LMFDB - Embedded newform 1003.2.a.h.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1003,2,Mod(1,1003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1003, 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("1003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1003 = 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1003.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:	$8.00899532273$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} - 5 x^{14} + 90 x^{13} - 82 x^{12} - 456 x^{11} + 723 x^{10} + 951 x^{9} - 2105 x^{8} + \cdots - 1 $ x^16 - 6x^15 - 5x^14 + 90x^13 - 82x^12 - 456x^11 + 723x^10 + 951x^9 - 2105x^8 - 695x^7 + 2641x^6 - 151x^5 - 1323x^4 + 301x^3 + 179x^2 - 50*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Root			$-2.67178$ of defining polynomial
Character	$\chi$	$=$	1003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.67178 q^{2} -2.26915 q^{3} +5.13841 q^{4} -3.81472 q^{5} -6.06267 q^{6} +0.767070 q^{7} +8.38515 q^{8} +2.14904 q^{9} +O(q^{10})$	\(q+2.67178 q^{2} -2.26915 q^{3} +5.13841 q^{4} -3.81472 q^{5} -6.06267 q^{6} +0.767070 q^{7} +8.38515 q^{8} +2.14904 q^{9} -10.1921 q^{10} -3.50387 q^{11} -11.6598 q^{12} -3.99988 q^{13} +2.04944 q^{14} +8.65616 q^{15} +12.1265 q^{16} +1.00000 q^{17} +5.74176 q^{18} -7.48497 q^{19} -19.6016 q^{20} -1.74060 q^{21} -9.36157 q^{22} -3.35147 q^{23} -19.0272 q^{24} +9.55206 q^{25} -10.6868 q^{26} +1.93096 q^{27} +3.94152 q^{28} -7.76321 q^{29} +23.1274 q^{30} +3.78202 q^{31} +15.6289 q^{32} +7.95080 q^{33} +2.67178 q^{34} -2.92616 q^{35} +11.0427 q^{36} -0.775849 q^{37} -19.9982 q^{38} +9.07632 q^{39} -31.9870 q^{40} -0.124996 q^{41} -4.65049 q^{42} +9.78511 q^{43} -18.0043 q^{44} -8.19798 q^{45} -8.95439 q^{46} -10.9899 q^{47} -27.5167 q^{48} -6.41160 q^{49} +25.5210 q^{50} -2.26915 q^{51} -20.5530 q^{52} -1.16150 q^{53} +5.15909 q^{54} +13.3663 q^{55} +6.43200 q^{56} +16.9845 q^{57} -20.7416 q^{58} +1.00000 q^{59} +44.4789 q^{60} +3.16854 q^{61} +10.1047 q^{62} +1.64846 q^{63} +17.5042 q^{64} +15.2584 q^{65} +21.2428 q^{66} +5.57191 q^{67} +5.13841 q^{68} +7.60498 q^{69} -7.81805 q^{70} +3.02937 q^{71} +18.0200 q^{72} +3.42854 q^{73} -2.07290 q^{74} -21.6751 q^{75} -38.4609 q^{76} -2.68771 q^{77} +24.2499 q^{78} +3.29209 q^{79} -46.2590 q^{80} -10.8287 q^{81} -0.333962 q^{82} -16.2473 q^{83} -8.94391 q^{84} -3.81472 q^{85} +26.1437 q^{86} +17.6159 q^{87} -29.3805 q^{88} +12.4772 q^{89} -21.9032 q^{90} -3.06819 q^{91} -17.2212 q^{92} -8.58196 q^{93} -29.3626 q^{94} +28.5530 q^{95} -35.4644 q^{96} +11.3482 q^{97} -17.1304 q^{98} -7.52995 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} - 7 q^{3} + 14 q^{4} - 21 q^{5} - 5 q^{6} - 11 q^{7} - 12 q^{8} + 17 q^{9}+O(q^{10}) $ 16 * q - 6 * q^2 - 7 * q^3 + 14 * q^4 - 21 * q^5 - 5 * q^6 - 11 * q^7 - 12 * q^8 + 17 * q^9	\( 16 q - 6 q^{2} - 7 q^{3} + 14 q^{4} - 21 q^{5} - 5 q^{6} - 11 q^{7} - 12 q^{8} + 17 q^{9} + 12 q^{10} - 7 q^{11} - 4 q^{12} - 16 q^{13} + 11 q^{14} + 7 q^{15} + 22 q^{16} + 16 q^{17} + 11 q^{18} + q^{19} - 43 q^{20} - 8 q^{21} - 18 q^{22} - 8 q^{23} - 39 q^{24} + 23 q^{25} - 49 q^{26} - 7 q^{27} - 15 q^{28} - 39 q^{29} + q^{30} - 3 q^{31} - 15 q^{33} - 6 q^{34} + 9 q^{35} - 17 q^{36} - 28 q^{37} - 27 q^{38} - 4 q^{39} + 26 q^{40} - 31 q^{41} - 45 q^{42} + 5 q^{43} - 19 q^{44} - 79 q^{45} - 39 q^{46} - 47 q^{47} - 31 q^{48} + 35 q^{49} - 13 q^{50} - 7 q^{51} + 9 q^{52} - 36 q^{53} + 9 q^{54} + 32 q^{55} + 3 q^{56} + 6 q^{57} + 22 q^{58} + 16 q^{59} + 6 q^{60} - 22 q^{61} + q^{62} - 19 q^{63} + 32 q^{64} - 19 q^{65} + 48 q^{66} + 4 q^{67} + 14 q^{68} + 14 q^{69} - 11 q^{70} - 5 q^{71} + 40 q^{72} - 35 q^{73} + 31 q^{74} - 12 q^{75} + q^{76} - 79 q^{77} + 31 q^{78} - 48 q^{79} - 127 q^{80} - 28 q^{81} - 7 q^{82} - 42 q^{83} + 28 q^{84} - 21 q^{85} + 58 q^{86} - 16 q^{87} - 2 q^{88} + 20 q^{89} - 14 q^{90} + 49 q^{91} - 21 q^{92} - 55 q^{93} - 22 q^{95} + 24 q^{96} - 2 q^{97} - 78 q^{98} - 35 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 - 7 * q^3 + 14 * q^4 - 21 * q^5 - 5 * q^6 - 11 * q^7 - 12 * q^8 + 17 * q^9 + 12 * q^10 - 7 * q^11 - 4 * q^12 - 16 * q^13 + 11 * q^14 + 7 * q^15 + 22 * q^16 + 16 * q^17 + 11 * q^18 + q^19 - 43 * q^20 - 8 * q^21 - 18 * q^22 - 8 * q^23 - 39 * q^24 + 23 * q^25 - 49 * q^26 - 7 * q^27 - 15 * q^28 - 39 * q^29 + q^30 - 3 * q^31 - 15 * q^33 - 6 * q^34 + 9 * q^35 - 17 * q^36 - 28 * q^37 - 27 * q^38 - 4 * q^39 + 26 * q^40 - 31 * q^41 - 45 * q^42 + 5 * q^43 - 19 * q^44 - 79 * q^45 - 39 * q^46 - 47 * q^47 - 31 * q^48 + 35 * q^49 - 13 * q^50 - 7 * q^51 + 9 * q^52 - 36 * q^53 + 9 * q^54 + 32 * q^55 + 3 * q^56 + 6 * q^57 + 22 * q^58 + 16 * q^59 + 6 * q^60 - 22 * q^61 + q^62 - 19 * q^63 + 32 * q^64 - 19 * q^65 + 48 * q^66 + 4 * q^67 + 14 * q^68 + 14 * q^69 - 11 * q^70 - 5 * q^71 + 40 * q^72 - 35 * q^73 + 31 * q^74 - 12 * q^75 + q^76 - 79 * q^77 + 31 * q^78 - 48 * q^79 - 127 * q^80 - 28 * q^81 - 7 * q^82 - 42 * q^83 + 28 * q^84 - 21 * q^85 + 58 * q^86 - 16 * q^87 - 2 * q^88 + 20 * q^89 - 14 * q^90 + 49 * q^91 - 21 * q^92 - 55 * q^93 - 22 * q^95 + 24 * q^96 - 2 * q^97 - 78 * q^98 - 35 * 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 $

$2$	2.67178	1.88923	0.944617	−	0.328174i	$-0.106433\pi$
$2$	2.67178	1.88923	0.944617	+	0.328174i	$0.106433\pi$
$3$	−2.26915	−1.31009	−0.655047	−	0.755588i	$-0.727351\pi$
$3$	−2.26915	−1.31009	−0.655047	+	0.755588i	$0.727351\pi$
$4$	5.13841	2.56921
$5$	−3.81472	−1.70599	−0.852997	−	0.521917i	$-0.825217\pi$
$5$	−3.81472	−1.70599	−0.852997	+	0.521917i	$0.825217\pi$
$6$	−6.06267	−2.47507
$7$	0.767070	0.289925	0.144963	−	0.989437i	$-0.453694\pi$
$7$	0.767070	0.289925	0.144963	+	0.989437i	$0.453694\pi$
$8$	8.38515	2.96460
$9$	2.14904	0.716347
$10$	−10.1921	−3.22302
$11$	−3.50387	−1.05646	−0.528228	−	0.849102i	$-0.677143\pi$
$11$	−3.50387	−1.05646	−0.528228	+	0.849102i	$0.677143\pi$
$12$	−11.6598	−3.36590
$13$	−3.99988	−1.10937	−0.554683	−	0.832062i	$-0.687160\pi$
$13$	−3.99988	−1.10937	−0.554683	+	0.832062i	$0.687160\pi$
$14$	2.04944	0.547737
$15$	8.65616	2.23501
$16$	12.1265	3.03161
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	5.74176	1.35335
$19$	−7.48497	−1.71717	−0.858585	−	0.512672i	$-0.828656\pi$
$19$	−7.48497	−1.71717	−0.858585	+	0.512672i	$0.828656\pi$
$20$	−19.6016	−4.38305
$21$	−1.74060	−0.379829
$22$	−9.36157	−1.99589
$23$	−3.35147	−0.698829	−0.349415	−	0.936968i	$-0.613620\pi$
$23$	−3.35147	−0.698829	−0.349415	+	0.936968i	$0.613620\pi$
$24$	−19.0272	−3.88390
$25$	9.55206	1.91041
$26$	−10.6868	−2.09585
$27$	1.93096	0.371613
$28$	3.94152	0.744878
$29$	−7.76321	−1.44159	−0.720796	−	0.693147i	$-0.756224\pi$
$29$	−7.76321	−1.44159	−0.720796	+	0.693147i	$0.756224\pi$
$30$	23.1274	4.22246
$31$	3.78202	0.679270	0.339635	−	0.940557i	$-0.389696\pi$
$31$	3.78202	0.679270	0.339635	+	0.940557i	$0.389696\pi$
$32$	15.6289	2.76283
$33$	7.95080	1.38406
$34$	2.67178	0.458207
$35$	−2.92616	−0.494611
$36$	11.0427	1.84044
$37$	−0.775849	−0.127549	−0.0637744	−	0.997964i	$-0.520314\pi$
$37$	−0.775849	−0.127549	−0.0637744	+	0.997964i	$0.520314\pi$
$38$	−19.9982	−3.24414
$39$	9.07632	1.45337
$40$	−31.9870	−5.05758
$41$	−0.124996	−0.0195211	−0.00976056	−	0.999952i	$-0.503107\pi$
$41$	−0.124996	−0.0195211	−0.00976056	+	0.999952i	$0.503107\pi$
$42$	−4.65049	−0.717587
$43$	9.78511	1.49222	0.746108	−	0.665825i	$-0.231920\pi$
$43$	9.78511	1.49222	0.746108	+	0.665825i	$0.231920\pi$
$44$	−18.0043	−2.71425
$45$	−8.19798	−1.22208
$46$	−8.95439	−1.32025
$47$	−10.9899	−1.60304	−0.801519	−	0.597969i	$-0.795975\pi$
$47$	−10.9899	−1.60304	−0.801519	+	0.597969i	$0.795975\pi$
$48$	−27.5167	−3.97170
$49$	−6.41160	−0.915943
$50$	25.5210	3.60922
$51$	−2.26915	−0.317744
$52$	−20.5530	−2.85019
$53$	−1.16150	−0.159544	−0.0797721	−	0.996813i	$-0.525419\pi$
$53$	−1.16150	−0.159544	−0.0797721	+	0.996813i	$0.525419\pi$
$54$	5.15909	0.702064
$55$	13.3663	1.80231
$56$	6.43200	0.859512
$57$	16.9845	2.24965
$58$	−20.7416	−2.72350
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	44.4789	5.74221
$61$	3.16854	0.405690	0.202845	−	0.979211i	$-0.434981\pi$
$61$	3.16854	0.405690	0.202845	+	0.979211i	$0.434981\pi$
$62$	10.1047	1.28330
$63$	1.64846	0.207687
$64$	17.5042	2.18802
$65$	15.2584	1.89257
$66$	21.2428	2.61481
$67$	5.57191	0.680717	0.340359	−	0.940296i	$-0.389452\pi$
$67$	5.57191	0.680717	0.340359	+	0.940296i	$0.389452\pi$
$68$	5.13841	0.623124
$69$	7.60498	0.915532
$70$	−7.81805	−0.934435
$71$	3.02937	0.359520	0.179760	−	0.983710i	$-0.442468\pi$
$71$	3.02937	0.359520	0.179760	+	0.983710i	$0.442468\pi$
$72$	18.0200	2.12368
$73$	3.42854	0.401280	0.200640	−	0.979665i	$-0.435698\pi$
$73$	3.42854	0.401280	0.200640	+	0.979665i	$0.435698\pi$
$74$	−2.07290	−0.240969
$75$	−21.6751	−2.50282
$76$	−38.4609	−4.41176
$77$	−2.68771	−0.306293
$78$	24.2499	2.74576
$79$	3.29209	0.370389	0.185195	−	0.982702i	$-0.440708\pi$
$79$	3.29209	0.370389	0.185195	+	0.982702i	$0.440708\pi$
$80$	−46.2590	−5.17191
$81$	−10.8287	−1.20319
$82$	−0.333962	−0.0368800
$83$	−16.2473	−1.78337	−0.891684	−	0.452658i	$-0.850476\pi$
$83$	−16.2473	−1.78337	−0.891684	+	0.452658i	$0.850476\pi$
$84$	−8.94391	−0.975860
$85$	−3.81472	−0.413764
$86$	26.1437	2.81914
$87$	17.6159	1.88862
$88$	−29.3805	−3.13197
$89$	12.4772	1.32258	0.661289	−	0.750132i	$-0.270010\pi$
$89$	12.4772	1.32258	0.661289	+	0.750132i	$0.270010\pi$
$90$	−21.9032	−2.30880
$91$	−3.06819	−0.321633
$92$	−17.2212	−1.79544
$93$	−8.58196	−0.889908
$94$	−29.3626	−3.02852
$95$	28.5530	2.92948
$96$	−35.4644	−3.61957
$97$	11.3482	1.15223	0.576117	−	0.817367i	$-0.304567\pi$
$97$	11.3482	1.15223	0.576117	+	0.817367i	$0.304567\pi$
$98$	−17.1304	−1.73043
$99$	−7.52995	−0.756789
$100$	49.0824	4.90824
$101$	10.2160	1.01653	0.508264	−	0.861201i	$-0.330287\pi$
$101$	10.2160	1.01653	0.508264	+	0.861201i	$0.330287\pi$
$102$	−6.06267	−0.600294
$103$	−4.33526	−0.427166	−0.213583	−	0.976925i	$-0.568513\pi$
$103$	−4.33526	−0.427166	−0.213583	+	0.976925i	$0.568513\pi$
$104$	−33.5396	−3.28882
$105$	6.63988	0.647986
$106$	−3.10327	−0.301416
$107$	15.7399	1.52163	0.760815	−	0.648969i	$-0.224799\pi$
$107$	15.7399	1.52163	0.760815	+	0.648969i	$0.224799\pi$
$108$	9.92205	0.954750
$109$	−18.8167	−1.80231	−0.901157	−	0.433492i	$-0.857281\pi$
$109$	−18.8167	−1.80231	−0.901157	+	0.433492i	$0.857281\pi$
$110$	35.7117	3.40498
$111$	1.76052	0.167101
$112$	9.30184	0.878942
$113$	3.80652	0.358088	0.179044	−	0.983841i	$-0.442700\pi$
$113$	3.80652	0.358088	0.179044	+	0.983841i	$0.442700\pi$
$114$	45.3789	4.25012
$115$	12.7849	1.19220
$116$	−39.8906	−3.70375
$117$	−8.59589	−0.794691
$118$	2.67178	0.245957
$119$	0.767070	0.0703172
$120$	72.5832	6.62591
$121$	1.27710	0.116100
$122$	8.46564	0.766443
$123$	0.283635	0.0255745
$124$	19.4336	1.74519
$125$	−17.3648	−1.55316
$126$	4.40434	0.392369
$127$	1.05083	0.0932461	0.0466231	−	0.998913i	$-0.485154\pi$
$127$	1.05083	0.0932461	0.0466231	+	0.998913i	$0.485154\pi$
$128$	15.5094	1.37085
$129$	−22.2039	−1.95494
$130$	40.7671	3.57551
$131$	1.64347	0.143590	0.0717951	−	0.997419i	$-0.477127\pi$
$131$	1.64347	0.143590	0.0717951	+	0.997419i	$0.477127\pi$
$132$	40.8545	3.55593
$133$	−5.74150	−0.497851
$134$	14.8869	1.28603
$135$	−7.36605	−0.633969
$136$	8.38515	0.719021
$137$	−6.24128	−0.533228	−0.266614	−	0.963803i	$-0.585905\pi$
$137$	−6.24128	−0.533228	−0.266614	+	0.963803i	$0.585905\pi$
$138$	20.3188	1.72966
$139$	16.1620	1.37084	0.685420	−	0.728148i	$-0.259619\pi$
$139$	16.1620	1.37084	0.685420	+	0.728148i	$0.259619\pi$
$140$	−15.0358	−1.27076
$141$	24.9377	2.10013
$142$	8.09382	0.679218
$143$	14.0150	1.17200
$144$	26.0602	2.17169
$145$	29.6144	2.45935
$146$	9.16031	0.758113
$147$	14.5489	1.19997
$148$	−3.98663	−0.327699
$149$	−2.77682	−0.227486	−0.113743	−	0.993510i	$-0.536284\pi$
$149$	−2.77682	−0.227486	−0.113743	+	0.993510i	$0.536284\pi$
$150$	−57.9110	−4.72841
$151$	−19.1274	−1.55656	−0.778281	−	0.627916i	$-0.783908\pi$
$151$	−19.1274	−1.55656	−0.778281	+	0.627916i	$0.783908\pi$
$152$	−62.7626	−5.09072
$153$	2.14904	0.173740
$154$	−7.18098	−0.578660
$155$	−14.4273	−1.15883
$156$	46.6379	3.73402
$157$	15.5064	1.23755	0.618773	−	0.785570i	$-0.287630\pi$
$157$	15.5064	1.23755	0.618773	+	0.785570i	$0.287630\pi$
$158$	8.79574	0.699752
$159$	2.63562	0.209018
$160$	−59.6200	−4.71337
$161$	−2.57081	−0.202608
$162$	−28.9320	−2.27312
$163$	−18.6605	−1.46160	−0.730802	−	0.682589i	$-0.760854\pi$
$163$	−18.6605	−1.46160	−0.730802	+	0.682589i	$0.760854\pi$
$164$	−0.642282	−0.0501538
$165$	−30.3301	−2.36119
$166$	−43.4091	−3.36920
$167$	−4.43275	−0.343016	−0.171508	−	0.985183i	$-0.554864\pi$
$167$	−4.43275	−0.343016	−0.171508	+	0.985183i	$0.554864\pi$
$168$	−14.5952	−1.12604
$169$	2.99901	0.230693
$170$	−10.1921	−0.781697
$171$	−16.0855	−1.23009
$172$	50.2799	3.83381
$173$	−12.3574	−0.939516	−0.469758	−	0.882795i	$-0.655659\pi$
$173$	−12.3574	−0.939516	−0.469758	+	0.882795i	$0.655659\pi$
$174$	47.0658	3.56805
$175$	7.32710	0.553877
$176$	−42.4895	−3.20277
$177$	−2.26915	−0.170560
$178$	33.3363	2.49866
$179$	13.8715	1.03681	0.518403	−	0.855136i	$-0.326527\pi$
$179$	13.8715	1.03681	0.518403	+	0.855136i	$0.326527\pi$
$180$	−42.1246	−3.13978
$181$	−4.42893	−0.329200	−0.164600	−	0.986360i	$-0.552633\pi$
$181$	−4.42893	−0.329200	−0.164600	+	0.986360i	$0.552633\pi$
$182$	−8.19752	−0.607641
$183$	−7.18989	−0.531492
$184$	−28.1026	−2.07175
$185$	2.95964	0.217597
$186$	−22.9291	−1.68124
$187$	−3.50387	−0.256228
$188$	−56.4705	−4.11854
$189$	1.48118	0.107740
$190$	76.2874	5.53447
$191$	−21.0811	−1.52537	−0.762687	−	0.646767i	$-0.776121\pi$
$191$	−21.0811	−1.52537	−0.762687	+	0.646767i	$0.776121\pi$
$192$	−39.7196	−2.86651
$193$	−13.7189	−0.987509	−0.493755	−	0.869601i	$-0.664376\pi$
$193$	−13.7189	−0.987509	−0.493755	+	0.869601i	$0.664376\pi$
$194$	30.3199	2.17684
$195$	−34.6236	−2.47945
$196$	−32.9455	−2.35325
$197$	−13.5079	−0.962400	−0.481200	−	0.876611i	$-0.659799\pi$
$197$	−13.5079	−0.962400	−0.481200	+	0.876611i	$0.659799\pi$
$198$	−20.1184	−1.42975
$199$	24.5871	1.74293	0.871465	−	0.490457i	$-0.163170\pi$
$199$	24.5871	1.74293	0.871465	+	0.490457i	$0.163170\pi$
$200$	80.0955	5.66360
$201$	−12.6435	−0.891803
$202$	27.2949	1.92046
$203$	−5.95493	−0.417954
$204$	−11.6598	−0.816351
$205$	0.476825	0.0333029
$206$	−11.5829	−0.807016
$207$	−7.20244	−0.500604
$208$	−48.5043	−3.36317
$209$	26.2263	1.81411
$210$	17.7403	1.22420
$211$	−10.7605	−0.740782	−0.370391	−	0.928876i	$-0.620776\pi$
$211$	−10.7605	−0.740782	−0.370391	+	0.928876i	$0.620776\pi$
$212$	−5.96826	−0.409902
$213$	−6.87410	−0.471005
$214$	42.0535	2.87472
$215$	−37.3274	−2.54571
$216$	16.1914	1.10168
$217$	2.90107	0.196938
$218$	−50.2741	−3.40499
$219$	−7.77987	−0.525715
$220$	68.6814	4.63050
$221$	−3.99988	−0.269061
$222$	4.70371	0.315693
$223$	0.960530	0.0643219	0.0321609	−	0.999483i	$-0.489761\pi$
$223$	0.960530	0.0643219	0.0321609	+	0.999483i	$0.489761\pi$
$224$	11.9885	0.801015
$225$	20.5278	1.36852
$226$	10.1702	0.676511
$227$	−24.1708	−1.60428	−0.802138	−	0.597139i	$-0.796304\pi$
$227$	−24.1708	−1.60428	−0.802138	+	0.597139i	$0.796304\pi$
$228$	87.2734	5.77982
$229$	−2.64948	−0.175082	−0.0875412	−	0.996161i	$-0.527901\pi$
$229$	−2.64948	−0.175082	−0.0875412	+	0.996161i	$0.527901\pi$
$230$	34.1585	2.25234
$231$	6.09882	0.401273
$232$	−65.0957	−4.27374
$233$	−19.1172	−1.25241	−0.626206	−	0.779658i	$-0.715393\pi$
$233$	−19.1172	−1.25241	−0.626206	+	0.779658i	$0.715393\pi$
$234$	−22.9663	−1.50136
$235$	41.9233	2.73477
$236$	5.13841	0.334482
$237$	−7.47025	−0.485245
$238$	2.04944	0.132846
$239$	−12.0938	−0.782282	−0.391141	−	0.920331i	$-0.627920\pi$
$239$	−12.0938	−0.782282	−0.391141	+	0.920331i	$0.627920\pi$
$240$	104.969	6.77569
$241$	−18.5384	−1.19416	−0.597081	−	0.802181i	$-0.703673\pi$
$241$	−18.5384	−1.19416	−0.597081	+	0.802181i	$0.703673\pi$
$242$	3.41213	0.219340
$243$	18.7792	1.20468
$244$	16.2813	1.04230
$245$	24.4584	1.56259
$246$	0.757811	0.0483163
$247$	29.9389	1.90497
$248$	31.7128	2.01376
$249$	36.8675	2.33638
$250$	−46.3950	−2.93428
$251$	23.6940	1.49555	0.747776	−	0.663951i	$-0.231122\pi$
$251$	23.6940	1.49555	0.747776	+	0.663951i	$0.231122\pi$
$252$	8.47049	0.533591
$253$	11.7431	0.738283
$254$	2.80759	0.176164
$255$	8.65616	0.542070
$256$	6.42948	0.401843
$257$	−30.2718	−1.88830	−0.944151	−	0.329514i	$-0.893115\pi$
$257$	−30.2718	−1.88830	−0.944151	+	0.329514i	$0.893115\pi$
$258$	−59.3239	−3.69334
$259$	−0.595130	−0.0369796
$260$	78.4039	4.86240
$261$	−16.6834	−1.03268
$262$	4.39098	0.271276
$263$	17.9576	1.10731	0.553655	−	0.832746i	$-0.313233\pi$
$263$	17.9576	1.10731	0.553655	+	0.832746i	$0.313233\pi$
$264$	66.6687	4.10317
$265$	4.43079	0.272181
$266$	−15.3400	−0.940557
$267$	−28.3126	−1.73270
$268$	28.6308	1.74890
$269$	−16.7717	−1.02259	−0.511294	−	0.859406i	$-0.670834\pi$
$269$	−16.7717	−1.02259	−0.511294	+	0.859406i	$0.670834\pi$
$270$	−19.6805	−1.19772
$271$	4.86900	0.295771	0.147885	−	0.989005i	$-0.452753\pi$
$271$	4.86900	0.295771	0.147885	+	0.989005i	$0.452753\pi$
$272$	12.1265	0.735274
$273$	6.96217	0.421370
$274$	−16.6753	−1.00739
$275$	−33.4692	−2.01827
$276$	39.0775	2.35219
$277$	−6.76053	−0.406201	−0.203100	−	0.979158i	$-0.565102\pi$
$277$	−6.76053	−0.406201	−0.203100	+	0.979158i	$0.565102\pi$
$278$	43.1812	2.58984
$279$	8.12770	0.486593
$280$	−24.5363	−1.46632
$281$	−15.6033	−0.930814	−0.465407	−	0.885097i	$-0.654092\pi$
$281$	−15.6033	−0.930814	−0.465407	+	0.885097i	$0.654092\pi$
$282$	66.6280	3.96764
$283$	−12.2312	−0.727070	−0.363535	−	0.931581i	$-0.618430\pi$
$283$	−12.2312	−0.727070	−0.363535	+	0.931581i	$0.618430\pi$
$284$	15.5662	0.923682
$285$	−64.7911	−3.83789
$286$	37.4451	2.21418
$287$	−0.0958809	−0.00565967
$288$	33.5872	1.97914
$289$	1.00000	0.0588235
$290$	79.1233	4.64628
$291$	−25.7507	−1.50953
$292$	17.6173	1.03097
$293$	−15.8721	−0.927257	−0.463629	−	0.886030i	$-0.653453\pi$
$293$	−15.8721	−0.927257	−0.463629	+	0.886030i	$0.653453\pi$
$294$	38.8714	2.26703
$295$	−3.81472	−0.222101
$296$	−6.50561	−0.378131
$297$	−6.76582	−0.392593
$298$	−7.41905	−0.429774
$299$	13.4055	0.775258
$300$	−111.375	−6.43026
$301$	7.50587	0.432631
$302$	−51.1041	−2.94071
$303$	−23.1816	−1.33175
$304$	−90.7661	−5.20580
$305$	−12.0871	−0.692104
$306$	5.74176	0.328235
$307$	−1.90522	−0.108737	−0.0543683	−	0.998521i	$-0.517314\pi$
$307$	−1.90522	−0.108737	−0.0543683	+	0.998521i	$0.517314\pi$
$308$	−13.8106	−0.786931
$309$	9.83735	0.559627
$310$	−38.5466	−2.18930
$311$	9.99366	0.566689	0.283344	−	0.959018i	$-0.408556\pi$
$311$	9.99366	0.566689	0.283344	+	0.959018i	$0.408556\pi$
$312$	76.1063	4.30867
$313$	−25.7403	−1.45493	−0.727464	−	0.686145i	$-0.759301\pi$
$313$	−25.7403	−1.45493	−0.727464	+	0.686145i	$0.759301\pi$
$314$	41.4297	2.33801
$315$	−6.28842	−0.354313
$316$	16.9161	0.951606
$317$	−0.205570	−0.0115459	−0.00577297	−	0.999983i	$-0.501838\pi$
$317$	−0.205570	−0.0115459	−0.00577297	+	0.999983i	$0.501838\pi$
$318$	7.04179	0.394884
$319$	27.2013	1.52298
$320$	−66.7735	−3.73275
$321$	−35.7161	−1.99348
$322$	−6.86865	−0.382775
$323$	−7.48497	−0.416475
$324$	−55.6426	−3.09125
$325$	−38.2071	−2.11935
$326$	−49.8568	−2.76131
$327$	42.6979	2.36120
$328$	−1.04811	−0.0578723
$329$	−8.43001	−0.464762
$330$	−81.0353	−4.46084
$331$	15.8494	0.871160	0.435580	−	0.900150i	$-0.356543\pi$
$331$	15.8494	0.871160	0.435580	+	0.900150i	$0.356543\pi$
$332$	−83.4851	−4.58184
$333$	−1.66733	−0.0913691
$334$	−11.8433	−0.648038
$335$	−21.2553	−1.16130
$336$	−21.1073	−1.15150
$337$	28.8732	1.57282	0.786412	−	0.617703i	$-0.211937\pi$
$337$	28.8732	1.57282	0.786412	+	0.617703i	$0.211937\pi$
$338$	8.01270	0.435833
$339$	−8.63757	−0.469128
$340$	−19.6016	−1.06305
$341$	−13.2517	−0.717619
$342$	−42.9769	−2.32393
$343$	−10.2876	−0.555480
$344$	82.0496	4.42382
$345$	−29.0109	−1.56189
$346$	−33.0163	−1.77497
$347$	8.01828	0.430444	0.215222	−	0.976565i	$-0.430953\pi$
$347$	8.01828	0.430444	0.215222	+	0.976565i	$0.430953\pi$
$348$	90.5177	4.85226
$349$	−27.8072	−1.48848	−0.744242	−	0.667910i	$-0.767189\pi$
$349$	−27.8072	−1.48848	−0.744242	+	0.667910i	$0.767189\pi$
$350$	19.5764	1.04640
$351$	−7.72359	−0.412255
$352$	−54.7617	−2.91881
$353$	−12.4845	−0.664480	−0.332240	−	0.943195i	$-0.607804\pi$
$353$	−12.4845	−0.664480	−0.332240	+	0.943195i	$0.607804\pi$
$354$	−6.06267	−0.322227
$355$	−11.5562	−0.613339
$356$	64.1128	3.39797
$357$	−1.74060	−0.0921222
$358$	37.0617	1.95877
$359$	37.2241	1.96461	0.982307	−	0.187276i	$-0.0599657\pi$
$359$	37.2241	1.96461	0.982307	+	0.187276i	$0.0599657\pi$
$360$	−68.7413	−3.62298
$361$	37.0248	1.94867
$362$	−11.8331	−0.621935
$363$	−2.89793	−0.152102
$364$	−15.7656	−0.826342
$365$	−13.0789	−0.684581
$366$	−19.2098	−1.00411
$367$	21.1015	1.10149	0.550745	−	0.834674i	$-0.314344\pi$
$367$	21.1015	1.10149	0.550745	+	0.834674i	$0.314344\pi$
$368$	−40.6414	−2.11858
$369$	−0.268622	−0.0139839
$370$	7.90752	0.411092
$371$	−0.890951	−0.0462559
$372$	−44.0977	−2.28636
$373$	26.1408	1.35352	0.676758	−	0.736205i	$-0.263384\pi$
$373$	26.1408	1.35352	0.676758	+	0.736205i	$0.263384\pi$
$374$	−9.36157	−0.484075
$375$	39.4034	2.03478
$376$	−92.1518	−4.75237
$377$	31.0519	1.59925
$378$	3.95739	0.203546
$379$	18.2354	0.936687	0.468344	−	0.883546i	$-0.344851\pi$
$379$	18.2354	0.936687	0.468344	+	0.883546i	$0.344851\pi$
$380$	146.717	7.52644
$381$	−2.38449	−0.122161
$382$	−56.3241	−2.88179
$383$	−8.90122	−0.454831	−0.227416	−	0.973798i	$-0.573028\pi$
$383$	−8.90122	−0.454831	−0.227416	+	0.973798i	$0.573028\pi$
$384$	−35.1932	−1.79595
$385$	10.2529	0.522534
$386$	−36.6539	−1.86564
$387$	21.0286	1.06894
$388$	58.3116	2.96033
$389$	−16.7355	−0.848524	−0.424262	−	0.905539i	$-0.639467\pi$
$389$	−16.7355	−0.848524	−0.424262	+	0.905539i	$0.639467\pi$
$390$	−92.5066	−4.68425
$391$	−3.35147	−0.169491
$392$	−53.7623	−2.71540
$393$	−3.72927	−0.188117
$394$	−36.0902	−1.81820
$395$	−12.5584	−0.631881
$396$	−38.6920	−1.94435
$397$	−0.222447	−0.0111643	−0.00558215	−	0.999984i	$-0.501777\pi$
$397$	−0.222447	−0.0111643	−0.00558215	+	0.999984i	$0.501777\pi$
$398$	65.6912	3.29280
$399$	13.0283	0.652232
$400$	115.833	5.79163
$401$	−31.4214	−1.56911	−0.784554	−	0.620060i	$-0.787108\pi$
$401$	−31.4214	−1.56911	−0.784554	+	0.620060i	$0.787108\pi$
$402$	−33.7806	−1.68483
$403$	−15.1276	−0.753559
$404$	52.4939	2.61167
$405$	41.3086	2.05264
$406$	−15.9103	−0.789613
$407$	2.71847	0.134750
$408$	−19.0272	−0.941985
$409$	34.2231	1.69222	0.846112	−	0.533005i	$-0.178937\pi$
$409$	34.2231	1.69222	0.846112	+	0.533005i	$0.178937\pi$
$410$	1.27397	0.0629170
$411$	14.1624	0.698579
$412$	−22.2763	−1.09748
$413$	0.767070	0.0377451
$414$	−19.2433	−0.945758
$415$	61.9787	3.04241
$416$	−62.5138	−3.06499
$417$	−36.6739	−1.79593
$418$	70.0711	3.42729
$419$	2.04697	0.100001	0.0500005	−	0.998749i	$-0.484078\pi$
$419$	2.04697	0.100001	0.0500005	+	0.998749i	$0.484078\pi$
$420$	34.1185	1.66481
$421$	6.70804	0.326930	0.163465	−	0.986549i	$-0.447733\pi$
$421$	6.70804	0.326930	0.163465	+	0.986549i	$0.447733\pi$
$422$	−28.7496	−1.39951
$423$	−23.6177	−1.14833
$424$	−9.73934	−0.472984
$425$	9.55206	0.463343
$426$	−18.3661	−0.889839
$427$	2.43049	0.117620
$428$	80.8779	3.90938
$429$	−31.8022	−1.53543
$430$	−99.7307	−4.80944
$431$	39.0860	1.88271	0.941354	−	0.337421i	$-0.109554\pi$
$431$	39.0860	1.88271	0.941354	+	0.337421i	$0.109554\pi$
$432$	23.4157	1.12659
$433$	−24.8823	−1.19577	−0.597883	−	0.801583i	$-0.703991\pi$
$433$	−24.8823	−1.19577	−0.597883	+	0.801583i	$0.703991\pi$
$434$	7.75103	0.372061
$435$	−67.1996	−3.22197
$436$	−96.6881	−4.63052
$437$	25.0856	1.20001
$438$	−20.7861	−0.993199
$439$	−25.1140	−1.19863	−0.599313	−	0.800515i	$-0.704560\pi$
$439$	−25.1140	−1.19863	−0.599313	+	0.800515i	$0.704560\pi$
$440$	112.078	5.34312
$441$	−13.7788	−0.656133
$442$	−10.6868	−0.508319
$443$	5.96511	0.283411	0.141706	−	0.989909i	$-0.454741\pi$
$443$	5.96511	0.283411	0.141706	+	0.989909i	$0.454741\pi$
$444$	9.04626	0.429317
$445$	−47.5969	−2.25631
$446$	2.56633	0.121519
$447$	6.30101	0.298028
$448$	13.4269	0.634363
$449$	3.99223	0.188405	0.0942026	−	0.995553i	$-0.469970\pi$
$449$	3.99223	0.188405	0.0942026	+	0.995553i	$0.469970\pi$
$450$	54.8457	2.58545
$451$	0.437970	0.0206232
$452$	19.5595	0.920001
$453$	43.4028	2.03924
$454$	−64.5792	−3.03085
$455$	11.7043	0.548704
$456$	142.418	6.66932
$457$	32.2678	1.50943	0.754713	−	0.656055i	$-0.227776\pi$
$457$	32.2678	1.50943	0.754713	+	0.656055i	$0.227776\pi$
$458$	−7.07882	−0.330772
$459$	1.93096	0.0901293
$460$	65.6941	3.06300
$461$	−11.2929	−0.525963	−0.262982	−	0.964801i	$-0.584706\pi$
$461$	−11.2929	−0.525963	−0.262982	+	0.964801i	$0.584706\pi$
$462$	16.2947	0.758099
$463$	4.17184	0.193882	0.0969410	−	0.995290i	$-0.469094\pi$
$463$	4.17184	0.193882	0.0969410	+	0.995290i	$0.469094\pi$
$464$	−94.1402	−4.37035
$465$	32.7378	1.51818
$466$	−51.0771	−2.36610
$467$	8.77446	0.406034	0.203017	−	0.979175i	$-0.434925\pi$
$467$	8.77446	0.406034	0.203017	+	0.979175i	$0.434925\pi$
$468$	−44.1692	−2.04172
$469$	4.27405	0.197357
$470$	112.010	5.16663
$471$	−35.1863	−1.62130
$472$	8.38515	0.385958
$473$	−34.2857	−1.57646
$474$	−19.9589	−0.916741
$475$	−71.4969	−3.28050
$476$	3.94152	0.180659
$477$	−2.49611	−0.114289
$478$	−32.3120	−1.47791
$479$	5.74847	0.262655	0.131327	−	0.991339i	$-0.458076\pi$
$479$	5.74847	0.262655	0.131327	+	0.991339i	$0.458076\pi$
$480$	135.287	6.17496
$481$	3.10330	0.141498
$482$	−49.5305	−2.25605
$483$	5.83356	0.265436
$484$	6.56226	0.298284
$485$	−43.2901	−1.96570
$486$	50.1738	2.27593
$487$	−15.1688	−0.687365	−0.343682	−	0.939086i	$-0.611674\pi$
$487$	−15.1688	−0.687365	−0.343682	+	0.939086i	$0.611674\pi$
$488$	26.5687	1.20271
$489$	42.3435	1.91484
$490$	65.3476	2.95210
$491$	20.4825	0.924361	0.462180	−	0.886786i	$-0.347067\pi$
$491$	20.4825	0.924361	0.462180	+	0.886786i	$0.347067\pi$
$492$	1.45743	0.0657062
$493$	−7.76321	−0.349637
$494$	79.9903	3.59893
$495$	28.7246	1.29108
$496$	45.8625	2.05929
$497$	2.32374	0.104234
$498$	98.5018	4.41397
$499$	−5.96562	−0.267058	−0.133529	−	0.991045i	$-0.542631\pi$
$499$	−5.96562	−0.267058	−0.133529	+	0.991045i	$0.542631\pi$
$500$	−89.2276	−3.99038
$501$	10.0586	0.449384
$502$	63.3052	2.82545
$503$	17.2200	0.767800	0.383900	−	0.923375i	$-0.374581\pi$
$503$	17.2200	0.767800	0.383900	+	0.923375i	$0.374581\pi$
$504$	13.8226	0.615708
$505$	−38.9711	−1.73419
$506$	31.3750	1.39479
$507$	−6.80520	−0.302230
$508$	5.39960	0.239569
$509$	−2.35476	−0.104373	−0.0521864	−	0.998637i	$-0.516619\pi$
$509$	−2.35476	−0.104373	−0.0521864	+	0.998637i	$0.516619\pi$
$510$	23.1274	1.02410
$511$	2.62993	0.116341
$512$	−13.8407	−0.611679
$513$	−14.4531	−0.638122
$514$	−80.8796	−3.56744
$515$	16.5378	0.728741
$516$	−114.093	−5.02265
$517$	38.5071	1.69354
$518$	−1.59006	−0.0698631
$519$	28.0408	1.23085
$520$	127.944	5.61071
$521$	−23.5218	−1.03051	−0.515255	−	0.857037i	$-0.672303\pi$
$521$	−23.5218	−1.03051	−0.515255	+	0.857037i	$0.672303\pi$
$522$	−44.5745	−1.95097
$523$	−23.0810	−1.00926	−0.504630	−	0.863336i	$-0.668371\pi$
$523$	−23.0810	−1.00926	−0.504630	+	0.863336i	$0.668371\pi$
$524$	8.44480	0.368913
$525$	−16.6263	−0.725631
$526$	47.9786	2.09197
$527$	3.78202	0.164747
$528$	96.4151	4.19593
$529$	−11.7677	−0.511637
$530$	11.8381	0.514214
$531$	2.14904	0.0932604
$532$	−29.5022	−1.27908
$533$	0.499969	0.0216561
$534$	−75.6449	−3.27348
$535$	−60.0431	−2.59589
$536$	46.7213	2.01805
$537$	−31.4766	−1.35831
$538$	−44.8103	−1.93191
$539$	22.4654	0.967654
$540$	−37.8498	−1.62880
$541$	22.8307	0.981566	0.490783	−	0.871282i	$-0.336711\pi$
$541$	22.8307	0.981566	0.490783	+	0.871282i	$0.336711\pi$
$542$	13.0089	0.558780
$543$	10.0499	0.431283
$544$	15.6289	0.670085
$545$	71.7804	3.07474
$546$	18.6014	0.796066
$547$	22.2941	0.953229	0.476614	−	0.879112i	$-0.341864\pi$
$547$	22.2941	0.953229	0.476614	+	0.879112i	$0.341864\pi$
$548$	−32.0703	−1.36997
$549$	6.80931	0.290614
$550$	−89.4223	−3.81298
$551$	58.1074	2.47546
$552$	63.7689	2.71419
$553$	2.52526	0.107385
$554$	−18.0627	−0.767409
$555$	−6.71587	−0.285073
$556$	83.0468	3.52197
$557$	4.54047	0.192386	0.0961930	−	0.995363i	$-0.469333\pi$
$557$	4.54047	0.192386	0.0961930	+	0.995363i	$0.469333\pi$
$558$	21.7154	0.919288
$559$	−39.1392	−1.65541
$560$	−35.4839	−1.49947
$561$	7.95080	0.335683
$562$	−41.6886	−1.75853
$563$	46.8592	1.97488	0.987440	−	0.157995i	$-0.0505031\pi$
$563$	46.8592	1.97488	0.987440	+	0.157995i	$0.0505031\pi$
$564$	128.140	5.39567
$565$	−14.5208	−0.610895
$566$	−32.6791	−1.37360
$567$	−8.30641	−0.348836
$568$	25.4017	1.06583
$569$	−1.78407	−0.0747919	−0.0373960	−	0.999301i	$-0.511906\pi$
$569$	−1.78407	−0.0747919	−0.0373960	+	0.999301i	$0.511906\pi$
$570$	−173.108	−7.25068
$571$	10.6689	0.446481	0.223241	−	0.974763i	$-0.428336\pi$
$571$	10.6689	0.446481	0.223241	+	0.974763i	$0.428336\pi$
$572$	72.0151	3.01110
$573$	47.8362	1.99838
$574$	−0.256173	−0.0106924
$575$	−32.0134	−1.33505
$576$	37.6172	1.56738
$577$	16.0025	0.666192	0.333096	−	0.942893i	$-0.391907\pi$
$577$	16.0025	0.666192	0.333096	+	0.942893i	$0.391907\pi$
$578$	2.67178	0.111131
$579$	31.1303	1.29373
$580$	152.171	6.31857
$581$	−12.4628	−0.517044
$582$	−68.8003	−2.85186
$583$	4.06974	0.168551
$584$	28.7488	1.18963
$585$	32.7909	1.35574
$586$	−42.4067	−1.75181
$587$	−42.0016	−1.73359	−0.866796	−	0.498662i	$-0.833825\pi$
$587$	−42.0016	−1.73359	−0.866796	+	0.498662i	$0.833825\pi$
$588$	74.7582	3.08298
$589$	−28.3083	−1.16642
$590$	−10.1921	−0.419602
$591$	30.6515	1.26083
$592$	−9.40830	−0.386679
$593$	−16.9108	−0.694443	−0.347221	−	0.937783i	$-0.612875\pi$
$593$	−16.9108	−0.694443	−0.347221	+	0.937783i	$0.612875\pi$
$594$	−18.0768	−0.741699
$595$	−2.92616	−0.119961
$596$	−14.2684	−0.584458
$597$	−55.7917	−2.28340
$598$	35.8164	1.46464
$599$	−6.45589	−0.263780	−0.131890	−	0.991264i	$-0.542105\pi$
$599$	−6.45589	−0.263780	−0.131890	+	0.991264i	$0.542105\pi$
$600$	−181.749	−7.41985
$601$	22.1832	0.904872	0.452436	−	0.891797i	$-0.350555\pi$
$601$	22.1832	0.904872	0.452436	+	0.891797i	$0.350555\pi$
$602$	20.0540	0.817341
$603$	11.9743	0.487629
$604$	−98.2842	−3.99913
$605$	−4.87177	−0.198066
$606$	−61.9361	−2.51598
$607$	−22.8614	−0.927916	−0.463958	−	0.885857i	$-0.653571\pi$
$607$	−22.8614	−0.927916	−0.463958	+	0.885857i	$0.653571\pi$
$608$	−116.982	−4.74425
$609$	13.5126	0.547559
$610$	−32.2940	−1.30755
$611$	43.9582	1.77836
$612$	11.0427	0.446373
$613$	−15.9785	−0.645367	−0.322684	−	0.946507i	$-0.604585\pi$
$613$	−15.9785	−0.645367	−0.322684	+	0.946507i	$0.604585\pi$
$614$	−5.09032	−0.205429
$615$	−1.08199	−0.0436299
$616$	−22.5369	−0.908037
$617$	−47.0320	−1.89344	−0.946719	−	0.322062i	$-0.895624\pi$
$617$	−47.0320	−1.89344	−0.946719	+	0.322062i	$0.895624\pi$
$618$	26.2832	1.05727
$619$	21.0374	0.845564	0.422782	−	0.906231i	$-0.361054\pi$
$619$	21.0374	0.845564	0.422782	+	0.906231i	$0.361054\pi$
$620$	−74.1335	−2.97727
$621$	−6.47154	−0.259694
$622$	26.7009	1.07061
$623$	9.57086	0.383449
$624$	110.064	4.40607
$625$	18.4816	0.739263
$626$	−68.7725	−2.74870
$627$	−59.5115	−2.37666
$628$	79.6783	3.17951
$629$	−0.775849	−0.0309351
$630$	−16.8013	−0.669379
$631$	−2.63139	−0.104754	−0.0523771	−	0.998627i	$-0.516680\pi$
$631$	−2.63139	−0.104754	−0.0523771	+	0.998627i	$0.516680\pi$
$632$	27.6047	1.09805
$633$	24.4171	0.970494
$634$	−0.549237	−0.0218130
$635$	−4.00862	−0.159077
$636$	13.5429	0.537010
$637$	25.6456	1.01612
$638$	72.6758	2.87726
$639$	6.51024	0.257541
$640$	−59.1641	−2.33867
$641$	−4.04389	−0.159724	−0.0798620	−	0.996806i	$-0.525448\pi$
$641$	−4.04389	−0.159724	−0.0798620	+	0.996806i	$0.525448\pi$
$642$	−95.4256	−3.76615
$643$	22.9665	0.905710	0.452855	−	0.891584i	$-0.350406\pi$
$643$	22.9665	0.905710	0.452855	+	0.891584i	$0.350406\pi$
$644$	−13.2099	−0.520543
$645$	84.7015	3.33512
$646$	−19.9982	−0.786818
$647$	28.8990	1.13614	0.568068	−	0.822982i	$-0.307691\pi$
$647$	28.8990	1.13614	0.568068	+	0.822982i	$0.307691\pi$
$648$	−90.8007	−3.56699
$649$	−3.50387	−0.137539
$650$	−102.081	−4.00394
$651$	−6.58297	−0.258007
$652$	−95.8854	−3.75516
$653$	2.23346	0.0874021	0.0437010	−	0.999045i	$-0.486085\pi$
$653$	2.23346	0.0874021	0.0437010	+	0.999045i	$0.486085\pi$
$654$	114.080	4.46086
$655$	−6.26936	−0.244964
$656$	−1.51576	−0.0591805
$657$	7.36807	0.287456
$658$	−22.5231	−0.878043
$659$	−23.6620	−0.921739	−0.460869	−	0.887468i	$-0.652462\pi$
$659$	−23.6620	−0.921739	−0.460869	+	0.887468i	$0.652462\pi$
$660$	−155.848	−6.06639
$661$	11.3385	0.441017	0.220509	−	0.975385i	$-0.429228\pi$
$661$	11.3385	0.441017	0.220509	+	0.975385i	$0.429228\pi$
$662$	42.3461	1.64583
$663$	9.07632	0.352495
$664$	−136.236	−5.28697
$665$	21.9022	0.849330
$666$	−4.45474	−0.172618
$667$	26.0182	1.00743
$668$	−22.7773	−0.881280
$669$	−2.17959	−0.0842677
$670$	−56.7894	−2.19397
$671$	−11.1021	−0.428593
$672$	−27.2037	−1.04940
$673$	−2.33543	−0.0900243	−0.0450121	−	0.998986i	$-0.514333\pi$
$673$	−2.33543	−0.0900243	−0.0450121	+	0.998986i	$0.514333\pi$
$674$	77.1428	2.97143
$675$	18.4446	0.709934
$676$	15.4101	0.592698
$677$	20.2424	0.777978	0.388989	−	0.921242i	$-0.372824\pi$
$677$	20.2424	0.777978	0.388989	+	0.921242i	$0.372824\pi$
$678$	−23.0777	−0.886293
$679$	8.70485	0.334062
$680$	−31.9870	−1.22664
$681$	54.8473	2.10175
$682$	−35.4056	−1.35575
$683$	−20.0654	−0.767780	−0.383890	−	0.923379i	$-0.625416\pi$
$683$	−20.0654	−0.767780	−0.383890	+	0.923379i	$0.625416\pi$
$684$	−82.6539	−3.16035
$685$	23.8087	0.909684
$686$	−27.4863	−1.04943
$687$	6.01206	0.229374
$688$	118.659	4.52382
$689$	4.64585	0.176993
$690$	−77.5106	−2.95078
$691$	37.7139	1.43470	0.717352	−	0.696711i	$-0.245354\pi$
$691$	37.7139	1.43470	0.717352	+	0.696711i	$0.245354\pi$
$692$	−63.4974	−2.41381
$693$	−5.77600	−0.219412
$694$	21.4231	0.813209
$695$	−61.6533	−2.33864
$696$	147.712	5.59900
$697$	−0.124996	−0.00473457
$698$	−74.2947	−2.81209
$699$	43.3799	1.64078
$700$	37.6497	1.42302
$701$	6.86230	0.259186	0.129593	−	0.991567i	$-0.458633\pi$
$701$	6.86230	0.259186	0.129593	+	0.991567i	$0.458633\pi$
$702$	−20.6357	−0.778845
$703$	5.80720	0.219023
$704$	−61.3323	−2.31155
$705$	−95.1302	−3.58281
$706$	−33.3557	−1.25536
$707$	7.83638	0.294717
$708$	−11.6598	−0.438203
$709$	31.9055	1.19824	0.599118	−	0.800661i	$-0.295518\pi$
$709$	31.9055	1.19824	0.599118	+	0.800661i	$0.295518\pi$
$710$	−30.8756	−1.15874
$711$	7.07483	0.265327
$712$	104.623	3.92091
$713$	−12.6753	−0.474694
$714$	−4.65049	−0.174040
$715$	−53.4634	−1.99942
$716$	71.2776	2.66377
$717$	27.4426	1.02486
$718$	99.4547	3.71162
$719$	−12.1883	−0.454546	−0.227273	−	0.973831i	$-0.572981\pi$
$719$	−12.1883	−0.454546	−0.227273	+	0.973831i	$0.572981\pi$
$720$	−99.4124	−3.70488
$721$	−3.32545	−0.123846
$722$	98.9220	3.68150
$723$	42.0663	1.56446
$724$	−22.7577	−0.845782
$725$	−74.1547	−2.75403
$726$	−7.74262	−0.287356
$727$	−35.3177	−1.30986	−0.654930	−	0.755690i	$-0.727302\pi$
$727$	−35.3177	−1.30986	−0.654930	+	0.755690i	$0.727302\pi$
$728$	−25.7272	−0.953513
$729$	−10.1265	−0.375056
$730$	−34.9440	−1.29333
$731$	9.78511	0.361915
$732$	−36.9446	−1.36551
$733$	−8.41218	−0.310711	−0.155355	−	0.987859i	$-0.549652\pi$
$733$	−8.41218	−0.310711	−0.155355	+	0.987859i	$0.549652\pi$
$734$	56.3786	2.08097
$735$	−55.4999	−2.04714
$736$	−52.3799	−1.93075
$737$	−19.5232	−0.719148
$738$	−0.717699	−0.0264188
$739$	22.5183	0.828348	0.414174	−	0.910198i	$-0.364071\pi$
$739$	22.5183	0.828348	0.414174	+	0.910198i	$0.364071\pi$
$740$	15.2079	0.559052
$741$	−67.9359	−2.49569
$742$	−2.38043	−0.0873882
$743$	−14.1883	−0.520520	−0.260260	−	0.965539i	$-0.583808\pi$
$743$	−14.1883	−0.520520	−0.260260	+	0.965539i	$0.583808\pi$
$744$	−71.9610	−2.63822
$745$	10.5928	0.388089
$746$	69.8424	2.55711
$747$	−34.9160	−1.27751
$748$	−18.0043	−0.658303
$749$	12.0736	0.441159
$750$	105.277	3.84418
$751$	15.7702	0.575464	0.287732	−	0.957711i	$-0.407099\pi$
$751$	15.7702	0.575464	0.287732	+	0.957711i	$0.407099\pi$
$752$	−133.268	−4.85980
$753$	−53.7653	−1.95931
$754$	82.9638	3.02136
$755$	72.9654	2.65548
$756$	7.61091	0.276806
$757$	−41.1460	−1.49548	−0.747739	−	0.663993i	$-0.768861\pi$
$757$	−41.1460	−1.49548	−0.747739	+	0.663993i	$0.768861\pi$
$758$	48.7209	1.76962
$759$	−26.6469	−0.967220
$760$	239.421	8.68473
$761$	44.3560	1.60790	0.803952	−	0.594694i	$-0.202727\pi$
$761$	44.3560	1.60790	0.803952	+	0.594694i	$0.202727\pi$
$762$	−6.37084	−0.230791
$763$	−14.4337	−0.522537
$764$	−108.323	−3.91900
$765$	−8.19798	−0.296398
$766$	−23.7821	−0.859283
$767$	−3.99988	−0.144427
$768$	−14.5895	−0.526452
$769$	−4.23858	−0.152847	−0.0764235	−	0.997075i	$-0.524350\pi$
$769$	−4.23858	−0.152847	−0.0764235	+	0.997075i	$0.524350\pi$
$770$	27.3934	0.987190
$771$	68.6912	2.47385
$772$	−70.4935	−2.53712
$773$	−51.2288	−1.84257	−0.921287	−	0.388884i	$-0.872861\pi$
$773$	−51.2288	−1.84257	−0.921287	+	0.388884i	$0.872861\pi$
$774$	56.1838	2.01948
$775$	36.1261	1.29769
$776$	95.1562	3.41591
$777$	1.35044	0.0484468
$778$	−44.7136	−1.60306
$779$	0.935593	0.0335211
$780$	−177.910	−6.37021
$781$	−10.6145	−0.379817
$782$	−8.95439	−0.320208
$783$	−14.9904	−0.535714
$784$	−77.7500	−2.77679
$785$	−59.1525	−2.11124
$786$	−9.96379	−0.355397
$787$	22.8310	0.813836	0.406918	−	0.913465i	$-0.366603\pi$
$787$	22.8310	0.813836	0.406918	+	0.913465i	$0.366603\pi$
$788$	−69.4093	−2.47260
$789$	−40.7484	−1.45068
$790$	−33.5533	−1.19377
$791$	2.91987	0.103819
$792$	−63.1398	−2.24357
$793$	−12.6738	−0.450058
$794$	−0.594330	−0.0210920
$795$	−10.0541	−0.356583
$796$	126.338	4.47795
$797$	−19.6521	−0.696112	−0.348056	−	0.937474i	$-0.613158\pi$
$797$	−19.6521	−0.696112	−0.348056	+	0.937474i	$0.613158\pi$
$798$	34.8088	1.23222
$799$	−10.9899	−0.388794
$800$	149.289	5.27815
$801$	26.8139	0.947423
$802$	−83.9510	−2.96441
$803$	−12.0132	−0.423935
$804$	−64.9675	−2.29123
$805$	9.80692	0.345648
$806$	−40.4176	−1.42365
$807$	38.0575	1.33969
$808$	85.6625	3.01360
$809$	11.6148	0.408355	0.204177	−	0.978934i	$-0.434548\pi$
$809$	11.6148	0.408355	0.204177	+	0.978934i	$0.434548\pi$
$810$	110.368	3.87792
$811$	−4.00231	−0.140540	−0.0702701	−	0.997528i	$-0.522386\pi$
$811$	−4.00231	−0.140540	−0.0702701	+	0.997528i	$0.522386\pi$
$812$	−30.5989	−1.07381
$813$	−11.0485	−0.387487
$814$	7.26316	0.254574
$815$	71.1846	2.49349
$816$	−27.5167	−0.963279
$817$	−73.2412	−2.56239
$818$	91.4366	3.19701
$819$	−6.59365	−0.230401
$820$	2.45012	0.0855620
$821$	−20.2533	−0.706845	−0.353423	−	0.935464i	$-0.614982\pi$
$821$	−20.2533	−0.706845	−0.353423	+	0.935464i	$0.614982\pi$
$822$	37.8388	1.31978
$823$	−11.4210	−0.398111	−0.199055	−	0.979988i	$-0.563787\pi$
$823$	−11.4210	−0.398111	−0.199055	+	0.979988i	$0.563787\pi$
$824$	−36.3518	−1.26637
$825$	75.9466	2.64412
$826$	2.04944	0.0713093
$827$	27.5765	0.958928	0.479464	−	0.877561i	$-0.340831\pi$
$827$	27.5765	0.958928	0.479464	+	0.877561i	$0.340831\pi$
$828$	−37.0091	−1.28616
$829$	46.8822	1.62829	0.814143	−	0.580665i	$-0.197207\pi$
$829$	46.8822	1.62829	0.814143	+	0.580665i	$0.197207\pi$
$830$	165.593	5.74783
$831$	15.3407	0.532161
$832$	−70.0145	−2.42732
$833$	−6.41160	−0.222149
$834$	−97.9846	−3.39293
$835$	16.9097	0.585183
$836$	134.762	4.66083
$837$	7.30291	0.252426
$838$	5.46906	0.188925
$839$	−40.0729	−1.38347	−0.691735	−	0.722151i	$-0.743153\pi$
$839$	−40.0729	−1.38347	−0.691735	+	0.722151i	$0.743153\pi$
$840$	55.6764	1.92102
$841$	31.2674	1.07819
$842$	17.9224	0.617647
$843$	35.4062	1.21945
$844$	−55.2918	−1.90322
$845$	−11.4404	−0.393561
$846$	−63.1013	−2.16947
$847$	0.979624	0.0336603
$848$	−14.0849	−0.483676
$849$	27.7544	0.952529
$850$	25.5210	0.875364
$851$	2.60023	0.0891348
$852$	−35.3219	−1.21011
$853$	−18.5871	−0.636410	−0.318205	−	0.948022i	$-0.603080\pi$
$853$	−18.5871	−0.636410	−0.318205	+	0.948022i	$0.603080\pi$
$854$	6.49374	0.222211
$855$	61.3616	2.09852
$856$	131.981	4.51102
$857$	5.34419	0.182554	0.0912770	−	0.995826i	$-0.470905\pi$
$857$	5.34419	0.182554	0.0912770	+	0.995826i	$0.470905\pi$
$858$	−84.9686	−2.90078
$859$	24.3690	0.831461	0.415730	−	0.909488i	$-0.363526\pi$
$859$	24.3690	0.831461	0.415730	+	0.909488i	$0.363526\pi$
$860$	−191.804	−6.54045
$861$	0.217568	0.00741470
$862$	104.429	3.55688
$863$	−42.4753	−1.44588	−0.722938	−	0.690913i	$-0.757209\pi$
$863$	−42.4753	−1.44588	−0.722938	+	0.690913i	$0.757209\pi$
$864$	30.1788	1.02670
$865$	47.1400	1.60281
$866$	−66.4800	−2.25908
$867$	−2.26915	−0.0770644
$868$	14.9069	0.505973
$869$	−11.5351	−0.391300
$870$	−179.543	−6.08706
$871$	−22.2869	−0.755164
$872$	−157.781	−5.34314
$873$	24.3877	0.825398
$874$	67.0233	2.26710
$875$	−13.3200	−0.450300
$876$	−39.9762	−1.35067
$877$	−22.1463	−0.747828	−0.373914	−	0.927463i	$-0.621985\pi$
$877$	−22.1463	−0.747828	−0.373914	+	0.927463i	$0.621985\pi$
$878$	−67.0991	−2.26449
$879$	36.0161	1.21479
$880$	162.085	5.46390
$881$	6.67204	0.224787	0.112393	−	0.993664i	$-0.464148\pi$
$881$	6.67204	0.224787	0.112393	+	0.993664i	$0.464148\pi$
$882$	−36.8139	−1.23959
$883$	−22.8348	−0.768451	−0.384226	−	0.923239i	$-0.625532\pi$
$883$	−22.8348	−0.768451	−0.384226	+	0.923239i	$0.625532\pi$
$884$	−20.5530	−0.691273
$885$	8.65616	0.290974
$886$	15.9375	0.535430
$887$	−42.9163	−1.44099	−0.720494	−	0.693461i	$-0.756085\pi$
$887$	−42.9163	−1.44099	−0.720494	+	0.693461i	$0.756085\pi$
$888$	14.7622	0.495387
$889$	0.806061	0.0270344
$890$	−127.168	−4.26269
$891$	37.9425	1.27112
$892$	4.93560	0.165256
$893$	82.2589	2.75269
$894$	16.8349	0.563044
$895$	−52.9159	−1.76878
$896$	11.8968	0.397445
$897$	−30.4190	−1.01566
$898$	10.6664	0.355942
$899$	−29.3606	−0.979231
$900$	105.480	3.51600
$901$	−1.16150	−0.0386951
$902$	1.17016	0.0389621
$903$	−17.0319	−0.566787
$904$	31.9183	1.06159
$905$	16.8951	0.561612
$906$	115.963	3.85261
$907$	−9.84282	−0.326825	−0.163413	−	0.986558i	$-0.552250\pi$
$907$	−9.84282	−0.326825	−0.163413	+	0.986558i	$0.552250\pi$
$908$	−124.200	−4.12171
$909$	21.9545	0.728186
$910$	31.2712	1.03663
$911$	−11.8399	−0.392274	−0.196137	−	0.980577i	$-0.562840\pi$
$911$	−11.8399	−0.392274	−0.196137	+	0.980577i	$0.562840\pi$
$912$	205.962	6.82008
$913$	56.9283	1.88405
$914$	86.2126	2.85166
$915$	27.4274	0.906721
$916$	−13.6141	−0.449823
$917$	1.26065	0.0416304
$918$	5.15909	0.170275
$919$	−5.14193	−0.169617	−0.0848083	−	0.996397i	$-0.527028\pi$
$919$	−5.14193	−0.169617	−0.0848083	+	0.996397i	$0.527028\pi$
$920$	107.203	3.53439
$921$	4.32322	0.142455
$922$	−30.1722	−0.993668
$923$	−12.1171	−0.398840
$924$	31.3383	1.03095
$925$	−7.41095	−0.243671
$926$	11.1462	0.366288
$927$	−9.31664	−0.305999
$928$	−121.331	−3.98288
$929$	−13.5741	−0.445351	−0.222675	−	0.974893i	$-0.571479\pi$
$929$	−13.5741	−0.445351	−0.222675	+	0.974893i	$0.571479\pi$
$930$	87.4681	2.86819
$931$	47.9906	1.57283
$932$	−98.2323	−3.21770
$933$	−22.6771	−0.742415
$934$	23.4434	0.767093
$935$	13.3663	0.437124
$936$	−72.0778	−2.35594
$937$	−46.4188	−1.51644	−0.758219	−	0.652000i	$-0.773930\pi$
$937$	−46.4188	−1.51644	−0.758219	+	0.652000i	$0.773930\pi$
$938$	11.4193	0.372854
$939$	58.4086	1.90609
$940$	215.419	7.02620
$941$	13.7666	0.448777	0.224388	−	0.974500i	$-0.427962\pi$
$941$	13.7666	0.448777	0.224388	+	0.974500i	$0.427962\pi$
$942$	−94.0102	−3.06302
$943$	0.418921	0.0136419
$944$	12.1265	0.394683
$945$	−5.65028	−0.183804
$946$	−91.6040	−2.97830
$947$	−24.3920	−0.792635	−0.396317	−	0.918114i	$-0.629712\pi$
$947$	−24.3920	−0.792635	−0.396317	+	0.918114i	$0.629712\pi$
$948$	−38.3852	−1.24669
$949$	−13.7137	−0.445167
$950$	−191.024	−6.19764
$951$	0.466468	0.0151263
$952$	6.43200	0.208462
$953$	−1.48563	−0.0481242	−0.0240621	−	0.999710i	$-0.507660\pi$
$953$	−1.48563	−0.0481242	−0.0240621	+	0.999710i	$0.507660\pi$
$954$	−6.66905	−0.215919
$955$	80.4184	2.60228
$956$	−62.1429	−2.00984
$957$	−61.7237	−1.99525
$958$	15.3587	0.496216
$959$	−4.78750	−0.154596
$960$	151.519	4.89025
$961$	−16.6963	−0.538592
$962$	8.29133	0.267323
$963$	33.8256	1.09001
$964$	−95.2578	−3.06805
$965$	52.3338	1.68468
$966$	15.5860	0.501471
$967$	−10.9743	−0.352910	−0.176455	−	0.984309i	$-0.556463\pi$
$967$	−10.9743	−0.352910	−0.176455	+	0.984309i	$0.556463\pi$
$968$	10.7087	0.344189
$969$	16.9845	0.545621
$970$	−115.662	−3.71367
$971$	−17.0103	−0.545887	−0.272943	−	0.962030i	$-0.587997\pi$
$971$	−17.0103	−0.545887	−0.272943	+	0.962030i	$0.587997\pi$
$972$	96.4952	3.09508
$973$	12.3974	0.397441
$974$	−40.5277	−1.29859
$975$	86.6975	2.77654
$976$	38.4231	1.22989
$977$	39.2934	1.25711	0.628553	−	0.777767i	$-0.283648\pi$
$977$	39.2934	1.25711	0.628553	+	0.777767i	$0.283648\pi$
$978$	113.133	3.61758
$979$	−43.7184	−1.39724
$980$	125.678	4.01462
$981$	−40.4379	−1.29108
$982$	54.7247	1.74633
$983$	16.4962	0.526148	0.263074	−	0.964776i	$-0.415264\pi$
$983$	16.4962	0.526148	0.263074	+	0.964776i	$0.415264\pi$
$984$	2.37832	0.0758182
$985$	51.5289	1.64185
$986$	−20.7416	−0.660547
$987$	19.1290	0.608881
$988$	153.839	4.89426
$989$	−32.7945	−1.04280
$990$	76.7459	2.43915
$991$	26.7174	0.848706	0.424353	−	0.905497i	$-0.360502\pi$
$991$	26.7174	0.848706	0.424353	+	0.905497i	$0.360502\pi$
$992$	59.1089	1.87671
$993$	−35.9646	−1.14130
$994$	6.20853	0.196922
$995$	−93.7927	−2.97343
$996$	189.440	6.00264
$997$	39.8210	1.26114	0.630572	−	0.776131i	$-0.282820\pi$
$997$	39.8210	1.26114	0.630572	+	0.776131i	$0.282820\pi$
$998$	−15.9388	−0.504534
$999$	−1.49813	−0.0473987

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1003.2.a.h.1.16	✓	16
3.2	odd	2		9027.2.a.n.1.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1003.2.a.h.1.16	✓	16	1.1	even	1	trivial
9027.2.a.n.1.1		16	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1003 = 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1003.a (trivial)

\(f(q)\)	\(=\)	\(q+2.67178 q^{2} -2.26915 q^{3} +5.13841 q^{4} -3.81472 q^{5} -6.06267 q^{6} +0.767070 q^{7} +8.38515 q^{8} +2.14904 q^{9} +O(q^{10})\)	\(q+2.67178 q^{2} -2.26915 q^{3} +5.13841 q^{4} -3.81472 q^{5} -6.06267 q^{6} +0.767070 q^{7} +8.38515 q^{8} +2.14904 q^{9} -10.1921 q^{10} -3.50387 q^{11} -11.6598 q^{12} -3.99988 q^{13} +2.04944 q^{14} +8.65616 q^{15} +12.1265 q^{16} +1.00000 q^{17} +5.74176 q^{18} -7.48497 q^{19} -19.6016 q^{20} -1.74060 q^{21} -9.36157 q^{22} -3.35147 q^{23} -19.0272 q^{24} +9.55206 q^{25} -10.6868 q^{26} +1.93096 q^{27} +3.94152 q^{28} -7.76321 q^{29} +23.1274 q^{30} +3.78202 q^{31} +15.6289 q^{32} +7.95080 q^{33} +2.67178 q^{34} -2.92616 q^{35} +11.0427 q^{36} -0.775849 q^{37} -19.9982 q^{38} +9.07632 q^{39} -31.9870 q^{40} -0.124996 q^{41} -4.65049 q^{42} +9.78511 q^{43} -18.0043 q^{44} -8.19798 q^{45} -8.95439 q^{46} -10.9899 q^{47} -27.5167 q^{48} -6.41160 q^{49} +25.5210 q^{50} -2.26915 q^{51} -20.5530 q^{52} -1.16150 q^{53} +5.15909 q^{54} +13.3663 q^{55} +6.43200 q^{56} +16.9845 q^{57} -20.7416 q^{58} +1.00000 q^{59} +44.4789 q^{60} +3.16854 q^{61} +10.1047 q^{62} +1.64846 q^{63} +17.5042 q^{64} +15.2584 q^{65} +21.2428 q^{66} +5.57191 q^{67} +5.13841 q^{68} +7.60498 q^{69} -7.81805 q^{70} +3.02937 q^{71} +18.0200 q^{72} +3.42854 q^{73} -2.07290 q^{74} -21.6751 q^{75} -38.4609 q^{76} -2.68771 q^{77} +24.2499 q^{78} +3.29209 q^{79} -46.2590 q^{80} -10.8287 q^{81} -0.333962 q^{82} -16.2473 q^{83} -8.94391 q^{84} -3.81472 q^{85} +26.1437 q^{86} +17.6159 q^{87} -29.3805 q^{88} +12.4772 q^{89} -21.9032 q^{90} -3.06819 q^{91} -17.2212 q^{92} -8.58196 q^{93} -29.3626 q^{94} +28.5530 q^{95} -35.4644 q^{96} +11.3482 q^{97} -17.1304 q^{98} -7.52995 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} - 7 q^{3} + 14 q^{4} - 21 q^{5} - 5 q^{6} - 11 q^{7} - 12 q^{8} + 17 q^{9}+O(q^{10}) \) 16 * q - 6 * q^2 - 7 * q^3 + 14 * q^4 - 21 * q^5 - 5 * q^6 - 11 * q^7 - 12 * q^8 + 17 * q^9	\( 16 q - 6 q^{2} - 7 q^{3} + 14 q^{4} - 21 q^{5} - 5 q^{6} - 11 q^{7} - 12 q^{8} + 17 q^{9} + 12 q^{10} - 7 q^{11} - 4 q^{12} - 16 q^{13} + 11 q^{14} + 7 q^{15} + 22 q^{16} + 16 q^{17} + 11 q^{18} + q^{19} - 43 q^{20} - 8 q^{21} - 18 q^{22} - 8 q^{23} - 39 q^{24} + 23 q^{25} - 49 q^{26} - 7 q^{27} - 15 q^{28} - 39 q^{29} + q^{30} - 3 q^{31} - 15 q^{33} - 6 q^{34} + 9 q^{35} - 17 q^{36} - 28 q^{37} - 27 q^{38} - 4 q^{39} + 26 q^{40} - 31 q^{41} - 45 q^{42} + 5 q^{43} - 19 q^{44} - 79 q^{45} - 39 q^{46} - 47 q^{47} - 31 q^{48} + 35 q^{49} - 13 q^{50} - 7 q^{51} + 9 q^{52} - 36 q^{53} + 9 q^{54} + 32 q^{55} + 3 q^{56} + 6 q^{57} + 22 q^{58} + 16 q^{59} + 6 q^{60} - 22 q^{61} + q^{62} - 19 q^{63} + 32 q^{64} - 19 q^{65} + 48 q^{66} + 4 q^{67} + 14 q^{68} + 14 q^{69} - 11 q^{70} - 5 q^{71} + 40 q^{72} - 35 q^{73} + 31 q^{74} - 12 q^{75} + q^{76} - 79 q^{77} + 31 q^{78} - 48 q^{79} - 127 q^{80} - 28 q^{81} - 7 q^{82} - 42 q^{83} + 28 q^{84} - 21 q^{85} + 58 q^{86} - 16 q^{87} - 2 q^{88} + 20 q^{89} - 14 q^{90} + 49 q^{91} - 21 q^{92} - 55 q^{93} - 22 q^{95} + 24 q^{96} - 2 q^{97} - 78 q^{98} - 35 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 - 7 * q^3 + 14 * q^4 - 21 * q^5 - 5 * q^6 - 11 * q^7 - 12 * q^8 + 17 * q^9 + 12 * q^10 - 7 * q^11 - 4 * q^12 - 16 * q^13 + 11 * q^14 + 7 * q^15 + 22 * q^16 + 16 * q^17 + 11 * q^18 + q^19 - 43 * q^20 - 8 * q^21 - 18 * q^22 - 8 * q^23 - 39 * q^24 + 23 * q^25 - 49 * q^26 - 7 * q^27 - 15 * q^28 - 39 * q^29 + q^30 - 3 * q^31 - 15 * q^33 - 6 * q^34 + 9 * q^35 - 17 * q^36 - 28 * q^37 - 27 * q^38 - 4 * q^39 + 26 * q^40 - 31 * q^41 - 45 * q^42 + 5 * q^43 - 19 * q^44 - 79 * q^45 - 39 * q^46 - 47 * q^47 - 31 * q^48 + 35 * q^49 - 13 * q^50 - 7 * q^51 + 9 * q^52 - 36 * q^53 + 9 * q^54 + 32 * q^55 + 3 * q^56 + 6 * q^57 + 22 * q^58 + 16 * q^59 + 6 * q^60 - 22 * q^61 + q^62 - 19 * q^63 + 32 * q^64 - 19 * q^65 + 48 * q^66 + 4 * q^67 + 14 * q^68 + 14 * q^69 - 11 * q^70 - 5 * q^71 + 40 * q^72 - 35 * q^73 + 31 * q^74 - 12 * q^75 + q^76 - 79 * q^77 + 31 * q^78 - 48 * q^79 - 127 * q^80 - 28 * q^81 - 7 * q^82 - 42 * q^83 + 28 * q^84 - 21 * q^85 + 58 * q^86 - 16 * q^87 - 2 * q^88 + 20 * q^89 - 14 * q^90 + 49 * q^91 - 21 * q^92 - 55 * q^93 - 22 * q^95 + 24 * q^96 - 2 * q^97 - 78 * q^98 - 35 * q^99

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