LMFDB - Embedded newform 2006.2.a.u.1.1

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:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - x^{8} - 23x^{7} + 18x^{6} + 185x^{5} - 91x^{4} - 615x^{3} + 126x^{2} + 668x - 44 $ x^9 - x^8 - 23x^7 + 18x^6 + 185x^5 - 91x^4 - 615x^3 + 126x^2 + 668*x - 44
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.90546$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.90546 q^{3} +1.00000 q^{4} +2.56462 q^{5} +2.90546 q^{6} -4.07426 q^{7} -1.00000 q^{8} +5.44169 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.90546 q^{3} +1.00000 q^{4} +2.56462 q^{5} +2.90546 q^{6} -4.07426 q^{7} -1.00000 q^{8} +5.44169 q^{9} -2.56462 q^{10} +6.17611 q^{11} -2.90546 q^{12} +2.23309 q^{13} +4.07426 q^{14} -7.45139 q^{15} +1.00000 q^{16} +1.00000 q^{17} -5.44169 q^{18} -1.36257 q^{19} +2.56462 q^{20} +11.8376 q^{21} -6.17611 q^{22} +0.247020 q^{23} +2.90546 q^{24} +1.57727 q^{25} -2.23309 q^{26} -7.09422 q^{27} -4.07426 q^{28} +6.05367 q^{29} +7.45139 q^{30} +0.381361 q^{31} -1.00000 q^{32} -17.9444 q^{33} -1.00000 q^{34} -10.4489 q^{35} +5.44169 q^{36} -4.40254 q^{37} +1.36257 q^{38} -6.48814 q^{39} -2.56462 q^{40} +6.97981 q^{41} -11.8376 q^{42} -10.4706 q^{43} +6.17611 q^{44} +13.9559 q^{45} -0.247020 q^{46} +3.56406 q^{47} -2.90546 q^{48} +9.59960 q^{49} -1.57727 q^{50} -2.90546 q^{51} +2.23309 q^{52} +5.87976 q^{53} +7.09422 q^{54} +15.8394 q^{55} +4.07426 q^{56} +3.95889 q^{57} -6.05367 q^{58} -1.00000 q^{59} -7.45139 q^{60} -7.73575 q^{61} -0.381361 q^{62} -22.1709 q^{63} +1.00000 q^{64} +5.72701 q^{65} +17.9444 q^{66} -6.76723 q^{67} +1.00000 q^{68} -0.717707 q^{69} +10.4489 q^{70} -7.84826 q^{71} -5.44169 q^{72} -1.14189 q^{73} +4.40254 q^{74} -4.58270 q^{75} -1.36257 q^{76} -25.1631 q^{77} +6.48814 q^{78} +0.645579 q^{79} +2.56462 q^{80} +4.28690 q^{81} -6.97981 q^{82} +8.73419 q^{83} +11.8376 q^{84} +2.56462 q^{85} +10.4706 q^{86} -17.5887 q^{87} -6.17611 q^{88} +9.82076 q^{89} -13.9559 q^{90} -9.09817 q^{91} +0.247020 q^{92} -1.10803 q^{93} -3.56406 q^{94} -3.49447 q^{95} +2.90546 q^{96} -18.5110 q^{97} -9.59960 q^{98} +33.6085 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 9 q^{2} - q^{3} + 9 q^{4} + 7 q^{5} + q^{6} - 9 q^{8} + 20 q^{9}+O(q^{10}) $ 9 * q - 9 * q^2 - q^3 + 9 * q^4 + 7 * q^5 + q^6 - 9 * q^8 + 20 * q^9	\( 9 q - 9 q^{2} - q^{3} + 9 q^{4} + 7 q^{5} + q^{6} - 9 q^{8} + 20 q^{9} - 7 q^{10} + 5 q^{11} - q^{12} + 25 q^{13} - 5 q^{15} + 9 q^{16} + 9 q^{17} - 20 q^{18} + 14 q^{19} + 7 q^{20} - 7 q^{21} - 5 q^{22} + 2 q^{23} + q^{24} + 20 q^{25} - 25 q^{26} - 10 q^{27} + 18 q^{29} + 5 q^{30} + 6 q^{31} - 9 q^{32} - 9 q^{33} - 9 q^{34} - 17 q^{35} + 20 q^{36} + 11 q^{37} - 14 q^{38} - 8 q^{39} - 7 q^{40} + 18 q^{41} + 7 q^{42} - 10 q^{43} + 5 q^{44} + 27 q^{45} - 2 q^{46} - 20 q^{47} - q^{48} + 13 q^{49} - 20 q^{50} - q^{51} + 25 q^{52} - 7 q^{53} + 10 q^{54} + 29 q^{55} + 17 q^{57} - 18 q^{58} - 9 q^{59} - 5 q^{60} + 30 q^{61} - 6 q^{62} - 47 q^{63} + 9 q^{64} + 8 q^{65} + 9 q^{66} + 6 q^{67} + 9 q^{68} + 20 q^{69} + 17 q^{70} + 30 q^{71} - 20 q^{72} - 11 q^{74} - 7 q^{75} + 14 q^{76} - 3 q^{77} + 8 q^{78} + 29 q^{79} + 7 q^{80} - 3 q^{81} - 18 q^{82} + 9 q^{83} - 7 q^{84} + 7 q^{85} + 10 q^{86} + 44 q^{87} - 5 q^{88} + 8 q^{89} - 27 q^{90} + 13 q^{91} + 2 q^{92} + 7 q^{93} + 20 q^{94} + 27 q^{95} + q^{96} - 13 q^{97} - 13 q^{98} - 19 q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - q^3 + 9 * q^4 + 7 * q^5 + q^6 - 9 * q^8 + 20 * q^9 - 7 * q^10 + 5 * q^11 - q^12 + 25 * q^13 - 5 * q^15 + 9 * q^16 + 9 * q^17 - 20 * q^18 + 14 * q^19 + 7 * q^20 - 7 * q^21 - 5 * q^22 + 2 * q^23 + q^24 + 20 * q^25 - 25 * q^26 - 10 * q^27 + 18 * q^29 + 5 * q^30 + 6 * q^31 - 9 * q^32 - 9 * q^33 - 9 * q^34 - 17 * q^35 + 20 * q^36 + 11 * q^37 - 14 * q^38 - 8 * q^39 - 7 * q^40 + 18 * q^41 + 7 * q^42 - 10 * q^43 + 5 * q^44 + 27 * q^45 - 2 * q^46 - 20 * q^47 - q^48 + 13 * q^49 - 20 * q^50 - q^51 + 25 * q^52 - 7 * q^53 + 10 * q^54 + 29 * q^55 + 17 * q^57 - 18 * q^58 - 9 * q^59 - 5 * q^60 + 30 * q^61 - 6 * q^62 - 47 * q^63 + 9 * q^64 + 8 * q^65 + 9 * q^66 + 6 * q^67 + 9 * q^68 + 20 * q^69 + 17 * q^70 + 30 * q^71 - 20 * q^72 - 11 * q^74 - 7 * q^75 + 14 * q^76 - 3 * q^77 + 8 * q^78 + 29 * q^79 + 7 * q^80 - 3 * q^81 - 18 * q^82 + 9 * q^83 - 7 * q^84 + 7 * q^85 + 10 * q^86 + 44 * q^87 - 5 * q^88 + 8 * q^89 - 27 * q^90 + 13 * q^91 + 2 * q^92 + 7 * q^93 + 20 * q^94 + 27 * q^95 + q^96 - 13 * q^97 - 13 * q^98 - 19 * 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
$3$	−2.90546	−1.67747	−0.838734	−	0.544542i	$-0.816703\pi$
$3$	−2.90546	−1.67747	−0.838734	+	0.544542i	$0.816703\pi$
$4$	1.00000	0.500000
$5$	2.56462	1.14693	0.573466	−	0.819229i	$-0.305598\pi$
$5$	2.56462	1.14693	0.573466	+	0.819229i	$0.305598\pi$
$6$	2.90546	1.18615
$7$	−4.07426	−1.53993	−0.769963	−	0.638089i	$-0.779725\pi$
$7$	−4.07426	−1.53993	−0.769963	+	0.638089i	$0.779725\pi$
$8$	−1.00000	−0.353553
$9$	5.44169	1.81390
$10$	−2.56462	−0.811004
$11$	6.17611	1.86217	0.931083	−	0.364806i	$-0.118865\pi$
$11$	6.17611	1.86217	0.931083	+	0.364806i	$0.118865\pi$
$12$	−2.90546	−0.838734
$13$	2.23309	0.619347	0.309673	−	0.950843i	$-0.399780\pi$
$13$	2.23309	0.619347	0.309673	+	0.950843i	$0.399780\pi$
$14$	4.07426	1.08889
$15$	−7.45139	−1.92394
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−5.44169	−1.28262
$19$	−1.36257	−0.312595	−0.156298	−	0.987710i	$-0.549956\pi$
$19$	−1.36257	−0.312595	−0.156298	+	0.987710i	$0.549956\pi$
$20$	2.56462	0.573466
$21$	11.8376	2.58318
$22$	−6.17611	−1.31675
$23$	0.247020	0.0515073	0.0257537	−	0.999668i	$-0.491801\pi$
$23$	0.247020	0.0515073	0.0257537	+	0.999668i	$0.491801\pi$
$24$	2.90546	0.593074
$25$	1.57727	0.315454
$26$	−2.23309	−0.437944
$27$	−7.09422	−1.36528
$28$	−4.07426	−0.769963
$29$	6.05367	1.12414	0.562069	−	0.827090i	$-0.310006\pi$
$29$	6.05367	1.12414	0.562069	+	0.827090i	$0.310006\pi$
$30$	7.45139	1.36043
$31$	0.381361	0.0684944	0.0342472	−	0.999413i	$-0.489097\pi$
$31$	0.381361	0.0684944	0.0342472	+	0.999413i	$0.489097\pi$
$32$	−1.00000	−0.176777
$33$	−17.9444	−3.12372
$34$	−1.00000	−0.171499
$35$	−10.4489	−1.76619
$36$	5.44169	0.906948
$37$	−4.40254	−0.723773	−0.361886	−	0.932222i	$-0.617867\pi$
$37$	−4.40254	−0.723773	−0.361886	+	0.932222i	$0.617867\pi$
$38$	1.36257	0.221038
$39$	−6.48814	−1.03893
$40$	−2.56462	−0.405502
$41$	6.97981	1.09006	0.545031	−	0.838416i	$-0.316518\pi$
$41$	6.97981	1.09006	0.545031	+	0.838416i	$0.316518\pi$
$42$	−11.8376	−1.82658
$43$	−10.4706	−1.59675	−0.798376	−	0.602160i	$-0.794307\pi$
$43$	−10.4706	−1.59675	−0.798376	+	0.602160i	$0.794307\pi$
$44$	6.17611	0.931083
$45$	13.9559	2.08042
$46$	−0.247020	−0.0364212
$47$	3.56406	0.519872	0.259936	−	0.965626i	$-0.416299\pi$
$47$	3.56406	0.519872	0.259936	+	0.965626i	$0.416299\pi$
$48$	−2.90546	−0.419367
$49$	9.59960	1.37137
$50$	−1.57727	−0.223060
$51$	−2.90546	−0.406846
$52$	2.23309	0.309673
$53$	5.87976	0.807648	0.403824	−	0.914837i	$-0.367681\pi$
$53$	5.87976	0.807648	0.403824	+	0.914837i	$0.367681\pi$
$54$	7.09422	0.965401
$55$	15.8394	2.13578
$56$	4.07426	0.544446
$57$	3.95889	0.524368
$58$	−6.05367	−0.794886
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−7.45139	−0.961971
$61$	−7.73575	−0.990461	−0.495230	−	0.868762i	$-0.664916\pi$
$61$	−7.73575	−0.990461	−0.495230	+	0.868762i	$0.664916\pi$
$62$	−0.381361	−0.0484329
$63$	−22.1709	−2.79327
$64$	1.00000	0.125000
$65$	5.72701	0.710349
$66$	17.9444	2.20881
$67$	−6.76723	−0.826748	−0.413374	−	0.910561i	$-0.635650\pi$
$67$	−6.76723	−0.826748	−0.413374	+	0.910561i	$0.635650\pi$
$68$	1.00000	0.121268
$69$	−0.717707	−0.0864018
$70$	10.4489	1.24889
$71$	−7.84826	−0.931417	−0.465709	−	0.884938i	$-0.654200\pi$
$71$	−7.84826	−0.931417	−0.465709	+	0.884938i	$0.654200\pi$
$72$	−5.44169	−0.641309
$73$	−1.14189	−0.133648	−0.0668241	−	0.997765i	$-0.521287\pi$
$73$	−1.14189	−0.133648	−0.0668241	+	0.997765i	$0.521287\pi$
$74$	4.40254	0.511784
$75$	−4.58270	−0.529164
$76$	−1.36257	−0.156298
$77$	−25.1631	−2.86760
$78$	6.48814	0.734637
$79$	0.645579	0.0726334	0.0363167	−	0.999340i	$-0.488437\pi$
$79$	0.645579	0.0726334	0.0363167	+	0.999340i	$0.488437\pi$
$80$	2.56462	0.286733
$81$	4.28690	0.476322
$82$	−6.97981	−0.770791
$83$	8.73419	0.958702	0.479351	−	0.877623i	$-0.340872\pi$
$83$	8.73419	0.958702	0.479351	+	0.877623i	$0.340872\pi$
$84$	11.8376	1.29159
$85$	2.56462	0.278172
$86$	10.4706	1.12907
$87$	−17.5887	−1.88570
$88$	−6.17611	−0.658375
$89$	9.82076	1.04100	0.520499	−	0.853862i	$-0.325746\pi$
$89$	9.82076	1.04100	0.520499	+	0.853862i	$0.325746\pi$
$90$	−13.9559	−1.47108
$91$	−9.09817	−0.953748
$92$	0.247020	0.0257537
$93$	−1.10803	−0.114897
$94$	−3.56406	−0.367605
$95$	−3.49447	−0.358526
$96$	2.90546	0.296537
$97$	−18.5110	−1.87950	−0.939752	−	0.341857i	$-0.888944\pi$
$97$	−18.5110	−1.87950	−0.939752	+	0.341857i	$0.888944\pi$
$98$	−9.59960	−0.969706
$99$	33.6085	3.37778
$100$	1.57727	0.157727
$101$	−5.44908	−0.542204	−0.271102	−	0.962551i	$-0.587388\pi$
$101$	−5.44908	−0.542204	−0.271102	+	0.962551i	$0.587388\pi$
$102$	2.90546	0.287683
$103$	18.8870	1.86099	0.930497	−	0.366298i	$-0.119375\pi$
$103$	18.8870	1.86099	0.930497	+	0.366298i	$0.119375\pi$
$104$	−2.23309	−0.218972
$105$	30.3589	2.96273
$106$	−5.87976	−0.571093
$107$	7.97115	0.770601	0.385300	−	0.922791i	$-0.374098\pi$
$107$	7.97115	0.770601	0.385300	+	0.922791i	$0.374098\pi$
$108$	−7.09422	−0.682642
$109$	−3.30249	−0.316321	−0.158161	−	0.987413i	$-0.550556\pi$
$109$	−3.30249	−0.316321	−0.158161	+	0.987413i	$0.550556\pi$
$110$	−15.8394	−1.51022
$111$	12.7914	1.21410
$112$	−4.07426	−0.384981
$113$	17.7052	1.66556	0.832781	−	0.553603i	$-0.186747\pi$
$113$	17.7052	1.66556	0.832781	+	0.553603i	$0.186747\pi$
$114$	−3.95889	−0.370784
$115$	0.633513	0.0590754
$116$	6.05367	0.562069
$117$	12.1518	1.12343
$118$	1.00000	0.0920575
$119$	−4.07426	−0.373487
$120$	7.45139	0.680216
$121$	27.1443	2.46767
$122$	7.73575	0.700362
$123$	−20.2795	−1.82854
$124$	0.381361	0.0342472
$125$	−8.77800	−0.785128
$126$	22.1709	1.97514
$127$	15.5840	1.38286	0.691428	−	0.722445i	$-0.256982\pi$
$127$	15.5840	1.38286	0.691428	+	0.722445i	$0.256982\pi$
$128$	−1.00000	−0.0883883
$129$	30.4219	2.67850
$130$	−5.72701	−0.502292
$131$	13.9064	1.21501	0.607506	−	0.794315i	$-0.292170\pi$
$131$	13.9064	1.21501	0.607506	+	0.794315i	$0.292170\pi$
$132$	−17.9444	−1.56186
$133$	5.55147	0.481373
$134$	6.76723	0.584599
$135$	−18.1940	−1.56589
$136$	−1.00000	−0.0857493
$137$	2.89694	0.247502	0.123751	−	0.992313i	$-0.460508\pi$
$137$	2.89694	0.247502	0.123751	+	0.992313i	$0.460508\pi$
$138$	0.717707	0.0610953
$139$	−9.72509	−0.824872	−0.412436	−	0.910987i	$-0.635322\pi$
$139$	−9.72509	−0.824872	−0.412436	+	0.910987i	$0.635322\pi$
$140$	−10.4489	−0.883096
$141$	−10.3552	−0.872068
$142$	7.84826	0.658611
$143$	13.7918	1.15333
$144$	5.44169	0.453474
$145$	15.5254	1.28931
$146$	1.14189	0.0945036
$147$	−27.8912	−2.30043
$148$	−4.40254	−0.361886
$149$	−3.71456	−0.304309	−0.152154	−	0.988357i	$-0.548621\pi$
$149$	−3.71456	−0.304309	−0.152154	+	0.988357i	$0.548621\pi$
$150$	4.58270	0.374176
$151$	−5.80620	−0.472502	−0.236251	−	0.971692i	$-0.575919\pi$
$151$	−5.80620	−0.472502	−0.236251	+	0.971692i	$0.575919\pi$
$152$	1.36257	0.110519
$153$	5.44169	0.439934
$154$	25.1631	2.02770
$155$	0.978045	0.0785585
$156$	−6.48814	−0.519467
$157$	20.7622	1.65701	0.828503	−	0.559985i	$-0.189193\pi$
$157$	20.7622	1.65701	0.828503	+	0.559985i	$0.189193\pi$
$158$	−0.645579	−0.0513595
$159$	−17.0834	−1.35480
$160$	−2.56462	−0.202751
$161$	−1.00643	−0.0793174
$162$	−4.28690	−0.336810
$163$	10.9773	0.859808	0.429904	−	0.902875i	$-0.358547\pi$
$163$	10.9773	0.859808	0.429904	+	0.902875i	$0.358547\pi$
$164$	6.97981	0.545031
$165$	−46.0206	−3.58270
$166$	−8.73419	−0.677905
$167$	7.84341	0.606941	0.303471	−	0.952841i	$-0.401855\pi$
$167$	7.84341	0.606941	0.303471	+	0.952841i	$0.401855\pi$
$168$	−11.8376	−0.913290
$169$	−8.01333	−0.616410
$170$	−2.56462	−0.196697
$171$	−7.41468	−0.567015
$172$	−10.4706	−0.798376
$173$	5.59950	0.425722	0.212861	−	0.977082i	$-0.431722\pi$
$173$	5.59950	0.425722	0.212861	+	0.977082i	$0.431722\pi$
$174$	17.5887	1.33339
$175$	−6.42622	−0.485776
$176$	6.17611	0.465542
$177$	2.90546	0.218388
$178$	−9.82076	−0.736097
$179$	−6.12370	−0.457707	−0.228854	−	0.973461i	$-0.573498\pi$
$179$	−6.12370	−0.457707	−0.228854	+	0.973461i	$0.573498\pi$
$180$	13.9559	1.04021
$181$	6.20302	0.461067	0.230533	−	0.973064i	$-0.425953\pi$
$181$	6.20302	0.461067	0.230533	+	0.973064i	$0.425953\pi$
$182$	9.09817	0.674402
$183$	22.4759	1.66147
$184$	−0.247020	−0.0182106
$185$	−11.2908	−0.830118
$186$	1.10803	0.0812445
$187$	6.17611	0.451642
$188$	3.56406	0.259936
$189$	28.9037	2.10244
$190$	3.49447	0.253516
$191$	−7.21342	−0.521945	−0.260972	−	0.965346i	$-0.584043\pi$
$191$	−7.21342	−0.521945	−0.260972	+	0.965346i	$0.584043\pi$
$192$	−2.90546	−0.209683
$193$	25.2994	1.82109	0.910547	−	0.413406i	$-0.135661\pi$
$193$	25.2994	1.82109	0.910547	+	0.413406i	$0.135661\pi$
$194$	18.5110	1.32901
$195$	−16.6396	−1.19159
$196$	9.59960	0.685686
$197$	18.8026	1.33963	0.669816	−	0.742527i	$-0.266373\pi$
$197$	18.8026	1.33963	0.669816	+	0.742527i	$0.266373\pi$
$198$	−33.6085	−2.38845
$199$	22.3251	1.58258	0.791291	−	0.611440i	$-0.209409\pi$
$199$	22.3251	1.58258	0.791291	+	0.611440i	$0.209409\pi$
$200$	−1.57727	−0.111530
$201$	19.6619	1.38684
$202$	5.44908	0.383396
$203$	−24.6642	−1.73109
$204$	−2.90546	−0.203423
$205$	17.9005	1.25023
$206$	−18.8870	−1.31592
$207$	1.34421	0.0934289
$208$	2.23309	0.154837
$209$	−8.41539	−0.582104
$210$	−30.3589	−2.09496
$211$	8.33848	0.574044	0.287022	−	0.957924i	$-0.407335\pi$
$211$	8.33848	0.574044	0.287022	+	0.957924i	$0.407335\pi$
$212$	5.87976	0.403824
$213$	22.8028	1.56242
$214$	−7.97115	−0.544897
$215$	−26.8531	−1.83137
$216$	7.09422	0.482701
$217$	−1.55376	−0.105476
$218$	3.30249	0.223673
$219$	3.31772	0.224190
$220$	15.8394	1.06789
$221$	2.23309	0.150214
$222$	−12.7914	−0.858502
$223$	−12.2579	−0.820850	−0.410425	−	0.911894i	$-0.634620\pi$
$223$	−12.2579	−0.820850	−0.410425	+	0.911894i	$0.634620\pi$
$224$	4.07426	0.272223
$225$	8.58302	0.572201
$226$	−17.7052	−1.17773
$227$	26.0736	1.73057	0.865283	−	0.501283i	$-0.167139\pi$
$227$	26.0736	1.73057	0.865283	+	0.501283i	$0.167139\pi$
$228$	3.95889	0.262184
$229$	−26.4356	−1.74692	−0.873458	−	0.486900i	$-0.838128\pi$
$229$	−26.4356	−1.74692	−0.873458	+	0.486900i	$0.838128\pi$
$230$	−0.633513	−0.0417726
$231$	73.1103	4.81030
$232$	−6.05367	−0.397443
$233$	4.42466	0.289869	0.144935	−	0.989441i	$-0.453703\pi$
$233$	4.42466	0.289869	0.144935	+	0.989441i	$0.453703\pi$
$234$	−12.1518	−0.794385
$235$	9.14046	0.596258
$236$	−1.00000	−0.0650945
$237$	−1.87570	−0.121840
$238$	4.07426	0.264095
$239$	15.3479	0.992776	0.496388	−	0.868101i	$-0.334659\pi$
$239$	15.3479	0.992776	0.496388	+	0.868101i	$0.334659\pi$
$240$	−7.45139	−0.480985
$241$	9.70773	0.625330	0.312665	−	0.949863i	$-0.398778\pi$
$241$	9.70773	0.625330	0.312665	+	0.949863i	$0.398778\pi$
$242$	−27.1443	−1.74490
$243$	8.82726	0.566269
$244$	−7.73575	−0.495230
$245$	24.6193	1.57287
$246$	20.2795	1.29298
$247$	−3.04274	−0.193605
$248$	−0.381361	−0.0242164
$249$	−25.3768	−1.60819
$250$	8.77800	0.555169
$251$	0.777866	0.0490985	0.0245492	−	0.999699i	$-0.492185\pi$
$251$	0.777866	0.0490985	0.0245492	+	0.999699i	$0.492185\pi$
$252$	−22.1709	−1.39663
$253$	1.52562	0.0959152
$254$	−15.5840	−0.977827
$255$	−7.45139	−0.466624
$256$	1.00000	0.0625000
$257$	−23.5749	−1.47056	−0.735280	−	0.677764i	$-0.762949\pi$
$257$	−23.5749	−1.47056	−0.735280	+	0.677764i	$0.762949\pi$
$258$	−30.4219	−1.89398
$259$	17.9371	1.11456
$260$	5.72701	0.355174
$261$	32.9422	2.03907
$262$	−13.9064	−0.859143
$263$	−17.1274	−1.05612	−0.528060	−	0.849207i	$-0.677080\pi$
$263$	−17.1274	−1.05612	−0.528060	+	0.849207i	$0.677080\pi$
$264$	17.9444	1.10440
$265$	15.0794	0.926317
$266$	−5.55147	−0.340382
$267$	−28.5338	−1.74624
$268$	−6.76723	−0.413374
$269$	17.0207	1.03777	0.518887	−	0.854843i	$-0.326347\pi$
$269$	17.0207	1.03777	0.518887	+	0.854843i	$0.326347\pi$
$270$	18.1940	1.10725
$271$	−1.41892	−0.0861933	−0.0430966	−	0.999071i	$-0.513722\pi$
$271$	−1.41892	−0.0861933	−0.0430966	+	0.999071i	$0.513722\pi$
$272$	1.00000	0.0606339
$273$	26.4344	1.59988
$274$	−2.89694	−0.175010
$275$	9.74140	0.587429
$276$	−0.717707	−0.0432009
$277$	−9.67682	−0.581424	−0.290712	−	0.956811i	$-0.593892\pi$
$277$	−9.67682	−0.581424	−0.290712	+	0.956811i	$0.593892\pi$
$278$	9.72509	0.583272
$279$	2.07525	0.124242
$280$	10.4489	0.624443
$281$	−10.0515	−0.599624	−0.299812	−	0.953998i	$-0.596924\pi$
$281$	−10.0515	−0.599624	−0.299812	+	0.953998i	$0.596924\pi$
$282$	10.3552	0.616645
$283$	14.4417	0.858467	0.429234	−	0.903193i	$-0.358784\pi$
$283$	14.4417	0.858467	0.429234	+	0.903193i	$0.358784\pi$
$284$	−7.84826	−0.465709
$285$	10.1531	0.601415
$286$	−13.7918	−0.815525
$287$	−28.4376	−1.67862
$288$	−5.44169	−0.320654
$289$	1.00000	0.0588235
$290$	−15.5254	−0.911680
$291$	53.7828	3.15281
$292$	−1.14189	−0.0668241
$293$	20.1544	1.17743	0.588715	−	0.808341i	$-0.299634\pi$
$293$	20.1544	1.17743	0.588715	+	0.808341i	$0.299634\pi$
$294$	27.8912	1.62665
$295$	−2.56462	−0.149318
$296$	4.40254	0.255892
$297$	−43.8147	−2.54239
$298$	3.71456	0.215179
$299$	0.551618	0.0319009
$300$	−4.58270	−0.264582
$301$	42.6600	2.45888
$302$	5.80620	0.334109
$303$	15.8321	0.909529
$304$	−1.36257	−0.0781488
$305$	−19.8392	−1.13599
$306$	−5.44169	−0.311081
$307$	−28.1158	−1.60465	−0.802327	−	0.596884i	$-0.796405\pi$
$307$	−28.1158	−1.60465	−0.802327	+	0.596884i	$0.796405\pi$
$308$	−25.1631	−1.43380
$309$	−54.8755	−3.12176
$310$	−0.978045	−0.0555492
$311$	13.2799	0.753036	0.376518	−	0.926409i	$-0.377121\pi$
$311$	13.2799	0.753036	0.376518	+	0.926409i	$0.377121\pi$
$312$	6.48814	0.367318
$313$	−13.2157	−0.746996	−0.373498	−	0.927631i	$-0.621842\pi$
$313$	−13.2157	−0.746996	−0.373498	+	0.927631i	$0.621842\pi$
$314$	−20.7622	−1.17168
$315$	−56.8598	−3.20369
$316$	0.645579	0.0363167
$317$	−10.3285	−0.580105	−0.290052	−	0.957011i	$-0.593673\pi$
$317$	−10.3285	−0.580105	−0.290052	+	0.957011i	$0.593673\pi$
$318$	17.0834	0.957990
$319$	37.3881	2.09333
$320$	2.56462	0.143367
$321$	−23.1599	−1.29266
$322$	1.00643	0.0560859
$323$	−1.36257	−0.0758155
$324$	4.28690	0.238161
$325$	3.52218	0.195376
$326$	−10.9773	−0.607976
$327$	9.59525	0.530619
$328$	−6.97981	−0.385395
$329$	−14.5209	−0.800564
$330$	46.0206	2.53335
$331$	−31.1282	−1.71096	−0.855481	−	0.517835i	$-0.826738\pi$
$331$	−31.1282	−1.71096	−0.855481	+	0.517835i	$0.826738\pi$
$332$	8.73419	0.479351
$333$	−23.9572	−1.31285
$334$	−7.84341	−0.429172
$335$	−17.3554	−0.948225
$336$	11.8376	0.645794
$337$	14.9051	0.811931	0.405966	−	0.913888i	$-0.366935\pi$
$337$	14.9051	0.811931	0.405966	+	0.913888i	$0.366935\pi$
$338$	8.01333	0.435868
$339$	−51.4416	−2.79392
$340$	2.56462	0.139086
$341$	2.35533	0.127548
$342$	7.41468	0.400940
$343$	−10.5915	−0.571885
$344$	10.4706	0.564537
$345$	−1.84065	−0.0990970
$346$	−5.59950	−0.301031
$347$	−21.0022	−1.12746	−0.563728	−	0.825960i	$-0.690633\pi$
$347$	−21.0022	−1.12746	−0.563728	+	0.825960i	$0.690633\pi$
$348$	−17.5887	−0.942852
$349$	25.1449	1.34598	0.672988	−	0.739653i	$-0.265011\pi$
$349$	25.1449	1.34598	0.672988	+	0.739653i	$0.265011\pi$
$350$	6.42622	0.343496
$351$	−15.8420	−0.845583
$352$	−6.17611	−0.329188
$353$	4.48230	0.238569	0.119284	−	0.992860i	$-0.461940\pi$
$353$	4.48230	0.238569	0.119284	+	0.992860i	$0.461940\pi$
$354$	−2.90546	−0.154423
$355$	−20.1278	−1.06827
$356$	9.82076	0.520499
$357$	11.8376	0.626512
$358$	6.12370	0.323648
$359$	0.749148	0.0395385	0.0197693	−	0.999805i	$-0.493707\pi$
$359$	0.749148	0.0395385	0.0197693	+	0.999805i	$0.493707\pi$
$360$	−13.9559	−0.735538
$361$	−17.1434	−0.902284
$362$	−6.20302	−0.326023
$363$	−78.8667	−4.13943
$364$	−9.09817	−0.476874
$365$	−2.92851	−0.153285
$366$	−22.4759	−1.17483
$367$	21.0588	1.09926	0.549630	−	0.835408i	$-0.314769\pi$
$367$	21.0588	1.09926	0.549630	+	0.835408i	$0.314769\pi$
$368$	0.247020	0.0128768
$369$	37.9819	1.97726
$370$	11.2908	0.586982
$371$	−23.9557	−1.24372
$372$	−1.10803	−0.0574486
$373$	16.4068	0.849511	0.424755	−	0.905308i	$-0.360360\pi$
$373$	16.4068	0.849511	0.424755	+	0.905308i	$0.360360\pi$
$374$	−6.17611	−0.319359
$375$	25.5041	1.31703
$376$	−3.56406	−0.183803
$377$	13.5184	0.696231
$378$	−28.9037	−1.48665
$379$	14.3567	0.737455	0.368728	−	0.929537i	$-0.379794\pi$
$379$	14.3567	0.737455	0.368728	+	0.929537i	$0.379794\pi$
$380$	−3.49447	−0.179263
$381$	−45.2787	−2.31970
$382$	7.21342	0.369071
$383$	−6.12201	−0.312820	−0.156410	−	0.987692i	$-0.549992\pi$
$383$	−6.12201	−0.312820	−0.156410	+	0.987692i	$0.549992\pi$
$384$	2.90546	0.148269
$385$	−64.5337	−3.28894
$386$	−25.2994	−1.28771
$387$	−56.9777	−2.89634
$388$	−18.5110	−0.939752
$389$	−19.1378	−0.970327	−0.485163	−	0.874424i	$-0.661240\pi$
$389$	−19.1378	−0.970327	−0.485163	+	0.874424i	$0.661240\pi$
$390$	16.6396	0.842579
$391$	0.247020	0.0124924
$392$	−9.59960	−0.484853
$393$	−40.4046	−2.03814
$394$	−18.8026	−0.947262
$395$	1.65567	0.0833056
$396$	33.6085	1.68889
$397$	22.3047	1.11944	0.559720	−	0.828682i	$-0.310909\pi$
$397$	22.3047	1.11944	0.559720	+	0.828682i	$0.310909\pi$
$398$	−22.3251	−1.11905
$399$	−16.1296	−0.807488
$400$	1.57727	0.0788636
$401$	6.11594	0.305416	0.152708	−	0.988271i	$-0.451201\pi$
$401$	6.11594	0.305416	0.152708	+	0.988271i	$0.451201\pi$
$402$	−19.6619	−0.980646
$403$	0.851611	0.0424218
$404$	−5.44908	−0.271102
$405$	10.9943	0.546309
$406$	24.6642	1.22406
$407$	−27.1905	−1.34779
$408$	2.90546	0.143842
$409$	14.0168	0.693087	0.346543	−	0.938034i	$-0.387355\pi$
$409$	14.0168	0.693087	0.346543	+	0.938034i	$0.387355\pi$
$410$	−17.9005	−0.884045
$411$	−8.41693	−0.415177
$412$	18.8870	0.930497
$413$	4.07426	0.200481
$414$	−1.34421	−0.0660642
$415$	22.3999	1.09957
$416$	−2.23309	−0.109486
$417$	28.2559	1.38369
$418$	8.41539	0.411610
$419$	−15.9078	−0.777149	−0.388574	−	0.921417i	$-0.627032\pi$
$419$	−15.9078	−0.777149	−0.388574	+	0.921417i	$0.627032\pi$
$420$	30.3589	1.48136
$421$	−26.7370	−1.30308	−0.651542	−	0.758613i	$-0.725878\pi$
$421$	−26.7370	−1.30308	−0.651542	+	0.758613i	$0.725878\pi$
$422$	−8.33848	−0.405911
$423$	19.3945	0.942994
$424$	−5.87976	−0.285547
$425$	1.57727	0.0765089
$426$	−22.8028	−1.10480
$427$	31.5175	1.52524
$428$	7.97115	0.385300
$429$	−40.0714	−1.93467
$430$	26.8531	1.29497
$431$	−27.6342	−1.33109	−0.665546	−	0.746357i	$-0.731801\pi$
$431$	−27.6342	−1.33109	−0.665546	+	0.746357i	$0.731801\pi$
$432$	−7.09422	−0.341321
$433$	−27.0870	−1.30172	−0.650859	−	0.759199i	$-0.725591\pi$
$433$	−27.0870	−1.30172	−0.650859	+	0.759199i	$0.725591\pi$
$434$	1.55376	0.0745830
$435$	−45.1083	−2.16278
$436$	−3.30249	−0.158161
$437$	−0.336583	−0.0161009
$438$	−3.31772	−0.158527
$439$	3.39928	0.162239	0.0811195	−	0.996704i	$-0.474150\pi$
$439$	3.39928	0.162239	0.0811195	+	0.996704i	$0.474150\pi$
$440$	−15.8394	−0.755112
$441$	52.2380	2.48753
$442$	−2.23309	−0.106217
$443$	−37.3948	−1.77668	−0.888339	−	0.459188i	$-0.848141\pi$
$443$	−37.3948	−1.77668	−0.888339	+	0.459188i	$0.848141\pi$
$444$	12.7914	0.607052
$445$	25.1865	1.19395
$446$	12.2579	0.580429
$447$	10.7925	0.510468
$448$	−4.07426	−0.192491
$449$	−31.5608	−1.48945	−0.744723	−	0.667373i	$-0.767419\pi$
$449$	−31.5608	−1.48945	−0.744723	+	0.667373i	$0.767419\pi$
$450$	−8.58302	−0.404607
$451$	43.1081	2.02988
$452$	17.7052	0.832781
$453$	16.8697	0.792606
$454$	−26.0736	−1.22370
$455$	−23.3334	−1.09388
$456$	−3.95889	−0.185392
$457$	−10.4575	−0.489182	−0.244591	−	0.969626i	$-0.578654\pi$
$457$	−10.4575	−0.489182	−0.244591	+	0.969626i	$0.578654\pi$
$458$	26.4356	1.23526
$459$	−7.09422	−0.331130
$460$	0.633513	0.0295377
$461$	25.2310	1.17512	0.587562	−	0.809179i	$-0.300088\pi$
$461$	25.2310	1.17512	0.587562	+	0.809179i	$0.300088\pi$
$462$	−73.1103	−3.40140
$463$	−8.91580	−0.414352	−0.207176	−	0.978304i	$-0.566427\pi$
$463$	−8.91580	−0.414352	−0.207176	+	0.978304i	$0.566427\pi$
$464$	6.05367	0.281034
$465$	−2.84167	−0.131779
$466$	−4.42466	−0.204969
$467$	19.4809	0.901469	0.450734	−	0.892658i	$-0.351162\pi$
$467$	19.4809	0.901469	0.450734	+	0.892658i	$0.351162\pi$
$468$	12.1518	0.561715
$469$	27.5714	1.27313
$470$	−9.14046	−0.421618
$471$	−60.3238	−2.77957
$472$	1.00000	0.0460287
$473$	−64.6676	−2.97342
$474$	1.87570	0.0861539
$475$	−2.14914	−0.0986095
$476$	−4.07426	−0.186743
$477$	31.9958	1.46499
$478$	−15.3479	−0.701998
$479$	7.12642	0.325615	0.162807	−	0.986658i	$-0.447945\pi$
$479$	7.12642	0.325615	0.162807	+	0.986658i	$0.447945\pi$
$480$	7.45139	0.340108
$481$	−9.83124	−0.448266
$482$	−9.70773	−0.442175
$483$	2.92413	0.133052
$484$	27.1443	1.23383
$485$	−47.4736	−2.15566
$486$	−8.82726	−0.400413
$487$	11.0747	0.501843	0.250922	−	0.968007i	$-0.419266\pi$
$487$	11.0747	0.501843	0.250922	+	0.968007i	$0.419266\pi$
$488$	7.73575	0.350181
$489$	−31.8941	−1.44230
$490$	−24.6193	−1.11219
$491$	−18.8634	−0.851292	−0.425646	−	0.904890i	$-0.639953\pi$
$491$	−18.8634	−0.851292	−0.425646	+	0.904890i	$0.639953\pi$
$492$	−20.2795	−0.914272
$493$	6.05367	0.272643
$494$	3.04274	0.136899
$495$	86.1929	3.87408
$496$	0.381361	0.0171236
$497$	31.9759	1.43431
$498$	25.3768	1.13716
$499$	19.8825	0.890065	0.445032	−	0.895514i	$-0.353192\pi$
$499$	19.8825	0.890065	0.445032	+	0.895514i	$0.353192\pi$
$500$	−8.77800	−0.392564
$501$	−22.7887	−1.01812
$502$	−0.777866	−0.0347179
$503$	−9.68502	−0.431834	−0.215917	−	0.976412i	$-0.569274\pi$
$503$	−9.68502	−0.431834	−0.215917	+	0.976412i	$0.569274\pi$
$504$	22.1709	0.987568
$505$	−13.9748	−0.621871
$506$	−1.52562	−0.0678223
$507$	23.2824	1.03401
$508$	15.5840	0.691428
$509$	31.1773	1.38191	0.690954	−	0.722899i	$-0.257191\pi$
$509$	31.1773	1.38191	0.690954	+	0.722899i	$0.257191\pi$
$510$	7.45139	0.329953
$511$	4.65236	0.205808
$512$	−1.00000	−0.0441942
$513$	9.66638	0.426781
$514$	23.5749	1.03984
$515$	48.4381	2.13444
$516$	30.4219	1.33925
$517$	22.0120	0.968089
$518$	−17.9371	−0.788110
$519$	−16.2691	−0.714135
$520$	−5.72701	−0.251146
$521$	37.9509	1.66266	0.831330	−	0.555780i	$-0.187580\pi$
$521$	37.9509	1.66266	0.831330	+	0.555780i	$0.187580\pi$
$522$	−32.9422	−1.44184
$523$	31.4744	1.37628	0.688139	−	0.725579i	$-0.258428\pi$
$523$	31.4744	1.37628	0.688139	+	0.725579i	$0.258428\pi$
$524$	13.9064	0.607506
$525$	18.6711	0.814874
$526$	17.1274	0.746789
$527$	0.381361	0.0166123
$528$	−17.9444	−0.780931
$529$	−22.9390	−0.997347
$530$	−15.0794	−0.655005
$531$	−5.44169	−0.236149
$532$	5.55147	0.240687
$533$	15.5865	0.675127
$534$	28.5338	1.23478
$535$	20.4430	0.883827
$536$	6.76723	0.292300
$537$	17.7922	0.767789
$538$	−17.0207	−0.733817
$539$	59.2882	2.55372
$540$	−18.1940	−0.782944
$541$	−12.9118	−0.555123	−0.277562	−	0.960708i	$-0.589526\pi$
$541$	−12.9118	−0.555123	−0.277562	+	0.960708i	$0.589526\pi$
$542$	1.41892	0.0609479
$543$	−18.0226	−0.773424
$544$	−1.00000	−0.0428746
$545$	−8.46963	−0.362799
$546$	−26.4344	−1.13129
$547$	−29.0806	−1.24340	−0.621698	−	0.783257i	$-0.713557\pi$
$547$	−29.0806	−1.24340	−0.621698	+	0.783257i	$0.713557\pi$
$548$	2.89694	0.123751
$549$	−42.0955	−1.79659
$550$	−9.74140	−0.415375
$551$	−8.24855	−0.351400
$552$	0.717707	0.0305477
$553$	−2.63026	−0.111850
$554$	9.67682	0.411129
$555$	32.8050	1.39250
$556$	−9.72509	−0.412436
$557$	26.5457	1.12478	0.562388	−	0.826873i	$-0.309883\pi$
$557$	26.5457	1.12478	0.562388	+	0.826873i	$0.309883\pi$
$558$	−2.07525	−0.0878521
$559$	−23.3817	−0.988942
$560$	−10.4489	−0.441548
$561$	−17.9444	−0.757614
$562$	10.0515	0.423998
$563$	31.7328	1.33738	0.668689	−	0.743542i	$-0.266856\pi$
$563$	31.7328	1.33738	0.668689	+	0.743542i	$0.266856\pi$
$564$	−10.3552	−0.436034
$565$	45.4070	1.91029
$566$	−14.4417	−0.607028
$567$	−17.4659	−0.733500
$568$	7.84826	0.329306
$569$	16.9595	0.710978	0.355489	−	0.934680i	$-0.384314\pi$
$569$	16.9595	0.710978	0.355489	+	0.934680i	$0.384314\pi$
$570$	−10.1531	−0.425265
$571$	31.9564	1.33734	0.668668	−	0.743562i	$-0.266865\pi$
$571$	31.9564	1.33734	0.668668	+	0.743562i	$0.266865\pi$
$572$	13.7918	0.576663
$573$	20.9583	0.875545
$574$	28.4376	1.18696
$575$	0.389618	0.0162482
$576$	5.44169	0.226737
$577$	−34.2145	−1.42437	−0.712184	−	0.701993i	$-0.752294\pi$
$577$	−34.2145	−1.42437	−0.712184	+	0.701993i	$0.752294\pi$
$578$	−1.00000	−0.0415945
$579$	−73.5065	−3.05482
$580$	15.5254	0.644655
$581$	−35.5854	−1.47633
$582$	−53.7828	−2.22937
$583$	36.3141	1.50397
$584$	1.14189	0.0472518
$585$	31.1646	1.28850
$586$	−20.1544	−0.832569
$587$	−41.7042	−1.72132	−0.860658	−	0.509183i	$-0.829948\pi$
$587$	−41.7042	−1.72132	−0.860658	+	0.509183i	$0.829948\pi$
$588$	−27.8912	−1.15022
$589$	−0.519631	−0.0214110
$590$	2.56462	0.105584
$591$	−54.6302	−2.24719
$592$	−4.40254	−0.180943
$593$	−18.4479	−0.757564	−0.378782	−	0.925486i	$-0.623657\pi$
$593$	−18.4479	−0.757564	−0.378782	+	0.925486i	$0.623657\pi$
$594$	43.8147	1.79774
$595$	−10.4489	−0.428364
$596$	−3.71456	−0.152154
$597$	−64.8645	−2.65473
$598$	−0.551618	−0.0225573
$599$	31.2317	1.27609	0.638046	−	0.769998i	$-0.279743\pi$
$599$	31.2317	1.27609	0.638046	+	0.769998i	$0.279743\pi$
$600$	4.58270	0.187088
$601$	32.5089	1.32607	0.663033	−	0.748590i	$-0.269269\pi$
$601$	32.5089	1.32607	0.663033	+	0.748590i	$0.269269\pi$
$602$	−42.6600	−1.73869
$603$	−36.8251	−1.49964
$604$	−5.80620	−0.236251
$605$	69.6149	2.83025
$606$	−15.8321	−0.643134
$607$	−39.9731	−1.62246	−0.811229	−	0.584729i	$-0.801201\pi$
$607$	−39.9731	−1.62246	−0.811229	+	0.584729i	$0.801201\pi$
$608$	1.36257	0.0552595
$609$	71.6609	2.90385
$610$	19.8392	0.803268
$611$	7.95886	0.321981
$612$	5.44169	0.219967
$613$	−11.0511	−0.446350	−0.223175	−	0.974778i	$-0.571642\pi$
$613$	−11.0511	−0.446350	−0.223175	+	0.974778i	$0.571642\pi$
$614$	28.1158	1.13466
$615$	−52.0093	−2.09722
$616$	25.1631	1.01385
$617$	−22.7028	−0.913981	−0.456991	−	0.889472i	$-0.651073\pi$
$617$	−22.7028	−0.913981	−0.456991	+	0.889472i	$0.651073\pi$
$618$	54.8755	2.20742
$619$	12.5822	0.505720	0.252860	−	0.967503i	$-0.418629\pi$
$619$	12.5822	0.505720	0.252860	+	0.967503i	$0.418629\pi$
$620$	0.978045	0.0392792
$621$	−1.75242	−0.0703221
$622$	−13.2799	−0.532477
$623$	−40.0123	−1.60306
$624$	−6.48814	−0.259733
$625$	−30.3986	−1.21594
$626$	13.2157	0.528206
$627$	24.4506	0.976461
$628$	20.7622	0.828503
$629$	−4.40254	−0.175541
$630$	56.8598	2.26535
$631$	42.2586	1.68229	0.841143	−	0.540813i	$-0.181883\pi$
$631$	42.2586	1.68229	0.841143	+	0.540813i	$0.181883\pi$
$632$	−0.645579	−0.0256798
$633$	−24.2271	−0.962941
$634$	10.3285	0.410196
$635$	39.9670	1.58604
$636$	−17.0834	−0.677401
$637$	21.4367	0.849354
$638$	−37.3881	−1.48021
$639$	−42.7078	−1.68949
$640$	−2.56462	−0.101375
$641$	35.2022	1.39040	0.695202	−	0.718814i	$-0.255315\pi$
$641$	35.2022	1.39040	0.695202	+	0.718814i	$0.255315\pi$
$642$	23.1599	0.914047
$643$	25.4456	1.00348	0.501739	−	0.865019i	$-0.332694\pi$
$643$	25.4456	1.00348	0.501739	+	0.865019i	$0.332694\pi$
$644$	−1.00643	−0.0396587
$645$	78.0206	3.07206
$646$	1.36257	0.0536096
$647$	10.7874	0.424095	0.212047	−	0.977259i	$-0.431987\pi$
$647$	10.7874	0.424095	0.212047	+	0.977259i	$0.431987\pi$
$648$	−4.28690	−0.168405
$649$	−6.17611	−0.242433
$650$	−3.52218	−0.138151
$651$	4.51439	0.176933
$652$	10.9773	0.429904
$653$	29.6569	1.16056	0.580281	−	0.814416i	$-0.302943\pi$
$653$	29.6569	1.16056	0.580281	+	0.814416i	$0.302943\pi$
$654$	−9.59525	−0.375204
$655$	35.6647	1.39354
$656$	6.97981	0.272516
$657$	−6.21381	−0.242424
$658$	14.5209	0.566085
$659$	28.3577	1.10466	0.552330	−	0.833626i	$-0.313739\pi$
$659$	28.3577	1.10466	0.552330	+	0.833626i	$0.313739\pi$
$660$	−46.0206	−1.79135
$661$	−6.51962	−0.253584	−0.126792	−	0.991929i	$-0.540468\pi$
$661$	−6.51962	−0.253584	−0.126792	+	0.991929i	$0.540468\pi$
$662$	31.1282	1.20983
$663$	−6.48814	−0.251978
$664$	−8.73419	−0.338952
$665$	14.2374	0.552103
$666$	23.9572	0.928324
$667$	1.49538	0.0579013
$668$	7.84341	0.303471
$669$	35.6148	1.37695
$670$	17.3554	0.670496
$671$	−47.7768	−1.84440
$672$	−11.8376	−0.456645
$673$	49.3830	1.90357	0.951787	−	0.306759i	$-0.0992446\pi$
$673$	49.3830	1.90357	0.951787	+	0.306759i	$0.0992446\pi$
$674$	−14.9051	−0.574122
$675$	−11.1895	−0.430684
$676$	−8.01333	−0.308205
$677$	6.84282	0.262991	0.131495	−	0.991317i	$-0.458022\pi$
$677$	6.84282	0.262991	0.131495	+	0.991317i	$0.458022\pi$
$678$	51.4416	1.97560
$679$	75.4185	2.89430
$680$	−2.56462	−0.0983487
$681$	−75.7558	−2.90297
$682$	−2.35533	−0.0901901
$683$	20.7156	0.792659	0.396329	−	0.918108i	$-0.370284\pi$
$683$	20.7156	0.792659	0.396329	+	0.918108i	$0.370284\pi$
$684$	−7.41468	−0.283508
$685$	7.42954	0.283868
$686$	10.5915	0.404384
$687$	76.8076	2.93039
$688$	−10.4706	−0.399188
$689$	13.1300	0.500214
$690$	1.84065	0.0700722
$691$	17.3105	0.658521	0.329260	−	0.944239i	$-0.393201\pi$
$691$	17.3105	0.658521	0.329260	+	0.944239i	$0.393201\pi$
$692$	5.59950	0.212861
$693$	−136.930	−5.20153
$694$	21.0022	0.797232
$695$	−24.9412	−0.946072
$696$	17.5887	0.666697
$697$	6.97981	0.264379
$698$	−25.1449	−0.951749
$699$	−12.8557	−0.486246
$700$	−6.42622	−0.242888
$701$	−24.5296	−0.926470	−0.463235	−	0.886236i	$-0.653311\pi$
$701$	−24.5296	−0.926470	−0.463235	+	0.886236i	$0.653311\pi$
$702$	15.8420	0.597918
$703$	5.99877	0.226248
$704$	6.17611	0.232771
$705$	−26.5572	−1.00020
$706$	−4.48230	−0.168693
$707$	22.2010	0.834954
$708$	2.90546	0.109194
$709$	14.9233	0.560457	0.280228	−	0.959933i	$-0.409590\pi$
$709$	14.9233	0.560457	0.280228	+	0.959933i	$0.409590\pi$
$710$	20.1278	0.755383
$711$	3.51304	0.131749
$712$	−9.82076	−0.368048
$713$	0.0942039	0.00352796
$714$	−11.8376	−0.443011
$715$	35.3707	1.32279
$716$	−6.12370	−0.228854
$717$	−44.5928	−1.66535
$718$	−0.749148	−0.0279579
$719$	37.6464	1.40397	0.701986	−	0.712190i	$-0.252297\pi$
$719$	37.6464	1.40397	0.701986	+	0.712190i	$0.252297\pi$
$720$	13.9559	0.520104
$721$	−76.9507	−2.86579
$722$	17.1434	0.638011
$723$	−28.2054	−1.04897
$724$	6.20302	0.230533
$725$	9.54828	0.354614
$726$	78.8667	2.92702
$727$	50.6917	1.88005	0.940025	−	0.341105i	$-0.110801\pi$
$727$	50.6917	1.88005	0.940025	+	0.341105i	$0.110801\pi$
$728$	9.09817	0.337201
$729$	−38.5079	−1.42622
$730$	2.92851	0.108389
$731$	−10.4706	−0.387269
$732$	22.4759	0.830733
$733$	−46.0250	−1.69997	−0.849987	−	0.526804i	$-0.823390\pi$
$733$	−46.0250	−1.69997	−0.849987	+	0.526804i	$0.823390\pi$
$734$	−21.0588	−0.777294
$735$	−71.5304	−2.63844
$736$	−0.247020	−0.00910529
$737$	−41.7951	−1.53954
$738$	−37.9819	−1.39813
$739$	49.1636	1.80851	0.904257	−	0.426989i	$-0.140426\pi$
$739$	49.1636	1.80851	0.904257	+	0.426989i	$0.140426\pi$
$740$	−11.2908	−0.415059
$741$	8.84055	0.324766
$742$	23.9557	0.879441
$743$	39.1802	1.43738	0.718692	−	0.695329i	$-0.244741\pi$
$743$	39.1802	1.43738	0.718692	+	0.695329i	$0.244741\pi$
$744$	1.10803	0.0406223
$745$	−9.52643	−0.349021
$746$	−16.4068	−0.600695
$747$	47.5287	1.73899
$748$	6.17611	0.225821
$749$	−32.4766	−1.18667
$750$	−25.5041	−0.931278
$751$	−49.7176	−1.81422	−0.907111	−	0.420892i	$-0.861717\pi$
$751$	−49.7176	−1.81422	−0.907111	+	0.420892i	$0.861717\pi$
$752$	3.56406	0.129968
$753$	−2.26006	−0.0823610
$754$	−13.5184	−0.492310
$755$	−14.8907	−0.541928
$756$	28.9037	1.05122
$757$	−39.8330	−1.44775	−0.723877	−	0.689929i	$-0.757642\pi$
$757$	−39.8330	−1.44775	−0.723877	+	0.689929i	$0.757642\pi$
$758$	−14.3567	−0.521460
$759$	−4.43264	−0.160895
$760$	3.49447	0.126758
$761$	−28.6011	−1.03679	−0.518395	−	0.855141i	$-0.673470\pi$
$761$	−28.6011	−1.03679	−0.518395	+	0.855141i	$0.673470\pi$
$762$	45.2787	1.64027
$763$	13.4552	0.487111
$764$	−7.21342	−0.260972
$765$	13.9559	0.504575
$766$	6.12201	0.221197
$767$	−2.23309	−0.0806321
$768$	−2.90546	−0.104842
$769$	6.51359	0.234886	0.117443	−	0.993080i	$-0.462530\pi$
$769$	6.51359	0.234886	0.117443	+	0.993080i	$0.462530\pi$
$770$	64.5337	2.32563
$771$	68.4958	2.46682
$772$	25.2994	0.910547
$773$	42.5209	1.52937	0.764686	−	0.644404i	$-0.222894\pi$
$773$	42.5209	1.52937	0.764686	+	0.644404i	$0.222894\pi$
$774$	56.9777	2.04802
$775$	0.601509	0.0216069
$776$	18.5110	0.664505
$777$	−52.1154	−1.86963
$778$	19.1378	0.686125
$779$	−9.51048	−0.340748
$780$	−16.6396	−0.595793
$781$	−48.4717	−1.73445
$782$	−0.247020	−0.00883343
$783$	−42.9461	−1.53477
$784$	9.59960	0.342843
$785$	53.2472	1.90047
$786$	40.4046	1.44118
$787$	−23.7857	−0.847870	−0.423935	−	0.905693i	$-0.639351\pi$
$787$	−23.7857	−0.847870	−0.423935	+	0.905693i	$0.639351\pi$
$788$	18.8026	0.669816
$789$	49.7629	1.77161
$790$	−1.65567	−0.0589059
$791$	−72.1355	−2.56484
$792$	−33.6085	−1.19422
$793$	−17.2746	−0.613439
$794$	−22.3047	−0.791563
$795$	−43.8124	−1.55387
$796$	22.3251	0.791291
$797$	15.8954	0.563044	0.281522	−	0.959555i	$-0.409161\pi$
$797$	15.8954	0.563044	0.281522	+	0.959555i	$0.409161\pi$
$798$	16.1296	0.570980
$799$	3.56406	0.126087
$800$	−1.57727	−0.0557650
$801$	53.4415	1.88826
$802$	−6.11594	−0.215961
$803$	−7.05244	−0.248875
$804$	19.6619	0.693422
$805$	−2.58110	−0.0909717
$806$	−0.851611	−0.0299967
$807$	−49.4531	−1.74083
$808$	5.44908	0.191698
$809$	−28.2050	−0.991636	−0.495818	−	0.868426i	$-0.665132\pi$
$809$	−28.2050	−0.991636	−0.495818	+	0.868426i	$0.665132\pi$
$810$	−10.9943	−0.386299
$811$	2.12500	0.0746188	0.0373094	−	0.999304i	$-0.488121\pi$
$811$	2.12500	0.0746188	0.0373094	+	0.999304i	$0.488121\pi$
$812$	−24.6642	−0.865545
$813$	4.12261	0.144586
$814$	27.1905	0.953028
$815$	28.1526	0.986142
$816$	−2.90546	−0.101711
$817$	14.2669	0.499137
$818$	−14.0168	−0.490086
$819$	−49.5094	−1.73000
$820$	17.9005	0.625114
$821$	−43.1948	−1.50751	−0.753754	−	0.657157i	$-0.771759\pi$
$821$	−43.1948	−1.50751	−0.753754	+	0.657157i	$0.771759\pi$
$822$	8.41693	0.293574
$823$	−34.9969	−1.21991	−0.609957	−	0.792435i	$-0.708813\pi$
$823$	−34.9969	−1.21991	−0.609957	+	0.792435i	$0.708813\pi$
$824$	−18.8870	−0.657961
$825$	−28.3032	−0.985392
$826$	−4.07426	−0.141762
$827$	−24.2368	−0.842797	−0.421399	−	0.906875i	$-0.638461\pi$
$827$	−24.2368	−0.842797	−0.421399	+	0.906875i	$0.638461\pi$
$828$	1.34421	0.0467144
$829$	−16.0804	−0.558495	−0.279248	−	0.960219i	$-0.590085\pi$
$829$	−16.0804	−0.558495	−0.279248	+	0.960219i	$0.590085\pi$
$830$	−22.3999	−0.777511
$831$	28.1156	0.975319
$832$	2.23309	0.0774183
$833$	9.59960	0.332607
$834$	−28.2559	−0.978420
$835$	20.1154	0.696121
$836$	−8.41539	−0.291052
$837$	−2.70546	−0.0935143
$838$	15.9078	0.549527
$839$	−21.5907	−0.745393	−0.372697	−	0.927953i	$-0.621567\pi$
$839$	−21.5907	−0.745393	−0.372697	+	0.927953i	$0.621567\pi$
$840$	−30.3589	−1.04748
$841$	7.64690	0.263686
$842$	26.7370	0.921419
$843$	29.2043	1.00585
$844$	8.33848	0.287022
$845$	−20.5511	−0.706981
$846$	−19.3945	−0.666797
$847$	−110.593	−3.80002
$848$	5.87976	0.201912
$849$	−41.9596	−1.44005
$850$	−1.57727	−0.0541000
$851$	−1.08752	−0.0372796
$852$	22.8028	0.781211
$853$	−31.7434	−1.08687	−0.543436	−	0.839451i	$-0.682877\pi$
$853$	−31.7434	−1.08687	−0.543436	+	0.839451i	$0.682877\pi$
$854$	−31.5175	−1.07851
$855$	−19.0158	−0.650328
$856$	−7.97115	−0.272448
$857$	−18.5008	−0.631975	−0.315987	−	0.948763i	$-0.602336\pi$
$857$	−18.5008	−0.631975	−0.315987	+	0.948763i	$0.602336\pi$
$858$	40.0714	1.36802
$859$	15.7621	0.537795	0.268898	−	0.963169i	$-0.413341\pi$
$859$	15.7621	0.537795	0.268898	+	0.963169i	$0.413341\pi$
$860$	−26.8531	−0.915683
$861$	82.6241	2.81582
$862$	27.6342	0.941224
$863$	23.6659	0.805597	0.402799	−	0.915289i	$-0.368038\pi$
$863$	23.6659	0.805597	0.402799	+	0.915289i	$0.368038\pi$
$864$	7.09422	0.241350
$865$	14.3606	0.488275
$866$	27.0870	0.920453
$867$	−2.90546	−0.0986745
$868$	−1.55376	−0.0527382
$869$	3.98717	0.135255
$870$	45.1083	1.52931
$871$	−15.1118	−0.512044
$872$	3.30249	0.111836
$873$	−100.731	−3.40922
$874$	0.336583	0.0113851
$875$	35.7638	1.20904
$876$	3.31772	0.112095
$877$	−17.5601	−0.592962	−0.296481	−	0.955039i	$-0.595813\pi$
$877$	−17.5601	−0.592962	−0.296481	+	0.955039i	$0.595813\pi$
$878$	−3.39928	−0.114720
$879$	−58.5577	−1.97510
$880$	15.8394	0.533945
$881$	−2.97564	−0.100252	−0.0501259	−	0.998743i	$-0.515962\pi$
$881$	−2.97564	−0.100252	−0.0501259	+	0.998743i	$0.515962\pi$
$882$	−52.2380	−1.75895
$883$	4.50650	0.151656	0.0758279	−	0.997121i	$-0.475840\pi$
$883$	4.50650	0.151656	0.0758279	+	0.997121i	$0.475840\pi$
$884$	2.23309	0.0751068
$885$	7.45139	0.250476
$886$	37.3948	1.25630
$887$	−43.4934	−1.46037	−0.730183	−	0.683252i	$-0.760565\pi$
$887$	−43.4934	−1.46037	−0.730183	+	0.683252i	$0.760565\pi$
$888$	−12.7914	−0.429251
$889$	−63.4933	−2.12950
$890$	−25.1865	−0.844253
$891$	26.4763	0.886991
$892$	−12.2579	−0.410425
$893$	−4.85629	−0.162509
$894$	−10.7925	−0.360955
$895$	−15.7050	−0.524959
$896$	4.07426	0.136112
$897$	−1.60270	−0.0535127
$898$	31.5608	1.05320
$899$	2.30863	0.0769972
$900$	8.58302	0.286101
$901$	5.87976	0.195883
$902$	−43.1081	−1.43534
$903$	−123.947	−4.12469
$904$	−17.7052	−0.588865
$905$	15.9084	0.528813
$906$	−16.8697	−0.560457
$907$	29.6935	0.985958	0.492979	−	0.870041i	$-0.335908\pi$
$907$	29.6935	0.985958	0.492979	+	0.870041i	$0.335908\pi$
$908$	26.0736	0.865283
$909$	−29.6522	−0.983501
$910$	23.3334	0.773493
$911$	26.4087	0.874958	0.437479	−	0.899229i	$-0.355871\pi$
$911$	26.4087	0.874958	0.437479	+	0.899229i	$0.355871\pi$
$912$	3.95889	0.131092
$913$	53.9433	1.78526
$914$	10.4575	0.345904
$915$	57.6421	1.90559
$916$	−26.4356	−0.873458
$917$	−56.6585	−1.87103
$918$	7.09422	0.234144
$919$	21.3191	0.703251	0.351626	−	0.936141i	$-0.385629\pi$
$919$	21.3191	0.703251	0.351626	+	0.936141i	$0.385629\pi$
$920$	−0.633513	−0.0208863
$921$	81.6893	2.69176
$922$	−25.2310	−0.830938
$923$	−17.5258	−0.576870
$924$	73.1103	2.40515
$925$	−6.94400	−0.228317
$926$	8.91580	0.292991
$927$	102.777	3.37565
$928$	−6.05367	−0.198721
$929$	−17.4047	−0.571031	−0.285515	−	0.958374i	$-0.592165\pi$
$929$	−17.4047	−0.571031	−0.285515	+	0.958374i	$0.592165\pi$
$930$	2.84167	0.0931820
$931$	−13.0801	−0.428684
$932$	4.42466	0.144935
$933$	−38.5843	−1.26319
$934$	−19.4809	−0.637435
$935$	15.8394	0.518003
$936$	−12.1518	−0.397192
$937$	−34.5172	−1.12763	−0.563815	−	0.825901i	$-0.690667\pi$
$937$	−34.5172	−1.12763	−0.563815	+	0.825901i	$0.690667\pi$
$938$	−27.5714	−0.900240
$939$	38.3977	1.25306
$940$	9.14046	0.298129
$941$	22.1248	0.721248	0.360624	−	0.932711i	$-0.382564\pi$
$941$	22.1248	0.721248	0.360624	+	0.932711i	$0.382564\pi$
$942$	60.3238	1.96545
$943$	1.72415	0.0561462
$944$	−1.00000	−0.0325472
$945$	74.1270	2.41135
$946$	64.6676	2.10252
$947$	29.1359	0.946790	0.473395	−	0.880850i	$-0.343028\pi$
$947$	29.1359	0.946790	0.473395	+	0.880850i	$0.343028\pi$
$948$	−1.87570	−0.0609200
$949$	−2.54994	−0.0827746
$950$	2.14914	0.0697274
$951$	30.0089	0.973106
$952$	4.07426	0.132048
$953$	17.3878	0.563245	0.281622	−	0.959525i	$-0.409127\pi$
$953$	17.3878	0.563245	0.281622	+	0.959525i	$0.409127\pi$
$954$	−31.9958	−1.03590
$955$	−18.4997	−0.598636
$956$	15.3479	0.496388
$957$	−108.630	−3.51150
$958$	−7.12642	−0.230244
$959$	−11.8029	−0.381135
$960$	−7.45139	−0.240493
$961$	−30.8546	−0.995309
$962$	9.83124	0.316972
$963$	43.3765	1.39779
$964$	9.70773	0.312665
$965$	64.8834	2.08867
$966$	−2.92413	−0.0940822
$967$	−27.4001	−0.881127	−0.440564	−	0.897721i	$-0.645221\pi$
$967$	−27.4001	−0.881127	−0.440564	+	0.897721i	$0.645221\pi$
$968$	−27.1443	−0.872452
$969$	3.95889	0.127178
$970$	47.4736	1.52428
$971$	−42.2910	−1.35718	−0.678592	−	0.734516i	$-0.737409\pi$
$971$	−42.2910	−1.35718	−0.678592	+	0.734516i	$0.737409\pi$
$972$	8.82726	0.283134
$973$	39.6226	1.27024
$974$	−11.0747	−0.354857
$975$	−10.2336	−0.327736
$976$	−7.73575	−0.247615
$977$	4.03738	0.129167	0.0645837	−	0.997912i	$-0.479428\pi$
$977$	4.03738	0.129167	0.0645837	+	0.997912i	$0.479428\pi$
$978$	31.8941	1.01986
$979$	60.6541	1.93851
$980$	24.6193	0.786436
$981$	−17.9711	−0.573774
$982$	18.8634	0.601955
$983$	−1.50453	−0.0479870	−0.0239935	−	0.999712i	$-0.507638\pi$
$983$	−1.50453	−0.0479870	−0.0239935	+	0.999712i	$0.507638\pi$
$984$	20.2795	0.646488
$985$	48.2216	1.53647
$986$	−6.05367	−0.192788
$987$	42.1899	1.34292
$988$	−3.04274	−0.0968024
$989$	−2.58645	−0.0822444
$990$	−86.1929	−2.73939
$991$	−48.0116	−1.52514	−0.762570	−	0.646906i	$-0.776063\pi$
$991$	−48.0116	−1.52514	−0.762570	+	0.646906i	$0.776063\pi$
$992$	−0.381361	−0.0121082
$993$	90.4417	2.87008
$994$	−31.9759	−1.01421
$995$	57.2553	1.81511
$996$	−25.3768	−0.804095
$997$	39.6617	1.25610	0.628049	−	0.778174i	$-0.283854\pi$
$997$	39.6617	1.25610	0.628049	+	0.778174i	$0.283854\pi$
$998$	−19.8825	−0.629371
$999$	31.2326	0.988154

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2006.2.a.u.1.1	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2006.2.a.u.1.1	✓	9	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.90546 q^{3} +1.00000 q^{4} +2.56462 q^{5} +2.90546 q^{6} -4.07426 q^{7} -1.00000 q^{8} +5.44169 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.90546 q^{3} +1.00000 q^{4} +2.56462 q^{5} +2.90546 q^{6} -4.07426 q^{7} -1.00000 q^{8} +5.44169 q^{9} -2.56462 q^{10} +6.17611 q^{11} -2.90546 q^{12} +2.23309 q^{13} +4.07426 q^{14} -7.45139 q^{15} +1.00000 q^{16} +1.00000 q^{17} -5.44169 q^{18} -1.36257 q^{19} +2.56462 q^{20} +11.8376 q^{21} -6.17611 q^{22} +0.247020 q^{23} +2.90546 q^{24} +1.57727 q^{25} -2.23309 q^{26} -7.09422 q^{27} -4.07426 q^{28} +6.05367 q^{29} +7.45139 q^{30} +0.381361 q^{31} -1.00000 q^{32} -17.9444 q^{33} -1.00000 q^{34} -10.4489 q^{35} +5.44169 q^{36} -4.40254 q^{37} +1.36257 q^{38} -6.48814 q^{39} -2.56462 q^{40} +6.97981 q^{41} -11.8376 q^{42} -10.4706 q^{43} +6.17611 q^{44} +13.9559 q^{45} -0.247020 q^{46} +3.56406 q^{47} -2.90546 q^{48} +9.59960 q^{49} -1.57727 q^{50} -2.90546 q^{51} +2.23309 q^{52} +5.87976 q^{53} +7.09422 q^{54} +15.8394 q^{55} +4.07426 q^{56} +3.95889 q^{57} -6.05367 q^{58} -1.00000 q^{59} -7.45139 q^{60} -7.73575 q^{61} -0.381361 q^{62} -22.1709 q^{63} +1.00000 q^{64} +5.72701 q^{65} +17.9444 q^{66} -6.76723 q^{67} +1.00000 q^{68} -0.717707 q^{69} +10.4489 q^{70} -7.84826 q^{71} -5.44169 q^{72} -1.14189 q^{73} +4.40254 q^{74} -4.58270 q^{75} -1.36257 q^{76} -25.1631 q^{77} +6.48814 q^{78} +0.645579 q^{79} +2.56462 q^{80} +4.28690 q^{81} -6.97981 q^{82} +8.73419 q^{83} +11.8376 q^{84} +2.56462 q^{85} +10.4706 q^{86} -17.5887 q^{87} -6.17611 q^{88} +9.82076 q^{89} -13.9559 q^{90} -9.09817 q^{91} +0.247020 q^{92} -1.10803 q^{93} -3.56406 q^{94} -3.49447 q^{95} +2.90546 q^{96} -18.5110 q^{97} -9.59960 q^{98} +33.6085 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 9 q^{2} - q^{3} + 9 q^{4} + 7 q^{5} + q^{6} - 9 q^{8} + 20 q^{9}+O(q^{10}) \) 9 * q - 9 * q^2 - q^3 + 9 * q^4 + 7 * q^5 + q^6 - 9 * q^8 + 20 * q^9	\( 9 q - 9 q^{2} - q^{3} + 9 q^{4} + 7 q^{5} + q^{6} - 9 q^{8} + 20 q^{9} - 7 q^{10} + 5 q^{11} - q^{12} + 25 q^{13} - 5 q^{15} + 9 q^{16} + 9 q^{17} - 20 q^{18} + 14 q^{19} + 7 q^{20} - 7 q^{21} - 5 q^{22} + 2 q^{23} + q^{24} + 20 q^{25} - 25 q^{26} - 10 q^{27} + 18 q^{29} + 5 q^{30} + 6 q^{31} - 9 q^{32} - 9 q^{33} - 9 q^{34} - 17 q^{35} + 20 q^{36} + 11 q^{37} - 14 q^{38} - 8 q^{39} - 7 q^{40} + 18 q^{41} + 7 q^{42} - 10 q^{43} + 5 q^{44} + 27 q^{45} - 2 q^{46} - 20 q^{47} - q^{48} + 13 q^{49} - 20 q^{50} - q^{51} + 25 q^{52} - 7 q^{53} + 10 q^{54} + 29 q^{55} + 17 q^{57} - 18 q^{58} - 9 q^{59} - 5 q^{60} + 30 q^{61} - 6 q^{62} - 47 q^{63} + 9 q^{64} + 8 q^{65} + 9 q^{66} + 6 q^{67} + 9 q^{68} + 20 q^{69} + 17 q^{70} + 30 q^{71} - 20 q^{72} - 11 q^{74} - 7 q^{75} + 14 q^{76} - 3 q^{77} + 8 q^{78} + 29 q^{79} + 7 q^{80} - 3 q^{81} - 18 q^{82} + 9 q^{83} - 7 q^{84} + 7 q^{85} + 10 q^{86} + 44 q^{87} - 5 q^{88} + 8 q^{89} - 27 q^{90} + 13 q^{91} + 2 q^{92} + 7 q^{93} + 20 q^{94} + 27 q^{95} + q^{96} - 13 q^{97} - 13 q^{98} - 19 q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - q^3 + 9 * q^4 + 7 * q^5 + q^6 - 9 * q^8 + 20 * q^9 - 7 * q^10 + 5 * q^11 - q^12 + 25 * q^13 - 5 * q^15 + 9 * q^16 + 9 * q^17 - 20 * q^18 + 14 * q^19 + 7 * q^20 - 7 * q^21 - 5 * q^22 + 2 * q^23 + q^24 + 20 * q^25 - 25 * q^26 - 10 * q^27 + 18 * q^29 + 5 * q^30 + 6 * q^31 - 9 * q^32 - 9 * q^33 - 9 * q^34 - 17 * q^35 + 20 * q^36 + 11 * q^37 - 14 * q^38 - 8 * q^39 - 7 * q^40 + 18 * q^41 + 7 * q^42 - 10 * q^43 + 5 * q^44 + 27 * q^45 - 2 * q^46 - 20 * q^47 - q^48 + 13 * q^49 - 20 * q^50 - q^51 + 25 * q^52 - 7 * q^53 + 10 * q^54 + 29 * q^55 + 17 * q^57 - 18 * q^58 - 9 * q^59 - 5 * q^60 + 30 * q^61 - 6 * q^62 - 47 * q^63 + 9 * q^64 + 8 * q^65 + 9 * q^66 + 6 * q^67 + 9 * q^68 + 20 * q^69 + 17 * q^70 + 30 * q^71 - 20 * q^72 - 11 * q^74 - 7 * q^75 + 14 * q^76 - 3 * q^77 + 8 * q^78 + 29 * q^79 + 7 * q^80 - 3 * q^81 - 18 * q^82 + 9 * q^83 - 7 * q^84 + 7 * q^85 + 10 * q^86 + 44 * q^87 - 5 * q^88 + 8 * q^89 - 27 * q^90 + 13 * q^91 + 2 * q^92 + 7 * q^93 + 20 * q^94 + 27 * q^95 + q^96 - 13 * q^97 - 13 * q^98 - 19 * q^99

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