LMFDB - Embedded newform 483.4.a.f.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:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 57x^{7} - 13x^{6} + 1042x^{5} + 331x^{4} - 6570x^{3} - 1782x^{2} + 9424x + 5112 $ x^9 - 57x^7 - 13x^6 + 1042x^5 + 331x^4 - 6570x^3 - 1782x^2 + 9424*x + 5112
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			$-1.05204$ 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)

$f(q)$	$=$	$q+1.05204 q^{2} -3.00000 q^{3} -6.89321 q^{4} -11.5074 q^{5} -3.15612 q^{6} +7.00000 q^{7} -15.6682 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+1.05204 q^{2} -3.00000 q^{3} -6.89321 q^{4} -11.5074 q^{5} -3.15612 q^{6} +7.00000 q^{7} -15.6682 q^{8} +9.00000 q^{9} -12.1063 q^{10} -58.4398 q^{11} +20.6796 q^{12} -37.9629 q^{13} +7.36428 q^{14} +34.5223 q^{15} +38.6621 q^{16} -131.447 q^{17} +9.46835 q^{18} +60.3971 q^{19} +79.3232 q^{20} -21.0000 q^{21} -61.4809 q^{22} +23.0000 q^{23} +47.0047 q^{24} +7.42099 q^{25} -39.9384 q^{26} -27.0000 q^{27} -48.2525 q^{28} -124.917 q^{29} +36.3188 q^{30} +294.792 q^{31} +166.020 q^{32} +175.319 q^{33} -138.287 q^{34} -80.5520 q^{35} -62.0389 q^{36} -43.6444 q^{37} +63.5401 q^{38} +113.889 q^{39} +180.301 q^{40} -174.663 q^{41} -22.0928 q^{42} -56.1216 q^{43} +402.838 q^{44} -103.567 q^{45} +24.1969 q^{46} +256.458 q^{47} -115.986 q^{48} +49.0000 q^{49} +7.80717 q^{50} +394.341 q^{51} +261.686 q^{52} +525.286 q^{53} -28.4051 q^{54} +672.492 q^{55} -109.678 q^{56} -181.191 q^{57} -131.417 q^{58} +35.2060 q^{59} -237.970 q^{60} +456.577 q^{61} +310.133 q^{62} +63.0000 q^{63} -134.637 q^{64} +436.855 q^{65} +184.443 q^{66} +610.737 q^{67} +906.091 q^{68} -69.0000 q^{69} -84.7439 q^{70} -397.663 q^{71} -141.014 q^{72} -450.519 q^{73} -45.9156 q^{74} -22.2630 q^{75} -416.330 q^{76} -409.078 q^{77} +119.815 q^{78} -891.829 q^{79} -444.901 q^{80} +81.0000 q^{81} -183.753 q^{82} +1306.14 q^{83} +144.757 q^{84} +1512.62 q^{85} -59.0421 q^{86} +374.750 q^{87} +915.649 q^{88} -125.040 q^{89} -108.956 q^{90} -265.740 q^{91} -158.544 q^{92} -884.375 q^{93} +269.804 q^{94} -695.015 q^{95} -498.060 q^{96} -179.753 q^{97} +51.5499 q^{98} -525.958 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 27 q^{3} + 42 q^{4} + 29 q^{5} + 63 q^{7} - 39 q^{8} + 81 q^{9}+O(q^{10}) $ 9 * q - 27 * q^3 + 42 * q^4 + 29 * q^5 + 63 * q^7 - 39 * q^8 + 81 * q^9	\( 9 q - 27 q^{3} + 42 q^{4} + 29 q^{5} + 63 q^{7} - 39 q^{8} + 81 q^{9} - 55 q^{10} + 12 q^{11} - 126 q^{12} + 199 q^{13} - 87 q^{15} + 170 q^{16} + 116 q^{17} + 260 q^{19} + 324 q^{20} - 189 q^{21} - 265 q^{22} + 207 q^{23} + 117 q^{24} + 438 q^{25} - 270 q^{26} - 243 q^{27} + 294 q^{28} - 107 q^{29} + 165 q^{30} + 440 q^{31} - 802 q^{32} - 36 q^{33} + 295 q^{34} + 203 q^{35} + 378 q^{36} + 563 q^{37} - 569 q^{38} - 597 q^{39} - 640 q^{40} + 243 q^{41} + 435 q^{43} + 1025 q^{44} + 261 q^{45} - 133 q^{47} - 510 q^{48} + 441 q^{49} + 104 q^{50} - 348 q^{51} + 2693 q^{52} + 958 q^{53} + 1846 q^{55} - 273 q^{56} - 780 q^{57} + 2796 q^{58} + 538 q^{59} - 972 q^{60} + 1374 q^{61} + 1263 q^{62} + 567 q^{63} - 83 q^{64} + 745 q^{65} + 795 q^{66} + 752 q^{67} + 5593 q^{68} - 621 q^{69} - 385 q^{70} - 418 q^{71} - 351 q^{72} + 2406 q^{73} + 352 q^{74} - 1314 q^{75} + 2765 q^{76} + 84 q^{77} + 810 q^{78} - 486 q^{79} + 5709 q^{80} + 729 q^{81} + 2726 q^{82} + 106 q^{83} - 882 q^{84} + 4130 q^{85} - 2576 q^{86} + 321 q^{87} + 1270 q^{88} + 234 q^{89} - 495 q^{90} + 1393 q^{91} + 966 q^{92} - 1320 q^{93} + 4967 q^{94} - 3074 q^{95} + 2406 q^{96} + 2409 q^{97} + 108 q^{99}+O(q^{100}) \) 9 * q - 27 * q^3 + 42 * q^4 + 29 * q^5 + 63 * q^7 - 39 * q^8 + 81 * q^9 - 55 * q^10 + 12 * q^11 - 126 * q^12 + 199 * q^13 - 87 * q^15 + 170 * q^16 + 116 * q^17 + 260 * q^19 + 324 * q^20 - 189 * q^21 - 265 * q^22 + 207 * q^23 + 117 * q^24 + 438 * q^25 - 270 * q^26 - 243 * q^27 + 294 * q^28 - 107 * q^29 + 165 * q^30 + 440 * q^31 - 802 * q^32 - 36 * q^33 + 295 * q^34 + 203 * q^35 + 378 * q^36 + 563 * q^37 - 569 * q^38 - 597 * q^39 - 640 * q^40 + 243 * q^41 + 435 * q^43 + 1025 * q^44 + 261 * q^45 - 133 * q^47 - 510 * q^48 + 441 * q^49 + 104 * q^50 - 348 * q^51 + 2693 * q^52 + 958 * q^53 + 1846 * q^55 - 273 * q^56 - 780 * q^57 + 2796 * q^58 + 538 * q^59 - 972 * q^60 + 1374 * q^61 + 1263 * q^62 + 567 * q^63 - 83 * q^64 + 745 * q^65 + 795 * q^66 + 752 * q^67 + 5593 * q^68 - 621 * q^69 - 385 * q^70 - 418 * q^71 - 351 * q^72 + 2406 * q^73 + 352 * q^74 - 1314 * q^75 + 2765 * q^76 + 84 * q^77 + 810 * q^78 - 486 * q^79 + 5709 * q^80 + 729 * q^81 + 2726 * q^82 + 106 * q^83 - 882 * q^84 + 4130 * q^85 - 2576 * q^86 + 321 * q^87 + 1270 * q^88 + 234 * q^89 - 495 * q^90 + 1393 * q^91 + 966 * q^92 - 1320 * q^93 + 4967 * q^94 - 3074 * q^95 + 2406 * q^96 + 2409 * q^97 + 108 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.05204	0.371952	0.185976	−	0.982554i	$-0.440455\pi$
$2$	1.05204	0.371952	0.185976	+	0.982554i	$0.440455\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−6.89321	−0.861652
$5$	−11.5074	−1.02926	−0.514628	−	0.857414i	$-0.672070\pi$
$5$	−11.5074	−1.02926	−0.514628	+	0.857414i	$0.672070\pi$
$6$	−3.15612	−0.214747
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−15.6682	−0.692445
$9$	9.00000	0.333333
$10$	−12.1063	−0.382834
$11$	−58.4398	−1.60184	−0.800920	−	0.598771i	$-0.795656\pi$
$11$	−58.4398	−1.60184	−0.800920	+	0.598771i	$0.795656\pi$
$12$	20.6796	0.497475
$13$	−37.9629	−0.809923	−0.404962	−	0.914334i	$-0.632715\pi$
$13$	−37.9629	−0.809923	−0.404962	+	0.914334i	$0.632715\pi$
$14$	7.36428	0.140585
$15$	34.5223	0.594241
$16$	38.6621	0.604095
$17$	−131.447	−1.87533	−0.937663	−	0.347545i	$-0.887015\pi$
$17$	−131.447	−1.87533	−0.937663	+	0.347545i	$0.887015\pi$
$18$	9.46835	0.123984
$19$	60.3971	0.729265	0.364633	−	0.931151i	$-0.381195\pi$
$19$	60.3971	0.729265	0.364633	+	0.931151i	$0.381195\pi$
$20$	79.3232	0.886860
$21$	−21.0000	−0.218218
$22$	−61.4809	−0.595808
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	47.0047	0.399783
$25$	7.42099	0.0593679
$26$	−39.9384	−0.301253
$27$	−27.0000	−0.192450
$28$	−48.2525	−0.325674
$29$	−124.917	−0.799876	−0.399938	−	0.916542i	$-0.630968\pi$
$29$	−124.917	−0.799876	−0.399938	+	0.916542i	$0.630968\pi$
$30$	36.3188	0.221029
$31$	294.792	1.70794	0.853971	−	0.520321i	$-0.174188\pi$
$31$	294.792	1.70794	0.853971	+	0.520321i	$0.174188\pi$
$32$	166.020	0.917140
$33$	175.319	0.924823
$34$	−138.287	−0.697532
$35$	−80.5520	−0.389022
$36$	−62.0389	−0.287217
$37$	−43.6444	−0.193921	−0.0969607	−	0.995288i	$-0.530912\pi$
$37$	−43.6444	−0.193921	−0.0969607	+	0.995288i	$0.530912\pi$
$38$	63.5401	0.271252
$39$	113.889	0.467609
$40$	180.301	0.712703
$41$	−174.663	−0.665313	−0.332656	−	0.943048i	$-0.607945\pi$
$41$	−174.663	−0.665313	−0.332656	+	0.943048i	$0.607945\pi$
$42$	−22.0928	−0.0811666
$43$	−56.1216	−0.199034	−0.0995170	−	0.995036i	$-0.531730\pi$
$43$	−56.1216	−0.199034	−0.0995170	+	0.995036i	$0.531730\pi$
$44$	402.838	1.38023
$45$	−103.567	−0.343085
$46$	24.1969	0.0775574
$47$	256.458	0.795921	0.397961	−	0.917402i	$-0.369718\pi$
$47$	256.458	0.795921	0.397961	+	0.917402i	$0.369718\pi$
$48$	−115.986	−0.348775
$49$	49.0000	0.142857
$50$	7.80717	0.0220820
$51$	394.341	1.08272
$52$	261.686	0.697872
$53$	525.286	1.36139	0.680695	−	0.732567i	$-0.261678\pi$
$53$	525.286	1.36139	0.680695	+	0.732567i	$0.261678\pi$
$54$	−28.4051	−0.0715822
$55$	672.492	1.64870
$56$	−109.678	−0.261720
$57$	−181.191	−0.421041
$58$	−131.417	−0.297516
$59$	35.2060	0.0776852	0.0388426	−	0.999245i	$-0.487633\pi$
$59$	35.2060	0.0776852	0.0388426	+	0.999245i	$0.487633\pi$
$60$	−237.970	−0.512029
$61$	456.577	0.958339	0.479169	−	0.877722i	$-0.340938\pi$
$61$	456.577	0.958339	0.479169	+	0.877722i	$0.340938\pi$
$62$	310.133	0.635272
$63$	63.0000	0.125988
$64$	−134.637	−0.262963
$65$	436.855	0.833619
$66$	184.443	0.343990
$67$	610.737	1.11363	0.556817	−	0.830635i	$-0.312023\pi$
$67$	610.737	1.11363	0.556817	+	0.830635i	$0.312023\pi$
$68$	906.091	1.61588
$69$	−69.0000	−0.120386
$70$	−84.7439	−0.144698
$71$	−397.663	−0.664702	−0.332351	−	0.943156i	$-0.607842\pi$
$71$	−397.663	−0.664702	−0.332351	+	0.943156i	$0.607842\pi$
$72$	−141.014	−0.230815
$73$	−450.519	−0.722318	−0.361159	−	0.932504i	$-0.617619\pi$
$73$	−450.519	−0.722318	−0.361159	+	0.932504i	$0.617619\pi$
$74$	−45.9156	−0.0721295
$75$	−22.2630	−0.0342761
$76$	−416.330	−0.628372
$77$	−409.078	−0.605439
$78$	119.815	0.173928
$79$	−891.829	−1.27011	−0.635054	−	0.772468i	$-0.719022\pi$
$79$	−891.829	−1.27011	−0.635054	+	0.772468i	$0.719022\pi$
$80$	−444.901	−0.621769
$81$	81.0000	0.111111
$82$	−183.753	−0.247464
$83$	1306.14	1.72732	0.863658	−	0.504077i	$-0.168167\pi$
$83$	1306.14	1.72732	0.863658	+	0.504077i	$0.168167\pi$
$84$	144.757	0.188028
$85$	1512.62	1.93019
$86$	−59.0421	−0.0740311
$87$	374.750	0.461809
$88$	915.649	1.10919
$89$	−125.040	−0.148924	−0.0744619	−	0.997224i	$-0.523724\pi$
$89$	−125.040	−0.148924	−0.0744619	+	0.997224i	$0.523724\pi$
$90$	−108.956	−0.127611
$91$	−265.740	−0.306122
$92$	−158.544	−0.179667
$93$	−884.375	−0.986080
$94$	269.804	0.296045
$95$	−695.015	−0.750600
$96$	−498.060	−0.529511
$97$	−179.753	−0.188157	−0.0940783	−	0.995565i	$-0.529990\pi$
$97$	−179.753	−0.188157	−0.0940783	+	0.995565i	$0.529990\pi$
$98$	51.5499	0.0531360
$99$	−525.958	−0.533947
$100$	−51.1545	−0.0511545
$101$	−1897.29	−1.86919	−0.934593	−	0.355718i	$-0.884236\pi$
$101$	−1897.29	−1.86919	−0.934593	+	0.355718i	$0.884236\pi$
$102$	414.862	0.402720
$103$	−1402.83	−1.34199	−0.670993	−	0.741463i	$-0.734132\pi$
$103$	−1402.83	−1.34199	−0.670993	+	0.741463i	$0.734132\pi$
$104$	594.812	0.560828
$105$	241.656	0.224602
$106$	552.622	0.506372
$107$	671.354	0.606563	0.303281	−	0.952901i	$-0.401918\pi$
$107$	671.354	0.606563	0.303281	+	0.952901i	$0.401918\pi$
$108$	186.117	0.165825
$109$	−685.095	−0.602020	−0.301010	−	0.953621i	$-0.597324\pi$
$109$	−685.095	−0.602020	−0.301010	+	0.953621i	$0.597324\pi$
$110$	707.488	0.613239
$111$	130.933	0.111961
$112$	270.635	0.228327
$113$	−742.519	−0.618144	−0.309072	−	0.951039i	$-0.600018\pi$
$113$	−742.519	−0.618144	−0.309072	+	0.951039i	$0.600018\pi$
$114$	−190.620	−0.156607
$115$	−264.671	−0.214615
$116$	861.076	0.689215
$117$	−341.666	−0.269974
$118$	37.0381	0.0288952
$119$	−920.128	−0.708807
$120$	−540.904	−0.411480
$121$	2084.21	1.56589
$122$	480.337	0.356456
$123$	523.990	0.384119
$124$	−2032.06	−1.47165
$125$	1353.03	0.968151
$126$	66.2785	0.0468616
$127$	−2207.73	−1.54256	−0.771279	−	0.636498i	$-0.780383\pi$
$127$	−2207.73	−1.54256	−0.771279	+	0.636498i	$0.780383\pi$
$128$	−1469.80	−1.01495
$129$	168.365	0.114912
$130$	459.589	0.310066
$131$	954.191	0.636398	0.318199	−	0.948024i	$-0.396922\pi$
$131$	954.191	0.636398	0.318199	+	0.948024i	$0.396922\pi$
$132$	−1208.51	−0.796876
$133$	422.779	0.275636
$134$	642.520	0.414218
$135$	310.701	0.198080
$136$	2059.54	1.29856
$137$	944.268	0.588863	0.294432	−	0.955673i	$-0.404870\pi$
$137$	944.268	0.588863	0.294432	+	0.955673i	$0.404870\pi$
$138$	−72.5907	−0.0447778
$139$	2724.16	1.66230	0.831152	−	0.556045i	$-0.187682\pi$
$139$	2724.16	1.66230	0.831152	+	0.556045i	$0.187682\pi$
$140$	555.262	0.335202
$141$	−769.375	−0.459525
$142$	−418.357	−0.247237
$143$	2218.54	1.29737
$144$	347.959	0.201365
$145$	1437.47	0.823278
$146$	−473.963	−0.268668
$147$	−147.000	−0.0824786
$148$	300.850	0.167093
$149$	−2103.44	−1.15651	−0.578257	−	0.815855i	$-0.696267\pi$
$149$	−2103.44	−1.15651	−0.578257	+	0.815855i	$0.696267\pi$
$150$	−23.4215	−0.0127491
$151$	100.617	0.0542256	0.0271128	−	0.999632i	$-0.491369\pi$
$151$	100.617	0.0542256	0.0271128	+	0.999632i	$0.491369\pi$
$152$	−946.316	−0.504976
$153$	−1183.02	−0.625109
$154$	−430.367	−0.225194
$155$	−3392.30	−1.75791
$156$	−785.058	−0.402916
$157$	1097.53	0.557912	0.278956	−	0.960304i	$-0.410012\pi$
$157$	1097.53	0.557912	0.278956	+	0.960304i	$0.410012\pi$
$158$	−938.239	−0.472420
$159$	−1575.86	−0.785998
$160$	−1910.46	−0.943972
$161$	161.000	0.0788110
$162$	85.2152	0.0413280
$163$	795.478	0.382249	0.191125	−	0.981566i	$-0.438787\pi$
$163$	795.478	0.382249	0.191125	+	0.981566i	$0.438787\pi$
$164$	1203.99	0.573268
$165$	−2017.47	−0.951880
$166$	1374.11	0.642479
$167$	−3693.50	−1.71145	−0.855724	−	0.517433i	$-0.826888\pi$
$167$	−3693.50	−1.71145	−0.855724	+	0.517433i	$0.826888\pi$
$168$	329.033	0.151104
$169$	−755.821	−0.344024
$170$	1591.33	0.717939
$171$	543.574	0.243088
$172$	386.858	0.171498
$173$	2127.03	0.934771	0.467386	−	0.884054i	$-0.345196\pi$
$173$	2127.03	0.934771	0.467386	+	0.884054i	$0.345196\pi$
$174$	394.251	0.171771
$175$	51.9469	0.0224390
$176$	−2259.40	−0.967664
$177$	−105.618	−0.0448516
$178$	−131.547	−0.0553925
$179$	−1724.06	−0.719899	−0.359950	−	0.932972i	$-0.617206\pi$
$179$	−1724.06	−0.719899	−0.359950	+	0.932972i	$0.617206\pi$
$180$	713.909	0.295620
$181$	2490.59	1.02279	0.511393	−	0.859347i	$-0.329130\pi$
$181$	2490.59	1.02279	0.511393	+	0.859347i	$0.329130\pi$
$182$	−279.569	−0.113863
$183$	−1369.73	−0.553297
$184$	−360.370	−0.144385
$185$	502.235	0.199595
$186$	−930.398	−0.366775
$187$	7681.72	3.00397
$188$	−1767.82	−0.685807
$189$	−189.000	−0.0727393
$190$	−731.183	−0.279187
$191$	−2876.47	−1.08971	−0.544853	−	0.838531i	$-0.683415\pi$
$191$	−2876.47	−1.08971	−0.544853	+	0.838531i	$0.683415\pi$
$192$	403.911	0.151822
$193$	−1680.29	−0.626685	−0.313342	−	0.949640i	$-0.601449\pi$
$193$	−1680.29	−0.626685	−0.313342	+	0.949640i	$0.601449\pi$
$194$	−189.108	−0.0699852
$195$	−1310.57	−0.481290
$196$	−337.767	−0.123093
$197$	4315.09	1.56060	0.780298	−	0.625408i	$-0.215068\pi$
$197$	4315.09	1.56060	0.780298	+	0.625408i	$0.215068\pi$
$198$	−553.328	−0.198603
$199$	2705.03	0.963589	0.481794	−	0.876284i	$-0.339985\pi$
$199$	2705.03	0.963589	0.481794	+	0.876284i	$0.339985\pi$
$200$	−116.274	−0.0411090
$201$	−1832.21	−0.642957
$202$	−1996.03	−0.695248
$203$	−874.416	−0.302325
$204$	−2718.27	−0.932928
$205$	2009.93	0.684777
$206$	−1475.83	−0.499155
$207$	207.000	0.0695048
$208$	−1467.72	−0.489271
$209$	−3529.59	−1.16817
$210$	254.232	0.0835412
$211$	1956.17	0.638237	0.319119	−	0.947715i	$-0.396613\pi$
$211$	1956.17	0.638237	0.319119	+	0.947715i	$0.396613\pi$
$212$	−3620.91	−1.17304
$213$	1192.99	0.383766
$214$	706.291	0.225612
$215$	645.815	0.204857
$216$	423.043	0.133261
$217$	2063.54	0.645541
$218$	−720.747	−0.223923
$219$	1351.56	0.417030
$220$	−4635.63	−1.42061
$221$	4990.10	1.51887
$222$	137.747	0.0416440
$223$	−2468.88	−0.741383	−0.370691	−	0.928756i	$-0.620879\pi$
$223$	−2468.88	−0.741383	−0.370691	+	0.928756i	$0.620879\pi$
$224$	1162.14	0.346646
$225$	66.7889	0.0197893
$226$	−781.159	−0.229920
$227$	−151.185	−0.0442049	−0.0221025	−	0.999756i	$-0.507036\pi$
$227$	−151.185	−0.0442049	−0.0221025	+	0.999756i	$0.507036\pi$
$228$	1248.99	0.362791
$229$	1267.37	0.365722	0.182861	−	0.983139i	$-0.441464\pi$
$229$	1267.37	0.365722	0.182861	+	0.983139i	$0.441464\pi$
$230$	−278.444	−0.0798264
$231$	1227.23	0.349550
$232$	1957.22	0.553871
$233$	−4649.22	−1.30721	−0.653606	−	0.756835i	$-0.726745\pi$
$233$	−4649.22	−1.30721	−0.653606	+	0.756835i	$0.726745\pi$
$234$	−359.446	−0.100418
$235$	−2951.18	−0.819207
$236$	−242.682	−0.0669376
$237$	2675.49	0.733297
$238$	−968.011	−0.263642
$239$	−4276.00	−1.15729	−0.578643	−	0.815581i	$-0.696417\pi$
$239$	−4276.00	−1.15729	−0.578643	+	0.815581i	$0.696417\pi$
$240$	1334.70	0.358978
$241$	5841.28	1.56129	0.780643	−	0.624977i	$-0.214892\pi$
$241$	5841.28	1.56129	0.780643	+	0.624977i	$0.214892\pi$
$242$	2192.67	0.582438
$243$	−243.000	−0.0641500
$244$	−3147.28	−0.825754
$245$	−563.864	−0.147037
$246$	551.258	0.142874
$247$	−2292.85	−0.590649
$248$	−4618.87	−1.18266
$249$	−3918.41	−0.997267
$250$	1423.44	0.360106
$251$	6331.37	1.59216	0.796080	−	0.605191i	$-0.206903\pi$
$251$	6331.37	1.59216	0.796080	+	0.605191i	$0.206903\pi$
$252$	−434.272	−0.108558
$253$	−1344.11	−0.334007
$254$	−2322.62	−0.573757
$255$	−4537.85	−1.11440
$256$	−469.195	−0.114549
$257$	2019.37	0.490136	0.245068	−	0.969506i	$-0.421190\pi$
$257$	2019.37	0.490136	0.245068	+	0.969506i	$0.421190\pi$
$258$	177.126	0.0427419
$259$	−305.511	−0.0732954
$260$	−3011.34	−0.718289
$261$	−1124.25	−0.266625
$262$	1003.85	0.236709
$263$	4394.67	1.03037	0.515184	−	0.857079i	$-0.327724\pi$
$263$	4394.67	1.03037	0.515184	+	0.857079i	$0.327724\pi$
$264$	−2746.95	−0.640390
$265$	−6044.70	−1.40122
$266$	444.781	0.102524
$267$	375.120	0.0859812
$268$	−4209.94	−0.959564
$269$	1062.63	0.240855	0.120427	−	0.992722i	$-0.461573\pi$
$269$	1062.63	0.240855	0.120427	+	0.992722i	$0.461573\pi$
$270$	326.869	0.0736764
$271$	3365.24	0.754330	0.377165	−	0.926146i	$-0.376899\pi$
$271$	3365.24	0.754330	0.377165	+	0.926146i	$0.376899\pi$
$272$	−5082.01	−1.13288
$273$	797.220	0.176740
$274$	993.407	0.219029
$275$	−433.681	−0.0950980
$276$	475.632	0.103731
$277$	−927.202	−0.201120	−0.100560	−	0.994931i	$-0.532063\pi$
$277$	−927.202	−0.201120	−0.100560	+	0.994931i	$0.532063\pi$
$278$	2865.92	0.618298
$279$	2653.13	0.569314
$280$	1262.11	0.269377
$281$	−3079.62	−0.653790	−0.326895	−	0.945061i	$-0.606002\pi$
$281$	−3079.62	−0.653790	−0.326895	+	0.945061i	$0.606002\pi$
$282$	−809.413	−0.170921
$283$	−7618.99	−1.60036	−0.800180	−	0.599760i	$-0.795263\pi$
$283$	−7618.99	−1.60036	−0.800180	+	0.599760i	$0.795263\pi$
$284$	2741.17	0.572742
$285$	2085.05	0.433359
$286$	2333.99	0.482559
$287$	−1222.64	−0.251465
$288$	1494.18	0.305713
$289$	12365.3	2.51685
$290$	1512.27	0.306220
$291$	539.260	0.108632
$292$	3105.52	0.622386
$293$	−9123.10	−1.81903	−0.909517	−	0.415666i	$-0.863549\pi$
$293$	−9123.10	−1.81903	−0.909517	+	0.415666i	$0.863549\pi$
$294$	−154.650	−0.0306781
$295$	−405.131	−0.0799580
$296$	683.831	0.134280
$297$	1577.87	0.308274
$298$	−2212.90	−0.430168
$299$	−873.146	−0.168881
$300$	153.463	0.0295340
$301$	−392.851	−0.0752278
$302$	105.853	0.0201693
$303$	5691.88	1.07918
$304$	2335.08	0.440546
$305$	−5254.03	−0.986376
$306$	−1244.59	−0.232511
$307$	6385.34	1.18707	0.593535	−	0.804808i	$-0.297732\pi$
$307$	6385.34	1.18707	0.593535	+	0.804808i	$0.297732\pi$
$308$	2819.86	0.521677
$309$	4208.48	0.774796
$310$	−3568.83	−0.653858
$311$	3798.57	0.692595	0.346298	−	0.938125i	$-0.387439\pi$
$311$	3798.57	0.692595	0.346298	+	0.938125i	$0.387439\pi$
$312$	−1784.43	−0.323794
$313$	6875.34	1.24159	0.620794	−	0.783973i	$-0.286810\pi$
$313$	6875.34	1.24159	0.620794	+	0.783973i	$0.286810\pi$
$314$	1154.64	0.207517
$315$	−724.968	−0.129674
$316$	6147.57	1.09439
$317$	−1063.45	−0.188420	−0.0942101	−	0.995552i	$-0.530033\pi$
$317$	−1063.45	−0.188420	−0.0942101	+	0.995552i	$0.530033\pi$
$318$	−1657.87	−0.292354
$319$	7300.09	1.28127
$320$	1549.33	0.270656
$321$	−2014.06	−0.350199
$322$	169.378	0.0293139
$323$	−7939.01	−1.36761
$324$	−558.350	−0.0957391
$325$	−281.722	−0.0480835
$326$	836.874	0.142178
$327$	2055.29	0.347577
$328$	2736.67	0.460693
$329$	1795.21	0.300830
$330$	−2122.46	−0.354054
$331$	−1052.20	−0.174725	−0.0873625	−	0.996177i	$-0.527844\pi$
$331$	−1052.20	−0.174725	−0.0873625	+	0.996177i	$0.527844\pi$
$332$	−9003.49	−1.48835
$333$	−392.800	−0.0646405
$334$	−3885.71	−0.636576
$335$	−7028.02	−1.14621
$336$	−811.904	−0.131824
$337$	−4269.30	−0.690099	−0.345050	−	0.938584i	$-0.612138\pi$
$337$	−4269.30	−0.690099	−0.345050	+	0.938584i	$0.612138\pi$
$338$	−795.153	−0.127960
$339$	2227.56	0.356886
$340$	−10426.8	−1.66315
$341$	−17227.6	−2.73585
$342$	571.861	0.0904172
$343$	343.000	0.0539949
$344$	879.327	0.137820
$345$	794.013	0.123908
$346$	2237.72	0.347690
$347$	10070.4	1.55794	0.778970	−	0.627061i	$-0.215743\pi$
$347$	10070.4	1.55794	0.778970	+	0.627061i	$0.215743\pi$
$348$	−2583.23	−0.397918
$349$	−8099.84	−1.24233	−0.621167	−	0.783678i	$-0.713341\pi$
$349$	−8099.84	−1.24233	−0.621167	+	0.783678i	$0.713341\pi$
$350$	54.6502	0.00834622
$351$	1025.00	0.155870
$352$	−9702.17	−1.46911
$353$	2527.31	0.381063	0.190532	−	0.981681i	$-0.438979\pi$
$353$	2527.31	0.381063	0.190532	+	0.981681i	$0.438979\pi$
$354$	−111.114	−0.0166826
$355$	4576.08	0.684149
$356$	861.928	0.128320
$357$	2760.38	0.409230
$358$	−1813.77	−0.267768
$359$	5046.63	0.741925	0.370962	−	0.928648i	$-0.379028\pi$
$359$	5046.63	0.741925	0.370962	+	0.928648i	$0.379028\pi$
$360$	1622.71	0.237568
$361$	−3211.19	−0.468172
$362$	2620.20	0.380428
$363$	−6252.62	−0.904070
$364$	1831.80	0.263771
$365$	5184.31	0.743450
$366$	−1441.01	−0.205800
$367$	6700.72	0.953065	0.476532	−	0.879157i	$-0.341893\pi$
$367$	6700.72	0.953065	0.476532	+	0.879157i	$0.341893\pi$
$368$	889.228	0.125963
$369$	−1571.97	−0.221771
$370$	528.371	0.0742397
$371$	3677.00	0.514557
$372$	6096.19	0.849658
$373$	1853.52	0.257296	0.128648	−	0.991690i	$-0.458936\pi$
$373$	1853.52	0.257296	0.128648	+	0.991690i	$0.458936\pi$
$374$	8081.48	1.11733
$375$	−4059.10	−0.558962
$376$	−4018.25	−0.551132
$377$	4742.19	0.647839
$378$	−198.835	−0.0270555
$379$	999.292	0.135436	0.0677179	−	0.997705i	$-0.478428\pi$
$379$	999.292	0.135436	0.0677179	+	0.997705i	$0.478428\pi$
$380$	4790.89	0.646756
$381$	6623.20	0.890596
$382$	−3026.16	−0.405319
$383$	−10859.5	−1.44881	−0.724404	−	0.689376i	$-0.757885\pi$
$383$	−10859.5	−1.44881	−0.724404	+	0.689376i	$0.757885\pi$
$384$	4409.41	0.585981
$385$	4707.44	0.623152
$386$	−1767.74	−0.233097
$387$	−505.094	−0.0663447
$388$	1239.08	0.162125
$389$	5895.92	0.768470	0.384235	−	0.923235i	$-0.374465\pi$
$389$	5895.92	0.768470	0.384235	+	0.923235i	$0.374465\pi$
$390$	−1378.77	−0.179017
$391$	−3023.28	−0.391033
$392$	−767.744	−0.0989207
$393$	−2862.57	−0.367424
$394$	4539.64	0.580467
$395$	10262.7	1.30727
$396$	3625.54	0.460076
$397$	12820.0	1.62070	0.810348	−	0.585949i	$-0.199278\pi$
$397$	12820.0	1.62070	0.810348	+	0.585949i	$0.199278\pi$
$398$	2845.79	0.358409
$399$	−1268.34	−0.159139
$400$	286.911	0.0358639
$401$	−1357.45	−0.169047	−0.0845236	−	0.996421i	$-0.526937\pi$
$401$	−1357.45	−0.169047	−0.0845236	+	0.996421i	$0.526937\pi$
$402$	−1927.56	−0.239149
$403$	−11191.1	−1.38330
$404$	13078.5	1.61059
$405$	−932.102	−0.114362
$406$	−919.920	−0.112450
$407$	2550.57	0.310631
$408$	−6178.63	−0.749725
$409$	−4543.38	−0.549281	−0.274640	−	0.961547i	$-0.588559\pi$
$409$	−4543.38	−0.549281	−0.274640	+	0.961547i	$0.588559\pi$
$410$	2114.52	0.254704
$411$	−2832.80	−0.339980
$412$	9669.98	1.15633
$413$	246.442	0.0293623
$414$	217.772	0.0258525
$415$	−15030.3	−1.77785
$416$	−6302.60	−0.742813
$417$	−8172.48	−0.959732
$418$	−3713.27	−0.434502
$419$	7976.02	0.929961	0.464981	−	0.885321i	$-0.346061\pi$
$419$	7976.02	0.929961	0.464981	+	0.885321i	$0.346061\pi$
$420$	−1665.79	−0.193529
$421$	−2993.41	−0.346531	−0.173266	−	0.984875i	$-0.555432\pi$
$421$	−2993.41	−0.346531	−0.173266	+	0.984875i	$0.555432\pi$
$422$	2057.96	0.237394
$423$	2308.13	0.265307
$424$	−8230.32	−0.942687
$425$	−975.466	−0.111334
$426$	1255.07	0.142743
$427$	3196.04	0.362218
$428$	−4627.79	−0.522646
$429$	−6655.62	−0.749036
$430$	679.423	0.0761970
$431$	−6123.56	−0.684365	−0.342183	−	0.939634i	$-0.611166\pi$
$431$	−6123.56	−0.684365	−0.342183	+	0.939634i	$0.611166\pi$
$432$	−1043.88	−0.116258
$433$	11225.8	1.24591	0.622953	−	0.782260i	$-0.285933\pi$
$433$	11225.8	1.24591	0.622953	+	0.782260i	$0.285933\pi$
$434$	2170.93	0.240110
$435$	−4312.40	−0.475320
$436$	4722.51	0.518732
$437$	1389.13	0.152062
$438$	1421.89	0.155115
$439$	15393.0	1.67350	0.836750	−	0.547585i	$-0.184453\pi$
$439$	15393.0	1.67350	0.836750	+	0.547585i	$0.184453\pi$
$440$	−10536.8	−1.14164
$441$	441.000	0.0476190
$442$	5249.78	0.564947
$443$	8429.13	0.904018	0.452009	−	0.892013i	$-0.350707\pi$
$443$	8429.13	0.904018	0.452009	+	0.892013i	$0.350707\pi$
$444$	−902.550	−0.0964710
$445$	1438.89	0.153281
$446$	−2597.36	−0.275759
$447$	6310.32	0.667714
$448$	−942.460	−0.0993907
$449$	16006.3	1.68237	0.841186	−	0.540746i	$-0.181858\pi$
$449$	16006.3	1.68237	0.841186	+	0.540746i	$0.181858\pi$
$450$	70.2646	0.00736067
$451$	10207.3	1.06573
$452$	5118.34	0.532625
$453$	−301.850	−0.0313071
$454$	−159.053	−0.0164421
$455$	3057.99	0.315078
$456$	2838.95	0.291548
$457$	−12620.9	−1.29186	−0.645930	−	0.763397i	$-0.723530\pi$
$457$	−12620.9	−1.29186	−0.645930	+	0.763397i	$0.723530\pi$
$458$	1333.32	0.136031
$459$	3549.07	0.360907
$460$	1824.43	0.184923
$461$	−3587.54	−0.362448	−0.181224	−	0.983442i	$-0.558006\pi$
$461$	−3587.54	−0.362448	−0.181224	+	0.983442i	$0.558006\pi$
$462$	1291.10	0.130016
$463$	6037.85	0.606054	0.303027	−	0.952982i	$-0.402003\pi$
$463$	6037.85	0.606054	0.303027	+	0.952982i	$0.402003\pi$
$464$	−4829.53	−0.483201
$465$	10176.9	1.01493
$466$	−4891.16	−0.486220
$467$	15082.1	1.49447	0.747233	−	0.664562i	$-0.231382\pi$
$467$	15082.1	1.49447	0.747233	+	0.664562i	$0.231382\pi$
$468$	2355.17	0.232624
$469$	4275.16	0.420914
$470$	−3104.76	−0.304706
$471$	−3292.58	−0.322111
$472$	−551.616	−0.0537928
$473$	3279.73	0.318821
$474$	2814.72	0.272752
$475$	448.206	0.0432950
$476$	6342.64	0.610745
$477$	4727.58	0.453796
$478$	−4498.52	−0.430455
$479$	−1315.02	−0.125438	−0.0627190	−	0.998031i	$-0.519977\pi$
$479$	−1315.02	−0.125438	−0.0627190	+	0.998031i	$0.519977\pi$
$480$	5731.39	0.545002
$481$	1656.87	0.157062
$482$	6145.26	0.580724
$483$	−483.000	−0.0455016
$484$	−14366.9	−1.34926
$485$	2068.50	0.193661
$486$	−255.646	−0.0238607
$487$	5647.77	0.525513	0.262757	−	0.964862i	$-0.415368\pi$
$487$	5647.77	0.525513	0.262757	+	0.964862i	$0.415368\pi$
$488$	−7153.76	−0.663597
$489$	−2386.43	−0.220692
$490$	−593.207	−0.0546906
$491$	−19855.6	−1.82499	−0.912493	−	0.409091i	$-0.865846\pi$
$491$	−19855.6	−1.82499	−0.912493	+	0.409091i	$0.865846\pi$
$492$	−3611.97	−0.330976
$493$	16419.9	1.50003
$494$	−2412.16	−0.219693
$495$	6052.42	0.549568
$496$	11397.3	1.03176
$497$	−2783.64	−0.251234
$498$	−4122.33	−0.370936
$499$	−11353.9	−1.01858	−0.509291	−	0.860595i	$-0.670092\pi$
$499$	−11353.9	−1.01858	−0.509291	+	0.860595i	$0.670092\pi$
$500$	−9326.74	−0.834209
$501$	11080.5	0.988104
$502$	6660.85	0.592208
$503$	15121.3	1.34041	0.670205	−	0.742176i	$-0.266206\pi$
$503$	15121.3	1.34041	0.670205	+	0.742176i	$0.266206\pi$
$504$	−987.100	−0.0872399
$505$	21833.0	1.92387
$506$	−1414.06	−0.124235
$507$	2267.46	0.198622
$508$	15218.4	1.32915
$509$	4819.60	0.419696	0.209848	−	0.977734i	$-0.432703\pi$
$509$	4819.60	0.419696	0.209848	+	0.977734i	$0.432703\pi$
$510$	−4774.00	−0.414502
$511$	−3153.63	−0.273010
$512$	11264.8	0.972342
$513$	−1630.72	−0.140347
$514$	2124.46	0.182307
$515$	16142.9	1.38125
$516$	−1160.57	−0.0990144
$517$	−14987.4	−1.27494
$518$	−321.409	−0.0272624
$519$	−6381.10	−0.539690
$520$	−6844.75	−0.577235
$521$	9010.06	0.757655	0.378827	−	0.925467i	$-0.376327\pi$
$521$	9010.06	0.757655	0.378827	+	0.925467i	$0.376327\pi$
$522$	−1182.75	−0.0991719
$523$	4230.86	0.353734	0.176867	−	0.984235i	$-0.443404\pi$
$523$	4230.86	0.353734	0.176867	+	0.984235i	$0.443404\pi$
$524$	−6577.44	−0.548353
$525$	−155.841	−0.0129551
$526$	4623.36	0.383248
$527$	−38749.5	−3.20295
$528$	6778.21	0.558681
$529$	529.000	0.0434783
$530$	−6359.26	−0.521186
$531$	316.854	0.0258951
$532$	−2914.31	−0.237502
$533$	6630.72	0.538852
$534$	394.641	0.0319809
$535$	−7725.56	−0.624308
$536$	−9569.19	−0.771130
$537$	5172.17	0.415634
$538$	1117.93	0.0895865
$539$	−2863.55	−0.228834
$540$	−2141.73	−0.170676
$541$	1109.88	0.0882021	0.0441011	−	0.999027i	$-0.485958\pi$
$541$	1109.88	0.0882021	0.0441011	+	0.999027i	$0.485958\pi$
$542$	3540.36	0.280575
$543$	−7471.78	−0.590506
$544$	−21822.8	−1.71994
$545$	7883.69	0.619633
$546$	838.707	0.0657387
$547$	632.641	0.0494511	0.0247256	−	0.999694i	$-0.492129\pi$
$547$	632.641	0.0494511	0.0247256	+	0.999694i	$0.492129\pi$
$548$	−6509.04	−0.507395
$549$	4109.19	0.319446
$550$	−456.249	−0.0353719
$551$	−7544.59	−0.583322
$552$	1081.11	0.0833606
$553$	−6242.80	−0.480056
$554$	−975.453	−0.0748069
$555$	−1506.70	−0.115236
$556$	−18778.2	−1.43233
$557$	3748.00	0.285112	0.142556	−	0.989787i	$-0.454468\pi$
$557$	3748.00	0.285112	0.142556	+	0.989787i	$0.454468\pi$
$558$	2791.19	0.211757
$559$	2130.54	0.161202
$560$	−3114.31	−0.235006
$561$	−23045.2	−1.73435
$562$	−3239.89	−0.243179
$563$	−18848.1	−1.41093	−0.705463	−	0.708747i	$-0.749261\pi$
$563$	−18848.1	−1.41093	−0.705463	+	0.708747i	$0.749261\pi$
$564$	5303.47	0.395951
$565$	8544.49	0.636229
$566$	−8015.48	−0.595257
$567$	567.000	0.0419961
$568$	6230.68	0.460270
$569$	6473.34	0.476936	0.238468	−	0.971150i	$-0.423355\pi$
$569$	6473.34	0.476936	0.238468	+	0.971150i	$0.423355\pi$
$570$	2193.55	0.161189
$571$	−2488.64	−0.182393	−0.0911965	−	0.995833i	$-0.529069\pi$
$571$	−2488.64	−0.182393	−0.0911965	+	0.995833i	$0.529069\pi$
$572$	−15292.9	−1.11788
$573$	8629.41	0.629142
$574$	−1286.27	−0.0935328
$575$	170.683	0.0123791
$576$	−1211.73	−0.0876544
$577$	1719.46	0.124059	0.0620295	−	0.998074i	$-0.480243\pi$
$577$	1719.46	0.124059	0.0620295	+	0.998074i	$0.480243\pi$
$578$	13008.8	0.936148
$579$	5040.88	0.361817
$580$	−9908.78	−0.709378
$581$	9142.97	0.652864
$582$	567.323	0.0404060
$583$	−30697.6	−2.18073
$584$	7058.84	0.500166
$585$	3931.70	0.277873
$586$	−9597.86	−0.676594
$587$	−4663.30	−0.327896	−0.163948	−	0.986469i	$-0.552423\pi$
$587$	−4663.30	−0.327896	−0.163948	+	0.986469i	$0.552423\pi$
$588$	1013.30	0.0710678
$589$	17804.6	1.24554
$590$	−426.213	−0.0297405
$591$	−12945.3	−0.901010
$592$	−1687.38	−0.117147
$593$	13086.8	0.906259	0.453129	−	0.891445i	$-0.350308\pi$
$593$	13086.8	0.906259	0.453129	+	0.891445i	$0.350308\pi$
$594$	1659.99	0.114663
$595$	10588.3	0.729544
$596$	14499.5	0.996512
$597$	−8115.08	−0.556328
$598$	−918.584	−0.0628155
$599$	−13990.5	−0.954320	−0.477160	−	0.878816i	$-0.658334\pi$
$599$	−13990.5	−0.954320	−0.477160	+	0.878816i	$0.658334\pi$
$600$	348.822	0.0237343
$601$	−26603.8	−1.80565	−0.902823	−	0.430013i	$-0.858509\pi$
$601$	−26603.8	−1.80565	−0.902823	+	0.430013i	$0.858509\pi$
$602$	−413.295	−0.0279811
$603$	5496.64	0.371211
$604$	−693.571	−0.0467235
$605$	−23983.9	−1.61171
$606$	5988.09	0.401402
$607$	24907.8	1.66553	0.832766	−	0.553625i	$-0.186756\pi$
$607$	24907.8	1.66553	0.832766	+	0.553625i	$0.186756\pi$
$608$	10027.1	0.668838
$609$	2623.25	0.174547
$610$	−5527.44	−0.366885
$611$	−9735.90	−0.644635
$612$	8154.82	0.538626
$613$	17527.2	1.15484	0.577419	−	0.816448i	$-0.304060\pi$
$613$	17527.2	1.15484	0.577419	+	0.816448i	$0.304060\pi$
$614$	6717.62	0.441533
$615$	−6029.78	−0.395356
$616$	6409.54	0.419233
$617$	6259.53	0.408426	0.204213	−	0.978926i	$-0.434536\pi$
$617$	6259.53	0.408426	0.204213	+	0.978926i	$0.434536\pi$
$618$	4427.49	0.288187
$619$	−6671.61	−0.433206	−0.216603	−	0.976260i	$-0.569498\pi$
$619$	−6671.61	−0.433206	−0.216603	+	0.976260i	$0.569498\pi$
$620$	23383.8	1.51470
$621$	−621.000	−0.0401286
$622$	3996.24	0.257612
$623$	−875.280	−0.0562879
$624$	4403.17	0.282481
$625$	−16497.6	−1.05584
$626$	7233.13	0.461812
$627$	10588.8	0.674441
$628$	−7565.49	−0.480726
$629$	5736.92	0.363666
$630$	−762.695	−0.0482325
$631$	−19637.6	−1.23892	−0.619460	−	0.785028i	$-0.712648\pi$
$631$	−19637.6	−1.23892	−0.619460	+	0.785028i	$0.712648\pi$
$632$	13973.4	0.879481
$633$	−5868.50	−0.368486
$634$	−1118.79	−0.0700833
$635$	25405.4	1.58769
$636$	10862.7	0.677257
$637$	−1860.18	−0.115703
$638$	7679.98	0.476573
$639$	−3578.96	−0.221567
$640$	16913.7	1.04464
$641$	19448.6	1.19840	0.599200	−	0.800600i	$-0.295486\pi$
$641$	19448.6	1.19840	0.599200	+	0.800600i	$0.295486\pi$
$642$	−2118.87	−0.130257
$643$	−29409.2	−1.80371	−0.901857	−	0.432036i	$-0.857795\pi$
$643$	−29409.2	−1.80371	−0.901857	+	0.432036i	$0.857795\pi$
$644$	−1109.81	−0.0679077
$645$	−1937.45	−0.118274
$646$	−8352.15	−0.508685
$647$	3249.78	0.197468	0.0987342	−	0.995114i	$-0.468521\pi$
$647$	3249.78	0.197468	0.0987342	+	0.995114i	$0.468521\pi$
$648$	−1269.13	−0.0769384
$649$	−2057.43	−0.124439
$650$	−296.383	−0.0178847
$651$	−6190.63	−0.372703
$652$	−5483.40	−0.329366
$653$	24372.7	1.46061	0.730304	−	0.683122i	$-0.239378\pi$
$653$	24372.7	1.46061	0.730304	+	0.683122i	$0.239378\pi$
$654$	2162.24	0.129282
$655$	−10980.3	−0.655016
$656$	−6752.85	−0.401912
$657$	−4054.67	−0.240773
$658$	1888.63	0.111894
$659$	−10976.6	−0.648844	−0.324422	−	0.945912i	$-0.605170\pi$
$659$	−10976.6	−0.648844	−0.324422	+	0.945912i	$0.605170\pi$
$660$	13906.9	0.820189
$661$	−9058.02	−0.533005	−0.266502	−	0.963834i	$-0.585868\pi$
$661$	−9058.02	−0.533005	−0.266502	+	0.963834i	$0.585868\pi$
$662$	−1106.95	−0.0649894
$663$	−14970.3	−0.876920
$664$	−20464.9	−1.19607
$665$	−4865.11	−0.283700
$666$	−413.241	−0.0240432
$667$	−2873.08	−0.166786
$668$	25460.1	1.47467
$669$	7406.64	0.428037
$670$	−7393.75	−0.426337
$671$	−26682.2	−1.53511
$672$	−3486.42	−0.200136
$673$	−29524.4	−1.69106	−0.845529	−	0.533930i	$-0.820715\pi$
$673$	−29524.4	−1.69106	−0.845529	+	0.533930i	$0.820715\pi$
$674$	−4491.47	−0.256684
$675$	−200.367	−0.0114254
$676$	5210.03	0.296429
$677$	−5132.51	−0.291372	−0.145686	−	0.989331i	$-0.546539\pi$
$677$	−5132.51	−0.291372	−0.145686	+	0.989331i	$0.546539\pi$
$678$	2343.48	0.132744
$679$	−1258.27	−0.0711165
$680$	−23700.0	−1.33655
$681$	453.556	0.0255217
$682$	−18124.1	−1.01761
$683$	−13707.3	−0.767927	−0.383964	−	0.923348i	$-0.625441\pi$
$683$	−13707.3	−0.767927	−0.383964	+	0.923348i	$0.625441\pi$
$684$	−3746.97	−0.209457
$685$	−10866.1	−0.606091
$686$	360.850	0.0200835
$687$	−3802.11	−0.211149
$688$	−2169.78	−0.120235
$689$	−19941.4	−1.10262
$690$	835.333	0.0460878
$691$	−12803.3	−0.704861	−0.352431	−	0.935838i	$-0.614645\pi$
$691$	−12803.3	−0.704861	−0.352431	+	0.935838i	$0.614645\pi$
$692$	−14662.1	−0.805447
$693$	−3681.70	−0.201813
$694$	10594.4	0.579479
$695$	−31348.1	−1.71094
$696$	−5871.67	−0.319777
$697$	22958.9	1.24768
$698$	−8521.35	−0.462089
$699$	13947.7	0.754719
$700$	−358.081	−0.0193346
$701$	2657.29	0.143173	0.0715867	−	0.997434i	$-0.477194\pi$
$701$	2657.29	0.143173	0.0715867	+	0.997434i	$0.477194\pi$
$702$	1078.34	0.0579761
$703$	−2635.99	−0.141420
$704$	7868.16	0.421225
$705$	8853.53	0.472969
$706$	2658.84	0.141737
$707$	−13281.1	−0.706486
$708$	728.047	0.0386465
$709$	3616.06	0.191543	0.0957714	−	0.995403i	$-0.469468\pi$
$709$	3616.06	0.191543	0.0957714	+	0.995403i	$0.469468\pi$
$710$	4814.21	0.254471
$711$	−8026.46	−0.423369
$712$	1959.16	0.103122
$713$	6780.21	0.356130
$714$	2904.03	0.152214
$715$	−25529.7	−1.33532
$716$	11884.3	0.620302
$717$	12828.0	0.668159
$718$	5309.26	0.275961
$719$	−7969.18	−0.413352	−0.206676	−	0.978409i	$-0.566265\pi$
$719$	−7969.18	−0.413352	−0.206676	+	0.978409i	$0.566265\pi$
$720$	−4004.11	−0.207256
$721$	−9819.79	−0.507223
$722$	−3378.30	−0.174138
$723$	−17523.8	−0.901409
$724$	−17168.2	−0.881286
$725$	−927.004	−0.0474870
$726$	−6578.00	−0.336271
$727$	−22654.0	−1.15569	−0.577847	−	0.816145i	$-0.696107\pi$
$727$	−22654.0	−1.15569	−0.577847	+	0.816145i	$0.696107\pi$
$728$	4163.68	0.211973
$729$	729.000	0.0370370
$730$	5454.10	0.276528
$731$	7377.01	0.373254
$732$	9441.84	0.476749
$733$	16963.5	0.854792	0.427396	−	0.904064i	$-0.359431\pi$
$733$	16963.5	0.854792	0.427396	+	0.904064i	$0.359431\pi$
$734$	7049.42	0.354494
$735$	1691.59	0.0848916
$736$	3818.46	0.191237
$737$	−35691.3	−1.78386
$738$	−1653.77	−0.0824882
$739$	−28555.4	−1.42142	−0.710709	−	0.703486i	$-0.751626\pi$
$739$	−28555.4	−1.42142	−0.710709	+	0.703486i	$0.751626\pi$
$740$	−3462.01	−0.171981
$741$	6878.54	0.341011
$742$	3868.35	0.191390
$743$	−36544.2	−1.80441	−0.902204	−	0.431309i	$-0.858052\pi$
$743$	−36544.2	−1.80441	−0.902204	+	0.431309i	$0.858052\pi$
$744$	13856.6	0.682807
$745$	24205.2	1.19035
$746$	1949.97	0.0957019
$747$	11755.2	0.575772
$748$	−52951.8	−2.58838
$749$	4699.48	0.229259
$750$	−4270.33	−0.207907
$751$	27019.0	1.31283	0.656417	−	0.754398i	$-0.272071\pi$
$751$	27019.0	1.31283	0.656417	+	0.754398i	$0.272071\pi$
$752$	9915.22	0.480812
$753$	−18994.1	−0.919235
$754$	4988.97	0.240965
$755$	−1157.84	−0.0558120
$756$	1302.82	0.0626759
$757$	28132.1	1.35070	0.675348	−	0.737499i	$-0.263993\pi$
$757$	28132.1	1.35070	0.675348	+	0.737499i	$0.263993\pi$
$758$	1051.29	0.0503756
$759$	4032.34	0.192839
$760$	10889.7	0.519750
$761$	−9242.97	−0.440286	−0.220143	−	0.975468i	$-0.570652\pi$
$761$	−9242.97	−0.440286	−0.220143	+	0.975468i	$0.570652\pi$
$762$	6967.87	0.331259
$763$	−4795.67	−0.227542
$764$	19828.1	0.938947
$765$	13613.5	0.643397
$766$	−11424.6	−0.538887
$767$	−1336.52	−0.0629191
$768$	1407.58	0.0661351
$769$	6057.93	0.284076	0.142038	−	0.989861i	$-0.454634\pi$
$769$	6057.93	0.284076	0.142038	+	0.989861i	$0.454634\pi$
$770$	4952.41	0.231783
$771$	−6058.11	−0.282980
$772$	11582.6	0.539984
$773$	25040.9	1.16515	0.582575	−	0.812777i	$-0.302045\pi$
$773$	25040.9	1.16515	0.582575	+	0.812777i	$0.302045\pi$
$774$	−531.379	−0.0246770
$775$	2187.65	0.101397
$776$	2816.42	0.130288
$777$	916.532	0.0423171
$778$	6202.74	0.285834
$779$	−10549.1	−0.485189
$780$	9034.01	0.414704
$781$	23239.3	1.06475
$782$	−3180.61	−0.145445
$783$	3372.75	0.153936
$784$	1894.44	0.0862993
$785$	−12629.7	−0.574235
$786$	−3011.54	−0.136664
$787$	5226.71	0.236737	0.118369	−	0.992970i	$-0.462234\pi$
$787$	5226.71	0.236737	0.118369	+	0.992970i	$0.462234\pi$
$788$	−29744.8	−1.34469
$789$	−13184.0	−0.594883
$790$	10796.7	0.486241
$791$	−5197.63	−0.233637
$792$	8240.84	0.369729
$793$	−17333.0	−0.776181
$794$	13487.1	0.602821
$795$	18134.1	0.808993
$796$	−18646.3	−0.830278
$797$	42939.3	1.90839	0.954195	−	0.299184i	$-0.0967144\pi$
$797$	42939.3	1.90839	0.954195	+	0.299184i	$0.0967144\pi$
$798$	−1334.34	−0.0591920
$799$	−33710.7	−1.49261
$800$	1232.03	0.0544487
$801$	−1125.36	−0.0496413
$802$	−1428.09	−0.0628774
$803$	26328.2	1.15704
$804$	12629.8	0.554005
$805$	−1852.70	−0.0811167
$806$	−11773.5	−0.514522
$807$	−3187.90	−0.139058
$808$	29727.3	1.29431
$809$	24276.4	1.05502	0.527512	−	0.849548i	$-0.323125\pi$
$809$	24276.4	1.05502	0.527512	+	0.849548i	$0.323125\pi$
$810$	−980.608	−0.0425371
$811$	−40151.4	−1.73848	−0.869238	−	0.494393i	$-0.835390\pi$
$811$	−40151.4	−1.73848	−0.869238	+	0.494393i	$0.835390\pi$
$812$	6027.53	0.260499
$813$	−10095.7	−0.435513
$814$	2683.30	0.115540
$815$	−9153.90	−0.393432
$816$	15246.0	0.654066
$817$	−3389.58	−0.145149
$818$	−4779.82	−0.204306
$819$	−2391.66	−0.102041
$820$	−13854.8	−0.590039
$821$	−36686.1	−1.55951	−0.779753	−	0.626087i	$-0.784655\pi$
$821$	−36686.1	−1.55951	−0.779753	+	0.626087i	$0.784655\pi$
$822$	−2980.22	−0.126456
$823$	−26221.3	−1.11059	−0.555297	−	0.831652i	$-0.687395\pi$
$823$	−26221.3	−1.11059	−0.555297	+	0.831652i	$0.687395\pi$
$824$	21979.8	0.929252
$825$	1301.04	0.0549048
$826$	259.267	0.0109214
$827$	14824.5	0.623337	0.311669	−	0.950191i	$-0.399112\pi$
$827$	14824.5	0.623337	0.311669	+	0.950191i	$0.399112\pi$
$828$	−1426.90	−0.0598889
$829$	11740.0	0.491853	0.245927	−	0.969288i	$-0.420908\pi$
$829$	11740.0	0.491853	0.245927	+	0.969288i	$0.420908\pi$
$830$	−15812.5	−0.661276
$831$	2781.61	0.116117
$832$	5111.21	0.212980
$833$	−6440.90	−0.267904
$834$	−8597.77	−0.356974
$835$	42502.7	1.76152
$836$	24330.2	1.00655
$837$	−7959.38	−0.328693
$838$	8391.08	0.345901
$839$	20270.8	0.834118	0.417059	−	0.908879i	$-0.363061\pi$
$839$	20270.8	0.834118	0.417059	+	0.908879i	$0.363061\pi$
$840$	−3786.33	−0.155525
$841$	−8784.86	−0.360198
$842$	−3149.18	−0.128893
$843$	9238.87	0.377466
$844$	−13484.3	−0.549938
$845$	8697.56	0.354089
$846$	2428.24	0.0986816
$847$	14589.4	0.591853
$848$	20308.7	0.822409
$849$	22857.0	0.923968
$850$	−1026.23	−0.0414110
$851$	−1003.82	−0.0404354
$852$	−8223.52	−0.330673
$853$	−13905.6	−0.558169	−0.279085	−	0.960267i	$-0.590031\pi$
$853$	−13905.6	−0.558169	−0.279085	+	0.960267i	$0.590031\pi$
$854$	3362.36	0.134728
$855$	−6255.14	−0.250200
$856$	−10518.9	−0.420012
$857$	−10316.6	−0.411212	−0.205606	−	0.978635i	$-0.565917\pi$
$857$	−10316.6	−0.411212	−0.205606	+	0.978635i	$0.565917\pi$
$858$	−7001.98	−0.278606
$859$	18090.8	0.718569	0.359285	−	0.933228i	$-0.383021\pi$
$859$	18090.8	0.718569	0.359285	+	0.933228i	$0.383021\pi$
$860$	−4451.74	−0.176515
$861$	3667.93	0.145183
$862$	−6442.22	−0.254551
$863$	11751.7	0.463536	0.231768	−	0.972771i	$-0.425549\pi$
$863$	11751.7	0.463536	0.231768	+	0.972771i	$0.425549\pi$
$864$	−4482.54	−0.176504
$865$	−24476.7	−0.962119
$866$	11810.0	0.463417
$867$	−37095.8	−1.45310
$868$	−14224.4	−0.556232
$869$	52118.3	2.03451
$870$	−4536.82	−0.176796
$871$	−23185.3	−0.901958
$872$	10734.2	0.416866
$873$	−1617.78	−0.0627189
$874$	1461.42	0.0565599
$875$	9471.23	0.365927
$876$	−9316.56	−0.359335
$877$	25359.8	0.976443	0.488221	−	0.872720i	$-0.337646\pi$
$877$	25359.8	0.976443	0.488221	+	0.872720i	$0.337646\pi$
$878$	16194.0	0.622462
$879$	27369.3	1.05022
$880$	25999.9	0.995974
$881$	2656.81	0.101601	0.0508004	−	0.998709i	$-0.483823\pi$
$881$	2656.81	0.101601	0.0508004	+	0.998709i	$0.483823\pi$
$882$	463.949	0.0177120
$883$	3369.55	0.128419	0.0642097	−	0.997936i	$-0.479547\pi$
$883$	3369.55	0.128419	0.0642097	+	0.997936i	$0.479547\pi$
$884$	−34397.8	−1.30874
$885$	1215.39	0.0461638
$886$	8867.78	0.336252
$887$	1284.23	0.0486135	0.0243068	−	0.999705i	$-0.492262\pi$
$887$	1284.23	0.0486135	0.0243068	+	0.999705i	$0.492262\pi$
$888$	−2051.49	−0.0775266
$889$	−15454.1	−0.583032
$890$	1513.77	0.0570131
$891$	−4733.62	−0.177982
$892$	17018.5	0.638814
$893$	15489.3	0.580438
$894$	6638.71	0.248358
$895$	19839.5	0.740961
$896$	−10288.6	−0.383615
$897$	2619.44	0.0975033
$898$	16839.3	0.625762
$899$	−36824.4	−1.36614
$900$	−460.390	−0.0170515
$901$	−69047.2	−2.55305
$902$	10738.5	0.396399
$903$	1178.55	0.0434328
$904$	11634.0	0.428031
$905$	−28660.3	−1.05271
$906$	−317.558	−0.0116448
$907$	29573.4	1.08266	0.541329	−	0.840811i	$-0.317921\pi$
$907$	29573.4	1.08266	0.541329	+	0.840811i	$0.317921\pi$
$908$	1042.15	0.0380892
$909$	−17075.7	−0.623062
$910$	3217.12	0.117194
$911$	49169.5	1.78821	0.894105	−	0.447857i	$-0.147813\pi$
$911$	49169.5	1.78821	0.894105	+	0.447857i	$0.147813\pi$
$912$	−7005.23	−0.254349
$913$	−76330.4	−2.76689
$914$	−13277.7	−0.480510
$915$	15762.1	0.569484
$916$	−8736.26	−0.315125
$917$	6679.34	0.240536
$918$	3733.76	0.134240
$919$	47639.6	1.70999	0.854997	−	0.518633i	$-0.173559\pi$
$919$	47639.6	1.70999	0.854997	+	0.518633i	$0.173559\pi$
$920$	4146.93	0.148609
$921$	−19156.0	−0.685355
$922$	−3774.24	−0.134813
$923$	15096.4	0.538358
$924$	−8459.59	−0.301191
$925$	−323.885	−0.0115127
$926$	6352.06	0.225423
$927$	−12625.4	−0.447329
$928$	−20738.6	−0.733598
$929$	33725.1	1.19105	0.595524	−	0.803338i	$-0.296945\pi$
$929$	33725.1	1.19105	0.595524	+	0.803338i	$0.296945\pi$
$930$	10706.5	0.377505
$931$	2959.46	0.104181
$932$	32048.0	1.12636
$933$	−11395.7	−0.399870
$934$	15867.0	0.555870
$935$	−88396.9	−3.09186
$936$	5353.30	0.186943
$937$	−1257.44	−0.0438407	−0.0219204	−	0.999760i	$-0.506978\pi$
$937$	−1257.44	−0.0438407	−0.0219204	+	0.999760i	$0.506978\pi$
$938$	4497.64	0.156560
$939$	−20626.0	−0.716832
$940$	20343.1	0.705871
$941$	25458.3	0.881952	0.440976	−	0.897519i	$-0.354632\pi$
$941$	25458.3	0.881952	0.440976	+	0.897519i	$0.354632\pi$
$942$	−3463.93	−0.119810
$943$	−4017.26	−0.138727
$944$	1361.14	0.0469293
$945$	2174.90	0.0748674
$946$	3450.41	0.118586
$947$	−10810.6	−0.370959	−0.185479	−	0.982648i	$-0.559384\pi$
$947$	−10810.6	−0.370959	−0.185479	+	0.982648i	$0.559384\pi$
$948$	−18442.7	−0.631847
$949$	17103.0	0.585022
$950$	471.530	0.0161036
$951$	3190.35	0.108784
$952$	14416.8	0.490810
$953$	10790.3	0.366771	0.183386	−	0.983041i	$-0.441294\pi$
$953$	10790.3	0.366771	0.183386	+	0.983041i	$0.441294\pi$
$954$	4973.60	0.168791
$955$	33100.8	1.12159
$956$	29475.3	0.997177
$957$	−21900.3	−0.739744
$958$	−1383.45	−0.0466569
$959$	6609.87	0.222569
$960$	−4647.98	−0.156264
$961$	57111.2	1.91706
$962$	1743.09	0.0584194
$963$	6042.18	0.202188
$964$	−40265.2	−1.34528
$965$	19335.9	0.645019
$966$	−508.135	−0.0169244
$967$	31507.2	1.04778	0.523889	−	0.851786i	$-0.324481\pi$
$967$	31507.2	1.04778	0.523889	+	0.851786i	$0.324481\pi$
$968$	−32655.8	−1.08430
$969$	23817.0	0.789590
$970$	2176.14	0.0720327
$971$	−4081.26	−0.134885	−0.0674427	−	0.997723i	$-0.521484\pi$
$971$	−4081.26	−0.134885	−0.0674427	+	0.997723i	$0.521484\pi$
$972$	1675.05	0.0552750
$973$	19069.1	0.628292
$974$	5941.68	0.195466
$975$	845.166	0.0277610
$976$	17652.2	0.578928
$977$	21784.9	0.713367	0.356683	−	0.934225i	$-0.383908\pi$
$977$	21784.9	0.713367	0.356683	+	0.934225i	$0.383908\pi$
$978$	−2510.62	−0.0820867
$979$	7307.31	0.238552
$980$	3886.84	0.126694
$981$	−6165.86	−0.200673
$982$	−20888.8	−0.678808
$983$	−23937.3	−0.776683	−0.388342	−	0.921515i	$-0.626952\pi$
$983$	−23937.3	−0.776683	−0.388342	+	0.921515i	$0.626952\pi$
$984$	−8210.00	−0.265981
$985$	−49655.6	−1.60625
$986$	17274.4	0.557939
$987$	−5385.63	−0.173684
$988$	15805.1	0.508934
$989$	−1290.80	−0.0415014
$990$	6367.39	0.204413
$991$	1362.92	0.0436877	0.0218439	−	0.999761i	$-0.493046\pi$
$991$	1362.92	0.0436877	0.0218439	+	0.999761i	$0.493046\pi$
$992$	48941.3	1.56642
$993$	3156.59	0.100878
$994$	−2928.50	−0.0934470
$995$	−31127.9	−0.991779
$996$	27010.5	0.859297
$997$	401.958	0.0127685	0.00638423	−	0.999980i	$-0.497968\pi$
$997$	401.958	0.0127685	0.00638423	+	0.999980i	$0.497968\pi$
$998$	−11944.8	−0.378863
$999$	1178.40	0.0373202

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.4.a.f.1.6	✓	9
3.2	odd	2		1449.4.a.m.1.4		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.4.a.f.1.6	✓	9	1.1	even	1	trivial
1449.4.a.m.1.4		9	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)

\(f(q)\)	\(=\)	\(q+1.05204 q^{2} -3.00000 q^{3} -6.89321 q^{4} -11.5074 q^{5} -3.15612 q^{6} +7.00000 q^{7} -15.6682 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+1.05204 q^{2} -3.00000 q^{3} -6.89321 q^{4} -11.5074 q^{5} -3.15612 q^{6} +7.00000 q^{7} -15.6682 q^{8} +9.00000 q^{9} -12.1063 q^{10} -58.4398 q^{11} +20.6796 q^{12} -37.9629 q^{13} +7.36428 q^{14} +34.5223 q^{15} +38.6621 q^{16} -131.447 q^{17} +9.46835 q^{18} +60.3971 q^{19} +79.3232 q^{20} -21.0000 q^{21} -61.4809 q^{22} +23.0000 q^{23} +47.0047 q^{24} +7.42099 q^{25} -39.9384 q^{26} -27.0000 q^{27} -48.2525 q^{28} -124.917 q^{29} +36.3188 q^{30} +294.792 q^{31} +166.020 q^{32} +175.319 q^{33} -138.287 q^{34} -80.5520 q^{35} -62.0389 q^{36} -43.6444 q^{37} +63.5401 q^{38} +113.889 q^{39} +180.301 q^{40} -174.663 q^{41} -22.0928 q^{42} -56.1216 q^{43} +402.838 q^{44} -103.567 q^{45} +24.1969 q^{46} +256.458 q^{47} -115.986 q^{48} +49.0000 q^{49} +7.80717 q^{50} +394.341 q^{51} +261.686 q^{52} +525.286 q^{53} -28.4051 q^{54} +672.492 q^{55} -109.678 q^{56} -181.191 q^{57} -131.417 q^{58} +35.2060 q^{59} -237.970 q^{60} +456.577 q^{61} +310.133 q^{62} +63.0000 q^{63} -134.637 q^{64} +436.855 q^{65} +184.443 q^{66} +610.737 q^{67} +906.091 q^{68} -69.0000 q^{69} -84.7439 q^{70} -397.663 q^{71} -141.014 q^{72} -450.519 q^{73} -45.9156 q^{74} -22.2630 q^{75} -416.330 q^{76} -409.078 q^{77} +119.815 q^{78} -891.829 q^{79} -444.901 q^{80} +81.0000 q^{81} -183.753 q^{82} +1306.14 q^{83} +144.757 q^{84} +1512.62 q^{85} -59.0421 q^{86} +374.750 q^{87} +915.649 q^{88} -125.040 q^{89} -108.956 q^{90} -265.740 q^{91} -158.544 q^{92} -884.375 q^{93} +269.804 q^{94} -695.015 q^{95} -498.060 q^{96} -179.753 q^{97} +51.5499 q^{98} -525.958 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 27 q^{3} + 42 q^{4} + 29 q^{5} + 63 q^{7} - 39 q^{8} + 81 q^{9}+O(q^{10}) \) 9 * q - 27 * q^3 + 42 * q^4 + 29 * q^5 + 63 * q^7 - 39 * q^8 + 81 * q^9	\( 9 q - 27 q^{3} + 42 q^{4} + 29 q^{5} + 63 q^{7} - 39 q^{8} + 81 q^{9} - 55 q^{10} + 12 q^{11} - 126 q^{12} + 199 q^{13} - 87 q^{15} + 170 q^{16} + 116 q^{17} + 260 q^{19} + 324 q^{20} - 189 q^{21} - 265 q^{22} + 207 q^{23} + 117 q^{24} + 438 q^{25} - 270 q^{26} - 243 q^{27} + 294 q^{28} - 107 q^{29} + 165 q^{30} + 440 q^{31} - 802 q^{32} - 36 q^{33} + 295 q^{34} + 203 q^{35} + 378 q^{36} + 563 q^{37} - 569 q^{38} - 597 q^{39} - 640 q^{40} + 243 q^{41} + 435 q^{43} + 1025 q^{44} + 261 q^{45} - 133 q^{47} - 510 q^{48} + 441 q^{49} + 104 q^{50} - 348 q^{51} + 2693 q^{52} + 958 q^{53} + 1846 q^{55} - 273 q^{56} - 780 q^{57} + 2796 q^{58} + 538 q^{59} - 972 q^{60} + 1374 q^{61} + 1263 q^{62} + 567 q^{63} - 83 q^{64} + 745 q^{65} + 795 q^{66} + 752 q^{67} + 5593 q^{68} - 621 q^{69} - 385 q^{70} - 418 q^{71} - 351 q^{72} + 2406 q^{73} + 352 q^{74} - 1314 q^{75} + 2765 q^{76} + 84 q^{77} + 810 q^{78} - 486 q^{79} + 5709 q^{80} + 729 q^{81} + 2726 q^{82} + 106 q^{83} - 882 q^{84} + 4130 q^{85} - 2576 q^{86} + 321 q^{87} + 1270 q^{88} + 234 q^{89} - 495 q^{90} + 1393 q^{91} + 966 q^{92} - 1320 q^{93} + 4967 q^{94} - 3074 q^{95} + 2406 q^{96} + 2409 q^{97} + 108 q^{99}+O(q^{100}) \) 9 * q - 27 * q^3 + 42 * q^4 + 29 * q^5 + 63 * q^7 - 39 * q^8 + 81 * q^9 - 55 * q^10 + 12 * q^11 - 126 * q^12 + 199 * q^13 - 87 * q^15 + 170 * q^16 + 116 * q^17 + 260 * q^19 + 324 * q^20 - 189 * q^21 - 265 * q^22 + 207 * q^23 + 117 * q^24 + 438 * q^25 - 270 * q^26 - 243 * q^27 + 294 * q^28 - 107 * q^29 + 165 * q^30 + 440 * q^31 - 802 * q^32 - 36 * q^33 + 295 * q^34 + 203 * q^35 + 378 * q^36 + 563 * q^37 - 569 * q^38 - 597 * q^39 - 640 * q^40 + 243 * q^41 + 435 * q^43 + 1025 * q^44 + 261 * q^45 - 133 * q^47 - 510 * q^48 + 441 * q^49 + 104 * q^50 - 348 * q^51 + 2693 * q^52 + 958 * q^53 + 1846 * q^55 - 273 * q^56 - 780 * q^57 + 2796 * q^58 + 538 * q^59 - 972 * q^60 + 1374 * q^61 + 1263 * q^62 + 567 * q^63 - 83 * q^64 + 745 * q^65 + 795 * q^66 + 752 * q^67 + 5593 * q^68 - 621 * q^69 - 385 * q^70 - 418 * q^71 - 351 * q^72 + 2406 * q^73 + 352 * q^74 - 1314 * q^75 + 2765 * q^76 + 84 * q^77 + 810 * q^78 - 486 * q^79 + 5709 * q^80 + 729 * q^81 + 2726 * q^82 + 106 * q^83 - 882 * q^84 + 4130 * q^85 - 2576 * q^86 + 321 * q^87 + 1270 * q^88 + 234 * q^89 - 495 * q^90 + 1393 * q^91 + 966 * q^92 - 1320 * q^93 + 4967 * q^94 - 3074 * q^95 + 2406 * q^96 + 2409 * q^97 + 108 * q^99

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