LMFDB - Embedded newform 547.2.a.b.1.13

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			1.13
Root			$-0.957552$ 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)

$f(q)$	$=$	$q+0.957552 q^{2} +0.564538 q^{3} -1.08309 q^{4} -4.10274 q^{5} +0.540575 q^{6} +4.97202 q^{7} -2.95222 q^{8} -2.68130 q^{9} +O(q^{10})$	\(q+0.957552 q^{2} +0.564538 q^{3} -1.08309 q^{4} -4.10274 q^{5} +0.540575 q^{6} +4.97202 q^{7} -2.95222 q^{8} -2.68130 q^{9} -3.92859 q^{10} +0.0769657 q^{11} -0.611448 q^{12} -3.33082 q^{13} +4.76097 q^{14} -2.31615 q^{15} -0.660720 q^{16} -5.96711 q^{17} -2.56748 q^{18} -7.28632 q^{19} +4.44365 q^{20} +2.80689 q^{21} +0.0736987 q^{22} +2.10873 q^{23} -1.66664 q^{24} +11.8325 q^{25} -3.18943 q^{26} -3.20731 q^{27} -5.38516 q^{28} +3.24142 q^{29} -2.21784 q^{30} -6.20019 q^{31} +5.27177 q^{32} +0.0434501 q^{33} -5.71382 q^{34} -20.3989 q^{35} +2.90410 q^{36} +2.16514 q^{37} -6.97703 q^{38} -1.88037 q^{39} +12.1122 q^{40} -5.00098 q^{41} +2.68775 q^{42} -1.06278 q^{43} -0.0833611 q^{44} +11.0007 q^{45} +2.01922 q^{46} +5.86219 q^{47} -0.373001 q^{48} +17.7210 q^{49} +11.3302 q^{50} -3.36866 q^{51} +3.60759 q^{52} -9.01187 q^{53} -3.07116 q^{54} -0.315771 q^{55} -14.6785 q^{56} -4.11340 q^{57} +3.10383 q^{58} -4.47532 q^{59} +2.50861 q^{60} +4.58346 q^{61} -5.93701 q^{62} -13.3315 q^{63} +6.36944 q^{64} +13.6655 q^{65} +0.0416057 q^{66} +10.6474 q^{67} +6.46294 q^{68} +1.19046 q^{69} -19.5330 q^{70} +3.35886 q^{71} +7.91579 q^{72} +14.7261 q^{73} +2.07323 q^{74} +6.67989 q^{75} +7.89177 q^{76} +0.382675 q^{77} -1.80056 q^{78} -2.00500 q^{79} +2.71076 q^{80} +6.23324 q^{81} -4.78870 q^{82} -8.56498 q^{83} -3.04013 q^{84} +24.4815 q^{85} -1.01767 q^{86} +1.82990 q^{87} -0.227220 q^{88} -8.84846 q^{89} +10.5337 q^{90} -16.5609 q^{91} -2.28395 q^{92} -3.50024 q^{93} +5.61336 q^{94} +29.8939 q^{95} +2.97612 q^{96} -0.394709 q^{97} +16.9688 q^{98} -0.206368 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.957552	0.677092	0.338546	−	0.940950i	$-0.390065\pi$
$2$	0.957552	0.677092	0.338546	+	0.940950i	$0.390065\pi$
$3$	0.564538	0.325936	0.162968	−	0.986631i	$-0.447893\pi$
$3$	0.564538	0.325936	0.162968	+	0.986631i	$0.447893\pi$
$4$	−1.08309	−0.541547
$5$	−4.10274	−1.83480	−0.917401	−	0.397964i	$-0.869717\pi$
$5$	−4.10274	−1.83480	−0.917401	+	0.397964i	$0.869717\pi$
$6$	0.540575	0.220689
$7$	4.97202	1.87925	0.939623	−	0.342210i	$-0.111176\pi$
$7$	4.97202	1.87925	0.939623	+	0.342210i	$0.111176\pi$
$8$	−2.95222	−1.04377
$9$	−2.68130	−0.893766
$10$	−3.92859	−1.24233
$11$	0.0769657	0.0232060	0.0116030	−	0.999933i	$-0.496307\pi$
$11$	0.0769657	0.0232060	0.0116030	+	0.999933i	$0.496307\pi$
$12$	−0.611448	−0.176510
$13$	−3.33082	−0.923803	−0.461901	−	0.886931i	$-0.652833\pi$
$13$	−3.33082	−0.923803	−0.461901	+	0.886931i	$0.652833\pi$
$14$	4.76097	1.27242
$15$	−2.31615	−0.598028
$16$	−0.660720	−0.165180
$17$	−5.96711	−1.44724	−0.723618	−	0.690200i	$-0.757522\pi$
$17$	−5.96711	−1.44724	−0.723618	+	0.690200i	$0.757522\pi$
$18$	−2.56748	−0.605161
$19$	−7.28632	−1.67160	−0.835798	−	0.549037i	$-0.814994\pi$
$19$	−7.28632	−1.67160	−0.835798	+	0.549037i	$0.814994\pi$
$20$	4.44365	0.993631
$21$	2.80689	0.612514
$22$	0.0736987	0.0157126
$23$	2.10873	0.439700	0.219850	−	0.975534i	$-0.429443\pi$
$23$	2.10873	0.439700	0.219850	+	0.975534i	$0.429443\pi$
$24$	−1.66664	−0.340202
$25$	11.8325	2.36650
$26$	−3.18943	−0.625499
$27$	−3.20731	−0.617247
$28$	−5.38516	−1.01770
$29$	3.24142	0.601916	0.300958	−	0.953637i	$-0.402694\pi$
$29$	3.24142	0.601916	0.300958	+	0.953637i	$0.402694\pi$
$30$	−2.21784	−0.404920
$31$	−6.20019	−1.11359	−0.556794	−	0.830651i	$-0.687969\pi$
$31$	−6.20019	−1.11359	−0.556794	+	0.830651i	$0.687969\pi$
$32$	5.27177	0.931927
$33$	0.0434501	0.00756369
$34$	−5.71382	−0.979912
$35$	−20.3989	−3.44805
$36$	2.90410	0.484016
$37$	2.16514	0.355946	0.177973	−	0.984035i	$-0.443046\pi$
$37$	2.16514	0.355946	0.177973	+	0.984035i	$0.443046\pi$
$38$	−6.97703	−1.13182
$39$	−1.88037	−0.301101
$40$	12.1122	1.91511
$41$	−5.00098	−0.781021	−0.390511	−	0.920598i	$-0.627702\pi$
$41$	−5.00098	−0.781021	−0.390511	+	0.920598i	$0.627702\pi$
$42$	2.68775	0.414728
$43$	−1.06278	−0.162072	−0.0810362	−	0.996711i	$-0.525823\pi$
$43$	−1.06278	−0.162072	−0.0810362	+	0.996711i	$0.525823\pi$
$44$	−0.0833611	−0.0125672
$45$	11.0007	1.63988
$46$	2.01922	0.297717
$47$	5.86219	0.855089	0.427544	−	0.903994i	$-0.359379\pi$
$47$	5.86219	0.855089	0.427544	+	0.903994i	$0.359379\pi$
$48$	−0.373001	−0.0538381
$49$	17.7210	2.53157
$50$	11.3302	1.60234
$51$	−3.36866	−0.471707
$52$	3.60759	0.500283
$53$	−9.01187	−1.23788	−0.618938	−	0.785440i	$-0.712437\pi$
$53$	−9.01187	−1.23788	−0.618938	+	0.785440i	$0.712437\pi$
$54$	−3.07116	−0.417933
$55$	−0.315771	−0.0425785
$56$	−14.6785	−1.96150
$57$	−4.11340	−0.544834
$58$	3.10383	0.407552
$59$	−4.47532	−0.582637	−0.291319	−	0.956626i	$-0.594094\pi$
$59$	−4.47532	−0.582637	−0.291319	+	0.956626i	$0.594094\pi$
$60$	2.50861	0.323860
$61$	4.58346	0.586851	0.293426	−	0.955982i	$-0.405205\pi$
$61$	4.58346	0.586851	0.293426	+	0.955982i	$0.405205\pi$
$62$	−5.93701	−0.754001
$63$	−13.3315	−1.67961
$64$	6.36944	0.796180
$65$	13.6655	1.69500
$66$	0.0416057	0.00512131
$67$	10.6474	1.30078	0.650391	−	0.759599i	$-0.274605\pi$
$67$	10.6474	1.30078	0.650391	+	0.759599i	$0.274605\pi$
$68$	6.46294	0.783747
$69$	1.19046	0.143314
$70$	−19.5330	−2.33464
$71$	3.35886	0.398624	0.199312	−	0.979936i	$-0.436129\pi$
$71$	3.35886	0.398624	0.199312	+	0.979936i	$0.436129\pi$
$72$	7.91579	0.932884
$73$	14.7261	1.72356	0.861779	−	0.507284i	$-0.169351\pi$
$73$	14.7261	1.72356	0.861779	+	0.507284i	$0.169351\pi$
$74$	2.07323	0.241008
$75$	6.67989	0.771327
$76$	7.89177	0.905248
$77$	0.382675	0.0436099
$78$	−1.80056	−0.203873
$79$	−2.00500	−0.225580	−0.112790	−	0.993619i	$-0.535979\pi$
$79$	−2.00500	−0.225580	−0.112790	+	0.993619i	$0.535979\pi$
$80$	2.71076	0.303072
$81$	6.23324	0.692583
$82$	−4.78870	−0.528823
$83$	−8.56498	−0.940129	−0.470065	−	0.882632i	$-0.655769\pi$
$83$	−8.56498	−0.940129	−0.470065	+	0.882632i	$0.655769\pi$
$84$	−3.04013	−0.331705
$85$	24.4815	2.65539
$86$	−1.01767	−0.109738
$87$	1.82990	0.196186
$88$	−0.227220	−0.0242217
$89$	−8.84846	−0.937935	−0.468967	−	0.883215i	$-0.655374\pi$
$89$	−8.84846	−0.937935	−0.468967	+	0.883215i	$0.655374\pi$
$90$	10.5337	1.11035
$91$	−16.5609	−1.73605
$92$	−2.28395	−0.238118
$93$	−3.50024	−0.362958
$94$	5.61336	0.578973
$95$	29.8939	3.06705
$96$	2.97612	0.303749
$97$	−0.394709	−0.0400766	−0.0200383	−	0.999799i	$-0.506379\pi$
$97$	−0.394709	−0.0400766	−0.0200383	+	0.999799i	$0.506379\pi$
$98$	16.9688	1.71410
$99$	−0.206368	−0.0207408
$100$	−12.8157	−1.28157
$101$	−5.67033	−0.564219	−0.282110	−	0.959382i	$-0.591034\pi$
$101$	−5.67033	−0.564219	−0.282110	+	0.959382i	$0.591034\pi$
$102$	−3.22567	−0.319389
$103$	−12.2307	−1.20513	−0.602565	−	0.798069i	$-0.705855\pi$
$103$	−12.2307	−1.20513	−0.602565	+	0.798069i	$0.705855\pi$
$104$	9.83332	0.964236
$105$	−11.5160	−1.12384
$106$	−8.62934	−0.838155
$107$	−8.31411	−0.803755	−0.401878	−	0.915693i	$-0.631642\pi$
$107$	−8.31411	−0.803755	−0.401878	+	0.915693i	$0.631642\pi$
$108$	3.47382	0.334268
$109$	0.677082	0.0648527	0.0324263	−	0.999474i	$-0.489677\pi$
$109$	0.677082	0.0648527	0.0324263	+	0.999474i	$0.489677\pi$
$110$	−0.302367	−0.0288295
$111$	1.22230	0.116016
$112$	−3.28511	−0.310414
$113$	−8.32143	−0.782814	−0.391407	−	0.920218i	$-0.628012\pi$
$113$	−8.32143	−0.782814	−0.391407	+	0.920218i	$0.628012\pi$
$114$	−3.93880	−0.368902
$115$	−8.65156	−0.806763
$116$	−3.51076	−0.325966
$117$	8.93091	0.825663
$118$	−4.28535	−0.394499
$119$	−29.6686	−2.71972
$120$	6.83780	0.624203
$121$	−10.9941	−0.999461
$122$	4.38890	0.397352
$123$	−2.82324	−0.254563
$124$	6.71539	0.603060
$125$	−28.0319	−2.50725
$126$	−12.7656	−1.13725
$127$	9.98242	0.885796	0.442898	−	0.896572i	$-0.353950\pi$
$127$	9.98242	0.885796	0.442898	+	0.896572i	$0.353950\pi$
$128$	−4.44448	−0.392840
$129$	−0.599980	−0.0528253
$130$	13.0854	1.14767
$131$	1.15417	0.100840	0.0504201	−	0.998728i	$-0.483944\pi$
$131$	1.15417	0.100840	0.0504201	+	0.998728i	$0.483944\pi$
$132$	−0.0470605	−0.00409609
$133$	−36.2277	−3.14134
$134$	10.1954	0.880749
$135$	13.1588	1.13253
$136$	17.6162	1.51058
$137$	5.05259	0.431672	0.215836	−	0.976430i	$-0.430752\pi$
$137$	5.05259	0.431672	0.215836	+	0.976430i	$0.430752\pi$
$138$	1.13992	0.0970368
$139$	−3.30416	−0.280256	−0.140128	−	0.990133i	$-0.544751\pi$
$139$	−3.30416	−0.280256	−0.140128	+	0.990133i	$0.544751\pi$
$140$	22.0939	1.86728
$141$	3.30943	0.278704
$142$	3.21629	0.269905
$143$	−0.256359	−0.0214378
$144$	1.77159	0.147632
$145$	−13.2987	−1.10440
$146$	14.1010	1.16701
$147$	10.0042	0.825130
$148$	−2.34505	−0.192762
$149$	−23.7638	−1.94680	−0.973402	−	0.229103i	$-0.926421\pi$
$149$	−23.7638	−1.94680	−0.973402	+	0.229103i	$0.926421\pi$
$150$	6.39634	0.522259
$151$	−5.72927	−0.466242	−0.233121	−	0.972448i	$-0.574894\pi$
$151$	−5.72927	−0.466242	−0.233121	+	0.972448i	$0.574894\pi$
$152$	21.5108	1.74476
$153$	15.9996	1.29349
$154$	0.366431	0.0295279
$155$	25.4378	2.04321
$156$	2.03662	0.163060
$157$	5.46006	0.435760	0.217880	−	0.975976i	$-0.430086\pi$
$157$	5.46006	0.435760	0.217880	+	0.975976i	$0.430086\pi$
$158$	−1.91989	−0.152738
$159$	−5.08754	−0.403468
$160$	−21.6287	−1.70990
$161$	10.4846	0.826305
$162$	5.96866	0.468942
$163$	−4.79414	−0.375506	−0.187753	−	0.982216i	$-0.560120\pi$
$163$	−4.79414	−0.375506	−0.187753	+	0.982216i	$0.560120\pi$
$164$	5.41653	0.422960
$165$	−0.178264	−0.0138779
$166$	−8.20142	−0.636554
$167$	8.88965	0.687902	0.343951	−	0.938988i	$-0.388235\pi$
$167$	8.88965	0.687902	0.343951	+	0.938988i	$0.388235\pi$
$168$	−8.28658	−0.639323
$169$	−1.90565	−0.146588
$170$	23.4423	1.79794
$171$	19.5368	1.49401
$172$	1.15109	0.0877698
$173$	18.2314	1.38611	0.693055	−	0.720885i	$-0.256264\pi$
$173$	18.2314	1.38611	0.693055	+	0.720885i	$0.256264\pi$
$174$	1.75223	0.132836
$175$	58.8314	4.44723
$176$	−0.0508528	−0.00383317
$177$	−2.52649	−0.189903
$178$	−8.47286	−0.635068
$179$	−10.4779	−0.783152	−0.391576	−	0.920146i	$-0.628070\pi$
$179$	−10.4779	−0.783152	−0.391576	+	0.920146i	$0.628070\pi$
$180$	−11.9148	−0.888074
$181$	−11.8241	−0.878881	−0.439441	−	0.898272i	$-0.644823\pi$
$181$	−11.8241	−0.878881	−0.439441	+	0.898272i	$0.644823\pi$
$182$	−15.8579	−1.17547
$183$	2.58753	0.191276
$184$	−6.22543	−0.458945
$185$	−8.88299	−0.653091
$186$	−3.35167	−0.245756
$187$	−0.459263	−0.0335846
$188$	−6.34931	−0.463071
$189$	−15.9468	−1.15996
$190$	28.6249	2.07667
$191$	−19.6548	−1.42217	−0.711087	−	0.703104i	$-0.751797\pi$
$191$	−19.6548	−1.42217	−0.711087	+	0.703104i	$0.751797\pi$
$192$	3.59579	0.259504
$193$	7.35743	0.529600	0.264800	−	0.964303i	$-0.414694\pi$
$193$	7.35743	0.529600	0.264800	+	0.964303i	$0.414694\pi$
$194$	−0.377955	−0.0271356
$195$	7.71469	0.552460
$196$	−19.1935	−1.37096
$197$	0.768399	0.0547462	0.0273731	−	0.999625i	$-0.491286\pi$
$197$	0.768399	0.0547462	0.0273731	+	0.999625i	$0.491286\pi$
$198$	−0.197608	−0.0140434
$199$	21.6917	1.53768	0.768841	−	0.639440i	$-0.220834\pi$
$199$	21.6917	1.53768	0.768841	+	0.639440i	$0.220834\pi$
$200$	−34.9321	−2.47008
$201$	6.01084	0.423972
$202$	−5.42964	−0.382028
$203$	16.1164	1.13115
$204$	3.64858	0.255451
$205$	20.5177	1.43302
$206$	−11.7116	−0.815984
$207$	−5.65412	−0.392989
$208$	2.20074	0.152594
$209$	−0.560797	−0.0387911
$210$	−11.0271	−0.760944
$211$	−10.4907	−0.722208	−0.361104	−	0.932526i	$-0.617600\pi$
$211$	−10.4907	−0.722208	−0.361104	+	0.932526i	$0.617600\pi$
$212$	9.76070	0.670368
$213$	1.89621	0.129926
$214$	−7.96119	−0.544216
$215$	4.36031	0.297371
$216$	9.46869	0.644263
$217$	−30.8275	−2.09271
$218$	0.648341	0.0439112
$219$	8.31343	0.561770
$220$	0.342009	0.0230583
$221$	19.8754	1.33696
$222$	1.17042	0.0785533
$223$	−18.6471	−1.24870	−0.624352	−	0.781143i	$-0.714637\pi$
$223$	−18.6471	−1.24870	−0.624352	+	0.781143i	$0.714637\pi$
$224$	26.2114	1.75132
$225$	−31.7264	−2.11509
$226$	−7.96820	−0.530037
$227$	27.9582	1.85565	0.927826	−	0.373014i	$-0.121676\pi$
$227$	27.9582	1.85565	0.927826	+	0.373014i	$0.121676\pi$
$228$	4.45520	0.295053
$229$	−9.73578	−0.643358	−0.321679	−	0.946849i	$-0.604247\pi$
$229$	−9.73578	−0.643358	−0.321679	+	0.946849i	$0.604247\pi$
$230$	−8.28432	−0.546252
$231$	0.216035	0.0142140
$232$	−9.56939	−0.628261
$233$	19.0910	1.25069	0.625347	−	0.780347i	$-0.284957\pi$
$233$	19.0910	1.25069	0.625347	+	0.780347i	$0.284957\pi$
$234$	8.55181	0.559050
$235$	−24.0511	−1.56892
$236$	4.84719	0.315525
$237$	−1.13190	−0.0735246
$238$	−28.4092	−1.84150
$239$	−26.9662	−1.74430	−0.872149	−	0.489241i	$-0.837274\pi$
$239$	−26.9662	−1.74430	−0.872149	+	0.489241i	$0.837274\pi$
$240$	1.53033	0.0987822
$241$	−6.54182	−0.421396	−0.210698	−	0.977551i	$-0.567574\pi$
$241$	−6.54182	−0.421396	−0.210698	+	0.977551i	$0.567574\pi$
$242$	−10.5274	−0.676727
$243$	13.1408	0.842984
$244$	−4.96431	−0.317808
$245$	−72.7046	−4.64493
$246$	−2.70340	−0.172363
$247$	24.2694	1.54422
$248$	18.3044	1.16233
$249$	−4.83526	−0.306422
$250$	−26.8420	−1.69764
$251$	−22.2725	−1.40583	−0.702914	−	0.711274i	$-0.748118\pi$
$251$	−22.2725	−1.40583	−0.702914	+	0.711274i	$0.748118\pi$
$252$	14.4392	0.909586
$253$	0.162300	0.0102037
$254$	9.55868	0.599765
$255$	13.8207	0.865489
$256$	−16.9947	−1.06217
$257$	−10.9352	−0.682119	−0.341060	−	0.940042i	$-0.610786\pi$
$257$	−10.9352	−0.682119	−0.341060	+	0.940042i	$0.610786\pi$
$258$	−0.574512	−0.0357675
$259$	10.7651	0.668911
$260$	−14.8010	−0.917920
$261$	−8.69120	−0.537972
$262$	1.10518	0.0682781
$263$	10.3267	0.636774	0.318387	−	0.947961i	$-0.396859\pi$
$263$	10.3267	0.636774	0.318387	+	0.947961i	$0.396859\pi$
$264$	−0.128274	−0.00789474
$265$	36.9734	2.27126
$266$	−34.6899	−2.12698
$267$	−4.99529	−0.305707
$268$	−11.5321	−0.704435
$269$	6.36422	0.388033	0.194017	−	0.980998i	$-0.437848\pi$
$269$	6.36422	0.388033	0.194017	+	0.980998i	$0.437848\pi$
$270$	12.6002	0.766823
$271$	−29.8982	−1.81619	−0.908095	−	0.418765i	$-0.862463\pi$
$271$	−29.8982	−1.81619	−0.908095	+	0.418765i	$0.862463\pi$
$272$	3.94259	0.239054
$273$	−9.34925	−0.565843
$274$	4.83812	0.292281
$275$	0.910696	0.0549171
$276$	−1.28938	−0.0776114
$277$	7.02599	0.422151	0.211076	−	0.977470i	$-0.432303\pi$
$277$	7.02599	0.422151	0.211076	+	0.977470i	$0.432303\pi$
$278$	−3.16391	−0.189759
$279$	16.6246	0.995286
$280$	60.2221	3.59896
$281$	19.7180	1.17628	0.588139	−	0.808760i	$-0.299861\pi$
$281$	19.7180	1.17628	0.588139	+	0.808760i	$0.299861\pi$
$282$	3.16895	0.188708
$283$	−3.99962	−0.237753	−0.118876	−	0.992909i	$-0.537929\pi$
$283$	−3.99962	−0.237753	−0.118876	+	0.992909i	$0.537929\pi$
$284$	−3.63796	−0.215873
$285$	16.8762	0.999662
$286$	−0.245477	−0.0145154
$287$	−24.8650	−1.46773
$288$	−14.1352	−0.832924
$289$	18.6064	1.09449
$290$	−12.7342	−0.747778
$291$	−0.222828	−0.0130624
$292$	−15.9497	−0.933387
$293$	−24.6884	−1.44231	−0.721156	−	0.692772i	$-0.756389\pi$
$293$	−24.6884	−1.44231	−0.721156	+	0.692772i	$0.756389\pi$
$294$	9.57951	0.558688
$295$	18.3611	1.06902
$296$	−6.39196	−0.371525
$297$	−0.246853	−0.0143239
$298$	−22.7551	−1.31816
$299$	−7.02379	−0.406196
$300$	−7.23495	−0.417710
$301$	−5.28416	−0.304574
$302$	−5.48608	−0.315688
$303$	−3.20112	−0.183899
$304$	4.81421	0.276114
$305$	−18.8047	−1.07676
$306$	15.3204	0.875812
$307$	5.06946	0.289329	0.144665	−	0.989481i	$-0.453790\pi$
$307$	5.06946	0.289329	0.144665	+	0.989481i	$0.453790\pi$
$308$	−0.414473	−0.0236168
$309$	−6.90472	−0.392796
$310$	24.3580	1.38344
$311$	3.96686	0.224940	0.112470	−	0.993655i	$-0.464124\pi$
$311$	3.96686	0.224940	0.112470	+	0.993655i	$0.464124\pi$
$312$	5.55128	0.314279
$313$	19.7218	1.11474	0.557371	−	0.830263i	$-0.311810\pi$
$313$	19.7218	1.11474	0.557371	+	0.830263i	$0.311810\pi$
$314$	5.22829	0.295049
$315$	54.6955	3.08174
$316$	2.17160	0.122162
$317$	−3.35701	−0.188548	−0.0942742	−	0.995546i	$-0.530053\pi$
$317$	−3.35701	−0.188548	−0.0942742	+	0.995546i	$0.530053\pi$
$318$	−4.87159	−0.273185
$319$	0.249478	0.0139681
$320$	−26.1322	−1.46083
$321$	−4.69363	−0.261973
$322$	10.0396	0.559484
$323$	43.4783	2.41919
$324$	−6.75119	−0.375066
$325$	−39.4119	−2.18618
$326$	−4.59064	−0.254252
$327$	0.382238	0.0211378
$328$	14.7640	0.815205
$329$	29.1469	1.60692
$330$	−0.170698	−0.00939659
$331$	20.3450	1.11826	0.559130	−	0.829080i	$-0.311135\pi$
$331$	20.3450	1.11826	0.559130	+	0.829080i	$0.311135\pi$
$332$	9.27668	0.509124
$333$	−5.80537	−0.318132
$334$	8.51231	0.465773
$335$	−43.6834	−2.38668
$336$	−1.85457	−0.101175
$337$	−36.6342	−1.99559	−0.997795	−	0.0663680i	$-0.978859\pi$
$337$	−36.6342	−1.99559	−0.997795	+	0.0663680i	$0.978859\pi$
$338$	−1.82476	−0.0992537
$339$	−4.69776	−0.255147
$340$	−26.5158	−1.43802
$341$	−0.477202	−0.0258420
$342$	18.7075	1.01158
$343$	53.3049	2.87820
$344$	3.13756	0.169166
$345$	−4.88414	−0.262953
$346$	17.4575	0.938523
$347$	−11.6505	−0.625434	−0.312717	−	0.949846i	$-0.601239\pi$
$347$	−11.6505	−0.625434	−0.312717	+	0.949846i	$0.601239\pi$
$348$	−1.98196	−0.106244
$349$	34.6972	1.85730	0.928650	−	0.370958i	$-0.120970\pi$
$349$	34.6972	1.85730	0.928650	+	0.370958i	$0.120970\pi$
$350$	56.3341	3.01118
$351$	10.6830	0.570214
$352$	0.405746	0.0216263
$353$	8.18793	0.435800	0.217900	−	0.975971i	$-0.430079\pi$
$353$	8.18793	0.435800	0.217900	+	0.975971i	$0.430079\pi$
$354$	−2.41924	−0.128581
$355$	−13.7805	−0.731395
$356$	9.58371	0.507936
$357$	−16.7490	−0.886454
$358$	−10.0331	−0.530266
$359$	−23.7939	−1.25579	−0.627896	−	0.778297i	$-0.716084\pi$
$359$	−23.7939	−1.25579	−0.627896	+	0.778297i	$0.716084\pi$
$360$	−32.4764	−1.71166
$361$	34.0904	1.79423
$362$	−11.3222	−0.595083
$363$	−6.20657	−0.325761
$364$	17.9370	0.940155
$365$	−60.4173	−3.16239
$366$	2.47770	0.129511
$367$	19.8468	1.03600	0.517998	−	0.855382i	$-0.326678\pi$
$367$	19.8468	1.03600	0.517998	+	0.855382i	$0.326678\pi$
$368$	−1.39328	−0.0726296
$369$	13.4091	0.698050
$370$	−8.50593	−0.442202
$371$	−44.8072	−2.32627
$372$	3.79109	0.196559
$373$	−26.5360	−1.37398	−0.686991	−	0.726666i	$-0.741069\pi$
$373$	−26.5360	−1.37398	−0.686991	+	0.726666i	$0.741069\pi$
$374$	−0.439768	−0.0227399
$375$	−15.8251	−0.817204
$376$	−17.3065	−0.892515
$377$	−10.7966	−0.556052
$378$	−15.2699	−0.785398
$379$	1.81485	0.0932226	0.0466113	−	0.998913i	$-0.485158\pi$
$379$	1.81485	0.0932226	0.0466113	+	0.998913i	$0.485158\pi$
$380$	−32.3779	−1.66095
$381$	5.63545	0.288713
$382$	−18.8205	−0.962942
$383$	20.8012	1.06289	0.531447	−	0.847092i	$-0.321649\pi$
$383$	20.8012	1.06289	0.531447	+	0.847092i	$0.321649\pi$
$384$	−2.50908	−0.128041
$385$	−1.57002	−0.0800155
$386$	7.04513	0.358588
$387$	2.84963	0.144855
$388$	0.427507	0.0217034
$389$	−9.93221	−0.503583	−0.251792	−	0.967782i	$-0.581020\pi$
$389$	−9.93221	−0.503583	−0.251792	+	0.967782i	$0.581020\pi$
$390$	7.38721	0.374066
$391$	−12.5830	−0.636350
$392$	−52.3163	−2.64237
$393$	0.651573	0.0328675
$394$	0.735782	0.0370682
$395$	8.22598	0.413894
$396$	0.223516	0.0112321
$397$	−27.7376	−1.39211	−0.696055	−	0.717989i	$-0.745063\pi$
$397$	−27.7376	−1.39211	−0.696055	+	0.717989i	$0.745063\pi$
$398$	20.7709	1.04115
$399$	−20.4519	−1.02388
$400$	−7.81796	−0.390898
$401$	37.8599	1.89063	0.945316	−	0.326157i	$-0.105754\pi$
$401$	37.8599	1.89063	0.945316	+	0.326157i	$0.105754\pi$
$402$	5.75569	0.287068
$403$	20.6517	1.02874
$404$	6.14150	0.305551
$405$	−25.5734	−1.27075
$406$	15.4323	0.765891
$407$	0.166641	0.00826010
$408$	9.94504	0.492353
$409$	3.63895	0.179934	0.0899672	−	0.995945i	$-0.471324\pi$
$409$	3.63895	0.179934	0.0899672	+	0.995945i	$0.471324\pi$
$410$	19.6468	0.970285
$411$	2.85238	0.140697
$412$	13.2470	0.652635
$413$	−22.2514	−1.09492
$414$	−5.41412	−0.266089
$415$	35.1399	1.72495
$416$	−17.5593	−0.860916
$417$	−1.86533	−0.0913454
$418$	−0.536992	−0.0262651
$419$	7.47377	0.365118	0.182559	−	0.983195i	$-0.441562\pi$
$419$	7.47377	0.365118	0.182559	+	0.983195i	$0.441562\pi$
$420$	12.4729	0.608614
$421$	23.1339	1.12748	0.563740	−	0.825952i	$-0.309362\pi$
$421$	23.1339	1.12748	0.563740	+	0.825952i	$0.309362\pi$
$422$	−10.0454	−0.489001
$423$	−15.7183	−0.764249
$424$	26.6051	1.29206
$425$	−70.6058	−3.42488
$426$	1.81572	0.0879717
$427$	22.7890	1.10284
$428$	9.00496	0.435271
$429$	−0.144724	−0.00698736
$430$	4.17523	0.201347
$431$	6.19805	0.298549	0.149275	−	0.988796i	$-0.452306\pi$
$431$	6.19805	0.298549	0.149275	+	0.988796i	$0.452306\pi$
$432$	2.11913	0.101957
$433$	2.84409	0.136678	0.0683390	−	0.997662i	$-0.478230\pi$
$433$	2.84409	0.136678	0.0683390	+	0.997662i	$0.478230\pi$
$434$	−29.5189	−1.41695
$435$	−7.50762	−0.359963
$436$	−0.733343	−0.0351208
$437$	−15.3649	−0.735001
$438$	7.96055	0.380370
$439$	5.09779	0.243304	0.121652	−	0.992573i	$-0.461181\pi$
$439$	5.09779	0.243304	0.121652	+	0.992573i	$0.461181\pi$
$440$	0.932225	0.0444421
$441$	−47.5152	−2.26263
$442$	19.0317	0.905245
$443$	13.7065	0.651217	0.325609	−	0.945505i	$-0.394431\pi$
$443$	13.7065	0.651217	0.325609	+	0.945505i	$0.394431\pi$
$444$	−1.32387	−0.0628280
$445$	36.3029	1.72092
$446$	−17.8556	−0.845487
$447$	−13.4156	−0.634534
$448$	31.6690	1.49622
$449$	30.5992	1.44407	0.722034	−	0.691858i	$-0.243207\pi$
$449$	30.5992	1.44407	0.722034	+	0.691858i	$0.243207\pi$
$450$	−30.3797	−1.43211
$451$	−0.384904	−0.0181244
$452$	9.01289	0.423931
$453$	−3.23439	−0.151965
$454$	26.7714	1.25645
$455$	67.9451	3.18531
$456$	12.1437	0.568680
$457$	17.9572	0.840001	0.420001	−	0.907524i	$-0.362030\pi$
$457$	17.9572	0.840001	0.420001	+	0.907524i	$0.362030\pi$
$458$	−9.32251	−0.435612
$459$	19.1384	0.893302
$460$	9.37046	0.436900
$461$	−18.3934	−0.856668	−0.428334	−	0.903620i	$-0.640899\pi$
$461$	−18.3934	−0.856668	−0.428334	+	0.903620i	$0.640899\pi$
$462$	0.206864	0.00962421
$463$	−34.4958	−1.60316	−0.801579	−	0.597889i	$-0.796006\pi$
$463$	−34.4958	−1.60316	−0.801579	+	0.597889i	$0.796006\pi$
$464$	−2.14167	−0.0994244
$465$	14.3606	0.665957
$466$	18.2806	0.846835
$467$	−17.7648	−0.822056	−0.411028	−	0.911623i	$-0.634830\pi$
$467$	−17.7648	−0.822056	−0.411028	+	0.911623i	$0.634830\pi$
$468$	−9.67302	−0.447135
$469$	52.9389	2.44449
$470$	−23.0301	−1.06230
$471$	3.08241	0.142030
$472$	13.2121	0.608138
$473$	−0.0817977	−0.00376106
$474$	−1.08385	−0.0497829
$475$	−86.2153	−3.95583
$476$	32.1339	1.47285
$477$	24.1635	1.10637
$478$	−25.8215	−1.18105
$479$	24.5625	1.12229	0.561145	−	0.827717i	$-0.310361\pi$
$479$	24.5625	1.12229	0.561145	+	0.827717i	$0.310361\pi$
$480$	−12.2102	−0.557318
$481$	−7.21167	−0.328824
$482$	−6.26414	−0.285324
$483$	5.91897	0.269323
$484$	11.9076	0.541255
$485$	1.61939	0.0735327
$486$	12.5830	0.570778
$487$	−35.4671	−1.60717	−0.803584	−	0.595191i	$-0.797076\pi$
$487$	−35.4671	−1.60717	−0.803584	+	0.595191i	$0.797076\pi$
$488$	−13.5314	−0.612537
$489$	−2.70648	−0.122391
$490$	−69.6184	−3.14504
$491$	27.8265	1.25579	0.627897	−	0.778296i	$-0.283916\pi$
$491$	27.8265	1.25579	0.627897	+	0.778296i	$0.283916\pi$
$492$	3.05784	0.137858
$493$	−19.3419	−0.871115
$494$	23.2392	1.04558
$495$	0.846675	0.0380552
$496$	4.09659	0.183942
$497$	16.7003	0.749112
$498$	−4.63001	−0.207476
$499$	−32.7456	−1.46590	−0.732948	−	0.680285i	$-0.761856\pi$
$499$	−32.7456	−1.46590	−0.732948	+	0.680285i	$0.761856\pi$
$500$	30.3612	1.35780
$501$	5.01855	0.224212
$502$	−21.3271	−0.951875
$503$	−8.43515	−0.376105	−0.188052	−	0.982159i	$-0.560217\pi$
$503$	−8.43515	−0.376105	−0.188052	+	0.982159i	$0.560217\pi$
$504$	39.3574	1.75312
$505$	23.2639	1.03523
$506$	0.155411	0.00690884
$507$	−1.07581	−0.0477784
$508$	−10.8119	−0.479700
$509$	−11.6347	−0.515698	−0.257849	−	0.966185i	$-0.583014\pi$
$509$	−11.6347	−0.515698	−0.257849	+	0.966185i	$0.583014\pi$
$510$	13.2341	0.586015
$511$	73.2184	3.23899
$512$	−7.38435	−0.326345
$513$	23.3695	1.03179
$514$	−10.4710	−0.461857
$515$	50.1796	2.21118
$516$	0.649834	0.0286074
$517$	0.451188	0.0198432
$518$	10.3081	0.452914
$519$	10.2923	0.451783
$520$	−40.3436	−1.76918
$521$	−6.18104	−0.270796	−0.135398	−	0.990791i	$-0.543231\pi$
$521$	−6.18104	−0.270796	−0.135398	+	0.990791i	$0.543231\pi$
$522$	−8.32228	−0.364256
$523$	−4.44108	−0.194195	−0.0970974	−	0.995275i	$-0.530956\pi$
$523$	−4.44108	−0.194195	−0.0970974	+	0.995275i	$0.530956\pi$
$524$	−1.25007	−0.0546098
$525$	33.2125	1.44951
$526$	9.88839	0.431154
$527$	36.9972	1.61162
$528$	−0.0287083	−0.00124937
$529$	−18.5533	−0.806664
$530$	35.4039	1.53785
$531$	11.9997	0.520741
$532$	39.2380	1.70118
$533$	16.6573	0.721510
$534$	−4.78325	−0.206992
$535$	34.1106	1.47473
$536$	−31.4334	−1.35772
$537$	−5.91515	−0.255258
$538$	6.09407	0.262734
$539$	1.36391	0.0587477
$540$	−14.2522	−0.613316
$541$	5.89672	0.253520	0.126760	−	0.991933i	$-0.459542\pi$
$541$	5.89672	0.253520	0.126760	+	0.991933i	$0.459542\pi$
$542$	−28.6291	−1.22973
$543$	−6.67517	−0.286459
$544$	−31.4573	−1.34872
$545$	−2.77789	−0.118992
$546$	−8.95240	−0.383127
$547$	−1.00000	−0.0427569
$547$	−1.00000	−0.0427569
$548$	−5.47243	−0.233771
$549$	−12.2896	−0.524508
$550$	0.872039	0.0371839
$551$	−23.6180	−1.00616
$552$	−3.51449	−0.149587
$553$	−9.96888	−0.423920
$554$	6.72776	0.285835
$555$	−5.01479	−0.212866
$556$	3.57872	0.151772
$557$	−1.66388	−0.0705009	−0.0352504	−	0.999379i	$-0.511223\pi$
$557$	−1.66388	−0.0705009	−0.0352504	+	0.999379i	$0.511223\pi$
$558$	15.9189	0.673900
$559$	3.53993	0.149723
$560$	13.4780	0.569548
$561$	−0.259271	−0.0109465
$562$	18.8810	0.796448
$563$	−5.94258	−0.250450	−0.125225	−	0.992128i	$-0.539965\pi$
$563$	−5.94258	−0.250450	−0.125225	+	0.992128i	$0.539965\pi$
$564$	−3.58442	−0.150931
$565$	34.1407	1.43631
$566$	−3.82985	−0.160980
$567$	30.9918	1.30153
$568$	−9.91611	−0.416071
$569$	16.7090	0.700476	0.350238	−	0.936661i	$-0.386101\pi$
$569$	16.7090	0.700476	0.350238	+	0.936661i	$0.386101\pi$
$570$	16.1599	0.676862
$571$	−12.6323	−0.528644	−0.264322	−	0.964434i	$-0.585148\pi$
$571$	−12.6323	−0.528644	−0.264322	+	0.964434i	$0.585148\pi$
$572$	0.277661	0.0116096
$573$	−11.0959	−0.463538
$574$	−23.8095	−0.993789
$575$	24.9515	1.04055
$576$	−17.0783	−0.711598
$577$	−28.5904	−1.19023	−0.595116	−	0.803640i	$-0.702894\pi$
$577$	−28.5904	−1.19023	−0.595116	+	0.803640i	$0.702894\pi$
$578$	17.8166	0.741073
$579$	4.15355	0.172616
$580$	14.4037	0.598083
$581$	−42.5853	−1.76673
$582$	−0.213370	−0.00884446
$583$	−0.693605	−0.0287262
$584$	−43.4747	−1.79900
$585$	−36.6412	−1.51493
$586$	−23.6404	−0.976578
$587$	−22.0036	−0.908187	−0.454094	−	0.890954i	$-0.650037\pi$
$587$	−22.0036	−0.908187	−0.454094	+	0.890954i	$0.650037\pi$
$588$	−10.8355	−0.446847
$589$	45.1766	1.86147
$590$	17.5817	0.723827
$591$	0.433791	0.0178438
$592$	−1.43055	−0.0587951
$593$	21.0528	0.864537	0.432268	−	0.901745i	$-0.357713\pi$
$593$	21.0528	0.864537	0.432268	+	0.901745i	$0.357713\pi$
$594$	−0.236374	−0.00969856
$595$	121.723	4.99014
$596$	25.7384	1.05429
$597$	12.2458	0.501186
$598$	−6.72564	−0.275032
$599$	10.0460	0.410468	0.205234	−	0.978713i	$-0.434204\pi$
$599$	10.0460	0.410468	0.205234	+	0.978713i	$0.434204\pi$
$600$	−19.7205	−0.805087
$601$	−24.1270	−0.984159	−0.492079	−	0.870550i	$-0.663763\pi$
$601$	−24.1270	−0.984159	−0.492079	+	0.870550i	$0.663763\pi$
$602$	−5.05986	−0.206225
$603$	−28.5487	−1.16259
$604$	6.20534	0.252492
$605$	45.1059	1.83381
$606$	−3.06524	−0.124517
$607$	−2.94817	−0.119662	−0.0598312	−	0.998209i	$-0.519056\pi$
$607$	−2.94817	−0.119662	−0.0598312	+	0.998209i	$0.519056\pi$
$608$	−38.4118	−1.55780
$609$	9.09832	0.368682
$610$	−18.0065	−0.729062
$611$	−19.5259	−0.789933
$612$	−17.3291	−0.700486
$613$	−6.60126	−0.266622	−0.133311	−	0.991074i	$-0.542561\pi$
$613$	−6.60126	−0.266622	−0.133311	+	0.991074i	$0.542561\pi$
$614$	4.85427	0.195902
$615$	11.5830	0.467073
$616$	−1.12974	−0.0455186
$617$	17.3067	0.696742	0.348371	−	0.937357i	$-0.386735\pi$
$617$	17.3067	0.696742	0.348371	+	0.937357i	$0.386735\pi$
$618$	−6.61163	−0.265959
$619$	15.8845	0.638451	0.319225	−	0.947679i	$-0.396577\pi$
$619$	15.8845	0.638451	0.319225	+	0.947679i	$0.396577\pi$
$620$	−27.5515	−1.10650
$621$	−6.76334	−0.271403
$622$	3.79847	0.152305
$623$	−43.9947	−1.76261
$624$	1.24240	0.0497358
$625$	55.8453	2.23381
$626$	18.8847	0.754783
$627$	−0.316591	−0.0126434
$628$	−5.91375	−0.235984
$629$	−12.9196	−0.515138
$630$	52.3738	2.08662
$631$	−17.6658	−0.703263	−0.351631	−	0.936139i	$-0.614373\pi$
$631$	−17.6658	−0.703263	−0.351631	+	0.936139i	$0.614373\pi$
$632$	5.91920	0.235453
$633$	−5.92238	−0.235394
$634$	−3.21451	−0.127665
$635$	−40.9553	−1.62526
$636$	5.51029	0.218497
$637$	−59.0254	−2.33867
$638$	0.238888	0.00945768
$639$	−9.00611	−0.356276
$640$	18.2345	0.720784
$641$	49.6629	1.96157	0.980783	−	0.195102i	$-0.0625037\pi$
$641$	49.6629	1.96157	0.980783	+	0.195102i	$0.0625037\pi$
$642$	−4.49439	−0.177380
$643$	−18.7162	−0.738096	−0.369048	−	0.929410i	$-0.620316\pi$
$643$	−18.7162	−0.738096	−0.369048	+	0.929410i	$0.620316\pi$
$644$	−11.3558	−0.447483
$645$	2.46156	0.0969239
$646$	41.6327	1.63802
$647$	−0.632028	−0.0248476	−0.0124238	−	0.999923i	$-0.503955\pi$
$647$	−0.632028	−0.0248476	−0.0124238	+	0.999923i	$0.503955\pi$
$648$	−18.4019	−0.722896
$649$	−0.344446	−0.0135207
$650$	−37.7389	−1.48024
$651$	−17.4033	−0.682088
$652$	5.19251	0.203354
$653$	12.2114	0.477869	0.238934	−	0.971036i	$-0.423202\pi$
$653$	12.2114	0.477869	0.238934	+	0.971036i	$0.423202\pi$
$654$	0.366013	0.0143122
$655$	−4.73526	−0.185022
$656$	3.30424	0.129009
$657$	−39.4850	−1.54046
$658$	27.9097	1.08803
$659$	−8.51707	−0.331778	−0.165889	−	0.986144i	$-0.553049\pi$
$659$	−8.51707	−0.331778	−0.165889	+	0.986144i	$0.553049\pi$
$660$	0.193077	0.00751552
$661$	−5.76560	−0.224256	−0.112128	−	0.993694i	$-0.535767\pi$
$661$	−5.76560	−0.224256	−0.112128	+	0.993694i	$0.535767\pi$
$662$	19.4814	0.757165
$663$	11.2204	0.435764
$664$	25.2857	0.981277
$665$	148.633	5.76374
$666$	−5.55895	−0.215405
$667$	6.83527	0.264663
$668$	−9.62833	−0.372531
$669$	−10.5270	−0.406998
$670$	−41.8291	−1.61600
$671$	0.352769	0.0136185
$672$	14.7973	0.570819
$673$	−18.9482	−0.730400	−0.365200	−	0.930929i	$-0.618999\pi$
$673$	−18.9482	−0.730400	−0.365200	+	0.930929i	$0.618999\pi$
$674$	−35.0791	−1.35120
$675$	−37.9504	−1.46071
$676$	2.06400	0.0793845
$677$	11.6427	0.447466	0.223733	−	0.974650i	$-0.428176\pi$
$677$	11.6427	0.447466	0.223733	+	0.974650i	$0.428176\pi$
$678$	−4.49835	−0.172758
$679$	−1.96250	−0.0753139
$680$	−72.2749	−2.77162
$681$	15.7835	0.604824
$682$	−0.456946	−0.0174974
$683$	32.4010	1.23979	0.619895	−	0.784685i	$-0.287175\pi$
$683$	32.4010	1.23979	0.619895	+	0.784685i	$0.287175\pi$
$684$	−21.1602	−0.809079
$685$	−20.7295	−0.792032
$686$	51.0422	1.94880
$687$	−5.49622	−0.209694
$688$	0.702199	0.0267711
$689$	30.0169	1.14355
$690$	−4.67682	−0.178043
$691$	33.5061	1.27463	0.637317	−	0.770602i	$-0.280044\pi$
$691$	33.5061	1.27463	0.637317	+	0.770602i	$0.280044\pi$
$692$	−19.7463	−0.750643
$693$	−1.02607	−0.0389770
$694$	−11.1560	−0.423476
$695$	13.5561	0.514213
$696$	−5.40228	−0.204773
$697$	29.8414	1.13032
$698$	33.2244	1.25756
$699$	10.7776	0.407647
$700$	−63.7199	−2.40839
$701$	−18.1131	−0.684122	−0.342061	−	0.939678i	$-0.611125\pi$
$701$	−18.1131	−0.684122	−0.342061	+	0.939678i	$0.611125\pi$
$702$	10.2295	0.386087
$703$	−15.7759	−0.594998
$704$	0.490228	0.0184762
$705$	−13.5777	−0.511367
$706$	7.84037	0.295076
$707$	−28.1930	−1.06031
$708$	2.73642	0.102841
$709$	−25.2354	−0.947736	−0.473868	−	0.880596i	$-0.657143\pi$
$709$	−25.2354	−0.947736	−0.473868	+	0.880596i	$0.657143\pi$
$710$	−13.1956	−0.495222
$711$	5.37599	0.201615
$712$	26.1226	0.978987
$713$	−13.0745	−0.489645
$714$	−16.0381	−0.600210
$715$	1.05177	0.0393341
$716$	11.3485	0.424114
$717$	−15.2234	−0.568530
$718$	−22.7839	−0.850287
$719$	1.53980	0.0574250	0.0287125	−	0.999588i	$-0.490859\pi$
$719$	1.53980	0.0574250	0.0287125	+	0.999588i	$0.490859\pi$
$720$	−7.26836	−0.270876
$721$	−60.8115	−2.26474
$722$	32.6433	1.21486
$723$	−3.69311	−0.137348
$724$	12.8067	0.475955
$725$	38.3540	1.42443
$726$	−5.94312	−0.220570
$727$	−29.6777	−1.10068	−0.550342	−	0.834939i	$-0.685503\pi$
$727$	−29.6777	−1.10068	−0.550342	+	0.834939i	$0.685503\pi$
$728$	48.8915	1.81204
$729$	−11.2812	−0.417823
$730$	−57.8527	−2.14123
$731$	6.34173	0.234557
$732$	−2.80254	−0.103585
$733$	−34.6887	−1.28126	−0.640629	−	0.767851i	$-0.721326\pi$
$733$	−34.6887	−1.28126	−0.640629	+	0.767851i	$0.721326\pi$
$734$	19.0044	0.701464
$735$	−41.0445	−1.51395
$736$	11.1167	0.409768
$737$	0.819482	0.0301860
$738$	12.8399	0.472644
$739$	−3.96845	−0.145982	−0.0729909	−	0.997333i	$-0.523254\pi$
$739$	−3.96845	−0.145982	−0.0729909	+	0.997333i	$0.523254\pi$
$740$	9.62112	0.353679
$741$	13.7010	0.503319
$742$	−42.9052	−1.57510
$743$	47.6574	1.74838	0.874190	−	0.485584i	$-0.161393\pi$
$743$	47.6574	1.74838	0.874190	+	0.485584i	$0.161393\pi$
$744$	10.3335	0.378845
$745$	97.4966	3.57200
$746$	−25.4096	−0.930312
$747$	22.9653	0.840255
$748$	0.497425	0.0181877
$749$	−41.3379	−1.51045
$750$	−15.1534	−0.553322
$751$	11.3760	0.415117	0.207558	−	0.978223i	$-0.433448\pi$
$751$	11.3760	0.415117	0.207558	+	0.978223i	$0.433448\pi$
$752$	−3.87327	−0.141243
$753$	−12.5737	−0.458210
$754$	−10.3383	−0.376498
$755$	23.5057	0.855461
$756$	17.2719	0.628172
$757$	35.7312	1.29867	0.649337	−	0.760501i	$-0.275047\pi$
$757$	35.7312	1.29867	0.649337	+	0.760501i	$0.275047\pi$
$758$	1.73781	0.0631202
$759$	0.0916244	0.00332575
$760$	−88.2534	−3.20129
$761$	45.2992	1.64209	0.821047	−	0.570861i	$-0.193390\pi$
$761$	45.2992	1.64209	0.821047	+	0.570861i	$0.193390\pi$
$762$	5.39624	0.195485
$763$	3.36646	0.121874
$764$	21.2880	0.770174
$765$	−65.6422	−2.37330
$766$	19.9183	0.719676
$767$	14.9065	0.538242
$768$	−9.59415	−0.346199
$769$	20.9580	0.755766	0.377883	−	0.925853i	$-0.376652\pi$
$769$	20.9580	0.755766	0.377883	+	0.925853i	$0.376652\pi$
$770$	−1.50337	−0.0541778
$771$	−6.17334	−0.222327
$772$	−7.96879	−0.286803
$773$	9.94311	0.357629	0.178814	−	0.983883i	$-0.442774\pi$
$773$	9.94311	0.357629	0.178814	+	0.983883i	$0.442774\pi$
$774$	2.72867	0.0980799
$775$	−73.3637	−2.63530
$776$	1.16527	0.0418307
$777$	6.07731	0.218022
$778$	−9.51061	−0.340972
$779$	36.4387	1.30555
$780$	−8.35573	−0.299183
$781$	0.258517	0.00925048
$782$	−12.0489	−0.430867
$783$	−10.3962	−0.371531
$784$	−11.7086	−0.418164
$785$	−22.4012	−0.799533
$786$	0.623915	0.0222543
$787$	43.0795	1.53562	0.767808	−	0.640680i	$-0.221347\pi$
$787$	43.0795	1.53562	0.767808	+	0.640680i	$0.221347\pi$
$788$	−0.832248	−0.0296476
$789$	5.82984	0.207548
$790$	7.87680	0.280244
$791$	−41.3743	−1.47110
$792$	0.609244	0.0216486
$793$	−15.2667	−0.542135
$794$	−26.5602	−0.942586
$795$	20.8729	0.740285
$796$	−23.4941	−0.832727
$797$	19.8313	0.702460	0.351230	−	0.936289i	$-0.385763\pi$
$797$	19.8313	0.702460	0.351230	+	0.936289i	$0.385763\pi$
$798$	−19.5838	−0.693258
$799$	−34.9804	−1.23752
$800$	62.3782	2.20540
$801$	23.7253	0.838294
$802$	36.2528	1.28013
$803$	1.13340	0.0399970
$804$	−6.51031	−0.229601
$805$	−43.0157	−1.51611
$806$	19.7751	0.696548
$807$	3.59284	0.126474
$808$	16.7401	0.588914
$809$	1.62413	0.0571014	0.0285507	−	0.999592i	$-0.490911\pi$
$809$	1.62413	0.0571014	0.0285507	+	0.999592i	$0.490911\pi$
$810$	−24.4879	−0.860415
$811$	41.7383	1.46563	0.732814	−	0.680428i	$-0.238206\pi$
$811$	41.7383	1.46563	0.732814	+	0.680428i	$0.238206\pi$
$812$	−17.4556	−0.612570
$813$	−16.8787	−0.591962
$814$	0.159568	0.00559285
$815$	19.6691	0.688979
$816$	2.22574	0.0779165
$817$	7.74375	0.270920
$818$	3.48448	0.121832
$819$	44.4047	1.55162
$820$	−22.2226	−0.776047
$821$	−34.5850	−1.20703	−0.603513	−	0.797353i	$-0.706233\pi$
$821$	−34.5850	−1.20703	−0.603513	+	0.797353i	$0.706233\pi$
$822$	2.73130	0.0952651
$823$	−22.0897	−0.769999	−0.384999	−	0.922917i	$-0.625798\pi$
$823$	−22.0897	−0.769999	−0.384999	+	0.922917i	$0.625798\pi$
$824$	36.1079	1.25788
$825$	0.514123	0.0178995
$826$	−21.3069	−0.741361
$827$	4.29638	0.149400	0.0746999	−	0.997206i	$-0.476200\pi$
$827$	4.29638	0.149400	0.0746999	+	0.997206i	$0.476200\pi$
$828$	6.12395	0.212822
$829$	9.89112	0.343533	0.171766	−	0.985138i	$-0.445053\pi$
$829$	9.89112	0.343533	0.171766	+	0.985138i	$0.445053\pi$
$830$	33.6483	1.16795
$831$	3.96644	0.137594
$832$	−21.2154	−0.735513
$833$	−105.743	−3.66378
$834$	−1.78615	−0.0618492
$835$	−36.4720	−1.26216
$836$	0.607396	0.0210072
$837$	19.8859	0.687358
$838$	7.15653	0.247218
$839$	−45.2914	−1.56363	−0.781817	−	0.623509i	$-0.785707\pi$
$839$	−45.2914	−1.56363	−0.781817	+	0.623509i	$0.785707\pi$
$840$	33.9977	1.17303
$841$	−18.4932	−0.637697
$842$	22.1520	0.763407
$843$	11.1316	0.383391
$844$	11.3624	0.391109
$845$	7.81838	0.268960
$846$	−15.0511	−0.517466
$847$	−54.6628	−1.87823
$848$	5.95432	0.204472
$849$	−2.25794	−0.0774922
$850$	−67.6087	−2.31896
$851$	4.56568	0.156510
$852$	−2.05377	−0.0703610
$853$	−54.9342	−1.88091	−0.940456	−	0.339916i	$-0.889601\pi$
$853$	−54.9342	−1.88091	−0.940456	+	0.339916i	$0.889601\pi$
$854$	21.8217	0.746723
$855$	−80.1544	−2.74122
$856$	24.5451	0.838934
$857$	−0.342745	−0.0117079	−0.00585397	−	0.999983i	$-0.501863\pi$
$857$	−0.342745	−0.0117079	−0.00585397	+	0.999983i	$0.501863\pi$
$858$	−0.138581	−0.00473108
$859$	13.8090	0.471157	0.235578	−	0.971855i	$-0.424302\pi$
$859$	13.8090	0.471157	0.235578	+	0.971855i	$0.424302\pi$
$860$	−4.72263	−0.161040
$861$	−14.0372	−0.478387
$862$	5.93495	0.202145
$863$	−27.0862	−0.922025	−0.461013	−	0.887394i	$-0.652514\pi$
$863$	−27.0862	−0.922025	−0.461013	+	0.887394i	$0.652514\pi$
$864$	−16.9082	−0.575229
$865$	−74.7988	−2.54324
$866$	2.72336	0.0925435
$867$	10.5040	0.356735
$868$	33.3891	1.13330
$869$	−0.154316	−0.00523481
$870$	−7.18894	−0.243728
$871$	−35.4644	−1.20167
$872$	−1.99890	−0.0676912
$873$	1.05833	0.0358191
$874$	−14.7127	−0.497663
$875$	−139.375	−4.71175
$876$	−9.00423	−0.304225
$877$	37.0243	1.25022	0.625111	−	0.780536i	$-0.285054\pi$
$877$	37.0243	1.25022	0.625111	+	0.780536i	$0.285054\pi$
$878$	4.88140	0.164739
$879$	−13.9376	−0.470102
$880$	0.208636	0.00703311
$881$	6.89398	0.232264	0.116132	−	0.993234i	$-0.462950\pi$
$881$	6.89398	0.232264	0.116132	+	0.993234i	$0.462950\pi$
$882$	−45.4983	−1.53201
$883$	9.37818	0.315601	0.157801	−	0.987471i	$-0.449560\pi$
$883$	9.37818	0.315601	0.157801	+	0.987471i	$0.449560\pi$
$884$	−21.5269	−0.724027
$885$	10.3655	0.348434
$886$	13.1247	0.440934
$887$	33.7032	1.13164	0.565822	−	0.824528i	$-0.308559\pi$
$887$	33.7032	1.13164	0.565822	+	0.824528i	$0.308559\pi$
$888$	−3.60851	−0.121094
$889$	49.6328	1.66463
$890$	34.7620	1.16522
$891$	0.479746	0.0160721
$892$	20.1966	0.676232
$893$	−42.7138	−1.42936
$894$	−12.8461	−0.429638
$895$	42.9879	1.43693
$896$	−22.0980	−0.738244
$897$	−3.96520	−0.132394
$898$	29.3004	0.977766
$899$	−20.0974	−0.670286
$900$	34.3627	1.14542
$901$	53.7748	1.79150
$902$	−0.368566	−0.0122719
$903$	−2.98311	−0.0992717
$904$	24.5667	0.817076
$905$	48.5114	1.61257
$906$	−3.09710	−0.102894
$907$	−25.0104	−0.830455	−0.415228	−	0.909718i	$-0.636298\pi$
$907$	−25.0104	−0.830455	−0.415228	+	0.909718i	$0.636298\pi$
$908$	−30.2814	−1.00492
$909$	15.2038	0.504280
$910$	65.0609	2.15675
$911$	−40.4013	−1.33855	−0.669277	−	0.743013i	$-0.733396\pi$
$911$	−40.4013	−1.33855	−0.669277	+	0.743013i	$0.733396\pi$
$912$	2.71781	0.0899955
$913$	−0.659210	−0.0218167
$914$	17.1949	0.568758
$915$	−10.6160	−0.350954
$916$	10.5448	0.348409
$917$	5.73856	0.189504
$918$	18.3260	0.604847
$919$	8.97289	0.295988	0.147994	−	0.988988i	$-0.452718\pi$
$919$	8.97289	0.295988	0.147994	+	0.988988i	$0.452718\pi$
$920$	25.5413	0.842073
$921$	2.86190	0.0943028
$922$	−17.6127	−0.580043
$923$	−11.1878	−0.368250
$924$	−0.233986	−0.00769757
$925$	25.6189	0.842346
$926$	−33.0316	−1.08548
$927$	32.7943	1.07710
$928$	17.0880	0.560942
$929$	−1.61228	−0.0528973	−0.0264487	−	0.999650i	$-0.508420\pi$
$929$	−1.61228	−0.0528973	−0.0264487	+	0.999650i	$0.508420\pi$
$930$	13.7510	0.450914
$931$	−129.121	−4.23176
$932$	−20.6774	−0.677310
$933$	2.23944	0.0733161
$934$	−17.0107	−0.556607
$935$	1.88424	0.0616212
$936$	−26.3660	−0.861801
$937$	−12.9284	−0.422351	−0.211176	−	0.977448i	$-0.567729\pi$
$937$	−12.9284	−0.422351	−0.211176	+	0.977448i	$0.567729\pi$
$938$	50.6918	1.65514
$939$	11.1337	0.363335
$940$	26.0496	0.849643
$941$	−18.4517	−0.601510	−0.300755	−	0.953701i	$-0.597239\pi$
$941$	−18.4517	−0.601510	−0.300755	+	0.953701i	$0.597239\pi$
$942$	2.95157	0.0961672
$943$	−10.5457	−0.343415
$944$	2.95693	0.0962399
$945$	65.4256	2.12829
$946$	−0.0783255	−0.00254658
$947$	12.2973	0.399607	0.199803	−	0.979836i	$-0.435970\pi$
$947$	12.2973	0.399607	0.199803	+	0.979836i	$0.435970\pi$
$948$	1.22595	0.0398170
$949$	−49.0499	−1.59223
$950$	−82.5556	−2.67846
$951$	−1.89516	−0.0614548
$952$	87.5883	2.83875
$953$	−2.51896	−0.0815970	−0.0407985	−	0.999167i	$-0.512990\pi$
$953$	−2.51896	−0.0815970	−0.0407985	+	0.999167i	$0.512990\pi$
$954$	23.1378	0.749114
$955$	80.6387	2.60941
$956$	29.2069	0.944619
$957$	0.140840	0.00455271
$958$	23.5199	0.759894
$959$	25.1216	0.811218
$960$	−14.7526	−0.476138
$961$	7.44239	0.240077
$962$	−6.90555	−0.222644
$963$	22.2926	0.718369
$964$	7.08541	0.228206
$965$	−30.1857	−0.971711
$966$	5.66773	0.182356
$967$	−45.0973	−1.45023	−0.725116	−	0.688627i	$-0.758214\pi$
$967$	−45.0973	−1.45023	−0.725116	+	0.688627i	$0.758214\pi$
$968$	32.4570	1.04321
$969$	24.5451	0.788503
$970$	1.55065	0.0497884
$971$	35.4672	1.13820	0.569098	−	0.822270i	$-0.307293\pi$
$971$	35.4672	1.13820	0.569098	+	0.822270i	$0.307293\pi$
$972$	−14.2328	−0.456516
$973$	−16.4284	−0.526669
$974$	−33.9616	−1.08820
$975$	−22.2495	−0.712554
$976$	−3.02838	−0.0969360
$977$	8.98700	0.287520	0.143760	−	0.989613i	$-0.454081\pi$
$977$	8.98700	0.287520	0.143760	+	0.989613i	$0.454081\pi$
$978$	−2.59159	−0.0828699
$979$	−0.681028	−0.0217658
$980$	78.7459	2.51545
$981$	−1.81546	−0.0579631
$982$	26.6454	0.850287
$983$	−8.91145	−0.284231	−0.142116	−	0.989850i	$-0.545390\pi$
$983$	−8.91145	−0.284231	−0.142116	+	0.989850i	$0.545390\pi$
$984$	8.33484	0.265705
$985$	−3.15254	−0.100448
$986$	−18.5209	−0.589825
$987$	16.4546	0.523754
$988$	−26.2860	−0.836270
$989$	−2.24111	−0.0712633
$990$	0.810735	0.0257669
$991$	24.7481	0.786149	0.393074	−	0.919507i	$-0.371411\pi$
$991$	24.7481	0.786149	0.393074	+	0.919507i	$0.371411\pi$
$992$	−32.6860	−1.03778
$993$	11.4855	0.364481
$994$	15.9914	0.507218
$995$	−88.9954	−2.82134
$996$	5.23704	0.165942
$997$	−39.8404	−1.26176	−0.630878	−	0.775882i	$-0.717305\pi$
$997$	−39.8404	−1.26176	−0.630878	+	0.775882i	$0.717305\pi$
$998$	−31.3557	−0.992546
$999$	−6.94426	−0.219707

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.2.a.b.1.13	✓	18
3.2	odd	2		4923.2.a.l.1.6		18
4.3	odd	2		8752.2.a.s.1.5		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.2.a.b.1.13	✓	18	1.1	even	1	trivial
4923.2.a.l.1.6		18	3.2	odd	2
8752.2.a.s.1.5		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)

\(f(q)\)	\(=\)	\(q+0.957552 q^{2} +0.564538 q^{3} -1.08309 q^{4} -4.10274 q^{5} +0.540575 q^{6} +4.97202 q^{7} -2.95222 q^{8} -2.68130 q^{9} +O(q^{10})\)	\(q+0.957552 q^{2} +0.564538 q^{3} -1.08309 q^{4} -4.10274 q^{5} +0.540575 q^{6} +4.97202 q^{7} -2.95222 q^{8} -2.68130 q^{9} -3.92859 q^{10} +0.0769657 q^{11} -0.611448 q^{12} -3.33082 q^{13} +4.76097 q^{14} -2.31615 q^{15} -0.660720 q^{16} -5.96711 q^{17} -2.56748 q^{18} -7.28632 q^{19} +4.44365 q^{20} +2.80689 q^{21} +0.0736987 q^{22} +2.10873 q^{23} -1.66664 q^{24} +11.8325 q^{25} -3.18943 q^{26} -3.20731 q^{27} -5.38516 q^{28} +3.24142 q^{29} -2.21784 q^{30} -6.20019 q^{31} +5.27177 q^{32} +0.0434501 q^{33} -5.71382 q^{34} -20.3989 q^{35} +2.90410 q^{36} +2.16514 q^{37} -6.97703 q^{38} -1.88037 q^{39} +12.1122 q^{40} -5.00098 q^{41} +2.68775 q^{42} -1.06278 q^{43} -0.0833611 q^{44} +11.0007 q^{45} +2.01922 q^{46} +5.86219 q^{47} -0.373001 q^{48} +17.7210 q^{49} +11.3302 q^{50} -3.36866 q^{51} +3.60759 q^{52} -9.01187 q^{53} -3.07116 q^{54} -0.315771 q^{55} -14.6785 q^{56} -4.11340 q^{57} +3.10383 q^{58} -4.47532 q^{59} +2.50861 q^{60} +4.58346 q^{61} -5.93701 q^{62} -13.3315 q^{63} +6.36944 q^{64} +13.6655 q^{65} +0.0416057 q^{66} +10.6474 q^{67} +6.46294 q^{68} +1.19046 q^{69} -19.5330 q^{70} +3.35886 q^{71} +7.91579 q^{72} +14.7261 q^{73} +2.07323 q^{74} +6.67989 q^{75} +7.89177 q^{76} +0.382675 q^{77} -1.80056 q^{78} -2.00500 q^{79} +2.71076 q^{80} +6.23324 q^{81} -4.78870 q^{82} -8.56498 q^{83} -3.04013 q^{84} +24.4815 q^{85} -1.01767 q^{86} +1.82990 q^{87} -0.227220 q^{88} -8.84846 q^{89} +10.5337 q^{90} -16.5609 q^{91} -2.28395 q^{92} -3.50024 q^{93} +5.61336 q^{94} +29.8939 q^{95} +2.97612 q^{96} -0.394709 q^{97} +16.9688 q^{98} -0.206368 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 4 q^{2} - 10 q^{3} + 16 q^{4} - 27 q^{5} - 3 q^{6} - 11 q^{7} - 12 q^{8} + 14 q^{9}+O(q^{10}) \) 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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