LMFDB - Embedded newform 2006.2.a.v.1.3

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:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 21 x^{10} + 62 x^{9} + 144 x^{8} - 418 x^{7} - 370 x^{6} + 1042 x^{5} + 417 x^{4} + \cdots + 62 $ x^12 - 3x^11 - 21x^10 + 62x^9 + 144x^8 - 418x^7 - 370x^6 + 1042x^5 + 417x^4 - 935x^3 - 233x^2 + 228*x + 62
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.03816$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.03816 q^{3} +1.00000 q^{4} +3.57691 q^{5} +2.03816 q^{6} -0.163425 q^{7} -1.00000 q^{8} +1.15408 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.03816 q^{3} +1.00000 q^{4} +3.57691 q^{5} +2.03816 q^{6} -0.163425 q^{7} -1.00000 q^{8} +1.15408 q^{9} -3.57691 q^{10} -0.327750 q^{11} -2.03816 q^{12} -3.91538 q^{13} +0.163425 q^{14} -7.29029 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.15408 q^{18} -4.04837 q^{19} +3.57691 q^{20} +0.333084 q^{21} +0.327750 q^{22} +5.81688 q^{23} +2.03816 q^{24} +7.79426 q^{25} +3.91538 q^{26} +3.76228 q^{27} -0.163425 q^{28} +5.71591 q^{29} +7.29029 q^{30} -0.947468 q^{31} -1.00000 q^{32} +0.668006 q^{33} +1.00000 q^{34} -0.584554 q^{35} +1.15408 q^{36} +3.22084 q^{37} +4.04837 q^{38} +7.98014 q^{39} -3.57691 q^{40} +8.14126 q^{41} -0.333084 q^{42} +3.84799 q^{43} -0.327750 q^{44} +4.12802 q^{45} -5.81688 q^{46} -11.5087 q^{47} -2.03816 q^{48} -6.97329 q^{49} -7.79426 q^{50} +2.03816 q^{51} -3.91538 q^{52} +3.68366 q^{53} -3.76228 q^{54} -1.17233 q^{55} +0.163425 q^{56} +8.25120 q^{57} -5.71591 q^{58} +1.00000 q^{59} -7.29029 q^{60} +3.66053 q^{61} +0.947468 q^{62} -0.188604 q^{63} +1.00000 q^{64} -14.0049 q^{65} -0.668006 q^{66} -10.9454 q^{67} -1.00000 q^{68} -11.8557 q^{69} +0.584554 q^{70} +9.50381 q^{71} -1.15408 q^{72} +11.1260 q^{73} -3.22084 q^{74} -15.8859 q^{75} -4.04837 q^{76} +0.0535624 q^{77} -7.98014 q^{78} -2.34874 q^{79} +3.57691 q^{80} -11.1303 q^{81} -8.14126 q^{82} -3.78764 q^{83} +0.333084 q^{84} -3.57691 q^{85} -3.84799 q^{86} -11.6499 q^{87} +0.327750 q^{88} +17.4324 q^{89} -4.12802 q^{90} +0.639869 q^{91} +5.81688 q^{92} +1.93109 q^{93} +11.5087 q^{94} -14.4806 q^{95} +2.03816 q^{96} +16.9514 q^{97} +6.97329 q^{98} -0.378249 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} - 3 q^{3} + 12 q^{4} - q^{5} + 3 q^{6} + 4 q^{7} - 12 q^{8} + 15 q^{9}+O(q^{10}) $ 12 * q - 12 * q^2 - 3 * q^3 + 12 * q^4 - q^5 + 3 * q^6 + 4 * q^7 - 12 * q^8 + 15 * q^9	\( 12 q - 12 q^{2} - 3 q^{3} + 12 q^{4} - q^{5} + 3 q^{6} + 4 q^{7} - 12 q^{8} + 15 q^{9} + q^{10} - 3 q^{11} - 3 q^{12} + 15 q^{13} - 4 q^{14} - 3 q^{15} + 12 q^{16} - 12 q^{17} - 15 q^{18} + 16 q^{19} - q^{20} + 15 q^{21} + 3 q^{22} - 14 q^{23} + 3 q^{24} + 19 q^{25} - 15 q^{26} - 12 q^{27} + 4 q^{28} + 14 q^{29} + 3 q^{30} + 26 q^{31} - 12 q^{32} + 13 q^{33} + 12 q^{34} - 5 q^{35} + 15 q^{36} + 15 q^{37} - 16 q^{38} + 4 q^{39} + q^{40} - 2 q^{41} - 15 q^{42} + 8 q^{43} - 3 q^{44} - 17 q^{45} + 14 q^{46} - 6 q^{47} - 3 q^{48} + 30 q^{49} - 19 q^{50} + 3 q^{51} + 15 q^{52} + q^{53} + 12 q^{54} + q^{55} - 4 q^{56} + 3 q^{57} - 14 q^{58} + 12 q^{59} - 3 q^{60} + 30 q^{61} - 26 q^{62} + q^{63} + 12 q^{64} - 4 q^{65} - 13 q^{66} + 10 q^{67} - 12 q^{68} + 8 q^{69} + 5 q^{70} + 6 q^{71} - 15 q^{72} + 26 q^{73} - 15 q^{74} + 7 q^{75} + 16 q^{76} + 45 q^{77} - 4 q^{78} - 11 q^{79} - q^{80} + 48 q^{81} + 2 q^{82} - 21 q^{83} + 15 q^{84} + q^{85} - 8 q^{86} + 2 q^{87} + 3 q^{88} - 2 q^{89} + 17 q^{90} + 31 q^{91} - 14 q^{92} + 41 q^{93} + 6 q^{94} - 29 q^{95} + 3 q^{96} + 27 q^{97} - 30 q^{98} + 9 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 - 3 * q^3 + 12 * q^4 - q^5 + 3 * q^6 + 4 * q^7 - 12 * q^8 + 15 * q^9 + q^10 - 3 * q^11 - 3 * q^12 + 15 * q^13 - 4 * q^14 - 3 * q^15 + 12 * q^16 - 12 * q^17 - 15 * q^18 + 16 * q^19 - q^20 + 15 * q^21 + 3 * q^22 - 14 * q^23 + 3 * q^24 + 19 * q^25 - 15 * q^26 - 12 * q^27 + 4 * q^28 + 14 * q^29 + 3 * q^30 + 26 * q^31 - 12 * q^32 + 13 * q^33 + 12 * q^34 - 5 * q^35 + 15 * q^36 + 15 * q^37 - 16 * q^38 + 4 * q^39 + q^40 - 2 * q^41 - 15 * q^42 + 8 * q^43 - 3 * q^44 - 17 * q^45 + 14 * q^46 - 6 * q^47 - 3 * q^48 + 30 * q^49 - 19 * q^50 + 3 * q^51 + 15 * q^52 + q^53 + 12 * q^54 + q^55 - 4 * q^56 + 3 * q^57 - 14 * q^58 + 12 * q^59 - 3 * q^60 + 30 * q^61 - 26 * q^62 + q^63 + 12 * q^64 - 4 * q^65 - 13 * q^66 + 10 * q^67 - 12 * q^68 + 8 * q^69 + 5 * q^70 + 6 * q^71 - 15 * q^72 + 26 * q^73 - 15 * q^74 + 7 * q^75 + 16 * q^76 + 45 * q^77 - 4 * q^78 - 11 * q^79 - q^80 + 48 * q^81 + 2 * q^82 - 21 * q^83 + 15 * q^84 + q^85 - 8 * q^86 + 2 * q^87 + 3 * q^88 - 2 * q^89 + 17 * q^90 + 31 * q^91 - 14 * q^92 + 41 * q^93 + 6 * q^94 - 29 * q^95 + 3 * q^96 + 27 * q^97 - 30 * q^98 + 9 * 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
$3$	−2.03816	−1.17673	−0.588365	−	0.808596i	$-0.700228\pi$
$3$	−2.03816	−1.17673	−0.588365	+	0.808596i	$0.700228\pi$
$4$	1.00000	0.500000
$5$	3.57691	1.59964	0.799821	−	0.600239i	$-0.204928\pi$
$5$	3.57691	1.59964	0.799821	+	0.600239i	$0.204928\pi$
$6$	2.03816	0.832073
$7$	−0.163425	−0.0617687	−0.0308843	−	0.999523i	$-0.509832\pi$
$7$	−0.163425	−0.0617687	−0.0308843	+	0.999523i	$0.509832\pi$
$8$	−1.00000	−0.353553
$9$	1.15408	0.384692
$10$	−3.57691	−1.13112
$11$	−0.327750	−0.0988204	−0.0494102	−	0.998779i	$-0.515734\pi$
$11$	−0.327750	−0.0988204	−0.0494102	+	0.998779i	$0.515734\pi$
$12$	−2.03816	−0.588365
$13$	−3.91538	−1.08593	−0.542965	−	0.839755i	$-0.682698\pi$
$13$	−3.91538	−1.08593	−0.542965	+	0.839755i	$0.682698\pi$
$14$	0.163425	0.0436770
$15$	−7.29029	−1.88234
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.15408	−0.272018
$19$	−4.04837	−0.928759	−0.464380	−	0.885636i	$-0.653723\pi$
$19$	−4.04837	−0.928759	−0.464380	+	0.885636i	$0.653723\pi$
$20$	3.57691	0.799821
$21$	0.333084	0.0726850
$22$	0.327750	0.0698766
$23$	5.81688	1.21290	0.606451	−	0.795121i	$-0.292592\pi$
$23$	5.81688	1.21290	0.606451	+	0.795121i	$0.292592\pi$
$24$	2.03816	0.416037
$25$	7.79426	1.55885
$26$	3.91538	0.767869
$27$	3.76228	0.724051
$28$	−0.163425	−0.0308843
$29$	5.71591	1.06142	0.530709	−	0.847554i	$-0.321926\pi$
$29$	5.71591	1.06142	0.530709	+	0.847554i	$0.321926\pi$
$30$	7.29029	1.33102
$31$	−0.947468	−0.170170	−0.0850851	−	0.996374i	$-0.527116\pi$
$31$	−0.947468	−0.170170	−0.0850851	+	0.996374i	$0.527116\pi$
$32$	−1.00000	−0.176777
$33$	0.668006	0.116285
$34$	1.00000	0.171499
$35$	−0.584554	−0.0988077
$36$	1.15408	0.192346
$37$	3.22084	0.529502	0.264751	−	0.964317i	$-0.414710\pi$
$37$	3.22084	0.529502	0.264751	+	0.964317i	$0.414710\pi$
$38$	4.04837	0.656732
$39$	7.98014	1.27785
$40$	−3.57691	−0.565559
$41$	8.14126	1.27145	0.635726	−	0.771915i	$-0.280701\pi$
$41$	8.14126	1.27145	0.635726	+	0.771915i	$0.280701\pi$
$42$	−0.333084	−0.0513961
$43$	3.84799	0.586812	0.293406	−	0.955988i	$-0.405211\pi$
$43$	3.84799	0.586812	0.293406	+	0.955988i	$0.405211\pi$
$44$	−0.327750	−0.0494102
$45$	4.12802	0.615369
$46$	−5.81688	−0.857652
$47$	−11.5087	−1.67871	−0.839355	−	0.543583i	$-0.817067\pi$
$47$	−11.5087	−1.67871	−0.839355	+	0.543583i	$0.817067\pi$
$48$	−2.03816	−0.294182
$49$	−6.97329	−0.996185
$50$	−7.79426	−1.10227
$51$	2.03816	0.285399
$52$	−3.91538	−0.542965
$53$	3.68366	0.505990	0.252995	−	0.967468i	$-0.418584\pi$
$53$	3.68366	0.505990	0.252995	+	0.967468i	$0.418584\pi$
$54$	−3.76228	−0.511981
$55$	−1.17233	−0.158077
$56$	0.163425	0.0218385
$57$	8.25120	1.09290
$58$	−5.71591	−0.750536
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	−7.29029	−0.941172
$61$	3.66053	0.468683	0.234342	−	0.972154i	$-0.424707\pi$
$61$	3.66053	0.468683	0.234342	+	0.972154i	$0.424707\pi$
$62$	0.947468	0.120329
$63$	−0.188604	−0.0237619
$64$	1.00000	0.125000
$65$	−14.0049	−1.73710
$66$	−0.668006	−0.0822258
$67$	−10.9454	−1.33719	−0.668594	−	0.743628i	$-0.733104\pi$
$67$	−10.9454	−1.33719	−0.668594	+	0.743628i	$0.733104\pi$
$68$	−1.00000	−0.121268
$69$	−11.8557	−1.42726
$70$	0.584554	0.0698676
$71$	9.50381	1.12789	0.563947	−	0.825811i	$-0.309282\pi$
$71$	9.50381	1.12789	0.563947	+	0.825811i	$0.309282\pi$
$72$	−1.15408	−0.136009
$73$	11.1260	1.30220	0.651102	−	0.758991i	$-0.274307\pi$
$73$	11.1260	1.30220	0.651102	+	0.758991i	$0.274307\pi$
$74$	−3.22084	−0.374415
$75$	−15.8859	−1.83435
$76$	−4.04837	−0.464380
$77$	0.0535624	0.00610400
$78$	−7.98014	−0.903573
$79$	−2.34874	−0.264254	−0.132127	−	0.991233i	$-0.542181\pi$
$79$	−2.34874	−0.264254	−0.132127	+	0.991233i	$0.542181\pi$
$80$	3.57691	0.399910
$81$	−11.1303	−1.23670
$82$	−8.14126	−0.899052
$83$	−3.78764	−0.415748	−0.207874	−	0.978156i	$-0.566654\pi$
$83$	−3.78764	−0.415748	−0.207874	+	0.978156i	$0.566654\pi$
$84$	0.333084	0.0363425
$85$	−3.57691	−0.387970
$86$	−3.84799	−0.414939
$87$	−11.6499	−1.24900
$88$	0.327750	0.0349383
$89$	17.4324	1.84783	0.923916	−	0.382595i	$-0.124970\pi$
$89$	17.4324	1.84783	0.923916	+	0.382595i	$0.124970\pi$
$90$	−4.12802	−0.435132
$91$	0.639869	0.0670764
$92$	5.81688	0.606451
$93$	1.93109	0.200244
$94$	11.5087	1.18703
$95$	−14.4806	−1.48568
$96$	2.03816	0.208018
$97$	16.9514	1.72116	0.860578	−	0.509319i	$-0.170103\pi$
$97$	16.9514	1.72116	0.860578	+	0.509319i	$0.170103\pi$
$98$	6.97329	0.704409
$99$	−0.378249	−0.0380154
$100$	7.79426	0.779426
$101$	12.6374	1.25747	0.628736	−	0.777619i	$-0.283573\pi$
$101$	12.6374	1.25747	0.628736	+	0.777619i	$0.283573\pi$
$102$	−2.03816	−0.201807
$103$	4.28360	0.422076	0.211038	−	0.977478i	$-0.432316\pi$
$103$	4.28360	0.422076	0.211038	+	0.977478i	$0.432316\pi$
$104$	3.91538	0.383934
$105$	1.19141	0.116270
$106$	−3.68366	−0.357789
$107$	4.63629	0.448207	0.224104	−	0.974565i	$-0.428055\pi$
$107$	4.63629	0.448207	0.224104	+	0.974565i	$0.428055\pi$
$108$	3.76228	0.362025
$109$	12.9471	1.24011	0.620053	−	0.784560i	$-0.287111\pi$
$109$	12.9471	1.24011	0.620053	+	0.784560i	$0.287111\pi$
$110$	1.17233	0.111777
$111$	−6.56456	−0.623081
$112$	−0.163425	−0.0154422
$113$	−13.3230	−1.25332	−0.626661	−	0.779292i	$-0.715579\pi$
$113$	−13.3230	−1.25332	−0.626661	+	0.779292i	$0.715579\pi$
$114$	−8.25120	−0.772796
$115$	20.8064	1.94021
$116$	5.71591	0.530709
$117$	−4.51864	−0.417749
$118$	−1.00000	−0.0920575
$119$	0.163425	0.0149811
$120$	7.29029	0.665509
$121$	−10.8926	−0.990235
$122$	−3.66053	−0.331409
$123$	−16.5932	−1.49615
$124$	−0.947468	−0.0850851
$125$	9.99479	0.893962
$126$	0.188604	0.0168022
$127$	−4.48947	−0.398376	−0.199188	−	0.979961i	$-0.563830\pi$
$127$	−4.48947	−0.398376	−0.199188	+	0.979961i	$0.563830\pi$
$128$	−1.00000	−0.0883883
$129$	−7.84279	−0.690519
$130$	14.0049	1.22831
$131$	3.85008	0.336383	0.168191	−	0.985754i	$-0.446207\pi$
$131$	3.85008	0.336383	0.168191	+	0.985754i	$0.446207\pi$
$132$	0.668006	0.0581424
$133$	0.661603	0.0573682
$134$	10.9454	0.945535
$135$	13.4573	1.15822
$136$	1.00000	0.0857493
$137$	−9.01175	−0.769926	−0.384963	−	0.922932i	$-0.625786\pi$
$137$	−9.01175	−0.769926	−0.384963	+	0.922932i	$0.625786\pi$
$138$	11.8557	1.00922
$139$	9.07518	0.769747	0.384873	−	0.922969i	$-0.374245\pi$
$139$	9.07518	0.769747	0.384873	+	0.922969i	$0.374245\pi$
$140$	−0.584554	−0.0494038
$141$	23.4564	1.97539
$142$	−9.50381	−0.797542
$143$	1.28327	0.107312
$144$	1.15408	0.0961730
$145$	20.4453	1.69789
$146$	−11.1260	−0.920797
$147$	14.2127	1.17224
$148$	3.22084	0.264751
$149$	20.5772	1.68575	0.842876	−	0.538108i	$-0.180861\pi$
$149$	20.5772	1.68575	0.842876	+	0.538108i	$0.180861\pi$
$150$	15.8859	1.29708
$151$	5.78136	0.470481	0.235240	−	0.971937i	$-0.424412\pi$
$151$	5.78136	0.470481	0.235240	+	0.971937i	$0.424412\pi$
$152$	4.04837	0.328366
$153$	−1.15408	−0.0933015
$154$	−0.0535624	−0.00431618
$155$	−3.38900	−0.272211
$156$	7.98014	0.638923
$157$	1.76684	0.141009	0.0705047	−	0.997511i	$-0.477539\pi$
$157$	1.76684	0.141009	0.0705047	+	0.997511i	$0.477539\pi$
$158$	2.34874	0.186856
$159$	−7.50787	−0.595413
$160$	−3.57691	−0.282779
$161$	−0.950620	−0.0749194
$162$	11.1303	0.874482
$163$	−17.3251	−1.35701	−0.678504	−	0.734596i	$-0.737372\pi$
$163$	−17.3251	−1.35701	−0.678504	+	0.734596i	$0.737372\pi$
$164$	8.14126	0.635726
$165$	2.38939	0.186014
$166$	3.78764	0.293978
$167$	−13.6389	−1.05541	−0.527705	−	0.849427i	$-0.676947\pi$
$167$	−13.6389	−1.05541	−0.527705	+	0.849427i	$0.676947\pi$
$168$	−0.333084	−0.0256980
$169$	2.33018	0.179244
$170$	3.57691	0.274336
$171$	−4.67213	−0.357286
$172$	3.84799	0.293406
$173$	8.08635	0.614794	0.307397	−	0.951581i	$-0.400542\pi$
$173$	8.08635	0.614794	0.307397	+	0.951581i	$0.400542\pi$
$174$	11.6499	0.883178
$175$	−1.27377	−0.0962882
$176$	−0.327750	−0.0247051
$177$	−2.03816	−0.153197
$178$	−17.4324	−1.30661
$179$	14.0694	1.05159	0.525797	−	0.850610i	$-0.323767\pi$
$179$	14.0694	1.05159	0.525797	+	0.850610i	$0.323767\pi$
$180$	4.12802	0.307685
$181$	−12.6860	−0.942942	−0.471471	−	0.881882i	$-0.656277\pi$
$181$	−12.6860	−0.942942	−0.471471	+	0.881882i	$0.656277\pi$
$182$	−0.639869	−0.0474302
$183$	−7.46074	−0.551514
$184$	−5.81688	−0.428826
$185$	11.5206	0.847013
$186$	−1.93109	−0.141594
$187$	0.327750	0.0239675
$188$	−11.5087	−0.839355
$189$	−0.614849	−0.0447237
$190$	14.4806	1.05054
$191$	−13.3232	−0.964036	−0.482018	−	0.876161i	$-0.660096\pi$
$191$	−13.3232	−0.964036	−0.482018	+	0.876161i	$0.660096\pi$
$192$	−2.03816	−0.147091
$193$	14.4083	1.03713	0.518566	−	0.855038i	$-0.326466\pi$
$193$	14.4083	1.03713	0.518566	+	0.855038i	$0.326466\pi$
$194$	−16.9514	−1.21704
$195$	28.5442	2.04409
$196$	−6.97329	−0.498092
$197$	−17.3303	−1.23474	−0.617368	−	0.786675i	$-0.711801\pi$
$197$	−17.3303	−1.23474	−0.617368	+	0.786675i	$0.711801\pi$
$198$	0.378249	0.0268810
$199$	15.0252	1.06511	0.532555	−	0.846395i	$-0.321232\pi$
$199$	15.0252	1.06511	0.532555	+	0.846395i	$0.321232\pi$
$200$	−7.79426	−0.551137
$201$	22.3083	1.57351
$202$	−12.6374	−0.889166
$203$	−0.934120	−0.0655624
$204$	2.03816	0.142699
$205$	29.1205	2.03387
$206$	−4.28360	−0.298453
$207$	6.71312	0.466594
$208$	−3.91538	−0.271483
$209$	1.32685	0.0917804
$210$	−1.19141	−0.0822152
$211$	14.8250	1.02060	0.510299	−	0.859997i	$-0.329535\pi$
$211$	14.8250	1.02060	0.510299	+	0.859997i	$0.329535\pi$
$212$	3.68366	0.252995
$213$	−19.3702	−1.32723
$214$	−4.63629	−0.316930
$215$	13.7639	0.938689
$216$	−3.76228	−0.255991
$217$	0.154839	0.0105112
$218$	−12.9471	−0.876887
$219$	−22.6766	−1.53234
$220$	−1.17233	−0.0790386
$221$	3.91538	0.263377
$222$	6.56456	0.440585
$223$	9.54153	0.638948	0.319474	−	0.947595i	$-0.396494\pi$
$223$	9.54153	0.638948	0.319474	+	0.947595i	$0.396494\pi$
$224$	0.163425	0.0109193
$225$	8.99516	0.599678
$226$	13.3230	0.886233
$227$	15.1458	1.00526	0.502631	−	0.864501i	$-0.332366\pi$
$227$	15.1458	1.00526	0.502631	+	0.864501i	$0.332366\pi$
$228$	8.25120	0.546449
$229$	23.4918	1.55238	0.776190	−	0.630499i	$-0.217150\pi$
$229$	23.4918	1.55238	0.776190	+	0.630499i	$0.217150\pi$
$230$	−20.8064	−1.37193
$231$	−0.109169	−0.00718276
$232$	−5.71591	−0.375268
$233$	−3.93456	−0.257762	−0.128881	−	0.991660i	$-0.541139\pi$
$233$	−3.93456	−0.257762	−0.128881	+	0.991660i	$0.541139\pi$
$234$	4.51864	0.295393
$235$	−41.1654	−2.68533
$236$	1.00000	0.0650945
$237$	4.78710	0.310956
$238$	−0.163425	−0.0105932
$239$	15.3320	0.991747	0.495874	−	0.868395i	$-0.334848\pi$
$239$	15.3320	0.991747	0.495874	+	0.868395i	$0.334848\pi$
$240$	−7.29029	−0.470586
$241$	27.9619	1.80118	0.900591	−	0.434668i	$-0.143134\pi$
$241$	27.9619	1.80118	0.900591	+	0.434668i	$0.143134\pi$
$242$	10.8926	0.700202
$243$	11.3985	0.731215
$244$	3.66053	0.234342
$245$	−24.9428	−1.59354
$246$	16.5932	1.05794
$247$	15.8509	1.00857
$248$	0.947468	0.0601643
$249$	7.71980	0.489223
$250$	−9.99479	−0.632126
$251$	−22.2075	−1.40172	−0.700861	−	0.713297i	$-0.747201\pi$
$251$	−22.2075	−1.40172	−0.700861	+	0.713297i	$0.747201\pi$
$252$	−0.188604	−0.0118810
$253$	−1.90648	−0.119860
$254$	4.48947	0.281694
$255$	7.29029	0.456536
$256$	1.00000	0.0625000
$257$	22.0402	1.37483	0.687416	−	0.726264i	$-0.258745\pi$
$257$	22.0402	1.37483	0.687416	+	0.726264i	$0.258745\pi$
$258$	7.84279	0.488271
$259$	−0.526364	−0.0327066
$260$	−14.0049	−0.868549
$261$	6.59660	0.408319
$262$	−3.85008	−0.237859
$263$	1.37630	0.0848664	0.0424332	−	0.999099i	$-0.486489\pi$
$263$	1.37630	0.0848664	0.0424332	+	0.999099i	$0.486489\pi$
$264$	−0.668006	−0.0411129
$265$	13.1761	0.809402
$266$	−0.661603	−0.0405655
$267$	−35.5300	−2.17440
$268$	−10.9454	−0.668594
$269$	29.6177	1.80582	0.902912	−	0.429825i	$-0.141425\pi$
$269$	29.6177	1.80582	0.902912	+	0.429825i	$0.141425\pi$
$270$	−13.4573	−0.818986
$271$	2.72418	0.165482	0.0827411	−	0.996571i	$-0.473633\pi$
$271$	2.72418	0.165482	0.0827411	+	0.996571i	$0.473633\pi$
$272$	−1.00000	−0.0606339
$273$	−1.30415	−0.0789308
$274$	9.01175	0.544420
$275$	−2.55457	−0.154046
$276$	−11.8557	−0.713629
$277$	−1.37547	−0.0826442	−0.0413221	−	0.999146i	$-0.513157\pi$
$277$	−1.37547	−0.0826442	−0.0413221	+	0.999146i	$0.513157\pi$
$278$	−9.07518	−0.544293
$279$	−1.09345	−0.0654631
$280$	0.584554	0.0349338
$281$	−1.11364	−0.0664343	−0.0332172	−	0.999448i	$-0.510575\pi$
$281$	−1.11364	−0.0664343	−0.0332172	+	0.999448i	$0.510575\pi$
$282$	−23.4564	−1.39681
$283$	32.5885	1.93718	0.968592	−	0.248657i	$-0.0799893\pi$
$283$	32.5885	1.93718	0.968592	+	0.248657i	$0.0799893\pi$
$284$	9.50381	0.563947
$285$	29.5138	1.74825
$286$	−1.28327	−0.0758811
$287$	−1.33048	−0.0785358
$288$	−1.15408	−0.0680046
$289$	1.00000	0.0588235
$290$	−20.4453	−1.20059
$291$	−34.5496	−2.02533
$292$	11.1260	0.651102
$293$	−25.5871	−1.49481	−0.747407	−	0.664366i	$-0.768701\pi$
$293$	−25.5871	−1.49481	−0.747407	+	0.664366i	$0.768701\pi$
$294$	−14.2127	−0.828899
$295$	3.57691	0.208256
$296$	−3.22084	−0.187207
$297$	−1.23309	−0.0715510
$298$	−20.5772	−1.19201
$299$	−22.7753	−1.31713
$300$	−15.8859	−0.917173
$301$	−0.628855	−0.0362466
$302$	−5.78136	−0.332680
$303$	−25.7570	−1.47970
$304$	−4.04837	−0.232190
$305$	13.0934	0.749725
$306$	1.15408	0.0659741
$307$	−16.3649	−0.933992	−0.466996	−	0.884259i	$-0.654664\pi$
$307$	−16.3649	−0.933992	−0.466996	+	0.884259i	$0.654664\pi$
$308$	0.0535624	0.00305200
$309$	−8.73064	−0.496669
$310$	3.38900	0.192482
$311$	2.68932	0.152497	0.0762487	−	0.997089i	$-0.475706\pi$
$311$	2.68932	0.152497	0.0762487	+	0.997089i	$0.475706\pi$
$312$	−7.98014	−0.451787
$313$	7.19020	0.406414	0.203207	−	0.979136i	$-0.434864\pi$
$313$	7.19020	0.406414	0.203207	+	0.979136i	$0.434864\pi$
$314$	−1.76684	−0.0997087
$315$	−0.674620	−0.0380105
$316$	−2.34874	−0.132127
$317$	−14.6442	−0.822500	−0.411250	−	0.911523i	$-0.634908\pi$
$317$	−14.6442	−0.822500	−0.411250	+	0.911523i	$0.634908\pi$
$318$	7.50787	0.421020
$319$	−1.87339	−0.104890
$320$	3.57691	0.199955
$321$	−9.44948	−0.527418
$322$	0.950620	0.0529760
$323$	4.04837	0.225257
$324$	−11.1303	−0.618352
$325$	−30.5175	−1.69280
$326$	17.3251	0.959550
$327$	−26.3882	−1.45927
$328$	−8.14126	−0.449526
$329$	1.88080	0.103692
$330$	−2.38939	−0.131532
$331$	−7.27635	−0.399944	−0.199972	−	0.979802i	$-0.564085\pi$
$331$	−7.27635	−0.399944	−0.199972	+	0.979802i	$0.564085\pi$
$332$	−3.78764	−0.207874
$333$	3.71709	0.203695
$334$	13.6389	0.746288
$335$	−39.1505	−2.13902
$336$	0.333084	0.0181712
$337$	−2.51930	−0.137235	−0.0686176	−	0.997643i	$-0.521859\pi$
$337$	−2.51930	−0.137235	−0.0686176	+	0.997643i	$0.521859\pi$
$338$	−2.33018	−0.126745
$339$	27.1543	1.47482
$340$	−3.57691	−0.193985
$341$	0.310533	0.0168163
$342$	4.67213	0.252640
$343$	2.28358	0.123302
$344$	−3.84799	−0.207469
$345$	−42.4067	−2.28310
$346$	−8.08635	−0.434725
$347$	10.3385	0.555002	0.277501	−	0.960725i	$-0.410494\pi$
$347$	10.3385	0.555002	0.277501	+	0.960725i	$0.410494\pi$
$348$	−11.6499	−0.624501
$349$	−18.9631	−1.01507	−0.507535	−	0.861631i	$-0.669443\pi$
$349$	−18.9631	−1.01507	−0.507535	+	0.861631i	$0.669443\pi$
$350$	1.27377	0.0680860
$351$	−14.7307	−0.786269
$352$	0.327750	0.0174691
$353$	−25.0973	−1.33580	−0.667898	−	0.744252i	$-0.732806\pi$
$353$	−25.0973	−1.33580	−0.667898	+	0.744252i	$0.732806\pi$
$354$	2.03816	0.108327
$355$	33.9942	1.80423
$356$	17.4324	0.923916
$357$	−0.333084	−0.0176287
$358$	−14.0694	−0.743590
$359$	−15.5717	−0.821841	−0.410920	−	0.911671i	$-0.634793\pi$
$359$	−15.5717	−0.821841	−0.410920	+	0.911671i	$0.634793\pi$
$360$	−4.12802	−0.217566
$361$	−2.61071	−0.137406
$362$	12.6860	0.666760
$363$	22.2008	1.16524
$364$	0.639869	0.0335382
$365$	39.7968	2.08306
$366$	7.46074	0.389979
$367$	−9.68451	−0.505528	−0.252764	−	0.967528i	$-0.581340\pi$
$367$	−9.68451	−0.505528	−0.252764	+	0.967528i	$0.581340\pi$
$368$	5.81688	0.303226
$369$	9.39563	0.489117
$370$	−11.5206	−0.598929
$371$	−0.602000	−0.0312543
$372$	1.93109	0.100122
$373$	12.7582	0.660596	0.330298	−	0.943877i	$-0.392851\pi$
$373$	12.7582	0.660596	0.330298	+	0.943877i	$0.392851\pi$
$374$	−0.327750	−0.0169476
$375$	−20.3709	−1.05195
$376$	11.5087	0.593514
$377$	−22.3800	−1.15263
$378$	0.614849	0.0316244
$379$	11.7280	0.602426	0.301213	−	0.953557i	$-0.402608\pi$
$379$	11.7280	0.602426	0.301213	+	0.953557i	$0.402608\pi$
$380$	−14.4806	−0.742841
$381$	9.15023	0.468781
$382$	13.3232	0.681677
$383$	−0.0324969	−0.00166052	−0.000830258	−	1.00000i	$-0.500264\pi$
$383$	−0.0324969	−0.00166052	−0.000830258		1.00000i	$0.500264\pi$
$384$	2.03816	0.104009
$385$	0.191588	0.00976422
$386$	−14.4083	−0.733363
$387$	4.44087	0.225742
$388$	16.9514	0.860578
$389$	30.9512	1.56929	0.784645	−	0.619946i	$-0.212845\pi$
$389$	30.9512	1.56929	0.784645	+	0.619946i	$0.212845\pi$
$390$	−28.5442	−1.44539
$391$	−5.81688	−0.294172
$392$	6.97329	0.352204
$393$	−7.84705	−0.395831
$394$	17.3303	0.873090
$395$	−8.40123	−0.422712
$396$	−0.378249	−0.0190077
$397$	−12.6326	−0.634010	−0.317005	−	0.948424i	$-0.602677\pi$
$397$	−12.6326	−0.634010	−0.317005	+	0.948424i	$0.602677\pi$
$398$	−15.0252	−0.753147
$399$	−1.34845	−0.0675069
$400$	7.79426	0.389713
$401$	−16.2469	−0.811332	−0.405666	−	0.914021i	$-0.632960\pi$
$401$	−16.2469	−0.811332	−0.405666	+	0.914021i	$0.632960\pi$
$402$	−22.3083	−1.11264
$403$	3.70969	0.184793
$404$	12.6374	0.628736
$405$	−39.8122	−1.97828
$406$	0.934120	0.0463596
$407$	−1.05563	−0.0523256
$408$	−2.03816	−0.100904
$409$	−25.9363	−1.28247	−0.641234	−	0.767345i	$-0.721577\pi$
$409$	−25.9363	−1.28247	−0.641234	+	0.767345i	$0.721577\pi$
$410$	−29.1205	−1.43816
$411$	18.3673	0.905995
$412$	4.28360	0.211038
$413$	−0.163425	−0.00804159
$414$	−6.71312	−0.329932
$415$	−13.5480	−0.665047
$416$	3.91538	0.191967
$417$	−18.4966	−0.905783
$418$	−1.32685	−0.0648985
$419$	9.56628	0.467343	0.233672	−	0.972316i	$-0.424926\pi$
$419$	9.56628	0.467343	0.233672	+	0.972316i	$0.424926\pi$
$420$	1.19141	0.0581349
$421$	−31.5436	−1.53734	−0.768669	−	0.639646i	$-0.779081\pi$
$421$	−31.5436	−1.53734	−0.768669	+	0.639646i	$0.779081\pi$
$422$	−14.8250	−0.721672
$423$	−13.2819	−0.645787
$424$	−3.68366	−0.178894
$425$	−7.79426	−0.378077
$426$	19.3702	0.938491
$427$	−0.598221	−0.0289499
$428$	4.63629	0.224104
$429$	−2.61549	−0.126277
$430$	−13.7639	−0.663753
$431$	−16.8606	−0.812145	−0.406073	−	0.913841i	$-0.633102\pi$
$431$	−16.8606	−0.812145	−0.406073	+	0.913841i	$0.633102\pi$
$432$	3.76228	0.181013
$433$	9.41721	0.452562	0.226281	−	0.974062i	$-0.427343\pi$
$433$	9.41721	0.452562	0.226281	+	0.974062i	$0.427343\pi$
$434$	−0.154839	−0.00743253
$435$	−41.6707	−1.99796
$436$	12.9471	0.620053
$437$	−23.5489	−1.12649
$438$	22.6766	1.08353
$439$	11.1344	0.531414	0.265707	−	0.964054i	$-0.414395\pi$
$439$	11.1344	0.531414	0.265707	+	0.964054i	$0.414395\pi$
$440$	1.17233	0.0558887
$441$	−8.04771	−0.383224
$442$	−3.91538	−0.186235
$443$	−33.8475	−1.60814	−0.804072	−	0.594532i	$-0.797337\pi$
$443$	−33.8475	−1.60814	−0.804072	+	0.594532i	$0.797337\pi$
$444$	−6.56456	−0.311540
$445$	62.3541	2.95587
$446$	−9.54153	−0.451805
$447$	−41.9396	−1.98367
$448$	−0.163425	−0.00772108
$449$	−31.1931	−1.47209	−0.736047	−	0.676930i	$-0.763310\pi$
$449$	−31.1931	−1.47209	−0.736047	+	0.676930i	$0.763310\pi$
$450$	−8.99516	−0.424036
$451$	−2.66830	−0.125645
$452$	−13.3230	−0.626661
$453$	−11.7833	−0.553628
$454$	−15.1458	−0.710827
$455$	2.28875	0.107298
$456$	−8.25120	−0.386398
$457$	39.7398	1.85895	0.929474	−	0.368888i	$-0.120261\pi$
$457$	39.7398	1.85895	0.929474	+	0.368888i	$0.120261\pi$
$458$	−23.4918	−1.09770
$459$	−3.76228	−0.175608
$460$	20.8064	0.970105
$461$	1.76732	0.0823123	0.0411562	−	0.999153i	$-0.486896\pi$
$461$	1.76732	0.0823123	0.0411562	+	0.999153i	$0.486896\pi$
$462$	0.109169	0.00507898
$463$	18.2176	0.846643	0.423322	−	0.905979i	$-0.360864\pi$
$463$	18.2176	0.846643	0.423322	+	0.905979i	$0.360864\pi$
$464$	5.71591	0.265355
$465$	6.90731	0.320319
$466$	3.93456	0.182265
$467$	−11.3214	−0.523890	−0.261945	−	0.965083i	$-0.584364\pi$
$467$	−11.3214	−0.523890	−0.261945	+	0.965083i	$0.584364\pi$
$468$	−4.51864	−0.208874
$469$	1.78874	0.0825963
$470$	41.1654	1.89882
$471$	−3.60110	−0.165930
$472$	−1.00000	−0.0460287
$473$	−1.26118	−0.0579890
$474$	−4.78710	−0.219879
$475$	−31.5540	−1.44780
$476$	0.163425	0.00749055
$477$	4.25122	0.194650
$478$	−15.3320	−0.701271
$479$	33.4721	1.52938	0.764690	−	0.644398i	$-0.222892\pi$
$479$	33.4721	1.52938	0.764690	+	0.644398i	$0.222892\pi$
$480$	7.29029	0.332755
$481$	−12.6108	−0.575002
$482$	−27.9619	−1.27363
$483$	1.93751	0.0881598
$484$	−10.8926	−0.495117
$485$	60.6336	2.75323
$486$	−11.3985	−0.517047
$487$	−26.8238	−1.21550	−0.607751	−	0.794127i	$-0.707928\pi$
$487$	−26.8238	−1.21550	−0.607751	+	0.794127i	$0.707928\pi$
$488$	−3.66053	−0.165705
$489$	35.3113	1.59683
$490$	24.9428	1.12680
$491$	9.03900	0.407924	0.203962	−	0.978979i	$-0.434618\pi$
$491$	9.03900	0.407924	0.203962	+	0.978979i	$0.434618\pi$
$492$	−16.5932	−0.748077
$493$	−5.71591	−0.257432
$494$	−15.8509	−0.713165
$495$	−1.35296	−0.0608110
$496$	−0.947468	−0.0425426
$497$	−1.55315	−0.0696685
$498$	−7.71980	−0.345933
$499$	5.32120	0.238210	0.119105	−	0.992882i	$-0.461998\pi$
$499$	5.32120	0.238210	0.119105	+	0.992882i	$0.461998\pi$
$500$	9.99479	0.446981
$501$	27.7982	1.24193
$502$	22.2075	0.991168
$503$	2.68974	0.119930	0.0599648	−	0.998200i	$-0.480901\pi$
$503$	2.68974	0.119930	0.0599648	+	0.998200i	$0.480901\pi$
$504$	0.188604	0.00840110
$505$	45.2029	2.01150
$506$	1.90648	0.0847535
$507$	−4.74926	−0.210922
$508$	−4.48947	−0.199188
$509$	−29.1827	−1.29350	−0.646751	−	0.762701i	$-0.723873\pi$
$509$	−29.1827	−1.29350	−0.646751	+	0.762701i	$0.723873\pi$
$510$	−7.29029	−0.322819
$511$	−1.81827	−0.0804353
$512$	−1.00000	−0.0441942
$513$	−15.2311	−0.672469
$514$	−22.0402	−0.972153
$515$	15.3220	0.675169
$516$	−7.84279	−0.345260
$517$	3.77197	0.165891
$518$	0.526364	0.0231271
$519$	−16.4812	−0.723446
$520$	14.0049	0.614157
$521$	15.2806	0.669457	0.334728	−	0.942315i	$-0.391355\pi$
$521$	15.2806	0.669457	0.334728	+	0.942315i	$0.391355\pi$
$522$	−6.59660	−0.288725
$523$	43.4924	1.90179	0.950896	−	0.309512i	$-0.100166\pi$
$523$	43.4924	1.90179	0.950896	+	0.309512i	$0.100166\pi$
$524$	3.85008	0.168191
$525$	2.59615	0.113305
$526$	−1.37630	−0.0600096
$527$	0.947468	0.0412723
$528$	0.668006	0.0290712
$529$	10.8361	0.471133
$530$	−13.1761	−0.572333
$531$	1.15408	0.0500826
$532$	0.661603	0.0286841
$533$	−31.8761	−1.38071
$534$	35.5300	1.53753
$535$	16.5836	0.716970
$536$	10.9454	0.472767
$537$	−28.6756	−1.23744
$538$	−29.6177	−1.27691
$539$	2.28550	0.0984434
$540$	13.4573	0.579111
$541$	1.66874	0.0717445	0.0358723	−	0.999356i	$-0.488579\pi$
$541$	1.66874	0.0717445	0.0358723	+	0.999356i	$0.488579\pi$
$542$	−2.72418	−0.117014
$543$	25.8560	1.10959
$544$	1.00000	0.0428746
$545$	46.3105	1.98372
$546$	1.30415	0.0558125
$547$	−26.7968	−1.14575	−0.572874	−	0.819644i	$-0.694171\pi$
$547$	−26.7968	−1.14575	−0.572874	+	0.819644i	$0.694171\pi$
$548$	−9.01175	−0.384963
$549$	4.22454	0.180299
$550$	2.55457	0.108927
$551$	−23.1401	−0.985802
$552$	11.8557	0.504612
$553$	0.383842	0.0163226
$554$	1.37547	0.0584383
$555$	−23.4808	−0.996706
$556$	9.07518	0.384873
$557$	−4.60941	−0.195307	−0.0976534	−	0.995220i	$-0.531134\pi$
$557$	−4.60941	−0.195307	−0.0976534	+	0.995220i	$0.531134\pi$
$558$	1.09345	0.0462894
$559$	−15.0663	−0.637237
$560$	−0.584554	−0.0247019
$561$	−0.668006	−0.0282032
$562$	1.11364	0.0469762
$563$	−22.8698	−0.963846	−0.481923	−	0.876213i	$-0.660062\pi$
$563$	−22.8698	−0.963846	−0.481923	+	0.876213i	$0.660062\pi$
$564$	23.4564	0.987694
$565$	−47.6551	−2.00487
$566$	−32.5885	−1.36980
$567$	1.81897	0.0763895
$568$	−9.50381	−0.398771
$569$	11.4131	0.478462	0.239231	−	0.970963i	$-0.423105\pi$
$569$	11.4131	0.478462	0.239231	+	0.970963i	$0.423105\pi$
$570$	−29.5138	−1.23620
$571$	−10.1932	−0.426571	−0.213286	−	0.976990i	$-0.568416\pi$
$571$	−10.1932	−0.426571	−0.213286	+	0.976990i	$0.568416\pi$
$572$	1.28327	0.0536560
$573$	27.1548	1.13441
$574$	1.33048	0.0555332
$575$	45.3382	1.89074
$576$	1.15408	0.0480865
$577$	2.50619	0.104334	0.0521670	−	0.998638i	$-0.483387\pi$
$577$	2.50619	0.104334	0.0521670	+	0.998638i	$0.483387\pi$
$578$	−1.00000	−0.0415945
$579$	−29.3663	−1.22042
$580$	20.4453	0.848944
$581$	0.618994	0.0256802
$582$	34.5496	1.43213
$583$	−1.20732	−0.0500021
$584$	−11.1260	−0.460398
$585$	−16.1628	−0.668248
$586$	25.5871	1.05699
$587$	−5.67337	−0.234165	−0.117082	−	0.993122i	$-0.537354\pi$
$587$	−5.67337	−0.234165	−0.117082	+	0.993122i	$0.537354\pi$
$588$	14.2127	0.586120
$589$	3.83570	0.158047
$590$	−3.57691	−0.147259
$591$	35.3219	1.45295
$592$	3.22084	0.132376
$593$	−21.8295	−0.896428	−0.448214	−	0.893926i	$-0.647940\pi$
$593$	−21.8295	−0.896428	−0.448214	+	0.893926i	$0.647940\pi$
$594$	1.23309	0.0505942
$595$	0.584554	0.0239644
$596$	20.5772	0.842876
$597$	−30.6237	−1.25335
$598$	22.7753	0.931350
$599$	16.0688	0.656555	0.328278	−	0.944581i	$-0.393532\pi$
$599$	16.0688	0.656555	0.328278	+	0.944581i	$0.393532\pi$
$600$	15.8859	0.648539
$601$	6.99542	0.285349	0.142675	−	0.989770i	$-0.454430\pi$
$601$	6.99542	0.285349	0.142675	+	0.989770i	$0.454430\pi$
$602$	0.628855	0.0256302
$603$	−12.6318	−0.514405
$604$	5.78136	0.235240
$605$	−38.9617	−1.58402
$606$	25.7570	1.04631
$607$	7.77002	0.315375	0.157688	−	0.987489i	$-0.449596\pi$
$607$	7.77002	0.315375	0.157688	+	0.987489i	$0.449596\pi$
$608$	4.04837	0.164183
$609$	1.90388	0.0771492
$610$	−13.0934	−0.530136
$611$	45.0607	1.82296
$612$	−1.15408	−0.0466508
$613$	40.9552	1.65417	0.827083	−	0.562080i	$-0.189999\pi$
$613$	40.9552	1.65417	0.827083	+	0.562080i	$0.189999\pi$
$614$	16.3649	0.660432
$615$	−59.3521	−2.39331
$616$	−0.0535624	−0.00215809
$617$	12.8332	0.516643	0.258322	−	0.966059i	$-0.416831\pi$
$617$	12.8332	0.516643	0.258322	+	0.966059i	$0.416831\pi$
$618$	8.73064	0.351198
$619$	26.0245	1.04601	0.523007	−	0.852328i	$-0.324810\pi$
$619$	26.0245	1.04601	0.523007	+	0.852328i	$0.324810\pi$
$620$	−3.38900	−0.136106
$621$	21.8847	0.878203
$622$	−2.68932	−0.107832
$623$	−2.84888	−0.114138
$624$	7.98014	0.319461
$625$	−3.22084	−0.128834
$626$	−7.19020	−0.287378
$627$	−2.70433	−0.108001
$628$	1.76684	0.0705047
$629$	−3.22084	−0.128423
$630$	0.674620	0.0268775
$631$	−29.4083	−1.17072	−0.585362	−	0.810772i	$-0.699048\pi$
$631$	−29.4083	−1.17072	−0.585362	+	0.810772i	$0.699048\pi$
$632$	2.34874	0.0934279
$633$	−30.2157	−1.20097
$634$	14.6442	0.581595
$635$	−16.0584	−0.637259
$636$	−7.50787	−0.297706
$637$	27.3031	1.08179
$638$	1.87339	0.0741683
$639$	10.9681	0.433892
$640$	−3.57691	−0.141390
$641$	−43.0551	−1.70058	−0.850288	−	0.526318i	$-0.823572\pi$
$641$	−43.0551	−1.70058	−0.850288	+	0.526318i	$0.823572\pi$
$642$	9.44948	0.372941
$643$	17.5634	0.692631	0.346315	−	0.938118i	$-0.387433\pi$
$643$	17.5634	0.692631	0.346315	+	0.938118i	$0.387433\pi$
$644$	−0.950620	−0.0374597
$645$	−28.0529	−1.10458
$646$	−4.04837	−0.159281
$647$	−3.91478	−0.153906	−0.0769529	−	0.997035i	$-0.524519\pi$
$647$	−3.91478	−0.153906	−0.0769529	+	0.997035i	$0.524519\pi$
$648$	11.1303	0.437241
$649$	−0.327750	−0.0128653
$650$	30.5175	1.19699
$651$	−0.315587	−0.0123688
$652$	−17.3251	−0.678504
$653$	−32.0322	−1.25352	−0.626759	−	0.779213i	$-0.715619\pi$
$653$	−32.0322	−1.25352	−0.626759	+	0.779213i	$0.715619\pi$
$654$	26.3882	1.03186
$655$	13.7714	0.538092
$656$	8.14126	0.317863
$657$	12.8403	0.500947
$658$	−1.88080	−0.0733211
$659$	33.5187	1.30571	0.652853	−	0.757485i	$-0.273572\pi$
$659$	33.5187	1.30571	0.652853	+	0.757485i	$0.273572\pi$
$660$	2.38939	0.0930070
$661$	13.8710	0.539521	0.269761	−	0.962927i	$-0.413055\pi$
$661$	13.8710	0.539521	0.269761	+	0.962927i	$0.413055\pi$
$662$	7.27635	0.282803
$663$	−7.98014	−0.309923
$664$	3.78764	0.146989
$665$	2.36649	0.0917686
$666$	−3.71709	−0.144034
$667$	33.2488	1.28740
$668$	−13.6389	−0.527705
$669$	−19.4471	−0.751869
$670$	39.1505	1.51252
$671$	−1.19974	−0.0463155
$672$	−0.333084	−0.0128490
$673$	10.6539	0.410676	0.205338	−	0.978691i	$-0.434171\pi$
$673$	10.6539	0.410676	0.205338	+	0.978691i	$0.434171\pi$
$674$	2.51930	0.0970399
$675$	29.3242	1.12869
$676$	2.33018	0.0896221
$677$	−16.9209	−0.650324	−0.325162	−	0.945658i	$-0.605419\pi$
$677$	−16.9209	−0.650324	−0.325162	+	0.945658i	$0.605419\pi$
$678$	−27.1543	−1.04286
$679$	−2.77028	−0.106313
$680$	3.57691	0.137168
$681$	−30.8695	−1.18292
$682$	−0.310533	−0.0118909
$683$	14.8699	0.568980	0.284490	−	0.958679i	$-0.408176\pi$
$683$	14.8699	0.568980	0.284490	+	0.958679i	$0.408176\pi$
$684$	−4.67213	−0.178643
$685$	−32.2342	−1.23161
$686$	−2.28358	−0.0871874
$687$	−47.8799	−1.82673
$688$	3.84799	0.146703
$689$	−14.4229	−0.549469
$690$	42.4067	1.61440
$691$	35.4181	1.34737	0.673685	−	0.739019i	$-0.264711\pi$
$691$	35.4181	1.34737	0.673685	+	0.739019i	$0.264711\pi$
$692$	8.08635	0.307397
$693$	0.0618151	0.00234816
$694$	−10.3385	−0.392446
$695$	32.4611	1.23132
$696$	11.6499	0.441589
$697$	−8.14126	−0.308372
$698$	18.9631	0.717762
$699$	8.01925	0.303316
$700$	−1.27377	−0.0481441
$701$	−28.9682	−1.09411	−0.547056	−	0.837096i	$-0.684252\pi$
$701$	−28.9682	−1.09411	−0.547056	+	0.837096i	$0.684252\pi$
$702$	14.7307	0.555976
$703$	−13.0391	−0.491780
$704$	−0.327750	−0.0123526
$705$	83.9015	3.15991
$706$	25.0973	0.944551
$707$	−2.06527	−0.0776723
$708$	−2.03816	−0.0765986
$709$	−5.50585	−0.206777	−0.103388	−	0.994641i	$-0.532968\pi$
$709$	−5.50585	−0.206777	−0.103388	+	0.994641i	$0.532968\pi$
$710$	−33.9942	−1.27578
$711$	−2.71063	−0.101656
$712$	−17.4324	−0.653307
$713$	−5.51130	−0.206400
$714$	0.333084	0.0124654
$715$	4.59012	0.171661
$716$	14.0694	0.525797
$717$	−31.2491	−1.16702
$718$	15.5717	0.581129
$719$	−45.2447	−1.68734	−0.843671	−	0.536860i	$-0.819610\pi$
$719$	−45.2447	−1.68734	−0.843671	+	0.536860i	$0.819610\pi$
$720$	4.12802	0.153842
$721$	−0.700045	−0.0260710
$722$	2.61071	0.0971606
$723$	−56.9906	−2.11950
$724$	−12.6860	−0.471471
$725$	44.5513	1.65459
$726$	−22.2008	−0.823948
$727$	−32.1300	−1.19164	−0.595818	−	0.803119i	$-0.703172\pi$
$727$	−32.1300	−1.19164	−0.595818	+	0.803119i	$0.703172\pi$
$728$	−0.639869	−0.0237151
$729$	10.1591	0.376262
$730$	−39.7968	−1.47294
$731$	−3.84799	−0.142323
$732$	−7.46074	−0.275757
$733$	−51.3985	−1.89845	−0.949224	−	0.314601i	$-0.898129\pi$
$733$	−51.3985	−1.89845	−0.949224	+	0.314601i	$0.898129\pi$
$734$	9.68451	0.357462
$735$	50.8373	1.87516
$736$	−5.81688	−0.214413
$737$	3.58734	0.132141
$738$	−9.39563	−0.345858
$739$	22.1235	0.813826	0.406913	−	0.913467i	$-0.366605\pi$
$739$	22.1235	0.813826	0.406913	+	0.913467i	$0.366605\pi$
$740$	11.5206	0.423507
$741$	−32.3066	−1.18681
$742$	0.602000	0.0221001
$743$	30.2530	1.10988	0.554938	−	0.831892i	$-0.312742\pi$
$743$	30.2530	1.10988	0.554938	+	0.831892i	$0.312742\pi$
$744$	−1.93109	−0.0707970
$745$	73.6028	2.69660
$746$	−12.7582	−0.467112
$747$	−4.37123	−0.159935
$748$	0.327750	0.0119837
$749$	−0.757683	−0.0276851
$750$	20.3709	0.743842
$751$	19.3730	0.706930	0.353465	−	0.935448i	$-0.385003\pi$
$751$	19.3730	0.706930	0.353465	+	0.935448i	$0.385003\pi$
$752$	−11.5087	−0.419678
$753$	45.2623	1.64945
$754$	22.3800	0.815030
$755$	20.6794	0.752600
$756$	−0.614849	−0.0223618
$757$	11.8338	0.430106	0.215053	−	0.976602i	$-0.431008\pi$
$757$	11.8338	0.430106	0.215053	+	0.976602i	$0.431008\pi$
$758$	−11.7280	−0.425980
$759$	3.88571	0.141042
$760$	14.4806	0.525268
$761$	15.4276	0.559250	0.279625	−	0.960109i	$-0.409790\pi$
$761$	15.4276	0.559250	0.279625	+	0.960109i	$0.409790\pi$
$762$	−9.15023	−0.331478
$763$	−2.11587	−0.0765996
$764$	−13.3232	−0.482018
$765$	−4.12802	−0.149249
$766$	0.0324969	0.00117416
$767$	−3.91538	−0.141376
$768$	−2.03816	−0.0735456
$769$	−39.4193	−1.42150	−0.710748	−	0.703447i	$-0.751643\pi$
$769$	−39.4193	−1.42150	−0.710748	+	0.703447i	$0.751643\pi$
$770$	−0.191588	−0.00690434
$771$	−44.9214	−1.61780
$772$	14.4083	0.518566
$773$	−27.9074	−1.00376	−0.501880	−	0.864937i	$-0.667358\pi$
$773$	−27.9074	−1.00376	−0.501880	+	0.864937i	$0.667358\pi$
$774$	−4.44087	−0.159624
$775$	−7.38481	−0.265270
$776$	−16.9514	−0.608520
$777$	1.07281	0.0384869
$778$	−30.9512	−1.10966
$779$	−32.9588	−1.18087
$780$	28.5442	1.02205
$781$	−3.11487	−0.111459
$782$	5.81688	0.208011
$783$	21.5049	0.768521
$784$	−6.97329	−0.249046
$785$	6.31983	0.225564
$786$	7.84705	0.279895
$787$	23.0090	0.820181	0.410090	−	0.912045i	$-0.365497\pi$
$787$	23.0090	0.820181	0.410090	+	0.912045i	$0.365497\pi$
$788$	−17.3303	−0.617368
$789$	−2.80512	−0.0998648
$790$	8.40123	0.298902
$791$	2.17730	0.0774160
$792$	0.378249	0.0134405
$793$	−14.3324	−0.508958
$794$	12.6326	0.448313
$795$	−26.8549	−0.952447
$796$	15.0252	0.532555
$797$	42.0131	1.48818	0.744089	−	0.668080i	$-0.232884\pi$
$797$	42.0131	1.48818	0.744089	+	0.668080i	$0.232884\pi$
$798$	1.34845	0.0477346
$799$	11.5087	0.407147
$800$	−7.79426	−0.275569
$801$	20.1183	0.710846
$802$	16.2469	0.573698
$803$	−3.64656	−0.128684
$804$	22.3083	0.786754
$805$	−3.40028	−0.119844
$806$	−3.70969	−0.130668
$807$	−60.3655	−2.12497
$808$	−12.6374	−0.444583
$809$	−3.46861	−0.121950	−0.0609749	−	0.998139i	$-0.519421\pi$
$809$	−3.46861	−0.121950	−0.0609749	+	0.998139i	$0.519421\pi$
$810$	39.8122	1.39886
$811$	54.0515	1.89801	0.949003	−	0.315267i	$-0.102094\pi$
$811$	54.0515	1.89801	0.949003	+	0.315267i	$0.102094\pi$
$812$	−0.934120	−0.0327812
$813$	−5.55230	−0.194728
$814$	1.05563	0.0369998
$815$	−61.9703	−2.17073
$816$	2.03816	0.0713497
$817$	−15.5781	−0.545008
$818$	25.9363	0.906843
$819$	0.738457	0.0258038
$820$	29.1205	1.01693
$821$	−28.9690	−1.01103	−0.505513	−	0.862819i	$-0.668697\pi$
$821$	−28.9690	−1.01103	−0.505513	+	0.862819i	$0.668697\pi$
$822$	−18.3673	−0.640635
$823$	−38.6046	−1.34567	−0.672835	−	0.739793i	$-0.734924\pi$
$823$	−38.6046	−1.34567	−0.672835	+	0.739793i	$0.734924\pi$
$824$	−4.28360	−0.149226
$825$	5.20661	0.181271
$826$	0.163425	0.00568627
$827$	39.8365	1.38525	0.692625	−	0.721297i	$-0.256454\pi$
$827$	39.8365	1.38525	0.692625	+	0.721297i	$0.256454\pi$
$828$	6.71312	0.233297
$829$	−26.1011	−0.906528	−0.453264	−	0.891376i	$-0.649741\pi$
$829$	−26.1011	−0.906528	−0.453264	+	0.891376i	$0.649741\pi$
$830$	13.5480	0.470259
$831$	2.80343	0.0972499
$832$	−3.91538	−0.135741
$833$	6.97329	0.241610
$834$	18.4966	0.640486
$835$	−48.7851	−1.68828
$836$	1.32685	0.0458902
$837$	−3.56464	−0.123212
$838$	−9.56628	−0.330462
$839$	15.1967	0.524647	0.262323	−	0.964980i	$-0.415511\pi$
$839$	15.1967	0.524647	0.262323	+	0.964980i	$0.415511\pi$
$840$	−1.19141	−0.0411076
$841$	3.67166	0.126609
$842$	31.5436	1.08706
$843$	2.26978	0.0781752
$844$	14.8250	0.510299
$845$	8.33482	0.286726
$846$	13.2819	0.456640
$847$	1.78011	0.0611655
$848$	3.68366	0.126497
$849$	−66.4203	−2.27954
$850$	7.79426	0.267341
$851$	18.7352	0.642235
$852$	−19.3702	−0.663613
$853$	−37.3052	−1.27730	−0.638652	−	0.769495i	$-0.720508\pi$
$853$	−37.3052	−1.27730	−0.638652	+	0.769495i	$0.720508\pi$
$854$	0.598221	0.0204707
$855$	−16.7118	−0.571530
$856$	−4.63629	−0.158465
$857$	−37.0562	−1.26582	−0.632909	−	0.774227i	$-0.718139\pi$
$857$	−37.0562	−1.26582	−0.632909	+	0.774227i	$0.718139\pi$
$858$	2.61549	0.0892915
$859$	−19.8127	−0.676000	−0.338000	−	0.941146i	$-0.609750\pi$
$859$	−19.8127	−0.676000	−0.338000	+	0.941146i	$0.609750\pi$
$860$	13.7639	0.469345
$861$	2.71173	0.0924154
$862$	16.8606	0.574273
$863$	−22.8641	−0.778303	−0.389152	−	0.921174i	$-0.627232\pi$
$863$	−22.8641	−0.778303	−0.389152	+	0.921174i	$0.627232\pi$
$864$	−3.76228	−0.127995
$865$	28.9241	0.983450
$866$	−9.41721	−0.320010
$867$	−2.03816	−0.0692194
$868$	0.154839	0.00525559
$869$	0.769801	0.0261137
$870$	41.6707	1.41277
$871$	42.8552	1.45209
$872$	−12.9471	−0.438443
$873$	19.5632	0.662115
$874$	23.5489	0.796552
$875$	−1.63339	−0.0552188
$876$	−22.6766	−0.766170
$877$	−3.88153	−0.131070	−0.0655350	−	0.997850i	$-0.520875\pi$
$877$	−3.88153	−0.131070	−0.0655350	+	0.997850i	$0.520875\pi$
$878$	−11.1344	−0.375766
$879$	52.1505	1.75899
$880$	−1.17233	−0.0395193
$881$	−38.4640	−1.29589	−0.647943	−	0.761689i	$-0.724371\pi$
$881$	−38.4640	−1.29589	−0.647943	+	0.761689i	$0.724371\pi$
$882$	8.04771	0.270980
$883$	−33.4397	−1.12534	−0.562668	−	0.826683i	$-0.690225\pi$
$883$	−33.4397	−1.12534	−0.562668	+	0.826683i	$0.690225\pi$
$884$	3.91538	0.131688
$885$	−7.29029	−0.245060
$886$	33.8475	1.13713
$887$	−9.40840	−0.315903	−0.157952	−	0.987447i	$-0.550489\pi$
$887$	−9.40840	−0.315903	−0.157952	+	0.987447i	$0.550489\pi$
$888$	6.56456	0.220292
$889$	0.733689	0.0246072
$890$	−62.3541	−2.09011
$891$	3.64797	0.122212
$892$	9.54153	0.319474
$893$	46.5913	1.55912
$894$	41.9396	1.40267
$895$	50.3248	1.68217
$896$	0.163425	0.00545963
$897$	46.4195	1.54990
$898$	31.1931	1.04093
$899$	−5.41564	−0.180622
$900$	8.99516	0.299839
$901$	−3.68366	−0.122721
$902$	2.66830	0.0888447
$903$	1.28170	0.0426524
$904$	13.3230	0.443116
$905$	−45.3766	−1.50837
$906$	11.7833	0.391474
$907$	18.2605	0.606329	0.303165	−	0.952938i	$-0.401957\pi$
$907$	18.2605	0.606329	0.303165	+	0.952938i	$0.401957\pi$
$908$	15.1458	0.502631
$909$	14.5846	0.483739
$910$	−2.28875	−0.0758713
$911$	−29.0907	−0.963817	−0.481908	−	0.876222i	$-0.660056\pi$
$911$	−29.0907	−0.963817	−0.481908	+	0.876222i	$0.660056\pi$
$912$	8.25120	0.273225
$913$	1.24140	0.0410844
$914$	−39.7398	−1.31447
$915$	−26.6864	−0.882224
$916$	23.4918	0.776190
$917$	−0.629197	−0.0207779
$918$	3.76228	0.124174
$919$	−32.7995	−1.08196	−0.540978	−	0.841037i	$-0.681946\pi$
$919$	−32.7995	−1.08196	−0.540978	+	0.841037i	$0.681946\pi$
$920$	−20.8064	−0.685967
$921$	33.3541	1.09906
$922$	−1.76732	−0.0582036
$923$	−37.2110	−1.22481
$924$	−0.109169	−0.00359138
$925$	25.1040	0.825415
$926$	−18.2176	−0.598667
$927$	4.94360	0.162369
$928$	−5.71591	−0.187634
$929$	−33.8745	−1.11139	−0.555693	−	0.831388i	$-0.687547\pi$
$929$	−33.8745	−1.11139	−0.555693	+	0.831388i	$0.687547\pi$
$930$	−6.90731	−0.226500
$931$	28.2305	0.925216
$932$	−3.93456	−0.128881
$933$	−5.48125	−0.179448
$934$	11.3214	0.370446
$935$	1.17233	0.0383393
$936$	4.51864	0.147696
$937$	51.4554	1.68098	0.840488	−	0.541830i	$-0.182268\pi$
$937$	51.4554	1.68098	0.840488	+	0.541830i	$0.182268\pi$
$938$	−1.78874	−0.0584044
$939$	−14.6548	−0.478240
$940$	−41.1654	−1.34267
$941$	−0.367896	−0.0119931	−0.00599654	−	0.999982i	$-0.501909\pi$
$941$	−0.367896	−0.0119931	−0.00599654	+	0.999982i	$0.501909\pi$
$942$	3.60110	0.117330
$943$	47.3567	1.54215
$944$	1.00000	0.0325472
$945$	−2.19926	−0.0715418
$946$	1.26118	0.0410044
$947$	−18.8234	−0.611679	−0.305840	−	0.952083i	$-0.598937\pi$
$947$	−18.8234	−0.611679	−0.305840	+	0.952083i	$0.598937\pi$
$948$	4.78710	0.155478
$949$	−43.5626	−1.41410
$950$	31.5540	1.02375
$951$	29.8472	0.967860
$952$	−0.163425	−0.00529662
$953$	−0.609849	−0.0197550	−0.00987748	−	0.999951i	$-0.503144\pi$
$953$	−0.609849	−0.0197550	−0.00987748	+	0.999951i	$0.503144\pi$
$954$	−4.25122	−0.137638
$955$	−47.6560	−1.54211
$956$	15.3320	0.495874
$957$	3.81826	0.123427
$958$	−33.4721	−1.08144
$959$	1.47274	0.0475573
$960$	−7.29029	−0.235293
$961$	−30.1023	−0.971042
$962$	12.6108	0.406588
$963$	5.35063	0.172422
$964$	27.9619	0.900591
$965$	51.5371	1.65904
$966$	−1.93751	−0.0623384
$967$	−37.1602	−1.19499	−0.597496	−	0.801872i	$-0.703838\pi$
$967$	−37.1602	−1.19499	−0.597496	+	0.801872i	$0.703838\pi$
$968$	10.8926	0.350101
$969$	−8.25120	−0.265067
$970$	−60.6336	−1.94683
$971$	−1.55098	−0.0497734	−0.0248867	−	0.999690i	$-0.507923\pi$
$971$	−1.55098	−0.0497734	−0.0248867	+	0.999690i	$0.507923\pi$
$972$	11.3985	0.365608
$973$	−1.48311	−0.0475462
$974$	26.8238	0.859490
$975$	62.1993	1.99197
$976$	3.66053	0.117171
$977$	−33.4851	−1.07128	−0.535642	−	0.844445i	$-0.679930\pi$
$977$	−33.4851	−1.07128	−0.535642	+	0.844445i	$0.679930\pi$
$978$	−35.3113	−1.12913
$979$	−5.71348	−0.182604
$980$	−24.9428	−0.796769
$981$	14.9419	0.477059
$982$	−9.03900	−0.288446
$983$	−17.7310	−0.565530	−0.282765	−	0.959189i	$-0.591252\pi$
$983$	−17.7310	−0.565530	−0.282765	+	0.959189i	$0.591252\pi$
$984$	16.5932	0.528970
$985$	−61.9890	−1.97513
$986$	5.71591	0.182032
$987$	−3.83336	−0.122017
$988$	15.8509	0.504284
$989$	22.3833	0.711746
$990$	1.35296	0.0429999
$991$	−10.3514	−0.328824	−0.164412	−	0.986392i	$-0.552573\pi$
$991$	−10.3514	−0.328824	−0.164412	+	0.986392i	$0.552573\pi$
$992$	0.947468	0.0300821
$993$	14.8303	0.470626
$994$	1.55315	0.0492631
$995$	53.7438	1.70379
$996$	7.71980	0.244611
$997$	−35.1067	−1.11184	−0.555921	−	0.831235i	$-0.687634\pi$
$997$	−35.1067	−1.11184	−0.555921	+	0.831235i	$0.687634\pi$
$998$	−5.32120	−0.168440
$999$	12.1177	0.383387

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2006.2.a.v.1.3	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2006.2.a.v.1.3	✓	12	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.03816 q^{3} +1.00000 q^{4} +3.57691 q^{5} +2.03816 q^{6} -0.163425 q^{7} -1.00000 q^{8} +1.15408 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.03816 q^{3} +1.00000 q^{4} +3.57691 q^{5} +2.03816 q^{6} -0.163425 q^{7} -1.00000 q^{8} +1.15408 q^{9} -3.57691 q^{10} -0.327750 q^{11} -2.03816 q^{12} -3.91538 q^{13} +0.163425 q^{14} -7.29029 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.15408 q^{18} -4.04837 q^{19} +3.57691 q^{20} +0.333084 q^{21} +0.327750 q^{22} +5.81688 q^{23} +2.03816 q^{24} +7.79426 q^{25} +3.91538 q^{26} +3.76228 q^{27} -0.163425 q^{28} +5.71591 q^{29} +7.29029 q^{30} -0.947468 q^{31} -1.00000 q^{32} +0.668006 q^{33} +1.00000 q^{34} -0.584554 q^{35} +1.15408 q^{36} +3.22084 q^{37} +4.04837 q^{38} +7.98014 q^{39} -3.57691 q^{40} +8.14126 q^{41} -0.333084 q^{42} +3.84799 q^{43} -0.327750 q^{44} +4.12802 q^{45} -5.81688 q^{46} -11.5087 q^{47} -2.03816 q^{48} -6.97329 q^{49} -7.79426 q^{50} +2.03816 q^{51} -3.91538 q^{52} +3.68366 q^{53} -3.76228 q^{54} -1.17233 q^{55} +0.163425 q^{56} +8.25120 q^{57} -5.71591 q^{58} +1.00000 q^{59} -7.29029 q^{60} +3.66053 q^{61} +0.947468 q^{62} -0.188604 q^{63} +1.00000 q^{64} -14.0049 q^{65} -0.668006 q^{66} -10.9454 q^{67} -1.00000 q^{68} -11.8557 q^{69} +0.584554 q^{70} +9.50381 q^{71} -1.15408 q^{72} +11.1260 q^{73} -3.22084 q^{74} -15.8859 q^{75} -4.04837 q^{76} +0.0535624 q^{77} -7.98014 q^{78} -2.34874 q^{79} +3.57691 q^{80} -11.1303 q^{81} -8.14126 q^{82} -3.78764 q^{83} +0.333084 q^{84} -3.57691 q^{85} -3.84799 q^{86} -11.6499 q^{87} +0.327750 q^{88} +17.4324 q^{89} -4.12802 q^{90} +0.639869 q^{91} +5.81688 q^{92} +1.93109 q^{93} +11.5087 q^{94} -14.4806 q^{95} +2.03816 q^{96} +16.9514 q^{97} +6.97329 q^{98} -0.378249 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} - 3 q^{3} + 12 q^{4} - q^{5} + 3 q^{6} + 4 q^{7} - 12 q^{8} + 15 q^{9}+O(q^{10}) \) 12 * q - 12 * q^2 - 3 * q^3 + 12 * q^4 - q^5 + 3 * q^6 + 4 * q^7 - 12 * q^8 + 15 * q^9	\( 12 q - 12 q^{2} - 3 q^{3} + 12 q^{4} - q^{5} + 3 q^{6} + 4 q^{7} - 12 q^{8} + 15 q^{9} + q^{10} - 3 q^{11} - 3 q^{12} + 15 q^{13} - 4 q^{14} - 3 q^{15} + 12 q^{16} - 12 q^{17} - 15 q^{18} + 16 q^{19} - q^{20} + 15 q^{21} + 3 q^{22} - 14 q^{23} + 3 q^{24} + 19 q^{25} - 15 q^{26} - 12 q^{27} + 4 q^{28} + 14 q^{29} + 3 q^{30} + 26 q^{31} - 12 q^{32} + 13 q^{33} + 12 q^{34} - 5 q^{35} + 15 q^{36} + 15 q^{37} - 16 q^{38} + 4 q^{39} + q^{40} - 2 q^{41} - 15 q^{42} + 8 q^{43} - 3 q^{44} - 17 q^{45} + 14 q^{46} - 6 q^{47} - 3 q^{48} + 30 q^{49} - 19 q^{50} + 3 q^{51} + 15 q^{52} + q^{53} + 12 q^{54} + q^{55} - 4 q^{56} + 3 q^{57} - 14 q^{58} + 12 q^{59} - 3 q^{60} + 30 q^{61} - 26 q^{62} + q^{63} + 12 q^{64} - 4 q^{65} - 13 q^{66} + 10 q^{67} - 12 q^{68} + 8 q^{69} + 5 q^{70} + 6 q^{71} - 15 q^{72} + 26 q^{73} - 15 q^{74} + 7 q^{75} + 16 q^{76} + 45 q^{77} - 4 q^{78} - 11 q^{79} - q^{80} + 48 q^{81} + 2 q^{82} - 21 q^{83} + 15 q^{84} + q^{85} - 8 q^{86} + 2 q^{87} + 3 q^{88} - 2 q^{89} + 17 q^{90} + 31 q^{91} - 14 q^{92} + 41 q^{93} + 6 q^{94} - 29 q^{95} + 3 q^{96} + 27 q^{97} - 30 q^{98} + 9 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 - 3 * q^3 + 12 * q^4 - q^5 + 3 * q^6 + 4 * q^7 - 12 * q^8 + 15 * q^9 + q^10 - 3 * q^11 - 3 * q^12 + 15 * q^13 - 4 * q^14 - 3 * q^15 + 12 * q^16 - 12 * q^17 - 15 * q^18 + 16 * q^19 - q^20 + 15 * q^21 + 3 * q^22 - 14 * q^23 + 3 * q^24 + 19 * q^25 - 15 * q^26 - 12 * q^27 + 4 * q^28 + 14 * q^29 + 3 * q^30 + 26 * q^31 - 12 * q^32 + 13 * q^33 + 12 * q^34 - 5 * q^35 + 15 * q^36 + 15 * q^37 - 16 * q^38 + 4 * q^39 + q^40 - 2 * q^41 - 15 * q^42 + 8 * q^43 - 3 * q^44 - 17 * q^45 + 14 * q^46 - 6 * q^47 - 3 * q^48 + 30 * q^49 - 19 * q^50 + 3 * q^51 + 15 * q^52 + q^53 + 12 * q^54 + q^55 - 4 * q^56 + 3 * q^57 - 14 * q^58 + 12 * q^59 - 3 * q^60 + 30 * q^61 - 26 * q^62 + q^63 + 12 * q^64 - 4 * q^65 - 13 * q^66 + 10 * q^67 - 12 * q^68 + 8 * q^69 + 5 * q^70 + 6 * q^71 - 15 * q^72 + 26 * q^73 - 15 * q^74 + 7 * q^75 + 16 * q^76 + 45 * q^77 - 4 * q^78 - 11 * q^79 - q^80 + 48 * q^81 + 2 * q^82 - 21 * q^83 + 15 * q^84 + q^85 - 8 * q^86 + 2 * q^87 + 3 * q^88 - 2 * q^89 + 17 * q^90 + 31 * q^91 - 14 * q^92 + 41 * q^93 + 6 * q^94 - 29 * q^95 + 3 * q^96 + 27 * q^97 - 30 * q^98 + 9 * q^99

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