LMFDB - Embedded newform 547.2.a.b.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [547,2,Mod(1,547)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(547, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("547.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	547.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:	$4.36781699056$
Analytic rank:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 4 x^{17} - 18 x^{16} + 84 x^{15} + 116 x^{14} - 708 x^{13} - 282 x^{12} + 3104 x^{11} + \cdots + 328 $ x^18 - 4x^17 - 18x^16 + 84x^15 + 116x^14 - 708x^13 - 282x^12 + 3104x^11 - 137x^10 - 7703x^9 + 2068x^8 + 11068x^7 - 4274x^6 - 9021x^5 + 4048x^4 + 3834x^3 - 1851x^2 - 654*x + 328
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Root			$-1.87675$ of defining polynomial
Character	$\chi$	$=$	547.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.87675 q^{2} -1.13919 q^{3} +1.52220 q^{4} -1.30620 q^{5} -2.13798 q^{6} -1.71403 q^{7} -0.896704 q^{8} -1.70224 q^{9} +O(q^{10})$	\(q+1.87675 q^{2} -1.13919 q^{3} +1.52220 q^{4} -1.30620 q^{5} -2.13798 q^{6} -1.71403 q^{7} -0.896704 q^{8} -1.70224 q^{9} -2.45142 q^{10} -5.30835 q^{11} -1.73408 q^{12} +2.18823 q^{13} -3.21682 q^{14} +1.48801 q^{15} -4.72730 q^{16} +0.392924 q^{17} -3.19469 q^{18} +0.498929 q^{19} -1.98831 q^{20} +1.95261 q^{21} -9.96246 q^{22} +8.33591 q^{23} +1.02152 q^{24} -3.29383 q^{25} +4.10676 q^{26} +5.35675 q^{27} -2.60911 q^{28} -4.50948 q^{29} +2.79264 q^{30} -2.96386 q^{31} -7.07857 q^{32} +6.04722 q^{33} +0.737421 q^{34} +2.23887 q^{35} -2.59116 q^{36} +3.06843 q^{37} +0.936368 q^{38} -2.49281 q^{39} +1.17128 q^{40} -10.0885 q^{41} +3.66457 q^{42} +9.93284 q^{43} -8.08039 q^{44} +2.22348 q^{45} +15.6444 q^{46} +0.714605 q^{47} +5.38530 q^{48} -4.06209 q^{49} -6.18172 q^{50} -0.447615 q^{51} +3.33093 q^{52} -10.3693 q^{53} +10.0533 q^{54} +6.93378 q^{55} +1.53698 q^{56} -0.568376 q^{57} -8.46318 q^{58} -6.58293 q^{59} +2.26506 q^{60} -0.889139 q^{61} -5.56243 q^{62} +2.91770 q^{63} -3.83013 q^{64} -2.85827 q^{65} +11.3491 q^{66} +4.67997 q^{67} +0.598110 q^{68} -9.49619 q^{69} +4.20181 q^{70} +11.4239 q^{71} +1.52641 q^{72} +5.35047 q^{73} +5.75869 q^{74} +3.75231 q^{75} +0.759473 q^{76} +9.09868 q^{77} -4.67838 q^{78} -7.79987 q^{79} +6.17481 q^{80} -0.995634 q^{81} -18.9336 q^{82} -17.9975 q^{83} +2.97227 q^{84} -0.513238 q^{85} +18.6415 q^{86} +5.13716 q^{87} +4.76002 q^{88} +13.3683 q^{89} +4.17292 q^{90} -3.75069 q^{91} +12.6890 q^{92} +3.37640 q^{93} +1.34114 q^{94} -0.651703 q^{95} +8.06385 q^{96} -13.2660 q^{97} -7.62355 q^{98} +9.03610 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 4 q^{2} - 10 q^{3} + 16 q^{4} - 27 q^{5} - 3 q^{6} - 11 q^{7} - 12 q^{8} + 14 q^{9}+O(q^{10}) $ 18 * q - 4 * q^2 - 10 * q^3 + 16 * q^4 - 27 * q^5 - 3 * q^6 - 11 * q^7 - 12 * q^8 + 14 * q^9	\( 18 q - 4 q^{2} - 10 q^{3} + 16 q^{4} - 27 q^{5} - 3 q^{6} - 11 q^{7} - 12 q^{8} + 14 q^{9} - 5 q^{10} + 2 q^{11} - 32 q^{12} - 25 q^{13} - 7 q^{14} + 9 q^{15} + 8 q^{16} - 30 q^{17} - 10 q^{18} + 4 q^{19} - 41 q^{20} - 16 q^{21} - 24 q^{22} - 26 q^{23} - 12 q^{24} + 31 q^{25} - 18 q^{26} - 37 q^{27} - 16 q^{28} - 18 q^{29} + 8 q^{30} - 5 q^{31} - 28 q^{32} - 10 q^{33} + 5 q^{34} - 9 q^{35} + 31 q^{36} - 18 q^{37} - 45 q^{38} + 7 q^{39} + 7 q^{40} - 17 q^{41} + 4 q^{42} + 8 q^{43} + 12 q^{44} - 44 q^{45} + 30 q^{46} - 52 q^{47} - 7 q^{48} + 29 q^{49} + 13 q^{50} + 19 q^{51} - 14 q^{52} - 60 q^{53} + 11 q^{54} + 11 q^{55} + 7 q^{56} + 4 q^{57} + 14 q^{58} - 8 q^{59} + 86 q^{60} - 26 q^{61} + 4 q^{62} - q^{63} + 44 q^{64} - 6 q^{65} + 18 q^{66} + 12 q^{67} - 61 q^{68} - 38 q^{69} + 35 q^{70} - q^{71} + 28 q^{72} - 2 q^{73} + 16 q^{74} - 17 q^{75} + 66 q^{76} - 73 q^{77} + 115 q^{78} + 18 q^{79} - 32 q^{80} + 18 q^{81} + 44 q^{82} - 43 q^{83} + 41 q^{84} + 51 q^{85} + 4 q^{86} + 3 q^{87} - 17 q^{88} - 28 q^{89} + 58 q^{90} - q^{91} - 68 q^{92} - 60 q^{93} + 78 q^{94} - 18 q^{95} + 29 q^{96} - 34 q^{97} + 34 q^{98} + 15 q^{99}+O(q^{100}) \) 18 * q - 4 * q^2 - 10 * q^3 + 16 * q^4 - 27 * q^5 - 3 * q^6 - 11 * q^7 - 12 * q^8 + 14 * q^9 - 5 * q^10 + 2 * q^11 - 32 * q^12 - 25 * q^13 - 7 * q^14 + 9 * q^15 + 8 * q^16 - 30 * q^17 - 10 * q^18 + 4 * q^19 - 41 * q^20 - 16 * q^21 - 24 * q^22 - 26 * q^23 - 12 * q^24 + 31 * q^25 - 18 * q^26 - 37 * q^27 - 16 * q^28 - 18 * q^29 + 8 * q^30 - 5 * q^31 - 28 * q^32 - 10 * q^33 + 5 * q^34 - 9 * q^35 + 31 * q^36 - 18 * q^37 - 45 * q^38 + 7 * q^39 + 7 * q^40 - 17 * q^41 + 4 * q^42 + 8 * q^43 + 12 * q^44 - 44 * q^45 + 30 * q^46 - 52 * q^47 - 7 * q^48 + 29 * q^49 + 13 * q^50 + 19 * q^51 - 14 * q^52 - 60 * q^53 + 11 * q^54 + 11 * q^55 + 7 * q^56 + 4 * q^57 + 14 * q^58 - 8 * q^59 + 86 * q^60 - 26 * q^61 + 4 * q^62 - q^63 + 44 * q^64 - 6 * q^65 + 18 * q^66 + 12 * q^67 - 61 * q^68 - 38 * q^69 + 35 * q^70 - q^71 + 28 * q^72 - 2 * q^73 + 16 * q^74 - 17 * q^75 + 66 * q^76 - 73 * q^77 + 115 * q^78 + 18 * q^79 - 32 * q^80 + 18 * q^81 + 44 * q^82 - 43 * q^83 + 41 * q^84 + 51 * q^85 + 4 * q^86 + 3 * q^87 - 17 * q^88 - 28 * q^89 + 58 * q^90 - q^91 - 68 * q^92 - 60 * q^93 + 78 * q^94 - 18 * q^95 + 29 * q^96 - 34 * q^97 + 34 * q^98 + 15 * 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 $

$2$	1.87675	1.32707	0.663533	−	0.748147i	$-0.269056\pi$
$2$	1.87675	1.32707	0.663533	+	0.748147i	$0.269056\pi$
$3$	−1.13919	−0.657712	−0.328856	−	0.944380i	$-0.606663\pi$
$3$	−1.13919	−0.657712	−0.328856	+	0.944380i	$0.606663\pi$
$4$	1.52220	0.761102
$5$	−1.30620	−0.584152	−0.292076	−	0.956395i	$-0.594346\pi$
$5$	−1.30620	−0.584152	−0.292076	+	0.956395i	$0.594346\pi$
$6$	−2.13798	−0.872827
$7$	−1.71403	−0.647843	−0.323922	−	0.946084i	$-0.605001\pi$
$7$	−1.71403	−0.647843	−0.323922	+	0.946084i	$0.605001\pi$
$8$	−0.896704	−0.317033
$9$	−1.70224	−0.567415
$10$	−2.45142	−0.775207
$11$	−5.30835	−1.60053	−0.800263	−	0.599649i	$-0.795307\pi$
$11$	−5.30835	−1.60053	−0.800263	+	0.599649i	$0.795307\pi$
$12$	−1.73408	−0.500586
$13$	2.18823	0.606905	0.303452	−	0.952847i	$-0.401861\pi$
$13$	2.18823	0.606905	0.303452	+	0.952847i	$0.401861\pi$
$14$	−3.21682	−0.859730
$15$	1.48801	0.384204
$16$	−4.72730	−1.18183
$17$	0.392924	0.0952980	0.0476490	−	0.998864i	$-0.484827\pi$
$17$	0.392924	0.0952980	0.0476490	+	0.998864i	$0.484827\pi$
$18$	−3.19469	−0.752996
$19$	0.498929	0.114462	0.0572311	−	0.998361i	$-0.481773\pi$
$19$	0.498929	0.114462	0.0572311	+	0.998361i	$0.481773\pi$
$20$	−1.98831	−0.444599
$21$	1.95261	0.426094
$22$	−9.96246	−2.12400
$23$	8.33591	1.73816	0.869079	−	0.494674i	$-0.164713\pi$
$23$	8.33591	1.73816	0.869079	+	0.494674i	$0.164713\pi$
$24$	1.02152	0.208516
$25$	−3.29383	−0.658767
$26$	4.10676	0.805402
$27$	5.35675	1.03091
$28$	−2.60911	−0.493075
$29$	−4.50948	−0.837389	−0.418695	−	0.908127i	$-0.637512\pi$
$29$	−4.50948	−0.837389	−0.418695	+	0.908127i	$0.637512\pi$
$30$	2.79264	0.509863
$31$	−2.96386	−0.532324	−0.266162	−	0.963928i	$-0.585756\pi$
$31$	−2.96386	−0.532324	−0.266162	+	0.963928i	$0.585756\pi$
$32$	−7.07857	−1.25133
$33$	6.04722	1.05269
$34$	0.737421	0.126467
$35$	2.23887	0.378439
$36$	−2.59116	−0.431861
$37$	3.06843	0.504447	0.252223	−	0.967669i	$-0.418838\pi$
$37$	3.06843	0.504447	0.252223	+	0.967669i	$0.418838\pi$
$38$	0.936368	0.151899
$39$	−2.49281	−0.399169
$40$	1.17128	0.185195
$41$	−10.0885	−1.57556	−0.787780	−	0.615957i	$-0.788770\pi$
$41$	−10.0885	−1.57556	−0.787780	+	0.615957i	$0.788770\pi$
$42$	3.66457	0.565455
$43$	9.93284	1.51474	0.757372	−	0.652984i	$-0.226483\pi$
$43$	9.93284	1.51474	0.757372	+	0.652984i	$0.226483\pi$
$44$	−8.08039	−1.21816
$45$	2.22348	0.331456
$46$	15.6444	2.30665
$47$	0.714605	0.104236	0.0521179	−	0.998641i	$-0.483403\pi$
$47$	0.714605	0.104236	0.0521179	+	0.998641i	$0.483403\pi$
$48$	5.38530	0.777301
$49$	−4.06209	−0.580299
$50$	−6.18172	−0.874227
$51$	−0.447615	−0.0626787
$52$	3.33093	0.461916
$53$	−10.3693	−1.42433	−0.712165	−	0.702012i	$-0.752285\pi$
$53$	−10.3693	−1.42433	−0.712165	+	0.702012i	$0.752285\pi$
$54$	10.0533	1.36808
$55$	6.93378	0.934950
$56$	1.53698	0.205388
$57$	−0.568376	−0.0752832
$58$	−8.46318	−1.11127
$59$	−6.58293	−0.857024	−0.428512	−	0.903536i	$-0.640962\pi$
$59$	−6.58293	−0.857024	−0.428512	+	0.903536i	$0.640962\pi$
$60$	2.26506	0.292418
$61$	−0.889139	−0.113843	−0.0569213	−	0.998379i	$-0.518128\pi$
$61$	−0.889139	−0.113843	−0.0569213	+	0.998379i	$0.518128\pi$
$62$	−5.56243	−0.706429
$63$	2.91770	0.367596
$64$	−3.83013	−0.478767
$65$	−2.85827	−0.354524
$66$	11.3491	1.39698
$67$	4.67997	0.571750	0.285875	−	0.958267i	$-0.407716\pi$
$67$	4.67997	0.571750	0.285875	+	0.958267i	$0.407716\pi$
$68$	0.598110	0.0725315
$69$	−9.49619	−1.14321
$70$	4.20181	0.502213
$71$	11.4239	1.35577	0.677886	−	0.735167i	$-0.262896\pi$
$71$	11.4239	1.35577	0.677886	+	0.735167i	$0.262896\pi$
$72$	1.52641	0.179889
$73$	5.35047	0.626225	0.313113	−	0.949716i	$-0.398628\pi$
$73$	5.35047	0.626225	0.313113	+	0.949716i	$0.398628\pi$
$74$	5.75869	0.669434
$75$	3.75231	0.433279
$76$	0.759473	0.0871175
$77$	9.09868	1.03689
$78$	−4.67838	−0.529723
$79$	−7.79987	−0.877554	−0.438777	−	0.898596i	$-0.644588\pi$
$79$	−7.79987	−0.877554	−0.438777	+	0.898596i	$0.644588\pi$
$80$	6.17481	0.690365
$81$	−0.995634	−0.110626
$82$	−18.9336	−2.09087
$83$	−17.9975	−1.97548	−0.987740	−	0.156107i	$-0.950105\pi$
$83$	−17.9975	−1.97548	−0.987740	+	0.156107i	$0.950105\pi$
$84$	2.97227	0.324301
$85$	−0.513238	−0.0556685
$86$	18.6415	2.01016
$87$	5.13716	0.550761
$88$	4.76002	0.507420
$89$	13.3683	1.41704	0.708519	−	0.705691i	$-0.249363\pi$
$89$	13.3683	1.41704	0.708519	+	0.705691i	$0.249363\pi$
$90$	4.17292	0.439864
$91$	−3.75069	−0.393179
$92$	12.6890	1.32292
$93$	3.37640	0.350116
$94$	1.34114	0.138328
$95$	−0.651703	−0.0668633
$96$	8.06385	0.823013
$97$	−13.2660	−1.34696	−0.673480	−	0.739206i	$-0.735201\pi$
$97$	−13.2660	−1.34696	−0.673480	+	0.739206i	$0.735201\pi$
$98$	−7.62355	−0.770095
$99$	9.03610	0.908162
$100$	−5.01389	−0.501389
$101$	−5.06820	−0.504305	−0.252152	−	0.967688i	$-0.581138\pi$
$101$	−5.06820	−0.504305	−0.252152	+	0.967688i	$0.581138\pi$
$102$	−0.840064	−0.0831787
$103$	−1.26789	−0.124929	−0.0624644	−	0.998047i	$-0.519896\pi$
$103$	−1.26789	−0.124929	−0.0624644	+	0.998047i	$0.519896\pi$
$104$	−1.96219	−0.192409
$105$	−2.55050	−0.248904
$106$	−19.4606	−1.89018
$107$	11.5228	1.11395	0.556974	−	0.830530i	$-0.311962\pi$
$107$	11.5228	1.11395	0.556974	+	0.830530i	$0.311962\pi$
$108$	8.15407	0.784626
$109$	1.84704	0.176914	0.0884570	−	0.996080i	$-0.471806\pi$
$109$	1.84704	0.176914	0.0884570	+	0.996080i	$0.471806\pi$
$110$	13.0130	1.24074
$111$	−3.49553	−0.331781
$112$	8.10275	0.765638
$113$	−10.8186	−1.01773	−0.508865	−	0.860846i	$-0.669935\pi$
$113$	−10.8186	−1.01773	−0.508865	+	0.860846i	$0.669935\pi$
$114$	−1.06670	−0.0999057
$115$	−10.8884	−1.01535
$116$	−6.86435	−0.637339
$117$	−3.72489	−0.344367
$118$	−12.3545	−1.13733
$119$	−0.673484	−0.0617382
$120$	−1.33431	−0.121805
$121$	17.1786	1.56169
$122$	−1.66869	−0.151077
$123$	11.4927	1.03626
$124$	−4.51159	−0.405153
$125$	10.8334	0.968971
$126$	5.47580	0.487823
$127$	16.9759	1.50637	0.753185	−	0.657809i	$-0.228517\pi$
$127$	16.9759	1.50637	0.753185	+	0.657809i	$0.228517\pi$
$128$	6.96893	0.615972
$129$	−11.3154	−0.996266
$130$	−5.36426	−0.470477
$131$	0.273878	0.0239289	0.0119644	−	0.999928i	$-0.496192\pi$
$131$	0.273878	0.0239289	0.0119644	+	0.999928i	$0.496192\pi$
$132$	9.20511	0.801202
$133$	−0.855181	−0.0741536
$134$	8.78316	0.758749
$135$	−6.99701	−0.602206
$136$	−0.352337	−0.0302126
$137$	−5.63213	−0.481185	−0.240593	−	0.970626i	$-0.577342\pi$
$137$	−5.63213	−0.481185	−0.240593	+	0.970626i	$0.577342\pi$
$138$	−17.8220	−1.51711
$139$	−22.7017	−1.92553	−0.962767	−	0.270333i	$-0.912866\pi$
$139$	−22.7017	−1.92553	−0.962767	+	0.270333i	$0.912866\pi$
$140$	3.40802	0.288030
$141$	−0.814072	−0.0685572
$142$	21.4399	1.79920
$143$	−11.6159	−0.971367
$144$	8.04702	0.670585
$145$	5.89029	0.489162
$146$	10.0415	0.831042
$147$	4.62750	0.381670
$148$	4.67078	0.383936
$149$	−3.23862	−0.265318	−0.132659	−	0.991162i	$-0.542352\pi$
$149$	−3.23862	−0.265318	−0.132659	+	0.991162i	$0.542352\pi$
$150$	7.04216	0.574990
$151$	18.3287	1.49157	0.745783	−	0.666189i	$-0.232076\pi$
$151$	18.3287	1.49157	0.745783	+	0.666189i	$0.232076\pi$
$152$	−0.447392	−0.0362883
$153$	−0.668852	−0.0540735
$154$	17.0760	1.37602
$155$	3.87140	0.310958
$156$	−3.79456	−0.303808
$157$	−2.10134	−0.167705	−0.0838527	−	0.996478i	$-0.526723\pi$
$157$	−2.10134	−0.167705	−0.0838527	+	0.996478i	$0.526723\pi$
$158$	−14.6384	−1.16457
$159$	11.8126	0.936799
$160$	9.24605	0.730965
$161$	−14.2880	−1.12605
$162$	−1.86856	−0.146808
$163$	−23.0706	−1.80703	−0.903514	−	0.428558i	$-0.859022\pi$
$163$	−23.0706	−1.80703	−0.903514	+	0.428558i	$0.859022\pi$
$164$	−15.3568	−1.19916
$165$	−7.89890	−0.614928
$166$	−33.7768	−2.62159
$167$	−11.3441	−0.877832	−0.438916	−	0.898528i	$-0.644637\pi$
$167$	−11.3441	−0.877832	−0.438916	+	0.898528i	$0.644637\pi$
$168$	−1.75091	−0.135086
$169$	−8.21167	−0.631667
$170$	−0.963222	−0.0738757
$171$	−0.849299	−0.0649476
$172$	15.1198	1.15287
$173$	−17.2109	−1.30852	−0.654259	−	0.756271i	$-0.727019\pi$
$173$	−17.2109	−1.30852	−0.654259	+	0.756271i	$0.727019\pi$
$174$	9.64118	0.730896
$175$	5.64574	0.426778
$176$	25.0942	1.89154
$177$	7.49921	0.563675
$178$	25.0890	1.88050
$179$	−11.9899	−0.896168	−0.448084	−	0.893991i	$-0.647893\pi$
$179$	−11.9899	−0.896168	−0.448084	+	0.893991i	$0.647893\pi$
$180$	3.38458	0.252272
$181$	1.09690	0.0815319	0.0407660	−	0.999169i	$-0.487020\pi$
$181$	1.09690	0.0815319	0.0407660	+	0.999169i	$0.487020\pi$
$182$	−7.03912	−0.521774
$183$	1.01290	0.0748756
$184$	−7.47485	−0.551053
$185$	−4.00799	−0.294673
$186$	6.33667	0.464627
$187$	−2.08578	−0.152527
$188$	1.08778	0.0793342
$189$	−9.18165	−0.667867
$190$	−1.22309	−0.0887320
$191$	1.44468	0.104533	0.0522667	−	0.998633i	$-0.483355\pi$
$191$	1.44468	0.104533	0.0522667	+	0.998633i	$0.483355\pi$
$192$	4.36325	0.314891
$193$	1.41359	0.101753	0.0508763	−	0.998705i	$-0.483799\pi$
$193$	1.41359	0.101753	0.0508763	+	0.998705i	$0.483799\pi$
$194$	−24.8970	−1.78750
$195$	3.25611	0.233175
$196$	−6.18334	−0.441667
$197$	−5.14237	−0.366379	−0.183189	−	0.983078i	$-0.558642\pi$
$197$	−5.14237	−0.366379	−0.183189	+	0.983078i	$0.558642\pi$
$198$	16.9585	1.20519
$199$	−16.7502	−1.18739	−0.593695	−	0.804690i	$-0.702332\pi$
$199$	−16.7502	−1.18739	−0.593695	+	0.804690i	$0.702332\pi$
$200$	2.95360	0.208851
$201$	−5.33139	−0.376047
$202$	−9.51176	−0.669245
$203$	7.72939	0.542497
$204$	−0.681362	−0.0477049
$205$	13.1776	0.920366
$206$	−2.37951	−0.165789
$207$	−14.1897	−0.986256
$208$	−10.3444	−0.717255
$209$	−2.64849	−0.183200
$210$	−4.78667	−0.330311
$211$	−11.7475	−0.808734	−0.404367	−	0.914597i	$-0.632508\pi$
$211$	−11.7475	−0.808734	−0.404367	+	0.914597i	$0.632508\pi$
$212$	−15.7842	−1.08406
$213$	−13.0141	−0.891708
$214$	21.6254	1.47828
$215$	−12.9743	−0.884840
$216$	−4.80343	−0.326832
$217$	5.08014	0.344863
$218$	3.46643	0.234777
$219$	−6.09521	−0.411876
$220$	10.5546	0.711593
$221$	0.859806	0.0578368
$222$	−6.56025	−0.440295
$223$	26.9958	1.80778	0.903888	−	0.427770i	$-0.140701\pi$
$223$	26.9958	1.80778	0.903888	+	0.427770i	$0.140701\pi$
$224$	12.1329	0.810664
$225$	5.60691	0.373794
$226$	−20.3039	−1.35059
$227$	−6.16279	−0.409039	−0.204519	−	0.978863i	$-0.565563\pi$
$227$	−6.16279	−0.409039	−0.204519	+	0.978863i	$0.565563\pi$
$228$	−0.865184	−0.0572982
$229$	5.04203	0.333187	0.166593	−	0.986026i	$-0.446723\pi$
$229$	5.04203	0.333187	0.166593	+	0.986026i	$0.446723\pi$
$230$	−20.4348	−1.34743
$231$	−10.3651	−0.681975
$232$	4.04367	0.265480
$233$	−8.21008	−0.537860	−0.268930	−	0.963160i	$-0.586670\pi$
$233$	−8.21008	−0.537860	−0.268930	+	0.963160i	$0.586670\pi$
$234$	−6.99071	−0.456997
$235$	−0.933419	−0.0608896
$236$	−10.0206	−0.652283
$237$	8.88554	0.577178
$238$	−1.26396	−0.0819306
$239$	25.4229	1.64447	0.822235	−	0.569148i	$-0.192727\pi$
$239$	25.4229	1.64447	0.822235	+	0.569148i	$0.192727\pi$
$240$	−7.03429	−0.454062
$241$	26.7739	1.72466	0.862328	−	0.506350i	$-0.169006\pi$
$241$	26.7739	1.72466	0.862328	+	0.506350i	$0.169006\pi$
$242$	32.2399	2.07246
$243$	−14.9360	−0.958148
$244$	−1.35345	−0.0866458
$245$	5.30592	0.338983
$246$	21.5690	1.37519
$247$	1.09177	0.0694677
$248$	2.65770	0.168764
$249$	20.5026	1.29930
$250$	20.3317	1.28589
$251$	23.7572	1.49954	0.749770	−	0.661699i	$-0.230164\pi$
$251$	23.7572	1.49954	0.749770	+	0.661699i	$0.230164\pi$
$252$	4.44134	0.279778
$253$	−44.2499	−2.78197
$254$	31.8596	1.99905
$255$	0.584676	0.0366138
$256$	20.7392	1.29620
$257$	−6.92184	−0.431773	−0.215886	−	0.976418i	$-0.569264\pi$
$257$	−6.92184	−0.431773	−0.215886	+	0.976418i	$0.569264\pi$
$258$	−21.2362	−1.32211
$259$	−5.25939	−0.326802
$260$	−4.35087	−0.269829
$261$	7.67623	0.475147
$262$	0.514002	0.0317551
$263$	−9.02135	−0.556281	−0.278140	−	0.960540i	$-0.589718\pi$
$263$	−9.02135	−0.556281	−0.278140	+	0.960540i	$0.589718\pi$
$264$	−5.42257	−0.333736
$265$	13.5444	0.832025
$266$	−1.60496	−0.0984066
$267$	−15.2291	−0.932004
$268$	7.12388	0.435160
$269$	7.43191	0.453131	0.226566	−	0.973996i	$-0.427250\pi$
$269$	7.43191	0.453131	0.226566	+	0.973996i	$0.427250\pi$
$270$	−13.1317	−0.799167
$271$	24.3754	1.48070	0.740351	−	0.672220i	$-0.234659\pi$
$271$	24.3754	1.48070	0.740351	+	0.672220i	$0.234659\pi$
$272$	−1.85747	−0.112626
$273$	4.27275	0.258599
$274$	−10.5701	−0.638564
$275$	17.4848	1.05437
$276$	−14.4551	−0.870098
$277$	15.8453	0.952052	0.476026	−	0.879431i	$-0.342077\pi$
$277$	15.8453	0.952052	0.476026	+	0.879431i	$0.342077\pi$
$278$	−42.6055	−2.55531
$279$	5.04520	0.302049
$280$	−2.00761	−0.119977
$281$	5.55329	0.331281	0.165641	−	0.986186i	$-0.447031\pi$
$281$	5.55329	0.331281	0.165641	+	0.986186i	$0.447031\pi$
$282$	−1.52781	−0.0909799
$283$	−21.5322	−1.27996	−0.639978	−	0.768394i	$-0.721056\pi$
$283$	−21.5322	−1.27996	−0.639978	+	0.768394i	$0.721056\pi$
$284$	17.3896	1.03188
$285$	0.742414	0.0439768
$286$	−21.8001	−1.28907
$287$	17.2920	1.02072
$288$	12.0495	0.710021
$289$	−16.8456	−0.990918
$290$	11.0546	0.649150
$291$	15.1125	0.885912
$292$	8.14451	0.476621
$293$	−23.9442	−1.39884	−0.699418	−	0.714713i	$-0.746557\pi$
$293$	−23.9442	−1.39884	−0.699418	+	0.714713i	$0.746557\pi$
$294$	8.68468	0.506501
$295$	8.59863	0.500632
$296$	−2.75148	−0.159926
$297$	−28.4355	−1.65000
$298$	−6.07809	−0.352094
$299$	18.2408	1.05490
$300$	5.71178	0.329770
$301$	−17.0252	−0.981316
$302$	34.3984	1.97941
$303$	5.77365	0.331687
$304$	−2.35859	−0.135274
$305$	1.16140	0.0665013
$306$	−1.25527	−0.0717591
$307$	1.31760	0.0751996	0.0375998	−	0.999293i	$-0.488029\pi$
$307$	1.31760	0.0751996	0.0375998	+	0.999293i	$0.488029\pi$
$308$	13.8500	0.789180
$309$	1.44437	0.0821672
$310$	7.26566	0.412662
$311$	−21.9974	−1.24736	−0.623679	−	0.781680i	$-0.714363\pi$
$311$	−21.9974	−1.24736	−0.623679	+	0.781680i	$0.714363\pi$
$312$	2.23531	0.126550
$313$	−0.891821	−0.0504087	−0.0252044	−	0.999682i	$-0.508024\pi$
$313$	−0.891821	−0.0504087	−0.0252044	+	0.999682i	$0.508024\pi$
$314$	−3.94370	−0.222556
$315$	−3.81111	−0.214732
$316$	−11.8730	−0.667908
$317$	−24.3281	−1.36640	−0.683202	−	0.730229i	$-0.739413\pi$
$317$	−24.3281	−1.36640	−0.683202	+	0.730229i	$0.739413\pi$
$318$	22.1693	1.24319
$319$	23.9379	1.34026
$320$	5.00293	0.279672
$321$	−13.1266	−0.732657
$322$	−26.8151	−1.49435
$323$	0.196041	0.0109080
$324$	−1.51556	−0.0841977
$325$	−7.20765	−0.399809
$326$	−43.2978	−2.39804
$327$	−2.10413	−0.116359
$328$	9.04641	0.499504
$329$	−1.22486	−0.0675285
$330$	−14.8243	−0.816050
$331$	27.7538	1.52549	0.762745	−	0.646700i	$-0.223851\pi$
$331$	27.7538	1.52549	0.762745	+	0.646700i	$0.223851\pi$
$332$	−27.3958	−1.50354
$333$	−5.22322	−0.286231
$334$	−21.2901	−1.16494
$335$	−6.11300	−0.333989
$336$	−9.23058	−0.503569
$337$	6.10740	0.332691	0.166346	−	0.986068i	$-0.446803\pi$
$337$	6.10740	0.332691	0.166346	+	0.986068i	$0.446803\pi$
$338$	−15.4113	−0.838263
$339$	12.3245	0.669374
$340$	−0.781253	−0.0423694
$341$	15.7332	0.851999
$342$	−1.59393	−0.0861896
$343$	18.9608	1.02379
$344$	−8.90682	−0.480224
$345$	12.4040	0.667806
$346$	−32.3005	−1.73649
$347$	27.7441	1.48938	0.744691	−	0.667409i	$-0.232597\pi$
$347$	27.7441	1.48938	0.744691	+	0.667409i	$0.232597\pi$
$348$	7.81981	0.419186
$349$	−14.3589	−0.768616	−0.384308	−	0.923205i	$-0.625560\pi$
$349$	−14.3589	−0.768616	−0.384308	+	0.923205i	$0.625560\pi$
$350$	10.5957	0.566362
$351$	11.7218	0.625663
$352$	37.5755	2.00278
$353$	1.89459	0.100839	0.0504194	−	0.998728i	$-0.483944\pi$
$353$	1.89459	0.100839	0.0504194	+	0.998728i	$0.483944\pi$
$354$	14.0742	0.748034
$355$	−14.9220	−0.791977
$356$	20.3493	1.07851
$357$	0.767227	0.0406060
$358$	−22.5021	−1.18927
$359$	10.0371	0.529740	0.264870	−	0.964284i	$-0.414671\pi$
$359$	10.0371	0.529740	0.264870	+	0.964284i	$0.414671\pi$
$360$	−1.99380	−0.105083
$361$	−18.7511	−0.986898
$362$	2.05861	0.108198
$363$	−19.5697	−1.02714
$364$	−5.70931	−0.299249
$365$	−6.98880	−0.365810
$366$	1.90096	0.0993649
$367$	5.02023	0.262054	0.131027	−	0.991379i	$-0.458173\pi$
$367$	5.02023	0.262054	0.131027	+	0.991379i	$0.458173\pi$
$368$	−39.4064	−2.05420
$369$	17.1731	0.893996
$370$	−7.52201	−0.391051
$371$	17.7733	0.922742
$372$	5.13957	0.266474
$373$	−3.12699	−0.161910	−0.0809548	−	0.996718i	$-0.525797\pi$
$373$	−3.12699	−0.161910	−0.0809548	+	0.996718i	$0.525797\pi$
$374$	−3.91449	−0.202413
$375$	−12.3413	−0.637304
$376$	−0.640790	−0.0330462
$377$	−9.86776	−0.508215
$378$	−17.2317	−0.886302
$379$	16.8372	0.864867	0.432433	−	0.901666i	$-0.357655\pi$
$379$	16.8372	0.864867	0.432433	+	0.901666i	$0.357655\pi$
$380$	−0.992025	−0.0508898
$381$	−19.3388	−0.990757
$382$	2.71131	0.138723
$383$	−3.31954	−0.169621	−0.0848104	−	0.996397i	$-0.527028\pi$
$383$	−3.31954	−0.169621	−0.0848104	+	0.996397i	$0.527028\pi$
$384$	−7.93894	−0.405132
$385$	−11.8847	−0.605701
$386$	2.65297	0.135032
$387$	−16.9081	−0.859488
$388$	−20.1936	−1.02517
$389$	−13.8035	−0.699867	−0.349933	−	0.936775i	$-0.613796\pi$
$389$	−13.8035	−0.699867	−0.349933	+	0.936775i	$0.613796\pi$
$390$	6.11092	0.309438
$391$	3.27538	0.165643
$392$	3.64250	0.183974
$393$	−0.312000	−0.0157383
$394$	−9.65096	−0.486208
$395$	10.1882	0.512625
$396$	13.7548	0.691204
$397$	13.6460	0.684875	0.342438	−	0.939541i	$-0.388747\pi$
$397$	13.6460	0.684875	0.342438	+	0.939541i	$0.388747\pi$
$398$	−31.4360	−1.57574
$399$	0.974214	0.0487717
$400$	15.5710	0.778548
$401$	−4.21927	−0.210700	−0.105350	−	0.994435i	$-0.533596\pi$
$401$	−4.21927	−0.210700	−0.105350	+	0.994435i	$0.533596\pi$
$402$	−10.0057	−0.499039
$403$	−6.48558	−0.323070
$404$	−7.71484	−0.383828
$405$	1.30050	0.0646224
$406$	14.5062	0.719929
$407$	−16.2883	−0.807381
$408$	0.401379	0.0198712
$409$	3.32926	0.164621	0.0823105	−	0.996607i	$-0.473770\pi$
$409$	3.32926	0.164621	0.0823105	+	0.996607i	$0.473770\pi$
$410$	24.7312	1.22139
$411$	6.41607	0.316481
$412$	−1.92999	−0.0950836
$413$	11.2833	0.555217
$414$	−26.6307	−1.30883
$415$	23.5084	1.15398
$416$	−15.4895	−0.759436
$417$	25.8616	1.26645
$418$	−4.97056	−0.243118
$419$	−17.2091	−0.840718	−0.420359	−	0.907358i	$-0.638096\pi$
$419$	−17.2091	−0.840718	−0.420359	+	0.907358i	$0.638096\pi$
$420$	−3.88239	−0.189441
$421$	5.90690	0.287884	0.143942	−	0.989586i	$-0.454022\pi$
$421$	5.90690	0.287884	0.143942	+	0.989586i	$0.454022\pi$
$422$	−22.0472	−1.07324
$423$	−1.21643	−0.0591450
$424$	9.29818	0.451559
$425$	−1.29423	−0.0627792
$426$	−24.4242	−1.18336
$427$	1.52401	0.0737521
$428$	17.5400	0.847828
$429$	13.2327	0.638880
$430$	−24.3496	−1.17424
$431$	−27.0646	−1.30366	−0.651829	−	0.758366i	$-0.725998\pi$
$431$	−27.0646	−1.30366	−0.651829	+	0.758366i	$0.725998\pi$
$432$	−25.3230	−1.21835
$433$	−5.65104	−0.271571	−0.135786	−	0.990738i	$-0.543356\pi$
$433$	−5.65104	−0.271571	−0.135786	+	0.990738i	$0.543356\pi$
$434$	9.53418	0.457655
$435$	−6.71017	−0.321728
$436$	2.81157	0.134650
$437$	4.15903	0.198953
$438$	−11.4392	−0.546586
$439$	−26.7713	−1.27772	−0.638861	−	0.769322i	$-0.720594\pi$
$439$	−26.7713	−1.27772	−0.638861	+	0.769322i	$0.720594\pi$
$440$	−6.21755	−0.296410
$441$	6.91468	0.329270
$442$	1.61364	0.0767532
$443$	34.1995	1.62487	0.812435	−	0.583052i	$-0.198142\pi$
$443$	34.1995	1.62487	0.812435	+	0.583052i	$0.198142\pi$
$444$	−5.32091	−0.252519
$445$	−17.4617	−0.827765
$446$	50.6646	2.39904
$447$	3.68940	0.174503
$448$	6.56497	0.310166
$449$	−7.11797	−0.335918	−0.167959	−	0.985794i	$-0.553718\pi$
$449$	−7.11797	−0.335918	−0.167959	+	0.985794i	$0.553718\pi$
$450$	10.5228	0.496049
$451$	53.5533	2.52173
$452$	−16.4682	−0.774597
$453$	−20.8799	−0.981021
$454$	−11.5660	−0.542821
$455$	4.89916	0.229676
$456$	0.509665	0.0238673
$457$	25.8336	1.20845	0.604223	−	0.796815i	$-0.293484\pi$
$457$	25.8336	1.20845	0.604223	+	0.796815i	$0.293484\pi$
$458$	9.46265	0.442161
$459$	2.10480	0.0982435
$460$	−16.5744	−0.772783
$461$	−38.8134	−1.80772	−0.903860	−	0.427829i	$-0.859279\pi$
$461$	−38.8134	−1.80772	−0.903860	+	0.427829i	$0.859279\pi$
$462$	−19.4528	−0.905026
$463$	22.8908	1.06383	0.531913	−	0.846799i	$-0.321473\pi$
$463$	22.8908	1.06383	0.531913	+	0.846799i	$0.321473\pi$
$464$	21.3177	0.989648
$465$	−4.41026	−0.204521
$466$	−15.4083	−0.713775
$467$	−12.1901	−0.564089	−0.282045	−	0.959401i	$-0.591013\pi$
$467$	−12.1901	−0.564089	−0.282045	+	0.959401i	$0.591013\pi$
$468$	−5.67005	−0.262098
$469$	−8.02163	−0.370404
$470$	−1.75180	−0.0808044
$471$	2.39383	0.110302
$472$	5.90294	0.271705
$473$	−52.7270	−2.42439
$474$	16.6760	0.765953
$475$	−1.64339	−0.0754039
$476$	−1.02518	−0.0469891
$477$	17.6510	0.808186
$478$	47.7125	2.18232
$479$	−35.1228	−1.60480	−0.802400	−	0.596786i	$-0.796444\pi$
$479$	−35.1228	−1.60480	−0.802400	+	0.596786i	$0.796444\pi$
$480$	−10.5330	−0.480764
$481$	6.71442	0.306151
$482$	50.2479	2.28873
$483$	16.2768	0.740619
$484$	26.1493	1.18860
$485$	17.3281	0.786828
$486$	−28.0313	−1.27152
$487$	7.59211	0.344031	0.172016	−	0.985094i	$-0.444972\pi$
$487$	7.59211	0.344031	0.172016	+	0.985094i	$0.444972\pi$
$488$	0.797295	0.0360918
$489$	26.2818	1.18850
$490$	9.95790	0.449852
$491$	18.2927	0.825537	0.412768	−	0.910836i	$-0.364562\pi$
$491$	18.2927	0.825537	0.412768	+	0.910836i	$0.364562\pi$
$492$	17.4943	0.788704
$493$	−1.77188	−0.0798015
$494$	2.04898	0.0921881
$495$	−11.8030	−0.530504
$496$	14.0110	0.629114
$497$	−19.5810	−0.878328
$498$	38.4783	1.72425
$499$	5.76535	0.258093	0.129046	−	0.991639i	$-0.458808\pi$
$499$	5.76535	0.258093	0.129046	+	0.991639i	$0.458808\pi$
$500$	16.4907	0.737486
$501$	12.9231	0.577361
$502$	44.5864	1.98999
$503$	−21.1805	−0.944394	−0.472197	−	0.881493i	$-0.656539\pi$
$503$	−21.1805	−0.944394	−0.472197	+	0.881493i	$0.656539\pi$
$504$	−2.61631	−0.116540
$505$	6.62010	0.294590
$506$	−83.0462	−3.69185
$507$	9.35466	0.415455
$508$	25.8408	1.14650
$509$	18.1907	0.806289	0.403145	−	0.915136i	$-0.367917\pi$
$509$	18.1907	0.806289	0.403145	+	0.915136i	$0.367917\pi$
$510$	1.09729	0.0485890
$511$	−9.17088	−0.405696
$512$	24.9846	1.10417
$513$	2.67264	0.118000
$514$	−12.9906	−0.572991
$515$	1.65612	0.0729773
$516$	−17.2244	−0.758260
$517$	−3.79337	−0.166832
$518$	−9.87058	−0.433688
$519$	19.6065	0.860628
$520$	2.56302	0.112396
$521$	21.4553	0.939976	0.469988	−	0.882673i	$-0.344258\pi$
$521$	21.4553	0.939976	0.469988	+	0.882673i	$0.344258\pi$
$522$	14.4064	0.630551
$523$	11.6184	0.508038	0.254019	−	0.967199i	$-0.418247\pi$
$523$	11.6184	0.508038	0.254019	+	0.967199i	$0.418247\pi$
$524$	0.416899	0.0182123
$525$	−6.43157	−0.280697
$526$	−16.9309	−0.738221
$527$	−1.16457	−0.0507294
$528$	−28.5870	−1.24409
$529$	46.4874	2.02119
$530$	25.4195	1.10415
$531$	11.2057	0.486288
$532$	−1.30176	−0.0564385
$533$	−22.0759	−0.956214
$534$	−28.5812	−1.23683
$535$	−15.0511	−0.650714
$536$	−4.19655	−0.181264
$537$	13.6588	0.589421
$538$	13.9479	0.601335
$539$	21.5630	0.928785
$540$	−10.6509	−0.458341
$541$	15.8443	0.681198	0.340599	−	0.940209i	$-0.389370\pi$
$541$	15.8443	0.681198	0.340599	+	0.940209i	$0.389370\pi$
$542$	45.7467	1.96499
$543$	−1.24958	−0.0536245
$544$	−2.78134	−0.119249
$545$	−2.41260	−0.103345
$546$	8.01890	0.343177
$547$	−1.00000	−0.0427569
$547$	−1.00000	−0.0427569
$548$	−8.57325	−0.366231
$549$	1.51353	0.0645959
$550$	32.8147	1.39922
$551$	−2.24991	−0.0958495
$552$	8.51528	0.362434
$553$	13.3692	0.568517
$554$	29.7377	1.26343
$555$	4.56587	0.193810
$556$	−34.5566	−1.46553
$557$	11.0799	0.469471	0.234735	−	0.972059i	$-0.424578\pi$
$557$	11.0799	0.469471	0.234735	+	0.972059i	$0.424578\pi$
$558$	9.46861	0.400838
$559$	21.7353	0.919305
$560$	−10.5838	−0.447248
$561$	2.37610	0.100319
$562$	10.4221	0.439632
$563$	41.1603	1.73470	0.867351	−	0.497697i	$-0.165821\pi$
$563$	41.1603	1.73470	0.867351	+	0.497697i	$0.165821\pi$
$564$	−1.23918	−0.0521791
$565$	14.1313	0.594509
$566$	−40.4106	−1.69858
$567$	1.70655	0.0716683
$568$	−10.2439	−0.429825
$569$	−9.52628	−0.399363	−0.199681	−	0.979861i	$-0.563991\pi$
$569$	−9.52628	−0.399363	−0.199681	+	0.979861i	$0.563991\pi$
$570$	1.39333	0.0583601
$571$	4.76393	0.199364	0.0996822	−	0.995019i	$-0.468217\pi$
$571$	4.76393	0.199364	0.0996822	+	0.995019i	$0.468217\pi$
$572$	−17.6817	−0.739310
$573$	−1.64577	−0.0687530
$574$	32.4529	1.35456
$575$	−27.4571	−1.14504
$576$	6.51982	0.271659
$577$	33.8345	1.40855	0.704274	−	0.709929i	$-0.251273\pi$
$577$	33.8345	1.40855	0.704274	+	0.709929i	$0.251273\pi$
$578$	−31.6151	−1.31501
$579$	−1.61035	−0.0669240
$580$	8.96623	0.372303
$581$	30.8483	1.27980
$582$	28.3625	1.17566
$583$	55.0437	2.27968
$584$	−4.79779	−0.198534
$585$	4.86547	0.201162
$586$	−44.9374	−1.85635
$587$	−12.2101	−0.503964	−0.251982	−	0.967732i	$-0.581082\pi$
$587$	−12.2101	−0.503964	−0.251982	+	0.967732i	$0.581082\pi$
$588$	7.04400	0.290490
$589$	−1.47875	−0.0609310
$590$	16.1375	0.664371
$591$	5.85814	0.240972
$592$	−14.5054	−0.596168
$593$	32.7830	1.34624	0.673118	−	0.739535i	$-0.264954\pi$
$593$	32.7830	1.34624	0.673118	+	0.739535i	$0.264954\pi$
$594$	−53.3664	−2.18965
$595$	0.879707	0.0360645
$596$	−4.92984	−0.201934
$597$	19.0817	0.780961
$598$	34.2336	1.39992
$599$	−26.1846	−1.06987	−0.534936	−	0.844892i	$-0.679664\pi$
$599$	−26.1846	−1.06987	−0.534936	+	0.844892i	$0.679664\pi$
$600$	−3.36471	−0.137364
$601$	−14.1011	−0.575196	−0.287598	−	0.957751i	$-0.592857\pi$
$601$	−14.1011	−0.575196	−0.287598	+	0.957751i	$0.592857\pi$
$602$	−31.9521	−1.30227
$603$	−7.96646	−0.324419
$604$	27.9000	1.13523
$605$	−22.4387	−0.912262
$606$	10.8357	0.440171
$607$	16.3651	0.664239	0.332120	−	0.943237i	$-0.392236\pi$
$607$	16.3651	0.664239	0.332120	+	0.943237i	$0.392236\pi$
$608$	−3.53171	−0.143230
$609$	−8.80525	−0.356807
$610$	2.17965	0.0882516
$611$	1.56372	0.0632612
$612$	−1.01813	−0.0411555
$613$	−13.3441	−0.538961	−0.269481	−	0.963006i	$-0.586852\pi$
$613$	−13.3441	−0.538961	−0.269481	+	0.963006i	$0.586852\pi$
$614$	2.47282	0.0997948
$615$	−15.0118	−0.605336
$616$	−8.15882	−0.328728
$617$	34.5802	1.39215	0.696074	−	0.717971i	$-0.254929\pi$
$617$	34.5802	1.39215	0.696074	+	0.717971i	$0.254929\pi$
$618$	2.71072	0.109041
$619$	−20.0240	−0.804832	−0.402416	−	0.915457i	$-0.631829\pi$
$619$	−20.0240	−0.804832	−0.402416	+	0.915457i	$0.631829\pi$
$620$	5.89306	0.236671
$621$	44.6534	1.79188
$622$	−41.2837	−1.65533
$623$	−22.9137	−0.918019
$624$	11.7843	0.471748
$625$	2.31852	0.0927408
$626$	−1.67373	−0.0668957
$627$	3.01714	0.120493
$628$	−3.19868	−0.127641
$629$	1.20566	0.0480728
$630$	−7.15251	−0.284963
$631$	−1.64737	−0.0655808	−0.0327904	−	0.999462i	$-0.510439\pi$
$631$	−1.64737	−0.0655808	−0.0327904	+	0.999462i	$0.510439\pi$
$632$	6.99418	0.278213
$633$	13.3827	0.531914
$634$	−45.6579	−1.81331
$635$	−22.1740	−0.879948
$636$	17.9812	0.713000
$637$	−8.88878	−0.352186
$638$	44.9255	1.77862
$639$	−19.4463	−0.769285
$640$	−9.10283	−0.359821
$641$	30.9733	1.22337	0.611686	−	0.791100i	$-0.290491\pi$
$641$	30.9733	1.22337	0.611686	+	0.791100i	$0.290491\pi$
$642$	−24.6354	−0.972283
$643$	24.8226	0.978907	0.489454	−	0.872029i	$-0.337196\pi$
$643$	24.8226	0.978907	0.489454	+	0.872029i	$0.337196\pi$
$644$	−21.7493	−0.857042
$645$	14.7802	0.581970
$646$	0.367921	0.0144757
$647$	36.5122	1.43544	0.717721	−	0.696331i	$-0.245185\pi$
$647$	36.5122	1.43544	0.717721	+	0.696331i	$0.245185\pi$
$648$	0.892790	0.0350721
$649$	34.9445	1.37169
$650$	−13.5270	−0.530572
$651$	−5.78725	−0.226820
$652$	−35.1182	−1.37533
$653$	−26.5164	−1.03767	−0.518834	−	0.854875i	$-0.673634\pi$
$653$	−26.5164	−1.03767	−0.518834	+	0.854875i	$0.673634\pi$
$654$	−3.94893	−0.154415
$655$	−0.357740	−0.0139781
$656$	47.6914	1.86204
$657$	−9.10781	−0.355329
$658$	−2.29875	−0.0896147
$659$	−25.7938	−1.00478	−0.502391	−	0.864641i	$-0.667546\pi$
$659$	−25.7938	−1.00478	−0.502391	+	0.864641i	$0.667546\pi$
$660$	−12.0237	−0.468023
$661$	−41.9540	−1.63182	−0.815910	−	0.578179i	$-0.803764\pi$
$661$	−41.9540	−1.63182	−0.815910	+	0.578179i	$0.803764\pi$
$662$	52.0871	2.02442
$663$	−0.979483	−0.0380400
$664$	16.1384	0.626292
$665$	1.11704	0.0433169
$666$	−9.80269	−0.379847
$667$	−37.5906	−1.45551
$668$	−17.2680	−0.668120
$669$	−30.7534	−1.18900
$670$	−11.4726	−0.443225
$671$	4.71986	0.182208
$672$	−13.8217	−0.533183
$673$	−3.20648	−0.123601	−0.0618003	−	0.998089i	$-0.519684\pi$
$673$	−3.20648	−0.123601	−0.0618003	+	0.998089i	$0.519684\pi$
$674$	11.4621	0.441503
$675$	−17.6443	−0.679128
$676$	−12.4998	−0.480763
$677$	4.84844	0.186341	0.0931704	−	0.995650i	$-0.470300\pi$
$677$	4.84844	0.186341	0.0931704	+	0.995650i	$0.470300\pi$
$678$	23.1300	0.888303
$679$	22.7384	0.872618
$680$	0.460223	0.0176487
$681$	7.02059	0.269030
$682$	29.5273	1.13066
$683$	−32.3263	−1.23693	−0.618466	−	0.785812i	$-0.712245\pi$
$683$	−32.3263	−1.23693	−0.618466	+	0.785812i	$0.712245\pi$
$684$	−1.29281	−0.0494317
$685$	7.35670	0.281085
$686$	35.5847	1.35863
$687$	−5.74384	−0.219141
$688$	−46.9555	−1.79016
$689$	−22.6903	−0.864432
$690$	23.2792	0.886223
$691$	−9.59431	−0.364985	−0.182492	−	0.983207i	$-0.558416\pi$
$691$	−9.59431	−0.364985	−0.182492	+	0.983207i	$0.558416\pi$
$692$	−26.1985	−0.995916
$693$	−15.4882	−0.588347
$694$	52.0689	1.97651
$695$	29.6530	1.12480
$696$	−4.60651	−0.174609
$697$	−3.96401	−0.150148
$698$	−26.9482	−1.02000
$699$	9.35285	0.353757
$700$	8.59397	0.324821
$701$	−48.0675	−1.81549	−0.907743	−	0.419527i	$-0.862196\pi$
$701$	−48.0675	−1.81549	−0.907743	+	0.419527i	$0.862196\pi$
$702$	21.9989	0.830295
$703$	1.53093	0.0577401
$704$	20.3317	0.766279
$705$	1.06334	0.0400478
$706$	3.55568	0.133820
$707$	8.68706	0.326710
$708$	11.4153	0.429014
$709$	12.6771	0.476099	0.238049	−	0.971253i	$-0.423492\pi$
$709$	12.6771	0.476099	0.238049	+	0.971253i	$0.423492\pi$
$710$	−28.0049	−1.05100
$711$	13.2773	0.497937
$712$	−11.9874	−0.449248
$713$	−24.7064	−0.925263
$714$	1.43990	0.0538867
$715$	15.1727	0.567426
$716$	−18.2511	−0.682076
$717$	−28.9615	−1.08159
$718$	18.8372	0.702999
$719$	14.9369	0.557053	0.278526	−	0.960429i	$-0.410154\pi$
$719$	14.9369	0.557053	0.278526	+	0.960429i	$0.410154\pi$
$720$	−10.5110	−0.391723
$721$	2.17320	0.0809343
$722$	−35.1911	−1.30968
$723$	−30.5005	−1.13433
$724$	1.66971	0.0620541
$725$	14.8535	0.551644
$726$	−36.7274	−1.36308
$727$	−16.9039	−0.626932	−0.313466	−	0.949599i	$-0.601490\pi$
$727$	−16.9039	−0.626932	−0.313466	+	0.949599i	$0.601490\pi$
$728$	3.36326	0.124651
$729$	20.0019	0.740811
$730$	−13.1163	−0.485454
$731$	3.90285	0.144352
$732$	1.54184	0.0569880
$733$	17.0731	0.630609	0.315305	−	0.948991i	$-0.397893\pi$
$733$	17.0731	0.630609	0.315305	+	0.948991i	$0.397893\pi$
$734$	9.42174	0.347763
$735$	−6.04445	−0.222953
$736$	−59.0063	−2.17500
$737$	−24.8429	−0.915101
$738$	32.2297	1.18639
$739$	−0.313121	−0.0115183	−0.00575917	−	0.999983i	$-0.501833\pi$
$739$	−0.313121	−0.0115183	−0.00575917	+	0.999983i	$0.501833\pi$
$740$	−6.10098	−0.224277
$741$	−1.24373	−0.0456897
$742$	33.3561	1.22454
$743$	−19.0657	−0.699451	−0.349726	−	0.936852i	$-0.613725\pi$
$743$	−19.0657	−0.699451	−0.349726	+	0.936852i	$0.613725\pi$
$744$	−3.02763	−0.110998
$745$	4.23029	0.154986
$746$	−5.86860	−0.214865
$747$	30.6361	1.12092
$748$	−3.17498	−0.116089
$749$	−19.7504	−0.721663
$750$	−23.1617	−0.845744
$751$	−14.1901	−0.517803	−0.258901	−	0.965904i	$-0.583360\pi$
$751$	−14.1901	−0.517803	−0.258901	+	0.965904i	$0.583360\pi$
$752$	−3.37816	−0.123189
$753$	−27.0640	−0.986266
$754$	−18.5194	−0.674435
$755$	−23.9410	−0.871301
$756$	−13.9763	−0.508315
$757$	−32.0979	−1.16662	−0.583309	−	0.812250i	$-0.698242\pi$
$757$	−32.0979	−1.16662	−0.583309	+	0.812250i	$0.698242\pi$
$758$	31.5992	1.14773
$759$	50.4091	1.82973
$760$	0.584385	0.0211979
$761$	27.3107	0.990013	0.495006	−	0.868889i	$-0.335166\pi$
$761$	27.3107	0.990013	0.495006	+	0.868889i	$0.335166\pi$
$762$	−36.2942	−1.31480
$763$	−3.16588	−0.114613
$764$	2.19910	0.0795607
$765$	0.873656	0.0315871
$766$	−6.22997	−0.225098
$767$	−14.4049	−0.520132
$768$	−23.6259	−0.852528
$769$	15.5549	0.560923	0.280461	−	0.959865i	$-0.409513\pi$
$769$	15.5549	0.560923	0.280461	+	0.959865i	$0.409513\pi$
$770$	−22.3047	−0.803805
$771$	7.88530	0.283982
$772$	2.15178	0.0774442
$773$	−49.6932	−1.78734	−0.893670	−	0.448724i	$-0.851878\pi$
$773$	−49.6932	−1.78734	−0.893670	+	0.448724i	$0.851878\pi$
$774$	−31.7324	−1.14060
$775$	9.76245	0.350678
$776$	11.8957	0.427030
$777$	5.99145	0.214942
$778$	−25.9058	−0.928769
$779$	−5.03345	−0.180342
$780$	4.95647	0.177470
$781$	−60.6423	−2.16995
$782$	6.14708	0.219819
$783$	−24.1562	−0.863271
$784$	19.2028	0.685813
$785$	2.74478	0.0979654
$786$	−0.585546	−0.0208858
$787$	−14.9449	−0.532729	−0.266365	−	0.963872i	$-0.585823\pi$
$787$	−14.9449	−0.532729	−0.266365	+	0.963872i	$0.585823\pi$
$788$	−7.82774	−0.278852
$789$	10.2770	0.365873
$790$	19.1208	0.680286
$791$	18.5435	0.659330
$792$	−8.10271	−0.287917
$793$	−1.94564	−0.0690916
$794$	25.6103	0.908874
$795$	−15.4296	−0.547233
$796$	−25.4972	−0.903726
$797$	−13.1154	−0.464573	−0.232286	−	0.972647i	$-0.574621\pi$
$797$	−13.1154	−0.464573	−0.232286	+	0.972647i	$0.574621\pi$
$798$	1.82836	0.0647233
$799$	0.280785	0.00993347
$800$	23.3157	0.824333
$801$	−22.7561	−0.804049
$802$	−7.91853	−0.279613
$803$	−28.4022	−1.00229
$804$	−8.11546	−0.286210
$805$	18.6630	0.657786
$806$	−12.1718	−0.428735
$807$	−8.46636	−0.298030
$808$	4.54468	0.159881
$809$	−19.4909	−0.685262	−0.342631	−	0.939470i	$-0.611318\pi$
$809$	−19.4909	−0.685262	−0.342631	+	0.939470i	$0.611318\pi$
$810$	2.44072	0.0857581
$811$	18.5367	0.650912	0.325456	−	0.945557i	$-0.394482\pi$
$811$	18.5367	0.650912	0.325456	+	0.945557i	$0.394482\pi$
$812$	11.7657	0.412896
$813$	−27.7683	−0.973876
$814$	−30.5691	−1.07145
$815$	30.1349	1.05558
$816$	2.11601	0.0740753
$817$	4.95579	0.173381
$818$	6.24819	0.218463
$819$	6.38459	0.223095
$820$	20.0590	0.700492
$821$	−12.1526	−0.424130	−0.212065	−	0.977256i	$-0.568019\pi$
$821$	−12.1526	−0.424130	−0.212065	+	0.977256i	$0.568019\pi$
$822$	12.0414	0.419992
$823$	15.5837	0.543214	0.271607	−	0.962408i	$-0.412445\pi$
$823$	15.5837	0.543214	0.271607	+	0.962408i	$0.412445\pi$
$824$	1.13692	0.0396065
$825$	−19.9185	−0.693475
$826$	21.1761	0.736809
$827$	14.2481	0.495456	0.247728	−	0.968830i	$-0.420316\pi$
$827$	14.2481	0.495456	0.247728	+	0.968830i	$0.420316\pi$
$828$	−21.5997	−0.750641
$829$	52.8914	1.83700	0.918498	−	0.395426i	$-0.129403\pi$
$829$	52.8914	1.83700	0.918498	+	0.395426i	$0.129403\pi$
$830$	44.1194	1.53141
$831$	−18.0508	−0.626176
$832$	−8.38120	−0.290566
$833$	−1.59609	−0.0553014
$834$	48.5358	1.68066
$835$	14.8177	0.512787
$836$	−4.03154	−0.139434
$837$	−15.8766	−0.548777
$838$	−32.2972	−1.11569
$839$	−25.6169	−0.884395	−0.442198	−	0.896918i	$-0.645801\pi$
$839$	−25.6169	−0.884395	−0.442198	+	0.896918i	$0.645801\pi$
$840$	2.28705	0.0789107
$841$	−8.66460	−0.298779
$842$	11.0858	0.382041
$843$	−6.32625	−0.217888
$844$	−17.8821	−0.615529
$845$	10.7261	0.368989
$846$	−2.28294	−0.0784892
$847$	−29.4446	−1.01173
$848$	49.0187	1.68331
$849$	24.5293	0.841842
$850$	−2.42894	−0.0833121
$851$	25.5782	0.876808
$852$	−19.8101	−0.678681
$853$	23.7883	0.814498	0.407249	−	0.913317i	$-0.366488\pi$
$853$	23.7883	0.814498	0.407249	+	0.913317i	$0.366488\pi$
$854$	2.86020	0.0978739
$855$	1.10936	0.0379392
$856$	−10.3325	−0.353158
$857$	−1.27557	−0.0435727	−0.0217863	−	0.999763i	$-0.506935\pi$
$857$	−1.27557	−0.0435727	−0.0217863	+	0.999763i	$0.506935\pi$
$858$	24.8345	0.847835
$859$	−38.6456	−1.31857	−0.659285	−	0.751893i	$-0.729141\pi$
$859$	−38.6456	−1.31857	−0.659285	+	0.751893i	$0.729141\pi$
$860$	−19.7495	−0.673454
$861$	−19.6989	−0.671337
$862$	−50.7937	−1.73004
$863$	13.3344	0.453908	0.226954	−	0.973905i	$-0.427123\pi$
$863$	13.3344	0.453908	0.226954	+	0.973905i	$0.427123\pi$
$864$	−37.9182	−1.29000
$865$	22.4809	0.764373
$866$	−10.6056	−0.360393
$867$	19.1904	0.651739
$868$	7.73302	0.262476
$869$	41.4044	1.40455
$870$	−12.5933	−0.426954
$871$	10.2408	0.346998
$872$	−1.65625	−0.0560876
$873$	22.5820	0.764284
$874$	7.80547	0.264024
$875$	−18.5688	−0.627741
$876$	−9.27815	−0.313480
$877$	−5.39699	−0.182244	−0.0911218	−	0.995840i	$-0.529045\pi$
$877$	−5.39699	−0.182244	−0.0911218	+	0.995840i	$0.529045\pi$
$878$	−50.2431	−1.69562
$879$	27.2770	0.920031
$880$	−32.7781	−1.10495
$881$	−5.04786	−0.170067	−0.0850333	−	0.996378i	$-0.527100\pi$
$881$	−5.04786	−0.170067	−0.0850333	+	0.996378i	$0.527100\pi$
$882$	12.9771	0.436963
$883$	−36.4145	−1.22545	−0.612723	−	0.790298i	$-0.709926\pi$
$883$	−36.4145	−1.22545	−0.612723	+	0.790298i	$0.709926\pi$
$884$	1.30880	0.0440197
$885$	−9.79549	−0.329272
$886$	64.1841	2.15631
$887$	−24.9346	−0.837224	−0.418612	−	0.908165i	$-0.637483\pi$
$887$	−24.9346	−0.837224	−0.418612	+	0.908165i	$0.637483\pi$
$888$	3.13446	0.105185
$889$	−29.0973	−0.975891
$890$	−32.7714	−1.09850
$891$	5.28517	0.177060
$892$	41.0932	1.37590
$893$	0.356538	0.0119311
$894$	6.92410	0.231577
$895$	15.6613	0.523498
$896$	−11.9450	−0.399053
$897$	−20.7798	−0.693818
$898$	−13.3587	−0.445785
$899$	13.3654	0.445763
$900$	8.53486	0.284495
$901$	−4.07434	−0.135736
$902$	100.506	3.34649
$903$	19.3950	0.645424
$904$	9.70111	0.322654
$905$	−1.43277	−0.0476270
$906$	−39.1863	−1.30188
$907$	−27.1951	−0.903000	−0.451500	−	0.892271i	$-0.649111\pi$
$907$	−27.1951	−0.903000	−0.451500	+	0.892271i	$0.649111\pi$
$908$	−9.38102	−0.311320
$909$	8.62731	0.286150
$910$	9.19451	0.304795
$911$	−47.9588	−1.58895	−0.794473	−	0.607299i	$-0.792253\pi$
$911$	−47.9588	−1.58895	−0.794473	+	0.607299i	$0.792253\pi$
$912$	2.68688	0.0889716
$913$	95.5369	3.16181
$914$	48.4834	1.60369
$915$	−1.32305	−0.0437387
$916$	7.67500	0.253589
$917$	−0.469436	−0.0155021
$918$	3.95018	0.130376
$919$	−20.3674	−0.671857	−0.335928	−	0.941887i	$-0.609050\pi$
$919$	−20.3674	−0.671857	−0.335928	+	0.941887i	$0.609050\pi$
$920$	9.76366	0.321898
$921$	−1.50100	−0.0494597
$922$	−72.8432	−2.39896
$923$	24.9982	0.822825
$924$	−15.7778	−0.519053
$925$	−10.1069	−0.332313
$926$	42.9604	1.41177
$927$	2.15826	0.0708864
$928$	31.9207	1.04785
$929$	3.43001	0.112535	0.0562675	−	0.998416i	$-0.482080\pi$
$929$	3.43001	0.112535	0.0562675	+	0.998416i	$0.482080\pi$
$930$	−8.27697	−0.271413
$931$	−2.02670	−0.0664224
$932$	−12.4974	−0.409367
$933$	25.0593	0.820403
$934$	−22.8778	−0.748583
$935$	2.72445	0.0890989
$936$	3.34013	0.109176
$937$	−55.8441	−1.82435	−0.912173	−	0.409805i	$-0.865597\pi$
$937$	−55.8441	−1.82435	−0.912173	+	0.409805i	$0.865597\pi$
$938$	−15.0546	−0.491551
$939$	1.01595	0.0331544
$940$	−1.42086	−0.0463432
$941$	−35.2757	−1.14996	−0.574978	−	0.818169i	$-0.694989\pi$
$941$	−35.2757	−1.14996	−0.574978	+	0.818169i	$0.694989\pi$
$942$	4.49263	0.146378
$943$	−84.0969	−2.73857
$944$	31.1195	1.01285
$945$	11.9931	0.390135
$946$	−98.9555	−3.21732
$947$	−45.2546	−1.47058	−0.735289	−	0.677754i	$-0.762954\pi$
$947$	−45.2546	−1.47058	−0.735289	+	0.677754i	$0.762954\pi$
$948$	13.5256	0.439291
$949$	11.7080	0.380059
$950$	−3.08424	−0.100066
$951$	27.7144	0.898701
$952$	0.603916	0.0195730
$953$	39.0690	1.26557	0.632784	−	0.774328i	$-0.281912\pi$
$953$	39.0690	1.26557	0.632784	+	0.774328i	$0.281912\pi$
$954$	33.1267	1.07252
$955$	−1.88705	−0.0610634
$956$	38.6988	1.25161
$957$	−27.2698	−0.881508
$958$	−65.9168	−2.12968
$959$	9.65365	0.311733
$960$	−5.69929	−0.183944
$961$	−22.2156	−0.716631
$962$	12.6013	0.406283
$963$	−19.6146	−0.632070
$964$	40.7553	1.31264
$965$	−1.84644	−0.0594390
$966$	30.5475	0.982850
$967$	11.8771	0.381942	0.190971	−	0.981596i	$-0.438836\pi$
$967$	11.8771	0.381942	0.190971	+	0.981596i	$0.438836\pi$
$968$	−15.4041	−0.495106
$969$	−0.223328	−0.00717434
$970$	32.5206	1.04417
$971$	−43.3430	−1.39094	−0.695471	−	0.718554i	$-0.744804\pi$
$971$	−43.3430	−1.39094	−0.695471	+	0.718554i	$0.744804\pi$
$972$	−22.7357	−0.729248
$973$	38.9115	1.24744
$974$	14.2485	0.456552
$975$	8.21089	0.262959
$976$	4.20323	0.134542
$977$	30.9084	0.988846	0.494423	−	0.869221i	$-0.335379\pi$
$977$	30.9084	0.988846	0.494423	+	0.869221i	$0.335379\pi$
$978$	49.3245	1.57722
$979$	−70.9637	−2.26801
$980$	8.07669	0.258001
$981$	−3.14411	−0.100384
$982$	34.3308	1.09554
$983$	35.0128	1.11673	0.558367	−	0.829594i	$-0.311428\pi$
$983$	35.0128	1.11673	0.558367	+	0.829594i	$0.311428\pi$
$984$	−10.3056	−0.328530
$985$	6.71698	0.214021
$986$	−3.32539	−0.105902
$987$	1.39535	0.0444143
$988$	1.66190	0.0528720
$989$	82.7992	2.63286
$990$	−22.1513	−0.704014
$991$	−22.7329	−0.722135	−0.361067	−	0.932540i	$-0.617588\pi$
$991$	−22.7329	−0.722135	−0.361067	+	0.932540i	$0.617588\pi$
$992$	20.9799	0.666112
$993$	−31.6169	−1.00333
$994$	−36.7487	−1.16560
$995$	21.8792	0.693616
$996$	31.2091	0.988898
$997$	−10.6754	−0.338095	−0.169047	−	0.985608i	$-0.554069\pi$
$997$	−10.6754	−0.338095	−0.169047	+	0.985608i	$0.554069\pi$
$998$	10.8201	0.342506
$999$	16.4368	0.520038

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.2.a.b.1.16	✓	18
3.2	odd	2		4923.2.a.l.1.3		18
4.3	odd	2		8752.2.a.s.1.11		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.2.a.b.1.16	✓	18	1.1	even	1	trivial
4923.2.a.l.1.3		18	3.2	odd	2
8752.2.a.s.1.11		18	4.3	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:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	547.a (trivial)

\(f(q)\)	\(=\)	\(q+1.87675 q^{2} -1.13919 q^{3} +1.52220 q^{4} -1.30620 q^{5} -2.13798 q^{6} -1.71403 q^{7} -0.896704 q^{8} -1.70224 q^{9} +O(q^{10})\)	\(q+1.87675 q^{2} -1.13919 q^{3} +1.52220 q^{4} -1.30620 q^{5} -2.13798 q^{6} -1.71403 q^{7} -0.896704 q^{8} -1.70224 q^{9} -2.45142 q^{10} -5.30835 q^{11} -1.73408 q^{12} +2.18823 q^{13} -3.21682 q^{14} +1.48801 q^{15} -4.72730 q^{16} +0.392924 q^{17} -3.19469 q^{18} +0.498929 q^{19} -1.98831 q^{20} +1.95261 q^{21} -9.96246 q^{22} +8.33591 q^{23} +1.02152 q^{24} -3.29383 q^{25} +4.10676 q^{26} +5.35675 q^{27} -2.60911 q^{28} -4.50948 q^{29} +2.79264 q^{30} -2.96386 q^{31} -7.07857 q^{32} +6.04722 q^{33} +0.737421 q^{34} +2.23887 q^{35} -2.59116 q^{36} +3.06843 q^{37} +0.936368 q^{38} -2.49281 q^{39} +1.17128 q^{40} -10.0885 q^{41} +3.66457 q^{42} +9.93284 q^{43} -8.08039 q^{44} +2.22348 q^{45} +15.6444 q^{46} +0.714605 q^{47} +5.38530 q^{48} -4.06209 q^{49} -6.18172 q^{50} -0.447615 q^{51} +3.33093 q^{52} -10.3693 q^{53} +10.0533 q^{54} +6.93378 q^{55} +1.53698 q^{56} -0.568376 q^{57} -8.46318 q^{58} -6.58293 q^{59} +2.26506 q^{60} -0.889139 q^{61} -5.56243 q^{62} +2.91770 q^{63} -3.83013 q^{64} -2.85827 q^{65} +11.3491 q^{66} +4.67997 q^{67} +0.598110 q^{68} -9.49619 q^{69} +4.20181 q^{70} +11.4239 q^{71} +1.52641 q^{72} +5.35047 q^{73} +5.75869 q^{74} +3.75231 q^{75} +0.759473 q^{76} +9.09868 q^{77} -4.67838 q^{78} -7.79987 q^{79} +6.17481 q^{80} -0.995634 q^{81} -18.9336 q^{82} -17.9975 q^{83} +2.97227 q^{84} -0.513238 q^{85} +18.6415 q^{86} +5.13716 q^{87} +4.76002 q^{88} +13.3683 q^{89} +4.17292 q^{90} -3.75069 q^{91} +12.6890 q^{92} +3.37640 q^{93} +1.34114 q^{94} -0.651703 q^{95} +8.06385 q^{96} -13.2660 q^{97} -7.62355 q^{98} +9.03610 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 4 q^{2} - 10 q^{3} + 16 q^{4} - 27 q^{5} - 3 q^{6} - 11 q^{7} - 12 q^{8} + 14 q^{9}+O(q^{10}) \) 18 * q - 4 * q^2 - 10 * q^3 + 16 * q^4 - 27 * q^5 - 3 * q^6 - 11 * q^7 - 12 * q^8 + 14 * q^9	\( 18 q - 4 q^{2} - 10 q^{3} + 16 q^{4} - 27 q^{5} - 3 q^{6} - 11 q^{7} - 12 q^{8} + 14 q^{9} - 5 q^{10} + 2 q^{11} - 32 q^{12} - 25 q^{13} - 7 q^{14} + 9 q^{15} + 8 q^{16} - 30 q^{17} - 10 q^{18} + 4 q^{19} - 41 q^{20} - 16 q^{21} - 24 q^{22} - 26 q^{23} - 12 q^{24} + 31 q^{25} - 18 q^{26} - 37 q^{27} - 16 q^{28} - 18 q^{29} + 8 q^{30} - 5 q^{31} - 28 q^{32} - 10 q^{33} + 5 q^{34} - 9 q^{35} + 31 q^{36} - 18 q^{37} - 45 q^{38} + 7 q^{39} + 7 q^{40} - 17 q^{41} + 4 q^{42} + 8 q^{43} + 12 q^{44} - 44 q^{45} + 30 q^{46} - 52 q^{47} - 7 q^{48} + 29 q^{49} + 13 q^{50} + 19 q^{51} - 14 q^{52} - 60 q^{53} + 11 q^{54} + 11 q^{55} + 7 q^{56} + 4 q^{57} + 14 q^{58} - 8 q^{59} + 86 q^{60} - 26 q^{61} + 4 q^{62} - q^{63} + 44 q^{64} - 6 q^{65} + 18 q^{66} + 12 q^{67} - 61 q^{68} - 38 q^{69} + 35 q^{70} - q^{71} + 28 q^{72} - 2 q^{73} + 16 q^{74} - 17 q^{75} + 66 q^{76} - 73 q^{77} + 115 q^{78} + 18 q^{79} - 32 q^{80} + 18 q^{81} + 44 q^{82} - 43 q^{83} + 41 q^{84} + 51 q^{85} + 4 q^{86} + 3 q^{87} - 17 q^{88} - 28 q^{89} + 58 q^{90} - q^{91} - 68 q^{92} - 60 q^{93} + 78 q^{94} - 18 q^{95} + 29 q^{96} - 34 q^{97} + 34 q^{98} + 15 q^{99}+O(q^{100}) \) 18 * q - 4 * q^2 - 10 * q^3 + 16 * q^4 - 27 * q^5 - 3 * q^6 - 11 * q^7 - 12 * q^8 + 14 * q^9 - 5 * q^10 + 2 * q^11 - 32 * q^12 - 25 * q^13 - 7 * q^14 + 9 * q^15 + 8 * q^16 - 30 * q^17 - 10 * q^18 + 4 * q^19 - 41 * q^20 - 16 * q^21 - 24 * q^22 - 26 * q^23 - 12 * q^24 + 31 * q^25 - 18 * q^26 - 37 * q^27 - 16 * q^28 - 18 * q^29 + 8 * q^30 - 5 * q^31 - 28 * q^32 - 10 * q^33 + 5 * q^34 - 9 * q^35 + 31 * q^36 - 18 * q^37 - 45 * q^38 + 7 * q^39 + 7 * q^40 - 17 * q^41 + 4 * q^42 + 8 * q^43 + 12 * q^44 - 44 * q^45 + 30 * q^46 - 52 * q^47 - 7 * q^48 + 29 * q^49 + 13 * q^50 + 19 * q^51 - 14 * q^52 - 60 * q^53 + 11 * q^54 + 11 * q^55 + 7 * q^56 + 4 * q^57 + 14 * q^58 - 8 * q^59 + 86 * q^60 - 26 * q^61 + 4 * q^62 - q^63 + 44 * q^64 - 6 * q^65 + 18 * q^66 + 12 * q^67 - 61 * q^68 - 38 * q^69 + 35 * q^70 - q^71 + 28 * q^72 - 2 * q^73 + 16 * q^74 - 17 * q^75 + 66 * q^76 - 73 * q^77 + 115 * q^78 + 18 * q^79 - 32 * q^80 + 18 * q^81 + 44 * q^82 - 43 * q^83 + 41 * q^84 + 51 * q^85 + 4 * q^86 + 3 * q^87 - 17 * q^88 - 28 * q^89 + 58 * q^90 - q^91 - 68 * q^92 - 60 * q^93 + 78 * q^94 - 18 * q^95 + 29 * q^96 - 34 * q^97 + 34 * q^98 + 15 * q^99

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