LMFDB - Embedded newform 4017.2.a.k.1.32

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, 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("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.0759064919$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.32
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.77069 q^{2} +1.00000 q^{3} +5.67673 q^{4} -3.19410 q^{5} +2.77069 q^{6} -4.02379 q^{7} +10.1871 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.77069 q^{2} +1.00000 q^{3} +5.67673 q^{4} -3.19410 q^{5} +2.77069 q^{6} -4.02379 q^{7} +10.1871 q^{8} +1.00000 q^{9} -8.84987 q^{10} +2.98765 q^{11} +5.67673 q^{12} +1.00000 q^{13} -11.1487 q^{14} -3.19410 q^{15} +16.8718 q^{16} -2.23404 q^{17} +2.77069 q^{18} +4.64741 q^{19} -18.1321 q^{20} -4.02379 q^{21} +8.27786 q^{22} +8.18315 q^{23} +10.1871 q^{24} +5.20228 q^{25} +2.77069 q^{26} +1.00000 q^{27} -22.8420 q^{28} +4.91843 q^{29} -8.84987 q^{30} +1.71323 q^{31} +26.3724 q^{32} +2.98765 q^{33} -6.18983 q^{34} +12.8524 q^{35} +5.67673 q^{36} +6.66821 q^{37} +12.8765 q^{38} +1.00000 q^{39} -32.5386 q^{40} +2.22147 q^{41} -11.1487 q^{42} -9.52411 q^{43} +16.9601 q^{44} -3.19410 q^{45} +22.6730 q^{46} +6.66120 q^{47} +16.8718 q^{48} +9.19091 q^{49} +14.4139 q^{50} -2.23404 q^{51} +5.67673 q^{52} -6.52915 q^{53} +2.77069 q^{54} -9.54286 q^{55} -40.9907 q^{56} +4.64741 q^{57} +13.6274 q^{58} -5.93929 q^{59} -18.1321 q^{60} -9.52660 q^{61} +4.74684 q^{62} -4.02379 q^{63} +39.3262 q^{64} -3.19410 q^{65} +8.27786 q^{66} +4.02241 q^{67} -12.6820 q^{68} +8.18315 q^{69} +35.6100 q^{70} +13.4186 q^{71} +10.1871 q^{72} +10.8591 q^{73} +18.4755 q^{74} +5.20228 q^{75} +26.3821 q^{76} -12.0217 q^{77} +2.77069 q^{78} -4.33437 q^{79} -53.8903 q^{80} +1.00000 q^{81} +6.15500 q^{82} -16.0370 q^{83} -22.8420 q^{84} +7.13574 q^{85} -26.3884 q^{86} +4.91843 q^{87} +30.4355 q^{88} -13.6059 q^{89} -8.84987 q^{90} -4.02379 q^{91} +46.4536 q^{92} +1.71323 q^{93} +18.4561 q^{94} -14.8443 q^{95} +26.3724 q^{96} -14.2561 q^{97} +25.4652 q^{98} +2.98765 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9} + 2 q^{10} + 17 q^{11} + 41 q^{12} + 32 q^{13} - 10 q^{14} + 7 q^{15} + 51 q^{16} + 2 q^{17} + 5 q^{18} + 36 q^{19} - 2 q^{20} + 25 q^{21} - 3 q^{22} + 37 q^{23} + 12 q^{24} + 43 q^{25} + 5 q^{26} + 32 q^{27} + 54 q^{28} + 2 q^{29} + 2 q^{30} + 44 q^{31} + 19 q^{32} + 17 q^{33} + 27 q^{34} - 10 q^{35} + 41 q^{36} + 46 q^{37} - 6 q^{38} + 32 q^{39} - 6 q^{40} + 5 q^{41} - 10 q^{42} + 19 q^{43} + 37 q^{44} + 7 q^{45} + 23 q^{46} + 50 q^{47} + 51 q^{48} + 67 q^{49} - 4 q^{50} + 2 q^{51} + 41 q^{52} + 5 q^{54} + 18 q^{55} - 54 q^{56} + 36 q^{57} + 27 q^{58} + 26 q^{59} - 2 q^{60} + 23 q^{61} + 27 q^{62} + 25 q^{63} + 70 q^{64} + 7 q^{65} - 3 q^{66} + 30 q^{67} - 22 q^{68} + 37 q^{69} + 59 q^{70} + 34 q^{71} + 12 q^{72} + 54 q^{73} + 18 q^{74} + 43 q^{75} + 40 q^{76} - 5 q^{77} + 5 q^{78} + 35 q^{79} - 46 q^{80} + 32 q^{81} + 23 q^{83} + 54 q^{84} + 59 q^{85} - 5 q^{86} + 2 q^{87} - 13 q^{88} + 16 q^{89} + 2 q^{90} + 25 q^{91} + 101 q^{92} + 44 q^{93} - 16 q^{94} - q^{95} + 19 q^{96} + 44 q^{97} - 44 q^{98} + 17 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9 + 2 * q^10 + 17 * q^11 + 41 * q^12 + 32 * q^13 - 10 * q^14 + 7 * q^15 + 51 * q^16 + 2 * q^17 + 5 * q^18 + 36 * q^19 - 2 * q^20 + 25 * q^21 - 3 * q^22 + 37 * q^23 + 12 * q^24 + 43 * q^25 + 5 * q^26 + 32 * q^27 + 54 * q^28 + 2 * q^29 + 2 * q^30 + 44 * q^31 + 19 * q^32 + 17 * q^33 + 27 * q^34 - 10 * q^35 + 41 * q^36 + 46 * q^37 - 6 * q^38 + 32 * q^39 - 6 * q^40 + 5 * q^41 - 10 * q^42 + 19 * q^43 + 37 * q^44 + 7 * q^45 + 23 * q^46 + 50 * q^47 + 51 * q^48 + 67 * q^49 - 4 * q^50 + 2 * q^51 + 41 * q^52 + 5 * q^54 + 18 * q^55 - 54 * q^56 + 36 * q^57 + 27 * q^58 + 26 * q^59 - 2 * q^60 + 23 * q^61 + 27 * q^62 + 25 * q^63 + 70 * q^64 + 7 * q^65 - 3 * q^66 + 30 * q^67 - 22 * q^68 + 37 * q^69 + 59 * q^70 + 34 * q^71 + 12 * q^72 + 54 * q^73 + 18 * q^74 + 43 * q^75 + 40 * q^76 - 5 * q^77 + 5 * q^78 + 35 * q^79 - 46 * q^80 + 32 * q^81 + 23 * q^83 + 54 * q^84 + 59 * q^85 - 5 * q^86 + 2 * q^87 - 13 * q^88 + 16 * q^89 + 2 * q^90 + 25 * q^91 + 101 * q^92 + 44 * q^93 - 16 * q^94 - q^95 + 19 * q^96 + 44 * q^97 - 44 * q^98 + 17 * 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 $

$2$	2.77069	1.95917	0.979587	−	0.201019i	$-0.0644252\pi$
$2$	2.77069	1.95917	0.979587	+	0.201019i	$0.0644252\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.67673	2.83837
$5$	−3.19410	−1.42845	−0.714223	−	0.699918i	$-0.753220\pi$
$5$	−3.19410	−1.42845	−0.714223	+	0.699918i	$0.753220\pi$
$6$	2.77069	1.13113
$7$	−4.02379	−1.52085	−0.760425	−	0.649425i	$-0.775010\pi$
$7$	−4.02379	−1.52085	−0.760425	+	0.649425i	$0.775010\pi$
$8$	10.1871	3.60168
$9$	1.00000	0.333333
$10$	−8.84987	−2.79857
$11$	2.98765	0.900810	0.450405	−	0.892824i	$-0.351280\pi$
$11$	2.98765	0.900810	0.450405	+	0.892824i	$0.351280\pi$
$12$	5.67673	1.63873
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−11.1487	−2.97961
$15$	−3.19410	−0.824713
$16$	16.8718	4.21796
$17$	−2.23404	−0.541833	−0.270917	−	0.962603i	$-0.587327\pi$
$17$	−2.23404	−0.541833	−0.270917	+	0.962603i	$0.587327\pi$
$18$	2.77069	0.653058
$19$	4.64741	1.06619	0.533094	−	0.846056i	$-0.321029\pi$
$19$	4.64741	1.06619	0.533094	+	0.846056i	$0.321029\pi$
$20$	−18.1321	−4.05445
$21$	−4.02379	−0.878064
$22$	8.27786	1.76485
$23$	8.18315	1.70631	0.853153	−	0.521661i	$-0.174688\pi$
$23$	8.18315	1.70631	0.853153	+	0.521661i	$0.174688\pi$
$24$	10.1871	2.07943
$25$	5.20228	1.04046
$26$	2.77069	0.543377
$27$	1.00000	0.192450
$28$	−22.8420	−4.31673
$29$	4.91843	0.913329	0.456665	−	0.889639i	$-0.349044\pi$
$29$	4.91843	0.913329	0.456665	+	0.889639i	$0.349044\pi$
$30$	−8.84987	−1.61576
$31$	1.71323	0.307706	0.153853	−	0.988094i	$-0.450832\pi$
$31$	1.71323	0.307706	0.153853	+	0.988094i	$0.450832\pi$
$32$	26.3724	4.66203
$33$	2.98765	0.520083
$34$	−6.18983	−1.06155
$35$	12.8524	2.17245
$36$	5.67673	0.946122
$37$	6.66821	1.09625	0.548123	−	0.836398i	$-0.315343\pi$
$37$	6.66821	1.09625	0.548123	+	0.836398i	$0.315343\pi$
$38$	12.8765	2.08885
$39$	1.00000	0.160128
$40$	−32.5386	−5.14480
$41$	2.22147	0.346935	0.173467	−	0.984840i	$-0.444503\pi$
$41$	2.22147	0.346935	0.173467	+	0.984840i	$0.444503\pi$
$42$	−11.1487	−1.72028
$43$	−9.52411	−1.45241	−0.726207	−	0.687476i	$-0.758718\pi$
$43$	−9.52411	−1.45241	−0.726207	+	0.687476i	$0.758718\pi$
$44$	16.9601	2.55683
$45$	−3.19410	−0.476149
$46$	22.6730	3.34295
$47$	6.66120	0.971636	0.485818	−	0.874060i	$-0.338522\pi$
$47$	6.66120	0.971636	0.485818	+	0.874060i	$0.338522\pi$
$48$	16.8718	2.43524
$49$	9.19091	1.31299
$50$	14.4139	2.03844
$51$	−2.23404	−0.312828
$52$	5.67673	0.787221
$53$	−6.52915	−0.896847	−0.448424	−	0.893821i	$-0.648014\pi$
$53$	−6.52915	−0.896847	−0.448424	+	0.893821i	$0.648014\pi$
$54$	2.77069	0.377043
$55$	−9.54286	−1.28676
$56$	−40.9907	−5.47762
$57$	4.64741	0.615564
$58$	13.6274	1.78937
$59$	−5.93929	−0.773229	−0.386615	−	0.922241i	$-0.626356\pi$
$59$	−5.93929	−0.773229	−0.386615	+	0.922241i	$0.626356\pi$
$60$	−18.1321	−2.34084
$61$	−9.52660	−1.21976	−0.609878	−	0.792495i	$-0.708782\pi$
$61$	−9.52660	−1.21976	−0.609878	+	0.792495i	$0.708782\pi$
$62$	4.74684	0.602849
$63$	−4.02379	−0.506950
$64$	39.3262	4.91578
$65$	−3.19410	−0.396180
$66$	8.27786	1.01893
$67$	4.02241	0.491415	0.245708	−	0.969344i	$-0.420980\pi$
$67$	4.02241	0.491415	0.245708	+	0.969344i	$0.420980\pi$
$68$	−12.6820	−1.53792
$69$	8.18315	0.985136
$70$	35.6100	4.25621
$71$	13.4186	1.59249	0.796247	−	0.604972i	$-0.206816\pi$
$71$	13.4186	1.59249	0.796247	+	0.604972i	$0.206816\pi$
$72$	10.1871	1.20056
$73$	10.8591	1.27096	0.635480	−	0.772117i	$-0.280802\pi$
$73$	10.8591	1.27096	0.635480	+	0.772117i	$0.280802\pi$
$74$	18.4755	2.14774
$75$	5.20228	0.600708
$76$	26.3821	3.02623
$77$	−12.0217	−1.37000
$78$	2.77069	0.313719
$79$	−4.33437	−0.487655	−0.243827	−	0.969819i	$-0.578403\pi$
$79$	−4.33437	−0.487655	−0.243827	+	0.969819i	$0.578403\pi$
$80$	−53.8903	−6.02512
$81$	1.00000	0.111111
$82$	6.15500	0.679706
$83$	−16.0370	−1.76028	−0.880142	−	0.474710i	$-0.842553\pi$
$83$	−16.0370	−1.76028	−0.880142	+	0.474710i	$0.842553\pi$
$84$	−22.8420	−2.49227
$85$	7.13574	0.773980
$86$	−26.3884	−2.84553
$87$	4.91843	0.527311
$88$	30.4355	3.24443
$89$	−13.6059	−1.44223	−0.721113	−	0.692818i	$-0.756369\pi$
$89$	−13.6059	−1.44223	−0.721113	+	0.692818i	$0.756369\pi$
$90$	−8.84987	−0.932858
$91$	−4.02379	−0.421808
$92$	46.4536	4.84312
$93$	1.71323	0.177654
$94$	18.4561	1.90360
$95$	−14.8443	−1.52299
$96$	26.3724	2.69163
$97$	−14.2561	−1.44749	−0.723743	−	0.690070i	$-0.757580\pi$
$97$	−14.2561	−1.44749	−0.723743	+	0.690070i	$0.757580\pi$
$98$	25.4652	2.57237
$99$	2.98765	0.300270
$100$	29.5320	2.95320
$101$	−5.14153	−0.511602	−0.255801	−	0.966730i	$-0.582339\pi$
$101$	−5.14153	−0.511602	−0.255801	+	0.966730i	$0.582339\pi$
$102$	−6.18983	−0.612884
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	10.1871	0.998926
$105$	12.8524	1.25427
$106$	−18.0902	−1.75708
$107$	−3.43727	−0.332293	−0.166147	−	0.986101i	$-0.553133\pi$
$107$	−3.43727	−0.332293	−0.166147	+	0.986101i	$0.553133\pi$
$108$	5.67673	0.546244
$109$	−1.98066	−0.189713	−0.0948563	−	0.995491i	$-0.530239\pi$
$109$	−1.98066	−0.189713	−0.0948563	+	0.995491i	$0.530239\pi$
$110$	−26.4403	−2.52099
$111$	6.66821	0.632918
$112$	−67.8887	−6.41488
$113$	9.16307	0.861989	0.430995	−	0.902355i	$-0.358163\pi$
$113$	9.16307	0.861989	0.430995	+	0.902355i	$0.358163\pi$
$114$	12.8765	1.20600
$115$	−26.1378	−2.43736
$116$	27.9206	2.59236
$117$	1.00000	0.0924500
$118$	−16.4559	−1.51489
$119$	8.98930	0.824048
$120$	−32.5386	−2.97035
$121$	−2.07395	−0.188541
$122$	−26.3953	−2.38972
$123$	2.22147	0.200303
$124$	9.72556	0.873381
$125$	−0.646112	−0.0577900
$126$	−11.1487	−0.993204
$127$	−16.1111	−1.42963	−0.714815	−	0.699314i	$-0.753489\pi$
$127$	−16.1111	−1.42963	−0.714815	+	0.699314i	$0.753489\pi$
$128$	56.2160	4.96884
$129$	−9.52411	−0.838551
$130$	−8.84987	−0.776185
$131$	−17.3936	−1.51968	−0.759841	−	0.650109i	$-0.774723\pi$
$131$	−17.3936	−1.51968	−0.759841	+	0.650109i	$0.774723\pi$
$132$	16.9601	1.47619
$133$	−18.7002	−1.62151
$134$	11.1449	0.962769
$135$	−3.19410	−0.274904
$136$	−22.7583	−1.95151
$137$	4.36300	0.372756	0.186378	−	0.982478i	$-0.440325\pi$
$137$	4.36300	0.372756	0.186378	+	0.982478i	$0.440325\pi$
$138$	22.6730	1.93005
$139$	−7.73988	−0.656488	−0.328244	−	0.944593i	$-0.606457\pi$
$139$	−7.73988	−0.656488	−0.328244	+	0.944593i	$0.606457\pi$
$140$	72.9597	6.16622
$141$	6.66120	0.560974
$142$	37.1788	3.11997
$143$	2.98765	0.249840
$144$	16.8718	1.40599
$145$	−15.7100	−1.30464
$146$	30.0872	2.49003
$147$	9.19091	0.758054
$148$	37.8536	3.11155
$149$	−13.0432	−1.06854	−0.534270	−	0.845314i	$-0.679413\pi$
$149$	−13.0432	−1.06854	−0.534270	+	0.845314i	$0.679413\pi$
$150$	14.4139	1.17689
$151$	5.05032	0.410989	0.205495	−	0.978658i	$-0.434120\pi$
$151$	5.05032	0.410989	0.205495	+	0.978658i	$0.434120\pi$
$152$	47.3435	3.84007
$153$	−2.23404	−0.180611
$154$	−33.3084	−2.68407
$155$	−5.47224	−0.439541
$156$	5.67673	0.454502
$157$	16.6954	1.33244	0.666218	−	0.745757i	$-0.267912\pi$
$157$	16.6954	1.33244	0.666218	+	0.745757i	$0.267912\pi$
$158$	−12.0092	−0.955401
$159$	−6.52915	−0.517795
$160$	−84.2362	−6.65946
$161$	−32.9273	−2.59504
$162$	2.77069	0.217686
$163$	2.86866	0.224691	0.112345	−	0.993669i	$-0.464164\pi$
$163$	2.86866	0.224691	0.112345	+	0.993669i	$0.464164\pi$
$164$	12.6107	0.984728
$165$	−9.54286	−0.742910
$166$	−44.4335	−3.44871
$167$	−14.2994	−1.10652	−0.553259	−	0.833010i	$-0.686616\pi$
$167$	−14.2994	−1.10652	−0.553259	+	0.833010i	$0.686616\pi$
$168$	−40.9907	−3.16250
$169$	1.00000	0.0769231
$170$	19.7709	1.51636
$171$	4.64741	0.355396
$172$	−54.0658	−4.12248
$173$	9.34325	0.710354	0.355177	−	0.934799i	$-0.384421\pi$
$173$	9.34325	0.710354	0.355177	+	0.934799i	$0.384421\pi$
$174$	13.6274	1.03309
$175$	−20.9329	−1.58238
$176$	50.4071	3.79958
$177$	−5.93929	−0.446424
$178$	−37.6978	−2.82557
$179$	−2.14820	−0.160564	−0.0802821	−	0.996772i	$-0.525582\pi$
$179$	−2.14820	−0.160564	−0.0802821	+	0.996772i	$0.525582\pi$
$180$	−18.1321	−1.35148
$181$	20.2391	1.50436	0.752179	−	0.658959i	$-0.229003\pi$
$181$	20.2391	1.50436	0.752179	+	0.658959i	$0.229003\pi$
$182$	−11.1487	−0.826396
$183$	−9.52660	−0.704227
$184$	83.3625	6.14557
$185$	−21.2989	−1.56593
$186$	4.74684	0.348055
$187$	−6.67452	−0.488089
$188$	37.8138	2.75786
$189$	−4.02379	−0.292688
$190$	−41.1289	−2.98381
$191$	−0.275815	−0.0199573	−0.00997863	−	0.999950i	$-0.503176\pi$
$191$	−0.275815	−0.0199573	−0.00997863	+	0.999950i	$0.503176\pi$
$192$	39.3262	2.83813
$193$	0.782680	0.0563385	0.0281693	−	0.999603i	$-0.491032\pi$
$193$	0.782680	0.0563385	0.0281693	+	0.999603i	$0.491032\pi$
$194$	−39.4992	−2.83588
$195$	−3.19410	−0.228734
$196$	52.1744	3.72674
$197$	17.4337	1.24210	0.621050	−	0.783771i	$-0.286707\pi$
$197$	17.4337	1.24210	0.621050	+	0.783771i	$0.286707\pi$
$198$	8.27786	0.588282
$199$	−0.181220	−0.0128463	−0.00642317	−	0.999979i	$-0.502045\pi$
$199$	−0.181220	−0.0128463	−0.00642317	+	0.999979i	$0.502045\pi$
$200$	52.9961	3.74739
$201$	4.02241	0.283719
$202$	−14.2456	−1.00232
$203$	−19.7907	−1.38904
$204$	−12.6820	−0.887920
$205$	−7.09559	−0.495578
$206$	2.77069	0.193043
$207$	8.18315	0.568768
$208$	16.8718	1.16985
$209$	13.8848	0.960433
$210$	35.6100	2.45733
$211$	−11.4610	−0.789010	−0.394505	−	0.918894i	$-0.629084\pi$
$211$	−11.4610	−0.789010	−0.394505	+	0.918894i	$0.629084\pi$
$212$	−37.0642	−2.54558
$213$	13.4186	0.919427
$214$	−9.52361	−0.651021
$215$	30.4210	2.07469
$216$	10.1871	0.693144
$217$	−6.89369	−0.467974
$218$	−5.48779	−0.371680
$219$	10.8591	0.733789
$220$	−54.1722	−3.65229
$221$	−2.23404	−0.150278
$222$	18.4755	1.24000
$223$	14.9346	1.00010	0.500048	−	0.865998i	$-0.333316\pi$
$223$	14.9346	1.00010	0.500048	+	0.865998i	$0.333316\pi$
$224$	−106.117	−7.09026
$225$	5.20228	0.346819
$226$	25.3880	1.68879
$227$	22.4950	1.49304	0.746522	−	0.665361i	$-0.231722\pi$
$227$	22.4950	1.49304	0.746522	+	0.665361i	$0.231722\pi$
$228$	26.3821	1.74720
$229$	11.7619	0.777250	0.388625	−	0.921396i	$-0.372950\pi$
$229$	11.7619	0.777250	0.388625	+	0.921396i	$0.372950\pi$
$230$	−72.4198	−4.77522
$231$	−12.0217	−0.790969
$232$	50.1045	3.28952
$233$	6.58181	0.431189	0.215594	−	0.976483i	$-0.430831\pi$
$233$	6.58181	0.431189	0.215594	+	0.976483i	$0.430831\pi$
$234$	2.77069	0.181126
$235$	−21.2765	−1.38793
$236$	−33.7157	−2.19471
$237$	−4.33437	−0.281548
$238$	24.9066	1.61445
$239$	−10.8047	−0.698900	−0.349450	−	0.936955i	$-0.613632\pi$
$239$	−10.8047	−0.698900	−0.349450	+	0.936955i	$0.613632\pi$
$240$	−53.8903	−3.47860
$241$	16.1274	1.03886	0.519429	−	0.854514i	$-0.326145\pi$
$241$	16.1274	1.03886	0.519429	+	0.854514i	$0.326145\pi$
$242$	−5.74626	−0.369384
$243$	1.00000	0.0641500
$244$	−54.0800	−3.46212
$245$	−29.3567	−1.87553
$246$	6.15500	0.392429
$247$	4.64741	0.295707
$248$	17.4529	1.10826
$249$	−16.0370	−1.01630
$250$	−1.79018	−0.113221
$251$	3.76684	0.237761	0.118880	−	0.992909i	$-0.462069\pi$
$251$	3.76684	0.237761	0.118880	+	0.992909i	$0.462069\pi$
$252$	−22.8420	−1.43891
$253$	24.4484	1.53706
$254$	−44.6389	−2.80089
$255$	7.13574	0.446857
$256$	77.1048	4.81905
$257$	6.23857	0.389151	0.194576	−	0.980888i	$-0.437667\pi$
$257$	6.23857	0.389151	0.194576	+	0.980888i	$0.437667\pi$
$258$	−26.3884	−1.64287
$259$	−26.8315	−1.66723
$260$	−18.1321	−1.12450
$261$	4.91843	0.304443
$262$	−48.1922	−2.97732
$263$	3.53804	0.218165	0.109083	−	0.994033i	$-0.465209\pi$
$263$	3.53804	0.218165	0.109083	+	0.994033i	$0.465209\pi$
$264$	30.4355	1.87317
$265$	20.8548	1.28110
$266$	−51.8125	−3.17683
$267$	−13.6059	−0.832669
$268$	22.8341	1.39482
$269$	−28.5441	−1.74036	−0.870182	−	0.492731i	$-0.835999\pi$
$269$	−28.5441	−1.74036	−0.870182	+	0.492731i	$0.835999\pi$
$270$	−8.84987	−0.538586
$271$	23.1786	1.40800	0.703999	−	0.710201i	$-0.251396\pi$
$271$	23.1786	1.40800	0.703999	+	0.710201i	$0.251396\pi$
$272$	−37.6923	−2.28543
$273$	−4.02379	−0.243531
$274$	12.0885	0.730294
$275$	15.5426	0.937254
$276$	46.4536	2.79618
$277$	−14.4005	−0.865245	−0.432622	−	0.901575i	$-0.642412\pi$
$277$	−14.4005	−0.865245	−0.432622	+	0.901575i	$0.642412\pi$
$278$	−21.4448	−1.28617
$279$	1.71323	0.102569
$280$	130.929	7.82448
$281$	−30.2595	−1.80513	−0.902566	−	0.430551i	$-0.858319\pi$
$281$	−30.2595	−1.80513	−0.902566	+	0.430551i	$0.858319\pi$
$282$	18.4561	1.09905
$283$	−15.4301	−0.917225	−0.458612	−	0.888636i	$-0.651653\pi$
$283$	−15.4301	−0.917225	−0.458612	+	0.888636i	$0.651653\pi$
$284$	76.1738	4.52008
$285$	−14.8443	−0.879299
$286$	8.27786	0.489480
$287$	−8.93873	−0.527636
$288$	26.3724	1.55401
$289$	−12.0091	−0.706416
$290$	−43.5275	−2.55602
$291$	−14.2561	−0.835706
$292$	61.6441	3.60745
$293$	19.6666	1.14894	0.574469	−	0.818527i	$-0.305209\pi$
$293$	19.6666	1.14894	0.574469	+	0.818527i	$0.305209\pi$
$294$	25.4652	1.48516
$295$	18.9707	1.10452
$296$	67.9296	3.94833
$297$	2.98765	0.173361
$298$	−36.1387	−2.09346
$299$	8.18315	0.473244
$300$	29.5320	1.70503
$301$	38.3231	2.20890
$302$	13.9929	0.805200
$303$	−5.14153	−0.295373
$304$	78.4102	4.49713
$305$	30.4289	1.74236
$306$	−6.18983	−0.353849
$307$	−32.1630	−1.83564	−0.917819	−	0.397000i	$-0.870051\pi$
$307$	−32.1630	−1.83564	−0.917819	+	0.397000i	$0.870051\pi$
$308$	−68.2439	−3.88856
$309$	1.00000	0.0568880
$310$	−15.1619	−0.861137
$311$	27.8763	1.58072	0.790361	−	0.612642i	$-0.209893\pi$
$311$	27.8763	1.58072	0.790361	+	0.612642i	$0.209893\pi$
$312$	10.1871	0.576730
$313$	30.4719	1.72237	0.861187	−	0.508289i	$-0.169722\pi$
$313$	30.4719	1.72237	0.861187	+	0.508289i	$0.169722\pi$
$314$	46.2578	2.61048
$315$	12.8524	0.724151
$316$	−24.6051	−1.38414
$317$	3.67196	0.206238	0.103119	−	0.994669i	$-0.467118\pi$
$317$	3.67196	0.206238	0.103119	+	0.994669i	$0.467118\pi$
$318$	−18.0902	−1.01445
$319$	14.6945	0.822737
$320$	−125.612	−7.02192
$321$	−3.43727	−0.191850
$322$	−91.2314	−5.08413
$323$	−10.3825	−0.577696
$324$	5.67673	0.315374
$325$	5.20228	0.288571
$326$	7.94818	0.440209
$327$	−1.98066	−0.109531
$328$	22.6303	1.24955
$329$	−26.8033	−1.47771
$330$	−26.4403	−1.45549
$331$	−8.17695	−0.449446	−0.224723	−	0.974423i	$-0.572148\pi$
$331$	−8.17695	−0.449446	−0.224723	+	0.974423i	$0.572148\pi$
$332$	−91.0375	−4.99633
$333$	6.66821	0.365415
$334$	−39.6191	−2.16786
$335$	−12.8480	−0.701960
$336$	−67.8887	−3.70363
$337$	−29.2713	−1.59451	−0.797254	−	0.603644i	$-0.793715\pi$
$337$	−29.2713	−1.59451	−0.797254	+	0.603644i	$0.793715\pi$
$338$	2.77069	0.150706
$339$	9.16307	0.497670
$340$	40.5077	2.19684
$341$	5.11854	0.277184
$342$	12.8765	0.696283
$343$	−8.81578	−0.476008
$344$	−97.0230	−5.23113
$345$	−26.1378	−1.40721
$346$	25.8873	1.39171
$347$	−21.9250	−1.17700	−0.588499	−	0.808498i	$-0.700281\pi$
$347$	−21.9250	−1.17700	−0.588499	+	0.808498i	$0.700281\pi$
$348$	27.9206	1.49670
$349$	−3.62744	−0.194172	−0.0970862	−	0.995276i	$-0.530952\pi$
$349$	−3.62744	−0.194172	−0.0970862	+	0.995276i	$0.530952\pi$
$350$	−57.9986	−3.10016
$351$	1.00000	0.0533761
$352$	78.7916	4.19961
$353$	−20.3298	−1.08205	−0.541024	−	0.841007i	$-0.681963\pi$
$353$	−20.3298	−1.08205	−0.541024	+	0.841007i	$0.681963\pi$
$354$	−16.4559	−0.874623
$355$	−42.8603	−2.27479
$356$	−77.2372	−4.09356
$357$	8.98930	0.475764
$358$	−5.95200	−0.314573
$359$	−29.6062	−1.56256	−0.781279	−	0.624183i	$-0.785432\pi$
$359$	−29.6062	−1.56256	−0.781279	+	0.624183i	$0.785432\pi$
$360$	−32.5386	−1.71493
$361$	2.59837	0.136757
$362$	56.0762	2.94730
$363$	−2.07395	−0.108854
$364$	−22.8420	−1.19725
$365$	−34.6850	−1.81550
$366$	−26.3953	−1.37970
$367$	35.5561	1.85601	0.928006	−	0.372564i	$-0.121521\pi$
$367$	35.5561	1.85601	0.928006	+	0.372564i	$0.121521\pi$
$368$	138.065	7.19712
$369$	2.22147	0.115645
$370$	−59.0128	−3.06793
$371$	26.2719	1.36397
$372$	9.72556	0.504247
$373$	11.3242	0.586347	0.293173	−	0.956059i	$-0.405289\pi$
$373$	11.3242	0.586347	0.293173	+	0.956059i	$0.405289\pi$
$374$	−18.4930	−0.956252
$375$	−0.646112	−0.0333651
$376$	67.8582	3.49952
$377$	4.91843	0.253312
$378$	−11.1487	−0.573427
$379$	30.9249	1.58850	0.794252	−	0.607588i	$-0.207863\pi$
$379$	30.9249	1.58850	0.794252	+	0.607588i	$0.207863\pi$
$380$	−84.2670	−4.32281
$381$	−16.1111	−0.825397
$382$	−0.764198	−0.0390998
$383$	17.5204	0.895250	0.447625	−	0.894221i	$-0.352270\pi$
$383$	17.5204	0.895250	0.447625	+	0.894221i	$0.352270\pi$
$384$	56.2160	2.86876
$385$	38.3985	1.95697
$386$	2.16856	0.110377
$387$	−9.52411	−0.484138
$388$	−80.9280	−4.10849
$389$	−20.1650	−1.02241	−0.511204	−	0.859459i	$-0.670800\pi$
$389$	−20.1650	−1.02241	−0.511204	+	0.859459i	$0.670800\pi$
$390$	−8.84987	−0.448131
$391$	−18.2815	−0.924533
$392$	93.6287	4.72896
$393$	−17.3936	−0.877389
$394$	48.3034	2.43349
$395$	13.8444	0.696588
$396$	16.9601	0.852277
$397$	10.0735	0.505574	0.252787	−	0.967522i	$-0.418653\pi$
$397$	10.0735	0.505574	0.252787	+	0.967522i	$0.418653\pi$
$398$	−0.502105	−0.0251682
$399$	−18.7002	−0.936181
$400$	87.7720	4.38860
$401$	4.18562	0.209020	0.104510	−	0.994524i	$-0.466673\pi$
$401$	4.18562	0.209020	0.104510	+	0.994524i	$0.466673\pi$
$402$	11.1449	0.555855
$403$	1.71323	0.0853422
$404$	−29.1871	−1.45211
$405$	−3.19410	−0.158716
$406$	−54.8340	−2.72137
$407$	19.9223	0.987510
$408$	−22.7583	−1.12671
$409$	11.1926	0.553437	0.276719	−	0.960951i	$-0.410753\pi$
$409$	11.1926	0.553437	0.276719	+	0.960951i	$0.410753\pi$
$410$	−19.6597	−0.970923
$411$	4.36300	0.215211
$412$	5.67673	0.279673
$413$	23.8985	1.17597
$414$	22.6730	1.11432
$415$	51.2237	2.51447
$416$	26.3724	1.29302
$417$	−7.73988	−0.379023
$418$	38.4706	1.88166
$419$	−29.1072	−1.42198	−0.710991	−	0.703201i	$-0.751753\pi$
$419$	−29.1072	−1.42198	−0.710991	+	0.703201i	$0.751753\pi$
$420$	72.9597	3.56007
$421$	−17.6502	−0.860219	−0.430109	−	0.902777i	$-0.641525\pi$
$421$	−17.6502	−0.860219	−0.430109	+	0.902777i	$0.641525\pi$
$422$	−31.7550	−1.54581
$423$	6.66120	0.323879
$424$	−66.5130	−3.23016
$425$	−11.6221	−0.563754
$426$	37.1788	1.80132
$427$	38.3331	1.85507
$428$	−19.5125	−0.943170
$429$	2.98765	0.144245
$430$	84.2871	4.06469
$431$	−2.10113	−0.101208	−0.0506038	−	0.998719i	$-0.516115\pi$
$431$	−2.10113	−0.101208	−0.0506038	+	0.998719i	$0.516115\pi$
$432$	16.8718	0.811746
$433$	4.89252	0.235120	0.117560	−	0.993066i	$-0.462493\pi$
$433$	4.89252	0.235120	0.117560	+	0.993066i	$0.462493\pi$
$434$	−19.1003	−0.916844
$435$	−15.7100	−0.753235
$436$	−11.2437	−0.538474
$437$	38.0304	1.81924
$438$	30.0872	1.43762
$439$	−32.5502	−1.55354	−0.776768	−	0.629787i	$-0.783142\pi$
$439$	−32.5502	−1.55354	−0.776768	+	0.629787i	$0.783142\pi$
$440$	−97.2140	−4.63449
$441$	9.19091	0.437663
$442$	−6.18983	−0.294420
$443$	4.38450	0.208314	0.104157	−	0.994561i	$-0.466786\pi$
$443$	4.38450	0.208314	0.104157	+	0.994561i	$0.466786\pi$
$444$	37.8536	1.79645
$445$	43.4587	2.06014
$446$	41.3792	1.95936
$447$	−13.0432	−0.616922
$448$	−158.241	−7.47617
$449$	−19.6094	−0.925423	−0.462711	−	0.886509i	$-0.653123\pi$
$449$	−19.6094	−0.925423	−0.462711	+	0.886509i	$0.653123\pi$
$450$	14.4139	0.679479
$451$	6.63697	0.312523
$452$	52.0163	2.44664
$453$	5.05032	0.237285
$454$	62.3266	2.92513
$455$	12.8524	0.602530
$456$	47.3435	2.21706
$457$	−8.70064	−0.406999	−0.203499	−	0.979075i	$-0.565231\pi$
$457$	−8.70064	−0.406999	−0.203499	+	0.979075i	$0.565231\pi$
$458$	32.5887	1.52277
$459$	−2.23404	−0.104276
$460$	−148.377	−6.91813
$461$	−31.4417	−1.46439	−0.732193	−	0.681098i	$-0.761503\pi$
$461$	−31.4417	−1.46439	−0.732193	+	0.681098i	$0.761503\pi$
$462$	−33.3084	−1.54965
$463$	−12.8447	−0.596945	−0.298473	−	0.954418i	$-0.596477\pi$
$463$	−12.8447	−0.596945	−0.298473	+	0.954418i	$0.596477\pi$
$464$	82.9829	3.85238
$465$	−5.47224	−0.253769
$466$	18.2362	0.844774
$467$	−18.5072	−0.856412	−0.428206	−	0.903681i	$-0.640854\pi$
$467$	−18.5072	−0.856412	−0.428206	+	0.903681i	$0.640854\pi$
$468$	5.67673	0.262407
$469$	−16.1853	−0.747370
$470$	−58.9508	−2.71920
$471$	16.6954	0.769283
$472$	−60.5041	−2.78492
$473$	−28.4547	−1.30835
$474$	−12.0092	−0.551601
$475$	24.1771	1.10932
$476$	51.0299	2.33895
$477$	−6.52915	−0.298949
$478$	−29.9366	−1.36927
$479$	−33.5922	−1.53487	−0.767433	−	0.641129i	$-0.778466\pi$
$479$	−33.5922	−1.53487	−0.767433	+	0.641129i	$0.778466\pi$
$480$	−84.2362	−3.84484
$481$	6.66821	0.304044
$482$	44.6841	2.03530
$483$	−32.9273	−1.49824
$484$	−11.7732	−0.535147
$485$	45.5354	2.06765
$486$	2.77069	0.125681
$487$	5.85672	0.265393	0.132697	−	0.991157i	$-0.457636\pi$
$487$	5.85672	0.265393	0.132697	+	0.991157i	$0.457636\pi$
$488$	−97.0484	−4.39317
$489$	2.86866	0.129725
$490$	−81.3384	−3.67449
$491$	40.3695	1.82185	0.910924	−	0.412573i	$-0.135370\pi$
$491$	40.3695	1.82185	0.910924	+	0.412573i	$0.135370\pi$
$492$	12.6107	0.568533
$493$	−10.9880	−0.494872
$494$	12.8765	0.579342
$495$	−9.54286	−0.428920
$496$	28.9054	1.29789
$497$	−53.9936	−2.42195
$498$	−44.4335	−1.99111
$499$	27.1496	1.21538	0.607691	−	0.794174i	$-0.292096\pi$
$499$	27.1496	1.21538	0.607691	+	0.794174i	$0.292096\pi$
$500$	−3.66781	−0.164029
$501$	−14.2994	−0.638848
$502$	10.4368	0.465815
$503$	2.34541	0.104577	0.0522884	−	0.998632i	$-0.483348\pi$
$503$	2.34541	0.104577	0.0522884	+	0.998632i	$0.483348\pi$
$504$	−40.9907	−1.82587
$505$	16.4226	0.730795
$506$	67.7390	3.01136
$507$	1.00000	0.0444116
$508$	−91.4584	−4.05781
$509$	−36.1086	−1.60048	−0.800242	−	0.599677i	$-0.795296\pi$
$509$	−36.1086	−1.60048	−0.800242	+	0.599677i	$0.795296\pi$
$510$	19.7709	0.875472
$511$	−43.6947	−1.93294
$512$	101.202	4.47252
$513$	4.64741	0.205188
$514$	17.2851	0.762415
$515$	−3.19410	−0.140749
$516$	−54.0658	−2.38012
$517$	19.9013	0.875260
$518$	−74.3418	−3.26639
$519$	9.34325	0.410123
$520$	−32.5386	−1.42691
$521$	−26.2284	−1.14909	−0.574543	−	0.818474i	$-0.694820\pi$
$521$	−26.2284	−1.14909	−0.574543	+	0.818474i	$0.694820\pi$
$522$	13.6274	0.596457
$523$	−44.0831	−1.92762	−0.963811	−	0.266588i	$-0.914104\pi$
$523$	−44.0831	−1.92762	−0.963811	+	0.266588i	$0.914104\pi$
$524$	−98.7385	−4.31341
$525$	−20.9329	−0.913587
$526$	9.80283	0.427424
$527$	−3.82742	−0.166725
$528$	50.4071	2.19369
$529$	43.9640	1.91148
$530$	57.7821	2.50989
$531$	−5.93929	−0.257743
$532$	−106.156	−4.60245
$533$	2.22147	0.0962224
$534$	−37.6978	−1.63134
$535$	10.9790	0.474663
$536$	40.9766	1.76992
$537$	−2.14820	−0.0927017
$538$	−79.0869	−3.40968
$539$	27.4592	1.18275
$540$	−18.1321	−0.780280
$541$	−18.6292	−0.800933	−0.400466	−	0.916311i	$-0.631152\pi$
$541$	−18.6292	−0.800933	−0.400466	+	0.916311i	$0.631152\pi$
$542$	64.2207	2.75851
$543$	20.2391	0.868541
$544$	−58.9170	−2.52605
$545$	6.32642	0.270994
$546$	−11.1487	−0.477120
$547$	−40.5116	−1.73215	−0.866076	−	0.499912i	$-0.833366\pi$
$547$	−40.5116	−1.73215	−0.866076	+	0.499912i	$0.833366\pi$
$548$	24.7676	1.05802
$549$	−9.52660	−0.406585
$550$	43.0638	1.83624
$551$	22.8579	0.973781
$552$	83.3625	3.54814
$553$	17.4406	0.741650
$554$	−39.8995	−1.69517
$555$	−21.2989	−0.904089
$556$	−43.9372	−1.86335
$557$	19.5221	0.827177	0.413588	−	0.910464i	$-0.364275\pi$
$557$	19.5221	0.827177	0.413588	+	0.910464i	$0.364275\pi$
$558$	4.74684	0.200950
$559$	−9.52411	−0.402827
$560$	216.843	9.16331
$561$	−6.67452	−0.281798
$562$	−83.8399	−3.53657
$563$	−5.08573	−0.214338	−0.107169	−	0.994241i	$-0.534179\pi$
$563$	−5.08573	−0.214338	−0.107169	+	0.994241i	$0.534179\pi$
$564$	37.8138	1.59225
$565$	−29.2678	−1.23130
$566$	−42.7521	−1.79700
$567$	−4.02379	−0.168983
$568$	136.696	5.73565
$569$	9.61669	0.403153	0.201576	−	0.979473i	$-0.435394\pi$
$569$	9.61669	0.403153	0.201576	+	0.979473i	$0.435394\pi$
$570$	−41.1289	−1.72270
$571$	11.5988	0.485396	0.242698	−	0.970102i	$-0.421968\pi$
$571$	11.5988	0.485396	0.242698	+	0.970102i	$0.421968\pi$
$572$	16.9601	0.709137
$573$	−0.275815	−0.0115223
$574$	−24.7665	−1.03373
$575$	42.5711	1.77534
$576$	39.3262	1.63859
$577$	−42.2654	−1.75953	−0.879766	−	0.475406i	$-0.842301\pi$
$577$	−42.2654	−1.75953	−0.879766	+	0.475406i	$0.842301\pi$
$578$	−33.2735	−1.38399
$579$	0.782680	0.0325271
$580$	−89.1812	−3.70305
$581$	64.5294	2.67713
$582$	−39.4992	−1.63729
$583$	−19.5068	−0.807889
$584$	110.622	4.57759
$585$	−3.19410	−0.132060
$586$	54.4902	2.25097
$587$	27.0312	1.11570	0.557848	−	0.829943i	$-0.311627\pi$
$587$	27.0312	1.11570	0.557848	+	0.829943i	$0.311627\pi$
$588$	52.1744	2.15163
$589$	7.96208	0.328072
$590$	52.5619	2.16394
$591$	17.4337	0.717126
$592$	112.505	4.62392
$593$	16.9317	0.695300	0.347650	−	0.937624i	$-0.386980\pi$
$593$	16.9317	0.695300	0.347650	+	0.937624i	$0.386980\pi$
$594$	8.27786	0.339645
$595$	−28.7127	−1.17711
$596$	−74.0427	−3.03291
$597$	−0.181220	−0.00741684
$598$	22.6730	0.927168
$599$	−15.6196	−0.638199	−0.319099	−	0.947721i	$-0.603380\pi$
$599$	−15.6196	−0.638199	−0.319099	+	0.947721i	$0.603380\pi$
$600$	52.9961	2.16356
$601$	−10.4846	−0.427675	−0.213838	−	0.976869i	$-0.568596\pi$
$601$	−10.4846	−0.427675	−0.213838	+	0.976869i	$0.568596\pi$
$602$	106.181	4.32763
$603$	4.02241	0.163805
$604$	28.6693	1.16654
$605$	6.62439	0.269320
$606$	−14.2456	−0.578688
$607$	30.2281	1.22692	0.613461	−	0.789725i	$-0.289777\pi$
$607$	30.2281	1.22692	0.613461	+	0.789725i	$0.289777\pi$
$608$	122.563	4.97060
$609$	−19.7907	−0.801961
$610$	84.3092	3.41358
$611$	6.66120	0.269483
$612$	−12.6820	−0.512641
$613$	31.8075	1.28469	0.642347	−	0.766414i	$-0.277961\pi$
$613$	31.8075	1.28469	0.642347	+	0.766414i	$0.277961\pi$
$614$	−89.1137	−3.59633
$615$	−7.09559	−0.286122
$616$	−122.466	−4.93430
$617$	26.3527	1.06092	0.530460	−	0.847710i	$-0.322019\pi$
$617$	26.3527	1.06092	0.530460	+	0.847710i	$0.322019\pi$
$618$	2.77069	0.111454
$619$	24.0003	0.964653	0.482326	−	0.875992i	$-0.339792\pi$
$619$	24.0003	0.964653	0.482326	+	0.875992i	$0.339792\pi$
$620$	−31.0644	−1.24758
$621$	8.18315	0.328379
$622$	77.2367	3.09691
$623$	54.7475	2.19341
$624$	16.8718	0.675413
$625$	−23.9477	−0.957907
$626$	84.4282	3.37443
$627$	13.8848	0.554506
$628$	94.7752	3.78194
$629$	−14.8970	−0.593983
$630$	35.6100	1.41874
$631$	18.5913	0.740107	0.370054	−	0.929010i	$-0.379339\pi$
$631$	18.5913	0.740107	0.370054	+	0.929010i	$0.379339\pi$
$632$	−44.1546	−1.75638
$633$	−11.4610	−0.455535
$634$	10.1739	0.404056
$635$	51.4605	2.04215
$636$	−37.0642	−1.46969
$637$	9.19091	0.364157
$638$	40.7141	1.61188
$639$	13.4186	0.530831
$640$	−179.560	−7.09772
$641$	7.48457	0.295623	0.147811	−	0.989016i	$-0.452777\pi$
$641$	7.48457	0.295623	0.147811	+	0.989016i	$0.452777\pi$
$642$	−9.52361	−0.375867
$643$	1.51349	0.0596864	0.0298432	−	0.999555i	$-0.490499\pi$
$643$	1.51349	0.0596864	0.0298432	+	0.999555i	$0.490499\pi$
$644$	−186.920	−7.36566
$645$	30.4210	1.19782
$646$	−28.7666	−1.13181
$647$	−39.8994	−1.56861	−0.784304	−	0.620377i	$-0.786980\pi$
$647$	−39.8994	−1.56861	−0.784304	+	0.620377i	$0.786980\pi$
$648$	10.1871	0.400187
$649$	−17.7445	−0.696533
$650$	14.4139	0.565361
$651$	−6.89369	−0.270185
$652$	16.2846	0.637755
$653$	−17.9434	−0.702179	−0.351089	−	0.936342i	$-0.614189\pi$
$653$	−17.9434	−0.702179	−0.351089	+	0.936342i	$0.614189\pi$
$654$	−5.48779	−0.214590
$655$	55.5568	2.17078
$656$	37.4802	1.46336
$657$	10.8591	0.423653
$658$	−74.2637	−2.89510
$659$	−32.8796	−1.28081	−0.640404	−	0.768038i	$-0.721233\pi$
$659$	−32.8796	−1.28081	−0.640404	+	0.768038i	$0.721233\pi$
$660$	−54.1722	−2.10865
$661$	32.1772	1.25155	0.625775	−	0.780004i	$-0.284783\pi$
$661$	32.1772	1.25155	0.625775	+	0.780004i	$0.284783\pi$
$662$	−22.6558	−0.880543
$663$	−2.23404	−0.0867628
$664$	−163.370	−6.33998
$665$	59.7303	2.31624
$666$	18.4755	0.715913
$667$	40.2483	1.55842
$668$	−81.1736	−3.14070
$669$	14.9346	0.577405
$670$	−35.5978	−1.37526
$671$	−28.4622	−1.09877
$672$	−106.117	−4.09356
$673$	16.3167	0.628963	0.314482	−	0.949264i	$-0.398169\pi$
$673$	16.3167	0.628963	0.314482	+	0.949264i	$0.398169\pi$
$674$	−81.1017	−3.12392
$675$	5.20228	0.200236
$676$	5.67673	0.218336
$677$	−44.2012	−1.69879	−0.849395	−	0.527758i	$-0.823033\pi$
$677$	−44.2012	−1.69879	−0.849395	+	0.527758i	$0.823033\pi$
$678$	25.3880	0.975022
$679$	57.3635	2.20141
$680$	72.6924	2.78763
$681$	22.4950	0.862009
$682$	14.1819	0.543053
$683$	9.21975	0.352784	0.176392	−	0.984320i	$-0.443557\pi$
$683$	9.21975	0.352784	0.176392	+	0.984320i	$0.443557\pi$
$684$	26.3821	1.00874
$685$	−13.9359	−0.532462
$686$	−24.4258	−0.932582
$687$	11.7619	0.448746
$688$	−160.689	−6.12622
$689$	−6.52915	−0.248741
$690$	−72.4198	−2.75698
$691$	−14.8240	−0.563931	−0.281966	−	0.959424i	$-0.590986\pi$
$691$	−14.8240	−0.563931	−0.281966	+	0.959424i	$0.590986\pi$
$692$	53.0391	2.01625
$693$	−12.0217	−0.456666
$694$	−60.7475	−2.30594
$695$	24.7220	0.937757
$696$	50.1045	1.89921
$697$	−4.96284	−0.187981
$698$	−10.0505	−0.380417
$699$	6.58181	0.248947
$700$	−118.831	−4.49137
$701$	28.1594	1.06356	0.531782	−	0.846881i	$-0.321522\pi$
$701$	28.1594	1.06356	0.531782	+	0.846881i	$0.321522\pi$
$702$	2.77069	0.104573
$703$	30.9899	1.16880
$704$	117.493	4.42819
$705$	−21.2765	−0.801321
$706$	−56.3277	−2.11992
$707$	20.6885	0.778070
$708$	−33.7157	−1.26712
$709$	50.2254	1.88626	0.943128	−	0.332430i	$-0.107869\pi$
$709$	50.2254	1.88626	0.943128	+	0.332430i	$0.107869\pi$
$710$	−118.753	−4.45671
$711$	−4.33437	−0.162552
$712$	−138.605	−5.19444
$713$	14.0196	0.525040
$714$	24.9066	0.932105
$715$	−9.54286	−0.356883
$716$	−12.1948	−0.455740
$717$	−10.8047	−0.403510
$718$	−82.0297	−3.06132
$719$	3.59322	0.134005	0.0670023	−	0.997753i	$-0.478657\pi$
$719$	3.59322	0.134005	0.0670023	+	0.997753i	$0.478657\pi$
$720$	−53.8903	−2.00837
$721$	−4.02379	−0.149854
$722$	7.19929	0.267930
$723$	16.1274	0.599785
$724$	114.892	4.26992
$725$	25.5871	0.950279
$726$	−5.74626	−0.213264
$727$	19.4433	0.721111	0.360556	−	0.932738i	$-0.382587\pi$
$727$	19.4433	0.721111	0.360556	+	0.932738i	$0.382587\pi$
$728$	−40.9907	−1.51922
$729$	1.00000	0.0370370
$730$	−96.1015	−3.55688
$731$	21.2772	0.786966
$732$	−54.0800	−1.99885
$733$	23.7742	0.878122	0.439061	−	0.898457i	$-0.355311\pi$
$733$	23.7742	0.878122	0.439061	+	0.898457i	$0.355311\pi$
$734$	98.5150	3.63625
$735$	−29.3567	−1.08284
$736$	215.810	7.95485
$737$	12.0176	0.442672
$738$	6.15500	0.226569
$739$	13.9763	0.514126	0.257063	−	0.966395i	$-0.417245\pi$
$739$	13.9763	0.514126	0.257063	+	0.966395i	$0.417245\pi$
$740$	−120.908	−4.44468
$741$	4.64741	0.170727
$742$	72.7914	2.67226
$743$	−22.8332	−0.837667	−0.418834	−	0.908063i	$-0.637561\pi$
$743$	−22.8332	−0.837667	−0.418834	+	0.908063i	$0.637561\pi$
$744$	17.4529	0.639853
$745$	41.6613	1.52635
$746$	31.3760	1.14876
$747$	−16.0370	−0.586762
$748$	−37.8895	−1.38538
$749$	13.8309	0.505369
$750$	−1.79018	−0.0653681
$751$	−6.86679	−0.250573	−0.125286	−	0.992121i	$-0.539985\pi$
$751$	−6.86679	−0.250573	−0.125286	+	0.992121i	$0.539985\pi$
$752$	112.387	4.09832
$753$	3.76684	0.137271
$754$	13.6274	0.496282
$755$	−16.1312	−0.587076
$756$	−22.8420	−0.830755
$757$	14.9099	0.541911	0.270956	−	0.962592i	$-0.412660\pi$
$757$	14.9099	0.541911	0.270956	+	0.962592i	$0.412660\pi$
$758$	85.6833	3.11216
$759$	24.4484	0.887421
$760$	−151.220	−5.48533
$761$	36.9043	1.33778	0.668890	−	0.743361i	$-0.266770\pi$
$761$	36.9043	1.33778	0.668890	+	0.743361i	$0.266770\pi$
$762$	−44.6389	−1.61710
$763$	7.96976	0.288525
$764$	−1.56573	−0.0566460
$765$	7.13574	0.257993
$766$	48.5436	1.75395
$767$	−5.93929	−0.214455
$768$	77.1048	2.78228
$769$	−41.2728	−1.48834	−0.744168	−	0.667992i	$-0.767154\pi$
$769$	−41.2728	−1.48834	−0.744168	+	0.667992i	$0.767154\pi$
$770$	106.390	3.83404
$771$	6.23857	0.224677
$772$	4.44306	0.159909
$773$	−0.839148	−0.0301820	−0.0150910	−	0.999886i	$-0.504804\pi$
$773$	−0.839148	−0.0301820	−0.0150910	+	0.999886i	$0.504804\pi$
$774$	−26.3884	−0.948511
$775$	8.91272	0.320154
$776$	−145.228	−5.21338
$777$	−26.8315	−0.962574
$778$	−55.8711	−2.00308
$779$	10.3241	0.369898
$780$	−18.1321	−0.649232
$781$	40.0901	1.43454
$782$	−50.6523	−1.81132
$783$	4.91843	0.175770
$784$	155.067	5.53812
$785$	−53.3267	−1.90331
$786$	−48.1922	−1.71896
$787$	37.6020	1.34036	0.670182	−	0.742196i	$-0.266216\pi$
$787$	37.6020	1.34036	0.670182	+	0.742196i	$0.266216\pi$
$788$	98.9664	3.52553
$789$	3.53804	0.125958
$790$	38.3586	1.36474
$791$	−36.8703	−1.31096
$792$	30.4355	1.08148
$793$	−9.52660	−0.338300
$794$	27.9105	0.990507
$795$	20.8548	0.739642
$796$	−1.02874	−0.0364626
$797$	−6.59055	−0.233449	−0.116725	−	0.993164i	$-0.537240\pi$
$797$	−6.59055	−0.233449	−0.116725	+	0.993164i	$0.537240\pi$
$798$	−51.8125	−1.83414
$799$	−14.8814	−0.526465
$800$	137.197	4.85064
$801$	−13.6059	−0.480742
$802$	11.5971	0.409507
$803$	32.4431	1.14489
$804$	22.8341	0.805298
$805$	105.173	3.70687
$806$	4.74684	0.167200
$807$	−28.5441	−1.00480
$808$	−52.3773	−1.84263
$809$	−1.88005	−0.0660991	−0.0330495	−	0.999454i	$-0.510522\pi$
$809$	−1.88005	−0.0660991	−0.0330495	+	0.999454i	$0.510522\pi$
$810$	−8.84987	−0.310953
$811$	−13.4778	−0.473271	−0.236636	−	0.971598i	$-0.576045\pi$
$811$	−13.4778	−0.473271	−0.236636	+	0.971598i	$0.576045\pi$
$812$	−112.347	−3.94260
$813$	23.1786	0.812908
$814$	55.1985	1.93471
$815$	−9.16280	−0.320959
$816$	−37.6923	−1.31949
$817$	−44.2624	−1.54855
$818$	31.0112	1.08428
$819$	−4.02379	−0.140603
$820$	−40.2798	−1.40663
$821$	−53.1440	−1.85474	−0.927369	−	0.374149i	$-0.877935\pi$
$821$	−53.1440	−1.85474	−0.927369	+	0.374149i	$0.877935\pi$
$822$	12.0885	0.421636
$823$	25.6266	0.893286	0.446643	−	0.894712i	$-0.352619\pi$
$823$	25.6266	0.893286	0.446643	+	0.894712i	$0.352619\pi$
$824$	10.1871	0.354884
$825$	15.5426	0.541124
$826$	66.2153	2.30392
$827$	−11.0862	−0.385506	−0.192753	−	0.981247i	$-0.561742\pi$
$827$	−11.0862	−0.385506	−0.192753	+	0.981247i	$0.561742\pi$
$828$	46.4536	1.61437
$829$	−56.8033	−1.97286	−0.986430	−	0.164180i	$-0.947502\pi$
$829$	−56.8033	−1.97286	−0.986430	+	0.164180i	$0.947502\pi$
$830$	141.925	4.92629
$831$	−14.4005	−0.499549
$832$	39.3262	1.36339
$833$	−20.5328	−0.711421
$834$	−21.4448	−0.742573
$835$	45.6736	1.58060
$836$	78.8204	2.72606
$837$	1.71323	0.0592180
$838$	−80.6472	−2.78591
$839$	9.61109	0.331812	0.165906	−	0.986142i	$-0.446945\pi$
$839$	9.61109	0.331812	0.165906	+	0.986142i	$0.446945\pi$
$840$	130.929	4.51747
$841$	−4.80906	−0.165830
$842$	−48.9033	−1.68532
$843$	−30.2595	−1.04219
$844$	−65.0612	−2.23950
$845$	−3.19410	−0.109880
$846$	18.4561	0.634535
$847$	8.34513	0.286742
$848$	−110.159	−3.78286
$849$	−15.4301	−0.529560
$850$	−32.2012	−1.10449
$851$	54.5669	1.87053
$852$	76.1738	2.60967
$853$	−1.86261	−0.0637744	−0.0318872	−	0.999491i	$-0.510152\pi$
$853$	−1.86261	−0.0637744	−0.0318872	+	0.999491i	$0.510152\pi$
$854$	106.209	3.63440
$855$	−14.8443	−0.507664
$856$	−35.0158	−1.19681
$857$	−16.2643	−0.555577	−0.277788	−	0.960642i	$-0.589601\pi$
$857$	−16.2643	−0.555577	−0.277788	+	0.960642i	$0.589601\pi$
$858$	8.27786	0.282601
$859$	−19.5221	−0.666085	−0.333043	−	0.942912i	$-0.608075\pi$
$859$	−19.5221	−0.666085	−0.333043	+	0.942912i	$0.608075\pi$
$860$	172.692	5.88874
$861$	−8.93873	−0.304631
$862$	−5.82157	−0.198283
$863$	−10.0365	−0.341647	−0.170824	−	0.985302i	$-0.554643\pi$
$863$	−10.0365	−0.341647	−0.170824	+	0.985302i	$0.554643\pi$
$864$	26.3724	0.897209
$865$	−29.8433	−1.01470
$866$	13.5557	0.460640
$867$	−12.0091	−0.407850
$868$	−39.1336	−1.32828
$869$	−12.9496	−0.439285
$870$	−43.5275	−1.47572
$871$	4.02241	0.136294
$872$	−20.1771	−0.683284
$873$	−14.2561	−0.482495
$874$	105.371	3.56421
$875$	2.59982	0.0878900
$876$	61.6441	2.08276
$877$	28.2860	0.955150	0.477575	−	0.878591i	$-0.341516\pi$
$877$	28.2860	0.955150	0.477575	+	0.878591i	$0.341516\pi$
$878$	−90.1866	−3.04365
$879$	19.6666	0.663339
$880$	−161.005	−5.42749
$881$	53.7449	1.81071	0.905356	−	0.424654i	$-0.139604\pi$
$881$	53.7449	1.81071	0.905356	+	0.424654i	$0.139604\pi$
$882$	25.4652	0.857457
$883$	25.7418	0.866282	0.433141	−	0.901326i	$-0.357405\pi$
$883$	25.7418	0.866282	0.433141	+	0.901326i	$0.357405\pi$
$884$	−12.6820	−0.426543
$885$	18.9707	0.637693
$886$	12.1481	0.408123
$887$	−7.89520	−0.265095	−0.132548	−	0.991177i	$-0.542316\pi$
$887$	−7.89520	−0.265095	−0.132548	+	0.991177i	$0.542316\pi$
$888$	67.9296	2.27957
$889$	64.8277	2.17425
$890$	120.411	4.03618
$891$	2.98765	0.100090
$892$	84.7798	2.83864
$893$	30.9573	1.03595
$894$	−36.1387	−1.20866
$895$	6.86157	0.229357
$896$	−226.202	−7.55687
$897$	8.18315	0.273228
$898$	−54.3315	−1.81307
$899$	8.42641	0.281037
$900$	29.5320	0.984399
$901$	14.5864	0.485942
$902$	18.3890	0.612286
$903$	38.3231	1.27531
$904$	93.3450	3.10461
$905$	−64.6456	−2.14889
$906$	13.9929	0.464883
$907$	32.2313	1.07022	0.535112	−	0.844781i	$-0.320269\pi$
$907$	32.2313	1.07022	0.535112	+	0.844781i	$0.320269\pi$
$908$	127.698	4.23780
$909$	−5.14153	−0.170534
$910$	35.6100	1.18046
$911$	−41.2403	−1.36635	−0.683175	−	0.730254i	$-0.739402\pi$
$911$	−41.2403	−1.36635	−0.683175	+	0.730254i	$0.739402\pi$
$912$	78.4102	2.59642
$913$	−47.9128	−1.58568
$914$	−24.1068	−0.797382
$915$	30.4289	1.00595
$916$	66.7693	2.20612
$917$	69.9881	2.31121
$918$	−6.18983	−0.204295
$919$	−34.4805	−1.13741	−0.568703	−	0.822543i	$-0.692555\pi$
$919$	−34.4805	−1.13741	−0.568703	+	0.822543i	$0.692555\pi$
$920$	−266.268	−8.77861
$921$	−32.1630	−1.05981
$922$	−87.1152	−2.86899
$923$	13.4186	0.441678
$924$	−68.2439	−2.24506
$925$	34.6899	1.14060
$926$	−35.5888	−1.16952
$927$	1.00000	0.0328443
$928$	129.711	4.25797
$929$	−5.28597	−0.173427	−0.0867136	−	0.996233i	$-0.527636\pi$
$929$	−5.28597	−0.173427	−0.0867136	+	0.996233i	$0.527636\pi$
$930$	−15.1619	−0.497178
$931$	42.7139	1.39989
$932$	37.3632	1.22387
$933$	27.8763	0.912630
$934$	−51.2778	−1.67786
$935$	21.3191	0.697209
$936$	10.1871	0.332975
$937$	−7.31565	−0.238992	−0.119496	−	0.992835i	$-0.538128\pi$
$937$	−7.31565	−0.238992	−0.119496	+	0.992835i	$0.538128\pi$
$938$	−44.8446	−1.46423
$939$	30.4719	0.994413
$940$	−120.781	−3.93945
$941$	−1.81847	−0.0592803	−0.0296402	−	0.999561i	$-0.509436\pi$
$941$	−1.81847	−0.0592803	−0.0296402	+	0.999561i	$0.509436\pi$
$942$	46.2578	1.50716
$943$	18.1786	0.591977
$944$	−100.207	−3.26145
$945$	12.8524	0.418089
$946$	−78.8392	−2.56328
$947$	−21.5867	−0.701473	−0.350737	−	0.936474i	$-0.614069\pi$
$947$	−21.5867	−0.701473	−0.350737	+	0.936474i	$0.614069\pi$
$948$	−24.6051	−0.799135
$949$	10.8591	0.352501
$950$	66.9873	2.17336
$951$	3.67196	0.119071
$952$	91.5748	2.96796
$953$	−16.4504	−0.532882	−0.266441	−	0.963851i	$-0.585848\pi$
$953$	−16.4504	−0.532882	−0.266441	+	0.963851i	$0.585848\pi$
$954$	−18.0902	−0.585693
$955$	0.880981	0.0285079
$956$	−61.3356	−1.98373
$957$	14.6945	0.475007
$958$	−93.0736	−3.00707
$959$	−17.5558	−0.566906
$960$	−125.612	−4.05411
$961$	−28.0648	−0.905317
$962$	18.4755	0.595675
$963$	−3.43727	−0.110764
$964$	91.5509	2.94866
$965$	−2.49996	−0.0804765
$966$	−91.2314	−2.93532
$967$	−34.4217	−1.10693	−0.553463	−	0.832874i	$-0.686694\pi$
$967$	−34.4217	−1.10693	−0.553463	+	0.832874i	$0.686694\pi$
$968$	−21.1275	−0.679063
$969$	−10.3825	−0.333533
$970$	126.164	4.05090
$971$	−33.3246	−1.06944	−0.534719	−	0.845030i	$-0.679582\pi$
$971$	−33.3246	−1.06944	−0.534719	+	0.845030i	$0.679582\pi$
$972$	5.67673	0.182081
$973$	31.1437	0.998420
$974$	16.2272	0.519952
$975$	5.20228	0.166606
$976$	−160.731	−5.14488
$977$	−31.2873	−1.00097	−0.500484	−	0.865746i	$-0.666845\pi$
$977$	−31.2873	−1.00097	−0.500484	+	0.865746i	$0.666845\pi$
$978$	7.94818	0.254155
$979$	−40.6498	−1.29917
$980$	−166.650	−5.32344
$981$	−1.98066	−0.0632375
$982$	111.851	3.56932
$983$	−35.9840	−1.14771	−0.573855	−	0.818957i	$-0.694553\pi$
$983$	−35.9840	−1.14771	−0.573855	+	0.818957i	$0.694553\pi$
$984$	22.6303	0.721427
$985$	−55.6850	−1.77427
$986$	−30.4442	−0.969542
$987$	−26.8033	−0.853158
$988$	26.3821	0.839326
$989$	−77.9373	−2.47826
$990$	−26.4403	−0.840328
$991$	−6.57731	−0.208935	−0.104468	−	0.994528i	$-0.533314\pi$
$991$	−6.57731	−0.208935	−0.104468	+	0.994528i	$0.533314\pi$
$992$	45.1821	1.43453
$993$	−8.17695	−0.259488
$994$	−149.600	−4.74502
$995$	0.578835	0.0183503
$996$	−91.0375	−2.88463
$997$	−16.7700	−0.531110	−0.265555	−	0.964096i	$-0.585555\pi$
$997$	−16.7700	−0.531110	−0.265555	+	0.964096i	$0.585555\pi$
$998$	75.2231	2.38115
$999$	6.66821	0.210973

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.k.1.32	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.k.1.32	✓	32	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q+2.77069 q^{2} +1.00000 q^{3} +5.67673 q^{4} -3.19410 q^{5} +2.77069 q^{6} -4.02379 q^{7} +10.1871 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.77069 q^{2} +1.00000 q^{3} +5.67673 q^{4} -3.19410 q^{5} +2.77069 q^{6} -4.02379 q^{7} +10.1871 q^{8} +1.00000 q^{9} -8.84987 q^{10} +2.98765 q^{11} +5.67673 q^{12} +1.00000 q^{13} -11.1487 q^{14} -3.19410 q^{15} +16.8718 q^{16} -2.23404 q^{17} +2.77069 q^{18} +4.64741 q^{19} -18.1321 q^{20} -4.02379 q^{21} +8.27786 q^{22} +8.18315 q^{23} +10.1871 q^{24} +5.20228 q^{25} +2.77069 q^{26} +1.00000 q^{27} -22.8420 q^{28} +4.91843 q^{29} -8.84987 q^{30} +1.71323 q^{31} +26.3724 q^{32} +2.98765 q^{33} -6.18983 q^{34} +12.8524 q^{35} +5.67673 q^{36} +6.66821 q^{37} +12.8765 q^{38} +1.00000 q^{39} -32.5386 q^{40} +2.22147 q^{41} -11.1487 q^{42} -9.52411 q^{43} +16.9601 q^{44} -3.19410 q^{45} +22.6730 q^{46} +6.66120 q^{47} +16.8718 q^{48} +9.19091 q^{49} +14.4139 q^{50} -2.23404 q^{51} +5.67673 q^{52} -6.52915 q^{53} +2.77069 q^{54} -9.54286 q^{55} -40.9907 q^{56} +4.64741 q^{57} +13.6274 q^{58} -5.93929 q^{59} -18.1321 q^{60} -9.52660 q^{61} +4.74684 q^{62} -4.02379 q^{63} +39.3262 q^{64} -3.19410 q^{65} +8.27786 q^{66} +4.02241 q^{67} -12.6820 q^{68} +8.18315 q^{69} +35.6100 q^{70} +13.4186 q^{71} +10.1871 q^{72} +10.8591 q^{73} +18.4755 q^{74} +5.20228 q^{75} +26.3821 q^{76} -12.0217 q^{77} +2.77069 q^{78} -4.33437 q^{79} -53.8903 q^{80} +1.00000 q^{81} +6.15500 q^{82} -16.0370 q^{83} -22.8420 q^{84} +7.13574 q^{85} -26.3884 q^{86} +4.91843 q^{87} +30.4355 q^{88} -13.6059 q^{89} -8.84987 q^{90} -4.02379 q^{91} +46.4536 q^{92} +1.71323 q^{93} +18.4561 q^{94} -14.8443 q^{95} +26.3724 q^{96} -14.2561 q^{97} +25.4652 q^{98} +2.98765 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9} + 2 q^{10} + 17 q^{11} + 41 q^{12} + 32 q^{13} - 10 q^{14} + 7 q^{15} + 51 q^{16} + 2 q^{17} + 5 q^{18} + 36 q^{19} - 2 q^{20} + 25 q^{21} - 3 q^{22} + 37 q^{23} + 12 q^{24} + 43 q^{25} + 5 q^{26} + 32 q^{27} + 54 q^{28} + 2 q^{29} + 2 q^{30} + 44 q^{31} + 19 q^{32} + 17 q^{33} + 27 q^{34} - 10 q^{35} + 41 q^{36} + 46 q^{37} - 6 q^{38} + 32 q^{39} - 6 q^{40} + 5 q^{41} - 10 q^{42} + 19 q^{43} + 37 q^{44} + 7 q^{45} + 23 q^{46} + 50 q^{47} + 51 q^{48} + 67 q^{49} - 4 q^{50} + 2 q^{51} + 41 q^{52} + 5 q^{54} + 18 q^{55} - 54 q^{56} + 36 q^{57} + 27 q^{58} + 26 q^{59} - 2 q^{60} + 23 q^{61} + 27 q^{62} + 25 q^{63} + 70 q^{64} + 7 q^{65} - 3 q^{66} + 30 q^{67} - 22 q^{68} + 37 q^{69} + 59 q^{70} + 34 q^{71} + 12 q^{72} + 54 q^{73} + 18 q^{74} + 43 q^{75} + 40 q^{76} - 5 q^{77} + 5 q^{78} + 35 q^{79} - 46 q^{80} + 32 q^{81} + 23 q^{83} + 54 q^{84} + 59 q^{85} - 5 q^{86} + 2 q^{87} - 13 q^{88} + 16 q^{89} + 2 q^{90} + 25 q^{91} + 101 q^{92} + 44 q^{93} - 16 q^{94} - q^{95} + 19 q^{96} + 44 q^{97} - 44 q^{98} + 17 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9 + 2 * q^10 + 17 * q^11 + 41 * q^12 + 32 * q^13 - 10 * q^14 + 7 * q^15 + 51 * q^16 + 2 * q^17 + 5 * q^18 + 36 * q^19 - 2 * q^20 + 25 * q^21 - 3 * q^22 + 37 * q^23 + 12 * q^24 + 43 * q^25 + 5 * q^26 + 32 * q^27 + 54 * q^28 + 2 * q^29 + 2 * q^30 + 44 * q^31 + 19 * q^32 + 17 * q^33 + 27 * q^34 - 10 * q^35 + 41 * q^36 + 46 * q^37 - 6 * q^38 + 32 * q^39 - 6 * q^40 + 5 * q^41 - 10 * q^42 + 19 * q^43 + 37 * q^44 + 7 * q^45 + 23 * q^46 + 50 * q^47 + 51 * q^48 + 67 * q^49 - 4 * q^50 + 2 * q^51 + 41 * q^52 + 5 * q^54 + 18 * q^55 - 54 * q^56 + 36 * q^57 + 27 * q^58 + 26 * q^59 - 2 * q^60 + 23 * q^61 + 27 * q^62 + 25 * q^63 + 70 * q^64 + 7 * q^65 - 3 * q^66 + 30 * q^67 - 22 * q^68 + 37 * q^69 + 59 * q^70 + 34 * q^71 + 12 * q^72 + 54 * q^73 + 18 * q^74 + 43 * q^75 + 40 * q^76 - 5 * q^77 + 5 * q^78 + 35 * q^79 - 46 * q^80 + 32 * q^81 + 23 * q^83 + 54 * q^84 + 59 * q^85 - 5 * q^86 + 2 * q^87 - 13 * q^88 + 16 * q^89 + 2 * q^90 + 25 * q^91 + 101 * q^92 + 44 * q^93 - 16 * q^94 - q^95 + 19 * q^96 + 44 * q^97 - 44 * q^98 + 17 * q^99

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