LMFDB - Embedded newform 6041.2.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6041,2,Mod(1,6041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6041, 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("6041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6041 = 7 \cdot 863 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6041.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:	$48.2376278611$
Analytic rank:	$1$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	6041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.381966 q^{3} -1.00000 q^{4} +1.61803 q^{5} -0.381966 q^{6} -1.00000 q^{7} +3.00000 q^{8} -2.85410 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.381966 q^{3} -1.00000 q^{4} +1.61803 q^{5} -0.381966 q^{6} -1.00000 q^{7} +3.00000 q^{8} -2.85410 q^{9} -1.61803 q^{10} -0.381966 q^{11} -0.381966 q^{12} +3.38197 q^{13} +1.00000 q^{14} +0.618034 q^{15} -1.00000 q^{16} +1.23607 q^{17} +2.85410 q^{18} +7.09017 q^{19} -1.61803 q^{20} -0.381966 q^{21} +0.381966 q^{22} -6.09017 q^{23} +1.14590 q^{24} -2.38197 q^{25} -3.38197 q^{26} -2.23607 q^{27} +1.00000 q^{28} +4.47214 q^{29} -0.618034 q^{30} -6.47214 q^{31} -5.00000 q^{32} -0.145898 q^{33} -1.23607 q^{34} -1.61803 q^{35} +2.85410 q^{36} -8.85410 q^{37} -7.09017 q^{38} +1.29180 q^{39} +4.85410 q^{40} -8.94427 q^{41} +0.381966 q^{42} +7.70820 q^{43} +0.381966 q^{44} -4.61803 q^{45} +6.09017 q^{46} -3.23607 q^{47} -0.381966 q^{48} +1.00000 q^{49} +2.38197 q^{50} +0.472136 q^{51} -3.38197 q^{52} +11.3262 q^{53} +2.23607 q^{54} -0.618034 q^{55} -3.00000 q^{56} +2.70820 q^{57} -4.47214 q^{58} -8.38197 q^{59} -0.618034 q^{60} +0.291796 q^{61} +6.47214 q^{62} +2.85410 q^{63} +7.00000 q^{64} +5.47214 q^{65} +0.145898 q^{66} -13.8541 q^{67} -1.23607 q^{68} -2.32624 q^{69} +1.61803 q^{70} +6.47214 q^{71} -8.56231 q^{72} +4.85410 q^{73} +8.85410 q^{74} -0.909830 q^{75} -7.09017 q^{76} +0.381966 q^{77} -1.29180 q^{78} -11.3820 q^{79} -1.61803 q^{80} +7.70820 q^{81} +8.94427 q^{82} +13.2361 q^{83} +0.381966 q^{84} +2.00000 q^{85} -7.70820 q^{86} +1.70820 q^{87} -1.14590 q^{88} +10.9443 q^{89} +4.61803 q^{90} -3.38197 q^{91} +6.09017 q^{92} -2.47214 q^{93} +3.23607 q^{94} +11.4721 q^{95} -1.90983 q^{96} +1.85410 q^{97} -1.00000 q^{98} +1.09017 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 3 q^{3} - 2 q^{4} + q^{5} - 3 q^{6} - 2 q^{7} + 6 q^{8} + q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 3 * q^3 - 2 * q^4 + q^5 - 3 * q^6 - 2 * q^7 + 6 * q^8 + q^9	$ 2 q - 2 q^{2} + 3 q^{3} - 2 q^{4} + q^{5} - 3 q^{6} - 2 q^{7} + 6 q^{8} + q^{9} - q^{10} - 3 q^{11} - 3 q^{12} + 9 q^{13} + 2 q^{14} - q^{15} - 2 q^{16} - 2 q^{17} - q^{18} + 3 q^{19} - q^{20} - 3 q^{21} + 3 q^{22} - q^{23} + 9 q^{24} - 7 q^{25} - 9 q^{26} + 2 q^{28} + q^{30} - 4 q^{31} - 10 q^{32} - 7 q^{33} + 2 q^{34} - q^{35} - q^{36} - 11 q^{37} - 3 q^{38} + 16 q^{39} + 3 q^{40} + 3 q^{42} + 2 q^{43} + 3 q^{44} - 7 q^{45} + q^{46} - 2 q^{47} - 3 q^{48} + 2 q^{49} + 7 q^{50} - 8 q^{51} - 9 q^{52} + 7 q^{53} + q^{55} - 6 q^{56} - 8 q^{57} - 19 q^{59} + q^{60} + 14 q^{61} + 4 q^{62} - q^{63} + 14 q^{64} + 2 q^{65} + 7 q^{66} - 21 q^{67} + 2 q^{68} + 11 q^{69} + q^{70} + 4 q^{71} + 3 q^{72} + 3 q^{73} + 11 q^{74} - 13 q^{75} - 3 q^{76} + 3 q^{77} - 16 q^{78} - 25 q^{79} - q^{80} + 2 q^{81} + 22 q^{83} + 3 q^{84} + 4 q^{85} - 2 q^{86} - 10 q^{87} - 9 q^{88} + 4 q^{89} + 7 q^{90} - 9 q^{91} + q^{92} + 4 q^{93} + 2 q^{94} + 14 q^{95} - 15 q^{96} - 3 q^{97} - 2 q^{98} - 9 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + 3 * q^3 - 2 * q^4 + q^5 - 3 * q^6 - 2 * q^7 + 6 * q^8 + q^9 - q^10 - 3 * q^11 - 3 * q^12 + 9 * q^13 + 2 * q^14 - q^15 - 2 * q^16 - 2 * q^17 - q^18 + 3 * q^19 - q^20 - 3 * q^21 + 3 * q^22 - q^23 + 9 * q^24 - 7 * q^25 - 9 * q^26 + 2 * q^28 + q^30 - 4 * q^31 - 10 * q^32 - 7 * q^33 + 2 * q^34 - q^35 - q^36 - 11 * q^37 - 3 * q^38 + 16 * q^39 + 3 * q^40 + 3 * q^42 + 2 * q^43 + 3 * q^44 - 7 * q^45 + q^46 - 2 * q^47 - 3 * q^48 + 2 * q^49 + 7 * q^50 - 8 * q^51 - 9 * q^52 + 7 * q^53 + q^55 - 6 * q^56 - 8 * q^57 - 19 * q^59 + q^60 + 14 * q^61 + 4 * q^62 - q^63 + 14 * q^64 + 2 * q^65 + 7 * q^66 - 21 * q^67 + 2 * q^68 + 11 * q^69 + q^70 + 4 * q^71 + 3 * q^72 + 3 * q^73 + 11 * q^74 - 13 * q^75 - 3 * q^76 + 3 * q^77 - 16 * q^78 - 25 * q^79 - q^80 + 2 * q^81 + 22 * q^83 + 3 * q^84 + 4 * q^85 - 2 * q^86 - 10 * q^87 - 9 * q^88 + 4 * q^89 + 7 * q^90 - 9 * q^91 + q^92 + 4 * q^93 + 2 * q^94 + 14 * q^95 - 15 * q^96 - 3 * q^97 - 2 * q^98 - 9 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107	−0.353553	−	0.935414i	$-0.615027\pi$
$2$	−1.00000	−0.707107	−0.353553	+	0.935414i	$0.615027\pi$
$3$	0.381966	0.220528	0.110264	−	0.993902i	$-0.464830\pi$
$3$	0.381966	0.220528	0.110264	+	0.993902i	$0.464830\pi$
$4$	−1.00000	−0.500000
$5$	1.61803	0.723607	0.361803	−	0.932254i	$-0.382161\pi$
$5$	1.61803	0.723607	0.361803	+	0.932254i	$0.382161\pi$
$6$	−0.381966	−0.155937
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	3.00000	1.06066
$9$	−2.85410	−0.951367
$10$	−1.61803	−0.511667
$11$	−0.381966	−0.115167	−0.0575835	−	0.998341i	$-0.518340\pi$
$11$	−0.381966	−0.115167	−0.0575835	+	0.998341i	$0.518340\pi$
$12$	−0.381966	−0.110264
$13$	3.38197	0.937989	0.468994	−	0.883201i	$-0.344616\pi$
$13$	3.38197	0.937989	0.468994	+	0.883201i	$0.344616\pi$
$14$	1.00000	0.267261
$15$	0.618034	0.159576
$16$	−1.00000	−0.250000
$17$	1.23607	0.299791	0.149895	−	0.988702i	$-0.452106\pi$
$17$	1.23607	0.299791	0.149895	+	0.988702i	$0.452106\pi$
$18$	2.85410	0.672718
$19$	7.09017	1.62660	0.813298	−	0.581847i	$-0.197670\pi$
$19$	7.09017	1.62660	0.813298	+	0.581847i	$0.197670\pi$
$20$	−1.61803	−0.361803
$21$	−0.381966	−0.0833518
$22$	0.381966	0.0814354
$23$	−6.09017	−1.26989	−0.634944	−	0.772558i	$-0.718977\pi$
$23$	−6.09017	−1.26989	−0.634944	+	0.772558i	$0.718977\pi$
$24$	1.14590	0.233905
$25$	−2.38197	−0.476393
$26$	−3.38197	−0.663258
$27$	−2.23607	−0.430331
$28$	1.00000	0.188982
$29$	4.47214	0.830455	0.415227	−	0.909718i	$-0.363702\pi$
$29$	4.47214	0.830455	0.415227	+	0.909718i	$0.363702\pi$
$30$	−0.618034	−0.112837
$31$	−6.47214	−1.16243	−0.581215	−	0.813750i	$-0.697422\pi$
$31$	−6.47214	−1.16243	−0.581215	+	0.813750i	$0.697422\pi$
$32$	−5.00000	−0.883883
$33$	−0.145898	−0.0253976
$34$	−1.23607	−0.211984
$35$	−1.61803	−0.273498
$36$	2.85410	0.475684
$37$	−8.85410	−1.45561	−0.727803	−	0.685787i	$-0.759458\pi$
$37$	−8.85410	−1.45561	−0.727803	+	0.685787i	$0.759458\pi$
$38$	−7.09017	−1.15018
$39$	1.29180	0.206853
$40$	4.85410	0.767501
$41$	−8.94427	−1.39686	−0.698430	−	0.715678i	$-0.746118\pi$
$41$	−8.94427	−1.39686	−0.698430	+	0.715678i	$0.746118\pi$
$42$	0.381966	0.0589386
$43$	7.70820	1.17549	0.587745	−	0.809046i	$-0.300016\pi$
$43$	7.70820	1.17549	0.587745	+	0.809046i	$0.300016\pi$
$44$	0.381966	0.0575835
$45$	−4.61803	−0.688416
$46$	6.09017	0.897947
$47$	−3.23607	−0.472029	−0.236015	−	0.971750i	$-0.575841\pi$
$47$	−3.23607	−0.472029	−0.236015	+	0.971750i	$0.575841\pi$
$48$	−0.381966	−0.0551320
$49$	1.00000	0.142857
$50$	2.38197	0.336861
$51$	0.472136	0.0661123
$52$	−3.38197	−0.468994
$53$	11.3262	1.55578	0.777889	−	0.628401i	$-0.216290\pi$
$53$	11.3262	1.55578	0.777889	+	0.628401i	$0.216290\pi$
$54$	2.23607	0.304290
$55$	−0.618034	−0.0833357
$56$	−3.00000	−0.400892
$57$	2.70820	0.358710
$58$	−4.47214	−0.587220
$59$	−8.38197	−1.09124	−0.545620	−	0.838033i	$-0.683706\pi$
$59$	−8.38197	−1.09124	−0.545620	+	0.838033i	$0.683706\pi$
$60$	−0.618034	−0.0797878
$61$	0.291796	0.0373607	0.0186803	−	0.999826i	$-0.494054\pi$
$61$	0.291796	0.0373607	0.0186803	+	0.999826i	$0.494054\pi$
$62$	6.47214	0.821962
$63$	2.85410	0.359583
$64$	7.00000	0.875000
$65$	5.47214	0.678735
$66$	0.145898	0.0179588
$67$	−13.8541	−1.69255	−0.846274	−	0.532748i	$-0.821159\pi$
$67$	−13.8541	−1.69255	−0.846274	+	0.532748i	$0.821159\pi$
$68$	−1.23607	−0.149895
$69$	−2.32624	−0.280046
$70$	1.61803	0.193392
$71$	6.47214	0.768101	0.384051	−	0.923312i	$-0.374529\pi$
$71$	6.47214	0.768101	0.384051	+	0.923312i	$0.374529\pi$
$72$	−8.56231	−1.00908
$73$	4.85410	0.568130	0.284065	−	0.958805i	$-0.408317\pi$
$73$	4.85410	0.568130	0.284065	+	0.958805i	$0.408317\pi$
$74$	8.85410	1.02927
$75$	−0.909830	−0.105058
$76$	−7.09017	−0.813298
$77$	0.381966	0.0435291
$78$	−1.29180	−0.146267
$79$	−11.3820	−1.28057	−0.640286	−	0.768137i	$-0.721184\pi$
$79$	−11.3820	−1.28057	−0.640286	+	0.768137i	$0.721184\pi$
$80$	−1.61803	−0.180902
$81$	7.70820	0.856467
$82$	8.94427	0.987730
$83$	13.2361	1.45285	0.726424	−	0.687247i	$-0.241181\pi$
$83$	13.2361	1.45285	0.726424	+	0.687247i	$0.241181\pi$
$84$	0.381966	0.0416759
$85$	2.00000	0.216930
$86$	−7.70820	−0.831197
$87$	1.70820	0.183139
$88$	−1.14590	−0.122153
$89$	10.9443	1.16009	0.580045	−	0.814584i	$-0.303035\pi$
$89$	10.9443	1.16009	0.580045	+	0.814584i	$0.303035\pi$
$90$	4.61803	0.486784
$91$	−3.38197	−0.354526
$92$	6.09017	0.634944
$93$	−2.47214	−0.256349
$94$	3.23607	0.333775
$95$	11.4721	1.17702
$96$	−1.90983	−0.194921
$97$	1.85410	0.188256	0.0941278	−	0.995560i	$-0.469994\pi$
$97$	1.85410	0.188256	0.0941278	+	0.995560i	$0.469994\pi$
$98$	−1.00000	−0.101015
$99$	1.09017	0.109566
$100$	2.38197	0.238197
$101$	4.47214	0.444994	0.222497	−	0.974933i	$-0.428579\pi$
$101$	4.47214	0.444994	0.222497	+	0.974933i	$0.428579\pi$
$102$	−0.472136	−0.0467484
$103$	5.90983	0.582313	0.291156	−	0.956675i	$-0.405960\pi$
$103$	5.90983	0.582313	0.291156	+	0.956675i	$0.405960\pi$
$104$	10.1459	0.994887
$105$	−0.618034	−0.0603139
$106$	−11.3262	−1.10010
$107$	6.00000	0.580042	0.290021	−	0.957020i	$-0.406338\pi$
$107$	6.00000	0.580042	0.290021	+	0.957020i	$0.406338\pi$
$108$	2.23607	0.215166
$109$	−3.14590	−0.301322	−0.150661	−	0.988585i	$-0.548140\pi$
$109$	−3.14590	−0.301322	−0.150661	+	0.988585i	$0.548140\pi$
$110$	0.618034	0.0589272
$111$	−3.38197	−0.321002
$112$	1.00000	0.0944911
$113$	−16.6180	−1.56329	−0.781647	−	0.623722i	$-0.785620\pi$
$113$	−16.6180	−1.56329	−0.781647	+	0.623722i	$0.785620\pi$
$114$	−2.70820	−0.253647
$115$	−9.85410	−0.918900
$116$	−4.47214	−0.415227
$117$	−9.65248	−0.892372
$118$	8.38197	0.771623
$119$	−1.23607	−0.113310
$120$	1.85410	0.169256
$121$	−10.8541	−0.986737
$122$	−0.291796	−0.0264180
$123$	−3.41641	−0.308047
$124$	6.47214	0.581215
$125$	−11.9443	−1.06833
$126$	−2.85410	−0.254264
$127$	−4.00000	−0.354943	−0.177471	−	0.984126i	$-0.556792\pi$
$127$	−4.00000	−0.354943	−0.177471	+	0.984126i	$0.556792\pi$
$128$	3.00000	0.265165
$129$	2.94427	0.259229
$130$	−5.47214	−0.479938
$131$	−19.7082	−1.72191	−0.860957	−	0.508678i	$-0.830134\pi$
$131$	−19.7082	−1.72191	−0.860957	+	0.508678i	$0.830134\pi$
$132$	0.145898	0.0126988
$133$	−7.09017	−0.614796
$134$	13.8541	1.19681
$135$	−3.61803	−0.311391
$136$	3.70820	0.317976
$137$	3.52786	0.301406	0.150703	−	0.988579i	$-0.451846\pi$
$137$	3.52786	0.301406	0.150703	+	0.988579i	$0.451846\pi$
$138$	2.32624	0.198023
$139$	15.4164	1.30760	0.653801	−	0.756666i	$-0.273173\pi$
$139$	15.4164	1.30760	0.653801	+	0.756666i	$0.273173\pi$
$140$	1.61803	0.136749
$141$	−1.23607	−0.104096
$142$	−6.47214	−0.543130
$143$	−1.29180	−0.108025
$144$	2.85410	0.237842
$145$	7.23607	0.600923
$146$	−4.85410	−0.401728
$147$	0.381966	0.0315040
$148$	8.85410	0.727803
$149$	21.4164	1.75450	0.877250	−	0.480033i	$-0.159375\pi$
$149$	21.4164	1.75450	0.877250	+	0.480033i	$0.159375\pi$
$150$	0.909830	0.0742873
$151$	−11.2361	−0.914378	−0.457189	−	0.889369i	$-0.651144\pi$
$151$	−11.2361	−0.914378	−0.457189	+	0.889369i	$0.651144\pi$
$152$	21.2705	1.72527
$153$	−3.52786	−0.285211
$154$	−0.381966	−0.0307797
$155$	−10.4721	−0.841142
$156$	−1.29180	−0.103426
$157$	9.85410	0.786443	0.393221	−	0.919444i	$-0.371361\pi$
$157$	9.85410	0.786443	0.393221	+	0.919444i	$0.371361\pi$
$158$	11.3820	0.905501
$159$	4.32624	0.343093
$160$	−8.09017	−0.639584
$161$	6.09017	0.479973
$162$	−7.70820	−0.605614
$163$	2.47214	0.193633	0.0968163	−	0.995302i	$-0.469134\pi$
$163$	2.47214	0.193633	0.0968163	+	0.995302i	$0.469134\pi$
$164$	8.94427	0.698430
$165$	−0.236068	−0.0183779
$166$	−13.2361	−1.02732
$167$	−10.1803	−0.787778	−0.393889	−	0.919158i	$-0.628871\pi$
$167$	−10.1803	−0.787778	−0.393889	+	0.919158i	$0.628871\pi$
$168$	−1.14590	−0.0884080
$169$	−1.56231	−0.120177
$170$	−2.00000	−0.153393
$171$	−20.2361	−1.54749
$172$	−7.70820	−0.587745
$173$	−18.5623	−1.41127	−0.705633	−	0.708578i	$-0.749337\pi$
$173$	−18.5623	−1.41127	−0.705633	+	0.708578i	$0.749337\pi$
$174$	−1.70820	−0.129499
$175$	2.38197	0.180060
$176$	0.381966	0.0287918
$177$	−3.20163	−0.240649
$178$	−10.9443	−0.820308
$179$	−12.3262	−0.921306	−0.460653	−	0.887580i	$-0.652385\pi$
$179$	−12.3262	−0.921306	−0.460653	+	0.887580i	$0.652385\pi$
$180$	4.61803	0.344208
$181$	14.9443	1.11080	0.555399	−	0.831584i	$-0.312565\pi$
$181$	14.9443	1.11080	0.555399	+	0.831584i	$0.312565\pi$
$182$	3.38197	0.250688
$183$	0.111456	0.00823908
$184$	−18.2705	−1.34692
$185$	−14.3262	−1.05329
$186$	2.47214	0.181266
$187$	−0.472136	−0.0345260
$188$	3.23607	0.236015
$189$	2.23607	0.162650
$190$	−11.4721	−0.832276
$191$	−17.8885	−1.29437	−0.647185	−	0.762333i	$-0.724054\pi$
$191$	−17.8885	−1.29437	−0.647185	+	0.762333i	$0.724054\pi$
$192$	2.67376	0.192962
$193$	−23.2361	−1.67257	−0.836284	−	0.548296i	$-0.815277\pi$
$193$	−23.2361	−1.67257	−0.836284	+	0.548296i	$0.815277\pi$
$194$	−1.85410	−0.133117
$195$	2.09017	0.149680
$196$	−1.00000	−0.0714286
$197$	−20.9443	−1.49222	−0.746109	−	0.665824i	$-0.768080\pi$
$197$	−20.9443	−1.49222	−0.746109	+	0.665824i	$0.768080\pi$
$198$	−1.09017	−0.0774750
$199$	−5.85410	−0.414986	−0.207493	−	0.978236i	$-0.566530\pi$
$199$	−5.85410	−0.414986	−0.207493	+	0.978236i	$0.566530\pi$
$200$	−7.14590	−0.505291
$201$	−5.29180	−0.373255
$202$	−4.47214	−0.314658
$203$	−4.47214	−0.313882
$204$	−0.472136	−0.0330561
$205$	−14.4721	−1.01078
$206$	−5.90983	−0.411757
$207$	17.3820	1.20813
$208$	−3.38197	−0.234497
$209$	−2.70820	−0.187330
$210$	0.618034	0.0426484
$211$	−6.43769	−0.443189	−0.221595	−	0.975139i	$-0.571126\pi$
$211$	−6.43769	−0.443189	−0.221595	+	0.975139i	$0.571126\pi$
$212$	−11.3262	−0.777889
$213$	2.47214	0.169388
$214$	−6.00000	−0.410152
$215$	12.4721	0.850593
$216$	−6.70820	−0.456435
$217$	6.47214	0.439357
$218$	3.14590	0.213067
$219$	1.85410	0.125289
$220$	0.618034	0.0416678
$221$	4.18034	0.281200
$222$	3.38197	0.226983
$223$	20.5623	1.37695	0.688477	−	0.725258i	$-0.258280\pi$
$223$	20.5623	1.37695	0.688477	+	0.725258i	$0.258280\pi$
$224$	5.00000	0.334077
$225$	6.79837	0.453225
$226$	16.6180	1.10542
$227$	1.05573	0.0700711	0.0350356	−	0.999386i	$-0.488846\pi$
$227$	1.05573	0.0700711	0.0350356	+	0.999386i	$0.488846\pi$
$228$	−2.70820	−0.179355
$229$	−0.180340	−0.0119172	−0.00595860	−	0.999982i	$-0.501897\pi$
$229$	−0.180340	−0.0119172	−0.00595860	+	0.999982i	$0.501897\pi$
$230$	9.85410	0.649760
$231$	0.145898	0.00959939
$232$	13.4164	0.880830
$233$	−24.1803	−1.58411	−0.792053	−	0.610452i	$-0.790988\pi$
$233$	−24.1803	−1.58411	−0.792053	+	0.610452i	$0.790988\pi$
$234$	9.65248	0.631002
$235$	−5.23607	−0.341563
$236$	8.38197	0.545620
$237$	−4.34752	−0.282402
$238$	1.23607	0.0801224
$239$	−29.2361	−1.89112	−0.945562	−	0.325442i	$-0.894487\pi$
$239$	−29.2361	−1.89112	−0.945562	+	0.325442i	$0.894487\pi$
$240$	−0.618034	−0.0398939
$241$	12.6180	0.812799	0.406400	−	0.913695i	$-0.366784\pi$
$241$	12.6180	0.812799	0.406400	+	0.913695i	$0.366784\pi$
$242$	10.8541	0.697728
$243$	9.65248	0.619207
$244$	−0.291796	−0.0186803
$245$	1.61803	0.103372
$246$	3.41641	0.217822
$247$	23.9787	1.52573
$248$	−19.4164	−1.23294
$249$	5.05573	0.320394
$250$	11.9443	0.755422
$251$	20.6525	1.30357	0.651786	−	0.758403i	$-0.274020\pi$
$251$	20.6525	1.30357	0.651786	+	0.758403i	$0.274020\pi$
$252$	−2.85410	−0.179792
$253$	2.32624	0.146249
$254$	4.00000	0.250982
$255$	0.763932	0.0478393
$256$	−17.0000	−1.06250
$257$	0.944272	0.0589021	0.0294510	−	0.999566i	$-0.490624\pi$
$257$	0.944272	0.0589021	0.0294510	+	0.999566i	$0.490624\pi$
$258$	−2.94427	−0.183302
$259$	8.85410	0.550167
$260$	−5.47214	−0.339367
$261$	−12.7639	−0.790068
$262$	19.7082	1.21758
$263$	−19.7426	−1.21738	−0.608692	−	0.793407i	$-0.708305\pi$
$263$	−19.7426	−1.21738	−0.608692	+	0.793407i	$0.708305\pi$
$264$	−0.437694	−0.0269382
$265$	18.3262	1.12577
$266$	7.09017	0.434726
$267$	4.18034	0.255833
$268$	13.8541	0.846274
$269$	5.70820	0.348035	0.174018	−	0.984743i	$-0.444325\pi$
$269$	5.70820	0.348035	0.174018	+	0.984743i	$0.444325\pi$
$270$	3.61803	0.220187
$271$	15.1246	0.918755	0.459377	−	0.888241i	$-0.348073\pi$
$271$	15.1246	0.918755	0.459377	+	0.888241i	$0.348073\pi$
$272$	−1.23607	−0.0749476
$273$	−1.29180	−0.0781831
$274$	−3.52786	−0.213126
$275$	0.909830	0.0548648
$276$	2.32624	0.140023
$277$	−14.4721	−0.869546	−0.434773	−	0.900540i	$-0.643171\pi$
$277$	−14.4721	−0.869546	−0.434773	+	0.900540i	$0.643171\pi$
$278$	−15.4164	−0.924615
$279$	18.4721	1.10590
$280$	−4.85410	−0.290088
$281$	8.27051	0.493377	0.246689	−	0.969095i	$-0.420658\pi$
$281$	8.27051	0.493377	0.246689	+	0.969095i	$0.420658\pi$
$282$	1.23607	0.0736068
$283$	16.3262	0.970494	0.485247	−	0.874377i	$-0.338730\pi$
$283$	16.3262	0.970494	0.485247	+	0.874377i	$0.338730\pi$
$284$	−6.47214	−0.384051
$285$	4.38197	0.259565
$286$	1.29180	0.0763855
$287$	8.94427	0.527964
$288$	14.2705	0.840898
$289$	−15.4721	−0.910126
$290$	−7.23607	−0.424917
$291$	0.708204	0.0415156
$292$	−4.85410	−0.284065
$293$	−7.52786	−0.439783	−0.219891	−	0.975524i	$-0.570570\pi$
$293$	−7.52786	−0.439783	−0.219891	+	0.975524i	$0.570570\pi$
$294$	−0.381966	−0.0222767
$295$	−13.5623	−0.789628
$296$	−26.5623	−1.54390
$297$	0.854102	0.0495600
$298$	−21.4164	−1.24062
$299$	−20.5967	−1.19114
$300$	0.909830	0.0525291
$301$	−7.70820	−0.444293
$302$	11.2361	0.646563
$303$	1.70820	0.0981338
$304$	−7.09017	−0.406649
$305$	0.472136	0.0270344
$306$	3.52786	0.201675
$307$	−5.20163	−0.296872	−0.148436	−	0.988922i	$-0.547424\pi$
$307$	−5.20163	−0.296872	−0.148436	+	0.988922i	$0.547424\pi$
$308$	−0.381966	−0.0217645
$309$	2.25735	0.128416
$310$	10.4721	0.594777
$311$	−8.94427	−0.507183	−0.253592	−	0.967311i	$-0.581612\pi$
$311$	−8.94427	−0.507183	−0.253592	+	0.967311i	$0.581612\pi$
$312$	3.87539	0.219401
$313$	−0.180340	−0.0101934	−0.00509671	−	0.999987i	$-0.501622\pi$
$313$	−0.180340	−0.0101934	−0.00509671	+	0.999987i	$0.501622\pi$
$314$	−9.85410	−0.556099
$315$	4.61803	0.260197
$316$	11.3820	0.640286
$317$	2.65248	0.148978	0.0744889	−	0.997222i	$-0.476267\pi$
$317$	2.65248	0.148978	0.0744889	+	0.997222i	$0.476267\pi$
$318$	−4.32624	−0.242603
$319$	−1.70820	−0.0956411
$320$	11.3262	0.633156
$321$	2.29180	0.127916
$322$	−6.09017	−0.339392
$323$	8.76393	0.487638
$324$	−7.70820	−0.428234
$325$	−8.05573	−0.446851
$326$	−2.47214	−0.136919
$327$	−1.20163	−0.0664501
$328$	−26.8328	−1.48159
$329$	3.23607	0.178410
$330$	0.236068	0.0129951
$331$	−13.5279	−0.743559	−0.371779	−	0.928321i	$-0.621252\pi$
$331$	−13.5279	−0.743559	−0.371779	+	0.928321i	$0.621252\pi$
$332$	−13.2361	−0.726424
$333$	25.2705	1.38482
$334$	10.1803	0.557043
$335$	−22.4164	−1.22474
$336$	0.381966	0.0208380
$337$	4.90983	0.267455	0.133728	−	0.991018i	$-0.457305\pi$
$337$	4.90983	0.267455	0.133728	+	0.991018i	$0.457305\pi$
$338$	1.56231	0.0849782
$339$	−6.34752	−0.344750
$340$	−2.00000	−0.108465
$341$	2.47214	0.133874
$342$	20.2361	1.09424
$343$	−1.00000	−0.0539949
$344$	23.1246	1.24680
$345$	−3.76393	−0.202643
$346$	18.5623	0.997916
$347$	23.4508	1.25891	0.629454	−	0.777038i	$-0.283279\pi$
$347$	23.4508	1.25891	0.629454	+	0.777038i	$0.283279\pi$
$348$	−1.70820	−0.0915693
$349$	−3.88854	−0.208149	−0.104074	−	0.994570i	$-0.533188\pi$
$349$	−3.88854	−0.208149	−0.104074	+	0.994570i	$0.533188\pi$
$350$	−2.38197	−0.127321
$351$	−7.56231	−0.403646
$352$	1.90983	0.101794
$353$	−0.291796	−0.0155307	−0.00776537	−	0.999970i	$-0.502472\pi$
$353$	−0.291796	−0.0155307	−0.00776537	+	0.999970i	$0.502472\pi$
$354$	3.20163	0.170165
$355$	10.4721	0.555803
$356$	−10.9443	−0.580045
$357$	−0.472136	−0.0249881
$358$	12.3262	0.651462
$359$	9.81966	0.518262	0.259131	−	0.965842i	$-0.416564\pi$
$359$	9.81966	0.518262	0.259131	+	0.965842i	$0.416564\pi$
$360$	−13.8541	−0.730175
$361$	31.2705	1.64582
$362$	−14.9443	−0.785453
$363$	−4.14590	−0.217603
$364$	3.38197	0.177263
$365$	7.85410	0.411102
$366$	−0.111456	−0.00582591
$367$	−30.0000	−1.56599	−0.782994	−	0.622030i	$-0.786308\pi$
$367$	−30.0000	−1.56599	−0.782994	+	0.622030i	$0.786308\pi$
$368$	6.09017	0.317472
$369$	25.5279	1.32893
$370$	14.3262	0.744786
$371$	−11.3262	−0.588029
$372$	2.47214	0.128174
$373$	−3.67376	−0.190220	−0.0951101	−	0.995467i	$-0.530320\pi$
$373$	−3.67376	−0.190220	−0.0951101	+	0.995467i	$0.530320\pi$
$374$	0.472136	0.0244136
$375$	−4.56231	−0.235596
$376$	−9.70820	−0.500662
$377$	15.1246	0.778957
$378$	−2.23607	−0.115011
$379$	−16.0344	−0.823634	−0.411817	−	0.911267i	$-0.635106\pi$
$379$	−16.0344	−0.823634	−0.411817	+	0.911267i	$0.635106\pi$
$380$	−11.4721	−0.588508
$381$	−1.52786	−0.0782748
$382$	17.8885	0.915258
$383$	−6.14590	−0.314041	−0.157020	−	0.987595i	$-0.550189\pi$
$383$	−6.14590	−0.314041	−0.157020	+	0.987595i	$0.550189\pi$
$384$	1.14590	0.0584764
$385$	0.618034	0.0314979
$386$	23.2361	1.18268
$387$	−22.0000	−1.11832
$388$	−1.85410	−0.0941278
$389$	−24.9787	−1.26647	−0.633236	−	0.773959i	$-0.718274\pi$
$389$	−24.9787	−1.26647	−0.633236	+	0.773959i	$0.718274\pi$
$390$	−2.09017	−0.105840
$391$	−7.52786	−0.380700
$392$	3.00000	0.151523
$393$	−7.52786	−0.379731
$394$	20.9443	1.05516
$395$	−18.4164	−0.926630
$396$	−1.09017	−0.0547831
$397$	−27.8885	−1.39969	−0.699843	−	0.714297i	$-0.746747\pi$
$397$	−27.8885	−1.39969	−0.699843	+	0.714297i	$0.746747\pi$
$398$	5.85410	0.293440
$399$	−2.70820	−0.135580
$400$	2.38197	0.119098
$401$	−18.9443	−0.946032	−0.473016	−	0.881054i	$-0.656835\pi$
$401$	−18.9443	−0.946032	−0.473016	+	0.881054i	$0.656835\pi$
$402$	5.29180	0.263931
$403$	−21.8885	−1.09035
$404$	−4.47214	−0.222497
$405$	12.4721	0.619745
$406$	4.47214	0.221948
$407$	3.38197	0.167638
$408$	1.41641	0.0701226
$409$	10.6525	0.526731	0.263366	−	0.964696i	$-0.415167\pi$
$409$	10.6525	0.526731	0.263366	+	0.964696i	$0.415167\pi$
$410$	14.4721	0.714728
$411$	1.34752	0.0664685
$412$	−5.90983	−0.291156
$413$	8.38197	0.412450
$414$	−17.3820	−0.854277
$415$	21.4164	1.05129
$416$	−16.9098	−0.829073
$417$	5.88854	0.288363
$418$	2.70820	0.132463
$419$	−20.0000	−0.977064	−0.488532	−	0.872546i	$-0.662467\pi$
$419$	−20.0000	−0.977064	−0.488532	+	0.872546i	$0.662467\pi$
$420$	0.618034	0.0301570
$421$	26.7984	1.30607	0.653036	−	0.757327i	$-0.273495\pi$
$421$	26.7984	1.30607	0.653036	+	0.757327i	$0.273495\pi$
$422$	6.43769	0.313382
$423$	9.23607	0.449073
$424$	33.9787	1.65015
$425$	−2.94427	−0.142818
$426$	−2.47214	−0.119775
$427$	−0.291796	−0.0141210
$428$	−6.00000	−0.290021
$429$	−0.493422	−0.0238226
$430$	−12.4721	−0.601460
$431$	−19.0557	−0.917882	−0.458941	−	0.888467i	$-0.651771\pi$
$431$	−19.0557	−0.917882	−0.458941	+	0.888467i	$0.651771\pi$
$432$	2.23607	0.107583
$433$	26.3607	1.26681	0.633407	−	0.773819i	$-0.281656\pi$
$433$	26.3607	1.26681	0.633407	+	0.773819i	$0.281656\pi$
$434$	−6.47214	−0.310672
$435$	2.76393	0.132520
$436$	3.14590	0.150661
$437$	−43.1803	−2.06560
$438$	−1.85410	−0.0885924
$439$	−23.1246	−1.10368	−0.551839	−	0.833951i	$-0.686074\pi$
$439$	−23.1246	−1.10368	−0.551839	+	0.833951i	$0.686074\pi$
$440$	−1.85410	−0.0883908
$441$	−2.85410	−0.135910
$442$	−4.18034	−0.198838
$443$	10.7984	0.513046	0.256523	−	0.966538i	$-0.417423\pi$
$443$	10.7984	0.513046	0.256523	+	0.966538i	$0.417423\pi$
$444$	3.38197	0.160501
$445$	17.7082	0.839449
$446$	−20.5623	−0.973653
$447$	8.18034	0.386917
$448$	−7.00000	−0.330719
$449$	−20.6869	−0.976276	−0.488138	−	0.872766i	$-0.662324\pi$
$449$	−20.6869	−0.976276	−0.488138	+	0.872766i	$0.662324\pi$
$450$	−6.79837	−0.320478
$451$	3.41641	0.160872
$452$	16.6180	0.781647
$453$	−4.29180	−0.201646
$454$	−1.05573	−0.0495478
$455$	−5.47214	−0.256538
$456$	8.12461	0.380470
$457$	−39.6869	−1.85648	−0.928238	−	0.371987i	$-0.878677\pi$
$457$	−39.6869	−1.85648	−0.928238	+	0.371987i	$0.878677\pi$
$458$	0.180340	0.00842673
$459$	−2.76393	−0.129009
$460$	9.85410	0.459450
$461$	−21.5967	−1.00586	−0.502930	−	0.864327i	$-0.667745\pi$
$461$	−21.5967	−1.00586	−0.502930	+	0.864327i	$0.667745\pi$
$462$	−0.145898	−0.00678779
$463$	−8.00000	−0.371792	−0.185896	−	0.982569i	$-0.559519\pi$
$463$	−8.00000	−0.371792	−0.185896	+	0.982569i	$0.559519\pi$
$464$	−4.47214	−0.207614
$465$	−4.00000	−0.185496
$466$	24.1803	1.12013
$467$	8.03444	0.371790	0.185895	−	0.982570i	$-0.440482\pi$
$467$	8.03444	0.371790	0.185895	+	0.982570i	$0.440482\pi$
$468$	9.65248	0.446186
$469$	13.8541	0.639723
$470$	5.23607	0.241522
$471$	3.76393	0.173433
$472$	−25.1459	−1.15743
$473$	−2.94427	−0.135378
$474$	4.34752	0.199688
$475$	−16.8885	−0.774900
$476$	1.23607	0.0566551
$477$	−32.3262	−1.48012
$478$	29.2361	1.33723
$479$	24.6525	1.12640	0.563200	−	0.826320i	$-0.309570\pi$
$479$	24.6525	1.12640	0.563200	+	0.826320i	$0.309570\pi$
$480$	−3.09017	−0.141046
$481$	−29.9443	−1.36534
$482$	−12.6180	−0.574736
$483$	2.32624	0.105847
$484$	10.8541	0.493368
$485$	3.00000	0.136223
$486$	−9.65248	−0.437845
$487$	1.41641	0.0641836	0.0320918	−	0.999485i	$-0.489783\pi$
$487$	1.41641	0.0641836	0.0320918	+	0.999485i	$0.489783\pi$
$488$	0.875388	0.0396270
$489$	0.944272	0.0427015
$490$	−1.61803	−0.0730953
$491$	−20.7426	−0.936102	−0.468051	−	0.883701i	$-0.655044\pi$
$491$	−20.7426	−0.936102	−0.468051	+	0.883701i	$0.655044\pi$
$492$	3.41641	0.154024
$493$	5.52786	0.248962
$494$	−23.9787	−1.07885
$495$	1.76393	0.0792828
$496$	6.47214	0.290607
$497$	−6.47214	−0.290315
$498$	−5.05573	−0.226553
$499$	−13.8885	−0.621737	−0.310868	−	0.950453i	$-0.600620\pi$
$499$	−13.8885	−0.621737	−0.310868	+	0.950453i	$0.600620\pi$
$500$	11.9443	0.534164
$501$	−3.88854	−0.173727
$502$	−20.6525	−0.921765
$503$	−16.9098	−0.753972	−0.376986	−	0.926219i	$-0.623040\pi$
$503$	−16.9098	−0.753972	−0.376986	+	0.926219i	$0.623040\pi$
$504$	8.56231	0.381395
$505$	7.23607	0.322001
$506$	−2.32624	−0.103414
$507$	−0.596748	−0.0265025
$508$	4.00000	0.177471
$509$	26.1459	1.15890	0.579448	−	0.815009i	$-0.303268\pi$
$509$	26.1459	1.15890	0.579448	+	0.815009i	$0.303268\pi$
$510$	−0.763932	−0.0338275
$511$	−4.85410	−0.214733
$512$	11.0000	0.486136
$513$	−15.8541	−0.699976
$514$	−0.944272	−0.0416500
$515$	9.56231	0.421366
$516$	−2.94427	−0.129614
$517$	1.23607	0.0543622
$518$	−8.85410	−0.389027
$519$	−7.09017	−0.311224
$520$	16.4164	0.719907
$521$	16.0902	0.704923	0.352462	−	0.935826i	$-0.385345\pi$
$521$	16.0902	0.704923	0.352462	+	0.935826i	$0.385345\pi$
$522$	12.7639	0.558662
$523$	−11.7426	−0.513470	−0.256735	−	0.966482i	$-0.582647\pi$
$523$	−11.7426	−0.513470	−0.256735	+	0.966482i	$0.582647\pi$
$524$	19.7082	0.860957
$525$	0.909830	0.0397082
$526$	19.7426	0.860820
$527$	−8.00000	−0.348485
$528$	0.145898	0.00634940
$529$	14.0902	0.612616
$530$	−18.3262	−0.796041
$531$	23.9230	1.03817
$532$	7.09017	0.307398
$533$	−30.2492	−1.31024
$534$	−4.18034	−0.180901
$535$	9.70820	0.419722
$536$	−41.5623	−1.79522
$537$	−4.70820	−0.203174
$538$	−5.70820	−0.246098
$539$	−0.381966	−0.0164524
$540$	3.61803	0.155695
$541$	−28.5410	−1.22707	−0.613537	−	0.789666i	$-0.710254\pi$
$541$	−28.5410	−1.22707	−0.613537	+	0.789666i	$0.710254\pi$
$542$	−15.1246	−0.649658
$543$	5.70820	0.244962
$544$	−6.18034	−0.264980
$545$	−5.09017	−0.218039
$546$	1.29180	0.0552838
$547$	14.0689	0.601542	0.300771	−	0.953696i	$-0.402756\pi$
$547$	14.0689	0.601542	0.300771	+	0.953696i	$0.402756\pi$
$548$	−3.52786	−0.150703
$549$	−0.832816	−0.0355437
$550$	−0.909830	−0.0387953
$551$	31.7082	1.35081
$552$	−6.97871	−0.297034
$553$	11.3820	0.484010
$554$	14.4721	0.614862
$555$	−5.47214	−0.232279
$556$	−15.4164	−0.653801
$557$	33.1246	1.40353	0.701767	−	0.712406i	$-0.252395\pi$
$557$	33.1246	1.40353	0.701767	+	0.712406i	$0.252395\pi$
$558$	−18.4721	−0.781988
$559$	26.0689	1.10260
$560$	1.61803	0.0683744
$561$	−0.180340	−0.00761396
$562$	−8.27051	−0.348870
$563$	−28.0689	−1.18296	−0.591481	−	0.806319i	$-0.701457\pi$
$563$	−28.0689	−1.18296	−0.591481	+	0.806319i	$0.701457\pi$
$564$	1.23607	0.0520479
$565$	−26.8885	−1.13121
$566$	−16.3262	−0.686243
$567$	−7.70820	−0.323714
$568$	19.4164	0.814694
$569$	26.0000	1.08998	0.544988	−	0.838444i	$-0.316534\pi$
$569$	26.0000	1.08998	0.544988	+	0.838444i	$0.316534\pi$
$570$	−4.38197	−0.183540
$571$	−36.0689	−1.50944	−0.754718	−	0.656049i	$-0.772226\pi$
$571$	−36.0689	−1.50944	−0.754718	+	0.656049i	$0.772226\pi$
$572$	1.29180	0.0540127
$573$	−6.83282	−0.285445
$574$	−8.94427	−0.373327
$575$	14.5066	0.604966
$576$	−19.9787	−0.832446
$577$	−37.5623	−1.56374	−0.781870	−	0.623442i	$-0.785734\pi$
$577$	−37.5623	−1.56374	−0.781870	+	0.623442i	$0.785734\pi$
$578$	15.4721	0.643556
$579$	−8.87539	−0.368849
$580$	−7.23607	−0.300461
$581$	−13.2361	−0.549125
$582$	−0.708204	−0.0293560
$583$	−4.32624	−0.179174
$584$	14.5623	0.602593
$585$	−15.6180	−0.645726
$586$	7.52786	0.310973
$587$	4.00000	0.165098	0.0825488	−	0.996587i	$-0.473694\pi$
$587$	4.00000	0.165098	0.0825488	+	0.996587i	$0.473694\pi$
$588$	−0.381966	−0.0157520
$589$	−45.8885	−1.89080
$590$	13.5623	0.558351
$591$	−8.00000	−0.329076
$592$	8.85410	0.363901
$593$	37.7082	1.54849	0.774245	−	0.632886i	$-0.218130\pi$
$593$	37.7082	1.54849	0.774245	+	0.632886i	$0.218130\pi$
$594$	−0.854102	−0.0350442
$595$	−2.00000	−0.0819920
$596$	−21.4164	−0.877250
$597$	−2.23607	−0.0915162
$598$	20.5967	0.842264
$599$	−18.6525	−0.762120	−0.381060	−	0.924550i	$-0.624441\pi$
$599$	−18.6525	−0.762120	−0.381060	+	0.924550i	$0.624441\pi$
$600$	−2.72949	−0.111431
$601$	−32.6525	−1.33192	−0.665961	−	0.745986i	$-0.731978\pi$
$601$	−32.6525	−1.33192	−0.665961	+	0.745986i	$0.731978\pi$
$602$	7.70820	0.314163
$603$	39.5410	1.61023
$604$	11.2361	0.457189
$605$	−17.5623	−0.714009
$606$	−1.70820	−0.0693910
$607$	15.0557	0.611093	0.305547	−	0.952177i	$-0.401161\pi$
$607$	15.0557	0.611093	0.305547	+	0.952177i	$0.401161\pi$
$608$	−35.4508	−1.43772
$609$	−1.70820	−0.0692199
$610$	−0.472136	−0.0191162
$611$	−10.9443	−0.442758
$612$	3.52786	0.142605
$613$	−32.4508	−1.31068	−0.655339	−	0.755335i	$-0.727474\pi$
$613$	−32.4508	−1.31068	−0.655339	+	0.755335i	$0.727474\pi$
$614$	5.20163	0.209921
$615$	−5.52786	−0.222905
$616$	1.14590	0.0461695
$617$	34.3607	1.38331	0.691654	−	0.722229i	$-0.256882\pi$
$617$	34.3607	1.38331	0.691654	+	0.722229i	$0.256882\pi$
$618$	−2.25735	−0.0908041
$619$	−7.70820	−0.309819	−0.154909	−	0.987929i	$-0.549509\pi$
$619$	−7.70820	−0.309819	−0.154909	+	0.987929i	$0.549509\pi$
$620$	10.4721	0.420571
$621$	13.6180	0.546473
$622$	8.94427	0.358633
$623$	−10.9443	−0.438473
$624$	−1.29180	−0.0517132
$625$	−7.41641	−0.296656
$626$	0.180340	0.00720783
$627$	−1.03444	−0.0413116
$628$	−9.85410	−0.393221
$629$	−10.9443	−0.436377
$630$	−4.61803	−0.183987
$631$	4.74265	0.188802	0.0944009	−	0.995534i	$-0.469906\pi$
$631$	4.74265	0.188802	0.0944009	+	0.995534i	$0.469906\pi$
$632$	−34.1459	−1.35825
$633$	−2.45898	−0.0977357
$634$	−2.65248	−0.105343
$635$	−6.47214	−0.256839
$636$	−4.32624	−0.171546
$637$	3.38197	0.133998
$638$	1.70820	0.0676284
$639$	−18.4721	−0.730746
$640$	4.85410	0.191875
$641$	41.0132	1.61992	0.809961	−	0.586484i	$-0.199488\pi$
$641$	41.0132	1.61992	0.809961	+	0.586484i	$0.199488\pi$
$642$	−2.29180	−0.0904500
$643$	1.63932	0.0646485	0.0323242	−	0.999477i	$-0.489709\pi$
$643$	1.63932	0.0646485	0.0323242	+	0.999477i	$0.489709\pi$
$644$	−6.09017	−0.239986
$645$	4.76393	0.187580
$646$	−8.76393	−0.344812
$647$	9.70820	0.381669	0.190834	−	0.981622i	$-0.438881\pi$
$647$	9.70820	0.381669	0.190834	+	0.981622i	$0.438881\pi$
$648$	23.1246	0.908421
$649$	3.20163	0.125675
$650$	8.05573	0.315972
$651$	2.47214	0.0968906
$652$	−2.47214	−0.0968163
$653$	32.9443	1.28921	0.644604	−	0.764516i	$-0.277022\pi$
$653$	32.9443	1.28921	0.644604	+	0.764516i	$0.277022\pi$
$654$	1.20163	0.0469873
$655$	−31.8885	−1.24599
$656$	8.94427	0.349215
$657$	−13.8541	−0.540500
$658$	−3.23607	−0.126155
$659$	−20.0344	−0.780431	−0.390216	−	0.920724i	$-0.627600\pi$
$659$	−20.0344	−0.780431	−0.390216	+	0.920724i	$0.627600\pi$
$660$	0.236068	0.00918893
$661$	−12.7639	−0.496459	−0.248230	−	0.968701i	$-0.579849\pi$
$661$	−12.7639	−0.496459	−0.248230	+	0.968701i	$0.579849\pi$
$662$	13.5279	0.525775
$663$	1.59675	0.0620125
$664$	39.7082	1.54098
$665$	−11.4721	−0.444870
$666$	−25.2705	−0.979212
$667$	−27.2361	−1.05458
$668$	10.1803	0.393889
$669$	7.85410	0.303657
$670$	22.4164	0.866021
$671$	−0.111456	−0.00430272
$672$	1.90983	0.0736733
$673$	−5.49342	−0.211756	−0.105878	−	0.994379i	$-0.533765\pi$
$673$	−5.49342	−0.211756	−0.105878	+	0.994379i	$0.533765\pi$
$674$	−4.90983	−0.189120
$675$	5.32624	0.205007
$676$	1.56231	0.0600887
$677$	−28.8541	−1.10895	−0.554477	−	0.832199i	$-0.687082\pi$
$677$	−28.8541	−1.10895	−0.554477	+	0.832199i	$0.687082\pi$
$678$	6.34752	0.243775
$679$	−1.85410	−0.0711539
$680$	6.00000	0.230089
$681$	0.403252	0.0154527
$682$	−2.47214	−0.0946630
$683$	−20.4721	−0.783345	−0.391672	−	0.920105i	$-0.628103\pi$
$683$	−20.4721	−0.783345	−0.391672	+	0.920105i	$0.628103\pi$
$684$	20.2361	0.773745
$685$	5.70820	0.218099
$686$	1.00000	0.0381802
$687$	−0.0688837	−0.00262808
$688$	−7.70820	−0.293873
$689$	38.3050	1.45930
$690$	3.76393	0.143290
$691$	20.2918	0.771936	0.385968	−	0.922512i	$-0.373867\pi$
$691$	20.2918	0.771936	0.385968	+	0.922512i	$0.373867\pi$
$692$	18.5623	0.705633
$693$	−1.09017	−0.0414121
$694$	−23.4508	−0.890182
$695$	24.9443	0.946190
$696$	5.12461	0.194248
$697$	−11.0557	−0.418766
$698$	3.88854	0.147184
$699$	−9.23607	−0.349340
$700$	−2.38197	−0.0900299
$701$	37.8885	1.43103	0.715515	−	0.698597i	$-0.246192\pi$
$701$	37.8885	1.43103	0.715515	+	0.698597i	$0.246192\pi$
$702$	7.56231	0.285421
$703$	−62.7771	−2.36768
$704$	−2.67376	−0.100771
$705$	−2.00000	−0.0753244
$706$	0.291796	0.0109819
$707$	−4.47214	−0.168192
$708$	3.20163	0.120324
$709$	−18.0000	−0.676004	−0.338002	−	0.941145i	$-0.609751\pi$
$709$	−18.0000	−0.676004	−0.338002	+	0.941145i	$0.609751\pi$
$710$	−10.4721	−0.393012
$711$	32.4853	1.21829
$712$	32.8328	1.23046
$713$	39.4164	1.47616
$714$	0.472136	0.0176692
$715$	−2.09017	−0.0781679
$716$	12.3262	0.460653
$717$	−11.1672	−0.417046
$718$	−9.81966	−0.366466
$719$	34.3607	1.28144	0.640719	−	0.767776i	$-0.278637\pi$
$719$	34.3607	1.28144	0.640719	+	0.767776i	$0.278637\pi$
$720$	4.61803	0.172104
$721$	−5.90983	−0.220094
$722$	−31.2705	−1.16377
$723$	4.81966	0.179245
$724$	−14.9443	−0.555399
$725$	−10.6525	−0.395623
$726$	4.14590	0.153869
$727$	−36.5410	−1.35523	−0.677616	−	0.735416i	$-0.736987\pi$
$727$	−36.5410	−1.35523	−0.677616	+	0.735416i	$0.736987\pi$
$728$	−10.1459	−0.376032
$729$	−19.4377	−0.719915
$730$	−7.85410	−0.290693
$731$	9.52786	0.352401
$732$	−0.111456	−0.00411954
$733$	−40.3262	−1.48948	−0.744742	−	0.667353i	$-0.767427\pi$
$733$	−40.3262	−1.48948	−0.744742	+	0.667353i	$0.767427\pi$
$734$	30.0000	1.10732
$735$	0.618034	0.0227965
$736$	30.4508	1.12243
$737$	5.29180	0.194926
$738$	−25.5279	−0.939694
$739$	13.5279	0.497631	0.248815	−	0.968551i	$-0.419959\pi$
$739$	13.5279	0.497631	0.248815	+	0.968551i	$0.419959\pi$
$740$	14.3262	0.526643
$741$	9.15905	0.336466
$742$	11.3262	0.415799
$743$	−2.29180	−0.0840778	−0.0420389	−	0.999116i	$-0.513385\pi$
$743$	−2.29180	−0.0840778	−0.0420389	+	0.999116i	$0.513385\pi$
$744$	−7.41641	−0.271899
$745$	34.6525	1.26957
$746$	3.67376	0.134506
$747$	−37.7771	−1.38219
$748$	0.472136	0.0172630
$749$	−6.00000	−0.219235
$750$	4.56231	0.166592
$751$	−31.7082	−1.15705	−0.578524	−	0.815665i	$-0.696371\pi$
$751$	−31.7082	−1.15705	−0.578524	+	0.815665i	$0.696371\pi$
$752$	3.23607	0.118007
$753$	7.88854	0.287475
$754$	−15.1246	−0.550806
$755$	−18.1803	−0.661650
$756$	−2.23607	−0.0813250
$757$	−31.7082	−1.15245	−0.576227	−	0.817290i	$-0.695476\pi$
$757$	−31.7082	−1.15245	−0.576227	+	0.817290i	$0.695476\pi$
$758$	16.0344	0.582397
$759$	0.888544	0.0322521
$760$	34.4164	1.24841
$761$	8.67376	0.314424	0.157212	−	0.987565i	$-0.449749\pi$
$761$	8.67376	0.314424	0.157212	+	0.987565i	$0.449749\pi$
$762$	1.52786	0.0553487
$763$	3.14590	0.113889
$764$	17.8885	0.647185
$765$	−5.70820	−0.206381
$766$	6.14590	0.222060
$767$	−28.3475	−1.02357
$768$	−6.49342	−0.234311
$769$	48.3607	1.74393	0.871965	−	0.489568i	$-0.162845\pi$
$769$	48.3607	1.74393	0.871965	+	0.489568i	$0.162845\pi$
$770$	−0.618034	−0.0222724
$771$	0.360680	0.0129896
$772$	23.2361	0.836284
$773$	−33.8885	−1.21889	−0.609443	−	0.792830i	$-0.708607\pi$
$773$	−33.8885	−1.21889	−0.609443	+	0.792830i	$0.708607\pi$
$774$	22.0000	0.790774
$775$	15.4164	0.553774
$776$	5.56231	0.199675
$777$	3.38197	0.121327
$778$	24.9787	0.895530
$779$	−63.4164	−2.27213
$780$	−2.09017	−0.0748401
$781$	−2.47214	−0.0884600
$782$	7.52786	0.269196
$783$	−10.0000	−0.357371
$784$	−1.00000	−0.0357143
$785$	15.9443	0.569075
$786$	7.52786	0.268510
$787$	−14.2918	−0.509448	−0.254724	−	0.967014i	$-0.581985\pi$
$787$	−14.2918	−0.509448	−0.254724	+	0.967014i	$0.581985\pi$
$788$	20.9443	0.746109
$789$	−7.54102	−0.268467
$790$	18.4164	0.655226
$791$	16.6180	0.590869
$792$	3.27051	0.116213
$793$	0.986844	0.0350439
$794$	27.8885	0.989727
$795$	7.00000	0.248264
$796$	5.85410	0.207493
$797$	26.5836	0.941639	0.470820	−	0.882230i	$-0.343958\pi$
$797$	26.5836	0.941639	0.470820	+	0.882230i	$0.343958\pi$
$798$	2.70820	0.0958694
$799$	−4.00000	−0.141510
$800$	11.9098	0.421076
$801$	−31.2361	−1.10367
$802$	18.9443	0.668945
$803$	−1.85410	−0.0654298
$804$	5.29180	0.186627
$805$	9.85410	0.347311
$806$	21.8885	0.770991
$807$	2.18034	0.0767516
$808$	13.4164	0.471988
$809$	−11.8885	−0.417979	−0.208989	−	0.977918i	$-0.567017\pi$
$809$	−11.8885	−0.417979	−0.208989	+	0.977918i	$0.567017\pi$
$810$	−12.4721	−0.438226
$811$	42.8541	1.50481	0.752406	−	0.658700i	$-0.228893\pi$
$811$	42.8541	1.50481	0.752406	+	0.658700i	$0.228893\pi$
$812$	4.47214	0.156941
$813$	5.77709	0.202611
$814$	−3.38197	−0.118538
$815$	4.00000	0.140114
$816$	−0.472136	−0.0165281
$817$	54.6525	1.91205
$818$	−10.6525	−0.372455
$819$	9.65248	0.337285
$820$	14.4721	0.505389
$821$	35.3262	1.23289	0.616447	−	0.787396i	$-0.288571\pi$
$821$	35.3262	1.23289	0.616447	+	0.787396i	$0.288571\pi$
$822$	−1.34752	−0.0470003
$823$	−14.1115	−0.491894	−0.245947	−	0.969283i	$-0.579099\pi$
$823$	−14.1115	−0.491894	−0.245947	+	0.969283i	$0.579099\pi$
$824$	17.7295	0.617636
$825$	0.347524	0.0120992
$826$	−8.38197	−0.291646
$827$	−44.6869	−1.55392	−0.776958	−	0.629552i	$-0.783238\pi$
$827$	−44.6869	−1.55392	−0.776958	+	0.629552i	$0.783238\pi$
$828$	−17.3820	−0.604065
$829$	42.1459	1.46379	0.731894	−	0.681419i	$-0.238637\pi$
$829$	42.1459	1.46379	0.731894	+	0.681419i	$0.238637\pi$
$830$	−21.4164	−0.743374
$831$	−5.52786	−0.191759
$832$	23.6738	0.820740
$833$	1.23607	0.0428272
$834$	−5.88854	−0.203904
$835$	−16.4721	−0.570042
$836$	2.70820	0.0936652
$837$	14.4721	0.500230
$838$	20.0000	0.690889
$839$	−31.2361	−1.07839	−0.539194	−	0.842181i	$-0.681271\pi$
$839$	−31.2361	−1.07839	−0.539194	+	0.842181i	$0.681271\pi$
$840$	−1.85410	−0.0639726
$841$	−9.00000	−0.310345
$842$	−26.7984	−0.923533
$843$	3.15905	0.108804
$844$	6.43769	0.221595
$845$	−2.52786	−0.0869612
$846$	−9.23607	−0.317543
$847$	10.8541	0.372951
$848$	−11.3262	−0.388945
$849$	6.23607	0.214021
$850$	2.94427	0.100988
$851$	53.9230	1.84846
$852$	−2.47214	−0.0846940
$853$	18.1803	0.622483	0.311241	−	0.950331i	$-0.399255\pi$
$853$	18.1803	0.622483	0.311241	+	0.950331i	$0.399255\pi$
$854$	0.291796	0.00998506
$855$	−32.7426	−1.11977
$856$	18.0000	0.615227
$857$	16.4721	0.562677	0.281339	−	0.959609i	$-0.409222\pi$
$857$	16.4721	0.562677	0.281339	+	0.959609i	$0.409222\pi$
$858$	0.493422	0.0168452
$859$	−17.5279	−0.598043	−0.299022	−	0.954246i	$-0.596660\pi$
$859$	−17.5279	−0.598043	−0.299022	+	0.954246i	$0.596660\pi$
$860$	−12.4721	−0.425296
$861$	3.41641	0.116431
$862$	19.0557	0.649041
$863$	−1.00000	−0.0340404
$863$	−1.00000	−0.0340404
$864$	11.1803	0.380363
$865$	−30.0344	−1.02120
$866$	−26.3607	−0.895772
$867$	−5.90983	−0.200708
$868$	−6.47214	−0.219679
$869$	4.34752	0.147480
$870$	−2.76393	−0.0937061
$871$	−46.8541	−1.58759
$872$	−9.43769	−0.319601
$873$	−5.29180	−0.179100
$874$	43.1803	1.46060
$875$	11.9443	0.403790
$876$	−1.85410	−0.0626443
$877$	−5.05573	−0.170720	−0.0853599	−	0.996350i	$-0.527204\pi$
$877$	−5.05573	−0.170720	−0.0853599	+	0.996350i	$0.527204\pi$
$878$	23.1246	0.780418
$879$	−2.87539	−0.0969844
$880$	0.618034	0.0208339
$881$	15.2361	0.513316	0.256658	−	0.966502i	$-0.417379\pi$
$881$	15.2361	0.513316	0.256658	+	0.966502i	$0.417379\pi$
$882$	2.85410	0.0961026
$883$	−52.9443	−1.78172	−0.890858	−	0.454281i	$-0.849896\pi$
$883$	−52.9443	−1.78172	−0.890858	+	0.454281i	$0.849896\pi$
$884$	−4.18034	−0.140600
$885$	−5.18034	−0.174135
$886$	−10.7984	−0.362778
$887$	51.1935	1.71891	0.859455	−	0.511212i	$-0.170803\pi$
$887$	51.1935	1.71891	0.859455	+	0.511212i	$0.170803\pi$
$888$	−10.1459	−0.340474
$889$	4.00000	0.134156
$890$	−17.7082	−0.593580
$891$	−2.94427	−0.0986368
$892$	−20.5623	−0.688477
$893$	−22.9443	−0.767801
$894$	−8.18034	−0.273591
$895$	−19.9443	−0.666663
$896$	−3.00000	−0.100223
$897$	−7.86726	−0.262680
$898$	20.6869	0.690331
$899$	−28.9443	−0.965346
$900$	−6.79837	−0.226612
$901$	14.0000	0.466408
$902$	−3.41641	−0.113754
$903$	−2.94427	−0.0979792
$904$	−49.8541	−1.65812
$905$	24.1803	0.803782
$906$	4.29180	0.142585
$907$	35.7426	1.18682	0.593408	−	0.804902i	$-0.297782\pi$
$907$	35.7426	1.18682	0.593408	+	0.804902i	$0.297782\pi$
$908$	−1.05573	−0.0350356
$909$	−12.7639	−0.423353
$910$	5.47214	0.181400
$911$	38.8328	1.28659	0.643294	−	0.765619i	$-0.277567\pi$
$911$	38.8328	1.28659	0.643294	+	0.765619i	$0.277567\pi$
$912$	−2.70820	−0.0896776
$913$	−5.05573	−0.167320
$914$	39.6869	1.31273
$915$	0.180340	0.00596185
$916$	0.180340	0.00595860
$917$	19.7082	0.650822
$918$	2.76393	0.0912234
$919$	−27.3820	−0.903248	−0.451624	−	0.892208i	$-0.649155\pi$
$919$	−27.3820	−0.903248	−0.451624	+	0.892208i	$0.649155\pi$
$920$	−29.5623	−0.974640
$921$	−1.98684	−0.0654687
$922$	21.5967	0.711251
$923$	21.8885	0.720470
$924$	−0.145898	−0.00479969
$925$	21.0902	0.693441
$926$	8.00000	0.262896
$927$	−16.8673	−0.553993
$928$	−22.3607	−0.734025
$929$	48.4508	1.58962	0.794810	−	0.606858i	$-0.207570\pi$
$929$	48.4508	1.58962	0.794810	+	0.606858i	$0.207570\pi$
$930$	4.00000	0.131165
$931$	7.09017	0.232371
$932$	24.1803	0.792053
$933$	−3.41641	−0.111848
$934$	−8.03444	−0.262895
$935$	−0.763932	−0.0249832
$936$	−28.9574	−0.946503
$937$	−8.65248	−0.282664	−0.141332	−	0.989962i	$-0.545139\pi$
$937$	−8.65248	−0.282664	−0.141332	+	0.989962i	$0.545139\pi$
$938$	−13.8541	−0.452352
$939$	−0.0688837	−0.00224793
$940$	5.23607	0.170782
$941$	−6.94427	−0.226377	−0.113188	−	0.993574i	$-0.536106\pi$
$941$	−6.94427	−0.226377	−0.113188	+	0.993574i	$0.536106\pi$
$942$	−3.76393	−0.122636
$943$	54.4721	1.77386
$944$	8.38197	0.272810
$945$	3.61803	0.117695
$946$	2.94427	0.0957265
$947$	−3.97871	−0.129291	−0.0646454	−	0.997908i	$-0.520592\pi$
$947$	−3.97871	−0.129291	−0.0646454	+	0.997908i	$0.520592\pi$
$948$	4.34752	0.141201
$949$	16.4164	0.532899
$950$	16.8885	0.547937
$951$	1.01316	0.0328538
$952$	−3.70820	−0.120184
$953$	−17.8885	−0.579467	−0.289733	−	0.957107i	$-0.593567\pi$
$953$	−17.8885	−0.579467	−0.289733	+	0.957107i	$0.593567\pi$
$954$	32.3262	1.04660
$955$	−28.9443	−0.936615
$956$	29.2361	0.945562
$957$	−0.652476	−0.0210915
$958$	−24.6525	−0.796485
$959$	−3.52786	−0.113921
$960$	4.32624	0.139629
$961$	10.8885	0.351243
$962$	29.9443	0.965442
$963$	−17.1246	−0.551833
$964$	−12.6180	−0.406400
$965$	−37.5967	−1.21028
$966$	−2.32624	−0.0748455
$967$	60.9787	1.96094	0.980472	−	0.196661i	$-0.0630097\pi$
$967$	60.9787	1.96094	0.980472	+	0.196661i	$0.0630097\pi$
$968$	−32.5623	−1.04659
$969$	3.34752	0.107538
$970$	−3.00000	−0.0963242
$971$	−48.7214	−1.56354	−0.781771	−	0.623565i	$-0.785684\pi$
$971$	−48.7214	−1.56354	−0.781771	+	0.623565i	$0.785684\pi$
$972$	−9.65248	−0.309603
$973$	−15.4164	−0.494227
$974$	−1.41641	−0.0453846
$975$	−3.07701	−0.0985433
$976$	−0.291796	−0.00934016
$977$	25.4164	0.813143	0.406571	−	0.913619i	$-0.366724\pi$
$977$	25.4164	0.813143	0.406571	+	0.913619i	$0.366724\pi$
$978$	−0.944272	−0.0301945
$979$	−4.18034	−0.133604
$980$	−1.61803	−0.0516862
$981$	8.97871	0.286668
$982$	20.7426	0.661924
$983$	16.0000	0.510321	0.255160	−	0.966899i	$-0.417872\pi$
$983$	16.0000	0.510321	0.255160	+	0.966899i	$0.417872\pi$
$984$	−10.2492	−0.326733
$985$	−33.8885	−1.07978
$986$	−5.52786	−0.176043
$987$	1.23607	0.0393445
$988$	−23.9787	−0.762865
$989$	−46.9443	−1.49274
$990$	−1.76393	−0.0560614
$991$	32.0000	1.01651	0.508257	−	0.861206i	$-0.330290\pi$
$991$	32.0000	1.01651	0.508257	+	0.861206i	$0.330290\pi$
$992$	32.3607	1.02745
$993$	−5.16718	−0.163976
$994$	6.47214	0.205284
$995$	−9.47214	−0.300287
$996$	−5.05573	−0.160197
$997$	−16.9787	−0.537721	−0.268861	−	0.963179i	$-0.586647\pi$
$997$	−16.9787	−0.537721	−0.268861	+	0.963179i	$0.586647\pi$
$998$	13.8885	0.439634
$999$	19.7984	0.626393

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6041.2.a.b.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6041.2.a.b.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:	\( N \)	\(=\)	\( 6041 = 7 \cdot 863 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6041.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.381966 q^{3} -1.00000 q^{4} +1.61803 q^{5} -0.381966 q^{6} -1.00000 q^{7} +3.00000 q^{8} -2.85410 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.381966 q^{3} -1.00000 q^{4} +1.61803 q^{5} -0.381966 q^{6} -1.00000 q^{7} +3.00000 q^{8} -2.85410 q^{9} -1.61803 q^{10} -0.381966 q^{11} -0.381966 q^{12} +3.38197 q^{13} +1.00000 q^{14} +0.618034 q^{15} -1.00000 q^{16} +1.23607 q^{17} +2.85410 q^{18} +7.09017 q^{19} -1.61803 q^{20} -0.381966 q^{21} +0.381966 q^{22} -6.09017 q^{23} +1.14590 q^{24} -2.38197 q^{25} -3.38197 q^{26} -2.23607 q^{27} +1.00000 q^{28} +4.47214 q^{29} -0.618034 q^{30} -6.47214 q^{31} -5.00000 q^{32} -0.145898 q^{33} -1.23607 q^{34} -1.61803 q^{35} +2.85410 q^{36} -8.85410 q^{37} -7.09017 q^{38} +1.29180 q^{39} +4.85410 q^{40} -8.94427 q^{41} +0.381966 q^{42} +7.70820 q^{43} +0.381966 q^{44} -4.61803 q^{45} +6.09017 q^{46} -3.23607 q^{47} -0.381966 q^{48} +1.00000 q^{49} +2.38197 q^{50} +0.472136 q^{51} -3.38197 q^{52} +11.3262 q^{53} +2.23607 q^{54} -0.618034 q^{55} -3.00000 q^{56} +2.70820 q^{57} -4.47214 q^{58} -8.38197 q^{59} -0.618034 q^{60} +0.291796 q^{61} +6.47214 q^{62} +2.85410 q^{63} +7.00000 q^{64} +5.47214 q^{65} +0.145898 q^{66} -13.8541 q^{67} -1.23607 q^{68} -2.32624 q^{69} +1.61803 q^{70} +6.47214 q^{71} -8.56231 q^{72} +4.85410 q^{73} +8.85410 q^{74} -0.909830 q^{75} -7.09017 q^{76} +0.381966 q^{77} -1.29180 q^{78} -11.3820 q^{79} -1.61803 q^{80} +7.70820 q^{81} +8.94427 q^{82} +13.2361 q^{83} +0.381966 q^{84} +2.00000 q^{85} -7.70820 q^{86} +1.70820 q^{87} -1.14590 q^{88} +10.9443 q^{89} +4.61803 q^{90} -3.38197 q^{91} +6.09017 q^{92} -2.47214 q^{93} +3.23607 q^{94} +11.4721 q^{95} -1.90983 q^{96} +1.85410 q^{97} -1.00000 q^{98} +1.09017 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 3 q^{3} - 2 q^{4} + q^{5} - 3 q^{6} - 2 q^{7} + 6 q^{8} + q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 3 * q^3 - 2 * q^4 + q^5 - 3 * q^6 - 2 * q^7 + 6 * q^8 + q^9	\( 2 q - 2 q^{2} + 3 q^{3} - 2 q^{4} + q^{5} - 3 q^{6} - 2 q^{7} + 6 q^{8} + q^{9} - q^{10} - 3 q^{11} - 3 q^{12} + 9 q^{13} + 2 q^{14} - q^{15} - 2 q^{16} - 2 q^{17} - q^{18} + 3 q^{19} - q^{20} - 3 q^{21} + 3 q^{22} - q^{23} + 9 q^{24} - 7 q^{25} - 9 q^{26} + 2 q^{28} + q^{30} - 4 q^{31} - 10 q^{32} - 7 q^{33} + 2 q^{34} - q^{35} - q^{36} - 11 q^{37} - 3 q^{38} + 16 q^{39} + 3 q^{40} + 3 q^{42} + 2 q^{43} + 3 q^{44} - 7 q^{45} + q^{46} - 2 q^{47} - 3 q^{48} + 2 q^{49} + 7 q^{50} - 8 q^{51} - 9 q^{52} + 7 q^{53} + q^{55} - 6 q^{56} - 8 q^{57} - 19 q^{59} + q^{60} + 14 q^{61} + 4 q^{62} - q^{63} + 14 q^{64} + 2 q^{65} + 7 q^{66} - 21 q^{67} + 2 q^{68} + 11 q^{69} + q^{70} + 4 q^{71} + 3 q^{72} + 3 q^{73} + 11 q^{74} - 13 q^{75} - 3 q^{76} + 3 q^{77} - 16 q^{78} - 25 q^{79} - q^{80} + 2 q^{81} + 22 q^{83} + 3 q^{84} + 4 q^{85} - 2 q^{86} - 10 q^{87} - 9 q^{88} + 4 q^{89} + 7 q^{90} - 9 q^{91} + q^{92} + 4 q^{93} + 2 q^{94} + 14 q^{95} - 15 q^{96} - 3 q^{97} - 2 q^{98} - 9 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 3 * q^3 - 2 * q^4 + q^5 - 3 * q^6 - 2 * q^7 + 6 * q^8 + q^9 - q^10 - 3 * q^11 - 3 * q^12 + 9 * q^13 + 2 * q^14 - q^15 - 2 * q^16 - 2 * q^17 - q^18 + 3 * q^19 - q^20 - 3 * q^21 + 3 * q^22 - q^23 + 9 * q^24 - 7 * q^25 - 9 * q^26 + 2 * q^28 + q^30 - 4 * q^31 - 10 * q^32 - 7 * q^33 + 2 * q^34 - q^35 - q^36 - 11 * q^37 - 3 * q^38 + 16 * q^39 + 3 * q^40 + 3 * q^42 + 2 * q^43 + 3 * q^44 - 7 * q^45 + q^46 - 2 * q^47 - 3 * q^48 + 2 * q^49 + 7 * q^50 - 8 * q^51 - 9 * q^52 + 7 * q^53 + q^55 - 6 * q^56 - 8 * q^57 - 19 * q^59 + q^60 + 14 * q^61 + 4 * q^62 - q^63 + 14 * q^64 + 2 * q^65 + 7 * q^66 - 21 * q^67 + 2 * q^68 + 11 * q^69 + q^70 + 4 * q^71 + 3 * q^72 + 3 * q^73 + 11 * q^74 - 13 * q^75 - 3 * q^76 + 3 * q^77 - 16 * q^78 - 25 * q^79 - q^80 + 2 * q^81 + 22 * q^83 + 3 * q^84 + 4 * q^85 - 2 * q^86 - 10 * q^87 - 9 * q^88 + 4 * q^89 + 7 * q^90 - 9 * q^91 + q^92 + 4 * q^93 + 2 * q^94 + 14 * q^95 - 15 * q^96 - 3 * q^97 - 2 * q^98 - 9 * q^99

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