LMFDB - Embedded newform 8033.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8033,2,Mod(1,8033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8033, 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("8033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8033 = 29 \cdot 277 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8033.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:	$64.1438279437$
Analytic rank:	$1$
Dimension:	$154$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	8033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.82218 q^{2} +1.84090 q^{3} +5.96471 q^{4} -0.0331224 q^{5} -5.19535 q^{6} +1.38101 q^{7} -11.1891 q^{8} +0.388906 q^{9} +O(q^{10})$	\(q-2.82218 q^{2} +1.84090 q^{3} +5.96471 q^{4} -0.0331224 q^{5} -5.19535 q^{6} +1.38101 q^{7} -11.1891 q^{8} +0.388906 q^{9} +0.0934774 q^{10} +5.36001 q^{11} +10.9804 q^{12} -3.33289 q^{13} -3.89746 q^{14} -0.0609750 q^{15} +19.6483 q^{16} +5.20672 q^{17} -1.09756 q^{18} -4.98067 q^{19} -0.197566 q^{20} +2.54230 q^{21} -15.1269 q^{22} -1.57301 q^{23} -20.5981 q^{24} -4.99890 q^{25} +9.40602 q^{26} -4.80676 q^{27} +8.23733 q^{28} +1.00000 q^{29} +0.172082 q^{30} +6.11201 q^{31} -33.0729 q^{32} +9.86724 q^{33} -14.6943 q^{34} -0.0457424 q^{35} +2.31971 q^{36} +10.6174 q^{37} +14.0563 q^{38} -6.13551 q^{39} +0.370611 q^{40} -11.4751 q^{41} -7.17483 q^{42} -4.28065 q^{43} +31.9709 q^{44} -0.0128815 q^{45} +4.43932 q^{46} -10.5792 q^{47} +36.1706 q^{48} -5.09281 q^{49} +14.1078 q^{50} +9.58504 q^{51} -19.8797 q^{52} +3.41995 q^{53} +13.5655 q^{54} -0.177537 q^{55} -15.4523 q^{56} -9.16890 q^{57} -2.82218 q^{58} -5.13617 q^{59} -0.363698 q^{60} -14.2040 q^{61} -17.2492 q^{62} +0.537083 q^{63} +54.0411 q^{64} +0.110393 q^{65} -27.8471 q^{66} -0.882964 q^{67} +31.0566 q^{68} -2.89575 q^{69} +0.129093 q^{70} -8.19808 q^{71} -4.35152 q^{72} -15.9154 q^{73} -29.9644 q^{74} -9.20247 q^{75} -29.7082 q^{76} +7.40224 q^{77} +17.3155 q^{78} -9.80982 q^{79} -0.650800 q^{80} -10.0155 q^{81} +32.3848 q^{82} -15.1356 q^{83} +15.1641 q^{84} -0.172459 q^{85} +12.0808 q^{86} +1.84090 q^{87} -59.9739 q^{88} +12.8508 q^{89} +0.0363539 q^{90} -4.60276 q^{91} -9.38254 q^{92} +11.2516 q^{93} +29.8564 q^{94} +0.164972 q^{95} -60.8839 q^{96} -1.24925 q^{97} +14.3728 q^{98} +2.08454 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 154 q - 12 q^{2} - 36 q^{3} + 142 q^{4} - 9 q^{5} - 11 q^{6} - 68 q^{7} - 33 q^{8} + 146 q^{9}+O(q^{10}) $ 154 * q - 12 * q^2 - 36 * q^3 + 142 * q^4 - 9 * q^5 - 11 * q^6 - 68 * q^7 - 33 * q^8 + 146 * q^9	\( 154 q - 12 q^{2} - 36 q^{3} + 142 q^{4} - 9 q^{5} - 11 q^{6} - 68 q^{7} - 33 q^{8} + 146 q^{9} - 40 q^{10} - 36 q^{11} - 67 q^{12} - 51 q^{13} - 19 q^{14} - 48 q^{15} + 122 q^{16} - 54 q^{17} - 46 q^{18} - 73 q^{19} - 21 q^{20} - 8 q^{21} - 23 q^{22} - 38 q^{23} - 17 q^{24} + 133 q^{25} - 20 q^{26} - 129 q^{27} - 99 q^{28} + 154 q^{29} - 10 q^{30} - 91 q^{31} - 88 q^{32} - 39 q^{33} - 42 q^{34} - 36 q^{35} + 101 q^{36} - 50 q^{37} - 17 q^{38} - 33 q^{39} - 92 q^{40} - 31 q^{41} - 62 q^{42} - 154 q^{43} - 42 q^{44} - 14 q^{45} - 24 q^{46} - 140 q^{47} - 118 q^{48} + 126 q^{49} - 5 q^{50} - 16 q^{51} - 133 q^{52} - 40 q^{53} + 14 q^{54} - 203 q^{55} - 44 q^{56} - 16 q^{57} - 12 q^{58} + 5 q^{59} - 28 q^{60} - 106 q^{61} - 30 q^{62} - 145 q^{63} + 111 q^{64} - 15 q^{65} - 49 q^{66} - 78 q^{67} - 118 q^{68} - 32 q^{69} - 43 q^{70} - 4 q^{71} - 152 q^{72} - 137 q^{73} + 9 q^{74} - 129 q^{75} - 204 q^{76} - 76 q^{77} + 15 q^{78} - 141 q^{79} - 44 q^{80} + 122 q^{81} - 71 q^{82} - 90 q^{83} + 92 q^{84} - 41 q^{85} + 9 q^{86} - 36 q^{87} - 109 q^{88} - 51 q^{89} - 82 q^{90} - 22 q^{91} - 8 q^{92} - 10 q^{93} - 106 q^{94} - 55 q^{95} - 49 q^{96} - 140 q^{97} - 4 q^{98} - 101 q^{99}+O(q^{100}) \) 154 * q - 12 * q^2 - 36 * q^3 + 142 * q^4 - 9 * q^5 - 11 * q^6 - 68 * q^7 - 33 * q^8 + 146 * q^9 - 40 * q^10 - 36 * q^11 - 67 * q^12 - 51 * q^13 - 19 * q^14 - 48 * q^15 + 122 * q^16 - 54 * q^17 - 46 * q^18 - 73 * q^19 - 21 * q^20 - 8 * q^21 - 23 * q^22 - 38 * q^23 - 17 * q^24 + 133 * q^25 - 20 * q^26 - 129 * q^27 - 99 * q^28 + 154 * q^29 - 10 * q^30 - 91 * q^31 - 88 * q^32 - 39 * q^33 - 42 * q^34 - 36 * q^35 + 101 * q^36 - 50 * q^37 - 17 * q^38 - 33 * q^39 - 92 * q^40 - 31 * q^41 - 62 * q^42 - 154 * q^43 - 42 * q^44 - 14 * q^45 - 24 * q^46 - 140 * q^47 - 118 * q^48 + 126 * q^49 - 5 * q^50 - 16 * q^51 - 133 * q^52 - 40 * q^53 + 14 * q^54 - 203 * q^55 - 44 * q^56 - 16 * q^57 - 12 * q^58 + 5 * q^59 - 28 * q^60 - 106 * q^61 - 30 * q^62 - 145 * q^63 + 111 * q^64 - 15 * q^65 - 49 * q^66 - 78 * q^67 - 118 * q^68 - 32 * q^69 - 43 * q^70 - 4 * q^71 - 152 * q^72 - 137 * q^73 + 9 * q^74 - 129 * q^75 - 204 * q^76 - 76 * q^77 + 15 * q^78 - 141 * q^79 - 44 * q^80 + 122 * q^81 - 71 * q^82 - 90 * q^83 + 92 * q^84 - 41 * q^85 + 9 * q^86 - 36 * q^87 - 109 * q^88 - 51 * q^89 - 82 * q^90 - 22 * q^91 - 8 * q^92 - 10 * q^93 - 106 * q^94 - 55 * q^95 - 49 * q^96 - 140 * q^97 - 4 * q^98 - 101 * 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 $

$2$	−2.82218	−1.99558	−0.997792	−	0.0664173i	$-0.978843\pi$
$2$	−2.82218	−1.99558	−0.997792	+	0.0664173i	$0.978843\pi$
$3$	1.84090	1.06284	0.531422	−	0.847108i	$-0.321658\pi$
$3$	1.84090	1.06284	0.531422	+	0.847108i	$0.321658\pi$
$4$	5.96471	2.98235
$5$	−0.0331224	−0.0148128	−0.00740640	−	0.999973i	$-0.502358\pi$
$5$	−0.0331224	−0.0148128	−0.00740640	+	0.999973i	$0.502358\pi$
$6$	−5.19535	−2.12099
$7$	1.38101	0.521973	0.260986	−	0.965342i	$-0.415952\pi$
$7$	1.38101	0.521973	0.260986	+	0.965342i	$0.415952\pi$
$8$	−11.1891	−3.95596
$9$	0.388906	0.129635
$10$	0.0934774	0.0295602
$11$	5.36001	1.61611	0.808053	−	0.589110i	$-0.200522\pi$
$11$	5.36001	1.61611	0.808053	+	0.589110i	$0.200522\pi$
$12$	10.9804	3.16978
$13$	−3.33289	−0.924378	−0.462189	−	0.886782i	$-0.652936\pi$
$13$	−3.33289	−0.924378	−0.462189	+	0.886782i	$0.652936\pi$
$14$	−3.89746	−1.04164
$15$	−0.0609750	−0.0157437
$16$	19.6483	4.91209
$17$	5.20672	1.26281	0.631407	−	0.775451i	$-0.282478\pi$
$17$	5.20672	1.26281	0.631407	+	0.775451i	$0.282478\pi$
$18$	−1.09756	−0.258698
$19$	−4.98067	−1.14264	−0.571322	−	0.820726i	$-0.693569\pi$
$19$	−4.98067	−1.14264	−0.571322	+	0.820726i	$0.693569\pi$
$20$	−0.197566	−0.0441770
$21$	2.54230	0.554775
$22$	−15.1269	−3.22507
$23$	−1.57301	−0.327995	−0.163998	−	0.986461i	$-0.552439\pi$
$23$	−1.57301	−0.327995	−0.163998	+	0.986461i	$0.552439\pi$
$24$	−20.5981	−4.20456
$25$	−4.99890	−0.999781
$26$	9.40602	1.84467
$27$	−4.80676	−0.925061
$28$	8.23733	1.55671
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	0.172082	0.0314178
$31$	6.11201	1.09775	0.548875	−	0.835905i	$-0.315056\pi$
$31$	6.11201	1.09775	0.548875	+	0.835905i	$0.315056\pi$
$32$	−33.0729	−5.84652
$33$	9.86724	1.71767
$34$	−14.6943	−2.52005
$35$	−0.0457424	−0.00773188
$36$	2.31971	0.386619
$37$	10.6174	1.74550	0.872749	−	0.488170i	$-0.162335\pi$
$37$	10.6174	1.74550	0.872749	+	0.488170i	$0.162335\pi$
$38$	14.0563	2.28024
$39$	−6.13551	−0.982468
$40$	0.370611	0.0585987
$41$	−11.4751	−1.79211	−0.896055	−	0.443943i	$-0.853579\pi$
$41$	−11.4751	−1.79211	−0.896055	+	0.443943i	$0.853579\pi$
$42$	−7.17483	−1.10710
$43$	−4.28065	−0.652793	−0.326396	−	0.945233i	$-0.605834\pi$
$43$	−4.28065	−0.652793	−0.326396	+	0.945233i	$0.605834\pi$
$44$	31.9709	4.81980
$45$	−0.0128815	−0.00192026
$46$	4.43932	0.654542
$47$	−10.5792	−1.54314	−0.771568	−	0.636147i	$-0.780527\pi$
$47$	−10.5792	−1.54314	−0.771568	+	0.636147i	$0.780527\pi$
$48$	36.1706	5.22078
$49$	−5.09281	−0.727544
$50$	14.1078	1.99515
$51$	9.58504	1.34217
$52$	−19.8797	−2.75682
$53$	3.41995	0.469766	0.234883	−	0.972024i	$-0.424529\pi$
$53$	3.41995	0.469766	0.234883	+	0.972024i	$0.424529\pi$
$54$	13.5655	1.84604
$55$	−0.177537	−0.0239390
$56$	−15.4523	−2.06490
$57$	−9.16890	−1.21445
$58$	−2.82218	−0.370571
$59$	−5.13617	−0.668673	−0.334336	−	0.942454i	$-0.608512\pi$
$59$	−5.13617	−0.668673	−0.334336	+	0.942454i	$0.608512\pi$
$60$	−0.363698	−0.0469532
$61$	−14.2040	−1.81863	−0.909316	−	0.416107i	$-0.863394\pi$
$61$	−14.2040	−1.81863	−0.909316	+	0.416107i	$0.863394\pi$
$62$	−17.2492	−2.19065
$63$	0.537083	0.0676662
$64$	54.0411	6.75514
$65$	0.110393	0.0136926
$66$	−27.8471	−3.42775
$67$	−0.882964	−0.107871	−0.0539356	−	0.998544i	$-0.517177\pi$
$67$	−0.882964	−0.107871	−0.0539356	+	0.998544i	$0.517177\pi$
$68$	31.0566	3.76616
$69$	−2.89575	−0.348607
$70$	0.129093	0.0154296
$71$	−8.19808	−0.972933	−0.486467	−	0.873699i	$-0.661714\pi$
$71$	−8.19808	−0.972933	−0.486467	+	0.873699i	$0.661714\pi$
$72$	−4.35152	−0.512832
$73$	−15.9154	−1.86276	−0.931381	−	0.364046i	$-0.881395\pi$
$73$	−15.9154	−1.86276	−0.931381	+	0.364046i	$0.881395\pi$
$74$	−29.9644	−3.48329
$75$	−9.20247	−1.06261
$76$	−29.7082	−3.40777
$77$	7.40224	0.843563
$78$	17.3155	1.96060
$79$	−9.80982	−1.10369	−0.551846	−	0.833946i	$-0.686076\pi$
$79$	−9.80982	−1.10369	−0.551846	+	0.833946i	$0.686076\pi$
$80$	−0.650800	−0.0727617
$81$	−10.0155	−1.11283
$82$	32.3848	3.57631
$83$	−15.1356	−1.66135	−0.830676	−	0.556757i	$-0.812046\pi$
$83$	−15.1356	−1.66135	−0.830676	+	0.556757i	$0.812046\pi$
$84$	15.1641	1.65454
$85$	−0.172459	−0.0187058
$86$	12.0808	1.30270
$87$	1.84090	0.197365
$88$	−59.9739	−6.39324
$89$	12.8508	1.36218	0.681090	−	0.732199i	$-0.261506\pi$
$89$	12.8508	1.36218	0.681090	+	0.732199i	$0.261506\pi$
$90$	0.0363539	0.00383204
$91$	−4.60276	−0.482500
$92$	−9.38254	−0.978198
$93$	11.2516	1.16674
$94$	29.8564	3.07946
$95$	0.164972	0.0169257
$96$	−60.8839	−6.21394
$97$	−1.24925	−0.126842	−0.0634211	−	0.997987i	$-0.520201\pi$
$97$	−1.24925	−0.126842	−0.0634211	+	0.997987i	$0.520201\pi$
$98$	14.3728	1.45188
$99$	2.08454	0.209504
$100$	−29.8170	−2.98170
$101$	14.8626	1.47888	0.739442	−	0.673220i	$-0.235089\pi$
$101$	14.8626	1.47888	0.739442	+	0.673220i	$0.235089\pi$
$102$	−27.0507	−2.67842
$103$	−16.5109	−1.62686	−0.813432	−	0.581660i	$-0.802403\pi$
$103$	−16.5109	−1.62686	−0.813432	+	0.581660i	$0.802403\pi$
$104$	37.2922	3.65680
$105$	−0.0842071	−0.00821777
$106$	−9.65172	−0.937458
$107$	4.32116	0.417742	0.208871	−	0.977943i	$-0.433021\pi$
$107$	4.32116	0.417742	0.208871	+	0.977943i	$0.433021\pi$
$108$	−28.6709	−2.75886
$109$	4.71263	0.451388	0.225694	−	0.974198i	$-0.427535\pi$
$109$	4.71263	0.451388	0.225694	+	0.974198i	$0.427535\pi$
$110$	0.501040	0.0477723
$111$	19.5456	1.85519
$112$	27.1346	2.56398
$113$	13.5279	1.27259	0.636297	−	0.771444i	$-0.280465\pi$
$113$	13.5279	1.27259	0.636297	+	0.771444i	$0.280465\pi$
$114$	25.8763	2.42354
$115$	0.0521019	0.00485852
$116$	5.96471	0.553809
$117$	−1.29618	−0.119832
$118$	14.4952	1.33439
$119$	7.19053	0.659155
$120$	0.682257	0.0622813
$121$	17.7298	1.61180
$122$	40.0862	3.62923
$123$	−21.1245	−1.90473
$124$	36.4564	3.27388
$125$	0.331188	0.0296223
$126$	−1.51575	−0.135033
$127$	−4.72631	−0.419392	−0.209696	−	0.977767i	$-0.567247\pi$
$127$	−4.72631	−0.419392	−0.209696	+	0.977767i	$0.567247\pi$
$128$	−86.3681	−7.63393
$129$	−7.88024	−0.693816
$130$	−0.311550	−0.0273248
$131$	2.64540	0.231130	0.115565	−	0.993300i	$-0.463132\pi$
$131$	2.64540	0.231130	0.115565	+	0.993300i	$0.463132\pi$
$132$	58.8552	5.12269
$133$	−6.87835	−0.596429
$134$	2.49188	0.215266
$135$	0.159211	0.0137027
$136$	−58.2587	−4.99564
$137$	11.7068	1.00018	0.500089	−	0.865974i	$-0.333301\pi$
$137$	11.7068	1.00018	0.500089	+	0.865974i	$0.333301\pi$
$138$	8.17233	0.695675
$139$	−3.98571	−0.338063	−0.169032	−	0.985611i	$-0.554064\pi$
$139$	−3.98571	−0.338063	−0.169032	+	0.985611i	$0.554064\pi$
$140$	−0.272840	−0.0230592
$141$	−19.4752	−1.64011
$142$	23.1365	1.94157
$143$	−17.8643	−1.49389
$144$	7.64136	0.636780
$145$	−0.0331224	−0.00275067
$146$	44.9163	3.71730
$147$	−9.37534	−0.773265
$148$	63.3300	5.20569
$149$	10.7166	0.877937	0.438968	−	0.898502i	$-0.355344\pi$
$149$	10.7166	0.877937	0.438968	+	0.898502i	$0.355344\pi$
$150$	25.9710	2.12053
$151$	0.972911	0.0791744	0.0395872	−	0.999216i	$-0.487396\pi$
$151$	0.972911	0.0791744	0.0395872	+	0.999216i	$0.487396\pi$
$152$	55.7293	4.52025
$153$	2.02492	0.163705
$154$	−20.8905	−1.68340
$155$	−0.202445	−0.0162607
$156$	−36.5966	−2.93007
$157$	−12.5991	−1.00552	−0.502759	−	0.864427i	$-0.667682\pi$
$157$	−12.5991	−1.00552	−0.502759	+	0.864427i	$0.667682\pi$
$158$	27.6851	2.20251
$159$	6.29578	0.499288
$160$	1.09546	0.0866033
$161$	−2.17234	−0.171205
$162$	28.2655	2.22075
$163$	4.07168	0.318919	0.159459	−	0.987204i	$-0.449025\pi$
$163$	4.07168	0.318919	0.159459	+	0.987204i	$0.449025\pi$
$164$	−68.4457	−5.34471
$165$	−0.326827	−0.0254434
$166$	42.7155	3.31537
$167$	14.2166	1.10011	0.550057	−	0.835127i	$-0.314606\pi$
$167$	14.2166	1.10011	0.550057	+	0.835127i	$0.314606\pi$
$168$	−28.4461	−2.19467
$169$	−1.89184	−0.145526
$170$	0.486711	0.0373290
$171$	−1.93701	−0.148127
$172$	−25.5328	−1.94686
$173$	−3.23652	−0.246068	−0.123034	−	0.992402i	$-0.539262\pi$
$173$	−3.23652	−0.246068	−0.123034	+	0.992402i	$0.539262\pi$
$174$	−5.19535	−0.393858
$175$	−6.90354	−0.521858
$176$	105.315	7.93845
$177$	−9.45517	−0.710694
$178$	−36.2673	−2.71835
$179$	−1.76550	−0.131960	−0.0659798	−	0.997821i	$-0.521017\pi$
$179$	−1.76550	−0.131960	−0.0659798	+	0.997821i	$0.521017\pi$
$180$	−0.0768344	−0.00572690
$181$	−20.9122	−1.55439	−0.777195	−	0.629260i	$-0.783358\pi$
$181$	−20.9122	−1.55439	−0.777195	+	0.629260i	$0.783358\pi$
$182$	12.9898	0.962869
$183$	−26.1481	−1.93292
$184$	17.6006	1.29753
$185$	−0.351675	−0.0258557
$186$	−31.7540	−2.32832
$187$	27.9081	2.04084
$188$	−63.1019	−4.60218
$189$	−6.63818	−0.482857
$190$	−0.465580	−0.0337767
$191$	−10.2802	−0.743847	−0.371923	−	0.928263i	$-0.621302\pi$
$191$	−10.2802	−0.743847	−0.371923	+	0.928263i	$0.621302\pi$
$192$	99.4843	7.17966
$193$	−7.04816	−0.507338	−0.253669	−	0.967291i	$-0.581637\pi$
$193$	−7.04816	−0.507338	−0.253669	+	0.967291i	$0.581637\pi$
$194$	3.52561	0.253124
$195$	0.203223	0.0145531
$196$	−30.3771	−2.16980
$197$	−1.13851	−0.0811157	−0.0405579	−	0.999177i	$-0.512914\pi$
$197$	−1.13851	−0.0811157	−0.0405579	+	0.999177i	$0.512914\pi$
$198$	−5.88296	−0.418084
$199$	−10.0017	−0.708998	−0.354499	−	0.935056i	$-0.615349\pi$
$199$	−10.0017	−0.708998	−0.354499	+	0.935056i	$0.615349\pi$
$200$	55.9334	3.95509
$201$	−1.62545	−0.114650
$202$	−41.9450	−2.95124
$203$	1.38101	0.0969279
$204$	57.1720	4.00284
$205$	0.380083	0.0265462
$206$	46.5967	3.24654
$207$	−0.611753	−0.0425198
$208$	−65.4858	−4.54062
$209$	−26.6964	−1.84663
$210$	0.237648	0.0163993
$211$	−1.11921	−0.0770498	−0.0385249	−	0.999258i	$-0.512266\pi$
$211$	−1.11921	−0.0770498	−0.0385249	+	0.999258i	$0.512266\pi$
$212$	20.3990	1.40101
$213$	−15.0918	−1.03408
$214$	−12.1951	−0.833640
$215$	0.141785	0.00966968
$216$	53.7835	3.65950
$217$	8.44075	0.572996
$218$	−13.2999	−0.900783
$219$	−29.2987	−1.97982
$220$	−1.05895	−0.0713947
$221$	−17.3534	−1.16732
$222$	−55.1613	−3.70219
$223$	13.8658	0.928522	0.464261	−	0.885699i	$-0.346320\pi$
$223$	13.8658	0.928522	0.464261	+	0.885699i	$0.346320\pi$
$224$	−45.6741	−3.05173
$225$	−1.94410	−0.129607
$226$	−38.1781	−2.53957
$227$	−11.7033	−0.776777	−0.388389	−	0.921496i	$-0.626968\pi$
$227$	−11.7033	−0.776777	−0.388389	+	0.921496i	$0.626968\pi$
$228$	−54.6898	−3.62192
$229$	11.1664	0.737897	0.368949	−	0.929450i	$-0.379718\pi$
$229$	11.1664	0.737897	0.368949	+	0.929450i	$0.379718\pi$
$230$	−0.147041	−0.00969559
$231$	13.6268	0.896575
$232$	−11.1891	−0.734603
$233$	−7.49585	−0.491069	−0.245535	−	0.969388i	$-0.578964\pi$
$233$	−7.49585	−0.491069	−0.245535	+	0.969388i	$0.578964\pi$
$234$	3.65806	0.239135
$235$	0.350409	0.0228581
$236$	−30.6358	−1.99422
$237$	−18.0589	−1.17305
$238$	−20.2930	−1.31540
$239$	11.9851	0.775250	0.387625	−	0.921817i	$-0.373296\pi$
$239$	11.9851	0.775250	0.387625	+	0.921817i	$0.373296\pi$
$240$	−1.19806	−0.0773343
$241$	5.56196	0.358277	0.179139	−	0.983824i	$-0.442669\pi$
$241$	5.56196	0.358277	0.179139	+	0.983824i	$0.442669\pi$
$242$	−50.0366	−3.21647
$243$	−4.01719	−0.257703
$244$	−84.7225	−5.42381
$245$	0.168686	0.0107770
$246$	59.6172	3.80105
$247$	16.6000	1.05623
$248$	−68.3881	−4.34265
$249$	−27.8632	−1.76576
$250$	−0.934672	−0.0591138
$251$	4.94828	0.312333	0.156166	−	0.987731i	$-0.450086\pi$
$251$	4.94828	0.312333	0.156166	+	0.987731i	$0.450086\pi$
$252$	3.20355	0.201804
$253$	−8.43135	−0.530075
$254$	13.3385	0.836933
$255$	−0.317479	−0.0198813
$256$	135.664	8.47901
$257$	11.1201	0.693650	0.346825	−	0.937930i	$-0.387260\pi$
$257$	11.1201	0.693650	0.346825	+	0.937930i	$0.387260\pi$
$258$	22.2395	1.38457
$259$	14.6628	0.911103
$260$	0.658464	0.0408362
$261$	0.388906	0.0240727
$262$	−7.46580	−0.461239
$263$	−18.1466	−1.11897	−0.559484	−	0.828841i	$-0.689001\pi$
$263$	−18.1466	−1.11897	−0.559484	+	0.828841i	$0.689001\pi$
$264$	−110.406	−6.79501
$265$	−0.113277	−0.00695855
$266$	19.4120	1.19022
$267$	23.6570	1.44778
$268$	−5.26662	−0.321710
$269$	23.1142	1.40930	0.704650	−	0.709555i	$-0.251104\pi$
$269$	23.1142	1.40930	0.704650	+	0.709555i	$0.251104\pi$
$270$	−0.449323	−0.0273450
$271$	2.86214	0.173863	0.0869314	−	0.996214i	$-0.472294\pi$
$271$	2.86214	0.173863	0.0869314	+	0.996214i	$0.472294\pi$
$272$	102.303	6.20305
$273$	−8.47321	−0.512822
$274$	−33.0386	−1.99594
$275$	−26.7942	−1.61575
$276$	−17.2723	−1.03967
$277$	1.00000	0.0600842
$277$	1.00000	0.0600842
$278$	11.2484	0.674634
$279$	2.37700	0.142307
$280$	0.511818	0.0305870
$281$	29.3061	1.74825	0.874126	−	0.485699i	$-0.161435\pi$
$281$	29.3061	1.74825	0.874126	+	0.485699i	$0.161435\pi$
$282$	54.9626	3.27298
$283$	−3.81395	−0.226716	−0.113358	−	0.993554i	$-0.536161\pi$
$283$	−3.81395	−0.226716	−0.113358	+	0.993554i	$0.536161\pi$
$284$	−48.8992	−2.90163
$285$	0.303696	0.0179894
$286$	50.4164	2.98119
$287$	−15.8472	−0.935433
$288$	−12.8623	−0.757916
$289$	10.1099	0.594700
$290$	0.0934774	0.00548918
$291$	−2.29974	−0.134813
$292$	−94.9310	−5.55542
$293$	−18.6153	−1.08752	−0.543759	−	0.839241i	$-0.683000\pi$
$293$	−18.6153	−1.08752	−0.543759	+	0.839241i	$0.683000\pi$
$294$	26.4589	1.54312
$295$	0.170122	0.00990491
$296$	−118.800	−6.90511
$297$	−25.7643	−1.49500
$298$	−30.2442	−1.75200
$299$	5.24267	0.303191
$300$	−54.8901	−3.16908
$301$	−5.91162	−0.340740
$302$	−2.74573	−0.157999
$303$	27.3605	1.57182
$304$	−97.8618	−5.61276
$305$	0.470470	0.0269390
$306$	−5.71470	−0.326688
$307$	1.42569	0.0813685	0.0406843	−	0.999172i	$-0.487046\pi$
$307$	1.42569	0.0813685	0.0406843	+	0.999172i	$0.487046\pi$
$308$	44.1522	2.51580
$309$	−30.3948	−1.72910
$310$	0.571335	0.0324497
$311$	6.23181	0.353374	0.176687	−	0.984267i	$-0.443462\pi$
$311$	6.23181	0.353374	0.176687	+	0.984267i	$0.443462\pi$
$312$	68.6511	3.88660
$313$	−11.3502	−0.641549	−0.320774	−	0.947156i	$-0.603943\pi$
$313$	−11.3502	−0.641549	−0.320774	+	0.947156i	$0.603943\pi$
$314$	35.5570	2.00660
$315$	−0.0177895	−0.00100232
$316$	−58.5127	−3.29160
$317$	−23.2866	−1.30790	−0.653952	−	0.756536i	$-0.726890\pi$
$317$	−23.2866	−1.30790	−0.653952	+	0.756536i	$0.726890\pi$
$318$	−17.7678	−0.996371
$319$	5.36001	0.300103
$320$	−1.78997	−0.100063
$321$	7.95481	0.443994
$322$	6.13075	0.341653
$323$	−25.9329	−1.44295
$324$	−59.7394	−3.31885
$325$	16.6608	0.924175
$326$	−11.4910	−0.636429
$327$	8.67547	0.479755
$328$	128.396	7.08951
$329$	−14.6100	−0.805475
$330$	0.922364	0.0507745
$331$	4.68008	0.257240	0.128620	−	0.991694i	$-0.458945\pi$
$331$	4.68008	0.257240	0.128620	+	0.991694i	$0.458945\pi$
$332$	−90.2796	−4.95474
$333$	4.12919	0.226278
$334$	−40.1218	−2.19537
$335$	0.0292459	0.00159787
$336$	49.9520	2.72510
$337$	14.1274	0.769570	0.384785	−	0.923006i	$-0.374276\pi$
$337$	14.1274	0.769570	0.384785	+	0.923006i	$0.374276\pi$
$338$	5.33911	0.290409
$339$	24.9034	1.35257
$340$	−1.02867	−0.0557874
$341$	32.7605	1.77408
$342$	5.46660	0.295600
$343$	−16.7003	−0.901731
$344$	47.8968	2.58242
$345$	0.0959142	0.00516385
$346$	9.13404	0.491049
$347$	−2.36819	−0.127131	−0.0635655	−	0.997978i	$-0.520247\pi$
$347$	−2.36819	−0.127131	−0.0635655	+	0.997978i	$0.520247\pi$
$348$	10.9804	0.588612
$349$	4.71387	0.252328	0.126164	−	0.992009i	$-0.459734\pi$
$349$	4.71387	0.252328	0.126164	+	0.992009i	$0.459734\pi$
$350$	19.4830	1.04141
$351$	16.0204	0.855106
$352$	−177.271	−9.44860
$353$	−18.0496	−0.960682	−0.480341	−	0.877082i	$-0.659487\pi$
$353$	−18.0496	−0.960682	−0.480341	+	0.877082i	$0.659487\pi$
$354$	26.6842	1.41825
$355$	0.271540	0.0144119
$356$	76.6512	4.06251
$357$	13.2370	0.700578
$358$	4.98256	0.263336
$359$	20.7492	1.09510	0.547549	−	0.836774i	$-0.315561\pi$
$359$	20.7492	1.09510	0.547549	+	0.836774i	$0.315561\pi$
$360$	0.144133	0.00759647
$361$	5.80703	0.305633
$362$	59.0179	3.10191
$363$	32.6387	1.71309
$364$	−27.4541	−1.43899
$365$	0.527158	0.0275927
$366$	73.7946	3.85730
$367$	−34.2217	−1.78636	−0.893179	−	0.449702i	$-0.851530\pi$
$367$	−34.2217	−1.78636	−0.893179	+	0.449702i	$0.851530\pi$
$368$	−30.9070	−1.61114
$369$	−4.46274	−0.232321
$370$	0.992492	0.0515972
$371$	4.72299	0.245205
$372$	67.1125	3.47962
$373$	−1.58170	−0.0818972	−0.0409486	−	0.999161i	$-0.513038\pi$
$373$	−1.58170	−0.0818972	−0.0409486	+	0.999161i	$0.513038\pi$
$374$	−78.7617	−4.07267
$375$	0.609683	0.0314839
$376$	118.372	6.10457
$377$	−3.33289	−0.171653
$378$	18.7342	0.963581
$379$	−9.22015	−0.473607	−0.236804	−	0.971558i	$-0.576100\pi$
$379$	−9.22015	−0.473607	−0.236804	+	0.971558i	$0.576100\pi$
$380$	0.984008	0.0504785
$381$	−8.70066	−0.445748
$382$	29.0125	1.48441
$383$	5.55000	0.283592	0.141796	−	0.989896i	$-0.454712\pi$
$383$	5.55000	0.283592	0.141796	+	0.989896i	$0.454712\pi$
$384$	−158.995	−8.11367
$385$	−0.245180	−0.0124955
$386$	19.8912	1.01243
$387$	−1.66477	−0.0846250
$388$	−7.45142	−0.378288
$389$	7.85534	0.398281	0.199141	−	0.979971i	$-0.436185\pi$
$389$	7.85534	0.398281	0.199141	+	0.979971i	$0.436185\pi$
$390$	−0.573532	−0.0290419
$391$	−8.19022	−0.414197
$392$	56.9841	2.87813
$393$	4.86992	0.245655
$394$	3.21309	0.161873
$395$	0.324925	0.0163487
$396$	12.4337	0.624816
$397$	6.66546	0.334530	0.167265	−	0.985912i	$-0.446507\pi$
$397$	6.66546	0.334530	0.167265	+	0.985912i	$0.446507\pi$
$398$	28.2265	1.41487
$399$	−12.6623	−0.633910
$400$	−98.2202	−4.91101
$401$	24.3325	1.21511	0.607553	−	0.794279i	$-0.292151\pi$
$401$	24.3325	1.21511	0.607553	+	0.794279i	$0.292151\pi$
$402$	4.58731	0.228794
$403$	−20.3707	−1.01474
$404$	88.6511	4.41056
$405$	0.331736	0.0164841
$406$	−3.89746	−0.193428
$407$	56.9097	2.82091
$408$	−107.248	−5.30958
$409$	22.2752	1.10144	0.550718	−	0.834691i	$-0.314354\pi$
$409$	22.2752	1.10144	0.550718	+	0.834691i	$0.314354\pi$
$410$	−1.07266	−0.0529751
$411$	21.5510	1.06303
$412$	−98.4825	−4.85188
$413$	−7.09311	−0.349029
$414$	1.72648	0.0848518
$415$	0.501328	0.0246092
$416$	110.228	5.40440
$417$	−7.33729	−0.359308
$418$	75.3422	3.68511
$419$	12.4466	0.608056	0.304028	−	0.952663i	$-0.401668\pi$
$419$	12.4466	0.608056	0.304028	+	0.952663i	$0.401668\pi$
$420$	−0.502271	−0.0245083
$421$	−26.2621	−1.27993	−0.639967	−	0.768402i	$-0.721052\pi$
$421$	−26.2621	−1.27993	−0.639967	+	0.768402i	$0.721052\pi$
$422$	3.15862	0.153759
$423$	−4.11432	−0.200045
$424$	−38.2663	−1.85838
$425$	−26.0279	−1.26254
$426$	42.5919	2.06358
$427$	−19.6158	−0.949277
$428$	25.7745	1.24586
$429$	−32.8864	−1.58777
$430$	−0.400144	−0.0192967
$431$	−31.4551	−1.51514	−0.757570	−	0.652753i	$-0.773614\pi$
$431$	−31.4551	−1.51514	−0.757570	+	0.652753i	$0.773614\pi$
$432$	−94.4448	−4.54398
$433$	13.8701	0.666552	0.333276	−	0.942829i	$-0.391846\pi$
$433$	13.8701	0.666552	0.333276	+	0.942829i	$0.391846\pi$
$434$	−23.8213	−1.14346
$435$	−0.0609750	−0.00292353
$436$	28.1095	1.34620
$437$	7.83463	0.374781
$438$	82.6863	3.95090
$439$	−29.6646	−1.41581	−0.707907	−	0.706305i	$-0.750361\pi$
$439$	−29.6646	−1.41581	−0.707907	+	0.706305i	$0.750361\pi$
$440$	1.98648	0.0947017
$441$	−1.98062	−0.0943155
$442$	48.9745	2.32948
$443$	−8.46938	−0.402392	−0.201196	−	0.979551i	$-0.564483\pi$
$443$	−8.46938	−0.402392	−0.201196	+	0.979551i	$0.564483\pi$
$444$	116.584	5.53284
$445$	−0.425649	−0.0201777
$446$	−39.1318	−1.85294
$447$	19.7281	0.933109
$448$	74.6314	3.52600
$449$	−11.0816	−0.522972	−0.261486	−	0.965207i	$-0.584213\pi$
$449$	−11.0816	−0.522972	−0.261486	+	0.965207i	$0.584213\pi$
$450$	5.48661	0.258641
$451$	−61.5067	−2.89624
$452$	80.6898	3.79533
$453$	1.79103	0.0841500
$454$	33.0289	1.55012
$455$	0.152454	0.00714717
$456$	102.592	4.80431
$457$	−18.6546	−0.872624	−0.436312	−	0.899795i	$-0.643716\pi$
$457$	−18.6546	−0.872624	−0.436312	+	0.899795i	$0.643716\pi$
$458$	−31.5136	−1.47254
$459$	−25.0274	−1.16818
$460$	0.310772	0.0144898
$461$	18.0801	0.842076	0.421038	−	0.907043i	$-0.361666\pi$
$461$	18.0801	0.842076	0.421038	+	0.907043i	$0.361666\pi$
$462$	−38.4572	−1.78919
$463$	33.7002	1.56618	0.783090	−	0.621908i	$-0.213642\pi$
$463$	33.7002	1.56618	0.783090	+	0.621908i	$0.213642\pi$
$464$	19.6483	0.912152
$465$	−0.372680	−0.0172826
$466$	21.1546	0.979970
$467$	−20.5903	−0.952807	−0.476404	−	0.879227i	$-0.658060\pi$
$467$	−20.5903	−0.952807	−0.476404	+	0.879227i	$0.658060\pi$
$468$	−7.73135	−0.357382
$469$	−1.21938	−0.0563059
$470$	−0.988917	−0.0456153
$471$	−23.1937	−1.06871
$472$	57.4693	2.64524
$473$	−22.9443	−1.05498
$474$	50.9654	2.34092
$475$	24.8979	1.14239
$476$	42.8894	1.96583
$477$	1.33004	0.0608983
$478$	−33.8241	−1.54708
$479$	23.5168	1.07451	0.537254	−	0.843420i	$-0.319462\pi$
$479$	23.5168	1.07451	0.537254	+	0.843420i	$0.319462\pi$
$480$	2.01662	0.0920458
$481$	−35.3868	−1.61350
$482$	−15.6969	−0.714972
$483$	−3.99906	−0.181964
$484$	105.753	4.80695
$485$	0.0413782	0.00187889
$486$	11.3372	0.514267
$487$	41.8468	1.89626	0.948130	−	0.317884i	$-0.102972\pi$
$487$	41.8468	1.89626	0.948130	+	0.317884i	$0.102972\pi$
$488$	158.930	7.19443
$489$	7.49555	0.338961
$490$	−0.476063	−0.0215063
$491$	−6.98677	−0.315309	−0.157654	−	0.987494i	$-0.550393\pi$
$491$	−6.98677	−0.315309	−0.157654	+	0.987494i	$0.550393\pi$
$492$	−126.002	−5.68059
$493$	5.20672	0.234499
$494$	−46.8483	−2.10780
$495$	−0.0690450	−0.00310334
$496$	120.091	5.39224
$497$	−11.3216	−0.507845
$498$	78.6349	3.52371
$499$	−5.41575	−0.242442	−0.121221	−	0.992626i	$-0.538681\pi$
$499$	−5.41575	−0.242442	−0.121221	+	0.992626i	$0.538681\pi$
$500$	1.97544	0.0883443
$501$	26.1713	1.16925
$502$	−13.9650	−0.623287
$503$	3.96120	0.176621	0.0883106	−	0.996093i	$-0.471853\pi$
$503$	3.96120	0.176621	0.0883106	+	0.996093i	$0.471853\pi$
$504$	−6.00950	−0.267684
$505$	−0.492285	−0.0219064
$506$	23.7948	1.05781
$507$	−3.48268	−0.154671
$508$	−28.1911	−1.25078
$509$	29.6123	1.31254	0.656272	−	0.754525i	$-0.272132\pi$
$509$	29.6123	1.31254	0.656272	+	0.754525i	$0.272132\pi$
$510$	0.895985	0.0396749
$511$	−21.9794	−0.972311
$512$	−210.133	−9.28664
$513$	23.9409	1.05701
$514$	−31.3828	−1.38424
$515$	0.546879	0.0240984
$516$	−47.0033	−2.06921
$517$	−56.7047	−2.49387
$518$	−41.3811	−1.81818
$519$	−5.95810	−0.261532
$520$	−1.23521	−0.0541674
$521$	38.6486	1.69323	0.846613	−	0.532209i	$-0.178638\pi$
$521$	38.6486	1.69323	0.846613	+	0.532209i	$0.178638\pi$
$522$	−1.09756	−0.0480391
$523$	−21.9042	−0.957804	−0.478902	−	0.877868i	$-0.658965\pi$
$523$	−21.9042	−0.957804	−0.478902	+	0.877868i	$0.658965\pi$
$524$	15.7791	0.689311
$525$	−12.7087	−0.554654
$526$	51.2130	2.23299
$527$	31.8235	1.38625
$528$	193.875	8.43732
$529$	−20.5256	−0.892419
$530$	0.319688	0.0138864
$531$	−1.99749	−0.0866836
$532$	−41.0274	−1.77876
$533$	38.2453	1.65659
$534$	−66.7643	−2.88918
$535$	−0.143127	−0.00618793
$536$	9.87960	0.426734
$537$	−3.25010	−0.140252
$538$	−65.2326	−2.81238
$539$	−27.2975	−1.17579
$540$	0.949650	0.0408664
$541$	−24.8152	−1.06689	−0.533445	−	0.845835i	$-0.679103\pi$
$541$	−24.8152	−1.06689	−0.533445	+	0.845835i	$0.679103\pi$
$542$	−8.07749	−0.346958
$543$	−38.4972	−1.65207
$544$	−172.201	−7.38308
$545$	−0.156094	−0.00668632
$546$	23.9129	1.02338
$547$	27.5057	1.17606	0.588029	−	0.808840i	$-0.299904\pi$
$547$	27.5057	1.17606	0.588029	+	0.808840i	$0.299904\pi$
$548$	69.8275	2.98288
$549$	−5.52401	−0.235759
$550$	75.6181	3.22437
$551$	−4.98067	−0.212183
$552$	32.4009	1.37908
$553$	−13.5475	−0.576097
$554$	−2.82218	−0.119903
$555$	−0.647399	−0.0274805
$556$	−23.7736	−1.00823
$557$	8.77003	0.371598	0.185799	−	0.982588i	$-0.440513\pi$
$557$	8.77003	0.371598	0.185799	+	0.982588i	$0.440513\pi$
$558$	−6.70832	−0.283986
$559$	14.2669	0.603427
$560$	−0.898762	−0.0379796
$561$	51.3759	2.16909
$562$	−82.7070	−3.48878
$563$	−25.5148	−1.07532	−0.537659	−	0.843162i	$-0.680691\pi$
$563$	−25.5148	−1.07532	−0.537659	+	0.843162i	$0.680691\pi$
$564$	−116.164	−4.89139
$565$	−0.448075	−0.0188507
$566$	10.7637	0.452430
$567$	−13.8315	−0.580867
$568$	91.7294	3.84888
$569$	45.8273	1.92118	0.960589	−	0.277971i	$-0.0896619\pi$
$569$	45.8273	1.92118	0.960589	+	0.277971i	$0.0896619\pi$
$570$	−0.857085	−0.0358993
$571$	3.34739	0.140084	0.0700419	−	0.997544i	$-0.477687\pi$
$571$	3.34739	0.140084	0.0700419	+	0.997544i	$0.477687\pi$
$572$	−106.556	−4.45531
$573$	−18.9247	−0.790592
$574$	44.7238	1.86674
$575$	7.86332	0.327923
$576$	21.0169	0.875705
$577$	11.3835	0.473899	0.236950	−	0.971522i	$-0.423852\pi$
$577$	11.3835	0.473899	0.236950	+	0.971522i	$0.423852\pi$
$578$	−28.5320	−1.18677
$579$	−12.9749	−0.539220
$580$	−0.197566	−0.00820346
$581$	−20.9025	−0.867180
$582$	6.49029	0.269031
$583$	18.3310	0.759192
$584$	178.080	7.36900
$585$	0.0429326	0.00177505
$586$	52.5358	2.17023
$587$	−21.5356	−0.888868	−0.444434	−	0.895812i	$-0.646595\pi$
$587$	−21.5356	−0.888868	−0.444434	+	0.895812i	$0.646595\pi$
$588$	−55.9212	−2.30615
$589$	−30.4419	−1.25434
$590$	−0.480116	−0.0197661
$591$	−2.09589	−0.0862133
$592$	208.615	8.57403
$593$	−26.3637	−1.08263	−0.541314	−	0.840820i	$-0.682073\pi$
$593$	−26.3637	−1.08263	−0.541314	+	0.840820i	$0.682073\pi$
$594$	72.7115	2.98339
$595$	−0.238168	−0.00976393
$596$	63.9213	2.61832
$597$	−18.4120	−0.753554
$598$	−14.7958	−0.605044
$599$	6.46669	0.264222	0.132111	−	0.991235i	$-0.457824\pi$
$599$	6.46669	0.264222	0.132111	+	0.991235i	$0.457824\pi$
$600$	102.968	4.20364
$601$	−16.5282	−0.674198	−0.337099	−	0.941469i	$-0.609446\pi$
$601$	−16.5282	−0.674198	−0.337099	+	0.941469i	$0.609446\pi$
$602$	16.6837	0.679976
$603$	−0.343390	−0.0139839
$604$	5.80313	0.236126
$605$	−0.587252	−0.0238752
$606$	−77.2164	−3.13670
$607$	12.9254	0.524626	0.262313	−	0.964983i	$-0.415515\pi$
$607$	12.9254	0.524626	0.262313	+	0.964983i	$0.415515\pi$
$608$	164.725	6.68049
$609$	2.54230	0.103019
$610$	−1.32775	−0.0537591
$611$	35.2593	1.42644
$612$	12.0781	0.488228
$613$	−11.7515	−0.474637	−0.237319	−	0.971432i	$-0.576269\pi$
$613$	−11.7515	−0.474637	−0.237319	+	0.971432i	$0.576269\pi$
$614$	−4.02356	−0.162378
$615$	0.699694	0.0282144
$616$	−82.8246	−3.33710
$617$	−22.2796	−0.896945	−0.448472	−	0.893797i	$-0.648032\pi$
$617$	−22.2796	−0.896945	−0.448472	+	0.893797i	$0.648032\pi$
$618$	85.7797	3.45057
$619$	4.34835	0.174775	0.0873875	−	0.996174i	$-0.472148\pi$
$619$	4.34835	0.174775	0.0873875	+	0.996174i	$0.472148\pi$
$620$	−1.20752	−0.0484953
$621$	7.56108	0.303415
$622$	−17.5873	−0.705187
$623$	17.7471	0.711022
$624$	−120.553	−4.82597
$625$	24.9835	0.999342
$626$	32.0322	1.28026
$627$	−49.1454	−1.96268
$628$	−75.1500	−2.99881
$629$	55.2821	2.20424
$630$	0.0502052	0.00200022
$631$	21.4306	0.853139	0.426569	−	0.904455i	$-0.359722\pi$
$631$	21.4306	0.853139	0.426569	+	0.904455i	$0.359722\pi$
$632$	109.763	4.36615
$633$	−2.06036	−0.0818919
$634$	65.7189	2.61003
$635$	0.156547	0.00621237
$636$	37.5525	1.48905
$637$	16.9738	0.672526
$638$	−15.1269	−0.598881
$639$	−3.18828	−0.126127
$640$	2.86072	0.113080
$641$	34.4643	1.36126	0.680630	−	0.732627i	$-0.261706\pi$
$641$	34.4643	1.36126	0.680630	+	0.732627i	$0.261706\pi$
$642$	−22.4499	−0.886028
$643$	15.5484	0.613169	0.306584	−	0.951843i	$-0.400814\pi$
$643$	15.5484	0.613169	0.306584	+	0.951843i	$0.400814\pi$
$644$	−12.9574	−0.510593
$645$	0.261012	0.0102774
$646$	73.1874	2.87952
$647$	12.7393	0.500835	0.250418	−	0.968138i	$-0.419432\pi$
$647$	12.7393	0.500835	0.250418	+	0.968138i	$0.419432\pi$
$648$	112.064	4.40231
$649$	−27.5300	−1.08065
$650$	−47.0198	−1.84427
$651$	15.5386	0.609004
$652$	24.2864	0.951129
$653$	9.07300	0.355054	0.177527	−	0.984116i	$-0.443190\pi$
$653$	9.07300	0.355054	0.177527	+	0.984116i	$0.443190\pi$
$654$	−24.4838	−0.957391
$655$	−0.0876221	−0.00342368
$656$	−225.467	−8.80300
$657$	−6.18961	−0.241480
$658$	41.2320	1.60739
$659$	−25.3569	−0.987766	−0.493883	−	0.869528i	$-0.664423\pi$
$659$	−25.3569	−0.987766	−0.493883	+	0.869528i	$0.664423\pi$
$660$	−1.94943	−0.0758813
$661$	−5.22377	−0.203181	−0.101590	−	0.994826i	$-0.532393\pi$
$661$	−5.22377	−0.203181	−0.101590	+	0.994826i	$0.532393\pi$
$662$	−13.2080	−0.513345
$663$	−31.9459	−1.24068
$664$	169.355	6.57223
$665$	0.227828	0.00883477
$666$	−11.6533	−0.451557
$667$	−1.57301	−0.0609072
$668$	84.7979	3.28093
$669$	25.5255	0.986873
$670$	−0.0825372	−0.00318869
$671$	−76.1335	−2.93910
$672$	−84.0813	−3.24351
$673$	−8.32132	−0.320763	−0.160382	−	0.987055i	$-0.551272\pi$
$673$	−8.32132	−0.320763	−0.160382	+	0.987055i	$0.551272\pi$
$674$	−39.8702	−1.53574
$675$	24.0285	0.924858
$676$	−11.2843	−0.434010
$677$	−1.03161	−0.0396481	−0.0198241	−	0.999803i	$-0.506311\pi$
$677$	−1.03161	−0.0396481	−0.0198241	+	0.999803i	$0.506311\pi$
$678$	−70.2820	−2.69916
$679$	−1.72523	−0.0662082
$680$	1.92967	0.0739993
$681$	−21.5446	−0.825592
$682$	−92.4560	−3.54032
$683$	3.04874	0.116657	0.0583285	−	0.998297i	$-0.481423\pi$
$683$	3.04874	0.116657	0.0583285	+	0.998297i	$0.481423\pi$
$684$	−11.5537	−0.441767
$685$	−0.387757	−0.0148154
$686$	47.1313	1.79948
$687$	20.5562	0.784269
$688$	−84.1077	−3.20658
$689$	−11.3983	−0.434242
$690$	−0.270687	−0.0103049
$691$	26.3981	1.00423	0.502116	−	0.864800i	$-0.332555\pi$
$691$	26.3981	1.00423	0.502116	+	0.864800i	$0.332555\pi$
$692$	−19.3049	−0.733862
$693$	2.87877	0.109356
$694$	6.68345	0.253700
$695$	0.132016	0.00500766
$696$	−20.5981	−0.780767
$697$	−59.7476	−2.26310
$698$	−13.3034	−0.503541
$699$	−13.7991	−0.521930
$700$	−41.1776	−1.55637
$701$	31.5066	1.18999	0.594994	−	0.803730i	$-0.297155\pi$
$701$	31.5066	1.18999	0.594994	+	0.803730i	$0.297155\pi$
$702$	−45.2125	−1.70644
$703$	−52.8820	−1.99448
$704$	289.661	10.9170
$705$	0.645067	0.0242946
$706$	50.9392	1.91712
$707$	20.5254	0.771937
$708$	−56.3974	−2.11954
$709$	22.4158	0.841845	0.420922	−	0.907097i	$-0.361706\pi$
$709$	22.4158	0.841845	0.420922	+	0.907097i	$0.361706\pi$
$710$	−0.766336	−0.0287601
$711$	−3.81510	−0.143077
$712$	−143.789	−5.38873
$713$	−9.61425	−0.360057
$714$	−37.3573	−1.39806
$715$	0.591710	0.0221287
$716$	−10.5307	−0.393550
$717$	22.0633	0.823969
$718$	−58.5579	−2.18536
$719$	1.16745	0.0435386	0.0217693	−	0.999763i	$-0.493070\pi$
$719$	1.16745	0.0435386	0.0217693	+	0.999763i	$0.493070\pi$
$720$	−0.253100	−0.00943249
$721$	−22.8017	−0.849179
$722$	−16.3885	−0.609917
$723$	10.2390	0.380793
$724$	−124.735	−4.63574
$725$	−4.99890	−0.185655
$726$	−92.1123	−3.41861
$727$	−41.7023	−1.54665	−0.773325	−	0.634009i	$-0.781408\pi$
$727$	−41.7023	−1.54665	−0.773325	+	0.634009i	$0.781408\pi$
$728$	51.5009	1.90875
$729$	22.6512	0.838933
$730$	−1.48774	−0.0550635
$731$	−22.2881	−0.824356
$732$	−155.966	−5.76465
$733$	−29.5021	−1.08969	−0.544843	−	0.838538i	$-0.683411\pi$
$733$	−29.5021	−1.08969	−0.544843	+	0.838538i	$0.683411\pi$
$734$	96.5798	3.56483
$735$	0.310534	0.0114542
$736$	52.0240	1.91763
$737$	−4.73270	−0.174331
$738$	12.5947	0.463616
$739$	5.39530	0.198469	0.0992347	−	0.995064i	$-0.468361\pi$
$739$	5.39530	0.198469	0.0992347	+	0.995064i	$0.468361\pi$
$740$	−2.09764	−0.0771108
$741$	30.5589	1.12261
$742$	−13.3291	−0.489328
$743$	28.4256	1.04283	0.521417	−	0.853302i	$-0.325404\pi$
$743$	28.4256	1.04283	0.521417	+	0.853302i	$0.325404\pi$
$744$	−125.896	−4.61555
$745$	−0.354959	−0.0130047
$746$	4.46384	0.163433
$747$	−5.88634	−0.215370
$748$	166.464	6.08651
$749$	5.96757	0.218050
$750$	−1.72064	−0.0628287
$751$	37.0646	1.35251	0.676253	−	0.736669i	$-0.263602\pi$
$751$	37.0646	1.35251	0.676253	+	0.736669i	$0.263602\pi$
$752$	−207.864	−7.58001
$753$	9.10929	0.331961
$754$	9.40602	0.342547
$755$	−0.0322252	−0.00117279
$756$	−39.5948	−1.44005
$757$	14.2083	0.516409	0.258204	−	0.966090i	$-0.416869\pi$
$757$	14.2083	0.516409	0.258204	+	0.966090i	$0.416869\pi$
$758$	26.0209	0.945123
$759$	−15.5213	−0.563386
$760$	−1.84589	−0.0669574
$761$	−22.4015	−0.812054	−0.406027	−	0.913861i	$-0.633086\pi$
$761$	−22.4015	−0.812054	−0.406027	+	0.913861i	$0.633086\pi$
$762$	24.5548	0.889528
$763$	6.50819	0.235612
$764$	−61.3182	−2.21842
$765$	−0.0670704	−0.00242493
$766$	−15.6631	−0.565931
$767$	17.1183	0.618106
$768$	249.744	9.01185
$769$	−38.9694	−1.40527	−0.702636	−	0.711550i	$-0.747994\pi$
$769$	−38.9694	−1.40527	−0.702636	+	0.711550i	$0.747994\pi$
$770$	0.691942	0.0249359
$771$	20.4709	0.737241
$772$	−42.0402	−1.51306
$773$	−35.4485	−1.27499	−0.637497	−	0.770452i	$-0.720030\pi$
$773$	−35.4485	−1.27499	−0.637497	+	0.770452i	$0.720030\pi$
$774$	4.69828	0.168876
$775$	−30.5534	−1.09751
$776$	13.9780	0.501782
$777$	26.9927	0.968359
$778$	−22.1692	−0.794804
$779$	57.1537	2.04774
$780$	1.21217	0.0434025
$781$	−43.9418	−1.57236
$782$	23.1143	0.826565
$783$	−4.80676	−0.171780
$784$	−100.065	−3.57376
$785$	0.417313	0.0148945
$786$	−13.7438	−0.490225
$787$	−8.37463	−0.298523	−0.149262	−	0.988798i	$-0.547690\pi$
$787$	−8.37463	−0.298523	−0.149262	+	0.988798i	$0.547690\pi$
$788$	−6.79090	−0.241916
$789$	−33.4060	−1.18929
$790$	−0.916997	−0.0326253
$791$	18.6821	0.664260
$792$	−23.3242	−0.828790
$793$	47.3403	1.68110
$794$	−18.8111	−0.667582
$795$	−0.208531	−0.00739585
$796$	−59.6570	−2.11449
$797$	−28.3126	−1.00288	−0.501441	−	0.865192i	$-0.667197\pi$
$797$	−28.3126	−1.00288	−0.501441	+	0.865192i	$0.667197\pi$
$798$	35.7354	1.26502
$799$	−55.0829	−1.94869
$800$	165.328	5.84524
$801$	4.99775	0.176587
$802$	−68.6706	−2.42484
$803$	−85.3070	−3.01042
$804$	−9.69532	−0.341928
$805$	0.0719532	0.00253602
$806$	57.4897	2.02499
$807$	42.5509	1.49786
$808$	−166.300	−5.85040
$809$	−2.84594	−0.100058	−0.0500290	−	0.998748i	$-0.515931\pi$
$809$	−2.84594	−0.100058	−0.0500290	+	0.998748i	$0.515931\pi$
$810$	−0.936221	−0.0328954
$811$	2.48979	0.0874284	0.0437142	−	0.999044i	$-0.486081\pi$
$811$	2.48979	0.0874284	0.0437142	+	0.999044i	$0.486081\pi$
$812$	8.23733	0.289074
$813$	5.26891	0.184789
$814$	−160.609	−5.62936
$815$	−0.134864	−0.00472408
$816$	188.330	6.59287
$817$	21.3205	0.745909
$818$	−62.8646	−2.19801
$819$	−1.79004	−0.0625491
$820$	2.26709	0.0791701
$821$	−46.8151	−1.63386	−0.816928	−	0.576739i	$-0.804325\pi$
$821$	−46.8151	−1.63386	−0.816928	+	0.576739i	$0.804325\pi$
$822$	−60.8208	−2.12137
$823$	25.5843	0.891813	0.445907	−	0.895079i	$-0.352881\pi$
$823$	25.5843	0.891813	0.445907	+	0.895079i	$0.352881\pi$
$824$	184.742	6.43580
$825$	−49.3254	−1.71729
$826$	20.0180	0.696517
$827$	−6.00641	−0.208863	−0.104432	−	0.994532i	$-0.533302\pi$
$827$	−6.00641	−0.208863	−0.104432	+	0.994532i	$0.533302\pi$
$828$	−3.64893	−0.126809
$829$	−44.8441	−1.55750	−0.778751	−	0.627334i	$-0.784146\pi$
$829$	−44.8441	−1.55750	−0.778751	+	0.627334i	$0.784146\pi$
$830$	−1.41484	−0.0491098
$831$	1.84090	0.0638600
$832$	−180.113	−6.24430
$833$	−26.5168	−0.918753
$834$	20.7072	0.717030
$835$	−0.470888	−0.0162958
$836$	−159.237	−5.50731
$837$	−29.3790	−1.01549
$838$	−35.1266	−1.21343
$839$	20.2827	0.700238	0.350119	−	0.936705i	$-0.386141\pi$
$839$	20.2827	0.700238	0.350119	+	0.936705i	$0.386141\pi$
$840$	0.942204	0.0325091
$841$	1.00000	0.0344828
$842$	74.1163	2.55422
$843$	53.9495	1.85812
$844$	−6.67578	−0.229790
$845$	0.0626622	0.00215565
$846$	11.6113	0.399206
$847$	24.4850	0.841314
$848$	67.1964	2.30753
$849$	−7.02109	−0.240963
$850$	73.4554	2.51950
$851$	−16.7013	−0.572515
$852$	−90.0184	−3.08398
$853$	47.7638	1.63540	0.817701	−	0.575643i	$-0.195248\pi$
$853$	47.7638	1.63540	0.817701	+	0.575643i	$0.195248\pi$
$854$	55.3594	1.89436
$855$	0.0641585	0.00219417
$856$	−48.3500	−1.65257
$857$	32.3311	1.10441	0.552205	−	0.833708i	$-0.313787\pi$
$857$	32.3311	1.10441	0.552205	+	0.833708i	$0.313787\pi$
$858$	92.8115	3.16853
$859$	2.68657	0.0916647	0.0458324	−	0.998949i	$-0.485406\pi$
$859$	2.68657	0.0916647	0.0458324	+	0.998949i	$0.485406\pi$
$860$	0.845709	0.0288384
$861$	−29.1732	−0.994219
$862$	88.7721	3.02359
$863$	−6.61248	−0.225092	−0.112546	−	0.993647i	$-0.535900\pi$
$863$	−6.61248	−0.225092	−0.112546	+	0.993647i	$0.535900\pi$
$864$	158.974	5.40839
$865$	0.107201	0.00364495
$866$	−39.1438	−1.33016
$867$	18.6113	0.632073
$868$	50.3466	1.70888
$869$	−52.5808	−1.78368
$870$	0.172082	0.00583414
$871$	2.94282	0.0997137
$872$	−52.7302	−1.78567
$873$	−0.485841	−0.0164432
$874$	−22.1108	−0.747908
$875$	0.457374	0.0154621
$876$	−174.758	−5.90454
$877$	−58.1852	−1.96477	−0.982387	−	0.186857i	$-0.940170\pi$
$877$	−58.1852	−1.96477	−0.982387	+	0.186857i	$0.940170\pi$
$878$	83.7189	2.82538
$879$	−34.2689	−1.15586
$880$	−3.48830	−0.117591
$881$	−44.8128	−1.50978	−0.754891	−	0.655850i	$-0.772310\pi$
$881$	−44.8128	−1.50978	−0.754891	+	0.655850i	$0.772310\pi$
$882$	5.58968	0.188214
$883$	−30.1434	−1.01440	−0.507202	−	0.861827i	$-0.669320\pi$
$883$	−30.1434	−1.01440	−0.507202	+	0.861827i	$0.669320\pi$
$884$	−103.508	−3.48136
$885$	0.313178	0.0105274
$886$	23.9021	0.803007
$887$	−7.96893	−0.267570	−0.133785	−	0.991010i	$-0.542713\pi$
$887$	−7.96893	−0.267570	−0.133785	+	0.991010i	$0.542713\pi$
$888$	−218.699	−7.33905
$889$	−6.52709	−0.218911
$890$	1.20126	0.0402663
$891$	−53.6831	−1.79845
$892$	82.7054	2.76918
$893$	52.6915	1.76325
$894$	−55.6764	−1.86210
$895$	0.0584776	0.00195469
$896$	−119.275	−3.98471
$897$	9.65122	0.322245
$898$	31.2743	1.04364
$899$	6.11201	0.203847
$900$	−11.5960	−0.386534
$901$	17.8067	0.593228
$902$	173.583	5.77969
$903$	−10.8827	−0.362153
$904$	−151.365	−5.03433
$905$	0.692661	0.0230248
$906$	−5.05461	−0.167928
$907$	−15.5789	−0.517288	−0.258644	−	0.965973i	$-0.583276\pi$
$907$	−15.5789	−0.517288	−0.258644	+	0.965973i	$0.583276\pi$
$908$	−69.8070	−2.31663
$909$	5.78015	0.191716
$910$	−0.430254	−0.0142628
$911$	−34.1473	−1.13135	−0.565675	−	0.824628i	$-0.691384\pi$
$911$	−34.1473	−1.13135	−0.565675	+	0.824628i	$0.691384\pi$
$912$	−180.154	−5.96548
$913$	−81.1272	−2.68492
$914$	52.6466	1.74139
$915$	0.866087	0.0286319
$916$	66.6044	2.20067
$917$	3.65333	0.120644
$918$	70.6320	2.33120
$919$	55.7090	1.83767	0.918834	−	0.394643i	$-0.129132\pi$
$919$	55.7090	1.83767	0.918834	+	0.394643i	$0.129132\pi$
$920$	−0.582975	−0.0192201
$921$	2.62455	0.0864820
$922$	−51.0254	−1.68043
$923$	27.3233	0.899358
$924$	81.2797	2.67391
$925$	−53.0756	−1.74511
$926$	−95.1081	−3.12544
$927$	−6.42117	−0.210899
$928$	−33.0729	−1.08567
$929$	23.3513	0.766131	0.383066	−	0.923721i	$-0.374868\pi$
$929$	23.3513	0.766131	0.383066	+	0.923721i	$0.374868\pi$
$930$	1.05177	0.0344889
$931$	25.3656	0.831323
$932$	−44.7106	−1.46454
$933$	11.4721	0.375581
$934$	58.1097	1.90141
$935$	−0.924383	−0.0302305
$936$	14.5031	0.474050
$937$	12.9063	0.421632	0.210816	−	0.977526i	$-0.432388\pi$
$937$	12.9063	0.421632	0.210816	+	0.977526i	$0.432388\pi$
$938$	3.44132	0.112363
$939$	−20.8945	−0.681866
$940$	2.09009	0.0681711
$941$	−9.70610	−0.316410	−0.158205	−	0.987406i	$-0.550571\pi$
$941$	−9.70610	−0.316410	−0.158205	+	0.987406i	$0.550571\pi$
$942$	65.4567	2.13270
$943$	18.0504	0.587803
$944$	−100.917	−3.28458
$945$	0.219873	0.00715246
$946$	64.7531	2.10530
$947$	5.31399	0.172682	0.0863408	−	0.996266i	$-0.472483\pi$
$947$	5.31399	0.172682	0.0863408	+	0.996266i	$0.472483\pi$
$948$	−107.716	−3.49845
$949$	53.0444	1.72190
$950$	−70.2663	−2.27974
$951$	−42.8682	−1.39010
$952$	−80.4558	−2.60759
$953$	−49.0998	−1.59050	−0.795249	−	0.606284i	$-0.792660\pi$
$953$	−49.0998	−1.59050	−0.795249	+	0.606284i	$0.792660\pi$
$954$	−3.75361	−0.121528
$955$	0.340504	0.0110184
$956$	71.4875	2.31207
$957$	9.86724	0.318963
$958$	−66.3686	−2.14427
$959$	16.1672	0.522066
$960$	−3.29516	−0.106351
$961$	6.35669	0.205054
$962$	99.8680	3.21987
$963$	1.68053	0.0541542
$964$	33.1755	1.06851
$965$	0.233452	0.00751509
$966$	11.2861	0.363124
$967$	42.2140	1.35751	0.678755	−	0.734365i	$-0.262520\pi$
$967$	42.2140	1.35751	0.678755	+	0.734365i	$0.262520\pi$
$968$	−198.381	−6.37619
$969$	−47.7399	−1.53363
$970$	−0.116777	−0.00374948
$971$	−53.2248	−1.70807	−0.854033	−	0.520219i	$-0.825850\pi$
$971$	−53.2248	−1.70807	−0.854033	+	0.520219i	$0.825850\pi$
$972$	−23.9614	−0.768561
$973$	−5.50431	−0.176460
$974$	−118.099	−3.78414
$975$	30.6708	0.982253
$976$	−279.084	−8.93328
$977$	16.0572	0.513716	0.256858	−	0.966449i	$-0.417313\pi$
$977$	16.0572	0.513716	0.256858	+	0.966449i	$0.417313\pi$
$978$	−21.1538	−0.676424
$979$	68.8804	2.20143
$980$	1.00616	0.0321407
$981$	1.83277	0.0585159
$982$	19.7179	0.629225
$983$	−53.9439	−1.72054	−0.860272	−	0.509835i	$-0.829706\pi$
$983$	−53.9439	−1.72054	−0.860272	+	0.509835i	$0.829706\pi$
$984$	236.365	7.53504
$985$	0.0377103	0.00120155
$986$	−14.6943	−0.467962
$987$	−26.8955	−0.856093
$988$	99.0143	3.15006
$989$	6.73350	0.214113
$990$	0.194858	0.00619298
$991$	−5.37978	−0.170894	−0.0854472	−	0.996343i	$-0.527232\pi$
$991$	−5.37978	−0.170894	−0.0854472	+	0.996343i	$0.527232\pi$
$992$	−202.142	−6.41802
$993$	8.61555	0.273406
$994$	31.9517	1.01345
$995$	0.331279	0.0105022
$996$	−166.196	−5.26611
$997$	−58.0764	−1.83930	−0.919649	−	0.392741i	$-0.871527\pi$
$997$	−58.0764	−1.83930	−0.919649	+	0.392741i	$0.871527\pi$
$998$	15.2842	0.483814
$999$	−51.0355	−1.61469

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8033.2.a.c.1.1	✓	154

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8033.2.a.c.1.1	✓	154	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:	\( N \)	\(=\)	\( 8033 = 29 \cdot 277 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.82218 q^{2} +1.84090 q^{3} +5.96471 q^{4} -0.0331224 q^{5} -5.19535 q^{6} +1.38101 q^{7} -11.1891 q^{8} +0.388906 q^{9} +O(q^{10})\)	\(q-2.82218 q^{2} +1.84090 q^{3} +5.96471 q^{4} -0.0331224 q^{5} -5.19535 q^{6} +1.38101 q^{7} -11.1891 q^{8} +0.388906 q^{9} +0.0934774 q^{10} +5.36001 q^{11} +10.9804 q^{12} -3.33289 q^{13} -3.89746 q^{14} -0.0609750 q^{15} +19.6483 q^{16} +5.20672 q^{17} -1.09756 q^{18} -4.98067 q^{19} -0.197566 q^{20} +2.54230 q^{21} -15.1269 q^{22} -1.57301 q^{23} -20.5981 q^{24} -4.99890 q^{25} +9.40602 q^{26} -4.80676 q^{27} +8.23733 q^{28} +1.00000 q^{29} +0.172082 q^{30} +6.11201 q^{31} -33.0729 q^{32} +9.86724 q^{33} -14.6943 q^{34} -0.0457424 q^{35} +2.31971 q^{36} +10.6174 q^{37} +14.0563 q^{38} -6.13551 q^{39} +0.370611 q^{40} -11.4751 q^{41} -7.17483 q^{42} -4.28065 q^{43} +31.9709 q^{44} -0.0128815 q^{45} +4.43932 q^{46} -10.5792 q^{47} +36.1706 q^{48} -5.09281 q^{49} +14.1078 q^{50} +9.58504 q^{51} -19.8797 q^{52} +3.41995 q^{53} +13.5655 q^{54} -0.177537 q^{55} -15.4523 q^{56} -9.16890 q^{57} -2.82218 q^{58} -5.13617 q^{59} -0.363698 q^{60} -14.2040 q^{61} -17.2492 q^{62} +0.537083 q^{63} +54.0411 q^{64} +0.110393 q^{65} -27.8471 q^{66} -0.882964 q^{67} +31.0566 q^{68} -2.89575 q^{69} +0.129093 q^{70} -8.19808 q^{71} -4.35152 q^{72} -15.9154 q^{73} -29.9644 q^{74} -9.20247 q^{75} -29.7082 q^{76} +7.40224 q^{77} +17.3155 q^{78} -9.80982 q^{79} -0.650800 q^{80} -10.0155 q^{81} +32.3848 q^{82} -15.1356 q^{83} +15.1641 q^{84} -0.172459 q^{85} +12.0808 q^{86} +1.84090 q^{87} -59.9739 q^{88} +12.8508 q^{89} +0.0363539 q^{90} -4.60276 q^{91} -9.38254 q^{92} +11.2516 q^{93} +29.8564 q^{94} +0.164972 q^{95} -60.8839 q^{96} -1.24925 q^{97} +14.3728 q^{98} +2.08454 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 154 q - 12 q^{2} - 36 q^{3} + 142 q^{4} - 9 q^{5} - 11 q^{6} - 68 q^{7} - 33 q^{8} + 146 q^{9}+O(q^{10}) \) 154 * q - 12 * q^2 - 36 * q^3 + 142 * q^4 - 9 * q^5 - 11 * q^6 - 68 * q^7 - 33 * q^8 + 146 * q^9	\( 154 q - 12 q^{2} - 36 q^{3} + 142 q^{4} - 9 q^{5} - 11 q^{6} - 68 q^{7} - 33 q^{8} + 146 q^{9} - 40 q^{10} - 36 q^{11} - 67 q^{12} - 51 q^{13} - 19 q^{14} - 48 q^{15} + 122 q^{16} - 54 q^{17} - 46 q^{18} - 73 q^{19} - 21 q^{20} - 8 q^{21} - 23 q^{22} - 38 q^{23} - 17 q^{24} + 133 q^{25} - 20 q^{26} - 129 q^{27} - 99 q^{28} + 154 q^{29} - 10 q^{30} - 91 q^{31} - 88 q^{32} - 39 q^{33} - 42 q^{34} - 36 q^{35} + 101 q^{36} - 50 q^{37} - 17 q^{38} - 33 q^{39} - 92 q^{40} - 31 q^{41} - 62 q^{42} - 154 q^{43} - 42 q^{44} - 14 q^{45} - 24 q^{46} - 140 q^{47} - 118 q^{48} + 126 q^{49} - 5 q^{50} - 16 q^{51} - 133 q^{52} - 40 q^{53} + 14 q^{54} - 203 q^{55} - 44 q^{56} - 16 q^{57} - 12 q^{58} + 5 q^{59} - 28 q^{60} - 106 q^{61} - 30 q^{62} - 145 q^{63} + 111 q^{64} - 15 q^{65} - 49 q^{66} - 78 q^{67} - 118 q^{68} - 32 q^{69} - 43 q^{70} - 4 q^{71} - 152 q^{72} - 137 q^{73} + 9 q^{74} - 129 q^{75} - 204 q^{76} - 76 q^{77} + 15 q^{78} - 141 q^{79} - 44 q^{80} + 122 q^{81} - 71 q^{82} - 90 q^{83} + 92 q^{84} - 41 q^{85} + 9 q^{86} - 36 q^{87} - 109 q^{88} - 51 q^{89} - 82 q^{90} - 22 q^{91} - 8 q^{92} - 10 q^{93} - 106 q^{94} - 55 q^{95} - 49 q^{96} - 140 q^{97} - 4 q^{98} - 101 q^{99}+O(q^{100}) \) 154 * q - 12 * q^2 - 36 * q^3 + 142 * q^4 - 9 * q^5 - 11 * q^6 - 68 * q^7 - 33 * q^8 + 146 * q^9 - 40 * q^10 - 36 * q^11 - 67 * q^12 - 51 * q^13 - 19 * q^14 - 48 * q^15 + 122 * q^16 - 54 * q^17 - 46 * q^18 - 73 * q^19 - 21 * q^20 - 8 * q^21 - 23 * q^22 - 38 * q^23 - 17 * q^24 + 133 * q^25 - 20 * q^26 - 129 * q^27 - 99 * q^28 + 154 * q^29 - 10 * q^30 - 91 * q^31 - 88 * q^32 - 39 * q^33 - 42 * q^34 - 36 * q^35 + 101 * q^36 - 50 * q^37 - 17 * q^38 - 33 * q^39 - 92 * q^40 - 31 * q^41 - 62 * q^42 - 154 * q^43 - 42 * q^44 - 14 * q^45 - 24 * q^46 - 140 * q^47 - 118 * q^48 + 126 * q^49 - 5 * q^50 - 16 * q^51 - 133 * q^52 - 40 * q^53 + 14 * q^54 - 203 * q^55 - 44 * q^56 - 16 * q^57 - 12 * q^58 + 5 * q^59 - 28 * q^60 - 106 * q^61 - 30 * q^62 - 145 * q^63 + 111 * q^64 - 15 * q^65 - 49 * q^66 - 78 * q^67 - 118 * q^68 - 32 * q^69 - 43 * q^70 - 4 * q^71 - 152 * q^72 - 137 * q^73 + 9 * q^74 - 129 * q^75 - 204 * q^76 - 76 * q^77 + 15 * q^78 - 141 * q^79 - 44 * q^80 + 122 * q^81 - 71 * q^82 - 90 * q^83 + 92 * q^84 - 41 * q^85 + 9 * q^86 - 36 * q^87 - 109 * q^88 - 51 * q^89 - 82 * q^90 - 22 * q^91 - 8 * q^92 - 10 * q^93 - 106 * q^94 - 55 * q^95 - 49 * q^96 - 140 * q^97 - 4 * q^98 - 101 * q^99

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