LMFDB - Embedded newform 483.4.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,4,Mod(1,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("483.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	483.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:	$28.4979225328$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.8184789.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 76x^{2} - 8x + 1048 $ x^4 - x^3 - 76x^2 - 8x + 1048
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$8.39513$ of defining polynomial
Character	$\chi$	$=$	483.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.70156 q^{2} +3.00000 q^{3} +5.70156 q^{4} -9.64642 q^{5} +11.1047 q^{6} -7.00000 q^{7} -8.50781 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+3.70156 q^{2} +3.00000 q^{3} +5.70156 q^{4} -9.64642 q^{5} +11.1047 q^{6} -7.00000 q^{7} -8.50781 q^{8} +9.00000 q^{9} -35.7068 q^{10} -5.31442 q^{11} +17.1047 q^{12} -36.0820 q^{13} -25.9109 q^{14} -28.9392 q^{15} -77.1047 q^{16} +94.2900 q^{17} +33.3141 q^{18} -148.494 q^{19} -54.9996 q^{20} -21.0000 q^{21} -19.6717 q^{22} -23.0000 q^{23} -25.5234 q^{24} -31.9467 q^{25} -133.560 q^{26} +27.0000 q^{27} -39.9109 q^{28} -125.676 q^{29} -107.120 q^{30} -32.7988 q^{31} -217.345 q^{32} -15.9433 q^{33} +349.020 q^{34} +67.5249 q^{35} +51.3141 q^{36} -183.714 q^{37} -549.659 q^{38} -108.246 q^{39} +82.0699 q^{40} +26.0115 q^{41} -77.7328 q^{42} +261.573 q^{43} -30.3005 q^{44} -86.8177 q^{45} -85.1359 q^{46} -207.760 q^{47} -231.314 q^{48} +49.0000 q^{49} -118.253 q^{50} +282.870 q^{51} -205.724 q^{52} -141.782 q^{53} +99.9422 q^{54} +51.2651 q^{55} +59.5547 q^{56} -445.482 q^{57} -465.199 q^{58} +545.402 q^{59} -164.999 q^{60} -233.698 q^{61} -121.407 q^{62} -63.0000 q^{63} -187.680 q^{64} +348.062 q^{65} -59.0150 q^{66} +64.1180 q^{67} +537.600 q^{68} -69.0000 q^{69} +249.948 q^{70} -674.596 q^{71} -76.5703 q^{72} +1157.65 q^{73} -680.027 q^{74} -95.8400 q^{75} -846.647 q^{76} +37.2010 q^{77} -400.679 q^{78} +492.386 q^{79} +743.784 q^{80} +81.0000 q^{81} +96.2831 q^{82} +695.468 q^{83} -119.733 q^{84} -909.561 q^{85} +968.230 q^{86} -377.029 q^{87} +45.2141 q^{88} -999.423 q^{89} -321.361 q^{90} +252.574 q^{91} -131.136 q^{92} -98.3964 q^{93} -769.035 q^{94} +1432.43 q^{95} -652.036 q^{96} +1046.59 q^{97} +181.377 q^{98} -47.8298 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 12 q^{3} + 10 q^{4} - 23 q^{5} + 6 q^{6} - 28 q^{7} + 30 q^{8} + 36 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 + 12 * q^3 + 10 * q^4 - 23 * q^5 + 6 * q^6 - 28 * q^7 + 30 * q^8 + 36 * q^9	\( 4 q + 2 q^{2} + 12 q^{3} + 10 q^{4} - 23 q^{5} + 6 q^{6} - 28 q^{7} + 30 q^{8} + 36 q^{9} - 32 q^{10} - 48 q^{11} + 30 q^{12} - 107 q^{13} - 14 q^{14} - 69 q^{15} - 270 q^{16} - 6 q^{17} + 18 q^{18} + 76 q^{19} - 78 q^{20} - 84 q^{21} - 106 q^{22} - 92 q^{23} + 90 q^{24} + 115 q^{25} - 320 q^{26} + 108 q^{27} - 70 q^{28} + 204 q^{29} - 96 q^{30} - 276 q^{31} - 498 q^{32} - 144 q^{33} - 126 q^{34} + 161 q^{35} + 90 q^{36} - 248 q^{37} - 372 q^{38} - 321 q^{39} - 70 q^{40} - 450 q^{41} - 42 q^{42} + 109 q^{43} - 202 q^{44} - 207 q^{45} - 46 q^{46} - 688 q^{47} - 810 q^{48} + 196 q^{49} - 1152 q^{50} - 18 q^{51} - 534 q^{52} - 633 q^{53} + 54 q^{54} + 581 q^{55} - 210 q^{56} + 228 q^{57} - 308 q^{58} + 585 q^{59} - 234 q^{60} + 1311 q^{61} + 846 q^{62} - 252 q^{63} + 722 q^{64} - 1614 q^{65} - 318 q^{66} + 365 q^{67} - 138 q^{68} - 276 q^{69} + 224 q^{70} - 3049 q^{71} + 270 q^{72} - 1164 q^{73} + 2090 q^{74} + 345 q^{75} - 220 q^{76} + 336 q^{77} - 960 q^{78} - 476 q^{79} + 1614 q^{80} + 324 q^{81} + 1784 q^{82} + 1462 q^{83} - 210 q^{84} - 891 q^{85} - 1032 q^{86} + 612 q^{87} + 50 q^{88} - 1767 q^{89} - 288 q^{90} + 749 q^{91} - 230 q^{92} - 828 q^{93} - 1246 q^{94} - 1927 q^{95} - 1494 q^{96} + 1788 q^{97} + 98 q^{98} - 432 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + 12 * q^3 + 10 * q^4 - 23 * q^5 + 6 * q^6 - 28 * q^7 + 30 * q^8 + 36 * q^9 - 32 * q^10 - 48 * q^11 + 30 * q^12 - 107 * q^13 - 14 * q^14 - 69 * q^15 - 270 * q^16 - 6 * q^17 + 18 * q^18 + 76 * q^19 - 78 * q^20 - 84 * q^21 - 106 * q^22 - 92 * q^23 + 90 * q^24 + 115 * q^25 - 320 * q^26 + 108 * q^27 - 70 * q^28 + 204 * q^29 - 96 * q^30 - 276 * q^31 - 498 * q^32 - 144 * q^33 - 126 * q^34 + 161 * q^35 + 90 * q^36 - 248 * q^37 - 372 * q^38 - 321 * q^39 - 70 * q^40 - 450 * q^41 - 42 * q^42 + 109 * q^43 - 202 * q^44 - 207 * q^45 - 46 * q^46 - 688 * q^47 - 810 * q^48 + 196 * q^49 - 1152 * q^50 - 18 * q^51 - 534 * q^52 - 633 * q^53 + 54 * q^54 + 581 * q^55 - 210 * q^56 + 228 * q^57 - 308 * q^58 + 585 * q^59 - 234 * q^60 + 1311 * q^61 + 846 * q^62 - 252 * q^63 + 722 * q^64 - 1614 * q^65 - 318 * q^66 + 365 * q^67 - 138 * q^68 - 276 * q^69 + 224 * q^70 - 3049 * q^71 + 270 * q^72 - 1164 * q^73 + 2090 * q^74 + 345 * q^75 - 220 * q^76 + 336 * q^77 - 960 * q^78 - 476 * q^79 + 1614 * q^80 + 324 * q^81 + 1784 * q^82 + 1462 * q^83 - 210 * q^84 - 891 * q^85 - 1032 * q^86 + 612 * q^87 + 50 * q^88 - 1767 * q^89 - 288 * q^90 + 749 * q^91 - 230 * q^92 - 828 * q^93 - 1246 * q^94 - 1927 * q^95 - 1494 * q^96 + 1788 * q^97 + 98 * q^98 - 432 * 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 $

$2$	3.70156	1.30870	0.654350	−	0.756192i	$-0.272942\pi$
$2$	3.70156	1.30870	0.654350	+	0.756192i	$0.272942\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	5.70156	0.712695
$5$	−9.64642	−0.862802	−0.431401	−	0.902160i	$-0.641981\pi$
$5$	−9.64642	−0.862802	−0.431401	+	0.902160i	$0.641981\pi$
$6$	11.1047	0.755578
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	−8.50781	−0.375996
$9$	9.00000	0.333333
$10$	−35.7068	−1.12915
$11$	−5.31442	−0.145669	−0.0728345	−	0.997344i	$-0.523204\pi$
$11$	−5.31442	−0.145669	−0.0728345	+	0.997344i	$0.523204\pi$
$12$	17.1047	0.411475
$13$	−36.0820	−0.769796	−0.384898	−	0.922959i	$-0.625763\pi$
$13$	−36.0820	−0.769796	−0.384898	+	0.922959i	$0.625763\pi$
$14$	−25.9109	−0.494642
$15$	−28.9392	−0.498139
$16$	−77.1047	−1.20476
$17$	94.2900	1.34522	0.672608	−	0.739999i	$-0.265174\pi$
$17$	94.2900	1.34522	0.672608	+	0.739999i	$0.265174\pi$
$18$	33.3141	0.436233
$19$	−148.494	−1.79299	−0.896496	−	0.443053i	$-0.853895\pi$
$19$	−148.494	−1.79299	−0.896496	+	0.443053i	$0.853895\pi$
$20$	−54.9996	−0.614915
$21$	−21.0000	−0.218218
$22$	−19.6717	−0.190637
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	−25.5234	−0.217081
$25$	−31.9467	−0.255573
$26$	−133.560	−1.00743
$27$	27.0000	0.192450
$28$	−39.9109	−0.269373
$29$	−125.676	−0.804742	−0.402371	−	0.915477i	$-0.631814\pi$
$29$	−125.676	−0.804742	−0.402371	+	0.915477i	$0.631814\pi$
$30$	−107.120	−0.651914
$31$	−32.7988	−0.190027	−0.0950136	−	0.995476i	$-0.530289\pi$
$31$	−32.7988	−0.190027	−0.0950136	+	0.995476i	$0.530289\pi$
$32$	−217.345	−1.20067
$33$	−15.9433	−0.0841021
$34$	349.020	1.76049
$35$	67.5249	0.326108
$36$	51.3141	0.237565
$37$	−183.714	−0.816279	−0.408140	−	0.912920i	$-0.633822\pi$
$37$	−183.714	−0.816279	−0.408140	+	0.912920i	$0.633822\pi$
$38$	−549.659	−2.34649
$39$	−108.246	−0.444442
$40$	82.0699	0.324410
$41$	26.0115	0.0990807	0.0495404	−	0.998772i	$-0.484224\pi$
$41$	26.0115	0.0990807	0.0495404	+	0.998772i	$0.484224\pi$
$42$	−77.7328	−0.285582
$43$	261.573	0.927665	0.463832	−	0.885923i	$-0.346474\pi$
$43$	261.573	0.927665	0.463832	+	0.885923i	$0.346474\pi$
$44$	−30.3005	−0.103818
$45$	−86.8177	−0.287601
$46$	−85.1359	−0.272883
$47$	−207.760	−0.644784	−0.322392	−	0.946606i	$-0.604487\pi$
$47$	−207.760	−0.644784	−0.322392	+	0.946606i	$0.604487\pi$
$48$	−231.314	−0.695569
$49$	49.0000	0.142857
$50$	−118.253	−0.334469
$51$	282.870	0.776661
$52$	−205.724	−0.548630
$53$	−141.782	−0.367457	−0.183728	−	0.982977i	$-0.558817\pi$
$53$	−141.782	−0.367457	−0.183728	+	0.982977i	$0.558817\pi$
$54$	99.9422	0.251859
$55$	51.2651	0.125683
$56$	59.5547	0.142113
$57$	−445.482	−1.03518
$58$	−465.199	−1.05317
$59$	545.402	1.20348	0.601740	−	0.798692i	$-0.294474\pi$
$59$	545.402	1.20348	0.601740	+	0.798692i	$0.294474\pi$
$60$	−164.999	−0.355021
$61$	−233.698	−0.490523	−0.245262	−	0.969457i	$-0.578874\pi$
$61$	−233.698	−0.490523	−0.245262	+	0.969457i	$0.578874\pi$
$62$	−121.407	−0.248688
$63$	−63.0000	−0.125988
$64$	−187.680	−0.366562
$65$	348.062	0.664181
$66$	−59.0150	−0.110064
$67$	64.1180	0.116914	0.0584572	−	0.998290i	$-0.481382\pi$
$67$	64.1180	0.116914	0.0584572	+	0.998290i	$0.481382\pi$
$68$	537.600	0.958730
$69$	−69.0000	−0.120386
$70$	249.948	0.426778
$71$	−674.596	−1.12760	−0.563802	−	0.825910i	$-0.690662\pi$
$71$	−674.596	−1.12760	−0.563802	+	0.825910i	$0.690662\pi$
$72$	−76.5703	−0.125332
$73$	1157.65	1.85606	0.928031	−	0.372504i	$-0.121501\pi$
$73$	1157.65	1.85606	0.928031	+	0.372504i	$0.121501\pi$
$74$	−680.027	−1.06826
$75$	−95.8400	−0.147555
$76$	−846.647	−1.27786
$77$	37.2010	0.0550577
$78$	−400.679	−0.581641
$79$	492.386	0.701237	0.350619	−	0.936518i	$-0.385971\pi$
$79$	492.386	0.701237	0.350619	+	0.936518i	$0.385971\pi$
$80$	743.784	1.03947
$81$	81.0000	0.111111
$82$	96.2831	0.129667
$83$	695.468	0.919730	0.459865	−	0.887989i	$-0.347898\pi$
$83$	695.468	0.919730	0.459865	+	0.887989i	$0.347898\pi$
$84$	−119.733	−0.155523
$85$	−909.561	−1.16066
$86$	968.230	1.21403
$87$	−377.029	−0.464618
$88$	45.2141	0.0547709
$89$	−999.423	−1.19032	−0.595161	−	0.803607i	$-0.702912\pi$
$89$	−999.423	−1.19032	−0.595161	+	0.803607i	$0.702912\pi$
$90$	−321.361	−0.376383
$91$	252.574	0.290955
$92$	−131.136	−0.148607
$93$	−98.3964	−0.109712
$94$	−769.035	−0.843829
$95$	1432.43	1.54700
$96$	−652.036	−0.693210
$97$	1046.59	1.09552	0.547759	−	0.836636i	$-0.315481\pi$
$97$	1046.59	1.09552	0.547759	+	0.836636i	$0.315481\pi$
$98$	181.377	0.186957
$99$	−47.8298	−0.0485563
$100$	−182.146	−0.182146
$101$	−788.294	−0.776616	−0.388308	−	0.921530i	$-0.626940\pi$
$101$	−788.294	−0.776616	−0.388308	+	0.921530i	$0.626940\pi$
$102$	1047.06	1.01642
$103$	568.773	0.544106	0.272053	−	0.962282i	$-0.412297\pi$
$103$	568.773	0.544106	0.272053	+	0.962282i	$0.412297\pi$
$104$	306.979	0.289440
$105$	202.575	0.188279
$106$	−524.814	−0.480891
$107$	830.519	0.750367	0.375184	−	0.926951i	$-0.377580\pi$
$107$	830.519	0.750367	0.375184	+	0.926951i	$0.377580\pi$
$108$	153.942	0.137158
$109$	−602.383	−0.529338	−0.264669	−	0.964339i	$-0.585263\pi$
$109$	−602.383	−0.529338	−0.264669	+	0.964339i	$0.585263\pi$
$110$	189.761	0.164482
$111$	−551.141	−0.471279
$112$	539.733	0.455357
$113$	418.091	0.348059	0.174030	−	0.984740i	$-0.444321\pi$
$113$	418.091	0.348059	0.174030	+	0.984740i	$0.444321\pi$
$114$	−1648.98	−1.35475
$115$	221.868	0.179907
$116$	−716.552	−0.573536
$117$	−324.738	−0.256599
$118$	2018.84	1.57499
$119$	−660.030	−0.508444
$120$	246.210	0.187298
$121$	−1302.76	−0.978781
$122$	−865.046	−0.641948
$123$	78.0344	0.0572043
$124$	−187.004	−0.135431
$125$	1513.97	1.08331
$126$	−233.198	−0.164881
$127$	−867.576	−0.606181	−0.303090	−	0.952962i	$-0.598018\pi$
$127$	−867.576	−0.606181	−0.303090	+	0.952962i	$0.598018\pi$
$128$	1044.05	0.720955
$129$	784.720	0.535587
$130$	1288.37	0.869213
$131$	−1716.98	−1.14514	−0.572570	−	0.819856i	$-0.694054\pi$
$131$	−1716.98	−1.14514	−0.572570	+	0.819856i	$0.694054\pi$
$132$	−90.9016	−0.0599391
$133$	1039.46	0.677687
$134$	237.337	0.153006
$135$	−260.453	−0.166046
$136$	−802.202	−0.505796
$137$	−277.542	−0.173081	−0.0865403	−	0.996248i	$-0.527581\pi$
$137$	−277.542	−0.173081	−0.0865403	+	0.996248i	$0.527581\pi$
$138$	−255.408	−0.157549
$139$	1105.94	0.674854	0.337427	−	0.941352i	$-0.390443\pi$
$139$	1105.94	0.674854	0.337427	+	0.941352i	$0.390443\pi$
$140$	384.997	0.232416
$141$	−623.279	−0.372266
$142$	−2497.06	−1.47569
$143$	191.755	0.112135
$144$	−693.942	−0.401587
$145$	1212.33	0.694333
$146$	4285.11	2.42903
$147$	147.000	0.0824786
$148$	−1047.45	−0.581758
$149$	−549.803	−0.302293	−0.151146	−	0.988511i	$-0.548297\pi$
$149$	−549.803	−0.302293	−0.151146	+	0.988511i	$0.548297\pi$
$150$	−354.758	−0.193106
$151$	−1486.02	−0.800863	−0.400431	−	0.916327i	$-0.631140\pi$
$151$	−1486.02	−0.800863	−0.400431	+	0.916327i	$0.631140\pi$
$152$	1263.36	0.674157
$153$	848.610	0.448406
$154$	137.702	0.0720540
$155$	316.391	0.163956
$156$	−617.171	−0.316751
$157$	−510.092	−0.259298	−0.129649	−	0.991560i	$-0.541385\pi$
$157$	−510.092	−0.259298	−0.129649	+	0.991560i	$0.541385\pi$
$158$	1822.60	0.917709
$159$	−425.345	−0.212151
$160$	2096.60	1.03594
$161$	161.000	0.0788110
$162$	299.827	0.145411
$163$	−3359.08	−1.61413	−0.807066	−	0.590462i	$-0.798946\pi$
$163$	−3359.08	−1.61413	−0.807066	+	0.590462i	$0.798946\pi$
$164$	148.306	0.0706144
$165$	153.795	0.0725634
$166$	2574.32	1.20365
$167$	−2445.65	−1.13323	−0.566617	−	0.823981i	$-0.691748\pi$
$167$	−2445.65	−1.13323	−0.566617	+	0.823981i	$0.691748\pi$
$168$	178.664	0.0820490
$169$	−895.090	−0.407415
$170$	−3366.80	−1.51895
$171$	−1336.44	−0.597664
$172$	1491.38	0.661142
$173$	−725.603	−0.318882	−0.159441	−	0.987207i	$-0.550969\pi$
$173$	−725.603	−0.318882	−0.159441	+	0.987207i	$0.550969\pi$
$174$	−1395.60	−0.608046
$175$	223.627	0.0965977
$176$	409.767	0.175496
$177$	1636.21	0.694829
$178$	−3699.42	−1.55777
$179$	−2395.97	−1.00046	−0.500232	−	0.865892i	$-0.666752\pi$
$179$	−2395.97	−1.00046	−0.500232	+	0.865892i	$0.666752\pi$
$180$	−494.997	−0.204972
$181$	809.971	0.332622	0.166311	−	0.986073i	$-0.446814\pi$
$181$	809.971	0.332622	0.166311	+	0.986073i	$0.446814\pi$
$182$	934.918	0.380773
$183$	−701.093	−0.283204
$184$	195.680	0.0784005
$185$	1772.18	0.704287
$186$	−364.221	−0.143580
$187$	−501.097	−0.195956
$188$	−1184.55	−0.459534
$189$	−189.000	−0.0727393
$190$	5302.24	2.02455
$191$	1658.76	0.628397	0.314198	−	0.949357i	$-0.398264\pi$
$191$	1658.76	0.628397	0.314198	+	0.949357i	$0.398264\pi$
$192$	−563.039	−0.211635
$193$	2772.79	1.03414	0.517071	−	0.855942i	$-0.327022\pi$
$193$	2772.79	1.03414	0.517071	+	0.855942i	$0.327022\pi$
$194$	3874.03	1.43371
$195$	1044.19	0.383465
$196$	279.377	0.101814
$197$	1453.19	0.525561	0.262781	−	0.964856i	$-0.415360\pi$
$197$	1453.19	0.525561	0.262781	+	0.964856i	$0.415360\pi$
$198$	−177.045	−0.0635457
$199$	3748.73	1.33538	0.667690	−	0.744439i	$-0.267283\pi$
$199$	3748.73	1.33538	0.667690	+	0.744439i	$0.267283\pi$
$200$	271.796	0.0960945
$201$	192.354	0.0675005
$202$	−2917.92	−1.01636
$203$	879.735	0.304164
$204$	1612.80	0.553523
$205$	−250.917	−0.0854870
$206$	2105.35	0.712071
$207$	−207.000	−0.0695048
$208$	2782.09	0.927419
$209$	789.160	0.261183
$210$	749.843	0.246400
$211$	−3536.74	−1.15393	−0.576964	−	0.816769i	$-0.695763\pi$
$211$	−3536.74	−1.15393	−0.576964	+	0.816769i	$0.695763\pi$
$212$	−808.377	−0.261885
$213$	−2023.79	−0.651022
$214$	3074.22	0.982005
$215$	−2523.25	−0.800390
$216$	−229.711	−0.0723604
$217$	229.592	0.0718235
$218$	−2229.76	−0.692744
$219$	3472.94	1.07160
$220$	292.291	0.0895740
$221$	−3402.17	−1.03554
$222$	−2040.08	−0.616763
$223$	1215.51	0.365006	0.182503	−	0.983205i	$-0.441580\pi$
$223$	1215.51	0.365006	0.182503	+	0.983205i	$0.441580\pi$
$224$	1521.42	0.453812
$225$	−287.520	−0.0851911
$226$	1547.59	0.455505
$227$	−2879.16	−0.841834	−0.420917	−	0.907099i	$-0.638292\pi$
$227$	−2879.16	−0.841834	−0.420917	+	0.907099i	$0.638292\pi$
$228$	−2539.94	−0.737771
$229$	2870.39	0.828299	0.414150	−	0.910209i	$-0.364079\pi$
$229$	2870.39	0.828299	0.414150	+	0.910209i	$0.364079\pi$
$230$	821.257	0.235444
$231$	111.603	0.0317876
$232$	1069.23	0.302580
$233$	−4244.34	−1.19337	−0.596687	−	0.802474i	$-0.703517\pi$
$233$	−4244.34	−1.19337	−0.596687	+	0.802474i	$0.703517\pi$
$234$	−1202.04	−0.335810
$235$	2004.13	0.556321
$236$	3109.64	0.857714
$237$	1477.16	0.404860
$238$	−2443.14	−0.665401
$239$	−5250.16	−1.42094	−0.710470	−	0.703727i	$-0.751518\pi$
$239$	−5250.16	−1.42094	−0.710470	+	0.703727i	$0.751518\pi$
$240$	2231.35	0.600138
$241$	1340.55	0.358310	0.179155	−	0.983821i	$-0.442664\pi$
$241$	1340.55	0.358310	0.179155	+	0.983821i	$0.442664\pi$
$242$	−4822.24	−1.28093
$243$	243.000	0.0641500
$244$	−1332.44	−0.349594
$245$	−472.674	−0.123257
$246$	288.849	0.0748632
$247$	5357.95	1.38024
$248$	279.046	0.0714494
$249$	2086.41	0.531006
$250$	5604.06	1.41773
$251$	−5801.74	−1.45897	−0.729487	−	0.683994i	$-0.760241\pi$
$251$	−5801.74	−1.45897	−0.729487	+	0.683994i	$0.760241\pi$
$252$	−359.198	−0.0897912
$253$	122.232	0.0303741
$254$	−3211.39	−0.793309
$255$	−2728.68	−0.670105
$256$	5366.07	1.31008
$257$	591.208	0.143496	0.0717481	−	0.997423i	$-0.477142\pi$
$257$	591.208	0.143496	0.0717481	+	0.997423i	$0.477142\pi$
$258$	2904.69	0.700923
$259$	1286.00	0.308525
$260$	1984.50	0.473359
$261$	−1131.09	−0.268247
$262$	−6355.51	−1.49865
$263$	−477.408	−0.111933	−0.0559663	−	0.998433i	$-0.517824\pi$
$263$	−477.408	−0.111933	−0.0559663	+	0.998433i	$0.517824\pi$
$264$	135.642	0.0316220
$265$	1367.68	0.317042
$266$	3847.62	0.886889
$267$	−2998.27	−0.687232
$268$	365.573	0.0833243
$269$	232.563	0.0527123	0.0263561	−	0.999653i	$-0.491610\pi$
$269$	232.563	0.0527123	0.0263561	+	0.999653i	$0.491610\pi$
$270$	−964.084	−0.217305
$271$	8592.41	1.92602	0.963011	−	0.269464i	$-0.0868464\pi$
$271$	8592.41	1.92602	0.963011	+	0.269464i	$0.0868464\pi$
$272$	−7270.20	−1.62066
$273$	757.722	0.167983
$274$	−1027.34	−0.226510
$275$	169.778	0.0372291
$276$	−393.408	−0.0857984
$277$	−7242.69	−1.57101	−0.785507	−	0.618853i	$-0.787598\pi$
$277$	−7242.69	−1.57101	−0.785507	+	0.618853i	$0.787598\pi$
$278$	4093.71	0.883182
$279$	−295.189	−0.0633424
$280$	−574.489	−0.122615
$281$	−2496.59	−0.530014	−0.265007	−	0.964246i	$-0.585374\pi$
$281$	−2496.59	−0.530014	−0.265007	+	0.964246i	$0.585374\pi$
$282$	−2307.10	−0.487185
$283$	−5016.23	−1.05365	−0.526827	−	0.849973i	$-0.676618\pi$
$283$	−5016.23	−1.05365	−0.526827	+	0.849973i	$0.676618\pi$
$284$	−3846.25	−0.803638
$285$	4297.30	0.893158
$286$	709.793	0.146752
$287$	−182.080	−0.0374490
$288$	−1956.11	−0.400225
$289$	3977.61	0.809609
$290$	4487.50	0.908673
$291$	3139.78	0.632498
$292$	6600.40	1.32281
$293$	251.249	0.0500959	0.0250480	−	0.999686i	$-0.492026\pi$
$293$	251.249	0.0500959	0.0250480	+	0.999686i	$0.492026\pi$
$294$	544.130	0.107940
$295$	−5261.17	−1.03836
$296$	1563.00	0.306917
$297$	−143.489	−0.0280340
$298$	−2035.13	−0.395611
$299$	829.886	0.160513
$300$	−546.438	−0.105162
$301$	−1831.01	−0.350624
$302$	−5500.58	−1.04809
$303$	−2364.88	−0.448379
$304$	11449.6	2.16013
$305$	2254.34	0.423224
$306$	3141.18	0.586828
$307$	3821.37	0.710414	0.355207	−	0.934788i	$-0.384410\pi$
$307$	3821.37	0.710414	0.355207	+	0.934788i	$0.384410\pi$
$308$	212.104	0.0392394
$309$	1706.32	0.314140
$310$	1171.14	0.214569
$311$	7496.39	1.36682	0.683410	−	0.730035i	$-0.260496\pi$
$311$	7496.39	1.36682	0.683410	+	0.730035i	$0.260496\pi$
$312$	920.936	0.167108
$313$	7820.36	1.41225	0.706123	−	0.708090i	$-0.250443\pi$
$313$	7820.36	1.41225	0.706123	+	0.708090i	$0.250443\pi$
$314$	−1888.14	−0.339343
$315$	607.724	0.108703
$316$	2807.37	0.499769
$317$	974.285	0.172622	0.0863112	−	0.996268i	$-0.472492\pi$
$317$	974.285	0.172622	0.0863112	+	0.996268i	$0.472492\pi$
$318$	−1574.44	−0.277642
$319$	667.898	0.117226
$320$	1810.44	0.316270
$321$	2491.56	0.433225
$322$	595.952	0.103140
$323$	−14001.5	−2.41196
$324$	461.827	0.0791884
$325$	1152.70	0.196739
$326$	−12433.8	−2.11241
$327$	−1807.15	−0.305613
$328$	−221.301	−0.0372539
$329$	1454.32	0.243705
$330$	569.283	0.0949637
$331$	−8734.67	−1.45046	−0.725228	−	0.688509i	$-0.758265\pi$
$331$	−8734.67	−1.45046	−0.725228	+	0.688509i	$0.758265\pi$
$332$	3965.26	0.655487
$333$	−1653.42	−0.272093
$334$	−9052.73	−1.48306
$335$	−618.509	−0.100874
$336$	1619.20	0.262900
$337$	1575.99	0.254746	0.127373	−	0.991855i	$-0.459345\pi$
$337$	1575.99	0.254746	0.127373	+	0.991855i	$0.459345\pi$
$338$	−3313.23	−0.533184
$339$	1254.27	0.200952
$340$	−5185.92	−0.827194
$341$	174.307	0.0276811
$342$	−4946.93	−0.782162
$343$	−343.000	−0.0539949
$344$	−2225.42	−0.348798
$345$	665.603	0.103869
$346$	−2685.87	−0.417321
$347$	8570.49	1.32590	0.662951	−	0.748663i	$-0.269304\pi$
$347$	8570.49	1.32590	0.662951	+	0.748663i	$0.269304\pi$
$348$	−2149.66	−0.331131
$349$	−7506.57	−1.15134	−0.575670	−	0.817682i	$-0.695259\pi$
$349$	−7506.57	−1.15134	−0.575670	+	0.817682i	$0.695259\pi$
$350$	827.768	0.126417
$351$	−974.214	−0.148147
$352$	1155.07	0.174901
$353$	−7111.33	−1.07223	−0.536116	−	0.844144i	$-0.680109\pi$
$353$	−7111.33	−1.07223	−0.536116	+	0.844144i	$0.680109\pi$
$354$	6056.52	0.909323
$355$	6507.44	0.972898
$356$	−5698.27	−0.848336
$357$	−1980.09	−0.293550
$358$	−8868.82	−1.30931
$359$	8389.83	1.23342	0.616711	−	0.787190i	$-0.288465\pi$
$359$	8389.83	1.23342	0.616711	+	0.787190i	$0.288465\pi$
$360$	738.629	0.108137
$361$	15191.4	2.21482
$362$	2998.16	0.435303
$363$	−3908.27	−0.565099
$364$	1440.07	0.207363
$365$	−11167.2	−1.60141
$366$	−2595.14	−0.370629
$367$	8337.35	1.18585	0.592924	−	0.805259i	$-0.297974\pi$
$367$	8337.35	1.18585	0.592924	+	0.805259i	$0.297974\pi$
$368$	1773.41	0.251210
$369$	234.103	0.0330269
$370$	6559.83	0.921700
$371$	992.471	0.138886
$372$	−561.013	−0.0781914
$373$	−2330.82	−0.323553	−0.161776	−	0.986827i	$-0.551722\pi$
$373$	−2330.82	−0.323553	−0.161776	+	0.986827i	$0.551722\pi$
$374$	−1854.84	−0.256448
$375$	4541.92	0.625450
$376$	1767.58	0.242436
$377$	4534.65	0.619487
$378$	−699.595	−0.0951939
$379$	12164.0	1.64861	0.824307	−	0.566143i	$-0.191565\pi$
$379$	12164.0	1.64861	0.824307	+	0.566143i	$0.191565\pi$
$380$	8167.11	1.10254
$381$	−2602.73	−0.349979
$382$	6140.01	0.822383
$383$	1944.68	0.259447	0.129724	−	0.991550i	$-0.458591\pi$
$383$	1944.68	0.259447	0.129724	+	0.991550i	$0.458591\pi$
$384$	3132.16	0.416244
$385$	−358.856	−0.0475039
$386$	10263.6	1.35338
$387$	2354.16	0.309222
$388$	5967.21	0.780771
$389$	−7002.41	−0.912689	−0.456345	−	0.889803i	$-0.650842\pi$
$389$	−7002.41	−0.912689	−0.456345	+	0.889803i	$0.650842\pi$
$390$	3865.12	0.501841
$391$	−2168.67	−0.280497
$392$	−416.883	−0.0537137
$393$	−5150.95	−0.661147
$394$	5379.08	0.687802
$395$	−4749.76	−0.605029
$396$	−272.705	−0.0346059
$397$	−3640.09	−0.460178	−0.230089	−	0.973170i	$-0.573902\pi$
$397$	−3640.09	−0.460178	−0.230089	+	0.973170i	$0.573902\pi$
$398$	13876.2	1.74761
$399$	3118.37	0.391263
$400$	2463.24	0.307905
$401$	−11319.2	−1.40961	−0.704803	−	0.709404i	$-0.748964\pi$
$401$	−11319.2	−1.40961	−0.704803	+	0.709404i	$0.748964\pi$
$402$	712.010	0.0883379
$403$	1183.45	0.146282
$404$	−4494.51	−0.553490
$405$	−781.360	−0.0958668
$406$	3256.39	0.398059
$407$	976.332	0.118907
$408$	−2406.60	−0.292021
$409$	−10008.4	−1.20998	−0.604992	−	0.796232i	$-0.706824\pi$
$409$	−10008.4	−1.20998	−0.604992	+	0.796232i	$0.706824\pi$
$410$	−928.787	−0.111877
$411$	−832.627	−0.0999281
$412$	3242.90	0.387781
$413$	−3817.81	−0.454873
$414$	−766.223	−0.0909609
$415$	−6708.78	−0.793544
$416$	7842.25	0.924274
$417$	3317.82	0.389627
$418$	2921.12	0.341811
$419$	−9521.34	−1.11014	−0.555069	−	0.831804i	$-0.687308\pi$
$419$	−9521.34	−1.11014	−0.555069	+	0.831804i	$0.687308\pi$
$420$	1154.99	0.134185
$421$	−6899.78	−0.798752	−0.399376	−	0.916787i	$-0.630773\pi$
$421$	−6899.78	−0.798752	−0.399376	+	0.916787i	$0.630773\pi$
$422$	−13091.4	−1.51015
$423$	−1869.84	−0.214928
$424$	1206.25	0.138162
$425$	−3012.25	−0.343802
$426$	−7491.18	−0.851993
$427$	1635.88	0.185400
$428$	4735.25	0.534783
$429$	575.265	0.0647414
$430$	−9339.95	−1.04747
$431$	−9802.42	−1.09551	−0.547756	−	0.836638i	$-0.684518\pi$
$431$	−9802.42	−1.09551	−0.547756	+	0.836638i	$0.684518\pi$
$432$	−2081.83	−0.231856
$433$	1700.80	0.188765	0.0943826	−	0.995536i	$-0.469912\pi$
$433$	1700.80	0.188765	0.0943826	+	0.995536i	$0.469912\pi$
$434$	849.848	0.0939954
$435$	3636.98	0.400873
$436$	−3434.52	−0.377257
$437$	3415.36	0.373865
$438$	12855.3	1.40240
$439$	−15259.6	−1.65900	−0.829502	−	0.558503i	$-0.811376\pi$
$439$	−15259.6	−1.65900	−0.829502	+	0.558503i	$0.811376\pi$
$440$	−436.154	−0.0472564
$441$	441.000	0.0476190
$442$	−12593.3	−1.35521
$443$	1287.78	0.138114	0.0690568	−	0.997613i	$-0.478001\pi$
$443$	1287.78	0.138114	0.0690568	+	0.997613i	$0.478001\pi$
$444$	−3142.36	−0.335878
$445$	9640.85	1.02701
$446$	4499.28	0.477684
$447$	−1649.41	−0.174529
$448$	1313.76	0.138547
$449$	−16115.8	−1.69388	−0.846941	−	0.531687i	$-0.821558\pi$
$449$	−16115.8	−1.69388	−0.846941	+	0.531687i	$0.821558\pi$
$450$	−1064.27	−0.111490
$451$	−138.236	−0.0144330
$452$	2383.77	0.248060
$453$	−4458.05	−0.462378
$454$	−10657.4	−1.10171
$455$	−2436.43	−0.251037
$456$	3790.07	0.389225
$457$	−14443.6	−1.47843	−0.739215	−	0.673470i	$-0.764803\pi$
$457$	−14443.6	−1.47843	−0.739215	+	0.673470i	$0.764803\pi$
$458$	10624.9	1.08400
$459$	2545.83	0.258887
$460$	1264.99	0.128219
$461$	−5358.10	−0.541327	−0.270663	−	0.962674i	$-0.587243\pi$
$461$	−5358.10	−0.541327	−0.270663	+	0.962674i	$0.587243\pi$
$462$	413.105	0.0416004
$463$	2652.97	0.266293	0.133147	−	0.991096i	$-0.457492\pi$
$463$	2652.97	0.266293	0.133147	+	0.991096i	$0.457492\pi$
$464$	9690.24	0.969522
$465$	949.173	0.0946599
$466$	−15710.7	−1.56177
$467$	−15904.9	−1.57600	−0.787999	−	0.615676i	$-0.788883\pi$
$467$	−15904.9	−1.57600	−0.787999	+	0.615676i	$0.788883\pi$
$468$	−1851.51	−0.182877
$469$	−448.826	−0.0441895
$470$	7418.43	0.728057
$471$	−1530.28	−0.149706
$472$	−4640.18	−0.452503
$473$	−1390.11	−0.135132
$474$	5467.79	0.529840
$475$	4743.89	0.458241
$476$	−3763.20	−0.362366
$477$	−1276.03	−0.122486
$478$	−19433.8	−1.85959
$479$	−9391.03	−0.895797	−0.447899	−	0.894084i	$-0.647827\pi$
$479$	−9391.03	−0.895797	−0.447899	+	0.894084i	$0.647827\pi$
$480$	6289.81	0.598102
$481$	6628.75	0.628368
$482$	4962.14	0.468920
$483$	483.000	0.0455016
$484$	−7427.75	−0.697572
$485$	−10095.9	−0.945215
$486$	899.480	0.0839531
$487$	−12373.8	−1.15136	−0.575679	−	0.817676i	$-0.695262\pi$
$487$	−12373.8	−1.15136	−0.575679	+	0.817676i	$0.695262\pi$
$488$	1988.26	0.184435
$489$	−10077.2	−0.931919
$490$	−1749.63	−0.161307
$491$	−9792.68	−0.900076	−0.450038	−	0.893009i	$-0.648590\pi$
$491$	−9792.68	−0.900076	−0.450038	+	0.893009i	$0.648590\pi$
$492$	444.918	0.0407692
$493$	−11850.0	−1.08255
$494$	19832.8	1.80632
$495$	461.386	0.0418945
$496$	2528.94	0.228937
$497$	4722.17	0.426194
$498$	7722.96	0.694928
$499$	−3701.57	−0.332074	−0.166037	−	0.986120i	$-0.553097\pi$
$499$	−3701.57	−0.332074	−0.166037	+	0.986120i	$0.553097\pi$
$500$	8632.01	0.772070
$501$	−7336.95	−0.654273
$502$	−21475.5	−1.90936
$503$	−21144.6	−1.87433	−0.937167	−	0.348881i	$-0.886562\pi$
$503$	−21144.6	−1.87433	−0.937167	+	0.348881i	$0.886562\pi$
$504$	535.992	0.0473710
$505$	7604.21	0.670065
$506$	452.448	0.0397506
$507$	−2685.27	−0.235221
$508$	−4946.54	−0.432022
$509$	8528.62	0.742681	0.371340	−	0.928497i	$-0.378898\pi$
$509$	8528.62	0.742681	0.371340	+	0.928497i	$0.378898\pi$
$510$	−10100.4	−0.876966
$511$	−8103.54	−0.701525
$512$	11510.4	0.993541
$513$	−4009.33	−0.345061
$514$	2188.39	0.187793
$515$	−5486.62	−0.469455
$516$	4474.13	0.381711
$517$	1104.12	0.0939250
$518$	4760.19	0.403766
$519$	−2176.81	−0.184107
$520$	−2961.24	−0.249729
$521$	12193.7	1.02536	0.512681	−	0.858579i	$-0.328652\pi$
$521$	12193.7	1.02536	0.512681	+	0.858579i	$0.328652\pi$
$522$	−4186.79	−0.351055
$523$	7520.53	0.628776	0.314388	−	0.949295i	$-0.398201\pi$
$523$	7520.53	0.628776	0.314388	+	0.949295i	$0.398201\pi$
$524$	−9789.48	−0.816136
$525$	670.880	0.0557707
$526$	−1767.16	−0.146486
$527$	−3092.60	−0.255628
$528$	1229.30	0.101323
$529$	529.000	0.0434783
$530$	5062.57	0.414913
$531$	4908.62	0.401160
$532$	5926.53	0.482984
$533$	−938.546	−0.0762719
$534$	−11098.3	−0.899381
$535$	−8011.53	−0.647418
$536$	−545.504	−0.0439593
$537$	−7187.90	−0.577618
$538$	860.845	0.0689845
$539$	−260.407	−0.0208099
$540$	−1484.99	−0.118340
$541$	8041.40	0.639052	0.319526	−	0.947578i	$-0.396476\pi$
$541$	8041.40	0.639052	0.319526	+	0.947578i	$0.396476\pi$
$542$	31805.3	2.52058
$543$	2429.91	0.192040
$544$	−20493.5	−1.61517
$545$	5810.84	0.456714
$546$	2804.75	0.219840
$547$	513.204	0.0401152	0.0200576	−	0.999799i	$-0.493615\pi$
$547$	513.204	0.0401152	0.0200576	+	0.999799i	$0.493615\pi$
$548$	−1582.42	−0.123354
$549$	−2103.28	−0.163508
$550$	628.445	0.0487218
$551$	18662.2	1.44290
$552$	587.039	0.0452646
$553$	−3446.70	−0.265043
$554$	−26809.3	−2.05599
$555$	5316.53	0.406620
$556$	6305.59	0.480965
$557$	14493.5	1.10253	0.551266	−	0.834330i	$-0.314145\pi$
$557$	14493.5	1.10253	0.551266	+	0.834330i	$0.314145\pi$
$558$	−1092.66	−0.0828962
$559$	−9438.09	−0.714112
$560$	−5206.49	−0.392883
$561$	−1503.29	−0.113136
$562$	−9241.28	−0.693630
$563$	24400.8	1.82659	0.913295	−	0.407299i	$-0.133529\pi$
$563$	24400.8	1.82659	0.913295	+	0.407299i	$0.133529\pi$
$564$	−3553.66	−0.265312
$565$	−4033.08	−0.300306
$566$	−18567.9	−1.37892
$567$	−567.000	−0.0419961
$568$	5739.34	0.423974
$569$	24818.9	1.82858	0.914290	−	0.405061i	$-0.132750\pi$
$569$	24818.9	1.82858	0.914290	+	0.405061i	$0.132750\pi$
$570$	15906.7	1.16888
$571$	−6852.31	−0.502207	−0.251103	−	0.967960i	$-0.580793\pi$
$571$	−6852.31	−0.502207	−0.251103	+	0.967960i	$0.580793\pi$
$572$	1093.30	0.0799183
$573$	4976.29	0.362805
$574$	−673.982	−0.0490095
$575$	734.774	0.0532907
$576$	−1689.12	−0.122187
$577$	−1225.62	−0.0884286	−0.0442143	−	0.999022i	$-0.514078\pi$
$577$	−1225.62	−0.0884286	−0.0442143	+	0.999022i	$0.514078\pi$
$578$	14723.4	1.05953
$579$	8318.36	0.597063
$580$	6912.16	0.494848
$581$	−4868.28	−0.347625
$582$	11622.1	0.827750
$583$	753.488	0.0535271
$584$	−9849.05	−0.697871
$585$	3132.56	0.221394
$586$	930.013	0.0655605
$587$	−20581.9	−1.44720	−0.723598	−	0.690221i	$-0.757513\pi$
$587$	−20581.9	−1.44720	−0.723598	+	0.690221i	$0.757513\pi$
$588$	838.130	0.0587821
$589$	4870.42	0.340717
$590$	−19474.6	−1.35891
$591$	4359.57	0.303433
$592$	14165.2	0.983421
$593$	17292.8	1.19752	0.598762	−	0.800927i	$-0.295660\pi$
$593$	17292.8	1.19752	0.598762	+	0.800927i	$0.295660\pi$
$594$	−531.135	−0.0366881
$595$	6366.92	0.438686
$596$	−3134.74	−0.215443
$597$	11246.2	0.770982
$598$	3071.87	0.210064
$599$	−12443.5	−0.848792	−0.424396	−	0.905477i	$-0.639514\pi$
$599$	−12443.5	−0.848792	−0.424396	+	0.905477i	$0.639514\pi$
$600$	815.389	0.0554802
$601$	−12864.8	−0.873152	−0.436576	−	0.899667i	$-0.643809\pi$
$601$	−12864.8	−0.873152	−0.436576	+	0.899667i	$0.643809\pi$
$602$	−6777.61	−0.458862
$603$	577.062	0.0389715
$604$	−8472.61	−0.570771
$605$	12566.9	0.844493
$606$	−8753.76	−0.586794
$607$	11968.9	0.800332	0.400166	−	0.916443i	$-0.368952\pi$
$607$	11968.9	0.800332	0.400166	+	0.916443i	$0.368952\pi$
$608$	32274.4	2.15280
$609$	2639.20	0.175609
$610$	8344.60	0.553874
$611$	7496.38	0.496352
$612$	4838.40	0.319577
$613$	4287.49	0.282496	0.141248	−	0.989974i	$-0.454889\pi$
$613$	4287.49	0.282496	0.141248	+	0.989974i	$0.454889\pi$
$614$	14145.0	0.929718
$615$	−752.752	−0.0493559
$616$	−316.499	−0.0207015
$617$	−6622.50	−0.432110	−0.216055	−	0.976381i	$-0.569319\pi$
$617$	−6622.50	−0.432110	−0.216055	+	0.976381i	$0.569319\pi$
$618$	6316.05	0.411114
$619$	19676.7	1.27766	0.638830	−	0.769348i	$-0.279419\pi$
$619$	19676.7	1.27766	0.638830	+	0.769348i	$0.279419\pi$
$620$	1803.92	0.116850
$621$	−621.000	−0.0401286
$622$	27748.3	1.78876
$623$	6995.96	0.449899
$624$	8346.27	0.535446
$625$	−10611.1	−0.679109
$626$	28947.5	1.84821
$627$	2367.48	0.150794
$628$	−2908.32	−0.184800
$629$	−17322.4	−1.09807
$630$	2249.53	0.142259
$631$	−5300.31	−0.334393	−0.167197	−	0.985924i	$-0.553471\pi$
$631$	−5300.31	−0.334393	−0.167197	+	0.985924i	$0.553471\pi$
$632$	−4189.13	−0.263662
$633$	−10610.2	−0.666221
$634$	3606.37	0.225911
$635$	8369.00	0.523014
$636$	−2425.13	−0.151199
$637$	−1768.02	−0.109971
$638$	2472.27	0.153414
$639$	−6071.37	−0.375868
$640$	−10071.4	−0.622041
$641$	17179.3	1.05857	0.529284	−	0.848445i	$-0.322461\pi$
$641$	17179.3	1.05857	0.529284	+	0.848445i	$0.322461\pi$
$642$	9222.65	0.566961
$643$	18473.1	1.13298	0.566491	−	0.824068i	$-0.308301\pi$
$643$	18473.1	1.13298	0.566491	+	0.824068i	$0.308301\pi$
$644$	917.952	0.0561683
$645$	−7569.74	−0.462106
$646$	−51827.4	−3.15653
$647$	25687.0	1.56084	0.780418	−	0.625258i	$-0.215006\pi$
$647$	25687.0	1.56084	0.780418	+	0.625258i	$0.215006\pi$
$648$	−689.133	−0.0417773
$649$	−2898.50	−0.175310
$650$	4266.79	0.257473
$651$	688.775	0.0414673
$652$	−19152.0	−1.15038
$653$	21578.7	1.29317	0.646584	−	0.762843i	$-0.276197\pi$
$653$	21578.7	1.29317	0.646584	+	0.762843i	$0.276197\pi$
$654$	−6689.27	−0.399956
$655$	16562.7	0.988029
$656$	−2005.61	−0.119369
$657$	10418.8	0.618687
$658$	5383.24	0.318937
$659$	−9815.17	−0.580189	−0.290095	−	0.956998i	$-0.593687\pi$
$659$	−9815.17	−0.580189	−0.290095	+	0.956998i	$0.593687\pi$
$660$	876.874	0.0517156
$661$	−12047.5	−0.708915	−0.354458	−	0.935072i	$-0.615334\pi$
$661$	−12047.5	−0.708915	−0.354458	+	0.935072i	$0.615334\pi$
$662$	−32331.9	−1.89821
$663$	−10206.5	−0.597870
$664$	−5916.91	−0.345814
$665$	−10027.0	−0.584709
$666$	−6120.25	−0.356088
$667$	2890.56	0.167800
$668$	−13944.0	−0.807651
$669$	3646.52	0.210736
$670$	−2289.45	−0.132014
$671$	1241.97	0.0714541
$672$	4564.25	0.262009
$673$	17399.7	0.996596	0.498298	−	0.867006i	$-0.333958\pi$
$673$	17399.7	0.996596	0.498298	+	0.867006i	$0.333958\pi$
$674$	5833.61	0.333386
$675$	−862.560	−0.0491851
$676$	−5103.41	−0.290363
$677$	−24203.7	−1.37404	−0.687018	−	0.726641i	$-0.741081\pi$
$677$	−24203.7	−1.37404	−0.687018	+	0.726641i	$0.741081\pi$
$678$	4642.77	0.262986
$679$	−7326.14	−0.414067
$680$	7738.37	0.436401
$681$	−8637.47	−0.486033
$682$	645.208	0.0362262
$683$	7366.09	0.412673	0.206336	−	0.978481i	$-0.433846\pi$
$683$	7366.09	0.412673	0.206336	+	0.978481i	$0.433846\pi$
$684$	−7619.82	−0.425952
$685$	2677.29	0.149334
$686$	−1269.64	−0.0706631
$687$	8611.16	0.478219
$688$	−20168.5	−1.11761
$689$	5115.76	0.282867
$690$	2463.77	0.135933
$691$	14400.7	0.792806	0.396403	−	0.918077i	$-0.370258\pi$
$691$	14400.7	0.792806	0.396403	+	0.918077i	$0.370258\pi$
$692$	−4137.07	−0.227266
$693$	334.809	0.0183526
$694$	31724.2	1.73521
$695$	−10668.4	−0.582265
$696$	3207.69	0.174694
$697$	2452.62	0.133285
$698$	−27786.0	−1.50676
$699$	−12733.0	−0.688995
$700$	1275.02	0.0688447
$701$	−4047.15	−0.218058	−0.109029	−	0.994039i	$-0.534774\pi$
$701$	−4047.15	−0.218058	−0.109029	+	0.994039i	$0.534774\pi$
$702$	−3606.11	−0.193880
$703$	27280.3	1.46358
$704$	997.409	0.0533967
$705$	6012.40	0.321192
$706$	−26323.0	−1.40323
$707$	5518.06	0.293533
$708$	9328.93	0.495202
$709$	−13757.1	−0.728713	−0.364357	−	0.931259i	$-0.618711\pi$
$709$	−13757.1	−0.728713	−0.364357	+	0.931259i	$0.618711\pi$
$710$	24087.7	1.27323
$711$	4431.47	0.233746
$712$	8502.90	0.447556
$713$	754.373	0.0396234
$714$	−7329.43	−0.384169
$715$	−1849.75	−0.0967506
$716$	−13660.8	−0.713026
$717$	−15750.5	−0.820381
$718$	31055.5	1.61418
$719$	14616.2	0.758128	0.379064	−	0.925370i	$-0.376246\pi$
$719$	14616.2	0.758128	0.379064	+	0.925370i	$0.376246\pi$
$720$	6694.05	0.346490
$721$	−3981.41	−0.205653
$722$	56232.0	2.89853
$723$	4021.66	0.206870
$724$	4618.10	0.237058
$725$	4014.94	0.205671
$726$	−14466.7	−0.739545
$727$	−8778.23	−0.447822	−0.223911	−	0.974610i	$-0.571882\pi$
$727$	−8778.23	−0.447822	−0.223911	+	0.974610i	$0.571882\pi$
$728$	−2148.85	−0.109398
$729$	729.000	0.0370370
$730$	−41335.9	−2.09577
$731$	24663.8	1.24791
$732$	−3997.33	−0.201838
$733$	−19947.1	−1.00513	−0.502566	−	0.864539i	$-0.667611\pi$
$733$	−19947.1	−1.00513	−0.502566	+	0.864539i	$0.667611\pi$
$734$	30861.2	1.55192
$735$	−1418.02	−0.0711627
$736$	4998.94	0.250358
$737$	−340.750	−0.0170308
$738$	866.548	0.0432223
$739$	17037.2	0.848069	0.424034	−	0.905646i	$-0.360614\pi$
$739$	17037.2	0.848069	0.424034	+	0.905646i	$0.360614\pi$
$740$	10104.2	0.501942
$741$	16073.9	0.796880
$742$	3673.69	0.181760
$743$	7014.58	0.346352	0.173176	−	0.984891i	$-0.444597\pi$
$743$	7014.58	0.346352	0.173176	+	0.984891i	$0.444597\pi$
$744$	837.138	0.0412513
$745$	5303.63	0.260819
$746$	−8627.67	−0.423433
$747$	6259.22	0.306577
$748$	−2857.04	−0.139657
$749$	−5813.63	−0.283612
$750$	16812.2	0.818526
$751$	20307.2	0.986709	0.493355	−	0.869828i	$-0.335771\pi$
$751$	20307.2	0.986709	0.493355	+	0.869828i	$0.335771\pi$
$752$	16019.2	0.776810
$753$	−17405.2	−0.842339
$754$	16785.3	0.810723
$755$	14334.7	0.690986
$756$	−1077.60	−0.0518410
$757$	−9644.24	−0.463046	−0.231523	−	0.972829i	$-0.574371\pi$
$757$	−9644.24	−0.463046	−0.231523	+	0.972829i	$0.574371\pi$
$758$	45025.9	2.15754
$759$	366.695	0.0175365
$760$	−12186.9	−0.581664
$761$	1677.07	0.0798868	0.0399434	−	0.999202i	$-0.487282\pi$
$761$	1677.07	0.0798868	0.0399434	+	0.999202i	$0.487282\pi$
$762$	−9634.16	−0.458017
$763$	4216.68	0.200071
$764$	9457.53	0.447855
$765$	−8186.05	−0.386885
$766$	7198.34	0.339539
$767$	−19679.2	−0.926433
$768$	16098.2	0.756373
$769$	38161.5	1.78952	0.894758	−	0.446552i	$-0.147348\pi$
$769$	38161.5	1.78952	0.894758	+	0.446552i	$0.147348\pi$
$770$	−1328.33	−0.0621683
$771$	1773.62	0.0828475
$772$	15809.2	0.737029
$773$	17275.9	0.803843	0.401922	−	0.915674i	$-0.368342\pi$
$773$	17275.9	0.803843	0.401922	+	0.915674i	$0.368342\pi$
$774$	8714.07	0.404678
$775$	1047.81	0.0485659
$776$	−8904.21	−0.411910
$777$	3857.99	0.178127
$778$	−25919.8	−1.19444
$779$	−3862.54	−0.177651
$780$	5953.49	0.273294
$781$	3585.09	0.164257
$782$	−8027.47	−0.367087
$783$	−3393.26	−0.154873
$784$	−3778.13	−0.172109
$785$	4920.56	0.223723
$786$	−19066.5	−0.865243
$787$	−23530.1	−1.06577	−0.532883	−	0.846189i	$-0.678892\pi$
$787$	−23530.1	−1.06577	−0.532883	+	0.846189i	$0.678892\pi$
$788$	8285.46	0.374565
$789$	−1432.22	−0.0646243
$790$	−17581.5	−0.791801
$791$	−2926.64	−0.131554
$792$	406.927	0.0182570
$793$	8432.28	0.377603
$794$	−13474.0	−0.602235
$795$	4103.05	0.183044
$796$	21373.6	0.951719
$797$	−27471.2	−1.22093	−0.610465	−	0.792043i	$-0.709017\pi$
$797$	−27471.2	−1.22093	−0.610465	+	0.792043i	$0.709017\pi$
$798$	11542.8	0.512046
$799$	−19589.6	−0.867374
$800$	6943.46	0.306860
$801$	−8994.80	−0.396774
$802$	−41898.6	−1.84475
$803$	−6152.23	−0.270371
$804$	1096.72	0.0481073
$805$	−1553.07	−0.0679983
$806$	4380.60	0.191439
$807$	697.688	0.0304334
$808$	6706.66	0.292004
$809$	20082.6	0.872765	0.436383	−	0.899761i	$-0.356259\pi$
$809$	20082.6	0.872765	0.436383	+	0.899761i	$0.356259\pi$
$810$	−2892.25	−0.125461
$811$	39875.9	1.72655	0.863274	−	0.504735i	$-0.168410\pi$
$811$	39875.9	1.72655	0.863274	+	0.504735i	$0.168410\pi$
$812$	5015.86	0.216776
$813$	25777.2	1.11199
$814$	3613.95	0.155613
$815$	32403.1	1.39268
$816$	−21810.6	−0.935691
$817$	−38842.1	−1.66329
$818$	−37046.7	−1.58350
$819$	2273.16	0.0969851
$820$	−1430.62	−0.0609262
$821$	23532.1	1.00034	0.500168	−	0.865928i	$-0.333272\pi$
$821$	23532.1	1.00034	0.500168	+	0.865928i	$0.333272\pi$
$822$	−3082.02	−0.130776
$823$	44102.8	1.86796	0.933978	−	0.357330i	$-0.116313\pi$
$823$	44102.8	1.86796	0.933978	+	0.357330i	$0.116313\pi$
$824$	−4839.01	−0.204581
$825$	509.335	0.0214942
$826$	−14131.9	−0.595292
$827$	27845.1	1.17082	0.585410	−	0.810737i	$-0.300934\pi$
$827$	27845.1	1.17082	0.585410	+	0.810737i	$0.300934\pi$
$828$	−1180.22	−0.0495357
$829$	40806.6	1.70962	0.854809	−	0.518943i	$-0.173674\pi$
$829$	40806.6	1.70962	0.854809	+	0.518943i	$0.173674\pi$
$830$	−24833.0	−1.03851
$831$	−21728.1	−0.907026
$832$	6771.85	0.282178
$833$	4620.21	0.192174
$834$	12281.1	0.509905
$835$	23591.8	0.977756
$836$	4499.44	0.186144
$837$	−885.568	−0.0365707
$838$	−35243.8	−1.45284
$839$	−17610.6	−0.724653	−0.362327	−	0.932051i	$-0.618017\pi$
$839$	−17610.6	−0.724653	−0.362327	+	0.932051i	$0.618017\pi$
$840$	−1723.47	−0.0707920
$841$	−8594.44	−0.352390
$842$	−25540.0	−1.04533
$843$	−7489.77	−0.306004
$844$	−20164.9	−0.822400
$845$	8634.41	0.351518
$846$	−6921.31	−0.281276
$847$	9119.30	0.369944
$848$	10932.0	0.442697
$849$	−15048.7	−0.608327
$850$	−11150.0	−0.449933
$851$	4225.41	0.170206
$852$	−11538.8	−0.463980
$853$	−40323.2	−1.61857	−0.809286	−	0.587415i	$-0.800145\pi$
$853$	−40323.2	−1.61857	−0.809286	+	0.587415i	$0.800145\pi$
$854$	6055.33	0.242633
$855$	12891.9	0.515665
$856$	−7065.90	−0.282135
$857$	2283.85	0.0910325	0.0455163	−	0.998964i	$-0.485507\pi$
$857$	2283.85	0.0910325	0.0455163	+	0.998964i	$0.485507\pi$
$858$	2129.38	0.0847270
$859$	13630.3	0.541398	0.270699	−	0.962664i	$-0.412745\pi$
$859$	13630.3	0.541398	0.270699	+	0.962664i	$0.412745\pi$
$860$	−14386.4	−0.570434
$861$	−546.241	−0.0216212
$862$	−36284.3	−1.43370
$863$	−25342.1	−0.999599	−0.499800	−	0.866141i	$-0.666593\pi$
$863$	−25342.1	−0.999599	−0.499800	+	0.866141i	$0.666593\pi$
$864$	−5868.32	−0.231070
$865$	6999.47	0.275132
$866$	6295.62	0.247037
$867$	11932.8	0.467428
$868$	1309.03	0.0511883
$869$	−2616.75	−0.102149
$870$	13462.5	0.524623
$871$	−2313.51	−0.0900001
$872$	5124.96	0.199029
$873$	9419.33	0.365173
$874$	12642.2	0.489276
$875$	−10597.8	−0.409453
$876$	19801.2	0.763722
$877$	−30758.1	−1.18429	−0.592147	−	0.805830i	$-0.701720\pi$
$877$	−30758.1	−1.18429	−0.592147	+	0.805830i	$0.701720\pi$
$878$	−56484.5	−2.17114
$879$	753.746	0.0289229
$880$	−3952.78	−0.151419
$881$	−32821.4	−1.25514	−0.627571	−	0.778559i	$-0.715951\pi$
$881$	−32821.4	−1.25514	−0.627571	+	0.778559i	$0.715951\pi$
$882$	1632.39	0.0623190
$883$	48437.6	1.84604	0.923021	−	0.384749i	$-0.125712\pi$
$883$	48437.6	1.84604	0.923021	+	0.384749i	$0.125712\pi$
$884$	−19397.7	−0.738026
$885$	−15783.5	−0.599500
$886$	4766.80	0.180749
$887$	12158.0	0.460232	0.230116	−	0.973163i	$-0.426090\pi$
$887$	12158.0	0.460232	0.230116	+	0.973163i	$0.426090\pi$
$888$	4689.00	0.177199
$889$	6073.03	0.229115
$890$	35686.2	1.34405
$891$	−430.468	−0.0161854
$892$	6930.29	0.260138
$893$	30851.0	1.15609
$894$	−6105.39	−0.228406
$895$	23112.5	0.863201
$896$	−7308.38	−0.272495
$897$	2489.66	0.0926725
$898$	−59653.7	−2.21678
$899$	4122.04	0.152923
$900$	−1639.31	−0.0607153
$901$	−13368.6	−0.494309
$902$	−511.689	−0.0188885
$903$	−5493.04	−0.202433
$904$	−3557.04	−0.130869
$905$	−7813.32	−0.286987
$906$	−16501.7	−0.605114
$907$	49889.8	1.82642	0.913211	−	0.407487i	$-0.133595\pi$
$907$	49889.8	1.82642	0.913211	+	0.407487i	$0.133595\pi$
$908$	−16415.7	−0.599971
$909$	−7094.65	−0.258872
$910$	−9018.61	−0.328532
$911$	28704.5	1.04393	0.521967	−	0.852966i	$-0.325198\pi$
$911$	28704.5	1.04393	0.521967	+	0.852966i	$0.325198\pi$
$912$	34348.7	1.24715
$913$	−3696.01	−0.133976
$914$	−53463.8	−1.93482
$915$	6763.03	0.244349
$916$	16365.7	0.590325
$917$	12018.9	0.432822
$918$	9423.55	0.338806
$919$	36821.3	1.32168	0.660839	−	0.750528i	$-0.270201\pi$
$919$	36821.3	1.32168	0.660839	+	0.750528i	$0.270201\pi$
$920$	−1887.61	−0.0676441
$921$	11464.1	0.410157
$922$	−19833.3	−0.708434
$923$	24340.8	0.868024
$924$	636.311	0.0226549
$925$	5869.04	0.208619
$926$	9820.12	0.348498
$927$	5118.96	0.181369
$928$	27315.2	0.966234
$929$	25025.7	0.883816	0.441908	−	0.897060i	$-0.354302\pi$
$929$	25025.7	0.883816	0.441908	+	0.897060i	$0.354302\pi$
$930$	3513.42	0.123881
$931$	−7276.20	−0.256142
$932$	−24199.4	−0.850512
$933$	22489.2	0.789134
$934$	−58873.0	−2.06251
$935$	4833.79	0.169072
$936$	2762.81	0.0964799
$937$	−33838.9	−1.17980	−0.589898	−	0.807478i	$-0.700832\pi$
$937$	−33838.9	−1.17980	−0.589898	+	0.807478i	$0.700832\pi$
$938$	−1661.36	−0.0578308
$939$	23461.1	0.815360
$940$	11426.7	0.396487
$941$	−55042.1	−1.90682	−0.953412	−	0.301673i	$-0.902455\pi$
$941$	−55042.1	−1.90682	−0.953412	+	0.301673i	$0.902455\pi$
$942$	−5664.41	−0.195920
$943$	−598.264	−0.0206598
$944$	−42053.1	−1.44990
$945$	1823.17	0.0627596
$946$	−5145.59	−0.176847
$947$	−16439.3	−0.564104	−0.282052	−	0.959399i	$-0.591015\pi$
$947$	−16439.3	−0.564104	−0.282052	+	0.959399i	$0.591015\pi$
$948$	8422.11	0.288541
$949$	−41770.2	−1.42879
$950$	17559.8	0.599700
$951$	2922.85	0.0996635
$952$	5615.41	0.191173
$953$	−17480.2	−0.594165	−0.297083	−	0.954852i	$-0.596014\pi$
$953$	−17480.2	−0.594165	−0.297083	+	0.954852i	$0.596014\pi$
$954$	−4723.32	−0.160297
$955$	−16001.1	−0.542182
$956$	−29934.1	−1.01270
$957$	2003.69	0.0676805
$958$	−34761.5	−1.17233
$959$	1942.80	0.0654183
$960$	5431.31	0.182599
$961$	−28715.2	−0.963890
$962$	24536.7	0.822345
$963$	7474.67	0.250122
$964$	7643.25	0.255366
$965$	−26747.5	−0.892260
$966$	1787.85	0.0595479
$967$	18106.6	0.602141	0.301071	−	0.953602i	$-0.402656\pi$
$967$	18106.6	0.602141	0.301071	+	0.953602i	$0.402656\pi$
$968$	11083.6	0.368017
$969$	−42004.5	−1.39255
$970$	−37370.5	−1.23700
$971$	7995.71	0.264258	0.132129	−	0.991233i	$-0.457819\pi$
$971$	7995.71	0.264258	0.132129	+	0.991233i	$0.457819\pi$
$972$	1385.48	0.0457194
$973$	−7741.59	−0.255071
$974$	−45802.4	−1.50678
$975$	3458.10	0.113587
$976$	18019.2	0.590963
$977$	−29163.7	−0.954995	−0.477498	−	0.878633i	$-0.658456\pi$
$977$	−29163.7	−0.954995	−0.477498	+	0.878633i	$0.658456\pi$
$978$	−37301.5	−1.21960
$979$	5311.36	0.173393
$980$	−2694.98	−0.0878449
$981$	−5421.45	−0.176446
$982$	−36248.2	−1.17793
$983$	−30677.4	−0.995378	−0.497689	−	0.867356i	$-0.665818\pi$
$983$	−30677.4	−0.995378	−0.497689	+	0.867356i	$0.665818\pi$
$984$	−663.902	−0.0215086
$985$	−14018.1	−0.453455
$986$	−43863.6	−1.41674
$987$	4362.95	0.140703
$988$	30548.7	0.983688
$989$	−6016.19	−0.193431
$990$	1707.85	0.0548273
$991$	−11856.9	−0.380067	−0.190034	−	0.981778i	$-0.560860\pi$
$991$	−11856.9	−0.380067	−0.190034	+	0.981778i	$0.560860\pi$
$992$	7128.67	0.228161
$993$	−26204.0	−0.837421
$994$	17479.4	0.557760
$995$	−36161.8	−1.15217
$996$	11895.8	0.378446
$997$	−53557.8	−1.70130	−0.850648	−	0.525736i	$-0.823790\pi$
$997$	−53557.8	−1.70130	−0.850648	+	0.525736i	$0.823790\pi$
$998$	−13701.6	−0.434585
$999$	−4960.27	−0.157093

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.4.a.b.1.3	✓	4
3.2	odd	2		1449.4.a.d.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.4.a.b.1.3	✓	4	1.1	even	1	trivial
1449.4.a.d.1.2		4	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	483.a (trivial)

\(f(q)\)	\(=\)	\(q+3.70156 q^{2} +3.00000 q^{3} +5.70156 q^{4} -9.64642 q^{5} +11.1047 q^{6} -7.00000 q^{7} -8.50781 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+3.70156 q^{2} +3.00000 q^{3} +5.70156 q^{4} -9.64642 q^{5} +11.1047 q^{6} -7.00000 q^{7} -8.50781 q^{8} +9.00000 q^{9} -35.7068 q^{10} -5.31442 q^{11} +17.1047 q^{12} -36.0820 q^{13} -25.9109 q^{14} -28.9392 q^{15} -77.1047 q^{16} +94.2900 q^{17} +33.3141 q^{18} -148.494 q^{19} -54.9996 q^{20} -21.0000 q^{21} -19.6717 q^{22} -23.0000 q^{23} -25.5234 q^{24} -31.9467 q^{25} -133.560 q^{26} +27.0000 q^{27} -39.9109 q^{28} -125.676 q^{29} -107.120 q^{30} -32.7988 q^{31} -217.345 q^{32} -15.9433 q^{33} +349.020 q^{34} +67.5249 q^{35} +51.3141 q^{36} -183.714 q^{37} -549.659 q^{38} -108.246 q^{39} +82.0699 q^{40} +26.0115 q^{41} -77.7328 q^{42} +261.573 q^{43} -30.3005 q^{44} -86.8177 q^{45} -85.1359 q^{46} -207.760 q^{47} -231.314 q^{48} +49.0000 q^{49} -118.253 q^{50} +282.870 q^{51} -205.724 q^{52} -141.782 q^{53} +99.9422 q^{54} +51.2651 q^{55} +59.5547 q^{56} -445.482 q^{57} -465.199 q^{58} +545.402 q^{59} -164.999 q^{60} -233.698 q^{61} -121.407 q^{62} -63.0000 q^{63} -187.680 q^{64} +348.062 q^{65} -59.0150 q^{66} +64.1180 q^{67} +537.600 q^{68} -69.0000 q^{69} +249.948 q^{70} -674.596 q^{71} -76.5703 q^{72} +1157.65 q^{73} -680.027 q^{74} -95.8400 q^{75} -846.647 q^{76} +37.2010 q^{77} -400.679 q^{78} +492.386 q^{79} +743.784 q^{80} +81.0000 q^{81} +96.2831 q^{82} +695.468 q^{83} -119.733 q^{84} -909.561 q^{85} +968.230 q^{86} -377.029 q^{87} +45.2141 q^{88} -999.423 q^{89} -321.361 q^{90} +252.574 q^{91} -131.136 q^{92} -98.3964 q^{93} -769.035 q^{94} +1432.43 q^{95} -652.036 q^{96} +1046.59 q^{97} +181.377 q^{98} -47.8298 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 12 q^{3} + 10 q^{4} - 23 q^{5} + 6 q^{6} - 28 q^{7} + 30 q^{8} + 36 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 + 12 * q^3 + 10 * q^4 - 23 * q^5 + 6 * q^6 - 28 * q^7 + 30 * q^8 + 36 * q^9	\( 4 q + 2 q^{2} + 12 q^{3} + 10 q^{4} - 23 q^{5} + 6 q^{6} - 28 q^{7} + 30 q^{8} + 36 q^{9} - 32 q^{10} - 48 q^{11} + 30 q^{12} - 107 q^{13} - 14 q^{14} - 69 q^{15} - 270 q^{16} - 6 q^{17} + 18 q^{18} + 76 q^{19} - 78 q^{20} - 84 q^{21} - 106 q^{22} - 92 q^{23} + 90 q^{24} + 115 q^{25} - 320 q^{26} + 108 q^{27} - 70 q^{28} + 204 q^{29} - 96 q^{30} - 276 q^{31} - 498 q^{32} - 144 q^{33} - 126 q^{34} + 161 q^{35} + 90 q^{36} - 248 q^{37} - 372 q^{38} - 321 q^{39} - 70 q^{40} - 450 q^{41} - 42 q^{42} + 109 q^{43} - 202 q^{44} - 207 q^{45} - 46 q^{46} - 688 q^{47} - 810 q^{48} + 196 q^{49} - 1152 q^{50} - 18 q^{51} - 534 q^{52} - 633 q^{53} + 54 q^{54} + 581 q^{55} - 210 q^{56} + 228 q^{57} - 308 q^{58} + 585 q^{59} - 234 q^{60} + 1311 q^{61} + 846 q^{62} - 252 q^{63} + 722 q^{64} - 1614 q^{65} - 318 q^{66} + 365 q^{67} - 138 q^{68} - 276 q^{69} + 224 q^{70} - 3049 q^{71} + 270 q^{72} - 1164 q^{73} + 2090 q^{74} + 345 q^{75} - 220 q^{76} + 336 q^{77} - 960 q^{78} - 476 q^{79} + 1614 q^{80} + 324 q^{81} + 1784 q^{82} + 1462 q^{83} - 210 q^{84} - 891 q^{85} - 1032 q^{86} + 612 q^{87} + 50 q^{88} - 1767 q^{89} - 288 q^{90} + 749 q^{91} - 230 q^{92} - 828 q^{93} - 1246 q^{94} - 1927 q^{95} - 1494 q^{96} + 1788 q^{97} + 98 q^{98} - 432 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + 12 * q^3 + 10 * q^4 - 23 * q^5 + 6 * q^6 - 28 * q^7 + 30 * q^8 + 36 * q^9 - 32 * q^10 - 48 * q^11 + 30 * q^12 - 107 * q^13 - 14 * q^14 - 69 * q^15 - 270 * q^16 - 6 * q^17 + 18 * q^18 + 76 * q^19 - 78 * q^20 - 84 * q^21 - 106 * q^22 - 92 * q^23 + 90 * q^24 + 115 * q^25 - 320 * q^26 + 108 * q^27 - 70 * q^28 + 204 * q^29 - 96 * q^30 - 276 * q^31 - 498 * q^32 - 144 * q^33 - 126 * q^34 + 161 * q^35 + 90 * q^36 - 248 * q^37 - 372 * q^38 - 321 * q^39 - 70 * q^40 - 450 * q^41 - 42 * q^42 + 109 * q^43 - 202 * q^44 - 207 * q^45 - 46 * q^46 - 688 * q^47 - 810 * q^48 + 196 * q^49 - 1152 * q^50 - 18 * q^51 - 534 * q^52 - 633 * q^53 + 54 * q^54 + 581 * q^55 - 210 * q^56 + 228 * q^57 - 308 * q^58 + 585 * q^59 - 234 * q^60 + 1311 * q^61 + 846 * q^62 - 252 * q^63 + 722 * q^64 - 1614 * q^65 - 318 * q^66 + 365 * q^67 - 138 * q^68 - 276 * q^69 + 224 * q^70 - 3049 * q^71 + 270 * q^72 - 1164 * q^73 + 2090 * q^74 + 345 * q^75 - 220 * q^76 + 336 * q^77 - 960 * q^78 - 476 * q^79 + 1614 * q^80 + 324 * q^81 + 1784 * q^82 + 1462 * q^83 - 210 * q^84 - 891 * q^85 - 1032 * q^86 + 612 * q^87 + 50 * q^88 - 1767 * q^89 - 288 * q^90 + 749 * q^91 - 230 * q^92 - 828 * q^93 - 1246 * q^94 - 1927 * q^95 - 1494 * q^96 + 1788 * q^97 + 98 * q^98 - 432 * q^99

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