LMFDB - Embedded newform 798.4.a.r.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [798,4,Mod(1,798)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(798, 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("798.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	798.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:	$47.0835241846$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 382x^{3} + 570x^{2} + 32160x - 9856 $ x^5 - 2x^4 - 382x^3 + 570x^2 + 32160x - 9856
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{3}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-16.0787$ of defining polynomial
Character	$\chi$	$=$	798.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +4.39114 q^{5} +6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +4.39114 q^{5} +6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +8.78228 q^{10} +50.1465 q^{11} +12.0000 q^{12} +11.4821 q^{13} +14.0000 q^{14} +13.1734 q^{15} +16.0000 q^{16} +107.299 q^{17} +18.0000 q^{18} +19.0000 q^{19} +17.5646 q^{20} +21.0000 q^{21} +100.293 q^{22} -181.876 q^{23} +24.0000 q^{24} -105.718 q^{25} +22.9642 q^{26} +27.0000 q^{27} +28.0000 q^{28} -286.643 q^{29} +26.3468 q^{30} -85.4861 q^{31} +32.0000 q^{32} +150.439 q^{33} +214.597 q^{34} +30.7380 q^{35} +36.0000 q^{36} +313.830 q^{37} +38.0000 q^{38} +34.4463 q^{39} +35.1291 q^{40} -18.8820 q^{41} +42.0000 q^{42} +395.779 q^{43} +200.586 q^{44} +39.5203 q^{45} -363.751 q^{46} +364.910 q^{47} +48.0000 q^{48} +49.0000 q^{49} -211.436 q^{50} +321.896 q^{51} +45.9283 q^{52} +152.250 q^{53} +54.0000 q^{54} +220.200 q^{55} +56.0000 q^{56} +57.0000 q^{57} -573.285 q^{58} -375.717 q^{59} +52.6937 q^{60} +253.815 q^{61} -170.972 q^{62} +63.0000 q^{63} +64.0000 q^{64} +50.4195 q^{65} +300.879 q^{66} -291.853 q^{67} +429.194 q^{68} -545.627 q^{69} +61.4760 q^{70} +587.770 q^{71} +72.0000 q^{72} -788.422 q^{73} +627.660 q^{74} -317.154 q^{75} +76.0000 q^{76} +351.025 q^{77} +68.8925 q^{78} +929.422 q^{79} +70.2582 q^{80} +81.0000 q^{81} -37.7641 q^{82} -371.206 q^{83} +84.0000 q^{84} +471.163 q^{85} +791.557 q^{86} -859.928 q^{87} +401.172 q^{88} +914.506 q^{89} +79.0405 q^{90} +80.3746 q^{91} -727.502 q^{92} -256.458 q^{93} +729.821 q^{94} +83.4317 q^{95} +96.0000 q^{96} +374.481 q^{97} +98.0000 q^{98} +451.318 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 10 q^{2} + 15 q^{3} + 20 q^{4} + 20 q^{5} + 30 q^{6} + 35 q^{7} + 40 q^{8} + 45 q^{9}+O(q^{10}) $ 5 * q + 10 * q^2 + 15 * q^3 + 20 * q^4 + 20 * q^5 + 30 * q^6 + 35 * q^7 + 40 * q^8 + 45 * q^9	\( 5 q + 10 q^{2} + 15 q^{3} + 20 q^{4} + 20 q^{5} + 30 q^{6} + 35 q^{7} + 40 q^{8} + 45 q^{9} + 40 q^{10} + 82 q^{11} + 60 q^{12} + 20 q^{13} + 70 q^{14} + 60 q^{15} + 80 q^{16} + 48 q^{17} + 90 q^{18} + 95 q^{19} + 80 q^{20} + 105 q^{21} + 164 q^{22} + 166 q^{23} + 120 q^{24} + 235 q^{25} + 40 q^{26} + 135 q^{27} + 140 q^{28} + 134 q^{29} + 120 q^{30} + 124 q^{31} + 160 q^{32} + 246 q^{33} + 96 q^{34} + 140 q^{35} + 180 q^{36} + 334 q^{37} + 190 q^{38} + 60 q^{39} + 160 q^{40} - 126 q^{41} + 210 q^{42} + 132 q^{43} + 328 q^{44} + 180 q^{45} + 332 q^{46} + 120 q^{47} + 240 q^{48} + 245 q^{49} + 470 q^{50} + 144 q^{51} + 80 q^{52} + 142 q^{53} + 270 q^{54} + 64 q^{55} + 280 q^{56} + 285 q^{57} + 268 q^{58} + 12 q^{59} + 240 q^{60} + 614 q^{61} + 248 q^{62} + 315 q^{63} + 320 q^{64} + 672 q^{65} + 492 q^{66} - 30 q^{67} + 192 q^{68} + 498 q^{69} + 280 q^{70} + 548 q^{71} + 360 q^{72} + 554 q^{73} + 668 q^{74} + 705 q^{75} + 380 q^{76} + 574 q^{77} + 120 q^{78} - 138 q^{79} + 320 q^{80} + 405 q^{81} - 252 q^{82} + 100 q^{83} + 420 q^{84} - 156 q^{85} + 264 q^{86} + 402 q^{87} + 656 q^{88} + 842 q^{89} + 360 q^{90} + 140 q^{91} + 664 q^{92} + 372 q^{93} + 240 q^{94} + 380 q^{95} + 480 q^{96} - 568 q^{97} + 490 q^{98} + 738 q^{99}+O(q^{100}) \) 5 * q + 10 * q^2 + 15 * q^3 + 20 * q^4 + 20 * q^5 + 30 * q^6 + 35 * q^7 + 40 * q^8 + 45 * q^9 + 40 * q^10 + 82 * q^11 + 60 * q^12 + 20 * q^13 + 70 * q^14 + 60 * q^15 + 80 * q^16 + 48 * q^17 + 90 * q^18 + 95 * q^19 + 80 * q^20 + 105 * q^21 + 164 * q^22 + 166 * q^23 + 120 * q^24 + 235 * q^25 + 40 * q^26 + 135 * q^27 + 140 * q^28 + 134 * q^29 + 120 * q^30 + 124 * q^31 + 160 * q^32 + 246 * q^33 + 96 * q^34 + 140 * q^35 + 180 * q^36 + 334 * q^37 + 190 * q^38 + 60 * q^39 + 160 * q^40 - 126 * q^41 + 210 * q^42 + 132 * q^43 + 328 * q^44 + 180 * q^45 + 332 * q^46 + 120 * q^47 + 240 * q^48 + 245 * q^49 + 470 * q^50 + 144 * q^51 + 80 * q^52 + 142 * q^53 + 270 * q^54 + 64 * q^55 + 280 * q^56 + 285 * q^57 + 268 * q^58 + 12 * q^59 + 240 * q^60 + 614 * q^61 + 248 * q^62 + 315 * q^63 + 320 * q^64 + 672 * q^65 + 492 * q^66 - 30 * q^67 + 192 * q^68 + 498 * q^69 + 280 * q^70 + 548 * q^71 + 360 * q^72 + 554 * q^73 + 668 * q^74 + 705 * q^75 + 380 * q^76 + 574 * q^77 + 120 * q^78 - 138 * q^79 + 320 * q^80 + 405 * q^81 - 252 * q^82 + 100 * q^83 + 420 * q^84 - 156 * q^85 + 264 * q^86 + 402 * q^87 + 656 * q^88 + 842 * q^89 + 360 * q^90 + 140 * q^91 + 664 * q^92 + 372 * q^93 + 240 * q^94 + 380 * q^95 + 480 * q^96 - 568 * q^97 + 490 * q^98 + 738 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	4.00000	0.500000
$5$	4.39114	0.392756	0.196378	−	0.980528i	$-0.437082\pi$
$5$	4.39114	0.392756	0.196378	+	0.980528i	$0.437082\pi$
$6$	6.00000	0.408248
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	8.78228	0.277720
$11$	50.1465	1.37452	0.687260	−	0.726411i	$-0.258813\pi$
$11$	50.1465	1.37452	0.687260	+	0.726411i	$0.258813\pi$
$12$	12.0000	0.288675
$13$	11.4821	0.244966	0.122483	−	0.992471i	$-0.460914\pi$
$13$	11.4821	0.244966	0.122483	+	0.992471i	$0.460914\pi$
$14$	14.0000	0.267261
$15$	13.1734	0.226758
$16$	16.0000	0.250000
$17$	107.299	1.53081	0.765404	−	0.643550i	$-0.222539\pi$
$17$	107.299	1.53081	0.765404	+	0.643550i	$0.222539\pi$
$18$	18.0000	0.235702
$19$	19.0000	0.229416
$19$	19.0000	0.229416
$20$	17.5646	0.196378
$21$	21.0000	0.218218
$22$	100.293	0.971933
$23$	−181.876	−1.64886	−0.824428	−	0.565967i	$-0.808503\pi$
$23$	−181.876	−1.64886	−0.824428	+	0.565967i	$0.808503\pi$
$24$	24.0000	0.204124
$25$	−105.718	−0.845743
$26$	22.9642	0.173217
$27$	27.0000	0.192450
$28$	28.0000	0.188982
$29$	−286.643	−1.83545	−0.917727	−	0.397211i	$-0.869978\pi$
$29$	−286.643	−1.83545	−0.917727	+	0.397211i	$0.869978\pi$
$30$	26.3468	0.160342
$31$	−85.4861	−0.495282	−0.247641	−	0.968852i	$-0.579655\pi$
$31$	−85.4861	−0.495282	−0.247641	+	0.968852i	$0.579655\pi$
$32$	32.0000	0.176777
$33$	150.439	0.793580
$34$	214.597	1.08244
$35$	30.7380	0.148448
$36$	36.0000	0.166667
$37$	313.830	1.39441	0.697207	−	0.716870i	$-0.254426\pi$
$37$	313.830	1.39441	0.697207	+	0.716870i	$0.254426\pi$
$38$	38.0000	0.162221
$39$	34.4463	0.141431
$40$	35.1291	0.138860
$41$	−18.8820	−0.0719239	−0.0359619	−	0.999353i	$-0.511450\pi$
$41$	−18.8820	−0.0719239	−0.0359619	+	0.999353i	$0.511450\pi$
$42$	42.0000	0.154303
$43$	395.779	1.40362	0.701810	−	0.712364i	$-0.252376\pi$
$43$	395.779	1.40362	0.701810	+	0.712364i	$0.252376\pi$
$44$	200.586	0.687260
$45$	39.5203	0.130919
$46$	−363.751	−1.16592
$47$	364.910	1.13250	0.566251	−	0.824233i	$-0.308393\pi$
$47$	364.910	1.13250	0.566251	+	0.824233i	$0.308393\pi$
$48$	48.0000	0.144338
$49$	49.0000	0.142857
$50$	−211.436	−0.598031
$51$	321.896	0.883812
$52$	45.9283	0.122483
$53$	152.250	0.394587	0.197294	−	0.980344i	$-0.436785\pi$
$53$	152.250	0.394587	0.197294	+	0.980344i	$0.436785\pi$
$54$	54.0000	0.136083
$55$	220.200	0.539851
$56$	56.0000	0.133631
$57$	57.0000	0.132453
$58$	−573.285	−1.29786
$59$	−375.717	−0.829055	−0.414527	−	0.910037i	$-0.636053\pi$
$59$	−375.717	−0.829055	−0.414527	+	0.910037i	$0.636053\pi$
$60$	52.6937	0.113379
$61$	253.815	0.532748	0.266374	−	0.963870i	$-0.414174\pi$
$61$	253.815	0.532748	0.266374	+	0.963870i	$0.414174\pi$
$62$	−170.972	−0.350217
$63$	63.0000	0.125988
$64$	64.0000	0.125000
$65$	50.4195	0.0962117
$66$	300.879	0.561146
$67$	−291.853	−0.532171	−0.266086	−	0.963949i	$-0.585730\pi$
$67$	−291.853	−0.532171	−0.266086	+	0.963949i	$0.585730\pi$
$68$	429.194	0.765404
$69$	−545.627	−0.951967
$70$	61.4760	0.104968
$71$	587.770	0.982472	0.491236	−	0.871027i	$-0.336545\pi$
$71$	587.770	0.982472	0.491236	+	0.871027i	$0.336545\pi$
$72$	72.0000	0.117851
$73$	−788.422	−1.26408	−0.632040	−	0.774936i	$-0.717782\pi$
$73$	−788.422	−1.26408	−0.632040	+	0.774936i	$0.717782\pi$
$74$	627.660	0.985999
$75$	−317.154	−0.488290
$76$	76.0000	0.114708
$77$	351.025	0.519520
$78$	68.8925	0.100007
$79$	929.422	1.32365	0.661823	−	0.749660i	$-0.269783\pi$
$79$	929.422	1.32365	0.661823	+	0.749660i	$0.269783\pi$
$80$	70.2582	0.0981889
$81$	81.0000	0.111111
$82$	−37.7641	−0.0508579
$83$	−371.206	−0.490905	−0.245453	−	0.969409i	$-0.578937\pi$
$83$	−371.206	−0.490905	−0.245453	+	0.969409i	$0.578937\pi$
$84$	84.0000	0.109109
$85$	471.163	0.601233
$86$	791.557	0.992509
$87$	−859.928	−1.05970
$88$	401.172	0.485966
$89$	914.506	1.08918	0.544592	−	0.838701i	$-0.316684\pi$
$89$	914.506	1.08918	0.544592	+	0.838701i	$0.316684\pi$
$90$	79.0405	0.0925734
$91$	80.3746	0.0925884
$92$	−727.502	−0.824428
$93$	−256.458	−0.285951
$94$	729.821	0.800800
$95$	83.4317	0.0901043
$96$	96.0000	0.102062
$97$	374.481	0.391988	0.195994	−	0.980605i	$-0.437207\pi$
$97$	374.481	0.391988	0.195994	+	0.980605i	$0.437207\pi$
$98$	98.0000	0.101015
$99$	451.318	0.458174
$100$	−422.872	−0.422872
$101$	1096.73	1.08048	0.540239	−	0.841512i	$-0.318334\pi$
$101$	1096.73	1.08048	0.540239	+	0.841512i	$0.318334\pi$
$102$	643.791	0.624950
$103$	−1936.65	−1.85266	−0.926329	−	0.376715i	$-0.877054\pi$
$103$	−1936.65	−1.85266	−0.926329	+	0.376715i	$0.877054\pi$
$104$	91.8567	0.0866086
$105$	92.2139	0.0857063
$106$	304.500	0.279015
$107$	−683.064	−0.617143	−0.308571	−	0.951201i	$-0.599851\pi$
$107$	−683.064	−0.617143	−0.308571	+	0.951201i	$0.599851\pi$
$108$	108.000	0.0962250
$109$	−339.420	−0.298262	−0.149131	−	0.988817i	$-0.547648\pi$
$109$	−339.420	−0.298262	−0.149131	+	0.988817i	$0.547648\pi$
$110$	440.400	0.381732
$111$	941.489	0.805065
$112$	112.000	0.0944911
$113$	−2012.18	−1.67513	−0.837565	−	0.546337i	$-0.816022\pi$
$113$	−2012.18	−1.67513	−0.837565	+	0.546337i	$0.816022\pi$
$114$	114.000	0.0936586
$115$	−798.641	−0.647597
$116$	−1146.57	−0.917727
$117$	103.339	0.0816553
$118$	−751.435	−0.586230
$119$	751.090	0.578591
$120$	105.387	0.0801709
$121$	1183.67	0.889307
$122$	507.630	0.376710
$123$	−56.6461	−0.0415253
$124$	−341.944	−0.247641
$125$	−1013.11	−0.724926
$126$	126.000	0.0890871
$127$	1646.24	1.15023	0.575117	−	0.818071i	$-0.304956\pi$
$127$	1646.24	1.15023	0.575117	+	0.818071i	$0.304956\pi$
$128$	128.000	0.0883883
$129$	1187.34	0.810381
$130$	100.839	0.0680320
$131$	−500.625	−0.333892	−0.166946	−	0.985966i	$-0.553391\pi$
$131$	−500.625	−0.333892	−0.166946	+	0.985966i	$0.553391\pi$
$132$	601.758	0.396790
$133$	133.000	0.0867110
$134$	−583.705	−0.376302
$135$	118.561	0.0755858
$136$	858.389	0.541222
$137$	769.300	0.479750	0.239875	−	0.970804i	$-0.422894\pi$
$137$	769.300	0.479750	0.239875	+	0.970804i	$0.422894\pi$
$138$	−1091.25	−0.673142
$139$	−1928.26	−1.17664	−0.588320	−	0.808628i	$-0.700210\pi$
$139$	−1928.26	−1.17664	−0.588320	+	0.808628i	$0.700210\pi$
$140$	122.952	0.0742238
$141$	1094.73	0.653851
$142$	1175.54	0.694712
$143$	575.786	0.336711
$144$	144.000	0.0833333
$145$	−1258.69	−0.720885
$146$	−1576.84	−0.893840
$147$	147.000	0.0824786
$148$	1255.32	0.697207
$149$	1538.09	0.845671	0.422836	−	0.906206i	$-0.361035\pi$
$149$	1538.09	0.845671	0.422836	+	0.906206i	$0.361035\pi$
$150$	−634.307	−0.345273
$151$	951.812	0.512963	0.256481	−	0.966549i	$-0.417437\pi$
$151$	951.812	0.512963	0.256481	+	0.966549i	$0.417437\pi$
$152$	152.000	0.0811107
$153$	965.687	0.510269
$154$	702.051	0.367356
$155$	−375.381	−0.194525
$156$	137.785	0.0707156
$157$	−172.640	−0.0877593	−0.0438796	−	0.999037i	$-0.513972\pi$
$157$	−172.640	−0.0877593	−0.0438796	+	0.999037i	$0.513972\pi$
$158$	1858.84	0.935960
$159$	456.750	0.227815
$160$	140.516	0.0694300
$161$	−1273.13	−0.623209
$162$	162.000	0.0785674
$163$	−2606.67	−1.25258	−0.626288	−	0.779592i	$-0.715427\pi$
$163$	−2606.67	−1.25258	−0.626288	+	0.779592i	$0.715427\pi$
$164$	−75.5282	−0.0359619
$165$	660.601	0.311683
$166$	−742.412	−0.347123
$167$	1514.43	0.701735	0.350868	−	0.936425i	$-0.385887\pi$
$167$	1514.43	0.701735	0.350868	+	0.936425i	$0.385887\pi$
$168$	168.000	0.0771517
$169$	−2065.16	−0.939992
$170$	942.326	0.425136
$171$	171.000	0.0764719
$172$	1583.11	0.701810
$173$	−276.369	−0.121456	−0.0607281	−	0.998154i	$-0.519342\pi$
$173$	−276.369	−0.121456	−0.0607281	+	0.998154i	$0.519342\pi$
$174$	−1719.86	−0.749321
$175$	−740.025	−0.319661
$176$	802.343	0.343630
$177$	−1127.15	−0.478655
$178$	1829.01	0.770170
$179$	−3173.73	−1.32523	−0.662614	−	0.748961i	$-0.730553\pi$
$179$	−3173.73	−1.32523	−0.662614	+	0.748961i	$0.730553\pi$
$180$	158.081	0.0654593
$181$	1647.82	0.676694	0.338347	−	0.941022i	$-0.390132\pi$
$181$	1647.82	0.676694	0.338347	+	0.941022i	$0.390132\pi$
$182$	160.749	0.0654699
$183$	761.444	0.307582
$184$	−1455.00	−0.582959
$185$	1378.07	0.547664
$186$	−512.916	−0.202198
$187$	5380.64	2.10413
$188$	1459.64	0.566251
$189$	189.000	0.0727393
$190$	166.863	0.0637134
$191$	−1464.59	−0.554839	−0.277420	−	0.960749i	$-0.589479\pi$
$191$	−1464.59	−0.554839	−0.277420	+	0.960749i	$0.589479\pi$
$192$	192.000	0.0721688
$193$	−2850.56	−1.06315	−0.531574	−	0.847012i	$-0.678399\pi$
$193$	−2850.56	−1.06315	−0.531574	+	0.847012i	$0.678399\pi$
$194$	748.962	0.277177
$195$	151.258	0.0555479
$196$	196.000	0.0714286
$197$	−411.592	−0.148856	−0.0744282	−	0.997226i	$-0.523713\pi$
$197$	−411.592	−0.148856	−0.0744282	+	0.997226i	$0.523713\pi$
$198$	902.636	0.323978
$199$	−768.466	−0.273744	−0.136872	−	0.990589i	$-0.543705\pi$
$199$	−768.466	−0.273744	−0.136872	+	0.990589i	$0.543705\pi$
$200$	−845.743	−0.299015
$201$	−875.558	−0.307249
$202$	2193.45	0.764013
$203$	−2006.50	−0.693737
$204$	1287.58	0.441906
$205$	−82.9137	−0.0282485
$206$	−3873.30	−1.31003
$207$	−1636.88	−0.549619
$208$	183.713	0.0612415
$209$	952.783	0.315337
$210$	184.428	0.0606035
$211$	−1646.14	−0.537084	−0.268542	−	0.963268i	$-0.586542\pi$
$211$	−1646.14	−0.537084	−0.268542	+	0.963268i	$0.586542\pi$
$212$	609.000	0.197294
$213$	1763.31	0.567230
$214$	−1366.13	−0.436386
$215$	1737.92	0.551280
$216$	216.000	0.0680414
$217$	−598.402	−0.187199
$218$	−678.839	−0.210903
$219$	−2365.27	−0.729817
$220$	880.801	0.269925
$221$	1232.01	0.374996
$222$	1882.98	0.569267
$223$	−1628.93	−0.489153	−0.244577	−	0.969630i	$-0.578649\pi$
$223$	−1628.93	−0.489153	−0.244577	+	0.969630i	$0.578649\pi$
$224$	224.000	0.0668153
$225$	−951.461	−0.281914
$226$	−4024.36	−1.18450
$227$	−4150.09	−1.21344	−0.606720	−	0.794916i	$-0.707515\pi$
$227$	−4150.09	−1.21344	−0.606720	+	0.794916i	$0.707515\pi$
$228$	228.000	0.0662266
$229$	−1154.76	−0.333225	−0.166613	−	0.986022i	$-0.553283\pi$
$229$	−1154.76	−0.333225	−0.166613	+	0.986022i	$0.553283\pi$
$230$	−1597.28	−0.457920
$231$	1053.08	0.299945
$232$	−2293.14	−0.648931
$233$	3179.44	0.893958	0.446979	−	0.894544i	$-0.352500\pi$
$233$	3179.44	0.893958	0.446979	+	0.894544i	$0.352500\pi$
$234$	206.678	0.0577390
$235$	1602.37	0.444797
$236$	−1502.87	−0.414527
$237$	2788.26	0.764208
$238$	1502.18	0.409126
$239$	3933.79	1.06467	0.532334	−	0.846535i	$-0.321315\pi$
$239$	3933.79	1.06467	0.532334	+	0.846535i	$0.321315\pi$
$240$	210.775	0.0566894
$241$	−5222.70	−1.39595	−0.697975	−	0.716123i	$-0.745915\pi$
$241$	−5222.70	−1.39595	−0.697975	+	0.716123i	$0.745915\pi$
$242$	2367.34	0.628835
$243$	243.000	0.0641500
$244$	1015.26	0.266374
$245$	215.166	0.0561079
$246$	−113.292	−0.0293628
$247$	218.160	0.0561991
$248$	−683.888	−0.175109
$249$	−1113.62	−0.283424
$250$	−2026.23	−0.512600
$251$	1030.69	0.259188	0.129594	−	0.991567i	$-0.458633\pi$
$251$	1030.69	0.259188	0.129594	+	0.991567i	$0.458633\pi$
$252$	252.000	0.0629941
$253$	−9120.42	−2.26639
$254$	3292.47	0.813339
$255$	1413.49	0.347122
$256$	256.000	0.0625000
$257$	−3753.70	−0.911088	−0.455544	−	0.890213i	$-0.650555\pi$
$257$	−3753.70	−0.911088	−0.455544	+	0.890213i	$0.650555\pi$
$258$	2374.67	0.573026
$259$	2196.81	0.527039
$260$	201.678	0.0481059
$261$	−2579.78	−0.611818
$262$	−1001.25	−0.236097
$263$	7056.32	1.65442	0.827208	−	0.561896i	$-0.189928\pi$
$263$	7056.32	1.65442	0.827208	+	0.561896i	$0.189928\pi$
$264$	1203.52	0.280573
$265$	668.551	0.154976
$266$	266.000	0.0613139
$267$	2743.52	0.628841
$268$	−1167.41	−0.266086
$269$	−401.217	−0.0909392	−0.0454696	−	0.998966i	$-0.514478\pi$
$269$	−401.217	−0.0909392	−0.0454696	+	0.998966i	$0.514478\pi$
$270$	237.122	0.0534473
$271$	2417.02	0.541785	0.270892	−	0.962610i	$-0.412681\pi$
$271$	2417.02	0.541785	0.270892	+	0.962610i	$0.412681\pi$
$272$	1716.78	0.382702
$273$	241.124	0.0534560
$274$	1538.60	0.339234
$275$	−5301.38	−1.16249
$276$	−2182.51	−0.475984
$277$	4167.82	0.904043	0.452022	−	0.892007i	$-0.350703\pi$
$277$	4167.82	0.904043	0.452022	+	0.892007i	$0.350703\pi$
$278$	−3856.52	−0.832010
$279$	−769.374	−0.165094
$280$	245.904	0.0524842
$281$	−4549.91	−0.965925	−0.482962	−	0.875641i	$-0.660439\pi$
$281$	−4549.91	−0.965925	−0.482962	+	0.875641i	$0.660439\pi$
$282$	2189.46	0.462342
$283$	−2192.05	−0.460437	−0.230218	−	0.973139i	$-0.573944\pi$
$283$	−2192.05	−0.460437	−0.230218	+	0.973139i	$0.573944\pi$
$284$	2351.08	0.491236
$285$	250.295	0.0520217
$286$	1151.57	0.238091
$287$	−132.174	−0.0271847
$288$	288.000	0.0589256
$289$	6599.99	1.34337
$290$	−2517.38	−0.509743
$291$	1123.44	0.226314
$292$	−3153.69	−0.632040
$293$	−300.922	−0.0600002	−0.0300001	−	0.999550i	$-0.509551\pi$
$293$	−300.922	−0.0600002	−0.0300001	+	0.999550i	$0.509551\pi$
$294$	294.000	0.0583212
$295$	−1649.83	−0.325616
$296$	2510.64	0.493000
$297$	1353.95	0.264527
$298$	3076.18	0.597980
$299$	−2088.31	−0.403914
$300$	−1268.61	−0.244145
$301$	2770.45	0.530519
$302$	1903.62	0.362719
$303$	3290.18	0.623814
$304$	304.000	0.0573539
$305$	1114.54	0.209240
$306$	1931.37	0.360815
$307$	−3262.41	−0.606501	−0.303251	−	0.952911i	$-0.598072\pi$
$307$	−3262.41	−0.606501	−0.303251	+	0.952911i	$0.598072\pi$
$308$	1404.10	0.259760
$309$	−5809.95	−1.06963
$310$	−750.763	−0.137550
$311$	−4420.21	−0.805940	−0.402970	−	0.915213i	$-0.632022\pi$
$311$	−4420.21	−0.805940	−0.402970	+	0.915213i	$0.632022\pi$
$312$	275.570	0.0500035
$313$	−3936.07	−0.710798	−0.355399	−	0.934715i	$-0.615655\pi$
$313$	−3936.07	−0.710798	−0.355399	+	0.934715i	$0.615655\pi$
$314$	−345.281	−0.0620552
$315$	276.642	0.0494825
$316$	3717.69	0.661823
$317$	−3459.22	−0.612900	−0.306450	−	0.951887i	$-0.599141\pi$
$317$	−3459.22	−0.612900	−0.306450	+	0.951887i	$0.599141\pi$
$318$	913.500	0.161090
$319$	−14374.1	−2.52287
$320$	281.033	0.0490944
$321$	−2049.19	−0.356307
$322$	−2546.26	−0.440675
$323$	2038.67	0.351191
$324$	324.000	0.0555556
$325$	−1213.86	−0.207178
$326$	−5213.33	−0.885705
$327$	−1018.26	−0.172201
$328$	−151.056	−0.0254289
$329$	2554.37	0.428046
$330$	1321.20	0.220393
$331$	3128.62	0.519530	0.259765	−	0.965672i	$-0.416355\pi$
$331$	3128.62	0.519530	0.259765	+	0.965672i	$0.416355\pi$
$332$	−1484.82	−0.245453
$333$	2824.47	0.464805
$334$	3028.85	0.496202
$335$	−1281.57	−0.209013
$336$	336.000	0.0545545
$337$	−9362.38	−1.51336	−0.756678	−	0.653787i	$-0.773179\pi$
$337$	−9362.38	−1.51336	−0.756678	+	0.653787i	$0.773179\pi$
$338$	−4130.32	−0.664674
$339$	−6036.53	−0.967137
$340$	1884.65	0.300617
$341$	−4286.82	−0.680776
$342$	342.000	0.0540738
$343$	343.000	0.0539949
$344$	3166.23	0.496255
$345$	−2395.92	−0.373890
$346$	−552.737	−0.0858825
$347$	7258.07	1.12286	0.561432	−	0.827523i	$-0.310251\pi$
$347$	7258.07	1.12286	0.561432	+	0.827523i	$0.310251\pi$
$348$	−3439.71	−0.529850
$349$	−8007.98	−1.22824	−0.614122	−	0.789211i	$-0.710490\pi$
$349$	−8007.98	−1.22824	−0.614122	+	0.789211i	$0.710490\pi$
$350$	−1480.05	−0.226034
$351$	310.016	0.0471437
$352$	1604.69	0.242983
$353$	2860.16	0.431250	0.215625	−	0.976476i	$-0.430821\pi$
$353$	2860.16	0.431250	0.215625	+	0.976476i	$0.430821\pi$
$354$	−2254.30	−0.338460
$355$	2580.98	0.385871
$356$	3658.02	0.544592
$357$	2253.27	0.334050
$358$	−6347.46	−0.937078
$359$	8797.51	1.29336	0.646678	−	0.762763i	$-0.276158\pi$
$359$	8797.51	1.29336	0.646678	+	0.762763i	$0.276158\pi$
$360$	316.162	0.0462867
$361$	361.000	0.0526316
$362$	3295.64	0.478495
$363$	3551.00	0.513442
$364$	321.498	0.0462942
$365$	−3462.07	−0.496475
$366$	1522.89	0.217494
$367$	−6800.65	−0.967278	−0.483639	−	0.875268i	$-0.660685\pi$
$367$	−6800.65	−0.967278	−0.483639	+	0.875268i	$0.660685\pi$
$368$	−2910.01	−0.412214
$369$	−169.938	−0.0239746
$370$	2756.14	0.387257
$371$	1065.75	0.149140
$372$	−1025.83	−0.142976
$373$	190.313	0.0264184	0.0132092	−	0.999913i	$-0.495795\pi$
$373$	190.313	0.0264184	0.0132092	+	0.999913i	$0.495795\pi$
$374$	10761.3	1.48784
$375$	−3039.34	−0.418536
$376$	2919.28	0.400400
$377$	−3291.26	−0.449624
$378$	378.000	0.0514344
$379$	5558.65	0.753374	0.376687	−	0.926341i	$-0.377063\pi$
$379$	5558.65	0.753374	0.376687	+	0.926341i	$0.377063\pi$
$380$	333.727	0.0450521
$381$	4938.71	0.664088
$382$	−2929.19	−0.392331
$383$	−6532.58	−0.871538	−0.435769	−	0.900059i	$-0.643524\pi$
$383$	−6532.58	−0.871538	−0.435769	+	0.900059i	$0.643524\pi$
$384$	384.000	0.0510310
$385$	1541.40	0.204044
$386$	−5701.12	−0.751760
$387$	3562.01	0.467873
$388$	1497.92	0.195994
$389$	−574.230	−0.0748448	−0.0374224	−	0.999300i	$-0.511915\pi$
$389$	−574.230	−0.0748448	−0.0374224	+	0.999300i	$0.511915\pi$
$390$	302.517	0.0392783
$391$	−19515.0	−2.52408
$392$	392.000	0.0505076
$393$	−1501.88	−0.192773
$394$	−823.184	−0.105257
$395$	4081.22	0.519870
$396$	1805.27	0.229087
$397$	−9013.89	−1.13953	−0.569766	−	0.821807i	$-0.692966\pi$
$397$	−9013.89	−1.13953	−0.569766	+	0.821807i	$0.692966\pi$
$398$	−1536.93	−0.193566
$399$	399.000	0.0500626
$400$	−1691.49	−0.211436
$401$	−4430.61	−0.551755	−0.275878	−	0.961193i	$-0.588968\pi$
$401$	−4430.61	−0.551755	−0.275878	+	0.961193i	$0.588968\pi$
$402$	−1751.12	−0.217258
$403$	−981.558	−0.121327
$404$	4386.90	0.540239
$405$	355.682	0.0436395
$406$	−4013.00	−0.490546
$407$	15737.5	1.91665
$408$	2575.17	0.312475
$409$	−1253.49	−0.151543	−0.0757713	−	0.997125i	$-0.524142\pi$
$409$	−1253.49	−0.151543	−0.0757713	+	0.997125i	$0.524142\pi$
$410$	−165.827	−0.0199747
$411$	2307.90	0.276984
$412$	−7746.60	−0.926329
$413$	−2630.02	−0.313353
$414$	−3273.76	−0.388639
$415$	−1630.02	−0.192806
$416$	367.427	0.0433043
$417$	−5784.78	−0.679333
$418$	1905.57	0.222977
$419$	−9134.15	−1.06499	−0.532497	−	0.846432i	$-0.678746\pi$
$419$	−9134.15	−1.06499	−0.532497	+	0.846432i	$0.678746\pi$
$420$	368.856	0.0428531
$421$	−3732.17	−0.432054	−0.216027	−	0.976387i	$-0.569310\pi$
$421$	−3732.17	−0.432054	−0.216027	+	0.976387i	$0.569310\pi$
$422$	−3292.27	−0.379776
$423$	3284.19	0.377501
$424$	1218.00	0.139508
$425$	−11343.4	−1.29467
$426$	3526.62	0.401092
$427$	1776.70	0.201360
$428$	−2732.26	−0.308571
$429$	1727.36	0.194400
$430$	3475.84	0.389814
$431$	17837.5	1.99351	0.996755	−	0.0805000i	$-0.0256517\pi$
$431$	17837.5	1.99351	0.996755	+	0.0805000i	$0.0256517\pi$
$432$	432.000	0.0481125
$433$	13832.2	1.53518	0.767589	−	0.640943i	$-0.221456\pi$
$433$	13832.2	1.53518	0.767589	+	0.640943i	$0.221456\pi$
$434$	−1196.80	−0.132370
$435$	−3776.06	−0.416203
$436$	−1357.68	−0.149131
$437$	−3455.64	−0.378273
$438$	−4730.53	−0.516059
$439$	−10107.7	−1.09889	−0.549445	−	0.835530i	$-0.685161\pi$
$439$	−10107.7	−1.09889	−0.549445	+	0.835530i	$0.685161\pi$
$440$	1761.60	0.190866
$441$	441.000	0.0476190
$442$	2464.02	0.265162
$443$	13324.6	1.42906	0.714529	−	0.699606i	$-0.246641\pi$
$443$	13324.6	1.42906	0.714529	+	0.699606i	$0.246641\pi$
$444$	3765.96	0.402533
$445$	4015.72	0.427783
$446$	−3257.86	−0.345883
$447$	4614.26	0.488249
$448$	448.000	0.0472456
$449$	9964.53	1.04734	0.523670	−	0.851921i	$-0.324563\pi$
$449$	9964.53	1.04734	0.523670	+	0.851921i	$0.324563\pi$
$450$	−1902.92	−0.199344
$451$	−946.868	−0.0988609
$452$	−8048.71	−0.837565
$453$	2855.44	0.296159
$454$	−8300.17	−0.858032
$455$	352.936	0.0363646
$456$	456.000	0.0468293
$457$	−3771.31	−0.386027	−0.193014	−	0.981196i	$-0.561826\pi$
$457$	−3771.31	−0.386027	−0.193014	+	0.981196i	$0.561826\pi$
$458$	−2309.52	−0.235626
$459$	2897.06	0.294604
$460$	−3194.56	−0.323799
$461$	18538.9	1.87298	0.936489	−	0.350697i	$-0.114055\pi$
$461$	18538.9	1.87298	0.936489	+	0.350697i	$0.114055\pi$
$462$	2106.15	0.212093
$463$	2229.46	0.223783	0.111892	−	0.993720i	$-0.464309\pi$
$463$	2229.46	0.223783	0.111892	+	0.993720i	$0.464309\pi$
$464$	−4586.28	−0.458864
$465$	−1126.14	−0.112309
$466$	6358.89	0.632124
$467$	−9794.58	−0.970534	−0.485267	−	0.874366i	$-0.661278\pi$
$467$	−9794.58	−0.970534	−0.485267	+	0.874366i	$0.661278\pi$
$468$	413.355	0.0408277
$469$	−2042.97	−0.201142
$470$	3204.74	0.314519
$471$	−517.921	−0.0506678
$472$	−3005.74	−0.293115
$473$	19846.9	1.92931
$474$	5576.53	0.540377
$475$	−2008.64	−0.194027
$476$	3004.36	0.289295
$477$	1370.25	0.131529
$478$	7867.57	0.752834
$479$	−19058.6	−1.81797	−0.908987	−	0.416825i	$-0.863143\pi$
$479$	−19058.6	−1.81797	−0.908987	+	0.416825i	$0.863143\pi$
$480$	421.549	0.0400854
$481$	3603.42	0.341584
$482$	−10445.4	−0.987085
$483$	−3819.39	−0.359810
$484$	4734.67	0.444654
$485$	1644.40	0.153955
$486$	486.000	0.0453609
$487$	−6011.67	−0.559373	−0.279687	−	0.960091i	$-0.590231\pi$
$487$	−6011.67	−0.559373	−0.279687	+	0.960091i	$0.590231\pi$
$488$	2030.52	0.188355
$489$	−7820.00	−0.723175
$490$	430.332	0.0396743
$491$	−12588.0	−1.15700	−0.578500	−	0.815682i	$-0.696362\pi$
$491$	−12588.0	−1.15700	−0.578500	+	0.815682i	$0.696362\pi$
$492$	−226.584	−0.0207626
$493$	−30756.3	−2.80973
$494$	436.319	0.0397387
$495$	1981.80	0.179950
$496$	−1367.78	−0.123821
$497$	4114.39	0.371339
$498$	−2227.24	−0.200411
$499$	−7266.39	−0.651880	−0.325940	−	0.945390i	$-0.605681\pi$
$499$	−7266.39	−0.651880	−0.325940	+	0.945390i	$0.605681\pi$
$500$	−4052.46	−0.362463
$501$	4543.28	0.405147
$502$	2061.37	0.183274
$503$	19027.0	1.68663	0.843314	−	0.537421i	$-0.180602\pi$
$503$	19027.0	1.68663	0.843314	+	0.537421i	$0.180602\pi$
$504$	504.000	0.0445435
$505$	4815.87	0.424364
$506$	−18240.8	−1.60258
$507$	−6195.49	−0.542704
$508$	6584.94	0.575117
$509$	16003.8	1.39362	0.696812	−	0.717253i	$-0.254601\pi$
$509$	16003.8	1.39362	0.696812	+	0.717253i	$0.254601\pi$
$510$	2826.98	0.245452
$511$	−5518.96	−0.477777
$512$	512.000	0.0441942
$513$	513.000	0.0441511
$514$	−7507.40	−0.644236
$515$	−8504.10	−0.727642
$516$	4749.34	0.405190
$517$	18299.0	1.55665
$518$	4393.62	0.372673
$519$	−829.106	−0.0701227
$520$	403.356	0.0340160
$521$	−17935.3	−1.50818	−0.754088	−	0.656774i	$-0.771921\pi$
$521$	−17935.3	−1.50818	−0.754088	+	0.656774i	$0.771921\pi$
$522$	−5159.57	−0.432621
$523$	−20949.2	−1.75152	−0.875761	−	0.482745i	$-0.839640\pi$
$523$	−20949.2	−1.75152	−0.875761	+	0.482745i	$0.839640\pi$
$524$	−2002.50	−0.166946
$525$	−2220.08	−0.184556
$526$	14112.6	1.16985
$527$	−9172.53	−0.758182
$528$	2407.03	0.198395
$529$	20911.7	1.71872
$530$	1337.10	0.109585
$531$	−3381.46	−0.276352
$532$	532.000	0.0433555
$533$	−216.805	−0.0176189
$534$	5487.04	0.444658
$535$	−2999.43	−0.242386
$536$	−2334.82	−0.188151
$537$	−9521.19	−0.765121
$538$	−802.434	−0.0643037
$539$	2457.18	0.196360
$540$	474.243	0.0377929
$541$	−10856.8	−0.862790	−0.431395	−	0.902163i	$-0.641978\pi$
$541$	−10856.8	−0.862790	−0.431395	+	0.902163i	$0.641978\pi$
$542$	4834.04	0.383100
$543$	4943.46	0.390689
$544$	3433.55	0.270611
$545$	−1490.44	−0.117144
$546$	482.248	0.0377991
$547$	−22509.3	−1.75947	−0.879733	−	0.475469i	$-0.842278\pi$
$547$	−22509.3	−1.75947	−0.879733	+	0.475469i	$0.842278\pi$
$548$	3077.20	0.239875
$549$	2284.33	0.177583
$550$	−10602.8	−0.822006
$551$	−5446.21	−0.421082
$552$	−4365.01	−0.336571
$553$	6505.95	0.500291
$554$	8335.64	0.639255
$555$	4134.21	0.316194
$556$	−7713.04	−0.588320
$557$	−3063.94	−0.233076	−0.116538	−	0.993186i	$-0.537180\pi$
$557$	−3063.94	−0.233076	−0.116538	+	0.993186i	$0.537180\pi$
$558$	−1538.75	−0.116739
$559$	4544.36	0.343839
$560$	491.808	0.0371119
$561$	16141.9	1.21482
$562$	−9099.82	−0.683012
$563$	15036.8	1.12562	0.562812	−	0.826585i	$-0.309720\pi$
$563$	15036.8	1.12562	0.562812	+	0.826585i	$0.309720\pi$
$564$	4378.92	0.326925
$565$	−8835.76	−0.657917
$566$	−4384.09	−0.325578
$567$	567.000	0.0419961
$568$	4702.16	0.347356
$569$	544.743	0.0401350	0.0200675	−	0.999799i	$-0.493612\pi$
$569$	544.743	0.0401350	0.0200675	+	0.999799i	$0.493612\pi$
$570$	500.590	0.0367849
$571$	23544.5	1.72558	0.862791	−	0.505560i	$-0.168714\pi$
$571$	23544.5	1.72558	0.862791	+	0.505560i	$0.168714\pi$
$572$	2303.14	0.168355
$573$	−4393.78	−0.320337
$574$	−264.349	−0.0192225
$575$	19227.5	1.39451
$576$	576.000	0.0416667
$577$	−3533.60	−0.254949	−0.127475	−	0.991842i	$-0.540687\pi$
$577$	−3533.60	−0.254949	−0.127475	+	0.991842i	$0.540687\pi$
$578$	13200.0	0.949907
$579$	−8551.67	−0.613809
$580$	−5034.75	−0.360443
$581$	−2598.44	−0.185545
$582$	2246.89	0.160028
$583$	7634.80	0.542369
$584$	−6307.38	−0.446920
$585$	453.775	0.0320706
$586$	−601.845	−0.0424266
$587$	12798.6	0.899921	0.449961	−	0.893048i	$-0.351438\pi$
$587$	12798.6	0.899921	0.449961	+	0.893048i	$0.351438\pi$
$588$	588.000	0.0412393
$589$	−1624.23	−0.113626
$590$	−3299.65	−0.230245
$591$	−1234.78	−0.0859423
$592$	5021.28	0.348603
$593$	−17771.7	−1.23069	−0.615344	−	0.788259i	$-0.710983\pi$
$593$	−17771.7	−1.23069	−0.615344	+	0.788259i	$0.710983\pi$
$594$	2707.91	0.187049
$595$	3298.14	0.227245
$596$	6152.35	0.422836
$597$	−2305.40	−0.158046
$598$	−4176.62	−0.285610
$599$	1677.41	0.114419	0.0572097	−	0.998362i	$-0.481780\pi$
$599$	1677.41	0.114419	0.0572097	+	0.998362i	$0.481780\pi$
$600$	−2537.23	−0.172637
$601$	8134.34	0.552091	0.276045	−	0.961145i	$-0.410976\pi$
$601$	8134.34	0.552091	0.276045	+	0.961145i	$0.410976\pi$
$602$	5540.90	0.375133
$603$	−2626.67	−0.177390
$604$	3807.25	0.256481
$605$	5197.65	0.349280
$606$	6580.35	0.441103
$607$	21535.5	1.44003	0.720017	−	0.693956i	$-0.244134\pi$
$607$	21535.5	1.44003	0.720017	+	0.693956i	$0.244134\pi$
$608$	608.000	0.0405554
$609$	−6019.49	−0.400529
$610$	2229.07	0.147955
$611$	4189.93	0.277425
$612$	3862.75	0.255135
$613$	−16113.0	−1.06166	−0.530829	−	0.847479i	$-0.678119\pi$
$613$	−16113.0	−1.06166	−0.530829	+	0.847479i	$0.678119\pi$
$614$	−6524.83	−0.428861
$615$	−248.741	−0.0163093
$616$	2808.20	0.183678
$617$	23836.5	1.55530	0.777652	−	0.628695i	$-0.216411\pi$
$617$	23836.5	1.55530	0.777652	+	0.628695i	$0.216411\pi$
$618$	−11619.9	−0.756345
$619$	−6268.65	−0.407041	−0.203520	−	0.979071i	$-0.565238\pi$
$619$	−6268.65	−0.407041	−0.203520	+	0.979071i	$0.565238\pi$
$620$	−1501.53	−0.0972624
$621$	−4910.64	−0.317322
$622$	−8840.43	−0.569885
$623$	6401.54	0.411673
$624$	551.140	0.0353578
$625$	8766.01	0.561024
$626$	−7872.14	−0.502610
$627$	2858.35	0.182060
$628$	−690.562	−0.0438796
$629$	33673.5	2.13458
$630$	553.284	0.0349894
$631$	−9776.06	−0.616765	−0.308383	−	0.951262i	$-0.599788\pi$
$631$	−9776.06	−0.616765	−0.308383	+	0.951262i	$0.599788\pi$
$632$	7435.37	0.467980
$633$	−4938.41	−0.310085
$634$	−6918.44	−0.433386
$635$	7228.85	0.451761
$636$	1827.00	0.113908
$637$	562.622	0.0349951
$638$	−28748.2	−1.78394
$639$	5289.93	0.327491
$640$	562.066	0.0347150
$641$	4888.63	0.301232	0.150616	−	0.988592i	$-0.451874\pi$
$641$	4888.63	0.301232	0.150616	+	0.988592i	$0.451874\pi$
$642$	−4098.38	−0.251947
$643$	2573.53	0.157839	0.0789194	−	0.996881i	$-0.474853\pi$
$643$	2573.53	0.157839	0.0789194	+	0.996881i	$0.474853\pi$
$644$	−5092.52	−0.311604
$645$	5213.76	0.318281
$646$	4077.35	0.248330
$647$	18864.2	1.14625	0.573127	−	0.819466i	$-0.305730\pi$
$647$	18864.2	1.14625	0.573127	+	0.819466i	$0.305730\pi$
$648$	648.000	0.0392837
$649$	−18840.9	−1.13955
$650$	−2427.72	−0.146497
$651$	−1795.21	−0.108079
$652$	−10426.7	−0.626288
$653$	−5849.51	−0.350550	−0.175275	−	0.984520i	$-0.556081\pi$
$653$	−5849.51	−0.350550	−0.175275	+	0.984520i	$0.556081\pi$
$654$	−2036.52	−0.121765
$655$	−2198.32	−0.131138
$656$	−302.113	−0.0179810
$657$	−7095.80	−0.421360
$658$	5108.74	0.302674
$659$	24592.3	1.45369	0.726843	−	0.686804i	$-0.240987\pi$
$659$	24592.3	1.45369	0.726843	+	0.686804i	$0.240987\pi$
$660$	2642.40	0.155841
$661$	−16173.2	−0.951687	−0.475844	−	0.879530i	$-0.657857\pi$
$661$	−16173.2	−0.951687	−0.475844	+	0.879530i	$0.657857\pi$
$662$	6257.24	0.367363
$663$	3696.03	0.216504
$664$	−2969.65	−0.173561
$665$	584.022	0.0340562
$666$	5648.94	0.328666
$667$	52133.3	3.02640
$668$	6057.70	0.350868
$669$	−4886.79	−0.282413
$670$	−2563.13	−0.147795
$671$	12727.9	0.732274
$672$	672.000	0.0385758
$673$	−15826.3	−0.906477	−0.453238	−	0.891389i	$-0.649731\pi$
$673$	−15826.3	−0.906477	−0.453238	+	0.891389i	$0.649731\pi$
$674$	−18724.8	−1.07010
$675$	−2854.38	−0.162763
$676$	−8260.65	−0.469996
$677$	−15746.9	−0.893946	−0.446973	−	0.894547i	$-0.647498\pi$
$677$	−15746.9	−0.893946	−0.446973	+	0.894547i	$0.647498\pi$
$678$	−12073.1	−0.683869
$679$	2621.37	0.148157
$680$	3769.30	0.212568
$681$	−12450.3	−0.700580
$682$	−8573.65	−0.481381
$683$	3938.37	0.220641	0.110320	−	0.993896i	$-0.464812\pi$
$683$	3938.37	0.220641	0.110320	+	0.993896i	$0.464812\pi$
$684$	684.000	0.0382360
$685$	3378.10	0.188424
$686$	686.000	0.0381802
$687$	−3464.27	−0.192388
$688$	6332.46	0.350905
$689$	1748.15	0.0966605
$690$	−4791.85	−0.264380
$691$	−15380.0	−0.846720	−0.423360	−	0.905962i	$-0.639149\pi$
$691$	−15380.0	−0.846720	−0.423360	+	0.905962i	$0.639149\pi$
$692$	−1105.47	−0.0607281
$693$	3159.23	0.173173
$694$	14516.1	0.793985
$695$	−8467.26	−0.462132
$696$	−6879.42	−0.374661
$697$	−2026.02	−0.110102
$698$	−16016.0	−0.868500
$699$	9538.33	0.516127
$700$	−2960.10	−0.159830
$701$	−14223.7	−0.766367	−0.383183	−	0.923672i	$-0.625172\pi$
$701$	−14223.7	−0.766367	−0.383183	+	0.923672i	$0.625172\pi$
$702$	620.033	0.0333356
$703$	5962.77	0.319900
$704$	3209.37	0.171815
$705$	4807.12	0.256804
$706$	5720.33	0.304940
$707$	7677.08	0.408382
$708$	−4508.61	−0.239327
$709$	−2248.14	−0.119084	−0.0595419	−	0.998226i	$-0.518964\pi$
$709$	−2248.14	−0.119084	−0.0595419	+	0.998226i	$0.518964\pi$
$710$	5161.96	0.272852
$711$	8364.79	0.441216
$712$	7316.05	0.385085
$713$	15547.8	0.816649
$714$	4506.54	0.236209
$715$	2528.36	0.132245
$716$	−12694.9	−0.662614
$717$	11801.4	0.614686
$718$	17595.0	0.914541
$719$	30958.5	1.60578	0.802890	−	0.596127i	$-0.203294\pi$
$719$	30958.5	1.60578	0.802890	+	0.596127i	$0.203294\pi$
$720$	632.324	0.0327296
$721$	−13556.6	−0.700239
$722$	722.000	0.0372161
$723$	−15668.1	−0.805952
$724$	6591.28	0.338347
$725$	30303.2	1.55232
$726$	7102.01	0.363058
$727$	20294.3	1.03532	0.517658	−	0.855588i	$-0.326804\pi$
$727$	20294.3	1.03532	0.517658	+	0.855588i	$0.326804\pi$
$728$	642.997	0.0327350
$729$	729.000	0.0370370
$730$	−6924.15	−0.351060
$731$	42466.5	2.14867
$732$	3045.78	0.153791
$733$	−18137.6	−0.913955	−0.456978	−	0.889478i	$-0.651068\pi$
$733$	−18137.6	−0.913955	−0.456978	+	0.889478i	$0.651068\pi$
$734$	−13601.3	−0.683969
$735$	645.498	0.0323939
$736$	−5820.02	−0.291479
$737$	−14635.4	−0.731480
$738$	−339.877	−0.0169526
$739$	36922.5	1.83791	0.918956	−	0.394361i	$-0.129034\pi$
$739$	36922.5	1.83791	0.918956	+	0.394361i	$0.129034\pi$
$740$	5512.28	0.273832
$741$	654.479	0.0324465
$742$	2131.50	0.105458
$743$	7653.03	0.377877	0.188938	−	0.981989i	$-0.439495\pi$
$743$	7653.03	0.377877	0.188938	+	0.981989i	$0.439495\pi$
$744$	−2051.67	−0.101099
$745$	6753.96	0.332142
$746$	380.627	0.0186806
$747$	−3340.85	−0.163635
$748$	21522.6	1.05206
$749$	−4781.45	−0.233258
$750$	−6078.69	−0.295950
$751$	−24883.8	−1.20908	−0.604542	−	0.796573i	$-0.706644\pi$
$751$	−24883.8	−1.20908	−0.604542	+	0.796573i	$0.706644\pi$
$752$	5838.56	0.283126
$753$	3092.06	0.149642
$754$	−6582.51	−0.317932
$755$	4179.54	0.201469
$756$	756.000	0.0363696
$757$	−8991.22	−0.431693	−0.215846	−	0.976427i	$-0.569251\pi$
$757$	−8991.22	−0.431693	−0.215846	+	0.976427i	$0.569251\pi$
$758$	11117.3	0.532716
$759$	−27361.3	−1.30850
$760$	667.453	0.0318567
$761$	29371.3	1.39909	0.699546	−	0.714588i	$-0.253386\pi$
$761$	29371.3	1.39909	0.699546	+	0.714588i	$0.253386\pi$
$762$	9877.41	0.469581
$763$	−2375.94	−0.112732
$764$	−5858.38	−0.277420
$765$	4240.47	0.200411
$766$	−13065.2	−0.616270
$767$	−4314.02	−0.203090
$768$	768.000	0.0360844
$769$	−22053.6	−1.03416	−0.517082	−	0.855936i	$-0.672982\pi$
$769$	−22053.6	−1.03416	−0.517082	+	0.855936i	$0.672982\pi$
$770$	3082.80	0.144281
$771$	−11261.1	−0.526017
$772$	−11402.2	−0.531574
$773$	1223.87	0.0569461	0.0284731	−	0.999595i	$-0.490936\pi$
$773$	1223.87	0.0569461	0.0284731	+	0.999595i	$0.490936\pi$
$774$	7124.01	0.330836
$775$	9037.40	0.418882
$776$	2995.85	0.138589
$777$	6590.43	0.304286
$778$	−1148.46	−0.0529233
$779$	−358.759	−0.0165005
$780$	605.033	0.0277739
$781$	29474.6	1.35043
$782$	−39030.0	−1.78479
$783$	−7739.35	−0.353233
$784$	784.000	0.0357143
$785$	−758.088	−0.0344679
$786$	−3003.75	−0.136311
$787$	28623.4	1.29646	0.648229	−	0.761445i	$-0.275510\pi$
$787$	28623.4	1.29646	0.648229	+	0.761445i	$0.275510\pi$
$788$	−1646.37	−0.0744282
$789$	21169.0	0.955177
$790$	8162.44	0.367603
$791$	−14085.2	−0.633140
$792$	3610.55	0.161989
$793$	2914.32	0.130505
$794$	−18027.8	−0.805770
$795$	2005.65	0.0894757
$796$	−3073.86	−0.136872
$797$	17685.6	0.786016	0.393008	−	0.919535i	$-0.371435\pi$
$797$	17685.6	0.786016	0.393008	+	0.919535i	$0.371435\pi$
$798$	798.000	0.0353996
$799$	39154.4	1.73364
$800$	−3382.97	−0.149508
$801$	8230.55	0.363062
$802$	−8861.21	−0.390150
$803$	−39536.6	−1.73750
$804$	−3502.23	−0.153625
$805$	−5590.49	−0.244769
$806$	−1963.12	−0.0857914
$807$	−1203.65	−0.0525038
$808$	8773.80	0.382007
$809$	−28722.6	−1.24825	−0.624124	−	0.781325i	$-0.714544\pi$
$809$	−28722.6	−1.24825	−0.624124	+	0.781325i	$0.714544\pi$
$810$	711.365	0.0308578
$811$	43620.9	1.88870	0.944350	−	0.328941i	$-0.106692\pi$
$811$	43620.9	1.88870	0.944350	+	0.328941i	$0.106692\pi$
$812$	−8025.99	−0.346868
$813$	7251.07	0.312800
$814$	31474.9	1.35528
$815$	−11446.2	−0.491956
$816$	5150.33	0.220953
$817$	7519.79	0.322013
$818$	−2506.97	−0.107157
$819$	723.371	0.0308628
$820$	−331.655	−0.0141243
$821$	−16692.0	−0.709567	−0.354784	−	0.934948i	$-0.615445\pi$
$821$	−16692.0	−0.709567	−0.354784	+	0.934948i	$0.615445\pi$
$822$	4615.80	0.195857
$823$	38403.2	1.62655	0.813276	−	0.581878i	$-0.197682\pi$
$823$	38403.2	1.62655	0.813276	+	0.581878i	$0.197682\pi$
$824$	−15493.2	−0.655014
$825$	−15904.1	−0.671165
$826$	−5260.04	−0.221574
$827$	−3903.55	−0.164135	−0.0820677	−	0.996627i	$-0.526152\pi$
$827$	−3903.55	−0.164135	−0.0820677	+	0.996627i	$0.526152\pi$
$828$	−6547.52	−0.274809
$829$	−45749.2	−1.91669	−0.958346	−	0.285611i	$-0.907803\pi$
$829$	−45749.2	−1.91669	−0.958346	+	0.285611i	$0.907803\pi$
$830$	−3260.04	−0.136334
$831$	12503.5	0.521950
$832$	734.854	0.0306207
$833$	5257.63	0.218687
$834$	−11569.6	−0.480361
$835$	6650.06	0.275610
$836$	3811.13	0.157668
$837$	−2308.12	−0.0953171
$838$	−18268.3	−0.753064
$839$	−23129.0	−0.951730	−0.475865	−	0.879518i	$-0.657865\pi$
$839$	−23129.0	−0.951730	−0.475865	+	0.879518i	$0.657865\pi$
$840$	737.712	0.0303017
$841$	57775.0	2.36889
$842$	−7464.33	−0.305508
$843$	−13649.7	−0.557677
$844$	−6584.54	−0.268542
$845$	−9068.41	−0.369187
$846$	6568.38	0.266933
$847$	8285.68	0.336127
$848$	2436.00	0.0986469
$849$	−6576.14	−0.265833
$850$	−22686.8	−0.915470
$851$	−57078.0	−2.29919
$852$	7053.24	0.283615
$853$	35307.7	1.41725	0.708623	−	0.705587i	$-0.249317\pi$
$853$	35307.7	1.41725	0.708623	+	0.705587i	$0.249317\pi$
$854$	3553.41	0.142383
$855$	750.885	0.0300348
$856$	−5464.51	−0.218193
$857$	−18374.8	−0.732407	−0.366203	−	0.930535i	$-0.619343\pi$
$857$	−18374.8	−0.732407	−0.366203	+	0.930535i	$0.619343\pi$
$858$	3454.72	0.137462
$859$	−5368.53	−0.213238	−0.106619	−	0.994300i	$-0.534003\pi$
$859$	−5368.53	−0.213238	−0.106619	+	0.994300i	$0.534003\pi$
$860$	6951.68	0.275640
$861$	−396.523	−0.0156951
$862$	35675.0	1.40962
$863$	−13324.7	−0.525584	−0.262792	−	0.964853i	$-0.584643\pi$
$863$	−13324.7	−0.525584	−0.262792	+	0.964853i	$0.584643\pi$
$864$	864.000	0.0340207
$865$	−1213.57	−0.0477026
$866$	27664.3	1.08553
$867$	19800.0	0.775596
$868$	−2393.61	−0.0935995
$869$	46607.2	1.81938
$870$	−7552.13	−0.294300
$871$	−3351.08	−0.130364
$872$	−2715.36	−0.105451
$873$	3370.33	0.130663
$874$	−6911.27	−0.267480
$875$	−7091.80	−0.273996
$876$	−9461.07	−0.364909
$877$	−36116.3	−1.39060	−0.695302	−	0.718718i	$-0.744729\pi$
$877$	−36116.3	−1.39060	−0.695302	+	0.718718i	$0.744729\pi$
$878$	−20215.3	−0.777032
$879$	−902.767	−0.0346412
$880$	3523.20	0.134963
$881$	3116.67	0.119187	0.0595933	−	0.998223i	$-0.481020\pi$
$881$	3116.67	0.119187	0.0595933	+	0.998223i	$0.481020\pi$
$882$	882.000	0.0336718
$883$	43281.3	1.64953	0.824763	−	0.565478i	$-0.191308\pi$
$883$	43281.3	1.64953	0.824763	+	0.565478i	$0.191308\pi$
$884$	4928.05	0.187498
$885$	−4949.48	−0.187994
$886$	26649.3	1.01050
$887$	23460.0	0.888060	0.444030	−	0.896012i	$-0.353548\pi$
$887$	23460.0	0.888060	0.444030	+	0.896012i	$0.353548\pi$
$888$	7531.92	0.284633
$889$	11523.6	0.434748
$890$	8031.45	0.302489
$891$	4061.86	0.152725
$892$	−6515.71	−0.244577
$893$	6933.29	0.259814
$894$	9228.53	0.345244
$895$	−13936.3	−0.520491
$896$	896.000	0.0334077
$897$	−6264.93	−0.233200
$898$	19929.1	0.740581
$899$	24503.9	0.909068
$900$	−3805.84	−0.140957
$901$	16336.2	0.604037
$902$	−1893.74	−0.0699052
$903$	8311.35	0.306295
$904$	−16097.4	−0.592248
$905$	7235.81	0.265775
$906$	5710.87	0.209416
$907$	17123.9	0.626892	0.313446	−	0.949606i	$-0.398517\pi$
$907$	17123.9	0.626892	0.313446	+	0.949606i	$0.398517\pi$
$908$	−16600.3	−0.606720
$909$	9870.53	0.360159
$910$	705.872	0.0257137
$911$	46213.5	1.68070	0.840351	−	0.542042i	$-0.182349\pi$
$911$	46213.5	1.68070	0.840351	+	0.542042i	$0.182349\pi$
$912$	912.000	0.0331133
$913$	−18614.7	−0.674760
$914$	−7542.62	−0.272963
$915$	3343.61	0.120805
$916$	−4619.03	−0.166613
$917$	−3504.38	−0.126199
$918$	5794.12	0.208317
$919$	7181.05	0.257760	0.128880	−	0.991660i	$-0.458862\pi$
$919$	7181.05	0.257760	0.128880	+	0.991660i	$0.458862\pi$
$920$	−6389.13	−0.228960
$921$	−9787.24	−0.350164
$922$	37077.8	1.32440
$923$	6748.83	0.240672
$924$	4212.30	0.149973
$925$	−33177.4	−1.17932
$926$	4458.91	0.158239
$927$	−17429.9	−0.617553
$928$	−9172.56	−0.324466
$929$	−28965.7	−1.02296	−0.511482	−	0.859294i	$-0.670903\pi$
$929$	−28965.7	−1.02296	−0.511482	+	0.859294i	$0.670903\pi$
$930$	−2252.29	−0.0794144
$931$	931.000	0.0327737
$932$	12717.8	0.446979
$933$	−13260.6	−0.465310
$934$	−19589.2	−0.686271
$935$	23627.2	0.826407
$936$	826.710	0.0288695
$937$	3209.62	0.111904	0.0559518	−	0.998433i	$-0.482181\pi$
$937$	3209.62	0.111904	0.0559518	+	0.998433i	$0.482181\pi$
$938$	−4085.94	−0.142229
$939$	−11808.2	−0.410380
$940$	6409.49	0.222398
$941$	50191.4	1.73878	0.869390	−	0.494126i	$-0.164512\pi$
$941$	50191.4	1.73878	0.869390	+	0.494126i	$0.164512\pi$
$942$	−1035.84	−0.0358276
$943$	3434.18	0.118592
$944$	−6011.48	−0.207264
$945$	829.926	0.0285688
$946$	39693.8	1.36422
$947$	−43950.9	−1.50814	−0.754072	−	0.656792i	$-0.771913\pi$
$947$	−43950.9	−1.50814	−0.754072	+	0.656792i	$0.771913\pi$
$948$	11153.1	0.382104
$949$	−9052.73	−0.309657
$950$	−4017.28	−0.137198
$951$	−10377.7	−0.353858
$952$	6008.72	0.204563
$953$	−12352.0	−0.419853	−0.209926	−	0.977717i	$-0.567322\pi$
$953$	−12352.0	−0.419853	−0.209926	+	0.977717i	$0.567322\pi$
$954$	2740.50	0.0930052
$955$	−6431.24	−0.217916
$956$	15735.1	0.532334
$957$	−43122.3	−1.45658
$958$	−38117.2	−1.28550
$959$	5385.10	0.181328
$960$	843.099	0.0283447
$961$	−22483.1	−0.754696
$962$	7206.84	0.241536
$963$	−6147.57	−0.205714
$964$	−20890.8	−0.697975
$965$	−12517.2	−0.417557
$966$	−7638.77	−0.254424
$967$	38663.2	1.28575	0.642877	−	0.765969i	$-0.277740\pi$
$967$	38663.2	1.28575	0.642877	+	0.765969i	$0.277740\pi$
$968$	9469.35	0.314418
$969$	6116.02	0.202760
$970$	3288.80	0.108863
$971$	10293.2	0.340190	0.170095	−	0.985428i	$-0.445593\pi$
$971$	10293.2	0.340190	0.170095	+	0.985428i	$0.445593\pi$
$972$	972.000	0.0320750
$973$	−13497.8	−0.444728
$974$	−12023.3	−0.395537
$975$	−3641.59	−0.119614
$976$	4061.04	0.133187
$977$	−14420.6	−0.472218	−0.236109	−	0.971727i	$-0.575872\pi$
$977$	−14420.6	−0.472218	−0.236109	+	0.971727i	$0.575872\pi$
$978$	−15640.0	−0.511362
$979$	45859.2	1.49711
$980$	860.664	0.0280540
$981$	−3054.78	−0.0994205
$982$	−25175.9	−0.818122
$983$	−40925.0	−1.32788	−0.663939	−	0.747787i	$-0.731117\pi$
$983$	−40925.0	−1.32788	−0.663939	+	0.747787i	$0.731117\pi$
$984$	−453.169	−0.0146814
$985$	−1807.36	−0.0584642
$986$	−61512.7	−1.98678
$987$	7663.12	0.247132
$988$	872.639	0.0280995
$989$	−71982.5	−2.31437
$990$	3963.60	0.127244
$991$	12984.4	0.416210	0.208105	−	0.978106i	$-0.433270\pi$
$991$	12984.4	0.416210	0.208105	+	0.978106i	$0.433270\pi$
$992$	−2735.55	−0.0875544
$993$	9385.86	0.299951
$994$	8228.78	0.262577
$995$	−3374.44	−0.107515
$996$	−4454.47	−0.141712
$997$	−7857.20	−0.249589	−0.124794	−	0.992183i	$-0.539827\pi$
$997$	−7857.20	−0.249589	−0.124794	+	0.992183i	$0.539827\pi$
$998$	−14532.8	−0.460949
$999$	8473.40	0.268355

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.4.a.r.1.3	✓	5
3.2	odd	2		2394.4.a.bb.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.4.a.r.1.3	✓	5	1.1	even	1	trivial
2394.4.a.bb.1.3		5	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:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	798.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +4.39114 q^{5} +6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +4.39114 q^{5} +6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +8.78228 q^{10} +50.1465 q^{11} +12.0000 q^{12} +11.4821 q^{13} +14.0000 q^{14} +13.1734 q^{15} +16.0000 q^{16} +107.299 q^{17} +18.0000 q^{18} +19.0000 q^{19} +17.5646 q^{20} +21.0000 q^{21} +100.293 q^{22} -181.876 q^{23} +24.0000 q^{24} -105.718 q^{25} +22.9642 q^{26} +27.0000 q^{27} +28.0000 q^{28} -286.643 q^{29} +26.3468 q^{30} -85.4861 q^{31} +32.0000 q^{32} +150.439 q^{33} +214.597 q^{34} +30.7380 q^{35} +36.0000 q^{36} +313.830 q^{37} +38.0000 q^{38} +34.4463 q^{39} +35.1291 q^{40} -18.8820 q^{41} +42.0000 q^{42} +395.779 q^{43} +200.586 q^{44} +39.5203 q^{45} -363.751 q^{46} +364.910 q^{47} +48.0000 q^{48} +49.0000 q^{49} -211.436 q^{50} +321.896 q^{51} +45.9283 q^{52} +152.250 q^{53} +54.0000 q^{54} +220.200 q^{55} +56.0000 q^{56} +57.0000 q^{57} -573.285 q^{58} -375.717 q^{59} +52.6937 q^{60} +253.815 q^{61} -170.972 q^{62} +63.0000 q^{63} +64.0000 q^{64} +50.4195 q^{65} +300.879 q^{66} -291.853 q^{67} +429.194 q^{68} -545.627 q^{69} +61.4760 q^{70} +587.770 q^{71} +72.0000 q^{72} -788.422 q^{73} +627.660 q^{74} -317.154 q^{75} +76.0000 q^{76} +351.025 q^{77} +68.8925 q^{78} +929.422 q^{79} +70.2582 q^{80} +81.0000 q^{81} -37.7641 q^{82} -371.206 q^{83} +84.0000 q^{84} +471.163 q^{85} +791.557 q^{86} -859.928 q^{87} +401.172 q^{88} +914.506 q^{89} +79.0405 q^{90} +80.3746 q^{91} -727.502 q^{92} -256.458 q^{93} +729.821 q^{94} +83.4317 q^{95} +96.0000 q^{96} +374.481 q^{97} +98.0000 q^{98} +451.318 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 10 q^{2} + 15 q^{3} + 20 q^{4} + 20 q^{5} + 30 q^{6} + 35 q^{7} + 40 q^{8} + 45 q^{9}+O(q^{10}) \) 5 * q + 10 * q^2 + 15 * q^3 + 20 * q^4 + 20 * q^5 + 30 * q^6 + 35 * q^7 + 40 * q^8 + 45 * q^9	\( 5 q + 10 q^{2} + 15 q^{3} + 20 q^{4} + 20 q^{5} + 30 q^{6} + 35 q^{7} + 40 q^{8} + 45 q^{9} + 40 q^{10} + 82 q^{11} + 60 q^{12} + 20 q^{13} + 70 q^{14} + 60 q^{15} + 80 q^{16} + 48 q^{17} + 90 q^{18} + 95 q^{19} + 80 q^{20} + 105 q^{21} + 164 q^{22} + 166 q^{23} + 120 q^{24} + 235 q^{25} + 40 q^{26} + 135 q^{27} + 140 q^{28} + 134 q^{29} + 120 q^{30} + 124 q^{31} + 160 q^{32} + 246 q^{33} + 96 q^{34} + 140 q^{35} + 180 q^{36} + 334 q^{37} + 190 q^{38} + 60 q^{39} + 160 q^{40} - 126 q^{41} + 210 q^{42} + 132 q^{43} + 328 q^{44} + 180 q^{45} + 332 q^{46} + 120 q^{47} + 240 q^{48} + 245 q^{49} + 470 q^{50} + 144 q^{51} + 80 q^{52} + 142 q^{53} + 270 q^{54} + 64 q^{55} + 280 q^{56} + 285 q^{57} + 268 q^{58} + 12 q^{59} + 240 q^{60} + 614 q^{61} + 248 q^{62} + 315 q^{63} + 320 q^{64} + 672 q^{65} + 492 q^{66} - 30 q^{67} + 192 q^{68} + 498 q^{69} + 280 q^{70} + 548 q^{71} + 360 q^{72} + 554 q^{73} + 668 q^{74} + 705 q^{75} + 380 q^{76} + 574 q^{77} + 120 q^{78} - 138 q^{79} + 320 q^{80} + 405 q^{81} - 252 q^{82} + 100 q^{83} + 420 q^{84} - 156 q^{85} + 264 q^{86} + 402 q^{87} + 656 q^{88} + 842 q^{89} + 360 q^{90} + 140 q^{91} + 664 q^{92} + 372 q^{93} + 240 q^{94} + 380 q^{95} + 480 q^{96} - 568 q^{97} + 490 q^{98} + 738 q^{99}+O(q^{100}) \) 5 * q + 10 * q^2 + 15 * q^3 + 20 * q^4 + 20 * q^5 + 30 * q^6 + 35 * q^7 + 40 * q^8 + 45 * q^9 + 40 * q^10 + 82 * q^11 + 60 * q^12 + 20 * q^13 + 70 * q^14 + 60 * q^15 + 80 * q^16 + 48 * q^17 + 90 * q^18 + 95 * q^19 + 80 * q^20 + 105 * q^21 + 164 * q^22 + 166 * q^23 + 120 * q^24 + 235 * q^25 + 40 * q^26 + 135 * q^27 + 140 * q^28 + 134 * q^29 + 120 * q^30 + 124 * q^31 + 160 * q^32 + 246 * q^33 + 96 * q^34 + 140 * q^35 + 180 * q^36 + 334 * q^37 + 190 * q^38 + 60 * q^39 + 160 * q^40 - 126 * q^41 + 210 * q^42 + 132 * q^43 + 328 * q^44 + 180 * q^45 + 332 * q^46 + 120 * q^47 + 240 * q^48 + 245 * q^49 + 470 * q^50 + 144 * q^51 + 80 * q^52 + 142 * q^53 + 270 * q^54 + 64 * q^55 + 280 * q^56 + 285 * q^57 + 268 * q^58 + 12 * q^59 + 240 * q^60 + 614 * q^61 + 248 * q^62 + 315 * q^63 + 320 * q^64 + 672 * q^65 + 492 * q^66 - 30 * q^67 + 192 * q^68 + 498 * q^69 + 280 * q^70 + 548 * q^71 + 360 * q^72 + 554 * q^73 + 668 * q^74 + 705 * q^75 + 380 * q^76 + 574 * q^77 + 120 * q^78 - 138 * q^79 + 320 * q^80 + 405 * q^81 - 252 * q^82 + 100 * q^83 + 420 * q^84 - 156 * q^85 + 264 * q^86 + 402 * q^87 + 656 * q^88 + 842 * q^89 + 360 * q^90 + 140 * q^91 + 664 * q^92 + 372 * q^93 + 240 * q^94 + 380 * q^95 + 480 * q^96 - 568 * q^97 + 490 * q^98 + 738 * q^99

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