LMFDB - Embedded newform 6042.2.a.q.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6042,2,Mod(1,6042)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6042, 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("6042.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6042 = 2 \cdot 3 \cdot 19 \cdot 53 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6042.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:	$48.2456129013$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.257.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 3 $ x^3 - x^2 - 4*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.713538$ of defining polynomial
Character	$\chi$	$=$	6042.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.49086 q^{5} +1.00000 q^{6} +1.77733 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.49086 q^{5} +1.00000 q^{6} +1.77733 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.49086 q^{10} -1.20440 q^{11} -1.00000 q^{12} -1.49086 q^{13} -1.77733 q^{14} -1.49086 q^{15} +1.00000 q^{16} +0.222674 q^{17} -1.00000 q^{18} +1.00000 q^{19} +1.49086 q^{20} -1.77733 q^{21} +1.20440 q^{22} -1.69527 q^{23} +1.00000 q^{24} -2.77733 q^{25} +1.49086 q^{26} -1.00000 q^{27} +1.77733 q^{28} +1.63671 q^{29} +1.49086 q^{30} -4.40880 q^{31} -1.00000 q^{32} +1.20440 q^{33} -0.222674 q^{34} +2.64975 q^{35} +1.00000 q^{36} +0.795598 q^{37} -1.00000 q^{38} +1.49086 q^{39} -1.49086 q^{40} +9.26819 q^{41} +1.77733 q^{42} +1.69527 q^{43} -1.20440 q^{44} +1.49086 q^{45} +1.69527 q^{46} -4.42708 q^{47} -1.00000 q^{48} -3.84111 q^{49} +2.77733 q^{50} -0.222674 q^{51} -1.49086 q^{52} -1.00000 q^{53} +1.00000 q^{54} -1.79560 q^{55} -1.77733 q^{56} -1.00000 q^{57} -1.63671 q^{58} +6.77209 q^{59} -1.49086 q^{60} -2.36329 q^{61} +4.40880 q^{62} +1.77733 q^{63} +1.00000 q^{64} -2.22267 q^{65} -1.20440 q^{66} +8.06379 q^{67} +0.222674 q^{68} +1.69527 q^{69} -2.64975 q^{70} +4.57292 q^{71} -1.00000 q^{72} -0.631477 q^{73} -0.795598 q^{74} +2.77733 q^{75} +1.00000 q^{76} -2.14061 q^{77} -1.49086 q^{78} +9.08580 q^{79} +1.49086 q^{80} +1.00000 q^{81} -9.26819 q^{82} +13.8228 q^{83} -1.77733 q^{84} +0.331977 q^{85} -1.69527 q^{86} -1.63671 q^{87} +1.20440 q^{88} +5.75905 q^{89} -1.49086 q^{90} -2.64975 q^{91} -1.69527 q^{92} +4.40880 q^{93} +4.42708 q^{94} +1.49086 q^{95} +1.00000 q^{96} +6.67699 q^{97} +3.84111 q^{98} -1.20440 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{5} + 3 q^{6} - q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^5 + 3 * q^6 - q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{5} + 3 q^{6} - q^{7} - 3 q^{8} + 3 q^{9} + 3 q^{10} + 5 q^{11} - 3 q^{12} + 3 q^{13} + q^{14} + 3 q^{15} + 3 q^{16} + 7 q^{17} - 3 q^{18} + 3 q^{19} - 3 q^{20} + q^{21} - 5 q^{22} + 11 q^{23} + 3 q^{24} - 2 q^{25} - 3 q^{26} - 3 q^{27} - q^{28} + 2 q^{29} - 3 q^{30} + 4 q^{31} - 3 q^{32} - 5 q^{33} - 7 q^{34} + 12 q^{35} + 3 q^{36} + 11 q^{37} - 3 q^{38} - 3 q^{39} + 3 q^{40} + 14 q^{41} - q^{42} - 11 q^{43} + 5 q^{44} - 3 q^{45} - 11 q^{46} - 11 q^{47} - 3 q^{48} + 2 q^{50} - 7 q^{51} + 3 q^{52} - 3 q^{53} + 3 q^{54} - 14 q^{55} + q^{56} - 3 q^{57} - 2 q^{58} + 6 q^{59} + 3 q^{60} - 10 q^{61} - 4 q^{62} - q^{63} + 3 q^{64} - 13 q^{65} + 5 q^{66} + 19 q^{67} + 7 q^{68} - 11 q^{69} - 12 q^{70} + 16 q^{71} - 3 q^{72} + 9 q^{73} - 11 q^{74} + 2 q^{75} + 3 q^{76} - 3 q^{77} + 3 q^{78} - 21 q^{79} - 3 q^{80} + 3 q^{81} - 14 q^{82} + 15 q^{83} + q^{84} - 18 q^{85} + 11 q^{86} - 2 q^{87} - 5 q^{88} - 4 q^{89} + 3 q^{90} - 12 q^{91} + 11 q^{92} - 4 q^{93} + 11 q^{94} - 3 q^{95} + 3 q^{96} - 11 q^{97} + 5 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^5 + 3 * q^6 - q^7 - 3 * q^8 + 3 * q^9 + 3 * q^10 + 5 * q^11 - 3 * q^12 + 3 * q^13 + q^14 + 3 * q^15 + 3 * q^16 + 7 * q^17 - 3 * q^18 + 3 * q^19 - 3 * q^20 + q^21 - 5 * q^22 + 11 * q^23 + 3 * q^24 - 2 * q^25 - 3 * q^26 - 3 * q^27 - q^28 + 2 * q^29 - 3 * q^30 + 4 * q^31 - 3 * q^32 - 5 * q^33 - 7 * q^34 + 12 * q^35 + 3 * q^36 + 11 * q^37 - 3 * q^38 - 3 * q^39 + 3 * q^40 + 14 * q^41 - q^42 - 11 * q^43 + 5 * q^44 - 3 * q^45 - 11 * q^46 - 11 * q^47 - 3 * q^48 + 2 * q^50 - 7 * q^51 + 3 * q^52 - 3 * q^53 + 3 * q^54 - 14 * q^55 + q^56 - 3 * q^57 - 2 * q^58 + 6 * q^59 + 3 * q^60 - 10 * q^61 - 4 * q^62 - q^63 + 3 * q^64 - 13 * q^65 + 5 * q^66 + 19 * q^67 + 7 * q^68 - 11 * q^69 - 12 * q^70 + 16 * q^71 - 3 * q^72 + 9 * q^73 - 11 * q^74 + 2 * q^75 + 3 * q^76 - 3 * q^77 + 3 * q^78 - 21 * q^79 - 3 * q^80 + 3 * q^81 - 14 * q^82 + 15 * q^83 + q^84 - 18 * q^85 + 11 * q^86 - 2 * q^87 - 5 * q^88 - 4 * q^89 + 3 * q^90 - 12 * q^91 + 11 * q^92 - 4 * q^93 + 11 * q^94 - 3 * q^95 + 3 * q^96 - 11 * q^97 + 5 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	1.49086	0.666734	0.333367	−	0.942797i	$-0.391815\pi$
$5$	1.49086	0.666734	0.333367	+	0.942797i	$0.391815\pi$
$6$	1.00000	0.408248
$7$	1.77733	0.671766	0.335883	−	0.941904i	$-0.390965\pi$
$7$	1.77733	0.671766	0.335883	+	0.941904i	$0.390965\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−1.49086	−0.471452
$11$	−1.20440	−0.363141	−0.181570	−	0.983378i	$-0.558118\pi$
$11$	−1.20440	−0.363141	−0.181570	+	0.983378i	$0.558118\pi$
$12$	−1.00000	−0.288675
$13$	−1.49086	−0.413491	−0.206746	−	0.978395i	$-0.566287\pi$
$13$	−1.49086	−0.413491	−0.206746	+	0.978395i	$0.566287\pi$
$14$	−1.77733	−0.475010
$15$	−1.49086	−0.384939
$16$	1.00000	0.250000
$17$	0.222674	0.0540065	0.0270032	−	0.999635i	$-0.491404\pi$
$17$	0.222674	0.0540065	0.0270032	+	0.999635i	$0.491404\pi$
$18$	−1.00000	−0.235702
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	1.49086	0.333367
$21$	−1.77733	−0.387844
$22$	1.20440	0.256779
$23$	−1.69527	−0.353487	−0.176744	−	0.984257i	$-0.556556\pi$
$23$	−1.69527	−0.353487	−0.176744	+	0.984257i	$0.556556\pi$
$24$	1.00000	0.204124
$25$	−2.77733	−0.555465
$26$	1.49086	0.292382
$27$	−1.00000	−0.192450
$28$	1.77733	0.335883
$29$	1.63671	0.303930	0.151965	−	0.988386i	$-0.451440\pi$
$29$	1.63671	0.303930	0.151965	+	0.988386i	$0.451440\pi$
$30$	1.49086	0.272193
$31$	−4.40880	−0.791844	−0.395922	−	0.918284i	$-0.629575\pi$
$31$	−4.40880	−0.791844	−0.395922	+	0.918284i	$0.629575\pi$
$32$	−1.00000	−0.176777
$33$	1.20440	0.209659
$34$	−0.222674	−0.0381883
$35$	2.64975	0.447890
$36$	1.00000	0.166667
$37$	0.795598	0.130796	0.0653978	−	0.997859i	$-0.479168\pi$
$37$	0.795598	0.130796	0.0653978	+	0.997859i	$0.479168\pi$
$38$	−1.00000	−0.162221
$39$	1.49086	0.238729
$40$	−1.49086	−0.235726
$41$	9.26819	1.44745	0.723724	−	0.690090i	$-0.242429\pi$
$41$	9.26819	1.44745	0.723724	+	0.690090i	$0.242429\pi$
$42$	1.77733	0.274247
$43$	1.69527	0.258526	0.129263	−	0.991610i	$-0.458739\pi$
$43$	1.69527	0.258526	0.129263	+	0.991610i	$0.458739\pi$
$44$	−1.20440	−0.181570
$45$	1.49086	0.222245
$46$	1.69527	0.249953
$47$	−4.42708	−0.645755	−0.322878	−	0.946441i	$-0.604650\pi$
$47$	−4.42708	−0.645755	−0.322878	+	0.946441i	$0.604650\pi$
$48$	−1.00000	−0.144338
$49$	−3.84111	−0.548730
$50$	2.77733	0.392773
$51$	−0.222674	−0.0311806
$52$	−1.49086	−0.206746
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	1.00000	0.136083
$55$	−1.79560	−0.242118
$56$	−1.77733	−0.237505
$57$	−1.00000	−0.132453
$58$	−1.63671	−0.214911
$59$	6.77209	0.881651	0.440826	−	0.897593i	$-0.354686\pi$
$59$	6.77209	0.881651	0.440826	+	0.897593i	$0.354686\pi$
$60$	−1.49086	−0.192470
$61$	−2.36329	−0.302588	−0.151294	−	0.988489i	$-0.548344\pi$
$61$	−2.36329	−0.302588	−0.151294	+	0.988489i	$0.548344\pi$
$62$	4.40880	0.559919
$63$	1.77733	0.223922
$64$	1.00000	0.125000
$65$	−2.22267	−0.275689
$66$	−1.20440	−0.148252
$67$	8.06379	0.985148	0.492574	−	0.870270i	$-0.336056\pi$
$67$	8.06379	0.985148	0.492574	+	0.870270i	$0.336056\pi$
$68$	0.222674	0.0270032
$69$	1.69527	0.204086
$70$	−2.64975	−0.316706
$71$	4.57292	0.542706	0.271353	−	0.962480i	$-0.412529\pi$
$71$	4.57292	0.542706	0.271353	+	0.962480i	$0.412529\pi$
$72$	−1.00000	−0.117851
$73$	−0.631477	−0.0739088	−0.0369544	−	0.999317i	$-0.511766\pi$
$73$	−0.631477	−0.0739088	−0.0369544	+	0.999317i	$0.511766\pi$
$74$	−0.795598	−0.0924864
$75$	2.77733	0.320698
$76$	1.00000	0.114708
$77$	−2.14061	−0.243946
$78$	−1.49086	−0.168807
$79$	9.08580	1.02223	0.511116	−	0.859512i	$-0.329232\pi$
$79$	9.08580	1.02223	0.511116	+	0.859512i	$0.329232\pi$
$80$	1.49086	0.166684
$81$	1.00000	0.111111
$82$	−9.26819	−1.02350
$83$	13.8228	1.51725	0.758627	−	0.651525i	$-0.225871\pi$
$83$	13.8228	1.51725	0.758627	+	0.651525i	$0.225871\pi$
$84$	−1.77733	−0.193922
$85$	0.331977	0.0360080
$86$	−1.69527	−0.182805
$87$	−1.63671	−0.175474
$88$	1.20440	0.128390
$89$	5.75905	0.610458	0.305229	−	0.952279i	$-0.401267\pi$
$89$	5.75905	0.610458	0.305229	+	0.952279i	$0.401267\pi$
$90$	−1.49086	−0.157151
$91$	−2.64975	−0.277769
$92$	−1.69527	−0.176744
$93$	4.40880	0.457172
$94$	4.42708	0.456618
$95$	1.49086	0.152959
$96$	1.00000	0.102062
$97$	6.67699	0.677946	0.338973	−	0.940796i	$-0.389920\pi$
$97$	6.67699	0.677946	0.338973	+	0.940796i	$0.389920\pi$
$98$	3.84111	0.388011
$99$	−1.20440	−0.121047
$100$	−2.77733	−0.277733
$101$	−10.8997	−1.08456	−0.542279	−	0.840199i	$-0.682438\pi$
$101$	−10.8997	−1.08456	−0.542279	+	0.840199i	$0.682438\pi$
$102$	0.222674	0.0220480
$103$	6.20440	0.611338	0.305669	−	0.952138i	$-0.401120\pi$
$103$	6.20440	0.611338	0.305669	+	0.952138i	$0.401120\pi$
$104$	1.49086	0.146191
$105$	−2.64975	−0.258589
$106$	1.00000	0.0971286
$107$	11.4909	1.11086	0.555432	−	0.831562i	$-0.312553\pi$
$107$	11.4909	1.11086	0.555432	+	0.831562i	$0.312553\pi$
$108$	−1.00000	−0.0962250
$109$	−0.923174	−0.0884240	−0.0442120	−	0.999022i	$-0.514078\pi$
$109$	−0.923174	−0.0884240	−0.0442120	+	0.999022i	$0.514078\pi$
$110$	1.79560	0.171204
$111$	−0.795598	−0.0755149
$112$	1.77733	0.167941
$113$	12.9635	1.21950	0.609750	−	0.792594i	$-0.291270\pi$
$113$	12.9635	1.21950	0.609750	+	0.792594i	$0.291270\pi$
$114$	1.00000	0.0936586
$115$	−2.52741	−0.235682
$116$	1.63671	0.151965
$117$	−1.49086	−0.137830
$118$	−6.77209	−0.623422
$119$	0.395765	0.0362797
$120$	1.49086	0.136097
$121$	−9.54942	−0.868129
$122$	2.36329	0.213962
$123$	−9.26819	−0.835684
$124$	−4.40880	−0.395922
$125$	−11.5949	−1.03708
$126$	−1.77733	−0.158337
$127$	−0.368523	−0.0327011	−0.0163505	−	0.999866i	$-0.505205\pi$
$127$	−0.368523	−0.0327011	−0.0163505	+	0.999866i	$0.505205\pi$
$128$	−1.00000	−0.0883883
$129$	−1.69527	−0.149260
$130$	2.22267	0.194941
$131$	18.3853	1.60633	0.803165	−	0.595756i	$-0.203148\pi$
$131$	18.3853	1.60633	0.803165	+	0.595756i	$0.203148\pi$
$132$	1.20440	0.104830
$133$	1.77733	0.154114
$134$	−8.06379	−0.696605
$135$	−1.49086	−0.128313
$136$	−0.222674	−0.0190942
$137$	22.0403	1.88303	0.941514	−	0.336974i	$-0.109403\pi$
$137$	22.0403	1.88303	0.941514	+	0.336974i	$0.109403\pi$
$138$	−1.69527	−0.144311
$139$	−3.90490	−0.331209	−0.165605	−	0.986192i	$-0.552958\pi$
$139$	−3.90490	−0.331209	−0.165605	+	0.986192i	$0.552958\pi$
$140$	2.64975	0.223945
$141$	4.42708	0.372827
$142$	−4.57292	−0.383751
$143$	1.79560	0.150155
$144$	1.00000	0.0833333
$145$	2.44011	0.202640
$146$	0.631477	0.0522614
$147$	3.84111	0.316810
$148$	0.795598	0.0653978
$149$	−7.57292	−0.620398	−0.310199	−	0.950672i	$-0.600396\pi$
$149$	−7.57292	−0.620398	−0.310199	+	0.950672i	$0.600396\pi$
$150$	−2.77733	−0.226768
$151$	−14.4088	−1.17257	−0.586286	−	0.810104i	$-0.699410\pi$
$151$	−14.4088	−1.17257	−0.586286	+	0.810104i	$0.699410\pi$
$152$	−1.00000	−0.0811107
$153$	0.222674	0.0180022
$154$	2.14061	0.172496
$155$	−6.57292	−0.527950
$156$	1.49086	0.119365
$157$	−1.50914	−0.120442	−0.0602211	−	0.998185i	$-0.519181\pi$
$157$	−1.50914	−0.120442	−0.0602211	+	0.998185i	$0.519181\pi$
$158$	−9.08580	−0.722827
$159$	1.00000	0.0793052
$160$	−1.49086	−0.117863
$161$	−3.01304	−0.237461
$162$	−1.00000	−0.0785674
$163$	11.9635	0.937050	0.468525	−	0.883450i	$-0.344786\pi$
$163$	11.9635	0.937050	0.468525	+	0.883450i	$0.344786\pi$
$164$	9.26819	0.723724
$165$	1.79560	0.139787
$166$	−13.8228	−1.07286
$167$	2.01827	0.156179	0.0780893	−	0.996946i	$-0.475118\pi$
$167$	2.01827	0.156179	0.0780893	+	0.996946i	$0.475118\pi$
$168$	1.77733	0.137124
$169$	−10.7773	−0.829025
$170$	−0.331977	−0.0254615
$171$	1.00000	0.0764719
$172$	1.69527	0.129263
$173$	−12.2902	−0.934406	−0.467203	−	0.884150i	$-0.654738\pi$
$173$	−12.2902	−0.934406	−0.467203	+	0.884150i	$0.654738\pi$
$174$	1.63671	0.124079
$175$	−4.93621	−0.373143
$176$	−1.20440	−0.0907852
$177$	−6.77209	−0.509022
$178$	−5.75905	−0.431659
$179$	−0.700500	−0.0523578	−0.0261789	−	0.999657i	$-0.508334\pi$
$179$	−0.700500	−0.0523578	−0.0261789	+	0.999657i	$0.508334\pi$
$180$	1.49086	0.111122
$181$	0.0402805	0.00299403	0.00149701	−	0.999999i	$-0.499523\pi$
$181$	0.0402805	0.00299403	0.00149701	+	0.999999i	$0.499523\pi$
$182$	2.64975	0.196413
$183$	2.36329	0.174699
$184$	1.69527	0.124977
$185$	1.18613	0.0872059
$186$	−4.40880	−0.323269
$187$	−0.268189	−0.0196119
$188$	−4.42708	−0.322878
$189$	−1.77733	−0.129281
$190$	−1.49086	−0.108159
$191$	−0.109303	−0.00790887	−0.00395443	−	0.999992i	$-0.501259\pi$
$191$	−0.109303	−0.00790887	−0.00395443	+	0.999992i	$0.501259\pi$
$192$	−1.00000	−0.0721688
$193$	−8.94518	−0.643888	−0.321944	−	0.946759i	$-0.604336\pi$
$193$	−8.94518	−0.643888	−0.321944	+	0.946759i	$0.604336\pi$
$194$	−6.67699	−0.479380
$195$	2.22267	0.159169
$196$	−3.84111	−0.274365
$197$	9.18613	0.654485	0.327242	−	0.944940i	$-0.393881\pi$
$197$	9.18613	0.654485	0.327242	+	0.944940i	$0.393881\pi$
$198$	1.20440	0.0855931
$199$	25.4308	1.80274	0.901371	−	0.433047i	$-0.142562\pi$
$199$	25.4308	1.80274	0.901371	+	0.433047i	$0.142562\pi$
$200$	2.77733	0.196387
$201$	−8.06379	−0.568776
$202$	10.8997	0.766898
$203$	2.90897	0.204170
$204$	−0.222674	−0.0155903
$205$	13.8176	0.965063
$206$	−6.20440	−0.432281
$207$	−1.69527	−0.117829
$208$	−1.49086	−0.103373
$209$	−1.20440	−0.0833102
$210$	2.64975	0.182850
$211$	−0.368523	−0.0253701	−0.0126851	−	0.999920i	$-0.504038\pi$
$211$	−0.368523	−0.0253701	−0.0126851	+	0.999920i	$0.504038\pi$
$212$	−1.00000	−0.0686803
$213$	−4.57292	−0.313332
$214$	−11.4909	−0.785499
$215$	2.52741	0.172368
$216$	1.00000	0.0680414
$217$	−7.83588	−0.531934
$218$	0.923174	0.0625252
$219$	0.631477	0.0426713
$220$	−1.79560	−0.121059
$221$	−0.331977	−0.0223312
$222$	0.795598	0.0533971
$223$	16.9504	1.13508	0.567542	−	0.823345i	$-0.307894\pi$
$223$	16.9504	1.13508	0.567542	+	0.823345i	$0.307894\pi$
$224$	−1.77733	−0.118753
$225$	−2.77733	−0.185155
$226$	−12.9635	−0.862316
$227$	−15.5767	−1.03386	−0.516930	−	0.856028i	$-0.672925\pi$
$227$	−15.5767	−1.03386	−0.516930	+	0.856028i	$0.672925\pi$
$228$	−1.00000	−0.0662266
$229$	−11.5625	−0.764069	−0.382034	−	0.924148i	$-0.624776\pi$
$229$	−11.5625	−0.764069	−0.382034	+	0.924148i	$0.624776\pi$
$230$	2.52741	0.166652
$231$	2.14061	0.140842
$232$	−1.63671	−0.107455
$233$	24.0675	1.57672	0.788358	−	0.615217i	$-0.210932\pi$
$233$	24.0675	1.57672	0.788358	+	0.615217i	$0.210932\pi$
$234$	1.49086	0.0974608
$235$	−6.60017	−0.430547
$236$	6.77209	0.440826
$237$	−9.08580	−0.590186
$238$	−0.395765	−0.0256536
$239$	−0.917939	−0.0593766	−0.0296883	−	0.999559i	$-0.509451\pi$
$239$	−0.917939	−0.0593766	−0.0296883	+	0.999559i	$0.509451\pi$
$240$	−1.49086	−0.0962348
$241$	17.3189	1.11561	0.557805	−	0.829972i	$-0.311644\pi$
$241$	17.3189	1.11561	0.557805	+	0.829972i	$0.311644\pi$
$242$	9.54942	0.613860
$243$	−1.00000	−0.0641500
$244$	−2.36329	−0.151294
$245$	−5.72658	−0.365858
$246$	9.26819	0.590918
$247$	−1.49086	−0.0948614
$248$	4.40880	0.279959
$249$	−13.8228	−0.875987
$250$	11.5949	0.733328
$251$	−20.9855	−1.32459	−0.662295	−	0.749243i	$-0.730418\pi$
$251$	−20.9855	−1.32459	−0.662295	+	0.749243i	$0.730418\pi$
$252$	1.77733	0.111961
$253$	2.04178	0.128366
$254$	0.368523	0.0231232
$255$	−0.331977	−0.0207892
$256$	1.00000	0.0625000
$257$	17.6367	1.10015	0.550074	−	0.835116i	$-0.314600\pi$
$257$	17.6367	1.10015	0.550074	+	0.835116i	$0.314600\pi$
$258$	1.69527	0.105543
$259$	1.41404	0.0878640
$260$	−2.22267	−0.137844
$261$	1.63671	0.101310
$262$	−18.3853	−1.13585
$263$	−20.4543	−1.26127	−0.630634	−	0.776081i	$-0.717205\pi$
$263$	−20.4543	−1.26127	−0.630634	+	0.776081i	$0.717205\pi$
$264$	−1.20440	−0.0741258
$265$	−1.49086	−0.0915830
$266$	−1.77733	−0.108975
$267$	−5.75905	−0.352448
$268$	8.06379	0.492574
$269$	−6.91271	−0.421475	−0.210738	−	0.977543i	$-0.567587\pi$
$269$	−6.91271	−0.421475	−0.210738	+	0.977543i	$0.567587\pi$
$270$	1.49086	0.0907311
$271$	−0.713538	−0.0433443	−0.0216722	−	0.999765i	$-0.506899\pi$
$271$	−0.713538	−0.0433443	−0.0216722	+	0.999765i	$0.506899\pi$
$272$	0.222674	0.0135016
$273$	2.64975	0.160370
$274$	−22.0403	−1.33150
$275$	3.34502	0.201712
$276$	1.69527	0.102043
$277$	−20.6222	−1.23907	−0.619533	−	0.784970i	$-0.712678\pi$
$277$	−20.6222	−1.23907	−0.619533	+	0.784970i	$0.712678\pi$
$278$	3.90490	0.234200
$279$	−4.40880	−0.263948
$280$	−2.64975	−0.158353
$281$	24.7941	1.47909	0.739546	−	0.673106i	$-0.235040\pi$
$281$	24.7941	1.47909	0.739546	+	0.673106i	$0.235040\pi$
$282$	−4.42708	−0.263629
$283$	20.1809	1.19963	0.599815	−	0.800139i	$-0.295241\pi$
$283$	20.1809	1.19963	0.599815	+	0.800139i	$0.295241\pi$
$284$	4.57292	0.271353
$285$	−1.49086	−0.0883111
$286$	−1.79560	−0.106176
$287$	16.4726	0.972346
$288$	−1.00000	−0.0589256
$289$	−16.9504	−0.997083
$290$	−2.44011	−0.143288
$291$	−6.67699	−0.391412
$292$	−0.631477	−0.0369544
$293$	16.2499	0.949330	0.474665	−	0.880166i	$-0.342569\pi$
$293$	16.2499	0.949330	0.474665	+	0.880166i	$0.342569\pi$
$294$	−3.84111	−0.224018
$295$	10.0963	0.587827
$296$	−0.795598	−0.0462432
$297$	1.20440	0.0698865
$298$	7.57292	0.438688
$299$	2.52741	0.146164
$300$	2.77733	0.160349
$301$	3.01304	0.173669
$302$	14.4088	0.829133
$303$	10.8997	0.626169
$304$	1.00000	0.0573539
$305$	−3.52334	−0.201746
$306$	−0.222674	−0.0127294
$307$	−8.06379	−0.460225	−0.230112	−	0.973164i	$-0.573909\pi$
$307$	−8.06379	−0.460225	−0.230112	+	0.973164i	$0.573909\pi$
$308$	−2.14061	−0.121973
$309$	−6.20440	−0.352956
$310$	6.57292	0.373317
$311$	−27.7460	−1.57333	−0.786666	−	0.617379i	$-0.788195\pi$
$311$	−27.7460	−1.57333	−0.786666	+	0.617379i	$0.788195\pi$
$312$	−1.49086	−0.0844035
$313$	−17.0325	−0.962733	−0.481366	−	0.876520i	$-0.659859\pi$
$313$	−17.0325	−0.962733	−0.481366	+	0.876520i	$0.659859\pi$
$314$	1.50914	0.0851655
$315$	2.64975	0.149297
$316$	9.08580	0.511116
$317$	9.19917	0.516677	0.258338	−	0.966055i	$-0.416825\pi$
$317$	9.19917	0.516677	0.258338	+	0.966055i	$0.416825\pi$
$318$	−1.00000	−0.0560772
$319$	−1.97126	−0.110369
$320$	1.49086	0.0833418
$321$	−11.4909	−0.641357
$322$	3.01304	0.167910
$323$	0.222674	0.0123899
$324$	1.00000	0.0555556
$325$	4.14061	0.229680
$326$	−11.9635	−0.662594
$327$	0.923174	0.0510516
$328$	−9.26819	−0.511750
$329$	−7.86836	−0.433796
$330$	−1.79560	−0.0988444
$331$	20.5233	1.12806	0.564032	−	0.825753i	$-0.309249\pi$
$331$	20.5233	1.12806	0.564032	+	0.825753i	$0.309249\pi$
$332$	13.8228	0.758627
$333$	0.795598	0.0435985
$334$	−2.01827	−0.110435
$335$	12.0220	0.656832
$336$	−1.77733	−0.0969611
$337$	−5.07683	−0.276552	−0.138276	−	0.990394i	$-0.544156\pi$
$337$	−5.07683	−0.276552	−0.138276	+	0.990394i	$0.544156\pi$
$338$	10.7773	0.586209
$339$	−12.9635	−0.704078
$340$	0.331977	0.0180040
$341$	5.30997	0.287551
$342$	−1.00000	−0.0540738
$343$	−19.2682	−1.04038
$344$	−1.69527	−0.0914026
$345$	2.52741	0.136071
$346$	12.2902	0.660725
$347$	−8.57816	−0.460500	−0.230250	−	0.973132i	$-0.573954\pi$
$347$	−8.57816	−0.460500	−0.230250	+	0.973132i	$0.573954\pi$
$348$	−1.63671	−0.0877370
$349$	14.3502	0.768151	0.384076	−	0.923302i	$-0.374520\pi$
$349$	14.3502	0.768151	0.384076	+	0.923302i	$0.374520\pi$
$350$	4.93621	0.263852
$351$	1.49086	0.0795764
$352$	1.20440	0.0641948
$353$	−2.21744	−0.118022	−0.0590112	−	0.998257i	$-0.518795\pi$
$353$	−2.21744	−0.118022	−0.0590112	+	0.998257i	$0.518795\pi$
$354$	6.77209	0.359933
$355$	6.81761	0.361841
$356$	5.75905	0.305229
$357$	−0.395765	−0.0209461
$358$	0.700500	0.0370226
$359$	−29.5845	−1.56141	−0.780704	−	0.624901i	$-0.785139\pi$
$359$	−29.5845	−1.56141	−0.780704	+	0.624901i	$0.785139\pi$
$360$	−1.49086	−0.0785754
$361$	1.00000	0.0526316
$362$	−0.0402805	−0.00211710
$363$	9.54942	0.501214
$364$	−2.64975	−0.138885
$365$	−0.941447	−0.0492776
$366$	−2.36329	−0.123531
$367$	−16.6770	−0.870532	−0.435266	−	0.900302i	$-0.643346\pi$
$367$	−16.6770	−0.870532	−0.435266	+	0.900302i	$0.643346\pi$
$368$	−1.69527	−0.0883718
$369$	9.26819	0.482483
$370$	−1.18613	−0.0616639
$371$	−1.77733	−0.0922742
$372$	4.40880	0.228586
$373$	−18.7538	−0.971036	−0.485518	−	0.874227i	$-0.661369\pi$
$373$	−18.7538	−0.971036	−0.485518	+	0.874227i	$0.661369\pi$
$374$	0.268189	0.0138677
$375$	11.5949	0.598760
$376$	4.42708	0.228309
$377$	−2.44011	−0.125672
$378$	1.77733	0.0914158
$379$	−5.11861	−0.262925	−0.131463	−	0.991321i	$-0.541967\pi$
$379$	−5.11861	−0.262925	−0.131463	+	0.991321i	$0.541967\pi$
$380$	1.49086	0.0764797
$381$	0.368523	0.0188800
$382$	0.109303	0.00559241
$383$	30.2056	1.54343	0.771716	−	0.635967i	$-0.219399\pi$
$383$	30.2056	1.54343	0.771716	+	0.635967i	$0.219399\pi$
$384$	1.00000	0.0510310
$385$	−3.19136	−0.162647
$386$	8.94518	0.455298
$387$	1.69527	0.0861752
$388$	6.67699	0.338973
$389$	39.1586	1.98542	0.992709	−	0.120538i	$-0.0384620\pi$
$389$	39.1586	1.98542	0.992709	+	0.120538i	$0.0384620\pi$
$390$	−2.22267	−0.112549
$391$	−0.377492	−0.0190906
$392$	3.84111	0.194006
$393$	−18.3853	−0.927415
$394$	−9.18613	−0.462790
$395$	13.5457	0.681557
$396$	−1.20440	−0.0605235
$397$	−14.7538	−0.740473	−0.370236	−	0.928938i	$-0.620723\pi$
$397$	−14.7538	−0.740473	−0.370236	+	0.928938i	$0.620723\pi$
$398$	−25.4308	−1.27473
$399$	−1.77733	−0.0889776
$400$	−2.77733	−0.138866
$401$	12.9765	0.648015	0.324008	−	0.946054i	$-0.394970\pi$
$401$	12.9765	0.648015	0.324008	+	0.946054i	$0.394970\pi$
$402$	8.06379	0.402185
$403$	6.57292	0.327421
$404$	−10.8997	−0.542279
$405$	1.49086	0.0740816
$406$	−2.90897	−0.144370
$407$	−0.958220	−0.0474972
$408$	0.222674	0.0110240
$409$	27.2537	1.34761	0.673803	−	0.738911i	$-0.264660\pi$
$409$	27.2537	1.34761	0.673803	+	0.738911i	$0.264660\pi$
$410$	−13.8176	−0.682403
$411$	−22.0403	−1.08717
$412$	6.20440	0.305669
$413$	12.0362	0.592263
$414$	1.69527	0.0833177
$415$	20.6080	1.01161
$416$	1.49086	0.0730956
$417$	3.90490	0.191224
$418$	1.20440	0.0589092
$419$	35.1443	1.71691	0.858457	−	0.512886i	$-0.171424\pi$
$419$	35.1443	1.71691	0.858457	+	0.512886i	$0.171424\pi$
$420$	−2.64975	−0.129295
$421$	31.0806	1.51477	0.757387	−	0.652966i	$-0.226476\pi$
$421$	31.0806	1.51477	0.757387	+	0.652966i	$0.226476\pi$
$422$	0.368523	0.0179394
$423$	−4.42708	−0.215252
$424$	1.00000	0.0485643
$425$	−0.618439	−0.0299987
$426$	4.57292	0.221559
$427$	−4.20033	−0.203268
$428$	11.4909	0.555432
$429$	−1.79560	−0.0866923
$430$	−2.52741	−0.121882
$431$	14.7501	0.710487	0.355243	−	0.934774i	$-0.384398\pi$
$431$	14.7501	0.710487	0.355243	+	0.934774i	$0.384398\pi$
$432$	−1.00000	−0.0481125
$433$	18.0638	0.868090	0.434045	−	0.900891i	$-0.357086\pi$
$433$	18.0638	0.868090	0.434045	+	0.900891i	$0.357086\pi$
$434$	7.83588	0.376134
$435$	−2.44011	−0.116995
$436$	−0.923174	−0.0442120
$437$	−1.69527	−0.0810955
$438$	−0.631477	−0.0301732
$439$	27.0220	1.28969	0.644845	−	0.764313i	$-0.276922\pi$
$439$	27.0220	1.28969	0.644845	+	0.764313i	$0.276922\pi$
$440$	1.79560	0.0856018
$441$	−3.84111	−0.182910
$442$	0.331977	0.0157905
$443$	18.0936	0.859653	0.429826	−	0.902912i	$-0.358575\pi$
$443$	18.0936	0.859653	0.429826	+	0.902912i	$0.358575\pi$
$444$	−0.795598	−0.0377574
$445$	8.58596	0.407014
$446$	−16.9504	−0.802625
$447$	7.57292	0.358187
$448$	1.77733	0.0839707
$449$	22.2589	1.05046	0.525231	−	0.850960i	$-0.323979\pi$
$449$	22.2589	1.05046	0.525231	+	0.850960i	$0.323979\pi$
$450$	2.77733	0.130924
$451$	−11.1626	−0.525627
$452$	12.9635	0.609750
$453$	14.4088	0.676985
$454$	15.5767	0.731049
$455$	−3.95042	−0.185198
$456$	1.00000	0.0468293
$457$	−2.43754	−0.114024	−0.0570118	−	0.998374i	$-0.518157\pi$
$457$	−2.43754	−0.114024	−0.0570118	+	0.998374i	$0.518157\pi$
$458$	11.5625	0.540278
$459$	−0.222674	−0.0103935
$460$	−2.52741	−0.117841
$461$	5.80864	0.270535	0.135268	−	0.990809i	$-0.456811\pi$
$461$	5.80864	0.270535	0.135268	+	0.990809i	$0.456811\pi$
$462$	−2.14061	−0.0995904
$463$	14.0858	0.654622	0.327311	−	0.944917i	$-0.393857\pi$
$463$	14.0858	0.654622	0.327311	+	0.944917i	$0.393857\pi$
$464$	1.63671	0.0759824
$465$	6.57292	0.304812
$466$	−24.0675	−1.11491
$467$	14.9728	0.692857	0.346428	−	0.938076i	$-0.387394\pi$
$467$	14.9728	0.692857	0.346428	+	0.938076i	$0.387394\pi$
$468$	−1.49086	−0.0689152
$469$	14.3320	0.661789
$470$	6.60017	0.304443
$471$	1.50914	0.0695373
$472$	−6.77209	−0.311711
$473$	−2.04178	−0.0938811
$474$	9.08580	0.417324
$475$	−2.77733	−0.127432
$476$	0.395765	0.0181398
$477$	−1.00000	−0.0457869
$478$	0.917939	0.0419856
$479$	24.3502	1.11259	0.556296	−	0.830984i	$-0.312222\pi$
$479$	24.3502	1.11259	0.556296	+	0.830984i	$0.312222\pi$
$480$	1.49086	0.0680483
$481$	−1.18613	−0.0540828
$482$	−17.3189	−0.788856
$483$	3.01304	0.137098
$484$	−9.54942	−0.434064
$485$	9.95449	0.452010
$486$	1.00000	0.0453609
$487$	−1.00897	−0.0457208	−0.0228604	−	0.999739i	$-0.507277\pi$
$487$	−1.00897	−0.0457208	−0.0228604	+	0.999739i	$0.507277\pi$
$488$	2.36329	0.106981
$489$	−11.9635	−0.541006
$490$	5.72658	0.258700
$491$	14.4648	0.652787	0.326393	−	0.945234i	$-0.394167\pi$
$491$	14.4648	0.652787	0.326393	+	0.945234i	$0.394167\pi$
$492$	−9.26819	−0.417842
$493$	0.364454	0.0164142
$494$	1.49086	0.0670771
$495$	−1.79560	−0.0807061
$496$	−4.40880	−0.197961
$497$	8.12758	0.364572
$498$	13.8228	0.619416
$499$	6.70573	0.300190	0.150095	−	0.988672i	$-0.452042\pi$
$499$	6.70573	0.300190	0.150095	+	0.988672i	$0.452042\pi$
$500$	−11.5949	−0.518541
$501$	−2.01827	−0.0901698
$502$	20.9855	0.936627
$503$	22.8944	1.02081	0.510406	−	0.859933i	$-0.329495\pi$
$503$	22.8944	1.02081	0.510406	+	0.859933i	$0.329495\pi$
$504$	−1.77733	−0.0791684
$505$	−16.2499	−0.723112
$506$	−2.04178	−0.0907682
$507$	10.7773	0.478638
$508$	−0.368523	−0.0163505
$509$	−27.1041	−1.20137	−0.600683	−	0.799487i	$-0.705105\pi$
$509$	−27.1041	−1.20137	−0.600683	+	0.799487i	$0.705105\pi$
$510$	0.331977	0.0147002
$511$	−1.12234	−0.0496494
$512$	−1.00000	−0.0441942
$513$	−1.00000	−0.0441511
$514$	−17.6367	−0.777922
$515$	9.24992	0.407600
$516$	−1.69527	−0.0746299
$517$	5.33198	0.234500
$518$	−1.41404	−0.0621292
$519$	12.2902	0.539480
$520$	2.22267	0.0974707
$521$	−33.4543	−1.46566	−0.732830	−	0.680412i	$-0.761801\pi$
$521$	−33.4543	−1.46566	−0.732830	+	0.680412i	$0.761801\pi$
$522$	−1.63671	−0.0716369
$523$	−0.894432	−0.0391108	−0.0195554	−	0.999809i	$-0.506225\pi$
$523$	−0.894432	−0.0391108	−0.0195554	+	0.999809i	$0.506225\pi$
$524$	18.3853	0.803165
$525$	4.93621	0.215434
$526$	20.4543	0.891851
$527$	−0.981727	−0.0427647
$528$	1.20440	0.0524148
$529$	−20.1261	−0.875047
$530$	1.49086	0.0647590
$531$	6.77209	0.293884
$532$	1.77733	0.0770568
$533$	−13.8176	−0.598507
$534$	5.75905	0.249219
$535$	17.1313	0.740651
$536$	−8.06379	−0.348303
$537$	0.700500	0.0302288
$538$	6.91271	0.298028
$539$	4.62624	0.199266
$540$	−1.49086	−0.0641566
$541$	−35.4946	−1.52603	−0.763016	−	0.646380i	$-0.776282\pi$
$541$	−35.4946	−1.52603	−0.763016	+	0.646380i	$0.776282\pi$
$542$	0.713538	0.0306491
$543$	−0.0402805	−0.00172860
$544$	−0.222674	−0.00954708
$545$	−1.37633	−0.0589553
$546$	−2.64975	−0.113399
$547$	−14.3540	−0.613732	−0.306866	−	0.951753i	$-0.599280\pi$
$547$	−14.3540	−0.613732	−0.306866	+	0.951753i	$0.599280\pi$
$548$	22.0403	0.941514
$549$	−2.36329	−0.100863
$550$	−3.34502	−0.142632
$551$	1.63671	0.0697263
$552$	−1.69527	−0.0721553
$553$	16.1484	0.686701
$554$	20.6222	0.876152
$555$	−1.18613	−0.0503484
$556$	−3.90490	−0.165605
$557$	45.0257	1.90780	0.953901	−	0.300122i	$-0.0970272\pi$
$557$	45.0257	1.90780	0.953901	+	0.300122i	$0.0970272\pi$
$558$	4.40880	0.186640
$559$	−2.52741	−0.106898
$560$	2.64975	0.111972
$561$	0.268189	0.0113230
$562$	−24.7941	−1.04588
$563$	27.4804	1.15816	0.579080	−	0.815271i	$-0.303412\pi$
$563$	27.4804	1.15816	0.579080	+	0.815271i	$0.303412\pi$
$564$	4.42708	0.186414
$565$	19.3267	0.813082
$566$	−20.1809	−0.848266
$567$	1.77733	0.0746407
$568$	−4.57292	−0.191876
$569$	8.86719	0.371732	0.185866	−	0.982575i	$-0.440491\pi$
$569$	8.86719	0.371732	0.185866	+	0.982575i	$0.440491\pi$
$570$	1.49086	0.0624454
$571$	27.1235	1.13508	0.567542	−	0.823345i	$-0.307895\pi$
$571$	27.1235	1.13508	0.567542	+	0.823345i	$0.307895\pi$
$572$	1.79560	0.0750777
$573$	0.109303	0.00456619
$574$	−16.4726	−0.687553
$575$	4.70830	0.196350
$576$	1.00000	0.0416667
$577$	3.74078	0.155731	0.0778654	−	0.996964i	$-0.475190\pi$
$577$	3.74078	0.155731	0.0778654	+	0.996964i	$0.475190\pi$
$578$	16.9504	0.705044
$579$	8.94518	0.371749
$580$	2.44011	0.101320
$581$	24.5677	1.01924
$582$	6.67699	0.276770
$583$	1.20440	0.0498812
$584$	0.631477	0.0261307
$585$	−2.22267	−0.0918963
$586$	−16.2499	−0.671278
$587$	27.8370	1.14896	0.574479	−	0.818519i	$-0.305205\pi$
$587$	27.8370	1.14896	0.574479	+	0.818519i	$0.305205\pi$
$588$	3.84111	0.158405
$589$	−4.40880	−0.181662
$590$	−10.0963	−0.415657
$591$	−9.18613	−0.377867
$592$	0.795598	0.0326989
$593$	−41.2772	−1.69505	−0.847525	−	0.530756i	$-0.821908\pi$
$593$	−41.2772	−1.69505	−0.847525	+	0.530756i	$0.821908\pi$
$594$	−1.20440	−0.0494172
$595$	0.590031	0.0241889
$596$	−7.57292	−0.310199
$597$	−25.4308	−1.04081
$598$	−2.52741	−0.103353
$599$	−3.06636	−0.125288	−0.0626440	−	0.998036i	$-0.519953\pi$
$599$	−3.06636	−0.125288	−0.0626440	+	0.998036i	$0.519953\pi$
$600$	−2.77733	−0.113384
$601$	−14.0350	−0.572501	−0.286251	−	0.958155i	$-0.592409\pi$
$601$	−14.0350	−0.572501	−0.286251	+	0.958155i	$0.592409\pi$
$602$	−3.01304	−0.122802
$603$	8.06379	0.328383
$604$	−14.4088	−0.586286
$605$	−14.2369	−0.578811
$606$	−10.8997	−0.442769
$607$	−17.6091	−0.714733	−0.357366	−	0.933964i	$-0.616325\pi$
$607$	−17.6091	−0.714733	−0.357366	+	0.933964i	$0.616325\pi$
$608$	−1.00000	−0.0405554
$609$	−2.90897	−0.117877
$610$	3.52334	0.142656
$611$	6.60017	0.267014
$612$	0.222674	0.00900108
$613$	8.66802	0.350098	0.175049	−	0.984560i	$-0.443992\pi$
$613$	8.66802	0.350098	0.175049	+	0.984560i	$0.443992\pi$
$614$	8.06379	0.325428
$615$	−13.8176	−0.557180
$616$	2.14061	0.0862478
$617$	0.275993	0.0111111	0.00555553	−	0.999985i	$-0.498232\pi$
$617$	0.275993	0.0111111	0.00555553	+	0.999985i	$0.498232\pi$
$618$	6.20440	0.249578
$619$	2.46362	0.0990213	0.0495107	−	0.998774i	$-0.484234\pi$
$619$	2.46362	0.0990213	0.0495107	+	0.998774i	$0.484234\pi$
$620$	−6.57292	−0.263975
$621$	1.69527	0.0680286
$622$	27.7460	1.11251
$623$	10.2357	0.410085
$624$	1.49086	0.0596823
$625$	−3.39983	−0.135993
$626$	17.0325	0.680755
$627$	1.20440	0.0480992
$628$	−1.50914	−0.0602211
$629$	0.177159	0.00706381
$630$	−2.64975	−0.105569
$631$	28.1899	1.12222	0.561110	−	0.827741i	$-0.310374\pi$
$631$	28.1899	1.12222	0.561110	+	0.827741i	$0.310374\pi$
$632$	−9.08580	−0.361414
$633$	0.368523	0.0146475
$634$	−9.19917	−0.365346
$635$	−0.549417	−0.0218029
$636$	1.00000	0.0396526
$637$	5.72658	0.226895
$638$	1.97126	0.0780429
$639$	4.57292	0.180902
$640$	−1.49086	−0.0589316
$641$	−8.63148	−0.340923	−0.170461	−	0.985364i	$-0.554526\pi$
$641$	−8.63148	−0.340923	−0.170461	+	0.985364i	$0.554526\pi$
$642$	11.4909	0.453508
$643$	−3.44385	−0.135812	−0.0679061	−	0.997692i	$-0.521632\pi$
$643$	−3.44385	−0.135812	−0.0679061	+	0.997692i	$0.521632\pi$
$644$	−3.01304	−0.118730
$645$	−2.52741	−0.0995166
$646$	−0.222674	−0.00876100
$647$	6.95042	0.273249	0.136625	−	0.990623i	$-0.456375\pi$
$647$	6.95042	0.273249	0.136625	+	0.990623i	$0.456375\pi$
$648$	−1.00000	−0.0392837
$649$	−8.15632	−0.320163
$650$	−4.14061	−0.162408
$651$	7.83588	0.307112
$652$	11.9635	0.468525
$653$	32.4685	1.27059	0.635296	−	0.772269i	$-0.280878\pi$
$653$	32.4685	1.27059	0.635296	+	0.772269i	$0.280878\pi$
$654$	−0.923174	−0.0360990
$655$	27.4100	1.07100
$656$	9.26819	0.361862
$657$	−0.631477	−0.0246363
$658$	7.86836	0.306740
$659$	0.301000	0.0117253	0.00586264	−	0.999983i	$-0.498134\pi$
$659$	0.301000	0.0117253	0.00586264	+	0.999983i	$0.498134\pi$
$660$	1.79560	0.0698936
$661$	−46.3760	−1.80382	−0.901909	−	0.431927i	$-0.857834\pi$
$661$	−46.3760	−1.80382	−0.901909	+	0.431927i	$0.857834\pi$
$662$	−20.5233	−0.797662
$663$	0.331977	0.0128929
$664$	−13.8228	−0.536430
$665$	2.64975	0.102753
$666$	−0.795598	−0.0308288
$667$	−2.77466	−0.107435
$668$	2.01827	0.0780893
$669$	−16.9504	−0.655341
$670$	−12.0220	−0.464451
$671$	2.84635	0.109882
$672$	1.77733	0.0685618
$673$	−27.9594	−1.07776	−0.538878	−	0.842384i	$-0.681151\pi$
$673$	−27.9594	−1.07776	−0.538878	+	0.842384i	$0.681151\pi$
$674$	5.07683	0.195552
$675$	2.77733	0.106899
$676$	−10.7773	−0.414513
$677$	−45.4305	−1.74604	−0.873018	−	0.487689i	$-0.837840\pi$
$677$	−45.4305	−1.74604	−0.873018	+	0.487689i	$0.837840\pi$
$678$	12.9635	0.497858
$679$	11.8672	0.455421
$680$	−0.331977	−0.0127307
$681$	15.5767	0.596899
$682$	−5.30997	−0.203329
$683$	26.6222	1.01867	0.509335	−	0.860569i	$-0.329892\pi$
$683$	26.6222	1.01867	0.509335	+	0.860569i	$0.329892\pi$
$684$	1.00000	0.0382360
$685$	32.8591	1.25548
$686$	19.2682	0.735663
$687$	11.5625	0.441135
$688$	1.69527	0.0646314
$689$	1.49086	0.0567974
$690$	−2.52741	−0.0962168
$691$	25.1041	0.955004	0.477502	−	0.878631i	$-0.341542\pi$
$691$	25.1041	0.955004	0.477502	+	0.878631i	$0.341542\pi$
$692$	−12.2902	−0.467203
$693$	−2.14061	−0.0813152
$694$	8.57816	0.325622
$695$	−5.82168	−0.220829
$696$	1.63671	0.0620394
$697$	2.06379	0.0781715
$698$	−14.3502	−0.543165
$699$	−24.0675	−0.910317
$700$	−4.93621	−0.186571
$701$	12.6625	0.478254	0.239127	−	0.970988i	$-0.423139\pi$
$701$	12.6625	0.478254	0.239127	+	0.970988i	$0.423139\pi$
$702$	−1.49086	−0.0562690
$703$	0.795598	0.0300066
$704$	−1.20440	−0.0453926
$705$	6.60017	0.248577
$706$	2.21744	0.0834545
$707$	−19.3723	−0.728569
$708$	−6.77209	−0.254511
$709$	−17.1496	−0.644066	−0.322033	−	0.946728i	$-0.604366\pi$
$709$	−17.1496	−0.644066	−0.322033	+	0.946728i	$0.604366\pi$
$710$	−6.81761	−0.255860
$711$	9.08580	0.340744
$712$	−5.75905	−0.215830
$713$	7.47409	0.279907
$714$	0.395765	0.0148111
$715$	2.67699	0.100114
$716$	−0.700500	−0.0261789
$717$	0.917939	0.0342811
$718$	29.5845	1.10408
$719$	15.0675	0.561924	0.280962	−	0.959719i	$-0.409347\pi$
$719$	15.0675	0.561924	0.280962	+	0.959719i	$0.409347\pi$
$720$	1.49086	0.0555612
$721$	11.0272	0.410676
$722$	−1.00000	−0.0372161
$723$	−17.3189	−0.644098
$724$	0.0402805	0.00149701
$725$	−4.54568	−0.168822
$726$	−9.54942	−0.354412
$727$	−7.91014	−0.293371	−0.146685	−	0.989183i	$-0.546860\pi$
$727$	−7.91014	−0.293371	−0.146685	+	0.989183i	$0.546860\pi$
$728$	2.64975	0.0982063
$729$	1.00000	0.0370370
$730$	0.941447	0.0348445
$731$	0.377492	0.0139620
$732$	2.36329	0.0873496
$733$	−10.0194	−0.370076	−0.185038	−	0.982731i	$-0.559241\pi$
$733$	−10.0194	−0.370076	−0.185038	+	0.982731i	$0.559241\pi$
$734$	16.6770	0.615559
$735$	5.72658	0.211228
$736$	1.69527	0.0624883
$737$	−9.71204	−0.357748
$738$	−9.26819	−0.341167
$739$	−32.4230	−1.19270	−0.596350	−	0.802725i	$-0.703383\pi$
$739$	−32.4230	−1.19270	−0.596350	+	0.802725i	$0.703383\pi$
$740$	1.18613	0.0436030
$741$	1.49086	0.0547682
$742$	1.77733	0.0652477
$743$	−23.5532	−0.864081	−0.432041	−	0.901854i	$-0.642206\pi$
$743$	−23.5532	−0.864081	−0.432041	+	0.901854i	$0.642206\pi$
$744$	−4.40880	−0.161635
$745$	−11.2902	−0.413641
$746$	18.7538	0.686626
$747$	13.8228	0.505751
$748$	−0.268189	−0.00980597
$749$	20.4230	0.746240
$750$	−11.5949	−0.423387
$751$	−17.7497	−0.647698	−0.323849	−	0.946109i	$-0.604977\pi$
$751$	−17.7497	−0.647698	−0.323849	+	0.946109i	$0.604977\pi$
$752$	−4.42708	−0.161439
$753$	20.9855	0.764753
$754$	2.44011	0.0888637
$755$	−21.4816	−0.781794
$756$	−1.77733	−0.0646407
$757$	1.11861	0.0406564	0.0203282	−	0.999793i	$-0.493529\pi$
$757$	1.11861	0.0406564	0.0203282	+	0.999793i	$0.493529\pi$
$758$	5.11861	0.185916
$759$	−2.04178	−0.0741119
$760$	−1.49086	−0.0540793
$761$	4.04551	0.146650	0.0733249	−	0.997308i	$-0.476639\pi$
$761$	4.04551	0.146650	0.0733249	+	0.997308i	$0.476639\pi$
$762$	−0.368523	−0.0133502
$763$	−1.64078	−0.0594003
$764$	−0.109303	−0.00395443
$765$	0.331977	0.0120027
$766$	−30.2056	−1.09137
$767$	−10.0963	−0.364555
$768$	−1.00000	−0.0360844
$769$	22.9399	0.827236	0.413618	−	0.910451i	$-0.364265\pi$
$769$	22.9399	0.827236	0.413618	+	0.910451i	$0.364265\pi$
$770$	3.19136	0.115009
$771$	−17.6367	−0.635171
$772$	−8.94518	−0.321944
$773$	14.0365	0.504859	0.252430	−	0.967615i	$-0.418770\pi$
$773$	14.0365	0.504859	0.252430	+	0.967615i	$0.418770\pi$
$774$	−1.69527	−0.0609350
$775$	12.2447	0.439842
$776$	−6.67699	−0.239690
$777$	−1.41404	−0.0507283
$778$	−39.1586	−1.40390
$779$	9.26819	0.332067
$780$	2.22267	0.0795845
$781$	−5.50764	−0.197079
$782$	0.377492	0.0134991
$783$	−1.63671	−0.0584913
$784$	−3.84111	−0.137183
$785$	−2.24992	−0.0803030
$786$	18.3853	0.655782
$787$	−2.47783	−0.0883249	−0.0441625	−	0.999024i	$-0.514062\pi$
$787$	−2.47783	−0.0883249	−0.0441625	+	0.999024i	$0.514062\pi$
$788$	9.18613	0.327242
$789$	20.4543	0.728193
$790$	−13.5457	−0.481934
$791$	23.0403	0.819218
$792$	1.20440	0.0427965
$793$	3.52334	0.125117
$794$	14.7538	0.523593
$795$	1.49086	0.0528755
$796$	25.4308	0.901371
$797$	−10.5949	−0.375292	−0.187646	−	0.982237i	$-0.560086\pi$
$797$	−10.5949	−0.375292	−0.187646	+	0.982237i	$0.560086\pi$
$798$	1.77733	0.0629166
$799$	−0.985796	−0.0348750
$800$	2.77733	0.0981933
$801$	5.75905	0.203486
$802$	−12.9765	−0.458216
$803$	0.760552	0.0268393
$804$	−8.06379	−0.284388
$805$	−4.49203	−0.158323
$806$	−6.57292	−0.231521
$807$	6.91271	0.243339
$808$	10.8997	0.383449
$809$	−10.3880	−0.365221	−0.182611	−	0.983185i	$-0.558455\pi$
$809$	−10.3880	−0.365221	−0.182611	+	0.983185i	$0.558455\pi$
$810$	−1.49086	−0.0523836
$811$	53.4345	1.87634	0.938170	−	0.346174i	$-0.112519\pi$
$811$	53.4345	1.87634	0.938170	+	0.346174i	$0.112519\pi$
$812$	2.90897	0.102085
$813$	0.713538	0.0250249
$814$	0.958220	0.0335856
$815$	17.8359	0.624764
$816$	−0.222674	−0.00779516
$817$	1.69527	0.0593098
$818$	−27.2537	−0.952902
$819$	−2.64975	−0.0925898
$820$	13.8176	0.482532
$821$	28.5767	0.997332	0.498666	−	0.866794i	$-0.333823\pi$
$821$	28.5767	0.997332	0.498666	+	0.866794i	$0.333823\pi$
$822$	22.0403	0.768743
$823$	−18.8176	−0.655941	−0.327970	−	0.944688i	$-0.606365\pi$
$823$	−18.8176	−0.655941	−0.327970	+	0.944688i	$0.606365\pi$
$824$	−6.20440	−0.216141
$825$	−3.34502	−0.116458
$826$	−12.0362	−0.418793
$827$	42.0492	1.46220	0.731098	−	0.682273i	$-0.239008\pi$
$827$	42.0492	1.46220	0.731098	+	0.682273i	$0.239008\pi$
$828$	−1.69527	−0.0589145
$829$	41.6184	1.44547	0.722734	−	0.691126i	$-0.242885\pi$
$829$	41.6184	1.44547	0.722734	+	0.691126i	$0.242885\pi$
$830$	−20.6080	−0.715313
$831$	20.6222	0.715375
$832$	−1.49086	−0.0516864
$833$	−0.855317	−0.0296350
$834$	−3.90490	−0.135216
$835$	3.00897	0.104130
$836$	−1.20440	−0.0416551
$837$	4.40880	0.152391
$838$	−35.1443	−1.21404
$839$	−34.0728	−1.17632	−0.588161	−	0.808744i	$-0.700148\pi$
$839$	−34.0728	−1.17632	−0.588161	+	0.808744i	$0.700148\pi$
$840$	2.64975	0.0914251
$841$	−26.3212	−0.907627
$842$	−31.0806	−1.07111
$843$	−24.7941	−0.853954
$844$	−0.368523	−0.0126851
$845$	−16.0675	−0.552740
$846$	4.42708	0.152206
$847$	−16.9724	−0.583179
$848$	−1.00000	−0.0343401
$849$	−20.1809	−0.692607
$850$	0.618439	0.0212123
$851$	−1.34875	−0.0462346
$852$	−4.57292	−0.156666
$853$	−9.48156	−0.324642	−0.162321	−	0.986738i	$-0.551898\pi$
$853$	−9.48156	−0.324642	−0.162321	+	0.986738i	$0.551898\pi$
$854$	4.20033	0.143732
$855$	1.49086	0.0509865
$856$	−11.4909	−0.392750
$857$	−34.8448	−1.19028	−0.595139	−	0.803623i	$-0.702903\pi$
$857$	−34.8448	−1.19028	−0.595139	+	0.803623i	$0.702903\pi$
$858$	1.79560	0.0613007
$859$	10.9205	0.372603	0.186301	−	0.982493i	$-0.440350\pi$
$859$	10.9205	0.372603	0.186301	+	0.982493i	$0.440350\pi$
$860$	2.52741	0.0861839
$861$	−16.4726	−0.561384
$862$	−14.7501	−0.502390
$863$	12.4218	0.422844	0.211422	−	0.977395i	$-0.432191\pi$
$863$	12.4218	0.422844	0.211422	+	0.977395i	$0.432191\pi$
$864$	1.00000	0.0340207
$865$	−18.3230	−0.623001
$866$	−18.0638	−0.613832
$867$	16.9504	0.575666
$868$	−7.83588	−0.265967
$869$	−10.9429	−0.371214
$870$	2.44011	0.0827276
$871$	−12.0220	−0.407350
$872$	0.923174	0.0312626
$873$	6.67699	0.225982
$874$	1.69527	0.0573432
$875$	−20.6080	−0.696677
$876$	0.631477	0.0213356
$877$	−54.8799	−1.85316	−0.926581	−	0.376095i	$-0.877267\pi$
$877$	−54.8799	−1.85316	−0.926581	+	0.376095i	$0.877267\pi$
$878$	−27.0220	−0.911949
$879$	−16.2499	−0.548096
$880$	−1.79560	−0.0605296
$881$	−20.2876	−0.683508	−0.341754	−	0.939790i	$-0.611021\pi$
$881$	−20.2876	−0.683508	−0.341754	+	0.939790i	$0.611021\pi$
$882$	3.84111	0.129337
$883$	48.6259	1.63639	0.818196	−	0.574939i	$-0.194974\pi$
$883$	48.6259	1.63639	0.818196	+	0.574939i	$0.194974\pi$
$884$	−0.331977	−0.0111656
$885$	−10.0963	−0.339382
$886$	−18.0936	−0.607866
$887$	12.4961	0.419578	0.209789	−	0.977747i	$-0.432722\pi$
$887$	12.4961	0.419578	0.209789	+	0.977747i	$0.432722\pi$
$888$	0.795598	0.0266985
$889$	−0.654985	−0.0219675
$890$	−8.58596	−0.287802
$891$	−1.20440	−0.0403490
$892$	16.9504	0.567542
$893$	−4.42708	−0.148146
$894$	−7.57292	−0.253276
$895$	−1.04435	−0.0349088
$896$	−1.77733	−0.0593763
$897$	−2.52741	−0.0843877
$898$	−22.2589	−0.742789
$899$	−7.21594	−0.240665
$900$	−2.77733	−0.0925775
$901$	−0.222674	−0.00741836
$902$	11.1626	0.371675
$903$	−3.01304	−0.100268
$904$	−12.9635	−0.431158
$905$	0.0600528	0.00199622
$906$	−14.4088	−0.478700
$907$	28.7251	0.953801	0.476900	−	0.878957i	$-0.341760\pi$
$907$	28.7251	0.953801	0.476900	+	0.878957i	$0.341760\pi$
$908$	−15.5767	−0.516930
$909$	−10.8997	−0.361519
$910$	3.95042	0.130955
$911$	−20.5782	−0.681785	−0.340892	−	0.940102i	$-0.610729\pi$
$911$	−20.5782	−0.681785	−0.340892	+	0.940102i	$0.610729\pi$
$912$	−1.00000	−0.0331133
$913$	−16.6483	−0.550977
$914$	2.43754	0.0806268
$915$	3.52334	0.116478
$916$	−11.5625	−0.382034
$917$	32.6767	1.07908
$918$	0.222674	0.00734935
$919$	−27.5547	−0.908944	−0.454472	−	0.890761i	$-0.650172\pi$
$919$	−27.5547	−0.908944	−0.454472	+	0.890761i	$0.650172\pi$
$920$	2.52741	0.0833262
$921$	8.06379	0.265711
$922$	−5.80864	−0.191297
$923$	−6.81761	−0.224404
$924$	2.14061	0.0704210
$925$	−2.20964	−0.0726524
$926$	−14.0858	−0.462888
$927$	6.20440	0.203779
$928$	−1.63671	−0.0537277
$929$	−25.7445	−0.844650	−0.422325	−	0.906444i	$-0.638786\pi$
$929$	−25.7445	−0.844650	−0.422325	+	0.906444i	$0.638786\pi$
$930$	−6.57292	−0.215535
$931$	−3.84111	−0.125887
$932$	24.0675	0.788358
$933$	27.7460	0.908364
$934$	−14.9728	−0.489924
$935$	−0.399834	−0.0130760
$936$	1.49086	0.0487304
$937$	42.5427	1.38981	0.694904	−	0.719102i	$-0.255447\pi$
$937$	42.5427	1.38981	0.694904	+	0.719102i	$0.255447\pi$
$938$	−14.3320	−0.467956
$939$	17.0325	0.555834
$940$	−6.60017	−0.215274
$941$	45.5752	1.48571	0.742854	−	0.669454i	$-0.233472\pi$
$941$	45.5752	1.48571	0.742854	+	0.669454i	$0.233472\pi$
$942$	−1.50914	−0.0491703
$943$	−15.7120	−0.511654
$944$	6.77209	0.220413
$945$	−2.64975	−0.0861964
$946$	2.04178	0.0663840
$947$	47.4256	1.54112	0.770562	−	0.637365i	$-0.219976\pi$
$947$	47.4256	1.54112	0.770562	+	0.637365i	$0.219976\pi$
$948$	−9.08580	−0.295093
$949$	0.941447	0.0305607
$950$	2.77733	0.0901083
$951$	−9.19917	−0.298303
$952$	−0.395765	−0.0128268
$953$	−7.01420	−0.227212	−0.113606	−	0.993526i	$-0.536240\pi$
$953$	−7.01420	−0.227212	−0.113606	+	0.993526i	$0.536240\pi$
$954$	1.00000	0.0323762
$955$	−0.162955	−0.00527311
$956$	−0.917939	−0.0296883
$957$	1.97126	0.0637217
$958$	−24.3502	−0.786721
$959$	39.1728	1.26495
$960$	−1.49086	−0.0481174
$961$	−11.5625	−0.372982
$962$	1.18613	0.0382423
$963$	11.4909	0.370288
$964$	17.3189	0.557805
$965$	−13.3360	−0.429303
$966$	−3.01304	−0.0969429
$967$	−34.7367	−1.11706	−0.558529	−	0.829485i	$-0.688634\pi$
$967$	−34.7367	−1.11706	−0.558529	+	0.829485i	$0.688634\pi$
$968$	9.54942	0.306930
$969$	−0.222674	−0.00715333
$970$	−9.95449	−0.319619
$971$	−33.6207	−1.07894	−0.539469	−	0.842005i	$-0.681375\pi$
$971$	−33.6207	−1.07894	−0.539469	+	0.842005i	$0.681375\pi$
$972$	−1.00000	−0.0320750
$973$	−6.94028	−0.222495
$974$	1.00897	0.0323295
$975$	−4.14061	−0.132606
$976$	−2.36329	−0.0756470
$977$	20.1354	0.644188	0.322094	−	0.946708i	$-0.395613\pi$
$977$	20.1354	0.644188	0.322094	+	0.946708i	$0.395613\pi$
$978$	11.9635	0.382549
$979$	−6.93621	−0.221682
$980$	−5.72658	−0.182929
$981$	−0.923174	−0.0294747
$982$	−14.4648	−0.461590
$983$	35.4621	1.13107	0.565533	−	0.824726i	$-0.308670\pi$
$983$	35.4621	1.13107	0.565533	+	0.824726i	$0.308670\pi$
$984$	9.26819	0.295459
$985$	13.6953	0.436367
$986$	−0.364454	−0.0116066
$987$	7.86836	0.250453
$988$	−1.49086	−0.0474307
$989$	−2.87392	−0.0913855
$990$	1.79560	0.0570679
$991$	30.5584	0.970719	0.485360	−	0.874315i	$-0.338689\pi$
$991$	30.5584	0.970719	0.485360	+	0.874315i	$0.338689\pi$
$992$	4.40880	0.139980
$993$	−20.5233	−0.651289
$994$	−8.12758	−0.257791
$995$	37.9139	1.20195
$996$	−13.8228	−0.437993
$997$	−14.5051	−0.459380	−0.229690	−	0.973264i	$-0.573771\pi$
$997$	−14.5051	−0.459380	−0.229690	+	0.973264i	$0.573771\pi$
$998$	−6.70573	−0.212266
$999$	−0.795598	−0.0251716

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6042.2.a.q.1.3	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6042.2.a.q.1.3	✓	3	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:	\( N \)	\(=\)	\( 6042 = 2 \cdot 3 \cdot 19 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6042.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.49086 q^{5} +1.00000 q^{6} +1.77733 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.49086 q^{5} +1.00000 q^{6} +1.77733 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.49086 q^{10} -1.20440 q^{11} -1.00000 q^{12} -1.49086 q^{13} -1.77733 q^{14} -1.49086 q^{15} +1.00000 q^{16} +0.222674 q^{17} -1.00000 q^{18} +1.00000 q^{19} +1.49086 q^{20} -1.77733 q^{21} +1.20440 q^{22} -1.69527 q^{23} +1.00000 q^{24} -2.77733 q^{25} +1.49086 q^{26} -1.00000 q^{27} +1.77733 q^{28} +1.63671 q^{29} +1.49086 q^{30} -4.40880 q^{31} -1.00000 q^{32} +1.20440 q^{33} -0.222674 q^{34} +2.64975 q^{35} +1.00000 q^{36} +0.795598 q^{37} -1.00000 q^{38} +1.49086 q^{39} -1.49086 q^{40} +9.26819 q^{41} +1.77733 q^{42} +1.69527 q^{43} -1.20440 q^{44} +1.49086 q^{45} +1.69527 q^{46} -4.42708 q^{47} -1.00000 q^{48} -3.84111 q^{49} +2.77733 q^{50} -0.222674 q^{51} -1.49086 q^{52} -1.00000 q^{53} +1.00000 q^{54} -1.79560 q^{55} -1.77733 q^{56} -1.00000 q^{57} -1.63671 q^{58} +6.77209 q^{59} -1.49086 q^{60} -2.36329 q^{61} +4.40880 q^{62} +1.77733 q^{63} +1.00000 q^{64} -2.22267 q^{65} -1.20440 q^{66} +8.06379 q^{67} +0.222674 q^{68} +1.69527 q^{69} -2.64975 q^{70} +4.57292 q^{71} -1.00000 q^{72} -0.631477 q^{73} -0.795598 q^{74} +2.77733 q^{75} +1.00000 q^{76} -2.14061 q^{77} -1.49086 q^{78} +9.08580 q^{79} +1.49086 q^{80} +1.00000 q^{81} -9.26819 q^{82} +13.8228 q^{83} -1.77733 q^{84} +0.331977 q^{85} -1.69527 q^{86} -1.63671 q^{87} +1.20440 q^{88} +5.75905 q^{89} -1.49086 q^{90} -2.64975 q^{91} -1.69527 q^{92} +4.40880 q^{93} +4.42708 q^{94} +1.49086 q^{95} +1.00000 q^{96} +6.67699 q^{97} +3.84111 q^{98} -1.20440 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{5} + 3 q^{6} - q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^5 + 3 * q^6 - q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{5} + 3 q^{6} - q^{7} - 3 q^{8} + 3 q^{9} + 3 q^{10} + 5 q^{11} - 3 q^{12} + 3 q^{13} + q^{14} + 3 q^{15} + 3 q^{16} + 7 q^{17} - 3 q^{18} + 3 q^{19} - 3 q^{20} + q^{21} - 5 q^{22} + 11 q^{23} + 3 q^{24} - 2 q^{25} - 3 q^{26} - 3 q^{27} - q^{28} + 2 q^{29} - 3 q^{30} + 4 q^{31} - 3 q^{32} - 5 q^{33} - 7 q^{34} + 12 q^{35} + 3 q^{36} + 11 q^{37} - 3 q^{38} - 3 q^{39} + 3 q^{40} + 14 q^{41} - q^{42} - 11 q^{43} + 5 q^{44} - 3 q^{45} - 11 q^{46} - 11 q^{47} - 3 q^{48} + 2 q^{50} - 7 q^{51} + 3 q^{52} - 3 q^{53} + 3 q^{54} - 14 q^{55} + q^{56} - 3 q^{57} - 2 q^{58} + 6 q^{59} + 3 q^{60} - 10 q^{61} - 4 q^{62} - q^{63} + 3 q^{64} - 13 q^{65} + 5 q^{66} + 19 q^{67} + 7 q^{68} - 11 q^{69} - 12 q^{70} + 16 q^{71} - 3 q^{72} + 9 q^{73} - 11 q^{74} + 2 q^{75} + 3 q^{76} - 3 q^{77} + 3 q^{78} - 21 q^{79} - 3 q^{80} + 3 q^{81} - 14 q^{82} + 15 q^{83} + q^{84} - 18 q^{85} + 11 q^{86} - 2 q^{87} - 5 q^{88} - 4 q^{89} + 3 q^{90} - 12 q^{91} + 11 q^{92} - 4 q^{93} + 11 q^{94} - 3 q^{95} + 3 q^{96} - 11 q^{97} + 5 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^5 + 3 * q^6 - q^7 - 3 * q^8 + 3 * q^9 + 3 * q^10 + 5 * q^11 - 3 * q^12 + 3 * q^13 + q^14 + 3 * q^15 + 3 * q^16 + 7 * q^17 - 3 * q^18 + 3 * q^19 - 3 * q^20 + q^21 - 5 * q^22 + 11 * q^23 + 3 * q^24 - 2 * q^25 - 3 * q^26 - 3 * q^27 - q^28 + 2 * q^29 - 3 * q^30 + 4 * q^31 - 3 * q^32 - 5 * q^33 - 7 * q^34 + 12 * q^35 + 3 * q^36 + 11 * q^37 - 3 * q^38 - 3 * q^39 + 3 * q^40 + 14 * q^41 - q^42 - 11 * q^43 + 5 * q^44 - 3 * q^45 - 11 * q^46 - 11 * q^47 - 3 * q^48 + 2 * q^50 - 7 * q^51 + 3 * q^52 - 3 * q^53 + 3 * q^54 - 14 * q^55 + q^56 - 3 * q^57 - 2 * q^58 + 6 * q^59 + 3 * q^60 - 10 * q^61 - 4 * q^62 - q^63 + 3 * q^64 - 13 * q^65 + 5 * q^66 + 19 * q^67 + 7 * q^68 - 11 * q^69 - 12 * q^70 + 16 * q^71 - 3 * q^72 + 9 * q^73 - 11 * q^74 + 2 * q^75 + 3 * q^76 - 3 * q^77 + 3 * q^78 - 21 * q^79 - 3 * q^80 + 3 * q^81 - 14 * q^82 + 15 * q^83 + q^84 - 18 * q^85 + 11 * q^86 - 2 * q^87 - 5 * q^88 - 4 * q^89 + 3 * q^90 - 12 * q^91 + 11 * q^92 - 4 * q^93 + 11 * q^94 - 3 * q^95 + 3 * q^96 - 11 * q^97 + 5 * q^99

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