LMFDB - Embedded newform 8049.2.a.a.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8049,2,Mod(1,8049)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8049, 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("8049.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8049 = 3 \cdot 2683 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8049.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:	$64.2715885869$
Analytic rank:	$1$
Dimension:	$95$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	8049.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.41240 q^{2} +1.00000 q^{3} +3.81966 q^{4} +4.15952 q^{5} -2.41240 q^{6} -1.40645 q^{7} -4.38975 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.41240 q^{2} +1.00000 q^{3} +3.81966 q^{4} +4.15952 q^{5} -2.41240 q^{6} -1.40645 q^{7} -4.38975 q^{8} +1.00000 q^{9} -10.0344 q^{10} -6.19250 q^{11} +3.81966 q^{12} -2.39681 q^{13} +3.39291 q^{14} +4.15952 q^{15} +2.95050 q^{16} +7.00317 q^{17} -2.41240 q^{18} +1.45744 q^{19} +15.8879 q^{20} -1.40645 q^{21} +14.9388 q^{22} -6.62802 q^{23} -4.38975 q^{24} +12.3016 q^{25} +5.78207 q^{26} +1.00000 q^{27} -5.37215 q^{28} -5.96265 q^{29} -10.0344 q^{30} -2.07440 q^{31} +1.66173 q^{32} -6.19250 q^{33} -16.8944 q^{34} -5.85014 q^{35} +3.81966 q^{36} -0.940689 q^{37} -3.51593 q^{38} -2.39681 q^{39} -18.2592 q^{40} +1.63477 q^{41} +3.39291 q^{42} -1.77847 q^{43} -23.6533 q^{44} +4.15952 q^{45} +15.9894 q^{46} -8.09655 q^{47} +2.95050 q^{48} -5.02191 q^{49} -29.6763 q^{50} +7.00317 q^{51} -9.15502 q^{52} +11.6970 q^{53} -2.41240 q^{54} -25.7578 q^{55} +6.17395 q^{56} +1.45744 q^{57} +14.3843 q^{58} +9.24612 q^{59} +15.8879 q^{60} +0.330691 q^{61} +5.00428 q^{62} -1.40645 q^{63} -9.90974 q^{64} -9.96959 q^{65} +14.9388 q^{66} -10.7175 q^{67} +26.7498 q^{68} -6.62802 q^{69} +14.1129 q^{70} -12.8497 q^{71} -4.38975 q^{72} -1.16282 q^{73} +2.26932 q^{74} +12.3016 q^{75} +5.56694 q^{76} +8.70942 q^{77} +5.78207 q^{78} +16.4427 q^{79} +12.2726 q^{80} +1.00000 q^{81} -3.94372 q^{82} -6.28201 q^{83} -5.37215 q^{84} +29.1298 q^{85} +4.29037 q^{86} -5.96265 q^{87} +27.1835 q^{88} +4.23970 q^{89} -10.0344 q^{90} +3.37099 q^{91} -25.3168 q^{92} -2.07440 q^{93} +19.5321 q^{94} +6.06226 q^{95} +1.66173 q^{96} -3.19042 q^{97} +12.1148 q^{98} -6.19250 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 95 q - 9 q^{2} + 95 q^{3} + 65 q^{4} - 15 q^{5} - 9 q^{6} - 36 q^{7} - 27 q^{8} + 95 q^{9}+O(q^{10}) $ 95 * q - 9 * q^2 + 95 * q^3 + 65 * q^4 - 15 * q^5 - 9 * q^6 - 36 * q^7 - 27 * q^8 + 95 * q^9	\( 95 q - 9 q^{2} + 95 q^{3} + 65 q^{4} - 15 q^{5} - 9 q^{6} - 36 q^{7} - 27 q^{8} + 95 q^{9} - 36 q^{10} - 48 q^{11} + 65 q^{12} - 73 q^{13} - 17 q^{14} - 15 q^{15} + 13 q^{16} - 9 q^{17} - 9 q^{18} - 66 q^{19} - 35 q^{20} - 36 q^{21} - 37 q^{22} - 58 q^{23} - 27 q^{24} + 24 q^{25} - 25 q^{26} + 95 q^{27} - 75 q^{28} - 31 q^{29} - 36 q^{30} - 129 q^{31} - 53 q^{32} - 48 q^{33} - 61 q^{34} - 38 q^{35} + 65 q^{36} - 127 q^{37} + q^{38} - 73 q^{39} - 74 q^{40} - 31 q^{41} - 17 q^{42} - 62 q^{43} - 76 q^{44} - 15 q^{45} - 60 q^{46} - 75 q^{47} + 13 q^{48} + 5 q^{49} - 30 q^{50} - 9 q^{51} - 137 q^{52} - 28 q^{53} - 9 q^{54} - 117 q^{55} - 23 q^{56} - 66 q^{57} - 90 q^{58} - 60 q^{59} - 35 q^{60} - 96 q^{61} + 10 q^{62} - 36 q^{63} - 75 q^{64} - 28 q^{65} - 37 q^{66} - 116 q^{67} + 3 q^{68} - 58 q^{69} - 73 q^{70} - 144 q^{71} - 27 q^{72} - 121 q^{73} - 16 q^{74} + 24 q^{75} - 118 q^{76} - 3 q^{77} - 25 q^{78} - 135 q^{79} - 36 q^{80} + 95 q^{81} - 102 q^{82} - 21 q^{83} - 75 q^{84} - 129 q^{85} - 46 q^{86} - 31 q^{87} - 77 q^{88} - 63 q^{89} - 36 q^{90} - 123 q^{91} - 42 q^{92} - 129 q^{93} - 44 q^{94} - 80 q^{95} - 53 q^{96} - 144 q^{97} + 10 q^{98} - 48 q^{99}+O(q^{100}) \) 95 * q - 9 * q^2 + 95 * q^3 + 65 * q^4 - 15 * q^5 - 9 * q^6 - 36 * q^7 - 27 * q^8 + 95 * q^9 - 36 * q^10 - 48 * q^11 + 65 * q^12 - 73 * q^13 - 17 * q^14 - 15 * q^15 + 13 * q^16 - 9 * q^17 - 9 * q^18 - 66 * q^19 - 35 * q^20 - 36 * q^21 - 37 * q^22 - 58 * q^23 - 27 * q^24 + 24 * q^25 - 25 * q^26 + 95 * q^27 - 75 * q^28 - 31 * q^29 - 36 * q^30 - 129 * q^31 - 53 * q^32 - 48 * q^33 - 61 * q^34 - 38 * q^35 + 65 * q^36 - 127 * q^37 + q^38 - 73 * q^39 - 74 * q^40 - 31 * q^41 - 17 * q^42 - 62 * q^43 - 76 * q^44 - 15 * q^45 - 60 * q^46 - 75 * q^47 + 13 * q^48 + 5 * q^49 - 30 * q^50 - 9 * q^51 - 137 * q^52 - 28 * q^53 - 9 * q^54 - 117 * q^55 - 23 * q^56 - 66 * q^57 - 90 * q^58 - 60 * q^59 - 35 * q^60 - 96 * q^61 + 10 * q^62 - 36 * q^63 - 75 * q^64 - 28 * q^65 - 37 * q^66 - 116 * q^67 + 3 * q^68 - 58 * q^69 - 73 * q^70 - 144 * q^71 - 27 * q^72 - 121 * q^73 - 16 * q^74 + 24 * q^75 - 118 * q^76 - 3 * q^77 - 25 * q^78 - 135 * q^79 - 36 * q^80 + 95 * q^81 - 102 * q^82 - 21 * q^83 - 75 * q^84 - 129 * q^85 - 46 * q^86 - 31 * q^87 - 77 * q^88 - 63 * q^89 - 36 * q^90 - 123 * q^91 - 42 * q^92 - 129 * q^93 - 44 * q^94 - 80 * q^95 - 53 * q^96 - 144 * q^97 + 10 * q^98 - 48 * 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 $

$2$	−2.41240	−1.70582	−0.852911	−	0.522056i	$-0.825165\pi$
$2$	−2.41240	−1.70582	−0.852911	+	0.522056i	$0.825165\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.81966	1.90983
$5$	4.15952	1.86019	0.930096	−	0.367316i	$-0.119723\pi$
$5$	4.15952	1.86019	0.930096	+	0.367316i	$0.119723\pi$
$6$	−2.41240	−0.984857
$7$	−1.40645	−0.531587	−0.265793	−	0.964030i	$-0.585634\pi$
$7$	−1.40645	−0.531587	−0.265793	+	0.964030i	$0.585634\pi$
$8$	−4.38975	−1.55201
$9$	1.00000	0.333333
$10$	−10.0344	−3.17316
$11$	−6.19250	−1.86711	−0.933554	−	0.358436i	$-0.883310\pi$
$11$	−6.19250	−1.86711	−0.933554	+	0.358436i	$0.883310\pi$
$12$	3.81966	1.10264
$13$	−2.39681	−0.664757	−0.332378	−	0.943146i	$-0.607851\pi$
$13$	−2.39681	−0.664757	−0.332378	+	0.943146i	$0.607851\pi$
$14$	3.39291	0.906793
$15$	4.15952	1.07398
$16$	2.95050	0.737624
$17$	7.00317	1.69852	0.849260	−	0.527976i	$-0.177049\pi$
$17$	7.00317	1.69852	0.849260	+	0.527976i	$0.177049\pi$
$18$	−2.41240	−0.568608
$19$	1.45744	0.334360	0.167180	−	0.985926i	$-0.446534\pi$
$19$	1.45744	0.334360	0.167180	+	0.985926i	$0.446534\pi$
$20$	15.8879	3.55265
$21$	−1.40645	−0.306912
$22$	14.9388	3.18496
$23$	−6.62802	−1.38204	−0.691019	−	0.722836i	$-0.742838\pi$
$23$	−6.62802	−1.38204	−0.691019	+	0.722836i	$0.742838\pi$
$24$	−4.38975	−0.896054
$25$	12.3016	2.46031
$26$	5.78207	1.13396
$27$	1.00000	0.192450
$28$	−5.37215	−1.01524
$29$	−5.96265	−1.10724	−0.553618	−	0.832771i	$-0.686753\pi$
$29$	−5.96265	−1.10724	−0.553618	+	0.832771i	$0.686753\pi$
$30$	−10.0344	−1.83202
$31$	−2.07440	−0.372573	−0.186287	−	0.982495i	$-0.559645\pi$
$31$	−2.07440	−0.372573	−0.186287	+	0.982495i	$0.559645\pi$
$32$	1.66173	0.293755
$33$	−6.19250	−1.07798
$34$	−16.8944	−2.89737
$35$	−5.85014	−0.988853
$36$	3.81966	0.636610
$37$	−0.940689	−0.154648	−0.0773242	−	0.997006i	$-0.524638\pi$
$37$	−0.940689	−0.154648	−0.0773242	+	0.997006i	$0.524638\pi$
$38$	−3.51593	−0.570360
$39$	−2.39681	−0.383798
$40$	−18.2592	−2.88704
$41$	1.63477	0.255308	0.127654	−	0.991819i	$-0.459255\pi$
$41$	1.63477	0.255308	0.127654	+	0.991819i	$0.459255\pi$
$42$	3.39291	0.523537
$43$	−1.77847	−0.271214	−0.135607	−	0.990763i	$-0.543298\pi$
$43$	−1.77847	−0.271214	−0.135607	+	0.990763i	$0.543298\pi$
$44$	−23.6533	−3.56586
$45$	4.15952	0.620064
$46$	15.9894	2.35751
$47$	−8.09655	−1.18100	−0.590502	−	0.807036i	$-0.701070\pi$
$47$	−8.09655	−1.18100	−0.590502	+	0.807036i	$0.701070\pi$
$48$	2.95050	0.425868
$49$	−5.02191	−0.717416
$50$	−29.6763	−4.19686
$51$	7.00317	0.980640
$52$	−9.15502	−1.26957
$53$	11.6970	1.60670	0.803351	−	0.595506i	$-0.203049\pi$
$53$	11.6970	1.60670	0.803351	+	0.595506i	$0.203049\pi$
$54$	−2.41240	−0.328286
$55$	−25.7578	−3.47318
$56$	6.17395	0.825028
$57$	1.45744	0.193043
$58$	14.3843	1.88875
$59$	9.24612	1.20374	0.601871	−	0.798593i	$-0.294422\pi$
$59$	9.24612	1.20374	0.601871	+	0.798593i	$0.294422\pi$
$60$	15.8879	2.05113
$61$	0.330691	0.0423407	0.0211703	−	0.999776i	$-0.493261\pi$
$61$	0.330691	0.0423407	0.0211703	+	0.999776i	$0.493261\pi$
$62$	5.00428	0.635544
$63$	−1.40645	−0.177196
$64$	−9.90974	−1.23872
$65$	−9.96959	−1.23658
$66$	14.9388	1.83884
$67$	−10.7175	−1.30935	−0.654674	−	0.755911i	$-0.727194\pi$
$67$	−10.7175	−1.30935	−0.654674	+	0.755911i	$0.727194\pi$
$68$	26.7498	3.24388
$69$	−6.62802	−0.797920
$70$	14.1129	1.68681
$71$	−12.8497	−1.52498	−0.762490	−	0.647000i	$-0.776023\pi$
$71$	−12.8497	−1.52498	−0.762490	+	0.647000i	$0.776023\pi$
$72$	−4.38975	−0.517337
$73$	−1.16282	−0.136098	−0.0680491	−	0.997682i	$-0.521677\pi$
$73$	−1.16282	−0.136098	−0.0680491	+	0.997682i	$0.521677\pi$
$74$	2.26932	0.263803
$75$	12.3016	1.42046
$76$	5.56694	0.638572
$77$	8.70942	0.992530
$78$	5.78207	0.654691
$79$	16.4427	1.84995	0.924973	−	0.380032i	$-0.124087\pi$
$79$	16.4427	1.84995	0.924973	+	0.380032i	$0.124087\pi$
$80$	12.2726	1.37212
$81$	1.00000	0.111111
$82$	−3.94372	−0.435511
$83$	−6.28201	−0.689540	−0.344770	−	0.938687i	$-0.612043\pi$
$83$	−6.28201	−0.689540	−0.344770	+	0.938687i	$0.612043\pi$
$84$	−5.37215	−0.586150
$85$	29.1298	3.15957
$86$	4.29037	0.462643
$87$	−5.96265	−0.639263
$88$	27.1835	2.89777
$89$	4.23970	0.449407	0.224703	−	0.974427i	$-0.427859\pi$
$89$	4.23970	0.449407	0.224703	+	0.974427i	$0.427859\pi$
$90$	−10.0344	−1.05772
$91$	3.37099	0.353376
$92$	−25.3168	−2.63946
$93$	−2.07440	−0.215105
$94$	19.5321	2.01458
$95$	6.06226	0.621975
$96$	1.66173	0.169599
$97$	−3.19042	−0.323938	−0.161969	−	0.986796i	$-0.551785\pi$
$97$	−3.19042	−0.323938	−0.161969	+	0.986796i	$0.551785\pi$
$98$	12.1148	1.22378
$99$	−6.19250	−0.622370
$100$	46.9879	4.69879
$101$	6.91550	0.688118	0.344059	−	0.938948i	$-0.388198\pi$
$101$	6.91550	0.688118	0.344059	+	0.938948i	$0.388198\pi$
$102$	−16.8944	−1.67280
$103$	5.24081	0.516392	0.258196	−	0.966093i	$-0.416872\pi$
$103$	5.24081	0.516392	0.258196	+	0.966093i	$0.416872\pi$
$104$	10.5214	1.03171
$105$	−5.85014	−0.570915
$106$	−28.2177	−2.74075
$107$	4.70012	0.454378	0.227189	−	0.973851i	$-0.427046\pi$
$107$	4.70012	0.454378	0.227189	+	0.973851i	$0.427046\pi$
$108$	3.81966	0.367547
$109$	−11.9562	−1.14520	−0.572598	−	0.819837i	$-0.694064\pi$
$109$	−11.9562	−1.14520	−0.572598	+	0.819837i	$0.694064\pi$
$110$	62.1381	5.92463
$111$	−0.940689	−0.0892863
$112$	−4.14972	−0.392111
$113$	−11.5615	−1.08762	−0.543809	−	0.839209i	$-0.683018\pi$
$113$	−11.5615	−1.08762	−0.543809	+	0.839209i	$0.683018\pi$
$114$	−3.51593	−0.329297
$115$	−27.5694	−2.57086
$116$	−22.7753	−2.11464
$117$	−2.39681	−0.221586
$118$	−22.3053	−2.05337
$119$	−9.84959	−0.902910
$120$	−18.2592	−1.66683
$121$	27.3470	2.48609
$122$	−0.797759	−0.0722257
$123$	1.63477	0.147402
$124$	−7.92351	−0.711552
$125$	30.3710	2.71647
$126$	3.39291	0.302264
$127$	3.72587	0.330618	0.165309	−	0.986242i	$-0.447138\pi$
$127$	3.72587	0.330618	0.165309	+	0.986242i	$0.447138\pi$
$128$	20.5828	1.81928
$129$	−1.77847	−0.156585
$130$	24.0506	2.10938
$131$	−8.32461	−0.727325	−0.363662	−	0.931531i	$-0.618474\pi$
$131$	−8.32461	−0.727325	−0.363662	+	0.931531i	$0.618474\pi$
$132$	−23.6533	−2.05875
$133$	−2.04982	−0.177742
$134$	25.8548	2.23352
$135$	4.15952	0.357994
$136$	−30.7422	−2.63612
$137$	−15.6155	−1.33413	−0.667063	−	0.745002i	$-0.732449\pi$
$137$	−15.6155	−1.33413	−0.667063	+	0.745002i	$0.732449\pi$
$138$	15.9894	1.36111
$139$	17.4917	1.48363	0.741813	−	0.670607i	$-0.233966\pi$
$139$	17.4917	1.48363	0.741813	+	0.670607i	$0.233966\pi$
$140$	−22.3455	−1.88854
$141$	−8.09655	−0.681853
$142$	30.9986	2.60135
$143$	14.8423	1.24117
$144$	2.95050	0.245875
$145$	−24.8017	−2.05967
$146$	2.80519	0.232160
$147$	−5.02191	−0.414200
$148$	−3.59312	−0.295352
$149$	12.3380	1.01077	0.505385	−	0.862894i	$-0.331350\pi$
$149$	12.3380	1.01077	0.505385	+	0.862894i	$0.331350\pi$
$150$	−29.6763	−2.42306
$151$	−18.8062	−1.53043	−0.765213	−	0.643777i	$-0.777367\pi$
$151$	−18.8062	−1.53043	−0.765213	+	0.643777i	$0.777367\pi$
$152$	−6.39781	−0.518931
$153$	7.00317	0.566173
$154$	−21.0106	−1.69308
$155$	−8.62850	−0.693058
$156$	−9.15502	−0.732989
$157$	−18.0445	−1.44011	−0.720056	−	0.693916i	$-0.755884\pi$
$157$	−18.0445	−1.44011	−0.720056	+	0.693916i	$0.755884\pi$
$158$	−39.6663	−3.15568
$159$	11.6970	0.927629
$160$	6.91198	0.546440
$161$	9.32196	0.734673
$162$	−2.41240	−0.189536
$163$	−18.7385	−1.46771	−0.733854	−	0.679307i	$-0.762281\pi$
$163$	−18.7385	−1.46771	−0.733854	+	0.679307i	$0.762281\pi$
$164$	6.24428	0.487596
$165$	−25.7578	−2.00524
$166$	15.1547	1.17623
$167$	−25.6590	−1.98556	−0.992778	−	0.119965i	$-0.961722\pi$
$167$	−25.6590	−1.98556	−0.992778	+	0.119965i	$0.961722\pi$
$168$	6.17395	0.476330
$169$	−7.25528	−0.558098
$170$	−70.2727	−5.38967
$171$	1.45744	0.111453
$172$	−6.79315	−0.517973
$173$	3.32682	0.252933	0.126467	−	0.991971i	$-0.459636\pi$
$173$	3.32682	0.252933	0.126467	+	0.991971i	$0.459636\pi$
$174$	14.3843	1.09047
$175$	−17.3015	−1.30787
$176$	−18.2710	−1.37722
$177$	9.24612	0.694981
$178$	−10.2278	−0.766609
$179$	1.86754	0.139587	0.0697933	−	0.997561i	$-0.477766\pi$
$179$	1.86754	0.139587	0.0697933	+	0.997561i	$0.477766\pi$
$180$	15.8879	1.18422
$181$	1.01217	0.0752337	0.0376168	−	0.999292i	$-0.488023\pi$
$181$	1.01217	0.0752337	0.0376168	+	0.999292i	$0.488023\pi$
$182$	−8.13217	−0.602797
$183$	0.330691	0.0244454
$184$	29.0954	2.14494
$185$	−3.91281	−0.287676
$186$	5.00428	0.366932
$187$	−43.3671	−3.17132
$188$	−30.9261	−2.25552
$189$	−1.40645	−0.102304
$190$	−14.6246	−1.06098
$191$	−8.96647	−0.648791	−0.324395	−	0.945922i	$-0.605161\pi$
$191$	−8.96647	−0.648791	−0.324395	+	0.945922i	$0.605161\pi$
$192$	−9.90974	−0.715174
$193$	−9.39997	−0.676625	−0.338312	−	0.941034i	$-0.609856\pi$
$193$	−9.39997	−0.676625	−0.338312	+	0.941034i	$0.609856\pi$
$194$	7.69657	0.552582
$195$	−9.96959	−0.713937
$196$	−19.1820	−1.37014
$197$	−0.383097	−0.0272946	−0.0136473	−	0.999907i	$-0.504344\pi$
$197$	−0.383097	−0.0272946	−0.0136473	+	0.999907i	$0.504344\pi$
$198$	14.9388	1.06165
$199$	−0.395802	−0.0280577	−0.0140288	−	0.999902i	$-0.504466\pi$
$199$	−0.395802	−0.0280577	−0.0140288	+	0.999902i	$0.504466\pi$
$200$	−54.0008	−3.81844
$201$	−10.7175	−0.755952
$202$	−16.6829	−1.17381
$203$	8.38615	0.588592
$204$	26.7498	1.87286
$205$	6.79986	0.474923
$206$	−12.6429	−0.880874
$207$	−6.62802	−0.460679
$208$	−7.07180	−0.490341
$209$	−9.02521	−0.624287
$210$	14.1129	0.973879
$211$	−20.0949	−1.38339	−0.691696	−	0.722189i	$-0.743136\pi$
$211$	−20.0949	−1.38339	−0.691696	+	0.722189i	$0.743136\pi$
$212$	44.6784	3.06853
$213$	−12.8497	−0.880448
$214$	−11.3386	−0.775088
$215$	−7.39757	−0.504510
$216$	−4.38975	−0.298685
$217$	2.91753	0.198055
$218$	28.8431	1.95350
$219$	−1.16282	−0.0785764
$220$	−98.3861	−6.63319
$221$	−16.7853	−1.12910
$222$	2.26932	0.152307
$223$	−10.3146	−0.690719	−0.345360	−	0.938470i	$-0.612243\pi$
$223$	−10.3146	−0.690719	−0.345360	+	0.938470i	$0.612243\pi$
$224$	−2.33713	−0.156156
$225$	12.3016	0.820105
$226$	27.8910	1.85528
$227$	19.9616	1.32490	0.662449	−	0.749107i	$-0.269517\pi$
$227$	19.9616	1.32490	0.662449	+	0.749107i	$0.269517\pi$
$228$	5.56694	0.368680
$229$	−15.8713	−1.04881	−0.524403	−	0.851470i	$-0.675711\pi$
$229$	−15.8713	−1.04881	−0.524403	+	0.851470i	$0.675711\pi$
$230$	66.5083	4.38543
$231$	8.70942	0.573038
$232$	26.1746	1.71844
$233$	22.1649	1.45207	0.726035	−	0.687658i	$-0.241361\pi$
$233$	22.1649	1.45207	0.726035	+	0.687658i	$0.241361\pi$
$234$	5.78207	0.377986
$235$	−33.6777	−2.19689
$236$	35.3170	2.29894
$237$	16.4427	1.06807
$238$	23.7611	1.54020
$239$	3.52549	0.228045	0.114022	−	0.993478i	$-0.463626\pi$
$239$	3.52549	0.228045	0.114022	+	0.993478i	$0.463626\pi$
$240$	12.2726	0.792196
$241$	−16.9024	−1.08878	−0.544391	−	0.838832i	$-0.683239\pi$
$241$	−16.9024	−1.08878	−0.544391	+	0.838832i	$0.683239\pi$
$242$	−65.9719	−4.24084
$243$	1.00000	0.0641500
$244$	1.26313	0.0808636
$245$	−20.8887	−1.33453
$246$	−3.94372	−0.251442
$247$	−3.49322	−0.222268
$248$	9.10610	0.578238
$249$	−6.28201	−0.398106
$250$	−73.2669	−4.63381
$251$	8.83247	0.557501	0.278750	−	0.960364i	$-0.410080\pi$
$251$	8.83247	0.557501	0.278750	+	0.960364i	$0.410080\pi$
$252$	−5.37215	−0.338414
$253$	41.0440	2.58042
$254$	−8.98829	−0.563975
$255$	29.1298	1.82418
$256$	−29.8344	−1.86465
$257$	−10.3549	−0.645922	−0.322961	−	0.946412i	$-0.604678\pi$
$257$	−10.3549	−0.645922	−0.322961	+	0.946412i	$0.604678\pi$
$258$	4.29037	0.267107
$259$	1.32303	0.0822090
$260$	−38.0805	−2.36165
$261$	−5.96265	−0.369079
$262$	20.0823	1.24069
$263$	−11.7933	−0.727203	−0.363602	−	0.931555i	$-0.618453\pi$
$263$	−11.7933	−0.727203	−0.363602	+	0.931555i	$0.618453\pi$
$264$	27.1835	1.67303
$265$	48.6537	2.98877
$266$	4.94497	0.303196
$267$	4.23970	0.259465
$268$	−40.9371	−2.50063
$269$	3.75479	0.228934	0.114467	−	0.993427i	$-0.463484\pi$
$269$	3.75479	0.228934	0.114467	+	0.993427i	$0.463484\pi$
$270$	−10.0344	−0.610675
$271$	−3.75057	−0.227831	−0.113915	−	0.993490i	$-0.536339\pi$
$271$	−3.75057	−0.227831	−0.113915	+	0.993490i	$0.536339\pi$
$272$	20.6628	1.25287
$273$	3.37099	0.204022
$274$	37.6709	2.27578
$275$	−76.1775	−4.59367
$276$	−25.3168	−1.52389
$277$	−26.9534	−1.61947	−0.809735	−	0.586795i	$-0.800389\pi$
$277$	−26.9534	−1.61947	−0.809735	+	0.586795i	$0.800389\pi$
$278$	−42.1969	−2.53080
$279$	−2.07440	−0.124191
$280$	25.6806	1.53471
$281$	−24.0107	−1.43236	−0.716180	−	0.697916i	$-0.754111\pi$
$281$	−24.0107	−1.43236	−0.716180	+	0.697916i	$0.754111\pi$
$282$	19.5321	1.16312
$283$	−0.0373547	−0.00222051	−0.00111025	−	0.999999i	$-0.500353\pi$
$283$	−0.0373547	−0.00222051	−0.00111025	+	0.999999i	$0.500353\pi$
$284$	−49.0816	−2.91245
$285$	6.06226	0.359097
$286$	−35.8055	−2.11722
$287$	−2.29922	−0.135719
$288$	1.66173	0.0979182
$289$	32.0444	1.88497
$290$	59.8317	3.51344
$291$	−3.19042	−0.187026
$292$	−4.44160	−0.259925
$293$	23.7910	1.38989	0.694944	−	0.719064i	$-0.255429\pi$
$293$	23.7910	1.38989	0.694944	+	0.719064i	$0.255429\pi$
$294$	12.1148	0.706552
$295$	38.4594	2.23919
$296$	4.12939	0.240016
$297$	−6.19250	−0.359325
$298$	−29.7642	−1.72420
$299$	15.8861	0.918719
$300$	46.9879	2.71285
$301$	2.50132	0.144174
$302$	45.3680	2.61064
$303$	6.91550	0.397285
$304$	4.30018	0.246632
$305$	1.37552	0.0787618
$306$	−16.8944	−0.965791
$307$	−23.4800	−1.34007	−0.670037	−	0.742328i	$-0.733722\pi$
$307$	−23.4800	−1.34007	−0.670037	+	0.742328i	$0.733722\pi$
$308$	33.2670	1.89557
$309$	5.24081	0.298139
$310$	20.8154	1.18223
$311$	−2.93378	−0.166359	−0.0831797	−	0.996535i	$-0.526508\pi$
$311$	−2.93378	−0.166359	−0.0831797	+	0.996535i	$0.526508\pi$
$312$	10.5214	0.595658
$313$	−4.44513	−0.251253	−0.125627	−	0.992078i	$-0.540094\pi$
$313$	−4.44513	−0.251253	−0.125627	+	0.992078i	$0.540094\pi$
$314$	43.5306	2.45658
$315$	−5.85014	−0.329618
$316$	62.8055	3.53309
$317$	7.71939	0.433564	0.216782	−	0.976220i	$-0.430444\pi$
$317$	7.71939	0.433564	0.216782	+	0.976220i	$0.430444\pi$
$318$	−28.2177	−1.58237
$319$	36.9237	2.06733
$320$	−41.2197	−2.30425
$321$	4.70012	0.262335
$322$	−22.4883	−1.25322
$323$	10.2067	0.567917
$324$	3.81966	0.212203
$325$	−29.4846	−1.63551
$326$	45.2046	2.50365
$327$	−11.9562	−0.661179
$328$	−7.17624	−0.396242
$329$	11.3874	0.627806
$330$	62.1381	3.42059
$331$	−28.2097	−1.55055	−0.775274	−	0.631625i	$-0.782388\pi$
$331$	−28.2097	−1.55055	−0.775274	+	0.631625i	$0.782388\pi$
$332$	−23.9952	−1.31691
$333$	−0.940689	−0.0515495
$334$	61.8998	3.38701
$335$	−44.5795	−2.43564
$336$	−4.14972	−0.226386
$337$	5.69349	0.310144	0.155072	−	0.987903i	$-0.450439\pi$
$337$	5.69349	0.310144	0.155072	+	0.987903i	$0.450439\pi$
$338$	17.5026	0.952017
$339$	−11.5615	−0.627937
$340$	111.266	6.03425
$341$	12.8457	0.695635
$342$	−3.51593	−0.190120
$343$	16.9082	0.912955
$344$	7.80703	0.420927
$345$	−27.5694	−1.48428
$346$	−8.02561	−0.431460
$347$	15.2493	0.818624	0.409312	−	0.912394i	$-0.365769\pi$
$347$	15.2493	0.818624	0.409312	+	0.912394i	$0.365769\pi$
$348$	−22.7753	−1.22089
$349$	−32.9978	−1.76633	−0.883165	−	0.469063i	$-0.844592\pi$
$349$	−32.9978	−1.76633	−0.883165	+	0.469063i	$0.844592\pi$
$350$	41.7381	2.23100
$351$	−2.39681	−0.127933
$352$	−10.2902	−0.548472
$353$	33.0994	1.76170	0.880852	−	0.473391i	$-0.156970\pi$
$353$	33.0994	1.76170	0.880852	+	0.473391i	$0.156970\pi$
$354$	−22.3053	−1.18551
$355$	−53.4486	−2.83676
$356$	16.1942	0.858291
$357$	−9.84959	−0.521295
$358$	−4.50526	−0.238110
$359$	34.2483	1.80755	0.903777	−	0.428004i	$-0.140783\pi$
$359$	34.2483	1.80755	0.903777	+	0.428004i	$0.140783\pi$
$360$	−18.2592	−0.962346
$361$	−16.8759	−0.888203
$362$	−2.44175	−0.128335
$363$	27.3470	1.43535
$364$	12.8760	0.674888
$365$	−4.83678	−0.253169
$366$	−0.797759	−0.0416995
$367$	17.2033	0.898006	0.449003	−	0.893530i	$-0.351779\pi$
$367$	17.2033	0.898006	0.449003	+	0.893530i	$0.351779\pi$
$368$	−19.5560	−1.01943
$369$	1.63477	0.0851028
$370$	9.43926	0.490724
$371$	−16.4511	−0.854101
$372$	−7.92351	−0.410815
$373$	−36.4930	−1.88953	−0.944767	−	0.327744i	$-0.893712\pi$
$373$	−36.4930	−1.88953	−0.944767	+	0.327744i	$0.893712\pi$
$374$	104.619	5.40971
$375$	30.3710	1.56835
$376$	35.5418	1.83293
$377$	14.2914	0.736043
$378$	3.39291	0.174512
$379$	−10.6313	−0.546093	−0.273047	−	0.962001i	$-0.588031\pi$
$379$	−10.6313	−0.546093	−0.273047	+	0.962001i	$0.588031\pi$
$380$	23.1558	1.18787
$381$	3.72587	0.190882
$382$	21.6307	1.10672
$383$	13.8621	0.708320	0.354160	−	0.935185i	$-0.384767\pi$
$383$	13.8621	0.708320	0.354160	+	0.935185i	$0.384767\pi$
$384$	20.5828	1.05036
$385$	36.2270	1.84630
$386$	22.6765	1.15420
$387$	−1.77847	−0.0904046
$388$	−12.1863	−0.618668
$389$	−23.4384	−1.18838	−0.594188	−	0.804326i	$-0.702527\pi$
$389$	−23.4384	−1.18838	−0.594188	+	0.804326i	$0.702527\pi$
$390$	24.0506	1.21785
$391$	−46.4172	−2.34742
$392$	22.0449	1.11344
$393$	−8.32461	−0.419921
$394$	0.924183	0.0465597
$395$	68.3936	3.44126
$396$	−23.6533	−1.18862
$397$	−13.0808	−0.656508	−0.328254	−	0.944590i	$-0.606460\pi$
$397$	−13.0808	−0.656508	−0.328254	+	0.944590i	$0.606460\pi$
$398$	0.954833	0.0478614
$399$	−2.04982	−0.102619
$400$	36.2958	1.81479
$401$	21.5464	1.07598	0.537988	−	0.842953i	$-0.319185\pi$
$401$	21.5464	1.07598	0.537988	+	0.842953i	$0.319185\pi$
$402$	25.8548	1.28952
$403$	4.97195	0.247671
$404$	26.4149	1.31419
$405$	4.15952	0.206688
$406$	−20.2307	−1.00403
$407$	5.82522	0.288745
$408$	−30.7422	−1.52196
$409$	−2.49018	−0.123131	−0.0615657	−	0.998103i	$-0.519609\pi$
$409$	−2.49018	−0.123131	−0.0615657	+	0.998103i	$0.519609\pi$
$410$	−16.4040	−0.810134
$411$	−15.6155	−0.770258
$412$	20.0181	0.986222
$413$	−13.0042	−0.639893
$414$	15.9894	0.785838
$415$	−26.1301	−1.28268
$416$	−3.98285	−0.195275
$417$	17.4917	0.856572
$418$	21.7724	1.06492
$419$	−36.1441	−1.76575	−0.882877	−	0.469605i	$-0.844396\pi$
$419$	−36.1441	−1.76575	−0.882877	+	0.469605i	$0.844396\pi$
$420$	−22.3455	−1.09035
$421$	−15.8960	−0.774726	−0.387363	−	0.921927i	$-0.626614\pi$
$421$	−15.8960	−0.774726	−0.387363	+	0.921927i	$0.626614\pi$
$422$	48.4770	2.35982
$423$	−8.09655	−0.393668
$424$	−51.3467	−2.49362
$425$	86.1500	4.17889
$426$	30.9986	1.50189
$427$	−0.465099	−0.0225077
$428$	17.9529	0.867785
$429$	14.8423	0.716592
$430$	17.8459	0.860605
$431$	9.99261	0.481327	0.240664	−	0.970609i	$-0.422635\pi$
$431$	9.99261	0.481327	0.240664	+	0.970609i	$0.422635\pi$
$432$	2.95050	0.141956
$433$	27.6090	1.32680	0.663401	−	0.748264i	$-0.269112\pi$
$433$	27.6090	1.32680	0.663401	+	0.748264i	$0.269112\pi$
$434$	−7.03825	−0.337847
$435$	−24.8017	−1.18915
$436$	−45.6686	−2.18713
$437$	−9.65997	−0.462099
$438$	2.80519	0.134037
$439$	16.2771	0.776865	0.388433	−	0.921477i	$-0.373017\pi$
$439$	16.2771	0.776865	0.388433	+	0.921477i	$0.373017\pi$
$440$	113.070	5.39041
$441$	−5.02191	−0.239139
$442$	40.4928	1.92605
$443$	−13.6722	−0.649588	−0.324794	−	0.945785i	$-0.605295\pi$
$443$	−13.6722	−0.649588	−0.324794	+	0.945785i	$0.605295\pi$
$444$	−3.59312	−0.170522
$445$	17.6351	0.835983
$446$	24.8830	1.17824
$447$	12.3380	0.583569
$448$	13.9375	0.658486
$449$	2.36459	0.111592	0.0557960	−	0.998442i	$-0.482230\pi$
$449$	2.36459	0.111592	0.0557960	+	0.998442i	$0.482230\pi$
$450$	−29.6763	−1.39895
$451$	−10.1233	−0.476689
$452$	−44.1612	−2.07717
$453$	−18.8062	−0.883592
$454$	−48.1553	−2.26004
$455$	14.0217	0.657347
$456$	−6.39781	−0.299605
$457$	26.5174	1.24043	0.620216	−	0.784431i	$-0.287045\pi$
$457$	26.5174	1.24043	0.620216	+	0.784431i	$0.287045\pi$
$458$	38.2879	1.78908
$459$	7.00317	0.326880
$460$	−105.306	−4.90990
$461$	−37.0284	−1.72458	−0.862292	−	0.506412i	$-0.830972\pi$
$461$	−37.0284	−1.72458	−0.862292	+	0.506412i	$0.830972\pi$
$462$	−21.0106	−0.977500
$463$	−33.3771	−1.55116	−0.775582	−	0.631247i	$-0.782544\pi$
$463$	−33.3771	−1.55116	−0.775582	+	0.631247i	$0.782544\pi$
$464$	−17.5928	−0.816725
$465$	−8.62850	−0.400137
$466$	−53.4705	−2.47697
$467$	3.34691	0.154876	0.0774382	−	0.996997i	$-0.475326\pi$
$467$	3.34691	0.154876	0.0774382	+	0.996997i	$0.475326\pi$
$468$	−9.15502	−0.423191
$469$	15.0736	0.696032
$470$	81.2441	3.74751
$471$	−18.0445	−0.831449
$472$	−40.5881	−1.86822
$473$	11.0132	0.506386
$474$	−39.6663	−1.82193
$475$	17.9288	0.822632
$476$	−37.6221	−1.72441
$477$	11.6970	0.535567
$478$	−8.50488	−0.389004
$479$	16.8534	0.770054	0.385027	−	0.922905i	$-0.374192\pi$
$479$	16.8534	0.770054	0.385027	+	0.922905i	$0.374192\pi$
$480$	6.91198	0.315487
$481$	2.25466	0.102804
$482$	40.7754	1.85727
$483$	9.32196	0.424164
$484$	104.456	4.74802
$485$	−13.2706	−0.602588
$486$	−2.41240	−0.109429
$487$	−40.8518	−1.85117	−0.925586	−	0.378538i	$-0.876427\pi$
$487$	−40.8518	−1.85117	−0.925586	+	0.378538i	$0.876427\pi$
$488$	−1.45165	−0.0657132
$489$	−18.7385	−0.847382
$490$	50.3919	2.27647
$491$	27.4663	1.23954	0.619768	−	0.784785i	$-0.287227\pi$
$491$	27.4663	1.23954	0.619768	+	0.784785i	$0.287227\pi$
$492$	6.24428	0.281514
$493$	−41.7575	−1.88066
$494$	8.42704	0.379150
$495$	−25.7578	−1.15773
$496$	−6.12051	−0.274819
$497$	18.0724	0.810659
$498$	15.1547	0.679098
$499$	3.54749	0.158807	0.0794037	−	0.996843i	$-0.474698\pi$
$499$	3.54749	0.158807	0.0794037	+	0.996843i	$0.474698\pi$
$500$	116.007	5.18799
$501$	−25.6590	−1.14636
$502$	−21.3074	−0.950997
$503$	14.7494	0.657642	0.328821	−	0.944392i	$-0.393349\pi$
$503$	14.7494	0.657642	0.328821	+	0.944392i	$0.393349\pi$
$504$	6.17395	0.275009
$505$	28.7651	1.28003
$506$	−99.0145	−4.40173
$507$	−7.25528	−0.322218
$508$	14.2316	0.631424
$509$	32.5242	1.44161	0.720805	−	0.693138i	$-0.243772\pi$
$509$	32.5242	1.44161	0.720805	+	0.693138i	$0.243772\pi$
$510$	−70.2727	−3.11173
$511$	1.63545	0.0723480
$512$	30.8068	1.36148
$513$	1.45744	0.0643477
$514$	24.9802	1.10183
$515$	21.7992	0.960589
$516$	−6.79315	−0.299052
$517$	50.1379	2.20506
$518$	−3.19167	−0.140234
$519$	3.32682	0.146031
$520$	43.7640	1.91918
$521$	−36.8120	−1.61276	−0.806381	−	0.591397i	$-0.798577\pi$
$521$	−36.8120	−1.61276	−0.806381	+	0.591397i	$0.798577\pi$
$522$	14.3843	0.629583
$523$	15.4582	0.675938	0.337969	−	0.941157i	$-0.390260\pi$
$523$	15.4582	0.675938	0.337969	+	0.941157i	$0.390260\pi$
$524$	−31.7972	−1.38907
$525$	−17.3015	−0.755099
$526$	28.4500	1.24048
$527$	−14.5274	−0.632823
$528$	−18.2710	−0.795141
$529$	20.9307	0.910030
$530$	−117.372	−5.09832
$531$	9.24612	0.401247
$532$	−7.82960	−0.339456
$533$	−3.91824	−0.169718
$534$	−10.2278	−0.442602
$535$	19.5502	0.845230
$536$	47.0470	2.03212
$537$	1.86754	0.0805904
$538$	−9.05805	−0.390520
$539$	31.0982	1.33949
$540$	15.8879	0.683708
$541$	−6.65491	−0.286117	−0.143058	−	0.989714i	$-0.545694\pi$
$541$	−6.65491	−0.286117	−0.143058	+	0.989714i	$0.545694\pi$
$542$	9.04786	0.388639
$543$	1.01217	0.0434362
$544$	11.6374	0.498948
$545$	−49.7319	−2.13028
$546$	−8.13217	−0.348025
$547$	6.08648	0.260239	0.130120	−	0.991498i	$-0.458464\pi$
$547$	6.08648	0.260239	0.130120	+	0.991498i	$0.458464\pi$
$548$	−59.6461	−2.54795
$549$	0.330691	0.0141136
$550$	183.770	7.83599
$551$	−8.69023	−0.370216
$552$	29.0954	1.23838
$553$	−23.1258	−0.983407
$554$	65.0222	2.76253
$555$	−3.91281	−0.166090
$556$	66.8124	2.83348
$557$	−22.6902	−0.961415	−0.480707	−	0.876881i	$-0.659620\pi$
$557$	−22.6902	−0.961415	−0.480707	+	0.876881i	$0.659620\pi$
$558$	5.00428	0.211848
$559$	4.26266	0.180291
$560$	−17.2608	−0.729402
$561$	−43.3671	−1.83096
$562$	57.9234	2.44335
$563$	12.5097	0.527220	0.263610	−	0.964629i	$-0.415087\pi$
$563$	12.5097	0.527220	0.263610	+	0.964629i	$0.415087\pi$
$564$	−30.9261	−1.30222
$565$	−48.0904	−2.02318
$566$	0.0901144	0.00378779
$567$	−1.40645	−0.0590652
$568$	56.4070	2.36679
$569$	−39.4343	−1.65317	−0.826585	−	0.562812i	$-0.809720\pi$
$569$	−39.4343	−1.65317	−0.826585	+	0.562812i	$0.809720\pi$
$570$	−14.6246	−0.612556
$571$	25.3750	1.06191	0.530955	−	0.847400i	$-0.321833\pi$
$571$	25.3750	1.06191	0.530955	+	0.847400i	$0.321833\pi$
$572$	56.6925	2.37043
$573$	−8.96647	−0.374580
$574$	5.54663	0.231512
$575$	−81.5351	−3.40025
$576$	−9.90974	−0.412906
$577$	33.6253	1.39984	0.699919	−	0.714222i	$-0.253219\pi$
$577$	33.6253	1.39984	0.699919	+	0.714222i	$0.253219\pi$
$578$	−77.3039	−3.21542
$579$	−9.39997	−0.390650
$580$	−94.7343	−3.93363
$581$	8.83531	0.366550
$582$	7.69657	0.319033
$583$	−72.4334	−2.99989
$584$	5.10451	0.211226
$585$	−9.96959	−0.412192
$586$	−57.3935	−2.37090
$587$	9.15931	0.378045	0.189023	−	0.981973i	$-0.439468\pi$
$587$	9.15931	0.378045	0.189023	+	0.981973i	$0.439468\pi$
$588$	−19.1820	−0.791052
$589$	−3.02332	−0.124574
$590$	−92.7793	−3.81966
$591$	−0.383097	−0.0157585
$592$	−2.77550	−0.114072
$593$	30.4665	1.25111	0.625555	−	0.780180i	$-0.284872\pi$
$593$	30.4665	1.25111	0.625555	+	0.780180i	$0.284872\pi$
$594$	14.9388	0.612945
$595$	−40.9695	−1.67959
$596$	47.1271	1.93040
$597$	−0.395802	−0.0161991
$598$	−38.3237	−1.56717
$599$	−41.8310	−1.70917	−0.854584	−	0.519314i	$-0.826188\pi$
$599$	−41.8310	−1.70917	−0.854584	+	0.519314i	$0.826188\pi$
$600$	−54.0008	−2.20457
$601$	−32.7789	−1.33708	−0.668540	−	0.743676i	$-0.733080\pi$
$601$	−32.7789	−1.33708	−0.668540	+	0.743676i	$0.733080\pi$
$602$	−6.03418	−0.245935
$603$	−10.7175	−0.436449
$604$	−71.8333	−2.92286
$605$	113.750	4.62461
$606$	−16.6829	−0.677698
$607$	7.96762	0.323396	0.161698	−	0.986840i	$-0.448303\pi$
$607$	7.96762	0.323396	0.161698	+	0.986840i	$0.448303\pi$
$608$	2.42187	0.0982199
$609$	8.38615	0.339824
$610$	−3.31829	−0.134354
$611$	19.4059	0.785080
$612$	26.7498	1.08129
$613$	−31.7900	−1.28399	−0.641993	−	0.766710i	$-0.721892\pi$
$613$	−31.7900	−1.28399	−0.641993	+	0.766710i	$0.721892\pi$
$614$	56.6431	2.28593
$615$	6.79986	0.274197
$616$	−38.2322	−1.54042
$617$	9.10085	0.366386	0.183193	−	0.983077i	$-0.441357\pi$
$617$	9.10085	0.366386	0.183193	+	0.983077i	$0.441357\pi$
$618$	−12.6429	−0.508573
$619$	−37.9631	−1.52587	−0.762933	−	0.646478i	$-0.776241\pi$
$619$	−37.9631	−1.52587	−0.762933	+	0.646478i	$0.776241\pi$
$620$	−32.9580	−1.32362
$621$	−6.62802	−0.265973
$622$	7.07745	0.283780
$623$	−5.96290	−0.238899
$624$	−7.07180	−0.283098
$625$	64.8208	2.59283
$626$	10.7234	0.428594
$627$	−9.02521	−0.360432
$628$	−68.9241	−2.75037
$629$	−6.58781	−0.262673
$630$	14.1129	0.562270
$631$	−10.1046	−0.402258	−0.201129	−	0.979565i	$-0.564461\pi$
$631$	−10.1046	−0.402258	−0.201129	+	0.979565i	$0.564461\pi$
$632$	−72.1793	−2.87114
$633$	−20.0949	−0.798702
$634$	−18.6222	−0.739584
$635$	15.4978	0.615013
$636$	44.6784	1.77162
$637$	12.0366	0.476907
$638$	−89.0747	−3.52650
$639$	−12.8497	−0.508327
$640$	85.6144	3.38421
$641$	15.9493	0.629960	0.314980	−	0.949098i	$-0.398002\pi$
$641$	15.9493	0.629960	0.314980	+	0.949098i	$0.398002\pi$
$642$	−11.3386	−0.447497
$643$	2.36283	0.0931809	0.0465905	−	0.998914i	$-0.485164\pi$
$643$	2.36283	0.0931809	0.0465905	+	0.998914i	$0.485164\pi$
$644$	35.6067	1.40310
$645$	−7.39757	−0.291279
$646$	−24.6227	−0.968767
$647$	2.79107	0.109728	0.0548641	−	0.998494i	$-0.482527\pi$
$647$	2.79107	0.109728	0.0548641	+	0.998494i	$0.482527\pi$
$648$	−4.38975	−0.172446
$649$	−57.2566	−2.24752
$650$	71.1286	2.78989
$651$	2.91753	0.114347
$652$	−71.5746	−2.80308
$653$	14.2363	0.557109	0.278555	−	0.960420i	$-0.410145\pi$
$653$	14.2363	0.557109	0.278555	+	0.960420i	$0.410145\pi$
$654$	28.8431	1.12785
$655$	−34.6263	−1.35296
$656$	4.82339	0.188322
$657$	−1.16282	−0.0453661
$658$	−27.4708	−1.07093
$659$	−0.170221	−0.00663085	−0.00331542	−	0.999995i	$-0.501055\pi$
$659$	−0.170221	−0.00663085	−0.00331542	+	0.999995i	$0.501055\pi$
$660$	−98.3861	−3.82967
$661$	16.1291	0.627349	0.313674	−	0.949531i	$-0.398440\pi$
$661$	16.1291	0.627349	0.313674	+	0.949531i	$0.398440\pi$
$662$	68.0531	2.64496
$663$	−16.7853	−0.651887
$664$	27.5764	1.07017
$665$	−8.52624	−0.330633
$666$	2.26932	0.0879343
$667$	39.5206	1.53024
$668$	−98.0089	−3.79208
$669$	−10.3146	−0.398787
$670$	107.543	4.15477
$671$	−2.04781	−0.0790546
$672$	−2.33713	−0.0901567
$673$	23.6003	0.909724	0.454862	−	0.890562i	$-0.349689\pi$
$673$	23.6003	0.909724	0.454862	+	0.890562i	$0.349689\pi$
$674$	−13.7350	−0.529051
$675$	12.3016	0.473488
$676$	−27.7127	−1.06587
$677$	−8.59833	−0.330461	−0.165230	−	0.986255i	$-0.552837\pi$
$677$	−8.59833	−0.330461	−0.165230	+	0.986255i	$0.552837\pi$
$678$	27.8910	1.07115
$679$	4.48716	0.172201
$680$	−127.873	−4.90369
$681$	19.9616	0.764930
$682$	−30.9890	−1.18663
$683$	−11.0211	−0.421709	−0.210855	−	0.977517i	$-0.567625\pi$
$683$	−11.0211	−0.421709	−0.210855	+	0.977517i	$0.567625\pi$
$684$	5.56694	0.212857
$685$	−64.9531	−2.48173
$686$	−40.7892	−1.55734
$687$	−15.8713	−0.605528
$688$	−5.24737	−0.200054
$689$	−28.0354	−1.06807
$690$	66.5083	2.53193
$691$	16.1058	0.612694	0.306347	−	0.951920i	$-0.400893\pi$
$691$	16.1058	0.612694	0.306347	+	0.951920i	$0.400893\pi$
$692$	12.7073	0.483060
$693$	8.70942	0.330843
$694$	−36.7873	−1.39643
$695$	72.7570	2.75983
$696$	26.1746	0.992144
$697$	11.4486	0.433646
$698$	79.6037	3.01304
$699$	22.1649	0.838353
$700$	−66.0859	−2.49781
$701$	−15.5678	−0.587988	−0.293994	−	0.955807i	$-0.594985\pi$
$701$	−15.5678	−0.587988	−0.293994	+	0.955807i	$0.594985\pi$
$702$	5.78207	0.218230
$703$	−1.37100	−0.0517083
$704$	61.3661	2.31282
$705$	−33.6777	−1.26838
$706$	−79.8490	−3.00516
$707$	−9.72627	−0.365794
$708$	35.3170	1.32730
$709$	31.2577	1.17391	0.586953	−	0.809621i	$-0.300327\pi$
$709$	31.2577	1.17391	0.586953	+	0.809621i	$0.300327\pi$
$710$	128.939	4.83900
$711$	16.4427	0.616649
$712$	−18.6112	−0.697484
$713$	13.7492	0.514911
$714$	23.7611	0.889238
$715$	61.7367	2.30882
$716$	7.13338	0.266587
$717$	3.52549	0.131662
$718$	−82.6204	−3.08337
$719$	−41.4039	−1.54410	−0.772052	−	0.635559i	$-0.780770\pi$
$719$	−41.4039	−1.54410	−0.772052	+	0.635559i	$0.780770\pi$
$720$	12.2726	0.457374
$721$	−7.37092	−0.274507
$722$	40.7113	1.51512
$723$	−16.9024	−0.628609
$724$	3.86613	0.143684
$725$	−73.3500	−2.72415
$726$	−65.9719	−2.44845
$727$	39.6373	1.47006	0.735032	−	0.678032i	$-0.237167\pi$
$727$	39.6373	1.47006	0.735032	+	0.678032i	$0.237167\pi$
$728$	−14.7978	−0.548443
$729$	1.00000	0.0370370
$730$	11.6682	0.431861
$731$	−12.4549	−0.460662
$732$	1.26313	0.0466866
$733$	5.36040	0.197991	0.0989954	−	0.995088i	$-0.468437\pi$
$733$	5.36040	0.197991	0.0989954	+	0.995088i	$0.468437\pi$
$734$	−41.5012	−1.53184
$735$	−20.8887	−0.770492
$736$	−11.0140	−0.405980
$737$	66.3680	2.44469
$738$	−3.94372	−0.145170
$739$	29.2008	1.07417	0.537084	−	0.843529i	$-0.319526\pi$
$739$	29.2008	1.07417	0.537084	+	0.843529i	$0.319526\pi$
$740$	−14.9456	−0.549412
$741$	−3.49322	−0.128327
$742$	39.6867	1.45694
$743$	5.97996	0.219383	0.109692	−	0.993966i	$-0.465014\pi$
$743$	5.97996	0.219383	0.109692	+	0.993966i	$0.465014\pi$
$744$	9.10610	0.333846
$745$	51.3202	1.88023
$746$	88.0355	3.22321
$747$	−6.28201	−0.229847
$748$	−165.648	−6.05669
$749$	−6.61047	−0.241541
$750$	−73.2669	−2.67533
$751$	−1.90699	−0.0695872	−0.0347936	−	0.999395i	$-0.511077\pi$
$751$	−1.90699	−0.0695872	−0.0347936	+	0.999395i	$0.511077\pi$
$752$	−23.8889	−0.871137
$753$	8.83247	0.321873
$754$	−34.4765	−1.25556
$755$	−78.2247	−2.84689
$756$	−5.37215	−0.195383
$757$	15.0747	0.547901	0.273951	−	0.961744i	$-0.411670\pi$
$757$	15.0747	0.547901	0.273951	+	0.961744i	$0.411670\pi$
$758$	25.6469	0.931538
$759$	41.0440	1.48980
$760$	−26.6118	−0.965311
$761$	7.51750	0.272509	0.136255	−	0.990674i	$-0.456493\pi$
$761$	7.51750	0.272509	0.136255	+	0.990674i	$0.456493\pi$
$762$	−8.98829	−0.325611
$763$	16.8157	0.608770
$764$	−34.2489	−1.23908
$765$	29.1298	1.05319
$766$	−33.4409	−1.20827
$767$	−22.1612	−0.800196
$768$	−29.8344	−1.07656
$769$	38.5555	1.39035	0.695174	−	0.718842i	$-0.255328\pi$
$769$	38.5555	1.39035	0.695174	+	0.718842i	$0.255328\pi$
$770$	−87.3938	−3.14945
$771$	−10.3549	−0.372923
$772$	−35.9047	−1.29224
$773$	44.2449	1.59138	0.795689	−	0.605705i	$-0.207109\pi$
$773$	44.2449	1.59138	0.795689	+	0.605705i	$0.207109\pi$
$774$	4.29037	0.154214
$775$	−25.5184	−0.916648
$776$	14.0052	0.502756
$777$	1.32303	0.0474634
$778$	56.5429	2.02716
$779$	2.38259	0.0853650
$780$	−38.0805	−1.36350
$781$	79.5718	2.84730
$782$	111.977	4.00428
$783$	−5.96265	−0.213088
$784$	−14.8171	−0.529183
$785$	−75.0566	−2.67888
$786$	20.0823	0.716311
$787$	23.2514	0.828822	0.414411	−	0.910090i	$-0.363988\pi$
$787$	23.2514	0.828822	0.414411	+	0.910090i	$0.363988\pi$
$788$	−1.46330	−0.0521280
$789$	−11.7933	−0.419851
$790$	−164.993	−5.87017
$791$	16.2607	0.578163
$792$	27.1835	0.965924
$793$	−0.792606	−0.0281463
$794$	31.5561	1.11989
$795$	48.6537	1.72557
$796$	−1.51183	−0.0535855
$797$	26.0005	0.920983	0.460492	−	0.887664i	$-0.347673\pi$
$797$	26.0005	0.920983	0.460492	+	0.887664i	$0.347673\pi$
$798$	4.94497	0.175050
$799$	−56.7015	−2.00596
$800$	20.4419	0.722729
$801$	4.23970	0.149802
$802$	−51.9785	−1.83542
$803$	7.20079	0.254110
$804$	−40.9371	−1.44374
$805$	38.7748	1.36663
$806$	−11.9943	−0.422482
$807$	3.75479	0.132175
$808$	−30.3573	−1.06797
$809$	−19.1483	−0.673218	−0.336609	−	0.941645i	$-0.609280\pi$
$809$	−19.1483	−0.673218	−0.336609	+	0.941645i	$0.609280\pi$
$810$	−10.0344	−0.352573
$811$	9.25277	0.324909	0.162454	−	0.986716i	$-0.448059\pi$
$811$	9.25277	0.324909	0.162454	+	0.986716i	$0.448059\pi$
$812$	32.0323	1.12411
$813$	−3.75057	−0.131538
$814$	−14.0527	−0.492548
$815$	−77.9429	−2.73022
$816$	20.6628	0.723344
$817$	−2.59202	−0.0906832
$818$	6.00730	0.210040
$819$	3.37099	0.117792
$820$	25.9732	0.907022
$821$	16.2117	0.565794	0.282897	−	0.959150i	$-0.408705\pi$
$821$	16.2117	0.565794	0.282897	+	0.959150i	$0.408705\pi$
$822$	37.6709	1.31392
$823$	34.3229	1.19642	0.598210	−	0.801339i	$-0.295879\pi$
$823$	34.3229	1.19642	0.598210	+	0.801339i	$0.295879\pi$
$824$	−23.0058	−0.801446
$825$	−76.1775	−2.65216
$826$	31.3712	1.09154
$827$	−18.7862	−0.653259	−0.326630	−	0.945152i	$-0.605913\pi$
$827$	−18.7862	−0.653259	−0.326630	+	0.945152i	$0.605913\pi$
$828$	−25.3168	−0.879820
$829$	−27.2098	−0.945036	−0.472518	−	0.881321i	$-0.656655\pi$
$829$	−27.2098	−0.945036	−0.472518	+	0.881321i	$0.656655\pi$
$830$	63.0362	2.18802
$831$	−26.9534	−0.935002
$832$	23.7518	0.823446
$833$	−35.1693	−1.21854
$834$	−42.1969	−1.46116
$835$	−106.729	−3.69352
$836$	−34.4733	−1.19228
$837$	−2.07440	−0.0717018
$838$	87.1939	3.01206
$839$	27.8786	0.962478	0.481239	−	0.876590i	$-0.340187\pi$
$839$	27.8786	0.962478	0.481239	+	0.876590i	$0.340187\pi$
$840$	25.6806	0.886066
$841$	6.55322	0.225973
$842$	38.3476	1.32154
$843$	−24.0107	−0.826973
$844$	−76.7558	−2.64205
$845$	−30.1784	−1.03817
$846$	19.5321	0.671527
$847$	−38.4621	−1.32157
$848$	34.5119	1.18514
$849$	−0.0373547	−0.00128201
$850$	−207.828	−7.12845
$851$	6.23491	0.213730
$852$	−49.0816	−1.68151
$853$	18.8288	0.644687	0.322344	−	0.946623i	$-0.395529\pi$
$853$	18.8288	0.644687	0.322344	+	0.946623i	$0.395529\pi$
$854$	1.12200	0.0383942
$855$	6.06226	0.207325
$856$	−20.6324	−0.705200
$857$	39.7947	1.35936	0.679681	−	0.733508i	$-0.262118\pi$
$857$	39.7947	1.35936	0.679681	+	0.733508i	$0.262118\pi$
$858$	−35.8055	−1.22238
$859$	26.5896	0.907225	0.453612	−	0.891199i	$-0.350135\pi$
$859$	26.5896	0.907225	0.453612	+	0.891199i	$0.350135\pi$
$860$	−28.2562	−0.963529
$861$	−2.29922	−0.0783572
$862$	−24.1061	−0.821059
$863$	32.1265	1.09360	0.546799	−	0.837264i	$-0.315846\pi$
$863$	32.1265	1.09360	0.546799	+	0.837264i	$0.315846\pi$
$864$	1.66173	0.0565331
$865$	13.8380	0.470505
$866$	−66.6038	−2.26329
$867$	32.0444	1.08829
$868$	11.1440	0.378252
$869$	−101.821	−3.45405
$870$	59.8317	2.02848
$871$	25.6878	0.870398
$872$	52.4847	1.77736
$873$	−3.19042	−0.107979
$874$	23.3037	0.788259
$875$	−42.7152	−1.44404
$876$	−4.44160	−0.150068
$877$	56.7935	1.91778	0.958889	−	0.283780i	$-0.0915886\pi$
$877$	56.7935	1.91778	0.958889	+	0.283780i	$0.0915886\pi$
$878$	−39.2669	−1.32519
$879$	23.7910	0.802452
$880$	−75.9983	−2.56190
$881$	−18.2522	−0.614932	−0.307466	−	0.951559i	$-0.599481\pi$
$881$	−18.2522	−0.614932	−0.307466	+	0.951559i	$0.599481\pi$
$882$	12.1148	0.407928
$883$	12.1186	0.407822	0.203911	−	0.978989i	$-0.434635\pi$
$883$	12.1186	0.407822	0.203911	+	0.978989i	$0.434635\pi$
$884$	−64.1142	−2.15639
$885$	38.4594	1.29280
$886$	32.9829	1.10808
$887$	−4.98447	−0.167362	−0.0836810	−	0.996493i	$-0.526668\pi$
$887$	−4.98447	−0.167362	−0.0836810	+	0.996493i	$0.526668\pi$
$888$	4.12939	0.138573
$889$	−5.24024	−0.175752
$890$	−42.5428	−1.42604
$891$	−6.19250	−0.207457
$892$	−39.3984	−1.31916
$893$	−11.8003	−0.394881
$894$	−29.7642	−0.995465
$895$	7.76807	0.259658
$896$	−28.9486	−0.967104
$897$	15.8861	0.530423
$898$	−5.70434	−0.190356
$899$	12.3689	0.412527
$900$	46.9879	1.56626
$901$	81.9158	2.72901
$902$	24.4215	0.813146
$903$	2.50132	0.0832387
$904$	50.7523	1.68800
$905$	4.21012	0.139949
$906$	45.3680	1.50725
$907$	21.4637	0.712690	0.356345	−	0.934354i	$-0.384023\pi$
$907$	21.4637	0.712690	0.356345	+	0.934354i	$0.384023\pi$
$908$	76.2465	2.53033
$909$	6.91550	0.229373
$910$	−33.8259	−1.12132
$911$	−41.0649	−1.36054	−0.680270	−	0.732962i	$-0.738137\pi$
$911$	−41.0649	−1.36054	−0.680270	+	0.732962i	$0.738137\pi$
$912$	4.30018	0.142393
$913$	38.9013	1.28745
$914$	−63.9706	−2.11596
$915$	1.37552	0.0454731
$916$	−60.6230	−2.00304
$917$	11.7081	0.386636
$918$	−16.8944	−0.557600
$919$	−40.6799	−1.34191	−0.670954	−	0.741499i	$-0.734115\pi$
$919$	−40.6799	−1.34191	−0.670954	+	0.741499i	$0.734115\pi$
$920$	121.023	3.99000
$921$	−23.4800	−0.773692
$922$	89.3272	2.94183
$923$	30.7984	1.01374
$924$	33.2670	1.09441
$925$	−11.5720	−0.380484
$926$	80.5188	2.64601
$927$	5.24081	0.172131
$928$	−9.90830	−0.325256
$929$	−8.95140	−0.293686	−0.146843	−	0.989160i	$-0.546911\pi$
$929$	−8.95140	−0.293686	−0.146843	+	0.989160i	$0.546911\pi$
$930$	20.8154	0.682563
$931$	−7.31915	−0.239875
$932$	84.6624	2.77321
$933$	−2.93378	−0.0960477
$934$	−8.07407	−0.264192
$935$	−180.386	−5.89926
$936$	10.5214	0.343903
$937$	−8.93036	−0.291742	−0.145871	−	0.989304i	$-0.546598\pi$
$937$	−8.93036	−0.291742	−0.145871	+	0.989304i	$0.546598\pi$
$938$	−36.3634	−1.18731
$939$	−4.44513	−0.145061
$940$	−128.638	−4.19569
$941$	−52.7291	−1.71892	−0.859461	−	0.511202i	$-0.829200\pi$
$941$	−52.7291	−1.71892	−0.859461	+	0.511202i	$0.829200\pi$
$942$	43.5306	1.41830
$943$	−10.8353	−0.352846
$944$	27.2806	0.887909
$945$	−5.85014	−0.190305
$946$	−26.5681	−0.863804
$947$	−5.56111	−0.180712	−0.0903559	−	0.995910i	$-0.528800\pi$
$947$	−5.56111	−0.180712	−0.0903559	+	0.995910i	$0.528800\pi$
$948$	62.8055	2.03983
$949$	2.78707	0.0904722
$950$	−43.2515	−1.40326
$951$	7.71939	0.250318
$952$	43.2372	1.40133
$953$	−56.2422	−1.82186	−0.910932	−	0.412557i	$-0.864636\pi$
$953$	−56.2422	−1.82186	−0.910932	+	0.412557i	$0.864636\pi$
$954$	−28.2177	−0.913582
$955$	−37.2962	−1.20688
$956$	13.4662	0.435527
$957$	36.9237	1.19357
$958$	−40.6572	−1.31358
$959$	21.9624	0.709203
$960$	−41.2197	−1.33036
$961$	−26.6969	−0.861189
$962$	−5.43913	−0.175365
$963$	4.70012	0.151459
$964$	−64.5616	−2.07939
$965$	−39.0993	−1.25865
$966$	−22.4883	−0.723548
$967$	−25.7067	−0.826671	−0.413336	−	0.910579i	$-0.635636\pi$
$967$	−25.7067	−0.826671	−0.413336	+	0.910579i	$0.635636\pi$
$968$	−120.047	−3.85845
$969$	10.2067	0.327887
$970$	32.0140	1.02791
$971$	−36.6294	−1.17549	−0.587747	−	0.809045i	$-0.699985\pi$
$971$	−36.6294	−1.17549	−0.587747	+	0.809045i	$0.699985\pi$
$972$	3.81966	0.122516
$973$	−24.6011	−0.788676
$974$	98.5508	3.15777
$975$	−29.4846	−0.944263
$976$	0.975704	0.0312315
$977$	−39.0615	−1.24969	−0.624844	−	0.780750i	$-0.714837\pi$
$977$	−39.0615	−1.24969	−0.624844	+	0.780750i	$0.714837\pi$
$978$	45.2046	1.44548
$979$	−26.2543	−0.839092
$980$	−79.7878	−2.54873
$981$	−11.9562	−0.381732
$982$	−66.2596	−2.11443
$983$	46.2531	1.47525	0.737623	−	0.675213i	$-0.235948\pi$
$983$	46.2531	1.47525	0.737623	+	0.675213i	$0.235948\pi$
$984$	−7.17624	−0.228770
$985$	−1.59350	−0.0507731
$986$	100.736	3.20808
$987$	11.3874	0.362464
$988$	−13.3429	−0.424495
$989$	11.7877	0.374828
$990$	62.1381	1.97488
$991$	−21.4773	−0.682248	−0.341124	−	0.940018i	$-0.610808\pi$
$991$	−21.4773	−0.682248	−0.341124	+	0.940018i	$0.610808\pi$
$992$	−3.44709	−0.109445
$993$	−28.2097	−0.895209
$994$	−43.5979	−1.38284
$995$	−1.64635	−0.0521927
$996$	−23.9952	−0.760316
$997$	18.0850	0.572756	0.286378	−	0.958117i	$-0.407549\pi$
$997$	18.0850	0.572756	0.286378	+	0.958117i	$0.407549\pi$
$998$	−8.55796	−0.270897
$999$	−0.940689	−0.0297621

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8049.2.a.a.1.9	✓	95

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8049.2.a.a.1.9	✓	95	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:	\( N \)	\(=\)	\( 8049 = 3 \cdot 2683 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8049.a (trivial)

\(f(q)\)	\(=\)	\(q-2.41240 q^{2} +1.00000 q^{3} +3.81966 q^{4} +4.15952 q^{5} -2.41240 q^{6} -1.40645 q^{7} -4.38975 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.41240 q^{2} +1.00000 q^{3} +3.81966 q^{4} +4.15952 q^{5} -2.41240 q^{6} -1.40645 q^{7} -4.38975 q^{8} +1.00000 q^{9} -10.0344 q^{10} -6.19250 q^{11} +3.81966 q^{12} -2.39681 q^{13} +3.39291 q^{14} +4.15952 q^{15} +2.95050 q^{16} +7.00317 q^{17} -2.41240 q^{18} +1.45744 q^{19} +15.8879 q^{20} -1.40645 q^{21} +14.9388 q^{22} -6.62802 q^{23} -4.38975 q^{24} +12.3016 q^{25} +5.78207 q^{26} +1.00000 q^{27} -5.37215 q^{28} -5.96265 q^{29} -10.0344 q^{30} -2.07440 q^{31} +1.66173 q^{32} -6.19250 q^{33} -16.8944 q^{34} -5.85014 q^{35} +3.81966 q^{36} -0.940689 q^{37} -3.51593 q^{38} -2.39681 q^{39} -18.2592 q^{40} +1.63477 q^{41} +3.39291 q^{42} -1.77847 q^{43} -23.6533 q^{44} +4.15952 q^{45} +15.9894 q^{46} -8.09655 q^{47} +2.95050 q^{48} -5.02191 q^{49} -29.6763 q^{50} +7.00317 q^{51} -9.15502 q^{52} +11.6970 q^{53} -2.41240 q^{54} -25.7578 q^{55} +6.17395 q^{56} +1.45744 q^{57} +14.3843 q^{58} +9.24612 q^{59} +15.8879 q^{60} +0.330691 q^{61} +5.00428 q^{62} -1.40645 q^{63} -9.90974 q^{64} -9.96959 q^{65} +14.9388 q^{66} -10.7175 q^{67} +26.7498 q^{68} -6.62802 q^{69} +14.1129 q^{70} -12.8497 q^{71} -4.38975 q^{72} -1.16282 q^{73} +2.26932 q^{74} +12.3016 q^{75} +5.56694 q^{76} +8.70942 q^{77} +5.78207 q^{78} +16.4427 q^{79} +12.2726 q^{80} +1.00000 q^{81} -3.94372 q^{82} -6.28201 q^{83} -5.37215 q^{84} +29.1298 q^{85} +4.29037 q^{86} -5.96265 q^{87} +27.1835 q^{88} +4.23970 q^{89} -10.0344 q^{90} +3.37099 q^{91} -25.3168 q^{92} -2.07440 q^{93} +19.5321 q^{94} +6.06226 q^{95} +1.66173 q^{96} -3.19042 q^{97} +12.1148 q^{98} -6.19250 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 95 q - 9 q^{2} + 95 q^{3} + 65 q^{4} - 15 q^{5} - 9 q^{6} - 36 q^{7} - 27 q^{8} + 95 q^{9}+O(q^{10}) \) 95 * q - 9 * q^2 + 95 * q^3 + 65 * q^4 - 15 * q^5 - 9 * q^6 - 36 * q^7 - 27 * q^8 + 95 * q^9	\( 95 q - 9 q^{2} + 95 q^{3} + 65 q^{4} - 15 q^{5} - 9 q^{6} - 36 q^{7} - 27 q^{8} + 95 q^{9} - 36 q^{10} - 48 q^{11} + 65 q^{12} - 73 q^{13} - 17 q^{14} - 15 q^{15} + 13 q^{16} - 9 q^{17} - 9 q^{18} - 66 q^{19} - 35 q^{20} - 36 q^{21} - 37 q^{22} - 58 q^{23} - 27 q^{24} + 24 q^{25} - 25 q^{26} + 95 q^{27} - 75 q^{28} - 31 q^{29} - 36 q^{30} - 129 q^{31} - 53 q^{32} - 48 q^{33} - 61 q^{34} - 38 q^{35} + 65 q^{36} - 127 q^{37} + q^{38} - 73 q^{39} - 74 q^{40} - 31 q^{41} - 17 q^{42} - 62 q^{43} - 76 q^{44} - 15 q^{45} - 60 q^{46} - 75 q^{47} + 13 q^{48} + 5 q^{49} - 30 q^{50} - 9 q^{51} - 137 q^{52} - 28 q^{53} - 9 q^{54} - 117 q^{55} - 23 q^{56} - 66 q^{57} - 90 q^{58} - 60 q^{59} - 35 q^{60} - 96 q^{61} + 10 q^{62} - 36 q^{63} - 75 q^{64} - 28 q^{65} - 37 q^{66} - 116 q^{67} + 3 q^{68} - 58 q^{69} - 73 q^{70} - 144 q^{71} - 27 q^{72} - 121 q^{73} - 16 q^{74} + 24 q^{75} - 118 q^{76} - 3 q^{77} - 25 q^{78} - 135 q^{79} - 36 q^{80} + 95 q^{81} - 102 q^{82} - 21 q^{83} - 75 q^{84} - 129 q^{85} - 46 q^{86} - 31 q^{87} - 77 q^{88} - 63 q^{89} - 36 q^{90} - 123 q^{91} - 42 q^{92} - 129 q^{93} - 44 q^{94} - 80 q^{95} - 53 q^{96} - 144 q^{97} + 10 q^{98} - 48 q^{99}+O(q^{100}) \) 95 * q - 9 * q^2 + 95 * q^3 + 65 * q^4 - 15 * q^5 - 9 * q^6 - 36 * q^7 - 27 * q^8 + 95 * q^9 - 36 * q^10 - 48 * q^11 + 65 * q^12 - 73 * q^13 - 17 * q^14 - 15 * q^15 + 13 * q^16 - 9 * q^17 - 9 * q^18 - 66 * q^19 - 35 * q^20 - 36 * q^21 - 37 * q^22 - 58 * q^23 - 27 * q^24 + 24 * q^25 - 25 * q^26 + 95 * q^27 - 75 * q^28 - 31 * q^29 - 36 * q^30 - 129 * q^31 - 53 * q^32 - 48 * q^33 - 61 * q^34 - 38 * q^35 + 65 * q^36 - 127 * q^37 + q^38 - 73 * q^39 - 74 * q^40 - 31 * q^41 - 17 * q^42 - 62 * q^43 - 76 * q^44 - 15 * q^45 - 60 * q^46 - 75 * q^47 + 13 * q^48 + 5 * q^49 - 30 * q^50 - 9 * q^51 - 137 * q^52 - 28 * q^53 - 9 * q^54 - 117 * q^55 - 23 * q^56 - 66 * q^57 - 90 * q^58 - 60 * q^59 - 35 * q^60 - 96 * q^61 + 10 * q^62 - 36 * q^63 - 75 * q^64 - 28 * q^65 - 37 * q^66 - 116 * q^67 + 3 * q^68 - 58 * q^69 - 73 * q^70 - 144 * q^71 - 27 * q^72 - 121 * q^73 - 16 * q^74 + 24 * q^75 - 118 * q^76 - 3 * q^77 - 25 * q^78 - 135 * q^79 - 36 * q^80 + 95 * q^81 - 102 * q^82 - 21 * q^83 - 75 * q^84 - 129 * q^85 - 46 * q^86 - 31 * q^87 - 77 * q^88 - 63 * q^89 - 36 * q^90 - 123 * q^91 - 42 * q^92 - 129 * q^93 - 44 * q^94 - 80 * q^95 - 53 * q^96 - 144 * q^97 + 10 * q^98 - 48 * q^99

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