LMFDB - Embedded newform 6034.2.a.p.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, 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("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$0$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.20972 q^{3} +1.00000 q^{4} -3.26323 q^{5} +3.20972 q^{6} +1.00000 q^{7} -1.00000 q^{8} +7.30232 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.20972 q^{3} +1.00000 q^{4} -3.26323 q^{5} +3.20972 q^{6} +1.00000 q^{7} -1.00000 q^{8} +7.30232 q^{9} +3.26323 q^{10} +1.75263 q^{11} -3.20972 q^{12} -5.78210 q^{13} -1.00000 q^{14} +10.4741 q^{15} +1.00000 q^{16} -4.31307 q^{17} -7.30232 q^{18} -1.34257 q^{19} -3.26323 q^{20} -3.20972 q^{21} -1.75263 q^{22} -3.06566 q^{23} +3.20972 q^{24} +5.64866 q^{25} +5.78210 q^{26} -13.8092 q^{27} +1.00000 q^{28} +4.81535 q^{29} -10.4741 q^{30} +2.52082 q^{31} -1.00000 q^{32} -5.62545 q^{33} +4.31307 q^{34} -3.26323 q^{35} +7.30232 q^{36} -1.68120 q^{37} +1.34257 q^{38} +18.5589 q^{39} +3.26323 q^{40} +9.19496 q^{41} +3.20972 q^{42} -4.91018 q^{43} +1.75263 q^{44} -23.8291 q^{45} +3.06566 q^{46} -0.249248 q^{47} -3.20972 q^{48} +1.00000 q^{49} -5.64866 q^{50} +13.8438 q^{51} -5.78210 q^{52} +5.24757 q^{53} +13.8092 q^{54} -5.71923 q^{55} -1.00000 q^{56} +4.30927 q^{57} -4.81535 q^{58} +2.05258 q^{59} +10.4741 q^{60} -8.52006 q^{61} -2.52082 q^{62} +7.30232 q^{63} +1.00000 q^{64} +18.8683 q^{65} +5.62545 q^{66} -14.7126 q^{67} -4.31307 q^{68} +9.83991 q^{69} +3.26323 q^{70} -9.97528 q^{71} -7.30232 q^{72} +3.94038 q^{73} +1.68120 q^{74} -18.1306 q^{75} -1.34257 q^{76} +1.75263 q^{77} -18.5589 q^{78} +7.76592 q^{79} -3.26323 q^{80} +22.4169 q^{81} -9.19496 q^{82} -2.26247 q^{83} -3.20972 q^{84} +14.0745 q^{85} +4.91018 q^{86} -15.4559 q^{87} -1.75263 q^{88} -11.5298 q^{89} +23.8291 q^{90} -5.78210 q^{91} -3.06566 q^{92} -8.09112 q^{93} +0.249248 q^{94} +4.38111 q^{95} +3.20972 q^{96} -16.2584 q^{97} -1.00000 q^{98} +12.7983 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9}+O(q^{10}) $ 27 * q - 27 * q^2 + 4 * q^3 + 27 * q^4 + 9 * q^5 - 4 * q^6 + 27 * q^7 - 27 * q^8 + 35 * q^9	\( 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9} - 9 q^{10} + 24 q^{11} + 4 q^{12} - 13 q^{13} - 27 q^{14} + 16 q^{15} + 27 q^{16} - 5 q^{17} - 35 q^{18} + q^{19} + 9 q^{20} + 4 q^{21} - 24 q^{22} + 32 q^{23} - 4 q^{24} + 30 q^{25} + 13 q^{26} + q^{27} + 27 q^{28} + 26 q^{29} - 16 q^{30} + 21 q^{31} - 27 q^{32} + 7 q^{33} + 5 q^{34} + 9 q^{35} + 35 q^{36} + 4 q^{37} - q^{38} + 13 q^{39} - 9 q^{40} + 31 q^{41} - 4 q^{42} - 13 q^{43} + 24 q^{44} + 19 q^{45} - 32 q^{46} + 41 q^{47} + 4 q^{48} + 27 q^{49} - 30 q^{50} + 21 q^{51} - 13 q^{52} + 29 q^{53} - q^{54} + 9 q^{55} - 27 q^{56} - 26 q^{58} + 36 q^{59} + 16 q^{60} + q^{61} - 21 q^{62} + 35 q^{63} + 27 q^{64} + 46 q^{65} - 7 q^{66} - 2 q^{67} - 5 q^{68} + 43 q^{69} - 9 q^{70} + 70 q^{71} - 35 q^{72} - 21 q^{73} - 4 q^{74} + 37 q^{75} + q^{76} + 24 q^{77} - 13 q^{78} + 19 q^{79} + 9 q^{80} + 67 q^{81} - 31 q^{82} + 25 q^{83} + 4 q^{84} - 6 q^{85} + 13 q^{86} - 9 q^{87} - 24 q^{88} + 85 q^{89} - 19 q^{90} - 13 q^{91} + 32 q^{92} + 23 q^{93} - 41 q^{94} + 77 q^{95} - 4 q^{96} - 2 q^{97} - 27 q^{98} + 38 q^{99}+O(q^{100}) \) 27 * q - 27 * q^2 + 4 * q^3 + 27 * q^4 + 9 * q^5 - 4 * q^6 + 27 * q^7 - 27 * q^8 + 35 * q^9 - 9 * q^10 + 24 * q^11 + 4 * q^12 - 13 * q^13 - 27 * q^14 + 16 * q^15 + 27 * q^16 - 5 * q^17 - 35 * q^18 + q^19 + 9 * q^20 + 4 * q^21 - 24 * q^22 + 32 * q^23 - 4 * q^24 + 30 * q^25 + 13 * q^26 + q^27 + 27 * q^28 + 26 * q^29 - 16 * q^30 + 21 * q^31 - 27 * q^32 + 7 * q^33 + 5 * q^34 + 9 * q^35 + 35 * q^36 + 4 * q^37 - q^38 + 13 * q^39 - 9 * q^40 + 31 * q^41 - 4 * q^42 - 13 * q^43 + 24 * q^44 + 19 * q^45 - 32 * q^46 + 41 * q^47 + 4 * q^48 + 27 * q^49 - 30 * q^50 + 21 * q^51 - 13 * q^52 + 29 * q^53 - q^54 + 9 * q^55 - 27 * q^56 - 26 * q^58 + 36 * q^59 + 16 * q^60 + q^61 - 21 * q^62 + 35 * q^63 + 27 * q^64 + 46 * q^65 - 7 * q^66 - 2 * q^67 - 5 * q^68 + 43 * q^69 - 9 * q^70 + 70 * q^71 - 35 * q^72 - 21 * q^73 - 4 * q^74 + 37 * q^75 + q^76 + 24 * q^77 - 13 * q^78 + 19 * q^79 + 9 * q^80 + 67 * q^81 - 31 * q^82 + 25 * q^83 + 4 * q^84 - 6 * q^85 + 13 * q^86 - 9 * q^87 - 24 * q^88 + 85 * q^89 - 19 * q^90 - 13 * q^91 + 32 * q^92 + 23 * q^93 - 41 * q^94 + 77 * q^95 - 4 * q^96 - 2 * q^97 - 27 * q^98 + 38 * 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
$3$	−3.20972	−1.85313	−0.926567	−	0.376130i	$-0.877255\pi$
$3$	−3.20972	−1.85313	−0.926567	+	0.376130i	$0.877255\pi$
$4$	1.00000	0.500000
$5$	−3.26323	−1.45936	−0.729680	−	0.683789i	$-0.760331\pi$
$5$	−3.26323	−1.45936	−0.729680	+	0.683789i	$0.760331\pi$
$6$	3.20972	1.31036
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	7.30232	2.43411
$10$	3.26323	1.03192
$11$	1.75263	0.528438	0.264219	−	0.964463i	$-0.414886\pi$
$11$	1.75263	0.528438	0.264219	+	0.964463i	$0.414886\pi$
$12$	−3.20972	−0.926567
$13$	−5.78210	−1.60367	−0.801833	−	0.597549i	$-0.796142\pi$
$13$	−5.78210	−1.60367	−0.801833	+	0.597549i	$0.796142\pi$
$14$	−1.00000	−0.267261
$15$	10.4741	2.70439
$16$	1.00000	0.250000
$17$	−4.31307	−1.04607	−0.523037	−	0.852310i	$-0.675201\pi$
$17$	−4.31307	−1.04607	−0.523037	+	0.852310i	$0.675201\pi$
$18$	−7.30232	−1.72117
$19$	−1.34257	−0.308006	−0.154003	−	0.988070i	$-0.549217\pi$
$19$	−1.34257	−0.308006	−0.154003	+	0.988070i	$0.549217\pi$
$20$	−3.26323	−0.729680
$21$	−3.20972	−0.700419
$22$	−1.75263	−0.373662
$23$	−3.06566	−0.639233	−0.319617	−	0.947547i	$-0.603554\pi$
$23$	−3.06566	−0.639233	−0.319617	+	0.947547i	$0.603554\pi$
$24$	3.20972	0.655182
$25$	5.64866	1.12973
$26$	5.78210	1.13396
$27$	−13.8092	−2.65759
$28$	1.00000	0.188982
$29$	4.81535	0.894187	0.447094	−	0.894487i	$-0.352459\pi$
$29$	4.81535	0.894187	0.447094	+	0.894487i	$0.352459\pi$
$30$	−10.4741	−1.91229
$31$	2.52082	0.452752	0.226376	−	0.974040i	$-0.427312\pi$
$31$	2.52082	0.452752	0.226376	+	0.974040i	$0.427312\pi$
$32$	−1.00000	−0.176777
$33$	−5.62545	−0.979266
$34$	4.31307	0.739686
$35$	−3.26323	−0.551586
$36$	7.30232	1.21705
$37$	−1.68120	−0.276387	−0.138194	−	0.990405i	$-0.544130\pi$
$37$	−1.68120	−0.276387	−0.138194	+	0.990405i	$0.544130\pi$
$38$	1.34257	0.217793
$39$	18.5589	2.97181
$40$	3.26323	0.515962
$41$	9.19496	1.43601	0.718005	−	0.696038i	$-0.245055\pi$
$41$	9.19496	1.43601	0.718005	+	0.696038i	$0.245055\pi$
$42$	3.20972	0.495271
$43$	−4.91018	−0.748796	−0.374398	−	0.927268i	$-0.622151\pi$
$43$	−4.91018	−0.748796	−0.374398	+	0.927268i	$0.622151\pi$
$44$	1.75263	0.264219
$45$	−23.8291	−3.55224
$46$	3.06566	0.452006
$47$	−0.249248	−0.0363566	−0.0181783	−	0.999835i	$-0.505787\pi$
$47$	−0.249248	−0.0363566	−0.0181783	+	0.999835i	$0.505787\pi$
$48$	−3.20972	−0.463284
$49$	1.00000	0.142857
$50$	−5.64866	−0.798842
$51$	13.8438	1.93851
$52$	−5.78210	−0.801833
$53$	5.24757	0.720809	0.360405	−	0.932796i	$-0.382639\pi$
$53$	5.24757	0.720809	0.360405	+	0.932796i	$0.382639\pi$
$54$	13.8092	1.87920
$55$	−5.71923	−0.771181
$56$	−1.00000	−0.133631
$57$	4.30927	0.570777
$58$	−4.81535	−0.632286
$59$	2.05258	0.267223	0.133611	−	0.991034i	$-0.457343\pi$
$59$	2.05258	0.267223	0.133611	+	0.991034i	$0.457343\pi$
$60$	10.4741	1.35220
$61$	−8.52006	−1.09088	−0.545441	−	0.838149i	$-0.683638\pi$
$61$	−8.52006	−1.09088	−0.545441	+	0.838149i	$0.683638\pi$
$62$	−2.52082	−0.320144
$63$	7.30232	0.920006
$64$	1.00000	0.125000
$65$	18.8683	2.34033
$66$	5.62545	0.692446
$67$	−14.7126	−1.79744	−0.898718	−	0.438527i	$-0.855500\pi$
$67$	−14.7126	−1.79744	−0.898718	+	0.438527i	$0.855500\pi$
$68$	−4.31307	−0.523037
$69$	9.83991	1.18459
$70$	3.26323	0.390030
$71$	−9.97528	−1.18385	−0.591924	−	0.805994i	$-0.701632\pi$
$71$	−9.97528	−1.18385	−0.591924	+	0.805994i	$0.701632\pi$
$72$	−7.30232	−0.860586
$73$	3.94038	0.461187	0.230594	−	0.973050i	$-0.425933\pi$
$73$	3.94038	0.461187	0.230594	+	0.973050i	$0.425933\pi$
$74$	1.68120	0.195435
$75$	−18.1306	−2.09355
$76$	−1.34257	−0.154003
$77$	1.75263	0.199731
$78$	−18.5589	−2.10139
$79$	7.76592	0.873735	0.436867	−	0.899526i	$-0.356088\pi$
$79$	7.76592	0.873735	0.436867	+	0.899526i	$0.356088\pi$
$80$	−3.26323	−0.364840
$81$	22.4169	2.49077
$82$	−9.19496	−1.01541
$83$	−2.26247	−0.248339	−0.124169	−	0.992261i	$-0.539627\pi$
$83$	−2.26247	−0.248339	−0.124169	+	0.992261i	$0.539627\pi$
$84$	−3.20972	−0.350209
$85$	14.0745	1.52660
$86$	4.91018	0.529479
$87$	−15.4559	−1.65705
$88$	−1.75263	−0.186831
$89$	−11.5298	−1.22216	−0.611081	−	0.791568i	$-0.709265\pi$
$89$	−11.5298	−1.22216	−0.611081	+	0.791568i	$0.709265\pi$
$90$	23.8291	2.51181
$91$	−5.78210	−0.606129
$92$	−3.06566	−0.319617
$93$	−8.09112	−0.839010
$94$	0.249248	0.0257080
$95$	4.38111	0.449492
$96$	3.20972	0.327591
$97$	−16.2584	−1.65079	−0.825393	−	0.564558i	$-0.809047\pi$
$97$	−16.2584	−1.65079	−0.825393	+	0.564558i	$0.809047\pi$
$98$	−1.00000	−0.101015
$99$	12.7983	1.28627
$100$	5.64866	0.564866
$101$	−6.03468	−0.600473	−0.300237	−	0.953865i	$-0.597066\pi$
$101$	−6.03468	−0.600473	−0.300237	+	0.953865i	$0.597066\pi$
$102$	−13.8438	−1.37074
$103$	2.35140	0.231691	0.115845	−	0.993267i	$-0.463042\pi$
$103$	2.35140	0.231691	0.115845	+	0.993267i	$0.463042\pi$
$104$	5.78210	0.566981
$105$	10.4741	1.02216
$106$	−5.24757	−0.509689
$107$	−1.84126	−0.178001	−0.0890006	−	0.996032i	$-0.528367\pi$
$107$	−1.84126	−0.178001	−0.0890006	+	0.996032i	$0.528367\pi$
$108$	−13.8092	−1.32880
$109$	−0.988387	−0.0946703	−0.0473351	−	0.998879i	$-0.515073\pi$
$109$	−0.988387	−0.0946703	−0.0473351	+	0.998879i	$0.515073\pi$
$110$	5.71923	0.545307
$111$	5.39618	0.512182
$112$	1.00000	0.0944911
$113$	−3.23106	−0.303952	−0.151976	−	0.988384i	$-0.548564\pi$
$113$	−3.23106	−0.303952	−0.151976	+	0.988384i	$0.548564\pi$
$114$	−4.30927	−0.403600
$115$	10.0039	0.932872
$116$	4.81535	0.447094
$117$	−42.2227	−3.90349
$118$	−2.05258	−0.188955
$119$	−4.31307	−0.395379
$120$	−10.4741	−0.956147
$121$	−7.92829	−0.720754
$122$	8.52006	0.771370
$123$	−29.5133	−2.66112
$124$	2.52082	0.226376
$125$	−2.11674	−0.189327
$126$	−7.30232	−0.650542
$127$	−13.0810	−1.16075	−0.580375	−	0.814349i	$-0.697094\pi$
$127$	−13.0810	−1.16075	−0.580375	+	0.814349i	$0.697094\pi$
$128$	−1.00000	−0.0883883
$129$	15.7603	1.38762
$130$	−18.8683	−1.65486
$131$	−1.28871	−0.112595	−0.0562973	−	0.998414i	$-0.517929\pi$
$131$	−1.28871	−0.112595	−0.0562973	+	0.998414i	$0.517929\pi$
$132$	−5.62545	−0.489633
$133$	−1.34257	−0.116415
$134$	14.7126	1.27098
$135$	45.0627	3.87838
$136$	4.31307	0.369843
$137$	3.34661	0.285920	0.142960	−	0.989728i	$-0.454338\pi$
$137$	3.34661	0.285920	0.142960	+	0.989728i	$0.454338\pi$
$138$	−9.83991	−0.837628
$139$	−17.4472	−1.47985	−0.739926	−	0.672688i	$-0.765140\pi$
$139$	−17.4472	−1.47985	−0.739926	+	0.672688i	$0.765140\pi$
$140$	−3.26323	−0.275793
$141$	0.800018	0.0673737
$142$	9.97528	0.837107
$143$	−10.1339	−0.847437
$144$	7.30232	0.608527
$145$	−15.7136	−1.30494
$146$	−3.94038	−0.326109
$147$	−3.20972	−0.264733
$148$	−1.68120	−0.138194
$149$	−10.3872	−0.850953	−0.425477	−	0.904969i	$-0.639894\pi$
$149$	−10.3872	−0.850953	−0.425477	+	0.904969i	$0.639894\pi$
$150$	18.1306	1.48036
$151$	−20.2165	−1.64520	−0.822599	−	0.568621i	$-0.807477\pi$
$151$	−20.2165	−1.64520	−0.822599	+	0.568621i	$0.807477\pi$
$152$	1.34257	0.108897
$153$	−31.4954	−2.54625
$154$	−1.75263	−0.141231
$155$	−8.22600	−0.660728
$156$	18.5589	1.48590
$157$	−4.91669	−0.392395	−0.196197	−	0.980564i	$-0.562859\pi$
$157$	−4.91669	−0.392395	−0.196197	+	0.980564i	$0.562859\pi$
$158$	−7.76592	−0.617824
$159$	−16.8432	−1.33576
$160$	3.26323	0.257981
$161$	−3.06566	−0.241608
$162$	−22.4169	−1.76124
$163$	−14.0830	−1.10307	−0.551534	−	0.834152i	$-0.685957\pi$
$163$	−14.0830	−1.10307	−0.551534	+	0.834152i	$0.685957\pi$
$164$	9.19496	0.718005
$165$	18.3571	1.42910
$166$	2.26247	0.175602
$167$	15.8303	1.22498	0.612491	−	0.790477i	$-0.290167\pi$
$167$	15.8303	1.22498	0.612491	+	0.790477i	$0.290167\pi$
$168$	3.20972	0.247635
$169$	20.4327	1.57174
$170$	−14.0745	−1.07947
$171$	−9.80386	−0.749720
$172$	−4.91018	−0.374398
$173$	7.73137	0.587805	0.293903	−	0.955835i	$-0.405046\pi$
$173$	7.73137	0.587805	0.293903	+	0.955835i	$0.405046\pi$
$174$	15.4559	1.17171
$175$	5.64866	0.426999
$176$	1.75263	0.132109
$177$	−6.58820	−0.495200
$178$	11.5298	0.864199
$179$	7.99270	0.597402	0.298701	−	0.954347i	$-0.403447\pi$
$179$	7.99270	0.597402	0.298701	+	0.954347i	$0.403447\pi$
$180$	−23.8291	−1.77612
$181$	−20.9632	−1.55818	−0.779091	−	0.626911i	$-0.784319\pi$
$181$	−20.9632	−1.55818	−0.779091	+	0.626911i	$0.784319\pi$
$182$	5.78210	0.428598
$183$	27.3470	2.02155
$184$	3.06566	0.226003
$185$	5.48613	0.403349
$186$	8.09112	0.593270
$187$	−7.55922	−0.552785
$188$	−0.249248	−0.0181783
$189$	−13.8092	−1.00447
$190$	−4.38111	−0.317839
$191$	7.33445	0.530702	0.265351	−	0.964152i	$-0.414512\pi$
$191$	7.33445	0.530702	0.265351	+	0.964152i	$0.414512\pi$
$192$	−3.20972	−0.231642
$193$	8.15652	0.587119	0.293560	−	0.955941i	$-0.405160\pi$
$193$	8.15652	0.587119	0.293560	+	0.955941i	$0.405160\pi$
$194$	16.2584	1.16728
$195$	−60.5620	−4.33694
$196$	1.00000	0.0714286
$197$	−14.4811	−1.03174	−0.515869	−	0.856667i	$-0.672531\pi$
$197$	−14.4811	−1.03174	−0.515869	+	0.856667i	$0.672531\pi$
$198$	−12.7983	−0.909533
$199$	7.88099	0.558669	0.279334	−	0.960194i	$-0.409886\pi$
$199$	7.88099	0.558669	0.279334	+	0.960194i	$0.409886\pi$
$200$	−5.64866	−0.399421
$201$	47.2235	3.33089
$202$	6.03468	0.424599
$203$	4.81535	0.337971
$204$	13.8438	0.969257
$205$	−30.0052	−2.09566
$206$	−2.35140	−0.163830
$207$	−22.3864	−1.55596
$208$	−5.78210	−0.400916
$209$	−2.35302	−0.162762
$210$	−10.4741	−0.722779
$211$	−3.08895	−0.212652	−0.106326	−	0.994331i	$-0.533909\pi$
$211$	−3.08895	−0.212652	−0.106326	+	0.994331i	$0.533909\pi$
$212$	5.24757	0.360405
$213$	32.0179	2.19383
$214$	1.84126	0.125866
$215$	16.0231	1.09276
$216$	13.8092	0.939600
$217$	2.52082	0.171124
$218$	0.988387	0.0669420
$219$	−12.6475	−0.854641
$220$	−5.71923	−0.385591
$221$	24.9386	1.67755
$222$	−5.39618	−0.362168
$223$	−5.96555	−0.399483	−0.199741	−	0.979849i	$-0.564010\pi$
$223$	−5.96555	−0.399483	−0.199741	+	0.979849i	$0.564010\pi$
$224$	−1.00000	−0.0668153
$225$	41.2484	2.74989
$226$	3.23106	0.214927
$227$	15.6138	1.03632	0.518161	−	0.855283i	$-0.326617\pi$
$227$	15.6138	1.03632	0.518161	+	0.855283i	$0.326617\pi$
$228$	4.30927	0.285388
$229$	0.765455	0.0505827	0.0252913	−	0.999680i	$-0.491949\pi$
$229$	0.765455	0.0505827	0.0252913	+	0.999680i	$0.491949\pi$
$230$	−10.0039	−0.659640
$231$	−5.62545	−0.370128
$232$	−4.81535	−0.316143
$233$	−7.86679	−0.515371	−0.257685	−	0.966229i	$-0.582960\pi$
$233$	−7.86679	−0.515371	−0.257685	+	0.966229i	$0.582960\pi$
$234$	42.2227	2.76019
$235$	0.813355	0.0530574
$236$	2.05258	0.133611
$237$	−24.9265	−1.61915
$238$	4.31307	0.279575
$239$	−18.3446	−1.18661	−0.593307	−	0.804976i	$-0.702178\pi$
$239$	−18.3446	−1.18661	−0.593307	+	0.804976i	$0.702178\pi$
$240$	10.4741	0.676098
$241$	0.0843460	0.00543320	0.00271660	−	0.999996i	$-0.499135\pi$
$241$	0.0843460	0.00543320	0.00271660	+	0.999996i	$0.499135\pi$
$242$	7.92829	0.509650
$243$	−30.5243	−1.95813
$244$	−8.52006	−0.545441
$245$	−3.26323	−0.208480
$246$	29.5133	1.88170
$247$	7.76286	0.493939
$248$	−2.52082	−0.160072
$249$	7.26191	0.460205
$250$	2.11674	0.133875
$251$	−11.7992	−0.744756	−0.372378	−	0.928081i	$-0.621458\pi$
$251$	−11.7992	−0.744756	−0.372378	+	0.928081i	$0.621458\pi$
$252$	7.30232	0.460003
$253$	−5.37296	−0.337795
$254$	13.0810	0.820774
$255$	−45.1754	−2.82899
$256$	1.00000	0.0625000
$257$	−2.67338	−0.166761	−0.0833805	−	0.996518i	$-0.526572\pi$
$257$	−2.67338	−0.166761	−0.0833805	+	0.996518i	$0.526572\pi$
$258$	−15.7603	−0.981195
$259$	−1.68120	−0.104465
$260$	18.8683	1.17016
$261$	35.1632	2.17655
$262$	1.28871	0.0796165
$263$	21.2094	1.30782	0.653912	−	0.756570i	$-0.273127\pi$
$263$	21.2094	1.30782	0.653912	+	0.756570i	$0.273127\pi$
$264$	5.62545	0.346223
$265$	−17.1240	−1.05192
$266$	1.34257	0.0823181
$267$	37.0076	2.26483
$268$	−14.7126	−0.898718
$269$	−22.3640	−1.36356	−0.681780	−	0.731557i	$-0.738794\pi$
$269$	−22.3640	−1.36356	−0.681780	+	0.731557i	$0.738794\pi$
$270$	−45.0627	−2.74243
$271$	24.5851	1.49344	0.746720	−	0.665139i	$-0.231628\pi$
$271$	24.5851	1.49344	0.746720	+	0.665139i	$0.231628\pi$
$272$	−4.31307	−0.261518
$273$	18.5589	1.12324
$274$	−3.34661	−0.202176
$275$	9.90002	0.596994
$276$	9.83991	0.592293
$277$	28.2020	1.69449	0.847247	−	0.531199i	$-0.178258\pi$
$277$	28.2020	1.69449	0.847247	+	0.531199i	$0.178258\pi$
$278$	17.4472	1.04641
$279$	18.4078	1.10205
$280$	3.26323	0.195015
$281$	0.195909	0.0116869	0.00584347	−	0.999983i	$-0.498140\pi$
$281$	0.195909	0.0116869	0.00584347	+	0.999983i	$0.498140\pi$
$282$	−0.800018	−0.0476404
$283$	30.4497	1.81004	0.905022	−	0.425365i	$-0.139854\pi$
$283$	30.4497	1.81004	0.905022	+	0.425365i	$0.139854\pi$
$284$	−9.97528	−0.591924
$285$	−14.0621	−0.832969
$286$	10.1339	0.599229
$287$	9.19496	0.542761
$288$	−7.30232	−0.430293
$289$	1.60259	0.0942702
$290$	15.7136	0.922733
$291$	52.1848	3.05913
$292$	3.94038	0.230594
$293$	1.33681	0.0780972	0.0390486	−	0.999237i	$-0.487567\pi$
$293$	1.33681	0.0780972	0.0390486	+	0.999237i	$0.487567\pi$
$294$	3.20972	0.187195
$295$	−6.69803	−0.389974
$296$	1.68120	0.0977176
$297$	−24.2025	−1.40437
$298$	10.3872	0.601715
$299$	17.7259	1.02512
$300$	−18.1306	−1.04677
$301$	−4.91018	−0.283018
$302$	20.2165	1.16333
$303$	19.3697	1.11276
$304$	−1.34257	−0.0770016
$305$	27.8029	1.59199
$306$	31.4954	1.80047
$307$	19.1761	1.09444	0.547219	−	0.836989i	$-0.315686\pi$
$307$	19.1761	1.09444	0.547219	+	0.836989i	$0.315686\pi$
$308$	1.75263	0.0998653
$309$	−7.54736	−0.429354
$310$	8.22600	0.467205
$311$	15.8505	0.898802	0.449401	−	0.893330i	$-0.351637\pi$
$311$	15.8505	0.898802	0.449401	+	0.893330i	$0.351637\pi$
$312$	−18.5589	−1.05069
$313$	−31.0957	−1.75763	−0.878816	−	0.477161i	$-0.841666\pi$
$313$	−31.0957	−1.75763	−0.878816	+	0.477161i	$0.841666\pi$
$314$	4.91669	0.277465
$315$	−23.8291	−1.34262
$316$	7.76592	0.436867
$317$	−5.87269	−0.329843	−0.164921	−	0.986307i	$-0.552737\pi$
$317$	−5.87269	−0.329843	−0.164921	+	0.986307i	$0.552737\pi$
$318$	16.8432	0.944522
$319$	8.43952	0.472522
$320$	−3.26323	−0.182420
$321$	5.90993	0.329860
$322$	3.06566	0.170842
$323$	5.79059	0.322197
$324$	22.4169	1.24538
$325$	−32.6611	−1.81171
$326$	14.0830	0.779988
$327$	3.17245	0.175437
$328$	−9.19496	−0.507706
$329$	−0.249248	−0.0137415
$330$	−18.3571	−1.01053
$331$	−34.2790	−1.88414	−0.942071	−	0.335412i	$-0.891124\pi$
$331$	−34.2790	−1.88414	−0.942071	+	0.335412i	$0.891124\pi$
$332$	−2.26247	−0.124169
$333$	−12.2766	−0.672756
$334$	−15.8303	−0.866194
$335$	48.0107	2.62311
$336$	−3.20972	−0.175105
$337$	5.97151	0.325289	0.162644	−	0.986685i	$-0.447998\pi$
$337$	5.97151	0.325289	0.162644	+	0.986685i	$0.447998\pi$
$338$	−20.4327	−1.11139
$339$	10.3708	0.563264
$340$	14.0745	0.763299
$341$	4.41806	0.239251
$342$	9.80386	0.530132
$343$	1.00000	0.0539949
$344$	4.91018	0.264739
$345$	−32.1099	−1.72874
$346$	−7.73137	−0.415641
$347$	34.7187	1.86380	0.931899	−	0.362717i	$-0.118151\pi$
$347$	34.7187	1.86380	0.931899	+	0.362717i	$0.118151\pi$
$348$	−15.4559	−0.828524
$349$	−10.7515	−0.575515	−0.287757	−	0.957703i	$-0.592910\pi$
$349$	−10.7515	−0.575515	−0.287757	+	0.957703i	$0.592910\pi$
$350$	−5.64866	−0.301934
$351$	79.8464	4.26189
$352$	−1.75263	−0.0934155
$353$	−14.1019	−0.750567	−0.375284	−	0.926910i	$-0.622455\pi$
$353$	−14.1019	−0.750567	−0.375284	+	0.926910i	$0.622455\pi$
$354$	6.58820	0.350159
$355$	32.5516	1.72766
$356$	−11.5298	−0.611081
$357$	13.8438	0.732690
$358$	−7.99270	−0.422427
$359$	2.36436	0.124786	0.0623929	−	0.998052i	$-0.480127\pi$
$359$	2.36436	0.124786	0.0623929	+	0.998052i	$0.480127\pi$
$360$	23.8291	1.25591
$361$	−17.1975	−0.905132
$362$	20.9632	1.10180
$363$	25.4476	1.33565
$364$	−5.78210	−0.303064
$365$	−12.8584	−0.673038
$366$	−27.3470	−1.42945
$367$	−13.3791	−0.698382	−0.349191	−	0.937052i	$-0.613544\pi$
$367$	−13.3791	−0.698382	−0.349191	+	0.937052i	$0.613544\pi$
$368$	−3.06566	−0.159808
$369$	67.1445	3.49540
$370$	−5.48613	−0.285210
$371$	5.24757	0.272440
$372$	−8.09112	−0.419505
$373$	8.95913	0.463886	0.231943	−	0.972729i	$-0.425492\pi$
$373$	8.95913	0.463886	0.231943	+	0.972729i	$0.425492\pi$
$374$	7.55922	0.390878
$375$	6.79416	0.350849
$376$	0.249248	0.0128540
$377$	−27.8428	−1.43398
$378$	13.8092	0.710271
$379$	−19.6213	−1.00788	−0.503940	−	0.863738i	$-0.668117\pi$
$379$	−19.6213	−1.00788	−0.503940	+	0.863738i	$0.668117\pi$
$380$	4.38111	0.224746
$381$	41.9863	2.15102
$382$	−7.33445	−0.375263
$383$	14.3949	0.735546	0.367773	−	0.929916i	$-0.380120\pi$
$383$	14.3949	0.735546	0.367773	+	0.929916i	$0.380120\pi$
$384$	3.20972	0.163795
$385$	−5.71923	−0.291479
$386$	−8.15652	−0.415156
$387$	−35.8557	−1.82265
$388$	−16.2584	−0.825393
$389$	−29.1139	−1.47614	−0.738068	−	0.674727i	$-0.764261\pi$
$389$	−29.1139	−1.47614	−0.738068	+	0.674727i	$0.764261\pi$
$390$	60.5620	3.06668
$391$	13.2224	0.668685
$392$	−1.00000	−0.0505076
$393$	4.13639	0.208653
$394$	14.4811	0.729550
$395$	−25.3420	−1.27509
$396$	12.7983	0.643137
$397$	2.64398	0.132698	0.0663488	−	0.997796i	$-0.478865\pi$
$397$	2.64398	0.132698	0.0663488	+	0.997796i	$0.478865\pi$
$398$	−7.88099	−0.395038
$399$	4.30927	0.215733
$400$	5.64866	0.282433
$401$	−9.34906	−0.466870	−0.233435	−	0.972372i	$-0.574997\pi$
$401$	−9.34906	−0.466870	−0.233435	+	0.972372i	$0.574997\pi$
$402$	−47.2235	−2.35530
$403$	−14.5756	−0.726063
$404$	−6.03468	−0.300237
$405$	−73.1515	−3.63493
$406$	−4.81535	−0.238982
$407$	−2.94652	−0.146053
$408$	−13.8438	−0.685369
$409$	25.8220	1.27681	0.638407	−	0.769699i	$-0.279594\pi$
$409$	25.8220	1.27681	0.638407	+	0.769699i	$0.279594\pi$
$410$	30.0052	1.48185
$411$	−10.7417	−0.529849
$412$	2.35140	0.115845
$413$	2.05258	0.101001
$414$	22.3864	1.10023
$415$	7.38297	0.362416
$416$	5.78210	0.283491
$417$	56.0007	2.74237
$418$	2.35302	0.115090
$419$	−30.5806	−1.49396	−0.746981	−	0.664846i	$-0.768497\pi$
$419$	−30.5806	−1.49396	−0.746981	+	0.664846i	$0.768497\pi$
$420$	10.4741	0.511082
$421$	8.20269	0.399775	0.199887	−	0.979819i	$-0.435942\pi$
$421$	8.20269	0.399775	0.199887	+	0.979819i	$0.435942\pi$
$422$	3.08895	0.150368
$423$	−1.82009	−0.0884959
$424$	−5.24757	−0.254845
$425$	−24.3631	−1.18178
$426$	−32.0179	−1.55127
$427$	−8.52006	−0.412315
$428$	−1.84126	−0.0890006
$429$	32.5269	1.57042
$430$	−16.0231	−0.772700
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	−13.8092	−0.664398
$433$	−12.6661	−0.608695	−0.304347	−	0.952561i	$-0.598438\pi$
$433$	−12.6661	−0.608695	−0.304347	+	0.952561i	$0.598438\pi$
$434$	−2.52082	−0.121003
$435$	50.4362	2.41823
$436$	−0.988387	−0.0473351
$437$	4.11585	0.196888
$438$	12.6475	0.604323
$439$	−30.8544	−1.47260	−0.736299	−	0.676656i	$-0.763428\pi$
$439$	−30.8544	−1.47260	−0.736299	+	0.676656i	$0.763428\pi$
$440$	5.71923	0.272654
$441$	7.30232	0.347729
$442$	−24.9386	−1.18621
$443$	20.3375	0.966265	0.483133	−	0.875547i	$-0.339499\pi$
$443$	20.3375	0.966265	0.483133	+	0.875547i	$0.339499\pi$
$444$	5.39618	0.256091
$445$	37.6245	1.78357
$446$	5.96555	0.282477
$447$	33.3400	1.57693
$448$	1.00000	0.0472456
$449$	33.7305	1.59184	0.795920	−	0.605402i	$-0.206988\pi$
$449$	33.7305	1.59184	0.795920	+	0.605402i	$0.206988\pi$
$450$	−41.2484	−1.94447
$451$	16.1154	0.758842
$452$	−3.23106	−0.151976
$453$	64.8895	3.04877
$454$	−15.6138	−0.732790
$455$	18.8683	0.884560
$456$	−4.30927	−0.201800
$457$	33.1453	1.55047	0.775235	−	0.631673i	$-0.217632\pi$
$457$	33.1453	1.55047	0.775235	+	0.631673i	$0.217632\pi$
$458$	−0.765455	−0.0357673
$459$	59.5603	2.78004
$460$	10.0039	0.466436
$461$	−19.4758	−0.907081	−0.453540	−	0.891236i	$-0.649839\pi$
$461$	−19.4758	−0.907081	−0.453540	+	0.891236i	$0.649839\pi$
$462$	5.62545	0.261720
$463$	7.68121	0.356976	0.178488	−	0.983942i	$-0.442879\pi$
$463$	7.68121	0.356976	0.178488	+	0.983942i	$0.442879\pi$
$464$	4.81535	0.223547
$465$	26.4032	1.22442
$466$	7.86679	0.364422
$467$	−14.0157	−0.648570	−0.324285	−	0.945959i	$-0.605124\pi$
$467$	−14.0157	−0.648570	−0.324285	+	0.945959i	$0.605124\pi$
$468$	−42.2227	−1.95175
$469$	−14.7126	−0.679367
$470$	−0.813355	−0.0375173
$471$	15.7812	0.727161
$472$	−2.05258	−0.0944775
$473$	−8.60574	−0.395692
$474$	24.9265	1.14491
$475$	−7.58372	−0.347965
$476$	−4.31307	−0.197689
$477$	38.3194	1.75453
$478$	18.3446	0.839063
$479$	−11.0015	−0.502672	−0.251336	−	0.967900i	$-0.580870\pi$
$479$	−11.0015	−0.502672	−0.251336	+	0.967900i	$0.580870\pi$
$480$	−10.4741	−0.478073
$481$	9.72085	0.443233
$482$	−0.0843460	−0.00384186
$483$	9.83991	0.447731
$484$	−7.92829	−0.360377
$485$	53.0548	2.40909
$486$	30.5243	1.38461
$487$	43.1683	1.95614	0.978071	−	0.208271i	$-0.0667836\pi$
$487$	43.1683	1.95614	0.978071	+	0.208271i	$0.0667836\pi$
$488$	8.52006	0.385685
$489$	45.2027	2.04413
$490$	3.26323	0.147418
$491$	12.7932	0.577349	0.288675	−	0.957427i	$-0.406785\pi$
$491$	12.7932	0.577349	0.288675	+	0.957427i	$0.406785\pi$
$492$	−29.5133	−1.33056
$493$	−20.7689	−0.935386
$494$	−7.76286	−0.349268
$495$	−41.7637	−1.87714
$496$	2.52082	0.113188
$497$	−9.97528	−0.447453
$498$	−7.26191	−0.325414
$499$	−9.60594	−0.430021	−0.215010	−	0.976612i	$-0.568979\pi$
$499$	−9.60594	−0.430021	−0.215010	+	0.976612i	$0.568979\pi$
$500$	−2.11674	−0.0946636
$501$	−50.8108	−2.27006
$502$	11.7992	0.526622
$503$	30.4654	1.35839	0.679193	−	0.733959i	$-0.262330\pi$
$503$	30.4654	1.35839	0.679193	+	0.733959i	$0.262330\pi$
$504$	−7.30232	−0.325271
$505$	19.6926	0.876307
$506$	5.37296	0.238857
$507$	−65.5832	−2.91265
$508$	−13.0810	−0.580375
$509$	27.8516	1.23450	0.617251	−	0.786766i	$-0.288246\pi$
$509$	27.8516	1.23450	0.617251	+	0.786766i	$0.288246\pi$
$510$	45.1754	2.00040
$511$	3.94038	0.174312
$512$	−1.00000	−0.0441942
$513$	18.5399	0.818555
$514$	2.67338	0.117918
$515$	−7.67317	−0.338120
$516$	15.7603	0.693810
$517$	−0.436840	−0.0192122
$518$	1.68120	0.0738676
$519$	−24.8155	−1.08928
$520$	−18.8683	−0.827430
$521$	33.3321	1.46031	0.730154	−	0.683283i	$-0.239448\pi$
$521$	33.3321	1.46031	0.730154	+	0.683283i	$0.239448\pi$
$522$	−35.1632	−1.53905
$523$	1.96097	0.0857474	0.0428737	−	0.999081i	$-0.486349\pi$
$523$	1.96097	0.0857474	0.0428737	+	0.999081i	$0.486349\pi$
$524$	−1.28871	−0.0562973
$525$	−18.1306	−0.791286
$526$	−21.2094	−0.924772
$527$	−10.8725	−0.473612
$528$	−5.62545	−0.244817
$529$	−13.6018	−0.591381
$530$	17.1240	0.743820
$531$	14.9886	0.650449
$532$	−1.34257	−0.0582077
$533$	−53.1661	−2.30288
$534$	−37.0076	−1.60148
$535$	6.00845	0.259768
$536$	14.7126	0.635490
$537$	−25.6543	−1.10707
$538$	22.3640	0.964183
$539$	1.75263	0.0754911
$540$	45.0627	1.93919
$541$	−30.1569	−1.29655	−0.648273	−	0.761408i	$-0.724509\pi$
$541$	−30.1569	−1.29655	−0.648273	+	0.761408i	$0.724509\pi$
$542$	−24.5851	−1.05602
$543$	67.2860	2.88752
$544$	4.31307	0.184921
$545$	3.22533	0.138158
$546$	−18.5589	−0.794249
$547$	−13.2867	−0.568098	−0.284049	−	0.958810i	$-0.591678\pi$
$547$	−13.2867	−0.568098	−0.284049	+	0.958810i	$0.591678\pi$
$548$	3.34661	0.142960
$549$	−62.2162	−2.65532
$550$	−9.90002	−0.422138
$551$	−6.46493	−0.275415
$552$	−9.83991	−0.418814
$553$	7.76592	0.330241
$554$	−28.2020	−1.19819
$555$	−17.6090	−0.747459
$556$	−17.4472	−0.739926
$557$	−1.36995	−0.0580466	−0.0290233	−	0.999579i	$-0.509240\pi$
$557$	−1.36995	−0.0580466	−0.0290233	+	0.999579i	$0.509240\pi$
$558$	−18.4078	−0.779264
$559$	28.3912	1.20082
$560$	−3.26323	−0.137897
$561$	24.2630	1.02438
$562$	−0.195909	−0.00826392
$563$	10.0779	0.424731	0.212365	−	0.977190i	$-0.431883\pi$
$563$	10.0779	0.424731	0.212365	+	0.977190i	$0.431883\pi$
$564$	0.800018	0.0336868
$565$	10.5437	0.443576
$566$	−30.4497	−1.27989
$567$	22.4169	0.941421
$568$	9.97528	0.418554
$569$	−30.6741	−1.28592	−0.642962	−	0.765898i	$-0.722295\pi$
$569$	−30.6741	−1.28592	−0.642962	+	0.765898i	$0.722295\pi$
$570$	14.0621	0.588998
$571$	24.1449	1.01043	0.505217	−	0.862992i	$-0.331412\pi$
$571$	24.1449	1.01043	0.505217	+	0.862992i	$0.331412\pi$
$572$	−10.1339	−0.423719
$573$	−23.5416	−0.983463
$574$	−9.19496	−0.383790
$575$	−17.3169	−0.722163
$576$	7.30232	0.304263
$577$	12.8905	0.536639	0.268319	−	0.963330i	$-0.413532\pi$
$577$	12.8905	0.536639	0.268319	+	0.963330i	$0.413532\pi$
$578$	−1.60259	−0.0666591
$579$	−26.1802	−1.08801
$580$	−15.7136	−0.652471
$581$	−2.26247	−0.0938632
$582$	−52.1848	−2.16313
$583$	9.19705	0.380903
$584$	−3.94038	−0.163054
$585$	137.782	5.69660
$586$	−1.33681	−0.0552231
$587$	−22.5017	−0.928746	−0.464373	−	0.885640i	$-0.653720\pi$
$587$	−22.5017	−0.928746	−0.464373	+	0.885640i	$0.653720\pi$
$588$	−3.20972	−0.132367
$589$	−3.38437	−0.139450
$590$	6.69803	0.275754
$591$	46.4805	1.91195
$592$	−1.68120	−0.0690968
$593$	14.3415	0.588936	0.294468	−	0.955661i	$-0.404858\pi$
$593$	14.3415	0.588936	0.294468	+	0.955661i	$0.404858\pi$
$594$	24.2025	0.993041
$595$	14.0745	0.577000
$596$	−10.3872	−0.425477
$597$	−25.2958	−1.03529
$598$	−17.7259	−0.724867
$599$	17.9173	0.732083	0.366041	−	0.930599i	$-0.380713\pi$
$599$	17.9173	0.732083	0.366041	+	0.930599i	$0.380713\pi$
$600$	18.1306	0.740181
$601$	−27.9251	−1.13909	−0.569545	−	0.821960i	$-0.692881\pi$
$601$	−27.9251	−1.13909	−0.569545	+	0.821960i	$0.692881\pi$
$602$	4.91018	0.200124
$603$	−107.436	−4.37515
$604$	−20.2165	−0.822599
$605$	25.8718	1.05184
$606$	−19.3697	−0.786839
$607$	−30.7461	−1.24795	−0.623973	−	0.781446i	$-0.714483\pi$
$607$	−30.7461	−1.24795	−0.623973	+	0.781446i	$0.714483\pi$
$608$	1.34257	0.0544483
$609$	−15.4559	−0.626306
$610$	−27.8029	−1.12571
$611$	1.44118	0.0583039
$612$	−31.4954	−1.27313
$613$	28.8431	1.16496	0.582482	−	0.812844i	$-0.302082\pi$
$613$	28.8431	1.16496	0.582482	+	0.812844i	$0.302082\pi$
$614$	−19.1761	−0.773885
$615$	96.3085	3.88353
$616$	−1.75263	−0.0706155
$617$	−43.2591	−1.74155	−0.870773	−	0.491685i	$-0.836381\pi$
$617$	−43.2591	−1.74155	−0.870773	+	0.491685i	$0.836381\pi$
$618$	7.54736	0.303599
$619$	32.5843	1.30967	0.654837	−	0.755770i	$-0.272737\pi$
$619$	32.5843	1.30967	0.654837	+	0.755770i	$0.272737\pi$
$620$	−8.22600	−0.330364
$621$	42.3344	1.69882
$622$	−15.8505	−0.635549
$623$	−11.5298	−0.461934
$624$	18.5589	0.742952
$625$	−21.3359	−0.853436
$626$	31.0957	1.24283
$627$	7.55256	0.301620
$628$	−4.91669	−0.196197
$629$	7.25113	0.289121
$630$	23.8291	0.949376
$631$	−6.62073	−0.263567	−0.131784	−	0.991279i	$-0.542070\pi$
$631$	−6.62073	−0.263567	−0.131784	+	0.991279i	$0.542070\pi$
$632$	−7.76592	−0.308912
$633$	9.91468	0.394073
$634$	5.87269	0.233234
$635$	42.6862	1.69395
$636$	−16.8432	−0.667878
$637$	−5.78210	−0.229095
$638$	−8.43952	−0.334124
$639$	−72.8427	−2.88161
$640$	3.26323	0.128990
$641$	43.4750	1.71716	0.858580	−	0.512680i	$-0.171347\pi$
$641$	43.4750	1.71716	0.858580	+	0.512680i	$0.171347\pi$
$642$	−5.90993	−0.233246
$643$	39.3148	1.55042	0.775212	−	0.631701i	$-0.217643\pi$
$643$	39.3148	1.55042	0.775212	+	0.631701i	$0.217643\pi$
$644$	−3.06566	−0.120804
$645$	−51.4296	−2.02504
$646$	−5.79059	−0.227828
$647$	12.7168	0.499950	0.249975	−	0.968252i	$-0.419578\pi$
$647$	12.7168	0.499950	0.249975	+	0.968252i	$0.419578\pi$
$648$	−22.4169	−0.880619
$649$	3.59741	0.141211
$650$	32.6611	1.28108
$651$	−8.09112	−0.317116
$652$	−14.0830	−0.551534
$653$	−46.0406	−1.80171	−0.900855	−	0.434121i	$-0.857059\pi$
$653$	−46.0406	−1.80171	−0.900855	+	0.434121i	$0.857059\pi$
$654$	−3.17245	−0.124053
$655$	4.20534	0.164316
$656$	9.19496	0.359003
$657$	28.7739	1.12258
$658$	0.249248	0.00971672
$659$	25.8876	1.00844	0.504220	−	0.863575i	$-0.331780\pi$
$659$	25.8876	1.00844	0.504220	+	0.863575i	$0.331780\pi$
$660$	18.3571	0.714551
$661$	−39.6231	−1.54116	−0.770580	−	0.637343i	$-0.780033\pi$
$661$	−39.6231	−1.54116	−0.770580	+	0.637343i	$0.780033\pi$
$662$	34.2790	1.33229
$663$	−80.0460	−3.10873
$664$	2.26247	0.0878010
$665$	4.38111	0.169892
$666$	12.2766	0.475710
$667$	−14.7622	−0.571594
$668$	15.8303	0.612491
$669$	19.1478	0.740295
$670$	−48.0107	−1.85482
$671$	−14.9325	−0.576463
$672$	3.20972	0.123818
$673$	32.7015	1.26055	0.630276	−	0.776371i	$-0.282942\pi$
$673$	32.7015	1.26055	0.630276	+	0.776371i	$0.282942\pi$
$674$	−5.97151	−0.230014
$675$	−78.0038	−3.00237
$676$	20.4327	0.785871
$677$	−15.9544	−0.613179	−0.306590	−	0.951842i	$-0.599188\pi$
$677$	−15.9544	−0.613179	−0.306590	+	0.951842i	$0.599188\pi$
$678$	−10.3708	−0.398288
$679$	−16.2584	−0.623939
$680$	−14.0745	−0.539734
$681$	−50.1158	−1.92044
$682$	−4.41806	−0.169176
$683$	−42.2365	−1.61614	−0.808068	−	0.589089i	$-0.799487\pi$
$683$	−42.2365	−1.61614	−0.808068	+	0.589089i	$0.799487\pi$
$684$	−9.80386	−0.374860
$685$	−10.9208	−0.417261
$686$	−1.00000	−0.0381802
$687$	−2.45690	−0.0937365
$688$	−4.91018	−0.187199
$689$	−30.3420	−1.15594
$690$	32.1099	1.22240
$691$	13.3826	0.509098	0.254549	−	0.967060i	$-0.418073\pi$
$691$	13.3826	0.509098	0.254549	+	0.967060i	$0.418073\pi$
$692$	7.73137	0.293903
$693$	12.7983	0.486166
$694$	−34.7187	−1.31790
$695$	56.9342	2.15964
$696$	15.4559	0.585855
$697$	−39.6585	−1.50217
$698$	10.7515	0.406950
$699$	25.2502	0.955051
$700$	5.64866	0.213499
$701$	36.4516	1.37676	0.688379	−	0.725351i	$-0.258323\pi$
$701$	36.4516	1.37676	0.688379	+	0.725351i	$0.258323\pi$
$702$	−79.8464	−3.01361
$703$	2.25712	0.0851290
$704$	1.75263	0.0660547
$705$	−2.61064	−0.0983225
$706$	14.1019	0.530731
$707$	−6.03468	−0.226958
$708$	−6.58820	−0.247600
$709$	−32.3793	−1.21603	−0.608015	−	0.793926i	$-0.708034\pi$
$709$	−32.3793	−1.21603	−0.608015	+	0.793926i	$0.708034\pi$
$710$	−32.5516	−1.22164
$711$	56.7093	2.12676
$712$	11.5298	0.432099
$713$	−7.72795	−0.289414
$714$	−13.8438	−0.518090
$715$	33.0692	1.23672
$716$	7.99270	0.298701
$717$	58.8811	2.19896
$718$	−2.36436	−0.0882370
$719$	5.89098	0.219696	0.109848	−	0.993948i	$-0.464964\pi$
$719$	5.89098	0.219696	0.109848	+	0.993948i	$0.464964\pi$
$720$	−23.8291	−0.888060
$721$	2.35140	0.0875709
$722$	17.1975	0.640025
$723$	−0.270727	−0.0100685
$724$	−20.9632	−0.779091
$725$	27.2003	1.01019
$726$	−25.4476	−0.944449
$727$	12.4458	0.461590	0.230795	−	0.973002i	$-0.425867\pi$
$727$	12.4458	0.461590	0.230795	+	0.973002i	$0.425867\pi$
$728$	5.78210	0.214299
$729$	30.7238	1.13792
$730$	12.8584	0.475910
$731$	21.1780	0.783296
$732$	27.3470	1.01078
$733$	−42.9398	−1.58602	−0.793009	−	0.609210i	$-0.791487\pi$
$733$	−42.9398	−1.58602	−0.793009	+	0.609210i	$0.791487\pi$
$734$	13.3791	0.493831
$735$	10.4741	0.386342
$736$	3.06566	0.113002
$737$	−25.7858	−0.949833
$738$	−67.1445	−2.47162
$739$	34.8747	1.28289	0.641444	−	0.767170i	$-0.278336\pi$
$739$	34.8747	1.28289	0.641444	+	0.767170i	$0.278336\pi$
$740$	5.48613	0.201674
$741$	−24.9166	−0.915335
$742$	−5.24757	−0.192644
$743$	4.74229	0.173978	0.0869889	−	0.996209i	$-0.472276\pi$
$743$	4.74229	0.173978	0.0869889	+	0.996209i	$0.472276\pi$
$744$	8.09112	0.296635
$745$	33.8958	1.24185
$746$	−8.95913	−0.328017
$747$	−16.5213	−0.604483
$748$	−7.55922	−0.276392
$749$	−1.84126	−0.0672781
$750$	−6.79416	−0.248088
$751$	−26.3085	−0.960010	−0.480005	−	0.877266i	$-0.659365\pi$
$751$	−26.3085	−0.960010	−0.480005	+	0.877266i	$0.659365\pi$
$752$	−0.249248	−0.00908916
$753$	37.8720	1.38013
$754$	27.8428	1.01397
$755$	65.9712	2.40094
$756$	−13.8092	−0.502237
$757$	−26.2754	−0.954995	−0.477497	−	0.878633i	$-0.658456\pi$
$757$	−26.2754	−0.954995	−0.477497	+	0.878633i	$0.658456\pi$
$758$	19.6213	0.712679
$759$	17.2457	0.625980
$760$	−4.38111	−0.158919
$761$	40.0053	1.45019	0.725096	−	0.688648i	$-0.241795\pi$
$761$	40.0053	1.45019	0.725096	+	0.688648i	$0.241795\pi$
$762$	−41.9863	−1.52100
$763$	−0.988387	−0.0357820
$764$	7.33445	0.265351
$765$	102.777	3.71590
$766$	−14.3949	−0.520110
$767$	−11.8682	−0.428536
$768$	−3.20972	−0.115821
$769$	46.2140	1.66652	0.833260	−	0.552882i	$-0.186472\pi$
$769$	46.2140	1.66652	0.833260	+	0.552882i	$0.186472\pi$
$770$	5.71923	0.206107
$771$	8.58081	0.309030
$772$	8.15652	0.293560
$773$	25.5356	0.918453	0.459226	−	0.888319i	$-0.348127\pi$
$773$	25.5356	0.918453	0.459226	+	0.888319i	$0.348127\pi$
$774$	35.8557	1.28881
$775$	14.2392	0.511489
$776$	16.2584	0.583641
$777$	5.39618	0.193587
$778$	29.1139	1.04379
$779$	−12.3449	−0.442300
$780$	−60.5620	−2.16847
$781$	−17.4830	−0.625590
$782$	−13.2224	−0.472832
$783$	−66.4963	−2.37638
$784$	1.00000	0.0357143
$785$	16.0443	0.572646
$786$	−4.13639	−0.147540
$787$	29.1506	1.03911	0.519554	−	0.854438i	$-0.326098\pi$
$787$	29.1506	1.03911	0.519554	+	0.854438i	$0.326098\pi$
$788$	−14.4811	−0.515869
$789$	−68.0761	−2.42357
$790$	25.3420	0.901628
$791$	−3.23106	−0.114883
$792$	−12.7983	−0.454766
$793$	49.2638	1.74941
$794$	−2.64398	−0.0938313
$795$	54.9634	1.94935
$796$	7.88099	0.279334
$797$	24.9448	0.883590	0.441795	−	0.897116i	$-0.354342\pi$
$797$	24.9448	0.883590	0.441795	+	0.897116i	$0.354342\pi$
$798$	−4.30927	−0.152547
$799$	1.07503	0.0380317
$800$	−5.64866	−0.199710
$801$	−84.1946	−2.97487
$802$	9.34906	0.330127
$803$	6.90603	0.243709
$804$	47.2235	1.66545
$805$	10.0039	0.352592
$806$	14.5756	0.513404
$807$	71.7824	2.52686
$808$	6.03468	0.212299
$809$	−47.1303	−1.65701	−0.828506	−	0.559980i	$-0.810809\pi$
$809$	−47.1303	−1.65701	−0.828506	+	0.559980i	$0.810809\pi$
$810$	73.1515	2.57028
$811$	46.1770	1.62149	0.810746	−	0.585398i	$-0.199062\pi$
$811$	46.1770	1.62149	0.810746	+	0.585398i	$0.199062\pi$
$812$	4.81535	0.168985
$813$	−78.9114	−2.76754
$814$	2.94652	0.103275
$815$	45.9562	1.60978
$816$	13.8438	0.484629
$817$	6.59226	0.230634
$818$	−25.8220	−0.902844
$819$	−42.2227	−1.47538
$820$	−30.0052	−1.04783
$821$	39.1698	1.36704	0.683518	−	0.729933i	$-0.260449\pi$
$821$	39.1698	1.36704	0.683518	+	0.729933i	$0.260449\pi$
$822$	10.7417	0.374660
$823$	7.82145	0.272639	0.136319	−	0.990665i	$-0.456473\pi$
$823$	7.82145	0.272639	0.136319	+	0.990665i	$0.456473\pi$
$824$	−2.35140	−0.0819151
$825$	−31.7763	−1.10631
$826$	−2.05258	−0.0714183
$827$	23.5866	0.820185	0.410093	−	0.912044i	$-0.365496\pi$
$827$	23.5866	0.820185	0.410093	+	0.912044i	$0.365496\pi$
$828$	−22.3864	−0.777981
$829$	13.6588	0.474390	0.237195	−	0.971462i	$-0.423772\pi$
$829$	13.6588	0.474390	0.237195	+	0.971462i	$0.423772\pi$
$830$	−7.38297	−0.256267
$831$	−90.5206	−3.14013
$832$	−5.78210	−0.200458
$833$	−4.31307	−0.149439
$834$	−56.0007	−1.93914
$835$	−51.6578	−1.78769
$836$	−2.35302	−0.0813811
$837$	−34.8106	−1.20323
$838$	30.5806	1.05639
$839$	−20.1760	−0.696552	−0.348276	−	0.937392i	$-0.613233\pi$
$839$	−20.1760	−0.696552	−0.348276	+	0.937392i	$0.613233\pi$
$840$	−10.4741	−0.361389
$841$	−5.81245	−0.200429
$842$	−8.20269	−0.282683
$843$	−0.628813	−0.0216575
$844$	−3.08895	−0.106326
$845$	−66.6764	−2.29374
$846$	1.82009	0.0625760
$847$	−7.92829	−0.272419
$848$	5.24757	0.180202
$849$	−97.7349	−3.35425
$850$	24.3631	0.835647
$851$	5.15397	0.176676
$852$	32.0179	1.09691
$853$	−6.25689	−0.214232	−0.107116	−	0.994247i	$-0.534162\pi$
$853$	−6.25689	−0.214232	−0.107116	+	0.994247i	$0.534162\pi$
$854$	8.52006	0.291550
$855$	31.9922	1.09411
$856$	1.84126	0.0629329
$857$	−1.73888	−0.0593988	−0.0296994	−	0.999559i	$-0.509455\pi$
$857$	−1.73888	−0.0593988	−0.0296994	+	0.999559i	$0.509455\pi$
$858$	−32.5269	−1.11045
$859$	−19.8656	−0.677805	−0.338903	−	0.940821i	$-0.610056\pi$
$859$	−19.8656	−0.677805	−0.338903	+	0.940821i	$0.610056\pi$
$860$	16.0231	0.546382
$861$	−29.5133	−1.00581
$862$	1.00000	0.0340601
$863$	−3.25327	−0.110743	−0.0553713	−	0.998466i	$-0.517634\pi$
$863$	−3.25327	−0.110743	−0.0553713	+	0.998466i	$0.517634\pi$
$864$	13.8092	0.469800
$865$	−25.2292	−0.857819
$866$	12.6661	0.430412
$867$	−5.14388	−0.174695
$868$	2.52082	0.0855621
$869$	13.6108	0.461714
$870$	−50.4362	−1.70995
$871$	85.0700	2.88249
$872$	0.988387	0.0334710
$873$	−118.724	−4.01819
$874$	−4.11585	−0.139221
$875$	−2.11674	−0.0715590
$876$	−12.6475	−0.427321
$877$	2.72621	0.0920576	0.0460288	−	0.998940i	$-0.485343\pi$
$877$	2.72621	0.0920576	0.0460288	+	0.998940i	$0.485343\pi$
$878$	30.8544	1.04128
$879$	−4.29079	−0.144725
$880$	−5.71923	−0.192795
$881$	38.3685	1.29267	0.646333	−	0.763055i	$-0.276302\pi$
$881$	38.3685	1.29267	0.646333	+	0.763055i	$0.276302\pi$
$882$	−7.30232	−0.245882
$883$	−7.12028	−0.239616	−0.119808	−	0.992797i	$-0.538228\pi$
$883$	−7.12028	−0.239616	−0.119808	+	0.992797i	$0.538228\pi$
$884$	24.9386	0.838776
$885$	21.4988	0.722675
$886$	−20.3375	−0.683253
$887$	53.1958	1.78614	0.893070	−	0.449917i	$-0.148546\pi$
$887$	53.1958	1.78614	0.893070	+	0.449917i	$0.148546\pi$
$888$	−5.39618	−0.181084
$889$	−13.0810	−0.438722
$890$	−37.6245	−1.26118
$891$	39.2885	1.31622
$892$	−5.96555	−0.199741
$893$	0.334633	0.0111981
$894$	−33.3400	−1.11506
$895$	−26.0820	−0.871825
$896$	−1.00000	−0.0334077
$897$	−56.8953	−1.89968
$898$	−33.7305	−1.12560
$899$	12.1386	0.404845
$900$	41.2484	1.37495
$901$	−22.6331	−0.754020
$902$	−16.1154	−0.536583
$903$	15.7603	0.524471
$904$	3.23106	0.107463
$905$	68.4077	2.27395
$906$	−64.8895	−2.15581
$907$	−26.3673	−0.875512	−0.437756	−	0.899094i	$-0.644227\pi$
$907$	−26.3673	−0.875512	−0.437756	+	0.899094i	$0.644227\pi$
$908$	15.6138	0.518161
$909$	−44.0672	−1.46162
$910$	−18.8683	−0.625478
$911$	−6.62153	−0.219381	−0.109690	−	0.993966i	$-0.534986\pi$
$911$	−6.62153	−0.219381	−0.109690	+	0.993966i	$0.534986\pi$
$912$	4.30927	0.142694
$913$	−3.96528	−0.131232
$914$	−33.1453	−1.09635
$915$	−89.2396	−2.95017
$916$	0.765455	0.0252913
$917$	−1.28871	−0.0425568
$918$	−59.5603	−1.96578
$919$	−10.2396	−0.337774	−0.168887	−	0.985635i	$-0.554017\pi$
$919$	−10.2396	−0.337774	−0.168887	+	0.985635i	$0.554017\pi$
$920$	−10.0039	−0.329820
$921$	−61.5500	−2.02814
$922$	19.4758	0.641403
$923$	57.6781	1.89850
$924$	−5.62545	−0.185064
$925$	−9.49652	−0.312244
$926$	−7.68121	−0.252420
$927$	17.1707	0.563960
$928$	−4.81535	−0.158071
$929$	−12.6900	−0.416345	−0.208172	−	0.978092i	$-0.566752\pi$
$929$	−12.6900	−0.416345	−0.208172	+	0.978092i	$0.566752\pi$
$930$	−26.4032	−0.865794
$931$	−1.34257	−0.0440009
$932$	−7.86679	−0.257685
$933$	−50.8758	−1.66560
$934$	14.0157	0.458608
$935$	24.6675	0.806712
$936$	42.2227	1.38009
$937$	−23.5871	−0.770558	−0.385279	−	0.922800i	$-0.625895\pi$
$937$	−23.5871	−0.770558	−0.385279	+	0.922800i	$0.625895\pi$
$938$	14.7126	0.480385
$939$	99.8085	3.25713
$940$	0.813355	0.0265287
$941$	30.9879	1.01018	0.505088	−	0.863068i	$-0.331460\pi$
$941$	30.9879	1.01018	0.505088	+	0.863068i	$0.331460\pi$
$942$	−15.7812	−0.514180
$943$	−28.1886	−0.917946
$944$	2.05258	0.0668057
$945$	45.0627	1.46589
$946$	8.60574	0.279797
$947$	45.2798	1.47140	0.735698	−	0.677310i	$-0.236854\pi$
$947$	45.2798	1.47140	0.735698	+	0.677310i	$0.236854\pi$
$948$	−24.9265	−0.809574
$949$	−22.7837	−0.739590
$950$	7.58372	0.246048
$951$	18.8497	0.611243
$952$	4.31307	0.139787
$953$	−19.9755	−0.647069	−0.323534	−	0.946216i	$-0.604871\pi$
$953$	−19.9755	−0.647069	−0.323534	+	0.946216i	$0.604871\pi$
$954$	−38.3194	−1.24064
$955$	−23.9340	−0.774486
$956$	−18.3446	−0.593307
$957$	−27.0885	−0.875647
$958$	11.0015	0.355443
$959$	3.34661	0.108068
$960$	10.4741	0.338049
$961$	−24.6455	−0.795016
$962$	−9.72085	−0.313413
$963$	−13.4454	−0.433274
$964$	0.0843460	0.00271660
$965$	−26.6166	−0.856818
$966$	−9.83991	−0.316594
$967$	−19.9699	−0.642190	−0.321095	−	0.947047i	$-0.604051\pi$
$967$	−19.9699	−0.642190	−0.321095	+	0.947047i	$0.604051\pi$
$968$	7.92829	0.254825
$969$	−18.5862	−0.597075
$970$	−53.0548	−1.70349
$971$	35.7460	1.14714	0.573572	−	0.819155i	$-0.305557\pi$
$971$	35.7460	1.14714	0.573572	+	0.819155i	$0.305557\pi$
$972$	−30.5243	−0.979067
$973$	−17.4472	−0.559332
$974$	−43.1683	−1.38320
$975$	104.833	3.35735
$976$	−8.52006	−0.272720
$977$	1.91439	0.0612467	0.0306234	−	0.999531i	$-0.490251\pi$
$977$	1.91439	0.0612467	0.0306234	+	0.999531i	$0.490251\pi$
$978$	−45.2027	−1.44542
$979$	−20.2076	−0.645836
$980$	−3.26323	−0.104240
$981$	−7.21751	−0.230438
$982$	−12.7932	−0.408248
$983$	45.2810	1.44424	0.722120	−	0.691768i	$-0.243168\pi$
$983$	45.2810	1.44424	0.722120	+	0.691768i	$0.243168\pi$
$984$	29.5133	0.940848
$985$	47.2553	1.50568
$986$	20.7689	0.661418
$987$	0.800018	0.0254649
$988$	7.76286	0.246970
$989$	15.0529	0.478656
$990$	41.7637	1.32734
$991$	15.0832	0.479135	0.239567	−	0.970880i	$-0.422994\pi$
$991$	15.0832	0.479135	0.239567	+	0.970880i	$0.422994\pi$
$992$	−2.52082	−0.0800360
$993$	110.026	3.49157
$994$	9.97528	0.316397
$995$	−25.7175	−0.815299
$996$	7.26191	0.230102
$997$	−29.1918	−0.924514	−0.462257	−	0.886746i	$-0.652960\pi$
$997$	−29.1918	−0.924514	−0.462257	+	0.886746i	$0.652960\pi$
$998$	9.60594	0.304071
$999$	23.2161	0.734524

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.p.1.2	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.p.1.2	✓	27	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.20972 q^{3} +1.00000 q^{4} -3.26323 q^{5} +3.20972 q^{6} +1.00000 q^{7} -1.00000 q^{8} +7.30232 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.20972 q^{3} +1.00000 q^{4} -3.26323 q^{5} +3.20972 q^{6} +1.00000 q^{7} -1.00000 q^{8} +7.30232 q^{9} +3.26323 q^{10} +1.75263 q^{11} -3.20972 q^{12} -5.78210 q^{13} -1.00000 q^{14} +10.4741 q^{15} +1.00000 q^{16} -4.31307 q^{17} -7.30232 q^{18} -1.34257 q^{19} -3.26323 q^{20} -3.20972 q^{21} -1.75263 q^{22} -3.06566 q^{23} +3.20972 q^{24} +5.64866 q^{25} +5.78210 q^{26} -13.8092 q^{27} +1.00000 q^{28} +4.81535 q^{29} -10.4741 q^{30} +2.52082 q^{31} -1.00000 q^{32} -5.62545 q^{33} +4.31307 q^{34} -3.26323 q^{35} +7.30232 q^{36} -1.68120 q^{37} +1.34257 q^{38} +18.5589 q^{39} +3.26323 q^{40} +9.19496 q^{41} +3.20972 q^{42} -4.91018 q^{43} +1.75263 q^{44} -23.8291 q^{45} +3.06566 q^{46} -0.249248 q^{47} -3.20972 q^{48} +1.00000 q^{49} -5.64866 q^{50} +13.8438 q^{51} -5.78210 q^{52} +5.24757 q^{53} +13.8092 q^{54} -5.71923 q^{55} -1.00000 q^{56} +4.30927 q^{57} -4.81535 q^{58} +2.05258 q^{59} +10.4741 q^{60} -8.52006 q^{61} -2.52082 q^{62} +7.30232 q^{63} +1.00000 q^{64} +18.8683 q^{65} +5.62545 q^{66} -14.7126 q^{67} -4.31307 q^{68} +9.83991 q^{69} +3.26323 q^{70} -9.97528 q^{71} -7.30232 q^{72} +3.94038 q^{73} +1.68120 q^{74} -18.1306 q^{75} -1.34257 q^{76} +1.75263 q^{77} -18.5589 q^{78} +7.76592 q^{79} -3.26323 q^{80} +22.4169 q^{81} -9.19496 q^{82} -2.26247 q^{83} -3.20972 q^{84} +14.0745 q^{85} +4.91018 q^{86} -15.4559 q^{87} -1.75263 q^{88} -11.5298 q^{89} +23.8291 q^{90} -5.78210 q^{91} -3.06566 q^{92} -8.09112 q^{93} +0.249248 q^{94} +4.38111 q^{95} +3.20972 q^{96} -16.2584 q^{97} -1.00000 q^{98} +12.7983 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9}+O(q^{10}) \) 27 * q - 27 * q^2 + 4 * q^3 + 27 * q^4 + 9 * q^5 - 4 * q^6 + 27 * q^7 - 27 * q^8 + 35 * q^9	\( 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9} - 9 q^{10} + 24 q^{11} + 4 q^{12} - 13 q^{13} - 27 q^{14} + 16 q^{15} + 27 q^{16} - 5 q^{17} - 35 q^{18} + q^{19} + 9 q^{20} + 4 q^{21} - 24 q^{22} + 32 q^{23} - 4 q^{24} + 30 q^{25} + 13 q^{26} + q^{27} + 27 q^{28} + 26 q^{29} - 16 q^{30} + 21 q^{31} - 27 q^{32} + 7 q^{33} + 5 q^{34} + 9 q^{35} + 35 q^{36} + 4 q^{37} - q^{38} + 13 q^{39} - 9 q^{40} + 31 q^{41} - 4 q^{42} - 13 q^{43} + 24 q^{44} + 19 q^{45} - 32 q^{46} + 41 q^{47} + 4 q^{48} + 27 q^{49} - 30 q^{50} + 21 q^{51} - 13 q^{52} + 29 q^{53} - q^{54} + 9 q^{55} - 27 q^{56} - 26 q^{58} + 36 q^{59} + 16 q^{60} + q^{61} - 21 q^{62} + 35 q^{63} + 27 q^{64} + 46 q^{65} - 7 q^{66} - 2 q^{67} - 5 q^{68} + 43 q^{69} - 9 q^{70} + 70 q^{71} - 35 q^{72} - 21 q^{73} - 4 q^{74} + 37 q^{75} + q^{76} + 24 q^{77} - 13 q^{78} + 19 q^{79} + 9 q^{80} + 67 q^{81} - 31 q^{82} + 25 q^{83} + 4 q^{84} - 6 q^{85} + 13 q^{86} - 9 q^{87} - 24 q^{88} + 85 q^{89} - 19 q^{90} - 13 q^{91} + 32 q^{92} + 23 q^{93} - 41 q^{94} + 77 q^{95} - 4 q^{96} - 2 q^{97} - 27 q^{98} + 38 q^{99}+O(q^{100}) \) 27 * q - 27 * q^2 + 4 * q^3 + 27 * q^4 + 9 * q^5 - 4 * q^6 + 27 * q^7 - 27 * q^8 + 35 * q^9 - 9 * q^10 + 24 * q^11 + 4 * q^12 - 13 * q^13 - 27 * q^14 + 16 * q^15 + 27 * q^16 - 5 * q^17 - 35 * q^18 + q^19 + 9 * q^20 + 4 * q^21 - 24 * q^22 + 32 * q^23 - 4 * q^24 + 30 * q^25 + 13 * q^26 + q^27 + 27 * q^28 + 26 * q^29 - 16 * q^30 + 21 * q^31 - 27 * q^32 + 7 * q^33 + 5 * q^34 + 9 * q^35 + 35 * q^36 + 4 * q^37 - q^38 + 13 * q^39 - 9 * q^40 + 31 * q^41 - 4 * q^42 - 13 * q^43 + 24 * q^44 + 19 * q^45 - 32 * q^46 + 41 * q^47 + 4 * q^48 + 27 * q^49 - 30 * q^50 + 21 * q^51 - 13 * q^52 + 29 * q^53 - q^54 + 9 * q^55 - 27 * q^56 - 26 * q^58 + 36 * q^59 + 16 * q^60 + q^61 - 21 * q^62 + 35 * q^63 + 27 * q^64 + 46 * q^65 - 7 * q^66 - 2 * q^67 - 5 * q^68 + 43 * q^69 - 9 * q^70 + 70 * q^71 - 35 * q^72 - 21 * q^73 - 4 * q^74 + 37 * q^75 + q^76 + 24 * q^77 - 13 * q^78 + 19 * q^79 + 9 * q^80 + 67 * q^81 - 31 * q^82 + 25 * q^83 + 4 * q^84 - 6 * q^85 + 13 * q^86 - 9 * q^87 - 24 * q^88 + 85 * q^89 - 19 * q^90 - 13 * q^91 + 32 * q^92 + 23 * q^93 - 41 * q^94 + 77 * q^95 - 4 * q^96 - 2 * q^97 - 27 * q^98 + 38 * q^99

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