LMFDB - Embedded newform 547.2.a.b.1.2

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			1.2
Root			$2.59964$ 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)

$f(q)$	$=$	$q-2.59964 q^{2} +2.09484 q^{3} +4.75812 q^{4} -3.02323 q^{5} -5.44583 q^{6} -0.561390 q^{7} -7.17011 q^{8} +1.38836 q^{9} +O(q^{10})$	\(q-2.59964 q^{2} +2.09484 q^{3} +4.75812 q^{4} -3.02323 q^{5} -5.44583 q^{6} -0.561390 q^{7} -7.17011 q^{8} +1.38836 q^{9} +7.85930 q^{10} +4.23111 q^{11} +9.96751 q^{12} -4.87964 q^{13} +1.45941 q^{14} -6.33319 q^{15} +9.12345 q^{16} -6.39965 q^{17} -3.60924 q^{18} +6.29628 q^{19} -14.3849 q^{20} -1.17602 q^{21} -10.9994 q^{22} -9.21357 q^{23} -15.0202 q^{24} +4.13991 q^{25} +12.6853 q^{26} -3.37612 q^{27} -2.67116 q^{28} +1.14750 q^{29} +16.4640 q^{30} -7.52167 q^{31} -9.37744 q^{32} +8.86351 q^{33} +16.6368 q^{34} +1.69721 q^{35} +6.60600 q^{36} +8.74347 q^{37} -16.3680 q^{38} -10.2221 q^{39} +21.6769 q^{40} +2.81890 q^{41} +3.05723 q^{42} -1.57023 q^{43} +20.1321 q^{44} -4.19734 q^{45} +23.9520 q^{46} -4.08126 q^{47} +19.1122 q^{48} -6.68484 q^{49} -10.7623 q^{50} -13.4063 q^{51} -23.2179 q^{52} -4.00434 q^{53} +8.77670 q^{54} -12.7916 q^{55} +4.02522 q^{56} +13.1897 q^{57} -2.98307 q^{58} -12.2872 q^{59} -30.1341 q^{60} -0.473603 q^{61} +19.5536 q^{62} -0.779413 q^{63} +6.13107 q^{64} +14.7523 q^{65} -23.0419 q^{66} +1.80684 q^{67} -30.4503 q^{68} -19.3010 q^{69} -4.41213 q^{70} -1.76871 q^{71} -9.95472 q^{72} +0.611682 q^{73} -22.7298 q^{74} +8.67247 q^{75} +29.9584 q^{76} -2.37530 q^{77} +26.5737 q^{78} -2.49642 q^{79} -27.5823 q^{80} -11.2375 q^{81} -7.32811 q^{82} +8.29336 q^{83} -5.59565 q^{84} +19.3476 q^{85} +4.08204 q^{86} +2.40382 q^{87} -30.3375 q^{88} -14.8521 q^{89} +10.9116 q^{90} +2.73938 q^{91} -43.8393 q^{92} -15.7567 q^{93} +10.6098 q^{94} -19.0351 q^{95} -19.6443 q^{96} -7.36588 q^{97} +17.3782 q^{98} +5.87432 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.59964	−1.83822	−0.919111	−	0.393999i	$-0.871091\pi$
$2$	−2.59964	−1.83822	−0.919111	+	0.393999i	$0.871091\pi$
$3$	2.09484	1.20946	0.604729	−	0.796431i	$-0.293281\pi$
$3$	2.09484	1.20946	0.604729	+	0.796431i	$0.293281\pi$
$4$	4.75812	2.37906
$5$	−3.02323	−1.35203	−0.676015	−	0.736888i	$-0.736294\pi$
$5$	−3.02323	−1.35203	−0.676015	+	0.736888i	$0.736294\pi$
$6$	−5.44583	−2.22325
$7$	−0.561390	−0.212185	−0.106093	−	0.994356i	$-0.533834\pi$
$7$	−0.561390	−0.212185	−0.106093	+	0.994356i	$0.533834\pi$
$8$	−7.17011	−2.53502
$9$	1.38836	0.462788
$10$	7.85930	2.48533
$11$	4.23111	1.27573	0.637864	−	0.770149i	$-0.279818\pi$
$11$	4.23111	1.27573	0.637864	+	0.770149i	$0.279818\pi$
$12$	9.96751	2.87737
$13$	−4.87964	−1.35337	−0.676684	−	0.736274i	$-0.736584\pi$
$13$	−4.87964	−1.35337	−0.676684	+	0.736274i	$0.736584\pi$
$14$	1.45941	0.390044
$15$	−6.33319	−1.63522
$16$	9.12345	2.28086
$17$	−6.39965	−1.55214	−0.776071	−	0.630645i	$-0.782790\pi$
$17$	−6.39965	−1.55214	−0.776071	+	0.630645i	$0.782790\pi$
$18$	−3.60924	−0.850707
$19$	6.29628	1.44447	0.722233	−	0.691650i	$-0.243116\pi$
$19$	6.29628	1.44447	0.722233	+	0.691650i	$0.243116\pi$
$20$	−14.3849	−3.21656
$21$	−1.17602	−0.256629
$22$	−10.9994	−2.34507
$23$	−9.21357	−1.92116	−0.960581	−	0.277999i	$-0.910329\pi$
$23$	−9.21357	−1.92116	−0.960581	+	0.277999i	$0.910329\pi$
$24$	−15.0202	−3.06599
$25$	4.13991	0.827983
$26$	12.6853	2.48779
$27$	−3.37612	−0.649735
$28$	−2.67116	−0.504801
$29$	1.14750	0.213085	0.106542	−	0.994308i	$-0.466022\pi$
$29$	1.14750	0.213085	0.106542	+	0.994308i	$0.466022\pi$
$30$	16.4640	3.00590
$31$	−7.52167	−1.35093	−0.675466	−	0.737391i	$-0.736058\pi$
$31$	−7.52167	−1.35093	−0.675466	+	0.737391i	$0.736058\pi$
$32$	−9.37744	−1.65771
$33$	8.86351	1.54294
$34$	16.6368	2.85318
$35$	1.69721	0.286881
$36$	6.60600	1.10100
$37$	8.74347	1.43742	0.718708	−	0.695312i	$-0.244734\pi$
$37$	8.74347	1.43742	0.718708	+	0.695312i	$0.244734\pi$
$38$	−16.3680	−2.65525
$39$	−10.2221	−1.63684
$40$	21.6769	3.42741
$41$	2.81890	0.440238	0.220119	−	0.975473i	$-0.429355\pi$
$41$	2.81890	0.440238	0.220119	+	0.975473i	$0.429355\pi$
$42$	3.05723	0.471741
$43$	−1.57023	−0.239458	−0.119729	−	0.992807i	$-0.538203\pi$
$43$	−1.57023	−0.239458	−0.119729	+	0.992807i	$0.538203\pi$
$44$	20.1321	3.03503
$45$	−4.19734	−0.625703
$46$	23.9520	3.53152
$47$	−4.08126	−0.595313	−0.297657	−	0.954673i	$-0.596205\pi$
$47$	−4.08126	−0.595313	−0.297657	+	0.954673i	$0.596205\pi$
$48$	19.1122	2.75861
$49$	−6.68484	−0.954977
$50$	−10.7623	−1.52202
$51$	−13.4063	−1.87725
$52$	−23.2179	−3.21974
$53$	−4.00434	−0.550039	−0.275019	−	0.961439i	$-0.588684\pi$
$53$	−4.00434	−0.550039	−0.275019	+	0.961439i	$0.588684\pi$
$54$	8.77670	1.19436
$55$	−12.7916	−1.72482
$56$	4.02522	0.537893
$57$	13.1897	1.74702
$58$	−2.98307	−0.391697
$59$	−12.2872	−1.59966	−0.799828	−	0.600229i	$-0.795076\pi$
$59$	−12.2872	−1.59966	−0.799828	+	0.600229i	$0.795076\pi$
$60$	−30.1341	−3.89029
$61$	−0.473603	−0.0606386	−0.0303193	−	0.999540i	$-0.509652\pi$
$61$	−0.473603	−0.0606386	−0.0303193	+	0.999540i	$0.509652\pi$
$62$	19.5536	2.48331
$63$	−0.779413	−0.0981968
$64$	6.13107	0.766383
$65$	14.7523	1.82979
$66$	−23.0419	−2.83626
$67$	1.80684	0.220740	0.110370	−	0.993891i	$-0.464796\pi$
$67$	1.80684	0.220740	0.110370	+	0.993891i	$0.464796\pi$
$68$	−30.4503	−3.69264
$69$	−19.3010	−2.32356
$70$	−4.41213	−0.527350
$71$	−1.76871	−0.209907	−0.104954	−	0.994477i	$-0.533469\pi$
$71$	−1.76871	−0.209907	−0.104954	+	0.994477i	$0.533469\pi$
$72$	−9.95472	−1.17317
$73$	0.611682	0.0715919	0.0357960	−	0.999359i	$-0.488603\pi$
$73$	0.611682	0.0715919	0.0357960	+	0.999359i	$0.488603\pi$
$74$	−22.7298	−2.64229
$75$	8.67247	1.00141
$76$	29.9584	3.43647
$77$	−2.37530	−0.270691
$78$	26.5737	3.00888
$79$	−2.49642	−0.280869	−0.140434	−	0.990090i	$-0.544850\pi$
$79$	−2.49642	−0.280869	−0.140434	+	0.990090i	$0.544850\pi$
$80$	−27.5823	−3.08379
$81$	−11.2375	−1.24862
$82$	−7.32811	−0.809254
$83$	8.29336	0.910315	0.455158	−	0.890411i	$-0.349583\pi$
$83$	8.29336	0.910315	0.455158	+	0.890411i	$0.349583\pi$
$84$	−5.59565	−0.610536
$85$	19.3476	2.09854
$86$	4.08204	0.440178
$87$	2.40382	0.257717
$88$	−30.3375	−3.23399
$89$	−14.8521	−1.57432	−0.787162	−	0.616746i	$-0.788450\pi$
$89$	−14.8521	−1.57432	−0.787162	+	0.616746i	$0.788450\pi$
$90$	10.9116	1.15018
$91$	2.73938	0.287165
$92$	−43.8393	−4.57056
$93$	−15.7567	−1.63390
$94$	10.6098	1.09432
$95$	−19.0351	−1.95296
$96$	−19.6443	−2.00493
$97$	−7.36588	−0.747891	−0.373946	−	0.927451i	$-0.621995\pi$
$97$	−7.36588	−0.747891	−0.373946	+	0.927451i	$0.621995\pi$
$98$	17.3782	1.75546
$99$	5.87432	0.590392
$100$	19.6982	1.96982
$101$	5.05569	0.503060	0.251530	−	0.967849i	$-0.419066\pi$
$101$	5.05569	0.503060	0.251530	+	0.967849i	$0.419066\pi$
$102$	34.8514	3.45080
$103$	1.90289	0.187497	0.0937486	−	0.995596i	$-0.470115\pi$
$103$	1.90289	0.187497	0.0937486	+	0.995596i	$0.470115\pi$
$104$	34.9875	3.43081
$105$	3.55539	0.346970
$106$	10.4098	1.01109
$107$	11.8307	1.14371	0.571856	−	0.820354i	$-0.306224\pi$
$107$	11.8307	1.14371	0.571856	+	0.820354i	$0.306224\pi$
$108$	−16.0640	−1.54576
$109$	4.76603	0.456503	0.228251	−	0.973602i	$-0.426699\pi$
$109$	4.76603	0.456503	0.228251	+	0.973602i	$0.426699\pi$
$110$	33.2536	3.17060
$111$	18.3162	1.73849
$112$	−5.12181	−0.483965
$113$	12.6049	1.18577	0.592886	−	0.805287i	$-0.297989\pi$
$113$	12.6049	1.18577	0.592886	+	0.805287i	$0.297989\pi$
$114$	−34.2885	−3.21141
$115$	27.8547	2.59747
$116$	5.45992	0.506941
$117$	−6.77471	−0.626322
$118$	31.9423	2.94052
$119$	3.59270	0.329342
$120$	45.4096	4.14531
$121$	6.90230	0.627482
$122$	1.23120	0.111467
$123$	5.90514	0.532449
$124$	−35.7890	−3.21395
$125$	2.60024	0.232572
$126$	2.02619	0.180508
$127$	−20.3142	−1.80260	−0.901298	−	0.433199i	$-0.857385\pi$
$127$	−20.3142	−1.80260	−0.901298	+	0.433199i	$0.857385\pi$
$128$	2.81634	0.248931
$129$	−3.28939	−0.289615
$130$	−38.3505	−3.36356
$131$	13.5167	1.18096	0.590478	−	0.807054i	$-0.298939\pi$
$131$	13.5167	1.18096	0.590478	+	0.807054i	$0.298939\pi$
$132$	42.1736	3.67074
$133$	−3.53467	−0.306494
$134$	−4.69712	−0.405770
$135$	10.2068	0.878461
$136$	45.8861	3.93470
$137$	8.32726	0.711446	0.355723	−	0.934591i	$-0.384235\pi$
$137$	8.32726	0.711446	0.355723	+	0.934591i	$0.384235\pi$
$138$	50.1756	4.27123
$139$	−16.6457	−1.41187	−0.705936	−	0.708275i	$-0.749474\pi$
$139$	−16.6457	−1.41187	−0.705936	+	0.708275i	$0.749474\pi$
$140$	8.07552	0.682506
$141$	−8.54960	−0.720006
$142$	4.59801	0.385856
$143$	−20.6463	−1.72653
$144$	12.6667	1.05556
$145$	−3.46914	−0.288096
$146$	−1.59015	−0.131602
$147$	−14.0037	−1.15500
$148$	41.6024	3.41970
$149$	9.40634	0.770598	0.385299	−	0.922792i	$-0.374098\pi$
$149$	9.40634	0.770598	0.385299	+	0.922792i	$0.374098\pi$
$150$	−22.5453	−1.84081
$151$	−20.3010	−1.65207	−0.826035	−	0.563619i	$-0.809409\pi$
$151$	−20.3010	−1.65207	−0.826035	+	0.563619i	$0.809409\pi$
$152$	−45.1450	−3.66174
$153$	−8.88504	−0.718313
$154$	6.17492	0.497590
$155$	22.7397	1.82650
$156$	−48.6378	−3.89414
$157$	−6.07853	−0.485120	−0.242560	−	0.970136i	$-0.577987\pi$
$157$	−6.07853	−0.485120	−0.242560	+	0.970136i	$0.577987\pi$
$158$	6.48978	0.516299
$159$	−8.38846	−0.665249
$160$	28.3502	2.24128
$161$	5.17240	0.407643
$162$	29.2135	2.29523
$163$	7.36070	0.576535	0.288267	−	0.957550i	$-0.406921\pi$
$163$	7.36070	0.576535	0.288267	+	0.957550i	$0.406921\pi$
$164$	13.4126	1.04735
$165$	−26.7964	−2.08610
$166$	−21.5597	−1.67336
$167$	7.50992	0.581135	0.290568	−	0.956854i	$-0.406156\pi$
$167$	7.50992	0.581135	0.290568	+	0.956854i	$0.406156\pi$
$168$	8.43221	0.650559
$169$	10.8108	0.831604
$170$	−50.2967	−3.85758
$171$	8.74153	0.668481
$172$	−7.47136	−0.569686
$173$	5.25063	0.399198	0.199599	−	0.979878i	$-0.436036\pi$
$173$	5.25063	0.399198	0.199599	+	0.979878i	$0.436036\pi$
$174$	−6.24907	−0.473740
$175$	−2.32410	−0.175686
$176$	38.6023	2.90976
$177$	−25.7397	−1.93472
$178$	38.6102	2.89396
$179$	−9.57025	−0.715314	−0.357657	−	0.933853i	$-0.616424\pi$
$179$	−9.57025	−0.715314	−0.357657	+	0.933853i	$0.616424\pi$
$180$	−19.9714	−1.48858
$181$	−1.66933	−0.124081	−0.0620403	−	0.998074i	$-0.519761\pi$
$181$	−1.66933	−0.124081	−0.0620403	+	0.998074i	$0.519761\pi$
$182$	−7.12139	−0.527872
$183$	−0.992123	−0.0733398
$184$	66.0623	4.87018
$185$	−26.4335	−1.94343
$186$	40.9618	3.00346
$187$	−27.0776	−1.98011
$188$	−19.4191	−1.41629
$189$	1.89532	0.137864
$190$	49.4843	3.58997
$191$	26.7101	1.93268	0.966339	−	0.257272i	$-0.0828236\pi$
$191$	26.7101	1.93268	0.966339	+	0.257272i	$0.0828236\pi$
$192$	12.8436	0.926908
$193$	17.1594	1.23516	0.617582	−	0.786506i	$-0.288112\pi$
$193$	17.1594	1.23516	0.617582	+	0.786506i	$0.288112\pi$
$194$	19.1486	1.37479
$195$	30.9037	2.21306
$196$	−31.8073	−2.27195
$197$	−5.98278	−0.426255	−0.213128	−	0.977024i	$-0.568365\pi$
$197$	−5.98278	−0.426255	−0.213128	+	0.977024i	$0.568365\pi$
$198$	−15.2711	−1.08527
$199$	16.0373	1.13685	0.568426	−	0.822734i	$-0.307552\pi$
$199$	16.0373	1.13685	0.568426	+	0.822734i	$0.307552\pi$
$200$	−29.6836	−2.09895
$201$	3.78504	0.266976
$202$	−13.1430	−0.924737
$203$	−0.644192	−0.0452134
$204$	−63.7885	−4.46609
$205$	−8.52217	−0.595214
$206$	−4.94682	−0.344661
$207$	−12.7918	−0.889091
$208$	−44.5191	−3.08684
$209$	26.6403	1.84274
$210$	−9.24272	−0.637808
$211$	11.5087	0.792291	0.396146	−	0.918188i	$-0.370348\pi$
$211$	11.5087	0.792291	0.396146	+	0.918188i	$0.370348\pi$
$212$	−19.0531	−1.30857
$213$	−3.70517	−0.253874
$214$	−30.7554	−2.10240
$215$	4.74718	0.323755
$216$	24.2072	1.64709
$217$	4.22259	0.286648
$218$	−12.3900	−0.839154
$219$	1.28138	0.0865874
$220$	−60.8640	−4.10345
$221$	31.2279	2.10062
$222$	−47.6154	−3.19574
$223$	4.40148	0.294745	0.147372	−	0.989081i	$-0.452918\pi$
$223$	4.40148	0.294745	0.147372	+	0.989081i	$0.452918\pi$
$224$	5.26440	0.351742
$225$	5.74771	0.383180
$226$	−32.7682	−2.17971
$227$	14.9252	0.990618	0.495309	−	0.868717i	$-0.335055\pi$
$227$	14.9252	0.990618	0.495309	+	0.868717i	$0.335055\pi$
$228$	62.7582	4.15626
$229$	4.19125	0.276966	0.138483	−	0.990365i	$-0.455777\pi$
$229$	4.19125	0.276966	0.138483	+	0.990365i	$0.455777\pi$
$230$	−72.4122	−4.77472
$231$	−4.97588	−0.327389
$232$	−8.22766	−0.540173
$233$	1.32186	0.0865980	0.0432990	−	0.999062i	$-0.486213\pi$
$233$	1.32186	0.0865980	0.0432990	+	0.999062i	$0.486213\pi$
$234$	17.6118	1.15132
$235$	12.3386	0.804881
$236$	−58.4639	−3.80568
$237$	−5.22960	−0.339699
$238$	−9.33971	−0.605403
$239$	−3.57501	−0.231248	−0.115624	−	0.993293i	$-0.536887\pi$
$239$	−3.57501	−0.231248	−0.115624	+	0.993293i	$0.536887\pi$
$240$	−57.7805	−3.72972
$241$	14.5198	0.935301	0.467650	−	0.883914i	$-0.345101\pi$
$241$	14.5198	0.935301	0.467650	+	0.883914i	$0.345101\pi$
$242$	−17.9435	−1.15345
$243$	−13.4125	−0.860412
$244$	−2.25346	−0.144263
$245$	20.2098	1.29116
$246$	−15.3512	−0.978759
$247$	−30.7235	−1.95489
$248$	53.9312	3.42464
$249$	17.3733	1.10099
$250$	−6.75968	−0.427520
$251$	5.30634	0.334933	0.167467	−	0.985878i	$-0.446441\pi$
$251$	5.30634	0.334933	0.167467	+	0.985878i	$0.446441\pi$
$252$	−3.70854	−0.233616
$253$	−38.9836	−2.45088
$254$	52.8097	3.31357
$255$	40.5302	2.53810
$256$	−19.5836	−1.22397
$257$	−2.08054	−0.129781	−0.0648903	−	0.997892i	$-0.520670\pi$
$257$	−2.08054	−0.129781	−0.0648903	+	0.997892i	$0.520670\pi$
$258$	8.55123	0.532376
$259$	−4.90849	−0.304999
$260$	70.1930	4.35318
$261$	1.59314	0.0986130
$262$	−35.1384	−2.17086
$263$	16.6250	1.02514	0.512570	−	0.858645i	$-0.328694\pi$
$263$	16.6250	1.02514	0.512570	+	0.858645i	$0.328694\pi$
$264$	−63.5523	−3.91137
$265$	12.1060	0.743668
$266$	9.18885	0.563405
$267$	−31.1129	−1.90408
$268$	8.59714	0.525154
$269$	−7.61200	−0.464112	−0.232056	−	0.972702i	$-0.574545\pi$
$269$	−7.61200	−0.464112	−0.232056	+	0.972702i	$0.574545\pi$
$270$	−26.5340	−1.61481
$271$	4.15827	0.252597	0.126298	−	0.991992i	$-0.459690\pi$
$271$	4.15827	0.252597	0.126298	+	0.991992i	$0.459690\pi$
$272$	−58.3868	−3.54022
$273$	5.73856	0.347314
$274$	−21.6479	−1.30779
$275$	17.5164	1.05628
$276$	−91.8363	−5.52790
$277$	9.42089	0.566047	0.283023	−	0.959113i	$-0.408663\pi$
$277$	9.42089	0.566047	0.283023	+	0.959113i	$0.408663\pi$
$278$	43.2729	2.59533
$279$	−10.4428	−0.625195
$280$	−12.1692	−0.727247
$281$	−23.1796	−1.38278	−0.691391	−	0.722481i	$-0.743002\pi$
$281$	−23.1796	−1.38278	−0.691391	+	0.722481i	$0.743002\pi$
$282$	22.2259	1.32353
$283$	−24.6282	−1.46399	−0.731997	−	0.681308i	$-0.761412\pi$
$283$	−24.6282	−1.46399	−0.731997	+	0.681308i	$0.761412\pi$
$284$	−8.41573	−0.499382
$285$	−39.8755	−2.36202
$286$	53.6729	3.17374
$287$	−1.58250	−0.0934120
$288$	−13.0193	−0.767170
$289$	23.9555	1.40915
$290$	9.01851	0.529585
$291$	−15.4303	−0.904543
$292$	2.91045	0.170321
$293$	23.3449	1.36382	0.681910	−	0.731436i	$-0.261149\pi$
$293$	23.3449	1.36382	0.681910	+	0.731436i	$0.261149\pi$
$294$	36.4045	2.12315
$295$	37.1470	2.16278
$296$	−62.6916	−3.64387
$297$	−14.2848	−0.828885
$298$	−24.4531	−1.41653
$299$	44.9589	2.60004
$300$	41.2646	2.38241
$301$	0.881513	0.0508096
$302$	52.7752	3.03687
$303$	10.5909	0.608430
$304$	57.4438	3.29463
$305$	1.43181	0.0819851
$306$	23.0979	1.32042
$307$	−13.1646	−0.751342	−0.375671	−	0.926753i	$-0.622588\pi$
$307$	−13.1646	−0.751342	−0.375671	+	0.926753i	$0.622588\pi$
$308$	−11.3020	−0.643989
$309$	3.98625	0.226770
$310$	−59.1151	−3.35751
$311$	−18.1219	−1.02760	−0.513800	−	0.857910i	$-0.671763\pi$
$311$	−18.1219	−1.02760	−0.513800	+	0.857910i	$0.671763\pi$
$312$	73.2933	4.14942
$313$	14.2295	0.804299	0.402150	−	0.915574i	$-0.368263\pi$
$313$	14.2295	0.804299	0.402150	+	0.915574i	$0.368263\pi$
$314$	15.8020	0.891758
$315$	2.35634	0.132765
$316$	−11.8783	−0.668204
$317$	0.706042	0.0396553	0.0198276	−	0.999803i	$-0.493688\pi$
$317$	0.706042	0.0396553	0.0198276	+	0.999803i	$0.493688\pi$
$318$	21.8070	1.22287
$319$	4.85518	0.271838
$320$	−18.5356	−1.03617
$321$	24.7834	1.38327
$322$	−13.4464	−0.749337
$323$	−40.2940	−2.24202
$324$	−53.4695	−2.97053
$325$	−20.2013	−1.12056
$326$	−19.1352	−1.05980
$327$	9.98408	0.552121
$328$	−20.2118	−1.11601
$329$	2.29118	0.126317
$330$	69.6610	3.83471
$331$	−1.50165	−0.0825381	−0.0412691	−	0.999148i	$-0.513140\pi$
$331$	−1.50165	−0.0825381	−0.0412691	+	0.999148i	$0.513140\pi$
$332$	39.4608	2.16569
$333$	12.1391	0.665219
$334$	−19.5231	−1.06825
$335$	−5.46248	−0.298447
$336$	−10.7294	−0.585336
$337$	−10.5820	−0.576437	−0.288219	−	0.957565i	$-0.593063\pi$
$337$	−10.5820	−0.576437	−0.288219	+	0.957565i	$0.593063\pi$
$338$	−28.1043	−1.52867
$339$	26.4053	1.43414
$340$	92.0581	4.99255
$341$	−31.8250	−1.72342
$342$	−22.7248	−1.22882
$343$	7.68253	0.414818
$344$	11.2587	0.607031
$345$	58.3513	3.14153
$346$	−13.6497	−0.733815
$347$	−21.9609	−1.17892	−0.589461	−	0.807797i	$-0.700660\pi$
$347$	−21.9609	−1.17892	−0.589461	+	0.807797i	$0.700660\pi$
$348$	11.4377	0.613123
$349$	−13.7632	−0.736727	−0.368364	−	0.929682i	$-0.620082\pi$
$349$	−13.7632	−0.736727	−0.368364	+	0.929682i	$0.620082\pi$
$350$	6.04183	0.322949
$351$	16.4743	0.879330
$352$	−39.6770	−2.11479
$353$	−33.1723	−1.76558	−0.882791	−	0.469766i	$-0.844338\pi$
$353$	−33.1723	−1.76558	−0.882791	+	0.469766i	$0.844338\pi$
$354$	66.9140	3.55644
$355$	5.34722	0.283801
$356$	−70.6682	−3.74541
$357$	7.52613	0.398325
$358$	24.8792	1.31491
$359$	−18.0716	−0.953782	−0.476891	−	0.878962i	$-0.658236\pi$
$359$	−18.0716	−0.953782	−0.476891	+	0.878962i	$0.658236\pi$
$360$	30.0954	1.58617
$361$	20.6431	1.08648
$362$	4.33966	0.228087
$363$	14.4592	0.758913
$364$	13.0343	0.683182
$365$	−1.84925	−0.0967944
$366$	2.57916	0.134815
$367$	−32.7727	−1.71072	−0.855361	−	0.518033i	$-0.826665\pi$
$367$	−32.7727	−1.71072	−0.855361	+	0.518033i	$0.826665\pi$
$368$	−84.0595	−4.38191
$369$	3.91365	0.203737
$370$	68.7175	3.57245
$371$	2.24800	0.116710
$372$	−74.9723	−3.88713
$373$	3.25311	0.168440	0.0842199	−	0.996447i	$-0.473160\pi$
$373$	3.25311	0.168440	0.0842199	+	0.996447i	$0.473160\pi$
$374$	70.3920	3.63988
$375$	5.44709	0.281287
$376$	29.2631	1.50913
$377$	−5.59936	−0.288382
$378$	−4.92715	−0.253425
$379$	−19.1603	−0.984198	−0.492099	−	0.870539i	$-0.663770\pi$
$379$	−19.1603	−0.984198	−0.492099	+	0.870539i	$0.663770\pi$
$380$	−90.5712	−4.64620
$381$	−42.5551	−2.18016
$382$	−69.4367	−3.55269
$383$	22.6686	1.15831	0.579155	−	0.815217i	$-0.303383\pi$
$383$	22.6686	1.15831	0.579155	+	0.815217i	$0.303383\pi$
$384$	5.89978	0.301072
$385$	7.18108	0.365982
$386$	−44.6084	−2.27051
$387$	−2.18006	−0.110818
$388$	−35.0477	−1.77928
$389$	−39.0808	−1.98148	−0.990738	−	0.135788i	$-0.956643\pi$
$389$	−39.0808	−1.98148	−0.990738	+	0.135788i	$0.956643\pi$
$390$	−80.3383	−4.06809
$391$	58.9636	2.98192
$392$	47.9310	2.42088
$393$	28.3153	1.42832
$394$	15.5531	0.783551
$395$	7.54724	0.379743
$396$	27.9507	1.40458
$397$	17.4671	0.876649	0.438324	−	0.898817i	$-0.355572\pi$
$397$	17.4671	0.876649	0.438324	+	0.898817i	$0.355572\pi$
$398$	−41.6911	−2.08979
$399$	−7.40457	−0.370692
$400$	37.7703	1.88851
$401$	7.16631	0.357868	0.178934	−	0.983861i	$-0.442735\pi$
$401$	7.16631	0.357868	0.178934	+	0.983861i	$0.442735\pi$
$402$	−9.83973	−0.490761
$403$	36.7030	1.82831
$404$	24.0556	1.19681
$405$	33.9736	1.68816
$406$	1.67467	0.0831123
$407$	36.9946	1.83375
$408$	96.1242	4.75886
$409$	−20.3350	−1.00550	−0.502750	−	0.864432i	$-0.667678\pi$
$409$	−20.3350	−1.00550	−0.502750	+	0.864432i	$0.667678\pi$
$410$	22.1546	1.09414
$411$	17.4443	0.860464
$412$	9.05417	0.446067
$413$	6.89791	0.339424
$414$	33.2540	1.63435
$415$	−25.0727	−1.23077
$416$	45.7585	2.24350
$417$	−34.8702	−1.70760
$418$	−69.2550	−3.38737
$419$	−28.3481	−1.38490	−0.692448	−	0.721468i	$-0.743468\pi$
$419$	−28.3481	−1.38490	−0.692448	+	0.721468i	$0.743468\pi$
$420$	16.9169	0.825462
$421$	−2.21872	−0.108134	−0.0540670	−	0.998537i	$-0.517218\pi$
$421$	−2.21872	−0.108134	−0.0540670	+	0.998537i	$0.517218\pi$
$422$	−29.9184	−1.45641
$423$	−5.66628	−0.275504
$424$	28.7116	1.39436
$425$	−26.4940	−1.28515
$426$	9.63210	0.466677
$427$	0.265876	0.0128666
$428$	56.2916	2.72096
$429$	−43.2507	−2.08816
$430$	−12.3409	−0.595133
$431$	−1.89601	−0.0913274	−0.0456637	−	0.998957i	$-0.514540\pi$
$431$	−1.89601	−0.0913274	−0.0456637	+	0.998957i	$0.514540\pi$
$432$	−30.8019	−1.48196
$433$	−33.8222	−1.62539	−0.812697	−	0.582687i	$-0.802001\pi$
$433$	−33.8222	−1.62539	−0.812697	+	0.582687i	$0.802001\pi$
$434$	−10.9772	−0.526923
$435$	−7.26730	−0.348440
$436$	22.6773	1.08605
$437$	−58.0112	−2.77505
$438$	−3.33112	−0.159167
$439$	6.31659	0.301474	0.150737	−	0.988574i	$-0.451835\pi$
$439$	6.31659	0.301474	0.150737	+	0.988574i	$0.451835\pi$
$440$	91.7173	4.37245
$441$	−9.28099	−0.441952
$442$	−81.1814	−3.86140
$443$	19.5315	0.927967	0.463984	−	0.885844i	$-0.346420\pi$
$443$	19.5315	0.927967	0.463984	+	0.885844i	$0.346420\pi$
$444$	87.1505	4.13598
$445$	44.9014	2.12853
$446$	−11.4423	−0.541807
$447$	19.7048	0.932005
$448$	−3.44192	−0.162615
$449$	−15.3252	−0.723242	−0.361621	−	0.932325i	$-0.617777\pi$
$449$	−15.3252	−0.723242	−0.361621	+	0.932325i	$0.617777\pi$
$450$	−14.9420	−0.704371
$451$	11.9271	0.561623
$452$	59.9757	2.82102
$453$	−42.5273	−1.99811
$454$	−38.8000	−1.82098
$455$	−8.28176	−0.388255
$456$	−94.5716	−4.42872
$457$	−14.7763	−0.691207	−0.345603	−	0.938381i	$-0.612326\pi$
$457$	−14.7763	−0.691207	−0.345603	+	0.938381i	$0.612326\pi$
$458$	−10.8957	−0.509124
$459$	21.6060	1.00848
$460$	132.536	6.17953
$461$	−28.1311	−1.31020	−0.655098	−	0.755544i	$-0.727373\pi$
$461$	−28.1311	−1.31020	−0.655098	+	0.755544i	$0.727373\pi$
$462$	12.9355	0.601814
$463$	16.7165	0.776880	0.388440	−	0.921474i	$-0.373014\pi$
$463$	16.7165	0.776880	0.388440	+	0.921474i	$0.373014\pi$
$464$	10.4691	0.486016
$465$	47.6362	2.20907
$466$	−3.43636	−0.159186
$467$	−22.4105	−1.03703	−0.518517	−	0.855067i	$-0.673516\pi$
$467$	−22.4105	−1.03703	−0.518517	+	0.855067i	$0.673516\pi$
$468$	−32.2349	−1.49006
$469$	−1.01434	−0.0468379
$470$	−32.0759	−1.47955
$471$	−12.7336	−0.586732
$472$	88.1005	4.05515
$473$	−6.64383	−0.305484
$474$	13.5951	0.624442
$475$	26.0660	1.19599
$476$	17.0945	0.783524
$477$	−5.55948	−0.254551
$478$	9.29372	0.425085
$479$	−15.0630	−0.688247	−0.344123	−	0.938924i	$-0.611824\pi$
$479$	−15.0630	−0.688247	−0.344123	+	0.938924i	$0.611824\pi$
$480$	59.3891	2.71073
$481$	−42.6649	−1.94535
$482$	−37.7462	−1.71929
$483$	10.8354	0.493026
$484$	32.8420	1.49282
$485$	22.2687	1.01117
$486$	34.8676	1.58163
$487$	39.0354	1.76886	0.884432	−	0.466669i	$-0.154546\pi$
$487$	39.0354	1.76886	0.884432	+	0.466669i	$0.154546\pi$
$488$	3.39578	0.153720
$489$	15.4195	0.697294
$490$	−52.5382	−2.37343
$491$	21.8721	0.987075	0.493537	−	0.869725i	$-0.335704\pi$
$491$	21.8721	0.987075	0.493537	+	0.869725i	$0.335704\pi$
$492$	28.0974	1.26673
$493$	−7.34356	−0.330737
$494$	79.8701	3.59353
$495$	−17.7594	−0.798227
$496$	−68.6236	−3.08129
$497$	0.992936	0.0445393
$498$	−45.1643	−2.02386
$499$	20.4160	0.913947	0.456973	−	0.889480i	$-0.348933\pi$
$499$	20.4160	0.913947	0.456973	+	0.889480i	$0.348933\pi$
$500$	12.3722	0.553304
$501$	15.7321	0.702858
$502$	−13.7946	−0.615681
$503$	−17.2592	−0.769551	−0.384776	−	0.923010i	$-0.625721\pi$
$503$	−17.2592	−0.769551	−0.384776	+	0.923010i	$0.625721\pi$
$504$	5.58848	0.248930
$505$	−15.2845	−0.680152
$506$	101.343	4.50526
$507$	22.6470	1.00579
$508$	−96.6575	−4.28848
$509$	−29.7166	−1.31717	−0.658584	−	0.752508i	$-0.728844\pi$
$509$	−29.7166	−1.31717	−0.658584	+	0.752508i	$0.728844\pi$
$510$	−105.364	−4.66559
$511$	−0.343392	−0.0151908
$512$	45.2776	2.00100
$513$	−21.2570	−0.938520
$514$	5.40865	0.238566
$515$	−5.75287	−0.253502
$516$	−15.6513	−0.689011
$517$	−17.2683	−0.759458
$518$	12.7603	0.560655
$519$	10.9992	0.482813
$520$	−105.775	−4.63855
$521$	32.4429	1.42135	0.710675	−	0.703520i	$-0.248390\pi$
$521$	32.4429	1.42135	0.710675	+	0.703520i	$0.248390\pi$
$522$	−4.14159	−0.181272
$523$	5.45155	0.238380	0.119190	−	0.992871i	$-0.461970\pi$
$523$	5.45155	0.238380	0.119190	+	0.992871i	$0.461970\pi$
$524$	64.3138	2.80956
$525$	−4.86863	−0.212485
$526$	−43.2189	−1.88443
$527$	48.1361	2.09684
$528$	80.8658	3.51923
$529$	61.8899	2.69087
$530$	−31.4713	−1.36703
$531$	−17.0591	−0.740302
$532$	−16.8184	−0.729168
$533$	−13.7552	−0.595803
$534$	80.8823	3.50012
$535$	−35.7668	−1.54633
$536$	−12.9552	−0.559580
$537$	−20.0482	−0.865142
$538$	19.7884	0.853140
$539$	−28.2843	−1.21829
$540$	48.5651	2.08991
$541$	31.1191	1.33792	0.668958	−	0.743301i	$-0.266741\pi$
$541$	31.1191	1.33792	0.668958	+	0.743301i	$0.266741\pi$
$542$	−10.8100	−0.464329
$543$	−3.49699	−0.150070
$544$	60.0123	2.57301
$545$	−14.4088	−0.617205
$546$	−14.9182	−0.638439
$547$	−1.00000	−0.0427569
$547$	−1.00000	−0.0427569
$548$	39.6221	1.69257
$549$	−0.657533	−0.0280628
$550$	−45.5364	−1.94168
$551$	7.22495	0.307793
$552$	138.390	5.89027
$553$	1.40146	0.0595963
$554$	−24.4909	−1.04052
$555$	−55.3740	−2.35050
$556$	−79.2023	−3.35893
$557$	41.0931	1.74117	0.870585	−	0.492017i	$-0.163740\pi$
$557$	41.0931	1.74117	0.870585	+	0.492017i	$0.163740\pi$
$558$	27.1476	1.14925
$559$	7.66217	0.324075
$560$	15.4844	0.654335
$561$	−56.7233	−2.39486
$562$	60.2587	2.54186
$563$	6.83856	0.288211	0.144105	−	0.989562i	$-0.453970\pi$
$563$	6.83856	0.288211	0.144105	+	0.989562i	$0.453970\pi$
$564$	−40.6800	−1.71294
$565$	−38.1076	−1.60320
$566$	64.0244	2.69115
$567$	6.30864	0.264938
$568$	12.6818	0.532118
$569$	−27.4209	−1.14955	−0.574773	−	0.818313i	$-0.694909\pi$
$569$	−27.4209	−1.14955	−0.574773	+	0.818313i	$0.694909\pi$
$570$	103.662	4.34192
$571$	−34.1032	−1.42718	−0.713588	−	0.700566i	$-0.752931\pi$
$571$	−34.1032	−1.42718	−0.713588	+	0.700566i	$0.752931\pi$
$572$	−98.2374	−4.10751
$573$	55.9535	2.33749
$574$	4.11392	0.171712
$575$	−38.1434	−1.59069
$576$	8.51215	0.354673
$577$	−33.6417	−1.40052	−0.700260	−	0.713888i	$-0.746933\pi$
$577$	−33.6417	−1.40052	−0.700260	+	0.713888i	$0.746933\pi$
$578$	−62.2756	−2.59032
$579$	35.9463	1.49388
$580$	−16.5066	−0.685398
$581$	−4.65581	−0.193155
$582$	40.1133	1.66275
$583$	−16.9428	−0.701700
$584$	−4.38582	−0.181487
$585$	20.4815	0.846806
$586$	−60.6882	−2.50701
$587$	−13.2895	−0.548516	−0.274258	−	0.961656i	$-0.588432\pi$
$587$	−13.2895	−0.548516	−0.274258	+	0.961656i	$0.588432\pi$
$588$	−66.6312	−2.74782
$589$	−47.3586	−1.95138
$590$	−96.5688	−3.97567
$591$	−12.5330	−0.515538
$592$	79.7705	3.27855
$593$	−44.2951	−1.81898	−0.909491	−	0.415724i	$-0.863528\pi$
$593$	−44.2951	−1.81898	−0.909491	+	0.415724i	$0.863528\pi$
$594$	37.1352	1.52367
$595$	−10.8615	−0.445280
$596$	44.7565	1.83330
$597$	33.5956	1.37498
$598$	−116.877	−4.77945
$599$	5.59011	0.228406	0.114203	−	0.993457i	$-0.463569\pi$
$599$	5.59011	0.228406	0.114203	+	0.993457i	$0.463569\pi$
$600$	−62.1825	−2.53859
$601$	25.4727	1.03905	0.519526	−	0.854454i	$-0.326108\pi$
$601$	25.4727	1.03905	0.519526	+	0.854454i	$0.326108\pi$
$602$	−2.29161	−0.0933992
$603$	2.50855	0.102156
$604$	−96.5944	−3.93037
$605$	−20.8672	−0.848374
$606$	−27.5325	−1.11843
$607$	−27.4291	−1.11331	−0.556657	−	0.830742i	$-0.687916\pi$
$607$	−27.4291	−1.11331	−0.556657	+	0.830742i	$0.687916\pi$
$608$	−59.0430	−2.39451
$609$	−1.34948	−0.0546837
$610$	−3.72218	−0.150707
$611$	19.9151	0.805678
$612$	−42.2761	−1.70891
$613$	16.8113	0.679000	0.339500	−	0.940606i	$-0.389742\pi$
$613$	16.8113	0.679000	0.339500	+	0.940606i	$0.389742\pi$
$614$	34.2231	1.38113
$615$	−17.8526	−0.719886
$616$	17.0312	0.686205
$617$	12.2317	0.492429	0.246215	−	0.969215i	$-0.420813\pi$
$617$	12.2317	0.492429	0.246215	+	0.969215i	$0.420813\pi$
$618$	−10.3628	−0.416854
$619$	−17.1538	−0.689471	−0.344736	−	0.938700i	$-0.612031\pi$
$619$	−17.1538	−0.689471	−0.344736	+	0.938700i	$0.612031\pi$
$620$	108.198	4.34535
$621$	31.1062	1.24825
$622$	47.1105	1.88896
$623$	8.33784	0.334048
$624$	−93.2605	−3.73341
$625$	−28.5607	−1.14243
$626$	−36.9916	−1.47848
$627$	55.8071	2.22872
$628$	−28.9224	−1.15413
$629$	−55.9551	−2.23108
$630$	−6.12564	−0.244051
$631$	−6.57839	−0.261882	−0.130941	−	0.991390i	$-0.541800\pi$
$631$	−6.57839	−0.261882	−0.130941	+	0.991390i	$0.541800\pi$
$632$	17.8996	0.712007
$633$	24.1089	0.958243
$634$	−1.83545	−0.0728952
$635$	61.4146	2.43716
$636$	−39.9133	−1.58267
$637$	32.6196	1.29244
$638$	−12.6217	−0.499698
$639$	−2.45561	−0.0971426
$640$	−8.51443	−0.336562
$641$	2.33872	0.0923737	0.0461868	−	0.998933i	$-0.485293\pi$
$641$	2.33872	0.0923737	0.0461868	+	0.998933i	$0.485293\pi$
$642$	−64.4277	−2.54276
$643$	−17.3754	−0.685218	−0.342609	−	0.939478i	$-0.611311\pi$
$643$	−17.3754	−0.685218	−0.342609	+	0.939478i	$0.611311\pi$
$644$	24.6109	0.969805
$645$	9.94459	0.391568
$646$	104.750	4.12132
$647$	38.9519	1.53136	0.765679	−	0.643223i	$-0.222403\pi$
$647$	38.9519	1.53136	0.765679	+	0.643223i	$0.222403\pi$
$648$	80.5743	3.16526
$649$	−51.9885	−2.04073
$650$	52.5160	2.05985
$651$	8.84566	0.346689
$652$	35.0231	1.37161
$653$	−7.75059	−0.303304	−0.151652	−	0.988434i	$-0.548459\pi$
$653$	−7.75059	−0.303304	−0.151652	+	0.988434i	$0.548459\pi$
$654$	−25.9550	−1.01492
$655$	−40.8639	−1.59669
$656$	25.7180	1.00412
$657$	0.849237	0.0331319
$658$	−5.95624	−0.232198
$659$	−22.3674	−0.871309	−0.435655	−	0.900114i	$-0.643483\pi$
$659$	−22.3674	−0.871309	−0.435655	+	0.900114i	$0.643483\pi$
$660$	−127.501	−4.96295
$661$	30.2526	1.17669	0.588345	−	0.808610i	$-0.299780\pi$
$661$	30.2526	1.17669	0.588345	+	0.808610i	$0.299780\pi$
$662$	3.90375	0.151723
$663$	65.4176	2.54061
$664$	−59.4643	−2.30766
$665$	10.6861	0.414389
$666$	−31.5573	−1.22282
$667$	−10.5725	−0.409370
$668$	35.7331	1.38255
$669$	9.22041	0.356482
$670$	14.2005	0.548612
$671$	−2.00386	−0.0773583
$672$	11.0281	0.425418
$673$	11.7416	0.452604	0.226302	−	0.974057i	$-0.427336\pi$
$673$	11.7416	0.452604	0.226302	+	0.974057i	$0.427336\pi$
$674$	27.5093	1.05962
$675$	−13.9769	−0.537969
$676$	51.4393	1.97843
$677$	−30.4285	−1.16946	−0.584732	−	0.811227i	$-0.698800\pi$
$677$	−30.4285	−1.16946	−0.584732	+	0.811227i	$0.698800\pi$
$678$	−68.6443	−2.63627
$679$	4.13513	0.158692
$680$	−138.724	−5.31984
$681$	31.2659	1.19811
$682$	82.7336	3.16803
$683$	−11.6989	−0.447647	−0.223823	−	0.974630i	$-0.571854\pi$
$683$	−11.6989	−0.447647	−0.223823	+	0.974630i	$0.571854\pi$
$684$	41.5932	1.59036
$685$	−25.1752	−0.961895
$686$	−19.9718	−0.762527
$687$	8.78001	0.334978
$688$	−14.3259	−0.546171
$689$	19.5397	0.744404
$690$	−151.692	−5.77482
$691$	27.2076	1.03502	0.517512	−	0.855676i	$-0.326858\pi$
$691$	27.2076	1.03502	0.517512	+	0.855676i	$0.326858\pi$
$692$	24.9831	0.949716
$693$	−3.29778	−0.125272
$694$	57.0903	2.16712
$695$	50.3239	1.90889
$696$	−17.2357	−0.653316
$697$	−18.0399	−0.683311
$698$	35.7794	1.35427
$699$	2.76909	0.104737
$700$	−11.0584	−0.417967
$701$	−21.2354	−0.802049	−0.401024	−	0.916067i	$-0.631346\pi$
$701$	−21.2354	−0.802049	−0.401024	+	0.916067i	$0.631346\pi$
$702$	−42.8271	−1.61640
$703$	55.0513	2.07630
$704$	25.9412	0.977697
$705$	25.8474	0.973470
$706$	86.2359	3.24553
$707$	−2.83821	−0.106742
$708$	−122.473	−4.60281
$709$	16.8807	0.633967	0.316983	−	0.948431i	$-0.397330\pi$
$709$	16.8807	0.633967	0.316983	+	0.948431i	$0.397330\pi$
$710$	−13.9008	−0.521689
$711$	−3.46594	−0.129983
$712$	106.491	3.99094
$713$	69.3015	2.59536
$714$	−19.5652	−0.732210
$715$	62.4184	2.33432
$716$	−45.5364	−1.70177
$717$	−7.48907	−0.279685
$718$	46.9796	1.75326
$719$	−20.3235	−0.757941	−0.378970	−	0.925409i	$-0.623722\pi$
$719$	−20.3235	−0.757941	−0.378970	+	0.925409i	$0.623722\pi$
$720$	−38.2942	−1.42714
$721$	−1.06826	−0.0397842
$722$	−53.6646	−1.99719
$723$	30.4166	1.13121
$724$	−7.94288	−0.295195
$725$	4.75053	0.176430
$726$	−37.5888	−1.39505
$727$	−9.13646	−0.338853	−0.169426	−	0.985543i	$-0.554191\pi$
$727$	−9.13646	−0.338853	−0.169426	+	0.985543i	$0.554191\pi$
$728$	−19.6416	−0.727967
$729$	5.61554	0.207983
$730$	4.80739	0.177929
$731$	10.0489	0.371674
$732$	−4.72064	−0.174480
$733$	−6.55001	−0.241930	−0.120965	−	0.992657i	$-0.538599\pi$
$733$	−6.55001	−0.241930	−0.120965	+	0.992657i	$0.538599\pi$
$734$	85.1972	3.14469
$735$	42.3364	1.56160
$736$	86.3997	3.18474
$737$	7.64493	0.281605
$738$	−10.1741	−0.374513
$739$	−37.2949	−1.37192	−0.685958	−	0.727641i	$-0.740617\pi$
$739$	−37.2949	−1.37192	−0.685958	+	0.727641i	$0.740617\pi$
$740$	−125.774	−4.62353
$741$	−64.3610	−2.36436
$742$	−5.84398	−0.214539
$743$	−45.7404	−1.67805	−0.839026	−	0.544092i	$-0.816874\pi$
$743$	−45.7404	−1.67805	−0.839026	+	0.544092i	$0.816874\pi$
$744$	112.977	4.14195
$745$	−28.4375	−1.04187
$746$	−8.45692	−0.309630
$747$	11.5142	0.421283
$748$	−128.838	−4.71080
$749$	−6.64161	−0.242679
$750$	−14.1605	−0.517067
$751$	−38.4995	−1.40487	−0.702434	−	0.711749i	$-0.747903\pi$
$751$	−38.4995	−1.40487	−0.702434	+	0.711749i	$0.747903\pi$
$752$	−37.2352	−1.35783
$753$	11.1159	0.405087
$754$	14.5563	0.530109
$755$	61.3745	2.23365
$756$	9.01816	0.327987
$757$	20.5989	0.748681	0.374340	−	0.927291i	$-0.377869\pi$
$757$	20.5989	0.748681	0.374340	+	0.927291i	$0.377869\pi$
$758$	49.8098	1.80917
$759$	−81.6646	−2.96424
$760$	136.484	4.95078
$761$	18.6360	0.675555	0.337778	−	0.941226i	$-0.390325\pi$
$761$	18.6360	0.675555	0.337778	+	0.941226i	$0.390325\pi$
$762$	110.628	4.00763
$763$	−2.67560	−0.0968632
$764$	127.090	4.59795
$765$	26.8615	0.971180
$766$	−58.9301	−2.12923
$767$	59.9571	2.16492
$768$	−41.0245	−1.48034
$769$	32.6001	1.17559	0.587795	−	0.809010i	$-0.299996\pi$
$769$	32.6001	1.17559	0.587795	+	0.809010i	$0.299996\pi$
$770$	−18.6682	−0.672756
$771$	−4.35841	−0.156964
$772$	81.6467	2.93853
$773$	−50.6910	−1.82323	−0.911614	−	0.411047i	$-0.865163\pi$
$773$	−50.6910	−1.82323	−0.911614	+	0.411047i	$0.865163\pi$
$774$	5.66736	0.203709
$775$	−31.1391	−1.11855
$776$	52.8141	1.89592
$777$	−10.2825	−0.368883
$778$	101.596	3.64239
$779$	17.7486	0.635908
$780$	147.043	5.26499
$781$	−7.48361	−0.267785
$782$	−153.284	−5.48143
$783$	−3.87409	−0.138449
$784$	−60.9888	−2.17817
$785$	18.3768	0.655896
$786$	−73.6094	−2.62556
$787$	17.5394	0.625213	0.312607	−	0.949883i	$-0.398798\pi$
$787$	17.5394	0.625213	0.312607	+	0.949883i	$0.398798\pi$
$788$	−28.4668	−1.01409
$789$	34.8267	1.23986
$790$	−19.6201	−0.698052
$791$	−7.07627	−0.251603
$792$	−42.1195	−1.49665
$793$	2.31101	0.0820663
$794$	−45.4081	−1.61147
$795$	25.3602	0.899435
$796$	76.3072	2.70464
$797$	−11.2655	−0.399044	−0.199522	−	0.979893i	$-0.563939\pi$
$797$	−11.2655	−0.399044	−0.199522	+	0.979893i	$0.563939\pi$
$798$	19.2492	0.681414
$799$	26.1186	0.924011
$800$	−38.8218	−1.37256
$801$	−20.6202	−0.728578
$802$	−18.6298	−0.657841
$803$	2.58809	0.0913318
$804$	18.0097	0.635152
$805$	−15.6374	−0.551145
$806$	−95.4146	−3.36084
$807$	−15.9459	−0.561323
$808$	−36.2499	−1.27527
$809$	−1.43789	−0.0505534	−0.0252767	−	0.999680i	$-0.508047\pi$
$809$	−1.43789	−0.0505534	−0.0252767	+	0.999680i	$0.508047\pi$
$810$	−88.3192	−3.10322
$811$	−39.2119	−1.37692	−0.688458	−	0.725276i	$-0.741712\pi$
$811$	−39.2119	−1.37692	−0.688458	+	0.725276i	$0.741712\pi$
$812$	−3.06514	−0.107565
$813$	8.71092	0.305505
$814$	−96.1725	−3.37084
$815$	−22.2531	−0.779492
$816$	−122.311	−4.28175
$817$	−9.88663	−0.345889
$818$	52.8636	1.84833
$819$	3.80325	0.132896
$820$	−40.5495	−1.41605
$821$	9.41950	0.328743	0.164371	−	0.986399i	$-0.447440\pi$
$821$	9.41950	0.328743	0.164371	+	0.986399i	$0.447440\pi$
$822$	−45.3488	−1.58172
$823$	−28.7149	−1.00094	−0.500470	−	0.865754i	$-0.666839\pi$
$823$	−28.7149	−1.00094	−0.500470	+	0.865754i	$0.666839\pi$
$824$	−13.6439	−0.475308
$825$	36.6942	1.27753
$826$	−17.9321	−0.623936
$827$	32.2145	1.12021	0.560104	−	0.828422i	$-0.310761\pi$
$827$	32.2145	1.12021	0.560104	+	0.828422i	$0.310761\pi$
$828$	−60.8648	−2.11520
$829$	−41.3853	−1.43737	−0.718685	−	0.695335i	$-0.755256\pi$
$829$	−41.3853	−1.43737	−0.718685	+	0.695335i	$0.755256\pi$
$830$	65.1800	2.26243
$831$	19.7353	0.684610
$832$	−29.9174	−1.03720
$833$	42.7806	1.48226
$834$	90.6498	3.13895
$835$	−22.7042	−0.785711
$836$	126.757	4.38400
$837$	25.3941	0.877748
$838$	73.6948	2.54575
$839$	31.6092	1.09127	0.545635	−	0.838023i	$-0.316289\pi$
$839$	31.6092	1.09127	0.545635	+	0.838023i	$0.316289\pi$
$840$	−25.4925	−0.879575
$841$	−27.6833	−0.954595
$842$	5.76788	0.198774
$843$	−48.5577	−1.67242
$844$	54.7597	1.88491
$845$	−32.6837	−1.12435
$846$	14.7303	0.506437
$847$	−3.87488	−0.133142
$848$	−36.5334	−1.25456
$849$	−51.5922	−1.77064
$850$	68.8748	2.36238
$851$	−80.5585	−2.76151
$852$	−17.6296	−0.603981
$853$	26.9128	0.921477	0.460739	−	0.887536i	$-0.347585\pi$
$853$	26.9128	0.921477	0.460739	+	0.887536i	$0.347585\pi$
$854$	−0.691180	−0.0236517
$855$	−26.4276	−0.903806
$856$	−84.8270	−2.89933
$857$	25.4512	0.869398	0.434699	−	0.900576i	$-0.356855\pi$
$857$	25.4512	0.869398	0.434699	+	0.900576i	$0.356855\pi$
$858$	112.436	3.83851
$859$	33.5688	1.14535	0.572676	−	0.819781i	$-0.305905\pi$
$859$	33.5688	1.14535	0.572676	+	0.819781i	$0.305905\pi$
$860$	22.5876	0.770231
$861$	−3.31509	−0.112978
$862$	4.92893	0.167880
$863$	21.3439	0.726554	0.363277	−	0.931681i	$-0.381658\pi$
$863$	21.3439	0.726554	0.363277	+	0.931681i	$0.381658\pi$
$864$	31.6594	1.07707
$865$	−15.8739	−0.539728
$866$	87.9256	2.98783
$867$	50.1829	1.70430
$868$	20.0916	0.681953
$869$	−10.5626	−0.358312
$870$	18.8924	0.640511
$871$	−8.81671	−0.298743
$872$	−34.1729	−1.15724
$873$	−10.2265	−0.346115
$874$	150.808	5.10116
$875$	−1.45975	−0.0493485
$876$	6.09694	0.205997
$877$	−32.2943	−1.09050	−0.545251	−	0.838273i	$-0.683566\pi$
$877$	−32.2943	−1.09050	−0.545251	+	0.838273i	$0.683566\pi$
$878$	−16.4208	−0.554176
$879$	48.9038	1.64948
$880$	−116.704	−3.93408
$881$	16.3456	0.550698	0.275349	−	0.961344i	$-0.411207\pi$
$881$	16.3456	0.550698	0.275349	+	0.961344i	$0.411207\pi$
$882$	24.1272	0.812406
$883$	7.21171	0.242693	0.121347	−	0.992610i	$-0.461279\pi$
$883$	7.21171	0.242693	0.121347	+	0.992610i	$0.461279\pi$
$884$	148.586	4.99750
$885$	77.8171	2.61579
$886$	−50.7747	−1.70581
$887$	35.6173	1.19591	0.597956	−	0.801529i	$-0.295980\pi$
$887$	35.6173	1.19591	0.597956	+	0.801529i	$0.295980\pi$
$888$	−131.329	−4.40711
$889$	11.4042	0.382485
$890$	−116.727	−3.91271
$891$	−47.5473	−1.59289
$892$	20.9428	0.701216
$893$	−25.6968	−0.859910
$894$	−51.2254	−1.71323
$895$	28.9330	0.967125
$896$	−1.58106	−0.0528196
$897$	94.1818	3.14464
$898$	39.8401	1.32948
$899$	−8.63109	−0.287863
$900$	27.3483	0.911609
$901$	25.6264	0.853738
$902$	−31.0060	−1.03239
$903$	1.84663	0.0614520
$904$	−90.3786	−3.00595
$905$	5.04677	0.167760
$906$	110.556	3.67297
$907$	−49.0472	−1.62859	−0.814293	−	0.580454i	$-0.802875\pi$
$907$	−49.0472	−1.62859	−0.814293	+	0.580454i	$0.802875\pi$
$908$	71.0157	2.35674
$909$	7.01914	0.232810
$910$	21.5296	0.713699
$911$	−45.6848	−1.51361	−0.756803	−	0.653643i	$-0.773240\pi$
$911$	−45.6848	−1.51361	−0.756803	+	0.653643i	$0.773240\pi$
$912$	120.336	3.98471
$913$	35.0901	1.16131
$914$	38.4131	1.27059
$915$	2.99941	0.0991576
$916$	19.9425	0.658917
$917$	−7.58811	−0.250581
$918$	−56.1678	−1.85381
$919$	−12.9459	−0.427045	−0.213522	−	0.976938i	$-0.568494\pi$
$919$	−12.9459	−0.427045	−0.213522	+	0.976938i	$0.568494\pi$
$920$	−199.721	−6.58462
$921$	−27.5777	−0.908716
$922$	73.1307	2.40843
$923$	8.63067	0.284082
$924$	−23.6758	−0.778878
$925$	36.1972	1.19016
$926$	−43.4568	−1.42808
$927$	2.64190	0.0867715
$928$	−10.7606	−0.353233
$929$	−4.49235	−0.147389	−0.0736946	−	0.997281i	$-0.523479\pi$
$929$	−4.49235	−0.147389	−0.0736946	+	0.997281i	$0.523479\pi$
$930$	−123.837	−4.06077
$931$	−42.0896	−1.37943
$932$	6.28957	0.206022
$933$	−37.9626	−1.24284
$934$	58.2592	1.90630
$935$	81.8618	2.67717
$936$	48.5754	1.58774
$937$	−1.90994	−0.0623951	−0.0311975	−	0.999513i	$-0.509932\pi$
$937$	−1.90994	−0.0623951	−0.0311975	+	0.999513i	$0.509932\pi$
$938$	2.63692	0.0860984
$939$	29.8086	0.972766
$940$	58.7085	1.91486
$941$	−1.34900	−0.0439761	−0.0219881	−	0.999758i	$-0.507000\pi$
$941$	−1.34900	−0.0439761	−0.0219881	+	0.999758i	$0.507000\pi$
$942$	33.1027	1.07854
$943$	−25.9721	−0.845768
$944$	−112.102	−3.64860
$945$	−5.72999	−0.186397
$946$	17.2716	0.561547
$947$	−23.5579	−0.765530	−0.382765	−	0.923846i	$-0.625028\pi$
$947$	−23.5579	−0.765530	−0.382765	+	0.923846i	$0.625028\pi$
$948$	−24.8831	−0.808164
$949$	−2.98478	−0.0968902
$950$	−67.7623	−2.19850
$951$	1.47905	0.0479614
$952$	−25.7600	−0.834887
$953$	44.6075	1.44498	0.722489	−	0.691383i	$-0.242998\pi$
$953$	44.6075	1.44498	0.722489	+	0.691383i	$0.242998\pi$
$954$	14.4526	0.467922
$955$	−80.7509	−2.61304
$956$	−17.0103	−0.550152
$957$	10.1708	0.328776
$958$	39.1584	1.26515
$959$	−4.67484	−0.150958
$960$	−38.8292	−1.25321
$961$	25.5756	0.825019
$962$	110.913	3.57599
$963$	16.4253	0.529296
$964$	69.0868	2.22514
$965$	−51.8769	−1.66998
$966$	−28.1680	−0.906292
$967$	−8.74032	−0.281070	−0.140535	−	0.990076i	$-0.544882\pi$
$967$	−8.74032	−0.281070	−0.140535	+	0.990076i	$0.544882\pi$
$968$	−49.4902	−1.59068
$969$	−84.4095	−2.71162
$970$	−57.8906	−1.85876
$971$	36.7867	1.18054	0.590271	−	0.807205i	$-0.299021\pi$
$971$	36.7867	1.18054	0.590271	+	0.807205i	$0.299021\pi$
$972$	−63.8182	−2.04697
$973$	9.34474	0.299579
$974$	−101.478	−3.25156
$975$	−42.3185	−1.35528
$976$	−4.32089	−0.138308
$977$	−17.6031	−0.563172	−0.281586	−	0.959536i	$-0.590860\pi$
$977$	−17.6031	−0.563172	−0.281586	+	0.959536i	$0.590860\pi$
$978$	−40.0851	−1.28178
$979$	−62.8411	−2.00841
$980$	96.1606	3.07174
$981$	6.61699	0.211264
$982$	−56.8596	−1.81446
$983$	−50.6464	−1.61537	−0.807684	−	0.589615i	$-0.799279\pi$
$983$	−50.6464	−1.61537	−0.807684	+	0.589615i	$0.799279\pi$
$984$	−42.3405	−1.34977
$985$	18.0873	0.576309
$986$	19.0906	0.607969
$987$	4.79966	0.152775
$988$	−146.186	−4.65080
$989$	14.4675	0.460039
$990$	46.1681	1.46732
$991$	4.79288	0.152251	0.0761254	−	0.997098i	$-0.475745\pi$
$991$	4.79288	0.152251	0.0761254	+	0.997098i	$0.475745\pi$
$992$	70.5341	2.23946
$993$	−3.14572	−0.0998264
$994$	−2.58127	−0.0818730
$995$	−48.4844	−1.53706
$996$	82.6642	2.61931
$997$	12.0839	0.382700	0.191350	−	0.981522i	$-0.438714\pi$
$997$	12.0839	0.382700	0.191350	+	0.981522i	$0.438714\pi$
$998$	−53.0743	−1.68004
$999$	−29.5190	−0.933940

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.2.a.b.1.2	✓	18
3.2	odd	2		4923.2.a.l.1.17		18
4.3	odd	2		8752.2.a.s.1.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.2.a.b.1.2	✓	18	1.1	even	1	trivial
4923.2.a.l.1.17		18	3.2	odd	2
8752.2.a.s.1.3		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)

\(f(q)\)	\(=\)	\(q-2.59964 q^{2} +2.09484 q^{3} +4.75812 q^{4} -3.02323 q^{5} -5.44583 q^{6} -0.561390 q^{7} -7.17011 q^{8} +1.38836 q^{9} +O(q^{10})\)	\(q-2.59964 q^{2} +2.09484 q^{3} +4.75812 q^{4} -3.02323 q^{5} -5.44583 q^{6} -0.561390 q^{7} -7.17011 q^{8} +1.38836 q^{9} +7.85930 q^{10} +4.23111 q^{11} +9.96751 q^{12} -4.87964 q^{13} +1.45941 q^{14} -6.33319 q^{15} +9.12345 q^{16} -6.39965 q^{17} -3.60924 q^{18} +6.29628 q^{19} -14.3849 q^{20} -1.17602 q^{21} -10.9994 q^{22} -9.21357 q^{23} -15.0202 q^{24} +4.13991 q^{25} +12.6853 q^{26} -3.37612 q^{27} -2.67116 q^{28} +1.14750 q^{29} +16.4640 q^{30} -7.52167 q^{31} -9.37744 q^{32} +8.86351 q^{33} +16.6368 q^{34} +1.69721 q^{35} +6.60600 q^{36} +8.74347 q^{37} -16.3680 q^{38} -10.2221 q^{39} +21.6769 q^{40} +2.81890 q^{41} +3.05723 q^{42} -1.57023 q^{43} +20.1321 q^{44} -4.19734 q^{45} +23.9520 q^{46} -4.08126 q^{47} +19.1122 q^{48} -6.68484 q^{49} -10.7623 q^{50} -13.4063 q^{51} -23.2179 q^{52} -4.00434 q^{53} +8.77670 q^{54} -12.7916 q^{55} +4.02522 q^{56} +13.1897 q^{57} -2.98307 q^{58} -12.2872 q^{59} -30.1341 q^{60} -0.473603 q^{61} +19.5536 q^{62} -0.779413 q^{63} +6.13107 q^{64} +14.7523 q^{65} -23.0419 q^{66} +1.80684 q^{67} -30.4503 q^{68} -19.3010 q^{69} -4.41213 q^{70} -1.76871 q^{71} -9.95472 q^{72} +0.611682 q^{73} -22.7298 q^{74} +8.67247 q^{75} +29.9584 q^{76} -2.37530 q^{77} +26.5737 q^{78} -2.49642 q^{79} -27.5823 q^{80} -11.2375 q^{81} -7.32811 q^{82} +8.29336 q^{83} -5.59565 q^{84} +19.3476 q^{85} +4.08204 q^{86} +2.40382 q^{87} -30.3375 q^{88} -14.8521 q^{89} +10.9116 q^{90} +2.73938 q^{91} -43.8393 q^{92} -15.7567 q^{93} +10.6098 q^{94} -19.0351 q^{95} -19.6443 q^{96} -7.36588 q^{97} +17.3782 q^{98} +5.87432 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 4 q^{2} - 10 q^{3} + 16 q^{4} - 27 q^{5} - 3 q^{6} - 11 q^{7} - 12 q^{8} + 14 q^{9}+O(q^{10}) \) 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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