LMFDB - Embedded newform 547.2.a.b.1.5

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			1.5
Root			$1.74487$ 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)

$f(q)$	$=$	$q-1.74487 q^{2} -1.27304 q^{3} +1.04455 q^{4} -3.61409 q^{5} +2.22129 q^{6} +4.28084 q^{7} +1.66712 q^{8} -1.37936 q^{9} +O(q^{10})$	\(q-1.74487 q^{2} -1.27304 q^{3} +1.04455 q^{4} -3.61409 q^{5} +2.22129 q^{6} +4.28084 q^{7} +1.66712 q^{8} -1.37936 q^{9} +6.30610 q^{10} -1.82207 q^{11} -1.32976 q^{12} +1.54763 q^{13} -7.46949 q^{14} +4.60089 q^{15} -4.99801 q^{16} +5.89804 q^{17} +2.40680 q^{18} +5.77207 q^{19} -3.77512 q^{20} -5.44969 q^{21} +3.17927 q^{22} -7.36494 q^{23} -2.12232 q^{24} +8.06166 q^{25} -2.70041 q^{26} +5.57511 q^{27} +4.47157 q^{28} -4.20778 q^{29} -8.02794 q^{30} -8.68625 q^{31} +5.38662 q^{32} +2.31958 q^{33} -10.2913 q^{34} -15.4714 q^{35} -1.44082 q^{36} -9.26711 q^{37} -10.0715 q^{38} -1.97020 q^{39} -6.02514 q^{40} +8.29157 q^{41} +9.50898 q^{42} -2.50047 q^{43} -1.90326 q^{44} +4.98514 q^{45} +12.8508 q^{46} -6.07577 q^{47} +6.36269 q^{48} +11.3256 q^{49} -14.0665 q^{50} -7.50845 q^{51} +1.61659 q^{52} -4.35174 q^{53} -9.72782 q^{54} +6.58514 q^{55} +7.13669 q^{56} -7.34809 q^{57} +7.34201 q^{58} -13.6982 q^{59} +4.80588 q^{60} -9.67314 q^{61} +15.1563 q^{62} -5.90483 q^{63} +0.597111 q^{64} -5.59329 q^{65} -4.04735 q^{66} -3.67729 q^{67} +6.16082 q^{68} +9.37589 q^{69} +26.9954 q^{70} +6.92649 q^{71} -2.29957 q^{72} +2.36768 q^{73} +16.1699 q^{74} -10.2628 q^{75} +6.02925 q^{76} -7.80001 q^{77} +3.43774 q^{78} +6.27816 q^{79} +18.0633 q^{80} -2.95927 q^{81} -14.4677 q^{82} -2.57942 q^{83} -5.69250 q^{84} -21.3161 q^{85} +4.36299 q^{86} +5.35668 q^{87} -3.03762 q^{88} +8.45581 q^{89} -8.69840 q^{90} +6.62517 q^{91} -7.69309 q^{92} +11.0580 q^{93} +10.6014 q^{94} -20.8608 q^{95} -6.85739 q^{96} -11.0935 q^{97} -19.7617 q^{98} +2.51330 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.74487	−1.23381	−0.616903	−	0.787039i	$-0.711613\pi$
$2$	−1.74487	−1.23381	−0.616903	+	0.787039i	$0.711613\pi$
$3$	−1.27304	−0.734991	−0.367496	−	0.930025i	$-0.619785\pi$
$3$	−1.27304	−0.734991	−0.367496	+	0.930025i	$0.619785\pi$
$4$	1.04455	0.522277
$5$	−3.61409	−1.61627	−0.808135	−	0.588997i	$-0.799523\pi$
$5$	−3.61409	−1.61627	−0.808135	+	0.588997i	$0.799523\pi$
$6$	2.22129	0.906837
$7$	4.28084	1.61801	0.809003	−	0.587804i	$-0.200008\pi$
$7$	4.28084	1.61801	0.809003	+	0.587804i	$0.200008\pi$
$8$	1.66712	0.589417
$9$	−1.37936	−0.459788
$10$	6.30610	1.99416
$11$	−1.82207	−0.549376	−0.274688	−	0.961533i	$-0.588575\pi$
$11$	−1.82207	−0.549376	−0.274688	+	0.961533i	$0.588575\pi$
$12$	−1.32976	−0.383869
$13$	1.54763	0.429236	0.214618	−	0.976698i	$-0.431149\pi$
$13$	1.54763	0.429236	0.214618	+	0.976698i	$0.431149\pi$
$14$	−7.46949	−1.99631
$15$	4.60089	1.18795
$16$	−4.99801	−1.24950
$17$	5.89804	1.43048	0.715242	−	0.698877i	$-0.246316\pi$
$17$	5.89804	1.43048	0.715242	+	0.698877i	$0.246316\pi$
$18$	2.40680	0.567289
$19$	5.77207	1.32420	0.662102	−	0.749414i	$-0.269664\pi$
$19$	5.77207	1.32420	0.662102	+	0.749414i	$0.269664\pi$
$20$	−3.77512	−0.844142
$21$	−5.44969	−1.18922
$22$	3.17927	0.677824
$23$	−7.36494	−1.53570	−0.767848	−	0.640632i	$-0.778673\pi$
$23$	−7.36494	−1.53570	−0.767848	+	0.640632i	$0.778673\pi$
$24$	−2.12232	−0.433217
$25$	8.06166	1.61233
$26$	−2.70041	−0.529594
$27$	5.57511	1.07293
$28$	4.47157	0.845048
$29$	−4.20778	−0.781365	−0.390683	−	0.920525i	$-0.627761\pi$
$29$	−4.20778	−0.781365	−0.390683	+	0.920525i	$0.627761\pi$
$30$	−8.02794	−1.46569
$31$	−8.68625	−1.56010	−0.780049	−	0.625719i	$-0.784806\pi$
$31$	−8.68625	−1.56010	−0.780049	+	0.625719i	$0.784806\pi$
$32$	5.38662	0.952228
$33$	2.31958	0.403787
$34$	−10.2913	−1.76494
$35$	−15.4714	−2.61514
$36$	−1.44082	−0.240137
$37$	−9.26711	−1.52350	−0.761752	−	0.647869i	$-0.775660\pi$
$37$	−9.26711	−1.52350	−0.761752	+	0.647869i	$0.775660\pi$
$38$	−10.0715	−1.63381
$39$	−1.97020	−0.315485
$40$	−6.02514	−0.952658
$41$	8.29157	1.29493	0.647463	−	0.762097i	$-0.275830\pi$
$41$	8.29157	1.29493	0.647463	+	0.762097i	$0.275830\pi$
$42$	9.50898	1.46727
$43$	−2.50047	−0.381319	−0.190659	−	0.981656i	$-0.561063\pi$
$43$	−2.50047	−0.381319	−0.190659	+	0.981656i	$0.561063\pi$
$44$	−1.90326	−0.286927
$45$	4.98514	0.743141
$46$	12.8508	1.89475
$47$	−6.07577	−0.886242	−0.443121	−	0.896462i	$-0.646129\pi$
$47$	−6.07577	−0.886242	−0.443121	+	0.896462i	$0.646129\pi$
$48$	6.36269	0.918375
$49$	11.3256	1.61794
$50$	−14.0665	−1.98930
$51$	−7.50845	−1.05139
$52$	1.61659	0.224180
$53$	−4.35174	−0.597757	−0.298879	−	0.954291i	$-0.596613\pi$
$53$	−4.35174	−0.597757	−0.298879	+	0.954291i	$0.596613\pi$
$54$	−9.72782	−1.32379
$55$	6.58514	0.887941
$56$	7.13669	0.953680
$57$	−7.34809	−0.973279
$58$	7.34201	0.964053
$59$	−13.6982	−1.78336	−0.891680	−	0.452667i	$-0.850473\pi$
$59$	−13.6982	−1.78336	−0.891680	+	0.452667i	$0.850473\pi$
$60$	4.80588	0.620437
$61$	−9.67314	−1.23852	−0.619259	−	0.785186i	$-0.712567\pi$
$61$	−9.67314	−1.23852	−0.619259	+	0.785186i	$0.712567\pi$
$62$	15.1563	1.92486
$63$	−5.90483	−0.743939
$64$	0.597111	0.0746389
$65$	−5.59329	−0.693762
$66$	−4.04735	−0.498194
$67$	−3.67729	−0.449253	−0.224626	−	0.974445i	$-0.572116\pi$
$67$	−3.67729	−0.449253	−0.224626	+	0.974445i	$0.572116\pi$
$68$	6.16082	0.747110
$69$	9.37589	1.12872
$70$	26.9954	3.22657
$71$	6.92649	0.822023	0.411012	−	0.911630i	$-0.365176\pi$
$71$	6.92649	0.822023	0.411012	+	0.911630i	$0.365176\pi$
$72$	−2.29957	−0.271007
$73$	2.36768	0.277116	0.138558	−	0.990354i	$-0.455753\pi$
$73$	2.36768	0.277116	0.138558	+	0.990354i	$0.455753\pi$
$74$	16.1699	1.87971
$75$	−10.2628	−1.18505
$76$	6.02925	0.691602
$77$	−7.80001	−0.888894
$78$	3.43774	0.389247
$79$	6.27816	0.706348	0.353174	−	0.935558i	$-0.385102\pi$
$79$	6.27816	0.706348	0.353174	+	0.935558i	$0.385102\pi$
$80$	18.0633	2.01954
$81$	−2.95927	−0.328808
$82$	−14.4677	−1.59769
$83$	−2.57942	−0.283128	−0.141564	−	0.989929i	$-0.545213\pi$
$83$	−2.57942	−0.283128	−0.141564	+	0.989929i	$0.545213\pi$
$84$	−5.69250	−0.621103
$85$	−21.3161	−2.31205
$86$	4.36299	0.470473
$87$	5.35668	0.574297
$88$	−3.03762	−0.323812
$89$	8.45581	0.896314	0.448157	−	0.893955i	$-0.352081\pi$
$89$	8.45581	0.896314	0.448157	+	0.893955i	$0.352081\pi$
$90$	−8.69840	−0.916892
$91$	6.62517	0.694507
$92$	−7.69309	−0.802060
$93$	11.0580	1.14666
$94$	10.6014	1.09345
$95$	−20.8608	−2.14027
$96$	−6.85739	−0.699880
$97$	−11.0935	−1.12637	−0.563187	−	0.826329i	$-0.690425\pi$
$97$	−11.0935	−1.12637	−0.563187	+	0.826329i	$0.690425\pi$
$98$	−19.7617	−1.99623
$99$	2.51330	0.252596
$100$	8.42084	0.842084
$101$	−12.1254	−1.20652	−0.603259	−	0.797545i	$-0.706131\pi$
$101$	−12.1254	−1.20652	−0.603259	+	0.797545i	$0.706131\pi$
$102$	13.1012	1.29722
$103$	−10.8356	−1.06767	−0.533833	−	0.845590i	$-0.679249\pi$
$103$	−10.8356	−1.06767	−0.533833	+	0.845590i	$0.679249\pi$
$104$	2.58010	0.252999
$105$	19.6957	1.92210
$106$	7.59320	0.737517
$107$	15.7365	1.52130	0.760652	−	0.649160i	$-0.224879\pi$
$107$	15.7365	1.52130	0.760652	+	0.649160i	$0.224879\pi$
$108$	5.82351	0.560368
$109$	−7.74111	−0.741464	−0.370732	−	0.928740i	$-0.620893\pi$
$109$	−7.74111	−0.741464	−0.370732	+	0.928740i	$0.620893\pi$
$110$	−11.4902	−1.09555
$111$	11.7974	1.11976
$112$	−21.3957	−2.02170
$113$	−0.0433232	−0.00407550	−0.00203775	−	0.999998i	$-0.500649\pi$
$113$	−0.0433232	−0.00407550	−0.00203775	+	0.999998i	$0.500649\pi$
$114$	12.8214	1.20084
$115$	26.6176	2.48210
$116$	−4.39526	−0.408089
$117$	−2.13475	−0.197358
$118$	23.9016	2.20032
$119$	25.2486	2.31453
$120$	7.67026	0.700195
$121$	−7.68004	−0.698186
$122$	16.8783	1.52809
$123$	−10.5555	−0.951760
$124$	−9.07327	−0.814803
$125$	−11.0651	−0.989694
$126$	10.3031	0.917877
$127$	0.557420	0.0494630	0.0247315	−	0.999694i	$-0.492127\pi$
$127$	0.557420	0.0494630	0.0247315	+	0.999694i	$0.492127\pi$
$128$	−11.8151	−1.04432
$129$	3.18321	0.280266
$130$	9.75954	0.855968
$131$	−4.31192	−0.376735	−0.188367	−	0.982099i	$-0.560320\pi$
$131$	−4.31192	−0.376735	−0.188367	+	0.982099i	$0.560320\pi$
$132$	2.42293	0.210889
$133$	24.7093	2.14257
$134$	6.41638	0.554291
$135$	−20.1490	−1.73415
$136$	9.83276	0.843152
$137$	−9.86688	−0.842985	−0.421492	−	0.906832i	$-0.638494\pi$
$137$	−9.86688	−0.842985	−0.421492	+	0.906832i	$0.638494\pi$
$138$	−16.3597	−1.39263
$139$	11.3673	0.964163	0.482082	−	0.876126i	$-0.339881\pi$
$139$	11.3673	0.964163	0.482082	+	0.876126i	$0.339881\pi$
$140$	−16.1607	−1.36583
$141$	7.73472	0.651381
$142$	−12.0858	−1.01422
$143$	−2.81990	−0.235812
$144$	6.89408	0.574506
$145$	15.2073	1.26290
$146$	−4.13128	−0.341907
$147$	−14.4180	−1.18917
$148$	−9.68001	−0.795692
$149$	14.2550	1.16781	0.583907	−	0.811821i	$-0.301523\pi$
$149$	14.2550	1.16781	0.583907	+	0.811821i	$0.301523\pi$
$150$	17.9073	1.46212
$151$	17.5151	1.42536	0.712680	−	0.701489i	$-0.247481\pi$
$151$	17.5151	1.42536	0.712680	+	0.701489i	$0.247481\pi$
$152$	9.62276	0.780509
$153$	−8.13554	−0.657719
$154$	13.6100	1.09672
$155$	31.3929	2.52154
$156$	−2.05798	−0.164771
$157$	−0.960703	−0.0766725	−0.0383362	−	0.999265i	$-0.512206\pi$
$157$	−0.960703	−0.0766725	−0.0383362	+	0.999265i	$0.512206\pi$
$158$	−10.9545	−0.871497
$159$	5.53995	0.439346
$160$	−19.4677	−1.53906
$161$	−31.5282	−2.48477
$162$	5.16353	0.405685
$163$	−8.10300	−0.634676	−0.317338	−	0.948313i	$-0.602789\pi$
$163$	−8.10300	−0.634676	−0.317338	+	0.948313i	$0.602789\pi$
$164$	8.66100	0.676311
$165$	−8.38317	−0.652629
$166$	4.50074	0.349325
$167$	−12.7559	−0.987083	−0.493541	−	0.869722i	$-0.664298\pi$
$167$	−12.7559	−0.987083	−0.493541	+	0.869722i	$0.664298\pi$
$168$	−9.08531	−0.700947
$169$	−10.6048	−0.815756
$170$	37.1936	2.85262
$171$	−7.96178	−0.608853
$172$	−2.61188	−0.199154
$173$	−6.36016	−0.483554	−0.241777	−	0.970332i	$-0.577730\pi$
$173$	−6.36016	−0.483554	−0.241777	+	0.970332i	$0.577730\pi$
$174$	−9.34669	−0.708571
$175$	34.5107	2.60876
$176$	9.10675	0.686447
$177$	17.4384	1.31075
$178$	−14.7542	−1.10588
$179$	15.6282	1.16811	0.584055	−	0.811714i	$-0.301465\pi$
$179$	15.6282	1.16811	0.584055	+	0.811714i	$0.301465\pi$
$180$	5.20726	0.388126
$181$	−12.0567	−0.896164	−0.448082	−	0.893992i	$-0.647893\pi$
$181$	−12.0567	−0.896164	−0.448082	+	0.893992i	$0.647893\pi$
$182$	−11.5600	−0.856887
$183$	12.3143	0.910301
$184$	−12.2783	−0.905166
$185$	33.4922	2.46240
$186$	−19.2947	−1.41475
$187$	−10.7467	−0.785874
$188$	−6.34648	−0.462864
$189$	23.8662	1.73601
$190$	36.3993	2.64068
$191$	−15.1622	−1.09710	−0.548550	−	0.836118i	$-0.684820\pi$
$191$	−15.1622	−1.09710	−0.548550	+	0.836118i	$0.684820\pi$
$192$	−0.760148	−0.0548590
$193$	−6.95522	−0.500648	−0.250324	−	0.968162i	$-0.580537\pi$
$193$	−6.95522	−0.500648	−0.250324	+	0.968162i	$0.580537\pi$
$194$	19.3567	1.38973
$195$	7.12049	0.509909
$196$	11.8302	0.845015
$197$	−14.5377	−1.03577	−0.517884	−	0.855451i	$-0.673280\pi$
$197$	−14.5377	−1.03577	−0.517884	+	0.855451i	$0.673280\pi$
$198$	−4.38537	−0.311655
$199$	−5.94365	−0.421334	−0.210667	−	0.977558i	$-0.567564\pi$
$199$	−5.94365	−0.421334	−0.210667	+	0.977558i	$0.567564\pi$
$200$	13.4398	0.950336
$201$	4.68135	0.330197
$202$	21.1571	1.48861
$203$	−18.0128	−1.26425
$204$	−7.84299	−0.549119
$205$	−29.9665	−2.09295
$206$	18.9067	1.31729
$207$	10.1589	0.706094
$208$	−7.73509	−0.536332
$209$	−10.5171	−0.727486
$210$	−34.3663	−2.37150
$211$	−27.1667	−1.87024	−0.935118	−	0.354337i	$-0.884707\pi$
$211$	−27.1667	−1.87024	−0.935118	+	0.354337i	$0.884707\pi$
$212$	−4.54563	−0.312195
$213$	−8.81772	−0.604180
$214$	−27.4581	−1.87699
$215$	9.03694	0.616314
$216$	9.29440	0.632404
$217$	−37.1845	−2.52425
$218$	13.5072	0.914823
$219$	−3.01415	−0.203678
$220$	6.87854	0.463751
$221$	9.12800	0.614016
$222$	−20.5849	−1.38157
$223$	3.41548	0.228717	0.114359	−	0.993440i	$-0.463519\pi$
$223$	3.41548	0.228717	0.114359	+	0.993440i	$0.463519\pi$
$224$	23.0592	1.54071
$225$	−11.1200	−0.741330
$226$	0.0755931	0.00502838
$227$	−22.1539	−1.47041	−0.735204	−	0.677846i	$-0.762914\pi$
$227$	−22.1539	−1.47041	−0.735204	+	0.677846i	$0.762914\pi$
$228$	−7.67549	−0.508321
$229$	1.65658	0.109470	0.0547350	−	0.998501i	$-0.482569\pi$
$229$	1.65658	0.109470	0.0547350	+	0.998501i	$0.482569\pi$
$230$	−46.4441	−3.06243
$231$	9.92975	0.653329
$232$	−7.01489	−0.460550
$233$	9.45846	0.619644	0.309822	−	0.950795i	$-0.399731\pi$
$233$	9.45846	0.619644	0.309822	+	0.950795i	$0.399731\pi$
$234$	3.72485	0.243501
$235$	21.9584	1.43241
$236$	−14.3086	−0.931408
$237$	−7.99236	−0.519160
$238$	−44.0554	−2.85568
$239$	−20.2498	−1.30985	−0.654926	−	0.755693i	$-0.727300\pi$
$239$	−20.2498	−1.30985	−0.654926	+	0.755693i	$0.727300\pi$
$240$	−22.9953	−1.48434
$241$	12.5021	0.805328	0.402664	−	0.915348i	$-0.368084\pi$
$241$	12.5021	0.805328	0.402664	+	0.915348i	$0.368084\pi$
$242$	13.4006	0.861426
$243$	−12.9581	−0.831260
$244$	−10.1041	−0.646850
$245$	−40.9318	−2.61504
$246$	18.4180	1.17429
$247$	8.93305	0.568397
$248$	−14.4811	−0.919548
$249$	3.28371	0.208097
$250$	19.3071	1.22109
$251$	15.4087	0.972590	0.486295	−	0.873795i	$-0.338348\pi$
$251$	15.4087	0.972590	0.486295	+	0.873795i	$0.338348\pi$
$252$	−6.16792	−0.388543
$253$	13.4195	0.843675
$254$	−0.972622	−0.0610277
$255$	27.1362	1.69934
$256$	19.4216	1.21385
$257$	−5.96426	−0.372040	−0.186020	−	0.982546i	$-0.559559\pi$
$257$	−5.96426	−0.372040	−0.186020	+	0.982546i	$0.559559\pi$
$258$	−5.55427	−0.345794
$259$	−39.6710	−2.46504
$260$	−5.84250	−0.362336
$261$	5.80406	0.359262
$262$	7.52373	0.464817
$263$	22.1233	1.36418	0.682089	−	0.731269i	$-0.261072\pi$
$263$	22.1233	1.36418	0.682089	+	0.731269i	$0.261072\pi$
$264$	3.86702	0.237999
$265$	15.7276	0.966138
$266$	−43.1144	−2.64352
$267$	−10.7646	−0.658783
$268$	−3.84113	−0.234635
$269$	−8.96149	−0.546391	−0.273196	−	0.961958i	$-0.588081\pi$
$269$	−8.96149	−0.546391	−0.273196	+	0.961958i	$0.588081\pi$
$270$	35.1572	2.13960
$271$	2.25602	0.137043	0.0685217	−	0.997650i	$-0.478172\pi$
$271$	2.25602	0.137043	0.0685217	+	0.997650i	$0.478172\pi$
$272$	−29.4785	−1.78740
$273$	−8.43413	−0.510457
$274$	17.2164	1.04008
$275$	−14.6889	−0.885777
$276$	9.79363	0.589507
$277$	−12.2849	−0.738128	−0.369064	−	0.929404i	$-0.620322\pi$
$277$	−12.2849	−0.738128	−0.369064	+	0.929404i	$0.620322\pi$
$278$	−19.8344	−1.18959
$279$	11.9815	0.717313
$280$	−25.7927	−1.54141
$281$	−31.3296	−1.86897	−0.934484	−	0.356005i	$-0.884139\pi$
$281$	−31.3296	−1.86897	−0.934484	+	0.356005i	$0.884139\pi$
$282$	−13.4960	−0.803677
$283$	26.8312	1.59495	0.797474	−	0.603353i	$-0.206169\pi$
$283$	26.8312	1.59495	0.797474	+	0.603353i	$0.206169\pi$
$284$	7.23510	0.429324
$285$	26.5567	1.57308
$286$	4.92035	0.290946
$287$	35.4949	2.09520
$288$	−7.43010	−0.437823
$289$	17.7869	1.04629
$290$	−26.5347	−1.55817
$291$	14.1225	0.827876
$292$	2.47317	0.144731
$293$	8.91567	0.520859	0.260430	−	0.965493i	$-0.416136\pi$
$293$	8.91567	0.520859	0.260430	+	0.965493i	$0.416136\pi$
$294$	25.1574	1.46721
$295$	49.5067	2.88239
$296$	−15.4494	−0.897979
$297$	−10.1583	−0.589443
$298$	−24.8730	−1.44086
$299$	−11.3982	−0.659177
$300$	−10.7201	−0.618925
$301$	−10.7041	−0.616976
$302$	−30.5615	−1.75862
$303$	15.4361	0.886780
$304$	−28.8489	−1.65460
$305$	34.9596	2.00178
$306$	14.1954	0.811498
$307$	−20.6821	−1.18039	−0.590195	−	0.807260i	$-0.700949\pi$
$307$	−20.6821	−1.18039	−0.590195	+	0.807260i	$0.700949\pi$
$308$	−8.14754	−0.464249
$309$	13.7942	0.784725
$310$	−54.7764	−3.11109
$311$	9.54165	0.541057	0.270529	−	0.962712i	$-0.412802\pi$
$311$	9.54165	0.541057	0.270529	+	0.962712i	$0.412802\pi$
$312$	−3.28457	−0.185952
$313$	−19.8618	−1.12265	−0.561327	−	0.827594i	$-0.689709\pi$
$313$	−19.8618	−1.12265	−0.561327	+	0.827594i	$0.689709\pi$
$314$	1.67630	0.0945989
$315$	21.3406	1.20241
$316$	6.55788	0.368910
$317$	−12.6386	−0.709857	−0.354929	−	0.934893i	$-0.615495\pi$
$317$	−12.6386	−0.709857	−0.354929	+	0.934893i	$0.615495\pi$
$318$	−9.66646	−0.542068
$319$	7.66689	0.429263
$320$	−2.15802	−0.120637
$321$	−20.0332	−1.11815
$322$	55.0124	3.06572
$323$	34.0439	1.89425
$324$	−3.09112	−0.171729
$325$	12.4765	0.692071
$326$	14.1386	0.783067
$327$	9.85477	0.544970
$328$	13.8231	0.763252
$329$	−26.0094	−1.43395
$330$	14.6275	0.805217
$331$	17.8621	0.981790	0.490895	−	0.871219i	$-0.336670\pi$
$331$	17.8621	0.981790	0.490895	+	0.871219i	$0.336670\pi$
$332$	−2.69434	−0.147871
$333$	12.7827	0.700488
$334$	22.2574	1.21787
$335$	13.2901	0.726114
$336$	27.2376	1.48594
$337$	11.1406	0.606865	0.303432	−	0.952853i	$-0.401867\pi$
$337$	11.1406	0.606865	0.303432	+	0.952853i	$0.401867\pi$
$338$	18.5040	1.00648
$339$	0.0551522	0.00299546
$340$	−22.2658	−1.20753
$341$	15.8270	0.857080
$342$	13.8922	0.751206
$343$	18.5172	0.999836
$344$	−4.16860	−0.224756
$345$	−33.8853	−1.82432
$346$	11.0976	0.596612
$347$	−0.533400	−0.0286344	−0.0143172	−	0.999898i	$-0.504557\pi$
$347$	−0.533400	−0.0286344	−0.0143172	+	0.999898i	$0.504557\pi$
$348$	5.59535	0.299942
$349$	26.6600	1.42708	0.713539	−	0.700616i	$-0.247091\pi$
$349$	26.6600	1.42708	0.713539	+	0.700616i	$0.247091\pi$
$350$	−60.2165	−3.21871
$351$	8.62823	0.460541
$352$	−9.81481	−0.523131
$353$	−2.12890	−0.113310	−0.0566548	−	0.998394i	$-0.518043\pi$
$353$	−2.12890	−0.113310	−0.0566548	+	0.998394i	$0.518043\pi$
$354$	−30.4277	−1.61722
$355$	−25.0330	−1.32861
$356$	8.83255	0.468124
$357$	−32.1425	−1.70116
$358$	−27.2692	−1.44122
$359$	1.54866	0.0817353	0.0408677	−	0.999165i	$-0.486988\pi$
$359$	1.54866	0.0817353	0.0408677	+	0.999165i	$0.486988\pi$
$360$	8.31085	0.438020
$361$	14.3168	0.753517
$362$	21.0372	1.10569
$363$	9.77702	0.513161
$364$	6.92036	0.362725
$365$	−8.55700	−0.447894
$366$	−21.4868	−1.12313
$367$	8.10473	0.423064	0.211532	−	0.977371i	$-0.432155\pi$
$367$	8.10473	0.423064	0.211532	+	0.977371i	$0.432155\pi$
$368$	36.8101	1.91886
$369$	−11.4371	−0.595391
$370$	−58.4394	−3.03812
$371$	−18.6291	−0.967175
$372$	11.5507	0.598874
$373$	36.4059	1.88503	0.942514	−	0.334167i	$-0.108455\pi$
$373$	36.4059	1.88503	0.942514	+	0.334167i	$0.108455\pi$
$374$	18.7515	0.969616
$375$	14.0864	0.727417
$376$	−10.1291	−0.522366
$377$	−6.51210	−0.335390
$378$	−41.6433	−2.14190
$379$	−1.17841	−0.0605309	−0.0302655	−	0.999542i	$-0.509635\pi$
$379$	−1.17841	−0.0605309	−0.0302655	+	0.999542i	$0.509635\pi$
$380$	−21.7902	−1.11782
$381$	−0.709619	−0.0363549
$382$	26.4560	1.35361
$383$	3.86230	0.197355	0.0986773	−	0.995119i	$-0.468539\pi$
$383$	3.86230	0.197355	0.0986773	+	0.995119i	$0.468539\pi$
$384$	15.0411	0.767565
$385$	28.1900	1.43669
$386$	12.1359	0.617702
$387$	3.44906	0.175326
$388$	−11.5878	−0.588280
$389$	−9.33318	−0.473211	−0.236605	−	0.971606i	$-0.576035\pi$
$389$	−9.33318	−0.473211	−0.236605	+	0.971606i	$0.576035\pi$
$390$	−12.4243	−0.629129
$391$	−43.4387	−2.19679
$392$	18.8812	0.953644
$393$	5.48926	0.276897
$394$	25.3663	1.27794
$395$	−22.6898	−1.14165
$396$	2.62528	0.131925
$397$	−29.7948	−1.49536	−0.747680	−	0.664059i	$-0.768832\pi$
$397$	−29.7948	−1.49536	−0.747680	+	0.664059i	$0.768832\pi$
$398$	10.3709	0.519844
$399$	−31.4560	−1.57477
$400$	−40.2923	−2.01461
$401$	5.34757	0.267045	0.133522	−	0.991046i	$-0.457371\pi$
$401$	5.34757	0.267045	0.133522	+	0.991046i	$0.457371\pi$
$402$	−8.16833	−0.407399
$403$	−13.4431	−0.669650
$404$	−12.6656	−0.630137
$405$	10.6951	0.531442
$406$	31.4300	1.55984
$407$	16.8854	0.836977
$408$	−12.5175	−0.619710
$409$	−6.05618	−0.299459	−0.149729	−	0.988727i	$-0.547840\pi$
$409$	−6.05618	−0.299459	−0.149729	+	0.988727i	$0.547840\pi$
$410$	52.2875	2.58230
$411$	12.5610	0.619587
$412$	−11.3184	−0.557617
$413$	−58.6400	−2.88549
$414$	−17.7260	−0.871184
$415$	9.32226	0.457612
$416$	8.33651	0.408731
$417$	−14.4711	−0.708652
$418$	18.3510	0.897577
$419$	8.84901	0.432303	0.216151	−	0.976360i	$-0.430650\pi$
$419$	8.84901	0.432303	0.216151	+	0.976360i	$0.430650\pi$
$420$	20.5732	1.00387
$421$	−18.4589	−0.899631	−0.449816	−	0.893121i	$-0.648510\pi$
$421$	−18.4589	−0.899631	−0.449816	+	0.893121i	$0.648510\pi$
$422$	47.4023	2.30751
$423$	8.38069	0.407483
$424$	−7.25489	−0.352328
$425$	47.5480	2.30642
$426$	15.3857	0.745441
$427$	−41.4092	−2.00393
$428$	16.4376	0.794543
$429$	3.58986	0.173320
$430$	−15.7682	−0.760413
$431$	17.9207	0.863212	0.431606	−	0.902062i	$-0.357947\pi$
$431$	17.9207	0.863212	0.431606	+	0.902062i	$0.357947\pi$
$432$	−27.8645	−1.34063
$433$	−39.6184	−1.90394	−0.951969	−	0.306193i	$-0.900945\pi$
$433$	−39.6184	−1.90394	−0.951969	+	0.306193i	$0.900945\pi$
$434$	64.8819	3.11443
$435$	−19.3595	−0.928219
$436$	−8.08602	−0.387250
$437$	−42.5110	−2.03358
$438$	5.25929	0.251299
$439$	14.0915	0.672553	0.336276	−	0.941763i	$-0.390832\pi$
$439$	14.0915	0.672553	0.336276	+	0.941763i	$0.390832\pi$
$440$	10.9782	0.523367
$441$	−15.6221	−0.743910
$442$	−15.9271	−0.757576
$443$	−24.4089	−1.15970	−0.579850	−	0.814723i	$-0.696889\pi$
$443$	−24.4089	−1.15970	−0.579850	+	0.814723i	$0.696889\pi$
$444$	12.3231	0.584826
$445$	−30.5601	−1.44869
$446$	−5.95955	−0.282193
$447$	−18.1472	−0.858333
$448$	2.55614	0.120766
$449$	25.2207	1.19024	0.595120	−	0.803637i	$-0.297105\pi$
$449$	25.2207	1.19024	0.595120	+	0.803637i	$0.297105\pi$
$450$	19.4028	0.914658
$451$	−15.1079	−0.711401
$452$	−0.0452534	−0.00212854
$453$	−22.2975	−1.04763
$454$	38.6556	1.81420
$455$	−23.9440	−1.12251
$456$	−12.2502	−0.573667
$457$	33.5255	1.56826	0.784128	−	0.620599i	$-0.213111\pi$
$457$	33.5255	1.56826	0.784128	+	0.620599i	$0.213111\pi$
$458$	−2.89051	−0.135065
$459$	32.8822	1.53481
$460$	27.8035	1.29635
$461$	8.70385	0.405379	0.202689	−	0.979243i	$-0.435032\pi$
$461$	8.70385	0.405379	0.202689	+	0.979243i	$0.435032\pi$
$462$	−17.3261	−0.806082
$463$	16.2456	0.754997	0.377498	−	0.926010i	$-0.376784\pi$
$463$	16.2456	0.754997	0.377498	+	0.926010i	$0.376784\pi$
$464$	21.0306	0.976319
$465$	−39.9645	−1.85331
$466$	−16.5037	−0.764521
$467$	13.7642	0.636932	0.318466	−	0.947934i	$-0.396832\pi$
$467$	13.7642	0.636932	0.318466	+	0.947934i	$0.396832\pi$
$468$	−2.22986	−0.103075
$469$	−15.7419	−0.726894
$470$	−38.3144	−1.76731
$471$	1.22302	0.0563536
$472$	−22.8367	−1.05114
$473$	4.55605	0.209487
$474$	13.9456	0.640542
$475$	46.5325	2.13506
$476$	26.3735	1.20883
$477$	6.00263	0.274841
$478$	35.3332	1.61610
$479$	5.69599	0.260256	0.130128	−	0.991497i	$-0.458461\pi$
$479$	5.69599	0.260256	0.130128	+	0.991497i	$0.458461\pi$
$480$	24.7832	1.13119
$481$	−14.3421	−0.653943
$482$	−21.8144	−0.993619
$483$	40.1367	1.82628
$484$	−8.02223	−0.364647
$485$	40.0930	1.82053
$486$	22.6101	1.02561
$487$	22.3309	1.01191	0.505954	−	0.862560i	$-0.331140\pi$
$487$	22.3309	1.01191	0.505954	+	0.862560i	$0.331140\pi$
$488$	−16.1263	−0.730004
$489$	10.3155	0.466481
$490$	71.4204	3.22645
$491$	27.1853	1.22686	0.613429	−	0.789750i	$-0.289790\pi$
$491$	27.1853	1.22686	0.613429	+	0.789750i	$0.289790\pi$
$492$	−11.0258	−0.497082
$493$	−24.8177	−1.11773
$494$	−15.5870	−0.701291
$495$	−9.08330	−0.408264
$496$	43.4140	1.94935
$497$	29.6512	1.33004
$498$	−5.72963	−0.256751
$499$	19.0533	0.852941	0.426470	−	0.904502i	$-0.359757\pi$
$499$	19.0533	0.852941	0.426470	+	0.904502i	$0.359757\pi$
$500$	−11.5581	−0.516895
$501$	16.2388	0.725497
$502$	−26.8861	−1.19999
$503$	−8.63613	−0.385066	−0.192533	−	0.981290i	$-0.561670\pi$
$503$	−8.63613	−0.385066	−0.192533	+	0.981290i	$0.561670\pi$
$504$	−9.84409	−0.438490
$505$	43.8222	1.95006
$506$	−23.4152	−1.04093
$507$	13.5004	0.599574
$508$	0.582255	0.0258334
$509$	25.5400	1.13204	0.566020	−	0.824392i	$-0.308483\pi$
$509$	25.5400	1.13204	0.566020	+	0.824392i	$0.308483\pi$
$510$	−47.3491	−2.09665
$511$	10.1356	0.448375
$512$	−10.2578	−0.453334
$513$	32.1800	1.42078
$514$	10.4068	0.459025
$515$	39.1609	1.72564
$516$	3.32504	0.146377
$517$	11.0705	0.486880
$518$	69.2206	3.04138
$519$	8.09676	0.355408
$520$	−9.32470	−0.408915
$521$	−39.4866	−1.72994	−0.864970	−	0.501824i	$-0.832663\pi$
$521$	−39.4866	−1.72994	−0.864970	+	0.501824i	$0.832663\pi$
$522$	−10.1273	−0.443260
$523$	−17.3341	−0.757967	−0.378984	−	0.925403i	$-0.623726\pi$
$523$	−17.3341	−0.757967	−0.378984	+	0.925403i	$0.623726\pi$
$524$	−4.50404	−0.196760
$525$	−43.9336	−1.91742
$526$	−38.6021	−1.68313
$527$	−51.2319	−2.23169
$528$	−11.5933	−0.504533
$529$	31.2424	1.35837
$530$	−27.4425	−1.19203
$531$	18.8948	0.819967
$532$	25.8102	1.11902
$533$	12.8323	0.555829
$534$	18.7828	0.812810
$535$	−56.8731	−2.45884
$536$	−6.13050	−0.264797
$537$	−19.8954	−0.858551
$538$	15.6366	0.674141
$539$	−20.6361	−0.888859
$540$	−21.0467	−0.905706
$541$	−26.4300	−1.13632	−0.568158	−	0.822919i	$-0.692344\pi$
$541$	−26.4300	−1.13632	−0.568158	+	0.822919i	$0.692344\pi$
$542$	−3.93645	−0.169085
$543$	15.3486	0.658673
$544$	31.7705	1.36215
$545$	27.9771	1.19841
$546$	14.7164	0.629804
$547$	−1.00000	−0.0427569
$547$	−1.00000	−0.0427569
$548$	−10.3065	−0.440272
$549$	13.3428	0.569456
$550$	25.6302	1.09288
$551$	−24.2876	−1.03469
$552$	15.6308	0.665289
$553$	26.8758	1.14288
$554$	21.4355	0.910706
$555$	−42.6370	−1.80984
$556$	11.8738	0.503561
$557$	1.27168	0.0538829	0.0269414	−	0.999637i	$-0.491423\pi$
$557$	1.27168	0.0538829	0.0269414	+	0.999637i	$0.491423\pi$
$558$	−20.9061	−0.885026
$559$	−3.86982	−0.163676
$560$	77.3261	3.26762
$561$	13.6810	0.577611
$562$	54.6660	2.30594
$563$	−3.96838	−0.167247	−0.0836237	−	0.996497i	$-0.526649\pi$
$563$	−3.96838	−0.167247	−0.0836237	+	0.996497i	$0.526649\pi$
$564$	8.07933	0.340201
$565$	0.156574	0.00658711
$566$	−46.8168	−1.96786
$567$	−12.6682	−0.532013
$568$	11.5473	0.484515
$569$	16.1671	0.677761	0.338881	−	0.940829i	$-0.389952\pi$
$569$	16.1671	0.677761	0.338881	+	0.940829i	$0.389952\pi$
$570$	−46.3378	−1.94088
$571$	17.9457	0.751005	0.375503	−	0.926821i	$-0.377470\pi$
$571$	17.9457	0.751005	0.375503	+	0.926821i	$0.377470\pi$
$572$	−2.94554	−0.123159
$573$	19.3022	0.806359
$574$	−61.9338	−2.58507
$575$	−59.3737	−2.47605
$576$	−0.823633	−0.0343180
$577$	16.6268	0.692184	0.346092	−	0.938200i	$-0.387508\pi$
$577$	16.6268	0.692184	0.346092	+	0.938200i	$0.387508\pi$
$578$	−31.0357	−1.29091
$579$	8.85429	0.367972
$580$	15.8849	0.659583
$581$	−11.0421	−0.458103
$582$	−24.6419	−1.02144
$583$	7.92919	0.328394
$584$	3.94721	0.163337
$585$	7.71517	0.318983
$586$	−15.5566	−0.642639
$587$	33.9183	1.39996	0.699979	−	0.714163i	$-0.253193\pi$
$587$	33.9183	1.39996	0.699979	+	0.714163i	$0.253193\pi$
$588$	−15.0604	−0.621079
$589$	−50.1377	−2.06589
$590$	−86.3825	−3.55631
$591$	18.5071	0.761280
$592$	46.3172	1.90362
$593$	23.7489	0.975252	0.487626	−	0.873053i	$-0.337863\pi$
$593$	23.7489	0.975252	0.487626	+	0.873053i	$0.337863\pi$
$594$	17.7248	0.727258
$595$	−91.2506	−3.74091
$596$	14.8901	0.609922
$597$	7.56651	0.309677
$598$	19.8884	0.813296
$599$	35.6788	1.45779	0.728897	−	0.684623i	$-0.240033\pi$
$599$	35.6788	1.45779	0.728897	+	0.684623i	$0.240033\pi$
$600$	−17.1094	−0.698489
$601$	−7.46392	−0.304460	−0.152230	−	0.988345i	$-0.548645\pi$
$601$	−7.46392	−0.304460	−0.152230	+	0.988345i	$0.548645\pi$
$602$	18.6773	0.761229
$603$	5.07232	0.206561
$604$	18.2955	0.744433
$605$	27.7564	1.12846
$606$	−26.9339	−1.09412
$607$	−3.18262	−0.129179	−0.0645893	−	0.997912i	$-0.520574\pi$
$607$	−3.18262	−0.129179	−0.0645893	+	0.997912i	$0.520574\pi$
$608$	31.0919	1.26094
$609$	22.9311	0.929216
$610$	−60.9998	−2.46981
$611$	−9.40307	−0.380407
$612$	−8.49801	−0.343512
$613$	−21.7245	−0.877446	−0.438723	−	0.898622i	$-0.644569\pi$
$613$	−21.7245	−0.877446	−0.438723	+	0.898622i	$0.644569\pi$
$614$	36.0875	1.45637
$615$	38.1486	1.53830
$616$	−13.0036	−0.523929
$617$	−6.04399	−0.243322	−0.121661	−	0.992572i	$-0.538822\pi$
$617$	−6.04399	−0.243322	−0.121661	+	0.992572i	$0.538822\pi$
$618$	−24.0690	−0.968198
$619$	−10.9041	−0.438272	−0.219136	−	0.975694i	$-0.570324\pi$
$619$	−10.9041	−0.438272	−0.219136	+	0.975694i	$0.570324\pi$
$620$	32.7916	1.31694
$621$	−41.0604	−1.64770
$622$	−16.6489	−0.667559
$623$	36.1980	1.45024
$624$	9.84710	0.394200
$625$	−0.317943	−0.0127177
$626$	34.6561	1.38514
$627$	13.3888	0.534696
$628$	−1.00351	−0.0400443
$629$	−54.6578	−2.17935
$630$	−37.2365	−1.48354
$631$	−6.17161	−0.245688	−0.122844	−	0.992426i	$-0.539201\pi$
$631$	−6.17161	−0.245688	−0.122844	+	0.992426i	$0.539201\pi$
$632$	10.4665	0.416334
$633$	34.5844	1.37461
$634$	22.0527	0.875826
$635$	−2.01457	−0.0799456
$636$	5.78678	0.229461
$637$	17.5279	0.694480
$638$	−13.3777	−0.529628
$639$	−9.55414	−0.377956
$640$	42.7009	1.68790
$641$	−4.63006	−0.182876	−0.0914382	−	0.995811i	$-0.529146\pi$
$641$	−4.63006	−0.182876	−0.0914382	+	0.995811i	$0.529146\pi$
$642$	34.9553	1.37957
$643$	−25.9357	−1.02281	−0.511403	−	0.859341i	$-0.670874\pi$
$643$	−25.9357	−1.02281	−0.511403	+	0.859341i	$0.670874\pi$
$644$	−32.9329	−1.29774
$645$	−11.5044	−0.452986
$646$	−59.4020	−2.33714
$647$	−18.9502	−0.745009	−0.372505	−	0.928030i	$-0.621501\pi$
$647$	−18.9502	−0.745009	−0.372505	+	0.928030i	$0.621501\pi$
$648$	−4.93347	−0.193805
$649$	24.9592	0.979735
$650$	−21.7698	−0.853882
$651$	47.3374	1.85530
$652$	−8.46403	−0.331477
$653$	−21.2753	−0.832568	−0.416284	−	0.909235i	$-0.636668\pi$
$653$	−21.2753	−0.832568	−0.416284	+	0.909235i	$0.636668\pi$
$654$	−17.1952	−0.672387
$655$	15.5837	0.608905
$656$	−41.4414	−1.61802
$657$	−3.26588	−0.127414
$658$	45.3829	1.76921
$659$	2.22303	0.0865968	0.0432984	−	0.999062i	$-0.486213\pi$
$659$	2.22303	0.0865968	0.0432984	+	0.999062i	$0.486213\pi$
$660$	−8.75668	−0.340853
$661$	−29.9111	−1.16341	−0.581704	−	0.813401i	$-0.697614\pi$
$661$	−29.9111	−1.16341	−0.581704	+	0.813401i	$0.697614\pi$
$662$	−31.1670	−1.21134
$663$	−11.6203	−0.451296
$664$	−4.30021	−0.166881
$665$	−89.3018	−3.46297
$666$	−22.3041	−0.864267
$667$	30.9901	1.19994
$668$	−13.3243	−0.515531
$669$	−4.34805	−0.168105
$670$	−23.1894	−0.895884
$671$	17.6252	0.680413
$672$	−29.3554	−1.13241
$673$	−2.14161	−0.0825530	−0.0412765	−	0.999148i	$-0.513142\pi$
$673$	−2.14161	−0.0825530	−0.0412765	+	0.999148i	$0.513142\pi$
$674$	−19.4388	−0.748754
$675$	44.9447	1.72992
$676$	−11.0773	−0.426051
$677$	46.7475	1.79665	0.898326	−	0.439329i	$-0.144784\pi$
$677$	46.7475	1.79665	0.898326	+	0.439329i	$0.144784\pi$
$678$	−0.0962332	−0.00369581
$679$	−47.4895	−1.82248
$680$	−35.5365	−1.36276
$681$	28.2029	1.08074
$682$	−27.6160	−1.05747
$683$	43.9641	1.68224	0.841119	−	0.540850i	$-0.181897\pi$
$683$	43.9641	1.68224	0.841119	+	0.540850i	$0.181897\pi$
$684$	−8.31652	−0.317990
$685$	35.6598	1.36249
$686$	−32.3101	−1.23360
$687$	−2.10890	−0.0804595
$688$	12.4974	0.476459
$689$	−6.73490	−0.256579
$690$	59.1253	2.25086
$691$	14.2320	0.541412	0.270706	−	0.962662i	$-0.412743\pi$
$691$	14.2320	0.541412	0.270706	+	0.962662i	$0.412743\pi$
$692$	−6.64354	−0.252549
$693$	10.7590	0.408702
$694$	0.930711	0.0353293
$695$	−41.0825	−1.55835
$696$	8.93025	0.338500
$697$	48.9040	1.85237
$698$	−46.5181	−1.76074
$699$	−12.0410	−0.455433
$700$	36.0483	1.36250
$701$	25.9017	0.978293	0.489147	−	0.872202i	$-0.337308\pi$
$701$	25.9017	0.978293	0.489147	+	0.872202i	$0.337308\pi$
$702$	−15.0551	−0.568218
$703$	−53.4904	−2.01743
$704$	−1.08798	−0.0410048
$705$	−27.9540	−1.05281
$706$	3.71464	0.139802
$707$	−51.9067	−1.95215
$708$	18.2154	0.684577
$709$	29.1752	1.09570	0.547849	−	0.836577i	$-0.315447\pi$
$709$	29.1752	1.09570	0.547849	+	0.836577i	$0.315447\pi$
$710$	43.6792	1.63925
$711$	−8.65986	−0.324770
$712$	14.0969	0.528303
$713$	63.9738	2.39584
$714$	56.0843	2.09890
$715$	10.1914	0.381136
$716$	16.3246	0.610077
$717$	25.7789	0.962730
$718$	−2.70221	−0.100846
$719$	−29.1591	−1.08745	−0.543725	−	0.839263i	$-0.682987\pi$
$719$	−29.1591	−1.08745	−0.543725	+	0.839263i	$0.682987\pi$
$720$	−24.9158	−0.928558
$721$	−46.3856	−1.72749
$722$	−24.9809	−0.929694
$723$	−15.9157	−0.591910
$724$	−12.5938	−0.468046
$725$	−33.9217	−1.25982
$726$	−17.0596	−0.633141
$727$	−24.6294	−0.913456	−0.456728	−	0.889606i	$-0.650979\pi$
$727$	−24.6294	−0.913456	−0.456728	+	0.889606i	$0.650979\pi$
$728$	11.0450	0.409354
$729$	25.3740	0.939777
$730$	14.9308	0.552614
$731$	−14.7479	−0.545471
$732$	12.8630	0.475429
$733$	−22.1022	−0.816362	−0.408181	−	0.912901i	$-0.633837\pi$
$733$	−22.1022	−0.816362	−0.408181	+	0.912901i	$0.633837\pi$
$734$	−14.1417	−0.521978
$735$	52.1079	1.92203
$736$	−39.6721	−1.46233
$737$	6.70030	0.246809
$738$	19.9562	0.734597
$739$	−9.16477	−0.337131	−0.168566	−	0.985690i	$-0.553914\pi$
$739$	−9.16477	−0.337131	−0.168566	+	0.985690i	$0.553914\pi$
$740$	34.9844	1.28605
$741$	−11.3722	−0.417767
$742$	32.5053	1.19331
$743$	32.0802	1.17691	0.588454	−	0.808531i	$-0.299737\pi$
$743$	32.0802	1.17691	0.588454	+	0.808531i	$0.299737\pi$
$744$	18.4350	0.675860
$745$	−51.5188	−1.88750
$746$	−63.5234	−2.32576
$747$	3.55796	0.130179
$748$	−11.2255	−0.410444
$749$	67.3654	2.46148
$750$	−24.5788	−0.897491
$751$	−19.3094	−0.704611	−0.352305	−	0.935885i	$-0.614602\pi$
$751$	−19.3094	−0.704611	−0.352305	+	0.935885i	$0.614602\pi$
$752$	30.3668	1.10736
$753$	−19.6160	−0.714845
$754$	11.3627	0.413807
$755$	−63.3012	−2.30377
$756$	24.9295	0.906678
$757$	9.52491	0.346189	0.173094	−	0.984905i	$-0.444623\pi$
$757$	9.52491	0.346189	0.173094	+	0.984905i	$0.444623\pi$
$758$	2.05617	0.0746834
$759$	−17.0836	−0.620094
$760$	−34.7775	−1.26151
$761$	26.1744	0.948823	0.474411	−	0.880303i	$-0.342661\pi$
$761$	26.1744	0.948823	0.474411	+	0.880303i	$0.342661\pi$
$762$	1.23819	0.0448549
$763$	−33.1385	−1.19969
$764$	−15.8378	−0.572991
$765$	29.4026	1.06305
$766$	−6.73920	−0.243497
$767$	−21.1999	−0.765483
$768$	−24.7245	−0.892167
$769$	28.8856	1.04164	0.520820	−	0.853666i	$-0.325626\pi$
$769$	28.8856	1.04164	0.520820	+	0.853666i	$0.325626\pi$
$770$	−49.1877	−1.77260
$771$	7.59275	0.273446
$772$	−7.26511	−0.261477
$773$	−4.07993	−0.146745	−0.0733725	−	0.997305i	$-0.523376\pi$
$773$	−4.07993	−0.146745	−0.0733725	+	0.997305i	$0.523376\pi$
$774$	−6.01815	−0.216318
$775$	−70.0256	−2.51539
$776$	−18.4942	−0.663905
$777$	50.5029	1.81178
$778$	16.2851	0.583851
$779$	47.8596	1.71475
$780$	7.43775	0.266314
$781$	−12.6206	−0.451600
$782$	75.7947	2.71041
$783$	−23.4589	−0.838351
$784$	−56.6055	−2.02163
$785$	3.47207	0.123923
$786$	−9.57802	−0.341637
$787$	−11.4800	−0.409219	−0.204609	−	0.978844i	$-0.565592\pi$
$787$	−11.4800	−0.409219	−0.204609	+	0.978844i	$0.565592\pi$
$788$	−15.1854	−0.540958
$789$	−28.1638	−1.00266
$790$	39.5907	1.40857
$791$	−0.185460	−0.00659418
$792$	4.18998	0.148885
$793$	−14.9705	−0.531617
$794$	51.9880	1.84498
$795$	−20.0219	−0.710103
$796$	−6.20846	−0.220053
$797$	−22.6786	−0.803316	−0.401658	−	0.915790i	$-0.631566\pi$
$797$	−22.6786	−0.803316	−0.401658	+	0.915790i	$0.631566\pi$
$798$	54.8865	1.94296
$799$	−35.8351	−1.26776
$800$	43.4251	1.53531
$801$	−11.6636	−0.412114
$802$	−9.33079	−0.329482
$803$	−4.31408	−0.152241
$804$	4.88993	0.172454
$805$	113.946	4.01606
$806$	23.4565	0.826219
$807$	11.4084	0.401593
$808$	−20.2145	−0.711142
$809$	−8.43197	−0.296452	−0.148226	−	0.988953i	$-0.547356\pi$
$809$	−8.43197	−0.296452	−0.148226	+	0.988953i	$0.547356\pi$
$810$	−18.6615	−0.655697
$811$	−25.0503	−0.879637	−0.439818	−	0.898087i	$-0.644957\pi$
$811$	−25.0503	−0.879637	−0.439818	+	0.898087i	$0.644957\pi$
$812$	−18.8154	−0.660291
$813$	−2.87201	−0.100726
$814$	−29.4627	−1.03267
$815$	29.2850	1.02581
$816$	37.5274	1.31372
$817$	−14.4329	−0.504944
$818$	10.5672	0.369474
$819$	−9.13852	−0.319326
$820$	−31.3017	−1.09310
$821$	3.90486	0.136280	0.0681402	−	0.997676i	$-0.478293\pi$
$821$	3.90486	0.136280	0.0681402	+	0.997676i	$0.478293\pi$
$822$	−21.9172	−0.764450
$823$	−19.1872	−0.668825	−0.334412	−	0.942427i	$-0.608538\pi$
$823$	−19.1872	−0.668825	−0.334412	+	0.942427i	$0.608538\pi$
$824$	−18.0643	−0.629300
$825$	18.6996	0.651038
$826$	102.319	3.56013
$827$	−32.9961	−1.14739	−0.573694	−	0.819070i	$-0.694490\pi$
$827$	−32.9961	−1.14739	−0.573694	+	0.819070i	$0.694490\pi$
$828$	10.6116	0.368777
$829$	−9.64456	−0.334969	−0.167485	−	0.985875i	$-0.553564\pi$
$829$	−9.64456	−0.334969	−0.167485	+	0.985875i	$0.553564\pi$
$830$	−16.2661	−0.564604
$831$	15.6392	0.542518
$832$	0.924109	0.0320377
$833$	66.7989	2.31444
$834$	25.2501	0.874339
$835$	46.1011	1.59539
$836$	−10.9857	−0.379950
$837$	−48.4269	−1.67388
$838$	−15.4403	−0.533378
$839$	49.6031	1.71249	0.856244	−	0.516572i	$-0.172792\pi$
$839$	49.6031	1.71249	0.856244	+	0.516572i	$0.172792\pi$
$840$	32.8351	1.13292
$841$	−11.2946	−0.389468
$842$	32.2083	1.10997
$843$	39.8839	1.37368
$844$	−28.3771	−0.976782
$845$	38.3268	1.31848
$846$	−14.6232	−0.502755
$847$	−32.8771	−1.12967
$848$	21.7501	0.746900
$849$	−34.1572	−1.17227
$850$	−82.9648	−2.84567
$851$	68.2518	2.33964
$852$	−9.21059	−0.315550
$853$	17.9174	0.613480	0.306740	−	0.951793i	$-0.400762\pi$
$853$	17.9174	0.613480	0.306740	+	0.951793i	$0.400762\pi$
$854$	72.2535	2.47246
$855$	28.7746	0.984071
$856$	26.2347	0.896683
$857$	−2.42086	−0.0826950	−0.0413475	−	0.999145i	$-0.513165\pi$
$857$	−2.42086	−0.0826950	−0.0413475	+	0.999145i	$0.513165\pi$
$858$	−6.26382	−0.213843
$859$	−16.6676	−0.568692	−0.284346	−	0.958722i	$-0.591776\pi$
$859$	−16.6676	−0.568692	−0.284346	+	0.958722i	$0.591776\pi$
$860$	9.43958	0.321887
$861$	−45.1865	−1.53995
$862$	−31.2693	−1.06504
$863$	34.8647	1.18681	0.593404	−	0.804905i	$-0.297784\pi$
$863$	34.8647	1.18681	0.593404	+	0.804905i	$0.297784\pi$
$864$	30.0310	1.02168
$865$	22.9862	0.781554
$866$	69.1288	2.34909
$867$	−22.6434	−0.769011
$868$	−38.8412	−1.31836
$869$	−11.4393	−0.388051
$870$	33.7798	1.14524
$871$	−5.69110	−0.192836
$872$	−12.9054	−0.437032
$873$	15.3020	0.517893
$874$	74.1760	2.50904
$875$	−47.3680	−1.60133
$876$	−3.14845	−0.106376
$877$	−6.48932	−0.219129	−0.109564	−	0.993980i	$-0.534946\pi$
$877$	−6.48932	−0.219129	−0.109564	+	0.993980i	$0.534946\pi$
$878$	−24.5879	−0.829800
$879$	−11.3500	−0.382827
$880$	−32.9126	−1.10949
$881$	−57.2243	−1.92794	−0.963968	−	0.266020i	$-0.914291\pi$
$881$	−57.2243	−1.92794	−0.963968	+	0.266020i	$0.914291\pi$
$882$	27.2585	0.917841
$883$	−24.1168	−0.811595	−0.405797	−	0.913963i	$-0.633006\pi$
$883$	−24.1168	−0.811595	−0.405797	+	0.913963i	$0.633006\pi$
$884$	9.53470	0.320687
$885$	−63.0241	−2.11853
$886$	42.5902	1.43084
$887$	42.1176	1.41417	0.707086	−	0.707128i	$-0.250010\pi$
$887$	42.1176	1.41417	0.707086	+	0.707128i	$0.250010\pi$
$888$	19.6678	0.660007
$889$	2.38622	0.0800314
$890$	53.3232	1.78740
$891$	5.39201	0.180639
$892$	3.56765	0.119454
$893$	−35.0698	−1.17357
$894$	31.6644	1.05902
$895$	−56.4819	−1.88798
$896$	−50.5786	−1.68971
$897$	14.5104	0.484489
$898$	−44.0068	−1.46852
$899$	36.5499	1.21901
$900$	−11.6154	−0.387180
$901$	−25.6667	−0.855083
$902$	26.3612	0.877731
$903$	13.6268	0.453472
$904$	−0.0722250	−0.00240217
$905$	43.5739	1.44844
$906$	38.9061	1.29257
$907$	25.8210	0.857371	0.428686	−	0.903454i	$-0.358977\pi$
$907$	25.8210	0.857371	0.428686	+	0.903454i	$0.358977\pi$
$908$	−23.1410	−0.767960
$909$	16.7253	0.554742
$910$	41.7790	1.38496
$911$	−20.3911	−0.675587	−0.337794	−	0.941220i	$-0.609681\pi$
$911$	−20.3911	−0.675587	−0.337794	+	0.941220i	$0.609681\pi$
$912$	36.7259	1.21612
$913$	4.69989	0.155544
$914$	−58.4974	−1.93492
$915$	−44.5051	−1.47129
$916$	1.73039	0.0571737
$917$	−18.4587	−0.609559
$918$	−57.3751	−1.89366
$919$	−23.0410	−0.760054	−0.380027	−	0.924975i	$-0.624085\pi$
$919$	−23.0410	−0.760054	−0.380027	+	0.924975i	$0.624085\pi$
$920$	44.3748	1.46299
$921$	26.3292	0.867577
$922$	−15.1870	−0.500159
$923$	10.7197	0.352842
$924$	10.3722	0.341219
$925$	−74.7083	−2.45639
$926$	−28.3464	−0.931520
$927$	14.9463	0.490899
$928$	−22.6657	−0.744038
$929$	−24.2154	−0.794483	−0.397241	−	0.917714i	$-0.630032\pi$
$929$	−24.2154	−0.794483	−0.397241	+	0.917714i	$0.630032\pi$
$930$	69.7327	2.28663
$931$	65.3722	2.14249
$932$	9.87987	0.323626
$933$	−12.1469	−0.397672
$934$	−24.0167	−0.785850
$935$	38.8394	1.27019
$936$	−3.55889	−0.116326
$937$	28.7273	0.938479	0.469239	−	0.883071i	$-0.344528\pi$
$937$	28.7273	0.938479	0.469239	+	0.883071i	$0.344528\pi$
$938$	27.4675	0.896846
$939$	25.2849	0.825141
$940$	22.9367	0.748114
$941$	−36.9396	−1.20420	−0.602098	−	0.798422i	$-0.705669\pi$
$941$	−36.9396	−1.20420	−0.602098	+	0.798422i	$0.705669\pi$
$942$	−2.13400	−0.0695294
$943$	−61.0670	−1.98861
$944$	68.4640	2.22831
$945$	−86.2546	−2.80586
$946$	−7.94969	−0.258467
$947$	−56.3251	−1.83032	−0.915160	−	0.403090i	$-0.867936\pi$
$947$	−56.3251	−1.83032	−0.915160	+	0.403090i	$0.867936\pi$
$948$	−8.34846	−0.271145
$949$	3.66430	0.118948
$950$	−81.1929	−2.63425
$951$	16.0895	0.521739
$952$	42.0925	1.36423
$953$	−10.9066	−0.353298	−0.176649	−	0.984274i	$-0.556526\pi$
$953$	−10.9066	−0.353298	−0.176649	+	0.984274i	$0.556526\pi$
$954$	−10.4738	−0.339101
$955$	54.7977	1.77321
$956$	−21.1520	−0.684106
$957$	−9.76028	−0.315505
$958$	−9.93873	−0.321106
$959$	−42.2386	−1.36395
$960$	2.74725	0.0886670
$961$	44.4510	1.43390
$962$	25.0250	0.806839
$963$	−21.7063	−0.699477
$964$	13.0591	0.420605
$965$	25.1368	0.809182
$966$	−70.0331	−2.25328
$967$	16.0179	0.515100	0.257550	−	0.966265i	$-0.417085\pi$
$967$	16.0179	0.515100	0.257550	+	0.966265i	$0.417085\pi$
$968$	−12.8036	−0.411523
$969$	−43.3393	−1.39226
$970$	−69.9568	−2.24618
$971$	24.3509	0.781457	0.390728	−	0.920506i	$-0.372223\pi$
$971$	24.3509	0.781457	0.390728	+	0.920506i	$0.372223\pi$
$972$	−13.5354	−0.434149
$973$	48.6617	1.56002
$974$	−38.9644	−1.24850
$975$	−15.8831	−0.508666
$976$	48.3465	1.54753
$977$	−9.25929	−0.296231	−0.148115	−	0.988970i	$-0.547321\pi$
$977$	−9.25929	−0.296231	−0.148115	+	0.988970i	$0.547321\pi$
$978$	−17.9991	−0.575547
$979$	−15.4071	−0.492413
$980$	−42.7555	−1.36577
$981$	10.6778	0.340916
$982$	−47.4348	−1.51370
$983$	−50.2659	−1.60323	−0.801617	−	0.597839i	$-0.796026\pi$
$983$	−50.2659	−1.60323	−0.801617	+	0.597839i	$0.796026\pi$
$984$	−17.5974	−0.560983
$985$	52.5405	1.67408
$986$	43.3035	1.37906
$987$	33.1111	1.05394
$988$	9.33106	0.296861
$989$	18.4159	0.585590
$990$	15.8491	0.503719
$991$	−37.3702	−1.18711	−0.593553	−	0.804795i	$-0.702275\pi$
$991$	−37.3702	−1.18711	−0.593553	+	0.804795i	$0.702275\pi$
$992$	−46.7895	−1.48557
$993$	−22.7392	−0.721607
$994$	−51.7374	−1.64101
$995$	21.4809	0.680990
$996$	3.43002	0.108684
$997$	−38.1667	−1.20875	−0.604375	−	0.796700i	$-0.706577\pi$
$997$	−38.1667	−1.20875	−0.604375	+	0.796700i	$0.706577\pi$
$998$	−33.2454	−1.05236
$999$	−51.6652	−1.63462

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.2.a.b.1.5	✓	18
3.2	odd	2		4923.2.a.l.1.14		18
4.3	odd	2		8752.2.a.s.1.12		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.2.a.b.1.5	✓	18	1.1	even	1	trivial
4923.2.a.l.1.14		18	3.2	odd	2
8752.2.a.s.1.12		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)

\(f(q)\)	\(=\)	\(q-1.74487 q^{2} -1.27304 q^{3} +1.04455 q^{4} -3.61409 q^{5} +2.22129 q^{6} +4.28084 q^{7} +1.66712 q^{8} -1.37936 q^{9} +O(q^{10})\)	\(q-1.74487 q^{2} -1.27304 q^{3} +1.04455 q^{4} -3.61409 q^{5} +2.22129 q^{6} +4.28084 q^{7} +1.66712 q^{8} -1.37936 q^{9} +6.30610 q^{10} -1.82207 q^{11} -1.32976 q^{12} +1.54763 q^{13} -7.46949 q^{14} +4.60089 q^{15} -4.99801 q^{16} +5.89804 q^{17} +2.40680 q^{18} +5.77207 q^{19} -3.77512 q^{20} -5.44969 q^{21} +3.17927 q^{22} -7.36494 q^{23} -2.12232 q^{24} +8.06166 q^{25} -2.70041 q^{26} +5.57511 q^{27} +4.47157 q^{28} -4.20778 q^{29} -8.02794 q^{30} -8.68625 q^{31} +5.38662 q^{32} +2.31958 q^{33} -10.2913 q^{34} -15.4714 q^{35} -1.44082 q^{36} -9.26711 q^{37} -10.0715 q^{38} -1.97020 q^{39} -6.02514 q^{40} +8.29157 q^{41} +9.50898 q^{42} -2.50047 q^{43} -1.90326 q^{44} +4.98514 q^{45} +12.8508 q^{46} -6.07577 q^{47} +6.36269 q^{48} +11.3256 q^{49} -14.0665 q^{50} -7.50845 q^{51} +1.61659 q^{52} -4.35174 q^{53} -9.72782 q^{54} +6.58514 q^{55} +7.13669 q^{56} -7.34809 q^{57} +7.34201 q^{58} -13.6982 q^{59} +4.80588 q^{60} -9.67314 q^{61} +15.1563 q^{62} -5.90483 q^{63} +0.597111 q^{64} -5.59329 q^{65} -4.04735 q^{66} -3.67729 q^{67} +6.16082 q^{68} +9.37589 q^{69} +26.9954 q^{70} +6.92649 q^{71} -2.29957 q^{72} +2.36768 q^{73} +16.1699 q^{74} -10.2628 q^{75} +6.02925 q^{76} -7.80001 q^{77} +3.43774 q^{78} +6.27816 q^{79} +18.0633 q^{80} -2.95927 q^{81} -14.4677 q^{82} -2.57942 q^{83} -5.69250 q^{84} -21.3161 q^{85} +4.36299 q^{86} +5.35668 q^{87} -3.03762 q^{88} +8.45581 q^{89} -8.69840 q^{90} +6.62517 q^{91} -7.69309 q^{92} +11.0580 q^{93} +10.6014 q^{94} -20.8608 q^{95} -6.85739 q^{96} -11.0935 q^{97} -19.7617 q^{98} +2.51330 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 4 q^{2} - 10 q^{3} + 16 q^{4} - 27 q^{5} - 3 q^{6} - 11 q^{7} - 12 q^{8} + 14 q^{9}+O(q^{10}) \) 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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