LMFDB - Embedded newform 8033.2.a.b.1.11

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:	$1$
Dimension:	$153$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
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)

$f(q)$	$=$	$q-2.56362 q^{2} +2.58113 q^{3} +4.57213 q^{4} +0.513446 q^{5} -6.61703 q^{6} +0.254616 q^{7} -6.59395 q^{8} +3.66224 q^{9} +O(q^{10})$	\(q-2.56362 q^{2} +2.58113 q^{3} +4.57213 q^{4} +0.513446 q^{5} -6.61703 q^{6} +0.254616 q^{7} -6.59395 q^{8} +3.66224 q^{9} -1.31628 q^{10} -1.89742 q^{11} +11.8013 q^{12} +1.22149 q^{13} -0.652738 q^{14} +1.32527 q^{15} +7.76009 q^{16} -2.48498 q^{17} -9.38859 q^{18} -3.52408 q^{19} +2.34754 q^{20} +0.657198 q^{21} +4.86426 q^{22} +5.64278 q^{23} -17.0198 q^{24} -4.73637 q^{25} -3.13142 q^{26} +1.70934 q^{27} +1.16414 q^{28} -1.00000 q^{29} -3.39749 q^{30} -3.94919 q^{31} -6.70601 q^{32} -4.89750 q^{33} +6.37053 q^{34} +0.130732 q^{35} +16.7442 q^{36} +3.40699 q^{37} +9.03438 q^{38} +3.15282 q^{39} -3.38563 q^{40} +1.34674 q^{41} -1.68480 q^{42} -7.06838 q^{43} -8.67526 q^{44} +1.88036 q^{45} -14.4659 q^{46} +7.66337 q^{47} +20.0298 q^{48} -6.93517 q^{49} +12.1422 q^{50} -6.41406 q^{51} +5.58479 q^{52} +4.65646 q^{53} -4.38209 q^{54} -0.974223 q^{55} -1.67893 q^{56} -9.09611 q^{57} +2.56362 q^{58} -12.6835 q^{59} +6.05931 q^{60} -0.953728 q^{61} +10.1242 q^{62} +0.932467 q^{63} +1.67144 q^{64} +0.627166 q^{65} +12.5553 q^{66} +4.38761 q^{67} -11.3616 q^{68} +14.5648 q^{69} -0.335146 q^{70} -9.23780 q^{71} -24.1486 q^{72} +13.4858 q^{73} -8.73420 q^{74} -12.2252 q^{75} -16.1125 q^{76} -0.483115 q^{77} -8.08261 q^{78} -12.9080 q^{79} +3.98439 q^{80} -6.57470 q^{81} -3.45253 q^{82} -13.1072 q^{83} +3.00479 q^{84} -1.27590 q^{85} +18.1206 q^{86} -2.58113 q^{87} +12.5115 q^{88} +6.95117 q^{89} -4.82053 q^{90} +0.311010 q^{91} +25.7995 q^{92} -10.1934 q^{93} -19.6459 q^{94} -1.80942 q^{95} -17.3091 q^{96} -0.132599 q^{97} +17.7791 q^{98} -6.94882 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 153 q - 3 q^{2} - 12 q^{3} + 135 q^{4} - 11 q^{5} - 17 q^{6} - 76 q^{7} - 12 q^{8} + 133 q^{9}+O(q^{10}) $ 153 * q - 3 * q^2 - 12 * q^3 + 135 * q^4 - 11 * q^5 - 17 * q^6 - 76 * q^7 - 12 * q^8 + 133 * q^9	\( 153 q - 3 q^{2} - 12 q^{3} + 135 q^{4} - 11 q^{5} - 17 q^{6} - 76 q^{7} - 12 q^{8} + 133 q^{9} - 30 q^{10} + 4 q^{11} - 39 q^{12} - 65 q^{13} + q^{14} - 26 q^{15} + 107 q^{16} - 20 q^{17} - 21 q^{18} - 65 q^{19} - 23 q^{20} - 24 q^{21} - 59 q^{22} - 62 q^{23} - 59 q^{24} + 102 q^{25} - 18 q^{26} - 57 q^{27} - 155 q^{28} - 153 q^{29} - 82 q^{30} - 49 q^{31} - 17 q^{32} - 59 q^{33} - 68 q^{34} - 36 q^{35} + 74 q^{36} - 30 q^{37} - 67 q^{38} - 47 q^{39} - 108 q^{40} - 9 q^{41} - 62 q^{42} - 90 q^{43} - 14 q^{44} - 56 q^{45} - 52 q^{46} - 54 q^{47} - 76 q^{48} + 101 q^{49} - 36 q^{50} - 60 q^{51} - 191 q^{52} - 38 q^{53} - 82 q^{54} - 215 q^{55} + 24 q^{56} - 52 q^{57} + 3 q^{58} - 55 q^{59} - 60 q^{60} - 90 q^{61} - 66 q^{62} - 229 q^{63} + 52 q^{64} - 67 q^{65} - 29 q^{66} - 114 q^{67} - 78 q^{68} - 68 q^{69} - 61 q^{70} - 52 q^{71} - 47 q^{72} - 83 q^{73} - 21 q^{74} - 47 q^{75} - 100 q^{76} - 32 q^{77} - 17 q^{78} - 151 q^{79} - 24 q^{80} + 81 q^{81} - 151 q^{82} - 94 q^{83} - 84 q^{84} - 77 q^{85} - 43 q^{86} + 12 q^{87} - 121 q^{88} + 11 q^{89} - 14 q^{90} - 66 q^{91} - 156 q^{92} - 66 q^{93} - 22 q^{94} - 67 q^{95} - 131 q^{96} - 78 q^{97} - 67 q^{98} - 41 q^{99}+O(q^{100}) \) 153 * q - 3 * q^2 - 12 * q^3 + 135 * q^4 - 11 * q^5 - 17 * q^6 - 76 * q^7 - 12 * q^8 + 133 * q^9 - 30 * q^10 + 4 * q^11 - 39 * q^12 - 65 * q^13 + q^14 - 26 * q^15 + 107 * q^16 - 20 * q^17 - 21 * q^18 - 65 * q^19 - 23 * q^20 - 24 * q^21 - 59 * q^22 - 62 * q^23 - 59 * q^24 + 102 * q^25 - 18 * q^26 - 57 * q^27 - 155 * q^28 - 153 * q^29 - 82 * q^30 - 49 * q^31 - 17 * q^32 - 59 * q^33 - 68 * q^34 - 36 * q^35 + 74 * q^36 - 30 * q^37 - 67 * q^38 - 47 * q^39 - 108 * q^40 - 9 * q^41 - 62 * q^42 - 90 * q^43 - 14 * q^44 - 56 * q^45 - 52 * q^46 - 54 * q^47 - 76 * q^48 + 101 * q^49 - 36 * q^50 - 60 * q^51 - 191 * q^52 - 38 * q^53 - 82 * q^54 - 215 * q^55 + 24 * q^56 - 52 * q^57 + 3 * q^58 - 55 * q^59 - 60 * q^60 - 90 * q^61 - 66 * q^62 - 229 * q^63 + 52 * q^64 - 67 * q^65 - 29 * q^66 - 114 * q^67 - 78 * q^68 - 68 * q^69 - 61 * q^70 - 52 * q^71 - 47 * q^72 - 83 * q^73 - 21 * q^74 - 47 * q^75 - 100 * q^76 - 32 * q^77 - 17 * q^78 - 151 * q^79 - 24 * q^80 + 81 * q^81 - 151 * q^82 - 94 * q^83 - 84 * q^84 - 77 * q^85 - 43 * q^86 + 12 * q^87 - 121 * q^88 + 11 * q^89 - 14 * q^90 - 66 * q^91 - 156 * q^92 - 66 * q^93 - 22 * q^94 - 67 * q^95 - 131 * q^96 - 78 * q^97 - 67 * q^98 - 41 * 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 $

$2$	−2.56362	−1.81275	−0.906375	−	0.422474i	$-0.861162\pi$
$2$	−2.56362	−1.81275	−0.906375	+	0.422474i	$0.861162\pi$
$3$	2.58113	1.49022	0.745109	−	0.666943i	$-0.232398\pi$
$3$	2.58113	1.49022	0.745109	+	0.666943i	$0.232398\pi$
$4$	4.57213	2.28606
$5$	0.513446	0.229620	0.114810	−	0.993387i	$-0.463374\pi$
$5$	0.513446	0.229620	0.114810	+	0.993387i	$0.463374\pi$
$6$	−6.61703	−2.70139
$7$	0.254616	0.0962359	0.0481180	−	0.998842i	$-0.484678\pi$
$7$	0.254616	0.0962359	0.0481180	+	0.998842i	$0.484678\pi$
$8$	−6.59395	−2.33131
$9$	3.66224	1.22075
$10$	−1.31628	−0.416244
$11$	−1.89742	−0.572094	−0.286047	−	0.958216i	$-0.592341\pi$
$11$	−1.89742	−0.572094	−0.286047	+	0.958216i	$0.592341\pi$
$12$	11.8013	3.40673
$13$	1.22149	0.338779	0.169390	−	0.985549i	$-0.445820\pi$
$13$	1.22149	0.338779	0.169390	+	0.985549i	$0.445820\pi$
$14$	−0.652738	−0.174452
$15$	1.32527	0.342184
$16$	7.76009	1.94002
$17$	−2.48498	−0.602696	−0.301348	−	0.953514i	$-0.597437\pi$
$17$	−2.48498	−0.602696	−0.301348	+	0.953514i	$0.597437\pi$
$18$	−9.38859	−2.21291
$19$	−3.52408	−0.808478	−0.404239	−	0.914653i	$-0.632464\pi$
$19$	−3.52408	−0.808478	−0.404239	+	0.914653i	$0.632464\pi$
$20$	2.34754	0.524926
$21$	0.657198	0.143412
$22$	4.86426	1.03706
$23$	5.64278	1.17660	0.588300	−	0.808643i	$-0.299797\pi$
$23$	5.64278	1.17660	0.588300	+	0.808643i	$0.299797\pi$
$24$	−17.0198	−3.47416
$25$	−4.73637	−0.947275
$26$	−3.13142	−0.614122
$27$	1.70934	0.328963
$28$	1.16414	0.220001
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−3.39749	−0.620293
$31$	−3.94919	−0.709295	−0.354648	−	0.935000i	$-0.615399\pi$
$31$	−3.94919	−0.709295	−0.354648	+	0.935000i	$0.615399\pi$
$32$	−6.70601	−1.18547
$33$	−4.89750	−0.852545
$34$	6.37053	1.09254
$35$	0.130732	0.0220977
$36$	16.7442	2.79071
$37$	3.40699	0.560105	0.280052	−	0.959985i	$-0.409648\pi$
$37$	3.40699	0.560105	0.280052	+	0.959985i	$0.409648\pi$
$38$	9.03438	1.46557
$39$	3.15282	0.504855
$40$	−3.38563	−0.535316
$41$	1.34674	0.210326	0.105163	−	0.994455i	$-0.466464\pi$
$41$	1.34674	0.210326	0.105163	+	0.994455i	$0.466464\pi$
$42$	−1.68480	−0.259971
$43$	−7.06838	−1.07792	−0.538959	−	0.842332i	$-0.681182\pi$
$43$	−7.06838	−1.07792	−0.538959	+	0.842332i	$0.681182\pi$
$44$	−8.67526	−1.30784
$45$	1.88036	0.280308
$46$	−14.4659	−2.13288
$47$	7.66337	1.11782	0.558908	−	0.829229i	$-0.311220\pi$
$47$	7.66337	1.11782	0.558908	+	0.829229i	$0.311220\pi$
$48$	20.0298	2.89106
$49$	−6.93517	−0.990739
$50$	12.1422	1.71717
$51$	−6.41406	−0.898148
$52$	5.58479	0.774471
$53$	4.65646	0.639614	0.319807	−	0.947483i	$-0.396382\pi$
$53$	4.65646	0.639614	0.319807	+	0.947483i	$0.396382\pi$
$54$	−4.38209	−0.596327
$55$	−0.974223	−0.131364
$56$	−1.67893	−0.224356
$57$	−9.09611	−1.20481
$58$	2.56362	0.336619
$59$	−12.6835	−1.65125	−0.825626	−	0.564218i	$-0.809178\pi$
$59$	−12.6835	−1.65125	−0.825626	+	0.564218i	$0.809178\pi$
$60$	6.05931	0.782253
$61$	−0.953728	−0.122112	−0.0610562	−	0.998134i	$-0.519447\pi$
$61$	−0.953728	−0.122112	−0.0610562	+	0.998134i	$0.519447\pi$
$62$	10.1242	1.28577
$63$	0.932467	0.117480
$64$	1.67144	0.208930
$65$	0.627166	0.0777904
$66$	12.5553	1.54545
$67$	4.38761	0.536032	0.268016	−	0.963414i	$-0.413632\pi$
$67$	4.38761	0.536032	0.268016	+	0.963414i	$0.413632\pi$
$68$	−11.3616	−1.37780
$69$	14.5648	1.75339
$70$	−0.335146	−0.0400576
$71$	−9.23780	−1.09632	−0.548162	−	0.836372i	$-0.684672\pi$
$71$	−9.23780	−1.09632	−0.548162	+	0.836372i	$0.684672\pi$
$72$	−24.1486	−2.84595
$73$	13.4858	1.57840	0.789198	−	0.614139i	$-0.210497\pi$
$73$	13.4858	1.57840	0.789198	+	0.614139i	$0.210497\pi$
$74$	−8.73420	−1.01533
$75$	−12.2252	−1.41165
$76$	−16.1125	−1.84823
$77$	−0.483115	−0.0550560
$78$	−8.08261	−0.915175
$79$	−12.9080	−1.45226	−0.726130	−	0.687558i	$-0.758683\pi$
$79$	−12.9080	−1.45226	−0.726130	+	0.687558i	$0.758683\pi$
$80$	3.98439	0.445468
$81$	−6.57470	−0.730522
$82$	−3.45253	−0.381268
$83$	−13.1072	−1.43870	−0.719351	−	0.694647i	$-0.755561\pi$
$83$	−13.1072	−1.43870	−0.719351	+	0.694647i	$0.755561\pi$
$84$	3.00479	0.327850
$85$	−1.27590	−0.138391
$86$	18.1206	1.95400
$87$	−2.58113	−0.276726
$88$	12.5115	1.33373
$89$	6.95117	0.736822	0.368411	−	0.929663i	$-0.379902\pi$
$89$	6.95117	0.736822	0.368411	+	0.929663i	$0.379902\pi$
$90$	−4.82053	−0.508129
$91$	0.311010	0.0326027
$92$	25.7995	2.68978
$93$	−10.1934	−1.05700
$94$	−19.6459	−2.02632
$95$	−1.80942	−0.185643
$96$	−17.3091	−1.76660
$97$	−0.132599	−0.0134634	−0.00673171	−	0.999977i	$-0.502143\pi$
$97$	−0.132599	−0.0134634	−0.00673171	+	0.999977i	$0.502143\pi$
$98$	17.7791	1.79596
$99$	−6.94882	−0.698383
$100$	−21.6553	−2.16553
$101$	0.886747	0.0882346	0.0441173	−	0.999026i	$-0.485952\pi$
$101$	0.886747	0.0882346	0.0441173	+	0.999026i	$0.485952\pi$
$102$	16.4432	1.62812
$103$	8.10578	0.798687	0.399343	−	0.916801i	$-0.369238\pi$
$103$	8.10578	0.798687	0.399343	+	0.916801i	$0.369238\pi$
$104$	−8.05441	−0.789800
$105$	0.337436	0.0329303
$106$	−11.9374	−1.15946
$107$	−2.93280	−0.283525	−0.141762	−	0.989901i	$-0.545277\pi$
$107$	−2.93280	−0.283525	−0.141762	+	0.989901i	$0.545277\pi$
$108$	7.81532	0.752030
$109$	−1.15822	−0.110937	−0.0554685	−	0.998460i	$-0.517665\pi$
$109$	−1.15822	−0.110937	−0.0554685	+	0.998460i	$0.517665\pi$
$110$	2.49753	0.238131
$111$	8.79388	0.834678
$112$	1.97585	0.186700
$113$	4.69779	0.441931	0.220965	−	0.975282i	$-0.429079\pi$
$113$	4.69779	0.441931	0.220965	+	0.975282i	$0.429079\pi$
$114$	23.3189	2.18402
$115$	2.89726	0.270171
$116$	−4.57213	−0.424511
$117$	4.47338	0.413564
$118$	32.5156	2.99331
$119$	−0.632716	−0.0580010
$120$	−8.73877	−0.797737
$121$	−7.39979	−0.672708
$122$	2.44499	0.221359
$123$	3.47612	0.313431
$124$	−18.0562	−1.62149
$125$	−4.99910	−0.447133
$126$	−2.39049	−0.212962
$127$	−4.53837	−0.402715	−0.201358	−	0.979518i	$-0.564535\pi$
$127$	−4.53837	−0.402715	−0.201358	+	0.979518i	$0.564535\pi$
$128$	9.12709	0.806728
$129$	−18.2444	−1.60633
$130$	−1.60781	−0.141015
$131$	−1.80311	−0.157538	−0.0787691	−	0.996893i	$-0.525099\pi$
$131$	−1.80311	−0.157538	−0.0787691	+	0.996893i	$0.525099\pi$
$132$	−22.3920	−1.94897
$133$	−0.897287	−0.0778047
$134$	−11.2481	−0.971692
$135$	0.877654	0.0755364
$136$	16.3858	1.40507
$137$	−6.09968	−0.521131	−0.260566	−	0.965456i	$-0.583909\pi$
$137$	−6.09968	−0.521131	−0.260566	+	0.965456i	$0.583909\pi$
$138$	−37.3384	−3.17846
$139$	−20.0507	−1.70068	−0.850339	−	0.526236i	$-0.823603\pi$
$139$	−20.0507	−1.70068	−0.850339	+	0.526236i	$0.823603\pi$
$140$	0.597722	0.0505167
$141$	19.7802	1.66579
$142$	23.6822	1.98736
$143$	−2.31767	−0.193814
$144$	28.4194	2.36828
$145$	−0.513446	−0.0426393
$146$	−34.5725	−2.86124
$147$	−17.9006	−1.47642
$148$	15.5772	1.28044
$149$	15.5589	1.27464	0.637319	−	0.770600i	$-0.280043\pi$
$149$	15.5589	1.27464	0.637319	+	0.770600i	$0.280043\pi$
$150$	31.3407	2.55896
$151$	8.18781	0.666315	0.333157	−	0.942871i	$-0.391886\pi$
$151$	8.18781	0.666315	0.333157	+	0.942871i	$0.391886\pi$
$152$	23.2376	1.88482
$153$	−9.10060	−0.735740
$154$	1.23852	0.0998028
$155$	−2.02769	−0.162868
$156$	14.4151	1.15413
$157$	5.06370	0.404128	0.202064	−	0.979372i	$-0.435235\pi$
$157$	5.06370	0.404128	0.202064	+	0.979372i	$0.435235\pi$
$158$	33.0911	2.63258
$159$	12.0189	0.953165
$160$	−3.44317	−0.272206
$161$	1.43674	0.113231
$162$	16.8550	1.32425
$163$	−14.7416	−1.15465	−0.577327	−	0.816513i	$-0.695904\pi$
$163$	−14.7416	−1.15465	−0.577327	+	0.816513i	$0.695904\pi$
$164$	6.15748	0.480818
$165$	−2.51460	−0.195761
$166$	33.6018	2.60801
$167$	2.23332	0.172819	0.0864097	−	0.996260i	$-0.472461\pi$
$167$	2.23332	0.172819	0.0864097	+	0.996260i	$0.472461\pi$
$168$	−4.33353	−0.334339
$169$	−11.5080	−0.885229
$170$	3.27092	0.250868
$171$	−12.9060	−0.986949
$172$	−32.3175	−2.46419
$173$	8.01417	0.609306	0.304653	−	0.952463i	$-0.401460\pi$
$173$	8.01417	0.609306	0.304653	+	0.952463i	$0.401460\pi$
$174$	6.61703	0.501636
$175$	−1.20596	−0.0911618
$176$	−14.7242	−1.10988
$177$	−32.7378	−2.46073
$178$	−17.8201	−1.33568
$179$	6.71288	0.501745	0.250872	−	0.968020i	$-0.419283\pi$
$179$	6.71288	0.501745	0.250872	+	0.968020i	$0.419283\pi$
$180$	8.59726	0.640802
$181$	−6.68080	−0.496580	−0.248290	−	0.968686i	$-0.579869\pi$
$181$	−6.68080	−0.496580	−0.248290	+	0.968686i	$0.579869\pi$
$182$	−0.797310	−0.0591006
$183$	−2.46170	−0.181974
$184$	−37.2082	−2.74302
$185$	1.74930	0.128611
$186$	26.1319	1.91608
$187$	4.71505	0.344799
$188$	35.0379	2.55540
$189$	0.435226	0.0316580
$190$	4.63866	0.336524
$191$	25.6822	1.85830	0.929148	−	0.369708i	$-0.120542\pi$
$191$	25.6822	1.85830	0.929148	+	0.369708i	$0.120542\pi$
$192$	4.31420	0.311351
$193$	−7.87942	−0.567173	−0.283587	−	0.958947i	$-0.591524\pi$
$193$	−7.87942	−0.567173	−0.283587	+	0.958947i	$0.591524\pi$
$194$	0.339934	0.0244058
$195$	1.61880	0.115925
$196$	−31.7085	−2.26489
$197$	23.8390	1.69846	0.849229	−	0.528024i	$-0.177067\pi$
$197$	23.8390	1.69846	0.849229	+	0.528024i	$0.177067\pi$
$198$	17.8141	1.26599
$199$	−9.08850	−0.644267	−0.322133	−	0.946694i	$-0.604400\pi$
$199$	−9.08850	−0.644267	−0.322133	+	0.946694i	$0.604400\pi$
$200$	31.2314	2.20839
$201$	11.3250	0.798804
$202$	−2.27328	−0.159947
$203$	−0.254616	−0.0178706
$204$	−29.3259	−2.05322
$205$	0.691479	0.0482950
$206$	−20.7801	−1.44782
$207$	20.6652	1.43633
$208$	9.47884	0.657239
$209$	6.68666	0.462526
$210$	−0.865055	−0.0596945
$211$	−22.0468	−1.51777	−0.758884	−	0.651226i	$-0.774255\pi$
$211$	−22.0468	−1.51777	−0.758884	+	0.651226i	$0.774255\pi$
$212$	21.2899	1.46220
$213$	−23.8440	−1.63376
$214$	7.51858	0.513959
$215$	−3.62923	−0.247511
$216$	−11.2713	−0.766915
$217$	−1.00553	−0.0682597
$218$	2.96922	0.201101
$219$	34.8087	2.35215
$220$	−4.45427	−0.300307
$221$	−3.03536	−0.204181
$222$	−22.5441	−1.51306
$223$	−24.0015	−1.60726	−0.803628	−	0.595131i	$-0.797100\pi$
$223$	−24.0015	−1.60726	−0.803628	+	0.595131i	$0.797100\pi$
$224$	−1.70746	−0.114084
$225$	−17.3458	−1.15638
$226$	−12.0433	−0.801110
$227$	−21.1743	−1.40539	−0.702695	−	0.711492i	$-0.748020\pi$
$227$	−21.1743	−1.40539	−0.702695	+	0.711492i	$0.748020\pi$
$228$	−41.5886	−2.75427
$229$	2.57196	0.169960	0.0849799	−	0.996383i	$-0.472917\pi$
$229$	2.57196	0.169960	0.0849799	+	0.996383i	$0.472917\pi$
$230$	−7.42746	−0.489752
$231$	−1.24698	−0.0820454
$232$	6.59395	0.432914
$233$	−4.68594	−0.306986	−0.153493	−	0.988150i	$-0.549052\pi$
$233$	−4.68594	−0.306986	−0.153493	+	0.988150i	$0.549052\pi$
$234$	−11.4680	−0.749688
$235$	3.93472	0.256673
$236$	−57.9906	−3.77487
$237$	−33.3172	−2.16418
$238$	1.62204	0.105141
$239$	−23.3853	−1.51267	−0.756335	−	0.654184i	$-0.773012\pi$
$239$	−23.3853	−1.51267	−0.756335	+	0.654184i	$0.773012\pi$
$240$	10.2842	0.663844
$241$	2.13895	0.137782	0.0688911	−	0.997624i	$-0.478054\pi$
$241$	2.13895	0.137782	0.0688911	+	0.997624i	$0.478054\pi$
$242$	18.9702	1.21945
$243$	−22.0982	−1.41760
$244$	−4.36057	−0.279157
$245$	−3.56083	−0.227493
$246$	−8.91144	−0.568173
$247$	−4.30461	−0.273896
$248$	26.0407	1.65359
$249$	−33.8314	−2.14398
$250$	12.8158	0.810540
$251$	7.00420	0.442101	0.221051	−	0.975262i	$-0.429051\pi$
$251$	7.00420	0.442101	0.221051	+	0.975262i	$0.429051\pi$
$252$	4.26336	0.268566
$253$	−10.7067	−0.673126
$254$	11.6346	0.730022
$255$	−3.29327	−0.206233
$256$	−26.7412	−1.67133
$257$	−23.3445	−1.45619	−0.728096	−	0.685475i	$-0.759595\pi$
$257$	−23.3445	−1.45619	−0.728096	+	0.685475i	$0.759595\pi$
$258$	46.7717	2.91188
$259$	0.867474	0.0539022
$260$	2.86748	0.177834
$261$	−3.66224	−0.226687
$262$	4.62247	0.285577
$263$	−0.193762	−0.0119479	−0.00597394	−	0.999982i	$-0.501902\pi$
$263$	−0.193762	−0.0119479	−0.00597394	+	0.999982i	$0.501902\pi$
$264$	32.2938	1.98755
$265$	2.39084	0.146868
$266$	2.30030	0.141040
$267$	17.9419	1.09803
$268$	20.0607	1.22540
$269$	−8.26678	−0.504034	−0.252017	−	0.967723i	$-0.581094\pi$
$269$	−8.26678	−0.504034	−0.252017	+	0.967723i	$0.581094\pi$
$270$	−2.24997	−0.136929
$271$	8.13687	0.494280	0.247140	−	0.968980i	$-0.420509\pi$
$271$	8.13687	0.494280	0.247140	+	0.968980i	$0.420509\pi$
$272$	−19.2837	−1.16924
$273$	0.802758	0.0485851
$274$	15.6372	0.944680
$275$	8.98690	0.541930
$276$	66.5919	4.00836
$277$	−1.00000	−0.0600842
$277$	−1.00000	−0.0600842
$278$	51.4023	3.08290
$279$	−14.4629	−0.865871
$280$	−0.862037	−0.0515166
$281$	−22.7640	−1.35799	−0.678994	−	0.734144i	$-0.737584\pi$
$281$	−22.7640	−1.35799	−0.678994	+	0.734144i	$0.737584\pi$
$282$	−50.7087	−3.01966
$283$	−2.56694	−0.152589	−0.0762943	−	0.997085i	$-0.524309\pi$
$283$	−2.56694	−0.152589	−0.0762943	+	0.997085i	$0.524309\pi$
$284$	−42.2364	−2.50627
$285$	−4.67036	−0.276648
$286$	5.94162	0.351336
$287$	0.342903	0.0202409
$288$	−24.5590	−1.44715
$289$	−10.8249	−0.636758
$290$	1.31628	0.0772945
$291$	−0.342256	−0.0200634
$292$	61.6589	3.60831
$293$	−24.6709	−1.44129	−0.720643	−	0.693306i	$-0.756153\pi$
$293$	−24.6709	−1.44129	−0.720643	+	0.693306i	$0.756153\pi$
$294$	45.8902	2.67637
$295$	−6.51229	−0.379160
$296$	−22.4655	−1.30578
$297$	−3.24334	−0.188198
$298$	−39.8872	−2.31060
$299$	6.89257	0.398608
$300$	−55.8952	−3.22711
$301$	−1.79972	−0.103734
$302$	−20.9904	−1.20786
$303$	2.28881	0.131489
$304$	−27.3472	−1.56847
$305$	−0.489688	−0.0280394
$306$	23.3304	1.33371
$307$	−22.7629	−1.29915	−0.649573	−	0.760299i	$-0.725052\pi$
$307$	−22.7629	−1.29915	−0.649573	+	0.760299i	$0.725052\pi$
$308$	−2.20886	−0.125862
$309$	20.9221	1.19022
$310$	5.19823	0.295239
$311$	13.0191	0.738246	0.369123	−	0.929381i	$-0.379658\pi$
$311$	13.0191	0.738246	0.369123	+	0.929381i	$0.379658\pi$
$312$	−20.7895	−1.17697
$313$	−5.08567	−0.287459	−0.143730	−	0.989617i	$-0.545910\pi$
$313$	−5.08567	−0.287459	−0.143730	+	0.989617i	$0.545910\pi$
$314$	−12.9814	−0.732582
$315$	0.478771	0.0269757
$316$	−59.0169	−3.31996
$317$	25.9990	1.46025	0.730126	−	0.683313i	$-0.239461\pi$
$317$	25.9990	1.46025	0.730126	+	0.683313i	$0.239461\pi$
$318$	−30.8120	−1.72785
$319$	1.89742	0.106235
$320$	0.858193	0.0479744
$321$	−7.56995	−0.422513
$322$	−3.68326	−0.205260
$323$	8.75725	0.487267
$324$	−30.0604	−1.67002
$325$	−5.78541	−0.320917
$326$	37.7919	2.09310
$327$	−2.98951	−0.165320
$328$	−8.88035	−0.490335
$329$	1.95122	0.107574
$330$	6.44647	0.354866
$331$	29.7429	1.63482	0.817410	−	0.576057i	$-0.195409\pi$
$331$	29.7429	1.63482	0.817410	+	0.576057i	$0.195409\pi$
$332$	−59.9278	−3.28896
$333$	12.4772	0.683747
$334$	−5.72537	−0.313279
$335$	2.25280	0.123084
$336$	5.09992	0.278223
$337$	12.6069	0.686743	0.343372	−	0.939200i	$-0.388431\pi$
$337$	12.6069	0.686743	0.343372	+	0.939200i	$0.388431\pi$
$338$	29.5020	1.60470
$339$	12.1256	0.658573
$340$	−5.83358	−0.316371
$341$	7.49328	0.405784
$342$	33.0861	1.78909
$343$	−3.54812	−0.191581
$344$	46.6085	2.51296
$345$	7.47821	0.402613
$346$	−20.5452	−1.10452
$347$	−25.9367	−1.39235	−0.696177	−	0.717871i	$-0.745117\pi$
$347$	−25.9367	−1.39235	−0.696177	+	0.717871i	$0.745117\pi$
$348$	−11.8013	−0.632614
$349$	−36.3242	−1.94439	−0.972195	−	0.234175i	$-0.924761\pi$
$349$	−36.3242	−1.94439	−0.972195	+	0.234175i	$0.924761\pi$
$350$	3.09161	0.165254
$351$	2.08793	0.111446
$352$	12.7241	0.678198
$353$	−0.146434	−0.00779392	−0.00389696	−	0.999992i	$-0.501240\pi$
$353$	−0.146434	−0.00779392	−0.00389696	+	0.999992i	$0.501240\pi$
$354$	83.9272	4.46068
$355$	−4.74311	−0.251738
$356$	31.7816	1.68442
$357$	−1.63312	−0.0864341
$358$	−17.2093	−0.909538
$359$	2.07499	0.109514	0.0547570	−	0.998500i	$-0.482562\pi$
$359$	2.07499	0.109514	0.0547570	+	0.998500i	$0.482562\pi$
$360$	−12.3990	−0.653486
$361$	−6.58089	−0.346363
$362$	17.1270	0.900175
$363$	−19.0998	−1.00248
$364$	1.42198	0.0745319
$365$	6.92424	0.362431
$366$	6.31085	0.329873
$367$	9.01812	0.470742	0.235371	−	0.971906i	$-0.424369\pi$
$367$	9.01812	0.470742	0.235371	+	0.971906i	$0.424369\pi$
$368$	43.7885	2.28263
$369$	4.93210	0.256755
$370$	−4.48454	−0.233140
$371$	1.18561	0.0615539
$372$	−46.6054	−2.41638
$373$	−15.5832	−0.806867	−0.403433	−	0.915009i	$-0.632183\pi$
$373$	−15.5832	−0.806867	−0.403433	+	0.915009i	$0.632183\pi$
$374$	−12.0876	−0.625034
$375$	−12.9033	−0.666325
$376$	−50.5318	−2.60598
$377$	−1.22149	−0.0629097
$378$	−1.11575	−0.0573881
$379$	19.8732	1.02082	0.510409	−	0.859932i	$-0.329494\pi$
$379$	19.8732	1.02082	0.510409	+	0.859932i	$0.329494\pi$
$380$	−8.27291	−0.424391
$381$	−11.7141	−0.600133
$382$	−65.8392	−3.36863
$383$	29.8769	1.52664	0.763319	−	0.646022i	$-0.223569\pi$
$383$	29.8769	1.52664	0.763319	+	0.646022i	$0.223569\pi$
$384$	23.5582	1.20220
$385$	−0.248053	−0.0126420
$386$	20.1998	1.02814
$387$	−25.8861	−1.31587
$388$	−0.606261	−0.0307782
$389$	26.4316	1.34013	0.670066	−	0.742301i	$-0.266266\pi$
$389$	26.4316	1.34013	0.670066	+	0.742301i	$0.266266\pi$
$390$	−4.14998	−0.210142
$391$	−14.0222	−0.709132
$392$	45.7301	2.30972
$393$	−4.65406	−0.234766
$394$	−61.1141	−3.07888
$395$	−6.62754	−0.333468
$396$	−31.7709	−1.59655
$397$	−27.0370	−1.35695	−0.678474	−	0.734624i	$-0.737358\pi$
$397$	−27.0370	−1.35695	−0.678474	+	0.734624i	$0.737358\pi$
$398$	23.2994	1.16789
$399$	−2.31602	−0.115946
$400$	−36.7547	−1.83773
$401$	−8.41234	−0.420092	−0.210046	−	0.977692i	$-0.567361\pi$
$401$	−8.41234	−0.420092	−0.210046	+	0.977692i	$0.567361\pi$
$402$	−29.0330	−1.44803
$403$	−4.82388	−0.240294
$404$	4.05432	0.201710
$405$	−3.37575	−0.167742
$406$	0.652738	0.0323949
$407$	−6.46449	−0.320433
$408$	42.2940	2.09386
$409$	15.5366	0.768236	0.384118	−	0.923284i	$-0.374506\pi$
$409$	15.5366	0.768236	0.384118	+	0.923284i	$0.374506\pi$
$410$	−1.77269	−0.0875468
$411$	−15.7441	−0.776599
$412$	37.0607	1.82585
$413$	−3.22943	−0.158910
$414$	−52.9777	−2.60371
$415$	−6.72984	−0.330355
$416$	−8.19129	−0.401611
$417$	−51.7535	−2.53438
$418$	−17.1420	−0.838444
$419$	28.7882	1.40639	0.703197	−	0.710995i	$-0.251755\pi$
$419$	28.7882	1.40639	0.703197	+	0.710995i	$0.251755\pi$
$420$	1.54280	0.0752809
$421$	12.8332	0.625451	0.312725	−	0.949844i	$-0.398758\pi$
$421$	12.8332	0.625451	0.312725	+	0.949844i	$0.398758\pi$
$422$	56.5196	2.75133
$423$	28.0651	1.36457
$424$	−30.7045	−1.49114
$425$	11.7698	0.570918
$426$	61.1268	2.96160
$427$	−0.242835	−0.0117516
$428$	−13.4091	−0.648155
$429$	−5.98222	−0.288824
$430$	9.30395	0.448676
$431$	−14.7352	−0.709767	−0.354884	−	0.934910i	$-0.615480\pi$
$431$	−14.7352	−0.709767	−0.354884	+	0.934910i	$0.615480\pi$
$432$	13.2646	0.638196
$433$	30.6955	1.47513	0.737566	−	0.675275i	$-0.235975\pi$
$433$	30.6955	1.47513	0.737566	+	0.675275i	$0.235975\pi$
$434$	2.57779	0.123738
$435$	−1.32527	−0.0635419
$436$	−5.29551	−0.253609
$437$	−19.8856	−0.951256
$438$	−89.2361	−4.26387
$439$	−17.4524	−0.832959	−0.416479	−	0.909145i	$-0.636736\pi$
$439$	−17.4524	−0.832959	−0.416479	+	0.909145i	$0.636736\pi$
$440$	6.42398	0.306251
$441$	−25.3983	−1.20944
$442$	7.78151	0.370129
$443$	−36.4548	−1.73202	−0.866010	−	0.500027i	$-0.833324\pi$
$443$	−36.4548	−1.73202	−0.866010	+	0.500027i	$0.833324\pi$
$444$	40.2067	1.90813
$445$	3.56905	0.169189
$446$	61.5305	2.91356
$447$	40.1597	1.89949
$448$	0.425575	0.0201065
$449$	30.4641	1.43769	0.718846	−	0.695169i	$-0.244671\pi$
$449$	30.4641	1.43769	0.718846	+	0.695169i	$0.244671\pi$
$450$	44.4679	2.09624
$451$	−2.55534	−0.120326
$452$	21.4789	1.01028
$453$	21.1338	0.992954
$454$	54.2828	2.54762
$455$	0.159687	0.00748623
$456$	59.9792	2.80879
$457$	−31.2817	−1.46330	−0.731649	−	0.681681i	$-0.761249\pi$
$457$	−31.2817	−1.46330	−0.731649	+	0.681681i	$0.761249\pi$
$458$	−6.59351	−0.308095
$459$	−4.24768	−0.198265
$460$	13.2466	0.617628
$461$	36.1359	1.68302	0.841509	−	0.540243i	$-0.181668\pi$
$461$	36.1359	1.68302	0.841509	+	0.540243i	$0.181668\pi$
$462$	3.19678	0.148728
$463$	−15.1764	−0.705308	−0.352654	−	0.935754i	$-0.614721\pi$
$463$	−15.1764	−0.705308	−0.352654	+	0.935754i	$0.614721\pi$
$464$	−7.76009	−0.360253
$465$	−5.23375	−0.242709
$466$	12.0130	0.556489
$467$	23.9976	1.11048	0.555239	−	0.831691i	$-0.312627\pi$
$467$	23.9976	1.11048	0.555239	+	0.831691i	$0.312627\pi$
$468$	20.4529	0.945434
$469$	1.11716	0.0515855
$470$	−10.0871	−0.465284
$471$	13.0701	0.602238
$472$	83.6344	3.84958
$473$	13.4117	0.616670
$474$	85.4124	3.92312
$475$	16.6913	0.765851
$476$	−2.89286	−0.132594
$477$	17.0531	0.780808
$478$	59.9510	2.74209
$479$	−0.444438	−0.0203069	−0.0101535	−	0.999948i	$-0.503232\pi$
$479$	−0.444438	−0.0203069	−0.0101535	+	0.999948i	$0.503232\pi$
$480$	−8.88728	−0.405647
$481$	4.16158	0.189752
$482$	−5.48346	−0.249765
$483$	3.70842	0.168739
$484$	−33.8328	−1.53785
$485$	−0.0680825	−0.00309147
$486$	56.6513	2.56975
$487$	9.21291	0.417477	0.208738	−	0.977972i	$-0.433064\pi$
$487$	9.21291	0.417477	0.208738	+	0.977972i	$0.433064\pi$
$488$	6.28883	0.284682
$489$	−38.0501	−1.72068
$490$	9.12861	0.412389
$491$	−41.3602	−1.86656	−0.933281	−	0.359147i	$-0.883068\pi$
$491$	−41.3602	−1.86656	−0.933281	+	0.359147i	$0.883068\pi$
$492$	15.8933	0.716524
$493$	2.48498	0.111918
$494$	11.0354	0.496504
$495$	−3.56784	−0.160363
$496$	−30.6461	−1.37605
$497$	−2.35209	−0.105506
$498$	86.7308	3.88650
$499$	13.6399	0.610607	0.305304	−	0.952255i	$-0.401242\pi$
$499$	13.6399	0.610607	0.305304	+	0.952255i	$0.401242\pi$
$500$	−22.8565	−1.02217
$501$	5.76449	0.257539
$502$	−17.9561	−0.801419
$503$	22.5793	1.00676	0.503381	−	0.864064i	$-0.332089\pi$
$503$	22.5793	1.00676	0.503381	+	0.864064i	$0.332089\pi$
$504$	−6.14864	−0.273882
$505$	0.455296	0.0202604
$506$	27.4479	1.22021
$507$	−29.7036	−1.31918
$508$	−20.7500	−0.920632
$509$	28.4561	1.26129	0.630646	−	0.776070i	$-0.282790\pi$
$509$	28.4561	1.26129	0.630646	+	0.776070i	$0.282790\pi$
$510$	8.44268	0.373848
$511$	3.43371	0.151898
$512$	50.3001	2.22297
$513$	−6.02385	−0.265959
$514$	59.8464	2.63971
$515$	4.16188	0.183394
$516$	−83.4158	−3.67218
$517$	−14.5406	−0.639497
$518$	−2.22387	−0.0977112
$519$	20.6856	0.907998
$520$	−4.13550	−0.181354
$521$	−40.0887	−1.75632	−0.878158	−	0.478370i	$-0.841228\pi$
$521$	−40.0887	−1.75632	−0.878158	+	0.478370i	$0.841228\pi$
$522$	9.38859	0.410927
$523$	17.0531	0.745678	0.372839	−	0.927896i	$-0.378384\pi$
$523$	17.0531	0.745678	0.372839	+	0.927896i	$0.378384\pi$
$524$	−8.24404	−0.360142
$525$	−3.11274	−0.135851
$526$	0.496731	0.0216585
$527$	9.81365	0.427489
$528$	−38.0050	−1.65396
$529$	8.84094	0.384389
$530$	−6.12920	−0.266235
$531$	−46.4501	−2.01576
$532$	−4.10251	−0.177866
$533$	1.64503	0.0712540
$534$	−45.9961	−1.99045
$535$	−1.50583	−0.0651029
$536$	−28.9317	−1.24966
$537$	17.3268	0.747709
$538$	21.1928	0.913688
$539$	13.1589	0.566796
$540$	4.01274	0.172681
$541$	20.7322	0.891346	0.445673	−	0.895196i	$-0.352964\pi$
$541$	20.7322	0.891346	0.445673	+	0.895196i	$0.352964\pi$
$542$	−20.8598	−0.896006
$543$	−17.2440	−0.740012
$544$	16.6643	0.714475
$545$	−0.594681	−0.0254733
$546$	−2.05796	−0.0880727
$547$	8.12728	0.347497	0.173749	−	0.984790i	$-0.444412\pi$
$547$	8.12728	0.347497	0.173749	+	0.984790i	$0.444412\pi$
$548$	−27.8885	−1.19134
$549$	−3.49279	−0.149068
$550$	−23.0390	−0.982385
$551$	3.52408	0.150131
$552$	−96.0392	−4.08770
$553$	−3.28658	−0.139759
$554$	2.56362	0.108918
$555$	4.51518	0.191659
$556$	−91.6743	−3.88786
$557$	−16.5438	−0.700984	−0.350492	−	0.936566i	$-0.613986\pi$
$557$	−16.5438	−0.700984	−0.350492	+	0.936566i	$0.613986\pi$
$558$	37.0773	1.56961
$559$	−8.63392	−0.365176
$560$	1.01449	0.0428700
$561$	12.1702	0.513825
$562$	58.3582	2.46169
$563$	−7.66565	−0.323069	−0.161534	−	0.986867i	$-0.551644\pi$
$563$	−7.66565	−0.323069	−0.161534	+	0.986867i	$0.551644\pi$
$564$	90.4374	3.80810
$565$	2.41206	0.101476
$566$	6.58064	0.276605
$567$	−1.67403	−0.0703025
$568$	60.9136	2.55588
$569$	−4.72814	−0.198214	−0.0991070	−	0.995077i	$-0.531599\pi$
$569$	−4.72814	−0.198214	−0.0991070	+	0.995077i	$0.531599\pi$
$570$	11.9730	0.501494
$571$	−4.87762	−0.204122	−0.102061	−	0.994778i	$-0.532544\pi$
$571$	−4.87762	−0.204122	−0.102061	+	0.994778i	$0.532544\pi$
$572$	−10.5967	−0.443070
$573$	66.2891	2.76927
$574$	−0.879071	−0.0366917
$575$	−26.7263	−1.11456
$576$	6.12121	0.255051
$577$	31.8484	1.32587	0.662934	−	0.748678i	$-0.269311\pi$
$577$	31.8484	1.32587	0.662934	+	0.748678i	$0.269311\pi$
$578$	27.7508	1.15428
$579$	−20.3378	−0.845212
$580$	−2.34754	−0.0974763
$581$	−3.33731	−0.138455
$582$	0.877414	0.0363700
$583$	−8.83528	−0.365920
$584$	−88.9248	−3.67973
$585$	2.29684	0.0949625
$586$	63.2466	2.61269
$587$	−8.83156	−0.364517	−0.182259	−	0.983251i	$-0.558341\pi$
$587$	−8.83156	−0.364517	−0.182259	+	0.983251i	$0.558341\pi$
$588$	−81.8438	−3.37518
$589$	13.9172	0.573450
$590$	16.6950	0.687323
$591$	61.5316	2.53107
$592$	26.4385	1.08662
$593$	33.3700	1.37034	0.685171	−	0.728382i	$-0.259728\pi$
$593$	33.3700	1.37034	0.685171	+	0.728382i	$0.259728\pi$
$594$	8.31468	0.341156
$595$	−0.324865	−0.0133182
$596$	71.1375	2.91390
$597$	−23.4586	−0.960097
$598$	−17.6699	−0.722576
$599$	21.8075	0.891031	0.445515	−	0.895274i	$-0.353020\pi$
$599$	21.8075	0.891031	0.445515	+	0.895274i	$0.353020\pi$
$600$	80.6124	3.29099
$601$	−37.1832	−1.51674	−0.758368	−	0.651827i	$-0.774003\pi$
$601$	−37.1832	−1.51674	−0.758368	+	0.651827i	$0.774003\pi$
$602$	4.61380	0.188045
$603$	16.0685	0.654360
$604$	37.4357	1.52324
$605$	−3.79939	−0.154467
$606$	−5.86763	−0.238356
$607$	−33.7901	−1.37150	−0.685750	−	0.727837i	$-0.740526\pi$
$607$	−33.7901	−1.37150	−0.685750	+	0.727837i	$0.740526\pi$
$608$	23.6325	0.958423
$609$	−0.657198	−0.0266310
$610$	1.25537	0.0508285
$611$	9.36069	0.378693
$612$	−41.6091	−1.68195
$613$	24.9596	1.00811	0.504055	−	0.863672i	$-0.331841\pi$
$613$	24.9596	1.00811	0.504055	+	0.863672i	$0.331841\pi$
$614$	58.3553	2.35503
$615$	1.78480	0.0719701
$616$	3.18563	0.128353
$617$	−16.4321	−0.661531	−0.330766	−	0.943713i	$-0.607307\pi$
$617$	−16.4321	−0.661531	−0.330766	+	0.943713i	$0.607307\pi$
$618$	−53.6362	−2.15757
$619$	40.5050	1.62803	0.814017	−	0.580841i	$-0.197276\pi$
$619$	40.5050	1.62803	0.814017	+	0.580841i	$0.197276\pi$
$620$	−9.27087	−0.372327
$621$	9.64543	0.387058
$622$	−33.3760	−1.33825
$623$	1.76988	0.0709088
$624$	24.4661	0.979430
$625$	21.1151	0.844604
$626$	13.0377	0.521091
$627$	17.2592	0.689264
$628$	23.1519	0.923861
$629$	−8.46628	−0.337573
$630$	−1.22739	−0.0489002
$631$	−3.25208	−0.129463	−0.0647316	−	0.997903i	$-0.520619\pi$
$631$	−3.25208	−0.129463	−0.0647316	+	0.997903i	$0.520619\pi$
$632$	85.1144	3.38567
$633$	−56.9058	−2.26180
$634$	−66.6516	−2.64707
$635$	−2.33021	−0.0924714
$636$	54.9522	2.17899
$637$	−8.47121	−0.335642
$638$	−4.86426	−0.192578
$639$	−33.8311	−1.33834
$640$	4.68626	0.185241
$641$	−19.6787	−0.777260	−0.388630	−	0.921394i	$-0.627052\pi$
$641$	−19.6787	−0.777260	−0.388630	+	0.921394i	$0.627052\pi$
$642$	19.4064	0.765911
$643$	20.8596	0.822623	0.411312	−	0.911495i	$-0.365071\pi$
$643$	20.8596	0.822623	0.411312	+	0.911495i	$0.365071\pi$
$644$	6.56897	0.258854
$645$	−9.36752	−0.368846
$646$	−22.4502	−0.883293
$647$	10.1844	0.400390	0.200195	−	0.979756i	$-0.435842\pi$
$647$	10.1844	0.400390	0.200195	+	0.979756i	$0.435842\pi$
$648$	43.3532	1.70307
$649$	24.0660	0.944672
$650$	14.8316	0.581742
$651$	−2.59540	−0.101722
$652$	−67.4006	−2.63961
$653$	27.3024	1.06842	0.534212	−	0.845351i	$-0.320608\pi$
$653$	27.3024	1.06842	0.534212	+	0.845351i	$0.320608\pi$
$654$	7.66395	0.299684
$655$	−0.925798	−0.0361739
$656$	10.4509	0.408037
$657$	49.3884	1.92682
$658$	−5.00217	−0.195005
$659$	−35.7345	−1.39202	−0.696009	−	0.718033i	$-0.745043\pi$
$659$	−35.7345	−1.39202	−0.696009	+	0.718033i	$0.745043\pi$
$660$	−11.4971	−0.447523
$661$	16.2979	0.633914	0.316957	−	0.948440i	$-0.397339\pi$
$661$	16.2979	0.633914	0.316957	+	0.948440i	$0.397339\pi$
$662$	−76.2494	−2.96352
$663$	−7.83468	−0.304274
$664$	86.4282	3.35406
$665$	−0.460708	−0.0178655
$666$	−31.9868	−1.23946
$667$	−5.64278	−0.218489
$668$	10.2110	0.395076
$669$	−61.9510	−2.39516
$670$	−5.77531	−0.223120
$671$	1.80963	0.0698598
$672$	−4.40718	−0.170010
$673$	41.8991	1.61509	0.807545	−	0.589806i	$-0.200796\pi$
$673$	41.8991	1.61509	0.807545	+	0.589806i	$0.200796\pi$
$674$	−32.3193	−1.24489
$675$	−8.09608	−0.311618
$676$	−52.6159	−2.02369
$677$	−7.70537	−0.296142	−0.148071	−	0.988977i	$-0.547306\pi$
$677$	−7.70537	−0.296142	−0.148071	+	0.988977i	$0.547306\pi$
$678$	−31.0854	−1.19383
$679$	−0.0337619	−0.00129566
$680$	8.41323	0.322632
$681$	−54.6537	−2.09434
$682$	−19.2099	−0.735584
$683$	26.1652	1.00118	0.500591	−	0.865684i	$-0.333116\pi$
$683$	26.1652	1.00118	0.500591	+	0.865684i	$0.333116\pi$
$684$	−59.0080	−2.25623
$685$	−3.13186	−0.119662
$686$	9.09602	0.347288
$687$	6.63856	0.253277
$688$	−54.8513	−2.09118
$689$	5.68780	0.216688
$690$	−19.1713	−0.729837
$691$	−7.78584	−0.296187	−0.148094	−	0.988973i	$-0.547314\pi$
$691$	−7.78584	−0.296187	−0.148094	+	0.988973i	$0.547314\pi$
$692$	36.6418	1.39291
$693$	−1.76928	−0.0672095
$694$	66.4917	2.52399
$695$	−10.2949	−0.390509
$696$	17.0198	0.645136
$697$	−3.34663	−0.126763
$698$	93.1213	3.52469
$699$	−12.0950	−0.457476
$700$	−5.51379	−0.208402
$701$	30.3634	1.14681	0.573406	−	0.819272i	$-0.305622\pi$
$701$	30.3634	1.14681	0.573406	+	0.819272i	$0.305622\pi$
$702$	−5.35266	−0.202023
$703$	−12.0065	−0.452833
$704$	−3.17142	−0.119528
$705$	10.1560	0.382499
$706$	0.375402	0.0141284
$707$	0.225780	0.00849134
$708$	−149.681	−5.62537
$709$	−41.7375	−1.56748	−0.783742	−	0.621086i	$-0.786692\pi$
$709$	−41.7375	−1.56748	−0.783742	+	0.621086i	$0.786692\pi$
$710$	12.1595	0.456338
$711$	−47.2721	−1.77284
$712$	−45.8356	−1.71776
$713$	−22.2844	−0.834557
$714$	4.18670	0.156683
$715$	−1.19000	−0.0445035
$716$	30.6922	1.14702
$717$	−60.3606	−2.25421
$718$	−5.31949	−0.198521
$719$	−0.421265	−0.0157105	−0.00785526	−	0.999969i	$-0.502500\pi$
$719$	−0.421265	−0.0157105	−0.00785526	+	0.999969i	$0.502500\pi$
$720$	14.5918	0.543804
$721$	2.06386	0.0768623
$722$	16.8709	0.627869
$723$	5.52092	0.205325
$724$	−30.5454	−1.13521
$725$	4.73637	0.175904
$726$	48.9646	1.81725
$727$	3.19380	0.118452	0.0592258	−	0.998245i	$-0.481137\pi$
$727$	3.19380	0.118452	0.0592258	+	0.998245i	$0.481137\pi$
$728$	−2.05078	−0.0760071
$729$	−37.3143	−1.38201
$730$	−17.7511	−0.656997
$731$	17.5648	0.649656
$732$	−11.2552	−0.416004
$733$	23.8361	0.880406	0.440203	−	0.897898i	$-0.354907\pi$
$733$	23.8361	0.880406	0.440203	+	0.897898i	$0.354907\pi$
$734$	−23.1190	−0.853338
$735$	−9.19098	−0.339015
$736$	−37.8405	−1.39482
$737$	−8.32515	−0.306661
$738$	−12.6440	−0.465433
$739$	38.5887	1.41951	0.709754	−	0.704449i	$-0.248806\pi$
$739$	38.5887	1.41951	0.709754	+	0.704449i	$0.248806\pi$
$740$	7.99803	0.294013
$741$	−11.1108	−0.408164
$742$	−3.03945	−0.111582
$743$	−33.9722	−1.24632	−0.623159	−	0.782095i	$-0.714151\pi$
$743$	−33.9722	−1.24632	−0.623159	+	0.782095i	$0.714151\pi$
$744$	67.2146	2.46421
$745$	7.98867	0.292682
$746$	39.9493	1.46265
$747$	−48.0018	−1.75629
$748$	21.5578	0.788232
$749$	−0.746739	−0.0272853
$750$	33.0792	1.20788
$751$	−32.5763	−1.18873	−0.594364	−	0.804196i	$-0.702596\pi$
$751$	−32.5763	−1.18873	−0.594364	+	0.804196i	$0.702596\pi$
$752$	59.4684	2.16859
$753$	18.0788	0.658827
$754$	3.13142	0.114040
$755$	4.20400	0.152999
$756$	1.98991	0.0723723
$757$	−46.0419	−1.67342	−0.836711	−	0.547645i	$-0.815524\pi$
$757$	−46.0419	−1.67342	−0.836711	+	0.547645i	$0.815524\pi$
$758$	−50.9472	−1.85049
$759$	−27.6355	−1.00310
$760$	11.9312	0.432791
$761$	−31.0176	−1.12439	−0.562193	−	0.827006i	$-0.690042\pi$
$761$	−31.0176	−1.12439	−0.562193	+	0.827006i	$0.690042\pi$
$762$	30.0305	1.08789
$763$	−0.294901	−0.0106761
$764$	117.422	4.24818
$765$	−4.67266	−0.168940
$766$	−76.5928	−2.76741
$767$	−15.4927	−0.559410
$768$	−69.0226	−2.49064
$769$	21.6088	0.779232	0.389616	−	0.920977i	$-0.372608\pi$
$769$	21.6088	0.779232	0.389616	+	0.920977i	$0.372608\pi$
$770$	0.635913	0.0229167
$771$	−60.2553	−2.17004
$772$	−36.0257	−1.29659
$773$	5.28228	0.189990	0.0949952	−	0.995478i	$-0.469716\pi$
$773$	5.28228	0.189990	0.0949952	+	0.995478i	$0.469716\pi$
$774$	66.3621	2.38534
$775$	18.7048	0.671897
$776$	0.874352	0.0313874
$777$	2.23906	0.0803260
$778$	−67.7604	−2.42933
$779$	−4.74602	−0.170044
$780$	7.40136	0.265011
$781$	17.5280	0.627201
$782$	35.9475	1.28548
$783$	−1.70934	−0.0610869
$784$	−53.8176	−1.92206
$785$	2.59994	0.0927957
$786$	11.9312	0.425573
$787$	9.41597	0.335643	0.167822	−	0.985817i	$-0.446327\pi$
$787$	9.41597	0.335643	0.167822	+	0.985817i	$0.446327\pi$
$788$	108.995	3.88278
$789$	−0.500125	−0.0178049
$790$	16.9905	0.604494
$791$	1.19613	0.0425296
$792$	45.8202	1.62815
$793$	−1.16497	−0.0413691
$794$	69.3125	2.45981
$795$	6.17108	0.218866
$796$	−41.5538	−1.47283
$797$	12.6737	0.448925	0.224463	−	0.974483i	$-0.427937\pi$
$797$	12.6737	0.448925	0.224463	+	0.974483i	$0.427937\pi$
$798$	5.93738	0.210181
$799$	−19.0433	−0.673704
$800$	31.7621	1.12296
$801$	25.4569	0.899475
$802$	21.5660	0.761522
$803$	−25.5883	−0.902991
$804$	51.7794	1.82612
$805$	0.737689	0.0260001
$806$	12.3666	0.435594
$807$	−21.3377	−0.751121
$808$	−5.84716	−0.205702
$809$	−12.9282	−0.454532	−0.227266	−	0.973833i	$-0.572979\pi$
$809$	−12.9282	−0.454532	−0.227266	+	0.973833i	$0.572979\pi$
$810$	8.65413	0.304075
$811$	34.1566	1.19940	0.599700	−	0.800225i	$-0.295287\pi$
$811$	34.1566	1.19940	0.599700	+	0.800225i	$0.295287\pi$
$812$	−1.16414	−0.0408532
$813$	21.0023	0.736584
$814$	16.5725	0.580865
$815$	−7.56902	−0.265131
$816$	−49.7737	−1.74243
$817$	24.9095	0.871473
$818$	−39.8299	−1.39262
$819$	1.13899	0.0397997
$820$	3.16153	0.110405
$821$	−11.1792	−0.390155	−0.195078	−	0.980788i	$-0.562496\pi$
$821$	−11.1792	−0.390155	−0.195078	+	0.980788i	$0.562496\pi$
$822$	40.3618	1.40778
$823$	−2.07984	−0.0724986	−0.0362493	−	0.999343i	$-0.511541\pi$
$823$	−2.07984	−0.0724986	−0.0362493	+	0.999343i	$0.511541\pi$
$824$	−53.4491	−1.86199
$825$	23.1964	0.807594
$826$	8.27901	0.288064
$827$	23.5493	0.818890	0.409445	−	0.912335i	$-0.365722\pi$
$827$	23.5493	0.818890	0.409445	+	0.912335i	$0.365722\pi$
$828$	94.4841	3.28355
$829$	30.2842	1.05181	0.525907	−	0.850542i	$-0.323726\pi$
$829$	30.2842	1.05181	0.525907	+	0.850542i	$0.323726\pi$
$830$	17.2527	0.598851
$831$	−2.58113	−0.0895385
$832$	2.04164	0.0707810
$833$	17.2337	0.597114
$834$	132.676	4.59420
$835$	1.14669	0.0396828
$836$	30.5723	1.05736
$837$	−6.75051	−0.233332
$838$	−73.8019	−2.54944
$839$	22.5403	0.778179	0.389089	−	0.921200i	$-0.372790\pi$
$839$	22.5403	0.778179	0.389089	+	0.921200i	$0.372790\pi$
$840$	−2.22503	−0.0767709
$841$	1.00000	0.0344828
$842$	−32.8993	−1.13379
$843$	−58.7569	−2.02370
$844$	−100.801	−3.46971
$845$	−5.90872	−0.203266
$846$	−71.9482	−2.47363
$847$	−1.88411	−0.0647387
$848$	36.1346	1.24087
$849$	−6.62560	−0.227390
$850$	−30.1732	−1.03493
$851$	19.2249	0.659020
$852$	−109.018	−3.73489
$853$	−13.6001	−0.465658	−0.232829	−	0.972518i	$-0.574798\pi$
$853$	−13.6001	−0.465658	−0.232829	+	0.972518i	$0.574798\pi$
$854$	0.622535	0.0213027
$855$	−6.62654	−0.226623
$856$	19.3387	0.660984
$857$	−8.53305	−0.291484	−0.145742	−	0.989323i	$-0.546557\pi$
$857$	−8.53305	−0.291484	−0.145742	+	0.989323i	$0.546557\pi$
$858$	15.3361	0.523567
$859$	−29.7844	−1.01623	−0.508115	−	0.861289i	$-0.669658\pi$
$859$	−29.7844	−1.01623	−0.508115	+	0.861289i	$0.669658\pi$
$860$	−16.5933	−0.565827
$861$	0.885077	0.0301634
$862$	37.7753	1.28663
$863$	29.8752	1.01696	0.508481	−	0.861073i	$-0.330207\pi$
$863$	29.8752	1.01696	0.508481	+	0.861073i	$0.330207\pi$
$864$	−11.4629	−0.389974
$865$	4.11484	0.139909
$866$	−78.6915	−2.67405
$867$	−27.9405	−0.948908
$868$	−4.59740	−0.156046
$869$	24.4919	0.830829
$870$	3.39749	0.115186
$871$	5.35940	0.181596
$872$	7.63721	0.258629
$873$	−0.485611	−0.0164354
$874$	50.9790	1.72439
$875$	−1.27285	−0.0430303
$876$	159.150	5.37717
$877$	44.8540	1.51461	0.757306	−	0.653060i	$-0.226515\pi$
$877$	44.8540	1.51461	0.757306	+	0.653060i	$0.226515\pi$
$878$	44.7413	1.50995
$879$	−63.6787	−2.14783
$880$	−7.56006	−0.254850
$881$	−13.8855	−0.467814	−0.233907	−	0.972259i	$-0.575151\pi$
$881$	−13.8855	−0.467814	−0.233907	+	0.972259i	$0.575151\pi$
$882$	65.1115	2.19242
$883$	5.97380	0.201034	0.100517	−	0.994935i	$-0.467950\pi$
$883$	5.97380	0.201034	0.100517	+	0.994935i	$0.467950\pi$
$884$	−13.8781	−0.466770
$885$	−16.8091	−0.565031
$886$	93.4561	3.13972
$887$	−41.1730	−1.38245	−0.691227	−	0.722637i	$-0.742930\pi$
$887$	−41.1730	−1.38245	−0.691227	+	0.722637i	$0.742930\pi$
$888$	−57.9864	−1.94590
$889$	−1.15554	−0.0387557
$890$	−9.14967	−0.306698
$891$	12.4750	0.417927
$892$	−109.738	−3.67429
$893$	−27.0063	−0.903731
$894$	−102.954	−3.44330
$895$	3.44670	0.115211
$896$	2.32390	0.0776362
$897$	17.7906	0.594012
$898$	−78.0984	−2.60618
$899$	3.94919	0.131713
$900$	−79.3070	−2.64357
$901$	−11.5712	−0.385493
$902$	6.55091	0.218121
$903$	−4.64533	−0.154587
$904$	−30.9770	−1.03028
$905$	−3.43023	−0.114025
$906$	−54.1790	−1.79998
$907$	−45.9392	−1.52539	−0.762694	−	0.646760i	$-0.776123\pi$
$907$	−45.9392	−1.52539	−0.762694	+	0.646760i	$0.776123\pi$
$908$	−96.8117	−3.21281
$909$	3.24748	0.107712
$910$	−0.409376	−0.0135707
$911$	15.6624	0.518918	0.259459	−	0.965754i	$-0.416456\pi$
$911$	15.6624	0.518918	0.259459	+	0.965754i	$0.416456\pi$
$912$	−70.5866	−2.33736
$913$	24.8699	0.823073
$914$	80.1944	2.65259
$915$	−1.26395	−0.0417849
$916$	11.7593	0.388539
$917$	−0.459100	−0.0151608
$918$	10.8894	0.359404
$919$	42.4647	1.40078	0.700390	−	0.713760i	$-0.253009\pi$
$919$	42.4647	1.40078	0.700390	+	0.713760i	$0.253009\pi$
$920$	−19.1044	−0.629853
$921$	−58.7540	−1.93601
$922$	−92.6386	−3.05089
$923$	−11.2838	−0.371412
$924$	−5.70136	−0.187561
$925$	−16.1368	−0.530573
$926$	38.9065	1.27855
$927$	29.6854	0.974995
$928$	6.70601	0.220135
$929$	36.4434	1.19567	0.597834	−	0.801620i	$-0.296028\pi$
$929$	36.4434	1.19567	0.597834	+	0.801620i	$0.296028\pi$
$930$	13.4173	0.439971
$931$	24.4401	0.800991
$932$	−21.4247	−0.701790
$933$	33.6040	1.10015
$934$	−61.5207	−2.01302
$935$	2.42092	0.0791727
$936$	−29.4972	−0.964147
$937$	12.4941	0.408165	0.204083	−	0.978954i	$-0.434579\pi$
$937$	12.4941	0.408165	0.204083	+	0.978954i	$0.434579\pi$
$938$	−2.86396	−0.0935117
$939$	−13.1268	−0.428376
$940$	17.9901	0.586771
$941$	−36.2973	−1.18326	−0.591630	−	0.806210i	$-0.701515\pi$
$941$	−36.2973	−1.18326	−0.591630	+	0.806210i	$0.701515\pi$
$942$	−33.5067	−1.09171
$943$	7.59937	0.247470
$944$	−98.4252	−3.20347
$945$	0.223465	0.00726931
$946$	−34.3824	−1.11787
$947$	−51.3877	−1.66988	−0.834938	−	0.550345i	$-0.814496\pi$
$947$	−51.3877	−1.66988	−0.834938	+	0.550345i	$0.814496\pi$
$948$	−152.330	−4.94746
$949$	16.4727	0.534728
$950$	−42.7902	−1.38830
$951$	67.1070	2.17609
$952$	4.17210	0.135218
$953$	−8.28565	−0.268398	−0.134199	−	0.990954i	$-0.542846\pi$
$953$	−8.28565	−0.268398	−0.134199	+	0.990954i	$0.542846\pi$
$954$	−43.7176	−1.41541
$955$	13.1864	0.426702
$956$	−106.921	−3.45806
$957$	4.89750	0.158314
$958$	1.13937	0.0368114
$959$	−1.55308	−0.0501515
$960$	2.21511	0.0714923
$961$	−15.4039	−0.496900
$962$	−10.6687	−0.343973
$963$	−10.7406	−0.346112
$964$	9.77957	0.314979
$965$	−4.04566	−0.130234
$966$	−9.50697	−0.305882
$967$	−7.30019	−0.234758	−0.117379	−	0.993087i	$-0.537449\pi$
$967$	−7.30019	−0.234758	−0.117379	+	0.993087i	$0.537449\pi$
$968$	48.7938	1.56829
$969$	22.6036	0.726133
$970$	0.174537	0.00560406
$971$	14.1050	0.452650	0.226325	−	0.974052i	$-0.427329\pi$
$971$	14.1050	0.452650	0.226325	+	0.974052i	$0.427329\pi$
$972$	−101.036	−3.24072
$973$	−5.10523	−0.163666
$974$	−23.6184	−0.756781
$975$	−14.9329	−0.478236
$976$	−7.40102	−0.236901
$977$	−39.6840	−1.26960	−0.634802	−	0.772675i	$-0.718918\pi$
$977$	−39.6840	−1.26960	−0.634802	+	0.772675i	$0.718918\pi$
$978$	97.5458	3.11917
$979$	−13.1893	−0.421532
$980$	−16.2806	−0.520064
$981$	−4.24167	−0.135426
$982$	106.032	3.38361
$983$	10.2025	0.325409	0.162704	−	0.986675i	$-0.447978\pi$
$983$	10.2025	0.325409	0.162704	+	0.986675i	$0.447978\pi$
$984$	−22.9214	−0.730706
$985$	12.2400	0.390000
$986$	−6.37053	−0.202879
$987$	5.03635	0.160309
$988$	−19.6812	−0.626143
$989$	−39.8853	−1.26828
$990$	9.14658	0.290697
$991$	−48.1192	−1.52856	−0.764278	−	0.644887i	$-0.776905\pi$
$991$	−48.1192	−1.52856	−0.764278	+	0.644887i	$0.776905\pi$
$992$	26.4833	0.840845
$993$	76.7704	2.43624
$994$	6.02987	0.191256
$995$	−4.66645	−0.147936
$996$	−154.682	−4.90127
$997$	6.80439	0.215497	0.107749	−	0.994178i	$-0.465636\pi$
$997$	6.80439	0.215497	0.107749	+	0.994178i	$0.465636\pi$
$998$	−34.9675	−1.10688
$999$	5.82370	0.184254

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8033.2.a.b.1.11	✓	153

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8033.2.a.b.1.11	✓	153	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)

\(f(q)\)	\(=\)	\(q-2.56362 q^{2} +2.58113 q^{3} +4.57213 q^{4} +0.513446 q^{5} -6.61703 q^{6} +0.254616 q^{7} -6.59395 q^{8} +3.66224 q^{9} +O(q^{10})\)	\(q-2.56362 q^{2} +2.58113 q^{3} +4.57213 q^{4} +0.513446 q^{5} -6.61703 q^{6} +0.254616 q^{7} -6.59395 q^{8} +3.66224 q^{9} -1.31628 q^{10} -1.89742 q^{11} +11.8013 q^{12} +1.22149 q^{13} -0.652738 q^{14} +1.32527 q^{15} +7.76009 q^{16} -2.48498 q^{17} -9.38859 q^{18} -3.52408 q^{19} +2.34754 q^{20} +0.657198 q^{21} +4.86426 q^{22} +5.64278 q^{23} -17.0198 q^{24} -4.73637 q^{25} -3.13142 q^{26} +1.70934 q^{27} +1.16414 q^{28} -1.00000 q^{29} -3.39749 q^{30} -3.94919 q^{31} -6.70601 q^{32} -4.89750 q^{33} +6.37053 q^{34} +0.130732 q^{35} +16.7442 q^{36} +3.40699 q^{37} +9.03438 q^{38} +3.15282 q^{39} -3.38563 q^{40} +1.34674 q^{41} -1.68480 q^{42} -7.06838 q^{43} -8.67526 q^{44} +1.88036 q^{45} -14.4659 q^{46} +7.66337 q^{47} +20.0298 q^{48} -6.93517 q^{49} +12.1422 q^{50} -6.41406 q^{51} +5.58479 q^{52} +4.65646 q^{53} -4.38209 q^{54} -0.974223 q^{55} -1.67893 q^{56} -9.09611 q^{57} +2.56362 q^{58} -12.6835 q^{59} +6.05931 q^{60} -0.953728 q^{61} +10.1242 q^{62} +0.932467 q^{63} +1.67144 q^{64} +0.627166 q^{65} +12.5553 q^{66} +4.38761 q^{67} -11.3616 q^{68} +14.5648 q^{69} -0.335146 q^{70} -9.23780 q^{71} -24.1486 q^{72} +13.4858 q^{73} -8.73420 q^{74} -12.2252 q^{75} -16.1125 q^{76} -0.483115 q^{77} -8.08261 q^{78} -12.9080 q^{79} +3.98439 q^{80} -6.57470 q^{81} -3.45253 q^{82} -13.1072 q^{83} +3.00479 q^{84} -1.27590 q^{85} +18.1206 q^{86} -2.58113 q^{87} +12.5115 q^{88} +6.95117 q^{89} -4.82053 q^{90} +0.311010 q^{91} +25.7995 q^{92} -10.1934 q^{93} -19.6459 q^{94} -1.80942 q^{95} -17.3091 q^{96} -0.132599 q^{97} +17.7791 q^{98} -6.94882 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 153 q - 3 q^{2} - 12 q^{3} + 135 q^{4} - 11 q^{5} - 17 q^{6} - 76 q^{7} - 12 q^{8} + 133 q^{9}+O(q^{10}) \) 153 * q - 3 * q^2 - 12 * q^3 + 135 * q^4 - 11 * q^5 - 17 * q^6 - 76 * q^7 - 12 * q^8 + 133 * q^9	\( 153 q - 3 q^{2} - 12 q^{3} + 135 q^{4} - 11 q^{5} - 17 q^{6} - 76 q^{7} - 12 q^{8} + 133 q^{9} - 30 q^{10} + 4 q^{11} - 39 q^{12} - 65 q^{13} + q^{14} - 26 q^{15} + 107 q^{16} - 20 q^{17} - 21 q^{18} - 65 q^{19} - 23 q^{20} - 24 q^{21} - 59 q^{22} - 62 q^{23} - 59 q^{24} + 102 q^{25} - 18 q^{26} - 57 q^{27} - 155 q^{28} - 153 q^{29} - 82 q^{30} - 49 q^{31} - 17 q^{32} - 59 q^{33} - 68 q^{34} - 36 q^{35} + 74 q^{36} - 30 q^{37} - 67 q^{38} - 47 q^{39} - 108 q^{40} - 9 q^{41} - 62 q^{42} - 90 q^{43} - 14 q^{44} - 56 q^{45} - 52 q^{46} - 54 q^{47} - 76 q^{48} + 101 q^{49} - 36 q^{50} - 60 q^{51} - 191 q^{52} - 38 q^{53} - 82 q^{54} - 215 q^{55} + 24 q^{56} - 52 q^{57} + 3 q^{58} - 55 q^{59} - 60 q^{60} - 90 q^{61} - 66 q^{62} - 229 q^{63} + 52 q^{64} - 67 q^{65} - 29 q^{66} - 114 q^{67} - 78 q^{68} - 68 q^{69} - 61 q^{70} - 52 q^{71} - 47 q^{72} - 83 q^{73} - 21 q^{74} - 47 q^{75} - 100 q^{76} - 32 q^{77} - 17 q^{78} - 151 q^{79} - 24 q^{80} + 81 q^{81} - 151 q^{82} - 94 q^{83} - 84 q^{84} - 77 q^{85} - 43 q^{86} + 12 q^{87} - 121 q^{88} + 11 q^{89} - 14 q^{90} - 66 q^{91} - 156 q^{92} - 66 q^{93} - 22 q^{94} - 67 q^{95} - 131 q^{96} - 78 q^{97} - 67 q^{98} - 41 q^{99}+O(q^{100}) \) 153 * q - 3 * q^2 - 12 * q^3 + 135 * q^4 - 11 * q^5 - 17 * q^6 - 76 * q^7 - 12 * q^8 + 133 * q^9 - 30 * q^10 + 4 * q^11 - 39 * q^12 - 65 * q^13 + q^14 - 26 * q^15 + 107 * q^16 - 20 * q^17 - 21 * q^18 - 65 * q^19 - 23 * q^20 - 24 * q^21 - 59 * q^22 - 62 * q^23 - 59 * q^24 + 102 * q^25 - 18 * q^26 - 57 * q^27 - 155 * q^28 - 153 * q^29 - 82 * q^30 - 49 * q^31 - 17 * q^32 - 59 * q^33 - 68 * q^34 - 36 * q^35 + 74 * q^36 - 30 * q^37 - 67 * q^38 - 47 * q^39 - 108 * q^40 - 9 * q^41 - 62 * q^42 - 90 * q^43 - 14 * q^44 - 56 * q^45 - 52 * q^46 - 54 * q^47 - 76 * q^48 + 101 * q^49 - 36 * q^50 - 60 * q^51 - 191 * q^52 - 38 * q^53 - 82 * q^54 - 215 * q^55 + 24 * q^56 - 52 * q^57 + 3 * q^58 - 55 * q^59 - 60 * q^60 - 90 * q^61 - 66 * q^62 - 229 * q^63 + 52 * q^64 - 67 * q^65 - 29 * q^66 - 114 * q^67 - 78 * q^68 - 68 * q^69 - 61 * q^70 - 52 * q^71 - 47 * q^72 - 83 * q^73 - 21 * q^74 - 47 * q^75 - 100 * q^76 - 32 * q^77 - 17 * q^78 - 151 * q^79 - 24 * q^80 + 81 * q^81 - 151 * q^82 - 94 * q^83 - 84 * q^84 - 77 * q^85 - 43 * q^86 + 12 * q^87 - 121 * q^88 + 11 * q^89 - 14 * q^90 - 66 * q^91 - 156 * q^92 - 66 * q^93 - 22 * q^94 - 67 * q^95 - 131 * q^96 - 78 * q^97 - 67 * q^98 - 41 * q^99

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