LMFDB - Embedded newform 8045.2.a.d.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8045,2,Mod(1,8045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8045, 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("8045.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8045 = 5 \cdot 1609 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8045.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:	$64.2396484261$
Analytic rank:	$0$
Dimension:	$141$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	8045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.75850 q^{2} -2.99511 q^{3} +5.60931 q^{4} -1.00000 q^{5} +8.26199 q^{6} +0.810789 q^{7} -9.95629 q^{8} +5.97065 q^{9} +O(q^{10})$	\(q-2.75850 q^{2} -2.99511 q^{3} +5.60931 q^{4} -1.00000 q^{5} +8.26199 q^{6} +0.810789 q^{7} -9.95629 q^{8} +5.97065 q^{9} +2.75850 q^{10} +2.99569 q^{11} -16.8005 q^{12} -3.56594 q^{13} -2.23656 q^{14} +2.99511 q^{15} +16.2458 q^{16} -1.15876 q^{17} -16.4700 q^{18} -2.54055 q^{19} -5.60931 q^{20} -2.42840 q^{21} -8.26361 q^{22} -1.21687 q^{23} +29.8201 q^{24} +1.00000 q^{25} +9.83664 q^{26} -8.89742 q^{27} +4.54797 q^{28} -7.49068 q^{29} -8.26199 q^{30} -6.00716 q^{31} -24.9014 q^{32} -8.97241 q^{33} +3.19644 q^{34} -0.810789 q^{35} +33.4913 q^{36} +0.121249 q^{37} +7.00812 q^{38} +10.6804 q^{39} +9.95629 q^{40} +0.894437 q^{41} +6.69874 q^{42} -5.87780 q^{43} +16.8038 q^{44} -5.97065 q^{45} +3.35674 q^{46} -6.84715 q^{47} -48.6578 q^{48} -6.34262 q^{49} -2.75850 q^{50} +3.47061 q^{51} -20.0025 q^{52} -13.3293 q^{53} +24.5435 q^{54} -2.99569 q^{55} -8.07245 q^{56} +7.60923 q^{57} +20.6630 q^{58} -4.48689 q^{59} +16.8005 q^{60} +4.66603 q^{61} +16.5707 q^{62} +4.84094 q^{63} +36.1989 q^{64} +3.56594 q^{65} +24.7504 q^{66} +5.90040 q^{67} -6.49986 q^{68} +3.64466 q^{69} +2.23656 q^{70} -13.1714 q^{71} -59.4456 q^{72} +3.90984 q^{73} -0.334464 q^{74} -2.99511 q^{75} -14.2508 q^{76} +2.42888 q^{77} -29.4618 q^{78} -8.63839 q^{79} -16.2458 q^{80} +8.73675 q^{81} -2.46730 q^{82} +2.27289 q^{83} -13.6217 q^{84} +1.15876 q^{85} +16.2139 q^{86} +22.4354 q^{87} -29.8260 q^{88} -5.91937 q^{89} +16.4700 q^{90} -2.89123 q^{91} -6.82582 q^{92} +17.9921 q^{93} +18.8879 q^{94} +2.54055 q^{95} +74.5822 q^{96} +13.5456 q^{97} +17.4961 q^{98} +17.8862 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 141 q - 8 q^{2} + 11 q^{3} + 158 q^{4} - 141 q^{5} + 23 q^{6} + 29 q^{7} - 21 q^{8} + 160 q^{9}+O(q^{10}) $ 141 * q - 8 * q^2 + 11 * q^3 + 158 * q^4 - 141 * q^5 + 23 * q^6 + 29 * q^7 - 21 * q^8 + 160 * q^9	\( 141 q - 8 q^{2} + 11 q^{3} + 158 q^{4} - 141 q^{5} + 23 q^{6} + 29 q^{7} - 21 q^{8} + 160 q^{9} + 8 q^{10} + 32 q^{11} + 17 q^{12} + 35 q^{13} + 18 q^{14} - 11 q^{15} + 188 q^{16} - 13 q^{17} - 16 q^{18} + 152 q^{19} - 158 q^{20} + 40 q^{21} + 14 q^{22} - 77 q^{23} + 69 q^{24} + 141 q^{25} + 27 q^{26} + 38 q^{27} + 67 q^{28} + 22 q^{29} - 23 q^{30} + 86 q^{31} - 65 q^{32} + 51 q^{33} + 79 q^{34} - 29 q^{35} + 191 q^{36} + 45 q^{37} - 9 q^{38} + 55 q^{39} + 21 q^{40} + 36 q^{41} + 6 q^{42} + 132 q^{43} + 74 q^{44} - 160 q^{45} + 72 q^{46} - 16 q^{47} + 22 q^{48} + 212 q^{49} - 8 q^{50} + 82 q^{51} + 106 q^{52} - 28 q^{53} + 86 q^{54} - 32 q^{55} + 27 q^{56} + 10 q^{57} + 23 q^{58} + 71 q^{59} - 17 q^{60} + 116 q^{61} - 36 q^{62} + 45 q^{63} + 237 q^{64} - 35 q^{65} + 69 q^{66} + 99 q^{67} - 7 q^{68} + 45 q^{69} - 18 q^{70} + 34 q^{71} - 53 q^{72} + 125 q^{73} + 50 q^{74} + 11 q^{75} + 271 q^{76} - 31 q^{77} + 2 q^{78} + 101 q^{79} - 188 q^{80} + 221 q^{81} + 67 q^{82} + 67 q^{83} + 141 q^{84} + 13 q^{85} + 48 q^{86} - 21 q^{87} + 71 q^{88} + 79 q^{89} + 16 q^{90} + 228 q^{91} - 198 q^{92} - 12 q^{93} + 114 q^{94} - 152 q^{95} + 129 q^{96} + 98 q^{97} - 31 q^{98} + 195 q^{99}+O(q^{100}) \) 141 * q - 8 * q^2 + 11 * q^3 + 158 * q^4 - 141 * q^5 + 23 * q^6 + 29 * q^7 - 21 * q^8 + 160 * q^9 + 8 * q^10 + 32 * q^11 + 17 * q^12 + 35 * q^13 + 18 * q^14 - 11 * q^15 + 188 * q^16 - 13 * q^17 - 16 * q^18 + 152 * q^19 - 158 * q^20 + 40 * q^21 + 14 * q^22 - 77 * q^23 + 69 * q^24 + 141 * q^25 + 27 * q^26 + 38 * q^27 + 67 * q^28 + 22 * q^29 - 23 * q^30 + 86 * q^31 - 65 * q^32 + 51 * q^33 + 79 * q^34 - 29 * q^35 + 191 * q^36 + 45 * q^37 - 9 * q^38 + 55 * q^39 + 21 * q^40 + 36 * q^41 + 6 * q^42 + 132 * q^43 + 74 * q^44 - 160 * q^45 + 72 * q^46 - 16 * q^47 + 22 * q^48 + 212 * q^49 - 8 * q^50 + 82 * q^51 + 106 * q^52 - 28 * q^53 + 86 * q^54 - 32 * q^55 + 27 * q^56 + 10 * q^57 + 23 * q^58 + 71 * q^59 - 17 * q^60 + 116 * q^61 - 36 * q^62 + 45 * q^63 + 237 * q^64 - 35 * q^65 + 69 * q^66 + 99 * q^67 - 7 * q^68 + 45 * q^69 - 18 * q^70 + 34 * q^71 - 53 * q^72 + 125 * q^73 + 50 * q^74 + 11 * q^75 + 271 * q^76 - 31 * q^77 + 2 * q^78 + 101 * q^79 - 188 * q^80 + 221 * q^81 + 67 * q^82 + 67 * q^83 + 141 * q^84 + 13 * q^85 + 48 * q^86 - 21 * q^87 + 71 * q^88 + 79 * q^89 + 16 * q^90 + 228 * q^91 - 198 * q^92 - 12 * q^93 + 114 * q^94 - 152 * q^95 + 129 * q^96 + 98 * q^97 - 31 * q^98 + 195 * 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 $

$2$	−2.75850	−1.95055	−0.975277	−	0.220988i	$-0.929072\pi$
$2$	−2.75850	−1.95055	−0.975277	+	0.220988i	$0.929072\pi$
$3$	−2.99511	−1.72922	−0.864612	−	0.502440i	$-0.832436\pi$
$3$	−2.99511	−1.72922	−0.864612	+	0.502440i	$0.832436\pi$
$4$	5.60931	2.80466
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	8.26199	3.37294
$7$	0.810789	0.306450	0.153225	−	0.988191i	$-0.451034\pi$
$7$	0.810789	0.306450	0.153225	+	0.988191i	$0.451034\pi$
$8$	−9.95629	−3.52008
$9$	5.97065	1.99022
$10$	2.75850	0.872314
$11$	2.99569	0.903235	0.451618	−	0.892212i	$-0.350847\pi$
$11$	2.99569	0.903235	0.451618	+	0.892212i	$0.350847\pi$
$12$	−16.8005	−4.84988
$13$	−3.56594	−0.989013	−0.494507	−	0.869174i	$-0.664651\pi$
$13$	−3.56594	−0.989013	−0.494507	+	0.869174i	$0.664651\pi$
$14$	−2.23656	−0.597746
$15$	2.99511	0.773333
$16$	16.2458	4.06144
$17$	−1.15876	−0.281041	−0.140521	−	0.990078i	$-0.544878\pi$
$17$	−1.15876	−0.281041	−0.140521	+	0.990078i	$0.544878\pi$
$18$	−16.4700	−3.88203
$19$	−2.54055	−0.582843	−0.291422	−	0.956595i	$-0.594128\pi$
$19$	−2.54055	−0.582843	−0.291422	+	0.956595i	$0.594128\pi$
$20$	−5.60931	−1.25428
$21$	−2.42840	−0.529920
$22$	−8.26361	−1.76181
$23$	−1.21687	−0.253735	−0.126868	−	0.991920i	$-0.540492\pi$
$23$	−1.21687	−0.253735	−0.126868	+	0.991920i	$0.540492\pi$
$24$	29.8201	6.08701
$25$	1.00000	0.200000
$26$	9.83664	1.92912
$27$	−8.89742	−1.71231
$28$	4.54797	0.859486
$29$	−7.49068	−1.39098	−0.695492	−	0.718534i	$-0.744813\pi$
$29$	−7.49068	−1.39098	−0.695492	+	0.718534i	$0.744813\pi$
$30$	−8.26199	−1.50843
$31$	−6.00716	−1.07892	−0.539459	−	0.842012i	$-0.681371\pi$
$31$	−6.00716	−1.07892	−0.539459	+	0.842012i	$0.681371\pi$
$32$	−24.9014	−4.40198
$33$	−8.97241	−1.56190
$34$	3.19644	0.548186
$35$	−0.810789	−0.137048
$36$	33.4913	5.58188
$37$	0.121249	0.0199331	0.00996657	−	0.999950i	$-0.496827\pi$
$37$	0.121249	0.0199331	0.00996657	+	0.999950i	$0.496827\pi$
$38$	7.00812	1.13687
$39$	10.6804	1.71023
$40$	9.95629	1.57423
$41$	0.894437	0.139688	0.0698438	−	0.997558i	$-0.477750\pi$
$41$	0.894437	0.139688	0.0698438	+	0.997558i	$0.477750\pi$
$42$	6.69874	1.03364
$43$	−5.87780	−0.896356	−0.448178	−	0.893944i	$-0.647927\pi$
$43$	−5.87780	−0.896356	−0.448178	+	0.893944i	$0.647927\pi$
$44$	16.8038	2.53327
$45$	−5.97065	−0.890053
$46$	3.35674	0.494924
$47$	−6.84715	−0.998760	−0.499380	−	0.866383i	$-0.666439\pi$
$47$	−6.84715	−0.998760	−0.499380	+	0.866383i	$0.666439\pi$
$48$	−48.6578	−7.02315
$49$	−6.34262	−0.906089
$50$	−2.75850	−0.390111
$51$	3.47061	0.485983
$52$	−20.0025	−2.77384
$53$	−13.3293	−1.83093	−0.915463	−	0.402403i	$-0.868175\pi$
$53$	−13.3293	−1.83093	−0.915463	+	0.402403i	$0.868175\pi$
$54$	24.5435	3.33995
$55$	−2.99569	−0.403939
$56$	−8.07245	−1.07873
$57$	7.60923	1.00787
$58$	20.6630	2.71319
$59$	−4.48689	−0.584143	−0.292071	−	0.956397i	$-0.594344\pi$
$59$	−4.48689	−0.584143	−0.292071	+	0.956397i	$0.594344\pi$
$60$	16.8005	2.16893
$61$	4.66603	0.597424	0.298712	−	0.954343i	$-0.403443\pi$
$61$	4.66603	0.597424	0.298712	+	0.954343i	$0.403443\pi$
$62$	16.5707	2.10449
$63$	4.84094	0.609902
$64$	36.1989	4.52486
$65$	3.56594	0.442300
$66$	24.7504	3.04656
$67$	5.90040	0.720849	0.360424	−	0.932788i	$-0.382632\pi$
$67$	5.90040	0.720849	0.360424	+	0.932788i	$0.382632\pi$
$68$	−6.49986	−0.788224
$69$	3.64466	0.438765
$70$	2.23656	0.267320
$71$	−13.1714	−1.56316	−0.781581	−	0.623804i	$-0.785586\pi$
$71$	−13.1714	−1.56316	−0.781581	+	0.623804i	$0.785586\pi$
$72$	−59.4456	−7.00573
$73$	3.90984	0.457612	0.228806	−	0.973472i	$-0.426518\pi$
$73$	3.90984	0.457612	0.228806	+	0.973472i	$0.426518\pi$
$74$	−0.334464	−0.0388807
$75$	−2.99511	−0.345845
$76$	−14.2508	−1.63468
$77$	2.42888	0.276796
$78$	−29.4618	−3.33589
$79$	−8.63839	−0.971895	−0.485947	−	0.873988i	$-0.661525\pi$
$79$	−8.63839	−0.971895	−0.485947	+	0.873988i	$0.661525\pi$
$80$	−16.2458	−1.81633
$81$	8.73675	0.970750
$82$	−2.46730	−0.272468
$83$	2.27289	0.249482	0.124741	−	0.992189i	$-0.460190\pi$
$83$	2.27289	0.249482	0.124741	+	0.992189i	$0.460190\pi$
$84$	−13.6217	−1.48624
$85$	1.15876	0.125685
$86$	16.2139	1.74839
$87$	22.4354	2.40532
$88$	−29.8260	−3.17946
$89$	−5.91937	−0.627452	−0.313726	−	0.949514i	$-0.601577\pi$
$89$	−5.91937	−0.627452	−0.313726	+	0.949514i	$0.601577\pi$
$90$	16.4700	1.73609
$91$	−2.89123	−0.303083
$92$	−6.82582	−0.711640
$93$	17.9921	1.86569
$94$	18.8879	1.94813
$95$	2.54055	0.260655
$96$	74.5822	7.61202
$97$	13.5456	1.37535	0.687673	−	0.726021i	$-0.258632\pi$
$97$	13.5456	1.37535	0.687673	+	0.726021i	$0.258632\pi$
$98$	17.4961	1.76737
$99$	17.8862	1.79763
$100$	5.60931	0.560931
$101$	−16.5078	−1.64258	−0.821292	−	0.570508i	$-0.806746\pi$
$101$	−16.5078	−1.64258	−0.821292	+	0.570508i	$0.806746\pi$
$102$	−9.57368	−0.947936
$103$	2.21208	0.217963	0.108982	−	0.994044i	$-0.465241\pi$
$103$	2.21208	0.217963	0.108982	+	0.994044i	$0.465241\pi$
$104$	35.5035	3.48141
$105$	2.42840	0.236988
$106$	36.7690	3.57132
$107$	8.44714	0.816616	0.408308	−	0.912844i	$-0.366119\pi$
$107$	8.44714	0.816616	0.408308	+	0.912844i	$0.366119\pi$
$108$	−49.9084	−4.80244
$109$	1.98514	0.190141	0.0950707	−	0.995471i	$-0.469692\pi$
$109$	1.98514	0.190141	0.0950707	+	0.995471i	$0.469692\pi$
$110$	8.26361	0.787905
$111$	−0.363152	−0.0344689
$112$	13.1719	1.24463
$113$	−2.07874	−0.195552	−0.0977759	−	0.995208i	$-0.531173\pi$
$113$	−2.07874	−0.195552	−0.0977759	+	0.995208i	$0.531173\pi$
$114$	−20.9900	−1.96590
$115$	1.21687	0.113474
$116$	−42.0176	−3.90123
$117$	−21.2910	−1.96835
$118$	12.3771	1.13940
$119$	−0.939512	−0.0861249
$120$	−29.8201	−2.72219
$121$	−2.02583	−0.184166
$122$	−12.8712	−1.16531
$123$	−2.67893	−0.241551
$124$	−33.6960	−3.02599
$125$	−1.00000	−0.0894427
$126$	−13.3537	−1.18965
$127$	−4.58119	−0.406515	−0.203257	−	0.979125i	$-0.565153\pi$
$127$	−4.58119	−0.406515	−0.203257	+	0.979125i	$0.565153\pi$
$128$	−50.0518	−4.42399
$129$	17.6046	1.55000
$130$	−9.83664	−0.862730
$131$	15.7241	1.37382	0.686909	−	0.726744i	$-0.258967\pi$
$131$	15.7241	1.37382	0.686909	+	0.726744i	$0.258967\pi$
$132$	−50.3291	−4.38058
$133$	−2.05985	−0.178612
$134$	−16.2763	−1.40605
$135$	8.89742	0.765768
$136$	11.5370	0.989287
$137$	−1.55447	−0.132807	−0.0664036	−	0.997793i	$-0.521152\pi$
$137$	−1.55447	−0.132807	−0.0664036	+	0.997793i	$0.521152\pi$
$138$	−10.0538	−0.855835
$139$	4.99972	0.424071	0.212035	−	0.977262i	$-0.431991\pi$
$139$	4.99972	0.424071	0.212035	+	0.977262i	$0.431991\pi$
$140$	−4.54797	−0.384374
$141$	20.5079	1.72708
$142$	36.3334	3.04903
$143$	−10.6825	−0.893312
$144$	96.9979	8.08316
$145$	7.49068	0.622067
$146$	−10.7853	−0.892596
$147$	18.9968	1.56683
$148$	0.680122	0.0559056
$149$	11.0821	0.907877	0.453939	−	0.891033i	$-0.350019\pi$
$149$	11.0821	0.907877	0.453939	+	0.891033i	$0.350019\pi$
$150$	8.26199	0.674589
$151$	−0.101258	−0.00824028	−0.00412014	−	0.999992i	$-0.501311\pi$
$151$	−0.101258	−0.00824028	−0.00412014	+	0.999992i	$0.501311\pi$
$152$	25.2945	2.05165
$153$	−6.91857	−0.559333
$154$	−6.70005	−0.539905
$155$	6.00716	0.482507
$156$	59.9095	4.79660
$157$	11.9362	0.952615	0.476308	−	0.879279i	$-0.341975\pi$
$157$	11.9362	0.952615	0.476308	+	0.879279i	$0.341975\pi$
$158$	23.8290	1.89573
$159$	39.9228	3.16608
$160$	24.9014	1.96863
$161$	−0.986627	−0.0777571
$162$	−24.1003	−1.89350
$163$	−3.41742	−0.267673	−0.133837	−	0.991003i	$-0.542730\pi$
$163$	−3.41742	−0.267673	−0.133837	+	0.991003i	$0.542730\pi$
$164$	5.01718	0.391776
$165$	8.97241	0.698501
$166$	−6.26977	−0.486629
$167$	−16.9490	−1.31155	−0.655775	−	0.754956i	$-0.727658\pi$
$167$	−16.9490	−1.31155	−0.655775	+	0.754956i	$0.727658\pi$
$168$	24.1778	1.86536
$169$	−0.284082	−0.0218524
$170$	−3.19644	−0.245156
$171$	−15.1688	−1.15998
$172$	−32.9704	−2.51397
$173$	2.71929	0.206744	0.103372	−	0.994643i	$-0.467037\pi$
$173$	2.71929	0.206744	0.103372	+	0.994643i	$0.467037\pi$
$174$	−61.8879	−4.69171
$175$	0.810789	0.0612899
$176$	48.6674	3.66844
$177$	13.4387	1.01011
$178$	16.3286	1.22388
$179$	−26.2066	−1.95877	−0.979386	−	0.201995i	$-0.935257\pi$
$179$	−26.2066	−1.95877	−0.979386	+	0.201995i	$0.935257\pi$
$180$	−33.4913	−2.49629
$181$	23.6253	1.75605	0.878026	−	0.478613i	$-0.158860\pi$
$181$	23.6253	1.75605	0.878026	+	0.478613i	$0.158860\pi$
$182$	7.97544	0.591179
$183$	−13.9753	−1.03308
$184$	12.1155	0.893168
$185$	−0.121249	−0.00891438
$186$	−49.6311	−3.63913
$187$	−3.47129	−0.253846
$188$	−38.4078	−2.80118
$189$	−7.21394	−0.524737
$190$	−7.00812	−0.508422
$191$	4.31848	0.312474	0.156237	−	0.987720i	$-0.450064\pi$
$191$	4.31848	0.312474	0.156237	+	0.987720i	$0.450064\pi$
$192$	−108.419	−7.82450
$193$	−5.43579	−0.391277	−0.195638	−	0.980676i	$-0.562678\pi$
$193$	−5.43579	−0.391277	−0.195638	+	0.980676i	$0.562678\pi$
$194$	−37.3655	−2.68268
$195$	−10.6804	−0.764837
$196$	−35.5778	−2.54127
$197$	8.38356	0.597304	0.298652	−	0.954362i	$-0.403463\pi$
$197$	8.38356	0.597304	0.298652	+	0.954362i	$0.403463\pi$
$198$	−49.3392	−3.50638
$199$	−0.783040	−0.0555082	−0.0277541	−	0.999615i	$-0.508836\pi$
$199$	−0.783040	−0.0555082	−0.0277541	+	0.999615i	$0.508836\pi$
$200$	−9.95629	−0.704016
$201$	−17.6723	−1.24651
$202$	45.5367	3.20395
$203$	−6.07336	−0.426266
$204$	19.4678	1.36302
$205$	−0.894437	−0.0624702
$206$	−6.10203	−0.425149
$207$	−7.26552	−0.504989
$208$	−57.9314	−4.01682
$209$	−7.61072	−0.526444
$210$	−6.69874	−0.462257
$211$	9.05381	0.623290	0.311645	−	0.950199i	$-0.399120\pi$
$211$	9.05381	0.623290	0.311645	+	0.950199i	$0.399120\pi$
$212$	−74.7685	−5.13512
$213$	39.4498	2.70306
$214$	−23.3014	−1.59285
$215$	5.87780	0.400863
$216$	88.5853	6.02747
$217$	−4.87054	−0.330634
$218$	−5.47599	−0.370881
$219$	−11.7104	−0.791313
$220$	−16.8038	−1.13291
$221$	4.13207	0.277953
$222$	1.00176	0.0672334
$223$	−17.9258	−1.20040	−0.600201	−	0.799849i	$-0.704913\pi$
$223$	−17.9258	−1.20040	−0.600201	+	0.799849i	$0.704913\pi$
$224$	−20.1898	−1.34899
$225$	5.97065	0.398044
$226$	5.73421	0.381434
$227$	13.5977	0.902510	0.451255	−	0.892395i	$-0.350976\pi$
$227$	13.5977	0.902510	0.451255	+	0.892395i	$0.350976\pi$
$228$	42.6825	2.82672
$229$	−17.3152	−1.14422	−0.572111	−	0.820176i	$-0.693875\pi$
$229$	−17.3152	−1.14422	−0.572111	+	0.820176i	$0.693875\pi$
$230$	−3.35674	−0.221337
$231$	−7.27474	−0.478643
$232$	74.5793	4.89637
$233$	−4.69004	−0.307255	−0.153628	−	0.988129i	$-0.549096\pi$
$233$	−4.69004	−0.307255	−0.153628	+	0.988129i	$0.549096\pi$
$234$	58.7312	3.83938
$235$	6.84715	0.446659
$236$	−25.1684	−1.63832
$237$	25.8729	1.68062
$238$	2.59164	0.167991
$239$	−22.2520	−1.43936	−0.719681	−	0.694305i	$-0.755712\pi$
$239$	−22.2520	−1.43936	−0.719681	+	0.694305i	$0.755712\pi$
$240$	48.6578	3.14085
$241$	14.2904	0.920524	0.460262	−	0.887783i	$-0.347755\pi$
$241$	14.2904	0.920524	0.460262	+	0.887783i	$0.347755\pi$
$242$	5.58824	0.359226
$243$	0.524785	0.0336649
$244$	26.1732	1.67557
$245$	6.34262	0.405215
$246$	7.38984	0.471159
$247$	9.05946	0.576440
$248$	59.8090	3.79788
$249$	−6.80755	−0.431411
$250$	2.75850	0.174463
$251$	19.9881	1.26164	0.630820	−	0.775929i	$-0.282719\pi$
$251$	19.9881	1.26164	0.630820	+	0.775929i	$0.282719\pi$
$252$	27.1544	1.71056
$253$	−3.64537	−0.229183
$254$	12.6372	0.792929
$255$	−3.47061	−0.217338
$256$	65.6700	4.10437
$257$	−10.7503	−0.670583	−0.335292	−	0.942114i	$-0.608835\pi$
$257$	−10.7503	−0.670583	−0.335292	+	0.942114i	$0.608835\pi$
$258$	−48.5624	−3.02336
$259$	0.0983071	0.00610851
$260$	20.0025	1.24050
$261$	−44.7242	−2.76836
$262$	−43.3748	−2.67970
$263$	−0.00377234	−0.000232612 0	−0.000116306	−	1.00000i	$-0.500037\pi$
$263$	−0.00377234	−0.000232612 0	−0.000116306		1.00000i	$0.500037\pi$
$264$	89.3319	5.49800
$265$	13.3293	0.818815
$266$	5.68211	0.348392
$267$	17.7291	1.08501
$268$	33.0972	2.02173
$269$	8.84341	0.539192	0.269596	−	0.962973i	$-0.413110\pi$
$269$	8.84341	0.539192	0.269596	+	0.962973i	$0.413110\pi$
$270$	−24.5435	−1.49367
$271$	−13.2462	−0.804651	−0.402325	−	0.915497i	$-0.631798\pi$
$271$	−13.2462	−0.804651	−0.402325	+	0.915497i	$0.631798\pi$
$272$	−18.8250	−1.14143
$273$	8.65952	0.524098
$274$	4.28800	0.259047
$275$	2.99569	0.180647
$276$	20.4440	1.23059
$277$	−20.1140	−1.20853	−0.604267	−	0.796782i	$-0.706534\pi$
$277$	−20.1140	−1.20853	−0.604267	+	0.796782i	$0.706534\pi$
$278$	−13.7917	−0.827172
$279$	−35.8667	−2.14728
$280$	8.07245	0.482421
$281$	−25.2303	−1.50512	−0.752558	−	0.658526i	$-0.771180\pi$
$281$	−25.2303	−1.50512	−0.752558	+	0.658526i	$0.771180\pi$
$282$	−56.5711	−3.36876
$283$	15.1129	0.898370	0.449185	−	0.893439i	$-0.351714\pi$
$283$	15.1129	0.898370	0.449185	+	0.893439i	$0.351714\pi$
$284$	−73.8827	−4.38413
$285$	−7.60923	−0.450732
$286$	29.4675	1.74245
$287$	0.725200	0.0428072
$288$	−148.678	−8.76091
$289$	−15.6573	−0.921016
$290$	−20.6630	−1.21337
$291$	−40.5704	−2.37828
$292$	21.9315	1.28344
$293$	−9.20169	−0.537568	−0.268784	−	0.963200i	$-0.586622\pi$
$293$	−9.20169	−0.537568	−0.268784	+	0.963200i	$0.586622\pi$
$294$	−52.4027	−3.05619
$295$	4.48689	0.261237
$296$	−1.20719	−0.0701663
$297$	−26.6539	−1.54662
$298$	−30.5698	−1.77086
$299$	4.33929	0.250948
$300$	−16.8005	−0.969976
$301$	−4.76566	−0.274688
$302$	0.279321	0.0160731
$303$	49.4425	2.84040
$304$	−41.2733	−2.36719
$305$	−4.66603	−0.267176
$306$	19.0849	1.09101
$307$	20.5784	1.17447	0.587236	−	0.809416i	$-0.300216\pi$
$307$	20.5784	1.17447	0.587236	+	0.809416i	$0.300216\pi$
$308$	13.6243	0.776318
$309$	−6.62542	−0.376907
$310$	−16.5707	−0.941155
$311$	−12.8500	−0.728656	−0.364328	−	0.931271i	$-0.618701\pi$
$311$	−12.8500	−0.728656	−0.364328	+	0.931271i	$0.618701\pi$
$312$	−106.337	−6.02013
$313$	21.2859	1.20315	0.601577	−	0.798815i	$-0.294539\pi$
$313$	21.2859	1.20315	0.601577	+	0.798815i	$0.294539\pi$
$314$	−32.9261	−1.85813
$315$	−4.84094	−0.272756
$316$	−48.4555	−2.72583
$317$	12.2480	0.687914	0.343957	−	0.938985i	$-0.388233\pi$
$317$	12.2480	0.687914	0.343957	+	0.938985i	$0.388233\pi$
$318$	−110.127	−6.17561
$319$	−22.4398	−1.25639
$320$	−36.1989	−2.02358
$321$	−25.3001	−1.41211
$322$	2.72161	0.151669
$323$	2.94390	0.163803
$324$	49.0072	2.72262
$325$	−3.56594	−0.197803
$326$	9.42696	0.522111
$327$	−5.94569	−0.328797
$328$	−8.90528	−0.491712
$329$	−5.55160	−0.306070
$330$	−24.7504	−1.36246
$331$	33.8289	1.85940	0.929702	−	0.368313i	$-0.120064\pi$
$331$	33.8289	1.85940	0.929702	+	0.368313i	$0.120064\pi$
$332$	12.7494	0.699713
$333$	0.723934	0.0396713
$334$	46.7537	2.55825
$335$	−5.90040	−0.322373
$336$	−39.4512	−2.15224
$337$	−27.6159	−1.50433	−0.752167	−	0.658972i	$-0.770991\pi$
$337$	−27.6159	−1.50433	−0.752167	+	0.658972i	$0.770991\pi$
$338$	0.783639	0.0426243
$339$	6.22605	0.338153
$340$	6.49986	0.352504
$341$	−17.9956	−0.974516
$342$	41.8430	2.26261
$343$	−10.8181	−0.584120
$344$	58.5211	3.15525
$345$	−3.64466	−0.196222
$346$	−7.50115	−0.403264
$347$	−29.9856	−1.60971	−0.804856	−	0.593470i	$-0.797758\pi$
$347$	−29.9856	−1.60971	−0.804856	+	0.593470i	$0.797758\pi$
$348$	125.847	6.74611
$349$	10.2205	0.547093	0.273546	−	0.961859i	$-0.411803\pi$
$349$	10.2205	0.547093	0.273546	+	0.961859i	$0.411803\pi$
$350$	−2.23656	−0.119549
$351$	31.7277	1.69350
$352$	−74.5969	−3.97603
$353$	−22.1074	−1.17666	−0.588330	−	0.808621i	$-0.700214\pi$
$353$	−22.1074	−1.17666	−0.588330	+	0.808621i	$0.700214\pi$
$354$	−37.0706	−1.97028
$355$	13.1714	0.699067
$356$	−33.2036	−1.75979
$357$	2.81394	0.148929
$358$	72.2909	3.82069
$359$	−19.6726	−1.03828	−0.519140	−	0.854689i	$-0.673748\pi$
$359$	−19.6726	−1.03828	−0.519140	+	0.854689i	$0.673748\pi$
$360$	59.4456	3.13306
$361$	−12.5456	−0.660294
$362$	−65.1703	−3.42527
$363$	6.06757	0.318465
$364$	−16.2178	−0.850043
$365$	−3.90984	−0.204650
$366$	38.5507	2.01508
$367$	31.9188	1.66615	0.833073	−	0.553163i	$-0.186579\pi$
$367$	31.9188	1.66615	0.833073	+	0.553163i	$0.186579\pi$
$368$	−19.7690	−1.03053
$369$	5.34038	0.278009
$370$	0.334464	0.0173880
$371$	−10.8073	−0.561086
$372$	100.923	5.23262
$373$	−28.6292	−1.48236	−0.741182	−	0.671305i	$-0.765734\pi$
$373$	−28.6292	−1.48236	−0.741182	+	0.671305i	$0.765734\pi$
$374$	9.57556	0.495140
$375$	2.99511	0.154667
$376$	68.1722	3.51571
$377$	26.7113	1.37570
$378$	19.8996	1.02353
$379$	−7.29589	−0.374765	−0.187382	−	0.982287i	$-0.560000\pi$
$379$	−7.29589	−0.374765	−0.187382	+	0.982287i	$0.560000\pi$
$380$	14.2508	0.731049
$381$	13.7211	0.702955
$382$	−11.9125	−0.609498
$383$	−28.6010	−1.46144	−0.730721	−	0.682676i	$-0.760816\pi$
$383$	−28.6010	−1.46144	−0.730721	+	0.682676i	$0.760816\pi$
$384$	149.910	7.65008
$385$	−2.42888	−0.123787
$386$	14.9946	0.763206
$387$	−35.0943	−1.78394
$388$	75.9814	3.85737
$389$	−5.59436	−0.283645	−0.141823	−	0.989892i	$-0.545296\pi$
$389$	−5.59436	−0.283645	−0.141823	+	0.989892i	$0.545296\pi$
$390$	29.4618	1.49185
$391$	1.41006	0.0713100
$392$	63.1490	3.18950
$393$	−47.0952	−2.37564
$394$	−23.1260	−1.16507
$395$	8.63839	0.434645
$396$	100.330	5.04175
$397$	−34.9851	−1.75585	−0.877926	−	0.478795i	$-0.841074\pi$
$397$	−34.9851	−1.75585	−0.877926	+	0.478795i	$0.841074\pi$
$398$	2.16001	0.108272
$399$	6.16948	0.308860
$400$	16.2458	0.812289
$401$	8.14247	0.406616	0.203308	−	0.979115i	$-0.434831\pi$
$401$	8.14247	0.406616	0.203308	+	0.979115i	$0.434831\pi$
$402$	48.7491	2.43138
$403$	21.4212	1.06706
$404$	−92.5973	−4.60689
$405$	−8.73675	−0.434133
$406$	16.7534	0.831455
$407$	0.363224	0.0180043
$408$	−34.5544	−1.71070
$409$	−10.3266	−0.510619	−0.255310	−	0.966859i	$-0.582177\pi$
$409$	−10.3266	−0.510619	−0.255310	+	0.966859i	$0.582177\pi$
$410$	2.46730	0.121851
$411$	4.65579	0.229653
$412$	12.4083	0.611312
$413$	−3.63792	−0.179010
$414$	20.0419	0.985007
$415$	−2.27289	−0.111572
$416$	88.7968	4.35362
$417$	−14.9747	−0.733313
$418$	20.9942	1.02686
$419$	−10.1440	−0.495568	−0.247784	−	0.968815i	$-0.579702\pi$
$419$	−10.1440	−0.495568	−0.247784	+	0.968815i	$0.579702\pi$
$420$	13.6217	0.664669
$421$	−31.7948	−1.54959	−0.774793	−	0.632215i	$-0.782146\pi$
$421$	−31.7948	−1.54959	−0.774793	+	0.632215i	$0.782146\pi$
$422$	−24.9749	−1.21576
$423$	−40.8820	−1.98775
$424$	132.711	6.44500
$425$	−1.15876	−0.0562082
$426$	−108.822	−5.27246
$427$	3.78317	0.183080
$428$	47.3827	2.29033
$429$	31.9951	1.54474
$430$	−16.2139	−0.781904
$431$	−5.75885	−0.277394	−0.138697	−	0.990335i	$-0.544291\pi$
$431$	−5.75885	−0.277394	−0.138697	+	0.990335i	$0.544291\pi$
$432$	−144.546	−6.95445
$433$	28.0035	1.34576	0.672881	−	0.739751i	$-0.265057\pi$
$433$	28.0035	1.34576	0.672881	+	0.739751i	$0.265057\pi$
$434$	13.4354	0.644919
$435$	−22.4354	−1.07569
$436$	11.1352	0.533282
$437$	3.09153	0.147888
$438$	32.3030	1.54350
$439$	21.5153	1.02687	0.513435	−	0.858128i	$-0.328373\pi$
$439$	21.5153	1.02687	0.513435	+	0.858128i	$0.328373\pi$
$440$	29.8260	1.42190
$441$	−37.8696	−1.80331
$442$	−11.3983	−0.542163
$443$	−2.84625	−0.135230	−0.0676148	−	0.997712i	$-0.521539\pi$
$443$	−2.84625	−0.135230	−0.0676148	+	0.997712i	$0.521539\pi$
$444$	−2.03704	−0.0966734
$445$	5.91937	0.280605
$446$	49.4484	2.34145
$447$	−33.1919	−1.56992
$448$	29.3497	1.38664
$449$	18.8504	0.889604	0.444802	−	0.895629i	$-0.353274\pi$
$449$	18.8504	0.889604	0.444802	+	0.895629i	$0.353274\pi$
$450$	−16.4700	−0.776405
$451$	2.67946	0.126171
$452$	−11.6603	−0.548456
$453$	0.303279	0.0142493
$454$	−37.5092	−1.76039
$455$	2.89123	0.135543
$456$	−75.7597	−3.54777
$457$	−15.8153	−0.739807	−0.369903	−	0.929070i	$-0.620609\pi$
$457$	−15.8153	−0.739807	−0.369903	+	0.929070i	$0.620609\pi$
$458$	47.7640	2.23187
$459$	10.3100	0.481229
$460$	6.82582	0.318255
$461$	12.4654	0.580571	0.290286	−	0.956940i	$-0.406250\pi$
$461$	12.4654	0.580571	0.290286	+	0.956940i	$0.406250\pi$
$462$	20.0674	0.933618
$463$	−15.1058	−0.702026	−0.351013	−	0.936370i	$-0.614163\pi$
$463$	−15.1058	−0.702026	−0.351013	+	0.936370i	$0.614163\pi$
$464$	−121.692	−5.64940
$465$	−17.9921	−0.834362
$466$	12.9375	0.599317
$467$	−20.1073	−0.930456	−0.465228	−	0.885191i	$-0.654028\pi$
$467$	−20.1073	−0.930456	−0.465228	+	0.885191i	$0.654028\pi$
$468$	−119.428	−5.52055
$469$	4.78398	0.220904
$470$	−18.8879	−0.871232
$471$	−35.7503	−1.64729
$472$	44.6727	2.05623
$473$	−17.6081	−0.809621
$474$	−71.3703	−3.27815
$475$	−2.54055	−0.116569
$476$	−5.27002	−0.241551
$477$	−79.5849	−3.64394
$478$	61.3821	2.80755
$479$	−16.8688	−0.770756	−0.385378	−	0.922759i	$-0.625929\pi$
$479$	−16.8688	−0.770756	−0.385378	+	0.922759i	$0.625929\pi$
$480$	−74.5822	−3.40420
$481$	−0.432365	−0.0197142
$482$	−39.4200	−1.79553
$483$	2.95505	0.134459
$484$	−11.3635	−0.516523
$485$	−13.5456	−0.615073
$486$	−1.44762	−0.0656653
$487$	10.0380	0.454865	0.227433	−	0.973794i	$-0.426967\pi$
$487$	10.0380	0.454865	0.227433	+	0.973794i	$0.426967\pi$
$488$	−46.4563	−2.10298
$489$	10.2355	0.462867
$490$	−17.4961	−0.790394
$491$	36.9793	1.66885	0.834427	−	0.551118i	$-0.185799\pi$
$491$	36.9793	1.66885	0.834427	+	0.551118i	$0.185799\pi$
$492$	−15.0270	−0.677469
$493$	8.67991	0.390924
$494$	−24.9905	−1.12438
$495$	−17.8862	−0.803927
$496$	−97.5910	−4.38196
$497$	−10.6793	−0.479030
$498$	18.7786	0.841490
$499$	29.5048	1.32081	0.660407	−	0.750908i	$-0.270384\pi$
$499$	29.5048	1.32081	0.660407	+	0.750908i	$0.270384\pi$
$500$	−5.60931	−0.250856
$501$	50.7639	2.26797
$502$	−55.1373	−2.46090
$503$	8.80203	0.392463	0.196232	−	0.980558i	$-0.437130\pi$
$503$	8.80203	0.392463	0.196232	+	0.980558i	$0.437130\pi$
$504$	−48.1978	−2.14690
$505$	16.5078	0.734586
$506$	10.0558	0.447033
$507$	0.850854	0.0377878
$508$	−25.6973	−1.14013
$509$	−15.1371	−0.670939	−0.335470	−	0.942051i	$-0.608895\pi$
$509$	−15.1371	−0.670939	−0.335470	+	0.942051i	$0.608895\pi$
$510$	9.57368	0.423930
$511$	3.17005	0.140235
$512$	−81.0470	−3.58180
$513$	22.6044	0.998008
$514$	29.6546	1.30801
$515$	−2.21208	−0.0974761
$516$	98.7499	4.34722
$517$	−20.5120	−0.902115
$518$	−0.271180	−0.0119150
$519$	−8.14455	−0.357506
$520$	−35.5035	−1.55693
$521$	34.2151	1.49899	0.749495	−	0.662010i	$-0.230296\pi$
$521$	34.2151	1.49899	0.749495	+	0.662010i	$0.230296\pi$
$522$	123.372	5.39984
$523$	−6.05729	−0.264867	−0.132433	−	0.991192i	$-0.542279\pi$
$523$	−6.05729	−0.264867	−0.132433	+	0.991192i	$0.542279\pi$
$524$	88.2012	3.85309
$525$	−2.42840	−0.105984
$526$	0.0104060	0.000453723 0
$527$	6.96087	0.303220
$528$	−145.764	−6.34356
$529$	−21.5192	−0.935618
$530$	−36.7690	−1.59714
$531$	−26.7896	−1.16257
$532$	−11.5544	−0.500946
$533$	−3.18951	−0.138153
$534$	−48.9058	−2.11636
$535$	−8.44714	−0.365202
$536$	−58.7461	−2.53745
$537$	78.4915	3.38716
$538$	−24.3945	−1.05172
$539$	−19.0005	−0.818411
$540$	49.9084	2.14772
$541$	17.8050	0.765499	0.382749	−	0.923852i	$-0.374977\pi$
$541$	17.8050	0.765499	0.382749	+	0.923852i	$0.374977\pi$
$542$	36.5397	1.56951
$543$	−70.7602	−3.03661
$544$	28.8548	1.23714
$545$	−1.98514	−0.0850339
$546$	−23.8873	−1.02228
$547$	31.7618	1.35804	0.679018	−	0.734122i	$-0.262406\pi$
$547$	31.7618	1.35804	0.679018	+	0.734122i	$0.262406\pi$
$548$	−8.71950	−0.372479
$549$	27.8593	1.18900
$550$	−8.26361	−0.352362
$551$	19.0305	0.810725
$552$	−36.2873	−1.54449
$553$	−7.00392	−0.297837
$554$	55.4845	2.35731
$555$	0.363152	0.0154150
$556$	28.0450	1.18937
$557$	27.5826	1.16871	0.584357	−	0.811497i	$-0.301347\pi$
$557$	27.5826	1.16871	0.584357	+	0.811497i	$0.301347\pi$
$558$	98.9382	4.18839
$559$	20.9599	0.886509
$560$	−13.1719	−0.556615
$561$	10.3969	0.438957
$562$	69.5978	2.93581
$563$	13.5427	0.570755	0.285377	−	0.958415i	$-0.407881\pi$
$563$	13.5427	0.570755	0.285377	+	0.958415i	$0.407881\pi$
$564$	115.036	4.84387
$565$	2.07874	0.0874534
$566$	−41.6890	−1.75232
$567$	7.08366	0.297486
$568$	131.139	5.50245
$569$	−21.4117	−0.897624	−0.448812	−	0.893626i	$-0.648153\pi$
$569$	−21.4117	−0.897624	−0.448812	+	0.893626i	$0.648153\pi$
$570$	20.9900	0.879176
$571$	17.9121	0.749598	0.374799	−	0.927106i	$-0.377712\pi$
$571$	17.9121	0.749598	0.374799	+	0.927106i	$0.377712\pi$
$572$	−59.9212	−2.50543
$573$	−12.9343	−0.540338
$574$	−2.00046	−0.0834978
$575$	−1.21687	−0.0507471
$576$	216.131	9.00545
$577$	−26.7325	−1.11289	−0.556444	−	0.830885i	$-0.687835\pi$
$577$	−26.7325	−1.11289	−0.556444	+	0.830885i	$0.687835\pi$
$578$	43.1906	1.79649
$579$	16.2808	0.676605
$580$	42.0176	1.74468
$581$	1.84284	0.0764538
$582$	111.914	4.63896
$583$	−39.9306	−1.65376
$584$	−38.9275	−1.61083
$585$	21.2910	0.880274
$586$	25.3828	1.04856
$587$	7.14123	0.294750	0.147375	−	0.989081i	$-0.452918\pi$
$587$	7.14123	0.294750	0.147375	+	0.989081i	$0.452918\pi$
$588$	106.559	4.39442
$589$	15.2615	0.628840
$590$	−12.3771	−0.509556
$591$	−25.1097	−1.03287
$592$	1.96978	0.0809574
$593$	10.6679	0.438079	0.219039	−	0.975716i	$-0.429708\pi$
$593$	10.6679	0.438079	0.219039	+	0.975716i	$0.429708\pi$
$594$	73.5248	3.01676
$595$	0.939512	0.0385162
$596$	62.1627	2.54628
$597$	2.34529	0.0959862
$598$	−11.9699	−0.489487
$599$	−19.9461	−0.814976	−0.407488	−	0.913211i	$-0.633595\pi$
$599$	−19.9461	−0.814976	−0.407488	+	0.913211i	$0.633595\pi$
$600$	29.8201	1.21740
$601$	−31.2028	−1.27279	−0.636394	−	0.771364i	$-0.719575\pi$
$601$	−31.2028	−1.27279	−0.636394	+	0.771364i	$0.719575\pi$
$602$	13.1461	0.535794
$603$	35.2293	1.43465
$604$	−0.567990	−0.0231112
$605$	2.02583	0.0823616
$606$	−136.387	−5.54035
$607$	1.43874	0.0583965	0.0291982	−	0.999574i	$-0.490705\pi$
$607$	1.43874	0.0583965	0.0291982	+	0.999574i	$0.490705\pi$
$608$	63.2633	2.56567
$609$	18.1904	0.737110
$610$	12.8712	0.521141
$611$	24.4165	0.987787
$612$	−38.8084	−1.56874
$613$	−22.7428	−0.918573	−0.459286	−	0.888288i	$-0.651895\pi$
$613$	−22.7428	−0.918573	−0.459286	+	0.888288i	$0.651895\pi$
$614$	−56.7655	−2.29087
$615$	2.67893	0.108025
$616$	−24.1826	−0.974344
$617$	30.3729	1.22277	0.611383	−	0.791335i	$-0.290614\pi$
$617$	30.3729	1.22277	0.611383	+	0.791335i	$0.290614\pi$
$618$	18.2762	0.735177
$619$	9.91896	0.398677	0.199338	−	0.979931i	$-0.436121\pi$
$619$	9.91896	0.398677	0.199338	+	0.979931i	$0.436121\pi$
$620$	33.6960	1.35327
$621$	10.8270	0.434473
$622$	35.4467	1.42128
$623$	−4.79936	−0.192282
$624$	173.511	6.94599
$625$	1.00000	0.0400000
$626$	−58.7173	−2.34681
$627$	22.7949	0.910341
$628$	66.9541	2.67176
$629$	−0.140498	−0.00560203
$630$	13.3537	0.532026
$631$	31.3889	1.24957	0.624785	−	0.780797i	$-0.285186\pi$
$631$	31.3889	1.24957	0.624785	+	0.780797i	$0.285186\pi$
$632$	86.0063	3.42115
$633$	−27.1171	−1.07781
$634$	−33.7860	−1.34181
$635$	4.58119	0.181799
$636$	223.939	8.87977
$637$	22.6174	0.896134
$638$	61.9001	2.45065
$639$	−78.6421	−3.11103
$640$	50.0518	1.97847
$641$	28.0597	1.10829	0.554147	−	0.832419i	$-0.313045\pi$
$641$	28.0597	1.10829	0.554147	+	0.832419i	$0.313045\pi$
$642$	69.7902	2.75440
$643$	0.294083	0.0115975	0.00579875	−	0.999983i	$-0.498154\pi$
$643$	0.294083	0.0115975	0.00579875	+	0.999983i	$0.498154\pi$
$644$	−5.53430	−0.218082
$645$	−17.6046	−0.693182
$646$	−8.12074	−0.319506
$647$	−15.5729	−0.612234	−0.306117	−	0.951994i	$-0.599030\pi$
$647$	−15.5729	−0.612234	−0.306117	+	0.951994i	$0.599030\pi$
$648$	−86.9856	−3.41712
$649$	−13.4413	−0.527618
$650$	9.83664	0.385825
$651$	14.5878	0.571740
$652$	−19.1694	−0.750732
$653$	−13.0530	−0.510802	−0.255401	−	0.966835i	$-0.582208\pi$
$653$	−13.0530	−0.510802	−0.255401	+	0.966835i	$0.582208\pi$
$654$	16.4012	0.641337
$655$	−15.7241	−0.614390
$656$	14.5308	0.567334
$657$	23.3443	0.910747
$658$	15.3141	0.597005
$659$	46.7135	1.81970	0.909850	−	0.414938i	$-0.136197\pi$
$659$	46.7135	1.81970	0.909850	+	0.414938i	$0.136197\pi$
$660$	50.3291	1.95906
$661$	−0.143747	−0.00559112	−0.00279556	−	0.999996i	$-0.500890\pi$
$661$	−0.143747	−0.00559112	−0.00279556	+	0.999996i	$0.500890\pi$
$662$	−93.3169	−3.62687
$663$	−12.3760	−0.480644
$664$	−22.6296	−0.878198
$665$	2.05985	0.0798777
$666$	−1.99697	−0.0773810
$667$	9.11519	0.352942
$668$	−95.0721	−3.67845
$669$	53.6898	2.07577
$670$	16.2763	0.628806
$671$	13.9780	0.539614
$672$	60.4705	2.33270
$673$	−24.7902	−0.955592	−0.477796	−	0.878471i	$-0.658564\pi$
$673$	−24.7902	−0.955592	−0.477796	+	0.878471i	$0.658564\pi$
$674$	76.1784	2.93428
$675$	−8.89742	−0.342462
$676$	−1.59350	−0.0612886
$677$	26.6293	1.02345	0.511724	−	0.859150i	$-0.329007\pi$
$677$	26.6293	1.02345	0.511724	+	0.859150i	$0.329007\pi$
$678$	−17.1746	−0.659585
$679$	10.9826	0.421474
$680$	−11.5370	−0.442423
$681$	−40.7265	−1.56064
$682$	49.6408	1.90085
$683$	−41.0438	−1.57050	−0.785249	−	0.619180i	$-0.787465\pi$
$683$	−41.0438	−1.57050	−0.785249	+	0.619180i	$0.787465\pi$
$684$	−85.0864	−3.25336
$685$	1.55447	0.0593932
$686$	29.8416	1.13936
$687$	51.8609	1.97862
$688$	−95.4895	−3.64050
$689$	47.5316	1.81081
$690$	10.0538	0.382741
$691$	33.7622	1.28437	0.642187	−	0.766548i	$-0.278027\pi$
$691$	33.7622	1.28437	0.642187	+	0.766548i	$0.278027\pi$
$692$	15.2533	0.579845
$693$	14.5020	0.550885
$694$	82.7153	3.13983
$695$	−4.99972	−0.189650
$696$	−223.373	−8.46693
$697$	−1.03644	−0.0392580
$698$	−28.1933	−1.06713
$699$	14.0472	0.531313
$700$	4.54797	0.171897
$701$	−28.1558	−1.06343	−0.531715	−	0.846924i	$-0.678452\pi$
$701$	−28.1558	−1.06343	−0.531715	+	0.846924i	$0.678452\pi$
$702$	−87.5207	−3.30326
$703$	−0.308039	−0.0116179
$704$	108.441	4.08701
$705$	−20.5079	−0.772374
$706$	60.9833	2.29514
$707$	−13.3843	−0.503369
$708$	75.3819	2.83302
$709$	−24.3663	−0.915097	−0.457548	−	0.889185i	$-0.651272\pi$
$709$	−24.3663	−0.915097	−0.457548	+	0.889185i	$0.651272\pi$
$710$	−36.3334	−1.36357
$711$	−51.5768	−1.93428
$712$	58.9349	2.20868
$713$	7.30994	0.273759
$714$	−7.76224	−0.290495
$715$	10.6825	0.399501
$716$	−147.001	−5.49369
$717$	66.6471	2.48898
$718$	54.2668	2.02522
$719$	34.5057	1.28685	0.643423	−	0.765511i	$-0.277514\pi$
$719$	34.5057	1.28685	0.643423	+	0.765511i	$0.277514\pi$
$720$	−96.9979	−3.61490
$721$	1.79353	0.0667947
$722$	34.6070	1.28794
$723$	−42.8012	−1.59179
$724$	132.522	4.92512
$725$	−7.49068	−0.278197
$726$	−16.7374	−0.621182
$727$	33.2892	1.23463	0.617313	−	0.786717i	$-0.288221\pi$
$727$	33.2892	1.23463	0.617313	+	0.786717i	$0.288221\pi$
$728$	28.7859	1.06688
$729$	−27.7820	−1.02896
$730$	10.7853	0.399181
$731$	6.81097	0.251913
$732$	−78.3916	−2.89744
$733$	13.6520	0.504248	0.252124	−	0.967695i	$-0.418871\pi$
$733$	13.6520	0.504248	0.252124	+	0.967695i	$0.418871\pi$
$734$	−88.0479	−3.24991
$735$	−18.9968	−0.700708
$736$	30.3018	1.11694
$737$	17.6758	0.651096
$738$	−14.7314	−0.542271
$739$	15.5644	0.572545	0.286272	−	0.958148i	$-0.407584\pi$
$739$	15.5644	0.572545	0.286272	+	0.958148i	$0.407584\pi$
$740$	−0.680122	−0.0250018
$741$	−27.1340	−0.996794
$742$	29.8119	1.09443
$743$	13.8510	0.508144	0.254072	−	0.967185i	$-0.418230\pi$
$743$	13.8510	0.508144	0.254072	+	0.967185i	$0.418230\pi$
$744$	−179.134	−6.56738
$745$	−11.0821	−0.406015
$746$	78.9736	2.89143
$747$	13.5707	0.496524
$748$	−19.4716	−0.711952
$749$	6.84885	0.250252
$750$	−8.26199	−0.301685
$751$	−30.1691	−1.10088	−0.550442	−	0.834873i	$-0.685541\pi$
$751$	−30.1691	−1.10088	−0.550442	+	0.834873i	$0.685541\pi$
$752$	−111.237	−4.05641
$753$	−59.8666	−2.18166
$754$	−73.6831	−2.68338
$755$	0.101258	0.00368517
$756$	−40.4652	−1.47171
$757$	−20.5236	−0.745943	−0.372972	−	0.927843i	$-0.621661\pi$
$757$	−20.5236	−0.745943	−0.372972	+	0.927843i	$0.621661\pi$
$758$	20.1257	0.730999
$759$	10.9183	0.396308
$760$	−25.2945	−0.917528
$761$	10.0623	0.364759	0.182380	−	0.983228i	$-0.441620\pi$
$761$	10.0623	0.364759	0.182380	+	0.983228i	$0.441620\pi$
$762$	−37.8498	−1.37115
$763$	1.60953	0.0582688
$764$	24.2237	0.876383
$765$	6.91857	0.250141
$766$	78.8958	2.85062
$767$	16.0000	0.577725
$768$	−196.688	−7.09738
$769$	6.74167	0.243111	0.121555	−	0.992585i	$-0.461212\pi$
$769$	6.74167	0.243111	0.121555	+	0.992585i	$0.461212\pi$
$770$	6.70005	0.241453
$771$	32.1982	1.15959
$772$	−30.4911	−1.09740
$773$	45.5457	1.63817	0.819083	−	0.573675i	$-0.194483\pi$
$773$	45.5457	1.63817	0.819083	+	0.573675i	$0.194483\pi$
$774$	96.8076	3.47968
$775$	−6.00716	−0.215784
$776$	−134.864	−4.84133
$777$	−0.294440	−0.0105630
$778$	15.4320	0.553265
$779$	−2.27237	−0.0814160
$780$	−59.9095	−2.14510
$781$	−39.4576	−1.41190
$782$	−3.88966	−0.139094
$783$	66.6477	2.38179
$784$	−103.041	−3.68003
$785$	−11.9362	−0.426022
$786$	129.912	4.63381
$787$	26.4163	0.941641	0.470820	−	0.882229i	$-0.343958\pi$
$787$	26.4163	0.941641	0.470820	+	0.882229i	$0.343958\pi$
$788$	47.0260	1.67523
$789$	0.0112986	0.000402239 0
$790$	−23.8290	−0.847797
$791$	−1.68542	−0.0599267
$792$	−178.081	−6.32782
$793$	−16.6388	−0.590860
$794$	96.5064	3.42488
$795$	−39.9228	−1.41591
$796$	−4.39232	−0.155682
$797$	22.8230	0.808434	0.404217	−	0.914663i	$-0.367544\pi$
$797$	22.8230	0.808434	0.404217	+	0.914663i	$0.367544\pi$
$798$	−17.0185	−0.602449
$799$	7.93422	0.280693
$800$	−24.9014	−0.880397
$801$	−35.3425	−1.24877
$802$	−22.4610	−0.793125
$803$	11.7127	0.413331
$804$	−99.1296	−3.49603
$805$	0.986627	0.0347740
$806$	−59.0902	−2.08137
$807$	−26.4869	−0.932385
$808$	164.356	5.78203
$809$	−8.31796	−0.292444	−0.146222	−	0.989252i	$-0.546711\pi$
$809$	−8.31796	−0.292444	−0.146222	+	0.989252i	$0.546711\pi$
$810$	24.1003	0.846798
$811$	−36.6543	−1.28711	−0.643553	−	0.765401i	$-0.722541\pi$
$811$	−36.6543	−1.28711	−0.643553	+	0.765401i	$0.722541\pi$
$812$	−34.0674	−1.19553
$813$	39.6738	1.39142
$814$	−1.00195	−0.0351184
$815$	3.41742	0.119707
$816$	56.3828	1.97379
$817$	14.9329	0.522435
$818$	28.4860	0.995990
$819$	−17.2625	−0.603201
$820$	−5.01718	−0.175208
$821$	−49.5483	−1.72925	−0.864624	−	0.502419i	$-0.832443\pi$
$821$	−49.5483	−1.72925	−0.864624	+	0.502419i	$0.832443\pi$
$822$	−12.8430	−0.447951
$823$	43.0968	1.50226	0.751131	−	0.660154i	$-0.229509\pi$
$823$	43.0968	1.50226	0.751131	+	0.660154i	$0.229509\pi$
$824$	−22.0241	−0.767247
$825$	−8.97241	−0.312379
$826$	10.0352	0.349169
$827$	−35.2865	−1.22703	−0.613516	−	0.789682i	$-0.710245\pi$
$827$	−35.2865	−1.22703	−0.613516	+	0.789682i	$0.710245\pi$
$828$	−40.7546	−1.41632
$829$	52.8493	1.83553	0.917765	−	0.397123i	$-0.129991\pi$
$829$	52.8493	1.83553	0.917765	+	0.397123i	$0.129991\pi$
$830$	6.26977	0.217627
$831$	60.2436	2.08983
$832$	−129.083	−4.47515
$833$	7.34959	0.254648
$834$	41.3076	1.43037
$835$	16.9490	0.586543
$836$	−42.6909	−1.47650
$837$	53.4482	1.84744
$838$	27.9823	0.966631
$839$	−21.8642	−0.754836	−0.377418	−	0.926043i	$-0.623188\pi$
$839$	−21.8642	−0.754836	−0.377418	+	0.926043i	$0.623188\pi$
$840$	−24.1778	−0.834215
$841$	27.1102	0.934836
$842$	87.7060	3.02255
$843$	75.5675	2.60268
$844$	50.7857	1.74811
$845$	0.284082	0.00977270
$846$	112.773	3.87721
$847$	−1.64252	−0.0564377
$848$	−216.546	−7.43620
$849$	−45.2648	−1.55348
$850$	3.19644	0.109637
$851$	−0.147544	−0.00505774
$852$	221.287	7.58115
$853$	21.0620	0.721148	0.360574	−	0.932731i	$-0.382581\pi$
$853$	21.0620	0.721148	0.360574	+	0.932731i	$0.382581\pi$
$854$	−10.4359	−0.357108
$855$	15.1688	0.518761
$856$	−84.1021	−2.87455
$857$	−44.7041	−1.52706	−0.763532	−	0.645770i	$-0.776537\pi$
$857$	−44.7041	−1.52706	−0.763532	+	0.645770i	$0.776537\pi$
$858$	−88.2584	−3.01309
$859$	−30.3335	−1.03497	−0.517483	−	0.855693i	$-0.673131\pi$
$859$	−30.3335	−1.03497	−0.517483	+	0.855693i	$0.673131\pi$
$860$	32.9704	1.12428
$861$	−2.17205	−0.0740233
$862$	15.8858	0.541072
$863$	35.4104	1.20538	0.602692	−	0.797974i	$-0.294095\pi$
$863$	35.4104	1.20538	0.602692	+	0.797974i	$0.294095\pi$
$864$	221.558	7.53756
$865$	−2.71929	−0.0924585
$866$	−77.2476	−2.62498
$867$	46.8952	1.59264
$868$	−27.3204	−0.927315
$869$	−25.8780	−0.877850
$870$	61.8879	2.09820
$871$	−21.0405	−0.712929
$872$	−19.7646	−0.669313
$873$	80.8760	2.73724
$874$	−8.52798	−0.288463
$875$	−0.810789	−0.0274097
$876$	−65.6871	−2.21936
$877$	−43.2690	−1.46109	−0.730545	−	0.682864i	$-0.760734\pi$
$877$	−43.2690	−1.46109	−0.730545	+	0.682864i	$0.760734\pi$
$878$	−59.3500	−2.00297
$879$	27.5600	0.929576
$880$	−48.6674	−1.64058
$881$	−24.4207	−0.822756	−0.411378	−	0.911465i	$-0.634952\pi$
$881$	−24.4207	−0.822756	−0.411378	+	0.911465i	$0.634952\pi$
$882$	104.463	3.51746
$883$	−20.2808	−0.682502	−0.341251	−	0.939972i	$-0.610851\pi$
$883$	−20.2808	−0.682502	−0.341251	+	0.939972i	$0.610851\pi$
$884$	23.1781	0.779564
$885$	−13.4387	−0.451737
$886$	7.85139	0.263773
$887$	−22.1542	−0.743867	−0.371933	−	0.928259i	$-0.621305\pi$
$887$	−22.1542	−0.743867	−0.371933	+	0.928259i	$0.621305\pi$
$888$	3.61565	0.121333
$889$	−3.71438	−0.124576
$890$	−16.3286	−0.547335
$891$	26.1726	0.876815
$892$	−100.552	−3.36672
$893$	17.3956	0.582120
$894$	91.5598	3.06222
$895$	26.2066	0.875990
$896$	−40.5814	−1.35573
$897$	−12.9966	−0.433945
$898$	−51.9987	−1.73522
$899$	44.9977	1.50076
$900$	33.4913	1.11638
$901$	15.4455	0.514565
$902$	−7.39128	−0.246103
$903$	14.2737	0.474997
$904$	20.6966	0.688358
$905$	−23.6253	−0.785330
$906$	−0.836595	−0.0277940
$907$	8.34453	0.277076	0.138538	−	0.990357i	$-0.455760\pi$
$907$	8.34453	0.277076	0.138538	+	0.990357i	$0.455760\pi$
$908$	76.2737	2.53123
$909$	−98.5622	−3.26910
$910$	−7.97544	−0.264383
$911$	31.9950	1.06004	0.530021	−	0.847984i	$-0.322184\pi$
$911$	31.9950	1.06004	0.530021	+	0.847984i	$0.322184\pi$
$912$	123.618	4.09339
$913$	6.80889	0.225341
$914$	43.6264	1.44303
$915$	13.9753	0.462008
$916$	−97.1265	−3.20915
$917$	12.7489	0.421006
$918$	−28.4401	−0.938663
$919$	31.1355	1.02707	0.513533	−	0.858070i	$-0.328336\pi$
$919$	31.1355	1.02707	0.513533	+	0.858070i	$0.328336\pi$
$920$	−12.1155	−0.399437
$921$	−61.6345	−2.03093
$922$	−34.3858	−1.13244
$923$	46.9685	1.54599
$924$	−40.8063	−1.34243
$925$	0.121249	0.00398663
$926$	41.6694	1.36934
$927$	13.2076	0.433794
$928$	186.528	6.12309
$929$	36.6350	1.20196	0.600978	−	0.799266i	$-0.294778\pi$
$929$	36.6350	1.20196	0.600978	+	0.799266i	$0.294778\pi$
$930$	49.6311	1.62747
$931$	16.1138	0.528108
$932$	−26.3079	−0.861745
$933$	38.4870	1.26001
$934$	55.4660	1.81490
$935$	3.47129	0.113523
$936$	211.979	6.92876
$937$	2.15404	0.0703693	0.0351846	−	0.999381i	$-0.488798\pi$
$937$	2.15404	0.0703693	0.0351846	+	0.999381i	$0.488798\pi$
$938$	−13.1966	−0.430885
$939$	−63.7537	−2.08052
$940$	38.4078	1.25273
$941$	−45.8837	−1.49577	−0.747884	−	0.663830i	$-0.768930\pi$
$941$	−45.8837	−1.49577	−0.747884	+	0.663830i	$0.768930\pi$
$942$	98.6171	3.21312
$943$	−1.08842	−0.0354437
$944$	−72.8929	−2.37246
$945$	7.21394	0.234669
$946$	48.5719	1.57921
$947$	16.8479	0.547482	0.273741	−	0.961803i	$-0.411739\pi$
$947$	16.8479	0.547482	0.273741	+	0.961803i	$0.411739\pi$
$948$	145.129	4.71358
$949$	−13.9422	−0.452584
$950$	7.00812	0.227373
$951$	−36.6839	−1.18956
$952$	9.35405	0.303167
$953$	27.8925	0.903526	0.451763	−	0.892138i	$-0.350795\pi$
$953$	27.8925	0.903526	0.451763	+	0.892138i	$0.350795\pi$
$954$	219.535	7.10770
$955$	−4.31848	−0.139743
$956$	−124.818	−4.03692
$957$	67.2094	2.17257
$958$	46.5326	1.50340
$959$	−1.26035	−0.0406987
$960$	108.419	3.49922
$961$	5.08596	0.164063
$962$	1.19268	0.0384535
$963$	50.4349	1.62524
$964$	80.1592	2.58175
$965$	5.43579	0.174984
$966$	−8.15150	−0.262270
$967$	36.4486	1.17211	0.586054	−	0.810272i	$-0.300681\pi$
$967$	36.4486	1.17211	0.586054	+	0.810272i	$0.300681\pi$
$968$	20.1697	0.648280
$969$	−8.81728	−0.283252
$970$	37.3655	1.19973
$971$	−1.92446	−0.0617587	−0.0308794	−	0.999523i	$-0.509831\pi$
$971$	−1.92446	−0.0617587	−0.0308794	+	0.999523i	$0.509831\pi$
$972$	2.94368	0.0944186
$973$	4.05372	0.129956
$974$	−27.6898	−0.887239
$975$	10.6804	0.342045
$976$	75.8033	2.42640
$977$	14.8345	0.474599	0.237300	−	0.971437i	$-0.423738\pi$
$977$	14.8345	0.474599	0.237300	+	0.971437i	$0.423738\pi$
$978$	−28.2347	−0.902847
$979$	−17.7326	−0.566737
$980$	35.5778	1.13649
$981$	11.8526	0.378423
$982$	−102.007	−3.25519
$983$	−27.8188	−0.887281	−0.443640	−	0.896205i	$-0.646313\pi$
$983$	−27.8188	−0.887281	−0.443640	+	0.896205i	$0.646313\pi$
$984$	26.6722	0.850280
$985$	−8.38356	−0.267123
$986$	−23.9435	−0.762517
$987$	16.6276	0.529263
$988$	50.8174	1.61672
$989$	7.15253	0.227437
$990$	49.3392	1.56810
$991$	25.7123	0.816778	0.408389	−	0.912808i	$-0.366091\pi$
$991$	25.7123	0.816778	0.408389	+	0.912808i	$0.366091\pi$
$992$	149.587	4.74938
$993$	−101.321	−3.21533
$994$	29.4587	0.934374
$995$	0.783040	0.0248240
$996$	−38.1857	−1.20996
$997$	47.0617	1.49046	0.745229	−	0.666808i	$-0.232340\pi$
$997$	47.0617	1.49046	0.745229	+	0.666808i	$0.232340\pi$
$998$	−81.3888	−2.57632
$999$	−1.07880	−0.0341317

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8045.2.a.d.1.4	✓	141

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8045.2.a.d.1.4	✓	141	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:	\( N \)	\(=\)	\( 8045 = 5 \cdot 1609 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8045.a (trivial)

\(f(q)\)	\(=\)	\(q-2.75850 q^{2} -2.99511 q^{3} +5.60931 q^{4} -1.00000 q^{5} +8.26199 q^{6} +0.810789 q^{7} -9.95629 q^{8} +5.97065 q^{9} +O(q^{10})\)	\(q-2.75850 q^{2} -2.99511 q^{3} +5.60931 q^{4} -1.00000 q^{5} +8.26199 q^{6} +0.810789 q^{7} -9.95629 q^{8} +5.97065 q^{9} +2.75850 q^{10} +2.99569 q^{11} -16.8005 q^{12} -3.56594 q^{13} -2.23656 q^{14} +2.99511 q^{15} +16.2458 q^{16} -1.15876 q^{17} -16.4700 q^{18} -2.54055 q^{19} -5.60931 q^{20} -2.42840 q^{21} -8.26361 q^{22} -1.21687 q^{23} +29.8201 q^{24} +1.00000 q^{25} +9.83664 q^{26} -8.89742 q^{27} +4.54797 q^{28} -7.49068 q^{29} -8.26199 q^{30} -6.00716 q^{31} -24.9014 q^{32} -8.97241 q^{33} +3.19644 q^{34} -0.810789 q^{35} +33.4913 q^{36} +0.121249 q^{37} +7.00812 q^{38} +10.6804 q^{39} +9.95629 q^{40} +0.894437 q^{41} +6.69874 q^{42} -5.87780 q^{43} +16.8038 q^{44} -5.97065 q^{45} +3.35674 q^{46} -6.84715 q^{47} -48.6578 q^{48} -6.34262 q^{49} -2.75850 q^{50} +3.47061 q^{51} -20.0025 q^{52} -13.3293 q^{53} +24.5435 q^{54} -2.99569 q^{55} -8.07245 q^{56} +7.60923 q^{57} +20.6630 q^{58} -4.48689 q^{59} +16.8005 q^{60} +4.66603 q^{61} +16.5707 q^{62} +4.84094 q^{63} +36.1989 q^{64} +3.56594 q^{65} +24.7504 q^{66} +5.90040 q^{67} -6.49986 q^{68} +3.64466 q^{69} +2.23656 q^{70} -13.1714 q^{71} -59.4456 q^{72} +3.90984 q^{73} -0.334464 q^{74} -2.99511 q^{75} -14.2508 q^{76} +2.42888 q^{77} -29.4618 q^{78} -8.63839 q^{79} -16.2458 q^{80} +8.73675 q^{81} -2.46730 q^{82} +2.27289 q^{83} -13.6217 q^{84} +1.15876 q^{85} +16.2139 q^{86} +22.4354 q^{87} -29.8260 q^{88} -5.91937 q^{89} +16.4700 q^{90} -2.89123 q^{91} -6.82582 q^{92} +17.9921 q^{93} +18.8879 q^{94} +2.54055 q^{95} +74.5822 q^{96} +13.5456 q^{97} +17.4961 q^{98} +17.8862 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 141 q - 8 q^{2} + 11 q^{3} + 158 q^{4} - 141 q^{5} + 23 q^{6} + 29 q^{7} - 21 q^{8} + 160 q^{9}+O(q^{10}) \) 141 * q - 8 * q^2 + 11 * q^3 + 158 * q^4 - 141 * q^5 + 23 * q^6 + 29 * q^7 - 21 * q^8 + 160 * q^9	\( 141 q - 8 q^{2} + 11 q^{3} + 158 q^{4} - 141 q^{5} + 23 q^{6} + 29 q^{7} - 21 q^{8} + 160 q^{9} + 8 q^{10} + 32 q^{11} + 17 q^{12} + 35 q^{13} + 18 q^{14} - 11 q^{15} + 188 q^{16} - 13 q^{17} - 16 q^{18} + 152 q^{19} - 158 q^{20} + 40 q^{21} + 14 q^{22} - 77 q^{23} + 69 q^{24} + 141 q^{25} + 27 q^{26} + 38 q^{27} + 67 q^{28} + 22 q^{29} - 23 q^{30} + 86 q^{31} - 65 q^{32} + 51 q^{33} + 79 q^{34} - 29 q^{35} + 191 q^{36} + 45 q^{37} - 9 q^{38} + 55 q^{39} + 21 q^{40} + 36 q^{41} + 6 q^{42} + 132 q^{43} + 74 q^{44} - 160 q^{45} + 72 q^{46} - 16 q^{47} + 22 q^{48} + 212 q^{49} - 8 q^{50} + 82 q^{51} + 106 q^{52} - 28 q^{53} + 86 q^{54} - 32 q^{55} + 27 q^{56} + 10 q^{57} + 23 q^{58} + 71 q^{59} - 17 q^{60} + 116 q^{61} - 36 q^{62} + 45 q^{63} + 237 q^{64} - 35 q^{65} + 69 q^{66} + 99 q^{67} - 7 q^{68} + 45 q^{69} - 18 q^{70} + 34 q^{71} - 53 q^{72} + 125 q^{73} + 50 q^{74} + 11 q^{75} + 271 q^{76} - 31 q^{77} + 2 q^{78} + 101 q^{79} - 188 q^{80} + 221 q^{81} + 67 q^{82} + 67 q^{83} + 141 q^{84} + 13 q^{85} + 48 q^{86} - 21 q^{87} + 71 q^{88} + 79 q^{89} + 16 q^{90} + 228 q^{91} - 198 q^{92} - 12 q^{93} + 114 q^{94} - 152 q^{95} + 129 q^{96} + 98 q^{97} - 31 q^{98} + 195 q^{99}+O(q^{100}) \) 141 * q - 8 * q^2 + 11 * q^3 + 158 * q^4 - 141 * q^5 + 23 * q^6 + 29 * q^7 - 21 * q^8 + 160 * q^9 + 8 * q^10 + 32 * q^11 + 17 * q^12 + 35 * q^13 + 18 * q^14 - 11 * q^15 + 188 * q^16 - 13 * q^17 - 16 * q^18 + 152 * q^19 - 158 * q^20 + 40 * q^21 + 14 * q^22 - 77 * q^23 + 69 * q^24 + 141 * q^25 + 27 * q^26 + 38 * q^27 + 67 * q^28 + 22 * q^29 - 23 * q^30 + 86 * q^31 - 65 * q^32 + 51 * q^33 + 79 * q^34 - 29 * q^35 + 191 * q^36 + 45 * q^37 - 9 * q^38 + 55 * q^39 + 21 * q^40 + 36 * q^41 + 6 * q^42 + 132 * q^43 + 74 * q^44 - 160 * q^45 + 72 * q^46 - 16 * q^47 + 22 * q^48 + 212 * q^49 - 8 * q^50 + 82 * q^51 + 106 * q^52 - 28 * q^53 + 86 * q^54 - 32 * q^55 + 27 * q^56 + 10 * q^57 + 23 * q^58 + 71 * q^59 - 17 * q^60 + 116 * q^61 - 36 * q^62 + 45 * q^63 + 237 * q^64 - 35 * q^65 + 69 * q^66 + 99 * q^67 - 7 * q^68 + 45 * q^69 - 18 * q^70 + 34 * q^71 - 53 * q^72 + 125 * q^73 + 50 * q^74 + 11 * q^75 + 271 * q^76 - 31 * q^77 + 2 * q^78 + 101 * q^79 - 188 * q^80 + 221 * q^81 + 67 * q^82 + 67 * q^83 + 141 * q^84 + 13 * q^85 + 48 * q^86 - 21 * q^87 + 71 * q^88 + 79 * q^89 + 16 * q^90 + 228 * q^91 - 198 * q^92 - 12 * q^93 + 114 * q^94 - 152 * q^95 + 129 * q^96 + 98 * q^97 - 31 * q^98 + 195 * q^99

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