LMFDB - Embedded newform 6026.2.a.k.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, 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("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.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:	$48.1178522580$
Analytic rank:	$0$
Dimension:	$35$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.41686 q^{3} +1.00000 q^{4} -1.19985 q^{5} -2.41686 q^{6} -1.78090 q^{7} +1.00000 q^{8} +2.84122 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.41686 q^{3} +1.00000 q^{4} -1.19985 q^{5} -2.41686 q^{6} -1.78090 q^{7} +1.00000 q^{8} +2.84122 q^{9} -1.19985 q^{10} +4.18860 q^{11} -2.41686 q^{12} -3.18514 q^{13} -1.78090 q^{14} +2.89987 q^{15} +1.00000 q^{16} -7.06162 q^{17} +2.84122 q^{18} +0.799427 q^{19} -1.19985 q^{20} +4.30420 q^{21} +4.18860 q^{22} -1.00000 q^{23} -2.41686 q^{24} -3.56036 q^{25} -3.18514 q^{26} +0.383756 q^{27} -1.78090 q^{28} +6.97022 q^{29} +2.89987 q^{30} +4.45062 q^{31} +1.00000 q^{32} -10.1233 q^{33} -7.06162 q^{34} +2.13682 q^{35} +2.84122 q^{36} +0.351218 q^{37} +0.799427 q^{38} +7.69803 q^{39} -1.19985 q^{40} -5.44451 q^{41} +4.30420 q^{42} -3.24491 q^{43} +4.18860 q^{44} -3.40903 q^{45} -1.00000 q^{46} -5.44806 q^{47} -2.41686 q^{48} -3.82838 q^{49} -3.56036 q^{50} +17.0670 q^{51} -3.18514 q^{52} -11.5139 q^{53} +0.383756 q^{54} -5.02568 q^{55} -1.78090 q^{56} -1.93210 q^{57} +6.97022 q^{58} +0.271844 q^{59} +2.89987 q^{60} -3.86669 q^{61} +4.45062 q^{62} -5.05993 q^{63} +1.00000 q^{64} +3.82168 q^{65} -10.1233 q^{66} +10.1968 q^{67} -7.06162 q^{68} +2.41686 q^{69} +2.13682 q^{70} +11.3358 q^{71} +2.84122 q^{72} +3.87297 q^{73} +0.351218 q^{74} +8.60490 q^{75} +0.799427 q^{76} -7.45949 q^{77} +7.69803 q^{78} -1.70043 q^{79} -1.19985 q^{80} -9.45114 q^{81} -5.44451 q^{82} -9.25325 q^{83} +4.30420 q^{84} +8.47287 q^{85} -3.24491 q^{86} -16.8461 q^{87} +4.18860 q^{88} +9.31098 q^{89} -3.40903 q^{90} +5.67242 q^{91} -1.00000 q^{92} -10.7565 q^{93} -5.44806 q^{94} -0.959191 q^{95} -2.41686 q^{96} +1.69125 q^{97} -3.82838 q^{98} +11.9007 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9}+O(q^{10}) $ 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9	\( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9} + 10 q^{10} + 9 q^{11} - 3 q^{12} + 19 q^{13} + 14 q^{14} + 14 q^{15} + 35 q^{16} + 28 q^{17} + 54 q^{18} + 21 q^{19} + 10 q^{20} + 28 q^{21} + 9 q^{22} - 35 q^{23} - 3 q^{24} + 81 q^{25} + 19 q^{26} - 21 q^{27} + 14 q^{28} + 35 q^{29} + 14 q^{30} + 5 q^{31} + 35 q^{32} + 26 q^{33} + 28 q^{34} - 7 q^{35} + 54 q^{36} + 51 q^{37} + 21 q^{38} + 21 q^{39} + 10 q^{40} + 3 q^{41} + 28 q^{42} + 43 q^{43} + 9 q^{44} + 2 q^{45} - 35 q^{46} + 10 q^{47} - 3 q^{48} + 85 q^{49} + 81 q^{50} + 26 q^{51} + 19 q^{52} + 39 q^{53} - 21 q^{54} + 2 q^{55} + 14 q^{56} + 50 q^{57} + 35 q^{58} - 42 q^{59} + 14 q^{60} + 47 q^{61} + 5 q^{62} + 23 q^{63} + 35 q^{64} + 61 q^{65} + 26 q^{66} + 22 q^{67} + 28 q^{68} + 3 q^{69} - 7 q^{70} + 54 q^{72} + 30 q^{73} + 51 q^{74} - 26 q^{75} + 21 q^{76} + 2 q^{77} + 21 q^{78} + 55 q^{79} + 10 q^{80} + 67 q^{81} + 3 q^{82} + 20 q^{83} + 28 q^{84} + 28 q^{85} + 43 q^{86} + 29 q^{87} + 9 q^{88} - 31 q^{89} + 2 q^{90} + 32 q^{91} - 35 q^{92} + 11 q^{93} + 10 q^{94} + 16 q^{95} - 3 q^{96} + 36 q^{97} + 85 q^{98} - 9 q^{99}+O(q^{100}) \) 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9 + 10 * q^10 + 9 * q^11 - 3 * q^12 + 19 * q^13 + 14 * q^14 + 14 * q^15 + 35 * q^16 + 28 * q^17 + 54 * q^18 + 21 * q^19 + 10 * q^20 + 28 * q^21 + 9 * q^22 - 35 * q^23 - 3 * q^24 + 81 * q^25 + 19 * q^26 - 21 * q^27 + 14 * q^28 + 35 * q^29 + 14 * q^30 + 5 * q^31 + 35 * q^32 + 26 * q^33 + 28 * q^34 - 7 * q^35 + 54 * q^36 + 51 * q^37 + 21 * q^38 + 21 * q^39 + 10 * q^40 + 3 * q^41 + 28 * q^42 + 43 * q^43 + 9 * q^44 + 2 * q^45 - 35 * q^46 + 10 * q^47 - 3 * q^48 + 85 * q^49 + 81 * q^50 + 26 * q^51 + 19 * q^52 + 39 * q^53 - 21 * q^54 + 2 * q^55 + 14 * q^56 + 50 * q^57 + 35 * q^58 - 42 * q^59 + 14 * q^60 + 47 * q^61 + 5 * q^62 + 23 * q^63 + 35 * q^64 + 61 * q^65 + 26 * q^66 + 22 * q^67 + 28 * q^68 + 3 * q^69 - 7 * q^70 + 54 * q^72 + 30 * q^73 + 51 * q^74 - 26 * q^75 + 21 * q^76 + 2 * q^77 + 21 * q^78 + 55 * q^79 + 10 * q^80 + 67 * q^81 + 3 * q^82 + 20 * q^83 + 28 * q^84 + 28 * q^85 + 43 * q^86 + 29 * q^87 + 9 * q^88 - 31 * q^89 + 2 * q^90 + 32 * q^91 - 35 * q^92 + 11 * q^93 + 10 * q^94 + 16 * q^95 - 3 * q^96 + 36 * q^97 + 85 * q^98 - 9 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.41686	−1.39538	−0.697688	−	0.716402i	$-0.745788\pi$
$3$	−2.41686	−1.39538	−0.697688	+	0.716402i	$0.745788\pi$
$4$	1.00000	0.500000
$5$	−1.19985	−0.536589	−0.268294	−	0.963337i	$-0.586460\pi$
$5$	−1.19985	−0.536589	−0.268294	+	0.963337i	$0.586460\pi$
$6$	−2.41686	−0.986679
$7$	−1.78090	−0.673118	−0.336559	−	0.941662i	$-0.609263\pi$
$7$	−1.78090	−0.673118	−0.336559	+	0.941662i	$0.609263\pi$
$8$	1.00000	0.353553
$9$	2.84122	0.947072
$10$	−1.19985	−0.379425
$11$	4.18860	1.26291	0.631455	−	0.775413i	$-0.282458\pi$
$11$	4.18860	1.26291	0.631455	+	0.775413i	$0.282458\pi$
$12$	−2.41686	−0.697688
$13$	−3.18514	−0.883398	−0.441699	−	0.897163i	$-0.645624\pi$
$13$	−3.18514	−0.883398	−0.441699	+	0.897163i	$0.645624\pi$
$14$	−1.78090	−0.475967
$15$	2.89987	0.748743
$16$	1.00000	0.250000
$17$	−7.06162	−1.71269	−0.856347	−	0.516401i	$-0.827271\pi$
$17$	−7.06162	−1.71269	−0.856347	+	0.516401i	$0.827271\pi$
$18$	2.84122	0.669681
$19$	0.799427	0.183401	0.0917005	−	0.995787i	$-0.470770\pi$
$19$	0.799427	0.183401	0.0917005	+	0.995787i	$0.470770\pi$
$20$	−1.19985	−0.268294
$21$	4.30420	0.939253
$22$	4.18860	0.893012
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−2.41686	−0.493340
$25$	−3.56036	−0.712073
$26$	−3.18514	−0.624657
$27$	0.383756	0.0738539
$28$	−1.78090	−0.336559
$29$	6.97022	1.29434	0.647169	−	0.762347i	$-0.275953\pi$
$29$	6.97022	1.29434	0.647169	+	0.762347i	$0.275953\pi$
$30$	2.89987	0.529441
$31$	4.45062	0.799356	0.399678	−	0.916656i	$-0.369122\pi$
$31$	4.45062	0.799356	0.399678	+	0.916656i	$0.369122\pi$
$32$	1.00000	0.176777
$33$	−10.1233	−1.76223
$34$	−7.06162	−1.21106
$35$	2.13682	0.361188
$36$	2.84122	0.473536
$37$	0.351218	0.0577398	0.0288699	−	0.999583i	$-0.490809\pi$
$37$	0.351218	0.0577398	0.0288699	+	0.999583i	$0.490809\pi$
$38$	0.799427	0.129684
$39$	7.69803	1.23267
$40$	−1.19985	−0.189713
$41$	−5.44451	−0.850289	−0.425145	−	0.905125i	$-0.639777\pi$
$41$	−5.44451	−0.850289	−0.425145	+	0.905125i	$0.639777\pi$
$42$	4.30420	0.664152
$43$	−3.24491	−0.494843	−0.247422	−	0.968908i	$-0.579583\pi$
$43$	−3.24491	−0.494843	−0.247422	+	0.968908i	$0.579583\pi$
$44$	4.18860	0.631455
$45$	−3.40903	−0.508188
$46$	−1.00000	−0.147442
$47$	−5.44806	−0.794682	−0.397341	−	0.917671i	$-0.630067\pi$
$47$	−5.44806	−0.794682	−0.397341	+	0.917671i	$0.630067\pi$
$48$	−2.41686	−0.348844
$49$	−3.82838	−0.546912
$50$	−3.56036	−0.503511
$51$	17.0670	2.38985
$52$	−3.18514	−0.441699
$53$	−11.5139	−1.58155	−0.790775	−	0.612107i	$-0.790322\pi$
$53$	−11.5139	−1.58155	−0.790775	+	0.612107i	$0.790322\pi$
$54$	0.383756	0.0522226
$55$	−5.02568	−0.677663
$56$	−1.78090	−0.237983
$57$	−1.93210	−0.255913
$58$	6.97022	0.915235
$59$	0.271844	0.0353911	0.0176956	−	0.999843i	$-0.494367\pi$
$59$	0.271844	0.0353911	0.0176956	+	0.999843i	$0.494367\pi$
$60$	2.89987	0.374371
$61$	−3.86669	−0.495079	−0.247540	−	0.968878i	$-0.579622\pi$
$61$	−3.86669	−0.495079	−0.247540	+	0.968878i	$0.579622\pi$
$62$	4.45062	0.565230
$63$	−5.05993	−0.637492
$64$	1.00000	0.125000
$65$	3.82168	0.474021
$66$	−10.1233	−1.24609
$67$	10.1968	1.24573	0.622866	−	0.782329i	$-0.285968\pi$
$67$	10.1968	1.24573	0.622866	+	0.782329i	$0.285968\pi$
$68$	−7.06162	−0.856347
$69$	2.41686	0.290956
$70$	2.13682	0.255398
$71$	11.3358	1.34531	0.672655	−	0.739956i	$-0.265154\pi$
$71$	11.3358	1.34531	0.672655	+	0.739956i	$0.265154\pi$
$72$	2.84122	0.334841
$73$	3.87297	0.453297	0.226648	−	0.973977i	$-0.427223\pi$
$73$	3.87297	0.453297	0.226648	+	0.973977i	$0.427223\pi$
$74$	0.351218	0.0408282
$75$	8.60490	0.993609
$76$	0.799427	0.0917005
$77$	−7.45949	−0.850088
$78$	7.69803	0.871631
$79$	−1.70043	−0.191314	−0.0956568	−	0.995414i	$-0.530495\pi$
$79$	−1.70043	−0.191314	−0.0956568	+	0.995414i	$0.530495\pi$
$80$	−1.19985	−0.134147
$81$	−9.45114	−1.05013
$82$	−5.44451	−0.601245
$83$	−9.25325	−1.01568	−0.507838	−	0.861453i	$-0.669555\pi$
$83$	−9.25325	−1.01568	−0.507838	+	0.861453i	$0.669555\pi$
$84$	4.30420	0.469626
$85$	8.47287	0.919012
$86$	−3.24491	−0.349907
$87$	−16.8461	−1.80609
$88$	4.18860	0.446506
$89$	9.31098	0.986961	0.493481	−	0.869757i	$-0.335724\pi$
$89$	9.31098	0.986961	0.493481	+	0.869757i	$0.335724\pi$
$90$	−3.40903	−0.359343
$91$	5.67242	0.594631
$92$	−1.00000	−0.104257
$93$	−10.7565	−1.11540
$94$	−5.44806	−0.561925
$95$	−0.959191	−0.0984109
$96$	−2.41686	−0.246670
$97$	1.69125	0.171721	0.0858603	−	0.996307i	$-0.472636\pi$
$97$	1.69125	0.171721	0.0858603	+	0.996307i	$0.472636\pi$
$98$	−3.82838	−0.386725
$99$	11.9007	1.19607
$100$	−3.56036	−0.356036
$101$	8.46163	0.841963	0.420982	−	0.907069i	$-0.361686\pi$
$101$	8.46163	0.841963	0.420982	+	0.907069i	$0.361686\pi$
$102$	17.0670	1.68988
$103$	−1.27977	−0.126099	−0.0630497	−	0.998010i	$-0.520083\pi$
$103$	−1.27977	−0.126099	−0.0630497	+	0.998010i	$0.520083\pi$
$104$	−3.18514	−0.312328
$105$	−5.16439	−0.503992
$106$	−11.5139	−1.11832
$107$	6.63915	0.641831	0.320915	−	0.947108i	$-0.396009\pi$
$107$	6.63915	0.641831	0.320915	+	0.947108i	$0.396009\pi$
$108$	0.383756	0.0369270
$109$	17.1038	1.63824	0.819122	−	0.573619i	$-0.194461\pi$
$109$	17.1038	1.63824	0.819122	+	0.573619i	$0.194461\pi$
$110$	−5.02568	−0.479180
$111$	−0.848845	−0.0805688
$112$	−1.78090	−0.168280
$113$	−8.86781	−0.834213	−0.417107	−	0.908858i	$-0.636956\pi$
$113$	−8.86781	−0.834213	−0.417107	+	0.908858i	$0.636956\pi$
$114$	−1.93210	−0.180958
$115$	1.19985	0.111886
$116$	6.97022	0.647169
$117$	−9.04966	−0.836642
$118$	0.271844	0.0250253
$119$	12.5761	1.15285
$120$	2.89987	0.264720
$121$	6.54434	0.594940
$122$	−3.86669	−0.350074
$123$	13.1586	1.18647
$124$	4.45062	0.399678
$125$	10.2711	0.918679
$126$	−5.05993	−0.450775
$127$	−12.8126	−1.13693	−0.568466	−	0.822707i	$-0.692463\pi$
$127$	−12.8126	−1.13693	−0.568466	+	0.822707i	$0.692463\pi$
$128$	1.00000	0.0883883
$129$	7.84249	0.690492
$130$	3.82168	0.335184
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	−10.1233	−0.881116
$133$	−1.42370	−0.123451
$134$	10.1968	0.880865
$135$	−0.460449	−0.0396292
$136$	−7.06162	−0.605529
$137$	19.5659	1.67163	0.835814	−	0.549013i	$-0.184996\pi$
$137$	19.5659	1.67163	0.835814	+	0.549013i	$0.184996\pi$
$138$	2.41686	0.205737
$139$	−7.02393	−0.595762	−0.297881	−	0.954603i	$-0.596280\pi$
$139$	−7.02393	−0.595762	−0.297881	+	0.954603i	$0.596280\pi$
$140$	2.13682	0.180594
$141$	13.1672	1.10888
$142$	11.3358	0.951278
$143$	−13.3413	−1.11565
$144$	2.84122	0.236768
$145$	−8.36321	−0.694527
$146$	3.87297	0.320529
$147$	9.25267	0.763147
$148$	0.351218	0.0288699
$149$	2.87617	0.235625	0.117813	−	0.993036i	$-0.462412\pi$
$149$	2.87617	0.235625	0.117813	+	0.993036i	$0.462412\pi$
$150$	8.60490	0.702587
$151$	−9.51227	−0.774098	−0.387049	−	0.922059i	$-0.626505\pi$
$151$	−9.51227	−0.774098	−0.387049	+	0.922059i	$0.626505\pi$
$152$	0.799427	0.0648421
$153$	−20.0636	−1.62205
$154$	−7.45949	−0.601103
$155$	−5.34008	−0.428925
$156$	7.69803	0.616336
$157$	3.13493	0.250194	0.125097	−	0.992144i	$-0.460076\pi$
$157$	3.13493	0.250194	0.125097	+	0.992144i	$0.460076\pi$
$158$	−1.70043	−0.135279
$159$	27.8274	2.20686
$160$	−1.19985	−0.0948564
$161$	1.78090	0.140355
$162$	−9.45114	−0.742551
$163$	5.90993	0.462902	0.231451	−	0.972847i	$-0.425653\pi$
$163$	5.90993	0.462902	0.231451	+	0.972847i	$0.425653\pi$
$164$	−5.44451	−0.425145
$165$	12.1464	0.945594
$166$	−9.25325	−0.718192
$167$	−12.8861	−0.997159	−0.498579	−	0.866844i	$-0.666145\pi$
$167$	−12.8861	−0.997159	−0.498579	+	0.866844i	$0.666145\pi$
$168$	4.30420	0.332076
$169$	−2.85491	−0.219608
$170$	8.47287	0.649840
$171$	2.27135	0.173694
$172$	−3.24491	−0.247422
$173$	7.22993	0.549682	0.274841	−	0.961490i	$-0.411375\pi$
$173$	7.22993	0.549682	0.274841	+	0.961490i	$0.411375\pi$
$174$	−16.8461	−1.27710
$175$	6.34066	0.479309
$176$	4.18860	0.315727
$177$	−0.657010	−0.0493839
$178$	9.31098	0.697887
$179$	−14.8345	−1.10878	−0.554390	−	0.832257i	$-0.687048\pi$
$179$	−14.8345	−1.10878	−0.554390	+	0.832257i	$0.687048\pi$
$180$	−3.40903	−0.254094
$181$	18.1290	1.34751	0.673757	−	0.738953i	$-0.264679\pi$
$181$	18.1290	1.34751	0.673757	+	0.738953i	$0.264679\pi$
$182$	5.67242	0.420468
$183$	9.34526	0.690822
$184$	−1.00000	−0.0737210
$185$	−0.421408	−0.0309825
$186$	−10.7565	−0.788708
$187$	−29.5783	−2.16298
$188$	−5.44806	−0.397341
$189$	−0.683433	−0.0497124
$190$	−0.959191	−0.0695870
$191$	13.3141	0.963377	0.481689	−	0.876342i	$-0.340024\pi$
$191$	13.3141	0.963377	0.481689	+	0.876342i	$0.340024\pi$
$192$	−2.41686	−0.174422
$193$	19.0948	1.37447	0.687236	−	0.726434i	$-0.258824\pi$
$193$	19.0948	1.37447	0.687236	+	0.726434i	$0.258824\pi$
$194$	1.69125	0.121425
$195$	−9.23647	−0.661438
$196$	−3.82838	−0.273456
$197$	26.9479	1.91996	0.959978	−	0.280074i	$-0.0903589\pi$
$197$	26.9479	1.91996	0.959978	+	0.280074i	$0.0903589\pi$
$198$	11.9007	0.845747
$199$	10.3107	0.730903	0.365451	−	0.930830i	$-0.380915\pi$
$199$	10.3107	0.730903	0.365451	+	0.930830i	$0.380915\pi$
$200$	−3.56036	−0.251756
$201$	−24.6441	−1.73826
$202$	8.46163	0.595358
$203$	−12.4133	−0.871242
$204$	17.0670	1.19493
$205$	6.53258	0.456255
$206$	−1.27977	−0.0891658
$207$	−2.84122	−0.197478
$208$	−3.18514	−0.220849
$209$	3.34848	0.231619
$210$	−5.16439	−0.356376
$211$	1.71860	0.118313	0.0591565	−	0.998249i	$-0.481159\pi$
$211$	1.71860	0.118313	0.0591565	+	0.998249i	$0.481159\pi$
$212$	−11.5139	−0.790775
$213$	−27.3970	−1.87721
$214$	6.63915	0.453843
$215$	3.89340	0.265527
$216$	0.383756	0.0261113
$217$	−7.92613	−0.538061
$218$	17.1038	1.15841
$219$	−9.36042	−0.632519
$220$	−5.02568	−0.338831
$221$	22.4922	1.51299
$222$	−0.848845	−0.0569707
$223$	1.64988	0.110484	0.0552419	−	0.998473i	$-0.482407\pi$
$223$	1.64988	0.110484	0.0552419	+	0.998473i	$0.482407\pi$
$224$	−1.78090	−0.118992
$225$	−10.1158	−0.674384
$226$	−8.86781	−0.589878
$227$	−1.64072	−0.108898	−0.0544491	−	0.998517i	$-0.517340\pi$
$227$	−1.64072	−0.108898	−0.0544491	+	0.998517i	$0.517340\pi$
$228$	−1.93210	−0.127957
$229$	1.32141	0.0873209	0.0436605	−	0.999046i	$-0.486098\pi$
$229$	1.32141	0.0873209	0.0436605	+	0.999046i	$0.486098\pi$
$230$	1.19985	0.0791157
$231$	18.0285	1.18619
$232$	6.97022	0.457617
$233$	5.09696	0.333913	0.166956	−	0.985964i	$-0.446606\pi$
$233$	5.09696	0.333913	0.166956	+	0.985964i	$0.446606\pi$
$234$	−9.04966	−0.591595
$235$	6.53685	0.426417
$236$	0.271844	0.0176956
$237$	4.10971	0.266954
$238$	12.5761	0.815185
$239$	20.1286	1.30201	0.651005	−	0.759073i	$-0.274348\pi$
$239$	20.1286	1.30201	0.651005	+	0.759073i	$0.274348\pi$
$240$	2.89987	0.187186
$241$	2.60691	0.167926	0.0839629	−	0.996469i	$-0.473242\pi$
$241$	2.60691	0.167926	0.0839629	+	0.996469i	$0.473242\pi$
$242$	6.54434	0.420686
$243$	21.6908	1.39147
$244$	−3.86669	−0.247540
$245$	4.59348	0.293467
$246$	13.1586	0.838963
$247$	−2.54628	−0.162016
$248$	4.45062	0.282615
$249$	22.3638	1.41725
$250$	10.2711	0.649604
$251$	23.5733	1.48793	0.743965	−	0.668218i	$-0.232943\pi$
$251$	23.5733	1.48793	0.743965	+	0.668218i	$0.232943\pi$
$252$	−5.05993	−0.318746
$253$	−4.18860	−0.263335
$254$	−12.8126	−0.803932
$255$	−20.4778	−1.28237
$256$	1.00000	0.0625000
$257$	22.0607	1.37611	0.688053	−	0.725660i	$-0.258465\pi$
$257$	22.0607	1.37611	0.688053	+	0.725660i	$0.258465\pi$
$258$	7.84249	0.488252
$259$	−0.625485	−0.0388658
$260$	3.82168	0.237011
$261$	19.8039	1.22583
$262$	−1.00000	−0.0617802
$263$	−24.5440	−1.51345	−0.756725	−	0.653734i	$-0.773202\pi$
$263$	−24.5440	−1.51345	−0.756725	+	0.653734i	$0.773202\pi$
$264$	−10.1233	−0.623043
$265$	13.8149	0.848642
$266$	−1.42370	−0.0872928
$267$	−22.5033	−1.37718
$268$	10.1968	0.622866
$269$	2.80645	0.171112	0.0855561	−	0.996333i	$-0.472733\pi$
$269$	2.80645	0.171112	0.0855561	+	0.996333i	$0.472733\pi$
$270$	−0.460449	−0.0280221
$271$	−21.1376	−1.28402	−0.642008	−	0.766698i	$-0.721898\pi$
$271$	−21.1376	−1.28402	−0.642008	+	0.766698i	$0.721898\pi$
$272$	−7.06162	−0.428174
$273$	−13.7095	−0.829734
$274$	19.5659	1.18202
$275$	−14.9129	−0.899283
$276$	2.41686	0.145478
$277$	−1.42273	−0.0854836	−0.0427418	−	0.999086i	$-0.513609\pi$
$277$	−1.42273	−0.0854836	−0.0427418	+	0.999086i	$0.513609\pi$
$278$	−7.02393	−0.421267
$279$	12.6452	0.757048
$280$	2.13682	0.127699
$281$	22.8406	1.36256	0.681278	−	0.732025i	$-0.261425\pi$
$281$	22.8406	1.36256	0.681278	+	0.732025i	$0.261425\pi$
$282$	13.1672	0.784096
$283$	15.4918	0.920894	0.460447	−	0.887687i	$-0.347689\pi$
$283$	15.4918	0.920894	0.460447	+	0.887687i	$0.347689\pi$
$284$	11.3358	0.672655
$285$	2.31823	0.137320
$286$	−13.3413	−0.788885
$287$	9.69614	0.572345
$288$	2.84122	0.167420
$289$	32.8665	1.93332
$290$	−8.36321	−0.491105
$291$	−4.08752	−0.239615
$292$	3.87297	0.226648
$293$	0.196112	0.0114570	0.00572851	−	0.999984i	$-0.498177\pi$
$293$	0.196112	0.0114570	0.00572851	+	0.999984i	$0.498177\pi$
$294$	9.25267	0.539626
$295$	−0.326172	−0.0189905
$296$	0.351218	0.0204141
$297$	1.60740	0.0932708
$298$	2.87617	0.166612
$299$	3.18514	0.184201
$300$	8.60490	0.496804
$301$	5.77886	0.333088
$302$	−9.51227	−0.547370
$303$	−20.4506	−1.17485
$304$	0.799427	0.0458503
$305$	4.63945	0.265654
$306$	−20.0636	−1.14696
$307$	27.4186	1.56486	0.782431	−	0.622737i	$-0.213979\pi$
$307$	27.4186	1.56486	0.782431	+	0.622737i	$0.213979\pi$
$308$	−7.45949	−0.425044
$309$	3.09303	0.175956
$310$	−5.34008	−0.303296
$311$	−25.5930	−1.45125	−0.725623	−	0.688093i	$-0.758448\pi$
$311$	−25.5930	−1.45125	−0.725623	+	0.688093i	$0.758448\pi$
$312$	7.69803	0.435815
$313$	−29.7716	−1.68279	−0.841395	−	0.540420i	$-0.818265\pi$
$313$	−29.7716	−1.68279	−0.841395	+	0.540420i	$0.818265\pi$
$314$	3.13493	0.176914
$315$	6.07116	0.342071
$316$	−1.70043	−0.0956568
$317$	−19.9112	−1.11832	−0.559161	−	0.829059i	$-0.688877\pi$
$317$	−19.9112	−1.11832	−0.559161	+	0.829059i	$0.688877\pi$
$318$	27.8274	1.56048
$319$	29.1954	1.63463
$320$	−1.19985	−0.0670736
$321$	−16.0459	−0.895595
$322$	1.78090	0.0992459
$323$	−5.64525	−0.314110
$324$	−9.45114	−0.525063
$325$	11.3402	0.629043
$326$	5.90993	0.327321
$327$	−41.3374	−2.28597
$328$	−5.44451	−0.300623
$329$	9.70248	0.534915
$330$	12.1464	0.668636
$331$	9.82390	0.539971	0.269985	−	0.962864i	$-0.412981\pi$
$331$	9.82390	0.539971	0.269985	+	0.962864i	$0.412981\pi$
$332$	−9.25325	−0.507838
$333$	0.997886	0.0546838
$334$	−12.8861	−0.705098
$335$	−12.2346	−0.668445
$336$	4.30420	0.234813
$337$	27.6746	1.50753	0.753766	−	0.657143i	$-0.228235\pi$
$337$	27.6746	1.50753	0.753766	+	0.657143i	$0.228235\pi$
$338$	−2.85491	−0.155286
$339$	21.4323	1.16404
$340$	8.47287	0.459506
$341$	18.6419	1.00951
$342$	2.27135	0.122820
$343$	19.2843	1.04125
$344$	−3.24491	−0.174954
$345$	−2.89987	−0.156124
$346$	7.22993	0.388684
$347$	26.2412	1.40870	0.704352	−	0.709851i	$-0.251238\pi$
$347$	26.2412	1.40870	0.704352	+	0.709851i	$0.251238\pi$
$348$	−16.8461	−0.903043
$349$	−22.4590	−1.20220	−0.601101	−	0.799173i	$-0.705271\pi$
$349$	−22.4590	−1.20220	−0.601101	+	0.799173i	$0.705271\pi$
$350$	6.34066	0.338923
$351$	−1.22232	−0.0652424
$352$	4.18860	0.223253
$353$	36.8826	1.96306	0.981530	−	0.191307i	$-0.0612726\pi$
$353$	36.8826	1.96306	0.981530	+	0.191307i	$0.0612726\pi$
$354$	−0.657010	−0.0349197
$355$	−13.6012	−0.721878
$356$	9.31098	0.493481
$357$	−30.3946	−1.60865
$358$	−14.8345	−0.784025
$359$	7.28513	0.384495	0.192247	−	0.981347i	$-0.438422\pi$
$359$	7.28513	0.384495	0.192247	+	0.981347i	$0.438422\pi$
$360$	−3.40903	−0.179672
$361$	−18.3609	−0.966364
$362$	18.1290	0.952837
$363$	−15.8168	−0.830165
$364$	5.67242	0.297316
$365$	−4.64698	−0.243234
$366$	9.34526	0.488485
$367$	4.55904	0.237980	0.118990	−	0.992895i	$-0.462034\pi$
$367$	4.55904	0.237980	0.118990	+	0.992895i	$0.462034\pi$
$368$	−1.00000	−0.0521286
$369$	−15.4690	−0.805285
$370$	−0.421408	−0.0219080
$371$	20.5051	1.06457
$372$	−10.7565	−0.557701
$373$	31.3090	1.62112	0.810560	−	0.585655i	$-0.199163\pi$
$373$	31.3090	1.62112	0.810560	+	0.585655i	$0.199163\pi$
$374$	−29.5783	−1.52946
$375$	−24.8239	−1.28190
$376$	−5.44806	−0.280962
$377$	−22.2011	−1.14341
$378$	−0.683433	−0.0351520
$379$	6.54430	0.336158	0.168079	−	0.985773i	$-0.446244\pi$
$379$	6.54430	0.336158	0.168079	+	0.985773i	$0.446244\pi$
$380$	−0.959191	−0.0492055
$381$	30.9662	1.58645
$382$	13.3141	0.681210
$383$	30.1980	1.54304	0.771522	−	0.636202i	$-0.219496\pi$
$383$	30.1980	1.54304	0.771522	+	0.636202i	$0.219496\pi$
$384$	−2.41686	−0.123335
$385$	8.95026	0.456147
$386$	19.0948	0.971899
$387$	−9.21948	−0.468653
$388$	1.69125	0.0858603
$389$	−28.2299	−1.43132	−0.715658	−	0.698451i	$-0.753873\pi$
$389$	−28.2299	−1.43132	−0.715658	+	0.698451i	$0.753873\pi$
$390$	−9.23647	−0.467707
$391$	7.06162	0.357121
$392$	−3.82838	−0.193362
$393$	2.41686	0.121915
$394$	26.9479	1.35761
$395$	2.04026	0.102657
$396$	11.9007	0.598033
$397$	−30.1533	−1.51335	−0.756675	−	0.653792i	$-0.773177\pi$
$397$	−30.1533	−1.51335	−0.756675	+	0.653792i	$0.773177\pi$
$398$	10.3107	0.516826
$399$	3.44089	0.172260
$400$	−3.56036	−0.178018
$401$	27.2003	1.35832	0.679160	−	0.733990i	$-0.262344\pi$
$401$	27.2003	1.35832	0.679160	+	0.733990i	$0.262344\pi$
$402$	−24.6441	−1.22914
$403$	−14.1758	−0.706149
$404$	8.46163	0.420982
$405$	11.3399	0.563486
$406$	−12.4133	−0.616061
$407$	1.47111	0.0729202
$408$	17.0670	0.844940
$409$	14.9139	0.737445	0.368722	−	0.929540i	$-0.379795\pi$
$409$	14.9139	0.737445	0.368722	+	0.929540i	$0.379795\pi$
$410$	6.53258	0.322621
$411$	−47.2881	−2.33255
$412$	−1.27977	−0.0630497
$413$	−0.484129	−0.0238224
$414$	−2.84122	−0.139638
$415$	11.1025	0.545000
$416$	−3.18514	−0.156164
$417$	16.9759	0.831312
$418$	3.34848	0.163779
$419$	−2.82188	−0.137858	−0.0689289	−	0.997622i	$-0.521958\pi$
$419$	−2.82188	−0.137858	−0.0689289	+	0.997622i	$0.521958\pi$
$420$	−5.16439	−0.251996
$421$	21.2694	1.03660	0.518302	−	0.855197i	$-0.326564\pi$
$421$	21.2694	1.03660	0.518302	+	0.855197i	$0.326564\pi$
$422$	1.71860	0.0836599
$423$	−15.4791	−0.752621
$424$	−11.5139	−0.559162
$425$	25.1419	1.21956
$426$	−27.3970	−1.32739
$427$	6.88621	0.333247
$428$	6.63915	0.320915
$429$	32.2440	1.55675
$430$	3.89340	0.187756
$431$	−7.39625	−0.356265	−0.178132	−	0.984007i	$-0.557006\pi$
$431$	−7.39625	−0.356265	−0.178132	+	0.984007i	$0.557006\pi$
$432$	0.383756	0.0184635
$433$	10.7840	0.518247	0.259123	−	0.965844i	$-0.416566\pi$
$433$	10.7840	0.518247	0.259123	+	0.965844i	$0.416566\pi$
$434$	−7.92613	−0.380467
$435$	20.2127	0.969126
$436$	17.1038	0.819122
$437$	−0.799427	−0.0382418
$438$	−9.36042	−0.447258
$439$	27.9476	1.33387	0.666933	−	0.745118i	$-0.267607\pi$
$439$	27.9476	1.33387	0.666933	+	0.745118i	$0.267607\pi$
$440$	−5.02568	−0.239590
$441$	−10.8773	−0.517965
$442$	22.4922	1.06985
$443$	24.8188	1.17918	0.589588	−	0.807704i	$-0.299290\pi$
$443$	24.8188	1.17918	0.589588	+	0.807704i	$0.299290\pi$
$444$	−0.848845	−0.0402844
$445$	−11.1718	−0.529592
$446$	1.64988	0.0781238
$447$	−6.95131	−0.328786
$448$	−1.78090	−0.0841398
$449$	−5.38435	−0.254103	−0.127052	−	0.991896i	$-0.540551\pi$
$449$	−5.38435	−0.254103	−0.127052	+	0.991896i	$0.540551\pi$
$450$	−10.1158	−0.476862
$451$	−22.8048	−1.07384
$452$	−8.86781	−0.417107
$453$	22.9898	1.08016
$454$	−1.64072	−0.0770026
$455$	−6.80605	−0.319072
$456$	−1.93210	−0.0904790
$457$	3.57380	0.167176	0.0835878	−	0.996500i	$-0.473362\pi$
$457$	3.57380	0.167176	0.0835878	+	0.996500i	$0.473362\pi$
$458$	1.32141	0.0617452
$459$	−2.70994	−0.126489
$460$	1.19985	0.0559432
$461$	13.0154	0.606188	0.303094	−	0.952961i	$-0.401980\pi$
$461$	13.0154	0.606188	0.303094	+	0.952961i	$0.401980\pi$
$462$	18.0285	0.838764
$463$	30.2372	1.40524	0.702621	−	0.711564i	$-0.252013\pi$
$463$	30.2372	1.40524	0.702621	+	0.711564i	$0.252013\pi$
$464$	6.97022	0.323584
$465$	12.9062	0.598512
$466$	5.09696	0.236112
$467$	−8.97180	−0.415165	−0.207583	−	0.978217i	$-0.566560\pi$
$467$	−8.97180	−0.415165	−0.207583	+	0.978217i	$0.566560\pi$
$468$	−9.04966	−0.418321
$469$	−18.1594	−0.838525
$470$	6.53685	0.301523
$471$	−7.57668	−0.349115
$472$	0.271844	0.0125127
$473$	−13.5916	−0.624943
$474$	4.10971	0.188765
$475$	−2.84625	−0.130595
$476$	12.5761	0.576423
$477$	−32.7134	−1.49784
$478$	20.1286	0.920660
$479$	2.62506	0.119942	0.0599711	−	0.998200i	$-0.480899\pi$
$479$	2.62506	0.119942	0.0599711	+	0.998200i	$0.480899\pi$
$480$	2.89987	0.132360
$481$	−1.11868	−0.0510073
$482$	2.60691	0.118741
$483$	−4.30420	−0.195848
$484$	6.54434	0.297470
$485$	−2.02925	−0.0921433
$486$	21.6908	0.983915
$487$	−4.90131	−0.222100	−0.111050	−	0.993815i	$-0.535421\pi$
$487$	−4.90131	−0.222100	−0.111050	+	0.993815i	$0.535421\pi$
$488$	−3.86669	−0.175037
$489$	−14.2835	−0.645921
$490$	4.59348	0.207512
$491$	−17.4694	−0.788384	−0.394192	−	0.919028i	$-0.628976\pi$
$491$	−17.4694	−0.788384	−0.394192	+	0.919028i	$0.628976\pi$
$492$	13.1586	0.593236
$493$	−49.2210	−2.21680
$494$	−2.54628	−0.114563
$495$	−14.2791	−0.641796
$496$	4.45062	0.199839
$497$	−20.1879	−0.905553
$498$	22.3638	1.00215
$499$	−38.0624	−1.70391	−0.851954	−	0.523616i	$-0.824583\pi$
$499$	−38.0624	−1.70391	−0.851954	+	0.523616i	$0.824583\pi$
$500$	10.2711	0.459339
$501$	31.1440	1.39141
$502$	23.5733	1.05213
$503$	−22.3632	−0.997125	−0.498562	−	0.866854i	$-0.666139\pi$
$503$	−22.3632	−0.997125	−0.498562	+	0.866854i	$0.666139\pi$
$504$	−5.05993	−0.225387
$505$	−10.1527	−0.451788
$506$	−4.18860	−0.186206
$507$	6.89991	0.306436
$508$	−12.8126	−0.568466
$509$	−2.67022	−0.118355	−0.0591777	−	0.998247i	$-0.518848\pi$
$509$	−2.67022	−0.118355	−0.0591777	+	0.998247i	$0.518848\pi$
$510$	−20.4778	−0.906770
$511$	−6.89738	−0.305122
$512$	1.00000	0.0441942
$513$	0.306785	0.0135449
$514$	22.0607	0.973054
$515$	1.53553	0.0676635
$516$	7.84249	0.345246
$517$	−22.8197	−1.00361
$518$	−0.625485	−0.0274822
$519$	−17.4737	−0.767012
$520$	3.82168	0.167592
$521$	−14.5438	−0.637177	−0.318588	−	0.947893i	$-0.603209\pi$
$521$	−14.5438	−0.637177	−0.318588	+	0.947893i	$0.603209\pi$
$522$	19.8039	0.866794
$523$	−16.0763	−0.702966	−0.351483	−	0.936194i	$-0.614323\pi$
$523$	−16.0763	−0.702966	−0.351483	+	0.936194i	$0.614323\pi$
$524$	−1.00000	−0.0436852
$525$	−15.3245	−0.668816
$526$	−24.5440	−1.07017
$527$	−31.4286	−1.36905
$528$	−10.1233	−0.440558
$529$	1.00000	0.0434783
$530$	13.8149	0.600080
$531$	0.772369	0.0335180
$532$	−1.42370	−0.0617253
$533$	17.3415	0.751144
$534$	−22.5033	−0.973814
$535$	−7.96597	−0.344399
$536$	10.1968	0.440433
$537$	35.8528	1.54716
$538$	2.80645	0.120995
$539$	−16.0355	−0.690700
$540$	−0.460449	−0.0198146
$541$	−14.6903	−0.631584	−0.315792	−	0.948829i	$-0.602270\pi$
$541$	−14.6903	−0.631584	−0.315792	+	0.948829i	$0.602270\pi$
$542$	−21.1376	−0.907937
$543$	−43.8152	−1.88029
$544$	−7.06162	−0.302764
$545$	−20.5219	−0.879063
$546$	−13.7095	−0.586711
$547$	33.6144	1.43725	0.718625	−	0.695398i	$-0.244772\pi$
$547$	33.6144	1.43725	0.718625	+	0.695398i	$0.244772\pi$
$548$	19.5659	0.835814
$549$	−10.9861	−0.468876
$550$	−14.9129	−0.635889
$551$	5.57218	0.237383
$552$	2.41686	0.102868
$553$	3.02831	0.128777
$554$	−1.42273	−0.0604460
$555$	1.01849	0.0432323
$556$	−7.02393	−0.297881
$557$	−29.8208	−1.26355	−0.631773	−	0.775153i	$-0.717673\pi$
$557$	−29.8208	−1.26355	−0.631773	+	0.775153i	$0.717673\pi$
$558$	12.6452	0.535314
$559$	10.3355	0.437144
$560$	2.13682	0.0902969
$561$	71.4866	3.01817
$562$	22.8406	0.963472
$563$	−1.80858	−0.0762225	−0.0381112	−	0.999274i	$-0.512134\pi$
$563$	−1.80858	−0.0762225	−0.0381112	+	0.999274i	$0.512134\pi$
$564$	13.1672	0.554440
$565$	10.6400	0.447629
$566$	15.4918	0.651170
$567$	16.8316	0.706859
$568$	11.3358	0.475639
$569$	−18.6876	−0.783423	−0.391712	−	0.920088i	$-0.628117\pi$
$569$	−18.6876	−0.783423	−0.391712	+	0.920088i	$0.628117\pi$
$570$	2.31823	0.0971001
$571$	30.6854	1.28414	0.642072	−	0.766645i	$-0.278075\pi$
$571$	30.6854	1.28414	0.642072	+	0.766645i	$0.278075\pi$
$572$	−13.3413	−0.557826
$573$	−32.1784	−1.34427
$574$	9.69614	0.404709
$575$	3.56036	0.148477
$576$	2.84122	0.118384
$577$	1.63046	0.0678769	0.0339385	−	0.999424i	$-0.489195\pi$
$577$	1.63046	0.0678769	0.0339385	+	0.999424i	$0.489195\pi$
$578$	32.8665	1.36706
$579$	−46.1494	−1.91790
$580$	−8.36321	−0.347263
$581$	16.4792	0.683670
$582$	−4.08752	−0.169433
$583$	−48.2269	−1.99735
$584$	3.87297	0.160265
$585$	10.8582	0.448932
$586$	0.196112	0.00810133
$587$	−35.1173	−1.44945	−0.724724	−	0.689039i	$-0.758033\pi$
$587$	−35.1173	−1.44945	−0.724724	+	0.689039i	$0.758033\pi$
$588$	9.25267	0.381574
$589$	3.55795	0.146603
$590$	−0.326172	−0.0134283
$591$	−65.1293	−2.67906
$592$	0.351218	0.0144350
$593$	−4.68425	−0.192359	−0.0961795	−	0.995364i	$-0.530662\pi$
$593$	−4.68425	−0.192359	−0.0961795	+	0.995364i	$0.530662\pi$
$594$	1.60740	0.0659524
$595$	−15.0894	−0.618604
$596$	2.87617	0.117813
$597$	−24.9194	−1.01988
$598$	3.18514	0.130250
$599$	16.2026	0.662019	0.331009	−	0.943627i	$-0.392611\pi$
$599$	16.2026	0.662019	0.331009	+	0.943627i	$0.392611\pi$
$600$	8.60490	0.351294
$601$	23.0303	0.939426	0.469713	−	0.882819i	$-0.344357\pi$
$601$	23.0303	0.939426	0.469713	+	0.882819i	$0.344357\pi$
$602$	5.77886	0.235529
$603$	28.9712	1.17980
$604$	−9.51227	−0.387049
$605$	−7.85222	−0.319238
$606$	−20.4506	−0.830748
$607$	−46.7461	−1.89736	−0.948682	−	0.316232i	$-0.897582\pi$
$607$	−46.7461	−1.89736	−0.948682	+	0.316232i	$0.897582\pi$
$608$	0.799427	0.0324210
$609$	30.0012	1.21571
$610$	4.63945	0.187846
$611$	17.3528	0.702020
$612$	−20.0636	−0.811023
$613$	−28.9369	−1.16875	−0.584376	−	0.811483i	$-0.698661\pi$
$613$	−28.9369	−1.16875	−0.584376	+	0.811483i	$0.698661\pi$
$614$	27.4186	1.10653
$615$	−15.7883	−0.636648
$616$	−7.45949	−0.300551
$617$	−40.6316	−1.63577	−0.817884	−	0.575383i	$-0.804853\pi$
$617$	−40.6316	−1.63577	−0.817884	+	0.575383i	$0.804853\pi$
$618$	3.09303	0.124420
$619$	9.88178	0.397182	0.198591	−	0.980082i	$-0.436363\pi$
$619$	9.88178	0.397182	0.198591	+	0.980082i	$0.436363\pi$
$620$	−5.34008	−0.214463
$621$	−0.383756	−0.0153996
$622$	−25.5930	−1.02619
$623$	−16.5820	−0.664342
$624$	7.69803	0.308168
$625$	5.47800	0.219120
$626$	−29.7716	−1.18991
$627$	−8.09280	−0.323195
$628$	3.13493	0.125097
$629$	−2.48017	−0.0988907
$630$	6.07116	0.241881
$631$	−49.0834	−1.95398	−0.976990	−	0.213286i	$-0.931583\pi$
$631$	−49.0834	−1.95398	−0.976990	+	0.213286i	$0.931583\pi$
$632$	−1.70043	−0.0676396
$633$	−4.15361	−0.165091
$634$	−19.9112	−0.790773
$635$	15.3731	0.610065
$636$	27.8274	1.10343
$637$	12.1939	0.483141
$638$	29.1954	1.15586
$639$	32.2074	1.27411
$640$	−1.19985	−0.0474282
$641$	8.69743	0.343528	0.171764	−	0.985138i	$-0.445053\pi$
$641$	8.69743	0.343528	0.171764	+	0.985138i	$0.445053\pi$
$642$	−16.0459	−0.633281
$643$	22.3642	0.881958	0.440979	−	0.897517i	$-0.354631\pi$
$643$	22.3642	0.881958	0.440979	+	0.897517i	$0.354631\pi$
$644$	1.78090	0.0701774
$645$	−9.40980	−0.370510
$646$	−5.64525	−0.222109
$647$	32.2354	1.26730	0.633652	−	0.773618i	$-0.281555\pi$
$647$	32.2354	1.26730	0.633652	+	0.773618i	$0.281555\pi$
$648$	−9.45114	−0.371276
$649$	1.13865	0.0446958
$650$	11.3402	0.444801
$651$	19.1564	0.750797
$652$	5.90993	0.231451
$653$	−4.64115	−0.181622	−0.0908111	−	0.995868i	$-0.528946\pi$
$653$	−4.64115	−0.181622	−0.0908111	+	0.995868i	$0.528946\pi$
$654$	−41.3374	−1.61642
$655$	1.19985	0.0468820
$656$	−5.44451	−0.212572
$657$	11.0039	0.429305
$658$	9.70248	0.378242
$659$	14.6862	0.572092	0.286046	−	0.958216i	$-0.407659\pi$
$659$	14.6862	0.572092	0.286046	+	0.958216i	$0.407659\pi$
$660$	12.1464	0.472797
$661$	−43.9197	−1.70828	−0.854139	−	0.520045i	$-0.825915\pi$
$661$	−43.9197	−1.70828	−0.854139	+	0.520045i	$0.825915\pi$
$662$	9.82390	0.381817
$663$	−54.3606	−2.11119
$664$	−9.25325	−0.359096
$665$	1.70823	0.0662422
$666$	0.997886	0.0386673
$667$	−6.97022	−0.269888
$668$	−12.8861	−0.498579
$669$	−3.98752	−0.154166
$670$	−12.2346	−0.472662
$671$	−16.1960	−0.625241
$672$	4.30420	0.166038
$673$	−10.8668	−0.418884	−0.209442	−	0.977821i	$-0.567165\pi$
$673$	−10.8668	−0.418884	−0.209442	+	0.977821i	$0.567165\pi$
$674$	27.6746	1.06599
$675$	−1.36631	−0.0525893
$676$	−2.85491	−0.109804
$677$	23.4611	0.901682	0.450841	−	0.892604i	$-0.351124\pi$
$677$	23.4611	0.901682	0.450841	+	0.892604i	$0.351124\pi$
$678$	21.4323	0.823101
$679$	−3.01196	−0.115588
$680$	8.47287	0.324920
$681$	3.96538	0.151954
$682$	18.6419	0.713834
$683$	−8.96790	−0.343147	−0.171574	−	0.985171i	$-0.554885\pi$
$683$	−8.96790	−0.343147	−0.171574	+	0.985171i	$0.554885\pi$
$684$	2.27135	0.0868471
$685$	−23.4761	−0.896976
$686$	19.2843	0.736278
$687$	−3.19365	−0.121845
$688$	−3.24491	−0.123711
$689$	36.6732	1.39714
$690$	−2.89987	−0.110396
$691$	−13.3501	−0.507863	−0.253931	−	0.967222i	$-0.581724\pi$
$691$	−13.3501	−0.507863	−0.253931	+	0.967222i	$0.581724\pi$
$692$	7.22993	0.274841
$693$	−21.1940	−0.805094
$694$	26.2412	0.996104
$695$	8.42766	0.319679
$696$	−16.8461	−0.638548
$697$	38.4470	1.45628
$698$	−22.4590	−0.850085
$699$	−12.3186	−0.465934
$700$	6.34066	0.239655
$701$	37.2639	1.40744	0.703718	−	0.710479i	$-0.251522\pi$
$701$	37.2639	1.40744	0.703718	+	0.710479i	$0.251522\pi$
$702$	−1.22232	−0.0461333
$703$	0.280773	0.0105896
$704$	4.18860	0.157864
$705$	−15.7987	−0.595012
$706$	36.8826	1.38809
$707$	−15.0693	−0.566741
$708$	−0.657010	−0.0246920
$709$	−20.4687	−0.768718	−0.384359	−	0.923184i	$-0.625578\pi$
$709$	−20.4687	−0.768718	−0.384359	+	0.923184i	$0.625578\pi$
$710$	−13.6012	−0.510445
$711$	−4.83130	−0.181188
$712$	9.31098	0.348944
$713$	−4.45062	−0.166677
$714$	−30.3946	−1.13749
$715$	16.0075	0.598646
$716$	−14.8345	−0.554390
$717$	−48.6480	−1.81679
$718$	7.28513	0.271879
$719$	1.92087	0.0716365	0.0358182	−	0.999358i	$-0.488596\pi$
$719$	1.92087	0.0716365	0.0358182	+	0.999358i	$0.488596\pi$
$720$	−3.40903	−0.127047
$721$	2.27915	0.0848799
$722$	−18.3609	−0.683323
$723$	−6.30054	−0.234319
$724$	18.1290	0.673757
$725$	−24.8165	−0.921662
$726$	−15.8168	−0.587015
$727$	36.5940	1.35720	0.678598	−	0.734510i	$-0.262588\pi$
$727$	36.5940	1.35720	0.678598	+	0.734510i	$0.262588\pi$
$728$	5.67242	0.210234
$729$	−24.0703	−0.891492
$730$	−4.64698	−0.171992
$731$	22.9143	0.847515
$732$	9.34526	0.345411
$733$	−42.2216	−1.55949	−0.779745	−	0.626097i	$-0.784651\pi$
$733$	−42.2216	−1.55949	−0.779745	+	0.626097i	$0.784651\pi$
$734$	4.55904	0.168277
$735$	−11.1018	−0.409496
$736$	−1.00000	−0.0368605
$737$	42.7101	1.57325
$738$	−15.4690	−0.569423
$739$	−45.3585	−1.66854	−0.834270	−	0.551356i	$-0.814111\pi$
$739$	−45.3585	−1.66854	−0.834270	+	0.551356i	$0.814111\pi$
$740$	−0.421408	−0.0154913
$741$	6.15401	0.226073
$742$	20.5051	0.752765
$743$	−45.0389	−1.65232	−0.826158	−	0.563439i	$-0.809478\pi$
$743$	−45.0389	−1.65232	−0.826158	+	0.563439i	$0.809478\pi$
$744$	−10.7565	−0.394354
$745$	−3.45097	−0.126434
$746$	31.3090	1.14631
$747$	−26.2905	−0.961919
$748$	−29.5783	−1.08149
$749$	−11.8237	−0.432028
$750$	−24.8239	−0.906441
$751$	7.73112	0.282113	0.141056	−	0.990002i	$-0.454950\pi$
$751$	7.73112	0.282113	0.141056	+	0.990002i	$0.454950\pi$
$752$	−5.44806	−0.198670
$753$	−56.9733	−2.07622
$754$	−22.2011	−0.808516
$755$	11.4133	0.415372
$756$	−0.683433	−0.0248562
$757$	1.28324	0.0466403	0.0233201	−	0.999728i	$-0.492576\pi$
$757$	1.28324	0.0466403	0.0233201	+	0.999728i	$0.492576\pi$
$758$	6.54430	0.237700
$759$	10.1233	0.367451
$760$	−0.959191	−0.0347935
$761$	−13.4788	−0.488605	−0.244303	−	0.969699i	$-0.578559\pi$
$761$	−13.4788	−0.488605	−0.244303	+	0.969699i	$0.578559\pi$
$762$	30.9662	1.12179
$763$	−30.4602	−1.10273
$764$	13.3141	0.481689
$765$	24.0733	0.870371
$766$	30.1980	1.09110
$767$	−0.865862	−0.0312645
$768$	−2.41686	−0.0872110
$769$	−27.0296	−0.974714	−0.487357	−	0.873203i	$-0.662039\pi$
$769$	−27.0296	−0.974714	−0.487357	+	0.873203i	$0.662039\pi$
$770$	8.95026	0.322545
$771$	−53.3176	−1.92019
$772$	19.0948	0.687236
$773$	−40.4186	−1.45376	−0.726878	−	0.686767i	$-0.759029\pi$
$773$	−40.4186	−1.45376	−0.726878	+	0.686767i	$0.759029\pi$
$774$	−9.21948	−0.331387
$775$	−15.8458	−0.569199
$776$	1.69125	0.0607124
$777$	1.51171	0.0542323
$778$	−28.2299	−1.01209
$779$	−4.35248	−0.155944
$780$	−9.23647	−0.330719
$781$	47.4810	1.69901
$782$	7.06162	0.252523
$783$	2.67486	0.0955919
$784$	−3.82838	−0.136728
$785$	−3.76144	−0.134251
$786$	2.41686	0.0862066
$787$	−4.00296	−0.142690	−0.0713451	−	0.997452i	$-0.522729\pi$
$787$	−4.00296	−0.142690	−0.0713451	+	0.997452i	$0.522729\pi$
$788$	26.9479	0.959978
$789$	59.3195	2.11183
$790$	2.04026	0.0725893
$791$	15.7927	0.561524
$792$	11.9007	0.422873
$793$	12.3159	0.437352
$794$	−30.1533	−1.07010
$795$	−33.3887	−1.18417
$796$	10.3107	0.365451
$797$	28.8625	1.02236	0.511180	−	0.859473i	$-0.329208\pi$
$797$	28.8625	1.02236	0.511180	+	0.859473i	$0.329208\pi$
$798$	3.44089	0.121806
$799$	38.4721	1.36105
$800$	−3.56036	−0.125878
$801$	26.4545	0.934724
$802$	27.2003	0.960477
$803$	16.2223	0.572473
$804$	−24.6441	−0.869132
$805$	−2.13682	−0.0753128
$806$	−14.1758	−0.499323
$807$	−6.78280	−0.238766
$808$	8.46163	0.297679
$809$	12.3811	0.435296	0.217648	−	0.976027i	$-0.430161\pi$
$809$	12.3811	0.435296	0.217648	+	0.976027i	$0.430161\pi$
$810$	11.3399	0.398445
$811$	12.0160	0.421940	0.210970	−	0.977492i	$-0.432338\pi$
$811$	12.0160	0.421940	0.210970	+	0.977492i	$0.432338\pi$
$812$	−12.4133	−0.435621
$813$	51.0866	1.79168
$814$	1.47111	0.0515624
$815$	−7.09102	−0.248388
$816$	17.0670	0.597463
$817$	−2.59406	−0.0907548
$818$	14.9139	0.521452
$819$	16.1166	0.563159
$820$	6.53258	0.228128
$821$	38.1537	1.33157	0.665787	−	0.746142i	$-0.268096\pi$
$821$	38.1537	1.33157	0.665787	+	0.746142i	$0.268096\pi$
$822$	−47.2881	−1.64936
$823$	16.5322	0.576277	0.288138	−	0.957589i	$-0.406964\pi$
$823$	16.5322	0.576277	0.288138	+	0.957589i	$0.406964\pi$
$824$	−1.27977	−0.0445829
$825$	36.0425	1.25484
$826$	−0.484129	−0.0168450
$827$	−46.6261	−1.62135	−0.810675	−	0.585497i	$-0.800899\pi$
$827$	−46.6261	−1.62135	−0.810675	+	0.585497i	$0.800899\pi$
$828$	−2.84122	−0.0987391
$829$	25.4993	0.885627	0.442814	−	0.896614i	$-0.353980\pi$
$829$	25.4993	0.885627	0.442814	+	0.896614i	$0.353980\pi$
$830$	11.1025	0.385373
$831$	3.43854	0.119282
$832$	−3.18514	−0.110425
$833$	27.0346	0.936692
$834$	16.9759	0.587826
$835$	15.4614	0.535064
$836$	3.34848	0.115809
$837$	1.70795	0.0590355
$838$	−2.82188	−0.0974802
$839$	−26.6685	−0.920698	−0.460349	−	0.887738i	$-0.652276\pi$
$839$	−26.6685	−0.920698	−0.460349	+	0.887738i	$0.652276\pi$
$840$	−5.16439	−0.178188
$841$	19.5840	0.675309
$842$	21.2694	0.732990
$843$	−55.2025	−1.90128
$844$	1.71860	0.0591565
$845$	3.42545	0.117839
$846$	−15.4791	−0.532184
$847$	−11.6548	−0.400465
$848$	−11.5139	−0.395387
$849$	−37.4416	−1.28499
$850$	25.1419	0.862361
$851$	−0.351218	−0.0120396
$852$	−27.3970	−0.938607
$853$	40.3062	1.38006	0.690028	−	0.723782i	$-0.257598\pi$
$853$	40.3062	1.38006	0.690028	+	0.723782i	$0.257598\pi$
$854$	6.88621	0.235641
$855$	−2.72527	−0.0932023
$856$	6.63915	0.226921
$857$	−5.90927	−0.201857	−0.100928	−	0.994894i	$-0.532181\pi$
$857$	−5.90927	−0.201857	−0.100928	+	0.994894i	$0.532181\pi$
$858$	32.2440	1.10079
$859$	−46.5023	−1.58664	−0.793319	−	0.608806i	$-0.791649\pi$
$859$	−46.5023	−1.58664	−0.793319	+	0.608806i	$0.791649\pi$
$860$	3.89340	0.132764
$861$	−23.4342	−0.798636
$862$	−7.39625	−0.251917
$863$	10.6397	0.362179	0.181089	−	0.983467i	$-0.442038\pi$
$863$	10.6397	0.362179	0.181089	+	0.983467i	$0.442038\pi$
$864$	0.383756	0.0130556
$865$	−8.67483	−0.294953
$866$	10.7840	0.366456
$867$	−79.4337	−2.69771
$868$	−7.92613	−0.269030
$869$	−7.12243	−0.241612
$870$	20.2127	0.685275
$871$	−32.4780	−1.10048
$872$	17.1038	0.579207
$873$	4.80521	0.162632
$874$	−0.799427	−0.0270410
$875$	−18.2919	−0.618380
$876$	−9.36042	−0.316259
$877$	52.6891	1.77918	0.889592	−	0.456756i	$-0.150989\pi$
$877$	52.6891	1.77918	0.889592	+	0.456756i	$0.150989\pi$
$878$	27.9476	0.943185
$879$	−0.473977	−0.0159868
$880$	−5.02568	−0.169416
$881$	−38.1168	−1.28419	−0.642093	−	0.766626i	$-0.721934\pi$
$881$	−38.1168	−1.28419	−0.642093	+	0.766626i	$0.721934\pi$
$882$	−10.8773	−0.366256
$883$	−31.9248	−1.07435	−0.537177	−	0.843470i	$-0.680509\pi$
$883$	−31.9248	−1.07435	−0.537177	+	0.843470i	$0.680509\pi$
$884$	22.4922	0.756495
$885$	0.788313	0.0264988
$886$	24.8188	0.833803
$887$	−2.27358	−0.0763394	−0.0381697	−	0.999271i	$-0.512153\pi$
$887$	−2.27358	−0.0763394	−0.0381697	+	0.999271i	$0.512153\pi$
$888$	−0.848845	−0.0284854
$889$	22.8180	0.765290
$890$	−11.1718	−0.374478
$891$	−39.5870	−1.32621
$892$	1.64988	0.0552419
$893$	−4.35533	−0.145746
$894$	−6.95131	−0.232487
$895$	17.7991	0.594958
$896$	−1.78090	−0.0594958
$897$	−7.69803	−0.257030
$898$	−5.38435	−0.179678
$899$	31.0218	1.03464
$900$	−10.1158	−0.337192
$901$	81.3065	2.70871
$902$	−22.8048	−0.759318
$903$	−13.9667	−0.464783
$904$	−8.86781	−0.294939
$905$	−21.7520	−0.723061
$906$	22.9898	0.763786
$907$	30.3532	1.00786	0.503930	−	0.863744i	$-0.331887\pi$
$907$	30.3532	1.00786	0.503930	+	0.863744i	$0.331887\pi$
$908$	−1.64072	−0.0544491
$909$	24.0413	0.797400
$910$	−6.80605	−0.225618
$911$	−4.78385	−0.158496	−0.0792481	−	0.996855i	$-0.525252\pi$
$911$	−4.78385	−0.158496	−0.0792481	+	0.996855i	$0.525252\pi$
$912$	−1.93210	−0.0639783
$913$	−38.7581	−1.28271
$914$	3.57380	0.118211
$915$	−11.2129	−0.370687
$916$	1.32141	0.0436605
$917$	1.78090	0.0588106
$918$	−2.70994	−0.0894413
$919$	24.5041	0.808316	0.404158	−	0.914689i	$-0.367565\pi$
$919$	24.5041	0.808316	0.404158	+	0.914689i	$0.367565\pi$
$920$	1.19985	0.0395578
$921$	−66.2670	−2.18357
$922$	13.0154	0.428640
$923$	−36.1060	−1.18844
$924$	18.0285	0.593096
$925$	−1.25046	−0.0411150
$926$	30.2372	0.993657
$927$	−3.63610	−0.119425
$928$	6.97022	0.228809
$929$	−15.0224	−0.492868	−0.246434	−	0.969160i	$-0.579259\pi$
$929$	−15.0224	−0.492868	−0.246434	+	0.969160i	$0.579259\pi$
$930$	12.9062	0.423212
$931$	−3.06051	−0.100304
$932$	5.09696	0.166956
$933$	61.8547	2.02503
$934$	−8.97180	−0.293566
$935$	35.4895	1.16063
$936$	−9.04966	−0.295798
$937$	29.4619	0.962477	0.481239	−	0.876590i	$-0.340187\pi$
$937$	29.4619	0.962477	0.481239	+	0.876590i	$0.340187\pi$
$938$	−18.1594	−0.592927
$939$	71.9538	2.34812
$940$	6.53685	0.213209
$941$	−20.6992	−0.674775	−0.337388	−	0.941366i	$-0.609543\pi$
$941$	−20.6992	−0.674775	−0.337388	+	0.941366i	$0.609543\pi$
$942$	−7.57668	−0.246862
$943$	5.44451	0.177298
$944$	0.271844	0.00884778
$945$	0.820016	0.0266751
$946$	−13.5916	−0.441901
$947$	−1.55148	−0.0504163	−0.0252081	−	0.999682i	$-0.508025\pi$
$947$	−1.55148	−0.0504163	−0.0252081	+	0.999682i	$0.508025\pi$
$948$	4.10971	0.133477
$949$	−12.3359	−0.400441
$950$	−2.84625	−0.0923445
$951$	48.1225	1.56048
$952$	12.5761	0.407593
$953$	5.55783	0.180036	0.0900179	−	0.995940i	$-0.471308\pi$
$953$	5.55783	0.180036	0.0900179	+	0.995940i	$0.471308\pi$
$954$	−32.7134	−1.05913
$955$	−15.9749	−0.516937
$956$	20.1286	0.651005
$957$	−70.5613	−2.28092
$958$	2.62506	0.0848120
$959$	−34.8450	−1.12520
$960$	2.89987	0.0935928
$961$	−11.1919	−0.361031
$962$	−1.11868	−0.0360676
$963$	18.8633	0.607860
$964$	2.60691	0.0839629
$965$	−22.9108	−0.737526
$966$	−4.30420	−0.138485
$967$	33.4478	1.07561	0.537805	−	0.843069i	$-0.319254\pi$
$967$	33.4478	1.07561	0.537805	+	0.843069i	$0.319254\pi$
$968$	6.54434	0.210343
$969$	13.6438	0.438301
$970$	−2.02925	−0.0651551
$971$	−40.8073	−1.30957	−0.654785	−	0.755816i	$-0.727241\pi$
$971$	−40.8073	−1.30957	−0.654785	+	0.755816i	$0.727241\pi$
$972$	21.6908	0.695733
$973$	12.5089	0.401018
$974$	−4.90131	−0.157048
$975$	−27.4078	−0.877752
$976$	−3.86669	−0.123770
$977$	−10.0659	−0.322036	−0.161018	−	0.986951i	$-0.551478\pi$
$977$	−10.0659	−0.322036	−0.161018	+	0.986951i	$0.551478\pi$
$978$	−14.2835	−0.456735
$979$	38.9999	1.24644
$980$	4.59348	0.146733
$981$	48.5955	1.55154
$982$	−17.4694	−0.557472
$983$	6.13057	0.195535	0.0977674	−	0.995209i	$-0.468830\pi$
$983$	6.13057	0.195535	0.0977674	+	0.995209i	$0.468830\pi$
$984$	13.1586	0.419481
$985$	−32.3334	−1.03023
$986$	−49.2210	−1.56752
$987$	−23.4495	−0.746407
$988$	−2.54628	−0.0810081
$989$	3.24491	0.103182
$990$	−14.2791	−0.453818
$991$	35.8645	1.13927	0.569637	−	0.821896i	$-0.307084\pi$
$991$	35.8645	1.13927	0.569637	+	0.821896i	$0.307084\pi$
$992$	4.45062	0.141307
$993$	−23.7430	−0.753462
$994$	−20.1879	−0.640323
$995$	−12.3712	−0.392194
$996$	22.3638	0.708625
$997$	39.8365	1.26163	0.630817	−	0.775932i	$-0.282720\pi$
$997$	39.8365	1.26163	0.630817	+	0.775932i	$0.282720\pi$
$998$	−38.0624	−1.20485
$999$	0.134782	0.00426431

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.k.1.8	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.k.1.8	✓	35	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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.41686 q^{3} +1.00000 q^{4} -1.19985 q^{5} -2.41686 q^{6} -1.78090 q^{7} +1.00000 q^{8} +2.84122 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.41686 q^{3} +1.00000 q^{4} -1.19985 q^{5} -2.41686 q^{6} -1.78090 q^{7} +1.00000 q^{8} +2.84122 q^{9} -1.19985 q^{10} +4.18860 q^{11} -2.41686 q^{12} -3.18514 q^{13} -1.78090 q^{14} +2.89987 q^{15} +1.00000 q^{16} -7.06162 q^{17} +2.84122 q^{18} +0.799427 q^{19} -1.19985 q^{20} +4.30420 q^{21} +4.18860 q^{22} -1.00000 q^{23} -2.41686 q^{24} -3.56036 q^{25} -3.18514 q^{26} +0.383756 q^{27} -1.78090 q^{28} +6.97022 q^{29} +2.89987 q^{30} +4.45062 q^{31} +1.00000 q^{32} -10.1233 q^{33} -7.06162 q^{34} +2.13682 q^{35} +2.84122 q^{36} +0.351218 q^{37} +0.799427 q^{38} +7.69803 q^{39} -1.19985 q^{40} -5.44451 q^{41} +4.30420 q^{42} -3.24491 q^{43} +4.18860 q^{44} -3.40903 q^{45} -1.00000 q^{46} -5.44806 q^{47} -2.41686 q^{48} -3.82838 q^{49} -3.56036 q^{50} +17.0670 q^{51} -3.18514 q^{52} -11.5139 q^{53} +0.383756 q^{54} -5.02568 q^{55} -1.78090 q^{56} -1.93210 q^{57} +6.97022 q^{58} +0.271844 q^{59} +2.89987 q^{60} -3.86669 q^{61} +4.45062 q^{62} -5.05993 q^{63} +1.00000 q^{64} +3.82168 q^{65} -10.1233 q^{66} +10.1968 q^{67} -7.06162 q^{68} +2.41686 q^{69} +2.13682 q^{70} +11.3358 q^{71} +2.84122 q^{72} +3.87297 q^{73} +0.351218 q^{74} +8.60490 q^{75} +0.799427 q^{76} -7.45949 q^{77} +7.69803 q^{78} -1.70043 q^{79} -1.19985 q^{80} -9.45114 q^{81} -5.44451 q^{82} -9.25325 q^{83} +4.30420 q^{84} +8.47287 q^{85} -3.24491 q^{86} -16.8461 q^{87} +4.18860 q^{88} +9.31098 q^{89} -3.40903 q^{90} +5.67242 q^{91} -1.00000 q^{92} -10.7565 q^{93} -5.44806 q^{94} -0.959191 q^{95} -2.41686 q^{96} +1.69125 q^{97} -3.82838 q^{98} +11.9007 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9}+O(q^{10}) \) 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9	\( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9} + 10 q^{10} + 9 q^{11} - 3 q^{12} + 19 q^{13} + 14 q^{14} + 14 q^{15} + 35 q^{16} + 28 q^{17} + 54 q^{18} + 21 q^{19} + 10 q^{20} + 28 q^{21} + 9 q^{22} - 35 q^{23} - 3 q^{24} + 81 q^{25} + 19 q^{26} - 21 q^{27} + 14 q^{28} + 35 q^{29} + 14 q^{30} + 5 q^{31} + 35 q^{32} + 26 q^{33} + 28 q^{34} - 7 q^{35} + 54 q^{36} + 51 q^{37} + 21 q^{38} + 21 q^{39} + 10 q^{40} + 3 q^{41} + 28 q^{42} + 43 q^{43} + 9 q^{44} + 2 q^{45} - 35 q^{46} + 10 q^{47} - 3 q^{48} + 85 q^{49} + 81 q^{50} + 26 q^{51} + 19 q^{52} + 39 q^{53} - 21 q^{54} + 2 q^{55} + 14 q^{56} + 50 q^{57} + 35 q^{58} - 42 q^{59} + 14 q^{60} + 47 q^{61} + 5 q^{62} + 23 q^{63} + 35 q^{64} + 61 q^{65} + 26 q^{66} + 22 q^{67} + 28 q^{68} + 3 q^{69} - 7 q^{70} + 54 q^{72} + 30 q^{73} + 51 q^{74} - 26 q^{75} + 21 q^{76} + 2 q^{77} + 21 q^{78} + 55 q^{79} + 10 q^{80} + 67 q^{81} + 3 q^{82} + 20 q^{83} + 28 q^{84} + 28 q^{85} + 43 q^{86} + 29 q^{87} + 9 q^{88} - 31 q^{89} + 2 q^{90} + 32 q^{91} - 35 q^{92} + 11 q^{93} + 10 q^{94} + 16 q^{95} - 3 q^{96} + 36 q^{97} + 85 q^{98} - 9 q^{99}+O(q^{100}) \) 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9 + 10 * q^10 + 9 * q^11 - 3 * q^12 + 19 * q^13 + 14 * q^14 + 14 * q^15 + 35 * q^16 + 28 * q^17 + 54 * q^18 + 21 * q^19 + 10 * q^20 + 28 * q^21 + 9 * q^22 - 35 * q^23 - 3 * q^24 + 81 * q^25 + 19 * q^26 - 21 * q^27 + 14 * q^28 + 35 * q^29 + 14 * q^30 + 5 * q^31 + 35 * q^32 + 26 * q^33 + 28 * q^34 - 7 * q^35 + 54 * q^36 + 51 * q^37 + 21 * q^38 + 21 * q^39 + 10 * q^40 + 3 * q^41 + 28 * q^42 + 43 * q^43 + 9 * q^44 + 2 * q^45 - 35 * q^46 + 10 * q^47 - 3 * q^48 + 85 * q^49 + 81 * q^50 + 26 * q^51 + 19 * q^52 + 39 * q^53 - 21 * q^54 + 2 * q^55 + 14 * q^56 + 50 * q^57 + 35 * q^58 - 42 * q^59 + 14 * q^60 + 47 * q^61 + 5 * q^62 + 23 * q^63 + 35 * q^64 + 61 * q^65 + 26 * q^66 + 22 * q^67 + 28 * q^68 + 3 * q^69 - 7 * q^70 + 54 * q^72 + 30 * q^73 + 51 * q^74 - 26 * q^75 + 21 * q^76 + 2 * q^77 + 21 * q^78 + 55 * q^79 + 10 * q^80 + 67 * q^81 + 3 * q^82 + 20 * q^83 + 28 * q^84 + 28 * q^85 + 43 * q^86 + 29 * q^87 + 9 * q^88 - 31 * q^89 + 2 * q^90 + 32 * q^91 - 35 * q^92 + 11 * q^93 + 10 * q^94 + 16 * q^95 - 3 * q^96 + 36 * q^97 + 85 * q^98 - 9 * q^99

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