LMFDB - Embedded newform 8033.2.a.e.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8033, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8033 = 29 \cdot 277 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8033.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.1438279437$
Analytic rank:	$0$
Dimension:	$169$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	8033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.31656 q^{2} -0.263356 q^{3} +3.36647 q^{4} -0.903221 q^{5} +0.610081 q^{6} +2.39669 q^{7} -3.16552 q^{8} -2.93064 q^{9} +O(q^{10})$	\(q-2.31656 q^{2} -0.263356 q^{3} +3.36647 q^{4} -0.903221 q^{5} +0.610081 q^{6} +2.39669 q^{7} -3.16552 q^{8} -2.93064 q^{9} +2.09237 q^{10} -2.46615 q^{11} -0.886580 q^{12} -6.17071 q^{13} -5.55208 q^{14} +0.237868 q^{15} +0.600187 q^{16} +5.93171 q^{17} +6.78903 q^{18} +0.563594 q^{19} -3.04067 q^{20} -0.631181 q^{21} +5.71299 q^{22} -7.46517 q^{23} +0.833658 q^{24} -4.18419 q^{25} +14.2948 q^{26} +1.56187 q^{27} +8.06837 q^{28} -1.00000 q^{29} -0.551038 q^{30} +5.73897 q^{31} +4.94067 q^{32} +0.649475 q^{33} -13.7412 q^{34} -2.16474 q^{35} -9.86593 q^{36} -2.21543 q^{37} -1.30560 q^{38} +1.62509 q^{39} +2.85916 q^{40} -1.21569 q^{41} +1.46217 q^{42} -1.07764 q^{43} -8.30222 q^{44} +2.64702 q^{45} +17.2936 q^{46} +1.61136 q^{47} -0.158063 q^{48} -1.25590 q^{49} +9.69295 q^{50} -1.56215 q^{51} -20.7735 q^{52} -5.73444 q^{53} -3.61817 q^{54} +2.22748 q^{55} -7.58675 q^{56} -0.148426 q^{57} +2.31656 q^{58} -10.0450 q^{59} +0.800777 q^{60} -5.26723 q^{61} -13.2947 q^{62} -7.02383 q^{63} -12.6457 q^{64} +5.57351 q^{65} -1.50455 q^{66} +2.74097 q^{67} +19.9689 q^{68} +1.96600 q^{69} +5.01475 q^{70} -11.5796 q^{71} +9.27701 q^{72} +10.0570 q^{73} +5.13218 q^{74} +1.10193 q^{75} +1.89732 q^{76} -5.91058 q^{77} -3.76463 q^{78} +16.2295 q^{79} -0.542102 q^{80} +8.38060 q^{81} +2.81622 q^{82} -14.4719 q^{83} -2.12485 q^{84} -5.35765 q^{85} +2.49642 q^{86} +0.263356 q^{87} +7.80664 q^{88} +8.92961 q^{89} -6.13199 q^{90} -14.7892 q^{91} -25.1313 q^{92} -1.51139 q^{93} -3.73281 q^{94} -0.509050 q^{95} -1.30115 q^{96} -9.69082 q^{97} +2.90938 q^{98} +7.22740 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 169 q + 3 q^{2} + 8 q^{3} + 183 q^{4} + 13 q^{5} + 17 q^{6} + 76 q^{7} + 6 q^{8} + 181 q^{9}+O(q^{10}) $ 169 * q + 3 * q^2 + 8 * q^3 + 183 * q^4 + 13 * q^5 + 17 * q^6 + 76 * q^7 + 6 * q^8 + 181 * q^9	\( 169 q + 3 q^{2} + 8 q^{3} + 183 q^{4} + 13 q^{5} + 17 q^{6} + 76 q^{7} + 6 q^{8} + 181 q^{9} + 30 q^{10} + 2 q^{11} + 25 q^{12} + 63 q^{13} - 3 q^{14} + 26 q^{15} + 219 q^{16} + 14 q^{17} + 31 q^{18} + 51 q^{19} + 49 q^{20} + 16 q^{21} + 53 q^{22} + 50 q^{23} + 43 q^{24} + 214 q^{25} - 2 q^{26} + 23 q^{27} + 149 q^{28} - 169 q^{29} + 26 q^{30} + 65 q^{31} + 25 q^{32} + 57 q^{33} + 60 q^{34} + 60 q^{35} + 218 q^{36} + 52 q^{37} + 35 q^{38} + 49 q^{39} + 72 q^{40} + 3 q^{41} + 78 q^{42} + 132 q^{43} + 64 q^{45} + 32 q^{46} + 54 q^{47} + 76 q^{48} + 245 q^{49} - 6 q^{50} + 44 q^{51} + 193 q^{52} + 58 q^{53} + 54 q^{54} + 213 q^{55} + 12 q^{56} + 52 q^{57} - 3 q^{58} + 25 q^{59} + 32 q^{60} + 100 q^{61} + 78 q^{62} + 227 q^{63} + 292 q^{64} + 37 q^{65} + 59 q^{66} + 110 q^{67} + 24 q^{68} - 20 q^{69} + 47 q^{70} + 44 q^{71} + 71 q^{72} + 139 q^{73} + 35 q^{74} + 53 q^{75} + 92 q^{76} + 22 q^{77} + 83 q^{78} + 137 q^{79} + 90 q^{80} + 177 q^{81} + 91 q^{82} + 126 q^{83} + 36 q^{84} + 95 q^{85} + 21 q^{86} - 8 q^{87} + 75 q^{88} + 19 q^{89} + 130 q^{90} + 102 q^{91} + 68 q^{92} + 22 q^{93} + 82 q^{94} + 37 q^{95} + 107 q^{96} + 116 q^{97} - 13 q^{98} - 11 q^{99}+O(q^{100}) \) 169 * q + 3 * q^2 + 8 * q^3 + 183 * q^4 + 13 * q^5 + 17 * q^6 + 76 * q^7 + 6 * q^8 + 181 * q^9 + 30 * q^10 + 2 * q^11 + 25 * q^12 + 63 * q^13 - 3 * q^14 + 26 * q^15 + 219 * q^16 + 14 * q^17 + 31 * q^18 + 51 * q^19 + 49 * q^20 + 16 * q^21 + 53 * q^22 + 50 * q^23 + 43 * q^24 + 214 * q^25 - 2 * q^26 + 23 * q^27 + 149 * q^28 - 169 * q^29 + 26 * q^30 + 65 * q^31 + 25 * q^32 + 57 * q^33 + 60 * q^34 + 60 * q^35 + 218 * q^36 + 52 * q^37 + 35 * q^38 + 49 * q^39 + 72 * q^40 + 3 * q^41 + 78 * q^42 + 132 * q^43 + 64 * q^45 + 32 * q^46 + 54 * q^47 + 76 * q^48 + 245 * q^49 - 6 * q^50 + 44 * q^51 + 193 * q^52 + 58 * q^53 + 54 * q^54 + 213 * q^55 + 12 * q^56 + 52 * q^57 - 3 * q^58 + 25 * q^59 + 32 * q^60 + 100 * q^61 + 78 * q^62 + 227 * q^63 + 292 * q^64 + 37 * q^65 + 59 * q^66 + 110 * q^67 + 24 * q^68 - 20 * q^69 + 47 * q^70 + 44 * q^71 + 71 * q^72 + 139 * q^73 + 35 * q^74 + 53 * q^75 + 92 * q^76 + 22 * q^77 + 83 * q^78 + 137 * q^79 + 90 * q^80 + 177 * q^81 + 91 * q^82 + 126 * q^83 + 36 * q^84 + 95 * q^85 + 21 * q^86 - 8 * q^87 + 75 * q^88 + 19 * q^89 + 130 * q^90 + 102 * q^91 + 68 * q^92 + 22 * q^93 + 82 * q^94 + 37 * q^95 + 107 * q^96 + 116 * q^97 - 13 * q^98 - 11 * 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 $

$2$	−2.31656	−1.63806	−0.819029	−	0.573752i	$-0.805487\pi$
$2$	−2.31656	−1.63806	−0.819029	+	0.573752i	$0.805487\pi$
$3$	−0.263356	−0.152049	−0.0760243	−	0.997106i	$-0.524223\pi$
$3$	−0.263356	−0.152049	−0.0760243	+	0.997106i	$0.524223\pi$
$4$	3.36647	1.68324
$5$	−0.903221	−0.403933	−0.201966	−	0.979392i	$-0.564733\pi$
$5$	−0.903221	−0.403933	−0.201966	+	0.979392i	$0.564733\pi$
$6$	0.610081	0.249064
$7$	2.39669	0.905862	0.452931	−	0.891546i	$-0.350378\pi$
$7$	2.39669	0.905862	0.452931	+	0.891546i	$0.350378\pi$
$8$	−3.16552	−1.11918
$9$	−2.93064	−0.976881
$10$	2.09237	0.661665
$11$	−2.46615	−0.743572	−0.371786	−	0.928318i	$-0.621254\pi$
$11$	−2.46615	−0.743572	−0.371786	+	0.928318i	$0.621254\pi$
$12$	−0.886580	−0.255934
$13$	−6.17071	−1.71145	−0.855723	−	0.517433i	$-0.826887\pi$
$13$	−6.17071	−1.71145	−0.855723	+	0.517433i	$0.826887\pi$
$14$	−5.55208	−1.48385
$15$	0.237868	0.0614174
$16$	0.600187	0.150047
$17$	5.93171	1.43865	0.719326	−	0.694673i	$-0.244451\pi$
$17$	5.93171	1.43865	0.719326	+	0.694673i	$0.244451\pi$
$18$	6.78903	1.60019
$19$	0.563594	0.129297	0.0646486	−	0.997908i	$-0.479407\pi$
$19$	0.563594	0.129297	0.0646486	+	0.997908i	$0.479407\pi$
$20$	−3.04067	−0.679914
$21$	−0.631181	−0.137735
$22$	5.71299	1.21801
$23$	−7.46517	−1.55660	−0.778298	−	0.627895i	$-0.783917\pi$
$23$	−7.46517	−1.55660	−0.778298	+	0.627895i	$0.783917\pi$
$24$	0.833658	0.170170
$25$	−4.18419	−0.836838
$26$	14.2948	2.80345
$27$	1.56187	0.300582
$28$	8.06837	1.52478
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−0.551038	−0.100605
$31$	5.73897	1.03075	0.515374	−	0.856965i	$-0.327653\pi$
$31$	5.73897	1.03075	0.515374	+	0.856965i	$0.327653\pi$
$32$	4.94067	0.873395
$33$	0.649475	0.113059
$34$	−13.7412	−2.35660
$35$	−2.16474	−0.365907
$36$	−9.86593	−1.64432
$37$	−2.21543	−0.364214	−0.182107	−	0.983279i	$-0.558292\pi$
$37$	−2.21543	−0.364214	−0.182107	+	0.983279i	$0.558292\pi$
$38$	−1.30560	−0.211796
$39$	1.62509	0.260223
$40$	2.85916	0.452073
$41$	−1.21569	−0.189859	−0.0949293	−	0.995484i	$-0.530263\pi$
$41$	−1.21569	−0.189859	−0.0949293	+	0.995484i	$0.530263\pi$
$42$	1.46217	0.225618
$43$	−1.07764	−0.164338	−0.0821692	−	0.996618i	$-0.526185\pi$
$43$	−1.07764	−0.164338	−0.0821692	+	0.996618i	$0.526185\pi$
$44$	−8.30222	−1.25161
$45$	2.64702	0.394594
$46$	17.2936	2.54980
$47$	1.61136	0.235041	0.117520	−	0.993070i	$-0.462505\pi$
$47$	1.61136	0.235041	0.117520	+	0.993070i	$0.462505\pi$
$48$	−0.158063	−0.0228144
$49$	−1.25590	−0.179414
$50$	9.69295	1.37079
$51$	−1.56215	−0.218745
$52$	−20.7735	−2.88077
$53$	−5.73444	−0.787686	−0.393843	−	0.919178i	$-0.628855\pi$
$53$	−5.73444	−0.787686	−0.393843	+	0.919178i	$0.628855\pi$
$54$	−3.61817	−0.492371
$55$	2.22748	0.300353
$56$	−7.58675	−1.01382
$57$	−0.148426	−0.0196595
$58$	2.31656	0.304180
$59$	−10.0450	−1.30774	−0.653871	−	0.756606i	$-0.726856\pi$
$59$	−10.0450	−1.30774	−0.653871	+	0.756606i	$0.726856\pi$
$60$	0.800777	0.103380
$61$	−5.26723	−0.674399	−0.337200	−	0.941433i	$-0.609480\pi$
$61$	−5.26723	−0.674399	−0.337200	+	0.941433i	$0.609480\pi$
$62$	−13.2947	−1.68843
$63$	−7.02383	−0.884919
$64$	−12.6457	−1.58072
$65$	5.57351	0.691309
$66$	−1.50455	−0.185197
$67$	2.74097	0.334863	0.167432	−	0.985884i	$-0.446453\pi$
$67$	2.74097	0.334863	0.167432	+	0.985884i	$0.446453\pi$
$68$	19.9689	2.42159
$69$	1.96600	0.236678
$70$	5.01475	0.599377
$71$	−11.5796	−1.37424	−0.687122	−	0.726542i	$-0.741126\pi$
$71$	−11.5796	−1.37424	−0.687122	+	0.726542i	$0.741126\pi$
$72$	9.27701	1.09331
$73$	10.0570	1.17708	0.588542	−	0.808467i	$-0.299702\pi$
$73$	10.0570	1.17708	0.588542	+	0.808467i	$0.299702\pi$
$74$	5.13218	0.596603
$75$	1.10193	0.127240
$76$	1.89732	0.217638
$77$	−5.91058	−0.673573
$78$	−3.76463	−0.426260
$79$	16.2295	1.82596	0.912981	−	0.408003i	$-0.133775\pi$
$79$	16.2295	1.82596	0.912981	+	0.408003i	$0.133775\pi$
$80$	−0.542102	−0.0606088
$81$	8.38060	0.931178
$82$	2.81622	0.311000
$83$	−14.4719	−1.58850	−0.794250	−	0.607591i	$-0.792136\pi$
$83$	−14.4719	−1.58850	−0.794250	+	0.607591i	$0.792136\pi$
$84$	−2.12485	−0.231840
$85$	−5.35765	−0.581118
$86$	2.49642	0.269196
$87$	0.263356	0.0282347
$88$	7.80664	0.832191
$89$	8.92961	0.946536	0.473268	−	0.880918i	$-0.343074\pi$
$89$	8.92961	0.946536	0.473268	+	0.880918i	$0.343074\pi$
$90$	−6.13199	−0.646368
$91$	−14.7892	−1.55033
$92$	−25.1313	−2.62012
$93$	−1.51139	−0.156724
$94$	−3.73281	−0.385010
$95$	−0.509050	−0.0522274
$96$	−1.30115	−0.132798
$97$	−9.69082	−0.983953	−0.491977	−	0.870608i	$-0.663725\pi$
$97$	−9.69082	−0.983953	−0.491977	+	0.870608i	$0.663725\pi$
$98$	2.90938	0.293891
$99$	7.22740	0.726381
$100$	−14.0860	−1.40860
$101$	−17.4111	−1.73246	−0.866232	−	0.499642i	$-0.833465\pi$
$101$	−17.4111	−1.73246	−0.866232	+	0.499642i	$0.833465\pi$
$102$	3.61882	0.358317
$103$	−3.94320	−0.388535	−0.194267	−	0.980949i	$-0.562233\pi$
$103$	−3.94320	−0.388535	−0.194267	+	0.980949i	$0.562233\pi$
$104$	19.5335	1.91542
$105$	0.570096	0.0556356
$106$	13.2842	1.29028
$107$	−14.9833	−1.44849	−0.724243	−	0.689545i	$-0.757811\pi$
$107$	−14.9833	−1.44849	−0.724243	+	0.689545i	$0.757811\pi$
$108$	5.25799	0.505950
$109$	−0.348814	−0.0334103	−0.0167052	−	0.999860i	$-0.505318\pi$
$109$	−0.348814	−0.0334103	−0.0167052	+	0.999860i	$0.505318\pi$
$110$	−5.16010	−0.491996
$111$	0.583445	0.0553781
$112$	1.43846	0.135922
$113$	9.65844	0.908590	0.454295	−	0.890851i	$-0.349891\pi$
$113$	9.65844	0.908590	0.454295	+	0.890851i	$0.349891\pi$
$114$	0.343838	0.0322033
$115$	6.74270	0.628760
$116$	−3.36647	−0.312569
$117$	18.0842	1.67188
$118$	23.2698	2.14216
$119$	14.2164	1.30322
$120$	−0.752977	−0.0687371
$121$	−4.91811	−0.447101
$122$	12.2019	1.10471
$123$	0.320159	0.0288677
$124$	19.3201	1.73499
$125$	8.29535	0.741959
$126$	16.2712	1.44955
$127$	−10.4370	−0.926135	−0.463067	−	0.886323i	$-0.653251\pi$
$127$	−10.4370	−0.926135	−0.463067	+	0.886323i	$0.653251\pi$
$128$	19.4134	1.71591
$129$	0.283803	0.0249874
$130$	−12.9114	−1.13241
$131$	18.0327	1.57552	0.787762	−	0.615980i	$-0.211240\pi$
$131$	18.0327	1.57552	0.787762	+	0.615980i	$0.211240\pi$
$132$	2.18644	0.190305
$133$	1.35076	0.117125
$134$	−6.34964	−0.548526
$135$	−1.41071	−0.121415
$136$	−18.7770	−1.61011
$137$	−5.23813	−0.447524	−0.223762	−	0.974644i	$-0.571834\pi$
$137$	−5.23813	−0.447524	−0.223762	+	0.974644i	$0.571834\pi$
$138$	−4.55436	−0.387693
$139$	5.47964	0.464777	0.232389	−	0.972623i	$-0.425346\pi$
$139$	5.47964	0.464777	0.232389	+	0.972623i	$0.425346\pi$
$140$	−7.28752	−0.615908
$141$	−0.424360	−0.0357376
$142$	26.8249	2.25109
$143$	15.2179	1.27258
$144$	−1.75894	−0.146578
$145$	0.903221	0.0750084
$146$	−23.2977	−1.92813
$147$	0.330749	0.0272797
$148$	−7.45817	−0.613057
$149$	−10.8243	−0.886760	−0.443380	−	0.896334i	$-0.646221\pi$
$149$	−10.8243	−0.886760	−0.443380	+	0.896334i	$0.646221\pi$
$150$	−2.55269	−0.208427
$151$	10.2242	0.832031	0.416016	−	0.909357i	$-0.363426\pi$
$151$	10.2242	0.832031	0.416016	+	0.909357i	$0.363426\pi$
$152$	−1.78407	−0.144707
$153$	−17.3837	−1.40539
$154$	13.6922	1.10335
$155$	−5.18355	−0.416353
$156$	5.47083	0.438017
$157$	4.75975	0.379869	0.189935	−	0.981797i	$-0.439172\pi$
$157$	4.75975	0.379869	0.189935	+	0.981797i	$0.439172\pi$
$158$	−37.5967	−2.99103
$159$	1.51020	0.119766
$160$	−4.46251	−0.352793
$161$	−17.8917	−1.41006
$162$	−19.4142	−1.52532
$163$	6.70085	0.524851	0.262426	−	0.964952i	$-0.415478\pi$
$163$	6.70085	0.524851	0.262426	+	0.964952i	$0.415478\pi$
$164$	−4.09258	−0.319577
$165$	−0.586619	−0.0456682
$166$	33.5252	2.60206
$167$	2.52255	0.195201	0.0976005	−	0.995226i	$-0.468883\pi$
$167$	2.52255	0.195201	0.0976005	+	0.995226i	$0.468883\pi$
$168$	1.99802	0.154150
$169$	25.0777	1.92905
$170$	12.4113	0.951906
$171$	−1.65169	−0.126308
$172$	−3.62784	−0.276620
$173$	13.9316	1.05920	0.529599	−	0.848248i	$-0.322343\pi$
$173$	13.9316	1.05920	0.529599	+	0.848248i	$0.322343\pi$
$174$	−0.610081	−0.0462501
$175$	−10.0282	−0.758060
$176$	−1.48015	−0.111571
$177$	2.64540	0.198840
$178$	−20.6860	−1.55048
$179$	7.62201	0.569696	0.284848	−	0.958573i	$-0.408057\pi$
$179$	7.62201	0.569696	0.284848	+	0.958573i	$0.408057\pi$
$180$	8.91111	0.664195
$181$	2.22713	0.165541	0.0827706	−	0.996569i	$-0.473623\pi$
$181$	2.22713	0.165541	0.0827706	+	0.996569i	$0.473623\pi$
$182$	34.2602	2.53954
$183$	1.38715	0.102541
$184$	23.6312	1.74211
$185$	2.00102	0.147118
$186$	3.50123	0.256723
$187$	−14.6285	−1.06974
$188$	5.42459	0.395629
$189$	3.74331	0.272286
$190$	1.17925	0.0855515
$191$	8.48427	0.613900	0.306950	−	0.951726i	$-0.400692\pi$
$191$	8.48427	0.613900	0.306950	+	0.951726i	$0.400692\pi$
$192$	3.33033	0.240346
$193$	5.43191	0.390997	0.195499	−	0.980704i	$-0.437368\pi$
$193$	5.43191	0.390997	0.195499	+	0.980704i	$0.437368\pi$
$194$	22.4494	1.61177
$195$	−1.46782	−0.105113
$196$	−4.22795	−0.301997
$197$	3.22231	0.229580	0.114790	−	0.993390i	$-0.463380\pi$
$197$	3.22231	0.229580	0.114790	+	0.993390i	$0.463380\pi$
$198$	−16.7427	−1.18986
$199$	12.1339	0.860151	0.430076	−	0.902793i	$-0.358487\pi$
$199$	12.1339	0.860151	0.430076	+	0.902793i	$0.358487\pi$
$200$	13.2451	0.936573
$201$	−0.721851	−0.0509155
$202$	40.3338	2.83788
$203$	−2.39669	−0.168214
$204$	−5.25894	−0.368199
$205$	1.09804	0.0766901
$206$	9.13467	0.636443
$207$	21.8778	1.52061
$208$	−3.70358	−0.256797
$209$	−1.38991	−0.0961418
$210$	−1.32066	−0.0911344
$211$	−2.97314	−0.204680	−0.102340	−	0.994749i	$-0.532633\pi$
$211$	−2.97314	−0.204680	−0.102340	+	0.994749i	$0.532633\pi$
$212$	−19.3048	−1.32586
$213$	3.04955	0.208952
$214$	34.7097	2.37271
$215$	0.973346	0.0663817
$216$	−4.94413	−0.336405
$217$	13.7545	0.933716
$218$	0.808051	0.0547281
$219$	−2.64857	−0.178974
$220$	7.49874	0.505565
$221$	−36.6029	−2.46218
$222$	−1.35159	−0.0907126
$223$	20.8793	1.39818	0.699091	−	0.715033i	$-0.253588\pi$
$223$	20.8793	1.39818	0.699091	+	0.715033i	$0.253588\pi$
$224$	11.8412	0.791175
$225$	12.2624	0.817492
$226$	−22.3744	−1.48832
$227$	−16.1545	−1.07221	−0.536104	−	0.844152i	$-0.680105\pi$
$227$	−16.1545	−1.07221	−0.536104	+	0.844152i	$0.680105\pi$
$228$	−0.499671	−0.0330915
$229$	−15.2897	−1.01037	−0.505184	−	0.863011i	$-0.668575\pi$
$229$	−15.2897	−1.01037	−0.505184	+	0.863011i	$0.668575\pi$
$230$	−15.6199	−1.02995
$231$	1.55659	0.102416
$232$	3.16552	0.207827
$233$	−11.4711	−0.751495	−0.375747	−	0.926722i	$-0.622614\pi$
$233$	−11.4711	−0.751495	−0.375747	+	0.926722i	$0.622614\pi$
$234$	−41.8931	−2.73864
$235$	−1.45541	−0.0949406
$236$	−33.8161	−2.20124
$237$	−4.27413	−0.277635
$238$	−32.9333	−2.13475
$239$	3.64144	0.235545	0.117773	−	0.993041i	$-0.462425\pi$
$239$	3.64144	0.235545	0.117773	+	0.993041i	$0.462425\pi$
$240$	0.142766	0.00921548
$241$	−11.8434	−0.762898	−0.381449	−	0.924390i	$-0.624575\pi$
$241$	−11.8434	−0.762898	−0.381449	+	0.924390i	$0.624575\pi$
$242$	11.3931	0.732377
$243$	−6.89269	−0.442166
$244$	−17.7320	−1.13517
$245$	1.13436	0.0724713
$246$	−0.741668	−0.0472870
$247$	−3.47777	−0.221285
$248$	−18.1668	−1.15359
$249$	3.81127	0.241529
$250$	−19.2167	−1.21537
$251$	−27.8181	−1.75586	−0.877930	−	0.478788i	$-0.841076\pi$
$251$	−27.8181	−1.75586	−0.877930	+	0.478788i	$0.841076\pi$
$252$	−23.6455	−1.48953
$253$	18.4102	1.15744
$254$	24.1780	1.51706
$255$	1.41097	0.0883582
$256$	−19.6808	−1.23005
$257$	28.0681	1.75084	0.875421	−	0.483362i	$-0.160584\pi$
$257$	28.0681	1.75084	0.875421	+	0.483362i	$0.160584\pi$
$258$	−0.657447	−0.0409309
$259$	−5.30968	−0.329927
$260$	18.7631	1.16364
$261$	2.93064	0.181402
$262$	−41.7739	−2.58080
$263$	−17.7293	−1.09323	−0.546617	−	0.837383i	$-0.684085\pi$
$263$	−17.7293	−1.09323	−0.546617	+	0.837383i	$0.684085\pi$
$264$	−2.05592	−0.126533
$265$	5.17946	0.318172
$266$	−3.12911	−0.191858
$267$	−2.35166	−0.143919
$268$	9.22741	0.563654
$269$	−21.1422	−1.28906	−0.644531	−	0.764578i	$-0.722947\pi$
$269$	−21.1422	−1.28906	−0.644531	+	0.764578i	$0.722947\pi$
$270$	3.26801	0.198885
$271$	10.7330	0.651980	0.325990	−	0.945373i	$-0.394302\pi$
$271$	10.7330	0.651980	0.325990	+	0.945373i	$0.394302\pi$
$272$	3.56014	0.215865
$273$	3.89483	0.235726
$274$	12.1345	0.733070
$275$	10.3188	0.622250
$276$	6.61847	0.398385
$277$	1.00000	0.0600842
$277$	1.00000	0.0600842
$278$	−12.6939	−0.761332
$279$	−16.8189	−1.00692
$280$	6.85251	0.409516
$281$	17.2400	1.02845	0.514226	−	0.857655i	$-0.328079\pi$
$281$	17.2400	1.02845	0.514226	+	0.857655i	$0.328079\pi$
$282$	0.983058	0.0585402
$283$	−28.4874	−1.69340	−0.846701	−	0.532068i	$-0.821415\pi$
$283$	−28.4874	−1.69340	−0.846701	+	0.532068i	$0.821415\pi$
$284$	−38.9824	−2.31318
$285$	0.134061	0.00794110
$286$	−35.2532	−2.08457
$287$	−2.91362	−0.171986
$288$	−14.4793	−0.853203
$289$	18.1852	1.06972
$290$	−2.09237	−0.122868
$291$	2.55213	0.149609
$292$	33.8566	1.98131
$293$	−19.1575	−1.11919	−0.559596	−	0.828766i	$-0.689044\pi$
$293$	−19.1575	−1.11919	−0.559596	+	0.828766i	$0.689044\pi$
$294$	−0.766201	−0.0446857
$295$	9.07282	0.528240
$296$	7.01297	0.407621
$297$	−3.85180	−0.223504
$298$	25.0752	1.45256
$299$	46.0654	2.66403
$300$	3.70962	0.214175
$301$	−2.58276	−0.148868
$302$	−23.6850	−1.36292
$303$	4.58530	0.263419
$304$	0.338262	0.0194006
$305$	4.75747	0.272412
$306$	40.2706	2.30211
$307$	14.4115	0.822507	0.411253	−	0.911521i	$-0.365091\pi$
$307$	14.4115	0.822507	0.411253	+	0.911521i	$0.365091\pi$
$308$	−19.8978	−1.13378
$309$	1.03846	0.0590761
$310$	12.0080	0.682011
$311$	−25.3576	−1.43790	−0.718949	−	0.695063i	$-0.755377\pi$
$311$	−25.3576	−1.43790	−0.718949	+	0.695063i	$0.755377\pi$
$312$	−5.14426	−0.291236
$313$	14.7425	0.833293	0.416646	−	0.909069i	$-0.363205\pi$
$313$	14.7425	0.833293	0.416646	+	0.909069i	$0.363205\pi$
$314$	−11.0263	−0.622248
$315$	6.34407	0.357448
$316$	54.6361	3.07352
$317$	10.8689	0.610458	0.305229	−	0.952279i	$-0.401267\pi$
$317$	10.8689	0.610458	0.305229	+	0.952279i	$0.401267\pi$
$318$	−3.49847	−0.196184
$319$	2.46615	0.138078
$320$	11.4219	0.638504
$321$	3.94593	0.220240
$322$	41.4472	2.30976
$323$	3.34308	0.186014
$324$	28.2131	1.56739
$325$	25.8194	1.43220
$326$	−15.5230	−0.859737
$327$	0.0918622	0.00507999
$328$	3.84829	0.212486
$329$	3.86192	0.212914
$330$	1.35894	0.0748072
$331$	−6.33321	−0.348105	−0.174052	−	0.984736i	$-0.555686\pi$
$331$	−6.33321	−0.348105	−0.174052	+	0.984736i	$0.555686\pi$
$332$	−48.7193	−2.67382
$333$	6.49262	0.355793
$334$	−5.84366	−0.319751
$335$	−2.47571	−0.135262
$336$	−0.378827	−0.0206667
$337$	−14.9602	−0.814933	−0.407466	−	0.913220i	$-0.633588\pi$
$337$	−14.9602	−0.814933	−0.407466	+	0.913220i	$0.633588\pi$
$338$	−58.0940	−3.15990
$339$	−2.54361	−0.138150
$340$	−18.0364	−0.978159
$341$	−14.1531	−0.766436
$342$	3.82625	0.206900
$343$	−19.7868	−1.06839
$344$	3.41129	0.183924
$345$	−1.77573	−0.0956020
$346$	−32.2734	−1.73503
$347$	−8.15269	−0.437659	−0.218830	−	0.975763i	$-0.570224\pi$
$347$	−8.15269	−0.437659	−0.218830	+	0.975763i	$0.570224\pi$
$348$	0.886580	0.0475257
$349$	33.8827	1.81370	0.906850	−	0.421454i	$-0.138480\pi$
$349$	33.8827	1.81370	0.906850	+	0.421454i	$0.138480\pi$
$350$	23.2310	1.24175
$351$	−9.63784	−0.514430
$352$	−12.1844	−0.649432
$353$	−7.14975	−0.380543	−0.190271	−	0.981732i	$-0.560937\pi$
$353$	−7.14975	−0.380543	−0.190271	+	0.981732i	$0.560937\pi$
$354$	−6.12823	−0.325712
$355$	10.4589	0.555102
$356$	30.0613	1.59324
$357$	−3.74398	−0.198153
$358$	−17.6569	−0.933195
$359$	−3.51005	−0.185254	−0.0926268	−	0.995701i	$-0.529526\pi$
$359$	−3.51005	−0.185254	−0.0926268	+	0.995701i	$0.529526\pi$
$360$	−8.37919	−0.441622
$361$	−18.6824	−0.983282
$362$	−5.15929	−0.271166
$363$	1.29521	0.0679810
$364$	−49.7876	−2.60958
$365$	−9.08370	−0.475463
$366$	−3.21343	−0.167969
$367$	25.6769	1.34032	0.670162	−	0.742215i	$-0.266224\pi$
$367$	25.6769	1.34032	0.670162	+	0.742215i	$0.266224\pi$
$368$	−4.48050	−0.233562
$369$	3.56275	0.185469
$370$	−4.63549	−0.240988
$371$	−13.7436	−0.713534
$372$	−5.08805	−0.263803
$373$	1.80211	0.0933096	0.0466548	−	0.998911i	$-0.485144\pi$
$373$	1.80211	0.0933096	0.0466548	+	0.998911i	$0.485144\pi$
$374$	33.8878	1.75230
$375$	−2.18463	−0.112814
$376$	−5.10078	−0.263053
$377$	6.17071	0.317808
$378$	−8.67162	−0.446020
$379$	22.2330	1.14203	0.571017	−	0.820938i	$-0.306549\pi$
$379$	22.2330	1.14203	0.571017	+	0.820938i	$0.306549\pi$
$380$	−1.71370	−0.0879110
$381$	2.74865	0.140817
$382$	−19.6544	−1.00560
$383$	−17.4826	−0.893319	−0.446660	−	0.894704i	$-0.647387\pi$
$383$	−17.4826	−0.893319	−0.446660	+	0.894704i	$0.647387\pi$
$384$	−5.11262	−0.260902
$385$	5.33856	0.272078
$386$	−12.5834	−0.640476
$387$	3.15818	0.160539
$388$	−32.6239	−1.65623
$389$	31.1938	1.58159	0.790794	−	0.612082i	$-0.209668\pi$
$389$	31.1938	1.58159	0.790794	+	0.612082i	$0.209668\pi$
$390$	3.40029	0.172181
$391$	−44.2813	−2.23940
$392$	3.97558	0.200797
$393$	−4.74902	−0.239556
$394$	−7.46468	−0.376065
$395$	−14.6588	−0.737565
$396$	24.3309	1.22267
$397$	30.7903	1.54532	0.772661	−	0.634818i	$-0.218925\pi$
$397$	30.7903	1.54532	0.772661	+	0.634818i	$0.218925\pi$
$398$	−28.1090	−1.40898
$399$	−0.355729	−0.0178087
$400$	−2.51130	−0.125565
$401$	34.5597	1.72583	0.862915	−	0.505350i	$-0.168636\pi$
$401$	34.5597	1.72583	0.862915	+	0.505350i	$0.168636\pi$
$402$	1.67222	0.0834025
$403$	−35.4135	−1.76407
$404$	−58.6138	−2.91615
$405$	−7.56954	−0.376133
$406$	5.55208	0.275545
$407$	5.46357	0.270819
$408$	4.94502	0.244815
$409$	3.10014	0.153292	0.0766460	−	0.997058i	$-0.475579\pi$
$409$	3.10014	0.153292	0.0766460	+	0.997058i	$0.475579\pi$
$410$	−2.54367	−0.125623
$411$	1.37949	0.0680453
$412$	−13.2747	−0.653996
$413$	−24.0746	−1.18463
$414$	−50.6812	−2.49085
$415$	13.0713	0.641647
$416$	−30.4874	−1.49477
$417$	−1.44310	−0.0706687
$418$	3.21981	0.157486
$419$	−30.4119	−1.48572	−0.742860	−	0.669447i	$-0.766531\pi$
$419$	−30.4119	−1.48572	−0.742860	+	0.669447i	$0.766531\pi$
$420$	1.91921	0.0936479
$421$	1.51806	0.0739857	0.0369929	−	0.999316i	$-0.488222\pi$
$421$	1.51806	0.0739857	0.0369929	+	0.999316i	$0.488222\pi$
$422$	6.88748	0.335277
$423$	−4.72231	−0.229607
$424$	18.1525	0.881562
$425$	−24.8194	−1.20392
$426$	−7.06448	−0.342275
$427$	−12.6239	−0.610913
$428$	−50.4407	−2.43814
$429$	−4.00772	−0.193494
$430$	−2.25482	−0.108737
$431$	13.5596	0.653142	0.326571	−	0.945173i	$-0.394107\pi$
$431$	13.5596	0.653142	0.326571	+	0.945173i	$0.394107\pi$
$432$	0.937414	0.0451014
$433$	22.8243	1.09687	0.548434	−	0.836194i	$-0.315224\pi$
$433$	22.8243	1.09687	0.548434	+	0.836194i	$0.315224\pi$
$434$	−31.8632	−1.52948
$435$	−0.237868	−0.0114049
$436$	−1.17427	−0.0562375
$437$	−4.20732	−0.201264
$438$	6.13559	0.293170
$439$	−14.8844	−0.710395	−0.355197	−	0.934791i	$-0.615586\pi$
$439$	−14.8844	−0.710395	−0.355197	+	0.934791i	$0.615586\pi$
$440$	−7.05112	−0.336149
$441$	3.68060	0.175267
$442$	84.7929	4.03319
$443$	10.7716	0.511772	0.255886	−	0.966707i	$-0.417633\pi$
$443$	10.7716	0.511772	0.255886	+	0.966707i	$0.417633\pi$
$444$	1.96415	0.0932145
$445$	−8.06541	−0.382337
$446$	−48.3682	−2.29030
$447$	2.85064	0.134831
$448$	−30.3079	−1.43191
$449$	−5.22038	−0.246365	−0.123182	−	0.992384i	$-0.539310\pi$
$449$	−5.22038	−0.246365	−0.123182	+	0.992384i	$0.539310\pi$
$450$	−28.4066	−1.33910
$451$	2.99807	0.141174
$452$	32.5149	1.52937
$453$	−2.69259	−0.126509
$454$	37.4228	1.75634
$455$	13.3580	0.626231
$456$	0.469844	0.0220025
$457$	2.61026	0.122103	0.0610515	−	0.998135i	$-0.480555\pi$
$457$	2.61026	0.122103	0.0610515	+	0.998135i	$0.480555\pi$
$458$	35.4195	1.65504
$459$	9.26456	0.432433
$460$	22.6991	1.05835
$461$	−6.49798	−0.302641	−0.151321	−	0.988485i	$-0.548353\pi$
$461$	−6.49798	−0.302641	−0.151321	+	0.988485i	$0.548353\pi$
$462$	−3.60593	−0.167763
$463$	1.88028	0.0873840	0.0436920	−	0.999045i	$-0.486088\pi$
$463$	1.88028	0.0873840	0.0436920	+	0.999045i	$0.486088\pi$
$464$	−0.600187	−0.0278630
$465$	1.36512	0.0633059
$466$	26.5735	1.23099
$467$	2.18607	0.101159	0.0505795	−	0.998720i	$-0.483893\pi$
$467$	2.18607	0.101159	0.0505795	+	0.998720i	$0.483893\pi$
$468$	60.8798	2.81417
$469$	6.56925	0.303340
$470$	3.37156	0.155518
$471$	−1.25351	−0.0577585
$472$	31.7975	1.46360
$473$	2.65762	0.122197
$474$	9.90130	0.454782
$475$	−2.35818	−0.108201
$476$	47.8593	2.19363
$477$	16.8056	0.769475
$478$	−8.43563	−0.385837
$479$	20.3557	0.930074	0.465037	−	0.885291i	$-0.346041\pi$
$479$	20.3557	0.930074	0.465037	+	0.885291i	$0.346041\pi$
$480$	1.17523	0.0536416
$481$	13.6707	0.623332
$482$	27.4359	1.24967
$483$	4.71187	0.214398
$484$	−16.5567	−0.752576
$485$	8.75295	0.397451
$486$	15.9674	0.724294
$487$	−12.3495	−0.559611	−0.279806	−	0.960057i	$-0.590270\pi$
$487$	−12.3495	−0.559611	−0.279806	+	0.960057i	$0.590270\pi$
$488$	16.6735	0.754775
$489$	−1.76471	−0.0798028
$490$	−2.62781	−0.118712
$491$	−3.85395	−0.173926	−0.0869632	−	0.996212i	$-0.527716\pi$
$491$	−3.85395	−0.173926	−0.0869632	+	0.996212i	$0.527716\pi$
$492$	1.07780	0.0485912
$493$	−5.93171	−0.267151
$494$	8.05648	0.362478
$495$	−6.52794	−0.293409
$496$	3.44446	0.154661
$497$	−27.7526	−1.24488
$498$	−8.82904	−0.395639
$499$	−27.6581	−1.23815	−0.619074	−	0.785332i	$-0.712492\pi$
$499$	−27.6581	−1.23815	−0.619074	+	0.785332i	$0.712492\pi$
$500$	27.9261	1.24889
$501$	−0.664329	−0.0296800
$502$	64.4423	2.87620
$503$	−1.49979	−0.0668725	−0.0334363	−	0.999441i	$-0.510645\pi$
$503$	−1.49979	−0.0668725	−0.0334363	+	0.999441i	$0.510645\pi$
$504$	22.2341	0.990384
$505$	15.7260	0.699799
$506$	−42.6485	−1.89596
$507$	−6.60434	−0.293309
$508$	−35.1359	−1.55890
$509$	−13.2365	−0.586697	−0.293349	−	0.956006i	$-0.594770\pi$
$509$	−13.2365	−0.586697	−0.293349	+	0.956006i	$0.594770\pi$
$510$	−3.26860	−0.144736
$511$	24.1035	1.06628
$512$	6.76514	0.298980
$513$	0.880260	0.0388644
$514$	−65.0216	−2.86798
$515$	3.56158	0.156942
$516$	0.955413	0.0420597
$517$	−3.97385	−0.174770
$518$	12.3002	0.540440
$519$	−3.66896	−0.161049
$520$	−17.6431	−0.773700
$521$	−20.1110	−0.881081	−0.440541	−	0.897733i	$-0.645213\pi$
$521$	−20.1110	−0.881081	−0.440541	+	0.897733i	$0.645213\pi$
$522$	−6.78903	−0.297148
$523$	21.7414	0.950685	0.475342	−	0.879801i	$-0.342324\pi$
$523$	21.7414	0.950685	0.475342	+	0.879801i	$0.342324\pi$
$524$	60.7066	2.65198
$525$	2.64098	0.115262
$526$	41.0710	1.79078
$527$	34.0419	1.48289
$528$	0.389806	0.0169641
$529$	32.7288	1.42299
$530$	−11.9986	−0.521184
$531$	29.4382	1.27751
$532$	4.54728	0.197150
$533$	7.50166	0.324933
$534$	5.44778	0.235748
$535$	13.5332	0.585091
$536$	−8.67661	−0.374772
$537$	−2.00730	−0.0866214
$538$	48.9773	2.11156
$539$	3.09724	0.133408
$540$	−4.74912	−0.204370
$541$	5.55927	0.239012	0.119506	−	0.992834i	$-0.461869\pi$
$541$	5.55927	0.239012	0.119506	+	0.992834i	$0.461869\pi$
$542$	−24.8636	−1.06798
$543$	−0.586527	−0.0251703
$544$	29.3066	1.25651
$545$	0.315056	0.0134955
$546$	−9.02263	−0.386133
$547$	8.51454	0.364055	0.182028	−	0.983293i	$-0.441734\pi$
$547$	8.51454	0.364055	0.182028	+	0.983293i	$0.441734\pi$
$548$	−17.6340	−0.753288
$549$	15.4364	0.658808
$550$	−23.9043	−1.01928
$551$	−0.563594	−0.0240099
$552$	−6.22340	−0.264885
$553$	38.8970	1.65407
$554$	−2.31656	−0.0984214
$555$	−0.526980	−0.0223690
$556$	18.4471	0.782330
$557$	33.6337	1.42510	0.712552	−	0.701619i	$-0.247539\pi$
$557$	33.6337	1.42510	0.712552	+	0.701619i	$0.247539\pi$
$558$	38.9620	1.64939
$559$	6.64980	0.281257
$560$	−1.29925	−0.0549032
$561$	3.85250	0.162653
$562$	−39.9376	−1.68467
$563$	−42.3907	−1.78655	−0.893277	−	0.449507i	$-0.851600\pi$
$563$	−42.3907	−1.78655	−0.893277	+	0.449507i	$0.851600\pi$
$564$	−1.42860	−0.0601548
$565$	−8.72371	−0.367009
$566$	65.9930	2.77389
$567$	20.0857	0.843519
$568$	36.6554	1.53803
$569$	−4.04277	−0.169482	−0.0847409	−	0.996403i	$-0.527006\pi$
$569$	−4.04277	−0.169482	−0.0847409	+	0.996403i	$0.527006\pi$
$570$	−0.310561	−0.0130080
$571$	−7.31309	−0.306043	−0.153022	−	0.988223i	$-0.548900\pi$
$571$	−7.31309	−0.306043	−0.153022	+	0.988223i	$0.548900\pi$
$572$	51.2306	2.14206
$573$	−2.23438	−0.0933426
$574$	6.74959	0.281723
$575$	31.2357	1.30262
$576$	37.0602	1.54417
$577$	36.3180	1.51194	0.755968	−	0.654608i	$-0.227166\pi$
$577$	36.3180	1.51194	0.755968	+	0.654608i	$0.227166\pi$
$578$	−42.1272	−1.75226
$579$	−1.43052	−0.0594505
$580$	3.04067	0.126257
$581$	−34.6847	−1.43896
$582$	−5.91218	−0.245068
$583$	14.1420	0.585701
$584$	−31.8357	−1.31737
$585$	−16.3340	−0.675327
$586$	44.3795	1.83330
$587$	−26.0352	−1.07459	−0.537294	−	0.843395i	$-0.680554\pi$
$587$	−26.0352	−1.07459	−0.537294	+	0.843395i	$0.680554\pi$
$588$	1.11346	0.0459182
$589$	3.23444	0.133273
$590$	−21.0178	−0.865288
$591$	−0.848613	−0.0349073
$592$	−1.32967	−0.0546491
$593$	−10.6742	−0.438335	−0.219168	−	0.975687i	$-0.570334\pi$
$593$	−10.6742	−0.438335	−0.219168	+	0.975687i	$0.570334\pi$
$594$	8.92295	0.366113
$595$	−12.8406	−0.526413
$596$	−36.4396	−1.49263
$597$	−3.19554	−0.130785
$598$	−106.714	−4.36384
$599$	5.62217	0.229716	0.114858	−	0.993382i	$-0.463359\pi$
$599$	5.62217	0.229716	0.114858	+	0.993382i	$0.463359\pi$
$600$	−3.48818	−0.142405
$601$	11.1937	0.456602	0.228301	−	0.973591i	$-0.426683\pi$
$601$	11.1937	0.456602	0.228301	+	0.973591i	$0.426683\pi$
$602$	5.98314	0.243854
$603$	−8.03282	−0.327122
$604$	34.4194	1.40050
$605$	4.44214	0.180599
$606$	−10.6221	−0.431495
$607$	3.15969	0.128248	0.0641240	−	0.997942i	$-0.479575\pi$
$607$	3.15969	0.128248	0.0641240	+	0.997942i	$0.479575\pi$
$608$	2.78453	0.112928
$609$	0.631181	0.0255767
$610$	−11.0210	−0.446227
$611$	−9.94322	−0.402260
$612$	−58.5219	−2.36561
$613$	−9.91213	−0.400347	−0.200174	−	0.979760i	$-0.564151\pi$
$613$	−9.91213	−0.400347	−0.200174	+	0.979760i	$0.564151\pi$
$614$	−33.3851	−1.34731
$615$	−0.289174	−0.0116606
$616$	18.7101	0.753850
$617$	−3.62288	−0.145851	−0.0729257	−	0.997337i	$-0.523234\pi$
$617$	−3.62288	−0.145851	−0.0729257	+	0.997337i	$0.523234\pi$
$618$	−2.40567	−0.0967702
$619$	19.0478	0.765597	0.382799	−	0.923832i	$-0.374960\pi$
$619$	19.0478	0.765597	0.382799	+	0.923832i	$0.374960\pi$
$620$	−17.4503	−0.700820
$621$	−11.6596	−0.467885
$622$	58.7426	2.35536
$623$	21.4015	0.857431
$624$	0.975360	0.0390456
$625$	13.4284	0.537137
$626$	−34.1518	−1.36498
$627$	0.366040	0.0146182
$628$	16.0236	0.639409
$629$	−13.1413	−0.523977
$630$	−14.6964	−0.585521
$631$	−5.17217	−0.205901	−0.102950	−	0.994686i	$-0.532828\pi$
$631$	−5.17217	−0.205901	−0.102950	+	0.994686i	$0.532828\pi$
$632$	−51.3748	−2.04358
$633$	0.782995	0.0311212
$634$	−25.1785	−0.999966
$635$	9.42693	0.374096
$636$	5.08404	0.201595
$637$	7.74980	0.307058
$638$	−5.71299	−0.226180
$639$	33.9357	1.34247
$640$	−17.5346	−0.693114
$641$	4.26079	0.168291	0.0841455	−	0.996453i	$-0.473184\pi$
$641$	4.26079	0.168291	0.0841455	+	0.996453i	$0.473184\pi$
$642$	−9.14100	−0.360766
$643$	33.7860	1.33239	0.666196	−	0.745777i	$-0.267922\pi$
$643$	33.7860	1.33239	0.666196	+	0.745777i	$0.267922\pi$
$644$	−60.2318	−2.37347
$645$	−0.256336	−0.0100932
$646$	−7.74445	−0.304701
$647$	−22.2849	−0.876110	−0.438055	−	0.898948i	$-0.644332\pi$
$647$	−22.2849	−0.876110	−0.438055	+	0.898948i	$0.644332\pi$
$648$	−26.5290	−1.04216
$649$	24.7724	0.972400
$650$	−59.8124	−2.34603
$651$	−3.62233	−0.141970
$652$	22.5582	0.883448
$653$	−4.21237	−0.164843	−0.0824214	−	0.996598i	$-0.526265\pi$
$653$	−4.21237	−0.164843	−0.0824214	+	0.996598i	$0.526265\pi$
$654$	−0.212805	−0.00832132
$655$	−16.2875	−0.636406
$656$	−0.729641	−0.0284877
$657$	−29.4735	−1.14987
$658$	−8.94638	−0.348766
$659$	−22.5401	−0.878039	−0.439020	−	0.898477i	$-0.644674\pi$
$659$	−22.5401	−0.878039	−0.439020	+	0.898477i	$0.644674\pi$
$660$	−1.97484	−0.0768704
$661$	20.9605	0.815269	0.407634	−	0.913145i	$-0.366354\pi$
$661$	20.9605	0.815269	0.407634	+	0.913145i	$0.366354\pi$
$662$	14.6713	0.570216
$663$	9.63958	0.374370
$664$	45.8112	1.77782
$665$	−1.22003	−0.0473108
$666$	−15.0406	−0.582811
$667$	7.46517	0.289053
$668$	8.49211	0.328569
$669$	−5.49868	−0.212591
$670$	5.73513	0.221567
$671$	12.9898	0.501464
$672$	−3.11845	−0.120297
$673$	−44.2860	−1.70710	−0.853549	−	0.521013i	$-0.825554\pi$
$673$	−44.2860	−1.70710	−0.853549	+	0.521013i	$0.825554\pi$
$674$	34.6562	1.33491
$675$	−6.53516	−0.251538
$676$	84.4232	3.24705
$677$	44.8834	1.72501	0.862504	−	0.506050i	$-0.168895\pi$
$677$	44.8834	1.72501	0.862504	+	0.506050i	$0.168895\pi$
$678$	5.89243	0.226297
$679$	−23.2258	−0.891326
$680$	16.9597	0.650376
$681$	4.25437	0.163028
$682$	32.7867	1.25547
$683$	50.7033	1.94011	0.970054	−	0.242891i	$-0.0780957\pi$
$683$	50.7033	1.94011	0.970054	+	0.242891i	$0.0780957\pi$
$684$	−5.56037	−0.212606
$685$	4.73119	0.180769
$686$	45.8374	1.75008
$687$	4.02662	0.153625
$688$	−0.646786	−0.0246585
$689$	35.3855	1.34808
$690$	4.11359	0.156602
$691$	8.88498	0.338001	0.169000	−	0.985616i	$-0.445946\pi$
$691$	8.88498	0.338001	0.169000	+	0.985616i	$0.445946\pi$
$692$	46.9002	1.78288
$693$	17.3218	0.658001
$694$	18.8862	0.716912
$695$	−4.94933	−0.187739
$696$	−0.833658	−0.0315997
$697$	−7.21112	−0.273140
$698$	−78.4915	−2.97095
$699$	3.02097	0.114264
$700$	−33.7596	−1.27599
$701$	−9.91077	−0.374325	−0.187162	−	0.982329i	$-0.559929\pi$
$701$	−9.91077	−0.374325	−0.187162	+	0.982329i	$0.559929\pi$
$702$	22.3267	0.842666
$703$	−1.24860	−0.0470918
$704$	31.1863	1.17538
$705$	0.383291	0.0144356
$706$	16.5629	0.623352
$707$	−41.7288	−1.56937
$708$	8.90565	0.334695
$709$	−1.65412	−0.0621219	−0.0310609	−	0.999517i	$-0.509889\pi$
$709$	−1.65412	−0.0621219	−0.0310609	+	0.999517i	$0.509889\pi$
$710$	−24.2288	−0.909290
$711$	−47.5629	−1.78375
$712$	−28.2668	−1.05934
$713$	−42.8424	−1.60446
$714$	8.67318	0.324586
$715$	−13.7451	−0.514038
$716$	25.6593	0.958932
$717$	−0.958994	−0.0358143
$718$	8.13127	0.303456
$719$	15.8866	0.592470	0.296235	−	0.955115i	$-0.404269\pi$
$719$	15.8866	0.592470	0.296235	+	0.955115i	$0.404269\pi$
$720$	1.58871	0.0592076
$721$	−9.45060	−0.351959
$722$	43.2789	1.61067
$723$	3.11902	0.115998
$724$	7.49757	0.278645
$725$	4.18419	0.155397
$726$	−3.00044	−0.111357
$727$	32.4126	1.20212	0.601058	−	0.799205i	$-0.294746\pi$
$727$	32.4126	1.20212	0.601058	+	0.799205i	$0.294746\pi$
$728$	46.8157	1.73510
$729$	−23.3266	−0.863948
$730$	21.0430	0.778836
$731$	−6.39225	−0.236426
$732$	4.66982	0.172601
$733$	34.0402	1.25730	0.628652	−	0.777687i	$-0.283607\pi$
$733$	34.0402	1.25730	0.628652	+	0.777687i	$0.283607\pi$
$734$	−59.4823	−2.19553
$735$	−0.298739	−0.0110192
$736$	−36.8829	−1.35952
$737$	−6.75965	−0.248995
$738$	−8.25334	−0.303810
$739$	17.9665	0.660907	0.330453	−	0.943822i	$-0.392798\pi$
$739$	17.9665	0.660907	0.330453	+	0.943822i	$0.392798\pi$
$740$	6.73637	0.247634
$741$	0.915891	0.0336461
$742$	31.8380	1.16881
$743$	−15.2118	−0.558068	−0.279034	−	0.960281i	$-0.590014\pi$
$743$	−15.2118	−0.558068	−0.279034	+	0.960281i	$0.590014\pi$
$744$	4.78433	0.175402
$745$	9.77672	0.358191
$746$	−4.17470	−0.152847
$747$	42.4121	1.55178
$748$	−49.2464	−1.80063
$749$	−35.9102	−1.31213
$750$	5.06083	0.184796
$751$	−23.5093	−0.857867	−0.428934	−	0.903336i	$-0.641111\pi$
$751$	−23.5093	−0.857867	−0.428934	+	0.903336i	$0.641111\pi$
$752$	0.967117	0.0352671
$753$	7.32605	0.266976
$754$	−14.2948	−0.520588
$755$	−9.23468	−0.336085
$756$	12.6017	0.458321
$757$	−2.83440	−0.103018	−0.0515090	−	0.998673i	$-0.516403\pi$
$757$	−2.83440	−0.103018	−0.0515090	+	0.998673i	$0.516403\pi$
$758$	−51.5042	−1.87072
$759$	−4.84844	−0.175987
$760$	1.61141	0.0584519
$761$	−36.3142	−1.31639	−0.658194	−	0.752848i	$-0.728679\pi$
$761$	−36.3142	−1.31639	−0.658194	+	0.752848i	$0.728679\pi$
$762$	−6.36742	−0.230667
$763$	−0.835998	−0.0302651
$764$	28.5620	1.03334
$765$	15.7014	0.567684
$766$	40.4996	1.46331
$767$	61.9845	2.23813
$768$	5.18305	0.187027
$769$	34.1384	1.23106	0.615530	−	0.788113i	$-0.288942\pi$
$769$	34.1384	1.23106	0.615530	+	0.788113i	$0.288942\pi$
$770$	−12.3671	−0.445680
$771$	−7.39190	−0.266213
$772$	18.2864	0.658140
$773$	45.7822	1.64667	0.823336	−	0.567554i	$-0.192110\pi$
$773$	45.7822	1.64667	0.823336	+	0.567554i	$0.192110\pi$
$774$	−7.31612	−0.262973
$775$	−24.0129	−0.862570
$776$	30.6765	1.10122
$777$	1.39833	0.0501649
$778$	−72.2624	−2.59073
$779$	−0.685154	−0.0245482
$780$	−4.94136	−0.176929
$781$	28.5570	1.02185
$782$	102.580	3.66827
$783$	−1.56187	−0.0558167
$784$	−0.753776	−0.0269206
$785$	−4.29910	−0.153442
$786$	11.0014	0.392407
$787$	−31.4895	−1.12248	−0.561239	−	0.827654i	$-0.689675\pi$
$787$	−31.4895	−1.12248	−0.561239	+	0.827654i	$0.689675\pi$
$788$	10.8478	0.386437
$789$	4.66911	0.166225
$790$	33.9581	1.20818
$791$	23.1482	0.823057
$792$	−22.8785	−0.812952
$793$	32.5025	1.15420
$794$	−71.3278	−2.53133
$795$	−1.36404	−0.0483776
$796$	40.8485	1.44784
$797$	38.4587	1.36228	0.681138	−	0.732155i	$-0.261485\pi$
$797$	38.4587	1.36228	0.681138	+	0.732155i	$0.261485\pi$
$798$	0.824070	0.0291718
$799$	9.55811	0.338142
$800$	−20.6727	−0.730890
$801$	−26.1695	−0.924654
$802$	−80.0598	−2.82701
$803$	−24.8021	−0.875247
$804$	−2.43009	−0.0857027
$805$	16.1601	0.569570
$806$	82.0376	2.88965
$807$	5.56792	0.196000
$808$	55.1150	1.93894
$809$	33.7656	1.18714	0.593568	−	0.804784i	$-0.297719\pi$
$809$	33.7656	1.18714	0.593568	+	0.804784i	$0.297719\pi$
$810$	17.5353	0.616128
$811$	13.6739	0.480155	0.240077	−	0.970754i	$-0.422827\pi$
$811$	13.6739	0.480155	0.240077	+	0.970754i	$0.422827\pi$
$812$	−8.06837	−0.283144
$813$	−2.82658	−0.0991326
$814$	−12.6567	−0.443617
$815$	−6.05235	−0.212005
$816$	−0.937583	−0.0328220
$817$	−0.607351	−0.0212485
$818$	−7.18167	−0.251101
$819$	43.3420	1.51449
$820$	3.69650	0.129088
$821$	−28.9638	−1.01084	−0.505421	−	0.862873i	$-0.668663\pi$
$821$	−28.9638	−1.01084	−0.505421	+	0.862873i	$0.668663\pi$
$822$	−3.19568	−0.111462
$823$	39.6410	1.38180	0.690899	−	0.722951i	$-0.257215\pi$
$823$	39.6410	1.38180	0.690899	+	0.722951i	$0.257215\pi$
$824$	12.4823	0.434840
$825$	−2.71753	−0.0946121
$826$	55.7704	1.94050
$827$	13.6433	0.474425	0.237213	−	0.971458i	$-0.423766\pi$
$827$	13.6433	0.474425	0.237213	+	0.971458i	$0.423766\pi$
$828$	73.6509	2.55954
$829$	−52.3451	−1.81802	−0.909010	−	0.416774i	$-0.863161\pi$
$829$	−52.3451	−1.81802	−0.909010	+	0.416774i	$0.863161\pi$
$830$	−30.2806	−1.05106
$831$	−0.263356	−0.00913571
$832$	78.0332	2.70532
$833$	−7.44964	−0.258115
$834$	3.34302	0.115759
$835$	−2.27842	−0.0788481
$836$	−4.67908	−0.161829
$837$	8.96351	0.309824
$838$	70.4512	2.43370
$839$	11.9817	0.413655	0.206828	−	0.978377i	$-0.433686\pi$
$839$	11.9817	0.413655	0.206828	+	0.978377i	$0.433686\pi$
$840$	−1.80465	−0.0622663
$841$	1.00000	0.0344828
$842$	−3.51668	−0.121193
$843$	−4.54025	−0.156375
$844$	−10.0090	−0.344524
$845$	−22.6507	−0.779206
$846$	10.9395	0.376109
$847$	−11.7872	−0.405012
$848$	−3.44174	−0.118190
$849$	7.50233	0.257479
$850$	57.4958	1.97209
$851$	16.5385	0.566934
$852$	10.2662	0.351715
$853$	3.43420	0.117585	0.0587924	−	0.998270i	$-0.481275\pi$
$853$	3.43420	0.117585	0.0587924	+	0.998270i	$0.481275\pi$
$854$	29.2441	1.00071
$855$	1.49184	0.0510200
$856$	47.4298	1.62112
$857$	6.55711	0.223987	0.111993	−	0.993709i	$-0.464276\pi$
$857$	6.55711	0.223987	0.111993	+	0.993709i	$0.464276\pi$
$858$	9.28414	0.316955
$859$	6.39955	0.218350	0.109175	−	0.994023i	$-0.465179\pi$
$859$	6.39955	0.218350	0.109175	+	0.994023i	$0.465179\pi$
$860$	3.27674	0.111736
$861$	0.767319	0.0261502
$862$	−31.4116	−1.06988
$863$	27.1358	0.923713	0.461856	−	0.886955i	$-0.347184\pi$
$863$	27.1358	0.923713	0.461856	+	0.886955i	$0.347184\pi$
$864$	7.71667	0.262527
$865$	−12.5833	−0.427844
$866$	−52.8741	−1.79673
$867$	−4.78918	−0.162649
$868$	46.3041	1.57166
$869$	−40.0244	−1.35773
$870$	0.551038	0.0186819
$871$	−16.9138	−0.573101
$872$	1.10418	0.0373922
$873$	28.4003	0.961205
$874$	9.74654	0.329682
$875$	19.8814	0.672112
$876$	−8.91634	−0.301255
$877$	29.3391	0.990711	0.495356	−	0.868690i	$-0.335038\pi$
$877$	29.3391	0.990711	0.495356	+	0.868690i	$0.335038\pi$
$878$	34.4807	1.16367
$879$	5.04523	0.170171
$880$	1.33690	0.0450670
$881$	−26.2554	−0.884567	−0.442284	−	0.896875i	$-0.645832\pi$
$881$	−26.2554	−0.884567	−0.442284	+	0.896875i	$0.645832\pi$
$882$	−8.52634	−0.287097
$883$	23.5626	0.792944	0.396472	−	0.918047i	$-0.370234\pi$
$883$	23.5626	0.792944	0.396472	+	0.918047i	$0.370234\pi$
$884$	−123.223	−4.14442
$885$	−2.38938	−0.0803181
$886$	−24.9530	−0.838312
$887$	44.8576	1.50617	0.753085	−	0.657923i	$-0.228565\pi$
$887$	44.8576	1.50617	0.753085	+	0.657923i	$0.228565\pi$
$888$	−1.84691	−0.0619781
$889$	−25.0142	−0.838950
$890$	18.6840	0.626290
$891$	−20.6678	−0.692398
$892$	70.2896	2.35347
$893$	0.908151	0.0303901
$894$	−6.60369	−0.220860
$895$	−6.88436	−0.230119
$896$	46.5277	1.55438
$897$	−12.1316	−0.405062
$898$	12.0933	0.403560
$899$	−5.73897	−0.191405
$900$	41.2809	1.37603
$901$	−34.0150	−1.13321
$902$	−6.94522	−0.231251
$903$	0.680185	0.0226351
$904$	−30.5740	−1.01688
$905$	−2.01159	−0.0668675
$906$	6.23757	0.207229
$907$	−13.4236	−0.445722	−0.222861	−	0.974850i	$-0.571540\pi$
$907$	−13.4236	−0.445722	−0.222861	+	0.974850i	$0.571540\pi$
$908$	−54.3835	−1.80478
$909$	51.0256	1.69241
$910$	−30.9446	−1.02580
$911$	19.8653	0.658167	0.329083	−	0.944301i	$-0.393260\pi$
$911$	19.8653	0.658167	0.329083	+	0.944301i	$0.393260\pi$
$912$	−0.0890832	−0.00294984
$913$	35.6899	1.18116
$914$	−6.04684	−0.200012
$915$	−1.25291	−0.0414198
$916$	−51.4722	−1.70069
$917$	43.2187	1.42721
$918$	−21.4620	−0.708350
$919$	2.66518	0.0879160	0.0439580	−	0.999033i	$-0.486003\pi$
$919$	2.66518	0.0879160	0.0439580	+	0.999033i	$0.486003\pi$
$920$	−21.3441	−0.703696
$921$	−3.79535	−0.125061
$922$	15.0530	0.495744
$923$	71.4543	2.35195
$924$	5.24020	0.172390
$925$	9.26976	0.304788
$926$	−4.35579	−0.143140
$927$	11.5561	0.379552
$928$	−4.94067	−0.162185
$929$	−3.31151	−0.108647	−0.0543235	−	0.998523i	$-0.517300\pi$
$929$	−3.31151	−0.108647	−0.0543235	+	0.998523i	$0.517300\pi$
$930$	−3.16239	−0.103699
$931$	−0.707818	−0.0231978
$932$	−38.6170	−1.26494
$933$	6.67807	0.218630
$934$	−5.06416	−0.165704
$935$	13.2128	0.432103
$936$	−57.2457	−1.87114
$937$	−7.79598	−0.254684	−0.127342	−	0.991859i	$-0.540645\pi$
$937$	−7.79598	−0.254684	−0.127342	+	0.991859i	$0.540645\pi$
$938$	−15.2181	−0.496889
$939$	−3.88251	−0.126701
$940$	−4.89960	−0.159807
$941$	−18.3652	−0.598689	−0.299345	−	0.954145i	$-0.596768\pi$
$941$	−18.3652	−0.598689	−0.299345	+	0.954145i	$0.596768\pi$
$942$	2.90383	0.0946119
$943$	9.07532	0.295533
$944$	−6.02886	−0.196223
$945$	−3.38103	−0.109985
$946$	−6.15655	−0.200167
$947$	−34.7337	−1.12869	−0.564347	−	0.825538i	$-0.690872\pi$
$947$	−34.7337	−1.12869	−0.564347	+	0.825538i	$0.690872\pi$
$948$	−14.3887	−0.467325
$949$	−62.0589	−2.01452
$950$	5.46289	0.177239
$951$	−2.86239	−0.0928192
$952$	−45.0024	−1.45854
$953$	28.8033	0.933029	0.466515	−	0.884513i	$-0.345509\pi$
$953$	28.8033	0.933029	0.466515	+	0.884513i	$0.345509\pi$
$954$	−38.9312	−1.26045
$955$	−7.66317	−0.247974
$956$	12.2588	0.396478
$957$	−0.649475	−0.0209945
$958$	−47.1552	−1.52352
$959$	−12.5541	−0.405395
$960$	−3.00802	−0.0970836
$961$	1.93574	0.0624431
$962$	−31.6692	−1.02105
$963$	43.9106	1.41500
$964$	−39.8703	−1.28414
$965$	−4.90621	−0.157937
$966$	−10.9154	−0.351196
$967$	39.2204	1.26124	0.630621	−	0.776091i	$-0.282800\pi$
$967$	39.2204	1.26124	0.630621	+	0.776091i	$0.282800\pi$
$968$	15.5684	0.500386
$969$	−0.880418	−0.0282831
$970$	−20.2768	−0.651048
$971$	46.2853	1.48537	0.742683	−	0.669643i	$-0.233553\pi$
$971$	46.2853	1.48537	0.742683	+	0.669643i	$0.233553\pi$
$972$	−23.2040	−0.744270
$973$	13.1330	0.421024
$974$	28.6085	0.916676
$975$	−6.79970	−0.217765
$976$	−3.16132	−0.101192
$977$	−35.2942	−1.12916	−0.564580	−	0.825378i	$-0.690962\pi$
$977$	−35.2942	−1.12916	−0.564580	+	0.825378i	$0.690962\pi$
$978$	4.08806	0.130722
$979$	−22.0217	−0.703818
$980$	3.81878	0.121986
$981$	1.02225	0.0326379
$982$	8.92793	0.284902
$983$	20.4697	0.652882	0.326441	−	0.945218i	$-0.394151\pi$
$983$	20.4697	0.652882	0.326441	+	0.945218i	$0.394151\pi$
$984$	−1.01347	−0.0323082
$985$	−2.91046	−0.0927348
$986$	13.7412	0.437609
$987$	−1.01706	−0.0323733
$988$	−11.7078	−0.372475
$989$	8.04476	0.255809
$990$	15.1224	0.480621
$991$	−8.97343	−0.285051	−0.142525	−	0.989791i	$-0.545522\pi$
$991$	−8.97343	−0.285051	−0.142525	+	0.989791i	$0.545522\pi$
$992$	28.3543	0.900250
$993$	1.66789	0.0529288
$994$	64.2908	2.03918
$995$	−10.9596	−0.347443
$996$	12.8305	0.406551
$997$	43.1875	1.36776	0.683880	−	0.729594i	$-0.260291\pi$
$997$	43.1875	1.36776	0.683880	+	0.729594i	$0.260291\pi$
$998$	64.0719	2.02816
$999$	−3.46020	−0.109476

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8033.2.a.e.1.18	✓	169

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8033.2.a.e.1.18	✓	169	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8033 = 29 \cdot 277 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.31656 q^{2} -0.263356 q^{3} +3.36647 q^{4} -0.903221 q^{5} +0.610081 q^{6} +2.39669 q^{7} -3.16552 q^{8} -2.93064 q^{9} +O(q^{10})\)	\(q-2.31656 q^{2} -0.263356 q^{3} +3.36647 q^{4} -0.903221 q^{5} +0.610081 q^{6} +2.39669 q^{7} -3.16552 q^{8} -2.93064 q^{9} +2.09237 q^{10} -2.46615 q^{11} -0.886580 q^{12} -6.17071 q^{13} -5.55208 q^{14} +0.237868 q^{15} +0.600187 q^{16} +5.93171 q^{17} +6.78903 q^{18} +0.563594 q^{19} -3.04067 q^{20} -0.631181 q^{21} +5.71299 q^{22} -7.46517 q^{23} +0.833658 q^{24} -4.18419 q^{25} +14.2948 q^{26} +1.56187 q^{27} +8.06837 q^{28} -1.00000 q^{29} -0.551038 q^{30} +5.73897 q^{31} +4.94067 q^{32} +0.649475 q^{33} -13.7412 q^{34} -2.16474 q^{35} -9.86593 q^{36} -2.21543 q^{37} -1.30560 q^{38} +1.62509 q^{39} +2.85916 q^{40} -1.21569 q^{41} +1.46217 q^{42} -1.07764 q^{43} -8.30222 q^{44} +2.64702 q^{45} +17.2936 q^{46} +1.61136 q^{47} -0.158063 q^{48} -1.25590 q^{49} +9.69295 q^{50} -1.56215 q^{51} -20.7735 q^{52} -5.73444 q^{53} -3.61817 q^{54} +2.22748 q^{55} -7.58675 q^{56} -0.148426 q^{57} +2.31656 q^{58} -10.0450 q^{59} +0.800777 q^{60} -5.26723 q^{61} -13.2947 q^{62} -7.02383 q^{63} -12.6457 q^{64} +5.57351 q^{65} -1.50455 q^{66} +2.74097 q^{67} +19.9689 q^{68} +1.96600 q^{69} +5.01475 q^{70} -11.5796 q^{71} +9.27701 q^{72} +10.0570 q^{73} +5.13218 q^{74} +1.10193 q^{75} +1.89732 q^{76} -5.91058 q^{77} -3.76463 q^{78} +16.2295 q^{79} -0.542102 q^{80} +8.38060 q^{81} +2.81622 q^{82} -14.4719 q^{83} -2.12485 q^{84} -5.35765 q^{85} +2.49642 q^{86} +0.263356 q^{87} +7.80664 q^{88} +8.92961 q^{89} -6.13199 q^{90} -14.7892 q^{91} -25.1313 q^{92} -1.51139 q^{93} -3.73281 q^{94} -0.509050 q^{95} -1.30115 q^{96} -9.69082 q^{97} +2.90938 q^{98} +7.22740 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 169 q + 3 q^{2} + 8 q^{3} + 183 q^{4} + 13 q^{5} + 17 q^{6} + 76 q^{7} + 6 q^{8} + 181 q^{9}+O(q^{10}) \) 169 * q + 3 * q^2 + 8 * q^3 + 183 * q^4 + 13 * q^5 + 17 * q^6 + 76 * q^7 + 6 * q^8 + 181 * q^9	\( 169 q + 3 q^{2} + 8 q^{3} + 183 q^{4} + 13 q^{5} + 17 q^{6} + 76 q^{7} + 6 q^{8} + 181 q^{9} + 30 q^{10} + 2 q^{11} + 25 q^{12} + 63 q^{13} - 3 q^{14} + 26 q^{15} + 219 q^{16} + 14 q^{17} + 31 q^{18} + 51 q^{19} + 49 q^{20} + 16 q^{21} + 53 q^{22} + 50 q^{23} + 43 q^{24} + 214 q^{25} - 2 q^{26} + 23 q^{27} + 149 q^{28} - 169 q^{29} + 26 q^{30} + 65 q^{31} + 25 q^{32} + 57 q^{33} + 60 q^{34} + 60 q^{35} + 218 q^{36} + 52 q^{37} + 35 q^{38} + 49 q^{39} + 72 q^{40} + 3 q^{41} + 78 q^{42} + 132 q^{43} + 64 q^{45} + 32 q^{46} + 54 q^{47} + 76 q^{48} + 245 q^{49} - 6 q^{50} + 44 q^{51} + 193 q^{52} + 58 q^{53} + 54 q^{54} + 213 q^{55} + 12 q^{56} + 52 q^{57} - 3 q^{58} + 25 q^{59} + 32 q^{60} + 100 q^{61} + 78 q^{62} + 227 q^{63} + 292 q^{64} + 37 q^{65} + 59 q^{66} + 110 q^{67} + 24 q^{68} - 20 q^{69} + 47 q^{70} + 44 q^{71} + 71 q^{72} + 139 q^{73} + 35 q^{74} + 53 q^{75} + 92 q^{76} + 22 q^{77} + 83 q^{78} + 137 q^{79} + 90 q^{80} + 177 q^{81} + 91 q^{82} + 126 q^{83} + 36 q^{84} + 95 q^{85} + 21 q^{86} - 8 q^{87} + 75 q^{88} + 19 q^{89} + 130 q^{90} + 102 q^{91} + 68 q^{92} + 22 q^{93} + 82 q^{94} + 37 q^{95} + 107 q^{96} + 116 q^{97} - 13 q^{98} - 11 q^{99}+O(q^{100}) \) 169 * q + 3 * q^2 + 8 * q^3 + 183 * q^4 + 13 * q^5 + 17 * q^6 + 76 * q^7 + 6 * q^8 + 181 * q^9 + 30 * q^10 + 2 * q^11 + 25 * q^12 + 63 * q^13 - 3 * q^14 + 26 * q^15 + 219 * q^16 + 14 * q^17 + 31 * q^18 + 51 * q^19 + 49 * q^20 + 16 * q^21 + 53 * q^22 + 50 * q^23 + 43 * q^24 + 214 * q^25 - 2 * q^26 + 23 * q^27 + 149 * q^28 - 169 * q^29 + 26 * q^30 + 65 * q^31 + 25 * q^32 + 57 * q^33 + 60 * q^34 + 60 * q^35 + 218 * q^36 + 52 * q^37 + 35 * q^38 + 49 * q^39 + 72 * q^40 + 3 * q^41 + 78 * q^42 + 132 * q^43 + 64 * q^45 + 32 * q^46 + 54 * q^47 + 76 * q^48 + 245 * q^49 - 6 * q^50 + 44 * q^51 + 193 * q^52 + 58 * q^53 + 54 * q^54 + 213 * q^55 + 12 * q^56 + 52 * q^57 - 3 * q^58 + 25 * q^59 + 32 * q^60 + 100 * q^61 + 78 * q^62 + 227 * q^63 + 292 * q^64 + 37 * q^65 + 59 * q^66 + 110 * q^67 + 24 * q^68 - 20 * q^69 + 47 * q^70 + 44 * q^71 + 71 * q^72 + 139 * q^73 + 35 * q^74 + 53 * q^75 + 92 * q^76 + 22 * q^77 + 83 * q^78 + 137 * q^79 + 90 * q^80 + 177 * q^81 + 91 * q^82 + 126 * q^83 + 36 * q^84 + 95 * q^85 + 21 * q^86 - 8 * q^87 + 75 * q^88 + 19 * q^89 + 130 * q^90 + 102 * q^91 + 68 * q^92 + 22 * q^93 + 82 * q^94 + 37 * q^95 + 107 * q^96 + 116 * q^97 - 13 * q^98 - 11 * q^99

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