LMFDB - Embedded newform 8027.2.a.e.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8027,2,Mod(1,8027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8027, 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("8027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8027 = 23 \cdot 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8027.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:	$64.0959177025$
Analytic rank:	$0$
Dimension:	$169$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	8027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.69664 q^{2} -0.711836 q^{3} +5.27186 q^{4} +2.29086 q^{5} +1.91957 q^{6} +3.32005 q^{7} -8.82303 q^{8} -2.49329 q^{9} +O(q^{10})$	\(q-2.69664 q^{2} -0.711836 q^{3} +5.27186 q^{4} +2.29086 q^{5} +1.91957 q^{6} +3.32005 q^{7} -8.82303 q^{8} -2.49329 q^{9} -6.17762 q^{10} +0.904642 q^{11} -3.75270 q^{12} +1.28544 q^{13} -8.95298 q^{14} -1.63072 q^{15} +13.2488 q^{16} +4.08802 q^{17} +6.72350 q^{18} +3.99557 q^{19} +12.0771 q^{20} -2.36333 q^{21} -2.43949 q^{22} -1.00000 q^{23} +6.28055 q^{24} +0.248038 q^{25} -3.46636 q^{26} +3.91032 q^{27} +17.5029 q^{28} +7.93772 q^{29} +4.39746 q^{30} +5.00419 q^{31} -18.0812 q^{32} -0.643957 q^{33} -11.0239 q^{34} +7.60578 q^{35} -13.1443 q^{36} +7.64650 q^{37} -10.7746 q^{38} -0.915022 q^{39} -20.2123 q^{40} +11.0075 q^{41} +6.37306 q^{42} +9.45927 q^{43} +4.76915 q^{44} -5.71178 q^{45} +2.69664 q^{46} +9.77018 q^{47} -9.43097 q^{48} +4.02275 q^{49} -0.668869 q^{50} -2.91000 q^{51} +6.77665 q^{52} +0.282322 q^{53} -10.5447 q^{54} +2.07241 q^{55} -29.2929 q^{56} -2.84419 q^{57} -21.4052 q^{58} -4.40461 q^{59} -8.59691 q^{60} +8.45036 q^{61} -13.4945 q^{62} -8.27785 q^{63} +22.2608 q^{64} +2.94476 q^{65} +1.73652 q^{66} -8.45806 q^{67} +21.5515 q^{68} +0.711836 q^{69} -20.5100 q^{70} -11.1405 q^{71} +21.9984 q^{72} +3.70320 q^{73} -20.6199 q^{74} -0.176563 q^{75} +21.0641 q^{76} +3.00346 q^{77} +2.46748 q^{78} +6.66572 q^{79} +30.3511 q^{80} +4.69636 q^{81} -29.6834 q^{82} -14.1619 q^{83} -12.4592 q^{84} +9.36509 q^{85} -25.5082 q^{86} -5.65035 q^{87} -7.98168 q^{88} -16.2403 q^{89} +15.4026 q^{90} +4.26772 q^{91} -5.27186 q^{92} -3.56217 q^{93} -26.3466 q^{94} +9.15329 q^{95} +12.8708 q^{96} +3.04337 q^{97} -10.8479 q^{98} -2.25553 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9}+O(q^{10}) $ 169 * q + 6 * q^2 + 2 * q^3 + 186 * q^4 + 28 * q^5 + 5 * q^6 + 38 * q^7 + 18 * q^8 + 185 * q^9	\( 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9} + 28 q^{10} + 17 q^{11} + 10 q^{12} + 91 q^{13} + 20 q^{14} + 29 q^{15} + 200 q^{16} + 16 q^{17} + 31 q^{18} + 30 q^{19} + 45 q^{20} + 49 q^{21} + 76 q^{22} - 169 q^{23} + 3 q^{24} + 241 q^{25} - 15 q^{26} + 14 q^{27} + 118 q^{28} + 23 q^{29} + 52 q^{30} + 45 q^{31} + 42 q^{32} + 62 q^{33} + 65 q^{34} - 16 q^{35} + 199 q^{36} + 226 q^{37} + 49 q^{38} + 17 q^{39} + 95 q^{40} + 19 q^{41} + 32 q^{42} + 71 q^{43} + 46 q^{44} + 127 q^{45} - 6 q^{46} + 27 q^{47} + 5 q^{48} + 239 q^{49} + 24 q^{50} + 39 q^{51} + 154 q^{52} + 111 q^{53} + 22 q^{54} + 47 q^{55} + 39 q^{56} + 122 q^{57} + 146 q^{58} - 73 q^{59} + 109 q^{60} + 125 q^{61} + 14 q^{62} + 109 q^{63} + 260 q^{64} + 73 q^{65} + 26 q^{66} + 152 q^{67} + 40 q^{68} - 2 q^{69} + 76 q^{70} - 79 q^{71} + 126 q^{72} + 106 q^{73} + 23 q^{74} + 12 q^{75} + 122 q^{76} + 63 q^{77} + 101 q^{78} + 82 q^{79} + 134 q^{80} + 225 q^{81} + 125 q^{82} + 28 q^{83} + 73 q^{84} + 197 q^{85} + 97 q^{86} + 18 q^{87} + 183 q^{88} + 54 q^{89} + 52 q^{90} + 106 q^{91} - 186 q^{92} + 194 q^{93} + q^{94} + 18 q^{95} - 39 q^{96} + 239 q^{97} + 5 q^{98} + 85 q^{99}+O(q^{100}) \) 169 * q + 6 * q^2 + 2 * q^3 + 186 * q^4 + 28 * q^5 + 5 * q^6 + 38 * q^7 + 18 * q^8 + 185 * q^9 + 28 * q^10 + 17 * q^11 + 10 * q^12 + 91 * q^13 + 20 * q^14 + 29 * q^15 + 200 * q^16 + 16 * q^17 + 31 * q^18 + 30 * q^19 + 45 * q^20 + 49 * q^21 + 76 * q^22 - 169 * q^23 + 3 * q^24 + 241 * q^25 - 15 * q^26 + 14 * q^27 + 118 * q^28 + 23 * q^29 + 52 * q^30 + 45 * q^31 + 42 * q^32 + 62 * q^33 + 65 * q^34 - 16 * q^35 + 199 * q^36 + 226 * q^37 + 49 * q^38 + 17 * q^39 + 95 * q^40 + 19 * q^41 + 32 * q^42 + 71 * q^43 + 46 * q^44 + 127 * q^45 - 6 * q^46 + 27 * q^47 + 5 * q^48 + 239 * q^49 + 24 * q^50 + 39 * q^51 + 154 * q^52 + 111 * q^53 + 22 * q^54 + 47 * q^55 + 39 * q^56 + 122 * q^57 + 146 * q^58 - 73 * q^59 + 109 * q^60 + 125 * q^61 + 14 * q^62 + 109 * q^63 + 260 * q^64 + 73 * q^65 + 26 * q^66 + 152 * q^67 + 40 * q^68 - 2 * q^69 + 76 * q^70 - 79 * q^71 + 126 * q^72 + 106 * q^73 + 23 * q^74 + 12 * q^75 + 122 * q^76 + 63 * q^77 + 101 * q^78 + 82 * q^79 + 134 * q^80 + 225 * q^81 + 125 * q^82 + 28 * q^83 + 73 * q^84 + 197 * q^85 + 97 * q^86 + 18 * q^87 + 183 * q^88 + 54 * q^89 + 52 * q^90 + 106 * q^91 - 186 * q^92 + 194 * q^93 + q^94 + 18 * q^95 - 39 * q^96 + 239 * q^97 + 5 * q^98 + 85 * 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 $

$2$	−2.69664	−1.90681	−0.953406	−	0.301691i	$-0.902449\pi$
$2$	−2.69664	−1.90681	−0.953406	+	0.301691i	$0.902449\pi$
$3$	−0.711836	−0.410979	−0.205489	−	0.978659i	$-0.565879\pi$
$3$	−0.711836	−0.410979	−0.205489	+	0.978659i	$0.565879\pi$
$4$	5.27186	2.63593
$5$	2.29086	1.02450	0.512252	−	0.858835i	$-0.328811\pi$
$5$	2.29086	1.02450	0.512252	+	0.858835i	$0.328811\pi$
$6$	1.91957	0.783659
$7$	3.32005	1.25486	0.627431	−	0.778672i	$-0.284106\pi$
$7$	3.32005	1.25486	0.627431	+	0.778672i	$0.284106\pi$
$8$	−8.82303	−3.11941
$9$	−2.49329	−0.831096
$10$	−6.17762	−1.95354
$11$	0.904642	0.272760	0.136380	−	0.990657i	$-0.456453\pi$
$11$	0.904642	0.272760	0.136380	+	0.990657i	$0.456453\pi$
$12$	−3.75270	−1.08331
$13$	1.28544	0.356516	0.178258	−	0.983984i	$-0.442954\pi$
$13$	1.28544	0.356516	0.178258	+	0.983984i	$0.442954\pi$
$14$	−8.95298	−2.39279
$15$	−1.63072	−0.421049
$16$	13.2488	3.31220
$17$	4.08802	0.991491	0.495746	−	0.868468i	$-0.334895\pi$
$17$	4.08802	0.991491	0.495746	+	0.868468i	$0.334895\pi$
$18$	6.72350	1.58474
$19$	3.99557	0.916647	0.458323	−	0.888785i	$-0.348450\pi$
$19$	3.99557	0.916647	0.458323	+	0.888785i	$0.348450\pi$
$20$	12.0771	2.70052
$21$	−2.36333	−0.515722
$22$	−2.43949	−0.520102
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	6.28055	1.28201
$25$	0.248038	0.0496076
$26$	−3.46636	−0.679810
$27$	3.91032	0.752542
$28$	17.5029	3.30773
$29$	7.93772	1.47400	0.736998	−	0.675894i	$-0.236242\pi$
$29$	7.93772	1.47400	0.736998	+	0.675894i	$0.236242\pi$
$30$	4.39746	0.802862
$31$	5.00419	0.898779	0.449390	−	0.893336i	$-0.351641\pi$
$31$	5.00419	0.898779	0.449390	+	0.893336i	$0.351641\pi$
$32$	−18.0812	−3.19633
$33$	−0.643957	−0.112099
$34$	−11.0239	−1.89059
$35$	7.60578	1.28561
$36$	−13.1443	−2.19071
$37$	7.64650	1.25708	0.628539	−	0.777778i	$-0.283653\pi$
$37$	7.64650	1.25708	0.628539	+	0.777778i	$0.283653\pi$
$38$	−10.7746	−1.74787
$39$	−0.915022	−0.146521
$40$	−20.2123	−3.19585
$41$	11.0075	1.71909	0.859545	−	0.511060i	$-0.170747\pi$
$41$	11.0075	1.71909	0.859545	+	0.511060i	$0.170747\pi$
$42$	6.37306	0.983384
$43$	9.45927	1.44253	0.721263	−	0.692661i	$-0.243562\pi$
$43$	9.45927	1.44253	0.721263	+	0.692661i	$0.243562\pi$
$44$	4.76915	0.718976
$45$	−5.71178	−0.851461
$46$	2.69664	0.397598
$47$	9.77018	1.42513	0.712564	−	0.701608i	$-0.247534\pi$
$47$	9.77018	1.42513	0.712564	+	0.701608i	$0.247534\pi$
$48$	−9.43097	−1.36124
$49$	4.02275	0.574679
$50$	−0.668869	−0.0945924
$51$	−2.91000	−0.407482
$52$	6.77665	0.939753
$53$	0.282322	0.0387799	0.0193899	−	0.999812i	$-0.493828\pi$
$53$	0.282322	0.0387799	0.0193899	+	0.999812i	$0.493828\pi$
$54$	−10.5447	−1.43496
$55$	2.07241	0.279444
$56$	−29.2929	−3.91443
$57$	−2.84419	−0.376723
$58$	−21.4052	−2.81063
$59$	−4.40461	−0.573431	−0.286715	−	0.958016i	$-0.592563\pi$
$59$	−4.40461	−0.573431	−0.286715	+	0.958016i	$0.592563\pi$
$60$	−8.59691	−1.10986
$61$	8.45036	1.08196	0.540979	−	0.841036i	$-0.318054\pi$
$61$	8.45036	1.08196	0.540979	+	0.841036i	$0.318054\pi$
$62$	−13.4945	−1.71380
$63$	−8.27785	−1.04291
$64$	22.2608	2.78260
$65$	2.94476	0.365252
$66$	1.73652	0.213751
$67$	−8.45806	−1.03332	−0.516658	−	0.856192i	$-0.672824\pi$
$67$	−8.45806	−1.03332	−0.516658	+	0.856192i	$0.672824\pi$
$68$	21.5515	2.61350
$69$	0.711836	0.0856950
$70$	−20.5100	−2.45142
$71$	−11.1405	−1.32213	−0.661065	−	0.750328i	$-0.729895\pi$
$71$	−11.1405	−1.32213	−0.661065	+	0.750328i	$0.729895\pi$
$72$	21.9984	2.59253
$73$	3.70320	0.433426	0.216713	−	0.976235i	$-0.430466\pi$
$73$	3.70320	0.433426	0.216713	+	0.976235i	$0.430466\pi$
$74$	−20.6199	−2.39701
$75$	−0.176563	−0.0203877
$76$	21.0641	2.41622
$77$	3.00346	0.342276
$78$	2.46748	0.279387
$79$	6.66572	0.749952	0.374976	−	0.927035i	$-0.377651\pi$
$79$	6.66572	0.749952	0.374976	+	0.927035i	$0.377651\pi$
$80$	30.3511	3.39336
$81$	4.69636	0.521817
$82$	−29.6834	−3.27798
$83$	−14.1619	−1.55447	−0.777236	−	0.629209i	$-0.783379\pi$
$83$	−14.1619	−1.55447	−0.777236	+	0.629209i	$0.783379\pi$
$84$	−12.4592	−1.35941
$85$	9.36509	1.01579
$86$	−25.5082	−2.75062
$87$	−5.65035	−0.605782
$88$	−7.98168	−0.850850
$89$	−16.2403	−1.72147	−0.860735	−	0.509052i	$-0.829996\pi$
$89$	−16.2403	−1.72147	−0.860735	+	0.509052i	$0.829996\pi$
$90$	15.4026	1.62358
$91$	4.26772	0.447379
$92$	−5.27186	−0.549630
$93$	−3.56217	−0.369379
$94$	−26.3466	−2.71745
$95$	9.15329	0.939108
$96$	12.8708	1.31362
$97$	3.04337	0.309008	0.154504	−	0.987992i	$-0.450622\pi$
$97$	3.04337	0.309008	0.154504	+	0.987992i	$0.450622\pi$
$98$	−10.8479	−1.09580
$99$	−2.25553	−0.226690
$100$	1.30762	0.130762
$101$	−16.1102	−1.60302	−0.801512	−	0.597978i	$-0.795971\pi$
$101$	−16.1102	−1.60302	−0.801512	+	0.597978i	$0.795971\pi$
$102$	7.84723	0.776991
$103$	−9.45884	−0.932007	−0.466004	−	0.884783i	$-0.654307\pi$
$103$	−9.45884	−0.932007	−0.466004	+	0.884783i	$0.654307\pi$
$104$	−11.3415	−1.11212
$105$	−5.41407	−0.528359
$106$	−0.761320	−0.0739460
$107$	18.0241	1.74246	0.871228	−	0.490879i	$-0.163324\pi$
$107$	18.0241	1.74246	0.871228	+	0.490879i	$0.163324\pi$
$108$	20.6147	1.98365
$109$	8.12577	0.778308	0.389154	−	0.921173i	$-0.372767\pi$
$109$	8.12577	0.778308	0.389154	+	0.921173i	$0.372767\pi$
$110$	−5.58854	−0.532846
$111$	−5.44306	−0.516632
$112$	43.9867	4.15635
$113$	−1.25194	−0.117773	−0.0588865	−	0.998265i	$-0.518755\pi$
$113$	−1.25194	−0.117773	−0.0588865	+	0.998265i	$0.518755\pi$
$114$	7.66976	0.718339
$115$	−2.29086	−0.213624
$116$	41.8465	3.88535
$117$	−3.20497	−0.296300
$118$	11.8776	1.09342
$119$	13.5725	1.24418
$120$	14.3879	1.31343
$121$	−10.1816	−0.925602
$122$	−22.7876	−2.06309
$123$	−7.83557	−0.706510
$124$	26.3814	2.36912
$125$	−10.8861	−0.973680
$126$	22.3224	1.98864
$127$	−15.5943	−1.38377	−0.691886	−	0.722007i	$-0.743220\pi$
$127$	−15.5943	−1.38377	−0.691886	+	0.722007i	$0.743220\pi$
$128$	−23.8669	−2.10956
$129$	−6.73345	−0.592848
$130$	−7.94095	−0.696468
$131$	3.38642	0.295873	0.147936	−	0.988997i	$-0.452737\pi$
$131$	3.38642	0.295873	0.147936	+	0.988997i	$0.452737\pi$
$132$	−3.39485	−0.295484
$133$	13.2655	1.15027
$134$	22.8083	1.97034
$135$	8.95800	0.770982
$136$	−36.0687	−3.09287
$137$	0.634307	0.0541925	0.0270962	−	0.999633i	$-0.491374\pi$
$137$	0.634307	0.0541925	0.0270962	+	0.999633i	$0.491374\pi$
$138$	−1.91957	−0.163404
$139$	−6.44454	−0.546618	−0.273309	−	0.961926i	$-0.588118\pi$
$139$	−6.44454	−0.546618	−0.273309	+	0.961926i	$0.588118\pi$
$140$	40.0966	3.38878
$141$	−6.95477	−0.585697
$142$	30.0418	2.52105
$143$	1.16286	0.0972434
$144$	−33.0331	−2.75276
$145$	18.1842	1.51012
$146$	−9.98618	−0.826462
$147$	−2.86354	−0.236181
$148$	40.3113	3.31357
$149$	13.4006	1.09782	0.548911	−	0.835881i	$-0.315043\pi$
$149$	13.4006	1.09782	0.548911	+	0.835881i	$0.315043\pi$
$150$	0.476125	0.0388755
$151$	23.2078	1.88863	0.944313	−	0.329049i	$-0.106728\pi$
$151$	23.2078	1.88863	0.944313	+	0.329049i	$0.106728\pi$
$152$	−35.2530	−2.85940
$153$	−10.1926	−0.824025
$154$	−8.09925	−0.652656
$155$	11.4639	0.920803
$156$	−4.82387	−0.386219
$157$	−14.2126	−1.13429	−0.567143	−	0.823619i	$-0.691951\pi$
$157$	−14.2126	−1.13429	−0.567143	+	0.823619i	$0.691951\pi$
$158$	−17.9750	−1.43002
$159$	−0.200967	−0.0159377
$160$	−41.4214	−3.27465
$161$	−3.32005	−0.261657
$162$	−12.6644	−0.995008
$163$	2.71697	0.212810	0.106405	−	0.994323i	$-0.466066\pi$
$163$	2.71697	0.212810	0.106405	+	0.994323i	$0.466066\pi$
$164$	58.0302	4.53140
$165$	−1.47522	−0.114845
$166$	38.1896	2.96409
$167$	−18.1129	−1.40162	−0.700809	−	0.713349i	$-0.747177\pi$
$167$	−18.1129	−1.40162	−0.700809	+	0.713349i	$0.747177\pi$
$168$	20.8518	1.60875
$169$	−11.3476	−0.872896
$170$	−25.2543	−1.93691
$171$	−9.96211	−0.761822
$172$	49.8680	3.80240
$173$	12.9622	0.985495	0.492748	−	0.870172i	$-0.335993\pi$
$173$	12.9622	0.985495	0.492748	+	0.870172i	$0.335993\pi$
$174$	15.2370	1.15511
$175$	0.823500	0.0622507
$176$	11.9854	0.903435
$177$	3.13536	0.235668
$178$	43.7943	3.28252
$179$	−16.1703	−1.20863	−0.604313	−	0.796747i	$-0.706552\pi$
$179$	−16.1703	−1.20863	−0.604313	+	0.796747i	$0.706552\pi$
$180$	−30.1117	−2.24439
$181$	−0.236626	−0.0175883	−0.00879415	−	0.999961i	$-0.502799\pi$
$181$	−0.236626	−0.0175883	−0.00879415	+	0.999961i	$0.502799\pi$
$182$	−11.5085	−0.853068
$183$	−6.01527	−0.444662
$184$	8.82303	0.650442
$185$	17.5171	1.28788
$186$	9.60587	0.704337
$187$	3.69820	0.270439
$188$	51.5070	3.75654
$189$	12.9825	0.944336
$190$	−24.6831	−1.79070
$191$	−8.68304	−0.628283	−0.314141	−	0.949376i	$-0.601717\pi$
$191$	−8.68304	−0.628283	−0.314141	+	0.949376i	$0.601717\pi$
$192$	−15.8460	−1.14359
$193$	16.5347	1.19020	0.595098	−	0.803653i	$-0.297113\pi$
$193$	16.5347	1.19020	0.595098	+	0.803653i	$0.297113\pi$
$194$	−8.20688	−0.589219
$195$	−2.09619	−0.150111
$196$	21.2074	1.51481
$197$	−13.7731	−0.981296	−0.490648	−	0.871358i	$-0.663240\pi$
$197$	−13.7731	−0.981296	−0.490648	+	0.871358i	$0.663240\pi$
$198$	6.08236	0.432255
$199$	12.8496	0.910884	0.455442	−	0.890266i	$-0.349481\pi$
$199$	12.8496	0.910884	0.455442	+	0.890266i	$0.349481\pi$
$200$	−2.18845	−0.154747
$201$	6.02075	0.424671
$202$	43.4434	3.05667
$203$	26.3536	1.84966
$204$	−15.3411	−1.07409
$205$	25.2167	1.76121
$206$	25.5071	1.77716
$207$	2.49329	0.173296
$208$	17.0305	1.18085
$209$	3.61456	0.250025
$210$	14.5998	1.00748
$211$	18.2059	1.25335	0.626674	−	0.779282i	$-0.284416\pi$
$211$	18.2059	1.25335	0.626674	+	0.779282i	$0.284416\pi$
$212$	1.48836	0.102221
$213$	7.93019	0.543368
$214$	−48.6045	−3.32254
$215$	21.6699	1.47787
$216$	−34.5009	−2.34749
$217$	16.6142	1.12784
$218$	−21.9123	−1.48409
$219$	−2.63607	−0.178129
$220$	10.9255	0.736594
$221$	5.25490	0.353483
$222$	14.6780	0.985121
$223$	27.3556	1.83187	0.915933	−	0.401332i	$-0.131453\pi$
$223$	27.3556	1.83187	0.915933	+	0.401332i	$0.131453\pi$
$224$	−60.0304	−4.01095
$225$	−0.618431	−0.0412287
$226$	3.37604	0.224571
$227$	3.05593	0.202829	0.101414	−	0.994844i	$-0.467663\pi$
$227$	3.05593	0.202829	0.101414	+	0.994844i	$0.467663\pi$
$228$	−14.9942	−0.993014
$229$	−19.9015	−1.31513	−0.657563	−	0.753400i	$-0.728412\pi$
$229$	−19.9015	−1.31513	−0.657563	+	0.753400i	$0.728412\pi$
$230$	6.17762	0.407340
$231$	−2.13797	−0.140668
$232$	−70.0347	−4.59800
$233$	10.5721	0.692604	0.346302	−	0.938123i	$-0.387437\pi$
$233$	10.5721	0.692604	0.346302	+	0.938123i	$0.387437\pi$
$234$	8.64265	0.564987
$235$	22.3821	1.46005
$236$	−23.2205	−1.51152
$237$	−4.74490	−0.308214
$238$	−36.6000	−2.37243
$239$	−18.6274	−1.20491	−0.602453	−	0.798154i	$-0.705810\pi$
$239$	−18.6274	−1.20491	−0.602453	+	0.798154i	$0.705810\pi$
$240$	−21.6050	−1.39460
$241$	24.9689	1.60839	0.804195	−	0.594366i	$-0.202597\pi$
$241$	24.9689	1.60839	0.804195	+	0.594366i	$0.202597\pi$
$242$	27.4562	1.76495
$243$	−15.0740	−0.966998
$244$	44.5491	2.85197
$245$	9.21556	0.588761
$246$	21.1297	1.34718
$247$	5.13606	0.326800
$248$	−44.1521	−2.80366
$249$	10.0810	0.638855
$250$	29.3558	1.85663
$251$	−27.4043	−1.72974	−0.864872	−	0.501992i	$-0.832601\pi$
$251$	−27.4043	−1.72974	−0.864872	+	0.501992i	$0.832601\pi$
$252$	−43.6397	−2.74904
$253$	−0.904642	−0.0568744
$254$	42.0522	2.63859
$255$	−6.66641	−0.417467
$256$	19.8390	1.23994
$257$	−21.8908	−1.36551	−0.682757	−	0.730646i	$-0.739219\pi$
$257$	−21.8908	−1.36551	−0.682757	+	0.730646i	$0.739219\pi$
$258$	18.1577	1.13045
$259$	25.3868	1.57746
$260$	15.5244	0.962780
$261$	−19.7910	−1.22503
$262$	−9.13195	−0.564174
$263$	2.92025	0.180070	0.0900351	−	0.995939i	$-0.471302\pi$
$263$	2.92025	0.180070	0.0900351	+	0.995939i	$0.471302\pi$
$264$	5.68165	0.349682
$265$	0.646760	0.0397301
$266$	−35.7723	−2.19334
$267$	11.5605	0.707488
$268$	−44.5897	−2.72375
$269$	−28.7995	−1.75594	−0.877969	−	0.478718i	$-0.841102\pi$
$269$	−28.7995	−1.75594	−0.877969	+	0.478718i	$0.841102\pi$
$270$	−24.1565	−1.47012
$271$	−24.6882	−1.49970	−0.749851	−	0.661607i	$-0.769875\pi$
$271$	−24.6882	−1.49970	−0.749851	+	0.661607i	$0.769875\pi$
$272$	54.1614	3.28402
$273$	−3.03792	−0.183863
$274$	−1.71050	−0.103335
$275$	0.224386	0.0135310
$276$	3.75270	0.225886
$277$	2.08510	0.125281	0.0626406	−	0.998036i	$-0.480048\pi$
$277$	2.08510	0.125281	0.0626406	+	0.998036i	$0.480048\pi$
$278$	17.3786	1.04230
$279$	−12.4769	−0.746972
$280$	−67.1060	−4.01035
$281$	−9.85673	−0.588003	−0.294001	−	0.955805i	$-0.594987\pi$
$281$	−9.85673	−0.588003	−0.294001	+	0.955805i	$0.594987\pi$
$282$	18.7545	1.11681
$283$	−16.9321	−1.00651	−0.503255	−	0.864138i	$-0.667864\pi$
$283$	−16.9321	−1.00651	−0.503255	+	0.864138i	$0.667864\pi$
$284$	−58.7310	−3.48504
$285$	−6.51565	−0.385954
$286$	−3.13582	−0.185425
$287$	36.5456	2.15722
$288$	45.0816	2.65646
$289$	−0.288063	−0.0169449
$290$	−49.0362	−2.87951
$291$	−2.16638	−0.126996
$292$	19.5227	1.14248
$293$	−21.2328	−1.24043	−0.620217	−	0.784430i	$-0.712956\pi$
$293$	−21.2328	−1.24043	−0.620217	+	0.784430i	$0.712956\pi$
$294$	7.72194	0.450353
$295$	−10.0903	−0.587482
$296$	−67.4653	−3.92134
$297$	3.53744	0.205263
$298$	−36.1367	−2.09334
$299$	−1.28544	−0.0743388
$300$	−0.930813	−0.0537405
$301$	31.4053	1.81017
$302$	−62.5831	−3.60125
$303$	11.4678	0.658809
$304$	52.9365	3.03612
$305$	19.3586	1.10847
$306$	27.4858	1.57126
$307$	1.58739	0.0905970	0.0452985	−	0.998973i	$-0.485576\pi$
$307$	1.58739	0.0905970	0.0452985	+	0.998973i	$0.485576\pi$
$308$	15.8338	0.902216
$309$	6.73315	0.383035
$310$	−30.9140	−1.75580
$311$	24.6168	1.39589	0.697946	−	0.716151i	$-0.254098\pi$
$311$	24.6168	1.39589	0.697946	+	0.716151i	$0.254098\pi$
$312$	8.07326	0.457058
$313$	−24.8035	−1.40198	−0.700988	−	0.713173i	$-0.747257\pi$
$313$	−24.8035	−1.40198	−0.700988	+	0.713173i	$0.747257\pi$
$314$	38.3261	2.16287
$315$	−18.9634	−1.06847
$316$	35.1407	1.97682
$317$	15.1546	0.851166	0.425583	−	0.904919i	$-0.360069\pi$
$317$	15.1546	0.851166	0.425583	+	0.904919i	$0.360069\pi$
$318$	0.541935	0.0303902
$319$	7.18079	0.402047
$320$	50.9963	2.85078
$321$	−12.8302	−0.716113
$322$	8.95298	0.498930
$323$	16.3340	0.908847
$324$	24.7585	1.37547
$325$	0.318838	0.0176859
$326$	−7.32669	−0.405788
$327$	−5.78422	−0.319868
$328$	−97.1199	−5.36255
$329$	32.4375	1.78834
$330$	3.97812	0.218989
$331$	0.0337366	0.00185433	0.000927166	−	1.00000i	$-0.499705\pi$
$331$	0.0337366	0.00185433	0.000927166		1.00000i	$0.499705\pi$
$332$	−74.6597	−4.09748
$333$	−19.0649	−1.04475
$334$	48.8439	2.67262
$335$	−19.3762	−1.05864
$336$	−31.3113	−1.70817
$337$	−1.67866	−0.0914425	−0.0457213	−	0.998954i	$-0.514559\pi$
$337$	−1.67866	−0.0914425	−0.0457213	+	0.998954i	$0.514559\pi$
$338$	30.6005	1.66445
$339$	0.891180	0.0484022
$340$	49.3714	2.67754
$341$	4.52700	0.245151
$342$	26.8642	1.45265
$343$	−9.88462	−0.533719
$344$	−83.4594	−4.49983
$345$	1.63072	0.0877949
$346$	−34.9543	−1.87915
$347$	−6.63133	−0.355989	−0.177994	−	0.984032i	$-0.556961\pi$
$347$	−6.63133	−0.355989	−0.177994	+	0.984032i	$0.556961\pi$
$348$	−29.7879	−1.59680
$349$	1.00000	0.0535288
$349$	1.00000	0.0535288
$350$	−2.22068	−0.118700
$351$	5.02648	0.268294
$352$	−16.3570	−0.871830
$353$	−28.9462	−1.54065	−0.770325	−	0.637651i	$-0.779906\pi$
$353$	−28.9462	−1.54065	−0.770325	+	0.637651i	$0.779906\pi$
$354$	−8.45493	−0.449375
$355$	−25.5213	−1.35453
$356$	−85.6167	−4.53768
$357$	−9.66137	−0.511334
$358$	43.6055	2.30462
$359$	−13.3695	−0.705614	−0.352807	−	0.935696i	$-0.614773\pi$
$359$	−13.3695	−0.705614	−0.352807	+	0.935696i	$0.614773\pi$
$360$	50.3951	2.65606
$361$	−3.03541	−0.159759
$362$	0.638096	0.0335376
$363$	7.24765	0.380403
$364$	22.4988	1.17926
$365$	8.48350	0.444047
$366$	16.2210	0.847886
$367$	32.5643	1.69984	0.849920	−	0.526911i	$-0.176650\pi$
$367$	32.5643	1.69984	0.849920	+	0.526911i	$0.176650\pi$
$368$	−13.2488	−0.690641
$369$	−27.4450	−1.42873
$370$	−47.2372	−2.45575
$371$	0.937324	0.0486634
$372$	−18.7792	−0.973658
$373$	−20.5365	−1.06334	−0.531670	−	0.846951i	$-0.678435\pi$
$373$	−20.5365	−1.06334	−0.531670	+	0.846951i	$0.678435\pi$
$374$	−9.97271	−0.515676
$375$	7.74911	0.400162
$376$	−86.2026	−4.44556
$377$	10.2034	0.525504
$378$	−35.0091	−1.80067
$379$	−17.3830	−0.892902	−0.446451	−	0.894808i	$-0.647312\pi$
$379$	−17.3830	−0.892902	−0.446451	+	0.894808i	$0.647312\pi$
$380$	48.2549	2.47542
$381$	11.1006	0.568701
$382$	23.4150	1.19802
$383$	35.3295	1.80525	0.902627	−	0.430423i	$-0.141636\pi$
$383$	35.3295	1.80525	0.902627	+	0.430423i	$0.141636\pi$
$384$	16.9894	0.866985
$385$	6.88051	0.350663
$386$	−44.5882	−2.26948
$387$	−23.5847	−1.19888
$388$	16.0442	0.814523
$389$	−11.7850	−0.597526	−0.298763	−	0.954327i	$-0.596574\pi$
$389$	−11.7850	−0.597526	−0.298763	+	0.954327i	$0.596574\pi$
$390$	5.65266	0.286233
$391$	−4.08802	−0.206740
$392$	−35.4929	−1.79266
$393$	−2.41058	−0.121598
$394$	37.1412	1.87115
$395$	15.2702	0.768328
$396$	−11.8909	−0.597539
$397$	−1.81497	−0.0910905	−0.0455453	−	0.998962i	$-0.514503\pi$
$397$	−1.81497	−0.0910905	−0.0455453	+	0.998962i	$0.514503\pi$
$398$	−34.6507	−1.73688
$399$	−9.44287	−0.472735
$400$	3.28621	0.164310
$401$	38.5441	1.92480	0.962400	−	0.271636i	$-0.0875646\pi$
$401$	38.5441	1.92480	0.962400	+	0.271636i	$0.0875646\pi$
$402$	−16.2358	−0.809768
$403$	6.43258	0.320430
$404$	−84.9307	−4.22546
$405$	10.7587	0.534604
$406$	−71.0662	−3.52696
$407$	6.91735	0.342880
$408$	25.6750	1.27110
$409$	−29.0200	−1.43495	−0.717474	−	0.696586i	$-0.754702\pi$
$409$	−29.0200	−1.43495	−0.717474	+	0.696586i	$0.754702\pi$
$410$	−68.0004	−3.35830
$411$	−0.451523	−0.0222720
$412$	−49.8657	−2.45671
$413$	−14.6235	−0.719577
$414$	−6.72350	−0.330442
$415$	−32.4430	−1.59256
$416$	−23.2422	−1.13954
$417$	4.58746	0.224649
$418$	−9.74717	−0.476750
$419$	−3.63850	−0.177752	−0.0888761	−	0.996043i	$-0.528328\pi$
$419$	−3.63850	−0.177752	−0.0888761	+	0.996043i	$0.528328\pi$
$420$	−28.5422	−1.39272
$421$	31.1141	1.51641	0.758205	−	0.652016i	$-0.226076\pi$
$421$	31.1141	1.51641	0.758205	+	0.652016i	$0.226076\pi$
$422$	−49.0948	−2.38990
$423$	−24.3599	−1.18442
$424$	−2.49093	−0.120970
$425$	1.01399	0.0491855
$426$	−21.3849	−1.03610
$427$	28.0556	1.35771
$428$	95.0206	4.59299
$429$	−0.827768	−0.0399650
$430$	−58.4358	−2.81802
$431$	−16.2735	−0.783868	−0.391934	−	0.919993i	$-0.628194\pi$
$431$	−16.2735	−0.783868	−0.391934	+	0.919993i	$0.628194\pi$
$432$	51.8071	2.49257
$433$	26.8692	1.29125	0.645625	−	0.763655i	$-0.276597\pi$
$433$	26.8692	1.29125	0.645625	+	0.763655i	$0.276597\pi$
$434$	−44.8024	−2.15059
$435$	−12.9442	−0.620625
$436$	42.8379	2.05156
$437$	−3.99557	−0.191134
$438$	7.10853	0.339659
$439$	−24.4438	−1.16664	−0.583319	−	0.812243i	$-0.698246\pi$
$439$	−24.4438	−1.16664	−0.583319	+	0.812243i	$0.698246\pi$
$440$	−18.2849	−0.871699
$441$	−10.0299	−0.477614
$442$	−14.1706	−0.674026
$443$	13.3195	0.632830	0.316415	−	0.948621i	$-0.397521\pi$
$443$	13.3195	0.632830	0.316415	+	0.948621i	$0.397521\pi$
$444$	−28.6951	−1.36181
$445$	−37.2043	−1.76365
$446$	−73.7681	−3.49302
$447$	−9.53906	−0.451182
$448$	73.9070	3.49178
$449$	−32.9812	−1.55648	−0.778241	−	0.627966i	$-0.783888\pi$
$449$	−32.9812	−1.55648	−0.778241	+	0.627966i	$0.783888\pi$
$450$	1.66768	0.0786154
$451$	9.95789	0.468899
$452$	−6.60008	−0.310442
$453$	−16.5202	−0.776185
$454$	−8.24073	−0.386757
$455$	9.77676	0.458341
$456$	25.0944	1.17515
$457$	23.4320	1.09610	0.548052	−	0.836444i	$-0.315370\pi$
$457$	23.4320	1.09610	0.548052	+	0.836444i	$0.315370\pi$
$458$	53.6670	2.50770
$459$	15.9855	0.746139
$460$	−12.0771	−0.563097
$461$	9.11184	0.424381	0.212190	−	0.977228i	$-0.431940\pi$
$461$	9.11184	0.424381	0.212190	+	0.977228i	$0.431940\pi$
$462$	5.76534	0.268228
$463$	8.77945	0.408016	0.204008	−	0.978969i	$-0.434603\pi$
$463$	8.77945	0.408016	0.204008	+	0.978969i	$0.434603\pi$
$464$	105.165	4.88217
$465$	−8.16042	−0.378430
$466$	−28.5092	−1.32067
$467$	0.678789	0.0314106	0.0157053	−	0.999877i	$-0.495001\pi$
$467$	0.678789	0.0314106	0.0157053	+	0.999877i	$0.495001\pi$
$468$	−16.8962	−0.781025
$469$	−28.0812	−1.29667
$470$	−60.3565	−2.78404
$471$	10.1170	0.466167
$472$	38.8620	1.78877
$473$	8.55726	0.393463
$474$	12.7953	0.587707
$475$	0.991054	0.0454727
$476$	71.5521	3.27959
$477$	−0.703910	−0.0322298
$478$	50.2314	2.29753
$479$	−13.8896	−0.634632	−0.317316	−	0.948320i	$-0.602782\pi$
$479$	−13.8896	−0.634632	−0.317316	+	0.948320i	$0.602782\pi$
$480$	29.4853	1.34581
$481$	9.82911	0.448169
$482$	−67.3322	−3.06690
$483$	2.36333	0.107535
$484$	−53.6761	−2.43982
$485$	6.97194	0.316580
$486$	40.6491	1.84388
$487$	14.7416	0.668005	0.334002	−	0.942572i	$-0.391601\pi$
$487$	14.7416	0.668005	0.334002	+	0.942572i	$0.391601\pi$
$488$	−74.5578	−3.37507
$489$	−1.93404	−0.0874603
$490$	−24.8510	−1.12266
$491$	13.8417	0.624669	0.312334	−	0.949972i	$-0.398889\pi$
$491$	13.8417	0.624669	0.312334	+	0.949972i	$0.398889\pi$
$492$	−41.3080	−1.86231
$493$	32.4496	1.46146
$494$	−13.8501	−0.623146
$495$	−5.16711	−0.232244
$496$	66.2995	2.97694
$497$	−36.9870	−1.65909
$498$	−27.1847	−1.21818
$499$	−2.66200	−0.119167	−0.0595836	−	0.998223i	$-0.518977\pi$
$499$	−2.66200	−0.119167	−0.0595836	+	0.998223i	$0.518977\pi$
$500$	−57.3899	−2.56655
$501$	12.8934	0.576035
$502$	73.8995	3.29830
$503$	34.5304	1.53963	0.769817	−	0.638265i	$-0.220348\pi$
$503$	34.5304	1.53963	0.769817	+	0.638265i	$0.220348\pi$
$504$	73.0357	3.25327
$505$	−36.9062	−1.64230
$506$	2.43949	0.108449
$507$	8.07767	0.358742
$508$	−82.2111	−3.64753
$509$	−38.7591	−1.71797	−0.858983	−	0.512004i	$-0.828903\pi$
$509$	−38.7591	−1.71797	−0.858983	+	0.512004i	$0.828903\pi$
$510$	17.9769	0.796031
$511$	12.2948	0.543890
$512$	−5.76467	−0.254765
$513$	15.6240	0.689815
$514$	59.0317	2.60378
$515$	−21.6689	−0.954845
$516$	−35.4978	−1.56271
$517$	8.83852	0.388718
$518$	−68.4590	−3.00792
$519$	−9.22694	−0.405018
$520$	−25.9817	−1.13937
$521$	22.8129	0.999453	0.499727	−	0.866183i	$-0.333434\pi$
$521$	22.8129	0.999453	0.499727	+	0.866183i	$0.333434\pi$
$522$	53.3692	2.33591
$523$	−15.8394	−0.692608	−0.346304	−	0.938122i	$-0.612563\pi$
$523$	−15.8394	−0.692608	−0.346304	+	0.938122i	$0.612563\pi$
$524$	17.8527	0.779900
$525$	−0.586197	−0.0255837
$526$	−7.87486	−0.343360
$527$	20.4573	0.891132
$528$	−8.53166	−0.371293
$529$	1.00000	0.0434783
$530$	−1.74408	−0.0757579
$531$	10.9820	0.476576
$532$	69.9339	3.03202
$533$	14.1495	0.612884
$534$	−31.1744	−1.34905
$535$	41.2907	1.78515
$536$	74.6257	3.22334
$537$	11.5106	0.496720
$538$	77.6619	3.34824
$539$	3.63915	0.156749
$540$	47.2253	2.03225
$541$	25.5431	1.09818	0.549092	−	0.835762i	$-0.314974\pi$
$541$	25.5431	1.09818	0.549092	+	0.835762i	$0.314974\pi$
$542$	66.5751	2.85965
$543$	0.168439	0.00722842
$544$	−73.9162	−3.16913
$545$	18.6150	0.797379
$546$	8.19218	0.350593
$547$	4.46191	0.190777	0.0953887	−	0.995440i	$-0.469591\pi$
$547$	4.46191	0.190777	0.0953887	+	0.995440i	$0.469591\pi$
$548$	3.34398	0.142848
$549$	−21.0692	−0.899211
$550$	−0.605087	−0.0258010
$551$	31.7157	1.35113
$552$	−6.28055	−0.267318
$553$	22.1305	0.941086
$554$	−5.62275	−0.238888
$555$	−12.4693	−0.529292
$556$	−33.9747	−1.44085
$557$	16.3326	0.692035	0.346018	−	0.938228i	$-0.387534\pi$
$557$	16.3326	0.692035	0.346018	+	0.938228i	$0.387534\pi$
$558$	33.6457	1.42434
$559$	12.1593	0.514284
$560$	100.767	4.25820
$561$	−2.63251	−0.111145
$562$	26.5800	1.12121
$563$	−5.34345	−0.225200	−0.112600	−	0.993640i	$-0.535918\pi$
$563$	−5.34345	−0.225200	−0.112600	+	0.993640i	$0.535918\pi$
$564$	−36.6646	−1.54386
$565$	−2.86803	−0.120659
$566$	45.6598	1.91923
$567$	15.5922	0.654809
$568$	98.2927	4.12427
$569$	−17.7330	−0.743407	−0.371704	−	0.928351i	$-0.621226\pi$
$569$	−17.7330	−0.743407	−0.371704	+	0.928351i	$0.621226\pi$
$570$	17.5703	0.735941
$571$	9.92432	0.415320	0.207660	−	0.978201i	$-0.433415\pi$
$571$	9.92432	0.415320	0.207660	+	0.978201i	$0.433415\pi$
$572$	6.13045	0.256327
$573$	6.18090	0.258211
$574$	−98.5504	−4.11341
$575$	−0.248038	−0.0103439
$576$	−55.5025	−2.31261
$577$	31.5001	1.31137	0.655683	−	0.755036i	$-0.272381\pi$
$577$	31.5001	1.31137	0.655683	+	0.755036i	$0.272381\pi$
$578$	0.776802	0.0323107
$579$	−11.7700	−0.489146
$580$	95.8645	3.98056
$581$	−47.0183	−1.95065
$582$	5.84195	0.242157
$583$	0.255400	0.0105776
$584$	−32.6734	−1.35203
$585$	−7.34214	−0.303560
$586$	57.2572	2.36527
$587$	13.4817	0.556448	0.278224	−	0.960516i	$-0.410254\pi$
$587$	13.4817	0.556448	0.278224	+	0.960516i	$0.410254\pi$
$588$	−15.0962	−0.622557
$589$	19.9946	0.823863
$590$	27.2100	1.12022
$591$	9.80422	0.403292
$592$	101.307	4.16369
$593$	30.6068	1.25687	0.628435	−	0.777862i	$-0.283696\pi$
$593$	30.6068	1.25687	0.628435	+	0.777862i	$0.283696\pi$
$594$	−9.53921	−0.391398
$595$	31.0926	1.27467
$596$	70.6463	2.89378
$597$	−9.14681	−0.374354
$598$	3.46636	0.141750
$599$	−17.0407	−0.696265	−0.348132	−	0.937445i	$-0.613184\pi$
$599$	−17.0407	−0.696265	−0.348132	+	0.937445i	$0.613184\pi$
$600$	1.55782	0.0635976
$601$	−6.67339	−0.272213	−0.136107	−	0.990694i	$-0.543459\pi$
$601$	−6.67339	−0.272213	−0.136107	+	0.990694i	$0.543459\pi$
$602$	−84.6887	−3.45165
$603$	21.0884	0.858785
$604$	122.348	4.97829
$605$	−23.3247	−0.948283
$606$	−30.9246	−1.25623
$607$	−29.5774	−1.20051	−0.600255	−	0.799809i	$-0.704934\pi$
$607$	−29.5774	−1.20051	−0.600255	+	0.799809i	$0.704934\pi$
$608$	−72.2446	−2.92990
$609$	−18.7595	−0.760172
$610$	−52.2031	−2.11364
$611$	12.5590	0.508081
$612$	−53.7341	−2.17207
$613$	24.9678	1.00844	0.504220	−	0.863575i	$-0.331780\pi$
$613$	24.9678	1.00844	0.504220	+	0.863575i	$0.331780\pi$
$614$	−4.28061	−0.172751
$615$	−17.9502	−0.723822
$616$	−26.4996	−1.06770
$617$	−45.1520	−1.81775	−0.908875	−	0.417068i	$-0.863058\pi$
$617$	−45.1520	−1.81775	−0.908875	+	0.417068i	$0.863058\pi$
$618$	−18.1569	−0.730376
$619$	−4.18816	−0.168337	−0.0841683	−	0.996452i	$-0.526823\pi$
$619$	−4.18816	−0.168337	−0.0841683	+	0.996452i	$0.526823\pi$
$620$	60.4361	2.42717
$621$	−3.91032	−0.156916
$622$	−66.3826	−2.66170
$623$	−53.9187	−2.16021
$624$	−12.1229	−0.485306
$625$	−26.1787	−1.04715
$626$	66.8861	2.67330
$627$	−2.57298	−0.102755
$628$	−74.9266	−2.98990
$629$	31.2591	1.24638
$630$	51.1374	2.03736
$631$	−18.0614	−0.719014	−0.359507	−	0.933142i	$-0.617055\pi$
$631$	−18.0614	−0.719014	−0.359507	+	0.933142i	$0.617055\pi$
$632$	−58.8118	−2.33941
$633$	−12.9596	−0.515100
$634$	−40.8664	−1.62301
$635$	−35.7244	−1.41768
$636$	−1.05947	−0.0420107
$637$	5.17100	0.204883
$638$	−19.3640	−0.766628
$639$	27.7764	1.09882
$640$	−54.6758	−2.16125
$641$	33.8431	1.33672	0.668360	−	0.743838i	$-0.266996\pi$
$641$	33.8431	1.33672	0.668360	+	0.743838i	$0.266996\pi$
$642$	34.5984	1.36549
$643$	1.74455	0.0687983	0.0343991	−	0.999408i	$-0.489048\pi$
$643$	1.74455	0.0687983	0.0343991	+	0.999408i	$0.489048\pi$
$644$	−17.5029	−0.689709
$645$	−15.4254	−0.607375
$646$	−44.0469	−1.73300
$647$	−31.0628	−1.22120	−0.610602	−	0.791938i	$-0.709072\pi$
$647$	−31.0628	−1.22120	−0.610602	+	0.791938i	$0.709072\pi$
$648$	−41.4361	−1.62776
$649$	−3.98459	−0.156409
$650$	−0.859790	−0.0337238
$651$	−11.8266	−0.463520
$652$	14.3235	0.560951
$653$	−4.04867	−0.158437	−0.0792184	−	0.996857i	$-0.525242\pi$
$653$	−4.04867	−0.158437	−0.0792184	+	0.996857i	$0.525242\pi$
$654$	15.5979	0.609928
$655$	7.75781	0.303123
$656$	145.837	5.69397
$657$	−9.23314	−0.360219
$658$	−87.4723	−3.41002
$659$	−11.0006	−0.428522	−0.214261	−	0.976776i	$-0.568734\pi$
$659$	−11.0006	−0.428522	−0.214261	+	0.976776i	$0.568734\pi$
$660$	−7.77713	−0.302724
$661$	−39.5130	−1.53688	−0.768440	−	0.639922i	$-0.778966\pi$
$661$	−39.5130	−1.53688	−0.768440	+	0.639922i	$0.778966\pi$
$662$	−0.0909755	−0.00353586
$663$	−3.74063	−0.145274
$664$	124.951	4.84904
$665$	30.3894	1.17845
$666$	51.4113	1.99215
$667$	−7.93772	−0.307350
$668$	−95.4887	−3.69457
$669$	−19.4727	−0.752858
$670$	52.2507	2.01862
$671$	7.64455	0.295115
$672$	42.7318	1.64842
$673$	51.0598	1.96821	0.984105	−	0.177587i	$-0.0568293\pi$
$673$	51.0598	1.96821	0.984105	+	0.177587i	$0.0568293\pi$
$674$	4.52674	0.174364
$675$	0.969909	0.0373318
$676$	−59.8232	−2.30089
$677$	44.9802	1.72873	0.864366	−	0.502864i	$-0.167720\pi$
$677$	44.9802	1.72873	0.864366	+	0.502864i	$0.167720\pi$
$678$	−2.40319	−0.0922939
$679$	10.1042	0.387762
$680$	−82.6284	−3.16866
$681$	−2.17532	−0.0833584
$682$	−12.2077	−0.467457
$683$	−26.9095	−1.02966	−0.514832	−	0.857291i	$-0.672146\pi$
$683$	−26.9095	−1.02966	−0.514832	+	0.857291i	$0.672146\pi$
$684$	−52.5189	−2.00811
$685$	1.45311	0.0555204
$686$	26.6552	1.01770
$687$	14.1666	0.540489
$688$	125.324	4.77793
$689$	0.362907	0.0138257
$690$	−4.39746	−0.167408
$691$	−11.6954	−0.444915	−0.222458	−	0.974942i	$-0.571408\pi$
$691$	−11.6954	−0.444915	−0.222458	+	0.974942i	$0.571408\pi$
$692$	68.3347	2.59770
$693$	−7.48850	−0.284464
$694$	17.8823	0.678803
$695$	−14.7635	−0.560013
$696$	49.8532	1.88968
$697$	44.9991	1.70446
$698$	−2.69664	−0.102069
$699$	−7.52563	−0.284646
$700$	4.34138	0.164089
$701$	15.7180	0.593659	0.296830	−	0.954930i	$-0.404071\pi$
$701$	15.7180	0.593659	0.296830	+	0.954930i	$0.404071\pi$
$702$	−13.5546	−0.511585
$703$	30.5522	1.15230
$704$	20.1380	0.758981
$705$	−15.9324	−0.600049
$706$	78.0574	2.93773
$707$	−53.4867	−2.01157
$708$	16.5292	0.621205
$709$	1.88790	0.0709016	0.0354508	−	0.999371i	$-0.488713\pi$
$709$	1.88790	0.0709016	0.0354508	+	0.999371i	$0.488713\pi$
$710$	68.8216	2.58283
$711$	−16.6196	−0.623282
$712$	143.289	5.36998
$713$	−5.00419	−0.187408
$714$	26.0532	0.975017
$715$	2.66395	0.0996262
$716$	−85.2477	−3.18585
$717$	13.2597	0.495191
$718$	36.0526	1.34547
$719$	18.7936	0.700883	0.350442	−	0.936585i	$-0.386032\pi$
$719$	18.7936	0.700883	0.350442	+	0.936585i	$0.386032\pi$
$720$	−75.6741	−2.82021
$721$	−31.4039	−1.16954
$722$	8.18541	0.304629
$723$	−17.7738	−0.661014
$724$	−1.24746	−0.0463615
$725$	1.96886	0.0731215
$726$	−19.5443	−0.725357
$727$	4.07579	0.151163	0.0755813	−	0.997140i	$-0.475919\pi$
$727$	4.07579	0.151163	0.0755813	+	0.997140i	$0.475919\pi$
$728$	−37.6542	−1.39556
$729$	−3.35885	−0.124402
$730$	−22.8769	−0.846714
$731$	38.6697	1.43025
$732$	−31.7117	−1.17210
$733$	−47.2237	−1.74425	−0.872124	−	0.489285i	$-0.837258\pi$
$733$	−47.2237	−1.74425	−0.872124	+	0.489285i	$0.837258\pi$
$734$	−87.8140	−3.24128
$735$	−6.55997	−0.241968
$736$	18.0812	0.666481
$737$	−7.65152	−0.281847
$738$	74.0092	2.72432
$739$	−28.5960	−1.05192	−0.525960	−	0.850510i	$-0.676294\pi$
$739$	−28.5960	−1.05192	−0.525960	+	0.850510i	$0.676294\pi$
$740$	92.3475	3.39476
$741$	−3.65603	−0.134308
$742$	−2.52762	−0.0927920
$743$	−22.1837	−0.813843	−0.406921	−	0.913463i	$-0.633398\pi$
$743$	−22.1837	−0.813843	−0.406921	+	0.913463i	$0.633398\pi$
$744$	31.4291	1.15225
$745$	30.6990	1.12472
$746$	55.3796	2.02759
$747$	35.3098	1.29192
$748$	19.4964	0.712859
$749$	59.8410	2.18654
$750$	−20.8965	−0.763034
$751$	43.6571	1.59307	0.796536	−	0.604591i	$-0.206664\pi$
$751$	43.6571	1.59307	0.796536	+	0.604591i	$0.206664\pi$
$752$	129.443	4.72030
$753$	19.5074	0.710889
$754$	−27.5150	−1.00204
$755$	53.1659	1.93490
$756$	68.4418	2.48921
$757$	−36.8626	−1.33980	−0.669898	−	0.742453i	$-0.733662\pi$
$757$	−36.8626	−1.33980	−0.669898	+	0.742453i	$0.733662\pi$
$758$	46.8756	1.70260
$759$	0.643957	0.0233742
$760$	−80.7598	−2.92946
$761$	−26.5900	−0.963887	−0.481944	−	0.876202i	$-0.660069\pi$
$761$	−26.5900	−0.963887	−0.481944	+	0.876202i	$0.660069\pi$
$762$	−29.9343	−1.08441
$763$	26.9780	0.976669
$764$	−45.7758	−1.65611
$765$	−23.3499	−0.844216
$766$	−95.2710	−3.44228
$767$	−5.66185	−0.204438
$768$	−14.1221	−0.509588
$769$	−43.5640	−1.57096	−0.785479	−	0.618889i	$-0.787583\pi$
$769$	−43.5640	−1.57096	−0.785479	+	0.618889i	$0.787583\pi$
$770$	−18.5542	−0.668648
$771$	15.5827	0.561197
$772$	87.1689	3.13728
$773$	4.92929	0.177294	0.0886472	−	0.996063i	$-0.471746\pi$
$773$	4.92929	0.177294	0.0886472	+	0.996063i	$0.471746\pi$
$774$	63.5994	2.28603
$775$	1.24123	0.0445863
$776$	−26.8518	−0.963922
$777$	−18.0712	−0.648302
$778$	31.7800	1.13937
$779$	43.9814	1.57580
$780$	−11.0508	−0.395682
$781$	−10.0781	−0.360624
$782$	11.0239	0.394215
$783$	31.0390	1.10924
$784$	53.2966	1.90345
$785$	−32.5590	−1.16208
$786$	6.50046	0.231864
$787$	2.67764	0.0954477	0.0477238	−	0.998861i	$-0.484803\pi$
$787$	2.67764	0.0954477	0.0477238	+	0.998861i	$0.484803\pi$
$788$	−72.6101	−2.58663
$789$	−2.07874	−0.0740051
$790$	−41.1783	−1.46506
$791$	−4.15652	−0.147789
$792$	19.9006	0.707139
$793$	10.8624	0.385736
$794$	4.89431	0.173693
$795$	−0.460387	−0.0163283
$796$	67.7413	2.40103
$797$	51.1012	1.81010	0.905049	−	0.425308i	$-0.139834\pi$
$797$	51.1012	1.81010	0.905049	+	0.425308i	$0.139834\pi$
$798$	25.4640	0.901416
$799$	39.9407	1.41300
$800$	−4.48482	−0.158562
$801$	40.4918	1.43071
$802$	−103.940	−3.67023
$803$	3.35007	0.118221
$804$	31.7406	1.11940
$805$	−7.60578	−0.268068
$806$	−17.3463	−0.610999
$807$	20.5005	0.721653
$808$	142.141	5.00049
$809$	−52.4321	−1.84341	−0.921707	−	0.387887i	$-0.873205\pi$
$809$	−52.4321	−1.84341	−0.921707	+	0.387887i	$0.873205\pi$
$810$	−29.0123	−1.01939
$811$	−11.7890	−0.413968	−0.206984	−	0.978344i	$-0.566365\pi$
$811$	−11.7890	−0.413968	−0.206984	+	0.978344i	$0.566365\pi$
$812$	138.933	4.87558
$813$	17.5740	0.616345
$814$	−18.6536	−0.653808
$815$	6.22420	0.218024
$816$	−38.5540	−1.34966
$817$	37.7952	1.32229
$818$	78.2565	2.73617
$819$	−10.6407	−0.371815
$820$	132.939	4.64244
$821$	−12.9644	−0.452461	−0.226230	−	0.974074i	$-0.572640\pi$
$821$	−12.9644	−0.452461	−0.226230	+	0.974074i	$0.572640\pi$
$822$	1.21759	0.0424684
$823$	24.7339	0.862168	0.431084	−	0.902312i	$-0.358131\pi$
$823$	24.7339	0.862168	0.431084	+	0.902312i	$0.358131\pi$
$824$	83.4556	2.90731
$825$	−0.159726	−0.00556094
$826$	39.4344	1.37210
$827$	−16.8827	−0.587067	−0.293534	−	0.955949i	$-0.594831\pi$
$827$	−16.8827	−0.587067	−0.293534	+	0.955949i	$0.594831\pi$
$828$	13.1443	0.456795
$829$	18.1980	0.632043	0.316022	−	0.948752i	$-0.397653\pi$
$829$	18.1980	0.632043	0.316022	+	0.948752i	$0.397653\pi$
$830$	87.4870	3.03672
$831$	−1.48425	−0.0514880
$832$	28.6149	0.992042
$833$	16.4451	0.569789
$834$	−12.3707	−0.428363
$835$	−41.4941	−1.43596
$836$	19.0555	0.659047
$837$	19.5680	0.676369
$838$	9.81171	0.338940
$839$	14.7718	0.509978	0.254989	−	0.966944i	$-0.417928\pi$
$839$	14.7718	0.509978	0.254989	+	0.966944i	$0.417928\pi$
$840$	47.7685	1.64817
$841$	34.0073	1.17267
$842$	−83.9036	−2.89151
$843$	7.01638	0.241657
$844$	95.9791	3.30374
$845$	−25.9959	−0.894285
$846$	65.6898	2.25846
$847$	−33.8035	−1.16150
$848$	3.74043	0.128447
$849$	12.0529	0.413655
$850$	−2.73435	−0.0937875
$851$	−7.64650	−0.262119
$852$	41.8069	1.43228
$853$	−38.7080	−1.32534	−0.662669	−	0.748913i	$-0.730576\pi$
$853$	−38.7080	−1.32534	−0.662669	+	0.748913i	$0.730576\pi$
$854$	−75.6559	−2.58889
$855$	−22.8218	−0.780489
$856$	−159.027	−5.43544
$857$	32.3889	1.10638	0.553192	−	0.833054i	$-0.313409\pi$
$857$	32.3889	1.10638	0.553192	+	0.833054i	$0.313409\pi$
$858$	2.23219	0.0762057
$859$	−26.1909	−0.893622	−0.446811	−	0.894628i	$-0.647440\pi$
$859$	−26.1909	−0.893622	−0.446811	+	0.894628i	$0.647440\pi$
$860$	114.241	3.89557
$861$	−26.0145	−0.886572
$862$	43.8838	1.49469
$863$	−18.8082	−0.640238	−0.320119	−	0.947377i	$-0.603723\pi$
$863$	−18.8082	−0.640238	−0.320119	+	0.947377i	$0.603723\pi$
$864$	−70.7032	−2.40537
$865$	29.6945	1.00964
$866$	−72.4564	−2.46217
$867$	0.205054	0.00696399
$868$	87.5877	2.97292
$869$	6.03009	0.204557
$870$	34.9058	1.18342
$871$	−10.8723	−0.368394
$872$	−71.6939	−2.42786
$873$	−7.58801	−0.256815
$874$	10.7746	0.364457
$875$	−36.1424	−1.22183
$876$	−13.8970	−0.469536
$877$	16.8129	0.567733	0.283866	−	0.958864i	$-0.408383\pi$
$877$	16.8129	0.567733	0.283866	+	0.958864i	$0.408383\pi$
$878$	65.9161	2.22456
$879$	15.1143	0.509792
$880$	27.4569	0.925573
$881$	−1.41066	−0.0475264	−0.0237632	−	0.999718i	$-0.507565\pi$
$881$	−1.41066	−0.0475264	−0.0237632	+	0.999718i	$0.507565\pi$
$882$	27.0470	0.910719
$883$	4.47001	0.150428	0.0752139	−	0.997167i	$-0.476036\pi$
$883$	4.47001	0.150428	0.0752139	+	0.997167i	$0.476036\pi$
$884$	27.7031	0.931757
$885$	7.18267	0.241443
$886$	−35.9179	−1.20669
$887$	−10.8053	−0.362806	−0.181403	−	0.983409i	$-0.558064\pi$
$887$	−10.8053	−0.362806	−0.181403	+	0.983409i	$0.558064\pi$
$888$	48.0243	1.61159
$889$	−51.7740	−1.73644
$890$	100.327	3.36295
$891$	4.24852	0.142331
$892$	144.215	4.82867
$893$	39.0374	1.30634
$894$	25.7234	0.860319
$895$	−37.0439	−1.23824
$896$	−79.2395	−2.64721
$897$	0.915022	0.0305517
$898$	88.9385	2.96792
$899$	39.7219	1.32480
$900$	−3.26028	−0.108676
$901$	1.15414	0.0384499
$902$	−26.8528	−0.894102
$903$	−22.3554	−0.743942
$904$	11.0459	0.367382
$905$	−0.542078	−0.0180193
$906$	44.5489	1.48004
$907$	0.0664075	0.00220503	0.00110251	−	0.999999i	$-0.499649\pi$
$907$	0.0664075	0.00220503	0.00110251	+	0.999999i	$0.499649\pi$
$908$	16.1104	0.534643
$909$	40.1674	1.33227
$910$	−26.3644	−0.873971
$911$	−5.43324	−0.180011	−0.0900057	−	0.995941i	$-0.528689\pi$
$911$	−5.43324	−0.180011	−0.0900057	+	0.995941i	$0.528689\pi$
$912$	−37.6821	−1.24778
$913$	−12.8115	−0.423998
$914$	−63.1877	−2.09006
$915$	−13.7801	−0.455558
$916$	−104.918	−3.46658
$917$	11.2431	0.371280
$918$	−43.1071	−1.42275
$919$	−46.0134	−1.51784	−0.758921	−	0.651183i	$-0.774273\pi$
$919$	−46.0134	−1.51784	−0.758921	+	0.651183i	$0.774273\pi$
$920$	20.2123	0.666380
$921$	−1.12996	−0.0372335
$922$	−24.5713	−0.809214
$923$	−14.3204	−0.471361
$924$	−11.2711	−0.370792
$925$	1.89662	0.0623606
$926$	−23.6750	−0.778009
$927$	23.5836	0.774588
$928$	−143.523	−4.71138
$929$	11.7304	0.384862	0.192431	−	0.981311i	$-0.438363\pi$
$929$	11.7304	0.384862	0.192431	+	0.981311i	$0.438363\pi$
$930$	22.0057	0.721596
$931$	16.0732	0.526778
$932$	55.7349	1.82566
$933$	−17.5231	−0.573682
$934$	−1.83045	−0.0598941
$935$	8.47206	0.277066
$936$	28.2775	0.924280
$937$	27.4994	0.898365	0.449183	−	0.893440i	$-0.351715\pi$
$937$	27.4994	0.898365	0.449183	+	0.893440i	$0.351715\pi$
$938$	75.7249	2.47250
$939$	17.6560	0.576183
$940$	117.995	3.84858
$941$	52.3499	1.70656	0.853279	−	0.521455i	$-0.174611\pi$
$941$	52.3499	1.70656	0.853279	+	0.521455i	$0.174611\pi$
$942$	−27.2819	−0.888893
$943$	−11.0075	−0.358455
$944$	−58.3557	−1.89932
$945$	29.7410	0.967476
$946$	−23.0758	−0.750260
$947$	−59.6308	−1.93774	−0.968871	−	0.247567i	$-0.920369\pi$
$947$	−59.6308	−1.93774	−0.968871	+	0.247567i	$0.920369\pi$
$948$	−25.0145	−0.812432
$949$	4.76023	0.154524
$950$	−2.67251	−0.0867078
$951$	−10.7876	−0.349811
$952$	−119.750	−3.88112
$953$	33.8521	1.09658	0.548289	−	0.836289i	$-0.315280\pi$
$953$	33.8521	1.09658	0.548289	+	0.836289i	$0.315280\pi$
$954$	1.89819	0.0614562
$955$	−19.8916	−0.643678
$956$	−98.2011	−3.17605
$957$	−5.11155	−0.165233
$958$	37.4552	1.21012
$959$	2.10593	0.0680041
$960$	−36.3010	−1.17161
$961$	−5.95807	−0.192196
$962$	−26.5056	−0.854574
$963$	−44.9393	−1.44815
$964$	131.633	4.23960
$965$	37.8788	1.21936
$966$	−6.37306	−0.205050
$967$	−7.38708	−0.237552	−0.118776	−	0.992921i	$-0.537897\pi$
$967$	−7.38708	−0.237552	−0.118776	+	0.992921i	$0.537897\pi$
$968$	89.8327	2.88733
$969$	−11.6271	−0.373517
$970$	−18.8008	−0.603657
$971$	19.4371	0.623765	0.311882	−	0.950121i	$-0.399041\pi$
$971$	19.4371	0.623765	0.311882	+	0.950121i	$0.399041\pi$
$972$	−79.4681	−2.54894
$973$	−21.3962	−0.685931
$974$	−39.7527	−1.27376
$975$	−0.226960	−0.00726855
$976$	111.957	3.58366
$977$	−16.7682	−0.536463	−0.268232	−	0.963354i	$-0.586439\pi$
$977$	−16.7682	−0.536463	−0.268232	+	0.963354i	$0.586439\pi$
$978$	5.21540	0.166770
$979$	−14.6917	−0.469548
$980$	48.5832	1.55193
$981$	−20.2599	−0.646849
$982$	−37.3262	−1.19113
$983$	−42.6494	−1.36030	−0.680152	−	0.733071i	$-0.738086\pi$
$983$	−42.6494	−1.36030	−0.680152	+	0.733071i	$0.738086\pi$
$984$	69.1335	2.20389
$985$	−31.5523	−1.00534
$986$	−87.5048	−2.78672
$987$	−23.0902	−0.734969
$988$	27.0766	0.861421
$989$	−9.45927	−0.300787
$990$	13.9338	0.442847
$991$	−45.0751	−1.43186	−0.715929	−	0.698173i	$-0.753997\pi$
$991$	−45.0751	−1.43186	−0.715929	+	0.698173i	$0.753997\pi$
$992$	−90.4816	−2.87279
$993$	−0.0240150	−0.000762092 0
$994$	99.7405	3.16358
$995$	29.4366	0.933204
$996$	53.1455	1.68398
$997$	62.2352	1.97101	0.985504	−	0.169654i	$-0.0542650\pi$
$997$	62.2352	1.97101	0.985504	+	0.169654i	$0.0542650\pi$
$998$	7.17844	0.227230
$999$	29.9003	0.946004

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.e.1.6	✓	169

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.e.1.6	✓	169	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:	\( N \)	\(=\)	\( 8027 = 23 \cdot 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.69664 q^{2} -0.711836 q^{3} +5.27186 q^{4} +2.29086 q^{5} +1.91957 q^{6} +3.32005 q^{7} -8.82303 q^{8} -2.49329 q^{9} +O(q^{10})\)	\(q-2.69664 q^{2} -0.711836 q^{3} +5.27186 q^{4} +2.29086 q^{5} +1.91957 q^{6} +3.32005 q^{7} -8.82303 q^{8} -2.49329 q^{9} -6.17762 q^{10} +0.904642 q^{11} -3.75270 q^{12} +1.28544 q^{13} -8.95298 q^{14} -1.63072 q^{15} +13.2488 q^{16} +4.08802 q^{17} +6.72350 q^{18} +3.99557 q^{19} +12.0771 q^{20} -2.36333 q^{21} -2.43949 q^{22} -1.00000 q^{23} +6.28055 q^{24} +0.248038 q^{25} -3.46636 q^{26} +3.91032 q^{27} +17.5029 q^{28} +7.93772 q^{29} +4.39746 q^{30} +5.00419 q^{31} -18.0812 q^{32} -0.643957 q^{33} -11.0239 q^{34} +7.60578 q^{35} -13.1443 q^{36} +7.64650 q^{37} -10.7746 q^{38} -0.915022 q^{39} -20.2123 q^{40} +11.0075 q^{41} +6.37306 q^{42} +9.45927 q^{43} +4.76915 q^{44} -5.71178 q^{45} +2.69664 q^{46} +9.77018 q^{47} -9.43097 q^{48} +4.02275 q^{49} -0.668869 q^{50} -2.91000 q^{51} +6.77665 q^{52} +0.282322 q^{53} -10.5447 q^{54} +2.07241 q^{55} -29.2929 q^{56} -2.84419 q^{57} -21.4052 q^{58} -4.40461 q^{59} -8.59691 q^{60} +8.45036 q^{61} -13.4945 q^{62} -8.27785 q^{63} +22.2608 q^{64} +2.94476 q^{65} +1.73652 q^{66} -8.45806 q^{67} +21.5515 q^{68} +0.711836 q^{69} -20.5100 q^{70} -11.1405 q^{71} +21.9984 q^{72} +3.70320 q^{73} -20.6199 q^{74} -0.176563 q^{75} +21.0641 q^{76} +3.00346 q^{77} +2.46748 q^{78} +6.66572 q^{79} +30.3511 q^{80} +4.69636 q^{81} -29.6834 q^{82} -14.1619 q^{83} -12.4592 q^{84} +9.36509 q^{85} -25.5082 q^{86} -5.65035 q^{87} -7.98168 q^{88} -16.2403 q^{89} +15.4026 q^{90} +4.26772 q^{91} -5.27186 q^{92} -3.56217 q^{93} -26.3466 q^{94} +9.15329 q^{95} +12.8708 q^{96} +3.04337 q^{97} -10.8479 q^{98} -2.25553 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9}+O(q^{10}) \) 169 * q + 6 * q^2 + 2 * q^3 + 186 * q^4 + 28 * q^5 + 5 * q^6 + 38 * q^7 + 18 * q^8 + 185 * q^9	\( 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9} + 28 q^{10} + 17 q^{11} + 10 q^{12} + 91 q^{13} + 20 q^{14} + 29 q^{15} + 200 q^{16} + 16 q^{17} + 31 q^{18} + 30 q^{19} + 45 q^{20} + 49 q^{21} + 76 q^{22} - 169 q^{23} + 3 q^{24} + 241 q^{25} - 15 q^{26} + 14 q^{27} + 118 q^{28} + 23 q^{29} + 52 q^{30} + 45 q^{31} + 42 q^{32} + 62 q^{33} + 65 q^{34} - 16 q^{35} + 199 q^{36} + 226 q^{37} + 49 q^{38} + 17 q^{39} + 95 q^{40} + 19 q^{41} + 32 q^{42} + 71 q^{43} + 46 q^{44} + 127 q^{45} - 6 q^{46} + 27 q^{47} + 5 q^{48} + 239 q^{49} + 24 q^{50} + 39 q^{51} + 154 q^{52} + 111 q^{53} + 22 q^{54} + 47 q^{55} + 39 q^{56} + 122 q^{57} + 146 q^{58} - 73 q^{59} + 109 q^{60} + 125 q^{61} + 14 q^{62} + 109 q^{63} + 260 q^{64} + 73 q^{65} + 26 q^{66} + 152 q^{67} + 40 q^{68} - 2 q^{69} + 76 q^{70} - 79 q^{71} + 126 q^{72} + 106 q^{73} + 23 q^{74} + 12 q^{75} + 122 q^{76} + 63 q^{77} + 101 q^{78} + 82 q^{79} + 134 q^{80} + 225 q^{81} + 125 q^{82} + 28 q^{83} + 73 q^{84} + 197 q^{85} + 97 q^{86} + 18 q^{87} + 183 q^{88} + 54 q^{89} + 52 q^{90} + 106 q^{91} - 186 q^{92} + 194 q^{93} + q^{94} + 18 q^{95} - 39 q^{96} + 239 q^{97} + 5 q^{98} + 85 q^{99}+O(q^{100}) \) 169 * q + 6 * q^2 + 2 * q^3 + 186 * q^4 + 28 * q^5 + 5 * q^6 + 38 * q^7 + 18 * q^8 + 185 * q^9 + 28 * q^10 + 17 * q^11 + 10 * q^12 + 91 * q^13 + 20 * q^14 + 29 * q^15 + 200 * q^16 + 16 * q^17 + 31 * q^18 + 30 * q^19 + 45 * q^20 + 49 * q^21 + 76 * q^22 - 169 * q^23 + 3 * q^24 + 241 * q^25 - 15 * q^26 + 14 * q^27 + 118 * q^28 + 23 * q^29 + 52 * q^30 + 45 * q^31 + 42 * q^32 + 62 * q^33 + 65 * q^34 - 16 * q^35 + 199 * q^36 + 226 * q^37 + 49 * q^38 + 17 * q^39 + 95 * q^40 + 19 * q^41 + 32 * q^42 + 71 * q^43 + 46 * q^44 + 127 * q^45 - 6 * q^46 + 27 * q^47 + 5 * q^48 + 239 * q^49 + 24 * q^50 + 39 * q^51 + 154 * q^52 + 111 * q^53 + 22 * q^54 + 47 * q^55 + 39 * q^56 + 122 * q^57 + 146 * q^58 - 73 * q^59 + 109 * q^60 + 125 * q^61 + 14 * q^62 + 109 * q^63 + 260 * q^64 + 73 * q^65 + 26 * q^66 + 152 * q^67 + 40 * q^68 - 2 * q^69 + 76 * q^70 - 79 * q^71 + 126 * q^72 + 106 * q^73 + 23 * q^74 + 12 * q^75 + 122 * q^76 + 63 * q^77 + 101 * q^78 + 82 * q^79 + 134 * q^80 + 225 * q^81 + 125 * q^82 + 28 * q^83 + 73 * q^84 + 197 * q^85 + 97 * q^86 + 18 * q^87 + 183 * q^88 + 54 * q^89 + 52 * q^90 + 106 * q^91 - 186 * q^92 + 194 * q^93 + q^94 + 18 * q^95 - 39 * q^96 + 239 * q^97 + 5 * q^98 + 85 * q^99

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