LMFDB - Embedded newform 8023.2.a.d.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8023, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8023 = 71 \cdot 113 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8023.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.0639775417$
Analytic rank:	$0$
Dimension:	$165$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	8023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.35257 q^{2} -0.106381 q^{3} +3.53459 q^{4} +1.14622 q^{5} +0.250270 q^{6} -0.376719 q^{7} -3.61023 q^{8} -2.98868 q^{9} +O(q^{10})$	\(q-2.35257 q^{2} -0.106381 q^{3} +3.53459 q^{4} +1.14622 q^{5} +0.250270 q^{6} -0.376719 q^{7} -3.61023 q^{8} -2.98868 q^{9} -2.69657 q^{10} +2.20181 q^{11} -0.376015 q^{12} +1.47383 q^{13} +0.886259 q^{14} -0.121937 q^{15} +1.42415 q^{16} -6.75687 q^{17} +7.03109 q^{18} +0.697065 q^{19} +4.05143 q^{20} +0.0400760 q^{21} -5.17991 q^{22} -2.06094 q^{23} +0.384062 q^{24} -3.68617 q^{25} -3.46729 q^{26} +0.637085 q^{27} -1.33155 q^{28} -8.88677 q^{29} +0.286866 q^{30} +4.95544 q^{31} +3.87006 q^{32} -0.234231 q^{33} +15.8960 q^{34} -0.431805 q^{35} -10.5638 q^{36} -9.22656 q^{37} -1.63990 q^{38} -0.156788 q^{39} -4.13814 q^{40} -0.380561 q^{41} -0.0942815 q^{42} -6.88593 q^{43} +7.78248 q^{44} -3.42570 q^{45} +4.84850 q^{46} +1.76553 q^{47} -0.151503 q^{48} -6.85808 q^{49} +8.67198 q^{50} +0.718806 q^{51} +5.20939 q^{52} +6.62593 q^{53} -1.49879 q^{54} +2.52376 q^{55} +1.36004 q^{56} -0.0741548 q^{57} +20.9068 q^{58} +9.40253 q^{59} -0.430998 q^{60} -5.30826 q^{61} -11.6580 q^{62} +1.12589 q^{63} -11.9529 q^{64} +1.68934 q^{65} +0.551046 q^{66} +3.37927 q^{67} -23.8828 q^{68} +0.219245 q^{69} +1.01585 q^{70} +1.00000 q^{71} +10.7898 q^{72} +6.97604 q^{73} +21.7061 q^{74} +0.392140 q^{75} +2.46384 q^{76} -0.829463 q^{77} +0.368855 q^{78} -8.58280 q^{79} +1.63239 q^{80} +8.89827 q^{81} +0.895296 q^{82} +2.23829 q^{83} +0.141652 q^{84} -7.74489 q^{85} +16.1996 q^{86} +0.945388 q^{87} -7.94903 q^{88} -12.5272 q^{89} +8.05921 q^{90} -0.555220 q^{91} -7.28457 q^{92} -0.527167 q^{93} -4.15354 q^{94} +0.798993 q^{95} -0.411703 q^{96} -4.43537 q^{97} +16.1341 q^{98} -6.58050 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9}+O(q^{10}) $ 165 * q + 22 * q^2 + 18 * q^3 + 166 * q^4 + 28 * q^5 + 16 * q^6 + 24 * q^7 + 66 * q^8 + 177 * q^9	\( 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9} + 14 q^{10} + 18 q^{11} + 54 q^{12} + 44 q^{13} + 26 q^{14} + 24 q^{15} + 168 q^{16} + 143 q^{17} + 57 q^{18} + 20 q^{19} + 49 q^{20} + 39 q^{21} + 25 q^{22} + 52 q^{23} + 27 q^{24} + 175 q^{25} + 48 q^{26} + 69 q^{27} + 28 q^{28} + 58 q^{29} - 11 q^{30} + 28 q^{31} + 114 q^{32} + 110 q^{33} + 55 q^{34} + 67 q^{35} + 202 q^{36} + 44 q^{37} + 35 q^{38} + 27 q^{39} + 53 q^{40} + 141 q^{41} + 40 q^{42} + 29 q^{43} + 52 q^{44} + 54 q^{45} + 29 q^{46} + 87 q^{47} + 53 q^{48} + 143 q^{49} + 16 q^{50} + 37 q^{51} + 105 q^{52} + 101 q^{53} - 36 q^{54} + 72 q^{55} + 57 q^{56} + 82 q^{57} + 4 q^{58} + 103 q^{59} + 53 q^{60} + 16 q^{61} + 54 q^{62} + 126 q^{63} + 136 q^{64} + 159 q^{65} + 53 q^{66} + 60 q^{67} + 220 q^{68} + 81 q^{69} + 16 q^{70} + 165 q^{71} + 176 q^{72} + 124 q^{73} + 29 q^{74} + 44 q^{75} + 18 q^{76} + 127 q^{77} - 91 q^{78} + 14 q^{79} + 158 q^{80} + 213 q^{81} + 20 q^{82} + 116 q^{83} + 67 q^{84} + 59 q^{85} + 30 q^{86} + 28 q^{87} + 79 q^{88} + 195 q^{89} + 16 q^{90} - 26 q^{91} + 173 q^{92} + 116 q^{93} + 53 q^{94} + 26 q^{95} - 36 q^{96} + 88 q^{97} + 150 q^{98} + 12 q^{99}+O(q^{100}) \) 165 * q + 22 * q^2 + 18 * q^3 + 166 * q^4 + 28 * q^5 + 16 * q^6 + 24 * q^7 + 66 * q^8 + 177 * q^9 + 14 * q^10 + 18 * q^11 + 54 * q^12 + 44 * q^13 + 26 * q^14 + 24 * q^15 + 168 * q^16 + 143 * q^17 + 57 * q^18 + 20 * q^19 + 49 * q^20 + 39 * q^21 + 25 * q^22 + 52 * q^23 + 27 * q^24 + 175 * q^25 + 48 * q^26 + 69 * q^27 + 28 * q^28 + 58 * q^29 - 11 * q^30 + 28 * q^31 + 114 * q^32 + 110 * q^33 + 55 * q^34 + 67 * q^35 + 202 * q^36 + 44 * q^37 + 35 * q^38 + 27 * q^39 + 53 * q^40 + 141 * q^41 + 40 * q^42 + 29 * q^43 + 52 * q^44 + 54 * q^45 + 29 * q^46 + 87 * q^47 + 53 * q^48 + 143 * q^49 + 16 * q^50 + 37 * q^51 + 105 * q^52 + 101 * q^53 - 36 * q^54 + 72 * q^55 + 57 * q^56 + 82 * q^57 + 4 * q^58 + 103 * q^59 + 53 * q^60 + 16 * q^61 + 54 * q^62 + 126 * q^63 + 136 * q^64 + 159 * q^65 + 53 * q^66 + 60 * q^67 + 220 * q^68 + 81 * q^69 + 16 * q^70 + 165 * q^71 + 176 * q^72 + 124 * q^73 + 29 * q^74 + 44 * q^75 + 18 * q^76 + 127 * q^77 - 91 * q^78 + 14 * q^79 + 158 * q^80 + 213 * q^81 + 20 * q^82 + 116 * q^83 + 67 * q^84 + 59 * q^85 + 30 * q^86 + 28 * q^87 + 79 * q^88 + 195 * q^89 + 16 * q^90 - 26 * q^91 + 173 * q^92 + 116 * q^93 + 53 * q^94 + 26 * q^95 - 36 * q^96 + 88 * q^97 + 150 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.35257	−1.66352	−0.831759	−	0.555136i	$-0.812666\pi$
$2$	−2.35257	−1.66352	−0.831759	+	0.555136i	$0.812666\pi$
$3$	−0.106381	−0.0614194	−0.0307097	−	0.999528i	$-0.509777\pi$
$3$	−0.106381	−0.0614194	−0.0307097	+	0.999528i	$0.509777\pi$
$4$	3.53459	1.76730
$5$	1.14622	0.512607	0.256304	−	0.966596i	$-0.417495\pi$
$5$	1.14622	0.512607	0.256304	+	0.966596i	$0.417495\pi$
$6$	0.250270	0.102172
$7$	−0.376719	−0.142387	−0.0711933	−	0.997463i	$-0.522681\pi$
$7$	−0.376719	−0.142387	−0.0711933	+	0.997463i	$0.522681\pi$
$8$	−3.61023	−1.27641
$9$	−2.98868	−0.996228
$10$	−2.69657	−0.852732
$11$	2.20181	0.663870	0.331935	−	0.943302i	$-0.392299\pi$
$11$	2.20181	0.663870	0.331935	+	0.943302i	$0.392299\pi$
$12$	−0.376015	−0.108546
$13$	1.47383	0.408767	0.204383	−	0.978891i	$-0.434481\pi$
$13$	1.47383	0.408767	0.204383	+	0.978891i	$0.434481\pi$
$14$	0.886259	0.236863
$15$	−0.121937	−0.0314840
$16$	1.42415	0.356037
$17$	−6.75687	−1.63878	−0.819391	−	0.573236i	$-0.805688\pi$
$17$	−6.75687	−1.63878	−0.819391	+	0.573236i	$0.805688\pi$
$18$	7.03109	1.65724
$19$	0.697065	0.159918	0.0799589	−	0.996798i	$-0.474521\pi$
$19$	0.697065	0.159918	0.0799589	+	0.996798i	$0.474521\pi$
$20$	4.05143	0.905928
$21$	0.0400760	0.00874529
$22$	−5.17991	−1.10436
$23$	−2.06094	−0.429735	−0.214867	−	0.976643i	$-0.568932\pi$
$23$	−2.06094	−0.429735	−0.214867	+	0.976643i	$0.568932\pi$
$24$	0.384062	0.0783963
$25$	−3.68617	−0.737234
$26$	−3.46729	−0.679991
$27$	0.637085	0.122607
$28$	−1.33155	−0.251639
$29$	−8.88677	−1.65023	−0.825116	−	0.564964i	$-0.808890\pi$
$29$	−8.88677	−1.65023	−0.825116	+	0.564964i	$0.808890\pi$
$30$	0.286866	0.0523742
$31$	4.95544	0.890024	0.445012	−	0.895525i	$-0.353199\pi$
$31$	4.95544	0.890024	0.445012	+	0.895525i	$0.353199\pi$
$32$	3.87006	0.684136
$33$	−0.234231	−0.0407745
$34$	15.8960	2.72614
$35$	−0.431805	−0.0729883
$36$	−10.5638	−1.76063
$37$	−9.22656	−1.51684	−0.758419	−	0.651768i	$-0.774028\pi$
$37$	−9.22656	−1.51684	−0.758419	+	0.651768i	$0.774028\pi$
$38$	−1.63990	−0.266026
$39$	−0.156788	−0.0251062
$40$	−4.13814	−0.654297
$41$	−0.380561	−0.0594336	−0.0297168	−	0.999558i	$-0.509461\pi$
$41$	−0.380561	−0.0594336	−0.0297168	+	0.999558i	$0.509461\pi$
$42$	−0.0942815	−0.0145480
$43$	−6.88593	−1.05009	−0.525047	−	0.851073i	$-0.675952\pi$
$43$	−6.88593	−1.05009	−0.525047	+	0.851073i	$0.675952\pi$
$44$	7.78248	1.17325
$45$	−3.42570	−0.510673
$46$	4.84850	0.714872
$47$	1.76553	0.257529	0.128765	−	0.991675i	$-0.458899\pi$
$47$	1.76553	0.257529	0.128765	+	0.991675i	$0.458899\pi$
$48$	−0.151503	−0.0218675
$49$	−6.85808	−0.979726
$50$	8.67198	1.22640
$51$	0.718806	0.100653
$52$	5.20939	0.722412
$53$	6.62593	0.910141	0.455070	−	0.890455i	$-0.349614\pi$
$53$	6.62593	0.910141	0.455070	+	0.890455i	$0.349614\pi$
$54$	−1.49879	−0.203959
$55$	2.52376	0.340304
$56$	1.36004	0.181744
$57$	−0.0741548	−0.00982205
$58$	20.9068	2.74519
$59$	9.40253	1.22410	0.612052	−	0.790817i	$-0.290344\pi$
$59$	9.40253	1.22410	0.612052	+	0.790817i	$0.290344\pi$
$60$	−0.430998	−0.0556415
$61$	−5.30826	−0.679653	−0.339827	−	0.940488i	$-0.610368\pi$
$61$	−5.30826	−0.679653	−0.339827	+	0.940488i	$0.610368\pi$
$62$	−11.6580	−1.48057
$63$	1.12589	0.141849
$64$	−11.9529	−1.49411
$65$	1.68934	0.209537
$66$	0.551046	0.0678291
$67$	3.37927	0.412843	0.206422	−	0.978463i	$-0.433818\pi$
$67$	3.37927	0.412843	0.206422	+	0.978463i	$0.433818\pi$
$68$	−23.8828	−2.89621
$69$	0.219245	0.0263941
$70$	1.01585	0.121417
$71$	1.00000	0.118678
$71$	1.00000	0.118678
$72$	10.7898	1.27159
$73$	6.97604	0.816484	0.408242	−	0.912874i	$-0.366142\pi$
$73$	6.97604	0.816484	0.408242	+	0.912874i	$0.366142\pi$
$74$	21.7061	2.52329
$75$	0.392140	0.0452804
$76$	2.46384	0.282622
$77$	−0.829463	−0.0945261
$78$	0.368855	0.0417647
$79$	−8.58280	−0.965640	−0.482820	−	0.875720i	$-0.660388\pi$
$79$	−8.58280	−0.965640	−0.482820	+	0.875720i	$0.660388\pi$
$80$	1.63239	0.182507
$81$	8.89827	0.988697
$82$	0.895296	0.0988689
$83$	2.23829	0.245684	0.122842	−	0.992426i	$-0.460799\pi$
$83$	2.23829	0.245684	0.122842	+	0.992426i	$0.460799\pi$
$84$	0.141652	0.0154555
$85$	−7.74489	−0.840051
$86$	16.1996	1.74685
$87$	0.945388	0.101356
$88$	−7.94903	−0.847370
$89$	−12.5272	−1.32788	−0.663940	−	0.747786i	$-0.731117\pi$
$89$	−12.5272	−1.32788	−0.663940	+	0.747786i	$0.731117\pi$
$90$	8.05921	0.849515
$91$	−0.555220	−0.0582029
$92$	−7.28457	−0.759469
$93$	−0.527167	−0.0546647
$94$	−4.15354	−0.428405
$95$	0.798993	0.0819750
$96$	−0.411703	−0.0420192
$97$	−4.43537	−0.450344	−0.225172	−	0.974319i	$-0.572294\pi$
$97$	−4.43537	−0.450344	−0.225172	+	0.974319i	$0.572294\pi$
$98$	16.1341	1.62979
$99$	−6.58050	−0.661365
$100$	−13.0291	−1.30291
$101$	10.5603	1.05079	0.525394	−	0.850859i	$-0.323918\pi$
$101$	10.5603	1.05079	0.525394	+	0.850859i	$0.323918\pi$
$102$	−1.69104	−0.167438
$103$	15.4931	1.52658	0.763289	−	0.646057i	$-0.223583\pi$
$103$	15.4931	1.52658	0.763289	+	0.646057i	$0.223583\pi$
$104$	−5.32087	−0.521754
$105$	0.0459360	0.00448290
$106$	−15.5880	−1.51404
$107$	2.60751	0.252078	0.126039	−	0.992025i	$-0.459774\pi$
$107$	2.60751	0.252078	0.126039	+	0.992025i	$0.459774\pi$
$108$	2.25183	0.216683
$109$	4.36285	0.417885	0.208942	−	0.977928i	$-0.432998\pi$
$109$	4.36285	0.417885	0.208942	+	0.977928i	$0.432998\pi$
$110$	−5.93734	−0.566103
$111$	0.981535	0.0931632
$112$	−0.536504	−0.0506948
$113$	−1.00000	−0.0940721
$113$	−1.00000	−0.0940721
$114$	0.174455	0.0163392
$115$	−2.36230	−0.220285
$116$	−31.4111	−2.91645
$117$	−4.40481	−0.407225
$118$	−22.1201	−2.03632
$119$	2.54544	0.233340
$120$	0.440221	0.0401865
$121$	−6.15205	−0.559277
$122$	12.4881	1.13062
$123$	0.0404846	0.00365038
$124$	17.5155	1.57293
$125$	−9.95630	−0.890519
$126$	−2.64875	−0.235969
$127$	10.6973	0.949232	0.474616	−	0.880193i	$-0.342587\pi$
$127$	10.6973	0.949232	0.474616	+	0.880193i	$0.342587\pi$
$128$	20.3799	1.80134
$129$	0.732535	0.0644961
$130$	−3.97429	−0.348569
$131$	3.50458	0.306197	0.153098	−	0.988211i	$-0.451075\pi$
$131$	3.50458	0.306197	0.153098	+	0.988211i	$0.451075\pi$
$132$	−0.827912	−0.0720605
$133$	−0.262598	−0.0227701
$134$	−7.94997	−0.686773
$135$	0.730242	0.0628493
$136$	24.3939	2.09176
$137$	11.1150	0.949620	0.474810	−	0.880088i	$-0.342517\pi$
$137$	11.1150	0.949620	0.474810	+	0.880088i	$0.342517\pi$
$138$	−0.515791	−0.0439070
$139$	13.9068	1.17956	0.589779	−	0.807565i	$-0.299215\pi$
$139$	13.9068	1.17956	0.589779	+	0.807565i	$0.299215\pi$
$140$	−1.52625	−0.128992
$141$	−0.187820	−0.0158173
$142$	−2.35257	−0.197423
$143$	3.24509	0.271368
$144$	−4.25632	−0.354694
$145$	−10.1862	−0.845920
$146$	−16.4116	−1.35824
$147$	0.729573	0.0601742
$148$	−32.6121	−2.68070
$149$	−10.6808	−0.875009	−0.437505	−	0.899216i	$-0.644138\pi$
$149$	−10.6808	−0.875009	−0.437505	+	0.899216i	$0.644138\pi$
$150$	−0.922538	−0.0753249
$151$	2.30221	0.187351	0.0936756	−	0.995603i	$-0.470138\pi$
$151$	2.30221	0.187351	0.0936756	+	0.995603i	$0.470138\pi$
$152$	−2.51657	−0.204121
$153$	20.1941	1.63260
$154$	1.95137	0.157246
$155$	5.68005	0.456232
$156$	−0.554182	−0.0443701
$157$	6.29718	0.502570	0.251285	−	0.967913i	$-0.419147\pi$
$157$	6.29718	0.502570	0.251285	+	0.967913i	$0.419147\pi$
$158$	20.1916	1.60636
$159$	−0.704876	−0.0559003
$160$	4.43596	0.350693
$161$	0.776395	0.0611885
$162$	−20.9338	−1.64472
$163$	−5.09060	−0.398726	−0.199363	−	0.979926i	$-0.563887\pi$
$163$	−5.09060	−0.398726	−0.199363	+	0.979926i	$0.563887\pi$
$164$	−1.34513	−0.105037
$165$	−0.268482	−0.0209013
$166$	−5.26573	−0.408700
$167$	24.5440	1.89927	0.949637	−	0.313354i	$-0.101452\pi$
$167$	24.5440	1.89927	0.949637	+	0.313354i	$0.101452\pi$
$168$	−0.144684	−0.0111626
$169$	−10.8278	−0.832910
$170$	18.2204	1.39744
$171$	−2.08331	−0.159314
$172$	−24.3389	−1.85583
$173$	19.0725	1.45006	0.725028	−	0.688719i	$-0.241827\pi$
$173$	19.0725	1.45006	0.725028	+	0.688719i	$0.241827\pi$
$174$	−2.22409	−0.168608
$175$	1.38865	0.104972
$176$	3.13570	0.236362
$177$	−1.00025	−0.0751837
$178$	29.4711	2.20895
$179$	1.91357	0.143027	0.0715135	−	0.997440i	$-0.477217\pi$
$179$	1.91357	0.143027	0.0715135	+	0.997440i	$0.477217\pi$
$180$	−12.1085	−0.902511
$181$	−4.58165	−0.340552	−0.170276	−	0.985396i	$-0.554466\pi$
$181$	−4.58165	−0.340552	−0.170276	+	0.985396i	$0.554466\pi$
$182$	1.30620	0.0968216
$183$	0.564701	0.0417439
$184$	7.44046	0.548518
$185$	−10.5757	−0.777542
$186$	1.24020	0.0909358
$187$	−14.8773	−1.08794
$188$	6.24043	0.455130
$189$	−0.240002	−0.0174576
$190$	−1.87969	−0.136367
$191$	19.0900	1.38130	0.690651	−	0.723189i	$-0.257324\pi$
$191$	19.0900	1.38130	0.690651	+	0.723189i	$0.257324\pi$
$192$	1.27157	0.0917673
$193$	17.7320	1.27637	0.638187	−	0.769881i	$-0.279684\pi$
$193$	17.7320	1.27637	0.638187	+	0.769881i	$0.279684\pi$
$194$	10.4345	0.749155
$195$	−0.179715	−0.0128696
$196$	−24.2405	−1.73147
$197$	9.80602	0.698650	0.349325	−	0.937002i	$-0.386411\pi$
$197$	9.80602	0.698650	0.349325	+	0.937002i	$0.386411\pi$
$198$	15.4811	1.10019
$199$	12.2963	0.871659	0.435829	−	0.900029i	$-0.356455\pi$
$199$	12.2963	0.871659	0.435829	+	0.900029i	$0.356455\pi$
$200$	13.3079	0.941013
$201$	−0.359492	−0.0253566
$202$	−24.8438	−1.74800
$203$	3.34782	0.234971
$204$	2.54068	0.177883
$205$	−0.436208	−0.0304661
$206$	−36.4486	−2.53949
$207$	6.15949	0.428114
$208$	2.09895	0.145536
$209$	1.53480	0.106165
$210$	−0.108068	−0.00745739
$211$	−17.0642	−1.17475	−0.587373	−	0.809317i	$-0.699838\pi$
$211$	−17.0642	−1.17475	−0.587373	+	0.809317i	$0.699838\pi$
$212$	23.4199	1.60849
$213$	−0.106381	−0.00728914
$214$	−6.13436	−0.419336
$215$	−7.89282	−0.538286
$216$	−2.30002	−0.156497
$217$	−1.86681	−0.126727
$218$	−10.2639	−0.695159
$219$	−0.742121	−0.0501479
$220$	8.92047	0.601418
$221$	−9.95848	−0.669880
$222$	−2.30913	−0.154979
$223$	8.85153	0.592742	0.296371	−	0.955073i	$-0.404223\pi$
$223$	8.85153	0.592742	0.296371	+	0.955073i	$0.404223\pi$
$224$	−1.45793	−0.0974117
$225$	11.0168	0.734453
$226$	2.35257	0.156491
$227$	−12.0431	−0.799325	−0.399663	−	0.916662i	$-0.630873\pi$
$227$	−12.0431	−0.799325	−0.399663	+	0.916662i	$0.630873\pi$
$228$	−0.262107	−0.0173585
$229$	−1.92014	−0.126887	−0.0634433	−	0.997985i	$-0.520208\pi$
$229$	−1.92014	−0.126887	−0.0634433	+	0.997985i	$0.520208\pi$
$230$	5.55747	0.366449
$231$	0.0882395	0.00580573
$232$	32.0833	2.10637
$233$	1.53606	0.100631	0.0503154	−	0.998733i	$-0.483977\pi$
$233$	1.53606	0.100631	0.0503154	+	0.998733i	$0.483977\pi$
$234$	10.3626	0.677426
$235$	2.02370	0.132011
$236$	33.2341	2.16335
$237$	0.913051	0.0593090
$238$	−5.98833	−0.388166
$239$	−3.17656	−0.205475	−0.102737	−	0.994709i	$-0.532760\pi$
$239$	−3.17656	−0.205475	−0.102737	+	0.994709i	$0.532760\pi$
$240$	−0.173656	−0.0112095
$241$	1.33218	0.0858130	0.0429065	−	0.999079i	$-0.486338\pi$
$241$	1.33218	0.0858130	0.0429065	+	0.999079i	$0.486338\pi$
$242$	14.4731	0.930368
$243$	−2.85787	−0.183332
$244$	−18.7625	−1.20115
$245$	−7.86090	−0.502215
$246$	−0.0952430	−0.00607247
$247$	1.02736	0.0653691
$248$	−17.8903	−1.13603
$249$	−0.238112	−0.0150898
$250$	23.4229	1.48139
$251$	9.71377	0.613128	0.306564	−	0.951850i	$-0.400821\pi$
$251$	9.71377	0.613128	0.306564	+	0.951850i	$0.400821\pi$
$252$	3.97958	0.250690
$253$	−4.53778	−0.285288
$254$	−25.1661	−1.57906
$255$	0.823913	0.0515954
$256$	−24.0394	−1.50246
$257$	−23.6152	−1.47308	−0.736539	−	0.676396i	$-0.763541\pi$
$257$	−23.6152	−1.47308	−0.736539	+	0.676396i	$0.763541\pi$
$258$	−1.72334	−0.107291
$259$	3.47582	0.215977
$260$	5.97112	0.370313
$261$	26.5597	1.64401
$262$	−8.24478	−0.509364
$263$	30.7267	1.89469	0.947345	−	0.320214i	$-0.103755\pi$
$263$	30.7267	1.89469	0.947345	+	0.320214i	$0.103755\pi$
$264$	0.845630	0.0520449
$265$	7.59480	0.466545
$266$	0.617780	0.0378785
$267$	1.33266	0.0815576
$268$	11.9443	0.729616
$269$	−12.5419	−0.764691	−0.382345	−	0.924019i	$-0.624884\pi$
$269$	−12.5419	−0.764691	−0.382345	+	0.924019i	$0.624884\pi$
$270$	−1.71795	−0.104551
$271$	21.4368	1.30219	0.651097	−	0.758994i	$-0.274309\pi$
$271$	21.4368	1.30219	0.651097	+	0.758994i	$0.274309\pi$
$272$	−9.62277	−0.583466
$273$	0.0590652	0.00357479
$274$	−26.1489	−1.57971
$275$	−8.11623	−0.489427
$276$	0.774943	0.0466461
$277$	16.1874	0.972607	0.486303	−	0.873790i	$-0.338345\pi$
$277$	16.1874	0.972607	0.486303	+	0.873790i	$0.338345\pi$
$278$	−32.7167	−1.96222
$279$	−14.8102	−0.886666
$280$	1.55892	0.0931630
$281$	3.94184	0.235151	0.117575	−	0.993064i	$-0.462488\pi$
$281$	3.94184	0.235151	0.117575	+	0.993064i	$0.462488\pi$
$282$	0.441860	0.0263124
$283$	17.9002	1.06406	0.532028	−	0.846726i	$-0.321430\pi$
$283$	17.9002	1.06406	0.532028	+	0.846726i	$0.321430\pi$
$284$	3.53459	0.209739
$285$	−0.0849981	−0.00503485
$286$	−7.63430	−0.451426
$287$	0.143365	0.00846255
$288$	−11.5664	−0.681555
$289$	28.6553	1.68560
$290$	23.9638	1.40720
$291$	0.471841	0.0276598
$292$	24.6574	1.44297
$293$	−33.1479	−1.93652	−0.968260	−	0.249945i	$-0.919587\pi$
$293$	−33.1479	−1.93652	−0.968260	+	0.249945i	$0.919587\pi$
$294$	−1.71637	−0.100101
$295$	10.7774	0.627485
$296$	33.3100	1.93611
$297$	1.40274	0.0813951
$298$	25.1275	1.45559
$299$	−3.03747	−0.175661
$300$	1.38605	0.0800239
$301$	2.59406	0.149519
$302$	−5.41611	−0.311662
$303$	−1.12342	−0.0645387
$304$	0.992723	0.0569366
$305$	−6.08446	−0.348395
$306$	−47.5081	−2.71586
$307$	9.21527	0.525943	0.262972	−	0.964804i	$-0.415297\pi$
$307$	9.21527	0.525943	0.262972	+	0.964804i	$0.415297\pi$
$308$	−2.93181	−0.167056
$309$	−1.64818	−0.0937615
$310$	−13.3627	−0.758951
$311$	19.2544	1.09182	0.545910	−	0.837844i	$-0.316184\pi$
$311$	19.2544	1.09182	0.545910	+	0.837844i	$0.316184\pi$
$312$	0.566042	0.0320458
$313$	−12.7897	−0.722919	−0.361459	−	0.932388i	$-0.617721\pi$
$313$	−12.7897	−0.722919	−0.361459	+	0.932388i	$0.617721\pi$
$314$	−14.8146	−0.836035
$315$	1.29053	0.0727130
$316$	−30.3367	−1.70657
$317$	3.79647	0.213231	0.106615	−	0.994300i	$-0.465999\pi$
$317$	3.79647	0.213231	0.106615	+	0.994300i	$0.465999\pi$
$318$	1.65827	0.0929912
$319$	−19.5669	−1.09554
$320$	−13.7007	−0.765891
$321$	−0.277391	−0.0154825
$322$	−1.82652	−0.101788
$323$	−4.70998	−0.262070
$324$	31.4518	1.74732
$325$	−5.43279	−0.301357
$326$	11.9760	0.663289
$327$	−0.464126	−0.0256662
$328$	1.37391	0.0758616
$329$	−0.665110	−0.0366687
$330$	0.631623	0.0347697
$331$	8.39924	0.461664	0.230832	−	0.972994i	$-0.425855\pi$
$331$	8.39924	0.461664	0.230832	+	0.972994i	$0.425855\pi$
$332$	7.91143	0.434196
$333$	27.5753	1.51112
$334$	−57.7415	−3.15948
$335$	3.87340	0.211626
$336$	0.0570740	0.00311364
$337$	1.55450	0.0846787	0.0423394	−	0.999103i	$-0.486519\pi$
$337$	1.55450	0.0846787	0.0423394	+	0.999103i	$0.486519\pi$
$338$	25.4732	1.38556
$339$	0.106381	0.00577785
$340$	−27.3750	−1.48462
$341$	10.9109	0.590860
$342$	4.90113	0.265023
$343$	5.22061	0.281886
$344$	24.8598	1.34035
$345$	0.251305	0.0135298
$346$	−44.8694	−2.41220
$347$	8.93267	0.479531	0.239766	−	0.970831i	$-0.422929\pi$
$347$	8.93267	0.479531	0.239766	+	0.970831i	$0.422929\pi$
$348$	3.34156	0.179126
$349$	2.08904	0.111824	0.0559120	−	0.998436i	$-0.482193\pi$
$349$	2.08904	0.111824	0.0559120	+	0.998436i	$0.482193\pi$
$350$	−3.26690	−0.174623
$351$	0.938955	0.0501177
$352$	8.52112	0.454177
$353$	−9.25285	−0.492479	−0.246240	−	0.969209i	$-0.579195\pi$
$353$	−9.25285	−0.492479	−0.246240	+	0.969209i	$0.579195\pi$
$354$	2.35317	0.125070
$355$	1.14622	0.0608353
$356$	−44.2785	−2.34676
$357$	−0.270788	−0.0143316
$358$	−4.50181	−0.237928
$359$	−16.5987	−0.876048	−0.438024	−	0.898963i	$-0.644321\pi$
$359$	−16.5987	−0.876048	−0.438024	+	0.898963i	$0.644321\pi$
$360$	12.3676	0.651829
$361$	−18.5141	−0.974426
$362$	10.7787	0.566514
$363$	0.654464	0.0343504
$364$	−1.96248	−0.102862
$365$	7.99611	0.418535
$366$	−1.32850	−0.0694417
$367$	−27.4007	−1.43031	−0.715154	−	0.698967i	$-0.753643\pi$
$367$	−27.4007	−1.43031	−0.715154	+	0.698967i	$0.753643\pi$
$368$	−2.93508	−0.153001
$369$	1.13738	0.0592094
$370$	24.8801	1.29346
$371$	−2.49611	−0.129592
$372$	−1.86332	−0.0966086
$373$	−13.5964	−0.703993	−0.351997	−	0.936001i	$-0.614497\pi$
$373$	−13.5964	−0.703993	−0.351997	+	0.936001i	$0.614497\pi$
$374$	34.9999	1.80980
$375$	1.05917	0.0546951
$376$	−6.37398	−0.328713
$377$	−13.0976	−0.674560
$378$	0.564622	0.0290410
$379$	−0.894448	−0.0459447	−0.0229723	−	0.999736i	$-0.507313\pi$
$379$	−0.894448	−0.0459447	−0.0229723	+	0.999736i	$0.507313\pi$
$380$	2.82411	0.144874
$381$	−1.13799	−0.0583012
$382$	−44.9105	−2.29782
$383$	−33.4590	−1.70967	−0.854837	−	0.518896i	$-0.826343\pi$
$383$	−33.4590	−1.70967	−0.854837	+	0.518896i	$0.826343\pi$
$384$	−2.16804	−0.110637
$385$	−0.950751	−0.0484548
$386$	−41.7157	−2.12327
$387$	20.5799	1.04613
$388$	−15.6772	−0.795890
$389$	26.0063	1.31857	0.659285	−	0.751893i	$-0.270859\pi$
$389$	26.0063	1.31857	0.659285	+	0.751893i	$0.270859\pi$
$390$	0.422791	0.0214089
$391$	13.9255	0.704242
$392$	24.7593	1.25053
$393$	−0.372823	−0.0188064
$394$	−23.0694	−1.16222
$395$	−9.83781	−0.494994
$396$	−23.2594	−1.16883
$397$	−36.5985	−1.83683	−0.918413	−	0.395623i	$-0.870529\pi$
$397$	−36.5985	−1.83683	−0.918413	+	0.395623i	$0.870529\pi$
$398$	−28.9278	−1.45002
$399$	0.0279356	0.00139853
$400$	−5.24965	−0.262482
$401$	28.1770	1.40709	0.703545	−	0.710651i	$-0.251599\pi$
$401$	28.1770	1.40709	0.703545	+	0.710651i	$0.251599\pi$
$402$	0.845729	0.0421812
$403$	7.30348	0.363812
$404$	37.3263	1.85705
$405$	10.1994	0.506813
$406$	−7.87598	−0.390878
$407$	−20.3151	−1.00698
$408$	−2.59506	−0.128474
$409$	−33.1222	−1.63779	−0.818893	−	0.573946i	$-0.805412\pi$
$409$	−33.1222	−1.63779	−0.818893	+	0.573946i	$0.805412\pi$
$410$	1.02621	0.0506809
$411$	−1.18243	−0.0583251
$412$	54.7617	2.69791
$413$	−3.54211	−0.174296
$414$	−14.4906	−0.712176
$415$	2.56558	0.125939
$416$	5.70381	0.279652
$417$	−1.47942	−0.0724477
$418$	−3.61073	−0.176607
$419$	−2.38602	−0.116565	−0.0582824	−	0.998300i	$-0.518562\pi$
$419$	−2.38602	−0.116565	−0.0582824	+	0.998300i	$0.518562\pi$
$420$	0.162365	0.00792260
$421$	−27.8864	−1.35910	−0.679550	−	0.733629i	$-0.737825\pi$
$421$	−27.8864	−1.35910	−0.679550	+	0.733629i	$0.737825\pi$
$422$	40.1446	1.95421
$423$	−5.27662	−0.256558
$424$	−23.9211	−1.16171
$425$	24.9070	1.20817
$426$	0.250270	0.0121256
$427$	1.99972	0.0967734
$428$	9.21648	0.445496
$429$	−0.345217	−0.0166673
$430$	18.5684	0.895449
$431$	2.78563	0.134179	0.0670896	−	0.997747i	$-0.478629\pi$
$431$	2.78563	0.134179	0.0670896	+	0.997747i	$0.478629\pi$
$432$	0.907302	0.0436526
$433$	6.15372	0.295729	0.147865	−	0.989008i	$-0.452760\pi$
$433$	6.15372	0.295729	0.147865	+	0.989008i	$0.452760\pi$
$434$	4.39180	0.210813
$435$	1.08363	0.0519559
$436$	15.4209	0.738526
$437$	−1.43661	−0.0687222
$438$	1.74589	0.0834220
$439$	−39.0801	−1.86519	−0.932596	−	0.360923i	$-0.882462\pi$
$439$	−39.0801	−1.86519	−0.932596	+	0.360923i	$0.882462\pi$
$440$	−9.11138	−0.434368
$441$	20.4966	0.976030
$442$	23.4280	1.11436
$443$	16.3716	0.777840	0.388920	−	0.921272i	$-0.372848\pi$
$443$	16.3716	0.777840	0.388920	+	0.921272i	$0.372848\pi$
$444$	3.46933	0.164647
$445$	−14.3590	−0.680681
$446$	−20.8239	−0.986038
$447$	1.13624	0.0537425
$448$	4.50288	0.212741
$449$	13.8994	0.655955	0.327978	−	0.944686i	$-0.393633\pi$
$449$	13.8994	0.655955	0.327978	+	0.944686i	$0.393633\pi$
$450$	−25.9178	−1.22178
$451$	−0.837922	−0.0394562
$452$	−3.53459	−0.166253
$453$	−0.244913	−0.0115070
$454$	28.3321	1.32969
$455$	−0.636407	−0.0298352
$456$	0.267716	0.0125370
$457$	−31.2045	−1.45968	−0.729841	−	0.683616i	$-0.760406\pi$
$457$	−31.2045	−1.45968	−0.729841	+	0.683616i	$0.760406\pi$
$458$	4.51727	0.211078
$459$	−4.30470	−0.200926
$460$	−8.34975	−0.389309
$461$	18.6645	0.869291	0.434645	−	0.900602i	$-0.356874\pi$
$461$	18.6645	0.869291	0.434645	+	0.900602i	$0.356874\pi$
$462$	−0.207590	−0.00965795
$463$	32.2840	1.50037	0.750184	−	0.661230i	$-0.229965\pi$
$463$	32.2840	1.50037	0.750184	+	0.661230i	$0.229965\pi$
$464$	−12.6561	−0.587543
$465$	−0.604252	−0.0280215
$466$	−3.61369	−0.167401
$467$	24.7341	1.14456	0.572280	−	0.820058i	$-0.306059\pi$
$467$	24.7341	1.14456	0.572280	+	0.820058i	$0.306059\pi$
$468$	−15.5692	−0.719687
$469$	−1.27304	−0.0587833
$470$	−4.76089	−0.219603
$471$	−0.669904	−0.0308675
$472$	−33.9453	−1.56246
$473$	−15.1615	−0.697126
$474$	−2.14802	−0.0986617
$475$	−2.56950	−0.117897
$476$	8.99710	0.412381
$477$	−19.8028	−0.906707
$478$	7.47309	0.341811
$479$	13.8146	0.631207	0.315604	−	0.948891i	$-0.397793\pi$
$479$	13.8146	0.631207	0.315604	+	0.948891i	$0.397793\pi$
$480$	−0.471903	−0.0215393
$481$	−13.5984	−0.620033
$482$	−3.13404	−0.142751
$483$	−0.0825940	−0.00375816
$484$	−21.7450	−0.988407
$485$	−5.08393	−0.230849
$486$	6.72333	0.304977
$487$	−27.5528	−1.24854	−0.624269	−	0.781209i	$-0.714603\pi$
$487$	−27.5528	−1.24854	−0.624269	+	0.781209i	$0.714603\pi$
$488$	19.1640	0.867516
$489$	0.541545	0.0244895
$490$	18.4933	0.835443
$491$	24.1862	1.09151	0.545755	−	0.837945i	$-0.316243\pi$
$491$	24.1862	1.09151	0.545755	+	0.837945i	$0.316243\pi$
$492$	0.143097	0.00645129
$493$	60.0467	2.70437
$494$	−2.41693	−0.108743
$495$	−7.54273	−0.339021
$496$	7.05728	0.316881
$497$	−0.376719	−0.0168982
$498$	0.560176	0.0251021
$499$	28.7298	1.28612	0.643061	−	0.765815i	$-0.277664\pi$
$499$	28.7298	1.28612	0.643061	+	0.765815i	$0.277664\pi$
$500$	−35.1914	−1.57381
$501$	−2.61103	−0.116652
$502$	−22.8523	−1.01995
$503$	−4.39310	−0.195879	−0.0979394	−	0.995192i	$-0.531225\pi$
$503$	−4.39310	−0.195879	−0.0979394	+	0.995192i	$0.531225\pi$
$504$	−4.06474	−0.181058
$505$	12.1045	0.538641
$506$	10.6755	0.474582
$507$	1.15188	0.0511568
$508$	37.8106	1.67757
$509$	−4.94066	−0.218991	−0.109495	−	0.993987i	$-0.534924\pi$
$509$	−4.94066	−0.218991	−0.109495	+	0.993987i	$0.534924\pi$
$510$	−1.93831	−0.0858299
$511$	−2.62801	−0.116256
$512$	15.7945	0.698026
$513$	0.444090	0.0196070
$514$	55.5565	2.45049
$515$	17.7585	0.782535
$516$	2.58921	0.113984
$517$	3.88736	0.170966
$518$	−8.17712	−0.359282
$519$	−2.02896	−0.0890615
$520$	−6.09891	−0.267455
$521$	−18.5080	−0.810851	−0.405426	−	0.914128i	$-0.632877\pi$
$521$	−18.5080	−0.810851	−0.405426	+	0.914128i	$0.632877\pi$
$522$	−62.4837	−2.73484
$523$	−18.2415	−0.797645	−0.398823	−	0.917028i	$-0.630581\pi$
$523$	−18.2415	−0.797645	−0.398823	+	0.917028i	$0.630581\pi$
$524$	12.3873	0.541140
$525$	−0.147727	−0.00644733
$526$	−72.2868	−3.15185
$527$	−33.4833	−1.45855
$528$	−0.333580	−0.0145172
$529$	−18.7525	−0.815328
$530$	−17.8673	−0.776106
$531$	−28.1012	−1.21949
$532$	−0.928176	−0.0402415
$533$	−0.560882	−0.0242945
$534$	−3.13518	−0.135673
$535$	2.98879	0.129217
$536$	−12.1999	−0.526957
$537$	−0.203568	−0.00878462
$538$	29.5056	1.27208
$539$	−15.1002	−0.650411
$540$	2.58111	0.111073
$541$	−21.6156	−0.929327	−0.464663	−	0.885487i	$-0.653825\pi$
$541$	−21.6156	−0.929327	−0.464663	+	0.885487i	$0.653825\pi$
$542$	−50.4317	−2.16623
$543$	0.487403	0.0209165
$544$	−26.1495	−1.12115
$545$	5.00080	0.214211
$546$	−0.138955	−0.00594672
$547$	25.1619	1.07584	0.537922	−	0.842995i	$-0.319210\pi$
$547$	25.1619	1.07584	0.537922	+	0.842995i	$0.319210\pi$
$548$	39.2870	1.67826
$549$	15.8647	0.677089
$550$	19.0940	0.814172
$551$	−6.19466	−0.263901
$552$	−0.791527	−0.0336896
$553$	3.23331	0.137494
$554$	−38.0820	−1.61795
$555$	1.12506	0.0477561
$556$	49.1547	2.08463
$557$	−36.8298	−1.56053	−0.780264	−	0.625450i	$-0.784915\pi$
$557$	−36.8298	−1.56053	−0.780264	+	0.625450i	$0.784915\pi$
$558$	34.8422	1.47499
$559$	−10.1487	−0.429244
$560$	−0.614953	−0.0259865
$561$	1.58267	0.0668204
$562$	−9.27347	−0.391178
$563$	−9.85782	−0.415457	−0.207729	−	0.978186i	$-0.566607\pi$
$563$	−9.85782	−0.415457	−0.207729	+	0.978186i	$0.566607\pi$
$564$	−0.663866	−0.0279538
$565$	−1.14622	−0.0482220
$566$	−42.1115	−1.77008
$567$	−3.35215	−0.140777
$568$	−3.61023	−0.151482
$569$	−2.50314	−0.104937	−0.0524685	−	0.998623i	$-0.516709\pi$
$569$	−2.50314	−0.104937	−0.0524685	+	0.998623i	$0.516709\pi$
$570$	0.199964	0.00837557
$571$	−9.53061	−0.398844	−0.199422	−	0.979914i	$-0.563906\pi$
$571$	−9.53061	−0.398844	−0.199422	+	0.979914i	$0.563906\pi$
$572$	11.4701	0.479587
$573$	−2.03082	−0.0848387
$574$	−0.337275	−0.0140776
$575$	7.59696	0.316815
$576$	35.7234	1.48847
$577$	−15.5619	−0.647852	−0.323926	−	0.946082i	$-0.605003\pi$
$577$	−15.5619	−0.647852	−0.323926	+	0.946082i	$0.605003\pi$
$578$	−67.4135	−2.80403
$579$	−1.88635	−0.0783942
$580$	−36.0041	−1.49499
$581$	−0.843206	−0.0349821
$582$	−1.11004	−0.0460127
$583$	14.5890	0.604215
$584$	−25.1851	−1.04217
$585$	−5.04890	−0.208746
$586$	77.9828	3.22144
$587$	−0.266480	−0.0109988	−0.00549941	−	0.999985i	$-0.501751\pi$
$587$	−0.266480	−0.0109988	−0.00549941	+	0.999985i	$0.501751\pi$
$588$	2.57874	0.106346
$589$	3.45427	0.142331
$590$	−25.3546	−1.04383
$591$	−1.04318	−0.0429106
$592$	−13.1400	−0.540050
$593$	36.1260	1.48352	0.741758	−	0.670667i	$-0.233992\pi$
$593$	36.1260	1.48352	0.741758	+	0.670667i	$0.233992\pi$
$594$	−3.30004	−0.135402
$595$	2.91765	0.119612
$596$	−37.7524	−1.54640
$597$	−1.30809	−0.0535367
$598$	7.14586	0.292216
$599$	8.35884	0.341533	0.170766	−	0.985312i	$-0.445376\pi$
$599$	8.35884	0.341533	0.170766	+	0.985312i	$0.445376\pi$
$600$	−1.41572	−0.0577964
$601$	13.1561	0.536647	0.268323	−	0.963329i	$-0.413530\pi$
$601$	13.1561	0.536647	0.268323	+	0.963329i	$0.413530\pi$
$602$	−6.10272	−0.248728
$603$	−10.0996	−0.411286
$604$	8.13737	0.331105
$605$	−7.05163	−0.286689
$606$	2.64292	0.107361
$607$	3.18549	0.129295	0.0646476	−	0.997908i	$-0.479408\pi$
$607$	3.18549	0.129295	0.0646476	+	0.997908i	$0.479408\pi$
$608$	2.69768	0.109405
$609$	−0.356146	−0.0144318
$610$	14.3141	0.579562
$611$	2.60209	0.105269
$612$	71.3780	2.88528
$613$	−21.7931	−0.880216	−0.440108	−	0.897945i	$-0.645060\pi$
$613$	−21.7931	−0.880216	−0.440108	+	0.897945i	$0.645060\pi$
$614$	−21.6796	−0.874917
$615$	0.0464045	0.00187121
$616$	2.99455	0.120654
$617$	23.0685	0.928702	0.464351	−	0.885651i	$-0.346288\pi$
$617$	23.0685	0.928702	0.464351	+	0.885651i	$0.346288\pi$
$618$	3.87745	0.155974
$619$	1.89456	0.0761487	0.0380744	−	0.999275i	$-0.487878\pi$
$619$	1.89456	0.0761487	0.0380744	+	0.999275i	$0.487878\pi$
$620$	20.0766	0.806297
$621$	−1.31299	−0.0526885
$622$	−45.2975	−1.81626
$623$	4.71924	0.189072
$624$	−0.223289	−0.00893873
$625$	7.01869	0.280748
$626$	30.0888	1.20259
$627$	−0.163275	−0.00652056
$628$	22.2580	0.888189
$629$	62.3427	2.48576
$630$	−3.03606	−0.120959
$631$	−30.1250	−1.19926	−0.599629	−	0.800278i	$-0.704685\pi$
$631$	−30.1250	−1.19926	−0.599629	+	0.800278i	$0.704685\pi$
$632$	30.9859	1.23255
$633$	1.81531	0.0721521
$634$	−8.93146	−0.354714
$635$	12.2615	0.486583
$636$	−2.49145	−0.0987923
$637$	−10.1076	−0.400480
$638$	46.0326	1.82245
$639$	−2.98868	−0.118230
$640$	23.3599	0.923382
$641$	11.5935	0.457915	0.228958	−	0.973436i	$-0.426468\pi$
$641$	11.5935	0.457915	0.228958	+	0.973436i	$0.426468\pi$
$642$	0.652582	0.0257554
$643$	12.2272	0.482195	0.241098	−	0.970501i	$-0.422493\pi$
$643$	12.2272	0.482195	0.241098	+	0.970501i	$0.422493\pi$
$644$	2.74424	0.108138
$645$	0.839650	0.0330612
$646$	11.0806	0.435959
$647$	−13.9013	−0.546518	−0.273259	−	0.961940i	$-0.588102\pi$
$647$	−13.9013	−0.546518	−0.273259	+	0.961940i	$0.588102\pi$
$648$	−32.1248	−1.26198
$649$	20.7025	0.812646
$650$	12.7810	0.501313
$651$	0.198594	0.00778352
$652$	−17.9932	−0.704667
$653$	48.9391	1.91513	0.957567	−	0.288209i	$-0.0930599\pi$
$653$	48.9391	1.91513	0.957567	+	0.288209i	$0.0930599\pi$
$654$	1.09189	0.0426962
$655$	4.01704	0.156959
$656$	−0.541974	−0.0211605
$657$	−20.8492	−0.813404
$658$	1.56472	0.0609991
$659$	3.69045	0.143759	0.0718797	−	0.997413i	$-0.477100\pi$
$659$	3.69045	0.143759	0.0718797	+	0.997413i	$0.477100\pi$
$660$	−0.948973	−0.0369387
$661$	−8.12858	−0.316165	−0.158083	−	0.987426i	$-0.550531\pi$
$661$	−8.12858	−0.316165	−0.158083	+	0.987426i	$0.550531\pi$
$662$	−19.7598	−0.767987
$663$	1.05940	0.0411436
$664$	−8.08074	−0.313593
$665$	−0.300996	−0.0116721
$666$	−64.8728	−2.51377
$667$	18.3151	0.709162
$668$	86.7530	3.35658
$669$	−0.941639	−0.0364059
$670$	−9.11245	−0.352045
$671$	−11.6878	−0.451201
$672$	0.155096	0.00598297
$673$	−8.37256	−0.322739	−0.161369	−	0.986894i	$-0.551591\pi$
$673$	−8.37256	−0.322739	−0.161369	+	0.986894i	$0.551591\pi$
$674$	−3.65706	−0.140865
$675$	−2.34840	−0.0903901
$676$	−38.2719	−1.47200
$677$	6.40645	0.246220	0.123110	−	0.992393i	$-0.460713\pi$
$677$	6.40645	0.246220	0.123110	+	0.992393i	$0.460713\pi$
$678$	−0.250270	−0.00961156
$679$	1.67089	0.0641229
$680$	27.9608	1.07225
$681$	1.28116	0.0490941
$682$	−25.6687	−0.982906
$683$	6.48170	0.248015	0.124008	−	0.992281i	$-0.460425\pi$
$683$	6.48170	0.248015	0.124008	+	0.992281i	$0.460425\pi$
$684$	−7.36364	−0.281556
$685$	12.7403	0.486782
$686$	−12.2818	−0.468923
$687$	0.204268	0.00779330
$688$	−9.80657	−0.373872
$689$	9.76549	0.372035
$690$	−0.591212	−0.0225070
$691$	−29.0486	−1.10506	−0.552531	−	0.833492i	$-0.686338\pi$
$691$	−29.0486	−1.10506	−0.552531	+	0.833492i	$0.686338\pi$
$692$	67.4135	2.56268
$693$	2.47900	0.0941695
$694$	−21.0147	−0.797709
$695$	15.9403	0.604650
$696$	−3.41307	−0.129372
$697$	2.57140	0.0973987
$698$	−4.91463	−0.186021
$699$	−0.163409	−0.00618068
$700$	4.90831	0.185517
$701$	−3.40186	−0.128486	−0.0642432	−	0.997934i	$-0.520463\pi$
$701$	−3.40186	−0.128486	−0.0642432	+	0.997934i	$0.520463\pi$
$702$	−2.20896	−0.0833718
$703$	−6.43152	−0.242569
$704$	−26.3179	−0.991894
$705$	−0.215284	−0.00810806
$706$	21.7680	0.819249
$707$	−3.97826	−0.149618
$708$	−3.53549	−0.132872
$709$	23.2827	0.874401	0.437200	−	0.899364i	$-0.355970\pi$
$709$	23.2827	0.874401	0.437200	+	0.899364i	$0.355970\pi$
$710$	−2.69657	−0.101201
$711$	25.6513	0.961997
$712$	45.2261	1.69492
$713$	−10.2129	−0.382474
$714$	0.637048	0.0238409
$715$	3.71960	0.139105
$716$	6.76368	0.252771
$717$	0.337927	0.0126201
$718$	39.0497	1.45732
$719$	4.06855	0.151731	0.0758656	−	0.997118i	$-0.475828\pi$
$719$	4.06855	0.151731	0.0758656	+	0.997118i	$0.475828\pi$
$720$	−4.87870	−0.181818
$721$	−5.83654	−0.217364
$722$	43.5557	1.62098
$723$	−0.141719	−0.00527058
$724$	−16.1943	−0.601855
$725$	32.7581	1.21661
$726$	−1.53967	−0.0571426
$727$	26.0601	0.966515	0.483257	−	0.875478i	$-0.339454\pi$
$727$	26.0601	0.966515	0.483257	+	0.875478i	$0.339454\pi$
$728$	2.00447	0.0742907
$729$	−26.3908	−0.977437
$730$	−18.8114	−0.696241
$731$	46.5273	1.72087
$732$	1.99598	0.0737737
$733$	32.0355	1.18326	0.591629	−	0.806210i	$-0.298485\pi$
$733$	32.0355	1.18326	0.591629	+	0.806210i	$0.298485\pi$
$734$	64.4622	2.37934
$735$	0.836254	0.0308457
$736$	−7.97594	−0.293997
$737$	7.44050	0.274074
$738$	−2.67576	−0.0984960
$739$	49.9085	1.83591	0.917957	−	0.396681i	$-0.129838\pi$
$739$	49.9085	1.83591	0.917957	+	0.396681i	$0.129838\pi$
$740$	−37.3808	−1.37415
$741$	−0.109292	−0.00401493
$742$	5.87229	0.215578
$743$	15.0293	0.551373	0.275687	−	0.961248i	$-0.411095\pi$
$743$	15.0293	0.551373	0.275687	+	0.961248i	$0.411095\pi$
$744$	1.90320	0.0697746
$745$	−12.2426	−0.448536
$746$	31.9864	1.17111
$747$	−6.68953	−0.244757
$748$	−52.5852	−1.92271
$749$	−0.982300	−0.0358925
$750$	−2.49176	−0.0909863
$751$	14.4974	0.529018	0.264509	−	0.964383i	$-0.414790\pi$
$751$	14.4974	0.529018	0.264509	+	0.964383i	$0.414790\pi$
$752$	2.51438	0.0916899
$753$	−1.03337	−0.0376579
$754$	30.8130	1.12214
$755$	2.63885	0.0960376
$756$	−0.848309	−0.0308527
$757$	51.3614	1.86676	0.933381	−	0.358887i	$-0.116844\pi$
$757$	51.3614	1.86676	0.933381	+	0.358887i	$0.116844\pi$
$758$	2.10425	0.0764299
$759$	0.482736	0.0175222
$760$	−2.88455	−0.104634
$761$	−2.04601	−0.0741678	−0.0370839	−	0.999312i	$-0.511807\pi$
$761$	−2.04601	−0.0741678	−0.0370839	+	0.999312i	$0.511807\pi$
$762$	2.67721	0.0969852
$763$	−1.64357	−0.0595012
$764$	67.4752	2.44117
$765$	23.1470	0.836882
$766$	78.7147	2.84408
$767$	13.8577	0.500373
$768$	2.55734	0.0922801
$769$	37.2157	1.34203	0.671016	−	0.741443i	$-0.265858\pi$
$769$	37.2157	1.34203	0.671016	+	0.741443i	$0.265858\pi$
$770$	2.23671	0.0806054
$771$	2.51222	0.0904755
$772$	62.6752	2.25573
$773$	−2.24772	−0.0808450	−0.0404225	−	0.999183i	$-0.512870\pi$
$773$	−2.24772	−0.0808450	−0.0404225	+	0.999183i	$0.512870\pi$
$774$	−48.4156	−1.74026
$775$	−18.2666	−0.656156
$776$	16.0127	0.574823
$777$	−0.369763	−0.0132652
$778$	−61.1816	−2.19347
$779$	−0.265276	−0.00950449
$780$	−0.635217	−0.0227444
$781$	2.20181	0.0787868
$782$	−32.7607	−1.17152
$783$	−5.66163	−0.202330
$784$	−9.76691	−0.348818
$785$	7.21799	0.257621
$786$	0.877092	0.0312848
$787$	30.5685	1.08965	0.544825	−	0.838550i	$-0.316596\pi$
$787$	30.5685	1.08965	0.544825	+	0.838550i	$0.316596\pi$
$788$	34.6603	1.23472
$789$	−3.26875	−0.116371
$790$	23.1442	0.823432
$791$	0.376719	0.0133946
$792$	23.7571	0.844173
$793$	−7.82347	−0.277820
$794$	86.1006	3.05559
$795$	−0.807946	−0.0286549
$796$	43.4622	1.54048
$797$	4.52167	0.160166	0.0800828	−	0.996788i	$-0.474482\pi$
$797$	4.52167	0.160166	0.0800828	+	0.996788i	$0.474482\pi$
$798$	−0.0657204	−0.00232648
$799$	−11.9295	−0.422034
$800$	−14.2657	−0.504368
$801$	37.4398	1.32287
$802$	−66.2883	−2.34072
$803$	15.3599	0.542039
$804$	−1.27066	−0.0448126
$805$	0.889922	0.0313656
$806$	−17.1820	−0.605208
$807$	1.33422	0.0469668
$808$	−38.1251	−1.34124
$809$	−11.1886	−0.393372	−0.196686	−	0.980467i	$-0.563018\pi$
$809$	−11.1886	−0.393372	−0.196686	+	0.980467i	$0.563018\pi$
$810$	−23.9949	−0.843093
$811$	6.01005	0.211041	0.105521	−	0.994417i	$-0.466349\pi$
$811$	6.01005	0.211041	0.105521	+	0.994417i	$0.466349\pi$
$812$	11.8332	0.415263
$813$	−2.28048	−0.0799800
$814$	47.7927	1.67513
$815$	−5.83497	−0.204390
$816$	1.02368	0.0358361
$817$	−4.79994	−0.167929
$818$	77.9223	2.72449
$819$	1.65938	0.0579833
$820$	−1.54182	−0.0538426
$821$	25.0781	0.875230	0.437615	−	0.899162i	$-0.355823\pi$
$821$	25.0781	0.875230	0.437615	+	0.899162i	$0.355823\pi$
$822$	2.78176	0.0970249
$823$	−26.0581	−0.908330	−0.454165	−	0.890918i	$-0.650062\pi$
$823$	−26.0581	−0.908330	−0.454165	+	0.890918i	$0.650062\pi$
$824$	−55.9336	−1.94854
$825$	0.863417	0.0300603
$826$	8.33307	0.289945
$827$	0.284894	0.00990675	0.00495337	−	0.999988i	$-0.498423\pi$
$827$	0.284894	0.00990675	0.00495337	+	0.999988i	$0.498423\pi$
$828$	21.7713	0.756604
$829$	10.2899	0.357382	0.178691	−	0.983905i	$-0.442814\pi$
$829$	10.2899	0.357382	0.178691	+	0.983905i	$0.442814\pi$
$830$	−6.03571	−0.209503
$831$	−1.72204	−0.0597369
$832$	−17.6165	−0.610743
$833$	46.3392	1.60556
$834$	3.48045	0.120518
$835$	28.1330	0.973581
$836$	5.42490	0.187624
$837$	3.15704	0.109123
$838$	5.61329	0.193908
$839$	−20.6564	−0.713138	−0.356569	−	0.934269i	$-0.616054\pi$
$839$	−20.6564	−0.713138	−0.356569	+	0.934269i	$0.616054\pi$
$840$	−0.165840	−0.00572202
$841$	49.9746	1.72326
$842$	65.6047	2.26089
$843$	−0.419339	−0.0144428
$844$	−60.3148	−2.07612
$845$	−12.4111	−0.426955
$846$	12.4136	0.426789
$847$	2.31759	0.0796335
$848$	9.43629	0.324043
$849$	−1.90425	−0.0653537
$850$	−58.5954	−2.00981
$851$	19.0154	0.651838
$852$	−0.376015	−0.0128821
$853$	21.2415	0.727296	0.363648	−	0.931536i	$-0.381531\pi$
$853$	21.2415	0.727296	0.363648	+	0.931536i	$0.381531\pi$
$854$	−4.70449	−0.160984
$855$	−2.38794	−0.0816657
$856$	−9.41372	−0.321754
$857$	11.7855	0.402585	0.201292	−	0.979531i	$-0.435486\pi$
$857$	11.7855	0.402585	0.201292	+	0.979531i	$0.435486\pi$
$858$	0.812148	0.0277263
$859$	22.2387	0.758775	0.379388	−	0.925238i	$-0.376135\pi$
$859$	22.2387	0.758775	0.379388	+	0.925238i	$0.376135\pi$
$860$	−27.8979	−0.951310
$861$	−0.0152513	−0.000519764 0
$862$	−6.55340	−0.223210
$863$	49.9747	1.70116	0.850580	−	0.525846i	$-0.176251\pi$
$863$	49.9747	1.70116	0.850580	+	0.525846i	$0.176251\pi$
$864$	2.46556	0.0838799
$865$	21.8614	0.743309
$866$	−14.4771	−0.491951
$867$	−3.04839	−0.103529
$868$	−6.59841	−0.223965
$869$	−18.8977	−0.641059
$870$	−2.54931	−0.0864296
$871$	4.98047	0.168757
$872$	−15.7509	−0.533392
$873$	13.2559	0.448645
$874$	3.37972	0.114321
$875$	3.75073	0.126798
$876$	−2.62309	−0.0886262
$877$	29.6158	1.00006	0.500028	−	0.866009i	$-0.333323\pi$
$877$	29.6158	1.00006	0.500028	+	0.866009i	$0.333323\pi$
$878$	91.9387	3.10278
$879$	3.52632	0.118940
$880$	3.59421	0.121161
$881$	11.1264	0.374858	0.187429	−	0.982278i	$-0.439984\pi$
$881$	11.1264	0.374858	0.187429	+	0.982278i	$0.439984\pi$
$882$	−48.2198	−1.62364
$883$	−7.91220	−0.266267	−0.133133	−	0.991098i	$-0.542504\pi$
$883$	−7.91220	−0.266267	−0.133133	+	0.991098i	$0.542504\pi$
$884$	−35.1991	−1.18387
$885$	−1.14652	−0.0385397
$886$	−38.5154	−1.29395
$887$	24.3705	0.818281	0.409141	−	0.912471i	$-0.365829\pi$
$887$	24.3705	0.818281	0.409141	+	0.912471i	$0.365829\pi$
$888$	−3.54357	−0.118914
$889$	−4.02988	−0.135158
$890$	33.7805	1.13233
$891$	19.5923	0.656366
$892$	31.2865	1.04755
$893$	1.23069	0.0411835
$894$	−2.67310	−0.0894017
$895$	2.19338	0.0733166
$896$	−7.67749	−0.256487
$897$	0.323131	0.0107890
$898$	−32.6994	−1.09119
$899$	−44.0379	−1.46874
$900$	38.9398	1.29799
$901$	−44.7705	−1.49152
$902$	1.97127	0.0656361
$903$	−0.275960	−0.00918338
$904$	3.61023	0.120075
$905$	−5.25160	−0.174569
$906$	0.576174	0.0191421
$907$	−36.6169	−1.21584	−0.607922	−	0.793997i	$-0.707997\pi$
$907$	−36.6169	−1.21584	−0.607922	+	0.793997i	$0.707997\pi$
$908$	−42.5673	−1.41264
$909$	−31.5613	−1.04682
$910$	1.49719	0.0496315
$911$	29.8929	0.990396	0.495198	−	0.868780i	$-0.335096\pi$
$911$	29.8929	0.990396	0.495198	+	0.868780i	$0.335096\pi$
$912$	−0.105607	−0.00349701
$913$	4.92828	0.163102
$914$	73.4107	2.42821
$915$	0.647274	0.0213982
$916$	−6.78692	−0.224246
$917$	−1.32024	−0.0435983
$918$	10.1271	0.334244
$919$	−57.6959	−1.90321	−0.951605	−	0.307323i	$-0.900567\pi$
$919$	−57.6959	−1.90321	−0.951605	+	0.307323i	$0.900567\pi$
$920$	8.52844	0.281174
$921$	−0.980334	−0.0323031
$922$	−43.9095	−1.44608
$923$	1.47383	0.0485117
$924$	0.311891	0.0102604
$925$	34.0107	1.11826
$926$	−75.9505	−2.49589
$927$	−46.3039	−1.52082
$928$	−34.3923	−1.12898
$929$	−27.5453	−0.903733	−0.451866	−	0.892086i	$-0.649242\pi$
$929$	−27.5453	−0.903733	−0.451866	+	0.892086i	$0.649242\pi$
$930$	1.42155	0.0466143
$931$	−4.78053	−0.156676
$932$	5.42935	0.177844
$933$	−2.04832	−0.0670589
$934$	−58.1888	−1.90400
$935$	−17.0527	−0.557684
$936$	15.9024	0.519786
$937$	28.4915	0.930775	0.465388	−	0.885107i	$-0.345915\pi$
$937$	28.4915	0.930775	0.465388	+	0.885107i	$0.345915\pi$
$938$	2.99491	0.0977872
$939$	1.36059	0.0444012
$940$	7.15294	0.233303
$941$	11.4355	0.372786	0.186393	−	0.982475i	$-0.440320\pi$
$941$	11.4355	0.372786	0.186393	+	0.982475i	$0.440320\pi$
$942$	1.57600	0.0513487
$943$	0.784312	0.0255407
$944$	13.3906	0.435826
$945$	−0.275096	−0.00894889
$946$	35.6685	1.15968
$947$	−19.6626	−0.638948	−0.319474	−	0.947595i	$-0.603506\pi$
$947$	−19.6626	−0.638948	−0.319474	+	0.947595i	$0.603506\pi$
$948$	3.22726	0.104817
$949$	10.2815	0.333752
$950$	6.04493	0.196124
$951$	−0.403874	−0.0130965
$952$	−9.18964	−0.297838
$953$	26.2048	0.848856	0.424428	−	0.905462i	$-0.360475\pi$
$953$	26.2048	0.848856	0.424428	+	0.905462i	$0.360475\pi$
$954$	46.5875	1.50833
$955$	21.8814	0.708065
$956$	−11.2278	−0.363135
$957$	2.08156	0.0672873
$958$	−32.4999	−1.05002
$959$	−4.18724	−0.135213
$960$	1.45750	0.0470406
$961$	−6.44360	−0.207858
$962$	31.9912	1.03144
$963$	−7.79303	−0.251127
$964$	4.70869	0.151657
$965$	20.3248	0.654279
$966$	0.194308	0.00625177
$967$	9.21272	0.296261	0.148131	−	0.988968i	$-0.452674\pi$
$967$	9.21272	0.296261	0.148131	+	0.988968i	$0.452674\pi$
$968$	22.2103	0.713866
$969$	0.501054	0.0160962
$970$	11.9603	0.384022
$971$	−26.4207	−0.847881	−0.423940	−	0.905690i	$-0.639353\pi$
$971$	−26.4207	−0.847881	−0.423940	+	0.905690i	$0.639353\pi$
$972$	−10.1014	−0.324002
$973$	−5.23895	−0.167953
$974$	64.8200	2.07697
$975$	0.577948	0.0185091
$976$	−7.55974	−0.241981
$977$	52.2887	1.67286	0.836431	−	0.548072i	$-0.184638\pi$
$977$	52.2887	1.67286	0.836431	+	0.548072i	$0.184638\pi$
$978$	−1.27402	−0.0407388
$979$	−27.5825	−0.881539
$980$	−27.7851	−0.887561
$981$	−13.0392	−0.416308
$982$	−56.8998	−1.81575
$983$	−29.3490	−0.936087	−0.468044	−	0.883705i	$-0.655041\pi$
$983$	−29.3490	−0.936087	−0.468044	+	0.883705i	$0.655041\pi$
$984$	−0.146159	−0.00465938
$985$	11.2399	0.358133
$986$	−141.264	−4.49877
$987$	0.0707554	0.00225217
$988$	3.63128	0.115526
$989$	14.1915	0.451262
$990$	17.7448	0.563967
$991$	−17.9228	−0.569338	−0.284669	−	0.958626i	$-0.591884\pi$
$991$	−17.9228	−0.569338	−0.284669	+	0.958626i	$0.591884\pi$
$992$	19.1778	0.608897
$993$	−0.893524	−0.0283551
$994$	0.886259	0.0281104
$995$	14.0943	0.446819
$996$	−0.841630	−0.0266681
$997$	51.4063	1.62805	0.814026	−	0.580828i	$-0.197271\pi$
$997$	51.4063	1.62805	0.814026	+	0.580828i	$0.197271\pi$
$998$	−67.5888	−2.13949
$999$	−5.87810	−0.185975

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8023.2.a.d.1.13	✓	165

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8023.2.a.d.1.13	✓	165	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8023 = 71 \cdot 113 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.35257 q^{2} -0.106381 q^{3} +3.53459 q^{4} +1.14622 q^{5} +0.250270 q^{6} -0.376719 q^{7} -3.61023 q^{8} -2.98868 q^{9} +O(q^{10})\)	\(q-2.35257 q^{2} -0.106381 q^{3} +3.53459 q^{4} +1.14622 q^{5} +0.250270 q^{6} -0.376719 q^{7} -3.61023 q^{8} -2.98868 q^{9} -2.69657 q^{10} +2.20181 q^{11} -0.376015 q^{12} +1.47383 q^{13} +0.886259 q^{14} -0.121937 q^{15} +1.42415 q^{16} -6.75687 q^{17} +7.03109 q^{18} +0.697065 q^{19} +4.05143 q^{20} +0.0400760 q^{21} -5.17991 q^{22} -2.06094 q^{23} +0.384062 q^{24} -3.68617 q^{25} -3.46729 q^{26} +0.637085 q^{27} -1.33155 q^{28} -8.88677 q^{29} +0.286866 q^{30} +4.95544 q^{31} +3.87006 q^{32} -0.234231 q^{33} +15.8960 q^{34} -0.431805 q^{35} -10.5638 q^{36} -9.22656 q^{37} -1.63990 q^{38} -0.156788 q^{39} -4.13814 q^{40} -0.380561 q^{41} -0.0942815 q^{42} -6.88593 q^{43} +7.78248 q^{44} -3.42570 q^{45} +4.84850 q^{46} +1.76553 q^{47} -0.151503 q^{48} -6.85808 q^{49} +8.67198 q^{50} +0.718806 q^{51} +5.20939 q^{52} +6.62593 q^{53} -1.49879 q^{54} +2.52376 q^{55} +1.36004 q^{56} -0.0741548 q^{57} +20.9068 q^{58} +9.40253 q^{59} -0.430998 q^{60} -5.30826 q^{61} -11.6580 q^{62} +1.12589 q^{63} -11.9529 q^{64} +1.68934 q^{65} +0.551046 q^{66} +3.37927 q^{67} -23.8828 q^{68} +0.219245 q^{69} +1.01585 q^{70} +1.00000 q^{71} +10.7898 q^{72} +6.97604 q^{73} +21.7061 q^{74} +0.392140 q^{75} +2.46384 q^{76} -0.829463 q^{77} +0.368855 q^{78} -8.58280 q^{79} +1.63239 q^{80} +8.89827 q^{81} +0.895296 q^{82} +2.23829 q^{83} +0.141652 q^{84} -7.74489 q^{85} +16.1996 q^{86} +0.945388 q^{87} -7.94903 q^{88} -12.5272 q^{89} +8.05921 q^{90} -0.555220 q^{91} -7.28457 q^{92} -0.527167 q^{93} -4.15354 q^{94} +0.798993 q^{95} -0.411703 q^{96} -4.43537 q^{97} +16.1341 q^{98} -6.58050 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9}+O(q^{10}) \) 165 * q + 22 * q^2 + 18 * q^3 + 166 * q^4 + 28 * q^5 + 16 * q^6 + 24 * q^7 + 66 * q^8 + 177 * q^9	\( 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9} + 14 q^{10} + 18 q^{11} + 54 q^{12} + 44 q^{13} + 26 q^{14} + 24 q^{15} + 168 q^{16} + 143 q^{17} + 57 q^{18} + 20 q^{19} + 49 q^{20} + 39 q^{21} + 25 q^{22} + 52 q^{23} + 27 q^{24} + 175 q^{25} + 48 q^{26} + 69 q^{27} + 28 q^{28} + 58 q^{29} - 11 q^{30} + 28 q^{31} + 114 q^{32} + 110 q^{33} + 55 q^{34} + 67 q^{35} + 202 q^{36} + 44 q^{37} + 35 q^{38} + 27 q^{39} + 53 q^{40} + 141 q^{41} + 40 q^{42} + 29 q^{43} + 52 q^{44} + 54 q^{45} + 29 q^{46} + 87 q^{47} + 53 q^{48} + 143 q^{49} + 16 q^{50} + 37 q^{51} + 105 q^{52} + 101 q^{53} - 36 q^{54} + 72 q^{55} + 57 q^{56} + 82 q^{57} + 4 q^{58} + 103 q^{59} + 53 q^{60} + 16 q^{61} + 54 q^{62} + 126 q^{63} + 136 q^{64} + 159 q^{65} + 53 q^{66} + 60 q^{67} + 220 q^{68} + 81 q^{69} + 16 q^{70} + 165 q^{71} + 176 q^{72} + 124 q^{73} + 29 q^{74} + 44 q^{75} + 18 q^{76} + 127 q^{77} - 91 q^{78} + 14 q^{79} + 158 q^{80} + 213 q^{81} + 20 q^{82} + 116 q^{83} + 67 q^{84} + 59 q^{85} + 30 q^{86} + 28 q^{87} + 79 q^{88} + 195 q^{89} + 16 q^{90} - 26 q^{91} + 173 q^{92} + 116 q^{93} + 53 q^{94} + 26 q^{95} - 36 q^{96} + 88 q^{97} + 150 q^{98} + 12 q^{99}+O(q^{100}) \) 165 * q + 22 * q^2 + 18 * q^3 + 166 * q^4 + 28 * q^5 + 16 * q^6 + 24 * q^7 + 66 * q^8 + 177 * q^9 + 14 * q^10 + 18 * q^11 + 54 * q^12 + 44 * q^13 + 26 * q^14 + 24 * q^15 + 168 * q^16 + 143 * q^17 + 57 * q^18 + 20 * q^19 + 49 * q^20 + 39 * q^21 + 25 * q^22 + 52 * q^23 + 27 * q^24 + 175 * q^25 + 48 * q^26 + 69 * q^27 + 28 * q^28 + 58 * q^29 - 11 * q^30 + 28 * q^31 + 114 * q^32 + 110 * q^33 + 55 * q^34 + 67 * q^35 + 202 * q^36 + 44 * q^37 + 35 * q^38 + 27 * q^39 + 53 * q^40 + 141 * q^41 + 40 * q^42 + 29 * q^43 + 52 * q^44 + 54 * q^45 + 29 * q^46 + 87 * q^47 + 53 * q^48 + 143 * q^49 + 16 * q^50 + 37 * q^51 + 105 * q^52 + 101 * q^53 - 36 * q^54 + 72 * q^55 + 57 * q^56 + 82 * q^57 + 4 * q^58 + 103 * q^59 + 53 * q^60 + 16 * q^61 + 54 * q^62 + 126 * q^63 + 136 * q^64 + 159 * q^65 + 53 * q^66 + 60 * q^67 + 220 * q^68 + 81 * q^69 + 16 * q^70 + 165 * q^71 + 176 * q^72 + 124 * q^73 + 29 * q^74 + 44 * q^75 + 18 * q^76 + 127 * q^77 - 91 * q^78 + 14 * q^79 + 158 * q^80 + 213 * q^81 + 20 * q^82 + 116 * q^83 + 67 * q^84 + 59 * q^85 + 30 * q^86 + 28 * q^87 + 79 * q^88 + 195 * q^89 + 16 * q^90 - 26 * q^91 + 173 * q^92 + 116 * q^93 + 53 * q^94 + 26 * q^95 - 36 * q^96 + 88 * q^97 + 150 * q^98 + 12 * q^99

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