882285	+	0.996100i	$0.471879\pi$
$264$	−108.607	−6.68429
$265$	−3.80658	−0.233836
$266$	−4.39682	−0.269586
$267$	−48.5696	−2.97241
$268$	−66.2966	−4.04971
$269$	−11.3992	−0.695022	−0.347511	−	0.937676i	$-0.612973\pi$
$269$	−11.3992	−0.695022	−0.347511	+	0.937676i	$0.612973\pi$
$270$	40.0932	2.43999
$271$	−11.0716	−0.672553	−0.336277	−	0.941763i	$-0.609168\pi$
$271$	−11.0716	−0.672553	−0.336277	+	0.941763i	$0.609168\pi$
$272$	39.5470	2.39789
$273$	−14.5808	−0.882469
$274$	28.5793	1.72654
$275$	−3.77948	−0.227911
$276$	102.695	6.18154
$277$	11.1087	0.667457	0.333729	−	0.942669i	$-0.391693\pi$
$277$	11.1087	0.667457	0.333729	+	0.942669i	$0.391693\pi$
$278$	−23.5614	−1.41312
$279$	76.4968	4.57974
$280$	−8.83812	−0.528179
$281$	−13.2698	−0.791608	−0.395804	−	0.918335i	$-0.629534\pi$
$281$	−13.2698	−0.791608	−0.395804	+	0.918335i	$0.629534\pi$
$282$	93.0357	5.54019
$283$	−3.65016	−0.216980	−0.108490	−	0.994098i	$-0.534601\pi$
$283$	−3.65016	−0.216980	−0.108490	+	0.994098i	$0.534601\pi$
$284$	−40.4434	−2.39987
$285$	−5.29962	−0.313923
$286$	45.7200	2.70348
$287$	2.24766	0.132675
$288$	−137.553	−8.10540
$289$	−8.14239	−0.478964
$290$	−10.2095	−0.599521
$291$	14.2997	0.838263
$292$	61.6511	3.60786
$293$	11.6070	0.678090	0.339045	−	0.940770i	$-0.389896\pi$
$293$	11.6070	0.678090	0.339045	+	0.940770i	$0.389896\pi$
$294$	8.77051	0.511506
$295$	−9.28006	−0.540306
$296$	28.5343	1.65853
$297$	56.1751	3.25961
$298$	26.2870	1.52276
$299$	−26.8448	−1.55248
$300$	−17.1556	−0.990479
$301$	−9.76674	−0.562946
$302$	−42.8680	−2.46677
$303$	1.91745	0.110155
$304$	21.6588	1.24222
$305$	−0.974217	−0.0557835
$306$	−60.7843	−3.47481
$307$	3.36474	0.192036	0.0960180	−	0.995380i	$-0.469389\pi$
$307$	3.36474	0.192036	0.0960180	+	0.995380i	$0.469389\pi$
$308$	−19.9422	−1.13631
$309$	−35.1708	−2.00080
$310$	−27.2539	−1.54792
$311$	5.04545	0.286101	0.143051	−	0.989715i	$-0.454309\pi$
$311$	5.04545	0.286101	0.143051	+	0.989715i	$0.454309\pi$
$312$	128.867	7.29565
$313$	−4.33804	−0.245200	−0.122600	−	0.992456i	$-0.539123\pi$
$313$	−4.33804	−0.245200	−0.122600	+	0.992456i	$0.539123\pi$
$314$	−52.0445	−2.93704
$315$	7.57137	0.426598
$316$	74.2803	4.17860
$317$	31.4392	1.76580	0.882900	−	0.469562i	$-0.155588\pi$
$317$	31.4392	1.76580	0.882900	+	0.469562i	$0.155588\pi$
$318$	−33.3856	−1.87217
$319$	−14.3046	−0.800905
$320$	22.4310	1.25393
$321$	6.82311	0.380829
$322$	16.1475	0.899864
$323$	4.85107	0.269921
$324$	135.137	7.50762
$325$	4.48451	0.248756
$326$	−37.9789	−2.10346
$327$	−43.4637	−2.40355
$328$	−19.8651	−1.09687
$329$	10.6078	0.584826
$330$	−33.1479	−1.82473
$331$	−20.6237	−1.13358	−0.566792	−	0.823861i	$-0.691816\pi$
$331$	−20.6237	−1.13358	−0.566792	+	0.823861i	$0.691816\pi$
$332$	−8.84189	−0.485262
$333$	−24.4446	−1.33955
$334$	−18.3278	−1.00285
$335$	−12.5647	−0.686482
$336$	−43.2036	−2.35695
$337$	−27.0878	−1.47557	−0.737784	−	0.675036i	$-0.764128\pi$
$337$	−27.0878	−1.47557	−0.737784	+	0.675036i	$0.764128\pi$
$338$	−19.1815	−1.04333
$339$	−50.7110	−2.75424
$340$	15.7036	0.851646
$341$	−38.1857	−2.06787
$342$	−33.2899	−1.80011
$343$	1.00000	0.0539949
$344$	86.3197	4.65404
$345$	19.4631	1.04786
$346$	32.8052	1.76362
$347$	−8.28562	−0.444796	−0.222398	−	0.974956i	$-0.571388\pi$
$347$	−8.28562	−0.444796	−0.222398	+	0.974956i	$0.571388\pi$
$348$	−64.9307	−3.48065
$349$	−1.55505	−0.0832398	−0.0416199	−	0.999134i	$-0.513252\pi$
$349$	−1.55505	−0.0832398	−0.0416199	+	0.999134i	$0.513252\pi$
$350$	−2.69749	−0.144187
$351$	−66.6541	−3.55773
$352$	68.6639	3.65980
$353$	−20.2833	−1.07957	−0.539786	−	0.841802i	$-0.681495\pi$
$353$	−20.2833	−1.07957	−0.539786	+	0.841802i	$0.681495\pi$
$354$	−81.3908	−4.32587
$355$	−7.66492	−0.406812
$356$	78.8205	4.17748
$357$	−9.67662	−0.512141
$358$	10.4373	0.551631
$359$	36.8100	1.94276	0.971380	−	0.237532i	$-0.0763383\pi$
$359$	36.8100	1.94276	0.971380	+	0.237532i	$0.0763383\pi$
$360$	−66.9167	−3.52682
$361$	−16.3432	−0.860168
$362$	38.4677	2.02182
$363$	−10.6790	−0.560501
$364$	23.6622	1.24024
$365$	11.6843	0.611582
$366$	−8.54438	−0.446622
$367$	−1.73071	−0.0903425	−0.0451713	−	0.998979i	$-0.514383\pi$
$367$	−1.73071	−0.0903425	−0.0451713	+	0.998979i	$0.514383\pi$
$368$	−79.5427	−4.14645
$369$	17.0179	0.885914
$370$	8.70898	0.452758
$371$	−3.80658	−0.197628
$372$	−173.330	−8.98677
$373$	17.1940	0.890270	0.445135	−	0.895463i	$-0.353156\pi$
$373$	17.1940	0.890270	0.445135	+	0.895463i	$0.353156\pi$
$374$	30.3424	1.56897
$375$	−3.25136	−0.167900
$376$	−93.7529	−4.83494
$377$	16.9731	0.874157
$378$	40.0932	2.06217
$379$	−5.79086	−0.297457	−0.148728	−	0.988878i	$-0.547518\pi$
$379$	−5.79086	−0.297457	−0.148728	+	0.988878i	$0.547518\pi$
$380$	8.60042	0.441192
$381$	16.6458	0.852791
$382$	−10.7627	−0.550666
$383$	21.8496	1.11646	0.558232	−	0.829685i	$-0.311480\pi$
$383$	21.8496	1.11646	0.558232	+	0.829685i	$0.311480\pi$
$384$	78.5926	4.01066
$385$	−3.77948	−0.192620
$386$	−72.7843	−3.70462
$387$	−73.9476	−3.75897
$388$	−23.2060	−1.17811
$389$	−6.98995	−0.354405	−0.177202	−	0.984174i	$-0.556705\pi$
$389$	−6.98995	−0.354405	−0.177202	+	0.984174i	$0.556705\pi$
$390$	39.3315	1.99163
$391$	−17.8157	−0.900981
$392$	−8.83812	−0.446393
$393$	−28.1220	−1.41856
$394$	65.2257	3.28602
$395$	14.0778	0.708329
$396$	−150.989	−7.58750
$397$	−29.7203	−1.49162	−0.745809	−	0.666160i	$-0.767937\pi$
$397$	−29.7203	−1.49162	−0.745809	+	0.666160i	$0.767937\pi$
$398$	54.0435	2.70896
$399$	−5.29962	−0.265313
$400$	13.2879	0.664393
$401$	11.1906	0.558831	0.279415	−	0.960170i	$-0.409859\pi$
$401$	11.1906	0.558831	0.279415	+	0.960170i	$0.409859\pi$
$402$	−110.199	−5.49621
$403$	45.3090	2.25700
$404$	−3.11171	−0.154814
$405$	25.6115	1.27265
$406$	−10.2095	−0.506688
$407$	12.2022	0.604843
$408$	85.5232	4.23403
$409$	−9.63495	−0.476417	−0.238209	−	0.971214i	$-0.576560\pi$
$409$	−9.63495	−0.476417	−0.238209	+	0.971214i	$0.576560\pi$
$410$	−6.06303	−0.299432
$411$	34.4475	1.69917
$412$	57.0765	2.81196
$413$	−9.28006	−0.456642
$414$	122.258	6.00868
$415$	−1.67573	−0.0822586
$416$	−81.4726	−3.99452
$417$	−28.3993	−1.39072
$418$	16.6177	0.812798
$419$	−6.97539	−0.340770	−0.170385	−	0.985378i	$-0.554501\pi$
$419$	−6.97539	−0.340770	−0.170385	+	0.985378i	$0.554501\pi$
$420$	−17.1556	−0.837107
$421$	−2.99705	−0.146067	−0.0730337	−	0.997329i	$-0.523268\pi$
$421$	−2.99705	−0.146067	−0.0730337	+	0.997329i	$0.523268\pi$
$422$	−56.0066	−2.72636
$423$	80.3154	3.90507
$424$	33.6430	1.63385
$425$	2.97617	0.144366
$426$	−67.2252	−3.25707
$427$	−0.974217	−0.0471457
$428$	−11.0728	−0.535224
$429$	55.1078	2.66063
$430$	26.3456	1.27050
$431$	−11.9575	−0.575972	−0.287986	−	0.957635i	$-0.592986\pi$
$431$	−11.9575	−0.575972	−0.287986	+	0.957635i	$0.592986\pi$
$432$	−197.500	−9.50221
$433$	−24.7739	−1.19056	−0.595278	−	0.803520i	$-0.702958\pi$
$433$	−24.7739	−1.19056	−0.595278	+	0.803520i	$0.702958\pi$
$434$	−27.2539	−1.30823
$435$	−12.3058	−0.590018
$436$	70.5344	3.37798
$437$	−9.75719	−0.466750
$438$	102.477	4.89653
$439$	−22.7405	−1.08535	−0.542673	−	0.839944i	$-0.682588\pi$
$439$	−22.7405	−1.08535	−0.542673	+	0.839944i	$0.682588\pi$
$440$	33.4035	1.59245
$441$	7.57137	0.360541
$442$	−36.0025	−1.71247
$443$	−20.3979	−0.969136	−0.484568	−	0.874754i	$-0.661023\pi$
$443$	−20.3979	−0.969136	−0.484568	+	0.874754i	$0.661023\pi$
$444$	55.3877	2.62859
$445$	14.9382	0.708140
$446$	36.9235	1.74838
$447$	31.6845	1.49863
$448$	22.4310	1.05976
$449$	−6.28365	−0.296544	−0.148272	−	0.988947i	$-0.547371\pi$
$449$	−6.28365	−0.296544	−0.148272	+	0.988947i	$0.547371\pi$
$450$	−20.4237	−0.962780
$451$	−8.49498	−0.400013
$452$	82.2956	3.87086
$453$	−51.6701	−2.42767
$454$	−38.0099	−1.78390
$455$	4.48451	0.210237
$456$	46.8387	2.19342
$457$	−2.44367	−0.114310	−0.0571550	−	0.998365i	$-0.518203\pi$
$457$	−2.44367	−0.114310	−0.0571550	+	0.998365i	$0.518203\pi$
$458$	−2.69749	−0.126045
$459$	−44.2354	−2.06473
$460$	−31.5853	−1.47267
$461$	−23.7746	−1.10729	−0.553647	−	0.832751i	$-0.686764\pi$
$461$	−23.7746	−1.10729	−0.553647	+	0.832751i	$0.686764\pi$
$462$	−33.1479	−1.54218
$463$	19.1777	0.891266	0.445633	−	0.895216i	$-0.352979\pi$
$463$	19.1777	0.891266	0.445633	+	0.895216i	$0.352979\pi$
$464$	50.2920	2.33475
$465$	−32.8499	−1.52338
$466$	−31.2424	−1.44728
$467$	−8.89474	−0.411599	−0.205800	−	0.978594i	$-0.565980\pi$
$467$	−8.89474	−0.411599	−0.205800	+	0.978594i	$0.565980\pi$
$468$	179.155	8.28146
$469$	−12.5647	−0.580183
$470$	−28.6143	−1.31988
$471$	−62.7308	−2.89048
$472$	82.0183	3.77520
$473$	36.9132	1.69727
$474$	123.469	5.67113
$475$	1.62997	0.0747881
$476$	15.7036	0.719772
$477$	−28.8210	−1.31962
$478$	−12.7961	−0.585280
$479$	−42.5536	−1.94432	−0.972161	−	0.234313i	$-0.924716\pi$
$479$	−42.5536	−1.94432	−0.972161	+	0.234313i	$0.924716\pi$
$480$	59.0693	2.69613
$481$	−14.4785	−0.660163
$482$	75.9923	3.46135
$483$	19.4631	0.885600
$484$	17.3302	0.787738
$485$	−4.39806	−0.199706
$486$	104.346	4.73324
$487$	−0.424274	−0.0192257	−0.00961284	−	0.999954i	$-0.503060\pi$
$487$	−0.424274	−0.0192257	−0.00961284	+	0.999954i	$0.503060\pi$
$488$	8.61025	0.389768
$489$	−45.7772	−2.07011
$490$	−2.69749	−0.121860
$491$	−22.3209	−1.00733	−0.503664	−	0.863900i	$-0.668015\pi$
$491$	−22.3209	−1.00733	−0.503664	+	0.863900i	$0.668015\pi$
$492$	−38.5599	−1.73842
$493$	11.2643	0.507317
$494$	−19.7176	−0.887137
$495$	−28.6158	−1.28619
$496$	134.253	6.02814
$497$	−7.66492	−0.343819
$498$	−14.6970	−0.658590
$499$	−31.3829	−1.40489	−0.702445	−	0.711738i	$-0.747908\pi$
$499$	−31.3829	−1.40489	−0.702445	+	0.711738i	$0.747908\pi$
$500$	5.27643	0.235969
$501$	−22.0911	−0.986956
$502$	−6.81745	−0.304278
$503$	−17.8923	−0.797779	−0.398889	−	0.916999i	$-0.630604\pi$
$503$	−17.8923	−0.797779	−0.398889	+	0.916999i	$0.630604\pi$
$504$	−66.9167	−2.98071
$505$	−0.589738	−0.0262430
$506$	−61.0291	−2.71307
$507$	−23.1200	−1.02680
$508$	−27.0134	−1.19853
$509$	44.6694	1.97994	0.989968	−	0.141293i	$-0.0451260\pi$
$509$	44.6694	1.97994	0.989968	+	0.141293i	$0.0451260\pi$
$510$	26.1026	1.15584
$511$	11.6843	0.516881
$512$	−6.52831	−0.288513
$513$	−24.2265	−1.06963
$514$	−38.3391	−1.69107
$515$	10.8173	0.476665
$516$	167.554	7.37616
$517$	−40.0919	−1.76324
$518$	8.70898	0.382650
$519$	39.5412	1.73566
$520$	−39.6347	−1.73810
$521$	20.2291	0.886253	0.443127	−	0.896459i	$-0.353869\pi$
$521$	20.2291	0.886253	0.443127	+	0.896459i	$0.353869\pi$
$522$	−77.2997	−3.38332
$523$	37.9650	1.66009	0.830047	−	0.557694i	$-0.188314\pi$
$523$	37.9650	1.66009	0.830047	+	0.557694i	$0.188314\pi$
$524$	45.6373	1.99368
$525$	−3.25136	−0.141901
$526$	−7.71926	−0.336576
$527$	30.0696	1.30985
$528$	163.287	7.10617
$529$	12.8336	0.557985
$530$	10.2682	0.446022
$531$	−70.2627	−3.04914
$532$	8.60042	0.372875
$533$	10.0797	0.436599
$534$	131.016	5.66961
$535$	−2.09854	−0.0907277
$536$	111.048	4.79655
$537$	12.5805	0.542886
$538$	30.7492	1.32569
$539$	−3.77948	−0.162794
$540$	−78.4245	−3.37485
$541$	−29.8584	−1.28371	−0.641857	−	0.766824i	$-0.721836\pi$
$541$	−29.8584	−1.28371	−0.641857	+	0.766824i	$0.721836\pi$
$542$	29.8656	1.28284
$543$	46.3663	1.98977
$544$	−54.0698	−2.31822
$545$	13.3678	0.572615
$546$	39.3315	1.68323
$547$	24.1031	1.03057	0.515287	−	0.857018i	$-0.327685\pi$
$547$	24.1031	1.03057	0.515287	+	0.857018i	$0.327685\pi$
$548$	−55.9026	−2.38804
$549$	−7.37616	−0.314807
$550$	10.1951	0.434720
$551$	6.16913	0.262814
$552$	−172.017	−7.32153
$553$	14.0778	0.598647
$554$	−29.9656	−1.27311
$555$	10.4972	0.445581
$556$	46.0874	1.95454
$557$	28.4994	1.20756	0.603779	−	0.797152i	$-0.293661\pi$
$557$	28.4994	1.20756	0.603779	+	0.797152i	$0.293661\pi$
$558$	−206.349	−8.73545
$559$	−43.7991	−1.85250
$560$	13.2879	0.561514
$561$	36.5726	1.54410
$562$	35.7950	1.50992
$563$	14.2135	0.599026	0.299513	−	0.954092i	$-0.403176\pi$
$563$	14.2135	0.599026	0.299513	+	0.954092i	$0.403176\pi$
$564$	−181.983	−7.66286
$565$	15.5968	0.656164
$566$	9.84626	0.413869
$567$	25.6115	1.07558
$568$	67.7435	2.84245
$569$	2.82868	0.118584	0.0592922	−	0.998241i	$-0.481116\pi$
$569$	2.82868	0.118584	0.0592922	+	0.998241i	$0.481116\pi$
$570$	14.2957	0.598779
$571$	37.2834	1.56026	0.780131	−	0.625617i	$-0.215153\pi$
$571$	37.2834	1.56026	0.780131	+	0.625617i	$0.215153\pi$
$572$	−89.4309	−3.73929
$573$	−12.9726	−0.541937
$574$	−6.06303	−0.253066
$575$	−5.98612	−0.249639
$576$	169.833	7.07639
$577$	0.331067	0.0137825	0.00689125	−	0.999976i	$-0.497806\pi$
$577$	0.331067	0.0137825	0.00689125	+	0.999976i	$0.497806\pi$
$578$	21.9640	0.913581
$579$	−87.7291	−3.64590
$580$	19.9703	0.829222
$581$	−1.67573	−0.0695212
$582$	−38.5732	−1.59891
$583$	14.3869	0.595844
$584$	−103.267	−4.27321
$585$	33.9539	1.40382
$586$	−31.3098	−1.29340
$587$	−27.8643	−1.15008	−0.575040	−	0.818125i	$-0.695014\pi$
$587$	−27.8643	−1.15008	−0.575040	+	0.818125i	$0.695014\pi$
$588$	−17.1556	−0.707485
$589$	16.4683	0.678564
$590$	25.0328	1.03059
$591$	78.6186	3.23394
$592$	−42.9005	−1.76320
$593$	33.6822	1.38316	0.691581	−	0.722299i	$-0.256914\pi$
$593$	33.6822	1.38316	0.691581	+	0.722299i	$0.256914\pi$
$594$	−151.531	−6.21741
$595$	2.97617	0.122011
$596$	−51.4188	−2.10619
$597$	65.1403	2.66601
$598$	72.4136	2.96121
$599$	26.9542	1.10132	0.550659	−	0.834731i	$-0.314377\pi$
$599$	26.9542	1.10132	0.550659	+	0.834731i	$0.314377\pi$
$600$	28.7360	1.17314
$601$	−1.78663	−0.0728782	−0.0364391	−	0.999336i	$-0.511601\pi$
$601$	−1.78663	−0.0728782	−0.0364391	+	0.999336i	$0.511601\pi$
$602$	26.3456	1.07377
$603$	−95.1318	−3.87407
$604$	83.8521	3.41189
$605$	3.28446	0.133532
$606$	−5.17231	−0.210111
$607$	−18.4756	−0.749903	−0.374952	−	0.927044i	$-0.622341\pi$
$607$	−18.4756	−0.749903	−0.374952	+	0.927044i	$0.622341\pi$
$608$	−29.6125	−1.20095
$609$	−12.3058	−0.498656
$610$	2.62794	0.106402
$611$	47.5708	1.92451
$612$	118.897	4.80615
$613$	40.8362	1.64936	0.824679	−	0.565601i	$-0.191356\pi$
$613$	40.8362	1.64936	0.824679	+	0.565601i	$0.191356\pi$
$614$	−9.07634	−0.366291
$615$	−7.30796	−0.294685
$616$	33.4035	1.34587
$617$	−43.7699	−1.76211	−0.881054	−	0.473016i	$-0.843165\pi$
$617$	−43.7699	−1.76211	−0.881054	+	0.473016i	$0.843165\pi$
$618$	94.8728	3.81634
$619$	−25.1113	−1.00931	−0.504654	−	0.863322i	$-0.668380\pi$
$619$	−25.1113	−1.00931	−0.504654	+	0.863322i	$0.668380\pi$
$620$	53.3101	2.14098
$621$	88.9728	3.57035
$622$	−13.6100	−0.545712
$623$	14.9382	0.598487
$624$	−193.747	−7.75610
$625$	1.00000	0.0400000
$626$	11.7018	0.467698
$627$	20.0298	0.799914
$628$	101.802	4.06233
$629$	−9.60874	−0.383125
$630$	−20.4237	−0.813698
$631$	7.94573	0.316315	0.158157	−	0.987414i	$-0.449445\pi$
$631$	7.94573	0.316315	0.158157	+	0.987414i	$0.449445\pi$
$632$	−124.421	−4.94920
$633$	−67.5065	−2.68314
$634$	−84.8067	−3.36810
$635$	−5.11964	−0.203167
$636$	65.3042	2.58948
$637$	4.48451	0.177683
$638$	38.5865	1.52765
$639$	−58.0339	−2.29579
$640$	−24.1722	−0.955490
$641$	4.38988	0.173390	0.0866950	−	0.996235i	$-0.472369\pi$
$641$	4.38988	0.173390	0.0866950	+	0.996235i	$0.472369\pi$
$642$	−18.4052	−0.726397
$643$	−1.26355	−0.0498296	−0.0249148	−	0.999690i	$-0.507931\pi$
$643$	−1.26355	−0.0498296	−0.0249148	+	0.999690i	$0.507931\pi$
$644$	−31.5853	−1.24464
$645$	31.7552	1.25036
$646$	−13.0857	−0.514850
$647$	50.2824	1.97680	0.988402	−	0.151861i	$-0.0485265\pi$
$647$	50.2824	1.97680	0.988402	+	0.151861i	$0.0485265\pi$
$648$	−226.357	−8.89216
$649$	35.0738	1.37677
$650$	−12.0969	−0.474480
$651$	−32.8499	−1.28749
$652$	74.2888	2.90937
$653$	33.5083	1.31128	0.655640	−	0.755074i	$-0.272399\pi$
$653$	33.5083	1.31128	0.655640	+	0.755074i	$0.272399\pi$
$654$	117.243	4.58455
$655$	8.64928	0.337955
$656$	29.8666	1.16609
$657$	88.4658	3.45138
$658$	−28.6143	−1.11550
$659$	31.2859	1.21872	0.609362	−	0.792892i	$-0.291426\pi$
$659$	31.2859	1.21872	0.609362	+	0.792892i	$0.291426\pi$
$660$	64.8392	2.52386
$661$	30.4441	1.18414	0.592070	−	0.805886i	$-0.298311\pi$
$661$	30.4441	1.18414	0.592070	+	0.805886i	$0.298311\pi$
$662$	55.6322	2.16221
$663$	−43.3950	−1.68532
$664$	14.8103	0.574753
$665$	1.62997	0.0632075
$666$	65.9389	2.55508
$667$	−22.6564	−0.877258
$668$	35.8502	1.38708
$669$	44.5050	1.72066
$670$	33.8930	1.30940
$671$	3.68203	0.142143
$672$	59.0693	2.27865
$673$	42.8427	1.65147	0.825733	−	0.564061i	$-0.190762\pi$
$673$	42.8427	1.65147	0.825733	+	0.564061i	$0.190762\pi$
$674$	73.0691	2.81452
$675$	−14.8632	−0.572084
$676$	37.5200	1.44308
$677$	7.57266	0.291041	0.145520	−	0.989355i	$-0.453514\pi$
$677$	7.57266	0.291041	0.145520	+	0.989355i	$0.453514\pi$
$678$	136.792	5.25347
$679$	−4.39806	−0.168782
$680$	−26.3038	−1.00870
$681$	−45.8146	−1.75562
$682$	103.005	3.94428
$683$	0.264454	0.0101191	0.00505953	−	0.999987i	$-0.498389\pi$
$683$	0.264454	0.0101191	0.00505953	+	0.999987i	$0.498389\pi$
$684$	65.1169	2.48981
$685$	−10.5948	−0.404806
$686$	−2.69749	−0.102990
$687$	−3.25136	−0.124047
$688$	−129.779	−4.94778
$689$	−17.0707	−0.650341
$690$	−52.5013	−1.99869
$691$	35.6755	1.35716	0.678579	−	0.734527i	$-0.262596\pi$
$691$	35.6755	1.35716	0.678579	+	0.734527i	$0.262596\pi$
$692$	−64.1688	−2.43933
$693$	−28.6158	−1.08703
$694$	22.3504	0.848408
$695$	8.73458	0.331321
$696$	108.760	4.12255
$697$	6.68942	0.253380
$698$	4.19472	0.158773
$699$	−37.6574	−1.42433
$700$	5.27643	0.199430
$701$	−1.52530	−0.0576099	−0.0288049	−	0.999585i	$-0.509170\pi$
$701$	−1.52530	−0.0576099	−0.0288049	+	0.999585i	$0.509170\pi$
$702$	179.799	6.78606
$703$	−5.26244	−0.198477
$704$	−84.7775	−3.19517
$705$	−34.4898	−1.29896
$706$	54.7140	2.05919
$707$	−0.589738	−0.0221794
$708$	159.205	5.98329
$709$	5.23210	0.196496	0.0982478	−	0.995162i	$-0.468676\pi$
$709$	5.23210	0.196496	0.0982478	+	0.995162i	$0.468676\pi$
$710$	20.6760	0.775957
$711$	106.588	3.99736
$712$	−132.026	−4.94788
$713$	−60.4804	−2.26501
$714$	26.1026	0.976864
$715$	−16.9491	−0.633862
$716$	−20.4160	−0.762982
$717$	−15.4235	−0.576002
$718$	−99.2946	−3.70564
$719$	31.4821	1.17409	0.587043	−	0.809556i	$-0.300292\pi$
$719$	31.4821	1.17409	0.587043	+	0.809556i	$0.300292\pi$
$720$	100.607	3.74941
$721$	10.8173	0.402856
$722$	44.0856	1.64069
$723$	91.5959	3.40649
$724$	−75.2448	−2.79645
$725$	3.78481	0.140564
$726$	28.8064	1.06911
$727$	33.1743	1.23037	0.615183	−	0.788384i	$-0.289082\pi$
$727$	33.1743	1.23037	0.615183	+	0.788384i	$0.289082\pi$
$728$	−39.6347	−1.46896
$729$	48.9372	1.81249
$730$	−31.5181	−1.16654
$731$	−29.0675	−1.07510
$732$	16.7133	0.617741
$733$	−14.1784	−0.523691	−0.261845	−	0.965110i	$-0.584331\pi$
$733$	−14.1784	−0.523691	−0.261845	+	0.965110i	$0.584331\pi$
$734$	4.66858	0.172320
$735$	−3.25136	−0.119928
$736$	108.753	4.00869
$737$	47.4879	1.74924
$738$	−45.9054	−1.68980
$739$	15.7702	0.580116	0.290058	−	0.957009i	$-0.406325\pi$
$739$	15.7702	0.580116	0.290058	+	0.957009i	$0.406325\pi$
$740$	−17.0352	−0.626228
$741$	−23.7662	−0.873075
$742$	10.2682	0.376957
$743$	−44.0162	−1.61480	−0.807398	−	0.590007i	$-0.799125\pi$
$743$	−44.0162	−1.61480	−0.807398	+	0.590007i	$0.799125\pi$
$744$	290.332	10.6441
$745$	−9.74499	−0.357029
$746$	−46.3805	−1.69811
$747$	−12.6876	−0.464215
$748$	−59.3513	−2.17010
$749$	−2.09854	−0.0766789
$750$	8.77051	0.320254
$751$	−22.1167	−0.807051	−0.403526	−	0.914968i	$-0.632215\pi$
$751$	−22.1167	−0.807051	−0.403526	+	0.914968i	$0.632215\pi$
$752$	140.955	5.14009
$753$	−8.21728	−0.299454
$754$	−45.7846	−1.66738
$755$	15.8918	0.578363
$756$	−78.4245	−2.85227
$757$	23.2572	0.845297	0.422649	−	0.906294i	$-0.361100\pi$
$757$	23.2572	0.845297	0.422649	+	0.906294i	$0.361100\pi$
$758$	15.6208	0.567372
$759$	−73.5602	−2.67007
$760$	−14.4059	−0.522556
$761$	42.9295	1.55619	0.778097	−	0.628144i	$-0.216185\pi$
$761$	42.9295	1.55619	0.778097	+	0.628144i	$0.216185\pi$
$762$	−44.9019	−1.62662
$763$	13.3678	0.483948
$764$	21.0524	0.761648
$765$	22.5337	0.814708
$766$	−58.9391	−2.12956
$767$	−41.6166	−1.50269
$768$	−66.1398	−2.38661
$769$	−26.2915	−0.948094	−0.474047	−	0.880499i	$-0.657207\pi$
$769$	−26.2915	−0.948094	−0.474047	+	0.880499i	$0.657207\pi$
$770$	10.1951	0.367406
$771$	−46.2113	−1.66426
$772$	142.370	5.12401
$773$	−18.8974	−0.679693	−0.339847	−	0.940481i	$-0.610375\pi$
$773$	−18.8974	−0.679693	−0.339847	+	0.940481i	$0.610375\pi$
$774$	199.473	7.16989
$775$	10.1034	0.362926
$776$	38.8706	1.39537
$777$	10.4972	0.376585
$778$	18.8553	0.675995
$779$	3.66362	0.131263
$780$	−76.9345	−2.75470
$781$	28.9694	1.03661
$782$	48.0577	1.71854
$783$	−56.2543	−2.01037
$784$	13.2879	0.474566
$785$	19.2937	0.688621
$786$	75.8586	2.70579
$787$	−17.0652	−0.608308	−0.304154	−	0.952623i	$-0.598374\pi$
$787$	−17.0652	−0.608308	−0.304154	+	0.952623i	$0.598374\pi$
$788$	−127.585	−4.54503
$789$	−9.30427	−0.331241
$790$	−37.9746	−1.35107
$791$	15.5968	0.554560
$792$	252.910	8.98677
$793$	−4.36889	−0.155144
$794$	80.1700	2.84513
$795$	12.3766	0.438952
$796$	−105.712	−3.74686
$797$	−22.7926	−0.807355	−0.403678	−	0.914901i	$-0.632268\pi$
$797$	−22.7926	−0.807355	−0.403678	+	0.914901i	$0.632268\pi$
$798$	14.2957	0.506061
$799$	31.5706	1.11689
$800$	−18.1675	−0.642320
$801$	113.103	3.99629
$802$	−30.1864	−1.06592
$803$	−44.1604	−1.55839
$804$	215.555	7.60202
$805$	−5.98612	−0.210983
$806$	−122.220	−4.30503
$807$	37.0630	1.30468
$808$	5.21218	0.183364
$809$	−37.9676	−1.33487	−0.667436	−	0.744668i	$-0.732608\pi$
$809$	−37.9676	−1.33487	−0.667436	+	0.744668i	$0.732608\pi$
$810$	−69.0866	−2.42746
$811$	43.7321	1.53564	0.767821	−	0.640664i	$-0.221341\pi$
$811$	43.7321	1.53564	0.767821	+	0.640664i	$0.221341\pi$
$812$	19.9703	0.700820
$813$	35.9979	1.26250
$814$	−32.9154	−1.15368
$815$	14.0794	0.493179
$816$	−128.582	−4.50125
$817$	−15.9195	−0.556952
$818$	25.9901	0.908724
$819$	33.9539	1.18645
$820$	11.8596	0.414156
$821$	−28.5128	−0.995102	−0.497551	−	0.867435i	$-0.665767\pi$
$821$	−28.5128	−0.995102	−0.497551	+	0.867435i	$0.665767\pi$
$822$	−92.9216	−3.24101
$823$	44.6747	1.55726	0.778632	−	0.627481i	$-0.215914\pi$
$823$	44.6747	1.55726	0.778632	+	0.627481i	$0.215914\pi$
$824$	−95.6042	−3.33053
$825$	12.2885	0.427829
$826$	25.0328	0.871003
$827$	−37.7119	−1.31137	−0.655685	−	0.755035i	$-0.727620\pi$
$827$	−37.7119	−1.31137	−0.655685	+	0.755035i	$0.727620\pi$
$828$	−239.144	−8.31084
$829$	−11.9402	−0.414700	−0.207350	−	0.978267i	$-0.566484\pi$
$829$	−11.9402	−0.414700	−0.207350	+	0.978267i	$0.566484\pi$
$830$	4.52027	0.156901
$831$	−36.1184	−1.25293
$832$	100.592	3.48740
$833$	2.97617	0.103118
$834$	76.6067	2.65267
$835$	6.79440	0.235130
$836$	−32.5051	−1.12421
$837$	−150.169	−5.19061
$838$	18.8160	0.649988
$839$	9.70917	0.335198	0.167599	−	0.985855i	$-0.446399\pi$
$839$	9.70917	0.335198	0.167599	+	0.985855i	$0.446399\pi$
$840$	28.7360	0.991485
$841$	−14.6752	−0.506041
$842$	8.08451	0.278611
$843$	43.1448	1.48599
$844$	109.552	3.77093
$845$	7.11087	0.244621
$846$	−216.650	−7.44857
$847$	3.28446	0.112855
$848$	−50.5813	−1.73697
$849$	11.8680	0.407309
$850$	−8.02819	−0.275365
$851$	19.3265	0.662504
$852$	131.496	4.50499
$853$	25.5200	0.873788	0.436894	−	0.899513i	$-0.356078\pi$
$853$	25.5200	0.873788	0.436894	+	0.899513i	$0.356078\pi$
$854$	2.62794	0.0899262
$855$	12.3411	0.422057
$856$	18.5471	0.633928
$857$	−35.3254	−1.20669	−0.603346	−	0.797480i	$-0.706166\pi$
$857$	−35.3254	−1.20669	−0.603346	+	0.797480i	$0.706166\pi$
$858$	−148.652	−5.07491
$859$	−17.6885	−0.603522	−0.301761	−	0.953384i	$-0.597574\pi$
$859$	−17.6885	−0.603522	−0.301761	+	0.953384i	$0.597574\pi$
$860$	−51.5335	−1.75728
$861$	−7.30796	−0.249055
$862$	32.2552	1.09862
$863$	−54.2408	−1.84638	−0.923189	−	0.384346i	$-0.874427\pi$
$863$	−54.2408	−1.84638	−0.923189	+	0.384346i	$0.874427\pi$
$864$	270.027	9.18652
$865$	−12.1614	−0.413500
$866$	66.8271	2.27088
$867$	26.4739	0.899100
$868$	53.3101	1.80946
$869$	−53.2066	−1.80491
$870$	33.1947	1.12541
$871$	−56.3465	−1.90923
$872$	−118.146	−4.00094
$873$	−33.2993	−1.12701
$874$	26.3199	0.890284
$875$	1.00000	0.0338062
$876$	−200.450	−6.77259
$877$	22.5569	0.761693	0.380846	−	0.924638i	$-0.375633\pi$
$877$	22.5569	0.761693	0.380846	+	0.924638i	$0.375633\pi$
$878$	61.3422	2.07020
$879$	−37.7387	−1.27289
$880$	−50.2212	−1.69295
$881$	38.4630	1.29585	0.647926	−	0.761703i	$-0.275637\pi$
$881$	38.4630	1.29585	0.647926	+	0.761703i	$0.275637\pi$
$882$	−20.4237	−0.687700
$883$	−11.5578	−0.388951	−0.194476	−	0.980907i	$-0.562301\pi$
$883$	−11.5578	−0.388951	−0.194476	+	0.980907i	$0.562301\pi$
$884$	70.4229	2.36858
$885$	30.1728	1.01425
$886$	55.0232	1.84854
$887$	26.0088	0.873289	0.436645	−	0.899634i	$-0.356167\pi$
$887$	26.0088	0.873289	0.436645	+	0.899634i	$0.356167\pi$
$888$	−92.7756	−3.11334
$889$	−5.11964	−0.171707
$890$	−40.2957	−1.35071
$891$	−96.7981	−3.24286
$892$	−72.2243	−2.41825
$893$	17.2904	0.578600
$894$	−85.4685	−2.85849
$895$	−3.86928	−0.129336
$896$	−24.1722	−0.807536
$897$	87.2824	2.91427
$898$	16.9501	0.565631
$899$	38.2396	1.27536
$900$	39.9498	1.33166
$901$	−11.3290	−0.377425
$902$	22.9151	0.762989
$903$	31.7552	1.05675
$904$	−137.847	−4.58471
$905$	−14.2606	−0.474037
$906$	139.379	4.63057
$907$	26.5241	0.880718	0.440359	−	0.897822i	$-0.354851\pi$
$907$	26.5241	0.880718	0.440359	+	0.897822i	$0.354851\pi$
$908$	74.3495	2.46738
$909$	−4.46513	−0.148099
$910$	−12.0969	−0.401009
$911$	10.9713	0.363495	0.181748	−	0.983345i	$-0.441825\pi$
$911$	10.9713	0.363495	0.181748	+	0.983345i	$0.441825\pi$
$912$	−70.4206	−2.33186
$913$	6.33340	0.209605
$914$	6.59176	0.218036
$915$	3.16754	0.104715
$916$	5.27643	0.174338
$917$	8.64928	0.285624
$918$	119.324	3.93829
$919$	−33.1024	−1.09195	−0.545973	−	0.837803i	$-0.683840\pi$
$919$	−33.1024	−1.09195	−0.545973	+	0.837803i	$0.683840\pi$
$920$	52.9061	1.74426
$921$	−10.9400	−0.360485
$922$	64.1317	2.11206
$923$	−34.3734	−1.13142
$924$	64.8392	2.13305
$925$	−3.22855	−0.106154
$926$	−51.7317	−1.70001
$927$	81.9014	2.68999
$928$	−68.7608	−2.25718
$929$	14.4482	0.474030	0.237015	−	0.971506i	$-0.423831\pi$
$929$	14.4482	0.474030	0.237015	+	0.971506i	$0.423831\pi$
$930$	88.6123	2.90571
$931$	1.62997	0.0534201
$932$	61.1118	2.00178
$933$	−16.4046	−0.537062
$934$	23.9934	0.785089
$935$	−11.2484	−0.367862
$936$	−300.089	−9.80871
$937$	−21.8598	−0.714128	−0.357064	−	0.934080i	$-0.616222\pi$
$937$	−21.8598	−0.714128	−0.357064	+	0.934080i	$0.616222\pi$
$938$	33.8930	1.10665
$939$	14.1045	0.460284
$940$	55.9712	1.82558
$941$	42.5725	1.38782	0.693912	−	0.720060i	$-0.255886\pi$
$941$	42.5725	1.38782	0.693912	+	0.720060i	$0.255886\pi$
$942$	169.215	5.51334
$943$	−13.4548	−0.438147
$944$	−123.312	−4.01347
$945$	−14.8632	−0.483499
$946$	−99.5728	−3.23739
$947$	−24.2602	−0.788351	−0.394176	−	0.919035i	$-0.628970\pi$
$947$	−24.2602	−0.788351	−0.394176	+	0.919035i	$0.628970\pi$
$948$	−241.512	−7.84396
$949$	52.3982	1.70092
$950$	−4.39682	−0.142652
$951$	−102.220	−3.31472
$952$	−26.3038	−0.852511
$953$	−53.9459	−1.74748	−0.873740	−	0.486394i	$-0.838312\pi$
$953$	−53.9459	−1.74748	−0.873740	+	0.486394i	$0.838312\pi$
$954$	77.7443	2.51706
$955$	3.98989	0.129110
$956$	25.0299	0.809523
$957$	46.5095	1.50344
$958$	114.788	3.70862
$959$	−10.5948	−0.342123
$960$	−72.9313	−2.35385
$961$	71.0794	2.29289
$962$	39.0555	1.25920
$963$	−15.8888	−0.512010
$964$	−148.645	−4.78754
$965$	26.9823	0.868590
$966$	−52.5013	−1.68920
$967$	14.6768	0.471973	0.235987	−	0.971756i	$-0.424168\pi$
$967$	14.6768	0.471973	0.235987	+	0.971756i	$0.424168\pi$
$968$	−29.0285	−0.933011
$969$	−15.7726	−0.506689
$970$	11.8637	0.380920
$971$	46.7049	1.49883	0.749417	−	0.662099i	$-0.230334\pi$
$971$	46.7049	1.49883	0.749417	+	0.662099i	$0.230334\pi$
$972$	−204.107	−6.54673
$973$	8.73458	0.280018
$974$	1.14447	0.0366713
$975$	−14.5808	−0.466959
$976$	−12.9453	−0.414368
$977$	4.27372	0.136728	0.0683642	−	0.997660i	$-0.478222\pi$
$977$	4.27372	0.136728	0.0683642	+	0.997660i	$0.478222\pi$
$978$	123.483	3.94856
$979$	−56.4587	−1.80443
$980$	5.27643	0.168549
$981$	101.213	3.23147
$982$	60.2103	1.92139
$983$	−15.4263	−0.492023	−0.246011	−	0.969267i	$-0.579120\pi$
$983$	−15.4263	−0.492023	−0.246011	+	0.969267i	$0.579120\pi$
$984$	64.5886	2.05901
$985$	−24.1802	−0.770445
$986$	−30.3852	−0.967662
$987$	−34.4898	−1.09782
$988$	38.5687	1.22703
$989$	58.4649	1.85908
$990$	77.1908	2.45328
$991$	50.2336	1.59572	0.797861	−	0.602841i	$-0.205965\pi$
$991$	50.2336	1.59572	0.797861	+	0.602841i	$0.205965\pi$
$992$	−183.555	−5.82787
$993$	67.0553	2.12793
$994$	20.6760	0.655803
$995$	−20.0348	−0.635145
$996$	28.7482	0.910922
$997$	37.3831	1.18394	0.591968	−	0.805962i	$-0.298351\pi$
$997$	37.3831	1.18394	0.591968	+	0.805962i	$0.298351\pi$
$998$	84.6549	2.67970
$999$	47.9866	1.51823

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.o.1.4	✓	73

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.o.1.4	✓	73	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.69749 q^{2} -3.25136 q^{3} +5.27643 q^{4} +1.00000 q^{5} +8.77051 q^{6} +1.00000 q^{7} -8.83812 q^{8} +7.57137 q^{9} +O(q^{10})\)	\(q-2.69749 q^{2} -3.25136 q^{3} +5.27643 q^{4} +1.00000 q^{5} +8.77051 q^{6} +1.00000 q^{7} -8.83812 q^{8} +7.57137 q^{9} -2.69749 q^{10} -3.77948 q^{11} -17.1556 q^{12} +4.48451 q^{13} -2.69749 q^{14} -3.25136 q^{15} +13.2879 q^{16} +2.97617 q^{17} -20.4237 q^{18} +1.62997 q^{19} +5.27643 q^{20} -3.25136 q^{21} +10.1951 q^{22} -5.98612 q^{23} +28.7360 q^{24} +1.00000 q^{25} -12.0969 q^{26} -14.8632 q^{27} +5.27643 q^{28} +3.78481 q^{29} +8.77051 q^{30} +10.1034 q^{31} -18.1675 q^{32} +12.2885 q^{33} -8.02819 q^{34} +1.00000 q^{35} +39.9498 q^{36} -3.22855 q^{37} -4.39682 q^{38} -14.5808 q^{39} -8.83812 q^{40} +2.24766 q^{41} +8.77051 q^{42} -9.76674 q^{43} -19.9422 q^{44} +7.57137 q^{45} +16.1475 q^{46} +10.6078 q^{47} -43.2036 q^{48} +1.00000 q^{49} -2.69749 q^{50} -9.67662 q^{51} +23.6622 q^{52} -3.80658 q^{53} +40.0932 q^{54} -3.77948 q^{55} -8.83812 q^{56} -5.29962 q^{57} -10.2095 q^{58} -9.28006 q^{59} -17.1556 q^{60} -0.974217 q^{61} -27.2539 q^{62} +7.57137 q^{63} +22.4310 q^{64} +4.48451 q^{65} -33.1479 q^{66} -12.5647 q^{67} +15.7036 q^{68} +19.4631 q^{69} -2.69749 q^{70} -7.66492 q^{71} -66.9167 q^{72} +11.6843 q^{73} +8.70898 q^{74} -3.25136 q^{75} +8.60042 q^{76} -3.77948 q^{77} +39.3315 q^{78} +14.0778 q^{79} +13.2879 q^{80} +25.6115 q^{81} -6.06303 q^{82} -1.67573 q^{83} -17.1556 q^{84} +2.97617 q^{85} +26.3456 q^{86} -12.3058 q^{87} +33.4035 q^{88} +14.9382 q^{89} -20.4237 q^{90} +4.48451 q^{91} -31.5853 q^{92} -32.8499 q^{93} -28.6143 q^{94} +1.62997 q^{95} +59.0693 q^{96} -4.39806 q^{97} -2.69749 q^{98} -28.6158 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 73 q + 7 q^{2} + 14 q^{3} + 95 q^{4} + 73 q^{5} - q^{6} + 73 q^{7} + 18 q^{8} + 111 q^{9}+O(q^{10}) \) 73 * q + 7 * q^2 + 14 * q^3 + 95 * q^4 + 73 * q^5 - q^6 + 73 * q^7 + 18 * q^8 + 111 * q^9	\( 73 q + 7 q^{2} + 14 q^{3} + 95 q^{4} + 73 q^{5} - q^{6} + 73 q^{7} + 18 q^{8} + 111 q^{9} + 7 q^{10} + 27 q^{11} + 21 q^{12} + 21 q^{13} + 7 q^{14} + 14 q^{15} + 135 q^{16} + 23 q^{17} + 41 q^{18} + 26 q^{19} + 95 q^{20} + 14 q^{21} + 48 q^{22} + 16 q^{23} - q^{24} + 73 q^{25} + 7 q^{26} + 44 q^{27} + 95 q^{28} + 66 q^{29} - q^{30} + 23 q^{31} + 3 q^{32} + 77 q^{33} + 29 q^{34} + 73 q^{35} + 142 q^{36} + 66 q^{37} - 12 q^{38} + 53 q^{39} + 18 q^{40} + 50 q^{41} - q^{42} + 43 q^{43} + 37 q^{44} + 111 q^{45} + 65 q^{46} + 28 q^{47} - 20 q^{48} + 73 q^{49} + 7 q^{50} + 71 q^{51} + 29 q^{52} - 7 q^{53} - 16 q^{54} + 27 q^{55} + 18 q^{56} + 33 q^{57} + 48 q^{58} + 16 q^{59} + 21 q^{60} + 42 q^{61} - 3 q^{62} + 111 q^{63} + 216 q^{64} + 21 q^{65} - 53 q^{66} + 48 q^{67} + 13 q^{68} + 73 q^{69} + 7 q^{70} + 68 q^{71} + 18 q^{72} + 65 q^{73} + 4 q^{74} + 14 q^{75} + 37 q^{76} + 27 q^{77} + 60 q^{78} + 116 q^{79} + 135 q^{80} + 177 q^{81} + 20 q^{82} + 40 q^{83} + 21 q^{84} + 23 q^{85} + 35 q^{86} - 14 q^{87} + 47 q^{88} + 59 q^{89} + 41 q^{90} + 21 q^{91} + 3 q^{92} + 37 q^{93} - 11 q^{94} + 26 q^{95} - 23 q^{96} + 70 q^{97} + 7 q^{98} + 49 q^{99}+O(q^{100}) \) 73 * q + 7 * q^2 + 14 * q^3 + 95 * q^4 + 73 * q^5 - q^6 + 73 * q^7 + 18 * q^8 + 111 * q^9 + 7 * q^10 + 27 * q^11 + 21 * q^12 + 21 * q^13 + 7 * q^14 + 14 * q^15 + 135 * q^16 + 23 * q^17 + 41 * q^18 + 26 * q^19 + 95 * q^20 + 14 * q^21 + 48 * q^22 + 16 * q^23 - q^24 + 73 * q^25 + 7 * q^26 + 44 * q^27 + 95 * q^28 + 66 * q^29 - q^30 + 23 * q^31 + 3 * q^32 + 77 * q^33 + 29 * q^34 + 73 * q^35 + 142 * q^36 + 66 * q^37 - 12 * q^38 + 53 * q^39 + 18 * q^40 + 50 * q^41 - q^42 + 43 * q^43 + 37 * q^44 + 111 * q^45 + 65 * q^46 + 28 * q^47 - 20 * q^48 + 73 * q^49 + 7 * q^50 + 71 * q^51 + 29 * q^52 - 7 * q^53 - 16 * q^54 + 27 * q^55 + 18 * q^56 + 33 * q^57 + 48 * q^58 + 16 * q^59 + 21 * q^60 + 42 * q^61 - 3 * q^62 + 111 * q^63 + 216 * q^64 + 21 * q^65 - 53 * q^66 + 48 * q^67 + 13 * q^68 + 73 * q^69 + 7 * q^70 + 68 * q^71 + 18 * q^72 + 65 * q^73 + 4 * q^74 + 14 * q^75 + 37 * q^76 + 27 * q^77 + 60 * q^78 + 116 * q^79 + 135 * q^80 + 177 * q^81 + 20 * q^82 + 40 * q^83 + 21 * q^84 + 23 * q^85 + 35 * q^86 - 14 * q^87 + 47 * q^88 + 59 * q^89 + 41 * q^90 + 21 * q^91 + 3 * q^92 + 37 * q^93 - 11 * q^94 + 26 * q^95 - 23 * q^96 + 70 * q^97 + 7 * q^98 + 49 * q^99

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