LMFDB - Embedded newform 579.2.a.g.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [579,2,Mod(1,579)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(579, 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("579.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 579 = 3 \cdot 193 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	579.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:	$4.62333827703$
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} - 2 x^{12} - 20 x^{11} + 39 x^{10} + 148 x^{9} - 275 x^{8} - 508 x^{7} + 865 x^{6} + 823 x^{5} + \cdots - 48 $ x^13 - 2x^12 - 20x^11 + 39x^10 + 148x^9 - 275x^8 - 508x^7 + 865x^6 + 823x^5 - 1187x^4 - 556x^3 + 576x^2 + 64x - 48
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-1.05223$ of defining polynomial
Character	$\chi$	$=$	579.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.05223 q^{2} +1.00000 q^{3} -0.892804 q^{4} +3.01396 q^{5} -1.05223 q^{6} +3.77896 q^{7} +3.04391 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.05223 q^{2} +1.00000 q^{3} -0.892804 q^{4} +3.01396 q^{5} -1.05223 q^{6} +3.77896 q^{7} +3.04391 q^{8} +1.00000 q^{9} -3.17139 q^{10} +4.93419 q^{11} -0.892804 q^{12} -5.50864 q^{13} -3.97635 q^{14} +3.01396 q^{15} -1.41729 q^{16} -7.70179 q^{17} -1.05223 q^{18} +5.52057 q^{19} -2.69088 q^{20} +3.77896 q^{21} -5.19193 q^{22} -7.92401 q^{23} +3.04391 q^{24} +4.08397 q^{25} +5.79638 q^{26} +1.00000 q^{27} -3.37387 q^{28} +4.62451 q^{29} -3.17139 q^{30} +3.53869 q^{31} -4.59649 q^{32} +4.93419 q^{33} +8.10408 q^{34} +11.3896 q^{35} -0.892804 q^{36} +5.57165 q^{37} -5.80892 q^{38} -5.50864 q^{39} +9.17422 q^{40} -4.18854 q^{41} -3.97635 q^{42} -0.0489147 q^{43} -4.40527 q^{44} +3.01396 q^{45} +8.33791 q^{46} +8.14508 q^{47} -1.41729 q^{48} +7.28054 q^{49} -4.29729 q^{50} -7.70179 q^{51} +4.91814 q^{52} -12.7647 q^{53} -1.05223 q^{54} +14.8715 q^{55} +11.5028 q^{56} +5.52057 q^{57} -4.86607 q^{58} -2.57352 q^{59} -2.69088 q^{60} -6.68322 q^{61} -3.72353 q^{62} +3.77896 q^{63} +7.67116 q^{64} -16.6028 q^{65} -5.19193 q^{66} -6.27347 q^{67} +6.87619 q^{68} -7.92401 q^{69} -11.9846 q^{70} +0.729787 q^{71} +3.04391 q^{72} +3.26717 q^{73} -5.86268 q^{74} +4.08397 q^{75} -4.92878 q^{76} +18.6461 q^{77} +5.79638 q^{78} +13.5577 q^{79} -4.27166 q^{80} +1.00000 q^{81} +4.40732 q^{82} -9.98298 q^{83} -3.37387 q^{84} -23.2129 q^{85} +0.0514697 q^{86} +4.62451 q^{87} +15.0192 q^{88} +3.67690 q^{89} -3.17139 q^{90} -20.8169 q^{91} +7.07459 q^{92} +3.53869 q^{93} -8.57052 q^{94} +16.6388 q^{95} -4.59649 q^{96} +0.726031 q^{97} -7.66083 q^{98} +4.93419 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 2 q^{2} + 13 q^{3} + 18 q^{4} + 6 q^{5} + 2 q^{6} + 15 q^{7} + 3 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q + 2 * q^2 + 13 * q^3 + 18 * q^4 + 6 * q^5 + 2 * q^6 + 15 * q^7 + 3 * q^8 + 13 * q^9	\( 13 q + 2 q^{2} + 13 q^{3} + 18 q^{4} + 6 q^{5} + 2 q^{6} + 15 q^{7} + 3 q^{8} + 13 q^{9} - q^{10} + 3 q^{11} + 18 q^{12} + 11 q^{13} - 4 q^{14} + 6 q^{15} + 20 q^{16} - 2 q^{17} + 2 q^{18} + 9 q^{19} - 9 q^{20} + 15 q^{21} - 8 q^{22} - 8 q^{23} + 3 q^{24} + 21 q^{25} - 15 q^{26} + 13 q^{27} + 16 q^{28} + 5 q^{29} - q^{30} + 25 q^{31} - 17 q^{32} + 3 q^{33} - 10 q^{34} - 10 q^{35} + 18 q^{36} + 29 q^{37} - 40 q^{38} + 11 q^{39} - 21 q^{40} - 11 q^{41} - 4 q^{42} + 8 q^{43} - 18 q^{44} + 6 q^{45} - 6 q^{46} - 12 q^{47} + 20 q^{48} + 20 q^{49} - 4 q^{50} - 2 q^{51} + 2 q^{52} + 14 q^{53} + 2 q^{54} + 12 q^{55} - 7 q^{56} + 9 q^{57} + 9 q^{58} + 10 q^{59} - 9 q^{60} + 6 q^{61} - 14 q^{62} + 15 q^{63} + 23 q^{64} - 15 q^{65} - 8 q^{66} + 25 q^{67} - 33 q^{68} - 8 q^{69} - 21 q^{70} + 3 q^{72} + 8 q^{73} - 2 q^{74} + 21 q^{75} + 20 q^{76} - 25 q^{77} - 15 q^{78} + 7 q^{79} - 40 q^{80} + 13 q^{81} - 19 q^{82} - 28 q^{83} + 16 q^{84} - 3 q^{85} + 2 q^{86} + 5 q^{87} - 21 q^{88} + 7 q^{89} - q^{90} + 7 q^{91} + 9 q^{92} + 25 q^{93} - 35 q^{94} - 26 q^{95} - 17 q^{96} + 26 q^{97} - 14 q^{98} + 3 q^{99}+O(q^{100}) \) 13 * q + 2 * q^2 + 13 * q^3 + 18 * q^4 + 6 * q^5 + 2 * q^6 + 15 * q^7 + 3 * q^8 + 13 * q^9 - q^10 + 3 * q^11 + 18 * q^12 + 11 * q^13 - 4 * q^14 + 6 * q^15 + 20 * q^16 - 2 * q^17 + 2 * q^18 + 9 * q^19 - 9 * q^20 + 15 * q^21 - 8 * q^22 - 8 * q^23 + 3 * q^24 + 21 * q^25 - 15 * q^26 + 13 * q^27 + 16 * q^28 + 5 * q^29 - q^30 + 25 * q^31 - 17 * q^32 + 3 * q^33 - 10 * q^34 - 10 * q^35 + 18 * q^36 + 29 * q^37 - 40 * q^38 + 11 * q^39 - 21 * q^40 - 11 * q^41 - 4 * q^42 + 8 * q^43 - 18 * q^44 + 6 * q^45 - 6 * q^46 - 12 * q^47 + 20 * q^48 + 20 * q^49 - 4 * q^50 - 2 * q^51 + 2 * q^52 + 14 * q^53 + 2 * q^54 + 12 * q^55 - 7 * q^56 + 9 * q^57 + 9 * q^58 + 10 * q^59 - 9 * q^60 + 6 * q^61 - 14 * q^62 + 15 * q^63 + 23 * q^64 - 15 * q^65 - 8 * q^66 + 25 * q^67 - 33 * q^68 - 8 * q^69 - 21 * q^70 + 3 * q^72 + 8 * q^73 - 2 * q^74 + 21 * q^75 + 20 * q^76 - 25 * q^77 - 15 * q^78 + 7 * q^79 - 40 * q^80 + 13 * q^81 - 19 * q^82 - 28 * q^83 + 16 * q^84 - 3 * q^85 + 2 * q^86 + 5 * q^87 - 21 * q^88 + 7 * q^89 - q^90 + 7 * q^91 + 9 * q^92 + 25 * q^93 - 35 * q^94 - 26 * q^95 - 17 * q^96 + 26 * q^97 - 14 * 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 $

$2$	−1.05223	−0.744042	−0.372021	−	0.928224i	$-0.621335\pi$
$2$	−1.05223	−0.744042	−0.372021	+	0.928224i	$0.621335\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.892804	−0.446402
$5$	3.01396	1.34789	0.673943	−	0.738784i	$-0.264600\pi$
$5$	3.01396	1.34789	0.673943	+	0.738784i	$0.264600\pi$
$6$	−1.05223	−0.429573
$7$	3.77896	1.42831	0.714156	−	0.699986i	$-0.246811\pi$
$7$	3.77896	1.42831	0.714156	+	0.699986i	$0.246811\pi$
$8$	3.04391	1.07618
$9$	1.00000	0.333333
$10$	−3.17139	−1.00288
$11$	4.93419	1.48772	0.743858	−	0.668338i	$-0.232994\pi$
$11$	4.93419	1.48772	0.743858	+	0.668338i	$0.232994\pi$
$12$	−0.892804	−0.257730
$13$	−5.50864	−1.52782	−0.763911	−	0.645321i	$-0.776723\pi$
$13$	−5.50864	−1.52782	−0.763911	+	0.645321i	$0.776723\pi$
$14$	−3.97635	−1.06272
$15$	3.01396	0.778202
$16$	−1.41729	−0.354323
$17$	−7.70179	−1.86796	−0.933979	−	0.357329i	$-0.883688\pi$
$17$	−7.70179	−1.86796	−0.933979	+	0.357329i	$0.883688\pi$
$18$	−1.05223	−0.248014
$19$	5.52057	1.26650	0.633252	−	0.773945i	$-0.281720\pi$
$19$	5.52057	1.26650	0.633252	+	0.773945i	$0.281720\pi$
$20$	−2.69088	−0.601699
$21$	3.77896	0.824637
$22$	−5.19193	−1.10692
$23$	−7.92401	−1.65227	−0.826136	−	0.563471i	$-0.809466\pi$
$23$	−7.92401	−1.65227	−0.826136	+	0.563471i	$0.809466\pi$
$24$	3.04391	0.621335
$25$	4.08397	0.816794
$26$	5.79638	1.13676
$27$	1.00000	0.192450
$28$	−3.37387	−0.637602
$29$	4.62451	0.858750	0.429375	−	0.903126i	$-0.358734\pi$
$29$	4.62451	0.858750	0.429375	+	0.903126i	$0.358734\pi$
$30$	−3.17139	−0.579015
$31$	3.53869	0.635568	0.317784	−	0.948163i	$-0.397061\pi$
$31$	3.53869	0.635568	0.317784	+	0.948163i	$0.397061\pi$
$32$	−4.59649	−0.812552
$33$	4.93419	0.858933
$34$	8.10408	1.38984
$35$	11.3896	1.92520
$36$	−0.892804	−0.148801
$37$	5.57165	0.915974	0.457987	−	0.888959i	$-0.348571\pi$
$37$	5.57165	0.915974	0.457987	+	0.888959i	$0.348571\pi$
$38$	−5.80892	−0.942332
$39$	−5.50864	−0.882089
$40$	9.17422	1.45057
$41$	−4.18854	−0.654140	−0.327070	−	0.945000i	$-0.606061\pi$
$41$	−4.18854	−0.654140	−0.327070	+	0.945000i	$0.606061\pi$
$42$	−3.97635	−0.613564
$43$	−0.0489147	−0.00745942	−0.00372971	−	0.999993i	$-0.501187\pi$
$43$	−0.0489147	−0.00745942	−0.00372971	+	0.999993i	$0.501187\pi$
$44$	−4.40527	−0.664119
$45$	3.01396	0.449295
$46$	8.33791	1.22936
$47$	8.14508	1.18808	0.594041	−	0.804435i	$-0.297532\pi$
$47$	8.14508	1.18808	0.594041	+	0.804435i	$0.297532\pi$
$48$	−1.41729	−0.204568
$49$	7.28054	1.04008
$50$	−4.29729	−0.607729
$51$	−7.70179	−1.07847
$52$	4.91814	0.682023
$53$	−12.7647	−1.75336	−0.876681	−	0.481072i	$-0.840248\pi$
$53$	−12.7647	−1.75336	−0.876681	+	0.481072i	$0.840248\pi$
$54$	−1.05223	−0.143191
$55$	14.8715	2.00527
$56$	11.5028	1.53713
$57$	5.52057	0.731217
$58$	−4.86607	−0.638946
$59$	−2.57352	−0.335044	−0.167522	−	0.985868i	$-0.553576\pi$
$59$	−2.57352	−0.335044	−0.167522	+	0.985868i	$0.553576\pi$
$60$	−2.69088	−0.347391
$61$	−6.68322	−0.855698	−0.427849	−	0.903850i	$-0.640729\pi$
$61$	−6.68322	−0.855698	−0.427849	+	0.903850i	$0.640729\pi$
$62$	−3.72353	−0.472889
$63$	3.77896	0.476104
$64$	7.67116	0.958896
$65$	−16.6028	−2.05933
$66$	−5.19193	−0.639082
$67$	−6.27347	−0.766426	−0.383213	−	0.923660i	$-0.625182\pi$
$67$	−6.27347	−0.766426	−0.383213	+	0.923660i	$0.625182\pi$
$68$	6.87619	0.833860
$69$	−7.92401	−0.953939
$70$	−11.9846	−1.43243
$71$	0.729787	0.0866097	0.0433049	−	0.999062i	$-0.486211\pi$
$71$	0.729787	0.0866097	0.0433049	+	0.999062i	$0.486211\pi$
$72$	3.04391	0.358728
$73$	3.26717	0.382393	0.191197	−	0.981552i	$-0.438763\pi$
$73$	3.26717	0.382393	0.191197	+	0.981552i	$0.438763\pi$
$74$	−5.86268	−0.681523
$75$	4.08397	0.471576
$76$	−4.92878	−0.565370
$77$	18.6461	2.12492
$78$	5.79638	0.656311
$79$	13.5577	1.52536	0.762679	−	0.646777i	$-0.223884\pi$
$79$	13.5577	1.52536	0.762679	+	0.646777i	$0.223884\pi$
$80$	−4.27166	−0.477587
$81$	1.00000	0.111111
$82$	4.40732	0.486707
$83$	−9.98298	−1.09577	−0.547887	−	0.836552i	$-0.684568\pi$
$83$	−9.98298	−1.09577	−0.547887	+	0.836552i	$0.684568\pi$
$84$	−3.37387	−0.368120
$85$	−23.2129	−2.51779
$86$	0.0514697	0.00555012
$87$	4.62451	0.495800
$88$	15.0192	1.60105
$89$	3.67690	0.389750	0.194875	−	0.980828i	$-0.437570\pi$
$89$	3.67690	0.389750	0.194875	+	0.980828i	$0.437570\pi$
$90$	−3.17139	−0.334294
$91$	−20.8169	−2.18221
$92$	7.07459	0.737577
$93$	3.53869	0.366945
$94$	−8.57052	−0.883982
$95$	16.6388	1.70710
$96$	−4.59649	−0.469127
$97$	0.726031	0.0737172	0.0368586	−	0.999320i	$-0.488265\pi$
$97$	0.726031	0.0737172	0.0368586	+	0.999320i	$0.488265\pi$
$98$	−7.66083	−0.773861
$99$	4.93419	0.495905
$100$	−3.64619	−0.364619
$101$	−6.63669	−0.660375	−0.330188	−	0.943915i	$-0.607112\pi$
$101$	−6.63669	−0.660375	−0.330188	+	0.943915i	$0.607112\pi$
$102$	8.10408	0.802423
$103$	−6.08147	−0.599225	−0.299613	−	0.954061i	$-0.596857\pi$
$103$	−6.08147	−0.599225	−0.299613	+	0.954061i	$0.596857\pi$
$104$	−16.7678	−1.64422
$105$	11.3896	1.11152
$106$	13.4314	1.30457
$107$	−4.39098	−0.424492	−0.212246	−	0.977216i	$-0.568078\pi$
$107$	−4.39098	−0.424492	−0.212246	+	0.977216i	$0.568078\pi$
$108$	−0.892804	−0.0859101
$109$	13.9009	1.33146	0.665731	−	0.746192i	$-0.268120\pi$
$109$	13.9009	1.33146	0.665731	+	0.746192i	$0.268120\pi$
$110$	−15.6483	−1.49200
$111$	5.57165	0.528838
$112$	−5.35589	−0.506084
$113$	17.9146	1.68526	0.842632	−	0.538489i	$-0.181005\pi$
$113$	17.9146	1.68526	0.842632	+	0.538489i	$0.181005\pi$
$114$	−5.80892	−0.544056
$115$	−23.8827	−2.22707
$116$	−4.12878	−0.383348
$117$	−5.50864	−0.509274
$118$	2.70794	0.249286
$119$	−29.1047	−2.66803
$120$	9.17422	0.837488
$121$	13.3463	1.21330
$122$	7.03230	0.636675
$123$	−4.18854	−0.377668
$124$	−3.15936	−0.283719
$125$	−2.76087	−0.246940
$126$	−3.97635	−0.354241
$127$	−4.10722	−0.364457	−0.182228	−	0.983256i	$-0.558331\pi$
$127$	−4.10722	−0.364457	−0.182228	+	0.983256i	$0.558331\pi$
$128$	1.12112	0.0990942
$129$	−0.0489147	−0.00430670
$130$	17.4701	1.53223
$131$	−8.72840	−0.762604	−0.381302	−	0.924451i	$-0.624524\pi$
$131$	−8.72840	−0.762604	−0.381302	+	0.924451i	$0.624524\pi$
$132$	−4.40527	−0.383430
$133$	20.8620	1.80896
$134$	6.60115	0.570253
$135$	3.01396	0.259401
$136$	−23.4435	−2.01026
$137$	−9.86915	−0.843178	−0.421589	−	0.906787i	$-0.638527\pi$
$137$	−9.86915	−0.843178	−0.421589	+	0.906787i	$0.638527\pi$
$138$	8.33791	0.709770
$139$	−11.1281	−0.943873	−0.471937	−	0.881632i	$-0.656445\pi$
$139$	−11.1281	−0.943873	−0.471937	+	0.881632i	$0.656445\pi$
$140$	−10.1687	−0.859414
$141$	8.14508	0.685939
$142$	−0.767906	−0.0644412
$143$	−27.1807	−2.27297
$144$	−1.41729	−0.118108
$145$	13.9381	1.15750
$146$	−3.43783	−0.284516
$147$	7.28054	0.600489
$148$	−4.97440	−0.408893
$149$	−4.12963	−0.338312	−0.169156	−	0.985589i	$-0.554104\pi$
$149$	−4.12963	−0.338312	−0.169156	+	0.985589i	$0.554104\pi$
$150$	−4.29729	−0.350872
$151$	−0.708420	−0.0576504	−0.0288252	−	0.999584i	$-0.509177\pi$
$151$	−0.708420	−0.0576504	−0.0288252	+	0.999584i	$0.509177\pi$
$152$	16.8041	1.36299
$153$	−7.70179	−0.622652
$154$	−19.6201	−1.58103
$155$	10.6655	0.856672
$156$	4.91814	0.393766
$157$	7.67216	0.612305	0.306152	−	0.951983i	$-0.400958\pi$
$157$	7.67216	0.612305	0.306152	+	0.951983i	$0.400958\pi$
$158$	−14.2658	−1.13493
$159$	−12.7647	−1.01230
$160$	−13.8537	−1.09523
$161$	−29.9445	−2.35996
$162$	−1.05223	−0.0826713
$163$	−3.90736	−0.306048	−0.153024	−	0.988222i	$-0.548901\pi$
$163$	−3.90736	−0.306048	−0.153024	+	0.988222i	$0.548901\pi$
$164$	3.73954	0.292009
$165$	14.8715	1.15774
$166$	10.5044	0.815301
$167$	8.60125	0.665585	0.332792	−	0.943000i	$-0.392009\pi$
$167$	8.60125	0.665585	0.332792	+	0.943000i	$0.392009\pi$
$168$	11.5028	0.887460
$169$	17.3451	1.33424
$170$	24.4254	1.87334
$171$	5.52057	0.422168
$172$	0.0436713	0.00332990
$173$	−11.2628	−0.856291	−0.428146	−	0.903710i	$-0.640833\pi$
$173$	−11.2628	−0.856291	−0.428146	+	0.903710i	$0.640833\pi$
$174$	−4.86607	−0.368895
$175$	15.4332	1.16664
$176$	−6.99319	−0.527132
$177$	−2.57352	−0.193437
$178$	−3.86895	−0.289990
$179$	4.73076	0.353594	0.176797	−	0.984247i	$-0.443426\pi$
$179$	4.73076	0.353594	0.176797	+	0.984247i	$0.443426\pi$
$180$	−2.69088	−0.200566
$181$	−6.26039	−0.465331	−0.232666	−	0.972557i	$-0.574745\pi$
$181$	−6.26039	−0.465331	−0.232666	+	0.972557i	$0.574745\pi$
$182$	21.9043	1.62365
$183$	−6.68322	−0.494038
$184$	−24.1200	−1.77815
$185$	16.7928	1.23463
$186$	−3.72353	−0.273022
$187$	−38.0021	−2.77899
$188$	−7.27196	−0.530362
$189$	3.77896	0.274879
$190$	−17.5079	−1.27016
$191$	−5.20719	−0.376779	−0.188390	−	0.982094i	$-0.560327\pi$
$191$	−5.20719	−0.376779	−0.188390	+	0.982094i	$0.560327\pi$
$192$	7.67116	0.553619
$193$	−1.00000	−0.0719816
$193$	−1.00000	−0.0719816
$194$	−0.763954	−0.0548487
$195$	−16.6028	−1.18895
$196$	−6.50010	−0.464293
$197$	−13.3487	−0.951057	−0.475528	−	0.879700i	$-0.657743\pi$
$197$	−13.3487	−0.951057	−0.475528	+	0.879700i	$0.657743\pi$
$198$	−5.19193	−0.368974
$199$	−3.36005	−0.238188	−0.119094	−	0.992883i	$-0.537999\pi$
$199$	−3.36005	−0.238188	−0.119094	+	0.992883i	$0.537999\pi$
$200$	12.4312	0.879021
$201$	−6.27347	−0.442496
$202$	6.98335	0.491347
$203$	17.4758	1.22656
$204$	6.87619	0.481429
$205$	−12.6241	−0.881705
$206$	6.39913	0.445848
$207$	−7.92401	−0.550757
$208$	7.80735	0.541342
$209$	27.2395	1.88420
$210$	−11.9846	−0.827014
$211$	−13.9904	−0.963139	−0.481570	−	0.876408i	$-0.659933\pi$
$211$	−13.9904	−0.963139	−0.481570	+	0.876408i	$0.659933\pi$
$212$	11.3964	0.782705
$213$	0.729787	0.0500042
$214$	4.62033	0.315839
$215$	−0.147427	−0.0100544
$216$	3.04391	0.207112
$217$	13.3726	0.907789
$218$	−14.6270	−0.990662
$219$	3.26717	0.220775
$220$	−13.2773	−0.895157
$221$	42.4264	2.85391
$222$	−5.86268	−0.393477
$223$	1.11740	0.0748264	0.0374132	−	0.999300i	$-0.488088\pi$
$223$	1.11740	0.0748264	0.0374132	+	0.999300i	$0.488088\pi$
$224$	−17.3700	−1.16058
$225$	4.08397	0.272265
$226$	−18.8504	−1.25391
$227$	8.01883	0.532229	0.266114	−	0.963941i	$-0.414260\pi$
$227$	8.01883	0.532229	0.266114	+	0.963941i	$0.414260\pi$
$228$	−4.92878	−0.326417
$229$	28.2834	1.86902	0.934511	−	0.355934i	$-0.115837\pi$
$229$	28.2834	1.86902	0.934511	+	0.355934i	$0.115837\pi$
$230$	25.1302	1.65703
$231$	18.6461	1.22682
$232$	14.0766	0.924172
$233$	0.459141	0.0300793	0.0150397	−	0.999887i	$-0.495213\pi$
$233$	0.459141	0.0300793	0.0150397	+	0.999887i	$0.495213\pi$
$234$	5.79638	0.378921
$235$	24.5490	1.60140
$236$	2.29765	0.149564
$237$	13.5577	0.880666
$238$	30.6250	1.98512
$239$	−19.0197	−1.23028	−0.615140	−	0.788418i	$-0.710900\pi$
$239$	−19.0197	−1.23028	−0.615140	+	0.788418i	$0.710900\pi$
$240$	−4.27166	−0.275735
$241$	−21.9125	−1.41151	−0.705755	−	0.708456i	$-0.749392\pi$
$241$	−21.9125	−1.41151	−0.705755	+	0.708456i	$0.749392\pi$
$242$	−14.0434	−0.902744
$243$	1.00000	0.0641500
$244$	5.96680	0.381986
$245$	21.9433	1.40190
$246$	4.40732	0.281000
$247$	−30.4108	−1.93499
$248$	10.7714	0.683987
$249$	−9.98298	−0.632645
$250$	2.90508	0.183734
$251$	16.0018	1.01003	0.505013	−	0.863111i	$-0.331488\pi$
$251$	16.0018	1.01003	0.505013	+	0.863111i	$0.331488\pi$
$252$	−3.37387	−0.212534
$253$	−39.0986	−2.45811
$254$	4.32175	0.271171
$255$	−23.2129	−1.45365
$256$	−16.5220	−1.03263
$257$	7.13264	0.444922	0.222461	−	0.974942i	$-0.428591\pi$
$257$	7.13264	0.444922	0.222461	+	0.974942i	$0.428591\pi$
$258$	0.0514697	0.00320436
$259$	21.0551	1.30830
$260$	14.8231	0.919289
$261$	4.62451	0.286250
$262$	9.18432	0.567409
$263$	16.1941	0.998572	0.499286	−	0.866437i	$-0.333596\pi$
$263$	16.1941	0.998572	0.499286	+	0.866437i	$0.333596\pi$
$264$	15.0192	0.924369
$265$	−38.4722	−2.36333
$266$	−21.9517	−1.34594
$267$	3.67690	0.225022
$268$	5.60098	0.342134
$269$	−29.5483	−1.80159	−0.900795	−	0.434245i	$-0.857015\pi$
$269$	−29.5483	−1.80159	−0.900795	+	0.434245i	$0.857015\pi$
$270$	−3.17139	−0.193005
$271$	−11.9367	−0.725101	−0.362550	−	0.931964i	$-0.618094\pi$
$271$	−11.9367	−0.725101	−0.362550	+	0.931964i	$0.618094\pi$
$272$	10.9157	0.661860
$273$	−20.8169	−1.25990
$274$	10.3846	0.627359
$275$	20.1511	1.21516
$276$	7.07459	0.425841
$277$	−11.9932	−0.720602	−0.360301	−	0.932836i	$-0.617326\pi$
$277$	−11.9932	−0.720602	−0.360301	+	0.932836i	$0.617326\pi$
$278$	11.7094	0.702281
$279$	3.53869	0.211856
$280$	34.6690	2.07187
$281$	−0.120341	−0.00717896	−0.00358948	−	0.999994i	$-0.501143\pi$
$281$	−0.120341	−0.00717896	−0.00358948	+	0.999994i	$0.501143\pi$
$282$	−8.57052	−0.510367
$283$	20.3583	1.21018	0.605088	−	0.796159i	$-0.293138\pi$
$283$	20.3583	1.21018	0.605088	+	0.796159i	$0.293138\pi$
$284$	−0.651557	−0.0386628
$285$	16.6388	0.985596
$286$	28.6005	1.69118
$287$	−15.8283	−0.934316
$288$	−4.59649	−0.270851
$289$	42.3175	2.48926
$290$	−14.6661	−0.861225
$291$	0.726031	0.0425607
$292$	−2.91694	−0.170701
$293$	11.0146	0.643480	0.321740	−	0.946828i	$-0.395732\pi$
$293$	11.0146	0.643480	0.321740	+	0.946828i	$0.395732\pi$
$294$	−7.66083	−0.446789
$295$	−7.75649	−0.451600
$296$	16.9596	0.985756
$297$	4.93419	0.286311
$298$	4.34533	0.251718
$299$	43.6506	2.52438
$300$	−3.64619	−0.210513
$301$	−0.184847	−0.0106544
$302$	0.745423	0.0428943
$303$	−6.63669	−0.381268
$304$	−7.82425	−0.448752
$305$	−20.1430	−1.15338
$306$	8.10408	0.463279
$307$	2.08748	0.119139	0.0595694	−	0.998224i	$-0.481027\pi$
$307$	2.08748	0.119139	0.0595694	+	0.998224i	$0.481027\pi$
$308$	−16.6473	−0.948570
$309$	−6.08147	−0.345963
$310$	−11.2226	−0.637400
$311$	−7.25318	−0.411290	−0.205645	−	0.978627i	$-0.565929\pi$
$311$	−7.25318	−0.411290	−0.205645	+	0.978627i	$0.565929\pi$
$312$	−16.7678	−0.949289
$313$	−6.58271	−0.372077	−0.186038	−	0.982542i	$-0.559565\pi$
$313$	−6.58271	−0.372077	−0.186038	+	0.982542i	$0.559565\pi$
$314$	−8.07290	−0.455580
$315$	11.3896	0.641734
$316$	−12.1044	−0.680923
$317$	22.9791	1.29063	0.645317	−	0.763915i	$-0.276725\pi$
$317$	22.9791	1.29063	0.645317	+	0.763915i	$0.276725\pi$
$318$	13.4314	0.753196
$319$	22.8182	1.27758
$320$	23.1206	1.29248
$321$	−4.39098	−0.245080
$322$	31.5086	1.75591
$323$	−42.5182	−2.36578
$324$	−0.892804	−0.0496002
$325$	−22.4971	−1.24792
$326$	4.11146	0.227713
$327$	13.9009	0.768719
$328$	−12.7495	−0.703974
$329$	30.7799	1.69695
$330$	−15.6483	−0.861409
$331$	27.2963	1.50034	0.750171	−	0.661244i	$-0.229971\pi$
$331$	27.2963	1.50034	0.750171	+	0.661244i	$0.229971\pi$
$332$	8.91284	0.489156
$333$	5.57165	0.305325
$334$	−9.05052	−0.495223
$335$	−18.9080	−1.03305
$336$	−5.35589	−0.292188
$337$	7.93185	0.432075	0.216038	−	0.976385i	$-0.430687\pi$
$337$	7.93185	0.432075	0.216038	+	0.976385i	$0.430687\pi$
$338$	−18.2511	−0.992731
$339$	17.9146	0.972988
$340$	20.7246	1.12395
$341$	17.4606	0.945544
$342$	−5.80892	−0.314111
$343$	1.06015	0.0572427
$344$	−0.148892	−0.00802771
$345$	−23.8827	−1.28580
$346$	11.8510	0.637116
$347$	4.00227	0.214853	0.107427	−	0.994213i	$-0.465739\pi$
$347$	4.00227	0.214853	0.107427	+	0.994213i	$0.465739\pi$
$348$	−4.12878	−0.221326
$349$	7.14623	0.382529	0.191265	−	0.981539i	$-0.438741\pi$
$349$	7.14623	0.382529	0.191265	+	0.981539i	$0.438741\pi$
$350$	−16.2393	−0.868027
$351$	−5.50864	−0.294030
$352$	−22.6800	−1.20885
$353$	−24.4226	−1.29988	−0.649941	−	0.759985i	$-0.725206\pi$
$353$	−24.4226	−1.29988	−0.649941	+	0.759985i	$0.725206\pi$
$354$	2.70794	0.143926
$355$	2.19955	0.116740
$356$	−3.28275	−0.173985
$357$	−29.1047	−1.54039
$358$	−4.97786	−0.263088
$359$	21.3702	1.12788	0.563939	−	0.825817i	$-0.309285\pi$
$359$	21.3702	1.12788	0.563939	+	0.825817i	$0.309285\pi$
$360$	9.17422	0.483524
$361$	11.4766	0.604034
$362$	6.58739	0.346226
$363$	13.3463	0.700498
$364$	18.5855	0.974142
$365$	9.84713	0.515422
$366$	7.03230	0.367584
$367$	11.7128	0.611404	0.305702	−	0.952127i	$-0.401109\pi$
$367$	11.7128	0.611404	0.305702	+	0.952127i	$0.401109\pi$
$368$	11.2306	0.585438
$369$	−4.18854	−0.218047
$370$	−17.6699	−0.918614
$371$	−48.2372	−2.50435
$372$	−3.15936	−0.163805
$373$	−9.30022	−0.481547	−0.240774	−	0.970581i	$-0.577401\pi$
$373$	−9.30022	−0.481547	−0.240774	+	0.970581i	$0.577401\pi$
$374$	39.9871	2.06768
$375$	−2.76087	−0.142571
$376$	24.7928	1.27859
$377$	−25.4748	−1.31202
$378$	−3.97635	−0.204521
$379$	−21.6015	−1.10959	−0.554797	−	0.831986i	$-0.687204\pi$
$379$	−21.6015	−1.10959	−0.554797	+	0.831986i	$0.687204\pi$
$380$	−14.8552	−0.762054
$381$	−4.10722	−0.210419
$382$	5.47918	0.280339
$383$	−35.1084	−1.79395	−0.896977	−	0.442077i	$-0.854242\pi$
$383$	−35.1084	−1.79395	−0.896977	+	0.442077i	$0.854242\pi$
$384$	1.12112	0.0572120
$385$	56.1987	2.86415
$386$	1.05223	0.0535573
$387$	−0.0489147	−0.00248647
$388$	−0.648203	−0.0329075
$389$	12.8340	0.650709	0.325355	−	0.945592i	$-0.394516\pi$
$389$	12.8340	0.650709	0.325355	+	0.945592i	$0.394516\pi$
$390$	17.4701	0.884631
$391$	61.0291	3.08637
$392$	22.1613	1.11931
$393$	−8.72840	−0.440290
$394$	14.0460	0.707626
$395$	40.8623	2.05601
$396$	−4.40527	−0.221373
$397$	−12.6635	−0.635565	−0.317783	−	0.948164i	$-0.602938\pi$
$397$	−12.6635	−0.635565	−0.317783	+	0.948164i	$0.602938\pi$
$398$	3.53556	0.177221
$399$	20.8620	1.04441
$400$	−5.78818	−0.289409
$401$	4.24500	0.211985	0.105993	−	0.994367i	$-0.466198\pi$
$401$	4.24500	0.211985	0.105993	+	0.994367i	$0.466198\pi$
$402$	6.60115	0.329236
$403$	−19.4934	−0.971034
$404$	5.92527	0.294793
$405$	3.01396	0.149765
$406$	−18.3887	−0.912614
$407$	27.4916	1.36271
$408$	−23.4435	−1.16063
$409$	13.3699	0.661099	0.330550	−	0.943789i	$-0.392766\pi$
$409$	13.3699	0.661099	0.330550	+	0.943789i	$0.392766\pi$
$410$	13.2835	0.656025
$411$	−9.86915	−0.486809
$412$	5.42956	0.267495
$413$	−9.72522	−0.478547
$414$	8.33791	0.409786
$415$	−30.0883	−1.47698
$416$	25.3204	1.24144
$417$	−11.1281	−0.544945
$418$	−28.6624	−1.40192
$419$	−24.9650	−1.21962	−0.609810	−	0.792547i	$-0.708754\pi$
$419$	−24.9650	−1.21962	−0.609810	+	0.792547i	$0.708754\pi$
$420$	−10.1687	−0.496183
$421$	23.3482	1.13792	0.568962	−	0.822364i	$-0.307345\pi$
$421$	23.3482	1.13792	0.568962	+	0.822364i	$0.307345\pi$
$422$	14.7212	0.716616
$423$	8.14508	0.396027
$424$	−38.8545	−1.88694
$425$	−31.4539	−1.52574
$426$	−0.767906	−0.0372052
$427$	−25.2556	−1.22220
$428$	3.92028	0.189494
$429$	−27.1807	−1.31230
$430$	0.155128	0.00748092
$431$	−22.4189	−1.07988	−0.539940	−	0.841703i	$-0.681553\pi$
$431$	−22.4189	−1.07988	−0.539940	+	0.841703i	$0.681553\pi$
$432$	−1.41729	−0.0681895
$433$	−30.0547	−1.44433	−0.722167	−	0.691718i	$-0.756854\pi$
$433$	−30.0547	−1.44433	−0.722167	+	0.691718i	$0.756854\pi$
$434$	−14.0711	−0.675433
$435$	13.9381	0.668281
$436$	−12.4107	−0.594367
$437$	−43.7450	−2.09261
$438$	−3.43783	−0.164266
$439$	−15.8831	−0.758058	−0.379029	−	0.925385i	$-0.623742\pi$
$439$	−15.8831	−0.758058	−0.379029	+	0.925385i	$0.623742\pi$
$440$	45.2674	2.15804
$441$	7.28054	0.346692
$442$	−44.6425	−2.12343
$443$	−14.2038	−0.674845	−0.337422	−	0.941353i	$-0.609555\pi$
$443$	−14.2038	−0.674845	−0.337422	+	0.941353i	$0.609555\pi$
$444$	−4.97440	−0.236074
$445$	11.0820	0.525339
$446$	−1.17576	−0.0556739
$447$	−4.12963	−0.195325
$448$	28.9890	1.36960
$449$	−19.6860	−0.929040	−0.464520	−	0.885563i	$-0.653773\pi$
$449$	−19.6860	−0.929040	−0.464520	+	0.885563i	$0.653773\pi$
$450$	−4.29729	−0.202576
$451$	−20.6671	−0.973174
$452$	−15.9942	−0.752306
$453$	−0.708420	−0.0332845
$454$	−8.43769	−0.396000
$455$	−62.7415	−2.94137
$456$	16.8041	0.786923
$457$	−18.6845	−0.874024	−0.437012	−	0.899456i	$-0.643963\pi$
$457$	−18.6845	−0.874024	−0.437012	+	0.899456i	$0.643963\pi$
$458$	−29.7608	−1.39063
$459$	−7.70179	−0.359489
$460$	21.3226	0.994170
$461$	−16.1678	−0.753012	−0.376506	−	0.926414i	$-0.622875\pi$
$461$	−16.1678	−0.753012	−0.376506	+	0.926414i	$0.622875\pi$
$462$	−19.6201	−0.912809
$463$	−6.67465	−0.310197	−0.155099	−	0.987899i	$-0.549570\pi$
$463$	−6.67465	−0.310197	−0.155099	+	0.987899i	$0.549570\pi$
$464$	−6.55428	−0.304275
$465$	10.6655	0.494600
$466$	−0.483124	−0.0223803
$467$	6.01221	0.278212	0.139106	−	0.990277i	$-0.455577\pi$
$467$	6.01221	0.278212	0.139106	+	0.990277i	$0.455577\pi$
$468$	4.91814	0.227341
$469$	−23.7072	−1.09470
$470$	−25.8312	−1.19151
$471$	7.67216	0.353514
$472$	−7.83355	−0.360568
$473$	−0.241355	−0.0110975
$474$	−14.2658	−0.655252
$475$	22.5458	1.03447
$476$	25.9848	1.19101
$477$	−12.7647	−0.584454
$478$	20.0131	0.915379
$479$	−7.74813	−0.354021	−0.177011	−	0.984209i	$-0.556643\pi$
$479$	−7.74813	−0.354021	−0.177011	+	0.984209i	$0.556643\pi$
$480$	−13.8537	−0.632330
$481$	−30.6922	−1.39945
$482$	23.0571	1.05022
$483$	−29.9445	−1.36252
$484$	−11.9156	−0.541619
$485$	2.18823	0.0993624
$486$	−1.05223	−0.0477303
$487$	23.7671	1.07699	0.538495	−	0.842629i	$-0.318993\pi$
$487$	23.7671	1.07699	0.538495	+	0.842629i	$0.318993\pi$
$488$	−20.3431	−0.920888
$489$	−3.90736	−0.176697
$490$	−23.0895	−1.04308
$491$	−18.9106	−0.853426	−0.426713	−	0.904387i	$-0.640328\pi$
$491$	−18.9106	−0.853426	−0.426713	+	0.904387i	$0.640328\pi$
$492$	3.73954	0.168592
$493$	−35.6170	−1.60411
$494$	31.9993	1.43972
$495$	14.8715	0.668423
$496$	−5.01536	−0.225196
$497$	2.75783	0.123706
$498$	10.5044	0.470714
$499$	−27.2736	−1.22093	−0.610466	−	0.792042i	$-0.709018\pi$
$499$	−27.2736	−1.22093	−0.610466	+	0.792042i	$0.709018\pi$
$500$	2.46492	0.110235
$501$	8.60125	0.384275
$502$	−16.8377	−0.751502
$503$	−1.64508	−0.0733507	−0.0366754	−	0.999327i	$-0.511677\pi$
$503$	−1.64508	−0.0733507	−0.0366754	+	0.999327i	$0.511677\pi$
$504$	11.5028	0.512375
$505$	−20.0027	−0.890110
$506$	41.1409	1.82894
$507$	17.3451	0.770324
$508$	3.66694	0.162694
$509$	31.0713	1.37721	0.688607	−	0.725135i	$-0.258223\pi$
$509$	31.0713	1.37721	0.688607	+	0.725135i	$0.258223\pi$
$510$	24.4254	1.08157
$511$	12.3465	0.546177
$512$	15.1428	0.669222
$513$	5.52057	0.243739
$514$	−7.50520	−0.331040
$515$	−18.3293	−0.807687
$516$	0.0436713	0.00192252
$517$	40.1894	1.76753
$518$	−22.1548	−0.973428
$519$	−11.2628	−0.494380
$520$	−50.5375	−2.21622
$521$	11.0807	0.485454	0.242727	−	0.970095i	$-0.421958\pi$
$521$	11.0807	0.485454	0.242727	+	0.970095i	$0.421958\pi$
$522$	−4.86607	−0.212982
$523$	20.4180	0.892816	0.446408	−	0.894830i	$-0.352703\pi$
$523$	20.4180	0.892816	0.446408	+	0.894830i	$0.352703\pi$
$524$	7.79275	0.340428
$525$	15.4332	0.673559
$526$	−17.0400	−0.742979
$527$	−27.2542	−1.18721
$528$	−6.99319	−0.304340
$529$	39.7900	1.73000
$530$	40.4818	1.75842
$531$	−2.57352	−0.111681
$532$	−18.6257	−0.807526
$533$	23.0732	0.999409
$534$	−3.86895	−0.167426
$535$	−13.2342	−0.572166
$536$	−19.0958	−0.824815
$537$	4.73076	0.204147
$538$	31.0917	1.34046
$539$	35.9236	1.54734
$540$	−2.69088	−0.115797
$541$	25.6550	1.10299	0.551496	−	0.834177i	$-0.314057\pi$
$541$	25.6550	1.10299	0.551496	+	0.834177i	$0.314057\pi$
$542$	12.5602	0.539505
$543$	−6.26039	−0.268659
$544$	35.4012	1.51781
$545$	41.8967	1.79466
$546$	21.9043	0.937417
$547$	21.9198	0.937222	0.468611	−	0.883405i	$-0.344755\pi$
$547$	21.9198	0.937222	0.468611	+	0.883405i	$0.344755\pi$
$548$	8.81122	0.376397
$549$	−6.68322	−0.285233
$550$	−21.2037	−0.904128
$551$	25.5299	1.08761
$552$	−24.1200	−1.02661
$553$	51.2339	2.17869
$554$	12.6197	0.536158
$555$	16.7928	0.712813
$556$	9.93522	0.421347
$557$	40.8767	1.73200	0.866001	−	0.500042i	$-0.166682\pi$
$557$	40.8767	1.73200	0.866001	+	0.500042i	$0.166682\pi$
$558$	−3.72353	−0.157630
$559$	0.269454	0.0113967
$560$	−16.1424	−0.682143
$561$	−38.0021	−1.60445
$562$	0.126627	0.00534144
$563$	26.8758	1.13268	0.566341	−	0.824171i	$-0.308359\pi$
$563$	26.8758	1.13268	0.566341	+	0.824171i	$0.308359\pi$
$564$	−7.27196	−0.306205
$565$	53.9940	2.27154
$566$	−21.4217	−0.900421
$567$	3.77896	0.158701
$568$	2.22140	0.0932080
$569$	−23.3458	−0.978709	−0.489354	−	0.872085i	$-0.662768\pi$
$569$	−23.3458	−0.978709	−0.489354	+	0.872085i	$0.662768\pi$
$570$	−17.5079	−0.733325
$571$	−36.1861	−1.51434	−0.757170	−	0.653218i	$-0.773419\pi$
$571$	−36.1861	−1.51434	−0.757170	+	0.653218i	$0.773419\pi$
$572$	24.2671	1.01466
$573$	−5.20719	−0.217534
$574$	16.6551	0.695170
$575$	−32.3615	−1.34957
$576$	7.67116	0.319632
$577$	35.2043	1.46557	0.732786	−	0.680459i	$-0.238219\pi$
$577$	35.2043	1.46557	0.732786	+	0.680459i	$0.238219\pi$
$578$	−44.5279	−1.85212
$579$	−1.00000	−0.0415586
$580$	−12.4440	−0.516709
$581$	−37.7253	−1.56511
$582$	−0.763954	−0.0316669
$583$	−62.9834	−2.60850
$584$	9.94496	0.411525
$585$	−16.6028	−0.686443
$586$	−11.5899	−0.478776
$587$	13.9848	0.577213	0.288607	−	0.957448i	$-0.406808\pi$
$587$	13.9848	0.577213	0.288607	+	0.957448i	$0.406808\pi$
$588$	−6.50010	−0.268060
$589$	19.5356	0.804949
$590$	8.16164	0.336009
$591$	−13.3487	−0.549093
$592$	−7.89666	−0.324551
$593$	−35.0102	−1.43769	−0.718847	−	0.695168i	$-0.755330\pi$
$593$	−35.0102	−1.43769	−0.718847	+	0.695168i	$0.755330\pi$
$594$	−5.19193	−0.213027
$595$	−87.7206	−3.59619
$596$	3.68695	0.151023
$597$	−3.36005	−0.137518
$598$	−45.9306	−1.87824
$599$	27.3102	1.11587	0.557933	−	0.829886i	$-0.311595\pi$
$599$	27.3102	1.11587	0.557933	+	0.829886i	$0.311595\pi$
$600$	12.4312	0.507503
$601$	18.6952	0.762593	0.381297	−	0.924453i	$-0.375478\pi$
$601$	18.6952	0.762593	0.381297	+	0.924453i	$0.375478\pi$
$602$	0.194502	0.00792731
$603$	−6.27347	−0.255475
$604$	0.632480	0.0257353
$605$	40.2252	1.63539
$606$	6.98335	0.283679
$607$	26.2091	1.06379	0.531897	−	0.846809i	$-0.321479\pi$
$607$	26.2091	1.06379	0.531897	+	0.846809i	$0.321479\pi$
$608$	−25.3752	−1.02910
$609$	17.4758	0.708157
$610$	21.1951	0.858165
$611$	−44.8683	−1.81518
$612$	6.87619	0.277953
$613$	39.7830	1.60682	0.803409	−	0.595427i	$-0.203017\pi$
$613$	39.7830	1.60682	0.803409	+	0.595427i	$0.203017\pi$
$614$	−2.19652	−0.0886442
$615$	−12.6241	−0.509053
$616$	56.7571	2.28681
$617$	4.60878	0.185543	0.0927713	−	0.995687i	$-0.470427\pi$
$617$	4.60878	0.185543	0.0927713	+	0.995687i	$0.470427\pi$
$618$	6.39913	0.257411
$619$	−5.75041	−0.231129	−0.115564	−	0.993300i	$-0.536868\pi$
$619$	−5.75041	−0.231129	−0.115564	+	0.993300i	$0.536868\pi$
$620$	−9.52219	−0.382420
$621$	−7.92401	−0.317980
$622$	7.63204	0.306017
$623$	13.8948	0.556685
$624$	7.80735	0.312544
$625$	−28.7410	−1.14964
$626$	6.92655	0.276840
$627$	27.2395	1.08784
$628$	−6.84974	−0.273334
$629$	−42.9117	−1.71100
$630$	−11.9846	−0.477477
$631$	21.8440	0.869595	0.434798	−	0.900528i	$-0.356820\pi$
$631$	21.8440	0.869595	0.434798	+	0.900528i	$0.356820\pi$
$632$	41.2683	1.64157
$633$	−13.9904	−0.556069
$634$	−24.1794	−0.960286
$635$	−12.3790	−0.491246
$636$	11.3964	0.451895
$637$	−40.1059	−1.58905
$638$	−24.0101	−0.950569
$639$	0.729787	0.0288699
$640$	3.37902	0.133568
$641$	38.2227	1.50970	0.754852	−	0.655895i	$-0.227709\pi$
$641$	38.2227	1.50970	0.754852	+	0.655895i	$0.227709\pi$
$642$	4.62033	0.182350
$643$	17.4577	0.688463	0.344232	−	0.938885i	$-0.388139\pi$
$643$	17.4577	0.688463	0.344232	+	0.938885i	$0.388139\pi$
$644$	26.7346	1.05349
$645$	−0.147427	−0.00580494
$646$	44.7391	1.76024
$647$	−5.94129	−0.233576	−0.116788	−	0.993157i	$-0.537260\pi$
$647$	−5.94129	−0.233576	−0.116788	+	0.993157i	$0.537260\pi$
$648$	3.04391	0.119576
$649$	−12.6982	−0.498450
$650$	23.6722	0.928502
$651$	13.3726	0.524112
$652$	3.48851	0.136621
$653$	28.2240	1.10449	0.552245	−	0.833682i	$-0.313771\pi$
$653$	28.2240	1.10449	0.552245	+	0.833682i	$0.313771\pi$
$654$	−14.6270	−0.571959
$655$	−26.3071	−1.02790
$656$	5.93638	0.231777
$657$	3.26717	0.127464
$658$	−32.3877	−1.26260
$659$	−16.1919	−0.630748	−0.315374	−	0.948967i	$-0.602130\pi$
$659$	−16.1919	−0.630748	−0.315374	+	0.948967i	$0.602130\pi$
$660$	−13.2773	−0.516819
$661$	28.8422	1.12183	0.560916	−	0.827872i	$-0.310449\pi$
$661$	28.8422	1.12183	0.560916	+	0.827872i	$0.310449\pi$
$662$	−28.7221	−1.11632
$663$	42.4264	1.64770
$664$	−30.3872	−1.17925
$665$	62.8773	2.43828
$666$	−5.86268	−0.227174
$667$	−36.6447	−1.41889
$668$	−7.67923	−0.297118
$669$	1.11740	0.0432010
$670$	19.8956	0.768635
$671$	−32.9763	−1.27304
$672$	−17.3700	−0.670060
$673$	−28.7029	−1.10642	−0.553208	−	0.833043i	$-0.686597\pi$
$673$	−28.7029	−1.10642	−0.553208	+	0.833043i	$0.686597\pi$
$674$	−8.34616	−0.321482
$675$	4.08397	0.157192
$676$	−15.4858	−0.595608
$677$	−3.50728	−0.134796	−0.0673978	−	0.997726i	$-0.521470\pi$
$677$	−3.50728	−0.134796	−0.0673978	+	0.997726i	$0.521470\pi$
$678$	−18.8504	−0.723944
$679$	2.74364	0.105291
$680$	−70.6579	−2.70961
$681$	8.01883	0.307282
$682$	−18.3726	−0.703524
$683$	1.68618	0.0645199	0.0322600	−	0.999480i	$-0.489730\pi$
$683$	1.68618	0.0645199	0.0322600	+	0.999480i	$0.489730\pi$
$684$	−4.92878	−0.188457
$685$	−29.7452	−1.13651
$686$	−1.11552	−0.0425909
$687$	28.2834	1.07908
$688$	0.0693264	0.00264304
$689$	70.3160	2.67883
$690$	25.1302	0.956689
$691$	44.3789	1.68825	0.844126	−	0.536145i	$-0.180120\pi$
$691$	44.3789	1.68825	0.844126	+	0.536145i	$0.180120\pi$
$692$	10.0554	0.382250
$693$	18.6461	0.708308
$694$	−4.21133	−0.159860
$695$	−33.5397	−1.27223
$696$	14.0766	0.533571
$697$	32.2592	1.22190
$698$	−7.51951	−0.284618
$699$	0.459141	0.0173663
$700$	−13.7788	−0.520790
$701$	−40.8579	−1.54318	−0.771591	−	0.636118i	$-0.780539\pi$
$701$	−40.8579	−1.54318	−0.771591	+	0.636118i	$0.780539\pi$
$702$	5.79638	0.218770
$703$	30.7587	1.16009
$704$	37.8510	1.42656
$705$	24.5490	0.924567
$706$	25.6982	0.967166
$707$	−25.0798	−0.943222
$708$	2.29765	0.0863509
$709$	5.05933	0.190007	0.0950036	−	0.995477i	$-0.469714\pi$
$709$	5.05933	0.190007	0.0950036	+	0.995477i	$0.469714\pi$
$710$	−2.31444	−0.0868594
$711$	13.5577	0.508453
$712$	11.1921	0.419443
$713$	−28.0406	−1.05013
$714$	30.6250	1.14611
$715$	−81.9216	−3.06370
$716$	−4.22364	−0.157845
$717$	−19.0197	−0.710302
$718$	−22.4865	−0.839188
$719$	−17.6286	−0.657437	−0.328719	−	0.944428i	$-0.606617\pi$
$719$	−17.6286	−0.657437	−0.328719	+	0.944428i	$0.606617\pi$
$720$	−4.27166	−0.159196
$721$	−22.9816	−0.855881
$722$	−12.0761	−0.449426
$723$	−21.9125	−0.814935
$724$	5.58930	0.207725
$725$	18.8864	0.701422
$726$	−14.0434	−0.521199
$727$	50.8085	1.88438	0.942192	−	0.335073i	$-0.108761\pi$
$727$	50.8085	1.88438	0.942192	+	0.335073i	$0.108761\pi$
$728$	−63.3648	−2.34846
$729$	1.00000	0.0370370
$730$	−10.3615	−0.383495
$731$	0.376731	0.0139339
$732$	5.96680	0.220539
$733$	−22.3958	−0.827208	−0.413604	−	0.910457i	$-0.635730\pi$
$733$	−22.3958	−0.827208	−0.413604	+	0.910457i	$0.635730\pi$
$734$	−12.3246	−0.454910
$735$	21.9433	0.809390
$736$	36.4227	1.34256
$737$	−30.9545	−1.14022
$738$	4.40732	0.162236
$739$	3.41760	0.125719	0.0628593	−	0.998022i	$-0.479978\pi$
$739$	3.41760	0.125719	0.0628593	+	0.998022i	$0.479978\pi$
$740$	−14.9926	−0.551141
$741$	−30.4108	−1.11717
$742$	50.7568	1.86334
$743$	−8.83892	−0.324268	−0.162134	−	0.986769i	$-0.551838\pi$
$743$	−8.83892	−0.324268	−0.162134	+	0.986769i	$0.551838\pi$
$744$	10.7714	0.394900
$745$	−12.4465	−0.456006
$746$	9.78601	0.358291
$747$	−9.98298	−0.365258
$748$	33.9284	1.24055
$749$	−16.5933	−0.606307
$750$	2.90508	0.106079
$751$	39.3748	1.43681	0.718403	−	0.695627i	$-0.244873\pi$
$751$	39.3748	1.43681	0.718403	+	0.695627i	$0.244873\pi$
$752$	−11.5439	−0.420964
$753$	16.0018	0.583139
$754$	26.8054	0.976195
$755$	−2.13515	−0.0777061
$756$	−3.37387	−0.122707
$757$	−43.8895	−1.59519	−0.797596	−	0.603192i	$-0.793895\pi$
$757$	−43.8895	−1.59519	−0.797596	+	0.603192i	$0.793895\pi$
$758$	22.7298	0.825584
$759$	−39.0986	−1.41919
$760$	50.6469	1.83716
$761$	−54.3535	−1.97031	−0.985156	−	0.171660i	$-0.945087\pi$
$761$	−54.3535	−1.97031	−0.985156	+	0.171660i	$0.945087\pi$
$762$	4.32175	0.156561
$763$	52.5308	1.90174
$764$	4.64900	0.168195
$765$	−23.2129	−0.839264
$766$	36.9422	1.33478
$767$	14.1766	0.511887
$768$	−16.5220	−0.596187
$769$	−25.6784	−0.925987	−0.462994	−	0.886362i	$-0.653225\pi$
$769$	−25.6784	−0.925987	−0.462994	+	0.886362i	$0.653225\pi$
$770$	−59.1342	−2.13105
$771$	7.13264	0.256876
$772$	0.892804	0.0321327
$773$	47.4057	1.70507	0.852533	−	0.522674i	$-0.175065\pi$
$773$	47.4057	1.70507	0.852533	+	0.522674i	$0.175065\pi$
$774$	0.0514697	0.00185004
$775$	14.4519	0.519128
$776$	2.20997	0.0793333
$777$	21.0551	0.755346
$778$	−13.5044	−0.484155
$779$	−23.1231	−0.828471
$780$	14.8231	0.530752
$781$	3.60091	0.128851
$782$	−64.2168	−2.29639
$783$	4.62451	0.165267
$784$	−10.3186	−0.368523
$785$	23.1236	0.825317
$786$	9.18432	0.327594
$787$	−29.5503	−1.05335	−0.526677	−	0.850065i	$-0.676562\pi$
$787$	−29.5503	−1.05335	−0.526677	+	0.850065i	$0.676562\pi$
$788$	11.9178	0.424554
$789$	16.1941	0.576526
$790$	−42.9967	−1.52976
$791$	67.6986	2.40708
$792$	15.0192	0.533685
$793$	36.8154	1.30735
$794$	13.3250	0.472887
$795$	−38.4722	−1.36447
$796$	2.99987	0.106327
$797$	−43.6617	−1.54658	−0.773289	−	0.634054i	$-0.781390\pi$
$797$	−43.6617	−1.54658	−0.773289	+	0.634054i	$0.781390\pi$
$798$	−21.9517	−0.777082
$799$	−62.7316	−2.21929
$800$	−18.7719	−0.663688
$801$	3.67690	0.129917
$802$	−4.46673	−0.157726
$803$	16.1208	0.568892
$804$	5.60098	0.197531
$805$	−90.2517	−3.18096
$806$	20.5116	0.722490
$807$	−29.5483	−1.04015
$808$	−20.2015	−0.710685
$809$	38.5615	1.35575	0.677875	−	0.735177i	$-0.262901\pi$
$809$	38.5615	1.35575	0.677875	+	0.735177i	$0.262901\pi$
$810$	−3.17139	−0.111431
$811$	44.9627	1.57885	0.789427	−	0.613844i	$-0.210378\pi$
$811$	44.9627	1.57885	0.789427	+	0.613844i	$0.210378\pi$
$812$	−15.6025	−0.547541
$813$	−11.9367	−0.418637
$814$	−28.9276	−1.01391
$815$	−11.7766	−0.412518
$816$	10.9157	0.382125
$817$	−0.270037	−0.00944739
$818$	−14.0683	−0.491885
$819$	−20.8169	−0.727403
$820$	11.2708	0.393595
$821$	30.6399	1.06934	0.534671	−	0.845061i	$-0.320436\pi$
$821$	30.6399	1.06934	0.534671	+	0.845061i	$0.320436\pi$
$822$	10.3846	0.362206
$823$	42.9964	1.49876	0.749380	−	0.662140i	$-0.230352\pi$
$823$	42.9964	1.49876	0.749380	+	0.662140i	$0.230352\pi$
$824$	−18.5114	−0.644876
$825$	20.1511	0.701572
$826$	10.2332	0.356059
$827$	53.4632	1.85910	0.929548	−	0.368700i	$-0.120197\pi$
$827$	53.4632	1.85910	0.929548	+	0.368700i	$0.120197\pi$
$828$	7.07459	0.245859
$829$	44.7236	1.55332	0.776658	−	0.629923i	$-0.216913\pi$
$829$	44.7236	1.55332	0.776658	+	0.629923i	$0.216913\pi$
$830$	31.6599	1.09893
$831$	−11.9932	−0.416040
$832$	−42.2577	−1.46502
$833$	−56.0732	−1.94282
$834$	11.7094	0.405462
$835$	25.9238	0.897132
$836$	−24.3196	−0.841110
$837$	3.53869	0.122315
$838$	26.2690	0.907448
$839$	−48.7683	−1.68367	−0.841834	−	0.539737i	$-0.818524\pi$
$839$	−48.7683	−1.68367	−0.841834	+	0.539737i	$0.818524\pi$
$840$	34.6690	1.19619
$841$	−7.61391	−0.262548
$842$	−24.5678	−0.846662
$843$	−0.120341	−0.00414477
$844$	12.4907	0.429947
$845$	52.2776	1.79840
$846$	−8.57052	−0.294661
$847$	50.4350	1.73297
$848$	18.0913	0.621256
$849$	20.3583	0.698695
$850$	33.0968	1.13521
$851$	−44.1499	−1.51344
$852$	−0.651557	−0.0223220
$853$	−53.3269	−1.82588	−0.912940	−	0.408095i	$-0.866193\pi$
$853$	−53.3269	−1.82588	−0.912940	+	0.408095i	$0.866193\pi$
$854$	26.5748	0.909371
$855$	16.6388	0.569034
$856$	−13.3657	−0.456831
$857$	43.4856	1.48544	0.742721	−	0.669602i	$-0.233535\pi$
$857$	43.4856	1.48544	0.742721	+	0.669602i	$0.233535\pi$
$858$	28.6005	0.976403
$859$	−21.9762	−0.749818	−0.374909	−	0.927062i	$-0.622326\pi$
$859$	−21.9762	−0.749818	−0.374909	+	0.927062i	$0.622326\pi$
$860$	0.131624	0.00448833
$861$	−15.8283	−0.539428
$862$	23.5899	0.803476
$863$	50.2611	1.71091	0.855454	−	0.517878i	$-0.173278\pi$
$863$	50.2611	1.71091	0.855454	+	0.517878i	$0.173278\pi$
$864$	−4.59649	−0.156376
$865$	−33.9455	−1.15418
$866$	31.6245	1.07465
$867$	42.3175	1.43718
$868$	−11.9391	−0.405239
$869$	66.8962	2.26930
$870$	−14.6661	−0.497229
$871$	34.5583	1.17096
$872$	42.3129	1.43290
$873$	0.726031	0.0245724
$874$	46.0300	1.55699
$875$	−10.4332	−0.352708
$876$	−2.91694	−0.0985544
$877$	3.36641	0.113676	0.0568378	−	0.998383i	$-0.481898\pi$
$877$	3.36641	0.113676	0.0568378	+	0.998383i	$0.481898\pi$
$878$	16.7127	0.564026
$879$	11.0146	0.371513
$880$	−21.0772	−0.710513
$881$	−1.50473	−0.0506956	−0.0253478	−	0.999679i	$-0.508069\pi$
$881$	−1.50473	−0.0506956	−0.0253478	+	0.999679i	$0.508069\pi$
$882$	−7.66083	−0.257954
$883$	−42.1862	−1.41968	−0.709839	−	0.704364i	$-0.751232\pi$
$883$	−42.1862	−1.41968	−0.709839	+	0.704364i	$0.751232\pi$
$884$	−37.8785	−1.27399
$885$	−7.75649	−0.260732
$886$	14.9458	0.502113
$887$	−16.5406	−0.555378	−0.277689	−	0.960671i	$-0.589568\pi$
$887$	−16.5406	−0.555378	−0.277689	+	0.960671i	$0.589568\pi$
$888$	16.9596	0.569126
$889$	−15.5210	−0.520558
$890$	−11.6609	−0.390874
$891$	4.93419	0.165302
$892$	−0.997616	−0.0334026
$893$	44.9654	1.50471
$894$	4.34533	0.145330
$895$	14.2583	0.476603
$896$	4.23668	0.141537
$897$	43.6506	1.45745
$898$	20.7143	0.691244
$899$	16.3647	0.545794
$900$	−3.64619	−0.121540
$901$	98.3108	3.27521
$902$	21.7466	0.724082
$903$	−0.184847	−0.00615131
$904$	54.5304	1.81365
$905$	−18.8686	−0.627213
$906$	0.745423	0.0247650
$907$	−16.8652	−0.560001	−0.280000	−	0.960000i	$-0.590335\pi$
$907$	−16.8652	−0.560001	−0.280000	+	0.960000i	$0.590335\pi$
$908$	−7.15925	−0.237588
$909$	−6.63669	−0.220125
$910$	66.0187	2.18850
$911$	28.7345	0.952018	0.476009	−	0.879440i	$-0.342083\pi$
$911$	28.7345	0.952018	0.476009	+	0.879440i	$0.342083\pi$
$912$	−7.82425	−0.259087
$913$	−49.2579	−1.63020
$914$	19.6604	0.650310
$915$	−20.1430	−0.665906
$916$	−25.2516	−0.834335
$917$	−32.9843	−1.08924
$918$	8.10408	0.267474
$919$	−37.6678	−1.24255	−0.621273	−	0.783594i	$-0.713384\pi$
$919$	−37.6678	−1.24255	−0.621273	+	0.783594i	$0.713384\pi$
$920$	−72.6967	−2.39674
$921$	2.08748	0.0687848
$922$	17.0124	0.560272
$923$	−4.02013	−0.132324
$924$	−16.6473	−0.547657
$925$	22.7545	0.748162
$926$	7.02329	0.230800
$927$	−6.08147	−0.199742
$928$	−21.2565	−0.697779
$929$	−15.8367	−0.519586	−0.259793	−	0.965664i	$-0.583654\pi$
$929$	−15.8367	−0.519586	−0.259793	+	0.965664i	$0.583654\pi$
$930$	−11.2226	−0.368003
$931$	40.1927	1.31726
$932$	−0.409923	−0.0134275
$933$	−7.25318	−0.237458
$934$	−6.32625	−0.207001
$935$	−114.537	−3.74576
$936$	−16.7678	−0.548072
$937$	−9.19075	−0.300249	−0.150124	−	0.988667i	$-0.547967\pi$
$937$	−9.19075	−0.300249	−0.150124	+	0.988667i	$0.547967\pi$
$938$	24.9455	0.814499
$939$	−6.58271	−0.214819
$940$	−21.9174	−0.714867
$941$	21.3247	0.695164	0.347582	−	0.937650i	$-0.387003\pi$
$941$	21.3247	0.695164	0.347582	+	0.937650i	$0.387003\pi$
$942$	−8.07290	−0.263029
$943$	33.1900	1.08082
$944$	3.64743	0.118714
$945$	11.3896	0.370505
$946$	0.253961	0.00825700
$947$	34.7747	1.13003	0.565013	−	0.825082i	$-0.308871\pi$
$947$	34.7747	1.13003	0.565013	+	0.825082i	$0.308871\pi$
$948$	−12.1044	−0.393131
$949$	−17.9977	−0.584229
$950$	−23.7235	−0.769692
$951$	22.9791	0.745148
$952$	−88.5921	−2.87129
$953$	−0.0530140	−0.00171729	−0.000858646	−	1.00000i	$-0.500273\pi$
$953$	−0.0530140	−0.00171729	−0.000858646		1.00000i	$0.500273\pi$
$954$	13.4314	0.434858
$955$	−15.6943	−0.507855
$956$	16.9808	0.549199
$957$	22.8182	0.737609
$958$	8.15284	0.263406
$959$	−37.2951	−1.20432
$960$	23.1206	0.746214
$961$	−18.4777	−0.596054
$962$	32.2954	1.04125
$963$	−4.39098	−0.141497
$964$	19.5636	0.630101
$965$	−3.01396	−0.0970229
$966$	31.5086	1.01377
$967$	25.2732	0.812733	0.406366	−	0.913710i	$-0.366796\pi$
$967$	25.2732	0.812733	0.406366	+	0.913710i	$0.366796\pi$
$968$	40.6248	1.30573
$969$	−42.5182	−1.36588
$970$	−2.30253	−0.0739297
$971$	22.8028	0.731775	0.365888	−	0.930659i	$-0.380765\pi$
$971$	22.8028	0.731775	0.365888	+	0.930659i	$0.380765\pi$
$972$	−0.892804	−0.0286367
$973$	−42.0527	−1.34815
$974$	−25.0085	−0.801325
$975$	−22.4971	−0.720485
$976$	9.47207	0.303193
$977$	−13.7179	−0.438876	−0.219438	−	0.975626i	$-0.570422\pi$
$977$	−13.7179	−0.438876	−0.219438	+	0.975626i	$0.570422\pi$
$978$	4.11146	0.131470
$979$	18.1425	0.579838
$980$	−19.5911	−0.625813
$981$	13.9009	0.443820
$982$	19.8984	0.634984
$983$	5.25861	0.167724	0.0838618	−	0.996477i	$-0.473275\pi$
$983$	5.25861	0.167724	0.0838618	+	0.996477i	$0.473275\pi$
$984$	−12.7495	−0.406440
$985$	−40.2325	−1.28192
$986$	37.4774	1.19352
$987$	30.7799	0.979736
$988$	27.1509	0.863786
$989$	0.387601	0.0123250
$990$	−15.6483	−0.497335
$991$	−29.5793	−0.939618	−0.469809	−	0.882768i	$-0.655677\pi$
$991$	−29.5793	−0.939618	−0.469809	+	0.882768i	$0.655677\pi$
$992$	−16.2656	−0.516432
$993$	27.2963	0.866223
$994$	−2.90189	−0.0920423
$995$	−10.1271	−0.321050
$996$	8.91284	0.282414
$997$	40.8901	1.29500	0.647502	−	0.762064i	$-0.275814\pi$
$997$	40.8901	1.29500	0.647502	+	0.762064i	$0.275814\pi$
$998$	28.6982	0.908425
$999$	5.57165	0.176279

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	579.2.a.g.1.5	✓	13
3.2	odd	2		1737.2.a.j.1.9		13
4.3	odd	2		9264.2.a.bp.1.10		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
579.2.a.g.1.5	✓	13	1.1	even	1	trivial
1737.2.a.j.1.9		13	3.2	odd	2
9264.2.a.bp.1.10		13	4.3	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:	\( N \)	\(=\)	\( 579 = 3 \cdot 193 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	579.a (trivial)

\(f(q)\)	\(=\)	\(q-1.05223 q^{2} +1.00000 q^{3} -0.892804 q^{4} +3.01396 q^{5} -1.05223 q^{6} +3.77896 q^{7} +3.04391 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.05223 q^{2} +1.00000 q^{3} -0.892804 q^{4} +3.01396 q^{5} -1.05223 q^{6} +3.77896 q^{7} +3.04391 q^{8} +1.00000 q^{9} -3.17139 q^{10} +4.93419 q^{11} -0.892804 q^{12} -5.50864 q^{13} -3.97635 q^{14} +3.01396 q^{15} -1.41729 q^{16} -7.70179 q^{17} -1.05223 q^{18} +5.52057 q^{19} -2.69088 q^{20} +3.77896 q^{21} -5.19193 q^{22} -7.92401 q^{23} +3.04391 q^{24} +4.08397 q^{25} +5.79638 q^{26} +1.00000 q^{27} -3.37387 q^{28} +4.62451 q^{29} -3.17139 q^{30} +3.53869 q^{31} -4.59649 q^{32} +4.93419 q^{33} +8.10408 q^{34} +11.3896 q^{35} -0.892804 q^{36} +5.57165 q^{37} -5.80892 q^{38} -5.50864 q^{39} +9.17422 q^{40} -4.18854 q^{41} -3.97635 q^{42} -0.0489147 q^{43} -4.40527 q^{44} +3.01396 q^{45} +8.33791 q^{46} +8.14508 q^{47} -1.41729 q^{48} +7.28054 q^{49} -4.29729 q^{50} -7.70179 q^{51} +4.91814 q^{52} -12.7647 q^{53} -1.05223 q^{54} +14.8715 q^{55} +11.5028 q^{56} +5.52057 q^{57} -4.86607 q^{58} -2.57352 q^{59} -2.69088 q^{60} -6.68322 q^{61} -3.72353 q^{62} +3.77896 q^{63} +7.67116 q^{64} -16.6028 q^{65} -5.19193 q^{66} -6.27347 q^{67} +6.87619 q^{68} -7.92401 q^{69} -11.9846 q^{70} +0.729787 q^{71} +3.04391 q^{72} +3.26717 q^{73} -5.86268 q^{74} +4.08397 q^{75} -4.92878 q^{76} +18.6461 q^{77} +5.79638 q^{78} +13.5577 q^{79} -4.27166 q^{80} +1.00000 q^{81} +4.40732 q^{82} -9.98298 q^{83} -3.37387 q^{84} -23.2129 q^{85} +0.0514697 q^{86} +4.62451 q^{87} +15.0192 q^{88} +3.67690 q^{89} -3.17139 q^{90} -20.8169 q^{91} +7.07459 q^{92} +3.53869 q^{93} -8.57052 q^{94} +16.6388 q^{95} -4.59649 q^{96} +0.726031 q^{97} -7.66083 q^{98} +4.93419 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 2 q^{2} + 13 q^{3} + 18 q^{4} + 6 q^{5} + 2 q^{6} + 15 q^{7} + 3 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q + 2 * q^2 + 13 * q^3 + 18 * q^4 + 6 * q^5 + 2 * q^6 + 15 * q^7 + 3 * q^8 + 13 * q^9	\( 13 q + 2 q^{2} + 13 q^{3} + 18 q^{4} + 6 q^{5} + 2 q^{6} + 15 q^{7} + 3 q^{8} + 13 q^{9} - q^{10} + 3 q^{11} + 18 q^{12} + 11 q^{13} - 4 q^{14} + 6 q^{15} + 20 q^{16} - 2 q^{17} + 2 q^{18} + 9 q^{19} - 9 q^{20} + 15 q^{21} - 8 q^{22} - 8 q^{23} + 3 q^{24} + 21 q^{25} - 15 q^{26} + 13 q^{27} + 16 q^{28} + 5 q^{29} - q^{30} + 25 q^{31} - 17 q^{32} + 3 q^{33} - 10 q^{34} - 10 q^{35} + 18 q^{36} + 29 q^{37} - 40 q^{38} + 11 q^{39} - 21 q^{40} - 11 q^{41} - 4 q^{42} + 8 q^{43} - 18 q^{44} + 6 q^{45} - 6 q^{46} - 12 q^{47} + 20 q^{48} + 20 q^{49} - 4 q^{50} - 2 q^{51} + 2 q^{52} + 14 q^{53} + 2 q^{54} + 12 q^{55} - 7 q^{56} + 9 q^{57} + 9 q^{58} + 10 q^{59} - 9 q^{60} + 6 q^{61} - 14 q^{62} + 15 q^{63} + 23 q^{64} - 15 q^{65} - 8 q^{66} + 25 q^{67} - 33 q^{68} - 8 q^{69} - 21 q^{70} + 3 q^{72} + 8 q^{73} - 2 q^{74} + 21 q^{75} + 20 q^{76} - 25 q^{77} - 15 q^{78} + 7 q^{79} - 40 q^{80} + 13 q^{81} - 19 q^{82} - 28 q^{83} + 16 q^{84} - 3 q^{85} + 2 q^{86} + 5 q^{87} - 21 q^{88} + 7 q^{89} - q^{90} + 7 q^{91} + 9 q^{92} + 25 q^{93} - 35 q^{94} - 26 q^{95} - 17 q^{96} + 26 q^{97} - 14 q^{98} + 3 q^{99}+O(q^{100}) \) 13 * q + 2 * q^2 + 13 * q^3 + 18 * q^4 + 6 * q^5 + 2 * q^6 + 15 * q^7 + 3 * q^8 + 13 * q^9 - q^10 + 3 * q^11 + 18 * q^12 + 11 * q^13 - 4 * q^14 + 6 * q^15 + 20 * q^16 - 2 * q^17 + 2 * q^18 + 9 * q^19 - 9 * q^20 + 15 * q^21 - 8 * q^22 - 8 * q^23 + 3 * q^24 + 21 * q^25 - 15 * q^26 + 13 * q^27 + 16 * q^28 + 5 * q^29 - q^30 + 25 * q^31 - 17 * q^32 + 3 * q^33 - 10 * q^34 - 10 * q^35 + 18 * q^36 + 29 * q^37 - 40 * q^38 + 11 * q^39 - 21 * q^40 - 11 * q^41 - 4 * q^42 + 8 * q^43 - 18 * q^44 + 6 * q^45 - 6 * q^46 - 12 * q^47 + 20 * q^48 + 20 * q^49 - 4 * q^50 - 2 * q^51 + 2 * q^52 + 14 * q^53 + 2 * q^54 + 12 * q^55 - 7 * q^56 + 9 * q^57 + 9 * q^58 + 10 * q^59 - 9 * q^60 + 6 * q^61 - 14 * q^62 + 15 * q^63 + 23 * q^64 - 15 * q^65 - 8 * q^66 + 25 * q^67 - 33 * q^68 - 8 * q^69 - 21 * q^70 + 3 * q^72 + 8 * q^73 - 2 * q^74 + 21 * q^75 + 20 * q^76 - 25 * q^77 - 15 * q^78 + 7 * q^79 - 40 * q^80 + 13 * q^81 - 19 * q^82 - 28 * q^83 + 16 * q^84 - 3 * q^85 + 2 * q^86 + 5 * q^87 - 21 * q^88 + 7 * q^89 - q^90 + 7 * q^91 + 9 * q^92 + 25 * q^93 - 35 * q^94 - 26 * q^95 - 17 * q^96 + 26 * q^97 - 14 * q^98 + 3 * q^99

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