LMFDB - Embedded newform 215.2.a.c.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [215,2,Mod(1,215)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(215, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("215.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 215 = 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	215.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:	$1.71678364346$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.1933097.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 7x^{3} + 13x^{2} + 5x - 4 $ x^5 - 2x^4 - 7x^3 + 13x^2 + 5x - 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$2.20940$ of defining polynomial
Character	$\chi$	$=$	215.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.20940 q^{2} +0.261901 q^{3} +2.88146 q^{4} +1.00000 q^{5} +0.578644 q^{6} -0.988801 q^{7} +1.94750 q^{8} -2.93141 q^{9} +O(q^{10})$	\(q+2.20940 q^{2} +0.261901 q^{3} +2.88146 q^{4} +1.00000 q^{5} +0.578644 q^{6} -0.988801 q^{7} +1.94750 q^{8} -2.93141 q^{9} +2.20940 q^{10} -3.47130 q^{11} +0.754656 q^{12} +5.78805 q^{13} -2.18466 q^{14} +0.261901 q^{15} -1.46010 q^{16} -7.13216 q^{17} -6.47666 q^{18} +6.26433 q^{19} +2.88146 q^{20} -0.258968 q^{21} -7.66951 q^{22} +1.36924 q^{23} +0.510052 q^{24} +1.00000 q^{25} +12.7881 q^{26} -1.55344 q^{27} -2.84919 q^{28} +7.74052 q^{29} +0.578644 q^{30} -9.06357 q^{31} -7.12096 q^{32} -0.909136 q^{33} -15.7578 q^{34} -0.988801 q^{35} -8.44674 q^{36} +6.07967 q^{37} +13.8404 q^{38} +1.51589 q^{39} +1.94750 q^{40} +3.31147 q^{41} -0.572164 q^{42} -1.00000 q^{43} -10.0024 q^{44} -2.93141 q^{45} +3.02520 q^{46} -6.18173 q^{47} -0.382402 q^{48} -6.02227 q^{49} +2.20940 q^{50} -1.86792 q^{51} +16.6780 q^{52} -0.867837 q^{53} -3.43217 q^{54} -3.47130 q^{55} -1.92569 q^{56} +1.64063 q^{57} +17.1019 q^{58} +0.261901 q^{59} +0.754656 q^{60} +13.5761 q^{61} -20.0251 q^{62} +2.89858 q^{63} -12.8129 q^{64} +5.78805 q^{65} -2.00865 q^{66} -0.229250 q^{67} -20.5510 q^{68} +0.358605 q^{69} -2.18466 q^{70} +12.2419 q^{71} -5.70892 q^{72} -2.02482 q^{73} +13.4324 q^{74} +0.261901 q^{75} +18.0504 q^{76} +3.43243 q^{77} +3.34922 q^{78} +9.66086 q^{79} -1.46010 q^{80} +8.38738 q^{81} +7.31636 q^{82} +1.04956 q^{83} -0.746205 q^{84} -7.13216 q^{85} -2.20940 q^{86} +2.02725 q^{87} -6.76037 q^{88} -6.15933 q^{89} -6.47666 q^{90} -5.72323 q^{91} +3.94541 q^{92} -2.37375 q^{93} -13.6579 q^{94} +6.26433 q^{95} -1.86498 q^{96} +1.10492 q^{97} -13.3056 q^{98} +10.1758 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 2 q^{2} - q^{3} + 8 q^{4} + 5 q^{5} - 12 q^{6} + 5 q^{7} + 3 q^{8} + 18 q^{9}+O(q^{10}) $ 5 * q + 2 * q^2 - q^3 + 8 * q^4 + 5 * q^5 - 12 * q^6 + 5 * q^7 + 3 * q^8 + 18 * q^9	\( 5 q + 2 q^{2} - q^{3} + 8 q^{4} + 5 q^{5} - 12 q^{6} + 5 q^{7} + 3 q^{8} + 18 q^{9} + 2 q^{10} - 6 q^{11} + 5 q^{13} + q^{14} - q^{15} + 14 q^{16} - 17 q^{17} - 5 q^{18} - 6 q^{19} + 8 q^{20} + 20 q^{21} - 8 q^{22} + q^{23} - 45 q^{24} + 5 q^{25} + 22 q^{26} - 22 q^{27} + 26 q^{28} + 6 q^{29} - 12 q^{30} + 6 q^{31} - 7 q^{32} - 20 q^{33} + 5 q^{35} + 36 q^{36} + 5 q^{37} - 16 q^{38} - 14 q^{39} + 3 q^{40} + 2 q^{41} - 58 q^{42} - 5 q^{43} - 15 q^{44} + 18 q^{45} - 14 q^{46} - 3 q^{48} + 18 q^{49} + 2 q^{50} - 10 q^{51} - 38 q^{52} - 23 q^{53} - 56 q^{54} - 6 q^{55} - 19 q^{56} + 28 q^{57} + 12 q^{58} - q^{59} + 20 q^{61} - 3 q^{62} + 26 q^{63} - 25 q^{64} + 5 q^{65} + 13 q^{66} + 21 q^{67} - 48 q^{68} + 10 q^{69} + q^{70} + 4 q^{71} + 20 q^{72} + 5 q^{73} + 24 q^{74} - q^{75} + 32 q^{76} - 26 q^{77} + 88 q^{78} + 41 q^{79} + 14 q^{80} + 41 q^{81} + 38 q^{82} - 7 q^{83} - 33 q^{84} - 17 q^{85} - 2 q^{86} - 40 q^{87} + 12 q^{88} + 20 q^{89} - 5 q^{90} - 42 q^{91} - 52 q^{92} - 36 q^{93} - 42 q^{94} - 6 q^{95} + 9 q^{96} + 37 q^{97} - 26 q^{98} + 12 q^{99}+O(q^{100}) \) 5 * q + 2 * q^2 - q^3 + 8 * q^4 + 5 * q^5 - 12 * q^6 + 5 * q^7 + 3 * q^8 + 18 * q^9 + 2 * q^10 - 6 * q^11 + 5 * q^13 + q^14 - q^15 + 14 * q^16 - 17 * q^17 - 5 * q^18 - 6 * q^19 + 8 * q^20 + 20 * q^21 - 8 * q^22 + q^23 - 45 * q^24 + 5 * q^25 + 22 * q^26 - 22 * q^27 + 26 * q^28 + 6 * q^29 - 12 * q^30 + 6 * q^31 - 7 * q^32 - 20 * q^33 + 5 * q^35 + 36 * q^36 + 5 * q^37 - 16 * q^38 - 14 * q^39 + 3 * q^40 + 2 * q^41 - 58 * q^42 - 5 * q^43 - 15 * q^44 + 18 * q^45 - 14 * q^46 - 3 * q^48 + 18 * q^49 + 2 * q^50 - 10 * q^51 - 38 * q^52 - 23 * q^53 - 56 * q^54 - 6 * q^55 - 19 * q^56 + 28 * q^57 + 12 * q^58 - q^59 + 20 * q^61 - 3 * q^62 + 26 * q^63 - 25 * q^64 + 5 * q^65 + 13 * q^66 + 21 * q^67 - 48 * q^68 + 10 * q^69 + q^70 + 4 * q^71 + 20 * q^72 + 5 * q^73 + 24 * q^74 - q^75 + 32 * q^76 - 26 * q^77 + 88 * q^78 + 41 * q^79 + 14 * q^80 + 41 * q^81 + 38 * q^82 - 7 * q^83 - 33 * q^84 - 17 * q^85 - 2 * q^86 - 40 * q^87 + 12 * q^88 + 20 * q^89 - 5 * q^90 - 42 * q^91 - 52 * q^92 - 36 * q^93 - 42 * q^94 - 6 * q^95 + 9 * q^96 + 37 * q^97 - 26 * q^98 + 12 * 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 $

$2$	2.20940	1.56228	0.781142	−	0.624354i	$-0.214638\pi$
$2$	2.20940	1.56228	0.781142	+	0.624354i	$0.214638\pi$
$3$	0.261901	0.151208	0.0756042	−	0.997138i	$-0.475911\pi$
$3$	0.261901	0.151208	0.0756042	+	0.997138i	$0.475911\pi$
$4$	2.88146	1.44073
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.578644	0.236230
$7$	−0.988801	−0.373732	−0.186866	−	0.982385i	$-0.559833\pi$
$7$	−0.988801	−0.373732	−0.186866	+	0.982385i	$0.559833\pi$
$8$	1.94750	0.688546
$9$	−2.93141	−0.977136
$10$	2.20940	0.698675
$11$	−3.47130	−1.04664	−0.523319	−	0.852137i	$-0.675306\pi$
$11$	−3.47130	−1.04664	−0.523319	+	0.852137i	$0.675306\pi$
$12$	0.754656	0.217850
$13$	5.78805	1.60532	0.802658	−	0.596440i	$-0.203419\pi$
$13$	5.78805	1.60532	0.802658	+	0.596440i	$0.203419\pi$
$14$	−2.18466	−0.583875
$15$	0.261901	0.0676224
$16$	−1.46010	−0.365026
$17$	−7.13216	−1.72980	−0.864902	−	0.501941i	$-0.832619\pi$
$17$	−7.13216	−1.72980	−0.864902	+	0.501941i	$0.832619\pi$
$18$	−6.47666	−1.52656
$19$	6.26433	1.43713	0.718567	−	0.695457i	$-0.244798\pi$
$19$	6.26433	1.43713	0.718567	+	0.695457i	$0.244798\pi$
$20$	2.88146	0.644314
$21$	−0.258968	−0.0565114
$22$	−7.66951	−1.63514
$23$	1.36924	0.285506	0.142753	−	0.989758i	$-0.454404\pi$
$23$	1.36924	0.285506	0.142753	+	0.989758i	$0.454404\pi$
$24$	0.510052	0.104114
$25$	1.00000	0.200000
$26$	12.7881	2.50796
$27$	−1.55344	−0.298959
$28$	−2.84919	−0.538447
$29$	7.74052	1.43738	0.718690	−	0.695331i	$-0.244742\pi$
$29$	7.74052	1.43738	0.718690	+	0.695331i	$0.244742\pi$
$30$	0.578644	0.105645
$31$	−9.06357	−1.62787	−0.813933	−	0.580959i	$-0.802678\pi$
$31$	−9.06357	−1.62787	−0.813933	+	0.580959i	$0.802678\pi$
$32$	−7.12096	−1.25882
$33$	−0.909136	−0.158260
$34$	−15.7578	−2.70244
$35$	−0.988801	−0.167138
$36$	−8.44674	−1.40779
$37$	6.07967	0.999491	0.499745	−	0.866172i	$-0.333427\pi$
$37$	6.07967	0.999491	0.499745	+	0.866172i	$0.333427\pi$
$38$	13.8404	2.24521
$39$	1.51589	0.242737
$40$	1.94750	0.307927
$41$	3.31147	0.517164	0.258582	−	0.965989i	$-0.416745\pi$
$41$	3.31147	0.517164	0.258582	+	0.965989i	$0.416745\pi$
$42$	−0.572164	−0.0882868
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−10.0024	−1.50792
$45$	−2.93141	−0.436989
$46$	3.02520	0.446042
$47$	−6.18173	−0.901698	−0.450849	−	0.892600i	$-0.648879\pi$
$47$	−6.18173	−0.901698	−0.450849	+	0.892600i	$0.648879\pi$
$48$	−0.382402	−0.0551950
$49$	−6.02227	−0.860325
$50$	2.20940	0.312457
$51$	−1.86792	−0.261561
$52$	16.6780	2.31283
$53$	−0.867837	−0.119207	−0.0596033	−	0.998222i	$-0.518984\pi$
$53$	−0.867837	−0.119207	−0.0596033	+	0.998222i	$0.518984\pi$
$54$	−3.43217	−0.467060
$55$	−3.47130	−0.468070
$56$	−1.92569	−0.257332
$57$	1.64063	0.217307
$58$	17.1019	2.24559
$59$	0.261901	0.0340965	0.0170483	−	0.999855i	$-0.494573\pi$
$59$	0.261901	0.0340965	0.0170483	+	0.999855i	$0.494573\pi$
$60$	0.754656	0.0974257
$61$	13.5761	1.73824	0.869120	−	0.494601i	$-0.164686\pi$
$61$	13.5761	1.73824	0.869120	+	0.494601i	$0.164686\pi$
$62$	−20.0251	−2.54319
$63$	2.89858	0.365187
$64$	−12.8129	−1.60161
$65$	5.78805	0.717919
$66$	−2.00865	−0.247247
$67$	−0.229250	−0.0280073	−0.0140037	−	0.999902i	$-0.504458\pi$
$67$	−0.229250	−0.0280073	−0.0140037	+	0.999902i	$0.504458\pi$
$68$	−20.5510	−2.49218
$69$	0.358605	0.0431710
$70$	−2.18466	−0.261117
$71$	12.2419	1.45285	0.726425	−	0.687246i	$-0.241181\pi$
$71$	12.2419	1.45285	0.726425	+	0.687246i	$0.241181\pi$
$72$	−5.70892	−0.672803
$73$	−2.02482	−0.236988	−0.118494	−	0.992955i	$-0.537807\pi$
$73$	−2.02482	−0.236988	−0.118494	+	0.992955i	$0.537807\pi$
$74$	13.4324	1.56149
$75$	0.261901	0.0302417
$76$	18.0504	2.07052
$77$	3.43243	0.391162
$78$	3.34922	0.379224
$79$	9.66086	1.08693	0.543466	−	0.839431i	$-0.317112\pi$
$79$	9.66086	1.08693	0.543466	+	0.839431i	$0.317112\pi$
$80$	−1.46010	−0.163245
$81$	8.38738	0.931931
$82$	7.31636	0.807957
$83$	1.04956	0.115205	0.0576023	−	0.998340i	$-0.481654\pi$
$83$	1.04956	0.115205	0.0576023	+	0.998340i	$0.481654\pi$
$84$	−0.746205	−0.0814176
$85$	−7.13216	−0.773592
$86$	−2.20940	−0.238246
$87$	2.02725	0.217344
$88$	−6.76037	−0.720658
$89$	−6.15933	−0.652888	−0.326444	−	0.945217i	$-0.605850\pi$
$89$	−6.15933	−0.652888	−0.326444	+	0.945217i	$0.605850\pi$
$90$	−6.47666	−0.682700
$91$	−5.72323	−0.599957
$92$	3.94541	0.411338
$93$	−2.37375	−0.246147
$94$	−13.6579	−1.40871
$95$	6.26433	0.642706
$96$	−1.86498	−0.190344
$97$	1.10492	0.112187	0.0560936	−	0.998426i	$-0.482135\pi$
$97$	1.10492	0.112187	0.0560936	+	0.998426i	$0.482135\pi$
$98$	−13.3056	−1.34407
$99$	10.1758	1.02271
$100$	2.88146	0.288146
$101$	−4.12096	−0.410051	−0.205026	−	0.978757i	$-0.565728\pi$
$101$	−4.12096	−0.410051	−0.205026	+	0.978757i	$0.565728\pi$
$102$	−4.12698	−0.408632
$103$	−11.3965	−1.12293	−0.561465	−	0.827501i	$-0.689762\pi$
$103$	−11.3965	−1.12293	−0.561465	+	0.827501i	$0.689762\pi$
$104$	11.2722	1.10533
$105$	−0.258968	−0.0252727
$106$	−1.91740	−0.186235
$107$	−13.2069	−1.27676	−0.638381	−	0.769720i	$-0.720396\pi$
$107$	−13.2069	−1.27676	−0.638381	+	0.769720i	$0.720396\pi$
$108$	−4.47617	−0.430720
$109$	14.6019	1.39860	0.699302	−	0.714826i	$-0.253494\pi$
$109$	14.6019	1.39860	0.699302	+	0.714826i	$0.253494\pi$
$110$	−7.66951	−0.731259
$111$	1.59227	0.151131
$112$	1.44375	0.136422
$113$	2.35531	0.221569	0.110785	−	0.993844i	$-0.464664\pi$
$113$	2.35531	0.221569	0.110785	+	0.993844i	$0.464664\pi$
$114$	3.62481	0.339495
$115$	1.36924	0.127682
$116$	22.3040	2.07088
$117$	−16.9671	−1.56861
$118$	0.578644	0.0532685
$119$	7.05229	0.646483
$120$	0.510052	0.0465612
$121$	1.04995	0.0954497
$122$	29.9951	2.71563
$123$	0.867275	0.0781995
$124$	−26.1163	−2.34532
$125$	1.00000	0.0894427
$126$	6.40413	0.570525
$127$	3.30904	0.293630	0.146815	−	0.989164i	$-0.453098\pi$
$127$	3.30904	0.293630	0.146815	+	0.989164i	$0.453098\pi$
$128$	−14.0669	−1.24335
$129$	−0.261901	−0.0230591
$130$	12.7881	1.12159
$131$	−3.17968	−0.277810	−0.138905	−	0.990306i	$-0.544358\pi$
$131$	−3.17968	−0.277810	−0.138905	+	0.990306i	$0.544358\pi$
$132$	−2.61964	−0.228010
$133$	−6.19417	−0.537103
$134$	−0.506505	−0.0437554
$135$	−1.55344	−0.133699
$136$	−13.8899	−1.19105
$137$	3.40189	0.290643	0.145322	−	0.989384i	$-0.453578\pi$
$137$	3.40189	0.290643	0.145322	+	0.989384i	$0.453578\pi$
$138$	0.792303	0.0674453
$139$	8.33667	0.707107	0.353554	−	0.935414i	$-0.384973\pi$
$139$	8.33667	0.707107	0.353554	+	0.935414i	$0.384973\pi$
$140$	−2.84919	−0.240801
$141$	−1.61900	−0.136344
$142$	27.0474	2.26976
$143$	−20.0921	−1.68018
$144$	4.28016	0.356680
$145$	7.74052	0.642816
$146$	−4.47365	−0.370242
$147$	−1.57724	−0.130088
$148$	17.5183	1.44000
$149$	14.9699	1.22638	0.613189	−	0.789936i	$-0.289886\pi$
$149$	14.9699	1.22638	0.613189	+	0.789936i	$0.289886\pi$
$150$	0.578644	0.0472461
$151$	−16.0999	−1.31019	−0.655095	−	0.755546i	$-0.727372\pi$
$151$	−16.0999	−1.31019	−0.655095	+	0.755546i	$0.727372\pi$
$152$	12.1998	0.989534
$153$	20.9073	1.69025
$154$	7.58362	0.611105
$155$	−9.06357	−0.728004
$156$	4.36799	0.349719
$157$	−2.87809	−0.229697	−0.114848	−	0.993383i	$-0.536638\pi$
$157$	−2.87809	−0.229697	−0.114848	+	0.993383i	$0.536638\pi$
$158$	21.3447	1.69810
$159$	−0.227287	−0.0180250
$160$	−7.12096	−0.562962
$161$	−1.35391	−0.106703
$162$	18.5311	1.45594
$163$	−14.8678	−1.16454	−0.582268	−	0.812997i	$-0.697834\pi$
$163$	−14.8678	−1.16454	−0.582268	+	0.812997i	$0.697834\pi$
$164$	9.54186	0.745094
$165$	−0.909136	−0.0707762
$166$	2.31891	0.179982
$167$	−19.6336	−1.51929	−0.759645	−	0.650337i	$-0.774628\pi$
$167$	−19.6336	−1.51929	−0.759645	+	0.650337i	$0.774628\pi$
$168$	−0.504340	−0.0389107
$169$	20.5015	1.57704
$170$	−15.7578	−1.20857
$171$	−18.3633	−1.40428
$172$	−2.88146	−0.219709
$173$	−12.6607	−0.962578	−0.481289	−	0.876562i	$-0.659831\pi$
$173$	−12.6607	−0.962578	−0.481289	+	0.876562i	$0.659831\pi$
$174$	4.47901	0.339553
$175$	−0.988801	−0.0747464
$176$	5.06847	0.382050
$177$	0.0685919	0.00515568
$178$	−13.6084	−1.02000
$179$	−5.10704	−0.381718	−0.190859	−	0.981617i	$-0.561127\pi$
$179$	−5.10704	−0.381718	−0.190859	+	0.981617i	$0.561127\pi$
$180$	−8.44674	−0.629583
$181$	16.5533	1.23040	0.615199	−	0.788372i	$-0.289076\pi$
$181$	16.5533	1.23040	0.615199	+	0.788372i	$0.289076\pi$
$182$	−12.6449	−0.937304
$183$	3.55559	0.262836
$184$	2.66660	0.196584
$185$	6.07967	0.446986
$186$	−5.24458	−0.384551
$187$	24.7579	1.81048
$188$	−17.8124	−1.29910
$189$	1.53604	0.111731
$190$	13.8404	1.00409
$191$	9.31662	0.674127	0.337063	−	0.941482i	$-0.390566\pi$
$191$	9.31662	0.674127	0.337063	+	0.941482i	$0.390566\pi$
$192$	−3.35570	−0.242177
$193$	3.79315	0.273037	0.136518	−	0.990638i	$-0.456409\pi$
$193$	3.79315	0.273037	0.136518	+	0.990638i	$0.456409\pi$
$194$	2.44120	0.175268
$195$	1.51589	0.108555
$196$	−17.3529	−1.23950
$197$	−18.7452	−1.33554	−0.667771	−	0.744367i	$-0.732751\pi$
$197$	−18.7452	−1.33554	−0.667771	+	0.744367i	$0.732751\pi$
$198$	22.4825	1.59776
$199$	−18.7881	−1.33185	−0.665927	−	0.746016i	$-0.731964\pi$
$199$	−18.7881	−1.33185	−0.665927	+	0.746016i	$0.731964\pi$
$200$	1.94750	0.137709
$201$	−0.0600406	−0.00423494
$202$	−9.10487	−0.640616
$203$	−7.65384	−0.537194
$204$	−5.38233	−0.376839
$205$	3.31147	0.231283
$206$	−25.1794	−1.75433
$207$	−4.01380	−0.278979
$208$	−8.45115	−0.585982
$209$	−21.7454	−1.50416
$210$	−0.572164	−0.0394831
$211$	5.92735	0.408056	0.204028	−	0.978965i	$-0.434597\pi$
$211$	5.92735	0.408056	0.204028	+	0.978965i	$0.434597\pi$
$212$	−2.50064	−0.171745
$213$	3.20617	0.219683
$214$	−29.1794	−1.99467
$215$	−1.00000	−0.0681994
$216$	−3.02533	−0.205847
$217$	8.96207	0.608385
$218$	32.2614	2.18502
$219$	−0.530302	−0.0358345
$220$	−10.0024	−0.674363
$221$	−41.2813	−2.77688
$222$	3.51796	0.236110
$223$	−8.62370	−0.577485	−0.288743	−	0.957407i	$-0.593237\pi$
$223$	−8.62370	−0.577485	−0.288743	+	0.957407i	$0.593237\pi$
$224$	7.04122	0.470461
$225$	−2.93141	−0.195427
$226$	5.20384	0.346154
$227$	−3.18032	−0.211085	−0.105543	−	0.994415i	$-0.533658\pi$
$227$	−3.18032	−0.211085	−0.105543	+	0.994415i	$0.533658\pi$
$228$	4.72741	0.313081
$229$	−22.5238	−1.48841	−0.744206	−	0.667950i	$-0.767172\pi$
$229$	−22.5238	−1.48841	−0.744206	+	0.667950i	$0.767172\pi$
$230$	3.02520	0.199476
$231$	0.898955	0.0591469
$232$	15.0747	0.989702
$233$	7.12267	0.466622	0.233311	−	0.972402i	$-0.425044\pi$
$233$	7.12267	0.466622	0.233311	+	0.972402i	$0.425044\pi$
$234$	−37.4872	−2.45062
$235$	−6.18173	−0.403251
$236$	0.754656	0.0491239
$237$	2.53018	0.164353
$238$	15.5814	1.00999
$239$	−28.3353	−1.83286	−0.916430	−	0.400195i	$-0.868942\pi$
$239$	−28.3353	−1.83286	−0.916430	+	0.400195i	$0.868942\pi$
$240$	−0.382402	−0.0246840
$241$	8.06020	0.519203	0.259602	−	0.965716i	$-0.416409\pi$
$241$	8.06020	0.519203	0.259602	+	0.965716i	$0.416409\pi$
$242$	2.31976	0.149120
$243$	6.85698	0.439875
$244$	39.1190	2.50434
$245$	−6.02227	−0.384749
$246$	1.91616	0.122170
$247$	36.2582	2.30705
$248$	−17.6513	−1.12086
$249$	0.274882	0.0174199
$250$	2.20940	0.139735
$251$	−11.0272	−0.696029	−0.348014	−	0.937489i	$-0.613144\pi$
$251$	−11.0272	−0.696029	−0.348014	+	0.937489i	$0.613144\pi$
$252$	8.35215	0.526136
$253$	−4.75305	−0.298822
$254$	7.31100	0.458733
$255$	−1.86792	−0.116974
$256$	−5.45362	−0.340852
$257$	−27.5410	−1.71796	−0.858979	−	0.512010i	$-0.828901\pi$
$257$	−27.5410	−1.71796	−0.858979	+	0.512010i	$0.828901\pi$
$258$	−0.578644	−0.0360248
$259$	−6.01158	−0.373541
$260$	16.6780	1.03433
$261$	−22.6906	−1.40452
$262$	−7.02520	−0.434019
$263$	7.08171	0.436677	0.218338	−	0.975873i	$-0.429936\pi$
$263$	7.08171	0.436677	0.218338	+	0.975873i	$0.429936\pi$
$264$	−1.77054	−0.108970
$265$	−0.867837	−0.0533108
$266$	−13.6854	−0.839107
$267$	−1.61313	−0.0987221
$268$	−0.660574	−0.0403510
$269$	10.3644	0.631930	0.315965	−	0.948771i	$-0.397672\pi$
$269$	10.3644	0.631930	0.315965	+	0.948771i	$0.397672\pi$
$270$	−3.43217	−0.208875
$271$	−14.6010	−0.886947	−0.443474	−	0.896287i	$-0.646254\pi$
$271$	−14.6010	−0.886947	−0.443474	+	0.896287i	$0.646254\pi$
$272$	10.4137	0.631424
$273$	−1.49892	−0.0907186
$274$	7.51615	0.454067
$275$	−3.47130	−0.209327
$276$	1.03331	0.0621977
$277$	−7.47965	−0.449409	−0.224704	−	0.974427i	$-0.572142\pi$
$277$	−7.47965	−0.449409	−0.224704	+	0.974427i	$0.572142\pi$
$278$	18.4191	1.10470
$279$	26.5690	1.59065
$280$	−1.92569	−0.115082
$281$	4.90271	0.292471	0.146236	−	0.989250i	$-0.453284\pi$
$281$	4.90271	0.292471	0.146236	+	0.989250i	$0.453284\pi$
$282$	−3.57702	−0.213008
$283$	31.4284	1.86823	0.934113	−	0.356977i	$-0.116193\pi$
$283$	31.4284	1.86823	0.934113	+	0.356977i	$0.116193\pi$
$284$	35.2746	2.09316
$285$	1.64063	0.0971825
$286$	−44.3915	−2.62492
$287$	−3.27438	−0.193281
$288$	20.8745	1.23004
$289$	33.8677	1.99222
$290$	17.1019	1.00426
$291$	0.289378	0.0169636
$292$	−5.83445	−0.341435
$293$	−3.45380	−0.201773	−0.100887	−	0.994898i	$-0.532168\pi$
$293$	−3.45380	−0.201773	−0.100887	+	0.994898i	$0.532168\pi$
$294$	−3.48475	−0.203235
$295$	0.261901	0.0152484
$296$	11.8402	0.688195
$297$	5.39246	0.312902
$298$	33.0744	1.91595
$299$	7.92523	0.458328
$300$	0.754656	0.0435701
$301$	0.988801	0.0569936
$302$	−35.5712	−2.04689
$303$	−1.07928	−0.0620032
$304$	−9.14657	−0.524592
$305$	13.5761	0.777365
$306$	46.1926	2.64066
$307$	33.1991	1.89477	0.947386	−	0.320092i	$-0.103714\pi$
$307$	33.1991	1.89477	0.947386	+	0.320092i	$0.103714\pi$
$308$	9.89041	0.563558
$309$	−2.98475	−0.169796
$310$	−20.0251	−1.13735
$311$	4.33667	0.245910	0.122955	−	0.992412i	$-0.460763\pi$
$311$	4.33667	0.245910	0.122955	+	0.992412i	$0.460763\pi$
$312$	2.95220	0.167136
$313$	18.3833	1.03909	0.519544	−	0.854444i	$-0.326102\pi$
$313$	18.3833	1.03909	0.519544	+	0.854444i	$0.326102\pi$
$314$	−6.35886	−0.358851
$315$	2.89858	0.163316
$316$	27.8374	1.56598
$317$	6.07477	0.341193	0.170597	−	0.985341i	$-0.445431\pi$
$317$	6.07477	0.341193	0.170597	+	0.985341i	$0.445431\pi$
$318$	−0.502169	−0.0281602
$319$	−26.8697	−1.50441
$320$	−12.8129	−0.716261
$321$	−3.45890	−0.193057
$322$	−2.99133	−0.166700
$323$	−44.6782	−2.48596
$324$	24.1679	1.34266
$325$	5.78805	0.321063
$326$	−32.8489	−1.81933
$327$	3.82424	0.211481
$328$	6.44909	0.356091
$329$	6.11250	0.336993
$330$	−2.00865	−0.110572
$331$	1.83557	0.100892	0.0504460	−	0.998727i	$-0.483936\pi$
$331$	1.83557	0.100892	0.0504460	+	0.998727i	$0.483936\pi$
$332$	3.02428	0.165979
$333$	−17.8220	−0.976638
$334$	−43.3785	−2.37356
$335$	−0.229250	−0.0125252
$336$	0.378120	0.0206281
$337$	−13.2447	−0.721483	−0.360741	−	0.932666i	$-0.617476\pi$
$337$	−13.2447	−0.721483	−0.360741	+	0.932666i	$0.617476\pi$
$338$	45.2960	2.46378
$339$	0.616858	0.0335031
$340$	−20.5510	−1.11454
$341$	31.4624	1.70378
$342$	−40.5719	−2.19388
$343$	12.8764	0.695262
$344$	−1.94750	−0.105002
$345$	0.358605	0.0193066
$346$	−27.9727	−1.50382
$347$	12.1293	0.651135	0.325568	−	0.945519i	$-0.394445\pi$
$347$	12.1293	0.651135	0.325568	+	0.945519i	$0.394445\pi$
$348$	5.84143	0.313134
$349$	26.6285	1.42539	0.712697	−	0.701472i	$-0.247474\pi$
$349$	26.6285	1.42539	0.712697	+	0.701472i	$0.247474\pi$
$350$	−2.18466	−0.116775
$351$	−8.99138	−0.479924
$352$	24.7190	1.31753
$353$	5.23129	0.278434	0.139217	−	0.990262i	$-0.455542\pi$
$353$	5.23129	0.278434	0.139217	+	0.990262i	$0.455542\pi$
$354$	0.151547	0.00805464
$355$	12.2419	0.649734
$356$	−17.7479	−0.940635
$357$	1.84700	0.0977536
$358$	−11.2835	−0.596352
$359$	4.75892	0.251166	0.125583	−	0.992083i	$-0.459920\pi$
$359$	4.75892	0.251166	0.125583	+	0.992083i	$0.459920\pi$
$360$	−5.70892	−0.300887
$361$	20.2418	1.06536
$362$	36.5729	1.92223
$363$	0.274982	0.0144328
$364$	−16.4913	−0.864377
$365$	−2.02482	−0.105984
$366$	7.85572	0.410625
$367$	−18.5236	−0.966921	−0.483461	−	0.875366i	$-0.660620\pi$
$367$	−18.5236	−0.966921	−0.483461	+	0.875366i	$0.660620\pi$
$368$	−1.99924	−0.104217
$369$	−9.70726	−0.505340
$370$	13.4324	0.698319
$371$	0.858119	0.0445513
$372$	−6.83988	−0.354631
$373$	−27.6040	−1.42928	−0.714640	−	0.699493i	$-0.753409\pi$
$373$	−27.6040	−1.42928	−0.714640	+	0.699493i	$0.753409\pi$
$374$	54.7002	2.82848
$375$	0.261901	0.0135245
$376$	−12.0389	−0.620860
$377$	44.8025	2.30745
$378$	3.39374	0.174555
$379$	−1.35652	−0.0696796	−0.0348398	−	0.999393i	$-0.511092\pi$
$379$	−1.35652	−0.0696796	−0.0348398	+	0.999393i	$0.511092\pi$
$380$	18.0504	0.925966
$381$	0.866639	0.0443993
$382$	20.5842	1.05318
$383$	18.9896	0.970322	0.485161	−	0.874425i	$-0.338761\pi$
$383$	18.9896	0.970322	0.485161	+	0.874425i	$0.338761\pi$
$384$	−3.68412	−0.188004
$385$	3.43243	0.174933
$386$	8.38059	0.426561
$387$	2.93141	0.149012
$388$	3.18377	0.161631
$389$	24.9697	1.26601	0.633007	−	0.774146i	$-0.281820\pi$
$389$	24.9697	1.26601	0.633007	+	0.774146i	$0.281820\pi$
$390$	3.34922	0.169594
$391$	−9.76565	−0.493870
$392$	−11.7284	−0.592373
$393$	−0.832761	−0.0420072
$394$	−41.4157	−2.08650
$395$	9.66086	0.486091
$396$	29.3212	1.47345
$397$	−20.8259	−1.04522	−0.522612	−	0.852571i	$-0.675042\pi$
$397$	−20.8259	−1.04522	−0.522612	+	0.852571i	$0.675042\pi$
$398$	−41.5105	−2.08074
$399$	−1.62226	−0.0812145
$400$	−1.46010	−0.0730052
$401$	−4.19770	−0.209623	−0.104811	−	0.994492i	$-0.533424\pi$
$401$	−4.19770	−0.209623	−0.104811	+	0.994492i	$0.533424\pi$
$402$	−0.132654	−0.00661617
$403$	−52.4604	−2.61324
$404$	−11.8744	−0.590773
$405$	8.38738	0.416772
$406$	−16.9104	−0.839250
$407$	−21.1044	−1.04610
$408$	−3.63777	−0.180097
$409$	−4.18173	−0.206773	−0.103387	−	0.994641i	$-0.532968\pi$
$409$	−4.18173	−0.206773	−0.103387	+	0.994641i	$0.532968\pi$
$410$	7.31636	0.361329
$411$	0.890957	0.0439477
$412$	−32.8385	−1.61784
$413$	−0.258968	−0.0127430
$414$	−8.86811	−0.435844
$415$	1.04956	0.0515211
$416$	−41.2165	−2.02080
$417$	2.18338	0.106920
$418$	−48.0443	−2.34992
$419$	−0.937506	−0.0458002	−0.0229001	−	0.999738i	$-0.507290\pi$
$419$	−0.937506	−0.0458002	−0.0229001	+	0.999738i	$0.507290\pi$
$420$	−0.746205	−0.0364111
$421$	15.1945	0.740534	0.370267	−	0.928925i	$-0.379266\pi$
$421$	15.1945	0.740534	0.370267	+	0.928925i	$0.379266\pi$
$422$	13.0959	0.637499
$423$	18.1212	0.881081
$424$	−1.69011	−0.0820792
$425$	−7.13216	−0.345961
$426$	7.08372	0.343207
$427$	−13.4241	−0.649636
$428$	−38.0553	−1.83947
$429$	−5.26212	−0.254058
$430$	−2.20940	−0.106547
$431$	0.650480	0.0313325	0.0156663	−	0.999877i	$-0.495013\pi$
$431$	0.650480	0.0313325	0.0156663	+	0.999877i	$0.495013\pi$
$432$	2.26818	0.109128
$433$	20.1847	0.970013	0.485006	−	0.874511i	$-0.338817\pi$
$433$	20.1847	0.970013	0.485006	+	0.874511i	$0.338817\pi$
$434$	19.8008	0.950470
$435$	2.02725	0.0971991
$436$	42.0747	2.01501
$437$	8.57737	0.410311
$438$	−1.17165	−0.0559836
$439$	−29.4009	−1.40323	−0.701614	−	0.712557i	$-0.747537\pi$
$439$	−29.4009	−1.40323	−0.701614	+	0.712557i	$0.747537\pi$
$440$	−6.76037	−0.322288
$441$	17.6537	0.840654
$442$	−91.2070	−4.33827
$443$	34.5625	1.64211	0.821056	−	0.570847i	$-0.193385\pi$
$443$	34.5625	1.64211	0.821056	+	0.570847i	$0.193385\pi$
$444$	4.58806	0.217740
$445$	−6.15933	−0.291980
$446$	−19.0532	−0.902196
$447$	3.92061	0.185439
$448$	12.6694	0.598572
$449$	7.23402	0.341395	0.170697	−	0.985324i	$-0.445398\pi$
$449$	7.23402	0.341395	0.170697	+	0.985324i	$0.445398\pi$
$450$	−6.47666	−0.305313
$451$	−11.4951	−0.541283
$452$	6.78675	0.319222
$453$	−4.21657	−0.198112
$454$	−7.02661	−0.329775
$455$	−5.72323	−0.268309
$456$	3.19513	0.149626
$457$	−9.93523	−0.464751	−0.232375	−	0.972626i	$-0.574650\pi$
$457$	−9.93523	−0.464751	−0.232375	+	0.972626i	$0.574650\pi$
$458$	−49.7641	−2.32532
$459$	11.0794	0.517141
$460$	3.94541	0.183956
$461$	−4.34399	−0.202320	−0.101160	−	0.994870i	$-0.532255\pi$
$461$	−4.34399	−0.202320	−0.101160	+	0.994870i	$0.532255\pi$
$462$	1.98615	0.0924042
$463$	3.21037	0.149199	0.0745993	−	0.997214i	$-0.476232\pi$
$463$	3.21037	0.149199	0.0745993	+	0.997214i	$0.476232\pi$
$464$	−11.3020	−0.524681
$465$	−2.37375	−0.110080
$466$	15.7369	0.728996
$467$	17.2961	0.800369	0.400184	−	0.916435i	$-0.368946\pi$
$467$	17.2961	0.800369	0.400184	+	0.916435i	$0.368946\pi$
$468$	−48.8901	−2.25995
$469$	0.226682	0.0104672
$470$	−13.6579	−0.629993
$471$	−0.753774	−0.0347321
$472$	0.510052	0.0234770
$473$	3.47130	0.159611
$474$	5.59020	0.256766
$475$	6.26433	0.287427
$476$	20.3209	0.931407
$477$	2.54398	0.116481
$478$	−62.6041	−2.86345
$479$	5.90118	0.269632	0.134816	−	0.990871i	$-0.456956\pi$
$479$	5.90118	0.269632	0.134816	+	0.990871i	$0.456956\pi$
$480$	−1.86498	−0.0851245
$481$	35.1894	1.60450
$482$	17.8082	0.811143
$483$	−0.354589	−0.0161344
$484$	3.02538	0.137517
$485$	1.10492	0.0501716
$486$	15.1498	0.687210
$487$	39.3612	1.78362	0.891812	−	0.452406i	$-0.149434\pi$
$487$	39.3612	1.78362	0.891812	+	0.452406i	$0.149434\pi$
$488$	26.4395	1.19686
$489$	−3.89388	−0.176087
$490$	−13.3056	−0.601087
$491$	−4.35860	−0.196701	−0.0983505	−	0.995152i	$-0.531357\pi$
$491$	−4.35860	−0.196701	−0.0983505	+	0.995152i	$0.531357\pi$
$492$	2.49902	0.112664
$493$	−55.2067	−2.48638
$494$	80.1090	3.60427
$495$	10.1758	0.457369
$496$	13.2338	0.594213
$497$	−12.1048	−0.542976
$498$	0.607324	0.0272148
$499$	25.6899	1.15004	0.575018	−	0.818141i	$-0.304995\pi$
$499$	25.6899	1.15004	0.575018	+	0.818141i	$0.304995\pi$
$500$	2.88146	0.128863
$501$	−5.14204	−0.229729
$502$	−24.3635	−1.08739
$503$	3.67703	0.163951	0.0819754	−	0.996634i	$-0.473877\pi$
$503$	3.67703	0.163951	0.0819754	+	0.996634i	$0.473877\pi$
$504$	5.64499	0.251448
$505$	−4.12096	−0.183380
$506$	−10.5014	−0.466844
$507$	5.36935	0.238461
$508$	9.53487	0.423041
$509$	−34.9139	−1.54753	−0.773767	−	0.633471i	$-0.781630\pi$
$509$	−34.9139	−1.54753	−0.773767	+	0.633471i	$0.781630\pi$
$510$	−4.12698	−0.182746
$511$	2.00215	0.0885698
$512$	16.0845	0.710840
$513$	−9.73125	−0.429645
$514$	−60.8491	−2.68394
$515$	−11.3965	−0.502189
$516$	−0.754656	−0.0332219
$517$	21.4587	0.943750
$518$	−13.2820	−0.583578
$519$	−3.31585	−0.145550
$520$	11.2722	0.494320
$521$	−15.4257	−0.675812	−0.337906	−	0.941180i	$-0.609719\pi$
$521$	−15.4257	−0.675812	−0.337906	+	0.941180i	$0.609719\pi$
$522$	−50.1328	−2.19425
$523$	32.2843	1.41169	0.705847	−	0.708364i	$-0.250567\pi$
$523$	32.2843	1.41169	0.705847	+	0.708364i	$0.250567\pi$
$524$	−9.16214	−0.400250
$525$	−0.258968	−0.0113023
$526$	15.6463	0.682213
$527$	64.6429	2.81589
$528$	1.32743	0.0577692
$529$	−21.1252	−0.918486
$530$	−1.91740	−0.0832866
$531$	−0.767737	−0.0333170
$532$	−17.8483	−0.773821
$533$	19.1669	0.830211
$534$	−3.56406	−0.154232
$535$	−13.2069	−0.570985
$536$	−0.446464	−0.0192843
$537$	−1.33754	−0.0577189
$538$	22.8992	0.987254
$539$	20.9051	0.900448
$540$	−4.47617	−0.192624
$541$	29.9794	1.28892	0.644459	−	0.764639i	$-0.277083\pi$
$541$	29.9794	1.28892	0.644459	+	0.764639i	$0.277083\pi$
$542$	−32.2595	−1.38566
$543$	4.33532	0.186046
$544$	50.7879	2.17751
$545$	14.6019	0.625475
$546$	−3.31171	−0.141728
$547$	−35.0520	−1.49871	−0.749357	−	0.662166i	$-0.769637\pi$
$547$	−35.0520	−1.49871	−0.749357	+	0.662166i	$0.769637\pi$
$548$	9.80242	0.418739
$549$	−39.7971	−1.69850
$550$	−7.66951	−0.327029
$551$	48.4892	2.06571
$552$	0.698384	0.0297252
$553$	−9.55267	−0.406221
$554$	−16.5256	−0.702104
$555$	1.59227	0.0675880
$556$	24.0218	1.01875
$557$	26.4107	1.11906	0.559529	−	0.828811i	$-0.310982\pi$
$557$	26.4107	1.11906	0.559529	+	0.828811i	$0.310982\pi$
$558$	58.7017	2.48504
$559$	−5.78805	−0.244808
$560$	1.44375	0.0610097
$561$	6.48411	0.273759
$562$	10.8321	0.456923
$563$	−29.9152	−1.26077	−0.630387	−	0.776281i	$-0.717104\pi$
$563$	−29.9152	−1.26077	−0.630387	+	0.776281i	$0.717104\pi$
$564$	−4.66508	−0.196435
$565$	2.35531	0.0990888
$566$	69.4381	2.91870
$567$	−8.29345	−0.348292
$568$	23.8412	1.00035
$569$	−31.5162	−1.32123	−0.660614	−	0.750726i	$-0.729704\pi$
$569$	−31.5162	−1.32123	−0.660614	+	0.750726i	$0.729704\pi$
$570$	3.62481	0.151827
$571$	17.6363	0.738056	0.369028	−	0.929418i	$-0.379691\pi$
$571$	17.6363	0.738056	0.369028	+	0.929418i	$0.379691\pi$
$572$	−57.8945	−2.42069
$573$	2.44003	0.101934
$574$	−7.23443	−0.301959
$575$	1.36924	0.0571013
$576$	37.5597	1.56499
$577$	28.5791	1.18976	0.594881	−	0.803814i	$-0.297199\pi$
$577$	28.5791	1.18976	0.594881	+	0.803814i	$0.297199\pi$
$578$	74.8275	3.11241
$579$	0.993427	0.0412854
$580$	22.3040	0.926124
$581$	−1.03781	−0.0430557
$582$	0.639352	0.0265020
$583$	3.01253	0.124766
$584$	−3.94335	−0.163177
$585$	−16.9671	−0.701504
$586$	−7.63084	−0.315227
$587$	−32.9257	−1.35899	−0.679494	−	0.733681i	$-0.737801\pi$
$587$	−32.9257	−1.35899	−0.679494	+	0.733681i	$0.737801\pi$
$588$	−4.54474	−0.187422
$589$	−56.7772	−2.33946
$590$	0.578644	0.0238224
$591$	−4.90938	−0.201945
$592$	−8.87695	−0.364840
$593$	−28.5886	−1.17399	−0.586996	−	0.809590i	$-0.699690\pi$
$593$	−28.5886	−1.17399	−0.586996	+	0.809590i	$0.699690\pi$
$594$	11.9141	0.488842
$595$	7.05229	0.289116
$596$	43.1351	1.76688
$597$	−4.92062	−0.201388
$598$	17.5100	0.716038
$599$	25.8590	1.05657	0.528286	−	0.849067i	$-0.322835\pi$
$599$	25.8590	1.05657	0.528286	+	0.849067i	$0.322835\pi$
$600$	0.510052	0.0208228
$601$	−19.3020	−0.787344	−0.393672	−	0.919251i	$-0.628795\pi$
$601$	−19.3020	−0.787344	−0.393672	+	0.919251i	$0.628795\pi$
$602$	2.18466	0.0890401
$603$	0.672024	0.0273669
$604$	−46.3912	−1.88763
$605$	1.04995	0.0426864
$606$	−2.38457	−0.0968665
$607$	41.0596	1.66656	0.833278	−	0.552854i	$-0.186461\pi$
$607$	41.0596	1.66656	0.833278	+	0.552854i	$0.186461\pi$
$608$	−44.6080	−1.80909
$609$	−2.00455	−0.0812283
$610$	29.9951	1.21446
$611$	−35.7801	−1.44751
$612$	60.2435	2.43520
$613$	1.39095	0.0561798	0.0280899	−	0.999605i	$-0.491058\pi$
$613$	1.39095	0.0561798	0.0280899	+	0.999605i	$0.491058\pi$
$614$	73.3502	2.96017
$615$	0.867275	0.0349719
$616$	6.68466	0.269333
$617$	−22.6207	−0.910676	−0.455338	−	0.890319i	$-0.650482\pi$
$617$	−22.6207	−0.910676	−0.455338	+	0.890319i	$0.650482\pi$
$618$	−6.59451	−0.265270
$619$	−1.20272	−0.0483413	−0.0241706	−	0.999708i	$-0.507695\pi$
$619$	−1.20272	−0.0483413	−0.0241706	+	0.999708i	$0.507695\pi$
$620$	−26.1163	−1.04886
$621$	−2.12703	−0.0853549
$622$	9.58145	0.384181
$623$	6.09035	0.244005
$624$	−2.21336	−0.0886054
$625$	1.00000	0.0400000
$626$	40.6162	1.62335
$627$	−5.69513	−0.227441
$628$	−8.29311	−0.330931
$629$	−43.3612	−1.72892
$630$	6.40413	0.255147
$631$	−4.37325	−0.174096	−0.0870481	−	0.996204i	$-0.527743\pi$
$631$	−4.37325	−0.174096	−0.0870481	+	0.996204i	$0.527743\pi$
$632$	18.8145	0.748402
$633$	1.55238	0.0617014
$634$	13.4216	0.533040
$635$	3.30904	0.131315
$636$	−0.654919	−0.0259692
$637$	−34.8572	−1.38109
$638$	−59.3660	−2.35032
$639$	−35.8861	−1.41963
$640$	−14.0669	−0.556042
$641$	16.6004	0.655675	0.327838	−	0.944734i	$-0.393680\pi$
$641$	16.6004	0.655675	0.327838	+	0.944734i	$0.393680\pi$
$642$	−7.64211	−0.301610
$643$	19.3762	0.764123	0.382062	−	0.924137i	$-0.375214\pi$
$643$	19.3762	0.764123	0.382062	+	0.924137i	$0.375214\pi$
$644$	−3.90123	−0.153730
$645$	−0.261901	−0.0103123
$646$	−98.7121	−3.88378
$647$	27.1872	1.06884	0.534420	−	0.845219i	$-0.320530\pi$
$647$	27.1872	1.06884	0.534420	+	0.845219i	$0.320530\pi$
$648$	16.3344	0.641677
$649$	−0.909136	−0.0356867
$650$	12.7881	0.501592
$651$	2.34717	0.0919929
$652$	−42.8410	−1.67778
$653$	22.8764	0.895223	0.447612	−	0.894228i	$-0.352275\pi$
$653$	22.8764	0.895223	0.447612	+	0.894228i	$0.352275\pi$
$654$	8.44928	0.330393
$655$	−3.17968	−0.124241
$656$	−4.83509	−0.188778
$657$	5.93558	0.231569
$658$	13.5050	0.526479
$659$	18.2273	0.710036	0.355018	−	0.934859i	$-0.384475\pi$
$659$	18.2273	0.710036	0.355018	+	0.934859i	$0.384475\pi$
$660$	−2.61964	−0.101969
$661$	−26.6129	−1.03512	−0.517562	−	0.855646i	$-0.673160\pi$
$661$	−26.6129	−1.03512	−0.517562	+	0.855646i	$0.673160\pi$
$662$	4.05551	0.157622
$663$	−10.8116	−0.419887
$664$	2.04403	0.0793237
$665$	−6.19417	−0.240200
$666$	−39.3759	−1.52579
$667$	10.5986	0.410381
$668$	−56.5734	−2.18889
$669$	−2.25855	−0.0873206
$670$	−0.506505	−0.0195680
$671$	−47.1267	−1.81931
$672$	1.84410	0.0711377
$673$	−32.7129	−1.26099	−0.630495	−	0.776193i	$-0.717148\pi$
$673$	−32.7129	−1.26099	−0.630495	+	0.776193i	$0.717148\pi$
$674$	−29.2628	−1.12716
$675$	−1.55344	−0.0597919
$676$	59.0742	2.27209
$677$	−35.5858	−1.36767	−0.683836	−	0.729636i	$-0.739690\pi$
$677$	−35.5858	−1.36767	−0.683836	+	0.729636i	$0.739690\pi$
$678$	1.36289	0.0523414
$679$	−1.09254	−0.0419279
$680$	−13.8899	−0.532653
$681$	−0.832928	−0.0319179
$682$	69.5131	2.66180
$683$	25.4303	0.973064	0.486532	−	0.873663i	$-0.338262\pi$
$683$	25.4303	0.973064	0.486532	+	0.873663i	$0.338262\pi$
$684$	−52.9131	−2.02318
$685$	3.40189	0.129980
$686$	28.4492	1.08620
$687$	−5.89898	−0.225060
$688$	1.46010	0.0556660
$689$	−5.02308	−0.191364
$690$	0.792303	0.0301625
$691$	16.0016	0.608731	0.304366	−	0.952555i	$-0.401556\pi$
$691$	16.0016	0.608731	0.304366	+	0.952555i	$0.401556\pi$
$692$	−36.4814	−1.38682
$693$	−10.0619	−0.382218
$694$	26.7985	1.01726
$695$	8.33667	0.316228
$696$	3.94807	0.149651
$697$	−23.6179	−0.894592
$698$	58.8332	2.22687
$699$	1.86543	0.0705571
$700$	−2.84919	−0.107689
$701$	18.6181	0.703196	0.351598	−	0.936151i	$-0.385638\pi$
$701$	18.6181	0.703196	0.351598	+	0.936151i	$0.385638\pi$
$702$	−19.8656	−0.749778
$703$	38.0850	1.43640
$704$	44.4774	1.67630
$705$	−1.61900	−0.0609750
$706$	11.5580	0.434992
$707$	4.07481	0.153249
$708$	0.197645	0.00742795
$709$	35.9746	1.35105	0.675527	−	0.737335i	$-0.263916\pi$
$709$	35.9746	1.35105	0.675527	+	0.737335i	$0.263916\pi$
$710$	27.0474	1.01507
$711$	−28.3199	−1.06208
$712$	−11.9953	−0.449543
$713$	−12.4102	−0.464766
$714$	4.08077	0.152719
$715$	−20.0921	−0.751401
$716$	−14.7157	−0.549953
$717$	−7.42104	−0.277144
$718$	10.5144	0.392393
$719$	28.6926	1.07006	0.535028	−	0.844835i	$-0.320301\pi$
$719$	28.6926	1.07006	0.535028	+	0.844835i	$0.320301\pi$
$720$	4.28016	0.159512
$721$	11.2689	0.419674
$722$	44.7222	1.66439
$723$	2.11097	0.0785079
$724$	47.6977	1.77267
$725$	7.74052	0.287476
$726$	0.607545	0.0225481
$727$	−32.2142	−1.19476	−0.597378	−	0.801960i	$-0.703791\pi$
$727$	−32.2142	−1.19476	−0.597378	+	0.801960i	$0.703791\pi$
$728$	−11.1460	−0.413098
$729$	−23.3663	−0.865418
$730$	−4.47365	−0.165577
$731$	7.13216	0.263793
$732$	10.2453	0.378677
$733$	−8.01974	−0.296216	−0.148108	−	0.988971i	$-0.547318\pi$
$733$	−8.01974	−0.296216	−0.148108	+	0.988971i	$0.547318\pi$
$734$	−40.9260	−1.51061
$735$	−1.57724	−0.0581772
$736$	−9.75032	−0.359401
$737$	0.795795	0.0293135
$738$	−21.4472	−0.789484
$739$	−53.8031	−1.97918	−0.989590	−	0.143915i	$-0.954031\pi$
$739$	−53.8031	−1.97918	−0.989590	+	0.143915i	$0.954031\pi$
$740$	17.5183	0.643986
$741$	9.49604	0.348846
$742$	1.89593	0.0696018
$743$	12.0967	0.443785	0.221893	−	0.975071i	$-0.428777\pi$
$743$	12.0967	0.443785	0.221893	+	0.975071i	$0.428777\pi$
$744$	−4.62289	−0.169483
$745$	14.9699	0.548453
$746$	−60.9883	−2.23294
$747$	−3.07670	−0.112571
$748$	71.3389	2.60841
$749$	13.0590	0.477167
$750$	0.578644	0.0211291
$751$	−29.0995	−1.06186	−0.530928	−	0.847417i	$-0.678156\pi$
$751$	−29.0995	−1.06186	−0.530928	+	0.847417i	$0.678156\pi$
$752$	9.02597	0.329143
$753$	−2.88802	−0.105245
$754$	98.9868	3.60489
$755$	−16.0999	−0.585935
$756$	4.42605	0.160974
$757$	18.5816	0.675359	0.337680	−	0.941261i	$-0.390358\pi$
$757$	18.5816	0.675359	0.337680	+	0.941261i	$0.390358\pi$
$758$	−2.99709	−0.108859
$759$	−1.24483	−0.0451843
$760$	12.1998	0.442533
$761$	1.78507	0.0647087	0.0323543	−	0.999476i	$-0.489699\pi$
$761$	1.78507	0.0647087	0.0323543	+	0.999476i	$0.489699\pi$
$762$	1.91476	0.0693643
$763$	−14.4383	−0.522703
$764$	26.8455	0.971235
$765$	20.9073	0.755904
$766$	41.9556	1.51592
$767$	1.51589	0.0547357
$768$	−1.42831	−0.0515396
$769$	16.4096	0.591747	0.295874	−	0.955227i	$-0.404389\pi$
$769$	16.4096	0.591747	0.295874	+	0.955227i	$0.404389\pi$
$770$	7.58362	0.273295
$771$	−7.21300	−0.259770
$772$	10.9298	0.393372
$773$	−30.1231	−1.08345	−0.541726	−	0.840555i	$-0.682229\pi$
$773$	−30.1231	−1.08345	−0.541726	+	0.840555i	$0.682229\pi$
$774$	6.47666	0.232799
$775$	−9.06357	−0.325573
$776$	2.15183	0.0772460
$777$	−1.57444	−0.0564826
$778$	55.1681	1.97787
$779$	20.7441	0.743234
$780$	4.36799	0.156399
$781$	−42.4954	−1.52061
$782$	−21.5763	−0.771565
$783$	−12.0244	−0.429718
$784$	8.79315	0.314041
$785$	−2.87809	−0.102723
$786$	−1.83990	−0.0656272
$787$	−16.8814	−0.601757	−0.300878	−	0.953663i	$-0.597280\pi$
$787$	−16.8814	−0.601757	−0.300878	+	0.953663i	$0.597280\pi$
$788$	−54.0136	−1.92416
$789$	1.85470	0.0660292
$790$	21.3447	0.759411
$791$	−2.32894	−0.0828075
$792$	19.8174	0.704181
$793$	78.5791	2.79042
$794$	−46.0129	−1.63294
$795$	−0.227287	−0.00806104
$796$	−54.1373	−1.91884
$797$	−37.1911	−1.31738	−0.658688	−	0.752416i	$-0.728888\pi$
$797$	−37.1911	−1.31738	−0.658688	+	0.752416i	$0.728888\pi$
$798$	−3.58422	−0.126880
$799$	44.0891	1.55976
$800$	−7.12096	−0.251764
$801$	18.0555	0.637960
$802$	−9.27440	−0.327491
$803$	7.02877	0.248040
$804$	−0.173005	−0.00610140
$805$	−1.35391	−0.0477190
$806$	−115.906	−4.08262
$807$	2.71445	0.0955531
$808$	−8.02559	−0.282339
$809$	36.3933	1.27952	0.639760	−	0.768575i	$-0.279034\pi$
$809$	36.3933	1.27952	0.639760	+	0.768575i	$0.279034\pi$
$810$	18.5311	0.651116
$811$	11.7890	0.413968	0.206984	−	0.978344i	$-0.433635\pi$
$811$	11.7890	0.413968	0.206984	+	0.978344i	$0.433635\pi$
$812$	−22.0542	−0.773952
$813$	−3.82401	−0.134114
$814$	−46.6280	−1.63431
$815$	−14.8678	−0.520796
$816$	2.72735	0.0954765
$817$	−6.26433	−0.219161
$818$	−9.23912	−0.323038
$819$	16.7771	0.586240
$820$	9.54186	0.333216
$821$	−39.6755	−1.38469	−0.692343	−	0.721569i	$-0.743421\pi$
$821$	−39.6755	−1.38469	−0.692343	+	0.721569i	$0.743421\pi$
$822$	1.96848	0.0686587
$823$	17.3869	0.606068	0.303034	−	0.952980i	$-0.402000\pi$
$823$	17.3869	0.606068	0.303034	+	0.952980i	$0.402000\pi$
$824$	−22.1947	−0.773189
$825$	−0.909136	−0.0316521
$826$	−0.572164	−0.0199081
$827$	20.8700	0.725720	0.362860	−	0.931844i	$-0.381800\pi$
$827$	20.8700	0.725720	0.362860	+	0.931844i	$0.381800\pi$
$828$	−11.5656	−0.401933
$829$	11.5430	0.400904	0.200452	−	0.979703i	$-0.435759\pi$
$829$	11.5430	0.400904	0.200452	+	0.979703i	$0.435759\pi$
$830$	2.31891	0.0804906
$831$	−1.95892	−0.0679543
$832$	−74.1615	−2.57109
$833$	42.9518	1.48819
$834$	4.82396	0.167040
$835$	−19.6336	−0.679448
$836$	−62.6584	−2.16709
$837$	14.0797	0.486666
$838$	−2.07133	−0.0715528
$839$	29.6682	1.02426	0.512131	−	0.858908i	$-0.328856\pi$
$839$	29.6682	1.02426	0.512131	+	0.858908i	$0.328856\pi$
$840$	−0.504340	−0.0174014
$841$	30.9157	1.06606
$842$	33.5707	1.15692
$843$	1.28402	0.0442241
$844$	17.0794	0.587898
$845$	20.5015	0.705272
$846$	40.0370	1.37650
$847$	−1.03819	−0.0356726
$848$	1.26713	0.0435135
$849$	8.23112	0.282491
$850$	−15.7578	−0.540489
$851$	8.32453	0.285361
$852$	9.23845	0.316504
$853$	5.54118	0.189726	0.0948632	−	0.995490i	$-0.469759\pi$
$853$	5.54118	0.189726	0.0948632	+	0.995490i	$0.469759\pi$
$854$	−29.6592	−1.01492
$855$	−18.3633	−0.628011
$856$	−25.7205	−0.879110
$857$	−15.6903	−0.535970	−0.267985	−	0.963423i	$-0.586358\pi$
$857$	−15.6903	−0.535970	−0.267985	+	0.963423i	$0.586358\pi$
$858$	−11.6261	−0.396910
$859$	−17.1962	−0.586727	−0.293364	−	0.956001i	$-0.594775\pi$
$859$	−17.1962	−0.586727	−0.293364	+	0.956001i	$0.594775\pi$
$860$	−2.88146	−0.0982570
$861$	−0.857562	−0.0292256
$862$	1.43717	0.0489503
$863$	−0.805293	−0.0274125	−0.0137063	−	0.999906i	$-0.504363\pi$
$863$	−0.805293	−0.0274125	−0.0137063	+	0.999906i	$0.504363\pi$
$864$	11.0620	0.376336
$865$	−12.6607	−0.430478
$866$	44.5960	1.51544
$867$	8.86998	0.301240
$868$	25.8239	0.876519
$869$	−33.5358	−1.13762
$870$	4.47901	0.151853
$871$	−1.32691	−0.0449605
$872$	28.4372	0.963004
$873$	−3.23896	−0.109622
$874$	18.9509	0.641023
$875$	−0.988801	−0.0334276
$876$	−1.52804	−0.0516278
$877$	−21.0222	−0.709870	−0.354935	−	0.934891i	$-0.615497\pi$
$877$	−21.0222	−0.709870	−0.354935	+	0.934891i	$0.615497\pi$
$878$	−64.9584	−2.19224
$879$	−0.904552	−0.0305098
$880$	5.06847	0.170858
$881$	37.1848	1.25279	0.626395	−	0.779506i	$-0.284530\pi$
$881$	37.1848	1.25279	0.626395	+	0.779506i	$0.284530\pi$
$882$	39.0042	1.31334
$883$	−45.7461	−1.53948	−0.769739	−	0.638359i	$-0.779614\pi$
$883$	−45.7461	−1.53948	−0.769739	+	0.638359i	$0.779614\pi$
$884$	−118.950	−4.00074
$885$	0.0685919	0.00230569
$886$	76.3624	2.56545
$887$	−28.6685	−0.962594	−0.481297	−	0.876558i	$-0.659834\pi$
$887$	−28.6685	−0.962594	−0.481297	+	0.876558i	$0.659834\pi$
$888$	3.10094	0.104061
$889$	−3.27198	−0.109739
$890$	−13.6084	−0.456156
$891$	−29.1151	−0.975394
$892$	−24.8488	−0.832001
$893$	−38.7244	−1.29586
$894$	8.66221	0.289708
$895$	−5.10704	−0.170709
$896$	13.9093	0.464678
$897$	2.07562	0.0693030
$898$	15.9829	0.533355
$899$	−70.1568	−2.33986
$900$	−8.44674	−0.281558
$901$	6.18956	0.206204
$902$	−25.3973	−0.845638
$903$	0.258968	0.00861790
$904$	4.58698	0.152561
$905$	16.5533	0.550251
$906$	−9.31610	−0.309507
$907$	16.6413	0.552566	0.276283	−	0.961076i	$-0.410897\pi$
$907$	16.6413	0.552566	0.276283	+	0.961076i	$0.410897\pi$
$908$	−9.16397	−0.304117
$909$	12.0802	0.400676
$910$	−12.6449	−0.419175
$911$	−26.1115	−0.865112	−0.432556	−	0.901607i	$-0.642388\pi$
$911$	−26.1115	−0.865112	−0.432556	+	0.901607i	$0.642388\pi$
$912$	−2.39549	−0.0793227
$913$	−3.64336	−0.120578
$914$	−21.9509	−0.726072
$915$	3.55559	0.117544
$916$	−64.9013	−2.14440
$917$	3.14408	0.103827
$918$	24.4788	0.807921
$919$	35.3733	1.16686	0.583429	−	0.812164i	$-0.301711\pi$
$919$	35.3733	1.16686	0.583429	+	0.812164i	$0.301711\pi$
$920$	2.66660	0.0879152
$921$	8.69486	0.286505
$922$	−9.59763	−0.316081
$923$	70.8569	2.33228
$924$	2.59030	0.0852147
$925$	6.07967	0.199898
$926$	7.09301	0.233091
$927$	33.4078	1.09725
$928$	−55.1200	−1.80940
$929$	−58.3105	−1.91311	−0.956553	−	0.291559i	$-0.905826\pi$
$929$	−58.3105	−1.91311	−0.956553	+	0.291559i	$0.905826\pi$
$930$	−5.24458	−0.171977
$931$	−37.7255	−1.23640
$932$	20.5237	0.672276
$933$	1.13578	0.0371836
$934$	38.2141	1.25040
$935$	24.7579	0.809670
$936$	−33.0435	−1.08006
$937$	−44.7746	−1.46272	−0.731362	−	0.681990i	$-0.761115\pi$
$937$	−44.7746	−1.46272	−0.731362	+	0.681990i	$0.761115\pi$
$938$	0.500833	0.0163528
$939$	4.81460	0.157119
$940$	−17.8124	−0.580977
$941$	−11.8845	−0.387424	−0.193712	−	0.981058i	$-0.562053\pi$
$941$	−11.8845	−0.387424	−0.193712	+	0.981058i	$0.562053\pi$
$942$	−1.66539	−0.0542613
$943$	4.53419	0.147654
$944$	−0.382402	−0.0124461
$945$	1.53604	0.0499675
$946$	7.66951	0.249357
$947$	19.2420	0.625281	0.312641	−	0.949871i	$-0.398786\pi$
$947$	19.2420	0.625281	0.312641	+	0.949871i	$0.398786\pi$
$948$	7.29063	0.236789
$949$	−11.7198	−0.380440
$950$	13.8404	0.449042
$951$	1.59099	0.0515912
$952$	13.7344	0.445133
$953$	31.5462	1.02188	0.510940	−	0.859616i	$-0.329297\pi$
$953$	31.5462	1.02188	0.510940	+	0.859616i	$0.329297\pi$
$954$	5.62069	0.181976
$955$	9.31662	0.301479
$956$	−81.6471	−2.64066
$957$	−7.03719	−0.227480
$958$	13.0381	0.421242
$959$	−3.36380	−0.108623
$960$	−3.35570	−0.108305
$961$	51.1483	1.64995
$962$	77.7475	2.50668
$963$	38.7149	1.24757
$964$	23.2252	0.748032
$965$	3.79315	0.122106
$966$	−0.783430	−0.0252064
$967$	19.0405	0.612302	0.306151	−	0.951983i	$-0.400959\pi$
$967$	19.0405	0.612302	0.306151	+	0.951983i	$0.400959\pi$
$968$	2.04477	0.0657215
$969$	−11.7012	−0.375898
$970$	2.44120	0.0783823
$971$	42.0227	1.34857	0.674286	−	0.738470i	$-0.264451\pi$
$971$	42.0227	1.34857	0.674286	+	0.738470i	$0.264451\pi$
$972$	19.7581	0.633742
$973$	−8.24331	−0.264268
$974$	86.9647	2.78653
$975$	1.51589	0.0485474
$976$	−19.8225	−0.634503
$977$	−16.7234	−0.535028	−0.267514	−	0.963554i	$-0.586202\pi$
$977$	−16.7234	−0.535028	−0.267514	+	0.963554i	$0.586202\pi$
$978$	−8.60316	−0.275099
$979$	21.3809	0.683337
$980$	−17.3529	−0.554319
$981$	−42.8040	−1.36663
$982$	−9.62991	−0.307303
$983$	−14.4984	−0.462427	−0.231213	−	0.972903i	$-0.574270\pi$
$983$	−14.4984	−0.462427	−0.231213	+	0.972903i	$0.574270\pi$
$984$	1.68902	0.0538440
$985$	−18.7452	−0.597272
$986$	−121.974	−3.88444
$987$	1.60087	0.0509562
$988$	104.477	3.32384
$989$	−1.36924	−0.0435393
$990$	22.4825	0.714539
$991$	−14.3810	−0.456828	−0.228414	−	0.973564i	$-0.573354\pi$
$991$	−14.3810	−0.456828	−0.228414	+	0.973564i	$0.573354\pi$
$992$	64.5414	2.04919
$993$	0.480736	0.0152557
$994$	−26.7445	−0.848283
$995$	−18.7881	−0.595624
$996$	0.792061	0.0250974
$997$	36.5886	1.15877	0.579386	−	0.815053i	$-0.303292\pi$
$997$	36.5886	1.15877	0.579386	+	0.815053i	$0.303292\pi$
$998$	56.7593	1.79668
$999$	−9.44439	−0.298807

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	215.2.a.c.1.4	✓	5
3.2	odd	2		1935.2.a.u.1.2		5
4.3	odd	2		3440.2.a.w.1.3		5
5.2	odd	4		1075.2.b.h.474.8		10
5.3	odd	4		1075.2.b.h.474.3		10
5.4	even	2		1075.2.a.m.1.2		5
15.14	odd	2		9675.2.a.ch.1.4		5
43.42	odd	2		9245.2.a.l.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
215.2.a.c.1.4	✓	5	1.1	even	1	trivial
1075.2.a.m.1.2		5	5.4	even	2
1075.2.b.h.474.3		10	5.3	odd	4
1075.2.b.h.474.8		10	5.2	odd	4
1935.2.a.u.1.2		5	3.2	odd	2
3440.2.a.w.1.3		5	4.3	odd	2
9245.2.a.l.1.2		5	43.42	odd	2
9675.2.a.ch.1.4		5	15.14	odd	2

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:	\( N \)	\(=\)	\( 215 = 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	215.a (trivial)

\(f(q)\)	\(=\)	\(q+2.20940 q^{2} +0.261901 q^{3} +2.88146 q^{4} +1.00000 q^{5} +0.578644 q^{6} -0.988801 q^{7} +1.94750 q^{8} -2.93141 q^{9} +O(q^{10})\)	\(q+2.20940 q^{2} +0.261901 q^{3} +2.88146 q^{4} +1.00000 q^{5} +0.578644 q^{6} -0.988801 q^{7} +1.94750 q^{8} -2.93141 q^{9} +2.20940 q^{10} -3.47130 q^{11} +0.754656 q^{12} +5.78805 q^{13} -2.18466 q^{14} +0.261901 q^{15} -1.46010 q^{16} -7.13216 q^{17} -6.47666 q^{18} +6.26433 q^{19} +2.88146 q^{20} -0.258968 q^{21} -7.66951 q^{22} +1.36924 q^{23} +0.510052 q^{24} +1.00000 q^{25} +12.7881 q^{26} -1.55344 q^{27} -2.84919 q^{28} +7.74052 q^{29} +0.578644 q^{30} -9.06357 q^{31} -7.12096 q^{32} -0.909136 q^{33} -15.7578 q^{34} -0.988801 q^{35} -8.44674 q^{36} +6.07967 q^{37} +13.8404 q^{38} +1.51589 q^{39} +1.94750 q^{40} +3.31147 q^{41} -0.572164 q^{42} -1.00000 q^{43} -10.0024 q^{44} -2.93141 q^{45} +3.02520 q^{46} -6.18173 q^{47} -0.382402 q^{48} -6.02227 q^{49} +2.20940 q^{50} -1.86792 q^{51} +16.6780 q^{52} -0.867837 q^{53} -3.43217 q^{54} -3.47130 q^{55} -1.92569 q^{56} +1.64063 q^{57} +17.1019 q^{58} +0.261901 q^{59} +0.754656 q^{60} +13.5761 q^{61} -20.0251 q^{62} +2.89858 q^{63} -12.8129 q^{64} +5.78805 q^{65} -2.00865 q^{66} -0.229250 q^{67} -20.5510 q^{68} +0.358605 q^{69} -2.18466 q^{70} +12.2419 q^{71} -5.70892 q^{72} -2.02482 q^{73} +13.4324 q^{74} +0.261901 q^{75} +18.0504 q^{76} +3.43243 q^{77} +3.34922 q^{78} +9.66086 q^{79} -1.46010 q^{80} +8.38738 q^{81} +7.31636 q^{82} +1.04956 q^{83} -0.746205 q^{84} -7.13216 q^{85} -2.20940 q^{86} +2.02725 q^{87} -6.76037 q^{88} -6.15933 q^{89} -6.47666 q^{90} -5.72323 q^{91} +3.94541 q^{92} -2.37375 q^{93} -13.6579 q^{94} +6.26433 q^{95} -1.86498 q^{96} +1.10492 q^{97} -13.3056 q^{98} +10.1758 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 2 q^{2} - q^{3} + 8 q^{4} + 5 q^{5} - 12 q^{6} + 5 q^{7} + 3 q^{8} + 18 q^{9}+O(q^{10}) \) 5 * q + 2 * q^2 - q^3 + 8 * q^4 + 5 * q^5 - 12 * q^6 + 5 * q^7 + 3 * q^8 + 18 * q^9	\( 5 q + 2 q^{2} - q^{3} + 8 q^{4} + 5 q^{5} - 12 q^{6} + 5 q^{7} + 3 q^{8} + 18 q^{9} + 2 q^{10} - 6 q^{11} + 5 q^{13} + q^{14} - q^{15} + 14 q^{16} - 17 q^{17} - 5 q^{18} - 6 q^{19} + 8 q^{20} + 20 q^{21} - 8 q^{22} + q^{23} - 45 q^{24} + 5 q^{25} + 22 q^{26} - 22 q^{27} + 26 q^{28} + 6 q^{29} - 12 q^{30} + 6 q^{31} - 7 q^{32} - 20 q^{33} + 5 q^{35} + 36 q^{36} + 5 q^{37} - 16 q^{38} - 14 q^{39} + 3 q^{40} + 2 q^{41} - 58 q^{42} - 5 q^{43} - 15 q^{44} + 18 q^{45} - 14 q^{46} - 3 q^{48} + 18 q^{49} + 2 q^{50} - 10 q^{51} - 38 q^{52} - 23 q^{53} - 56 q^{54} - 6 q^{55} - 19 q^{56} + 28 q^{57} + 12 q^{58} - q^{59} + 20 q^{61} - 3 q^{62} + 26 q^{63} - 25 q^{64} + 5 q^{65} + 13 q^{66} + 21 q^{67} - 48 q^{68} + 10 q^{69} + q^{70} + 4 q^{71} + 20 q^{72} + 5 q^{73} + 24 q^{74} - q^{75} + 32 q^{76} - 26 q^{77} + 88 q^{78} + 41 q^{79} + 14 q^{80} + 41 q^{81} + 38 q^{82} - 7 q^{83} - 33 q^{84} - 17 q^{85} - 2 q^{86} - 40 q^{87} + 12 q^{88} + 20 q^{89} - 5 q^{90} - 42 q^{91} - 52 q^{92} - 36 q^{93} - 42 q^{94} - 6 q^{95} + 9 q^{96} + 37 q^{97} - 26 q^{98} + 12 q^{99}+O(q^{100}) \) 5 * q + 2 * q^2 - q^3 + 8 * q^4 + 5 * q^5 - 12 * q^6 + 5 * q^7 + 3 * q^8 + 18 * q^9 + 2 * q^10 - 6 * q^11 + 5 * q^13 + q^14 - q^15 + 14 * q^16 - 17 * q^17 - 5 * q^18 - 6 * q^19 + 8 * q^20 + 20 * q^21 - 8 * q^22 + q^23 - 45 * q^24 + 5 * q^25 + 22 * q^26 - 22 * q^27 + 26 * q^28 + 6 * q^29 - 12 * q^30 + 6 * q^31 - 7 * q^32 - 20 * q^33 + 5 * q^35 + 36 * q^36 + 5 * q^37 - 16 * q^38 - 14 * q^39 + 3 * q^40 + 2 * q^41 - 58 * q^42 - 5 * q^43 - 15 * q^44 + 18 * q^45 - 14 * q^46 - 3 * q^48 + 18 * q^49 + 2 * q^50 - 10 * q^51 - 38 * q^52 - 23 * q^53 - 56 * q^54 - 6 * q^55 - 19 * q^56 + 28 * q^57 + 12 * q^58 - q^59 + 20 * q^61 - 3 * q^62 + 26 * q^63 - 25 * q^64 + 5 * q^65 + 13 * q^66 + 21 * q^67 - 48 * q^68 + 10 * q^69 + q^70 + 4 * q^71 + 20 * q^72 + 5 * q^73 + 24 * q^74 - q^75 + 32 * q^76 - 26 * q^77 + 88 * q^78 + 41 * q^79 + 14 * q^80 + 41 * q^81 + 38 * q^82 - 7 * q^83 - 33 * q^84 - 17 * q^85 - 2 * q^86 - 40 * q^87 + 12 * q^88 + 20 * q^89 - 5 * q^90 - 42 * q^91 - 52 * q^92 - 36 * q^93 - 42 * q^94 - 6 * q^95 + 9 * q^96 + 37 * q^97 - 26 * q^98 + 12 * q^99

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