LMFDB - Embedded newform 979.2.a.d.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [979,2,Mod(1,979)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(979, 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("979.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 979 = 11 \cdot 89 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	979.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:	$7.81735435788$
Analytic rank:	$1$
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} - 4 x^{16} - 16 x^{15} + 74 x^{14} + 95 x^{13} - 547 x^{12} - 241 x^{11} + 2054 x^{10} + 141 x^{9} + \cdots + 1 $ x^17 - 4x^16 - 16x^15 + 74x^14 + 95x^13 - 547x^12 - 241x^11 + 2054x^10 + 141x^9 - 4103x^8 + 489x^7 + 4118x^6 - 966x^5 - 1663x^4 + 596x^3 + 94x^2 - 43x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.50646$ of defining polynomial
Character	$\chi$	$=$	979.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.50646 q^{2} -1.47186 q^{3} +4.28233 q^{4} -3.57592 q^{5} +3.68915 q^{6} -1.01713 q^{7} -5.72057 q^{8} -0.833639 q^{9} +O(q^{10})$	\(q-2.50646 q^{2} -1.47186 q^{3} +4.28233 q^{4} -3.57592 q^{5} +3.68915 q^{6} -1.01713 q^{7} -5.72057 q^{8} -0.833639 q^{9} +8.96289 q^{10} -1.00000 q^{11} -6.30298 q^{12} +6.20886 q^{13} +2.54939 q^{14} +5.26324 q^{15} +5.77371 q^{16} -2.01119 q^{17} +2.08948 q^{18} +2.66748 q^{19} -15.3133 q^{20} +1.49706 q^{21} +2.50646 q^{22} +3.98165 q^{23} +8.41986 q^{24} +7.78720 q^{25} -15.5623 q^{26} +5.64257 q^{27} -4.35568 q^{28} -2.68526 q^{29} -13.1921 q^{30} -8.75357 q^{31} -3.03043 q^{32} +1.47186 q^{33} +5.04097 q^{34} +3.63716 q^{35} -3.56992 q^{36} +4.44011 q^{37} -6.68592 q^{38} -9.13856 q^{39} +20.4563 q^{40} +7.01882 q^{41} -3.75233 q^{42} +2.27129 q^{43} -4.28233 q^{44} +2.98103 q^{45} -9.97983 q^{46} +10.4767 q^{47} -8.49808 q^{48} -5.96545 q^{49} -19.5183 q^{50} +2.96019 q^{51} +26.5884 q^{52} -3.38979 q^{53} -14.1429 q^{54} +3.57592 q^{55} +5.81855 q^{56} -3.92614 q^{57} +6.73050 q^{58} -8.56153 q^{59} +22.5389 q^{60} +4.77597 q^{61} +21.9405 q^{62} +0.847917 q^{63} -3.95179 q^{64} -22.2024 q^{65} -3.68915 q^{66} +8.28168 q^{67} -8.61259 q^{68} -5.86041 q^{69} -9.11640 q^{70} +8.11785 q^{71} +4.76889 q^{72} -12.5915 q^{73} -11.1290 q^{74} -11.4616 q^{75} +11.4230 q^{76} +1.01713 q^{77} +22.9054 q^{78} -11.0148 q^{79} -20.6463 q^{80} -5.80413 q^{81} -17.5924 q^{82} +0.243961 q^{83} +6.41093 q^{84} +7.19186 q^{85} -5.69290 q^{86} +3.95232 q^{87} +5.72057 q^{88} -1.00000 q^{89} -7.47182 q^{90} -6.31520 q^{91} +17.0507 q^{92} +12.8840 q^{93} -26.2595 q^{94} -9.53868 q^{95} +4.46035 q^{96} -0.199119 q^{97} +14.9522 q^{98} +0.833639 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 4 q^{2} - q^{3} + 14 q^{4} - 14 q^{5} - 6 q^{6} - 5 q^{7} - 18 q^{8} + 6 q^{9}+O(q^{10}) $ 17 * q - 4 * q^2 - q^3 + 14 * q^4 - 14 * q^5 - 6 * q^6 - 5 * q^7 - 18 * q^8 + 6 * q^9	\( 17 q - 4 q^{2} - q^{3} + 14 q^{4} - 14 q^{5} - 6 q^{6} - 5 q^{7} - 18 q^{8} + 6 q^{9} - 6 q^{10} - 17 q^{11} + q^{12} - 6 q^{13} - 17 q^{14} - 3 q^{15} + 8 q^{16} - 19 q^{17} - 9 q^{19} - 29 q^{20} - 35 q^{21} + 4 q^{22} - 13 q^{23} - 20 q^{24} + 19 q^{25} - 19 q^{27} + q^{28} - 54 q^{29} + q^{30} + 8 q^{31} - 35 q^{32} + q^{33} + 14 q^{34} - 22 q^{35} - 20 q^{36} - 3 q^{38} - 18 q^{39} + 16 q^{40} - 16 q^{41} - 37 q^{42} - 21 q^{43} - 14 q^{44} - 31 q^{45} - 31 q^{46} - 3 q^{47} + 34 q^{48} + 2 q^{49} - 5 q^{50} - 13 q^{51} + 14 q^{52} - 43 q^{53} - 19 q^{54} + 14 q^{55} + 14 q^{56} - 29 q^{57} + 22 q^{58} - q^{59} - 11 q^{60} - 29 q^{61} + 32 q^{62} + 17 q^{63} - 22 q^{64} - 44 q^{65} + 6 q^{66} + 17 q^{67} - 43 q^{68} - 21 q^{69} + 76 q^{70} + 6 q^{71} + 17 q^{72} + 3 q^{73} - 10 q^{74} - 11 q^{75} - 17 q^{76} + 5 q^{77} + 35 q^{78} - 43 q^{79} - 32 q^{80} + 13 q^{81} - 10 q^{82} - 14 q^{83} + 44 q^{84} + 5 q^{85} - 37 q^{86} - 3 q^{87} + 18 q^{88} - 17 q^{89} - 2 q^{90} - 12 q^{91} + 23 q^{92} - 26 q^{93} - 4 q^{94} - 35 q^{95} - 20 q^{96} - 6 q^{97} + q^{98} - 6 q^{99}+O(q^{100}) \) 17 * q - 4 * q^2 - q^3 + 14 * q^4 - 14 * q^5 - 6 * q^6 - 5 * q^7 - 18 * q^8 + 6 * q^9 - 6 * q^10 - 17 * q^11 + q^12 - 6 * q^13 - 17 * q^14 - 3 * q^15 + 8 * q^16 - 19 * q^17 - 9 * q^19 - 29 * q^20 - 35 * q^21 + 4 * q^22 - 13 * q^23 - 20 * q^24 + 19 * q^25 - 19 * q^27 + q^28 - 54 * q^29 + q^30 + 8 * q^31 - 35 * q^32 + q^33 + 14 * q^34 - 22 * q^35 - 20 * q^36 - 3 * q^38 - 18 * q^39 + 16 * q^40 - 16 * q^41 - 37 * q^42 - 21 * q^43 - 14 * q^44 - 31 * q^45 - 31 * q^46 - 3 * q^47 + 34 * q^48 + 2 * q^49 - 5 * q^50 - 13 * q^51 + 14 * q^52 - 43 * q^53 - 19 * q^54 + 14 * q^55 + 14 * q^56 - 29 * q^57 + 22 * q^58 - q^59 - 11 * q^60 - 29 * q^61 + 32 * q^62 + 17 * q^63 - 22 * q^64 - 44 * q^65 + 6 * q^66 + 17 * q^67 - 43 * q^68 - 21 * q^69 + 76 * q^70 + 6 * q^71 + 17 * q^72 + 3 * q^73 - 10 * q^74 - 11 * q^75 - 17 * q^76 + 5 * q^77 + 35 * q^78 - 43 * q^79 - 32 * q^80 + 13 * q^81 - 10 * q^82 - 14 * q^83 + 44 * q^84 + 5 * q^85 - 37 * q^86 - 3 * q^87 + 18 * q^88 - 17 * q^89 - 2 * q^90 - 12 * q^91 + 23 * q^92 - 26 * q^93 - 4 * q^94 - 35 * q^95 - 20 * q^96 - 6 * q^97 + q^98 - 6 * 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 $

$2$	−2.50646	−1.77233	−0.886167	−	0.463366i	$-0.846641\pi$
$2$	−2.50646	−1.77233	−0.886167	+	0.463366i	$0.846641\pi$
$3$	−1.47186	−0.849777	−0.424888	−	0.905246i	$-0.639687\pi$
$3$	−1.47186	−0.849777	−0.424888	+	0.905246i	$0.639687\pi$
$4$	4.28233	2.14117
$5$	−3.57592	−1.59920	−0.799600	−	0.600533i	$-0.794955\pi$
$5$	−3.57592	−1.59920	−0.799600	+	0.600533i	$0.794955\pi$
$6$	3.68915	1.50609
$7$	−1.01713	−0.384438	−0.192219	−	0.981352i	$-0.561568\pi$
$7$	−1.01713	−0.384438	−0.192219	+	0.981352i	$0.561568\pi$
$8$	−5.72057	−2.02253
$9$	−0.833639	−0.277880
$10$	8.96289	2.83432
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−6.30298	−1.81951
$13$	6.20886	1.72203	0.861014	−	0.508580i	$-0.169830\pi$
$13$	6.20886	1.72203	0.861014	+	0.508580i	$0.169830\pi$
$14$	2.54939	0.681352
$15$	5.26324	1.35896
$16$	5.77371	1.44343
$17$	−2.01119	−0.487786	−0.243893	−	0.969802i	$-0.578425\pi$
$17$	−2.01119	−0.487786	−0.243893	+	0.969802i	$0.578425\pi$
$18$	2.08948	0.492496
$19$	2.66748	0.611961	0.305981	−	0.952038i	$-0.401016\pi$
$19$	2.66748	0.611961	0.305981	+	0.952038i	$0.401016\pi$
$20$	−15.3133	−3.42415
$21$	1.49706	0.326686
$22$	2.50646	0.534379
$23$	3.98165	0.830231	0.415115	−	0.909769i	$-0.363741\pi$
$23$	3.98165	0.830231	0.415115	+	0.909769i	$0.363741\pi$
$24$	8.41986	1.71870
$25$	7.78720	1.55744
$26$	−15.5623	−3.05201
$27$	5.64257	1.08591
$28$	−4.35568	−0.823146
$29$	−2.68526	−0.498641	−0.249320	−	0.968421i	$-0.580207\pi$
$29$	−2.68526	−0.498641	−0.249320	+	0.968421i	$0.580207\pi$
$30$	−13.1921	−2.40854
$31$	−8.75357	−1.57219	−0.786094	−	0.618108i	$-0.787900\pi$
$31$	−8.75357	−1.57219	−0.786094	+	0.618108i	$0.787900\pi$
$32$	−3.03043	−0.535709
$33$	1.47186	0.256217
$34$	5.04097	0.864519
$35$	3.63716	0.614793
$36$	−3.56992	−0.594987
$37$	4.44011	0.729950	0.364975	−	0.931017i	$-0.381077\pi$
$37$	4.44011	0.729950	0.364975	+	0.931017i	$0.381077\pi$
$38$	−6.68592	−1.08460
$39$	−9.13856	−1.46334
$40$	20.4563	3.23443
$41$	7.01882	1.09616	0.548078	−	0.836427i	$-0.315360\pi$
$41$	7.01882	1.09616	0.548078	+	0.836427i	$0.315360\pi$
$42$	−3.75233	−0.578997
$43$	2.27129	0.346369	0.173185	−	0.984889i	$-0.444594\pi$
$43$	2.27129	0.346369	0.173185	+	0.984889i	$0.444594\pi$
$44$	−4.28233	−0.645586
$45$	2.98103	0.444385
$46$	−9.97983	−1.47145
$47$	10.4767	1.52819	0.764095	−	0.645104i	$-0.223186\pi$
$47$	10.4767	1.52819	0.764095	+	0.645104i	$0.223186\pi$
$48$	−8.49808	−1.22659
$49$	−5.96545	−0.852208
$50$	−19.5183	−2.76030
$51$	2.96019	0.414509
$52$	26.5884	3.68715
$53$	−3.38979	−0.465624	−0.232812	−	0.972522i	$-0.574793\pi$
$53$	−3.38979	−0.465624	−0.232812	+	0.972522i	$0.574793\pi$
$54$	−14.1429	−1.92460
$55$	3.57592	0.482177
$56$	5.81855	0.777537
$57$	−3.92614	−0.520030
$58$	6.73050	0.883758
$59$	−8.56153	−1.11462	−0.557308	−	0.830306i	$-0.688166\pi$
$59$	−8.56153	−1.11462	−0.557308	+	0.830306i	$0.688166\pi$
$60$	22.5389	2.90977
$61$	4.77597	0.611501	0.305750	−	0.952112i	$-0.401093\pi$
$61$	4.77597	0.611501	0.305750	+	0.952112i	$0.401093\pi$
$62$	21.9405	2.78644
$63$	0.847917	0.106827
$64$	−3.95179	−0.493974
$65$	−22.2024	−2.75387
$66$	−3.68915	−0.454103
$67$	8.28168	1.01177	0.505884	−	0.862602i	$-0.331166\pi$
$67$	8.28168	1.01177	0.505884	+	0.862602i	$0.331166\pi$
$68$	−8.61259	−1.04443
$69$	−5.86041	−0.705511
$70$	−9.11640	−1.08962
$71$	8.11785	0.963412	0.481706	−	0.876333i	$-0.340017\pi$
$71$	8.11785	0.963412	0.481706	+	0.876333i	$0.340017\pi$
$72$	4.76889	0.562020
$73$	−12.5915	−1.47372	−0.736862	−	0.676044i	$-0.763693\pi$
$73$	−12.5915	−1.47372	−0.736862	+	0.676044i	$0.763693\pi$
$74$	−11.1290	−1.29372
$75$	−11.4616	−1.32348
$76$	11.4230	1.31031
$77$	1.01713	0.115912
$78$	22.9054	2.59353
$79$	−11.0148	−1.23927	−0.619633	−	0.784892i	$-0.712719\pi$
$79$	−11.0148	−1.23927	−0.619633	+	0.784892i	$0.712719\pi$
$80$	−20.6463	−2.30833
$81$	−5.80413	−0.644903
$82$	−17.5924	−1.94275
$83$	0.243961	0.0267782	0.0133891	−	0.999910i	$-0.495738\pi$
$83$	0.243961	0.0267782	0.0133891	+	0.999910i	$0.495738\pi$
$84$	6.41093	0.699490
$85$	7.19186	0.780067
$86$	−5.69290	−0.613882
$87$	3.95232	0.423733
$88$	5.72057	0.609815
$89$	−1.00000	−0.106000
$89$	−1.00000	−0.106000
$90$	−7.47182	−0.787599
$91$	−6.31520	−0.662013
$92$	17.0507	1.77766
$93$	12.8840	1.33601
$94$	−26.2595	−2.70846
$95$	−9.53868	−0.978648
$96$	4.46035	0.455233
$97$	−0.199119	−0.0202174	−0.0101087	−	0.999949i	$-0.503218\pi$
$97$	−0.199119	−0.0202174	−0.0101087	+	0.999949i	$0.503218\pi$
$98$	14.9522	1.51040
$99$	0.833639	0.0837839
$100$	33.3474	3.33474
$101$	−6.83138	−0.679747	−0.339874	−	0.940471i	$-0.610384\pi$
$101$	−6.83138	−0.679747	−0.339874	+	0.940471i	$0.610384\pi$
$102$	−7.41958	−0.734648
$103$	−5.82961	−0.574408	−0.287204	−	0.957869i	$-0.592726\pi$
$103$	−5.82961	−0.574408	−0.287204	+	0.957869i	$0.592726\pi$
$104$	−35.5183	−3.48285
$105$	−5.35338	−0.522437
$106$	8.49638	0.825241
$107$	−13.1979	−1.27589	−0.637946	−	0.770081i	$-0.720216\pi$
$107$	−13.1979	−1.27589	−0.637946	+	0.770081i	$0.720216\pi$
$108$	24.1633	2.32512
$109$	−11.5790	−1.10907	−0.554533	−	0.832162i	$-0.687103\pi$
$109$	−11.5790	−1.10907	−0.554533	+	0.832162i	$0.687103\pi$
$110$	−8.96289	−0.854578
$111$	−6.53521	−0.620295
$112$	−5.87260	−0.554909
$113$	−4.99175	−0.469584	−0.234792	−	0.972046i	$-0.575441\pi$
$113$	−4.99175	−0.469584	−0.234792	+	0.972046i	$0.575441\pi$
$114$	9.84072	0.921667
$115$	−14.2380	−1.32770
$116$	−11.4992	−1.06767
$117$	−5.17595	−0.478517
$118$	21.4591	1.97547
$119$	2.04564	0.187523
$120$	−30.1088	−2.74854
$121$	1.00000	0.0909091
$122$	−11.9708	−1.08378
$123$	−10.3307	−0.931488
$124$	−37.4857	−3.36631
$125$	−9.96680	−0.891457
$126$	−2.12527	−0.189334
$127$	−19.8674	−1.76295	−0.881473	−	0.472234i	$-0.843448\pi$
$127$	−19.8674	−1.76295	−0.881473	+	0.472234i	$0.843448\pi$
$128$	15.9659	1.41120
$129$	−3.34302	−0.294336
$130$	55.6494	4.88077
$131$	−13.0596	−1.14102	−0.570511	−	0.821290i	$-0.693255\pi$
$131$	−13.0596	−1.14102	−0.570511	+	0.821290i	$0.693255\pi$
$132$	6.30298	0.548604
$133$	−2.71316	−0.235261
$134$	−20.7577	−1.79319
$135$	−20.1774	−1.73659
$136$	11.5052	0.986560
$137$	20.6181	1.76153	0.880763	−	0.473558i	$-0.157030\pi$
$137$	20.6181	1.76153	0.880763	+	0.473558i	$0.157030\pi$
$138$	14.6889	1.25040
$139$	2.28507	0.193817	0.0969084	−	0.995293i	$-0.469105\pi$
$139$	2.28507	0.193817	0.0969084	+	0.995293i	$0.469105\pi$
$140$	15.5755	1.31637
$141$	−15.4203	−1.29862
$142$	−20.3471	−1.70749
$143$	−6.20886	−0.519211
$144$	−4.81319	−0.401100
$145$	9.60228	0.797426
$146$	31.5601	2.61193
$147$	8.78029	0.724186
$148$	19.0140	1.56295
$149$	3.67550	0.301109	0.150554	−	0.988602i	$-0.451894\pi$
$149$	3.67550	0.301109	0.150554	+	0.988602i	$0.451894\pi$
$150$	28.7281	2.34564
$151$	15.3344	1.24790	0.623949	−	0.781465i	$-0.285527\pi$
$151$	15.3344	1.24790	0.623949	+	0.781465i	$0.285527\pi$
$152$	−15.2595	−1.23771
$153$	1.67661	0.135546
$154$	−2.54939	−0.205435
$155$	31.3020	2.51424
$156$	−39.1343	−3.13326
$157$	−6.99032	−0.557888	−0.278944	−	0.960307i	$-0.589984\pi$
$157$	−6.99032	−0.557888	−0.278944	+	0.960307i	$0.589984\pi$
$158$	27.6082	2.19639
$159$	4.98929	0.395676
$160$	10.8366	0.856705
$161$	−4.04984	−0.319172
$162$	14.5478	1.14298
$163$	−17.5507	−1.37468	−0.687338	−	0.726338i	$-0.741221\pi$
$163$	−17.5507	−1.37468	−0.687338	+	0.726338i	$0.741221\pi$
$164$	30.0569	2.34705
$165$	−5.26324	−0.409743
$166$	−0.611478	−0.0474599
$167$	13.1267	1.01578	0.507888	−	0.861423i	$-0.330426\pi$
$167$	13.1267	1.01578	0.507888	+	0.861423i	$0.330426\pi$
$168$	−8.56407	−0.660732
$169$	25.5500	1.96538
$170$	−18.0261	−1.38254
$171$	−2.22371	−0.170052
$172$	9.72644	0.741634
$173$	−21.9569	−1.66935	−0.834677	−	0.550740i	$-0.814346\pi$
$173$	−21.9569	−1.66935	−0.834677	+	0.550740i	$0.814346\pi$
$174$	−9.90632	−0.750996
$175$	−7.92057	−0.598739
$176$	−5.77371	−0.435210
$177$	12.6013	0.947175
$178$	2.50646	0.187867
$179$	−2.43301	−0.181851	−0.0909257	−	0.995858i	$-0.528983\pi$
$179$	−2.43301	−0.181851	−0.0909257	+	0.995858i	$0.528983\pi$
$180$	12.7657	0.951503
$181$	0.445787	0.0331351	0.0165675	−	0.999863i	$-0.494726\pi$
$181$	0.445787	0.0331351	0.0165675	+	0.999863i	$0.494726\pi$
$182$	15.8288	1.17331
$183$	−7.02955	−0.519639
$184$	−22.7773	−1.67917
$185$	−15.8775	−1.16734
$186$	−32.2932	−2.36785
$187$	2.01119	0.147073
$188$	44.8649	3.27211
$189$	−5.73921	−0.417466
$190$	23.9083	1.73449
$191$	−1.26605	−0.0916082	−0.0458041	−	0.998950i	$-0.514585\pi$
$191$	−1.26605	−0.0916082	−0.0458041	+	0.998950i	$0.514585\pi$
$192$	5.81647	0.419767
$193$	7.84475	0.564678	0.282339	−	0.959315i	$-0.408890\pi$
$193$	7.84475	0.564678	0.282339	+	0.959315i	$0.408890\pi$
$194$	0.499082	0.0358320
$195$	32.6787	2.34017
$196$	−25.5461	−1.82472
$197$	−10.6112	−0.756015	−0.378007	−	0.925803i	$-0.623391\pi$
$197$	−10.6112	−0.756015	−0.378007	+	0.925803i	$0.623391\pi$
$198$	−2.08948	−0.148493
$199$	19.0568	1.35090	0.675449	−	0.737406i	$-0.263950\pi$
$199$	19.0568	1.35090	0.675449	+	0.737406i	$0.263950\pi$
$200$	−44.5472	−3.14997
$201$	−12.1894	−0.859777
$202$	17.1226	1.20474
$203$	2.73125	0.191696
$204$	12.6765	0.887533
$205$	−25.0987	−1.75297
$206$	14.6117	1.01804
$207$	−3.31926	−0.230704
$208$	35.8482	2.48563
$209$	−2.66748	−0.184513
$210$	13.4180	0.925932
$211$	11.7469	0.808689	0.404345	−	0.914607i	$-0.367500\pi$
$211$	11.7469	0.808689	0.404345	+	0.914607i	$0.367500\pi$
$212$	−14.5162	−0.996979
$213$	−11.9483	−0.818685
$214$	33.0801	2.26131
$215$	−8.12196	−0.553913
$216$	−32.2787	−2.19629
$217$	8.90349	0.604408
$218$	29.0223	1.96563
$219$	18.5329	1.25234
$220$	15.3133	1.03242
$221$	−12.4872	−0.839981
$222$	16.3802	1.09937
$223$	26.5358	1.77697	0.888484	−	0.458908i	$-0.151759\pi$
$223$	26.5358	1.77697	0.888484	+	0.458908i	$0.151759\pi$
$224$	3.08233	0.205947
$225$	−6.49171	−0.432781
$226$	12.5116	0.832260
$227$	1.59420	0.105811	0.0529054	−	0.998600i	$-0.483152\pi$
$227$	1.59420	0.105811	0.0529054	+	0.998600i	$0.483152\pi$
$228$	−16.8131	−1.11347
$229$	1.79027	0.118304	0.0591522	−	0.998249i	$-0.481160\pi$
$229$	1.79027	0.118304	0.0591522	+	0.998249i	$0.481160\pi$
$230$	35.6871	2.35314
$231$	−1.49706	−0.0984996
$232$	15.3612	1.00851
$233$	−15.5858	−1.02106	−0.510529	−	0.859860i	$-0.670551\pi$
$233$	−15.5858	−1.02106	−0.510529	+	0.859860i	$0.670551\pi$
$234$	12.9733	0.848092
$235$	−37.4640	−2.44388
$236$	−36.6633	−2.38658
$237$	16.2123	1.05310
$238$	−5.12730	−0.332354
$239$	−17.9060	−1.15824	−0.579122	−	0.815241i	$-0.696605\pi$
$239$	−17.9060	−1.15824	−0.579122	+	0.815241i	$0.696605\pi$
$240$	30.3884	1.96157
$241$	8.14685	0.524785	0.262392	−	0.964961i	$-0.415489\pi$
$241$	8.14685	0.524785	0.262392	+	0.964961i	$0.415489\pi$
$242$	−2.50646	−0.161121
$243$	−8.38485	−0.537889
$244$	20.4523	1.30932
$245$	21.3320	1.36285
$246$	25.8935	1.65091
$247$	16.5620	1.05382
$248$	50.0754	3.17979
$249$	−0.359076	−0.0227555
$250$	24.9814	1.57996
$251$	26.7541	1.68870	0.844352	−	0.535789i	$-0.179986\pi$
$251$	26.7541	1.68870	0.844352	+	0.535789i	$0.179986\pi$
$252$	3.63106	0.228735
$253$	−3.98165	−0.250324
$254$	49.7968	3.12453
$255$	−10.5854	−0.662882
$256$	−32.1142	−2.00714
$257$	12.9941	0.810550	0.405275	−	0.914195i	$-0.367176\pi$
$257$	12.9941	0.810550	0.405275	+	0.914195i	$0.367176\pi$
$258$	8.37914	0.521662
$259$	−4.51616	−0.280621
$260$	−95.0781	−5.89649
$261$	2.23854	0.138562
$262$	32.7333	2.02227
$263$	28.0544	1.72991	0.864954	−	0.501851i	$-0.167348\pi$
$263$	28.0544	1.72991	0.864954	+	0.501851i	$0.167348\pi$
$264$	−8.41986	−0.518207
$265$	12.1216	0.744626
$266$	6.80043	0.416961
$267$	1.47186	0.0900761
$268$	35.4649	2.16636
$269$	−20.6969	−1.26191	−0.630957	−	0.775818i	$-0.717338\pi$
$269$	−20.6969	−1.26191	−0.630957	+	0.775818i	$0.717338\pi$
$270$	50.5737	3.07782
$271$	4.08361	0.248062	0.124031	−	0.992278i	$-0.460418\pi$
$271$	4.08361	0.248062	0.124031	+	0.992278i	$0.460418\pi$
$272$	−11.6120	−0.704084
$273$	9.29507	0.562563
$274$	−51.6785	−3.12201
$275$	−7.78720	−0.469586
$276$	−25.0962	−1.51062
$277$	−15.3276	−0.920947	−0.460473	−	0.887674i	$-0.652320\pi$
$277$	−15.3276	−0.920947	−0.460473	+	0.887674i	$0.652320\pi$
$278$	−5.72742	−0.343508
$279$	7.29732	0.436879
$280$	−20.8067	−1.24344
$281$	−24.1872	−1.44289	−0.721444	−	0.692473i	$-0.756521\pi$
$281$	−24.1872	−1.44289	−0.721444	+	0.692473i	$0.756521\pi$
$282$	38.6502	2.30159
$283$	−28.1915	−1.67581	−0.837906	−	0.545814i	$-0.816220\pi$
$283$	−28.1915	−1.67581	−0.837906	+	0.545814i	$0.816220\pi$
$284$	34.7634	2.06283
$285$	14.0396	0.831633
$286$	15.5623	0.920216
$287$	−7.13904	−0.421404
$288$	2.52628	0.148863
$289$	−12.9551	−0.762065
$290$	−24.0677	−1.41330
$291$	0.293074	0.0171803
$292$	−53.9210	−3.15549
$293$	−14.7673	−0.862713	−0.431357	−	0.902182i	$-0.641965\pi$
$293$	−14.7673	−0.862713	−0.431357	+	0.902182i	$0.641965\pi$
$294$	−22.0074	−1.28350
$295$	30.6153	1.78249
$296$	−25.4000	−1.47635
$297$	−5.64257	−0.327415
$298$	−9.21249	−0.533665
$299$	24.7215	1.42968
$300$	−49.0826	−2.83378
$301$	−2.31019	−0.133157
$302$	−38.4351	−2.21169
$303$	10.0548	0.577633
$304$	15.4013	0.883323
$305$	−17.0785	−0.977912
$306$	−4.20235	−0.240232
$307$	12.2897	0.701410	0.350705	−	0.936486i	$-0.385942\pi$
$307$	12.2897	0.701410	0.350705	+	0.936486i	$0.385942\pi$
$308$	4.35568	0.248188
$309$	8.58035	0.488119
$310$	−78.4573	−4.45607
$311$	5.50880	0.312375	0.156188	−	0.987727i	$-0.450080\pi$
$311$	5.50880	0.312375	0.156188	+	0.987727i	$0.450080\pi$
$312$	52.2778	2.95965
$313$	31.4486	1.77758	0.888789	−	0.458317i	$-0.151548\pi$
$313$	31.4486	1.77758	0.888789	+	0.458317i	$0.151548\pi$
$314$	17.5209	0.988764
$315$	−3.03208	−0.170838
$316$	−47.1692	−2.65348
$317$	−23.0138	−1.29258	−0.646291	−	0.763091i	$-0.723681\pi$
$317$	−23.0138	−1.29258	−0.646291	+	0.763091i	$0.723681\pi$
$318$	−12.5054	−0.701270
$319$	2.68526	0.150346
$320$	14.1313	0.789963
$321$	19.4255	1.08422
$322$	10.1508	0.565680
$323$	−5.36481	−0.298506
$324$	−24.8552	−1.38085
$325$	48.3497	2.68196
$326$	43.9901	2.43638
$327$	17.0426	0.942458
$328$	−40.1517	−2.21701
$329$	−10.6562	−0.587494
$330$	13.1921	0.726201
$331$	−26.1047	−1.43484	−0.717421	−	0.696640i	$-0.754677\pi$
$331$	−26.1047	−1.43484	−0.717421	+	0.696640i	$0.754677\pi$
$332$	1.04472	0.0573366
$333$	−3.70145	−0.202838
$334$	−32.9016	−1.80029
$335$	−29.6146	−1.61802
$336$	8.64362	0.471548
$337$	−18.2255	−0.992804	−0.496402	−	0.868093i	$-0.665346\pi$
$337$	−18.2255	−0.992804	−0.496402	+	0.868093i	$0.665346\pi$
$338$	−64.0400	−3.48332
$339$	7.34714	0.399042
$340$	30.7979	1.67025
$341$	8.75357	0.474032
$342$	5.57365	0.301388
$343$	13.1875	0.712059
$344$	−12.9931	−0.700541
$345$	20.9564	1.12825
$346$	55.0341	2.95865
$347$	−5.79825	−0.311267	−0.155633	−	0.987815i	$-0.549742\pi$
$347$	−5.79825	−0.311267	−0.155633	+	0.987815i	$0.549742\pi$
$348$	16.9252	0.907283
$349$	−12.4230	−0.664989	−0.332494	−	0.943105i	$-0.607890\pi$
$349$	−12.4230	−0.664989	−0.332494	+	0.943105i	$0.607890\pi$
$350$	19.8526	1.06116
$351$	35.0339	1.86997
$352$	3.03043	0.161522
$353$	23.7572	1.26447	0.632233	−	0.774778i	$-0.282138\pi$
$353$	23.7572	1.26447	0.632233	+	0.774778i	$0.282138\pi$
$354$	−31.5847	−1.67871
$355$	−29.0288	−1.54069
$356$	−4.28233	−0.226963
$357$	−3.01088	−0.159353
$358$	6.09823	0.322301
$359$	23.7264	1.25223	0.626117	−	0.779729i	$-0.284643\pi$
$359$	23.7264	1.25223	0.626117	+	0.779729i	$0.284643\pi$
$360$	−17.0532	−0.898782
$361$	−11.8846	−0.625503
$362$	−1.11735	−0.0587265
$363$	−1.47186	−0.0772524
$364$	−27.0438	−1.41748
$365$	45.0262	2.35678
$366$	17.6193	0.920974
$367$	−13.8475	−0.722832	−0.361416	−	0.932405i	$-0.617707\pi$
$367$	−13.8475	−0.722832	−0.361416	+	0.932405i	$0.617707\pi$
$368$	22.9889	1.19838
$369$	−5.85117	−0.304600
$370$	39.7963	2.06891
$371$	3.44785	0.179003
$372$	55.1736	2.86062
$373$	21.5061	1.11354	0.556771	−	0.830666i	$-0.312040\pi$
$373$	21.5061	1.11354	0.556771	+	0.830666i	$0.312040\pi$
$374$	−5.04097	−0.260662
$375$	14.6697	0.757540
$376$	−59.9330	−3.09081
$377$	−16.6724	−0.858674
$378$	14.3851	0.739889
$379$	12.8614	0.660644	0.330322	−	0.943868i	$-0.392843\pi$
$379$	12.8614	0.660644	0.330322	+	0.943868i	$0.392843\pi$
$380$	−40.8478	−2.09545
$381$	29.2420	1.49811
$382$	3.17330	0.162360
$383$	−10.4701	−0.534996	−0.267498	−	0.963558i	$-0.586197\pi$
$383$	−10.4701	−0.534996	−0.267498	+	0.963558i	$0.586197\pi$
$384$	−23.4994	−1.19920
$385$	−3.63716	−0.185367
$386$	−19.6626	−1.00080
$387$	−1.89344	−0.0962489
$388$	−0.852692	−0.0432889
$389$	−23.5228	−1.19265	−0.596327	−	0.802741i	$-0.703374\pi$
$389$	−23.5228	−1.19265	−0.596327	+	0.802741i	$0.703374\pi$
$390$	−81.9079	−4.14757
$391$	−8.00786	−0.404975
$392$	34.1258	1.72361
$393$	19.2218	0.969614
$394$	26.5965	1.33991
$395$	39.3882	1.98183
$396$	3.56992	0.179395
$397$	−1.31522	−0.0660090	−0.0330045	−	0.999455i	$-0.510508\pi$
$397$	−1.31522	−0.0660090	−0.0330045	+	0.999455i	$0.510508\pi$
$398$	−47.7650	−2.39424
$399$	3.99339	0.199919
$400$	44.9611	2.24805
$401$	12.5724	0.627833	0.313917	−	0.949451i	$-0.398359\pi$
$401$	12.5724	0.627833	0.313917	+	0.949451i	$0.398359\pi$
$402$	30.5523	1.52381
$403$	−54.3497	−2.70735
$404$	−29.2542	−1.45545
$405$	20.7551	1.03133
$406$	−6.84577	−0.339750
$407$	−4.44011	−0.220088
$408$	−16.9340	−0.838356
$409$	−29.6391	−1.46556	−0.732779	−	0.680467i	$-0.761777\pi$
$409$	−29.6391	−1.46556	−0.732779	+	0.680467i	$0.761777\pi$
$410$	62.9090	3.10685
$411$	−30.3469	−1.49690
$412$	−24.9643	−1.22990
$413$	8.70816	0.428501
$414$	8.31958	0.408885
$415$	−0.872385	−0.0428237
$416$	−18.8155	−0.922506
$417$	−3.36329	−0.164701
$418$	6.68592	0.327019
$419$	−13.7629	−0.672360	−0.336180	−	0.941798i	$-0.609135\pi$
$419$	−13.7629	−0.672360	−0.336180	+	0.941798i	$0.609135\pi$
$420$	−22.9250	−1.11862
$421$	−27.6706	−1.34858	−0.674291	−	0.738466i	$-0.735551\pi$
$421$	−27.6706	−1.34858	−0.674291	+	0.738466i	$0.735551\pi$
$422$	−29.4431	−1.43327
$423$	−8.73382	−0.424653
$424$	19.3916	0.941738
$425$	−15.6615	−0.759697
$426$	29.9480	1.45098
$427$	−4.85777	−0.235084
$428$	−56.5180	−2.73190
$429$	9.13856	0.441214
$430$	20.3574	0.981719
$431$	2.66151	0.128200	0.0641002	−	0.997943i	$-0.479582\pi$
$431$	2.66151	0.128200	0.0641002	+	0.997943i	$0.479582\pi$
$432$	32.5786	1.56744
$433$	−22.0369	−1.05902	−0.529512	−	0.848302i	$-0.677625\pi$
$433$	−22.0369	−1.05902	−0.529512	+	0.848302i	$0.677625\pi$
$434$	−22.3162	−1.07121
$435$	−14.1332	−0.677634
$436$	−49.5851	−2.37470
$437$	10.6210	0.508069
$438$	−46.4519	−2.21956
$439$	−38.5318	−1.83902	−0.919510	−	0.393066i	$-0.871414\pi$
$439$	−38.5318	−1.83902	−0.919510	+	0.393066i	$0.871414\pi$
$440$	−20.4563	−0.975216
$441$	4.97303	0.236811
$442$	31.2987	1.48873
$443$	13.3314	0.633395	0.316698	−	0.948527i	$-0.397426\pi$
$443$	13.3314	0.633395	0.316698	+	0.948527i	$0.397426\pi$
$444$	−27.9859	−1.32815
$445$	3.57592	0.169515
$446$	−66.5108	−3.14938
$447$	−5.40981	−0.255875
$448$	4.01947	0.189902
$449$	−6.04443	−0.285254	−0.142627	−	0.989776i	$-0.545555\pi$
$449$	−6.04443	−0.285254	−0.142627	+	0.989776i	$0.545555\pi$
$450$	16.2712	0.767032
$451$	−7.01882	−0.330504
$452$	−21.3763	−1.00546
$453$	−22.5701	−1.06044
$454$	−3.99580	−0.187532
$455$	22.5827	1.05869
$456$	22.4598	1.05178
$457$	−31.3400	−1.46602	−0.733012	−	0.680216i	$-0.761886\pi$
$457$	−31.3400	−1.46602	−0.733012	+	0.680216i	$0.761886\pi$
$458$	−4.48724	−0.209675
$459$	−11.3483	−0.529692
$460$	−60.9721	−2.84284
$461$	−4.95003	−0.230546	−0.115273	−	0.993334i	$-0.536774\pi$
$461$	−4.95003	−0.230546	−0.115273	+	0.993334i	$0.536774\pi$
$462$	3.75233	0.174574
$463$	5.48111	0.254729	0.127364	−	0.991856i	$-0.459348\pi$
$463$	5.48111	0.254729	0.127364	+	0.991856i	$0.459348\pi$
$464$	−15.5039	−0.719752
$465$	−46.0721	−2.13654
$466$	39.0651	1.80966
$467$	27.2117	1.25921	0.629604	−	0.776916i	$-0.283217\pi$
$467$	27.2117	1.25921	0.629604	+	0.776916i	$0.283217\pi$
$468$	−22.1652	−1.02458
$469$	−8.42352	−0.388962
$470$	93.9019	4.33137
$471$	10.2887	0.474080
$472$	48.9769	2.25434
$473$	−2.27129	−0.104434
$474$	−40.6354	−1.86644
$475$	20.7722	0.953093
$476$	8.76010	0.401519
$477$	2.82586	0.129387
$478$	44.8807	2.05280
$479$	30.4419	1.39092	0.695462	−	0.718563i	$-0.255200\pi$
$479$	30.4419	1.39092	0.695462	+	0.718563i	$0.255200\pi$
$480$	−15.9499	−0.728008
$481$	27.5681	1.25700
$482$	−20.4197	−0.930094
$483$	5.96078	0.271225
$484$	4.28233	0.194652
$485$	0.712032	0.0323317
$486$	21.0163	0.953318
$487$	7.21432	0.326912	0.163456	−	0.986551i	$-0.447736\pi$
$487$	7.21432	0.326912	0.163456	+	0.986551i	$0.447736\pi$
$488$	−27.3213	−1.23678
$489$	25.8321	1.16817
$490$	−53.4677	−2.41543
$491$	30.3375	1.36911	0.684557	−	0.728959i	$-0.259996\pi$
$491$	30.3375	1.36911	0.684557	+	0.728959i	$0.259996\pi$
$492$	−44.2395	−1.99447
$493$	5.40058	0.243230
$494$	−41.5120	−1.86771
$495$	−2.98103	−0.133987
$496$	−50.5406	−2.26934
$497$	−8.25689	−0.370372
$498$	0.900008	0.0403303
$499$	−10.9360	−0.489564	−0.244782	−	0.969578i	$-0.578716\pi$
$499$	−10.9360	−0.489564	−0.244782	+	0.969578i	$0.578716\pi$
$500$	−42.6811	−1.90876
$501$	−19.3206	−0.863182
$502$	−67.0580	−2.99295
$503$	−20.5727	−0.917292	−0.458646	−	0.888619i	$-0.651665\pi$
$503$	−20.5727	−0.917292	−0.458646	+	0.888619i	$0.651665\pi$
$504$	−4.85057	−0.216062
$505$	24.4284	1.08705
$506$	9.97983	0.443658
$507$	−37.6059	−1.67014
$508$	−85.0788	−3.77476
$509$	−12.4301	−0.550954	−0.275477	−	0.961308i	$-0.588836\pi$
$509$	−12.4301	−0.550954	−0.275477	+	0.961308i	$0.588836\pi$
$510$	26.5318	1.17485
$511$	12.8072	0.566555
$512$	48.5611	2.14612
$513$	15.0514	0.664536
$514$	−32.5692	−1.43657
$515$	20.8462	0.918594
$516$	−14.3159	−0.630223
$517$	−10.4767	−0.460767
$518$	11.3196	0.497353
$519$	32.3174	1.41858
$520$	127.010	5.56978
$521$	−38.5439	−1.68864	−0.844318	−	0.535842i	$-0.819994\pi$
$521$	−38.5439	−1.68864	−0.844318	+	0.535842i	$0.819994\pi$
$522$	−5.61081	−0.245578
$523$	−0.363663	−0.0159019	−0.00795095	−	0.999968i	$-0.502531\pi$
$523$	−0.363663	−0.0159019	−0.00795095	+	0.999968i	$0.502531\pi$
$524$	−55.9255	−2.44312
$525$	11.6579	0.508794
$526$	−70.3172	−3.06597
$527$	17.6051	0.766890
$528$	8.49808	0.369831
$529$	−7.14649	−0.310717
$530$	−30.3824	−1.31973
$531$	7.13722	0.309729
$532$	−11.6187	−0.503733
$533$	43.5789	1.88761
$534$	−3.68915	−0.159645
$535$	47.1948	2.04041
$536$	−47.3760	−2.04633
$537$	3.58104	0.154533
$538$	51.8760	2.23653
$539$	5.96545	0.256950
$540$	−86.4062	−3.71833
$541$	−6.80137	−0.292414	−0.146207	−	0.989254i	$-0.546707\pi$
$541$	−6.80137	−0.292414	−0.146207	+	0.989254i	$0.546707\pi$
$542$	−10.2354	−0.439648
$543$	−0.656135	−0.0281574
$544$	6.09477	0.261311
$545$	41.4055	1.77362
$546$	−23.2977	−0.997050
$547$	24.8512	1.06256	0.531281	−	0.847196i	$-0.321711\pi$
$547$	24.8512	1.06256	0.531281	+	0.847196i	$0.321711\pi$
$548$	88.2937	3.77172
$549$	−3.98144	−0.169924
$550$	19.5183	0.832263
$551$	−7.16288	−0.305149
$552$	33.5249	1.42692
$553$	11.2035	0.476421
$554$	38.4180	1.63223
$555$	23.3694	0.991975
$556$	9.78542	0.414994
$557$	−42.5647	−1.80352	−0.901762	−	0.432232i	$-0.857726\pi$
$557$	−42.5647	−1.80352	−0.901762	+	0.432232i	$0.857726\pi$
$558$	−18.2904	−0.774295
$559$	14.1022	0.596458
$560$	20.9999	0.887410
$561$	−2.96019	−0.124979
$562$	60.6242	2.55728
$563$	3.26170	0.137464	0.0687322	−	0.997635i	$-0.478105\pi$
$563$	3.26170	0.137464	0.0687322	+	0.997635i	$0.478105\pi$
$564$	−66.0347	−2.78056
$565$	17.8501	0.750959
$566$	70.6609	2.97010
$567$	5.90354	0.247925
$568$	−46.4388	−1.94853
$569$	−0.207915	−0.00871626	−0.00435813	−	0.999991i	$-0.501387\pi$
$569$	−0.207915	−0.00871626	−0.00435813	+	0.999991i	$0.501387\pi$
$570$	−35.1896	−1.47393
$571$	−13.9526	−0.583898	−0.291949	−	0.956434i	$-0.594304\pi$
$571$	−13.9526	−0.583898	−0.291949	+	0.956434i	$0.594304\pi$
$572$	−26.5884	−1.11172
$573$	1.86344	0.0778465
$574$	17.8937	0.746868
$575$	31.0059	1.29303
$576$	3.29437	0.137265
$577$	43.9130	1.82812	0.914061	−	0.405577i	$-0.132929\pi$
$577$	43.9130	1.82812	0.914061	+	0.405577i	$0.132929\pi$
$578$	32.4714	1.35063
$579$	−11.5464	−0.479850
$580$	41.1202	1.70742
$581$	−0.248139	−0.0102946
$582$	−0.734578	−0.0304492
$583$	3.38979	0.140391
$584$	72.0306	2.98065
$585$	18.5088	0.765244
$586$	37.0135	1.52902
$587$	−31.3976	−1.29592	−0.647958	−	0.761676i	$-0.724377\pi$
$587$	−31.3976	−1.29592	−0.647958	+	0.761676i	$0.724377\pi$
$588$	37.6001	1.55060
$589$	−23.3499	−0.962118
$590$	−76.7361	−3.15917
$591$	15.6181	0.642444
$592$	25.6360	1.05363
$593$	−15.7973	−0.648716	−0.324358	−	0.945934i	$-0.605148\pi$
$593$	−15.7973	−0.648716	−0.324358	+	0.945934i	$0.605148\pi$
$594$	14.1429	0.580288
$595$	−7.31503	−0.299887
$596$	15.7397	0.644724
$597$	−28.0488	−1.14796
$598$	−61.9634	−2.53387
$599$	−42.8462	−1.75065	−0.875325	−	0.483536i	$-0.839352\pi$
$599$	−42.8462	−1.75065	−0.875325	+	0.483536i	$0.839352\pi$
$600$	65.5671	2.67677
$601$	16.6476	0.679069	0.339535	−	0.940594i	$-0.389730\pi$
$601$	16.6476	0.679069	0.339535	+	0.940594i	$0.389730\pi$
$602$	5.79041	0.235999
$603$	−6.90393	−0.281150
$604$	65.6672	2.67196
$605$	−3.57592	−0.145382
$606$	−25.2019	−1.02376
$607$	18.7548	0.761235	0.380618	−	0.924733i	$-0.375711\pi$
$607$	18.7548	0.761235	0.380618	+	0.924733i	$0.375711\pi$
$608$	−8.08360	−0.327833
$609$	−4.02001	−0.162899
$610$	42.8065	1.73319
$611$	65.0487	2.63159
$612$	7.17979	0.290226
$613$	−1.89705	−0.0766210	−0.0383105	−	0.999266i	$-0.512198\pi$
$613$	−1.89705	−0.0766210	−0.0383105	+	0.999266i	$0.512198\pi$
$614$	−30.8036	−1.24313
$615$	36.9418	1.48964
$616$	−5.81855	−0.234436
$617$	−33.4249	−1.34564	−0.672819	−	0.739807i	$-0.734917\pi$
$617$	−33.4249	−1.34564	−0.672819	+	0.739807i	$0.734917\pi$
$618$	−21.5063	−0.865110
$619$	26.5436	1.06688	0.533440	−	0.845838i	$-0.320899\pi$
$619$	26.5436	1.06688	0.533440	+	0.845838i	$0.320899\pi$
$620$	134.046	5.38341
$621$	22.4667	0.901558
$622$	−13.8076	−0.553633
$623$	1.01713	0.0407503
$624$	−52.7634	−2.11223
$625$	−3.29553	−0.131821
$626$	−78.8245	−3.15046
$627$	3.92614	0.156795
$628$	−29.9349	−1.19453
$629$	−8.92992	−0.356059
$630$	7.59979	0.302783
$631$	−0.120135	−0.00478250	−0.00239125	−	0.999997i	$-0.500761\pi$
$631$	−0.120135	−0.00478250	−0.00239125	+	0.999997i	$0.500761\pi$
$632$	63.0112	2.50645
$633$	−17.2897	−0.687205
$634$	57.6831	2.29089
$635$	71.0442	2.81930
$636$	21.3658	0.847209
$637$	−37.0387	−1.46753
$638$	−6.73050	−0.266463
$639$	−6.76736	−0.267713
$640$	−57.0926	−2.25678
$641$	27.2744	1.07728	0.538638	−	0.842537i	$-0.318939\pi$
$641$	27.2744	1.07728	0.538638	+	0.842537i	$0.318939\pi$
$642$	−48.6891	−1.92161
$643$	−18.4170	−0.726295	−0.363147	−	0.931732i	$-0.618298\pi$
$643$	−18.4170	−0.726295	−0.363147	+	0.931732i	$0.618298\pi$
$644$	−17.3428	−0.683401
$645$	11.9544	0.470703
$646$	13.4467	0.529052
$647$	15.8858	0.624535	0.312268	−	0.949994i	$-0.398911\pi$
$647$	15.8858	0.624535	0.312268	+	0.949994i	$0.398911\pi$
$648$	33.2030	1.30434
$649$	8.56153	0.336069
$650$	−121.186	−4.75332
$651$	−13.1047	−0.513612
$652$	−75.1579	−2.94341
$653$	3.96377	0.155114	0.0775571	−	0.996988i	$-0.475288\pi$
$653$	3.96377	0.155114	0.0775571	+	0.996988i	$0.475288\pi$
$654$	−42.7166	−1.67035
$655$	46.7001	1.82472
$656$	40.5247	1.58222
$657$	10.4968	0.409518
$658$	26.7093	1.04124
$659$	22.9097	0.892437	0.446218	−	0.894924i	$-0.352770\pi$
$659$	22.9097	0.892437	0.446218	+	0.894924i	$0.352770\pi$
$660$	−22.5389	−0.877327
$661$	−15.2854	−0.594531	−0.297266	−	0.954795i	$-0.596075\pi$
$661$	−15.2854	−0.594531	−0.297266	+	0.954795i	$0.596075\pi$
$662$	65.4302	2.54302
$663$	18.3794	0.713796
$664$	−1.39560	−0.0541597
$665$	9.70205	0.376229
$666$	9.27754	0.359497
$667$	−10.6918	−0.413987
$668$	56.2130	2.17495
$669$	−39.0569	−1.51003
$670$	74.2278	2.86767
$671$	−4.77597	−0.184374
$672$	−4.53675	−0.175009
$673$	49.5418	1.90970	0.954849	−	0.297093i	$-0.0960171\pi$
$673$	49.5418	1.90970	0.954849	+	0.297093i	$0.0960171\pi$
$674$	45.6814	1.75958
$675$	43.9398	1.69124
$676$	109.414	4.20821
$677$	−10.5455	−0.405297	−0.202649	−	0.979252i	$-0.564955\pi$
$677$	−10.5455	−0.405297	−0.202649	+	0.979252i	$0.564955\pi$
$678$	−18.4153	−0.707235
$679$	0.202529	0.00777235
$680$	−41.1416	−1.57771
$681$	−2.34643	−0.0899155
$682$	−21.9405	−0.840143
$683$	−34.1683	−1.30741	−0.653707	−	0.756747i	$-0.726787\pi$
$683$	−34.1683	−1.30741	−0.653707	+	0.756747i	$0.726787\pi$
$684$	−9.52268	−0.364109
$685$	−73.7288	−2.81703
$686$	−33.0539	−1.26201
$687$	−2.63502	−0.100532
$688$	13.1138	0.499959
$689$	−21.0468	−0.801818
$690$	−52.5262	−1.99964
$691$	−4.90095	−0.186441	−0.0932204	−	0.995645i	$-0.529716\pi$
$691$	−4.90095	−0.186441	−0.0932204	+	0.995645i	$0.529716\pi$
$692$	−94.0269	−3.57437
$693$	−0.847917	−0.0322097
$694$	14.5331	0.551668
$695$	−8.17121	−0.309952
$696$	−22.6095	−0.857012
$697$	−14.1162	−0.534689
$698$	31.1378	1.17858
$699$	22.9400	0.867672
$700$	−33.9185	−1.28200
$701$	−15.0988	−0.570275	−0.285138	−	0.958487i	$-0.592039\pi$
$701$	−15.0988	−0.570275	−0.285138	+	0.958487i	$0.592039\pi$
$702$	−87.8111	−3.31422
$703$	11.8439	0.446701
$704$	3.95179	0.148939
$705$	55.1416	2.07675
$706$	−59.5464	−2.24106
$707$	6.94838	0.261321
$708$	53.9631	2.02806
$709$	7.54403	0.283322	0.141661	−	0.989915i	$-0.454756\pi$
$709$	7.54403	0.283322	0.141661	+	0.989915i	$0.454756\pi$
$710$	72.7594	2.73061
$711$	9.18240	0.344367
$712$	5.72057	0.214388
$713$	−34.8536	−1.30528
$714$	7.54666	0.282426
$715$	22.2024	0.830323
$716$	−10.4189	−0.389374
$717$	26.3551	0.984249
$718$	−59.4693	−2.21938
$719$	1.35817	0.0506512	0.0253256	−	0.999679i	$-0.491938\pi$
$719$	1.35817	0.0506512	0.0253256	+	0.999679i	$0.491938\pi$
$720$	17.2116	0.641438
$721$	5.92945	0.220824
$722$	29.7882	1.10860
$723$	−11.9910	−0.445950
$724$	1.90901	0.0709478
$725$	−20.9107	−0.776603
$726$	3.68915	0.136917
$727$	2.86654	0.106314	0.0531570	−	0.998586i	$-0.483072\pi$
$727$	2.86654	0.106314	0.0531570	+	0.998586i	$0.483072\pi$
$728$	36.1266	1.33894
$729$	29.7537	1.10199
$730$	−112.856	−4.17700
$731$	−4.56801	−0.168954
$732$	−30.1029	−1.11263
$733$	10.9676	0.405098	0.202549	−	0.979272i	$-0.435077\pi$
$733$	10.9676	0.405098	0.202549	+	0.979272i	$0.435077\pi$
$734$	34.7081	1.28110
$735$	−31.3976	−1.15812
$736$	−12.0661	−0.444762
$737$	−8.28168	−0.305060
$738$	14.6657	0.539852
$739$	−54.0283	−1.98746	−0.993732	−	0.111785i	$-0.964343\pi$
$739$	−54.0283	−1.98746	−0.993732	+	0.111785i	$0.964343\pi$
$740$	−67.9927	−2.49946
$741$	−24.3769	−0.895507
$742$	−8.64189	−0.317254
$743$	−41.5566	−1.52456	−0.762281	−	0.647246i	$-0.775921\pi$
$743$	−41.5566	−1.52456	−0.762281	+	0.647246i	$0.775921\pi$
$744$	−73.7038	−2.70211
$745$	−13.1433	−0.481533
$746$	−53.9041	−1.97357
$747$	−0.203375	−0.00744112
$748$	8.61259	0.314908
$749$	13.4240	0.490502
$750$	−36.7690	−1.34261
$751$	−36.2524	−1.32287	−0.661434	−	0.750003i	$-0.730052\pi$
$751$	−36.2524	−1.32287	−0.661434	+	0.750003i	$0.730052\pi$
$752$	60.4897	2.20583
$753$	−39.3782	−1.43502
$754$	41.7887	1.52186
$755$	−54.8347	−1.99564
$756$	−24.5772	−0.893864
$757$	−40.6051	−1.47582	−0.737909	−	0.674901i	$-0.764187\pi$
$757$	−40.6051	−1.47582	−0.737909	+	0.674901i	$0.764187\pi$
$758$	−32.2365	−1.17088
$759$	5.86041	0.212719
$760$	54.5668	1.97934
$761$	−14.1590	−0.513262	−0.256631	−	0.966509i	$-0.582613\pi$
$761$	−14.1590	−0.513262	−0.256631	+	0.966509i	$0.582613\pi$
$762$	−73.2937	−2.65515
$763$	11.7773	0.426367
$764$	−5.42165	−0.196148
$765$	−5.99541	−0.216765
$766$	26.2428	0.948192
$767$	−53.1574	−1.91940
$768$	47.2674	1.70562
$769$	−39.3408	−1.41866	−0.709332	−	0.704874i	$-0.751003\pi$
$769$	−39.3408	−1.41866	−0.709332	+	0.704874i	$0.751003\pi$
$770$	9.11640	0.328532
$771$	−19.1255	−0.688787
$772$	33.5939	1.20907
$773$	2.63279	0.0946950	0.0473475	−	0.998878i	$-0.484923\pi$
$773$	2.63279	0.0946950	0.0473475	+	0.998878i	$0.484923\pi$
$774$	4.74583	0.170585
$775$	−68.1658	−2.44859
$776$	1.13907	0.0408903
$777$	6.64714	0.238465
$778$	58.9590	2.11378
$779$	18.7226	0.670805
$780$	139.941	5.01070
$781$	−8.11785	−0.290480
$782$	20.0714	0.717750
$783$	−15.1518	−0.541480
$784$	−34.4428	−1.23010
$785$	24.9968	0.892175
$786$	−48.1788	−1.71848
$787$	−4.85411	−0.173030	−0.0865152	−	0.996251i	$-0.527573\pi$
$787$	−4.85411	−0.173030	−0.0865152	+	0.996251i	$0.527573\pi$
$788$	−45.4406	−1.61875
$789$	−41.2920	−1.47004
$790$	−98.7248	−3.51247
$791$	5.07724	0.180526
$792$	−4.76889	−0.169455
$793$	29.6534	1.05302
$794$	3.29655	0.116990
$795$	−17.8413	−0.632765
$796$	81.6075	2.89250
$797$	47.4366	1.68029	0.840144	−	0.542363i	$-0.182470\pi$
$797$	47.4366	1.68029	0.840144	+	0.542363i	$0.182470\pi$
$798$	−10.0093	−0.354324
$799$	−21.0707	−0.745429
$800$	−23.5985	−0.834334
$801$	0.833639	0.0294552
$802$	−31.5121	−1.11273
$803$	12.5915	0.444344
$804$	−52.1992	−1.84093
$805$	14.4819	0.510420
$806$	136.225	4.79833
$807$	30.4629	1.07235
$808$	39.0794	1.37481
$809$	−10.3495	−0.363868	−0.181934	−	0.983311i	$-0.558236\pi$
$809$	−10.3495	−0.363868	−0.181934	+	0.983311i	$0.558236\pi$
$810$	−52.0218	−1.82786
$811$	33.2810	1.16865	0.584327	−	0.811519i	$-0.301359\pi$
$811$	33.2810	1.16865	0.584327	+	0.811519i	$0.301359\pi$
$812$	11.6961	0.410454
$813$	−6.01049	−0.210797
$814$	11.1290	0.390070
$815$	62.7598	2.19838
$816$	17.0913	0.598314
$817$	6.05863	0.211964
$818$	74.2891	2.59746
$819$	5.26460	0.183960
$820$	−107.481	−3.75341
$821$	−40.5469	−1.41510	−0.707549	−	0.706665i	$-0.750199\pi$
$821$	−40.5469	−1.41510	−0.707549	+	0.706665i	$0.750199\pi$
$822$	76.0633	2.65301
$823$	24.6889	0.860602	0.430301	−	0.902686i	$-0.358407\pi$
$823$	24.6889	0.860602	0.430301	+	0.902686i	$0.358407\pi$
$824$	33.3487	1.16176
$825$	11.4616	0.399043
$826$	−21.8266	−0.759446
$827$	11.6012	0.403414	0.201707	−	0.979446i	$-0.435351\pi$
$827$	11.6012	0.403414	0.201707	+	0.979446i	$0.435351\pi$
$828$	−14.2142	−0.493976
$829$	−40.8260	−1.41794	−0.708972	−	0.705237i	$-0.750841\pi$
$829$	−40.8260	−1.41794	−0.708972	+	0.705237i	$0.750841\pi$
$830$	2.18660	0.0758979
$831$	22.5600	0.782599
$832$	−24.5361	−0.850637
$833$	11.9977	0.415695
$834$	8.42995	0.291905
$835$	−46.9401	−1.62443
$836$	−11.4230	−0.395074
$837$	−49.3926	−1.70726
$838$	34.4961	1.19165
$839$	−8.12573	−0.280531	−0.140266	−	0.990114i	$-0.544796\pi$
$839$	−8.12573	−0.280531	−0.140266	+	0.990114i	$0.544796\pi$
$840$	30.6244	1.05664
$841$	−21.7894	−0.751358
$842$	69.3552	2.39014
$843$	35.6001	1.22613
$844$	50.3041	1.73154
$845$	−91.3647	−3.14304
$846$	21.8910	0.752627
$847$	−1.01713	−0.0349489
$848$	−19.5717	−0.672095
$849$	41.4939	1.42407
$850$	39.2550	1.34644
$851$	17.6790	0.606027
$852$	−51.1667	−1.75294
$853$	34.4812	1.18061	0.590307	−	0.807179i	$-0.299007\pi$
$853$	34.4812	1.18061	0.590307	+	0.807179i	$0.299007\pi$
$854$	12.1758	0.416647
$855$	7.95182	0.271947
$856$	75.4998	2.58053
$857$	−18.9026	−0.645700	−0.322850	−	0.946450i	$-0.604641\pi$
$857$	−18.9026	−0.645700	−0.322850	+	0.946450i	$0.604641\pi$
$858$	−22.9054	−0.781978
$859$	7.56724	0.258191	0.129095	−	0.991632i	$-0.458793\pi$
$859$	7.56724	0.258191	0.129095	+	0.991632i	$0.458793\pi$
$860$	−34.7810	−1.18602
$861$	10.5076	0.358099
$862$	−6.67097	−0.227214
$863$	−19.8164	−0.674560	−0.337280	−	0.941404i	$-0.609507\pi$
$863$	−19.8164	−0.674560	−0.337280	+	0.941404i	$0.609507\pi$
$864$	−17.0994	−0.581733
$865$	78.5162	2.66963
$866$	55.2345	1.87694
$867$	19.0681	0.647585
$868$	38.1277	1.29414
$869$	11.0148	0.373653
$870$	35.4242	1.20099
$871$	51.4198	1.74229
$872$	66.2385	2.24312
$873$	0.165993	0.00561801
$874$	−26.6210	−0.900468
$875$	10.1375	0.342710
$876$	79.3639	2.68146
$877$	−24.6383	−0.831977	−0.415989	−	0.909370i	$-0.636564\pi$
$877$	−24.6383	−0.831977	−0.415989	+	0.909370i	$0.636564\pi$
$878$	96.5782	3.25936
$879$	21.7353	0.733113
$880$	20.6463	0.695988
$881$	13.0073	0.438227	0.219114	−	0.975699i	$-0.429683\pi$
$881$	13.0073	0.438227	0.219114	+	0.975699i	$0.429683\pi$
$882$	−12.4647	−0.419708
$883$	50.1150	1.68650	0.843252	−	0.537518i	$-0.180638\pi$
$883$	50.1150	1.68650	0.843252	+	0.537518i	$0.180638\pi$
$884$	−53.4744	−1.79854
$885$	−45.0614	−1.51472
$886$	−33.4147	−1.12259
$887$	−17.7233	−0.595089	−0.297544	−	0.954708i	$-0.596168\pi$
$887$	−17.7233	−0.595089	−0.297544	+	0.954708i	$0.596168\pi$
$888$	37.3852	1.25456
$889$	20.2077	0.677743
$890$	−8.96289	−0.300437
$891$	5.80413	0.194446
$892$	113.635	3.80478
$893$	27.9465	0.935193
$894$	13.5595	0.453496
$895$	8.70023	0.290817
$896$	−16.2393	−0.542517
$897$	−36.3865	−1.21491
$898$	15.1501	0.505566
$899$	23.5056	0.783956
$900$	−27.7997	−0.926656
$901$	6.81752	0.227125
$902$	17.5924	0.585763
$903$	3.40027	0.113154
$904$	28.5557	0.949748
$905$	−1.59410	−0.0529896
$906$	56.5710	1.87945
$907$	15.7371	0.522542	0.261271	−	0.965266i	$-0.415858\pi$
$907$	15.7371	0.522542	0.261271	+	0.965266i	$0.415858\pi$
$908$	6.82690	0.226559
$909$	5.69490	0.188888
$910$	−56.6025	−1.87635
$911$	−14.5458	−0.481924	−0.240962	−	0.970535i	$-0.577463\pi$
$911$	−14.5458	−0.481924	−0.240962	+	0.970535i	$0.577463\pi$
$912$	−22.6684	−0.750627
$913$	−0.243961	−0.00807393
$914$	78.5525	2.59828
$915$	25.1371	0.831006
$916$	7.66654	0.253310
$917$	13.2833	0.438652
$918$	28.4440	0.938792
$919$	−24.4688	−0.807151	−0.403576	−	0.914946i	$-0.632233\pi$
$919$	−24.4688	−0.807151	−0.403576	+	0.914946i	$0.632233\pi$
$920$	81.4498	2.68532
$921$	−18.0887	−0.596041
$922$	12.4071	0.408605
$923$	50.4026	1.65902
$924$	−6.41093	−0.210904
$925$	34.5760	1.13685
$926$	−13.7382	−0.451465
$927$	4.85979	0.159616
$928$	8.13749	0.267126
$929$	−6.23973	−0.204719	−0.102360	−	0.994747i	$-0.532639\pi$
$929$	−6.23973	−0.204719	−0.102360	+	0.994747i	$0.532639\pi$
$930$	115.478	3.78667
$931$	−15.9127	−0.521518
$932$	−66.7436	−2.18626
$933$	−8.10816	−0.265449
$934$	−68.2051	−2.23174
$935$	−7.19186	−0.235199
$936$	29.6094	0.967814
$937$	−54.9480	−1.79507	−0.897537	−	0.440940i	$-0.854645\pi$
$937$	−54.9480	−1.79507	−0.897537	+	0.440940i	$0.854645\pi$
$938$	21.1132	0.689370
$939$	−46.2878	−1.51054
$940$	−160.433	−5.23276
$941$	27.8302	0.907238	0.453619	−	0.891196i	$-0.350133\pi$
$941$	27.8302	0.907238	0.453619	+	0.891196i	$0.350133\pi$
$942$	−25.7883	−0.840229
$943$	27.9465	0.910063
$944$	−49.4318	−1.60887
$945$	20.5229	0.667611
$946$	5.69290	0.185092
$947$	38.9727	1.26644	0.633221	−	0.773971i	$-0.281732\pi$
$947$	38.9727	1.26644	0.633221	+	0.773971i	$0.281732\pi$
$948$	69.4263	2.25486
$949$	−78.1789	−2.53779
$950$	−52.0646	−1.68920
$951$	33.8730	1.09841
$952$	−11.7022	−0.379271
$953$	−21.9453	−0.710880	−0.355440	−	0.934699i	$-0.615669\pi$
$953$	−21.9453	−0.710880	−0.355440	+	0.934699i	$0.615669\pi$
$954$	−7.08291	−0.229318
$955$	4.52729	0.146500
$956$	−76.6796	−2.48000
$957$	−3.95232	−0.127760
$958$	−76.3012	−2.46518
$959$	−20.9713	−0.677197
$960$	−20.7992	−0.671292
$961$	45.6249	1.47177
$962$	−69.0982	−2.22782
$963$	11.0023	0.354545
$964$	34.8875	1.12365
$965$	−28.0522	−0.903033
$966$	−14.9405	−0.480701
$967$	−61.5634	−1.97974	−0.989872	−	0.141960i	$-0.954660\pi$
$967$	−61.5634	−1.97974	−0.989872	+	0.141960i	$0.954660\pi$
$968$	−5.72057	−0.183866
$969$	7.89623	0.253663
$970$	−1.78468	−0.0573026
$971$	−35.8270	−1.14974	−0.574871	−	0.818244i	$-0.694948\pi$
$971$	−35.8270	−1.14974	−0.574871	+	0.818244i	$0.694948\pi$
$972$	−35.9067	−1.15171
$973$	−2.32420	−0.0745105
$974$	−18.0824	−0.579397
$975$	−71.1637	−2.27906
$976$	27.5751	0.882658
$977$	60.4248	1.93316	0.966580	−	0.256367i	$-0.0825256\pi$
$977$	60.4248	1.93316	0.966580	+	0.256367i	$0.0825256\pi$
$978$	−64.7470	−2.07038
$979$	1.00000	0.0319601
$980$	91.3506	2.91809
$981$	9.65270	0.308187
$982$	−76.0398	−2.42653
$983$	44.0288	1.40430	0.702150	−	0.712029i	$-0.252224\pi$
$983$	44.0288	1.40430	0.702150	+	0.712029i	$0.252224\pi$
$984$	59.0975	1.88396
$985$	37.9447	1.20902
$986$	−13.5363	−0.431084
$987$	15.6844	0.499239
$988$	70.9240	2.25639
$989$	9.04349	0.287566
$990$	7.47182	0.237470
$991$	−36.8630	−1.17099	−0.585495	−	0.810676i	$-0.699100\pi$
$991$	−36.8630	−1.17099	−0.585495	+	0.810676i	$0.699100\pi$
$992$	26.5270	0.842235
$993$	38.4223	1.21929
$994$	20.6955	0.656423
$995$	−68.1455	−2.16036
$996$	−1.53768	−0.0487233
$997$	−32.3243	−1.02372	−0.511860	−	0.859069i	$-0.671043\pi$
$997$	−32.3243	−1.02372	−0.511860	+	0.859069i	$0.671043\pi$
$998$	27.4107	0.867670
$999$	25.0536	0.792662

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	979.2.a.d.1.3	✓	17
3.2	odd	2		8811.2.a.p.1.15		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
979.2.a.d.1.3	✓	17	1.1	even	1	trivial
8811.2.a.p.1.15		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:	\( N \)	\(=\)	\( 979 = 11 \cdot 89 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	979.a (trivial)

\(f(q)\)	\(=\)	\(q-2.50646 q^{2} -1.47186 q^{3} +4.28233 q^{4} -3.57592 q^{5} +3.68915 q^{6} -1.01713 q^{7} -5.72057 q^{8} -0.833639 q^{9} +O(q^{10})\)	\(q-2.50646 q^{2} -1.47186 q^{3} +4.28233 q^{4} -3.57592 q^{5} +3.68915 q^{6} -1.01713 q^{7} -5.72057 q^{8} -0.833639 q^{9} +8.96289 q^{10} -1.00000 q^{11} -6.30298 q^{12} +6.20886 q^{13} +2.54939 q^{14} +5.26324 q^{15} +5.77371 q^{16} -2.01119 q^{17} +2.08948 q^{18} +2.66748 q^{19} -15.3133 q^{20} +1.49706 q^{21} +2.50646 q^{22} +3.98165 q^{23} +8.41986 q^{24} +7.78720 q^{25} -15.5623 q^{26} +5.64257 q^{27} -4.35568 q^{28} -2.68526 q^{29} -13.1921 q^{30} -8.75357 q^{31} -3.03043 q^{32} +1.47186 q^{33} +5.04097 q^{34} +3.63716 q^{35} -3.56992 q^{36} +4.44011 q^{37} -6.68592 q^{38} -9.13856 q^{39} +20.4563 q^{40} +7.01882 q^{41} -3.75233 q^{42} +2.27129 q^{43} -4.28233 q^{44} +2.98103 q^{45} -9.97983 q^{46} +10.4767 q^{47} -8.49808 q^{48} -5.96545 q^{49} -19.5183 q^{50} +2.96019 q^{51} +26.5884 q^{52} -3.38979 q^{53} -14.1429 q^{54} +3.57592 q^{55} +5.81855 q^{56} -3.92614 q^{57} +6.73050 q^{58} -8.56153 q^{59} +22.5389 q^{60} +4.77597 q^{61} +21.9405 q^{62} +0.847917 q^{63} -3.95179 q^{64} -22.2024 q^{65} -3.68915 q^{66} +8.28168 q^{67} -8.61259 q^{68} -5.86041 q^{69} -9.11640 q^{70} +8.11785 q^{71} +4.76889 q^{72} -12.5915 q^{73} -11.1290 q^{74} -11.4616 q^{75} +11.4230 q^{76} +1.01713 q^{77} +22.9054 q^{78} -11.0148 q^{79} -20.6463 q^{80} -5.80413 q^{81} -17.5924 q^{82} +0.243961 q^{83} +6.41093 q^{84} +7.19186 q^{85} -5.69290 q^{86} +3.95232 q^{87} +5.72057 q^{88} -1.00000 q^{89} -7.47182 q^{90} -6.31520 q^{91} +17.0507 q^{92} +12.8840 q^{93} -26.2595 q^{94} -9.53868 q^{95} +4.46035 q^{96} -0.199119 q^{97} +14.9522 q^{98} +0.833639 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 4 q^{2} - q^{3} + 14 q^{4} - 14 q^{5} - 6 q^{6} - 5 q^{7} - 18 q^{8} + 6 q^{9}+O(q^{10}) \) 17 * q - 4 * q^2 - q^3 + 14 * q^4 - 14 * q^5 - 6 * q^6 - 5 * q^7 - 18 * q^8 + 6 * q^9	\( 17 q - 4 q^{2} - q^{3} + 14 q^{4} - 14 q^{5} - 6 q^{6} - 5 q^{7} - 18 q^{8} + 6 q^{9} - 6 q^{10} - 17 q^{11} + q^{12} - 6 q^{13} - 17 q^{14} - 3 q^{15} + 8 q^{16} - 19 q^{17} - 9 q^{19} - 29 q^{20} - 35 q^{21} + 4 q^{22} - 13 q^{23} - 20 q^{24} + 19 q^{25} - 19 q^{27} + q^{28} - 54 q^{29} + q^{30} + 8 q^{31} - 35 q^{32} + q^{33} + 14 q^{34} - 22 q^{35} - 20 q^{36} - 3 q^{38} - 18 q^{39} + 16 q^{40} - 16 q^{41} - 37 q^{42} - 21 q^{43} - 14 q^{44} - 31 q^{45} - 31 q^{46} - 3 q^{47} + 34 q^{48} + 2 q^{49} - 5 q^{50} - 13 q^{51} + 14 q^{52} - 43 q^{53} - 19 q^{54} + 14 q^{55} + 14 q^{56} - 29 q^{57} + 22 q^{58} - q^{59} - 11 q^{60} - 29 q^{61} + 32 q^{62} + 17 q^{63} - 22 q^{64} - 44 q^{65} + 6 q^{66} + 17 q^{67} - 43 q^{68} - 21 q^{69} + 76 q^{70} + 6 q^{71} + 17 q^{72} + 3 q^{73} - 10 q^{74} - 11 q^{75} - 17 q^{76} + 5 q^{77} + 35 q^{78} - 43 q^{79} - 32 q^{80} + 13 q^{81} - 10 q^{82} - 14 q^{83} + 44 q^{84} + 5 q^{85} - 37 q^{86} - 3 q^{87} + 18 q^{88} - 17 q^{89} - 2 q^{90} - 12 q^{91} + 23 q^{92} - 26 q^{93} - 4 q^{94} - 35 q^{95} - 20 q^{96} - 6 q^{97} + q^{98} - 6 q^{99}+O(q^{100}) \) 17 * q - 4 * q^2 - q^3 + 14 * q^4 - 14 * q^5 - 6 * q^6 - 5 * q^7 - 18 * q^8 + 6 * q^9 - 6 * q^10 - 17 * q^11 + q^12 - 6 * q^13 - 17 * q^14 - 3 * q^15 + 8 * q^16 - 19 * q^17 - 9 * q^19 - 29 * q^20 - 35 * q^21 + 4 * q^22 - 13 * q^23 - 20 * q^24 + 19 * q^25 - 19 * q^27 + q^28 - 54 * q^29 + q^30 + 8 * q^31 - 35 * q^32 + q^33 + 14 * q^34 - 22 * q^35 - 20 * q^36 - 3 * q^38 - 18 * q^39 + 16 * q^40 - 16 * q^41 - 37 * q^42 - 21 * q^43 - 14 * q^44 - 31 * q^45 - 31 * q^46 - 3 * q^47 + 34 * q^48 + 2 * q^49 - 5 * q^50 - 13 * q^51 + 14 * q^52 - 43 * q^53 - 19 * q^54 + 14 * q^55 + 14 * q^56 - 29 * q^57 + 22 * q^58 - q^59 - 11 * q^60 - 29 * q^61 + 32 * q^62 + 17 * q^63 - 22 * q^64 - 44 * q^65 + 6 * q^66 + 17 * q^67 - 43 * q^68 - 21 * q^69 + 76 * q^70 + 6 * q^71 + 17 * q^72 + 3 * q^73 - 10 * q^74 - 11 * q^75 - 17 * q^76 + 5 * q^77 + 35 * q^78 - 43 * q^79 - 32 * q^80 + 13 * q^81 - 10 * q^82 - 14 * q^83 + 44 * q^84 + 5 * q^85 - 37 * q^86 - 3 * q^87 + 18 * q^88 - 17 * q^89 - 2 * q^90 - 12 * q^91 + 23 * q^92 - 26 * q^93 - 4 * q^94 - 35 * q^95 - 20 * q^96 - 6 * q^97 + q^98 - 6 * q^99

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