LMFDB - Embedded newform 8023.2.a.e.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:	$172$
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)

$f(q)$	$=$	$q-2.39224 q^{2} -1.88283 q^{3} +3.72279 q^{4} -1.64189 q^{5} +4.50418 q^{6} -4.12017 q^{7} -4.12133 q^{8} +0.545055 q^{9} +O(q^{10})$	\(q-2.39224 q^{2} -1.88283 q^{3} +3.72279 q^{4} -1.64189 q^{5} +4.50418 q^{6} -4.12017 q^{7} -4.12133 q^{8} +0.545055 q^{9} +3.92779 q^{10} -0.677131 q^{11} -7.00939 q^{12} +1.00669 q^{13} +9.85642 q^{14} +3.09140 q^{15} +2.41360 q^{16} -0.318979 q^{17} -1.30390 q^{18} -2.15768 q^{19} -6.11242 q^{20} +7.75759 q^{21} +1.61986 q^{22} +6.24353 q^{23} +7.75976 q^{24} -2.30419 q^{25} -2.40824 q^{26} +4.62225 q^{27} -15.3385 q^{28} -9.11087 q^{29} -7.39537 q^{30} +5.12303 q^{31} +2.46875 q^{32} +1.27492 q^{33} +0.763074 q^{34} +6.76487 q^{35} +2.02913 q^{36} -9.04261 q^{37} +5.16169 q^{38} -1.89543 q^{39} +6.76677 q^{40} +6.95614 q^{41} -18.5580 q^{42} +6.90844 q^{43} -2.52082 q^{44} -0.894921 q^{45} -14.9360 q^{46} +0.717228 q^{47} -4.54440 q^{48} +9.97581 q^{49} +5.51218 q^{50} +0.600584 q^{51} +3.74770 q^{52} -3.38528 q^{53} -11.0575 q^{54} +1.11178 q^{55} +16.9806 q^{56} +4.06255 q^{57} +21.7953 q^{58} -14.2294 q^{59} +11.5087 q^{60} +3.73935 q^{61} -12.2555 q^{62} -2.24572 q^{63} -10.7330 q^{64} -1.65288 q^{65} -3.04992 q^{66} -4.38506 q^{67} -1.18749 q^{68} -11.7555 q^{69} -16.1832 q^{70} -1.00000 q^{71} -2.24635 q^{72} +11.5743 q^{73} +21.6321 q^{74} +4.33841 q^{75} -8.03261 q^{76} +2.78990 q^{77} +4.53432 q^{78} +2.73076 q^{79} -3.96287 q^{80} -10.3381 q^{81} -16.6407 q^{82} -18.1230 q^{83} +28.8799 q^{84} +0.523729 q^{85} -16.5266 q^{86} +17.1542 q^{87} +2.79068 q^{88} -0.986400 q^{89} +2.14086 q^{90} -4.14774 q^{91} +23.2434 q^{92} -9.64580 q^{93} -1.71578 q^{94} +3.54268 q^{95} -4.64825 q^{96} +1.67168 q^{97} -23.8645 q^{98} -0.369074 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 172 q + 24 q^{2} + 18 q^{3} + 180 q^{4} + 28 q^{5} + 16 q^{6} + 4 q^{7} + 72 q^{8} + 198 q^{9}+O(q^{10}) $ 172 * q + 24 * q^2 + 18 * q^3 + 180 * q^4 + 28 * q^5 + 16 * q^6 + 4 * q^7 + 72 * q^8 + 198 * q^9	\( 172 q + 24 q^{2} + 18 q^{3} + 180 q^{4} + 28 q^{5} + 16 q^{6} + 4 q^{7} + 72 q^{8} + 198 q^{9} + 14 q^{10} + 20 q^{11} + 54 q^{12} + 36 q^{13} + 26 q^{14} + 32 q^{15} + 196 q^{16} + 123 q^{17} + 74 q^{18} + 20 q^{19} + 70 q^{20} + 37 q^{21} + 11 q^{22} + 22 q^{23} + 62 q^{24} + 210 q^{25} + 50 q^{26} + 69 q^{27} + 42 q^{28} + 58 q^{29} + 36 q^{30} + 10 q^{31} + 168 q^{32} + 124 q^{33} + 5 q^{34} + 59 q^{35} + 192 q^{36} + 40 q^{37} + 58 q^{38} + 15 q^{39} + 7 q^{40} + 155 q^{41} - 6 q^{42} + 19 q^{43} + 22 q^{44} + 76 q^{45} + q^{46} + 71 q^{47} + 144 q^{48} + 206 q^{49} + 126 q^{50} + 33 q^{51} + 71 q^{52} + 101 q^{53} + 92 q^{54} - 2 q^{55} + 57 q^{56} + 114 q^{57} + 4 q^{58} + 71 q^{59} + 38 q^{60} + 50 q^{61} + 86 q^{62} + 14 q^{63} + 240 q^{64} + 143 q^{65} + 21 q^{66} + 8 q^{67} + 192 q^{68} + 41 q^{69} - 12 q^{70} - 172 q^{71} + 156 q^{72} + 128 q^{73} + 30 q^{74} + 72 q^{75} + 74 q^{76} + 127 q^{77} + 107 q^{78} + 2 q^{79} + 50 q^{80} + 236 q^{81} + 42 q^{82} + 140 q^{83} + 71 q^{84} + 55 q^{85} + 46 q^{86} + 100 q^{87} - 31 q^{88} + 215 q^{89} - 7 q^{90} + 22 q^{91} - 15 q^{92} + 60 q^{93} + 5 q^{94} + 74 q^{95} + 182 q^{96} + 120 q^{97} + 164 q^{98} + 60 q^{99}+O(q^{100}) \) 172 * q + 24 * q^2 + 18 * q^3 + 180 * q^4 + 28 * q^5 + 16 * q^6 + 4 * q^7 + 72 * q^8 + 198 * q^9 + 14 * q^10 + 20 * q^11 + 54 * q^12 + 36 * q^13 + 26 * q^14 + 32 * q^15 + 196 * q^16 + 123 * q^17 + 74 * q^18 + 20 * q^19 + 70 * q^20 + 37 * q^21 + 11 * q^22 + 22 * q^23 + 62 * q^24 + 210 * q^25 + 50 * q^26 + 69 * q^27 + 42 * q^28 + 58 * q^29 + 36 * q^30 + 10 * q^31 + 168 * q^32 + 124 * q^33 + 5 * q^34 + 59 * q^35 + 192 * q^36 + 40 * q^37 + 58 * q^38 + 15 * q^39 + 7 * q^40 + 155 * q^41 - 6 * q^42 + 19 * q^43 + 22 * q^44 + 76 * q^45 + q^46 + 71 * q^47 + 144 * q^48 + 206 * q^49 + 126 * q^50 + 33 * q^51 + 71 * q^52 + 101 * q^53 + 92 * q^54 - 2 * q^55 + 57 * q^56 + 114 * q^57 + 4 * q^58 + 71 * q^59 + 38 * q^60 + 50 * q^61 + 86 * q^62 + 14 * q^63 + 240 * q^64 + 143 * q^65 + 21 * q^66 + 8 * q^67 + 192 * q^68 + 41 * q^69 - 12 * q^70 - 172 * q^71 + 156 * q^72 + 128 * q^73 + 30 * q^74 + 72 * q^75 + 74 * q^76 + 127 * q^77 + 107 * q^78 + 2 * q^79 + 50 * q^80 + 236 * q^81 + 42 * q^82 + 140 * q^83 + 71 * q^84 + 55 * q^85 + 46 * q^86 + 100 * q^87 - 31 * q^88 + 215 * q^89 - 7 * q^90 + 22 * q^91 - 15 * q^92 + 60 * q^93 + 5 * q^94 + 74 * q^95 + 182 * q^96 + 120 * q^97 + 164 * q^98 + 60 * 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 $

$2$	−2.39224	−1.69157	−0.845783	−	0.533527i	$-0.820866\pi$
$2$	−2.39224	−1.69157	−0.845783	+	0.533527i	$0.820866\pi$
$3$	−1.88283	−1.08705	−0.543527	−	0.839392i	$-0.682911\pi$
$3$	−1.88283	−1.08705	−0.543527	+	0.839392i	$0.682911\pi$
$4$	3.72279	1.86140
$5$	−1.64189	−0.734276	−0.367138	−	0.930167i	$-0.619662\pi$
$5$	−1.64189	−0.734276	−0.367138	+	0.930167i	$0.619662\pi$
$6$	4.50418	1.83882
$7$	−4.12017	−1.55728	−0.778639	−	0.627472i	$-0.784090\pi$
$7$	−4.12017	−1.55728	−0.778639	+	0.627472i	$0.784090\pi$
$8$	−4.12133	−1.45711
$9$	0.545055	0.181685
$10$	3.92779	1.24208
$11$	−0.677131	−0.204163	−0.102081	−	0.994776i	$-0.532550\pi$
$11$	−0.677131	−0.204163	−0.102081	+	0.994776i	$0.532550\pi$
$12$	−7.00939	−2.02344
$13$	1.00669	0.279206	0.139603	−	0.990208i	$-0.455417\pi$
$13$	1.00669	0.279206	0.139603	+	0.990208i	$0.455417\pi$
$14$	9.85642	2.63424
$15$	3.09140	0.798197
$16$	2.41360	0.603400
$17$	−0.318979	−0.0773639	−0.0386819	−	0.999252i	$-0.512316\pi$
$17$	−0.318979	−0.0773639	−0.0386819	+	0.999252i	$0.512316\pi$
$18$	−1.30390	−0.307332
$19$	−2.15768	−0.495006	−0.247503	−	0.968887i	$-0.579610\pi$
$19$	−2.15768	−0.495006	−0.247503	+	0.968887i	$0.579610\pi$
$20$	−6.11242	−1.36678
$21$	7.75759	1.69284
$22$	1.61986	0.345355
$23$	6.24353	1.30187	0.650933	−	0.759135i	$-0.274378\pi$
$23$	6.24353	1.30187	0.650933	+	0.759135i	$0.274378\pi$
$24$	7.75976	1.58396
$25$	−2.30419	−0.460839
$26$	−2.40824	−0.472295
$27$	4.62225	0.889552
$28$	−15.3385	−2.89871
$29$	−9.11087	−1.69185	−0.845923	−	0.533305i	$-0.820950\pi$
$29$	−9.11087	−1.69185	−0.845923	+	0.533305i	$0.820950\pi$
$30$	−7.39537	−1.35020
$31$	5.12303	0.920123	0.460061	−	0.887887i	$-0.347827\pi$
$31$	5.12303	0.920123	0.460061	+	0.887887i	$0.347827\pi$
$32$	2.46875	0.436418
$33$	1.27492	0.221936
$34$	0.763074	0.130866
$35$	6.76487	1.14347
$36$	2.02913	0.338188
$37$	−9.04261	−1.48660	−0.743298	−	0.668961i	$-0.766740\pi$
$37$	−9.04261	−1.48660	−0.743298	+	0.668961i	$0.766740\pi$
$38$	5.16169	0.837336
$39$	−1.89543	−0.303512
$40$	6.76677	1.06992
$41$	6.95614	1.08637	0.543183	−	0.839614i	$-0.317219\pi$
$41$	6.95614	1.08637	0.543183	+	0.839614i	$0.317219\pi$
$42$	−18.5580	−2.86356
$43$	6.90844	1.05353	0.526763	−	0.850012i	$-0.323405\pi$
$43$	6.90844	1.05353	0.526763	+	0.850012i	$0.323405\pi$
$44$	−2.52082	−0.380028
$45$	−0.894921	−0.133407
$46$	−14.9360	−2.20219
$47$	0.717228	0.104618	0.0523092	−	0.998631i	$-0.483342\pi$
$47$	0.717228	0.104618	0.0523092	+	0.998631i	$0.483342\pi$
$48$	−4.54440	−0.655928
$49$	9.97581	1.42512
$50$	5.51218	0.779540
$51$	0.600584	0.0840986
$52$	3.74770	0.519713
$53$	−3.38528	−0.465004	−0.232502	−	0.972596i	$-0.574691\pi$
$53$	−3.38528	−0.465004	−0.232502	+	0.972596i	$0.574691\pi$
$54$	−11.0575	−1.50474
$55$	1.11178	0.149912
$56$	16.9806	2.26912
$57$	4.06255	0.538098
$58$	21.7953	2.86187
$59$	−14.2294	−1.85251	−0.926253	−	0.376902i	$-0.876989\pi$
$59$	−14.2294	−1.85251	−0.926253	+	0.376902i	$0.876989\pi$
$60$	11.5087	1.48576
$61$	3.73935	0.478774	0.239387	−	0.970924i	$-0.423053\pi$
$61$	3.73935	0.478774	0.239387	+	0.970924i	$0.423053\pi$
$62$	−12.2555	−1.55645
$63$	−2.24572	−0.282934
$64$	−10.7330	−1.34163
$65$	−1.65288	−0.205014
$66$	−3.04992	−0.375419
$67$	−4.38506	−0.535720	−0.267860	−	0.963458i	$-0.586316\pi$
$67$	−4.38506	−0.535720	−0.267860	+	0.963458i	$0.586316\pi$
$68$	−1.18749	−0.144005
$69$	−11.7555	−1.41520
$70$	−16.1832	−1.93426
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	−2.24635	−0.264735
$73$	11.5743	1.35467	0.677337	−	0.735673i	$-0.263134\pi$
$73$	11.5743	1.35467	0.677337	+	0.735673i	$0.263134\pi$
$74$	21.6321	2.51468
$75$	4.33841	0.500957
$76$	−8.03261	−0.921403
$77$	2.78990	0.317938
$78$	4.53432	0.513410
$79$	2.73076	0.307234	0.153617	−	0.988130i	$-0.450908\pi$
$79$	2.73076	0.307234	0.153617	+	0.988130i	$0.450908\pi$
$80$	−3.96287	−0.443062
$81$	−10.3381	−1.14868
$82$	−16.6407	−1.83766
$83$	−18.1230	−1.98926	−0.994629	−	0.103505i	$-0.966994\pi$
$83$	−18.1230	−1.98926	−0.994629	+	0.103505i	$0.966994\pi$
$84$	28.8799	3.15105
$85$	0.523729	0.0568064
$86$	−16.5266	−1.78211
$87$	17.1542	1.83913
$88$	2.79068	0.297487
$89$	−0.986400	−0.104558	−0.0522791	−	0.998633i	$-0.516649\pi$
$89$	−0.986400	−0.104558	−0.0522791	+	0.998633i	$0.516649\pi$
$90$	2.14086	0.225667
$91$	−4.14774	−0.434801
$92$	23.2434	2.42329
$93$	−9.64580	−1.00022
$94$	−1.71578	−0.176969
$95$	3.54268	0.363471
$96$	−4.64825	−0.474410
$97$	1.67168	0.169734	0.0848669	−	0.996392i	$-0.472954\pi$
$97$	1.67168	0.169734	0.0848669	+	0.996392i	$0.472954\pi$
$98$	−23.8645	−2.41068
$99$	−0.369074	−0.0370933
$100$	−8.57804	−0.857804
$101$	−13.2151	−1.31496	−0.657478	−	0.753474i	$-0.728377\pi$
$101$	−13.2151	−1.31496	−0.657478	+	0.753474i	$0.728377\pi$
$102$	−1.43674	−0.142258
$103$	−2.33889	−0.230457	−0.115229	−	0.993339i	$-0.536760\pi$
$103$	−2.33889	−0.230457	−0.115229	+	0.993339i	$0.536760\pi$
$104$	−4.14890	−0.406834
$105$	−12.7371	−1.24301
$106$	8.09838	0.786585
$107$	15.0521	1.45514	0.727569	−	0.686035i	$-0.240650\pi$
$107$	15.0521	1.45514	0.727569	+	0.686035i	$0.240650\pi$
$108$	17.2077	1.65581
$109$	−2.26376	−0.216829	−0.108415	−	0.994106i	$-0.534577\pi$
$109$	−2.26376	−0.216829	−0.108415	+	0.994106i	$0.534577\pi$
$110$	−2.65963	−0.253586
$111$	17.0257	1.61601
$112$	−9.94445	−0.939662
$113$	1.00000	0.0940721
$113$	1.00000	0.0940721
$114$	−9.71859	−0.910229
$115$	−10.2512	−0.955929
$116$	−33.9179	−3.14920
$117$	0.548702	0.0507275
$118$	34.0400	3.13364
$119$	1.31425	0.120477
$120$	−12.7407	−1.16306
$121$	−10.5415	−0.958318
$122$	−8.94540	−0.809878
$123$	−13.0972	−1.18094
$124$	19.0720	1.71271
$125$	11.9927	1.07266
$126$	5.37229	0.478602
$127$	−19.3902	−1.72060	−0.860300	−	0.509789i	$-0.829724\pi$
$127$	−19.3902	−1.72060	−0.860300	+	0.509789i	$0.829724\pi$
$128$	20.7385	1.83304
$129$	−13.0074	−1.14524
$130$	3.95407	0.346795
$131$	−8.23120	−0.719163	−0.359582	−	0.933114i	$-0.617081\pi$
$131$	−8.23120	−0.719163	−0.359582	+	0.933114i	$0.617081\pi$
$132$	4.74628	0.413111
$133$	8.89002	0.770863
$134$	10.4901	0.906206
$135$	−7.58923	−0.653177
$136$	1.31462	0.112728
$137$	7.54486	0.644601	0.322300	−	0.946637i	$-0.395544\pi$
$137$	7.54486	0.644601	0.322300	+	0.946637i	$0.395544\pi$
$138$	28.1220	2.39390
$139$	−20.3889	−1.72936	−0.864680	−	0.502322i	$-0.832479\pi$
$139$	−20.3889	−1.72936	−0.864680	+	0.502322i	$0.832479\pi$
$140$	25.1842	2.12845
$141$	−1.35042	−0.113726
$142$	2.39224	0.200752
$143$	−0.681662	−0.0570035
$144$	1.31554	0.109629
$145$	14.9591	1.24228
$146$	−27.6885	−2.29152
$147$	−18.7828	−1.54918
$148$	−33.6638	−2.76714
$149$	−10.8259	−0.886889	−0.443445	−	0.896302i	$-0.646244\pi$
$149$	−10.8259	−0.886889	−0.443445	+	0.896302i	$0.646244\pi$
$150$	−10.3785	−0.847401
$151$	6.48241	0.527531	0.263765	−	0.964587i	$-0.415036\pi$
$151$	6.48241	0.527531	0.263765	+	0.964587i	$0.415036\pi$
$152$	8.89252	0.721278
$153$	−0.173861	−0.0140559
$154$	−6.67409	−0.537814
$155$	−8.41145	−0.675624
$156$	−7.05630	−0.564956
$157$	−22.9955	−1.83524	−0.917621	−	0.397456i	$-0.869893\pi$
$157$	−22.9955	−1.83524	−0.917621	+	0.397456i	$0.869893\pi$
$158$	−6.53262	−0.519707
$159$	6.37391	0.505484
$160$	−4.05342	−0.320451
$161$	−25.7244	−2.02737
$162$	24.7311	1.94306
$163$	−3.72756	−0.291965	−0.145982	−	0.989287i	$-0.546634\pi$
$163$	−3.72756	−0.291965	−0.145982	+	0.989287i	$0.546634\pi$
$164$	25.8963	2.02216
$165$	−2.09329	−0.162962
$166$	43.3545	3.36496
$167$	−7.35112	−0.568846	−0.284423	−	0.958699i	$-0.591802\pi$
$167$	−7.35112	−0.568846	−0.284423	+	0.958699i	$0.591802\pi$
$168$	−31.9716	−2.46666
$169$	−11.9866	−0.922044
$170$	−1.25288	−0.0960918
$171$	−1.17606	−0.0899353
$172$	25.7187	1.96103
$173$	12.7796	0.971611	0.485806	−	0.874067i	$-0.338526\pi$
$173$	12.7796	0.971611	0.485806	+	0.874067i	$0.338526\pi$
$174$	−41.0370	−3.11100
$175$	9.49368	0.717655
$176$	−1.63432	−0.123192
$177$	26.7915	2.01377
$178$	2.35970	0.176867
$179$	4.42484	0.330728	0.165364	−	0.986233i	$-0.447120\pi$
$179$	4.42484	0.330728	0.165364	+	0.986233i	$0.447120\pi$
$180$	−3.33160	−0.248323
$181$	−16.2203	−1.20564	−0.602822	−	0.797876i	$-0.705957\pi$
$181$	−16.2203	−1.20564	−0.602822	+	0.797876i	$0.705957\pi$
$182$	9.92238	0.735495
$183$	−7.04056	−0.520453
$184$	−25.7316	−1.89696
$185$	14.8470	1.09157
$186$	23.0750	1.69194
$187$	0.215991	0.0157948
$188$	2.67009	0.194736
$189$	−19.0445	−1.38528
$190$	−8.47493	−0.614836
$191$	14.1085	1.02086	0.510428	−	0.859920i	$-0.329487\pi$
$191$	14.1085	1.02086	0.510428	+	0.859920i	$0.329487\pi$
$192$	20.2085	1.45842
$193$	−5.72868	−0.412359	−0.206180	−	0.978514i	$-0.566103\pi$
$193$	−5.72868	−0.412359	−0.206180	+	0.978514i	$0.566103\pi$
$194$	−3.99906	−0.287116
$195$	3.11209	0.222861
$196$	37.1379	2.65271
$197$	12.3986	0.883365	0.441682	−	0.897172i	$-0.354382\pi$
$197$	12.3986	0.883365	0.441682	+	0.897172i	$0.354382\pi$
$198$	0.882912	0.0627458
$199$	−6.90196	−0.489267	−0.244634	−	0.969616i	$-0.578668\pi$
$199$	−6.90196	−0.489267	−0.244634	+	0.969616i	$0.578668\pi$
$200$	9.49634	0.671493
$201$	8.25632	0.582356
$202$	31.6137	2.22434
$203$	37.5383	2.63468
$204$	2.23585	0.156541
$205$	−11.4212	−0.797692
$206$	5.59517	0.389834
$207$	3.40307	0.236530
$208$	2.42975	0.168473
$209$	1.46103	0.101062
$210$	30.4702	2.10264
$211$	−10.2725	−0.707191	−0.353596	−	0.935398i	$-0.615041\pi$
$211$	−10.2725	−0.707191	−0.353596	+	0.935398i	$0.615041\pi$
$212$	−12.6027	−0.865556
$213$	1.88283	0.129009
$214$	−36.0081	−2.46146
$215$	−11.3429	−0.773579
$216$	−19.0498	−1.29617
$217$	−21.1078	−1.43289
$218$	5.41545	0.366781
$219$	−21.7925	−1.47260
$220$	4.13891	0.279045
$221$	−0.321114	−0.0216005
$222$	−40.7295	−2.73359
$223$	21.0258	1.40799	0.703997	−	0.710203i	$-0.251397\pi$
$223$	21.0258	1.40799	0.703997	+	0.710203i	$0.251397\pi$
$224$	−10.1717	−0.679624
$225$	−1.25591	−0.0837275
$226$	−2.39224	−0.159129
$227$	−11.5156	−0.764317	−0.382159	−	0.924097i	$-0.624819\pi$
$227$	−11.5156	−0.764317	−0.382159	+	0.924097i	$0.624819\pi$
$228$	15.1240	1.00161
$229$	15.1250	0.999491	0.499745	−	0.866172i	$-0.333427\pi$
$229$	15.1250	0.999491	0.499745	+	0.866172i	$0.333427\pi$
$230$	24.5233	1.61702
$231$	−5.25291	−0.345616
$232$	37.5489	2.46520
$233$	12.9294	0.847030	0.423515	−	0.905889i	$-0.360796\pi$
$233$	12.9294	0.847030	0.423515	+	0.905889i	$0.360796\pi$
$234$	−1.31263	−0.0858090
$235$	−1.17761	−0.0768188
$236$	−52.9730	−3.44825
$237$	−5.14156	−0.333980
$238$	−3.14400	−0.203795
$239$	8.60228	0.556435	0.278217	−	0.960518i	$-0.410256\pi$
$239$	8.60228	0.556435	0.278217	+	0.960518i	$0.410256\pi$
$240$	7.46141	0.481632
$241$	4.38697	0.282589	0.141295	−	0.989968i	$-0.454873\pi$
$241$	4.38697	0.282589	0.141295	+	0.989968i	$0.454873\pi$
$242$	25.2177	1.62106
$243$	5.59812	0.359120
$244$	13.9208	0.891189
$245$	−16.3792	−1.04643
$246$	31.3317	1.99763
$247$	−2.17212	−0.138209
$248$	−21.1137	−1.34072
$249$	34.1226	2.16243
$250$	−28.6893	−1.81447
$251$	−29.8367	−1.88328	−0.941638	−	0.336628i	$-0.890713\pi$
$251$	−29.8367	−1.88328	−0.941638	+	0.336628i	$0.890713\pi$
$252$	−8.36035	−0.526653
$253$	−4.22769	−0.265793
$254$	46.3859	2.91051
$255$	−0.986094	−0.0617516
$256$	−28.1452	−1.75907
$257$	11.5936	0.723189	0.361595	−	0.932335i	$-0.382232\pi$
$257$	11.5936	0.723189	0.361595	+	0.932335i	$0.382232\pi$
$258$	31.1168	1.93725
$259$	37.2571	2.31504
$260$	−6.15332	−0.381613
$261$	−4.96593	−0.307383
$262$	19.6910	1.21651
$263$	21.6111	1.33260	0.666298	−	0.745686i	$-0.267878\pi$
$263$	21.6111	1.33260	0.666298	+	0.745686i	$0.267878\pi$
$264$	−5.25438	−0.323385
$265$	5.55826	0.341441
$266$	−21.2670	−1.30397
$267$	1.85723	0.113660
$268$	−16.3247	−0.997187
$269$	−3.79804	−0.231570	−0.115785	−	0.993274i	$-0.536938\pi$
$269$	−3.79804	−0.231570	−0.115785	+	0.993274i	$0.536938\pi$
$270$	18.1552	1.10489
$271$	−18.0899	−1.09889	−0.549443	−	0.835531i	$-0.685160\pi$
$271$	−18.0899	−1.09889	−0.549443	+	0.835531i	$0.685160\pi$
$272$	−0.769889	−0.0466814
$273$	7.80950	0.472652
$274$	−18.0491	−1.09039
$275$	1.56024	0.0940862
$276$	−43.7634	−2.63425
$277$	−15.9371	−0.957568	−0.478784	−	0.877933i	$-0.658922\pi$
$277$	−15.9371	−0.957568	−0.478784	+	0.877933i	$0.658922\pi$
$278$	48.7750	2.92533
$279$	2.79233	0.167173
$280$	−27.8802	−1.66616
$281$	−16.9561	−1.01152	−0.505759	−	0.862675i	$-0.668788\pi$
$281$	−16.9561	−1.01152	−0.505759	+	0.862675i	$0.668788\pi$
$282$	3.23052	0.192375
$283$	−13.3655	−0.794495	−0.397248	−	0.917712i	$-0.630035\pi$
$283$	−13.3655	−0.794495	−0.397248	+	0.917712i	$0.630035\pi$
$284$	−3.72279	−0.220907
$285$	−6.67027	−0.395113
$286$	1.63070	0.0964251
$287$	−28.6605	−1.69177
$288$	1.34561	0.0792906
$289$	−16.8983	−0.994015
$290$	−35.7856	−2.10140
$291$	−3.14750	−0.184510
$292$	43.0889	2.52158
$293$	−16.7596	−0.979103	−0.489552	−	0.871974i	$-0.662840\pi$
$293$	−16.7596	−0.979103	−0.489552	+	0.871974i	$0.662840\pi$
$294$	44.9328	2.62054
$295$	23.3631	1.36025
$296$	37.2675	2.16613
$297$	−3.12987	−0.181613
$298$	25.8980	1.50023
$299$	6.28531	0.363489
$300$	16.1510	0.932479
$301$	−28.4639	−1.64063
$302$	−15.5074	−0.892353
$303$	24.8819	1.42943
$304$	−5.20778	−0.298687
$305$	−6.13960	−0.351552
$306$	0.415917	0.0237764
$307$	−32.9885	−1.88276	−0.941378	−	0.337354i	$-0.890468\pi$
$307$	−32.9885	−1.88276	−0.941378	+	0.337354i	$0.890468\pi$
$308$	10.3862	0.591809
$309$	4.40373	0.250519
$310$	20.1222	1.14286
$311$	10.3734	0.588223	0.294111	−	0.955771i	$-0.404976\pi$
$311$	10.3734	0.588223	0.294111	+	0.955771i	$0.404976\pi$
$312$	7.81169	0.442250
$313$	−16.0969	−0.909852	−0.454926	−	0.890529i	$-0.650334\pi$
$313$	−16.0969	−0.909852	−0.454926	+	0.890529i	$0.650334\pi$
$314$	55.0107	3.10443
$315$	3.68723	0.207752
$316$	10.1660	0.571885
$317$	7.56205	0.424727	0.212363	−	0.977191i	$-0.431884\pi$
$317$	7.56205	0.424727	0.212363	+	0.977191i	$0.431884\pi$
$318$	−15.2479	−0.855059
$319$	6.16926	0.345412
$320$	17.6225	0.985126
$321$	−28.3405	−1.58181
$322$	61.5389	3.42943
$323$	0.688256	0.0382956
$324$	−38.4865	−2.13814
$325$	−2.31961	−0.128669
$326$	8.91719	0.493878
$327$	4.26228	0.235705
$328$	−28.6685	−1.58295
$329$	−2.95510	−0.162920
$330$	5.00763	0.275661
$331$	−30.0217	−1.65014	−0.825070	−	0.565030i	$-0.808865\pi$
$331$	−30.0217	−1.65014	−0.825070	+	0.565030i	$0.808865\pi$
$332$	−67.4682	−3.70280
$333$	−4.92872	−0.270092
$334$	17.5856	0.962241
$335$	7.19978	0.393366
$336$	18.7237	1.02146
$337$	4.53904	0.247257	0.123629	−	0.992329i	$-0.460547\pi$
$337$	4.53904	0.247257	0.123629	+	0.992329i	$0.460547\pi$
$338$	28.6747	1.55970
$339$	−1.88283	−0.102261
$340$	1.94974	0.105739
$341$	−3.46896	−0.187855
$342$	2.81340	0.152131
$343$	−12.2609	−0.662024
$344$	−28.4719	−1.53510
$345$	19.3013	1.03915
$346$	−30.5717	−1.64355
$347$	−11.1228	−0.597103	−0.298552	−	0.954393i	$-0.596504\pi$
$347$	−11.1228	−0.597103	−0.298552	+	0.954393i	$0.596504\pi$
$348$	63.8617	3.42334
$349$	14.3591	0.768627	0.384313	−	0.923203i	$-0.374438\pi$
$349$	14.3591	0.768627	0.384313	+	0.923203i	$0.374438\pi$
$350$	−22.7111	−1.21396
$351$	4.65318	0.248368
$352$	−1.67167	−0.0891003
$353$	12.1060	0.644335	0.322167	−	0.946683i	$-0.395589\pi$
$353$	12.1060	0.644335	0.322167	+	0.946683i	$0.395589\pi$
$354$	−64.0916	−3.40643
$355$	1.64189	0.0871425
$356$	−3.67216	−0.194624
$357$	−2.47451	−0.130965
$358$	−10.5853	−0.559449
$359$	−26.6117	−1.40451	−0.702256	−	0.711924i	$-0.747824\pi$
$359$	−26.6117	−1.40451	−0.702256	+	0.711924i	$0.747824\pi$
$360$	3.68826	0.194388
$361$	−14.3444	−0.754969
$362$	38.8027	2.03943
$363$	19.8479	1.04174
$364$	−15.4412	−0.809338
$365$	−19.0038	−0.994704
$366$	16.8427	0.880381
$367$	−36.6644	−1.91387	−0.956933	−	0.290307i	$-0.906242\pi$
$367$	−36.6644	−1.91387	−0.956933	+	0.290307i	$0.906242\pi$
$368$	15.0694	0.785546
$369$	3.79148	0.197376
$370$	−35.5175	−1.84647
$371$	13.9479	0.724140
$372$	−35.9093	−1.86181
$373$	−25.8617	−1.33907	−0.669533	−	0.742782i	$-0.733506\pi$
$373$	−25.8617	−1.33907	−0.669533	+	0.742782i	$0.733506\pi$
$374$	−0.516701	−0.0267180
$375$	−22.5802	−1.16604
$376$	−2.95593	−0.152440
$377$	−9.17184	−0.472374
$378$	45.5588	2.34329
$379$	−9.11850	−0.468386	−0.234193	−	0.972190i	$-0.575245\pi$
$379$	−9.11850	−0.468386	−0.234193	+	0.972190i	$0.575245\pi$
$380$	13.1887	0.676564
$381$	36.5084	1.87038
$382$	−33.7509	−1.72685
$383$	13.6237	0.696138	0.348069	−	0.937469i	$-0.386838\pi$
$383$	13.6237	0.696138	0.348069	+	0.937469i	$0.386838\pi$
$384$	−39.0470	−1.99261
$385$	−4.58071	−0.233454
$386$	13.7043	0.697533
$387$	3.76548	0.191410
$388$	6.22333	0.315942
$389$	19.4304	0.985159	0.492579	−	0.870267i	$-0.336054\pi$
$389$	19.4304	0.985159	0.492579	+	0.870267i	$0.336054\pi$
$390$	−7.44485	−0.376985
$391$	−1.99156	−0.100717
$392$	−41.1136	−2.07655
$393$	15.4980	0.781769
$394$	−29.6604	−1.49427
$395$	−4.48361	−0.225595
$396$	−1.37399	−0.0690454
$397$	16.3681	0.821493	0.410746	−	0.911750i	$-0.365268\pi$
$397$	16.3681	0.821493	0.410746	+	0.911750i	$0.365268\pi$
$398$	16.5111	0.827628
$399$	−16.7384	−0.837969
$400$	−5.56140	−0.278070
$401$	36.8298	1.83919	0.919595	−	0.392867i	$-0.128517\pi$
$401$	36.8298	1.83919	0.919595	+	0.392867i	$0.128517\pi$
$402$	−19.7511	−0.985094
$403$	5.15731	0.256904
$404$	−49.1972	−2.44765
$405$	16.9740	0.843445
$406$	−89.8006	−4.45673
$407$	6.12303	0.303508
$408$	−2.47520	−0.122541
$409$	−12.6801	−0.626989	−0.313495	−	0.949590i	$-0.601500\pi$
$409$	−12.6801	−0.626989	−0.313495	+	0.949590i	$0.601500\pi$
$410$	27.3222	1.34935
$411$	−14.2057	−0.700716
$412$	−8.70719	−0.428972
$413$	58.6275	2.88487
$414$	−8.14094	−0.400106
$415$	29.7560	1.46066
$416$	2.48527	0.121850
$417$	38.3888	1.87991
$418$	−3.49514	−0.170953
$419$	−30.7943	−1.50440	−0.752199	−	0.658936i	$-0.771007\pi$
$419$	−30.7943	−1.50440	−0.752199	+	0.658936i	$0.771007\pi$
$420$	−47.4176	−2.31374
$421$	−27.5493	−1.34267	−0.671336	−	0.741153i	$-0.734279\pi$
$421$	−27.5493	−1.34267	−0.671336	+	0.741153i	$0.734279\pi$
$422$	24.5743	1.19626
$423$	0.390929	0.0190076
$424$	13.9518	0.677561
$425$	0.734991	0.0356523
$426$	−4.50418	−0.218228
$427$	−15.4067	−0.745585
$428$	56.0357	2.70859
$429$	1.28346	0.0619658
$430$	27.1349	1.30856
$431$	6.25447	0.301267	0.150633	−	0.988590i	$-0.451869\pi$
$431$	6.25447	0.301267	0.150633	+	0.988590i	$0.451869\pi$
$432$	11.1563	0.536756
$433$	−31.1175	−1.49541	−0.747706	−	0.664029i	$-0.768845\pi$
$433$	−31.1175	−1.49541	−0.747706	+	0.664029i	$0.768845\pi$
$434$	50.4947	2.42382
$435$	−28.1654	−1.35043
$436$	−8.42751	−0.403605
$437$	−13.4716	−0.644433
$438$	52.1329	2.49100
$439$	3.05895	0.145996	0.0729978	−	0.997332i	$-0.476743\pi$
$439$	3.05895	0.145996	0.0729978	+	0.997332i	$0.476743\pi$
$440$	−4.58199	−0.218438
$441$	5.43737	0.258922
$442$	0.768180	0.0365386
$443$	22.1817	1.05388	0.526941	−	0.849902i	$-0.323339\pi$
$443$	22.1817	1.05388	0.526941	+	0.849902i	$0.323339\pi$
$444$	63.3832	3.00803
$445$	1.61956	0.0767746
$446$	−50.2987	−2.38171
$447$	20.3833	0.964096
$448$	44.2220	2.08929
$449$	−10.0631	−0.474908	−0.237454	−	0.971399i	$-0.576313\pi$
$449$	−10.0631	−0.474908	−0.237454	+	0.971399i	$0.576313\pi$
$450$	3.00444	0.141631
$451$	−4.71022	−0.221796
$452$	3.72279	0.175105
$453$	−12.2053	−0.573454
$454$	27.5480	1.29289
$455$	6.81014	0.319264
$456$	−16.7431	−0.784068
$457$	28.3868	1.32788	0.663940	−	0.747786i	$-0.268883\pi$
$457$	28.3868	1.32788	0.663940	+	0.747786i	$0.268883\pi$
$458$	−36.1827	−1.69071
$459$	−1.47440	−0.0688192
$460$	−38.1631	−1.77936
$461$	15.8947	0.740290	0.370145	−	0.928974i	$-0.379308\pi$
$461$	15.8947	0.740290	0.370145	+	0.928974i	$0.379308\pi$
$462$	12.5662	0.584632
$463$	−41.4418	−1.92596	−0.962982	−	0.269567i	$-0.913119\pi$
$463$	−41.4418	−1.92596	−0.962982	+	0.269567i	$0.913119\pi$
$464$	−21.9900	−1.02086
$465$	15.8373	0.734439
$466$	−30.9301	−1.43281
$467$	22.4178	1.03737	0.518687	−	0.854964i	$-0.326421\pi$
$467$	22.4178	1.03737	0.518687	+	0.854964i	$0.326421\pi$
$468$	2.04270	0.0944241
$469$	18.0672	0.834265
$470$	2.81712	0.129944
$471$	43.2967	1.99501
$472$	58.6439	2.69930
$473$	−4.67792	−0.215091
$474$	12.2998	0.564950
$475$	4.97172	0.228118
$476$	4.89268	0.224256
$477$	−1.84516	−0.0844842
$478$	−20.5787	−0.941247
$479$	−42.8941	−1.95988	−0.979942	−	0.199285i	$-0.936138\pi$
$479$	−42.8941	−1.95988	−0.979942	+	0.199285i	$0.936138\pi$
$480$	7.63191	0.348347
$481$	−9.10312	−0.415066
$482$	−10.4947	−0.478019
$483$	48.4348	2.20386
$484$	−39.2438	−1.78381
$485$	−2.74472	−0.124631
$486$	−13.3920	−0.607475
$487$	2.20781	0.100046	0.0500228	−	0.998748i	$-0.484071\pi$
$487$	2.20781	0.100046	0.0500228	+	0.998748i	$0.484071\pi$
$488$	−15.4111	−0.697626
$489$	7.01836	0.317381
$490$	39.1829	1.77010
$491$	9.24662	0.417294	0.208647	−	0.977991i	$-0.433094\pi$
$491$	9.24662	0.417294	0.208647	+	0.977991i	$0.433094\pi$
$492$	−48.7583	−2.19819
$493$	2.90618	0.130888
$494$	5.19623	0.233789
$495$	0.605979	0.0272367
$496$	12.3649	0.555202
$497$	4.12017	0.184815
$498$	−81.6292	−3.65789
$499$	16.1985	0.725144	0.362572	−	0.931956i	$-0.381899\pi$
$499$	16.1985	0.725144	0.362572	+	0.931956i	$0.381899\pi$
$500$	44.6463	1.99664
$501$	13.8409	0.618366
$502$	71.3764	3.18569
$503$	−32.0717	−1.43001	−0.715003	−	0.699122i	$-0.753575\pi$
$503$	−32.0717	−1.43001	−0.715003	+	0.699122i	$0.753575\pi$
$504$	9.25535	0.412266
$505$	21.6978	0.965540
$506$	10.1136	0.449606
$507$	22.5687	1.00231
$508$	−72.1856	−3.20272
$509$	−25.6390	−1.13643	−0.568215	−	0.822880i	$-0.692366\pi$
$509$	−25.6390	−1.13643	−0.568215	+	0.822880i	$0.692366\pi$
$510$	2.35897	0.104457
$511$	−47.6883	−2.10960
$512$	25.8530	1.14255
$513$	−9.97335	−0.440334
$514$	−27.7346	−1.22332
$515$	3.84019	0.169219
$516$	−48.4240	−2.13175
$517$	−0.485657	−0.0213592
$518$	−89.1278	−3.91605
$519$	−24.0617	−1.05619
$520$	6.81205	0.298728
$521$	38.9873	1.70807	0.854033	−	0.520219i	$-0.174150\pi$
$521$	38.9873	1.70807	0.854033	+	0.520219i	$0.174150\pi$
$522$	11.8797	0.519959
$523$	−16.1220	−0.704966	−0.352483	−	0.935818i	$-0.614663\pi$
$523$	−16.1220	−0.704966	−0.352483	+	0.935818i	$0.614663\pi$
$524$	−30.6430	−1.33865
$525$	−17.8750	−0.780129
$526$	−51.6988	−2.25417
$527$	−1.63414	−0.0711843
$528$	3.07716	0.133916
$529$	15.9817	0.694857
$530$	−13.2967	−0.577570
$531$	−7.75579	−0.336573
$532$	33.0957	1.43488
$533$	7.00268	0.303320
$534$	−4.44292	−0.192264
$535$	−24.7138	−1.06847
$536$	18.0722	0.780602
$537$	−8.33123	−0.359519
$538$	9.08580	0.391717
$539$	−6.75493	−0.290956
$540$	−28.2531	−1.21582
$541$	−43.7349	−1.88031	−0.940156	−	0.340745i	$-0.889321\pi$
$541$	−43.7349	−1.88031	−0.940156	+	0.340745i	$0.889321\pi$
$542$	43.2754	1.85884
$543$	30.5401	1.31060
$544$	−0.787481	−0.0337630
$545$	3.71685	0.159212
$546$	−18.6822	−0.799523
$547$	14.0212	0.599503	0.299752	−	0.954017i	$-0.403096\pi$
$547$	14.0212	0.599503	0.299752	+	0.954017i	$0.403096\pi$
$548$	28.0879	1.19986
$549$	2.03815	0.0869861
$550$	−3.73247	−0.159153
$551$	19.6584	0.837475
$552$	48.4483	2.06210
$553$	−11.2512	−0.478449
$554$	38.1253	1.61979
$555$	−27.9544	−1.18660
$556$	−75.9035	−3.21903
$557$	3.95770	0.167693	0.0838466	−	0.996479i	$-0.473279\pi$
$557$	3.95770	0.167693	0.0838466	+	0.996479i	$0.473279\pi$
$558$	−6.67992	−0.282783
$559$	6.95467	0.294151
$560$	16.3277	0.689971
$561$	−0.406675	−0.0171698
$562$	40.5631	1.71105
$563$	21.1206	0.890129	0.445065	−	0.895498i	$-0.353181\pi$
$563$	21.1206	0.890129	0.445065	+	0.895498i	$0.353181\pi$
$564$	−5.02733	−0.211689
$565$	−1.64189	−0.0690749
$566$	31.9734	1.34394
$567$	42.5947	1.78881
$568$	4.12133	0.172927
$569$	−18.5598	−0.778066	−0.389033	−	0.921224i	$-0.627191\pi$
$569$	−18.5598	−0.778066	−0.389033	+	0.921224i	$0.627191\pi$
$570$	15.9569	0.668359
$571$	−23.1627	−0.969328	−0.484664	−	0.874700i	$-0.661058\pi$
$571$	−23.1627	−0.969328	−0.484664	+	0.874700i	$0.661058\pi$
$572$	−2.53769	−0.106106
$573$	−26.5640	−1.10973
$574$	68.5626	2.86175
$575$	−14.3863	−0.599951
$576$	−5.85010	−0.243754
$577$	1.76739	0.0735773	0.0367887	−	0.999323i	$-0.488287\pi$
$577$	1.76739	0.0735773	0.0367887	+	0.999323i	$0.488287\pi$
$578$	40.4246	1.68144
$579$	10.7861	0.448256
$580$	55.6894	2.31238
$581$	74.6699	3.09783
$582$	7.52956	0.312110
$583$	2.29228	0.0949364
$584$	−47.7016	−1.97391
$585$	−0.900909	−0.0372480
$586$	40.0928	1.65622
$587$	−9.79389	−0.404237	−0.202118	−	0.979361i	$-0.564783\pi$
$587$	−9.79389	−0.404237	−0.202118	+	0.979361i	$0.564783\pi$
$588$	−69.9244	−2.88363
$589$	−11.0539	−0.455467
$590$	−55.8900	−2.30095
$591$	−23.3445	−0.960264
$592$	−21.8252	−0.897012
$593$	28.2676	1.16081	0.580406	−	0.814327i	$-0.302894\pi$
$593$	28.2676	1.16081	0.580406	+	0.814327i	$0.302894\pi$
$594$	7.48739	0.307211
$595$	−2.15785	−0.0884634
$596$	−40.3025	−1.65085
$597$	12.9952	0.531860
$598$	−15.0360	−0.614866
$599$	3.48645	0.142453	0.0712263	−	0.997460i	$-0.477309\pi$
$599$	3.48645	0.142453	0.0712263	+	0.997460i	$0.477309\pi$
$600$	−17.8800	−0.729948
$601$	32.0186	1.30607	0.653033	−	0.757329i	$-0.273496\pi$
$601$	32.0186	1.30607	0.653033	+	0.757329i	$0.273496\pi$
$602$	68.0925	2.77524
$603$	−2.39010	−0.0973323
$604$	24.1327	0.981944
$605$	17.3080	0.703669
$606$	−59.5234	−2.41797
$607$	8.11339	0.329312	0.164656	−	0.986351i	$-0.447349\pi$
$607$	8.11339	0.329312	0.164656	+	0.986351i	$0.447349\pi$
$608$	−5.32679	−0.216030
$609$	−70.6784	−2.86403
$610$	14.6874	0.594674
$611$	0.722027	0.0292101
$612$	−0.647250	−0.0261635
$613$	39.6109	1.59987	0.799934	−	0.600087i	$-0.204868\pi$
$613$	39.6109	1.59987	0.799934	+	0.600087i	$0.204868\pi$
$614$	78.9164	3.18481
$615$	21.5042	0.867134
$616$	−11.4981	−0.463271
$617$	−21.8120	−0.878116	−0.439058	−	0.898459i	$-0.644688\pi$
$617$	−21.8120	−0.878116	−0.439058	+	0.898459i	$0.644688\pi$
$618$	−10.5348	−0.423770
$619$	20.2009	0.811944	0.405972	−	0.913885i	$-0.366933\pi$
$619$	20.2009	0.811944	0.405972	+	0.913885i	$0.366933\pi$
$620$	−31.3141	−1.25760
$621$	28.8592	1.15808
$622$	−24.8157	−0.995018
$623$	4.06414	0.162826
$624$	−4.57481	−0.183139
$625$	−8.16971	−0.326788
$626$	38.5077	1.53908
$627$	−2.75088	−0.109860
$628$	−85.6076	−3.41611
$629$	2.88441	0.115009
$630$	−8.82072	−0.351426
$631$	−6.82079	−0.271531	−0.135766	−	0.990741i	$-0.543349\pi$
$631$	−6.82079	−0.271531	−0.135766	+	0.990741i	$0.543349\pi$
$632$	−11.2543	−0.447674
$633$	19.3415	0.768754
$634$	−18.0902	−0.718454
$635$	31.8365	1.26339
$636$	23.7287	0.940906
$637$	10.0426	0.397901
$638$	−14.7583	−0.584287
$639$	−0.545055	−0.0215620
$640$	−34.0503	−1.34596
$641$	25.3754	1.00227	0.501134	−	0.865370i	$-0.332916\pi$
$641$	25.3754	1.00227	0.501134	+	0.865370i	$0.332916\pi$
$642$	67.7971	2.67574
$643$	21.2765	0.839062	0.419531	−	0.907741i	$-0.362195\pi$
$643$	21.2765	0.839062	0.419531	+	0.907741i	$0.362195\pi$
$644$	−95.7667	−3.77374
$645$	21.3568	0.840922
$646$	−1.64647	−0.0647796
$647$	1.28665	0.0505834	0.0252917	−	0.999680i	$-0.491949\pi$
$647$	1.28665	0.0505834	0.0252917	+	0.999680i	$0.491949\pi$
$648$	42.6066	1.67375
$649$	9.63515	0.378213
$650$	5.54906	0.217652
$651$	39.7423	1.55763
$652$	−13.8769	−0.543462
$653$	25.6765	1.00480	0.502400	−	0.864635i	$-0.332450\pi$
$653$	25.6765	1.00480	0.502400	+	0.864635i	$0.332450\pi$
$654$	−10.1964	−0.398710
$655$	13.5147	0.528064
$656$	16.7893	0.655513
$657$	6.30865	0.246124
$658$	7.06930	0.275590
$659$	−1.27253	−0.0495707	−0.0247854	−	0.999693i	$-0.507890\pi$
$659$	−1.27253	−0.0495707	−0.0247854	+	0.999693i	$0.507890\pi$
$660$	−7.79287	−0.303337
$661$	33.7000	1.31078	0.655390	−	0.755291i	$-0.272504\pi$
$661$	33.7000	1.31078	0.655390	+	0.755291i	$0.272504\pi$
$662$	71.8189	2.79132
$663$	0.604603	0.0234808
$664$	74.6908	2.89857
$665$	−14.5964	−0.566026
$666$	11.7907	0.456879
$667$	−56.8840	−2.20256
$668$	−27.3667	−1.05885
$669$	−39.5881	−1.53056
$670$	−17.2236	−0.665405
$671$	−2.53203	−0.0977479
$672$	19.1516	0.738788
$673$	24.8968	0.959701	0.479850	−	0.877350i	$-0.340691\pi$
$673$	24.8968	0.959701	0.479850	+	0.877350i	$0.340691\pi$
$674$	−10.8585	−0.418252
$675$	−10.6506	−0.409940
$676$	−44.6235	−1.71629
$677$	−3.08894	−0.118718	−0.0593588	−	0.998237i	$-0.518906\pi$
$677$	−3.08894	−0.118718	−0.0593588	+	0.998237i	$0.518906\pi$
$678$	4.50418	0.172982
$679$	−6.88762	−0.264323
$680$	−2.15846	−0.0827731
$681$	21.6819	0.830854
$682$	8.29858	0.317769
$683$	−1.66982	−0.0638939	−0.0319469	−	0.999490i	$-0.510171\pi$
$683$	−1.66982	−0.0638939	−0.0319469	+	0.999490i	$0.510171\pi$
$684$	−4.37821	−0.167405
$685$	−12.3878	−0.473315
$686$	29.3308	1.11986
$687$	−28.4779	−1.08650
$688$	16.6742	0.635698
$689$	−3.40793	−0.129832
$690$	−46.1732	−1.75778
$691$	32.8851	1.25101	0.625504	−	0.780221i	$-0.284894\pi$
$691$	32.8851	1.25101	0.625504	+	0.780221i	$0.284894\pi$
$692$	47.5756	1.80855
$693$	1.52065	0.0577646
$694$	26.6084	1.01004
$695$	33.4763	1.26983
$696$	−70.6982	−2.67981
$697$	−2.21886	−0.0840455
$698$	−34.3504	−1.30018
$699$	−24.3438	−0.920767
$700$	35.3430	1.33584
$701$	−4.24119	−0.160188	−0.0800938	−	0.996787i	$-0.525522\pi$
$701$	−4.24119	−0.160188	−0.0800938	+	0.996787i	$0.525522\pi$
$702$	−11.1315	−0.420131
$703$	19.5111	0.735875
$704$	7.26768	0.273911
$705$	2.21724	0.0835061
$706$	−28.9603	−1.08993
$707$	54.4487	2.04775
$708$	99.7393	3.74843
$709$	39.9791	1.50145	0.750724	−	0.660616i	$-0.229705\pi$
$709$	39.9791	1.50145	0.750724	+	0.660616i	$0.229705\pi$
$710$	−3.92779	−0.147407
$711$	1.48841	0.0558199
$712$	4.06528	0.152353
$713$	31.9858	1.19788
$714$	5.91961	0.221536
$715$	1.11922	0.0418563
$716$	16.4728	0.615616
$717$	−16.1966	−0.604875
$718$	63.6615	2.37583
$719$	−30.6522	−1.14314	−0.571568	−	0.820555i	$-0.693665\pi$
$719$	−30.6522	−1.14314	−0.571568	+	0.820555i	$0.693665\pi$
$720$	−2.15998	−0.0804977
$721$	9.63661	0.358886
$722$	34.3152	1.27708
$723$	−8.25992	−0.307190
$724$	−60.3848	−2.24418
$725$	20.9932	0.779669
$726$	−47.4808	−1.76218
$727$	23.6974	0.878887	0.439443	−	0.898270i	$-0.355176\pi$
$727$	23.6974	0.878887	0.439443	+	0.898270i	$0.355176\pi$
$728$	17.0942	0.633553
$729$	20.4739	0.758293
$730$	45.4616	1.68261
$731$	−2.20365	−0.0815049
$732$	−26.2105	−0.968770
$733$	−31.6560	−1.16924	−0.584621	−	0.811307i	$-0.698757\pi$
$733$	−31.6560	−1.16924	−0.584621	+	0.811307i	$0.698757\pi$
$734$	87.7099	3.23743
$735$	30.8393	1.13752
$736$	15.4137	0.568158
$737$	2.96926	0.109374
$738$	−9.07011	−0.333875
$739$	36.4492	1.34080	0.670402	−	0.741998i	$-0.266122\pi$
$739$	36.4492	1.34080	0.670402	+	0.741998i	$0.266122\pi$
$740$	55.2722	2.03185
$741$	4.08974	0.150240
$742$	−33.3667	−1.22493
$743$	20.2532	0.743019	0.371509	−	0.928429i	$-0.378840\pi$
$743$	20.2532	0.743019	0.371509	+	0.928429i	$0.378840\pi$
$744$	39.7535	1.45743
$745$	17.7749	0.651221
$746$	61.8672	2.26512
$747$	−9.87803	−0.361418
$748$	0.804089	0.0294004
$749$	−62.0170	−2.26605
$750$	54.0172	1.97243
$751$	−37.7972	−1.37924	−0.689620	−	0.724172i	$-0.742222\pi$
$751$	−37.7972	−1.37924	−0.689620	+	0.724172i	$0.742222\pi$
$752$	1.73110	0.0631268
$753$	56.1775	2.04722
$754$	21.9412	0.799051
$755$	−10.6434	−0.387353
$756$	−70.8986	−2.57856
$757$	−29.0164	−1.05462	−0.527309	−	0.849674i	$-0.676799\pi$
$757$	−29.0164	−1.05462	−0.527309	+	0.849674i	$0.676799\pi$
$758$	21.8136	0.792305
$759$	7.96003	0.288931
$760$	−14.6005	−0.529617
$761$	23.5760	0.854628	0.427314	−	0.904103i	$-0.359460\pi$
$761$	23.5760	0.854628	0.427314	+	0.904103i	$0.359460\pi$
$762$	−87.3368	−3.16388
$763$	9.32708	0.337663
$764$	52.5231	1.90022
$765$	0.285461	0.0103209
$766$	−32.5911	−1.17756
$767$	−14.3246	−0.517231
$768$	52.9927	1.91221
$769$	−1.31365	−0.0473714	−0.0236857	−	0.999719i	$-0.507540\pi$
$769$	−1.31365	−0.0473714	−0.0236857	+	0.999719i	$0.507540\pi$
$770$	10.9581	0.394904
$771$	−21.8288	−0.786145
$772$	−21.3267	−0.767564
$773$	−10.3690	−0.372947	−0.186474	−	0.982460i	$-0.559706\pi$
$773$	−10.3690	−0.372947	−0.186474	+	0.982460i	$0.559706\pi$
$774$	−9.00791	−0.323783
$775$	−11.8045	−0.424028
$776$	−6.88955	−0.247321
$777$	−70.1488	−2.51658
$778$	−46.4820	−1.66646
$779$	−15.0091	−0.537758
$780$	11.5857	0.414833
$781$	0.677131	0.0242297
$782$	4.76428	0.170370
$783$	−42.1127	−1.50499
$784$	24.0776	0.859915
$785$	37.7561	1.34757
$786$	−37.0748	−1.32241
$787$	−7.93118	−0.282716	−0.141358	−	0.989959i	$-0.545147\pi$
$787$	−7.93118	−0.282716	−0.141358	+	0.989959i	$0.545147\pi$
$788$	46.1575	1.64429
$789$	−40.6900	−1.44860
$790$	10.7258	0.381609
$791$	−4.12017	−0.146496
$792$	1.52107	0.0540490
$793$	3.76437	0.133677
$794$	−39.1564	−1.38961
$795$	−10.4653	−0.371165
$796$	−25.6946	−0.910720
$797$	−55.1764	−1.95445	−0.977225	−	0.212208i	$-0.931935\pi$
$797$	−55.1764	−1.95445	−0.977225	+	0.212208i	$0.931935\pi$
$798$	40.0422	1.41748
$799$	−0.228781	−0.00809369
$800$	−5.68849	−0.201118
$801$	−0.537643	−0.0189967
$802$	−88.1055	−3.11111
$803$	−7.83735	−0.276574
$804$	30.7366	1.08400
$805$	42.2367	1.48865
$806$	−12.3375	−0.434570
$807$	7.15106	0.251729
$808$	54.4639	1.91603
$809$	−35.8655	−1.26096	−0.630481	−	0.776205i	$-0.717142\pi$
$809$	−35.8655	−1.26096	−0.630481	+	0.776205i	$0.717142\pi$
$810$	−40.6058	−1.42674
$811$	39.4377	1.38485	0.692423	−	0.721492i	$-0.256543\pi$
$811$	39.4377	1.38485	0.692423	+	0.721492i	$0.256543\pi$
$812$	139.747	4.90417
$813$	34.0603	1.19455
$814$	−14.6477	−0.513403
$815$	6.12024	0.214383
$816$	1.44957	0.0507451
$817$	−14.9062	−0.521503
$818$	30.3337	1.06059
$819$	−2.26075	−0.0789969
$820$	−42.5188	−1.48482
$821$	38.9289	1.35863	0.679314	−	0.733848i	$-0.262277\pi$
$821$	38.9289	1.35863	0.679314	+	0.733848i	$0.262277\pi$
$822$	33.9834	1.18531
$823$	−24.7519	−0.862796	−0.431398	−	0.902162i	$-0.641979\pi$
$823$	−24.7519	−0.862796	−0.431398	+	0.902162i	$0.641979\pi$
$824$	9.63931	0.335801
$825$	−2.93767	−0.102277
$826$	−140.251	−4.87995
$827$	3.74323	0.130165	0.0650825	−	0.997880i	$-0.479269\pi$
$827$	3.74323	0.130165	0.0650825	+	0.997880i	$0.479269\pi$
$828$	12.6689	0.440275
$829$	−19.6146	−0.681245	−0.340622	−	0.940200i	$-0.610638\pi$
$829$	−19.6146	−0.681245	−0.340622	+	0.940200i	$0.610638\pi$
$830$	−71.1833	−2.47081
$831$	30.0069	1.04093
$832$	−10.8049	−0.374591
$833$	−3.18208	−0.110252
$834$	−91.8351	−3.17999
$835$	12.0697	0.417690
$836$	5.43913	0.188116
$837$	23.6799	0.818497
$838$	73.6671	2.54479
$839$	1.25908	0.0434684	0.0217342	−	0.999764i	$-0.493081\pi$
$839$	1.25908	0.0434684	0.0217342	+	0.999764i	$0.493081\pi$
$840$	52.4938	1.81121
$841$	54.0079	1.86234
$842$	65.9045	2.27122
$843$	31.9256	1.09958
$844$	−38.2425	−1.31636
$845$	19.6806	0.677035
$846$	−0.935193	−0.0321526
$847$	43.4328	1.49237
$848$	−8.17071	−0.280583
$849$	25.1649	0.863659
$850$	−1.75827	−0.0603082
$851$	−56.4578	−1.93535
$852$	7.00939	0.240138
$853$	46.8502	1.60412	0.802060	−	0.597244i	$-0.203738\pi$
$853$	46.8502	1.60412	0.802060	+	0.597244i	$0.203738\pi$
$854$	36.8566	1.26121
$855$	1.93096	0.0660373
$856$	−62.0344	−2.12029
$857$	41.0887	1.40356	0.701782	−	0.712392i	$-0.252388\pi$
$857$	41.0887	1.40356	0.701782	+	0.712392i	$0.252388\pi$
$858$	−3.07033	−0.104819
$859$	36.1464	1.23330	0.616650	−	0.787237i	$-0.288489\pi$
$859$	36.1464	1.23330	0.616650	+	0.787237i	$0.288489\pi$
$860$	−42.2273	−1.43994
$861$	53.9628	1.83905
$862$	−14.9622	−0.509613
$863$	27.3890	0.932333	0.466166	−	0.884697i	$-0.345635\pi$
$863$	27.3890	0.932333	0.466166	+	0.884697i	$0.345635\pi$
$864$	11.4112	0.388216
$865$	−20.9826	−0.713431
$866$	74.4405	2.52959
$867$	31.8166	1.08055
$868$	−78.5798	−2.66717
$869$	−1.84908	−0.0627258
$870$	67.3782	2.28434
$871$	−4.41440	−0.149576
$872$	9.32970	0.315943
$873$	0.911159	0.0308381
$874$	32.2272	1.09010
$875$	−49.4119	−1.67043
$876$	−81.1291	−2.74110
$877$	−11.8726	−0.400908	−0.200454	−	0.979703i	$-0.564242\pi$
$877$	−11.8726	−0.400908	−0.200454	+	0.979703i	$0.564242\pi$
$878$	−7.31772	−0.246961
$879$	31.5554	1.06434
$880$	2.68338	0.0904568
$881$	17.6400	0.594308	0.297154	−	0.954830i	$-0.403963\pi$
$881$	17.6400	0.594308	0.297154	+	0.954830i	$0.403963\pi$
$882$	−13.0075	−0.437984
$883$	−6.27678	−0.211231	−0.105615	−	0.994407i	$-0.533681\pi$
$883$	−6.27678	−0.211231	−0.105615	+	0.994407i	$0.533681\pi$
$884$	−1.19544	−0.0402070
$885$	−43.9887	−1.47867
$886$	−53.0637	−1.78271
$887$	−36.8764	−1.23819	−0.619094	−	0.785317i	$-0.712500\pi$
$887$	−36.8764	−1.23819	−0.619094	+	0.785317i	$0.712500\pi$
$888$	−70.1685	−2.35470
$889$	79.8908	2.67945
$890$	−3.87437	−0.129869
$891$	7.00024	0.234517
$892$	78.2748	2.62083
$893$	−1.54755	−0.0517868
$894$	−48.7616	−1.63083
$895$	−7.26510	−0.242846
$896$	−85.4460	−2.85455
$897$	−11.8342	−0.395132
$898$	24.0733	0.803338
$899$	−46.6752	−1.55671
$900$	−4.67550	−0.155850
$901$	1.07983	0.0359745
$902$	11.2680	0.375182
$903$	53.5928	1.78346
$904$	−4.12133	−0.137073
$905$	26.6319	0.885275
$906$	29.1979	0.970036
$907$	22.1318	0.734874	0.367437	−	0.930049i	$-0.380235\pi$
$907$	22.1318	0.734874	0.367437	+	0.930049i	$0.380235\pi$
$908$	−42.8702	−1.42270
$909$	−7.20298	−0.238908
$910$	−16.2915	−0.540057
$911$	−57.1121	−1.89221	−0.946105	−	0.323861i	$-0.895019\pi$
$911$	−57.1121	−1.89221	−0.946105	+	0.323861i	$0.895019\pi$
$912$	9.80538	0.324689
$913$	12.2717	0.406132
$914$	−67.9080	−2.24620
$915$	11.5598	0.382156
$916$	56.3074	1.86045
$917$	33.9139	1.11994
$918$	3.52712	0.116412
$919$	15.1108	0.498460	0.249230	−	0.968444i	$-0.419822\pi$
$919$	15.1108	0.498460	0.249230	+	0.968444i	$0.419822\pi$
$920$	42.2485	1.39289
$921$	62.1119	2.04666
$922$	−38.0239	−1.25225
$923$	−1.00669	−0.0331357
$924$	−19.5555	−0.643328
$925$	20.8359	0.685081
$926$	99.1385	3.25789
$927$	−1.27482	−0.0418706
$928$	−22.4925	−0.738352
$929$	45.8689	1.50491	0.752455	−	0.658644i	$-0.228869\pi$
$929$	45.8689	1.50491	0.752455	+	0.658644i	$0.228869\pi$
$930$	−37.8867	−1.24235
$931$	−21.5246	−0.705442
$932$	48.1333	1.57666
$933$	−19.5314	−0.639430
$934$	−53.6288	−1.75479
$935$	−0.354634	−0.0115978
$936$	−2.26138	−0.0739156
$937$	−46.2669	−1.51147	−0.755736	−	0.654876i	$-0.772721\pi$
$937$	−46.2669	−1.51147	−0.755736	+	0.654876i	$0.772721\pi$
$938$	−43.2210	−1.41121
$939$	30.3078	0.989058
$940$	−4.38400	−0.142990
$941$	3.61808	0.117946	0.0589731	−	0.998260i	$-0.481217\pi$
$941$	3.61808	0.117946	0.0589731	+	0.998260i	$0.481217\pi$
$942$	−103.576	−3.37469
$943$	43.4309	1.41430
$944$	−34.3440	−1.11780
$945$	31.2689	1.01718
$946$	11.1907	0.363841
$947$	−45.2001	−1.46881	−0.734403	−	0.678713i	$-0.762538\pi$
$947$	−45.2001	−1.46881	−0.734403	+	0.678713i	$0.762538\pi$
$948$	−19.1410	−0.621669
$949$	11.6518	0.378233
$950$	−11.8935	−0.385877
$951$	−14.2381	−0.461701
$952$	−5.41645	−0.175548
$953$	−3.69976	−0.119847	−0.0599235	−	0.998203i	$-0.519086\pi$
$953$	−3.69976	−0.119847	−0.0599235	+	0.998203i	$0.519086\pi$
$954$	4.41406	0.142911
$955$	−23.1646	−0.749590
$956$	32.0245	1.03575
$957$	−11.6157	−0.375481
$958$	102.613	3.31527
$959$	−31.0861	−1.00382
$960$	−33.1802	−1.07088
$961$	−4.75459	−0.153374
$962$	21.7768	0.702112
$963$	8.20420	0.264377
$964$	16.3318	0.526011
$965$	9.40586	0.302785
$966$	−115.867	−3.72797
$967$	−9.77015	−0.314187	−0.157093	−	0.987584i	$-0.550212\pi$
$967$	−9.77015	−0.314187	−0.157093	+	0.987584i	$0.550212\pi$
$968$	43.4449	1.39637
$969$	−1.29587	−0.0416294
$970$	6.56602	0.210822
$971$	50.3707	1.61647	0.808236	−	0.588858i	$-0.200422\pi$
$971$	50.3707	1.61647	0.808236	+	0.588858i	$0.200422\pi$
$972$	20.8406	0.668464
$973$	84.0056	2.69310
$974$	−5.28161	−0.169234
$975$	4.36744	0.139870
$976$	9.02529	0.288892
$977$	38.1269	1.21979	0.609894	−	0.792483i	$-0.291212\pi$
$977$	38.1269	1.21979	0.609894	+	0.792483i	$0.291212\pi$
$978$	−16.7896	−0.536871
$979$	0.667923	0.0213469
$980$	−60.9763	−1.94782
$981$	−1.23387	−0.0393946
$982$	−22.1201	−0.705881
$983$	59.4871	1.89734	0.948672	−	0.316263i	$-0.102428\pi$
$983$	59.4871	1.89734	0.948672	+	0.316263i	$0.102428\pi$
$984$	53.9780	1.72076
$985$	−20.3572	−0.648633
$986$	−6.95227	−0.221405
$987$	5.56396	0.177103
$988$	−8.08636	−0.257261
$989$	43.1331	1.37155
$990$	−1.44964	−0.0460727
$991$	−8.80134	−0.279584	−0.139792	−	0.990181i	$-0.544643\pi$
$991$	−8.80134	−0.279584	−0.139792	+	0.990181i	$0.544643\pi$
$992$	12.6475	0.401558
$993$	56.5258	1.79379
$994$	−9.85642	−0.312627
$995$	11.3323	0.359257
$996$	127.031	4.02514
$997$	54.6485	1.73074	0.865368	−	0.501137i	$-0.167085\pi$
$997$	54.6485	1.73074	0.865368	+	0.501137i	$0.167085\pi$
$998$	−38.7506	−1.22663
$999$	−41.7972	−1.32240

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8023.2.a.e.1.13	✓	172

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8023.2.a.e.1.13	✓	172	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)

\(f(q)\)	\(=\)	\(q-2.39224 q^{2} -1.88283 q^{3} +3.72279 q^{4} -1.64189 q^{5} +4.50418 q^{6} -4.12017 q^{7} -4.12133 q^{8} +0.545055 q^{9} +O(q^{10})\)	\(q-2.39224 q^{2} -1.88283 q^{3} +3.72279 q^{4} -1.64189 q^{5} +4.50418 q^{6} -4.12017 q^{7} -4.12133 q^{8} +0.545055 q^{9} +3.92779 q^{10} -0.677131 q^{11} -7.00939 q^{12} +1.00669 q^{13} +9.85642 q^{14} +3.09140 q^{15} +2.41360 q^{16} -0.318979 q^{17} -1.30390 q^{18} -2.15768 q^{19} -6.11242 q^{20} +7.75759 q^{21} +1.61986 q^{22} +6.24353 q^{23} +7.75976 q^{24} -2.30419 q^{25} -2.40824 q^{26} +4.62225 q^{27} -15.3385 q^{28} -9.11087 q^{29} -7.39537 q^{30} +5.12303 q^{31} +2.46875 q^{32} +1.27492 q^{33} +0.763074 q^{34} +6.76487 q^{35} +2.02913 q^{36} -9.04261 q^{37} +5.16169 q^{38} -1.89543 q^{39} +6.76677 q^{40} +6.95614 q^{41} -18.5580 q^{42} +6.90844 q^{43} -2.52082 q^{44} -0.894921 q^{45} -14.9360 q^{46} +0.717228 q^{47} -4.54440 q^{48} +9.97581 q^{49} +5.51218 q^{50} +0.600584 q^{51} +3.74770 q^{52} -3.38528 q^{53} -11.0575 q^{54} +1.11178 q^{55} +16.9806 q^{56} +4.06255 q^{57} +21.7953 q^{58} -14.2294 q^{59} +11.5087 q^{60} +3.73935 q^{61} -12.2555 q^{62} -2.24572 q^{63} -10.7330 q^{64} -1.65288 q^{65} -3.04992 q^{66} -4.38506 q^{67} -1.18749 q^{68} -11.7555 q^{69} -16.1832 q^{70} -1.00000 q^{71} -2.24635 q^{72} +11.5743 q^{73} +21.6321 q^{74} +4.33841 q^{75} -8.03261 q^{76} +2.78990 q^{77} +4.53432 q^{78} +2.73076 q^{79} -3.96287 q^{80} -10.3381 q^{81} -16.6407 q^{82} -18.1230 q^{83} +28.8799 q^{84} +0.523729 q^{85} -16.5266 q^{86} +17.1542 q^{87} +2.79068 q^{88} -0.986400 q^{89} +2.14086 q^{90} -4.14774 q^{91} +23.2434 q^{92} -9.64580 q^{93} -1.71578 q^{94} +3.54268 q^{95} -4.64825 q^{96} +1.67168 q^{97} -23.8645 q^{98} -0.369074 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 172 q + 24 q^{2} + 18 q^{3} + 180 q^{4} + 28 q^{5} + 16 q^{6} + 4 q^{7} + 72 q^{8} + 198 q^{9}+O(q^{10}) \) 172 * q + 24 * q^2 + 18 * q^3 + 180 * q^4 + 28 * q^5 + 16 * q^6 + 4 * q^7 + 72 * q^8 + 198 * q^9	\( 172 q + 24 q^{2} + 18 q^{3} + 180 q^{4} + 28 q^{5} + 16 q^{6} + 4 q^{7} + 72 q^{8} + 198 q^{9} + 14 q^{10} + 20 q^{11} + 54 q^{12} + 36 q^{13} + 26 q^{14} + 32 q^{15} + 196 q^{16} + 123 q^{17} + 74 q^{18} + 20 q^{19} + 70 q^{20} + 37 q^{21} + 11 q^{22} + 22 q^{23} + 62 q^{24} + 210 q^{25} + 50 q^{26} + 69 q^{27} + 42 q^{28} + 58 q^{29} + 36 q^{30} + 10 q^{31} + 168 q^{32} + 124 q^{33} + 5 q^{34} + 59 q^{35} + 192 q^{36} + 40 q^{37} + 58 q^{38} + 15 q^{39} + 7 q^{40} + 155 q^{41} - 6 q^{42} + 19 q^{43} + 22 q^{44} + 76 q^{45} + q^{46} + 71 q^{47} + 144 q^{48} + 206 q^{49} + 126 q^{50} + 33 q^{51} + 71 q^{52} + 101 q^{53} + 92 q^{54} - 2 q^{55} + 57 q^{56} + 114 q^{57} + 4 q^{58} + 71 q^{59} + 38 q^{60} + 50 q^{61} + 86 q^{62} + 14 q^{63} + 240 q^{64} + 143 q^{65} + 21 q^{66} + 8 q^{67} + 192 q^{68} + 41 q^{69} - 12 q^{70} - 172 q^{71} + 156 q^{72} + 128 q^{73} + 30 q^{74} + 72 q^{75} + 74 q^{76} + 127 q^{77} + 107 q^{78} + 2 q^{79} + 50 q^{80} + 236 q^{81} + 42 q^{82} + 140 q^{83} + 71 q^{84} + 55 q^{85} + 46 q^{86} + 100 q^{87} - 31 q^{88} + 215 q^{89} - 7 q^{90} + 22 q^{91} - 15 q^{92} + 60 q^{93} + 5 q^{94} + 74 q^{95} + 182 q^{96} + 120 q^{97} + 164 q^{98} + 60 q^{99}+O(q^{100}) \) 172 * q + 24 * q^2 + 18 * q^3 + 180 * q^4 + 28 * q^5 + 16 * q^6 + 4 * q^7 + 72 * q^8 + 198 * q^9 + 14 * q^10 + 20 * q^11 + 54 * q^12 + 36 * q^13 + 26 * q^14 + 32 * q^15 + 196 * q^16 + 123 * q^17 + 74 * q^18 + 20 * q^19 + 70 * q^20 + 37 * q^21 + 11 * q^22 + 22 * q^23 + 62 * q^24 + 210 * q^25 + 50 * q^26 + 69 * q^27 + 42 * q^28 + 58 * q^29 + 36 * q^30 + 10 * q^31 + 168 * q^32 + 124 * q^33 + 5 * q^34 + 59 * q^35 + 192 * q^36 + 40 * q^37 + 58 * q^38 + 15 * q^39 + 7 * q^40 + 155 * q^41 - 6 * q^42 + 19 * q^43 + 22 * q^44 + 76 * q^45 + q^46 + 71 * q^47 + 144 * q^48 + 206 * q^49 + 126 * q^50 + 33 * q^51 + 71 * q^52 + 101 * q^53 + 92 * q^54 - 2 * q^55 + 57 * q^56 + 114 * q^57 + 4 * q^58 + 71 * q^59 + 38 * q^60 + 50 * q^61 + 86 * q^62 + 14 * q^63 + 240 * q^64 + 143 * q^65 + 21 * q^66 + 8 * q^67 + 192 * q^68 + 41 * q^69 - 12 * q^70 - 172 * q^71 + 156 * q^72 + 128 * q^73 + 30 * q^74 + 72 * q^75 + 74 * q^76 + 127 * q^77 + 107 * q^78 + 2 * q^79 + 50 * q^80 + 236 * q^81 + 42 * q^82 + 140 * q^83 + 71 * q^84 + 55 * q^85 + 46 * q^86 + 100 * q^87 - 31 * q^88 + 215 * q^89 - 7 * q^90 + 22 * q^91 - 15 * q^92 + 60 * q^93 + 5 * q^94 + 74 * q^95 + 182 * q^96 + 120 * q^97 + 164 * q^98 + 60 * q^99

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