LMFDB - Embedded newform 8027.2.a.e.1.7

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			1.7
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)

$f(q)$	$=$	$q-2.69608 q^{2} +1.22457 q^{3} +5.26883 q^{4} -1.75306 q^{5} -3.30153 q^{6} +4.29034 q^{7} -8.81301 q^{8} -1.50043 q^{9} +O(q^{10})$	\(q-2.69608 q^{2} +1.22457 q^{3} +5.26883 q^{4} -1.75306 q^{5} -3.30153 q^{6} +4.29034 q^{7} -8.81301 q^{8} -1.50043 q^{9} +4.72638 q^{10} -4.51051 q^{11} +6.45203 q^{12} -0.196284 q^{13} -11.5671 q^{14} -2.14674 q^{15} +13.2229 q^{16} +2.15376 q^{17} +4.04529 q^{18} +0.277638 q^{19} -9.23657 q^{20} +5.25381 q^{21} +12.1607 q^{22} -1.00000 q^{23} -10.7921 q^{24} -1.92678 q^{25} +0.529197 q^{26} -5.51109 q^{27} +22.6051 q^{28} -5.36745 q^{29} +5.78778 q^{30} -6.13197 q^{31} -18.0239 q^{32} -5.52342 q^{33} -5.80670 q^{34} -7.52123 q^{35} -7.90553 q^{36} -2.46086 q^{37} -0.748533 q^{38} -0.240363 q^{39} +15.4497 q^{40} +2.49889 q^{41} -14.1647 q^{42} +8.34476 q^{43} -23.7651 q^{44} +2.63035 q^{45} +2.69608 q^{46} +1.28549 q^{47} +16.1923 q^{48} +11.4070 q^{49} +5.19475 q^{50} +2.63742 q^{51} -1.03419 q^{52} -1.65103 q^{53} +14.8583 q^{54} +7.90719 q^{55} -37.8108 q^{56} +0.339986 q^{57} +14.4711 q^{58} +8.94494 q^{59} -11.3108 q^{60} -4.32081 q^{61} +16.5323 q^{62} -6.43738 q^{63} +22.1480 q^{64} +0.344098 q^{65} +14.8916 q^{66} -2.31689 q^{67} +11.3478 q^{68} -1.22457 q^{69} +20.2778 q^{70} -0.145135 q^{71} +13.2233 q^{72} +3.50498 q^{73} +6.63466 q^{74} -2.35947 q^{75} +1.46283 q^{76} -19.3516 q^{77} +0.648038 q^{78} +8.97026 q^{79} -23.1805 q^{80} -2.24739 q^{81} -6.73719 q^{82} -7.06773 q^{83} +27.6814 q^{84} -3.77567 q^{85} -22.4981 q^{86} -6.57280 q^{87} +39.7511 q^{88} +11.2791 q^{89} -7.09163 q^{90} -0.842127 q^{91} -5.26883 q^{92} -7.50901 q^{93} -3.46577 q^{94} -0.486716 q^{95} -22.0715 q^{96} -11.6350 q^{97} -30.7542 q^{98} +6.76772 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.69608	−1.90641	−0.953207	−	0.302319i	$-0.902239\pi$
$2$	−2.69608	−1.90641	−0.953207	+	0.302319i	$0.902239\pi$
$3$	1.22457	0.707004	0.353502	−	0.935434i	$-0.384991\pi$
$3$	1.22457	0.707004	0.353502	+	0.935434i	$0.384991\pi$
$4$	5.26883	2.63441
$5$	−1.75306	−0.783992	−0.391996	−	0.919967i	$-0.628215\pi$
$5$	−1.75306	−0.783992	−0.391996	+	0.919967i	$0.628215\pi$
$6$	−3.30153	−1.34784
$7$	4.29034	1.62160	0.810798	−	0.585325i	$-0.199033\pi$
$7$	4.29034	1.62160	0.810798	+	0.585325i	$0.199033\pi$
$8$	−8.81301	−3.11587
$9$	−1.50043	−0.500145
$10$	4.72638	1.49461
$11$	−4.51051	−1.35997	−0.679985	−	0.733226i	$-0.738014\pi$
$11$	−4.51051	−1.35997	−0.679985	+	0.733226i	$0.738014\pi$
$12$	6.45203	1.86254
$13$	−0.196284	−0.0544395	−0.0272197	−	0.999629i	$-0.508665\pi$
$13$	−0.196284	−0.0544395	−0.0272197	+	0.999629i	$0.508665\pi$
$14$	−11.5671	−3.09143
$15$	−2.14674	−0.554286
$16$	13.2229	3.30572
$17$	2.15376	0.522363	0.261182	−	0.965290i	$-0.415888\pi$
$17$	2.15376	0.522363	0.261182	+	0.965290i	$0.415888\pi$
$18$	4.04529	0.953483
$19$	0.277638	0.0636945	0.0318473	−	0.999493i	$-0.489861\pi$
$19$	0.277638	0.0636945	0.0318473	+	0.999493i	$0.489861\pi$
$20$	−9.23657	−2.06536
$21$	5.25381	1.14648
$22$	12.1607	2.59266
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−10.7921	−2.20293
$25$	−1.92678	−0.385356
$26$	0.529197	0.103784
$27$	−5.51109	−1.06061
$28$	22.6051	4.27196
$29$	−5.36745	−0.996710	−0.498355	−	0.866973i	$-0.666062\pi$
$29$	−5.36745	−0.996710	−0.498355	+	0.866973i	$0.666062\pi$
$30$	5.78778	1.05670
$31$	−6.13197	−1.10133	−0.550667	−	0.834725i	$-0.685627\pi$
$31$	−6.13197	−1.10133	−0.550667	+	0.834725i	$0.685627\pi$
$32$	−18.0239	−3.18620
$33$	−5.52342	−0.961504
$34$	−5.80670	−0.995841
$35$	−7.52123	−1.27132
$36$	−7.90553	−1.31759
$37$	−2.46086	−0.404562	−0.202281	−	0.979327i	$-0.564835\pi$
$37$	−2.46086	−0.404562	−0.202281	+	0.979327i	$0.564835\pi$
$38$	−0.748533	−0.121428
$39$	−0.240363	−0.0384889
$40$	15.4497	2.44282
$41$	2.49889	0.390261	0.195130	−	0.980777i	$-0.437487\pi$
$41$	2.49889	0.390261	0.195130	+	0.980777i	$0.437487\pi$
$42$	−14.1647	−2.18566
$43$	8.34476	1.27256	0.636282	−	0.771456i	$-0.280471\pi$
$43$	8.34476	1.27256	0.636282	+	0.771456i	$0.280471\pi$
$44$	−23.7651	−3.58272
$45$	2.63035	0.392110
$46$	2.69608	0.397515
$47$	1.28549	0.187508	0.0937538	−	0.995595i	$-0.470113\pi$
$47$	1.28549	0.187508	0.0937538	+	0.995595i	$0.470113\pi$
$48$	16.1923	2.33716
$49$	11.4070	1.62958
$50$	5.19475	0.734648
$51$	2.63742	0.369313
$52$	−1.03419	−0.143416
$53$	−1.65103	−0.226786	−0.113393	−	0.993550i	$-0.536172\pi$
$53$	−1.65103	−0.226786	−0.113393	+	0.993550i	$0.536172\pi$
$54$	14.8583	2.02196
$55$	7.90719	1.06621
$56$	−37.8108	−5.05268
$57$	0.339986	0.0450323
$58$	14.4711	1.90014
$59$	8.94494	1.16453	0.582266	−	0.812998i	$-0.302166\pi$
$59$	8.94494	1.16453	0.582266	+	0.812998i	$0.302166\pi$
$60$	−11.3108	−1.46022
$61$	−4.32081	−0.553222	−0.276611	−	0.960982i	$-0.589211\pi$
$61$	−4.32081	−0.553222	−0.276611	+	0.960982i	$0.589211\pi$
$62$	16.5323	2.09960
$63$	−6.43738	−0.811033
$64$	22.1480	2.76850
$65$	0.344098	0.0426801
$66$	14.8916	1.83302
$67$	−2.31689	−0.283053	−0.141527	−	0.989934i	$-0.545201\pi$
$67$	−2.31689	−0.283053	−0.141527	+	0.989934i	$0.545201\pi$
$68$	11.3478	1.37612
$69$	−1.22457	−0.147421
$70$	20.2778	2.42366
$71$	−0.145135	−0.0172243	−0.00861216	−	0.999963i	$-0.502741\pi$
$71$	−0.145135	−0.0172243	−0.00861216	+	0.999963i	$0.502741\pi$
$72$	13.2233	1.55839
$73$	3.50498	0.410227	0.205113	−	0.978738i	$-0.434244\pi$
$73$	3.50498	0.410227	0.205113	+	0.978738i	$0.434244\pi$
$74$	6.63466	0.771263
$75$	−2.35947	−0.272448
$76$	1.46283	0.167798
$77$	−19.3516	−2.20532
$78$	0.648038	0.0733759
$79$	8.97026	1.00923	0.504617	−	0.863343i	$-0.331634\pi$
$79$	8.97026	1.00923	0.504617	+	0.863343i	$0.331634\pi$
$80$	−23.1805	−2.59166
$81$	−2.24739	−0.249710
$82$	−6.73719	−0.743998
$83$	−7.06773	−0.775784	−0.387892	−	0.921705i	$-0.626797\pi$
$83$	−7.06773	−0.775784	−0.387892	+	0.921705i	$0.626797\pi$
$84$	27.6814	3.02029
$85$	−3.77567	−0.409529
$86$	−22.4981	−2.42603
$87$	−6.57280	−0.704679
$88$	39.7511	4.23749
$89$	11.2791	1.19559	0.597793	−	0.801650i	$-0.296044\pi$
$89$	11.2791	1.19559	0.597793	+	0.801650i	$0.296044\pi$
$90$	−7.09163	−0.747523
$91$	−0.842127	−0.0882789
$92$	−5.26883	−0.549313
$93$	−7.50901	−0.778648
$94$	−3.46577	−0.357467
$95$	−0.486716	−0.0499360
$96$	−22.0715	−2.25266
$97$	−11.6350	−1.18135	−0.590676	−	0.806909i	$-0.701139\pi$
$97$	−11.6350	−1.18135	−0.590676	+	0.806909i	$0.701139\pi$
$98$	−30.7542	−3.10665
$99$	6.76772	0.680181
$100$	−10.1519	−1.01519
$101$	2.37553	0.236374	0.118187	−	0.992991i	$-0.462292\pi$
$101$	2.37553	0.236374	0.118187	+	0.992991i	$0.462292\pi$
$102$	−7.11070	−0.704064
$103$	−8.77433	−0.864560	−0.432280	−	0.901739i	$-0.642291\pi$
$103$	−8.77433	−0.864560	−0.432280	+	0.901739i	$0.642291\pi$
$104$	1.72985	0.169626
$105$	−9.21025	−0.898829
$106$	4.45129	0.432348
$107$	−10.9974	−1.06316	−0.531580	−	0.847008i	$-0.678401\pi$
$107$	−10.9974	−1.06316	−0.531580	+	0.847008i	$0.678401\pi$
$108$	−29.0370	−2.79408
$109$	11.8995	1.13976	0.569880	−	0.821728i	$-0.306990\pi$
$109$	11.8995	1.13976	0.569880	+	0.821728i	$0.306990\pi$
$110$	−21.3184	−2.03263
$111$	−3.01349	−0.286027
$112$	56.7307	5.36055
$113$	−7.03749	−0.662031	−0.331016	−	0.943625i	$-0.607391\pi$
$113$	−7.03749	−0.662031	−0.331016	+	0.943625i	$0.607391\pi$
$114$	−0.916629	−0.0858502
$115$	1.75306	0.163474
$116$	−28.2802	−2.62575
$117$	0.294512	0.0272276
$118$	−24.1162	−2.22008
$119$	9.24037	0.847063
$120$	18.9192	1.72708
$121$	9.34468	0.849516
$122$	11.6492	1.05467
$123$	3.06006	0.275916
$124$	−32.3083	−2.90137
$125$	12.1431	1.08611
$126$	17.3557	1.54616
$127$	1.40671	0.124825	0.0624125	−	0.998050i	$-0.480121\pi$
$127$	1.40671	0.124825	0.0624125	+	0.998050i	$0.480121\pi$
$128$	−23.6649	−2.09171
$129$	10.2187	0.899708
$130$	−0.927715	−0.0813660
$131$	12.4698	1.08949	0.544745	−	0.838602i	$-0.316627\pi$
$131$	12.4698	1.08949	0.544745	+	0.838602i	$0.316627\pi$
$132$	−29.1020	−2.53300
$133$	1.19116	0.103287
$134$	6.24651	0.539616
$135$	9.66126	0.831509
$136$	−18.9811	−1.62762
$137$	−3.23878	−0.276708	−0.138354	−	0.990383i	$-0.544181\pi$
$137$	−3.23878	−0.276708	−0.138354	+	0.990383i	$0.544181\pi$
$138$	3.30153	0.281045
$139$	4.34100	0.368199	0.184099	−	0.982908i	$-0.441063\pi$
$139$	4.34100	0.368199	0.184099	+	0.982908i	$0.441063\pi$
$140$	−39.6280	−3.34918
$141$	1.57417	0.132569
$142$	0.391294	0.0328367
$143$	0.885342	0.0740360
$144$	−19.8401	−1.65334
$145$	9.40946	0.781413
$146$	−9.44969	−0.782062
$147$	13.9687	1.15212
$148$	−12.9658	−1.06578
$149$	−6.97798	−0.571658	−0.285829	−	0.958281i	$-0.592269\pi$
$149$	−6.97798	−0.571658	−0.285829	+	0.958281i	$0.592269\pi$
$150$	6.36132	0.519399
$151$	17.2249	1.40175	0.700873	−	0.713286i	$-0.252794\pi$
$151$	17.2249	1.40175	0.700873	+	0.713286i	$0.252794\pi$
$152$	−2.44683	−0.198464
$153$	−3.23157	−0.261257
$154$	52.1734	4.20426
$155$	10.7497	0.863438
$156$	−1.26643	−0.101396
$157$	21.9005	1.74785	0.873925	−	0.486061i	$-0.161567\pi$
$157$	21.9005	1.74785	0.873925	+	0.486061i	$0.161567\pi$
$158$	−24.1845	−1.92402
$159$	−2.02179	−0.160339
$160$	31.5970	2.49796
$161$	−4.29034	−0.338126
$162$	6.05915	0.476051
$163$	−0.847536	−0.0663842	−0.0331921	−	0.999449i	$-0.510567\pi$
$163$	−0.847536	−0.0663842	−0.0331921	+	0.999449i	$0.510567\pi$
$164$	13.1662	1.02811
$165$	9.68289	0.753812
$166$	19.0551	1.47897
$167$	13.5787	1.05075	0.525374	−	0.850871i	$-0.323925\pi$
$167$	13.5787	1.05075	0.525374	+	0.850871i	$0.323925\pi$
$168$	−46.3019	−3.57227
$169$	−12.9615	−0.997036
$170$	10.1795	0.780732
$171$	−0.416578	−0.0318565
$172$	43.9671	3.35246
$173$	23.2578	1.76826	0.884130	−	0.467242i	$-0.154752\pi$
$173$	23.2578	1.76826	0.884130	+	0.467242i	$0.154752\pi$
$174$	17.7208	1.34341
$175$	−8.26655	−0.624892
$176$	−59.6419	−4.49568
$177$	10.9537	0.823329
$178$	−30.4094	−2.27928
$179$	−2.70655	−0.202297	−0.101149	−	0.994871i	$-0.532252\pi$
$179$	−2.70655	−0.202297	−0.101149	+	0.994871i	$0.532252\pi$
$180$	13.8589	1.03298
$181$	19.6929	1.46376	0.731881	−	0.681433i	$-0.238643\pi$
$181$	19.6929	1.46376	0.731881	+	0.681433i	$0.238643\pi$
$182$	2.27044	0.168296
$183$	−5.29112	−0.391131
$184$	8.81301	0.649703
$185$	4.31403	0.317174
$186$	20.2449	1.48443
$187$	−9.71455	−0.710398
$188$	6.77301	0.493973
$189$	−23.6444	−1.71988
$190$	1.31222	0.0951987
$191$	6.18858	0.447790	0.223895	−	0.974613i	$-0.428123\pi$
$191$	6.18858	0.447790	0.223895	+	0.974613i	$0.428123\pi$
$192$	27.1217	1.95734
$193$	7.30963	0.526159	0.263080	−	0.964774i	$-0.415262\pi$
$193$	7.30963	0.526159	0.263080	+	0.964774i	$0.415262\pi$
$194$	31.3688	2.25215
$195$	0.421371	0.0301750
$196$	60.1017	4.29298
$197$	5.02970	0.358351	0.179176	−	0.983817i	$-0.442657\pi$
$197$	5.02970	0.358351	0.179176	+	0.983817i	$0.442657\pi$
$198$	−18.2463	−1.29671
$199$	−9.49525	−0.673101	−0.336550	−	0.941665i	$-0.609260\pi$
$199$	−9.49525	−0.673101	−0.336550	+	0.941665i	$0.609260\pi$
$200$	16.9807	1.20072
$201$	−2.83719	−0.200120
$202$	−6.40461	−0.450627
$203$	−23.0282	−1.61626
$204$	13.8961	0.972924
$205$	−4.38070	−0.305961
$206$	23.6563	1.64821
$207$	1.50043	0.104287
$208$	−2.59544	−0.179962
$209$	−1.25229	−0.0866226
$210$	24.8315	1.71354
$211$	−1.81145	−0.124705	−0.0623527	−	0.998054i	$-0.519860\pi$
$211$	−1.81145	−0.124705	−0.0623527	+	0.998054i	$0.519860\pi$
$212$	−8.69897	−0.597448
$213$	−0.177727	−0.0121777
$214$	29.6499	2.02682
$215$	−14.6289	−0.997681
$216$	48.5692	3.30472
$217$	−26.3082	−1.78592
$218$	−32.0818	−2.17286
$219$	4.29208	0.290032
$220$	41.6616	2.80883
$221$	−0.422749	−0.0284372
$222$	8.12459	0.545287
$223$	3.79762	0.254307	0.127154	−	0.991883i	$-0.459416\pi$
$223$	3.79762	0.254307	0.127154	+	0.991883i	$0.459416\pi$
$224$	−77.3287	−5.16674
$225$	2.89101	0.192734
$226$	18.9736	1.26211
$227$	16.8105	1.11575	0.557875	−	0.829925i	$-0.311617\pi$
$227$	16.8105	1.11575	0.557875	+	0.829925i	$0.311617\pi$
$228$	1.79133	0.118634
$229$	25.3827	1.67734	0.838669	−	0.544641i	$-0.183334\pi$
$229$	25.3827	1.67734	0.838669	+	0.544641i	$0.183334\pi$
$230$	−4.72638	−0.311649
$231$	−23.6974	−1.55917
$232$	47.3034	3.10562
$233$	5.99366	0.392658	0.196329	−	0.980538i	$-0.437098\pi$
$233$	5.99366	0.392658	0.196329	+	0.980538i	$0.437098\pi$
$234$	−0.794026	−0.0519071
$235$	−2.25354	−0.147005
$236$	47.1294	3.06786
$237$	10.9847	0.713533
$238$	−24.9127	−1.61485
$239$	2.39610	0.154991	0.0774953	−	0.996993i	$-0.475308\pi$
$239$	2.39610	0.154991	0.0774953	+	0.996993i	$0.475308\pi$
$240$	−28.3861	−1.83231
$241$	−3.38969	−0.218349	−0.109175	−	0.994023i	$-0.534821\pi$
$241$	−3.38969	−0.218349	−0.109175	+	0.994023i	$0.534821\pi$
$242$	−25.1940	−1.61953
$243$	13.7812	0.884063
$244$	−22.7656	−1.45742
$245$	−19.9972	−1.27758
$246$	−8.25015	−0.526010
$247$	−0.0544960	−0.00346750
$248$	54.0411	3.43161
$249$	−8.65491	−0.548483
$250$	−32.7386	−2.07057
$251$	−13.5722	−0.856673	−0.428336	−	0.903619i	$-0.640900\pi$
$251$	−13.5722	−0.856673	−0.428336	+	0.903619i	$0.640900\pi$
$252$	−33.9174	−2.13660
$253$	4.51051	0.283573
$254$	−3.79259	−0.237968
$255$	−4.62356	−0.289539
$256$	19.5065	1.21915
$257$	−14.1829	−0.884706	−0.442353	−	0.896841i	$-0.645856\pi$
$257$	−14.1829	−0.884706	−0.442353	+	0.896841i	$0.645856\pi$
$258$	−27.5505	−1.71522
$259$	−10.5579	−0.656037
$260$	1.81299	0.112437
$261$	8.05350	0.498499
$262$	−33.6195	−2.07702
$263$	−4.95428	−0.305494	−0.152747	−	0.988265i	$-0.548812\pi$
$263$	−4.95428	−0.305494	−0.152747	+	0.988265i	$0.548812\pi$
$264$	48.6779	2.99592
$265$	2.89435	0.177798
$266$	−3.21146	−0.196907
$267$	13.8121	0.845285
$268$	−12.2073	−0.745679
$269$	−15.6371	−0.953411	−0.476705	−	0.879063i	$-0.658169\pi$
$269$	−15.6371	−0.953411	−0.476705	+	0.879063i	$0.658169\pi$
$270$	−26.0475	−1.58520
$271$	10.0497	0.610475	0.305238	−	0.952276i	$-0.401264\pi$
$271$	10.0497	0.610475	0.305238	+	0.952276i	$0.401264\pi$
$272$	28.4789	1.72679
$273$	−1.03124	−0.0624136
$274$	8.73199	0.527519
$275$	8.69076	0.524072
$276$	−6.45203	−0.388367
$277$	−23.2589	−1.39749	−0.698745	−	0.715371i	$-0.746258\pi$
$277$	−23.2589	−1.39749	−0.698745	+	0.715371i	$0.746258\pi$
$278$	−11.7037	−0.701939
$279$	9.20062	0.550827
$280$	66.2846	3.96126
$281$	27.4223	1.63588	0.817938	−	0.575306i	$-0.195117\pi$
$281$	27.4223	1.63588	0.817938	+	0.575306i	$0.195117\pi$
$282$	−4.24407	−0.252731
$283$	−5.01902	−0.298350	−0.149175	−	0.988811i	$-0.547662\pi$
$283$	−5.01902	−0.298350	−0.149175	+	0.988811i	$0.547662\pi$
$284$	−0.764689	−0.0453760
$285$	−0.596017	−0.0353050
$286$	−2.38695	−0.141143
$287$	10.7211	0.632845
$288$	27.0437	1.59356
$289$	−12.3613	−0.727136
$290$	−25.3686	−1.48970
$291$	−14.2478	−0.835221
$292$	18.4671	1.08071
$293$	24.9839	1.45958	0.729788	−	0.683673i	$-0.239619\pi$
$293$	24.9839	1.45958	0.729788	+	0.683673i	$0.239619\pi$
$294$	−37.6606	−2.19641
$295$	−15.6810	−0.912984
$296$	21.6875	1.26056
$297$	24.8578	1.44240
$298$	18.8132	1.08982
$299$	0.196284	0.0113514
$300$	−12.4317	−0.717742
$301$	35.8019	2.06359
$302$	−46.4397	−2.67231
$303$	2.90900	0.167118
$304$	3.67117	0.210556
$305$	7.57463	0.433722
$306$	8.71257	0.498065
$307$	3.95405	0.225669	0.112835	−	0.993614i	$-0.464007\pi$
$307$	3.95405	0.225669	0.112835	+	0.993614i	$0.464007\pi$
$308$	−101.960	−5.80973
$309$	−10.7448	−0.611248
$310$	−28.9820	−1.64607
$311$	−4.88249	−0.276860	−0.138430	−	0.990372i	$-0.544206\pi$
$311$	−4.88249	−0.276860	−0.138430	+	0.990372i	$0.544206\pi$
$312$	2.11832	0.119926
$313$	31.4534	1.77785	0.888925	−	0.458053i	$-0.151453\pi$
$313$	31.4534	1.77785	0.888925	+	0.458053i	$0.151453\pi$
$314$	−59.0454	−3.33212
$315$	11.2851	0.635844
$316$	47.2628	2.65874
$317$	−23.0276	−1.29336	−0.646679	−	0.762762i	$-0.723843\pi$
$317$	−23.0276	−1.29336	−0.646679	+	0.762762i	$0.723843\pi$
$318$	5.45091	0.305672
$319$	24.2099	1.35550
$320$	−38.8268	−2.17048
$321$	−13.4671	−0.751659
$322$	11.5671	0.644609
$323$	0.597966	0.0332717
$324$	−11.8411	−0.657841
$325$	0.378197	0.0209786
$326$	2.28502	0.126556
$327$	14.5717	0.805816
$328$	−22.0227	−1.21600
$329$	5.51518	0.304062
$330$	−26.1058	−1.43708
$331$	17.4919	0.961442	0.480721	−	0.876873i	$-0.340375\pi$
$331$	17.4919	0.961442	0.480721	+	0.876873i	$0.340375\pi$
$332$	−37.2386	−2.04374
$333$	3.69235	0.202340
$334$	−36.6091	−2.00316
$335$	4.06165	0.221911
$336$	69.4706	3.78993
$337$	25.3532	1.38108	0.690539	−	0.723295i	$-0.257373\pi$
$337$	25.3532	1.38108	0.690539	+	0.723295i	$0.257373\pi$
$338$	34.9451	1.90076
$339$	−8.61788	−0.468059
$340$	−19.8934	−1.07887
$341$	27.6583	1.49778
$342$	1.12312	0.0607316
$343$	18.9077	1.02092
$344$	−73.5424	−3.96514
$345$	2.14674	0.115577
$346$	−62.7049	−3.37103
$347$	20.0750	1.07768	0.538842	−	0.842407i	$-0.318862\pi$
$347$	20.0750	1.07768	0.538842	+	0.842407i	$0.318862\pi$
$348$	−34.6310	−1.85641
$349$	1.00000	0.0535288
$349$	1.00000	0.0535288
$350$	22.2872	1.19130
$351$	1.08174	0.0577390
$352$	81.2969	4.33314
$353$	−1.67403	−0.0890997	−0.0445499	−	0.999007i	$-0.514185\pi$
$353$	−1.67403	−0.0890997	−0.0445499	+	0.999007i	$0.514185\pi$
$354$	−29.5320	−1.56961
$355$	0.254430	0.0135037
$356$	59.4278	3.14967
$357$	11.3155	0.598877
$358$	7.29707	0.385662
$359$	1.26280	0.0666480	0.0333240	−	0.999445i	$-0.489391\pi$
$359$	1.26280	0.0666480	0.0333240	+	0.999445i	$0.489391\pi$
$360$	−23.1813	−1.22176
$361$	−18.9229	−0.995943
$362$	−53.0935	−2.79053
$363$	11.4432	0.600612
$364$	−4.43702	−0.232563
$365$	−6.14444	−0.321615
$366$	14.2653	0.745657
$367$	−25.7432	−1.34378	−0.671891	−	0.740650i	$-0.734518\pi$
$367$	−25.7432	−1.34378	−0.671891	+	0.740650i	$0.734518\pi$
$368$	−13.2229	−0.689290
$369$	−3.74942	−0.195187
$370$	−11.6310	−0.604665
$371$	−7.08347	−0.367755
$372$	−39.5637	−2.05128
$373$	−10.5169	−0.544544	−0.272272	−	0.962220i	$-0.587775\pi$
$373$	−10.5169	−0.544544	−0.272272	+	0.962220i	$0.587775\pi$
$374$	26.1912	1.35431
$375$	14.8700	0.767884
$376$	−11.3290	−0.584249
$377$	1.05355	0.0542604
$378$	63.7472	3.27880
$379$	21.6103	1.11005	0.555024	−	0.831834i	$-0.312709\pi$
$379$	21.6103	1.11005	0.555024	+	0.831834i	$0.312709\pi$
$380$	−2.56442	−0.131552
$381$	1.72261	0.0882519
$382$	−16.6849	−0.853673
$383$	−6.27339	−0.320555	−0.160278	−	0.987072i	$-0.551239\pi$
$383$	−6.27339	−0.320555	−0.160278	+	0.987072i	$0.551239\pi$
$384$	−28.9793	−1.47884
$385$	33.9246	1.72896
$386$	−19.7073	−1.00308
$387$	−12.5208	−0.636466
$388$	−61.3026	−3.11217
$389$	0.628992	0.0318912	0.0159456	−	0.999873i	$-0.494924\pi$
$389$	0.628992	0.0318912	0.0159456	+	0.999873i	$0.494924\pi$
$390$	−1.13605	−0.0575261
$391$	−2.15376	−0.108920
$392$	−100.530	−5.07755
$393$	15.2701	0.770274
$394$	−13.5605	−0.683166
$395$	−15.7254	−0.791231
$396$	35.6579	1.79188
$397$	10.5168	0.527823	0.263911	−	0.964547i	$-0.414987\pi$
$397$	10.5168	0.527823	0.263911	+	0.964547i	$0.414987\pi$
$398$	25.5999	1.28321
$399$	1.45866	0.0730243
$400$	−25.4776	−1.27388
$401$	−17.9995	−0.898852	−0.449426	−	0.893318i	$-0.648371\pi$
$401$	−17.9995	−0.898852	−0.449426	+	0.893318i	$0.648371\pi$
$402$	7.64928	0.381511
$403$	1.20361	0.0599561
$404$	12.5163	0.622708
$405$	3.93982	0.195771
$406$	62.0858	3.08126
$407$	11.0997	0.550192
$408$	−23.2436	−1.15073
$409$	−12.3353	−0.609939	−0.304969	−	0.952362i	$-0.598646\pi$
$409$	−12.3353	−0.609939	−0.304969	+	0.952362i	$0.598646\pi$
$410$	11.8107	0.583289
$411$	−3.96610	−0.195633
$412$	−46.2304	−2.27761
$413$	38.3769	1.88840
$414$	−4.04529	−0.198815
$415$	12.3902	0.608209
$416$	3.53781	0.173455
$417$	5.31585	0.260318
$418$	3.37626	0.165139
$419$	19.5326	0.954228	0.477114	−	0.878841i	$-0.341683\pi$
$419$	19.5326	0.954228	0.477114	+	0.878841i	$0.341683\pi$
$420$	−48.5272	−2.36789
$421$	10.8473	0.528664	0.264332	−	0.964432i	$-0.414848\pi$
$421$	10.8473	0.528664	0.264332	+	0.964432i	$0.414848\pi$
$422$	4.88381	0.237740
$423$	−1.92879	−0.0937810
$424$	14.5505	0.706635
$425$	−4.14982	−0.201296
$426$	0.479166	0.0232157
$427$	−18.5377	−0.897104
$428$	−57.9434	−2.80080
$429$	1.08416	0.0523438
$430$	39.4405	1.90199
$431$	−6.99673	−0.337021	−0.168510	−	0.985700i	$-0.553896\pi$
$431$	−6.99673	−0.337021	−0.168510	+	0.985700i	$0.553896\pi$
$432$	−72.8724	−3.50608
$433$	−37.5527	−1.80467	−0.902334	−	0.431037i	$-0.858148\pi$
$433$	−37.5527	−1.80467	−0.902334	+	0.431037i	$0.858148\pi$
$434$	70.9290	3.40470
$435$	11.5225	0.552463
$436$	62.6962	3.00260
$437$	−0.277638	−0.0132812
$438$	−11.5718	−0.552921
$439$	−4.15736	−0.198420	−0.0992100	−	0.995067i	$-0.531632\pi$
$439$	−4.15736	−0.198420	−0.0992100	+	0.995067i	$0.531632\pi$
$440$	−69.6861	−3.32216
$441$	−17.1155	−0.815024
$442$	1.13976	0.0542130
$443$	10.3221	0.490419	0.245210	−	0.969470i	$-0.421143\pi$
$443$	10.3221	0.490419	0.245210	+	0.969470i	$0.421143\pi$
$444$	−15.8775	−0.753514
$445$	−19.7730	−0.937330
$446$	−10.2387	−0.484815
$447$	−8.54500	−0.404165
$448$	95.0225	4.48939
$449$	−15.2573	−0.720038	−0.360019	−	0.932945i	$-0.617230\pi$
$449$	−15.2573	−0.720038	−0.360019	+	0.932945i	$0.617230\pi$
$450$	−7.79438	−0.367430
$451$	−11.2713	−0.530742
$452$	−37.0793	−1.74406
$453$	21.0931	0.991040
$454$	−45.3223	−2.12708
$455$	1.47630	0.0692100
$456$	−2.99630	−0.140315
$457$	30.2543	1.41524	0.707619	−	0.706594i	$-0.249769\pi$
$457$	30.2543	1.41524	0.707619	+	0.706594i	$0.249769\pi$
$458$	−68.4338	−3.19770
$459$	−11.8696	−0.554023
$460$	9.23657	0.430657
$461$	34.3530	1.59998	0.799989	−	0.600014i	$-0.204838\pi$
$461$	34.3530	1.59998	0.799989	+	0.600014i	$0.204838\pi$
$462$	63.8899	2.97243
$463$	−30.6099	−1.42256	−0.711282	−	0.702907i	$-0.751885\pi$
$463$	−30.6099	−1.42256	−0.711282	+	0.702907i	$0.751885\pi$
$464$	−70.9732	−3.29485
$465$	13.1637	0.610454
$466$	−16.1594	−0.748568
$467$	−9.45740	−0.437636	−0.218818	−	0.975766i	$-0.570220\pi$
$467$	−9.45740	−0.437636	−0.218818	+	0.975766i	$0.570220\pi$
$468$	1.55173	0.0717288
$469$	−9.94025	−0.458998
$470$	6.07571	0.280252
$471$	26.8186	1.23574
$472$	−78.8318	−3.62853
$473$	−37.6391	−1.73065
$474$	−29.6156	−1.36029
$475$	−0.534947	−0.0245451
$476$	48.6859	2.23151
$477$	2.47726	0.113426
$478$	−6.46006	−0.295476
$479$	−38.7210	−1.76921	−0.884603	−	0.466345i	$-0.845570\pi$
$479$	−38.7210	−1.76921	−0.884603	+	0.466345i	$0.845570\pi$
$480$	38.6926	1.76607
$481$	0.483028	0.0220242
$482$	9.13886	0.416264
$483$	−5.25381	−0.239057
$484$	49.2355	2.23798
$485$	20.3968	0.926171
$486$	−37.1551	−1.68539
$487$	−10.8877	−0.493368	−0.246684	−	0.969096i	$-0.579341\pi$
$487$	−10.8877	−0.493368	−0.246684	+	0.969096i	$0.579341\pi$
$488$	38.0793	1.72377
$489$	−1.03787	−0.0469339
$490$	53.9140	2.43559
$491$	16.8445	0.760181	0.380091	−	0.924949i	$-0.375893\pi$
$491$	16.8445	0.760181	0.380091	+	0.924949i	$0.375893\pi$
$492$	16.1229	0.726877
$493$	−11.5602	−0.520645
$494$	0.146925	0.00661048
$495$	−11.8642	−0.533257
$496$	−81.0823	−3.64070
$497$	−0.622677	−0.0279309
$498$	23.3343	1.04564
$499$	24.1294	1.08018	0.540091	−	0.841606i	$-0.318390\pi$
$499$	24.1294	1.08018	0.540091	+	0.841606i	$0.318390\pi$
$500$	63.9797	2.86126
$501$	16.6280	0.742884
$502$	36.5918	1.63317
$503$	−9.50524	−0.423818	−0.211909	−	0.977289i	$-0.567968\pi$
$503$	−9.50524	−0.423818	−0.211909	+	0.977289i	$0.567968\pi$
$504$	56.7326	2.52707
$505$	−4.16445	−0.185316
$506$	−12.1607	−0.540608
$507$	−15.8722	−0.704909
$508$	7.41170	0.328841
$509$	12.1970	0.540622	0.270311	−	0.962773i	$-0.412873\pi$
$509$	12.1970	0.540622	0.270311	+	0.962773i	$0.412873\pi$
$510$	12.4655	0.551981
$511$	15.0376	0.665222
$512$	−5.26106	−0.232508
$513$	−1.53009	−0.0675550
$514$	38.2382	1.68662
$515$	15.3819	0.677808
$516$	53.8407	2.37020
$517$	−5.79820	−0.255005
$518$	28.4650	1.25068
$519$	28.4808	1.25017
$520$	−3.03254	−0.132986
$521$	37.4202	1.63941	0.819704	−	0.572787i	$-0.194138\pi$
$521$	37.4202	1.63941	0.819704	+	0.572787i	$0.194138\pi$
$522$	−21.7129	−0.950346
$523$	27.3516	1.19600	0.598002	−	0.801495i	$-0.295962\pi$
$523$	27.3516	1.19600	0.598002	+	0.801495i	$0.295962\pi$
$524$	65.7011	2.87017
$525$	−10.1229	−0.441802
$526$	13.3571	0.582398
$527$	−13.2068	−0.575297
$528$	−73.0356	−3.17846
$529$	1.00000	0.0434783
$530$	−7.80338	−0.338957
$531$	−13.4213	−0.582435
$532$	6.27603	0.272100
$533$	−0.490492	−0.0212456
$534$	−37.2384	−1.61146
$535$	19.2791	0.833509
$536$	20.4188	0.881956
$537$	−3.31435	−0.143025
$538$	42.1588	1.81760
$539$	−51.4515	−2.21617
$540$	50.9035	2.19054
$541$	−18.1818	−0.781697	−0.390849	−	0.920455i	$-0.627818\pi$
$541$	−18.1818	−0.781697	−0.390849	+	0.920455i	$0.627818\pi$
$542$	−27.0947	−1.16382
$543$	24.1153	1.03489
$544$	−38.8191	−1.66436
$545$	−20.8605	−0.893564
$546$	2.78030	0.118986
$547$	19.1193	0.817484	0.408742	−	0.912650i	$-0.365968\pi$
$547$	19.1193	0.817484	0.408742	+	0.912650i	$0.365968\pi$
$548$	−17.0646	−0.728962
$549$	6.48308	0.276691
$550$	−23.4309	−0.999099
$551$	−1.49021	−0.0634850
$552$	10.7921	0.459343
$553$	38.4855	1.63657
$554$	62.7077	2.66419
$555$	5.28282	0.224243
$556$	22.8720	0.969988
$557$	−15.9251	−0.674767	−0.337384	−	0.941367i	$-0.609542\pi$
$557$	−15.9251	−0.674767	−0.337384	+	0.941367i	$0.609542\pi$
$558$	−24.8056	−1.05010
$559$	−1.63795	−0.0692777
$560$	−99.4523	−4.20263
$561$	−11.8961	−0.502255
$562$	−73.9326	−3.11866
$563$	25.3894	1.07004	0.535019	−	0.844840i	$-0.320305\pi$
$563$	25.3894	1.07004	0.535019	+	0.844840i	$0.320305\pi$
$564$	8.29401	0.349241
$565$	12.3371	0.519027
$566$	13.5317	0.568778
$567$	−9.64209	−0.404930
$568$	1.27907	0.0536687
$569$	−30.5475	−1.28062	−0.640309	−	0.768117i	$-0.721194\pi$
$569$	−30.5475	−1.28062	−0.640309	+	0.768117i	$0.721194\pi$
$570$	1.60691	0.0673059
$571$	−39.1053	−1.63651	−0.818253	−	0.574858i	$-0.805057\pi$
$571$	−39.1053	−1.63651	−0.818253	+	0.574858i	$0.805057\pi$
$572$	4.66471	0.195041
$573$	7.57833	0.316589
$574$	−28.9049	−1.20647
$575$	1.92678	0.0803523
$576$	−33.2316	−1.38465
$577$	−15.2761	−0.635951	−0.317976	−	0.948099i	$-0.603003\pi$
$577$	−15.2761	−0.635951	−0.317976	+	0.948099i	$0.603003\pi$
$578$	33.3271	1.38622
$579$	8.95114	0.371997
$580$	49.5768	2.05857
$581$	−30.3230	−1.25801
$582$	38.4132	1.59228
$583$	7.44697	0.308422
$584$	−30.8894	−1.27821
$585$	−0.516297	−0.0213462
$586$	−67.3586	−2.78256
$587$	20.2674	0.836523	0.418262	−	0.908327i	$-0.362640\pi$
$587$	20.2674	0.836523	0.418262	+	0.908327i	$0.362640\pi$
$588$	73.5986	3.03515
$589$	−1.70247	−0.0701490
$590$	42.2772	1.74053
$591$	6.15921	0.253356
$592$	−32.5396	−1.33737
$593$	4.85104	0.199208	0.0996042	−	0.995027i	$-0.468242\pi$
$593$	4.85104	0.199208	0.0996042	+	0.995027i	$0.468242\pi$
$594$	−67.0185	−2.74980
$595$	−16.1989	−0.664091
$596$	−36.7658	−1.50598
$597$	−11.6276	−0.475885
$598$	−0.529197	−0.0216405
$599$	−36.5931	−1.49515	−0.747576	−	0.664176i	$-0.768783\pi$
$599$	−36.5931	−1.49515	−0.747576	+	0.664176i	$0.768783\pi$
$600$	20.7940	0.848913
$601$	−18.0705	−0.737109	−0.368555	−	0.929606i	$-0.620147\pi$
$601$	−18.0705	−0.737109	−0.368555	+	0.929606i	$0.620147\pi$
$602$	−96.5246	−3.93405
$603$	3.47634	0.141568
$604$	90.7552	3.69278
$605$	−16.3818	−0.666014
$606$	−7.84288	−0.318595
$607$	27.9055	1.13265	0.566324	−	0.824183i	$-0.308365\pi$
$607$	27.9055	1.13265	0.566324	+	0.824183i	$0.308365\pi$
$608$	−5.00412	−0.202944
$609$	−28.1996	−1.14270
$610$	−20.4218	−0.826854
$611$	−0.252321	−0.0102078
$612$	−17.0266	−0.688260
$613$	−27.1988	−1.09855	−0.549275	−	0.835641i	$-0.685096\pi$
$613$	−27.1988	−1.09855	−0.549275	+	0.835641i	$0.685096\pi$
$614$	−10.6604	−0.430219
$615$	−5.36446	−0.216316
$616$	170.546	6.87149
$617$	−6.80222	−0.273847	−0.136924	−	0.990582i	$-0.543721\pi$
$617$	−6.80222	−0.273847	−0.136924	+	0.990582i	$0.543721\pi$
$618$	28.9687	1.16529
$619$	−17.3486	−0.697301	−0.348650	−	0.937253i	$-0.613360\pi$
$619$	−17.3486	−0.697301	−0.348650	+	0.937253i	$0.613360\pi$
$620$	56.6384	2.27465
$621$	5.51109	0.221152
$622$	13.1636	0.527811
$623$	48.3914	1.93876
$624$	−3.17830	−0.127234
$625$	−11.6536	−0.466145
$626$	−84.8007	−3.38932
$627$	−1.53351	−0.0612426
$628$	115.390	4.60456
$629$	−5.30009	−0.211329
$630$	−30.4255	−1.21218
$631$	7.97280	0.317392	0.158696	−	0.987327i	$-0.449271\pi$
$631$	7.97280	0.317392	0.158696	+	0.987327i	$0.449271\pi$
$632$	−79.0550	−3.14464
$633$	−2.21825	−0.0881673
$634$	62.0841	2.46568
$635$	−2.46604	−0.0978619
$636$	−10.6525	−0.422398
$637$	−2.23902	−0.0887133
$638$	−65.2718	−2.58413
$639$	0.217765	0.00861465
$640$	41.4861	1.63988
$641$	−13.6184	−0.537895	−0.268948	−	0.963155i	$-0.586676\pi$
$641$	−13.6184	−0.537895	−0.268948	+	0.963155i	$0.586676\pi$
$642$	36.3082	1.43297
$643$	32.3395	1.27534	0.637672	−	0.770308i	$-0.279898\pi$
$643$	32.3395	1.27534	0.637672	+	0.770308i	$0.279898\pi$
$644$	−22.6051	−0.890765
$645$	−17.9140	−0.705365
$646$	−1.61216	−0.0634296
$647$	−19.6647	−0.773100	−0.386550	−	0.922268i	$-0.626333\pi$
$647$	−19.6647	−0.773100	−0.386550	+	0.922268i	$0.626333\pi$
$648$	19.8063	0.778065
$649$	−40.3462	−1.58373
$650$	−1.01965	−0.0399938
$651$	−32.2162	−1.26265
$652$	−4.46552	−0.174883
$653$	34.5694	1.35280	0.676402	−	0.736533i	$-0.263538\pi$
$653$	34.5694	1.35280	0.676402	+	0.736533i	$0.263538\pi$
$654$	−39.2864	−1.53622
$655$	−21.8603	−0.854152
$656$	33.0425	1.29009
$657$	−5.25899	−0.205173
$658$	−14.8694	−0.579668
$659$	12.8761	0.501580	0.250790	−	0.968042i	$-0.419310\pi$
$659$	12.8761	0.501580	0.250790	+	0.968042i	$0.419310\pi$
$660$	51.0175	1.98585
$661$	−4.79989	−0.186694	−0.0933471	−	0.995634i	$-0.529757\pi$
$661$	−4.79989	−0.186694	−0.0933471	+	0.995634i	$0.529757\pi$
$662$	−47.1595	−1.83291
$663$	−0.517685	−0.0201052
$664$	62.2880	2.41724
$665$	−2.08818	−0.0809761
$666$	−9.95487	−0.385743
$667$	5.36745	0.207828
$668$	71.5436	2.76811
$669$	4.65044	0.179796
$670$	−10.9505	−0.423055
$671$	19.4890	0.752365
$672$	−94.6942	−3.65291
$673$	−7.00735	−0.270114	−0.135057	−	0.990838i	$-0.543122\pi$
$673$	−7.00735	−0.270114	−0.135057	+	0.990838i	$0.543122\pi$
$674$	−68.3542	−2.63291
$675$	10.6187	0.408712
$676$	−68.2918	−2.62661
$677$	−11.9779	−0.460349	−0.230174	−	0.973149i	$-0.573930\pi$
$677$	−11.9779	−0.460349	−0.230174	+	0.973149i	$0.573930\pi$
$678$	23.2345	0.892314
$679$	−49.9180	−1.91568
$680$	33.2750	1.27604
$681$	20.5856	0.788841
$682$	−74.5689	−2.85539
$683$	45.1763	1.72862	0.864311	−	0.502958i	$-0.167755\pi$
$683$	45.1763	1.72862	0.864311	+	0.502958i	$0.167755\pi$
$684$	−2.19488	−0.0839231
$685$	5.67777	0.216937
$686$	−50.9766	−1.94630
$687$	31.0829	1.18589
$688$	110.342	4.20674
$689$	0.324071	0.0123461
$690$	−5.78778	−0.220337
$691$	−7.55218	−0.287298	−0.143649	−	0.989629i	$-0.545884\pi$
$691$	−7.55218	−0.287298	−0.143649	+	0.989629i	$0.545884\pi$
$692$	122.541	4.65833
$693$	29.0358	1.10298
$694$	−54.1238	−2.05451
$695$	−7.61003	−0.288665
$696$	57.9262	2.19569
$697$	5.38200	0.203858
$698$	−2.69608	−0.102048
$699$	7.33965	0.277611
$700$	−43.5550	−1.64622
$701$	12.1827	0.460134	0.230067	−	0.973175i	$-0.426105\pi$
$701$	12.1827	0.460134	0.230067	+	0.973175i	$0.426105\pi$
$702$	−2.91645	−0.110074
$703$	−0.683227	−0.0257684
$704$	−99.8988	−3.76508
$705$	−2.75961	−0.103933
$706$	4.51332	0.169861
$707$	10.1918	0.383304
$708$	57.7131	2.16899
$709$	−37.8373	−1.42101	−0.710505	−	0.703692i	$-0.751534\pi$
$709$	−37.8373	−1.42101	−0.710505	+	0.703692i	$0.751534\pi$
$710$	−0.685962	−0.0257437
$711$	−13.4593	−0.504763
$712$	−99.4031	−3.72529
$713$	6.13197	0.229644
$714$	−30.5073	−1.14171
$715$	−1.55206	−0.0580437
$716$	−14.2604	−0.532934
$717$	2.93418	0.109579
$718$	−3.40460	−0.127059
$719$	43.5069	1.62253	0.811266	−	0.584677i	$-0.198779\pi$
$719$	43.5069	1.62253	0.811266	+	0.584677i	$0.198779\pi$
$720$	34.7808	1.29621
$721$	−37.6449	−1.40197
$722$	51.0176	1.89868
$723$	−4.15091	−0.154374
$724$	103.758	3.85615
$725$	10.3419	0.384088
$726$	−30.8517	−1.14501
$727$	−49.4621	−1.83445	−0.917223	−	0.398373i	$-0.869575\pi$
$727$	−49.4621	−1.83445	−0.917223	+	0.398373i	$0.869575\pi$
$728$	7.42167	0.275065
$729$	23.6182	0.874747
$730$	16.5659	0.613130
$731$	17.9726	0.664741
$732$	−27.8780	−1.03040
$733$	−17.6745	−0.652824	−0.326412	−	0.945228i	$-0.605840\pi$
$733$	−17.6745	−0.652824	−0.326412	+	0.945228i	$0.605840\pi$
$734$	69.4055	2.56180
$735$	−24.4879	−0.903252
$736$	18.0239	0.664369
$737$	10.4503	0.384944
$738$	10.1087	0.372107
$739$	35.5640	1.30824	0.654122	−	0.756389i	$-0.273038\pi$
$739$	35.5640	1.30824	0.654122	+	0.756389i	$0.273038\pi$
$740$	22.7299	0.835567
$741$	−0.0667340	−0.00245154
$742$	19.0976	0.701094
$743$	−11.1097	−0.407574	−0.203787	−	0.979015i	$-0.565325\pi$
$743$	−11.1097	−0.407574	−0.203787	+	0.979015i	$0.565325\pi$
$744$	66.1770	2.42617
$745$	12.2328	0.448176
$746$	28.3543	1.03813
$747$	10.6047	0.388004
$748$	−51.1843	−1.87148
$749$	−47.1826	−1.72402
$750$	−40.0907	−1.46390
$751$	−41.6539	−1.51997	−0.759987	−	0.649939i	$-0.774795\pi$
$751$	−41.6539	−1.51997	−0.759987	+	0.649939i	$0.774795\pi$
$752$	16.9979	0.619848
$753$	−16.6201	−0.605671
$754$	−2.84044	−0.103443
$755$	−30.1963	−1.09896
$756$	−124.578	−4.53088
$757$	42.0688	1.52902	0.764508	−	0.644615i	$-0.222982\pi$
$757$	42.0688	1.52902	0.764508	+	0.644615i	$0.222982\pi$
$758$	−58.2631	−2.11621
$759$	5.52342	0.200487
$760$	4.28943	0.155594
$761$	26.3062	0.953599	0.476799	−	0.879012i	$-0.341797\pi$
$761$	26.3062	0.953599	0.476799	+	0.879012i	$0.341797\pi$
$762$	−4.64428	−0.168245
$763$	51.0527	1.84823
$764$	32.6066	1.17966
$765$	5.66515	0.204824
$766$	16.9135	0.611111
$767$	−1.75575	−0.0633965
$768$	23.8870	0.861948
$769$	20.6944	0.746260	0.373130	−	0.927779i	$-0.378284\pi$
$769$	20.6944	0.746260	0.373130	+	0.927779i	$0.378284\pi$
$770$	−91.4632	−3.29610
$771$	−17.3679	−0.625491
$772$	38.5132	1.38612
$773$	−51.5609	−1.85452	−0.927258	−	0.374423i	$-0.877841\pi$
$773$	−51.5609	−1.85452	−0.927258	+	0.374423i	$0.877841\pi$
$774$	33.7569	1.21337
$775$	11.8150	0.424406
$776$	102.539	3.68094
$777$	−12.9289	−0.463821
$778$	−1.69581	−0.0607978
$779$	0.693786	0.0248575
$780$	2.22013	0.0794935
$781$	0.654631	0.0234245
$782$	5.80670	0.207647
$783$	29.5805	1.05712
$784$	150.834	5.38693
$785$	−38.3929	−1.37030
$786$	−41.1693	−1.46846
$787$	21.9918	0.783923	0.391961	−	0.919982i	$-0.371797\pi$
$787$	21.9918	0.783923	0.391961	+	0.919982i	$0.371797\pi$
$788$	26.5006	0.944046
$789$	−6.06685	−0.215986
$790$	42.3969	1.50841
$791$	−30.1932	−1.07355
$792$	−59.6440	−2.11936
$793$	0.848106	0.0301171
$794$	−28.3541	−1.00625
$795$	3.54433	0.125704
$796$	−50.0289	−1.77323
$797$	48.3936	1.71419	0.857095	−	0.515158i	$-0.172267\pi$
$797$	48.3936	1.71419	0.857095	+	0.515158i	$0.172267\pi$
$798$	−3.93265	−0.139214
$799$	2.76863	0.0979472
$800$	34.7281	1.22782
$801$	−16.9236	−0.597966
$802$	48.5280	1.71358
$803$	−15.8092	−0.557896
$804$	−14.9487	−0.527198
$805$	7.52123	0.265088
$806$	−3.24502	−0.114301
$807$	−19.1487	−0.674066
$808$	−20.9356	−0.736511
$809$	−6.44033	−0.226430	−0.113215	−	0.993571i	$-0.536115\pi$
$809$	−6.44033	−0.226430	−0.113215	+	0.993571i	$0.536115\pi$
$810$	−10.6220	−0.373221
$811$	−23.1606	−0.813279	−0.406640	−	0.913589i	$-0.633299\pi$
$811$	−23.1606	−0.813279	−0.406640	+	0.913589i	$0.633299\pi$
$812$	−121.332	−4.25790
$813$	12.3065	0.431609
$814$	−29.9257	−1.04889
$815$	1.48578	0.0520447
$816$	34.8744	1.22085
$817$	2.31682	0.0810554
$818$	33.2568	1.16280
$819$	1.26356	0.0441522
$820$	−23.0811	−0.806029
$821$	27.9004	0.973732	0.486866	−	0.873477i	$-0.338140\pi$
$821$	27.9004	0.973732	0.486866	+	0.873477i	$0.338140\pi$
$822$	10.6929	0.372958
$823$	12.3305	0.429815	0.214908	−	0.976634i	$-0.431055\pi$
$823$	12.3305	0.429815	0.214908	+	0.976634i	$0.431055\pi$
$824$	77.3282	2.69386
$825$	10.6424	0.370521
$826$	−103.467	−3.60008
$827$	−52.8663	−1.83834	−0.919171	−	0.393859i	$-0.871140\pi$
$827$	−52.8663	−1.83834	−0.919171	+	0.393859i	$0.871140\pi$
$828$	7.90553	0.274736
$829$	1.28480	0.0446228	0.0223114	−	0.999751i	$-0.492897\pi$
$829$	1.28480	0.0446228	0.0223114	+	0.999751i	$0.492897\pi$
$830$	−33.4048	−1.15950
$831$	−28.4820	−0.988031
$832$	−4.34731	−0.150716
$833$	24.5680	0.851231
$834$	−14.3319	−0.496274
$835$	−23.8042	−0.823779
$836$	−6.59809	−0.228200
$837$	33.7938	1.16809
$838$	−52.6613	−1.81915
$839$	21.3459	0.736943	0.368471	−	0.929639i	$-0.379881\pi$
$839$	21.3459	0.736943	0.368471	+	0.929639i	$0.379881\pi$
$840$	81.1700	2.80063
$841$	−0.190489	−0.00656860
$842$	−29.2451	−1.00785
$843$	33.5804	1.15657
$844$	−9.54423	−0.328526
$845$	22.7222	0.781669
$846$	5.20017	0.178785
$847$	40.0919	1.37757
$848$	−21.8313	−0.749691
$849$	−6.14613	−0.210934
$850$	11.1882	0.383753
$851$	2.46086	0.0843571
$852$	−0.936414	−0.0320810
$853$	38.8040	1.32862	0.664311	−	0.747456i	$-0.268725\pi$
$853$	38.8040	1.32862	0.664311	+	0.747456i	$0.268725\pi$
$854$	49.9791	1.71025
$855$	0.730286	0.0249752
$856$	96.9202	3.31267
$857$	21.0927	0.720512	0.360256	−	0.932853i	$-0.382689\pi$
$857$	21.0927	0.720512	0.360256	+	0.932853i	$0.382689\pi$
$858$	−2.92298	−0.0997889
$859$	−11.9406	−0.407406	−0.203703	−	0.979033i	$-0.565298\pi$
$859$	−11.9406	−0.407406	−0.203703	+	0.979033i	$0.565298\pi$
$860$	−77.0770	−2.62830
$861$	13.1287	0.447425
$862$	18.8637	0.642501
$863$	49.2780	1.67744	0.838721	−	0.544561i	$-0.183304\pi$
$863$	49.2780	1.67744	0.838721	+	0.544561i	$0.183304\pi$
$864$	99.3312	3.37932
$865$	−40.7724	−1.38630
$866$	101.245	3.44044
$867$	−15.1373	−0.514089
$868$	−138.614	−4.70485
$869$	−40.4604	−1.37253
$870$	−31.0656	−1.05322
$871$	0.454769	0.0154093
$872$	−104.870	−3.55134
$873$	17.4575	0.590847
$874$	0.748533	0.0253195
$875$	52.0979	1.76123
$876$	22.6142	0.764064
$877$	7.03319	0.237494	0.118747	−	0.992925i	$-0.462112\pi$
$877$	7.03319	0.237494	0.118747	+	0.992925i	$0.462112\pi$
$878$	11.2086	0.378271
$879$	30.5945	1.03193
$880$	104.556	3.52458
$881$	−4.81983	−0.162384	−0.0811921	−	0.996698i	$-0.525873\pi$
$881$	−4.81983	−0.162384	−0.0811921	+	0.996698i	$0.525873\pi$
$882$	46.1447	1.55377
$883$	2.75473	0.0927042	0.0463521	−	0.998925i	$-0.485240\pi$
$883$	2.75473	0.0927042	0.0463521	+	0.998925i	$0.485240\pi$
$884$	−2.22739	−0.0749153
$885$	−19.2025	−0.645484
$886$	−27.8293	−0.934942
$887$	22.8169	0.766115	0.383057	−	0.923725i	$-0.374871\pi$
$887$	22.8169	0.766115	0.383057	+	0.923725i	$0.374871\pi$
$888$	26.5579	0.891224
$889$	6.03526	0.202416
$890$	53.3095	1.78694
$891$	10.1369	0.339599
$892$	20.0090	0.669951
$893$	0.356900	0.0119432
$894$	23.0380	0.770505
$895$	4.74475	0.158599
$896$	−101.531	−3.39190
$897$	0.240363	0.00802550
$898$	41.1349	1.37269
$899$	32.9130	1.09771
$900$	15.2322	0.507741
$901$	−3.55591	−0.118465
$902$	30.3882	1.01181
$903$	43.8418	1.45896
$904$	62.0214	2.06280
$905$	−34.5228	−1.14758
$906$	−56.8686	−1.88933
$907$	44.7284	1.48518	0.742591	−	0.669745i	$-0.233597\pi$
$907$	44.7284	1.48518	0.742591	+	0.669745i	$0.233597\pi$
$908$	88.5715	2.93935
$909$	−3.56433	−0.118221
$910$	−3.98021	−0.131943
$911$	27.7355	0.918918	0.459459	−	0.888199i	$-0.348043\pi$
$911$	27.7355	0.918918	0.459459	+	0.888199i	$0.348043\pi$
$912$	4.49560	0.148864
$913$	31.8791	1.05504
$914$	−81.5680	−2.69803
$915$	9.27565	0.306643
$916$	133.737	4.41880
$917$	53.4996	1.76671
$918$	32.0012	1.05620
$919$	−35.9739	−1.18667	−0.593334	−	0.804956i	$-0.702189\pi$
$919$	−35.9739	−1.18667	−0.593334	+	0.804956i	$0.702189\pi$
$920$	−15.4497	−0.509363
$921$	4.84200	0.159549
$922$	−92.6183	−3.05022
$923$	0.0284877	0.000937683 0
$924$	−124.857	−4.10750
$925$	4.74153	0.155901
$926$	82.5267	2.71199
$927$	13.1653	0.432405
$928$	96.7423	3.17572
$929$	7.69948	0.252612	0.126306	−	0.991991i	$-0.459688\pi$
$929$	7.69948	0.252612	0.126306	+	0.991991i	$0.459688\pi$
$930$	−35.4905	−1.16378
$931$	3.16703	0.103795
$932$	31.5796	1.03442
$933$	−5.97893	−0.195742
$934$	25.4979	0.834316
$935$	17.0302	0.556947
$936$	−2.59553	−0.0848377
$937$	−26.3697	−0.861460	−0.430730	−	0.902481i	$-0.641744\pi$
$937$	−26.3697	−0.861460	−0.430730	+	0.902481i	$0.641744\pi$
$938$	26.7997	0.875040
$939$	38.5168	1.25695
$940$	−11.8735	−0.387271
$941$	27.0683	0.882403	0.441201	−	0.897408i	$-0.354552\pi$
$941$	27.0683	0.882403	0.441201	+	0.897408i	$0.354552\pi$
$942$	−72.3051	−2.35583
$943$	−2.49889	−0.0813750
$944$	118.278	3.84962
$945$	41.4501	1.34837
$946$	101.478	3.29933
$947$	27.2381	0.885120	0.442560	−	0.896739i	$-0.354070\pi$
$947$	27.2381	0.885120	0.442560	+	0.896739i	$0.354070\pi$
$948$	57.8765	1.87974
$949$	−0.687972	−0.0223325
$950$	1.44226	0.0467931
$951$	−28.1988	−0.914410
$952$	−81.4354	−2.63934
$953$	47.4256	1.53626	0.768132	−	0.640291i	$-0.221186\pi$
$953$	47.4256	1.53626	0.768132	+	0.640291i	$0.221186\pi$
$954$	−6.67887	−0.216236
$955$	−10.8490	−0.351064
$956$	12.6246	0.408309
$957$	29.6467	0.958341
$958$	104.395	3.37284
$959$	−13.8955	−0.448708
$960$	−47.5460	−1.53454
$961$	6.60105	0.212937
$962$	−1.30228	−0.0419872
$963$	16.5009	0.531734
$964$	−17.8597	−0.575222
$965$	−12.8142	−0.412505
$966$	14.1647	0.455741
$967$	24.3078	0.781685	0.390842	−	0.920458i	$-0.372184\pi$
$967$	24.3078	0.781685	0.390842	+	0.920458i	$0.372184\pi$
$968$	−82.3547	−2.64698
$969$	0.732249	0.0235232
$970$	−54.9913	−1.76567
$971$	6.91359	0.221868	0.110934	−	0.993828i	$-0.464616\pi$
$971$	6.91359	0.221868	0.110934	+	0.993828i	$0.464616\pi$
$972$	72.6106	2.32899
$973$	18.6244	0.597070
$974$	29.3540	0.940563
$975$	0.463127	0.0148319
$976$	−57.1335	−1.82880
$977$	−27.3667	−0.875539	−0.437769	−	0.899087i	$-0.644231\pi$
$977$	−27.3667	−0.875539	−0.437769	+	0.899087i	$0.644231\pi$
$978$	2.79816	0.0894754
$979$	−50.8746	−1.62596
$980$	−105.362	−3.36566
$981$	−17.8543	−0.570045
$982$	−45.4140	−1.44922
$983$	36.1260	1.15224	0.576120	−	0.817365i	$-0.304566\pi$
$983$	36.1260	1.15224	0.576120	+	0.817365i	$0.304566\pi$
$984$	−26.9683	−0.859718
$985$	−8.81737	−0.280945
$986$	31.1672	0.992565
$987$	6.75371	0.214973
$988$	−0.287130	−0.00913482
$989$	−8.34476	−0.265348
$990$	31.9868	1.01661
$991$	46.3610	1.47271	0.736353	−	0.676597i	$-0.236546\pi$
$991$	46.3610	1.47271	0.736353	+	0.676597i	$0.236546\pi$
$992$	110.522	3.50908
$993$	21.4200	0.679744
$994$	1.67879	0.0532478
$995$	16.6458	0.527706
$996$	−45.6012	−1.44493
$997$	36.6646	1.16118	0.580590	−	0.814196i	$-0.302822\pi$
$997$	36.6646	1.16118	0.580590	+	0.814196i	$0.302822\pi$
$998$	−65.0548	−2.05927
$999$	13.5620	0.429083

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.e.1.7	✓	169

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.e.1.7	✓	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)

\(f(q)\)	\(=\)	\(q-2.69608 q^{2} +1.22457 q^{3} +5.26883 q^{4} -1.75306 q^{5} -3.30153 q^{6} +4.29034 q^{7} -8.81301 q^{8} -1.50043 q^{9} +O(q^{10})\)	\(q-2.69608 q^{2} +1.22457 q^{3} +5.26883 q^{4} -1.75306 q^{5} -3.30153 q^{6} +4.29034 q^{7} -8.81301 q^{8} -1.50043 q^{9} +4.72638 q^{10} -4.51051 q^{11} +6.45203 q^{12} -0.196284 q^{13} -11.5671 q^{14} -2.14674 q^{15} +13.2229 q^{16} +2.15376 q^{17} +4.04529 q^{18} +0.277638 q^{19} -9.23657 q^{20} +5.25381 q^{21} +12.1607 q^{22} -1.00000 q^{23} -10.7921 q^{24} -1.92678 q^{25} +0.529197 q^{26} -5.51109 q^{27} +22.6051 q^{28} -5.36745 q^{29} +5.78778 q^{30} -6.13197 q^{31} -18.0239 q^{32} -5.52342 q^{33} -5.80670 q^{34} -7.52123 q^{35} -7.90553 q^{36} -2.46086 q^{37} -0.748533 q^{38} -0.240363 q^{39} +15.4497 q^{40} +2.49889 q^{41} -14.1647 q^{42} +8.34476 q^{43} -23.7651 q^{44} +2.63035 q^{45} +2.69608 q^{46} +1.28549 q^{47} +16.1923 q^{48} +11.4070 q^{49} +5.19475 q^{50} +2.63742 q^{51} -1.03419 q^{52} -1.65103 q^{53} +14.8583 q^{54} +7.90719 q^{55} -37.8108 q^{56} +0.339986 q^{57} +14.4711 q^{58} +8.94494 q^{59} -11.3108 q^{60} -4.32081 q^{61} +16.5323 q^{62} -6.43738 q^{63} +22.1480 q^{64} +0.344098 q^{65} +14.8916 q^{66} -2.31689 q^{67} +11.3478 q^{68} -1.22457 q^{69} +20.2778 q^{70} -0.145135 q^{71} +13.2233 q^{72} +3.50498 q^{73} +6.63466 q^{74} -2.35947 q^{75} +1.46283 q^{76} -19.3516 q^{77} +0.648038 q^{78} +8.97026 q^{79} -23.1805 q^{80} -2.24739 q^{81} -6.73719 q^{82} -7.06773 q^{83} +27.6814 q^{84} -3.77567 q^{85} -22.4981 q^{86} -6.57280 q^{87} +39.7511 q^{88} +11.2791 q^{89} -7.09163 q^{90} -0.842127 q^{91} -5.26883 q^{92} -7.50901 q^{93} -3.46577 q^{94} -0.486716 q^{95} -22.0715 q^{96} -11.6350 q^{97} -30.7542 q^{98} +6.76772 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9}+O(q^{10}) \) 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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