LMFDB - Embedded newform 983.2.a.a.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [983,2,Mod(1,983)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(983, 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("983.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 983 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	983.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:	$7.84929451869$
Analytic rank:	$1$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	983.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.05764 q^{2} -2.81984 q^{3} +2.23388 q^{4} +0.650217 q^{5} +5.80222 q^{6} +0.324376 q^{7} -0.481237 q^{8} +4.95151 q^{9} +O(q^{10})$	\(q-2.05764 q^{2} -2.81984 q^{3} +2.23388 q^{4} +0.650217 q^{5} +5.80222 q^{6} +0.324376 q^{7} -0.481237 q^{8} +4.95151 q^{9} -1.33791 q^{10} -3.65411 q^{11} -6.29918 q^{12} -4.76319 q^{13} -0.667449 q^{14} -1.83351 q^{15} -3.47754 q^{16} -1.11307 q^{17} -10.1884 q^{18} +7.62389 q^{19} +1.45250 q^{20} -0.914690 q^{21} +7.51884 q^{22} +5.96176 q^{23} +1.35701 q^{24} -4.57722 q^{25} +9.80093 q^{26} -5.50294 q^{27} +0.724617 q^{28} +9.04679 q^{29} +3.77270 q^{30} -1.52211 q^{31} +8.11801 q^{32} +10.3040 q^{33} +2.29029 q^{34} +0.210915 q^{35} +11.0611 q^{36} -3.84129 q^{37} -15.6872 q^{38} +13.4314 q^{39} -0.312908 q^{40} +4.18281 q^{41} +1.88210 q^{42} +6.53148 q^{43} -8.16284 q^{44} +3.21955 q^{45} -12.2672 q^{46} -1.70240 q^{47} +9.80612 q^{48} -6.89478 q^{49} +9.41826 q^{50} +3.13867 q^{51} -10.6404 q^{52} -11.5527 q^{53} +11.3231 q^{54} -2.37596 q^{55} -0.156102 q^{56} -21.4982 q^{57} -18.6150 q^{58} +10.7873 q^{59} -4.09583 q^{60} +5.03032 q^{61} +3.13196 q^{62} +1.60615 q^{63} -9.74883 q^{64} -3.09711 q^{65} -21.2019 q^{66} -9.87654 q^{67} -2.48645 q^{68} -16.8112 q^{69} -0.433987 q^{70} -10.8109 q^{71} -2.38285 q^{72} -13.4507 q^{73} +7.90398 q^{74} +12.9070 q^{75} +17.0308 q^{76} -1.18531 q^{77} -27.6371 q^{78} +10.6157 q^{79} -2.26116 q^{80} +0.662898 q^{81} -8.60671 q^{82} +13.2312 q^{83} -2.04331 q^{84} -0.723734 q^{85} -13.4394 q^{86} -25.5105 q^{87} +1.75849 q^{88} -10.4765 q^{89} -6.62468 q^{90} -1.54507 q^{91} +13.3179 q^{92} +4.29212 q^{93} +3.50293 q^{94} +4.95718 q^{95} -22.8915 q^{96} -4.36580 q^{97} +14.1870 q^{98} -18.0934 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 7 q^{2} - 6 q^{3} + 17 q^{4} - 7 q^{5} - 7 q^{6} - 25 q^{7} - 15 q^{8} + 6 q^{9}+O(q^{10}) $ 28 * q - 7 * q^2 - 6 * q^3 + 17 * q^4 - 7 * q^5 - 7 * q^6 - 25 * q^7 - 15 * q^8 + 6 * q^9	\( 28 q - 7 q^{2} - 6 q^{3} + 17 q^{4} - 7 q^{5} - 7 q^{6} - 25 q^{7} - 15 q^{8} + 6 q^{9} - 17 q^{10} - 10 q^{11} - 10 q^{12} - 28 q^{13} + 5 q^{14} - 9 q^{15} + 3 q^{16} - 24 q^{17} - 23 q^{18} - 13 q^{19} - 4 q^{20} - 21 q^{21} - 21 q^{22} - 9 q^{23} - 19 q^{24} - 33 q^{25} + 2 q^{26} - 12 q^{27} - 58 q^{28} - 14 q^{29} - 8 q^{30} - 16 q^{31} - 27 q^{32} - 34 q^{33} - 6 q^{34} - 2 q^{35} - 6 q^{36} - 58 q^{37} + 6 q^{38} - 12 q^{39} - 24 q^{40} - 24 q^{41} + 22 q^{42} - 43 q^{43} - 19 q^{45} - 28 q^{46} + 2 q^{47} + 19 q^{48} - 21 q^{49} + 17 q^{50} - 6 q^{51} - 47 q^{52} - 16 q^{53} + 16 q^{54} - 16 q^{55} + 30 q^{56} - 70 q^{57} - 31 q^{58} + 12 q^{59} - q^{60} - 22 q^{61} - 15 q^{63} - 3 q^{64} - 24 q^{65} + 41 q^{66} - 38 q^{67} + 11 q^{68} + 2 q^{69} + 19 q^{70} + 2 q^{71} - 15 q^{72} - 124 q^{73} + 14 q^{74} + 8 q^{75} + 3 q^{76} - 20 q^{77} + 21 q^{78} - 16 q^{79} + 10 q^{80} - 36 q^{81} + 2 q^{82} + 12 q^{83} + 6 q^{84} - 73 q^{85} + 41 q^{86} - 15 q^{87} - 61 q^{88} - 3 q^{89} + 39 q^{90} + 5 q^{91} + 44 q^{92} - 21 q^{93} + 9 q^{94} + 17 q^{95} - 3 q^{96} - 105 q^{97} + 16 q^{98} - 15 q^{99}+O(q^{100}) \) 28 * q - 7 * q^2 - 6 * q^3 + 17 * q^4 - 7 * q^5 - 7 * q^6 - 25 * q^7 - 15 * q^8 + 6 * q^9 - 17 * q^10 - 10 * q^11 - 10 * q^12 - 28 * q^13 + 5 * q^14 - 9 * q^15 + 3 * q^16 - 24 * q^17 - 23 * q^18 - 13 * q^19 - 4 * q^20 - 21 * q^21 - 21 * q^22 - 9 * q^23 - 19 * q^24 - 33 * q^25 + 2 * q^26 - 12 * q^27 - 58 * q^28 - 14 * q^29 - 8 * q^30 - 16 * q^31 - 27 * q^32 - 34 * q^33 - 6 * q^34 - 2 * q^35 - 6 * q^36 - 58 * q^37 + 6 * q^38 - 12 * q^39 - 24 * q^40 - 24 * q^41 + 22 * q^42 - 43 * q^43 - 19 * q^45 - 28 * q^46 + 2 * q^47 + 19 * q^48 - 21 * q^49 + 17 * q^50 - 6 * q^51 - 47 * q^52 - 16 * q^53 + 16 * q^54 - 16 * q^55 + 30 * q^56 - 70 * q^57 - 31 * q^58 + 12 * q^59 - q^60 - 22 * q^61 - 15 * q^63 - 3 * q^64 - 24 * q^65 + 41 * q^66 - 38 * q^67 + 11 * q^68 + 2 * q^69 + 19 * q^70 + 2 * q^71 - 15 * q^72 - 124 * q^73 + 14 * q^74 + 8 * q^75 + 3 * q^76 - 20 * q^77 + 21 * q^78 - 16 * q^79 + 10 * q^80 - 36 * q^81 + 2 * q^82 + 12 * q^83 + 6 * q^84 - 73 * q^85 + 41 * q^86 - 15 * q^87 - 61 * q^88 - 3 * q^89 + 39 * q^90 + 5 * q^91 + 44 * q^92 - 21 * q^93 + 9 * q^94 + 17 * q^95 - 3 * q^96 - 105 * q^97 + 16 * q^98 - 15 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.05764	−1.45497	−0.727485	−	0.686123i	$-0.759311\pi$
$2$	−2.05764	−1.45497	−0.727485	+	0.686123i	$0.759311\pi$
$3$	−2.81984	−1.62804	−0.814018	−	0.580839i	$-0.802724\pi$
$3$	−2.81984	−1.62804	−0.814018	+	0.580839i	$0.802724\pi$
$4$	2.23388	1.11694
$5$	0.650217	0.290786	0.145393	−	0.989374i	$-0.453555\pi$
$5$	0.650217	0.290786	0.145393	+	0.989374i	$0.453555\pi$
$6$	5.80222	2.36874
$7$	0.324376	0.122603	0.0613013	−	0.998119i	$-0.480475\pi$
$7$	0.324376	0.122603	0.0613013	+	0.998119i	$0.480475\pi$
$8$	−0.481237	−0.170143
$9$	4.95151	1.65050
$10$	−1.33791	−0.423085
$11$	−3.65411	−1.10176	−0.550878	−	0.834586i	$-0.685707\pi$
$11$	−3.65411	−1.10176	−0.550878	+	0.834586i	$0.685707\pi$
$12$	−6.29918	−1.81842
$13$	−4.76319	−1.32107	−0.660536	−	0.750794i	$-0.729671\pi$
$13$	−4.76319	−1.32107	−0.660536	+	0.750794i	$0.729671\pi$
$14$	−0.667449	−0.178383
$15$	−1.83351	−0.473410
$16$	−3.47754	−0.869386
$17$	−1.11307	−0.269958	−0.134979	−	0.990848i	$-0.543097\pi$
$17$	−1.11307	−0.269958	−0.134979	+	0.990848i	$0.543097\pi$
$18$	−10.1884	−2.40143
$19$	7.62389	1.74904	0.874520	−	0.484989i	$-0.161176\pi$
$19$	7.62389	1.74904	0.874520	+	0.484989i	$0.161176\pi$
$20$	1.45250	0.324790
$21$	−0.914690	−0.199602
$22$	7.51884	1.60302
$23$	5.96176	1.24311	0.621557	−	0.783369i	$-0.286501\pi$
$23$	5.96176	1.24311	0.621557	+	0.783369i	$0.286501\pi$
$24$	1.35701	0.276999
$25$	−4.57722	−0.915444
$26$	9.80093	1.92212
$27$	−5.50294	−1.05904
$28$	0.724617	0.136940
$29$	9.04679	1.67995	0.839973	−	0.542628i	$-0.182571\pi$
$29$	9.04679	1.67995	0.839973	+	0.542628i	$0.182571\pi$
$30$	3.77270	0.688797
$31$	−1.52211	−0.273380	−0.136690	−	0.990614i	$-0.543646\pi$
$31$	−1.52211	−0.273380	−0.136690	+	0.990614i	$0.543646\pi$
$32$	8.11801	1.43507
$33$	10.3040	1.79370
$34$	2.29029	0.392781
$35$	0.210915	0.0356511
$36$	11.0611	1.84351
$37$	−3.84129	−0.631504	−0.315752	−	0.948842i	$-0.602257\pi$
$37$	−3.84129	−0.631504	−0.315752	+	0.948842i	$0.602257\pi$
$38$	−15.6872	−2.54480
$39$	13.4314	2.15075
$40$	−0.312908	−0.0494751
$41$	4.18281	0.653245	0.326622	−	0.945155i	$-0.394089\pi$
$41$	4.18281	0.653245	0.326622	+	0.945155i	$0.394089\pi$
$42$	1.88210	0.290414
$43$	6.53148	0.996041	0.498021	−	0.867165i	$-0.334060\pi$
$43$	6.53148	0.996041	0.498021	+	0.867165i	$0.334060\pi$
$44$	−8.16284	−1.23059
$45$	3.21955	0.479942
$46$	−12.2672	−1.80869
$47$	−1.70240	−0.248321	−0.124161	−	0.992262i	$-0.539624\pi$
$47$	−1.70240	−0.248321	−0.124161	+	0.992262i	$0.539624\pi$
$48$	9.80612	1.41539
$49$	−6.89478	−0.984969
$50$	9.41826	1.33194
$51$	3.13867	0.439502
$52$	−10.6404	−1.47556
$53$	−11.5527	−1.58689	−0.793445	−	0.608642i	$-0.791714\pi$
$53$	−11.5527	−1.58689	−0.793445	+	0.608642i	$0.791714\pi$
$54$	11.3231	1.54087
$55$	−2.37596	−0.320375
$56$	−0.156102	−0.0208600
$57$	−21.4982	−2.84750
$58$	−18.6150	−2.44427
$59$	10.7873	1.40438	0.702191	−	0.711988i	$-0.252205\pi$
$59$	10.7873	1.40438	0.702191	+	0.711988i	$0.252205\pi$
$60$	−4.09583	−0.528770
$61$	5.03032	0.644066	0.322033	−	0.946728i	$-0.395634\pi$
$61$	5.03032	0.644066	0.322033	+	0.946728i	$0.395634\pi$
$62$	3.13196	0.397759
$63$	1.60615	0.202356
$64$	−9.74883	−1.21860
$65$	−3.09711	−0.384149
$66$	−21.2019	−2.60978
$67$	−9.87654	−1.20661	−0.603306	−	0.797510i	$-0.706150\pi$
$67$	−9.87654	−1.20661	−0.603306	+	0.797510i	$0.706150\pi$
$68$	−2.48645	−0.301527
$69$	−16.8112	−2.02383
$70$	−0.433987	−0.0518713
$71$	−10.8109	−1.28301	−0.641507	−	0.767117i	$-0.721690\pi$
$71$	−10.8109	−1.28301	−0.641507	+	0.767117i	$0.721690\pi$
$72$	−2.38285	−0.280821
$73$	−13.4507	−1.57428	−0.787141	−	0.616773i	$-0.788440\pi$
$73$	−13.4507	−1.57428	−0.787141	+	0.616773i	$0.788440\pi$
$74$	7.90398	0.918819
$75$	12.9070	1.49038
$76$	17.0308	1.95357
$77$	−1.18531	−0.135078
$78$	−27.6371	−3.12928
$79$	10.6157	1.19436	0.597180	−	0.802107i	$-0.296288\pi$
$79$	10.6157	1.19436	0.597180	+	0.802107i	$0.296288\pi$
$80$	−2.26116	−0.252805
$81$	0.662898	0.0736554
$82$	−8.60671	−0.950452
$83$	13.2312	1.45231	0.726157	−	0.687529i	$-0.241304\pi$
$83$	13.2312	1.45231	0.726157	+	0.687529i	$0.241304\pi$
$84$	−2.04331	−0.222943
$85$	−0.723734	−0.0785000
$86$	−13.4394	−1.44921
$87$	−25.5105	−2.73501
$88$	1.75849	0.187456
$89$	−10.4765	−1.11051	−0.555256	−	0.831680i	$-0.687380\pi$
$89$	−10.4765	−1.11051	−0.555256	+	0.831680i	$0.687380\pi$
$90$	−6.62468	−0.698302
$91$	−1.54507	−0.161967
$92$	13.3179	1.38848
$93$	4.29212	0.445072
$94$	3.50293	0.361300
$95$	4.95718	0.508596
$96$	−22.8915	−2.33635
$97$	−4.36580	−0.443280	−0.221640	−	0.975129i	$-0.571141\pi$
$97$	−4.36580	−0.443280	−0.221640	+	0.975129i	$0.571141\pi$
$98$	14.1870	1.43310
$99$	−18.0934	−1.81845
$100$	−10.2249	−1.02249
$101$	2.60935	0.259640	0.129820	−	0.991538i	$-0.458560\pi$
$101$	2.60935	0.259640	0.129820	+	0.991538i	$0.458560\pi$
$102$	−6.45825	−0.639462
$103$	−7.11892	−0.701448	−0.350724	−	0.936479i	$-0.614065\pi$
$103$	−7.11892	−0.701448	−0.350724	+	0.936479i	$0.614065\pi$
$104$	2.29222	0.224771
$105$	−0.594746	−0.0580413
$106$	23.7713	2.30888
$107$	15.4681	1.49535	0.747677	−	0.664062i	$-0.231169\pi$
$107$	15.4681	1.49535	0.747677	+	0.664062i	$0.231169\pi$
$108$	−12.2929	−1.18288
$109$	13.8408	1.32571	0.662853	−	0.748750i	$-0.269345\pi$
$109$	13.8408	1.32571	0.662853	+	0.748750i	$0.269345\pi$
$110$	4.88888	0.466136
$111$	10.8318	1.02811
$112$	−1.12803	−0.106589
$113$	3.62460	0.340974	0.170487	−	0.985360i	$-0.445466\pi$
$113$	3.62460	0.340974	0.170487	+	0.985360i	$0.445466\pi$
$114$	44.2355	4.14303
$115$	3.87644	0.361480
$116$	20.2094	1.87640
$117$	−23.5850	−2.18043
$118$	−22.1963	−2.04333
$119$	−0.361052	−0.0330976
$120$	0.882352	0.0805473
$121$	2.35253	0.213866
$122$	−10.3506	−0.937097
$123$	−11.7949	−1.06351
$124$	−3.40022	−0.305349
$125$	−6.22727	−0.556984
$126$	−3.30488	−0.294422
$127$	−15.2063	−1.34934	−0.674672	−	0.738117i	$-0.735715\pi$
$127$	−15.2063	−1.34934	−0.674672	+	0.738117i	$0.735715\pi$
$128$	3.82357	0.337959
$129$	−18.4177	−1.62159
$130$	6.37273	0.558925
$131$	−20.4981	−1.79092	−0.895462	−	0.445138i	$-0.853155\pi$
$131$	−20.4981	−1.79092	−0.895462	+	0.445138i	$0.853155\pi$
$132$	23.0179	2.00345
$133$	2.47301	0.214437
$134$	20.3224	1.75558
$135$	−3.57810	−0.307954
$136$	0.535648	0.0459315
$137$	−7.72907	−0.660339	−0.330170	−	0.943922i	$-0.607106\pi$
$137$	−7.72907	−0.660339	−0.330170	+	0.943922i	$0.607106\pi$
$138$	34.5914	2.94462
$139$	−16.3773	−1.38911	−0.694554	−	0.719441i	$-0.744398\pi$
$139$	−16.3773	−1.38911	−0.694554	+	0.719441i	$0.744398\pi$
$140$	0.471158	0.0398201
$141$	4.80051	0.404276
$142$	22.2449	1.86675
$143$	17.4052	1.45550
$144$	−17.2191	−1.43492
$145$	5.88237	0.488504
$146$	27.6766	2.29053
$147$	19.4422	1.60356
$148$	−8.58097	−0.705351
$149$	−13.4417	−1.10119	−0.550593	−	0.834774i	$-0.685598\pi$
$149$	−13.4417	−1.10119	−0.550593	+	0.834774i	$0.685598\pi$
$150$	−26.5580	−2.16845
$151$	−12.4246	−1.01110	−0.505550	−	0.862797i	$-0.668710\pi$
$151$	−12.4246	−1.01110	−0.505550	+	0.862797i	$0.668710\pi$
$152$	−3.66890	−0.297587
$153$	−5.51135	−0.445566
$154$	2.43893	0.196535
$155$	−0.989704	−0.0794949
$156$	30.0042	2.40226
$157$	−17.9167	−1.42990	−0.714952	−	0.699173i	$-0.753552\pi$
$157$	−17.9167	−1.42990	−0.714952	+	0.699173i	$0.753552\pi$
$158$	−21.8433	−1.73776
$159$	32.5769	2.58351
$160$	5.27846	0.417299
$161$	1.93385	0.152409
$162$	−1.36401	−0.107166
$163$	−22.0446	−1.72666	−0.863331	−	0.504637i	$-0.831626\pi$
$163$	−22.0446	−1.72666	−0.863331	+	0.504637i	$0.831626\pi$
$164$	9.34388	0.729635
$165$	6.69984	0.521582
$166$	−27.2251	−2.11307
$167$	−8.20127	−0.634634	−0.317317	−	0.948320i	$-0.602782\pi$
$167$	−8.20127	−0.634634	−0.317317	+	0.948320i	$0.602782\pi$
$168$	0.440182	0.0339608
$169$	9.68800	0.745231
$170$	1.48918	0.114215
$171$	37.7498	2.88680
$172$	14.5905	1.11252
$173$	6.79143	0.516343	0.258171	−	0.966099i	$-0.416880\pi$
$173$	6.79143	0.516343	0.258171	+	0.966099i	$0.416880\pi$
$174$	52.4914	3.97936
$175$	−1.48474	−0.112236
$176$	12.7073	0.957851
$177$	−30.4184	−2.28639
$178$	21.5570	1.61576
$179$	7.42622	0.555062	0.277531	−	0.960717i	$-0.410484\pi$
$179$	7.42622	0.555062	0.277531	+	0.960717i	$0.410484\pi$
$180$	7.19209	0.536067
$181$	7.20353	0.535434	0.267717	−	0.963498i	$-0.413731\pi$
$181$	7.20353	0.535434	0.267717	+	0.963498i	$0.413731\pi$
$182$	3.17919	0.235657
$183$	−14.1847	−1.04856
$184$	−2.86902	−0.211507
$185$	−2.49767	−0.183632
$186$	−8.83163	−0.647567
$187$	4.06727	0.297428
$188$	−3.80296	−0.277360
$189$	−1.78502	−0.129841
$190$	−10.2001	−0.739992
$191$	−11.8577	−0.857995	−0.428998	−	0.903306i	$-0.641133\pi$
$191$	−11.8577	−0.857995	−0.428998	+	0.903306i	$0.641133\pi$
$192$	27.4902	1.98393
$193$	−18.8329	−1.35563	−0.677813	−	0.735235i	$-0.737072\pi$
$193$	−18.8329	−1.35563	−0.677813	+	0.735235i	$0.737072\pi$
$194$	8.98324	0.644959
$195$	8.73335	0.625408
$196$	−15.4021	−1.10015
$197$	2.29679	0.163640	0.0818199	−	0.996647i	$-0.473927\pi$
$197$	2.29679	0.163640	0.0818199	+	0.996647i	$0.473927\pi$
$198$	37.2296	2.64579
$199$	−11.7041	−0.829681	−0.414841	−	0.909894i	$-0.636163\pi$
$199$	−11.7041	−0.829681	−0.414841	+	0.909894i	$0.636163\pi$
$200$	2.20273	0.155756
$201$	27.8503	1.96441
$202$	−5.36911	−0.377769
$203$	2.93456	0.205966
$204$	7.01140	0.490897
$205$	2.71973	0.189954
$206$	14.6482	1.02059
$207$	29.5197	2.05176
$208$	16.5642	1.14852
$209$	−27.8585	−1.92702
$210$	1.22377	0.0844484
$211$	21.0046	1.44602	0.723010	−	0.690838i	$-0.242758\pi$
$211$	21.0046	1.44602	0.723010	+	0.690838i	$0.242758\pi$
$212$	−25.8074	−1.77246
$213$	30.4849	2.08879
$214$	−31.8277	−2.17570
$215$	4.24688	0.289635
$216$	2.64822	0.180188
$217$	−0.493738	−0.0335171
$218$	−28.4793	−1.92886
$219$	37.9288	2.56299
$220$	−5.30761	−0.357839
$221$	5.30175	0.356634
$222$	−22.2880	−1.49587
$223$	1.54989	0.103789	0.0518943	−	0.998653i	$-0.483474\pi$
$223$	1.54989	0.103789	0.0518943	+	0.998653i	$0.483474\pi$
$224$	2.63329	0.175944
$225$	−22.6641	−1.51094
$226$	−7.45812	−0.496107
$227$	26.1374	1.73480	0.867402	−	0.497609i	$-0.165788\pi$
$227$	26.1374	1.73480	0.867402	+	0.497609i	$0.165788\pi$
$228$	−48.0243	−3.18049
$229$	10.3584	0.684505	0.342252	−	0.939608i	$-0.388810\pi$
$229$	10.3584	0.684505	0.342252	+	0.939608i	$0.388810\pi$
$230$	−7.97631	−0.525942
$231$	3.34238	0.219912
$232$	−4.35365	−0.285831
$233$	−19.6878	−1.28979	−0.644895	−	0.764271i	$-0.723099\pi$
$233$	−19.6878	−1.28979	−0.644895	+	0.764271i	$0.723099\pi$
$234$	48.5294	3.17246
$235$	−1.10693	−0.0722082
$236$	24.0974	1.56861
$237$	−29.9346	−1.94446
$238$	0.742915	0.0481560
$239$	5.63700	0.364627	0.182314	−	0.983240i	$-0.441641\pi$
$239$	5.63700	0.364627	0.182314	+	0.983240i	$0.441641\pi$
$240$	6.37611	0.411576
$241$	16.4507	1.05968	0.529842	−	0.848097i	$-0.322251\pi$
$241$	16.4507	1.05968	0.529842	+	0.848097i	$0.322251\pi$
$242$	−4.84065	−0.311169
$243$	14.6396	0.939128
$244$	11.2371	0.719382
$245$	−4.48310	−0.286415
$246$	24.2696	1.54737
$247$	−36.3141	−2.31061
$248$	0.732498	0.0465136
$249$	−37.3099	−2.36442
$250$	12.8135	0.810395
$251$	−0.797075	−0.0503109	−0.0251555	−	0.999684i	$-0.508008\pi$
$251$	−0.797075	−0.0503109	−0.0251555	+	0.999684i	$0.508008\pi$
$252$	3.58795	0.226019
$253$	−21.7849	−1.36961
$254$	31.2892	1.96326
$255$	2.04082	0.127801
$256$	11.6301	0.726884
$257$	9.90950	0.618138	0.309069	−	0.951040i	$-0.399983\pi$
$257$	9.90950	0.618138	0.309069	+	0.951040i	$0.399983\pi$
$258$	37.8971	2.35937
$259$	−1.24602	−0.0774240
$260$	−6.91856	−0.429071
$261$	44.7952	2.77275
$262$	42.1776	2.60574
$263$	2.43009	0.149845	0.0749227	−	0.997189i	$-0.476129\pi$
$263$	2.43009	0.149845	0.0749227	+	0.997189i	$0.476129\pi$
$264$	−4.95867	−0.305185
$265$	−7.51178	−0.461445
$266$	−5.08856	−0.312000
$267$	29.5422	1.80795
$268$	−22.0630	−1.34771
$269$	−13.8009	−0.841455	−0.420728	−	0.907187i	$-0.638225\pi$
$269$	−13.8009	−0.841455	−0.420728	+	0.907187i	$0.638225\pi$
$270$	7.36244	0.448064
$271$	5.88150	0.357276	0.178638	−	0.983915i	$-0.442831\pi$
$271$	5.88150	0.357276	0.178638	+	0.983915i	$0.442831\pi$
$272$	3.87074	0.234698
$273$	4.35684	0.263688
$274$	15.9036	0.960774
$275$	16.7257	1.00860
$276$	−37.5542	−2.26050
$277$	−21.8369	−1.31205	−0.656026	−	0.754738i	$-0.727764\pi$
$277$	−21.8369	−1.31205	−0.656026	+	0.754738i	$0.727764\pi$
$278$	33.6987	2.02111
$279$	−7.53676	−0.451214
$280$	−0.101500	−0.00606579
$281$	−11.4070	−0.680486	−0.340243	−	0.940338i	$-0.610509\pi$
$281$	−11.4070	−0.680486	−0.340243	+	0.940338i	$0.610509\pi$
$282$	−9.87772	−0.588209
$283$	−13.7847	−0.819416	−0.409708	−	0.912217i	$-0.634369\pi$
$283$	−13.7847	−0.819416	−0.409708	+	0.912217i	$0.634369\pi$
$284$	−24.1502	−1.43305
$285$	−13.9785	−0.828013
$286$	−35.8137	−2.11771
$287$	1.35680	0.0800896
$288$	40.1964	2.36859
$289$	−15.7611	−0.927123
$290$	−12.1038	−0.710759
$291$	12.3109	0.721675
$292$	−30.0472	−1.75838
$293$	−12.7189	−0.743045	−0.371523	−	0.928424i	$-0.621164\pi$
$293$	−12.7189	−0.743045	−0.371523	+	0.928424i	$0.621164\pi$
$294$	−40.0050	−2.33314
$295$	7.01406	0.408374
$296$	1.84857	0.107446
$297$	20.1084	1.16680
$298$	27.6581	1.60219
$299$	−28.3970	−1.64224
$300$	28.8327	1.66466
$301$	2.11866	0.122117
$302$	25.5654	1.47112
$303$	−7.35797	−0.422704
$304$	−26.5124	−1.52059
$305$	3.27079	0.187285
$306$	11.3404	0.648286
$307$	−24.7185	−1.41076	−0.705379	−	0.708830i	$-0.749223\pi$
$307$	−24.7185	−1.41076	−0.705379	+	0.708830i	$0.749223\pi$
$308$	−2.64783	−0.150874
$309$	20.0742	1.14198
$310$	2.03645	0.115663
$311$	28.7343	1.62937	0.814686	−	0.579903i	$-0.196910\pi$
$311$	28.7343	1.62937	0.814686	+	0.579903i	$0.196910\pi$
$312$	−6.46371	−0.365935
$313$	1.59654	0.0902417	0.0451209	−	0.998982i	$-0.485633\pi$
$313$	1.59654	0.0902417	0.0451209	+	0.998982i	$0.485633\pi$
$314$	36.8660	2.08047
$315$	1.04435	0.0588422
$316$	23.7142	1.33403
$317$	14.5164	0.815323	0.407661	−	0.913133i	$-0.366344\pi$
$317$	14.5164	0.815323	0.407661	+	0.913133i	$0.366344\pi$
$318$	−67.0314	−3.75894
$319$	−33.0580	−1.85089
$320$	−6.33885	−0.354353
$321$	−43.6175	−2.43449
$322$	−3.97917	−0.221751
$323$	−8.48589	−0.472168
$324$	1.48083	0.0822685
$325$	21.8022	1.20937
$326$	45.3597	2.51224
$327$	−39.0288	−2.15830
$328$	−2.01292	−0.111145
$329$	−0.552219	−0.0304448
$330$	−13.7859	−0.758886
$331$	−8.96489	−0.492755	−0.246377	−	0.969174i	$-0.579240\pi$
$331$	−8.96489	−0.492755	−0.246377	+	0.969174i	$0.579240\pi$
$332$	29.5569	1.62215
$333$	−19.0202	−1.04230
$334$	16.8753	0.923373
$335$	−6.42189	−0.350865
$336$	3.18087	0.173531
$337$	−26.9613	−1.46868	−0.734339	−	0.678783i	$-0.762508\pi$
$337$	−26.9613	−1.46868	−0.734339	+	0.678783i	$0.762508\pi$
$338$	−19.9344	−1.08429
$339$	−10.2208	−0.555117
$340$	−1.61673	−0.0876797
$341$	5.56197	0.301198
$342$	−77.6754	−4.20020
$343$	−4.50714	−0.243362
$344$	−3.14319	−0.169469
$345$	−10.9309	−0.588502
$346$	−13.9743	−0.751263
$347$	12.4896	0.670478	0.335239	−	0.942133i	$-0.391183\pi$
$347$	12.4896	0.670478	0.335239	+	0.942133i	$0.391183\pi$
$348$	−56.9874	−3.05484
$349$	−16.5437	−0.885562	−0.442781	−	0.896630i	$-0.646008\pi$
$349$	−16.5437	−0.885562	−0.442781	+	0.896630i	$0.646008\pi$
$350$	3.05506	0.163300
$351$	26.2116	1.39907
$352$	−29.6641	−1.58110
$353$	18.9951	1.01101	0.505503	−	0.862825i	$-0.331307\pi$
$353$	18.9951	1.01101	0.505503	+	0.862825i	$0.331307\pi$
$354$	62.5900	3.32662
$355$	−7.02941	−0.373082
$356$	−23.4033	−1.24037
$357$	1.01811	0.0538841
$358$	−15.2805	−0.807598
$359$	10.9630	0.578605	0.289303	−	0.957238i	$-0.406577\pi$
$359$	10.9630	0.578605	0.289303	+	0.957238i	$0.406577\pi$
$360$	−1.54937	−0.0816588
$361$	39.1237	2.05914
$362$	−14.8223	−0.779041
$363$	−6.63376	−0.348182
$364$	−3.45149	−0.180907
$365$	−8.74585	−0.457779
$366$	29.1870	1.52563
$367$	14.1886	0.740638	0.370319	−	0.928905i	$-0.379248\pi$
$367$	14.1886	0.740638	0.370319	+	0.928905i	$0.379248\pi$
$368$	−20.7323	−1.08075
$369$	20.7112	1.07818
$370$	5.13930	0.267179
$371$	−3.74743	−0.194557
$372$	9.58807	0.497118
$373$	−3.04232	−0.157525	−0.0787626	−	0.996893i	$-0.525097\pi$
$373$	−3.04232	−0.157525	−0.0787626	+	0.996893i	$0.525097\pi$
$374$	−8.36897	−0.432749
$375$	17.5599	0.906790
$376$	0.819260	0.0422501
$377$	−43.0916	−2.21933
$378$	3.67293	0.188915
$379$	−16.5122	−0.848175	−0.424087	−	0.905621i	$-0.639405\pi$
$379$	−16.5122	−0.848175	−0.424087	+	0.905621i	$0.639405\pi$
$380$	11.0737	0.568071
$381$	42.8795	2.19678
$382$	24.3989	1.24836
$383$	3.36203	0.171792	0.0858960	−	0.996304i	$-0.472625\pi$
$383$	3.36203	0.171792	0.0858960	+	0.996304i	$0.472625\pi$
$384$	−10.7819	−0.550210
$385$	−0.770706	−0.0392788
$386$	38.7514	1.97239
$387$	32.3407	1.64397
$388$	−9.75266	−0.495116
$389$	11.4511	0.580593	0.290297	−	0.956937i	$-0.406246\pi$
$389$	11.4511	0.580593	0.290297	+	0.956937i	$0.406246\pi$
$390$	−17.9701	−0.909951
$391$	−6.63583	−0.335589
$392$	3.31802	0.167585
$393$	57.8013	2.91569
$394$	−4.72597	−0.238091
$395$	6.90251	0.347303
$396$	−40.4184	−2.03110
$397$	36.7389	1.84387	0.921937	−	0.387340i	$-0.126606\pi$
$397$	36.7389	1.84387	0.921937	+	0.387340i	$0.126606\pi$
$398$	24.0828	1.20716
$399$	−6.97349	−0.349111
$400$	15.9175	0.795874
$401$	−19.4218	−0.969880	−0.484940	−	0.874547i	$-0.661159\pi$
$401$	−19.4218	−0.969880	−0.484940	+	0.874547i	$0.661159\pi$
$402$	−57.3058	−2.85815
$403$	7.25012	0.361154
$404$	5.82898	0.290003
$405$	0.431027	0.0214179
$406$	−6.03827	−0.299674
$407$	14.0365	0.695763
$408$	−1.51044	−0.0747781
$409$	−2.28157	−0.112817	−0.0564083	−	0.998408i	$-0.517965\pi$
$409$	−2.28157	−0.112817	−0.0564083	+	0.998408i	$0.517965\pi$
$410$	−5.59622	−0.276378
$411$	21.7948	1.07506
$412$	−15.9028	−0.783475
$413$	3.49913	0.172181
$414$	−60.7409	−2.98525
$415$	8.60315	0.422312
$416$	−38.6676	−1.89584
$417$	46.1815	2.26152
$418$	57.3228	2.80375
$419$	−5.50484	−0.268929	−0.134465	−	0.990918i	$-0.542931\pi$
$419$	−5.50484	−0.268929	−0.134465	+	0.990918i	$0.542931\pi$
$420$	−1.32859	−0.0648286
$421$	5.66018	0.275860	0.137930	−	0.990442i	$-0.455955\pi$
$421$	5.66018	0.275860	0.137930	+	0.990442i	$0.455955\pi$
$422$	−43.2200	−2.10392
$423$	−8.42946	−0.409855
$424$	5.55960	0.269998
$425$	5.09475	0.247131
$426$	−62.7270	−3.03913
$427$	1.63171	0.0789642
$428$	34.5538	1.67022
$429$	−49.0800	−2.36960
$430$	−8.73854	−0.421410
$431$	−32.0215	−1.54242	−0.771210	−	0.636580i	$-0.780348\pi$
$431$	−32.0215	−1.54242	−0.771210	+	0.636580i	$0.780348\pi$
$432$	19.1367	0.920716
$433$	20.4619	0.983338	0.491669	−	0.870782i	$-0.336387\pi$
$433$	20.4619	0.983338	0.491669	+	0.870782i	$0.336387\pi$
$434$	1.01593	0.0487664
$435$	−16.5874	−0.795303
$436$	30.9186	1.48073
$437$	45.4518	2.17426
$438$	−78.0437	−3.72907
$439$	5.53178	0.264018	0.132009	−	0.991249i	$-0.457857\pi$
$439$	5.53178	0.264018	0.132009	+	0.991249i	$0.457857\pi$
$440$	1.14340	0.0545095
$441$	−34.1395	−1.62569
$442$	−10.9091	−0.518892
$443$	−9.33636	−0.443584	−0.221792	−	0.975094i	$-0.571191\pi$
$443$	−9.33636	−0.443584	−0.221792	+	0.975094i	$0.571191\pi$
$444$	24.1970	1.14834
$445$	−6.81203	−0.322921
$446$	−3.18912	−0.151009
$447$	37.9034	1.79277
$448$	−3.16229	−0.149404
$449$	−27.4943	−1.29754	−0.648769	−	0.760985i	$-0.724716\pi$
$449$	−27.4943	−1.29754	−0.648769	+	0.760985i	$0.724716\pi$
$450$	46.6346	2.19838
$451$	−15.2844	−0.719716
$452$	8.09691	0.380847
$453$	35.0354	1.64611
$454$	−53.7814	−2.52409
$455$	−1.00463	−0.0470977
$456$	10.3457	0.484482
$457$	28.8270	1.34847	0.674234	−	0.738518i	$-0.264474\pi$
$457$	28.8270	1.34847	0.674234	+	0.738518i	$0.264474\pi$
$458$	−21.3139	−0.995935
$459$	6.12513	0.285897
$460$	8.65949	0.403751
$461$	−3.84216	−0.178947	−0.0894737	−	0.995989i	$-0.528518\pi$
$461$	−3.84216	−0.178947	−0.0894737	+	0.995989i	$0.528518\pi$
$462$	−6.87741	−0.319966
$463$	32.8378	1.52610	0.763051	−	0.646338i	$-0.223700\pi$
$463$	32.8378	1.52610	0.763051	+	0.646338i	$0.223700\pi$
$464$	−31.4606	−1.46052
$465$	2.79081	0.129421
$466$	40.5104	1.87661
$467$	−24.9477	−1.15444	−0.577221	−	0.816588i	$-0.695863\pi$
$467$	−24.9477	−1.15444	−0.577221	+	0.816588i	$0.695863\pi$
$468$	−52.6860	−2.43541
$469$	−3.20371	−0.147934
$470$	2.27767	0.105061
$471$	50.5221	2.32794
$472$	−5.19123	−0.238946
$473$	−23.8668	−1.09739
$474$	61.5946	2.82913
$475$	−34.8962	−1.60115
$476$	−0.806546	−0.0369680
$477$	−57.2034	−2.61916
$478$	−11.5989	−0.530522
$479$	−33.8396	−1.54617	−0.773086	−	0.634301i	$-0.781288\pi$
$479$	−33.8396	−1.54617	−0.773086	+	0.634301i	$0.781288\pi$
$480$	−14.8844	−0.679378
$481$	18.2968	0.834262
$482$	−33.8496	−1.54181
$483$	−5.45316	−0.248127
$484$	5.25526	0.238876
$485$	−2.83871	−0.128899
$486$	−30.1229	−1.36640
$487$	−7.85118	−0.355771	−0.177885	−	0.984051i	$-0.556926\pi$
$487$	−7.85118	−0.355771	−0.177885	+	0.984051i	$0.556926\pi$
$488$	−2.42077	−0.109583
$489$	62.1622	2.81107
$490$	9.22460	0.416725
$491$	−26.7845	−1.20877	−0.604383	−	0.796694i	$-0.706580\pi$
$491$	−26.7845	−1.20877	−0.604383	+	0.796694i	$0.706580\pi$
$492$	−26.3483	−1.18787
$493$	−10.0697	−0.453515
$494$	74.7212	3.36187
$495$	−11.7646	−0.528779
$496$	5.29322	0.237673
$497$	−3.50679	−0.157301
$498$	76.7704	3.44016
$499$	−10.3270	−0.462298	−0.231149	−	0.972918i	$-0.574249\pi$
$499$	−10.3270	−0.462298	−0.231149	+	0.972918i	$0.574249\pi$
$500$	−13.9110	−0.622117
$501$	23.1263	1.03321
$502$	1.64009	0.0732009
$503$	−35.7634	−1.59461	−0.797307	−	0.603575i	$-0.793743\pi$
$503$	−35.7634	−1.59461	−0.797307	+	0.603575i	$0.793743\pi$
$504$	−0.772939	−0.0344295
$505$	1.69665	0.0754997
$506$	44.8256	1.99274
$507$	−27.3186	−1.21326
$508$	−33.9691	−1.50714
$509$	4.21479	0.186817	0.0934087	−	0.995628i	$-0.470224\pi$
$509$	4.21479	0.186817	0.0934087	+	0.995628i	$0.470224\pi$
$510$	−4.19926	−0.185946
$511$	−4.36308	−0.193011
$512$	−31.5778	−1.39555
$513$	−41.9538	−1.85231
$514$	−20.3902	−0.899372
$515$	−4.62884	−0.203971
$516$	−41.1430	−1.81122
$517$	6.22077	0.273589
$518$	2.56386	0.112650
$519$	−19.1507	−0.840624
$520$	1.49044	0.0653602
$521$	6.79130	0.297532	0.148766	−	0.988872i	$-0.452470\pi$
$521$	6.79130	0.297532	0.148766	+	0.988872i	$0.452470\pi$
$522$	−92.1724	−4.03428
$523$	14.8759	0.650480	0.325240	−	0.945632i	$-0.394555\pi$
$523$	14.8759	0.650480	0.325240	+	0.945632i	$0.394555\pi$
$524$	−45.7902	−2.00035
$525$	4.18673	0.182724
$526$	−5.00024	−0.218021
$527$	1.69421	0.0738011
$528$	−35.8327	−1.55942
$529$	12.5426	0.545331
$530$	15.4565	0.671388
$531$	53.4132	2.31794
$532$	5.52440	0.239513
$533$	−19.9235	−0.862983
$534$	−60.7872	−2.63052
$535$	10.0576	0.434828
$536$	4.75296	0.205296
$537$	−20.9408	−0.903661
$538$	28.3973	1.22429
$539$	25.1943	1.08520
$540$	−7.99305	−0.343966
$541$	−10.5492	−0.453545	−0.226773	−	0.973948i	$-0.572817\pi$
$541$	−10.5492	−0.453545	−0.226773	+	0.973948i	$0.572817\pi$
$542$	−12.1020	−0.519826
$543$	−20.3128	−0.871706
$544$	−9.03587	−0.387410
$545$	8.99950	0.385496
$546$	−8.96481	−0.383658
$547$	35.8052	1.53092	0.765460	−	0.643483i	$-0.222511\pi$
$547$	35.8052	1.53092	0.765460	+	0.643483i	$0.222511\pi$
$548$	−17.2658	−0.737559
$549$	24.9076	1.06303
$550$	−34.4154	−1.46748
$551$	68.9717	2.93829
$552$	8.09018	0.344341
$553$	3.44348	0.146432
$554$	44.9325	1.90900
$555$	7.04303	0.298960
$556$	−36.5850	−1.55155
$557$	−20.3498	−0.862247	−0.431124	−	0.902293i	$-0.641883\pi$
$557$	−20.3498	−0.862247	−0.431124	+	0.902293i	$0.641883\pi$
$558$	15.5079	0.656503
$559$	−31.1107	−1.31584
$560$	−0.733466	−0.0309946
$561$	−11.4690	−0.484224
$562$	23.4715	0.990086
$563$	−7.29639	−0.307506	−0.153753	−	0.988109i	$-0.549136\pi$
$563$	−7.29639	−0.307506	−0.153753	+	0.988109i	$0.549136\pi$
$564$	10.7238	0.451551
$565$	2.35677	0.0991503
$566$	28.3640	1.19223
$567$	0.215028	0.00903034
$568$	5.20259	0.218296
$569$	36.7558	1.54088	0.770441	−	0.637511i	$-0.220036\pi$
$569$	36.7558	1.54088	0.770441	+	0.637511i	$0.220036\pi$
$570$	28.7626	1.20473
$571$	−19.3533	−0.809912	−0.404956	−	0.914336i	$-0.632713\pi$
$571$	−19.3533	−0.809912	−0.404956	+	0.914336i	$0.632713\pi$
$572$	38.8812	1.62570
$573$	33.4369	1.39685
$574$	−2.79181	−0.116528
$575$	−27.2883	−1.13800
$576$	−48.2714	−2.01131
$577$	−22.3441	−0.930199	−0.465099	−	0.885259i	$-0.653981\pi$
$577$	−22.3441	−0.930199	−0.465099	+	0.885259i	$0.653981\pi$
$578$	32.4306	1.34894
$579$	53.1059	2.20701
$580$	13.1405	0.545630
$581$	4.29189	0.178058
$582$	−25.3313	−1.05002
$583$	42.2150	1.74836
$584$	6.47296	0.267853
$585$	−15.3353	−0.634039
$586$	26.1709	1.08111
$587$	18.2446	0.753036	0.376518	−	0.926409i	$-0.377121\pi$
$587$	18.2446	0.753036	0.376518	+	0.926409i	$0.377121\pi$
$588$	43.4315	1.79108
$589$	−11.6044	−0.478152
$590$	−14.4324	−0.594173
$591$	−6.47659	−0.266411
$592$	13.3582	0.549020
$593$	−23.3716	−0.959755	−0.479877	−	0.877336i	$-0.659319\pi$
$593$	−23.3716	−0.959755	−0.479877	+	0.877336i	$0.659319\pi$
$594$	−41.3757	−1.69767
$595$	−0.234762	−0.00962431
$596$	−30.0271	−1.22996
$597$	33.0037	1.35075
$598$	58.4308	2.38941
$599$	−13.7853	−0.563252	−0.281626	−	0.959524i	$-0.590874\pi$
$599$	−13.7853	−0.563252	−0.281626	+	0.959524i	$0.590874\pi$
$600$	−6.21134	−0.253577
$601$	6.20194	0.252983	0.126491	−	0.991968i	$-0.459628\pi$
$601$	6.20194	0.252983	0.126491	+	0.991968i	$0.459628\pi$
$602$	−4.35943	−0.177677
$603$	−48.9037	−1.99151
$604$	−27.7551	−1.12934
$605$	1.52965	0.0621892
$606$	15.1400	0.615022
$607$	25.9287	1.05241	0.526206	−	0.850357i	$-0.323614\pi$
$607$	25.9287	1.05241	0.526206	+	0.850357i	$0.323614\pi$
$608$	61.8908	2.51000
$609$	−8.27500	−0.335320
$610$	−6.73011	−0.272494
$611$	8.10888	0.328050
$612$	−12.3117	−0.497671
$613$	29.8917	1.20731	0.603656	−	0.797245i	$-0.293710\pi$
$613$	29.8917	1.20731	0.603656	+	0.797245i	$0.293710\pi$
$614$	50.8617	2.05261
$615$	−7.66921	−0.309252
$616$	0.570413	0.0229826
$617$	23.9446	0.963972	0.481986	−	0.876179i	$-0.339916\pi$
$617$	23.9446	0.963972	0.481986	+	0.876179i	$0.339916\pi$
$618$	−41.3055	−1.66155
$619$	24.5983	0.988687	0.494344	−	0.869267i	$-0.335408\pi$
$619$	24.5983	0.988687	0.494344	+	0.869267i	$0.335408\pi$
$620$	−2.21088	−0.0887910
$621$	−32.8072	−1.31651
$622$	−59.1248	−2.37069
$623$	−3.39834	−0.136152
$624$	−46.7085	−1.86983
$625$	18.8370	0.753481
$626$	−3.28510	−0.131299
$627$	78.5567	3.13725
$628$	−40.0236	−1.59712
$629$	4.27560	0.170479
$630$	−2.14889	−0.0856137
$631$	−9.90019	−0.394121	−0.197060	−	0.980391i	$-0.563139\pi$
$631$	−9.90019	−0.394121	−0.197060	+	0.980391i	$0.563139\pi$
$632$	−5.10867	−0.203212
$633$	−59.2298	−2.35417
$634$	−29.8695	−1.18627
$635$	−9.88742	−0.392370
$636$	72.7727	2.88563
$637$	32.8412	1.30121
$638$	68.0214	2.69299
$639$	−53.5301	−2.11762
$640$	2.48615	0.0982737
$641$	−3.86513	−0.152664	−0.0763318	−	0.997082i	$-0.524321\pi$
$641$	−3.86513	−0.152664	−0.0763318	+	0.997082i	$0.524321\pi$
$642$	89.7490	3.54211
$643$	−14.9802	−0.590762	−0.295381	−	0.955380i	$-0.595447\pi$
$643$	−14.9802	−0.590762	−0.295381	+	0.955380i	$0.595447\pi$
$644$	4.31999	0.170232
$645$	−11.9755	−0.471536
$646$	17.4609	0.686990
$647$	−5.23677	−0.205879	−0.102939	−	0.994688i	$-0.532825\pi$
$647$	−5.23677	−0.205879	−0.102939	+	0.994688i	$0.532825\pi$
$648$	−0.319011	−0.0125319
$649$	−39.4179	−1.54729
$650$	−44.8610	−1.75959
$651$	1.39226	0.0545670
$652$	−49.2449	−1.92858
$653$	−16.0921	−0.629732	−0.314866	−	0.949136i	$-0.601960\pi$
$653$	−16.0921	−0.629732	−0.314866	+	0.949136i	$0.601960\pi$
$654$	80.3072	3.14026
$655$	−13.3282	−0.520775
$656$	−14.5459	−0.567922
$657$	−66.6011	−2.59836
$658$	1.13627	0.0442963
$659$	−1.04848	−0.0408431	−0.0204216	−	0.999791i	$-0.506501\pi$
$659$	−1.04848	−0.0408431	−0.0204216	+	0.999791i	$0.506501\pi$
$660$	14.9666	0.582575
$661$	19.3308	0.751881	0.375940	−	0.926644i	$-0.377320\pi$
$661$	19.3308	0.751881	0.375940	+	0.926644i	$0.377320\pi$
$662$	18.4465	0.716944
$663$	−14.9501	−0.580613
$664$	−6.36735	−0.247101
$665$	1.60799	0.0623552
$666$	39.1366	1.51651
$667$	53.9348	2.08836
$668$	−18.3206	−0.708847
$669$	−4.37045	−0.168972
$670$	13.2139	0.510499
$671$	−18.3813	−0.709603
$672$	−7.42545	−0.286443
$673$	29.1303	1.12289	0.561446	−	0.827514i	$-0.310245\pi$
$673$	29.1303	1.12289	0.561446	+	0.827514i	$0.310245\pi$
$674$	55.4767	2.13688
$675$	25.1882	0.969493
$676$	21.6418	0.832377
$677$	−11.6307	−0.447006	−0.223503	−	0.974703i	$-0.571749\pi$
$677$	−11.6307	−0.447006	−0.223503	+	0.974703i	$0.571749\pi$
$678$	21.0307	0.807679
$679$	−1.41616	−0.0543473
$680$	0.348288	0.0133562
$681$	−73.7035	−2.82432
$682$	−11.4445	−0.438234
$683$	−13.0938	−0.501022	−0.250511	−	0.968114i	$-0.580599\pi$
$683$	−13.0938	−0.501022	−0.250511	+	0.968114i	$0.580599\pi$
$684$	84.3283	3.22438
$685$	−5.02557	−0.192017
$686$	9.27406	0.354085
$687$	−29.2092	−1.11440
$688$	−22.7135	−0.865944
$689$	55.0279	2.09639
$690$	22.4919	0.856253
$691$	−13.0192	−0.495274	−0.247637	−	0.968853i	$-0.579654\pi$
$691$	−13.0192	−0.495274	−0.247637	+	0.968853i	$0.579654\pi$
$692$	15.1712	0.576723
$693$	−5.86905	−0.222947
$694$	−25.6991	−0.975526
$695$	−10.6488	−0.403933
$696$	12.2766	0.465343
$697$	−4.65574	−0.176349
$698$	34.0409	1.28847
$699$	55.5165	2.09983
$700$	−3.31673	−0.125361
$701$	−49.4583	−1.86802	−0.934008	−	0.357252i	$-0.883714\pi$
$701$	−49.4583	−1.86802	−0.934008	+	0.357252i	$0.883714\pi$
$702$	−53.9339	−2.03560
$703$	−29.2855	−1.10453
$704$	35.6233	1.34260
$705$	3.12137	0.117558
$706$	−39.0850	−1.47098
$707$	0.846412	0.0318326
$708$	−67.9510	−2.55375
$709$	−43.6332	−1.63868	−0.819339	−	0.573309i	$-0.805659\pi$
$709$	−43.6332	−1.63868	−0.819339	+	0.573309i	$0.805659\pi$
$710$	14.4640	0.542824
$711$	52.5637	1.97129
$712$	5.04170	0.188946
$713$	−9.07448	−0.339842
$714$	−2.09490	−0.0783997
$715$	11.3172	0.423238
$716$	16.5893	0.619970
$717$	−15.8954	−0.593626
$718$	−22.5579	−0.841853
$719$	21.9099	0.817102	0.408551	−	0.912736i	$-0.366034\pi$
$719$	21.9099	0.817102	0.408551	+	0.912736i	$0.366034\pi$
$720$	−11.1961	−0.417255
$721$	−2.30921	−0.0859995
$722$	−80.5025	−2.99599
$723$	−46.3884	−1.72520
$724$	16.0918	0.598047
$725$	−41.4091	−1.53790
$726$	13.6499	0.506594
$727$	14.6615	0.543764	0.271882	−	0.962331i	$-0.412354\pi$
$727$	14.6615	0.543764	0.271882	+	0.962331i	$0.412354\pi$
$728$	0.743543	0.0275575
$729$	−43.2699	−1.60259
$730$	17.9958	0.666055
$731$	−7.26997	−0.268889
$732$	−31.6869	−1.17118
$733$	14.0095	0.517453	0.258726	−	0.965951i	$-0.416697\pi$
$733$	14.0095	0.517453	0.258726	+	0.965951i	$0.416697\pi$
$734$	−29.1950	−1.07761
$735$	12.6416	0.466294
$736$	48.3976	1.78396
$737$	36.0900	1.32939
$738$	−42.6162	−1.56872
$739$	−5.98789	−0.220268	−0.110134	−	0.993917i	$-0.535128\pi$
$739$	−5.98789	−0.220268	−0.110134	+	0.993917i	$0.535128\pi$
$740$	−5.57949	−0.205106
$741$	102.400	3.76175
$742$	7.71086	0.283075
$743$	21.8420	0.801303	0.400652	−	0.916230i	$-0.368784\pi$
$743$	21.8420	0.801303	0.400652	+	0.916230i	$0.368784\pi$
$744$	−2.06553	−0.0757259
$745$	−8.74001	−0.320209
$746$	6.25999	0.229195
$747$	65.5144	2.39705
$748$	9.08578	0.332209
$749$	5.01747	0.183334
$750$	−36.1319	−1.31935
$751$	−35.6788	−1.30194	−0.650968	−	0.759105i	$-0.725637\pi$
$751$	−35.6788	−1.30194	−0.650968	+	0.759105i	$0.725637\pi$
$752$	5.92019	0.215887
$753$	2.24762	0.0819080
$754$	88.6669	3.22906
$755$	−8.07868	−0.294013
$756$	−3.98752	−0.145025
$757$	15.2780	0.555287	0.277644	−	0.960684i	$-0.410447\pi$
$757$	15.2780	0.555287	0.277644	+	0.960684i	$0.410447\pi$
$758$	33.9761	1.23407
$759$	61.4301	2.22977
$760$	−2.38558	−0.0865341
$761$	29.2771	1.06129	0.530646	−	0.847593i	$-0.321949\pi$
$761$	29.2771	1.06129	0.530646	+	0.847593i	$0.321949\pi$
$762$	−88.2305	−3.19625
$763$	4.48962	0.162535
$764$	−26.4887	−0.958329
$765$	−3.58357	−0.129564
$766$	−6.91785	−0.249952
$767$	−51.3818	−1.85529
$768$	−32.7951	−1.18339
$769$	−43.2216	−1.55861	−0.779305	−	0.626645i	$-0.784428\pi$
$769$	−43.2216	−1.55861	−0.779305	+	0.626645i	$0.784428\pi$
$770$	1.58584	0.0571495
$771$	−27.9432	−1.00635
$772$	−42.0705	−1.51415
$773$	41.1691	1.48075	0.740375	−	0.672194i	$-0.234648\pi$
$773$	41.1691	1.48075	0.740375	+	0.672194i	$0.234648\pi$
$774$	−66.5454	−2.39193
$775$	6.96705	0.250264
$776$	2.10098	0.0754209
$777$	3.51358	0.126049
$778$	−23.5622	−0.844746
$779$	31.8893	1.14255
$780$	19.5092	0.698543
$781$	39.5041	1.41357
$782$	13.6542	0.488271
$783$	−49.7839	−1.77913
$784$	23.9769	0.856318
$785$	−11.6497	−0.415796
$786$	−118.934	−4.24224
$787$	42.3486	1.50957	0.754783	−	0.655975i	$-0.227742\pi$
$787$	42.3486	1.50957	0.754783	+	0.655975i	$0.227742\pi$
$788$	5.13076	0.182776
$789$	−6.85246	−0.243954
$790$	−14.2029	−0.505315
$791$	1.17573	0.0418043
$792$	8.70719	0.309397
$793$	−23.9604	−0.850857
$794$	−75.5955	−2.68278
$795$	21.1820	0.751249
$796$	−26.1455	−0.926703
$797$	−10.6543	−0.377396	−0.188698	−	0.982035i	$-0.560427\pi$
$797$	−10.6543	−0.377396	−0.188698	+	0.982035i	$0.560427\pi$
$798$	14.3489	0.507947
$799$	1.89489	0.0670363
$800$	−37.1579	−1.31373
$801$	−51.8747	−1.83290
$802$	39.9631	1.41115
$803$	49.1503	1.73447
$804$	62.2141	2.19412
$805$	1.25742	0.0443184
$806$	−14.9181	−0.525469
$807$	38.9163	1.36992
$808$	−1.25572	−0.0441760
$809$	35.5895	1.25126	0.625630	−	0.780120i	$-0.284842\pi$
$809$	35.5895	1.25126	0.625630	+	0.780120i	$0.284842\pi$
$810$	−0.886899	−0.0311624
$811$	41.6818	1.46365	0.731823	−	0.681494i	$-0.238670\pi$
$811$	41.6818	1.46365	0.731823	+	0.681494i	$0.238670\pi$
$812$	6.55546	0.230051
$813$	−16.5849	−0.581658
$814$	−28.8820	−1.01231
$815$	−14.3337	−0.502089
$816$	−10.9149	−0.382097
$817$	49.7953	1.74212
$818$	4.69466	0.164145
$819$	−7.65041	−0.267327
$820$	6.07555	0.212167
$821$	8.22752	0.287142	0.143571	−	0.989640i	$-0.454141\pi$
$821$	8.22752	0.287142	0.143571	+	0.989640i	$0.454141\pi$
$822$	−44.8458	−1.56418
$823$	−8.51588	−0.296845	−0.148422	−	0.988924i	$-0.547420\pi$
$823$	−8.51588	−0.296845	−0.148422	+	0.988924i	$0.547420\pi$
$824$	3.42589	0.119347
$825$	−47.1637	−1.64203
$826$	−7.19995	−0.250518
$827$	−0.128745	−0.00447690	−0.00223845	−	0.999997i	$-0.500713\pi$
$827$	−0.128745	−0.00447690	−0.00223845	+	0.999997i	$0.500713\pi$
$828$	65.9434	2.29169
$829$	−25.1286	−0.872752	−0.436376	−	0.899764i	$-0.643738\pi$
$829$	−25.1286	−0.872752	−0.436376	+	0.899764i	$0.643738\pi$
$830$	−17.7022	−0.614452
$831$	61.5766	2.13607
$832$	46.4356	1.60986
$833$	7.67434	0.265900
$834$	−95.0249	−3.29044
$835$	−5.33260	−0.184542
$836$	−62.2326	−2.15236
$837$	8.37610	0.289520
$838$	11.3270	0.391284
$839$	−13.0943	−0.452066	−0.226033	−	0.974120i	$-0.572576\pi$
$839$	−13.0943	−0.452066	−0.226033	+	0.974120i	$0.572576\pi$
$840$	0.286214	0.00987532
$841$	52.8444	1.82222
$842$	−11.6466	−0.401368
$843$	32.1660	1.10786
$844$	46.9218	1.61512
$845$	6.29930	0.216702
$846$	17.3448	0.596326
$847$	0.763104	0.0262206
$848$	40.1751	1.37962
$849$	38.8707	1.33404
$850$	−10.4831	−0.359569
$851$	−22.9008	−0.785031
$852$	68.0996	2.33306
$853$	−50.3854	−1.72516	−0.862581	−	0.505919i	$-0.831153\pi$
$853$	−50.3854	−1.72516	−0.862581	+	0.505919i	$0.831153\pi$
$854$	−3.35748	−0.114891
$855$	24.5455	0.839439
$856$	−7.44380	−0.254424
$857$	−34.4254	−1.17595	−0.587974	−	0.808880i	$-0.700074\pi$
$857$	−34.4254	−1.17595	−0.587974	+	0.808880i	$0.700074\pi$
$858$	100.989	3.44771
$859$	3.18794	0.108771	0.0543855	−	0.998520i	$-0.482680\pi$
$859$	3.18794	0.108771	0.0543855	+	0.998520i	$0.482680\pi$
$860$	9.48701	0.323504
$861$	−3.82597	−0.130389
$862$	65.8887	2.24418
$863$	16.0755	0.547217	0.273608	−	0.961841i	$-0.411783\pi$
$863$	16.0755	0.547217	0.273608	+	0.961841i	$0.411783\pi$
$864$	−44.6729	−1.51980
$865$	4.41590	0.150145
$866$	−42.1033	−1.43073
$867$	44.4438	1.50939
$868$	−1.10295	−0.0374365
$869$	−38.7910	−1.31589
$870$	34.1308	1.15714
$871$	47.0439	1.59402
$872$	−6.66069	−0.225560
$873$	−21.6173	−0.731634
$874$	−93.5235	−3.16348
$875$	−2.01998	−0.0682877
$876$	84.7283	2.86270
$877$	−50.5940	−1.70844	−0.854219	−	0.519914i	$-0.825964\pi$
$877$	−50.5940	−1.70844	−0.854219	+	0.519914i	$0.825964\pi$
$878$	−11.3824	−0.384138
$879$	35.8652	1.20970
$880$	8.26252	0.278529
$881$	−19.7235	−0.664502	−0.332251	−	0.943191i	$-0.607808\pi$
$881$	−19.7235	−0.664502	−0.332251	+	0.943191i	$0.607808\pi$
$882$	70.2469	2.36534
$883$	19.3151	0.650005	0.325002	−	0.945713i	$-0.394635\pi$
$883$	19.3151	0.650005	0.325002	+	0.945713i	$0.394635\pi$
$884$	11.8435	0.398339
$885$	−19.7785	−0.664848
$886$	19.2109	0.645402
$887$	5.88942	0.197748	0.0988738	−	0.995100i	$-0.468476\pi$
$887$	5.88942	0.197748	0.0988738	+	0.995100i	$0.468476\pi$
$888$	−5.21267	−0.174926
$889$	−4.93257	−0.165433
$890$	14.0167	0.469840
$891$	−2.42230	−0.0811502
$892$	3.46227	0.115925
$893$	−12.9789	−0.434324
$894$	−77.9916	−2.60843
$895$	4.82865	0.161404
$896$	1.24028	0.0414347
$897$	80.0751	2.67363
$898$	56.5734	1.88788
$899$	−13.7702	−0.459263
$900$	−50.6289	−1.68763
$901$	12.8589	0.428394
$902$	31.4499	1.04717
$903$	−5.97428	−0.198811
$904$	−1.74429	−0.0580143
$905$	4.68385	0.155697
$906$	−72.0902	−2.39504
$907$	−38.3326	−1.27281	−0.636406	−	0.771354i	$-0.719580\pi$
$907$	−38.3326	−1.27281	−0.636406	+	0.771354i	$0.719580\pi$
$908$	58.3879	1.93767
$909$	12.9202	0.428537
$910$	2.06716	0.0685257
$911$	11.5809	0.383692	0.191846	−	0.981425i	$-0.438553\pi$
$911$	11.5809	0.383692	0.191846	+	0.981425i	$0.438553\pi$
$912$	74.7608	2.47558
$913$	−48.3483	−1.60010
$914$	−59.3155	−1.96198
$915$	−9.22312	−0.304907
$916$	23.1395	0.764550
$917$	−6.64908	−0.219572
$918$	−12.6033	−0.415971
$919$	−36.1376	−1.19207	−0.596035	−	0.802959i	$-0.703258\pi$
$919$	−36.1376	−1.19207	−0.596035	+	0.802959i	$0.703258\pi$
$920$	−1.86549	−0.0615032
$921$	69.7022	2.29677
$922$	7.90578	0.260363
$923$	51.4942	1.69495
$924$	7.46646	0.245629
$925$	17.5824	0.578106
$926$	−67.5684	−2.22043
$927$	−35.2494	−1.15774
$928$	73.4419	2.41085
$929$	−19.8107	−0.649967	−0.324983	−	0.945720i	$-0.605359\pi$
$929$	−19.8107	−0.649967	−0.324983	+	0.945720i	$0.605359\pi$
$930$	−5.74248	−0.188303
$931$	−52.5651	−1.72275
$932$	−43.9801	−1.44062
$933$	−81.0261	−2.65268
$934$	51.3334	1.67968
$935$	2.64460	0.0864878
$936$	11.3500	0.370985
$937$	20.9691	0.685031	0.342515	−	0.939512i	$-0.388721\pi$
$937$	20.9691	0.685031	0.342515	+	0.939512i	$0.388721\pi$
$938$	6.59209	0.215239
$939$	−4.50199	−0.146917
$940$	−2.47275	−0.0806522
$941$	10.8801	0.354682	0.177341	−	0.984149i	$-0.443250\pi$
$941$	10.8801	0.354682	0.177341	+	0.984149i	$0.443250\pi$
$942$	−103.956	−3.38708
$943$	24.9369	0.812057
$944$	−37.5132	−1.22095
$945$	−1.16065	−0.0377560
$946$	49.1092	1.59668
$947$	44.1980	1.43624	0.718121	−	0.695919i	$-0.245003\pi$
$947$	44.1980	1.43624	0.718121	+	0.695919i	$0.245003\pi$
$948$	−66.8702	−2.17184
$949$	64.0681	2.07974
$950$	71.8038	2.32962
$951$	−40.9340	−1.32737
$952$	0.173752	0.00563132
$953$	14.3023	0.463296	0.231648	−	0.972800i	$-0.425588\pi$
$953$	14.3023	0.463296	0.231648	+	0.972800i	$0.425588\pi$
$954$	117.704	3.81081
$955$	−7.71009	−0.249493
$956$	12.5924	0.407266
$957$	93.2182	3.01332
$958$	69.6297	2.24963
$959$	−2.50713	−0.0809594
$960$	17.8746	0.576899
$961$	−28.6832	−0.925264
$962$	−37.6482	−1.21383
$963$	76.5902	2.46809
$964$	36.7489	1.18360
$965$	−12.2455	−0.394196
$966$	11.2206	0.361018
$967$	0.107776	0.00346583	0.00173291	−	0.999998i	$-0.499448\pi$
$967$	0.107776	0.00346583	0.00173291	+	0.999998i	$0.499448\pi$
$968$	−1.13212	−0.0363878
$969$	23.9289	0.768706
$970$	5.84105	0.187545
$971$	−30.9750	−0.994035	−0.497018	−	0.867740i	$-0.665572\pi$
$971$	−30.9750	−0.994035	−0.497018	+	0.867740i	$0.665572\pi$
$972$	32.7030	1.04895
$973$	−5.31242	−0.170308
$974$	16.1549	0.517636
$975$	−61.4787	−1.96889
$976$	−17.4931	−0.559942
$977$	29.7053	0.950355	0.475178	−	0.879890i	$-0.342384\pi$
$977$	29.7053	0.950355	0.475178	+	0.879890i	$0.342384\pi$
$978$	−127.907	−4.09002
$979$	38.2825	1.22351
$980$	−10.0147	−0.319908
$981$	68.5327	2.18808
$982$	55.1128	1.75872
$983$	−1.00000	−0.0318950
$983$	−1.00000	−0.0318950
$984$	5.67612	0.180948
$985$	1.49341	0.0475841
$986$	20.7197	0.659851
$987$	1.55717	0.0495653
$988$	−81.1212	−2.58081
$989$	38.9391	1.23819
$990$	24.2073	0.769359
$991$	−14.0954	−0.447756	−0.223878	−	0.974617i	$-0.571872\pi$
$991$	−14.0954	−0.447756	−0.223878	+	0.974617i	$0.571872\pi$
$992$	−12.3565	−0.392320
$993$	25.2796	0.802223
$994$	7.21571	0.228868
$995$	−7.61020	−0.241259
$996$	−83.3458	−2.64091
$997$	34.6917	1.09870	0.549348	−	0.835594i	$-0.314876\pi$
$997$	34.6917	1.09870	0.549348	+	0.835594i	$0.314876\pi$
$998$	21.2492	0.672631
$999$	21.1384	0.668788

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.2.a.a.1.5	✓	28
3.2	odd	2		8847.2.a.b.1.24		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.2.a.a.1.5	✓	28	1.1	even	1	trivial
8847.2.a.b.1.24		28	3.2	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:	\( N \)	\(=\)	\( 983 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	983.a (trivial)

\(f(q)\)	\(=\)	\(q-2.05764 q^{2} -2.81984 q^{3} +2.23388 q^{4} +0.650217 q^{5} +5.80222 q^{6} +0.324376 q^{7} -0.481237 q^{8} +4.95151 q^{9} +O(q^{10})\)	\(q-2.05764 q^{2} -2.81984 q^{3} +2.23388 q^{4} +0.650217 q^{5} +5.80222 q^{6} +0.324376 q^{7} -0.481237 q^{8} +4.95151 q^{9} -1.33791 q^{10} -3.65411 q^{11} -6.29918 q^{12} -4.76319 q^{13} -0.667449 q^{14} -1.83351 q^{15} -3.47754 q^{16} -1.11307 q^{17} -10.1884 q^{18} +7.62389 q^{19} +1.45250 q^{20} -0.914690 q^{21} +7.51884 q^{22} +5.96176 q^{23} +1.35701 q^{24} -4.57722 q^{25} +9.80093 q^{26} -5.50294 q^{27} +0.724617 q^{28} +9.04679 q^{29} +3.77270 q^{30} -1.52211 q^{31} +8.11801 q^{32} +10.3040 q^{33} +2.29029 q^{34} +0.210915 q^{35} +11.0611 q^{36} -3.84129 q^{37} -15.6872 q^{38} +13.4314 q^{39} -0.312908 q^{40} +4.18281 q^{41} +1.88210 q^{42} +6.53148 q^{43} -8.16284 q^{44} +3.21955 q^{45} -12.2672 q^{46} -1.70240 q^{47} +9.80612 q^{48} -6.89478 q^{49} +9.41826 q^{50} +3.13867 q^{51} -10.6404 q^{52} -11.5527 q^{53} +11.3231 q^{54} -2.37596 q^{55} -0.156102 q^{56} -21.4982 q^{57} -18.6150 q^{58} +10.7873 q^{59} -4.09583 q^{60} +5.03032 q^{61} +3.13196 q^{62} +1.60615 q^{63} -9.74883 q^{64} -3.09711 q^{65} -21.2019 q^{66} -9.87654 q^{67} -2.48645 q^{68} -16.8112 q^{69} -0.433987 q^{70} -10.8109 q^{71} -2.38285 q^{72} -13.4507 q^{73} +7.90398 q^{74} +12.9070 q^{75} +17.0308 q^{76} -1.18531 q^{77} -27.6371 q^{78} +10.6157 q^{79} -2.26116 q^{80} +0.662898 q^{81} -8.60671 q^{82} +13.2312 q^{83} -2.04331 q^{84} -0.723734 q^{85} -13.4394 q^{86} -25.5105 q^{87} +1.75849 q^{88} -10.4765 q^{89} -6.62468 q^{90} -1.54507 q^{91} +13.3179 q^{92} +4.29212 q^{93} +3.50293 q^{94} +4.95718 q^{95} -22.8915 q^{96} -4.36580 q^{97} +14.1870 q^{98} -18.0934 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 7 q^{2} - 6 q^{3} + 17 q^{4} - 7 q^{5} - 7 q^{6} - 25 q^{7} - 15 q^{8} + 6 q^{9}+O(q^{10}) \) 28 * q - 7 * q^2 - 6 * q^3 + 17 * q^4 - 7 * q^5 - 7 * q^6 - 25 * q^7 - 15 * q^8 + 6 * q^9	\( 28 q - 7 q^{2} - 6 q^{3} + 17 q^{4} - 7 q^{5} - 7 q^{6} - 25 q^{7} - 15 q^{8} + 6 q^{9} - 17 q^{10} - 10 q^{11} - 10 q^{12} - 28 q^{13} + 5 q^{14} - 9 q^{15} + 3 q^{16} - 24 q^{17} - 23 q^{18} - 13 q^{19} - 4 q^{20} - 21 q^{21} - 21 q^{22} - 9 q^{23} - 19 q^{24} - 33 q^{25} + 2 q^{26} - 12 q^{27} - 58 q^{28} - 14 q^{29} - 8 q^{30} - 16 q^{31} - 27 q^{32} - 34 q^{33} - 6 q^{34} - 2 q^{35} - 6 q^{36} - 58 q^{37} + 6 q^{38} - 12 q^{39} - 24 q^{40} - 24 q^{41} + 22 q^{42} - 43 q^{43} - 19 q^{45} - 28 q^{46} + 2 q^{47} + 19 q^{48} - 21 q^{49} + 17 q^{50} - 6 q^{51} - 47 q^{52} - 16 q^{53} + 16 q^{54} - 16 q^{55} + 30 q^{56} - 70 q^{57} - 31 q^{58} + 12 q^{59} - q^{60} - 22 q^{61} - 15 q^{63} - 3 q^{64} - 24 q^{65} + 41 q^{66} - 38 q^{67} + 11 q^{68} + 2 q^{69} + 19 q^{70} + 2 q^{71} - 15 q^{72} - 124 q^{73} + 14 q^{74} + 8 q^{75} + 3 q^{76} - 20 q^{77} + 21 q^{78} - 16 q^{79} + 10 q^{80} - 36 q^{81} + 2 q^{82} + 12 q^{83} + 6 q^{84} - 73 q^{85} + 41 q^{86} - 15 q^{87} - 61 q^{88} - 3 q^{89} + 39 q^{90} + 5 q^{91} + 44 q^{92} - 21 q^{93} + 9 q^{94} + 17 q^{95} - 3 q^{96} - 105 q^{97} + 16 q^{98} - 15 q^{99}+O(q^{100}) \) 28 * q - 7 * q^2 - 6 * q^3 + 17 * q^4 - 7 * q^5 - 7 * q^6 - 25 * q^7 - 15 * q^8 + 6 * q^9 - 17 * q^10 - 10 * q^11 - 10 * q^12 - 28 * q^13 + 5 * q^14 - 9 * q^15 + 3 * q^16 - 24 * q^17 - 23 * q^18 - 13 * q^19 - 4 * q^20 - 21 * q^21 - 21 * q^22 - 9 * q^23 - 19 * q^24 - 33 * q^25 + 2 * q^26 - 12 * q^27 - 58 * q^28 - 14 * q^29 - 8 * q^30 - 16 * q^31 - 27 * q^32 - 34 * q^33 - 6 * q^34 - 2 * q^35 - 6 * q^36 - 58 * q^37 + 6 * q^38 - 12 * q^39 - 24 * q^40 - 24 * q^41 + 22 * q^42 - 43 * q^43 - 19 * q^45 - 28 * q^46 + 2 * q^47 + 19 * q^48 - 21 * q^49 + 17 * q^50 - 6 * q^51 - 47 * q^52 - 16 * q^53 + 16 * q^54 - 16 * q^55 + 30 * q^56 - 70 * q^57 - 31 * q^58 + 12 * q^59 - q^60 - 22 * q^61 - 15 * q^63 - 3 * q^64 - 24 * q^65 + 41 * q^66 - 38 * q^67 + 11 * q^68 + 2 * q^69 + 19 * q^70 + 2 * q^71 - 15 * q^72 - 124 * q^73 + 14 * q^74 + 8 * q^75 + 3 * q^76 - 20 * q^77 + 21 * q^78 - 16 * q^79 + 10 * q^80 - 36 * q^81 + 2 * q^82 + 12 * q^83 + 6 * q^84 - 73 * q^85 + 41 * q^86 - 15 * q^87 - 61 * q^88 - 3 * q^89 + 39 * q^90 + 5 * q^91 + 44 * q^92 - 21 * q^93 + 9 * q^94 + 17 * q^95 - 3 * q^96 - 105 * q^97 + 16 * q^98 - 15 * q^99

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