LMFDB - Embedded newform 1502.2.a.h.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1502,2,Mod(1,1502)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1502, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1502.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1502 = 2 \cdot 751 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1502.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:	$11.9935303836$
Analytic rank:	$0$
Dimension:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - 6 x^{18} - 23 x^{17} + 190 x^{16} + 128 x^{15} - 2394 x^{14} + 749 x^{13} + 15539 x^{12} + \cdots + 4222 $ x^19 - 6x^18 - 23x^17 + 190x^16 + 128x^15 - 2394x^14 + 749x^13 + 15539x^12 - 11338x^11 - 56744x^10 + 50183x^9 + 120237x^8 - 102992x^7 - 148539x^6 + 99519x^5 + 104388x^4 - 41081x^3 - 35733x^2 + 5542x + 4222
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Root			$3.41483$ of defining polynomial
Character	$\chi$	$=$	1502.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +3.41483 q^{3} +1.00000 q^{4} +1.24390 q^{5} -3.41483 q^{6} +3.09855 q^{7} -1.00000 q^{8} +8.66107 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +3.41483 q^{3} +1.00000 q^{4} +1.24390 q^{5} -3.41483 q^{6} +3.09855 q^{7} -1.00000 q^{8} +8.66107 q^{9} -1.24390 q^{10} -0.904638 q^{11} +3.41483 q^{12} -5.39604 q^{13} -3.09855 q^{14} +4.24772 q^{15} +1.00000 q^{16} -0.870030 q^{17} -8.66107 q^{18} -3.19528 q^{19} +1.24390 q^{20} +10.5810 q^{21} +0.904638 q^{22} +8.26173 q^{23} -3.41483 q^{24} -3.45271 q^{25} +5.39604 q^{26} +19.3316 q^{27} +3.09855 q^{28} -4.98170 q^{29} -4.24772 q^{30} +9.63616 q^{31} -1.00000 q^{32} -3.08918 q^{33} +0.870030 q^{34} +3.85430 q^{35} +8.66107 q^{36} -2.39269 q^{37} +3.19528 q^{38} -18.4266 q^{39} -1.24390 q^{40} +1.85762 q^{41} -10.5810 q^{42} -2.07034 q^{43} -0.904638 q^{44} +10.7735 q^{45} -8.26173 q^{46} -5.19288 q^{47} +3.41483 q^{48} +2.60103 q^{49} +3.45271 q^{50} -2.97101 q^{51} -5.39604 q^{52} -9.37920 q^{53} -19.3316 q^{54} -1.12528 q^{55} -3.09855 q^{56} -10.9113 q^{57} +4.98170 q^{58} +7.32378 q^{59} +4.24772 q^{60} -0.973323 q^{61} -9.63616 q^{62} +26.8368 q^{63} +1.00000 q^{64} -6.71215 q^{65} +3.08918 q^{66} +10.5286 q^{67} -0.870030 q^{68} +28.2124 q^{69} -3.85430 q^{70} -11.5385 q^{71} -8.66107 q^{72} +5.80679 q^{73} +2.39269 q^{74} -11.7904 q^{75} -3.19528 q^{76} -2.80307 q^{77} +18.4266 q^{78} -1.73998 q^{79} +1.24390 q^{80} +40.0309 q^{81} -1.85762 q^{82} -15.3378 q^{83} +10.5810 q^{84} -1.08223 q^{85} +2.07034 q^{86} -17.0117 q^{87} +0.904638 q^{88} -13.3012 q^{89} -10.7735 q^{90} -16.7199 q^{91} +8.26173 q^{92} +32.9058 q^{93} +5.19288 q^{94} -3.97462 q^{95} -3.41483 q^{96} -0.715847 q^{97} -2.60103 q^{98} -7.83513 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q - 19 q^{2} + 6 q^{3} + 19 q^{4} + 2 q^{5} - 6 q^{6} + 13 q^{7} - 19 q^{8} + 25 q^{9}+O(q^{10}) $ 19 * q - 19 * q^2 + 6 * q^3 + 19 * q^4 + 2 * q^5 - 6 * q^6 + 13 * q^7 - 19 * q^8 + 25 * q^9	\( 19 q - 19 q^{2} + 6 q^{3} + 19 q^{4} + 2 q^{5} - 6 q^{6} + 13 q^{7} - 19 q^{8} + 25 q^{9} - 2 q^{10} - 7 q^{11} + 6 q^{12} + 19 q^{13} - 13 q^{14} + 6 q^{15} + 19 q^{16} + 11 q^{17} - 25 q^{18} + 7 q^{19} + 2 q^{20} + 7 q^{21} + 7 q^{22} + 12 q^{23} - 6 q^{24} + 37 q^{25} - 19 q^{26} + 24 q^{27} + 13 q^{28} - 8 q^{29} - 6 q^{30} + 32 q^{31} - 19 q^{32} + 24 q^{33} - 11 q^{34} - 19 q^{35} + 25 q^{36} + 41 q^{37} - 7 q^{38} - 2 q^{39} - 2 q^{40} + 15 q^{41} - 7 q^{42} + 15 q^{43} - 7 q^{44} + 28 q^{45} - 12 q^{46} - 6 q^{47} + 6 q^{48} + 42 q^{49} - 37 q^{50} + 8 q^{51} + 19 q^{52} + 6 q^{53} - 24 q^{54} + 22 q^{55} - 13 q^{56} + 24 q^{57} + 8 q^{58} - 4 q^{59} + 6 q^{60} + 13 q^{61} - 32 q^{62} + 37 q^{63} + 19 q^{64} + 20 q^{65} - 24 q^{66} + 47 q^{67} + 11 q^{68} + 15 q^{69} + 19 q^{70} - 25 q^{72} + 64 q^{73} - 41 q^{74} - 3 q^{75} + 7 q^{76} - 4 q^{77} + 2 q^{78} + 34 q^{79} + 2 q^{80} + 27 q^{81} - 15 q^{82} + 4 q^{83} + 7 q^{84} + 21 q^{85} - 15 q^{86} + 7 q^{88} + 18 q^{89} - 28 q^{90} + 28 q^{91} + 12 q^{92} + 43 q^{93} + 6 q^{94} - 8 q^{95} - 6 q^{96} + 82 q^{97} - 42 q^{98} - 2 q^{99}+O(q^{100}) \) 19 * q - 19 * q^2 + 6 * q^3 + 19 * q^4 + 2 * q^5 - 6 * q^6 + 13 * q^7 - 19 * q^8 + 25 * q^9 - 2 * q^10 - 7 * q^11 + 6 * q^12 + 19 * q^13 - 13 * q^14 + 6 * q^15 + 19 * q^16 + 11 * q^17 - 25 * q^18 + 7 * q^19 + 2 * q^20 + 7 * q^21 + 7 * q^22 + 12 * q^23 - 6 * q^24 + 37 * q^25 - 19 * q^26 + 24 * q^27 + 13 * q^28 - 8 * q^29 - 6 * q^30 + 32 * q^31 - 19 * q^32 + 24 * q^33 - 11 * q^34 - 19 * q^35 + 25 * q^36 + 41 * q^37 - 7 * q^38 - 2 * q^39 - 2 * q^40 + 15 * q^41 - 7 * q^42 + 15 * q^43 - 7 * q^44 + 28 * q^45 - 12 * q^46 - 6 * q^47 + 6 * q^48 + 42 * q^49 - 37 * q^50 + 8 * q^51 + 19 * q^52 + 6 * q^53 - 24 * q^54 + 22 * q^55 - 13 * q^56 + 24 * q^57 + 8 * q^58 - 4 * q^59 + 6 * q^60 + 13 * q^61 - 32 * q^62 + 37 * q^63 + 19 * q^64 + 20 * q^65 - 24 * q^66 + 47 * q^67 + 11 * q^68 + 15 * q^69 + 19 * q^70 - 25 * q^72 + 64 * q^73 - 41 * q^74 - 3 * q^75 + 7 * q^76 - 4 * q^77 + 2 * q^78 + 34 * q^79 + 2 * q^80 + 27 * q^81 - 15 * q^82 + 4 * q^83 + 7 * q^84 + 21 * q^85 - 15 * q^86 + 7 * q^88 + 18 * q^89 - 28 * q^90 + 28 * q^91 + 12 * q^92 + 43 * q^93 + 6 * q^94 - 8 * q^95 - 6 * q^96 + 82 * q^97 - 42 * q^98 - 2 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	3.41483	1.97155	0.985777	−	0.168061i	$-0.0537506\pi$
$3$	3.41483	1.97155	0.985777	+	0.168061i	$0.0537506\pi$
$4$	1.00000	0.500000
$5$	1.24390	0.556290	0.278145	−	0.960539i	$-0.410280\pi$
$5$	1.24390	0.556290	0.278145	+	0.960539i	$0.410280\pi$
$6$	−3.41483	−1.39410
$7$	3.09855	1.17114	0.585572	−	0.810621i	$-0.300870\pi$
$7$	3.09855	1.17114	0.585572	+	0.810621i	$0.300870\pi$
$8$	−1.00000	−0.353553
$9$	8.66107	2.88702
$10$	−1.24390	−0.393357
$11$	−0.904638	−0.272759	−0.136379	−	0.990657i	$-0.543547\pi$
$11$	−0.904638	−0.272759	−0.136379	+	0.990657i	$0.543547\pi$
$12$	3.41483	0.985777
$13$	−5.39604	−1.49659	−0.748296	−	0.663365i	$-0.769128\pi$
$13$	−5.39604	−1.49659	−0.748296	+	0.663365i	$0.769128\pi$
$14$	−3.09855	−0.828123
$15$	4.24772	1.09676
$16$	1.00000	0.250000
$17$	−0.870030	−0.211013	−0.105507	−	0.994419i	$-0.533646\pi$
$17$	−0.870030	−0.211013	−0.105507	+	0.994419i	$0.533646\pi$
$18$	−8.66107	−2.04143
$19$	−3.19528	−0.733048	−0.366524	−	0.930409i	$-0.619452\pi$
$19$	−3.19528	−0.733048	−0.366524	+	0.930409i	$0.619452\pi$
$20$	1.24390	0.278145
$21$	10.5810	2.30897
$22$	0.904638	0.192869
$23$	8.26173	1.72269	0.861345	−	0.508020i	$-0.169622\pi$
$23$	8.26173	1.72269	0.861345	+	0.508020i	$0.169622\pi$
$24$	−3.41483	−0.697049
$25$	−3.45271	−0.690541
$26$	5.39604	1.05825
$27$	19.3316	3.72036
$28$	3.09855	0.585572
$29$	−4.98170	−0.925079	−0.462539	−	0.886599i	$-0.653062\pi$
$29$	−4.98170	−0.925079	−0.462539	+	0.886599i	$0.653062\pi$
$30$	−4.24772	−0.775523
$31$	9.63616	1.73070	0.865352	−	0.501164i	$-0.167095\pi$
$31$	9.63616	1.73070	0.865352	+	0.501164i	$0.167095\pi$
$32$	−1.00000	−0.176777
$33$	−3.08918	−0.537758
$34$	0.870030	0.149209
$35$	3.85430	0.651495
$36$	8.66107	1.44351
$37$	−2.39269	−0.393355	−0.196678	−	0.980468i	$-0.563015\pi$
$37$	−2.39269	−0.393355	−0.196678	+	0.980468i	$0.563015\pi$
$38$	3.19528	0.518343
$39$	−18.4266	−2.95061
$40$	−1.24390	−0.196678
$41$	1.85762	0.290112	0.145056	−	0.989423i	$-0.453664\pi$
$41$	1.85762	0.290112	0.145056	+	0.989423i	$0.453664\pi$
$42$	−10.5810	−1.63269
$43$	−2.07034	−0.315725	−0.157862	−	0.987461i	$-0.550460\pi$
$43$	−2.07034	−0.315725	−0.157862	+	0.987461i	$0.550460\pi$
$44$	−0.904638	−0.136379
$45$	10.7735	1.60602
$46$	−8.26173	−1.21813
$47$	−5.19288	−0.757459	−0.378730	−	0.925507i	$-0.623639\pi$
$47$	−5.19288	−0.757459	−0.378730	+	0.925507i	$0.623639\pi$
$48$	3.41483	0.492888
$49$	2.60103	0.371576
$50$	3.45271	0.488286
$51$	−2.97101	−0.416024
$52$	−5.39604	−0.748296
$53$	−9.37920	−1.28833	−0.644166	−	0.764885i	$-0.722796\pi$
$53$	−9.37920	−1.28833	−0.644166	+	0.764885i	$0.722796\pi$
$54$	−19.3316	−2.63069
$55$	−1.12528	−0.151733
$56$	−3.09855	−0.414062
$57$	−10.9113	−1.44524
$58$	4.98170	0.654129
$59$	7.32378	0.953475	0.476737	−	0.879046i	$-0.341819\pi$
$59$	7.32378	0.953475	0.476737	+	0.879046i	$0.341819\pi$
$60$	4.24772	0.548378
$61$	−0.973323	−0.124621	−0.0623106	−	0.998057i	$-0.519847\pi$
$61$	−0.973323	−0.124621	−0.0623106	+	0.998057i	$0.519847\pi$
$62$	−9.63616	−1.22379
$63$	26.8368	3.38112
$64$	1.00000	0.125000
$65$	−6.71215	−0.832539
$66$	3.08918	0.380252
$67$	10.5286	1.28627	0.643135	−	0.765753i	$-0.277633\pi$
$67$	10.5286	1.28627	0.643135	+	0.765753i	$0.277633\pi$
$68$	−0.870030	−0.105507
$69$	28.2124	3.39638
$70$	−3.85430	−0.460677
$71$	−11.5385	−1.36936	−0.684681	−	0.728842i	$-0.740059\pi$
$71$	−11.5385	−1.36936	−0.684681	+	0.728842i	$0.740059\pi$
$72$	−8.66107	−1.02072
$73$	5.80679	0.679633	0.339816	−	0.940492i	$-0.389635\pi$
$73$	5.80679	0.679633	0.339816	+	0.940492i	$0.389635\pi$
$74$	2.39269	0.278144
$75$	−11.7904	−1.36144
$76$	−3.19528	−0.366524
$77$	−2.80307	−0.319439
$78$	18.4266	2.08640
$79$	−1.73998	−0.195763	−0.0978817	−	0.995198i	$-0.531207\pi$
$79$	−1.73998	−0.195763	−0.0978817	+	0.995198i	$0.531207\pi$
$80$	1.24390	0.139073
$81$	40.0309	4.44787
$82$	−1.85762	−0.205140
$83$	−15.3378	−1.68354	−0.841770	−	0.539837i	$-0.818486\pi$
$83$	−15.3378	−1.68354	−0.841770	+	0.539837i	$0.818486\pi$
$84$	10.5810	1.15449
$85$	−1.08223	−0.117385
$86$	2.07034	0.223251
$87$	−17.0117	−1.82384
$88$	0.904638	0.0964347
$89$	−13.3012	−1.40993	−0.704963	−	0.709244i	$-0.749036\pi$
$89$	−13.3012	−1.40993	−0.704963	+	0.709244i	$0.749036\pi$
$90$	−10.7735	−1.13563
$91$	−16.7199	−1.75272
$92$	8.26173	0.861345
$93$	32.9058	3.41218
$94$	5.19288	0.535605
$95$	−3.97462	−0.407787
$96$	−3.41483	−0.348525
$97$	−0.715847	−0.0726833	−0.0363416	−	0.999339i	$-0.511570\pi$
$97$	−0.715847	−0.0726833	−0.0363416	+	0.999339i	$0.511570\pi$
$98$	−2.60103	−0.262744
$99$	−7.83513	−0.787460
$100$	−3.45271	−0.345271
$101$	−10.6797	−1.06267	−0.531337	−	0.847161i	$-0.678310\pi$
$101$	−10.6797	−1.06267	−0.531337	+	0.847161i	$0.678310\pi$
$102$	2.97101	0.294173
$103$	13.2393	1.30451	0.652255	−	0.757999i	$-0.273823\pi$
$103$	13.2393	1.30451	0.652255	+	0.757999i	$0.273823\pi$
$104$	5.39604	0.529125
$105$	13.1618	1.28446
$106$	9.37920	0.910989
$107$	3.86877	0.374008	0.187004	−	0.982359i	$-0.440122\pi$
$107$	3.86877	0.374008	0.187004	+	0.982359i	$0.440122\pi$
$108$	19.3316	1.86018
$109$	6.75692	0.647196	0.323598	−	0.946195i	$-0.395107\pi$
$109$	6.75692	0.647196	0.323598	+	0.946195i	$0.395107\pi$
$110$	1.12528	0.107291
$111$	−8.17062	−0.775521
$112$	3.09855	0.292786
$113$	−9.25477	−0.870616	−0.435308	−	0.900282i	$-0.643360\pi$
$113$	−9.25477	−0.870616	−0.435308	+	0.900282i	$0.643360\pi$
$114$	10.9113	1.02194
$115$	10.2768	0.958316
$116$	−4.98170	−0.462539
$117$	−46.7354	−4.32069
$118$	−7.32378	−0.674208
$119$	−2.69584	−0.247127
$120$	−4.24772	−0.387762
$121$	−10.1816	−0.925603
$122$	0.973323	0.0881205
$123$	6.34346	0.571971
$124$	9.63616	0.865352
$125$	−10.5143	−0.940432
$126$	−26.8368	−2.39081
$127$	−11.0551	−0.980981	−0.490491	−	0.871446i	$-0.663182\pi$
$127$	−11.0551	−0.980981	−0.490491	+	0.871446i	$0.663182\pi$
$128$	−1.00000	−0.0883883
$129$	−7.06988	−0.622468
$130$	6.71215	0.588694
$131$	−6.84521	−0.598068	−0.299034	−	0.954242i	$-0.596664\pi$
$131$	−6.84521	−0.598068	−0.299034	+	0.954242i	$0.596664\pi$
$132$	−3.08918	−0.268879
$133$	−9.90075	−0.858504
$134$	−10.5286	−0.909530
$135$	24.0466	2.06960
$136$	0.870030	0.0746045
$137$	8.04294	0.687154	0.343577	−	0.939124i	$-0.388361\pi$
$137$	8.04294	0.687154	0.343577	+	0.939124i	$0.388361\pi$
$138$	−28.2124	−2.40160
$139$	7.30936	0.619972	0.309986	−	0.950741i	$-0.399676\pi$
$139$	7.30936	0.619972	0.309986	+	0.950741i	$0.399676\pi$
$140$	3.85430	0.325748
$141$	−17.7328	−1.49337
$142$	11.5385	0.968286
$143$	4.88146	0.408208
$144$	8.66107	0.721755
$145$	−6.19675	−0.514612
$146$	−5.80679	−0.480573
$147$	8.88209	0.732582
$148$	−2.39269	−0.196678
$149$	−3.77239	−0.309046	−0.154523	−	0.987989i	$-0.549384\pi$
$149$	−3.77239	−0.309046	−0.154523	+	0.987989i	$0.549384\pi$
$150$	11.7904	0.962682
$151$	23.6880	1.92770	0.963852	−	0.266437i	$-0.0858463\pi$
$151$	23.6880	1.92770	0.963852	+	0.266437i	$0.0858463\pi$
$152$	3.19528	0.259171
$153$	−7.53539	−0.609200
$154$	2.80307	0.225878
$155$	11.9864	0.962774
$156$	−18.4266	−1.47530
$157$	−9.78526	−0.780948	−0.390474	−	0.920614i	$-0.627689\pi$
$157$	−9.78526	−0.780948	−0.390474	+	0.920614i	$0.627689\pi$
$158$	1.73998	0.138426
$159$	−32.0284	−2.54002
$160$	−1.24390	−0.0983391
$161$	25.5994	2.01752
$162$	−40.0309	−3.14512
$163$	21.1432	1.65606	0.828030	−	0.560684i	$-0.189462\pi$
$163$	21.1432	1.65606	0.828030	+	0.560684i	$0.189462\pi$
$164$	1.85762	0.145056
$165$	−3.84265	−0.299150
$166$	15.3378	1.19044
$167$	10.9803	0.849684	0.424842	−	0.905267i	$-0.360330\pi$
$167$	10.9803	0.849684	0.424842	+	0.905267i	$0.360330\pi$
$168$	−10.5810	−0.816344
$169$	16.1172	1.23979
$170$	1.08223	0.0830035
$171$	−27.6745	−2.11632
$172$	−2.07034	−0.157862
$173$	−6.06140	−0.460840	−0.230420	−	0.973091i	$-0.574010\pi$
$173$	−6.06140	−0.460840	−0.230420	+	0.973091i	$0.574010\pi$
$174$	17.0117	1.28965
$175$	−10.6984	−0.808723
$176$	−0.904638	−0.0681896
$177$	25.0095	1.87983
$178$	13.3012	0.996968
$179$	1.21656	0.0909303	0.0454652	−	0.998966i	$-0.485523\pi$
$179$	1.21656	0.0909303	0.0454652	+	0.998966i	$0.485523\pi$
$180$	10.7735	0.803011
$181$	−5.30210	−0.394102	−0.197051	−	0.980393i	$-0.563136\pi$
$181$	−5.30210	−0.394102	−0.197051	+	0.980393i	$0.563136\pi$
$182$	16.7199	1.23936
$183$	−3.32373	−0.245697
$184$	−8.26173	−0.609063
$185$	−2.97627	−0.218820
$186$	−32.9058	−2.41277
$187$	0.787062	0.0575557
$188$	−5.19288	−0.378730
$189$	59.8999	4.35708
$190$	3.97462	0.288349
$191$	−8.39529	−0.607462	−0.303731	−	0.952758i	$-0.598232\pi$
$191$	−8.39529	−0.607462	−0.303731	+	0.952758i	$0.598232\pi$
$192$	3.41483	0.246444
$193$	5.93474	0.427192	0.213596	−	0.976922i	$-0.431482\pi$
$193$	5.93474	0.427192	0.213596	+	0.976922i	$0.431482\pi$
$194$	0.715847	0.0513948
$195$	−22.9208	−1.64140
$196$	2.60103	0.185788
$197$	−17.0402	−1.21406	−0.607032	−	0.794677i	$-0.707640\pi$
$197$	−17.0402	−1.21406	−0.607032	+	0.794677i	$0.707640\pi$
$198$	7.83513	0.556818
$199$	−4.82937	−0.342345	−0.171173	−	0.985241i	$-0.554756\pi$
$199$	−4.82937	−0.342345	−0.171173	+	0.985241i	$0.554756\pi$
$200$	3.45271	0.244143
$201$	35.9533	2.53595
$202$	10.6797	0.751423
$203$	−15.4361	−1.08340
$204$	−2.97101	−0.208012
$205$	2.31070	0.161386
$206$	−13.2393	−0.922428
$207$	71.5554	4.97344
$208$	−5.39604	−0.374148
$209$	2.89057	0.199945
$210$	−13.1618	−0.908249
$211$	−5.16797	−0.355778	−0.177889	−	0.984051i	$-0.556927\pi$
$211$	−5.16797	−0.355778	−0.177889	+	0.984051i	$0.556927\pi$
$212$	−9.37920	−0.644166
$213$	−39.4019	−2.69977
$214$	−3.86877	−0.264463
$215$	−2.57531	−0.175635
$216$	−19.3316	−1.31535
$217$	29.8581	2.02690
$218$	−6.75692	−0.457637
$219$	19.8292	1.33993
$220$	−1.12528	−0.0758665
$221$	4.69472	0.315801
$222$	8.17062	0.548376
$223$	−26.6511	−1.78469	−0.892345	−	0.451354i	$-0.850941\pi$
$223$	−26.6511	−1.78469	−0.892345	+	0.451354i	$0.850941\pi$
$224$	−3.09855	−0.207031
$225$	−29.9041	−1.99361
$226$	9.25477	0.615618
$227$	11.0154	0.731116	0.365558	−	0.930789i	$-0.380878\pi$
$227$	11.0154	0.731116	0.365558	+	0.930789i	$0.380878\pi$
$228$	−10.9113	−0.722621
$229$	3.24907	0.214705	0.107352	−	0.994221i	$-0.465763\pi$
$229$	3.24907	0.214705	0.107352	+	0.994221i	$0.465763\pi$
$230$	−10.2768	−0.677632
$231$	−9.57200	−0.629792
$232$	4.98170	0.327065
$233$	3.44063	0.225403	0.112702	−	0.993629i	$-0.464050\pi$
$233$	3.44063	0.225403	0.112702	+	0.993629i	$0.464050\pi$
$234$	46.7354	3.05519
$235$	−6.45944	−0.421367
$236$	7.32378	0.476737
$237$	−5.94175	−0.385958
$238$	2.69584	0.174745
$239$	21.6580	1.40094	0.700469	−	0.713683i	$-0.252974\pi$
$239$	21.6580	1.40094	0.700469	+	0.713683i	$0.252974\pi$
$240$	4.24772	0.274189
$241$	28.9020	1.86174	0.930871	−	0.365349i	$-0.119050\pi$
$241$	28.9020	1.86174	0.930871	+	0.365349i	$0.119050\pi$
$242$	10.1816	0.654500
$243$	78.7038	5.04885
$244$	−0.973323	−0.0623106
$245$	3.23543	0.206704
$246$	−6.34346	−0.404444
$247$	17.2419	1.09707
$248$	−9.63616	−0.611897
$249$	−52.3759	−3.31919
$250$	10.5143	0.664986
$251$	−13.1263	−0.828525	−0.414262	−	0.910157i	$-0.635960\pi$
$251$	−13.1263	−0.828525	−0.414262	+	0.910157i	$0.635960\pi$
$252$	26.8368	1.69056
$253$	−7.47388	−0.469879
$254$	11.0551	0.693659
$255$	−3.69564	−0.231430
$256$	1.00000	0.0625000
$257$	25.6236	1.59836	0.799178	−	0.601094i	$-0.205268\pi$
$257$	25.6236	1.59836	0.799178	+	0.601094i	$0.205268\pi$
$258$	7.06988	0.440151
$259$	−7.41387	−0.460675
$260$	−6.71215	−0.416270
$261$	−43.1468	−2.67072
$262$	6.84521	0.422898
$263$	13.9147	0.858017	0.429009	−	0.903300i	$-0.358863\pi$
$263$	13.9147	0.858017	0.429009	+	0.903300i	$0.358863\pi$
$264$	3.08918	0.190126
$265$	−11.6668	−0.716687
$266$	9.90075	0.607054
$267$	−45.4214	−2.77974
$268$	10.5286	0.643135
$269$	26.4475	1.61253	0.806266	−	0.591553i	$-0.201485\pi$
$269$	26.4475	1.61253	0.806266	+	0.591553i	$0.201485\pi$
$270$	−24.0466	−1.46343
$271$	−13.7462	−0.835024	−0.417512	−	0.908671i	$-0.637098\pi$
$271$	−13.7462	−0.835024	−0.417512	+	0.908671i	$0.637098\pi$
$272$	−0.870030	−0.0527533
$273$	−57.0957	−3.45559
$274$	−8.04294	−0.485892
$275$	3.12345	0.188351
$276$	28.2124	1.69819
$277$	−7.94386	−0.477300	−0.238650	−	0.971106i	$-0.576705\pi$
$277$	−7.94386	−0.477300	−0.238650	+	0.971106i	$0.576705\pi$
$278$	−7.30936	−0.438386
$279$	83.4594	4.99658
$280$	−3.85430	−0.230338
$281$	−15.3656	−0.916634	−0.458317	−	0.888789i	$-0.651548\pi$
$281$	−15.3656	−0.916634	−0.458317	+	0.888789i	$0.651548\pi$
$282$	17.7328	1.05597
$283$	11.8841	0.706435	0.353218	−	0.935541i	$-0.385088\pi$
$283$	11.8841	0.706435	0.353218	+	0.935541i	$0.385088\pi$
$284$	−11.5385	−0.684681
$285$	−13.5726	−0.803974
$286$	−4.88146	−0.288647
$287$	5.75594	0.339762
$288$	−8.66107	−0.510358
$289$	−16.2430	−0.955473
$290$	6.19675	0.363886
$291$	−2.44450	−0.143299
$292$	5.80679	0.339816
$293$	−31.4917	−1.83977	−0.919884	−	0.392191i	$-0.871717\pi$
$293$	−31.4917	−1.83977	−0.919884	+	0.392191i	$0.871717\pi$
$294$	−8.88209	−0.518014
$295$	9.11007	0.530409
$296$	2.39269	0.139072
$297$	−17.4881	−1.01476
$298$	3.77239	0.218528
$299$	−44.5806	−2.57816
$300$	−11.7904	−0.680719
$301$	−6.41507	−0.369759
$302$	−23.6880	−1.36309
$303$	−36.4695	−2.09512
$304$	−3.19528	−0.183262
$305$	−1.21072	−0.0693256
$306$	7.53539	0.430770
$307$	29.9432	1.70895	0.854475	−	0.519492i	$-0.173879\pi$
$307$	29.9432	1.70895	0.854475	+	0.519492i	$0.173879\pi$
$308$	−2.80307	−0.159720
$309$	45.2101	2.57191
$310$	−11.9864	−0.680784
$311$	6.34343	0.359703	0.179851	−	0.983694i	$-0.442438\pi$
$311$	6.34343	0.359703	0.179851	+	0.983694i	$0.442438\pi$
$312$	18.4266	1.04320
$313$	13.6050	0.769000	0.384500	−	0.923125i	$-0.374374\pi$
$313$	13.6050	0.769000	0.384500	+	0.923125i	$0.374374\pi$
$314$	9.78526	0.552214
$315$	33.3823	1.88088
$316$	−1.73998	−0.0978817
$317$	−25.8780	−1.45345	−0.726727	−	0.686926i	$-0.758960\pi$
$317$	−25.8780	−1.45345	−0.726727	+	0.686926i	$0.758960\pi$
$318$	32.0284	1.79606
$319$	4.50664	0.252323
$320$	1.24390	0.0695363
$321$	13.2112	0.737376
$322$	−25.5994	−1.42660
$323$	2.77999	0.154683
$324$	40.0309	2.22394
$325$	18.6309	1.03346
$326$	−21.1432	−1.17101
$327$	23.0737	1.27598
$328$	−1.85762	−0.102570
$329$	−16.0904	−0.887093
$330$	3.84265	0.211531
$331$	3.73294	0.205181	0.102590	−	0.994724i	$-0.467287\pi$
$331$	3.73294	0.205181	0.102590	+	0.994724i	$0.467287\pi$
$332$	−15.3378	−0.841770
$333$	−20.7232	−1.13562
$334$	−10.9803	−0.600818
$335$	13.0965	0.715540
$336$	10.5810	0.577243
$337$	26.4947	1.44326	0.721630	−	0.692279i	$-0.243393\pi$
$337$	26.4947	1.44326	0.721630	+	0.692279i	$0.243393\pi$
$338$	−16.1172	−0.876661
$339$	−31.6035	−1.71647
$340$	−1.08223	−0.0586923
$341$	−8.71723	−0.472065
$342$	27.6745	1.49647
$343$	−13.6304	−0.735974
$344$	2.07034	0.111626
$345$	35.0935	1.88937
$346$	6.06140	0.325863
$347$	0.391525	0.0210181	0.0105091	−	0.999945i	$-0.496655\pi$
$347$	0.391525	0.0210181	0.0105091	+	0.999945i	$0.496655\pi$
$348$	−17.0117	−0.911921
$349$	−22.5839	−1.20889	−0.604444	−	0.796648i	$-0.706605\pi$
$349$	−22.5839	−1.20889	−0.604444	+	0.796648i	$0.706605\pi$
$350$	10.6984	0.571853
$351$	−104.314	−5.56786
$352$	0.904638	0.0482174
$353$	−10.2268	−0.544317	−0.272159	−	0.962252i	$-0.587738\pi$
$353$	−10.2268	−0.544317	−0.272159	+	0.962252i	$0.587738\pi$
$354$	−25.0095	−1.32924
$355$	−14.3527	−0.761763
$356$	−13.3012	−0.704963
$357$	−9.20582	−0.487224
$358$	−1.21656	−0.0642975
$359$	21.7133	1.14598	0.572991	−	0.819562i	$-0.305783\pi$
$359$	21.7133	1.14598	0.572991	+	0.819562i	$0.305783\pi$
$360$	−10.7735	−0.567815
$361$	−8.79018	−0.462641
$362$	5.30210	0.278672
$363$	−34.7685	−1.82488
$364$	−16.7199	−0.876361
$365$	7.22308	0.378073
$366$	3.32373	0.173734
$367$	−22.8035	−1.19033	−0.595165	−	0.803603i	$-0.702913\pi$
$367$	−22.8035	−1.19033	−0.595165	+	0.803603i	$0.702913\pi$
$368$	8.26173	0.430673
$369$	16.0890	0.837559
$370$	2.97627	0.154729
$371$	−29.0620	−1.50882
$372$	32.9058	1.70609
$373$	−33.7018	−1.74501	−0.872507	−	0.488602i	$-0.837507\pi$
$373$	−33.7018	−1.74501	−0.872507	+	0.488602i	$0.837507\pi$
$374$	−0.787062	−0.0406980
$375$	−35.9047	−1.85411
$376$	5.19288	0.267802
$377$	26.8814	1.38447
$378$	−59.8999	−3.08092
$379$	−10.0392	−0.515678	−0.257839	−	0.966188i	$-0.583010\pi$
$379$	−10.0392	−0.515678	−0.257839	+	0.966188i	$0.583010\pi$
$380$	−3.97462	−0.203894
$381$	−37.7513	−1.93406
$382$	8.39529	0.429540
$383$	−9.63150	−0.492147	−0.246073	−	0.969251i	$-0.579140\pi$
$383$	−9.63150	−0.492147	−0.246073	+	0.969251i	$0.579140\pi$
$384$	−3.41483	−0.174262
$385$	−3.48674	−0.177701
$386$	−5.93474	−0.302071
$387$	−17.9314	−0.911504
$388$	−0.715847	−0.0363416
$389$	−32.0546	−1.62523	−0.812617	−	0.582798i	$-0.801958\pi$
$389$	−32.0546	−1.62523	−0.812617	+	0.582798i	$0.801958\pi$
$390$	22.9208	1.16064
$391$	−7.18796	−0.363511
$392$	−2.60103	−0.131372
$393$	−23.3752	−1.17912
$394$	17.0402	0.858473
$395$	−2.16437	−0.108901
$396$	−7.83513	−0.393730
$397$	35.2925	1.77128	0.885640	−	0.464372i	$-0.153720\pi$
$397$	35.2925	1.77128	0.885640	+	0.464372i	$0.153720\pi$
$398$	4.82937	0.242075
$399$	−33.8094	−1.69259
$400$	−3.45271	−0.172635
$401$	5.52326	0.275818	0.137909	−	0.990445i	$-0.455962\pi$
$401$	5.52326	0.275818	0.137909	+	0.990445i	$0.455962\pi$
$402$	−35.9533	−1.79319
$403$	−51.9971	−2.59016
$404$	−10.6797	−0.531337
$405$	49.7945	2.47431
$406$	15.4361	0.766079
$407$	2.16451	0.107291
$408$	2.97101	0.147087
$409$	−14.6740	−0.725584	−0.362792	−	0.931870i	$-0.618176\pi$
$409$	−14.6740	−0.725584	−0.362792	+	0.931870i	$0.618176\pi$
$410$	−2.31070	−0.114117
$411$	27.4653	1.35476
$412$	13.2393	0.652255
$413$	22.6931	1.11666
$414$	−71.5554	−3.51676
$415$	−19.0787	−0.936536
$416$	5.39604	0.264562
$417$	24.9602	1.22231
$418$	−2.89057	−0.141382
$419$	4.12239	0.201392	0.100696	−	0.994917i	$-0.467893\pi$
$419$	4.12239	0.201392	0.100696	+	0.994917i	$0.467893\pi$
$420$	13.1618	0.642229
$421$	−2.56075	−0.124803	−0.0624017	−	0.998051i	$-0.519876\pi$
$421$	−2.56075	−0.124803	−0.0624017	+	0.998051i	$0.519876\pi$
$422$	5.16797	0.251573
$423$	−44.9759	−2.18680
$424$	9.37920	0.455494
$425$	3.00396	0.145713
$426$	39.4019	1.90903
$427$	−3.01589	−0.145949
$428$	3.86877	0.187004
$429$	16.6694	0.804804
$430$	2.57531	0.124192
$431$	40.8475	1.96756	0.983778	−	0.179388i	$-0.0574118\pi$
$431$	40.8475	1.96756	0.983778	+	0.179388i	$0.0574118\pi$
$432$	19.3316	0.930091
$433$	−35.0312	−1.68349	−0.841746	−	0.539873i	$-0.818472\pi$
$433$	−35.0312	−1.68349	−0.841746	+	0.539873i	$0.818472\pi$
$434$	−29.8581	−1.43324
$435$	−21.1609	−1.01459
$436$	6.75692	0.323598
$437$	−26.3986	−1.26281
$438$	−19.8292	−0.947475
$439$	3.81776	0.182212	0.0911059	−	0.995841i	$-0.470960\pi$
$439$	3.81776	0.182212	0.0911059	+	0.995841i	$0.470960\pi$
$440$	1.12528	0.0536457
$441$	22.5277	1.07275
$442$	−4.69472	−0.223305
$443$	−2.50385	−0.118962	−0.0594808	−	0.998229i	$-0.518945\pi$
$443$	−2.50385	−0.118962	−0.0594808	+	0.998229i	$0.518945\pi$
$444$	−8.17062	−0.387760
$445$	−16.5454	−0.784328
$446$	26.6511	1.26197
$447$	−12.8821	−0.609300
$448$	3.09855	0.146393
$449$	25.2736	1.19273	0.596367	−	0.802712i	$-0.296610\pi$
$449$	25.2736	1.19273	0.596367	+	0.802712i	$0.296610\pi$
$450$	29.9041	1.40969
$451$	−1.68047	−0.0791304
$452$	−9.25477	−0.435308
$453$	80.8906	3.80057
$454$	−11.0154	−0.516977
$455$	−20.7979	−0.975023
$456$	10.9113	0.510970
$457$	33.9539	1.58829	0.794147	−	0.607726i	$-0.207918\pi$
$457$	33.9539	1.58829	0.794147	+	0.607726i	$0.207918\pi$
$458$	−3.24907	−0.151819
$459$	−16.8191	−0.785046
$460$	10.2768	0.479158
$461$	−13.6987	−0.638011	−0.319005	−	0.947753i	$-0.603349\pi$
$461$	−13.6987	−0.638011	−0.319005	+	0.947753i	$0.603349\pi$
$462$	9.57200	0.445330
$463$	−24.2717	−1.12800	−0.564000	−	0.825775i	$-0.690738\pi$
$463$	−24.2717	−1.12800	−0.564000	+	0.825775i	$0.690738\pi$
$464$	−4.98170	−0.231270
$465$	40.9317	1.89816
$466$	−3.44063	−0.159384
$467$	−34.8800	−1.61405	−0.807027	−	0.590515i	$-0.798925\pi$
$467$	−34.8800	−1.61405	−0.807027	+	0.590515i	$0.798925\pi$
$468$	−46.7354	−2.16035
$469$	32.6234	1.50641
$470$	6.45944	0.297952
$471$	−33.4150	−1.53968
$472$	−7.32378	−0.337104
$473$	1.87291	0.0861166
$474$	5.94175	0.272914
$475$	11.0324	0.506200
$476$	−2.69584	−0.123563
$477$	−81.2339	−3.71944
$478$	−21.6580	−0.990612
$479$	13.7868	0.629933	0.314967	−	0.949103i	$-0.398007\pi$
$479$	13.7868	0.629933	0.314967	+	0.949103i	$0.398007\pi$
$480$	−4.24772	−0.193881
$481$	12.9110	0.588692
$482$	−28.9020	−1.31645
$483$	87.4177	3.97764
$484$	−10.1816	−0.462801
$485$	−0.890444	−0.0404330
$486$	−78.7038	−3.57008
$487$	−21.9635	−0.995260	−0.497630	−	0.867389i	$-0.665796\pi$
$487$	−21.9635	−0.995260	−0.497630	+	0.867389i	$0.665796\pi$
$488$	0.973323	0.0440603
$489$	72.2003	3.26501
$490$	−3.23543	−0.146162
$491$	−6.01546	−0.271474	−0.135737	−	0.990745i	$-0.543340\pi$
$491$	−6.01546	−0.271474	−0.135737	+	0.990745i	$0.543340\pi$
$492$	6.34346	0.285985
$493$	4.33423	0.195204
$494$	−17.2419	−0.775748
$495$	−9.74614	−0.438056
$496$	9.63616	0.432676
$497$	−35.7525	−1.60372
$498$	52.3759	2.34702
$499$	−9.19291	−0.411531	−0.205766	−	0.978601i	$-0.565968\pi$
$499$	−9.19291	−0.411531	−0.205766	+	0.978601i	$0.565968\pi$
$500$	−10.5143	−0.470216
$501$	37.4960	1.67520
$502$	13.1263	0.585856
$503$	12.0329	0.536522	0.268261	−	0.963346i	$-0.413551\pi$
$503$	12.0329	0.536522	0.268261	+	0.963346i	$0.413551\pi$
$504$	−26.8368	−1.19540
$505$	−13.2845	−0.591155
$506$	7.47388	0.332254
$507$	55.0376	2.44430
$508$	−11.0551	−0.490491
$509$	43.1348	1.91192	0.955959	−	0.293500i	$-0.0948201\pi$
$509$	43.1348	1.91192	0.955959	+	0.293500i	$0.0948201\pi$
$510$	3.69564	0.163646
$511$	17.9926	0.795947
$512$	−1.00000	−0.0441942
$513$	−61.7698	−2.72720
$514$	−25.6236	−1.13021
$515$	16.4684	0.725686
$516$	−7.06988	−0.311234
$517$	4.69767	0.206603
$518$	7.41387	0.325747
$519$	−20.6986	−0.908570
$520$	6.71215	0.294347
$521$	1.42387	0.0623809	0.0311904	−	0.999513i	$-0.490070\pi$
$521$	1.42387	0.0623809	0.0311904	+	0.999513i	$0.490070\pi$
$522$	43.1468	1.88849
$523$	24.0241	1.05050	0.525249	−	0.850948i	$-0.323972\pi$
$523$	24.0241	1.05050	0.525249	+	0.850948i	$0.323972\pi$
$524$	−6.84521	−0.299034
$525$	−36.5332	−1.59444
$526$	−13.9147	−0.606710
$527$	−8.38375	−0.365202
$528$	−3.08918	−0.134440
$529$	45.2562	1.96766
$530$	11.6668	0.506774
$531$	63.4317	2.75270
$532$	−9.90075	−0.429252
$533$	−10.0238	−0.434179
$534$	45.4214	1.96557
$535$	4.81237	0.208057
$536$	−10.5286	−0.454765
$537$	4.15436	0.179274
$538$	−26.4475	−1.14023
$539$	−2.35299	−0.101351
$540$	24.0466	1.03480
$541$	19.5474	0.840408	0.420204	−	0.907430i	$-0.361958\pi$
$541$	19.5474	0.840408	0.420204	+	0.907430i	$0.361958\pi$
$542$	13.7462	0.590451
$543$	−18.1058	−0.776994
$544$	0.870030	0.0373022
$545$	8.40496	0.360029
$546$	57.0957	2.44347
$547$	−13.6126	−0.582032	−0.291016	−	0.956718i	$-0.593993\pi$
$547$	−13.6126	−0.582032	−0.291016	+	0.956718i	$0.593993\pi$
$548$	8.04294	0.343577
$549$	−8.43001	−0.359784
$550$	−3.12345	−0.133184
$551$	15.9179	0.678127
$552$	−28.2124	−1.20080
$553$	−5.39143	−0.229267
$554$	7.94386	0.337502
$555$	−10.1635	−0.431415
$556$	7.30936	0.309986
$557$	7.85030	0.332628	0.166314	−	0.986073i	$-0.446813\pi$
$557$	7.85030	0.332628	0.166314	+	0.986073i	$0.446813\pi$
$558$	−83.4594	−3.53312
$559$	11.1717	0.472511
$560$	3.85430	0.162874
$561$	2.68768	0.113474
$562$	15.3656	0.648158
$563$	−1.53452	−0.0646724	−0.0323362	−	0.999477i	$-0.510295\pi$
$563$	−1.53452	−0.0646724	−0.0323362	+	0.999477i	$0.510295\pi$
$564$	−17.7328	−0.746685
$565$	−11.5120	−0.484315
$566$	−11.8841	−0.499525
$567$	124.038	5.20910
$568$	11.5385	0.484143
$569$	−27.5234	−1.15384	−0.576920	−	0.816801i	$-0.695745\pi$
$569$	−27.5234	−1.15384	−0.576920	+	0.816801i	$0.695745\pi$
$570$	13.5726	0.568496
$571$	25.6020	1.07141	0.535705	−	0.844405i	$-0.320046\pi$
$571$	25.6020	1.07141	0.535705	+	0.844405i	$0.320046\pi$
$572$	4.88146	0.204104
$573$	−28.6685	−1.19764
$574$	−5.75594	−0.240248
$575$	−28.5253	−1.18959
$576$	8.66107	0.360878
$577$	−15.3078	−0.637274	−0.318637	−	0.947877i	$-0.603225\pi$
$577$	−15.3078	−0.637274	−0.318637	+	0.947877i	$0.603225\pi$
$578$	16.2430	0.675622
$579$	20.2661	0.842232
$580$	−6.19675	−0.257306
$581$	−47.5249	−1.97167
$582$	2.44450	0.101328
$583$	8.48478	0.351404
$584$	−5.80679	−0.240286
$585$	−58.1343	−2.40356
$586$	31.4917	1.30091
$587$	−6.29352	−0.259762	−0.129881	−	0.991530i	$-0.541459\pi$
$587$	−6.29352	−0.259762	−0.129881	+	0.991530i	$0.541459\pi$
$588$	8.88209	0.366291
$589$	−30.7902	−1.26869
$590$	−9.11007	−0.375056
$591$	−58.1894	−2.39359
$592$	−2.39269	−0.0983388
$593$	4.28040	0.175775	0.0878875	−	0.996130i	$-0.471988\pi$
$593$	4.28040	0.175775	0.0878875	+	0.996130i	$0.471988\pi$
$594$	17.4881	0.717544
$595$	−3.35336	−0.137474
$596$	−3.77239	−0.154523
$597$	−16.4915	−0.674952
$598$	44.5806	1.82304
$599$	−2.43243	−0.0993864	−0.0496932	−	0.998765i	$-0.515824\pi$
$599$	−2.43243	−0.0993864	−0.0496932	+	0.998765i	$0.515824\pi$
$600$	11.7904	0.481341
$601$	45.9592	1.87472	0.937358	−	0.348366i	$-0.113264\pi$
$601$	45.9592	1.87472	0.937358	+	0.348366i	$0.113264\pi$
$602$	6.41507	0.261459
$603$	91.1887	3.71349
$604$	23.6880	0.963852
$605$	−12.6650	−0.514904
$606$	36.4695	1.48147
$607$	18.2703	0.741569	0.370784	−	0.928719i	$-0.379089\pi$
$607$	18.2703	0.741569	0.370784	+	0.928719i	$0.379089\pi$
$608$	3.19528	0.129586
$609$	−52.7116	−2.13598
$610$	1.21072	0.0490206
$611$	28.0210	1.13361
$612$	−7.53539	−0.304600
$613$	−3.62218	−0.146299	−0.0731493	−	0.997321i	$-0.523305\pi$
$613$	−3.62218	−0.146299	−0.0731493	+	0.997321i	$0.523305\pi$
$614$	−29.9432	−1.20841
$615$	7.89065	0.318182
$616$	2.80307	0.112939
$617$	7.58495	0.305359	0.152679	−	0.988276i	$-0.451210\pi$
$617$	7.58495	0.305359	0.152679	+	0.988276i	$0.451210\pi$
$618$	−45.2101	−1.81862
$619$	−8.85329	−0.355844	−0.177922	−	0.984045i	$-0.556937\pi$
$619$	−8.85329	−0.355844	−0.177922	+	0.984045i	$0.556937\pi$
$620$	11.9864	0.481387
$621$	159.712	6.40903
$622$	−6.34343	−0.254348
$623$	−41.2145	−1.65122
$624$	−18.4266	−0.737652
$625$	4.18471	0.167388
$626$	−13.6050	−0.543765
$627$	9.87081	0.394202
$628$	−9.78526	−0.390474
$629$	2.08171	0.0830032
$630$	−33.3823	−1.32998
$631$	−9.39253	−0.373911	−0.186955	−	0.982368i	$-0.559862\pi$
$631$	−9.39253	−0.373911	−0.186955	+	0.982368i	$0.559862\pi$
$632$	1.73998	0.0692128
$633$	−17.6478	−0.701435
$634$	25.8780	1.02775
$635$	−13.7515	−0.545710
$636$	−32.0284	−1.27001
$637$	−14.0353	−0.556098
$638$	−4.50664	−0.178419
$639$	−99.9353	−3.95338
$640$	−1.24390	−0.0491696
$641$	−25.1449	−0.993165	−0.496582	−	0.867990i	$-0.665412\pi$
$641$	−25.1449	−0.993165	−0.496582	+	0.867990i	$0.665412\pi$
$642$	−13.2112	−0.521404
$643$	23.9773	0.945572	0.472786	−	0.881177i	$-0.343248\pi$
$643$	23.9773	0.945572	0.472786	+	0.881177i	$0.343248\pi$
$644$	25.5994	1.00876
$645$	−8.79424	−0.346273
$646$	−2.77999	−0.109377
$647$	−17.3870	−0.683553	−0.341776	−	0.939781i	$-0.611029\pi$
$647$	−17.3870	−0.683553	−0.341776	+	0.939781i	$0.611029\pi$
$648$	−40.0309	−1.57256
$649$	−6.62537	−0.260068
$650$	−18.6309	−0.730765
$651$	101.961	3.99615
$652$	21.1432	0.828030
$653$	0.732416	0.0286617	0.0143308	−	0.999897i	$-0.495438\pi$
$653$	0.732416	0.0286617	0.0143308	+	0.999897i	$0.495438\pi$
$654$	−23.0737	−0.902255
$655$	−8.51477	−0.332700
$656$	1.85762	0.0725279
$657$	50.2929	1.96211
$658$	16.0904	0.627270
$659$	−10.5572	−0.411251	−0.205625	−	0.978631i	$-0.565923\pi$
$659$	−10.5572	−0.411251	−0.205625	+	0.978631i	$0.565923\pi$
$660$	−3.84265	−0.149575
$661$	13.7940	0.536523	0.268262	−	0.963346i	$-0.413551\pi$
$661$	13.7940	0.536523	0.268262	+	0.963346i	$0.413551\pi$
$662$	−3.73294	−0.145085
$663$	16.0317	0.622618
$664$	15.3378	0.595221
$665$	−12.3156	−0.477577
$666$	20.7232	0.803008
$667$	−41.1575	−1.59362
$668$	10.9803	0.424842
$669$	−91.0090	−3.51861
$670$	−13.0965	−0.505963
$671$	0.880505	0.0339915
$672$	−10.5810	−0.408172
$673$	17.1368	0.660576	0.330288	−	0.943880i	$-0.392854\pi$
$673$	17.1368	0.660576	0.330288	+	0.943880i	$0.392854\pi$
$674$	−26.4947	−1.02054
$675$	−66.7462	−2.56906
$676$	16.1172	0.619893
$677$	−28.3237	−1.08857	−0.544284	−	0.838901i	$-0.683199\pi$
$677$	−28.3237	−1.08857	−0.544284	+	0.838901i	$0.683199\pi$
$678$	31.6035	1.21372
$679$	−2.21809	−0.0851225
$680$	1.08223	0.0415017
$681$	37.6156	1.44143
$682$	8.71723	0.333800
$683$	31.3592	1.19993	0.599963	−	0.800028i	$-0.295182\pi$
$683$	31.3592	1.19993	0.599963	+	0.800028i	$0.295182\pi$
$684$	−27.6745	−1.05816
$685$	10.0046	0.382257
$686$	13.6304	0.520412
$687$	11.0950	0.423302
$688$	−2.07034	−0.0789312
$689$	50.6105	1.92811
$690$	−35.0935	−1.33599
$691$	−41.1061	−1.56375	−0.781875	−	0.623435i	$-0.785737\pi$
$691$	−41.1061	−1.56375	−0.781875	+	0.623435i	$0.785737\pi$
$692$	−6.06140	−0.230420
$693$	−24.2776	−0.922228
$694$	−0.391525	−0.0148621
$695$	9.09213	0.344884
$696$	17.0117	0.644826
$697$	−1.61619	−0.0612174
$698$	22.5839	0.854813
$699$	11.7492	0.444395
$700$	−10.6984	−0.404361
$701$	−15.0461	−0.568284	−0.284142	−	0.958782i	$-0.591709\pi$
$701$	−15.0461	−0.568284	−0.284142	+	0.958782i	$0.591709\pi$
$702$	104.314	3.93707
$703$	7.64530	0.288348
$704$	−0.904638	−0.0340948
$705$	−22.0579	−0.830748
$706$	10.2268	0.384890
$707$	−33.0917	−1.24454
$708$	25.0095	0.939913
$709$	43.7695	1.64380	0.821899	−	0.569633i	$-0.192914\pi$
$709$	43.7695	1.64380	0.821899	+	0.569633i	$0.192914\pi$
$710$	14.3527	0.538648
$711$	−15.0701	−0.565173
$712$	13.3012	0.498484
$713$	79.6114	2.98147
$714$	9.20582	0.344519
$715$	6.07206	0.227082
$716$	1.21656	0.0454652
$717$	73.9583	2.76202
$718$	−21.7133	−0.810331
$719$	−53.2287	−1.98510	−0.992548	−	0.121858i	$-0.961115\pi$
$719$	−53.2287	−1.98510	−0.992548	+	0.121858i	$0.961115\pi$
$720$	10.7735	0.401505
$721$	41.0228	1.52777
$722$	8.79018	0.327137
$723$	98.6954	3.67052
$724$	−5.30210	−0.197051
$725$	17.2004	0.638805
$726$	34.7685	1.29038
$727$	9.53237	0.353536	0.176768	−	0.984253i	$-0.443436\pi$
$727$	9.53237	0.353536	0.176768	+	0.984253i	$0.443436\pi$
$728$	16.7199	0.619681
$729$	148.668	5.50621
$730$	−7.22308	−0.267338
$731$	1.80126	0.0666221
$732$	−3.32373	−0.122849
$733$	−17.5353	−0.647683	−0.323841	−	0.946111i	$-0.604974\pi$
$733$	−17.5353	−0.647683	−0.323841	+	0.946111i	$0.604974\pi$
$734$	22.8035	0.841691
$735$	11.0485	0.407528
$736$	−8.26173	−0.304532
$737$	−9.52455	−0.350841
$738$	−16.0890	−0.592243
$739$	5.12397	0.188488	0.0942442	−	0.995549i	$-0.469957\pi$
$739$	5.12397	0.188488	0.0942442	+	0.995549i	$0.469957\pi$
$740$	−2.97627	−0.109410
$741$	58.8780	2.16294
$742$	29.0620	1.06690
$743$	−47.9930	−1.76069	−0.880346	−	0.474332i	$-0.842690\pi$
$743$	−47.9930	−1.76069	−0.880346	+	0.474332i	$0.842690\pi$
$744$	−32.9058	−1.20639
$745$	−4.69248	−0.171919
$746$	33.7018	1.23391
$747$	−132.841	−4.86041
$748$	0.787062	0.0287779
$749$	11.9876	0.438017
$750$	35.9047	1.31105
$751$	1.00000	0.0364905
$751$	1.00000	0.0364905
$752$	−5.19288	−0.189365
$753$	−44.8241	−1.63348
$754$	−26.8814	−0.978965
$755$	29.4656	1.07236
$756$	59.8999	2.17854
$757$	22.1696	0.805769	0.402884	−	0.915251i	$-0.368008\pi$
$757$	22.1696	0.805769	0.402884	+	0.915251i	$0.368008\pi$
$758$	10.0392	0.364639
$759$	−25.5220	−0.926391
$760$	3.97462	0.144175
$761$	6.70551	0.243075	0.121537	−	0.992587i	$-0.461218\pi$
$761$	6.70551	0.243075	0.121537	+	0.992587i	$0.461218\pi$
$762$	37.7513	1.36758
$763$	20.9367	0.757959
$764$	−8.39529	−0.303731
$765$	−9.37329	−0.338892
$766$	9.63150	0.348000
$767$	−39.5194	−1.42696
$768$	3.41483	0.123222
$769$	−13.0233	−0.469632	−0.234816	−	0.972040i	$-0.575449\pi$
$769$	−13.0233	−0.469632	−0.234816	+	0.972040i	$0.575449\pi$
$770$	3.48674	0.125654
$771$	87.5003	3.15125
$772$	5.93474	0.213596
$773$	30.3935	1.09318	0.546589	−	0.837401i	$-0.315926\pi$
$773$	30.3935	1.09318	0.546589	+	0.837401i	$0.315926\pi$
$774$	17.9314	0.644531
$775$	−33.2708	−1.19512
$776$	0.715847	0.0256974
$777$	−25.3171	−0.908246
$778$	32.0546	1.14921
$779$	−5.93562	−0.212666
$780$	−22.9208	−0.820698
$781$	10.4381	0.373505
$782$	7.18796	0.257041
$783$	−96.3041	−3.44163
$784$	2.60103	0.0928940
$785$	−12.1719	−0.434434
$786$	23.3752	0.833766
$787$	22.7849	0.812194	0.406097	−	0.913830i	$-0.366890\pi$
$787$	22.7849	0.812194	0.406097	+	0.913830i	$0.366890\pi$
$788$	−17.0402	−0.607032
$789$	47.5163	1.69163
$790$	2.16437	0.0770048
$791$	−28.6764	−1.01962
$792$	7.83513	0.278409
$793$	5.25209	0.186507
$794$	−35.2925	−1.25248
$795$	−39.8402	−1.41299
$796$	−4.82937	−0.171173
$797$	−44.7134	−1.58383	−0.791914	−	0.610633i	$-0.790915\pi$
$797$	−44.7134	−1.58383	−0.791914	+	0.610633i	$0.790915\pi$
$798$	33.8094	1.19684
$799$	4.51796	0.159834
$800$	3.45271	0.122072
$801$	−115.203	−4.07049
$802$	−5.52326	−0.195033
$803$	−5.25304	−0.185376
$804$	35.9533	1.26797
$805$	31.8432	1.12233
$806$	51.9971	1.83152
$807$	90.3137	3.17919
$808$	10.6797	0.375712
$809$	40.2829	1.41627	0.708135	−	0.706077i	$-0.249537\pi$
$809$	40.2829	1.41627	0.708135	+	0.706077i	$0.249537\pi$
$810$	−49.7945	−1.74960
$811$	−37.7764	−1.32651	−0.663254	−	0.748395i	$-0.730825\pi$
$811$	−37.7764	−1.32651	−0.663254	+	0.748395i	$0.730825\pi$
$812$	−15.4361	−0.541700
$813$	−46.9410	−1.64629
$814$	−2.16451	−0.0758662
$815$	26.3000	0.921250
$816$	−2.97101	−0.104006
$817$	6.61533	0.231441
$818$	14.6740	0.513066
$819$	−144.812	−5.06015
$820$	2.31070	0.0806931
$821$	44.9106	1.56739	0.783696	−	0.621144i	$-0.213332\pi$
$821$	44.9106	1.56739	0.783696	+	0.621144i	$0.213332\pi$
$822$	−27.4653	−0.957961
$823$	11.6319	0.405463	0.202732	−	0.979234i	$-0.435018\pi$
$823$	11.6319	0.405463	0.202732	+	0.979234i	$0.435018\pi$
$824$	−13.2393	−0.461214
$825$	10.6660	0.371344
$826$	−22.6931	−0.789594
$827$	39.5255	1.37444	0.687219	−	0.726451i	$-0.258831\pi$
$827$	39.5255	1.37444	0.687219	+	0.726451i	$0.258831\pi$
$828$	71.5554	2.48672
$829$	−14.5000	−0.503606	−0.251803	−	0.967779i	$-0.581023\pi$
$829$	−14.5000	−0.503606	−0.251803	+	0.967779i	$0.581023\pi$
$830$	19.0787	0.662231
$831$	−27.1269	−0.941023
$832$	−5.39604	−0.187074
$833$	−2.26298	−0.0784075
$834$	−24.9602	−0.864302
$835$	13.6585	0.472671
$836$	2.89057	0.0999725
$837$	186.282	6.43885
$838$	−4.12239	−0.142406
$839$	48.4100	1.67130	0.835650	−	0.549263i	$-0.185092\pi$
$839$	48.4100	1.67130	0.835650	+	0.549263i	$0.185092\pi$
$840$	−13.1618	−0.454124
$841$	−4.18265	−0.144229
$842$	2.56075	0.0882493
$843$	−52.4709	−1.80719
$844$	−5.16797	−0.177889
$845$	20.0483	0.689681
$846$	44.9759	1.54630
$847$	−31.5483	−1.08401
$848$	−9.37920	−0.322083
$849$	40.5821	1.39277
$850$	−3.00396	−0.103035
$851$	−19.7677	−0.677629
$852$	−39.4019	−1.34989
$853$	−1.19804	−0.0410200	−0.0205100	−	0.999790i	$-0.506529\pi$
$853$	−1.19804	−0.0410200	−0.0205100	+	0.999790i	$0.506529\pi$
$854$	3.01589	0.103202
$855$	−34.4244	−1.17729
$856$	−3.86877	−0.132232
$857$	16.9658	0.579541	0.289771	−	0.957096i	$-0.406421\pi$
$857$	16.9658	0.579541	0.289771	+	0.957096i	$0.406421\pi$
$858$	−16.6694	−0.569082
$859$	42.6432	1.45497	0.727484	−	0.686125i	$-0.240690\pi$
$859$	42.6432	1.45497	0.727484	+	0.686125i	$0.240690\pi$
$860$	−2.57531	−0.0878173
$861$	19.6556	0.669859
$862$	−40.8475	−1.39127
$863$	−6.18166	−0.210426	−0.105213	−	0.994450i	$-0.533552\pi$
$863$	−6.18166	−0.210426	−0.105213	+	0.994450i	$0.533552\pi$
$864$	−19.3316	−0.657674
$865$	−7.53979	−0.256361
$866$	35.0312	1.19041
$867$	−55.4672	−1.88377
$868$	29.8581	1.01345
$869$	1.57406	0.0533962
$870$	21.1609	0.717420
$871$	−56.8126	−1.92502
$872$	−6.75692	−0.228818
$873$	−6.20000	−0.209838
$874$	26.3986	0.892944
$875$	−32.5793	−1.10138
$876$	19.8292	0.669966
$877$	16.2640	0.549197	0.274599	−	0.961559i	$-0.411455\pi$
$877$	16.2640	0.549197	0.274599	+	0.961559i	$0.411455\pi$
$878$	−3.81776	−0.128843
$879$	−107.539	−3.62720
$880$	−1.12528	−0.0379332
$881$	5.63364	0.189802	0.0949010	−	0.995487i	$-0.469747\pi$
$881$	5.63364	0.189802	0.0949010	+	0.995487i	$0.469747\pi$
$882$	−22.5277	−0.758548
$883$	12.7642	0.429550	0.214775	−	0.976664i	$-0.431098\pi$
$883$	12.7642	0.429550	0.214775	+	0.976664i	$0.431098\pi$
$884$	4.69472	0.157900
$885$	31.1093	1.04573
$886$	2.50385	0.0841185
$887$	−11.6423	−0.390910	−0.195455	−	0.980713i	$-0.562618\pi$
$887$	−11.6423	−0.390910	−0.195455	+	0.980713i	$0.562618\pi$
$888$	8.17062	0.274188
$889$	−34.2548	−1.14887
$890$	16.5454	0.554603
$891$	−36.2134	−1.21320
$892$	−26.6511	−0.892345
$893$	16.5927	0.555254
$894$	12.8821	0.430840
$895$	1.51329	0.0505837
$896$	−3.09855	−0.103515
$897$	−152.235	−5.08299
$898$	−25.2736	−0.843390
$899$	−48.0045	−1.60104
$900$	−29.9041	−0.996804
$901$	8.16019	0.271855
$902$	1.68047	0.0559537
$903$	−21.9064	−0.728999
$904$	9.25477	0.307809
$905$	−6.59530	−0.219235
$906$	−80.8906	−2.68741
$907$	44.0857	1.46384	0.731921	−	0.681389i	$-0.238624\pi$
$907$	44.0857	1.46384	0.731921	+	0.681389i	$0.238624\pi$
$908$	11.0154	0.365558
$909$	−92.4979	−3.06796
$910$	20.7979	0.689445
$911$	−8.89673	−0.294762	−0.147381	−	0.989080i	$-0.547084\pi$
$911$	−8.89673	−0.294762	−0.147381	+	0.989080i	$0.547084\pi$
$912$	−10.9113	−0.361311
$913$	13.8751	0.459200
$914$	−33.9539	−1.12309
$915$	−4.13440	−0.136679
$916$	3.24907	0.107352
$917$	−21.2102	−0.700424
$918$	16.8191	0.555112
$919$	−37.8432	−1.24833	−0.624165	−	0.781292i	$-0.714561\pi$
$919$	−37.8432	−1.24833	−0.624165	+	0.781292i	$0.714561\pi$
$920$	−10.2768	−0.338816
$921$	102.251	3.36929
$922$	13.6987	0.451142
$923$	62.2619	2.04938
$924$	−9.57200	−0.314896
$925$	8.26124	0.271628
$926$	24.2717	0.797617
$927$	114.667	3.76615
$928$	4.98170	0.163532
$929$	13.5876	0.445795	0.222897	−	0.974842i	$-0.428449\pi$
$929$	13.5876	0.445795	0.222897	+	0.974842i	$0.428449\pi$
$930$	−40.9317	−1.34220
$931$	−8.31103	−0.272383
$932$	3.44063	0.112702
$933$	21.6617	0.709173
$934$	34.8800	1.14131
$935$	0.979029	0.0320177
$936$	46.7354	1.52760
$937$	43.5976	1.42427	0.712135	−	0.702042i	$-0.247728\pi$
$937$	43.5976	1.42427	0.712135	+	0.702042i	$0.247728\pi$
$938$	−32.6234	−1.06519
$939$	46.4588	1.51612
$940$	−6.45944	−0.210684
$941$	18.4068	0.600046	0.300023	−	0.953932i	$-0.403006\pi$
$941$	18.4068	0.600046	0.300023	+	0.953932i	$0.403006\pi$
$942$	33.4150	1.08872
$943$	15.3472	0.499773
$944$	7.32378	0.238369
$945$	74.5097	2.42380
$946$	−1.87291	−0.0608936
$947$	36.6815	1.19199	0.595995	−	0.802988i	$-0.296758\pi$
$947$	36.6815	1.19199	0.595995	+	0.802988i	$0.296758\pi$
$948$	−5.94175	−0.192979
$949$	−31.3336	−1.01713
$950$	−11.0324	−0.357937
$951$	−88.3690	−2.86556
$952$	2.69584	0.0873725
$953$	1.36230	0.0441291	0.0220645	−	0.999757i	$-0.492976\pi$
$953$	1.36230	0.0441291	0.0220645	+	0.999757i	$0.492976\pi$
$954$	81.2339	2.63004
$955$	−10.4429	−0.337925
$956$	21.6580	0.700469
$957$	15.3894	0.497469
$958$	−13.7868	−0.445430
$959$	24.9215	0.804756
$960$	4.24772	0.137094
$961$	61.8555	1.99534
$962$	−12.9110	−0.416268
$963$	33.5076	1.07977
$964$	28.9020	0.930871
$965$	7.38224	0.237643
$966$	−87.4177	−2.81262
$967$	19.8234	0.637478	0.318739	−	0.947843i	$-0.396741\pi$
$967$	19.8234	0.637478	0.318739	+	0.947843i	$0.396741\pi$
$968$	10.1816	0.327250
$969$	9.49320	0.304965
$970$	0.890444	0.0285904
$971$	−27.7068	−0.889155	−0.444577	−	0.895740i	$-0.646646\pi$
$971$	−27.7068	−0.889155	−0.444577	+	0.895740i	$0.646646\pi$
$972$	78.7038	2.52443
$973$	22.6484	0.726076
$974$	21.9635	0.703755
$975$	63.6215	2.03752
$976$	−0.973323	−0.0311553
$977$	−11.5989	−0.371083	−0.185542	−	0.982636i	$-0.559404\pi$
$977$	−11.5989	−0.371083	−0.185542	+	0.982636i	$0.559404\pi$
$978$	−72.2003	−2.30871
$979$	12.0328	0.384569
$980$	3.23543	0.103352
$981$	58.5222	1.86847
$982$	6.01546	0.191961
$983$	41.7653	1.33211	0.666053	−	0.745904i	$-0.267982\pi$
$983$	41.7653	1.33211	0.666053	+	0.745904i	$0.267982\pi$
$984$	−6.34346	−0.202222
$985$	−21.1964	−0.675372
$986$	−4.33423	−0.138030
$987$	−54.9460	−1.74895
$988$	17.2419	0.548536
$989$	−17.1046	−0.543896
$990$	9.74614	0.309753
$991$	−19.6431	−0.623984	−0.311992	−	0.950085i	$-0.600996\pi$
$991$	−19.6431	−0.623984	−0.311992	+	0.950085i	$0.600996\pi$
$992$	−9.63616	−0.305948
$993$	12.7474	0.404525
$994$	35.7525	1.13400
$995$	−6.00727	−0.190443
$996$	−52.3759	−1.65959
$997$	56.4685	1.78838	0.894188	−	0.447692i	$-0.147754\pi$
$997$	56.4685	1.78838	0.894188	+	0.447692i	$0.147754\pi$
$998$	9.19291	0.290996
$999$	−46.2544	−1.46342

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1502.2.a.h.1.19	✓	19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1502.2.a.h.1.19	✓	19	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1502 = 2 \cdot 751 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1502.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +3.41483 q^{3} +1.00000 q^{4} +1.24390 q^{5} -3.41483 q^{6} +3.09855 q^{7} -1.00000 q^{8} +8.66107 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +3.41483 q^{3} +1.00000 q^{4} +1.24390 q^{5} -3.41483 q^{6} +3.09855 q^{7} -1.00000 q^{8} +8.66107 q^{9} -1.24390 q^{10} -0.904638 q^{11} +3.41483 q^{12} -5.39604 q^{13} -3.09855 q^{14} +4.24772 q^{15} +1.00000 q^{16} -0.870030 q^{17} -8.66107 q^{18} -3.19528 q^{19} +1.24390 q^{20} +10.5810 q^{21} +0.904638 q^{22} +8.26173 q^{23} -3.41483 q^{24} -3.45271 q^{25} +5.39604 q^{26} +19.3316 q^{27} +3.09855 q^{28} -4.98170 q^{29} -4.24772 q^{30} +9.63616 q^{31} -1.00000 q^{32} -3.08918 q^{33} +0.870030 q^{34} +3.85430 q^{35} +8.66107 q^{36} -2.39269 q^{37} +3.19528 q^{38} -18.4266 q^{39} -1.24390 q^{40} +1.85762 q^{41} -10.5810 q^{42} -2.07034 q^{43} -0.904638 q^{44} +10.7735 q^{45} -8.26173 q^{46} -5.19288 q^{47} +3.41483 q^{48} +2.60103 q^{49} +3.45271 q^{50} -2.97101 q^{51} -5.39604 q^{52} -9.37920 q^{53} -19.3316 q^{54} -1.12528 q^{55} -3.09855 q^{56} -10.9113 q^{57} +4.98170 q^{58} +7.32378 q^{59} +4.24772 q^{60} -0.973323 q^{61} -9.63616 q^{62} +26.8368 q^{63} +1.00000 q^{64} -6.71215 q^{65} +3.08918 q^{66} +10.5286 q^{67} -0.870030 q^{68} +28.2124 q^{69} -3.85430 q^{70} -11.5385 q^{71} -8.66107 q^{72} +5.80679 q^{73} +2.39269 q^{74} -11.7904 q^{75} -3.19528 q^{76} -2.80307 q^{77} +18.4266 q^{78} -1.73998 q^{79} +1.24390 q^{80} +40.0309 q^{81} -1.85762 q^{82} -15.3378 q^{83} +10.5810 q^{84} -1.08223 q^{85} +2.07034 q^{86} -17.0117 q^{87} +0.904638 q^{88} -13.3012 q^{89} -10.7735 q^{90} -16.7199 q^{91} +8.26173 q^{92} +32.9058 q^{93} +5.19288 q^{94} -3.97462 q^{95} -3.41483 q^{96} -0.715847 q^{97} -2.60103 q^{98} -7.83513 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q - 19 q^{2} + 6 q^{3} + 19 q^{4} + 2 q^{5} - 6 q^{6} + 13 q^{7} - 19 q^{8} + 25 q^{9}+O(q^{10}) \) 19 * q - 19 * q^2 + 6 * q^3 + 19 * q^4 + 2 * q^5 - 6 * q^6 + 13 * q^7 - 19 * q^8 + 25 * q^9	\( 19 q - 19 q^{2} + 6 q^{3} + 19 q^{4} + 2 q^{5} - 6 q^{6} + 13 q^{7} - 19 q^{8} + 25 q^{9} - 2 q^{10} - 7 q^{11} + 6 q^{12} + 19 q^{13} - 13 q^{14} + 6 q^{15} + 19 q^{16} + 11 q^{17} - 25 q^{18} + 7 q^{19} + 2 q^{20} + 7 q^{21} + 7 q^{22} + 12 q^{23} - 6 q^{24} + 37 q^{25} - 19 q^{26} + 24 q^{27} + 13 q^{28} - 8 q^{29} - 6 q^{30} + 32 q^{31} - 19 q^{32} + 24 q^{33} - 11 q^{34} - 19 q^{35} + 25 q^{36} + 41 q^{37} - 7 q^{38} - 2 q^{39} - 2 q^{40} + 15 q^{41} - 7 q^{42} + 15 q^{43} - 7 q^{44} + 28 q^{45} - 12 q^{46} - 6 q^{47} + 6 q^{48} + 42 q^{49} - 37 q^{50} + 8 q^{51} + 19 q^{52} + 6 q^{53} - 24 q^{54} + 22 q^{55} - 13 q^{56} + 24 q^{57} + 8 q^{58} - 4 q^{59} + 6 q^{60} + 13 q^{61} - 32 q^{62} + 37 q^{63} + 19 q^{64} + 20 q^{65} - 24 q^{66} + 47 q^{67} + 11 q^{68} + 15 q^{69} + 19 q^{70} - 25 q^{72} + 64 q^{73} - 41 q^{74} - 3 q^{75} + 7 q^{76} - 4 q^{77} + 2 q^{78} + 34 q^{79} + 2 q^{80} + 27 q^{81} - 15 q^{82} + 4 q^{83} + 7 q^{84} + 21 q^{85} - 15 q^{86} + 7 q^{88} + 18 q^{89} - 28 q^{90} + 28 q^{91} + 12 q^{92} + 43 q^{93} + 6 q^{94} - 8 q^{95} - 6 q^{96} + 82 q^{97} - 42 q^{98} - 2 q^{99}+O(q^{100}) \) 19 * q - 19 * q^2 + 6 * q^3 + 19 * q^4 + 2 * q^5 - 6 * q^6 + 13 * q^7 - 19 * q^8 + 25 * q^9 - 2 * q^10 - 7 * q^11 + 6 * q^12 + 19 * q^13 - 13 * q^14 + 6 * q^15 + 19 * q^16 + 11 * q^17 - 25 * q^18 + 7 * q^19 + 2 * q^20 + 7 * q^21 + 7 * q^22 + 12 * q^23 - 6 * q^24 + 37 * q^25 - 19 * q^26 + 24 * q^27 + 13 * q^28 - 8 * q^29 - 6 * q^30 + 32 * q^31 - 19 * q^32 + 24 * q^33 - 11 * q^34 - 19 * q^35 + 25 * q^36 + 41 * q^37 - 7 * q^38 - 2 * q^39 - 2 * q^40 + 15 * q^41 - 7 * q^42 + 15 * q^43 - 7 * q^44 + 28 * q^45 - 12 * q^46 - 6 * q^47 + 6 * q^48 + 42 * q^49 - 37 * q^50 + 8 * q^51 + 19 * q^52 + 6 * q^53 - 24 * q^54 + 22 * q^55 - 13 * q^56 + 24 * q^57 + 8 * q^58 - 4 * q^59 + 6 * q^60 + 13 * q^61 - 32 * q^62 + 37 * q^63 + 19 * q^64 + 20 * q^65 - 24 * q^66 + 47 * q^67 + 11 * q^68 + 15 * q^69 + 19 * q^70 - 25 * q^72 + 64 * q^73 - 41 * q^74 - 3 * q^75 + 7 * q^76 - 4 * q^77 + 2 * q^78 + 34 * q^79 + 2 * q^80 + 27 * q^81 - 15 * q^82 + 4 * q^83 + 7 * q^84 + 21 * q^85 - 15 * q^86 + 7 * q^88 + 18 * q^89 - 28 * q^90 + 28 * q^91 + 12 * q^92 + 43 * q^93 + 6 * q^94 - 8 * q^95 - 6 * q^96 + 82 * q^97 - 42 * q^98 - 2 * q^99

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