LMFDB - Embedded newform 547.2.a.b.1.1

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			1.1
Root			$2.72204$ 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)

$f(q)$	$=$	$q-2.72204 q^{2} -1.76734 q^{3} +5.40952 q^{4} +0.469688 q^{5} +4.81078 q^{6} +1.03831 q^{7} -9.28087 q^{8} +0.123492 q^{9} +O(q^{10})$	\(q-2.72204 q^{2} -1.76734 q^{3} +5.40952 q^{4} +0.469688 q^{5} +4.81078 q^{6} +1.03831 q^{7} -9.28087 q^{8} +0.123492 q^{9} -1.27851 q^{10} -1.84194 q^{11} -9.56047 q^{12} -0.700934 q^{13} -2.82633 q^{14} -0.830099 q^{15} +14.4439 q^{16} +0.793975 q^{17} -0.336150 q^{18} +3.65845 q^{19} +2.54079 q^{20} -1.83505 q^{21} +5.01384 q^{22} -3.65159 q^{23} +16.4025 q^{24} -4.77939 q^{25} +1.90797 q^{26} +5.08377 q^{27} +5.61677 q^{28} +5.52848 q^{29} +2.25957 q^{30} +6.13605 q^{31} -20.7552 q^{32} +3.25534 q^{33} -2.16124 q^{34} +0.487683 q^{35} +0.668032 q^{36} -2.73114 q^{37} -9.95846 q^{38} +1.23879 q^{39} -4.35911 q^{40} -9.69220 q^{41} +4.99509 q^{42} -4.25340 q^{43} -9.96402 q^{44} +0.0580027 q^{45} +9.93978 q^{46} -5.21084 q^{47} -25.5273 q^{48} -5.92191 q^{49} +13.0097 q^{50} -1.40322 q^{51} -3.79172 q^{52} -7.01107 q^{53} -13.8382 q^{54} -0.865138 q^{55} -9.63643 q^{56} -6.46572 q^{57} -15.0488 q^{58} +6.98691 q^{59} -4.49044 q^{60} -3.87686 q^{61} -16.7026 q^{62} +0.128223 q^{63} +27.6087 q^{64} -0.329220 q^{65} -8.86117 q^{66} -5.10753 q^{67} +4.29503 q^{68} +6.45360 q^{69} -1.32749 q^{70} +1.33192 q^{71} -1.14611 q^{72} -7.83377 q^{73} +7.43429 q^{74} +8.44681 q^{75} +19.7905 q^{76} -1.91251 q^{77} -3.37204 q^{78} +4.36166 q^{79} +6.78412 q^{80} -9.35523 q^{81} +26.3826 q^{82} -13.3348 q^{83} -9.92674 q^{84} +0.372921 q^{85} +11.5779 q^{86} -9.77071 q^{87} +17.0948 q^{88} -0.208861 q^{89} -0.157886 q^{90} -0.727788 q^{91} -19.7533 q^{92} -10.8445 q^{93} +14.1841 q^{94} +1.71833 q^{95} +36.6814 q^{96} +3.08809 q^{97} +16.1197 q^{98} -0.227465 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.72204	−1.92478	−0.962388	−	0.271679i	$-0.912421\pi$
$2$	−2.72204	−1.92478	−0.962388	+	0.271679i	$0.912421\pi$
$3$	−1.76734	−1.02037	−0.510187	−	0.860063i	$-0.670424\pi$
$3$	−1.76734	−1.02037	−0.510187	+	0.860063i	$0.670424\pi$
$4$	5.40952	2.70476
$5$	0.469688	0.210051	0.105025	−	0.994470i	$-0.466508\pi$
$5$	0.469688	0.210051	0.105025	+	0.994470i	$0.466508\pi$
$6$	4.81078	1.96399
$7$	1.03831	0.392445	0.196222	−	0.980559i	$-0.437133\pi$
$7$	1.03831	0.392445	0.196222	+	0.980559i	$0.437133\pi$
$8$	−9.28087	−3.28128
$9$	0.123492	0.0411640
$10$	−1.27851	−0.404301
$11$	−1.84194	−0.555366	−0.277683	−	0.960673i	$-0.589566\pi$
$11$	−1.84194	−0.555366	−0.277683	+	0.960673i	$0.589566\pi$
$12$	−9.56047	−2.75987
$13$	−0.700934	−0.194404	−0.0972021	−	0.995265i	$-0.530989\pi$
$13$	−0.700934	−0.194404	−0.0972021	+	0.995265i	$0.530989\pi$
$14$	−2.82633	−0.755368
$15$	−0.830099	−0.214331
$16$	14.4439	3.61097
$17$	0.793975	0.192567	0.0962837	−	0.995354i	$-0.469304\pi$
$17$	0.793975	0.192567	0.0962837	+	0.995354i	$0.469304\pi$
$18$	−0.336150	−0.0792314
$19$	3.65845	0.839306	0.419653	−	0.907685i	$-0.362152\pi$
$19$	3.65845	0.839306	0.419653	+	0.907685i	$0.362152\pi$
$20$	2.54079	0.568138
$21$	−1.83505	−0.400441
$22$	5.01384	1.06895
$23$	−3.65159	−0.761409	−0.380704	−	0.924697i	$-0.624318\pi$
$23$	−3.65159	−0.761409	−0.380704	+	0.924697i	$0.624318\pi$
$24$	16.4025	3.34814
$25$	−4.77939	−0.955879
$26$	1.90797	0.374184
$27$	5.08377	0.978372
$28$	5.61677	1.06147
$29$	5.52848	1.02661	0.513307	−	0.858205i	$-0.328420\pi$
$29$	5.52848	1.02661	0.513307	+	0.858205i	$0.328420\pi$
$30$	2.25957	0.412538
$31$	6.13605	1.10207	0.551034	−	0.834483i	$-0.314234\pi$
$31$	6.13605	1.10207	0.551034	+	0.834483i	$0.314234\pi$
$32$	−20.7552	−3.66903
$33$	3.25534	0.566681
$34$	−2.16124	−0.370649
$35$	0.487683	0.0824334
$36$	0.668032	0.111339
$37$	−2.73114	−0.448997	−0.224498	−	0.974474i	$-0.572074\pi$
$37$	−2.73114	−0.448997	−0.224498	+	0.974474i	$0.572074\pi$
$38$	−9.95846	−1.61547
$39$	1.23879	0.198365
$40$	−4.35911	−0.689237
$41$	−9.69220	−1.51367	−0.756833	−	0.653608i	$-0.773255\pi$
$41$	−9.69220	−1.51367	−0.756833	+	0.653608i	$0.773255\pi$
$42$	4.99509	0.770758
$43$	−4.25340	−0.648638	−0.324319	−	0.945948i	$-0.605135\pi$
$43$	−4.25340	−0.648638	−0.324319	+	0.945948i	$0.605135\pi$
$44$	−9.96402	−1.50213
$45$	0.0580027	0.00864653
$46$	9.93978	1.46554
$47$	−5.21084	−0.760078	−0.380039	−	0.924970i	$-0.624090\pi$
$47$	−5.21084	−0.760078	−0.380039	+	0.924970i	$0.624090\pi$
$48$	−25.5273	−3.68454
$49$	−5.92191	−0.845987
$50$	13.0097	1.83985
$51$	−1.40322	−0.196491
$52$	−3.79172	−0.525817
$53$	−7.01107	−0.963044	−0.481522	−	0.876434i	$-0.659916\pi$
$53$	−7.01107	−0.963044	−0.481522	+	0.876434i	$0.659916\pi$
$54$	−13.8382	−1.88315
$55$	−0.865138	−0.116655
$56$	−9.63643	−1.28772
$57$	−6.46572	−0.856406
$58$	−15.0488	−1.97600
$59$	6.98691	0.909619	0.454809	−	0.890589i	$-0.349707\pi$
$59$	6.98691	0.909619	0.454809	+	0.890589i	$0.349707\pi$
$60$	−4.49044	−0.579713
$61$	−3.87686	−0.496381	−0.248191	−	0.968711i	$-0.579836\pi$
$61$	−3.87686	−0.496381	−0.248191	+	0.968711i	$0.579836\pi$
$62$	−16.7026	−2.12123
$63$	0.128223	0.0161546
$64$	27.6087	3.45109
$65$	−0.329220	−0.0408348
$66$	−8.86117	−1.09073
$67$	−5.10753	−0.623984	−0.311992	−	0.950085i	$-0.600996\pi$
$67$	−5.10753	−0.623984	−0.311992	+	0.950085i	$0.600996\pi$
$68$	4.29503	0.520849
$69$	6.45360	0.776922
$70$	−1.32749	−0.158666
$71$	1.33192	0.158070	0.0790350	−	0.996872i	$-0.474816\pi$
$71$	1.33192	0.158070	0.0790350	+	0.996872i	$0.474816\pi$
$72$	−1.14611	−0.135071
$73$	−7.83377	−0.916874	−0.458437	−	0.888727i	$-0.651591\pi$
$73$	−7.83377	−0.916874	−0.458437	+	0.888727i	$0.651591\pi$
$74$	7.43429	0.864218
$75$	8.44681	0.975354
$76$	19.7905	2.27012
$77$	−1.91251	−0.217950
$78$	−3.37204	−0.381808
$79$	4.36166	0.490726	0.245363	−	0.969431i	$-0.421093\pi$
$79$	4.36166	0.490726	0.245363	+	0.969431i	$0.421093\pi$
$80$	6.78412	0.758488
$81$	−9.35523	−1.03947
$82$	26.3826	2.91347
$83$	−13.3348	−1.46368	−0.731842	−	0.681475i	$-0.761339\pi$
$83$	−13.3348	−1.46368	−0.731842	+	0.681475i	$0.761339\pi$
$84$	−9.92674	−1.08310
$85$	0.372921	0.0404489
$86$	11.5779	1.24848
$87$	−9.77071	−1.04753
$88$	17.0948	1.82231
$89$	−0.208861	−0.0221393	−0.0110696	−	0.999939i	$-0.503524\pi$
$89$	−0.208861	−0.0221393	−0.0110696	+	0.999939i	$0.503524\pi$
$90$	−0.157886	−0.0166426
$91$	−0.727788	−0.0762929
$92$	−19.7533	−2.05943
$93$	−10.8445	−1.12452
$94$	14.1841	1.46298
$95$	1.71833	0.176297
$96$	36.6814	3.74378
$97$	3.08809	0.313549	0.156774	−	0.987634i	$-0.449890\pi$
$97$	3.08809	0.313549	0.156774	+	0.987634i	$0.449890\pi$
$98$	16.1197	1.62834
$99$	−0.227465	−0.0228611
$100$	−25.8542	−2.58542
$101$	−8.00261	−0.796290	−0.398145	−	0.917323i	$-0.630346\pi$
$101$	−8.00261	−0.796290	−0.398145	+	0.917323i	$0.630346\pi$
$102$	3.81964	0.378201
$103$	−3.26470	−0.321681	−0.160840	−	0.986980i	$-0.551420\pi$
$103$	−3.26470	−0.321681	−0.160840	+	0.986980i	$0.551420\pi$
$104$	6.50528	0.637895
$105$	−0.861901	−0.0841129
$106$	19.0844	1.85364
$107$	−18.4884	−1.78735	−0.893673	−	0.448719i	$-0.851880\pi$
$107$	−18.4884	−1.78735	−0.893673	+	0.448719i	$0.851880\pi$
$108$	27.5008	2.64626
$109$	−18.6769	−1.78893	−0.894463	−	0.447141i	$-0.852442\pi$
$109$	−18.6769	−1.78893	−0.894463	+	0.447141i	$0.852442\pi$
$110$	2.35494	0.224535
$111$	4.82686	0.458145
$112$	14.9973	1.41711
$113$	7.85874	0.739288	0.369644	−	0.929173i	$-0.379480\pi$
$113$	7.85874	0.739288	0.369644	+	0.929173i	$0.379480\pi$
$114$	17.6000	1.64839
$115$	−1.71511	−0.159935
$116$	29.9064	2.77674
$117$	−0.0865597	−0.00800245
$118$	−19.0187	−1.75081
$119$	0.824394	0.0755720
$120$	7.70404	0.703279
$121$	−7.60726	−0.691569
$122$	10.5530	0.955422
$123$	17.1294	1.54451
$124$	33.1931	2.98083
$125$	−4.59326	−0.410834
$126$	−0.349029	−0.0310940
$127$	9.84052	0.873205	0.436602	−	0.899655i	$-0.356182\pi$
$127$	9.84052	0.873205	0.436602	+	0.899655i	$0.356182\pi$
$128$	−33.6417	−2.97354
$129$	7.51721	0.661854
$130$	0.896152	0.0785978
$131$	8.02091	0.700791	0.350395	−	0.936602i	$-0.386047\pi$
$131$	8.02091	0.700791	0.350395	+	0.936602i	$0.386047\pi$
$132$	17.6098	1.53274
$133$	3.79861	0.329381
$134$	13.9029	1.20103
$135$	2.38779	0.205508
$136$	−7.36878	−0.631868
$137$	16.8434	1.43903	0.719516	−	0.694476i	$-0.244364\pi$
$137$	16.8434	1.43903	0.719516	+	0.694476i	$0.244364\pi$
$138$	−17.5670	−1.49540
$139$	11.2506	0.954260	0.477130	−	0.878833i	$-0.341677\pi$
$139$	11.2506	0.954260	0.477130	+	0.878833i	$0.341677\pi$
$140$	2.63813	0.222963
$141$	9.20932	0.775565
$142$	−3.62555	−0.304249
$143$	1.29108	0.107965
$144$	1.78370	0.148642
$145$	2.59666	0.215641
$146$	21.3239	1.76478
$147$	10.4660	0.863224
$148$	−14.7742	−1.21443
$149$	−18.8662	−1.54558	−0.772788	−	0.634664i	$-0.781138\pi$
$149$	−18.8662	−1.54558	−0.772788	+	0.634664i	$0.781138\pi$
$150$	−22.9926	−1.87734
$151$	−6.40292	−0.521062	−0.260531	−	0.965465i	$-0.583898\pi$
$151$	−6.40292	−0.521062	−0.260531	+	0.965465i	$0.583898\pi$
$152$	−33.9536	−2.75400
$153$	0.0980495	0.00792684
$154$	5.20593	0.419506
$155$	2.88203	0.231490
$156$	6.70126	0.536530
$157$	−14.9254	−1.19118	−0.595589	−	0.803290i	$-0.703081\pi$
$157$	−14.9254	−1.19118	−0.595589	+	0.803290i	$0.703081\pi$
$158$	−11.8726	−0.944537
$159$	12.3909	0.982665
$160$	−9.74845	−0.770683
$161$	−3.79148	−0.298811
$162$	25.4653	2.00075
$163$	−20.3834	−1.59655	−0.798274	−	0.602294i	$-0.794253\pi$
$163$	−20.3834	−1.59655	−0.798274	+	0.602294i	$0.794253\pi$
$164$	−52.4302	−4.09411
$165$	1.52899	0.119032
$166$	36.2979	2.81726
$167$	15.8853	1.22924	0.614622	−	0.788822i	$-0.289309\pi$
$167$	15.8853	1.22924	0.614622	+	0.788822i	$0.289309\pi$
$168$	17.0309	1.31396
$169$	−12.5087	−0.962207
$170$	−1.01511	−0.0778551
$171$	0.451789	0.0345492
$172$	−23.0089	−1.75441
$173$	16.4110	1.24771	0.623854	−	0.781541i	$-0.285566\pi$
$173$	16.4110	1.24771	0.623854	+	0.781541i	$0.285566\pi$
$174$	26.5963	2.01626
$175$	−4.96250	−0.375130
$176$	−26.6048	−2.00541
$177$	−12.3483	−0.928151
$178$	0.568530	0.0426131
$179$	−20.4269	−1.52678	−0.763390	−	0.645938i	$-0.776466\pi$
$179$	−20.4269	−1.52678	−0.763390	+	0.645938i	$0.776466\pi$
$180$	0.313767	0.0233868
$181$	−10.3683	−0.770666	−0.385333	−	0.922778i	$-0.625913\pi$
$181$	−10.3683	−0.770666	−0.385333	+	0.922778i	$0.625913\pi$
$182$	1.98107	0.146847
$183$	6.85173	0.506495
$184$	33.8899	2.49840
$185$	−1.28279	−0.0943122
$186$	29.5192	2.16445
$187$	−1.46246	−0.106945
$188$	−28.1881	−2.05583
$189$	5.27853	0.383957
$190$	−4.67737	−0.339332
$191$	−7.95483	−0.575591	−0.287796	−	0.957692i	$-0.592922\pi$
$191$	−7.95483	−0.575591	−0.287796	+	0.957692i	$0.592922\pi$
$192$	−48.7939	−3.52140
$193$	23.9566	1.72443	0.862217	−	0.506539i	$-0.169075\pi$
$193$	23.9566	1.72443	0.862217	+	0.506539i	$0.169075\pi$
$194$	−8.40593	−0.603511
$195$	0.581845	0.0416668
$196$	−32.0347	−2.28819
$197$	5.15127	0.367013	0.183506	−	0.983019i	$-0.441255\pi$
$197$	5.15127	0.367013	0.183506	+	0.983019i	$0.441255\pi$
$198$	0.619169	0.0440024
$199$	1.54311	0.109388	0.0546940	−	0.998503i	$-0.482582\pi$
$199$	1.54311	0.109388	0.0546940	+	0.998503i	$0.482582\pi$
$200$	44.3569	3.13651
$201$	9.02674	0.636697
$202$	21.7835	1.53268
$203$	5.74028	0.402889
$204$	−7.59078	−0.531461
$205$	−4.55231	−0.317947
$206$	8.88666	0.619163
$207$	−0.450942	−0.0313426
$208$	−10.1242	−0.701988
$209$	−6.73864	−0.466122
$210$	2.34613	0.161899
$211$	8.81178	0.606628	0.303314	−	0.952891i	$-0.401907\pi$
$211$	8.81178	0.606628	0.303314	+	0.952891i	$0.401907\pi$
$212$	−37.9265	−2.60480
$213$	−2.35396	−0.161291
$214$	50.3264	3.44024
$215$	−1.99777	−0.136247
$216$	−47.1818	−3.21031
$217$	6.37113	0.432501
$218$	50.8395	3.44328
$219$	13.8449	0.935555
$220$	−4.67998	−0.315524
$221$	−0.556524	−0.0374359
$222$	−13.1389	−0.881826
$223$	24.2050	1.62089	0.810445	−	0.585815i	$-0.199226\pi$
$223$	24.2050	1.62089	0.810445	+	0.585815i	$0.199226\pi$
$224$	−21.5503	−1.43989
$225$	−0.590216	−0.0393478
$226$	−21.3918	−1.42296
$227$	−3.55162	−0.235729	−0.117865	−	0.993030i	$-0.537605\pi$
$227$	−3.55162	−0.235729	−0.117865	+	0.993030i	$0.537605\pi$
$228$	−34.9765	−2.31637
$229$	−18.8164	−1.24342	−0.621711	−	0.783247i	$-0.713562\pi$
$229$	−18.8164	−1.24342	−0.621711	+	0.783247i	$0.713562\pi$
$230$	4.66860	0.307838
$231$	3.38005	0.222391
$232$	−51.3091	−3.36861
$233$	12.1897	0.798575	0.399288	−	0.916826i	$-0.369258\pi$
$233$	12.1897	0.798575	0.399288	+	0.916826i	$0.369258\pi$
$234$	0.235619	0.0154029
$235$	−2.44747	−0.159655
$236$	37.7959	2.46030
$237$	−7.70855	−0.500724
$238$	−2.24404	−0.145459
$239$	30.6423	1.98208	0.991042	−	0.133553i	$-0.0426385\pi$
$239$	30.6423	1.98208	0.991042	+	0.133553i	$0.0426385\pi$
$240$	−11.9899	−0.773942
$241$	−7.26294	−0.467847	−0.233924	−	0.972255i	$-0.575157\pi$
$241$	−7.26294	−0.467847	−0.233924	+	0.972255i	$0.575157\pi$
$242$	20.7073	1.33111
$243$	1.28256	0.0822763
$244$	−20.9720	−1.34259
$245$	−2.78145	−0.177700
$246$	−46.6270	−2.97283
$247$	−2.56433	−0.163164
$248$	−56.9479	−3.61620
$249$	23.5671	1.49350
$250$	12.5031	0.790764
$251$	−25.2813	−1.59574	−0.797871	−	0.602828i	$-0.794041\pi$
$251$	−25.2813	−1.59574	−0.797871	+	0.602828i	$0.794041\pi$
$252$	0.693626	0.0436943
$253$	6.72601	0.422860
$254$	−26.7863	−1.68072
$255$	−0.659078	−0.0412731
$256$	36.3569	2.27230
$257$	−26.5017	−1.65313	−0.826564	−	0.562842i	$-0.809708\pi$
$257$	−26.5017	−1.65313	−0.826564	+	0.562842i	$0.809708\pi$
$258$	−20.4622	−1.27392
$259$	−2.83578	−0.176207
$260$	−1.78093	−0.110448
$261$	0.682723	0.0422595
$262$	−21.8333	−1.34886
$263$	12.5983	0.776845	0.388422	−	0.921481i	$-0.373020\pi$
$263$	12.5983	0.776845	0.388422	+	0.921481i	$0.373020\pi$
$264$	−30.2123	−1.85944
$265$	−3.29301	−0.202288
$266$	−10.3400	−0.633985
$267$	0.369129	0.0225903
$268$	−27.6293	−1.68773
$269$	1.45914	0.0889652	0.0444826	−	0.999010i	$-0.485836\pi$
$269$	1.45914	0.0889652	0.0444826	+	0.999010i	$0.485836\pi$
$270$	−6.49966	−0.395557
$271$	5.16205	0.313572	0.156786	−	0.987633i	$-0.449887\pi$
$271$	5.16205	0.313572	0.156786	+	0.987633i	$0.449887\pi$
$272$	11.4681	0.695355
$273$	1.28625	0.0778473
$274$	−45.8486	−2.76981
$275$	8.80336	0.530862
$276$	34.9109	2.10139
$277$	14.0110	0.841837	0.420918	−	0.907098i	$-0.361708\pi$
$277$	14.0110	0.841837	0.420918	+	0.907098i	$0.361708\pi$
$278$	−30.6245	−1.83674
$279$	0.757753	0.0453655
$280$	−4.52612	−0.270487
$281$	16.3617	0.976059	0.488030	−	0.872827i	$-0.337716\pi$
$281$	16.3617	0.976059	0.488030	+	0.872827i	$0.337716\pi$
$282$	−25.0682	−1.49279
$283$	18.5182	1.10079	0.550397	−	0.834903i	$-0.314476\pi$
$283$	18.5182	1.10079	0.550397	+	0.834903i	$0.314476\pi$
$284$	7.20506	0.427542
$285$	−3.03687	−0.179889
$286$	−3.51437	−0.207809
$287$	−10.0635	−0.594031
$288$	−2.56310	−0.151032
$289$	−16.3696	−0.962918
$290$	−7.06823	−0.415061
$291$	−5.45771	−0.319937
$292$	−42.3770	−2.47993
$293$	30.5239	1.78323	0.891613	−	0.452798i	$-0.149574\pi$
$293$	30.5239	1.78323	0.891613	+	0.452798i	$0.149574\pi$
$294$	−28.4890	−1.66151
$295$	3.28167	0.191066
$296$	25.3474	1.47329
$297$	−9.36400	−0.543354
$298$	51.3545	2.97489
$299$	2.55952	0.148021
$300$	45.6932	2.63810
$301$	−4.41636	−0.254555
$302$	17.4290	1.00293
$303$	14.1433	0.812514
$304$	52.8422	3.03071
$305$	−1.82092	−0.104265
$306$	−0.266895	−0.0152574
$307$	3.36035	0.191785	0.0958926	−	0.995392i	$-0.469429\pi$
$307$	3.36035	0.191785	0.0958926	+	0.995392i	$0.469429\pi$
$308$	−10.3458	−0.589504
$309$	5.76984	0.328235
$310$	−7.84501	−0.445567
$311$	26.0631	1.47791	0.738953	−	0.673757i	$-0.235321\pi$
$311$	26.0631	1.47791	0.738953	+	0.673757i	$0.235321\pi$
$312$	−11.4970	−0.650892
$313$	−28.4960	−1.61069	−0.805345	−	0.592807i	$-0.798020\pi$
$313$	−28.4960	−1.61069	−0.805345	+	0.592807i	$0.798020\pi$
$314$	40.6276	2.29275
$315$	0.0602249	0.00339329
$316$	23.5945	1.32730
$317$	−8.26530	−0.464225	−0.232113	−	0.972689i	$-0.574564\pi$
$317$	−8.26530	−0.464225	−0.232113	+	0.972689i	$0.574564\pi$
$318$	−33.7287	−1.89141
$319$	−10.1831	−0.570146
$320$	12.9675	0.724904
$321$	32.6754	1.82376
$322$	10.3206	0.575144
$323$	2.90472	0.161623
$324$	−50.6073	−2.81152
$325$	3.35004	0.185827
$326$	55.4844	3.07300
$327$	33.0085	1.82537
$328$	89.9520	4.96677
$329$	−5.41047	−0.298289
$330$	−4.16198	−0.229110
$331$	12.5162	0.687951	0.343976	−	0.938979i	$-0.388226\pi$
$331$	12.5162	0.687951	0.343976	+	0.938979i	$0.388226\pi$
$332$	−72.1348	−3.95891
$333$	−0.337274	−0.0184825
$334$	−43.2406	−2.36602
$335$	−2.39895	−0.131068
$336$	−26.5053	−1.44598
$337$	−20.0461	−1.09198	−0.545990	−	0.837792i	$-0.683846\pi$
$337$	−20.0461	−1.09198	−0.545990	+	0.837792i	$0.683846\pi$
$338$	34.0492	1.85203
$339$	−13.8891	−0.754351
$340$	2.01732	0.109405
$341$	−11.3022	−0.612051
$342$	−1.22979	−0.0664994
$343$	−13.4170	−0.724448
$344$	39.4753	2.12836
$345$	3.03118	0.163193
$346$	−44.6716	−2.40156
$347$	0.748255	0.0401684	0.0200842	−	0.999798i	$-0.493607\pi$
$347$	0.748255	0.0401684	0.0200842	+	0.999798i	$0.493607\pi$
$348$	−52.8549	−2.83332
$349$	4.16941	0.223183	0.111592	−	0.993754i	$-0.464405\pi$
$349$	4.16941	0.223183	0.111592	+	0.993754i	$0.464405\pi$
$350$	13.5081	0.722040
$351$	−3.56339	−0.190200
$352$	38.2298	2.03765
$353$	28.9002	1.53820	0.769100	−	0.639128i	$-0.220705\pi$
$353$	28.9002	1.53820	0.769100	+	0.639128i	$0.220705\pi$
$354$	33.6125	1.78648
$355$	0.625588	0.0332028
$356$	−1.12984	−0.0598814
$357$	−1.45698	−0.0771118
$358$	55.6030	2.93871
$359$	22.5238	1.18876	0.594380	−	0.804185i	$-0.297398\pi$
$359$	22.5238	1.18876	0.594380	+	0.804185i	$0.297398\pi$
$360$	−0.538315	−0.0283717
$361$	−5.61576	−0.295566
$362$	28.2228	1.48336
$363$	13.4446	0.705659
$364$	−3.93698	−0.206354
$365$	−3.67943	−0.192590
$366$	−18.6507	−0.974888
$367$	−3.07935	−0.160741	−0.0803705	−	0.996765i	$-0.525610\pi$
$367$	−3.07935	−0.160741	−0.0803705	+	0.996765i	$0.525610\pi$
$368$	−52.7431	−2.74943
$369$	−1.19691	−0.0623085
$370$	3.49180	0.181530
$371$	−7.27967	−0.377942
$372$	−58.6635	−3.04156
$373$	−23.8756	−1.23623	−0.618115	−	0.786088i	$-0.712103\pi$
$373$	−23.8756	−1.23623	−0.618115	+	0.786088i	$0.712103\pi$
$374$	3.98087	0.205846
$375$	8.11786	0.419205
$376$	48.3611	2.49403
$377$	−3.87510	−0.199578
$378$	−14.3684	−0.739031
$379$	3.60479	0.185166	0.0925828	−	0.995705i	$-0.470488\pi$
$379$	3.60479	0.185166	0.0925828	+	0.995705i	$0.470488\pi$
$380$	9.29534	0.476841
$381$	−17.3915	−0.890996
$382$	21.6534	1.10788
$383$	−3.63594	−0.185788	−0.0928939	−	0.995676i	$-0.529612\pi$
$383$	−3.63594	−0.185788	−0.0928939	+	0.995676i	$0.529612\pi$
$384$	59.4564	3.03412
$385$	−0.898282	−0.0457807
$386$	−65.2109	−3.31915
$387$	−0.525261	−0.0267005
$388$	16.7051	0.848074
$389$	21.6735	1.09889	0.549445	−	0.835530i	$-0.314839\pi$
$389$	21.6735	1.09889	0.549445	+	0.835530i	$0.314839\pi$
$390$	−1.58381	−0.0801992
$391$	−2.89927	−0.146622
$392$	54.9605	2.77592
$393$	−14.1757	−0.715069
$394$	−14.0220	−0.706417
$395$	2.04862	0.103077
$396$	−1.23048	−0.0618337
$397$	6.59119	0.330802	0.165401	−	0.986226i	$-0.447108\pi$
$397$	6.59119	0.330802	0.165401	+	0.986226i	$0.447108\pi$
$398$	−4.20041	−0.210547
$399$	−6.71343	−0.336092
$400$	−69.0330	−3.45165
$401$	−4.35340	−0.217398	−0.108699	−	0.994075i	$-0.534668\pi$
$401$	−4.35340	−0.217398	−0.108699	+	0.994075i	$0.534668\pi$
$402$	−24.5712	−1.22550
$403$	−4.30097	−0.214246
$404$	−43.2903	−2.15377
$405$	−4.39404	−0.218342
$406$	−15.6253	−0.775471
$407$	5.03060	0.249358
$408$	13.0231	0.644742
$409$	31.8412	1.57445	0.787223	−	0.616668i	$-0.211518\pi$
$409$	31.8412	1.57445	0.787223	+	0.616668i	$0.211518\pi$
$410$	12.3916	0.611977
$411$	−29.7681	−1.46835
$412$	−17.6605	−0.870069
$413$	7.25459	0.356975
$414$	1.22748	0.0603275
$415$	−6.26319	−0.307448
$416$	14.5480	0.713274
$417$	−19.8836	−0.973703
$418$	18.3429	0.897180
$419$	−29.8225	−1.45692	−0.728462	−	0.685087i	$-0.759764\pi$
$419$	−29.8225	−1.45692	−0.728462	+	0.685087i	$0.759764\pi$
$420$	−4.66247	−0.227505
$421$	−7.93092	−0.386530	−0.193265	−	0.981147i	$-0.561908\pi$
$421$	−7.93092	−0.386530	−0.193265	+	0.981147i	$0.561908\pi$
$422$	−23.9860	−1.16762
$423$	−0.643496	−0.0312879
$424$	65.0688	3.16002
$425$	−3.79472	−0.184071
$426$	6.40758	0.310448
$427$	−4.02539	−0.194802
$428$	−100.014	−4.83434
$429$	−2.28178	−0.110165
$430$	5.43803	0.262245
$431$	−24.9537	−1.20198	−0.600988	−	0.799258i	$-0.705226\pi$
$431$	−24.9537	−1.20198	−0.600988	+	0.799258i	$0.705226\pi$
$432$	73.4294	3.53287
$433$	23.1505	1.11254	0.556272	−	0.831000i	$-0.312231\pi$
$433$	23.1505	1.11254	0.556272	+	0.831000i	$0.312231\pi$
$434$	−17.3425	−0.832467
$435$	−4.58918	−0.220035
$436$	−101.033	−4.83862
$437$	−13.3591	−0.639054
$438$	−37.6865	−1.80073
$439$	18.9654	0.905167	0.452584	−	0.891722i	$-0.350502\pi$
$439$	18.9654	0.905167	0.452584	+	0.891722i	$0.350502\pi$
$440$	8.02923	0.382778
$441$	−0.731308	−0.0348242
$442$	1.51488	0.0720557
$443$	21.6203	1.02721	0.513606	−	0.858026i	$-0.328309\pi$
$443$	21.6203	1.02721	0.513606	+	0.858026i	$0.328309\pi$
$444$	26.1110	1.23917
$445$	−0.0980997	−0.00465037
$446$	−65.8872	−3.11985
$447$	33.3429	1.57707
$448$	28.6664	1.35436
$449$	15.1299	0.714023	0.357011	−	0.934100i	$-0.383796\pi$
$449$	15.1299	0.714023	0.357011	+	0.934100i	$0.383796\pi$
$450$	1.60660	0.0757356
$451$	17.8524	0.840639
$452$	42.5121	1.99960
$453$	11.3161	0.531678
$454$	9.66767	0.453726
$455$	−0.341833	−0.0160254
$456$	60.0075	2.81011
$457$	−7.87882	−0.368556	−0.184278	−	0.982874i	$-0.558995\pi$
$457$	−7.87882	−0.368556	−0.184278	+	0.982874i	$0.558995\pi$
$458$	51.2190	2.39331
$459$	4.03639	0.188402
$460$	−9.27791	−0.432585
$461$	−33.2729	−1.54967	−0.774836	−	0.632162i	$-0.782168\pi$
$461$	−33.2729	−1.54967	−0.774836	+	0.632162i	$0.782168\pi$
$462$	−9.20065	−0.428053
$463$	31.9493	1.48481	0.742405	−	0.669951i	$-0.233685\pi$
$463$	31.9493	1.48481	0.742405	+	0.669951i	$0.233685\pi$
$464$	79.8528	3.70707
$465$	−5.09353	−0.236207
$466$	−33.1810	−1.53708
$467$	6.03218	0.279136	0.139568	−	0.990213i	$-0.455429\pi$
$467$	6.03218	0.279136	0.139568	+	0.990213i	$0.455429\pi$
$468$	−0.468247	−0.0216447
$469$	−5.30320	−0.244879
$470$	6.66211	0.307300
$471$	26.3783	1.21545
$472$	−64.8446	−2.98472
$473$	7.83451	0.360231
$474$	20.9830	0.963781
$475$	−17.4852	−0.802274
$476$	4.45958	0.204404
$477$	−0.865810	−0.0396427
$478$	−83.4096	−3.81507
$479$	18.1368	0.828693	0.414347	−	0.910119i	$-0.364010\pi$
$479$	18.1368	0.828693	0.414347	+	0.910119i	$0.364010\pi$
$480$	17.2288	0.786385
$481$	1.91435	0.0872869
$482$	19.7700	0.900501
$483$	6.70084	0.304899
$484$	−41.1516	−1.87053
$485$	1.45044	0.0658612
$486$	−3.49119	−0.158363
$487$	−23.3591	−1.05850	−0.529251	−	0.848465i	$-0.677527\pi$
$487$	−23.3591	−1.05850	−0.529251	+	0.848465i	$0.677527\pi$
$488$	35.9806	1.62877
$489$	36.0243	1.62908
$490$	7.57123	0.342033
$491$	−4.28889	−0.193555	−0.0967775	−	0.995306i	$-0.530854\pi$
$491$	−4.28889	−0.193555	−0.0967775	+	0.995306i	$0.530854\pi$
$492$	92.6619	4.17752
$493$	4.38948	0.197692
$494$	6.98022	0.314055
$495$	−0.106838	−0.00480199
$496$	88.6285	3.97954
$497$	1.38295	0.0620338
$498$	−64.1507	−2.87466
$499$	−12.0079	−0.537549	−0.268775	−	0.963203i	$-0.586619\pi$
$499$	−12.0079	−0.537549	−0.268775	+	0.963203i	$0.586619\pi$
$500$	−24.8474	−1.11121
$501$	−28.0748	−1.25429
$502$	68.8169	3.07145
$503$	−22.0435	−0.982872	−0.491436	−	0.870914i	$-0.663528\pi$
$503$	−22.0435	−0.982872	−0.491436	+	0.870914i	$0.663528\pi$
$504$	−1.19002	−0.0530078
$505$	−3.75873	−0.167261
$506$	−18.3085	−0.813911
$507$	22.1071	0.981811
$508$	53.2325	2.36181
$509$	−11.9642	−0.530302	−0.265151	−	0.964207i	$-0.585422\pi$
$509$	−11.9642	−0.530302	−0.265151	+	0.964207i	$0.585422\pi$
$510$	1.79404	0.0794414
$511$	−8.13390	−0.359822
$512$	−31.6816	−1.40014
$513$	18.5987	0.821153
$514$	72.1387	3.18190
$515$	−1.53339	−0.0675693
$516$	40.6645	1.79016
$517$	9.59805	0.422122
$518$	7.71911	0.339158
$519$	−29.0039	−1.27313
$520$	3.05545	0.133990
$521$	−5.47217	−0.239740	−0.119870	−	0.992790i	$-0.538248\pi$
$521$	−5.47217	−0.239740	−0.119870	+	0.992790i	$0.538248\pi$
$522$	−1.85840	−0.0813400
$523$	−31.1363	−1.36149	−0.680747	−	0.732519i	$-0.738345\pi$
$523$	−31.1363	−1.36149	−0.680747	+	0.732519i	$0.738345\pi$
$524$	43.3893	1.89547
$525$	8.77042	0.382773
$526$	−34.2931	−1.49525
$527$	4.87187	0.212222
$528$	47.0197	2.04627
$529$	−9.66591	−0.420257
$530$	8.96373	0.389360
$531$	0.862827	0.0374435
$532$	20.5487	0.890897
$533$	6.79359	0.294263
$534$	−1.00479	−0.0434813
$535$	−8.68380	−0.375434
$536$	47.4023	2.04747
$537$	36.1013	1.55789
$538$	−3.97183	−0.171238
$539$	10.9078	0.469832
$540$	12.9168	0.555850
$541$	−15.0578	−0.647387	−0.323694	−	0.946162i	$-0.604925\pi$
$541$	−15.0578	−0.647387	−0.323694	+	0.946162i	$0.604925\pi$
$542$	−14.0513	−0.603556
$543$	18.3242	0.786368
$544$	−16.4791	−0.706535
$545$	−8.77234	−0.375766
$546$	−3.50123	−0.149839
$547$	−1.00000	−0.0427569
$547$	−1.00000	−0.0427569
$548$	91.1150	3.89224
$549$	−0.478761	−0.0204330
$550$	−23.9631	−1.02179
$551$	20.2257	0.861642
$552$	−59.8950	−2.54930
$553$	4.52877	0.192583
$554$	−38.1384	−1.62035
$555$	2.26712	0.0962338
$556$	60.8602	2.58105
$557$	23.5488	0.997796	0.498898	−	0.866661i	$-0.333738\pi$
$557$	23.5488	0.997796	0.498898	+	0.866661i	$0.333738\pi$
$558$	−2.06264	−0.0873184
$559$	2.98136	0.126098
$560$	7.04403	0.297665
$561$	2.58466	0.109124
$562$	−44.5374	−1.87869
$563$	−29.0653	−1.22496	−0.612478	−	0.790488i	$-0.709827\pi$
$563$	−29.0653	−1.22496	−0.612478	+	0.790488i	$0.709827\pi$
$564$	49.8180	2.09772
$565$	3.69116	0.155288
$566$	−50.4074	−2.11878
$567$	−9.71364	−0.407934
$568$	−12.3614	−0.518673
$569$	−0.227367	−0.00953174	−0.00476587	−	0.999989i	$-0.501517\pi$
$569$	−0.227367	−0.00953174	−0.00476587	+	0.999989i	$0.501517\pi$
$570$	8.26650	0.346246
$571$	0.874566	0.0365994	0.0182997	−	0.999833i	$-0.494175\pi$
$571$	0.874566	0.0365994	0.0182997	+	0.999833i	$0.494175\pi$
$572$	6.98412	0.292021
$573$	14.0589	0.587319
$574$	27.3933	1.14338
$575$	17.4524	0.727814
$576$	3.40945	0.142060
$577$	−29.2997	−1.21976	−0.609882	−	0.792492i	$-0.708783\pi$
$577$	−29.2997	−1.21976	−0.609882	+	0.792492i	$0.708783\pi$
$578$	44.5588	1.85340
$579$	−42.3395	−1.75957
$580$	14.0467	0.583257
$581$	−13.8457	−0.574415
$582$	14.8561	0.615807
$583$	12.9140	0.534842
$584$	72.7042	3.00852
$585$	−0.0406561	−0.00168092
$586$	−83.0875	−3.43231
$587$	−10.9789	−0.453149	−0.226574	−	0.973994i	$-0.572753\pi$
$587$	−10.9789	−0.453149	−0.226574	+	0.973994i	$0.572753\pi$
$588$	56.6162	2.33481
$589$	22.4484	0.924971
$590$	−8.93285	−0.367760
$591$	−9.10404	−0.374490
$592$	−39.4483	−1.62132
$593$	−42.7926	−1.75728	−0.878641	−	0.477483i	$-0.841549\pi$
$593$	−42.7926	−1.75728	−0.878641	+	0.477483i	$0.841549\pi$
$594$	25.4892	1.04584
$595$	0.387208	0.0158740
$596$	−102.057	−4.18042
$597$	−2.72720	−0.111617
$598$	−6.96713	−0.284907
$599$	0.841737	0.0343925	0.0171962	−	0.999852i	$-0.494526\pi$
$599$	0.841737	0.0343925	0.0171962	+	0.999852i	$0.494526\pi$
$600$	−78.3938	−3.20041
$601$	−19.7479	−0.805536	−0.402768	−	0.915302i	$-0.631952\pi$
$601$	−19.7479	−0.805536	−0.402768	+	0.915302i	$0.631952\pi$
$602$	12.0215	0.489960
$603$	−0.630738	−0.0256857
$604$	−34.6367	−1.40935
$605$	−3.57304	−0.145265
$606$	−38.4988	−1.56391
$607$	−0.928802	−0.0376989	−0.0188495	−	0.999822i	$-0.506000\pi$
$607$	−0.928802	−0.0376989	−0.0188495	+	0.999822i	$0.506000\pi$
$608$	−75.9317	−3.07944
$609$	−10.1450	−0.411098
$610$	4.95661	0.200687
$611$	3.65245	0.147762
$612$	0.530401	0.0214402
$613$	20.1162	0.812485	0.406242	−	0.913765i	$-0.366839\pi$
$613$	20.1162	0.812485	0.406242	+	0.913765i	$0.366839\pi$
$614$	−9.14702	−0.369144
$615$	8.04548	0.324425
$616$	17.7497	0.715157
$617$	−13.2513	−0.533479	−0.266739	−	0.963769i	$-0.585946\pi$
$617$	−13.2513	−0.533479	−0.266739	+	0.963769i	$0.585946\pi$
$618$	−15.7058	−0.631778
$619$	−29.2870	−1.17714	−0.588572	−	0.808445i	$-0.700310\pi$
$619$	−29.2870	−1.17714	−0.588572	+	0.808445i	$0.700310\pi$
$620$	15.5904	0.626126
$621$	−18.5638	−0.744941
$622$	−70.9450	−2.84464
$623$	−0.216863	−0.00868844
$624$	17.8929	0.716291
$625$	21.7396	0.869583
$626$	77.5674	3.10022
$627$	11.9095	0.475619
$628$	−80.7393	−3.22185
$629$	−2.16846	−0.0864621
$630$	−0.163935	−0.00653131
$631$	−46.5766	−1.85418	−0.927092	−	0.374834i	$-0.877700\pi$
$631$	−46.5766	−1.85418	−0.927092	+	0.374834i	$0.877700\pi$
$632$	−40.4800	−1.61021
$633$	−15.5734	−0.618987
$634$	22.4985	0.893530
$635$	4.62197	0.183417
$636$	67.0291	2.65788
$637$	4.15087	0.164463
$638$	27.7189	1.09740
$639$	0.164482	0.00650679
$640$	−15.8011	−0.624594
$641$	−5.11165	−0.201898	−0.100949	−	0.994892i	$-0.532188\pi$
$641$	−5.11165	−0.201898	−0.100949	+	0.994892i	$0.532188\pi$
$642$	−88.9438	−3.51033
$643$	−4.32994	−0.170756	−0.0853781	−	0.996349i	$-0.527210\pi$
$643$	−4.32994	−0.170756	−0.0853781	+	0.996349i	$0.527210\pi$
$644$	−20.5101	−0.808212
$645$	3.53074	0.139023
$646$	−7.90677	−0.311088
$647$	−12.0401	−0.473343	−0.236672	−	0.971590i	$-0.576057\pi$
$647$	−12.0401	−0.473343	−0.236672	+	0.971590i	$0.576057\pi$
$648$	86.8246	3.41079
$649$	−12.8695	−0.505171
$650$	−9.11895	−0.357675
$651$	−11.2600	−0.441313
$652$	−110.264	−4.31828
$653$	39.4366	1.54327	0.771636	−	0.636064i	$-0.219439\pi$
$653$	39.4366	1.54327	0.771636	+	0.636064i	$0.219439\pi$
$654$	−89.8506	−3.51344
$655$	3.76733	0.147202
$656$	−139.993	−5.46581
$657$	−0.967408	−0.0377422
$658$	14.7275	0.574139
$659$	43.8625	1.70864	0.854320	−	0.519748i	$-0.173974\pi$
$659$	43.8625	1.70864	0.854320	+	0.519748i	$0.173974\pi$
$660$	8.27112	0.321953
$661$	−5.18941	−0.201845	−0.100922	−	0.994894i	$-0.532179\pi$
$661$	−5.18941	−0.201845	−0.100922	+	0.994894i	$0.532179\pi$
$662$	−34.0696	−1.32415
$663$	0.983568	0.0381986
$664$	123.758	4.80276
$665$	1.78416	0.0691868
$666$	0.918075	0.0355747
$667$	−20.1877	−0.781672
$668$	85.9321	3.32481
$669$	−42.7785	−1.65391
$670$	6.53003	0.252277
$671$	7.14094	0.275673
$672$	38.0868	1.46923
$673$	37.7606	1.45557	0.727783	−	0.685808i	$-0.240551\pi$
$673$	37.7606	1.45557	0.727783	+	0.685808i	$0.240551\pi$
$674$	54.5663	2.10182
$675$	−24.2973	−0.935205
$676$	−67.6661	−2.60254
$677$	−36.6368	−1.40806	−0.704032	−	0.710168i	$-0.748619\pi$
$677$	−36.6368	−1.40806	−0.704032	+	0.710168i	$0.748619\pi$
$678$	37.8067	1.45196
$679$	3.20640	0.123050
$680$	−3.46103	−0.132724
$681$	6.27692	0.240532
$682$	30.7652	1.17806
$683$	31.5096	1.20568	0.602841	−	0.797861i	$-0.294035\pi$
$683$	31.5096	1.20568	0.602841	+	0.797861i	$0.294035\pi$
$684$	2.44396	0.0934472
$685$	7.91116	0.302270
$686$	36.5216	1.39440
$687$	33.2549	1.26876
$688$	−61.4357	−2.34221
$689$	4.91430	0.187220
$690$	−8.25100	−0.314110
$691$	18.9407	0.720540	0.360270	−	0.932848i	$-0.382685\pi$
$691$	18.9407	0.720540	0.360270	+	0.932848i	$0.382685\pi$
$692$	88.7759	3.37475
$693$	−0.236179	−0.00897171
$694$	−2.03678	−0.0773153
$695$	5.28426	0.200443
$696$	90.6807	3.43724
$697$	−7.69537	−0.291483
$698$	−11.3493	−0.429578
$699$	−21.5434	−0.814846
$700$	−26.8447	−1.01464
$701$	42.8730	1.61929	0.809646	−	0.586919i	$-0.199659\pi$
$701$	42.8730	1.61929	0.809646	+	0.586919i	$0.199659\pi$
$702$	9.69970	0.366091
$703$	−9.99174	−0.376846
$704$	−50.8535	−1.91662
$705$	4.32551	0.162908
$706$	−78.6675	−2.96069
$707$	−8.30921	−0.312500
$708$	−66.7982	−2.51043
$709$	35.4811	1.33252	0.666260	−	0.745719i	$-0.267894\pi$
$709$	35.4811	1.33252	0.666260	+	0.745719i	$0.267894\pi$
$710$	−1.70288	−0.0639079
$711$	0.538630	0.0202002
$712$	1.93842	0.0726452
$713$	−22.4063	−0.839124
$714$	3.96597	0.148423
$715$	0.606404	0.0226782
$716$	−110.500	−4.12957
$717$	−54.1553	−2.02247
$718$	−61.3107	−2.28810
$719$	−24.4790	−0.912913	−0.456456	−	0.889746i	$-0.650882\pi$
$719$	−24.4790	−0.912913	−0.456456	+	0.889746i	$0.650882\pi$
$720$	0.837785	0.0312224
$721$	−3.38978	−0.126242
$722$	15.2863	0.568899
$723$	12.8361	0.477379
$724$	−56.0873	−2.08447
$725$	−26.4228	−0.981317
$726$	−36.5968	−1.35824
$727$	−28.7796	−1.06737	−0.533687	−	0.845682i	$-0.679194\pi$
$727$	−28.7796	−1.06737	−0.533687	+	0.845682i	$0.679194\pi$
$728$	6.75450	0.250339
$729$	25.7990	0.955517
$730$	10.0156	0.370693
$731$	−3.37710	−0.124906
$732$	37.0646	1.36995
$733$	23.0494	0.851350	0.425675	−	0.904876i	$-0.360037\pi$
$733$	23.0494	0.851350	0.425675	+	0.904876i	$0.360037\pi$
$734$	8.38213	0.309390
$735$	4.91577	0.181321
$736$	75.7893	2.79363
$737$	9.40776	0.346539
$738$	3.25804	0.119930
$739$	−9.02906	−0.332139	−0.166070	−	0.986114i	$-0.553108\pi$
$739$	−9.02906	−0.332139	−0.166070	+	0.986114i	$0.553108\pi$
$740$	−6.93925	−0.255092
$741$	4.53205	0.166489
$742$	19.8156	0.727453
$743$	−47.5028	−1.74271	−0.871355	−	0.490653i	$-0.836758\pi$
$743$	−47.5028	−1.74271	−0.871355	+	0.490653i	$0.836758\pi$
$744$	100.646	3.68987
$745$	−8.86121	−0.324650
$746$	64.9903	2.37947
$747$	−1.64674	−0.0602510
$748$	−7.91118	−0.289262
$749$	−19.1968	−0.701434
$750$	−22.0972	−0.806875
$751$	−20.5388	−0.749473	−0.374737	−	0.927131i	$-0.622267\pi$
$751$	−20.5388	−0.749473	−0.374737	+	0.927131i	$0.622267\pi$
$752$	−75.2647	−2.74462
$753$	44.6807	1.62825
$754$	10.5482	0.384143
$755$	−3.00737	−0.109450
$756$	28.5544	1.03851
$757$	36.3077	1.31962	0.659812	−	0.751430i	$-0.270636\pi$
$757$	36.3077	1.31962	0.659812	+	0.751430i	$0.270636\pi$
$758$	−9.81240	−0.356402
$759$	−11.8871	−0.431476
$760$	−15.9476	−0.578480
$761$	23.0597	0.835915	0.417957	−	0.908467i	$-0.362746\pi$
$761$	23.0597	0.835915	0.417957	+	0.908467i	$0.362746\pi$
$762$	47.3405	1.71497
$763$	−19.3925	−0.702055
$764$	−43.0318	−1.55684
$765$	0.0460527	0.00166504
$766$	9.89719	0.357600
$767$	−4.89737	−0.176834
$768$	−64.2550	−2.31860
$769$	4.40403	0.158813	0.0794066	−	0.996842i	$-0.474697\pi$
$769$	4.40403	0.158813	0.0794066	+	0.996842i	$0.474697\pi$
$770$	2.44516	0.0881176
$771$	46.8375	1.68681
$772$	129.594	4.66418
$773$	−25.6259	−0.921699	−0.460849	−	0.887478i	$-0.652455\pi$
$773$	−25.6259	−0.921699	−0.460849	+	0.887478i	$0.652455\pi$
$774$	1.42978	0.0513925
$775$	−29.3266	−1.05344
$776$	−28.6602	−1.02884
$777$	5.01178	0.179797
$778$	−58.9962	−2.11512
$779$	−35.4584	−1.27043
$780$	3.14750	0.112699
$781$	−2.45332	−0.0877867
$782$	7.89194	0.282215
$783$	28.1055	1.00441
$784$	−85.5354	−3.05484
$785$	−7.01029	−0.250208
$786$	38.5868	1.37635
$787$	46.4038	1.65412	0.827059	−	0.562115i	$-0.190012\pi$
$787$	46.4038	1.65412	0.827059	+	0.562115i	$0.190012\pi$
$788$	27.8659	0.992681
$789$	−22.2655	−0.792673
$790$	−5.57644	−0.198401
$791$	8.15982	0.290130
$792$	2.11107	0.0750136
$793$	2.71742	0.0964985
$794$	−17.9415	−0.636720
$795$	5.81988	0.206410
$796$	8.34748	0.295868
$797$	−33.6692	−1.19262	−0.596312	−	0.802753i	$-0.703368\pi$
$797$	−33.6692	−1.19262	−0.596312	+	0.802753i	$0.703368\pi$
$798$	18.2743	0.646902
$799$	−4.13727	−0.146366
$800$	99.1971	3.50715
$801$	−0.0257927	−0.000911340 0
$802$	11.8501	0.418443
$803$	14.4293	0.509200
$804$	48.8304	1.72211
$805$	−1.78082	−0.0627655
$806$	11.7074	0.412376
$807$	−2.57879	−0.0907778
$808$	74.2712	2.61285
$809$	32.2939	1.13539	0.567696	−	0.823238i	$-0.307835\pi$
$809$	32.2939	1.13539	0.567696	+	0.823238i	$0.307835\pi$
$810$	11.9608	0.420258
$811$	27.4278	0.963119	0.481559	−	0.876413i	$-0.340071\pi$
$811$	27.4278	0.963119	0.481559	+	0.876413i	$0.340071\pi$
$812$	31.0522	1.08972
$813$	−9.12310	−0.319961
$814$	−13.6935	−0.479957
$815$	−9.57382	−0.335356
$816$	−20.2680	−0.709523
$817$	−15.5609	−0.544405
$818$	−86.6732	−3.03046
$819$	−0.0898759	−0.00314052
$820$	−24.6258	−0.859971
$821$	−17.5646	−0.613008	−0.306504	−	0.951869i	$-0.599159\pi$
$821$	−17.5646	−0.613008	−0.306504	+	0.951869i	$0.599159\pi$
$822$	81.0301	2.82625
$823$	−7.94705	−0.277017	−0.138508	−	0.990361i	$-0.544231\pi$
$823$	−7.94705	−0.277017	−0.138508	+	0.990361i	$0.544231\pi$
$824$	30.2993	1.05552
$825$	−15.5585	−0.541678
$826$	−19.7473	−0.687097
$827$	−5.16367	−0.179558	−0.0897792	−	0.995962i	$-0.528616\pi$
$827$	−5.16367	−0.179558	−0.0897792	+	0.995962i	$0.528616\pi$
$828$	−2.43938	−0.0847743
$829$	−20.0606	−0.696734	−0.348367	−	0.937358i	$-0.613264\pi$
$829$	−20.0606	−0.696734	−0.348367	+	0.937358i	$0.613264\pi$
$830$	17.0487	0.591768
$831$	−24.7621	−0.858989
$832$	−19.3519	−0.670905
$833$	−4.70185	−0.162909
$834$	54.1240	1.87416
$835$	7.46115	0.258204
$836$	−36.4528	−1.26075
$837$	31.1943	1.07823
$838$	81.1781	2.80425
$839$	39.3019	1.35685	0.678426	−	0.734669i	$-0.262662\pi$
$839$	39.3019	1.35685	0.678426	+	0.734669i	$0.262662\pi$
$840$	7.99919	0.275998
$841$	1.56409	0.0539343
$842$	21.5883	0.743983
$843$	−28.9168	−0.995946
$844$	47.6675	1.64078
$845$	−5.87518	−0.202112
$846$	1.75162	0.0602221
$847$	−7.89870	−0.271403
$848$	−101.267	−3.47753
$849$	−32.7280	−1.12322
$850$	10.3294	0.354295
$851$	9.97300	0.341870
$852$	−12.7338	−0.436253
$853$	41.2623	1.41280	0.706398	−	0.707815i	$-0.250319\pi$
$853$	41.2623	1.41280	0.706398	+	0.707815i	$0.250319\pi$
$854$	10.9573	0.374950
$855$	0.212200	0.00725708
$856$	171.589	5.86479
$857$	4.93880	0.168706	0.0843532	−	0.996436i	$-0.473118\pi$
$857$	4.93880	0.168706	0.0843532	+	0.996436i	$0.473118\pi$
$858$	6.21109	0.212043
$859$	−38.1044	−1.30011	−0.650053	−	0.759889i	$-0.725253\pi$
$859$	−38.1044	−1.30011	−0.650053	+	0.759889i	$0.725253\pi$
$860$	−10.8070	−0.368516
$861$	17.7857	0.606134
$862$	67.9250	2.31353
$863$	−1.71273	−0.0583019	−0.0291510	−	0.999575i	$-0.509280\pi$
$863$	−1.71273	−0.0583019	−0.0291510	+	0.999575i	$0.509280\pi$
$864$	−105.514	−3.58967
$865$	7.70808	0.262082
$866$	−63.0168	−2.14140
$867$	28.9307	0.982537
$868$	34.4648	1.16981
$869$	−8.03393	−0.272532
$870$	12.4920	0.423517
$871$	3.58004	0.121305
$872$	173.338	5.86997
$873$	0.381355	0.0129069
$874$	36.3642	1.23004
$875$	−4.76924	−0.161230
$876$	74.8945	2.53045
$877$	19.2114	0.648724	0.324362	−	0.945933i	$-0.394850\pi$
$877$	19.2114	0.648724	0.324362	+	0.945933i	$0.394850\pi$
$878$	−51.6245	−1.74224
$879$	−53.9462	−1.81956
$880$	−12.4960	−0.421238
$881$	0.0458679	0.00154533	0.000772664	−	1.00000i	$-0.499754\pi$
$881$	0.0458679	0.00154533	0.000772664		1.00000i	$0.499754\pi$
$882$	1.99065	0.0670288
$883$	42.1763	1.41935	0.709674	−	0.704531i	$-0.248842\pi$
$883$	42.1763	1.41935	0.709674	+	0.704531i	$0.248842\pi$
$884$	−3.01053	−0.101255
$885$	−5.79983	−0.194959
$886$	−58.8515	−1.97715
$887$	36.1371	1.21337	0.606683	−	0.794944i	$-0.292500\pi$
$887$	36.1371	1.21337	0.606683	+	0.794944i	$0.292500\pi$
$888$	−44.7974	−1.50330
$889$	10.2175	0.342685
$890$	0.267032	0.00895093
$891$	17.2318	0.577286
$892$	130.938	4.38412
$893$	−19.0636	−0.637938
$894$	−90.7609	−3.03550
$895$	−9.59428	−0.320701
$896$	−34.9306	−1.16695
$897$	−4.52355	−0.151037
$898$	−41.1842	−1.37433
$899$	33.9230	1.13140
$900$	−3.19279	−0.106426
$901$	−5.56661	−0.185451
$902$	−48.5951	−1.61804
$903$	7.80520	0.259741
$904$	−72.9360	−2.42581
$905$	−4.86985	−0.161879
$906$	−30.8030	−1.02336
$907$	−21.2700	−0.706259	−0.353129	−	0.935574i	$-0.614882\pi$
$907$	−21.2700	−0.706259	−0.353129	+	0.935574i	$0.614882\pi$
$908$	−19.2126	−0.637592
$909$	−0.988258	−0.0327785
$910$	0.930485	0.0308453
$911$	−10.2529	−0.339694	−0.169847	−	0.985470i	$-0.554327\pi$
$911$	−10.2529	−0.339694	−0.169847	+	0.985470i	$0.554327\pi$
$912$	−93.3902	−3.09246
$913$	24.5619	0.812880
$914$	21.4465	0.709387
$915$	3.21818	0.106390
$916$	−101.788	−3.36316
$917$	8.32821	0.275022
$918$	−10.9872	−0.362632
$919$	−39.3681	−1.29864	−0.649318	−	0.760517i	$-0.724945\pi$
$919$	−39.3681	−1.29864	−0.649318	+	0.760517i	$0.724945\pi$
$920$	15.9177	0.524791
$921$	−5.93888	−0.195693
$922$	90.5703	2.98277
$923$	−0.933589	−0.0307295
$924$	18.2845	0.601515
$925$	13.0532	0.429187
$926$	−86.9674	−2.85793
$927$	−0.403164	−0.0132416
$928$	−114.745	−3.76667
$929$	48.6956	1.59765	0.798826	−	0.601562i	$-0.205455\pi$
$929$	48.6956	1.59765	0.798826	+	0.601562i	$0.205455\pi$
$930$	13.8648	0.454645
$931$	−21.6650	−0.710042
$932$	65.9406	2.15996
$933$	−46.0625	−1.50802
$934$	−16.4198	−0.537274
$935$	−0.686898	−0.0224640
$936$	0.803349	0.0262583
$937$	−12.4806	−0.407723	−0.203862	−	0.979000i	$-0.565349\pi$
$937$	−12.4806	−0.407723	−0.203862	+	0.979000i	$0.565349\pi$
$938$	14.4356	0.471338
$939$	50.3621	1.64351
$940$	−13.2396	−0.431829
$941$	−44.4531	−1.44913	−0.724565	−	0.689207i	$-0.757959\pi$
$941$	−44.4531	−1.44913	−0.724565	+	0.689207i	$0.757959\pi$
$942$	−71.8028	−2.33946
$943$	35.3919	1.15252
$944$	100.918	3.28461
$945$	2.47927	0.0806505
$946$	−21.3259	−0.693365
$947$	−7.49160	−0.243444	−0.121722	−	0.992564i	$-0.538842\pi$
$947$	−7.49160	−0.243444	−0.121722	+	0.992564i	$0.538842\pi$
$948$	−41.6996	−1.35434
$949$	5.49096	0.178244
$950$	47.5954	1.54420
$951$	14.6076	0.473684
$952$	−7.65109	−0.247973
$953$	−14.6341	−0.474045	−0.237023	−	0.971504i	$-0.576172\pi$
$953$	−14.6341	−0.474045	−0.237023	+	0.971504i	$0.576172\pi$
$954$	2.35677	0.0763033
$955$	−3.73629	−0.120903
$956$	165.760	5.36106
$957$	17.9971	0.581762
$958$	−49.3693	−1.59505
$959$	17.4887	0.564741
$960$	−22.9179	−0.739673
$961$	6.65114	0.214553
$962$	−5.21095	−0.168008
$963$	−2.28317	−0.0735743
$964$	−39.2891	−1.26542
$965$	11.2521	0.362219
$966$	−18.2400	−0.586862
$967$	1.24602	0.0400692	0.0200346	−	0.999799i	$-0.493622\pi$
$967$	1.24602	0.0400692	0.0200346	+	0.999799i	$0.493622\pi$
$968$	70.6020	2.26923
$969$	−5.13362	−0.164916
$970$	−3.94817	−0.126768
$971$	15.4693	0.496434	0.248217	−	0.968704i	$-0.420155\pi$
$971$	15.4693	0.496434	0.248217	+	0.968704i	$0.420155\pi$
$972$	6.93804	0.222538
$973$	11.6816	0.374494
$974$	63.5846	2.03738
$975$	−5.92066	−0.189613
$976$	−55.9969	−1.79242
$977$	29.2177	0.934757	0.467379	−	0.884057i	$-0.345199\pi$
$977$	29.2177	0.934757	0.467379	+	0.884057i	$0.345199\pi$
$978$	−98.0598	−3.13561
$979$	0.384710	0.0122954
$980$	−15.0463	−0.480637
$981$	−2.30645	−0.0736393
$982$	11.6745	0.372550
$983$	−2.39930	−0.0765259	−0.0382629	−	0.999268i	$-0.512182\pi$
$983$	−2.39930	−0.0765259	−0.0382629	+	0.999268i	$0.512182\pi$
$984$	−158.976	−5.06796
$985$	2.41949	0.0770913
$986$	−11.9483	−0.380513
$987$	9.56214	0.304366
$988$	−13.8718	−0.441321
$989$	15.5317	0.493878
$990$	0.290816	0.00924275
$991$	51.4773	1.63523	0.817614	−	0.575766i	$-0.195296\pi$
$991$	51.4773	1.63523	0.817614	+	0.575766i	$0.195296\pi$
$992$	−127.355	−4.04352
$993$	−22.1203	−0.701968
$994$	−3.76445	−0.119401
$995$	0.724779	0.0229771
$996$	127.487	4.03957
$997$	−41.2171	−1.30536	−0.652680	−	0.757634i	$-0.726355\pi$
$997$	−41.2171	−1.30536	−0.652680	+	0.757634i	$0.726355\pi$
$998$	32.6862	1.03466
$999$	−13.8845	−0.439286

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.2.a.b.1.1	✓	18
3.2	odd	2		4923.2.a.l.1.18		18
4.3	odd	2		8752.2.a.s.1.13		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.2.a.b.1.1	✓	18	1.1	even	1	trivial
4923.2.a.l.1.18		18	3.2	odd	2
8752.2.a.s.1.13		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)

\(f(q)\)	\(=\)	\(q-2.72204 q^{2} -1.76734 q^{3} +5.40952 q^{4} +0.469688 q^{5} +4.81078 q^{6} +1.03831 q^{7} -9.28087 q^{8} +0.123492 q^{9} +O(q^{10})\)	\(q-2.72204 q^{2} -1.76734 q^{3} +5.40952 q^{4} +0.469688 q^{5} +4.81078 q^{6} +1.03831 q^{7} -9.28087 q^{8} +0.123492 q^{9} -1.27851 q^{10} -1.84194 q^{11} -9.56047 q^{12} -0.700934 q^{13} -2.82633 q^{14} -0.830099 q^{15} +14.4439 q^{16} +0.793975 q^{17} -0.336150 q^{18} +3.65845 q^{19} +2.54079 q^{20} -1.83505 q^{21} +5.01384 q^{22} -3.65159 q^{23} +16.4025 q^{24} -4.77939 q^{25} +1.90797 q^{26} +5.08377 q^{27} +5.61677 q^{28} +5.52848 q^{29} +2.25957 q^{30} +6.13605 q^{31} -20.7552 q^{32} +3.25534 q^{33} -2.16124 q^{34} +0.487683 q^{35} +0.668032 q^{36} -2.73114 q^{37} -9.95846 q^{38} +1.23879 q^{39} -4.35911 q^{40} -9.69220 q^{41} +4.99509 q^{42} -4.25340 q^{43} -9.96402 q^{44} +0.0580027 q^{45} +9.93978 q^{46} -5.21084 q^{47} -25.5273 q^{48} -5.92191 q^{49} +13.0097 q^{50} -1.40322 q^{51} -3.79172 q^{52} -7.01107 q^{53} -13.8382 q^{54} -0.865138 q^{55} -9.63643 q^{56} -6.46572 q^{57} -15.0488 q^{58} +6.98691 q^{59} -4.49044 q^{60} -3.87686 q^{61} -16.7026 q^{62} +0.128223 q^{63} +27.6087 q^{64} -0.329220 q^{65} -8.86117 q^{66} -5.10753 q^{67} +4.29503 q^{68} +6.45360 q^{69} -1.32749 q^{70} +1.33192 q^{71} -1.14611 q^{72} -7.83377 q^{73} +7.43429 q^{74} +8.44681 q^{75} +19.7905 q^{76} -1.91251 q^{77} -3.37204 q^{78} +4.36166 q^{79} +6.78412 q^{80} -9.35523 q^{81} +26.3826 q^{82} -13.3348 q^{83} -9.92674 q^{84} +0.372921 q^{85} +11.5779 q^{86} -9.77071 q^{87} +17.0948 q^{88} -0.208861 q^{89} -0.157886 q^{90} -0.727788 q^{91} -19.7533 q^{92} -10.8445 q^{93} +14.1841 q^{94} +1.71833 q^{95} +36.6814 q^{96} +3.08809 q^{97} +16.1197 q^{98} -0.227465 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 4 q^{2} - 10 q^{3} + 16 q^{4} - 27 q^{5} - 3 q^{6} - 11 q^{7} - 12 q^{8} + 14 q^{9}+O(q^{10}) \) 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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