LMFDB - Embedded newform 8023.2.a.d.1.40

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8023,2,Mod(1,8023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8023, 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("8023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8023 = 71 \cdot 113 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8023.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:	$64.0639775417$
Analytic rank:	$0$
Dimension:	$165$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.40
Character	$\chi$	$=$	8023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.50512 q^{2} -2.15769 q^{3} +0.265401 q^{4} -0.274643 q^{5} +3.24759 q^{6} -3.10640 q^{7} +2.61079 q^{8} +1.65562 q^{9} +O(q^{10})$	\(q-1.50512 q^{2} -2.15769 q^{3} +0.265401 q^{4} -0.274643 q^{5} +3.24759 q^{6} -3.10640 q^{7} +2.61079 q^{8} +1.65562 q^{9} +0.413372 q^{10} -0.546289 q^{11} -0.572653 q^{12} +0.316996 q^{13} +4.67552 q^{14} +0.592594 q^{15} -4.46036 q^{16} +6.19549 q^{17} -2.49191 q^{18} +0.859770 q^{19} -0.0728906 q^{20} +6.70264 q^{21} +0.822233 q^{22} -3.62122 q^{23} -5.63327 q^{24} -4.92457 q^{25} -0.477119 q^{26} +2.90076 q^{27} -0.824442 q^{28} +5.63617 q^{29} -0.891929 q^{30} -5.22891 q^{31} +1.49183 q^{32} +1.17872 q^{33} -9.32498 q^{34} +0.853152 q^{35} +0.439403 q^{36} +11.9159 q^{37} -1.29406 q^{38} -0.683979 q^{39} -0.717035 q^{40} +8.57919 q^{41} -10.0883 q^{42} +7.71508 q^{43} -0.144986 q^{44} -0.454704 q^{45} +5.45038 q^{46} -3.18828 q^{47} +9.62407 q^{48} +2.64972 q^{49} +7.41209 q^{50} -13.3679 q^{51} +0.0841311 q^{52} -10.3141 q^{53} -4.36600 q^{54} +0.150035 q^{55} -8.11015 q^{56} -1.85511 q^{57} -8.48315 q^{58} +1.09249 q^{59} +0.157275 q^{60} +10.1584 q^{61} +7.87016 q^{62} -5.14301 q^{63} +6.67534 q^{64} -0.0870609 q^{65} -1.77412 q^{66} -1.09757 q^{67} +1.64429 q^{68} +7.81345 q^{69} -1.28410 q^{70} +1.00000 q^{71} +4.32247 q^{72} -6.15734 q^{73} -17.9349 q^{74} +10.6257 q^{75} +0.228184 q^{76} +1.69699 q^{77} +1.02947 q^{78} +8.78720 q^{79} +1.22501 q^{80} -11.2258 q^{81} -12.9127 q^{82} -12.1859 q^{83} +1.77889 q^{84} -1.70155 q^{85} -11.6122 q^{86} -12.1611 q^{87} -1.42624 q^{88} -0.385834 q^{89} +0.684386 q^{90} -0.984717 q^{91} -0.961075 q^{92} +11.2824 q^{93} +4.79876 q^{94} -0.236130 q^{95} -3.21890 q^{96} +18.2474 q^{97} -3.98816 q^{98} -0.904445 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9}+O(q^{10}) $ 165 * q + 22 * q^2 + 18 * q^3 + 166 * q^4 + 28 * q^5 + 16 * q^6 + 24 * q^7 + 66 * q^8 + 177 * q^9	\( 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9} + 14 q^{10} + 18 q^{11} + 54 q^{12} + 44 q^{13} + 26 q^{14} + 24 q^{15} + 168 q^{16} + 143 q^{17} + 57 q^{18} + 20 q^{19} + 49 q^{20} + 39 q^{21} + 25 q^{22} + 52 q^{23} + 27 q^{24} + 175 q^{25} + 48 q^{26} + 69 q^{27} + 28 q^{28} + 58 q^{29} - 11 q^{30} + 28 q^{31} + 114 q^{32} + 110 q^{33} + 55 q^{34} + 67 q^{35} + 202 q^{36} + 44 q^{37} + 35 q^{38} + 27 q^{39} + 53 q^{40} + 141 q^{41} + 40 q^{42} + 29 q^{43} + 52 q^{44} + 54 q^{45} + 29 q^{46} + 87 q^{47} + 53 q^{48} + 143 q^{49} + 16 q^{50} + 37 q^{51} + 105 q^{52} + 101 q^{53} - 36 q^{54} + 72 q^{55} + 57 q^{56} + 82 q^{57} + 4 q^{58} + 103 q^{59} + 53 q^{60} + 16 q^{61} + 54 q^{62} + 126 q^{63} + 136 q^{64} + 159 q^{65} + 53 q^{66} + 60 q^{67} + 220 q^{68} + 81 q^{69} + 16 q^{70} + 165 q^{71} + 176 q^{72} + 124 q^{73} + 29 q^{74} + 44 q^{75} + 18 q^{76} + 127 q^{77} - 91 q^{78} + 14 q^{79} + 158 q^{80} + 213 q^{81} + 20 q^{82} + 116 q^{83} + 67 q^{84} + 59 q^{85} + 30 q^{86} + 28 q^{87} + 79 q^{88} + 195 q^{89} + 16 q^{90} - 26 q^{91} + 173 q^{92} + 116 q^{93} + 53 q^{94} + 26 q^{95} - 36 q^{96} + 88 q^{97} + 150 q^{98} + 12 q^{99}+O(q^{100}) \) 165 * q + 22 * q^2 + 18 * q^3 + 166 * q^4 + 28 * q^5 + 16 * q^6 + 24 * q^7 + 66 * q^8 + 177 * q^9 + 14 * q^10 + 18 * q^11 + 54 * q^12 + 44 * q^13 + 26 * q^14 + 24 * q^15 + 168 * q^16 + 143 * q^17 + 57 * q^18 + 20 * q^19 + 49 * q^20 + 39 * q^21 + 25 * q^22 + 52 * q^23 + 27 * q^24 + 175 * q^25 + 48 * q^26 + 69 * q^27 + 28 * q^28 + 58 * q^29 - 11 * q^30 + 28 * q^31 + 114 * q^32 + 110 * q^33 + 55 * q^34 + 67 * q^35 + 202 * q^36 + 44 * q^37 + 35 * q^38 + 27 * q^39 + 53 * q^40 + 141 * q^41 + 40 * q^42 + 29 * q^43 + 52 * q^44 + 54 * q^45 + 29 * q^46 + 87 * q^47 + 53 * q^48 + 143 * q^49 + 16 * q^50 + 37 * q^51 + 105 * q^52 + 101 * q^53 - 36 * q^54 + 72 * q^55 + 57 * q^56 + 82 * q^57 + 4 * q^58 + 103 * q^59 + 53 * q^60 + 16 * q^61 + 54 * q^62 + 126 * q^63 + 136 * q^64 + 159 * q^65 + 53 * q^66 + 60 * q^67 + 220 * q^68 + 81 * q^69 + 16 * q^70 + 165 * q^71 + 176 * q^72 + 124 * q^73 + 29 * q^74 + 44 * q^75 + 18 * q^76 + 127 * q^77 - 91 * q^78 + 14 * q^79 + 158 * q^80 + 213 * q^81 + 20 * q^82 + 116 * q^83 + 67 * q^84 + 59 * q^85 + 30 * q^86 + 28 * q^87 + 79 * q^88 + 195 * q^89 + 16 * q^90 - 26 * q^91 + 173 * q^92 + 116 * q^93 + 53 * q^94 + 26 * q^95 - 36 * q^96 + 88 * q^97 + 150 * q^98 + 12 * 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 $

$2$	−1.50512	−1.06428	−0.532142	−	0.846655i	$-0.678613\pi$
$2$	−1.50512	−1.06428	−0.532142	+	0.846655i	$0.678613\pi$
$3$	−2.15769	−1.24574	−0.622871	−	0.782325i	$-0.714034\pi$
$3$	−2.15769	−1.24574	−0.622871	+	0.782325i	$0.714034\pi$
$4$	0.265401	0.132701
$5$	−0.274643	−0.122824	−0.0614121	−	0.998112i	$-0.519560\pi$
$5$	−0.274643	−0.122824	−0.0614121	+	0.998112i	$0.519560\pi$
$6$	3.24759	1.32582
$7$	−3.10640	−1.17411	−0.587054	−	0.809547i	$-0.699713\pi$
$7$	−3.10640	−1.17411	−0.587054	+	0.809547i	$0.699713\pi$
$8$	2.61079	0.923053
$9$	1.65562	0.551872
$10$	0.413372	0.130720
$11$	−0.546289	−0.164712	−0.0823561	−	0.996603i	$-0.526244\pi$
$11$	−0.546289	−0.164712	−0.0823561	+	0.996603i	$0.526244\pi$
$12$	−0.572653	−0.165311
$13$	0.316996	0.0879189	0.0439595	−	0.999033i	$-0.486003\pi$
$13$	0.316996	0.0879189	0.0439595	+	0.999033i	$0.486003\pi$
$14$	4.67552	1.24959
$15$	0.592594	0.153007
$16$	−4.46036	−1.11509
$17$	6.19549	1.50263	0.751313	−	0.659946i	$-0.229421\pi$
$17$	6.19549	1.50263	0.751313	+	0.659946i	$0.229421\pi$
$18$	−2.49191	−0.587349
$19$	0.859770	0.197245	0.0986224	−	0.995125i	$-0.468556\pi$
$19$	0.859770	0.197245	0.0986224	+	0.995125i	$0.468556\pi$
$20$	−0.0728906	−0.0162988
$21$	6.70264	1.46264
$22$	0.822233	0.175301
$23$	−3.62122	−0.755076	−0.377538	−	0.925994i	$-0.623229\pi$
$23$	−3.62122	−0.755076	−0.377538	+	0.925994i	$0.623229\pi$
$24$	−5.63327	−1.14989
$25$	−4.92457	−0.984914
$26$	−0.477119	−0.0935707
$27$	2.90076	0.558251
$28$	−0.824442	−0.155805
$29$	5.63617	1.04661	0.523306	−	0.852145i	$-0.324699\pi$
$29$	5.63617	1.04661	0.523306	+	0.852145i	$0.324699\pi$
$30$	−0.891929	−0.162843
$31$	−5.22891	−0.939140	−0.469570	−	0.882895i	$-0.655591\pi$
$31$	−5.22891	−0.939140	−0.469570	+	0.882895i	$0.655591\pi$
$32$	1.49183	0.263721
$33$	1.17872	0.205189
$34$	−9.32498	−1.59922
$35$	0.853152	0.144209
$36$	0.439403	0.0732338
$37$	11.9159	1.95896	0.979479	−	0.201547i	$-0.0645968\pi$
$37$	11.9159	1.95896	0.979479	+	0.201547i	$0.0645968\pi$
$38$	−1.29406	−0.209924
$39$	−0.683979	−0.109524
$40$	−0.717035	−0.113373
$41$	8.57919	1.33984	0.669922	−	0.742432i	$-0.266328\pi$
$41$	8.57919	1.33984	0.669922	+	0.742432i	$0.266328\pi$
$42$	−10.0883	−1.55666
$43$	7.71508	1.17654	0.588269	−	0.808665i	$-0.299810\pi$
$43$	7.71508	1.17654	0.588269	+	0.808665i	$0.299810\pi$
$44$	−0.144986	−0.0218574
$45$	−0.454704	−0.0677833
$46$	5.45038	0.803615
$47$	−3.18828	−0.465058	−0.232529	−	0.972589i	$-0.574700\pi$
$47$	−3.18828	−0.465058	−0.232529	+	0.972589i	$0.574700\pi$
$48$	9.62407	1.38912
$49$	2.64972	0.378532
$50$	7.41209	1.04823
$51$	−13.3679	−1.87188
$52$	0.0841311	0.0116669
$53$	−10.3141	−1.41675	−0.708374	−	0.705837i	$-0.750571\pi$
$53$	−10.3141	−1.41675	−0.708374	+	0.705837i	$0.750571\pi$
$54$	−4.36600	−0.594138
$55$	0.150035	0.0202307
$56$	−8.11015	−1.08376
$57$	−1.85511	−0.245716
$58$	−8.48315	−1.11389
$59$	1.09249	0.142230	0.0711150	−	0.997468i	$-0.477344\pi$
$59$	1.09249	0.142230	0.0711150	+	0.997468i	$0.477344\pi$
$60$	0.157275	0.0203041
$61$	10.1584	1.30065	0.650324	−	0.759657i	$-0.274633\pi$
$61$	10.1584	1.30065	0.650324	+	0.759657i	$0.274633\pi$
$62$	7.87016	0.999512
$63$	−5.14301	−0.647958
$64$	6.67534	0.834417
$65$	−0.0870609	−0.0107986
$66$	−1.77412	−0.218379
$67$	−1.09757	−0.134089	−0.0670445	−	0.997750i	$-0.521357\pi$
$67$	−1.09757	−0.134089	−0.0670445	+	0.997750i	$0.521357\pi$
$68$	1.64429	0.199399
$69$	7.81345	0.940629
$70$	−1.28410	−0.153479
$71$	1.00000	0.118678
$71$	1.00000	0.118678
$72$	4.32247	0.509407
$73$	−6.15734	−0.720662	−0.360331	−	0.932825i	$-0.617336\pi$
$73$	−6.15734	−0.720662	−0.360331	+	0.932825i	$0.617336\pi$
$74$	−17.9349	−2.08489
$75$	10.6257	1.22695
$76$	0.228184	0.0261745
$77$	1.69699	0.193390
$78$	1.02947	0.116565
$79$	8.78720	0.988637	0.494319	−	0.869281i	$-0.335418\pi$
$79$	8.78720	0.988637	0.494319	+	0.869281i	$0.335418\pi$
$80$	1.22501	0.136960
$81$	−11.2258	−1.24731
$82$	−12.9127	−1.42597
$83$	−12.1859	−1.33758	−0.668789	−	0.743453i	$-0.733187\pi$
$83$	−12.1859	−1.33758	−0.668789	+	0.743453i	$0.733187\pi$
$84$	1.77889	0.194093
$85$	−1.70155	−0.184559
$86$	−11.6122	−1.25217
$87$	−12.1611	−1.30381
$88$	−1.42624	−0.152038
$89$	−0.385834	−0.0408983	−0.0204491	−	0.999791i	$-0.506510\pi$
$89$	−0.385834	−0.0408983	−0.0204491	+	0.999791i	$0.506510\pi$
$90$	0.684386	0.0721407
$91$	−0.984717	−0.103226
$92$	−0.961075	−0.100199
$93$	11.2824	1.16993
$94$	4.79876	0.494954
$95$	−0.236130	−0.0242264
$96$	−3.21890	−0.328528
$97$	18.2474	1.85274	0.926370	−	0.376615i	$-0.122912\pi$
$97$	18.2474	1.85274	0.926370	+	0.376615i	$0.122912\pi$
$98$	−3.98816	−0.402865
$99$	−0.904445	−0.0909002
$100$	−1.30699	−0.130699
$101$	6.12319	0.609281	0.304640	−	0.952467i	$-0.401464\pi$
$101$	6.12319	0.609281	0.304640	+	0.952467i	$0.401464\pi$
$102$	20.1204	1.99222
$103$	−3.46628	−0.341543	−0.170771	−	0.985311i	$-0.554626\pi$
$103$	−3.46628	−0.341543	−0.170771	+	0.985311i	$0.554626\pi$
$104$	0.827610	0.0811538
$105$	−1.84084	−0.179647
$106$	15.5240	1.50782
$107$	6.24652	0.603874	0.301937	−	0.953328i	$-0.402367\pi$
$107$	6.24652	0.603874	0.301937	+	0.953328i	$0.402367\pi$
$108$	0.769865	0.0740803
$109$	7.10392	0.680432	0.340216	−	0.940347i	$-0.389500\pi$
$109$	7.10392	0.680432	0.340216	+	0.940347i	$0.389500\pi$
$110$	−0.225821	−0.0215312
$111$	−25.7107	−2.44036
$112$	13.8557	1.30924
$113$	−1.00000	−0.0940721
$113$	−1.00000	−0.0940721
$114$	2.79218	0.261512
$115$	0.994543	0.0927416
$116$	1.49585	0.138886
$117$	0.524824	0.0485200
$118$	−1.64433	−0.151373
$119$	−19.2457	−1.76425
$120$	1.54714	0.141234
$121$	−10.7016	−0.972870
$122$	−15.2896	−1.38426
$123$	−18.5112	−1.66910
$124$	−1.38776	−0.124624
$125$	2.72572	0.243796
$126$	7.74087	0.689612
$127$	9.83120	0.872378	0.436189	−	0.899855i	$-0.356328\pi$
$127$	9.83120	0.872378	0.436189	+	0.899855i	$0.356328\pi$
$128$	−13.0309	−1.15178
$129$	−16.6467	−1.46566
$130$	0.131037	0.0114927
$131$	6.51339	0.569077	0.284539	−	0.958665i	$-0.408160\pi$
$131$	6.51339	0.569077	0.284539	+	0.958665i	$0.408160\pi$
$132$	0.312834	0.0272287
$133$	−2.67079	−0.231587
$134$	1.65197	0.142709
$135$	−0.796674	−0.0685668
$136$	16.1751	1.38700
$137$	−2.68591	−0.229473	−0.114737	−	0.993396i	$-0.536602\pi$
$137$	−2.68591	−0.229473	−0.114737	+	0.993396i	$0.536602\pi$
$138$	−11.7602	−1.00110
$139$	4.54095	0.385159	0.192579	−	0.981281i	$-0.438315\pi$
$139$	4.54095	0.385159	0.192579	+	0.981281i	$0.438315\pi$
$140$	0.226427	0.0191366
$141$	6.87931	0.579342
$142$	−1.50512	−0.126307
$143$	−0.173171	−0.0144813
$144$	−7.38466	−0.615388
$145$	−1.54794	−0.128549
$146$	9.26756	0.766989
$147$	−5.71727	−0.471553
$148$	3.16249	0.259955
$149$	−24.3085	−1.99143	−0.995715	−	0.0924781i	$-0.970521\pi$
$149$	−24.3085	−1.99143	−0.995715	+	0.0924781i	$0.970521\pi$
$150$	−15.9930	−1.30582
$151$	−20.8872	−1.69978	−0.849889	−	0.526961i	$-0.823331\pi$
$151$	−20.8872	−1.69978	−0.849889	+	0.526961i	$0.823331\pi$
$152$	2.24468	0.182067
$153$	10.2574	0.829258
$154$	−2.55418	−0.205822
$155$	1.43609	0.115349
$156$	−0.181529	−0.0145339
$157$	−17.1689	−1.37023	−0.685115	−	0.728435i	$-0.740248\pi$
$157$	−17.1689	−1.37023	−0.685115	+	0.728435i	$0.740248\pi$
$158$	−13.2258	−1.05219
$159$	22.2546	1.76490
$160$	−0.409721	−0.0323913
$161$	11.2489	0.886541
$162$	16.8962	1.32749
$163$	3.47458	0.272150	0.136075	−	0.990699i	$-0.456551\pi$
$163$	3.47458	0.272150	0.136075	+	0.990699i	$0.456551\pi$
$164$	2.27693	0.177798
$165$	−0.323728	−0.0252022
$166$	18.3413	1.42356
$167$	−19.4128	−1.50221	−0.751104	−	0.660184i	$-0.770478\pi$
$167$	−19.4128	−1.50221	−0.751104	+	0.660184i	$0.770478\pi$
$168$	17.4992	1.35009
$169$	−12.8995	−0.992270
$170$	2.56104	0.196423
$171$	1.42345	0.108854
$172$	2.04759	0.156127
$173$	−15.1891	−1.15481	−0.577404	−	0.816459i	$-0.695934\pi$
$173$	−15.1891	−1.15481	−0.577404	+	0.816459i	$0.695934\pi$
$174$	18.3040	1.38762
$175$	15.2977	1.15640
$176$	2.43665	0.183669
$177$	−2.35725	−0.177182
$178$	0.580728	0.0435274
$179$	−18.1135	−1.35386	−0.676931	−	0.736046i	$-0.736691\pi$
$179$	−18.1135	−1.35386	−0.676931	+	0.736046i	$0.736691\pi$
$180$	−0.120679	−0.00899488
$181$	8.48107	0.630393	0.315196	−	0.949026i	$-0.397930\pi$
$181$	8.48107	0.630393	0.315196	+	0.949026i	$0.397930\pi$
$182$	1.48212	0.109862
$183$	−21.9186	−1.62027
$184$	−9.45423	−0.696975
$185$	−3.27262	−0.240607
$186$	−16.9814	−1.24513
$187$	−3.38453	−0.247501
$188$	−0.846173	−0.0617135
$189$	−9.01092	−0.655448
$190$	0.355405	0.0257838
$191$	5.94962	0.430500	0.215250	−	0.976559i	$-0.430943\pi$
$191$	5.94962	0.430500	0.215250	+	0.976559i	$0.430943\pi$
$192$	−14.4033	−1.03947
$193$	6.10300	0.439304	0.219652	−	0.975578i	$-0.429508\pi$
$193$	6.10300	0.439304	0.219652	+	0.975578i	$0.429508\pi$
$194$	−27.4646	−1.97184
$195$	0.187850	0.0134522
$196$	0.703239	0.0502314
$197$	25.5627	1.82127	0.910634	−	0.413213i	$-0.135594\pi$
$197$	25.5627	1.82127	0.910634	+	0.413213i	$0.135594\pi$
$198$	1.36130	0.0967436
$199$	−24.7805	−1.75664	−0.878320	−	0.478073i	$-0.841335\pi$
$199$	−24.7805	−1.75664	−0.878320	+	0.478073i	$0.841335\pi$
$200$	−12.8570	−0.909128
$201$	2.36820	0.167040
$202$	−9.21617	−0.648448
$203$	−17.5082	−1.22884
$204$	−3.54786	−0.248400
$205$	−2.35622	−0.164565
$206$	5.21718	0.363498
$207$	−5.99535	−0.416705
$208$	−1.41392	−0.0980376
$209$	−0.469683	−0.0324886
$210$	2.77069	0.191196
$211$	−6.19624	−0.426567	−0.213283	−	0.976990i	$-0.568416\pi$
$211$	−6.19624	−0.426567	−0.213283	+	0.976990i	$0.568416\pi$
$212$	−2.73737	−0.188003
$213$	−2.15769	−0.147842
$214$	−9.40180	−0.642694
$215$	−2.11889	−0.144507
$216$	7.57327	0.515296
$217$	16.2431	1.10265
$218$	−10.6923	−0.724173
$219$	13.2856	0.897758
$220$	0.0398193	0.00268462
$221$	1.96395	0.132109
$222$	38.6979	2.59723
$223$	6.86720	0.459862	0.229931	−	0.973207i	$-0.426150\pi$
$223$	6.86720	0.459862	0.229931	+	0.973207i	$0.426150\pi$
$224$	−4.63422	−0.309637
$225$	−8.15320	−0.543547
$226$	1.50512	0.100119
$227$	12.3240	0.817974	0.408987	−	0.912540i	$-0.365882\pi$
$227$	12.3240	0.817974	0.408987	+	0.912540i	$0.365882\pi$
$228$	−0.492350	−0.0326066
$229$	22.3484	1.47682	0.738412	−	0.674350i	$-0.235576\pi$
$229$	22.3484	1.47682	0.738412	+	0.674350i	$0.235576\pi$
$230$	−1.49691	−0.0987034
$231$	−3.66158	−0.240914
$232$	14.7149	0.966078
$233$	13.9165	0.911701	0.455850	−	0.890056i	$-0.349335\pi$
$233$	13.9165	0.911701	0.455850	+	0.890056i	$0.349335\pi$
$234$	−0.789926	−0.0516391
$235$	0.875639	0.0571204
$236$	0.289948	0.0188740
$237$	−18.9600	−1.23159
$238$	28.9671	1.87766
$239$	2.85002	0.184353	0.0921764	−	0.995743i	$-0.470618\pi$
$239$	2.85002	0.184353	0.0921764	+	0.995743i	$0.470618\pi$
$240$	−2.64319	−0.170617
$241$	−10.2119	−0.657805	−0.328903	−	0.944364i	$-0.606679\pi$
$241$	−10.2119	−0.657805	−0.328903	+	0.944364i	$0.606679\pi$
$242$	16.1072	1.03541
$243$	15.5195	0.995574
$244$	2.69605	0.172597
$245$	−0.727728	−0.0464929
$246$	27.8617	1.77640
$247$	0.272544	0.0173415
$248$	−13.6516	−0.866876
$249$	26.2934	1.66628
$250$	−4.10254	−0.259468
$251$	−4.10956	−0.259393	−0.129697	−	0.991554i	$-0.541400\pi$
$251$	−4.10956	−0.259393	−0.129697	+	0.991554i	$0.541400\pi$
$252$	−1.36496	−0.0859844
$253$	1.97823	0.124370
$254$	−14.7972	−0.928458
$255$	3.67141	0.229913
$256$	6.26242	0.391401
$257$	1.10815	0.0691243	0.0345622	−	0.999403i	$-0.488996\pi$
$257$	1.10815	0.0691243	0.0345622	+	0.999403i	$0.488996\pi$
$258$	25.0554	1.55988
$259$	−37.0155	−2.30003
$260$	−0.0231060	−0.00143298
$261$	9.33135	0.577596
$262$	−9.80346	−0.605660
$263$	1.72831	0.106572	0.0532861	−	0.998579i	$-0.483030\pi$
$263$	1.72831	0.106572	0.0532861	+	0.998579i	$0.483030\pi$
$264$	3.07739	0.189400
$265$	2.83269	0.174011
$266$	4.01987	0.246474
$267$	0.832509	0.0509487
$268$	−0.291295	−0.0177937
$269$	3.91069	0.238439	0.119220	−	0.992868i	$-0.461961\pi$
$269$	3.91069	0.238439	0.119220	+	0.992868i	$0.461961\pi$
$270$	1.19909	0.0729745
$271$	−26.0048	−1.57968	−0.789839	−	0.613315i	$-0.789836\pi$
$271$	−26.0048	−1.57968	−0.789839	+	0.613315i	$0.789836\pi$
$272$	−27.6341	−1.67557
$273$	2.12471	0.128593
$274$	4.04263	0.244224
$275$	2.69024	0.162227
$276$	2.07370	0.124822
$277$	20.8374	1.25200	0.625998	−	0.779824i	$-0.284692\pi$
$277$	20.8374	1.25200	0.625998	+	0.779824i	$0.284692\pi$
$278$	−6.83470	−0.409918
$279$	−8.65707	−0.518285
$280$	2.22740	0.133113
$281$	−5.02376	−0.299692	−0.149846	−	0.988709i	$-0.547878\pi$
$281$	−5.02376	−0.299692	−0.149846	+	0.988709i	$0.547878\pi$
$282$	−10.3542	−0.616585
$283$	5.54268	0.329478	0.164739	−	0.986337i	$-0.447322\pi$
$283$	5.54268	0.329478	0.164739	+	0.986337i	$0.447322\pi$
$284$	0.265401	0.0157487
$285$	0.509495	0.0301799
$286$	0.260645	0.0154122
$287$	−26.6504	−1.57312
$288$	2.46990	0.145540
$289$	21.3841	1.25789
$290$	2.32984	0.136813
$291$	−39.3721	−2.30804
$292$	−1.63416	−0.0956322
$293$	2.16392	0.126418	0.0632089	−	0.998000i	$-0.479867\pi$
$293$	2.16392	0.126418	0.0632089	+	0.998000i	$0.479867\pi$
$294$	8.60521	0.501866
$295$	−0.300045	−0.0174693
$296$	31.1098	1.80822
$297$	−1.58465	−0.0919508
$298$	36.5873	2.11945
$299$	−1.14791	−0.0663854
$300$	2.82007	0.162817
$301$	−23.9661	−1.38138
$302$	31.4379	1.80905
$303$	−13.2119	−0.759006
$304$	−3.83489	−0.219946
$305$	−2.78993	−0.159751
$306$	−15.4386	−0.882566
$307$	−30.1349	−1.71989	−0.859945	−	0.510387i	$-0.829502\pi$
$307$	−30.1349	−1.71989	−0.859945	+	0.510387i	$0.829502\pi$
$308$	0.450384	0.0256630
$309$	7.47915	0.425474
$310$	−2.16149	−0.122764
$311$	−7.10691	−0.402996	−0.201498	−	0.979489i	$-0.564581\pi$
$311$	−7.10691	−0.402996	−0.201498	+	0.979489i	$0.564581\pi$
$312$	−1.78572	−0.101097
$313$	28.5148	1.61175	0.805875	−	0.592085i	$-0.201695\pi$
$313$	28.5148	1.61175	0.805875	+	0.592085i	$0.201695\pi$
$314$	25.8414	1.45831
$315$	1.41249	0.0795850
$316$	2.33213	0.131193
$317$	−27.2740	−1.53186	−0.765931	−	0.642922i	$-0.777722\pi$
$317$	−27.2740	−1.53186	−0.765931	+	0.642922i	$0.777722\pi$
$318$	−33.4959	−1.87836
$319$	−3.07898	−0.172390
$320$	−1.83334	−0.102487
$321$	−13.4780	−0.752271
$322$	−16.9311	−0.943531
$323$	5.32669	0.296385
$324$	−2.97934	−0.165519
$325$	−1.56107	−0.0865926
$326$	−5.22968	−0.289645
$327$	−15.3280	−0.847643
$328$	22.3984	1.23675
$329$	9.90407	0.546029
$330$	0.487251	0.0268223
$331$	22.8980	1.25859	0.629294	−	0.777168i	$-0.283344\pi$
$331$	22.8980	1.25859	0.629294	+	0.777168i	$0.283344\pi$
$332$	−3.23415	−0.177497
$333$	19.7281	1.08109
$334$	29.2187	1.59878
$335$	0.301439	0.0164694
$336$	−29.8962	−1.63097
$337$	−30.3874	−1.65531	−0.827653	−	0.561241i	$-0.810324\pi$
$337$	−30.3874	−1.65531	−0.827653	+	0.561241i	$0.810324\pi$
$338$	19.4154	1.05606
$339$	2.15769	0.117190
$340$	−0.451593	−0.0244911
$341$	2.85650	0.154688
$342$	−2.14247	−0.115851
$343$	13.5137	0.729671
$344$	20.1424	1.08601
$345$	−2.14591	−0.115532
$346$	22.8615	1.22904
$347$	17.5481	0.942031	0.471015	−	0.882125i	$-0.343888\pi$
$347$	17.5481	0.942031	0.471015	+	0.882125i	$0.343888\pi$
$348$	−3.22757	−0.173016
$349$	−12.9713	−0.694337	−0.347169	−	0.937803i	$-0.612857\pi$
$349$	−12.9713	−0.694337	−0.347169	+	0.937803i	$0.612857\pi$
$350$	−23.0249	−1.23073
$351$	0.919529	0.0490808
$352$	−0.814970	−0.0434380
$353$	1.86608	0.0993216	0.0496608	−	0.998766i	$-0.484186\pi$
$353$	1.86608	0.0993216	0.0496608	+	0.998766i	$0.484186\pi$
$354$	3.54796	0.188572
$355$	−0.274643	−0.0145766
$356$	−0.102401	−0.00542723
$357$	41.5261	2.19780
$358$	27.2630	1.44089
$359$	23.9287	1.26291	0.631454	−	0.775413i	$-0.282458\pi$
$359$	23.9287	1.26291	0.631454	+	0.775413i	$0.282458\pi$
$360$	−1.18714	−0.0625676
$361$	−18.2608	−0.961095
$362$	−12.7651	−0.670917
$363$	23.0906	1.21194
$364$	−0.261345	−0.0136982
$365$	1.69107	0.0885147
$366$	32.9903	1.72443
$367$	0.313032	0.0163401	0.00817007	−	0.999967i	$-0.497399\pi$
$367$	0.313032	0.0163401	0.00817007	+	0.999967i	$0.497399\pi$
$368$	16.1519	0.841978
$369$	14.2038	0.739423
$370$	4.92569	0.256075
$371$	32.0397	1.66342
$372$	2.99435	0.155250
$373$	8.72964	0.452004	0.226002	−	0.974127i	$-0.427434\pi$
$373$	8.72964	0.452004	0.226002	+	0.974127i	$0.427434\pi$
$374$	5.09414	0.263411
$375$	−5.88125	−0.303706
$376$	−8.32392	−0.429273
$377$	1.78665	0.0920169
$378$	13.5626	0.697583
$379$	9.60202	0.493223	0.246611	−	0.969114i	$-0.420683\pi$
$379$	9.60202	0.493223	0.246611	+	0.969114i	$0.420683\pi$
$380$	−0.0626692	−0.00321486
$381$	−21.2127	−1.08676
$382$	−8.95493	−0.458174
$383$	−20.7433	−1.05993	−0.529966	−	0.848019i	$-0.677795\pi$
$383$	−20.7433	−1.05993	−0.529966	+	0.848019i	$0.677795\pi$
$384$	28.1166	1.43482
$385$	−0.466067	−0.0237530
$386$	−9.18578	−0.467544
$387$	12.7732	0.649299
$388$	4.84287	0.245860
$389$	1.26113	0.0639418	0.0319709	−	0.999489i	$-0.489822\pi$
$389$	1.26113	0.0639418	0.0319709	+	0.999489i	$0.489822\pi$
$390$	−0.282738	−0.0143170
$391$	−22.4352	−1.13460
$392$	6.91786	0.349405
$393$	−14.0539	−0.708923
$394$	−38.4751	−1.93835
$395$	−2.41335	−0.121429
$396$	−0.240041	−0.0120625
$397$	−6.52199	−0.327329	−0.163665	−	0.986516i	$-0.552332\pi$
$397$	−6.52199	−0.327329	−0.163665	+	0.986516i	$0.552332\pi$
$398$	37.2977	1.86956
$399$	5.76273	0.288497
$400$	21.9654	1.09827
$401$	14.9842	0.748275	0.374137	−	0.927373i	$-0.377939\pi$
$401$	14.9842	0.748275	0.374137	+	0.927373i	$0.377939\pi$
$402$	−3.56444	−0.177778
$403$	−1.65754	−0.0825682
$404$	1.62510	0.0808519
$405$	3.08309	0.153200
$406$	26.3520	1.30783
$407$	−6.50951	−0.322664
$408$	−34.9008	−1.72785
$409$	4.11664	0.203555	0.101777	−	0.994807i	$-0.467547\pi$
$409$	4.11664	0.203555	0.101777	+	0.994807i	$0.467547\pi$
$410$	3.54640	0.175144
$411$	5.79536	0.285864
$412$	−0.919955	−0.0453229
$413$	−3.39371	−0.166994
$414$	9.02374	0.443493
$415$	3.34678	0.164287
$416$	0.472904	0.0231860
$417$	−9.79796	−0.479808
$418$	0.706931	0.0345771
$419$	−34.4793	−1.68442	−0.842212	−	0.539146i	$-0.818747\pi$
$419$	−34.4793	−1.68442	−0.842212	+	0.539146i	$0.818747\pi$
$420$	−0.488560	−0.0238393
$421$	9.29292	0.452909	0.226455	−	0.974022i	$-0.427287\pi$
$421$	9.29292	0.452909	0.226455	+	0.974022i	$0.427287\pi$
$422$	9.32612	0.453988
$423$	−5.27857	−0.256653
$424$	−26.9279	−1.30773
$425$	−30.5101	−1.47996
$426$	3.24759	0.157346
$427$	−31.5560	−1.52710
$428$	1.65783	0.0801344
$429$	0.373650	0.0180400
$430$	3.18920	0.153797
$431$	11.5104	0.554435	0.277218	−	0.960807i	$-0.410588\pi$
$431$	11.5104	0.554435	0.277218	+	0.960807i	$0.410588\pi$
$432$	−12.9384	−0.622501
$433$	−23.9146	−1.14926	−0.574631	−	0.818413i	$-0.694854\pi$
$433$	−23.9146	−1.14926	−0.574631	+	0.818413i	$0.694854\pi$
$434$	−24.4479	−1.17354
$435$	3.33997	0.160139
$436$	1.88539	0.0902937
$437$	−3.11341	−0.148935
$438$	−19.9965	−0.955470
$439$	−27.7167	−1.32285	−0.661423	−	0.750013i	$-0.730047\pi$
$439$	−27.7167	−1.32285	−0.661423	+	0.750013i	$0.730047\pi$
$440$	0.391708	0.0186740
$441$	4.38692	0.208901
$442$	−2.95598	−0.140602
$443$	−11.0351	−0.524292	−0.262146	−	0.965028i	$-0.584430\pi$
$443$	−11.0351	−0.524292	−0.262146	+	0.965028i	$0.584430\pi$
$444$	−6.82366	−0.323837
$445$	0.105967	0.00502330
$446$	−10.3360	−0.489423
$447$	52.4501	2.48081
$448$	−20.7363	−0.979697
$449$	0.321561	0.0151754	0.00758770	−	0.999971i	$-0.497585\pi$
$449$	0.321561	0.0151754	0.00758770	+	0.999971i	$0.497585\pi$
$450$	12.2716	0.578488
$451$	−4.68671	−0.220689
$452$	−0.265401	−0.0124834
$453$	45.0681	2.11749
$454$	−18.5492	−0.870557
$455$	0.270446	0.0126787
$456$	−4.84331	−0.226809
$457$	−13.7606	−0.643695	−0.321847	−	0.946792i	$-0.604304\pi$
$457$	−13.7606	−0.643695	−0.321847	+	0.946792i	$0.604304\pi$
$458$	−33.6371	−1.57176
$459$	17.9716	0.838843
$460$	0.263953	0.0123069
$461$	24.1819	1.12626	0.563131	−	0.826368i	$-0.309597\pi$
$461$	24.1819	1.12626	0.563131	+	0.826368i	$0.309597\pi$
$462$	5.51113	0.256401
$463$	18.1274	0.842452	0.421226	−	0.906956i	$-0.361600\pi$
$463$	18.1274	0.842452	0.421226	+	0.906956i	$0.361600\pi$
$464$	−25.1394	−1.16707
$465$	−3.09862	−0.143695
$466$	−20.9461	−0.970309
$467$	24.3454	1.12657	0.563285	−	0.826263i	$-0.309538\pi$
$467$	24.3454	1.12657	0.563285	+	0.826263i	$0.309538\pi$
$468$	0.139289	0.00643863
$469$	3.40948	0.157435
$470$	−1.31795	−0.0607923
$471$	37.0452	1.70695
$472$	2.85226	0.131286
$473$	−4.21466	−0.193790
$474$	28.5372	1.31076
$475$	−4.23400	−0.194269
$476$	−5.10782	−0.234117
$477$	−17.0762	−0.781864
$478$	−4.28964	−0.196204
$479$	0.0528351	0.00241410	0.00120705	−	0.999999i	$-0.499616\pi$
$479$	0.0528351	0.00241410	0.00120705	+	0.999999i	$0.499616\pi$
$480$	0.884050	0.0403512
$481$	3.77729	0.172229
$482$	15.3702	0.700092
$483$	−24.2717	−1.10440
$484$	−2.84021	−0.129100
$485$	−5.01152	−0.227561
$486$	−23.3587	−1.05957
$487$	−15.9534	−0.722919	−0.361459	−	0.932388i	$-0.617721\pi$
$487$	−15.9534	−0.722919	−0.361459	+	0.932388i	$0.617721\pi$
$488$	26.5214	1.20057
$489$	−7.49707	−0.339029
$490$	1.09532	0.0494816
$491$	−12.6352	−0.570220	−0.285110	−	0.958495i	$-0.592030\pi$
$491$	−12.6352	−0.570220	−0.285110	+	0.958495i	$0.592030\pi$
$492$	−4.91289	−0.221490
$493$	34.9189	1.57267
$494$	−0.410212	−0.0184563
$495$	0.248400	0.0111647
$496$	23.3228	1.04723
$497$	−3.10640	−0.139341
$498$	−39.5748	−1.77339
$499$	−4.24928	−0.190224	−0.0951121	−	0.995467i	$-0.530321\pi$
$499$	−4.24928	−0.190224	−0.0951121	+	0.995467i	$0.530321\pi$
$500$	0.723408	0.0323518
$501$	41.8868	1.87136
$502$	6.18540	0.276068
$503$	−6.68111	−0.297896	−0.148948	−	0.988845i	$-0.547589\pi$
$503$	−6.68111	−0.297896	−0.148948	+	0.988845i	$0.547589\pi$
$504$	−13.4273	−0.598100
$505$	−1.68169	−0.0748344
$506$	−2.97748	−0.132365
$507$	27.8331	1.23611
$508$	2.60921	0.115765
$509$	34.7861	1.54187	0.770934	−	0.636915i	$-0.219790\pi$
$509$	34.7861	1.54187	0.770934	+	0.636915i	$0.219790\pi$
$510$	−5.52593	−0.244693
$511$	19.1272	0.846135
$512$	16.6360	0.735216
$513$	2.49398	0.110112
$514$	−1.66790	−0.0735679
$515$	0.951991	0.0419497
$516$	−4.41806	−0.194494
$517$	1.74172	0.0766008
$518$	55.7129	2.44789
$519$	32.7734	1.43859
$520$	−0.227297	−0.00996765
$521$	−25.3149	−1.10907	−0.554533	−	0.832162i	$-0.687103\pi$
$521$	−25.3149	−1.10907	−0.554533	+	0.832162i	$0.687103\pi$
$522$	−14.0448	−0.614726
$523$	−7.45888	−0.326154	−0.163077	−	0.986613i	$-0.552142\pi$
$523$	−7.45888	−0.326154	−0.163077	+	0.986613i	$0.552142\pi$
$524$	1.72866	0.0755169
$525$	−33.0076	−1.44057
$526$	−2.60132	−0.113423
$527$	−32.3957	−1.41118
$528$	−5.25752	−0.228804
$529$	−9.88680	−0.429861
$530$	−4.26356	−0.185197
$531$	1.80874	0.0784928
$532$	−0.708830	−0.0307317
$533$	2.71957	0.117798
$534$	−1.25303	−0.0542239
$535$	−1.71557	−0.0741704
$536$	−2.86551	−0.123771
$537$	39.0832	1.68656
$538$	−5.88608	−0.253767
$539$	−1.44751	−0.0623488
$540$	−0.211438	−0.00909885
$541$	−10.4434	−0.448995	−0.224497	−	0.974475i	$-0.572074\pi$
$541$	−10.4434	−0.448995	−0.224497	+	0.974475i	$0.572074\pi$
$542$	39.1404	1.68123
$543$	−18.2995	−0.785307
$544$	9.24261	0.396274
$545$	−1.95104	−0.0835735
$546$	−3.19796	−0.136860
$547$	14.6446	0.626156	0.313078	−	0.949727i	$-0.398640\pi$
$547$	14.6446	0.626156	0.313078	+	0.949727i	$0.398640\pi$
$548$	−0.712844	−0.0304512
$549$	16.8184	0.717791
$550$	−4.04914	−0.172656
$551$	4.84581	0.206439
$552$	20.3993	0.868251
$553$	−27.2966	−1.16077
$554$	−31.3629	−1.33248
$555$	7.06128	0.299735
$556$	1.20517	0.0511108
$557$	6.80787	0.288459	0.144229	−	0.989544i	$-0.453930\pi$
$557$	6.80787	0.288459	0.144229	+	0.989544i	$0.453930\pi$
$558$	13.0300	0.551603
$559$	2.44565	0.103440
$560$	−3.80537	−0.160806
$561$	7.30275	0.308322
$562$	7.56138	0.318958
$563$	23.0386	0.970961	0.485480	−	0.874248i	$-0.338645\pi$
$563$	23.0386	0.970961	0.485480	+	0.874248i	$0.338645\pi$
$564$	1.82578	0.0768791
$565$	0.274643	0.0115543
$566$	−8.34243	−0.350658
$567$	34.8718	1.46448
$568$	2.61079	0.109546
$569$	42.1892	1.76866	0.884331	−	0.466861i	$-0.154615\pi$
$569$	42.1892	1.76866	0.884331	+	0.466861i	$0.154615\pi$
$570$	−0.766853	−0.0321200
$571$	10.6471	0.445565	0.222783	−	0.974868i	$-0.428486\pi$
$571$	10.6471	0.445565	0.222783	+	0.974868i	$0.428486\pi$
$572$	−0.0459599	−0.00192168
$573$	−12.8374	−0.536291
$574$	40.1122	1.67425
$575$	17.8329	0.743685
$576$	11.0518	0.460492
$577$	42.0181	1.74924	0.874618	−	0.484813i	$-0.161112\pi$
$577$	42.0181	1.74924	0.874618	+	0.484813i	$0.161112\pi$
$578$	−32.1857	−1.33875
$579$	−13.1684	−0.547259
$580$	−0.410824	−0.0170586
$581$	37.8543	1.57046
$582$	59.2600	2.45641
$583$	5.63447	0.233356
$584$	−16.0755	−0.665209
$585$	−0.144139	−0.00595943
$586$	−3.25697	−0.134544
$587$	26.8402	1.10781	0.553906	−	0.832579i	$-0.313137\pi$
$587$	26.8402	1.10781	0.553906	+	0.832579i	$0.313137\pi$
$588$	−1.51737	−0.0625753
$589$	−4.49566	−0.185240
$590$	0.451605	0.0185923
$591$	−55.1564	−2.26883
$592$	−53.1491	−2.18442
$593$	−21.8512	−0.897322	−0.448661	−	0.893702i	$-0.648099\pi$
$593$	−21.8512	−0.897322	−0.448661	+	0.893702i	$0.648099\pi$
$594$	2.38510	0.0978618
$595$	5.28569	0.216692
$596$	−6.45150	−0.264264
$597$	53.4685	2.18832
$598$	1.72775	0.0706530
$599$	31.1989	1.27475	0.637377	−	0.770552i	$-0.280019\pi$
$599$	31.1989	1.27475	0.637377	+	0.770552i	$0.280019\pi$
$600$	27.7414	1.13254
$601$	−27.8378	−1.13553	−0.567763	−	0.823192i	$-0.692191\pi$
$601$	−27.8378	−1.13553	−0.567763	+	0.823192i	$0.692191\pi$
$602$	36.0720	1.47019
$603$	−1.81715	−0.0740000
$604$	−5.54349	−0.225562
$605$	2.93911	0.119492
$606$	19.8856	0.807798
$607$	24.8308	1.00785	0.503925	−	0.863747i	$-0.331889\pi$
$607$	24.8308	1.00785	0.503925	+	0.863747i	$0.331889\pi$
$608$	1.28263	0.0520175
$609$	37.7773	1.53081
$610$	4.19920	0.170020
$611$	−1.01067	−0.0408874
$612$	2.72231	0.110043
$613$	33.9573	1.37152	0.685762	−	0.727826i	$-0.259469\pi$
$613$	33.9573	1.37152	0.685762	+	0.727826i	$0.259469\pi$
$614$	45.3568	1.83045
$615$	5.08398	0.205006
$616$	4.43049	0.178509
$617$	−31.5495	−1.27014	−0.635068	−	0.772456i	$-0.719028\pi$
$617$	−31.5495	−1.27014	−0.635068	+	0.772456i	$0.719028\pi$
$618$	−11.2571	−0.452825
$619$	−3.80309	−0.152859	−0.0764295	−	0.997075i	$-0.524352\pi$
$619$	−3.80309	−0.152859	−0.0764295	+	0.997075i	$0.524352\pi$
$620$	0.381139	0.0153069
$621$	−10.5043	−0.421522
$622$	10.6968	0.428902
$623$	1.19855	0.0480190
$624$	3.05079	0.122130
$625$	23.8743	0.954970
$626$	−42.9183	−1.71536
$627$	1.01343	0.0404724
$628$	−4.55666	−0.181830
$629$	73.8247	2.94358
$630$	−2.12598	−0.0847010
$631$	−0.521806	−0.0207728	−0.0103864	−	0.999946i	$-0.503306\pi$
$631$	−0.521806	−0.0207728	−0.0103864	+	0.999946i	$0.503306\pi$
$632$	22.9415	0.912565
$633$	13.3696	0.531392
$634$	41.0508	1.63034
$635$	−2.70007	−0.107149
$636$	5.90639	0.234203
$637$	0.839952	0.0332801
$638$	4.63425	0.183472
$639$	1.65562	0.0654952
$640$	3.57884	0.141466
$641$	−14.7359	−0.582034	−0.291017	−	0.956718i	$-0.593994\pi$
$641$	−14.7359	−0.582034	−0.291017	+	0.956718i	$0.593994\pi$
$642$	20.2861	0.800630
$643$	23.8941	0.942292	0.471146	−	0.882055i	$-0.343841\pi$
$643$	23.8941	0.942292	0.471146	+	0.882055i	$0.343841\pi$
$644$	2.98548	0.117644
$645$	4.57191	0.180019
$646$	−8.01734	−0.315438
$647$	28.7925	1.13195	0.565975	−	0.824422i	$-0.308500\pi$
$647$	28.7925	1.13195	0.565975	+	0.824422i	$0.308500\pi$
$648$	−29.3081	−1.15133
$649$	−0.596815	−0.0234270
$650$	2.34961	0.0921591
$651$	−35.0475	−1.37362
$652$	0.922158	0.0361145
$653$	29.5932	1.15807	0.579036	−	0.815302i	$-0.303429\pi$
$653$	29.5932	1.15807	0.579036	+	0.815302i	$0.303429\pi$
$654$	23.0706	0.902132
$655$	−1.78886	−0.0698965
$656$	−38.2663	−1.49405
$657$	−10.1942	−0.397713
$658$	−14.9069	−0.581130
$659$	26.8072	1.04426	0.522130	−	0.852866i	$-0.325138\pi$
$659$	26.8072	1.04426	0.522130	+	0.852866i	$0.325138\pi$
$660$	−0.0859177	−0.00334434
$661$	20.7050	0.805332	0.402666	−	0.915347i	$-0.368084\pi$
$661$	20.7050	0.805332	0.402666	+	0.915347i	$0.368084\pi$
$662$	−34.4643	−1.33949
$663$	−4.23758	−0.164574
$664$	−31.8148	−1.23465
$665$	0.733514	0.0284445
$666$	−29.6933	−1.15059
$667$	−20.4098	−0.790271
$668$	−5.15218	−0.199344
$669$	−14.8173	−0.572869
$670$	−0.453704	−0.0175281
$671$	−5.54941	−0.214233
$672$	9.99920	0.385728
$673$	25.2151	0.971971	0.485986	−	0.873967i	$-0.338461\pi$
$673$	25.2151	0.971971	0.485986	+	0.873967i	$0.338461\pi$
$674$	45.7368	1.76172
$675$	−14.2850	−0.549830
$676$	−3.42355	−0.131675
$677$	31.4382	1.20827	0.604134	−	0.796883i	$-0.293519\pi$
$677$	31.4382	1.20827	0.604134	+	0.796883i	$0.293519\pi$
$678$	−3.24759	−0.124723
$679$	−56.6836	−2.17532
$680$	−4.44238	−0.170358
$681$	−26.5914	−1.01898
$682$	−4.29938	−0.164632
$683$	23.0679	0.882670	0.441335	−	0.897342i	$-0.354505\pi$
$683$	23.0679	0.882670	0.441335	+	0.897342i	$0.354505\pi$
$684$	0.377785	0.0144450
$685$	0.737668	0.0281848
$686$	−20.3398	−0.776578
$687$	−48.2209	−1.83974
$688$	−34.4121	−1.31195
$689$	−3.26952	−0.124559
$690$	3.22987	0.122959
$691$	43.9907	1.67349	0.836743	−	0.547596i	$-0.184457\pi$
$691$	43.9907	1.67349	0.836743	+	0.547596i	$0.184457\pi$
$692$	−4.03121	−0.153244
$693$	2.80957	0.106727
$694$	−26.4121	−1.00259
$695$	−1.24714	−0.0473068
$696$	−31.7501	−1.20348
$697$	53.1522	2.01328
$698$	19.5234	0.738972
$699$	−30.0275	−1.13574
$700$	4.06002	0.153454
$701$	−21.4554	−0.810359	−0.405180	−	0.914237i	$-0.632791\pi$
$701$	−21.4554	−0.810359	−0.405180	+	0.914237i	$0.632791\pi$
$702$	−1.38401	−0.0522360
$703$	10.2449	0.386394
$704$	−3.64666	−0.137439
$705$	−1.88936	−0.0711573
$706$	−2.80869	−0.105706
$707$	−19.0211	−0.715362
$708$	−0.625617	−0.0235121
$709$	9.23509	0.346831	0.173416	−	0.984849i	$-0.444520\pi$
$709$	9.23509	0.346831	0.173416	+	0.984849i	$0.444520\pi$
$710$	0.413372	0.0155136
$711$	14.5482	0.545602
$712$	−1.00733	−0.0377513
$713$	18.9350	0.709122
$714$	−62.5020	−2.33908
$715$	0.0475604	0.00177866
$716$	−4.80733	−0.179658
$717$	−6.14946	−0.229656
$718$	−36.0157	−1.34409
$719$	26.4945	0.988076	0.494038	−	0.869440i	$-0.335520\pi$
$719$	26.4945	0.988076	0.494038	+	0.869440i	$0.335520\pi$
$720$	2.02815	0.0755845
$721$	10.7677	0.401008
$722$	27.4848	1.02288
$723$	22.0341	0.819455
$724$	2.25089	0.0836535
$725$	−27.7557	−1.03082
$726$	−34.7543	−1.28985
$727$	−29.9486	−1.11073	−0.555366	−	0.831606i	$-0.687422\pi$
$727$	−29.9486	−1.11073	−0.555366	+	0.831606i	$0.687422\pi$
$728$	−2.57089	−0.0952834
$729$	0.191199	0.00708146
$730$	−2.54527	−0.0942048
$731$	47.7987	1.76790
$732$	−5.81723	−0.215011
$733$	−3.81455	−0.140894	−0.0704468	−	0.997516i	$-0.522442\pi$
$733$	−3.81455	−0.140894	−0.0704468	+	0.997516i	$0.522442\pi$
$734$	−0.471153	−0.0173906
$735$	1.57021	0.0579181
$736$	−5.40224	−0.199129
$737$	0.599588	0.0220861
$738$	−21.3786	−0.786956
$739$	10.6674	0.392406	0.196203	−	0.980563i	$-0.437139\pi$
$739$	10.6674	0.392406	0.196203	+	0.980563i	$0.437139\pi$
$740$	−0.868556	−0.0319287
$741$	−0.588064	−0.0216031
$742$	−48.2237	−1.77035
$743$	−6.25912	−0.229625	−0.114813	−	0.993387i	$-0.536627\pi$
$743$	−6.25912	−0.229625	−0.114813	+	0.993387i	$0.536627\pi$
$744$	29.4558	1.07990
$745$	6.67616	0.244596
$746$	−13.1392	−0.481060
$747$	−20.1752	−0.738172
$748$	−0.898257	−0.0328435
$749$	−19.4042	−0.709014
$750$	8.85201	0.323230
$751$	−42.9883	−1.56867	−0.784333	−	0.620340i	$-0.786994\pi$
$751$	−42.9883	−1.56867	−0.784333	+	0.620340i	$0.786994\pi$
$752$	14.2209	0.518582
$753$	8.86715	0.323137
$754$	−2.68912	−0.0979321
$755$	5.73654	0.208774
$756$	−2.39151	−0.0869783
$757$	5.69801	0.207098	0.103549	−	0.994624i	$-0.466980\pi$
$757$	5.69801	0.207098	0.103549	+	0.994624i	$0.466980\pi$
$758$	−14.4522	−0.524929
$759$	−4.26840	−0.154933
$760$	−0.616485	−0.0223623
$761$	−39.2768	−1.42378	−0.711891	−	0.702290i	$-0.752161\pi$
$761$	−39.2768	−1.42378	−0.711891	+	0.702290i	$0.752161\pi$
$762$	31.9277	1.15662
$763$	−22.0676	−0.798901
$764$	1.57904	0.0571276
$765$	−2.81711	−0.101853
$766$	31.2212	1.12807
$767$	0.346315	0.0125047
$768$	−13.5124	−0.487585
$769$	2.97879	0.107418	0.0537089	−	0.998557i	$-0.482896\pi$
$769$	2.97879	0.107418	0.0537089	+	0.998557i	$0.482896\pi$
$770$	0.701490	0.0252799
$771$	−2.39104	−0.0861111
$772$	1.61974	0.0582958
$773$	25.4148	0.914108	0.457054	−	0.889439i	$-0.348905\pi$
$773$	25.4148	0.914108	0.457054	+	0.889439i	$0.348905\pi$
$774$	−19.2253	−0.691039
$775$	25.7501	0.924972
$776$	47.6400	1.71018
$777$	79.8678	2.86524
$778$	−1.89816	−0.0680522
$779$	7.37612	0.264277
$780$	0.0498556	0.00178512
$781$	−0.546289	−0.0195478
$782$	33.7678	1.20753
$783$	16.3492	0.584272
$784$	−11.8187	−0.422097
$785$	4.71533	0.168297
$786$	21.1528	0.754496
$787$	23.8172	0.848992	0.424496	−	0.905430i	$-0.360451\pi$
$787$	23.8172	0.848992	0.424496	+	0.905430i	$0.360451\pi$
$788$	6.78438	0.241683
$789$	−3.72915	−0.132761
$790$	3.63239	0.129235
$791$	3.10640	0.110451
$792$	−2.36131	−0.0839057
$793$	3.22017	0.114352
$794$	9.81641	0.348371
$795$	−6.11207	−0.216773
$796$	−6.57676	−0.233107
$797$	8.00493	0.283549	0.141775	−	0.989899i	$-0.454719\pi$
$797$	8.00493	0.283549	0.141775	+	0.989899i	$0.454719\pi$
$798$	−8.67363	−0.307043
$799$	−19.7529	−0.698809
$800$	−7.34662	−0.259742
$801$	−0.638793	−0.0225706
$802$	−22.5531	−0.796377
$803$	3.36368	0.118702
$804$	0.628524	0.0221663
$805$	−3.08945	−0.108889
$806$	2.49481	0.0878760
$807$	−8.43806	−0.297034
$808$	15.9864	0.562398
$809$	26.8407	0.943669	0.471834	−	0.881687i	$-0.343592\pi$
$809$	26.8407	0.943669	0.471834	+	0.881687i	$0.343592\pi$
$810$	−4.64043	−0.163048
$811$	−19.5090	−0.685054	−0.342527	−	0.939508i	$-0.611283\pi$
$811$	−19.5090	−0.685054	−0.342527	+	0.939508i	$0.611283\pi$
$812$	−4.64670	−0.163067
$813$	56.1102	1.96787
$814$	9.79763	0.343407
$815$	−0.954271	−0.0334267
$816$	59.6258	2.08732
$817$	6.63319	0.232066
$818$	−6.19605	−0.216640
$819$	−1.63031	−0.0569678
$820$	−0.625342	−0.0218379
$821$	−23.6047	−0.823810	−0.411905	−	0.911227i	$-0.635136\pi$
$821$	−23.6047	−0.823810	−0.411905	+	0.911227i	$0.635136\pi$
$822$	−8.72274	−0.304241
$823$	3.10010	0.108063	0.0540314	−	0.998539i	$-0.482793\pi$
$823$	3.10010	0.108063	0.0540314	+	0.998539i	$0.482793\pi$
$824$	−9.04972	−0.315262
$825$	−5.80469	−0.202094
$826$	5.10796	0.177729
$827$	−6.73995	−0.234371	−0.117186	−	0.993110i	$-0.537387\pi$
$827$	−6.73995	−0.234371	−0.117186	+	0.993110i	$0.537387\pi$
$828$	−1.59117	−0.0552970
$829$	−39.1098	−1.35834	−0.679170	−	0.733981i	$-0.737660\pi$
$829$	−39.1098	−1.35834	−0.679170	+	0.733981i	$0.737660\pi$
$830$	−5.03732	−0.174848
$831$	−44.9606	−1.55966
$832$	2.11606	0.0733611
$833$	16.4163	0.568792
$834$	14.7472	0.510652
$835$	5.33159	0.184507
$836$	−0.124654	−0.00431126
$837$	−15.1678	−0.524276
$838$	51.8957	1.79271
$839$	−7.86601	−0.271565	−0.135782	−	0.990739i	$-0.543355\pi$
$839$	−7.86601	−0.271565	−0.135782	+	0.990739i	$0.543355\pi$
$840$	−4.80603	−0.165824
$841$	2.76646	0.0953952
$842$	−13.9870	−0.482024
$843$	10.8397	0.373339
$844$	−1.64449	−0.0566057
$845$	3.54276	0.121875
$846$	7.94491	0.273151
$847$	33.2434	1.14226
$848$	46.0046	1.57980
$849$	−11.9594	−0.410445
$850$	45.9216	1.57510
$851$	−43.1500	−1.47916
$852$	−0.572653	−0.0196188
$853$	−8.47561	−0.290200	−0.145100	−	0.989417i	$-0.546350\pi$
$853$	−8.47561	−0.290200	−0.145100	+	0.989417i	$0.546350\pi$
$854$	47.4957	1.62527
$855$	−0.390941	−0.0133699
$856$	16.3083	0.557408
$857$	20.2472	0.691630	0.345815	−	0.938303i	$-0.387602\pi$
$857$	20.2472	0.691630	0.345815	+	0.938303i	$0.387602\pi$
$858$	−0.562390	−0.0191997
$859$	38.3306	1.30782	0.653911	−	0.756571i	$-0.273127\pi$
$859$	38.3306	1.30782	0.653911	+	0.756571i	$0.273127\pi$
$860$	−0.562357	−0.0191762
$861$	57.5032	1.95970
$862$	−17.3245	−0.590076
$863$	30.7468	1.04663	0.523317	−	0.852138i	$-0.324694\pi$
$863$	30.7468	1.04663	0.523317	+	0.852138i	$0.324694\pi$
$864$	4.32744	0.147222
$865$	4.17159	0.141838
$866$	35.9944	1.22314
$867$	−46.1402	−1.56700
$868$	4.31093	0.146323
$869$	−4.80035	−0.162841
$870$	−5.02707	−0.170434
$871$	−0.347924	−0.0117890
$872$	18.5468	0.628075
$873$	30.2107	1.02248
$874$	4.68607	0.158509
$875$	−8.46717	−0.286242
$876$	3.52602	0.119133
$877$	−4.80436	−0.162232	−0.0811158	−	0.996705i	$-0.525848\pi$
$877$	−4.80436	−0.162232	−0.0811158	+	0.996705i	$0.525848\pi$
$878$	41.7171	1.40788
$879$	−4.66907	−0.157484
$880$	−0.669209	−0.0225590
$881$	26.0826	0.878744	0.439372	−	0.898305i	$-0.355201\pi$
$881$	26.0826	0.878744	0.439372	+	0.898305i	$0.355201\pi$
$882$	−6.60287	−0.222330
$883$	50.2124	1.68978	0.844890	−	0.534940i	$-0.179666\pi$
$883$	50.2124	1.68978	0.844890	+	0.534940i	$0.179666\pi$
$884$	0.521233	0.0175310
$885$	0.647404	0.0217622
$886$	16.6092	0.557995
$887$	11.0503	0.371033	0.185517	−	0.982641i	$-0.440604\pi$
$887$	11.0503	0.371033	0.185517	+	0.982641i	$0.440604\pi$
$888$	−67.1253	−2.25258
$889$	−30.5396	−1.02427
$890$	−0.159493	−0.00534622
$891$	6.13252	0.205447
$892$	1.82256	0.0610239
$893$	−2.74119	−0.0917303
$894$	−78.9440	−2.64028
$895$	4.97474	0.166287
$896$	40.4791	1.35231
$897$	2.47683	0.0826991
$898$	−0.483989	−0.0161509
$899$	−29.4711	−0.982915
$900$	−2.16387	−0.0721290
$901$	−63.9008	−2.12884
$902$	7.05409	0.234875
$903$	51.7114	1.72085
$904$	−2.61079	−0.0868335
$905$	−2.32927	−0.0774275
$906$	−67.8332	−2.25361
$907$	−1.64847	−0.0547364	−0.0273682	−	0.999625i	$-0.508713\pi$
$907$	−1.64847	−0.0547364	−0.0273682	+	0.999625i	$0.508713\pi$
$908$	3.27081	0.108546
$909$	10.1377	0.336245
$910$	−0.407055	−0.0134937
$911$	19.4788	0.645361	0.322681	−	0.946508i	$-0.395416\pi$
$911$	19.4788	0.645361	0.322681	+	0.946508i	$0.395416\pi$
$912$	8.27449	0.273996
$913$	6.65703	0.220315
$914$	20.7114	0.685074
$915$	6.01980	0.199008
$916$	5.93129	0.195975
$917$	−20.2332	−0.668159
$918$	−27.0495	−0.892768
$919$	−40.1644	−1.32490	−0.662451	−	0.749105i	$-0.730484\pi$
$919$	−40.1644	−1.32490	−0.662451	+	0.749105i	$0.730484\pi$
$920$	2.59654	0.0856054
$921$	65.0217	2.14254
$922$	−36.3967	−1.19866
$923$	0.316996	0.0104341
$924$	−0.971787	−0.0319694
$925$	−58.6806	−1.92941
$926$	−27.2840	−0.896609
$927$	−5.73883	−0.188488
$928$	8.40821	0.276013
$929$	15.7106	0.515448	0.257724	−	0.966219i	$-0.417027\pi$
$929$	15.7106	0.515448	0.257724	+	0.966219i	$0.417027\pi$
$930$	4.66382	0.152933
$931$	2.27815	0.0746634
$932$	3.69346	0.120983
$933$	15.3345	0.502029
$934$	−36.6428	−1.19899
$935$	0.929537	0.0303991
$936$	1.37020	0.0447865
$937$	34.3160	1.12105	0.560527	−	0.828136i	$-0.310598\pi$
$937$	34.3160	1.12105	0.560527	+	0.828136i	$0.310598\pi$
$938$	−5.13169	−0.167556
$939$	−61.5260	−2.00782
$940$	0.232396	0.00757991
$941$	−33.8658	−1.10399	−0.551996	−	0.833847i	$-0.686134\pi$
$941$	−33.8658	−1.10399	−0.551996	+	0.833847i	$0.686134\pi$
$942$	−55.7577	−1.81668
$943$	−31.0671	−1.01168
$944$	−4.87290	−0.158599
$945$	2.47479	0.0805049
$946$	6.34359	0.206248
$947$	19.3076	0.627412	0.313706	−	0.949520i	$-0.398429\pi$
$947$	19.3076	0.627412	0.313706	+	0.949520i	$0.398429\pi$
$948$	−5.03201	−0.163432
$949$	−1.95185	−0.0633598
$950$	6.37270	0.206758
$951$	58.8489	1.90831
$952$	−50.2464	−1.62849
$953$	−4.42661	−0.143392	−0.0716960	−	0.997427i	$-0.522841\pi$
$953$	−4.42661	−0.143392	−0.0716960	+	0.997427i	$0.522841\pi$
$954$	25.7018	0.832125
$955$	−1.63402	−0.0528758
$956$	0.756400	0.0244637
$957$	6.64348	0.214753
$958$	−0.0795234	−0.00256928
$959$	8.34352	0.269426
$960$	3.95577	0.127672
$961$	−3.65850	−0.118016
$962$	−5.68529	−0.183301
$963$	10.3418	0.333261
$964$	−2.71025	−0.0872911
$965$	−1.67615	−0.0539571
$966$	36.5320	1.17540
$967$	−3.30433	−0.106260	−0.0531300	−	0.998588i	$-0.516920\pi$
$967$	−3.30433	−0.106260	−0.0531300	+	0.998588i	$0.516920\pi$
$968$	−27.9395	−0.898010
$969$	−11.4933	−0.369219
$970$	7.54296	0.242190
$971$	−5.00273	−0.160545	−0.0802726	−	0.996773i	$-0.525579\pi$
$971$	−5.00273	−0.160545	−0.0802726	+	0.996773i	$0.525579\pi$
$972$	4.11888	0.132113
$973$	−14.1060	−0.452218
$974$	24.0119	0.769391
$975$	3.36830	0.107872
$976$	−45.3101	−1.45034
$977$	−3.19054	−0.102074	−0.0510372	−	0.998697i	$-0.516253\pi$
$977$	−3.19054	−0.102074	−0.0510372	+	0.998697i	$0.516253\pi$
$978$	11.2840	0.360823
$979$	0.210777	0.00673645
$980$	−0.193140	−0.00616963
$981$	11.7614	0.375512
$982$	19.0176	0.606876
$983$	40.0440	1.27720	0.638602	−	0.769537i	$-0.279513\pi$
$983$	40.0440	1.27720	0.638602	+	0.769537i	$0.279513\pi$
$984$	−48.3288	−1.54067
$985$	−7.02063	−0.223696
$986$	−52.5572	−1.67376
$987$	−21.3699	−0.680211
$988$	0.0723334	0.00230123
$989$	−27.9380	−0.888376
$990$	−0.373873	−0.0118825
$991$	−44.4409	−1.41171	−0.705855	−	0.708356i	$-0.749437\pi$
$991$	−44.4409	−1.41171	−0.705855	+	0.708356i	$0.749437\pi$
$992$	−7.80064	−0.247671
$993$	−49.4067	−1.56787
$994$	4.67552	0.148299
$995$	6.80579	0.215758
$996$	6.97830	0.221116
$997$	4.08118	0.129252	0.0646261	−	0.997910i	$-0.479415\pi$
$997$	4.08118	0.129252	0.0646261	+	0.997910i	$0.479415\pi$
$998$	6.39570	0.202452
$999$	34.5651	1.09359

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8023.2.a.d.1.40	✓	165

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8023.2.a.d.1.40	✓	165	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:	\( N \)	\(=\)	\( 8023 = 71 \cdot 113 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8023.a (trivial)

\(f(q)\)	\(=\)	\(q-1.50512 q^{2} -2.15769 q^{3} +0.265401 q^{4} -0.274643 q^{5} +3.24759 q^{6} -3.10640 q^{7} +2.61079 q^{8} +1.65562 q^{9} +O(q^{10})\)	\(q-1.50512 q^{2} -2.15769 q^{3} +0.265401 q^{4} -0.274643 q^{5} +3.24759 q^{6} -3.10640 q^{7} +2.61079 q^{8} +1.65562 q^{9} +0.413372 q^{10} -0.546289 q^{11} -0.572653 q^{12} +0.316996 q^{13} +4.67552 q^{14} +0.592594 q^{15} -4.46036 q^{16} +6.19549 q^{17} -2.49191 q^{18} +0.859770 q^{19} -0.0728906 q^{20} +6.70264 q^{21} +0.822233 q^{22} -3.62122 q^{23} -5.63327 q^{24} -4.92457 q^{25} -0.477119 q^{26} +2.90076 q^{27} -0.824442 q^{28} +5.63617 q^{29} -0.891929 q^{30} -5.22891 q^{31} +1.49183 q^{32} +1.17872 q^{33} -9.32498 q^{34} +0.853152 q^{35} +0.439403 q^{36} +11.9159 q^{37} -1.29406 q^{38} -0.683979 q^{39} -0.717035 q^{40} +8.57919 q^{41} -10.0883 q^{42} +7.71508 q^{43} -0.144986 q^{44} -0.454704 q^{45} +5.45038 q^{46} -3.18828 q^{47} +9.62407 q^{48} +2.64972 q^{49} +7.41209 q^{50} -13.3679 q^{51} +0.0841311 q^{52} -10.3141 q^{53} -4.36600 q^{54} +0.150035 q^{55} -8.11015 q^{56} -1.85511 q^{57} -8.48315 q^{58} +1.09249 q^{59} +0.157275 q^{60} +10.1584 q^{61} +7.87016 q^{62} -5.14301 q^{63} +6.67534 q^{64} -0.0870609 q^{65} -1.77412 q^{66} -1.09757 q^{67} +1.64429 q^{68} +7.81345 q^{69} -1.28410 q^{70} +1.00000 q^{71} +4.32247 q^{72} -6.15734 q^{73} -17.9349 q^{74} +10.6257 q^{75} +0.228184 q^{76} +1.69699 q^{77} +1.02947 q^{78} +8.78720 q^{79} +1.22501 q^{80} -11.2258 q^{81} -12.9127 q^{82} -12.1859 q^{83} +1.77889 q^{84} -1.70155 q^{85} -11.6122 q^{86} -12.1611 q^{87} -1.42624 q^{88} -0.385834 q^{89} +0.684386 q^{90} -0.984717 q^{91} -0.961075 q^{92} +11.2824 q^{93} +4.79876 q^{94} -0.236130 q^{95} -3.21890 q^{96} +18.2474 q^{97} -3.98816 q^{98} -0.904445 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9}+O(q^{10}) \) 165 * q + 22 * q^2 + 18 * q^3 + 166 * q^4 + 28 * q^5 + 16 * q^6 + 24 * q^7 + 66 * q^8 + 177 * q^9	\( 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9} + 14 q^{10} + 18 q^{11} + 54 q^{12} + 44 q^{13} + 26 q^{14} + 24 q^{15} + 168 q^{16} + 143 q^{17} + 57 q^{18} + 20 q^{19} + 49 q^{20} + 39 q^{21} + 25 q^{22} + 52 q^{23} + 27 q^{24} + 175 q^{25} + 48 q^{26} + 69 q^{27} + 28 q^{28} + 58 q^{29} - 11 q^{30} + 28 q^{31} + 114 q^{32} + 110 q^{33} + 55 q^{34} + 67 q^{35} + 202 q^{36} + 44 q^{37} + 35 q^{38} + 27 q^{39} + 53 q^{40} + 141 q^{41} + 40 q^{42} + 29 q^{43} + 52 q^{44} + 54 q^{45} + 29 q^{46} + 87 q^{47} + 53 q^{48} + 143 q^{49} + 16 q^{50} + 37 q^{51} + 105 q^{52} + 101 q^{53} - 36 q^{54} + 72 q^{55} + 57 q^{56} + 82 q^{57} + 4 q^{58} + 103 q^{59} + 53 q^{60} + 16 q^{61} + 54 q^{62} + 126 q^{63} + 136 q^{64} + 159 q^{65} + 53 q^{66} + 60 q^{67} + 220 q^{68} + 81 q^{69} + 16 q^{70} + 165 q^{71} + 176 q^{72} + 124 q^{73} + 29 q^{74} + 44 q^{75} + 18 q^{76} + 127 q^{77} - 91 q^{78} + 14 q^{79} + 158 q^{80} + 213 q^{81} + 20 q^{82} + 116 q^{83} + 67 q^{84} + 59 q^{85} + 30 q^{86} + 28 q^{87} + 79 q^{88} + 195 q^{89} + 16 q^{90} - 26 q^{91} + 173 q^{92} + 116 q^{93} + 53 q^{94} + 26 q^{95} - 36 q^{96} + 88 q^{97} + 150 q^{98} + 12 q^{99}+O(q^{100}) \) 165 * q + 22 * q^2 + 18 * q^3 + 166 * q^4 + 28 * q^5 + 16 * q^6 + 24 * q^7 + 66 * q^8 + 177 * q^9 + 14 * q^10 + 18 * q^11 + 54 * q^12 + 44 * q^13 + 26 * q^14 + 24 * q^15 + 168 * q^16 + 143 * q^17 + 57 * q^18 + 20 * q^19 + 49 * q^20 + 39 * q^21 + 25 * q^22 + 52 * q^23 + 27 * q^24 + 175 * q^25 + 48 * q^26 + 69 * q^27 + 28 * q^28 + 58 * q^29 - 11 * q^30 + 28 * q^31 + 114 * q^32 + 110 * q^33 + 55 * q^34 + 67 * q^35 + 202 * q^36 + 44 * q^37 + 35 * q^38 + 27 * q^39 + 53 * q^40 + 141 * q^41 + 40 * q^42 + 29 * q^43 + 52 * q^44 + 54 * q^45 + 29 * q^46 + 87 * q^47 + 53 * q^48 + 143 * q^49 + 16 * q^50 + 37 * q^51 + 105 * q^52 + 101 * q^53 - 36 * q^54 + 72 * q^55 + 57 * q^56 + 82 * q^57 + 4 * q^58 + 103 * q^59 + 53 * q^60 + 16 * q^61 + 54 * q^62 + 126 * q^63 + 136 * q^64 + 159 * q^65 + 53 * q^66 + 60 * q^67 + 220 * q^68 + 81 * q^69 + 16 * q^70 + 165 * q^71 + 176 * q^72 + 124 * q^73 + 29 * q^74 + 44 * q^75 + 18 * q^76 + 127 * q^77 - 91 * q^78 + 14 * q^79 + 158 * q^80 + 213 * q^81 + 20 * q^82 + 116 * q^83 + 67 * q^84 + 59 * q^85 + 30 * q^86 + 28 * q^87 + 79 * q^88 + 195 * q^89 + 16 * q^90 - 26 * q^91 + 173 * q^92 + 116 * q^93 + 53 * q^94 + 26 * q^95 - 36 * q^96 + 88 * q^97 + 150 * q^98 + 12 * q^99

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