LMFDB - Embedded newform 471.4.a.c.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [471,4,Mod(1,471)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(471, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("471.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 471 = 3 \cdot 157 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	471.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:	$27.7898996127$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	471.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.22585 q^{2} -3.00000 q^{3} -6.49728 q^{4} -2.10116 q^{5} +3.67756 q^{6} +35.0092 q^{7} +17.7716 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-1.22585 q^{2} -3.00000 q^{3} -6.49728 q^{4} -2.10116 q^{5} +3.67756 q^{6} +35.0092 q^{7} +17.7716 q^{8} +9.00000 q^{9} +2.57572 q^{10} -11.3828 q^{11} +19.4918 q^{12} -54.5332 q^{13} -42.9161 q^{14} +6.30348 q^{15} +30.1929 q^{16} -9.39716 q^{17} -11.0327 q^{18} -15.5321 q^{19} +13.6518 q^{20} -105.027 q^{21} +13.9537 q^{22} +183.958 q^{23} -53.3147 q^{24} -120.585 q^{25} +66.8498 q^{26} -27.0000 q^{27} -227.464 q^{28} -139.496 q^{29} -7.72715 q^{30} -236.609 q^{31} -179.185 q^{32} +34.1485 q^{33} +11.5195 q^{34} -73.5599 q^{35} -58.4755 q^{36} +156.703 q^{37} +19.0401 q^{38} +163.600 q^{39} -37.3409 q^{40} +182.457 q^{41} +128.748 q^{42} +423.810 q^{43} +73.9574 q^{44} -18.9104 q^{45} -225.506 q^{46} +439.359 q^{47} -90.5788 q^{48} +882.642 q^{49} +147.820 q^{50} +28.1915 q^{51} +354.318 q^{52} -497.712 q^{53} +33.0981 q^{54} +23.9171 q^{55} +622.167 q^{56} +46.5963 q^{57} +171.002 q^{58} +216.123 q^{59} -40.9555 q^{60} -325.040 q^{61} +290.048 q^{62} +315.082 q^{63} -21.8893 q^{64} +114.583 q^{65} -41.8610 q^{66} +505.112 q^{67} +61.0560 q^{68} -551.875 q^{69} +90.1737 q^{70} +993.848 q^{71} +159.944 q^{72} +370.314 q^{73} -192.095 q^{74} +361.755 q^{75} +100.916 q^{76} -398.503 q^{77} -200.549 q^{78} -810.923 q^{79} -63.4402 q^{80} +81.0000 q^{81} -223.666 q^{82} +655.000 q^{83} +682.393 q^{84} +19.7450 q^{85} -519.529 q^{86} +418.488 q^{87} -202.290 q^{88} +1077.51 q^{89} +23.1814 q^{90} -1909.16 q^{91} -1195.23 q^{92} +709.826 q^{93} -538.590 q^{94} +32.6355 q^{95} +537.554 q^{96} -844.529 q^{97} -1081.99 q^{98} -102.445 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 4 q^{2} - 66 q^{3} + 90 q^{4} + 32 q^{5} - 12 q^{6} - 4 q^{7} + 27 q^{8} + 198 q^{9}+O(q^{10}) $ 22 * q + 4 * q^2 - 66 * q^3 + 90 * q^4 + 32 * q^5 - 12 * q^6 - 4 * q^7 + 27 * q^8 + 198 * q^9	\( 22 q + 4 q^{2} - 66 q^{3} + 90 q^{4} + 32 q^{5} - 12 q^{6} - 4 q^{7} + 27 q^{8} + 198 q^{9} + 13 q^{10} + 61 q^{11} - 270 q^{12} + 4 q^{13} + 133 q^{14} - 96 q^{15} + 342 q^{16} + 308 q^{17} + 36 q^{18} + 32 q^{19} + 407 q^{20} + 12 q^{21} - 166 q^{22} + 53 q^{23} - 81 q^{24} + 746 q^{25} + 467 q^{26} - 594 q^{27} + 85 q^{28} + 634 q^{29} - 39 q^{30} - 163 q^{31} + 150 q^{32} - 183 q^{33} + 37 q^{34} + 782 q^{35} + 810 q^{36} - 2 q^{37} + 584 q^{38} - 12 q^{39} + 864 q^{40} + 1593 q^{41} - 399 q^{42} - 891 q^{43} + 2093 q^{44} + 288 q^{45} + 108 q^{46} + 1200 q^{47} - 1026 q^{48} + 2816 q^{49} + 4703 q^{50} - 924 q^{51} + 1866 q^{52} + 1182 q^{53} - 108 q^{54} + 970 q^{55} + 5362 q^{56} - 96 q^{57} + 1814 q^{58} + 2802 q^{59} - 1221 q^{60} + 2629 q^{61} + 2378 q^{62} - 36 q^{63} + 625 q^{64} + 2264 q^{65} + 498 q^{66} - 1074 q^{67} + 4383 q^{68} - 159 q^{69} + 4009 q^{70} + 3920 q^{71} + 243 q^{72} + 1086 q^{73} + 4904 q^{74} - 2238 q^{75} + 3750 q^{76} + 2966 q^{77} - 1401 q^{78} - 30 q^{79} + 7777 q^{80} + 1782 q^{81} + 2932 q^{82} + 1900 q^{83} - 255 q^{84} + 524 q^{85} + 3209 q^{86} - 1902 q^{87} - 100 q^{88} + 4488 q^{89} + 117 q^{90} - 818 q^{91} + 6210 q^{92} + 489 q^{93} + 3220 q^{94} + 3500 q^{95} - 450 q^{96} + 2178 q^{97} + 7629 q^{98} + 549 q^{99}+O(q^{100}) \) 22 * q + 4 * q^2 - 66 * q^3 + 90 * q^4 + 32 * q^5 - 12 * q^6 - 4 * q^7 + 27 * q^8 + 198 * q^9 + 13 * q^10 + 61 * q^11 - 270 * q^12 + 4 * q^13 + 133 * q^14 - 96 * q^15 + 342 * q^16 + 308 * q^17 + 36 * q^18 + 32 * q^19 + 407 * q^20 + 12 * q^21 - 166 * q^22 + 53 * q^23 - 81 * q^24 + 746 * q^25 + 467 * q^26 - 594 * q^27 + 85 * q^28 + 634 * q^29 - 39 * q^30 - 163 * q^31 + 150 * q^32 - 183 * q^33 + 37 * q^34 + 782 * q^35 + 810 * q^36 - 2 * q^37 + 584 * q^38 - 12 * q^39 + 864 * q^40 + 1593 * q^41 - 399 * q^42 - 891 * q^43 + 2093 * q^44 + 288 * q^45 + 108 * q^46 + 1200 * q^47 - 1026 * q^48 + 2816 * q^49 + 4703 * q^50 - 924 * q^51 + 1866 * q^52 + 1182 * q^53 - 108 * q^54 + 970 * q^55 + 5362 * q^56 - 96 * q^57 + 1814 * q^58 + 2802 * q^59 - 1221 * q^60 + 2629 * q^61 + 2378 * q^62 - 36 * q^63 + 625 * q^64 + 2264 * q^65 + 498 * q^66 - 1074 * q^67 + 4383 * q^68 - 159 * q^69 + 4009 * q^70 + 3920 * q^71 + 243 * q^72 + 1086 * q^73 + 4904 * q^74 - 2238 * q^75 + 3750 * q^76 + 2966 * q^77 - 1401 * q^78 - 30 * q^79 + 7777 * q^80 + 1782 * q^81 + 2932 * q^82 + 1900 * q^83 - 255 * q^84 + 524 * q^85 + 3209 * q^86 - 1902 * q^87 - 100 * q^88 + 4488 * q^89 + 117 * q^90 - 818 * q^91 + 6210 * q^92 + 489 * q^93 + 3220 * q^94 + 3500 * q^95 - 450 * q^96 + 2178 * q^97 + 7629 * q^98 + 549 * 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 $

$2$	−1.22585	−0.433405	−0.216702	−	0.976238i	$-0.569530\pi$
$2$	−1.22585	−0.433405	−0.216702	+	0.976238i	$0.569530\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−6.49728	−0.812160
$5$	−2.10116	−0.187934	−0.0939668	−	0.995575i	$-0.529955\pi$
$5$	−2.10116	−0.187934	−0.0939668	+	0.995575i	$0.529955\pi$
$6$	3.67756	0.250226
$7$	35.0092	1.89032	0.945159	−	0.326612i	$-0.105907\pi$
$7$	35.0092	1.89032	0.945159	+	0.326612i	$0.105907\pi$
$8$	17.7716	0.785399
$9$	9.00000	0.333333
$10$	2.57572	0.0814513
$11$	−11.3828	−0.312004	−0.156002	−	0.987757i	$-0.549861\pi$
$11$	−11.3828	−0.312004	−0.156002	+	0.987757i	$0.549861\pi$
$12$	19.4918	0.468901
$13$	−54.5332	−1.16345	−0.581723	−	0.813387i	$-0.697621\pi$
$13$	−54.5332	−1.16345	−0.581723	+	0.813387i	$0.697621\pi$
$14$	−42.9161	−0.819273
$15$	6.30348	0.108503
$16$	30.1929	0.471764
$17$	−9.39716	−0.134067	−0.0670337	−	0.997751i	$-0.521354\pi$
$17$	−9.39716	−0.134067	−0.0670337	+	0.997751i	$0.521354\pi$
$18$	−11.0327	−0.144468
$19$	−15.5321	−0.187543	−0.0937713	−	0.995594i	$-0.529892\pi$
$19$	−15.5321	−0.187543	−0.0937713	+	0.995594i	$0.529892\pi$
$20$	13.6518	0.152632
$21$	−105.027	−1.09138
$22$	13.9537	0.135224
$23$	183.958	1.66774	0.833869	−	0.551962i	$-0.186121\pi$
$23$	183.958	1.66774	0.833869	+	0.551962i	$0.186121\pi$
$24$	−53.3147	−0.453450
$25$	−120.585	−0.964681
$26$	66.8498	0.504243
$27$	−27.0000	−0.192450
$28$	−227.464	−1.53524
$29$	−139.496	−0.893232	−0.446616	−	0.894726i	$-0.647371\pi$
$29$	−139.496	−0.893232	−0.446616	+	0.894726i	$0.647371\pi$
$30$	−7.72715	−0.0470259
$31$	−236.609	−1.37084	−0.685422	−	0.728146i	$-0.740382\pi$
$31$	−236.609	−1.37084	−0.685422	+	0.728146i	$0.740382\pi$
$32$	−179.185	−0.989864
$33$	34.1485	0.180136
$34$	11.5195	0.0581055
$35$	−73.5599	−0.355254
$36$	−58.4755	−0.270720
$37$	156.703	0.696265	0.348132	−	0.937445i	$-0.386816\pi$
$37$	156.703	0.696265	0.348132	+	0.937445i	$0.386816\pi$
$38$	19.0401	0.0812819
$39$	163.600	0.671716
$40$	−37.3409	−0.147603
$41$	182.457	0.694999	0.347500	−	0.937680i	$-0.387031\pi$
$41$	182.457	0.694999	0.347500	+	0.937680i	$0.387031\pi$
$42$	128.748	0.473007
$43$	423.810	1.50303	0.751516	−	0.659715i	$-0.229323\pi$
$43$	423.810	1.50303	0.751516	+	0.659715i	$0.229323\pi$
$44$	73.9574	0.253398
$45$	−18.9104	−0.0626445
$46$	−225.506	−0.722806
$47$	439.359	1.36355	0.681777	−	0.731560i	$-0.261207\pi$
$47$	439.359	1.36355	0.681777	+	0.731560i	$0.261207\pi$
$48$	−90.5788	−0.272373
$49$	882.642	2.57330
$50$	147.820	0.418097
$51$	28.1915	0.0774039
$52$	354.318	0.944905
$53$	−497.712	−1.28993	−0.644963	−	0.764214i	$-0.723127\pi$
$53$	−497.712	−1.28993	−0.644963	+	0.764214i	$0.723127\pi$
$54$	33.0981	0.0834088
$55$	23.9171	0.0586361
$56$	622.167	1.48465
$57$	46.5963	0.108278
$58$	171.002	0.387131
$59$	216.123	0.476895	0.238448	−	0.971155i	$-0.423361\pi$
$59$	216.123	0.476895	0.238448	+	0.971155i	$0.423361\pi$
$60$	−40.9555	−0.0881222
$61$	−325.040	−0.682248	−0.341124	−	0.940018i	$-0.610808\pi$
$61$	−325.040	−0.682248	−0.341124	+	0.940018i	$0.610808\pi$
$62$	290.048	0.594131
$63$	315.082	0.630106
$64$	−21.8893	−0.0427526
$65$	114.583	0.218651
$66$	−41.8610	−0.0780718
$67$	505.112	0.921034	0.460517	−	0.887651i	$-0.347664\pi$
$67$	505.112	0.921034	0.460517	+	0.887651i	$0.347664\pi$
$68$	61.0560	0.108884
$69$	−551.875	−0.962870
$70$	90.1737	0.153969
$71$	993.848	1.66124	0.830620	−	0.556840i	$-0.187986\pi$
$71$	993.848	1.66124	0.830620	+	0.556840i	$0.187986\pi$
$72$	159.944	0.261800
$73$	370.314	0.593725	0.296863	−	0.954920i	$-0.404060\pi$
$73$	370.314	0.593725	0.296863	+	0.954920i	$0.404060\pi$
$74$	−192.095	−0.301765
$75$	361.755	0.556959
$76$	100.916	0.152315
$77$	−398.503	−0.589787
$78$	−200.549	−0.291125
$79$	−810.923	−1.15489	−0.577443	−	0.816431i	$-0.695949\pi$
$79$	−810.923	−1.15489	−0.577443	+	0.816431i	$0.695949\pi$
$80$	−63.4402	−0.0886604
$81$	81.0000	0.111111
$82$	−223.666	−0.301216
$83$	655.000	0.866212	0.433106	−	0.901343i	$-0.357418\pi$
$83$	655.000	0.866212	0.433106	+	0.901343i	$0.357418\pi$
$84$	682.393	0.886372
$85$	19.7450	0.0251958
$86$	−519.529	−0.651422
$87$	418.488	0.515708
$88$	−202.290	−0.245048
$89$	1077.51	1.28333	0.641663	−	0.766987i	$-0.278245\pi$
$89$	1077.51	1.28333	0.641663	+	0.766987i	$0.278245\pi$
$90$	23.1814	0.0271504
$91$	−1909.16	−2.19928
$92$	−1195.23	−1.35447
$93$	709.826	0.791458
$94$	−538.590	−0.590971
$95$	32.6355	0.0352455
$96$	537.554	0.571498
$97$	−844.529	−0.884010	−0.442005	−	0.897013i	$-0.645733\pi$
$97$	−844.529	−0.884010	−0.442005	+	0.897013i	$0.645733\pi$
$98$	−1081.99	−1.11528
$99$	−102.445	−0.104001
$100$	783.476	0.783476
$101$	−1026.10	−1.01090	−0.505450	−	0.862856i	$-0.668673\pi$
$101$	−1026.10	−1.01090	−0.505450	+	0.862856i	$0.668673\pi$
$102$	−34.5586	−0.0335472
$103$	1830.57	1.75118	0.875588	−	0.483059i	$-0.160474\pi$
$103$	1830.57	1.75118	0.875588	+	0.483059i	$0.160474\pi$
$104$	−969.140	−0.913770
$105$	220.680	0.205106
$106$	610.123	0.559060
$107$	1755.73	1.58629	0.793146	−	0.609032i	$-0.208442\pi$
$107$	1755.73	1.58629	0.793146	+	0.609032i	$0.208442\pi$
$108$	175.427	0.156300
$109$	−1030.83	−0.905834	−0.452917	−	0.891553i	$-0.649617\pi$
$109$	−1030.83	−0.905834	−0.452917	+	0.891553i	$0.649617\pi$
$110$	−29.3189	−0.0254132
$111$	−470.109	−0.401989
$112$	1057.03	0.891785
$113$	1418.97	1.18129	0.590645	−	0.806931i	$-0.298873\pi$
$113$	1418.97	1.18129	0.590645	+	0.806931i	$0.298873\pi$
$114$	−57.1203	−0.0469281
$115$	−386.526	−0.313424
$116$	906.344	0.725448
$117$	−490.799	−0.387815
$118$	−264.935	−0.206689
$119$	−328.987	−0.253430
$120$	112.023	0.0852185
$121$	−1201.43	−0.902653
$122$	398.451	0.295689
$123$	−547.371	−0.401258
$124$	1537.31	1.11335
$125$	516.014	0.369229
$126$	−386.245	−0.273091
$127$	1052.24	0.735205	0.367603	−	0.929983i	$-0.380179\pi$
$127$	1052.24	0.735205	0.367603	+	0.929983i	$0.380179\pi$
$128$	1460.31	1.00839
$129$	−1271.43	−0.867776
$130$	−140.462	−0.0947642
$131$	−352.936	−0.235390	−0.117695	−	0.993050i	$-0.537551\pi$
$131$	−352.936	−0.235390	−0.117695	+	0.993050i	$0.537551\pi$
$132$	−221.872	−0.146299
$133$	−543.766	−0.354515
$134$	−619.194	−0.399180
$135$	56.7313	0.0361678
$136$	−167.002	−0.105296
$137$	−1006.65	−0.627768	−0.313884	−	0.949461i	$-0.601630\pi$
$137$	−1006.65	−0.627768	−0.313884	+	0.949461i	$0.601630\pi$
$138$	676.519	0.417312
$139$	2906.88	1.77380	0.886900	−	0.461961i	$-0.152854\pi$
$139$	2906.88	1.77380	0.886900	+	0.461961i	$0.152854\pi$
$140$	477.939	0.288523
$141$	−1318.08	−0.787249
$142$	−1218.31	−0.719989
$143$	620.742	0.363000
$144$	271.736	0.157255
$145$	293.103	0.167868
$146$	−453.950	−0.257323
$147$	−2647.92	−1.48569
$148$	−1018.14	−0.565479
$149$	2556.24	1.40547	0.702735	−	0.711452i	$-0.251962\pi$
$149$	2556.24	1.40547	0.702735	+	0.711452i	$0.251962\pi$
$150$	−443.459	−0.241389
$151$	−3187.07	−1.71762	−0.858809	−	0.512296i	$-0.828795\pi$
$151$	−3187.07	−1.71762	−0.858809	+	0.512296i	$0.828795\pi$
$152$	−276.030	−0.147296
$153$	−84.5745	−0.0446892
$154$	488.507	0.255617
$155$	497.153	0.257628
$156$	−1062.95	−0.545541
$157$	−157.000	−0.0798087
$157$	−157.000	−0.0798087
$158$	994.073	0.500533
$159$	1493.14	0.744739
$160$	376.496	0.186029
$161$	6440.23	3.15256
$162$	−99.2942	−0.0481561
$163$	−2742.49	−1.31784	−0.658921	−	0.752212i	$-0.728987\pi$
$163$	−2742.49	−1.31784	−0.658921	+	0.752212i	$0.728987\pi$
$164$	−1185.47	−0.564451
$165$	−71.7514	−0.0338536
$166$	−802.934	−0.375420
$167$	3131.43	1.45100	0.725500	−	0.688222i	$-0.241608\pi$
$167$	3131.43	1.45100	0.725500	+	0.688222i	$0.241608\pi$
$168$	−1866.50	−0.857165
$169$	776.875	0.353607
$170$	−24.2044	−0.0109200
$171$	−139.789	−0.0625142
$172$	−2753.61	−1.22070
$173$	2636.88	1.15883	0.579416	−	0.815032i	$-0.303281\pi$
$173$	2636.88	1.15883	0.579416	+	0.815032i	$0.303281\pi$
$174$	−513.005	−0.223510
$175$	−4221.58	−1.82355
$176$	−343.681	−0.147193
$177$	−648.369	−0.275336
$178$	−1320.87	−0.556199
$179$	−1432.82	−0.598291	−0.299145	−	0.954208i	$-0.596702\pi$
$179$	−1432.82	−0.598291	−0.299145	+	0.954208i	$0.596702\pi$
$180$	122.867	0.0508774
$181$	−1028.51	−0.422368	−0.211184	−	0.977446i	$-0.567732\pi$
$181$	−1028.51	−0.422368	−0.211184	+	0.977446i	$0.567732\pi$
$182$	2340.36	0.953180
$183$	975.120	0.393896
$184$	3269.23	1.30984
$185$	−329.258	−0.130851
$186$	−870.143	−0.343022
$187$	106.966	0.0418296
$188$	−2854.64	−1.10742
$189$	−945.247	−0.363792
$190$	−40.0063	−0.0152756
$191$	−2249.54	−0.852203	−0.426102	−	0.904675i	$-0.640113\pi$
$191$	−2249.54	−0.852203	−0.426102	+	0.904675i	$0.640113\pi$
$192$	65.6680	0.0246832
$193$	1609.34	0.600223	0.300112	−	0.953904i	$-0.402976\pi$
$193$	1609.34	0.600223	0.300112	+	0.953904i	$0.402976\pi$
$194$	1035.27	0.383134
$195$	−343.749	−0.126238
$196$	−5734.77	−2.08993
$197$	2012.72	0.727921	0.363961	−	0.931414i	$-0.381424\pi$
$197$	2012.72	0.727921	0.363961	+	0.931414i	$0.381424\pi$
$198$	125.583	0.0450748
$199$	885.226	0.315337	0.157668	−	0.987492i	$-0.449602\pi$
$199$	885.226	0.315337	0.157668	+	0.987492i	$0.449602\pi$
$200$	−2142.98	−0.757660
$201$	−1515.34	−0.531759
$202$	1257.85	0.438129
$203$	−4883.64	−1.68849
$204$	−183.168	−0.0628644
$205$	−383.371	−0.130614
$206$	−2244.01	−0.758968
$207$	1655.63	0.555913
$208$	−1646.52	−0.548873
$209$	176.799	0.0585141
$210$	−270.521	−0.0888939
$211$	−398.548	−0.130034	−0.0650169	−	0.997884i	$-0.520710\pi$
$211$	−398.548	−0.130034	−0.0650169	+	0.997884i	$0.520710\pi$
$212$	3233.78	1.04763
$213$	−2981.54	−0.959117
$214$	−2152.27	−0.687506
$215$	−890.493	−0.282470
$216$	−479.832	−0.151150
$217$	−8283.48	−2.59133
$218$	1263.65	0.392593
$219$	−1110.94	−0.342787
$220$	−155.396	−0.0476219
$221$	512.458	0.155980
$222$	576.285	0.174224
$223$	5536.20	1.66247	0.831236	−	0.555920i	$-0.187634\pi$
$223$	5536.20	1.66247	0.831236	+	0.555920i	$0.187634\pi$
$224$	−6273.10	−1.87116
$225$	−1085.27	−0.321560
$226$	−1739.46	−0.511977
$227$	5303.38	1.55065	0.775325	−	0.631563i	$-0.217586\pi$
$227$	5303.38	1.55065	0.775325	+	0.631563i	$0.217586\pi$
$228$	−302.749	−0.0879389
$229$	3213.66	0.927357	0.463678	−	0.886004i	$-0.346529\pi$
$229$	3213.66	0.927357	0.463678	+	0.886004i	$0.346529\pi$
$230$	473.825	0.135840
$231$	1195.51	0.340514
$232$	−2479.06	−0.701544
$233$	2209.69	0.621294	0.310647	−	0.950525i	$-0.399454\pi$
$233$	2209.69	0.621294	0.310647	+	0.950525i	$0.399454\pi$
$234$	601.648	0.168081
$235$	−923.163	−0.256258
$236$	−1404.21	−0.387315
$237$	2432.77	0.666773
$238$	403.290	0.109838
$239$	5086.23	1.37657	0.688286	−	0.725440i	$-0.258364\pi$
$239$	5086.23	1.37657	0.688286	+	0.725440i	$0.258364\pi$
$240$	190.321	0.0511881
$241$	1393.90	0.372569	0.186285	−	0.982496i	$-0.440355\pi$
$241$	1393.90	0.372569	0.186285	+	0.982496i	$0.440355\pi$
$242$	1472.78	0.391214
$243$	−243.000	−0.0641500
$244$	2111.88	0.554094
$245$	−1854.57	−0.483609
$246$	670.997	0.173907
$247$	847.016	0.218196
$248$	−4204.90	−1.07666
$249$	−1965.00	−0.500107
$250$	−632.558	−0.160026
$251$	−1871.35	−0.470593	−0.235297	−	0.971924i	$-0.575606\pi$
$251$	−1871.35	−0.470593	−0.235297	+	0.971924i	$0.575606\pi$
$252$	−2047.18	−0.511747
$253$	−2093.97	−0.520342
$254$	−1289.89	−0.318642
$255$	−59.2349	−0.0145468
$256$	−1615.01	−0.394290
$257$	4269.63	1.03631	0.518156	−	0.855286i	$-0.326619\pi$
$257$	4269.63	1.03631	0.518156	+	0.855286i	$0.326619\pi$
$258$	1558.59	0.376098
$259$	5486.04	1.31616
$260$	−744.479	−0.177579
$261$	−1255.46	−0.297744
$262$	432.648	0.102019
$263$	−355.244	−0.0832900	−0.0416450	−	0.999132i	$-0.513260\pi$
$263$	−355.244	−0.0832900	−0.0416450	+	0.999132i	$0.513260\pi$
$264$	606.871	0.141479
$265$	1045.77	0.242420
$266$	666.578	0.153649
$267$	−3232.53	−0.740928
$268$	−3281.86	−0.748027
$269$	4685.00	1.06189	0.530947	−	0.847405i	$-0.321836\pi$
$269$	4685.00	1.06189	0.530947	+	0.847405i	$0.321836\pi$
$270$	−69.5443	−0.0156753
$271$	−2319.48	−0.519920	−0.259960	−	0.965619i	$-0.583709\pi$
$271$	−2319.48	−0.519920	−0.259960	+	0.965619i	$0.583709\pi$
$272$	−283.728	−0.0632483
$273$	5727.49	1.26976
$274$	1234.01	0.272078
$275$	1372.60	0.300985
$276$	3585.69	0.782004
$277$	−351.134	−0.0761646	−0.0380823	−	0.999275i	$-0.512125\pi$
$277$	−351.134	−0.0761646	−0.0380823	+	0.999275i	$0.512125\pi$
$278$	−3563.41	−0.768774
$279$	−2129.48	−0.456948
$280$	−1307.27	−0.279016
$281$	−5545.88	−1.17737	−0.588683	−	0.808364i	$-0.700353\pi$
$281$	−5545.88	−1.17737	−0.588683	+	0.808364i	$0.700353\pi$
$282$	1615.77	0.341197
$283$	6719.35	1.41139	0.705695	−	0.708515i	$-0.250635\pi$
$283$	6719.35	1.41139	0.705695	+	0.708515i	$0.250635\pi$
$284$	−6457.31	−1.34919
$285$	−97.9064	−0.0203490
$286$	−760.939	−0.157326
$287$	6387.66	1.31377
$288$	−1612.66	−0.329955
$289$	−4824.69	−0.982026
$290$	−359.302	−0.0727549
$291$	2533.59	0.510383
$292$	−2406.03	−0.482200
$293$	−8781.03	−1.75083	−0.875415	−	0.483373i	$-0.839412\pi$
$293$	−8781.03	−1.75083	−0.875415	+	0.483373i	$0.839412\pi$
$294$	3245.97	0.643907
$295$	−454.109	−0.0896246
$296$	2784.85	0.546846
$297$	307.336	0.0600453
$298$	−3133.57	−0.609138
$299$	−10031.9	−1.94032
$300$	−2350.43	−0.452340
$301$	14837.2	2.84121
$302$	3906.89	0.744424
$303$	3078.30	0.583643
$304$	−468.960	−0.0884759
$305$	682.961	0.128217
$306$	103.676	0.0193685
$307$	−8808.81	−1.63761	−0.818803	−	0.574074i	$-0.805362\pi$
$307$	−8808.81	−1.63761	−0.818803	+	0.574074i	$0.805362\pi$
$308$	2589.19	0.479002
$309$	−5491.70	−1.01104
$310$	−609.437	−0.111657
$311$	−2447.29	−0.446216	−0.223108	−	0.974794i	$-0.571620\pi$
$311$	−2447.29	−0.446216	−0.223108	+	0.974794i	$0.571620\pi$
$312$	2907.42	0.527565
$313$	−878.776	−0.158694	−0.0793472	−	0.996847i	$-0.525284\pi$
$313$	−878.776	−0.158694	−0.0793472	+	0.996847i	$0.525284\pi$
$314$	192.459	0.0345895
$315$	−662.039	−0.118418
$316$	5268.79	0.937952
$317$	−7283.36	−1.29045	−0.645227	−	0.763991i	$-0.723237\pi$
$317$	−7283.36	−1.29045	−0.645227	+	0.763991i	$0.723237\pi$
$318$	−1830.37	−0.322773
$319$	1587.86	0.278693
$320$	45.9930	0.00803465
$321$	−5267.20	−0.915846
$322$	−7894.79	−1.36633
$323$	145.958	0.0251434
$324$	−526.280	−0.0902400
$325$	6575.90	1.12235
$326$	3361.89	0.571160
$327$	3092.50	0.522983
$328$	3242.54	0.545852
$329$	15381.6	2.57755
$330$	87.9568	0.0146723
$331$	−482.642	−0.0801463	−0.0400731	−	0.999197i	$-0.512759\pi$
$331$	−482.642	−0.0801463	−0.0400731	+	0.999197i	$0.512759\pi$
$332$	−4255.72	−0.703503
$333$	1410.33	0.232088
$334$	−3838.67	−0.628871
$335$	−1061.32	−0.173093
$336$	−3171.09	−0.514872
$337$	1096.19	0.177191	0.0885957	−	0.996068i	$-0.471762\pi$
$337$	1096.19	0.177191	0.0885957	+	0.996068i	$0.471762\pi$
$338$	−952.335	−0.153255
$339$	−4256.92	−0.682019
$340$	−128.289	−0.0204630
$341$	2693.28	0.427710
$342$	171.361	0.0270940
$343$	18892.4	2.97403
$344$	7531.76	1.18048
$345$	1159.58	0.180955
$346$	−3232.42	−0.502243
$347$	−3360.55	−0.519895	−0.259948	−	0.965623i	$-0.583705\pi$
$347$	−3360.55	−0.519895	−0.259948	+	0.965623i	$0.583705\pi$
$348$	−2719.03	−0.418838
$349$	−3285.70	−0.503952	−0.251976	−	0.967733i	$-0.581080\pi$
$349$	−3285.70	−0.503952	−0.251976	+	0.967733i	$0.581080\pi$
$350$	5175.05	0.790337
$351$	1472.40	0.223905
$352$	2039.63	0.308842
$353$	10482.1	1.58047	0.790236	−	0.612803i	$-0.209958\pi$
$353$	10482.1	1.58047	0.790236	+	0.612803i	$0.209958\pi$
$354$	794.806	0.119332
$355$	−2088.23	−0.312203
$356$	−7000.89	−1.04227
$357$	986.960	0.146318
$358$	1756.43	0.259302
$359$	759.706	0.111687	0.0558437	−	0.998440i	$-0.482215\pi$
$359$	759.706	0.111687	0.0558437	+	0.998440i	$0.482215\pi$
$360$	−336.068	−0.0492009
$361$	−6617.75	−0.964828
$362$	1260.80	0.183056
$363$	3604.29	0.521147
$364$	12404.4	1.78617
$365$	−778.089	−0.111581
$366$	−1195.35	−0.170716
$367$	1482.82	0.210905	0.105453	−	0.994424i	$-0.466371\pi$
$367$	1482.82	0.210905	0.105453	+	0.994424i	$0.466371\pi$
$368$	5554.25	0.786780
$369$	1642.11	0.231666
$370$	403.622	0.0567117
$371$	−17424.5	−2.43837
$372$	−4611.94	−0.642790
$373$	246.654	0.0342394	0.0171197	−	0.999853i	$-0.494550\pi$
$373$	246.654	0.0342394	0.0171197	+	0.999853i	$0.494550\pi$
$374$	−131.125	−0.0181292
$375$	−1548.04	−0.213175
$376$	7808.09	1.07093
$377$	7607.16	1.03923
$378$	1158.74	0.157669
$379$	−144.337	−0.0195622	−0.00978110	−	0.999952i	$-0.503113\pi$
$379$	−144.337	−0.0195622	−0.00978110	+	0.999952i	$0.503113\pi$
$380$	−212.042	−0.0286250
$381$	−3156.72	−0.424471
$382$	2757.60	0.369349
$383$	−9445.99	−1.26023	−0.630114	−	0.776502i	$-0.716992\pi$
$383$	−9445.99	−1.26023	−0.630114	+	0.776502i	$0.716992\pi$
$384$	−4380.93	−0.582196
$385$	837.319	0.110841
$386$	−1972.82	−0.260140
$387$	3814.29	0.501011
$388$	5487.14	0.717957
$389$	−5993.23	−0.781153	−0.390577	−	0.920570i	$-0.627724\pi$
$389$	−5993.23	−0.781153	−0.390577	+	0.920570i	$0.627724\pi$
$390$	421.387	0.0547121
$391$	−1728.69	−0.223590
$392$	15685.9	2.02107
$393$	1058.81	0.135903
$394$	−2467.30	−0.315485
$395$	1703.88	0.217042
$396$	665.617	0.0844659
$397$	4626.85	0.584925	0.292462	−	0.956277i	$-0.405525\pi$
$397$	4626.85	0.584925	0.292462	+	0.956277i	$0.405525\pi$
$398$	−1085.16	−0.136668
$399$	1631.30	0.204679
$400$	−3640.82	−0.455102
$401$	8686.45	1.08175	0.540874	−	0.841104i	$-0.318094\pi$
$401$	8686.45	1.08175	0.540874	+	0.841104i	$0.318094\pi$
$402$	1857.58	0.230467
$403$	12903.0	1.59490
$404$	6666.87	0.821013
$405$	−170.194	−0.0208815
$406$	5986.62	0.731801
$407$	−1783.72	−0.217238
$408$	501.006	0.0607929
$409$	12232.1	1.47882	0.739411	−	0.673254i	$-0.235104\pi$
$409$	12232.1	1.47882	0.739411	+	0.673254i	$0.235104\pi$
$410$	469.957	0.0566086
$411$	3019.96	0.362442
$412$	−11893.7	−1.42223
$413$	7566.28	0.901483
$414$	−2029.56	−0.240935
$415$	−1376.26	−0.162790
$416$	9771.51	1.15165
$417$	−8720.64	−1.02410
$418$	−216.730	−0.0253603
$419$	1583.17	0.184590	0.0922948	−	0.995732i	$-0.470580\pi$
$419$	1583.17	0.184590	0.0922948	+	0.995732i	$0.470580\pi$
$420$	−1433.82	−0.166579
$421$	−12749.4	−1.47593	−0.737967	−	0.674837i	$-0.764214\pi$
$421$	−12749.4	−1.47593	−0.737967	+	0.674837i	$0.764214\pi$
$422$	488.561	0.0563573
$423$	3954.23	0.454518
$424$	−8845.12	−1.01311
$425$	1133.16	0.129332
$426$	3654.94	0.415686
$427$	−11379.4	−1.28966
$428$	−11407.5	−1.28832
$429$	−1862.23	−0.209578
$430$	1091.61	0.122424
$431$	−10142.2	−1.13348	−0.566742	−	0.823895i	$-0.691796\pi$
$431$	−10142.2	−1.13348	−0.566742	+	0.823895i	$0.691796\pi$
$432$	−815.209	−0.0907911
$433$	−2042.43	−0.226681	−0.113340	−	0.993556i	$-0.536155\pi$
$433$	−2042.43	−0.226681	−0.113340	+	0.993556i	$0.536155\pi$
$434$	10154.3	1.12310
$435$	−879.310	−0.0969188
$436$	6697.61	0.735682
$437$	−2857.26	−0.312772
$438$	1361.85	0.148566
$439$	868.305	0.0944007	0.0472004	−	0.998885i	$-0.484970\pi$
$439$	868.305	0.0944007	0.0472004	+	0.998885i	$0.484970\pi$
$440$	425.045	0.0460527
$441$	7943.77	0.857766
$442$	−628.198	−0.0676026
$443$	4635.38	0.497141	0.248571	−	0.968614i	$-0.420039\pi$
$443$	4635.38	0.497141	0.248571	+	0.968614i	$0.420039\pi$
$444$	3054.43	0.326479
$445$	−2264.02	−0.241180
$446$	−6786.57	−0.720523
$447$	−7668.71	−0.811449
$448$	−766.328	−0.0808160
$449$	7932.63	0.833772	0.416886	−	0.908959i	$-0.363121\pi$
$449$	7932.63	0.833772	0.416886	+	0.908959i	$0.363121\pi$
$450$	1330.38	0.139366
$451$	−2076.87	−0.216843
$452$	−9219.48	−0.959398
$453$	9561.22	0.991667
$454$	−6501.16	−0.672059
$455$	4011.46	0.413319
$456$	828.089	0.0850413
$457$	7160.20	0.732911	0.366455	−	0.930436i	$-0.380571\pi$
$457$	7160.20	0.732911	0.366455	+	0.930436i	$0.380571\pi$
$458$	−3939.48	−0.401921
$459$	253.723	0.0258013
$460$	2511.37	0.254551
$461$	16445.7	1.66151	0.830753	−	0.556641i	$-0.187910\pi$
$461$	16445.7	1.66151	0.830753	+	0.556641i	$0.187910\pi$
$462$	−1465.52	−0.147580
$463$	10663.0	1.07031	0.535154	−	0.844754i	$-0.320253\pi$
$463$	10663.0	1.07031	0.535154	+	0.844754i	$0.320253\pi$
$464$	−4211.79	−0.421395
$465$	−1491.46	−0.148741
$466$	−2708.76	−0.269272
$467$	−1397.49	−0.138476	−0.0692378	−	0.997600i	$-0.522057\pi$
$467$	−1397.49	−0.138476	−0.0692378	+	0.997600i	$0.522057\pi$
$468$	3188.86	0.314968
$469$	17683.6	1.74105
$470$	1131.66	0.111063
$471$	471.000	0.0460776
$472$	3840.84	0.374553
$473$	−4824.15	−0.468953
$474$	−2982.22	−0.288983
$475$	1872.94	0.180919
$476$	2137.52	0.205826
$477$	−4479.41	−0.429975
$478$	−6234.97	−0.596613
$479$	−10475.9	−0.999279	−0.499639	−	0.866234i	$-0.666534\pi$
$479$	−10475.9	−0.999279	−0.499639	+	0.866234i	$0.666534\pi$
$480$	−1129.49	−0.107404
$481$	−8545.52	−0.810067
$482$	−1708.72	−0.161473
$483$	−19320.7	−1.82013
$484$	7806.04	0.733099
$485$	1774.49	0.166135
$486$	297.883	0.0278029
$487$	−6835.80	−0.636056	−0.318028	−	0.948081i	$-0.603021\pi$
$487$	−6835.80	−0.636056	−0.318028	+	0.948081i	$0.603021\pi$
$488$	−5776.46	−0.535837
$489$	8227.47	0.760857
$490$	2273.43	0.209599
$491$	8578.17	0.788447	0.394223	−	0.919015i	$-0.371014\pi$
$491$	8578.17	0.788447	0.394223	+	0.919015i	$0.371014\pi$
$492$	3556.42	0.325886
$493$	1310.87	0.119753
$494$	−1038.32	−0.0945671
$495$	215.254	0.0195454
$496$	−7143.91	−0.646716
$497$	34793.8	3.14027
$498$	2408.80	0.216749
$499$	−20727.7	−1.85952	−0.929761	−	0.368165i	$-0.879986\pi$
$499$	−20727.7	−1.85952	−0.929761	+	0.368165i	$0.879986\pi$
$500$	−3352.69	−0.299873
$501$	−9394.28	−0.837736
$502$	2294.01	0.203957
$503$	4641.01	0.411396	0.205698	−	0.978616i	$-0.434054\pi$
$503$	4641.01	0.411396	0.205698	+	0.978616i	$0.434054\pi$
$504$	5599.50	0.494884
$505$	2156.00	0.189982
$506$	2566.90	0.225519
$507$	−2330.62	−0.204155
$508$	−6836.69	−0.597104
$509$	−20483.4	−1.78371	−0.891857	−	0.452318i	$-0.850597\pi$
$509$	−20483.4	−1.78371	−0.891857	+	0.452318i	$0.850597\pi$
$510$	72.6133	0.00630465
$511$	12964.4	1.12233
$512$	−9702.71	−0.837506
$513$	419.367	0.0360926
$514$	−5233.94	−0.449142
$515$	−3846.31	−0.329105
$516$	8260.84	0.704773
$517$	−5001.14	−0.425435
$518$	−6725.08	−0.570431
$519$	−7910.63	−0.669052
$520$	2036.32	0.171728
$521$	3292.45	0.276861	0.138431	−	0.990372i	$-0.455794\pi$
$521$	3292.45	0.276861	0.138431	+	0.990372i	$0.455794\pi$
$522$	1539.01	0.129044
$523$	−8793.14	−0.735176	−0.367588	−	0.929989i	$-0.619816\pi$
$523$	−8793.14	−0.735176	−0.367588	+	0.929989i	$0.619816\pi$
$524$	2293.12	0.191175
$525$	12664.8	1.05283
$526$	435.477	0.0360983
$527$	2223.45	0.183786
$528$	1031.04	0.0849817
$529$	21673.7	1.78135
$530$	−1281.97	−0.105066
$531$	1945.11	0.158965
$532$	3533.00	0.287923
$533$	−9949.97	−0.808595
$534$	3962.61	0.321122
$535$	−3689.08	−0.298117
$536$	8976.62	0.723379
$537$	4298.46	0.345423
$538$	−5743.13	−0.460230
$539$	−10047.0	−0.802881
$540$	−368.600	−0.0293741
$541$	21262.3	1.68972	0.844858	−	0.534991i	$-0.179685\pi$
$541$	21262.3	1.68972	0.844858	+	0.534991i	$0.179685\pi$
$542$	2843.34	0.225336
$543$	3085.53	0.243854
$544$	1683.83	0.132709
$545$	2165.95	0.170237
$546$	−7021.07	−0.550319
$547$	−14327.2	−1.11990	−0.559950	−	0.828526i	$-0.689180\pi$
$547$	−14327.2	−1.11990	−0.559950	+	0.828526i	$0.689180\pi$
$548$	6540.52	0.509849
$549$	−2925.36	−0.227416
$550$	−1682.61	−0.130448
$551$	2166.67	0.167519
$552$	−9807.68	−0.756237
$553$	−28389.7	−2.18310
$554$	430.439	0.0330101
$555$	987.774	0.0755471
$556$	−18886.8	−1.44061
$557$	−6091.49	−0.463384	−0.231692	−	0.972789i	$-0.574426\pi$
$557$	−6091.49	−0.463384	−0.231692	+	0.972789i	$0.574426\pi$
$558$	2610.43	0.198044
$559$	−23111.7	−1.74870
$560$	−2220.99	−0.167596
$561$	−320.899	−0.0241504
$562$	6798.44	0.510276
$563$	−25818.3	−1.93270	−0.966352	−	0.257222i	$-0.917193\pi$
$563$	−25818.3	−1.93270	−0.966352	+	0.257222i	$0.917193\pi$
$564$	8563.91	0.639372
$565$	−2981.49	−0.222004
$566$	−8236.94	−0.611704
$567$	2835.74	0.210035
$568$	17662.2	1.30474
$569$	5738.15	0.422769	0.211385	−	0.977403i	$-0.432203\pi$
$569$	5738.15	0.422769	0.211385	+	0.977403i	$0.432203\pi$
$570$	120.019	0.00881937
$571$	6970.19	0.510846	0.255423	−	0.966829i	$-0.417785\pi$
$571$	6970.19	0.510846	0.255423	+	0.966829i	$0.417785\pi$
$572$	−4033.14	−0.294815
$573$	6748.61	0.492020
$574$	−7830.34	−0.569394
$575$	−22182.7	−1.60884
$576$	−197.004	−0.0142509
$577$	−4842.66	−0.349398	−0.174699	−	0.984622i	$-0.555895\pi$
$577$	−4842.66	−0.349398	−0.174699	+	0.984622i	$0.555895\pi$
$578$	5914.37	0.425615
$579$	−4828.03	−0.346539
$580$	−1904.38	−0.136336
$581$	22931.0	1.63741
$582$	−3105.81	−0.221203
$583$	5665.37	0.402462
$584$	6581.05	0.466311
$585$	1031.25	0.0728835
$586$	10764.3	0.758818
$587$	−10114.4	−0.711183	−0.355591	−	0.934641i	$-0.615721\pi$
$587$	−10114.4	−0.711183	−0.355591	+	0.934641i	$0.615721\pi$
$588$	17204.3	1.20662
$589$	3675.03	0.257092
$590$	556.671	0.0388437
$591$	−6038.16	−0.420265
$592$	4731.32	0.328473
$593$	−2202.51	−0.152523	−0.0762617	−	0.997088i	$-0.524298\pi$
$593$	−2202.51	−0.152523	−0.0762617	+	0.997088i	$0.524298\pi$
$594$	−376.749	−0.0260239
$595$	691.254	0.0476280
$596$	−16608.6	−1.14147
$597$	−2655.68	−0.182060
$598$	12297.6	0.840946
$599$	21001.7	1.43256	0.716281	−	0.697812i	$-0.245843\pi$
$599$	21001.7	1.43256	0.716281	+	0.697812i	$0.245843\pi$
$600$	6428.95	0.437435
$601$	−1491.65	−0.101241	−0.0506205	−	0.998718i	$-0.516120\pi$
$601$	−1491.65	−0.101241	−0.0506205	+	0.998718i	$0.516120\pi$
$602$	−18188.3	−1.23139
$603$	4546.01	0.307011
$604$	20707.3	1.39498
$605$	2524.40	0.169639
$606$	−3773.55	−0.252954
$607$	3233.17	0.216195	0.108097	−	0.994140i	$-0.465524\pi$
$607$	3233.17	0.216195	0.108097	+	0.994140i	$0.465524\pi$
$608$	2783.11	0.185642
$609$	14650.9	0.974852
$610$	−837.211	−0.0555700
$611$	−23959.7	−1.58642
$612$	549.504	0.0362948
$613$	17686.7	1.16535	0.582676	−	0.812704i	$-0.302006\pi$
$613$	17686.7	1.16535	0.582676	+	0.812704i	$0.302006\pi$
$614$	10798.3	0.709747
$615$	1150.11	0.0754099
$616$	−7082.02	−0.463218
$617$	−25478.4	−1.66244	−0.831218	−	0.555946i	$-0.812356\pi$
$617$	−25478.4	−1.66244	−0.831218	+	0.555946i	$0.812356\pi$
$618$	6732.02	0.438190
$619$	5041.25	0.327342	0.163671	−	0.986515i	$-0.447666\pi$
$619$	5041.25	0.327342	0.163671	+	0.986515i	$0.447666\pi$
$620$	−3230.14	−0.209235
$621$	−4966.88	−0.320957
$622$	3000.02	0.193392
$623$	37722.8	2.42589
$624$	4939.56	0.316892
$625$	13988.9	0.895290
$626$	1077.25	0.0687789
$627$	−530.397	−0.0337832
$628$	1020.07	0.0648174
$629$	−1472.56	−0.0933464
$630$	811.563	0.0513229
$631$	−9004.01	−0.568057	−0.284029	−	0.958816i	$-0.591671\pi$
$631$	−9004.01	−0.568057	−0.284029	+	0.958816i	$0.591671\pi$
$632$	−14411.4	−0.907046
$633$	1195.64	0.0750751
$634$	8928.33	0.559289
$635$	−2210.92	−0.138170
$636$	−9701.33	−0.604847
$637$	−48133.3	−2.99390
$638$	−1946.48	−0.120787
$639$	8944.63	0.553746
$640$	−3068.34	−0.189511
$641$	−15633.8	−0.963338	−0.481669	−	0.876353i	$-0.659969\pi$
$641$	−15633.8	−0.963338	−0.481669	+	0.876353i	$0.659969\pi$
$642$	6456.82	0.396932
$643$	19495.8	1.19571	0.597853	−	0.801605i	$-0.296020\pi$
$643$	19495.8	1.19571	0.597853	+	0.801605i	$0.296020\pi$
$644$	−41844.0	−2.56038
$645$	2671.48	0.163084
$646$	−178.923	−0.0108973
$647$	−4841.85	−0.294209	−0.147104	−	0.989121i	$-0.546995\pi$
$647$	−4841.85	−0.294209	−0.147104	+	0.989121i	$0.546995\pi$
$648$	1439.50	0.0872666
$649$	−2460.09	−0.148793
$650$	−8061.09	−0.486434
$651$	24850.4	1.49611
$652$	17818.7	1.07030
$653$	−14689.2	−0.880296	−0.440148	−	0.897925i	$-0.645074\pi$
$653$	−14689.2	−0.880296	−0.440148	+	0.897925i	$0.645074\pi$
$654$	−3790.95	−0.226664
$655$	741.575	0.0442377
$656$	5508.91	0.327876
$657$	3332.82	0.197908
$658$	−18855.6	−1.11712
$659$	798.289	0.0471881	0.0235940	−	0.999722i	$-0.492489\pi$
$659$	798.289	0.0471881	0.0235940	+	0.999722i	$0.492489\pi$
$660$	466.189	0.0274945
$661$	−4387.58	−0.258180	−0.129090	−	0.991633i	$-0.541206\pi$
$661$	−4387.58	−0.258180	−0.129090	+	0.991633i	$0.541206\pi$
$662$	591.649	0.0347358
$663$	−1537.37	−0.0900553
$664$	11640.4	0.680322
$665$	1142.54	0.0666253
$666$	−1728.85	−0.100588
$667$	−25661.5	−1.48968
$668$	−20345.8	−1.17844
$669$	−16608.6	−0.959829
$670$	1301.03	0.0750194
$671$	3699.87	0.212864
$672$	18819.3	1.08031
$673$	−29802.3	−1.70698	−0.853488	−	0.521113i	$-0.825517\pi$
$673$	−29802.3	−1.70698	−0.853488	+	0.521113i	$0.825517\pi$
$674$	−1343.77	−0.0767957
$675$	3255.80	0.185653
$676$	−5047.58	−0.287186
$677$	−28424.8	−1.61367	−0.806833	−	0.590780i	$-0.798820\pi$
$677$	−28424.8	−1.61367	−0.806833	+	0.590780i	$0.798820\pi$
$678$	5218.37	0.295590
$679$	−29566.3	−1.67106
$680$	350.898	0.0197887
$681$	−15910.1	−0.895268
$682$	−3301.56	−0.185371
$683$	24960.1	1.39835	0.699175	−	0.714950i	$-0.253551\pi$
$683$	24960.1	1.39835	0.699175	+	0.714950i	$0.253551\pi$
$684$	908.248	0.0507715
$685$	2115.14	0.117979
$686$	−23159.3	−1.28896
$687$	−9640.99	−0.535410
$688$	12796.1	0.709077
$689$	27141.9	1.50076
$690$	−1421.47	−0.0784270
$691$	12571.5	0.692100	0.346050	−	0.938216i	$-0.387523\pi$
$691$	12571.5	0.692100	0.346050	+	0.938216i	$0.387523\pi$
$692$	−17132.5	−0.941157
$693$	−3586.53	−0.196596
$694$	4119.54	0.225325
$695$	−6107.82	−0.333357
$696$	7437.18	0.405037
$697$	−1714.58	−0.0931768
$698$	4027.79	0.218415
$699$	−6629.07	−0.358704
$700$	27428.8	1.48102
$701$	12554.8	0.676446	0.338223	−	0.941066i	$-0.390174\pi$
$701$	12554.8	0.676446	0.338223	+	0.941066i	$0.390174\pi$
$702$	−1804.94	−0.0970417
$703$	−2433.93	−0.130579
$704$	249.162	0.0133390
$705$	2769.49	0.147950
$706$	−12849.5	−0.684984
$707$	−35922.9	−1.91092
$708$	4212.64	0.223617
$709$	−24665.7	−1.30654	−0.653271	−	0.757124i	$-0.726604\pi$
$709$	−24665.7	−1.30654	−0.653271	+	0.757124i	$0.726604\pi$
$710$	2559.87	0.135310
$711$	−7298.30	−0.384962
$712$	19149.0	1.00792
$713$	−43526.2	−2.28621
$714$	−1209.87	−0.0634149
$715$	−1304.28	−0.0682200
$716$	9309.44	0.485908
$717$	−15258.7	−0.794764
$718$	−931.289	−0.0484058
$719$	−6846.01	−0.355095	−0.177547	−	0.984112i	$-0.556816\pi$
$719$	−6846.01	−0.355095	−0.177547	+	0.984112i	$0.556816\pi$
$720$	−570.962	−0.0295535
$721$	64086.6	3.31028
$722$	8112.40	0.418161
$723$	−4181.71	−0.215103
$724$	6682.52	0.343030
$725$	16821.1	0.861684
$726$	−4418.34	−0.225868
$727$	2281.14	0.116372	0.0581861	−	0.998306i	$-0.481468\pi$
$727$	2281.14	0.116372	0.0581861	+	0.998306i	$0.481468\pi$
$728$	−33928.8	−1.72731
$729$	729.000	0.0370370
$730$	953.823	0.0483597
$731$	−3982.61	−0.201508
$732$	−6335.63	−0.319906
$733$	−1630.09	−0.0821404	−0.0410702	−	0.999156i	$-0.513077\pi$
$733$	−1630.09	−0.0821404	−0.0410702	+	0.999156i	$0.513077\pi$
$734$	−1817.71	−0.0914075
$735$	5563.72	0.279212
$736$	−32962.5	−1.65083
$737$	−5749.60	−0.287367
$738$	−2012.99	−0.100405
$739$	−8910.21	−0.443528	−0.221764	−	0.975100i	$-0.571181\pi$
$739$	−8910.21	−0.443528	−0.221764	+	0.975100i	$0.571181\pi$
$740$	2139.28	0.106272
$741$	−2541.05	−0.125975
$742$	21359.9	1.05680
$743$	−23621.8	−1.16635	−0.583176	−	0.812346i	$-0.698190\pi$
$743$	−23621.8	−1.16635	−0.583176	+	0.812346i	$0.698190\pi$
$744$	12614.7	0.621610
$745$	−5371.06	−0.264135
$746$	−302.362	−0.0148395
$747$	5895.00	0.288737
$748$	−694.990	−0.0339724
$749$	61466.8	2.99859
$750$	1897.67	0.0923910
$751$	24419.0	1.18650	0.593250	−	0.805019i	$-0.297845\pi$
$751$	24419.0	1.18650	0.593250	+	0.805019i	$0.297845\pi$
$752$	13265.5	0.643277
$753$	5614.06	0.271697
$754$	−9325.27	−0.450406
$755$	6696.55	0.322798
$756$	6141.54	0.295457
$757$	10441.1	0.501304	0.250652	−	0.968077i	$-0.419355\pi$
$757$	10441.1	0.501304	0.250652	+	0.968077i	$0.419355\pi$
$758$	176.936	0.00847835
$759$	6281.90	0.300420
$760$	579.983	0.0276818
$761$	11363.2	0.541284	0.270642	−	0.962680i	$-0.412764\pi$
$761$	11363.2	0.541284	0.270642	+	0.962680i	$0.412764\pi$
$762$	3869.67	0.183968
$763$	−36088.6	−1.71231
$764$	14615.9	0.692126
$765$	177.705	0.00839859
$766$	11579.4	0.546189
$767$	−11785.9	−0.554842
$768$	4845.03	0.227643
$769$	3558.77	0.166882	0.0834411	−	0.996513i	$-0.473409\pi$
$769$	3558.77	0.166882	0.0834411	+	0.996513i	$0.473409\pi$
$770$	−1026.43	−0.0480390
$771$	−12808.9	−0.598314
$772$	−10456.4	−0.487477
$773$	29595.4	1.37706	0.688532	−	0.725206i	$-0.258255\pi$
$773$	29595.4	1.37706	0.688532	+	0.725206i	$0.258255\pi$
$774$	−4675.76	−0.217141
$775$	28531.5	1.32243
$776$	−15008.6	−0.694300
$777$	−16458.1	−0.759886
$778$	7346.82	0.338556
$779$	−2833.94	−0.130342
$780$	2233.44	0.102525
$781$	−11312.8	−0.518314
$782$	2119.12	0.0969048
$783$	3766.39	0.171903
$784$	26649.5	1.21399
$785$	329.882	0.0149987
$786$	−1297.94	−0.0589009
$787$	−42507.3	−1.92531	−0.962656	−	0.270727i	$-0.912736\pi$
$787$	−42507.3	−1.92531	−0.962656	+	0.270727i	$0.912736\pi$
$788$	−13077.2	−0.591189
$789$	1065.73	0.0480875
$790$	−2088.71	−0.0940669
$791$	49677.1	2.23301
$792$	−1820.61	−0.0816827
$793$	17725.5	0.793758
$794$	−5671.85	−0.253509
$795$	−3137.32	−0.139961
$796$	−5751.56	−0.256104
$797$	−2889.95	−0.128441	−0.0642204	−	0.997936i	$-0.520456\pi$
$797$	−2889.95	−0.128441	−0.0642204	+	0.997936i	$0.520456\pi$
$798$	−1999.73	−0.0887090
$799$	−4128.73	−0.182808
$800$	21607.0	0.954903
$801$	9697.60	0.427775
$802$	−10648.3	−0.468834
$803$	−4215.21	−0.185245
$804$	9845.57	0.431874
$805$	−13532.0	−0.592471
$806$	−15817.2	−0.691239
$807$	−14055.0	−0.613085
$808$	−18235.4	−0.793960
$809$	−28947.4	−1.25802	−0.629009	−	0.777398i	$-0.716539\pi$
$809$	−28947.4	−1.25802	−0.629009	+	0.777398i	$0.716539\pi$
$810$	208.633	0.00905015
$811$	390.359	0.0169018	0.00845089	−	0.999964i	$-0.497310\pi$
$811$	390.359	0.0169018	0.00845089	+	0.999964i	$0.497310\pi$
$812$	31730.4	1.37133
$813$	6958.44	0.300176
$814$	2186.58	0.0941519
$815$	5762.41	0.247667
$816$	851.184	0.0365164
$817$	−6582.66	−0.281883
$818$	−14994.8	−0.640929
$819$	−17182.5	−0.733094
$820$	2490.87	0.106079
$821$	36351.3	1.54527	0.772637	−	0.634849i	$-0.218938\pi$
$821$	36351.3	1.54527	0.772637	+	0.634849i	$0.218938\pi$
$822$	−3702.03	−0.157084
$823$	−22892.1	−0.969585	−0.484792	−	0.874629i	$-0.661105\pi$
$823$	−22892.1	−0.969585	−0.484792	+	0.874629i	$0.661105\pi$
$824$	32532.0	1.37537
$825$	−4117.80	−0.173774
$826$	−9275.16	−0.390707
$827$	−12195.7	−0.512801	−0.256400	−	0.966571i	$-0.582537\pi$
$827$	−12195.7	−0.512801	−0.256400	+	0.966571i	$0.582537\pi$
$828$	−10757.1	−0.451490
$829$	16451.3	0.689235	0.344618	−	0.938743i	$-0.388009\pi$
$829$	16451.3	0.689235	0.344618	+	0.938743i	$0.388009\pi$
$830$	1687.09	0.0705541
$831$	1053.40	0.0439736
$832$	1193.70	0.0497404
$833$	−8294.33	−0.344996
$834$	10690.2	0.443852
$835$	−6579.63	−0.272692
$836$	−1148.71	−0.0475229
$837$	6388.44	0.263819
$838$	−1940.74	−0.0800021
$839$	5020.47	0.206586	0.103293	−	0.994651i	$-0.467062\pi$
$839$	5020.47	0.206586	0.103293	+	0.994651i	$0.467062\pi$
$840$	3921.82	0.161090
$841$	−4929.89	−0.202136
$842$	15628.9	0.639677
$843$	16637.7	0.679752
$844$	2589.48	0.105608
$845$	−1632.34	−0.0664546
$846$	−4847.31	−0.196990
$847$	−42061.1	−1.70630
$848$	−15027.4	−0.608541
$849$	−20158.0	−0.814867
$850$	−1389.09	−0.0560533
$851$	28826.8	1.16119
$852$	19371.9	0.778957
$853$	27607.8	1.10818	0.554088	−	0.832458i	$-0.313067\pi$
$853$	27607.8	1.10818	0.554088	+	0.832458i	$0.313067\pi$
$854$	13949.5	0.558947
$855$	293.719	0.0117485
$856$	31202.1	1.24587
$857$	−49487.3	−1.97253	−0.986263	−	0.165184i	$-0.947178\pi$
$857$	−49487.3	−1.97253	−0.986263	+	0.165184i	$0.947178\pi$
$858$	2282.82	0.0908323
$859$	22552.5	0.895788	0.447894	−	0.894087i	$-0.352174\pi$
$859$	22552.5	0.895788	0.447894	+	0.894087i	$0.352174\pi$
$860$	5785.78	0.229411
$861$	−19163.0	−0.758505
$862$	12432.8	0.491258
$863$	−14795.1	−0.583580	−0.291790	−	0.956482i	$-0.594251\pi$
$863$	−14795.1	−0.583580	−0.291790	+	0.956482i	$0.594251\pi$
$864$	4837.98	0.190499
$865$	−5540.50	−0.217783
$866$	2503.72	0.0982446
$867$	14474.1	0.566973
$868$	53820.1	2.10458
$869$	9230.59	0.360329
$870$	1077.91	0.0420051
$871$	−27545.4	−1.07157
$872$	−18319.5	−0.711441
$873$	−7600.76	−0.294670
$874$	3502.59	0.135557
$875$	18065.2	0.697961
$876$	7218.10	0.278398
$877$	21331.2	0.821327	0.410663	−	0.911787i	$-0.365297\pi$
$877$	21331.2	0.821327	0.410663	+	0.911787i	$0.365297\pi$
$878$	−1064.41	−0.0409137
$879$	26343.1	1.01084
$880$	722.128	0.0276624
$881$	−39773.0	−1.52098	−0.760491	−	0.649348i	$-0.775042\pi$
$881$	−39773.0	−1.52098	−0.760491	+	0.649348i	$0.775042\pi$
$882$	−9737.91	−0.371760
$883$	2492.14	0.0949797	0.0474898	−	0.998872i	$-0.484878\pi$
$883$	2492.14	0.0949797	0.0474898	+	0.998872i	$0.484878\pi$
$884$	−3329.58	−0.126681
$885$	1362.33	0.0517448
$886$	−5682.30	−0.215463
$887$	8725.44	0.330295	0.165147	−	0.986269i	$-0.447190\pi$
$887$	8725.44	0.330295	0.165147	+	0.986269i	$0.447190\pi$
$888$	−8354.56	−0.315721
$889$	36838.0	1.38977
$890$	2775.36	0.104529
$891$	−922.008	−0.0346672
$892$	−35970.2	−1.35019
$893$	−6824.17	−0.255725
$894$	9400.72	0.351686
$895$	3010.59	0.112439
$896$	51124.2	1.90618
$897$	30095.6	1.12025
$898$	−9724.24	−0.361361
$899$	33006.0	1.22448
$900$	7051.28	0.261159
$901$	4677.08	0.172937
$902$	2545.94	0.0939808
$903$	−44511.7	−1.64037
$904$	25217.4	0.927785
$905$	2161.07	0.0793771
$906$	−11720.7	−0.429793
$907$	−16648.7	−0.609495	−0.304748	−	0.952433i	$-0.598572\pi$
$907$	−16648.7	−0.609495	−0.304748	+	0.952433i	$0.598572\pi$
$908$	−34457.5	−1.25938
$909$	−9234.91	−0.336967
$910$	−4917.46	−0.179134
$911$	11559.8	0.420409	0.210205	−	0.977657i	$-0.432587\pi$
$911$	11559.8	0.420409	0.210205	+	0.977657i	$0.432587\pi$
$912$	1406.88	0.0510816
$913$	−7455.74	−0.270262
$914$	−8777.36	−0.317647
$915$	−2048.88	−0.0740262
$916$	−20880.1	−0.753162
$917$	−12356.0	−0.444962
$918$	−311.028	−0.0111824
$919$	−21327.4	−0.765534	−0.382767	−	0.923845i	$-0.625029\pi$
$919$	−21327.4	−0.765534	−0.382767	+	0.923845i	$0.625029\pi$
$920$	−6869.17	−0.246163
$921$	26426.4	0.945473
$922$	−20160.1	−0.720105
$923$	−54197.7	−1.93276
$924$	−7767.56	−0.276552
$925$	−18896.0	−0.671673
$926$	−13071.3	−0.463877
$927$	16475.1	0.583725
$928$	24995.5	0.884179
$929$	14863.5	0.524927	0.262463	−	0.964942i	$-0.415465\pi$
$929$	14863.5	0.524927	0.262463	+	0.964942i	$0.415465\pi$
$930$	1828.31	0.0644653
$931$	−13709.3	−0.482603
$932$	−14357.0	−0.504590
$933$	7341.87	0.257623
$934$	1713.12	0.0600160
$935$	−224.753	−0.00786119
$936$	−8722.26	−0.304590
$937$	4266.37	0.148747	0.0743737	−	0.997230i	$-0.476304\pi$
$937$	4266.37	0.148747	0.0743737	+	0.997230i	$0.476304\pi$
$938$	−21677.5	−0.754578
$939$	2636.33	0.0916223
$940$	5998.05	0.208122
$941$	−21228.8	−0.735430	−0.367715	−	0.929939i	$-0.619860\pi$
$941$	−21228.8	−0.735430	−0.367715	+	0.929939i	$0.619860\pi$
$942$	−577.377	−0.0199702
$943$	33564.5	1.15908
$944$	6525.38	0.224982
$945$	1986.12	0.0683687
$946$	5913.71	0.203246
$947$	−23570.5	−0.808806	−0.404403	−	0.914581i	$-0.632521\pi$
$947$	−23570.5	−0.808806	−0.404403	+	0.914581i	$0.632521\pi$
$948$	−15806.4	−0.541527
$949$	−20194.4	−0.690767
$950$	−2295.95	−0.0784111
$951$	21850.1	0.745044
$952$	−5846.61	−0.199044
$953$	−32519.5	−1.10536	−0.552681	−	0.833393i	$-0.686395\pi$
$953$	−32519.5	−1.10536	−0.552681	+	0.833393i	$0.686395\pi$
$954$	5491.10	0.186353
$955$	4726.64	0.160158
$956$	−33046.6	−1.11800
$957$	−4763.57	−0.160903
$958$	12841.9	0.433092
$959$	−35242.1	−1.18668
$960$	−137.979	−0.00463881
$961$	26192.7	0.879216
$962$	10475.6	0.351087
$963$	15801.6	0.528764
$964$	−9056.58	−0.302586
$965$	−3381.49	−0.112802
$966$	23684.4	0.788853
$967$	23136.2	0.769402	0.384701	−	0.923041i	$-0.374305\pi$
$967$	23136.2	0.769402	0.384701	+	0.923041i	$0.374305\pi$
$968$	−21351.3	−0.708943
$969$	−437.873	−0.0145165
$970$	−2175.27	−0.0720037
$971$	25537.7	0.844019	0.422010	−	0.906591i	$-0.361325\pi$
$971$	25537.7	0.844019	0.422010	+	0.906591i	$0.361325\pi$
$972$	1578.84	0.0521001
$973$	101767.	3.35305
$974$	8379.69	0.275670
$975$	−19727.7	−0.647992
$976$	−9813.91	−0.321860
$977$	44463.2	1.45599	0.727996	−	0.685581i	$-0.240452\pi$
$977$	44463.2	1.45599	0.727996	+	0.685581i	$0.240452\pi$
$978$	−10085.7	−0.329759
$979$	−12265.1	−0.400403
$980$	12049.7	0.392768
$981$	−9277.50	−0.301945
$982$	−10515.6	−0.341717
$983$	37311.3	1.21063	0.605313	−	0.795987i	$-0.293048\pi$
$983$	37311.3	1.21063	0.605313	+	0.795987i	$0.293048\pi$
$984$	−9727.63	−0.315148
$985$	−4229.05	−0.136801
$986$	−1606.93	−0.0519017
$987$	−46144.8	−1.48815
$988$	−5503.30	−0.177210
$989$	77963.4	2.50667
$990$	−263.870	−0.00847106
$991$	−405.099	−0.0129853	−0.00649263	−	0.999979i	$-0.502067\pi$
$991$	−405.099	−0.0129853	−0.00649263	+	0.999979i	$0.502067\pi$
$992$	42396.6	1.35695
$993$	1447.93	0.0462725
$994$	−42652.1	−1.36101
$995$	−1860.00	−0.0592623
$996$	12767.2	0.406167
$997$	−28485.3	−0.904855	−0.452427	−	0.891801i	$-0.649442\pi$
$997$	−28485.3	−0.904855	−0.452427	+	0.891801i	$0.649442\pi$
$998$	25409.2	0.805925
$999$	−4230.98	−0.133996

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.4.a.c.1.10	✓	22
3.2	odd	2		1413.4.a.e.1.13		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.4.a.c.1.10	✓	22	1.1	even	1	trivial
1413.4.a.e.1.13		22	3.2	odd	2

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:	\( N \)	\(=\)	\( 471 = 3 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	471.a (trivial)

\(f(q)\)	\(=\)	\(q-1.22585 q^{2} -3.00000 q^{3} -6.49728 q^{4} -2.10116 q^{5} +3.67756 q^{6} +35.0092 q^{7} +17.7716 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-1.22585 q^{2} -3.00000 q^{3} -6.49728 q^{4} -2.10116 q^{5} +3.67756 q^{6} +35.0092 q^{7} +17.7716 q^{8} +9.00000 q^{9} +2.57572 q^{10} -11.3828 q^{11} +19.4918 q^{12} -54.5332 q^{13} -42.9161 q^{14} +6.30348 q^{15} +30.1929 q^{16} -9.39716 q^{17} -11.0327 q^{18} -15.5321 q^{19} +13.6518 q^{20} -105.027 q^{21} +13.9537 q^{22} +183.958 q^{23} -53.3147 q^{24} -120.585 q^{25} +66.8498 q^{26} -27.0000 q^{27} -227.464 q^{28} -139.496 q^{29} -7.72715 q^{30} -236.609 q^{31} -179.185 q^{32} +34.1485 q^{33} +11.5195 q^{34} -73.5599 q^{35} -58.4755 q^{36} +156.703 q^{37} +19.0401 q^{38} +163.600 q^{39} -37.3409 q^{40} +182.457 q^{41} +128.748 q^{42} +423.810 q^{43} +73.9574 q^{44} -18.9104 q^{45} -225.506 q^{46} +439.359 q^{47} -90.5788 q^{48} +882.642 q^{49} +147.820 q^{50} +28.1915 q^{51} +354.318 q^{52} -497.712 q^{53} +33.0981 q^{54} +23.9171 q^{55} +622.167 q^{56} +46.5963 q^{57} +171.002 q^{58} +216.123 q^{59} -40.9555 q^{60} -325.040 q^{61} +290.048 q^{62} +315.082 q^{63} -21.8893 q^{64} +114.583 q^{65} -41.8610 q^{66} +505.112 q^{67} +61.0560 q^{68} -551.875 q^{69} +90.1737 q^{70} +993.848 q^{71} +159.944 q^{72} +370.314 q^{73} -192.095 q^{74} +361.755 q^{75} +100.916 q^{76} -398.503 q^{77} -200.549 q^{78} -810.923 q^{79} -63.4402 q^{80} +81.0000 q^{81} -223.666 q^{82} +655.000 q^{83} +682.393 q^{84} +19.7450 q^{85} -519.529 q^{86} +418.488 q^{87} -202.290 q^{88} +1077.51 q^{89} +23.1814 q^{90} -1909.16 q^{91} -1195.23 q^{92} +709.826 q^{93} -538.590 q^{94} +32.6355 q^{95} +537.554 q^{96} -844.529 q^{97} -1081.99 q^{98} -102.445 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 4 q^{2} - 66 q^{3} + 90 q^{4} + 32 q^{5} - 12 q^{6} - 4 q^{7} + 27 q^{8} + 198 q^{9}+O(q^{10}) \) 22 * q + 4 * q^2 - 66 * q^3 + 90 * q^4 + 32 * q^5 - 12 * q^6 - 4 * q^7 + 27 * q^8 + 198 * q^9	\( 22 q + 4 q^{2} - 66 q^{3} + 90 q^{4} + 32 q^{5} - 12 q^{6} - 4 q^{7} + 27 q^{8} + 198 q^{9} + 13 q^{10} + 61 q^{11} - 270 q^{12} + 4 q^{13} + 133 q^{14} - 96 q^{15} + 342 q^{16} + 308 q^{17} + 36 q^{18} + 32 q^{19} + 407 q^{20} + 12 q^{21} - 166 q^{22} + 53 q^{23} - 81 q^{24} + 746 q^{25} + 467 q^{26} - 594 q^{27} + 85 q^{28} + 634 q^{29} - 39 q^{30} - 163 q^{31} + 150 q^{32} - 183 q^{33} + 37 q^{34} + 782 q^{35} + 810 q^{36} - 2 q^{37} + 584 q^{38} - 12 q^{39} + 864 q^{40} + 1593 q^{41} - 399 q^{42} - 891 q^{43} + 2093 q^{44} + 288 q^{45} + 108 q^{46} + 1200 q^{47} - 1026 q^{48} + 2816 q^{49} + 4703 q^{50} - 924 q^{51} + 1866 q^{52} + 1182 q^{53} - 108 q^{54} + 970 q^{55} + 5362 q^{56} - 96 q^{57} + 1814 q^{58} + 2802 q^{59} - 1221 q^{60} + 2629 q^{61} + 2378 q^{62} - 36 q^{63} + 625 q^{64} + 2264 q^{65} + 498 q^{66} - 1074 q^{67} + 4383 q^{68} - 159 q^{69} + 4009 q^{70} + 3920 q^{71} + 243 q^{72} + 1086 q^{73} + 4904 q^{74} - 2238 q^{75} + 3750 q^{76} + 2966 q^{77} - 1401 q^{78} - 30 q^{79} + 7777 q^{80} + 1782 q^{81} + 2932 q^{82} + 1900 q^{83} - 255 q^{84} + 524 q^{85} + 3209 q^{86} - 1902 q^{87} - 100 q^{88} + 4488 q^{89} + 117 q^{90} - 818 q^{91} + 6210 q^{92} + 489 q^{93} + 3220 q^{94} + 3500 q^{95} - 450 q^{96} + 2178 q^{97} + 7629 q^{98} + 549 q^{99}+O(q^{100}) \) 22 * q + 4 * q^2 - 66 * q^3 + 90 * q^4 + 32 * q^5 - 12 * q^6 - 4 * q^7 + 27 * q^8 + 198 * q^9 + 13 * q^10 + 61 * q^11 - 270 * q^12 + 4 * q^13 + 133 * q^14 - 96 * q^15 + 342 * q^16 + 308 * q^17 + 36 * q^18 + 32 * q^19 + 407 * q^20 + 12 * q^21 - 166 * q^22 + 53 * q^23 - 81 * q^24 + 746 * q^25 + 467 * q^26 - 594 * q^27 + 85 * q^28 + 634 * q^29 - 39 * q^30 - 163 * q^31 + 150 * q^32 - 183 * q^33 + 37 * q^34 + 782 * q^35 + 810 * q^36 - 2 * q^37 + 584 * q^38 - 12 * q^39 + 864 * q^40 + 1593 * q^41 - 399 * q^42 - 891 * q^43 + 2093 * q^44 + 288 * q^45 + 108 * q^46 + 1200 * q^47 - 1026 * q^48 + 2816 * q^49 + 4703 * q^50 - 924 * q^51 + 1866 * q^52 + 1182 * q^53 - 108 * q^54 + 970 * q^55 + 5362 * q^56 - 96 * q^57 + 1814 * q^58 + 2802 * q^59 - 1221 * q^60 + 2629 * q^61 + 2378 * q^62 - 36 * q^63 + 625 * q^64 + 2264 * q^65 + 498 * q^66 - 1074 * q^67 + 4383 * q^68 - 159 * q^69 + 4009 * q^70 + 3920 * q^71 + 243 * q^72 + 1086 * q^73 + 4904 * q^74 - 2238 * q^75 + 3750 * q^76 + 2966 * q^77 - 1401 * q^78 - 30 * q^79 + 7777 * q^80 + 1782 * q^81 + 2932 * q^82 + 1900 * q^83 - 255 * q^84 + 524 * q^85 + 3209 * q^86 - 1902 * q^87 - 100 * q^88 + 4488 * q^89 + 117 * q^90 - 818 * q^91 + 6210 * q^92 + 489 * q^93 + 3220 * q^94 + 3500 * q^95 - 450 * q^96 + 2178 * q^97 + 7629 * q^98 + 549 * q^99

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