LMFDB - Embedded newform 6029.2.a.b.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6029,2,Mod(1,6029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6029, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6029 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6029.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:	$48.1418073786$
Analytic rank:	$0$
Dimension:	$268$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	6029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.71891 q^{2} -2.75648 q^{3} +5.39247 q^{4} -2.65361 q^{5} +7.49462 q^{6} -3.09784 q^{7} -9.22383 q^{8} +4.59818 q^{9} +O(q^{10})$	\(q-2.71891 q^{2} -2.75648 q^{3} +5.39247 q^{4} -2.65361 q^{5} +7.49462 q^{6} -3.09784 q^{7} -9.22383 q^{8} +4.59818 q^{9} +7.21494 q^{10} -6.00726 q^{11} -14.8642 q^{12} -3.01496 q^{13} +8.42275 q^{14} +7.31463 q^{15} +14.2938 q^{16} -0.630155 q^{17} -12.5020 q^{18} +5.65656 q^{19} -14.3095 q^{20} +8.53913 q^{21} +16.3332 q^{22} +2.26570 q^{23} +25.4253 q^{24} +2.04167 q^{25} +8.19740 q^{26} -4.40534 q^{27} -16.7050 q^{28} +7.80191 q^{29} -19.8878 q^{30} +5.29682 q^{31} -20.4159 q^{32} +16.5589 q^{33} +1.71334 q^{34} +8.22047 q^{35} +24.7955 q^{36} -0.567352 q^{37} -15.3797 q^{38} +8.31067 q^{39} +24.4765 q^{40} -12.5843 q^{41} -23.2171 q^{42} -4.73797 q^{43} -32.3940 q^{44} -12.2018 q^{45} -6.16023 q^{46} +6.76665 q^{47} -39.4006 q^{48} +2.59661 q^{49} -5.55112 q^{50} +1.73701 q^{51} -16.2581 q^{52} +2.19672 q^{53} +11.9777 q^{54} +15.9409 q^{55} +28.5739 q^{56} -15.5922 q^{57} -21.2127 q^{58} -9.44726 q^{59} +39.4440 q^{60} -4.99859 q^{61} -14.4016 q^{62} -14.2444 q^{63} +26.9215 q^{64} +8.00054 q^{65} -45.0221 q^{66} +6.49640 q^{67} -3.39809 q^{68} -6.24535 q^{69} -22.3507 q^{70} -3.44103 q^{71} -42.4128 q^{72} -8.05091 q^{73} +1.54258 q^{74} -5.62782 q^{75} +30.5028 q^{76} +18.6095 q^{77} -22.5960 q^{78} +1.82930 q^{79} -37.9303 q^{80} -1.65130 q^{81} +34.2156 q^{82} -15.9578 q^{83} +46.0470 q^{84} +1.67219 q^{85} +12.8821 q^{86} -21.5058 q^{87} +55.4099 q^{88} -14.4025 q^{89} +33.1756 q^{90} +9.33986 q^{91} +12.2177 q^{92} -14.6006 q^{93} -18.3979 q^{94} -15.0103 q^{95} +56.2761 q^{96} +8.11577 q^{97} -7.05996 q^{98} -27.6224 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 268 q + 8 q^{2} + 43 q^{3} + 300 q^{4} + 18 q^{5} + 34 q^{6} + 59 q^{7} + 21 q^{8} + 295 q^{9}+O(q^{10}) $ 268 * q + 8 * q^2 + 43 * q^3 + 300 * q^4 + 18 * q^5 + 34 * q^6 + 59 * q^7 + 21 * q^8 + 295 * q^9	\( 268 q + 8 q^{2} + 43 q^{3} + 300 q^{4} + 18 q^{5} + 34 q^{6} + 59 q^{7} + 21 q^{8} + 295 q^{9} + 91 q^{10} + 49 q^{11} + 77 q^{12} + 45 q^{13} + 42 q^{14} + 37 q^{15} + 356 q^{16} + 40 q^{17} + 36 q^{18} + 245 q^{19} + 40 q^{20} + 66 q^{21} + 51 q^{22} + 26 q^{23} + 90 q^{24} + 314 q^{25} + 24 q^{26} + 160 q^{27} + 117 q^{28} + 54 q^{29} + 25 q^{30} + 181 q^{31} + 35 q^{32} + 49 q^{33} + 84 q^{34} + 73 q^{35} + 348 q^{36} + 77 q^{37} + 20 q^{38} + 96 q^{39} + 257 q^{40} + 62 q^{41} + 22 q^{42} + 199 q^{43} + 59 q^{44} + 60 q^{45} + 116 q^{46} + 41 q^{47} + 106 q^{48} + 381 q^{49} + 21 q^{50} + 248 q^{51} + 101 q^{52} + 4 q^{53} + 98 q^{54} + 136 q^{55} + 79 q^{56} + 47 q^{57} + 14 q^{58} + 170 q^{59} + 31 q^{60} + 247 q^{61} + 17 q^{62} + 143 q^{63} + 437 q^{64} + 29 q^{65} + 38 q^{66} + 114 q^{67} + 62 q^{68} + 101 q^{69} + 48 q^{70} + 64 q^{71} + 54 q^{72} + 115 q^{73} + 22 q^{74} + 250 q^{75} + 448 q^{76} + 8 q^{77} - 50 q^{78} + 271 q^{79} + 39 q^{80} + 336 q^{81} + 132 q^{82} + 74 q^{83} + 122 q^{84} + 58 q^{85} + 27 q^{86} + 105 q^{87} + 127 q^{88} + 63 q^{89} + 179 q^{90} + 406 q^{91} + 13 q^{92} + q^{93} + 263 q^{94} + 76 q^{95} + 161 q^{96} + 123 q^{97} - 7 q^{98} + 180 q^{99}+O(q^{100}) \) 268 * q + 8 * q^2 + 43 * q^3 + 300 * q^4 + 18 * q^5 + 34 * q^6 + 59 * q^7 + 21 * q^8 + 295 * q^9 + 91 * q^10 + 49 * q^11 + 77 * q^12 + 45 * q^13 + 42 * q^14 + 37 * q^15 + 356 * q^16 + 40 * q^17 + 36 * q^18 + 245 * q^19 + 40 * q^20 + 66 * q^21 + 51 * q^22 + 26 * q^23 + 90 * q^24 + 314 * q^25 + 24 * q^26 + 160 * q^27 + 117 * q^28 + 54 * q^29 + 25 * q^30 + 181 * q^31 + 35 * q^32 + 49 * q^33 + 84 * q^34 + 73 * q^35 + 348 * q^36 + 77 * q^37 + 20 * q^38 + 96 * q^39 + 257 * q^40 + 62 * q^41 + 22 * q^42 + 199 * q^43 + 59 * q^44 + 60 * q^45 + 116 * q^46 + 41 * q^47 + 106 * q^48 + 381 * q^49 + 21 * q^50 + 248 * q^51 + 101 * q^52 + 4 * q^53 + 98 * q^54 + 136 * q^55 + 79 * q^56 + 47 * q^57 + 14 * q^58 + 170 * q^59 + 31 * q^60 + 247 * q^61 + 17 * q^62 + 143 * q^63 + 437 * q^64 + 29 * q^65 + 38 * q^66 + 114 * q^67 + 62 * q^68 + 101 * q^69 + 48 * q^70 + 64 * q^71 + 54 * q^72 + 115 * q^73 + 22 * q^74 + 250 * q^75 + 448 * q^76 + 8 * q^77 - 50 * q^78 + 271 * q^79 + 39 * q^80 + 336 * q^81 + 132 * q^82 + 74 * q^83 + 122 * q^84 + 58 * q^85 + 27 * q^86 + 105 * q^87 + 127 * q^88 + 63 * q^89 + 179 * q^90 + 406 * q^91 + 13 * q^92 + q^93 + 263 * q^94 + 76 * q^95 + 161 * q^96 + 123 * q^97 - 7 * q^98 + 180 * 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 $

$2$	−2.71891	−1.92256	−0.961280	−	0.275574i	$-0.911132\pi$
$2$	−2.71891	−1.92256	−0.961280	+	0.275574i	$0.911132\pi$
$3$	−2.75648	−1.59145	−0.795727	−	0.605656i	$-0.792911\pi$
$3$	−2.75648	−1.59145	−0.795727	+	0.605656i	$0.792911\pi$
$4$	5.39247	2.69624
$5$	−2.65361	−1.18673	−0.593366	−	0.804933i	$-0.702201\pi$
$5$	−2.65361	−1.18673	−0.593366	+	0.804933i	$0.702201\pi$
$6$	7.49462	3.05967
$7$	−3.09784	−1.17087	−0.585437	−	0.810718i	$-0.699077\pi$
$7$	−3.09784	−1.17087	−0.585437	+	0.810718i	$0.699077\pi$
$8$	−9.22383	−3.26111
$9$	4.59818	1.53273
$10$	7.21494	2.28156
$11$	−6.00726	−1.81126	−0.905628	−	0.424073i	$-0.860600\pi$
$11$	−6.00726	−1.81126	−0.905628	+	0.424073i	$0.860600\pi$
$12$	−14.8642	−4.29094
$13$	−3.01496	−0.836199	−0.418100	−	0.908401i	$-0.637304\pi$
$13$	−3.01496	−0.836199	−0.418100	+	0.908401i	$0.637304\pi$
$14$	8.42275	2.25107
$15$	7.31463	1.88863
$16$	14.2938	3.57345
$17$	−0.630155	−0.152835	−0.0764175	−	0.997076i	$-0.524348\pi$
$17$	−0.630155	−0.152835	−0.0764175	+	0.997076i	$0.524348\pi$
$18$	−12.5020	−2.94676
$19$	5.65656	1.29770	0.648852	−	0.760915i	$-0.275250\pi$
$19$	5.65656	1.29770	0.648852	+	0.760915i	$0.275250\pi$
$20$	−14.3095	−3.19971
$21$	8.53913	1.86339
$22$	16.3332	3.48225
$23$	2.26570	0.472431	0.236215	−	0.971701i	$-0.424093\pi$
$23$	2.26570	0.472431	0.236215	+	0.971701i	$0.424093\pi$
$24$	25.4253	5.18991
$25$	2.04167	0.408334
$26$	8.19740	1.60764
$27$	−4.40534	−0.847808
$28$	−16.7050	−3.15695
$29$	7.80191	1.44878	0.724389	−	0.689391i	$-0.242122\pi$
$29$	7.80191	1.44878	0.724389	+	0.689391i	$0.242122\pi$
$30$	−19.8878	−3.63100
$31$	5.29682	0.951337	0.475669	−	0.879625i	$-0.342206\pi$
$31$	5.29682	0.951337	0.475669	+	0.879625i	$0.342206\pi$
$32$	−20.4159	−3.60906
$33$	16.5589	2.88253
$34$	1.71334	0.293835
$35$	8.22047	1.38951
$36$	24.7955	4.13259
$37$	−0.567352	−0.0932721	−0.0466361	−	0.998912i	$-0.514850\pi$
$37$	−0.567352	−0.0932721	−0.0466361	+	0.998912i	$0.514850\pi$
$38$	−15.3797	−2.49491
$39$	8.31067	1.33077
$40$	24.4765	3.87007
$41$	−12.5843	−1.96534	−0.982670	−	0.185362i	$-0.940654\pi$
$41$	−12.5843	−1.96534	−0.982670	+	0.185362i	$0.940654\pi$
$42$	−23.2171	−3.58248
$43$	−4.73797	−0.722533	−0.361267	−	0.932463i	$-0.617656\pi$
$43$	−4.73797	−0.722533	−0.361267	+	0.932463i	$0.617656\pi$
$44$	−32.3940	−4.88357
$45$	−12.2018	−1.81894
$46$	−6.16023	−0.908276
$47$	6.76665	0.987017	0.493509	−	0.869741i	$-0.335714\pi$
$47$	6.76665	0.987017	0.493509	+	0.869741i	$0.335714\pi$
$48$	−39.4006	−5.68698
$49$	2.59661	0.370945
$50$	−5.55112	−0.785047
$51$	1.73701	0.243230
$52$	−16.2581	−2.25459
$53$	2.19672	0.301743	0.150872	−	0.988553i	$-0.451792\pi$
$53$	2.19672	0.301743	0.150872	+	0.988553i	$0.451792\pi$
$54$	11.9777	1.62996
$55$	15.9409	2.14948
$56$	28.5739	3.81835
$57$	−15.5922	−2.06524
$58$	−21.2127	−2.78536
$59$	−9.44726	−1.22993	−0.614965	−	0.788555i	$-0.710830\pi$
$59$	−9.44726	−1.22993	−0.614965	+	0.788555i	$0.710830\pi$
$60$	39.4440	5.09219
$61$	−4.99859	−0.640004	−0.320002	−	0.947417i	$-0.603684\pi$
$61$	−4.99859	−0.640004	−0.320002	+	0.947417i	$0.603684\pi$
$62$	−14.4016	−1.82900
$63$	−14.2444	−1.79463
$64$	26.9215	3.36518
$65$	8.00054	0.992345
$66$	−45.0221	−5.54184
$67$	6.49640	0.793662	0.396831	−	0.917892i	$-0.370110\pi$
$67$	6.49640	0.793662	0.396831	+	0.917892i	$0.370110\pi$
$68$	−3.39809	−0.412079
$69$	−6.24535	−0.751852
$70$	−22.3507	−2.67142
$71$	−3.44103	−0.408375	−0.204187	−	0.978932i	$-0.565455\pi$
$71$	−3.44103	−0.408375	−0.204187	+	0.978932i	$0.565455\pi$
$72$	−42.4128	−4.99839
$73$	−8.05091	−0.942287	−0.471144	−	0.882056i	$-0.656159\pi$
$73$	−8.05091	−0.942287	−0.471144	+	0.882056i	$0.656159\pi$
$74$	1.54258	0.179321
$75$	−5.62782	−0.649845
$76$	30.5028	3.49892
$77$	18.6095	2.12075
$78$	−22.5960	−2.55849
$79$	1.82930	0.205812	0.102906	−	0.994691i	$-0.467186\pi$
$79$	1.82930	0.205812	0.102906	+	0.994691i	$0.467186\pi$
$80$	−37.9303	−4.24073
$81$	−1.65130	−0.183478
$82$	34.2156	3.77848
$83$	−15.9578	−1.75159	−0.875796	−	0.482682i	$-0.839663\pi$
$83$	−15.9578	−1.75159	−0.875796	+	0.482682i	$0.839663\pi$
$84$	46.0470	5.02414
$85$	1.67219	0.181374
$86$	12.8821	1.38911
$87$	−21.5058	−2.30566
$88$	55.4099	5.90671
$89$	−14.4025	−1.52667	−0.763333	−	0.646005i	$-0.776439\pi$
$89$	−14.4025	−1.52667	−0.763333	+	0.646005i	$0.776439\pi$
$90$	33.1756	3.49701
$91$	9.33986	0.979084
$92$	12.2177	1.27378
$93$	−14.6006	−1.51401
$94$	−18.3979	−1.89760
$95$	−15.0103	−1.54003
$96$	56.2761	5.74365
$97$	8.11577	0.824032	0.412016	−	0.911177i	$-0.364825\pi$
$97$	8.11577	0.824032	0.412016	+	0.911177i	$0.364825\pi$
$98$	−7.05996	−0.713163
$99$	−27.6224	−2.77616
$100$	11.0097	1.10097
$101$	11.5766	1.15192	0.575959	−	0.817479i	$-0.304629\pi$
$101$	11.5766	1.15192	0.575959	+	0.817479i	$0.304629\pi$
$102$	−4.72277	−0.467624
$103$	2.57728	0.253947	0.126973	−	0.991906i	$-0.459474\pi$
$103$	2.57728	0.253947	0.126973	+	0.991906i	$0.459474\pi$
$104$	27.8095	2.72694
$105$	−22.6596	−2.21135
$106$	−5.97270	−0.580120
$107$	−16.0137	−1.54810	−0.774051	−	0.633123i	$-0.781773\pi$
$107$	−16.0137	−1.54810	−0.774051	+	0.633123i	$0.781773\pi$
$108$	−23.7557	−2.28589
$109$	9.04409	0.866267	0.433134	−	0.901330i	$-0.357408\pi$
$109$	9.04409	0.866267	0.433134	+	0.901330i	$0.357408\pi$
$110$	−43.3420	−4.13250
$111$	1.56389	0.148438
$112$	−44.2799	−4.18406
$113$	−16.7891	−1.57939	−0.789693	−	0.613502i	$-0.789760\pi$
$113$	−16.7891	−1.57939	−0.789693	+	0.613502i	$0.789760\pi$
$114$	42.3938	3.97054
$115$	−6.01229	−0.560649
$116$	42.0716	3.90625
$117$	−13.8633	−1.28166
$118$	25.6863	2.36461
$119$	1.95212	0.178951
$120$	−67.4689	−6.15904
$121$	25.0871	2.28065
$122$	13.5907	1.23045
$123$	34.6884	3.12775
$124$	28.5630	2.56503
$125$	7.85027	0.702149
$126$	38.7293	3.45028
$127$	−18.3217	−1.62579	−0.812895	−	0.582410i	$-0.802110\pi$
$127$	−18.3217	−1.62579	−0.812895	+	0.582410i	$0.802110\pi$
$128$	−32.3652	−2.86070
$129$	13.0601	1.14988
$130$	−21.7527	−1.90784
$131$	19.4905	1.70290	0.851448	−	0.524439i	$-0.175725\pi$
$131$	19.4905	1.70290	0.851448	+	0.524439i	$0.175725\pi$
$132$	89.2933	7.77198
$133$	−17.5231	−1.51945
$134$	−17.6631	−1.52586
$135$	11.6901	1.00612
$136$	5.81244	0.498413
$137$	−16.6544	−1.42289	−0.711443	−	0.702744i	$-0.751958\pi$
$137$	−16.6544	−1.42289	−0.711443	+	0.702744i	$0.751958\pi$
$138$	16.9805	1.44548
$139$	−4.77838	−0.405297	−0.202648	−	0.979252i	$-0.564955\pi$
$139$	−4.77838	−0.405297	−0.202648	+	0.979252i	$0.564955\pi$
$140$	44.3287	3.74646
$141$	−18.6521	−1.57079
$142$	9.35584	0.785125
$143$	18.1116	1.51457
$144$	65.7255	5.47712
$145$	−20.7033	−1.71931
$146$	21.8897	1.81160
$147$	−7.15751	−0.590341
$148$	−3.05943	−0.251484
$149$	8.56775	0.701897	0.350949	−	0.936395i	$-0.385859\pi$
$149$	8.56775	0.701897	0.350949	+	0.936395i	$0.385859\pi$
$150$	15.3015	1.24937
$151$	−15.9882	−1.30110	−0.650550	−	0.759464i	$-0.725462\pi$
$151$	−15.9882	−1.30110	−0.650550	+	0.759464i	$0.725462\pi$
$152$	−52.1751	−4.23196
$153$	−2.89756	−0.234254
$154$	−50.5976	−4.07727
$155$	−14.0557	−1.12898
$156$	44.8151	3.58808
$157$	−9.20697	−0.734796	−0.367398	−	0.930064i	$-0.619751\pi$
$157$	−9.20697	−0.734796	−0.367398	+	0.930064i	$0.619751\pi$
$158$	−4.97369	−0.395686
$159$	−6.05523	−0.480211
$160$	54.1760	4.28299
$161$	−7.01877	−0.553157
$162$	4.48974	0.352747
$163$	−15.4756	−1.21214	−0.606072	−	0.795410i	$-0.707256\pi$
$163$	−15.4756	−1.21214	−0.606072	+	0.795410i	$0.707256\pi$
$164$	−67.8606	−5.29902
$165$	−43.9409	−3.42079
$166$	43.3877	3.36754
$167$	5.20231	0.402567	0.201283	−	0.979533i	$-0.435489\pi$
$167$	5.20231	0.402567	0.201283	+	0.979533i	$0.435489\pi$
$168$	−78.7635	−6.07673
$169$	−3.91002	−0.300771
$170$	−4.54653	−0.348703
$171$	26.0099	1.98902
$172$	−25.5494	−1.94812
$173$	−1.06593	−0.0810414	−0.0405207	−	0.999179i	$-0.512902\pi$
$173$	−1.06593	−0.0810414	−0.0405207	+	0.999179i	$0.512902\pi$
$174$	58.4723	4.43278
$175$	−6.32477	−0.478108
$176$	−85.8666	−6.47244
$177$	26.0412	1.95738
$178$	39.1592	2.93511
$179$	−3.29694	−0.246425	−0.123213	−	0.992380i	$-0.539320\pi$
$179$	−3.29694	−0.246425	−0.123213	+	0.992380i	$0.539320\pi$
$180$	−65.7978	−4.90428
$181$	−0.146384	−0.0108807	−0.00544033	−	0.999985i	$-0.501732\pi$
$181$	−0.146384	−0.0108807	−0.00544033	+	0.999985i	$0.501732\pi$
$182$	−25.3942	−1.88235
$183$	13.7785	1.01854
$184$	−20.8984	−1.54065
$185$	1.50553	0.110689
$186$	39.6977	2.91077
$187$	3.78550	0.276823
$188$	36.4890	2.66123
$189$	13.6470	0.992676
$190$	40.8117	2.96079
$191$	−12.9093	−0.934083	−0.467041	−	0.884235i	$-0.654680\pi$
$191$	−12.9093	−0.934083	−0.467041	+	0.884235i	$0.654680\pi$
$192$	−74.2084	−5.35553
$193$	14.0852	1.01387	0.506937	−	0.861983i	$-0.330778\pi$
$193$	14.0852	1.01387	0.506937	+	0.861983i	$0.330778\pi$
$194$	−22.0661	−1.58425
$195$	−22.0533	−1.57927
$196$	14.0022	1.00015
$197$	−13.7450	−0.979290	−0.489645	−	0.871922i	$-0.662874\pi$
$197$	−13.7450	−0.979290	−0.489645	+	0.871922i	$0.662874\pi$
$198$	75.1029	5.33733
$199$	10.4866	0.743375	0.371688	−	0.928358i	$-0.378779\pi$
$199$	10.4866	0.743375	0.371688	+	0.928358i	$0.378779\pi$
$200$	−18.8320	−1.33162
$201$	−17.9072	−1.26308
$202$	−31.4758	−2.21463
$203$	−24.1691	−1.69634
$204$	9.36677	0.655805
$205$	33.3939	2.33233
$206$	−7.00739	−0.488228
$207$	10.4181	0.724107
$208$	−43.0953	−2.98812
$209$	−33.9804	−2.35047
$210$	61.6093	4.25145
$211$	16.4300	1.13109	0.565544	−	0.824718i	$-0.308666\pi$
$211$	16.4300	1.13109	0.565544	+	0.824718i	$0.308666\pi$
$212$	11.8458	0.813571
$213$	9.48512	0.649909
$214$	43.5398	2.97632
$215$	12.5727	0.857454
$216$	40.6341	2.76480
$217$	−16.4087	−1.11390
$218$	−24.5901	−1.66545
$219$	22.1922	1.49961
$220$	85.9611	5.79550
$221$	1.89989	0.127801
$222$	−4.25209	−0.285382
$223$	−15.4980	−1.03783	−0.518913	−	0.854827i	$-0.673663\pi$
$223$	−15.4980	−1.03783	−0.518913	+	0.854827i	$0.673663\pi$
$224$	63.2453	4.22575
$225$	9.38796	0.625864
$226$	45.6481	3.03646
$227$	15.5188	1.03002	0.515008	−	0.857185i	$-0.327789\pi$
$227$	15.5188	1.03002	0.515008	+	0.857185i	$0.327789\pi$
$228$	−84.0804	−5.56836
$229$	−12.1440	−0.802496	−0.401248	−	0.915970i	$-0.631423\pi$
$229$	−12.1440	−0.802496	−0.401248	+	0.915970i	$0.631423\pi$
$230$	16.3469	1.07788
$231$	−51.2968	−3.37508
$232$	−71.9634	−4.72463
$233$	−14.4964	−0.949693	−0.474847	−	0.880069i	$-0.657496\pi$
$233$	−14.4964	−0.949693	−0.474847	+	0.880069i	$0.657496\pi$
$234$	37.6931	2.46408
$235$	−17.9561	−1.17133
$236$	−50.9441	−3.31618
$237$	−5.04242	−0.327540
$238$	−5.30764	−0.344043
$239$	−21.0292	−1.36026	−0.680132	−	0.733090i	$-0.738078\pi$
$239$	−21.0292	−1.36026	−0.680132	+	0.733090i	$0.738078\pi$
$240$	104.554	6.74893
$241$	−25.2107	−1.62397	−0.811983	−	0.583681i	$-0.801612\pi$
$241$	−25.2107	−1.62397	−0.811983	+	0.583681i	$0.801612\pi$
$242$	−68.2097	−4.38468
$243$	17.7678	1.13980
$244$	−26.9548	−1.72560
$245$	−6.89041	−0.440212
$246$	−94.3147	−6.01328
$247$	−17.0543	−1.08514
$248$	−48.8570	−3.10242
$249$	43.9872	2.78758
$250$	−21.3442	−1.34992
$251$	1.31310	0.0828819	0.0414409	−	0.999141i	$-0.486805\pi$
$251$	1.31310	0.0828819	0.0414409	+	0.999141i	$0.486805\pi$
$252$	−76.8126	−4.83874
$253$	−13.6106	−0.855693
$254$	49.8151	3.12568
$255$	−4.60935	−0.288649
$256$	34.1550	2.13469
$257$	−25.4601	−1.58816	−0.794080	−	0.607814i	$-0.792047\pi$
$257$	−25.4601	−1.58816	−0.794080	+	0.607814i	$0.792047\pi$
$258$	−35.5093	−2.21071
$259$	1.75757	0.109210
$260$	43.1427	2.67560
$261$	35.8746	2.22058
$262$	−52.9930	−3.27392
$263$	0.985931	0.0607951	0.0303975	−	0.999538i	$-0.490323\pi$
$263$	0.985931	0.0607951	0.0303975	+	0.999538i	$0.490323\pi$
$264$	−152.736	−9.40026
$265$	−5.82926	−0.358089
$266$	47.6438	2.92123
$267$	39.7003	2.42962
$268$	35.0317	2.13990
$269$	−11.3702	−0.693254	−0.346627	−	0.938003i	$-0.612673\pi$
$269$	−11.3702	−0.693254	−0.346627	+	0.938003i	$0.612673\pi$
$270$	−31.7843	−1.93433
$271$	28.5927	1.73688	0.868441	−	0.495793i	$-0.165122\pi$
$271$	28.5927	1.73688	0.868441	+	0.495793i	$0.165122\pi$
$272$	−9.00732	−0.546149
$273$	−25.7451	−1.55817
$274$	45.2819	2.73558
$275$	−12.2648	−0.739598
$276$	−33.6779	−2.02717
$277$	12.1981	0.732913	0.366457	−	0.930435i	$-0.380571\pi$
$277$	12.1981	0.732913	0.366457	+	0.930435i	$0.380571\pi$
$278$	12.9920	0.779207
$279$	24.3557	1.45814
$280$	−75.8242	−4.53136
$281$	−9.19674	−0.548631	−0.274316	−	0.961640i	$-0.588451\pi$
$281$	−9.19674	−0.548631	−0.274316	+	0.961640i	$0.588451\pi$
$282$	50.7135	3.01994
$283$	16.9302	1.00640	0.503198	−	0.864171i	$-0.332157\pi$
$283$	16.9302	1.00640	0.503198	+	0.864171i	$0.332157\pi$
$284$	−18.5556	−1.10107
$285$	41.3757	2.45088
$286$	−49.2439	−2.91185
$287$	38.9842	2.30117
$288$	−93.8760	−5.53170
$289$	−16.6029	−0.976641
$290$	56.2903	3.30548
$291$	−22.3710	−1.31141
$292$	−43.4143	−2.54063
$293$	15.4841	0.904591	0.452295	−	0.891868i	$-0.350605\pi$
$293$	15.4841	0.904591	0.452295	+	0.891868i	$0.350605\pi$
$294$	19.4606	1.13497
$295$	25.0694	1.45960
$296$	5.23316	0.304171
$297$	26.4640	1.53560
$298$	−23.2949	−1.34944
$299$	−6.83099	−0.395046
$300$	−30.3479	−1.75214
$301$	14.6775	0.845995
$302$	43.4704	2.50144
$303$	−31.9107	−1.83322
$304$	80.8538	4.63728
$305$	13.2643	0.759514
$306$	7.87822	0.450368
$307$	−25.6463	−1.46371	−0.731857	−	0.681459i	$-0.761346\pi$
$307$	−25.6463	−1.46371	−0.731857	+	0.681459i	$0.761346\pi$
$308$	100.351	5.71805
$309$	−7.10421	−0.404145
$310$	38.2162	2.17054
$311$	−11.6923	−0.663010	−0.331505	−	0.943453i	$-0.607556\pi$
$311$	−11.6923	−0.663010	−0.331505	+	0.943453i	$0.607556\pi$
$312$	−76.6562	−4.33980
$313$	−7.44191	−0.420642	−0.210321	−	0.977632i	$-0.567451\pi$
$313$	−7.44191	−0.420642	−0.210321	+	0.977632i	$0.567451\pi$
$314$	25.0329	1.41269
$315$	37.7992	2.12974
$316$	9.86443	0.554918
$317$	1.98729	0.111617	0.0558086	−	0.998441i	$-0.482226\pi$
$317$	1.98729	0.111617	0.0558086	+	0.998441i	$0.482226\pi$
$318$	16.4636	0.923234
$319$	−46.8681	−2.62411
$320$	−71.4392	−3.99357
$321$	44.1414	2.46373
$322$	19.0834	1.06348
$323$	−3.56451	−0.198335
$324$	−8.90459	−0.494700
$325$	−6.15555	−0.341449
$326$	42.0768	2.33042
$327$	−24.9299	−1.37862
$328$	116.076	6.40920
$329$	−20.9620	−1.15567
$330$	119.471	6.57668
$331$	−31.0316	−1.70565	−0.852825	−	0.522197i	$-0.825112\pi$
$331$	−31.0316	−1.70565	−0.852825	+	0.522197i	$0.825112\pi$
$332$	−86.0517	−4.72270
$333$	−2.60879	−0.142961
$334$	−14.1446	−0.773959
$335$	−17.2390	−0.941865
$336$	122.057	6.65874
$337$	−3.74314	−0.203902	−0.101951	−	0.994789i	$-0.532508\pi$
$337$	−3.74314	−0.203902	−0.101951	+	0.994789i	$0.532508\pi$
$338$	10.6310	0.578250
$339$	46.2788	2.51352
$340$	9.01723	0.489028
$341$	−31.8194	−1.72312
$342$	−70.7185	−3.82402
$343$	13.6410	0.736544
$344$	43.7022	2.35626
$345$	16.5727	0.892247
$346$	2.89818	0.155807
$347$	13.8268	0.742262	0.371131	−	0.928580i	$-0.378970\pi$
$347$	13.8268	0.742262	0.371131	+	0.928580i	$0.378970\pi$
$348$	−115.969	−6.21661
$349$	28.1676	1.50777	0.753887	−	0.657004i	$-0.228176\pi$
$349$	28.1676	1.50777	0.753887	+	0.657004i	$0.228176\pi$
$350$	17.1965	0.919190
$351$	13.2819	0.708937
$352$	122.644	6.53693
$353$	−9.61827	−0.511929	−0.255964	−	0.966686i	$-0.582393\pi$
$353$	−9.61827	−0.511929	−0.255964	+	0.966686i	$0.582393\pi$
$354$	−70.8036	−3.76317
$355$	9.13116	0.484631
$356$	−77.6653	−4.11625
$357$	−5.38098	−0.284792
$358$	8.96409	0.473767
$359$	9.11804	0.481232	0.240616	−	0.970620i	$-0.422651\pi$
$359$	9.11804	0.481232	0.240616	+	0.970620i	$0.422651\pi$
$360$	112.547	5.93176
$361$	12.9967	0.684035
$362$	0.398006	0.0209187
$363$	−69.1522	−3.62955
$364$	50.3649	2.63984
$365$	21.3640	1.11824
$366$	−37.4625	−1.95820
$367$	−30.4827	−1.59119	−0.795593	−	0.605831i	$-0.792841\pi$
$367$	−30.4827	−1.59119	−0.795593	+	0.605831i	$0.792841\pi$
$368$	32.3855	1.68821
$369$	−57.8649	−3.01233
$370$	−4.09341	−0.212806
$371$	−6.80510	−0.353303
$372$	−78.7332	−4.08213
$373$	−0.939887	−0.0486655	−0.0243328	−	0.999704i	$-0.507746\pi$
$373$	−0.939887	−0.0486655	−0.0243328	+	0.999704i	$0.507746\pi$
$374$	−10.2924	−0.532210
$375$	−21.6391	−1.11744
$376$	−62.4144	−3.21878
$377$	−23.5224	−1.21147
$378$	−37.1051	−1.90848
$379$	10.6706	0.548113	0.274056	−	0.961714i	$-0.411635\pi$
$379$	10.6706	0.548113	0.274056	+	0.961714i	$0.411635\pi$
$380$	−80.9428	−4.15228
$381$	50.5034	2.58737
$382$	35.0992	1.79583
$383$	−0.394692	−0.0201678	−0.0100839	−	0.999949i	$-0.503210\pi$
$383$	−0.394692	−0.0201678	−0.0100839	+	0.999949i	$0.503210\pi$
$384$	89.2139	4.55268
$385$	−49.3825	−2.51677
$386$	−38.2964	−1.94923
$387$	−21.7860	−1.10745
$388$	43.7641	2.22178
$389$	−31.1904	−1.58142	−0.790708	−	0.612194i	$-0.790287\pi$
$389$	−31.1904	−1.58142	−0.790708	+	0.612194i	$0.790287\pi$
$390$	59.9610	3.03624
$391$	−1.42774	−0.0722040
$392$	−23.9507	−1.20969
$393$	−53.7253	−2.71008
$394$	37.3714	1.88274
$395$	−4.85425	−0.244244
$396$	−148.953	−7.48518
$397$	2.42087	0.121500	0.0607500	−	0.998153i	$-0.480651\pi$
$397$	2.42087	0.121500	0.0607500	+	0.998153i	$0.480651\pi$
$398$	−28.5121	−1.42918
$399$	48.3021	2.41813
$400$	29.1832	1.45916
$401$	−21.1338	−1.05537	−0.527686	−	0.849440i	$-0.676940\pi$
$401$	−21.1338	−1.05537	−0.527686	+	0.849440i	$0.676940\pi$
$402$	48.6881	2.42834
$403$	−15.9697	−0.795507
$404$	62.4266	3.10584
$405$	4.38192	0.217739
$406$	65.7135	3.26131
$407$	3.40823	0.168940
$408$	−16.0219	−0.793201
$409$	−4.37821	−0.216489	−0.108244	−	0.994124i	$-0.534523\pi$
$409$	−4.37821	−0.216489	−0.108244	+	0.994124i	$0.534523\pi$
$410$	−90.7951	−4.48405
$411$	45.9076	2.26446
$412$	13.8979	0.684700
$413$	29.2661	1.44009
$414$	−28.3258	−1.39214
$415$	42.3457	2.07867
$416$	61.5532	3.01789
$417$	13.1715	0.645011
$418$	92.3897	4.51893
$419$	−5.49859	−0.268624	−0.134312	−	0.990939i	$-0.542882\pi$
$419$	−5.49859	−0.268624	−0.134312	+	0.990939i	$0.542882\pi$
$420$	−122.191	−5.96231
$421$	−15.8180	−0.770924	−0.385462	−	0.922724i	$-0.625958\pi$
$421$	−15.8180	−0.770924	−0.385462	+	0.922724i	$0.625958\pi$
$422$	−44.6717	−2.17458
$423$	31.1143	1.51283
$424$	−20.2622	−0.984020
$425$	−1.28657	−0.0624078
$426$	−25.7892	−1.24949
$427$	15.4848	0.749364
$428$	−86.3534	−4.17405
$429$	−49.9243	−2.41037
$430$	−34.1842	−1.64851
$431$	0.437165	0.0210575	0.0105287	−	0.999945i	$-0.496649\pi$
$431$	0.437165	0.0210575	0.0105287	+	0.999945i	$0.496649\pi$
$432$	−62.9691	−3.02960
$433$	−8.51482	−0.409196	−0.204598	−	0.978846i	$-0.565589\pi$
$433$	−8.51482	−0.409196	−0.204598	+	0.978846i	$0.565589\pi$
$434$	44.6138	2.14153
$435$	57.0681	2.73621
$436$	48.7700	2.33566
$437$	12.8161	0.613075
$438$	−60.3385	−2.88308
$439$	−27.0374	−1.29043	−0.645213	−	0.764002i	$-0.723232\pi$
$439$	−27.0374	−1.29043	−0.645213	+	0.764002i	$0.723232\pi$
$440$	−147.037	−7.00969
$441$	11.9397	0.568556
$442$	−5.16564	−0.245704
$443$	26.2514	1.24724	0.623622	−	0.781726i	$-0.285661\pi$
$443$	26.2514	1.24724	0.623622	+	0.781726i	$0.285661\pi$
$444$	8.43326	0.400225
$445$	38.2188	1.81175
$446$	42.1378	1.99528
$447$	−23.6168	−1.11704
$448$	−83.3984	−3.94020
$449$	−14.1309	−0.666877	−0.333438	−	0.942772i	$-0.608209\pi$
$449$	−14.1309	−0.666877	−0.333438	+	0.942772i	$0.608209\pi$
$450$	−25.5250	−1.20326
$451$	75.5973	3.55974
$452$	−90.5348	−4.25840
$453$	44.0711	2.07064
$454$	−42.1941	−1.98027
$455$	−24.7844	−1.16191
$456$	143.820	6.73497
$457$	−27.5978	−1.29097	−0.645486	−	0.763772i	$-0.723345\pi$
$457$	−27.5978	−1.29097	−0.645486	+	0.763772i	$0.723345\pi$
$458$	33.0183	1.54285
$459$	2.77605	0.129575
$460$	−32.4211	−1.51164
$461$	−29.3047	−1.36486	−0.682429	−	0.730952i	$-0.739076\pi$
$461$	−29.3047	−1.36486	−0.682429	+	0.730952i	$0.739076\pi$
$462$	139.471	6.48879
$463$	23.6922	1.10107	0.550535	−	0.834812i	$-0.314424\pi$
$463$	23.6922	1.10107	0.550535	+	0.834812i	$0.314424\pi$
$464$	111.519	5.17714
$465$	38.7443	1.79672
$466$	39.4145	1.82584
$467$	4.46313	0.206529	0.103265	−	0.994654i	$-0.467071\pi$
$467$	4.46313	0.206529	0.103265	+	0.994654i	$0.467071\pi$
$468$	−74.7575	−3.45567
$469$	−20.1248	−0.929278
$470$	48.8210	2.25194
$471$	25.3788	1.16939
$472$	87.1399	4.01094
$473$	28.4622	1.30869
$474$	13.7099	0.629716
$475$	11.5488	0.529897
$476$	10.5268	0.482493
$477$	10.1009	0.462490
$478$	57.1764	2.61519
$479$	32.7747	1.49751	0.748757	−	0.662845i	$-0.230651\pi$
$479$	32.7747	1.49751	0.748757	+	0.662845i	$0.230651\pi$
$480$	−149.335	−6.81618
$481$	1.71054	0.0779941
$482$	68.5457	3.12217
$483$	19.3471	0.880323
$484$	135.282	6.14917
$485$	−21.5361	−0.977906
$486$	−48.3090	−2.19134
$487$	−9.39555	−0.425753	−0.212877	−	0.977079i	$-0.568283\pi$
$487$	−9.39555	−0.425753	−0.212877	+	0.977079i	$0.568283\pi$
$488$	46.1061	2.08713
$489$	42.6582	1.92907
$490$	18.7344	0.846334
$491$	21.9263	0.989519	0.494760	−	0.869030i	$-0.335256\pi$
$491$	21.9263	0.989519	0.494760	+	0.869030i	$0.335256\pi$
$492$	187.056	8.43315
$493$	−4.91641	−0.221424
$494$	46.3691	2.08624
$495$	73.2993	3.29456
$496$	75.7117	3.39956
$497$	10.6597	0.478155
$498$	−119.597	−5.35928
$499$	−19.2879	−0.863444	−0.431722	−	0.902007i	$-0.642094\pi$
$499$	−19.2879	−0.863444	−0.431722	+	0.902007i	$0.642094\pi$
$500$	42.3323	1.89316
$501$	−14.3401	−0.640667
$502$	−3.57019	−0.159345
$503$	38.1751	1.70214	0.851071	−	0.525051i	$-0.175954\pi$
$503$	38.1751	1.70214	0.851071	+	0.525051i	$0.175954\pi$
$504$	131.388	5.85249
$505$	−30.7199	−1.36702
$506$	37.0061	1.64512
$507$	10.7779	0.478663
$508$	−98.7994	−4.38351
$509$	−26.7759	−1.18682	−0.593410	−	0.804900i	$-0.702219\pi$
$509$	−26.7759	−1.18682	−0.593410	+	0.804900i	$0.702219\pi$
$510$	12.5324	0.554945
$511$	24.9404	1.10330
$512$	−28.1342	−1.24337
$513$	−24.9191	−1.10020
$514$	69.2238	3.05333
$515$	−6.83910	−0.301367
$516$	70.4263	3.10034
$517$	−40.6490	−1.78774
$518$	−4.77867	−0.209963
$519$	2.93822	0.128974
$520$	−73.7956	−3.23615
$521$	12.2589	0.537073	0.268536	−	0.963270i	$-0.413460\pi$
$521$	12.2589	0.537073	0.268536	+	0.963270i	$0.413460\pi$
$522$	−97.5397	−4.26920
$523$	15.1909	0.664251	0.332126	−	0.943235i	$-0.392234\pi$
$523$	15.1909	0.664251	0.332126	+	0.943235i	$0.392234\pi$
$524$	105.102	4.59141
$525$	17.4341	0.760886
$526$	−2.68066	−0.116882
$527$	−3.33782	−0.145398
$528$	236.689	10.3006
$529$	−17.8666	−0.776809
$530$	15.8492	0.688447
$531$	−43.4402	−1.88514
$532$	−94.4929	−4.09679
$533$	37.9412	1.64342
$534$	−107.942	−4.67109
$535$	42.4942	1.83718
$536$	−59.9217	−2.58822
$537$	9.08796	0.392174
$538$	30.9146	1.33282
$539$	−15.5985	−0.671876
$540$	63.0384	2.71274
$541$	−12.3252	−0.529901	−0.264950	−	0.964262i	$-0.585356\pi$
$541$	−12.3252	−0.529901	−0.264950	+	0.964262i	$0.585356\pi$
$542$	−77.7409	−3.33926
$543$	0.403505	0.0173161
$544$	12.8652	0.551591
$545$	−23.9995	−1.02803
$546$	69.9987	2.99567
$547$	−29.2640	−1.25124	−0.625619	−	0.780129i	$-0.715153\pi$
$547$	−29.2640	−1.25124	−0.625619	+	0.780129i	$0.715153\pi$
$548$	−89.8086	−3.83643
$549$	−22.9844	−0.980951
$550$	33.3470	1.42192
$551$	44.1320	1.88008
$552$	57.6060	2.45187
$553$	−5.66687	−0.240980
$554$	−33.1655	−1.40907
$555$	−4.14997	−0.176157
$556$	−25.7673	−1.09278
$557$	12.4722	0.528463	0.264231	−	0.964459i	$-0.414882\pi$
$557$	12.4722	0.528463	0.264231	+	0.964459i	$0.414882\pi$
$558$	−66.2210	−2.80336
$559$	14.2848	0.604182
$560$	117.502	4.96536
$561$	−10.4347	−0.440552
$562$	25.0051	1.05478
$563$	−25.2880	−1.06576	−0.532882	−	0.846190i	$-0.678891\pi$
$563$	−25.2880	−1.06576	−0.532882	+	0.846190i	$0.678891\pi$
$564$	−100.581	−4.23523
$565$	44.5518	1.87431
$566$	−46.0317	−1.93486
$567$	5.11547	0.214829
$568$	31.7394	1.33176
$569$	−22.0100	−0.922706	−0.461353	−	0.887217i	$-0.652636\pi$
$569$	−22.0100	−0.922706	−0.461353	+	0.887217i	$0.652636\pi$
$570$	−112.497	−4.71197
$571$	31.9929	1.33886	0.669431	−	0.742874i	$-0.266538\pi$
$571$	31.9929	1.33886	0.669431	+	0.742874i	$0.266538\pi$
$572$	97.6665	4.08364
$573$	35.5842	1.48655
$574$	−105.995	−4.42413
$575$	4.62581	0.192910
$576$	123.790	5.15790
$577$	−25.6123	−1.06625	−0.533127	−	0.846035i	$-0.678983\pi$
$577$	−25.6123	−1.06625	−0.533127	+	0.846035i	$0.678983\pi$
$578$	45.1418	1.87765
$579$	−38.8255	−1.61353
$580$	−111.642	−4.63567
$581$	49.4346	2.05089
$582$	60.8246	2.52126
$583$	−13.1963	−0.546535
$584$	74.2602	3.07291
$585$	36.7879	1.52099
$586$	−42.0999	−1.73913
$587$	22.9962	0.949156	0.474578	−	0.880213i	$-0.342601\pi$
$587$	22.9962	0.949156	0.474578	+	0.880213i	$0.342601\pi$
$588$	−38.5967	−1.59170
$589$	29.9618	1.23455
$590$	−68.1614	−2.80616
$591$	37.8878	1.55850
$592$	−8.10963	−0.333304
$593$	−27.1549	−1.11512	−0.557560	−	0.830137i	$-0.688262\pi$
$593$	−27.1549	−1.11512	−0.557560	+	0.830137i	$0.688262\pi$
$594$	−71.9533	−2.95228
$595$	−5.18017	−0.212366
$596$	46.2013	1.89248
$597$	−28.9061	−1.18305
$598$	18.5728	0.759500
$599$	−23.5897	−0.963847	−0.481924	−	0.876213i	$-0.660062\pi$
$599$	−23.5897	−0.963847	−0.481924	+	0.876213i	$0.660062\pi$
$600$	51.9101	2.11922
$601$	45.8599	1.87067	0.935333	−	0.353769i	$-0.115100\pi$
$601$	45.8599	1.87067	0.935333	+	0.353769i	$0.115100\pi$
$602$	−39.9067	−1.62648
$603$	29.8716	1.21647
$604$	−86.2158	−3.50807
$605$	−66.5716	−2.70652
$606$	86.7624	3.52448
$607$	3.53313	0.143405	0.0717026	−	0.997426i	$-0.477157\pi$
$607$	3.53313	0.143405	0.0717026	+	0.997426i	$0.477157\pi$
$608$	−115.484	−4.68349
$609$	66.6215	2.69964
$610$	−36.0645	−1.46021
$611$	−20.4012	−0.825343
$612$	−15.6250	−0.631605
$613$	−11.8827	−0.479936	−0.239968	−	0.970781i	$-0.577137\pi$
$613$	−11.8827	−0.479936	−0.239968	+	0.970781i	$0.577137\pi$
$614$	69.7301	2.81408
$615$	−92.0497	−3.71180
$616$	−171.651	−6.91602
$617$	11.2283	0.452034	0.226017	−	0.974123i	$-0.427430\pi$
$617$	11.2283	0.452034	0.226017	+	0.974123i	$0.427430\pi$
$618$	19.3157	0.776992
$619$	−36.0493	−1.44895	−0.724473	−	0.689304i	$-0.757917\pi$
$619$	−36.0493	−1.44895	−0.724473	+	0.689304i	$0.757917\pi$
$620$	−75.7951	−3.04400
$621$	−9.98117	−0.400531
$622$	31.7904	1.27468
$623$	44.6168	1.78753
$624$	118.791	4.75545
$625$	−31.0399	−1.24160
$626$	20.2339	0.808709
$627$	93.6663	3.74067
$628$	−49.6483	−1.98118
$629$	0.357520	0.0142553
$630$	−102.773	−4.09456
$631$	4.04880	0.161180	0.0805901	−	0.996747i	$-0.474320\pi$
$631$	4.04880	0.161180	0.0805901	+	0.996747i	$0.474320\pi$
$632$	−16.8731	−0.671177
$633$	−45.2889	−1.80007
$634$	−5.40326	−0.214591
$635$	48.6188	1.92938
$636$	−32.6526	−1.29476
$637$	−7.82868	−0.310184
$638$	127.430	5.04500
$639$	−15.8224	−0.625926
$640$	85.8847	3.39489
$641$	17.3868	0.686736	0.343368	−	0.939201i	$-0.388432\pi$
$641$	17.3868	0.686736	0.343368	+	0.939201i	$0.388432\pi$
$642$	−120.017	−4.73667
$643$	8.15915	0.321766	0.160883	−	0.986974i	$-0.448566\pi$
$643$	8.15915	0.321766	0.160883	+	0.986974i	$0.448566\pi$
$644$	−37.8485	−1.49144
$645$	−34.6565	−1.36460
$646$	9.69158	0.381310
$647$	1.07843	0.0423974	0.0211987	−	0.999775i	$-0.493252\pi$
$647$	1.07843	0.0423974	0.0211987	+	0.999775i	$0.493252\pi$
$648$	15.2313	0.598342
$649$	56.7522	2.22772
$650$	16.7364	0.656456
$651$	45.2302	1.77271
$652$	−83.4518	−3.26823
$653$	9.28542	0.363366	0.181683	−	0.983357i	$-0.441845\pi$
$653$	9.28542	0.363366	0.181683	+	0.983357i	$0.441845\pi$
$654$	67.7820	2.65049
$655$	−51.7204	−2.02088
$656$	−179.878	−7.02305
$657$	−37.0195	−1.44427
$658$	56.9938	2.22185
$659$	27.0377	1.05324	0.526620	−	0.850101i	$-0.323459\pi$
$659$	27.0377	1.05324	0.526620	+	0.850101i	$0.323459\pi$
$660$	−236.950	−9.22327
$661$	−24.7004	−0.960735	−0.480367	−	0.877067i	$-0.659497\pi$
$661$	−24.7004	−0.960735	−0.480367	+	0.877067i	$0.659497\pi$
$662$	84.3720	3.27921
$663$	−5.23701	−0.203389
$664$	147.192	5.71214
$665$	46.4996	1.80318
$666$	7.09305	0.274850
$667$	17.6768	0.684447
$668$	28.0533	1.08542
$669$	42.7200	1.65165
$670$	46.8712	1.81079
$671$	30.0278	1.15921
$672$	−174.334	−6.72509
$673$	−7.83669	−0.302082	−0.151041	−	0.988527i	$-0.548263\pi$
$673$	−7.83669	−0.302082	−0.151041	+	0.988527i	$0.548263\pi$
$674$	10.1773	0.392013
$675$	−8.99425	−0.346189
$676$	−21.0847	−0.810949
$677$	3.14285	0.120790	0.0603948	−	0.998175i	$-0.480764\pi$
$677$	3.14285	0.120790	0.0603948	+	0.998175i	$0.480764\pi$
$678$	−125.828	−4.83239
$679$	−25.1414	−0.964837
$680$	−15.4240	−0.591483
$681$	−42.7771	−1.63922
$682$	86.5140	3.31279
$683$	46.1437	1.76564	0.882820	−	0.469712i	$-0.155642\pi$
$683$	46.1437	1.76564	0.882820	+	0.469712i	$0.155642\pi$
$684$	140.257	5.36288
$685$	44.1945	1.68858
$686$	−37.0886	−1.41605
$687$	33.4746	1.27713
$688$	−67.7236	−2.58194
$689$	−6.62304	−0.252318
$690$	−45.0598	−1.71540
$691$	−23.2880	−0.885917	−0.442959	−	0.896542i	$-0.646071\pi$
$691$	−23.2880	−0.885917	−0.442959	+	0.896542i	$0.646071\pi$
$692$	−5.74801	−0.218507
$693$	85.5699	3.25053
$694$	−37.5939	−1.42704
$695$	12.6800	0.480979
$696$	198.366	7.51903
$697$	7.93007	0.300373
$698$	−76.5850	−2.89879
$699$	39.9591	1.51139
$700$	−34.1061	−1.28909
$701$	−34.2374	−1.29313	−0.646565	−	0.762859i	$-0.723795\pi$
$701$	−34.2374	−1.29313	−0.646565	+	0.762859i	$0.723795\pi$
$702$	−36.1124	−1.36297
$703$	−3.20926	−0.121040
$704$	−161.724	−6.09521
$705$	49.4956	1.86411
$706$	26.1512	0.984214
$707$	−35.8625	−1.34875
$708$	140.426	5.27755
$709$	−3.48456	−0.130865	−0.0654327	−	0.997857i	$-0.520843\pi$
$709$	−3.48456	−0.130865	−0.0654327	+	0.997857i	$0.520843\pi$
$710$	−24.8268	−0.931733
$711$	8.41143	0.315453
$712$	132.847	4.97864
$713$	12.0010	0.449441
$714$	14.6304	0.547529
$715$	−48.0613	−1.79739
$716$	−17.7787	−0.664420
$717$	57.9665	2.16480
$718$	−24.7911	−0.925196
$719$	−49.8958	−1.86080	−0.930399	−	0.366547i	$-0.880540\pi$
$719$	−49.8958	−1.86080	−0.930399	+	0.366547i	$0.880540\pi$
$720$	−174.410	−6.49988
$721$	−7.98400	−0.297340
$722$	−35.3367	−1.31510
$723$	69.4928	2.58447
$724$	−0.789373	−0.0293368
$725$	15.9289	0.591585
$726$	188.019	6.97802
$727$	32.7956	1.21632	0.608161	−	0.793814i	$-0.291907\pi$
$727$	32.7956	1.21632	0.608161	+	0.793814i	$0.291907\pi$
$728$	−86.1493	−3.19290
$729$	−44.0227	−1.63047
$730$	−58.0868	−2.14989
$731$	2.98566	0.110428
$732$	74.3002	2.74622
$733$	−29.4822	−1.08895	−0.544474	−	0.838777i	$-0.683271\pi$
$733$	−29.4822	−1.08895	−0.544474	+	0.838777i	$0.683271\pi$
$734$	82.8798	3.05915
$735$	18.9933	0.700577
$736$	−46.2563	−1.70503
$737$	−39.0256	−1.43753
$738$	157.330	5.79138
$739$	19.3523	0.711884	0.355942	−	0.934508i	$-0.384160\pi$
$739$	19.3523	0.711884	0.355942	+	0.934508i	$0.384160\pi$
$740$	8.11855	0.298444
$741$	47.0098	1.72695
$742$	18.5025	0.679247
$743$	35.4914	1.30205	0.651027	−	0.759054i	$-0.274338\pi$
$743$	35.4914	1.30205	0.651027	+	0.759054i	$0.274338\pi$
$744$	134.673	4.93736
$745$	−22.7355	−0.832964
$746$	2.55547	0.0935624
$747$	−73.3766	−2.68471
$748$	20.4132	0.746381
$749$	49.6079	1.81263
$750$	58.8348	2.14834
$751$	23.6280	0.862200	0.431100	−	0.902304i	$-0.358126\pi$
$751$	23.6280	0.862200	0.431100	+	0.902304i	$0.358126\pi$
$752$	96.7212	3.52706
$753$	−3.61952	−0.131903
$754$	63.9554	2.32912
$755$	42.4265	1.54406
$756$	73.5913	2.67649
$757$	−36.7632	−1.33618	−0.668091	−	0.744080i	$-0.732888\pi$
$757$	−36.7632	−1.33618	−0.668091	+	0.744080i	$0.732888\pi$
$758$	−29.0124	−1.05378
$759$	37.5174	1.36180
$760$	138.453	5.02221
$761$	−25.3381	−0.918506	−0.459253	−	0.888305i	$-0.651883\pi$
$761$	−25.3381	−0.918506	−0.459253	+	0.888305i	$0.651883\pi$
$762$	−137.314	−4.97437
$763$	−28.0172	−1.01429
$764$	−69.6129	−2.51851
$765$	7.68902	0.277997
$766$	1.07313	0.0387738
$767$	28.4831	1.02847
$768$	−94.1477	−3.39726
$769$	−9.57445	−0.345264	−0.172632	−	0.984986i	$-0.555227\pi$
$769$	−9.57445	−0.345264	−0.172632	+	0.984986i	$0.555227\pi$
$770$	134.267	4.83863
$771$	70.1803	2.52748
$772$	75.9540	2.73364
$773$	−25.4929	−0.916915	−0.458458	−	0.888716i	$-0.651598\pi$
$773$	−25.4929	−0.916915	−0.458458	+	0.888716i	$0.651598\pi$
$774$	59.2342	2.12913
$775$	10.8144	0.388463
$776$	−74.8585	−2.68726
$777$	−4.84470	−0.173802
$778$	84.8038	3.04036
$779$	−71.1840	−2.55043
$780$	−118.922	−4.25809
$781$	20.6711	0.739671
$782$	3.88190	0.138816
$783$	−34.3701	−1.22829
$784$	37.1155	1.32555
$785$	24.4317	0.872006
$786$	146.074	5.21029
$787$	16.5107	0.588544	0.294272	−	0.955722i	$-0.404923\pi$
$787$	16.5107	0.588544	0.294272	+	0.955722i	$0.404923\pi$
$788$	−74.1195	−2.64040
$789$	−2.71770	−0.0967526
$790$	13.1983	0.469573
$791$	52.0100	1.84926
$792$	254.784	9.05337
$793$	15.0706	0.535171
$794$	−6.58213	−0.233591
$795$	16.0682	0.569882
$796$	56.5487	2.00431
$797$	46.4174	1.64419	0.822094	−	0.569352i	$-0.192806\pi$
$797$	46.4174	1.64419	0.822094	+	0.569352i	$0.192806\pi$
$798$	−131.329	−4.64900
$799$	−4.26404	−0.150851
$800$	−41.6826	−1.47370
$801$	−66.2255	−2.33996
$802$	57.4609	2.02901
$803$	48.3639	1.70672
$804$	−96.5641	−3.40555
$805$	18.6251	0.656449
$806$	43.4202	1.52941
$807$	31.3418	1.10328
$808$	−106.781	−3.75653
$809$	−9.33859	−0.328327	−0.164164	−	0.986433i	$-0.552493\pi$
$809$	−9.33859	−0.328327	−0.164164	+	0.986433i	$0.552493\pi$
$810$	−11.9140	−0.418617
$811$	−28.9899	−1.01797	−0.508986	−	0.860775i	$-0.669979\pi$
$811$	−28.9899	−1.01797	−0.508986	+	0.860775i	$0.669979\pi$
$812$	−130.331	−4.57372
$813$	−78.8151	−2.76417
$814$	−9.26667	−0.324797
$815$	41.0663	1.43849
$816$	24.8285	0.869171
$817$	−26.8006	−0.937634
$818$	11.9040	0.416213
$819$	42.9463	1.50067
$820$	180.076	6.28852
$821$	46.0374	1.60672	0.803358	−	0.595496i	$-0.203045\pi$
$821$	46.0374	1.60672	0.803358	+	0.595496i	$0.203045\pi$
$822$	−124.819	−4.35355
$823$	8.37419	0.291906	0.145953	−	0.989292i	$-0.453375\pi$
$823$	8.37419	0.291906	0.145953	+	0.989292i	$0.453375\pi$
$824$	−23.7724	−0.828150
$825$	33.8078	1.17704
$826$	−79.5719	−2.76866
$827$	−38.6933	−1.34550	−0.672749	−	0.739871i	$-0.734887\pi$
$827$	−38.6933	−1.34550	−0.672749	+	0.739871i	$0.734887\pi$
$828$	56.1792	1.95236
$829$	−28.5033	−0.989960	−0.494980	−	0.868904i	$-0.664825\pi$
$829$	−28.5033	−0.989960	−0.494980	+	0.868904i	$0.664825\pi$
$830$	−115.134	−3.99637
$831$	−33.6238	−1.16640
$832$	−81.1671	−2.81396
$833$	−1.63627	−0.0566934
$834$	−35.8121	−1.24007
$835$	−13.8049	−0.477739
$836$	−183.238	−6.33743
$837$	−23.3343	−0.806551
$838$	14.9502	0.516445
$839$	−14.5872	−0.503605	−0.251803	−	0.967779i	$-0.581023\pi$
$839$	−14.5872	−0.503605	−0.251803	+	0.967779i	$0.581023\pi$
$840$	209.008	7.21146
$841$	31.8698	1.09896
$842$	43.0078	1.48215
$843$	25.3506	0.873122
$844$	88.5983	3.04968
$845$	10.3757	0.356934
$846$	−84.5969	−2.90850
$847$	−77.7159	−2.67035
$848$	31.3996	1.07827
$849$	−46.6677	−1.60163
$850$	3.49807	0.119983
$851$	−1.28545	−0.0440646
$852$	51.1482	1.75231
$853$	−40.2239	−1.37724	−0.688619	−	0.725123i	$-0.741783\pi$
$853$	−40.2239	−1.37724	−0.688619	+	0.725123i	$0.741783\pi$
$854$	−42.1019	−1.44070
$855$	−69.0201	−2.36044
$856$	147.707	5.04854
$857$	33.7348	1.15236	0.576180	−	0.817323i	$-0.304543\pi$
$857$	33.7348	1.15236	0.576180	+	0.817323i	$0.304543\pi$
$858$	135.740	4.63408
$859$	−12.8311	−0.437793	−0.218897	−	0.975748i	$-0.570246\pi$
$859$	−12.8311	−0.437793	−0.218897	+	0.975748i	$0.570246\pi$
$860$	67.7982	2.31190
$861$	−107.459	−3.66220
$862$	−1.18861	−0.0404843
$863$	−14.1666	−0.482236	−0.241118	−	0.970496i	$-0.577514\pi$
$863$	−14.1666	−0.482236	−0.241118	+	0.970496i	$0.577514\pi$
$864$	89.9391	3.05979
$865$	2.82857	0.0961744
$866$	23.1510	0.786704
$867$	45.7656	1.55428
$868$	−88.4835	−3.00332
$869$	−10.9891	−0.372778
$870$	−155.163	−5.26052
$871$	−19.5864	−0.663660
$872$	−83.4212	−2.82500
$873$	37.3178	1.26301
$874$	−34.8457	−1.17867
$875$	−24.3189	−0.822128
$876$	119.671	4.04329
$877$	22.5304	0.760799	0.380399	−	0.924822i	$-0.375787\pi$
$877$	22.5304	0.760799	0.380399	+	0.924822i	$0.375787\pi$
$878$	73.5124	2.48092
$879$	−42.6816	−1.43961
$880$	227.857	7.68105
$881$	1.69095	0.0569696	0.0284848	−	0.999594i	$-0.490932\pi$
$881$	1.69095	0.0569696	0.0284848	+	0.999594i	$0.490932\pi$
$882$	−32.4629	−1.09308
$883$	−29.5498	−0.994431	−0.497216	−	0.867627i	$-0.665644\pi$
$883$	−29.5498	−0.994431	−0.497216	+	0.867627i	$0.665644\pi$
$884$	10.2451	0.344580
$885$	−69.1033	−2.32288
$886$	−71.3753	−2.39790
$887$	22.8265	0.766440	0.383220	−	0.923657i	$-0.374815\pi$
$887$	22.8265	0.766440	0.383220	+	0.923657i	$0.374815\pi$
$888$	−14.4251	−0.484074
$889$	56.7578	1.90359
$890$	−103.913	−3.48319
$891$	9.91979	0.332325
$892$	−83.5727	−2.79822
$893$	38.2760	1.28086
$894$	64.2120	2.14757
$895$	8.74882	0.292441
$896$	100.262	3.34952
$897$	18.8295	0.628698
$898$	38.4205	1.28211
$899$	41.3253	1.37828
$900$	50.6243	1.68748
$901$	−1.38428	−0.0461170
$902$	−205.542	−6.84380
$903$	−40.4581	−1.34636
$904$	154.860	5.15056
$905$	0.388448	0.0129124
$906$	−119.825	−3.98093
$907$	13.4243	0.445745	0.222873	−	0.974848i	$-0.428457\pi$
$907$	13.4243	0.445745	0.222873	+	0.974848i	$0.428457\pi$
$908$	83.6845	2.77717
$909$	53.2314	1.76557
$910$	67.3865	2.23384
$911$	41.1266	1.36259	0.681293	−	0.732011i	$-0.261418\pi$
$911$	41.1266	1.36259	0.681293	+	0.732011i	$0.261418\pi$
$912$	−222.872	−7.38002
$913$	95.8623	3.17258
$914$	75.0361	2.48197
$915$	−36.5629	−1.20873
$916$	−65.4860	−2.16372
$917$	−60.3786	−1.99388
$918$	−7.54782	−0.249115
$919$	−31.7499	−1.04733	−0.523666	−	0.851924i	$-0.675436\pi$
$919$	−31.7499	−1.04733	−0.523666	+	0.851924i	$0.675436\pi$
$920$	55.4563	1.82834
$921$	70.6936	2.32943
$922$	79.6770	2.62402
$923$	10.3746	0.341483
$924$	−276.616	−9.10001
$925$	−1.15835	−0.0380862
$926$	−64.4170	−2.11687
$927$	11.8508	0.389231
$928$	−159.283	−5.22873
$929$	−42.7735	−1.40335	−0.701677	−	0.712495i	$-0.747565\pi$
$929$	−42.7735	−1.40335	−0.701677	+	0.712495i	$0.747565\pi$
$930$	−105.342	−3.45431
$931$	14.6879	0.481376
$932$	−78.1716	−2.56060
$933$	32.2296	1.05515
$934$	−12.1348	−0.397064
$935$	−10.0453	−0.328515
$936$	127.873	4.17965
$937$	−2.08180	−0.0680094	−0.0340047	−	0.999422i	$-0.510826\pi$
$937$	−2.08180	−0.0680094	−0.0340047	+	0.999422i	$0.510826\pi$
$938$	54.7176	1.78659
$939$	20.5135	0.669432
$940$	−96.8277	−3.15817
$941$	27.7796	0.905589	0.452795	−	0.891615i	$-0.350427\pi$
$941$	27.7796	0.905589	0.452795	+	0.891615i	$0.350427\pi$
$942$	−69.0027	−2.24823
$943$	−28.5123	−0.928487
$944$	−135.037	−4.39509
$945$	−36.2140	−1.17804
$946$	−77.3862	−2.51604
$947$	−16.0048	−0.520086	−0.260043	−	0.965597i	$-0.583737\pi$
$947$	−16.0048	−0.520086	−0.260043	+	0.965597i	$0.583737\pi$
$948$	−27.1911	−0.883126
$949$	24.2732	0.787940
$950$	−31.4002	−1.01876
$951$	−5.47792	−0.177634
$952$	−18.0060	−0.583578
$953$	−42.3669	−1.37240	−0.686200	−	0.727413i	$-0.740722\pi$
$953$	−42.3669	−1.37240	−0.686200	+	0.727413i	$0.740722\pi$
$954$	−27.4635	−0.889164
$955$	34.2563	1.10851
$956$	−113.399	−3.66759
$957$	129.191	4.17615
$958$	−89.1114	−2.87906
$959$	51.5928	1.66602
$960$	196.921	6.35558
$961$	−2.94369	−0.0949578
$962$	−4.65082	−0.149948
$963$	−73.6338	−2.37282
$964$	−135.948	−4.37859
$965$	−37.3767	−1.20320
$966$	−52.6030	−1.69247
$967$	3.44228	0.110696	0.0553482	−	0.998467i	$-0.482373\pi$
$967$	3.44228	0.110696	0.0553482	+	0.998467i	$0.482373\pi$
$968$	−231.399	−7.43746
$969$	9.82550	0.315640
$970$	58.5548	1.88008
$971$	−0.812065	−0.0260604	−0.0130302	−	0.999915i	$-0.504148\pi$
$971$	−0.812065	−0.0260604	−0.0130302	+	0.999915i	$0.504148\pi$
$972$	95.8124	3.07318
$973$	14.8026	0.474551
$974$	25.5457	0.818536
$975$	16.9677	0.543400
$976$	−71.4489	−2.28702
$977$	−15.0490	−0.481460	−0.240730	−	0.970592i	$-0.577387\pi$
$977$	−15.0490	−0.481460	−0.240730	+	0.970592i	$0.577387\pi$
$978$	−115.984	−3.70875
$979$	86.5198	2.76518
$980$	−37.1563	−1.18692
$981$	41.5863	1.32775
$982$	−59.6156	−1.90241
$983$	53.8782	1.71845	0.859224	−	0.511599i	$-0.170947\pi$
$983$	53.8782	1.71845	0.859224	+	0.511599i	$0.170947\pi$
$984$	−319.960	−10.1999
$985$	36.4739	1.16216
$986$	13.3673	0.425701
$987$	57.7813	1.83920
$988$	−91.9648	−2.92579
$989$	−10.7348	−0.341347
$990$	−199.294	−6.33398
$991$	−1.76083	−0.0559345	−0.0279673	−	0.999609i	$-0.508903\pi$
$991$	−1.76083	−0.0559345	−0.0279673	+	0.999609i	$0.508903\pi$
$992$	−108.140	−3.43343
$993$	85.5379	2.71446
$994$	−28.9829	−0.919282
$995$	−27.8274	−0.882187
$996$	237.200	7.51596
$997$	20.1550	0.638314	0.319157	−	0.947702i	$-0.396600\pi$
$997$	20.1550	0.638314	0.319157	+	0.947702i	$0.396600\pi$
$998$	52.4420	1.66002
$999$	2.49938	0.0790769

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6029.2.a.b.1.7	✓	268

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6029.2.a.b.1.7	✓	268	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:	\( N \)	\(=\)	\( 6029 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6029.a (trivial)

\(f(q)\)	\(=\)	\(q-2.71891 q^{2} -2.75648 q^{3} +5.39247 q^{4} -2.65361 q^{5} +7.49462 q^{6} -3.09784 q^{7} -9.22383 q^{8} +4.59818 q^{9} +O(q^{10})\)	\(q-2.71891 q^{2} -2.75648 q^{3} +5.39247 q^{4} -2.65361 q^{5} +7.49462 q^{6} -3.09784 q^{7} -9.22383 q^{8} +4.59818 q^{9} +7.21494 q^{10} -6.00726 q^{11} -14.8642 q^{12} -3.01496 q^{13} +8.42275 q^{14} +7.31463 q^{15} +14.2938 q^{16} -0.630155 q^{17} -12.5020 q^{18} +5.65656 q^{19} -14.3095 q^{20} +8.53913 q^{21} +16.3332 q^{22} +2.26570 q^{23} +25.4253 q^{24} +2.04167 q^{25} +8.19740 q^{26} -4.40534 q^{27} -16.7050 q^{28} +7.80191 q^{29} -19.8878 q^{30} +5.29682 q^{31} -20.4159 q^{32} +16.5589 q^{33} +1.71334 q^{34} +8.22047 q^{35} +24.7955 q^{36} -0.567352 q^{37} -15.3797 q^{38} +8.31067 q^{39} +24.4765 q^{40} -12.5843 q^{41} -23.2171 q^{42} -4.73797 q^{43} -32.3940 q^{44} -12.2018 q^{45} -6.16023 q^{46} +6.76665 q^{47} -39.4006 q^{48} +2.59661 q^{49} -5.55112 q^{50} +1.73701 q^{51} -16.2581 q^{52} +2.19672 q^{53} +11.9777 q^{54} +15.9409 q^{55} +28.5739 q^{56} -15.5922 q^{57} -21.2127 q^{58} -9.44726 q^{59} +39.4440 q^{60} -4.99859 q^{61} -14.4016 q^{62} -14.2444 q^{63} +26.9215 q^{64} +8.00054 q^{65} -45.0221 q^{66} +6.49640 q^{67} -3.39809 q^{68} -6.24535 q^{69} -22.3507 q^{70} -3.44103 q^{71} -42.4128 q^{72} -8.05091 q^{73} +1.54258 q^{74} -5.62782 q^{75} +30.5028 q^{76} +18.6095 q^{77} -22.5960 q^{78} +1.82930 q^{79} -37.9303 q^{80} -1.65130 q^{81} +34.2156 q^{82} -15.9578 q^{83} +46.0470 q^{84} +1.67219 q^{85} +12.8821 q^{86} -21.5058 q^{87} +55.4099 q^{88} -14.4025 q^{89} +33.1756 q^{90} +9.33986 q^{91} +12.2177 q^{92} -14.6006 q^{93} -18.3979 q^{94} -15.0103 q^{95} +56.2761 q^{96} +8.11577 q^{97} -7.05996 q^{98} -27.6224 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 268 q + 8 q^{2} + 43 q^{3} + 300 q^{4} + 18 q^{5} + 34 q^{6} + 59 q^{7} + 21 q^{8} + 295 q^{9}+O(q^{10}) \) 268 * q + 8 * q^2 + 43 * q^3 + 300 * q^4 + 18 * q^5 + 34 * q^6 + 59 * q^7 + 21 * q^8 + 295 * q^9	\( 268 q + 8 q^{2} + 43 q^{3} + 300 q^{4} + 18 q^{5} + 34 q^{6} + 59 q^{7} + 21 q^{8} + 295 q^{9} + 91 q^{10} + 49 q^{11} + 77 q^{12} + 45 q^{13} + 42 q^{14} + 37 q^{15} + 356 q^{16} + 40 q^{17} + 36 q^{18} + 245 q^{19} + 40 q^{20} + 66 q^{21} + 51 q^{22} + 26 q^{23} + 90 q^{24} + 314 q^{25} + 24 q^{26} + 160 q^{27} + 117 q^{28} + 54 q^{29} + 25 q^{30} + 181 q^{31} + 35 q^{32} + 49 q^{33} + 84 q^{34} + 73 q^{35} + 348 q^{36} + 77 q^{37} + 20 q^{38} + 96 q^{39} + 257 q^{40} + 62 q^{41} + 22 q^{42} + 199 q^{43} + 59 q^{44} + 60 q^{45} + 116 q^{46} + 41 q^{47} + 106 q^{48} + 381 q^{49} + 21 q^{50} + 248 q^{51} + 101 q^{52} + 4 q^{53} + 98 q^{54} + 136 q^{55} + 79 q^{56} + 47 q^{57} + 14 q^{58} + 170 q^{59} + 31 q^{60} + 247 q^{61} + 17 q^{62} + 143 q^{63} + 437 q^{64} + 29 q^{65} + 38 q^{66} + 114 q^{67} + 62 q^{68} + 101 q^{69} + 48 q^{70} + 64 q^{71} + 54 q^{72} + 115 q^{73} + 22 q^{74} + 250 q^{75} + 448 q^{76} + 8 q^{77} - 50 q^{78} + 271 q^{79} + 39 q^{80} + 336 q^{81} + 132 q^{82} + 74 q^{83} + 122 q^{84} + 58 q^{85} + 27 q^{86} + 105 q^{87} + 127 q^{88} + 63 q^{89} + 179 q^{90} + 406 q^{91} + 13 q^{92} + q^{93} + 263 q^{94} + 76 q^{95} + 161 q^{96} + 123 q^{97} - 7 q^{98} + 180 q^{99}+O(q^{100}) \) 268 * q + 8 * q^2 + 43 * q^3 + 300 * q^4 + 18 * q^5 + 34 * q^6 + 59 * q^7 + 21 * q^8 + 295 * q^9 + 91 * q^10 + 49 * q^11 + 77 * q^12 + 45 * q^13 + 42 * q^14 + 37 * q^15 + 356 * q^16 + 40 * q^17 + 36 * q^18 + 245 * q^19 + 40 * q^20 + 66 * q^21 + 51 * q^22 + 26 * q^23 + 90 * q^24 + 314 * q^25 + 24 * q^26 + 160 * q^27 + 117 * q^28 + 54 * q^29 + 25 * q^30 + 181 * q^31 + 35 * q^32 + 49 * q^33 + 84 * q^34 + 73 * q^35 + 348 * q^36 + 77 * q^37 + 20 * q^38 + 96 * q^39 + 257 * q^40 + 62 * q^41 + 22 * q^42 + 199 * q^43 + 59 * q^44 + 60 * q^45 + 116 * q^46 + 41 * q^47 + 106 * q^48 + 381 * q^49 + 21 * q^50 + 248 * q^51 + 101 * q^52 + 4 * q^53 + 98 * q^54 + 136 * q^55 + 79 * q^56 + 47 * q^57 + 14 * q^58 + 170 * q^59 + 31 * q^60 + 247 * q^61 + 17 * q^62 + 143 * q^63 + 437 * q^64 + 29 * q^65 + 38 * q^66 + 114 * q^67 + 62 * q^68 + 101 * q^69 + 48 * q^70 + 64 * q^71 + 54 * q^72 + 115 * q^73 + 22 * q^74 + 250 * q^75 + 448 * q^76 + 8 * q^77 - 50 * q^78 + 271 * q^79 + 39 * q^80 + 336 * q^81 + 132 * q^82 + 74 * q^83 + 122 * q^84 + 58 * q^85 + 27 * q^86 + 105 * q^87 + 127 * q^88 + 63 * q^89 + 179 * q^90 + 406 * q^91 + 13 * q^92 + q^93 + 263 * q^94 + 76 * q^95 + 161 * q^96 + 123 * q^97 - 7 * q^98 + 180 * q^99

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