LMFDB - Embedded newform 483.4.a.c.1.6

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:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 34x^{5} + 7x^{4} + 295x^{3} + 84x^{2} - 524x - 288 $ x^7 - x^6 - 34x^5 + 7x^4 + 295x^3 + 84x^2 - 524*x - 288
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			1.6
Root			$3.29766$ 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)

$f(q)$	$=$	$q+2.29766 q^{2} +3.00000 q^{3} -2.72078 q^{4} -7.00327 q^{5} +6.89297 q^{6} +7.00000 q^{7} -24.6327 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+2.29766 q^{2} +3.00000 q^{3} -2.72078 q^{4} -7.00327 q^{5} +6.89297 q^{6} +7.00000 q^{7} -24.6327 q^{8} +9.00000 q^{9} -16.0911 q^{10} +60.7102 q^{11} -8.16233 q^{12} -64.2411 q^{13} +16.0836 q^{14} -21.0098 q^{15} -34.8311 q^{16} -97.1763 q^{17} +20.6789 q^{18} -40.7073 q^{19} +19.0543 q^{20} +21.0000 q^{21} +139.491 q^{22} +23.0000 q^{23} -73.8980 q^{24} -75.9542 q^{25} -147.604 q^{26} +27.0000 q^{27} -19.0454 q^{28} -36.5752 q^{29} -48.2733 q^{30} -139.396 q^{31} +117.031 q^{32} +182.131 q^{33} -223.278 q^{34} -49.0229 q^{35} -24.4870 q^{36} -46.2359 q^{37} -93.5313 q^{38} -192.723 q^{39} +172.509 q^{40} -414.519 q^{41} +48.2508 q^{42} -194.226 q^{43} -165.179 q^{44} -63.0294 q^{45} +52.8461 q^{46} -366.705 q^{47} -104.493 q^{48} +49.0000 q^{49} -174.517 q^{50} -291.529 q^{51} +174.786 q^{52} +414.043 q^{53} +62.0367 q^{54} -425.170 q^{55} -172.429 q^{56} -122.122 q^{57} -84.0371 q^{58} -323.891 q^{59} +57.1630 q^{60} +144.604 q^{61} -320.283 q^{62} +63.0000 q^{63} +547.547 q^{64} +449.898 q^{65} +418.474 q^{66} +155.076 q^{67} +264.395 q^{68} +69.0000 q^{69} -112.638 q^{70} -852.980 q^{71} -221.694 q^{72} +790.043 q^{73} -106.234 q^{74} -227.863 q^{75} +110.756 q^{76} +424.972 q^{77} -442.812 q^{78} -656.006 q^{79} +243.932 q^{80} +81.0000 q^{81} -952.421 q^{82} +369.386 q^{83} -57.1363 q^{84} +680.551 q^{85} -446.266 q^{86} -109.725 q^{87} -1495.45 q^{88} +497.973 q^{89} -144.820 q^{90} -449.688 q^{91} -62.5779 q^{92} -418.187 q^{93} -842.563 q^{94} +285.084 q^{95} +351.094 q^{96} -1728.17 q^{97} +112.585 q^{98} +546.392 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 6 q^{2} + 21 q^{3} + 18 q^{4} - 41 q^{5} - 18 q^{6} + 49 q^{7} - 33 q^{8} + 63 q^{9}+O(q^{10}) $ 7 * q - 6 * q^2 + 21 * q^3 + 18 * q^4 - 41 * q^5 - 18 * q^6 + 49 * q^7 - 33 * q^8 + 63 * q^9	\( 7 q - 6 q^{2} + 21 q^{3} + 18 q^{4} - 41 q^{5} - 18 q^{6} + 49 q^{7} - 33 q^{8} + 63 q^{9} + q^{10} - 126 q^{11} + 54 q^{12} - 87 q^{13} - 42 q^{14} - 123 q^{15} + 2 q^{16} - 204 q^{17} - 54 q^{18} - 286 q^{19} - 418 q^{20} + 147 q^{21} + 329 q^{22} + 161 q^{23} - 99 q^{24} + 440 q^{25} - 360 q^{26} + 189 q^{27} + 126 q^{28} - 329 q^{29} + 3 q^{30} + 296 q^{31} - 270 q^{32} - 378 q^{33} - 919 q^{34} - 287 q^{35} + 162 q^{36} - 691 q^{37} - 367 q^{38} - 261 q^{39} + 138 q^{40} - 343 q^{41} - 126 q^{42} - 171 q^{43} - 1279 q^{44} - 369 q^{45} - 138 q^{46} - 1403 q^{47} + 6 q^{48} + 343 q^{49} + 230 q^{50} - 612 q^{51} + 2157 q^{52} - 1024 q^{53} - 162 q^{54} - 158 q^{55} - 231 q^{56} - 858 q^{57} + 2608 q^{58} - 1388 q^{59} - 1254 q^{60} - 52 q^{61} - 309 q^{62} + 441 q^{63} - 187 q^{64} - 1067 q^{65} + 987 q^{66} - 1148 q^{67} + 1293 q^{68} + 483 q^{69} + 7 q^{70} - 1590 q^{71} - 297 q^{72} - 802 q^{73} - 878 q^{74} + 1320 q^{75} - 2505 q^{76} - 882 q^{77} - 1080 q^{78} + 618 q^{79} + 195 q^{80} + 567 q^{81} - 1040 q^{82} - 1818 q^{83} + 378 q^{84} - 1526 q^{85} + 1188 q^{86} - 987 q^{87} + 1664 q^{88} - 354 q^{89} + 9 q^{90} - 609 q^{91} + 414 q^{92} + 888 q^{93} + 663 q^{94} + 78 q^{95} - 810 q^{96} - 1575 q^{97} - 294 q^{98} - 1134 q^{99}+O(q^{100}) \) 7 * q - 6 * q^2 + 21 * q^3 + 18 * q^4 - 41 * q^5 - 18 * q^6 + 49 * q^7 - 33 * q^8 + 63 * q^9 + q^10 - 126 * q^11 + 54 * q^12 - 87 * q^13 - 42 * q^14 - 123 * q^15 + 2 * q^16 - 204 * q^17 - 54 * q^18 - 286 * q^19 - 418 * q^20 + 147 * q^21 + 329 * q^22 + 161 * q^23 - 99 * q^24 + 440 * q^25 - 360 * q^26 + 189 * q^27 + 126 * q^28 - 329 * q^29 + 3 * q^30 + 296 * q^31 - 270 * q^32 - 378 * q^33 - 919 * q^34 - 287 * q^35 + 162 * q^36 - 691 * q^37 - 367 * q^38 - 261 * q^39 + 138 * q^40 - 343 * q^41 - 126 * q^42 - 171 * q^43 - 1279 * q^44 - 369 * q^45 - 138 * q^46 - 1403 * q^47 + 6 * q^48 + 343 * q^49 + 230 * q^50 - 612 * q^51 + 2157 * q^52 - 1024 * q^53 - 162 * q^54 - 158 * q^55 - 231 * q^56 - 858 * q^57 + 2608 * q^58 - 1388 * q^59 - 1254 * q^60 - 52 * q^61 - 309 * q^62 + 441 * q^63 - 187 * q^64 - 1067 * q^65 + 987 * q^66 - 1148 * q^67 + 1293 * q^68 + 483 * q^69 + 7 * q^70 - 1590 * q^71 - 297 * q^72 - 802 * q^73 - 878 * q^74 + 1320 * q^75 - 2505 * q^76 - 882 * q^77 - 1080 * q^78 + 618 * q^79 + 195 * q^80 + 567 * q^81 - 1040 * q^82 - 1818 * q^83 + 378 * q^84 - 1526 * q^85 + 1188 * q^86 - 987 * q^87 + 1664 * q^88 - 354 * q^89 + 9 * q^90 - 609 * q^91 + 414 * q^92 + 888 * q^93 + 663 * q^94 + 78 * q^95 - 810 * q^96 - 1575 * q^97 - 294 * q^98 - 1134 * 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 $

$2$	2.29766	0.812344	0.406172	−	0.913797i	$-0.366863\pi$
$2$	2.29766	0.812344	0.406172	+	0.913797i	$0.366863\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−2.72078	−0.340097
$5$	−7.00327	−0.626391	−0.313196	−	0.949689i	$-0.601400\pi$
$5$	−7.00327	−0.626391	−0.313196	+	0.949689i	$0.601400\pi$
$6$	6.89297	0.469007
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−24.6327	−1.08862
$9$	9.00000	0.333333
$10$	−16.0911	−0.508845
$11$	60.7102	1.66407	0.832037	−	0.554720i	$-0.187175\pi$
$11$	60.7102	1.66407	0.832037	+	0.554720i	$0.187175\pi$
$12$	−8.16233	−0.196355
$13$	−64.2411	−1.37056	−0.685280	−	0.728280i	$-0.740320\pi$
$13$	−64.2411	−1.37056	−0.685280	+	0.728280i	$0.740320\pi$
$14$	16.0836	0.307037
$15$	−21.0098	−0.361647
$16$	−34.8311	−0.544237
$17$	−97.1763	−1.38639	−0.693197	−	0.720748i	$-0.743799\pi$
$17$	−97.1763	−1.38639	−0.693197	+	0.720748i	$0.743799\pi$
$18$	20.6789	0.270781
$19$	−40.7073	−0.491521	−0.245760	−	0.969331i	$-0.579038\pi$
$19$	−40.7073	−0.491521	−0.245760	+	0.969331i	$0.579038\pi$
$20$	19.0543	0.213034
$21$	21.0000	0.218218
$22$	139.491	1.35180
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	−73.8980	−0.628515
$25$	−75.9542	−0.607634
$26$	−147.604	−1.11337
$27$	27.0000	0.192450
$28$	−19.0454	−0.128545
$29$	−36.5752	−0.234201	−0.117101	−	0.993120i	$-0.537360\pi$
$29$	−36.5752	−0.234201	−0.117101	+	0.993120i	$0.537360\pi$
$30$	−48.2733	−0.293782
$31$	−139.396	−0.807619	−0.403809	−	0.914843i	$-0.632314\pi$
$31$	−139.396	−0.807619	−0.403809	+	0.914843i	$0.632314\pi$
$32$	117.031	0.646513
$33$	182.131	0.960754
$34$	−223.278	−1.12623
$35$	−49.0229	−0.236754
$36$	−24.4870	−0.113366
$37$	−46.2359	−0.205436	−0.102718	−	0.994711i	$-0.532754\pi$
$37$	−46.2359	−0.205436	−0.102718	+	0.994711i	$0.532754\pi$
$38$	−93.5313	−0.399284
$39$	−192.723	−0.791293
$40$	172.509	0.681902
$41$	−414.519	−1.57895	−0.789475	−	0.613783i	$-0.789647\pi$
$41$	−414.519	−1.57895	−0.789475	+	0.613783i	$0.789647\pi$
$42$	48.2508	0.177268
$43$	−194.226	−0.688820	−0.344410	−	0.938819i	$-0.611921\pi$
$43$	−194.226	−0.688820	−0.344410	+	0.938819i	$0.611921\pi$
$44$	−165.179	−0.565947
$45$	−63.0294	−0.208797
$46$	52.8461	0.169385
$47$	−366.705	−1.13807	−0.569037	−	0.822312i	$-0.692684\pi$
$47$	−366.705	−1.13807	−0.569037	+	0.822312i	$0.692684\pi$
$48$	−104.493	−0.314215
$49$	49.0000	0.142857
$50$	−174.517	−0.493608
$51$	−291.529	−0.800435
$52$	174.786	0.466123
$53$	414.043	1.07308	0.536539	−	0.843875i	$-0.319731\pi$
$53$	414.043	1.07308	0.536539	+	0.843875i	$0.319731\pi$
$54$	62.0367	0.156336
$55$	−425.170	−1.04236
$56$	−172.429	−0.411460
$57$	−122.122	−0.283780
$58$	−84.0371	−0.190252
$59$	−323.891	−0.714696	−0.357348	−	0.933971i	$-0.616319\pi$
$59$	−323.891	−0.714696	−0.357348	+	0.933971i	$0.616319\pi$
$60$	57.1630	0.122995
$61$	144.604	0.303518	0.151759	−	0.988418i	$-0.451506\pi$
$61$	144.604	0.303518	0.151759	+	0.988418i	$0.451506\pi$
$62$	−320.283	−0.656064
$63$	63.0000	0.125988
$64$	547.547	1.06943
$65$	449.898	0.858506
$66$	418.474	0.780463
$67$	155.076	0.282769	0.141385	−	0.989955i	$-0.454845\pi$
$67$	155.076	0.282769	0.141385	+	0.989955i	$0.454845\pi$
$68$	264.395	0.471509
$69$	69.0000	0.120386
$70$	−112.638	−0.192325
$71$	−852.980	−1.42578	−0.712888	−	0.701278i	$-0.752613\pi$
$71$	−852.980	−1.42578	−0.712888	+	0.701278i	$0.752613\pi$
$72$	−221.694	−0.362873
$73$	790.043	1.26668	0.633340	−	0.773874i	$-0.281684\pi$
$73$	790.043	1.26668	0.633340	+	0.773874i	$0.281684\pi$
$74$	−106.234	−0.166885
$75$	−227.863	−0.350818
$76$	110.756	0.167165
$77$	424.972	0.628961
$78$	−442.812	−0.642802
$79$	−656.006	−0.934258	−0.467129	−	0.884189i	$-0.654712\pi$
$79$	−656.006	−0.934258	−0.467129	+	0.884189i	$0.654712\pi$
$80$	243.932	0.340905
$81$	81.0000	0.111111
$82$	−952.421	−1.28265
$83$	369.386	0.488499	0.244249	−	0.969712i	$-0.421458\pi$
$83$	369.386	0.488499	0.244249	+	0.969712i	$0.421458\pi$
$84$	−57.1363	−0.0742153
$85$	680.551	0.868426
$86$	−446.266	−0.559559
$87$	−109.725	−0.135216
$88$	−1495.45	−1.81154
$89$	497.973	0.593090	0.296545	−	0.955019i	$-0.404166\pi$
$89$	497.973	0.593090	0.296545	+	0.955019i	$0.404166\pi$
$90$	−144.820	−0.169615
$91$	−449.688	−0.518023
$92$	−62.5779	−0.0709152
$93$	−418.187	−0.466279
$94$	−842.563	−0.924508
$95$	285.084	0.307884
$96$	351.094	0.373264
$97$	−1728.17	−1.80896	−0.904481	−	0.426514i	$-0.859741\pi$
$97$	−1728.17	−1.80896	−0.904481	+	0.426514i	$0.859741\pi$
$98$	112.585	0.116049
$99$	546.392	0.554692
$100$	206.655	0.206655
$101$	2026.19	1.99617	0.998087	−	0.0618288i	$-0.0196933\pi$
$101$	2026.19	1.99617	0.998087	+	0.0618288i	$0.0196933\pi$
$102$	−669.833	−0.650229
$103$	2066.63	1.97700	0.988502	−	0.151211i	$-0.0483172\pi$
$103$	2066.63	1.97700	0.988502	+	0.151211i	$0.0483172\pi$
$104$	1582.43	1.49202
$105$	−147.069	−0.136690
$106$	951.328	0.871709
$107$	762.366	0.688792	0.344396	−	0.938825i	$-0.388084\pi$
$107$	762.366	0.688792	0.344396	+	0.938825i	$0.388084\pi$
$108$	−73.4610	−0.0654517
$109$	−1305.58	−1.14726	−0.573632	−	0.819113i	$-0.694466\pi$
$109$	−1305.58	−1.14726	−0.573632	+	0.819113i	$0.694466\pi$
$110$	−976.894	−0.846756
$111$	−138.708	−0.118608
$112$	−243.818	−0.205702
$113$	1565.58	1.30334	0.651670	−	0.758503i	$-0.274069\pi$
$113$	1565.58	1.30334	0.651670	+	0.758503i	$0.274069\pi$
$114$	−280.594	−0.230527
$115$	−161.075	−0.130612
$116$	99.5129	0.0796512
$117$	−578.170	−0.456853
$118$	−744.191	−0.580579
$119$	−680.234	−0.524008
$120$	517.527	0.393696
$121$	2354.73	1.76914
$122$	332.250	0.246561
$123$	−1243.56	−0.911607
$124$	379.264	0.274669
$125$	1407.34	1.00701
$126$	144.752	0.102346
$127$	1239.91	0.866336	0.433168	−	0.901313i	$-0.357396\pi$
$127$	1239.91	0.866336	0.433168	+	0.901313i	$0.357396\pi$
$128$	321.824	0.222230
$129$	−582.679	−0.397690
$130$	1033.71	0.697403
$131$	−2020.45	−1.34754	−0.673770	−	0.738941i	$-0.735326\pi$
$131$	−2020.45	−1.34754	−0.673770	+	0.738941i	$0.735326\pi$
$132$	−495.537	−0.326750
$133$	−284.951	−0.185777
$134$	356.311	0.229706
$135$	−189.088	−0.120549
$136$	2393.71	1.50926
$137$	−2655.53	−1.65604	−0.828019	−	0.560700i	$-0.810532\pi$
$137$	−2655.53	−1.65604	−0.828019	+	0.560700i	$0.810532\pi$
$138$	158.538	0.0977947
$139$	553.732	0.337892	0.168946	−	0.985625i	$-0.445964\pi$
$139$	553.732	0.337892	0.168946	+	0.985625i	$0.445964\pi$
$140$	133.380	0.0805193
$141$	−1100.12	−0.657067
$142$	−1959.85	−1.15822
$143$	−3900.09	−2.28071
$144$	−313.480	−0.181412
$145$	256.146	0.146702
$146$	1815.25	1.02898
$147$	147.000	0.0824786
$148$	125.798	0.0698682
$149$	1480.67	0.814101	0.407050	−	0.913406i	$-0.366557\pi$
$149$	1480.67	0.814101	0.407050	+	0.913406i	$0.366557\pi$
$150$	−523.550	−0.284985
$151$	−2923.61	−1.57563	−0.787814	−	0.615914i	$-0.788787\pi$
$151$	−2923.61	−1.57563	−0.787814	+	0.615914i	$0.788787\pi$
$152$	1002.73	0.535079
$153$	−874.586	−0.462132
$154$	976.438	0.510933
$155$	976.224	0.505885
$156$	524.357	0.269117
$157$	816.791	0.415204	0.207602	−	0.978213i	$-0.433434\pi$
$157$	816.791	0.415204	0.207602	+	0.978213i	$0.433434\pi$
$158$	−1507.28	−0.758939
$159$	1242.13	0.619542
$160$	−819.601	−0.404970
$161$	161.000	0.0788110
$162$	186.110	0.0902604
$163$	2571.15	1.23551	0.617754	−	0.786371i	$-0.288043\pi$
$163$	2571.15	1.23551	0.617754	+	0.786371i	$0.288043\pi$
$164$	1127.81	0.536997
$165$	−1275.51	−0.601808
$166$	848.722	0.396829
$167$	−4153.75	−1.92471	−0.962356	−	0.271793i	$-0.912383\pi$
$167$	−4153.75	−1.92471	−0.962356	+	0.271793i	$0.912383\pi$
$168$	−517.286	−0.237556
$169$	1929.92	0.878433
$170$	1563.67	0.705460
$171$	−366.366	−0.163840
$172$	528.447	0.234266
$173$	−3535.27	−1.55365	−0.776826	−	0.629716i	$-0.783171\pi$
$173$	−3535.27	−1.55365	−0.776826	+	0.629716i	$0.783171\pi$
$174$	−252.111	−0.109842
$175$	−531.680	−0.229664
$176$	−2114.61	−0.905650
$177$	−971.674	−0.412630
$178$	1144.17	0.481793
$179$	2475.37	1.03362	0.516809	−	0.856101i	$-0.327120\pi$
$179$	2475.37	1.03362	0.516809	+	0.856101i	$0.327120\pi$
$180$	171.489	0.0710113
$181$	3760.97	1.54448	0.772240	−	0.635330i	$-0.219136\pi$
$181$	3760.97	1.54448	0.772240	+	0.635330i	$0.219136\pi$
$182$	−1033.23	−0.420813
$183$	433.811	0.175236
$184$	−566.551	−0.226993
$185$	323.802	0.128683
$186$	−960.849	−0.378779
$187$	−5899.59	−2.30706
$188$	997.724	0.387056
$189$	189.000	0.0727393
$190$	655.025	0.250108
$191$	−2164.14	−0.819854	−0.409927	−	0.912118i	$-0.634446\pi$
$191$	−2164.14	−0.819854	−0.409927	+	0.912118i	$0.634446\pi$
$192$	1642.64	0.617434
$193$	1269.71	0.473553	0.236776	−	0.971564i	$-0.423909\pi$
$193$	1269.71	0.473553	0.236776	+	0.971564i	$0.423909\pi$
$194$	−3970.74	−1.46950
$195$	1349.69	0.495659
$196$	−133.318	−0.0485853
$197$	−3881.51	−1.40379	−0.701894	−	0.712282i	$-0.747662\pi$
$197$	−3881.51	−1.40379	−0.701894	+	0.712282i	$0.747662\pi$
$198$	1255.42	0.450600
$199$	−258.180	−0.0919694	−0.0459847	−	0.998942i	$-0.514643\pi$
$199$	−258.180	−0.0919694	−0.0459847	+	0.998942i	$0.514643\pi$
$200$	1870.95	0.661482
$201$	465.228	0.163257
$202$	4655.49	1.62158
$203$	−256.026	−0.0885198
$204$	793.185	0.272226
$205$	2902.99	0.989041
$206$	4748.41	1.60601
$207$	207.000	0.0695048
$208$	2237.59	0.745909
$209$	−2471.35	−0.817927
$210$	−337.913	−0.111039
$211$	3833.58	1.25078	0.625390	−	0.780313i	$-0.284940\pi$
$211$	3833.58	1.25078	0.625390	+	0.780313i	$0.284940\pi$
$212$	−1126.52	−0.364951
$213$	−2558.94	−0.823172
$214$	1751.65	0.559536
$215$	1360.22	0.431471
$216$	−665.082	−0.209505
$217$	−975.769	−0.305251
$218$	−2999.77	−0.931973
$219$	2370.13	0.731318
$220$	1156.79	0.354504
$221$	6242.71	1.90014
$222$	−318.702	−0.0963509
$223$	3448.87	1.03566	0.517832	−	0.855482i	$-0.326739\pi$
$223$	3448.87	1.03566	0.517832	+	0.855482i	$0.326739\pi$
$224$	819.219	0.244359
$225$	−683.588	−0.202545
$226$	3597.17	1.05876
$227$	−3053.29	−0.892748	−0.446374	−	0.894847i	$-0.647285\pi$
$227$	−3053.29	−0.892748	−0.446374	+	0.894847i	$0.647285\pi$
$228$	332.267	0.0965127
$229$	−4710.10	−1.35918	−0.679590	−	0.733592i	$-0.737842\pi$
$229$	−4710.10	−1.35918	−0.679590	+	0.733592i	$0.737842\pi$
$230$	−370.095	−0.106102
$231$	1274.91	0.363131
$232$	900.943	0.254956
$233$	2669.22	0.750498	0.375249	−	0.926924i	$-0.377557\pi$
$233$	2669.22	0.750498	0.375249	+	0.926924i	$0.377557\pi$
$234$	−1328.44	−0.371122
$235$	2568.14	0.712880
$236$	881.237	0.243066
$237$	−1968.02	−0.539394
$238$	−1562.94	−0.425675
$239$	6821.27	1.84616	0.923079	−	0.384611i	$-0.125664\pi$
$239$	6821.27	1.84616	0.923079	+	0.384611i	$0.125664\pi$
$240$	731.795	0.196822
$241$	1359.98	0.363502	0.181751	−	0.983345i	$-0.441824\pi$
$241$	1359.98	0.363502	0.181751	+	0.983345i	$0.441824\pi$
$242$	5410.36	1.43715
$243$	243.000	0.0641500
$244$	−393.435	−0.103226
$245$	−343.160	−0.0894845
$246$	−2857.26	−0.740539
$247$	2615.08	0.673658
$248$	3433.68	0.879190
$249$	1108.16	0.282035
$250$	3233.57	0.818037
$251$	−3483.80	−0.876078	−0.438039	−	0.898956i	$-0.644327\pi$
$251$	−3483.80	−0.876078	−0.438039	+	0.898956i	$0.644327\pi$
$252$	−171.409	−0.0428482
$253$	1396.34	0.346984
$254$	2848.90	0.703763
$255$	2041.65	0.501386
$256$	−3640.93	−0.888900
$257$	−3076.61	−0.746747	−0.373373	−	0.927681i	$-0.621799\pi$
$257$	−3076.61	−0.746747	−0.373373	+	0.927681i	$0.621799\pi$
$258$	−1338.80	−0.323061
$259$	−323.651	−0.0776475
$260$	−1224.07	−0.291976
$261$	−329.176	−0.0780671
$262$	−4642.30	−1.09467
$263$	−6248.71	−1.46506	−0.732532	−	0.680732i	$-0.761662\pi$
$263$	−6248.71	−1.46506	−0.732532	+	0.680732i	$0.761662\pi$
$264$	−4486.36	−1.04590
$265$	−2899.65	−0.672167
$266$	−654.719	−0.150915
$267$	1493.92	0.342421
$268$	−421.927	−0.0961690
$269$	−1224.94	−0.277642	−0.138821	−	0.990318i	$-0.544331\pi$
$269$	−1224.94	−0.277642	−0.138821	+	0.990318i	$0.544331\pi$
$270$	−434.460	−0.0979273
$271$	6040.60	1.35402	0.677011	−	0.735973i	$-0.263275\pi$
$271$	6040.60	1.35402	0.677011	+	0.735973i	$0.263275\pi$
$272$	3384.76	0.754527
$273$	−1349.06	−0.299081
$274$	−6101.50	−1.34527
$275$	−4611.20	−1.01115
$276$	−187.734	−0.0409429
$277$	−482.924	−0.104751	−0.0523756	−	0.998627i	$-0.516679\pi$
$277$	−482.924	−0.104751	−0.0523756	+	0.998627i	$0.516679\pi$
$278$	1272.29	0.274484
$279$	−1254.56	−0.269206
$280$	1207.56	0.257735
$281$	5970.96	1.26761	0.633804	−	0.773494i	$-0.281493\pi$
$281$	5970.96	1.26761	0.633804	+	0.773494i	$0.281493\pi$
$282$	−2527.69	−0.533765
$283$	1171.75	0.246126	0.123063	−	0.992399i	$-0.460728\pi$
$283$	1171.75	0.246126	0.123063	+	0.992399i	$0.460728\pi$
$284$	2320.77	0.484903
$285$	855.252	0.177757
$286$	−8961.07	−1.85272
$287$	−2901.63	−0.596787
$288$	1053.28	0.215504
$289$	4530.23	0.922090
$290$	588.535	0.119172
$291$	−5184.52	−1.04440
$292$	−2149.53	−0.430794
$293$	423.736	0.0844878	0.0422439	−	0.999107i	$-0.486549\pi$
$293$	423.736	0.0844878	0.0422439	+	0.999107i	$0.486549\pi$
$294$	337.755	0.0670010
$295$	2268.30	0.447680
$296$	1138.91	0.223642
$297$	1639.18	0.320251
$298$	3402.06	0.661330
$299$	−1477.54	−0.285781
$300$	619.964	0.119312
$301$	−1359.59	−0.260350
$302$	−6717.44	−1.27995
$303$	6078.57	1.15249
$304$	1417.88	0.267504
$305$	−1012.70	−0.190121
$306$	−2009.50	−0.375410
$307$	1450.13	0.269587	0.134794	−	0.990874i	$-0.456963\pi$
$307$	1450.13	0.269587	0.134794	+	0.990874i	$0.456963\pi$
$308$	−1156.25	−0.213908
$309$	6199.90	1.14142
$310$	2243.03	0.410953
$311$	−6480.33	−1.18156	−0.590781	−	0.806832i	$-0.701180\pi$
$311$	−6480.33	−1.18156	−0.590781	+	0.806832i	$0.701180\pi$
$312$	4747.29	0.861417
$313$	−4059.15	−0.733025	−0.366513	−	0.930413i	$-0.619448\pi$
$313$	−4059.15	−0.733025	−0.366513	+	0.930413i	$0.619448\pi$
$314$	1876.70	0.337288
$315$	−441.206	−0.0789179
$316$	1784.85	0.317739
$317$	−8165.35	−1.44672	−0.723362	−	0.690469i	$-0.757404\pi$
$317$	−8165.35	−1.44672	−0.723362	+	0.690469i	$0.757404\pi$
$318$	2853.98	0.503281
$319$	−2220.49	−0.389728
$320$	−3834.62	−0.669880
$321$	2287.10	0.397674
$322$	369.923	0.0640217
$323$	3955.78	0.681442
$324$	−220.383	−0.0377886
$325$	4879.38	0.832798
$326$	5907.62	1.00366
$327$	−3916.74	−0.662373
$328$	10210.7	1.71888
$329$	−2566.94	−0.430152
$330$	−2930.68	−0.488875
$331$	2964.68	0.492307	0.246154	−	0.969231i	$-0.420833\pi$
$331$	2964.68	0.492307	0.246154	+	0.969231i	$0.420833\pi$
$332$	−1005.02	−0.166137
$333$	−416.123	−0.0684786
$334$	−9543.89	−1.56353
$335$	−1086.04	−0.177124
$336$	−731.454	−0.118762
$337$	11582.4	1.87220	0.936101	−	0.351731i	$-0.114407\pi$
$337$	11582.4	1.87220	0.936101	+	0.351731i	$0.114407\pi$
$338$	4434.29	0.713590
$339$	4696.74	0.752484
$340$	−1851.63	−0.295349
$341$	−8462.73	−1.34394
$342$	−841.782	−0.133095
$343$	343.000	0.0539949
$344$	4784.31	0.749863
$345$	−483.225	−0.0754086
$346$	−8122.83	−1.26210
$347$	4437.69	0.686534	0.343267	−	0.939238i	$-0.388466\pi$
$347$	4437.69	0.686534	0.343267	+	0.939238i	$0.388466\pi$
$348$	298.539	0.0459867
$349$	843.065	0.129307	0.0646536	−	0.997908i	$-0.479406\pi$
$349$	843.065	0.129307	0.0646536	+	0.997908i	$0.479406\pi$
$350$	−1221.62	−0.186566
$351$	−1734.51	−0.263764
$352$	7105.00	1.07585
$353$	−7702.20	−1.16132	−0.580661	−	0.814145i	$-0.697206\pi$
$353$	−7702.20	−1.16132	−0.580661	+	0.814145i	$0.697206\pi$
$354$	−2232.57	−0.335198
$355$	5973.65	0.893094
$356$	−1354.87	−0.201708
$357$	−2040.70	−0.302536
$358$	5687.54	0.839653
$359$	−11014.2	−1.61924	−0.809621	−	0.586953i	$-0.800327\pi$
$359$	−11014.2	−1.61924	−0.809621	+	0.586953i	$0.800327\pi$
$360$	1552.58	0.227301
$361$	−5201.92	−0.758407
$362$	8641.42	1.25465
$363$	7064.19	1.02142
$364$	1223.50	0.176178
$365$	−5532.88	−0.793437
$366$	996.749	0.142352
$367$	−8956.29	−1.27388	−0.636941	−	0.770913i	$-0.719800\pi$
$367$	−8956.29	−1.27388	−0.636941	+	0.770913i	$0.719800\pi$
$368$	−801.116	−0.113481
$369$	−3730.67	−0.526317
$370$	743.986	0.104535
$371$	2898.30	0.405585
$372$	1137.79	0.158580
$373$	−2116.01	−0.293735	−0.146867	−	0.989156i	$-0.546919\pi$
$373$	−2116.01	−0.293735	−0.146867	+	0.989156i	$0.546919\pi$
$374$	−13555.2	−1.87413
$375$	4222.01	0.581396
$376$	9032.93	1.23893
$377$	2349.63	0.320987
$378$	434.257	0.0590893
$379$	−6234.79	−0.845013	−0.422506	−	0.906360i	$-0.638850\pi$
$379$	−6234.79	−0.845013	−0.422506	+	0.906360i	$0.638850\pi$
$380$	−775.650	−0.104711
$381$	3719.74	0.500179
$382$	−4972.46	−0.666003
$383$	192.636	0.0257003	0.0128502	−	0.999917i	$-0.495910\pi$
$383$	192.636	0.0257003	0.0128502	+	0.999917i	$0.495910\pi$
$384$	965.471	0.128305
$385$	−2976.19	−0.393976
$386$	2917.35	0.384688
$387$	−1748.04	−0.229607
$388$	4701.97	0.615223
$389$	−935.352	−0.121913	−0.0609566	−	0.998140i	$-0.519415\pi$
$389$	−935.352	−0.121913	−0.0609566	+	0.998140i	$0.519415\pi$
$390$	3101.13	0.402646
$391$	−2235.05	−0.289083
$392$	−1207.00	−0.155517
$393$	−6061.35	−0.778002
$394$	−8918.38	−1.14036
$395$	4594.18	0.585211
$396$	−1486.61	−0.188649
$397$	5290.08	0.668770	0.334385	−	0.942437i	$-0.391471\pi$
$397$	5290.08	0.668770	0.334385	+	0.942437i	$0.391471\pi$
$398$	−593.210	−0.0747108
$399$	−854.853	−0.107259
$400$	2645.57	0.330697
$401$	−2406.82	−0.299728	−0.149864	−	0.988707i	$-0.547884\pi$
$401$	−2406.82	−0.299728	−0.149864	+	0.988707i	$0.547884\pi$
$402$	1068.93	0.132621
$403$	8954.92	1.10689
$404$	−5512.82	−0.678893
$405$	−567.265	−0.0695990
$406$	−588.260	−0.0719085
$407$	−2806.99	−0.341861
$408$	7181.13	0.871370
$409$	6035.14	0.729629	0.364814	−	0.931080i	$-0.381132\pi$
$409$	6035.14	0.729629	0.364814	+	0.931080i	$0.381132\pi$
$410$	6670.06	0.803441
$411$	−7966.59	−0.956114
$412$	−5622.85	−0.672373
$413$	−2267.24	−0.270130
$414$	475.615	0.0564618
$415$	−2586.91	−0.305991
$416$	−7518.22	−0.886084
$417$	1661.20	0.195082
$418$	−5678.31	−0.664438
$419$	−750.256	−0.0874760	−0.0437380	−	0.999043i	$-0.513927\pi$
$419$	−750.256	−0.0874760	−0.0437380	+	0.999043i	$0.513927\pi$
$420$	400.141	0.0464878
$421$	−11803.2	−1.36640	−0.683200	−	0.730231i	$-0.739412\pi$
$421$	−11803.2	−1.36640	−0.683200	+	0.730231i	$0.739412\pi$
$422$	8808.24	1.01606
$423$	−3300.35	−0.379358
$424$	−10199.0	−1.16817
$425$	7380.95	0.842420
$426$	−5879.56	−0.668699
$427$	1012.23	0.114719
$428$	−2074.23	−0.234256
$429$	−11700.3	−1.31677
$430$	3125.32	0.350503
$431$	−11532.8	−1.28889	−0.644447	−	0.764649i	$-0.722912\pi$
$431$	−11532.8	−1.28889	−0.644447	+	0.764649i	$0.722912\pi$
$432$	−940.441	−0.104738
$433$	1805.92	0.200432	0.100216	−	0.994966i	$-0.468047\pi$
$433$	1805.92	0.200432	0.100216	+	0.994966i	$0.468047\pi$
$434$	−2241.98	−0.247969
$435$	768.437	0.0846982
$436$	3552.19	0.390182
$437$	−936.268	−0.102489
$438$	5445.74	0.594081
$439$	3765.45	0.409374	0.204687	−	0.978827i	$-0.434382\pi$
$439$	3765.45	0.409374	0.204687	+	0.978827i	$0.434382\pi$
$440$	10473.1	1.13474
$441$	441.000	0.0476190
$442$	14343.6	1.54356
$443$	−7352.72	−0.788574	−0.394287	−	0.918987i	$-0.629008\pi$
$443$	−7352.72	−0.788574	−0.394287	+	0.918987i	$0.629008\pi$
$444$	377.393	0.0403384
$445$	−3487.44	−0.371506
$446$	7924.31	0.841316
$447$	4442.00	0.470021
$448$	3832.83	0.404206
$449$	13724.5	1.44253	0.721267	−	0.692657i	$-0.243560\pi$
$449$	13724.5	1.44253	0.721267	+	0.692657i	$0.243560\pi$
$450$	−1570.65	−0.164536
$451$	−25165.5	−2.62749
$452$	−4259.60	−0.443262
$453$	−8770.82	−0.909689
$454$	−7015.40	−0.725218
$455$	3149.28	0.324485
$456$	3008.19	0.308928
$457$	−9179.81	−0.939635	−0.469818	−	0.882763i	$-0.655680\pi$
$457$	−9179.81	−0.939635	−0.469818	+	0.882763i	$0.655680\pi$
$458$	−10822.2	−1.10412
$459$	−2623.76	−0.266812
$460$	438.250	0.0444206
$461$	1204.51	0.121691	0.0608453	−	0.998147i	$-0.480620\pi$
$461$	1204.51	0.121691	0.0608453	+	0.998147i	$0.480620\pi$
$462$	2929.31	0.294987
$463$	−10852.3	−1.08930	−0.544652	−	0.838662i	$-0.683338\pi$
$463$	−10852.3	−1.08930	−0.544652	+	0.838662i	$0.683338\pi$
$464$	1273.95	0.127461
$465$	2928.67	0.292073
$466$	6132.94	0.609663
$467$	−4892.35	−0.484777	−0.242388	−	0.970179i	$-0.577931\pi$
$467$	−4892.35	−0.484777	−0.242388	+	0.970179i	$0.577931\pi$
$468$	1573.07	0.155374
$469$	1085.53	0.106877
$470$	5900.69	0.579104
$471$	2450.37	0.239718
$472$	7978.31	0.778033
$473$	−11791.5	−1.14625
$474$	−4521.83	−0.438174
$475$	3091.89	0.298665
$476$	1850.77	0.178214
$477$	3726.38	0.357693
$478$	15672.9	1.49971
$479$	−6620.33	−0.631504	−0.315752	−	0.948842i	$-0.602257\pi$
$479$	−6620.33	−0.631504	−0.315752	+	0.948842i	$0.602257\pi$
$480$	−2458.80	−0.233809
$481$	2970.24	0.281562
$482$	3124.76	0.295288
$483$	483.000	0.0455016
$484$	−6406.70	−0.601681
$485$	12102.9	1.13312
$486$	558.330	0.0521119
$487$	−11914.7	−1.10863	−0.554317	−	0.832306i	$-0.687020\pi$
$487$	−11914.7	−1.10863	−0.554317	+	0.832306i	$0.687020\pi$
$488$	−3561.97	−0.330416
$489$	7713.45	0.713321
$490$	−788.464	−0.0726922
$491$	17879.2	1.64334	0.821668	−	0.569966i	$-0.193044\pi$
$491$	17879.2	1.64334	0.821668	+	0.569966i	$0.193044\pi$
$492$	3383.44	0.310035
$493$	3554.24	0.324695
$494$	6008.56	0.547242
$495$	−3826.53	−0.347454
$496$	4855.31	0.439536
$497$	−5970.86	−0.538893
$498$	2546.17	0.229109
$499$	501.758	0.0450136	0.0225068	−	0.999747i	$-0.492835\pi$
$499$	501.758	0.0450136	0.0225068	+	0.999747i	$0.492835\pi$
$500$	−3829.05	−0.342481
$501$	−12461.2	−1.11123
$502$	−8004.57	−0.711676
$503$	−5212.75	−0.462077	−0.231039	−	0.972945i	$-0.574212\pi$
$503$	−5212.75	−0.462077	−0.231039	+	0.972945i	$0.574212\pi$
$504$	−1551.86	−0.137153
$505$	−14190.0	−1.25039
$506$	3208.30	0.281870
$507$	5789.75	0.507163
$508$	−3373.53	−0.294638
$509$	−9951.59	−0.866595	−0.433297	−	0.901251i	$-0.642650\pi$
$509$	−9951.59	−0.866595	−0.433297	+	0.901251i	$0.642650\pi$
$510$	4691.02	0.407298
$511$	5530.30	0.478760
$512$	−10940.2	−0.944323
$513$	−1099.10	−0.0945932
$514$	−7069.00	−0.606615
$515$	−14473.2	−1.23838
$516$	1585.34	0.135253
$517$	−22262.8	−1.89384
$518$	−743.639	−0.0630765
$519$	−10605.8	−0.897001
$520$	−11082.2	−0.934587
$521$	−9777.02	−0.822148	−0.411074	−	0.911602i	$-0.634846\pi$
$521$	−9777.02	−0.822148	−0.411074	+	0.911602i	$0.634846\pi$
$522$	−756.334	−0.0634173
$523$	−4679.94	−0.391280	−0.195640	−	0.980676i	$-0.562678\pi$
$523$	−4679.94	−0.391280	−0.195640	+	0.980676i	$0.562678\pi$
$524$	5497.20	0.458294
$525$	−1595.04	−0.132597
$526$	−14357.4	−1.19014
$527$	13545.9	1.11968
$528$	−6343.82	−0.522877
$529$	529.000	0.0434783
$530$	−6662.40	−0.546031
$531$	−2915.02	−0.238232
$532$	775.289	0.0631824
$533$	26629.1	2.16404
$534$	3432.51	0.278163
$535$	−5339.05	−0.431453
$536$	−3819.93	−0.307828
$537$	7426.10	0.596759
$538$	−2814.48	−0.225541
$539$	2974.80	0.237725
$540$	514.467	0.0409984
$541$	2164.34	0.172001	0.0860003	−	0.996295i	$-0.472591\pi$
$541$	2164.34	0.172001	0.0860003	+	0.996295i	$0.472591\pi$
$542$	13879.2	1.09993
$543$	11282.9	0.891706
$544$	−11372.7	−0.896322
$545$	9143.32	0.718637
$546$	−3099.68	−0.242956
$547$	−3690.06	−0.288438	−0.144219	−	0.989546i	$-0.546067\pi$
$547$	−3690.06	−0.288438	−0.144219	+	0.989546i	$0.546067\pi$
$548$	7225.11	0.563214
$549$	1301.43	0.101173
$550$	−10594.9	−0.821400
$551$	1488.88	0.115115
$552$	−1699.65	−0.131054
$553$	−4592.04	−0.353116
$554$	−1109.59	−0.0850941
$555$	971.406	0.0742953
$556$	−1506.58	−0.114916
$557$	2516.49	0.191431	0.0957157	−	0.995409i	$-0.469486\pi$
$557$	2516.49	0.191431	0.0957157	+	0.995409i	$0.469486\pi$
$558$	−2882.55	−0.218688
$559$	12477.3	0.944069
$560$	1707.52	0.128850
$561$	−17698.8	−1.33198
$562$	13719.2	1.02973
$563$	−4543.79	−0.340138	−0.170069	−	0.985432i	$-0.554399\pi$
$563$	−4543.79	−0.340138	−0.170069	+	0.985432i	$0.554399\pi$
$564$	2993.17	0.223467
$565$	−10964.2	−0.816401
$566$	2692.29	0.199939
$567$	567.000	0.0419961
$568$	21011.2	1.55213
$569$	7350.75	0.541581	0.270790	−	0.962638i	$-0.412715\pi$
$569$	7350.75	0.541581	0.270790	+	0.962638i	$0.412715\pi$
$570$	1965.08	0.144400
$571$	11998.5	0.879370	0.439685	−	0.898152i	$-0.355090\pi$
$571$	11998.5	0.879370	0.439685	+	0.898152i	$0.355090\pi$
$572$	10611.3	0.775664
$573$	−6492.43	−0.473343
$574$	−6666.95	−0.484796
$575$	−1746.95	−0.126700
$576$	4927.92	0.356476
$577$	20754.3	1.49743	0.748713	−	0.662894i	$-0.230672\pi$
$577$	20754.3	1.49743	0.748713	+	0.662894i	$0.230672\pi$
$578$	10408.9	0.749054
$579$	3809.13	0.273406
$580$	−696.915	−0.0498928
$581$	2585.70	0.184635
$582$	−11912.2	−0.848416
$583$	25136.6	1.78568
$584$	−19460.9	−1.37893
$585$	4049.08	0.286169
$586$	973.599	0.0686331
$587$	15217.9	1.07003	0.535017	−	0.844841i	$-0.320305\pi$
$587$	15217.9	1.07003	0.535017	+	0.844841i	$0.320305\pi$
$588$	−399.954	−0.0280507
$589$	5674.42	0.396961
$590$	5211.77	0.363670
$591$	−11644.5	−0.810477
$592$	1610.45	0.111806
$593$	−12474.1	−0.863827	−0.431914	−	0.901915i	$-0.642161\pi$
$593$	−12474.1	−0.863827	−0.431914	+	0.901915i	$0.642161\pi$
$594$	3766.26	0.260154
$595$	4763.86	0.328234
$596$	−4028.57	−0.276873
$597$	−774.541	−0.0530986
$598$	−3394.89	−0.232153
$599$	−709.905	−0.0484239	−0.0242120	−	0.999707i	$-0.507708\pi$
$599$	−709.905	−0.0484239	−0.0242120	+	0.999707i	$0.507708\pi$
$600$	5612.86	0.381907
$601$	14436.6	0.979835	0.489918	−	0.871769i	$-0.337027\pi$
$601$	14436.6	0.979835	0.489918	+	0.871769i	$0.337027\pi$
$602$	−3123.86	−0.211493
$603$	1395.68	0.0942564
$604$	7954.48	0.535866
$605$	−16490.8	−1.10818
$606$	13966.5	0.936219
$607$	6447.47	0.431128	0.215564	−	0.976490i	$-0.430841\pi$
$607$	6447.47	0.431128	0.215564	+	0.976490i	$0.430841\pi$
$608$	−4764.03	−0.317774
$609$	−768.078	−0.0511069
$610$	−2326.83	−0.154444
$611$	23557.6	1.55980
$612$	2379.56	0.157170
$613$	−20852.1	−1.37391	−0.686955	−	0.726700i	$-0.741053\pi$
$613$	−20852.1	−1.37391	−0.686955	+	0.726700i	$0.741053\pi$
$614$	3331.90	0.218998
$615$	8708.96	0.571023
$616$	−10468.2	−0.684700
$617$	24712.5	1.61246	0.806231	−	0.591601i	$-0.201504\pi$
$617$	24712.5	1.61246	0.806231	+	0.591601i	$0.201504\pi$
$618$	14245.2	0.927228
$619$	−8533.91	−0.554130	−0.277065	−	0.960851i	$-0.589362\pi$
$619$	−8533.91	−0.554130	−0.277065	+	0.960851i	$0.589362\pi$
$620$	−2656.09	−0.172050
$621$	621.000	0.0401286
$622$	−14889.6	−0.959834
$623$	3485.81	0.224167
$624$	6712.77	0.430651
$625$	−361.672	−0.0231470
$626$	−9326.53	−0.595469
$627$	−7414.05	−0.472230
$628$	−2222.31	−0.141210
$629$	4493.03	0.284815
$630$	−1013.74	−0.0641085
$631$	4401.53	0.277689	0.138845	−	0.990314i	$-0.455661\pi$
$631$	4401.53	0.277689	0.138845	+	0.990314i	$0.455661\pi$
$632$	16159.2	1.01705
$633$	11500.7	0.722138
$634$	−18761.2	−1.17524
$635$	−8683.46	−0.542665
$636$	−3379.56	−0.210705
$637$	−3147.81	−0.195794
$638$	−5101.91	−0.316594
$639$	−7676.82	−0.475259
$640$	−2253.82	−0.139203
$641$	−2302.29	−0.141864	−0.0709322	−	0.997481i	$-0.522597\pi$
$641$	−2302.29	−0.141864	−0.0709322	+	0.997481i	$0.522597\pi$
$642$	5254.96	0.323048
$643$	−28118.6	−1.72455	−0.862277	−	0.506438i	$-0.830962\pi$
$643$	−28118.6	−1.72455	−0.862277	+	0.506438i	$0.830962\pi$
$644$	−438.045	−0.0268034
$645$	4080.66	0.249110
$646$	9089.03	0.553565
$647$	−22429.8	−1.36291	−0.681457	−	0.731858i	$-0.738653\pi$
$647$	−22429.8	−1.36291	−0.681457	+	0.731858i	$0.738653\pi$
$648$	−1995.25	−0.120958
$649$	−19663.5	−1.18931
$650$	11211.1	0.676519
$651$	−2927.31	−0.176237
$652$	−6995.53	−0.420193
$653$	−7198.81	−0.431411	−0.215705	−	0.976458i	$-0.569205\pi$
$653$	−7198.81	−0.431411	−0.215705	+	0.976458i	$0.569205\pi$
$654$	−8999.32	−0.538075
$655$	14149.8	0.844087
$656$	14438.2	0.859322
$657$	7110.39	0.422226
$658$	−5897.94	−0.349431
$659$	−5884.71	−0.347854	−0.173927	−	0.984759i	$-0.555646\pi$
$659$	−5884.71	−0.347854	−0.173927	+	0.984759i	$0.555646\pi$
$660$	3470.38	0.204673
$661$	−14830.2	−0.872662	−0.436331	−	0.899786i	$-0.643722\pi$
$661$	−14830.2	−0.872662	−0.436331	+	0.899786i	$0.643722\pi$
$662$	6811.82	0.399923
$663$	18728.1	1.09704
$664$	−9098.96	−0.531789
$665$	1995.59	0.116369
$666$	−956.107	−0.0556282
$667$	−841.229	−0.0488343
$668$	11301.4	0.654589
$669$	10346.6	0.597941
$670$	−2495.34	−0.143886
$671$	8778.93	0.505077
$672$	2457.66	0.141081
$673$	2039.80	0.116833	0.0584164	−	0.998292i	$-0.481395\pi$
$673$	2039.80	0.116833	0.0584164	+	0.998292i	$0.481395\pi$
$674$	26612.3	1.52087
$675$	−2050.76	−0.116939
$676$	−5250.88	−0.298753
$677$	−5051.89	−0.286795	−0.143397	−	0.989665i	$-0.545803\pi$
$677$	−5051.89	−0.286795	−0.143397	+	0.989665i	$0.545803\pi$
$678$	10791.5	0.611276
$679$	−12097.2	−0.683723
$680$	−16763.8	−0.945385
$681$	−9159.86	−0.515428
$682$	−19444.5	−1.09174
$683$	−2796.72	−0.156681	−0.0783407	−	0.996927i	$-0.524962\pi$
$683$	−2796.72	−0.156681	−0.0783407	+	0.996927i	$0.524962\pi$
$684$	996.800	0.0557216
$685$	18597.4	1.03733
$686$	788.096	0.0438625
$687$	−14130.3	−0.784723
$688$	6765.13	0.374881
$689$	−26598.6	−1.47072
$690$	−1110.29	−0.0612578
$691$	21378.7	1.17697	0.588483	−	0.808510i	$-0.299725\pi$
$691$	21378.7	1.17697	0.588483	+	0.808510i	$0.299725\pi$
$692$	9618.69	0.528392
$693$	3824.74	0.209654
$694$	10196.3	0.557702
$695$	−3877.93	−0.211652
$696$	2702.83	0.147199
$697$	40281.4	2.18905
$698$	1937.07	0.105042
$699$	8007.65	0.433300
$700$	1446.58	0.0781081
$701$	13713.9	0.738896	0.369448	−	0.929251i	$-0.379547\pi$
$701$	13713.9	0.738896	0.369448	+	0.929251i	$0.379547\pi$
$702$	−3985.31	−0.214267
$703$	1882.14	0.100976
$704$	33241.7	1.77961
$705$	7704.41	0.411581
$706$	−17697.0	−0.943394
$707$	14183.3	0.754483
$708$	2643.71	0.140334
$709$	−8107.18	−0.429438	−0.214719	−	0.976676i	$-0.568884\pi$
$709$	−8107.18	−0.429438	−0.214719	+	0.976676i	$0.568884\pi$
$710$	13725.4	0.725499
$711$	−5904.05	−0.311419
$712$	−12266.4	−0.645650
$713$	−3206.10	−0.168400
$714$	−4688.83	−0.245763
$715$	27313.4	1.42862
$716$	−6734.92	−0.351530
$717$	20463.8	1.06588
$718$	−25306.9	−1.31538
$719$	−14304.1	−0.741935	−0.370967	−	0.928646i	$-0.620974\pi$
$719$	−14304.1	−0.741935	−0.370967	+	0.928646i	$0.620974\pi$
$720$	2195.39	0.113635
$721$	14466.4	0.747237
$722$	−11952.2	−0.616088
$723$	4079.93	0.209868
$724$	−10232.8	−0.525274
$725$	2778.04	0.142309
$726$	16231.1	0.829741
$727$	−3315.08	−0.169119	−0.0845595	−	0.996418i	$-0.526948\pi$
$727$	−3315.08	−0.169119	−0.0845595	+	0.996418i	$0.526948\pi$
$728$	11077.0	0.563930
$729$	729.000	0.0370370
$730$	−12712.7	−0.644544
$731$	18874.2	0.954976
$732$	−1180.30	−0.0595974
$733$	28858.2	1.45416	0.727081	−	0.686552i	$-0.240876\pi$
$733$	28858.2	1.45416	0.727081	+	0.686552i	$0.240876\pi$
$734$	−20578.5	−1.03483
$735$	−1029.48	−0.0516639
$736$	2691.72	0.134807
$737$	9414.69	0.470549
$738$	−8571.79	−0.427550
$739$	18305.2	0.911186	0.455593	−	0.890188i	$-0.349427\pi$
$739$	18305.2	0.911186	0.455593	+	0.890188i	$0.349427\pi$
$740$	−880.994	−0.0437648
$741$	7845.24	0.388937
$742$	6659.29	0.329475
$743$	−14181.5	−0.700228	−0.350114	−	0.936707i	$-0.613857\pi$
$743$	−14181.5	−0.700228	−0.350114	+	0.936707i	$0.613857\pi$
$744$	10301.0	0.507600
$745$	−10369.5	−0.509945
$746$	−4861.87	−0.238614
$747$	3324.47	0.162833
$748$	16051.5	0.784626
$749$	5336.56	0.260339
$750$	9700.72	0.472294
$751$	31483.8	1.52977	0.764887	−	0.644164i	$-0.222795\pi$
$751$	31483.8	1.52977	0.764887	+	0.644164i	$0.222795\pi$
$752$	12772.8	0.619382
$753$	−10451.4	−0.505804
$754$	5398.64	0.260752
$755$	20474.8	0.986959
$756$	−514.227	−0.0247384
$757$	298.278	0.0143211	0.00716056	−	0.999974i	$-0.497721\pi$
$757$	298.278	0.0143211	0.00716056	+	0.999974i	$0.497721\pi$
$758$	−14325.4	−0.686441
$759$	4189.01	0.200331
$760$	−7022.38	−0.335169
$761$	31543.3	1.50255	0.751276	−	0.659988i	$-0.229439\pi$
$761$	31543.3	1.50255	0.751276	+	0.659988i	$0.229439\pi$
$762$	8546.69	0.406318
$763$	−9139.06	−0.433625
$764$	5888.16	0.278830
$765$	6124.96	0.289475
$766$	442.611	0.0208775
$767$	20807.1	0.979534
$768$	−10922.8	−0.513207
$769$	23876.3	1.11964	0.559819	−	0.828615i	$-0.310871\pi$
$769$	23876.3	1.11964	0.559819	+	0.828615i	$0.310871\pi$
$770$	−6838.26	−0.320044
$771$	−9229.84	−0.431134
$772$	−3454.60	−0.161054
$773$	10792.4	0.502170	0.251085	−	0.967965i	$-0.419213\pi$
$773$	10792.4	0.502170	0.251085	+	0.967965i	$0.419213\pi$
$774$	−4016.39	−0.186520
$775$	10587.7	0.490737
$776$	42569.5	1.96927
$777$	−970.953	−0.0448298
$778$	−2149.12	−0.0990354
$779$	16873.9	0.776087
$780$	−3672.21	−0.168572
$781$	−51784.6	−2.37260
$782$	−5135.39	−0.234835
$783$	−987.529	−0.0450721
$784$	−1706.73	−0.0777481
$785$	−5720.21	−0.260080
$786$	−13926.9	−0.632005
$787$	41071.9	1.86030	0.930150	−	0.367180i	$-0.119677\pi$
$787$	41071.9	1.86030	0.930150	+	0.367180i	$0.119677\pi$
$788$	10560.7	0.477424
$789$	−18746.1	−0.845856
$790$	10555.9	0.475393
$791$	10959.1	0.492616
$792$	−13459.1	−0.603848
$793$	−9289.50	−0.415990
$794$	12154.8	0.543271
$795$	−8698.96	−0.388076
$796$	702.451	0.0312786
$797$	−34785.1	−1.54599	−0.772994	−	0.634413i	$-0.781242\pi$
$797$	−34785.1	−1.54599	−0.772994	+	0.634413i	$0.781242\pi$
$798$	−1964.16	−0.0871309
$799$	35635.1	1.57782
$800$	−8889.02	−0.392843
$801$	4481.76	0.197697
$802$	−5530.05	−0.243482
$803$	47963.7	2.10785
$804$	−1265.78	−0.0555232
$805$	−1127.53	−0.0493665
$806$	20575.3	0.899175
$807$	−3674.81	−0.160297
$808$	−49910.5	−2.17307
$809$	−5486.63	−0.238442	−0.119221	−	0.992868i	$-0.538040\pi$
$809$	−5486.63	−0.238442	−0.119221	+	0.992868i	$0.538040\pi$
$810$	−1303.38	−0.0565384
$811$	8416.45	0.364416	0.182208	−	0.983260i	$-0.441676\pi$
$811$	8416.45	0.364416	0.182208	+	0.983260i	$0.441676\pi$
$812$	696.590	0.0301053
$813$	18121.8	0.781745
$814$	−6449.49	−0.277708
$815$	−18006.4	−0.773912
$816$	10154.3	0.435626
$817$	7906.43	0.338569
$818$	13866.7	0.592710
$819$	−4047.19	−0.172674
$820$	−7898.38	−0.336370
$821$	−23087.3	−0.981428	−0.490714	−	0.871321i	$-0.663264\pi$
$821$	−23087.3	−0.981428	−0.490714	+	0.871321i	$0.663264\pi$
$822$	−18304.5	−0.776694
$823$	−32949.4	−1.39556	−0.697780	−	0.716312i	$-0.745829\pi$
$823$	−32949.4	−1.39556	−0.697780	+	0.716312i	$0.745829\pi$
$824$	−50906.6	−2.15221
$825$	−13833.6	−0.583787
$826$	−5209.34	−0.219438
$827$	−772.254	−0.0324715	−0.0162357	−	0.999868i	$-0.505168\pi$
$827$	−772.254	−0.0324715	−0.0162357	+	0.999868i	$0.505168\pi$
$828$	−563.201	−0.0236384
$829$	20879.8	0.874772	0.437386	−	0.899274i	$-0.355904\pi$
$829$	20879.8	0.874772	0.437386	+	0.899274i	$0.355904\pi$
$830$	−5943.83	−0.248570
$831$	−1448.77	−0.0604782
$832$	−35175.0	−1.46571
$833$	−4761.64	−0.198056
$834$	3816.86	0.158474
$835$	29089.8	1.20562
$836$	6723.99	0.278175
$837$	−3763.68	−0.155426
$838$	−1723.83	−0.0710606
$839$	32106.4	1.32114	0.660571	−	0.750764i	$-0.270314\pi$
$839$	32106.4	1.32114	0.660571	+	0.750764i	$0.270314\pi$
$840$	3622.69	0.148803
$841$	−23051.3	−0.945150
$842$	−27119.8	−1.10999
$843$	17912.9	0.731853
$844$	−10430.3	−0.425387
$845$	−13515.7	−0.550243
$846$	−7583.07	−0.308169
$847$	16483.1	0.668674
$848$	−14421.6	−0.584008
$849$	3515.26	0.142101
$850$	16958.9	0.684335
$851$	−1063.42	−0.0428363
$852$	6962.31	0.279959
$853$	−18457.1	−0.740865	−0.370432	−	0.928859i	$-0.620791\pi$
$853$	−18457.1	−0.740865	−0.370432	+	0.928859i	$0.620791\pi$
$854$	2325.75	0.0931914
$855$	2565.76	0.102628
$856$	−18779.1	−0.749832
$857$	−11394.0	−0.454154	−0.227077	−	0.973877i	$-0.572917\pi$
$857$	−11394.0	−0.454154	−0.227077	+	0.973877i	$0.572917\pi$
$858$	−26883.2	−1.06967
$859$	−19305.3	−0.766808	−0.383404	−	0.923581i	$-0.625248\pi$
$859$	−19305.3	−0.766808	−0.383404	+	0.923581i	$0.625248\pi$
$860$	−3700.86	−0.146742
$861$	−8704.89	−0.344555
$862$	−26498.3	−1.04703
$863$	37067.9	1.46212	0.731059	−	0.682315i	$-0.239027\pi$
$863$	37067.9	1.46212	0.731059	+	0.682315i	$0.239027\pi$
$864$	3159.84	0.124421
$865$	24758.4	0.973194
$866$	4149.39	0.162820
$867$	13590.7	0.532369
$868$	2654.85	0.103815
$869$	−39826.3	−1.55468
$870$	1765.60	0.0688041
$871$	−9962.24	−0.387552
$872$	32159.9	1.24894
$873$	−15553.5	−0.602987
$874$	−2151.22	−0.0832564
$875$	9851.35	0.380613
$876$	−6448.60	−0.248719
$877$	−14060.1	−0.541364	−0.270682	−	0.962669i	$-0.587249\pi$
$877$	−14060.1	−0.541364	−0.270682	+	0.962669i	$0.587249\pi$
$878$	8651.71	0.332553
$879$	1271.21	0.0487790
$880$	14809.2	0.567291
$881$	31541.5	1.20620	0.603098	−	0.797667i	$-0.293933\pi$
$881$	31541.5	1.20620	0.603098	+	0.797667i	$0.293933\pi$
$882$	1013.27	0.0386830
$883$	−9697.52	−0.369590	−0.184795	−	0.982777i	$-0.559162\pi$
$883$	−9697.52	−0.369590	−0.184795	+	0.982777i	$0.559162\pi$
$884$	−16985.0	−0.646231
$885$	6804.90	0.258468
$886$	−16894.0	−0.640593
$887$	−34036.2	−1.28842	−0.644208	−	0.764851i	$-0.722813\pi$
$887$	−34036.2	−1.28842	−0.644208	+	0.764851i	$0.722813\pi$
$888$	3416.74	0.129120
$889$	8679.40	0.327444
$890$	−8012.93	−0.301791
$891$	4917.53	0.184897
$892$	−9383.60	−0.352227
$893$	14927.6	0.559387
$894$	10206.2	0.381819
$895$	−17335.6	−0.647449
$896$	2252.77	0.0839951
$897$	−4432.63	−0.164996
$898$	31534.1	1.17183
$899$	5098.42	0.189145
$900$	1859.89	0.0688849
$901$	−40235.1	−1.48771
$902$	−57821.7	−2.13443
$903$	−4078.76	−0.150313
$904$	−38564.4	−1.41884
$905$	−26339.1	−0.967449
$906$	−20152.3	−0.738980
$907$	−41495.9	−1.51913	−0.759564	−	0.650432i	$-0.774588\pi$
$907$	−41495.9	−1.51913	−0.759564	+	0.650432i	$0.774588\pi$
$908$	8307.31	0.303621
$909$	18235.7	0.665391
$910$	7235.97	0.263593
$911$	41970.5	1.52640	0.763198	−	0.646165i	$-0.223628\pi$
$911$	41970.5	1.52640	0.763198	+	0.646165i	$0.223628\pi$
$912$	4253.64	0.154443
$913$	22425.5	0.812898
$914$	−21092.0	−0.763307
$915$	−3038.10	−0.109767
$916$	12815.1	0.462253
$917$	−14143.2	−0.509322
$918$	−6028.50	−0.216743
$919$	21174.7	0.760053	0.380026	−	0.924976i	$-0.375915\pi$
$919$	21174.7	0.760053	0.380026	+	0.924976i	$0.375915\pi$
$920$	3967.71	0.142186
$921$	4350.39	0.155646
$922$	2767.54	0.0988547
$923$	54796.4	1.95411
$924$	−3468.76	−0.123500
$925$	3511.81	0.124830
$926$	−24934.8	−0.884889
$927$	18599.7	0.659001
$928$	−4280.44	−0.151414
$929$	−5893.24	−0.208128	−0.104064	−	0.994571i	$-0.533185\pi$
$929$	−5893.24	−0.208128	−0.104064	+	0.994571i	$0.533185\pi$
$930$	6729.08	0.237264
$931$	−1994.66	−0.0702172
$932$	−7262.34	−0.255242
$933$	−19441.0	−0.682175
$934$	−11240.9	−0.393806
$935$	41316.4	1.44512
$936$	14241.9	0.497339
$937$	−7266.96	−0.253363	−0.126682	−	0.991943i	$-0.540433\pi$
$937$	−7266.96	−0.253363	−0.126682	+	0.991943i	$0.540433\pi$
$938$	2494.18	0.0868206
$939$	−12177.5	−0.423212
$940$	−6987.33	−0.242448
$941$	32852.3	1.13810	0.569052	−	0.822302i	$-0.307310\pi$
$941$	32852.3	1.13810	0.569052	+	0.822302i	$0.307310\pi$
$942$	5630.11	0.194734
$943$	−9533.93	−0.329234
$944$	11281.5	0.388964
$945$	−1323.62	−0.0455633
$946$	−27092.9	−0.931148
$947$	−36264.6	−1.24439	−0.622197	−	0.782861i	$-0.713760\pi$
$947$	−36264.6	−1.24439	−0.622197	+	0.782861i	$0.713760\pi$
$948$	5354.54	0.183447
$949$	−50753.2	−1.73606
$950$	7104.10	0.242618
$951$	−24496.0	−0.835267
$952$	16756.0	0.570445
$953$	−36071.9	−1.22611	−0.613056	−	0.790040i	$-0.710060\pi$
$953$	−36071.9	−1.22611	−0.613056	+	0.790040i	$0.710060\pi$
$954$	8561.95	0.290570
$955$	15156.1	0.513549
$956$	−18559.2	−0.627873
$957$	−6661.46	−0.225010
$958$	−15211.2	−0.512999
$959$	−18588.7	−0.625924
$960$	−11503.8	−0.386755
$961$	−10359.9	−0.347752
$962$	6824.59	0.228725
$963$	6861.30	0.229597
$964$	−3700.20	−0.123626
$965$	−8892.11	−0.296629
$966$	1109.77	0.0369629
$967$	37598.1	1.25033	0.625167	−	0.780491i	$-0.285031\pi$
$967$	37598.1	1.25033	0.625167	+	0.780491i	$0.285031\pi$
$968$	−58003.3	−1.92593
$969$	11867.3	0.393431
$970$	27808.2	0.920481
$971$	−41734.5	−1.37932	−0.689662	−	0.724131i	$-0.742241\pi$
$971$	−41734.5	−1.37932	−0.689662	+	0.724131i	$0.742241\pi$
$972$	−661.149	−0.0218172
$973$	3876.13	0.127711
$974$	−27375.8	−0.900592
$975$	14638.1	0.480816
$976$	−5036.71	−0.165186
$977$	−18255.1	−0.597782	−0.298891	−	0.954287i	$-0.596617\pi$
$977$	−18255.1	−0.597782	−0.298891	+	0.954287i	$0.596617\pi$
$978$	17722.8	0.579462
$979$	30232.0	0.986946
$980$	933.662	0.0304334
$981$	−11750.2	−0.382422
$982$	41080.3	1.33495
$983$	38495.5	1.24905	0.624525	−	0.781004i	$-0.285292\pi$
$983$	38495.5	1.24905	0.624525	+	0.781004i	$0.285292\pi$
$984$	30632.1	0.992394
$985$	27183.3	0.879320
$986$	8166.42	0.263764
$987$	−7700.81	−0.248348
$988$	−7115.05	−0.229109
$989$	−4467.21	−0.143629
$990$	−8792.05	−0.282252
$991$	23163.4	0.742494	0.371247	−	0.928534i	$-0.378930\pi$
$991$	23163.4	0.742494	0.371247	+	0.928534i	$0.378930\pi$
$992$	−16313.6	−0.522136
$993$	8894.04	0.284234
$994$	−13719.0	−0.437766
$995$	1808.11	0.0576089
$996$	−3015.05	−0.0959193
$997$	−34698.5	−1.10222	−0.551110	−	0.834433i	$-0.685795\pi$
$997$	−34698.5	−1.10222	−0.551110	+	0.834433i	$0.685795\pi$
$998$	1152.87	0.0365665
$999$	−1248.37	−0.0395362

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.4.a.c.1.6	✓	7
3.2	odd	2		1449.4.a.h.1.2		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.4.a.c.1.6	✓	7	1.1	even	1	trivial
1449.4.a.h.1.2		7	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)

\(f(q)\)	\(=\)	\(q+2.29766 q^{2} +3.00000 q^{3} -2.72078 q^{4} -7.00327 q^{5} +6.89297 q^{6} +7.00000 q^{7} -24.6327 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+2.29766 q^{2} +3.00000 q^{3} -2.72078 q^{4} -7.00327 q^{5} +6.89297 q^{6} +7.00000 q^{7} -24.6327 q^{8} +9.00000 q^{9} -16.0911 q^{10} +60.7102 q^{11} -8.16233 q^{12} -64.2411 q^{13} +16.0836 q^{14} -21.0098 q^{15} -34.8311 q^{16} -97.1763 q^{17} +20.6789 q^{18} -40.7073 q^{19} +19.0543 q^{20} +21.0000 q^{21} +139.491 q^{22} +23.0000 q^{23} -73.8980 q^{24} -75.9542 q^{25} -147.604 q^{26} +27.0000 q^{27} -19.0454 q^{28} -36.5752 q^{29} -48.2733 q^{30} -139.396 q^{31} +117.031 q^{32} +182.131 q^{33} -223.278 q^{34} -49.0229 q^{35} -24.4870 q^{36} -46.2359 q^{37} -93.5313 q^{38} -192.723 q^{39} +172.509 q^{40} -414.519 q^{41} +48.2508 q^{42} -194.226 q^{43} -165.179 q^{44} -63.0294 q^{45} +52.8461 q^{46} -366.705 q^{47} -104.493 q^{48} +49.0000 q^{49} -174.517 q^{50} -291.529 q^{51} +174.786 q^{52} +414.043 q^{53} +62.0367 q^{54} -425.170 q^{55} -172.429 q^{56} -122.122 q^{57} -84.0371 q^{58} -323.891 q^{59} +57.1630 q^{60} +144.604 q^{61} -320.283 q^{62} +63.0000 q^{63} +547.547 q^{64} +449.898 q^{65} +418.474 q^{66} +155.076 q^{67} +264.395 q^{68} +69.0000 q^{69} -112.638 q^{70} -852.980 q^{71} -221.694 q^{72} +790.043 q^{73} -106.234 q^{74} -227.863 q^{75} +110.756 q^{76} +424.972 q^{77} -442.812 q^{78} -656.006 q^{79} +243.932 q^{80} +81.0000 q^{81} -952.421 q^{82} +369.386 q^{83} -57.1363 q^{84} +680.551 q^{85} -446.266 q^{86} -109.725 q^{87} -1495.45 q^{88} +497.973 q^{89} -144.820 q^{90} -449.688 q^{91} -62.5779 q^{92} -418.187 q^{93} -842.563 q^{94} +285.084 q^{95} +351.094 q^{96} -1728.17 q^{97} +112.585 q^{98} +546.392 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 6 q^{2} + 21 q^{3} + 18 q^{4} - 41 q^{5} - 18 q^{6} + 49 q^{7} - 33 q^{8} + 63 q^{9}+O(q^{10}) \) 7 * q - 6 * q^2 + 21 * q^3 + 18 * q^4 - 41 * q^5 - 18 * q^6 + 49 * q^7 - 33 * q^8 + 63 * q^9	\( 7 q - 6 q^{2} + 21 q^{3} + 18 q^{4} - 41 q^{5} - 18 q^{6} + 49 q^{7} - 33 q^{8} + 63 q^{9} + q^{10} - 126 q^{11} + 54 q^{12} - 87 q^{13} - 42 q^{14} - 123 q^{15} + 2 q^{16} - 204 q^{17} - 54 q^{18} - 286 q^{19} - 418 q^{20} + 147 q^{21} + 329 q^{22} + 161 q^{23} - 99 q^{24} + 440 q^{25} - 360 q^{26} + 189 q^{27} + 126 q^{28} - 329 q^{29} + 3 q^{30} + 296 q^{31} - 270 q^{32} - 378 q^{33} - 919 q^{34} - 287 q^{35} + 162 q^{36} - 691 q^{37} - 367 q^{38} - 261 q^{39} + 138 q^{40} - 343 q^{41} - 126 q^{42} - 171 q^{43} - 1279 q^{44} - 369 q^{45} - 138 q^{46} - 1403 q^{47} + 6 q^{48} + 343 q^{49} + 230 q^{50} - 612 q^{51} + 2157 q^{52} - 1024 q^{53} - 162 q^{54} - 158 q^{55} - 231 q^{56} - 858 q^{57} + 2608 q^{58} - 1388 q^{59} - 1254 q^{60} - 52 q^{61} - 309 q^{62} + 441 q^{63} - 187 q^{64} - 1067 q^{65} + 987 q^{66} - 1148 q^{67} + 1293 q^{68} + 483 q^{69} + 7 q^{70} - 1590 q^{71} - 297 q^{72} - 802 q^{73} - 878 q^{74} + 1320 q^{75} - 2505 q^{76} - 882 q^{77} - 1080 q^{78} + 618 q^{79} + 195 q^{80} + 567 q^{81} - 1040 q^{82} - 1818 q^{83} + 378 q^{84} - 1526 q^{85} + 1188 q^{86} - 987 q^{87} + 1664 q^{88} - 354 q^{89} + 9 q^{90} - 609 q^{91} + 414 q^{92} + 888 q^{93} + 663 q^{94} + 78 q^{95} - 810 q^{96} - 1575 q^{97} - 294 q^{98} - 1134 q^{99}+O(q^{100}) \) 7 * q - 6 * q^2 + 21 * q^3 + 18 * q^4 - 41 * q^5 - 18 * q^6 + 49 * q^7 - 33 * q^8 + 63 * q^9 + q^10 - 126 * q^11 + 54 * q^12 - 87 * q^13 - 42 * q^14 - 123 * q^15 + 2 * q^16 - 204 * q^17 - 54 * q^18 - 286 * q^19 - 418 * q^20 + 147 * q^21 + 329 * q^22 + 161 * q^23 - 99 * q^24 + 440 * q^25 - 360 * q^26 + 189 * q^27 + 126 * q^28 - 329 * q^29 + 3 * q^30 + 296 * q^31 - 270 * q^32 - 378 * q^33 - 919 * q^34 - 287 * q^35 + 162 * q^36 - 691 * q^37 - 367 * q^38 - 261 * q^39 + 138 * q^40 - 343 * q^41 - 126 * q^42 - 171 * q^43 - 1279 * q^44 - 369 * q^45 - 138 * q^46 - 1403 * q^47 + 6 * q^48 + 343 * q^49 + 230 * q^50 - 612 * q^51 + 2157 * q^52 - 1024 * q^53 - 162 * q^54 - 158 * q^55 - 231 * q^56 - 858 * q^57 + 2608 * q^58 - 1388 * q^59 - 1254 * q^60 - 52 * q^61 - 309 * q^62 + 441 * q^63 - 187 * q^64 - 1067 * q^65 + 987 * q^66 - 1148 * q^67 + 1293 * q^68 + 483 * q^69 + 7 * q^70 - 1590 * q^71 - 297 * q^72 - 802 * q^73 - 878 * q^74 + 1320 * q^75 - 2505 * q^76 - 882 * q^77 - 1080 * q^78 + 618 * q^79 + 195 * q^80 + 567 * q^81 - 1040 * q^82 - 1818 * q^83 + 378 * q^84 - 1526 * q^85 + 1188 * q^86 - 987 * q^87 + 1664 * q^88 - 354 * q^89 + 9 * q^90 - 609 * q^91 + 414 * q^92 + 888 * q^93 + 663 * q^94 + 78 * q^95 - 810 * q^96 - 1575 * q^97 - 294 * q^98 - 1134 * q^99

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