LMFDB - Embedded newform 547.2.a.b.1.8

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			1.8
Root			$0.826129$ 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)

$f(q)$	$=$	$q-0.826129 q^{2} +2.26041 q^{3} -1.31751 q^{4} -0.786316 q^{5} -1.86739 q^{6} -5.06179 q^{7} +2.74069 q^{8} +2.10946 q^{9} +O(q^{10})$	\(q-0.826129 q^{2} +2.26041 q^{3} -1.31751 q^{4} -0.786316 q^{5} -1.86739 q^{6} -5.06179 q^{7} +2.74069 q^{8} +2.10946 q^{9} +0.649598 q^{10} +3.16492 q^{11} -2.97812 q^{12} -2.09157 q^{13} +4.18169 q^{14} -1.77740 q^{15} +0.370855 q^{16} -0.108946 q^{17} -1.74269 q^{18} -6.43031 q^{19} +1.03598 q^{20} -11.4417 q^{21} -2.61463 q^{22} -2.45365 q^{23} +6.19509 q^{24} -4.38171 q^{25} +1.72790 q^{26} -2.01298 q^{27} +6.66896 q^{28} -6.82278 q^{29} +1.46836 q^{30} -4.03224 q^{31} -5.78776 q^{32} +7.15403 q^{33} +0.0900034 q^{34} +3.98016 q^{35} -2.77924 q^{36} -5.74026 q^{37} +5.31227 q^{38} -4.72780 q^{39} -2.15505 q^{40} +9.42512 q^{41} +9.45235 q^{42} +6.98045 q^{43} -4.16982 q^{44} -1.65870 q^{45} +2.02703 q^{46} +4.86990 q^{47} +0.838285 q^{48} +18.6217 q^{49} +3.61986 q^{50} -0.246263 q^{51} +2.75566 q^{52} -13.4156 q^{53} +1.66299 q^{54} -2.48863 q^{55} -13.8728 q^{56} -14.5351 q^{57} +5.63650 q^{58} +5.35027 q^{59} +2.34174 q^{60} +6.38066 q^{61} +3.33115 q^{62} -10.6776 q^{63} +4.03973 q^{64} +1.64463 q^{65} -5.91015 q^{66} -10.0563 q^{67} +0.143537 q^{68} -5.54626 q^{69} -3.28813 q^{70} +13.7032 q^{71} +5.78138 q^{72} +12.7591 q^{73} +4.74220 q^{74} -9.90446 q^{75} +8.47200 q^{76} -16.0202 q^{77} +3.90578 q^{78} -0.423068 q^{79} -0.291609 q^{80} -10.8786 q^{81} -7.78637 q^{82} +2.31035 q^{83} +15.0746 q^{84} +0.0856659 q^{85} -5.76676 q^{86} -15.4223 q^{87} +8.67408 q^{88} -12.2474 q^{89} +1.37030 q^{90} +10.5871 q^{91} +3.23271 q^{92} -9.11453 q^{93} -4.02317 q^{94} +5.05625 q^{95} -13.0827 q^{96} +0.251761 q^{97} -15.3839 q^{98} +6.67628 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.826129	−0.584162	−0.292081	−	0.956394i	$-0.594348\pi$
$2$	−0.826129	−0.584162	−0.292081	+	0.956394i	$0.594348\pi$
$3$	2.26041	1.30505	0.652525	−	0.757767i	$-0.273710\pi$
$3$	2.26041	1.30505	0.652525	+	0.757767i	$0.273710\pi$
$4$	−1.31751	−0.658755
$5$	−0.786316	−0.351651	−0.175826	−	0.984421i	$-0.556259\pi$
$5$	−0.786316	−0.351651	−0.175826	+	0.984421i	$0.556259\pi$
$6$	−1.86739	−0.762360
$7$	−5.06179	−1.91318	−0.956588	−	0.291442i	$-0.905865\pi$
$7$	−5.06179	−1.91318	−0.956588	+	0.291442i	$0.905865\pi$
$8$	2.74069	0.968981
$9$	2.10946	0.703154
$10$	0.649598	0.205421
$11$	3.16492	0.954260	0.477130	−	0.878833i	$-0.341677\pi$
$11$	3.16492	0.954260	0.477130	+	0.878833i	$0.341677\pi$
$12$	−2.97812	−0.859708
$13$	−2.09157	−0.580096	−0.290048	−	0.957012i	$-0.593671\pi$
$13$	−2.09157	−0.580096	−0.290048	+	0.957012i	$0.593671\pi$
$14$	4.18169	1.11760
$15$	−1.77740	−0.458922
$16$	0.370855	0.0927137
$17$	−0.108946	−0.0264233	−0.0132116	−	0.999913i	$-0.504206\pi$
$17$	−0.108946	−0.0264233	−0.0132116	+	0.999913i	$0.504206\pi$
$18$	−1.74269	−0.410755
$19$	−6.43031	−1.47521	−0.737607	−	0.675230i	$-0.764044\pi$
$19$	−6.43031	−1.47521	−0.737607	+	0.675230i	$0.764044\pi$
$20$	1.03598	0.231652
$21$	−11.4417	−2.49679
$22$	−2.61463	−0.557442
$23$	−2.45365	−0.511621	−0.255811	−	0.966727i	$-0.582342\pi$
$23$	−2.45365	−0.511621	−0.255811	+	0.966727i	$0.582342\pi$
$24$	6.19509	1.26457
$25$	−4.38171	−0.876342
$26$	1.72790	0.338870
$27$	−2.01298	−0.387399
$28$	6.66896	1.26032
$29$	−6.82278	−1.26696	−0.633480	−	0.773759i	$-0.718374\pi$
$29$	−6.82278	−1.26696	−0.633480	+	0.773759i	$0.718374\pi$
$30$	1.46836	0.268085
$31$	−4.03224	−0.724212	−0.362106	−	0.932137i	$-0.617942\pi$
$31$	−4.03224	−0.724212	−0.362106	+	0.932137i	$0.617942\pi$
$32$	−5.78776	−1.02314
$33$	7.15403	1.24536
$34$	0.0900034	0.0154355
$35$	3.98016	0.672771
$36$	−2.77924	−0.463206
$37$	−5.74026	−0.943693	−0.471847	−	0.881681i	$-0.656412\pi$
$37$	−5.74026	−0.943693	−0.471847	+	0.881681i	$0.656412\pi$
$38$	5.31227	0.861764
$39$	−4.72780	−0.757054
$40$	−2.15505	−0.340743
$41$	9.42512	1.47196	0.735978	−	0.677005i	$-0.236723\pi$
$41$	9.42512	1.47196	0.735978	+	0.677005i	$0.236723\pi$
$42$	9.45235	1.45853
$43$	6.98045	1.06451	0.532255	−	0.846584i	$-0.321345\pi$
$43$	6.98045	1.06451	0.532255	+	0.846584i	$0.321345\pi$
$44$	−4.16982	−0.628624
$45$	−1.65870	−0.247265
$46$	2.02703	0.298869
$47$	4.86990	0.710348	0.355174	−	0.934800i	$-0.384422\pi$
$47$	4.86990	0.710348	0.355174	+	0.934800i	$0.384422\pi$
$48$	0.838285	0.120996
$49$	18.6217	2.66025
$50$	3.61986	0.511925
$51$	−0.246263	−0.0344837
$52$	2.75566	0.382141
$53$	−13.4156	−1.84278	−0.921388	−	0.388645i	$-0.872943\pi$
$53$	−13.4156	−1.84278	−0.921388	+	0.388645i	$0.872943\pi$
$54$	1.66299	0.226304
$55$	−2.48863	−0.335566
$56$	−13.8728	−1.85383
$57$	−14.5351	−1.92523
$58$	5.63650	0.740109
$59$	5.35027	0.696546	0.348273	−	0.937393i	$-0.386768\pi$
$59$	5.35027	0.696546	0.348273	+	0.937393i	$0.386768\pi$
$60$	2.34174	0.302317
$61$	6.38066	0.816959	0.408480	−	0.912767i	$-0.366059\pi$
$61$	6.38066	0.816959	0.408480	+	0.912767i	$0.366059\pi$
$62$	3.33115	0.423057
$63$	−10.6776	−1.34526
$64$	4.03973	0.504966
$65$	1.64463	0.203991
$66$	−5.91015	−0.727489
$67$	−10.0563	−1.22858	−0.614288	−	0.789082i	$-0.710557\pi$
$67$	−10.0563	−1.22858	−0.614288	+	0.789082i	$0.710557\pi$
$68$	0.143537	0.0174065
$69$	−5.54626	−0.667691
$70$	−3.28813	−0.393007
$71$	13.7032	1.62627	0.813133	−	0.582077i	$-0.197760\pi$
$71$	13.7032	1.62627	0.813133	+	0.582077i	$0.197760\pi$
$72$	5.78138	0.681343
$73$	12.7591	1.49334	0.746668	−	0.665196i	$-0.231652\pi$
$73$	12.7591	1.49334	0.746668	+	0.665196i	$0.231652\pi$
$74$	4.74220	0.551269
$75$	−9.90446	−1.14367
$76$	8.47200	0.971805
$77$	−16.0202	−1.82567
$78$	3.90578	0.442242
$79$	−0.423068	−0.0475989	−0.0237994	−	0.999717i	$-0.507576\pi$
$79$	−0.423068	−0.0475989	−0.0237994	+	0.999717i	$0.507576\pi$
$80$	−0.291609	−0.0326029
$81$	−10.8786	−1.20873
$82$	−7.78637	−0.859860
$83$	2.31035	0.253594	0.126797	−	0.991929i	$-0.459530\pi$
$83$	2.31035	0.253594	0.126797	+	0.991929i	$0.459530\pi$
$84$	15.0746	1.64477
$85$	0.0856659	0.00929177
$86$	−5.76676	−0.621845
$87$	−15.4223	−1.65344
$88$	8.67408	0.924660
$89$	−12.2474	−1.29823	−0.649113	−	0.760692i	$-0.724860\pi$
$89$	−12.2474	−1.29823	−0.649113	+	0.760692i	$0.724860\pi$
$90$	1.37030	0.144443
$91$	10.5871	1.10983
$92$	3.23271	0.337033
$93$	−9.11453	−0.945133
$94$	−4.02317	−0.414958
$95$	5.05625	0.518761
$96$	−13.0827	−1.33525
$97$	0.251761	0.0255625	0.0127812	−	0.999918i	$-0.495931\pi$
$97$	0.251761	0.0255625	0.0127812	+	0.999918i	$0.495931\pi$
$98$	−15.3839	−1.55401
$99$	6.67628	0.670991
$100$	5.77295	0.577295
$101$	−0.761643	−0.0757863	−0.0378931	−	0.999282i	$-0.512065\pi$
$101$	−0.761643	−0.0757863	−0.0378931	+	0.999282i	$0.512065\pi$
$102$	0.203445	0.0201440
$103$	−8.12573	−0.800652	−0.400326	−	0.916373i	$-0.631103\pi$
$103$	−8.12573	−0.800652	−0.400326	+	0.916373i	$0.631103\pi$
$104$	−5.73234	−0.562102
$105$	8.99681	0.877999
$106$	11.0830	1.07648
$107$	6.91809	0.668797	0.334399	−	0.942432i	$-0.391467\pi$
$107$	6.91809	0.668797	0.334399	+	0.942432i	$0.391467\pi$
$108$	2.65213	0.255201
$109$	7.83918	0.750857	0.375428	−	0.926851i	$-0.377496\pi$
$109$	7.83918	0.750857	0.375428	+	0.926851i	$0.377496\pi$
$110$	2.05593	0.196025
$111$	−12.9754	−1.23157
$112$	−1.87719	−0.177378
$113$	−9.98412	−0.939227	−0.469614	−	0.882872i	$-0.655607\pi$
$113$	−9.98412	−0.939227	−0.469614	+	0.882872i	$0.655607\pi$
$114$	12.0079	1.12464
$115$	1.92934	0.179912
$116$	8.98909	0.834616
$117$	−4.41208	−0.407897
$118$	−4.42002	−0.406896
$119$	0.551462	0.0505524
$120$	−4.87130	−0.444687
$121$	−0.983273	−0.0893884
$122$	−5.27125	−0.477236
$123$	21.3047	1.92098
$124$	5.31252	0.477079
$125$	7.37698	0.659817
$126$	8.82112	0.785848
$127$	19.1377	1.69820	0.849099	−	0.528234i	$-0.177146\pi$
$127$	19.1377	1.69820	0.849099	+	0.528234i	$0.177146\pi$
$128$	8.23818	0.728159
$129$	15.7787	1.38924
$130$	−1.35868	−0.119164
$131$	−20.0684	−1.75339	−0.876693	−	0.481051i	$-0.840255\pi$
$131$	−20.0684	−1.75339	−0.876693	+	0.481051i	$0.840255\pi$
$132$	−9.42550	−0.820385
$133$	32.5489	2.82235
$134$	8.30782	0.717686
$135$	1.58284	0.136229
$136$	−0.298587	−0.0256037
$137$	0.483338	0.0412944	0.0206472	−	0.999787i	$-0.493427\pi$
$137$	0.483338	0.0412944	0.0206472	+	0.999787i	$0.493427\pi$
$138$	4.58192	0.390039
$139$	11.7671	0.998071	0.499035	−	0.866582i	$-0.333688\pi$
$139$	11.7671	0.998071	0.499035	+	0.866582i	$0.333688\pi$
$140$	−5.24391	−0.443191
$141$	11.0080	0.927039
$142$	−11.3206	−0.950003
$143$	−6.61964	−0.553563
$144$	0.782304	0.0651920
$145$	5.36486	0.445528
$146$	−10.5406	−0.872350
$147$	42.0927	3.47175
$148$	7.56286	0.621663
$149$	3.59414	0.294443	0.147222	−	0.989104i	$-0.452967\pi$
$149$	3.59414	0.294443	0.147222	+	0.989104i	$0.452967\pi$
$150$	8.18237	0.668087
$151$	−12.3861	−1.00797	−0.503984	−	0.863713i	$-0.668133\pi$
$151$	−12.3861	−1.00797	−0.503984	+	0.863713i	$0.668133\pi$
$152$	−17.6235	−1.42945
$153$	−0.229817	−0.0185796
$154$	13.2347	1.06648
$155$	3.17062	0.254670
$156$	6.22893	0.498713
$157$	−22.4520	−1.79187	−0.895933	−	0.444188i	$-0.853492\pi$
$157$	−22.4520	−1.79187	−0.895933	+	0.444188i	$0.853492\pi$
$158$	0.349509	0.0278054
$159$	−30.3248	−2.40491
$160$	4.55101	0.359789
$161$	12.4199	0.978822
$162$	8.98709	0.706093
$163$	−3.40571	−0.266756	−0.133378	−	0.991065i	$-0.542582\pi$
$163$	−3.40571	−0.266756	−0.133378	+	0.991065i	$0.542582\pi$
$164$	−12.4177	−0.969659
$165$	−5.62532	−0.437931
$166$	−1.90865	−0.148140
$167$	−0.617110	−0.0477534	−0.0238767	−	0.999715i	$-0.507601\pi$
$167$	−0.617110	−0.0477534	−0.0238767	+	0.999715i	$0.507601\pi$
$168$	−31.3583	−2.41934
$169$	−8.62535	−0.663488
$170$	−0.0707711	−0.00542790
$171$	−13.5645	−1.03730
$172$	−9.19682	−0.701251
$173$	8.12121	0.617444	0.308722	−	0.951152i	$-0.400099\pi$
$173$	8.12121	0.617444	0.308722	+	0.951152i	$0.400099\pi$
$174$	12.7408	0.965879
$175$	22.1793	1.67660
$176$	1.17373	0.0884730
$177$	12.0938	0.909027
$178$	10.1180	0.758374
$179$	−5.38653	−0.402608	−0.201304	−	0.979529i	$-0.564518\pi$
$179$	−5.38653	−0.402608	−0.201304	+	0.979529i	$0.564518\pi$
$180$	2.18536	0.162887
$181$	7.68451	0.571185	0.285593	−	0.958351i	$-0.407810\pi$
$181$	7.68451	0.571185	0.285593	+	0.958351i	$0.407810\pi$
$182$	−8.74629	−0.648318
$183$	14.4229	1.06617
$184$	−6.72470	−0.495751
$185$	4.51366	0.331851
$186$	7.52978	0.552110
$187$	−0.344805	−0.0252147
$188$	−6.41615	−0.467946
$189$	10.1893	0.741163
$190$	−4.17712	−0.303040
$191$	−16.2735	−1.17751	−0.588753	−	0.808313i	$-0.700381\pi$
$191$	−16.2735	−1.17751	−0.588753	+	0.808313i	$0.700381\pi$
$192$	9.13145	0.659005
$193$	−1.47963	−0.106506	−0.0532531	−	0.998581i	$-0.516959\pi$
$193$	−1.47963	−0.106506	−0.0532531	+	0.998581i	$0.516959\pi$
$194$	−0.207987	−0.0149326
$195$	3.71755	0.266219
$196$	−24.5343	−1.75245
$197$	4.77839	0.340446	0.170223	−	0.985406i	$-0.445551\pi$
$197$	4.77839	0.340446	0.170223	+	0.985406i	$0.445551\pi$
$198$	−5.51547	−0.391967
$199$	13.8921	0.984784	0.492392	−	0.870373i	$-0.336123\pi$
$199$	13.8921	0.984784	0.492392	+	0.870373i	$0.336123\pi$
$200$	−12.0089	−0.849158
$201$	−22.7314	−1.60335
$202$	0.629215	0.0442714
$203$	34.5355	2.42392
$204$	0.324454	0.0227163
$205$	−7.41112	−0.517615
$206$	6.71291	0.467710
$207$	−5.17588	−0.359748
$208$	−0.775668	−0.0537829
$209$	−20.3514	−1.40774
$210$	−7.43253	−0.512893
$211$	−24.6663	−1.69810	−0.849049	−	0.528314i	$-0.822824\pi$
$211$	−24.6663	−1.69810	−0.849049	+	0.528314i	$0.822824\pi$
$212$	17.6752	1.21394
$213$	30.9748	2.12236
$214$	−5.71524	−0.390686
$215$	−5.48884	−0.374336
$216$	−5.51697	−0.375382
$217$	20.4104	1.38555
$218$	−6.47617	−0.438622
$219$	28.8408	1.94888
$220$	3.27879	0.221056
$221$	0.227868	0.0153280
$222$	10.7193	0.719434
$223$	−8.58640	−0.574988	−0.287494	−	0.957782i	$-0.592822\pi$
$223$	−8.58640	−0.574988	−0.287494	+	0.957782i	$0.592822\pi$
$224$	29.2964	1.95745
$225$	−9.24304	−0.616203
$226$	8.24818	0.548660
$227$	−25.2376	−1.67508	−0.837540	−	0.546375i	$-0.816007\pi$
$227$	−25.2376	−1.67508	−0.837540	+	0.546375i	$0.816007\pi$
$228$	19.1502	1.26825
$229$	−10.2627	−0.678176	−0.339088	−	0.940755i	$-0.610119\pi$
$229$	−10.2627	−0.678176	−0.339088	+	0.940755i	$0.610119\pi$
$230$	−1.59389	−0.105098
$231$	−36.2122	−2.38259
$232$	−18.6992	−1.22766
$233$	0.393334	0.0257682	0.0128841	−	0.999917i	$-0.495899\pi$
$233$	0.393334	0.0257682	0.0128841	+	0.999917i	$0.495899\pi$
$234$	3.64495	0.238278
$235$	−3.82928	−0.249795
$236$	−7.04904	−0.458854
$237$	−0.956308	−0.0621189
$238$	−0.455578	−0.0295308
$239$	−4.68089	−0.302782	−0.151391	−	0.988474i	$-0.548375\pi$
$239$	−4.68089	−0.302782	−0.151391	+	0.988474i	$0.548375\pi$
$240$	−0.659156	−0.0425484
$241$	15.4761	0.996905	0.498452	−	0.866917i	$-0.333902\pi$
$241$	15.4761	0.996905	0.498452	+	0.866917i	$0.333902\pi$
$242$	0.812310	0.0522173
$243$	−18.5511	−1.19005
$244$	−8.40658	−0.538176
$245$	−14.6425	−0.935478
$246$	−17.6004	−1.12216
$247$	13.4494	0.855766
$248$	−11.0511	−0.701748
$249$	5.22235	0.330953
$250$	−6.09434	−0.385440
$251$	7.93354	0.500761	0.250380	−	0.968148i	$-0.419444\pi$
$251$	7.93354	0.500761	0.250380	+	0.968148i	$0.419444\pi$
$252$	14.0679	0.886195
$253$	−7.76561	−0.488219
$254$	−15.8102	−0.992022
$255$	0.193640	0.0121262
$256$	−14.8853	−0.930329
$257$	−21.8790	−1.36478	−0.682389	−	0.730990i	$-0.739059\pi$
$257$	−21.8790	−1.36478	−0.682389	+	0.730990i	$0.739059\pi$
$258$	−13.0352	−0.811539
$259$	29.0560	1.80545
$260$	−2.16682	−0.134380
$261$	−14.3924	−0.890867
$262$	16.5791	1.02426
$263$	16.8492	1.03897	0.519484	−	0.854480i	$-0.326124\pi$
$263$	16.8492	1.03897	0.519484	+	0.854480i	$0.326124\pi$
$264$	19.6070	1.20673
$265$	10.5489	0.648014
$266$	−26.8896	−1.64871
$267$	−27.6843	−1.69425
$268$	13.2493	0.809330
$269$	6.42681	0.391849	0.195925	−	0.980619i	$-0.437229\pi$
$269$	6.42681	0.391849	0.195925	+	0.980619i	$0.437229\pi$
$270$	−1.30763	−0.0795799
$271$	19.9132	1.20964	0.604820	−	0.796362i	$-0.293245\pi$
$271$	19.9132	1.20964	0.604820	+	0.796362i	$0.293245\pi$
$272$	−0.0404031	−0.00244980
$273$	23.9311	1.44838
$274$	−0.399300	−0.0241226
$275$	−13.8678	−0.836257
$276$	7.30725	0.439845
$277$	−2.56259	−0.153971	−0.0769854	−	0.997032i	$-0.524529\pi$
$277$	−2.56259	−0.153971	−0.0769854	+	0.997032i	$0.524529\pi$
$278$	−9.72113	−0.583035
$279$	−8.50586	−0.509233
$280$	10.9084	0.651902
$281$	−9.17907	−0.547577	−0.273789	−	0.961790i	$-0.588277\pi$
$281$	−9.17907	−0.547577	−0.273789	+	0.961790i	$0.588277\pi$
$282$	−9.09402	−0.541541
$283$	−16.3038	−0.969158	−0.484579	−	0.874748i	$-0.661027\pi$
$283$	−16.3038	−0.969158	−0.484579	+	0.874748i	$0.661027\pi$
$284$	−18.0541	−1.07131
$285$	11.4292	0.677008
$286$	5.46868	0.323370
$287$	−47.7080	−2.81611
$288$	−12.2091	−0.719425
$289$	−16.9881	−0.999302
$290$	−4.43207	−0.260260
$291$	0.569084	0.0333603
$292$	−16.8102	−0.983743
$293$	−8.66768	−0.506371	−0.253186	−	0.967418i	$-0.581478\pi$
$293$	−8.66768	−0.506371	−0.253186	+	0.967418i	$0.581478\pi$
$294$	−34.7741	−2.02806
$295$	−4.20700	−0.244941
$296$	−15.7323	−0.914421
$297$	−6.37094	−0.369679
$298$	−2.96922	−0.172002
$299$	5.13197	0.296790
$300$	13.0492	0.753398
$301$	−35.3336	−2.03659
$302$	10.2325	0.588817
$303$	−1.72163	−0.0989048
$304$	−2.38471	−0.136773
$305$	−5.01721	−0.287285
$306$	0.189859	0.0108535
$307$	11.3930	0.650233	0.325116	−	0.945674i	$-0.394597\pi$
$307$	11.3930	0.650233	0.325116	+	0.945674i	$0.394597\pi$
$308$	21.1067	1.20267
$309$	−18.3675	−1.04489
$310$	−2.61934	−0.148768
$311$	−14.0569	−0.797096	−0.398548	−	0.917147i	$-0.630486\pi$
$311$	−14.0569	−0.797096	−0.398548	+	0.917147i	$0.630486\pi$
$312$	−12.9575	−0.733571
$313$	−30.2403	−1.70928	−0.854640	−	0.519221i	$-0.826222\pi$
$313$	−30.2403	−1.70928	−0.854640	+	0.519221i	$0.826222\pi$
$314$	18.5483	1.04674
$315$	8.39600	0.473061
$316$	0.557397	0.0313560
$317$	31.2545	1.75543	0.877715	−	0.479184i	$-0.159067\pi$
$317$	31.2545	1.75543	0.877715	+	0.479184i	$0.159067\pi$
$318$	25.0522	1.40486
$319$	−21.5936	−1.20901
$320$	−3.17650	−0.177572
$321$	15.6377	0.872813
$322$	−10.2604	−0.571790
$323$	0.700556	0.0389800
$324$	14.3326	0.796256
$325$	9.16463	0.508362
$326$	2.81356	0.155829
$327$	17.7198	0.979905
$328$	25.8314	1.42630
$329$	−24.6504	−1.35902
$330$	4.64724	0.255822
$331$	34.5967	1.90161	0.950803	−	0.309797i	$-0.100261\pi$
$331$	34.5967	1.90161	0.950803	+	0.309797i	$0.100261\pi$
$332$	−3.04391	−0.167056
$333$	−12.1089	−0.663562
$334$	0.509813	0.0278957
$335$	7.90744	0.432030
$336$	−4.24322	−0.231487
$337$	1.53217	0.0834625	0.0417312	−	0.999129i	$-0.486713\pi$
$337$	1.53217	0.0834625	0.0417312	+	0.999129i	$0.486713\pi$
$338$	7.12565	0.387584
$339$	−22.5682	−1.22574
$340$	−0.112866	−0.00612100
$341$	−12.7617	−0.691087
$342$	11.2060	0.605952
$343$	−58.8267	−3.17634
$344$	19.1313	1.03149
$345$	4.36111	0.234794
$346$	−6.70917	−0.360687
$347$	16.8369	0.903851	0.451926	−	0.892056i	$-0.350737\pi$
$347$	16.8369	0.903851	0.451926	+	0.892056i	$0.350737\pi$
$348$	20.3190	1.08922
$349$	−23.7566	−1.27166	−0.635830	−	0.771829i	$-0.719342\pi$
$349$	−23.7566	−1.27166	−0.635830	+	0.771829i	$0.719342\pi$
$350$	−18.3230	−0.979403
$351$	4.21029	0.224729
$352$	−18.3178	−0.976342
$353$	1.39136	0.0740545	0.0370273	−	0.999314i	$-0.488211\pi$
$353$	1.39136	0.0740545	0.0370273	+	0.999314i	$0.488211\pi$
$354$	−9.99106	−0.531019
$355$	−10.7750	−0.571878
$356$	16.1361	0.855213
$357$	1.24653	0.0659734
$358$	4.44997	0.235188
$359$	28.2644	1.49174	0.745868	−	0.666094i	$-0.232035\pi$
$359$	28.2644	1.49174	0.745868	+	0.666094i	$0.232035\pi$
$360$	−4.54599	−0.239595
$361$	22.3489	1.17626
$362$	−6.34840	−0.333665
$363$	−2.22260	−0.116656
$364$	−13.9486	−0.731104
$365$	−10.0327	−0.525133
$366$	−11.9152	−0.622817
$367$	−3.01566	−0.157416	−0.0787082	−	0.996898i	$-0.525080\pi$
$367$	−3.01566	−0.157416	−0.0787082	+	0.996898i	$0.525080\pi$
$368$	−0.909948	−0.0474343
$369$	19.8819	1.03501
$370$	−3.72887	−0.193854
$371$	67.9070	3.52556
$372$	12.0085	0.622611
$373$	−31.1754	−1.61420	−0.807101	−	0.590413i	$-0.798965\pi$
$373$	−31.1754	−1.61420	−0.807101	+	0.590413i	$0.798965\pi$
$374$	0.284854	0.0147294
$375$	16.6750	0.861094
$376$	13.3469	0.688314
$377$	14.2703	0.734958
$378$	−8.41768	−0.432959
$379$	21.4740	1.10304	0.551522	−	0.834161i	$-0.314047\pi$
$379$	21.4740	1.10304	0.551522	+	0.834161i	$0.314047\pi$
$380$	−6.66167	−0.341736
$381$	43.2591	2.21623
$382$	13.4440	0.687854
$383$	−28.8202	−1.47265	−0.736323	−	0.676630i	$-0.763440\pi$
$383$	−28.8202	−1.47265	−0.736323	+	0.676630i	$0.763440\pi$
$384$	18.6217	0.950284
$385$	12.5969	0.641998
$386$	1.22237	0.0622169
$387$	14.7250	0.748514
$388$	−0.331698	−0.0168394
$389$	−18.9124	−0.958896	−0.479448	−	0.877570i	$-0.659163\pi$
$389$	−18.9124	−0.958896	−0.479448	+	0.877570i	$0.659163\pi$
$390$	−3.07117	−0.155515
$391$	0.267315	0.0135187
$392$	51.0364	2.57773
$393$	−45.3629	−2.28825
$394$	−3.94756	−0.198875
$395$	0.332665	0.0167382
$396$	−8.79607	−0.442019
$397$	8.57041	0.430137	0.215068	−	0.976599i	$-0.431003\pi$
$397$	8.57041	0.430137	0.215068	+	0.976599i	$0.431003\pi$
$398$	−11.4767	−0.575273
$399$	73.5739	3.68330
$400$	−1.62498	−0.0812489
$401$	8.96307	0.447595	0.223797	−	0.974636i	$-0.428155\pi$
$401$	8.96307	0.447595	0.223797	+	0.974636i	$0.428155\pi$
$402$	18.7791	0.936616
$403$	8.43371	0.420113
$404$	1.00347	0.0499246
$405$	8.55398	0.425051
$406$	−28.5308	−1.41596
$407$	−18.1675	−0.900529
$408$	−0.674930	−0.0334140
$409$	−3.36946	−0.166609	−0.0833045	−	0.996524i	$-0.526547\pi$
$409$	−3.36946	−0.166609	−0.0833045	+	0.996524i	$0.526547\pi$
$410$	6.12254	0.302371
$411$	1.09254	0.0538912
$412$	10.7057	0.527434
$413$	−27.0820	−1.33262
$414$	4.27594	0.210151
$415$	−1.81667	−0.0891766
$416$	12.1055	0.593520
$417$	26.5984	1.30253
$418$	16.8129	0.822346
$419$	21.4455	1.04768	0.523841	−	0.851816i	$-0.324499\pi$
$419$	21.4455	1.04768	0.523841	+	0.851816i	$0.324499\pi$
$420$	−11.8534	−0.578386
$421$	30.3392	1.47864	0.739321	−	0.673353i	$-0.235146\pi$
$421$	30.3392	1.47864	0.739321	+	0.673353i	$0.235146\pi$
$422$	20.3776	0.991964
$423$	10.2729	0.499484
$424$	−36.7681	−1.78561
$425$	0.477369	0.0231558
$426$	−25.5892	−1.23980
$427$	−32.2975	−1.56299
$428$	−9.11466	−0.440574
$429$	−14.9631	−0.722426
$430$	4.53449	0.218673
$431$	16.9804	0.817915	0.408958	−	0.912553i	$-0.365892\pi$
$431$	16.9804	0.817915	0.408958	+	0.912553i	$0.365892\pi$
$432$	−0.746525	−0.0359172
$433$	6.02425	0.289507	0.144753	−	0.989468i	$-0.453761\pi$
$433$	6.02425	0.289507	0.144753	+	0.989468i	$0.453761\pi$
$434$	−16.8616	−0.809383
$435$	12.1268	0.581435
$436$	−10.3282	−0.494631
$437$	15.7777	0.754751
$438$	−23.8262	−1.13846
$439$	11.3630	0.542328	0.271164	−	0.962533i	$-0.412592\pi$
$439$	11.3630	0.542328	0.271164	+	0.962533i	$0.412592\pi$
$440$	−6.82056	−0.325158
$441$	39.2818	1.87056
$442$	−0.188248	−0.00895405
$443$	11.0858	0.526703	0.263351	−	0.964700i	$-0.415172\pi$
$443$	11.0858	0.526703	0.263351	+	0.964700i	$0.415172\pi$
$444$	17.0952	0.811301
$445$	9.63035	0.456522
$446$	7.09348	0.335886
$447$	8.12423	0.384263
$448$	−20.4482	−0.966089
$449$	−18.5315	−0.874554	−0.437277	−	0.899327i	$-0.644057\pi$
$449$	−18.5315	−0.874554	−0.437277	+	0.899327i	$0.644057\pi$
$450$	7.63595	0.359962
$451$	29.8298	1.40463
$452$	13.1542	0.618721
$453$	−27.9978	−1.31545
$454$	20.8496	0.978518
$455$	−8.32478	−0.390272
$456$	−39.8364	−1.86551
$457$	3.77862	0.176756	0.0883782	−	0.996087i	$-0.471832\pi$
$457$	3.77862	0.176756	0.0883782	+	0.996087i	$0.471832\pi$
$458$	8.47829	0.396165
$459$	0.219307	0.0102364
$460$	−2.54193	−0.118518
$461$	−12.7036	−0.591665	−0.295833	−	0.955240i	$-0.595597\pi$
$461$	−12.7036	−0.591665	−0.295833	+	0.955240i	$0.595597\pi$
$462$	29.9159	1.39182
$463$	−8.23426	−0.382678	−0.191339	−	0.981524i	$-0.561283\pi$
$463$	−8.23426	−0.382678	−0.191339	+	0.981524i	$0.561283\pi$
$464$	−2.53026	−0.117465
$465$	7.16690	0.332357
$466$	−0.324945	−0.0150528
$467$	3.12314	0.144521	0.0722607	−	0.997386i	$-0.476979\pi$
$467$	3.12314	0.144521	0.0722607	+	0.997386i	$0.476979\pi$
$468$	5.81296	0.268704
$469$	50.9030	2.35048
$470$	3.16348	0.145920
$471$	−50.7508	−2.33847
$472$	14.6635	0.674940
$473$	22.0926	1.01582
$474$	0.790034	0.0362875
$475$	28.1757	1.29279
$476$	−0.726556	−0.0333017
$477$	−28.2997	−1.29575
$478$	3.86702	0.176874
$479$	−4.21771	−0.192712	−0.0963561	−	0.995347i	$-0.530719\pi$
$479$	−4.21771	−0.192712	−0.0963561	+	0.995347i	$0.530719\pi$
$480$	10.2871	0.469542
$481$	12.0061	0.547433
$482$	−12.7853	−0.582353
$483$	28.0740	1.27741
$484$	1.29547	0.0588851
$485$	−0.197964	−0.00898908
$486$	15.3256	0.695182
$487$	22.7931	1.03285	0.516427	−	0.856331i	$-0.327262\pi$
$487$	22.7931	1.03285	0.516427	+	0.856331i	$0.327262\pi$
$488$	17.4874	0.791618
$489$	−7.69831	−0.348130
$490$	12.0966	0.546470
$491$	−6.80067	−0.306910	−0.153455	−	0.988156i	$-0.549040\pi$
$491$	−6.80067	−0.306910	−0.153455	+	0.988156i	$0.549040\pi$
$492$	−28.0691	−1.26545
$493$	0.743315	0.0334772
$494$	−11.1110	−0.499906
$495$	−5.24966	−0.235955
$496$	−1.49538	−0.0671444
$497$	−69.3626	−3.11134
$498$	−4.31433	−0.193330
$499$	5.63452	0.252236	0.126118	−	0.992015i	$-0.459748\pi$
$499$	5.63452	0.252236	0.126118	+	0.992015i	$0.459748\pi$
$500$	−9.71925	−0.434658
$501$	−1.39492	−0.0623206
$502$	−6.55413	−0.292525
$503$	−23.7525	−1.05907	−0.529535	−	0.848288i	$-0.677634\pi$
$503$	−23.7525	−1.05907	−0.529535	+	0.848288i	$0.677634\pi$
$504$	−29.2642	−1.30353
$505$	0.598892	0.0266503
$506$	6.41539	0.285199
$507$	−19.4968	−0.865885
$508$	−25.2141	−1.11870
$509$	−38.4562	−1.70454	−0.852270	−	0.523101i	$-0.824775\pi$
$509$	−38.4562	−1.70454	−0.852270	+	0.523101i	$0.824775\pi$
$510$	−0.159972	−0.00708367
$511$	−64.5838	−2.85702
$512$	−4.17922	−0.184697
$513$	12.9441	0.571497
$514$	18.0749	0.797250
$515$	6.38939	0.281550
$516$	−20.7886	−0.915167
$517$	15.4129	0.677857
$518$	−24.0040	−1.05468
$519$	18.3573	0.805795
$520$	4.50743	0.197664
$521$	14.0011	0.613401	0.306701	−	0.951806i	$-0.400775\pi$
$521$	14.0011	0.613401	0.306701	+	0.951806i	$0.400775\pi$
$522$	11.8900	0.520410
$523$	−9.02076	−0.394450	−0.197225	−	0.980358i	$-0.563193\pi$
$523$	−9.02076	−0.394450	−0.197225	+	0.980358i	$0.563193\pi$
$524$	26.4403	1.15505
$525$	50.1343	2.18804
$526$	−13.9197	−0.606926
$527$	0.439297	0.0191361
$528$	2.65311	0.115462
$529$	−16.9796	−0.738244
$530$	−8.71476	−0.378545
$531$	11.2862	0.489779
$532$	−42.8835	−1.85924
$533$	−19.7133	−0.853876
$534$	22.8708	0.989715
$535$	−5.43980	−0.235183
$536$	−27.5613	−1.19047
$537$	−12.1758	−0.525423
$538$	−5.30937	−0.228903
$539$	58.9363	2.53857
$540$	−2.08541	−0.0897418
$541$	−40.7851	−1.75349	−0.876743	−	0.480959i	$-0.840289\pi$
$541$	−40.7851	−1.75349	−0.876743	+	0.480959i	$0.840289\pi$
$542$	−16.4509	−0.706626
$543$	17.3702	0.745425
$544$	0.630553	0.0270347
$545$	−6.16407	−0.264040
$546$	−19.7702	−0.846087
$547$	−1.00000	−0.0427569
$547$	−1.00000	−0.0427569
$548$	−0.636803	−0.0272029
$549$	13.4597	0.574448
$550$	11.4566	0.488509
$551$	43.8726	1.86904
$552$	−15.2006	−0.646980
$553$	2.14148	0.0910651
$554$	2.11703	0.0899439
$555$	10.2027	0.433082
$556$	−15.5033	−0.657484
$557$	−35.9029	−1.52125	−0.760627	−	0.649190i	$-0.775108\pi$
$557$	−35.9029	−1.52125	−0.760627	+	0.649190i	$0.775108\pi$
$558$	7.02694	0.297474
$559$	−14.6001	−0.617518
$560$	1.47606	0.0623751
$561$	−0.779402	−0.0329064
$562$	7.58310	0.319874
$563$	15.3436	0.646657	0.323329	−	0.946287i	$-0.395198\pi$
$563$	15.3436	0.646657	0.323329	+	0.946287i	$0.395198\pi$
$564$	−14.5031	−0.610692
$565$	7.85067	0.330280
$566$	13.4690	0.566145
$567$	55.0650	2.31251
$568$	37.5562	1.57582
$569$	−5.21447	−0.218602	−0.109301	−	0.994009i	$-0.534861\pi$
$569$	−5.21447	−0.218602	−0.109301	+	0.994009i	$0.534861\pi$
$570$	−9.44201	−0.395482
$571$	4.18745	0.175239	0.0876196	−	0.996154i	$-0.472074\pi$
$571$	4.18745	0.175239	0.0876196	+	0.996154i	$0.472074\pi$
$572$	8.72145	0.364662
$573$	−36.7847	−1.53670
$574$	39.4130	1.64507
$575$	10.7512	0.448355
$576$	8.52165	0.355069
$577$	2.13588	0.0889176	0.0444588	−	0.999011i	$-0.485844\pi$
$577$	2.13588	0.0889176	0.0444588	+	0.999011i	$0.485844\pi$
$578$	14.0344	0.583754
$579$	−3.34458	−0.138996
$580$	−7.06826	−0.293494
$581$	−11.6945	−0.485170
$582$	−0.470137	−0.0194878
$583$	−42.4593	−1.75849
$584$	34.9687	1.44702
$585$	3.46929	0.143437
$586$	7.16062	0.295803
$587$	−4.54834	−0.187730	−0.0938650	−	0.995585i	$-0.529922\pi$
$587$	−4.54834	−0.187730	−0.0938650	+	0.995585i	$0.529922\pi$
$588$	−55.4576	−2.28703
$589$	25.9286	1.06837
$590$	3.47553	0.143085
$591$	10.8011	0.444299
$592$	−2.12881	−0.0874933
$593$	−21.3019	−0.874766	−0.437383	−	0.899275i	$-0.644095\pi$
$593$	−21.3019	−0.874766	−0.437383	+	0.899275i	$0.644095\pi$
$594$	5.26322	0.215952
$595$	−0.433623	−0.0177768
$596$	−4.73531	−0.193966
$597$	31.4018	1.28519
$598$	−4.23967	−0.173373
$599$	−3.77034	−0.154052	−0.0770260	−	0.997029i	$-0.524542\pi$
$599$	−3.77034	−0.154052	−0.0770260	+	0.997029i	$0.524542\pi$
$600$	−27.1451	−1.10819
$601$	−3.60143	−0.146905	−0.0734527	−	0.997299i	$-0.523402\pi$
$601$	−3.60143	−0.146905	−0.0734527	+	0.997299i	$0.523402\pi$
$602$	29.1901	1.18970
$603$	−21.2134	−0.863877
$604$	16.3189	0.664005
$605$	0.773163	0.0314335
$606$	1.42229	0.0577764
$607$	0.723525	0.0293670	0.0146835	−	0.999892i	$-0.495326\pi$
$607$	0.723525	0.0293670	0.0146835	+	0.999892i	$0.495326\pi$
$608$	37.2171	1.50935
$609$	78.0644	3.16333
$610$	4.14486	0.167821
$611$	−10.1857	−0.412070
$612$	0.302787	0.0122394
$613$	−31.8621	−1.28690	−0.643449	−	0.765489i	$-0.722497\pi$
$613$	−31.8621	−1.28690	−0.643449	+	0.765489i	$0.722497\pi$
$614$	−9.41209	−0.379841
$615$	−16.7522	−0.675513
$616$	−43.9064	−1.76904
$617$	−19.2818	−0.776255	−0.388128	−	0.921606i	$-0.626878\pi$
$617$	−19.2818	−0.776255	−0.388128	+	0.921606i	$0.626878\pi$
$618$	15.1739	0.610385
$619$	22.6679	0.911099	0.455549	−	0.890210i	$-0.349443\pi$
$619$	22.6679	0.911099	0.455549	+	0.890210i	$0.349443\pi$
$620$	−4.17732	−0.167765
$621$	4.93916	0.198202
$622$	11.6129	0.465633
$623$	61.9940	2.48374
$624$	−1.75333	−0.0701893
$625$	16.1079	0.644316
$626$	24.9824	0.998496
$627$	−46.0026	−1.83717
$628$	29.5808	1.18040
$629$	0.625378	0.0249355
$630$	−6.93618	−0.276344
$631$	19.6329	0.781574	0.390787	−	0.920481i	$-0.372203\pi$
$631$	19.6329	0.781574	0.390787	+	0.920481i	$0.372203\pi$
$632$	−1.15950	−0.0461224
$633$	−55.7560	−2.21610
$634$	−25.8203	−1.02545
$635$	−15.0483	−0.597173
$636$	39.9532	1.58425
$637$	−38.9486	−1.54320
$638$	17.8391	0.706256
$639$	28.9063	1.14352
$640$	−6.47781	−0.256058
$641$	−1.12354	−0.0443773	−0.0221887	−	0.999754i	$-0.507063\pi$
$641$	−1.12354	−0.0443773	−0.0221887	+	0.999754i	$0.507063\pi$
$642$	−12.9188	−0.509864
$643$	−37.6799	−1.48595	−0.742975	−	0.669319i	$-0.766586\pi$
$643$	−37.6799	−1.48595	−0.742975	+	0.669319i	$0.766586\pi$
$644$	−16.3633	−0.644804
$645$	−12.4070	−0.488527
$646$	−0.578750	−0.0227706
$647$	20.2406	0.795740	0.397870	−	0.917442i	$-0.369749\pi$
$647$	20.2406	0.795740	0.397870	+	0.917442i	$0.369749\pi$
$648$	−29.8148	−1.17124
$649$	16.9332	0.664686
$650$	−7.57117	−0.296966
$651$	46.1358	1.80821
$652$	4.48706	0.175727
$653$	−36.3954	−1.42426	−0.712131	−	0.702046i	$-0.752270\pi$
$653$	−36.3954	−1.42426	−0.712131	+	0.702046i	$0.752270\pi$
$654$	−14.6388	−0.572423
$655$	15.7801	0.616580
$656$	3.49535	0.136471
$657$	26.9148	1.05005
$658$	20.3644	0.793888
$659$	21.1203	0.822729	0.411365	−	0.911471i	$-0.365052\pi$
$659$	21.1203	0.822729	0.411365	+	0.911471i	$0.365052\pi$
$660$	7.41142	0.288489
$661$	−21.2739	−0.827458	−0.413729	−	0.910400i	$-0.635774\pi$
$661$	−21.2739	−0.827458	−0.413729	+	0.910400i	$0.635774\pi$
$662$	−28.5813	−1.11084
$663$	0.515075	0.0200039
$664$	6.33197	0.245728
$665$	−25.5937	−0.992481
$666$	10.0035	0.387627
$667$	16.7407	0.648203
$668$	0.813049	0.0314578
$669$	−19.4088	−0.750388
$670$	−6.53257	−0.252375
$671$	20.1943	0.779591
$672$	66.2220	2.55457
$673$	−39.9319	−1.53926	−0.769631	−	0.638489i	$-0.779560\pi$
$673$	−39.9319	−1.53926	−0.769631	+	0.638489i	$0.779560\pi$
$674$	−1.26577	−0.0487556
$675$	8.82031	0.339494
$676$	11.3640	0.437076
$677$	−42.0748	−1.61706	−0.808532	−	0.588452i	$-0.799738\pi$
$677$	−42.0748	−1.61706	−0.808532	+	0.588452i	$0.799738\pi$
$678$	18.6443	0.716029
$679$	−1.27436	−0.0489056
$680$	0.234784	0.00900355
$681$	−57.0475	−2.18606
$682$	10.5428	0.403706
$683$	−24.1077	−0.922454	−0.461227	−	0.887282i	$-0.652591\pi$
$683$	−24.1077	−0.922454	−0.461227	+	0.887282i	$0.652591\pi$
$684$	17.8714	0.683328
$685$	−0.380057	−0.0145212
$686$	48.5985	1.85550
$687$	−23.1979	−0.885054
$688$	2.58874	0.0986946
$689$	28.0596	1.06899
$690$	−3.60284	−0.137158
$691$	1.60780	0.0611638	0.0305819	−	0.999532i	$-0.490264\pi$
$691$	1.60780	0.0611638	0.0305819	+	0.999532i	$0.490264\pi$
$692$	−10.6998	−0.406745
$693$	−33.7939	−1.28372
$694$	−13.9094	−0.527995
$695$	−9.25264	−0.350973
$696$	−42.2678	−1.60216
$697$	−1.02683	−0.0388939
$698$	19.6260	0.742854
$699$	0.889097	0.0336287
$700$	−29.2214	−1.10447
$701$	−3.38942	−0.128017	−0.0640083	−	0.997949i	$-0.520388\pi$
$701$	−3.38942	−0.128017	−0.0640083	+	0.997949i	$0.520388\pi$
$702$	−3.47825	−0.131278
$703$	36.9117	1.39215
$704$	12.7854	0.481869
$705$	−8.65575	−0.325994
$706$	−1.14944	−0.0432598
$707$	3.85528	0.144993
$708$	−15.9337	−0.598827
$709$	−5.79060	−0.217471	−0.108735	−	0.994071i	$-0.534680\pi$
$709$	−5.79060	−0.217471	−0.108735	+	0.994071i	$0.534680\pi$
$710$	8.90156	0.334069
$711$	−0.892446	−0.0334693
$712$	−33.5665	−1.25796
$713$	9.89371	0.370522
$714$	−1.02979	−0.0385391
$715$	5.20513	0.194661
$716$	7.09681	0.265220
$717$	−10.5807	−0.395145
$718$	−23.3500	−0.871415
$719$	−22.6574	−0.844980	−0.422490	−	0.906368i	$-0.638844\pi$
$719$	−22.6574	−0.844980	−0.422490	+	0.906368i	$0.638844\pi$
$720$	−0.615138	−0.0229248
$721$	41.1308	1.53179
$722$	−18.4631	−0.687125
$723$	34.9824	1.30101
$724$	−10.1244	−0.376271
$725$	29.8954	1.11029
$726$	1.83616	0.0681461
$727$	16.0566	0.595507	0.297753	−	0.954643i	$-0.403763\pi$
$727$	16.0566	0.595507	0.297753	+	0.954643i	$0.403763\pi$
$728$	29.0159	1.07540
$729$	−9.29737	−0.344347
$730$	8.28827	0.306763
$731$	−0.760492	−0.0281278
$732$	−19.0023	−0.702347
$733$	33.7217	1.24554	0.622770	−	0.782405i	$-0.286007\pi$
$733$	33.7217	1.24554	0.622770	+	0.782405i	$0.286007\pi$
$734$	2.49133	0.0919566
$735$	−33.0982	−1.22085
$736$	14.2011	0.523461
$737$	−31.8275	−1.17238
$738$	−16.4250	−0.604614
$739$	28.8700	1.06200	0.530999	−	0.847372i	$-0.321817\pi$
$739$	28.8700	1.06200	0.530999	+	0.847372i	$0.321817\pi$
$740$	−5.94679	−0.218608
$741$	30.4012	1.11682
$742$	−56.0999	−2.05949
$743$	49.2010	1.80501	0.902505	−	0.430678i	$-0.141726\pi$
$743$	49.2010	1.80501	0.902505	+	0.430678i	$0.141726\pi$
$744$	−24.9801	−0.915816
$745$	−2.82613	−0.103541
$746$	25.7549	0.942955
$747$	4.87360	0.178316
$748$	0.454285	0.0166103
$749$	−35.0179	−1.27953
$750$	−13.7757	−0.503018
$751$	−2.75859	−0.100663	−0.0503313	−	0.998733i	$-0.516028\pi$
$751$	−2.75859	−0.100663	−0.0503313	+	0.998733i	$0.516028\pi$
$752$	1.80603	0.0658590
$753$	17.9331	0.653518
$754$	−11.7891	−0.429334
$755$	9.73941	0.354453
$756$	−13.4245	−0.488245
$757$	4.96288	0.180379	0.0901894	−	0.995925i	$-0.471253\pi$
$757$	4.96288	0.180379	0.0901894	+	0.995925i	$0.471253\pi$
$758$	−17.7403	−0.644356
$759$	−17.5535	−0.637150
$760$	13.8576	0.502669
$761$	24.3799	0.883772	0.441886	−	0.897071i	$-0.354310\pi$
$761$	24.3799	0.883772	0.441886	+	0.897071i	$0.354310\pi$
$762$	−35.7376	−1.29464
$763$	−39.6803	−1.43652
$764$	21.4405	0.775689
$765$	0.180709	0.00653354
$766$	23.8092	0.860263
$767$	−11.1905	−0.404064
$768$	−33.6468	−1.21412
$769$	−17.9443	−0.647089	−0.323544	−	0.946213i	$-0.604875\pi$
$769$	−17.9443	−0.647089	−0.323544	+	0.946213i	$0.604875\pi$
$770$	−10.4067	−0.375031
$771$	−49.4556	−1.78110
$772$	1.94943	0.0701616
$773$	−19.3616	−0.696387	−0.348193	−	0.937423i	$-0.613205\pi$
$773$	−19.3616	−0.696387	−0.348193	+	0.937423i	$0.613205\pi$
$774$	−12.1647	−0.437253
$775$	17.6681	0.634657
$776$	0.690001	0.0247696
$777$	65.6785	2.35620
$778$	15.6241	0.560150
$779$	−60.6065	−2.17145
$780$	−4.89790	−0.175373
$781$	43.3694	1.55188
$782$	−0.220837	−0.00789711
$783$	13.7342	0.490819
$784$	6.90596	0.246641
$785$	17.6544	0.630112
$786$	37.4756	1.33671
$787$	39.9866	1.42537	0.712684	−	0.701486i	$-0.247480\pi$
$787$	39.9866	1.42537	0.712684	+	0.701486i	$0.247480\pi$
$788$	−6.29557	−0.224271
$789$	38.0862	1.35591
$790$	−0.274824	−0.00977781
$791$	50.5375	1.79691
$792$	18.2976	0.650178
$793$	−13.3456	−0.473915
$794$	−7.08027	−0.251269
$795$	23.8449	0.845690
$796$	−18.3030	−0.648732
$797$	8.61344	0.305104	0.152552	−	0.988295i	$-0.451251\pi$
$797$	8.61344	0.305104	0.152552	+	0.988295i	$0.451251\pi$
$798$	−60.7815	−2.15164
$799$	−0.530556	−0.0187697
$800$	25.3603	0.896621
$801$	−25.8355	−0.912852
$802$	−7.40466	−0.261468
$803$	40.3815	1.42503
$804$	29.9489	1.05622
$805$	−9.76593	−0.344204
$806$	−6.96733	−0.245414
$807$	14.5272	0.511383
$808$	−2.08743	−0.0734355
$809$	29.8360	1.04898	0.524488	−	0.851418i	$-0.324257\pi$
$809$	29.8360	1.04898	0.524488	+	0.851418i	$0.324257\pi$
$810$	−7.06669	−0.248298
$811$	−41.9510	−1.47310	−0.736549	−	0.676384i	$-0.763546\pi$
$811$	−41.9510	−1.47310	−0.736549	+	0.676384i	$0.763546\pi$
$812$	−45.5009	−1.59677
$813$	45.0120	1.57864
$814$	15.0087	0.526054
$815$	2.67796	0.0938050
$816$	−0.0913277	−0.00319711
$817$	−44.8865	−1.57038
$818$	2.78361	0.0973266
$819$	22.3330	0.780379
$820$	9.76423	0.340982
$821$	31.0960	1.08526	0.542628	−	0.839973i	$-0.317429\pi$
$821$	31.0960	1.08526	0.542628	+	0.839973i	$0.317429\pi$
$822$	−0.902582	−0.0314812
$823$	33.1740	1.15637	0.578186	−	0.815905i	$-0.303761\pi$
$823$	33.1740	1.15637	0.578186	+	0.815905i	$0.303761\pi$
$824$	−22.2701	−0.775817
$825$	−31.3468	−1.09136
$826$	22.3732	0.778463
$827$	−38.5228	−1.33957	−0.669785	−	0.742555i	$-0.733614\pi$
$827$	−38.5228	−1.33957	−0.669785	+	0.742555i	$0.733614\pi$
$828$	6.81927	0.236986
$829$	19.7333	0.685366	0.342683	−	0.939451i	$-0.388664\pi$
$829$	19.7333	0.685366	0.342683	+	0.939451i	$0.388664\pi$
$830$	1.50080	0.0520936
$831$	−5.79250	−0.200940
$832$	−8.44936	−0.292929
$833$	−2.02876	−0.0702924
$834$	−21.9738	−0.760889
$835$	0.485243	0.0167925
$836$	26.8132	0.927355
$837$	8.11685	0.280559
$838$	−17.7168	−0.612015
$839$	46.0637	1.59030	0.795149	−	0.606415i	$-0.207393\pi$
$839$	46.0637	1.59030	0.795149	+	0.606415i	$0.207393\pi$
$840$	24.6575	0.850764
$841$	17.5504	0.605185
$842$	−25.0641	−0.863766
$843$	−20.7485	−0.714615
$844$	32.4981	1.11863
$845$	6.78225	0.233316
$846$	−8.48672	−0.291779
$847$	4.97712	0.171016
$848$	−4.97524	−0.170851
$849$	−36.8532	−1.26480
$850$	−0.394369	−0.0135267
$851$	14.0846	0.482814
$852$	−40.8096	−1.39811
$853$	−28.2328	−0.966672	−0.483336	−	0.875435i	$-0.660575\pi$
$853$	−28.2328	−0.966672	−0.483336	+	0.875435i	$0.660575\pi$
$854$	26.6819	0.913037
$855$	10.6660	0.364769
$856$	18.9604	0.648052
$857$	−14.6620	−0.500845	−0.250422	−	0.968137i	$-0.580569\pi$
$857$	−14.6620	−0.500845	−0.250422	+	0.968137i	$0.580569\pi$
$858$	12.3615	0.422014
$859$	12.2615	0.418356	0.209178	−	0.977878i	$-0.432921\pi$
$859$	12.2615	0.418356	0.209178	+	0.977878i	$0.432921\pi$
$860$	7.23160	0.246596
$861$	−107.840	−3.67517
$862$	−14.0280	−0.477795
$863$	−27.6201	−0.940199	−0.470099	−	0.882613i	$-0.655782\pi$
$863$	−27.6201	−0.940199	−0.470099	+	0.882613i	$0.655782\pi$
$864$	11.6507	0.396364
$865$	−6.38584	−0.217125
$866$	−4.97681	−0.169119
$867$	−38.4002	−1.30414
$868$	−26.8909	−0.912736
$869$	−1.33898	−0.0454217
$870$	−10.0183	−0.339652
$871$	21.0335	0.712692
$872$	21.4848	0.727566
$873$	0.531081	0.0179744
$874$	−13.0344	−0.440896
$875$	−37.3407	−1.26235
$876$	−37.9980	−1.28383
$877$	−13.7496	−0.464293	−0.232146	−	0.972681i	$-0.574575\pi$
$877$	−13.7496	−0.464293	−0.232146	+	0.972681i	$0.574575\pi$
$878$	−9.38733	−0.316807
$879$	−19.5925	−0.660839
$880$	−0.922920	−0.0311116
$881$	−38.5777	−1.29972	−0.649858	−	0.760055i	$-0.725172\pi$
$881$	−38.5777	−1.29972	−0.649858	+	0.760055i	$0.725172\pi$
$882$	−32.4518	−1.09271
$883$	52.1427	1.75474	0.877371	−	0.479813i	$-0.159296\pi$
$883$	52.1427	1.75474	0.877371	+	0.479813i	$0.159296\pi$
$884$	−0.300218	−0.0100974
$885$	−9.50956	−0.319660
$886$	−9.15831	−0.307680
$887$	3.23758	0.108707	0.0543537	−	0.998522i	$-0.482690\pi$
$887$	3.23758	0.108707	0.0543537	+	0.998522i	$0.482690\pi$
$888$	−35.5615	−1.19336
$889$	−96.8711	−3.24895
$890$	−7.95592	−0.266683
$891$	−34.4298	−1.15344
$892$	11.3127	0.378776
$893$	−31.3150	−1.04792
$894$	−6.71166	−0.224472
$895$	4.23551	0.141577
$896$	−41.6999	−1.39310
$897$	11.6004	0.387325
$898$	15.3094	0.510881
$899$	27.5111	0.917548
$900$	12.1778	0.405927
$901$	1.46158	0.0486922
$902$	−24.6432	−0.820530
$903$	−79.8685	−2.65786
$904$	−27.3634	−0.910093
$905$	−6.04245	−0.200858
$906$	23.1298	0.768435
$907$	25.8082	0.856946	0.428473	−	0.903555i	$-0.359052\pi$
$907$	25.8082	0.856946	0.428473	+	0.903555i	$0.359052\pi$
$908$	33.2509	1.10347
$909$	−1.60666	−0.0532894
$910$	6.87734	0.227982
$911$	50.0860	1.65942	0.829712	−	0.558192i	$-0.188505\pi$
$911$	50.0860	1.65942	0.829712	+	0.558192i	$0.188505\pi$
$912$	−5.39043	−0.178495
$913$	7.31208	0.241995
$914$	−3.12163	−0.103254
$915$	−11.3410	−0.374921
$916$	13.5212	0.446752
$917$	101.582	3.35454
$918$	−0.181176	−0.00597968
$919$	−1.51395	−0.0499407	−0.0249703	−	0.999688i	$-0.507949\pi$
$919$	−1.51395	−0.0499407	−0.0249703	+	0.999688i	$0.507949\pi$
$920$	5.28773	0.174331
$921$	25.7529	0.848586
$922$	10.4948	0.345628
$923$	−28.6611	−0.943391
$924$	47.7099	1.56954
$925$	25.1522	0.826998
$926$	6.80256	0.223546
$927$	−17.1409	−0.562982
$928$	39.4886	1.29628
$929$	−23.3902	−0.767408	−0.383704	−	0.923456i	$-0.625352\pi$
$929$	−23.3902	−0.767408	−0.383704	+	0.923456i	$0.625352\pi$
$930$	−5.92078	−0.194150
$931$	−119.743	−3.92443
$932$	−0.518222	−0.0169749
$933$	−31.7745	−1.04025
$934$	−2.58011	−0.0844239
$935$	0.271126	0.00886676
$936$	−12.0922	−0.395244
$937$	−1.93988	−0.0633731	−0.0316865	−	0.999498i	$-0.510088\pi$
$937$	−1.93988	−0.0633731	−0.0316865	+	0.999498i	$0.510088\pi$
$938$	−42.0524	−1.37306
$939$	−68.3554	−2.23070
$940$	5.04512	0.164554
$941$	58.8179	1.91741	0.958705	−	0.284403i	$-0.0917954\pi$
$941$	58.8179	1.91741	0.958705	+	0.284403i	$0.0917954\pi$
$942$	41.9267	1.36605
$943$	−23.1259	−0.753084
$944$	1.98418	0.0645794
$945$	−8.01201	−0.260631
$946$	−18.2513	−0.593402
$947$	15.6362	0.508107	0.254054	−	0.967190i	$-0.418236\pi$
$947$	15.6362	0.508107	0.254054	+	0.967190i	$0.418236\pi$
$948$	1.25995	0.0409212
$949$	−26.6865	−0.866279
$950$	−23.2768	−0.755199
$951$	70.6481	2.29092
$952$	1.51139	0.0489843
$953$	37.3601	1.21021	0.605106	−	0.796145i	$-0.293131\pi$
$953$	37.3601	1.21021	0.605106	+	0.796145i	$0.293131\pi$
$954$	23.3792	0.756930
$955$	12.7961	0.414072
$956$	6.16713	0.199459
$957$	−48.8104	−1.57782
$958$	3.48438	0.112575
$959$	−2.44656	−0.0790035
$960$	−7.18020	−0.231740
$961$	−14.7410	−0.475516
$962$	−9.91863	−0.319789
$963$	14.5934	0.470267
$964$	−20.3900	−0.656716
$965$	1.16346	0.0374530
$966$	−23.1927	−0.746214
$967$	−16.6383	−0.535051	−0.267526	−	0.963551i	$-0.586206\pi$
$967$	−16.6383	−0.535051	−0.267526	+	0.963551i	$0.586206\pi$
$968$	−2.69485	−0.0866157
$969$	1.58355	0.0508708
$970$	0.163544	0.00525107
$971$	−4.34862	−0.139554	−0.0697770	−	0.997563i	$-0.522229\pi$
$971$	−4.34862	−0.139554	−0.0697770	+	0.997563i	$0.522229\pi$
$972$	24.4412	0.783953
$973$	−59.5625	−1.90949
$974$	−18.8300	−0.603353
$975$	20.7158	0.663438
$976$	2.36630	0.0757433
$977$	52.0366	1.66480	0.832399	−	0.554177i	$-0.186967\pi$
$977$	52.0366	1.66480	0.832399	+	0.554177i	$0.186967\pi$
$978$	6.35980	0.203364
$979$	−38.7622	−1.23884
$980$	19.2917	0.616251
$981$	16.5364	0.527968
$982$	5.61823	0.179285
$983$	3.76181	0.119983	0.0599916	−	0.998199i	$-0.480893\pi$
$983$	3.76181	0.119983	0.0599916	+	0.998199i	$0.480893\pi$
$984$	58.3895	1.86139
$985$	−3.75732	−0.119718
$986$	−0.614074	−0.0195561
$987$	−55.7201	−1.77359
$988$	−17.7198	−0.563741
$989$	−17.1276	−0.544625
$990$	4.33690	0.137836
$991$	−41.0075	−1.30265	−0.651323	−	0.758801i	$-0.725786\pi$
$991$	−41.0075	−1.30265	−0.651323	+	0.758801i	$0.725786\pi$
$992$	23.3377	0.740971
$993$	78.2027	2.48169
$994$	57.3024	1.81752
$995$	−10.9236	−0.346300
$996$	−6.88050	−0.218017
$997$	12.7824	0.404823	0.202411	−	0.979301i	$-0.435122\pi$
$997$	12.7824	0.404823	0.202411	+	0.979301i	$0.435122\pi$
$998$	−4.65484	−0.147346
$999$	11.5551	0.365586

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.2.a.b.1.8	✓	18
3.2	odd	2		4923.2.a.l.1.11		18
4.3	odd	2		8752.2.a.s.1.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.2.a.b.1.8	✓	18	1.1	even	1	trivial
4923.2.a.l.1.11		18	3.2	odd	2
8752.2.a.s.1.1		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)

\(f(q)\)	\(=\)	\(q-0.826129 q^{2} +2.26041 q^{3} -1.31751 q^{4} -0.786316 q^{5} -1.86739 q^{6} -5.06179 q^{7} +2.74069 q^{8} +2.10946 q^{9} +O(q^{10})\)	\(q-0.826129 q^{2} +2.26041 q^{3} -1.31751 q^{4} -0.786316 q^{5} -1.86739 q^{6} -5.06179 q^{7} +2.74069 q^{8} +2.10946 q^{9} +0.649598 q^{10} +3.16492 q^{11} -2.97812 q^{12} -2.09157 q^{13} +4.18169 q^{14} -1.77740 q^{15} +0.370855 q^{16} -0.108946 q^{17} -1.74269 q^{18} -6.43031 q^{19} +1.03598 q^{20} -11.4417 q^{21} -2.61463 q^{22} -2.45365 q^{23} +6.19509 q^{24} -4.38171 q^{25} +1.72790 q^{26} -2.01298 q^{27} +6.66896 q^{28} -6.82278 q^{29} +1.46836 q^{30} -4.03224 q^{31} -5.78776 q^{32} +7.15403 q^{33} +0.0900034 q^{34} +3.98016 q^{35} -2.77924 q^{36} -5.74026 q^{37} +5.31227 q^{38} -4.72780 q^{39} -2.15505 q^{40} +9.42512 q^{41} +9.45235 q^{42} +6.98045 q^{43} -4.16982 q^{44} -1.65870 q^{45} +2.02703 q^{46} +4.86990 q^{47} +0.838285 q^{48} +18.6217 q^{49} +3.61986 q^{50} -0.246263 q^{51} +2.75566 q^{52} -13.4156 q^{53} +1.66299 q^{54} -2.48863 q^{55} -13.8728 q^{56} -14.5351 q^{57} +5.63650 q^{58} +5.35027 q^{59} +2.34174 q^{60} +6.38066 q^{61} +3.33115 q^{62} -10.6776 q^{63} +4.03973 q^{64} +1.64463 q^{65} -5.91015 q^{66} -10.0563 q^{67} +0.143537 q^{68} -5.54626 q^{69} -3.28813 q^{70} +13.7032 q^{71} +5.78138 q^{72} +12.7591 q^{73} +4.74220 q^{74} -9.90446 q^{75} +8.47200 q^{76} -16.0202 q^{77} +3.90578 q^{78} -0.423068 q^{79} -0.291609 q^{80} -10.8786 q^{81} -7.78637 q^{82} +2.31035 q^{83} +15.0746 q^{84} +0.0856659 q^{85} -5.76676 q^{86} -15.4223 q^{87} +8.67408 q^{88} -12.2474 q^{89} +1.37030 q^{90} +10.5871 q^{91} +3.23271 q^{92} -9.11453 q^{93} -4.02317 q^{94} +5.05625 q^{95} -13.0827 q^{96} +0.251761 q^{97} -15.3839 q^{98} +6.67628 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 4 q^{2} - 10 q^{3} + 16 q^{4} - 27 q^{5} - 3 q^{6} - 11 q^{7} - 12 q^{8} + 14 q^{9}+O(q^{10}) \) 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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