LMFDB - Embedded newform 2006.2.a.w.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2006,2,Mod(1,2006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2006, 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("2006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2006 = 2 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2006.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:	$16.0179906455$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 6 x^{12} - 9 x^{11} + 91 x^{10} + 14 x^{9} - 517 x^{8} + 70 x^{7} + 1296 x^{6} - 300 x^{5} + \cdots + 16 $ x^13 - 6x^12 - 9x^11 + 91x^10 + 14x^9 - 517x^8 + 70x^7 + 1296x^6 - 300x^5 - 1312x^4 + 472x^3 + 368x^2 - 176x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$0.129950$ of defining polynomial
Character	$\chi$	$=$	2006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.870050 q^{3} +1.00000 q^{4} +1.72202 q^{5} +0.870050 q^{6} +2.12442 q^{7} +1.00000 q^{8} -2.24301 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.870050 q^{3} +1.00000 q^{4} +1.72202 q^{5} +0.870050 q^{6} +2.12442 q^{7} +1.00000 q^{8} -2.24301 q^{9} +1.72202 q^{10} +5.37607 q^{11} +0.870050 q^{12} -0.704926 q^{13} +2.12442 q^{14} +1.49825 q^{15} +1.00000 q^{16} +1.00000 q^{17} -2.24301 q^{18} -0.612083 q^{19} +1.72202 q^{20} +1.84836 q^{21} +5.37607 q^{22} +1.69087 q^{23} +0.870050 q^{24} -2.03463 q^{25} -0.704926 q^{26} -4.56168 q^{27} +2.12442 q^{28} +9.79004 q^{29} +1.49825 q^{30} -10.5805 q^{31} +1.00000 q^{32} +4.67745 q^{33} +1.00000 q^{34} +3.65831 q^{35} -2.24301 q^{36} -6.44758 q^{37} -0.612083 q^{38} -0.613321 q^{39} +1.72202 q^{40} +1.44573 q^{41} +1.84836 q^{42} -9.06020 q^{43} +5.37607 q^{44} -3.86252 q^{45} +1.69087 q^{46} +10.9940 q^{47} +0.870050 q^{48} -2.48682 q^{49} -2.03463 q^{50} +0.870050 q^{51} -0.704926 q^{52} +9.23011 q^{53} -4.56168 q^{54} +9.25772 q^{55} +2.12442 q^{56} -0.532543 q^{57} +9.79004 q^{58} +1.00000 q^{59} +1.49825 q^{60} +5.29474 q^{61} -10.5805 q^{62} -4.76511 q^{63} +1.00000 q^{64} -1.21390 q^{65} +4.67745 q^{66} +7.38999 q^{67} +1.00000 q^{68} +1.47114 q^{69} +3.65831 q^{70} -15.7531 q^{71} -2.24301 q^{72} -12.7750 q^{73} -6.44758 q^{74} -1.77023 q^{75} -0.612083 q^{76} +11.4211 q^{77} -0.613321 q^{78} -4.10590 q^{79} +1.72202 q^{80} +2.76014 q^{81} +1.44573 q^{82} +4.34938 q^{83} +1.84836 q^{84} +1.72202 q^{85} -9.06020 q^{86} +8.51782 q^{87} +5.37607 q^{88} +0.0795409 q^{89} -3.86252 q^{90} -1.49756 q^{91} +1.69087 q^{92} -9.20553 q^{93} +10.9940 q^{94} -1.05402 q^{95} +0.870050 q^{96} +3.93492 q^{97} -2.48682 q^{98} -12.0586 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 13 q^{2} + 7 q^{3} + 13 q^{4} + q^{5} + 7 q^{6} + 8 q^{7} + 13 q^{8} + 16 q^{9}+O(q^{10}) $ 13 * q + 13 * q^2 + 7 * q^3 + 13 * q^4 + q^5 + 7 * q^6 + 8 * q^7 + 13 * q^8 + 16 * q^9	\( 13 q + 13 q^{2} + 7 q^{3} + 13 q^{4} + q^{5} + 7 q^{6} + 8 q^{7} + 13 q^{8} + 16 q^{9} + q^{10} + 13 q^{11} + 7 q^{12} + 9 q^{13} + 8 q^{14} - 9 q^{15} + 13 q^{16} + 13 q^{17} + 16 q^{18} + 16 q^{19} + q^{20} - 3 q^{21} + 13 q^{22} + 18 q^{23} + 7 q^{24} + 14 q^{25} + 9 q^{26} + 10 q^{27} + 8 q^{28} + 8 q^{29} - 9 q^{30} + 32 q^{31} + 13 q^{32} + 13 q^{33} + 13 q^{34} - q^{35} + 16 q^{36} - 3 q^{37} + 16 q^{38} + 20 q^{39} + q^{40} + 24 q^{41} - 3 q^{42} - 2 q^{43} + 13 q^{44} - 3 q^{45} + 18 q^{46} + 26 q^{47} + 7 q^{48} + 23 q^{49} + 14 q^{50} + 7 q^{51} + 9 q^{52} - 27 q^{53} + 10 q^{54} - 7 q^{55} + 8 q^{56} - 21 q^{57} + 8 q^{58} + 13 q^{59} - 9 q^{60} + 20 q^{61} + 32 q^{62} - 3 q^{63} + 13 q^{64} + 16 q^{65} + 13 q^{66} + 4 q^{67} + 13 q^{68} - 2 q^{69} - q^{70} - 8 q^{71} + 16 q^{72} + 10 q^{73} - 3 q^{74} + 39 q^{75} + 16 q^{76} - 15 q^{77} + 20 q^{78} + 35 q^{79} + q^{80} + 29 q^{81} + 24 q^{82} - q^{83} - 3 q^{84} + q^{85} - 2 q^{86} - 32 q^{87} + 13 q^{88} - 20 q^{89} - 3 q^{90} - 15 q^{91} + 18 q^{92} - 7 q^{93} + 26 q^{94} - 3 q^{95} + 7 q^{96} - 3 q^{97} + 23 q^{98} + 65 q^{99}+O(q^{100}) \) 13 * q + 13 * q^2 + 7 * q^3 + 13 * q^4 + q^5 + 7 * q^6 + 8 * q^7 + 13 * q^8 + 16 * q^9 + q^10 + 13 * q^11 + 7 * q^12 + 9 * q^13 + 8 * q^14 - 9 * q^15 + 13 * q^16 + 13 * q^17 + 16 * q^18 + 16 * q^19 + q^20 - 3 * q^21 + 13 * q^22 + 18 * q^23 + 7 * q^24 + 14 * q^25 + 9 * q^26 + 10 * q^27 + 8 * q^28 + 8 * q^29 - 9 * q^30 + 32 * q^31 + 13 * q^32 + 13 * q^33 + 13 * q^34 - q^35 + 16 * q^36 - 3 * q^37 + 16 * q^38 + 20 * q^39 + q^40 + 24 * q^41 - 3 * q^42 - 2 * q^43 + 13 * q^44 - 3 * q^45 + 18 * q^46 + 26 * q^47 + 7 * q^48 + 23 * q^49 + 14 * q^50 + 7 * q^51 + 9 * q^52 - 27 * q^53 + 10 * q^54 - 7 * q^55 + 8 * q^56 - 21 * q^57 + 8 * q^58 + 13 * q^59 - 9 * q^60 + 20 * q^61 + 32 * q^62 - 3 * q^63 + 13 * q^64 + 16 * q^65 + 13 * q^66 + 4 * q^67 + 13 * q^68 - 2 * q^69 - q^70 - 8 * q^71 + 16 * q^72 + 10 * q^73 - 3 * q^74 + 39 * q^75 + 16 * q^76 - 15 * q^77 + 20 * q^78 + 35 * q^79 + q^80 + 29 * q^81 + 24 * q^82 - q^83 - 3 * q^84 + q^85 - 2 * q^86 - 32 * q^87 + 13 * q^88 - 20 * q^89 - 3 * q^90 - 15 * q^91 + 18 * q^92 - 7 * q^93 + 26 * q^94 - 3 * q^95 + 7 * q^96 - 3 * q^97 + 23 * q^98 + 65 * 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
$3$	0.870050	0.502324	0.251162	−	0.967945i	$-0.419187\pi$
$3$	0.870050	0.502324	0.251162	+	0.967945i	$0.419187\pi$
$4$	1.00000	0.500000
$5$	1.72202	0.770113	0.385056	−	0.922893i	$-0.374182\pi$
$5$	1.72202	0.770113	0.385056	+	0.922893i	$0.374182\pi$
$6$	0.870050	0.355197
$7$	2.12442	0.802957	0.401478	−	0.915869i	$-0.368496\pi$
$7$	2.12442	0.802957	0.401478	+	0.915869i	$0.368496\pi$
$8$	1.00000	0.353553
$9$	−2.24301	−0.747671
$10$	1.72202	0.544552
$11$	5.37607	1.62095	0.810473	−	0.585776i	$-0.199210\pi$
$11$	5.37607	1.62095	0.810473	+	0.585776i	$0.199210\pi$
$12$	0.870050	0.251162
$13$	−0.704926	−0.195511	−0.0977556	−	0.995210i	$-0.531166\pi$
$13$	−0.704926	−0.195511	−0.0977556	+	0.995210i	$0.531166\pi$
$14$	2.12442	0.567776
$15$	1.49825	0.386846
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.24301	−0.528683
$19$	−0.612083	−0.140421	−0.0702107	−	0.997532i	$-0.522367\pi$
$19$	−0.612083	−0.140421	−0.0702107	+	0.997532i	$0.522367\pi$
$20$	1.72202	0.385056
$21$	1.84836	0.403344
$22$	5.37607	1.14618
$23$	1.69087	0.352571	0.176285	−	0.984339i	$-0.443592\pi$
$23$	1.69087	0.352571	0.176285	+	0.984339i	$0.443592\pi$
$24$	0.870050	0.177598
$25$	−2.03463	−0.406927
$26$	−0.704926	−0.138247
$27$	−4.56168	−0.877897
$28$	2.12442	0.401478
$29$	9.79004	1.81796	0.908982	−	0.416835i	$-0.136861\pi$
$29$	9.79004	1.81796	0.908982	+	0.416835i	$0.136861\pi$
$30$	1.49825	0.273541
$31$	−10.5805	−1.90031	−0.950153	−	0.311784i	$-0.899074\pi$
$31$	−10.5805	−1.90031	−0.950153	+	0.311784i	$0.899074\pi$
$32$	1.00000	0.176777
$33$	4.67745	0.814240
$34$	1.00000	0.171499
$35$	3.65831	0.618367
$36$	−2.24301	−0.373835
$37$	−6.44758	−1.05998	−0.529988	−	0.848005i	$-0.677804\pi$
$37$	−6.44758	−1.05998	−0.529988	+	0.848005i	$0.677804\pi$
$38$	−0.612083	−0.0992929
$39$	−0.613321	−0.0982100
$40$	1.72202	0.272276
$41$	1.44573	0.225785	0.112893	−	0.993607i	$-0.463988\pi$
$41$	1.44573	0.225785	0.112893	+	0.993607i	$0.463988\pi$
$42$	1.84836	0.285207
$43$	−9.06020	−1.38167	−0.690834	−	0.723014i	$-0.742756\pi$
$43$	−9.06020	−1.38167	−0.690834	+	0.723014i	$0.742756\pi$
$44$	5.37607	0.810473
$45$	−3.86252	−0.575791
$46$	1.69087	0.249305
$47$	10.9940	1.60364	0.801821	−	0.597565i	$-0.203865\pi$
$47$	10.9940	1.60364	0.801821	+	0.597565i	$0.203865\pi$
$48$	0.870050	0.125581
$49$	−2.48682	−0.355261
$50$	−2.03463	−0.287741
$51$	0.870050	0.121831
$52$	−0.704926	−0.0977556
$53$	9.23011	1.26785	0.633927	−	0.773393i	$-0.281442\pi$
$53$	9.23011	1.26785	0.633927	+	0.773393i	$0.281442\pi$
$54$	−4.56168	−0.620767
$55$	9.25772	1.24831
$56$	2.12442	0.283888
$57$	−0.532543	−0.0705370
$58$	9.79004	1.28549
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	1.49825	0.193423
$61$	5.29474	0.677922	0.338961	−	0.940800i	$-0.389925\pi$
$61$	5.29474	0.677922	0.338961	+	0.940800i	$0.389925\pi$
$62$	−10.5805	−1.34372
$63$	−4.76511	−0.600347
$64$	1.00000	0.125000
$65$	−1.21390	−0.150566
$66$	4.67745	0.575754
$67$	7.38999	0.902831	0.451416	−	0.892314i	$-0.350919\pi$
$67$	7.38999	0.902831	0.451416	+	0.892314i	$0.350919\pi$
$68$	1.00000	0.121268
$69$	1.47114	0.177105
$70$	3.65831	0.437252
$71$	−15.7531	−1.86955	−0.934776	−	0.355239i	$-0.884399\pi$
$71$	−15.7531	−1.86955	−0.934776	+	0.355239i	$0.884399\pi$
$72$	−2.24301	−0.264342
$73$	−12.7750	−1.49520	−0.747602	−	0.664147i	$-0.768795\pi$
$73$	−12.7750	−1.49520	−0.747602	+	0.664147i	$0.768795\pi$
$74$	−6.44758	−0.749516
$75$	−1.77023	−0.204409
$76$	−0.612083	−0.0702107
$77$	11.4211	1.30155
$78$	−0.613321	−0.0694449
$79$	−4.10590	−0.461950	−0.230975	−	0.972960i	$-0.574192\pi$
$79$	−4.10590	−0.461950	−0.230975	+	0.972960i	$0.574192\pi$
$80$	1.72202	0.192528
$81$	2.76014	0.306683
$82$	1.44573	0.159654
$83$	4.34938	0.477407	0.238703	−	0.971093i	$-0.423278\pi$
$83$	4.34938	0.477407	0.238703	+	0.971093i	$0.423278\pi$
$84$	1.84836	0.201672
$85$	1.72202	0.186780
$86$	−9.06020	−0.976986
$87$	8.51782	0.913206
$88$	5.37607	0.573091
$89$	0.0795409	0.00843132	0.00421566	−	0.999991i	$-0.498658\pi$
$89$	0.0795409	0.00843132	0.00421566	+	0.999991i	$0.498658\pi$
$90$	−3.86252	−0.407146
$91$	−1.49756	−0.156987
$92$	1.69087	0.176285
$93$	−9.20553	−0.954569
$94$	10.9940	1.13395
$95$	−1.05402	−0.108140
$96$	0.870050	0.0887991
$97$	3.93492	0.399531	0.199765	−	0.979844i	$-0.435982\pi$
$97$	3.93492	0.399531	0.199765	+	0.979844i	$0.435982\pi$
$98$	−2.48682	−0.251207
$99$	−12.0586	−1.21193
$100$	−2.03463	−0.203463
$101$	1.59746	0.158953	0.0794764	−	0.996837i	$-0.474675\pi$
$101$	1.59746	0.158953	0.0794764	+	0.996837i	$0.474675\pi$
$102$	0.870050	0.0861478
$103$	5.28366	0.520614	0.260307	−	0.965526i	$-0.416176\pi$
$103$	5.28366	0.520614	0.260307	+	0.965526i	$0.416176\pi$
$104$	−0.704926	−0.0691237
$105$	3.18291	0.310620
$106$	9.23011	0.896507
$107$	−15.0118	−1.45125	−0.725624	−	0.688091i	$-0.758449\pi$
$107$	−15.0118	−1.45125	−0.725624	+	0.688091i	$0.758449\pi$
$108$	−4.56168	−0.438948
$109$	6.03352	0.577906	0.288953	−	0.957343i	$-0.406693\pi$
$109$	6.03352	0.577906	0.288953	+	0.957343i	$0.406693\pi$
$110$	9.25772	0.882689
$111$	−5.60972	−0.532451
$112$	2.12442	0.200739
$113$	8.99813	0.846473	0.423237	−	0.906019i	$-0.360894\pi$
$113$	8.99813	0.846473	0.423237	+	0.906019i	$0.360894\pi$
$114$	−0.532543	−0.0498772
$115$	2.91172	0.271519
$116$	9.79004	0.908982
$117$	1.58116	0.146178
$118$	1.00000	0.0920575
$119$	2.12442	0.194746
$120$	1.49825	0.136771
$121$	17.9021	1.62747
$122$	5.29474	0.479363
$123$	1.25786	0.113417
$124$	−10.5805	−0.950153
$125$	−12.1138	−1.08349
$126$	−4.76511	−0.424510
$127$	−1.57697	−0.139933	−0.0699665	−	0.997549i	$-0.522289\pi$
$127$	−1.57697	−0.139933	−0.0699665	+	0.997549i	$0.522289\pi$
$128$	1.00000	0.0883883
$129$	−7.88283	−0.694044
$130$	−1.21390	−0.106466
$131$	−5.58477	−0.487944	−0.243972	−	0.969782i	$-0.578450\pi$
$131$	−5.58477	−0.487944	−0.243972	+	0.969782i	$0.578450\pi$
$132$	4.67745	0.407120
$133$	−1.30032	−0.112752
$134$	7.38999	0.638398
$135$	−7.85533	−0.676079
$136$	1.00000	0.0857493
$137$	−19.0763	−1.62980	−0.814899	−	0.579603i	$-0.803208\pi$
$137$	−19.0763	−1.62980	−0.814899	+	0.579603i	$0.803208\pi$
$138$	1.47114	0.125232
$139$	12.7792	1.08392	0.541958	−	0.840406i	$-0.317683\pi$
$139$	12.7792	1.08392	0.541958	+	0.840406i	$0.317683\pi$
$140$	3.65831	0.309184
$141$	9.56534	0.805547
$142$	−15.7531	−1.32197
$143$	−3.78973	−0.316913
$144$	−2.24301	−0.186918
$145$	16.8587	1.40004
$146$	−12.7750	−1.05727
$147$	−2.16366	−0.178456
$148$	−6.44758	−0.529988
$149$	7.59358	0.622090	0.311045	−	0.950395i	$-0.399321\pi$
$149$	7.59358	0.622090	0.311045	+	0.950395i	$0.399321\pi$
$150$	−1.77023	−0.144539
$151$	−16.6352	−1.35375	−0.676877	−	0.736096i	$-0.736667\pi$
$151$	−16.6352	−1.35375	−0.676877	+	0.736096i	$0.736667\pi$
$152$	−0.612083	−0.0496465
$153$	−2.24301	−0.181337
$154$	11.4211	0.920334
$155$	−18.2198	−1.46345
$156$	−0.613321	−0.0491050
$157$	−5.90501	−0.471271	−0.235636	−	0.971841i	$-0.575717\pi$
$157$	−5.90501	−0.471271	−0.235636	+	0.971841i	$0.575717\pi$
$158$	−4.10590	−0.326648
$159$	8.03066	0.636873
$160$	1.72202	0.136138
$161$	3.59212	0.283099
$162$	2.76014	0.216857
$163$	4.22967	0.331293	0.165647	−	0.986185i	$-0.447029\pi$
$163$	4.22967	0.331293	0.165647	+	0.986185i	$0.447029\pi$
$164$	1.44573	0.112893
$165$	8.05468	0.627056
$166$	4.34938	0.337578
$167$	1.33810	0.103545	0.0517725	−	0.998659i	$-0.483513\pi$
$167$	1.33810	0.103545	0.0517725	+	0.998659i	$0.483513\pi$
$168$	1.84836	0.142604
$169$	−12.5031	−0.961775
$170$	1.72202	0.132073
$171$	1.37291	0.104989
$172$	−9.06020	−0.690834
$173$	−7.37948	−0.561051	−0.280526	−	0.959847i	$-0.590509\pi$
$173$	−7.37948	−0.561051	−0.280526	+	0.959847i	$0.590509\pi$
$174$	8.51782	0.645734
$175$	−4.32242	−0.326745
$176$	5.37607	0.405237
$177$	0.870050	0.0653970
$178$	0.0795409	0.00596184
$179$	23.6229	1.76566	0.882830	−	0.469694i	$-0.155636\pi$
$179$	23.6229	1.76566	0.882830	+	0.469694i	$0.155636\pi$
$180$	−3.86252	−0.287895
$181$	21.5306	1.60035	0.800177	−	0.599764i	$-0.204739\pi$
$181$	21.5306	1.60035	0.800177	+	0.599764i	$0.204739\pi$
$182$	−1.49756	−0.111007
$183$	4.60669	0.340536
$184$	1.69087	0.124653
$185$	−11.1029	−0.816301
$186$	−9.20553	−0.674982
$187$	5.37607	0.393137
$188$	10.9940	0.801821
$189$	−9.69095	−0.704913
$190$	−1.05402	−0.0764667
$191$	−12.8084	−0.926784	−0.463392	−	0.886153i	$-0.653368\pi$
$191$	−12.8084	−0.926784	−0.463392	+	0.886153i	$0.653368\pi$
$192$	0.870050	0.0627905
$193$	−11.0497	−0.795375	−0.397688	−	0.917521i	$-0.630187\pi$
$193$	−11.0497	−0.795375	−0.397688	+	0.917521i	$0.630187\pi$
$194$	3.93492	0.282511
$195$	−1.05615	−0.0756327
$196$	−2.48682	−0.177630
$197$	−15.0424	−1.07173	−0.535863	−	0.844305i	$-0.680014\pi$
$197$	−15.0424	−1.07173	−0.535863	+	0.844305i	$0.680014\pi$
$198$	−12.0586	−0.856967
$199$	21.9590	1.55663	0.778316	−	0.627873i	$-0.216074\pi$
$199$	21.9590	1.55663	0.778316	+	0.627873i	$0.216074\pi$
$200$	−2.03463	−0.143870
$201$	6.42966	0.453514
$202$	1.59746	0.112397
$203$	20.7982	1.45975
$204$	0.870050	0.0609157
$205$	2.48958	0.173880
$206$	5.28366	0.368130
$207$	−3.79264	−0.263607
$208$	−0.704926	−0.0488778
$209$	−3.29060	−0.227616
$210$	3.18291	0.219642
$211$	−11.7676	−0.810112	−0.405056	−	0.914292i	$-0.632748\pi$
$211$	−11.7676	−0.810112	−0.405056	+	0.914292i	$0.632748\pi$
$212$	9.23011	0.633927
$213$	−13.7060	−0.939120
$214$	−15.0118	−1.02619
$215$	−15.6019	−1.06404
$216$	−4.56168	−0.310383
$217$	−22.4774	−1.52586
$218$	6.03352	0.408642
$219$	−11.1149	−0.751076
$220$	9.25772	0.624155
$221$	−0.704926	−0.0474185
$222$	−5.60972	−0.376500
$223$	−9.50289	−0.636361	−0.318180	−	0.948030i	$-0.603072\pi$
$223$	−9.50289	−0.636361	−0.318180	+	0.948030i	$0.603072\pi$
$224$	2.12442	0.141944
$225$	4.56371	0.304247
$226$	8.99813	0.598547
$227$	8.30482	0.551210	0.275605	−	0.961271i	$-0.411122\pi$
$227$	8.30482	0.551210	0.275605	+	0.961271i	$0.411122\pi$
$228$	−0.532543	−0.0352685
$229$	−10.5202	−0.695192	−0.347596	−	0.937644i	$-0.613002\pi$
$229$	−10.5202	−0.695192	−0.347596	+	0.937644i	$0.613002\pi$
$230$	2.91172	0.191993
$231$	9.93689	0.653799
$232$	9.79004	0.642747
$233$	12.6064	0.825875	0.412937	−	0.910759i	$-0.364503\pi$
$233$	12.6064	0.825875	0.412937	+	0.910759i	$0.364503\pi$
$234$	1.58116	0.103364
$235$	18.9320	1.23498
$236$	1.00000	0.0650945
$237$	−3.57234	−0.232049
$238$	2.12442	0.137706
$239$	−0.448659	−0.0290213	−0.0145107	−	0.999895i	$-0.504619\pi$
$239$	−0.448659	−0.0290213	−0.0145107	+	0.999895i	$0.504619\pi$
$240$	1.49825	0.0967114
$241$	−13.1225	−0.845296	−0.422648	−	0.906294i	$-0.638899\pi$
$241$	−13.1225	−0.845296	−0.422648	+	0.906294i	$0.638899\pi$
$242$	17.9021	1.15079
$243$	16.0865	1.03195
$244$	5.29474	0.338961
$245$	−4.28237	−0.273591
$246$	1.25786	0.0801981
$247$	0.431473	0.0274540
$248$	−10.5805	−0.671860
$249$	3.78418	0.239813
$250$	−12.1138	−0.766144
$251$	0.0382849	0.00241652	0.00120826	−	0.999999i	$-0.499615\pi$
$251$	0.0382849	0.00241652	0.00120826	+	0.999999i	$0.499615\pi$
$252$	−4.76511	−0.300174
$253$	9.09023	0.571498
$254$	−1.57697	−0.0989476
$255$	1.49825	0.0938239
$256$	1.00000	0.0625000
$257$	1.49431	0.0932124	0.0466062	−	0.998913i	$-0.485159\pi$
$257$	1.49431	0.0932124	0.0466062	+	0.998913i	$0.485159\pi$
$258$	−7.88283	−0.490763
$259$	−13.6974	−0.851115
$260$	−1.21390	−0.0752828
$261$	−21.9592	−1.35924
$262$	−5.58477	−0.345028
$263$	22.7441	1.40246	0.701230	−	0.712936i	$-0.252635\pi$
$263$	22.7441	1.40246	0.701230	+	0.712936i	$0.252635\pi$
$264$	4.67745	0.287877
$265$	15.8945	0.976390
$266$	−1.30032	−0.0797279
$267$	0.0692046	0.00423525
$268$	7.38999	0.451416
$269$	18.6816	1.13904	0.569518	−	0.821979i	$-0.307130\pi$
$269$	18.6816	1.13904	0.569518	+	0.821979i	$0.307130\pi$
$270$	−7.85533	−0.478060
$271$	−18.1994	−1.10554	−0.552768	−	0.833335i	$-0.686428\pi$
$271$	−18.1994	−1.10554	−0.552768	+	0.833335i	$0.686428\pi$
$272$	1.00000	0.0606339
$273$	−1.30295	−0.0788583
$274$	−19.0763	−1.15244
$275$	−10.9383	−0.659606
$276$	1.47114	0.0885523
$277$	−6.98659	−0.419784	−0.209892	−	0.977725i	$-0.567311\pi$
$277$	−6.98659	−0.419784	−0.209892	+	0.977725i	$0.567311\pi$
$278$	12.7792	0.766444
$279$	23.7321	1.42080
$280$	3.65831	0.218626
$281$	−18.8118	−1.12222	−0.561109	−	0.827742i	$-0.689625\pi$
$281$	−18.8118	−1.12222	−0.561109	+	0.827742i	$0.689625\pi$
$282$	9.56534	0.569608
$283$	19.0384	1.13171	0.565857	−	0.824503i	$-0.308545\pi$
$283$	19.0384	1.13171	0.565857	+	0.824503i	$0.308545\pi$
$284$	−15.7531	−0.934776
$285$	−0.917051	−0.0543214
$286$	−3.78973	−0.224092
$287$	3.07134	0.181296
$288$	−2.24301	−0.132171
$289$	1.00000	0.0588235
$290$	16.8587	0.989975
$291$	3.42358	0.200694
$292$	−12.7750	−0.747602
$293$	−26.3511	−1.53945	−0.769724	−	0.638377i	$-0.779606\pi$
$293$	−26.3511	−1.53945	−0.769724	+	0.638377i	$0.779606\pi$
$294$	−2.16366	−0.126187
$295$	1.72202	0.100260
$296$	−6.44758	−0.374758
$297$	−24.5239	−1.42302
$298$	7.59358	0.439884
$299$	−1.19194	−0.0689315
$300$	−1.77023	−0.102204
$301$	−19.2477	−1.10942
$302$	−16.6352	−0.957249
$303$	1.38987	0.0798458
$304$	−0.612083	−0.0351054
$305$	9.11766	0.522076
$306$	−2.24301	−0.128224
$307$	28.1312	1.60553	0.802767	−	0.596293i	$-0.203360\pi$
$307$	28.1312	1.60553	0.802767	+	0.596293i	$0.203360\pi$
$308$	11.4211	0.650775
$309$	4.59705	0.261517
$310$	−18.2198	−1.03482
$311$	2.49966	0.141743	0.0708714	−	0.997485i	$-0.477422\pi$
$311$	2.49966	0.141743	0.0708714	+	0.997485i	$0.477422\pi$
$312$	−0.613321	−0.0347225
$313$	−21.6039	−1.22113	−0.610563	−	0.791968i	$-0.709057\pi$
$313$	−21.6039	−1.22113	−0.610563	+	0.791968i	$0.709057\pi$
$314$	−5.90501	−0.333239
$315$	−8.20563	−0.462335
$316$	−4.10590	−0.230975
$317$	−8.73791	−0.490770	−0.245385	−	0.969426i	$-0.578914\pi$
$317$	−8.73791	−0.490770	−0.245385	+	0.969426i	$0.578914\pi$
$318$	8.03066	0.450337
$319$	52.6319	2.94682
$320$	1.72202	0.0962641
$321$	−13.0610	−0.728996
$322$	3.59212	0.200181
$323$	−0.612083	−0.0340572
$324$	2.76014	0.153341
$325$	1.43427	0.0795588
$326$	4.22967	0.234260
$327$	5.24947	0.290296
$328$	1.44573	0.0798271
$329$	23.3559	1.28765
$330$	8.05468	0.443396
$331$	−10.9389	−0.601258	−0.300629	−	0.953741i	$-0.597197\pi$
$331$	−10.9389	−0.601258	−0.300629	+	0.953741i	$0.597197\pi$
$332$	4.34938	0.238703
$333$	14.4620	0.792513
$334$	1.33810	0.0732174
$335$	12.7257	0.695282
$336$	1.84836	0.100836
$337$	−21.0421	−1.14623	−0.573117	−	0.819474i	$-0.694266\pi$
$337$	−21.0421	−1.14623	−0.573117	+	0.819474i	$0.694266\pi$
$338$	−12.5031	−0.680078
$339$	7.82883	0.425203
$340$	1.72202	0.0933899
$341$	−56.8813	−3.08029
$342$	1.37291	0.0742384
$343$	−20.1540	−1.08822
$344$	−9.06020	−0.488493
$345$	2.53334	0.136390
$346$	−7.37948	−0.396723
$347$	−34.1138	−1.83132	−0.915662	−	0.401949i	$-0.868333\pi$
$347$	−34.1138	−1.83132	−0.915662	+	0.401949i	$0.868333\pi$
$348$	8.51782	0.456603
$349$	−7.26955	−0.389130	−0.194565	−	0.980890i	$-0.562330\pi$
$349$	−7.26955	−0.389130	−0.194565	+	0.980890i	$0.562330\pi$
$350$	−4.32242	−0.231043
$351$	3.21565	0.171639
$352$	5.37607	0.286545
$353$	−16.3705	−0.871316	−0.435658	−	0.900112i	$-0.643484\pi$
$353$	−16.3705	−0.871316	−0.435658	+	0.900112i	$0.643484\pi$
$354$	0.870050	0.0462426
$355$	−27.1272	−1.43976
$356$	0.0795409	0.00421566
$357$	1.84836	0.0978253
$358$	23.6229	1.24851
$359$	−18.3793	−0.970025	−0.485012	−	0.874507i	$-0.661185\pi$
$359$	−18.3793	−0.970025	−0.485012	+	0.874507i	$0.661185\pi$
$360$	−3.86252	−0.203573
$361$	−18.6254	−0.980282
$362$	21.5306	1.13162
$363$	15.5757	0.817515
$364$	−1.49756	−0.0784936
$365$	−21.9989	−1.15147
$366$	4.60669	0.240795
$367$	−21.9697	−1.14681	−0.573404	−	0.819273i	$-0.694377\pi$
$367$	−21.9697	−1.14681	−0.573404	+	0.819273i	$0.694377\pi$
$368$	1.69087	0.0881426
$369$	−3.24279	−0.168813
$370$	−11.1029	−0.577212
$371$	19.6087	1.01803
$372$	−9.20553	−0.477284
$373$	26.4848	1.37133	0.685665	−	0.727917i	$-0.259511\pi$
$373$	26.4848	1.37133	0.685665	+	0.727917i	$0.259511\pi$
$374$	5.37607	0.277990
$375$	−10.5396	−0.544264
$376$	10.9940	0.566973
$377$	−6.90125	−0.355432
$378$	−9.69095	−0.498449
$379$	−3.66374	−0.188194	−0.0940969	−	0.995563i	$-0.529996\pi$
$379$	−3.66374	−0.188194	−0.0940969	+	0.995563i	$0.529996\pi$
$380$	−1.05402	−0.0540701
$381$	−1.37204	−0.0702917
$382$	−12.8084	−0.655335
$383$	8.95765	0.457715	0.228857	−	0.973460i	$-0.426501\pi$
$383$	8.95765	0.457715	0.228857	+	0.973460i	$0.426501\pi$
$384$	0.870050	0.0443996
$385$	19.6673	1.00234
$386$	−11.0497	−0.562415
$387$	20.3221	1.03303
$388$	3.93492	0.199765
$389$	−11.5476	−0.585485	−0.292742	−	0.956191i	$-0.594568\pi$
$389$	−11.5476	−0.585485	−0.292742	+	0.956191i	$0.594568\pi$
$390$	−1.05615	−0.0534804
$391$	1.69087	0.0855109
$392$	−2.48682	−0.125604
$393$	−4.85903	−0.245106
$394$	−15.0424	−0.757825
$395$	−7.07047	−0.355754
$396$	−12.0586	−0.605967
$397$	−5.34050	−0.268032	−0.134016	−	0.990979i	$-0.542787\pi$
$397$	−5.34050	−0.268032	−0.134016	+	0.990979i	$0.542787\pi$
$398$	21.9590	1.10070
$399$	−1.13135	−0.0566382
$400$	−2.03463	−0.101732
$401$	−24.0545	−1.20123	−0.600613	−	0.799540i	$-0.705077\pi$
$401$	−24.0545	−1.20123	−0.600613	+	0.799540i	$0.705077\pi$
$402$	6.42966	0.320682
$403$	7.45844	0.371531
$404$	1.59746	0.0794764
$405$	4.75303	0.236180
$406$	20.7982	1.03220
$407$	−34.6627	−1.71816
$408$	0.870050	0.0430739
$409$	−23.5707	−1.16550	−0.582748	−	0.812653i	$-0.698023\pi$
$409$	−23.5707	−1.16550	−0.582748	+	0.812653i	$0.698023\pi$
$410$	2.48958	0.122952
$411$	−16.5973	−0.818686
$412$	5.28366	0.260307
$413$	2.12442	0.104536
$414$	−3.79264	−0.186398
$415$	7.48974	0.367657
$416$	−0.704926	−0.0345618
$417$	11.1185	0.544477
$418$	−3.29060	−0.160948
$419$	13.5572	0.662312	0.331156	−	0.943576i	$-0.392561\pi$
$419$	13.5572	0.662312	0.331156	+	0.943576i	$0.392561\pi$
$420$	3.18291	0.155310
$421$	35.9585	1.75251	0.876256	−	0.481846i	$-0.160033\pi$
$421$	35.9585	1.75251	0.876256	+	0.481846i	$0.160033\pi$
$422$	−11.7676	−0.572836
$423$	−24.6597	−1.19900
$424$	9.23011	0.448254
$425$	−2.03463	−0.0986942
$426$	−13.7060	−0.664058
$427$	11.2483	0.544342
$428$	−15.0118	−0.725624
$429$	−3.29726	−0.159193
$430$	−15.6019	−0.752389
$431$	7.69311	0.370564	0.185282	−	0.982685i	$-0.440680\pi$
$431$	7.69311	0.370564	0.185282	+	0.982685i	$0.440680\pi$
$432$	−4.56168	−0.219474
$433$	14.1764	0.681272	0.340636	−	0.940195i	$-0.389358\pi$
$433$	14.1764	0.681272	0.340636	+	0.940195i	$0.389358\pi$
$434$	−22.4774	−1.07895
$435$	14.6679	0.703272
$436$	6.03352	0.288953
$437$	−1.03495	−0.0495085
$438$	−11.1149	−0.531091
$439$	23.3973	1.11669	0.558346	−	0.829608i	$-0.311436\pi$
$439$	23.3973	1.11669	0.558346	+	0.829608i	$0.311436\pi$
$440$	9.25772	0.441345
$441$	5.57798	0.265618
$442$	−0.704926	−0.0335299
$443$	4.59269	0.218205	0.109103	−	0.994031i	$-0.465202\pi$
$443$	4.59269	0.218205	0.109103	+	0.994031i	$0.465202\pi$
$444$	−5.60972	−0.266226
$445$	0.136971	0.00649306
$446$	−9.50289	−0.449975
$447$	6.60679	0.312491
$448$	2.12442	0.100370
$449$	24.7441	1.16774	0.583872	−	0.811845i	$-0.301537\pi$
$449$	24.7441	1.16774	0.583872	+	0.811845i	$0.301537\pi$
$450$	4.56371	0.215135
$451$	7.77235	0.365986
$452$	8.99813	0.423237
$453$	−14.4735	−0.680023
$454$	8.30482	0.389765
$455$	−2.57884	−0.120898
$456$	−0.532543	−0.0249386
$457$	29.0343	1.35817	0.679083	−	0.734061i	$-0.262377\pi$
$457$	29.0343	1.35817	0.679083	+	0.734061i	$0.262377\pi$
$458$	−10.5202	−0.491575
$459$	−4.56168	−0.212921
$460$	2.91172	0.135759
$461$	−6.31274	−0.294013	−0.147007	−	0.989135i	$-0.546964\pi$
$461$	−6.31274	−0.294013	−0.147007	+	0.989135i	$0.546964\pi$
$462$	9.93689	0.462306
$463$	2.87760	0.133734	0.0668668	−	0.997762i	$-0.478700\pi$
$463$	2.87760	0.133734	0.0668668	+	0.997762i	$0.478700\pi$
$464$	9.79004	0.454491
$465$	−15.8521	−0.735125
$466$	12.6064	0.583982
$467$	13.7367	0.635658	0.317829	−	0.948148i	$-0.397046\pi$
$467$	13.7367	0.635658	0.317829	+	0.948148i	$0.397046\pi$
$468$	1.58116	0.0730891
$469$	15.6995	0.724934
$470$	18.9320	0.873266
$471$	−5.13766	−0.236731
$472$	1.00000	0.0460287
$473$	−48.7083	−2.23961
$474$	−3.57234	−0.164083
$475$	1.24536	0.0571412
$476$	2.12442	0.0973728
$477$	−20.7033	−0.947937
$478$	−0.448659	−0.0205212
$479$	−3.82075	−0.174574	−0.0872872	−	0.996183i	$-0.527820\pi$
$479$	−3.82075	−0.174574	−0.0872872	+	0.996183i	$0.527820\pi$
$480$	1.49825	0.0683853
$481$	4.54507	0.207237
$482$	−13.1225	−0.597714
$483$	3.12533	0.142207
$484$	17.9021	0.813733
$485$	6.77603	0.307684
$486$	16.0865	0.729699
$487$	−12.5630	−0.569285	−0.284643	−	0.958634i	$-0.591875\pi$
$487$	−12.5630	−0.569285	−0.284643	+	0.958634i	$0.591875\pi$
$488$	5.29474	0.239681
$489$	3.68002	0.166416
$490$	−4.28237	−0.193458
$491$	30.1739	1.36173	0.680864	−	0.732410i	$-0.261605\pi$
$491$	30.1739	1.36173	0.680864	+	0.732410i	$0.261605\pi$
$492$	1.25786	0.0567086
$493$	9.79004	0.440921
$494$	0.431473	0.0194129
$495$	−20.7652	−0.933326
$496$	−10.5805	−0.475077
$497$	−33.4663	−1.50117
$498$	3.78418	0.169573
$499$	−21.6368	−0.968597	−0.484298	−	0.874903i	$-0.660925\pi$
$499$	−21.6368	−0.968597	−0.484298	+	0.874903i	$0.660925\pi$
$500$	−12.1138	−0.541746
$501$	1.16421	0.0520132
$502$	0.0382849	0.00170874
$503$	33.8747	1.51040	0.755199	−	0.655496i	$-0.227540\pi$
$503$	33.8747	1.51040	0.755199	+	0.655496i	$0.227540\pi$
$504$	−4.76511	−0.212255
$505$	2.75086	0.122412
$506$	9.09023	0.404110
$507$	−10.8783	−0.483123
$508$	−1.57697	−0.0699665
$509$	28.5711	1.26639	0.633196	−	0.773992i	$-0.281743\pi$
$509$	28.5711	1.26639	0.633196	+	0.773992i	$0.281743\pi$
$510$	1.49825	0.0663435
$511$	−27.1396	−1.20058
$512$	1.00000	0.0441942
$513$	2.79213	0.123275
$514$	1.49431	0.0659111
$515$	9.09858	0.400932
$516$	−7.88283	−0.347022
$517$	59.1046	2.59942
$518$	−13.6974	−0.601829
$519$	−6.42051	−0.281829
$520$	−1.21390	−0.0532330
$521$	12.4663	0.546161	0.273080	−	0.961991i	$-0.411958\pi$
$521$	12.4663	0.546161	0.273080	+	0.961991i	$0.411958\pi$
$522$	−21.9592	−0.961127
$523$	−2.28172	−0.0997725	−0.0498863	−	0.998755i	$-0.515886\pi$
$523$	−2.28172	−0.0997725	−0.0498863	+	0.998755i	$0.515886\pi$
$524$	−5.58477	−0.243972
$525$	−3.76073	−0.164132
$526$	22.7441	0.991688
$527$	−10.5805	−0.460892
$528$	4.67745	0.203560
$529$	−20.1410	−0.875694
$530$	15.8945	0.690412
$531$	−2.24301	−0.0973385
$532$	−1.30032	−0.0563762
$533$	−1.01913	−0.0441436
$534$	0.0692046	0.00299477
$535$	−25.8507	−1.11762
$536$	7.38999	0.319199
$537$	20.5531	0.886932
$538$	18.6816	0.805421
$539$	−13.3693	−0.575858
$540$	−7.85533	−0.338040
$541$	−23.2094	−0.997851	−0.498925	−	0.866645i	$-0.666272\pi$
$541$	−23.2094	−0.997851	−0.498925	+	0.866645i	$0.666272\pi$
$542$	−18.1994	−0.781731
$543$	18.7327	0.803896
$544$	1.00000	0.0428746
$545$	10.3899	0.445053
$546$	−1.30295	−0.0557613
$547$	−0.00445098	−0.000190310 0	−9.51551e−5	−	1.00000i	$-0.500030\pi$
$547$	−0.00445098	−0.000190310 0	−9.51551e−5		1.00000i	$0.500030\pi$
$548$	−19.0763	−0.814899
$549$	−11.8762	−0.506862
$550$	−10.9383	−0.466412
$551$	−5.99231	−0.255281
$552$	1.47114	0.0626159
$553$	−8.72268	−0.370926
$554$	−6.98659	−0.296832
$555$	−9.66008	−0.410047
$556$	12.7792	0.541958
$557$	−6.35306	−0.269188	−0.134594	−	0.990901i	$-0.542973\pi$
$557$	−6.35306	−0.269188	−0.134594	+	0.990901i	$0.542973\pi$
$558$	23.7321	1.00466
$559$	6.38677	0.270132
$560$	3.65831	0.154592
$561$	4.67745	0.197482
$562$	−18.8118	−0.793528
$563$	−23.2410	−0.979491	−0.489746	−	0.871865i	$-0.662910\pi$
$563$	−23.2410	−0.979491	−0.489746	+	0.871865i	$0.662910\pi$
$564$	9.56534	0.402774
$565$	15.4950	0.651879
$566$	19.0384	0.800242
$567$	5.86371	0.246253
$568$	−15.7531	−0.660986
$569$	3.93276	0.164870	0.0824350	−	0.996596i	$-0.473730\pi$
$569$	3.93276	0.164870	0.0824350	+	0.996596i	$0.473730\pi$
$570$	−0.917051	−0.0384111
$571$	32.5747	1.36321	0.681604	−	0.731721i	$-0.261283\pi$
$571$	32.5747	1.36321	0.681604	+	0.731721i	$0.261283\pi$
$572$	−3.78973	−0.158457
$573$	−11.1440	−0.465546
$574$	3.07134	0.128195
$575$	−3.44030	−0.143470
$576$	−2.24301	−0.0934589
$577$	−7.72066	−0.321415	−0.160708	−	0.987002i	$-0.551378\pi$
$577$	−7.72066	−0.321415	−0.160708	+	0.987002i	$0.551378\pi$
$578$	1.00000	0.0415945
$579$	−9.61380	−0.399536
$580$	16.8587	0.700018
$581$	9.23993	0.383337
$582$	3.42358	0.141912
$583$	49.6217	2.05512
$584$	−12.7750	−0.528634
$585$	2.72279	0.112574
$586$	−26.3511	−1.08855
$587$	7.88516	0.325455	0.162728	−	0.986671i	$-0.447971\pi$
$587$	7.88516	0.325455	0.162728	+	0.986671i	$0.447971\pi$
$588$	−2.16366	−0.0892279
$589$	6.47611	0.266844
$590$	1.72202	0.0708946
$591$	−13.0876	−0.538354
$592$	−6.44758	−0.264994
$593$	−7.32432	−0.300774	−0.150387	−	0.988627i	$-0.548052\pi$
$593$	−7.32432	−0.300774	−0.150387	+	0.988627i	$0.548052\pi$
$594$	−24.5239	−1.00623
$595$	3.65831	0.149976
$596$	7.59358	0.311045
$597$	19.1054	0.781933
$598$	−1.19194	−0.0487419
$599$	−25.8032	−1.05429	−0.527145	−	0.849775i	$-0.676738\pi$
$599$	−25.8032	−1.05429	−0.527145	+	0.849775i	$0.676738\pi$
$600$	−1.77023	−0.0722695
$601$	−46.5355	−1.89822	−0.949111	−	0.314941i	$-0.898015\pi$
$601$	−46.5355	−1.89822	−0.949111	+	0.314941i	$0.898015\pi$
$602$	−19.2477	−0.784478
$603$	−16.5758	−0.675021
$604$	−16.6352	−0.676877
$605$	30.8279	1.25333
$606$	1.38987	0.0564595
$607$	−31.1372	−1.26382	−0.631911	−	0.775041i	$-0.717729\pi$
$607$	−31.1372	−1.26382	−0.631911	+	0.775041i	$0.717729\pi$
$608$	−0.612083	−0.0248232
$609$	18.0955	0.733265
$610$	9.11766	0.369163
$611$	−7.74996	−0.313530
$612$	−2.24301	−0.0906684
$613$	−1.98795	−0.0802926	−0.0401463	−	0.999194i	$-0.512782\pi$
$613$	−1.98795	−0.0802926	−0.0401463	+	0.999194i	$0.512782\pi$
$614$	28.1312	1.13528
$615$	2.16606	0.0873441
$616$	11.4211	0.460167
$617$	20.2989	0.817203	0.408602	−	0.912713i	$-0.366017\pi$
$617$	20.2989	0.817203	0.408602	+	0.912713i	$0.366017\pi$
$618$	4.59705	0.184920
$619$	−45.6188	−1.83357	−0.916787	−	0.399377i	$-0.869226\pi$
$619$	−45.6188	−1.83357	−0.916787	+	0.399377i	$0.869226\pi$
$620$	−18.2198	−0.731725
$621$	−7.71321	−0.309520
$622$	2.49966	0.100227
$623$	0.168979	0.00676998
$624$	−0.613321	−0.0245525
$625$	−10.6871	−0.427484
$626$	−21.6039	−0.863467
$627$	−2.86299	−0.114337
$628$	−5.90501	−0.235636
$629$	−6.44758	−0.257082
$630$	−8.20563	−0.326920
$631$	−9.58637	−0.381628	−0.190814	−	0.981626i	$-0.561113\pi$
$631$	−9.58637	−0.381628	−0.190814	+	0.981626i	$0.561113\pi$
$632$	−4.10590	−0.163324
$633$	−10.2384	−0.406938
$634$	−8.73791	−0.347027
$635$	−2.71557	−0.107764
$636$	8.03066	0.318436
$637$	1.75303	0.0694574
$638$	52.6319	2.08372
$639$	35.3344	1.39781
$640$	1.72202	0.0680690
$641$	3.37658	0.133367	0.0666834	−	0.997774i	$-0.478758\pi$
$641$	3.37658	0.133367	0.0666834	+	0.997774i	$0.478758\pi$
$642$	−13.0610	−0.515478
$643$	22.9561	0.905300	0.452650	−	0.891688i	$-0.350479\pi$
$643$	22.9561	0.905300	0.452650	+	0.891688i	$0.350479\pi$
$644$	3.59212	0.141549
$645$	−13.5744	−0.534492
$646$	−0.612083	−0.0240821
$647$	22.0582	0.867196	0.433598	−	0.901106i	$-0.357244\pi$
$647$	22.0582	0.867196	0.433598	+	0.901106i	$0.357244\pi$
$648$	2.76014	0.108429
$649$	5.37607	0.211029
$650$	1.43427	0.0562565
$651$	−19.5564	−0.766477
$652$	4.22967	0.165647
$653$	20.0755	0.785615	0.392807	−	0.919621i	$-0.371504\pi$
$653$	20.0755	0.785615	0.392807	+	0.919621i	$0.371504\pi$
$654$	5.24947	0.205270
$655$	−9.61711	−0.375772
$656$	1.44573	0.0564463
$657$	28.6545	1.11792
$658$	23.3559	0.910509
$659$	26.3271	1.02556	0.512780	−	0.858520i	$-0.328616\pi$
$659$	26.3271	1.02556	0.512780	+	0.858520i	$0.328616\pi$
$660$	8.05468	0.313528
$661$	13.4158	0.521812	0.260906	−	0.965364i	$-0.415979\pi$
$661$	13.4158	0.521812	0.260906	+	0.965364i	$0.415979\pi$
$662$	−10.9389	−0.425154
$663$	−0.613321	−0.0238194
$664$	4.34938	0.168789
$665$	−2.23919	−0.0868320
$666$	14.4620	0.560392
$667$	16.5537	0.640961
$668$	1.33810	0.0517725
$669$	−8.26799	−0.319659
$670$	12.7257	0.491638
$671$	28.4649	1.09887
$672$	1.84836	0.0713019
$673$	11.1866	0.431212	0.215606	−	0.976480i	$-0.430827\pi$
$673$	11.1866	0.431212	0.215606	+	0.976480i	$0.430827\pi$
$674$	−21.0421	−0.810510
$675$	9.28136	0.357240
$676$	−12.5031	−0.480888
$677$	11.0358	0.424141	0.212071	−	0.977254i	$-0.431979\pi$
$677$	11.0358	0.424141	0.212071	+	0.977254i	$0.431979\pi$
$678$	7.82883	0.300664
$679$	8.35944	0.320806
$680$	1.72202	0.0660366
$681$	7.22561	0.276886
$682$	−56.8813	−2.17810
$683$	8.90720	0.340825	0.170412	−	0.985373i	$-0.445490\pi$
$683$	8.90720	0.340825	0.170412	+	0.985373i	$0.445490\pi$
$684$	1.37291	0.0524945
$685$	−32.8499	−1.25513
$686$	−20.1540	−0.769485
$687$	−9.15308	−0.349212
$688$	−9.06020	−0.345417
$689$	−6.50654	−0.247880
$690$	2.53334	0.0964426
$691$	20.4686	0.778660	0.389330	−	0.921098i	$-0.372707\pi$
$691$	20.4686	0.778660	0.389330	+	0.921098i	$0.372707\pi$
$692$	−7.37948	−0.280526
$693$	−25.6176	−0.973131
$694$	−34.1138	−1.29494
$695$	22.0061	0.834737
$696$	8.51782	0.322867
$697$	1.44573	0.0547610
$698$	−7.26955	−0.275157
$699$	10.9682	0.414856
$700$	−4.32242	−0.163372
$701$	−34.0974	−1.28784	−0.643921	−	0.765092i	$-0.722694\pi$
$701$	−34.0974	−1.28784	−0.643921	+	0.765092i	$0.722694\pi$
$702$	3.21565	0.121367
$703$	3.94645	0.148843
$704$	5.37607	0.202618
$705$	16.4717	0.620362
$706$	−16.3705	−0.616113
$707$	3.39367	0.127632
$708$	0.870050	0.0326985
$709$	6.03883	0.226793	0.113397	−	0.993550i	$-0.463827\pi$
$709$	6.03883	0.226793	0.113397	+	0.993550i	$0.463827\pi$
$710$	−27.1272	−1.01807
$711$	9.20960	0.345387
$712$	0.0795409	0.00298092
$713$	−17.8902	−0.669992
$714$	1.84836	0.0691730
$715$	−6.52601	−0.244059
$716$	23.6229	0.882830
$717$	−0.390356	−0.0145781
$718$	−18.3793	−0.685911
$719$	5.37109	0.200308	0.100154	−	0.994972i	$-0.468066\pi$
$719$	5.37109	0.200308	0.100154	+	0.994972i	$0.468066\pi$
$720$	−3.86252	−0.143948
$721$	11.2247	0.418031
$722$	−18.6254	−0.693164
$723$	−11.4173	−0.424612
$724$	21.5306	0.800177
$725$	−19.9191	−0.739778
$726$	15.5757	0.578070
$727$	−30.7853	−1.14176	−0.570882	−	0.821032i	$-0.693398\pi$
$727$	−30.7853	−1.14176	−0.570882	+	0.821032i	$0.693398\pi$
$728$	−1.49756	−0.0555033
$729$	5.71565	0.211691
$730$	−21.9989	−0.814216
$731$	−9.06020	−0.335104
$732$	4.60669	0.170268
$733$	−18.3721	−0.678587	−0.339294	−	0.940681i	$-0.610188\pi$
$733$	−18.3721	−0.678587	−0.339294	+	0.940681i	$0.610188\pi$
$734$	−21.9697	−0.810915
$735$	−3.72588	−0.137431
$736$	1.69087	0.0623263
$737$	39.7291	1.46344
$738$	−3.24279	−0.119369
$739$	9.01751	0.331714	0.165857	−	0.986150i	$-0.446961\pi$
$739$	9.01751	0.331714	0.165857	+	0.986150i	$0.446961\pi$
$740$	−11.1029	−0.408151
$741$	0.375403	0.0137908
$742$	19.6087	0.719857
$743$	32.3714	1.18759	0.593795	−	0.804616i	$-0.297629\pi$
$743$	32.3714	1.18759	0.593795	+	0.804616i	$0.297629\pi$
$744$	−9.20553	−0.337491
$745$	13.0763	0.479079
$746$	26.4848	0.969677
$747$	−9.75572	−0.356943
$748$	5.37607	0.196569
$749$	−31.8915	−1.16529
$750$	−10.5396	−0.384853
$751$	17.5041	0.638733	0.319367	−	0.947631i	$-0.396530\pi$
$751$	17.5041	0.638733	0.319367	+	0.947631i	$0.396530\pi$
$752$	10.9940	0.400910
$753$	0.0333098	0.00121388
$754$	−6.90125	−0.251329
$755$	−28.6462	−1.04254
$756$	−9.69095	−0.352456
$757$	37.8227	1.37469	0.687345	−	0.726331i	$-0.258776\pi$
$757$	37.8227	1.37469	0.687345	+	0.726331i	$0.258776\pi$
$758$	−3.66374	−0.133073
$759$	7.90896	0.287077
$760$	−1.05402	−0.0382334
$761$	37.9534	1.37581	0.687906	−	0.725800i	$-0.258530\pi$
$761$	37.9534	1.37581	0.687906	+	0.725800i	$0.258530\pi$
$762$	−1.37204	−0.0497037
$763$	12.8178	0.464034
$764$	−12.8084	−0.463392
$765$	−3.86252	−0.139650
$766$	8.95765	0.323653
$767$	−0.704926	−0.0254534
$768$	0.870050	0.0313952
$769$	−53.2994	−1.92203	−0.961013	−	0.276504i	$-0.910824\pi$
$769$	−53.2994	−1.92203	−0.961013	+	0.276504i	$0.910824\pi$
$770$	19.6673	0.708761
$771$	1.30012	0.0468228
$772$	−11.0497	−0.397688
$773$	31.4012	1.12942	0.564711	−	0.825289i	$-0.308988\pi$
$773$	31.4012	1.12942	0.564711	+	0.825289i	$0.308988\pi$
$774$	20.3221	0.730464
$775$	21.5274	0.773285
$776$	3.93492	0.141255
$777$	−11.9174	−0.427535
$778$	−11.5476	−0.414000
$779$	−0.884907	−0.0317051
$780$	−1.05615	−0.0378164
$781$	−84.6899	−3.03044
$782$	1.69087	0.0604654
$783$	−44.6590	−1.59598
$784$	−2.48682	−0.0888151
$785$	−10.1686	−0.362932
$786$	−4.85903	−0.173316
$787$	49.9882	1.78189	0.890944	−	0.454114i	$-0.150044\pi$
$787$	49.9882	1.78189	0.890944	+	0.454114i	$0.150044\pi$
$788$	−15.0424	−0.535863
$789$	19.7885	0.704489
$790$	−7.07047	−0.251556
$791$	19.1158	0.679681
$792$	−12.0586	−0.428483
$793$	−3.73240	−0.132541
$794$	−5.34050	−0.189527
$795$	13.8290	0.490464
$796$	21.9590	0.778316
$797$	7.56719	0.268044	0.134022	−	0.990978i	$-0.457211\pi$
$797$	7.56719	0.268044	0.134022	+	0.990978i	$0.457211\pi$
$798$	−1.13135	−0.0400492
$799$	10.9940	0.388940
$800$	−2.03463	−0.0719352
$801$	−0.178411	−0.00630385
$802$	−24.0545	−0.849396
$803$	−68.6794	−2.42364
$804$	6.42966	0.226757
$805$	6.18572	0.218018
$806$	7.45844	0.262712
$807$	16.2539	0.572165
$808$	1.59746	0.0561983
$809$	13.1694	0.463013	0.231506	−	0.972833i	$-0.425635\pi$
$809$	13.1694	0.463013	0.231506	+	0.972833i	$0.425635\pi$
$810$	4.75303	0.167005
$811$	34.0251	1.19478	0.597392	−	0.801950i	$-0.296204\pi$
$811$	34.0251	1.19478	0.597392	+	0.801950i	$0.296204\pi$
$812$	20.7982	0.729873
$813$	−15.8344	−0.555337
$814$	−34.6627	−1.21493
$815$	7.28359	0.255133
$816$	0.870050	0.0304578
$817$	5.54559	0.194016
$818$	−23.5707	−0.824131
$819$	3.35905	0.117375
$820$	2.48958	0.0869400
$821$	−42.3987	−1.47972	−0.739862	−	0.672758i	$-0.765109\pi$
$821$	−42.3987	−1.47972	−0.739862	+	0.672758i	$0.765109\pi$
$822$	−16.5973	−0.578899
$823$	−0.753269	−0.0262573	−0.0131287	−	0.999914i	$-0.504179\pi$
$823$	−0.753269	−0.0262573	−0.0131287	+	0.999914i	$0.504179\pi$
$824$	5.28366	0.184065
$825$	−9.51690	−0.331336
$826$	2.12442	0.0739182
$827$	47.9693	1.66806	0.834028	−	0.551723i	$-0.186029\pi$
$827$	47.9693	1.66806	0.834028	+	0.551723i	$0.186029\pi$
$828$	−3.79264	−0.131803
$829$	33.4478	1.16169	0.580845	−	0.814014i	$-0.302722\pi$
$829$	33.4478	1.16169	0.580845	+	0.814014i	$0.302722\pi$
$830$	7.48974	0.259973
$831$	−6.07869	−0.210867
$832$	−0.704926	−0.0244389
$833$	−2.48682	−0.0861633
$834$	11.1185	0.385003
$835$	2.30424	0.0797414
$836$	−3.29060	−0.113808
$837$	48.2647	1.66827
$838$	13.5572	0.468325
$839$	41.7208	1.44036	0.720181	−	0.693786i	$-0.244059\pi$
$839$	41.7208	1.44036	0.720181	+	0.693786i	$0.244059\pi$
$840$	3.18291	0.109821
$841$	66.8448	2.30499
$842$	35.9585	1.23921
$843$	−16.3672	−0.563717
$844$	−11.7676	−0.405056
$845$	−21.5306	−0.740675
$846$	−24.6597	−0.847818
$847$	38.0317	1.30678
$848$	9.23011	0.316963
$849$	16.5643	0.568487
$850$	−2.03463	−0.0697874
$851$	−10.9020	−0.373716
$852$	−13.7060	−0.469560
$853$	−51.5462	−1.76491	−0.882455	−	0.470397i	$-0.844111\pi$
$853$	−51.5462	−1.76491	−0.882455	+	0.470397i	$0.844111\pi$
$854$	11.2483	0.384908
$855$	2.36418	0.0808533
$856$	−15.0118	−0.513094
$857$	−3.94169	−0.134645	−0.0673227	−	0.997731i	$-0.521446\pi$
$857$	−3.94169	−0.134645	−0.0673227	+	0.997731i	$0.521446\pi$
$858$	−3.29726	−0.112566
$859$	14.6746	0.500690	0.250345	−	0.968157i	$-0.419456\pi$
$859$	14.6746	0.500690	0.250345	+	0.968157i	$0.419456\pi$
$860$	−15.6019	−0.532020
$861$	2.67222	0.0910691
$862$	7.69311	0.262028
$863$	−46.0929	−1.56902	−0.784510	−	0.620116i	$-0.787086\pi$
$863$	−46.0929	−1.56902	−0.784510	+	0.620116i	$0.787086\pi$
$864$	−4.56168	−0.155192
$865$	−12.7076	−0.432072
$866$	14.1764	0.481732
$867$	0.870050	0.0295485
$868$	−22.4774	−0.762932
$869$	−22.0736	−0.748797
$870$	14.6679	0.497288
$871$	−5.20940	−0.176514
$872$	6.03352	0.204321
$873$	−8.82608	−0.298717
$874$	−1.03495	−0.0350078
$875$	−25.7349	−0.869997
$876$	−11.1149	−0.375538
$877$	9.48525	0.320294	0.160147	−	0.987093i	$-0.448803\pi$
$877$	9.48525	0.320294	0.160147	+	0.987093i	$0.448803\pi$
$878$	23.3973	0.789620
$879$	−22.9268	−0.773301
$880$	9.25772	0.312078
$881$	−7.04142	−0.237231	−0.118616	−	0.992940i	$-0.537846\pi$
$881$	−7.04142	−0.237231	−0.118616	+	0.992940i	$0.537846\pi$
$882$	5.57798	0.187820
$883$	31.2740	1.05245	0.526227	−	0.850344i	$-0.323606\pi$
$883$	31.2740	1.05245	0.526227	+	0.850344i	$0.323606\pi$
$884$	−0.704926	−0.0237092
$885$	1.49825	0.0503630
$886$	4.59269	0.154294
$887$	−13.3564	−0.448462	−0.224231	−	0.974536i	$-0.571987\pi$
$887$	−13.3564	−0.448462	−0.224231	+	0.974536i	$0.571987\pi$
$888$	−5.60972	−0.188250
$889$	−3.35014	−0.112360
$890$	0.136971	0.00459129
$891$	14.8387	0.497116
$892$	−9.50289	−0.318180
$893$	−6.72924	−0.225186
$894$	6.60679	0.220964
$895$	40.6792	1.35976
$896$	2.12442	0.0709720
$897$	−1.03705	−0.0346259
$898$	24.7441	0.825720
$899$	−103.583	−3.45469
$900$	4.56371	0.152124
$901$	9.23011	0.307500
$902$	7.77235	0.258791
$903$	−16.7465	−0.557287
$904$	8.99813	0.299273
$905$	37.0762	1.23245
$906$	−14.4735	−0.480849
$907$	−14.2160	−0.472033	−0.236017	−	0.971749i	$-0.575842\pi$
$907$	−14.2160	−0.472033	−0.236017	+	0.971749i	$0.575842\pi$
$908$	8.30482	0.275605
$909$	−3.58312	−0.118844
$910$	−2.57884	−0.0854876
$911$	1.89321	0.0627247	0.0313624	−	0.999508i	$-0.490015\pi$
$911$	1.89321	0.0627247	0.0313624	+	0.999508i	$0.490015\pi$
$912$	−0.532543	−0.0176343
$913$	23.3826	0.773850
$914$	29.0343	0.960369
$915$	7.93283	0.262251
$916$	−10.5202	−0.347596
$917$	−11.8644	−0.391798
$918$	−4.56168	−0.150558
$919$	13.1249	0.432949	0.216474	−	0.976288i	$-0.430544\pi$
$919$	13.1249	0.432949	0.216474	+	0.976288i	$0.430544\pi$
$920$	2.91172	0.0959965
$921$	24.4756	0.806498
$922$	−6.31274	−0.207899
$923$	11.1048	0.365518
$924$	9.93689	0.326900
$925$	13.1185	0.431333
$926$	2.87760	0.0945639
$927$	−11.8513	−0.389248
$928$	9.79004	0.321374
$929$	39.5753	1.29842	0.649212	−	0.760608i	$-0.275099\pi$
$929$	39.5753	1.29842	0.649212	+	0.760608i	$0.275099\pi$
$930$	−15.8521	−0.519812
$931$	1.52214	0.0498862
$932$	12.6064	0.412937
$933$	2.17483	0.0712008
$934$	13.7367	0.449478
$935$	9.25772	0.302760
$936$	1.58116	0.0516818
$937$	59.5802	1.94640	0.973201	−	0.229957i	$-0.0738585\pi$
$937$	59.5802	1.94640	0.973201	+	0.229957i	$0.0738585\pi$
$938$	15.6995	0.512606
$939$	−18.7965	−0.613401
$940$	18.9320	0.617492
$941$	32.6948	1.06582	0.532910	−	0.846172i	$-0.321099\pi$
$941$	32.6948	1.06582	0.532910	+	0.846172i	$0.321099\pi$
$942$	−5.13766	−0.167394
$943$	2.44454	0.0796052
$944$	1.00000	0.0325472
$945$	−16.6880	−0.542862
$946$	−48.7083	−1.58364
$947$	−13.2388	−0.430203	−0.215102	−	0.976592i	$-0.569008\pi$
$947$	−13.2388	−0.430203	−0.215102	+	0.976592i	$0.569008\pi$
$948$	−3.57234	−0.116024
$949$	9.00545	0.292329
$950$	1.24536	0.0404049
$951$	−7.60242	−0.246525
$952$	2.12442	0.0688530
$953$	37.7502	1.22285	0.611424	−	0.791303i	$-0.290597\pi$
$953$	37.7502	1.22285	0.611424	+	0.791303i	$0.290597\pi$
$954$	−20.7033	−0.670293
$955$	−22.0564	−0.713728
$956$	−0.448659	−0.0145107
$957$	45.7924	1.48026
$958$	−3.82075	−0.123443
$959$	−40.5262	−1.30866
$960$	1.49825	0.0483557
$961$	80.9461	2.61116
$962$	4.54507	0.146539
$963$	33.6717	1.08506
$964$	−13.1225	−0.422648
$965$	−19.0279	−0.612529
$966$	3.12533	0.100556
$967$	59.0634	1.89935	0.949675	−	0.313237i	$-0.101414\pi$
$967$	59.0634	1.89935	0.949675	+	0.313237i	$0.101414\pi$
$968$	17.9021	0.575396
$969$	−0.532543	−0.0171077
$970$	6.77603	0.217565
$971$	22.7537	0.730202	0.365101	−	0.930968i	$-0.381034\pi$
$971$	22.7537	0.730202	0.365101	+	0.930968i	$0.381034\pi$
$972$	16.0865	0.515975
$973$	27.1484	0.870338
$974$	−12.5630	−0.402545
$975$	1.24788	0.0399643
$976$	5.29474	0.169480
$977$	−10.1351	−0.324252	−0.162126	−	0.986770i	$-0.551835\pi$
$977$	−10.1351	−0.324252	−0.162126	+	0.986770i	$0.551835\pi$
$978$	3.68002	0.117674
$979$	0.427617	0.0136667
$980$	−4.28237	−0.136795
$981$	−13.5333	−0.432084
$982$	30.1739	0.962887
$983$	58.2602	1.85821	0.929106	−	0.369812i	$-0.120578\pi$
$983$	58.2602	1.85821	0.929106	+	0.369812i	$0.120578\pi$
$984$	1.25786	0.0400991
$985$	−25.9034	−0.825350
$986$	9.79004	0.311778
$987$	20.3208	0.646819
$988$	0.431473	0.0137270
$989$	−15.3196	−0.487135
$990$	−20.7652	−0.659961
$991$	−15.2799	−0.485381	−0.242691	−	0.970104i	$-0.578030\pi$
$991$	−15.2799	−0.485381	−0.242691	+	0.970104i	$0.578030\pi$
$992$	−10.5805	−0.335930
$993$	−9.51742	−0.302026
$994$	−33.4663	−1.06149
$995$	37.8139	1.19878
$996$	3.78418	0.119906
$997$	−20.3548	−0.644644	−0.322322	−	0.946630i	$-0.604463\pi$
$997$	−20.3548	−0.644644	−0.322322	+	0.946630i	$0.604463\pi$
$998$	−21.6368	−0.684901
$999$	29.4118	0.930550

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2006.2.a.w.1.8	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2006.2.a.w.1.8	✓	13	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:	\( N \)	\(=\)	\( 2006 = 2 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2006.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.870050 q^{3} +1.00000 q^{4} +1.72202 q^{5} +0.870050 q^{6} +2.12442 q^{7} +1.00000 q^{8} -2.24301 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.870050 q^{3} +1.00000 q^{4} +1.72202 q^{5} +0.870050 q^{6} +2.12442 q^{7} +1.00000 q^{8} -2.24301 q^{9} +1.72202 q^{10} +5.37607 q^{11} +0.870050 q^{12} -0.704926 q^{13} +2.12442 q^{14} +1.49825 q^{15} +1.00000 q^{16} +1.00000 q^{17} -2.24301 q^{18} -0.612083 q^{19} +1.72202 q^{20} +1.84836 q^{21} +5.37607 q^{22} +1.69087 q^{23} +0.870050 q^{24} -2.03463 q^{25} -0.704926 q^{26} -4.56168 q^{27} +2.12442 q^{28} +9.79004 q^{29} +1.49825 q^{30} -10.5805 q^{31} +1.00000 q^{32} +4.67745 q^{33} +1.00000 q^{34} +3.65831 q^{35} -2.24301 q^{36} -6.44758 q^{37} -0.612083 q^{38} -0.613321 q^{39} +1.72202 q^{40} +1.44573 q^{41} +1.84836 q^{42} -9.06020 q^{43} +5.37607 q^{44} -3.86252 q^{45} +1.69087 q^{46} +10.9940 q^{47} +0.870050 q^{48} -2.48682 q^{49} -2.03463 q^{50} +0.870050 q^{51} -0.704926 q^{52} +9.23011 q^{53} -4.56168 q^{54} +9.25772 q^{55} +2.12442 q^{56} -0.532543 q^{57} +9.79004 q^{58} +1.00000 q^{59} +1.49825 q^{60} +5.29474 q^{61} -10.5805 q^{62} -4.76511 q^{63} +1.00000 q^{64} -1.21390 q^{65} +4.67745 q^{66} +7.38999 q^{67} +1.00000 q^{68} +1.47114 q^{69} +3.65831 q^{70} -15.7531 q^{71} -2.24301 q^{72} -12.7750 q^{73} -6.44758 q^{74} -1.77023 q^{75} -0.612083 q^{76} +11.4211 q^{77} -0.613321 q^{78} -4.10590 q^{79} +1.72202 q^{80} +2.76014 q^{81} +1.44573 q^{82} +4.34938 q^{83} +1.84836 q^{84} +1.72202 q^{85} -9.06020 q^{86} +8.51782 q^{87} +5.37607 q^{88} +0.0795409 q^{89} -3.86252 q^{90} -1.49756 q^{91} +1.69087 q^{92} -9.20553 q^{93} +10.9940 q^{94} -1.05402 q^{95} +0.870050 q^{96} +3.93492 q^{97} -2.48682 q^{98} -12.0586 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 13 q^{2} + 7 q^{3} + 13 q^{4} + q^{5} + 7 q^{6} + 8 q^{7} + 13 q^{8} + 16 q^{9}+O(q^{10}) \) 13 * q + 13 * q^2 + 7 * q^3 + 13 * q^4 + q^5 + 7 * q^6 + 8 * q^7 + 13 * q^8 + 16 * q^9	\( 13 q + 13 q^{2} + 7 q^{3} + 13 q^{4} + q^{5} + 7 q^{6} + 8 q^{7} + 13 q^{8} + 16 q^{9} + q^{10} + 13 q^{11} + 7 q^{12} + 9 q^{13} + 8 q^{14} - 9 q^{15} + 13 q^{16} + 13 q^{17} + 16 q^{18} + 16 q^{19} + q^{20} - 3 q^{21} + 13 q^{22} + 18 q^{23} + 7 q^{24} + 14 q^{25} + 9 q^{26} + 10 q^{27} + 8 q^{28} + 8 q^{29} - 9 q^{30} + 32 q^{31} + 13 q^{32} + 13 q^{33} + 13 q^{34} - q^{35} + 16 q^{36} - 3 q^{37} + 16 q^{38} + 20 q^{39} + q^{40} + 24 q^{41} - 3 q^{42} - 2 q^{43} + 13 q^{44} - 3 q^{45} + 18 q^{46} + 26 q^{47} + 7 q^{48} + 23 q^{49} + 14 q^{50} + 7 q^{51} + 9 q^{52} - 27 q^{53} + 10 q^{54} - 7 q^{55} + 8 q^{56} - 21 q^{57} + 8 q^{58} + 13 q^{59} - 9 q^{60} + 20 q^{61} + 32 q^{62} - 3 q^{63} + 13 q^{64} + 16 q^{65} + 13 q^{66} + 4 q^{67} + 13 q^{68} - 2 q^{69} - q^{70} - 8 q^{71} + 16 q^{72} + 10 q^{73} - 3 q^{74} + 39 q^{75} + 16 q^{76} - 15 q^{77} + 20 q^{78} + 35 q^{79} + q^{80} + 29 q^{81} + 24 q^{82} - q^{83} - 3 q^{84} + q^{85} - 2 q^{86} - 32 q^{87} + 13 q^{88} - 20 q^{89} - 3 q^{90} - 15 q^{91} + 18 q^{92} - 7 q^{93} + 26 q^{94} - 3 q^{95} + 7 q^{96} - 3 q^{97} + 23 q^{98} + 65 q^{99}+O(q^{100}) \) 13 * q + 13 * q^2 + 7 * q^3 + 13 * q^4 + q^5 + 7 * q^6 + 8 * q^7 + 13 * q^8 + 16 * q^9 + q^10 + 13 * q^11 + 7 * q^12 + 9 * q^13 + 8 * q^14 - 9 * q^15 + 13 * q^16 + 13 * q^17 + 16 * q^18 + 16 * q^19 + q^20 - 3 * q^21 + 13 * q^22 + 18 * q^23 + 7 * q^24 + 14 * q^25 + 9 * q^26 + 10 * q^27 + 8 * q^28 + 8 * q^29 - 9 * q^30 + 32 * q^31 + 13 * q^32 + 13 * q^33 + 13 * q^34 - q^35 + 16 * q^36 - 3 * q^37 + 16 * q^38 + 20 * q^39 + q^40 + 24 * q^41 - 3 * q^42 - 2 * q^43 + 13 * q^44 - 3 * q^45 + 18 * q^46 + 26 * q^47 + 7 * q^48 + 23 * q^49 + 14 * q^50 + 7 * q^51 + 9 * q^52 - 27 * q^53 + 10 * q^54 - 7 * q^55 + 8 * q^56 - 21 * q^57 + 8 * q^58 + 13 * q^59 - 9 * q^60 + 20 * q^61 + 32 * q^62 - 3 * q^63 + 13 * q^64 + 16 * q^65 + 13 * q^66 + 4 * q^67 + 13 * q^68 - 2 * q^69 - q^70 - 8 * q^71 + 16 * q^72 + 10 * q^73 - 3 * q^74 + 39 * q^75 + 16 * q^76 - 15 * q^77 + 20 * q^78 + 35 * q^79 + q^80 + 29 * q^81 + 24 * q^82 - q^83 - 3 * q^84 + q^85 - 2 * q^86 - 32 * q^87 + 13 * q^88 - 20 * q^89 - 3 * q^90 - 15 * q^91 + 18 * q^92 - 7 * q^93 + 26 * q^94 - 3 * q^95 + 7 * q^96 - 3 * q^97 + 23 * q^98 + 65 * q^99

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