LMFDB - Embedded newform 6026.2.a.k.1.17

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			1.17
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)

$f(q)$	$=$	$q+1.00000 q^{2} -0.339838 q^{3} +1.00000 q^{4} -2.83329 q^{5} -0.339838 q^{6} -3.26036 q^{7} +1.00000 q^{8} -2.88451 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.339838 q^{3} +1.00000 q^{4} -2.83329 q^{5} -0.339838 q^{6} -3.26036 q^{7} +1.00000 q^{8} -2.88451 q^{9} -2.83329 q^{10} -2.84996 q^{11} -0.339838 q^{12} -5.10163 q^{13} -3.26036 q^{14} +0.962858 q^{15} +1.00000 q^{16} -6.71263 q^{17} -2.88451 q^{18} -0.852694 q^{19} -2.83329 q^{20} +1.10800 q^{21} -2.84996 q^{22} -1.00000 q^{23} -0.339838 q^{24} +3.02752 q^{25} -5.10163 q^{26} +1.99978 q^{27} -3.26036 q^{28} -5.13561 q^{29} +0.962858 q^{30} +9.14925 q^{31} +1.00000 q^{32} +0.968523 q^{33} -6.71263 q^{34} +9.23755 q^{35} -2.88451 q^{36} +3.06834 q^{37} -0.852694 q^{38} +1.73373 q^{39} -2.83329 q^{40} -7.10528 q^{41} +1.10800 q^{42} -1.19417 q^{43} -2.84996 q^{44} +8.17265 q^{45} -1.00000 q^{46} -10.0714 q^{47} -0.339838 q^{48} +3.62998 q^{49} +3.02752 q^{50} +2.28120 q^{51} -5.10163 q^{52} -0.435017 q^{53} +1.99978 q^{54} +8.07475 q^{55} -3.26036 q^{56} +0.289778 q^{57} -5.13561 q^{58} -1.02869 q^{59} +0.962858 q^{60} +10.3396 q^{61} +9.14925 q^{62} +9.40455 q^{63} +1.00000 q^{64} +14.4544 q^{65} +0.968523 q^{66} +5.64707 q^{67} -6.71263 q^{68} +0.339838 q^{69} +9.23755 q^{70} -15.4654 q^{71} -2.88451 q^{72} -9.82625 q^{73} +3.06834 q^{74} -1.02886 q^{75} -0.852694 q^{76} +9.29190 q^{77} +1.73373 q^{78} +4.13277 q^{79} -2.83329 q^{80} +7.97393 q^{81} -7.10528 q^{82} +16.5885 q^{83} +1.10800 q^{84} +19.0188 q^{85} -1.19417 q^{86} +1.74528 q^{87} -2.84996 q^{88} -6.78312 q^{89} +8.17265 q^{90} +16.6332 q^{91} -1.00000 q^{92} -3.10926 q^{93} -10.0714 q^{94} +2.41593 q^{95} -0.339838 q^{96} -9.73695 q^{97} +3.62998 q^{98} +8.22073 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.339838	−0.196205	−0.0981027	−	0.995176i	$-0.531277\pi$
$3$	−0.339838	−0.196205	−0.0981027	+	0.995176i	$0.531277\pi$
$4$	1.00000	0.500000
$5$	−2.83329	−1.26708	−0.633542	−	0.773708i	$-0.718400\pi$
$5$	−2.83329	−1.26708	−0.633542	+	0.773708i	$0.718400\pi$
$6$	−0.339838	−0.138738
$7$	−3.26036	−1.23230	−0.616151	−	0.787628i	$-0.711309\pi$
$7$	−3.26036	−1.23230	−0.616151	+	0.787628i	$0.711309\pi$
$8$	1.00000	0.353553
$9$	−2.88451	−0.961503
$10$	−2.83329	−0.895964
$11$	−2.84996	−0.859294	−0.429647	−	0.902997i	$-0.641362\pi$
$11$	−2.84996	−0.859294	−0.429647	+	0.902997i	$0.641362\pi$
$12$	−0.339838	−0.0981027
$13$	−5.10163	−1.41494	−0.707469	−	0.706744i	$-0.750163\pi$
$13$	−5.10163	−1.41494	−0.707469	+	0.706744i	$0.750163\pi$
$14$	−3.26036	−0.871369
$15$	0.962858	0.248609
$16$	1.00000	0.250000
$17$	−6.71263	−1.62805	−0.814025	−	0.580829i	$-0.802728\pi$
$17$	−6.71263	−1.62805	−0.814025	+	0.580829i	$0.802728\pi$
$18$	−2.88451	−0.679886
$19$	−0.852694	−0.195621	−0.0978107	−	0.995205i	$-0.531184\pi$
$19$	−0.852694	−0.195621	−0.0978107	+	0.995205i	$0.531184\pi$
$20$	−2.83329	−0.633542
$21$	1.10800	0.241784
$22$	−2.84996	−0.607613
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−0.339838	−0.0693691
$25$	3.02752	0.605503
$26$	−5.10163	−1.00051
$27$	1.99978	0.384858
$28$	−3.26036	−0.616151
$29$	−5.13561	−0.953660	−0.476830	−	0.878996i	$-0.658214\pi$
$29$	−5.13561	−0.953660	−0.476830	+	0.878996i	$0.658214\pi$
$30$	0.962858	0.175793
$31$	9.14925	1.64325	0.821627	−	0.570026i	$-0.193067\pi$
$31$	9.14925	1.64325	0.821627	+	0.570026i	$0.193067\pi$
$32$	1.00000	0.176777
$33$	0.968523	0.168598
$34$	−6.71263	−1.15121
$35$	9.23755	1.56143
$36$	−2.88451	−0.480752
$37$	3.06834	0.504433	0.252216	−	0.967671i	$-0.418841\pi$
$37$	3.06834	0.504433	0.252216	+	0.967671i	$0.418841\pi$
$38$	−0.852694	−0.138325
$39$	1.73373	0.277619
$40$	−2.83329	−0.447982
$41$	−7.10528	−1.10966	−0.554829	−	0.831965i	$-0.687216\pi$
$41$	−7.10528	−1.10966	−0.554829	+	0.831965i	$0.687216\pi$
$42$	1.10800	0.170967
$43$	−1.19417	−0.182109	−0.0910547	−	0.995846i	$-0.529024\pi$
$43$	−1.19417	−0.182109	−0.0910547	+	0.995846i	$0.529024\pi$
$44$	−2.84996	−0.429647
$45$	8.17265	1.21831
$46$	−1.00000	−0.147442
$47$	−10.0714	−1.46906	−0.734532	−	0.678574i	$-0.762598\pi$
$47$	−10.0714	−1.46906	−0.734532	+	0.678574i	$0.762598\pi$
$48$	−0.339838	−0.0490514
$49$	3.62998	0.518568
$50$	3.02752	0.428156
$51$	2.28120	0.319432
$52$	−5.10163	−0.707469
$53$	−0.435017	−0.0597542	−0.0298771	−	0.999554i	$-0.509512\pi$
$53$	−0.435017	−0.0597542	−0.0298771	+	0.999554i	$0.509512\pi$
$54$	1.99978	0.272136
$55$	8.07475	1.08880
$56$	−3.26036	−0.435685
$57$	0.289778	0.0383820
$58$	−5.13561	−0.674339
$59$	−1.02869	−0.133924	−0.0669618	−	0.997756i	$-0.521331\pi$
$59$	−1.02869	−0.133924	−0.0669618	+	0.997756i	$0.521331\pi$
$60$	0.962858	0.124304
$61$	10.3396	1.32385	0.661925	−	0.749570i	$-0.269740\pi$
$61$	10.3396	1.32385	0.661925	+	0.749570i	$0.269740\pi$
$62$	9.14925	1.16196
$63$	9.40455	1.18486
$64$	1.00000	0.125000
$65$	14.4544	1.79285
$66$	0.968523	0.119217
$67$	5.64707	0.689899	0.344950	−	0.938621i	$-0.387896\pi$
$67$	5.64707	0.689899	0.344950	+	0.938621i	$0.387896\pi$
$68$	−6.71263	−0.814025
$69$	0.339838	0.0409117
$70$	9.23755	1.10410
$71$	−15.4654	−1.83540	−0.917700	−	0.397274i	$-0.869956\pi$
$71$	−15.4654	−1.83540	−0.917700	+	0.397274i	$0.869956\pi$
$72$	−2.88451	−0.339943
$73$	−9.82625	−1.15008	−0.575038	−	0.818127i	$-0.695013\pi$
$73$	−9.82625	−1.15008	−0.575038	+	0.818127i	$0.695013\pi$
$74$	3.06834	0.356688
$75$	−1.02886	−0.118803
$76$	−0.852694	−0.0978107
$77$	9.29190	1.05891
$78$	1.73373	0.196306
$79$	4.13277	0.464973	0.232487	−	0.972600i	$-0.425314\pi$
$79$	4.13277	0.464973	0.232487	+	0.972600i	$0.425314\pi$
$80$	−2.83329	−0.316771
$81$	7.97393	0.885992
$82$	−7.10528	−0.784646
$83$	16.5885	1.82083	0.910413	−	0.413701i	$-0.135764\pi$
$83$	16.5885	1.82083	0.910413	+	0.413701i	$0.135764\pi$
$84$	1.10800	0.120892
$85$	19.0188	2.06288
$86$	−1.19417	−0.128771
$87$	1.74528	0.187113
$88$	−2.84996	−0.303806
$89$	−6.78312	−0.719009	−0.359504	−	0.933143i	$-0.617054\pi$
$89$	−6.78312	−0.719009	−0.359504	+	0.933143i	$0.617054\pi$
$90$	8.17265	0.861473
$91$	16.6332	1.74363
$92$	−1.00000	−0.104257
$93$	−3.10926	−0.322415
$94$	−10.0714	−1.03879
$95$	2.41593	0.247869
$96$	−0.339838	−0.0346846
$97$	−9.73695	−0.988637	−0.494319	−	0.869281i	$-0.664582\pi$
$97$	−9.73695	−0.988637	−0.494319	+	0.869281i	$0.664582\pi$
$98$	3.62998	0.366683
$99$	8.22073	0.826215
$100$	3.02752	0.302752
$101$	−18.0641	−1.79744	−0.898721	−	0.438522i	$-0.855502\pi$
$101$	−18.0641	−1.79744	−0.898721	+	0.438522i	$0.855502\pi$
$102$	2.28120	0.225873
$103$	−0.620291	−0.0611191	−0.0305596	−	0.999533i	$-0.509729\pi$
$103$	−0.620291	−0.0611191	−0.0305596	+	0.999533i	$0.509729\pi$
$104$	−5.10163	−0.500256
$105$	−3.13927	−0.306361
$106$	−0.435017	−0.0422526
$107$	1.12026	0.108299	0.0541497	−	0.998533i	$-0.482755\pi$
$107$	1.12026	0.108299	0.0541497	+	0.998533i	$0.482755\pi$
$108$	1.99978	0.192429
$109$	10.1244	0.969742	0.484871	−	0.874586i	$-0.338867\pi$
$109$	10.1244	0.969742	0.484871	+	0.874586i	$0.338867\pi$
$110$	8.07475	0.769897
$111$	−1.04274	−0.0989725
$112$	−3.26036	−0.308075
$113$	1.37838	0.129667	0.0648336	−	0.997896i	$-0.479348\pi$
$113$	1.37838	0.129667	0.0648336	+	0.997896i	$0.479348\pi$
$114$	0.289778	0.0271402
$115$	2.83329	0.264205
$116$	−5.13561	−0.476830
$117$	14.7157	1.36047
$118$	−1.02869	−0.0946982
$119$	21.8856	2.00625
$120$	0.962858	0.0878965
$121$	−2.87774	−0.261613
$122$	10.3396	0.936103
$123$	2.41464	0.217721
$124$	9.14925	0.821627
$125$	5.58861	0.499861
$126$	9.40455	0.837824
$127$	12.5675	1.11519	0.557593	−	0.830115i	$-0.311725\pi$
$127$	12.5675	1.11519	0.557593	+	0.830115i	$0.311725\pi$
$128$	1.00000	0.0883883
$129$	0.405824	0.0357308
$130$	14.4544	1.26773
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	0.968523	0.0842991
$133$	2.78009	0.241065
$134$	5.64707	0.487832
$135$	−5.66595	−0.487647
$136$	−6.71263	−0.575603
$137$	6.33054	0.540854	0.270427	−	0.962740i	$-0.412835\pi$
$137$	6.33054	0.540854	0.270427	+	0.962740i	$0.412835\pi$
$138$	0.339838	0.0289289
$139$	2.81575	0.238829	0.119414	−	0.992845i	$-0.461898\pi$
$139$	2.81575	0.238829	0.119414	+	0.992845i	$0.461898\pi$
$140$	9.23755	0.780715
$141$	3.42264	0.288239
$142$	−15.4654	−1.29782
$143$	14.5394	1.21585
$144$	−2.88451	−0.240376
$145$	14.5507	1.20837
$146$	−9.82625	−0.813226
$147$	−1.23360	−0.101746
$148$	3.06834	0.252216
$149$	−20.0553	−1.64299	−0.821495	−	0.570216i	$-0.806860\pi$
$149$	−20.0553	−1.64299	−0.821495	+	0.570216i	$0.806860\pi$
$150$	−1.02886	−0.0840065
$151$	4.46931	0.363707	0.181854	−	0.983326i	$-0.441790\pi$
$151$	4.46931	0.363707	0.181854	+	0.983326i	$0.441790\pi$
$152$	−0.852694	−0.0691626
$153$	19.3626	1.56538
$154$	9.29190	0.748763
$155$	−25.9224	−2.08214
$156$	1.73373	0.138809
$157$	−16.4381	−1.31191	−0.655953	−	0.754802i	$-0.727733\pi$
$157$	−16.4381	−1.31191	−0.655953	+	0.754802i	$0.727733\pi$
$158$	4.13277	0.328786
$159$	0.147835	0.0117241
$160$	−2.83329	−0.223991
$161$	3.26036	0.256953
$162$	7.97393	0.626491
$163$	−5.17214	−0.405114	−0.202557	−	0.979271i	$-0.564925\pi$
$163$	−5.17214	−0.405114	−0.202557	+	0.979271i	$0.564925\pi$
$164$	−7.10528	−0.554829
$165$	−2.74410	−0.213628
$166$	16.5885	1.28752
$167$	5.71922	0.442566	0.221283	−	0.975210i	$-0.428976\pi$
$167$	5.71922	0.442566	0.221283	+	0.975210i	$0.428976\pi$
$168$	1.10800	0.0854837
$169$	13.0266	1.00205
$170$	19.0188	1.45868
$171$	2.45961	0.188091
$172$	−1.19417	−0.0910547
$173$	−4.19883	−0.319231	−0.159615	−	0.987179i	$-0.551025\pi$
$173$	−4.19883	−0.319231	−0.159615	+	0.987179i	$0.551025\pi$
$174$	1.74528	0.132309
$175$	−9.87081	−0.746163
$176$	−2.84996	−0.214824
$177$	0.349586	0.0262765
$178$	−6.78312	−0.508416
$179$	11.7403	0.877508	0.438754	−	0.898607i	$-0.355420\pi$
$179$	11.7403	0.877508	0.438754	+	0.898607i	$0.355420\pi$
$180$	8.17265	0.609153
$181$	−23.7017	−1.76174	−0.880868	−	0.473362i	$-0.843040\pi$
$181$	−23.7017	−1.76174	−0.880868	+	0.473362i	$0.843040\pi$
$182$	16.6332	1.23293
$183$	−3.51379	−0.259747
$184$	−1.00000	−0.0737210
$185$	−8.69350	−0.639159
$186$	−3.10926	−0.227982
$187$	19.1307	1.39897
$188$	−10.0714	−0.734532
$189$	−6.52001	−0.474261
$190$	2.41593	0.175270
$191$	−14.0796	−1.01876	−0.509382	−	0.860541i	$-0.670126\pi$
$191$	−14.0796	−1.01876	−0.509382	+	0.860541i	$0.670126\pi$
$192$	−0.339838	−0.0245257
$193$	−16.0160	−1.15286	−0.576428	−	0.817148i	$-0.695554\pi$
$193$	−16.0160	−1.15286	−0.576428	+	0.817148i	$0.695554\pi$
$194$	−9.73695	−0.699072
$195$	−4.91215	−0.351766
$196$	3.62998	0.259284
$197$	−21.7646	−1.55066	−0.775330	−	0.631556i	$-0.782416\pi$
$197$	−21.7646	−1.55066	−0.775330	+	0.631556i	$0.782416\pi$
$198$	8.22073	0.584222
$199$	6.24870	0.442958	0.221479	−	0.975165i	$-0.428912\pi$
$199$	6.24870	0.442958	0.221479	+	0.975165i	$0.428912\pi$
$200$	3.02752	0.214078
$201$	−1.91909	−0.135362
$202$	−18.0641	−1.27098
$203$	16.7440	1.17520
$204$	2.28120	0.159716
$205$	20.1313	1.40603
$206$	−0.620291	−0.0432177
$207$	2.88451	0.200487
$208$	−5.10163	−0.353735
$209$	2.43014	0.168096
$210$	−3.13927	−0.216630
$211$	−0.830866	−0.0571992	−0.0285996	−	0.999591i	$-0.509105\pi$
$211$	−0.830866	−0.0571992	−0.0285996	+	0.999591i	$0.509105\pi$
$212$	−0.435017	−0.0298771
$213$	5.25571	0.360115
$214$	1.12026	0.0765792
$215$	3.38343	0.230748
$216$	1.99978	0.136068
$217$	−29.8299	−2.02498
$218$	10.1244	0.685711
$219$	3.33933	0.225651
$220$	8.07475	0.544399
$221$	34.2453	2.30359
$222$	−1.04274	−0.0699841
$223$	−17.3081	−1.15903	−0.579517	−	0.814960i	$-0.696759\pi$
$223$	−17.3081	−1.15903	−0.579517	+	0.814960i	$0.696759\pi$
$224$	−3.26036	−0.217842
$225$	−8.73290	−0.582194
$226$	1.37838	0.0916885
$227$	1.23585	0.0820263	0.0410131	−	0.999159i	$-0.486941\pi$
$227$	1.23585	0.0820263	0.0410131	+	0.999159i	$0.486941\pi$
$228$	0.289778	0.0191910
$229$	6.22950	0.411657	0.205829	−	0.978588i	$-0.434011\pi$
$229$	6.22950	0.411657	0.205829	+	0.978588i	$0.434011\pi$
$230$	2.83329	0.186821
$231$	−3.15774	−0.207764
$232$	−5.13561	−0.337170
$233$	5.71750	0.374566	0.187283	−	0.982306i	$-0.440032\pi$
$233$	5.71750	0.374566	0.187283	+	0.982306i	$0.440032\pi$
$234$	14.7157	0.961996
$235$	28.5352	1.86143
$236$	−1.02869	−0.0669618
$237$	−1.40447	−0.0912303
$238$	21.8856	1.41863
$239$	−17.1158	−1.10713	−0.553564	−	0.832807i	$-0.686733\pi$
$239$	−17.1158	−1.10713	−0.553564	+	0.832807i	$0.686733\pi$
$240$	0.962858	0.0621522
$241$	−4.71052	−0.303431	−0.151716	−	0.988424i	$-0.548480\pi$
$241$	−4.71052	−0.303431	−0.151716	+	0.988424i	$0.548480\pi$
$242$	−2.87774	−0.184988
$243$	−8.70918	−0.558694
$244$	10.3396	0.661925
$245$	−10.2848	−0.657070
$246$	2.41464	0.153952
$247$	4.35013	0.276792
$248$	9.14925	0.580978
$249$	−5.63740	−0.357256
$250$	5.58861	0.353455
$251$	1.87519	0.118361	0.0591805	−	0.998247i	$-0.481151\pi$
$251$	1.87519	0.118361	0.0591805	+	0.998247i	$0.481151\pi$
$252$	9.40455	0.592431
$253$	2.84996	0.179175
$254$	12.5675	0.788555
$255$	−6.46331	−0.404748
$256$	1.00000	0.0625000
$257$	−18.8136	−1.17356	−0.586780	−	0.809746i	$-0.699605\pi$
$257$	−18.8136	−1.17356	−0.586780	+	0.809746i	$0.699605\pi$
$258$	0.405824	0.0252655
$259$	−10.0039	−0.621613
$260$	14.4544	0.896423
$261$	14.8137	0.916947
$262$	−1.00000	−0.0617802
$263$	−8.30344	−0.512012	−0.256006	−	0.966675i	$-0.582407\pi$
$263$	−8.30344	−0.512012	−0.256006	+	0.966675i	$0.582407\pi$
$264$	0.968523	0.0596085
$265$	1.23253	0.0757136
$266$	2.78009	0.170459
$267$	2.30516	0.141073
$268$	5.64707	0.344950
$269$	12.7062	0.774711	0.387356	−	0.921930i	$-0.373389\pi$
$269$	12.7062	0.774711	0.387356	+	0.921930i	$0.373389\pi$
$270$	−5.66595	−0.344819
$271$	14.1750	0.861067	0.430534	−	0.902575i	$-0.358325\pi$
$271$	14.1750	0.861067	0.430534	+	0.902575i	$0.358325\pi$
$272$	−6.71263	−0.407013
$273$	−5.65258	−0.342110
$274$	6.33054	0.382442
$275$	−8.62829	−0.520306
$276$	0.339838	0.0204558
$277$	−10.2651	−0.616769	−0.308385	−	0.951262i	$-0.599788\pi$
$277$	−10.2651	−0.616769	−0.308385	+	0.951262i	$0.599788\pi$
$278$	2.81575	0.168877
$279$	−26.3911	−1.57999
$280$	9.23755	0.552049
$281$	14.4965	0.864791	0.432396	−	0.901684i	$-0.357668\pi$
$281$	14.4965	0.864791	0.432396	+	0.901684i	$0.357668\pi$
$282$	3.42264	0.203815
$283$	−26.4321	−1.57123	−0.785613	−	0.618719i	$-0.787652\pi$
$283$	−26.4321	−1.57123	−0.785613	+	0.618719i	$0.787652\pi$
$284$	−15.4654	−0.917700
$285$	−0.821024	−0.0486333
$286$	14.5394	0.859735
$287$	23.1658	1.36743
$288$	−2.88451	−0.169971
$289$	28.0593	1.65055
$290$	14.5507	0.854445
$291$	3.30898	0.193976
$292$	−9.82625	−0.575038
$293$	30.7222	1.79481	0.897406	−	0.441206i	$-0.145449\pi$
$293$	30.7222	1.79481	0.897406	+	0.441206i	$0.145449\pi$
$294$	−1.23360	−0.0719452
$295$	2.91456	0.169692
$296$	3.06834	0.178344
$297$	−5.69929	−0.330706
$298$	−20.0553	−1.16177
$299$	5.10163	0.295035
$300$	−1.02886	−0.0594015
$301$	3.89343	0.224414
$302$	4.46931	0.257180
$303$	6.13885	0.352668
$304$	−0.852694	−0.0489054
$305$	−29.2951	−1.67743
$306$	19.3626	1.10689
$307$	−17.9332	−1.02350	−0.511752	−	0.859133i	$-0.671003\pi$
$307$	−17.9332	−1.02350	−0.511752	+	0.859133i	$0.671003\pi$
$308$	9.29190	0.529455
$309$	0.210798	0.0119919
$310$	−25.9224	−1.47230
$311$	−7.75658	−0.439836	−0.219918	−	0.975518i	$-0.570579\pi$
$311$	−7.75658	−0.439836	−0.219918	+	0.975518i	$0.570579\pi$
$312$	1.73373	0.0981530
$313$	4.58307	0.259050	0.129525	−	0.991576i	$-0.458655\pi$
$313$	4.58307	0.259050	0.129525	+	0.991576i	$0.458655\pi$
$314$	−16.4381	−0.927657
$315$	−26.6458	−1.50132
$316$	4.13277	0.232487
$317$	−13.1677	−0.739570	−0.369785	−	0.929117i	$-0.620569\pi$
$317$	−13.1677	−0.739570	−0.369785	+	0.929117i	$0.620569\pi$
$318$	0.147835	0.00829019
$319$	14.6363	0.819474
$320$	−2.83329	−0.158386
$321$	−0.380706	−0.0212489
$322$	3.26036	0.181693
$323$	5.72382	0.318482
$324$	7.97393	0.442996
$325$	−15.4453	−0.856750
$326$	−5.17214	−0.286459
$327$	−3.44066	−0.190269
$328$	−7.10528	−0.392323
$329$	32.8364	1.81033
$330$	−2.74410	−0.151058
$331$	24.7531	1.36055	0.680276	−	0.732956i	$-0.261860\pi$
$331$	24.7531	1.36055	0.680276	+	0.732956i	$0.261860\pi$
$332$	16.5885	0.910413
$333$	−8.85067	−0.485014
$334$	5.71922	0.312942
$335$	−15.9998	−0.874160
$336$	1.10800	0.0604461
$337$	30.8819	1.68224	0.841121	−	0.540847i	$-0.181896\pi$
$337$	30.8819	1.68224	0.841121	+	0.540847i	$0.181896\pi$
$338$	13.0266	0.708556
$339$	−0.468426	−0.0254414
$340$	19.0188	1.03144
$341$	−26.0750	−1.41204
$342$	2.45961	0.133000
$343$	10.9875	0.593270
$344$	−1.19417	−0.0643854
$345$	−0.962858	−0.0518385
$346$	−4.19883	−0.225730
$347$	−17.4806	−0.938408	−0.469204	−	0.883090i	$-0.655459\pi$
$347$	−17.4806	−0.938408	−0.469204	+	0.883090i	$0.655459\pi$
$348$	1.74528	0.0935566
$349$	−12.6657	−0.677979	−0.338989	−	0.940790i	$-0.610085\pi$
$349$	−12.6657	−0.677979	−0.338989	+	0.940790i	$0.610085\pi$
$350$	−9.87081	−0.527617
$351$	−10.2021	−0.544550
$352$	−2.84996	−0.151903
$353$	−2.43026	−0.129350	−0.0646749	−	0.997906i	$-0.520601\pi$
$353$	−2.43026	−0.129350	−0.0646749	+	0.997906i	$0.520601\pi$
$354$	0.349586	0.0185803
$355$	43.8178	2.32561
$356$	−6.78312	−0.359504
$357$	−7.43756	−0.393637
$358$	11.7403	0.620492
$359$	23.4962	1.24008	0.620042	−	0.784569i	$-0.287116\pi$
$359$	23.4962	1.24008	0.620042	+	0.784569i	$0.287116\pi$
$360$	8.17265	0.430736
$361$	−18.2729	−0.961732
$362$	−23.7017	−1.24574
$363$	0.977967	0.0513299
$364$	16.6332	0.871815
$365$	27.8406	1.45724
$366$	−3.51379	−0.183669
$367$	−30.0524	−1.56872	−0.784360	−	0.620306i	$-0.787009\pi$
$367$	−30.0524	−1.56872	−0.784360	+	0.620306i	$0.787009\pi$
$368$	−1.00000	−0.0521286
$369$	20.4952	1.06694
$370$	−8.69350	−0.451954
$371$	1.41831	0.0736352
$372$	−3.10926	−0.161208
$373$	31.4474	1.62829	0.814143	−	0.580665i	$-0.197207\pi$
$373$	31.4474	1.62829	0.814143	+	0.580665i	$0.197207\pi$
$374$	19.1307	0.989225
$375$	−1.89922	−0.0980754
$376$	−10.0714	−0.519393
$377$	26.2000	1.34937
$378$	−6.52001	−0.335353
$379$	−0.189882	−0.00975357	−0.00487678	−	0.999988i	$-0.501552\pi$
$379$	−0.189882	−0.00975357	−0.00487678	+	0.999988i	$0.501552\pi$
$380$	2.41593	0.123934
$381$	−4.27091	−0.218805
$382$	−14.0796	−0.720374
$383$	30.1459	1.54039	0.770193	−	0.637811i	$-0.220160\pi$
$383$	30.1459	1.54039	0.770193	+	0.637811i	$0.220160\pi$
$384$	−0.339838	−0.0173423
$385$	−26.3266	−1.34173
$386$	−16.0160	−0.815192
$387$	3.44460	0.175099
$388$	−9.73695	−0.494319
$389$	20.2627	1.02736	0.513680	−	0.857982i	$-0.328282\pi$
$389$	20.2627	1.02736	0.513680	+	0.857982i	$0.328282\pi$
$390$	−4.91215	−0.248736
$391$	6.71263	0.339472
$392$	3.62998	0.183341
$393$	0.339838	0.0171426
$394$	−21.7646	−1.09648
$395$	−11.7093	−0.589160
$396$	8.22073	0.413107
$397$	−21.2759	−1.06781	−0.533905	−	0.845545i	$-0.679276\pi$
$397$	−21.2759	−1.06781	−0.533905	+	0.845545i	$0.679276\pi$
$398$	6.24870	0.313219
$399$	−0.944781	−0.0472982
$400$	3.02752	0.151376
$401$	−9.83257	−0.491015	−0.245508	−	0.969395i	$-0.578955\pi$
$401$	−9.83257	−0.491015	−0.245508	+	0.969395i	$0.578955\pi$
$402$	−1.91909	−0.0957154
$403$	−46.6761	−2.32510
$404$	−18.0641	−0.898721
$405$	−22.5924	−1.12263
$406$	16.7440	0.830990
$407$	−8.74465	−0.433456
$408$	2.28120	0.112936
$409$	16.5953	0.820585	0.410293	−	0.911954i	$-0.365427\pi$
$409$	16.5953	0.820585	0.410293	+	0.911954i	$0.365427\pi$
$410$	20.1313	0.994213
$411$	−2.15136	−0.106119
$412$	−0.620291	−0.0305596
$413$	3.35389	0.165034
$414$	2.88451	0.141766
$415$	−47.0000	−2.30714
$416$	−5.10163	−0.250128
$417$	−0.956898	−0.0468595
$418$	2.43014	0.118862
$419$	−7.75782	−0.378994	−0.189497	−	0.981881i	$-0.560686\pi$
$419$	−7.75782	−0.378994	−0.189497	+	0.981881i	$0.560686\pi$
$420$	−3.13927	−0.153181
$421$	−17.8653	−0.870700	−0.435350	−	0.900261i	$-0.643375\pi$
$421$	−17.8653	−0.870700	−0.435350	+	0.900261i	$0.643375\pi$
$422$	−0.830866	−0.0404459
$423$	29.0511	1.41251
$424$	−0.435017	−0.0211263
$425$	−20.3226	−0.985790
$426$	5.25571	0.254640
$427$	−33.7109	−1.63138
$428$	1.12026	0.0541497
$429$	−4.94105	−0.238556
$430$	3.38343	0.163163
$431$	−18.1598	−0.874727	−0.437364	−	0.899285i	$-0.644088\pi$
$431$	−18.1598	−0.874727	−0.437364	+	0.899285i	$0.644088\pi$
$432$	1.99978	0.0962144
$433$	−17.0880	−0.821198	−0.410599	−	0.911816i	$-0.634680\pi$
$433$	−17.0880	−0.821198	−0.410599	+	0.911816i	$0.634680\pi$
$434$	−29.8299	−1.43188
$435$	−4.94487	−0.237088
$436$	10.1244	0.484871
$437$	0.852694	0.0407899
$438$	3.33933	0.159559
$439$	1.51144	0.0721370	0.0360685	−	0.999349i	$-0.488517\pi$
$439$	1.51144	0.0721370	0.0360685	+	0.999349i	$0.488517\pi$
$440$	8.07475	0.384948
$441$	−10.4707	−0.498605
$442$	34.2453	1.62888
$443$	−32.5538	−1.54668	−0.773339	−	0.633993i	$-0.781415\pi$
$443$	−32.5538	−1.54668	−0.773339	+	0.633993i	$0.781415\pi$
$444$	−1.04274	−0.0494862
$445$	19.2185	0.911045
$446$	−17.3081	−0.819561
$447$	6.81553	0.322364
$448$	−3.26036	−0.154038
$449$	5.71486	0.269701	0.134850	−	0.990866i	$-0.456945\pi$
$449$	5.71486	0.269701	0.134850	+	0.990866i	$0.456945\pi$
$450$	−8.73290	−0.411673
$451$	20.2497	0.953523
$452$	1.37838	0.0648336
$453$	−1.51884	−0.0713614
$454$	1.23585	0.0580013
$455$	−47.1266	−2.20933
$456$	0.289778	0.0135701
$457$	9.53035	0.445811	0.222905	−	0.974840i	$-0.428446\pi$
$457$	9.53035	0.445811	0.222905	+	0.974840i	$0.428446\pi$
$458$	6.22950	0.291086
$459$	−13.4238	−0.626568
$460$	2.83329	0.132103
$461$	12.5940	0.586563	0.293282	−	0.956026i	$-0.405253\pi$
$461$	12.5940	0.586563	0.293282	+	0.956026i	$0.405253\pi$
$462$	−3.15774	−0.146911
$463$	14.0189	0.651513	0.325757	−	0.945454i	$-0.394381\pi$
$463$	14.0189	0.651513	0.325757	+	0.945454i	$0.394381\pi$
$464$	−5.13561	−0.238415
$465$	8.80943	0.408527
$466$	5.71750	0.264858
$467$	15.1757	0.702247	0.351124	−	0.936329i	$-0.385800\pi$
$467$	15.1757	0.702247	0.351124	+	0.936329i	$0.385800\pi$
$468$	14.7157	0.680234
$469$	−18.4115	−0.850164
$470$	28.5352	1.31623
$471$	5.58630	0.257403
$472$	−1.02869	−0.0473491
$473$	3.40334	0.156486
$474$	−1.40447	−0.0645095
$475$	−2.58155	−0.118449
$476$	21.8856	1.00313
$477$	1.25481	0.0574538
$478$	−17.1158	−0.782858
$479$	14.5786	0.666114	0.333057	−	0.942907i	$-0.391920\pi$
$479$	14.5786	0.666114	0.333057	+	0.942907i	$0.391920\pi$
$480$	0.962858	0.0439483
$481$	−15.6536	−0.713741
$482$	−4.71052	−0.214558
$483$	−1.10800	−0.0504155
$484$	−2.87774	−0.130807
$485$	27.5876	1.25269
$486$	−8.70918	−0.395057
$487$	4.26500	0.193265	0.0966327	−	0.995320i	$-0.469193\pi$
$487$	4.26500	0.193265	0.0966327	+	0.995320i	$0.469193\pi$
$488$	10.3396	0.468052
$489$	1.75769	0.0794855
$490$	−10.2848	−0.464618
$491$	1.59962	0.0721901	0.0360950	−	0.999348i	$-0.488508\pi$
$491$	1.59962	0.0721901	0.0360950	+	0.999348i	$0.488508\pi$
$492$	2.41464	0.108860
$493$	34.4735	1.55261
$494$	4.35013	0.195722
$495$	−23.2917	−1.04688
$496$	9.14925	0.410813
$497$	50.4227	2.26177
$498$	−5.63740	−0.252618
$499$	−8.79091	−0.393535	−0.196768	−	0.980450i	$-0.563044\pi$
$499$	−8.79091	−0.393535	−0.196768	+	0.980450i	$0.563044\pi$
$500$	5.58861	0.249930
$501$	−1.94361	−0.0868339
$502$	1.87519	0.0836939
$503$	−16.0430	−0.715322	−0.357661	−	0.933852i	$-0.616426\pi$
$503$	−16.0430	−0.715322	−0.357661	+	0.933852i	$0.616426\pi$
$504$	9.40455	0.418912
$505$	51.1807	2.27751
$506$	2.84996	0.126696
$507$	−4.42695	−0.196608
$508$	12.5675	0.557593
$509$	−7.80873	−0.346116	−0.173058	−	0.984912i	$-0.555365\pi$
$509$	−7.80873	−0.346116	−0.173058	+	0.984912i	$0.555365\pi$
$510$	−6.46331	−0.286200
$511$	32.0372	1.41724
$512$	1.00000	0.0441942
$513$	−1.70520	−0.0752864
$514$	−18.8136	−0.829833
$515$	1.75746	0.0774431
$516$	0.405824	0.0178654
$517$	28.7031	1.26236
$518$	−10.0039	−0.439547
$519$	1.42692	0.0626349
$520$	14.4544	0.633867
$521$	14.0184	0.614156	0.307078	−	0.951684i	$-0.400649\pi$
$521$	14.0184	0.614156	0.307078	+	0.951684i	$0.400649\pi$
$522$	14.8137	0.648380
$523$	−33.2747	−1.45500	−0.727501	−	0.686106i	$-0.759318\pi$
$523$	−33.2747	−1.45500	−0.727501	+	0.686106i	$0.759318\pi$
$524$	−1.00000	−0.0436852
$525$	3.35447	0.146401
$526$	−8.30344	−0.362047
$527$	−61.4155	−2.67530
$528$	0.968523	0.0421496
$529$	1.00000	0.0434783
$530$	1.23253	0.0535376
$531$	2.96726	0.128768
$532$	2.78009	0.120532
$533$	36.2485	1.57010
$534$	2.30516	0.0997540
$535$	−3.17401	−0.137224
$536$	5.64707	0.243916
$537$	−3.98978	−0.172172
$538$	12.7062	0.547804
$539$	−10.3453	−0.445603
$540$	−5.66595	−0.243824
$541$	38.2456	1.64431	0.822153	−	0.569266i	$-0.192773\pi$
$541$	38.2456	1.64431	0.822153	+	0.569266i	$0.192773\pi$
$542$	14.1750	0.608866
$543$	8.05475	0.345662
$544$	−6.71263	−0.287801
$545$	−28.6853	−1.22874
$546$	−5.65258	−0.241908
$547$	−10.4113	−0.445156	−0.222578	−	0.974915i	$-0.571447\pi$
$547$	−10.4113	−0.445156	−0.222578	+	0.974915i	$0.571447\pi$
$548$	6.33054	0.270427
$549$	−29.8247	−1.27289
$550$	−8.62829	−0.367912
$551$	4.37911	0.186556
$552$	0.339838	0.0144645
$553$	−13.4743	−0.572987
$554$	−10.2651	−0.436122
$555$	2.95438	0.125406
$556$	2.81575	0.119414
$557$	−20.5914	−0.872487	−0.436243	−	0.899829i	$-0.643691\pi$
$557$	−20.5914	−0.872487	−0.436243	+	0.899829i	$0.643691\pi$
$558$	−26.3911	−1.11722
$559$	6.09222	0.257673
$560$	9.23755	0.390358
$561$	−6.50133	−0.274487
$562$	14.4965	0.611500
$563$	38.0492	1.60358	0.801790	−	0.597605i	$-0.203881\pi$
$563$	38.0492	1.60358	0.801790	+	0.597605i	$0.203881\pi$
$564$	3.42264	0.144119
$565$	−3.90535	−0.164299
$566$	−26.4321	−1.11102
$567$	−25.9979	−1.09181
$568$	−15.4654	−0.648912
$569$	23.7333	0.994951	0.497476	−	0.867478i	$-0.334260\pi$
$569$	23.7333	0.994951	0.497476	+	0.867478i	$0.334260\pi$
$570$	−0.821024	−0.0343889
$571$	−10.2418	−0.428605	−0.214303	−	0.976767i	$-0.568748\pi$
$571$	−10.2418	−0.428605	−0.214303	+	0.976767i	$0.568748\pi$
$572$	14.5394	0.607924
$573$	4.78478	0.199887
$574$	23.1658	0.966921
$575$	−3.02752	−0.126256
$576$	−2.88451	−0.120188
$577$	−11.2801	−0.469598	−0.234799	−	0.972044i	$-0.575443\pi$
$577$	−11.2801	−0.469598	−0.234799	+	0.972044i	$0.575443\pi$
$578$	28.0593	1.16711
$579$	5.44284	0.226197
$580$	14.5507	0.604184
$581$	−54.0846	−2.24381
$582$	3.30898	0.137162
$583$	1.23978	0.0513464
$584$	−9.82625	−0.406613
$585$	−41.6938	−1.72383
$586$	30.7222	1.26912
$587$	−34.5003	−1.42398	−0.711990	−	0.702189i	$-0.752206\pi$
$587$	−34.5003	−1.42398	−0.711990	+	0.702189i	$0.752206\pi$
$588$	−1.23360	−0.0508729
$589$	−7.80151	−0.321456
$590$	2.91456	0.119991
$591$	7.39642	0.304248
$592$	3.06834	0.126108
$593$	−43.3766	−1.78126	−0.890632	−	0.454724i	$-0.849738\pi$
$593$	−43.3766	−1.78126	−0.890632	+	0.454724i	$0.849738\pi$
$594$	−5.69929	−0.233845
$595$	−62.0082	−2.54209
$596$	−20.0553	−0.821495
$597$	−2.12354	−0.0869108
$598$	5.10163	0.208621
$599$	19.5834	0.800157	0.400079	−	0.916481i	$-0.368983\pi$
$599$	19.5834	0.800157	0.400079	+	0.916481i	$0.368983\pi$
$600$	−1.02886	−0.0420032
$601$	−5.79174	−0.236250	−0.118125	−	0.992999i	$-0.537688\pi$
$601$	−5.79174	−0.236250	−0.118125	+	0.992999i	$0.537688\pi$
$602$	3.89343	0.158684
$603$	−16.2890	−0.663340
$604$	4.46931	0.181854
$605$	8.15348	0.331486
$606$	6.13885	0.249374
$607$	21.8779	0.887995	0.443997	−	0.896028i	$-0.353560\pi$
$607$	21.8779	0.887995	0.443997	+	0.896028i	$0.353560\pi$
$608$	−0.852694	−0.0345813
$609$	−5.69024	−0.230580
$610$	−29.2951	−1.18612
$611$	51.3806	2.07864
$612$	19.3626	0.782688
$613$	−6.46980	−0.261313	−0.130656	−	0.991428i	$-0.541708\pi$
$613$	−6.46980	−0.261313	−0.130656	+	0.991428i	$0.541708\pi$
$614$	−17.9332	−0.723727
$615$	−6.84137	−0.275871
$616$	9.29190	0.374381
$617$	30.1998	1.21580	0.607899	−	0.794014i	$-0.292012\pi$
$617$	30.1998	1.21580	0.607899	+	0.794014i	$0.292012\pi$
$618$	0.210798	0.00847956
$619$	−2.06753	−0.0831009	−0.0415504	−	0.999136i	$-0.513230\pi$
$619$	−2.06753	−0.0831009	−0.0415504	+	0.999136i	$0.513230\pi$
$620$	−25.9224	−1.04107
$621$	−1.99978	−0.0802484
$622$	−7.75658	−0.311011
$623$	22.1154	0.886036
$624$	1.73373	0.0694047
$625$	−30.9717	−1.23887
$626$	4.58307	0.183176
$627$	−0.825854	−0.0329814
$628$	−16.4381	−0.655953
$629$	−20.5966	−0.821242
$630$	−26.6458	−1.06159
$631$	3.55412	0.141487	0.0707437	−	0.997495i	$-0.477463\pi$
$631$	3.55412	0.141487	0.0707437	+	0.997495i	$0.477463\pi$
$632$	4.13277	0.164393
$633$	0.282360	0.0112228
$634$	−13.1677	−0.522955
$635$	−35.6073	−1.41303
$636$	0.147835	0.00586205
$637$	−18.5188	−0.733742
$638$	14.6363	0.579456
$639$	44.6100	1.76474
$640$	−2.83329	−0.111996
$641$	14.0597	0.555325	0.277663	−	0.960679i	$-0.410440\pi$
$641$	14.0597	0.555325	0.277663	+	0.960679i	$0.410440\pi$
$642$	−0.380706	−0.0150253
$643$	−27.4603	−1.08293	−0.541465	−	0.840723i	$-0.682130\pi$
$643$	−27.4603	−1.08293	−0.541465	+	0.840723i	$0.682130\pi$
$644$	3.26036	0.128476
$645$	−1.14982	−0.0452740
$646$	5.72382	0.225201
$647$	17.9358	0.705131	0.352565	−	0.935787i	$-0.385309\pi$
$647$	17.9358	0.705131	0.352565	+	0.935787i	$0.385309\pi$
$648$	7.97393	0.313246
$649$	2.93171	0.115080
$650$	−15.4453	−0.605814
$651$	10.1373	0.397313
$652$	−5.17214	−0.202557
$653$	−37.6166	−1.47205	−0.736026	−	0.676953i	$-0.763300\pi$
$653$	−37.6166	−1.47205	−0.736026	+	0.676953i	$0.763300\pi$
$654$	−3.44066	−0.134540
$655$	2.83329	0.110706
$656$	−7.10528	−0.277414
$657$	28.3439	1.10580
$658$	32.8364	1.28010
$659$	−38.1419	−1.48580	−0.742898	−	0.669404i	$-0.766549\pi$
$659$	−38.1419	−1.48580	−0.742898	+	0.669404i	$0.766549\pi$
$660$	−2.74410	−0.106814
$661$	−36.3229	−1.41280	−0.706398	−	0.707815i	$-0.749681\pi$
$661$	−36.3229	−1.41280	−0.706398	+	0.707815i	$0.749681\pi$
$662$	24.7531	0.962055
$663$	−11.6379	−0.451977
$664$	16.5885	0.643759
$665$	−7.87681	−0.305449
$666$	−8.85067	−0.342957
$667$	5.13561	0.198852
$668$	5.71922	0.221283
$669$	5.88194	0.227409
$670$	−15.9998	−0.618125
$671$	−29.4674	−1.13758
$672$	1.10800	0.0427418
$673$	13.7690	0.530755	0.265377	−	0.964145i	$-0.414503\pi$
$673$	13.7690	0.530755	0.265377	+	0.964145i	$0.414503\pi$
$674$	30.8819	1.18952
$675$	6.05437	0.233033
$676$	13.0266	0.501025
$677$	21.6052	0.830354	0.415177	−	0.909741i	$-0.363720\pi$
$677$	21.6052	0.830354	0.415177	+	0.909741i	$0.363720\pi$
$678$	−0.468426	−0.0179898
$679$	31.7460	1.21830
$680$	19.0188	0.729338
$681$	−0.419989	−0.0160940
$682$	−26.0750	−0.998462
$683$	−24.6924	−0.944827	−0.472413	−	0.881377i	$-0.656617\pi$
$683$	−24.6924	−0.944827	−0.472413	+	0.881377i	$0.656617\pi$
$684$	2.45961	0.0940454
$685$	−17.9362	−0.685308
$686$	10.9875	0.419505
$687$	−2.11702	−0.0807694
$688$	−1.19417	−0.0455273
$689$	2.21930	0.0845485
$690$	−0.962858	−0.0366554
$691$	10.9287	0.415747	0.207874	−	0.978156i	$-0.433346\pi$
$691$	10.9287	0.415747	0.207874	+	0.978156i	$0.433346\pi$
$692$	−4.19883	−0.159615
$693$	−26.8026	−1.01815
$694$	−17.4806	−0.663554
$695$	−7.97783	−0.302616
$696$	1.74528	0.0661545
$697$	47.6951	1.80658
$698$	−12.6657	−0.479403
$699$	−1.94302	−0.0734918
$700$	−9.87081	−0.373081
$701$	−3.37725	−0.127557	−0.0637785	−	0.997964i	$-0.520315\pi$
$701$	−3.37725	−0.127557	−0.0637785	+	0.997964i	$0.520315\pi$
$702$	−10.2021	−0.385055
$703$	−2.61636	−0.0986779
$704$	−2.84996	−0.107412
$705$	−9.69733	−0.365223
$706$	−2.43026	−0.0914641
$707$	58.8954	2.21499
$708$	0.349586	0.0131383
$709$	4.84902	0.182109	0.0910543	−	0.995846i	$-0.470976\pi$
$709$	4.84902	0.182109	0.0910543	+	0.995846i	$0.470976\pi$
$710$	43.8178	1.64445
$711$	−11.9210	−0.447073
$712$	−6.78312	−0.254208
$713$	−9.14925	−0.342642
$714$	−7.43756	−0.278344
$715$	−41.1944	−1.54058
$716$	11.7403	0.438754
$717$	5.81659	0.217225
$718$	23.4962	0.876872
$719$	36.1203	1.34706	0.673530	−	0.739160i	$-0.264777\pi$
$719$	36.1203	1.34706	0.673530	+	0.739160i	$0.264777\pi$
$720$	8.17265	0.304577
$721$	2.02238	0.0753172
$722$	−18.2729	−0.680047
$723$	1.60081	0.0595348
$724$	−23.7017	−0.880868
$725$	−15.5482	−0.577444
$726$	0.977967	0.0362957
$727$	−15.3296	−0.568543	−0.284272	−	0.958744i	$-0.591752\pi$
$727$	−15.3296	−0.568543	−0.284272	+	0.958744i	$0.591752\pi$
$728$	16.6332	0.616467
$729$	−20.9621	−0.776373
$730$	27.8406	1.03043
$731$	8.01602	0.296483
$732$	−3.51379	−0.129873
$733$	−28.6382	−1.05778	−0.528888	−	0.848692i	$-0.677391\pi$
$733$	−28.6382	−1.05778	−0.528888	+	0.848692i	$0.677391\pi$
$734$	−30.0524	−1.10925
$735$	3.49515	0.128921
$736$	−1.00000	−0.0368605
$737$	−16.0939	−0.592826
$738$	20.4952	0.754440
$739$	35.3141	1.29905	0.649524	−	0.760341i	$-0.274968\pi$
$739$	35.3141	1.29905	0.649524	+	0.760341i	$0.274968\pi$
$740$	−8.69350	−0.319579
$741$	−1.47834	−0.0543082
$742$	1.41831	0.0520679
$743$	13.6257	0.499878	0.249939	−	0.968262i	$-0.419589\pi$
$743$	13.6257	0.499878	0.249939	+	0.968262i	$0.419589\pi$
$744$	−3.10926	−0.113991
$745$	56.8223	2.08181
$746$	31.4474	1.15137
$747$	−47.8497	−1.75073
$748$	19.1307	0.699487
$749$	−3.65245	−0.133458
$750$	−1.89922	−0.0693498
$751$	15.4313	0.563098	0.281549	−	0.959547i	$-0.409152\pi$
$751$	15.4313	0.563098	0.281549	+	0.959547i	$0.409152\pi$
$752$	−10.0714	−0.367266
$753$	−0.637261	−0.0232231
$754$	26.2000	0.954148
$755$	−12.6628	−0.460848
$756$	−6.52001	−0.237130
$757$	−15.7508	−0.572473	−0.286237	−	0.958159i	$-0.592404\pi$
$757$	−15.7508	−0.572473	−0.286237	+	0.958159i	$0.592404\pi$
$758$	−0.189882	−0.00689681
$759$	−0.968523	−0.0351552
$760$	2.41593	0.0876349
$761$	−38.2429	−1.38631	−0.693153	−	0.720791i	$-0.743779\pi$
$761$	−38.2429	−1.38631	−0.693153	+	0.720791i	$0.743779\pi$
$762$	−4.27091	−0.154719
$763$	−33.0092	−1.19501
$764$	−14.0796	−0.509382
$765$	−54.8599	−1.98346
$766$	30.1459	1.08922
$767$	5.24798	0.189493
$768$	−0.339838	−0.0122628
$769$	−45.3773	−1.63635	−0.818175	−	0.574970i	$-0.805014\pi$
$769$	−45.3773	−1.63635	−0.818175	+	0.574970i	$0.805014\pi$
$770$	−26.3266	−0.948745
$771$	6.39358	0.230259
$772$	−16.0160	−0.576428
$773$	42.0014	1.51069	0.755343	−	0.655329i	$-0.227470\pi$
$773$	42.0014	1.51069	0.755343	+	0.655329i	$0.227470\pi$
$774$	3.44460	0.123813
$775$	27.6995	0.994995
$776$	−9.73695	−0.349536
$777$	3.39971	0.121964
$778$	20.2627	0.726454
$779$	6.05863	0.217073
$780$	−4.91215	−0.175883
$781$	44.0756	1.57715
$782$	6.71263	0.240043
$783$	−10.2701	−0.367023
$784$	3.62998	0.129642
$785$	46.5739	1.66230
$786$	0.339838	0.0121216
$787$	1.52247	0.0542703	0.0271352	−	0.999632i	$-0.491362\pi$
$787$	1.52247	0.0542703	0.0271352	+	0.999632i	$0.491362\pi$
$788$	−21.7646	−0.775330
$789$	2.82182	0.100460
$790$	−11.7093	−0.416599
$791$	−4.49402	−0.159789
$792$	8.22073	0.292111
$793$	−52.7488	−1.87317
$794$	−21.2759	−0.755055
$795$	−0.418860	−0.0148554
$796$	6.24870	0.221479
$797$	−1.77008	−0.0626996	−0.0313498	−	0.999508i	$-0.509981\pi$
$797$	−1.77008	−0.0626996	−0.0313498	+	0.999508i	$0.509981\pi$
$798$	−0.944781	−0.0334449
$799$	67.6055	2.39171
$800$	3.02752	0.107039
$801$	19.5660	0.691329
$802$	−9.83257	−0.347200
$803$	28.0044	0.988253
$804$	−1.91909	−0.0676810
$805$	−9.23755	−0.325581
$806$	−46.6761	−1.64409
$807$	−4.31805	−0.152003
$808$	−18.0641	−0.635491
$809$	26.0677	0.916490	0.458245	−	0.888826i	$-0.348478\pi$
$809$	26.0677	0.916490	0.458245	+	0.888826i	$0.348478\pi$
$810$	−22.5924	−0.793817
$811$	−2.90730	−0.102089	−0.0510446	−	0.998696i	$-0.516255\pi$
$811$	−2.90730	−0.102089	−0.0510446	+	0.998696i	$0.516255\pi$
$812$	16.7440	0.587598
$813$	−4.81719	−0.168946
$814$	−8.74465	−0.306500
$815$	14.6542	0.513313
$816$	2.28120	0.0798581
$817$	1.01826	0.0356245
$818$	16.5953	0.580241
$819$	−47.9786	−1.67651
$820$	20.1313	0.703015
$821$	7.24874	0.252983	0.126491	−	0.991968i	$-0.459628\pi$
$821$	7.24874	0.252983	0.126491	+	0.991968i	$0.459628\pi$
$822$	−2.15136	−0.0750372
$823$	48.5172	1.69120	0.845602	−	0.533813i	$-0.179241\pi$
$823$	48.5172	1.69120	0.845602	+	0.533813i	$0.179241\pi$
$824$	−0.620291	−0.0216089
$825$	2.93222	0.102087
$826$	3.35389	0.116697
$827$	−42.1490	−1.46567	−0.732833	−	0.680409i	$-0.761802\pi$
$827$	−42.1490	−1.46567	−0.732833	+	0.680409i	$0.761802\pi$
$828$	2.88451	0.100244
$829$	15.3620	0.533545	0.266772	−	0.963760i	$-0.414043\pi$
$829$	15.3620	0.533545	0.266772	+	0.963760i	$0.414043\pi$
$830$	−47.0000	−1.63139
$831$	3.48847	0.121014
$832$	−5.10163	−0.176867
$833$	−24.3667	−0.844255
$834$	−0.956898	−0.0331347
$835$	−16.2042	−0.560769
$836$	2.43014	0.0840482
$837$	18.2965	0.632419
$838$	−7.75782	−0.267989
$839$	−0.875609	−0.0302294	−0.0151147	−	0.999886i	$-0.504811\pi$
$839$	−0.875609	−0.0302294	−0.0151147	+	0.999886i	$0.504811\pi$
$840$	−3.13927	−0.108315
$841$	−2.62546	−0.0905331
$842$	−17.8653	−0.615678
$843$	−4.92647	−0.169677
$844$	−0.830866	−0.0285996
$845$	−36.9082	−1.26968
$846$	29.0511	0.998796
$847$	9.38250	0.322386
$848$	−0.435017	−0.0149385
$849$	8.98263	0.308283
$850$	−20.3226	−0.697059
$851$	−3.06834	−0.105181
$852$	5.25571	0.180058
$853$	−33.3255	−1.14104	−0.570522	−	0.821282i	$-0.693259\pi$
$853$	−33.3255	−1.14104	−0.570522	+	0.821282i	$0.693259\pi$
$854$	−33.7109	−1.15356
$855$	−6.96877	−0.238327
$856$	1.12026	0.0382896
$857$	−16.5450	−0.565166	−0.282583	−	0.959243i	$-0.591191\pi$
$857$	−16.5450	−0.565166	−0.282583	+	0.959243i	$0.591191\pi$
$858$	−4.94105	−0.168685
$859$	28.5919	0.975542	0.487771	−	0.872972i	$-0.337810\pi$
$859$	28.5919	0.975542	0.487771	+	0.872972i	$0.337810\pi$
$860$	3.38343	0.115374
$861$	−7.87261	−0.268298
$862$	−18.1598	−0.618525
$863$	42.6436	1.45161	0.725803	−	0.687903i	$-0.241469\pi$
$863$	42.6436	1.45161	0.725803	+	0.687903i	$0.241469\pi$
$864$	1.99978	0.0680339
$865$	11.8965	0.404493
$866$	−17.0880	−0.580675
$867$	−9.53563	−0.323847
$868$	−29.8299	−1.01249
$869$	−11.7782	−0.399549
$870$	−4.94487	−0.167647
$871$	−28.8093	−0.976164
$872$	10.1244	0.342856
$873$	28.0863	0.950578
$874$	0.852694	0.0288428
$875$	−18.2209	−0.615979
$876$	3.33933	0.112826
$877$	−45.0546	−1.52139	−0.760693	−	0.649112i	$-0.775141\pi$
$877$	−45.0546	−1.52139	−0.760693	+	0.649112i	$0.775141\pi$
$878$	1.51144	0.0510086
$879$	−10.4406	−0.352152
$880$	8.07475	0.272200
$881$	21.5304	0.725378	0.362689	−	0.931910i	$-0.381859\pi$
$881$	21.5304	0.725378	0.362689	+	0.931910i	$0.381859\pi$
$882$	−10.4707	−0.352567
$883$	58.0081	1.95213	0.976063	−	0.217486i	$-0.0697857\pi$
$883$	58.0081	1.95213	0.976063	+	0.217486i	$0.0697857\pi$
$884$	34.2453	1.15180
$885$	−0.990479	−0.0332946
$886$	−32.5538	−1.09367
$887$	−34.1053	−1.14514	−0.572572	−	0.819855i	$-0.694054\pi$
$887$	−34.1053	−1.14514	−0.572572	+	0.819855i	$0.694054\pi$
$888$	−1.04274	−0.0349920
$889$	−40.9746	−1.37424
$890$	19.2185	0.644206
$891$	−22.7254	−0.761328
$892$	−17.3081	−0.579517
$893$	8.58783	0.287381
$894$	6.81553	0.227946
$895$	−33.2635	−1.11188
$896$	−3.26036	−0.108921
$897$	−1.73373	−0.0578875
$898$	5.71486	0.190707
$899$	−46.9870	−1.56710
$900$	−8.73290	−0.291097
$901$	2.92011	0.0972828
$902$	20.2497	0.674242
$903$	−1.32314	−0.0440312
$904$	1.37838	0.0458443
$905$	67.1538	2.23227
$906$	−1.51884	−0.0504601
$907$	−47.4198	−1.57455	−0.787275	−	0.616602i	$-0.788509\pi$
$907$	−47.4198	−1.57455	−0.787275	+	0.616602i	$0.788509\pi$
$908$	1.23585	0.0410131
$909$	52.1060	1.72825
$910$	−47.1266	−1.56223
$911$	5.90323	0.195583	0.0977913	−	0.995207i	$-0.468822\pi$
$911$	5.90323	0.195583	0.0977913	+	0.995207i	$0.468822\pi$
$912$	0.289778	0.00959550
$913$	−47.2765	−1.56463
$914$	9.53035	0.315236
$915$	9.95557	0.329121
$916$	6.22950	0.205829
$917$	3.26036	0.107667
$918$	−13.4238	−0.443050
$919$	−2.67057	−0.0880938	−0.0440469	−	0.999029i	$-0.514025\pi$
$919$	−2.67057	−0.0880938	−0.0440469	+	0.999029i	$0.514025\pi$
$920$	2.83329	0.0934107
$921$	6.09440	0.200817
$922$	12.5940	0.414763
$923$	78.8985	2.59698
$924$	−3.15774	−0.103882
$925$	9.28946	0.305436
$926$	14.0189	0.460690
$927$	1.78924	0.0587662
$928$	−5.13561	−0.168585
$929$	34.3342	1.12647	0.563235	−	0.826297i	$-0.309557\pi$
$929$	34.3342	1.12647	0.563235	+	0.826297i	$0.309557\pi$
$930$	8.80943	0.288873
$931$	−3.09526	−0.101443
$932$	5.71750	0.187283
$933$	2.63598	0.0862982
$934$	15.1757	0.496564
$935$	−54.2028	−1.77262
$936$	14.7157	0.480998
$937$	55.5671	1.81530	0.907649	−	0.419731i	$-0.137876\pi$
$937$	55.5671	1.81530	0.907649	+	0.419731i	$0.137876\pi$
$938$	−18.4115	−0.601157
$939$	−1.55750	−0.0508271
$940$	28.5352	0.930715
$941$	3.77228	0.122973	0.0614864	−	0.998108i	$-0.480416\pi$
$941$	3.77228	0.122973	0.0614864	+	0.998108i	$0.480416\pi$
$942$	5.58630	0.182011
$943$	7.10528	0.231380
$944$	−1.02869	−0.0334809
$945$	18.4731	0.600929
$946$	3.40334	0.110652
$947$	−13.1880	−0.428552	−0.214276	−	0.976773i	$-0.568739\pi$
$947$	−13.1880	−0.428552	−0.214276	+	0.976773i	$0.568739\pi$
$948$	−1.40447	−0.0456151
$949$	50.1299	1.62729
$950$	−2.58155	−0.0837564
$951$	4.47488	0.145108
$952$	21.8856	0.709317
$953$	−55.7693	−1.80654	−0.903272	−	0.429068i	$-0.858842\pi$
$953$	−55.7693	−1.80654	−0.903272	+	0.429068i	$0.858842\pi$
$954$	1.25481	0.0406260
$955$	39.8915	1.29086
$956$	−17.1158	−0.553564
$957$	−4.97396	−0.160785
$958$	14.5786	0.471013
$959$	−20.6399	−0.666496
$960$	0.962858	0.0310761
$961$	52.7087	1.70028
$962$	−15.6536	−0.504691
$963$	−3.23139	−0.104130
$964$	−4.71052	−0.151716
$965$	45.3779	1.46077
$966$	−1.10800	−0.0356492
$967$	18.2872	0.588076	0.294038	−	0.955794i	$-0.405001\pi$
$967$	18.2872	0.588076	0.294038	+	0.955794i	$0.405001\pi$
$968$	−2.87774	−0.0924942
$969$	−1.94517	−0.0624879
$970$	27.5876	0.885783
$971$	−58.0733	−1.86366	−0.931830	−	0.362894i	$-0.881789\pi$
$971$	−58.0733	−1.86366	−0.931830	+	0.362894i	$0.881789\pi$
$972$	−8.70918	−0.279347
$973$	−9.18037	−0.294309
$974$	4.26500	0.136659
$975$	5.24889	0.168099
$976$	10.3396	0.330963
$977$	−32.9155	−1.05306	−0.526531	−	0.850156i	$-0.676507\pi$
$977$	−32.9155	−1.05306	−0.526531	+	0.850156i	$0.676507\pi$
$978$	1.75769	0.0562047
$979$	19.3316	0.617840
$980$	−10.2848	−0.328535
$981$	−29.2039	−0.932410
$982$	1.59962	0.0510461
$983$	4.19115	0.133677	0.0668385	−	0.997764i	$-0.478709\pi$
$983$	4.19115	0.133677	0.0668385	+	0.997764i	$0.478709\pi$
$984$	2.41464	0.0769760
$985$	61.6652	1.96482
$986$	34.4735	1.09786
$987$	−11.1591	−0.355197
$988$	4.35013	0.138396
$989$	1.19417	0.0379724
$990$	−23.2917	−0.740259
$991$	−29.0426	−0.922569	−0.461285	−	0.887252i	$-0.652611\pi$
$991$	−29.0426	−0.922569	−0.461285	+	0.887252i	$0.652611\pi$
$992$	9.14925	0.290489
$993$	−8.41203	−0.266948
$994$	50.4227	1.59931
$995$	−17.7043	−0.561266
$996$	−5.63740	−0.178628
$997$	11.5569	0.366010	0.183005	−	0.983112i	$-0.441417\pi$
$997$	11.5569	0.366010	0.183005	+	0.983112i	$0.441417\pi$
$998$	−8.79091	−0.278272
$999$	6.13601	0.194135

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.k.1.17	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.k.1.17	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.339838 q^{3} +1.00000 q^{4} -2.83329 q^{5} -0.339838 q^{6} -3.26036 q^{7} +1.00000 q^{8} -2.88451 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.339838 q^{3} +1.00000 q^{4} -2.83329 q^{5} -0.339838 q^{6} -3.26036 q^{7} +1.00000 q^{8} -2.88451 q^{9} -2.83329 q^{10} -2.84996 q^{11} -0.339838 q^{12} -5.10163 q^{13} -3.26036 q^{14} +0.962858 q^{15} +1.00000 q^{16} -6.71263 q^{17} -2.88451 q^{18} -0.852694 q^{19} -2.83329 q^{20} +1.10800 q^{21} -2.84996 q^{22} -1.00000 q^{23} -0.339838 q^{24} +3.02752 q^{25} -5.10163 q^{26} +1.99978 q^{27} -3.26036 q^{28} -5.13561 q^{29} +0.962858 q^{30} +9.14925 q^{31} +1.00000 q^{32} +0.968523 q^{33} -6.71263 q^{34} +9.23755 q^{35} -2.88451 q^{36} +3.06834 q^{37} -0.852694 q^{38} +1.73373 q^{39} -2.83329 q^{40} -7.10528 q^{41} +1.10800 q^{42} -1.19417 q^{43} -2.84996 q^{44} +8.17265 q^{45} -1.00000 q^{46} -10.0714 q^{47} -0.339838 q^{48} +3.62998 q^{49} +3.02752 q^{50} +2.28120 q^{51} -5.10163 q^{52} -0.435017 q^{53} +1.99978 q^{54} +8.07475 q^{55} -3.26036 q^{56} +0.289778 q^{57} -5.13561 q^{58} -1.02869 q^{59} +0.962858 q^{60} +10.3396 q^{61} +9.14925 q^{62} +9.40455 q^{63} +1.00000 q^{64} +14.4544 q^{65} +0.968523 q^{66} +5.64707 q^{67} -6.71263 q^{68} +0.339838 q^{69} +9.23755 q^{70} -15.4654 q^{71} -2.88451 q^{72} -9.82625 q^{73} +3.06834 q^{74} -1.02886 q^{75} -0.852694 q^{76} +9.29190 q^{77} +1.73373 q^{78} +4.13277 q^{79} -2.83329 q^{80} +7.97393 q^{81} -7.10528 q^{82} +16.5885 q^{83} +1.10800 q^{84} +19.0188 q^{85} -1.19417 q^{86} +1.74528 q^{87} -2.84996 q^{88} -6.78312 q^{89} +8.17265 q^{90} +16.6332 q^{91} -1.00000 q^{92} -3.10926 q^{93} -10.0714 q^{94} +2.41593 q^{95} -0.339838 q^{96} -9.73695 q^{97} +3.62998 q^{98} +8.22073 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9}+O(q^{10}) \) 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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