LMFDB - Embedded newform 2667.2.a.l.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2667,2,Mod(1,2667)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2667, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2667.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2667 = 3 \cdot 7 \cdot 127 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2667.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:	$21.2961022191$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 4 x^{12} - 10 x^{11} + 53 x^{10} + 19 x^{9} - 242 x^{8} + 61 x^{7} + 467 x^{6} - 211 x^{5} + \cdots - 8 $ x^13 - 4x^12 - 10x^11 + 53x^10 + 19x^9 - 242x^8 + 61x^7 + 467x^6 - 211x^5 - 372x^4 + 146x^3 + 116x^2 - 12x - 8
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$0.307326$ of defining polynomial
Character	$\chi$	$=$	2667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.307326 q^{2} -1.00000 q^{3} -1.90555 q^{4} -0.988649 q^{5} -0.307326 q^{6} +1.00000 q^{7} -1.20028 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.307326 q^{2} -1.00000 q^{3} -1.90555 q^{4} -0.988649 q^{5} -0.307326 q^{6} +1.00000 q^{7} -1.20028 q^{8} +1.00000 q^{9} -0.303838 q^{10} +2.00682 q^{11} +1.90555 q^{12} -0.289737 q^{13} +0.307326 q^{14} +0.988649 q^{15} +3.44222 q^{16} +0.186210 q^{17} +0.307326 q^{18} +0.852422 q^{19} +1.88392 q^{20} -1.00000 q^{21} +0.616750 q^{22} -3.33599 q^{23} +1.20028 q^{24} -4.02257 q^{25} -0.0890436 q^{26} -1.00000 q^{27} -1.90555 q^{28} -4.37763 q^{29} +0.303838 q^{30} -5.73898 q^{31} +3.45844 q^{32} -2.00682 q^{33} +0.0572272 q^{34} -0.988649 q^{35} -1.90555 q^{36} -7.05580 q^{37} +0.261972 q^{38} +0.289737 q^{39} +1.18665 q^{40} +3.81974 q^{41} -0.307326 q^{42} +9.06384 q^{43} -3.82411 q^{44} -0.988649 q^{45} -1.02524 q^{46} +1.34856 q^{47} -3.44222 q^{48} +1.00000 q^{49} -1.23624 q^{50} -0.186210 q^{51} +0.552108 q^{52} +3.75486 q^{53} -0.307326 q^{54} -1.98405 q^{55} -1.20028 q^{56} -0.852422 q^{57} -1.34536 q^{58} -4.26624 q^{59} -1.88392 q^{60} +3.08411 q^{61} -1.76374 q^{62} +1.00000 q^{63} -5.82158 q^{64} +0.286448 q^{65} -0.616750 q^{66} -10.8349 q^{67} -0.354832 q^{68} +3.33599 q^{69} -0.303838 q^{70} +13.0932 q^{71} -1.20028 q^{72} +14.9066 q^{73} -2.16843 q^{74} +4.02257 q^{75} -1.62433 q^{76} +2.00682 q^{77} +0.0890436 q^{78} +16.7593 q^{79} -3.40315 q^{80} +1.00000 q^{81} +1.17391 q^{82} +15.1974 q^{83} +1.90555 q^{84} -0.184096 q^{85} +2.78556 q^{86} +4.37763 q^{87} -2.40875 q^{88} -0.526198 q^{89} -0.303838 q^{90} -0.289737 q^{91} +6.35689 q^{92} +5.73898 q^{93} +0.414448 q^{94} -0.842746 q^{95} -3.45844 q^{96} +6.83150 q^{97} +0.307326 q^{98} +2.00682 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 4 q^{2} - 13 q^{3} + 10 q^{4} + 12 q^{5} - 4 q^{6} + 13 q^{7} + 9 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q + 4 * q^2 - 13 * q^3 + 10 * q^4 + 12 * q^5 - 4 * q^6 + 13 * q^7 + 9 * q^8 + 13 * q^9	\( 13 q + 4 q^{2} - 13 q^{3} + 10 q^{4} + 12 q^{5} - 4 q^{6} + 13 q^{7} + 9 q^{8} + 13 q^{9} + 6 q^{10} + 3 q^{11} - 10 q^{12} + 21 q^{13} + 4 q^{14} - 12 q^{15} + 8 q^{16} + 17 q^{17} + 4 q^{18} + 5 q^{19} + 29 q^{20} - 13 q^{21} + q^{22} + 4 q^{23} - 9 q^{24} + q^{25} + 22 q^{26} - 13 q^{27} + 10 q^{28} + 21 q^{29} - 6 q^{30} - 7 q^{31} + 12 q^{32} - 3 q^{33} + 2 q^{34} + 12 q^{35} + 10 q^{36} + 7 q^{37} - 9 q^{38} - 21 q^{39} + 29 q^{40} + 21 q^{41} - 4 q^{42} - 9 q^{43} - 2 q^{44} + 12 q^{45} - 28 q^{46} + 23 q^{47} - 8 q^{48} + 13 q^{49} + 15 q^{50} - 17 q^{51} + 15 q^{52} + 31 q^{53} - 4 q^{54} - 8 q^{55} + 9 q^{56} - 5 q^{57} - 25 q^{58} + 28 q^{59} - 29 q^{60} + 29 q^{61} - 3 q^{62} + 13 q^{63} + 9 q^{64} + 30 q^{65} - q^{66} - 18 q^{67} + 34 q^{68} - 4 q^{69} + 6 q^{70} + 10 q^{71} + 9 q^{72} + 24 q^{73} - 19 q^{74} - q^{75} + 3 q^{77} - 22 q^{78} - 28 q^{79} + 26 q^{80} + 13 q^{81} + 18 q^{82} + 26 q^{83} - 10 q^{84} + 20 q^{85} - 2 q^{86} - 21 q^{87} - 17 q^{88} + 44 q^{89} + 6 q^{90} + 21 q^{91} + 6 q^{92} + 7 q^{93} - 9 q^{94} - 2 q^{95} - 12 q^{96} + 17 q^{97} + 4 q^{98} + 3 q^{99}+O(q^{100}) \) 13 * q + 4 * q^2 - 13 * q^3 + 10 * q^4 + 12 * q^5 - 4 * q^6 + 13 * q^7 + 9 * q^8 + 13 * q^9 + 6 * q^10 + 3 * q^11 - 10 * q^12 + 21 * q^13 + 4 * q^14 - 12 * q^15 + 8 * q^16 + 17 * q^17 + 4 * q^18 + 5 * q^19 + 29 * q^20 - 13 * q^21 + q^22 + 4 * q^23 - 9 * q^24 + q^25 + 22 * q^26 - 13 * q^27 + 10 * q^28 + 21 * q^29 - 6 * q^30 - 7 * q^31 + 12 * q^32 - 3 * q^33 + 2 * q^34 + 12 * q^35 + 10 * q^36 + 7 * q^37 - 9 * q^38 - 21 * q^39 + 29 * q^40 + 21 * q^41 - 4 * q^42 - 9 * q^43 - 2 * q^44 + 12 * q^45 - 28 * q^46 + 23 * q^47 - 8 * q^48 + 13 * q^49 + 15 * q^50 - 17 * q^51 + 15 * q^52 + 31 * q^53 - 4 * q^54 - 8 * q^55 + 9 * q^56 - 5 * q^57 - 25 * q^58 + 28 * q^59 - 29 * q^60 + 29 * q^61 - 3 * q^62 + 13 * q^63 + 9 * q^64 + 30 * q^65 - q^66 - 18 * q^67 + 34 * q^68 - 4 * q^69 + 6 * q^70 + 10 * q^71 + 9 * q^72 + 24 * q^73 - 19 * q^74 - q^75 + 3 * q^77 - 22 * q^78 - 28 * q^79 + 26 * q^80 + 13 * q^81 + 18 * q^82 + 26 * q^83 - 10 * q^84 + 20 * q^85 - 2 * q^86 - 21 * q^87 - 17 * q^88 + 44 * q^89 + 6 * q^90 + 21 * q^91 + 6 * q^92 + 7 * q^93 - 9 * q^94 - 2 * q^95 - 12 * q^96 + 17 * q^97 + 4 * q^98 + 3 * 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 $

$2$	0.307326	0.217312	0.108656	−	0.994079i	$-0.465345\pi$
$2$	0.307326	0.217312	0.108656	+	0.994079i	$0.465345\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.90555	−0.952775
$5$	−0.988649	−0.442137	−0.221069	−	0.975258i	$-0.570954\pi$
$5$	−0.988649	−0.442137	−0.221069	+	0.975258i	$0.570954\pi$
$6$	−0.307326	−0.125465
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.20028	−0.424362
$9$	1.00000	0.333333
$10$	−0.303838	−0.0960819
$11$	2.00682	0.605081	0.302540	−	0.953137i	$-0.402165\pi$
$11$	2.00682	0.605081	0.302540	+	0.953137i	$0.402165\pi$
$12$	1.90555	0.550085
$13$	−0.289737	−0.0803585	−0.0401792	−	0.999192i	$-0.512793\pi$
$13$	−0.289737	−0.0803585	−0.0401792	+	0.999192i	$0.512793\pi$
$14$	0.307326	0.0821364
$15$	0.988649	0.255268
$16$	3.44222	0.860556
$17$	0.186210	0.0451625	0.0225813	−	0.999745i	$-0.492812\pi$
$17$	0.186210	0.0451625	0.0225813	+	0.999745i	$0.492812\pi$
$18$	0.307326	0.0724375
$19$	0.852422	0.195559	0.0977795	−	0.995208i	$-0.468826\pi$
$19$	0.852422	0.195559	0.0977795	+	0.995208i	$0.468826\pi$
$20$	1.88392	0.421257
$21$	−1.00000	−0.218218
$22$	0.616750	0.131491
$23$	−3.33599	−0.695601	−0.347801	−	0.937569i	$-0.613071\pi$
$23$	−3.33599	−0.695601	−0.347801	+	0.937569i	$0.613071\pi$
$24$	1.20028	0.245006
$25$	−4.02257	−0.804515
$26$	−0.0890436	−0.0174629
$27$	−1.00000	−0.192450
$28$	−1.90555	−0.360115
$29$	−4.37763	−0.812905	−0.406452	−	0.913672i	$-0.633234\pi$
$29$	−4.37763	−0.812905	−0.406452	+	0.913672i	$0.633234\pi$
$30$	0.303838	0.0554729
$31$	−5.73898	−1.03075	−0.515376	−	0.856964i	$-0.672348\pi$
$31$	−5.73898	−1.03075	−0.515376	+	0.856964i	$0.672348\pi$
$32$	3.45844	0.611372
$33$	−2.00682	−0.349343
$34$	0.0572272	0.00981438
$35$	−0.988649	−0.167112
$36$	−1.90555	−0.317592
$37$	−7.05580	−1.15997	−0.579983	−	0.814629i	$-0.696941\pi$
$37$	−7.05580	−1.15997	−0.579983	+	0.814629i	$0.696941\pi$
$38$	0.261972	0.0424974
$39$	0.289737	0.0463950
$40$	1.18665	0.187626
$41$	3.81974	0.596544	0.298272	−	0.954481i	$-0.403590\pi$
$41$	3.81974	0.596544	0.298272	+	0.954481i	$0.403590\pi$
$42$	−0.307326	−0.0474214
$43$	9.06384	1.38222	0.691112	−	0.722748i	$-0.257121\pi$
$43$	9.06384	1.38222	0.691112	+	0.722748i	$0.257121\pi$
$44$	−3.82411	−0.576506
$45$	−0.988649	−0.147379
$46$	−1.02524	−0.151163
$47$	1.34856	0.196708	0.0983540	−	0.995151i	$-0.468642\pi$
$47$	1.34856	0.196708	0.0983540	+	0.995151i	$0.468642\pi$
$48$	−3.44222	−0.496842
$49$	1.00000	0.142857
$50$	−1.23624	−0.174831
$51$	−0.186210	−0.0260746
$52$	0.552108	0.0765636
$53$	3.75486	0.515770	0.257885	−	0.966176i	$-0.416974\pi$
$53$	3.75486	0.515770	0.257885	+	0.966176i	$0.416974\pi$
$54$	−0.307326	−0.0418218
$55$	−1.98405	−0.267529
$56$	−1.20028	−0.160394
$57$	−0.852422	−0.112906
$58$	−1.34536	−0.176654
$59$	−4.26624	−0.555418	−0.277709	−	0.960665i	$-0.589575\pi$
$59$	−4.26624	−0.555418	−0.277709	+	0.960665i	$0.589575\pi$
$60$	−1.88392	−0.243213
$61$	3.08411	0.394880	0.197440	−	0.980315i	$-0.436737\pi$
$61$	3.08411	0.394880	0.197440	+	0.980315i	$0.436737\pi$
$62$	−1.76374	−0.223995
$63$	1.00000	0.125988
$64$	−5.82158	−0.727698
$65$	0.286448	0.0355295
$66$	−0.616750	−0.0759166
$67$	−10.8349	−1.32370	−0.661850	−	0.749636i	$-0.730228\pi$
$67$	−10.8349	−1.32370	−0.661850	+	0.749636i	$0.730228\pi$
$68$	−0.354832	−0.0430297
$69$	3.33599	0.401606
$70$	−0.303838	−0.0363155
$71$	13.0932	1.55387	0.776937	−	0.629579i	$-0.216773\pi$
$71$	13.0932	1.55387	0.776937	+	0.629579i	$0.216773\pi$
$72$	−1.20028	−0.141454
$73$	14.9066	1.74469	0.872343	−	0.488894i	$-0.162600\pi$
$73$	14.9066	1.74469	0.872343	+	0.488894i	$0.162600\pi$
$74$	−2.16843	−0.252075
$75$	4.02257	0.464487
$76$	−1.62433	−0.186324
$77$	2.00682	0.228699
$78$	0.0890436	0.0100822
$79$	16.7593	1.88557	0.942785	−	0.333400i	$-0.108196\pi$
$79$	16.7593	1.88557	0.942785	+	0.333400i	$0.108196\pi$
$80$	−3.40315	−0.380484
$81$	1.00000	0.111111
$82$	1.17391	0.129636
$83$	15.1974	1.66813	0.834067	−	0.551663i	$-0.186007\pi$
$83$	15.1974	1.66813	0.834067	+	0.551663i	$0.186007\pi$
$84$	1.90555	0.207913
$85$	−0.184096	−0.0199680
$86$	2.78556	0.300374
$87$	4.37763	0.469331
$88$	−2.40875	−0.256773
$89$	−0.526198	−0.0557769	−0.0278884	−	0.999611i	$-0.508878\pi$
$89$	−0.526198	−0.0557769	−0.0278884	+	0.999611i	$0.508878\pi$
$90$	−0.303838	−0.0320273
$91$	−0.289737	−0.0303726
$92$	6.35689	0.662752
$93$	5.73898	0.595105
$94$	0.414448	0.0427471
$95$	−0.842746	−0.0864639
$96$	−3.45844	−0.352976
$97$	6.83150	0.693634	0.346817	−	0.937933i	$-0.387262\pi$
$97$	6.83150	0.693634	0.346817	+	0.937933i	$0.387262\pi$
$98$	0.307326	0.0310446
$99$	2.00682	0.201694
$100$	7.66522	0.766522
$101$	13.4337	1.33670	0.668350	−	0.743847i	$-0.267001\pi$
$101$	13.4337	1.33670	0.668350	+	0.743847i	$0.267001\pi$
$102$	−0.0572272	−0.00566633
$103$	−2.29311	−0.225947	−0.112973	−	0.993598i	$-0.536037\pi$
$103$	−2.29311	−0.225947	−0.112973	+	0.993598i	$0.536037\pi$
$104$	0.347764	0.0341011
$105$	0.988649	0.0964823
$106$	1.15397	0.112083
$107$	4.90083	0.473781	0.236890	−	0.971536i	$-0.423872\pi$
$107$	4.90083	0.473781	0.236890	+	0.971536i	$0.423872\pi$
$108$	1.90555	0.183362
$109$	2.58229	0.247339	0.123669	−	0.992323i	$-0.460534\pi$
$109$	2.58229	0.247339	0.123669	+	0.992323i	$0.460534\pi$
$110$	−0.609749	−0.0581373
$111$	7.05580	0.669707
$112$	3.44222	0.325260
$113$	−1.77268	−0.166760	−0.0833799	−	0.996518i	$-0.526572\pi$
$113$	−1.77268	−0.166760	−0.0833799	+	0.996518i	$0.526572\pi$
$114$	−0.261972	−0.0245359
$115$	3.29812	0.307551
$116$	8.34179	0.774516
$117$	−0.289737	−0.0267862
$118$	−1.31113	−0.120699
$119$	0.186210	0.0170698
$120$	−1.18665	−0.108326
$121$	−6.97265	−0.633878
$122$	0.947829	0.0858124
$123$	−3.81974	−0.344415
$124$	10.9359	0.982075
$125$	8.92016	0.797843
$126$	0.307326	0.0273788
$127$	−1.00000	−0.0887357
$127$	−1.00000	−0.0887357
$128$	−8.70601	−0.769509
$129$	−9.06384	−0.798027
$130$	0.0880329	0.00772099
$131$	−11.9789	−1.04661	−0.523303	−	0.852147i	$-0.675300\pi$
$131$	−11.9789	−1.04661	−0.523303	+	0.852147i	$0.675300\pi$
$132$	3.82411	0.332846
$133$	0.852422	0.0739144
$134$	−3.32986	−0.287656
$135$	0.988649	0.0850894
$136$	−0.223504	−0.0191653
$137$	−13.4775	−1.15146	−0.575731	−	0.817639i	$-0.695282\pi$
$137$	−13.4775	−1.15146	−0.575731	+	0.817639i	$0.695282\pi$
$138$	1.02524	0.0872738
$139$	6.28920	0.533443	0.266721	−	0.963774i	$-0.414060\pi$
$139$	6.28920	0.533443	0.266721	+	0.963774i	$0.414060\pi$
$140$	1.88392	0.159220
$141$	−1.34856	−0.113569
$142$	4.02387	0.337676
$143$	−0.581451	−0.0486233
$144$	3.44222	0.286852
$145$	4.32794	0.359416
$146$	4.58119	0.379142
$147$	−1.00000	−0.0824786
$148$	13.4452	1.10519
$149$	2.21608	0.181548	0.0907740	−	0.995872i	$-0.471066\pi$
$149$	2.21608	0.181548	0.0907740	+	0.995872i	$0.471066\pi$
$150$	1.23624	0.100939
$151$	−11.7145	−0.953316	−0.476658	−	0.879089i	$-0.658152\pi$
$151$	−11.7145	−0.953316	−0.476658	+	0.879089i	$0.658152\pi$
$152$	−1.02314	−0.0829879
$153$	0.186210	0.0150542
$154$	0.616750	0.0496991
$155$	5.67384	0.455734
$156$	−0.552108	−0.0442040
$157$	−3.95965	−0.316014	−0.158007	−	0.987438i	$-0.550507\pi$
$157$	−3.95965	−0.316014	−0.158007	+	0.987438i	$0.550507\pi$
$158$	5.15058	0.409758
$159$	−3.75486	−0.297780
$160$	−3.41918	−0.270310
$161$	−3.33599	−0.262913
$162$	0.307326	0.0241458
$163$	22.5680	1.76766	0.883832	−	0.467805i	$-0.154955\pi$
$163$	22.5680	1.76766	0.883832	+	0.467805i	$0.154955\pi$
$164$	−7.27872	−0.568372
$165$	1.98405	0.154458
$166$	4.67056	0.362506
$167$	15.6225	1.20891	0.604453	−	0.796641i	$-0.293392\pi$
$167$	15.6225	1.20891	0.604453	+	0.796641i	$0.293392\pi$
$168$	1.20028	0.0926034
$169$	−12.9161	−0.993543
$170$	−0.0565776	−0.00433930
$171$	0.852422	0.0651863
$172$	−17.2716	−1.31695
$173$	16.8019	1.27743	0.638713	−	0.769445i	$-0.279467\pi$
$173$	16.8019	1.27743	0.638713	+	0.769445i	$0.279467\pi$
$174$	1.34536	0.101991
$175$	−4.02257	−0.304078
$176$	6.90794	0.520706
$177$	4.26624	0.320671
$178$	−0.161714	−0.0121210
$179$	18.5086	1.38340	0.691699	−	0.722186i	$-0.256862\pi$
$179$	18.5086	1.38340	0.691699	+	0.722186i	$0.256862\pi$
$180$	1.88392	0.140419
$181$	5.16665	0.384034	0.192017	−	0.981392i	$-0.438497\pi$
$181$	5.16665	0.384034	0.192017	+	0.981392i	$0.438497\pi$
$182$	−0.0890436	−0.00660035
$183$	−3.08411	−0.227984
$184$	4.00411	0.295187
$185$	6.97571	0.512864
$186$	1.76374	0.129324
$187$	0.373691	0.0273270
$188$	−2.56975	−0.187418
$189$	−1.00000	−0.0727393
$190$	−0.258998	−0.0187897
$191$	−1.27980	−0.0926027	−0.0463014	−	0.998928i	$-0.514743\pi$
$191$	−1.27980	−0.0926027	−0.0463014	+	0.998928i	$0.514743\pi$
$192$	5.82158	0.420136
$193$	5.02979	0.362052	0.181026	−	0.983478i	$-0.442058\pi$
$193$	5.02979	0.362052	0.181026	+	0.983478i	$0.442058\pi$
$194$	2.09950	0.150735
$195$	−0.286448	−0.0205130
$196$	−1.90555	−0.136111
$197$	−5.69293	−0.405604	−0.202802	−	0.979220i	$-0.565005\pi$
$197$	−5.69293	−0.405604	−0.202802	+	0.979220i	$0.565005\pi$
$198$	0.616750	0.0438305
$199$	0.823780	0.0583962	0.0291981	−	0.999574i	$-0.490705\pi$
$199$	0.823780	0.0583962	0.0291981	+	0.999574i	$0.490705\pi$
$200$	4.82820	0.341406
$201$	10.8349	0.764238
$202$	4.12852	0.290482
$203$	−4.37763	−0.307249
$204$	0.354832	0.0248432
$205$	−3.77639	−0.263754
$206$	−0.704732	−0.0491010
$207$	−3.33599	−0.231867
$208$	−0.997338	−0.0691530
$209$	1.71066	0.118329
$210$	0.303838	0.0209668
$211$	−15.1264	−1.04135	−0.520674	−	0.853756i	$-0.674319\pi$
$211$	−15.1264	−1.04135	−0.520674	+	0.853756i	$0.674319\pi$
$212$	−7.15508	−0.491413
$213$	−13.0932	−0.897129
$214$	1.50615	0.102958
$215$	−8.96096	−0.611132
$216$	1.20028	0.0816685
$217$	−5.73898	−0.389587
$218$	0.793606	0.0537498
$219$	−14.9066	−1.00729
$220$	3.78070	0.254895
$221$	−0.0539518	−0.00362919
$222$	2.16843	0.145536
$223$	4.14354	0.277472	0.138736	−	0.990329i	$-0.455696\pi$
$223$	4.14354	0.277472	0.138736	+	0.990329i	$0.455696\pi$
$224$	3.45844	0.231077
$225$	−4.02257	−0.268172
$226$	−0.544791	−0.0362390
$227$	−17.7163	−1.17587	−0.587935	−	0.808908i	$-0.700059\pi$
$227$	−17.7163	−1.17587	−0.587935	+	0.808908i	$0.700059\pi$
$228$	1.62433	0.107574
$229$	27.6285	1.82574	0.912871	−	0.408249i	$-0.133860\pi$
$229$	27.6285	1.82574	0.912871	+	0.408249i	$0.133860\pi$
$230$	1.01360	0.0668347
$231$	−2.00682	−0.132039
$232$	5.25437	0.344966
$233$	21.6658	1.41937	0.709687	−	0.704517i	$-0.248836\pi$
$233$	21.6658	1.41937	0.709687	+	0.704517i	$0.248836\pi$
$234$	−0.0890436	−0.00582096
$235$	−1.33325	−0.0869719
$236$	8.12954	0.529188
$237$	−16.7593	−1.08863
$238$	0.0572272	0.00370949
$239$	3.33796	0.215915	0.107957	−	0.994156i	$-0.465569\pi$
$239$	3.33796	0.215915	0.107957	+	0.994156i	$0.465569\pi$
$240$	3.40315	0.219673
$241$	−13.4703	−0.867701	−0.433851	−	0.900985i	$-0.642845\pi$
$241$	−13.4703	−0.867701	−0.433851	+	0.900985i	$0.642845\pi$
$242$	−2.14288	−0.137749
$243$	−1.00000	−0.0641500
$244$	−5.87693	−0.376232
$245$	−0.988649	−0.0631625
$246$	−1.17391	−0.0748456
$247$	−0.246978	−0.0157148
$248$	6.88837	0.437412
$249$	−15.1974	−0.963097
$250$	2.74140	0.173381
$251$	3.19071	0.201396	0.100698	−	0.994917i	$-0.467892\pi$
$251$	3.19071	0.201396	0.100698	+	0.994917i	$0.467892\pi$
$252$	−1.90555	−0.120038
$253$	−6.69474	−0.420895
$254$	−0.307326	−0.0192834
$255$	0.184096	0.0115286
$256$	8.96758	0.560474
$257$	9.04475	0.564196	0.282098	−	0.959386i	$-0.408970\pi$
$257$	9.04475	0.564196	0.282098	+	0.959386i	$0.408970\pi$
$258$	−2.78556	−0.173421
$259$	−7.05580	−0.438426
$260$	−0.545841	−0.0338516
$261$	−4.37763	−0.270968
$262$	−3.68144	−0.227440
$263$	28.1759	1.73740	0.868700	−	0.495339i	$-0.164956\pi$
$263$	28.1759	1.73740	0.868700	+	0.495339i	$0.164956\pi$
$264$	2.40875	0.148248
$265$	−3.71224	−0.228041
$266$	0.261972	0.0160625
$267$	0.526198	0.0322028
$268$	20.6465	1.26119
$269$	28.9671	1.76616	0.883078	−	0.469226i	$-0.155467\pi$
$269$	28.9671	1.76616	0.883078	+	0.469226i	$0.155467\pi$
$270$	0.303838	0.0184910
$271$	−2.61077	−0.158593	−0.0792964	−	0.996851i	$-0.525267\pi$
$271$	−2.61077	−0.158593	−0.0792964	+	0.996851i	$0.525267\pi$
$272$	0.640976	0.0388649
$273$	0.289737	0.0175357
$274$	−4.14199	−0.250227
$275$	−8.07260	−0.486796
$276$	−6.35689	−0.382640
$277$	−15.2284	−0.914988	−0.457494	−	0.889213i	$-0.651253\pi$
$277$	−15.2284	−0.914988	−0.457494	+	0.889213i	$0.651253\pi$
$278$	1.93283	0.115924
$279$	−5.73898	−0.343584
$280$	1.18665	0.0709161
$281$	−16.7836	−1.00122	−0.500612	−	0.865672i	$-0.666892\pi$
$281$	−16.7836	−1.00122	−0.500612	+	0.865672i	$0.666892\pi$
$282$	−0.414448	−0.0246800
$283$	−5.84420	−0.347401	−0.173701	−	0.984798i	$-0.555573\pi$
$283$	−5.84420	−0.347401	−0.173701	+	0.984798i	$0.555573\pi$
$284$	−24.9497	−1.48049
$285$	0.842746	0.0499200
$286$	−0.178695	−0.0105665
$287$	3.81974	0.225472
$288$	3.45844	0.203791
$289$	−16.9653	−0.997960
$290$	1.33009	0.0781054
$291$	−6.83150	−0.400470
$292$	−28.4053	−1.66229
$293$	2.88058	0.168285	0.0841427	−	0.996454i	$-0.473185\pi$
$293$	2.88058	0.168285	0.0841427	+	0.996454i	$0.473185\pi$
$294$	−0.307326	−0.0179236
$295$	4.21782	0.245571
$296$	8.46892	0.492246
$297$	−2.00682	−0.116448
$298$	0.681058	0.0394526
$299$	0.966557	0.0558974
$300$	−7.66522	−0.442552
$301$	9.06384	0.522431
$302$	−3.60018	−0.207167
$303$	−13.4337	−0.771744
$304$	2.93423	0.168290
$305$	−3.04911	−0.174591
$306$	0.0572272	0.00327146
$307$	2.95818	0.168832	0.0844161	−	0.996431i	$-0.473098\pi$
$307$	2.95818	0.168832	0.0844161	+	0.996431i	$0.473098\pi$
$308$	−3.82411	−0.217899
$309$	2.29311	0.130450
$310$	1.74372	0.0990366
$311$	−7.79466	−0.441995	−0.220997	−	0.975274i	$-0.570931\pi$
$311$	−7.79466	−0.441995	−0.220997	+	0.975274i	$0.570931\pi$
$312$	−0.347764	−0.0196883
$313$	7.56008	0.427321	0.213660	−	0.976908i	$-0.431461\pi$
$313$	7.56008	0.427321	0.213660	+	0.976908i	$0.431461\pi$
$314$	−1.21690	−0.0686738
$315$	−0.988649	−0.0557041
$316$	−31.9357	−1.79653
$317$	31.2502	1.75519	0.877593	−	0.479406i	$-0.159148\pi$
$317$	31.2502	1.75519	0.877593	+	0.479406i	$0.159148\pi$
$318$	−1.15397	−0.0647112
$319$	−8.78513	−0.491873
$320$	5.75550	0.321742
$321$	−4.90083	−0.273538
$322$	−1.02524	−0.0571341
$323$	0.158729	0.00883194
$324$	−1.90555	−0.105864
$325$	1.16549	0.0646496
$326$	6.93574	0.384135
$327$	−2.58229	−0.142801
$328$	−4.58475	−0.253151
$329$	1.34856	0.0743486
$330$	0.609749	0.0335656
$331$	12.3799	0.680461	0.340230	−	0.940342i	$-0.389495\pi$
$331$	12.3799	0.680461	0.340230	+	0.940342i	$0.389495\pi$
$332$	−28.9595	−1.58936
$333$	−7.05580	−0.386655
$334$	4.80120	0.262710
$335$	10.7120	0.585257
$336$	−3.44222	−0.187789
$337$	24.7975	1.35081	0.675403	−	0.737448i	$-0.263970\pi$
$337$	24.7975	1.35081	0.675403	+	0.737448i	$0.263970\pi$
$338$	−3.96944	−0.215909
$339$	1.77268	0.0962788
$340$	0.350805	0.0190251
$341$	−11.5171	−0.623688
$342$	0.261972	0.0141658
$343$	1.00000	0.0539949
$344$	−10.8791	−0.586563
$345$	−3.29812	−0.177565
$346$	5.16367	0.277601
$347$	−36.3026	−1.94883	−0.974413	−	0.224763i	$-0.927839\pi$
$347$	−36.3026	−1.94883	−0.974413	+	0.224763i	$0.927839\pi$
$348$	−8.34179	−0.447167
$349$	11.0963	0.593973	0.296986	−	0.954882i	$-0.404018\pi$
$349$	11.0963	0.593973	0.296986	+	0.954882i	$0.404018\pi$
$350$	−1.23624	−0.0660799
$351$	0.289737	0.0154650
$352$	6.94049	0.369929
$353$	10.7528	0.572312	0.286156	−	0.958183i	$-0.407622\pi$
$353$	10.7528	0.572312	0.286156	+	0.958183i	$0.407622\pi$
$354$	1.31113	0.0696857
$355$	−12.9445	−0.687025
$356$	1.00270	0.0531428
$357$	−0.186210	−0.00985527
$358$	5.68818	0.300630
$359$	−4.97551	−0.262598	−0.131299	−	0.991343i	$-0.541915\pi$
$359$	−4.97551	−0.262598	−0.131299	+	0.991343i	$0.541915\pi$
$360$	1.18665	0.0625421
$361$	−18.2734	−0.961757
$362$	1.58785	0.0834554
$363$	6.97265	0.365969
$364$	0.552108	0.0289383
$365$	−14.7374	−0.771391
$366$	−0.947829	−0.0495438
$367$	−21.4750	−1.12099	−0.560493	−	0.828159i	$-0.689388\pi$
$367$	−21.4750	−1.12099	−0.560493	+	0.828159i	$0.689388\pi$
$368$	−11.4832	−0.598604
$369$	3.81974	0.198848
$370$	2.14382	0.111452
$371$	3.75486	0.194943
$372$	−10.9359	−0.567001
$373$	19.7237	1.02125	0.510627	−	0.859803i	$-0.329413\pi$
$373$	19.7237	1.02125	0.510627	+	0.859803i	$0.329413\pi$
$374$	0.114845	0.00593849
$375$	−8.92016	−0.460635
$376$	−1.61865	−0.0834754
$377$	1.26836	0.0653238
$378$	−0.307326	−0.0158071
$379$	−0.520876	−0.0267556	−0.0133778	−	0.999911i	$-0.504258\pi$
$379$	−0.520876	−0.0267556	−0.0133778	+	0.999911i	$0.504258\pi$
$380$	1.60590	0.0823807
$381$	1.00000	0.0512316
$382$	−0.393314	−0.0201237
$383$	24.9559	1.27519	0.637594	−	0.770372i	$-0.279930\pi$
$383$	24.9559	1.27519	0.637594	+	0.770372i	$0.279930\pi$
$384$	8.70601	0.444276
$385$	−1.98405	−0.101116
$386$	1.54579	0.0786785
$387$	9.06384	0.460741
$388$	−13.0178	−0.660877
$389$	14.5891	0.739696	0.369848	−	0.929092i	$-0.379410\pi$
$389$	14.5891	0.739696	0.369848	+	0.929092i	$0.379410\pi$
$390$	−0.0880329	−0.00445772
$391$	−0.621194	−0.0314151
$392$	−1.20028	−0.0606232
$393$	11.9789	0.604258
$394$	−1.74959	−0.0881429
$395$	−16.5691	−0.833681
$396$	−3.82411	−0.192169
$397$	−5.87002	−0.294608	−0.147304	−	0.989091i	$-0.547060\pi$
$397$	−5.87002	−0.294608	−0.147304	+	0.989091i	$0.547060\pi$
$398$	0.253169	0.0126902
$399$	−0.852422	−0.0426745
$400$	−13.8466	−0.692330
$401$	5.35527	0.267429	0.133715	−	0.991020i	$-0.457309\pi$
$401$	5.35527	0.267429	0.133715	+	0.991020i	$0.457309\pi$
$402$	3.32986	0.166078
$403$	1.66279	0.0828296
$404$	−25.5985	−1.27358
$405$	−0.988649	−0.0491264
$406$	−1.34536	−0.0667690
$407$	−14.1598	−0.701873
$408$	0.223504	0.0110651
$409$	−35.4278	−1.75179	−0.875896	−	0.482500i	$-0.839729\pi$
$409$	−35.4278	−1.75179	−0.875896	+	0.482500i	$0.839729\pi$
$410$	−1.16058	−0.0573171
$411$	13.4775	0.664797
$412$	4.36963	0.215276
$413$	−4.26624	−0.209928
$414$	−1.02524	−0.0503876
$415$	−15.0249	−0.737544
$416$	−1.00204	−0.0491289
$417$	−6.28920	−0.307983
$418$	0.525731	0.0257143
$419$	15.6038	0.762293	0.381147	−	0.924515i	$-0.375529\pi$
$419$	15.6038	0.762293	0.381147	+	0.924515i	$0.375529\pi$
$420$	−1.88392	−0.0919259
$421$	25.4791	1.24177	0.620887	−	0.783900i	$-0.286773\pi$
$421$	25.4791	1.24177	0.620887	+	0.783900i	$0.286773\pi$
$422$	−4.64875	−0.226298
$423$	1.34856	0.0655693
$424$	−4.50688	−0.218873
$425$	−0.749043	−0.0363339
$426$	−4.02387	−0.194957
$427$	3.08411	0.149251
$428$	−9.33878	−0.451407
$429$	0.581451	0.0280727
$430$	−2.75394	−0.132807
$431$	2.51062	0.120932	0.0604661	−	0.998170i	$-0.480741\pi$
$431$	2.51062	0.120932	0.0604661	+	0.998170i	$0.480741\pi$
$432$	−3.44222	−0.165614
$433$	−26.5601	−1.27640	−0.638198	−	0.769872i	$-0.720320\pi$
$433$	−26.5601	−1.27640	−0.638198	+	0.769872i	$0.720320\pi$
$434$	−1.76374	−0.0846622
$435$	−4.32794	−0.207509
$436$	−4.92069	−0.235658
$437$	−2.84367	−0.136031
$438$	−4.58119	−0.218898
$439$	2.59419	0.123814	0.0619070	−	0.998082i	$-0.480282\pi$
$439$	2.59419	0.123814	0.0619070	+	0.998082i	$0.480282\pi$
$440$	2.38141	0.113529
$441$	1.00000	0.0476190
$442$	−0.0165808	−0.000788668 0
$443$	24.0954	1.14481	0.572404	−	0.819972i	$-0.306011\pi$
$443$	24.0954	1.14481	0.572404	+	0.819972i	$0.306011\pi$
$444$	−13.4452	−0.638080
$445$	0.520225	0.0246610
$446$	1.27342	0.0602981
$447$	−2.21608	−0.104817
$448$	−5.82158	−0.275044
$449$	−11.0719	−0.522514	−0.261257	−	0.965269i	$-0.584137\pi$
$449$	−11.0719	−0.522514	−0.261257	+	0.965269i	$0.584137\pi$
$450$	−1.23624	−0.0582770
$451$	7.66556	0.360957
$452$	3.37793	0.158885
$453$	11.7145	0.550397
$454$	−5.44467	−0.255531
$455$	0.286448	0.0134289
$456$	1.02314	0.0479131
$457$	7.11118	0.332647	0.166324	−	0.986071i	$-0.446810\pi$
$457$	7.11118	0.332647	0.166324	+	0.986071i	$0.446810\pi$
$458$	8.49095	0.396756
$459$	−0.186210	−0.00869153
$460$	−6.28473	−0.293027
$461$	24.0587	1.12052	0.560262	−	0.828315i	$-0.310700\pi$
$461$	24.0587	1.12052	0.560262	+	0.828315i	$0.310700\pi$
$462$	−0.616750	−0.0286938
$463$	−18.9750	−0.881842	−0.440921	−	0.897546i	$-0.645348\pi$
$463$	−18.9750	−0.881842	−0.440921	+	0.897546i	$0.645348\pi$
$464$	−15.0688	−0.699550
$465$	−5.67384	−0.263118
$466$	6.65847	0.308448
$467$	7.40649	0.342732	0.171366	−	0.985207i	$-0.445182\pi$
$467$	7.40649	0.342732	0.171366	+	0.985207i	$0.445182\pi$
$468$	0.552108	0.0255212
$469$	−10.8349	−0.500311
$470$	−0.409744	−0.0189001
$471$	3.95965	0.182451
$472$	5.12068	0.235698
$473$	18.1895	0.836356
$474$	−5.15058	−0.236574
$475$	−3.42893	−0.157330
$476$	−0.354832	−0.0162637
$477$	3.75486	0.171923
$478$	1.02584	0.0469209
$479$	−4.92351	−0.224961	−0.112481	−	0.993654i	$-0.535880\pi$
$479$	−4.92351	−0.224961	−0.112481	+	0.993654i	$0.535880\pi$
$480$	3.41918	0.156064
$481$	2.04432	0.0932131
$482$	−4.13979	−0.188562
$483$	3.33599	0.151793
$484$	13.2867	0.603943
$485$	−6.75396	−0.306681
$486$	−0.307326	−0.0139406
$487$	9.85082	0.446383	0.223192	−	0.974775i	$-0.428352\pi$
$487$	9.85082	0.446383	0.223192	+	0.974775i	$0.428352\pi$
$488$	−3.70179	−0.167572
$489$	−22.5680	−1.02056
$490$	−0.303838	−0.0137260
$491$	−31.4542	−1.41951	−0.709755	−	0.704449i	$-0.751194\pi$
$491$	−31.4542	−1.41951	−0.709755	+	0.704449i	$0.751194\pi$
$492$	7.27872	0.328150
$493$	−0.815157	−0.0367128
$494$	−0.0759027	−0.00341503
$495$	−1.98405	−0.0891762
$496$	−19.7549	−0.887020
$497$	13.0932	0.587309
$498$	−4.67056	−0.209293
$499$	−15.4537	−0.691801	−0.345900	−	0.938271i	$-0.612426\pi$
$499$	−15.4537	−0.691801	−0.345900	+	0.938271i	$0.612426\pi$
$500$	−16.9978	−0.760165
$501$	−15.6225	−0.697962
$502$	0.980590	0.0437659
$503$	34.8449	1.55366	0.776829	−	0.629712i	$-0.216827\pi$
$503$	34.8449	1.55366	0.776829	+	0.629712i	$0.216827\pi$
$504$	−1.20028	−0.0534646
$505$	−13.2812	−0.591005
$506$	−2.05747	−0.0914656
$507$	12.9161	0.573622
$508$	1.90555	0.0845451
$509$	22.9563	1.01752	0.508761	−	0.860908i	$-0.330104\pi$
$509$	22.9563	1.01752	0.508761	+	0.860908i	$0.330104\pi$
$510$	0.0565776	0.00250530
$511$	14.9066	0.659429
$512$	20.1680	0.891307
$513$	−0.852422	−0.0376354
$514$	2.77969	0.122607
$515$	2.26708	0.0998994
$516$	17.2716	0.760340
$517$	2.70633	0.119024
$518$	−2.16843	−0.0952754
$519$	−16.8019	−0.737522
$520$	−0.343817	−0.0150774
$521$	23.8812	1.04625	0.523127	−	0.852255i	$-0.324765\pi$
$521$	23.8812	1.04625	0.523127	+	0.852255i	$0.324765\pi$
$522$	−1.34536	−0.0588848
$523$	−42.3363	−1.85124	−0.925620	−	0.378455i	$-0.876455\pi$
$523$	−42.3363	−1.85124	−0.925620	+	0.378455i	$0.876455\pi$
$524$	22.8265	0.997180
$525$	4.02257	0.175559
$526$	8.65919	0.377558
$527$	−1.06866	−0.0465514
$528$	−6.90794	−0.300630
$529$	−11.8712	−0.516139
$530$	−1.14087	−0.0495561
$531$	−4.26624	−0.185139
$532$	−1.62433	−0.0704238
$533$	−1.10672	−0.0479373
$534$	0.161714	0.00699807
$535$	−4.84520	−0.209476
$536$	13.0049	0.561728
$537$	−18.5086	−0.798705
$538$	8.90235	0.383808
$539$	2.00682	0.0864401
$540$	−1.88392	−0.0810710
$541$	−10.0291	−0.431186	−0.215593	−	0.976483i	$-0.569168\pi$
$541$	−10.0291	−0.431186	−0.215593	+	0.976483i	$0.569168\pi$
$542$	−0.802357	−0.0344642
$543$	−5.16665	−0.221722
$544$	0.643996	0.0276111
$545$	−2.55298	−0.109358
$546$	0.0890436	0.00381071
$547$	−38.5584	−1.64864	−0.824318	−	0.566127i	$-0.808441\pi$
$547$	−38.5584	−1.64864	−0.824318	+	0.566127i	$0.808441\pi$
$548$	25.6821	1.09708
$549$	3.08411	0.131627
$550$	−2.48092	−0.105787
$551$	−3.73159	−0.158971
$552$	−4.00411	−0.170426
$553$	16.7593	0.712679
$554$	−4.68010	−0.198838
$555$	−6.97571	−0.296102
$556$	−11.9844	−0.508251
$557$	−27.3968	−1.16084	−0.580420	−	0.814317i	$-0.697112\pi$
$557$	−27.3968	−1.16084	−0.580420	+	0.814317i	$0.697112\pi$
$558$	−1.76374	−0.0746650
$559$	−2.62613	−0.111073
$560$	−3.40315	−0.143809
$561$	−0.373691	−0.0157772
$562$	−5.15803	−0.217578
$563$	−39.9956	−1.68561	−0.842807	−	0.538216i	$-0.819098\pi$
$563$	−39.9956	−1.68561	−0.842807	+	0.538216i	$0.819098\pi$
$564$	2.56975	0.108206
$565$	1.75256	0.0737307
$566$	−1.79607	−0.0754946
$567$	1.00000	0.0419961
$568$	−15.7154	−0.659405
$569$	−39.2508	−1.64548	−0.822740	−	0.568418i	$-0.807556\pi$
$569$	−39.2508	−1.64548	−0.822740	+	0.568418i	$0.807556\pi$
$570$	0.258998	0.0108482
$571$	−14.5997	−0.610978	−0.305489	−	0.952196i	$-0.598820\pi$
$571$	−14.5997	−0.610978	−0.305489	+	0.952196i	$0.598820\pi$
$572$	1.10798	0.0463271
$573$	1.27980	0.0534642
$574$	1.17391	0.0489979
$575$	13.4192	0.559621
$576$	−5.82158	−0.242566
$577$	22.3677	0.931181	0.465591	−	0.885000i	$-0.345842\pi$
$577$	22.3677	0.931181	0.465591	+	0.885000i	$0.345842\pi$
$578$	−5.21389	−0.216869
$579$	−5.02979	−0.209031
$580$	−8.24710	−0.342442
$581$	15.1974	0.630495
$582$	−2.09950	−0.0870270
$583$	7.53535	0.312082
$584$	−17.8921	−0.740379
$585$	0.286448	0.0118432
$586$	0.885278	0.0365705
$587$	37.4645	1.54633	0.773164	−	0.634207i	$-0.218673\pi$
$587$	37.4645	1.54633	0.773164	+	0.634207i	$0.218673\pi$
$588$	1.90555	0.0785836
$589$	−4.89204	−0.201573
$590$	1.29625	0.0533656
$591$	5.69293	0.234176
$592$	−24.2876	−0.998216
$593$	48.5027	1.99177	0.995883	−	0.0906456i	$-0.0288930\pi$
$593$	48.5027	1.99177	0.995883	+	0.0906456i	$0.0288930\pi$
$594$	−0.616750	−0.0253055
$595$	−0.184096	−0.00754721
$596$	−4.22284	−0.172974
$597$	−0.823780	−0.0337151
$598$	0.297048	0.0121472
$599$	26.4798	1.08194	0.540968	−	0.841043i	$-0.318058\pi$
$599$	26.4798	1.08194	0.540968	+	0.841043i	$0.318058\pi$
$600$	−4.82820	−0.197111
$601$	44.0904	1.79849	0.899243	−	0.437449i	$-0.144118\pi$
$601$	44.0904	1.79849	0.899243	+	0.437449i	$0.144118\pi$
$602$	2.78556	0.113531
$603$	−10.8349	−0.441233
$604$	22.3227	0.908296
$605$	6.89351	0.280261
$606$	−4.12852	−0.167710
$607$	36.8393	1.49526	0.747630	−	0.664116i	$-0.231192\pi$
$607$	36.8393	1.49526	0.747630	+	0.664116i	$0.231192\pi$
$608$	2.94805	0.119559
$609$	4.37763	0.177390
$610$	−0.937070	−0.0379408
$611$	−0.390728	−0.0158071
$612$	−0.354832	−0.0143432
$613$	−43.1987	−1.74478	−0.872389	−	0.488812i	$-0.837430\pi$
$613$	−43.1987	−1.74478	−0.872389	+	0.488812i	$0.837430\pi$
$614$	0.909125	0.0366893
$615$	3.77639	0.152279
$616$	−2.40875	−0.0970512
$617$	8.35601	0.336400	0.168200	−	0.985753i	$-0.446205\pi$
$617$	8.35601	0.336400	0.168200	+	0.985753i	$0.446205\pi$
$618$	0.704732	0.0283485
$619$	−33.1859	−1.33385	−0.666927	−	0.745123i	$-0.732391\pi$
$619$	−33.1859	−1.33385	−0.666927	+	0.745123i	$0.732391\pi$
$620$	−10.8118	−0.434212
$621$	3.33599	0.133869
$622$	−2.39550	−0.0960509
$623$	−0.526198	−0.0210817
$624$	0.997338	0.0399255
$625$	11.2940	0.451758
$626$	2.32341	0.0928621
$627$	−1.71066	−0.0683173
$628$	7.54531	0.301091
$629$	−1.31386	−0.0523870
$630$	−0.303838	−0.0121052
$631$	−33.3707	−1.32847	−0.664234	−	0.747525i	$-0.731242\pi$
$631$	−33.3707	−1.32847	−0.664234	+	0.747525i	$0.731242\pi$
$632$	−20.1158	−0.800165
$633$	15.1264	0.601222
$634$	9.60400	0.381424
$635$	0.988649	0.0392333
$636$	7.15508	0.283717
$637$	−0.289737	−0.0114798
$638$	−2.69990	−0.106890
$639$	13.0932	0.517958
$640$	8.60718	0.340229
$641$	11.9243	0.470982	0.235491	−	0.971877i	$-0.424330\pi$
$641$	11.9243	0.470982	0.235491	+	0.971877i	$0.424330\pi$
$642$	−1.50615	−0.0594431
$643$	−28.5011	−1.12397	−0.561987	−	0.827146i	$-0.689963\pi$
$643$	−28.5011	−1.12397	−0.561987	+	0.827146i	$0.689963\pi$
$644$	6.35689	0.250497
$645$	8.96096	0.352837
$646$	0.0487817	0.00191929
$647$	−13.0053	−0.511291	−0.255645	−	0.966771i	$-0.582288\pi$
$647$	−13.0053	−0.511291	−0.255645	+	0.966771i	$0.582288\pi$
$648$	−1.20028	−0.0471514
$649$	−8.56161	−0.336072
$650$	0.358184	0.0140491
$651$	5.73898	0.224928
$652$	−43.0045	−1.68419
$653$	−25.3698	−0.992797	−0.496398	−	0.868095i	$-0.665344\pi$
$653$	−25.3698	−0.992797	−0.496398	+	0.868095i	$0.665344\pi$
$654$	−0.793606	−0.0310325
$655$	11.8430	0.462743
$656$	13.1484	0.513359
$657$	14.9066	0.581562
$658$	0.414448	0.0161569
$659$	38.0906	1.48380	0.741899	−	0.670511i	$-0.233925\pi$
$659$	38.0906	1.48380	0.741899	+	0.670511i	$0.233925\pi$
$660$	−3.78070	−0.147164
$661$	29.6423	1.15295	0.576477	−	0.817114i	$-0.304427\pi$
$661$	29.6423	1.15295	0.576477	+	0.817114i	$0.304427\pi$
$662$	3.80467	0.147873
$663$	0.0539518	0.00209531
$664$	−18.2411	−0.707893
$665$	−0.842746	−0.0326803
$666$	−2.16843	−0.0840250
$667$	14.6037	0.565458
$668$	−29.7695	−1.15182
$669$	−4.14354	−0.160198
$670$	3.29207	0.127184
$671$	6.18928	0.238934
$672$	−3.45844	−0.133412
$673$	13.5428	0.522038	0.261019	−	0.965334i	$-0.415941\pi$
$673$	13.5428	0.522038	0.261019	+	0.965334i	$0.415941\pi$
$674$	7.62092	0.293547
$675$	4.02257	0.154829
$676$	24.6122	0.946623
$677$	15.8075	0.607533	0.303767	−	0.952746i	$-0.401756\pi$
$677$	15.8075	0.607533	0.303767	+	0.952746i	$0.401756\pi$
$678$	0.544791	0.0209226
$679$	6.83150	0.262169
$680$	0.220967	0.00847368
$681$	17.7163	0.678889
$682$	−3.53952	−0.135535
$683$	−3.33700	−0.127687	−0.0638433	−	0.997960i	$-0.520336\pi$
$683$	−3.33700	−0.127687	−0.0638433	+	0.997960i	$0.520336\pi$
$684$	−1.62433	−0.0621079
$685$	13.3245	0.509104
$686$	0.307326	0.0117338
$687$	−27.6285	−1.05409
$688$	31.1998	1.18948
$689$	−1.08792	−0.0414465
$690$	−1.01360	−0.0385870
$691$	18.9842	0.722191	0.361096	−	0.932529i	$-0.382403\pi$
$691$	18.9842	0.722191	0.361096	+	0.932529i	$0.382403\pi$
$692$	−32.0169	−1.21710
$693$	2.00682	0.0762330
$694$	−11.1567	−0.423504
$695$	−6.21781	−0.235855
$696$	−5.25437	−0.199166
$697$	0.711274	0.0269414
$698$	3.41019	0.129078
$699$	−21.6658	−0.819476
$700$	7.66522	0.289718
$701$	6.87293	0.259587	0.129793	−	0.991541i	$-0.458569\pi$
$701$	6.87293	0.259587	0.129793	+	0.991541i	$0.458569\pi$
$702$	0.0890436	0.00336073
$703$	−6.01452	−0.226842
$704$	−11.6829	−0.440316
$705$	1.33325	0.0502133
$706$	3.30461	0.124371
$707$	13.4337	0.505225
$708$	−8.12954	−0.305527
$709$	15.3156	0.575188	0.287594	−	0.957752i	$-0.407145\pi$
$709$	15.3156	0.575188	0.287594	+	0.957752i	$0.407145\pi$
$710$	−3.97820	−0.149299
$711$	16.7593	0.628524
$712$	0.631584	0.0236696
$713$	19.1452	0.716992
$714$	−0.0572272	−0.00214167
$715$	0.574851	0.0214982
$716$	−35.2691	−1.31807
$717$	−3.33796	−0.124658
$718$	−1.52911	−0.0570657
$719$	28.3904	1.05878	0.529391	−	0.848378i	$-0.322421\pi$
$719$	28.3904	1.05878	0.529391	+	0.848378i	$0.322421\pi$
$720$	−3.40315	−0.126828
$721$	−2.29311	−0.0853998
$722$	−5.61589	−0.209002
$723$	13.4703	0.500967
$724$	−9.84532	−0.365898
$725$	17.6093	0.653994
$726$	2.14288	0.0795297
$727$	3.08701	0.114491	0.0572454	−	0.998360i	$-0.481768\pi$
$727$	3.08701	0.114491	0.0572454	+	0.998360i	$0.481768\pi$
$728$	0.347764	0.0128890
$729$	1.00000	0.0370370
$730$	−4.52919	−0.167633
$731$	1.68778	0.0624247
$732$	5.87693	0.217218
$733$	−35.7181	−1.31928	−0.659638	−	0.751583i	$-0.729291\pi$
$733$	−35.7181	−1.31928	−0.659638	+	0.751583i	$0.729291\pi$
$734$	−6.59983	−0.243604
$735$	0.988649	0.0364669
$736$	−11.5373	−0.425271
$737$	−21.7438	−0.800945
$738$	1.17391	0.0432121
$739$	−19.6678	−0.723490	−0.361745	−	0.932277i	$-0.617819\pi$
$739$	−19.6678	−0.723490	−0.361745	+	0.932277i	$0.617819\pi$
$740$	−13.2926	−0.488644
$741$	0.246978	0.00907296
$742$	1.15397	0.0423634
$743$	38.7753	1.42253	0.711264	−	0.702925i	$-0.248123\pi$
$743$	38.7753	1.42253	0.711264	+	0.702925i	$0.248123\pi$
$744$	−6.88837	−0.252540
$745$	−2.19092	−0.0802691
$746$	6.06160	0.221931
$747$	15.1974	0.556045
$748$	−0.712086	−0.0260365
$749$	4.90083	0.179072
$750$	−2.74140	−0.100102
$751$	−14.9648	−0.546074	−0.273037	−	0.962003i	$-0.588028\pi$
$751$	−14.9648	−0.546074	−0.273037	+	0.962003i	$0.588028\pi$
$752$	4.64205	0.169278
$753$	−3.19071	−0.116276
$754$	0.389800	0.0141957
$755$	11.5816	0.421497
$756$	1.90555	0.0693042
$757$	−54.7349	−1.98937	−0.994687	−	0.102946i	$-0.967173\pi$
$757$	−54.7349	−1.98937	−0.994687	+	0.102946i	$0.967173\pi$
$758$	−0.160079	−0.00581432
$759$	6.69474	0.243004
$760$	1.01153	0.0366920
$761$	−16.9679	−0.615087	−0.307543	−	0.951534i	$-0.599507\pi$
$761$	−16.9679	−0.615087	−0.307543	+	0.951534i	$0.599507\pi$
$762$	0.307326	0.0111332
$763$	2.58229	0.0934853
$764$	2.43871	0.0882296
$765$	−0.184096	−0.00665601
$766$	7.66961	0.277114
$767$	1.23609	0.0446325
$768$	−8.96758	−0.323590
$769$	−12.4821	−0.450116	−0.225058	−	0.974345i	$-0.572257\pi$
$769$	−12.4821	−0.450116	−0.225058	+	0.974345i	$0.572257\pi$
$770$	−0.609749	−0.0219738
$771$	−9.04475	−0.325739
$772$	−9.58452	−0.344955
$773$	−7.72207	−0.277744	−0.138872	−	0.990310i	$-0.544348\pi$
$773$	−7.72207	−0.277744	−0.138872	+	0.990310i	$0.544348\pi$
$774$	2.78556	0.100125
$775$	23.0855	0.829255
$776$	−8.19970	−0.294352
$777$	7.05580	0.253125
$778$	4.48361	0.160745
$779$	3.25603	0.116660
$780$	0.545841	0.0195442
$781$	26.2757	0.940218
$782$	−0.190909	−0.00682689
$783$	4.37763	0.156444
$784$	3.44222	0.122937
$785$	3.91470	0.139722
$786$	3.68144	0.131313
$787$	4.74326	0.169079	0.0845396	−	0.996420i	$-0.473058\pi$
$787$	4.74326	0.169079	0.0845396	+	0.996420i	$0.473058\pi$
$788$	10.8482	0.386450
$789$	−28.1759	−1.00309
$790$	−5.09211	−0.181169
$791$	−1.77268	−0.0630293
$792$	−2.40875	−0.0855911
$793$	−0.893580	−0.0317320
$794$	−1.80401	−0.0640220
$795$	3.71224	0.131660
$796$	−1.56975	−0.0556385
$797$	46.3762	1.64273	0.821365	−	0.570403i	$-0.193213\pi$
$797$	46.3762	1.64273	0.821365	+	0.570403i	$0.193213\pi$
$798$	−0.261972	−0.00927369
$799$	0.251116	0.00888383
$800$	−13.9118	−0.491858
$801$	−0.526198	−0.0185923
$802$	1.64581	0.0581157
$803$	29.9149	1.05568
$804$	−20.6465	−0.728147
$805$	3.29812	0.116243
$806$	0.511020	0.0179999
$807$	−28.9671	−1.01969
$808$	−16.1241	−0.567245
$809$	−38.5949	−1.35693	−0.678463	−	0.734635i	$-0.737354\pi$
$809$	−38.5949	−1.35693	−0.678463	+	0.734635i	$0.737354\pi$
$810$	−0.303838	−0.0106758
$811$	6.69385	0.235053	0.117527	−	0.993070i	$-0.462503\pi$
$811$	6.69385	0.235053	0.117527	+	0.993070i	$0.462503\pi$
$812$	8.34179	0.292739
$813$	2.61077	0.0915636
$814$	−4.35166	−0.152526
$815$	−22.3119	−0.781550
$816$	−0.640976	−0.0224387
$817$	7.72622	0.270306
$818$	−10.8879	−0.380686
$819$	−0.289737	−0.0101242
$820$	7.19610	0.251299
$821$	−27.8784	−0.972964	−0.486482	−	0.873690i	$-0.661720\pi$
$821$	−27.8784	−0.972964	−0.486482	+	0.873690i	$0.661720\pi$
$822$	4.14199	0.144469
$823$	−22.7329	−0.792419	−0.396209	−	0.918160i	$-0.629675\pi$
$823$	−22.7329	−0.792419	−0.396209	+	0.918160i	$0.629675\pi$
$824$	2.75237	0.0958832
$825$	8.07260	0.281052
$826$	−1.31113	−0.0456200
$827$	−5.40384	−0.187910	−0.0939549	−	0.995576i	$-0.529951\pi$
$827$	−5.40384	−0.187910	−0.0939549	+	0.995576i	$0.529951\pi$
$828$	6.35689	0.220917
$829$	38.4471	1.33532	0.667661	−	0.744466i	$-0.267296\pi$
$829$	38.4471	1.33532	0.667661	+	0.744466i	$0.267296\pi$
$830$	−4.61755	−0.160277
$831$	15.2284	0.528269
$832$	1.68672	0.0584767
$833$	0.186210	0.00645179
$834$	−1.93283	−0.0669286
$835$	−15.4452	−0.534502
$836$	−3.25975	−0.112741
$837$	5.73898	0.198368
$838$	4.79544	0.165656
$839$	−22.6601	−0.782313	−0.391157	−	0.920324i	$-0.627925\pi$
$839$	−22.6601	−0.782313	−0.391157	+	0.920324i	$0.627925\pi$
$840$	−1.18665	−0.0409434
$841$	−9.83638	−0.339186
$842$	7.83038	0.269853
$843$	16.7836	0.578057
$844$	28.8242	0.992170
$845$	12.7694	0.439282
$846$	0.414448	0.0142490
$847$	−6.97265	−0.239583
$848$	12.9251	0.443849
$849$	5.84420	0.200572
$850$	−0.230200	−0.00789581
$851$	23.5380	0.806874
$852$	24.9497	0.854762
$853$	22.6319	0.774902	0.387451	−	0.921890i	$-0.373356\pi$
$853$	22.6319	0.774902	0.387451	+	0.921890i	$0.373356\pi$
$854$	0.947829	0.0324340
$855$	−0.842746	−0.0288213
$856$	−5.88235	−0.201055
$857$	−38.6289	−1.31954	−0.659770	−	0.751468i	$-0.729346\pi$
$857$	−38.6289	−1.31954	−0.659770	+	0.751468i	$0.729346\pi$
$858$	0.178695	0.00610054
$859$	−2.75056	−0.0938481	−0.0469240	−	0.998898i	$-0.514942\pi$
$859$	−2.75056	−0.0938481	−0.0469240	+	0.998898i	$0.514942\pi$
$860$	17.0756	0.582272
$861$	−3.81974	−0.130177
$862$	0.771579	0.0262801
$863$	−18.8268	−0.640871	−0.320435	−	0.947270i	$-0.603829\pi$
$863$	−18.8268	−0.640871	−0.320435	+	0.947270i	$0.603829\pi$
$864$	−3.45844	−0.117659
$865$	−16.6112	−0.564798
$866$	−8.16261	−0.277377
$867$	16.9653	0.576173
$868$	10.9359	0.371189
$869$	33.6330	1.14092
$870$	−1.33009	−0.0450942
$871$	3.13928	0.106370
$872$	−3.09947	−0.104961
$873$	6.83150	0.231211
$874$	−0.873933	−0.0295612
$875$	8.92016	0.301556
$876$	28.4053	0.959726
$877$	5.91209	0.199637	0.0998186	−	0.995006i	$-0.468174\pi$
$877$	5.91209	0.199637	0.0998186	+	0.995006i	$0.468174\pi$
$878$	0.797262	0.0269063
$879$	−2.88058	−0.0971596
$880$	−6.82953	−0.230223
$881$	23.3170	0.785569	0.392785	−	0.919630i	$-0.371512\pi$
$881$	23.3170	0.785569	0.392785	+	0.919630i	$0.371512\pi$
$882$	0.307326	0.0103482
$883$	−20.2527	−0.681558	−0.340779	−	0.940143i	$-0.610691\pi$
$883$	−20.2527	−0.681558	−0.340779	+	0.940143i	$0.610691\pi$
$884$	0.102808	0.00345780
$885$	−4.21782	−0.141780
$886$	7.40515	0.248781
$887$	−59.2402	−1.98909	−0.994545	−	0.104309i	$-0.966737\pi$
$887$	−59.2402	−1.98909	−0.994545	+	0.104309i	$0.966737\pi$
$888$	−8.46892	−0.284198
$889$	−1.00000	−0.0335389
$890$	0.159879	0.00535915
$891$	2.00682	0.0672312
$892$	−7.89572	−0.264368
$893$	1.14954	0.0384680
$894$	−0.681058	−0.0227780
$895$	−18.2985	−0.611652
$896$	−8.70601	−0.290847
$897$	−0.966557	−0.0322724
$898$	−3.40268	−0.113549
$899$	25.1231	0.837903
$900$	7.66522	0.255507
$901$	0.699192	0.0232935
$902$	2.35583	0.0784404
$903$	−9.06384	−0.301626
$904$	2.12771	0.0707666
$905$	−5.10801	−0.169796
$906$	3.60018	0.119608
$907$	3.28126	0.108953	0.0544763	−	0.998515i	$-0.482651\pi$
$907$	3.28126	0.108953	0.0544763	+	0.998515i	$0.482651\pi$
$908$	33.7592	1.12034
$909$	13.4337	0.445567
$910$	0.0880329	0.00291826
$911$	−53.0856	−1.75880	−0.879402	−	0.476080i	$-0.842057\pi$
$911$	−53.0856	−1.75880	−0.879402	+	0.476080i	$0.842057\pi$
$912$	−2.93423	−0.0971620
$913$	30.4986	1.00936
$914$	2.18545	0.0722883
$915$	3.04911	0.100800
$916$	−52.6475	−1.73952
$917$	−11.9789	−0.395580
$918$	−0.0572272	−0.00188878
$919$	−10.1491	−0.334787	−0.167394	−	0.985890i	$-0.553535\pi$
$919$	−10.1491	−0.334787	−0.167394	+	0.985890i	$0.553535\pi$
$920$	−3.95866	−0.130513
$921$	−2.95818	−0.0974753
$922$	7.39386	0.243504
$923$	−3.79357	−0.124867
$924$	3.82411	0.125804
$925$	28.3825	0.933210
$926$	−5.83151	−0.191635
$927$	−2.29311	−0.0753156
$928$	−15.1398	−0.496987
$929$	−26.8433	−0.880699	−0.440350	−	0.897826i	$-0.645145\pi$
$929$	−26.8433	−0.880699	−0.440350	+	0.897826i	$0.645145\pi$
$930$	−1.74372	−0.0571788
$931$	0.852422	0.0279370
$932$	−41.2853	−1.35235
$933$	7.79466	0.255186
$934$	2.27621	0.0744798
$935$	−0.369449	−0.0120823
$936$	0.347764	0.0113670
$937$	43.6904	1.42730	0.713651	−	0.700501i	$-0.247040\pi$
$937$	43.6904	1.42730	0.713651	+	0.700501i	$0.247040\pi$
$938$	−3.32986	−0.108724
$939$	−7.56008	−0.246714
$940$	2.54058	0.0828647
$941$	−9.59031	−0.312635	−0.156318	−	0.987707i	$-0.549962\pi$
$941$	−9.59031	−0.312635	−0.156318	+	0.987707i	$0.549962\pi$
$942$	1.21690	0.0396489
$943$	−12.7426	−0.414957
$944$	−14.6854	−0.477968
$945$	0.988649	0.0321608
$946$	5.59012	0.181751
$947$	3.89541	0.126584	0.0632918	−	0.997995i	$-0.479840\pi$
$947$	3.89541	0.126584	0.0632918	+	0.997995i	$0.479840\pi$
$948$	31.9357	1.03722
$949$	−4.31899	−0.140200
$950$	−1.05380	−0.0341898
$951$	−31.2502	−1.01336
$952$	−0.223504	−0.00724379
$953$	−0.685511	−0.0222059	−0.0111029	−	0.999938i	$-0.503534\pi$
$953$	−0.685511	−0.0222059	−0.0111029	+	0.999938i	$0.503534\pi$
$954$	1.15397	0.0373610
$955$	1.26527	0.0409431
$956$	−6.36065	−0.205718
$957$	8.78513	0.283983
$958$	−1.51312	−0.0488868
$959$	−13.4775	−0.435212
$960$	−5.75550	−0.185758
$961$	1.93592	0.0624489
$962$	0.628274	0.0202564
$963$	4.90083	0.157927
$964$	25.6684	0.826724
$965$	−4.97270	−0.160077
$966$	1.02524	0.0329864
$967$	−38.2729	−1.23077	−0.615386	−	0.788226i	$-0.711000\pi$
$967$	−38.2729	−1.23077	−0.615386	+	0.788226i	$0.711000\pi$
$968$	8.36912	0.268994
$969$	−0.158729	−0.00509912
$970$	−2.07567	−0.0666457
$971$	2.76859	0.0888482	0.0444241	−	0.999013i	$-0.485855\pi$
$971$	2.76859	0.0888482	0.0444241	+	0.999013i	$0.485855\pi$
$972$	1.90555	0.0611206
$973$	6.28920	0.201622
$974$	3.02741	0.0970046
$975$	−1.16549	−0.0373254
$976$	10.6162	0.339817
$977$	25.2322	0.807249	0.403625	−	0.914925i	$-0.367750\pi$
$977$	25.2322	0.807249	0.403625	+	0.914925i	$0.367750\pi$
$978$	−6.93574	−0.221781
$979$	−1.05599	−0.0337495
$980$	1.88392	0.0601796
$981$	2.58229	0.0824463
$982$	−9.66671	−0.308477
$983$	27.4799	0.876472	0.438236	−	0.898860i	$-0.355603\pi$
$983$	27.4799	0.876472	0.438236	+	0.898860i	$0.355603\pi$
$984$	4.58475	0.146157
$985$	5.62831	0.179333
$986$	−0.250519	−0.00797816
$987$	−1.34856	−0.0429252
$988$	0.470629	0.0149727
$989$	−30.2369	−0.961476
$990$	−0.609749	−0.0193791
$991$	−26.6965	−0.848043	−0.424021	−	0.905652i	$-0.639382\pi$
$991$	−26.6965	−0.848043	−0.424021	+	0.905652i	$0.639382\pi$
$992$	−19.8479	−0.630172
$993$	−12.3799	−0.392864
$994$	4.02387	0.127629
$995$	−0.814429	−0.0258191
$996$	28.9595	0.917615
$997$	−4.92865	−0.156092	−0.0780459	−	0.996950i	$-0.524868\pi$
$997$	−4.92865	−0.156092	−0.0780459	+	0.996950i	$0.524868\pi$
$998$	−4.74931	−0.150337
$999$	7.05580	0.223236

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2667.2.a.l.1.7	✓	13
3.2	odd	2		8001.2.a.o.1.7		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2667.2.a.l.1.7	✓	13	1.1	even	1	trivial
8001.2.a.o.1.7		13	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:	\( N \)	\(=\)	\( 2667 = 3 \cdot 7 \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2667.a (trivial)

\(f(q)\)	\(=\)	\(q+0.307326 q^{2} -1.00000 q^{3} -1.90555 q^{4} -0.988649 q^{5} -0.307326 q^{6} +1.00000 q^{7} -1.20028 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.307326 q^{2} -1.00000 q^{3} -1.90555 q^{4} -0.988649 q^{5} -0.307326 q^{6} +1.00000 q^{7} -1.20028 q^{8} +1.00000 q^{9} -0.303838 q^{10} +2.00682 q^{11} +1.90555 q^{12} -0.289737 q^{13} +0.307326 q^{14} +0.988649 q^{15} +3.44222 q^{16} +0.186210 q^{17} +0.307326 q^{18} +0.852422 q^{19} +1.88392 q^{20} -1.00000 q^{21} +0.616750 q^{22} -3.33599 q^{23} +1.20028 q^{24} -4.02257 q^{25} -0.0890436 q^{26} -1.00000 q^{27} -1.90555 q^{28} -4.37763 q^{29} +0.303838 q^{30} -5.73898 q^{31} +3.45844 q^{32} -2.00682 q^{33} +0.0572272 q^{34} -0.988649 q^{35} -1.90555 q^{36} -7.05580 q^{37} +0.261972 q^{38} +0.289737 q^{39} +1.18665 q^{40} +3.81974 q^{41} -0.307326 q^{42} +9.06384 q^{43} -3.82411 q^{44} -0.988649 q^{45} -1.02524 q^{46} +1.34856 q^{47} -3.44222 q^{48} +1.00000 q^{49} -1.23624 q^{50} -0.186210 q^{51} +0.552108 q^{52} +3.75486 q^{53} -0.307326 q^{54} -1.98405 q^{55} -1.20028 q^{56} -0.852422 q^{57} -1.34536 q^{58} -4.26624 q^{59} -1.88392 q^{60} +3.08411 q^{61} -1.76374 q^{62} +1.00000 q^{63} -5.82158 q^{64} +0.286448 q^{65} -0.616750 q^{66} -10.8349 q^{67} -0.354832 q^{68} +3.33599 q^{69} -0.303838 q^{70} +13.0932 q^{71} -1.20028 q^{72} +14.9066 q^{73} -2.16843 q^{74} +4.02257 q^{75} -1.62433 q^{76} +2.00682 q^{77} +0.0890436 q^{78} +16.7593 q^{79} -3.40315 q^{80} +1.00000 q^{81} +1.17391 q^{82} +15.1974 q^{83} +1.90555 q^{84} -0.184096 q^{85} +2.78556 q^{86} +4.37763 q^{87} -2.40875 q^{88} -0.526198 q^{89} -0.303838 q^{90} -0.289737 q^{91} +6.35689 q^{92} +5.73898 q^{93} +0.414448 q^{94} -0.842746 q^{95} -3.45844 q^{96} +6.83150 q^{97} +0.307326 q^{98} +2.00682 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 4 q^{2} - 13 q^{3} + 10 q^{4} + 12 q^{5} - 4 q^{6} + 13 q^{7} + 9 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q + 4 * q^2 - 13 * q^3 + 10 * q^4 + 12 * q^5 - 4 * q^6 + 13 * q^7 + 9 * q^8 + 13 * q^9	\( 13 q + 4 q^{2} - 13 q^{3} + 10 q^{4} + 12 q^{5} - 4 q^{6} + 13 q^{7} + 9 q^{8} + 13 q^{9} + 6 q^{10} + 3 q^{11} - 10 q^{12} + 21 q^{13} + 4 q^{14} - 12 q^{15} + 8 q^{16} + 17 q^{17} + 4 q^{18} + 5 q^{19} + 29 q^{20} - 13 q^{21} + q^{22} + 4 q^{23} - 9 q^{24} + q^{25} + 22 q^{26} - 13 q^{27} + 10 q^{28} + 21 q^{29} - 6 q^{30} - 7 q^{31} + 12 q^{32} - 3 q^{33} + 2 q^{34} + 12 q^{35} + 10 q^{36} + 7 q^{37} - 9 q^{38} - 21 q^{39} + 29 q^{40} + 21 q^{41} - 4 q^{42} - 9 q^{43} - 2 q^{44} + 12 q^{45} - 28 q^{46} + 23 q^{47} - 8 q^{48} + 13 q^{49} + 15 q^{50} - 17 q^{51} + 15 q^{52} + 31 q^{53} - 4 q^{54} - 8 q^{55} + 9 q^{56} - 5 q^{57} - 25 q^{58} + 28 q^{59} - 29 q^{60} + 29 q^{61} - 3 q^{62} + 13 q^{63} + 9 q^{64} + 30 q^{65} - q^{66} - 18 q^{67} + 34 q^{68} - 4 q^{69} + 6 q^{70} + 10 q^{71} + 9 q^{72} + 24 q^{73} - 19 q^{74} - q^{75} + 3 q^{77} - 22 q^{78} - 28 q^{79} + 26 q^{80} + 13 q^{81} + 18 q^{82} + 26 q^{83} - 10 q^{84} + 20 q^{85} - 2 q^{86} - 21 q^{87} - 17 q^{88} + 44 q^{89} + 6 q^{90} + 21 q^{91} + 6 q^{92} + 7 q^{93} - 9 q^{94} - 2 q^{95} - 12 q^{96} + 17 q^{97} + 4 q^{98} + 3 q^{99}+O(q^{100}) \) 13 * q + 4 * q^2 - 13 * q^3 + 10 * q^4 + 12 * q^5 - 4 * q^6 + 13 * q^7 + 9 * q^8 + 13 * q^9 + 6 * q^10 + 3 * q^11 - 10 * q^12 + 21 * q^13 + 4 * q^14 - 12 * q^15 + 8 * q^16 + 17 * q^17 + 4 * q^18 + 5 * q^19 + 29 * q^20 - 13 * q^21 + q^22 + 4 * q^23 - 9 * q^24 + q^25 + 22 * q^26 - 13 * q^27 + 10 * q^28 + 21 * q^29 - 6 * q^30 - 7 * q^31 + 12 * q^32 - 3 * q^33 + 2 * q^34 + 12 * q^35 + 10 * q^36 + 7 * q^37 - 9 * q^38 - 21 * q^39 + 29 * q^40 + 21 * q^41 - 4 * q^42 - 9 * q^43 - 2 * q^44 + 12 * q^45 - 28 * q^46 + 23 * q^47 - 8 * q^48 + 13 * q^49 + 15 * q^50 - 17 * q^51 + 15 * q^52 + 31 * q^53 - 4 * q^54 - 8 * q^55 + 9 * q^56 - 5 * q^57 - 25 * q^58 + 28 * q^59 - 29 * q^60 + 29 * q^61 - 3 * q^62 + 13 * q^63 + 9 * q^64 + 30 * q^65 - q^66 - 18 * q^67 + 34 * q^68 - 4 * q^69 + 6 * q^70 + 10 * q^71 + 9 * q^72 + 24 * q^73 - 19 * q^74 - q^75 + 3 * q^77 - 22 * q^78 - 28 * q^79 + 26 * q^80 + 13 * q^81 + 18 * q^82 + 26 * q^83 - 10 * q^84 + 20 * q^85 - 2 * q^86 - 21 * q^87 - 17 * q^88 + 44 * q^89 + 6 * q^90 + 21 * q^91 + 6 * q^92 + 7 * q^93 - 9 * q^94 - 2 * q^95 - 12 * q^96 + 17 * q^97 + 4 * q^98 + 3 * q^99

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