LMFDB - Embedded newform 799.2.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [799,2,Mod(1,799)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(799, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("799.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 799 = 17 \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	799.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:	$6.38004712150$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 3 x^{16} - 22 x^{15} + 70 x^{14} + 184 x^{13} - 644 x^{12} - 713 x^{11} + 2975 x^{10} + \cdots + 11 $ x^17 - 3x^16 - 22x^15 + 70x^14 + 184x^13 - 644x^12 - 713x^11 + 2975x^10 + 1130x^9 - 7241x^8 + 309x^7 + 8675x^6 - 2943x^5 - 3739x^4 + 2446x^3 - 300x^2 - 60x + 11
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.61092$ of defining polynomial
Character	$\chi$	$=$	799.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.61092 q^{2} -2.05419 q^{3} +4.81692 q^{4} -0.541341 q^{5} +5.36334 q^{6} -3.52380 q^{7} -7.35476 q^{8} +1.21971 q^{9} +O(q^{10})$	\(q-2.61092 q^{2} -2.05419 q^{3} +4.81692 q^{4} -0.541341 q^{5} +5.36334 q^{6} -3.52380 q^{7} -7.35476 q^{8} +1.21971 q^{9} +1.41340 q^{10} +1.19730 q^{11} -9.89489 q^{12} -4.15112 q^{13} +9.20038 q^{14} +1.11202 q^{15} +9.56887 q^{16} +1.00000 q^{17} -3.18458 q^{18} -2.49371 q^{19} -2.60759 q^{20} +7.23857 q^{21} -3.12606 q^{22} -1.46369 q^{23} +15.1081 q^{24} -4.70695 q^{25} +10.8382 q^{26} +3.65705 q^{27} -16.9739 q^{28} -1.91529 q^{29} -2.90339 q^{30} -7.86064 q^{31} -10.2741 q^{32} -2.45949 q^{33} -2.61092 q^{34} +1.90758 q^{35} +5.87526 q^{36} -4.71226 q^{37} +6.51089 q^{38} +8.52720 q^{39} +3.98143 q^{40} +2.04230 q^{41} -18.8994 q^{42} -11.5594 q^{43} +5.76730 q^{44} -0.660280 q^{45} +3.82159 q^{46} -1.00000 q^{47} -19.6563 q^{48} +5.41719 q^{49} +12.2895 q^{50} -2.05419 q^{51} -19.9956 q^{52} +5.53881 q^{53} -9.54829 q^{54} -0.648147 q^{55} +25.9167 q^{56} +5.12257 q^{57} +5.00068 q^{58} -3.66113 q^{59} +5.35650 q^{60} +7.64495 q^{61} +20.5235 q^{62} -4.29803 q^{63} +7.68706 q^{64} +2.24717 q^{65} +6.42153 q^{66} +12.5704 q^{67} +4.81692 q^{68} +3.00671 q^{69} -4.98054 q^{70} +1.13750 q^{71} -8.97070 q^{72} +10.7927 q^{73} +12.3033 q^{74} +9.66899 q^{75} -12.0120 q^{76} -4.21905 q^{77} -22.2639 q^{78} +2.03646 q^{79} -5.18002 q^{80} -11.1714 q^{81} -5.33229 q^{82} -4.24125 q^{83} +34.8676 q^{84} -0.541341 q^{85} +30.1808 q^{86} +3.93438 q^{87} -8.80586 q^{88} +16.2288 q^{89} +1.72394 q^{90} +14.6277 q^{91} -7.05050 q^{92} +16.1473 q^{93} +2.61092 q^{94} +1.34995 q^{95} +21.1049 q^{96} +16.5488 q^{97} -14.1439 q^{98} +1.46036 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + 3 q^{2} + q^{3} + 19 q^{4} + 11 q^{5} + 5 q^{6} + q^{7} + 3 q^{8} + 30 q^{9}+O(q^{10}) $ 17 * q + 3 * q^2 + q^3 + 19 * q^4 + 11 * q^5 + 5 * q^6 + q^7 + 3 * q^8 + 30 * q^9	\( 17 q + 3 q^{2} + q^{3} + 19 q^{4} + 11 q^{5} + 5 q^{6} + q^{7} + 3 q^{8} + 30 q^{9} + 12 q^{10} + 8 q^{11} + 12 q^{12} + q^{13} + 11 q^{14} - 7 q^{15} + 15 q^{16} + 17 q^{17} - 26 q^{18} - q^{19} + 13 q^{20} + 14 q^{21} + 3 q^{22} + 12 q^{23} - 24 q^{24} + 33 q^{26} + 22 q^{27} + q^{28} + 10 q^{29} + q^{30} + 2 q^{31} - q^{32} + 3 q^{33} + 3 q^{34} + 9 q^{35} + 50 q^{36} + 10 q^{37} + 23 q^{38} + 13 q^{39} + q^{40} + 65 q^{41} - 41 q^{42} - 3 q^{43} + 10 q^{44} + 31 q^{45} - 17 q^{47} - 16 q^{48} + 14 q^{49} + 5 q^{50} + q^{51} - 32 q^{52} - 13 q^{53} - 15 q^{54} - 11 q^{55} + 46 q^{56} + 36 q^{57} - q^{58} + 39 q^{59} + 43 q^{60} + 23 q^{61} + 33 q^{62} - 15 q^{63} - 27 q^{64} - 10 q^{65} - 86 q^{66} - 14 q^{67} + 19 q^{68} + 45 q^{69} - 13 q^{70} + 21 q^{71} - 42 q^{72} + 24 q^{73} + 25 q^{74} - 32 q^{75} - 5 q^{76} - 2 q^{77} + 36 q^{78} - 26 q^{79} - 14 q^{80} + 41 q^{81} - 37 q^{82} - 5 q^{83} - 60 q^{84} + 11 q^{85} - 24 q^{86} - 5 q^{87} - 25 q^{88} + 61 q^{89} + 6 q^{90} + 29 q^{91} - 12 q^{92} - 3 q^{93} - 3 q^{94} - 6 q^{95} + 12 q^{96} + 3 q^{97} + 36 q^{98} - 27 q^{99}+O(q^{100}) \) 17 * q + 3 * q^2 + q^3 + 19 * q^4 + 11 * q^5 + 5 * q^6 + q^7 + 3 * q^8 + 30 * q^9 + 12 * q^10 + 8 * q^11 + 12 * q^12 + q^13 + 11 * q^14 - 7 * q^15 + 15 * q^16 + 17 * q^17 - 26 * q^18 - q^19 + 13 * q^20 + 14 * q^21 + 3 * q^22 + 12 * q^23 - 24 * q^24 + 33 * q^26 + 22 * q^27 + q^28 + 10 * q^29 + q^30 + 2 * q^31 - q^32 + 3 * q^33 + 3 * q^34 + 9 * q^35 + 50 * q^36 + 10 * q^37 + 23 * q^38 + 13 * q^39 + q^40 + 65 * q^41 - 41 * q^42 - 3 * q^43 + 10 * q^44 + 31 * q^45 - 17 * q^47 - 16 * q^48 + 14 * q^49 + 5 * q^50 + q^51 - 32 * q^52 - 13 * q^53 - 15 * q^54 - 11 * q^55 + 46 * q^56 + 36 * q^57 - q^58 + 39 * q^59 + 43 * q^60 + 23 * q^61 + 33 * q^62 - 15 * q^63 - 27 * q^64 - 10 * q^65 - 86 * q^66 - 14 * q^67 + 19 * q^68 + 45 * q^69 - 13 * q^70 + 21 * q^71 - 42 * q^72 + 24 * q^73 + 25 * q^74 - 32 * q^75 - 5 * q^76 - 2 * q^77 + 36 * q^78 - 26 * q^79 - 14 * q^80 + 41 * q^81 - 37 * q^82 - 5 * q^83 - 60 * q^84 + 11 * q^85 - 24 * q^86 - 5 * q^87 - 25 * q^88 + 61 * q^89 + 6 * q^90 + 29 * q^91 - 12 * q^92 - 3 * q^93 - 3 * q^94 - 6 * q^95 + 12 * q^96 + 3 * q^97 + 36 * q^98 - 27 * 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 $

$2$	−2.61092	−1.84620	−0.923101	−	0.384558i	$-0.874354\pi$
$2$	−2.61092	−1.84620	−0.923101	+	0.384558i	$0.874354\pi$
$3$	−2.05419	−1.18599	−0.592995	−	0.805206i	$-0.702055\pi$
$3$	−2.05419	−1.18599	−0.592995	+	0.805206i	$0.702055\pi$
$4$	4.81692	2.40846
$5$	−0.541341	−0.242095	−0.121047	−	0.992647i	$-0.538625\pi$
$5$	−0.541341	−0.242095	−0.121047	+	0.992647i	$0.538625\pi$
$6$	5.36334	2.18958
$7$	−3.52380	−1.33187	−0.665936	−	0.746009i	$-0.731968\pi$
$7$	−3.52380	−1.33187	−0.665936	+	0.746009i	$0.731968\pi$
$8$	−7.35476	−2.60030
$9$	1.21971	0.406571
$10$	1.41340	0.446956
$11$	1.19730	0.361000	0.180500	−	0.983575i	$-0.442228\pi$
$11$	1.19730	0.361000	0.180500	+	0.983575i	$0.442228\pi$
$12$	−9.89489	−2.85641
$13$	−4.15112	−1.15131	−0.575656	−	0.817692i	$-0.695253\pi$
$13$	−4.15112	−1.15131	−0.575656	+	0.817692i	$0.695253\pi$
$14$	9.20038	2.45890
$15$	1.11202	0.287122
$16$	9.56887	2.39222
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−3.18458	−0.750612
$19$	−2.49371	−0.572097	−0.286048	−	0.958215i	$-0.592342\pi$
$19$	−2.49371	−0.572097	−0.286048	+	0.958215i	$0.592342\pi$
$20$	−2.60759	−0.583076
$21$	7.23857	1.57959
$22$	−3.12606	−0.666478
$23$	−1.46369	−0.305201	−0.152601	−	0.988288i	$-0.548765\pi$
$23$	−1.46369	−0.305201	−0.152601	+	0.988288i	$0.548765\pi$
$24$	15.1081	3.08393
$25$	−4.70695	−0.941390
$26$	10.8382	2.12556
$27$	3.65705	0.703801
$28$	−16.9739	−3.20776
$29$	−1.91529	−0.355661	−0.177831	−	0.984061i	$-0.556908\pi$
$29$	−1.91529	−0.355661	−0.177831	+	0.984061i	$0.556908\pi$
$30$	−2.90339	−0.530085
$31$	−7.86064	−1.41181	−0.705907	−	0.708305i	$-0.749460\pi$
$31$	−7.86064	−1.41181	−0.705907	+	0.708305i	$0.749460\pi$
$32$	−10.2741	−1.81622
$33$	−2.45949	−0.428142
$34$	−2.61092	−0.447770
$35$	1.90758	0.322439
$36$	5.87526	0.979210
$37$	−4.71226	−0.774691	−0.387345	−	0.921935i	$-0.626608\pi$
$37$	−4.71226	−0.774691	−0.387345	+	0.921935i	$0.626608\pi$
$38$	6.51089	1.05621
$39$	8.52720	1.36544
$40$	3.98143	0.629519
$41$	2.04230	0.318954	0.159477	−	0.987202i	$-0.449019\pi$
$41$	2.04230	0.318954	0.159477	+	0.987202i	$0.449019\pi$
$42$	−18.8994	−2.91623
$43$	−11.5594	−1.76280	−0.881398	−	0.472374i	$-0.843397\pi$
$43$	−11.5594	−1.76280	−0.881398	+	0.472374i	$0.843397\pi$
$44$	5.76730	0.869453
$45$	−0.660280	−0.0984287
$46$	3.82159	0.563463
$47$	−1.00000	−0.145865
$47$	−1.00000	−0.145865
$48$	−19.6563	−2.83715
$49$	5.41719	0.773884
$50$	12.2895	1.73800
$51$	−2.05419	−0.287645
$52$	−19.9956	−2.77289
$53$	5.53881	0.760815	0.380407	−	0.924819i	$-0.375784\pi$
$53$	5.53881	0.760815	0.380407	+	0.924819i	$0.375784\pi$
$54$	−9.54829	−1.29936
$55$	−0.648147	−0.0873962
$56$	25.9167	3.46327
$57$	5.12257	0.678500
$58$	5.00068	0.656622
$59$	−3.66113	−0.476638	−0.238319	−	0.971187i	$-0.576596\pi$
$59$	−3.66113	−0.476638	−0.238319	+	0.971187i	$0.576596\pi$
$60$	5.35650	0.691522
$61$	7.64495	0.978835	0.489418	−	0.872049i	$-0.337209\pi$
$61$	7.64495	0.978835	0.489418	+	0.872049i	$0.337209\pi$
$62$	20.5235	2.60649
$63$	−4.29803	−0.541501
$64$	7.68706	0.960882
$65$	2.24717	0.278727
$66$	6.42153	0.790436
$67$	12.5704	1.53572	0.767859	−	0.640619i	$-0.221322\pi$
$67$	12.5704	1.53572	0.767859	+	0.640619i	$0.221322\pi$
$68$	4.81692	0.584137
$69$	3.00671	0.361966
$70$	−4.98054	−0.595288
$71$	1.13750	0.134996	0.0674982	−	0.997719i	$-0.478498\pi$
$71$	1.13750	0.134996	0.0674982	+	0.997719i	$0.478498\pi$
$72$	−8.97070	−1.05721
$73$	10.7927	1.26319	0.631593	−	0.775300i	$-0.282401\pi$
$73$	10.7927	1.26319	0.631593	+	0.775300i	$0.282401\pi$
$74$	12.3033	1.43023
$75$	9.66899	1.11648
$76$	−12.0120	−1.37787
$77$	−4.21905	−0.480805
$78$	−22.2639	−2.52089
$79$	2.03646	0.229120	0.114560	−	0.993416i	$-0.463454\pi$
$79$	2.03646	0.229120	0.114560	+	0.993416i	$0.463454\pi$
$80$	−5.18002	−0.579144
$81$	−11.1714	−1.24127
$82$	−5.33229	−0.588853
$83$	−4.24125	−0.465538	−0.232769	−	0.972532i	$-0.574779\pi$
$83$	−4.24125	−0.465538	−0.232769	+	0.972532i	$0.574779\pi$
$84$	34.8676	3.80437
$85$	−0.541341	−0.0587166
$86$	30.1808	3.25448
$87$	3.93438	0.421810
$88$	−8.80586	−0.938708
$89$	16.2288	1.72025	0.860125	−	0.510083i	$-0.170385\pi$
$89$	16.2288	1.72025	0.860125	+	0.510083i	$0.170385\pi$
$90$	1.72394	0.181719
$91$	14.6277	1.53340
$92$	−7.05050	−0.735065
$93$	16.1473	1.67440
$94$	2.61092	0.269296
$95$	1.34995	0.138502
$96$	21.1049	2.15401
$97$	16.5488	1.68028	0.840138	−	0.542373i	$-0.182474\pi$
$97$	16.5488	1.68028	0.840138	+	0.542373i	$0.182474\pi$
$98$	−14.1439	−1.42875
$99$	1.46036	0.146772
$100$	−22.6730	−2.26730
$101$	1.91761	0.190809	0.0954046	−	0.995439i	$-0.469586\pi$
$101$	1.91761	0.190809	0.0954046	+	0.995439i	$0.469586\pi$
$102$	5.36334	0.531050
$103$	−1.47350	−0.145188	−0.0725940	−	0.997362i	$-0.523128\pi$
$103$	−1.47350	−0.145188	−0.0725940	+	0.997362i	$0.523128\pi$
$104$	30.5305	2.99376
$105$	−3.91853	−0.382410
$106$	−14.4614	−1.40462
$107$	−5.33502	−0.515756	−0.257878	−	0.966177i	$-0.583023\pi$
$107$	−5.33502	−0.515756	−0.257878	+	0.966177i	$0.583023\pi$
$108$	17.6157	1.69508
$109$	13.1922	1.26358	0.631792	−	0.775138i	$-0.282320\pi$
$109$	13.1922	1.26358	0.631792	+	0.775138i	$0.282320\pi$
$110$	1.69226	0.161351
$111$	9.67989	0.918775
$112$	−33.7188	−3.18613
$113$	−6.49642	−0.611132	−0.305566	−	0.952171i	$-0.598846\pi$
$113$	−6.49642	−0.611132	−0.305566	+	0.952171i	$0.598846\pi$
$114$	−13.3746	−1.25265
$115$	0.792357	0.0738877
$116$	−9.22581	−0.856595
$117$	−5.06317	−0.468090
$118$	9.55892	0.879970
$119$	−3.52380	−0.323026
$120$	−8.17863	−0.746603
$121$	−9.56647	−0.869679
$122$	−19.9604	−1.80713
$123$	−4.19528	−0.378276
$124$	−37.8641	−3.40029
$125$	5.25477	0.470001
$126$	11.2218	0.999719
$127$	−4.48008	−0.397543	−0.198771	−	0.980046i	$-0.563695\pi$
$127$	−4.48008	−0.397543	−0.198771	+	0.980046i	$0.563695\pi$
$128$	0.477818	0.0422335
$129$	23.7453	2.09066
$130$	−5.86718	−0.514586
$131$	−6.91998	−0.604602	−0.302301	−	0.953213i	$-0.597755\pi$
$131$	−6.91998	−0.604602	−0.302301	+	0.953213i	$0.597755\pi$
$132$	−11.8472	−1.03116
$133$	8.78735	0.761959
$134$	−32.8203	−2.83524
$135$	−1.97971	−0.170386
$136$	−7.35476	−0.630665
$137$	15.2952	1.30676	0.653381	−	0.757030i	$-0.273350\pi$
$137$	15.2952	1.30676	0.653381	+	0.757030i	$0.273350\pi$
$138$	−7.85030	−0.668262
$139$	−13.0572	−1.10750	−0.553749	−	0.832684i	$-0.686803\pi$
$139$	−13.0572	−1.10750	−0.553749	+	0.832684i	$0.686803\pi$
$140$	9.18864	0.776582
$141$	2.05419	0.172994
$142$	−2.96993	−0.249231
$143$	−4.97013	−0.415624
$144$	11.6713	0.972606
$145$	1.03683	0.0861037
$146$	−28.1788	−2.33210
$147$	−11.1280	−0.917818
$148$	−22.6986	−1.86581
$149$	13.9505	1.14287	0.571434	−	0.820648i	$-0.306387\pi$
$149$	13.9505	1.14287	0.571434	+	0.820648i	$0.306387\pi$
$150$	−25.2450	−2.06124
$151$	−1.55469	−0.126519	−0.0632593	−	0.997997i	$-0.520150\pi$
$151$	−1.55469	−0.126519	−0.0632593	+	0.997997i	$0.520150\pi$
$152$	18.3406	1.48762
$153$	1.21971	0.0986080
$154$	11.0156	0.887664
$155$	4.25528	0.341793
$156$	41.0748	3.28862
$157$	−23.6518	−1.88762	−0.943810	−	0.330489i	$-0.892786\pi$
$157$	−23.6518	−1.88762	−0.943810	+	0.330489i	$0.892786\pi$
$158$	−5.31704	−0.423001
$159$	−11.3778	−0.902318
$160$	5.56177	0.439696
$161$	5.15777	0.406489
$162$	29.1678	2.29164
$163$	20.8748	1.63504	0.817519	−	0.575902i	$-0.195349\pi$
$163$	20.8748	1.63504	0.817519	+	0.575902i	$0.195349\pi$
$164$	9.83759	0.768187
$165$	1.33142	0.103651
$166$	11.0736	0.859477
$167$	0.133912	0.0103624	0.00518121	−	0.999987i	$-0.498351\pi$
$167$	0.133912	0.0103624	0.00518121	+	0.999987i	$0.498351\pi$
$168$	−53.2380	−4.10740
$169$	4.23177	0.325521
$170$	1.41340	0.108403
$171$	−3.04161	−0.232598
$172$	−55.6808	−4.24562
$173$	6.05012	0.459982	0.229991	−	0.973193i	$-0.426130\pi$
$173$	6.05012	0.459982	0.229991	+	0.973193i	$0.426130\pi$
$174$	−10.2724	−0.778747
$175$	16.5864	1.25381
$176$	11.4568	0.863590
$177$	7.52067	0.565288
$178$	−42.3722	−3.17593
$179$	−4.79335	−0.358272	−0.179136	−	0.983824i	$-0.557330\pi$
$179$	−4.79335	−0.358272	−0.179136	+	0.983824i	$0.557330\pi$
$180$	−3.18052	−0.237062
$181$	−3.11441	−0.231492	−0.115746	−	0.993279i	$-0.536926\pi$
$181$	−3.11441	−0.231492	−0.115746	+	0.993279i	$0.536926\pi$
$182$	−38.1918	−2.83097
$183$	−15.7042	−1.16089
$184$	10.7651	0.793615
$185$	2.55094	0.187549
$186$	−42.1593	−3.09127
$187$	1.19730	0.0875553
$188$	−4.81692	−0.351310
$189$	−12.8867	−0.937372
$190$	−3.52461	−0.255702
$191$	−10.7592	−0.778507	−0.389254	−	0.921131i	$-0.627267\pi$
$191$	−10.7592	−0.778507	−0.389254	+	0.921131i	$0.627267\pi$
$192$	−15.7907	−1.13960
$193$	−7.31107	−0.526262	−0.263131	−	0.964760i	$-0.584755\pi$
$193$	−7.31107	−0.526262	−0.263131	+	0.964760i	$0.584755\pi$
$194$	−43.2076	−3.10213
$195$	−4.61612	−0.330567
$196$	26.0941	1.86387
$197$	−0.369375	−0.0263169	−0.0131584	−	0.999913i	$-0.504189\pi$
$197$	−0.369375	−0.0263169	−0.0131584	+	0.999913i	$0.504189\pi$
$198$	−3.81290	−0.270971
$199$	9.16532	0.649712	0.324856	−	0.945763i	$-0.394684\pi$
$199$	9.16532	0.649712	0.324856	+	0.945763i	$0.394684\pi$
$200$	34.6185	2.44790
$201$	−25.8220	−1.82135
$202$	−5.00673	−0.352272
$203$	6.74912	0.473695
$204$	−9.89489	−0.692781
$205$	−1.10558	−0.0772170
$206$	3.84719	0.268046
$207$	−1.78529	−0.124086
$208$	−39.7215	−2.75419
$209$	−2.98572	−0.206527
$210$	10.2310	0.706005
$211$	−7.19418	−0.495268	−0.247634	−	0.968854i	$-0.579653\pi$
$211$	−7.19418	−0.495268	−0.247634	+	0.968854i	$0.579653\pi$
$212$	26.6800	1.83239
$213$	−2.33665	−0.160104
$214$	13.9293	0.952190
$215$	6.25759	0.426764
$216$	−26.8968	−1.83009
$217$	27.6994	1.88035
$218$	−34.4438	−2.33283
$219$	−22.1702	−1.49812
$220$	−3.12207	−0.210490
$221$	−4.15112	−0.279234
$222$	−25.2735	−1.69624
$223$	11.2237	0.751591	0.375796	−	0.926703i	$-0.377369\pi$
$223$	11.2237	0.751591	0.375796	+	0.926703i	$0.377369\pi$
$224$	36.2038	2.41897
$225$	−5.74113	−0.382742
$226$	16.9617	1.12827
$227$	21.9478	1.45672	0.728362	−	0.685192i	$-0.240282\pi$
$227$	21.9478	1.45672	0.728362	+	0.685192i	$0.240282\pi$
$228$	24.6750	1.63414
$229$	18.6310	1.23117	0.615585	−	0.788070i	$-0.288920\pi$
$229$	18.6310	1.23117	0.615585	+	0.788070i	$0.288920\pi$
$230$	−2.06878	−0.136412
$231$	8.66675	0.570230
$232$	14.0865	0.924825
$233$	26.0657	1.70762	0.853809	−	0.520587i	$-0.174287\pi$
$233$	26.0657	1.70762	0.853809	+	0.520587i	$0.174287\pi$
$234$	13.2196	0.864189
$235$	0.541341	0.0353132
$236$	−17.6354	−1.14796
$237$	−4.18329	−0.271734
$238$	9.20038	0.596372
$239$	−24.7016	−1.59782	−0.798908	−	0.601454i	$-0.794588\pi$
$239$	−24.7016	−1.59782	−0.798908	+	0.601454i	$0.794588\pi$
$240$	10.6408	0.686858
$241$	−7.53872	−0.485612	−0.242806	−	0.970075i	$-0.578068\pi$
$241$	−7.53872	−0.485612	−0.242806	+	0.970075i	$0.578068\pi$
$242$	24.9773	1.60560
$243$	11.9771	0.768334
$244$	36.8251	2.35749
$245$	−2.93254	−0.187353
$246$	10.9536	0.698373
$247$	10.3517	0.658662
$248$	57.8131	3.67114
$249$	8.71235	0.552123
$250$	−13.7198	−0.867716
$251$	22.1917	1.40073	0.700363	−	0.713787i	$-0.253021\pi$
$251$	22.1917	1.40073	0.700363	+	0.713787i	$0.253021\pi$
$252$	−20.7033	−1.30418
$253$	−1.75248	−0.110178
$254$	11.6971	0.733944
$255$	1.11202	0.0696373
$256$	−16.6217	−1.03885
$257$	16.1246	1.00583	0.502914	−	0.864337i	$-0.332261\pi$
$257$	16.1246	1.00583	0.502914	+	0.864337i	$0.332261\pi$
$258$	−61.9972	−3.85977
$259$	16.6051	1.03179
$260$	10.8244	0.671302
$261$	−2.33611	−0.144601
$262$	18.0675	1.11622
$263$	−12.3827	−0.763549	−0.381775	−	0.924255i	$-0.624687\pi$
$263$	−12.3827	−0.763549	−0.381775	+	0.924255i	$0.624687\pi$
$264$	18.0889	1.11330
$265$	−2.99838	−0.184189
$266$	−22.9431	−1.40673
$267$	−33.3371	−2.04020
$268$	60.5506	3.69871
$269$	26.4396	1.61205	0.806025	−	0.591881i	$-0.201614\pi$
$269$	26.4396	1.61205	0.806025	+	0.591881i	$0.201614\pi$
$270$	5.16888	0.314568
$271$	−13.0389	−0.792058	−0.396029	−	0.918238i	$-0.629612\pi$
$271$	−13.0389	−0.792058	−0.396029	+	0.918238i	$0.629612\pi$
$272$	9.56887	0.580198
$273$	−30.0482	−1.81860
$274$	−39.9347	−2.41254
$275$	−5.63563	−0.339842
$276$	14.4831	0.871780
$277$	−18.0358	−1.08367	−0.541834	−	0.840486i	$-0.682270\pi$
$277$	−18.0358	−1.08367	−0.541834	+	0.840486i	$0.682270\pi$
$278$	34.0914	2.04466
$279$	−9.58773	−0.574002
$280$	−14.0298	−0.838439
$281$	−15.2905	−0.912153	−0.456077	−	0.889941i	$-0.650746\pi$
$281$	−15.2905	−0.912153	−0.456077	+	0.889941i	$0.650746\pi$
$282$	−5.36334	−0.319382
$283$	−13.9407	−0.828688	−0.414344	−	0.910120i	$-0.635989\pi$
$283$	−13.9407	−0.828688	−0.414344	+	0.910120i	$0.635989\pi$
$284$	5.47925	0.325133
$285$	−2.77305	−0.164261
$286$	12.9766	0.767325
$287$	−7.19666	−0.424805
$288$	−12.5314	−0.738421
$289$	1.00000	0.0588235
$290$	−2.70707	−0.158965
$291$	−33.9944	−1.99279
$292$	51.9874	3.04233
$293$	−25.2539	−1.47535	−0.737674	−	0.675157i	$-0.764076\pi$
$293$	−25.2539	−1.47535	−0.737674	+	0.675157i	$0.764076\pi$
$294$	29.0542	1.69448
$295$	1.98192	0.115392
$296$	34.6575	2.01443
$297$	4.37859	0.254072
$298$	−36.4236	−2.10996
$299$	6.07597	0.351382
$300$	46.5747	2.68899
$301$	40.7331	2.34782
$302$	4.05916	0.233579
$303$	−3.93914	−0.226298
$304$	−23.8620	−1.36858
$305$	−4.13852	−0.236971
$306$	−3.18458	−0.182050
$307$	−30.3515	−1.73225	−0.866124	−	0.499828i	$-0.833396\pi$
$307$	−30.3515	−1.73225	−0.866124	+	0.499828i	$0.833396\pi$
$308$	−20.3228	−1.15800
$309$	3.02685	0.172192
$310$	−11.1102	−0.631018
$311$	−3.55456	−0.201561	−0.100780	−	0.994909i	$-0.532134\pi$
$311$	−3.55456	−0.201561	−0.100780	+	0.994909i	$0.532134\pi$
$312$	−62.7155	−3.55057
$313$	11.6660	0.659400	0.329700	−	0.944086i	$-0.393052\pi$
$313$	11.6660	0.659400	0.329700	+	0.944086i	$0.393052\pi$
$314$	61.7531	3.48493
$315$	2.32670	0.131095
$316$	9.80947	0.551826
$317$	−28.3699	−1.59342	−0.796708	−	0.604365i	$-0.793427\pi$
$317$	−28.3699	−1.59342	−0.796708	+	0.604365i	$0.793427\pi$
$318$	29.7066	1.66586
$319$	−2.29318	−0.128394
$320$	−4.16132	−0.232625
$321$	10.9592	0.611681
$322$	−13.4665	−0.750461
$323$	−2.49371	−0.138754
$324$	−53.8119	−2.98955
$325$	19.5391	1.08383
$326$	−54.5024	−3.01861
$327$	−27.0993	−1.49860
$328$	−15.0206	−0.829375
$329$	3.52380	0.194274
$330$	−3.47624	−0.191360
$331$	19.5653	1.07541	0.537703	−	0.843134i	$-0.319292\pi$
$331$	19.5653	1.07541	0.537703	+	0.843134i	$0.319292\pi$
$332$	−20.4298	−1.12123
$333$	−5.74760	−0.314967
$334$	−0.349634	−0.0191311
$335$	−6.80486	−0.371789
$336$	69.2650	3.77871
$337$	28.1264	1.53214	0.766072	−	0.642755i	$-0.222209\pi$
$337$	28.1264	1.53214	0.766072	+	0.642755i	$0.222209\pi$
$338$	−11.0488	−0.600977
$339$	13.3449	0.724796
$340$	−2.60759	−0.141417
$341$	−9.41155	−0.509664
$342$	7.94141	0.429423
$343$	5.57753	0.301158
$344$	85.0168	4.58380
$345$	−1.62766	−0.0876300
$346$	−15.7964	−0.849219
$347$	−34.4695	−1.85042	−0.925211	−	0.379453i	$-0.876112\pi$
$347$	−34.4695	−1.85042	−0.925211	+	0.379453i	$0.876112\pi$
$348$	18.9516	1.01591
$349$	−31.7500	−1.69954	−0.849770	−	0.527153i	$-0.823259\pi$
$349$	−31.7500	−1.69954	−0.849770	+	0.527153i	$0.823259\pi$
$350$	−43.3057	−2.31479
$351$	−15.1809	−0.810295
$352$	−12.3011	−0.655653
$353$	−9.16866	−0.487999	−0.243999	−	0.969775i	$-0.578459\pi$
$353$	−9.16866	−0.487999	−0.243999	+	0.969775i	$0.578459\pi$
$354$	−19.6359	−1.04364
$355$	−0.615775	−0.0326819
$356$	78.1729	4.14315
$357$	7.23857	0.383106
$358$	12.5151	0.661442
$359$	−12.7554	−0.673205	−0.336603	−	0.941647i	$-0.609278\pi$
$359$	−12.7554	−0.673205	−0.336603	+	0.941647i	$0.609278\pi$
$360$	4.85620	0.255944
$361$	−12.7814	−0.672706
$362$	8.13148	0.427381
$363$	19.6514	1.03143
$364$	70.4605	3.69314
$365$	−5.84251	−0.305811
$366$	41.0025	2.14323
$367$	5.85164	0.305453	0.152727	−	0.988268i	$-0.451195\pi$
$367$	5.85164	0.305453	0.152727	+	0.988268i	$0.451195\pi$
$368$	−14.0059	−0.730108
$369$	2.49102	0.129677
$370$	−6.66030	−0.346252
$371$	−19.5177	−1.01331
$372$	77.7802	4.03271
$373$	1.55972	0.0807593	0.0403796	−	0.999184i	$-0.487143\pi$
$373$	1.55972	0.0807593	0.0403796	+	0.999184i	$0.487143\pi$
$374$	−3.12606	−0.161645
$375$	−10.7943	−0.557416
$376$	7.35476	0.379293
$377$	7.95061	0.409477
$378$	33.6463	1.73058
$379$	9.84168	0.505533	0.252767	−	0.967527i	$-0.418659\pi$
$379$	9.84168	0.505533	0.252767	+	0.967527i	$0.418659\pi$
$380$	6.50258	0.333576
$381$	9.20295	0.471482
$382$	28.0914	1.43728
$383$	26.7655	1.36765	0.683825	−	0.729646i	$-0.260315\pi$
$383$	26.7655	1.36765	0.683825	+	0.729646i	$0.260315\pi$
$384$	−0.981530	−0.0500885
$385$	2.28394	0.116401
$386$	19.0886	0.971586
$387$	−14.0992	−0.716702
$388$	79.7142	4.04688
$389$	−36.4269	−1.84692	−0.923459	−	0.383697i	$-0.874651\pi$
$389$	−36.4269	−1.84692	−0.923459	+	0.383697i	$0.874651\pi$
$390$	12.0523	0.610294
$391$	−1.46369	−0.0740222
$392$	−39.8421	−2.01233
$393$	14.2150	0.717051
$394$	0.964410	0.0485863
$395$	−1.10242	−0.0554687
$396$	7.03445	0.353494
$397$	−0.414927	−0.0208246	−0.0104123	−	0.999946i	$-0.503314\pi$
$397$	−0.414927	−0.0208246	−0.0104123	+	0.999946i	$0.503314\pi$
$398$	−23.9299	−1.19950
$399$	−18.0509	−0.903676
$400$	−45.0402	−2.25201
$401$	10.4493	0.521812	0.260906	−	0.965364i	$-0.415979\pi$
$401$	10.4493	0.521812	0.260906	+	0.965364i	$0.415979\pi$
$402$	67.4193	3.36257
$403$	32.6305	1.62544
$404$	9.23697	0.459556
$405$	6.04755	0.300505
$406$	−17.6214	−0.874536
$407$	−5.64199	−0.279663
$408$	15.1081	0.747962
$409$	18.0496	0.892498	0.446249	−	0.894909i	$-0.352760\pi$
$409$	18.0496	0.892498	0.446249	+	0.894909i	$0.352760\pi$
$410$	2.88658	0.142558
$411$	−31.4194	−1.54981
$412$	−7.09772	−0.349680
$413$	12.9011	0.634821
$414$	4.66125	0.229088
$415$	2.29596	0.112704
$416$	42.6489	2.09103
$417$	26.8220	1.31348
$418$	7.79549	0.381290
$419$	34.3586	1.67853	0.839263	−	0.543725i	$-0.182987\pi$
$419$	34.3586	1.67853	0.839263	+	0.543725i	$0.182987\pi$
$420$	−18.8753	−0.921018
$421$	−10.9039	−0.531422	−0.265711	−	0.964053i	$-0.585607\pi$
$421$	−10.9039	−0.531422	−0.265711	+	0.964053i	$0.585607\pi$
$422$	18.7834	0.914364
$423$	−1.21971	−0.0593045
$424$	−40.7366	−1.97835
$425$	−4.70695	−0.228321
$426$	6.10080	0.295585
$427$	−26.9393	−1.30368
$428$	−25.6984	−1.24218
$429$	10.2096	0.492925
$430$	−16.3381	−0.787892
$431$	−24.9918	−1.20381	−0.601907	−	0.798566i	$-0.705592\pi$
$431$	−24.9918	−1.20381	−0.601907	+	0.798566i	$0.705592\pi$
$432$	34.9939	1.68364
$433$	−17.6814	−0.849713	−0.424856	−	0.905261i	$-0.639675\pi$
$433$	−17.6814	−0.849713	−0.424856	+	0.905261i	$0.639675\pi$
$434$	−72.3209	−3.47151
$435$	−2.12984	−0.102118
$436$	63.5457	3.04329
$437$	3.65003	0.174605
$438$	57.8847	2.76584
$439$	18.4729	0.881663	0.440831	−	0.897590i	$-0.354684\pi$
$439$	18.4729	0.881663	0.440831	+	0.897590i	$0.354684\pi$
$440$	4.76697	0.227256
$441$	6.60741	0.314639
$442$	10.8382	0.515523
$443$	−16.3906	−0.778741	−0.389371	−	0.921081i	$-0.627307\pi$
$443$	−16.3906	−0.778741	−0.389371	+	0.921081i	$0.627307\pi$
$444$	46.6273	2.21283
$445$	−8.78531	−0.416464
$446$	−29.3041	−1.38759
$447$	−28.6570	−1.35543
$448$	−27.0877	−1.27977
$449$	14.4625	0.682529	0.341265	−	0.939967i	$-0.389145\pi$
$449$	14.4625	0.682529	0.341265	+	0.939967i	$0.389145\pi$
$450$	14.9896	0.706619
$451$	2.44525	0.115142
$452$	−31.2928	−1.47189
$453$	3.19363	0.150050
$454$	−57.3039	−2.68941
$455$	−7.91858	−0.371229
$456$	−37.6752	−1.76430
$457$	37.5707	1.75748	0.878741	−	0.477300i	$-0.158384\pi$
$457$	37.5707	1.75748	0.878741	+	0.477300i	$0.158384\pi$
$458$	−48.6441	−2.27299
$459$	3.65705	0.170697
$460$	3.81672	0.177956
$461$	−6.63797	−0.309161	−0.154581	−	0.987980i	$-0.549403\pi$
$461$	−6.63797	−0.309161	−0.154581	+	0.987980i	$0.549403\pi$
$462$	−22.6282	−1.05276
$463$	10.4161	0.484080	0.242040	−	0.970266i	$-0.422184\pi$
$463$	10.4161	0.484080	0.242040	+	0.970266i	$0.422184\pi$
$464$	−18.3272	−0.850819
$465$	−8.74118	−0.405363
$466$	−68.0554	−3.15261
$467$	25.7924	1.19353	0.596766	−	0.802416i	$-0.296452\pi$
$467$	25.7924	1.19353	0.596766	+	0.802416i	$0.296452\pi$
$468$	−24.3889	−1.12738
$469$	−44.2956	−2.04538
$470$	−1.41340	−0.0651952
$471$	48.5854	2.23870
$472$	26.9267	1.23940
$473$	−13.8401	−0.636369
$474$	10.9222	0.501675
$475$	11.7378	0.538566
$476$	−16.9739	−0.777996
$477$	6.75576	0.309325
$478$	64.4940	2.94989
$479$	38.1855	1.74474	0.872370	−	0.488846i	$-0.162582\pi$
$479$	38.1855	1.74474	0.872370	+	0.488846i	$0.162582\pi$
$480$	−11.4250	−0.521475
$481$	19.5611	0.891911
$482$	19.6830	0.896537
$483$	−10.5951	−0.482092
$484$	−46.0809	−2.09459
$485$	−8.95853	−0.406786
$486$	−31.2714	−1.41850
$487$	17.6204	0.798458	0.399229	−	0.916851i	$-0.369278\pi$
$487$	17.6204	0.798458	0.399229	+	0.916851i	$0.369278\pi$
$488$	−56.2268	−2.54527
$489$	−42.8808	−1.93914
$490$	7.65664	0.345892
$491$	−6.35998	−0.287022	−0.143511	−	0.989649i	$-0.545839\pi$
$491$	−6.35998	−0.287022	−0.143511	+	0.989649i	$0.545839\pi$
$492$	−20.2083	−0.911061
$493$	−1.91529	−0.0862605
$494$	−27.0275	−1.21602
$495$	−0.790554	−0.0355327
$496$	−75.2175	−3.37736
$497$	−4.00833	−0.179798
$498$	−22.7473	−1.01933
$499$	−15.3551	−0.687390	−0.343695	−	0.939081i	$-0.611679\pi$
$499$	−15.3551	−0.687390	−0.343695	+	0.939081i	$0.611679\pi$
$500$	25.3118	1.13198
$501$	−0.275081	−0.0122897
$502$	−57.9408	−2.58602
$503$	33.6228	1.49917	0.749583	−	0.661910i	$-0.230254\pi$
$503$	33.6228	1.49917	0.749583	+	0.661910i	$0.230254\pi$
$504$	31.6110	1.40806
$505$	−1.03808	−0.0461939
$506$	4.57560	0.203410
$507$	−8.69288	−0.386065
$508$	−21.5802	−0.957466
$509$	−8.78059	−0.389193	−0.194596	−	0.980883i	$-0.562340\pi$
$509$	−8.78059	−0.389193	−0.194596	+	0.980883i	$0.562340\pi$
$510$	−2.90339	−0.128564
$511$	−38.0312	−1.68240
$512$	42.4422	1.87570
$513$	−9.11964	−0.402642
$514$	−42.1002	−1.85696
$515$	0.797664	0.0351493
$516$	114.379	5.03526
$517$	−1.19730	−0.0526572
$518$	−43.3546	−1.90489
$519$	−12.4281	−0.545534
$520$	−16.5274	−0.724773
$521$	5.75870	0.252293	0.126147	−	0.992012i	$-0.459739\pi$
$521$	5.75870	0.252293	0.126147	+	0.992012i	$0.459739\pi$
$522$	6.09940	0.266963
$523$	−21.9255	−0.958735	−0.479368	−	0.877614i	$-0.659134\pi$
$523$	−21.9255	−0.958735	−0.479368	+	0.877614i	$0.659134\pi$
$524$	−33.3330	−1.45616
$525$	−34.0716	−1.48701
$526$	32.3302	1.40967
$527$	−7.86064	−0.342415
$528$	−23.5345	−1.02421
$529$	−20.8576	−0.906852
$530$	7.82855	0.340051
$531$	−4.46553	−0.193787
$532$	42.3279	1.83515
$533$	−8.47782	−0.367215
$534$	87.0407	3.76662
$535$	2.88806	0.124862
$536$	−92.4522	−3.99333
$537$	9.84647	0.424907
$538$	−69.0318	−2.97617
$539$	6.48600	0.279372
$540$	−9.53611	−0.410369
$541$	−21.9024	−0.941660	−0.470830	−	0.882224i	$-0.656045\pi$
$541$	−21.9024	−0.941660	−0.470830	+	0.882224i	$0.656045\pi$
$542$	34.0436	1.46230
$543$	6.39760	0.274547
$544$	−10.2741	−0.440497
$545$	−7.14147	−0.305907
$546$	78.4535	3.35750
$547$	21.0783	0.901245	0.450622	−	0.892715i	$-0.351202\pi$
$547$	21.0783	0.901245	0.450622	+	0.892715i	$0.351202\pi$
$548$	73.6760	3.14728
$549$	9.32464	0.397966
$550$	14.7142	0.627416
$551$	4.77619	0.203472
$552$	−22.1136	−0.941219
$553$	−7.17609	−0.305158
$554$	47.0902	2.00067
$555$	−5.24012	−0.222431
$556$	−62.8955	−2.66736
$557$	−11.8122	−0.500499	−0.250249	−	0.968181i	$-0.580513\pi$
$557$	−11.8122	−0.500499	−0.250249	+	0.968181i	$0.580513\pi$
$558$	25.0328	1.05972
$559$	47.9845	2.02953
$560$	18.2534	0.771345
$561$	−2.45949	−0.103840
$562$	39.9222	1.68402
$563$	12.7909	0.539073	0.269536	−	0.962990i	$-0.413130\pi$
$563$	12.7909	0.539073	0.269536	+	0.962990i	$0.413130\pi$
$564$	9.89489	0.416650
$565$	3.51678	0.147952
$566$	36.3981	1.52992
$567$	39.3659	1.65321
$568$	−8.36604	−0.351031
$569$	37.1587	1.55777	0.778887	−	0.627164i	$-0.215784\pi$
$569$	37.1587	1.55777	0.778887	+	0.627164i	$0.215784\pi$
$570$	7.24023	0.303260
$571$	−25.4240	−1.06396	−0.531980	−	0.846757i	$-0.678552\pi$
$571$	−25.4240	−1.06396	−0.531980	+	0.846757i	$0.678552\pi$
$572$	−23.9407	−1.00101
$573$	22.1015	0.923302
$574$	18.7899	0.784276
$575$	6.88954	0.287314
$576$	9.37601	0.390667
$577$	−22.9028	−0.953458	−0.476729	−	0.879050i	$-0.658178\pi$
$577$	−22.9028	−0.953458	−0.476729	+	0.879050i	$0.658178\pi$
$578$	−2.61092	−0.108600
$579$	15.0184	0.624141
$580$	4.99431	0.207377
$581$	14.9453	0.620037
$582$	88.7569	3.67909
$583$	6.63163	0.274654
$584$	−79.3774	−3.28466
$585$	2.74090	0.113322
$586$	65.9360	2.72379
$587$	−1.51141	−0.0623826	−0.0311913	−	0.999513i	$-0.509930\pi$
$587$	−1.51141	−0.0623826	−0.0311913	+	0.999513i	$0.509930\pi$
$588$	−53.6024	−2.21053
$589$	19.6022	0.807693
$590$	−5.17463	−0.213036
$591$	0.758768	0.0312115
$592$	−45.0910	−1.85323
$593$	−1.58736	−0.0651852	−0.0325926	−	0.999469i	$-0.510376\pi$
$593$	−1.58736	−0.0651852	−0.0325926	+	0.999469i	$0.510376\pi$
$594$	−11.4322	−0.469068
$595$	1.90758	0.0782030
$596$	67.1983	2.75255
$597$	−18.8273	−0.770552
$598$	−15.8639	−0.648722
$599$	−8.98115	−0.366960	−0.183480	−	0.983023i	$-0.558736\pi$
$599$	−8.98115	−0.366960	−0.183480	+	0.983023i	$0.558736\pi$
$600$	−71.1131	−2.90318
$601$	−20.6089	−0.840656	−0.420328	−	0.907372i	$-0.638085\pi$
$601$	−20.6089	−0.840656	−0.420328	+	0.907372i	$0.638085\pi$
$602$	−106.351	−4.33455
$603$	15.3323	0.624378
$604$	−7.48879	−0.304715
$605$	5.17872	0.210545
$606$	10.2848	0.417791
$607$	28.0214	1.13736	0.568678	−	0.822560i	$-0.307455\pi$
$607$	28.0214	1.13736	0.568678	+	0.822560i	$0.307455\pi$
$608$	25.6206	1.03905
$609$	−13.8640	−0.561797
$610$	10.8054	0.437496
$611$	4.15112	0.167936
$612$	5.87526	0.237493
$613$	−27.9577	−1.12920	−0.564601	−	0.825364i	$-0.690970\pi$
$613$	−27.9577	−1.12920	−0.564601	+	0.825364i	$0.690970\pi$
$614$	79.2453	3.19808
$615$	2.27107	0.0915786
$616$	31.0301	1.25024
$617$	14.3503	0.577720	0.288860	−	0.957371i	$-0.406724\pi$
$617$	14.3503	0.577720	0.288860	+	0.957371i	$0.406724\pi$
$618$	−7.90287	−0.317900
$619$	−12.5065	−0.502678	−0.251339	−	0.967899i	$-0.580871\pi$
$619$	−12.5065	−0.502678	−0.251339	+	0.967899i	$0.580871\pi$
$620$	20.4974	0.823194
$621$	−5.35281	−0.214801
$622$	9.28069	0.372122
$623$	−57.1871	−2.29115
$624$	81.5957	3.26644
$625$	20.6901	0.827605
$626$	−30.4590	−1.21739
$627$	6.13325	0.244938
$628$	−113.929	−4.54626
$629$	−4.71226	−0.187890
$630$	−6.07483	−0.242027
$631$	−1.11455	−0.0443696	−0.0221848	−	0.999754i	$-0.507062\pi$
$631$	−1.11455	−0.0443696	−0.0221848	+	0.999754i	$0.507062\pi$
$632$	−14.9777	−0.595780
$633$	14.7782	0.587382
$634$	74.0718	2.94177
$635$	2.42525	0.0962431
$636$	−54.8059	−2.17320
$637$	−22.4874	−0.890982
$638$	5.98732	0.237040
$639$	1.38742	0.0548856
$640$	−0.258662	−0.0102245
$641$	45.8518	1.81104	0.905519	−	0.424306i	$-0.139482\pi$
$641$	45.8518	1.81104	0.905519	+	0.424306i	$0.139482\pi$
$642$	−28.6135	−1.12929
$643$	21.2470	0.837901	0.418950	−	0.908009i	$-0.362398\pi$
$643$	21.2470	0.837901	0.418950	+	0.908009i	$0.362398\pi$
$644$	24.8446	0.979013
$645$	−12.8543	−0.506137
$646$	6.51089	0.256167
$647$	10.0668	0.395766	0.197883	−	0.980226i	$-0.436593\pi$
$647$	10.0668	0.395766	0.197883	+	0.980226i	$0.436593\pi$
$648$	82.1632	3.22768
$649$	−4.38347	−0.172066
$650$	−51.0151	−2.00098
$651$	−56.8999	−2.23008
$652$	100.552	3.93792
$653$	15.6020	0.610555	0.305277	−	0.952264i	$-0.401251\pi$
$653$	15.6020	0.610555	0.305277	+	0.952264i	$0.401251\pi$
$654$	70.7543	2.76671
$655$	3.74607	0.146371
$656$	19.5425	0.763006
$657$	13.1640	0.513575
$658$	−9.20038	−0.358668
$659$	−42.8375	−1.66871	−0.834355	−	0.551227i	$-0.814160\pi$
$659$	−42.8375	−1.66871	−0.834355	+	0.551227i	$0.814160\pi$
$660$	6.41334	0.249639
$661$	33.2433	1.29301	0.646507	−	0.762908i	$-0.276229\pi$
$661$	33.2433	1.29301	0.646507	+	0.762908i	$0.276229\pi$
$662$	−51.0835	−1.98542
$663$	8.52720	0.331169
$664$	31.1934	1.21054
$665$	−4.75695	−0.184466
$666$	15.0066	0.581492
$667$	2.80340	0.108548
$668$	0.645044	0.0249575
$669$	−23.0556	−0.891380
$670$	17.7670	0.686398
$671$	9.15330	0.353359
$672$	−74.3696	−2.86887
$673$	−8.74618	−0.337141	−0.168570	−	0.985690i	$-0.553915\pi$
$673$	−8.74618	−0.337141	−0.168570	+	0.985690i	$0.553915\pi$
$674$	−73.4359	−2.82865
$675$	−17.2136	−0.662551
$676$	20.3841	0.784004
$677$	−39.5258	−1.51910	−0.759550	−	0.650449i	$-0.774581\pi$
$677$	−39.5258	−1.51910	−0.759550	+	0.650449i	$0.774581\pi$
$678$	−34.8425	−1.33812
$679$	−58.3147	−2.23791
$680$	3.98143	0.152681
$681$	−45.0850	−1.72766
$682$	24.5728	0.940943
$683$	−4.00327	−0.153181	−0.0765905	−	0.997063i	$-0.524403\pi$
$683$	−4.00327	−0.153181	−0.0765905	+	0.997063i	$0.524403\pi$
$684$	−14.6512	−0.560203
$685$	−8.27994	−0.316360
$686$	−14.5625	−0.555998
$687$	−38.2717	−1.46016
$688$	−110.611	−4.21699
$689$	−22.9923	−0.875936
$690$	4.24968	0.161783
$691$	−44.7924	−1.70398	−0.851991	−	0.523556i	$-0.824605\pi$
$691$	−44.7924	−1.70398	−0.851991	+	0.523556i	$0.824605\pi$
$692$	29.1429	1.10785
$693$	−5.14603	−0.195482
$694$	89.9973	3.41625
$695$	7.06840	0.268120
$696$	−28.9364	−1.09683
$697$	2.04230	0.0773576
$698$	82.8969	3.13769
$699$	−53.5439	−2.02522
$700$	79.8952	3.01975
$701$	32.9444	1.24429	0.622147	−	0.782900i	$-0.286261\pi$
$701$	32.9444	1.24429	0.622147	+	0.782900i	$0.286261\pi$
$702$	39.6361	1.49597
$703$	11.7510	0.443198
$704$	9.20372	0.346878
$705$	−1.11202	−0.0418810
$706$	23.9387	0.900944
$707$	−6.75728	−0.254134
$708$	36.2264	1.36147
$709$	24.8512	0.933305	0.466652	−	0.884441i	$-0.345460\pi$
$709$	24.8512	0.933305	0.466652	+	0.884441i	$0.345460\pi$
$710$	1.60774	0.0603374
$711$	2.48390	0.0931534
$712$	−119.359	−4.47317
$713$	11.5056	0.430887
$714$	−18.8994	−0.707291
$715$	2.69054	0.100620
$716$	−23.0892	−0.862883
$717$	50.7419	1.89499
$718$	33.3034	1.24287
$719$	2.19012	0.0816776	0.0408388	−	0.999166i	$-0.486997\pi$
$719$	2.19012	0.0816776	0.0408388	+	0.999166i	$0.486997\pi$
$720$	−6.31814	−0.235463
$721$	5.19232	0.193372
$722$	33.3713	1.24195
$723$	15.4860	0.575930
$724$	−15.0019	−0.557540
$725$	9.01519	0.334816
$726$	−51.3083	−1.90423
$727$	−6.42639	−0.238341	−0.119171	−	0.992874i	$-0.538024\pi$
$727$	−6.42639	−0.238341	−0.119171	+	0.992874i	$0.538024\pi$
$728$	−107.583	−3.98730
$729$	8.91095	0.330035
$730$	15.2543	0.564588
$731$	−11.5594	−0.427541
$732$	−75.6459	−2.79595
$733$	−21.4865	−0.793622	−0.396811	−	0.917900i	$-0.629883\pi$
$733$	−21.4865	−0.793622	−0.396811	+	0.917900i	$0.629883\pi$
$734$	−15.2782	−0.563928
$735$	6.02401	0.222199
$736$	15.0381	0.554312
$737$	15.0505	0.554394
$738$	−6.50386	−0.239410
$739$	36.0005	1.32430	0.662149	−	0.749372i	$-0.269644\pi$
$739$	36.0005	1.32430	0.662149	+	0.749372i	$0.269644\pi$
$740$	12.2877	0.451703
$741$	−21.2644	−0.781166
$742$	50.9592	1.87077
$743$	−16.9047	−0.620174	−0.310087	−	0.950708i	$-0.600358\pi$
$743$	−16.9047	−0.620174	−0.310087	+	0.950708i	$0.600358\pi$
$744$	−118.759	−4.35393
$745$	−7.55196	−0.276682
$746$	−4.07231	−0.149098
$747$	−5.17311	−0.189274
$748$	5.76730	0.210873
$749$	18.7996	0.686921
$750$	28.1831	1.02910
$751$	7.70546	0.281176	0.140588	−	0.990068i	$-0.455101\pi$
$751$	7.70546	0.281176	0.140588	+	0.990068i	$0.455101\pi$
$752$	−9.56887	−0.348941
$753$	−45.5860	−1.66125
$754$	−20.7584	−0.755977
$755$	0.841614	0.0306295
$756$	−62.0744	−2.25762
$757$	−21.9875	−0.799149	−0.399574	−	0.916701i	$-0.630842\pi$
$757$	−21.9875	−0.799149	−0.399574	+	0.916701i	$0.630842\pi$
$758$	−25.6959	−0.933316
$759$	3.59994	0.130670
$760$	−9.92853	−0.360146
$761$	12.1632	0.440915	0.220458	−	0.975397i	$-0.429245\pi$
$761$	12.1632	0.440915	0.220458	+	0.975397i	$0.429245\pi$
$762$	−24.0282	−0.870450
$763$	−46.4867	−1.68293
$764$	−51.8261	−1.87500
$765$	−0.660280	−0.0238725
$766$	−69.8825	−2.52496
$767$	15.1978	0.548760
$768$	34.1441	1.23207
$769$	51.6038	1.86088	0.930439	−	0.366446i	$-0.119425\pi$
$769$	51.6038	1.86088	0.930439	+	0.366446i	$0.119425\pi$
$770$	−5.96320	−0.214899
$771$	−33.1231	−1.19290
$772$	−35.2168	−1.26748
$773$	−45.9894	−1.65412	−0.827062	−	0.562111i	$-0.809989\pi$
$773$	−45.9894	−1.65412	−0.827062	+	0.562111i	$0.809989\pi$
$774$	36.8119	1.32318
$775$	36.9997	1.32907
$776$	−121.712	−4.36922
$777$	−34.1100	−1.22369
$778$	95.1079	3.40978
$779$	−5.09290	−0.182472
$780$	−22.2355	−0.796158
$781$	1.36193	0.0487337
$782$	3.82159	0.136660
$783$	−7.00433	−0.250314
$784$	51.8363	1.85130
$785$	12.8037	0.456983
$786$	−37.1142	−1.32382
$787$	42.2208	1.50501	0.752504	−	0.658587i	$-0.228846\pi$
$787$	42.2208	1.50501	0.752504	+	0.658587i	$0.228846\pi$
$788$	−1.77925	−0.0633831
$789$	25.4364	0.905561
$790$	2.87833	0.102406
$791$	22.8921	0.813950
$792$	−10.7406	−0.381651
$793$	−31.7351	−1.12695
$794$	1.08334	0.0384464
$795$	6.15926	0.218447
$796$	44.1486	1.56481
$797$	39.4428	1.39713	0.698567	−	0.715544i	$-0.253821\pi$
$797$	39.4428	1.39713	0.698567	+	0.715544i	$0.253821\pi$
$798$	47.1295	1.66837
$799$	−1.00000	−0.0353775
$800$	48.3595	1.70977
$801$	19.7945	0.699404
$802$	−27.2823	−0.963371
$803$	12.9221	0.456010
$804$	−124.383	−4.38664
$805$	−2.79211	−0.0984090
$806$	−85.1956	−3.00089
$807$	−54.3121	−1.91188
$808$	−14.1036	−0.496161
$809$	33.2096	1.16759	0.583793	−	0.811902i	$-0.301568\pi$
$809$	33.2096	1.16759	0.583793	+	0.811902i	$0.301568\pi$
$810$	−15.7897	−0.554793
$811$	7.09691	0.249206	0.124603	−	0.992207i	$-0.460234\pi$
$811$	7.09691	0.249206	0.124603	+	0.992207i	$0.460234\pi$
$812$	32.5099	1.14088
$813$	26.7845	0.939372
$814$	14.7308	0.516314
$815$	−11.3004	−0.395834
$816$	−19.6563	−0.688109
$817$	28.8259	1.00849
$818$	−47.1262	−1.64773
$819$	17.8416	0.623437
$820$	−5.32549	−0.185974
$821$	−24.6984	−0.861980	−0.430990	−	0.902357i	$-0.641836\pi$
$821$	−24.6984	−0.861980	−0.430990	+	0.902357i	$0.641836\pi$
$822$	82.0337	2.86125
$823$	−45.4935	−1.58580	−0.792902	−	0.609349i	$-0.791431\pi$
$823$	−45.4935	−1.58580	−0.792902	+	0.609349i	$0.791431\pi$
$824$	10.8372	0.377533
$825$	11.5767	0.403048
$826$	−33.6838	−1.17201
$827$	−27.2340	−0.947018	−0.473509	−	0.880789i	$-0.657013\pi$
$827$	−27.2340	−0.947018	−0.473509	+	0.880789i	$0.657013\pi$
$828$	−8.59959	−0.298856
$829$	47.1784	1.63857	0.819287	−	0.573384i	$-0.194370\pi$
$829$	47.1784	1.63857	0.819287	+	0.573384i	$0.194370\pi$
$830$	−5.99458	−0.208075
$831$	37.0491	1.28522
$832$	−31.9099	−1.10628
$833$	5.41719	0.187694
$834$	−70.0303	−2.42495
$835$	−0.0724920	−0.00250869
$836$	−14.3820	−0.497411
$837$	−28.7468	−0.993635
$838$	−89.7076	−3.09890
$839$	47.5832	1.64275	0.821377	−	0.570386i	$-0.193206\pi$
$839$	47.5832	1.64275	0.821377	+	0.570386i	$0.193206\pi$
$840$	28.8199	0.994380
$841$	−25.3317	−0.873505
$842$	28.4691	0.981112
$843$	31.4096	1.08180
$844$	−34.6538	−1.19283
$845$	−2.29083	−0.0788070
$846$	3.18458	0.109488
$847$	33.7104	1.15830
$848$	53.0002	1.82003
$849$	28.6369	0.982815
$850$	12.2895	0.421526
$851$	6.89731	0.236437
$852$	−11.2554	−0.385605
$853$	−46.6082	−1.59583	−0.797917	−	0.602768i	$-0.794065\pi$
$853$	−46.6082	−1.59583	−0.797917	+	0.602768i	$0.794065\pi$
$854$	70.3364	2.40686
$855$	1.64655	0.0563107
$856$	39.2378	1.34112
$857$	−33.4114	−1.14131	−0.570656	−	0.821189i	$-0.693311\pi$
$857$	−33.4114	−1.14131	−0.570656	+	0.821189i	$0.693311\pi$
$858$	−26.6565	−0.910039
$859$	12.4572	0.425035	0.212518	−	0.977157i	$-0.431834\pi$
$859$	12.4572	0.425035	0.212518	+	0.977157i	$0.431834\pi$
$860$	30.1423	1.02784
$861$	14.7833	0.503815
$862$	65.2518	2.22248
$863$	35.7001	1.21525	0.607623	−	0.794225i	$-0.292123\pi$
$863$	35.7001	1.21525	0.607623	+	0.794225i	$0.292123\pi$
$864$	−37.5728	−1.27825
$865$	−3.27517	−0.111359
$866$	46.1647	1.56874
$867$	−2.05419	−0.0697641
$868$	133.426	4.52876
$869$	2.43826	0.0827121
$870$	5.56085	0.188531
$871$	−52.1812	−1.76809
$872$	−97.0254	−3.28570
$873$	20.1848	0.683151
$874$	−9.52995	−0.322355
$875$	−18.5168	−0.625981
$876$	−106.792	−3.60817
$877$	36.1709	1.22141	0.610703	−	0.791860i	$-0.290887\pi$
$877$	36.1709	1.22141	0.610703	+	0.791860i	$0.290887\pi$
$878$	−48.2313	−1.62773
$879$	51.8764	1.74975
$880$	−6.20204	−0.209071
$881$	−49.4627	−1.66644	−0.833221	−	0.552940i	$-0.813506\pi$
$881$	−49.4627	−1.66644	−0.833221	+	0.552940i	$0.813506\pi$
$882$	−17.2514	−0.580886
$883$	10.9349	0.367989	0.183994	−	0.982927i	$-0.441097\pi$
$883$	10.9349	0.367989	0.183994	+	0.982927i	$0.441097\pi$
$884$	−19.9956	−0.672525
$885$	−4.07124	−0.136853
$886$	42.7946	1.43771
$887$	17.2111	0.577894	0.288947	−	0.957345i	$-0.406695\pi$
$887$	17.2111	0.577894	0.288947	+	0.957345i	$0.406695\pi$
$888$	−71.1933	−2.38909
$889$	15.7869	0.529476
$890$	22.9378	0.768876
$891$	−13.3756	−0.448098
$892$	54.0634	1.81018
$893$	2.49371	0.0834489
$894$	74.8212	2.50239
$895$	2.59483	0.0867358
$896$	−1.68374	−0.0562496
$897$	−12.4812	−0.416736
$898$	−37.7606	−1.26009
$899$	15.0554	0.502127
$900$	−27.6546	−0.921818
$901$	5.53881	0.184525
$902$	−6.38435	−0.212576
$903$	−83.6738	−2.78449
$904$	47.7796	1.58913
$905$	1.68596	0.0560431
$906$	−8.33831	−0.277022
$907$	43.9477	1.45926	0.729629	−	0.683843i	$-0.239693\pi$
$907$	43.9477	1.45926	0.729629	+	0.683843i	$0.239693\pi$
$908$	105.721	3.50846
$909$	2.33893	0.0775775
$910$	20.6748	0.685363
$911$	−44.5759	−1.47687	−0.738433	−	0.674327i	$-0.764434\pi$
$911$	−44.5759	−1.47687	−0.738433	+	0.674327i	$0.764434\pi$
$912$	49.0172	1.62312
$913$	−5.07805	−0.168059
$914$	−98.0941	−3.24466
$915$	8.50132	0.281045
$916$	89.7440	2.96522
$917$	24.3847	0.805252
$918$	−9.54829	−0.315140
$919$	23.6650	0.780636	0.390318	−	0.920680i	$-0.372365\pi$
$919$	23.6650	0.780636	0.390318	+	0.920680i	$0.372365\pi$
$920$	−5.82760	−0.192130
$921$	62.3478	2.05443
$922$	17.3312	0.570774
$923$	−4.72190	−0.155423
$924$	41.7470	1.37338
$925$	22.1804	0.729286
$926$	−27.1958	−0.893708
$927$	−1.79724	−0.0590293
$928$	19.6779	0.645957
$929$	−35.8969	−1.17774	−0.588870	−	0.808228i	$-0.700427\pi$
$929$	−35.8969	−1.17774	−0.588870	+	0.808228i	$0.700427\pi$
$930$	22.8225	0.748381
$931$	−13.5089	−0.442736
$932$	125.556	4.11273
$933$	7.30176	0.239049
$934$	−67.3420	−2.20350
$935$	−0.648147	−0.0211967
$936$	37.2384	1.21718
$937$	55.0012	1.79681	0.898406	−	0.439165i	$-0.144726\pi$
$937$	55.0012	1.79681	0.898406	+	0.439165i	$0.144726\pi$
$938$	115.652	3.77618
$939$	−23.9642	−0.782041
$940$	2.60759	0.0850503
$941$	36.8089	1.19994	0.599968	−	0.800024i	$-0.295180\pi$
$941$	36.8089	1.19994	0.599968	+	0.800024i	$0.295180\pi$
$942$	−126.853	−4.13309
$943$	−2.98930	−0.0973451
$944$	−35.0329	−1.14022
$945$	6.97611	0.226933
$946$	36.1355	1.17487
$947$	29.0596	0.944312	0.472156	−	0.881515i	$-0.343476\pi$
$947$	29.0596	0.944312	0.472156	+	0.881515i	$0.343476\pi$
$948$	−20.1505	−0.654459
$949$	−44.8016	−1.45432
$950$	−30.6464	−0.994301
$951$	58.2774	1.88977
$952$	25.9167	0.839966
$953$	11.1322	0.360609	0.180304	−	0.983611i	$-0.442292\pi$
$953$	11.1322	0.360609	0.180304	+	0.983611i	$0.442292\pi$
$954$	−17.6388	−0.571077
$955$	5.82438	0.188473
$956$	−118.986	−3.84827
$957$	4.71064	0.152273
$958$	−99.6994	−3.22114
$959$	−53.8974	−1.74044
$960$	8.54815	0.275890
$961$	30.7897	0.993216
$962$	−51.0726	−1.64665
$963$	−6.50720	−0.209691
$964$	−36.3134	−1.16958
$965$	3.95778	0.127405
$966$	27.6629	0.890039
$967$	−42.8197	−1.37699	−0.688494	−	0.725242i	$-0.741728\pi$
$967$	−42.8197	−1.37699	−0.688494	+	0.725242i	$0.741728\pi$
$968$	70.3591	2.26143
$969$	5.12257	0.164561
$970$	23.3900	0.751009
$971$	6.15711	0.197591	0.0987956	−	0.995108i	$-0.468501\pi$
$971$	6.15711	0.197591	0.0987956	+	0.995108i	$0.468501\pi$
$972$	57.6929	1.85050
$973$	46.0110	1.47505
$974$	−46.0056	−1.47411
$975$	−40.1371	−1.28542
$976$	73.1535	2.34159
$977$	48.7697	1.56028	0.780141	−	0.625604i	$-0.215147\pi$
$977$	48.7697	1.56028	0.780141	+	0.625604i	$0.215147\pi$
$978$	111.958	3.58004
$979$	19.4308	0.621010
$980$	−14.1258	−0.451233
$981$	16.0907	0.513736
$982$	16.6054	0.529900
$983$	−48.4848	−1.54642	−0.773212	−	0.634148i	$-0.781351\pi$
$983$	−48.4848	−1.54642	−0.773212	+	0.634148i	$0.781351\pi$
$984$	30.8553	0.983630
$985$	0.199958	0.00637118
$986$	5.00068	0.159254
$987$	−7.23857	−0.230406
$988$	49.8632	1.58636
$989$	16.9195	0.538008
$990$	2.06408	0.0656006
$991$	25.2531	0.802192	0.401096	−	0.916036i	$-0.368629\pi$
$991$	25.2531	0.802192	0.401096	+	0.916036i	$0.368629\pi$
$992$	80.7608	2.56416
$993$	−40.1910	−1.27542
$994$	10.4654	0.331943
$995$	−4.96156	−0.157292
$996$	41.9667	1.32977
$997$	14.3910	0.455766	0.227883	−	0.973688i	$-0.426820\pi$
$997$	14.3910	0.455766	0.227883	+	0.973688i	$0.426820\pi$
$998$	40.0910	1.26906
$999$	−17.2330	−0.545228

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	799.2.a.f.1.1	✓	17
3.2	odd	2		7191.2.a.y.1.17		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
799.2.a.f.1.1	✓	17	1.1	even	1	trivial
7191.2.a.y.1.17		17	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:	\( N \)	\(=\)	\( 799 = 17 \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	799.a (trivial)

\(f(q)\)	\(=\)	\(q-2.61092 q^{2} -2.05419 q^{3} +4.81692 q^{4} -0.541341 q^{5} +5.36334 q^{6} -3.52380 q^{7} -7.35476 q^{8} +1.21971 q^{9} +O(q^{10})\)	\(q-2.61092 q^{2} -2.05419 q^{3} +4.81692 q^{4} -0.541341 q^{5} +5.36334 q^{6} -3.52380 q^{7} -7.35476 q^{8} +1.21971 q^{9} +1.41340 q^{10} +1.19730 q^{11} -9.89489 q^{12} -4.15112 q^{13} +9.20038 q^{14} +1.11202 q^{15} +9.56887 q^{16} +1.00000 q^{17} -3.18458 q^{18} -2.49371 q^{19} -2.60759 q^{20} +7.23857 q^{21} -3.12606 q^{22} -1.46369 q^{23} +15.1081 q^{24} -4.70695 q^{25} +10.8382 q^{26} +3.65705 q^{27} -16.9739 q^{28} -1.91529 q^{29} -2.90339 q^{30} -7.86064 q^{31} -10.2741 q^{32} -2.45949 q^{33} -2.61092 q^{34} +1.90758 q^{35} +5.87526 q^{36} -4.71226 q^{37} +6.51089 q^{38} +8.52720 q^{39} +3.98143 q^{40} +2.04230 q^{41} -18.8994 q^{42} -11.5594 q^{43} +5.76730 q^{44} -0.660280 q^{45} +3.82159 q^{46} -1.00000 q^{47} -19.6563 q^{48} +5.41719 q^{49} +12.2895 q^{50} -2.05419 q^{51} -19.9956 q^{52} +5.53881 q^{53} -9.54829 q^{54} -0.648147 q^{55} +25.9167 q^{56} +5.12257 q^{57} +5.00068 q^{58} -3.66113 q^{59} +5.35650 q^{60} +7.64495 q^{61} +20.5235 q^{62} -4.29803 q^{63} +7.68706 q^{64} +2.24717 q^{65} +6.42153 q^{66} +12.5704 q^{67} +4.81692 q^{68} +3.00671 q^{69} -4.98054 q^{70} +1.13750 q^{71} -8.97070 q^{72} +10.7927 q^{73} +12.3033 q^{74} +9.66899 q^{75} -12.0120 q^{76} -4.21905 q^{77} -22.2639 q^{78} +2.03646 q^{79} -5.18002 q^{80} -11.1714 q^{81} -5.33229 q^{82} -4.24125 q^{83} +34.8676 q^{84} -0.541341 q^{85} +30.1808 q^{86} +3.93438 q^{87} -8.80586 q^{88} +16.2288 q^{89} +1.72394 q^{90} +14.6277 q^{91} -7.05050 q^{92} +16.1473 q^{93} +2.61092 q^{94} +1.34995 q^{95} +21.1049 q^{96} +16.5488 q^{97} -14.1439 q^{98} +1.46036 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 3 q^{2} + q^{3} + 19 q^{4} + 11 q^{5} + 5 q^{6} + q^{7} + 3 q^{8} + 30 q^{9}+O(q^{10}) \) 17 * q + 3 * q^2 + q^3 + 19 * q^4 + 11 * q^5 + 5 * q^6 + q^7 + 3 * q^8 + 30 * q^9	\( 17 q + 3 q^{2} + q^{3} + 19 q^{4} + 11 q^{5} + 5 q^{6} + q^{7} + 3 q^{8} + 30 q^{9} + 12 q^{10} + 8 q^{11} + 12 q^{12} + q^{13} + 11 q^{14} - 7 q^{15} + 15 q^{16} + 17 q^{17} - 26 q^{18} - q^{19} + 13 q^{20} + 14 q^{21} + 3 q^{22} + 12 q^{23} - 24 q^{24} + 33 q^{26} + 22 q^{27} + q^{28} + 10 q^{29} + q^{30} + 2 q^{31} - q^{32} + 3 q^{33} + 3 q^{34} + 9 q^{35} + 50 q^{36} + 10 q^{37} + 23 q^{38} + 13 q^{39} + q^{40} + 65 q^{41} - 41 q^{42} - 3 q^{43} + 10 q^{44} + 31 q^{45} - 17 q^{47} - 16 q^{48} + 14 q^{49} + 5 q^{50} + q^{51} - 32 q^{52} - 13 q^{53} - 15 q^{54} - 11 q^{55} + 46 q^{56} + 36 q^{57} - q^{58} + 39 q^{59} + 43 q^{60} + 23 q^{61} + 33 q^{62} - 15 q^{63} - 27 q^{64} - 10 q^{65} - 86 q^{66} - 14 q^{67} + 19 q^{68} + 45 q^{69} - 13 q^{70} + 21 q^{71} - 42 q^{72} + 24 q^{73} + 25 q^{74} - 32 q^{75} - 5 q^{76} - 2 q^{77} + 36 q^{78} - 26 q^{79} - 14 q^{80} + 41 q^{81} - 37 q^{82} - 5 q^{83} - 60 q^{84} + 11 q^{85} - 24 q^{86} - 5 q^{87} - 25 q^{88} + 61 q^{89} + 6 q^{90} + 29 q^{91} - 12 q^{92} - 3 q^{93} - 3 q^{94} - 6 q^{95} + 12 q^{96} + 3 q^{97} + 36 q^{98} - 27 q^{99}+O(q^{100}) \) 17 * q + 3 * q^2 + q^3 + 19 * q^4 + 11 * q^5 + 5 * q^6 + q^7 + 3 * q^8 + 30 * q^9 + 12 * q^10 + 8 * q^11 + 12 * q^12 + q^13 + 11 * q^14 - 7 * q^15 + 15 * q^16 + 17 * q^17 - 26 * q^18 - q^19 + 13 * q^20 + 14 * q^21 + 3 * q^22 + 12 * q^23 - 24 * q^24 + 33 * q^26 + 22 * q^27 + q^28 + 10 * q^29 + q^30 + 2 * q^31 - q^32 + 3 * q^33 + 3 * q^34 + 9 * q^35 + 50 * q^36 + 10 * q^37 + 23 * q^38 + 13 * q^39 + q^40 + 65 * q^41 - 41 * q^42 - 3 * q^43 + 10 * q^44 + 31 * q^45 - 17 * q^47 - 16 * q^48 + 14 * q^49 + 5 * q^50 + q^51 - 32 * q^52 - 13 * q^53 - 15 * q^54 - 11 * q^55 + 46 * q^56 + 36 * q^57 - q^58 + 39 * q^59 + 43 * q^60 + 23 * q^61 + 33 * q^62 - 15 * q^63 - 27 * q^64 - 10 * q^65 - 86 * q^66 - 14 * q^67 + 19 * q^68 + 45 * q^69 - 13 * q^70 + 21 * q^71 - 42 * q^72 + 24 * q^73 + 25 * q^74 - 32 * q^75 - 5 * q^76 - 2 * q^77 + 36 * q^78 - 26 * q^79 - 14 * q^80 + 41 * q^81 - 37 * q^82 - 5 * q^83 - 60 * q^84 + 11 * q^85 - 24 * q^86 - 5 * q^87 - 25 * q^88 + 61 * q^89 + 6 * q^90 + 29 * q^91 - 12 * q^92 - 3 * q^93 - 3 * q^94 - 6 * q^95 + 12 * q^96 + 3 * q^97 + 36 * q^98 - 27 * q^99

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