LMFDB - Embedded newform 667.2.a.d.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [667,2,Mod(1,667)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(667, 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("667.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 667 = 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	667.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:	$5.32602181482$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} - 22 x^{14} + 68 x^{13} + 187 x^{12} - 597 x^{11} - 795 x^{10} + 2592 x^{9} + \cdots + 64 $ x^16 - 3x^15 - 22x^14 + 68x^13 + 187x^12 - 597x^11 - 795x^10 + 2592x^9 + 1860x^8 - 5877x^7 - 2496x^6 + 6612x^5 + 1842x^4 - 3011x^3 - 505x^2 + 336*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.80038$ of defining polynomial
Character	$\chi$	$=$	667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.80038 q^{2} -3.34524 q^{3} +1.24138 q^{4} +2.67126 q^{5} +6.02272 q^{6} +1.66993 q^{7} +1.36580 q^{8} +8.19063 q^{9} +O(q^{10})$	\(q-1.80038 q^{2} -3.34524 q^{3} +1.24138 q^{4} +2.67126 q^{5} +6.02272 q^{6} +1.66993 q^{7} +1.36580 q^{8} +8.19063 q^{9} -4.80929 q^{10} -2.09236 q^{11} -4.15273 q^{12} +2.30892 q^{13} -3.00652 q^{14} -8.93599 q^{15} -4.94173 q^{16} +3.16946 q^{17} -14.7463 q^{18} +0.855823 q^{19} +3.31605 q^{20} -5.58633 q^{21} +3.76705 q^{22} +1.00000 q^{23} -4.56893 q^{24} +2.13561 q^{25} -4.15695 q^{26} -17.3639 q^{27} +2.07303 q^{28} -1.00000 q^{29} +16.0882 q^{30} -7.33040 q^{31} +6.16542 q^{32} +6.99945 q^{33} -5.70624 q^{34} +4.46082 q^{35} +10.1677 q^{36} +6.32439 q^{37} -1.54081 q^{38} -7.72390 q^{39} +3.64840 q^{40} -0.237540 q^{41} +10.0575 q^{42} +9.69447 q^{43} -2.59742 q^{44} +21.8793 q^{45} -1.80038 q^{46} +6.83751 q^{47} +16.5313 q^{48} -4.21132 q^{49} -3.84491 q^{50} -10.6026 q^{51} +2.86626 q^{52} +2.54640 q^{53} +31.2617 q^{54} -5.58923 q^{55} +2.28080 q^{56} -2.86293 q^{57} +1.80038 q^{58} +9.30330 q^{59} -11.0930 q^{60} +5.36437 q^{61} +13.1975 q^{62} +13.6778 q^{63} -1.21665 q^{64} +6.16772 q^{65} -12.6017 q^{66} -4.05341 q^{67} +3.93451 q^{68} -3.34524 q^{69} -8.03120 q^{70} -9.77123 q^{71} +11.1868 q^{72} -14.4287 q^{73} -11.3863 q^{74} -7.14412 q^{75} +1.06241 q^{76} -3.49410 q^{77} +13.9060 q^{78} -5.24323 q^{79} -13.2006 q^{80} +33.5145 q^{81} +0.427664 q^{82} +14.5348 q^{83} -6.93478 q^{84} +8.46643 q^{85} -17.4538 q^{86} +3.34524 q^{87} -2.85775 q^{88} +4.00108 q^{89} -39.3911 q^{90} +3.85575 q^{91} +1.24138 q^{92} +24.5219 q^{93} -12.3101 q^{94} +2.28612 q^{95} -20.6248 q^{96} -18.5247 q^{97} +7.58199 q^{98} -17.1377 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{2} + 5 q^{3} + 21 q^{4} + 16 q^{5} + 6 q^{6} + q^{7} + 9 q^{8} + 23 q^{9}+O(q^{10}) $ 16 * q + 3 * q^2 + 5 * q^3 + 21 * q^4 + 16 * q^5 + 6 * q^6 + q^7 + 9 * q^8 + 23 * q^9	\( 16 q + 3 q^{2} + 5 q^{3} + 21 q^{4} + 16 q^{5} + 6 q^{6} + q^{7} + 9 q^{8} + 23 q^{9} - 14 q^{10} + 4 q^{11} + 3 q^{12} + 15 q^{13} + 8 q^{14} + 8 q^{15} + 23 q^{16} + 20 q^{17} + 2 q^{18} - 4 q^{19} + 25 q^{20} + 5 q^{21} + 13 q^{22} + 16 q^{23} - 24 q^{24} + 30 q^{25} + 25 q^{26} + 8 q^{27} - 13 q^{28} - 16 q^{29} - 45 q^{30} - 19 q^{32} + q^{33} - 23 q^{34} + 5 q^{35} + 37 q^{36} + 5 q^{37} + 38 q^{38} - 10 q^{39} - 20 q^{40} + 7 q^{41} + 14 q^{42} - 17 q^{43} - 21 q^{44} + 48 q^{45} + 3 q^{46} + 29 q^{47} + 35 q^{48} + 31 q^{49} - 44 q^{50} - 14 q^{51} + 20 q^{52} + 63 q^{53} - 13 q^{54} + q^{55} - 19 q^{56} - 22 q^{57} - 3 q^{58} + 11 q^{59} - 3 q^{60} + 33 q^{62} - 33 q^{63} + 29 q^{64} + 53 q^{65} - 43 q^{66} - 13 q^{67} + 63 q^{68} + 5 q^{69} - 46 q^{70} - 23 q^{71} + 46 q^{72} - 38 q^{73} - 47 q^{74} + 37 q^{75} - 56 q^{76} + 97 q^{77} - 24 q^{78} - 27 q^{79} + 8 q^{80} + 40 q^{81} + 9 q^{82} + 36 q^{83} + 22 q^{84} + 6 q^{85} - 11 q^{86} - 5 q^{87} - 24 q^{88} - 16 q^{89} - 95 q^{90} - 47 q^{91} + 21 q^{92} + 62 q^{93} + 37 q^{94} - 12 q^{95} - 74 q^{96} - 30 q^{97} - 27 q^{98} - 42 q^{99}+O(q^{100}) \) 16 * q + 3 * q^2 + 5 * q^3 + 21 * q^4 + 16 * q^5 + 6 * q^6 + q^7 + 9 * q^8 + 23 * q^9 - 14 * q^10 + 4 * q^11 + 3 * q^12 + 15 * q^13 + 8 * q^14 + 8 * q^15 + 23 * q^16 + 20 * q^17 + 2 * q^18 - 4 * q^19 + 25 * q^20 + 5 * q^21 + 13 * q^22 + 16 * q^23 - 24 * q^24 + 30 * q^25 + 25 * q^26 + 8 * q^27 - 13 * q^28 - 16 * q^29 - 45 * q^30 - 19 * q^32 + q^33 - 23 * q^34 + 5 * q^35 + 37 * q^36 + 5 * q^37 + 38 * q^38 - 10 * q^39 - 20 * q^40 + 7 * q^41 + 14 * q^42 - 17 * q^43 - 21 * q^44 + 48 * q^45 + 3 * q^46 + 29 * q^47 + 35 * q^48 + 31 * q^49 - 44 * q^50 - 14 * q^51 + 20 * q^52 + 63 * q^53 - 13 * q^54 + q^55 - 19 * q^56 - 22 * q^57 - 3 * q^58 + 11 * q^59 - 3 * q^60 + 33 * q^62 - 33 * q^63 + 29 * q^64 + 53 * q^65 - 43 * q^66 - 13 * q^67 + 63 * q^68 + 5 * q^69 - 46 * q^70 - 23 * q^71 + 46 * q^72 - 38 * q^73 - 47 * q^74 + 37 * q^75 - 56 * q^76 + 97 * q^77 - 24 * q^78 - 27 * q^79 + 8 * q^80 + 40 * q^81 + 9 * q^82 + 36 * q^83 + 22 * q^84 + 6 * q^85 - 11 * q^86 - 5 * q^87 - 24 * q^88 - 16 * q^89 - 95 * q^90 - 47 * q^91 + 21 * q^92 + 62 * q^93 + 37 * q^94 - 12 * q^95 - 74 * q^96 - 30 * q^97 - 27 * q^98 - 42 * 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 $

$2$	−1.80038	−1.27306	−0.636532	−	0.771250i	$-0.719632\pi$
$2$	−1.80038	−1.27306	−0.636532	+	0.771250i	$0.719632\pi$
$3$	−3.34524	−1.93138	−0.965688	−	0.259706i	$-0.916374\pi$
$3$	−3.34524	−1.93138	−0.965688	+	0.259706i	$0.916374\pi$
$4$	1.24138	0.620692
$5$	2.67126	1.19462	0.597311	−	0.802010i	$-0.296236\pi$
$5$	2.67126	1.19462	0.597311	+	0.802010i	$0.296236\pi$
$6$	6.02272	2.45876
$7$	1.66993	0.631176	0.315588	−	0.948896i	$-0.397798\pi$
$7$	1.66993	0.631176	0.315588	+	0.948896i	$0.397798\pi$
$8$	1.36580	0.482884
$9$	8.19063	2.73021
$10$	−4.80929	−1.52083
$11$	−2.09236	−0.630870	−0.315435	−	0.948947i	$-0.602150\pi$
$11$	−2.09236	−0.630870	−0.315435	+	0.948947i	$0.602150\pi$
$12$	−4.15273	−1.19879
$13$	2.30892	0.640380	0.320190	−	0.947353i	$-0.396253\pi$
$13$	2.30892	0.640380	0.320190	+	0.947353i	$0.396253\pi$
$14$	−3.00652	−0.803527
$15$	−8.93599	−2.30726
$16$	−4.94173	−1.23543
$17$	3.16946	0.768706	0.384353	−	0.923186i	$-0.374425\pi$
$17$	3.16946	0.768706	0.384353	+	0.923186i	$0.374425\pi$
$18$	−14.7463	−3.47573
$19$	0.855823	0.196339	0.0981697	−	0.995170i	$-0.468701\pi$
$19$	0.855823	0.196339	0.0981697	+	0.995170i	$0.468701\pi$
$20$	3.31605	0.741492
$21$	−5.58633	−1.21904
$22$	3.76705	0.803138
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−4.56893	−0.932630
$25$	2.13561	0.427122
$26$	−4.15695	−0.815244
$27$	−17.3639	−3.34169
$28$	2.07303	0.391766
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	16.0882	2.93729
$31$	−7.33040	−1.31658	−0.658289	−	0.752765i	$-0.728720\pi$
$31$	−7.33040	−1.31658	−0.658289	+	0.752765i	$0.728720\pi$
$32$	6.16542	1.08990
$33$	6.99945	1.21845
$34$	−5.70624	−0.978612
$35$	4.46082	0.754017
$36$	10.1677	1.69462
$37$	6.32439	1.03972	0.519862	−	0.854251i	$-0.325984\pi$
$37$	6.32439	1.03972	0.519862	+	0.854251i	$0.325984\pi$
$38$	−1.54081	−0.249953
$39$	−7.72390	−1.23681
$40$	3.64840	0.576863
$41$	−0.237540	−0.0370976	−0.0185488	−	0.999828i	$-0.505905\pi$
$41$	−0.237540	−0.0370976	−0.0185488	+	0.999828i	$0.505905\pi$
$42$	10.0575	1.55191
$43$	9.69447	1.47839	0.739196	−	0.673490i	$-0.235206\pi$
$43$	9.69447	1.47839	0.739196	+	0.673490i	$0.235206\pi$
$44$	−2.59742	−0.391576
$45$	21.8793	3.26157
$46$	−1.80038	−0.265452
$47$	6.83751	0.997353	0.498677	−	0.866788i	$-0.333819\pi$
$47$	6.83751	0.997353	0.498677	+	0.866788i	$0.333819\pi$
$48$	16.5313	2.38609
$49$	−4.21132	−0.601617
$50$	−3.84491	−0.543753
$51$	−10.6026	−1.48466
$52$	2.86626	0.397478
$53$	2.54640	0.349775	0.174888	−	0.984588i	$-0.444044\pi$
$53$	2.54640	0.349775	0.174888	+	0.984588i	$0.444044\pi$
$54$	31.2617	4.25418
$55$	−5.58923	−0.753651
$56$	2.28080	0.304785
$57$	−2.86293	−0.379205
$58$	1.80038	0.236402
$59$	9.30330	1.21119	0.605593	−	0.795774i	$-0.292936\pi$
$59$	9.30330	1.21119	0.605593	+	0.795774i	$0.292936\pi$
$60$	−11.0930	−1.43210
$61$	5.36437	0.686837	0.343419	−	0.939182i	$-0.388415\pi$
$61$	5.36437	0.686837	0.343419	+	0.939182i	$0.388415\pi$
$62$	13.1975	1.67609
$63$	13.6778	1.72324
$64$	−1.21665	−0.152082
$65$	6.16772	0.765011
$66$	−12.6017	−1.55116
$67$	−4.05341	−0.495202	−0.247601	−	0.968862i	$-0.579642\pi$
$67$	−4.05341	−0.495202	−0.247601	+	0.968862i	$0.579642\pi$
$68$	3.93451	0.477129
$69$	−3.34524	−0.402720
$70$	−8.03120	−0.959911
$71$	−9.77123	−1.15963	−0.579816	−	0.814747i	$-0.696876\pi$
$71$	−9.77123	−1.15963	−0.579816	+	0.814747i	$0.696876\pi$
$72$	11.1868	1.31837
$73$	−14.4287	−1.68875	−0.844375	−	0.535753i	$-0.820028\pi$
$73$	−14.4287	−1.68875	−0.844375	+	0.535753i	$0.820028\pi$
$74$	−11.3863	−1.32363
$75$	−7.14412	−0.824932
$76$	1.06241	0.121866
$77$	−3.49410	−0.398190
$78$	13.9060	1.57454
$79$	−5.24323	−0.589909	−0.294955	−	0.955511i	$-0.595305\pi$
$79$	−5.24323	−0.589909	−0.294955	+	0.955511i	$0.595305\pi$
$80$	−13.2006	−1.47588
$81$	33.5145	3.72384
$82$	0.427664	0.0472276
$83$	14.5348	1.59540	0.797700	−	0.603054i	$-0.206050\pi$
$83$	14.5348	1.59540	0.797700	+	0.603054i	$0.206050\pi$
$84$	−6.93478	−0.756647
$85$	8.46643	0.918313
$86$	−17.4538	−1.88209
$87$	3.34524	0.358647
$88$	−2.85775	−0.304637
$89$	4.00108	0.424113	0.212057	−	0.977257i	$-0.431984\pi$
$89$	4.00108	0.424113	0.212057	+	0.977257i	$0.431984\pi$
$90$	−39.3911	−4.15219
$91$	3.85575	0.404192
$92$	1.24138	0.129423
$93$	24.5219	2.54281
$94$	−12.3101	−1.26969
$95$	2.28612	0.234551
$96$	−20.6248	−2.10501
$97$	−18.5247	−1.88090	−0.940448	−	0.339938i	$-0.889594\pi$
$97$	−18.5247	−1.88090	−0.940448	+	0.339938i	$0.889594\pi$
$98$	7.58199	0.765897
$99$	−17.1377	−1.72241
$100$	2.65111	0.265111
$101$	9.44544	0.939856	0.469928	−	0.882705i	$-0.344280\pi$
$101$	9.44544	0.939856	0.469928	+	0.882705i	$0.344280\pi$
$102$	19.0887	1.89007
$103$	10.1223	0.997377	0.498688	−	0.866781i	$-0.333815\pi$
$103$	10.1223	0.997377	0.498688	+	0.866781i	$0.333815\pi$
$104$	3.15353	0.309229
$105$	−14.9225	−1.45629
$106$	−4.58450	−0.445286
$107$	6.37046	0.615856	0.307928	−	0.951410i	$-0.400364\pi$
$107$	6.37046	0.615856	0.307928	+	0.951410i	$0.400364\pi$
$108$	−21.5553	−2.07416
$109$	−0.657653	−0.0629917	−0.0314958	−	0.999504i	$-0.510027\pi$
$109$	−0.657653	−0.0629917	−0.0314958	+	0.999504i	$0.510027\pi$
$110$	10.0628	0.959446
$111$	−21.1566	−2.00810
$112$	−8.25237	−0.779776
$113$	2.91640	0.274351	0.137176	−	0.990547i	$-0.456198\pi$
$113$	2.91640	0.274351	0.137176	+	0.990547i	$0.456198\pi$
$114$	5.15438	0.482752
$115$	2.67126	0.249096
$116$	−1.24138	−0.115260
$117$	18.9115	1.74837
$118$	−16.7495	−1.54192
$119$	5.29278	0.485189
$120$	−12.2048	−1.11414
$121$	−6.62203	−0.602003
$122$	−9.65793	−0.874388
$123$	0.794629	0.0716493
$124$	−9.09983	−0.817189
$125$	−7.65152	−0.684373
$126$	−24.6253	−2.19380
$127$	−1.13798	−0.100979	−0.0504895	−	0.998725i	$-0.516078\pi$
$127$	−1.13798	−0.100979	−0.0504895	+	0.998725i	$0.516078\pi$
$128$	−10.1404	−0.896293
$129$	−32.4303	−2.85533
$130$	−11.1043	−0.973909
$131$	2.97772	0.260165	0.130082	−	0.991503i	$-0.458476\pi$
$131$	2.97772	0.260165	0.130082	+	0.991503i	$0.458476\pi$
$132$	8.68900	0.756280
$133$	1.42917	0.123925
$134$	7.29769	0.630424
$135$	−46.3834	−3.99205
$136$	4.32885	0.371196
$137$	22.1228	1.89008	0.945040	−	0.326954i	$-0.106022\pi$
$137$	22.1228	1.89008	0.945040	+	0.326954i	$0.106022\pi$
$138$	6.02272	0.512688
$139$	14.5315	1.23255	0.616275	−	0.787531i	$-0.288641\pi$
$139$	14.5315	1.23255	0.616275	+	0.787531i	$0.288641\pi$
$140$	5.53759	0.468012
$141$	−22.8731	−1.92626
$142$	17.5920	1.47629
$143$	−4.83109	−0.403996
$144$	−40.4759	−3.37299
$145$	−2.67126	−0.221836
$146$	25.9772	2.14989
$147$	14.0879	1.16195
$148$	7.85099	0.645348
$149$	9.69697	0.794407	0.397203	−	0.917731i	$-0.369981\pi$
$149$	9.69697	0.794407	0.397203	+	0.917731i	$0.369981\pi$
$150$	12.8622	1.05019
$151$	18.7262	1.52392	0.761958	−	0.647627i	$-0.224238\pi$
$151$	18.7262	1.52392	0.761958	+	0.647627i	$0.224238\pi$
$152$	1.16888	0.0948091
$153$	25.9598	2.09873
$154$	6.29073	0.506922
$155$	−19.5814	−1.57281
$156$	−9.58832	−0.767680
$157$	16.7286	1.33508	0.667542	−	0.744572i	$-0.267346\pi$
$157$	16.7286	1.33508	0.667542	+	0.744572i	$0.267346\pi$
$158$	9.43983	0.750992
$159$	−8.51832	−0.675547
$160$	16.4694	1.30202
$161$	1.66993	0.131609
$162$	−60.3391	−4.74068
$163$	−15.6039	−1.22219	−0.611095	−	0.791557i	$-0.709271\pi$
$163$	−15.6039	−1.22219	−0.611095	+	0.791557i	$0.709271\pi$
$164$	−0.294879	−0.0230261
$165$	18.6973	1.45558
$166$	−26.1682	−2.03105
$167$	12.0575	0.933041	0.466521	−	0.884510i	$-0.345507\pi$
$167$	12.0575	0.933041	0.466521	+	0.884510i	$0.345507\pi$
$168$	−7.62982	−0.588653
$169$	−7.66888	−0.589914
$170$	−15.2428	−1.16907
$171$	7.00973	0.536048
$172$	12.0346	0.917626
$173$	18.7908	1.42863	0.714317	−	0.699822i	$-0.246737\pi$
$173$	18.7908	1.42863	0.714317	+	0.699822i	$0.246737\pi$
$174$	−6.02272	−0.456581
$175$	3.56633	0.269589
$176$	10.3399	0.779398
$177$	−31.1218	−2.33926
$178$	−7.20348	−0.539923
$179$	−11.4827	−0.858257	−0.429129	−	0.903243i	$-0.641179\pi$
$179$	−11.4827	−0.858257	−0.429129	+	0.903243i	$0.641179\pi$
$180$	27.1606	2.02443
$181$	5.39334	0.400884	0.200442	−	0.979706i	$-0.435762\pi$
$181$	5.39334	0.400884	0.200442	+	0.979706i	$0.435762\pi$
$182$	−6.94183	−0.514563
$183$	−17.9451	−1.32654
$184$	1.36580	0.100688
$185$	16.8941	1.24208
$186$	−44.1489	−3.23716
$187$	−6.63164	−0.484954
$188$	8.48797	0.619049
$189$	−28.9966	−2.10919
$190$	−4.11590	−0.298599
$191$	22.0948	1.59873	0.799363	−	0.600848i	$-0.205170\pi$
$191$	22.0948	1.59873	0.799363	+	0.600848i	$0.205170\pi$
$192$	4.07000	0.293727
$193$	16.9225	1.21811	0.609053	−	0.793130i	$-0.291550\pi$
$193$	16.9225	1.21811	0.609053	+	0.793130i	$0.291550\pi$
$194$	33.3515	2.39450
$195$	−20.6325	−1.47752
$196$	−5.22786	−0.373419
$197$	−9.01852	−0.642543	−0.321272	−	0.946987i	$-0.604110\pi$
$197$	−9.01852	−0.642543	−0.321272	+	0.946987i	$0.604110\pi$
$198$	30.8545	2.19274
$199$	−19.6161	−1.39055	−0.695274	−	0.718745i	$-0.744717\pi$
$199$	−19.6161	−1.39055	−0.695274	+	0.718745i	$0.744717\pi$
$200$	2.91682	0.206250
$201$	13.5596	0.956422
$202$	−17.0054	−1.19650
$203$	−1.66993	−0.117206
$204$	−13.1619	−0.921516
$205$	−0.634531	−0.0443176
$206$	−18.2240	−1.26972
$207$	8.19063	0.569288
$208$	−11.4101	−0.791146
$209$	−1.79069	−0.123865
$210$	26.8663	1.85395
$211$	17.7261	1.22032	0.610159	−	0.792279i	$-0.291106\pi$
$211$	17.7261	1.22032	0.610159	+	0.792279i	$0.291106\pi$
$212$	3.16106	0.217103
$213$	32.6871	2.23968
$214$	−11.4693	−0.784023
$215$	25.8964	1.76612
$216$	−23.7156	−1.61365
$217$	−12.2413	−0.830993
$218$	1.18403	0.0801925
$219$	48.2674	3.26161
$220$	−6.93838	−0.467785
$221$	7.31802	0.492264
$222$	38.0900	2.55643
$223$	−9.50918	−0.636782	−0.318391	−	0.947959i	$-0.603142\pi$
$223$	−9.50918	−0.636782	−0.318391	+	0.947959i	$0.603142\pi$
$224$	10.2958	0.687920
$225$	17.4920	1.16613
$226$	−5.25063	−0.349267
$227$	−9.15505	−0.607642	−0.303821	−	0.952729i	$-0.598263\pi$
$227$	−9.15505	−0.607642	−0.303821	+	0.952729i	$0.598263\pi$
$228$	−3.55400	−0.235369
$229$	16.5585	1.09422	0.547108	−	0.837062i	$-0.315729\pi$
$229$	16.5585	1.09422	0.547108	+	0.837062i	$0.315729\pi$
$230$	−4.80929	−0.317115
$231$	11.6886	0.769055
$232$	−1.36580	−0.0896692
$233$	5.52661	0.362060	0.181030	−	0.983478i	$-0.442057\pi$
$233$	5.52661	0.362060	0.181030	+	0.983478i	$0.442057\pi$
$234$	−34.0480	−2.22579
$235$	18.2647	1.19146
$236$	11.5490	0.751773
$237$	17.5399	1.13934
$238$	−9.52905	−0.617676
$239$	−19.4467	−1.25790	−0.628950	−	0.777446i	$-0.716515\pi$
$239$	−19.4467	−1.25790	−0.628950	+	0.777446i	$0.716515\pi$
$240$	44.1593	2.85047
$241$	−18.1428	−1.16868	−0.584341	−	0.811508i	$-0.698647\pi$
$241$	−18.1428	−1.16868	−0.584341	+	0.811508i	$0.698647\pi$
$242$	11.9222	0.766388
$243$	−60.0225	−3.85044
$244$	6.65924	0.426314
$245$	−11.2495	−0.718705
$246$	−1.43064	−0.0912141
$247$	1.97603	0.125732
$248$	−10.0119	−0.635754
$249$	−48.6224	−3.08132
$250$	13.7757	0.871251
$251$	27.9363	1.76332	0.881661	−	0.471883i	$-0.156425\pi$
$251$	27.9363	1.76332	0.881661	+	0.471883i	$0.156425\pi$
$252$	16.9794	1.06960
$253$	−2.09236	−0.131546
$254$	2.04879	0.128553
$255$	−28.3222	−1.77361
$256$	20.6899	1.29312
$257$	−24.5000	−1.52827	−0.764133	−	0.645059i	$-0.776833\pi$
$257$	−24.5000	−1.52827	−0.764133	+	0.645059i	$0.776833\pi$
$258$	58.3870	3.63502
$259$	10.5613	0.656248
$260$	7.65651	0.474836
$261$	−8.19063	−0.506987
$262$	−5.36104	−0.331206
$263$	26.5801	1.63900	0.819500	−	0.573079i	$-0.194251\pi$
$263$	26.5801	1.63900	0.819500	+	0.573079i	$0.194251\pi$
$264$	9.55985	0.588368
$265$	6.80209	0.417849
$266$	−2.57305	−0.157764
$267$	−13.3846	−0.819122
$268$	−5.03183	−0.307368
$269$	−11.6472	−0.710145	−0.355072	−	0.934839i	$-0.615544\pi$
$269$	−11.6472	−0.710145	−0.355072	+	0.934839i	$0.615544\pi$
$270$	83.5080	5.08214
$271$	3.26194	0.198149	0.0990744	−	0.995080i	$-0.468412\pi$
$271$	3.26194	0.198149	0.0990744	+	0.995080i	$0.468412\pi$
$272$	−15.6626	−0.949685
$273$	−12.8984	−0.780647
$274$	−39.8296	−2.40619
$275$	−4.46846	−0.269458
$276$	−4.15273	−0.249965
$277$	−30.3851	−1.82567	−0.912833	−	0.408333i	$-0.866110\pi$
$277$	−30.3851	−1.82567	−0.912833	+	0.408333i	$0.866110\pi$
$278$	−26.1624	−1.56911
$279$	−60.0406	−3.59454
$280$	6.09260	0.364102
$281$	2.54033	0.151544	0.0757718	−	0.997125i	$-0.475858\pi$
$281$	2.54033	0.151544	0.0757718	+	0.997125i	$0.475858\pi$
$282$	41.1804	2.45226
$283$	−7.86054	−0.467260	−0.233630	−	0.972326i	$-0.575061\pi$
$283$	−7.86054	−0.467260	−0.233630	+	0.972326i	$0.575061\pi$
$284$	−12.1298	−0.719774
$285$	−7.64763	−0.453007
$286$	8.69783	0.514313
$287$	−0.396677	−0.0234151
$288$	50.4987	2.97566
$289$	−6.95455	−0.409091
$290$	4.80929	0.282411
$291$	61.9695	3.63272
$292$	−17.9115	−1.04819
$293$	−21.4677	−1.25416	−0.627079	−	0.778955i	$-0.715750\pi$
$293$	−21.4677	−1.25416	−0.627079	+	0.778955i	$0.715750\pi$
$294$	−25.3636	−1.47923
$295$	24.8515	1.44691
$296$	8.63786	0.502065
$297$	36.3315	2.10817
$298$	−17.4583	−1.01133
$299$	2.30892	0.133528
$300$	−8.86859	−0.512028
$301$	16.1891	0.933126
$302$	−33.7143	−1.94004
$303$	−31.5973	−1.81522
$304$	−4.22925	−0.242564
$305$	14.3296	0.820511
$306$	−46.7377	−2.67182
$307$	−10.7356	−0.612715	−0.306358	−	0.951916i	$-0.599110\pi$
$307$	−10.7356	−0.612715	−0.306358	+	0.951916i	$0.599110\pi$
$308$	−4.33752	−0.247153
$309$	−33.8614	−1.92631
$310$	35.2540	2.00229
$311$	2.06047	0.116838	0.0584192	−	0.998292i	$-0.481394\pi$
$311$	2.06047	0.116838	0.0584192	+	0.998292i	$0.481394\pi$
$312$	−10.5493	−0.597237
$313$	21.2563	1.20148	0.600738	−	0.799446i	$-0.294873\pi$
$313$	21.2563	1.20148	0.600738	+	0.799446i	$0.294873\pi$
$314$	−30.1178	−1.69965
$315$	36.5370	2.05862
$316$	−6.50886	−0.366152
$317$	2.75770	0.154888	0.0774439	−	0.996997i	$-0.475324\pi$
$317$	2.75770	0.154888	0.0774439	+	0.996997i	$0.475324\pi$
$318$	15.3363	0.860014
$319$	2.09236	0.117150
$320$	−3.24999	−0.181680
$321$	−21.3107	−1.18945
$322$	−3.00652	−0.167547
$323$	2.71249	0.150927
$324$	41.6044	2.31136
$325$	4.93095	0.273520
$326$	28.0930	1.55593
$327$	2.20001	0.121661
$328$	−0.324433	−0.0179138
$329$	11.4182	0.629506
$330$	−33.6623	−1.85305
$331$	−11.5054	−0.632394	−0.316197	−	0.948694i	$-0.602406\pi$
$331$	−11.5054	−0.632394	−0.316197	+	0.948694i	$0.602406\pi$
$332$	18.0432	0.990252
$333$	51.8007	2.83866
$334$	−21.7082	−1.18782
$335$	−10.8277	−0.591580
$336$	27.6062	1.50604
$337$	33.6508	1.83307	0.916537	−	0.399950i	$-0.130972\pi$
$337$	33.6508	1.83307	0.916537	+	0.399950i	$0.130972\pi$
$338$	13.8069	0.750998
$339$	−9.75604	−0.529875
$340$	10.5101	0.569989
$341$	15.3378	0.830590
$342$	−12.6202	−0.682423
$343$	−18.7222	−1.01090
$344$	13.2407	0.713892
$345$	−8.93599	−0.481098
$346$	−33.8306	−1.81874
$347$	13.9776	0.750355	0.375178	−	0.926953i	$-0.377582\pi$
$347$	13.9776	0.750355	0.375178	+	0.926953i	$0.377582\pi$
$348$	4.15273	0.222609
$349$	1.32730	0.0710485	0.0355243	−	0.999369i	$-0.488690\pi$
$349$	1.32730	0.0710485	0.0355243	+	0.999369i	$0.488690\pi$
$350$	−6.42076	−0.343204
$351$	−40.0919	−2.13995
$352$	−12.9003	−0.687587
$353$	−1.02867	−0.0547506	−0.0273753	−	0.999625i	$-0.508715\pi$
$353$	−1.02867	−0.0547506	−0.0273753	+	0.999625i	$0.508715\pi$
$354$	56.0312	2.97802
$355$	−26.1015	−1.38532
$356$	4.96687	0.263244
$357$	−17.7056	−0.937081
$358$	20.6733	1.09262
$359$	−20.5700	−1.08564	−0.542822	−	0.839848i	$-0.682644\pi$
$359$	−20.5700	−1.08564	−0.542822	+	0.839848i	$0.682644\pi$
$360$	29.8827	1.57496
$361$	−18.2676	−0.961451
$362$	−9.71008	−0.510350
$363$	22.1523	1.16269
$364$	4.78646	0.250879
$365$	−38.5427	−2.01742
$366$	32.3081	1.68877
$367$	−24.0628	−1.25607	−0.628033	−	0.778187i	$-0.716140\pi$
$367$	−24.0628	−1.25607	−0.628033	+	0.778187i	$0.716140\pi$
$368$	−4.94173	−0.257606
$369$	−1.94560	−0.101284
$370$	−30.4158	−1.58124
$371$	4.25232	0.220770
$372$	30.4411	1.57830
$373$	10.9453	0.566726	0.283363	−	0.959013i	$-0.408550\pi$
$373$	10.9453	0.566726	0.283363	+	0.959013i	$0.408550\pi$
$374$	11.9395	0.617377
$375$	25.5962	1.32178
$376$	9.33868	0.481606
$377$	−2.30892	−0.118916
$378$	52.2050	2.68514
$379$	−12.4616	−0.640110	−0.320055	−	0.947399i	$-0.603701\pi$
$379$	−12.4616	−0.640110	−0.320055	+	0.947399i	$0.603701\pi$
$380$	2.83796	0.145584
$381$	3.80680	0.195028
$382$	−39.7792	−2.03528
$383$	0.0834058	0.00426184	0.00213092	−	0.999998i	$-0.499322\pi$
$383$	0.0834058	0.00426184	0.00213092	+	0.999998i	$0.499322\pi$
$384$	33.9220	1.73108
$385$	−9.33365	−0.475687
$386$	−30.4669	−1.55073
$387$	79.4038	4.03632
$388$	−22.9962	−1.16746
$389$	−13.6022	−0.689659	−0.344830	−	0.938665i	$-0.612063\pi$
$389$	−13.6022	−0.689659	−0.344830	+	0.938665i	$0.612063\pi$
$390$	37.1464	1.88098
$391$	3.16946	0.160286
$392$	−5.75182	−0.290511
$393$	−9.96119	−0.502476
$394$	16.2368	0.817999
$395$	−14.0060	−0.704719
$396$	−21.2745	−1.06908
$397$	26.2001	1.31495	0.657474	−	0.753477i	$-0.271625\pi$
$397$	26.2001	1.31495	0.657474	+	0.753477i	$0.271625\pi$
$398$	35.3165	1.77026
$399$	−4.78091	−0.239345
$400$	−10.5536	−0.527680
$401$	27.3144	1.36402	0.682009	−	0.731344i	$-0.261106\pi$
$401$	27.3144	1.36402	0.682009	+	0.731344i	$0.261106\pi$
$402$	−24.4125	−1.21759
$403$	−16.9253	−0.843110
$404$	11.7254	0.583361
$405$	89.5259	4.44858
$406$	3.00652	0.149211
$407$	−13.2329	−0.655930
$408$	−14.4810	−0.716918
$409$	33.3682	1.64995	0.824975	−	0.565169i	$-0.191189\pi$
$409$	33.3682	1.64995	0.824975	+	0.565169i	$0.191189\pi$
$410$	1.14240	0.0564191
$411$	−74.0061	−3.65045
$412$	12.5656	0.619064
$413$	15.5359	0.764472
$414$	−14.7463	−0.724740
$415$	38.8261	1.90590
$416$	14.2355	0.697951
$417$	−48.6115	−2.38052
$418$	3.22393	0.157688
$419$	21.6033	1.05539	0.527696	−	0.849433i	$-0.323056\pi$
$419$	21.6033	1.05539	0.527696	+	0.849433i	$0.323056\pi$
$420$	−18.5246	−0.903907
$421$	−27.2802	−1.32956	−0.664779	−	0.747040i	$-0.731474\pi$
$421$	−27.2802	−1.32956	−0.664779	+	0.747040i	$0.731474\pi$
$422$	−31.9139	−1.55354
$423$	56.0035	2.72298
$424$	3.47788	0.168901
$425$	6.76871	0.328331
$426$	−58.8494	−2.85126
$427$	8.95815	0.433515
$428$	7.90818	0.382256
$429$	16.1612	0.780269
$430$	−46.6235	−2.24838
$431$	−9.04837	−0.435845	−0.217922	−	0.975966i	$-0.569928\pi$
$431$	−9.04837	−0.435845	−0.217922	+	0.975966i	$0.569928\pi$
$432$	85.8078	4.12843
$433$	16.4712	0.791554	0.395777	−	0.918347i	$-0.370475\pi$
$433$	16.4712	0.791554	0.395777	+	0.918347i	$0.370475\pi$
$434$	22.0390	1.05791
$435$	8.93599	0.428448
$436$	−0.816399	−0.0390984
$437$	0.855823	0.0409396
$438$	−86.8999	−4.15224
$439$	−18.3212	−0.874424	−0.437212	−	0.899359i	$-0.644034\pi$
$439$	−18.3212	−0.874424	−0.437212	+	0.899359i	$0.644034\pi$
$440$	−7.63378	−0.363926
$441$	−34.4933	−1.64254
$442$	−13.1753	−0.626683
$443$	−32.7174	−1.55445	−0.777226	−	0.629221i	$-0.783374\pi$
$443$	−32.7174	−1.55445	−0.777226	+	0.629221i	$0.783374\pi$
$444$	−26.2635	−1.24641
$445$	10.6879	0.506655
$446$	17.1202	0.810664
$447$	−32.4387	−1.53430
$448$	−2.03173	−0.0959903
$449$	−39.3491	−1.85700	−0.928499	−	0.371336i	$-0.878900\pi$
$449$	−39.3491	−1.85700	−0.928499	+	0.371336i	$0.878900\pi$
$450$	−31.4923	−1.48456
$451$	0.497020	0.0234037
$452$	3.62036	0.170288
$453$	−62.6436	−2.94325
$454$	16.4826	0.773567
$455$	10.2997	0.482857
$456$	−3.91020	−0.183112
$457$	34.7280	1.62451	0.812255	−	0.583303i	$-0.198240\pi$
$457$	34.7280	1.62451	0.812255	+	0.583303i	$0.198240\pi$
$458$	−29.8117	−1.39301
$459$	−55.0341	−2.56877
$460$	3.31605	0.154612
$461$	1.30696	0.0608714	0.0304357	−	0.999537i	$-0.490311\pi$
$461$	1.30696	0.0608714	0.0304357	+	0.999537i	$0.490311\pi$
$462$	−21.0440	−0.979056
$463$	28.5878	1.32859	0.664293	−	0.747472i	$-0.268733\pi$
$463$	28.5878	1.32859	0.664293	+	0.747472i	$0.268733\pi$
$464$	4.94173	0.229414
$465$	65.5044	3.03769
$466$	−9.95002	−0.460926
$467$	6.56840	0.303950	0.151975	−	0.988384i	$-0.451437\pi$
$467$	6.56840	0.303950	0.151975	+	0.988384i	$0.451437\pi$
$468$	23.4765	1.08520
$469$	−6.76892	−0.312560
$470$	−32.8836	−1.51681
$471$	−55.9611	−2.57855
$472$	12.7065	0.584862
$473$	−20.2843	−0.932674
$474$	−31.5785	−1.45045
$475$	1.82770	0.0838608
$476$	6.57037	0.301153
$477$	20.8566	0.954960
$478$	35.0115	1.60139
$479$	31.5136	1.43989	0.719947	−	0.694029i	$-0.244166\pi$
$479$	31.5136	1.43989	0.719947	+	0.694029i	$0.244166\pi$
$480$	−55.0941	−2.51469
$481$	14.6025	0.665817
$482$	32.6641	1.48781
$483$	−5.58633	−0.254187
$484$	−8.22048	−0.373658
$485$	−49.4842	−2.24696
$486$	108.064	4.90186
$487$	−8.38768	−0.380082	−0.190041	−	0.981776i	$-0.560862\pi$
$487$	−8.38768	−0.380082	−0.190041	+	0.981776i	$0.560862\pi$
$488$	7.32666	0.331662
$489$	52.1987	2.36051
$490$	20.2534	0.914957
$491$	−10.0413	−0.453155	−0.226578	−	0.973993i	$-0.572754\pi$
$491$	−10.0413	−0.453155	−0.226578	+	0.973993i	$0.572754\pi$
$492$	0.986439	0.0444721
$493$	−3.16946	−0.142745
$494$	−3.55761	−0.160065
$495$	−45.7793	−2.05763
$496$	36.2249	1.62654
$497$	−16.3173	−0.731932
$498$	87.5389	3.92271
$499$	11.9821	0.536392	0.268196	−	0.963364i	$-0.413573\pi$
$499$	11.9821	0.536392	0.268196	+	0.963364i	$0.413573\pi$
$500$	−9.49848	−0.424785
$501$	−40.3354	−1.80205
$502$	−50.2961	−2.24482
$503$	−6.68248	−0.297957	−0.148979	−	0.988840i	$-0.547599\pi$
$503$	−6.68248	−0.297957	−0.148979	+	0.988840i	$0.547599\pi$
$504$	18.6812	0.832126
$505$	25.2312	1.12277
$506$	3.76705	0.167466
$507$	25.6543	1.13935
$508$	−1.41266	−0.0626768
$509$	−20.9085	−0.926753	−0.463377	−	0.886161i	$-0.653362\pi$
$509$	−20.9085	−0.926753	−0.463377	+	0.886161i	$0.653362\pi$
$510$	50.9909	2.25791
$511$	−24.0950	−1.06590
$512$	−16.9690	−0.749931
$513$	−14.8604	−0.656104
$514$	44.1094	1.94558
$515$	27.0392	1.19149
$516$	−40.2585	−1.77228
$517$	−14.3065	−0.629201
$518$	−19.0144	−0.835446
$519$	−62.8596	−2.75923
$520$	8.42388	0.369412
$521$	13.9056	0.609216	0.304608	−	0.952478i	$-0.401474\pi$
$521$	13.9056	0.609216	0.304608	+	0.952478i	$0.401474\pi$
$522$	14.7463	0.645427
$523$	−10.5453	−0.461115	−0.230557	−	0.973059i	$-0.574055\pi$
$523$	−10.5453	−0.461115	−0.230557	+	0.973059i	$0.574055\pi$
$524$	3.69649	0.161482
$525$	−11.9302	−0.520677
$526$	−47.8544	−2.08655
$527$	−23.2334	−1.01206
$528$	−34.5894	−1.50531
$529$	1.00000	0.0434783
$530$	−12.2464	−0.531948
$531$	76.1999	3.30679
$532$	1.77415	0.0769190
$533$	−0.548462	−0.0237565
$534$	24.0974	1.04279
$535$	17.0171	0.735715
$536$	−5.53615	−0.239125
$537$	38.4124	1.65762
$538$	20.9695	0.904060
$539$	8.81159	0.379542
$540$	−57.5796	−2.47783
$541$	−34.2114	−1.47086	−0.735431	−	0.677600i	$-0.763020\pi$
$541$	−34.2114	−1.47086	−0.735431	+	0.677600i	$0.763020\pi$
$542$	−5.87275	−0.252256
$543$	−18.0420	−0.774257
$544$	19.5410	0.837814
$545$	−1.75676	−0.0752513
$546$	23.2221	0.993813
$547$	6.74782	0.288516	0.144258	−	0.989540i	$-0.453920\pi$
$547$	6.74782	0.288516	0.144258	+	0.989540i	$0.453920\pi$
$548$	27.4629	1.17316
$549$	43.9376	1.87521
$550$	8.04494	0.343038
$551$	−0.855823	−0.0364593
$552$	−4.56893	−0.194467
$553$	−8.75585	−0.372337
$554$	54.7049	2.32419
$555$	−56.5147	−2.39891
$556$	18.0392	0.765033
$557$	−19.2080	−0.813870	−0.406935	−	0.913457i	$-0.633403\pi$
$557$	−19.2080	−0.813870	−0.406935	+	0.913457i	$0.633403\pi$
$558$	108.096	4.57607
$559$	22.3838	0.946732
$560$	−22.0442	−0.931538
$561$	22.1844	0.936627
$562$	−4.57358	−0.192925
$563$	−6.69581	−0.282195	−0.141097	−	0.989996i	$-0.545063\pi$
$563$	−6.69581	−0.282195	−0.141097	+	0.989996i	$0.545063\pi$
$564$	−28.3943	−1.19562
$565$	7.79044	0.327746
$566$	14.1520	0.594852
$567$	55.9671	2.35040
$568$	−13.3456	−0.559967
$569$	−30.4923	−1.27830	−0.639151	−	0.769081i	$-0.720714\pi$
$569$	−30.4923	−1.27830	−0.639151	+	0.769081i	$0.720714\pi$
$570$	13.7687	0.576706
$571$	−4.84450	−0.202736	−0.101368	−	0.994849i	$-0.532322\pi$
$571$	−4.84450	−0.202736	−0.101368	+	0.994849i	$0.532322\pi$
$572$	−5.99724	−0.250757
$573$	−73.9125	−3.08774
$574$	0.714171	0.0298089
$575$	2.13561	0.0890610
$576$	−9.96515	−0.415215
$577$	18.2641	0.760346	0.380173	−	0.924915i	$-0.375865\pi$
$577$	18.2641	0.760346	0.380173	+	0.924915i	$0.375865\pi$
$578$	12.5209	0.520799
$579$	−56.6097	−2.35262
$580$	−3.31605	−0.137692
$581$	24.2722	1.00698
$582$	−111.569	−4.62468
$583$	−5.32799	−0.220663
$584$	−19.7067	−0.815470
$585$	50.5175	2.08864
$586$	38.6502	1.59662
$587$	−19.6519	−0.811121	−0.405560	−	0.914068i	$-0.632924\pi$
$587$	−19.6519	−0.811121	−0.405560	+	0.914068i	$0.632924\pi$
$588$	17.4884	0.721211
$589$	−6.27353	−0.258496
$590$	−44.7422	−1.84201
$591$	30.1691	1.24099
$592$	−31.2534	−1.28451
$593$	−28.3554	−1.16442	−0.582208	−	0.813040i	$-0.697811\pi$
$593$	−28.3554	−1.16442	−0.582208	+	0.813040i	$0.697811\pi$
$594$	−65.4107	−2.68383
$595$	14.1384	0.579617
$596$	12.0377	0.493082
$597$	65.6205	2.68567
$598$	−4.15695	−0.169990
$599$	−13.6995	−0.559745	−0.279873	−	0.960037i	$-0.590292\pi$
$599$	−13.6995	−0.559745	−0.279873	+	0.960037i	$0.590292\pi$
$600$	−9.75745	−0.398346
$601$	32.9585	1.34440	0.672202	−	0.740367i	$-0.265348\pi$
$601$	32.9585	1.34440	0.672202	+	0.740367i	$0.265348\pi$
$602$	−29.1467	−1.18793
$603$	−33.2000	−1.35201
$604$	23.2464	0.945882
$605$	−17.6891	−0.719166
$606$	56.8872	2.31089
$607$	−31.6252	−1.28363	−0.641815	−	0.766860i	$-0.721818\pi$
$607$	−31.6252	−1.28363	−0.641815	+	0.766860i	$0.721818\pi$
$608$	5.27651	0.213991
$609$	5.58633	0.226370
$610$	−25.7988	−1.04456
$611$	15.7873	0.638685
$612$	32.2261	1.30266
$613$	−23.3793	−0.944281	−0.472141	−	0.881523i	$-0.656519\pi$
$613$	−23.3793	−0.944281	−0.472141	+	0.881523i	$0.656519\pi$
$614$	19.3283	0.780026
$615$	2.12266	0.0855938
$616$	−4.77225	−0.192280
$617$	2.70486	0.108894	0.0544469	−	0.998517i	$-0.482660\pi$
$617$	2.70486	0.108894	0.0544469	+	0.998517i	$0.482660\pi$
$618$	60.9636	2.45231
$619$	−6.20806	−0.249523	−0.124762	−	0.992187i	$-0.539817\pi$
$619$	−6.20806	−0.249523	−0.124762	+	0.992187i	$0.539817\pi$
$620$	−24.3080	−0.976232
$621$	−17.3639	−0.696790
$622$	−3.70964	−0.148743
$623$	6.68154	0.267690
$624$	38.1694	1.52800
$625$	−31.1172	−1.24469
$626$	−38.2695	−1.52956
$627$	5.99029	0.239229
$628$	20.7666	0.828676
$629$	20.0449	0.799241
$630$	−65.7806	−2.62076
$631$	8.78362	0.349670	0.174835	−	0.984598i	$-0.444061\pi$
$631$	8.78362	0.349670	0.174835	+	0.984598i	$0.444061\pi$
$632$	−7.16121	−0.284858
$633$	−59.2982	−2.35689
$634$	−4.96492	−0.197182
$635$	−3.03982	−0.120632
$636$	−10.5745	−0.419306
$637$	−9.72360	−0.385263
$638$	−3.76705	−0.149139
$639$	−80.0326	−3.16604
$640$	−27.0876	−1.07073
$641$	37.1787	1.46847	0.734235	−	0.678896i	$-0.237541\pi$
$641$	37.1787	1.46847	0.734235	+	0.678896i	$0.237541\pi$
$642$	38.3675	1.51424
$643$	37.4545	1.47706	0.738531	−	0.674220i	$-0.235520\pi$
$643$	37.4545	1.47706	0.738531	+	0.674220i	$0.235520\pi$
$644$	2.07303	0.0816888
$645$	−86.6297	−3.41104
$646$	−4.88353	−0.192140
$647$	−12.1024	−0.475796	−0.237898	−	0.971290i	$-0.576458\pi$
$647$	−12.1024	−0.475796	−0.237898	+	0.971290i	$0.576458\pi$
$648$	45.7742	1.79818
$649$	−19.4659	−0.764102
$650$	−8.87760	−0.348208
$651$	40.9500	1.60496
$652$	−19.3704	−0.758603
$653$	−27.0887	−1.06006	−0.530032	−	0.847978i	$-0.677820\pi$
$653$	−27.0887	−1.06006	−0.530032	+	0.847978i	$0.677820\pi$
$654$	−3.96086	−0.154882
$655$	7.95426	0.310798
$656$	1.17386	0.0458316
$657$	−118.180	−4.61064
$658$	−20.5571	−0.801401
$659$	−33.9335	−1.32186	−0.660930	−	0.750448i	$-0.729838\pi$
$659$	−33.9335	−1.32186	−0.660930	+	0.750448i	$0.729838\pi$
$660$	23.2105	0.903469
$661$	2.59247	0.100835	0.0504176	−	0.998728i	$-0.483945\pi$
$661$	2.59247	0.100835	0.0504176	+	0.998728i	$0.483945\pi$
$662$	20.7141	0.805078
$663$	−24.4805	−0.950746
$664$	19.8516	0.770393
$665$	3.81768	0.148043
$666$	−93.2612	−3.61380
$667$	−1.00000	−0.0387202
$668$	14.9680	0.579131
$669$	31.8105	1.22987
$670$	19.4940	0.753119
$671$	−11.2242	−0.433305
$672$	−34.4421	−1.32863
$673$	−36.9053	−1.42260	−0.711298	−	0.702891i	$-0.751892\pi$
$673$	−36.9053	−1.42260	−0.711298	+	0.702891i	$0.751892\pi$
$674$	−60.5843	−2.33362
$675$	−37.0825	−1.42731
$676$	−9.52002	−0.366155
$677$	5.47441	0.210399	0.105199	−	0.994451i	$-0.466452\pi$
$677$	5.47441	0.210399	0.105199	+	0.994451i	$0.466452\pi$
$678$	17.5646	0.674565
$679$	−30.9350	−1.18718
$680$	11.5635	0.443438
$681$	30.6258	1.17358
$682$	−27.6140	−1.05739
$683$	−0.415708	−0.0159066	−0.00795331	−	0.999968i	$-0.502532\pi$
$683$	−0.415708	−0.0159066	−0.00795331	+	0.999968i	$0.502532\pi$
$684$	8.70177	0.332720
$685$	59.0957	2.25793
$686$	33.7071	1.28694
$687$	−55.3922	−2.11334
$688$	−47.9075	−1.82646
$689$	5.87944	0.223989
$690$	16.0882	0.612468
$691$	29.9264	1.13845	0.569227	−	0.822180i	$-0.307243\pi$
$691$	29.9264	1.13845	0.569227	+	0.822180i	$0.307243\pi$
$692$	23.3265	0.886742
$693$	−28.6189	−1.08714
$694$	−25.1650	−0.955250
$695$	38.8175	1.47243
$696$	4.56893	0.173185
$697$	−0.752873	−0.0285171
$698$	−2.38964	−0.0904493
$699$	−18.4878	−0.699274
$700$	4.42718	0.167332
$701$	−14.4942	−0.547439	−0.273720	−	0.961810i	$-0.588254\pi$
$701$	−14.4942	−0.547439	−0.273720	+	0.961810i	$0.588254\pi$
$702$	72.1808	2.72429
$703$	5.41256	0.204139
$704$	2.54568	0.0959438
$705$	−61.0999	−2.30116
$706$	1.85200	0.0697010
$707$	15.7733	0.593215
$708$	−38.6341	−1.45196
$709$	−19.8992	−0.747332	−0.373666	−	0.927563i	$-0.621899\pi$
$709$	−19.8992	−0.747332	−0.373666	+	0.927563i	$0.621899\pi$
$710$	46.9927	1.76360
$711$	−42.9454	−1.61058
$712$	5.46468	0.204797
$713$	−7.33040	−0.274526
$714$	31.8769	1.19296
$715$	−12.9051	−0.482623
$716$	−14.2544	−0.532713
$717$	65.0537	2.42948
$718$	37.0340	1.38210
$719$	−8.34648	−0.311271	−0.155636	−	0.987815i	$-0.549743\pi$
$719$	−8.34648	−0.311271	−0.155636	+	0.987815i	$0.549743\pi$
$720$	−108.122	−4.02945
$721$	16.9035	0.629520
$722$	32.8886	1.22399
$723$	60.6921	2.25716
$724$	6.69520	0.248825
$725$	−2.13561	−0.0793145
$726$	−39.8826	−1.48018
$727$	13.8747	0.514583	0.257292	−	0.966334i	$-0.417170\pi$
$727$	13.8747	0.514583	0.257292	+	0.966334i	$0.417170\pi$
$728$	5.26619	0.195178
$729$	100.246	3.71281
$730$	69.3917	2.56830
$731$	30.7262	1.13645
$732$	−22.2768	−0.823373
$733$	22.9744	0.848577	0.424289	−	0.905527i	$-0.360524\pi$
$733$	22.9744	0.848577	0.424289	+	0.905527i	$0.360524\pi$
$734$	43.3222	1.59905
$735$	37.6323	1.38809
$736$	6.16542	0.227260
$737$	8.48118	0.312408
$738$	3.50284	0.128941
$739$	20.9037	0.768954	0.384477	−	0.923135i	$-0.374382\pi$
$739$	20.9037	0.768954	0.384477	+	0.923135i	$0.374382\pi$
$740$	20.9720	0.770946
$741$	−6.61029	−0.242835
$742$	−7.65582	−0.281054
$743$	51.6364	1.89436	0.947178	−	0.320707i	$-0.103921\pi$
$743$	51.6364	1.89436	0.947178	+	0.320707i	$0.103921\pi$
$744$	33.4921	1.22788
$745$	25.9031	0.949016
$746$	−19.7057	−0.721478
$747$	119.049	4.35578
$748$	−8.23241	−0.301007
$749$	10.6383	0.388713
$750$	−46.0830	−1.68271
$751$	−44.0079	−1.60587	−0.802935	−	0.596067i	$-0.796729\pi$
$751$	−44.0079	−1.60587	−0.802935	+	0.596067i	$0.796729\pi$
$752$	−33.7892	−1.23216
$753$	−93.4536	−3.40564
$754$	4.15695	0.151387
$755$	50.0224	1.82050
$756$	−35.9959	−1.30916
$757$	−20.1006	−0.730569	−0.365284	−	0.930896i	$-0.619028\pi$
$757$	−20.1006	−0.730569	−0.365284	+	0.930896i	$0.619028\pi$
$758$	22.4357	0.814901
$759$	6.99945	0.254064
$760$	3.12239	0.113261
$761$	−14.4611	−0.524216	−0.262108	−	0.965039i	$-0.584418\pi$
$761$	−14.4611	−0.524216	−0.262108	+	0.965039i	$0.584418\pi$
$762$	−6.85371	−0.248284
$763$	−1.09824	−0.0397588
$764$	27.4282	0.992316
$765$	69.3454	2.50719
$766$	−0.150163	−0.00542559
$767$	21.4806	0.775619
$768$	−69.2127	−2.49750
$769$	−24.8366	−0.895629	−0.447815	−	0.894126i	$-0.647798\pi$
$769$	−24.8366	−0.895629	−0.447815	+	0.894126i	$0.647798\pi$
$770$	16.8042	0.605580
$771$	81.9583	2.95166
$772$	21.0073	0.756068
$773$	8.57947	0.308582	0.154291	−	0.988025i	$-0.450691\pi$
$773$	8.57947	0.308582	0.154291	+	0.988025i	$0.450691\pi$
$774$	−142.957	−5.13850
$775$	−15.6549	−0.562339
$776$	−25.3010	−0.908254
$777$	−35.3301	−1.26746
$778$	24.4892	0.877980
$779$	−0.203292	−0.00728371
$780$	−25.6128	−0.917087
$781$	20.4449	0.731577
$782$	−5.70624	−0.204055
$783$	17.3639	0.620535
$784$	20.8112	0.743258
$785$	44.6863	1.59492
$786$	17.9340	0.639684
$787$	8.68947	0.309746	0.154873	−	0.987934i	$-0.450503\pi$
$787$	8.68947	0.309746	0.154873	+	0.987934i	$0.450503\pi$
$788$	−11.1954	−0.398821
$789$	−88.9169	−3.16552
$790$	25.2162	0.897152
$791$	4.87019	0.173164
$792$	−23.4068	−0.831723
$793$	12.3859	0.439837
$794$	−47.1703	−1.67401
$795$	−22.7546	−0.807023
$796$	−24.3511	−0.863102
$797$	40.9587	1.45083	0.725417	−	0.688310i	$-0.241647\pi$
$797$	40.9587	1.45083	0.725417	+	0.688310i	$0.241647\pi$
$798$	8.60748	0.304702
$799$	21.6712	0.766671
$800$	13.1669	0.465521
$801$	32.7714	1.15792
$802$	−49.1765	−1.73648
$803$	30.1900	1.06538
$804$	16.8327	0.593643
$805$	4.46082	0.157223
$806$	30.4721	1.07333
$807$	38.9628	1.37156
$808$	12.9006	0.453841
$809$	−29.3151	−1.03066	−0.515332	−	0.856990i	$-0.672331\pi$
$809$	−29.3151	−1.03066	−0.515332	+	0.856990i	$0.672331\pi$
$810$	−161.181	−5.66332
$811$	47.2670	1.65977	0.829884	−	0.557936i	$-0.188407\pi$
$811$	47.2670	1.65977	0.829884	+	0.557936i	$0.188407\pi$
$812$	−2.07303	−0.0727491
$813$	−10.9120	−0.382700
$814$	23.8243	0.835041
$815$	−41.6820	−1.46006
$816$	52.3952	1.83420
$817$	8.29675	0.290267
$818$	−60.0756	−2.10049
$819$	31.5810	1.10353
$820$	−0.787696	−0.0275075
$821$	−4.71487	−0.164550	−0.0822750	−	0.996610i	$-0.526219\pi$
$821$	−4.71487	−0.164550	−0.0822750	+	0.996610i	$0.526219\pi$
$822$	133.240	4.64726
$823$	20.6481	0.719747	0.359873	−	0.933001i	$-0.382820\pi$
$823$	20.6481	0.719747	0.359873	+	0.933001i	$0.382820\pi$
$824$	13.8250	0.481617
$825$	14.9481	0.520425
$826$	−27.9706	−0.973222
$827$	−25.6122	−0.890624	−0.445312	−	0.895375i	$-0.646907\pi$
$827$	−25.6122	−0.890624	−0.445312	+	0.895375i	$0.646907\pi$
$828$	10.1677	0.353352
$829$	2.63616	0.0915576	0.0457788	−	0.998952i	$-0.485423\pi$
$829$	2.63616	0.0915576	0.0457788	+	0.998952i	$0.485423\pi$
$830$	−69.9020	−2.42633
$831$	101.646	3.52605
$832$	−2.80916	−0.0973900
$833$	−13.3476	−0.462466
$834$	87.5194	3.03055
$835$	32.2088	1.11463
$836$	−2.22293	−0.0768818
$837$	127.284	4.39959
$838$	−38.8943	−1.34358
$839$	17.0389	0.588247	0.294124	−	0.955767i	$-0.404972\pi$
$839$	17.0389	0.588247	0.294124	+	0.955767i	$0.404972\pi$
$840$	−20.3812	−0.703218
$841$	1.00000	0.0344828
$842$	49.1149	1.69261
$843$	−8.49803	−0.292688
$844$	22.0049	0.757441
$845$	−20.4855	−0.704724
$846$	−100.828	−3.46653
$847$	−11.0584	−0.379970
$848$	−12.5836	−0.432124
$849$	26.2954	0.902455
$850$	−12.1863	−0.417986
$851$	6.32439	0.216797
$852$	40.5773	1.39015
$853$	0.598601	0.0204957	0.0102479	−	0.999947i	$-0.496738\pi$
$853$	0.598601	0.0204957	0.0102479	+	0.999947i	$0.496738\pi$
$854$	−16.1281	−0.551893
$855$	18.7248	0.640374
$856$	8.70078	0.297387
$857$	8.72118	0.297910	0.148955	−	0.988844i	$-0.452409\pi$
$857$	8.72118	0.297910	0.148955	+	0.988844i	$0.452409\pi$
$858$	−29.0963	−0.993332
$859$	20.4118	0.696443	0.348221	−	0.937412i	$-0.386786\pi$
$859$	20.4118	0.696443	0.348221	+	0.937412i	$0.386786\pi$
$860$	32.1474	1.09622
$861$	1.32698	0.0452233
$862$	16.2905	0.554858
$863$	−4.12094	−0.140278	−0.0701391	−	0.997537i	$-0.522344\pi$
$863$	−4.12094	−0.140278	−0.0701391	+	0.997537i	$0.522344\pi$
$864$	−107.056	−3.64211
$865$	50.1949	1.70668
$866$	−29.6545	−1.00770
$867$	23.2646	0.790109
$868$	−15.1961	−0.515790
$869$	10.9707	0.372156
$870$	−16.0882	−0.545442
$871$	−9.35900	−0.317117
$872$	−0.898223	−0.0304177
$873$	−151.729	−5.13524
$874$	−1.54081	−0.0521187
$875$	−12.7775	−0.431960
$876$	59.9184	2.02445
$877$	4.80288	0.162182	0.0810909	−	0.996707i	$-0.474160\pi$
$877$	4.80288	0.162182	0.0810909	+	0.996707i	$0.474160\pi$
$878$	32.9852	1.11320
$879$	71.8148	2.42225
$880$	27.6205	0.931086
$881$	4.55946	0.153612	0.0768060	−	0.997046i	$-0.475528\pi$
$881$	4.55946	0.153612	0.0768060	+	0.997046i	$0.475528\pi$
$882$	62.1013	2.09106
$883$	−22.6282	−0.761500	−0.380750	−	0.924678i	$-0.624334\pi$
$883$	−22.6282	−0.761500	−0.380750	+	0.924678i	$0.624334\pi$
$884$	9.08447	0.305544
$885$	−83.1342	−2.79453
$886$	58.9040	1.97892
$887$	4.58047	0.153797	0.0768985	−	0.997039i	$-0.475498\pi$
$887$	4.58047	0.153797	0.0768985	+	0.997039i	$0.475498\pi$
$888$	−28.8957	−0.969677
$889$	−1.90035	−0.0637355
$890$	−19.2423	−0.645004
$891$	−70.1245	−2.34926
$892$	−11.8045	−0.395245
$893$	5.85170	0.195820
$894$	58.4021	1.95326
$895$	−30.6732	−1.02529
$896$	−16.9338	−0.565718
$897$	−7.72390	−0.257893
$898$	70.8434	2.36408
$899$	7.33040	0.244482
$900$	21.7142	0.723808
$901$	8.07071	0.268874
$902$	−0.894826	−0.0297945
$903$	−54.1565	−1.80222
$904$	3.98322	0.132480
$905$	14.4070	0.478904
$906$	112.783	3.74695
$907$	35.3993	1.17542	0.587708	−	0.809073i	$-0.300031\pi$
$907$	35.3993	1.17542	0.587708	+	0.809073i	$0.300031\pi$
$908$	−11.3649	−0.377158
$909$	77.3641	2.56601
$910$	−18.5434	−0.614708
$911$	−25.8326	−0.855872	−0.427936	−	0.903809i	$-0.640759\pi$
$911$	−25.8326	−0.855872	−0.427936	+	0.903809i	$0.640759\pi$
$912$	14.1479	0.468483
$913$	−30.4120	−1.00649
$914$	−62.5238	−2.06810
$915$	−47.9360	−1.58471
$916$	20.5555	0.679171
$917$	4.97260	0.164210
$918$	99.0826	3.27021
$919$	19.5672	0.645464	0.322732	−	0.946490i	$-0.395399\pi$
$919$	19.5672	0.645464	0.322732	+	0.946490i	$0.395399\pi$
$920$	3.64840	0.120284
$921$	35.9133	1.18338
$922$	−2.35304	−0.0774931
$923$	−22.5610	−0.742605
$924$	14.5101	0.477346
$925$	13.5064	0.444088
$926$	−51.4689	−1.69137
$927$	82.9078	2.72305
$928$	−6.16542	−0.202390
$929$	−52.3694	−1.71818	−0.859092	−	0.511820i	$-0.828971\pi$
$929$	−52.3694	−1.71818	−0.859092	+	0.511820i	$0.828971\pi$
$930$	−117.933	−3.86718
$931$	−3.60414	−0.118121
$932$	6.86064	0.224728
$933$	−6.89276	−0.225659
$934$	−11.8257	−0.386947
$935$	−17.7148	−0.579336
$936$	25.8294	0.844260
$937$	−18.8943	−0.617251	−0.308625	−	0.951184i	$-0.599869\pi$
$937$	−18.8943	−0.617251	−0.308625	+	0.951184i	$0.599869\pi$
$938$	12.1867	0.397909
$939$	−71.1074	−2.32050
$940$	22.6735	0.739530
$941$	−0.101917	−0.00332241	−0.00166120	−	0.999999i	$-0.500529\pi$
$941$	−0.101917	−0.00332241	−0.00166120	+	0.999999i	$0.500529\pi$
$942$	100.751	3.28266
$943$	−0.237540	−0.00773537
$944$	−45.9744	−1.49634
$945$	−77.4573	−2.51969
$946$	36.5196	1.18735
$947$	−8.17439	−0.265632	−0.132816	−	0.991141i	$-0.542402\pi$
$947$	−8.17439	−0.265632	−0.132816	+	0.991141i	$0.542402\pi$
$948$	21.7737	0.707177
$949$	−33.3147	−1.08144
$950$	−3.29057	−0.106760
$951$	−9.22517	−0.299146
$952$	7.22889	0.234290
$953$	−34.2815	−1.11049	−0.555243	−	0.831688i	$-0.687375\pi$
$953$	−34.2815	−1.11049	−0.555243	+	0.831688i	$0.687375\pi$
$954$	−37.5500	−1.21572
$955$	59.0210	1.90987
$956$	−24.1408	−0.780768
$957$	−6.99945	−0.226260
$958$	−56.7366	−1.83308
$959$	36.9437	1.19297
$960$	10.8720	0.350892
$961$	22.7347	0.733378
$962$	−26.2901	−0.847628
$963$	52.1781	1.68142
$964$	−22.5222	−0.725391
$965$	45.2042	1.45518
$966$	10.0575	0.323596
$967$	−25.8018	−0.829731	−0.414866	−	0.909883i	$-0.636171\pi$
$967$	−25.8018	−0.829731	−0.414866	+	0.909883i	$0.636171\pi$
$968$	−9.04438	−0.290697
$969$	−9.07394	−0.291497
$970$	89.0905	2.86052
$971$	37.7530	1.21155	0.605776	−	0.795635i	$-0.292863\pi$
$971$	37.7530	1.21155	0.605776	+	0.795635i	$0.292863\pi$
$972$	−74.5109	−2.38994
$973$	24.2667	0.777956
$974$	15.1011	0.483869
$975$	−16.4952	−0.528270
$976$	−26.5093	−0.848542
$977$	5.08937	0.162823	0.0814116	−	0.996681i	$-0.474057\pi$
$977$	5.08937	0.162823	0.0814116	+	0.996681i	$0.474057\pi$
$978$	−93.9778	−3.00508
$979$	−8.37169	−0.267561
$980$	−13.9650	−0.446094
$981$	−5.38659	−0.171981
$982$	18.0781	0.576896
$983$	−1.25574	−0.0400520	−0.0200260	−	0.999799i	$-0.506375\pi$
$983$	−1.25574	−0.0400520	−0.0200260	+	0.999799i	$0.506375\pi$
$984$	1.08531	0.0345983
$985$	−24.0908	−0.767596
$986$	5.70624	0.181724
$987$	−38.1966	−1.21581
$988$	2.45301	0.0780406
$989$	9.69447	0.308266
$990$	82.4203	2.61949
$991$	−33.1445	−1.05287	−0.526435	−	0.850215i	$-0.676472\pi$
$991$	−33.1445	−1.05287	−0.526435	+	0.850215i	$0.676472\pi$
$992$	−45.1950	−1.43494
$993$	38.4883	1.22139
$994$	29.3775	0.931796
$995$	−52.3996	−1.66118
$996$	−60.3590	−1.91255
$997$	−22.4065	−0.709621	−0.354810	−	0.934938i	$-0.615455\pi$
$997$	−22.4065	−0.709621	−0.354810	+	0.934938i	$0.615455\pi$
$998$	−21.5724	−0.682861
$999$	−109.816	−3.47443

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.2.a.d.1.3	✓	16
3.2	odd	2		6003.2.a.q.1.14		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.2.a.d.1.3	✓	16	1.1	even	1	trivial
6003.2.a.q.1.14		16	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 667 = 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	667.a (trivial)

\(f(q)\)	\(=\)	\(q-1.80038 q^{2} -3.34524 q^{3} +1.24138 q^{4} +2.67126 q^{5} +6.02272 q^{6} +1.66993 q^{7} +1.36580 q^{8} +8.19063 q^{9} +O(q^{10})\)	\(q-1.80038 q^{2} -3.34524 q^{3} +1.24138 q^{4} +2.67126 q^{5} +6.02272 q^{6} +1.66993 q^{7} +1.36580 q^{8} +8.19063 q^{9} -4.80929 q^{10} -2.09236 q^{11} -4.15273 q^{12} +2.30892 q^{13} -3.00652 q^{14} -8.93599 q^{15} -4.94173 q^{16} +3.16946 q^{17} -14.7463 q^{18} +0.855823 q^{19} +3.31605 q^{20} -5.58633 q^{21} +3.76705 q^{22} +1.00000 q^{23} -4.56893 q^{24} +2.13561 q^{25} -4.15695 q^{26} -17.3639 q^{27} +2.07303 q^{28} -1.00000 q^{29} +16.0882 q^{30} -7.33040 q^{31} +6.16542 q^{32} +6.99945 q^{33} -5.70624 q^{34} +4.46082 q^{35} +10.1677 q^{36} +6.32439 q^{37} -1.54081 q^{38} -7.72390 q^{39} +3.64840 q^{40} -0.237540 q^{41} +10.0575 q^{42} +9.69447 q^{43} -2.59742 q^{44} +21.8793 q^{45} -1.80038 q^{46} +6.83751 q^{47} +16.5313 q^{48} -4.21132 q^{49} -3.84491 q^{50} -10.6026 q^{51} +2.86626 q^{52} +2.54640 q^{53} +31.2617 q^{54} -5.58923 q^{55} +2.28080 q^{56} -2.86293 q^{57} +1.80038 q^{58} +9.30330 q^{59} -11.0930 q^{60} +5.36437 q^{61} +13.1975 q^{62} +13.6778 q^{63} -1.21665 q^{64} +6.16772 q^{65} -12.6017 q^{66} -4.05341 q^{67} +3.93451 q^{68} -3.34524 q^{69} -8.03120 q^{70} -9.77123 q^{71} +11.1868 q^{72} -14.4287 q^{73} -11.3863 q^{74} -7.14412 q^{75} +1.06241 q^{76} -3.49410 q^{77} +13.9060 q^{78} -5.24323 q^{79} -13.2006 q^{80} +33.5145 q^{81} +0.427664 q^{82} +14.5348 q^{83} -6.93478 q^{84} +8.46643 q^{85} -17.4538 q^{86} +3.34524 q^{87} -2.85775 q^{88} +4.00108 q^{89} -39.3911 q^{90} +3.85575 q^{91} +1.24138 q^{92} +24.5219 q^{93} -12.3101 q^{94} +2.28612 q^{95} -20.6248 q^{96} -18.5247 q^{97} +7.58199 q^{98} -17.1377 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} + 5 q^{3} + 21 q^{4} + 16 q^{5} + 6 q^{6} + q^{7} + 9 q^{8} + 23 q^{9}+O(q^{10}) \) 16 * q + 3 * q^2 + 5 * q^3 + 21 * q^4 + 16 * q^5 + 6 * q^6 + q^7 + 9 * q^8 + 23 * q^9	\( 16 q + 3 q^{2} + 5 q^{3} + 21 q^{4} + 16 q^{5} + 6 q^{6} + q^{7} + 9 q^{8} + 23 q^{9} - 14 q^{10} + 4 q^{11} + 3 q^{12} + 15 q^{13} + 8 q^{14} + 8 q^{15} + 23 q^{16} + 20 q^{17} + 2 q^{18} - 4 q^{19} + 25 q^{20} + 5 q^{21} + 13 q^{22} + 16 q^{23} - 24 q^{24} + 30 q^{25} + 25 q^{26} + 8 q^{27} - 13 q^{28} - 16 q^{29} - 45 q^{30} - 19 q^{32} + q^{33} - 23 q^{34} + 5 q^{35} + 37 q^{36} + 5 q^{37} + 38 q^{38} - 10 q^{39} - 20 q^{40} + 7 q^{41} + 14 q^{42} - 17 q^{43} - 21 q^{44} + 48 q^{45} + 3 q^{46} + 29 q^{47} + 35 q^{48} + 31 q^{49} - 44 q^{50} - 14 q^{51} + 20 q^{52} + 63 q^{53} - 13 q^{54} + q^{55} - 19 q^{56} - 22 q^{57} - 3 q^{58} + 11 q^{59} - 3 q^{60} + 33 q^{62} - 33 q^{63} + 29 q^{64} + 53 q^{65} - 43 q^{66} - 13 q^{67} + 63 q^{68} + 5 q^{69} - 46 q^{70} - 23 q^{71} + 46 q^{72} - 38 q^{73} - 47 q^{74} + 37 q^{75} - 56 q^{76} + 97 q^{77} - 24 q^{78} - 27 q^{79} + 8 q^{80} + 40 q^{81} + 9 q^{82} + 36 q^{83} + 22 q^{84} + 6 q^{85} - 11 q^{86} - 5 q^{87} - 24 q^{88} - 16 q^{89} - 95 q^{90} - 47 q^{91} + 21 q^{92} + 62 q^{93} + 37 q^{94} - 12 q^{95} - 74 q^{96} - 30 q^{97} - 27 q^{98} - 42 q^{99}+O(q^{100}) \) 16 * q + 3 * q^2 + 5 * q^3 + 21 * q^4 + 16 * q^5 + 6 * q^6 + q^7 + 9 * q^8 + 23 * q^9 - 14 * q^10 + 4 * q^11 + 3 * q^12 + 15 * q^13 + 8 * q^14 + 8 * q^15 + 23 * q^16 + 20 * q^17 + 2 * q^18 - 4 * q^19 + 25 * q^20 + 5 * q^21 + 13 * q^22 + 16 * q^23 - 24 * q^24 + 30 * q^25 + 25 * q^26 + 8 * q^27 - 13 * q^28 - 16 * q^29 - 45 * q^30 - 19 * q^32 + q^33 - 23 * q^34 + 5 * q^35 + 37 * q^36 + 5 * q^37 + 38 * q^38 - 10 * q^39 - 20 * q^40 + 7 * q^41 + 14 * q^42 - 17 * q^43 - 21 * q^44 + 48 * q^45 + 3 * q^46 + 29 * q^47 + 35 * q^48 + 31 * q^49 - 44 * q^50 - 14 * q^51 + 20 * q^52 + 63 * q^53 - 13 * q^54 + q^55 - 19 * q^56 - 22 * q^57 - 3 * q^58 + 11 * q^59 - 3 * q^60 + 33 * q^62 - 33 * q^63 + 29 * q^64 + 53 * q^65 - 43 * q^66 - 13 * q^67 + 63 * q^68 + 5 * q^69 - 46 * q^70 - 23 * q^71 + 46 * q^72 - 38 * q^73 - 47 * q^74 + 37 * q^75 - 56 * q^76 + 97 * q^77 - 24 * q^78 - 27 * q^79 + 8 * q^80 + 40 * q^81 + 9 * q^82 + 36 * q^83 + 22 * q^84 + 6 * q^85 - 11 * q^86 - 5 * q^87 - 24 * q^88 - 16 * q^89 - 95 * q^90 - 47 * q^91 + 21 * q^92 + 62 * q^93 + 37 * q^94 - 12 * q^95 - 74 * q^96 - 30 * q^97 - 27 * q^98 - 42 * q^99

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