LMFDB - Embedded newform 6007.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6007,2,Mod(1,6007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6007, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6007 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6007.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:	$47.9661364942$
Analytic rank:	$2$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	6007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.61803 q^{2} -0.381966 q^{3} +0.618034 q^{4} -0.618034 q^{5} +0.618034 q^{6} -3.00000 q^{7} +2.23607 q^{8} -2.85410 q^{9} +O(q^{10})$	\(q-1.61803 q^{2} -0.381966 q^{3} +0.618034 q^{4} -0.618034 q^{5} +0.618034 q^{6} -3.00000 q^{7} +2.23607 q^{8} -2.85410 q^{9} +1.00000 q^{10} +4.23607 q^{11} -0.236068 q^{12} -3.00000 q^{13} +4.85410 q^{14} +0.236068 q^{15} -4.85410 q^{16} -3.38197 q^{17} +4.61803 q^{18} -3.00000 q^{19} -0.381966 q^{20} +1.14590 q^{21} -6.85410 q^{22} -7.23607 q^{23} -0.854102 q^{24} -4.61803 q^{25} +4.85410 q^{26} +2.23607 q^{27} -1.85410 q^{28} -8.47214 q^{29} -0.381966 q^{30} -1.14590 q^{31} +3.38197 q^{32} -1.61803 q^{33} +5.47214 q^{34} +1.85410 q^{35} -1.76393 q^{36} +1.14590 q^{37} +4.85410 q^{38} +1.14590 q^{39} -1.38197 q^{40} -6.00000 q^{41} -1.85410 q^{42} +0.0901699 q^{43} +2.61803 q^{44} +1.76393 q^{45} +11.7082 q^{46} +1.47214 q^{47} +1.85410 q^{48} +2.00000 q^{49} +7.47214 q^{50} +1.29180 q^{51} -1.85410 q^{52} +1.38197 q^{53} -3.61803 q^{54} -2.61803 q^{55} -6.70820 q^{56} +1.14590 q^{57} +13.7082 q^{58} +5.09017 q^{59} +0.145898 q^{60} -2.76393 q^{61} +1.85410 q^{62} +8.56231 q^{63} +4.23607 q^{64} +1.85410 q^{65} +2.61803 q^{66} +3.00000 q^{67} -2.09017 q^{68} +2.76393 q^{69} -3.00000 q^{70} -13.3820 q^{71} -6.38197 q^{72} -1.85410 q^{74} +1.76393 q^{75} -1.85410 q^{76} -12.7082 q^{77} -1.85410 q^{78} +7.32624 q^{79} +3.00000 q^{80} +7.70820 q^{81} +9.70820 q^{82} -13.1803 q^{83} +0.708204 q^{84} +2.09017 q^{85} -0.145898 q^{86} +3.23607 q^{87} +9.47214 q^{88} -0.472136 q^{89} -2.85410 q^{90} +9.00000 q^{91} -4.47214 q^{92} +0.437694 q^{93} -2.38197 q^{94} +1.85410 q^{95} -1.29180 q^{96} -2.52786 q^{97} -3.23607 q^{98} -12.0902 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - 3 q^{3} - q^{4} + q^{5} - q^{6} - 6 q^{7} + q^{9}+O(q^{10}) $ 2 * q - q^2 - 3 * q^3 - q^4 + q^5 - q^6 - 6 * q^7 + q^9	\( 2 q - q^{2} - 3 q^{3} - q^{4} + q^{5} - q^{6} - 6 q^{7} + q^{9} + 2 q^{10} + 4 q^{11} + 4 q^{12} - 6 q^{13} + 3 q^{14} - 4 q^{15} - 3 q^{16} - 9 q^{17} + 7 q^{18} - 6 q^{19} - 3 q^{20} + 9 q^{21} - 7 q^{22} - 10 q^{23} + 5 q^{24} - 7 q^{25} + 3 q^{26} + 3 q^{28} - 8 q^{29} - 3 q^{30} - 9 q^{31} + 9 q^{32} - q^{33} + 2 q^{34} - 3 q^{35} - 8 q^{36} + 9 q^{37} + 3 q^{38} + 9 q^{39} - 5 q^{40} - 12 q^{41} + 3 q^{42} - 11 q^{43} + 3 q^{44} + 8 q^{45} + 10 q^{46} - 6 q^{47} - 3 q^{48} + 4 q^{49} + 6 q^{50} + 16 q^{51} + 3 q^{52} + 5 q^{53} - 5 q^{54} - 3 q^{55} + 9 q^{57} + 14 q^{58} - q^{59} + 7 q^{60} - 10 q^{61} - 3 q^{62} - 3 q^{63} + 4 q^{64} - 3 q^{65} + 3 q^{66} + 6 q^{67} + 7 q^{68} + 10 q^{69} - 6 q^{70} - 29 q^{71} - 15 q^{72} + 3 q^{74} + 8 q^{75} + 3 q^{76} - 12 q^{77} + 3 q^{78} - q^{79} + 6 q^{80} + 2 q^{81} + 6 q^{82} - 4 q^{83} - 12 q^{84} - 7 q^{85} - 7 q^{86} + 2 q^{87} + 10 q^{88} + 8 q^{89} + q^{90} + 18 q^{91} + 21 q^{93} - 7 q^{94} - 3 q^{95} - 16 q^{96} - 14 q^{97} - 2 q^{98} - 13 q^{99}+O(q^{100}) \) 2 * q - q^2 - 3 * q^3 - q^4 + q^5 - q^6 - 6 * q^7 + q^9 + 2 * q^10 + 4 * q^11 + 4 * q^12 - 6 * q^13 + 3 * q^14 - 4 * q^15 - 3 * q^16 - 9 * q^17 + 7 * q^18 - 6 * q^19 - 3 * q^20 + 9 * q^21 - 7 * q^22 - 10 * q^23 + 5 * q^24 - 7 * q^25 + 3 * q^26 + 3 * q^28 - 8 * q^29 - 3 * q^30 - 9 * q^31 + 9 * q^32 - q^33 + 2 * q^34 - 3 * q^35 - 8 * q^36 + 9 * q^37 + 3 * q^38 + 9 * q^39 - 5 * q^40 - 12 * q^41 + 3 * q^42 - 11 * q^43 + 3 * q^44 + 8 * q^45 + 10 * q^46 - 6 * q^47 - 3 * q^48 + 4 * q^49 + 6 * q^50 + 16 * q^51 + 3 * q^52 + 5 * q^53 - 5 * q^54 - 3 * q^55 + 9 * q^57 + 14 * q^58 - q^59 + 7 * q^60 - 10 * q^61 - 3 * q^62 - 3 * q^63 + 4 * q^64 - 3 * q^65 + 3 * q^66 + 6 * q^67 + 7 * q^68 + 10 * q^69 - 6 * q^70 - 29 * q^71 - 15 * q^72 + 3 * q^74 + 8 * q^75 + 3 * q^76 - 12 * q^77 + 3 * q^78 - q^79 + 6 * q^80 + 2 * q^81 + 6 * q^82 - 4 * q^83 - 12 * q^84 - 7 * q^85 - 7 * q^86 + 2 * q^87 + 10 * q^88 + 8 * q^89 + q^90 + 18 * q^91 + 21 * q^93 - 7 * q^94 - 3 * q^95 - 16 * q^96 - 14 * q^97 - 2 * q^98 - 13 * 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 $

$2$	−1.61803	−1.14412	−0.572061	−	0.820211i	$-0.693856\pi$
$2$	−1.61803	−1.14412	−0.572061	+	0.820211i	$0.693856\pi$
$3$	−0.381966	−0.220528	−0.110264	−	0.993902i	$-0.535170\pi$
$3$	−0.381966	−0.220528	−0.110264	+	0.993902i	$0.535170\pi$
$4$	0.618034	0.309017
$5$	−0.618034	−0.276393	−0.138197	−	0.990405i	$-0.544131\pi$
$5$	−0.618034	−0.276393	−0.138197	+	0.990405i	$0.544131\pi$
$6$	0.618034	0.252311
$7$	−3.00000	−1.13389	−0.566947	−	0.823754i	$-0.691875\pi$
$7$	−3.00000	−1.13389	−0.566947	+	0.823754i	$0.691875\pi$
$8$	2.23607	0.790569
$9$	−2.85410	−0.951367
$10$	1.00000	0.316228
$11$	4.23607	1.27722	0.638611	−	0.769529i	$-0.279509\pi$
$11$	4.23607	1.27722	0.638611	+	0.769529i	$0.279509\pi$
$12$	−0.236068	−0.0681470
$13$	−3.00000	−0.832050	−0.416025	−	0.909353i	$-0.636577\pi$
$13$	−3.00000	−0.832050	−0.416025	+	0.909353i	$0.636577\pi$
$14$	4.85410	1.29731
$15$	0.236068	0.0609525
$16$	−4.85410	−1.21353
$17$	−3.38197	−0.820247	−0.410124	−	0.912030i	$-0.634514\pi$
$17$	−3.38197	−0.820247	−0.410124	+	0.912030i	$0.634514\pi$
$18$	4.61803	1.08848
$19$	−3.00000	−0.688247	−0.344124	−	0.938924i	$-0.611824\pi$
$19$	−3.00000	−0.688247	−0.344124	+	0.938924i	$0.611824\pi$
$20$	−0.381966	−0.0854102
$21$	1.14590	0.250055
$22$	−6.85410	−1.46130
$23$	−7.23607	−1.50882	−0.754412	−	0.656401i	$-0.772078\pi$
$23$	−7.23607	−1.50882	−0.754412	+	0.656401i	$0.772078\pi$
$24$	−0.854102	−0.174343
$25$	−4.61803	−0.923607
$26$	4.85410	0.951968
$27$	2.23607	0.430331
$28$	−1.85410	−0.350392
$29$	−8.47214	−1.57324	−0.786618	−	0.617440i	$-0.788170\pi$
$29$	−8.47214	−1.57324	−0.786618	+	0.617440i	$0.788170\pi$
$30$	−0.381966	−0.0697371
$31$	−1.14590	−0.205809	−0.102905	−	0.994691i	$-0.532814\pi$
$31$	−1.14590	−0.205809	−0.102905	+	0.994691i	$0.532814\pi$
$32$	3.38197	0.597853
$33$	−1.61803	−0.281664
$34$	5.47214	0.938464
$35$	1.85410	0.313400
$36$	−1.76393	−0.293989
$37$	1.14590	0.188384	0.0941922	−	0.995554i	$-0.469973\pi$
$37$	1.14590	0.188384	0.0941922	+	0.995554i	$0.469973\pi$
$38$	4.85410	0.787439
$39$	1.14590	0.183491
$40$	−1.38197	−0.218508
$41$	−6.00000	−0.937043	−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000	−0.937043	−0.468521	+	0.883452i	$0.655213\pi$
$42$	−1.85410	−0.286094
$43$	0.0901699	0.0137508	0.00687539	−	0.999976i	$-0.497811\pi$
$43$	0.0901699	0.0137508	0.00687539	+	0.999976i	$0.497811\pi$
$44$	2.61803	0.394683
$45$	1.76393	0.262951
$46$	11.7082	1.72628
$47$	1.47214	0.214733	0.107367	−	0.994220i	$-0.465758\pi$
$47$	1.47214	0.214733	0.107367	+	0.994220i	$0.465758\pi$
$48$	1.85410	0.267617
$49$	2.00000	0.285714
$50$	7.47214	1.05672
$51$	1.29180	0.180888
$52$	−1.85410	−0.257118
$53$	1.38197	0.189828	0.0949138	−	0.995485i	$-0.469742\pi$
$53$	1.38197	0.189828	0.0949138	+	0.995485i	$0.469742\pi$
$54$	−3.61803	−0.492352
$55$	−2.61803	−0.353016
$56$	−6.70820	−0.896421
$57$	1.14590	0.151778
$58$	13.7082	1.79998
$59$	5.09017	0.662684	0.331342	−	0.943511i	$-0.392499\pi$
$59$	5.09017	0.662684	0.331342	+	0.943511i	$0.392499\pi$
$60$	0.145898	0.0188354
$61$	−2.76393	−0.353885	−0.176943	−	0.984221i	$-0.556621\pi$
$61$	−2.76393	−0.353885	−0.176943	+	0.984221i	$0.556621\pi$
$62$	1.85410	0.235471
$63$	8.56231	1.07875
$64$	4.23607	0.529508
$65$	1.85410	0.229973
$66$	2.61803	0.322258
$67$	3.00000	0.366508	0.183254	−	0.983066i	$-0.441337\pi$
$67$	3.00000	0.366508	0.183254	+	0.983066i	$0.441337\pi$
$68$	−2.09017	−0.253470
$69$	2.76393	0.332738
$70$	−3.00000	−0.358569
$71$	−13.3820	−1.58815	−0.794074	−	0.607822i	$-0.792044\pi$
$71$	−13.3820	−1.58815	−0.794074	+	0.607822i	$0.792044\pi$
$72$	−6.38197	−0.752122
$73$	0	0		−	1.00000i	$-0.5\pi$
$73$	0	0			1.00000i	$0.5\pi$
$74$	−1.85410	−0.215535
$75$	1.76393	0.203681
$76$	−1.85410	−0.212680
$77$	−12.7082	−1.44823
$78$	−1.85410	−0.209936
$79$	7.32624	0.824266	0.412133	−	0.911124i	$-0.364784\pi$
$79$	7.32624	0.824266	0.412133	+	0.911124i	$0.364784\pi$
$80$	3.00000	0.335410
$81$	7.70820	0.856467
$82$	9.70820	1.07209
$83$	−13.1803	−1.44673	−0.723365	−	0.690466i	$-0.757406\pi$
$83$	−13.1803	−1.44673	−0.723365	+	0.690466i	$0.757406\pi$
$84$	0.708204	0.0772714
$85$	2.09017	0.226711
$86$	−0.145898	−0.0157326
$87$	3.23607	0.346943
$88$	9.47214	1.00973
$89$	−0.472136	−0.0500463	−0.0250232	−	0.999687i	$-0.507966\pi$
$89$	−0.472136	−0.0500463	−0.0250232	+	0.999687i	$0.507966\pi$
$90$	−2.85410	−0.300849
$91$	9.00000	0.943456
$92$	−4.47214	−0.466252
$93$	0.437694	0.0453868
$94$	−2.38197	−0.245681
$95$	1.85410	0.190227
$96$	−1.29180	−0.131843
$97$	−2.52786	−0.256666	−0.128333	−	0.991731i	$-0.540963\pi$
$97$	−2.52786	−0.256666	−0.128333	+	0.991731i	$0.540963\pi$
$98$	−3.23607	−0.326892
$99$	−12.0902	−1.21511
$100$	−2.85410	−0.285410
$101$	−7.47214	−0.743505	−0.371753	−	0.928332i	$-0.621243\pi$
$101$	−7.47214	−0.743505	−0.371753	+	0.928332i	$0.621243\pi$
$102$	−2.09017	−0.206958
$103$	−17.5623	−1.73047	−0.865233	−	0.501370i	$-0.832829\pi$
$103$	−17.5623	−1.73047	−0.865233	+	0.501370i	$0.832829\pi$
$104$	−6.70820	−0.657794
$105$	−0.708204	−0.0691136
$106$	−2.23607	−0.217186
$107$	7.85410	0.759285	0.379642	−	0.925133i	$-0.376047\pi$
$107$	7.85410	0.759285	0.379642	+	0.925133i	$0.376047\pi$
$108$	1.38197	0.132980
$109$	−15.9443	−1.52718	−0.763592	−	0.645699i	$-0.776566\pi$
$109$	−15.9443	−1.52718	−0.763592	+	0.645699i	$0.776566\pi$
$110$	4.23607	0.403893
$111$	−0.437694	−0.0415441
$112$	14.5623	1.37601
$113$	−16.3820	−1.54109	−0.770543	−	0.637388i	$-0.780015\pi$
$113$	−16.3820	−1.54109	−0.770543	+	0.637388i	$0.780015\pi$
$114$	−1.85410	−0.173653
$115$	4.47214	0.417029
$116$	−5.23607	−0.486157
$117$	8.56231	0.791585
$118$	−8.23607	−0.758192
$119$	10.1459	0.930073
$120$	0.527864	0.0481872
$121$	6.94427	0.631297
$122$	4.47214	0.404888
$123$	2.29180	0.206644
$124$	−0.708204	−0.0635986
$125$	5.94427	0.531672
$126$	−13.8541	−1.23422
$127$	17.6525	1.56640	0.783202	−	0.621767i	$-0.213585\pi$
$127$	17.6525	1.56640	0.783202	+	0.621767i	$0.213585\pi$
$128$	−13.6180	−1.20368
$129$	−0.0344419	−0.00303244
$130$	−3.00000	−0.263117
$131$	−15.0902	−1.31843	−0.659217	−	0.751953i	$-0.729112\pi$
$131$	−15.0902	−1.31843	−0.659217	+	0.751953i	$0.729112\pi$
$132$	−1.00000	−0.0870388
$133$	9.00000	0.780399
$134$	−4.85410	−0.419331
$135$	−1.38197	−0.118941
$136$	−7.56231	−0.648462
$137$	−19.9443	−1.70395	−0.851977	−	0.523579i	$-0.824596\pi$
$137$	−19.9443	−1.70395	−0.851977	+	0.523579i	$0.824596\pi$
$138$	−4.47214	−0.380693
$139$	−16.3262	−1.38477	−0.692387	−	0.721527i	$-0.743441\pi$
$139$	−16.3262	−1.38477	−0.692387	+	0.721527i	$0.743441\pi$
$140$	1.14590	0.0968461
$141$	−0.562306	−0.0473547
$142$	21.6525	1.81704
$143$	−12.7082	−1.06271
$144$	13.8541	1.15451
$145$	5.23607	0.434832
$146$	0	0
$147$	−0.763932	−0.0630081
$148$	0.708204	0.0582140
$149$	−4.47214	−0.366372	−0.183186	−	0.983078i	$-0.558641\pi$
$149$	−4.47214	−0.366372	−0.183186	+	0.983078i	$0.558641\pi$
$150$	−2.85410	−0.233036
$151$	−13.8541	−1.12743	−0.563715	−	0.825969i	$-0.690629\pi$
$151$	−13.8541	−1.12743	−0.563715	+	0.825969i	$0.690629\pi$
$152$	−6.70820	−0.544107
$153$	9.65248	0.780356
$154$	20.5623	1.65696
$155$	0.708204	0.0568843
$156$	0.708204	0.0567017
$157$	−0.562306	−0.0448769	−0.0224384	−	0.999748i	$-0.507143\pi$
$157$	−0.562306	−0.0448769	−0.0224384	+	0.999748i	$0.507143\pi$
$158$	−11.8541	−0.943062
$159$	−0.527864	−0.0418623
$160$	−2.09017	−0.165242
$161$	21.7082	1.71085
$162$	−12.4721	−0.979904
$163$	8.52786	0.667954	0.333977	−	0.942581i	$-0.391609\pi$
$163$	8.52786	0.667954	0.333977	+	0.942581i	$0.391609\pi$
$164$	−3.70820	−0.289562
$165$	1.00000	0.0778499
$166$	21.3262	1.65524
$167$	18.3820	1.42244	0.711220	−	0.702970i	$-0.248143\pi$
$167$	18.3820	1.42244	0.711220	+	0.702970i	$0.248143\pi$
$168$	2.56231	0.197686
$169$	−4.00000	−0.307692
$170$	−3.38197	−0.259385
$171$	8.56231	0.654776
$172$	0.0557281	0.00424923
$173$	−7.47214	−0.568096	−0.284048	−	0.958810i	$-0.591678\pi$
$173$	−7.47214	−0.568096	−0.284048	+	0.958810i	$0.591678\pi$
$174$	−5.23607	−0.396945
$175$	13.8541	1.04727
$176$	−20.5623	−1.54994
$177$	−1.94427	−0.146140
$178$	0.763932	0.0572591
$179$	19.9443	1.49070	0.745352	−	0.666671i	$-0.232281\pi$
$179$	19.9443	1.49070	0.745352	+	0.666671i	$0.232281\pi$
$180$	1.09017	0.0812565
$181$	−15.1803	−1.12835	−0.564173	−	0.825657i	$-0.690805\pi$
$181$	−15.1803	−1.12835	−0.564173	+	0.825657i	$0.690805\pi$
$182$	−14.5623	−1.07943
$183$	1.05573	0.0780417
$184$	−16.1803	−1.19283
$185$	−0.708204	−0.0520682
$186$	−0.708204	−0.0519280
$187$	−14.3262	−1.04764
$188$	0.909830	0.0663562
$189$	−6.70820	−0.487950
$190$	−3.00000	−0.217643
$191$	−18.4721	−1.33660	−0.668298	−	0.743893i	$-0.732977\pi$
$191$	−18.4721	−1.33660	−0.668298	+	0.743893i	$0.732977\pi$
$192$	−1.61803	−0.116772
$193$	−7.00000	−0.503871	−0.251936	−	0.967744i	$-0.581067\pi$
$193$	−7.00000	−0.503871	−0.251936	+	0.967744i	$0.581067\pi$
$194$	4.09017	0.293657
$195$	−0.708204	−0.0507155
$196$	1.23607	0.0882906
$197$	8.23607	0.586796	0.293398	−	0.955990i	$-0.405214\pi$
$197$	8.23607	0.586796	0.293398	+	0.955990i	$0.405214\pi$
$198$	19.5623	1.39023
$199$	20.1246	1.42660	0.713298	−	0.700861i	$-0.247201\pi$
$199$	20.1246	1.42660	0.713298	+	0.700861i	$0.247201\pi$
$200$	−10.3262	−0.730175
$201$	−1.14590	−0.0808254
$202$	12.0902	0.850661
$203$	25.4164	1.78388
$204$	0.798374	0.0558974
$205$	3.70820	0.258992
$206$	28.4164	1.97986
$207$	20.6525	1.43545
$208$	14.5623	1.00971
$209$	−12.7082	−0.879045
$210$	1.14590	0.0790745
$211$	−5.14590	−0.354258	−0.177129	−	0.984188i	$-0.556681\pi$
$211$	−5.14590	−0.354258	−0.177129	+	0.984188i	$0.556681\pi$
$212$	0.854102	0.0586600
$213$	5.11146	0.350231
$214$	−12.7082	−0.868715
$215$	−0.0557281	−0.00380062
$216$	5.00000	0.340207
$217$	3.43769	0.233366
$218$	25.7984	1.74729
$219$	0	0
$220$	−1.61803	−0.109088
$221$	10.1459	0.682487
$222$	0.708204	0.0475315
$223$	−3.14590	−0.210665	−0.105332	−	0.994437i	$-0.533591\pi$
$223$	−3.14590	−0.210665	−0.105332	+	0.994437i	$0.533591\pi$
$224$	−10.1459	−0.677901
$225$	13.1803	0.878689
$226$	26.5066	1.76319
$227$	24.3262	1.61459	0.807295	−	0.590149i	$-0.200931\pi$
$227$	24.3262	1.61459	0.807295	+	0.590149i	$0.200931\pi$
$228$	0.708204	0.0469020
$229$	0.291796	0.0192824	0.00964121	−	0.999954i	$-0.496931\pi$
$229$	0.291796	0.0192824	0.00964121	+	0.999954i	$0.496931\pi$
$230$	−7.23607	−0.477132
$231$	4.85410	0.319376
$232$	−18.9443	−1.24375
$233$	−4.94427	−0.323910	−0.161955	−	0.986798i	$-0.551780\pi$
$233$	−4.94427	−0.323910	−0.161955	+	0.986798i	$0.551780\pi$
$234$	−13.8541	−0.905671
$235$	−0.909830	−0.0593508
$236$	3.14590	0.204781
$237$	−2.79837	−0.181774
$238$	−16.4164	−1.06412
$239$	−3.81966	−0.247073	−0.123537	−	0.992340i	$-0.539424\pi$
$239$	−3.81966	−0.247073	−0.123537	+	0.992340i	$0.539424\pi$
$240$	−1.14590	−0.0739674
$241$	22.7639	1.46635	0.733177	−	0.680038i	$-0.238037\pi$
$241$	22.7639	1.46635	0.733177	+	0.680038i	$0.238037\pi$
$242$	−11.2361	−0.722282
$243$	−9.65248	−0.619207
$244$	−1.70820	−0.109357
$245$	−1.23607	−0.0789695
$246$	−3.70820	−0.236426
$247$	9.00000	0.572656
$248$	−2.56231	−0.162707
$249$	5.03444	0.319045
$250$	−9.61803	−0.608298
$251$	−4.52786	−0.285796	−0.142898	−	0.989737i	$-0.545642\pi$
$251$	−4.52786	−0.285796	−0.142898	+	0.989737i	$0.545642\pi$
$252$	5.29180	0.333352
$253$	−30.6525	−1.92710
$254$	−28.5623	−1.79216
$255$	−0.798374	−0.0499961
$256$	13.5623	0.847644
$257$	12.0000	0.748539	0.374270	−	0.927320i	$-0.377893\pi$
$257$	12.0000	0.748539	0.374270	+	0.927320i	$0.377893\pi$
$258$	0.0557281	0.00346948
$259$	−3.43769	−0.213608
$260$	1.14590	0.0710656
$261$	24.1803	1.49673
$262$	24.4164	1.50845
$263$	−23.2361	−1.43280	−0.716399	−	0.697691i	$-0.754211\pi$
$263$	−23.2361	−1.43280	−0.716399	+	0.697691i	$0.754211\pi$
$264$	−3.61803	−0.222675
$265$	−0.854102	−0.0524671
$266$	−14.5623	−0.892872
$267$	0.180340	0.0110366
$268$	1.85410	0.113257
$269$	−14.5623	−0.887879	−0.443940	−	0.896057i	$-0.646420\pi$
$269$	−14.5623	−0.887879	−0.443940	+	0.896057i	$0.646420\pi$
$270$	2.23607	0.136083
$271$	19.2361	1.16851	0.584254	−	0.811571i	$-0.301387\pi$
$271$	19.2361	1.16851	0.584254	+	0.811571i	$0.301387\pi$
$272$	16.4164	0.995391
$273$	−3.43769	−0.208059
$274$	32.2705	1.94953
$275$	−19.5623	−1.17965
$276$	1.70820	0.102822
$277$	−5.43769	−0.326719	−0.163360	−	0.986567i	$-0.552233\pi$
$277$	−5.43769	−0.326719	−0.163360	+	0.986567i	$0.552233\pi$
$278$	26.4164	1.58435
$279$	3.27051	0.195800
$280$	4.14590	0.247765
$281$	9.00000	0.536895	0.268447	−	0.963294i	$-0.413489\pi$
$281$	9.00000	0.536895	0.268447	+	0.963294i	$0.413489\pi$
$282$	0.909830	0.0541796
$283$	22.1459	1.31644	0.658218	−	0.752827i	$-0.271310\pi$
$283$	22.1459	1.31644	0.658218	+	0.752827i	$0.271310\pi$
$284$	−8.27051	−0.490764
$285$	−0.708204	−0.0419504
$286$	20.5623	1.21587
$287$	18.0000	1.06251
$288$	−9.65248	−0.568778
$289$	−5.56231	−0.327194
$290$	−8.47214	−0.497501
$291$	0.965558	0.0566020
$292$	0	0
$293$	23.3262	1.36273	0.681367	−	0.731942i	$-0.261386\pi$
$293$	23.3262	1.36273	0.681367	+	0.731942i	$0.261386\pi$
$294$	1.23607	0.0720889
$295$	−3.14590	−0.183161
$296$	2.56231	0.148931
$297$	9.47214	0.549629
$298$	7.23607	0.419174
$299$	21.7082	1.25542
$300$	1.09017	0.0629410
$301$	−0.270510	−0.0155919
$302$	22.4164	1.28992
$303$	2.85410	0.163964
$304$	14.5623	0.835206
$305$	1.70820	0.0978115
$306$	−15.6180	−0.892824
$307$	−17.6525	−1.00748	−0.503740	−	0.863855i	$-0.668043\pi$
$307$	−17.6525	−1.00748	−0.503740	+	0.863855i	$0.668043\pi$
$308$	−7.85410	−0.447529
$309$	6.70820	0.381616
$310$	−1.14590	−0.0650826
$311$	−15.3262	−0.869071	−0.434536	−	0.900655i	$-0.643087\pi$
$311$	−15.3262	−0.869071	−0.434536	+	0.900655i	$0.643087\pi$
$312$	2.56231	0.145062
$313$	−29.1246	−1.64622	−0.823110	−	0.567882i	$-0.807763\pi$
$313$	−29.1246	−1.64622	−0.823110	+	0.567882i	$0.807763\pi$
$314$	0.909830	0.0513447
$315$	−5.29180	−0.298159
$316$	4.52786	0.254712
$317$	34.3607	1.92989	0.964944	−	0.262456i	$-0.0845324\pi$
$317$	34.3607	1.92989	0.964944	+	0.262456i	$0.0845324\pi$
$318$	0.854102	0.0478957
$319$	−35.8885	−2.00937
$320$	−2.61803	−0.146353
$321$	−3.00000	−0.167444
$322$	−35.1246	−1.95742
$323$	10.1459	0.564533
$324$	4.76393	0.264663
$325$	13.8541	0.768487
$326$	−13.7984	−0.764221
$327$	6.09017	0.336787
$328$	−13.4164	−0.740797
$329$	−4.41641	−0.243484
$330$	−1.61803	−0.0890698
$331$	35.4721	1.94972	0.974862	−	0.222807i	$-0.0715221\pi$
$331$	35.4721	1.94972	0.974862	+	0.222807i	$0.0715221\pi$
$332$	−8.14590	−0.447064
$333$	−3.27051	−0.179223
$334$	−29.7426	−1.62745
$335$	−1.85410	−0.101300
$336$	−5.56231	−0.303449
$337$	−28.5967	−1.55776	−0.778882	−	0.627170i	$-0.784213\pi$
$337$	−28.5967	−1.55776	−0.778882	+	0.627170i	$0.784213\pi$
$338$	6.47214	0.352038
$339$	6.25735	0.339853
$340$	1.29180	0.0700575
$341$	−4.85410	−0.262864
$342$	−13.8541	−0.749144
$343$	15.0000	0.809924
$344$	0.201626	0.0108710
$345$	−1.70820	−0.0919666
$346$	12.0902	0.649972
$347$	15.0344	0.807091	0.403546	−	0.914960i	$-0.367778\pi$
$347$	15.0344	0.807091	0.403546	+	0.914960i	$0.367778\pi$
$348$	2.00000	0.107211
$349$	−20.6525	−1.10550	−0.552751	−	0.833347i	$-0.686422\pi$
$349$	−20.6525	−1.10550	−0.552751	+	0.833347i	$0.686422\pi$
$350$	−22.4164	−1.19821
$351$	−6.70820	−0.358057
$352$	14.3262	0.763591
$353$	31.0344	1.65180	0.825898	−	0.563819i	$-0.190668\pi$
$353$	31.0344	1.65180	0.825898	+	0.563819i	$0.190668\pi$
$354$	3.14590	0.167203
$355$	8.27051	0.438953
$356$	−0.291796	−0.0154652
$357$	−3.87539	−0.205107
$358$	−32.2705	−1.70555
$359$	−15.6525	−0.826106	−0.413053	−	0.910707i	$-0.635538\pi$
$359$	−15.6525	−0.826106	−0.413053	+	0.910707i	$0.635538\pi$
$360$	3.94427	0.207881
$361$	−10.0000	−0.526316
$362$	24.5623	1.29097
$363$	−2.65248	−0.139219
$364$	5.56231	0.291544
$365$	0	0
$366$	−1.70820	−0.0892892
$367$	−20.5623	−1.07334	−0.536672	−	0.843791i	$-0.680319\pi$
$367$	−20.5623	−1.07334	−0.536672	+	0.843791i	$0.680319\pi$
$368$	35.1246	1.83100
$369$	17.1246	0.891472
$370$	1.14590	0.0595724
$371$	−4.14590	−0.215244
$372$	0.270510	0.0140253
$373$	33.5623	1.73779	0.868895	−	0.494996i	$-0.164831\pi$
$373$	33.5623	1.73779	0.868895	+	0.494996i	$0.164831\pi$
$374$	23.1803	1.19863
$375$	−2.27051	−0.117249
$376$	3.29180	0.169761
$377$	25.4164	1.30901
$378$	10.8541	0.558275
$379$	24.0344	1.23457	0.617283	−	0.786741i	$-0.288233\pi$
$379$	24.0344	1.23457	0.617283	+	0.786741i	$0.288233\pi$
$380$	1.14590	0.0587833
$381$	−6.74265	−0.345436
$382$	29.8885	1.52923
$383$	3.52786	0.180265	0.0901327	−	0.995930i	$-0.471271\pi$
$383$	3.52786	0.180265	0.0901327	+	0.995930i	$0.471271\pi$
$384$	5.20163	0.265444
$385$	7.85410	0.400282
$386$	11.3262	0.576490
$387$	−0.257354	−0.0130820
$388$	−1.56231	−0.0793141
$389$	−35.0902	−1.77914	−0.889571	−	0.456797i	$-0.848997\pi$
$389$	−35.0902	−1.77914	−0.889571	+	0.456797i	$0.848997\pi$
$390$	1.14590	0.0580248
$391$	24.4721	1.23761
$392$	4.47214	0.225877
$393$	5.76393	0.290752
$394$	−13.3262	−0.671366
$395$	−4.52786	−0.227822
$396$	−7.47214	−0.375489
$397$	−0.527864	−0.0264927	−0.0132464	−	0.999912i	$-0.504217\pi$
$397$	−0.527864	−0.0264927	−0.0132464	+	0.999912i	$0.504217\pi$
$398$	−32.5623	−1.63220
$399$	−3.43769	−0.172100
$400$	22.4164	1.12082
$401$	−36.9787	−1.84663	−0.923314	−	0.384045i	$-0.874531\pi$
$401$	−36.9787	−1.84663	−0.923314	+	0.384045i	$0.874531\pi$
$402$	1.85410	0.0924742
$403$	3.43769	0.171244
$404$	−4.61803	−0.229756
$405$	−4.76393	−0.236722
$406$	−41.1246	−2.04098
$407$	4.85410	0.240609
$408$	2.88854	0.143004
$409$	−26.7082	−1.32064	−0.660318	−	0.750986i	$-0.729578\pi$
$409$	−26.7082	−1.32064	−0.660318	+	0.750986i	$0.729578\pi$
$410$	−6.00000	−0.296319
$411$	7.61803	0.375770
$412$	−10.8541	−0.534743
$413$	−15.2705	−0.751413
$414$	−33.4164	−1.64233
$415$	8.14590	0.399866
$416$	−10.1459	−0.497444
$417$	6.23607	0.305382
$418$	20.5623	1.00574
$419$	−11.1803	−0.546195	−0.273098	−	0.961986i	$-0.588048\pi$
$419$	−11.1803	−0.546195	−0.273098	+	0.961986i	$0.588048\pi$
$420$	−0.437694	−0.0213573
$421$	24.8328	1.21028	0.605139	−	0.796120i	$-0.293118\pi$
$421$	24.8328	1.21028	0.605139	+	0.796120i	$0.293118\pi$
$422$	8.32624	0.405315
$423$	−4.20163	−0.204290
$424$	3.09017	0.150072
$425$	15.6180	0.757586
$426$	−8.27051	−0.400708
$427$	8.29180	0.401268
$428$	4.85410	0.234632
$429$	4.85410	0.234358
$430$	0.0901699	0.00434838
$431$	−12.3262	−0.593734	−0.296867	−	0.954919i	$-0.595942\pi$
$431$	−12.3262	−0.593734	−0.296867	+	0.954919i	$0.595942\pi$
$432$	−10.8541	−0.522218
$433$	−25.2705	−1.21442	−0.607212	−	0.794540i	$-0.707712\pi$
$433$	−25.2705	−1.21442	−0.607212	+	0.794540i	$0.707712\pi$
$434$	−5.56231	−0.266999
$435$	−2.00000	−0.0958927
$436$	−9.85410	−0.471926
$437$	21.7082	1.03844
$438$	0	0
$439$	−15.0000	−0.715911	−0.357955	−	0.933739i	$-0.616526\pi$
$439$	−15.0000	−0.715911	−0.357955	+	0.933739i	$0.616526\pi$
$440$	−5.85410	−0.279083
$441$	−5.70820	−0.271819
$442$	−16.4164	−0.780849
$443$	11.1246	0.528546	0.264273	−	0.964448i	$-0.414868\pi$
$443$	11.1246	0.528546	0.264273	+	0.964448i	$0.414868\pi$
$444$	−0.270510	−0.0128378
$445$	0.291796	0.0138325
$446$	5.09017	0.241027
$447$	1.70820	0.0807953
$448$	−12.7082	−0.600406
$449$	−22.4164	−1.05790	−0.528948	−	0.848654i	$-0.677413\pi$
$449$	−22.4164	−1.05790	−0.528948	+	0.848654i	$0.677413\pi$
$450$	−21.3262	−1.00533
$451$	−25.4164	−1.19681
$452$	−10.1246	−0.476222
$453$	5.29180	0.248630
$454$	−39.3607	−1.84729
$455$	−5.56231	−0.260765
$456$	2.56231	0.119991
$457$	33.7426	1.57841	0.789207	−	0.614127i	$-0.210492\pi$
$457$	33.7426	1.57841	0.789207	+	0.614127i	$0.210492\pi$
$458$	−0.472136	−0.0220615
$459$	−7.56231	−0.352978
$460$	2.76393	0.128869
$461$	30.1803	1.40564	0.702819	−	0.711368i	$-0.251924\pi$
$461$	30.1803	1.40564	0.702819	+	0.711368i	$0.251924\pi$
$462$	−7.85410	−0.365406
$463$	−38.5410	−1.79115	−0.895577	−	0.444907i	$-0.853237\pi$
$463$	−38.5410	−1.79115	−0.895577	+	0.444907i	$0.853237\pi$
$464$	41.1246	1.90916
$465$	−0.270510	−0.0125446
$466$	8.00000	0.370593
$467$	12.2705	0.567811	0.283906	−	0.958852i	$-0.408370\pi$
$467$	12.2705	0.567811	0.283906	+	0.958852i	$0.408370\pi$
$468$	5.29180	0.244613
$469$	−9.00000	−0.415581
$470$	1.47214	0.0679046
$471$	0.214782	0.00989662
$472$	11.3820	0.523897
$473$	0.381966	0.0175628
$474$	4.52786	0.207972
$475$	13.8541	0.635670
$476$	6.27051	0.287408
$477$	−3.94427	−0.180596
$478$	6.18034	0.282682
$479$	7.67376	0.350623	0.175312	−	0.984513i	$-0.443907\pi$
$479$	7.67376	0.350623	0.175312	+	0.984513i	$0.443907\pi$
$480$	0.798374	0.0364406
$481$	−3.43769	−0.156745
$482$	−36.8328	−1.67769
$483$	−8.29180	−0.377290
$484$	4.29180	0.195082
$485$	1.56231	0.0709407
$486$	15.6180	0.708448
$487$	−16.2705	−0.737287	−0.368644	−	0.929571i	$-0.620178\pi$
$487$	−16.2705	−0.737287	−0.368644	+	0.929571i	$0.620178\pi$
$488$	−6.18034	−0.279771
$489$	−3.25735	−0.147303
$490$	2.00000	0.0903508
$491$	1.32624	0.0598523	0.0299261	−	0.999552i	$-0.490473\pi$
$491$	1.32624	0.0598523	0.0299261	+	0.999552i	$0.490473\pi$
$492$	1.41641	0.0638566
$493$	28.6525	1.29044
$494$	−14.5623	−0.655189
$495$	7.47214	0.335848
$496$	5.56231	0.249755
$497$	40.1459	1.80079
$498$	−8.14590	−0.365026
$499$	18.8885	0.845567	0.422784	−	0.906231i	$-0.361053\pi$
$499$	18.8885	0.845567	0.422784	+	0.906231i	$0.361053\pi$
$500$	3.67376	0.164296
$501$	−7.02129	−0.313688
$502$	7.32624	0.326986
$503$	32.3951	1.44443	0.722214	−	0.691670i	$-0.243125\pi$
$503$	32.3951	1.44443	0.722214	+	0.691670i	$0.243125\pi$
$504$	19.1459	0.852826
$505$	4.61803	0.205500
$506$	49.5967	2.20484
$507$	1.52786	0.0678548
$508$	10.9098	0.484045
$509$	15.4721	0.685790	0.342895	−	0.939374i	$-0.388592\pi$
$509$	15.4721	0.685790	0.342895	+	0.939374i	$0.388592\pi$
$510$	1.29180	0.0572017
$511$	0	0
$512$	5.29180	0.233867
$513$	−6.70820	−0.296174
$514$	−19.4164	−0.856421
$515$	10.8541	0.478289
$516$	−0.0212862	−0.000937074 0
$517$	6.23607	0.274262
$518$	5.56231	0.244394
$519$	2.85410	0.125281
$520$	4.14590	0.181810
$521$	34.7771	1.52361	0.761806	−	0.647805i	$-0.224313\pi$
$521$	34.7771	1.52361	0.761806	+	0.647805i	$0.224313\pi$
$522$	−39.1246	−1.71244
$523$	9.27051	0.405371	0.202686	−	0.979244i	$-0.435033\pi$
$523$	9.27051	0.405371	0.202686	+	0.979244i	$0.435033\pi$
$524$	−9.32624	−0.407419
$525$	−5.29180	−0.230953
$526$	37.5967	1.63930
$527$	3.87539	0.168815
$528$	7.85410	0.341806
$529$	29.3607	1.27655
$530$	1.38197	0.0600288
$531$	−14.5279	−0.630456
$532$	5.56231	0.241157
$533$	18.0000	0.779667
$534$	−0.291796	−0.0126273
$535$	−4.85410	−0.209861
$536$	6.70820	0.289750
$537$	−7.61803	−0.328742
$538$	23.5623	1.01584
$539$	8.47214	0.364921
$540$	−0.854102	−0.0367547
$541$	−21.1246	−0.908218	−0.454109	−	0.890946i	$-0.650042\pi$
$541$	−21.1246	−0.908218	−0.454109	+	0.890946i	$0.650042\pi$
$542$	−31.1246	−1.33692
$543$	5.79837	0.248832
$544$	−11.4377	−0.490387
$545$	9.85410	0.422103
$546$	5.56231	0.238045
$547$	7.27051	0.310865	0.155432	−	0.987847i	$-0.450323\pi$
$547$	7.27051	0.310865	0.155432	+	0.987847i	$0.450323\pi$
$548$	−12.3262	−0.526551
$549$	7.88854	0.336675
$550$	31.6525	1.34967
$551$	25.4164	1.08278
$552$	6.18034	0.263053
$553$	−21.9787	−0.934630
$554$	8.79837	0.373807
$555$	0.270510	0.0114825
$556$	−10.0902	−0.427919
$557$	6.18034	0.261869	0.130935	−	0.991391i	$-0.458202\pi$
$557$	6.18034	0.261869	0.130935	+	0.991391i	$0.458202\pi$
$558$	−5.29180	−0.224020
$559$	−0.270510	−0.0114413
$560$	−9.00000	−0.380319
$561$	5.47214	0.231034
$562$	−14.5623	−0.614274
$563$	−14.1803	−0.597630	−0.298815	−	0.954311i	$-0.596591\pi$
$563$	−14.1803	−0.597630	−0.298815	+	0.954311i	$0.596591\pi$
$564$	−0.347524	−0.0146334
$565$	10.1246	0.425946
$566$	−35.8328	−1.50617
$567$	−23.1246	−0.971142
$568$	−29.9230	−1.25554
$569$	−0.673762	−0.0282456	−0.0141228	−	0.999900i	$-0.504496\pi$
$569$	−0.673762	−0.0282456	−0.0141228	+	0.999900i	$0.504496\pi$
$570$	1.14590	0.0479964
$571$	6.20163	0.259530	0.129765	−	0.991545i	$-0.458578\pi$
$571$	6.20163	0.259530	0.129765	+	0.991545i	$0.458578\pi$
$572$	−7.85410	−0.328397
$573$	7.05573	0.294757
$574$	−29.1246	−1.21564
$575$	33.4164	1.39356
$576$	−12.0902	−0.503757
$577$	8.56231	0.356453	0.178227	−	0.983989i	$-0.442964\pi$
$577$	8.56231	0.356453	0.178227	+	0.983989i	$0.442964\pi$
$578$	9.00000	0.374351
$579$	2.67376	0.111118
$580$	3.23607	0.134370
$581$	39.5410	1.64044
$582$	−1.56231	−0.0647597
$583$	5.85410	0.242452
$584$	0	0
$585$	−5.29180	−0.218789
$586$	−37.7426	−1.55913
$587$	10.3820	0.428510	0.214255	−	0.976778i	$-0.431268\pi$
$587$	10.3820	0.428510	0.214255	+	0.976778i	$0.431268\pi$
$588$	−0.472136	−0.0194706
$589$	3.43769	0.141648
$590$	5.09017	0.209559
$591$	−3.14590	−0.129405
$592$	−5.56231	−0.228609
$593$	−17.3262	−0.711503	−0.355752	−	0.934581i	$-0.615775\pi$
$593$	−17.3262	−0.711503	−0.355752	+	0.934581i	$0.615775\pi$
$594$	−15.3262	−0.628843
$595$	−6.27051	−0.257066
$596$	−2.76393	−0.113215
$597$	−7.68692	−0.314605
$598$	−35.1246	−1.43635
$599$	−16.2016	−0.661980	−0.330990	−	0.943634i	$-0.607383\pi$
$599$	−16.2016	−0.661980	−0.330990	+	0.943634i	$0.607383\pi$
$600$	3.94427	0.161024
$601$	−34.1803	−1.39425	−0.697123	−	0.716952i	$-0.745537\pi$
$601$	−34.1803	−1.39425	−0.697123	+	0.716952i	$0.745537\pi$
$602$	0.437694	0.0178391
$603$	−8.56231	−0.348684
$604$	−8.56231	−0.348395
$605$	−4.29180	−0.174486
$606$	−4.61803	−0.187595
$607$	−34.4164	−1.39692	−0.698459	−	0.715650i	$-0.746131\pi$
$607$	−34.4164	−1.39692	−0.698459	+	0.715650i	$0.746131\pi$
$608$	−10.1459	−0.411470
$609$	−9.70820	−0.393396
$610$	−2.76393	−0.111908
$611$	−4.41641	−0.178669
$612$	5.96556	0.241143
$613$	11.4377	0.461964	0.230982	−	0.972958i	$-0.425806\pi$
$613$	11.4377	0.461964	0.230982	+	0.972958i	$0.425806\pi$
$614$	28.5623	1.15268
$615$	−1.41641	−0.0571151
$616$	−28.4164	−1.14493
$617$	42.0132	1.69139	0.845693	−	0.533670i	$-0.179187\pi$
$617$	42.0132	1.69139	0.845693	+	0.533670i	$0.179187\pi$
$618$	−10.8541	−0.436616
$619$	29.1246	1.17062	0.585308	−	0.810811i	$-0.300973\pi$
$619$	29.1246	1.17062	0.585308	+	0.810811i	$0.300973\pi$
$620$	0.437694	0.0175782
$621$	−16.1803	−0.649295
$622$	24.7984	0.994324
$623$	1.41641	0.0567472
$624$	−5.56231	−0.222670
$625$	19.4164	0.776656
$626$	47.1246	1.88348
$627$	4.85410	0.193854
$628$	−0.347524	−0.0138677
$629$	−3.87539	−0.154522
$630$	8.56231	0.341130
$631$	−9.14590	−0.364092	−0.182046	−	0.983290i	$-0.558272\pi$
$631$	−9.14590	−0.364092	−0.182046	+	0.983290i	$0.558272\pi$
$632$	16.3820	0.651640
$633$	1.96556	0.0781239
$634$	−55.5967	−2.20803
$635$	−10.9098	−0.432943
$636$	−0.326238	−0.0129362
$637$	−6.00000	−0.237729
$638$	58.0689	2.29897
$639$	38.1935	1.51091
$640$	8.41641	0.332688
$641$	−3.52786	−0.139342	−0.0696711	−	0.997570i	$-0.522195\pi$
$641$	−3.52786	−0.139342	−0.0696711	+	0.997570i	$0.522195\pi$
$642$	4.85410	0.191576
$643$	28.6869	1.13130	0.565651	−	0.824645i	$-0.308625\pi$
$643$	28.6869	1.13130	0.565651	+	0.824645i	$0.308625\pi$
$644$	13.4164	0.528681
$645$	0.0212862	0.000838145 0
$646$	−16.4164	−0.645895
$647$	−28.5279	−1.12155	−0.560773	−	0.827970i	$-0.689496\pi$
$647$	−28.5279	−1.12155	−0.560773	+	0.827970i	$0.689496\pi$
$648$	17.2361	0.677097
$649$	21.5623	0.846395
$650$	−22.4164	−0.879244
$651$	−1.31308	−0.0514638
$652$	5.27051	0.206409
$653$	8.72949	0.341611	0.170806	−	0.985305i	$-0.445363\pi$
$653$	8.72949	0.341611	0.170806	+	0.985305i	$0.445363\pi$
$654$	−9.85410	−0.385326
$655$	9.32624	0.364406
$656$	29.1246	1.13713
$657$	0	0
$658$	7.14590	0.278576
$659$	30.0132	1.16915	0.584573	−	0.811341i	$-0.301262\pi$
$659$	30.0132	1.16915	0.584573	+	0.811341i	$0.301262\pi$
$660$	0.618034	0.0240569
$661$	−19.8197	−0.770895	−0.385448	−	0.922730i	$-0.625953\pi$
$661$	−19.8197	−0.770895	−0.385448	+	0.922730i	$0.625953\pi$
$662$	−57.3951	−2.23072
$663$	−3.87539	−0.150508
$664$	−29.4721	−1.14374
$665$	−5.56231	−0.215697
$666$	5.29180	0.205053
$667$	61.3050	2.37374
$668$	11.3607	0.439558
$669$	1.20163	0.0464575
$670$	3.00000	0.115900
$671$	−11.7082	−0.451990
$672$	3.87539	0.149496
$673$	−27.1246	−1.04558	−0.522788	−	0.852462i	$-0.675108\pi$
$673$	−27.1246	−1.04558	−0.522788	+	0.852462i	$0.675108\pi$
$674$	46.2705	1.78227
$675$	−10.3262	−0.397457
$676$	−2.47214	−0.0950822
$677$	−0.506578	−0.0194694	−0.00973468	−	0.999953i	$-0.503099\pi$
$677$	−0.506578	−0.0194694	−0.00973468	+	0.999953i	$0.503099\pi$
$678$	−10.1246	−0.388833
$679$	7.58359	0.291032
$680$	4.67376	0.179231
$681$	−9.29180	−0.356062
$682$	7.85410	0.300749
$683$	−35.3050	−1.35091	−0.675453	−	0.737403i	$-0.736052\pi$
$683$	−35.3050	−1.35091	−0.675453	+	0.737403i	$0.736052\pi$
$684$	5.29180	0.202337
$685$	12.3262	0.470961
$686$	−24.2705	−0.926652
$687$	−0.111456	−0.00425232
$688$	−0.437694	−0.0166869
$689$	−4.14590	−0.157946
$690$	2.76393	0.105221
$691$	11.7082	0.445401	0.222701	−	0.974887i	$-0.428513\pi$
$691$	11.7082	0.445401	0.222701	+	0.974887i	$0.428513\pi$
$692$	−4.61803	−0.175551
$693$	36.2705	1.37780
$694$	−24.3262	−0.923411
$695$	10.0902	0.382742
$696$	7.23607	0.274282
$697$	20.2918	0.768607
$698$	33.4164	1.26483
$699$	1.88854	0.0714313
$700$	8.56231	0.323625
$701$	15.6180	0.589885	0.294943	−	0.955515i	$-0.404700\pi$
$701$	15.6180	0.589885	0.294943	+	0.955515i	$0.404700\pi$
$702$	10.8541	0.409662
$703$	−3.43769	−0.129655
$704$	17.9443	0.676300
$705$	0.347524	0.0130885
$706$	−50.2148	−1.88986
$707$	22.4164	0.843056
$708$	−1.20163	−0.0451599
$709$	26.8328	1.00773	0.503864	−	0.863783i	$-0.331911\pi$
$709$	26.8328	1.00773	0.503864	+	0.863783i	$0.331911\pi$
$710$	−13.3820	−0.502216
$711$	−20.9098	−0.784180
$712$	−1.05573	−0.0395651
$713$	8.29180	0.310530
$714$	6.27051	0.234668
$715$	7.85410	0.293727
$716$	12.3262	0.460653
$717$	1.45898	0.0544866
$718$	25.3262	0.945167
$719$	42.5410	1.58651	0.793256	−	0.608888i	$-0.208384\pi$
$719$	42.5410	1.58651	0.793256	+	0.608888i	$0.208384\pi$
$720$	−8.56231	−0.319098
$721$	52.6869	1.96216
$722$	16.1803	0.602170
$723$	−8.69505	−0.323372
$724$	−9.38197	−0.348678
$725$	39.1246	1.45305
$726$	4.29180	0.159283
$727$	−51.7214	−1.91824	−0.959120	−	0.283001i	$-0.908670\pi$
$727$	−51.7214	−1.91824	−0.959120	+	0.283001i	$0.908670\pi$
$728$	20.1246	0.745868
$729$	−19.4377	−0.719915
$730$	0	0
$731$	−0.304952	−0.0112790
$732$	0.652476	0.0241162
$733$	16.3262	0.603023	0.301512	−	0.953462i	$-0.402509\pi$
$733$	16.3262	0.603023	0.301512	+	0.953462i	$0.402509\pi$
$734$	33.2705	1.22804
$735$	0.472136	0.0174150
$736$	−24.4721	−0.902055
$737$	12.7082	0.468113
$738$	−27.7082	−1.01995
$739$	0.291796	0.0107339	0.00536695	−	0.999986i	$-0.498292\pi$
$739$	0.291796	0.0107339	0.00536695	+	0.999986i	$0.498292\pi$
$740$	−0.437694	−0.0160900
$741$	−3.43769	−0.126287
$742$	6.70820	0.246266
$743$	−1.11146	−0.0407754	−0.0203877	−	0.999792i	$-0.506490\pi$
$743$	−1.11146	−0.0407754	−0.0203877	+	0.999792i	$0.506490\pi$
$744$	0.978714	0.0358814
$745$	2.76393	0.101263
$746$	−54.3050	−1.98825
$747$	37.6180	1.37637
$748$	−8.85410	−0.323738
$749$	−23.5623	−0.860948
$750$	3.67376	0.134147
$751$	−15.7426	−0.574457	−0.287229	−	0.957862i	$-0.592734\pi$
$751$	−15.7426	−0.574457	−0.287229	+	0.957862i	$0.592734\pi$
$752$	−7.14590	−0.260584
$753$	1.72949	0.0630261
$754$	−41.1246	−1.49767
$755$	8.56231	0.311614
$756$	−4.14590	−0.150785
$757$	−13.4164	−0.487628	−0.243814	−	0.969822i	$-0.578399\pi$
$757$	−13.4164	−0.487628	−0.243814	+	0.969822i	$0.578399\pi$
$758$	−38.8885	−1.41250
$759$	11.7082	0.424981
$760$	4.14590	0.150388
$761$	36.4853	1.32259	0.661295	−	0.750126i	$-0.270007\pi$
$761$	36.4853	1.32259	0.661295	+	0.750126i	$0.270007\pi$
$762$	10.9098	0.395221
$763$	47.8328	1.73166
$764$	−11.4164	−0.413031
$765$	−5.96556	−0.215685
$766$	−5.70820	−0.206246
$767$	−15.2705	−0.551386
$768$	−5.18034	−0.186929
$769$	−47.6312	−1.71762	−0.858812	−	0.512290i	$-0.828797\pi$
$769$	−47.6312	−1.71762	−0.858812	+	0.512290i	$0.828797\pi$
$770$	−12.7082	−0.457972
$771$	−4.58359	−0.165074
$772$	−4.32624	−0.155705
$773$	−13.2361	−0.476068	−0.238034	−	0.971257i	$-0.576503\pi$
$773$	−13.2361	−0.476068	−0.238034	+	0.971257i	$0.576503\pi$
$774$	0.416408	0.0149675
$775$	5.29180	0.190087
$776$	−5.65248	−0.202912
$777$	1.31308	0.0471066
$778$	56.7771	2.03556
$779$	18.0000	0.644917
$780$	−0.437694	−0.0156720
$781$	−56.6869	−2.02842
$782$	−39.5967	−1.41598
$783$	−18.9443	−0.677013
$784$	−9.70820	−0.346722
$785$	0.347524	0.0124037
$786$	−9.32624	−0.332656
$787$	44.3607	1.58129	0.790644	−	0.612276i	$-0.209746\pi$
$787$	44.3607	1.58129	0.790644	+	0.612276i	$0.209746\pi$
$788$	5.09017	0.181330
$789$	8.87539	0.315972
$790$	7.32624	0.260656
$791$	49.1459	1.74743
$792$	−27.0344	−0.960627
$793$	8.29180	0.294450
$794$	0.854102	0.0303109
$795$	0.326238	0.0115705
$796$	12.4377	0.440842
$797$	−21.4377	−0.759362	−0.379681	−	0.925117i	$-0.623966\pi$
$797$	−21.4377	−0.759362	−0.379681	+	0.925117i	$0.623966\pi$
$798$	5.56231	0.196903
$799$	−4.97871	−0.176134
$800$	−15.6180	−0.552181
$801$	1.34752	0.0476124
$802$	59.8328	2.11277
$803$	0	0
$804$	−0.708204	−0.0249764
$805$	−13.4164	−0.472866
$806$	−5.56231	−0.195924
$807$	5.56231	0.195802
$808$	−16.7082	−0.587793
$809$	−23.5623	−0.828407	−0.414203	−	0.910184i	$-0.635940\pi$
$809$	−23.5623	−0.828407	−0.414203	+	0.910184i	$0.635940\pi$
$810$	7.70820	0.270839
$811$	21.4164	0.752032	0.376016	−	0.926613i	$-0.377294\pi$
$811$	21.4164	0.752032	0.376016	+	0.926613i	$0.377294\pi$
$812$	15.7082	0.551250
$813$	−7.34752	−0.257689
$814$	−7.85410	−0.275286
$815$	−5.27051	−0.184618
$816$	−6.27051	−0.219512
$817$	−0.270510	−0.00946394
$818$	43.2148	1.51097
$819$	−25.6869	−0.897574
$820$	2.29180	0.0800330
$821$	25.3050	0.883149	0.441574	−	0.897225i	$-0.354420\pi$
$821$	25.3050	0.883149	0.441574	+	0.897225i	$0.354420\pi$
$822$	−12.3262	−0.429927
$823$	15.4377	0.538124	0.269062	−	0.963123i	$-0.413286\pi$
$823$	15.4377	0.538124	0.269062	+	0.963123i	$0.413286\pi$
$824$	−39.2705	−1.36805
$825$	7.47214	0.260146
$826$	24.7082	0.859708
$827$	−32.8328	−1.14171	−0.570854	−	0.821051i	$-0.693388\pi$
$827$	−32.8328	−1.14171	−0.570854	+	0.821051i	$0.693388\pi$
$828$	12.7639	0.443577
$829$	−4.59675	−0.159652	−0.0798258	−	0.996809i	$-0.525436\pi$
$829$	−4.59675	−0.159652	−0.0798258	+	0.996809i	$0.525436\pi$
$830$	−13.1803	−0.457496
$831$	2.07701	0.0720508
$832$	−12.7082	−0.440578
$833$	−6.76393	−0.234356
$834$	−10.0902	−0.349394
$835$	−11.3607	−0.393153
$836$	−7.85410	−0.271640
$837$	−2.56231	−0.0885662
$838$	18.0902	0.624915
$839$	−47.0689	−1.62500	−0.812499	−	0.582962i	$-0.801894\pi$
$839$	−47.0689	−1.62500	−0.812499	+	0.582962i	$0.801894\pi$
$840$	−1.58359	−0.0546391
$841$	42.7771	1.47507
$842$	−40.1803	−1.38471
$843$	−3.43769	−0.118400
$844$	−3.18034	−0.109472
$845$	2.47214	0.0850441
$846$	6.79837	0.233733
$847$	−20.8328	−0.715824
$848$	−6.70820	−0.230361
$849$	−8.45898	−0.290311
$850$	−25.2705	−0.866771
$851$	−8.29180	−0.284239
$852$	3.15905	0.108227
$853$	4.58359	0.156939	0.0784696	−	0.996917i	$-0.474997\pi$
$853$	4.58359	0.156939	0.0784696	+	0.996917i	$0.474997\pi$
$854$	−13.4164	−0.459100
$855$	−5.29180	−0.180976
$856$	17.5623	0.600267
$857$	26.8328	0.916592	0.458296	−	0.888800i	$-0.348460\pi$
$857$	26.8328	0.916592	0.458296	+	0.888800i	$0.348460\pi$
$858$	−7.85410	−0.268135
$859$	−15.2918	−0.521749	−0.260875	−	0.965373i	$-0.584011\pi$
$859$	−15.2918	−0.521749	−0.260875	+	0.965373i	$0.584011\pi$
$860$	−0.0344419	−0.00117446
$861$	−6.87539	−0.234313
$862$	19.9443	0.679305
$863$	4.81966	0.164063	0.0820316	−	0.996630i	$-0.473859\pi$
$863$	4.81966	0.164063	0.0820316	+	0.996630i	$0.473859\pi$
$864$	7.56231	0.257275
$865$	4.61803	0.157018
$866$	40.8885	1.38945
$867$	2.12461	0.0721556
$868$	2.12461	0.0721140
$869$	31.0344	1.05277
$870$	3.23607	0.109713
$871$	−9.00000	−0.304953
$872$	−35.6525	−1.20735
$873$	7.21478	0.244183
$874$	−35.1246	−1.18811
$875$	−17.8328	−0.602859
$876$	0	0
$877$	7.32624	0.247389	0.123695	−	0.992320i	$-0.460526\pi$
$877$	7.32624	0.247389	0.123695	+	0.992320i	$0.460526\pi$
$878$	24.2705	0.819090
$879$	−8.90983	−0.300521
$880$	12.7082	0.428393
$881$	−21.4377	−0.722254	−0.361127	−	0.932517i	$-0.617608\pi$
$881$	−21.4377	−0.722254	−0.361127	+	0.932517i	$0.617608\pi$
$882$	9.23607	0.310995
$883$	−15.1803	−0.510859	−0.255430	−	0.966828i	$-0.582217\pi$
$883$	−15.1803	−0.510859	−0.255430	+	0.966828i	$0.582217\pi$
$884$	6.27051	0.210900
$885$	1.20163	0.0403922
$886$	−18.0000	−0.604722
$887$	−12.8197	−0.430442	−0.215221	−	0.976565i	$-0.569047\pi$
$887$	−12.8197	−0.430442	−0.215221	+	0.976565i	$0.569047\pi$
$888$	−0.978714	−0.0328435
$889$	−52.9574	−1.77614
$890$	−0.472136	−0.0158260
$891$	32.6525	1.09390
$892$	−1.94427	−0.0650990
$893$	−4.41641	−0.147789
$894$	−2.76393	−0.0924397
$895$	−12.3262	−0.412021
$896$	40.8541	1.36484
$897$	−8.29180	−0.276855
$898$	36.2705	1.21036
$899$	9.70820	0.323787
$900$	8.14590	0.271530
$901$	−4.67376	−0.155706
$902$	41.1246	1.36930
$903$	0.103326	0.00343846
$904$	−36.6312	−1.21834
$905$	9.38197	0.311867
$906$	−8.56231	−0.284464
$907$	−20.7082	−0.687605	−0.343802	−	0.939042i	$-0.611715\pi$
$907$	−20.7082	−0.687605	−0.343802	+	0.939042i	$0.611715\pi$
$908$	15.0344	0.498935
$909$	21.3262	0.707347
$910$	9.00000	0.298347
$911$	−11.5066	−0.381230	−0.190615	−	0.981665i	$-0.561048\pi$
$911$	−11.5066	−0.381230	−0.190615	+	0.981665i	$0.561048\pi$
$912$	−5.56231	−0.184186
$913$	−55.8328	−1.84780
$914$	−54.5967	−1.80590
$915$	−0.652476	−0.0215702
$916$	0.180340	0.00595860
$917$	45.2705	1.49496
$918$	12.2361	0.403850
$919$	−38.7082	−1.27687	−0.638433	−	0.769677i	$-0.720417\pi$
$919$	−38.7082	−1.27687	−0.638433	+	0.769677i	$0.720417\pi$
$920$	10.0000	0.329690
$921$	6.74265	0.222178
$922$	−48.8328	−1.60822
$923$	40.1459	1.32142
$924$	3.00000	0.0986928
$925$	−5.29180	−0.173993
$926$	62.3607	2.04930
$927$	50.1246	1.64631
$928$	−28.6525	−0.940564
$929$	3.05573	0.100255	0.0501276	−	0.998743i	$-0.484037\pi$
$929$	3.05573	0.100255	0.0501276	+	0.998743i	$0.484037\pi$
$930$	0.437694	0.0143526
$931$	−6.00000	−0.196642
$932$	−3.05573	−0.100094
$933$	5.85410	0.191655
$934$	−19.8541	−0.649646
$935$	8.85410	0.289560
$936$	19.1459	0.625803
$937$	39.5410	1.29175	0.645874	−	0.763444i	$-0.276493\pi$
$937$	39.5410	1.29175	0.645874	+	0.763444i	$0.276493\pi$
$938$	14.5623	0.475476
$939$	11.1246	0.363038
$940$	−0.562306	−0.0183404
$941$	23.9098	0.779438	0.389719	−	0.920934i	$-0.372572\pi$
$941$	23.9098	0.779438	0.389719	+	0.920934i	$0.372572\pi$
$942$	−0.347524	−0.0113229
$943$	43.4164	1.41383
$944$	−24.7082	−0.804184
$945$	4.14590	0.134866
$946$	−0.618034	−0.0200940
$947$	14.8328	0.482002	0.241001	−	0.970525i	$-0.422524\pi$
$947$	14.8328	0.482002	0.241001	+	0.970525i	$0.422524\pi$
$948$	−1.72949	−0.0561712
$949$	0	0
$950$	−22.4164	−0.727284
$951$	−13.1246	−0.425595
$952$	22.6869	0.735287
$953$	40.9098	1.32520	0.662600	−	0.748974i	$-0.269453\pi$
$953$	40.9098	1.32520	0.662600	+	0.748974i	$0.269453\pi$
$954$	6.38197	0.206624
$955$	11.4164	0.369426
$956$	−2.36068	−0.0763498
$957$	13.7082	0.443123
$958$	−12.4164	−0.401156
$959$	59.8328	1.93210
$960$	1.00000	0.0322749
$961$	−29.6869	−0.957643
$962$	5.56231	0.179336
$963$	−22.4164	−0.722359
$964$	14.0689	0.453128
$965$	4.32624	0.139267
$966$	13.4164	0.431666
$967$	−16.0000	−0.514525	−0.257263	−	0.966342i	$-0.582821\pi$
$967$	−16.0000	−0.514525	−0.257263	+	0.966342i	$0.582821\pi$
$968$	15.5279	0.499084
$969$	−3.87539	−0.124495
$970$	−2.52786	−0.0811648
$971$	−24.4377	−0.784243	−0.392121	−	0.919913i	$-0.628259\pi$
$971$	−24.4377	−0.784243	−0.392121	+	0.919913i	$0.628259\pi$
$972$	−5.96556	−0.191345
$973$	48.9787	1.57019
$974$	26.3262	0.843547
$975$	−5.29180	−0.169473
$976$	13.4164	0.429449
$977$	57.7771	1.84845	0.924226	−	0.381845i	$-0.124711\pi$
$977$	57.7771	1.84845	0.924226	+	0.381845i	$0.124711\pi$
$978$	5.27051	0.168532
$979$	−2.00000	−0.0639203
$980$	−0.763932	−0.0244029
$981$	45.5066	1.45291
$982$	−2.14590	−0.0684784
$983$	11.8328	0.377408	0.188704	−	0.982034i	$-0.439571\pi$
$983$	11.8328	0.377408	0.188704	+	0.982034i	$0.439571\pi$
$984$	5.12461	0.163367
$985$	−5.09017	−0.162186
$986$	−46.3607	−1.47642
$987$	1.68692	0.0536952
$988$	5.56231	0.176961
$989$	−0.652476	−0.0207475
$990$	−12.0902	−0.384251
$991$	−34.3820	−1.09218	−0.546090	−	0.837727i	$-0.683884\pi$
$991$	−34.3820	−1.09218	−0.546090	+	0.837727i	$0.683884\pi$
$992$	−3.87539	−0.123044
$993$	−13.5492	−0.429969
$994$	−64.9574	−2.06032
$995$	−12.4377	−0.394301
$996$	3.11146	0.0985903
$997$	−29.1246	−0.922386	−0.461193	−	0.887300i	$-0.652578\pi$
$997$	−29.1246	−0.922386	−0.461193	+	0.887300i	$0.652578\pi$
$998$	−30.5623	−0.967433
$999$	2.56231	0.0810678

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6007.2.a.a.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6007.2.a.a.1.1	✓	2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6007 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6007.a (trivial)

\(f(q)\)	\(=\)	\(q-1.61803 q^{2} -0.381966 q^{3} +0.618034 q^{4} -0.618034 q^{5} +0.618034 q^{6} -3.00000 q^{7} +2.23607 q^{8} -2.85410 q^{9} +O(q^{10})\)	\(q-1.61803 q^{2} -0.381966 q^{3} +0.618034 q^{4} -0.618034 q^{5} +0.618034 q^{6} -3.00000 q^{7} +2.23607 q^{8} -2.85410 q^{9} +1.00000 q^{10} +4.23607 q^{11} -0.236068 q^{12} -3.00000 q^{13} +4.85410 q^{14} +0.236068 q^{15} -4.85410 q^{16} -3.38197 q^{17} +4.61803 q^{18} -3.00000 q^{19} -0.381966 q^{20} +1.14590 q^{21} -6.85410 q^{22} -7.23607 q^{23} -0.854102 q^{24} -4.61803 q^{25} +4.85410 q^{26} +2.23607 q^{27} -1.85410 q^{28} -8.47214 q^{29} -0.381966 q^{30} -1.14590 q^{31} +3.38197 q^{32} -1.61803 q^{33} +5.47214 q^{34} +1.85410 q^{35} -1.76393 q^{36} +1.14590 q^{37} +4.85410 q^{38} +1.14590 q^{39} -1.38197 q^{40} -6.00000 q^{41} -1.85410 q^{42} +0.0901699 q^{43} +2.61803 q^{44} +1.76393 q^{45} +11.7082 q^{46} +1.47214 q^{47} +1.85410 q^{48} +2.00000 q^{49} +7.47214 q^{50} +1.29180 q^{51} -1.85410 q^{52} +1.38197 q^{53} -3.61803 q^{54} -2.61803 q^{55} -6.70820 q^{56} +1.14590 q^{57} +13.7082 q^{58} +5.09017 q^{59} +0.145898 q^{60} -2.76393 q^{61} +1.85410 q^{62} +8.56231 q^{63} +4.23607 q^{64} +1.85410 q^{65} +2.61803 q^{66} +3.00000 q^{67} -2.09017 q^{68} +2.76393 q^{69} -3.00000 q^{70} -13.3820 q^{71} -6.38197 q^{72} -1.85410 q^{74} +1.76393 q^{75} -1.85410 q^{76} -12.7082 q^{77} -1.85410 q^{78} +7.32624 q^{79} +3.00000 q^{80} +7.70820 q^{81} +9.70820 q^{82} -13.1803 q^{83} +0.708204 q^{84} +2.09017 q^{85} -0.145898 q^{86} +3.23607 q^{87} +9.47214 q^{88} -0.472136 q^{89} -2.85410 q^{90} +9.00000 q^{91} -4.47214 q^{92} +0.437694 q^{93} -2.38197 q^{94} +1.85410 q^{95} -1.29180 q^{96} -2.52786 q^{97} -3.23607 q^{98} -12.0902 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - 3 q^{3} - q^{4} + q^{5} - q^{6} - 6 q^{7} + q^{9}+O(q^{10}) \) 2 * q - q^2 - 3 * q^3 - q^4 + q^5 - q^6 - 6 * q^7 + q^9	\( 2 q - q^{2} - 3 q^{3} - q^{4} + q^{5} - q^{6} - 6 q^{7} + q^{9} + 2 q^{10} + 4 q^{11} + 4 q^{12} - 6 q^{13} + 3 q^{14} - 4 q^{15} - 3 q^{16} - 9 q^{17} + 7 q^{18} - 6 q^{19} - 3 q^{20} + 9 q^{21} - 7 q^{22} - 10 q^{23} + 5 q^{24} - 7 q^{25} + 3 q^{26} + 3 q^{28} - 8 q^{29} - 3 q^{30} - 9 q^{31} + 9 q^{32} - q^{33} + 2 q^{34} - 3 q^{35} - 8 q^{36} + 9 q^{37} + 3 q^{38} + 9 q^{39} - 5 q^{40} - 12 q^{41} + 3 q^{42} - 11 q^{43} + 3 q^{44} + 8 q^{45} + 10 q^{46} - 6 q^{47} - 3 q^{48} + 4 q^{49} + 6 q^{50} + 16 q^{51} + 3 q^{52} + 5 q^{53} - 5 q^{54} - 3 q^{55} + 9 q^{57} + 14 q^{58} - q^{59} + 7 q^{60} - 10 q^{61} - 3 q^{62} - 3 q^{63} + 4 q^{64} - 3 q^{65} + 3 q^{66} + 6 q^{67} + 7 q^{68} + 10 q^{69} - 6 q^{70} - 29 q^{71} - 15 q^{72} + 3 q^{74} + 8 q^{75} + 3 q^{76} - 12 q^{77} + 3 q^{78} - q^{79} + 6 q^{80} + 2 q^{81} + 6 q^{82} - 4 q^{83} - 12 q^{84} - 7 q^{85} - 7 q^{86} + 2 q^{87} + 10 q^{88} + 8 q^{89} + q^{90} + 18 q^{91} + 21 q^{93} - 7 q^{94} - 3 q^{95} - 16 q^{96} - 14 q^{97} - 2 q^{98} - 13 q^{99}+O(q^{100}) \) 2 * q - q^2 - 3 * q^3 - q^4 + q^5 - q^6 - 6 * q^7 + q^9 + 2 * q^10 + 4 * q^11 + 4 * q^12 - 6 * q^13 + 3 * q^14 - 4 * q^15 - 3 * q^16 - 9 * q^17 + 7 * q^18 - 6 * q^19 - 3 * q^20 + 9 * q^21 - 7 * q^22 - 10 * q^23 + 5 * q^24 - 7 * q^25 + 3 * q^26 + 3 * q^28 - 8 * q^29 - 3 * q^30 - 9 * q^31 + 9 * q^32 - q^33 + 2 * q^34 - 3 * q^35 - 8 * q^36 + 9 * q^37 + 3 * q^38 + 9 * q^39 - 5 * q^40 - 12 * q^41 + 3 * q^42 - 11 * q^43 + 3 * q^44 + 8 * q^45 + 10 * q^46 - 6 * q^47 - 3 * q^48 + 4 * q^49 + 6 * q^50 + 16 * q^51 + 3 * q^52 + 5 * q^53 - 5 * q^54 - 3 * q^55 + 9 * q^57 + 14 * q^58 - q^59 + 7 * q^60 - 10 * q^61 - 3 * q^62 - 3 * q^63 + 4 * q^64 - 3 * q^65 + 3 * q^66 + 6 * q^67 + 7 * q^68 + 10 * q^69 - 6 * q^70 - 29 * q^71 - 15 * q^72 + 3 * q^74 + 8 * q^75 + 3 * q^76 - 12 * q^77 + 3 * q^78 - q^79 + 6 * q^80 + 2 * q^81 + 6 * q^82 - 4 * q^83 - 12 * q^84 - 7 * q^85 - 7 * q^86 + 2 * q^87 + 10 * q^88 + 8 * q^89 + q^90 + 18 * q^91 + 21 * q^93 - 7 * q^94 - 3 * q^95 - 16 * q^96 - 14 * q^97 - 2 * q^98 - 13 * q^99

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