LMFDB - Embedded newform 6015.2.a.d.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.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:	$48.0300168158$
Analytic rank:	$1$
Dimension:	$29$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.705071 q^{2} -1.00000 q^{3} -1.50287 q^{4} +1.00000 q^{5} +0.705071 q^{6} -2.52019 q^{7} +2.46978 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.705071 q^{2} -1.00000 q^{3} -1.50287 q^{4} +1.00000 q^{5} +0.705071 q^{6} -2.52019 q^{7} +2.46978 q^{8} +1.00000 q^{9} -0.705071 q^{10} -2.77748 q^{11} +1.50287 q^{12} +6.65116 q^{13} +1.77691 q^{14} -1.00000 q^{15} +1.26438 q^{16} -3.40959 q^{17} -0.705071 q^{18} +4.59586 q^{19} -1.50287 q^{20} +2.52019 q^{21} +1.95832 q^{22} -2.73589 q^{23} -2.46978 q^{24} +1.00000 q^{25} -4.68954 q^{26} -1.00000 q^{27} +3.78753 q^{28} -7.54808 q^{29} +0.705071 q^{30} +3.53469 q^{31} -5.83103 q^{32} +2.77748 q^{33} +2.40400 q^{34} -2.52019 q^{35} -1.50287 q^{36} -6.87002 q^{37} -3.24041 q^{38} -6.65116 q^{39} +2.46978 q^{40} -12.3315 q^{41} -1.77691 q^{42} +8.84765 q^{43} +4.17420 q^{44} +1.00000 q^{45} +1.92899 q^{46} -12.9489 q^{47} -1.26438 q^{48} -0.648639 q^{49} -0.705071 q^{50} +3.40959 q^{51} -9.99585 q^{52} +9.96419 q^{53} +0.705071 q^{54} -2.77748 q^{55} -6.22431 q^{56} -4.59586 q^{57} +5.32193 q^{58} +12.1325 q^{59} +1.50287 q^{60} +3.52643 q^{61} -2.49221 q^{62} -2.52019 q^{63} +1.58253 q^{64} +6.65116 q^{65} -1.95832 q^{66} +11.0862 q^{67} +5.12419 q^{68} +2.73589 q^{69} +1.77691 q^{70} +12.7725 q^{71} +2.46978 q^{72} -1.94932 q^{73} +4.84386 q^{74} -1.00000 q^{75} -6.90700 q^{76} +6.99978 q^{77} +4.68954 q^{78} +8.73644 q^{79} +1.26438 q^{80} +1.00000 q^{81} +8.69462 q^{82} +16.7749 q^{83} -3.78753 q^{84} -3.40959 q^{85} -6.23822 q^{86} +7.54808 q^{87} -6.85976 q^{88} +7.69143 q^{89} -0.705071 q^{90} -16.7622 q^{91} +4.11169 q^{92} -3.53469 q^{93} +9.12989 q^{94} +4.59586 q^{95} +5.83103 q^{96} +11.2323 q^{97} +0.457337 q^{98} -2.77748 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 29 q - q^{2} - 29 q^{3} + 27 q^{4} + 29 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 29 q^{9}+O(q^{10}) $ 29 * q - q^2 - 29 * q^3 + 27 * q^4 + 29 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 29 * q^9	\( 29 q - q^{2} - 29 q^{3} + 27 q^{4} + 29 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 29 q^{9} - q^{10} - 21 q^{11} - 27 q^{12} - 8 q^{13} - 30 q^{14} - 29 q^{15} + 23 q^{16} - 28 q^{17} - q^{18} - 9 q^{19} + 27 q^{20} - 2 q^{21} - 9 q^{22} + 6 q^{24} + 29 q^{25} - 34 q^{26} - 29 q^{27} + 6 q^{28} - 61 q^{29} + q^{30} - 19 q^{31} - 8 q^{32} + 21 q^{33} - 16 q^{34} + 2 q^{35} + 27 q^{36} - 4 q^{37} + 4 q^{38} + 8 q^{39} - 6 q^{40} - 85 q^{41} + 30 q^{42} + 29 q^{43} - 69 q^{44} + 29 q^{45} - 35 q^{46} - 2 q^{47} - 23 q^{48} + q^{49} - q^{50} + 28 q^{51} - 28 q^{52} - 5 q^{53} + q^{54} - 21 q^{55} - 97 q^{56} + 9 q^{57} + 6 q^{58} - 43 q^{59} - 27 q^{60} - 59 q^{61} - 17 q^{62} + 2 q^{63} - 6 q^{64} - 8 q^{65} + 9 q^{66} + 28 q^{67} - 44 q^{68} - 30 q^{70} - 44 q^{71} - 6 q^{72} - 41 q^{73} - 50 q^{74} - 29 q^{75} - 62 q^{76} - 20 q^{77} + 34 q^{78} - 25 q^{79} + 23 q^{80} + 29 q^{81} - 29 q^{82} - 7 q^{83} - 6 q^{84} - 28 q^{85} - 43 q^{86} + 61 q^{87} - 3 q^{88} - 109 q^{89} - q^{90} - q^{91} - 11 q^{92} + 19 q^{93} - 20 q^{94} - 9 q^{95} + 8 q^{96} - 51 q^{97} - 12 q^{98} - 21 q^{99}+O(q^{100}) \) 29 * q - q^2 - 29 * q^3 + 27 * q^4 + 29 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 29 * q^9 - q^10 - 21 * q^11 - 27 * q^12 - 8 * q^13 - 30 * q^14 - 29 * q^15 + 23 * q^16 - 28 * q^17 - q^18 - 9 * q^19 + 27 * q^20 - 2 * q^21 - 9 * q^22 + 6 * q^24 + 29 * q^25 - 34 * q^26 - 29 * q^27 + 6 * q^28 - 61 * q^29 + q^30 - 19 * q^31 - 8 * q^32 + 21 * q^33 - 16 * q^34 + 2 * q^35 + 27 * q^36 - 4 * q^37 + 4 * q^38 + 8 * q^39 - 6 * q^40 - 85 * q^41 + 30 * q^42 + 29 * q^43 - 69 * q^44 + 29 * q^45 - 35 * q^46 - 2 * q^47 - 23 * q^48 + q^49 - q^50 + 28 * q^51 - 28 * q^52 - 5 * q^53 + q^54 - 21 * q^55 - 97 * q^56 + 9 * q^57 + 6 * q^58 - 43 * q^59 - 27 * q^60 - 59 * q^61 - 17 * q^62 + 2 * q^63 - 6 * q^64 - 8 * q^65 + 9 * q^66 + 28 * q^67 - 44 * q^68 - 30 * q^70 - 44 * q^71 - 6 * q^72 - 41 * q^73 - 50 * q^74 - 29 * q^75 - 62 * q^76 - 20 * q^77 + 34 * q^78 - 25 * q^79 + 23 * q^80 + 29 * q^81 - 29 * q^82 - 7 * q^83 - 6 * q^84 - 28 * q^85 - 43 * q^86 + 61 * q^87 - 3 * q^88 - 109 * q^89 - q^90 - q^91 - 11 * q^92 + 19 * q^93 - 20 * q^94 - 9 * q^95 + 8 * q^96 - 51 * q^97 - 12 * q^98 - 21 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.705071	−0.498561	−0.249280	−	0.968431i	$-0.580194\pi$
$2$	−0.705071	−0.498561	−0.249280	+	0.968431i	$0.580194\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.50287	−0.751437
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.705071	0.287844
$7$	−2.52019	−0.952543	−0.476271	−	0.879298i	$-0.658012\pi$
$7$	−2.52019	−0.952543	−0.476271	+	0.879298i	$0.658012\pi$
$8$	2.46978	0.873198
$9$	1.00000	0.333333
$10$	−0.705071	−0.222963
$11$	−2.77748	−0.837442	−0.418721	−	0.908115i	$-0.637521\pi$
$11$	−2.77748	−0.837442	−0.418721	+	0.908115i	$0.637521\pi$
$12$	1.50287	0.433842
$13$	6.65116	1.84470	0.922349	−	0.386357i	$-0.126267\pi$
$13$	6.65116	1.84470	0.922349	+	0.386357i	$0.126267\pi$
$14$	1.77691	0.474900
$15$	−1.00000	−0.258199
$16$	1.26438	0.316095
$17$	−3.40959	−0.826947	−0.413474	−	0.910516i	$-0.635685\pi$
$17$	−3.40959	−0.826947	−0.413474	+	0.910516i	$0.635685\pi$
$18$	−0.705071	−0.166187
$19$	4.59586	1.05436	0.527181	−	0.849753i	$-0.323249\pi$
$19$	4.59586	1.05436	0.527181	+	0.849753i	$0.323249\pi$
$20$	−1.50287	−0.336053
$21$	2.52019	0.549951
$22$	1.95832	0.417516
$23$	−2.73589	−0.570472	−0.285236	−	0.958457i	$-0.592072\pi$
$23$	−2.73589	−0.570472	−0.285236	+	0.958457i	$0.592072\pi$
$24$	−2.46978	−0.504141
$25$	1.00000	0.200000
$26$	−4.68954	−0.919694
$27$	−1.00000	−0.192450
$28$	3.78753	0.715776
$29$	−7.54808	−1.40164	−0.700821	−	0.713337i	$-0.747183\pi$
$29$	−7.54808	−1.40164	−0.700821	+	0.713337i	$0.747183\pi$
$30$	0.705071	0.128728
$31$	3.53469	0.634850	0.317425	−	0.948283i	$-0.397182\pi$
$31$	3.53469	0.634850	0.317425	+	0.948283i	$0.397182\pi$
$32$	−5.83103	−1.03079
$33$	2.77748	0.483497
$34$	2.40400	0.412283
$35$	−2.52019	−0.425990
$36$	−1.50287	−0.250479
$37$	−6.87002	−1.12943	−0.564713	−	0.825288i	$-0.691013\pi$
$37$	−6.87002	−1.12943	−0.564713	+	0.825288i	$0.691013\pi$
$38$	−3.24041	−0.525664
$39$	−6.65116	−1.06504
$40$	2.46978	0.390506
$41$	−12.3315	−1.92586	−0.962932	−	0.269745i	$-0.913061\pi$
$41$	−12.3315	−1.92586	−0.962932	+	0.269745i	$0.913061\pi$
$42$	−1.77691	−0.274184
$43$	8.84765	1.34925	0.674627	−	0.738159i	$-0.264305\pi$
$43$	8.84765	1.34925	0.674627	+	0.738159i	$0.264305\pi$
$44$	4.17420	0.629285
$45$	1.00000	0.149071
$46$	1.92899	0.284415
$47$	−12.9489	−1.88879	−0.944395	−	0.328814i	$-0.893351\pi$
$47$	−12.9489	−1.88879	−0.944395	+	0.328814i	$0.893351\pi$
$48$	−1.26438	−0.182498
$49$	−0.648639	−0.0926628
$50$	−0.705071	−0.0997121
$51$	3.40959	0.477438
$52$	−9.99585	−1.38618
$53$	9.96419	1.36869	0.684344	−	0.729160i	$-0.260089\pi$
$53$	9.96419	1.36869	0.684344	+	0.729160i	$0.260089\pi$
$54$	0.705071	0.0959481
$55$	−2.77748	−0.374515
$56$	−6.22431	−0.831758
$57$	−4.59586	−0.608736
$58$	5.32193	0.698804
$59$	12.1325	1.57951	0.789755	−	0.613422i	$-0.210208\pi$
$59$	12.1325	1.57951	0.789755	+	0.613422i	$0.210208\pi$
$60$	1.50287	0.194020
$61$	3.52643	0.451513	0.225756	−	0.974184i	$-0.427515\pi$
$61$	3.52643	0.451513	0.225756	+	0.974184i	$0.427515\pi$
$62$	−2.49221	−0.316511
$63$	−2.52019	−0.317514
$64$	1.58253	0.197817
$65$	6.65116	0.824974
$66$	−1.95832	−0.241053
$67$	11.0862	1.35439	0.677195	−	0.735804i	$-0.263196\pi$
$67$	11.0862	1.35439	0.677195	+	0.735804i	$0.263196\pi$
$68$	5.12419	0.621399
$69$	2.73589	0.329362
$70$	1.77691	0.212382
$71$	12.7725	1.51581	0.757906	−	0.652364i	$-0.226223\pi$
$71$	12.7725	1.51581	0.757906	+	0.652364i	$0.226223\pi$
$72$	2.46978	0.291066
$73$	−1.94932	−0.228150	−0.114075	−	0.993472i	$-0.536390\pi$
$73$	−1.94932	−0.228150	−0.114075	+	0.993472i	$0.536390\pi$
$74$	4.84386	0.563087
$75$	−1.00000	−0.115470
$76$	−6.90700	−0.792287
$77$	6.99978	0.797699
$78$	4.68954	0.530986
$79$	8.73644	0.982926	0.491463	−	0.870898i	$-0.336462\pi$
$79$	8.73644	0.982926	0.491463	+	0.870898i	$0.336462\pi$
$80$	1.26438	0.141362
$81$	1.00000	0.111111
$82$	8.69462	0.960160
$83$	16.7749	1.84129	0.920644	−	0.390404i	$-0.127665\pi$
$83$	16.7749	1.84129	0.920644	+	0.390404i	$0.127665\pi$
$84$	−3.78753	−0.413253
$85$	−3.40959	−0.369822
$86$	−6.23822	−0.672685
$87$	7.54808	0.809239
$88$	−6.85976	−0.731252
$89$	7.69143	0.815290	0.407645	−	0.913141i	$-0.366350\pi$
$89$	7.69143	0.815290	0.407645	+	0.913141i	$0.366350\pi$
$90$	−0.705071	−0.0743210
$91$	−16.7622	−1.75715
$92$	4.11169	0.428674
$93$	−3.53469	−0.366531
$94$	9.12989	0.941676
$95$	4.59586	0.471525
$96$	5.83103	0.595127
$97$	11.2323	1.14046	0.570231	−	0.821484i	$-0.306854\pi$
$97$	11.2323	1.14046	0.570231	+	0.821484i	$0.306854\pi$
$98$	0.457337	0.0461980
$99$	−2.77748	−0.279147
$100$	−1.50287	−0.150287
$101$	−8.36618	−0.832466	−0.416233	−	0.909258i	$-0.636650\pi$
$101$	−8.36618	−0.832466	−0.416233	+	0.909258i	$0.636650\pi$
$102$	−2.40400	−0.238032
$103$	−16.3046	−1.60654	−0.803268	−	0.595618i	$-0.796907\pi$
$103$	−16.3046	−1.60654	−0.803268	+	0.595618i	$0.796907\pi$
$104$	16.4269	1.61079
$105$	2.52019	0.245945
$106$	−7.02547	−0.682374
$107$	−15.4779	−1.49631	−0.748154	−	0.663525i	$-0.769059\pi$
$107$	−15.4779	−1.49631	−0.748154	+	0.663525i	$0.769059\pi$
$108$	1.50287	0.144614
$109$	−9.19070	−0.880309	−0.440155	−	0.897922i	$-0.645076\pi$
$109$	−9.19070	−0.880309	−0.440155	+	0.897922i	$0.645076\pi$
$110$	1.95832	0.186719
$111$	6.87002	0.652074
$112$	−3.18648	−0.301094
$113$	−6.95547	−0.654316	−0.327158	−	0.944970i	$-0.606091\pi$
$113$	−6.95547	−0.654316	−0.327158	+	0.944970i	$0.606091\pi$
$114$	3.24041	0.303492
$115$	−2.73589	−0.255123
$116$	11.3438	1.05325
$117$	6.65116	0.614900
$118$	−8.55424	−0.787482
$119$	8.59282	0.787702
$120$	−2.46978	−0.225459
$121$	−3.28560	−0.298691
$122$	−2.48638	−0.225106
$123$	12.3315	1.11190
$124$	−5.31220	−0.477050
$125$	1.00000	0.0894427
$126$	1.77691	0.158300
$127$	13.2874	1.17906	0.589531	−	0.807746i	$-0.299312\pi$
$127$	13.2874	1.17906	0.589531	+	0.807746i	$0.299312\pi$
$128$	10.5463	0.932167
$129$	−8.84765	−0.778992
$130$	−4.68954	−0.411300
$131$	−7.35328	−0.642459	−0.321229	−	0.947001i	$-0.604096\pi$
$131$	−7.35328	−0.642459	−0.321229	+	0.947001i	$0.604096\pi$
$132$	−4.17420	−0.363318
$133$	−11.5824	−1.00433
$134$	−7.81653	−0.675245
$135$	−1.00000	−0.0860663
$136$	−8.42093	−0.722089
$137$	15.5818	1.33124	0.665620	−	0.746291i	$-0.268167\pi$
$137$	15.5818	1.33124	0.665620	+	0.746291i	$0.268167\pi$
$138$	−1.92899	−0.164207
$139$	−18.8003	−1.59462	−0.797308	−	0.603572i	$-0.793743\pi$
$139$	−18.8003	−1.59462	−0.797308	+	0.603572i	$0.793743\pi$
$140$	3.78753	0.320105
$141$	12.9489	1.09049
$142$	−9.00549	−0.755724
$143$	−18.4735	−1.54483
$144$	1.26438	0.105365
$145$	−7.54808	−0.626834
$146$	1.37441	0.113747
$147$	0.648639	0.0534989
$148$	10.3248	0.848692
$149$	−19.4765	−1.59557	−0.797787	−	0.602939i	$-0.793996\pi$
$149$	−19.4765	−1.59557	−0.797787	+	0.602939i	$0.793996\pi$
$150$	0.705071	0.0575688
$151$	6.47083	0.526589	0.263294	−	0.964716i	$-0.415191\pi$
$151$	6.47083	0.526589	0.263294	+	0.964716i	$0.415191\pi$
$152$	11.3507	0.920667
$153$	−3.40959	−0.275649
$154$	−4.93534	−0.397701
$155$	3.53469	0.283913
$156$	9.99585	0.800309
$157$	−3.61436	−0.288457	−0.144229	−	0.989544i	$-0.546070\pi$
$157$	−3.61436	−0.288457	−0.144229	+	0.989544i	$0.546070\pi$
$158$	−6.15981	−0.490048
$159$	−9.96419	−0.790212
$160$	−5.83103	−0.460983
$161$	6.89495	0.543399
$162$	−0.705071	−0.0553956
$163$	−7.77101	−0.608673	−0.304336	−	0.952565i	$-0.598435\pi$
$163$	−7.77101	−0.608673	−0.304336	+	0.952565i	$0.598435\pi$
$164$	18.5328	1.44717
$165$	2.77748	0.216227
$166$	−11.8275	−0.917994
$167$	−7.22835	−0.559346	−0.279673	−	0.960095i	$-0.590226\pi$
$167$	−7.22835	−0.559346	−0.279673	+	0.960095i	$0.590226\pi$
$168$	6.22431	0.480216
$169$	31.2379	2.40291
$170$	2.40400	0.184379
$171$	4.59586	0.351454
$172$	−13.2969	−1.01388
$173$	0.266337	0.0202493	0.0101246	−	0.999949i	$-0.496777\pi$
$173$	0.266337	0.0202493	0.0101246	+	0.999949i	$0.496777\pi$
$174$	−5.32193	−0.403455
$175$	−2.52019	−0.190509
$176$	−3.51179	−0.264711
$177$	−12.1325	−0.911931
$178$	−5.42300	−0.406471
$179$	−17.9350	−1.34052	−0.670261	−	0.742126i	$-0.733818\pi$
$179$	−17.9350	−1.34052	−0.670261	+	0.742126i	$0.733818\pi$
$180$	−1.50287	−0.112018
$181$	11.8497	0.880782	0.440391	−	0.897806i	$-0.354840\pi$
$181$	11.8497	0.880782	0.440391	+	0.897806i	$0.354840\pi$
$182$	11.8185	0.876048
$183$	−3.52643	−0.260681
$184$	−6.75703	−0.498135
$185$	−6.87002	−0.505094
$186$	2.49221	0.182738
$187$	9.47007	0.692520
$188$	19.4606	1.41931
$189$	2.52019	0.183317
$190$	−3.24041	−0.235084
$191$	16.5841	1.19999	0.599993	−	0.800006i	$-0.295170\pi$
$191$	16.5841	1.19999	0.599993	+	0.800006i	$0.295170\pi$
$192$	−1.58253	−0.114209
$193$	−21.0480	−1.51507	−0.757535	−	0.652794i	$-0.773597\pi$
$193$	−21.0480	−1.51507	−0.757535	+	0.652794i	$0.773597\pi$
$194$	−7.91954	−0.568590
$195$	−6.65116	−0.476299
$196$	0.974823	0.0696302
$197$	−0.0657754	−0.00468630	−0.00234315	−	0.999997i	$-0.500746\pi$
$197$	−0.0657754	−0.00468630	−0.00234315	+	0.999997i	$0.500746\pi$
$198$	1.95832	0.139172
$199$	19.5040	1.38260	0.691302	−	0.722566i	$-0.257038\pi$
$199$	19.5040	1.38260	0.691302	+	0.722566i	$0.257038\pi$
$200$	2.46978	0.174640
$201$	−11.0862	−0.781957
$202$	5.89875	0.415035
$203$	19.0226	1.33512
$204$	−5.12419	−0.358765
$205$	−12.3315	−0.861272
$206$	11.4959	0.800956
$207$	−2.73589	−0.190157
$208$	8.40959	0.583100
$209$	−12.7649	−0.882967
$210$	−1.77691	−0.122619
$211$	3.16035	0.217567	0.108784	−	0.994065i	$-0.465304\pi$
$211$	3.16035	0.217567	0.108784	+	0.994065i	$0.465304\pi$
$212$	−14.9749	−1.02848
$213$	−12.7725	−0.875154
$214$	10.9130	0.746000
$215$	8.84765	0.603405
$216$	−2.46978	−0.168047
$217$	−8.90810	−0.604721
$218$	6.48010	0.438888
$219$	1.94932	0.131723
$220$	4.17420	0.281425
$221$	−22.6777	−1.52547
$222$	−4.84386	−0.325098
$223$	3.59997	0.241072	0.120536	−	0.992709i	$-0.461539\pi$
$223$	3.59997	0.241072	0.120536	+	0.992709i	$0.461539\pi$
$224$	14.6953	0.981872
$225$	1.00000	0.0666667
$226$	4.90410	0.326216
$227$	0.0448940	0.00297972	0.00148986	−	0.999999i	$-0.499526\pi$
$227$	0.0448940	0.00297972	0.00148986	+	0.999999i	$0.499526\pi$
$228$	6.90700	0.457427
$229$	1.83993	0.121586	0.0607931	−	0.998150i	$-0.480637\pi$
$229$	1.83993	0.121586	0.0607931	+	0.998150i	$0.480637\pi$
$230$	1.92899	0.127194
$231$	−6.99978	−0.460552
$232$	−18.6421	−1.22391
$233$	−17.5212	−1.14785	−0.573927	−	0.818906i	$-0.694581\pi$
$233$	−17.5212	−1.14785	−0.573927	+	0.818906i	$0.694581\pi$
$234$	−4.68954	−0.306565
$235$	−12.9489	−0.844692
$236$	−18.2335	−1.18690
$237$	−8.73644	−0.567493
$238$	−6.05855	−0.392717
$239$	−25.6500	−1.65916	−0.829580	−	0.558388i	$-0.811420\pi$
$239$	−25.6500	−1.65916	−0.829580	+	0.558388i	$0.811420\pi$
$240$	−1.26438	−0.0816154
$241$	0.0539818	0.00347727	0.00173864	−	0.999998i	$-0.499447\pi$
$241$	0.0539818	0.00347727	0.00173864	+	0.999998i	$0.499447\pi$
$242$	2.31658	0.148916
$243$	−1.00000	−0.0641500
$244$	−5.29977	−0.339283
$245$	−0.648639	−0.0414400
$246$	−8.69462	−0.554349
$247$	30.5678	1.94498
$248$	8.72990	0.554349
$249$	−16.7749	−1.06307
$250$	−0.705071	−0.0445926
$251$	−21.4670	−1.35498	−0.677492	−	0.735530i	$-0.736933\pi$
$251$	−21.4670	−1.35498	−0.677492	+	0.735530i	$0.736933\pi$
$252$	3.78753	0.238592
$253$	7.59887	0.477737
$254$	−9.36854	−0.587834
$255$	3.40959	0.213517
$256$	−10.6009	−0.662558
$257$	−11.1246	−0.693934	−0.346967	−	0.937877i	$-0.612788\pi$
$257$	−11.1246	−0.693934	−0.346967	+	0.937877i	$0.612788\pi$
$258$	6.23822	0.388375
$259$	17.3138	1.07583
$260$	−9.99585	−0.619916
$261$	−7.54808	−0.467214
$262$	5.18459	0.320305
$263$	24.0556	1.48333	0.741666	−	0.670770i	$-0.234036\pi$
$263$	24.0556	1.48333	0.741666	+	0.670770i	$0.234036\pi$
$264$	6.85976	0.422189
$265$	9.96419	0.612096
$266$	8.16645	0.500717
$267$	−7.69143	−0.470708
$268$	−16.6611	−1.01774
$269$	12.8612	0.784160	0.392080	−	0.919931i	$-0.371756\pi$
$269$	12.8612	0.784160	0.392080	+	0.919931i	$0.371756\pi$
$270$	0.705071	0.0429093
$271$	−28.9919	−1.76113	−0.880566	−	0.473923i	$-0.842837\pi$
$271$	−28.9919	−1.76113	−0.880566	+	0.473923i	$0.842837\pi$
$272$	−4.31102	−0.261394
$273$	16.7622	1.01449
$274$	−10.9863	−0.663704
$275$	−2.77748	−0.167488
$276$	−4.11169	−0.247495
$277$	15.4951	0.931010	0.465505	−	0.885045i	$-0.345873\pi$
$277$	15.4951	0.931010	0.465505	+	0.885045i	$0.345873\pi$
$278$	13.2555	0.795013
$279$	3.53469	0.211617
$280$	−6.22431	−0.371974
$281$	3.13265	0.186878	0.0934391	−	0.995625i	$-0.470214\pi$
$281$	3.13265	0.186878	0.0934391	+	0.995625i	$0.470214\pi$
$282$	−9.12989	−0.543677
$283$	4.75563	0.282693	0.141346	−	0.989960i	$-0.454857\pi$
$283$	4.75563	0.282693	0.141346	+	0.989960i	$0.454857\pi$
$284$	−19.1954	−1.13904
$285$	−4.59586	−0.272235
$286$	13.0251	0.770191
$287$	31.0778	1.83447
$288$	−5.83103	−0.343597
$289$	−5.37469	−0.316158
$290$	5.32193	0.312515
$291$	−11.2323	−0.658446
$292$	2.92958	0.171441
$293$	−26.2040	−1.53085	−0.765426	−	0.643523i	$-0.777472\pi$
$293$	−26.2040	−1.53085	−0.765426	+	0.643523i	$0.777472\pi$
$294$	−0.457337	−0.0266724
$295$	12.1325	0.706379
$296$	−16.9674	−0.986212
$297$	2.77748	0.161166
$298$	13.7323	0.795491
$299$	−18.1968	−1.05235
$300$	1.50287	0.0867685
$301$	−22.2978	−1.28522
$302$	−4.56240	−0.262537
$303$	8.36618	0.480624
$304$	5.81091	0.333279
$305$	3.52643	0.201923
$306$	2.40400	0.137428
$307$	−16.9318	−0.966351	−0.483175	−	0.875524i	$-0.660517\pi$
$307$	−16.9318	−0.966351	−0.483175	+	0.875524i	$0.660517\pi$
$308$	−10.5198	−0.599421
$309$	16.3046	0.927534
$310$	−2.49221	−0.141548
$311$	−11.9940	−0.680116	−0.340058	−	0.940404i	$-0.610447\pi$
$311$	−11.9940	−0.680116	−0.340058	+	0.940404i	$0.610447\pi$
$312$	−16.4269	−0.929988
$313$	5.11102	0.288892	0.144446	−	0.989513i	$-0.453860\pi$
$313$	5.11102	0.288892	0.144446	+	0.989513i	$0.453860\pi$
$314$	2.54838	0.143813
$315$	−2.52019	−0.141997
$316$	−13.1298	−0.738607
$317$	−5.22567	−0.293503	−0.146751	−	0.989173i	$-0.546882\pi$
$317$	−5.22567	−0.293503	−0.146751	+	0.989173i	$0.546882\pi$
$318$	7.02547	0.393969
$319$	20.9646	1.17379
$320$	1.58253	0.0884663
$321$	15.4779	0.863893
$322$	−4.86143	−0.270917
$323$	−15.6700	−0.871902
$324$	−1.50287	−0.0834930
$325$	6.65116	0.368940
$326$	5.47912	0.303460
$327$	9.19070	0.508247
$328$	−30.4562	−1.68166
$329$	32.6337	1.79915
$330$	−1.95832	−0.107802
$331$	−6.26140	−0.344158	−0.172079	−	0.985083i	$-0.555048\pi$
$331$	−6.26140	−0.344158	−0.172079	+	0.985083i	$0.555048\pi$
$332$	−25.2106	−1.38361
$333$	−6.87002	−0.376475
$334$	5.09650	0.278868
$335$	11.0862	0.605701
$336$	3.18648	0.173837
$337$	−3.62326	−0.197372	−0.0986858	−	0.995119i	$-0.531464\pi$
$337$	−3.62326	−0.197372	−0.0986858	+	0.995119i	$0.531464\pi$
$338$	−22.0249	−1.19800
$339$	6.95547	0.377769
$340$	5.12419	0.277898
$341$	−9.81754	−0.531650
$342$	−3.24041	−0.175221
$343$	19.2760	1.04081
$344$	21.8517	1.17817
$345$	2.73589	0.147295
$346$	−0.187787	−0.0100955
$347$	4.00539	0.215020	0.107510	−	0.994204i	$-0.465712\pi$
$347$	4.00539	0.215020	0.107510	+	0.994204i	$0.465712\pi$
$348$	−11.3438	−0.608092
$349$	−7.10363	−0.380248	−0.190124	−	0.981760i	$-0.560889\pi$
$349$	−7.10363	−0.380248	−0.190124	+	0.981760i	$0.560889\pi$
$350$	1.77691	0.0949801
$351$	−6.65116	−0.355012
$352$	16.1956	0.863227
$353$	6.28850	0.334703	0.167351	−	0.985897i	$-0.446479\pi$
$353$	6.28850	0.334703	0.167351	+	0.985897i	$0.446479\pi$
$354$	8.55424	0.454653
$355$	12.7725	0.677891
$356$	−11.5592	−0.612639
$357$	−8.59282	−0.454780
$358$	12.6454	0.668332
$359$	3.88197	0.204882	0.102441	−	0.994739i	$-0.467335\pi$
$359$	3.88197	0.204882	0.102441	+	0.994739i	$0.467335\pi$
$360$	2.46978	0.130169
$361$	2.12192	0.111680
$362$	−8.35489	−0.439123
$363$	3.28560	0.172449
$364$	25.1915	1.32039
$365$	−1.94932	−0.102032
$366$	2.48638	0.129965
$367$	25.3244	1.32192	0.660962	−	0.750419i	$-0.270148\pi$
$367$	25.3244	1.32192	0.660962	+	0.750419i	$0.270148\pi$
$368$	−3.45920	−0.180323
$369$	−12.3315	−0.641955
$370$	4.84386	0.251820
$371$	−25.1117	−1.30373
$372$	5.31220	0.275425
$373$	−9.95371	−0.515384	−0.257692	−	0.966227i	$-0.582962\pi$
$373$	−9.95371	−0.515384	−0.257692	+	0.966227i	$0.582962\pi$
$374$	−6.67708	−0.345263
$375$	−1.00000	−0.0516398
$376$	−31.9809	−1.64929
$377$	−50.2034	−2.58561
$378$	−1.77691	−0.0913946
$379$	−19.8406	−1.01915	−0.509573	−	0.860428i	$-0.670197\pi$
$379$	−19.8406	−1.01915	−0.509573	+	0.860428i	$0.670197\pi$
$380$	−6.90700	−0.354322
$381$	−13.2874	−0.680732
$382$	−11.6930	−0.598266
$383$	18.1170	0.925735	0.462868	−	0.886427i	$-0.346821\pi$
$383$	18.1170	0.925735	0.462868	+	0.886427i	$0.346821\pi$
$384$	−10.5463	−0.538187
$385$	6.99978	0.356742
$386$	14.8404	0.755354
$387$	8.84765	0.449751
$388$	−16.8807	−0.856986
$389$	−29.3543	−1.48832	−0.744160	−	0.668002i	$-0.767150\pi$
$389$	−29.3543	−1.48832	−0.744160	+	0.668002i	$0.767150\pi$
$390$	4.68954	0.237464
$391$	9.32825	0.471750
$392$	−1.60199	−0.0809129
$393$	7.35328	0.370924
$394$	0.0463763	0.00233641
$395$	8.73644	0.439578
$396$	4.17420	0.209762
$397$	−34.1587	−1.71438	−0.857189	−	0.515002i	$-0.827791\pi$
$397$	−34.1587	−1.71438	−0.857189	+	0.515002i	$0.827791\pi$
$398$	−13.7517	−0.689312
$399$	11.5824	0.579847
$400$	1.26438	0.0632190
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	7.81653	0.389853
$403$	23.5098	1.17111
$404$	12.5733	0.625546
$405$	1.00000	0.0496904
$406$	−13.4123	−0.665640
$407$	19.0814	0.945828
$408$	8.42093	0.416898
$409$	−36.2910	−1.79448	−0.897238	−	0.441546i	$-0.854430\pi$
$409$	−36.2910	−1.79448	−0.897238	+	0.441546i	$0.854430\pi$
$410$	8.69462	0.429397
$411$	−15.5818	−0.768592
$412$	24.5037	1.20721
$413$	−30.5761	−1.50455
$414$	1.92899	0.0948049
$415$	16.7749	0.823449
$416$	−38.7831	−1.90150
$417$	18.8003	0.920652
$418$	9.00017	0.440213
$419$	−30.9440	−1.51171	−0.755856	−	0.654738i	$-0.772779\pi$
$419$	−30.9440	−1.51171	−0.755856	+	0.654738i	$0.772779\pi$
$420$	−3.78753	−0.184813
$421$	−22.2090	−1.08240	−0.541200	−	0.840894i	$-0.682030\pi$
$421$	−22.2090	−1.08240	−0.541200	+	0.840894i	$0.682030\pi$
$422$	−2.22827	−0.108470
$423$	−12.9489	−0.629596
$424$	24.6093	1.19513
$425$	−3.40959	−0.165389
$426$	9.00549	0.436317
$427$	−8.88726	−0.430085
$428$	23.2614	1.12438
$429$	18.4735	0.891907
$430$	−6.23822	−0.300834
$431$	26.4015	1.27171	0.635857	−	0.771807i	$-0.280647\pi$
$431$	26.4015	1.27171	0.635857	+	0.771807i	$0.280647\pi$
$432$	−1.26438	−0.0608325
$433$	17.7919	0.855024	0.427512	−	0.904010i	$-0.359390\pi$
$433$	17.7919	0.855024	0.427512	+	0.904010i	$0.359390\pi$
$434$	6.28085	0.301490
$435$	7.54808	0.361903
$436$	13.8125	0.661497
$437$	−12.5737	−0.601484
$438$	−1.37441	−0.0656718
$439$	−28.1815	−1.34503	−0.672516	−	0.740083i	$-0.734786\pi$
$439$	−28.1815	−1.34503	−0.672516	+	0.740083i	$0.734786\pi$
$440$	−6.85976	−0.327026
$441$	−0.648639	−0.0308876
$442$	15.9894	0.760539
$443$	25.7172	1.22186	0.610931	−	0.791684i	$-0.290795\pi$
$443$	25.7172	1.22186	0.610931	+	0.791684i	$0.290795\pi$
$444$	−10.3248	−0.489993
$445$	7.69143	0.364609
$446$	−2.53823	−0.120189
$447$	19.4765	0.921205
$448$	−3.98828	−0.188429
$449$	10.4312	0.492277	0.246138	−	0.969235i	$-0.420838\pi$
$449$	10.4312	0.492277	0.246138	+	0.969235i	$0.420838\pi$
$450$	−0.705071	−0.0332374
$451$	34.2506	1.61280
$452$	10.4532	0.491677
$453$	−6.47083	−0.304026
$454$	−0.0316535	−0.00148557
$455$	−16.7622	−0.785823
$456$	−11.3507	−0.531547
$457$	−16.0270	−0.749709	−0.374855	−	0.927084i	$-0.622307\pi$
$457$	−16.0270	−0.749709	−0.374855	+	0.927084i	$0.622307\pi$
$458$	−1.29728	−0.0606181
$459$	3.40959	0.159146
$460$	4.11169	0.191709
$461$	−29.6953	−1.38305	−0.691525	−	0.722352i	$-0.743061\pi$
$461$	−29.6953	−1.38305	−0.691525	+	0.722352i	$0.743061\pi$
$462$	4.93534	0.229613
$463$	−36.7064	−1.70589	−0.852945	−	0.522000i	$-0.825186\pi$
$463$	−36.7064	−1.70589	−0.852945	+	0.522000i	$0.825186\pi$
$464$	−9.54364	−0.443052
$465$	−3.53469	−0.163918
$466$	12.3537	0.572275
$467$	29.7194	1.37525	0.687625	−	0.726066i	$-0.258653\pi$
$467$	29.7194	1.37525	0.687625	+	0.726066i	$0.258653\pi$
$468$	−9.99585	−0.462058
$469$	−27.9392	−1.29011
$470$	9.12989	0.421130
$471$	3.61436	0.166541
$472$	29.9644	1.37923
$473$	−24.5742	−1.12992
$474$	6.15981	0.282930
$475$	4.59586	0.210872
$476$	−12.9139	−0.591909
$477$	9.96419	0.456229
$478$	18.0851	0.827192
$479$	7.45188	0.340485	0.170243	−	0.985402i	$-0.445545\pi$
$479$	7.45188	0.340485	0.170243	+	0.985402i	$0.445545\pi$
$480$	5.83103	0.266149
$481$	−45.6936	−2.08345
$482$	−0.0380610	−0.00173363
$483$	−6.89495	−0.313731
$484$	4.93785	0.224448
$485$	11.2323	0.510030
$486$	0.705071	0.0319827
$487$	11.0697	0.501614	0.250807	−	0.968037i	$-0.419304\pi$
$487$	11.0697	0.501614	0.250807	+	0.968037i	$0.419304\pi$
$488$	8.70948	0.394260
$489$	7.77101	0.351417
$490$	0.457337	0.0206604
$491$	−24.1693	−1.09075	−0.545374	−	0.838193i	$-0.683612\pi$
$491$	−24.1693	−1.09075	−0.545374	+	0.838193i	$0.683612\pi$
$492$	−18.5328	−0.835521
$493$	25.7358	1.15908
$494$	−21.5525	−0.969691
$495$	−2.77748	−0.124838
$496$	4.46920	0.200673
$497$	−32.1890	−1.44387
$498$	11.8275	0.530004
$499$	−33.4103	−1.49565	−0.747825	−	0.663896i	$-0.768902\pi$
$499$	−33.4103	−1.49565	−0.747825	+	0.663896i	$0.768902\pi$
$500$	−1.50287	−0.0672106
$501$	7.22835	0.322939
$502$	15.1358	0.675542
$503$	−2.91744	−0.130082	−0.0650411	−	0.997883i	$-0.520718\pi$
$503$	−2.91744	−0.130082	−0.0650411	+	0.997883i	$0.520718\pi$
$504$	−6.22431	−0.277253
$505$	−8.36618	−0.372290
$506$	−5.35775	−0.238181
$507$	−31.2379	−1.38732
$508$	−19.9692	−0.885991
$509$	26.4723	1.17336	0.586682	−	0.809818i	$-0.300434\pi$
$509$	26.4723	1.17336	0.586682	+	0.809818i	$0.300434\pi$
$510$	−2.40400	−0.106451
$511$	4.91265	0.217323
$512$	−13.6181	−0.601841
$513$	−4.59586	−0.202912
$514$	7.84365	0.345968
$515$	−16.3046	−0.718465
$516$	13.2969	0.585364
$517$	35.9653	1.58175
$518$	−12.2074	−0.536364
$519$	−0.266337	−0.0116909
$520$	16.4269	0.720366
$521$	14.9443	0.654720	0.327360	−	0.944900i	$-0.393841\pi$
$521$	14.9443	0.654720	0.327360	+	0.944900i	$0.393841\pi$
$522$	5.32193	0.232935
$523$	−9.03819	−0.395212	−0.197606	−	0.980281i	$-0.563317\pi$
$523$	−9.03819	−0.395212	−0.197606	+	0.980281i	$0.563317\pi$
$524$	11.0511	0.482767
$525$	2.52019	0.109990
$526$	−16.9609	−0.739531
$527$	−12.0519	−0.524987
$528$	3.51179	0.152831
$529$	−15.5149	−0.674562
$530$	−7.02547	−0.305167
$531$	12.1325	0.526504
$532$	17.4070	0.754687
$533$	−82.0190	−3.55264
$534$	5.42300	0.234676
$535$	−15.4779	−0.669169
$536$	27.3803	1.18265
$537$	17.9350	0.773951
$538$	−9.06805	−0.390951
$539$	1.80158	0.0775997
$540$	1.50287	0.0646734
$541$	−7.79903	−0.335306	−0.167653	−	0.985846i	$-0.553619\pi$
$541$	−7.79903	−0.335306	−0.167653	+	0.985846i	$0.553619\pi$
$542$	20.4414	0.878031
$543$	−11.8497	−0.508520
$544$	19.8814	0.852409
$545$	−9.19070	−0.393686
$546$	−11.8185	−0.505787
$547$	−8.34265	−0.356706	−0.178353	−	0.983967i	$-0.557077\pi$
$547$	−8.34265	−0.356706	−0.178353	+	0.983967i	$0.557077\pi$
$548$	−23.4174	−1.00034
$549$	3.52643	0.150504
$550$	1.95832	0.0835031
$551$	−34.6899	−1.47784
$552$	6.75703	0.287598
$553$	−22.0175	−0.936279
$554$	−10.9251	−0.464165
$555$	6.87002	0.291616
$556$	28.2544	1.19825
$557$	−1.32446	−0.0561191	−0.0280596	−	0.999606i	$-0.508933\pi$
$557$	−1.32446	−0.0561191	−0.0280596	+	0.999606i	$0.508933\pi$
$558$	−2.49221	−0.105504
$559$	58.8471	2.48897
$560$	−3.18648	−0.134653
$561$	−9.47007	−0.399827
$562$	−2.20874	−0.0931701
$563$	12.2217	0.515083	0.257542	−	0.966267i	$-0.417088\pi$
$563$	12.2217	0.515083	0.257542	+	0.966267i	$0.417088\pi$
$564$	−19.4606	−0.819437
$565$	−6.95547	−0.292619
$566$	−3.35306	−0.140939
$567$	−2.52019	−0.105838
$568$	31.5451	1.32360
$569$	1.71603	0.0719399	0.0359700	−	0.999353i	$-0.488548\pi$
$569$	1.71603	0.0719399	0.0359700	+	0.999353i	$0.488548\pi$
$570$	3.24041	0.135726
$571$	27.6530	1.15724	0.578621	−	0.815596i	$-0.303591\pi$
$571$	27.6530	1.15724	0.578621	+	0.815596i	$0.303591\pi$
$572$	27.7633	1.16084
$573$	−16.5841	−0.692812
$574$	−21.9121	−0.914593
$575$	−2.73589	−0.114094
$576$	1.58253	0.0659389
$577$	−14.1934	−0.590879	−0.295440	−	0.955361i	$-0.595466\pi$
$577$	−14.1934	−0.590879	−0.295440	+	0.955361i	$0.595466\pi$
$578$	3.78954	0.157624
$579$	21.0480	0.874726
$580$	11.3438	0.471026
$581$	−42.2760	−1.75390
$582$	7.91954	0.328275
$583$	−27.6754	−1.14620
$584$	−4.81438	−0.199220
$585$	6.65116	0.274991
$586$	18.4757	0.763223
$587$	36.8371	1.52043	0.760215	−	0.649671i	$-0.225094\pi$
$587$	36.8371	1.52043	0.760215	+	0.649671i	$0.225094\pi$
$588$	−0.974823	−0.0402010
$589$	16.2450	0.669362
$590$	−8.55424	−0.352173
$591$	0.0657754	0.00270564
$592$	−8.68632	−0.357006
$593$	−18.9570	−0.778472	−0.389236	−	0.921138i	$-0.627261\pi$
$593$	−18.9570	−0.778472	−0.389236	+	0.921138i	$0.627261\pi$
$594$	−1.95832	−0.0803509
$595$	8.59282	0.352271
$596$	29.2707	1.19897
$597$	−19.5040	−0.798246
$598$	12.8300	0.524660
$599$	10.7957	0.441101	0.220550	−	0.975376i	$-0.429215\pi$
$599$	10.7957	0.441101	0.220550	+	0.975376i	$0.429215\pi$
$600$	−2.46978	−0.100828
$601$	8.89351	0.362774	0.181387	−	0.983412i	$-0.441941\pi$
$601$	8.89351	0.362774	0.181387	+	0.983412i	$0.441941\pi$
$602$	15.7215	0.640761
$603$	11.0862	0.451463
$604$	−9.72485	−0.395698
$605$	−3.28560	−0.133579
$606$	−5.89875	−0.239621
$607$	10.1839	0.413353	0.206676	−	0.978409i	$-0.433735\pi$
$607$	10.1839	0.413353	0.206676	+	0.978409i	$0.433735\pi$
$608$	−26.7986	−1.08683
$609$	−19.0226	−0.770834
$610$	−2.48638	−0.100671
$611$	−86.1251	−3.48425
$612$	5.12419	0.207133
$613$	6.03743	0.243850	0.121925	−	0.992539i	$-0.461093\pi$
$613$	6.03743	0.243850	0.121925	+	0.992539i	$0.461093\pi$
$614$	11.9381	0.481784
$615$	12.3315	0.497256
$616$	17.2879	0.696549
$617$	7.98361	0.321408	0.160704	−	0.987003i	$-0.448624\pi$
$617$	7.98361	0.321408	0.160704	+	0.987003i	$0.448624\pi$
$618$	−11.4959	−0.462432
$619$	−6.00168	−0.241228	−0.120614	−	0.992699i	$-0.538486\pi$
$619$	−6.00168	−0.241228	−0.120614	+	0.992699i	$0.538486\pi$
$620$	−5.31220	−0.213343
$621$	2.73589	0.109787
$622$	8.45661	0.339079
$623$	−19.3839	−0.776598
$624$	−8.40959	−0.336653
$625$	1.00000	0.0400000
$626$	−3.60363	−0.144030
$627$	12.7649	0.509781
$628$	5.43193	0.216757
$629$	23.4240	0.933975
$630$	1.77691	0.0707940
$631$	4.96753	0.197754	0.0988772	−	0.995100i	$-0.468475\pi$
$631$	4.96753	0.197754	0.0988772	+	0.995100i	$0.468475\pi$
$632$	21.5771	0.858289
$633$	−3.16035	−0.125612
$634$	3.68447	0.146329
$635$	13.2874	0.527293
$636$	14.9749	0.593795
$637$	−4.31420	−0.170935
$638$	−14.7816	−0.585208
$639$	12.7725	0.505270
$640$	10.5463	0.416878
$641$	−32.3876	−1.27923	−0.639616	−	0.768695i	$-0.720906\pi$
$641$	−32.3876	−1.27923	−0.639616	+	0.768695i	$0.720906\pi$
$642$	−10.9130	−0.430703
$643$	−21.2274	−0.837126	−0.418563	−	0.908188i	$-0.637466\pi$
$643$	−21.2274	−0.837126	−0.418563	+	0.908188i	$0.637466\pi$
$644$	−10.3622	−0.408330
$645$	−8.84765	−0.348376
$646$	11.0485	0.434696
$647$	−9.90368	−0.389354	−0.194677	−	0.980867i	$-0.562366\pi$
$647$	−9.90368	−0.389354	−0.194677	+	0.980867i	$0.562366\pi$
$648$	2.46978	0.0970220
$649$	−33.6976	−1.32275
$650$	−4.68954	−0.183939
$651$	8.90810	0.349136
$652$	11.6789	0.457379
$653$	31.2388	1.22247	0.611234	−	0.791450i	$-0.290674\pi$
$653$	31.2388	1.22247	0.611234	+	0.791450i	$0.290674\pi$
$654$	−6.48010	−0.253392
$655$	−7.35328	−0.287316
$656$	−15.5918	−0.608756
$657$	−1.94932	−0.0760501
$658$	−23.0091	−0.896987
$659$	−49.1934	−1.91630	−0.958151	−	0.286263i	$-0.907587\pi$
$659$	−49.1934	−1.91630	−0.958151	+	0.286263i	$0.907587\pi$
$660$	−4.17420	−0.162481
$661$	−7.37660	−0.286917	−0.143458	−	0.989656i	$-0.545822\pi$
$661$	−7.37660	−0.286917	−0.143458	+	0.989656i	$0.545822\pi$
$662$	4.41473	0.171583
$663$	22.6777	0.880730
$664$	41.4303	1.60781
$665$	−11.5824	−0.449148
$666$	4.84386	0.187696
$667$	20.6507	0.799597
$668$	10.8633	0.420314
$669$	−3.59997	−0.139183
$670$	−7.81653	−0.301979
$671$	−9.79458	−0.378116
$672$	−14.6953	−0.566884
$673$	−3.36627	−0.129760	−0.0648801	−	0.997893i	$-0.520666\pi$
$673$	−3.36627	−0.129760	−0.0648801	+	0.997893i	$0.520666\pi$
$674$	2.55466	0.0984017
$675$	−1.00000	−0.0384900
$676$	−46.9466	−1.80564
$677$	−9.65034	−0.370893	−0.185446	−	0.982654i	$-0.559373\pi$
$677$	−9.65034	−0.370893	−0.185446	+	0.982654i	$0.559373\pi$
$678$	−4.90410	−0.188341
$679$	−28.3074	−1.08634
$680$	−8.42093	−0.322928
$681$	−0.0448940	−0.00172034
$682$	6.92207	0.265060
$683$	−19.3612	−0.740834	−0.370417	−	0.928866i	$-0.620785\pi$
$683$	−19.3612	−0.740834	−0.370417	+	0.928866i	$0.620785\pi$
$684$	−6.90700	−0.264096
$685$	15.5818	0.595349
$686$	−13.5910	−0.518906
$687$	−1.83993	−0.0701978
$688$	11.1868	0.426492
$689$	66.2734	2.52482
$690$	−1.92899	−0.0734356
$691$	−14.2628	−0.542583	−0.271292	−	0.962497i	$-0.587451\pi$
$691$	−14.2628	−0.542583	−0.271292	+	0.962497i	$0.587451\pi$
$692$	−0.400272	−0.0152160
$693$	6.99978	0.265900
$694$	−2.82408	−0.107201
$695$	−18.8003	−0.713134
$696$	18.6421	0.706625
$697$	42.0455	1.59259
$698$	5.00856	0.189577
$699$	17.5212	0.662714
$700$	3.78753	0.143155
$701$	−21.6183	−0.816514	−0.408257	−	0.912867i	$-0.633863\pi$
$701$	−21.6183	−0.816514	−0.408257	+	0.912867i	$0.633863\pi$
$702$	4.68954	0.176995
$703$	−31.5737	−1.19082
$704$	−4.39545	−0.165660
$705$	12.9489	0.487683
$706$	−4.43384	−0.166870
$707$	21.0844	0.792959
$708$	18.2335	0.685259
$709$	−7.37182	−0.276855	−0.138427	−	0.990373i	$-0.544205\pi$
$709$	−7.37182	−0.276855	−0.138427	+	0.990373i	$0.544205\pi$
$710$	−9.00549	−0.337970
$711$	8.73644	0.327642
$712$	18.9961	0.711909
$713$	−9.67052	−0.362164
$714$	6.05855	0.226736
$715$	−18.4735	−0.690868
$716$	26.9540	1.00732
$717$	25.6500	0.957917
$718$	−2.73706	−0.102146
$719$	−43.2839	−1.61422	−0.807109	−	0.590403i	$-0.798969\pi$
$719$	−43.2839	−1.61422	−0.807109	+	0.590403i	$0.798969\pi$
$720$	1.26438	0.0471207
$721$	41.0906	1.53029
$722$	−1.49611	−0.0556794
$723$	−0.0539818	−0.00200761
$724$	−17.8086	−0.661852
$725$	−7.54808	−0.280328
$726$	−2.31658	−0.0859765
$727$	16.3014	0.604584	0.302292	−	0.953215i	$-0.402248\pi$
$727$	16.3014	0.604584	0.302292	+	0.953215i	$0.402248\pi$
$728$	−41.3988	−1.53434
$729$	1.00000	0.0370370
$730$	1.37441	0.0508691
$731$	−30.1669	−1.11576
$732$	5.29977	0.195885
$733$	−3.77640	−0.139484	−0.0697422	−	0.997565i	$-0.522218\pi$
$733$	−3.77640	−0.139484	−0.0697422	+	0.997565i	$0.522218\pi$
$734$	−17.8555	−0.659060
$735$	0.648639	0.0239254
$736$	15.9530	0.588037
$737$	−30.7916	−1.13422
$738$	8.69462	0.320053
$739$	29.8250	1.09713	0.548566	−	0.836107i	$-0.315174\pi$
$739$	29.8250	1.09713	0.548566	+	0.836107i	$0.315174\pi$
$740$	10.3248	0.379547
$741$	−30.5678	−1.12294
$742$	17.7055	0.649990
$743$	36.3591	1.33389	0.666944	−	0.745108i	$-0.267602\pi$
$743$	36.3591	1.33389	0.666944	+	0.745108i	$0.267602\pi$
$744$	−8.72990	−0.320054
$745$	−19.4765	−0.713563
$746$	7.01808	0.256950
$747$	16.7749	0.613762
$748$	−14.2323	−0.520385
$749$	39.0073	1.42530
$750$	0.705071	0.0257456
$751$	−33.3800	−1.21805	−0.609026	−	0.793150i	$-0.708439\pi$
$751$	−33.3800	−1.21805	−0.609026	+	0.793150i	$0.708439\pi$
$752$	−16.3723	−0.597037
$753$	21.4670	0.782301
$754$	35.3970	1.28908
$755$	6.47083	0.235498
$756$	−3.78753	−0.137751
$757$	−28.5763	−1.03862	−0.519311	−	0.854585i	$-0.673811\pi$
$757$	−28.5763	−1.03862	−0.519311	+	0.854585i	$0.673811\pi$
$758$	13.9891	0.508106
$759$	−7.59887	−0.275822
$760$	11.3507	0.411735
$761$	−40.8875	−1.48217	−0.741086	−	0.671410i	$-0.765689\pi$
$761$	−40.8875	−1.48217	−0.741086	+	0.671410i	$0.765689\pi$
$762$	9.36854	0.339386
$763$	23.1623	0.838532
$764$	−24.9239	−0.901714
$765$	−3.40959	−0.123274
$766$	−12.7738	−0.461535
$767$	80.6948	2.91372
$768$	10.6009	0.382528
$769$	40.6464	1.46575	0.732873	−	0.680365i	$-0.238179\pi$
$769$	40.6464	1.46575	0.732873	+	0.680365i	$0.238179\pi$
$770$	−4.93534	−0.177857
$771$	11.1246	0.400643
$772$	31.6325	1.13848
$773$	41.0628	1.47693	0.738464	−	0.674293i	$-0.235552\pi$
$773$	41.0628	1.47693	0.738464	+	0.674293i	$0.235552\pi$
$774$	−6.23822	−0.224228
$775$	3.53469	0.126970
$776$	27.7412	0.995849
$777$	−17.3138	−0.621128
$778$	20.6968	0.742018
$779$	−56.6740	−2.03056
$780$	9.99585	0.357909
$781$	−35.4752	−1.26940
$782$	−6.57708	−0.235196
$783$	7.54808	0.269746
$784$	−0.820127	−0.0292902
$785$	−3.61436	−0.129002
$786$	−5.18459	−0.184928
$787$	29.4169	1.04860	0.524300	−	0.851534i	$-0.324327\pi$
$787$	29.4169	1.04860	0.524300	+	0.851534i	$0.324327\pi$
$788$	0.0988521	0.00352146
$789$	−24.0556	−0.856402
$790$	−6.15981	−0.219156
$791$	17.5291	0.623263
$792$	−6.85976	−0.243751
$793$	23.4548	0.832905
$794$	24.0843	0.854721
$795$	−9.96419	−0.353394
$796$	−29.3121	−1.03894
$797$	5.40002	0.191278	0.0956392	−	0.995416i	$-0.469511\pi$
$797$	5.40002	0.191278	0.0956392	+	0.995416i	$0.469511\pi$
$798$	−8.16645	−0.289089
$799$	44.1504	1.56193
$800$	−5.83103	−0.206158
$801$	7.69143	0.271763
$802$	−0.705071	−0.0248969
$803$	5.41419	0.191063
$804$	16.6611	0.587591
$805$	6.89495	0.243015
$806$	−16.5761	−0.583868
$807$	−12.8612	−0.452735
$808$	−20.6626	−0.726908
$809$	−15.5219	−0.545722	−0.272861	−	0.962054i	$-0.587970\pi$
$809$	−15.5219	−0.545722	−0.272861	+	0.962054i	$0.587970\pi$
$810$	−0.705071	−0.0247737
$811$	19.8542	0.697174	0.348587	−	0.937276i	$-0.386662\pi$
$811$	19.8542	0.697174	0.348587	+	0.937276i	$0.386662\pi$
$812$	−28.5886	−1.00326
$813$	28.9919	1.01679
$814$	−13.4537	−0.471553
$815$	−7.77101	−0.272207
$816$	4.31102	0.150916
$817$	40.6626	1.42260
$818$	25.5878	0.894656
$819$	−16.7622	−0.585718
$820$	18.5328	0.647192
$821$	−1.97007	−0.0687559	−0.0343780	−	0.999409i	$-0.510945\pi$
$821$	−1.97007	−0.0687559	−0.0343780	+	0.999409i	$0.510945\pi$
$822$	10.9863	0.383190
$823$	−28.8124	−1.00434	−0.502168	−	0.864770i	$-0.667464\pi$
$823$	−28.8124	−1.00434	−0.502168	+	0.864770i	$0.667464\pi$
$824$	−40.2686	−1.40282
$825$	2.77748	0.0966995
$826$	21.5583	0.750110
$827$	−28.9319	−1.00606	−0.503030	−	0.864269i	$-0.667781\pi$
$827$	−28.9319	−1.00606	−0.503030	+	0.864269i	$0.667781\pi$
$828$	4.11169	0.142891
$829$	2.97721	0.103403	0.0517014	−	0.998663i	$-0.483536\pi$
$829$	2.97721	0.103403	0.0517014	+	0.998663i	$0.483536\pi$
$830$	−11.8275	−0.410539
$831$	−15.4951	−0.537519
$832$	10.5257	0.364912
$833$	2.21159	0.0766272
$834$	−13.2555	−0.459001
$835$	−7.22835	−0.250147
$836$	19.1841	0.663494
$837$	−3.53469	−0.122177
$838$	21.8177	0.753680
$839$	26.4851	0.914367	0.457183	−	0.889372i	$-0.348858\pi$
$839$	26.4851	0.914367	0.457183	+	0.889372i	$0.348858\pi$
$840$	6.22431	0.214759
$841$	27.9734	0.964601
$842$	15.6589	0.539642
$843$	−3.13265	−0.107894
$844$	−4.74960	−0.163488
$845$	31.2379	1.07462
$846$	9.12989	0.313892
$847$	8.28034	0.284516
$848$	12.5985	0.432635
$849$	−4.75563	−0.163213
$850$	2.40400	0.0824567
$851$	18.7956	0.644305
$852$	19.1954	0.657623
$853$	2.80152	0.0959222	0.0479611	−	0.998849i	$-0.484728\pi$
$853$	2.80152	0.0959222	0.0479611	+	0.998849i	$0.484728\pi$
$854$	6.26616	0.214423
$855$	4.59586	0.157175
$856$	−38.2270	−1.30657
$857$	−0.632041	−0.0215901	−0.0107951	−	0.999942i	$-0.503436\pi$
$857$	−0.632041	−0.0215901	−0.0107951	+	0.999942i	$0.503436\pi$
$858$	−13.0251	−0.444670
$859$	17.7006	0.603937	0.301968	−	0.953318i	$-0.402356\pi$
$859$	17.7006	0.603937	0.301968	+	0.953318i	$0.402356\pi$
$860$	−13.2969	−0.453421
$861$	−31.0778	−1.05913
$862$	−18.6149	−0.634026
$863$	−21.1324	−0.719356	−0.359678	−	0.933076i	$-0.617114\pi$
$863$	−21.1324	−0.719356	−0.359678	+	0.933076i	$0.617114\pi$
$864$	5.83103	0.198376
$865$	0.266337	0.00905574
$866$	−12.5446	−0.426281
$867$	5.37469	0.182534
$868$	13.3878	0.454410
$869$	−24.2653	−0.823144
$870$	−5.32193	−0.180430
$871$	73.7357	2.49844
$872$	−22.6990	−0.768684
$873$	11.2323	0.380154
$874$	8.86539	0.299876
$875$	−2.52019	−0.0851980
$876$	−2.92958	−0.0989813
$877$	−52.2404	−1.76403	−0.882017	−	0.471218i	$-0.843814\pi$
$877$	−52.2404	−1.76403	−0.882017	+	0.471218i	$0.843814\pi$
$878$	19.8700	0.670580
$879$	26.2040	0.883838
$880$	−3.51179	−0.118382
$881$	−35.7591	−1.20476	−0.602378	−	0.798211i	$-0.705780\pi$
$881$	−35.7591	−1.20476	−0.602378	+	0.798211i	$0.705780\pi$
$882$	0.457337	0.0153993
$883$	36.7309	1.23609	0.618046	−	0.786142i	$-0.287924\pi$
$883$	36.7309	1.23609	0.618046	+	0.786142i	$0.287924\pi$
$884$	34.0818	1.14629
$885$	−12.1325	−0.407828
$886$	−18.1325	−0.609172
$887$	−4.11956	−0.138321	−0.0691606	−	0.997606i	$-0.522032\pi$
$887$	−4.11956	−0.138321	−0.0691606	+	0.997606i	$0.522032\pi$
$888$	16.9674	0.569390
$889$	−33.4867	−1.12311
$890$	−5.42300	−0.181780
$891$	−2.77748	−0.0930491
$892$	−5.41030	−0.181150
$893$	−59.5113	−1.99147
$894$	−13.7323	−0.459277
$895$	−17.9350	−0.599500
$896$	−26.5786	−0.887929
$897$	18.1968	0.607574
$898$	−7.35471	−0.245430
$899$	−26.6801	−0.889832
$900$	−1.50287	−0.0500958
$901$	−33.9738	−1.13183
$902$	−24.1491	−0.804078
$903$	22.2978	0.742023
$904$	−17.1785	−0.571347
$905$	11.8497	0.393898
$906$	4.56240	0.151576
$907$	19.2704	0.639864	0.319932	−	0.947441i	$-0.396340\pi$
$907$	19.2704	0.639864	0.319932	+	0.947441i	$0.396340\pi$
$908$	−0.0674701	−0.00223907
$909$	−8.36618	−0.277489
$910$	11.8185	0.391781
$911$	43.3864	1.43746	0.718728	−	0.695292i	$-0.244725\pi$
$911$	43.3864	1.43746	0.718728	+	0.695292i	$0.244725\pi$
$912$	−5.81091	−0.192419
$913$	−46.5920	−1.54197
$914$	11.3001	0.373776
$915$	−3.52643	−0.116580
$916$	−2.76519	−0.0913644
$917$	18.5317	0.611969
$918$	−2.40400	−0.0793440
$919$	−60.4557	−1.99425	−0.997124	−	0.0757813i	$-0.975855\pi$
$919$	−60.4557	−1.99425	−0.997124	+	0.0757813i	$0.975855\pi$
$920$	−6.75703	−0.222773
$921$	16.9318	0.557923
$922$	20.9373	0.689535
$923$	84.9516	2.79621
$924$	10.5198	0.346076
$925$	−6.87002	−0.225885
$926$	25.8806	0.850490
$927$	−16.3046	−0.535512
$928$	44.0131	1.44480
$929$	−13.8451	−0.454244	−0.227122	−	0.973866i	$-0.572932\pi$
$929$	−13.8451	−0.454244	−0.227122	+	0.973866i	$0.572932\pi$
$930$	2.49221	0.0817228
$931$	−2.98106	−0.0977001
$932$	26.3322	0.862541
$933$	11.9940	0.392665
$934$	−20.9543	−0.685646
$935$	9.47007	0.309704
$936$	16.4269	0.536929
$937$	41.2250	1.34676	0.673381	−	0.739296i	$-0.264841\pi$
$937$	41.2250	1.34676	0.673381	+	0.739296i	$0.264841\pi$
$938$	19.6991	0.643200
$939$	−5.11102	−0.166792
$940$	19.4606	0.634733
$941$	−31.0082	−1.01084	−0.505420	−	0.862874i	$-0.668662\pi$
$941$	−31.0082	−1.01084	−0.505420	+	0.862874i	$0.668662\pi$
$942$	−2.54838	−0.0830307
$943$	33.7377	1.09865
$944$	15.3400	0.499275
$945$	2.52019	0.0819818
$946$	17.3265	0.563335
$947$	−21.7324	−0.706209	−0.353105	−	0.935584i	$-0.614874\pi$
$947$	−21.7324	−0.706209	−0.353105	+	0.935584i	$0.614874\pi$
$948$	13.1298	0.426435
$949$	−12.9652	−0.420869
$950$	−3.24041	−0.105133
$951$	5.22567	0.169454
$952$	21.2223	0.687820
$953$	22.2478	0.720676	0.360338	−	0.932822i	$-0.382661\pi$
$953$	22.2478	0.720676	0.360338	+	0.932822i	$0.382661\pi$
$954$	−7.02547	−0.227458
$955$	16.5841	0.536650
$956$	38.5487	1.24675
$957$	−20.9646	−0.677690
$958$	−5.25411	−0.169753
$959$	−39.2690	−1.26806
$960$	−1.58253	−0.0510760
$961$	−18.5059	−0.596966
$962$	32.2173	1.03873
$963$	−15.4779	−0.498769
$964$	−0.0811279	−0.00261295
$965$	−21.0480	−0.677560
$966$	4.86143	0.156414
$967$	55.3691	1.78055	0.890275	−	0.455422i	$-0.150512\pi$
$967$	55.3691	1.78055	0.890275	+	0.455422i	$0.150512\pi$
$968$	−8.11470	−0.260816
$969$	15.6700	0.503393
$970$	−7.91954	−0.254281
$971$	−27.0436	−0.867870	−0.433935	−	0.900944i	$-0.642875\pi$
$971$	−27.0436	−0.867870	−0.433935	+	0.900944i	$0.642875\pi$
$972$	1.50287	0.0482047
$973$	47.3802	1.51894
$974$	−7.80490	−0.250085
$975$	−6.65116	−0.213007
$976$	4.45874	0.142721
$977$	−19.0427	−0.609230	−0.304615	−	0.952476i	$-0.598528\pi$
$977$	−19.0427	−0.609230	−0.304615	+	0.952476i	$0.598528\pi$
$978$	−5.47912	−0.175203
$979$	−21.3628	−0.682758
$980$	0.974823	0.0311396
$981$	−9.19070	−0.293436
$982$	17.0411	0.543804
$983$	−4.56125	−0.145481	−0.0727407	−	0.997351i	$-0.523175\pi$
$983$	−4.56125	−0.145481	−0.0727407	+	0.997351i	$0.523175\pi$
$984$	30.4562	0.970907
$985$	−0.0657754	−0.00209578
$986$	−18.1456	−0.577874
$987$	−32.6337	−1.03874
$988$	−45.9395	−1.46153
$989$	−24.2062	−0.769711
$990$	1.95832	0.0622396
$991$	25.9709	0.824993	0.412496	−	0.910959i	$-0.364657\pi$
$991$	25.9709	0.824993	0.412496	+	0.910959i	$0.364657\pi$
$992$	−20.6109	−0.654397
$993$	6.26140	0.198700
$994$	22.6955	0.719859
$995$	19.5040	0.618319
$996$	25.2106	0.798829
$997$	11.1323	0.352563	0.176281	−	0.984340i	$-0.443593\pi$
$997$	11.1323	0.352563	0.176281	+	0.984340i	$0.443593\pi$
$998$	23.5566	0.745673
$999$	6.87002	0.217358

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.d.1.11	✓	29

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.d.1.11	✓	29	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q-0.705071 q^{2} -1.00000 q^{3} -1.50287 q^{4} +1.00000 q^{5} +0.705071 q^{6} -2.52019 q^{7} +2.46978 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.705071 q^{2} -1.00000 q^{3} -1.50287 q^{4} +1.00000 q^{5} +0.705071 q^{6} -2.52019 q^{7} +2.46978 q^{8} +1.00000 q^{9} -0.705071 q^{10} -2.77748 q^{11} +1.50287 q^{12} +6.65116 q^{13} +1.77691 q^{14} -1.00000 q^{15} +1.26438 q^{16} -3.40959 q^{17} -0.705071 q^{18} +4.59586 q^{19} -1.50287 q^{20} +2.52019 q^{21} +1.95832 q^{22} -2.73589 q^{23} -2.46978 q^{24} +1.00000 q^{25} -4.68954 q^{26} -1.00000 q^{27} +3.78753 q^{28} -7.54808 q^{29} +0.705071 q^{30} +3.53469 q^{31} -5.83103 q^{32} +2.77748 q^{33} +2.40400 q^{34} -2.52019 q^{35} -1.50287 q^{36} -6.87002 q^{37} -3.24041 q^{38} -6.65116 q^{39} +2.46978 q^{40} -12.3315 q^{41} -1.77691 q^{42} +8.84765 q^{43} +4.17420 q^{44} +1.00000 q^{45} +1.92899 q^{46} -12.9489 q^{47} -1.26438 q^{48} -0.648639 q^{49} -0.705071 q^{50} +3.40959 q^{51} -9.99585 q^{52} +9.96419 q^{53} +0.705071 q^{54} -2.77748 q^{55} -6.22431 q^{56} -4.59586 q^{57} +5.32193 q^{58} +12.1325 q^{59} +1.50287 q^{60} +3.52643 q^{61} -2.49221 q^{62} -2.52019 q^{63} +1.58253 q^{64} +6.65116 q^{65} -1.95832 q^{66} +11.0862 q^{67} +5.12419 q^{68} +2.73589 q^{69} +1.77691 q^{70} +12.7725 q^{71} +2.46978 q^{72} -1.94932 q^{73} +4.84386 q^{74} -1.00000 q^{75} -6.90700 q^{76} +6.99978 q^{77} +4.68954 q^{78} +8.73644 q^{79} +1.26438 q^{80} +1.00000 q^{81} +8.69462 q^{82} +16.7749 q^{83} -3.78753 q^{84} -3.40959 q^{85} -6.23822 q^{86} +7.54808 q^{87} -6.85976 q^{88} +7.69143 q^{89} -0.705071 q^{90} -16.7622 q^{91} +4.11169 q^{92} -3.53469 q^{93} +9.12989 q^{94} +4.59586 q^{95} +5.83103 q^{96} +11.2323 q^{97} +0.457337 q^{98} -2.77748 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 29 q - q^{2} - 29 q^{3} + 27 q^{4} + 29 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 29 q^{9}+O(q^{10}) \) 29 * q - q^2 - 29 * q^3 + 27 * q^4 + 29 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 29 * q^9	\( 29 q - q^{2} - 29 q^{3} + 27 q^{4} + 29 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 29 q^{9} - q^{10} - 21 q^{11} - 27 q^{12} - 8 q^{13} - 30 q^{14} - 29 q^{15} + 23 q^{16} - 28 q^{17} - q^{18} - 9 q^{19} + 27 q^{20} - 2 q^{21} - 9 q^{22} + 6 q^{24} + 29 q^{25} - 34 q^{26} - 29 q^{27} + 6 q^{28} - 61 q^{29} + q^{30} - 19 q^{31} - 8 q^{32} + 21 q^{33} - 16 q^{34} + 2 q^{35} + 27 q^{36} - 4 q^{37} + 4 q^{38} + 8 q^{39} - 6 q^{40} - 85 q^{41} + 30 q^{42} + 29 q^{43} - 69 q^{44} + 29 q^{45} - 35 q^{46} - 2 q^{47} - 23 q^{48} + q^{49} - q^{50} + 28 q^{51} - 28 q^{52} - 5 q^{53} + q^{54} - 21 q^{55} - 97 q^{56} + 9 q^{57} + 6 q^{58} - 43 q^{59} - 27 q^{60} - 59 q^{61} - 17 q^{62} + 2 q^{63} - 6 q^{64} - 8 q^{65} + 9 q^{66} + 28 q^{67} - 44 q^{68} - 30 q^{70} - 44 q^{71} - 6 q^{72} - 41 q^{73} - 50 q^{74} - 29 q^{75} - 62 q^{76} - 20 q^{77} + 34 q^{78} - 25 q^{79} + 23 q^{80} + 29 q^{81} - 29 q^{82} - 7 q^{83} - 6 q^{84} - 28 q^{85} - 43 q^{86} + 61 q^{87} - 3 q^{88} - 109 q^{89} - q^{90} - q^{91} - 11 q^{92} + 19 q^{93} - 20 q^{94} - 9 q^{95} + 8 q^{96} - 51 q^{97} - 12 q^{98} - 21 q^{99}+O(q^{100}) \) 29 * q - q^2 - 29 * q^3 + 27 * q^4 + 29 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 29 * q^9 - q^10 - 21 * q^11 - 27 * q^12 - 8 * q^13 - 30 * q^14 - 29 * q^15 + 23 * q^16 - 28 * q^17 - q^18 - 9 * q^19 + 27 * q^20 - 2 * q^21 - 9 * q^22 + 6 * q^24 + 29 * q^25 - 34 * q^26 - 29 * q^27 + 6 * q^28 - 61 * q^29 + q^30 - 19 * q^31 - 8 * q^32 + 21 * q^33 - 16 * q^34 + 2 * q^35 + 27 * q^36 - 4 * q^37 + 4 * q^38 + 8 * q^39 - 6 * q^40 - 85 * q^41 + 30 * q^42 + 29 * q^43 - 69 * q^44 + 29 * q^45 - 35 * q^46 - 2 * q^47 - 23 * q^48 + q^49 - q^50 + 28 * q^51 - 28 * q^52 - 5 * q^53 + q^54 - 21 * q^55 - 97 * q^56 + 9 * q^57 + 6 * q^58 - 43 * q^59 - 27 * q^60 - 59 * q^61 - 17 * q^62 + 2 * q^63 - 6 * q^64 - 8 * q^65 + 9 * q^66 + 28 * q^67 - 44 * q^68 - 30 * q^70 - 44 * q^71 - 6 * q^72 - 41 * q^73 - 50 * q^74 - 29 * q^75 - 62 * q^76 - 20 * q^77 + 34 * q^78 - 25 * q^79 + 23 * q^80 + 29 * q^81 - 29 * q^82 - 7 * q^83 - 6 * q^84 - 28 * q^85 - 43 * q^86 + 61 * q^87 - 3 * q^88 - 109 * q^89 - q^90 - q^91 - 11 * q^92 + 19 * q^93 - 20 * q^94 - 9 * q^95 + 8 * q^96 - 51 * q^97 - 12 * q^98 - 21 * q^99

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