LMFDB - Embedded newform 209.2.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [209,2,Mod(1,209)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(209, 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("209.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 209 = 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	209.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:	$1.66887340224$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 14x^{5} + 10x^{4} + 59x^{3} - 27x^{2} - 66x + 30 $ x^7 - x^6 - 14x^5 + 10x^4 + 59x^3 - 27x^2 - 66*x + 30
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.61330$ of defining polynomial
Character	$\chi$	$=$	209.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.61330 q^{2} +1.19599 q^{3} +4.82936 q^{4} +4.07680 q^{5} -3.12549 q^{6} +3.61829 q^{7} -7.39397 q^{8} -1.56960 q^{9} +O(q^{10})$	\(q-2.61330 q^{2} +1.19599 q^{3} +4.82936 q^{4} +4.07680 q^{5} -3.12549 q^{6} +3.61829 q^{7} -7.39397 q^{8} -1.56960 q^{9} -10.6539 q^{10} -1.00000 q^{11} +5.77587 q^{12} -1.47857 q^{13} -9.45570 q^{14} +4.87582 q^{15} +9.66398 q^{16} -3.27003 q^{17} +4.10185 q^{18} +1.00000 q^{19} +19.6883 q^{20} +4.32745 q^{21} +2.61330 q^{22} -7.45793 q^{23} -8.84313 q^{24} +11.6203 q^{25} +3.86395 q^{26} -5.46521 q^{27} +17.4740 q^{28} +1.02535 q^{29} -12.7420 q^{30} +1.64921 q^{31} -10.4670 q^{32} -1.19599 q^{33} +8.54558 q^{34} +14.7511 q^{35} -7.58018 q^{36} -6.71293 q^{37} -2.61330 q^{38} -1.76836 q^{39} -30.1438 q^{40} -3.92451 q^{41} -11.3089 q^{42} +5.38113 q^{43} -4.82936 q^{44} -6.39896 q^{45} +19.4898 q^{46} -3.71597 q^{47} +11.5580 q^{48} +6.09205 q^{49} -30.3674 q^{50} -3.91093 q^{51} -7.14054 q^{52} -0.102902 q^{53} +14.2823 q^{54} -4.07680 q^{55} -26.7536 q^{56} +1.19599 q^{57} -2.67955 q^{58} +13.2986 q^{59} +23.5471 q^{60} -6.49664 q^{61} -4.30989 q^{62} -5.67929 q^{63} +8.02543 q^{64} -6.02783 q^{65} +3.12549 q^{66} -3.70989 q^{67} -15.7921 q^{68} -8.91962 q^{69} -38.5490 q^{70} +6.32968 q^{71} +11.6056 q^{72} -1.37759 q^{73} +17.5429 q^{74} +13.8978 q^{75} +4.82936 q^{76} -3.61829 q^{77} +4.62125 q^{78} +13.6725 q^{79} +39.3981 q^{80} -1.82753 q^{81} +10.2559 q^{82} +5.44061 q^{83} +20.8988 q^{84} -13.3313 q^{85} -14.0625 q^{86} +1.22631 q^{87} +7.39397 q^{88} +12.1357 q^{89} +16.7224 q^{90} -5.34990 q^{91} -36.0170 q^{92} +1.97244 q^{93} +9.71096 q^{94} +4.07680 q^{95} -12.5184 q^{96} -13.7910 q^{97} -15.9204 q^{98} +1.56960 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - q^{2} + 2 q^{3} + 15 q^{4} + 2 q^{5} - 2 q^{6} + 10 q^{7} - 9 q^{8} + 11 q^{9}+O(q^{10}) $ 7 * q - q^2 + 2 * q^3 + 15 * q^4 + 2 * q^5 - 2 * q^6 + 10 * q^7 - 9 * q^8 + 11 * q^9	\( 7 q - q^{2} + 2 q^{3} + 15 q^{4} + 2 q^{5} - 2 q^{6} + 10 q^{7} - 9 q^{8} + 11 q^{9} - 6 q^{10} - 7 q^{11} - 16 q^{12} - 4 q^{13} + 6 q^{14} + 12 q^{15} + 27 q^{16} + 2 q^{17} + 9 q^{18} + 7 q^{19} - 4 q^{20} - 14 q^{21} + q^{22} + 10 q^{23} - 2 q^{24} + 9 q^{25} - 8 q^{26} - 4 q^{27} + 26 q^{28} - 18 q^{29} - 42 q^{30} + 24 q^{31} - 49 q^{32} - 2 q^{33} - 6 q^{34} + 8 q^{35} + 29 q^{36} - q^{38} + 24 q^{39} - 2 q^{40} - 12 q^{41} - 44 q^{42} + 2 q^{43} - 15 q^{44} - 4 q^{45} - 4 q^{46} + 8 q^{47} - 72 q^{48} + 17 q^{49} - 33 q^{50} - 24 q^{51} - 60 q^{52} + 2 q^{53} - 52 q^{54} - 2 q^{55} + 26 q^{56} + 2 q^{57} - 8 q^{58} - 10 q^{59} + 42 q^{60} + 14 q^{61} + 14 q^{62} + 55 q^{64} - 14 q^{65} + 2 q^{66} + 8 q^{67} - 18 q^{68} - 6 q^{69} - 66 q^{70} + 10 q^{71} + 53 q^{72} - 6 q^{73} + 26 q^{74} + 26 q^{75} + 15 q^{76} - 10 q^{77} + 22 q^{78} + 52 q^{79} - 12 q^{80} - q^{81} + 24 q^{82} - 10 q^{83} - 6 q^{84} - 12 q^{85} + 8 q^{86} + 6 q^{87} + 9 q^{88} + 20 q^{90} + 12 q^{91} + 2 q^{93} + 24 q^{94} + 2 q^{95} + 6 q^{96} - 24 q^{97} + 19 q^{98} - 11 q^{99}+O(q^{100}) \) 7 * q - q^2 + 2 * q^3 + 15 * q^4 + 2 * q^5 - 2 * q^6 + 10 * q^7 - 9 * q^8 + 11 * q^9 - 6 * q^10 - 7 * q^11 - 16 * q^12 - 4 * q^13 + 6 * q^14 + 12 * q^15 + 27 * q^16 + 2 * q^17 + 9 * q^18 + 7 * q^19 - 4 * q^20 - 14 * q^21 + q^22 + 10 * q^23 - 2 * q^24 + 9 * q^25 - 8 * q^26 - 4 * q^27 + 26 * q^28 - 18 * q^29 - 42 * q^30 + 24 * q^31 - 49 * q^32 - 2 * q^33 - 6 * q^34 + 8 * q^35 + 29 * q^36 - q^38 + 24 * q^39 - 2 * q^40 - 12 * q^41 - 44 * q^42 + 2 * q^43 - 15 * q^44 - 4 * q^45 - 4 * q^46 + 8 * q^47 - 72 * q^48 + 17 * q^49 - 33 * q^50 - 24 * q^51 - 60 * q^52 + 2 * q^53 - 52 * q^54 - 2 * q^55 + 26 * q^56 + 2 * q^57 - 8 * q^58 - 10 * q^59 + 42 * q^60 + 14 * q^61 + 14 * q^62 + 55 * q^64 - 14 * q^65 + 2 * q^66 + 8 * q^67 - 18 * q^68 - 6 * q^69 - 66 * q^70 + 10 * q^71 + 53 * q^72 - 6 * q^73 + 26 * q^74 + 26 * q^75 + 15 * q^76 - 10 * q^77 + 22 * q^78 + 52 * q^79 - 12 * q^80 - q^81 + 24 * q^82 - 10 * q^83 - 6 * q^84 - 12 * q^85 + 8 * q^86 + 6 * q^87 + 9 * q^88 + 20 * q^90 + 12 * q^91 + 2 * q^93 + 24 * q^94 + 2 * q^95 + 6 * q^96 - 24 * q^97 + 19 * q^98 - 11 * 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 $

$2$	−2.61330	−1.84789	−0.923943	−	0.382531i	$-0.875052\pi$
$2$	−2.61330	−1.84789	−0.923943	+	0.382531i	$0.875052\pi$
$3$	1.19599	0.690506	0.345253	−	0.938510i	$-0.387793\pi$
$3$	1.19599	0.690506	0.345253	+	0.938510i	$0.387793\pi$
$4$	4.82936	2.41468
$5$	4.07680	1.82320	0.911600	−	0.411078i	$-0.134847\pi$
$5$	4.07680	1.82320	0.911600	+	0.411078i	$0.134847\pi$
$6$	−3.12549	−1.27598
$7$	3.61829	1.36759	0.683793	−	0.729676i	$-0.260329\pi$
$7$	3.61829	1.36759	0.683793	+	0.729676i	$0.260329\pi$
$8$	−7.39397	−2.61416
$9$	−1.56960	−0.523201
$10$	−10.6539	−3.36907
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	5.77587	1.66735
$13$	−1.47857	−0.410081	−0.205041	−	0.978753i	$-0.565733\pi$
$13$	−1.47857	−0.410081	−0.205041	+	0.978753i	$0.565733\pi$
$14$	−9.45570	−2.52714
$15$	4.87582	1.25893
$16$	9.66398	2.41600
$17$	−3.27003	−0.793099	−0.396549	−	0.918013i	$-0.629792\pi$
$17$	−3.27003	−0.793099	−0.396549	+	0.918013i	$0.629792\pi$
$18$	4.10185	0.966816
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	19.6883	4.40244
$21$	4.32745	0.944327
$22$	2.61330	0.557158
$23$	−7.45793	−1.55509	−0.777543	−	0.628830i	$-0.783534\pi$
$23$	−7.45793	−1.55509	−0.777543	+	0.628830i	$0.783534\pi$
$24$	−8.84313	−1.80510
$25$	11.6203	2.32406
$26$	3.86395	0.757783
$27$	−5.46521	−1.05178
$28$	17.4740	3.30228
$29$	1.02535	0.190403	0.0952013	−	0.995458i	$-0.469651\pi$
$29$	1.02535	0.190403	0.0952013	+	0.995458i	$0.469651\pi$
$30$	−12.7420	−2.32636
$31$	1.64921	0.296207	0.148104	−	0.988972i	$-0.452683\pi$
$31$	1.64921	0.296207	0.148104	+	0.988972i	$0.452683\pi$
$32$	−10.4670	−1.85032
$33$	−1.19599	−0.208195
$34$	8.54558	1.46556
$35$	14.7511	2.49338
$36$	−7.58018	−1.26336
$37$	−6.71293	−1.10360	−0.551799	−	0.833977i	$-0.686059\pi$
$37$	−6.71293	−1.10360	−0.551799	+	0.833977i	$0.686059\pi$
$38$	−2.61330	−0.423934
$39$	−1.76836	−0.283164
$40$	−30.1438	−4.76615
$41$	−3.92451	−0.612905	−0.306453	−	0.951886i	$-0.599142\pi$
$41$	−3.92451	−0.612905	−0.306453	+	0.951886i	$0.599142\pi$
$42$	−11.3089	−1.74501
$43$	5.38113	0.820614	0.410307	−	0.911947i	$-0.365422\pi$
$43$	5.38113	0.820614	0.410307	+	0.911947i	$0.365422\pi$
$44$	−4.82936	−0.728053
$45$	−6.39896	−0.953901
$46$	19.4898	2.87362
$47$	−3.71597	−0.542030	−0.271015	−	0.962575i	$-0.587359\pi$
$47$	−3.71597	−0.542030	−0.271015	+	0.962575i	$0.587359\pi$
$48$	11.5580	1.66826
$49$	6.09205	0.870292
$50$	−30.3674	−4.29460
$51$	−3.91093	−0.547640
$52$	−7.14054	−0.990215
$53$	−0.102902	−0.0141347	−0.00706733	−	0.999975i	$-0.502250\pi$
$53$	−0.102902	−0.0141347	−0.00706733	+	0.999975i	$0.502250\pi$
$54$	14.2823	1.94357
$55$	−4.07680	−0.549716
$56$	−26.7536	−3.57509
$57$	1.19599	0.158413
$58$	−2.67955	−0.351842
$59$	13.2986	1.73134	0.865668	−	0.500619i	$-0.166894\pi$
$59$	13.2986	1.73134	0.865668	+	0.500619i	$0.166894\pi$
$60$	23.5471	3.03991
$61$	−6.49664	−0.831809	−0.415905	−	0.909408i	$-0.636535\pi$
$61$	−6.49664	−0.831809	−0.415905	+	0.909408i	$0.636535\pi$
$62$	−4.30989	−0.547357
$63$	−5.67929	−0.715523
$64$	8.02543	1.00318
$65$	−6.02783	−0.747661
$66$	3.12549	0.384721
$67$	−3.70989	−0.453235	−0.226618	−	0.973984i	$-0.572767\pi$
$67$	−3.70989	−0.453235	−0.226618	+	0.973984i	$0.572767\pi$
$68$	−15.7921	−1.91508
$69$	−8.91962	−1.07380
$70$	−38.5490	−4.60749
$71$	6.32968	0.751194	0.375597	−	0.926783i	$-0.377438\pi$
$71$	6.32968	0.751194	0.375597	+	0.926783i	$0.377438\pi$
$72$	11.6056	1.36773
$73$	−1.37759	−0.161235	−0.0806173	−	0.996745i	$-0.525689\pi$
$73$	−1.37759	−0.161235	−0.0806173	+	0.996745i	$0.525689\pi$
$74$	17.5429	2.03932
$75$	13.8978	1.60478
$76$	4.82936	0.553965
$77$	−3.61829	−0.412343
$78$	4.62125	0.523254
$79$	13.6725	1.53828	0.769141	−	0.639079i	$-0.220684\pi$
$79$	13.6725	1.53828	0.769141	+	0.639079i	$0.220684\pi$
$80$	39.3981	4.40484
$81$	−1.82753	−0.203059
$82$	10.2559	1.13258
$83$	5.44061	0.597184	0.298592	−	0.954381i	$-0.403483\pi$
$83$	5.44061	0.597184	0.298592	+	0.954381i	$0.403483\pi$
$84$	20.8988	2.28025
$85$	−13.3313	−1.44598
$86$	−14.0625	−1.51640
$87$	1.22631	0.131474
$88$	7.39397	0.788200
$89$	12.1357	1.28638	0.643191	−	0.765706i	$-0.277610\pi$
$89$	12.1357	1.28638	0.643191	+	0.765706i	$0.277610\pi$
$90$	16.7224	1.76270
$91$	−5.34990	−0.560822
$92$	−36.0170	−3.75503
$93$	1.97244	0.204533
$94$	9.71096	1.00161
$95$	4.07680	0.418271
$96$	−12.5184	−1.27766
$97$	−13.7910	−1.40026	−0.700131	−	0.714014i	$-0.746875\pi$
$97$	−13.7910	−1.40026	−0.700131	+	0.714014i	$0.746875\pi$
$98$	−15.9204	−1.60820
$99$	1.56960	0.157751
$100$	56.1186	5.61186
$101$	−11.0029	−1.09483	−0.547413	−	0.836863i	$-0.684387\pi$
$101$	−11.0029	−1.09483	−0.547413	+	0.836863i	$0.684387\pi$
$102$	10.2204	1.01198
$103$	−4.99191	−0.491867	−0.245934	−	0.969287i	$-0.579094\pi$
$103$	−4.99191	−0.491867	−0.245934	+	0.969287i	$0.579094\pi$
$104$	10.9325	1.07202
$105$	17.6421	1.72170
$106$	0.268914	0.0261192
$107$	7.31345	0.707018	0.353509	−	0.935431i	$-0.384988\pi$
$107$	7.31345	0.707018	0.353509	+	0.935431i	$0.384988\pi$
$108$	−26.3934	−2.53971
$109$	−1.44482	−0.138389	−0.0691944	−	0.997603i	$-0.522043\pi$
$109$	−1.44482	−0.138389	−0.0691944	+	0.997603i	$0.522043\pi$
$110$	10.6539	1.01581
$111$	−8.02861	−0.762042
$112$	34.9671	3.30408
$113$	−12.0369	−1.13234	−0.566169	−	0.824289i	$-0.691575\pi$
$113$	−12.0369	−1.13234	−0.566169	+	0.824289i	$0.691575\pi$
$114$	−3.12549	−0.292729
$115$	−30.4045	−2.83523
$116$	4.95178	0.459761
$117$	2.32077	0.214555
$118$	−34.7534	−3.19931
$119$	−11.8319	−1.08463
$120$	−36.0517	−3.29105
$121$	1.00000	0.0909091
$122$	16.9777	1.53709
$123$	−4.69368	−0.423215
$124$	7.96463	0.715245
$125$	26.9897	2.41403
$126$	14.8417	1.32220
$127$	−4.69692	−0.416784	−0.208392	−	0.978045i	$-0.566823\pi$
$127$	−4.69692	−0.416784	−0.208392	+	0.978045i	$0.566823\pi$
$128$	−0.0389415	−0.00344197
$129$	6.43578	0.566639
$130$	15.7526	1.38159
$131$	3.74466	0.327173	0.163586	−	0.986529i	$-0.447694\pi$
$131$	3.74466	0.327173	0.163586	+	0.986529i	$0.447694\pi$
$132$	−5.77587	−0.502725
$133$	3.61829	0.313746
$134$	9.69507	0.837526
$135$	−22.2806	−1.91761
$136$	24.1785	2.07329
$137$	−15.7595	−1.34643	−0.673213	−	0.739449i	$-0.735086\pi$
$137$	−15.7595	−1.34643	−0.673213	+	0.739449i	$0.735086\pi$
$138$	23.3097	1.98425
$139$	−2.52822	−0.214440	−0.107220	−	0.994235i	$-0.534195\pi$
$139$	−2.52822	−0.214440	−0.107220	+	0.994235i	$0.534195\pi$
$140$	71.2381	6.02072
$141$	−4.44427	−0.374275
$142$	−16.5414	−1.38812
$143$	1.47857	0.123644
$144$	−15.1686	−1.26405
$145$	4.18015	0.347142
$146$	3.60006	0.297943
$147$	7.28604	0.600942
$148$	−32.4191	−2.66484
$149$	1.84902	0.151477	0.0757387	−	0.997128i	$-0.475869\pi$
$149$	1.84902	0.151477	0.0757387	+	0.997128i	$0.475869\pi$
$150$	−36.3191	−2.96545
$151$	−15.3184	−1.24659	−0.623296	−	0.781986i	$-0.714207\pi$
$151$	−15.3184	−1.24659	−0.623296	+	0.781986i	$0.714207\pi$
$152$	−7.39397	−0.599730
$153$	5.13265	0.414950
$154$	9.45570	0.761962
$155$	6.72351	0.540045
$156$	−8.54003	−0.683750
$157$	24.6631	1.96833	0.984165	−	0.177254i	$-0.0567215\pi$
$157$	24.6631	1.96833	0.984165	+	0.177254i	$0.0567215\pi$
$158$	−35.7305	−2.84257
$159$	−0.123070	−0.00976006
$160$	−42.6718	−3.37350
$161$	−26.9850	−2.12671
$162$	4.77590	0.375230
$163$	−3.72149	−0.291490	−0.145745	−	0.989322i	$-0.546558\pi$
$163$	−3.72149	−0.291490	−0.145745	+	0.989322i	$0.546558\pi$
$164$	−18.9529	−1.47997
$165$	−4.87582	−0.379582
$166$	−14.2180	−1.10353
$167$	2.64758	0.204876	0.102438	−	0.994739i	$-0.467336\pi$
$167$	2.64758	0.204876	0.102438	+	0.994739i	$0.467336\pi$
$168$	−31.9970	−2.46863
$169$	−10.8138	−0.831833
$170$	34.8386	2.67200
$171$	−1.56960	−0.120031
$172$	25.9874	1.98152
$173$	7.34552	0.558469	0.279235	−	0.960223i	$-0.409919\pi$
$173$	7.34552	0.558469	0.279235	+	0.960223i	$0.409919\pi$
$174$	−3.20472	−0.242949
$175$	42.0457	3.17835
$176$	−9.66398	−0.728450
$177$	15.9051	1.19550
$178$	−31.7143	−2.37708
$179$	9.55394	0.714095	0.357047	−	0.934086i	$-0.383783\pi$
$179$	9.55394	0.714095	0.357047	+	0.934086i	$0.383783\pi$
$180$	−30.9029	−2.30336
$181$	6.02638	0.447937	0.223969	−	0.974596i	$-0.428099\pi$
$181$	6.02638	0.447937	0.223969	+	0.974596i	$0.428099\pi$
$182$	13.9809	1.03633
$183$	−7.76993	−0.574369
$184$	55.1437	4.06525
$185$	−27.3673	−2.01208
$186$	−5.15459	−0.377953
$187$	3.27003	0.239128
$188$	−17.9458	−1.30883
$189$	−19.7747	−1.43840
$190$	−10.6539	−0.772917
$191$	17.7069	1.28123	0.640613	−	0.767864i	$-0.278680\pi$
$191$	17.7069	1.28123	0.640613	+	0.767864i	$0.278680\pi$
$192$	9.59835	0.692701
$193$	3.69348	0.265863	0.132931	−	0.991125i	$-0.457561\pi$
$193$	3.69348	0.265863	0.132931	+	0.991125i	$0.457561\pi$
$194$	36.0400	2.58752
$195$	−7.20924	−0.516264
$196$	29.4207	2.10148
$197$	−25.7789	−1.83667	−0.918336	−	0.395802i	$-0.870467\pi$
$197$	−25.7789	−1.83667	−0.918336	+	0.395802i	$0.870467\pi$
$198$	−4.10185	−0.291506
$199$	18.8953	1.33945	0.669726	−	0.742608i	$-0.266411\pi$
$199$	18.8953	1.33945	0.669726	+	0.742608i	$0.266411\pi$
$200$	−85.9202	−6.07548
$201$	−4.43700	−0.312962
$202$	28.7538	2.02311
$203$	3.71002	0.260392
$204$	−18.8873	−1.32237
$205$	−15.9994	−1.11745
$206$	13.0454	0.908914
$207$	11.7060	0.813623
$208$	−14.2889	−0.990755
$209$	−1.00000	−0.0691714
$210$	−46.1043	−3.18150
$211$	−10.1993	−0.702150	−0.351075	−	0.936347i	$-0.614184\pi$
$211$	−10.1993	−0.702150	−0.351075	+	0.936347i	$0.614184\pi$
$212$	−0.496950	−0.0341306
$213$	7.57024	0.518704
$214$	−19.1123	−1.30649
$215$	21.9378	1.49614
$216$	40.4096	2.74953
$217$	5.96733	0.405089
$218$	3.77576	0.255727
$219$	−1.64759	−0.111334
$220$	−19.6883	−1.32739
$221$	4.83497	0.325235
$222$	20.9812	1.40817
$223$	−0.262700	−0.0175917	−0.00879584	−	0.999961i	$-0.502800\pi$
$223$	−0.262700	−0.0175917	−0.00879584	+	0.999961i	$0.502800\pi$
$224$	−37.8726	−2.53047
$225$	−18.2393	−1.21595
$226$	31.4561	2.09243
$227$	27.3256	1.81367	0.906834	−	0.421489i	$-0.138492\pi$
$227$	27.3256	1.81367	0.906834	+	0.421489i	$0.138492\pi$
$228$	5.77587	0.382516
$229$	−5.53171	−0.365546	−0.182773	−	0.983155i	$-0.558507\pi$
$229$	−5.53171	−0.365546	−0.182773	+	0.983155i	$0.558507\pi$
$230$	79.4562	5.23918
$231$	−4.32745	−0.284725
$232$	−7.58141	−0.497744
$233$	27.4733	1.79984	0.899918	−	0.436059i	$-0.143626\pi$
$233$	27.4733	1.79984	0.899918	+	0.436059i	$0.143626\pi$
$234$	−6.06487	−0.396473
$235$	−15.1493	−0.988229
$236$	64.2239	4.18062
$237$	16.3523	1.06219
$238$	30.9204	2.00427
$239$	1.40339	0.0907781	0.0453890	−	0.998969i	$-0.485547\pi$
$239$	1.40339	0.0907781	0.0453890	+	0.998969i	$0.485547\pi$
$240$	47.1198	3.04157
$241$	−20.7696	−1.33789	−0.668944	−	0.743312i	$-0.733254\pi$
$241$	−20.7696	−1.33789	−0.668944	+	0.743312i	$0.733254\pi$
$242$	−2.61330	−0.167990
$243$	14.2099	0.911566
$244$	−31.3746	−2.00855
$245$	24.8361	1.58672
$246$	12.2660	0.782052
$247$	−1.47857	−0.0940791
$248$	−12.1942	−0.774334
$249$	6.50692	0.412359
$250$	−70.5322	−4.46085
$251$	−1.29936	−0.0820148	−0.0410074	−	0.999159i	$-0.513057\pi$
$251$	−1.29936	−0.0820148	−0.0410074	+	0.999159i	$0.513057\pi$
$252$	−27.4273	−1.72776
$253$	7.45793	0.468876
$254$	12.2745	0.770169
$255$	−15.9441	−0.998457
$256$	−15.9491	−0.996819
$257$	3.41219	0.212847	0.106423	−	0.994321i	$-0.466060\pi$
$257$	3.41219	0.212847	0.106423	+	0.994321i	$0.466060\pi$
$258$	−16.8187	−1.04708
$259$	−24.2893	−1.50927
$260$	−29.1106	−1.80536
$261$	−1.60939	−0.0996189
$262$	−9.78594	−0.604577
$263$	14.2418	0.878189	0.439094	−	0.898441i	$-0.355299\pi$
$263$	14.2418	0.878189	0.439094	+	0.898441i	$0.355299\pi$
$264$	8.84313	0.544257
$265$	−0.419510	−0.0257703
$266$	−9.45570	−0.579766
$267$	14.5142	0.888254
$268$	−17.9164	−1.09442
$269$	5.39477	0.328925	0.164462	−	0.986383i	$-0.447411\pi$
$269$	5.39477	0.328925	0.164462	+	0.986383i	$0.447411\pi$
$270$	58.2259	3.54351
$271$	−11.0624	−0.671995	−0.335998	−	0.941863i	$-0.609073\pi$
$271$	−11.0624	−0.671995	−0.335998	+	0.941863i	$0.609073\pi$
$272$	−31.6015	−1.91612
$273$	−6.39843	−0.387251
$274$	41.1844	2.48804
$275$	−11.6203	−0.700731
$276$	−43.0760	−2.59287
$277$	14.0808	0.846036	0.423018	−	0.906121i	$-0.360971\pi$
$277$	14.0808	0.846036	0.423018	+	0.906121i	$0.360971\pi$
$278$	6.60700	0.396261
$279$	−2.58861	−0.154976
$280$	−109.069	−6.51812
$281$	−10.8199	−0.645459	−0.322729	−	0.946491i	$-0.604600\pi$
$281$	−10.8199	−0.645459	−0.322729	+	0.946491i	$0.604600\pi$
$282$	11.6142	0.691617
$283$	1.90947	0.113506	0.0567532	−	0.998388i	$-0.481925\pi$
$283$	1.90947	0.113506	0.0567532	+	0.998388i	$0.481925\pi$
$284$	30.5683	1.81389
$285$	4.87582	0.288819
$286$	−3.86395	−0.228480
$287$	−14.2000	−0.838201
$288$	16.4290	0.968089
$289$	−6.30690	−0.370994
$290$	−10.9240	−0.641479
$291$	−16.4939	−0.966890
$292$	−6.65287	−0.389330
$293$	3.63550	0.212388	0.106194	−	0.994345i	$-0.466133\pi$
$293$	3.63550	0.212388	0.106194	+	0.994345i	$0.466133\pi$
$294$	−19.0406	−1.11047
$295$	54.2159	3.15657
$296$	49.6352	2.88499
$297$	5.46521	0.317124
$298$	−4.83205	−0.279913
$299$	11.0271	0.637712
$300$	67.1174	3.87502
$301$	19.4705	1.12226
$302$	40.0316	2.30356
$303$	−13.1593	−0.755984
$304$	9.66398	0.554267
$305$	−26.4855	−1.51656
$306$	−13.4132	−0.766781
$307$	−23.5329	−1.34310	−0.671548	−	0.740961i	$-0.734370\pi$
$307$	−23.5329	−1.34310	−0.671548	+	0.740961i	$0.734370\pi$
$308$	−17.4740	−0.995675
$309$	−5.97028	−0.339637
$310$	−17.5706	−0.997941
$311$	−16.0026	−0.907425	−0.453713	−	0.891148i	$-0.649901\pi$
$311$	−16.0026	−0.907425	−0.453713	+	0.891148i	$0.649901\pi$
$312$	13.0752	0.740237
$313$	16.0034	0.904566	0.452283	−	0.891875i	$-0.350610\pi$
$313$	16.0034	0.904566	0.452283	+	0.891875i	$0.350610\pi$
$314$	−64.4522	−3.63725
$315$	−23.1533	−1.30454
$316$	66.0296	3.71446
$317$	−20.8766	−1.17255	−0.586273	−	0.810113i	$-0.699405\pi$
$317$	−20.8766	−1.17255	−0.586273	+	0.810113i	$0.699405\pi$
$318$	0.321619	0.0180355
$319$	−1.02535	−0.0574086
$320$	32.7181	1.82900
$321$	8.74683	0.488200
$322$	70.5199	3.92992
$323$	−3.27003	−0.181949
$324$	−8.82581	−0.490323
$325$	−17.1814	−0.953054
$326$	9.72539	0.538640
$327$	−1.72800	−0.0955584
$328$	29.0177	1.60224
$329$	−13.4455	−0.741273
$330$	12.7420	0.701424
$331$	15.1136	0.830721	0.415360	−	0.909657i	$-0.363655\pi$
$331$	15.1136	0.830721	0.415360	+	0.909657i	$0.363655\pi$
$332$	26.2746	1.44201
$333$	10.5366	0.577404
$334$	−6.91893	−0.378587
$335$	−15.1245	−0.826339
$336$	41.8204	2.28149
$337$	−12.2766	−0.668751	−0.334376	−	0.942440i	$-0.608525\pi$
$337$	−12.2766	−0.668751	−0.334376	+	0.942440i	$0.608525\pi$
$338$	28.2598	1.53713
$339$	−14.3961	−0.781886
$340$	−64.3814	−3.49157
$341$	−1.64921	−0.0893098
$342$	4.10185	0.221803
$343$	−3.28525	−0.177387
$344$	−39.7879	−2.14522
$345$	−36.3635	−1.95775
$346$	−19.1961	−1.03199
$347$	−30.9067	−1.65916	−0.829580	−	0.558387i	$-0.811420\pi$
$347$	−30.9067	−1.65916	−0.829580	+	0.558387i	$0.811420\pi$
$348$	5.92229	0.317468
$349$	−23.9024	−1.27947	−0.639733	−	0.768597i	$-0.720955\pi$
$349$	−23.9024	−1.27947	−0.639733	+	0.768597i	$0.720955\pi$
$350$	−109.878	−5.87323
$351$	8.08069	0.431315
$352$	10.4670	0.557892
$353$	15.0158	0.799210	0.399605	−	0.916687i	$-0.369147\pi$
$353$	15.0158	0.799210	0.399605	+	0.916687i	$0.369147\pi$
$354$	−41.5648	−2.20914
$355$	25.8048	1.36958
$356$	58.6076	3.10620
$357$	−14.1509	−0.748945
$358$	−24.9673	−1.31957
$359$	14.0826	0.743251	0.371626	−	0.928383i	$-0.378800\pi$
$359$	14.0826	0.743251	0.371626	+	0.928383i	$0.378800\pi$
$360$	47.3137	2.49365
$361$	1.00000	0.0526316
$362$	−15.7488	−0.827737
$363$	1.19599	0.0627733
$364$	−25.8366	−1.35420
$365$	−5.61616	−0.293963
$366$	20.3052	1.06137
$367$	21.3142	1.11259	0.556296	−	0.830984i	$-0.312222\pi$
$367$	21.3142	1.11259	0.556296	+	0.830984i	$0.312222\pi$
$368$	−72.0733	−3.75708
$369$	6.15992	0.320673
$370$	71.5190	3.71810
$371$	−0.372329	−0.0193304
$372$	9.52564	0.493881
$373$	−2.42088	−0.125349	−0.0626743	−	0.998034i	$-0.519963\pi$
$373$	−2.42088	−0.125349	−0.0626743	+	0.998034i	$0.519963\pi$
$374$	−8.54558	−0.441882
$375$	32.2794	1.66690
$376$	27.4758	1.41696
$377$	−1.51605	−0.0780806
$378$	51.6774	2.65800
$379$	8.87535	0.455896	0.227948	−	0.973673i	$-0.426798\pi$
$379$	8.87535	0.455896	0.227948	+	0.973673i	$0.426798\pi$
$380$	19.6883	1.00999
$381$	−5.61748	−0.287792
$382$	−46.2735	−2.36756
$383$	−3.54065	−0.180919	−0.0904595	−	0.995900i	$-0.528834\pi$
$383$	−3.54065	−0.180919	−0.0904595	+	0.995900i	$0.528834\pi$
$384$	−0.0465737	−0.00237670
$385$	−14.7511	−0.751784
$386$	−9.65219	−0.491284
$387$	−8.44624	−0.429346
$388$	−66.6016	−3.38118
$389$	−16.7041	−0.846933	−0.423466	−	0.905912i	$-0.639187\pi$
$389$	−16.7041	−0.846933	−0.423466	+	0.905912i	$0.639187\pi$
$390$	18.8399	0.953997
$391$	24.3877	1.23334
$392$	−45.0444	−2.27509
$393$	4.47858	0.225915
$394$	67.3681	3.39396
$395$	55.7403	2.80460
$396$	7.58018	0.380918
$397$	28.2073	1.41568	0.707841	−	0.706372i	$-0.249669\pi$
$397$	28.2073	1.41568	0.707841	+	0.706372i	$0.249669\pi$
$398$	−49.3792	−2.47515
$399$	4.32745	0.216643
$400$	112.298	5.61492
$401$	−36.2078	−1.80813	−0.904065	−	0.427395i	$-0.859431\pi$
$401$	−36.2078	−1.80813	−0.904065	+	0.427395i	$0.859431\pi$
$402$	11.5952	0.578317
$403$	−2.43847	−0.121469
$404$	−53.1368	−2.64365
$405$	−7.45049	−0.370218
$406$	−9.69540	−0.481175
$407$	6.71293	0.332748
$408$	28.9173	1.43162
$409$	36.9236	1.82576	0.912878	−	0.408233i	$-0.133855\pi$
$409$	36.9236	1.82576	0.912878	+	0.408233i	$0.133855\pi$
$410$	41.8114	2.06492
$411$	−18.8482	−0.929715
$412$	−24.1077	−1.18770
$413$	48.1184	2.36775
$414$	−30.5913	−1.50348
$415$	22.1803	1.08879
$416$	15.4762	0.758781
$417$	−3.02373	−0.148072
$418$	2.61330	0.127821
$419$	18.0690	0.882726	0.441363	−	0.897329i	$-0.354495\pi$
$419$	18.0690	0.882726	0.441363	+	0.897329i	$0.354495\pi$
$420$	85.2002	4.15735
$421$	−8.57629	−0.417983	−0.208991	−	0.977918i	$-0.567018\pi$
$421$	−8.57629	−0.417983	−0.208991	+	0.977918i	$0.567018\pi$
$422$	26.6539	1.29749
$423$	5.83260	0.283591
$424$	0.760853	0.0369503
$425$	−37.9987	−1.84321
$426$	−19.7833	−0.958506
$427$	−23.5067	−1.13757
$428$	35.3193	1.70722
$429$	1.76836	0.0853771
$430$	−57.3301	−2.76470
$431$	4.28147	0.206231	0.103116	−	0.994669i	$-0.467119\pi$
$431$	4.28147	0.206231	0.103116	+	0.994669i	$0.467119\pi$
$432$	−52.8157	−2.54110
$433$	18.2035	0.874804	0.437402	−	0.899266i	$-0.355899\pi$
$433$	18.2035	0.874804	0.437402	+	0.899266i	$0.355899\pi$
$434$	−15.5945	−0.748558
$435$	4.99942	0.239704
$436$	−6.97756	−0.334165
$437$	−7.45793	−0.356761
$438$	4.30564	0.205732
$439$	29.4442	1.40529	0.702647	−	0.711538i	$-0.252001\pi$
$439$	29.4442	1.40529	0.702647	+	0.711538i	$0.252001\pi$
$440$	30.1438	1.43705
$441$	−9.56210	−0.455338
$442$	−12.6352	−0.600997
$443$	−24.3633	−1.15753	−0.578767	−	0.815493i	$-0.696466\pi$
$443$	−24.3633	−1.15753	−0.578767	+	0.815493i	$0.696466\pi$
$444$	−38.7730	−1.84009
$445$	49.4748	2.34533
$446$	0.686514	0.0325074
$447$	2.21141	0.104596
$448$	29.0384	1.37193
$449$	38.7776	1.83003	0.915015	−	0.403421i	$-0.132179\pi$
$449$	38.7776	1.83003	0.915015	+	0.403421i	$0.132179\pi$
$450$	47.6648	2.24694
$451$	3.92451	0.184798
$452$	−58.1306	−2.73423
$453$	−18.3206	−0.860779
$454$	−71.4102	−3.35145
$455$	−21.8105	−1.02249
$456$	−8.84313	−0.414118
$457$	−7.47672	−0.349746	−0.174873	−	0.984591i	$-0.555952\pi$
$457$	−7.47672	−0.349746	−0.174873	+	0.984591i	$0.555952\pi$
$458$	14.4560	0.675487
$459$	17.8714	0.834165
$460$	−146.834	−6.84618
$461$	15.9782	0.744181	0.372091	−	0.928196i	$-0.378641\pi$
$461$	15.9782	0.744181	0.372091	+	0.928196i	$0.378641\pi$
$462$	11.3089	0.526139
$463$	−6.10221	−0.283594	−0.141797	−	0.989896i	$-0.545288\pi$
$463$	−6.10221	−0.283594	−0.141797	+	0.989896i	$0.545288\pi$
$464$	9.90896	0.460012
$465$	8.04126	0.372904
$466$	−71.7961	−3.32589
$467$	−26.6373	−1.23263	−0.616313	−	0.787502i	$-0.711374\pi$
$467$	−26.6373	−1.23263	−0.616313	+	0.787502i	$0.711374\pi$
$468$	11.2078	0.518082
$469$	−13.4235	−0.619838
$470$	39.5896	1.82613
$471$	29.4969	1.35914
$472$	−98.3298	−4.52599
$473$	−5.38113	−0.247424
$474$	−42.7334	−1.96281
$475$	11.6203	0.533176
$476$	−57.1406	−2.61904
$477$	0.161515	0.00739527
$478$	−3.66750	−0.167747
$479$	−16.2094	−0.740626	−0.370313	−	0.928907i	$-0.620750\pi$
$479$	−16.2094	−0.740626	−0.370313	+	0.928907i	$0.620750\pi$
$480$	−51.0351	−2.32942
$481$	9.92553	0.452565
$482$	54.2773	2.47226
$483$	−32.2738	−1.46851
$484$	4.82936	0.219516
$485$	−56.2231	−2.55296
$486$	−37.1348	−1.68447
$487$	−4.82448	−0.218618	−0.109309	−	0.994008i	$-0.534864\pi$
$487$	−4.82448	−0.218618	−0.109309	+	0.994008i	$0.534864\pi$
$488$	48.0360	2.17449
$489$	−4.45088	−0.201276
$490$	−64.9042	−2.93207
$491$	−8.53579	−0.385215	−0.192607	−	0.981276i	$-0.561694\pi$
$491$	−8.53579	−0.385215	−0.192607	+	0.981276i	$0.561694\pi$
$492$	−22.6675	−1.02193
$493$	−3.35293	−0.151008
$494$	3.86395	0.173847
$495$	6.39896	0.287612
$496$	15.9380	0.715635
$497$	22.9026	1.02732
$498$	−17.0046	−0.761993
$499$	−13.4325	−0.601319	−0.300660	−	0.953732i	$-0.597207\pi$
$499$	−13.4325	−0.601319	−0.300660	+	0.953732i	$0.597207\pi$
$500$	130.343	5.82910
$501$	3.16648	0.141468
$502$	3.39562	0.151554
$503$	−1.66487	−0.0742327	−0.0371163	−	0.999311i	$-0.511817\pi$
$503$	−1.66487	−0.0742327	−0.0371163	+	0.999311i	$0.511817\pi$
$504$	41.9925	1.87049
$505$	−44.8565	−1.99609
$506$	−19.4898	−0.866429
$507$	−12.9333	−0.574386
$508$	−22.6831	−1.00640
$509$	−14.9684	−0.663463	−0.331731	−	0.943374i	$-0.607633\pi$
$509$	−14.9684	−0.663463	−0.331731	+	0.943374i	$0.607633\pi$
$510$	41.6667	1.84503
$511$	−4.98452	−0.220502
$512$	41.7577	1.84545
$513$	−5.46521	−0.241295
$514$	−8.91709	−0.393316
$515$	−20.3510	−0.896772
$516$	31.0807	1.36825
$517$	3.71597	0.163428
$518$	63.4754	2.78895
$519$	8.78518	0.385627
$520$	44.5696	1.95451
$521$	−7.89123	−0.345721	−0.172861	−	0.984946i	$-0.555301\pi$
$521$	−7.89123	−0.345721	−0.172861	+	0.984946i	$0.555301\pi$
$522$	4.20583	0.184084
$523$	−22.3062	−0.975381	−0.487690	−	0.873017i	$-0.662160\pi$
$523$	−22.3062	−0.975381	−0.487690	+	0.873017i	$0.662160\pi$
$524$	18.0843	0.790017
$525$	50.2863	2.19467
$526$	−37.2182	−1.62279
$527$	−5.39297	−0.234922
$528$	−11.5580	−0.502999
$529$	32.6207	1.41829
$530$	1.09631	0.0476206
$531$	−20.8736	−0.905837
$532$	17.4740	0.757595
$533$	5.80266	0.251341
$534$	−37.9300	−1.64139
$535$	29.8155	1.28904
$536$	27.4308	1.18483
$537$	11.4264	0.493087
$538$	−14.0982	−0.607815
$539$	−6.09205	−0.262403
$540$	−107.601	−4.63040
$541$	38.9694	1.67542	0.837712	−	0.546112i	$-0.183893\pi$
$541$	38.9694	1.67542	0.837712	+	0.546112i	$0.183893\pi$
$542$	28.9095	1.24177
$543$	7.20750	0.309304
$544$	34.2273	1.46749
$545$	−5.89025	−0.252311
$546$	16.7211	0.715595
$547$	37.7503	1.61409	0.807043	−	0.590492i	$-0.201066\pi$
$547$	37.7503	1.61409	0.807043	+	0.590492i	$0.201066\pi$
$548$	−76.1083	−3.25119
$549$	10.1971	0.435204
$550$	30.3674	1.29487
$551$	1.02535	0.0436814
$552$	65.9514	2.80708
$553$	49.4713	2.10373
$554$	−36.7975	−1.56338
$555$	−32.7310	−1.38935
$556$	−12.2097	−0.517805
$557$	−3.17436	−0.134502	−0.0672511	−	0.997736i	$-0.521423\pi$
$557$	−3.17436	−0.134502	−0.0672511	+	0.997736i	$0.521423\pi$
$558$	6.76482	0.286378
$559$	−7.95637	−0.336519
$560$	142.554	6.02401
$561$	3.91093	0.165120
$562$	28.2756	1.19273
$563$	−19.9431	−0.840503	−0.420252	−	0.907408i	$-0.638058\pi$
$563$	−19.9431	−0.840503	−0.420252	+	0.907408i	$0.638058\pi$
$564$	−21.4630	−0.903754
$565$	−49.0721	−2.06448
$566$	−4.99004	−0.209747
$567$	−6.61255	−0.277701
$568$	−46.8015	−1.96375
$569$	36.6424	1.53613	0.768064	−	0.640374i	$-0.221220\pi$
$569$	36.6424	1.53613	0.768064	+	0.640374i	$0.221220\pi$
$570$	−12.7420	−0.533704
$571$	11.5300	0.482515	0.241258	−	0.970461i	$-0.422440\pi$
$571$	11.5300	0.482515	0.241258	+	0.970461i	$0.422440\pi$
$572$	7.14054	0.298561
$573$	21.1773	0.884694
$574$	37.1090	1.54890
$575$	−86.6634	−3.61411
$576$	−12.5968	−0.524865
$577$	28.5590	1.18893	0.594463	−	0.804123i	$-0.297365\pi$
$577$	28.5590	1.18893	0.594463	+	0.804123i	$0.297365\pi$
$578$	16.4818	0.685554
$579$	4.41737	0.183580
$580$	20.1874	0.838237
$581$	19.6857	0.816701
$582$	43.1036	1.78670
$583$	0.102902	0.00426176
$584$	10.1859	0.421494
$585$	9.46131	0.391177
$586$	−9.50067	−0.392469
$587$	18.1461	0.748969	0.374484	−	0.927233i	$-0.377820\pi$
$587$	18.1461	0.748969	0.374484	+	0.927233i	$0.377820\pi$
$588$	35.1869	1.45108
$589$	1.64921	0.0679546
$590$	−141.683	−5.83298
$591$	−30.8314	−1.26823
$592$	−64.8736	−2.66629
$593$	15.3085	0.628644	0.314322	−	0.949316i	$-0.398223\pi$
$593$	15.3085	0.628644	0.314322	+	0.949316i	$0.398223\pi$
$594$	−14.2823	−0.586008
$595$	−48.2364	−1.97750
$596$	8.92957	0.365769
$597$	22.5986	0.924900
$598$	−28.8171	−1.17842
$599$	17.8806	0.730580	0.365290	−	0.930894i	$-0.380970\pi$
$599$	17.8806	0.730580	0.365290	+	0.930894i	$0.380970\pi$
$600$	−102.760	−4.19515
$601$	−32.5803	−1.32898	−0.664489	−	0.747298i	$-0.731351\pi$
$601$	−32.5803	−1.32898	−0.664489	+	0.747298i	$0.731351\pi$
$602$	−50.8823	−2.07381
$603$	5.82306	0.237133
$604$	−73.9779	−3.01012
$605$	4.07680	0.165746
$606$	34.3893	1.39697
$607$	43.6494	1.77167	0.885837	−	0.463997i	$-0.153585\pi$
$607$	43.6494	1.77167	0.885837	+	0.463997i	$0.153585\pi$
$608$	−10.4670	−0.424492
$609$	4.43715	0.179802
$610$	69.2147	2.80242
$611$	5.49432	0.222276
$612$	24.7874	1.00197
$613$	0.843061	0.0340509	0.0170254	−	0.999855i	$-0.494580\pi$
$613$	0.843061	0.0340509	0.0170254	+	0.999855i	$0.494580\pi$
$614$	61.4987	2.48189
$615$	−19.1352	−0.771606
$616$	26.7536	1.07793
$617$	4.89882	0.197219	0.0986094	−	0.995126i	$-0.468561\pi$
$617$	4.89882	0.197219	0.0986094	+	0.995126i	$0.468561\pi$
$618$	15.6021	0.627611
$619$	−14.8704	−0.597691	−0.298846	−	0.954301i	$-0.596602\pi$
$619$	−14.8704	−0.597691	−0.298846	+	0.954301i	$0.596602\pi$
$620$	32.4702	1.30404
$621$	40.7591	1.63561
$622$	41.8197	1.67682
$623$	43.9105	1.75924
$624$	−17.0894	−0.684122
$625$	51.9299	2.07720
$626$	−41.8217	−1.67153
$627$	−1.19599	−0.0477633
$628$	119.107	4.75289
$629$	21.9515	0.875263
$630$	60.5067	2.41064
$631$	2.83922	0.113027	0.0565137	−	0.998402i	$-0.482002\pi$
$631$	2.83922	0.113027	0.0565137	+	0.998402i	$0.482002\pi$
$632$	−101.094	−4.02132
$633$	−12.1983	−0.484839
$634$	54.5569	2.16673
$635$	−19.1484	−0.759881
$636$	−0.594348	−0.0235674
$637$	−9.00751	−0.356891
$638$	2.67955	0.106084
$639$	−9.93508	−0.393026
$640$	−0.158757	−0.00627541
$641$	20.6746	0.816599	0.408299	−	0.912848i	$-0.366122\pi$
$641$	20.6746	0.816599	0.408299	+	0.912848i	$0.366122\pi$
$642$	−22.8581	−0.902138
$643$	−24.6254	−0.971130	−0.485565	−	0.874201i	$-0.661386\pi$
$643$	−24.6254	−0.971130	−0.485565	+	0.874201i	$0.661386\pi$
$644$	−130.320	−5.13533
$645$	26.2374	1.03310
$646$	8.54558	0.336222
$647$	45.3626	1.78339	0.891693	−	0.452640i	$-0.149518\pi$
$647$	45.3626	1.78339	0.891693	+	0.452640i	$0.149518\pi$
$648$	13.5127	0.530830
$649$	−13.2986	−0.522017
$650$	44.9003	1.76113
$651$	7.13688	0.279716
$652$	−17.9724	−0.703854
$653$	26.1012	1.02142	0.510710	−	0.859753i	$-0.329383\pi$
$653$	26.1012	1.02142	0.510710	+	0.859753i	$0.329383\pi$
$654$	4.51578	0.176581
$655$	15.2662	0.596501
$656$	−37.9264	−1.48078
$657$	2.16227	0.0843582
$658$	35.1371	1.36979
$659$	−45.8507	−1.78609	−0.893045	−	0.449967i	$-0.851436\pi$
$659$	−45.8507	−1.78609	−0.893045	+	0.449967i	$0.851436\pi$
$660$	−23.5471	−0.916569
$661$	−15.4225	−0.599864	−0.299932	−	0.953961i	$-0.596964\pi$
$661$	−15.4225	−0.599864	−0.299932	+	0.953961i	$0.596964\pi$
$662$	−39.4965	−1.53508
$663$	5.78258	0.224577
$664$	−40.2277	−1.56114
$665$	14.7511	0.572022
$666$	−27.5354	−1.06698
$667$	−7.64698	−0.296092
$668$	12.7861	0.494709
$669$	−0.314187	−0.0121472
$670$	39.5249	1.52698
$671$	6.49664	0.250800
$672$	−45.2953	−1.74730
$673$	−37.8633	−1.45952	−0.729762	−	0.683702i	$-0.760369\pi$
$673$	−37.8633	−1.45952	−0.729762	+	0.683702i	$0.760369\pi$
$674$	32.0826	1.23578
$675$	−63.5074	−2.44440
$676$	−52.2239	−2.00861
$677$	−25.3510	−0.974320	−0.487160	−	0.873313i	$-0.661967\pi$
$677$	−25.3510	−0.974320	−0.487160	+	0.873313i	$0.661967\pi$
$678$	37.6213	1.44484
$679$	−49.8998	−1.91498
$680$	98.5710	3.78003
$681$	32.6812	1.25235
$682$	4.30989	0.165034
$683$	−21.7513	−0.832290	−0.416145	−	0.909298i	$-0.636619\pi$
$683$	−21.7513	−0.832290	−0.416145	+	0.909298i	$0.636619\pi$
$684$	−7.58018	−0.289835
$685$	−64.2484	−2.45480
$686$	8.58534	0.327790
$687$	−6.61588	−0.252412
$688$	52.0031	1.98260
$689$	0.152147	0.00579636
$690$	95.0289	3.61769
$691$	17.3051	0.658318	0.329159	−	0.944275i	$-0.393235\pi$
$691$	17.3051	0.658318	0.329159	+	0.944275i	$0.393235\pi$
$692$	35.4741	1.34852
$693$	5.67929	0.215738
$694$	80.7687	3.06594
$695$	−10.3070	−0.390968
$696$	−9.06730	−0.343695
$697$	12.8333	0.486095
$698$	62.4643	2.36431
$699$	32.8578	1.24280
$700$	203.054	7.67470
$701$	−29.6923	−1.12146	−0.560732	−	0.827997i	$-0.689480\pi$
$701$	−29.6923	−1.12146	−0.560732	+	0.827997i	$0.689480\pi$
$702$	−21.1173	−0.797021
$703$	−6.71293	−0.253183
$704$	−8.02543	−0.302470
$705$	−18.1184	−0.682378
$706$	−39.2409	−1.47685
$707$	−39.8116	−1.49727
$708$	76.8112	2.88674
$709$	−21.4898	−0.807067	−0.403534	−	0.914965i	$-0.632218\pi$
$709$	−21.4898	−0.807067	−0.403534	+	0.914965i	$0.632218\pi$
$710$	−67.4359	−2.53082
$711$	−21.4605	−0.804831
$712$	−89.7310	−3.36281
$713$	−12.2997	−0.460627
$714$	36.9806	1.38396
$715$	6.02783	0.225428
$716$	46.1394	1.72431
$717$	1.67845	0.0626828
$718$	−36.8021	−1.37344
$719$	9.61388	0.358537	0.179269	−	0.983800i	$-0.442627\pi$
$719$	9.61388	0.358537	0.179269	+	0.983800i	$0.442627\pi$
$720$	−61.8395	−2.30462
$721$	−18.0622	−0.672671
$722$	−2.61330	−0.0972571
$723$	−24.8403	−0.923821
$724$	29.1036	1.08163
$725$	11.9149	0.442507
$726$	−3.12549	−0.115998
$727$	6.84046	0.253699	0.126849	−	0.991922i	$-0.459514\pi$
$727$	6.84046	0.253699	0.126849	+	0.991922i	$0.459514\pi$
$728$	39.5570	1.46608
$729$	22.4775	0.832501
$730$	14.6767	0.543210
$731$	−17.5965	−0.650828
$732$	−37.5238	−1.38692
$733$	38.2277	1.41197	0.705987	−	0.708225i	$-0.250504\pi$
$733$	38.2277	1.41197	0.705987	+	0.708225i	$0.250504\pi$
$734$	−55.7005	−2.05594
$735$	29.7037	1.09564
$736$	78.0620	2.87740
$737$	3.70989	0.136656
$738$	−16.0978	−0.592567
$739$	−17.7157	−0.651682	−0.325841	−	0.945425i	$-0.605647\pi$
$739$	−17.7157	−0.651682	−0.325841	+	0.945425i	$0.605647\pi$
$740$	−132.166	−4.85853
$741$	−1.76836	−0.0649622
$742$	0.973009	0.0357203
$743$	21.3028	0.781525	0.390763	−	0.920491i	$-0.372211\pi$
$743$	21.3028	0.781525	0.390763	+	0.920491i	$0.372211\pi$
$744$	−14.5842	−0.534682
$745$	7.53808	0.276174
$746$	6.32650	0.231630
$747$	−8.53960	−0.312447
$748$	15.7921	0.577418
$749$	26.4622	0.966908
$750$	−84.3559	−3.08024
$751$	25.1552	0.917926	0.458963	−	0.888455i	$-0.348221\pi$
$751$	25.1552	0.917926	0.458963	+	0.888455i	$0.348221\pi$
$752$	−35.9111	−1.30954
$753$	−1.55402	−0.0566317
$754$	3.96190	0.144284
$755$	−62.4499	−2.27279
$756$	−95.4992	−3.47327
$757$	15.5116	0.563780	0.281890	−	0.959447i	$-0.409039\pi$
$757$	15.5116	0.563780	0.281890	+	0.959447i	$0.409039\pi$
$758$	−23.1940	−0.842443
$759$	8.91962	0.323762
$760$	−30.1438	−1.09343
$761$	35.2085	1.27631	0.638154	−	0.769908i	$-0.279698\pi$
$761$	35.2085	1.27631	0.638154	+	0.769908i	$0.279698\pi$
$762$	14.6802	0.531807
$763$	−5.22779	−0.189259
$764$	85.5129	3.09375
$765$	20.9248	0.756538
$766$	9.25280	0.334317
$767$	−19.6630	−0.709988
$768$	−19.0750	−0.688310
$769$	−5.57667	−0.201100	−0.100550	−	0.994932i	$-0.532060\pi$
$769$	−5.57667	−0.201100	−0.100550	+	0.994932i	$0.532060\pi$
$770$	38.5490	1.38921
$771$	4.08095	0.146972
$772$	17.8371	0.641973
$773$	35.9175	1.29186	0.645931	−	0.763396i	$-0.276469\pi$
$773$	35.9175	1.29186	0.645931	+	0.763396i	$0.276469\pi$
$774$	22.0726	0.793383
$775$	19.1643	0.688403
$776$	101.970	3.66052
$777$	−29.0499	−1.04216
$778$	43.6530	1.56503
$779$	−3.92451	−0.140610
$780$	−34.8160	−1.24661
$781$	−6.32968	−0.226494
$782$	−63.7324	−2.27906
$783$	−5.60375	−0.200262
$784$	58.8734	2.10262
$785$	100.547	3.58866
$786$	−11.7039	−0.417464
$787$	7.53242	0.268502	0.134251	−	0.990947i	$-0.457137\pi$
$787$	7.53242	0.268502	0.134251	+	0.990947i	$0.457137\pi$
$788$	−124.496	−4.43497
$789$	17.0331	0.606395
$790$	−145.666	−5.18257
$791$	−43.5531	−1.54857
$792$	−11.6056	−0.412387
$793$	9.60573	0.341110
$794$	−73.7141	−2.61602
$795$	−0.501731	−0.0177946
$796$	91.2522	3.23435
$797$	−49.3837	−1.74926	−0.874629	−	0.484792i	$-0.838895\pi$
$797$	−49.3837	−1.74926	−0.874629	+	0.484792i	$0.838895\pi$
$798$	−11.3089	−0.400332
$799$	12.1513	0.429883
$800$	−121.629	−4.30025
$801$	−19.0482	−0.673036
$802$	94.6219	3.34122
$803$	1.37759	0.0486141
$804$	−21.4278	−0.755702
$805$	−110.012	−3.87743
$806$	6.37247	0.224461
$807$	6.45210	0.227125
$808$	81.3549	2.86205
$809$	34.4637	1.21168	0.605840	−	0.795587i	$-0.292837\pi$
$809$	34.4637	1.21168	0.605840	+	0.795587i	$0.292837\pi$
$810$	19.4704	0.684120
$811$	20.0278	0.703272	0.351636	−	0.936137i	$-0.385625\pi$
$811$	20.0278	0.703272	0.351636	+	0.936137i	$0.385625\pi$
$812$	17.9170	0.628763
$813$	−13.2306	−0.464017
$814$	−17.5429	−0.614879
$815$	−15.1718	−0.531444
$816$	−37.7952	−1.32310
$817$	5.38113	0.188262
$818$	−96.4926	−3.37379
$819$	8.39722	0.293423
$820$	−77.2670	−2.69828
$821$	6.45245	0.225192	0.112596	−	0.993641i	$-0.464083\pi$
$821$	6.45245	0.225192	0.112596	+	0.993641i	$0.464083\pi$
$822$	49.2562	1.71801
$823$	−43.0190	−1.49955	−0.749774	−	0.661694i	$-0.769838\pi$
$823$	−43.0190	−1.49955	−0.749774	+	0.661694i	$0.769838\pi$
$824$	36.9100	1.28582
$825$	−13.8978	−0.483859
$826$	−125.748	−4.37533
$827$	−43.1557	−1.50067	−0.750335	−	0.661058i	$-0.770108\pi$
$827$	−43.1557	−1.50067	−0.750335	+	0.661058i	$0.770108\pi$
$828$	56.5324	1.96464
$829$	13.4937	0.468656	0.234328	−	0.972158i	$-0.424711\pi$
$829$	13.4937	0.468656	0.234328	+	0.972158i	$0.424711\pi$
$830$	−57.9638	−2.01195
$831$	16.8406	0.584193
$832$	−11.8662	−0.411385
$833$	−19.9212	−0.690228
$834$	7.90191	0.273621
$835$	10.7937	0.373530
$836$	−4.82936	−0.167027
$837$	−9.01329	−0.311545
$838$	−47.2197	−1.63118
$839$	−14.6851	−0.506988	−0.253494	−	0.967337i	$-0.581580\pi$
$839$	−14.6851	−0.506988	−0.253494	+	0.967337i	$0.581580\pi$
$840$	−130.446	−4.50080
$841$	−27.9487	−0.963747
$842$	22.4124	0.772384
$843$	−12.9405	−0.445693
$844$	−49.2562	−1.69547
$845$	−44.0858	−1.51660
$846$	−15.2424	−0.524043
$847$	3.61829	0.124326
$848$	−0.994441	−0.0341493
$849$	2.28372	0.0783769
$850$	99.3023	3.40604
$851$	50.0645	1.71619
$852$	36.5594	1.25250
$853$	−51.5775	−1.76598	−0.882990	−	0.469392i	$-0.844473\pi$
$853$	−51.5775	−1.76598	−0.882990	+	0.469392i	$0.844473\pi$
$854$	61.4303	2.10210
$855$	−6.39896	−0.218840
$856$	−54.0755	−1.84826
$857$	−46.6355	−1.59304	−0.796520	−	0.604612i	$-0.793328\pi$
$857$	−46.6355	−1.59304	−0.796520	+	0.604612i	$0.793328\pi$
$858$	−4.62125	−0.157767
$859$	−18.6711	−0.637048	−0.318524	−	0.947915i	$-0.603187\pi$
$859$	−18.6711	−0.637048	−0.318524	+	0.947915i	$0.603187\pi$
$860$	105.945	3.61271
$861$	−16.9831	−0.578783
$862$	−11.1888	−0.381091
$863$	43.0160	1.46428	0.732141	−	0.681153i	$-0.238521\pi$
$863$	43.0160	1.46428	0.732141	+	0.681153i	$0.238521\pi$
$864$	57.2042	1.94613
$865$	29.9462	1.01820
$866$	−47.5712	−1.61654
$867$	−7.54300	−0.256174
$868$	28.8184	0.978160
$869$	−13.6725	−0.463809
$870$	−13.0650	−0.442945
$871$	5.48533	0.185863
$872$	10.6830	0.361771
$873$	21.6464	0.732619
$874$	19.4898	0.659253
$875$	97.6565	3.30139
$876$	−7.95678	−0.268835
$877$	56.0429	1.89243	0.946217	−	0.323534i	$-0.104871\pi$
$877$	56.0429	1.89243	0.946217	+	0.323534i	$0.104871\pi$
$878$	−76.9466	−2.59682
$879$	4.34803	0.146655
$880$	−39.3981	−1.32811
$881$	17.9947	0.606257	0.303128	−	0.952950i	$-0.401969\pi$
$881$	17.9947	0.606257	0.303128	+	0.952950i	$0.401969\pi$
$882$	24.9887	0.841412
$883$	1.99550	0.0671540	0.0335770	−	0.999436i	$-0.489310\pi$
$883$	1.99550	0.0671540	0.0335770	+	0.999436i	$0.489310\pi$
$884$	23.3498	0.785339
$885$	64.8418	2.17963
$886$	63.6687	2.13899
$887$	7.20927	0.242063	0.121032	−	0.992649i	$-0.461380\pi$
$887$	7.20927	0.242063	0.121032	+	0.992649i	$0.461380\pi$
$888$	59.3633	1.99210
$889$	−16.9948	−0.569988
$890$	−129.293	−4.33390
$891$	1.82753	0.0612246
$892$	−1.26867	−0.0424782
$893$	−3.71597	−0.124350
$894$	−5.77909	−0.193282
$895$	38.9495	1.30194
$896$	−0.140902	−0.00470720
$897$	13.1883	0.440344
$898$	−101.338	−3.38168
$899$	1.69102	0.0563986
$900$	−88.0840	−2.93613
$901$	0.336492	0.0112102
$902$	−10.2559	−0.341485
$903$	23.2866	0.774928
$904$	89.0006	2.96012
$905$	24.5684	0.816680
$906$	47.8774	1.59062
$907$	−25.7832	−0.856116	−0.428058	−	0.903751i	$-0.640802\pi$
$907$	−25.7832	−0.856116	−0.428058	+	0.903751i	$0.640802\pi$
$908$	131.965	4.37942
$909$	17.2701	0.572814
$910$	56.9974	1.88945
$911$	31.1334	1.03149	0.515747	−	0.856741i	$-0.327514\pi$
$911$	31.1334	1.03149	0.515747	+	0.856741i	$0.327514\pi$
$912$	11.5580	0.382725
$913$	−5.44061	−0.180058
$914$	19.5389	0.646291
$915$	−31.6764	−1.04719
$916$	−26.7146	−0.882676
$917$	13.5493	0.447437
$918$	−46.7034	−1.54144
$919$	5.42725	0.179029	0.0895143	−	0.995986i	$-0.471469\pi$
$919$	5.42725	0.179029	0.0895143	+	0.995986i	$0.471469\pi$
$920$	224.810	7.41176
$921$	−28.1452	−0.927416
$922$	−41.7560	−1.37516
$923$	−9.35887	−0.308051
$924$	−20.8988	−0.687520
$925$	−78.0063	−2.56483
$926$	15.9469	0.524049
$927$	7.83531	0.257345
$928$	−10.7323	−0.352305
$929$	−21.6025	−0.708756	−0.354378	−	0.935102i	$-0.615307\pi$
$929$	−21.6025	−0.708756	−0.354378	+	0.935102i	$0.615307\pi$
$930$	−21.0143	−0.689085
$931$	6.09205	0.199659
$932$	132.678	4.34603
$933$	−19.1390	−0.626583
$934$	69.6113	2.27775
$935$	13.3313	0.435979
$936$	−17.1597	−0.560882
$937$	31.6840	1.03507	0.517536	−	0.855661i	$-0.326849\pi$
$937$	31.6840	1.03507	0.517536	+	0.855661i	$0.326849\pi$
$938$	35.0796	1.14539
$939$	19.1399	0.624608
$940$	−73.1612	−2.38626
$941$	−5.63987	−0.183854	−0.0919272	−	0.995766i	$-0.529303\pi$
$941$	−5.63987	−0.183854	−0.0919272	+	0.995766i	$0.529303\pi$
$942$	−77.0843	−2.51154
$943$	29.2687	0.953120
$944$	128.518	4.18290
$945$	−80.6176	−2.62249
$946$	14.0625	0.457212
$947$	−51.7369	−1.68122	−0.840611	−	0.541639i	$-0.817804\pi$
$947$	−51.7369	−1.68122	−0.840611	+	0.541639i	$0.817804\pi$
$948$	78.9709	2.56486
$949$	2.03686	0.0661194
$950$	−30.3674	−0.985248
$951$	−24.9682	−0.809650
$952$	87.4850	2.83540
$953$	−16.2553	−0.526561	−0.263281	−	0.964719i	$-0.584804\pi$
$953$	−16.2553	−0.526561	−0.263281	+	0.964719i	$0.584804\pi$
$954$	−0.422088	−0.0136656
$955$	72.1874	2.33593
$956$	6.77750	0.219200
$957$	−1.22631	−0.0396410
$958$	42.3601	1.36859
$959$	−57.0225	−1.84135
$960$	39.1306	1.26293
$961$	−28.2801	−0.912261
$962$	−25.9384	−0.836289
$963$	−11.4792	−0.369913
$964$	−100.304	−3.23057
$965$	15.0576	0.484721
$966$	84.3413	2.71364
$967$	−54.5004	−1.75261	−0.876307	−	0.481754i	$-0.840000\pi$
$967$	−54.5004	−1.75261	−0.876307	+	0.481754i	$0.840000\pi$
$968$	−7.39397	−0.237651
$969$	−3.91093	−0.125637
$970$	146.928	4.71758
$971$	−34.2679	−1.09971	−0.549855	−	0.835260i	$-0.685317\pi$
$971$	−34.2679	−1.09971	−0.549855	+	0.835260i	$0.685317\pi$
$972$	68.6247	2.20114
$973$	−9.14783	−0.293266
$974$	12.6078	0.403981
$975$	−20.5488	−0.658090
$976$	−62.7834	−2.00965
$977$	55.5644	1.77766	0.888831	−	0.458234i	$-0.151518\pi$
$977$	55.5644	1.77766	0.888831	+	0.458234i	$0.151518\pi$
$978$	11.6315	0.371934
$979$	−12.1357	−0.387858
$980$	119.942	3.83141
$981$	2.26780	0.0724052
$982$	22.3066	0.711832
$983$	−41.3971	−1.32036	−0.660181	−	0.751106i	$-0.729521\pi$
$983$	−41.3971	−1.32036	−0.660181	+	0.751106i	$0.729521\pi$
$984$	34.7049	1.10635
$985$	−105.095	−3.34862
$986$	8.76221	0.279046
$987$	−16.0807	−0.511853
$988$	−7.14054	−0.227171
$989$	−40.1321	−1.27613
$990$	−16.7224	−0.531474
$991$	60.8219	1.93207	0.966036	−	0.258406i	$-0.0831973\pi$
$991$	60.8219	1.93207	0.966036	+	0.258406i	$0.0831973\pi$
$992$	−17.2623	−0.548077
$993$	18.0758	0.573618
$994$	−59.8515	−1.89837
$995$	77.0324	2.44209
$996$	31.4242	0.995715
$997$	26.0627	0.825414	0.412707	−	0.910864i	$-0.364583\pi$
$997$	26.0627	0.825414	0.412707	+	0.910864i	$0.364583\pi$
$998$	35.1031	1.11117
$999$	36.6876	1.16074

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	209.2.a.d.1.2	✓	7
3.2	odd	2		1881.2.a.p.1.6		7
4.3	odd	2		3344.2.a.ba.1.4		7
5.4	even	2		5225.2.a.n.1.6		7
11.10	odd	2		2299.2.a.q.1.6		7
19.18	odd	2		3971.2.a.i.1.6		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
209.2.a.d.1.2	✓	7	1.1	even	1	trivial
1881.2.a.p.1.6		7	3.2	odd	2
2299.2.a.q.1.6		7	11.10	odd	2
3344.2.a.ba.1.4		7	4.3	odd	2
3971.2.a.i.1.6		7	19.18	odd	2
5225.2.a.n.1.6		7	5.4	even	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:	\( N \)	\(=\)	\( 209 = 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	209.a (trivial)

\(f(q)\)	\(=\)	\(q-2.61330 q^{2} +1.19599 q^{3} +4.82936 q^{4} +4.07680 q^{5} -3.12549 q^{6} +3.61829 q^{7} -7.39397 q^{8} -1.56960 q^{9} +O(q^{10})\)	\(q-2.61330 q^{2} +1.19599 q^{3} +4.82936 q^{4} +4.07680 q^{5} -3.12549 q^{6} +3.61829 q^{7} -7.39397 q^{8} -1.56960 q^{9} -10.6539 q^{10} -1.00000 q^{11} +5.77587 q^{12} -1.47857 q^{13} -9.45570 q^{14} +4.87582 q^{15} +9.66398 q^{16} -3.27003 q^{17} +4.10185 q^{18} +1.00000 q^{19} +19.6883 q^{20} +4.32745 q^{21} +2.61330 q^{22} -7.45793 q^{23} -8.84313 q^{24} +11.6203 q^{25} +3.86395 q^{26} -5.46521 q^{27} +17.4740 q^{28} +1.02535 q^{29} -12.7420 q^{30} +1.64921 q^{31} -10.4670 q^{32} -1.19599 q^{33} +8.54558 q^{34} +14.7511 q^{35} -7.58018 q^{36} -6.71293 q^{37} -2.61330 q^{38} -1.76836 q^{39} -30.1438 q^{40} -3.92451 q^{41} -11.3089 q^{42} +5.38113 q^{43} -4.82936 q^{44} -6.39896 q^{45} +19.4898 q^{46} -3.71597 q^{47} +11.5580 q^{48} +6.09205 q^{49} -30.3674 q^{50} -3.91093 q^{51} -7.14054 q^{52} -0.102902 q^{53} +14.2823 q^{54} -4.07680 q^{55} -26.7536 q^{56} +1.19599 q^{57} -2.67955 q^{58} +13.2986 q^{59} +23.5471 q^{60} -6.49664 q^{61} -4.30989 q^{62} -5.67929 q^{63} +8.02543 q^{64} -6.02783 q^{65} +3.12549 q^{66} -3.70989 q^{67} -15.7921 q^{68} -8.91962 q^{69} -38.5490 q^{70} +6.32968 q^{71} +11.6056 q^{72} -1.37759 q^{73} +17.5429 q^{74} +13.8978 q^{75} +4.82936 q^{76} -3.61829 q^{77} +4.62125 q^{78} +13.6725 q^{79} +39.3981 q^{80} -1.82753 q^{81} +10.2559 q^{82} +5.44061 q^{83} +20.8988 q^{84} -13.3313 q^{85} -14.0625 q^{86} +1.22631 q^{87} +7.39397 q^{88} +12.1357 q^{89} +16.7224 q^{90} -5.34990 q^{91} -36.0170 q^{92} +1.97244 q^{93} +9.71096 q^{94} +4.07680 q^{95} -12.5184 q^{96} -13.7910 q^{97} -15.9204 q^{98} +1.56960 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - q^{2} + 2 q^{3} + 15 q^{4} + 2 q^{5} - 2 q^{6} + 10 q^{7} - 9 q^{8} + 11 q^{9}+O(q^{10}) \) 7 * q - q^2 + 2 * q^3 + 15 * q^4 + 2 * q^5 - 2 * q^6 + 10 * q^7 - 9 * q^8 + 11 * q^9	\( 7 q - q^{2} + 2 q^{3} + 15 q^{4} + 2 q^{5} - 2 q^{6} + 10 q^{7} - 9 q^{8} + 11 q^{9} - 6 q^{10} - 7 q^{11} - 16 q^{12} - 4 q^{13} + 6 q^{14} + 12 q^{15} + 27 q^{16} + 2 q^{17} + 9 q^{18} + 7 q^{19} - 4 q^{20} - 14 q^{21} + q^{22} + 10 q^{23} - 2 q^{24} + 9 q^{25} - 8 q^{26} - 4 q^{27} + 26 q^{28} - 18 q^{29} - 42 q^{30} + 24 q^{31} - 49 q^{32} - 2 q^{33} - 6 q^{34} + 8 q^{35} + 29 q^{36} - q^{38} + 24 q^{39} - 2 q^{40} - 12 q^{41} - 44 q^{42} + 2 q^{43} - 15 q^{44} - 4 q^{45} - 4 q^{46} + 8 q^{47} - 72 q^{48} + 17 q^{49} - 33 q^{50} - 24 q^{51} - 60 q^{52} + 2 q^{53} - 52 q^{54} - 2 q^{55} + 26 q^{56} + 2 q^{57} - 8 q^{58} - 10 q^{59} + 42 q^{60} + 14 q^{61} + 14 q^{62} + 55 q^{64} - 14 q^{65} + 2 q^{66} + 8 q^{67} - 18 q^{68} - 6 q^{69} - 66 q^{70} + 10 q^{71} + 53 q^{72} - 6 q^{73} + 26 q^{74} + 26 q^{75} + 15 q^{76} - 10 q^{77} + 22 q^{78} + 52 q^{79} - 12 q^{80} - q^{81} + 24 q^{82} - 10 q^{83} - 6 q^{84} - 12 q^{85} + 8 q^{86} + 6 q^{87} + 9 q^{88} + 20 q^{90} + 12 q^{91} + 2 q^{93} + 24 q^{94} + 2 q^{95} + 6 q^{96} - 24 q^{97} + 19 q^{98} - 11 q^{99}+O(q^{100}) \) 7 * q - q^2 + 2 * q^3 + 15 * q^4 + 2 * q^5 - 2 * q^6 + 10 * q^7 - 9 * q^8 + 11 * q^9 - 6 * q^10 - 7 * q^11 - 16 * q^12 - 4 * q^13 + 6 * q^14 + 12 * q^15 + 27 * q^16 + 2 * q^17 + 9 * q^18 + 7 * q^19 - 4 * q^20 - 14 * q^21 + q^22 + 10 * q^23 - 2 * q^24 + 9 * q^25 - 8 * q^26 - 4 * q^27 + 26 * q^28 - 18 * q^29 - 42 * q^30 + 24 * q^31 - 49 * q^32 - 2 * q^33 - 6 * q^34 + 8 * q^35 + 29 * q^36 - q^38 + 24 * q^39 - 2 * q^40 - 12 * q^41 - 44 * q^42 + 2 * q^43 - 15 * q^44 - 4 * q^45 - 4 * q^46 + 8 * q^47 - 72 * q^48 + 17 * q^49 - 33 * q^50 - 24 * q^51 - 60 * q^52 + 2 * q^53 - 52 * q^54 - 2 * q^55 + 26 * q^56 + 2 * q^57 - 8 * q^58 - 10 * q^59 + 42 * q^60 + 14 * q^61 + 14 * q^62 + 55 * q^64 - 14 * q^65 + 2 * q^66 + 8 * q^67 - 18 * q^68 - 6 * q^69 - 66 * q^70 + 10 * q^71 + 53 * q^72 - 6 * q^73 + 26 * q^74 + 26 * q^75 + 15 * q^76 - 10 * q^77 + 22 * q^78 + 52 * q^79 - 12 * q^80 - q^81 + 24 * q^82 - 10 * q^83 - 6 * q^84 - 12 * q^85 + 8 * q^86 + 6 * q^87 + 9 * q^88 + 20 * q^90 + 12 * q^91 + 2 * q^93 + 24 * q^94 + 2 * q^95 + 6 * q^96 - 24 * q^97 + 19 * q^98 - 11 * q^99

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