LMFDB - Embedded newform 6013.2.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6013,2,Mod(1,6013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6013, 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("6013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6013 = 7 \cdot 859 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6013.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:	$48.0140467354$
Analytic rank:	$1$
Dimension:	$104$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	6013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.80884 q^{2} +0.402205 q^{3} +5.88959 q^{4} +2.13491 q^{5} -1.12973 q^{6} +1.00000 q^{7} -10.9252 q^{8} -2.83823 q^{9} +O(q^{10})$	\(q-2.80884 q^{2} +0.402205 q^{3} +5.88959 q^{4} +2.13491 q^{5} -1.12973 q^{6} +1.00000 q^{7} -10.9252 q^{8} -2.83823 q^{9} -5.99663 q^{10} -1.23558 q^{11} +2.36882 q^{12} +6.48478 q^{13} -2.80884 q^{14} +0.858673 q^{15} +18.9081 q^{16} +3.21777 q^{17} +7.97214 q^{18} -0.699472 q^{19} +12.5738 q^{20} +0.402205 q^{21} +3.47056 q^{22} +3.50363 q^{23} -4.39419 q^{24} -0.442149 q^{25} -18.2147 q^{26} -2.34817 q^{27} +5.88959 q^{28} -3.81011 q^{29} -2.41188 q^{30} -6.49620 q^{31} -31.2594 q^{32} -0.496958 q^{33} -9.03822 q^{34} +2.13491 q^{35} -16.7160 q^{36} -0.935098 q^{37} +1.96471 q^{38} +2.60821 q^{39} -23.3245 q^{40} -7.17691 q^{41} -1.12973 q^{42} -5.22719 q^{43} -7.27708 q^{44} -6.05937 q^{45} -9.84116 q^{46} -10.9881 q^{47} +7.60494 q^{48} +1.00000 q^{49} +1.24193 q^{50} +1.29421 q^{51} +38.1927 q^{52} +6.66871 q^{53} +6.59563 q^{54} -2.63786 q^{55} -10.9252 q^{56} -0.281331 q^{57} +10.7020 q^{58} -9.88444 q^{59} +5.05723 q^{60} -8.59996 q^{61} +18.2468 q^{62} -2.83823 q^{63} +49.9865 q^{64} +13.8444 q^{65} +1.39588 q^{66} -15.0280 q^{67} +18.9514 q^{68} +1.40918 q^{69} -5.99663 q^{70} -12.3597 q^{71} +31.0084 q^{72} -5.58671 q^{73} +2.62654 q^{74} -0.177835 q^{75} -4.11960 q^{76} -1.23558 q^{77} -7.32605 q^{78} +4.39586 q^{79} +40.3672 q^{80} +7.57025 q^{81} +20.1588 q^{82} -8.42086 q^{83} +2.36882 q^{84} +6.86967 q^{85} +14.6824 q^{86} -1.53245 q^{87} +13.4991 q^{88} -3.33813 q^{89} +17.0198 q^{90} +6.48478 q^{91} +20.6350 q^{92} -2.61281 q^{93} +30.8639 q^{94} -1.49331 q^{95} -12.5727 q^{96} +6.50349 q^{97} -2.80884 q^{98} +3.50687 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 104 q - 17 q^{2} - 34 q^{3} + 99 q^{4} - 46 q^{5} - 18 q^{6} + 104 q^{7} - 48 q^{8} + 98 q^{9}+O(q^{10}) $ 104 * q - 17 * q^2 - 34 * q^3 + 99 * q^4 - 46 * q^5 - 18 * q^6 + 104 * q^7 - 48 * q^8 + 98 * q^9	\( 104 q - 17 q^{2} - 34 q^{3} + 99 q^{4} - 46 q^{5} - 18 q^{6} + 104 q^{7} - 48 q^{8} + 98 q^{9} - 17 q^{10} - 46 q^{11} - 62 q^{12} - 37 q^{13} - 17 q^{14} - 17 q^{15} + 93 q^{16} - 75 q^{17} - 41 q^{18} - 40 q^{19} - 106 q^{20} - 34 q^{21} - 14 q^{22} - 57 q^{23} - 38 q^{24} + 102 q^{25} - 45 q^{26} - 121 q^{27} + 99 q^{28} - 29 q^{29} + 26 q^{30} - 42 q^{31} - 113 q^{32} - 42 q^{33} - 7 q^{34} - 46 q^{35} + 99 q^{36} - 31 q^{37} - 62 q^{38} - 9 q^{39} - 36 q^{40} - 106 q^{41} - 18 q^{42} - 29 q^{43} - 60 q^{44} - 121 q^{45} + 21 q^{46} - 141 q^{47} - 88 q^{48} + 104 q^{49} - 70 q^{50} - 2 q^{51} - 58 q^{52} - 70 q^{53} - 49 q^{54} - 14 q^{55} - 48 q^{56} - 11 q^{57} - 28 q^{58} - 202 q^{59} + 17 q^{60} - 79 q^{61} - 41 q^{62} + 98 q^{63} + 110 q^{64} - 34 q^{65} - 21 q^{66} - 57 q^{67} - 180 q^{68} - 99 q^{69} - 17 q^{70} - 109 q^{71} - 73 q^{72} - 46 q^{73} - 7 q^{74} - 146 q^{75} - 54 q^{76} - 46 q^{77} - 42 q^{78} - 12 q^{79} - 187 q^{80} + 100 q^{81} - 45 q^{82} - 156 q^{83} - 62 q^{84} - 13 q^{85} - 8 q^{86} - 76 q^{87} - 6 q^{88} - 140 q^{89} - 5 q^{90} - 37 q^{91} - 98 q^{92} - q^{93} - 17 q^{94} - 48 q^{95} - 12 q^{96} - 63 q^{97} - 17 q^{98} - 78 q^{99}+O(q^{100}) \) 104 * q - 17 * q^2 - 34 * q^3 + 99 * q^4 - 46 * q^5 - 18 * q^6 + 104 * q^7 - 48 * q^8 + 98 * q^9 - 17 * q^10 - 46 * q^11 - 62 * q^12 - 37 * q^13 - 17 * q^14 - 17 * q^15 + 93 * q^16 - 75 * q^17 - 41 * q^18 - 40 * q^19 - 106 * q^20 - 34 * q^21 - 14 * q^22 - 57 * q^23 - 38 * q^24 + 102 * q^25 - 45 * q^26 - 121 * q^27 + 99 * q^28 - 29 * q^29 + 26 * q^30 - 42 * q^31 - 113 * q^32 - 42 * q^33 - 7 * q^34 - 46 * q^35 + 99 * q^36 - 31 * q^37 - 62 * q^38 - 9 * q^39 - 36 * q^40 - 106 * q^41 - 18 * q^42 - 29 * q^43 - 60 * q^44 - 121 * q^45 + 21 * q^46 - 141 * q^47 - 88 * q^48 + 104 * q^49 - 70 * q^50 - 2 * q^51 - 58 * q^52 - 70 * q^53 - 49 * q^54 - 14 * q^55 - 48 * q^56 - 11 * q^57 - 28 * q^58 - 202 * q^59 + 17 * q^60 - 79 * q^61 - 41 * q^62 + 98 * q^63 + 110 * q^64 - 34 * q^65 - 21 * q^66 - 57 * q^67 - 180 * q^68 - 99 * q^69 - 17 * q^70 - 109 * q^71 - 73 * q^72 - 46 * q^73 - 7 * q^74 - 146 * q^75 - 54 * q^76 - 46 * q^77 - 42 * q^78 - 12 * q^79 - 187 * q^80 + 100 * q^81 - 45 * q^82 - 156 * q^83 - 62 * q^84 - 13 * q^85 - 8 * q^86 - 76 * q^87 - 6 * q^88 - 140 * q^89 - 5 * q^90 - 37 * q^91 - 98 * q^92 - q^93 - 17 * q^94 - 48 * q^95 - 12 * q^96 - 63 * q^97 - 17 * q^98 - 78 * 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 $

$2$	−2.80884	−1.98615	−0.993076	−	0.117477i	$-0.962519\pi$
$2$	−2.80884	−1.98615	−0.993076	+	0.117477i	$0.962519\pi$
$3$	0.402205	0.232213	0.116107	−	0.993237i	$-0.462959\pi$
$3$	0.402205	0.232213	0.116107	+	0.993237i	$0.462959\pi$
$4$	5.88959	2.94480
$5$	2.13491	0.954762	0.477381	−	0.878696i	$-0.341586\pi$
$5$	2.13491	0.954762	0.477381	+	0.878696i	$0.341586\pi$
$6$	−1.12973	−0.461211
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−10.9252	−3.86266
$9$	−2.83823	−0.946077
$10$	−5.99663	−1.89630
$11$	−1.23558	−0.372542	−0.186271	−	0.982498i	$-0.559640\pi$
$11$	−1.23558	−0.372542	−0.186271	+	0.982498i	$0.559640\pi$
$12$	2.36882	0.683821
$13$	6.48478	1.79855	0.899277	−	0.437380i	$-0.144093\pi$
$13$	6.48478	1.79855	0.899277	+	0.437380i	$0.144093\pi$
$14$	−2.80884	−0.750695
$15$	0.858673	0.221708
$16$	18.9081	4.72703
$17$	3.21777	0.780425	0.390212	−	0.920725i	$-0.372402\pi$
$17$	3.21777	0.780425	0.390212	+	0.920725i	$0.372402\pi$
$18$	7.97214	1.87905
$19$	−0.699472	−0.160470	−0.0802349	−	0.996776i	$-0.525567\pi$
$19$	−0.699472	−0.160470	−0.0802349	+	0.996776i	$0.525567\pi$
$20$	12.5738	2.81158
$21$	0.402205	0.0877683
$22$	3.47056	0.739925
$23$	3.50363	0.730558	0.365279	−	0.930898i	$-0.380974\pi$
$23$	3.50363	0.730558	0.365279	+	0.930898i	$0.380974\pi$
$24$	−4.39419	−0.896960
$25$	−0.442149	−0.0884298
$26$	−18.2147	−3.57220
$27$	−2.34817	−0.451905
$28$	5.88959	1.11303
$29$	−3.81011	−0.707520	−0.353760	−	0.935336i	$-0.615097\pi$
$29$	−3.81011	−0.707520	−0.353760	+	0.935336i	$0.615097\pi$
$30$	−2.41188	−0.440346
$31$	−6.49620	−1.16675	−0.583376	−	0.812202i	$-0.698269\pi$
$31$	−6.49620	−1.16675	−0.583376	+	0.812202i	$0.698269\pi$
$32$	−31.2594	−5.52593
$33$	−0.496958	−0.0865093
$34$	−9.03822	−1.55004
$35$	2.13491	0.360866
$36$	−16.7160	−2.78600
$37$	−0.935098	−0.153729	−0.0768646	−	0.997042i	$-0.524491\pi$
$37$	−0.935098	−0.153729	−0.0768646	+	0.997042i	$0.524491\pi$
$38$	1.96471	0.318717
$39$	2.60821	0.417648
$40$	−23.3245	−3.68792
$41$	−7.17691	−1.12085	−0.560423	−	0.828207i	$-0.689361\pi$
$41$	−7.17691	−1.12085	−0.560423	+	0.828207i	$0.689361\pi$
$42$	−1.12973	−0.174321
$43$	−5.22719	−0.797139	−0.398570	−	0.917138i	$-0.630493\pi$
$43$	−5.22719	−0.797139	−0.398570	+	0.917138i	$0.630493\pi$
$44$	−7.27708	−1.09706
$45$	−6.05937	−0.903278
$46$	−9.84116	−1.45100
$47$	−10.9881	−1.60278	−0.801392	−	0.598140i	$-0.795907\pi$
$47$	−10.9881	−1.60278	−0.801392	+	0.598140i	$0.795907\pi$
$48$	7.60494	1.09768
$49$	1.00000	0.142857
$50$	1.24193	0.175635
$51$	1.29421	0.181225
$52$	38.1927	5.29637
$53$	6.66871	0.916018	0.458009	−	0.888948i	$-0.348563\pi$
$53$	6.66871	0.916018	0.458009	+	0.888948i	$0.348563\pi$
$54$	6.59563	0.897551
$55$	−2.63786	−0.355689
$56$	−10.9252	−1.45995
$57$	−0.281331	−0.0372632
$58$	10.7020	1.40524
$59$	−9.88444	−1.28684	−0.643422	−	0.765511i	$-0.722486\pi$
$59$	−9.88444	−1.28684	−0.643422	+	0.765511i	$0.722486\pi$
$60$	5.05723	0.652886
$61$	−8.59996	−1.10111	−0.550556	−	0.834798i	$-0.685584\pi$
$61$	−8.59996	−1.10111	−0.550556	+	0.834798i	$0.685584\pi$
$62$	18.2468	2.31735
$63$	−2.83823	−0.357584
$64$	49.9865	6.24831
$65$	13.8444	1.71719
$66$	1.39588	0.171820
$67$	−15.0280	−1.83596	−0.917979	−	0.396628i	$-0.870180\pi$
$67$	−15.0280	−1.83596	−0.917979	+	0.396628i	$0.870180\pi$
$68$	18.9514	2.29819
$69$	1.40918	0.169645
$70$	−5.99663	−0.716735
$71$	−12.3597	−1.46683	−0.733415	−	0.679781i	$-0.762075\pi$
$71$	−12.3597	−1.46683	−0.733415	+	0.679781i	$0.762075\pi$
$72$	31.0084	3.65437
$73$	−5.58671	−0.653876	−0.326938	−	0.945046i	$-0.606017\pi$
$73$	−5.58671	−0.653876	−0.326938	+	0.945046i	$0.606017\pi$
$74$	2.62654	0.305330
$75$	−0.177835	−0.0205346
$76$	−4.11960	−0.472551
$77$	−1.23558	−0.140808
$78$	−7.32605	−0.829512
$79$	4.39586	0.494572	0.247286	−	0.968942i	$-0.420461\pi$
$79$	4.39586	0.494572	0.247286	+	0.968942i	$0.420461\pi$
$80$	40.3672	4.51319
$81$	7.57025	0.841139
$82$	20.1588	2.22617
$83$	−8.42086	−0.924309	−0.462155	−	0.886799i	$-0.652923\pi$
$83$	−8.42086	−0.924309	−0.462155	+	0.886799i	$0.652923\pi$
$84$	2.36882	0.258460
$85$	6.86967	0.745120
$86$	14.6824	1.58324
$87$	−1.53245	−0.164296
$88$	13.4991	1.43900
$89$	−3.33813	−0.353841	−0.176920	−	0.984225i	$-0.556613\pi$
$89$	−3.33813	−0.353841	−0.176920	+	0.984225i	$0.556613\pi$
$90$	17.0198	1.79405
$91$	6.48478	0.679789
$92$	20.6350	2.15135
$93$	−2.61281	−0.270935
$94$	30.8639	3.18337
$95$	−1.49331	−0.153210
$96$	−12.5727	−1.28319
$97$	6.50349	0.660330	0.330165	−	0.943923i	$-0.392896\pi$
$97$	6.50349	0.660330	0.330165	+	0.943923i	$0.392896\pi$
$98$	−2.80884	−0.283736
$99$	3.50687	0.352454
$100$	−2.60408	−0.260408
$101$	−8.48409	−0.844198	−0.422099	−	0.906550i	$-0.638707\pi$
$101$	−8.48409	−0.844198	−0.422099	+	0.906550i	$0.638707\pi$
$102$	−3.63522	−0.359940
$103$	18.5653	1.82929	0.914647	−	0.404254i	$-0.132469\pi$
$103$	18.5653	1.82929	0.914647	+	0.404254i	$0.132469\pi$
$104$	−70.8478	−6.94720
$105$	0.858673	0.0837979
$106$	−18.7314	−1.81935
$107$	−9.24268	−0.893524	−0.446762	−	0.894653i	$-0.647423\pi$
$107$	−9.24268	−0.893524	−0.446762	+	0.894653i	$0.647423\pi$
$108$	−13.8297	−1.33077
$109$	10.2208	0.978973	0.489487	−	0.872011i	$-0.337184\pi$
$109$	10.2208	0.978973	0.489487	+	0.872011i	$0.337184\pi$
$110$	7.40934	0.706453
$111$	−0.376101	−0.0356980
$112$	18.9081	1.78665
$113$	12.5391	1.17958	0.589788	−	0.807558i	$-0.299211\pi$
$113$	12.5391	1.17958	0.589788	+	0.807558i	$0.299211\pi$
$114$	0.790214	0.0740104
$115$	7.47995	0.697509
$116$	−22.4400	−2.08350
$117$	−18.4053	−1.70157
$118$	27.7638	2.55587
$119$	3.21777	0.294973
$120$	−9.38121	−0.856384
$121$	−9.47333	−0.861212
$122$	24.1559	2.18697
$123$	−2.88659	−0.260275
$124$	−38.2600	−3.43585
$125$	−11.6185	−1.03919
$126$	7.97214	0.710215
$127$	−5.88417	−0.522135	−0.261068	−	0.965321i	$-0.584075\pi$
$127$	−5.88417	−0.522135	−0.261068	+	0.965321i	$0.584075\pi$
$128$	−77.8853	−6.88416
$129$	−2.10240	−0.185106
$130$	−38.8868	−3.41060
$131$	−14.1638	−1.23750	−0.618749	−	0.785589i	$-0.712360\pi$
$131$	−14.1638	−1.23750	−0.618749	+	0.785589i	$0.712360\pi$
$132$	−2.92688	−0.254752
$133$	−0.699472	−0.0606519
$134$	42.2112	3.64649
$135$	−5.01313	−0.431461
$136$	−35.1550	−3.01452
$137$	−13.8491	−1.18321	−0.591605	−	0.806228i	$-0.701506\pi$
$137$	−13.8491	−1.18321	−0.591605	+	0.806228i	$0.701506\pi$
$138$	−3.95816	−0.336941
$139$	10.9465	0.928469	0.464234	−	0.885712i	$-0.346330\pi$
$139$	10.9465	0.928469	0.464234	+	0.885712i	$0.346330\pi$
$140$	12.5738	1.06268
$141$	−4.41948	−0.372188
$142$	34.7165	2.91335
$143$	−8.01248	−0.670037
$144$	−53.6656	−4.47213
$145$	−8.13426	−0.675514
$146$	15.6922	1.29870
$147$	0.402205	0.0331733
$148$	−5.50735	−0.452701
$149$	11.4322	0.936558	0.468279	−	0.883581i	$-0.344874\pi$
$149$	11.4322	0.936558	0.468279	+	0.883581i	$0.344874\pi$
$150$	0.499509	0.0407848
$151$	−15.6870	−1.27659	−0.638294	−	0.769793i	$-0.720359\pi$
$151$	−15.6870	−1.27659	−0.638294	+	0.769793i	$0.720359\pi$
$152$	7.64190	0.619840
$153$	−9.13279	−0.738342
$154$	3.47056	0.279666
$155$	−13.8688	−1.11397
$156$	15.3613	1.22989
$157$	13.9167	1.11067	0.555335	−	0.831627i	$-0.312590\pi$
$157$	13.9167	1.11067	0.555335	+	0.831627i	$0.312590\pi$
$158$	−12.3473	−0.982295
$159$	2.68219	0.212711
$160$	−66.7361	−5.27595
$161$	3.50363	0.276125
$162$	−21.2636	−1.67063
$163$	−3.28302	−0.257146	−0.128573	−	0.991700i	$-0.541040\pi$
$163$	−3.28302	−0.257146	−0.128573	+	0.991700i	$0.541040\pi$
$164$	−42.2691	−3.30066
$165$	−1.06096	−0.0825957
$166$	23.6529	1.83582
$167$	−13.0860	−1.01262	−0.506312	−	0.862350i	$-0.668992\pi$
$167$	−13.0860	−1.01262	−0.506312	+	0.862350i	$0.668992\pi$
$168$	−4.39419	−0.339019
$169$	29.0523	2.23480
$170$	−19.2958	−1.47992
$171$	1.98526	0.151817
$172$	−30.7860	−2.34741
$173$	4.84763	0.368558	0.184279	−	0.982874i	$-0.441005\pi$
$173$	4.84763	0.368558	0.184279	+	0.982874i	$0.441005\pi$
$174$	4.30440	0.326316
$175$	−0.442149	−0.0334233
$176$	−23.3625	−1.76102
$177$	−3.97557	−0.298822
$178$	9.37627	0.702781
$179$	13.2525	0.990538	0.495269	−	0.868740i	$-0.335070\pi$
$179$	13.2525	0.990538	0.495269	+	0.868740i	$0.335070\pi$
$180$	−35.6872	−2.65997
$181$	5.21099	0.387330	0.193665	−	0.981068i	$-0.437963\pi$
$181$	5.21099	0.387330	0.193665	+	0.981068i	$0.437963\pi$
$182$	−18.2147	−1.35016
$183$	−3.45895	−0.255693
$184$	−38.2781	−2.82190
$185$	−1.99635	−0.146775
$186$	7.33896	0.538118
$187$	−3.97583	−0.290741
$188$	−64.7156	−4.71987
$189$	−2.34817	−0.170804
$190$	4.19447	0.304299
$191$	−11.4583	−0.829095	−0.414548	−	0.910028i	$-0.636060\pi$
$191$	−11.4583	−0.829095	−0.414548	+	0.910028i	$0.636060\pi$
$192$	20.1048	1.45094
$193$	−17.0573	−1.22781	−0.613906	−	0.789379i	$-0.710403\pi$
$193$	−17.0573	−1.22781	−0.613906	+	0.789379i	$0.710403\pi$
$194$	−18.2673	−1.31151
$195$	5.56830	0.398754
$196$	5.88959	0.420685
$197$	3.02056	0.215206	0.107603	−	0.994194i	$-0.465683\pi$
$197$	3.02056	0.215206	0.107603	+	0.994194i	$0.465683\pi$
$198$	−9.85024	−0.700026
$199$	11.8791	0.842084	0.421042	−	0.907041i	$-0.361664\pi$
$199$	11.8791	0.842084	0.421042	+	0.907041i	$0.361664\pi$
$200$	4.83059	0.341574
$201$	−6.04433	−0.426334
$202$	23.8305	1.67671
$203$	−3.81011	−0.267418
$204$	7.62234	0.533671
$205$	−15.3221	−1.07014
$206$	−52.1470	−3.63325
$207$	−9.94413	−0.691165
$208$	122.615	8.50182
$209$	0.864255	0.0597818
$210$	−2.41188	−0.166435
$211$	16.2220	1.11677	0.558384	−	0.829582i	$-0.311422\pi$
$211$	16.2220	1.11677	0.558384	+	0.829582i	$0.311422\pi$
$212$	39.2760	2.69749
$213$	−4.97115	−0.340617
$214$	25.9612	1.77467
$215$	−11.1596	−0.761078
$216$	25.6543	1.74555
$217$	−6.49620	−0.440991
$218$	−28.7086	−1.94439
$219$	−2.24701	−0.151839
$220$	−15.5359	−1.04743
$221$	20.8666	1.40364
$222$	1.05641	0.0709015
$223$	−2.46309	−0.164941	−0.0824703	−	0.996594i	$-0.526281\pi$
$223$	−2.46309	−0.164941	−0.0824703	+	0.996594i	$0.526281\pi$
$224$	−31.2594	−2.08861
$225$	1.25492	0.0836614
$226$	−35.2202	−2.34281
$227$	−3.00123	−0.199198	−0.0995992	−	0.995028i	$-0.531756\pi$
$227$	−3.00123	−0.199198	−0.0995992	+	0.995028i	$0.531756\pi$
$228$	−1.65693	−0.109733
$229$	−11.1367	−0.735932	−0.367966	−	0.929839i	$-0.619946\pi$
$229$	−11.1367	−0.735932	−0.367966	+	0.929839i	$0.619946\pi$
$230$	−21.0100	−1.38536
$231$	−0.496958	−0.0326974
$232$	41.6264	2.73291
$233$	−19.5058	−1.27787	−0.638934	−	0.769262i	$-0.720624\pi$
$233$	−19.5058	−1.27787	−0.638934	+	0.769262i	$0.720624\pi$
$234$	51.6976	3.37958
$235$	−23.4587	−1.53028
$236$	−58.2153	−3.78950
$237$	1.76804	0.114846
$238$	−9.03822	−0.585861
$239$	16.6789	1.07887	0.539435	−	0.842028i	$-0.318638\pi$
$239$	16.6789	1.07887	0.539435	+	0.842028i	$0.318638\pi$
$240$	16.2359	1.04802
$241$	29.1104	1.87516	0.937582	−	0.347763i	$-0.113059\pi$
$241$	29.1104	1.87516	0.937582	+	0.347763i	$0.113059\pi$
$242$	26.6091	1.71050
$243$	10.0893	0.647228
$244$	−50.6502	−3.24255
$245$	2.13491	0.136395
$246$	8.10797	0.516946
$247$	−4.53592	−0.288614
$248$	70.9726	4.50677
$249$	−3.38691	−0.214637
$250$	32.6346	2.06399
$251$	20.8679	1.31717	0.658585	−	0.752506i	$-0.271155\pi$
$251$	20.8679	1.31717	0.658585	+	0.752506i	$0.271155\pi$
$252$	−16.7160	−1.05301
$253$	−4.32903	−0.272164
$254$	16.5277	1.03704
$255$	2.76301	0.173027
$256$	118.795	7.42466
$257$	−12.7199	−0.793444	−0.396722	−	0.917939i	$-0.629852\pi$
$257$	−12.7199	−0.793444	−0.396722	+	0.917939i	$0.629852\pi$
$258$	5.90532	0.367649
$259$	−0.935098	−0.0581042
$260$	81.5381	5.05678
$261$	10.8140	0.669369
$262$	39.7839	2.45786
$263$	31.4811	1.94121	0.970605	−	0.240677i	$-0.0773696\pi$
$263$	31.4811	1.94121	0.970605	+	0.240677i	$0.0773696\pi$
$264$	5.42939	0.334156
$265$	14.2371	0.874579
$266$	1.96471	0.120464
$267$	−1.34261	−0.0821665
$268$	−88.5086	−5.40653
$269$	−26.7896	−1.63339	−0.816697	−	0.577067i	$-0.804197\pi$
$269$	−26.7896	−1.63339	−0.816697	+	0.577067i	$0.804197\pi$
$270$	14.0811	0.856948
$271$	18.4652	1.12168	0.560841	−	0.827924i	$-0.310478\pi$
$271$	18.4652	1.12168	0.560841	+	0.827924i	$0.310478\pi$
$272$	60.8420	3.68909
$273$	2.60821	0.157856
$274$	38.9000	2.35003
$275$	0.546312	0.0329439
$276$	8.29949	0.499571
$277$	−10.1068	−0.607259	−0.303629	−	0.952790i	$-0.598198\pi$
$277$	−10.1068	−0.607259	−0.303629	+	0.952790i	$0.598198\pi$
$278$	−30.7469	−1.84408
$279$	18.4377	1.10384
$280$	−23.3245	−1.39390
$281$	24.7220	1.47479	0.737394	−	0.675463i	$-0.236056\pi$
$281$	24.7220	1.47479	0.737394	+	0.675463i	$0.236056\pi$
$282$	12.4136	0.739221
$283$	1.63546	0.0972178	0.0486089	−	0.998818i	$-0.484521\pi$
$283$	1.63546	0.0972178	0.0486089	+	0.998818i	$0.484521\pi$
$284$	−72.7938	−4.31952
$285$	−0.600617	−0.0355775
$286$	22.5058	1.33080
$287$	−7.17691	−0.423640
$288$	88.7214	5.22796
$289$	−6.64593	−0.390937
$290$	22.8478	1.34167
$291$	2.61574	0.153337
$292$	−32.9035	−1.92553
$293$	18.3162	1.07004	0.535022	−	0.844838i	$-0.320303\pi$
$293$	18.3162	1.07004	0.535022	+	0.844838i	$0.320303\pi$
$294$	−1.12973	−0.0658872
$295$	−21.1024	−1.22863
$296$	10.2162	0.593804
$297$	2.90135	0.168354
$298$	−32.1111	−1.86015
$299$	22.7203	1.31395
$300$	−1.04737	−0.0604701
$301$	−5.22719	−0.301290
$302$	44.0622	2.53549
$303$	−3.41234	−0.196034
$304$	−13.2257	−0.758545
$305$	−18.3602	−1.05130
$306$	25.6526	1.46646
$307$	−30.7369	−1.75425	−0.877125	−	0.480263i	$-0.840541\pi$
$307$	−30.7369	−1.75425	−0.877125	+	0.480263i	$0.840541\pi$
$308$	−7.27708	−0.414650
$309$	7.46706	0.424786
$310$	38.9553	2.21251
$311$	19.2915	1.09392	0.546960	−	0.837159i	$-0.315785\pi$
$311$	19.2915	1.09392	0.546960	+	0.837159i	$0.315785\pi$
$312$	−28.4954	−1.61323
$313$	−23.1535	−1.30871	−0.654356	−	0.756186i	$-0.727060\pi$
$313$	−23.1535	−1.30871	−0.654356	+	0.756186i	$0.727060\pi$
$314$	−39.0897	−2.20596
$315$	−6.05937	−0.341407
$316$	25.8898	1.45641
$317$	−28.0752	−1.57686	−0.788429	−	0.615126i	$-0.789105\pi$
$317$	−28.0752	−1.57686	−0.788429	+	0.615126i	$0.789105\pi$
$318$	−7.53384	−0.422477
$319$	4.70771	0.263581
$320$	106.717	5.96565
$321$	−3.71745	−0.207488
$322$	−9.84116	−0.548426
$323$	−2.25074	−0.125235
$324$	44.5857	2.47698
$325$	−2.86724	−0.159046
$326$	9.22149	0.510731
$327$	4.11085	0.227331
$328$	78.4095	4.32944
$329$	−10.9881	−0.605795
$330$	2.98007	0.164048
$331$	−7.67343	−0.421770	−0.210885	−	0.977511i	$-0.567635\pi$
$331$	−7.67343	−0.421770	−0.210885	+	0.977511i	$0.567635\pi$
$332$	−49.5954	−2.72190
$333$	2.65403	0.145440
$334$	36.7565	2.01122
$335$	−32.0834	−1.75290
$336$	7.60494	0.414883
$337$	27.8164	1.51525	0.757627	−	0.652688i	$-0.226359\pi$
$337$	27.8164	1.51525	0.757627	+	0.652688i	$0.226359\pi$
$338$	−81.6034	−4.43864
$339$	5.04327	0.273913
$340$	40.4595	2.19423
$341$	8.02660	0.434665
$342$	−5.57629	−0.301531
$343$	1.00000	0.0539949
$344$	57.1084	3.07908
$345$	3.00848	0.161971
$346$	−13.6162	−0.732012
$347$	−14.9114	−0.800485	−0.400243	−	0.916409i	$-0.631074\pi$
$347$	−14.9114	−0.800485	−0.400243	+	0.916409i	$0.631074\pi$
$348$	−9.02549	−0.483817
$349$	32.5218	1.74085	0.870427	−	0.492297i	$-0.163843\pi$
$349$	32.5218	1.74085	0.870427	+	0.492297i	$0.163843\pi$
$350$	1.24193	0.0663838
$351$	−15.2273	−0.812775
$352$	38.6236	2.05864
$353$	24.3870	1.29799	0.648995	−	0.760792i	$-0.275189\pi$
$353$	24.3870	1.29799	0.648995	+	0.760792i	$0.275189\pi$
$354$	11.1668	0.593506
$355$	−26.3869	−1.40047
$356$	−19.6602	−1.04199
$357$	1.29421	0.0684966
$358$	−37.2241	−1.96736
$359$	−18.1269	−0.956699	−0.478349	−	0.878170i	$-0.658765\pi$
$359$	−18.1269	−0.956699	−0.478349	+	0.878170i	$0.658765\pi$
$360$	66.2002	3.48906
$361$	−18.5107	−0.974249
$362$	−14.6368	−0.769295
$363$	−3.81022	−0.199985
$364$	38.1927	2.00184
$365$	−11.9271	−0.624295
$366$	9.71563	0.507844
$367$	−4.80503	−0.250821	−0.125410	−	0.992105i	$-0.540025\pi$
$367$	−4.80503	−0.250821	−0.125410	+	0.992105i	$0.540025\pi$
$368$	66.2471	3.45337
$369$	20.3697	1.06041
$370$	5.60744	0.291517
$371$	6.66871	0.346222
$372$	−15.3884	−0.797849
$373$	−28.7825	−1.49030	−0.745151	−	0.666895i	$-0.767623\pi$
$373$	−28.7825	−1.49030	−0.745151	+	0.666895i	$0.767623\pi$
$374$	11.1675	0.577456
$375$	−4.67302	−0.241314
$376$	120.048	6.19101
$377$	−24.7077	−1.27251
$378$	6.59563	0.339242
$379$	−20.9012	−1.07362	−0.536811	−	0.843702i	$-0.680371\pi$
$379$	−20.9012	−1.07362	−0.536811	+	0.843702i	$0.680371\pi$
$380$	−8.79499	−0.451174
$381$	−2.36664	−0.121247
$382$	32.1846	1.64671
$383$	−0.818245	−0.0418104	−0.0209052	−	0.999781i	$-0.506655\pi$
$383$	−0.818245	−0.0418104	−0.0209052	+	0.999781i	$0.506655\pi$
$384$	−31.3259	−1.59859
$385$	−2.63786	−0.134438
$386$	47.9113	2.43862
$387$	14.8360	0.754155
$388$	38.3029	1.94454
$389$	−20.4547	−1.03710	−0.518548	−	0.855049i	$-0.673527\pi$
$389$	−20.4547	−1.03710	−0.518548	+	0.855049i	$0.673527\pi$
$390$	−15.6405	−0.791986
$391$	11.2739	0.570146
$392$	−10.9252	−0.551808
$393$	−5.69676	−0.287363
$394$	−8.48426	−0.427431
$395$	9.38477	0.472199
$396$	20.6540	1.03790
$397$	25.7548	1.29260	0.646299	−	0.763085i	$-0.276316\pi$
$397$	25.7548	1.29260	0.646299	+	0.763085i	$0.276316\pi$
$398$	−33.3664	−1.67251
$399$	−0.281331	−0.0140842
$400$	−8.36021	−0.418010
$401$	−9.31241	−0.465039	−0.232520	−	0.972592i	$-0.574697\pi$
$401$	−9.31241	−0.465039	−0.232520	+	0.972592i	$0.574697\pi$
$402$	16.9776	0.846764
$403$	−42.1264	−2.09847
$404$	−49.9678	−2.48599
$405$	16.1618	0.803087
$406$	10.7020	0.531132
$407$	1.15539	0.0572707
$408$	−14.1395	−0.700010
$409$	2.09921	0.103799	0.0518997	−	0.998652i	$-0.483472\pi$
$409$	2.09921	0.103799	0.0518997	+	0.998652i	$0.483472\pi$
$410$	43.0373	2.12546
$411$	−5.57019	−0.274757
$412$	109.342	5.38690
$413$	−9.88444	−0.486382
$414$	27.9315	1.37276
$415$	−17.9778	−0.882495
$416$	−202.710	−9.93869
$417$	4.40273	0.215603
$418$	−2.42756	−0.118736
$419$	9.18802	0.448864	0.224432	−	0.974490i	$-0.427947\pi$
$419$	9.18802	0.448864	0.224432	+	0.974490i	$0.427947\pi$
$420$	5.05723	0.246768
$421$	3.59668	0.175292	0.0876458	−	0.996152i	$-0.472066\pi$
$421$	3.59668	0.175292	0.0876458	+	0.996152i	$0.472066\pi$
$422$	−45.5650	−2.21807
$423$	31.1869	1.51636
$424$	−72.8573	−3.53826
$425$	−1.42274	−0.0690128
$426$	13.9632	0.676517
$427$	−8.59996	−0.416181
$428$	−54.4356	−2.63125
$429$	−3.22266	−0.155592
$430$	31.3455	1.51162
$431$	1.95088	0.0939706	0.0469853	−	0.998896i	$-0.485039\pi$
$431$	1.95088	0.0939706	0.0469853	+	0.998896i	$0.485039\pi$
$432$	−44.3994	−2.13617
$433$	−15.6257	−0.750924	−0.375462	−	0.926838i	$-0.622516\pi$
$433$	−15.6257	−0.750924	−0.375462	+	0.926838i	$0.622516\pi$
$434$	18.2468	0.875875
$435$	−3.27164	−0.156863
$436$	60.1962	2.88288
$437$	−2.45069	−0.117233
$438$	6.31148	0.301574
$439$	−24.7918	−1.18325	−0.591624	−	0.806214i	$-0.701513\pi$
$439$	−24.7918	−1.18325	−0.591624	+	0.806214i	$0.701513\pi$
$440$	28.8193	1.37391
$441$	−2.83823	−0.135154
$442$	−58.6108	−2.78783
$443$	12.2142	0.580315	0.290157	−	0.956979i	$-0.406292\pi$
$443$	12.2142	0.580315	0.290157	+	0.956979i	$0.406292\pi$
$444$	−2.21508	−0.105123
$445$	−7.12660	−0.337833
$446$	6.91843	0.327597
$447$	4.59807	0.217481
$448$	49.9865	2.36164
$449$	14.3374	0.676623	0.338312	−	0.941034i	$-0.390144\pi$
$449$	14.3374	0.676623	0.338312	+	0.941034i	$0.390144\pi$
$450$	−3.52488	−0.166164
$451$	8.86767	0.417562
$452$	73.8499	3.47361
$453$	−6.30938	−0.296440
$454$	8.42997	0.395638
$455$	13.8444	0.649037
$456$	3.07361	0.143935
$457$	35.7273	1.67125	0.835626	−	0.549299i	$-0.185105\pi$
$457$	35.7273	1.67125	0.835626	+	0.549299i	$0.185105\pi$
$458$	31.2812	1.46167
$459$	−7.55587	−0.352678
$460$	44.0539	2.05402
$461$	6.39151	0.297682	0.148841	−	0.988861i	$-0.452446\pi$
$461$	6.39151	0.297682	0.148841	+	0.988861i	$0.452446\pi$
$462$	1.39588	0.0649420
$463$	−7.12165	−0.330971	−0.165486	−	0.986212i	$-0.552919\pi$
$463$	−7.12165	−0.330971	−0.165486	+	0.986212i	$0.552919\pi$
$464$	−72.0421	−3.34447
$465$	−5.57811	−0.258679
$466$	54.7887	2.53804
$467$	8.52466	0.394474	0.197237	−	0.980356i	$-0.436803\pi$
$467$	8.52466	0.394474	0.197237	+	0.980356i	$0.436803\pi$
$468$	−108.400	−5.01078
$469$	−15.0280	−0.693927
$470$	65.8918	3.03936
$471$	5.59735	0.257912
$472$	107.990	4.97064
$473$	6.45863	0.296968
$474$	−4.96613	−0.228102
$475$	0.309271	0.0141903
$476$	18.9514	0.868635
$477$	−18.9273	−0.866623
$478$	−46.8484	−2.14280
$479$	28.2961	1.29288	0.646441	−	0.762964i	$-0.276256\pi$
$479$	28.2961	1.29288	0.646441	+	0.762964i	$0.276256\pi$
$480$	−26.8416	−1.22515
$481$	−6.06391	−0.276490
$482$	−81.7665	−3.72436
$483$	1.40918	0.0641199
$484$	−55.7941	−2.53609
$485$	13.8844	0.630457
$486$	−28.3392	−1.28549
$487$	4.94720	0.224179	0.112090	−	0.993698i	$-0.464246\pi$
$487$	4.94720	0.224179	0.112090	+	0.993698i	$0.464246\pi$
$488$	93.9567	4.25322
$489$	−1.32045	−0.0597127
$490$	−5.99663	−0.270900
$491$	7.18391	0.324205	0.162103	−	0.986774i	$-0.448172\pi$
$491$	7.18391	0.324205	0.162103	+	0.986774i	$0.448172\pi$
$492$	−17.0008	−0.766457
$493$	−12.2601	−0.552167
$494$	12.7407	0.573230
$495$	7.48686	0.336509
$496$	−122.831	−5.51527
$497$	−12.3597	−0.554410
$498$	9.51330	0.426301
$499$	−40.1146	−1.79577	−0.897887	−	0.440226i	$-0.854898\pi$
$499$	−40.1146	−1.79577	−0.897887	+	0.440226i	$0.854898\pi$
$500$	−68.4283	−3.06021
$501$	−5.26325	−0.235145
$502$	−58.6146	−2.61610
$503$	10.5155	0.468861	0.234431	−	0.972133i	$-0.424677\pi$
$503$	10.5155	0.468861	0.234431	+	0.972133i	$0.424677\pi$
$504$	31.0084	1.38122
$505$	−18.1128	−0.806008
$506$	12.1596	0.540559
$507$	11.6850	0.518949
$508$	−34.6553	−1.53758
$509$	−17.2666	−0.765327	−0.382664	−	0.923888i	$-0.624993\pi$
$509$	−17.2666	−0.765327	−0.382664	+	0.923888i	$0.624993\pi$
$510$	−7.76087	−0.343657
$511$	−5.58671	−0.247142
$512$	−177.905	−7.86235
$513$	1.64248	0.0725171
$514$	35.7281	1.57590
$515$	39.6353	1.74654
$516$	−12.3823	−0.545100
$517$	13.5768	0.597105
$518$	2.62654	0.115404
$519$	1.94974	0.0855841
$520$	−151.254	−6.63292
$521$	34.6996	1.52021	0.760107	−	0.649797i	$-0.225146\pi$
$521$	34.6996	1.52021	0.760107	+	0.649797i	$0.225146\pi$
$522$	−30.3748	−1.32947
$523$	−11.4225	−0.499472	−0.249736	−	0.968314i	$-0.580344\pi$
$523$	−11.4225	−0.499472	−0.249736	+	0.968314i	$0.580344\pi$
$524$	−83.4191	−3.64418
$525$	−0.177835	−0.00776134
$526$	−88.4255	−3.85554
$527$	−20.9033	−0.910563
$528$	−9.39654	−0.408932
$529$	−10.7245	−0.466284
$530$	−39.9898	−1.73705
$531$	28.0543	1.21745
$532$	−4.11960	−0.178607
$533$	−46.5407	−2.01590
$534$	3.77118	0.163195
$535$	−19.7323	−0.853102
$536$	164.184	7.09168
$537$	5.33022	0.230016
$538$	75.2479	3.24417
$539$	−1.23558	−0.0532203
$540$	−29.5253	−1.27057
$541$	−1.69415	−0.0728373	−0.0364187	−	0.999337i	$-0.511595\pi$
$541$	−1.69415	−0.0728373	−0.0364187	+	0.999337i	$0.511595\pi$
$542$	−51.8658	−2.22783
$543$	2.09589	0.0899431
$544$	−100.586	−4.31258
$545$	21.8205	0.934686
$546$	−7.32605	−0.313526
$547$	17.5258	0.749351	0.374675	−	0.927156i	$-0.377754\pi$
$547$	17.5258	0.749351	0.374675	+	0.927156i	$0.377754\pi$
$548$	−81.5657	−3.48431
$549$	24.4087	1.04174
$550$	−1.53450	−0.0654315
$551$	2.66507	0.113536
$552$	−15.3956	−0.655282
$553$	4.39586	0.186931
$554$	28.3884	1.20611
$555$	−0.802943	−0.0340831
$556$	64.4703	2.73415
$557$	−20.9347	−0.887032	−0.443516	−	0.896267i	$-0.646269\pi$
$557$	−20.9347	−0.887032	−0.443516	+	0.896267i	$0.646269\pi$
$558$	−51.7886	−2.19239
$559$	−33.8972	−1.43370
$560$	40.3672	1.70582
$561$	−1.59910	−0.0675140
$562$	−69.4401	−2.92915
$563$	19.9460	0.840624	0.420312	−	0.907380i	$-0.361921\pi$
$563$	19.9460	0.840624	0.420312	+	0.907380i	$0.361921\pi$
$564$	−26.0290	−1.09602
$565$	26.7698	1.12621
$566$	−4.59374	−0.193089
$567$	7.57025	0.317921
$568$	135.033	5.66586
$569$	37.2702	1.56245	0.781225	−	0.624250i	$-0.214595\pi$
$569$	37.2702	1.56245	0.781225	+	0.624250i	$0.214595\pi$
$570$	1.68704	0.0706623
$571$	17.5726	0.735390	0.367695	−	0.929946i	$-0.380147\pi$
$571$	17.5726	0.735390	0.367695	+	0.929946i	$0.380147\pi$
$572$	−47.1903	−1.97312
$573$	−4.60860	−0.192527
$574$	20.1588	0.841412
$575$	−1.54913	−0.0646031
$576$	−141.873	−5.91138
$577$	17.8359	0.742518	0.371259	−	0.928529i	$-0.378926\pi$
$577$	17.8359	0.742518	0.371259	+	0.928529i	$0.378926\pi$
$578$	18.6674	0.776460
$579$	−6.86054	−0.285114
$580$	−47.9075	−1.98925
$581$	−8.42086	−0.349356
$582$	−7.34719	−0.304551
$583$	−8.23975	−0.341255
$584$	61.0363	2.52570
$585$	−39.2937	−1.62459
$586$	−51.4473	−2.12527
$587$	2.57919	0.106455	0.0532273	−	0.998582i	$-0.483049\pi$
$587$	2.57919	0.106455	0.0532273	+	0.998582i	$0.483049\pi$
$588$	2.36882	0.0976887
$589$	4.54391	0.187229
$590$	59.2733	2.44025
$591$	1.21488	0.0499736
$592$	−17.6809	−0.726683
$593$	8.77942	0.360527	0.180264	−	0.983618i	$-0.442305\pi$
$593$	8.77942	0.360527	0.180264	+	0.983618i	$0.442305\pi$
$594$	−8.14945	−0.334376
$595$	6.86967	0.281629
$596$	67.3307	2.75797
$597$	4.77782	0.195543
$598$	−63.8177	−2.60970
$599$	−39.0015	−1.59356	−0.796779	−	0.604271i	$-0.793465\pi$
$599$	−39.0015	−1.59356	−0.796779	+	0.604271i	$0.793465\pi$
$600$	1.94289	0.0793181
$601$	16.3063	0.665148	0.332574	−	0.943077i	$-0.392083\pi$
$601$	16.3063	0.665148	0.332574	+	0.943077i	$0.392083\pi$
$602$	14.6824	0.598408
$603$	42.6529	1.73696
$604$	−92.3898	−3.75929
$605$	−20.2247	−0.822253
$606$	9.58473	0.389353
$607$	−6.55872	−0.266210	−0.133105	−	0.991102i	$-0.542495\pi$
$607$	−6.55872	−0.266210	−0.133105	+	0.991102i	$0.542495\pi$
$608$	21.8651	0.886746
$609$	−1.53245	−0.0620979
$610$	51.5708	2.08804
$611$	−71.2556	−2.88269
$612$	−53.7884	−2.17427
$613$	48.6797	1.96615	0.983077	−	0.183192i	$-0.0586430\pi$
$613$	48.6797	1.96615	0.983077	+	0.183192i	$0.0586430\pi$
$614$	86.3352	3.48420
$615$	−6.16262	−0.248501
$616$	13.4991	0.543892
$617$	−24.5490	−0.988307	−0.494153	−	0.869375i	$-0.664522\pi$
$617$	−24.5490	−0.988307	−0.494153	+	0.869375i	$0.664522\pi$
$618$	−20.9738	−0.843690
$619$	−2.70108	−0.108565	−0.0542827	−	0.998526i	$-0.517287\pi$
$619$	−2.70108	−0.108565	−0.0542827	+	0.998526i	$0.517287\pi$
$620$	−81.6817	−3.28042
$621$	−8.22712	−0.330143
$622$	−54.1868	−2.17269
$623$	−3.33813	−0.133739
$624$	49.3163	1.97423
$625$	−22.5938	−0.903750
$626$	65.0345	2.59930
$627$	0.347608	0.0138821
$628$	81.9634	3.27070
$629$	−3.00894	−0.119974
$630$	17.0198	0.678086
$631$	−20.2104	−0.804562	−0.402281	−	0.915516i	$-0.631783\pi$
$631$	−20.2104	−0.804562	−0.402281	+	0.915516i	$0.631783\pi$
$632$	−48.0258	−1.91036
$633$	6.52457	0.259328
$634$	78.8587	3.13188
$635$	−12.5622	−0.498515
$636$	15.7970	0.626392
$637$	6.48478	0.256936
$638$	−13.2232	−0.523512
$639$	35.0798	1.38773
$640$	−166.278	−6.57273
$641$	−25.5087	−1.00753	−0.503766	−	0.863840i	$-0.668053\pi$
$641$	−25.5087	−1.00753	−0.503766	+	0.863840i	$0.668053\pi$
$642$	10.4417	0.412103
$643$	0.261361	0.0103071	0.00515354	−	0.999987i	$-0.498360\pi$
$643$	0.261361	0.0103071	0.00515354	+	0.999987i	$0.498360\pi$
$644$	20.6350	0.813132
$645$	−4.48845	−0.176732
$646$	6.32198	0.248735
$647$	3.63307	0.142831	0.0714153	−	0.997447i	$-0.477248\pi$
$647$	3.63307	0.142831	0.0714153	+	0.997447i	$0.477248\pi$
$648$	−82.7069	−3.24903
$649$	12.2130	0.479404
$650$	8.05362	0.315889
$651$	−2.61281	−0.102404
$652$	−19.3357	−0.757243
$653$	−10.5774	−0.413927	−0.206963	−	0.978349i	$-0.566358\pi$
$653$	−10.5774	−0.413927	−0.206963	+	0.978349i	$0.566358\pi$
$654$	−11.5467	−0.451513
$655$	−30.2385	−1.18152
$656$	−135.702	−5.29827
$657$	15.8564	0.618617
$658$	30.8639	1.20320
$659$	−11.2464	−0.438098	−0.219049	−	0.975714i	$-0.570296\pi$
$659$	−11.2464	−0.438098	−0.219049	+	0.975714i	$0.570296\pi$
$660$	−6.24863	−0.243228
$661$	−27.9009	−1.08522	−0.542611	−	0.839984i	$-0.682564\pi$
$661$	−27.9009	−1.08522	−0.542611	+	0.839984i	$0.682564\pi$
$662$	21.5534	0.837698
$663$	8.39263	0.325943
$664$	92.0000	3.57029
$665$	−1.49331	−0.0579081
$666$	−7.45474	−0.288865
$667$	−13.3492	−0.516885
$668$	−77.0711	−2.98197
$669$	−0.990667	−0.0383014
$670$	90.1172	3.48153
$671$	10.6260	0.410211
$672$	−12.5727	−0.485002
$673$	−3.94938	−0.152238	−0.0761188	−	0.997099i	$-0.524253\pi$
$673$	−3.94938	−0.152238	−0.0761188	+	0.997099i	$0.524253\pi$
$674$	−78.1318	−3.00952
$675$	1.03824	0.0399619
$676$	171.106	6.58102
$677$	0.337697	0.0129788	0.00648938	−	0.999979i	$-0.497934\pi$
$677$	0.337697	0.0129788	0.00648938	+	0.999979i	$0.497934\pi$
$678$	−14.1658	−0.544033
$679$	6.50349	0.249581
$680$	−75.0528	−2.87814
$681$	−1.20711	−0.0462565
$682$	−22.5454	−0.863310
$683$	−20.6429	−0.789880	−0.394940	−	0.918707i	$-0.629235\pi$
$683$	−20.6429	−0.789880	−0.394940	+	0.918707i	$0.629235\pi$
$684$	11.6924	0.447070
$685$	−29.5667	−1.12968
$686$	−2.80884	−0.107242
$687$	−4.47923	−0.170893
$688$	−98.8364	−3.76810
$689$	43.2451	1.64751
$690$	−8.45033	−0.321699
$691$	5.45841	0.207648	0.103824	−	0.994596i	$-0.466892\pi$
$691$	5.45841	0.207648	0.103824	+	0.994596i	$0.466892\pi$
$692$	28.5505	1.08533
$693$	3.50687	0.133215
$694$	41.8837	1.58988
$695$	23.3698	0.886466
$696$	16.7424	0.634618
$697$	−23.0937	−0.874735
$698$	−91.3487	−3.45760
$699$	−7.84533	−0.296738
$700$	−2.60408	−0.0984249
$701$	2.19821	0.0830253	0.0415126	−	0.999138i	$-0.486782\pi$
$701$	2.19821	0.0830253	0.0415126	+	0.999138i	$0.486782\pi$
$702$	42.7712	1.61429
$703$	0.654075	0.0246689
$704$	−61.7625	−2.32776
$705$	−9.43521	−0.355351
$706$	−68.4993	−2.57801
$707$	−8.48409	−0.319077
$708$	−23.4145	−0.879971
$709$	31.0211	1.16502	0.582511	−	0.812823i	$-0.302070\pi$
$709$	31.0211	1.16502	0.582511	+	0.812823i	$0.302070\pi$
$710$	74.1167	2.78155
$711$	−12.4765	−0.467904
$712$	36.4699	1.36677
$713$	−22.7603	−0.852381
$714$	−3.63522	−0.136045
$715$	−17.1059	−0.639726
$716$	78.0518	2.91693
$717$	6.70834	0.250528
$718$	50.9155	1.90015
$719$	−48.3531	−1.80327	−0.901633	−	0.432503i	$-0.857631\pi$
$719$	−48.3531	−1.80327	−0.901633	+	0.432503i	$0.857631\pi$
$720$	−114.571	−4.26982
$721$	18.5653	0.691408
$722$	51.9937	1.93501
$723$	11.7083	0.435438
$724$	30.6906	1.14061
$725$	1.68464	0.0625659
$726$	10.7023	0.397200
$727$	−7.26454	−0.269427	−0.134713	−	0.990885i	$-0.543011\pi$
$727$	−7.26454	−0.269427	−0.134713	+	0.990885i	$0.543011\pi$
$728$	−70.8478	−2.62579
$729$	−18.6528	−0.690844
$730$	33.5015	1.23995
$731$	−16.8199	−0.622108
$732$	−20.3718	−0.752963
$733$	−51.8343	−1.91454	−0.957271	−	0.289191i	$-0.906614\pi$
$733$	−51.8343	−1.91454	−0.957271	+	0.289191i	$0.906614\pi$
$734$	13.4966	0.498168
$735$	0.858673	0.0316726
$736$	−109.522	−4.03702
$737$	18.5683	0.683972
$738$	−57.2153	−2.10613
$739$	34.4364	1.26676	0.633382	−	0.773839i	$-0.281666\pi$
$739$	34.4364	1.26676	0.633382	+	0.773839i	$0.281666\pi$
$740$	−11.7577	−0.432222
$741$	−1.82437	−0.0670199
$742$	−18.7314	−0.687650
$743$	−47.5605	−1.74482	−0.872412	−	0.488771i	$-0.837445\pi$
$743$	−47.5605	−1.74482	−0.872412	+	0.488771i	$0.837445\pi$
$744$	28.5456	1.04653
$745$	24.4066	0.894190
$746$	80.8456	2.95997
$747$	23.9003	0.874468
$748$	−23.4160	−0.856174
$749$	−9.24268	−0.337720
$750$	13.1258	0.479286
$751$	0.0598266	0.00218310	0.00109155	−	0.999999i	$-0.499653\pi$
$751$	0.0598266	0.00218310	0.00109155	+	0.999999i	$0.499653\pi$
$752$	−207.765	−7.57641
$753$	8.39317	0.305864
$754$	69.4001	2.52740
$755$	−33.4903	−1.21884
$756$	−13.8297	−0.502983
$757$	3.80600	0.138331	0.0691657	−	0.997605i	$-0.477966\pi$
$757$	3.80600	0.138331	0.0691657	+	0.997605i	$0.477966\pi$
$758$	58.7081	2.13238
$759$	−1.74116	−0.0632001
$760$	16.3148	0.591800
$761$	20.2616	0.734484	0.367242	−	0.930125i	$-0.380302\pi$
$761$	20.2616	0.734484	0.367242	+	0.930125i	$0.380302\pi$
$762$	6.64752	0.240814
$763$	10.2208	0.370017
$764$	−67.4849	−2.44152
$765$	−19.4977	−0.704941
$766$	2.29832	0.0830417
$767$	−64.0984	−2.31446
$768$	47.7798	1.72410
$769$	38.5318	1.38949	0.694746	−	0.719255i	$-0.255517\pi$
$769$	38.5318	1.38949	0.694746	+	0.719255i	$0.255517\pi$
$770$	7.40934	0.267014
$771$	−5.11600	−0.184248
$772$	−100.461	−3.61566
$773$	17.8599	0.642376	0.321188	−	0.947015i	$-0.395918\pi$
$773$	17.8599	0.642376	0.321188	+	0.947015i	$0.395918\pi$
$774$	−41.6719	−1.49787
$775$	2.87229	0.103176
$776$	−71.0523	−2.55063
$777$	−0.376101	−0.0134926
$778$	57.4541	2.05983
$779$	5.02005	0.179862
$780$	32.7950	1.17425
$781$	15.2715	0.546456
$782$	−31.6666	−1.13240
$783$	8.94678	0.319732
$784$	18.9081	0.675290
$785$	29.7108	1.06043
$786$	16.0013	0.570747
$787$	−39.5901	−1.41123	−0.705617	−	0.708594i	$-0.749330\pi$
$787$	−39.5901	−1.41123	−0.705617	+	0.708594i	$0.749330\pi$
$788$	17.7898	0.633737
$789$	12.6619	0.450775
$790$	−26.3603	−0.937858
$791$	12.5391	0.445838
$792$	−38.3134	−1.36141
$793$	−55.7688	−1.98041
$794$	−72.3412	−2.56729
$795$	5.72624	0.203089
$796$	69.9628	2.47977
$797$	14.6212	0.517911	0.258955	−	0.965889i	$-0.416622\pi$
$797$	14.6212	0.517911	0.258955	+	0.965889i	$0.416622\pi$
$798$	0.790214	0.0279733
$799$	−35.3573	−1.25085
$800$	13.8213	0.488657
$801$	9.47437	0.334760
$802$	26.1571	0.923639
$803$	6.90285	0.243596
$804$	−35.5986	−1.25547
$805$	7.47995	0.263634
$806$	118.326	4.16787
$807$	−10.7749	−0.379296
$808$	92.6908	3.26085
$809$	23.5634	0.828446	0.414223	−	0.910175i	$-0.364053\pi$
$809$	23.5634	0.828446	0.414223	+	0.910175i	$0.364053\pi$
$810$	−45.3960	−1.59505
$811$	10.6792	0.374998	0.187499	−	0.982265i	$-0.439962\pi$
$811$	10.6792	0.374998	0.187499	+	0.982265i	$0.439962\pi$
$812$	−22.4400	−0.787490
$813$	7.42680	0.260469
$814$	−3.24531	−0.113748
$815$	−7.00897	−0.245513
$816$	24.4710	0.856656
$817$	3.65627	0.127917
$818$	−5.89636	−0.206161
$819$	−18.4053	−0.643133
$820$	−90.2408	−3.15134
$821$	42.4109	1.48015	0.740075	−	0.672525i	$-0.234790\pi$
$821$	42.4109	1.48015	0.740075	+	0.672525i	$0.234790\pi$
$822$	15.6458	0.545709
$823$	10.8136	0.376938	0.188469	−	0.982079i	$-0.439648\pi$
$823$	10.8136	0.376938	0.188469	+	0.982079i	$0.439648\pi$
$824$	−202.831	−7.06594
$825$	0.219729	0.00765000
$826$	27.7638	0.966027
$827$	22.5914	0.785578	0.392789	−	0.919629i	$-0.371510\pi$
$827$	22.5914	0.785578	0.392789	+	0.919629i	$0.371510\pi$
$828$	−58.5668	−2.03534
$829$	26.8994	0.934255	0.467128	−	0.884190i	$-0.345289\pi$
$829$	26.8994	0.934255	0.467128	+	0.884190i	$0.345289\pi$
$830$	50.4968	1.75277
$831$	−4.06501	−0.141014
$832$	324.151	11.2379
$833$	3.21777	0.111489
$834$	−12.3666	−0.428219
$835$	−27.9374	−0.966815
$836$	5.09011	0.176045
$837$	15.2542	0.527261
$838$	−25.8077	−0.891512
$839$	−25.0677	−0.865432	−0.432716	−	0.901530i	$-0.642445\pi$
$839$	−25.0677	−0.865432	−0.432716	+	0.901530i	$0.642445\pi$
$840$	−9.38121	−0.323683
$841$	−14.4830	−0.499415
$842$	−10.1025	−0.348155
$843$	9.94330	0.342465
$844$	95.5410	3.28866
$845$	62.0242	2.13370
$846$	−87.5990	−3.01171
$847$	−9.47333	−0.325508
$848$	126.093	4.33004
$849$	0.657789	0.0225753
$850$	3.99624	0.137070
$851$	−3.27624	−0.112308
$852$	−29.2780	−1.00305
$853$	50.7751	1.73850	0.869252	−	0.494369i	$-0.164601\pi$
$853$	50.7751	1.73850	0.869252	+	0.494369i	$0.164601\pi$
$854$	24.1559	0.826598
$855$	4.23836	0.144949
$856$	100.979	3.45138
$857$	4.31475	0.147389	0.0736945	−	0.997281i	$-0.476521\pi$
$857$	4.31475	0.147389	0.0736945	+	0.997281i	$0.476521\pi$
$858$	9.05195	0.309028
$859$	1.00000	0.0341196
$859$	1.00000	0.0341196
$860$	−65.7255	−2.24122
$861$	−2.88659	−0.0983747
$862$	−5.47972	−0.186640
$863$	27.5322	0.937207	0.468604	−	0.883409i	$-0.344757\pi$
$863$	27.5322	0.937207	0.468604	+	0.883409i	$0.344757\pi$
$864$	73.4023	2.49720
$865$	10.3493	0.351885
$866$	43.8902	1.49145
$867$	−2.67303	−0.0907807
$868$	−38.2600	−1.29863
$869$	−5.43144	−0.184249
$870$	9.18952	0.311554
$871$	−97.4531	−3.30207
$872$	−111.665	−3.78144
$873$	−18.4584	−0.624723
$874$	6.88361	0.232842
$875$	−11.6185	−0.392777
$876$	−13.2339	−0.447134
$877$	6.02583	0.203478	0.101739	−	0.994811i	$-0.467559\pi$
$877$	6.02583	0.203478	0.101739	+	0.994811i	$0.467559\pi$
$878$	69.6362	2.35011
$879$	7.36687	0.248478
$880$	−49.8770	−1.68135
$881$	−10.3897	−0.350038	−0.175019	−	0.984565i	$-0.555999\pi$
$881$	−10.3897	−0.350038	−0.175019	+	0.984565i	$0.555999\pi$
$882$	7.97214	0.268436
$883$	21.6004	0.726912	0.363456	−	0.931611i	$-0.381597\pi$
$883$	21.6004	0.726912	0.363456	+	0.931611i	$0.381597\pi$
$884$	122.895	4.13342
$885$	−8.48750	−0.285304
$886$	−34.3078	−1.15259
$887$	2.75052	0.0923535	0.0461768	−	0.998933i	$-0.485296\pi$
$887$	2.75052	0.0923535	0.0461768	+	0.998933i	$0.485296\pi$
$888$	4.10900	0.137889
$889$	−5.88417	−0.197349
$890$	20.0175	0.670988
$891$	−9.35367	−0.313360
$892$	−14.5066	−0.485717
$893$	7.68589	0.257198
$894$	−12.9152	−0.431951
$895$	28.2929	0.945728
$896$	−77.8853	−2.60197
$897$	9.13822	0.305116
$898$	−40.2715	−1.34388
$899$	24.7513	0.825501
$900$	7.39098	0.246366
$901$	21.4584	0.714883
$902$	−24.9079	−0.829342
$903$	−2.10240	−0.0699636
$904$	−136.992	−4.55630
$905$	11.1250	0.369808
$906$	17.7220	0.588775
$907$	31.7047	1.05274	0.526369	−	0.850256i	$-0.323553\pi$
$907$	31.7047	1.05274	0.526369	+	0.850256i	$0.323553\pi$
$908$	−17.6760	−0.586599
$909$	24.0798	0.798677
$910$	−38.8868	−1.28909
$911$	−14.4558	−0.478942	−0.239471	−	0.970903i	$-0.576974\pi$
$911$	−14.4558	−0.478942	−0.239471	+	0.970903i	$0.576974\pi$
$912$	−5.31944	−0.176144
$913$	10.4047	0.344344
$914$	−100.352	−3.31936
$915$	−7.38455	−0.244126
$916$	−65.5905	−2.16717
$917$	−14.1638	−0.467730
$918$	21.2232	0.700471
$919$	22.1916	0.732034	0.366017	−	0.930608i	$-0.380721\pi$
$919$	22.1916	0.732034	0.366017	+	0.930608i	$0.380721\pi$
$920$	−81.7204	−2.69424
$921$	−12.3625	−0.407360
$922$	−17.9527	−0.591242
$923$	−80.1501	−2.63817
$924$	−2.92688	−0.0962873
$925$	0.413453	0.0135942
$926$	20.0036	0.657359
$927$	−52.6926	−1.73065
$928$	119.102	3.90971
$929$	−5.15535	−0.169142	−0.0845708	−	0.996417i	$-0.526952\pi$
$929$	−5.15535	−0.169142	−0.0845708	+	0.996417i	$0.526952\pi$
$930$	15.6680	0.513775
$931$	−0.699472	−0.0229243
$932$	−114.881	−3.76306
$933$	7.75914	0.254023
$934$	−23.9444	−0.783485
$935$	−8.48804	−0.277589
$936$	201.082	6.57259
$937$	−31.6207	−1.03300	−0.516501	−	0.856287i	$-0.672766\pi$
$937$	−31.6207	−1.03300	−0.516501	+	0.856287i	$0.672766\pi$
$938$	42.2112	1.37824
$939$	−9.31245	−0.303900
$940$	−138.162	−4.50635
$941$	−36.0089	−1.17386	−0.586928	−	0.809639i	$-0.699663\pi$
$941$	−36.0089	−1.17386	−0.586928	+	0.809639i	$0.699663\pi$
$942$	−15.7221	−0.512253
$943$	−25.1453	−0.818843
$944$	−186.896	−6.08295
$945$	−5.01313	−0.163077
$946$	−18.1413	−0.589824
$947$	5.61943	0.182607	0.0913035	−	0.995823i	$-0.470897\pi$
$947$	5.61943	0.182607	0.0913035	+	0.995823i	$0.470897\pi$
$948$	10.4130	0.338199
$949$	−36.2286	−1.17603
$950$	−0.868693	−0.0281841
$951$	−11.2920	−0.366167
$952$	−35.1550	−1.13938
$953$	−42.4549	−1.37525	−0.687625	−	0.726066i	$-0.741347\pi$
$953$	−42.4549	−1.37525	−0.687625	+	0.726066i	$0.741347\pi$
$954$	53.1639	1.72125
$955$	−24.4625	−0.791589
$956$	98.2320	3.17705
$957$	1.89347	0.0612071
$958$	−79.4793	−2.56786
$959$	−13.8491	−0.447211
$960$	42.9220	1.38530
$961$	11.2006	0.361311
$962$	17.0326	0.549152
$963$	26.2329	0.845342
$964$	171.448	5.52198
$965$	−36.4159	−1.17227
$966$	−3.95816	−0.127352
$967$	51.8114	1.66614	0.833071	−	0.553166i	$-0.186581\pi$
$967$	51.8114	1.66614	0.833071	+	0.553166i	$0.186581\pi$
$968$	103.499	3.32657
$969$	−0.905260	−0.0290811
$970$	−38.9990	−1.25218
$971$	5.35879	0.171972	0.0859859	−	0.996296i	$-0.472596\pi$
$971$	5.35879	0.171972	0.0859859	+	0.996296i	$0.472596\pi$
$972$	59.4218	1.90596
$973$	10.9465	0.350928
$974$	−13.8959	−0.445254
$975$	−1.15322	−0.0369325
$976$	−162.609	−5.20499
$977$	−5.28041	−0.168935	−0.0844677	−	0.996426i	$-0.526919\pi$
$977$	−5.28041	−0.168935	−0.0844677	+	0.996426i	$0.526919\pi$
$978$	3.70893	0.118599
$979$	4.12453	0.131821
$980$	12.5738	0.401654
$981$	−29.0089	−0.926184
$982$	−20.1785	−0.643920
$983$	0.999669	0.0318845	0.0159422	−	0.999873i	$-0.494925\pi$
$983$	0.999669	0.0318845	0.0159422	+	0.999873i	$0.494925\pi$
$984$	31.5367	1.00535
$985$	6.44862	0.205470
$986$	34.4366	1.09669
$987$	−4.41948	−0.140674
$988$	−26.7147	−0.849908
$989$	−18.3142	−0.582357
$990$	−21.0294	−0.668359
$991$	−27.8076	−0.883337	−0.441669	−	0.897178i	$-0.645613\pi$
$991$	−27.8076	−0.883337	−0.441669	+	0.897178i	$0.645613\pi$
$992$	203.067	6.44740
$993$	−3.08629	−0.0979405
$994$	34.7165	1.10114
$995$	25.3608	0.803990
$996$	−19.9475	−0.632062
$997$	−11.4470	−0.362530	−0.181265	−	0.983434i	$-0.558019\pi$
$997$	−11.4470	−0.362530	−0.181265	+	0.983434i	$0.558019\pi$
$998$	112.675	3.56668
$999$	2.19577	0.0694710

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6013.2.a.d.1.2	✓	104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6013.2.a.d.1.2	✓	104	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:	\( N \)	\(=\)	\( 6013 = 7 \cdot 859 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.80884 q^{2} +0.402205 q^{3} +5.88959 q^{4} +2.13491 q^{5} -1.12973 q^{6} +1.00000 q^{7} -10.9252 q^{8} -2.83823 q^{9} +O(q^{10})\)	\(q-2.80884 q^{2} +0.402205 q^{3} +5.88959 q^{4} +2.13491 q^{5} -1.12973 q^{6} +1.00000 q^{7} -10.9252 q^{8} -2.83823 q^{9} -5.99663 q^{10} -1.23558 q^{11} +2.36882 q^{12} +6.48478 q^{13} -2.80884 q^{14} +0.858673 q^{15} +18.9081 q^{16} +3.21777 q^{17} +7.97214 q^{18} -0.699472 q^{19} +12.5738 q^{20} +0.402205 q^{21} +3.47056 q^{22} +3.50363 q^{23} -4.39419 q^{24} -0.442149 q^{25} -18.2147 q^{26} -2.34817 q^{27} +5.88959 q^{28} -3.81011 q^{29} -2.41188 q^{30} -6.49620 q^{31} -31.2594 q^{32} -0.496958 q^{33} -9.03822 q^{34} +2.13491 q^{35} -16.7160 q^{36} -0.935098 q^{37} +1.96471 q^{38} +2.60821 q^{39} -23.3245 q^{40} -7.17691 q^{41} -1.12973 q^{42} -5.22719 q^{43} -7.27708 q^{44} -6.05937 q^{45} -9.84116 q^{46} -10.9881 q^{47} +7.60494 q^{48} +1.00000 q^{49} +1.24193 q^{50} +1.29421 q^{51} +38.1927 q^{52} +6.66871 q^{53} +6.59563 q^{54} -2.63786 q^{55} -10.9252 q^{56} -0.281331 q^{57} +10.7020 q^{58} -9.88444 q^{59} +5.05723 q^{60} -8.59996 q^{61} +18.2468 q^{62} -2.83823 q^{63} +49.9865 q^{64} +13.8444 q^{65} +1.39588 q^{66} -15.0280 q^{67} +18.9514 q^{68} +1.40918 q^{69} -5.99663 q^{70} -12.3597 q^{71} +31.0084 q^{72} -5.58671 q^{73} +2.62654 q^{74} -0.177835 q^{75} -4.11960 q^{76} -1.23558 q^{77} -7.32605 q^{78} +4.39586 q^{79} +40.3672 q^{80} +7.57025 q^{81} +20.1588 q^{82} -8.42086 q^{83} +2.36882 q^{84} +6.86967 q^{85} +14.6824 q^{86} -1.53245 q^{87} +13.4991 q^{88} -3.33813 q^{89} +17.0198 q^{90} +6.48478 q^{91} +20.6350 q^{92} -2.61281 q^{93} +30.8639 q^{94} -1.49331 q^{95} -12.5727 q^{96} +6.50349 q^{97} -2.80884 q^{98} +3.50687 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 104 q - 17 q^{2} - 34 q^{3} + 99 q^{4} - 46 q^{5} - 18 q^{6} + 104 q^{7} - 48 q^{8} + 98 q^{9}+O(q^{10}) \) 104 * q - 17 * q^2 - 34 * q^3 + 99 * q^4 - 46 * q^5 - 18 * q^6 + 104 * q^7 - 48 * q^8 + 98 * q^9	\( 104 q - 17 q^{2} - 34 q^{3} + 99 q^{4} - 46 q^{5} - 18 q^{6} + 104 q^{7} - 48 q^{8} + 98 q^{9} - 17 q^{10} - 46 q^{11} - 62 q^{12} - 37 q^{13} - 17 q^{14} - 17 q^{15} + 93 q^{16} - 75 q^{17} - 41 q^{18} - 40 q^{19} - 106 q^{20} - 34 q^{21} - 14 q^{22} - 57 q^{23} - 38 q^{24} + 102 q^{25} - 45 q^{26} - 121 q^{27} + 99 q^{28} - 29 q^{29} + 26 q^{30} - 42 q^{31} - 113 q^{32} - 42 q^{33} - 7 q^{34} - 46 q^{35} + 99 q^{36} - 31 q^{37} - 62 q^{38} - 9 q^{39} - 36 q^{40} - 106 q^{41} - 18 q^{42} - 29 q^{43} - 60 q^{44} - 121 q^{45} + 21 q^{46} - 141 q^{47} - 88 q^{48} + 104 q^{49} - 70 q^{50} - 2 q^{51} - 58 q^{52} - 70 q^{53} - 49 q^{54} - 14 q^{55} - 48 q^{56} - 11 q^{57} - 28 q^{58} - 202 q^{59} + 17 q^{60} - 79 q^{61} - 41 q^{62} + 98 q^{63} + 110 q^{64} - 34 q^{65} - 21 q^{66} - 57 q^{67} - 180 q^{68} - 99 q^{69} - 17 q^{70} - 109 q^{71} - 73 q^{72} - 46 q^{73} - 7 q^{74} - 146 q^{75} - 54 q^{76} - 46 q^{77} - 42 q^{78} - 12 q^{79} - 187 q^{80} + 100 q^{81} - 45 q^{82} - 156 q^{83} - 62 q^{84} - 13 q^{85} - 8 q^{86} - 76 q^{87} - 6 q^{88} - 140 q^{89} - 5 q^{90} - 37 q^{91} - 98 q^{92} - q^{93} - 17 q^{94} - 48 q^{95} - 12 q^{96} - 63 q^{97} - 17 q^{98} - 78 q^{99}+O(q^{100}) \) 104 * q - 17 * q^2 - 34 * q^3 + 99 * q^4 - 46 * q^5 - 18 * q^6 + 104 * q^7 - 48 * q^8 + 98 * q^9 - 17 * q^10 - 46 * q^11 - 62 * q^12 - 37 * q^13 - 17 * q^14 - 17 * q^15 + 93 * q^16 - 75 * q^17 - 41 * q^18 - 40 * q^19 - 106 * q^20 - 34 * q^21 - 14 * q^22 - 57 * q^23 - 38 * q^24 + 102 * q^25 - 45 * q^26 - 121 * q^27 + 99 * q^28 - 29 * q^29 + 26 * q^30 - 42 * q^31 - 113 * q^32 - 42 * q^33 - 7 * q^34 - 46 * q^35 + 99 * q^36 - 31 * q^37 - 62 * q^38 - 9 * q^39 - 36 * q^40 - 106 * q^41 - 18 * q^42 - 29 * q^43 - 60 * q^44 - 121 * q^45 + 21 * q^46 - 141 * q^47 - 88 * q^48 + 104 * q^49 - 70 * q^50 - 2 * q^51 - 58 * q^52 - 70 * q^53 - 49 * q^54 - 14 * q^55 - 48 * q^56 - 11 * q^57 - 28 * q^58 - 202 * q^59 + 17 * q^60 - 79 * q^61 - 41 * q^62 + 98 * q^63 + 110 * q^64 - 34 * q^65 - 21 * q^66 - 57 * q^67 - 180 * q^68 - 99 * q^69 - 17 * q^70 - 109 * q^71 - 73 * q^72 - 46 * q^73 - 7 * q^74 - 146 * q^75 - 54 * q^76 - 46 * q^77 - 42 * q^78 - 12 * q^79 - 187 * q^80 + 100 * q^81 - 45 * q^82 - 156 * q^83 - 62 * q^84 - 13 * q^85 - 8 * q^86 - 76 * q^87 - 6 * q^88 - 140 * q^89 - 5 * q^90 - 37 * q^91 - 98 * q^92 - q^93 - 17 * q^94 - 48 * q^95 - 12 * q^96 - 63 * q^97 - 17 * q^98 - 78 * q^99

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