LMFDB - Embedded newform 5290.2.a.bb.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5290,2,Mod(1,5290)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5290, 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("5290.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5290 = 2 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5290.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:	$42.2408626693$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.4752.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 3x^{2} + 4x + 1 $ x^4 - 2x^3 - 3x^2 + 4*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.219687$ of defining polynomial
Character	$\chi$	$=$	5290.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.60020 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.60020 q^{6} +2.60020 q^{7} +1.00000 q^{8} -0.439374 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.60020 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.60020 q^{6} +2.60020 q^{7} +1.00000 q^{8} -0.439374 q^{9} +1.00000 q^{10} -0.439374 q^{11} +1.60020 q^{12} -1.20039 q^{13} +2.60020 q^{14} +1.60020 q^{15} +1.00000 q^{16} -2.33225 q^{17} -0.439374 q^{18} +2.97103 q^{19} +1.00000 q^{20} +4.16082 q^{21} -0.439374 q^{22} +1.60020 q^{24} +1.00000 q^{25} -1.20039 q^{26} -5.50367 q^{27} +2.60020 q^{28} +3.47894 q^{29} +1.60020 q^{30} -0.600196 q^{31} +1.00000 q^{32} -0.703084 q^{33} -2.33225 q^{34} +2.60020 q^{35} -0.439374 q^{36} +7.20039 q^{37} +2.97103 q^{38} -1.92086 q^{39} +1.00000 q^{40} +8.56797 q^{41} +4.16082 q^{42} +10.1971 q^{43} -0.439374 q^{44} -0.439374 q^{45} -0.960431 q^{47} +1.60020 q^{48} -0.238982 q^{49} +1.00000 q^{50} -3.73205 q^{51} -1.20039 q^{52} +8.60020 q^{53} -5.50367 q^{54} -0.439374 q^{55} +2.60020 q^{56} +4.75423 q^{57} +3.47894 q^{58} +0.824336 q^{59} +1.60020 q^{60} +4.26371 q^{61} -0.600196 q^{62} -1.14246 q^{63} +1.00000 q^{64} -1.20039 q^{65} -0.703084 q^{66} +11.2901 q^{67} -2.33225 q^{68} +2.60020 q^{70} +7.52840 q^{71} -0.439374 q^{72} -16.0716 q^{73} +7.20039 q^{74} +1.60020 q^{75} +2.97103 q^{76} -1.14246 q^{77} -1.92086 q^{78} +3.03957 q^{79} +1.00000 q^{80} -7.48883 q^{81} +8.56797 q^{82} +3.84342 q^{83} +4.16082 q^{84} -2.33225 q^{85} +10.1971 q^{86} +5.56699 q^{87} -0.439374 q^{88} +9.98261 q^{89} -0.439374 q^{90} -3.12125 q^{91} -0.960431 q^{93} -0.960431 q^{94} +2.97103 q^{95} +1.60020 q^{96} +6.92820 q^{97} -0.238982 q^{98} +0.193049 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 2 q^{3} + 4 q^{4} + 4 q^{5} + 2 q^{6} + 6 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 + 4 * q^5 + 2 * q^6 + 6 * q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} + 2 q^{3} + 4 q^{4} + 4 q^{5} + 2 q^{6} + 6 q^{7} + 4 q^{8} + 4 q^{9} + 4 q^{10} + 4 q^{11} + 2 q^{12} + 4 q^{13} + 6 q^{14} + 2 q^{15} + 4 q^{16} + 2 q^{17} + 4 q^{18} + 8 q^{19} + 4 q^{20} + 18 q^{21} + 4 q^{22} + 2 q^{24} + 4 q^{25} + 4 q^{26} + 2 q^{27} + 6 q^{28} - 2 q^{29} + 2 q^{30} + 2 q^{31} + 4 q^{32} + 8 q^{33} + 2 q^{34} + 6 q^{35} + 4 q^{36} + 20 q^{37} + 8 q^{38} - 28 q^{39} + 4 q^{40} - 8 q^{41} + 18 q^{42} - 2 q^{43} + 4 q^{44} + 4 q^{45} - 14 q^{47} + 2 q^{48} - 4 q^{49} + 4 q^{50} - 8 q^{51} + 4 q^{52} + 30 q^{53} + 2 q^{54} + 4 q^{55} + 6 q^{56} - 38 q^{57} - 2 q^{58} + 4 q^{59} + 2 q^{60} + 12 q^{61} + 2 q^{62} + 12 q^{63} + 4 q^{64} + 4 q^{65} + 8 q^{66} + 2 q^{67} + 2 q^{68} + 6 q^{70} - 2 q^{71} + 4 q^{72} + 2 q^{73} + 20 q^{74} + 2 q^{75} + 8 q^{76} + 12 q^{77} - 28 q^{78} + 2 q^{79} + 4 q^{80} - 8 q^{81} - 8 q^{82} + 26 q^{83} + 18 q^{84} + 2 q^{85} - 2 q^{86} + 2 q^{87} + 4 q^{88} + 4 q^{90} - 24 q^{91} - 14 q^{93} - 14 q^{94} + 8 q^{95} + 2 q^{96} - 4 q^{98} + 40 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 + 4 * q^5 + 2 * q^6 + 6 * q^7 + 4 * q^8 + 4 * q^9 + 4 * q^10 + 4 * q^11 + 2 * q^12 + 4 * q^13 + 6 * q^14 + 2 * q^15 + 4 * q^16 + 2 * q^17 + 4 * q^18 + 8 * q^19 + 4 * q^20 + 18 * q^21 + 4 * q^22 + 2 * q^24 + 4 * q^25 + 4 * q^26 + 2 * q^27 + 6 * q^28 - 2 * q^29 + 2 * q^30 + 2 * q^31 + 4 * q^32 + 8 * q^33 + 2 * q^34 + 6 * q^35 + 4 * q^36 + 20 * q^37 + 8 * q^38 - 28 * q^39 + 4 * q^40 - 8 * q^41 + 18 * q^42 - 2 * q^43 + 4 * q^44 + 4 * q^45 - 14 * q^47 + 2 * q^48 - 4 * q^49 + 4 * q^50 - 8 * q^51 + 4 * q^52 + 30 * q^53 + 2 * q^54 + 4 * q^55 + 6 * q^56 - 38 * q^57 - 2 * q^58 + 4 * q^59 + 2 * q^60 + 12 * q^61 + 2 * q^62 + 12 * q^63 + 4 * q^64 + 4 * q^65 + 8 * q^66 + 2 * q^67 + 2 * q^68 + 6 * q^70 - 2 * q^71 + 4 * q^72 + 2 * q^73 + 20 * q^74 + 2 * q^75 + 8 * q^76 + 12 * q^77 - 28 * q^78 + 2 * q^79 + 4 * q^80 - 8 * q^81 - 8 * q^82 + 26 * q^83 + 18 * q^84 + 2 * q^85 - 2 * q^86 + 2 * q^87 + 4 * q^88 + 4 * q^90 - 24 * q^91 - 14 * q^93 - 14 * q^94 + 8 * q^95 + 2 * q^96 - 4 * q^98 + 40 * 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
$2$	1.00000	0.707107
$3$	1.60020	0.923873	0.461937	−	0.886913i	$-0.347155\pi$
$3$	1.60020	0.923873	0.461937	+	0.886913i	$0.347155\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.60020	0.653277
$7$	2.60020	0.982782	0.491391	−	0.870939i	$-0.336489\pi$
$7$	2.60020	0.982782	0.491391	+	0.870939i	$0.336489\pi$
$8$	1.00000	0.353553
$9$	−0.439374	−0.146458
$10$	1.00000	0.316228
$11$	−0.439374	−0.132476	−0.0662381	−	0.997804i	$-0.521100\pi$
$11$	−0.439374	−0.132476	−0.0662381	+	0.997804i	$0.521100\pi$
$12$	1.60020	0.461937
$13$	−1.20039	−0.332929	−0.166464	−	0.986047i	$-0.553235\pi$
$13$	−1.20039	−0.332929	−0.166464	+	0.986047i	$0.553235\pi$
$14$	2.60020	0.694932
$15$	1.60020	0.413169
$16$	1.00000	0.250000
$17$	−2.33225	−0.565653	−0.282826	−	0.959171i	$-0.591272\pi$
$17$	−2.33225	−0.565653	−0.282826	+	0.959171i	$0.591272\pi$
$18$	−0.439374	−0.103561
$19$	2.97103	0.681602	0.340801	−	0.940136i	$-0.389302\pi$
$19$	2.97103	0.681602	0.340801	+	0.940136i	$0.389302\pi$
$20$	1.00000	0.223607
$21$	4.16082	0.907966
$22$	−0.439374	−0.0936748
$23$	0	0
$23$	0	0
$24$	1.60020	0.326639
$25$	1.00000	0.200000
$26$	−1.20039	−0.235416
$27$	−5.50367	−1.05918
$28$	2.60020	0.491391
$29$	3.47894	0.646024	0.323012	−	0.946395i	$-0.395305\pi$
$29$	3.47894	0.646024	0.323012	+	0.946395i	$0.395305\pi$
$30$	1.60020	0.292154
$31$	−0.600196	−0.107798	−0.0538992	−	0.998546i	$-0.517165\pi$
$31$	−0.600196	−0.107798	−0.0538992	+	0.998546i	$0.517165\pi$
$32$	1.00000	0.176777
$33$	−0.703084	−0.122391
$34$	−2.33225	−0.399977
$35$	2.60020	0.439513
$36$	−0.439374	−0.0732290
$37$	7.20039	1.18374	0.591869	−	0.806035i	$-0.298390\pi$
$37$	7.20039	1.18374	0.591869	+	0.806035i	$0.298390\pi$
$38$	2.97103	0.481965
$39$	−1.92086	−0.307584
$40$	1.00000	0.158114
$41$	8.56797	1.33809	0.669046	−	0.743221i	$-0.266703\pi$
$41$	8.56797	1.33809	0.669046	+	0.743221i	$0.266703\pi$
$42$	4.16082	0.642029
$43$	10.1971	1.55505	0.777524	−	0.628853i	$-0.216475\pi$
$43$	10.1971	1.55505	0.777524	+	0.628853i	$0.216475\pi$
$44$	−0.439374	−0.0662381
$45$	−0.439374	−0.0654980
$46$	0	0
$47$	−0.960431	−0.140093	−0.0700466	−	0.997544i	$-0.522315\pi$
$47$	−0.960431	−0.140093	−0.0700466	+	0.997544i	$0.522315\pi$
$48$	1.60020	0.230968
$49$	−0.238982	−0.0341403
$50$	1.00000	0.141421
$51$	−3.73205	−0.522592
$52$	−1.20039	−0.166464
$53$	8.60020	1.18133	0.590664	−	0.806918i	$-0.298866\pi$
$53$	8.60020	1.18133	0.590664	+	0.806918i	$0.298866\pi$
$54$	−5.50367	−0.748955
$55$	−0.439374	−0.0592451
$56$	2.60020	0.347466
$57$	4.75423	0.629714
$58$	3.47894	0.456808
$59$	0.824336	0.107319	0.0536597	−	0.998559i	$-0.482911\pi$
$59$	0.824336	0.107319	0.0536597	+	0.998559i	$0.482911\pi$
$60$	1.60020	0.206584
$61$	4.26371	0.545912	0.272956	−	0.962026i	$-0.411999\pi$
$61$	4.26371	0.545912	0.272956	+	0.962026i	$0.411999\pi$
$62$	−0.600196	−0.0762249
$63$	−1.14246	−0.143936
$64$	1.00000	0.125000
$65$	−1.20039	−0.148890
$66$	−0.703084	−0.0865437
$67$	11.2901	1.37931	0.689655	−	0.724138i	$-0.257762\pi$
$67$	11.2901	1.37931	0.689655	+	0.724138i	$0.257762\pi$
$68$	−2.33225	−0.282826
$69$	0	0
$70$	2.60020	0.310783
$71$	7.52840	0.893457	0.446728	−	0.894670i	$-0.352589\pi$
$71$	7.52840	0.893457	0.446728	+	0.894670i	$0.352589\pi$
$72$	−0.439374	−0.0517807
$73$	−16.0716	−1.88104	−0.940522	−	0.339734i	$-0.889663\pi$
$73$	−16.0716	−1.88104	−0.940522	+	0.339734i	$0.889663\pi$
$74$	7.20039	0.837028
$75$	1.60020	0.184775
$76$	2.97103	0.340801
$77$	−1.14246	−0.130195
$78$	−1.92086	−0.217495
$79$	3.03957	0.341978	0.170989	−	0.985273i	$-0.445304\pi$
$79$	3.03957	0.341978	0.170989	+	0.985273i	$0.445304\pi$
$80$	1.00000	0.111803
$81$	−7.48883	−0.832092
$82$	8.56797	0.946174
$83$	3.84342	0.421870	0.210935	−	0.977500i	$-0.432349\pi$
$83$	3.84342	0.421870	0.210935	+	0.977500i	$0.432349\pi$
$84$	4.16082	0.453983
$85$	−2.33225	−0.252968
$86$	10.1971	1.09958
$87$	5.56699	0.596844
$88$	−0.439374	−0.0468374
$89$	9.98261	1.05815	0.529077	−	0.848574i	$-0.322538\pi$
$89$	9.98261	1.05815	0.529077	+	0.848574i	$0.322538\pi$
$90$	−0.439374	−0.0463141
$91$	−3.12125	−0.327196
$92$	0	0
$93$	−0.960431	−0.0995920
$94$	−0.960431	−0.0990608
$95$	2.97103	0.304822
$96$	1.60020	0.163319
$97$	6.92820	0.703452	0.351726	−	0.936103i	$-0.385595\pi$
$97$	6.92820	0.703452	0.351726	+	0.936103i	$0.385595\pi$
$98$	−0.238982	−0.0241409
$99$	0.193049	0.0194022
$100$	1.00000	0.100000
$101$	−9.32899	−0.928269	−0.464134	−	0.885765i	$-0.653635\pi$
$101$	−9.32899	−0.928269	−0.464134	+	0.885765i	$0.653635\pi$
$102$	−3.73205	−0.369528
$103$	−19.0073	−1.87285	−0.936425	−	0.350869i	$-0.885886\pi$
$103$	−19.0073	−1.87285	−0.936425	+	0.350869i	$0.885886\pi$
$104$	−1.20039	−0.117708
$105$	4.16082	0.406055
$106$	8.60020	0.835325
$107$	−13.9935	−1.35280	−0.676400	−	0.736534i	$-0.736461\pi$
$107$	−13.9935	−1.35280	−0.676400	+	0.736534i	$0.736461\pi$
$108$	−5.50367	−0.529591
$109$	3.51753	0.336919	0.168459	−	0.985709i	$-0.446121\pi$
$109$	3.51753	0.336919	0.168459	+	0.985709i	$0.446121\pi$
$110$	−0.439374	−0.0418926
$111$	11.5220	1.09362
$112$	2.60020	0.245695
$113$	6.02799	0.567065	0.283533	−	0.958963i	$-0.408494\pi$
$113$	6.02799	0.567065	0.283533	+	0.958963i	$0.408494\pi$
$114$	4.75423	0.445275
$115$	0	0
$116$	3.47894	0.323012
$117$	0.527420	0.0487600
$118$	0.824336	0.0758863
$119$	−6.06430	−0.555913
$120$	1.60020	0.146077
$121$	−10.8070	−0.982450
$122$	4.26371	0.386018
$123$	13.7104	1.23623
$124$	−0.600196	−0.0538992
$125$	1.00000	0.0894427
$126$	−1.14246	−0.101778
$127$	−17.0890	−1.51641	−0.758203	−	0.652019i	$-0.773922\pi$
$127$	−17.0890	−1.51641	−0.758203	+	0.652019i	$0.773922\pi$
$128$	1.00000	0.0883883
$129$	16.3174	1.43667
$130$	−1.20039	−0.105281
$131$	9.25480	0.808596	0.404298	−	0.914627i	$-0.367516\pi$
$131$	9.25480	0.808596	0.404298	+	0.914627i	$0.367516\pi$
$132$	−0.703084	−0.0611956
$133$	7.72527	0.669866
$134$	11.2901	0.975319
$135$	−5.50367	−0.473681
$136$	−2.33225	−0.199988
$137$	−20.0126	−1.70979	−0.854894	−	0.518802i	$-0.826378\pi$
$137$	−20.0126	−1.70979	−0.854894	+	0.518802i	$0.826378\pi$
$138$	0	0
$139$	−15.7050	−1.33208	−0.666042	−	0.745914i	$-0.732013\pi$
$139$	−15.7050	−1.33208	−0.666042	+	0.745914i	$0.732013\pi$
$140$	2.60020	0.219757
$141$	−1.53688	−0.129428
$142$	7.52840	0.631769
$143$	0.527420	0.0441051
$144$	−0.439374	−0.0366145
$145$	3.47894	0.288911
$146$	−16.0716	−1.33010
$147$	−0.382419	−0.0315413
$148$	7.20039	0.591869
$149$	−3.65461	−0.299397	−0.149699	−	0.988732i	$-0.547830\pi$
$149$	−3.65461	−0.299397	−0.149699	+	0.988732i	$0.547830\pi$
$150$	1.60020	0.130655
$151$	8.79309	0.715571	0.357786	−	0.933804i	$-0.383532\pi$
$151$	8.79309	0.715571	0.357786	+	0.933804i	$0.383532\pi$
$152$	2.97103	0.240983
$153$	1.02473	0.0828443
$154$	−1.14246	−0.0920619
$155$	−0.600196	−0.0482089
$156$	−1.92086	−0.153792
$157$	−5.59270	−0.446346	−0.223173	−	0.974779i	$-0.571641\pi$
$157$	−5.59270	−0.446346	−0.223173	+	0.974779i	$0.571641\pi$
$158$	3.03957	0.241815
$159$	13.7620	1.09140
$160$	1.00000	0.0790569
$161$	0	0
$162$	−7.48883	−0.588378
$163$	11.2498	0.881156	0.440578	−	0.897714i	$-0.354774\pi$
$163$	11.2498	0.881156	0.440578	+	0.897714i	$0.354774\pi$
$164$	8.56797	0.669046
$165$	−0.703084	−0.0547350
$166$	3.84342	0.298307
$167$	−20.0257	−1.54964	−0.774818	−	0.632185i	$-0.782158\pi$
$167$	−20.0257	−1.54964	−0.774818	+	0.632185i	$0.782158\pi$
$168$	4.16082	0.321014
$169$	−11.5591	−0.889159
$170$	−2.33225	−0.178875
$171$	−1.30539	−0.0998260
$172$	10.1971	0.777524
$173$	−1.08903	−0.0827971	−0.0413985	−	0.999143i	$-0.513181\pi$
$173$	−1.08903	−0.0827971	−0.0413985	+	0.999143i	$0.513181\pi$
$174$	5.56699	0.422032
$175$	2.60020	0.196556
$176$	−0.439374	−0.0331190
$177$	1.31910	0.0991496
$178$	9.98261	0.748229
$179$	17.2746	1.29116	0.645581	−	0.763692i	$-0.276615\pi$
$179$	17.2746	1.29116	0.645581	+	0.763692i	$0.276615\pi$
$180$	−0.439374	−0.0327490
$181$	−26.4155	−1.96345	−0.981723	−	0.190315i	$-0.939049\pi$
$181$	−26.4155	−1.96345	−0.981723	+	0.190315i	$0.939049\pi$
$182$	−3.12125	−0.231363
$183$	6.82277	0.504354
$184$	0	0
$185$	7.20039	0.529383
$186$	−0.960431	−0.0704222
$187$	1.02473	0.0749355
$188$	−0.960431	−0.0700466
$189$	−14.3106	−1.04094
$190$	2.97103	0.215541
$191$	16.6323	1.20347	0.601734	−	0.798696i	$-0.294477\pi$
$191$	16.6323	1.20347	0.601734	+	0.798696i	$0.294477\pi$
$192$	1.60020	0.115484
$193$	−9.23996	−0.665107	−0.332553	−	0.943084i	$-0.607910\pi$
$193$	−9.23996	−0.665107	−0.332553	+	0.943084i	$0.607910\pi$
$194$	6.92820	0.497416
$195$	−1.92086	−0.137556
$196$	−0.238982	−0.0170702
$197$	7.52204	0.535923	0.267961	−	0.963430i	$-0.413650\pi$
$197$	7.52204	0.535923	0.267961	+	0.963430i	$0.413650\pi$
$198$	0.193049	0.0137194
$199$	2.23996	0.158787	0.0793933	−	0.996843i	$-0.474702\pi$
$199$	2.23996	0.158787	0.0793933	+	0.996843i	$0.474702\pi$
$200$	1.00000	0.0707107
$201$	18.0664	1.27431
$202$	−9.32899	−0.656385
$203$	9.04593	0.634900
$204$	−3.73205	−0.261296
$205$	8.56797	0.598413
$206$	−19.0073	−1.32430
$207$	0	0
$208$	−1.20039	−0.0832322
$209$	−1.30539	−0.0902960
$210$	4.16082	0.287124
$211$	10.8946	0.750013	0.375006	−	0.927022i	$-0.377640\pi$
$211$	10.8946	0.750013	0.375006	+	0.927022i	$0.377640\pi$
$212$	8.60020	0.590664
$213$	12.0469	0.825441
$214$	−13.9935	−0.956575
$215$	10.1971	0.695439
$216$	−5.50367	−0.374477
$217$	−1.56063	−0.105942
$218$	3.51753	0.238237
$219$	−25.7178	−1.73785
$220$	−0.439374	−0.0296226
$221$	2.79961	0.188322
$222$	11.5220	0.773308
$223$	−11.2414	−0.752778	−0.376389	−	0.926462i	$-0.622834\pi$
$223$	−11.2414	−0.752778	−0.376389	+	0.926462i	$0.622834\pi$
$224$	2.60020	0.173733
$225$	−0.439374	−0.0292916
$226$	6.02799	0.400976
$227$	−5.21099	−0.345866	−0.172933	−	0.984934i	$-0.555324\pi$
$227$	−5.21099	−0.345866	−0.172933	+	0.984934i	$0.555324\pi$
$228$	4.75423	0.314857
$229$	−10.4542	−0.690834	−0.345417	−	0.938449i	$-0.612263\pi$
$229$	−10.4542	−0.690834	−0.345417	+	0.938449i	$0.612263\pi$
$230$	0	0
$231$	−1.82816	−0.120284
$232$	3.47894	0.228404
$233$	9.44769	0.618939	0.309470	−	0.950909i	$-0.399849\pi$
$233$	9.44769	0.618939	0.309470	+	0.950909i	$0.399849\pi$
$234$	0.527420	0.0344786
$235$	−0.960431	−0.0626516
$236$	0.824336	0.0536597
$237$	4.86391	0.315945
$238$	−6.06430	−0.393090
$239$	−15.9355	−1.03078	−0.515392	−	0.856954i	$-0.672354\pi$
$239$	−15.9355	−1.03078	−0.515392	+	0.856954i	$0.672354\pi$
$240$	1.60020	0.103292
$241$	−25.4618	−1.64014	−0.820070	−	0.572263i	$-0.806066\pi$
$241$	−25.4618	−1.64014	−0.820070	+	0.572263i	$0.806066\pi$
$242$	−10.8070	−0.694697
$243$	4.52742	0.290434
$244$	4.26371	0.272956
$245$	−0.238982	−0.0152680
$246$	13.7104	0.874145
$247$	−3.56640	−0.226925
$248$	−0.600196	−0.0381125
$249$	6.15022	0.389754
$250$	1.00000	0.0632456
$251$	−12.0189	−0.758628	−0.379314	−	0.925268i	$-0.623840\pi$
$251$	−12.0189	−0.758628	−0.379314	+	0.925268i	$0.623840\pi$
$252$	−1.14246	−0.0719681
$253$	0	0
$254$	−17.0890	−1.07226
$255$	−3.73205	−0.233710
$256$	1.00000	0.0625000
$257$	−10.2350	−0.638442	−0.319221	−	0.947680i	$-0.603421\pi$
$257$	−10.2350	−0.638442	−0.319221	+	0.947680i	$0.603421\pi$
$258$	16.3174	1.01588
$259$	18.7224	1.16335
$260$	−1.20039	−0.0744451
$261$	−1.52856	−0.0946153
$262$	9.25480	0.571764
$263$	−5.51356	−0.339981	−0.169990	−	0.985446i	$-0.554374\pi$
$263$	−5.51356	−0.339981	−0.169990	+	0.985446i	$0.554374\pi$
$264$	−0.703084	−0.0432718
$265$	8.60020	0.528306
$266$	7.72527	0.473667
$267$	15.9741	0.977601
$268$	11.2901	0.689655
$269$	−29.2236	−1.78179	−0.890896	−	0.454208i	$-0.849922\pi$
$269$	−29.2236	−1.78179	−0.890896	+	0.454208i	$0.849922\pi$
$270$	−5.50367	−0.334943
$271$	−13.6204	−0.827382	−0.413691	−	0.910417i	$-0.635761\pi$
$271$	−13.6204	−0.827382	−0.413691	+	0.910417i	$0.635761\pi$
$272$	−2.33225	−0.141413
$273$	−4.99461	−0.302288
$274$	−20.0126	−1.20900
$275$	−0.439374	−0.0264952
$276$	0	0
$277$	−7.99550	−0.480403	−0.240201	−	0.970723i	$-0.577214\pi$
$277$	−7.99550	−0.480403	−0.240201	+	0.970723i	$0.577214\pi$
$278$	−15.7050	−0.941926
$279$	0.263710	0.0157879
$280$	2.60020	0.155391
$281$	−31.5993	−1.88506	−0.942529	−	0.334125i	$-0.891559\pi$
$281$	−31.5993	−1.88506	−0.942529	+	0.334125i	$0.891559\pi$
$282$	−1.53688	−0.0915197
$283$	−5.73841	−0.341113	−0.170557	−	0.985348i	$-0.554557\pi$
$283$	−5.73841	−0.341113	−0.170557	+	0.985348i	$0.554557\pi$
$284$	7.52840	0.446728
$285$	4.75423	0.281617
$286$	0.527420	0.0311870
$287$	22.2784	1.31505
$288$	−0.439374	−0.0258903
$289$	−11.5606	−0.680037
$290$	3.47894	0.204291
$291$	11.0865	0.649901
$292$	−16.0716	−0.940522
$293$	15.1425	0.884632	0.442316	−	0.896859i	$-0.354157\pi$
$293$	15.1425	0.884632	0.442316	+	0.896859i	$0.354157\pi$
$294$	−0.382419	−0.0223031
$295$	0.824336	0.0479947
$296$	7.20039	0.418514
$297$	2.41817	0.140316
$298$	−3.65461	−0.211706
$299$	0	0
$300$	1.60020	0.0923873
$301$	26.5145	1.52827
$302$	8.79309	0.505985
$303$	−14.9282	−0.857603
$304$	2.97103	0.170400
$305$	4.26371	0.244139
$306$	1.02473	0.0585798
$307$	27.1369	1.54879	0.774393	−	0.632705i	$-0.218055\pi$
$307$	27.1369	1.54879	0.774393	+	0.632705i	$0.218055\pi$
$308$	−1.14246	−0.0650976
$309$	−30.4155	−1.73028
$310$	−0.600196	−0.0340888
$311$	−17.5991	−0.997951	−0.498976	−	0.866616i	$-0.666290\pi$
$311$	−17.5991	−0.997951	−0.498976	+	0.866616i	$0.666290\pi$
$312$	−1.92086	−0.108747
$313$	−4.90021	−0.276977	−0.138488	−	0.990364i	$-0.544224\pi$
$313$	−4.90021	−0.276977	−0.138488	+	0.990364i	$0.544224\pi$
$314$	−5.59270	−0.315614
$315$	−1.14246	−0.0643702
$316$	3.03957	0.170989
$317$	26.3601	1.48053	0.740265	−	0.672316i	$-0.234700\pi$
$317$	26.3601	1.48053	0.740265	+	0.672316i	$0.234700\pi$
$318$	13.7620	0.771734
$319$	−1.52856	−0.0855827
$320$	1.00000	0.0559017
$321$	−22.3923	−1.24982
$322$	0	0
$323$	−6.92918	−0.385550
$324$	−7.48883	−0.416046
$325$	−1.20039	−0.0665857
$326$	11.2498	0.623071
$327$	5.62874	0.311270
$328$	8.56797	0.473087
$329$	−2.49731	−0.137681
$330$	−0.703084	−0.0387035
$331$	28.7213	1.57866	0.789332	−	0.613966i	$-0.210427\pi$
$331$	28.7213	1.57866	0.789332	+	0.613966i	$0.210427\pi$
$332$	3.84342	0.210935
$333$	−3.16366	−0.173368
$334$	−20.0257	−1.09576
$335$	11.2901	0.616846
$336$	4.16082	0.226991
$337$	−22.5206	−1.22678	−0.613389	−	0.789781i	$-0.710194\pi$
$337$	−22.5206	−1.22678	−0.613389	+	0.789781i	$0.710194\pi$
$338$	−11.5591	−0.628730
$339$	9.64596	0.523897
$340$	−2.33225	−0.126484
$341$	0.263710	0.0142807
$342$	−1.30539	−0.0705876
$343$	−18.8228	−1.01633
$344$	10.1971	0.549792
$345$	0	0
$346$	−1.08903	−0.0585464
$347$	23.3620	1.25414	0.627070	−	0.778963i	$-0.284254\pi$
$347$	23.3620	1.25414	0.627070	+	0.778963i	$0.284254\pi$
$348$	5.56699	0.298422
$349$	−17.2645	−0.924149	−0.462075	−	0.886841i	$-0.652895\pi$
$349$	−17.2645	−0.924149	−0.462075	+	0.886841i	$0.652895\pi$
$350$	2.60020	0.138986
$351$	6.60656	0.352632
$352$	−0.439374	−0.0234187
$353$	21.4457	1.14144	0.570721	−	0.821144i	$-0.306664\pi$
$353$	21.4457	1.14144	0.570721	+	0.821144i	$0.306664\pi$
$354$	1.31910	0.0701094
$355$	7.52840	0.399566
$356$	9.98261	0.529077
$357$	−9.70406	−0.513593
$358$	17.2746	0.912990
$359$	−12.9341	−0.682638	−0.341319	−	0.939948i	$-0.610874\pi$
$359$	−12.9341	−0.682638	−0.341319	+	0.939948i	$0.610874\pi$
$360$	−0.439374	−0.0231570
$361$	−10.1730	−0.535419
$362$	−26.4155	−1.38837
$363$	−17.2932	−0.907659
$364$	−3.12125	−0.163598
$365$	−16.0716	−0.841228
$366$	6.82277	0.356632
$367$	8.78672	0.458663	0.229332	−	0.973348i	$-0.426346\pi$
$367$	8.78672	0.458663	0.229332	+	0.973348i	$0.426346\pi$
$368$	0	0
$369$	−3.76454	−0.195974
$370$	7.20039	0.374331
$371$	22.3622	1.16099
$372$	−0.960431	−0.0497960
$373$	33.7856	1.74935	0.874676	−	0.484709i	$-0.161074\pi$
$373$	33.7856	1.74935	0.874676	+	0.484709i	$0.161074\pi$
$374$	1.02473	0.0529874
$375$	1.60020	0.0826338
$376$	−0.960431	−0.0495304
$377$	−4.17609	−0.215080
$378$	−14.3106	−0.736059
$379$	−8.61080	−0.442307	−0.221153	−	0.975239i	$-0.570982\pi$
$379$	−8.61080	−0.442307	−0.221153	+	0.975239i	$0.570982\pi$
$380$	2.97103	0.152411
$381$	−27.3458	−1.40097
$382$	16.6323	0.850981
$383$	15.9143	0.813185	0.406592	−	0.913610i	$-0.366717\pi$
$383$	15.9143	0.813185	0.406592	+	0.913610i	$0.366717\pi$
$384$	1.60020	0.0816596
$385$	−1.14246	−0.0582250
$386$	−9.23996	−0.470302
$387$	−4.48035	−0.227749
$388$	6.92820	0.351726
$389$	1.49183	0.0756387	0.0378193	−	0.999285i	$-0.487959\pi$
$389$	1.49183	0.0756387	0.0378193	+	0.999285i	$0.487959\pi$
$390$	−1.92086	−0.0972666
$391$	0	0
$392$	−0.238982	−0.0120704
$393$	14.8095	0.747040
$394$	7.52204	0.378955
$395$	3.03957	0.152937
$396$	0.193049	0.00970109
$397$	−18.0766	−0.907238	−0.453619	−	0.891196i	$-0.649867\pi$
$397$	−18.0766	−0.907238	−0.453619	+	0.891196i	$0.649867\pi$
$398$	2.23996	0.112279
$399$	12.3619	0.618871
$400$	1.00000	0.0500000
$401$	22.5920	1.12819	0.564095	−	0.825710i	$-0.309225\pi$
$401$	22.5920	1.12819	0.564095	+	0.825710i	$0.309225\pi$
$402$	18.0664	0.901071
$403$	0.720470	0.0358892
$404$	−9.32899	−0.464134
$405$	−7.48883	−0.372123
$406$	9.04593	0.448942
$407$	−3.16366	−0.156817
$408$	−3.73205	−0.184764
$409$	16.3973	0.810792	0.405396	−	0.914141i	$-0.367134\pi$
$409$	16.3973	0.810792	0.405396	+	0.914141i	$0.367134\pi$
$410$	8.56797	0.423142
$411$	−32.0240	−1.57963
$412$	−19.0073	−0.936425
$413$	2.14344	0.105472
$414$	0	0
$415$	3.84342	0.188666
$416$	−1.20039	−0.0588540
$417$	−25.1311	−1.23068
$418$	−1.30539	−0.0638489
$419$	−30.9768	−1.51332	−0.756658	−	0.653811i	$-0.773169\pi$
$419$	−30.9768	−1.51332	−0.756658	+	0.653811i	$0.773169\pi$
$420$	4.16082	0.203027
$421$	0.737698	0.0359532	0.0179766	−	0.999838i	$-0.494278\pi$
$421$	0.737698	0.0359532	0.0179766	+	0.999838i	$0.494278\pi$
$422$	10.8946	0.530339
$423$	0.421988	0.0205178
$424$	8.60020	0.417662
$425$	−2.33225	−0.113131
$426$	12.0469	0.583675
$427$	11.0865	0.536512
$428$	−13.9935	−0.676400
$429$	0.843976	0.0407475
$430$	10.1971	0.491749
$431$	19.3502	0.932066	0.466033	−	0.884767i	$-0.345683\pi$
$431$	19.3502	0.932066	0.466033	+	0.884767i	$0.345683\pi$
$432$	−5.50367	−0.264795
$433$	15.0954	0.725438	0.362719	−	0.931899i	$-0.381848\pi$
$433$	15.0954	0.725438	0.362719	+	0.931899i	$0.381848\pi$
$434$	−1.56063	−0.0749125
$435$	5.56699	0.266917
$436$	3.51753	0.168459
$437$	0	0
$438$	−25.7178	−1.22884
$439$	22.3987	1.06903	0.534515	−	0.845159i	$-0.320494\pi$
$439$	22.3987	1.06903	0.534515	+	0.845159i	$0.320494\pi$
$440$	−0.439374	−0.0209463
$441$	0.105003	0.00500012
$442$	2.79961	0.133164
$443$	0.993636	0.0472091	0.0236045	−	0.999721i	$-0.492486\pi$
$443$	0.993636	0.0472091	0.0236045	+	0.999721i	$0.492486\pi$
$444$	11.5220	0.546812
$445$	9.98261	0.473221
$446$	−11.2414	−0.532294
$447$	−5.84809	−0.276605
$448$	2.60020	0.122848
$449$	39.5737	1.86760	0.933800	−	0.357795i	$-0.116471\pi$
$449$	39.5737	1.86760	0.933800	+	0.357795i	$0.116471\pi$
$450$	−0.439374	−0.0207123
$451$	−3.76454	−0.177265
$452$	6.02799	0.283533
$453$	14.0707	0.661097
$454$	−5.21099	−0.244564
$455$	−3.12125	−0.146327
$456$	4.75423	0.222637
$457$	3.44290	0.161052	0.0805260	−	0.996753i	$-0.474340\pi$
$457$	3.44290	0.161052	0.0805260	+	0.996753i	$0.474340\pi$
$458$	−10.4542	−0.488493
$459$	12.8359	0.599129
$460$	0	0
$461$	8.61308	0.401151	0.200576	−	0.979678i	$-0.435719\pi$
$461$	8.61308	0.401151	0.200576	+	0.979678i	$0.435719\pi$
$462$	−1.82816	−0.0850535
$463$	0.934724	0.0434403	0.0217202	−	0.999764i	$-0.493086\pi$
$463$	0.934724	0.0434403	0.0217202	+	0.999764i	$0.493086\pi$
$464$	3.47894	0.161506
$465$	−0.960431	−0.0445389
$466$	9.44769	0.437656
$467$	−10.2340	−0.473574	−0.236787	−	0.971562i	$-0.576094\pi$
$467$	−10.2340	−0.473574	−0.236787	+	0.971562i	$0.576094\pi$
$468$	0.527420	0.0243800
$469$	29.3566	1.35556
$470$	−0.960431	−0.0443014
$471$	−8.94941	−0.412367
$472$	0.824336	0.0379432
$473$	−4.48035	−0.206007
$474$	4.86391	0.223407
$475$	2.97103	0.136320
$476$	−6.06430	−0.277957
$477$	−3.77870	−0.173015
$478$	−15.9355	−0.728875
$479$	−9.83918	−0.449564	−0.224782	−	0.974409i	$-0.572167\pi$
$479$	−9.83918	−0.449564	−0.224782	+	0.974409i	$0.572167\pi$
$480$	1.60020	0.0730386
$481$	−8.64329	−0.394100
$482$	−25.4618	−1.15975
$483$	0	0
$484$	−10.8070	−0.491225
$485$	6.92820	0.314594
$486$	4.52742	0.205368
$487$	0.537855	0.0243726	0.0121863	−	0.999926i	$-0.496121\pi$
$487$	0.537855	0.0243726	0.0121863	+	0.999926i	$0.496121\pi$
$488$	4.26371	0.193009
$489$	18.0020	0.814077
$490$	−0.238982	−0.0107961
$491$	13.9464	0.629393	0.314696	−	0.949192i	$-0.398097\pi$
$491$	13.9464	0.629393	0.314696	+	0.949192i	$0.398097\pi$
$492$	13.7104	0.618114
$493$	−8.11375	−0.365425
$494$	−3.56640	−0.160460
$495$	0.193049	0.00867692
$496$	−0.600196	−0.0269496
$497$	19.5753	0.878073
$498$	6.15022	0.275598
$499$	−40.6847	−1.82130	−0.910648	−	0.413184i	$-0.864417\pi$
$499$	−40.6847	−1.82130	−0.910648	+	0.413184i	$0.864417\pi$
$500$	1.00000	0.0447214
$501$	−32.0450	−1.43167
$502$	−12.0189	−0.536431
$503$	16.8425	0.750972	0.375486	−	0.926828i	$-0.377476\pi$
$503$	16.8425	0.750972	0.375486	+	0.926828i	$0.377476\pi$
$504$	−1.14246	−0.0508891
$505$	−9.32899	−0.415134
$506$	0	0
$507$	−18.4968	−0.821470
$508$	−17.0890	−0.758203
$509$	−15.9871	−0.708616	−0.354308	−	0.935129i	$-0.615284\pi$
$509$	−15.9871	−0.708616	−0.354308	+	0.935129i	$0.615284\pi$
$510$	−3.73205	−0.165258
$511$	−41.7894	−1.84865
$512$	1.00000	0.0441942
$513$	−16.3516	−0.721940
$514$	−10.2350	−0.451447
$515$	−19.0073	−0.837564
$516$	16.3174	0.718334
$517$	0.421988	0.0185590
$518$	18.7224	0.822616
$519$	−1.74265	−0.0764940
$520$	−1.20039	−0.0526406
$521$	9.87575	0.432664	0.216332	−	0.976320i	$-0.430591\pi$
$521$	9.87575	0.432664	0.216332	+	0.976320i	$0.430591\pi$
$522$	−1.52856	−0.0669031
$523$	−15.0356	−0.657461	−0.328730	−	0.944424i	$-0.606621\pi$
$523$	−15.0356	−0.657461	−0.328730	+	0.944424i	$0.606621\pi$
$524$	9.25480	0.404298
$525$	4.16082	0.181593
$526$	−5.51356	−0.240403
$527$	1.39980	0.0609764
$528$	−0.703084	−0.0305978
$529$	0	0
$530$	8.60020	0.373569
$531$	−0.362192	−0.0157178
$532$	7.72527	0.334933
$533$	−10.2849	−0.445489
$534$	15.9741	0.691268
$535$	−13.9935	−0.604991
$536$	11.2901	0.487659
$537$	27.6427	1.19287
$538$	−29.2236	−1.25992
$539$	0.105003	0.00452278
$540$	−5.50367	−0.236840
$541$	12.4269	0.534275	0.267137	−	0.963658i	$-0.413922\pi$
$541$	12.4269	0.534275	0.267137	+	0.963658i	$0.413922\pi$
$542$	−13.6204	−0.585047
$543$	−42.2699	−1.81398
$544$	−2.33225	−0.0999942
$545$	3.51753	0.150675
$546$	−4.99461	−0.213750
$547$	−33.2966	−1.42366	−0.711830	−	0.702352i	$-0.752133\pi$
$547$	−33.2966	−1.42366	−0.711830	+	0.702352i	$0.752133\pi$
$548$	−20.0126	−0.854894
$549$	−1.87336	−0.0799532
$550$	−0.439374	−0.0187350
$551$	10.3361	0.440331
$552$	0	0
$553$	7.90348	0.336090
$554$	−7.99550	−0.339696
$555$	11.5220	0.489083
$556$	−15.7050	−0.666042
$557$	27.4659	1.16377	0.581884	−	0.813272i	$-0.302316\pi$
$557$	27.4659	1.16377	0.581884	+	0.813272i	$0.302316\pi$
$558$	0.263710	0.0111637
$559$	−12.2405	−0.517720
$560$	2.60020	0.109878
$561$	1.63977	0.0692309
$562$	−31.5993	−1.33294
$563$	−19.6721	−0.829080	−0.414540	−	0.910031i	$-0.636058\pi$
$563$	−19.6721	−0.829080	−0.414540	+	0.910031i	$0.636058\pi$
$564$	−1.53688	−0.0647142
$565$	6.02799	0.253599
$566$	−5.73841	−0.241204
$567$	−19.4724	−0.817765
$568$	7.52840	0.315885
$569$	17.8150	0.746844	0.373422	−	0.927662i	$-0.378184\pi$
$569$	17.8150	0.746844	0.373422	+	0.927662i	$0.378184\pi$
$570$	4.75423	0.199133
$571$	19.7853	0.827990	0.413995	−	0.910279i	$-0.364133\pi$
$571$	19.7853	0.827990	0.413995	+	0.910279i	$0.364133\pi$
$572$	0.527420	0.0220526
$573$	26.6149	1.11185
$574$	22.2784	0.929882
$575$	0	0
$576$	−0.439374	−0.0183072
$577$	−12.3098	−0.512464	−0.256232	−	0.966615i	$-0.582481\pi$
$577$	−12.3098	−0.512464	−0.256232	+	0.966615i	$0.582481\pi$
$578$	−11.5606	−0.480859
$579$	−14.7857	−0.614475
$580$	3.47894	0.144455
$581$	9.99364	0.414606
$582$	11.0865	0.459549
$583$	−3.77870	−0.156498
$584$	−16.0716	−0.665049
$585$	0.527420	0.0218062
$586$	15.1425	0.625529
$587$	−9.96891	−0.411461	−0.205730	−	0.978609i	$-0.565957\pi$
$587$	−9.96891	−0.411461	−0.205730	+	0.978609i	$0.565957\pi$
$588$	−0.382419	−0.0157707
$589$	−1.78320	−0.0734755
$590$	0.824336	0.0339374
$591$	12.0367	0.495125
$592$	7.20039	0.295934
$593$	43.9968	1.80673	0.903367	−	0.428869i	$-0.141088\pi$
$593$	43.9968	1.80673	0.903367	+	0.428869i	$0.141088\pi$
$594$	2.41817	0.0992187
$595$	−6.06430	−0.248612
$596$	−3.65461	−0.149699
$597$	3.58438	0.146699
$598$	0	0
$599$	−21.6584	−0.884939	−0.442470	−	0.896783i	$-0.645898\pi$
$599$	−21.6584	−0.884939	−0.442470	+	0.896783i	$0.645898\pi$
$600$	1.60020	0.0653277
$601$	29.0776	1.18610	0.593049	−	0.805166i	$-0.297924\pi$
$601$	29.0776	1.18610	0.593049	+	0.805166i	$0.297924\pi$
$602$	26.5145	1.08065
$603$	−4.96059	−0.202011
$604$	8.79309	0.357786
$605$	−10.8070	−0.439365
$606$	−14.9282	−0.606417
$607$	15.2091	0.617320	0.308660	−	0.951172i	$-0.400119\pi$
$607$	15.2091	0.617320	0.308660	+	0.951172i	$0.400119\pi$
$608$	2.97103	0.120491
$609$	14.4753	0.586567
$610$	4.26371	0.172633
$611$	1.15289	0.0466410
$612$	1.02473	0.0414222
$613$	−8.38398	−0.338626	−0.169313	−	0.985562i	$-0.554155\pi$
$613$	−8.38398	−0.338626	−0.169313	+	0.985562i	$0.554155\pi$
$614$	27.1369	1.09516
$615$	13.7104	0.552858
$616$	−1.14246	−0.0460309
$617$	−37.0585	−1.49192	−0.745959	−	0.665991i	$-0.768009\pi$
$617$	−37.0585	−1.49192	−0.745959	+	0.665991i	$0.768009\pi$
$618$	−30.4155	−1.22349
$619$	−17.4815	−0.702640	−0.351320	−	0.936255i	$-0.614267\pi$
$619$	−17.4815	−0.702640	−0.351320	+	0.936255i	$0.614267\pi$
$620$	−0.600196	−0.0241044
$621$	0	0
$622$	−17.5991	−0.705658
$623$	25.9568	1.03994
$624$	−1.92086	−0.0768960
$625$	1.00000	0.0400000
$626$	−4.90021	−0.195852
$627$	−2.08889	−0.0834221
$628$	−5.59270	−0.223173
$629$	−16.7931	−0.669584
$630$	−1.14246	−0.0455166
$631$	46.7247	1.86008	0.930040	−	0.367459i	$-0.119772\pi$
$631$	46.7247	1.86008	0.930040	+	0.367459i	$0.119772\pi$
$632$	3.03957	0.120908
$633$	17.4334	0.692917
$634$	26.3601	1.04689
$635$	−17.0890	−0.678157
$636$	13.7620	0.545699
$637$	0.286872	0.0113663
$638$	−1.52856	−0.0605161
$639$	−3.30778	−0.130854
$640$	1.00000	0.0395285
$641$	11.1552	0.440603	0.220301	−	0.975432i	$-0.429296\pi$
$641$	11.1552	0.440603	0.220301	+	0.975432i	$0.429296\pi$
$642$	−22.3923	−0.883754
$643$	20.2487	0.798531	0.399266	−	0.916835i	$-0.369265\pi$
$643$	20.2487	0.798531	0.399266	+	0.916835i	$0.369265\pi$
$644$	0	0
$645$	16.3174	0.642497
$646$	−6.92918	−0.272625
$647$	−38.6297	−1.51869	−0.759346	−	0.650688i	$-0.774481\pi$
$647$	−38.6297	−1.51869	−0.759346	+	0.650688i	$0.774481\pi$
$648$	−7.48883	−0.294189
$649$	−0.362192	−0.0142173
$650$	−1.20039	−0.0470832
$651$	−2.49731	−0.0978772
$652$	11.2498	0.440578
$653$	−27.0805	−1.05974	−0.529872	−	0.848078i	$-0.677760\pi$
$653$	−27.0805	−1.05974	−0.529872	+	0.848078i	$0.677760\pi$
$654$	5.62874	0.220101
$655$	9.25480	0.361615
$656$	8.56797	0.334523
$657$	7.06146	0.275494
$658$	−2.49731	−0.0973552
$659$	3.29268	0.128264	0.0641322	−	0.997941i	$-0.479572\pi$
$659$	3.29268	0.128264	0.0641322	+	0.997941i	$0.479572\pi$
$660$	−0.703084	−0.0273675
$661$	2.18907	0.0851451	0.0425725	−	0.999093i	$-0.486445\pi$
$661$	2.18907	0.0851451	0.0425725	+	0.999093i	$0.486445\pi$
$662$	28.7213	1.11628
$663$	4.47992	0.173986
$664$	3.84342	0.149154
$665$	7.72527	0.299573
$666$	−3.16366	−0.122589
$667$	0	0
$668$	−20.0257	−0.774818
$669$	−17.9884	−0.695471
$670$	11.2901	0.436176
$671$	−1.87336	−0.0723204
$672$	4.16082	0.160507
$673$	−35.4026	−1.36467	−0.682335	−	0.731040i	$-0.739035\pi$
$673$	−35.4026	−1.36467	−0.682335	+	0.731040i	$0.739035\pi$
$674$	−22.5206	−0.867463
$675$	−5.50367	−0.211836
$676$	−11.5591	−0.444579
$677$	28.2998	1.08765	0.543824	−	0.839199i	$-0.316976\pi$
$677$	28.2998	1.08765	0.543824	+	0.839199i	$0.316976\pi$
$678$	9.64596	0.370451
$679$	18.0147	0.691340
$680$	−2.33225	−0.0894376
$681$	−8.33861	−0.319536
$682$	0.263710	0.0100980
$683$	10.8520	0.415240	0.207620	−	0.978210i	$-0.433428\pi$
$683$	10.8520	0.415240	0.207620	+	0.978210i	$0.433428\pi$
$684$	−1.30539	−0.0499130
$685$	−20.0126	−0.764641
$686$	−18.8228	−0.718657
$687$	−16.7288	−0.638243
$688$	10.1971	0.388762
$689$	−10.3236	−0.393298
$690$	0	0
$691$	46.0830	1.75308	0.876539	−	0.481331i	$-0.159846\pi$
$691$	46.0830	1.75308	0.876539	+	0.481331i	$0.159846\pi$
$692$	−1.08903	−0.0413985
$693$	0.501966	0.0190681
$694$	23.3620	0.886811
$695$	−15.7050	−0.595726
$696$	5.56699	0.211016
$697$	−19.9826	−0.756895
$698$	−17.2645	−0.653472
$699$	15.1182	0.571821
$700$	2.60020	0.0982782
$701$	14.5121	0.548116	0.274058	−	0.961713i	$-0.411634\pi$
$701$	14.5121	0.548116	0.274058	+	0.961713i	$0.411634\pi$
$702$	6.60656	0.249349
$703$	21.3926	0.806837
$704$	−0.439374	−0.0165595
$705$	−1.53688	−0.0578821
$706$	21.4457	0.807121
$707$	−24.2572	−0.912285
$708$	1.31910	0.0495748
$709$	3.73375	0.140224	0.0701119	−	0.997539i	$-0.477664\pi$
$709$	3.73375	0.140224	0.0701119	+	0.997539i	$0.477664\pi$
$710$	7.52840	0.282536
$711$	−1.33551	−0.0500854
$712$	9.98261	0.374114
$713$	0	0
$714$	−9.70406	−0.363165
$715$	0.527420	0.0197244
$716$	17.2746	0.645581
$717$	−25.5000	−0.952315
$718$	−12.9341	−0.482698
$719$	−23.2794	−0.868174	−0.434087	−	0.900871i	$-0.642929\pi$
$719$	−23.2794	−0.868174	−0.434087	+	0.900871i	$0.642929\pi$
$720$	−0.439374	−0.0163745
$721$	−49.4228	−1.84060
$722$	−10.1730	−0.378598
$723$	−40.7439	−1.51528
$724$	−26.4155	−0.981723
$725$	3.47894	0.129205
$726$	−17.2932	−0.641812
$727$	30.7094	1.13895	0.569474	−	0.822009i	$-0.307147\pi$
$727$	30.7094	1.13895	0.569474	+	0.822009i	$0.307147\pi$
$728$	−3.12125	−0.115681
$729$	29.7112	1.10042
$730$	−16.0716	−0.594838
$731$	−23.7822	−0.879617
$732$	6.82277	0.252177
$733$	11.9801	0.442494	0.221247	−	0.975218i	$-0.428987\pi$
$733$	11.9801	0.442494	0.221247	+	0.975218i	$0.428987\pi$
$734$	8.78672	0.324324
$735$	−0.382419	−0.0141057
$736$	0	0
$737$	−4.96059	−0.182726
$738$	−3.76454	−0.138575
$739$	−29.6248	−1.08976	−0.544882	−	0.838513i	$-0.683426\pi$
$739$	−29.6248	−1.08976	−0.544882	+	0.838513i	$0.683426\pi$
$740$	7.20039	0.264692
$741$	−5.70694	−0.209650
$742$	22.3622	0.820942
$743$	−37.7890	−1.38634	−0.693172	−	0.720773i	$-0.743787\pi$
$743$	−37.7890	−1.38634	−0.693172	+	0.720773i	$0.743787\pi$
$744$	−0.960431	−0.0352111
$745$	−3.65461	−0.133894
$746$	33.7856	1.23698
$747$	−1.68870	−0.0617862
$748$	1.02473	0.0374678
$749$	−36.3858	−1.32951
$750$	1.60020	0.0584309
$751$	−12.7668	−0.465867	−0.232933	−	0.972493i	$-0.574832\pi$
$751$	−12.7668	−0.465867	−0.232933	+	0.972493i	$0.574832\pi$
$752$	−0.960431	−0.0350233
$753$	−19.2326	−0.700876
$754$	−4.17609	−0.152084
$755$	8.79309	0.320013
$756$	−14.3106	−0.520472
$757$	−2.00636	−0.0729225	−0.0364613	−	0.999335i	$-0.511609\pi$
$757$	−2.00636	−0.0729225	−0.0364613	+	0.999335i	$0.511609\pi$
$758$	−8.61080	−0.312758
$759$	0	0
$760$	2.97103	0.107771
$761$	6.60499	0.239431	0.119715	−	0.992808i	$-0.461802\pi$
$761$	6.60499	0.239431	0.119715	+	0.992808i	$0.461802\pi$
$762$	−27.3458	−0.990633
$763$	9.14628	0.331117
$764$	16.6323	0.601734
$765$	1.02473	0.0370491
$766$	15.9143	0.575008
$767$	−0.989526	−0.0357297
$768$	1.60020	0.0577421
$769$	−17.4382	−0.628839	−0.314419	−	0.949284i	$-0.601810\pi$
$769$	−17.4382	−0.628839	−0.314419	+	0.949284i	$0.601810\pi$
$770$	−1.14246	−0.0411713
$771$	−16.3780	−0.589840
$772$	−9.23996	−0.332553
$773$	−0.990701	−0.0356330	−0.0178165	−	0.999841i	$-0.505671\pi$
$773$	−0.990701	−0.0356330	−0.0178165	+	0.999841i	$0.505671\pi$
$774$	−4.48035	−0.161043
$775$	−0.600196	−0.0215597
$776$	6.92820	0.248708
$777$	29.9595	1.07479
$778$	1.49183	0.0534846
$779$	25.4557	0.912046
$780$	−1.92086	−0.0687779
$781$	−3.30778	−0.118362
$782$	0	0
$783$	−19.1470	−0.684256
$784$	−0.238982	−0.00853508
$785$	−5.59270	−0.199612
$786$	14.8095	0.528237
$787$	17.4983	0.623747	0.311873	−	0.950124i	$-0.399044\pi$
$787$	17.4983	0.623747	0.311873	+	0.950124i	$0.399044\pi$
$788$	7.52204	0.267961
$789$	−8.82277	−0.314099
$790$	3.03957	0.108143
$791$	15.6739	0.557301
$792$	0.193049	0.00685971
$793$	−5.11812	−0.181750
$794$	−18.0766	−0.641514
$795$	13.7620	0.488088
$796$	2.23996	0.0793933
$797$	−28.4269	−1.00693	−0.503467	−	0.864015i	$-0.667942\pi$
$797$	−28.4269	−1.00693	−0.503467	+	0.864015i	$0.667942\pi$
$798$	12.3619	0.437608
$799$	2.23996	0.0792441
$800$	1.00000	0.0353553
$801$	−4.38610	−0.154975
$802$	22.5920	0.797751
$803$	7.06146	0.249193
$804$	18.0664	0.637154
$805$	0	0
$806$	0.720470	0.0253775
$807$	−46.7634	−1.64615
$808$	−9.32899	−0.328193
$809$	−17.7630	−0.624513	−0.312256	−	0.949998i	$-0.601085\pi$
$809$	−17.7630	−0.624513	−0.312256	+	0.949998i	$0.601085\pi$
$810$	−7.48883	−0.263131
$811$	−12.4344	−0.436631	−0.218316	−	0.975878i	$-0.570056\pi$
$811$	−12.4344	−0.436631	−0.218316	+	0.975878i	$0.570056\pi$
$812$	9.04593	0.317450
$813$	−21.7953	−0.764396
$814$	−3.16366	−0.110886
$815$	11.2498	0.394065
$816$	−3.73205	−0.130648
$817$	30.2960	1.05992
$818$	16.3973	0.573317
$819$	1.37140	0.0479205
$820$	8.56797	0.299206
$821$	42.6000	1.48675	0.743376	−	0.668874i	$-0.233223\pi$
$821$	42.6000	1.48675	0.743376	+	0.668874i	$0.233223\pi$
$822$	−32.0240	−1.11697
$823$	1.33805	0.0466415	0.0233208	−	0.999728i	$-0.492576\pi$
$823$	1.33805	0.0466415	0.0233208	+	0.999728i	$0.492576\pi$
$824$	−19.0073	−0.662152
$825$	−0.703084	−0.0244782
$826$	2.14344	0.0745797
$827$	52.1609	1.81381	0.906907	−	0.421332i	$-0.138437\pi$
$827$	52.1609	1.81381	0.906907	+	0.421332i	$0.138437\pi$
$828$	0	0
$829$	−3.13625	−0.108927	−0.0544633	−	0.998516i	$-0.517345\pi$
$829$	−3.13625	−0.108927	−0.0544633	+	0.998516i	$0.517345\pi$
$830$	3.84342	0.133407
$831$	−12.7944	−0.443832
$832$	−1.20039	−0.0416161
$833$	0.557366	0.0193116
$834$	−25.1311	−0.870220
$835$	−20.0257	−0.693018
$836$	−1.30539	−0.0451480
$837$	3.30328	0.114178
$838$	−30.9768	−1.07008
$839$	55.2928	1.90892	0.954459	−	0.298341i	$-0.0964332\pi$
$839$	55.2928	1.90892	0.954459	+	0.298341i	$0.0964332\pi$
$840$	4.16082	0.143562
$841$	−16.8970	−0.582654
$842$	0.737698	0.0254228
$843$	−50.5651	−1.74155
$844$	10.8946	0.375006
$845$	−11.5591	−0.397644
$846$	0.421988	0.0145082
$847$	−28.1002	−0.965534
$848$	8.60020	0.295332
$849$	−9.18259	−0.315146
$850$	−2.33225	−0.0799954
$851$	0	0
$852$	12.0469	0.412720
$853$	29.4030	1.00674	0.503370	−	0.864071i	$-0.332093\pi$
$853$	29.4030	1.00674	0.503370	+	0.864071i	$0.332093\pi$
$854$	11.0865	0.379372
$855$	−1.30539	−0.0446435
$856$	−13.9935	−0.478287
$857$	−50.9453	−1.74026	−0.870129	−	0.492824i	$-0.835965\pi$
$857$	−50.9453	−1.74026	−0.870129	+	0.492824i	$0.835965\pi$
$858$	0.843976	0.0288129
$859$	−25.2804	−0.862554	−0.431277	−	0.902219i	$-0.641937\pi$
$859$	−25.2804	−0.862554	−0.431277	+	0.902219i	$0.641937\pi$
$860$	10.1971	0.347719
$861$	35.6498	1.21494
$862$	19.3502	0.659070
$863$	7.86886	0.267859	0.133930	−	0.990991i	$-0.457240\pi$
$863$	7.86886	0.267859	0.133930	+	0.990991i	$0.457240\pi$
$864$	−5.50367	−0.187239
$865$	−1.08903	−0.0370280
$866$	15.0954	0.512962
$867$	−18.4993	−0.628268
$868$	−1.56063	−0.0529711
$869$	−1.33551	−0.0453040
$870$	5.56699	0.188739
$871$	−13.5526	−0.459212
$872$	3.51753	0.119119
$873$	−3.04407	−0.103026
$874$	0	0
$875$	2.60020	0.0879027
$876$	−25.7178	−0.868923
$877$	−44.9494	−1.51783	−0.758917	−	0.651188i	$-0.774271\pi$
$877$	−44.9494	−1.51783	−0.758917	+	0.651188i	$0.774271\pi$
$878$	22.3987	0.755918
$879$	24.2309	0.817288
$880$	−0.439374	−0.0148113
$881$	−0.782223	−0.0263538	−0.0131769	−	0.999913i	$-0.504194\pi$
$881$	−0.782223	−0.0263538	−0.0131769	+	0.999913i	$0.504194\pi$
$882$	0.105003	0.00353562
$883$	23.4590	0.789458	0.394729	−	0.918798i	$-0.370839\pi$
$883$	23.4590	0.789458	0.394729	+	0.918798i	$0.370839\pi$
$884$	2.79961	0.0941610
$885$	1.31910	0.0443411
$886$	0.993636	0.0333819
$887$	−22.7100	−0.762526	−0.381263	−	0.924467i	$-0.624511\pi$
$887$	−22.7100	−0.762526	−0.381263	+	0.924467i	$0.624511\pi$
$888$	11.5220	0.386654
$889$	−44.4348	−1.49030
$890$	9.98261	0.334618
$891$	3.29040	0.110232
$892$	−11.2414	−0.376389
$893$	−2.85347	−0.0954878
$894$	−5.84809	−0.195589
$895$	17.2746	0.577425
$896$	2.60020	0.0868664
$897$	0	0
$898$	39.5737	1.32059
$899$	−2.08805	−0.0696403
$900$	−0.439374	−0.0146458
$901$	−20.0578	−0.668221
$902$	−3.76454	−0.125345
$903$	42.4284	1.41193
$904$	6.02799	0.200488
$905$	−26.4155	−0.878080
$906$	14.0707	0.467466
$907$	−28.4132	−0.943446	−0.471723	−	0.881747i	$-0.656368\pi$
$907$	−28.4132	−0.943446	−0.471723	+	0.881747i	$0.656368\pi$
$908$	−5.21099	−0.172933
$909$	4.09891	0.135952
$910$	−3.12125	−0.103469
$911$	−58.0359	−1.92281	−0.961407	−	0.275129i	$-0.911280\pi$
$911$	−58.0359	−1.92281	−0.961407	+	0.275129i	$0.911280\pi$
$912$	4.75423	0.157428
$913$	−1.68870	−0.0558877
$914$	3.44290	0.113881
$915$	6.82277	0.225554
$916$	−10.4542	−0.345417
$917$	24.0643	0.794673
$918$	12.8359	0.423648
$919$	−10.6732	−0.352078	−0.176039	−	0.984383i	$-0.556328\pi$
$919$	−10.6732	−0.352078	−0.176039	+	0.984383i	$0.556328\pi$
$920$	0	0
$921$	43.4244	1.43088
$922$	8.61308	0.283657
$923$	−9.03703	−0.297457
$924$	−1.82816	−0.0601419
$925$	7.20039	0.236747
$926$	0.934724	0.0307169
$927$	8.35133	0.274294
$928$	3.47894	0.114202
$929$	−2.17609	−0.0713953	−0.0356977	−	0.999363i	$-0.511365\pi$
$929$	−2.17609	−0.0713953	−0.0356977	+	0.999363i	$0.511365\pi$
$930$	−0.960431	−0.0314938
$931$	−0.710025	−0.0232701
$932$	9.44769	0.309470
$933$	−28.1619	−0.921981
$934$	−10.2340	−0.334868
$935$	1.02473	0.0335122
$936$	0.527420	0.0172393
$937$	43.2102	1.41162	0.705809	−	0.708403i	$-0.250584\pi$
$937$	43.2102	1.41162	0.705809	+	0.708403i	$0.250584\pi$
$938$	29.3566	0.958525
$939$	−7.84130	−0.255891
$940$	−0.960431	−0.0313258
$941$	53.9929	1.76012	0.880059	−	0.474864i	$-0.157503\pi$
$941$	53.9929	1.76012	0.880059	+	0.474864i	$0.157503\pi$
$942$	−8.94941	−0.291587
$943$	0	0
$944$	0.824336	0.0268299
$945$	−14.3106	−0.465525
$946$	−4.48035	−0.145669
$947$	16.7361	0.543851	0.271926	−	0.962318i	$-0.412340\pi$
$947$	16.7361	0.543851	0.271926	+	0.962318i	$0.412340\pi$
$948$	4.86391	0.157972
$949$	19.2923	0.626253
$950$	2.97103	0.0963930
$951$	42.1813	1.36782
$952$	−6.06430	−0.196545
$953$	3.82391	0.123868	0.0619342	−	0.998080i	$-0.480273\pi$
$953$	3.82391	0.123868	0.0619342	+	0.998080i	$0.480273\pi$
$954$	−3.77870	−0.122340
$955$	16.6323	0.538207
$956$	−15.9355	−0.515392
$957$	−2.44599	−0.0790676
$958$	−9.83918	−0.317889
$959$	−52.0366	−1.68035
$960$	1.60020	0.0516461
$961$	−30.6398	−0.988380
$962$	−8.64329	−0.278671
$963$	6.14837	0.198128
$964$	−25.4618	−0.820070
$965$	−9.23996	−0.297445
$966$	0	0
$967$	−20.9748	−0.674505	−0.337253	−	0.941414i	$-0.609498\pi$
$967$	−20.9748	−0.674505	−0.337253	+	0.941414i	$0.609498\pi$
$968$	−10.8070	−0.347349
$969$	−11.0880	−0.356199
$970$	6.92820	0.222451
$971$	−47.2203	−1.51537	−0.757685	−	0.652620i	$-0.773670\pi$
$971$	−47.2203	−1.51537	−0.757685	+	0.652620i	$0.773670\pi$
$972$	4.52742	0.145217
$973$	−40.8362	−1.30915
$974$	0.537855	0.0172340
$975$	−1.92086	−0.0615168
$976$	4.26371	0.136478
$977$	16.3988	0.524645	0.262322	−	0.964980i	$-0.415512\pi$
$977$	16.3988	0.524645	0.262322	+	0.964980i	$0.415512\pi$
$978$	18.0020	0.575639
$979$	−4.38610	−0.140180
$980$	−0.238982	−0.00763401
$981$	−1.54551	−0.0493444
$982$	13.9464	0.445048
$983$	−13.5150	−0.431061	−0.215531	−	0.976497i	$-0.569148\pi$
$983$	−13.5150	−0.431061	−0.215531	+	0.976497i	$0.569148\pi$
$984$	13.7104	0.437072
$985$	7.52204	0.239672
$986$	−8.11375	−0.258395
$987$	−3.99618	−0.127200
$988$	−3.56640	−0.113462
$989$	0	0
$990$	0.193049	0.00613551
$991$	−14.8425	−0.471489	−0.235744	−	0.971815i	$-0.575753\pi$
$991$	−14.8425	−0.471489	−0.235744	+	0.971815i	$0.575753\pi$
$992$	−0.600196	−0.0190562
$993$	45.9597	1.45849
$994$	19.5753	0.620891
$995$	2.23996	0.0710115
$996$	6.15022	0.194877
$997$	−39.8781	−1.26295	−0.631477	−	0.775395i	$-0.717551\pi$
$997$	−39.8781	−1.26295	−0.631477	+	0.775395i	$0.717551\pi$
$998$	−40.6847	−1.28785
$999$	−39.6286	−1.25379

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5290.2.a.bb.1.3	yes	4
23.22	odd	2		5290.2.a.ba.1.3	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5290.2.a.ba.1.3	✓	4	23.22	odd	2
5290.2.a.bb.1.3	yes	4	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:	\( N \)	\(=\)	\( 5290 = 2 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5290.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.60020 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.60020 q^{6} +2.60020 q^{7} +1.00000 q^{8} -0.439374 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.60020 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.60020 q^{6} +2.60020 q^{7} +1.00000 q^{8} -0.439374 q^{9} +1.00000 q^{10} -0.439374 q^{11} +1.60020 q^{12} -1.20039 q^{13} +2.60020 q^{14} +1.60020 q^{15} +1.00000 q^{16} -2.33225 q^{17} -0.439374 q^{18} +2.97103 q^{19} +1.00000 q^{20} +4.16082 q^{21} -0.439374 q^{22} +1.60020 q^{24} +1.00000 q^{25} -1.20039 q^{26} -5.50367 q^{27} +2.60020 q^{28} +3.47894 q^{29} +1.60020 q^{30} -0.600196 q^{31} +1.00000 q^{32} -0.703084 q^{33} -2.33225 q^{34} +2.60020 q^{35} -0.439374 q^{36} +7.20039 q^{37} +2.97103 q^{38} -1.92086 q^{39} +1.00000 q^{40} +8.56797 q^{41} +4.16082 q^{42} +10.1971 q^{43} -0.439374 q^{44} -0.439374 q^{45} -0.960431 q^{47} +1.60020 q^{48} -0.238982 q^{49} +1.00000 q^{50} -3.73205 q^{51} -1.20039 q^{52} +8.60020 q^{53} -5.50367 q^{54} -0.439374 q^{55} +2.60020 q^{56} +4.75423 q^{57} +3.47894 q^{58} +0.824336 q^{59} +1.60020 q^{60} +4.26371 q^{61} -0.600196 q^{62} -1.14246 q^{63} +1.00000 q^{64} -1.20039 q^{65} -0.703084 q^{66} +11.2901 q^{67} -2.33225 q^{68} +2.60020 q^{70} +7.52840 q^{71} -0.439374 q^{72} -16.0716 q^{73} +7.20039 q^{74} +1.60020 q^{75} +2.97103 q^{76} -1.14246 q^{77} -1.92086 q^{78} +3.03957 q^{79} +1.00000 q^{80} -7.48883 q^{81} +8.56797 q^{82} +3.84342 q^{83} +4.16082 q^{84} -2.33225 q^{85} +10.1971 q^{86} +5.56699 q^{87} -0.439374 q^{88} +9.98261 q^{89} -0.439374 q^{90} -3.12125 q^{91} -0.960431 q^{93} -0.960431 q^{94} +2.97103 q^{95} +1.60020 q^{96} +6.92820 q^{97} -0.238982 q^{98} +0.193049 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 2 q^{3} + 4 q^{4} + 4 q^{5} + 2 q^{6} + 6 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 + 4 * q^5 + 2 * q^6 + 6 * q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} + 2 q^{3} + 4 q^{4} + 4 q^{5} + 2 q^{6} + 6 q^{7} + 4 q^{8} + 4 q^{9} + 4 q^{10} + 4 q^{11} + 2 q^{12} + 4 q^{13} + 6 q^{14} + 2 q^{15} + 4 q^{16} + 2 q^{17} + 4 q^{18} + 8 q^{19} + 4 q^{20} + 18 q^{21} + 4 q^{22} + 2 q^{24} + 4 q^{25} + 4 q^{26} + 2 q^{27} + 6 q^{28} - 2 q^{29} + 2 q^{30} + 2 q^{31} + 4 q^{32} + 8 q^{33} + 2 q^{34} + 6 q^{35} + 4 q^{36} + 20 q^{37} + 8 q^{38} - 28 q^{39} + 4 q^{40} - 8 q^{41} + 18 q^{42} - 2 q^{43} + 4 q^{44} + 4 q^{45} - 14 q^{47} + 2 q^{48} - 4 q^{49} + 4 q^{50} - 8 q^{51} + 4 q^{52} + 30 q^{53} + 2 q^{54} + 4 q^{55} + 6 q^{56} - 38 q^{57} - 2 q^{58} + 4 q^{59} + 2 q^{60} + 12 q^{61} + 2 q^{62} + 12 q^{63} + 4 q^{64} + 4 q^{65} + 8 q^{66} + 2 q^{67} + 2 q^{68} + 6 q^{70} - 2 q^{71} + 4 q^{72} + 2 q^{73} + 20 q^{74} + 2 q^{75} + 8 q^{76} + 12 q^{77} - 28 q^{78} + 2 q^{79} + 4 q^{80} - 8 q^{81} - 8 q^{82} + 26 q^{83} + 18 q^{84} + 2 q^{85} - 2 q^{86} + 2 q^{87} + 4 q^{88} + 4 q^{90} - 24 q^{91} - 14 q^{93} - 14 q^{94} + 8 q^{95} + 2 q^{96} - 4 q^{98} + 40 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 + 4 * q^5 + 2 * q^6 + 6 * q^7 + 4 * q^8 + 4 * q^9 + 4 * q^10 + 4 * q^11 + 2 * q^12 + 4 * q^13 + 6 * q^14 + 2 * q^15 + 4 * q^16 + 2 * q^17 + 4 * q^18 + 8 * q^19 + 4 * q^20 + 18 * q^21 + 4 * q^22 + 2 * q^24 + 4 * q^25 + 4 * q^26 + 2 * q^27 + 6 * q^28 - 2 * q^29 + 2 * q^30 + 2 * q^31 + 4 * q^32 + 8 * q^33 + 2 * q^34 + 6 * q^35 + 4 * q^36 + 20 * q^37 + 8 * q^38 - 28 * q^39 + 4 * q^40 - 8 * q^41 + 18 * q^42 - 2 * q^43 + 4 * q^44 + 4 * q^45 - 14 * q^47 + 2 * q^48 - 4 * q^49 + 4 * q^50 - 8 * q^51 + 4 * q^52 + 30 * q^53 + 2 * q^54 + 4 * q^55 + 6 * q^56 - 38 * q^57 - 2 * q^58 + 4 * q^59 + 2 * q^60 + 12 * q^61 + 2 * q^62 + 12 * q^63 + 4 * q^64 + 4 * q^65 + 8 * q^66 + 2 * q^67 + 2 * q^68 + 6 * q^70 - 2 * q^71 + 4 * q^72 + 2 * q^73 + 20 * q^74 + 2 * q^75 + 8 * q^76 + 12 * q^77 - 28 * q^78 + 2 * q^79 + 4 * q^80 - 8 * q^81 - 8 * q^82 + 26 * q^83 + 18 * q^84 + 2 * q^85 - 2 * q^86 + 2 * q^87 + 4 * q^88 + 4 * q^90 - 24 * q^91 - 14 * q^93 - 14 * q^94 + 8 * q^95 + 2 * q^96 - 4 * q^98 + 40 * q^99

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