LMFDB - Embedded newform 1441.4.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1441,4,Mod(1,1441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1441, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1441.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1441 = 11 \cdot 131 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1441.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:	$85.0217523183$
Analytic rank:	$1$
Dimension:	$77$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1441.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.64162 q^{2} -7.12045 q^{3} +23.8278 q^{4} +12.2922 q^{5} +40.1708 q^{6} +10.9151 q^{7} -89.2945 q^{8} +23.7008 q^{9} +O(q^{10})$	\(q-5.64162 q^{2} -7.12045 q^{3} +23.8278 q^{4} +12.2922 q^{5} +40.1708 q^{6} +10.9151 q^{7} -89.2945 q^{8} +23.7008 q^{9} -69.3477 q^{10} -11.0000 q^{11} -169.665 q^{12} -34.4337 q^{13} -61.5790 q^{14} -87.5258 q^{15} +313.143 q^{16} +116.026 q^{17} -133.711 q^{18} -17.4856 q^{19} +292.896 q^{20} -77.7206 q^{21} +62.0578 q^{22} +43.6875 q^{23} +635.817 q^{24} +26.0976 q^{25} +194.262 q^{26} +23.4916 q^{27} +260.084 q^{28} -23.3181 q^{29} +493.787 q^{30} -122.466 q^{31} -1052.28 q^{32} +78.3250 q^{33} -654.576 q^{34} +134.171 q^{35} +564.739 q^{36} +28.4397 q^{37} +98.6473 q^{38} +245.184 q^{39} -1097.62 q^{40} -14.4261 q^{41} +438.470 q^{42} +495.729 q^{43} -262.106 q^{44} +291.335 q^{45} -246.468 q^{46} -416.993 q^{47} -2229.72 q^{48} -223.860 q^{49} -147.233 q^{50} -826.160 q^{51} -820.482 q^{52} +215.603 q^{53} -132.531 q^{54} -135.214 q^{55} -974.661 q^{56} +124.506 q^{57} +131.552 q^{58} -888.606 q^{59} -2085.55 q^{60} -520.137 q^{61} +690.905 q^{62} +258.697 q^{63} +3431.39 q^{64} -423.266 q^{65} -441.879 q^{66} -194.531 q^{67} +2764.66 q^{68} -311.075 q^{69} -756.939 q^{70} -543.298 q^{71} -2116.35 q^{72} +686.401 q^{73} -160.446 q^{74} -185.827 q^{75} -416.645 q^{76} -120.066 q^{77} -1383.23 q^{78} -426.863 q^{79} +3849.21 q^{80} -807.193 q^{81} +81.3865 q^{82} -89.7343 q^{83} -1851.91 q^{84} +1426.22 q^{85} -2796.71 q^{86} +166.035 q^{87} +982.240 q^{88} +393.400 q^{89} -1643.60 q^{90} -375.849 q^{91} +1040.98 q^{92} +872.011 q^{93} +2352.52 q^{94} -214.937 q^{95} +7492.67 q^{96} +621.569 q^{97} +1262.93 q^{98} -260.709 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 77 q - 14 q^{2} - 10 q^{3} + 296 q^{4} - 42 q^{5} - 13 q^{6} - 59 q^{7} - 150 q^{8} + 541 q^{9}+O(q^{10}) $ 77 * q - 14 * q^2 - 10 * q^3 + 296 * q^4 - 42 * q^5 - 13 * q^6 - 59 * q^7 - 150 * q^8 + 541 * q^9	\( 77 q - 14 q^{2} - 10 q^{3} + 296 q^{4} - 42 q^{5} - 13 q^{6} - 59 q^{7} - 150 q^{8} + 541 q^{9} + 2 q^{10} - 847 q^{11} - 88 q^{12} - 20 q^{13} - 282 q^{14} - 330 q^{15} + 936 q^{16} - 56 q^{17} - 343 q^{18} - 157 q^{19} - 450 q^{20} - 122 q^{21} + 154 q^{22} - 764 q^{23} - 346 q^{24} + 1413 q^{25} - 408 q^{26} - 358 q^{27} - 228 q^{28} - 557 q^{29} - 267 q^{30} - 780 q^{31} - 1739 q^{32} + 110 q^{33} - 1104 q^{34} - 1254 q^{35} + 375 q^{36} - 541 q^{37} - 2133 q^{38} - 1458 q^{39} - 554 q^{40} - 1723 q^{41} - 5 q^{42} - 688 q^{43} - 3256 q^{44} - 1588 q^{45} + 276 q^{46} - 3086 q^{47} - 4280 q^{48} + 2452 q^{49} - 2234 q^{50} - 1570 q^{51} - 715 q^{52} - 1230 q^{53} - 5166 q^{54} + 462 q^{55} - 3203 q^{56} + 1024 q^{57} - 3016 q^{58} - 5408 q^{59} - 8221 q^{60} + 566 q^{61} - 3642 q^{62} - 3035 q^{63} + 1084 q^{64} - 1794 q^{65} + 143 q^{66} - 1925 q^{67} - 1105 q^{68} - 3710 q^{69} - 5875 q^{70} - 9614 q^{71} - 2198 q^{72} - 384 q^{73} - 2378 q^{74} - 3888 q^{75} - 2809 q^{76} + 649 q^{77} - 1731 q^{78} - 1086 q^{79} - 4357 q^{80} + 2329 q^{81} - 3167 q^{82} - 3045 q^{83} - 5359 q^{84} + 2582 q^{85} - 6468 q^{86} - 4432 q^{87} + 1650 q^{88} - 2831 q^{89} + 512 q^{90} - 6002 q^{91} - 7134 q^{92} - 4428 q^{93} + 1697 q^{94} - 10434 q^{95} + 195 q^{96} - 2506 q^{97} - 3435 q^{98} - 5951 q^{99}+O(q^{100}) \) 77 * q - 14 * q^2 - 10 * q^3 + 296 * q^4 - 42 * q^5 - 13 * q^6 - 59 * q^7 - 150 * q^8 + 541 * q^9 + 2 * q^10 - 847 * q^11 - 88 * q^12 - 20 * q^13 - 282 * q^14 - 330 * q^15 + 936 * q^16 - 56 * q^17 - 343 * q^18 - 157 * q^19 - 450 * q^20 - 122 * q^21 + 154 * q^22 - 764 * q^23 - 346 * q^24 + 1413 * q^25 - 408 * q^26 - 358 * q^27 - 228 * q^28 - 557 * q^29 - 267 * q^30 - 780 * q^31 - 1739 * q^32 + 110 * q^33 - 1104 * q^34 - 1254 * q^35 + 375 * q^36 - 541 * q^37 - 2133 * q^38 - 1458 * q^39 - 554 * q^40 - 1723 * q^41 - 5 * q^42 - 688 * q^43 - 3256 * q^44 - 1588 * q^45 + 276 * q^46 - 3086 * q^47 - 4280 * q^48 + 2452 * q^49 - 2234 * q^50 - 1570 * q^51 - 715 * q^52 - 1230 * q^53 - 5166 * q^54 + 462 * q^55 - 3203 * q^56 + 1024 * q^57 - 3016 * q^58 - 5408 * q^59 - 8221 * q^60 + 566 * q^61 - 3642 * q^62 - 3035 * q^63 + 1084 * q^64 - 1794 * q^65 + 143 * q^66 - 1925 * q^67 - 1105 * q^68 - 3710 * q^69 - 5875 * q^70 - 9614 * q^71 - 2198 * q^72 - 384 * q^73 - 2378 * q^74 - 3888 * q^75 - 2809 * q^76 + 649 * q^77 - 1731 * q^78 - 1086 * q^79 - 4357 * q^80 + 2329 * q^81 - 3167 * q^82 - 3045 * q^83 - 5359 * q^84 + 2582 * q^85 - 6468 * q^86 - 4432 * q^87 + 1650 * q^88 - 2831 * q^89 + 512 * q^90 - 6002 * q^91 - 7134 * q^92 - 4428 * q^93 + 1697 * q^94 - 10434 * q^95 + 195 * q^96 - 2506 * q^97 - 3435 * q^98 - 5951 * 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 $

$2$	−5.64162	−1.99461	−0.997306	−	0.0733507i	$-0.976631\pi$
$2$	−5.64162	−1.99461	−0.997306	+	0.0733507i	$0.976631\pi$
$3$	−7.12045	−1.37033	−0.685166	−	0.728387i	$-0.740270\pi$
$3$	−7.12045	−1.37033	−0.685166	+	0.728387i	$0.740270\pi$
$4$	23.8278	2.97848
$5$	12.2922	1.09945	0.549723	−	0.835347i	$-0.314733\pi$
$5$	12.2922	1.09945	0.549723	+	0.835347i	$0.314733\pi$
$6$	40.1708	2.73328
$7$	10.9151	0.589361	0.294681	−	0.955596i	$-0.404787\pi$
$7$	10.9151	0.589361	0.294681	+	0.955596i	$0.404787\pi$
$8$	−89.2945	−3.94630
$9$	23.7008	0.877808
$10$	−69.3477	−2.19297
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−169.665	−4.08150
$13$	−34.4337	−0.734631	−0.367316	−	0.930096i	$-0.619723\pi$
$13$	−34.4337	−0.734631	−0.367316	+	0.930096i	$0.619723\pi$
$14$	−61.5790	−1.17555
$15$	−87.5258	−1.50660
$16$	313.143	4.89286
$17$	116.026	1.65533	0.827663	−	0.561226i	$-0.189670\pi$
$17$	116.026	1.65533	0.827663	+	0.561226i	$0.189670\pi$
$18$	−133.711	−1.75089
$19$	−17.4856	−0.211131	−0.105565	−	0.994412i	$-0.533665\pi$
$19$	−17.4856	−0.211131	−0.105565	+	0.994412i	$0.533665\pi$
$20$	292.896	3.27468
$21$	−77.7206	−0.807621
$22$	62.0578	0.601398
$23$	43.6875	0.396064	0.198032	−	0.980196i	$-0.436545\pi$
$23$	43.6875	0.396064	0.198032	+	0.980196i	$0.436545\pi$
$24$	635.817	5.40774
$25$	26.0976	0.208781
$26$	194.262	1.46530
$27$	23.4916	0.167443
$28$	260.084	1.75540
$29$	−23.3181	−0.149312	−0.0746562	−	0.997209i	$-0.523786\pi$
$29$	−23.3181	−0.149312	−0.0746562	+	0.997209i	$0.523786\pi$
$30$	493.787	3.00509
$31$	−122.466	−0.709532	−0.354766	−	0.934955i	$-0.615439\pi$
$31$	−122.466	−0.709532	−0.354766	+	0.934955i	$0.615439\pi$
$32$	−1052.28	−5.81305
$33$	78.3250	0.413170
$34$	−654.576	−3.30173
$35$	134.171	0.647971
$36$	564.739	2.61453
$37$	28.4397	0.126364	0.0631819	−	0.998002i	$-0.479875\pi$
$37$	28.4397	0.126364	0.0631819	+	0.998002i	$0.479875\pi$
$38$	98.6473	0.421124
$39$	245.184	1.00669
$40$	−1097.62	−4.33874
$41$	−14.4261	−0.0549507	−0.0274754	−	0.999622i	$-0.508747\pi$
$41$	−14.4261	−0.0549507	−0.0274754	+	0.999622i	$0.508747\pi$
$42$	438.470	1.61089
$43$	495.729	1.75809	0.879046	−	0.476736i	$-0.158180\pi$
$43$	495.729	1.75809	0.879046	+	0.476736i	$0.158180\pi$
$44$	−262.106	−0.898045
$45$	291.335	0.965102
$46$	−246.468	−0.789994
$47$	−416.993	−1.29414	−0.647071	−	0.762429i	$-0.724006\pi$
$47$	−416.993	−1.29414	−0.647071	+	0.762429i	$0.724006\pi$
$48$	−2229.72	−6.70484
$49$	−223.860	−0.652653
$50$	−147.233	−0.416437
$51$	−826.160	−2.26835
$52$	−820.482	−2.18808
$53$	215.603	0.558779	0.279390	−	0.960178i	$-0.409868\pi$
$53$	215.603	0.558779	0.279390	+	0.960178i	$0.409868\pi$
$54$	−132.531	−0.333984
$55$	−135.214	−0.331495
$56$	−974.661	−2.32580
$57$	124.506	0.289319
$58$	131.552	0.297820
$59$	−888.606	−1.96079	−0.980396	−	0.197039i	$-0.936867\pi$
$59$	−888.606	−1.96079	−0.980396	+	0.197039i	$0.936867\pi$
$60$	−2085.55	−4.48739
$61$	−520.137	−1.09175	−0.545875	−	0.837867i	$-0.683802\pi$
$61$	−520.137	−1.09175	−0.545875	+	0.837867i	$0.683802\pi$
$62$	690.905	1.41524
$63$	258.697	0.517346
$64$	3431.39	6.70193
$65$	−423.266	−0.807687
$66$	−441.879	−0.824115
$67$	−194.531	−0.354712	−0.177356	−	0.984147i	$-0.556754\pi$
$67$	−194.531	−0.354712	−0.177356	+	0.984147i	$0.556754\pi$
$68$	2764.66	4.93035
$69$	−311.075	−0.542739
$70$	−756.939	−1.29245
$71$	−543.298	−0.908135	−0.454068	−	0.890967i	$-0.650028\pi$
$71$	−543.298	−0.908135	−0.454068	+	0.890967i	$0.650028\pi$
$72$	−2116.35	−3.46409
$73$	686.401	1.10051	0.550255	−	0.834997i	$-0.314531\pi$
$73$	686.401	1.10051	0.550255	+	0.834997i	$0.314531\pi$
$74$	−160.446	−0.252047
$75$	−185.827	−0.286099
$76$	−416.645	−0.628848
$77$	−120.066	−0.177699
$78$	−1383.23	−2.00795
$79$	−426.863	−0.607921	−0.303961	−	0.952685i	$-0.598309\pi$
$79$	−426.863	−0.607921	−0.303961	+	0.952685i	$0.598309\pi$
$80$	3849.21	5.37943
$81$	−807.193	−1.10726
$82$	81.3865	0.109605
$83$	−89.7343	−0.118670	−0.0593350	−	0.998238i	$-0.518898\pi$
$83$	−89.7343	−0.118670	−0.0593350	+	0.998238i	$0.518898\pi$
$84$	−1851.91	−2.40548
$85$	1426.22	1.81994
$86$	−2796.71	−3.50671
$87$	166.035	0.204607
$88$	982.240	1.18985
$89$	393.400	0.468543	0.234271	−	0.972171i	$-0.424730\pi$
$89$	393.400	0.468543	0.234271	+	0.972171i	$0.424730\pi$
$90$	−1643.60	−1.92501
$91$	−375.849	−0.432963
$92$	1040.98	1.17967
$93$	872.011	0.972294
$94$	2352.52	2.58131
$95$	−214.937	−0.232127
$96$	7492.67	7.96581
$97$	621.569	0.650626	0.325313	−	0.945606i	$-0.394530\pi$
$97$	621.569	0.650626	0.325313	+	0.945606i	$0.394530\pi$
$98$	1262.93	1.30179
$99$	−260.709	−0.264669
$100$	621.849	0.621849
$101$	863.712	0.850916	0.425458	−	0.904978i	$-0.360113\pi$
$101$	863.712	0.850916	0.425458	+	0.904978i	$0.360113\pi$
$102$	4660.88	4.52447
$103$	1101.94	1.05415	0.527073	−	0.849820i	$-0.323289\pi$
$103$	1101.94	1.05415	0.527073	+	0.849820i	$0.323289\pi$
$104$	3074.75	2.89907
$105$	−955.356	−0.887935
$106$	−1216.35	−1.11455
$107$	−1295.90	−1.17083	−0.585416	−	0.810733i	$-0.699069\pi$
$107$	−1295.90	−1.17083	−0.585416	+	0.810733i	$0.699069\pi$
$108$	559.755	0.498726
$109$	1501.51	1.31944	0.659720	−	0.751512i	$-0.270675\pi$
$109$	1501.51	1.31944	0.659720	+	0.751512i	$0.270675\pi$
$110$	762.825	0.661205
$111$	−202.504	−0.173160
$112$	3417.99	2.88366
$113$	−2380.65	−1.98188	−0.990941	−	0.134299i	$-0.957122\pi$
$113$	−2380.65	−1.98188	−0.990941	+	0.134299i	$0.957122\pi$
$114$	−702.413	−0.577079
$115$	537.014	0.435451
$116$	−555.619	−0.444724
$117$	−816.108	−0.644865
$118$	5013.18	3.91102
$119$	1266.44	0.975585
$120$	7815.58	5.94551
$121$	121.000	0.0909091
$122$	2934.41	2.17762
$123$	102.720	0.0753007
$124$	−2918.09	−2.11333
$125$	−1215.73	−0.869903
$126$	−1459.47	−1.03191
$127$	1376.96	0.962088	0.481044	−	0.876696i	$-0.340258\pi$
$127$	1376.96	0.962088	0.481044	+	0.876696i	$0.340258\pi$
$128$	−10940.4	−7.55471
$129$	−3529.82	−2.40917
$130$	2387.90	1.61102
$131$	131.000	0.0873704
$131$	131.000	0.0873704
$132$	1866.31	1.23062
$133$	−190.858	−0.124432
$134$	1097.47	0.707513
$135$	288.763	0.184095
$136$	−10360.5	−6.53241
$137$	−1714.92	−1.06946	−0.534730	−	0.845023i	$-0.679587\pi$
$137$	−1714.92	−1.06946	−0.534730	+	0.845023i	$0.679587\pi$
$138$	1754.96	1.08255
$139$	−1633.79	−0.996952	−0.498476	−	0.866903i	$-0.666107\pi$
$139$	−1633.79	−0.996952	−0.498476	+	0.866903i	$0.666107\pi$
$140$	3197.00	1.92997
$141$	2969.18	1.77340
$142$	3065.08	1.81138
$143$	378.771	0.221500
$144$	7421.74	4.29499
$145$	−286.630	−0.164161
$146$	−3872.41	−2.19509
$147$	1593.98	0.894351
$148$	677.657	0.376372
$149$	−464.560	−0.255424	−0.127712	−	0.991811i	$-0.540763\pi$
$149$	−464.560	−0.255424	−0.127712	+	0.991811i	$0.540763\pi$
$150$	1048.36	0.570656
$151$	1301.04	0.701174	0.350587	−	0.936530i	$-0.385982\pi$
$151$	1301.04	0.701174	0.350587	+	0.936530i	$0.385982\pi$
$152$	1561.37	0.833184
$153$	2749.92	1.45306
$154$	677.368	0.354441
$155$	−1505.37	−0.780092
$156$	5842.20	2.99840
$157$	915.012	0.465133	0.232567	−	0.972580i	$-0.425288\pi$
$157$	915.012	0.465133	0.232567	+	0.972580i	$0.425288\pi$
$158$	2408.19	1.21257
$159$	−1535.19	−0.765713
$160$	−12934.8	−6.39114
$161$	476.855	0.233425
$162$	4553.87	2.20856
$163$	−14.2692	−0.00685673	−0.00342836	−	0.999994i	$-0.501091\pi$
$163$	−14.2692	−0.00685673	−0.00342836	+	0.999994i	$0.501091\pi$
$164$	−343.743	−0.163669
$165$	962.784	0.454258
$166$	506.246	0.236701
$167$	−1934.39	−0.896331	−0.448165	−	0.893951i	$-0.647922\pi$
$167$	−1934.39	−0.896331	−0.448165	+	0.893951i	$0.647922\pi$
$168$	6940.03	3.18711
$169$	−1011.32	−0.460317
$170$	−8046.17	−3.63008
$171$	−414.424	−0.185332
$172$	11812.2	5.23644
$173$	3442.32	1.51280	0.756400	−	0.654109i	$-0.226956\pi$
$173$	3442.32	1.51280	0.756400	+	0.654109i	$0.226956\pi$
$174$	−936.707	−0.408112
$175$	284.858	0.123047
$176$	−3444.57	−1.47525
$177$	6327.28	2.68693
$178$	−2219.41	−0.934561
$179$	−809.650	−0.338079	−0.169039	−	0.985609i	$-0.554066\pi$
$179$	−809.650	−0.338079	−0.169039	+	0.985609i	$0.554066\pi$
$180$	6941.87	2.87454
$181$	−2320.92	−0.953107	−0.476554	−	0.879145i	$-0.658114\pi$
$181$	−2320.92	−0.953107	−0.476554	+	0.879145i	$0.658114\pi$
$182$	2120.39	0.863594
$183$	3703.61	1.49606
$184$	−3901.05	−1.56299
$185$	349.586	0.138930
$186$	−4919.55	−1.93935
$187$	−1276.29	−0.499100
$188$	−9936.04	−3.85458
$189$	256.414	0.0986846
$190$	1212.59	0.463003
$191$	573.920	0.217421	0.108710	−	0.994073i	$-0.465328\pi$
$191$	573.920	0.217421	0.108710	+	0.994073i	$0.465328\pi$
$192$	−24433.0	−9.18387
$193$	1965.16	0.732928	0.366464	−	0.930432i	$-0.380568\pi$
$193$	1965.16	0.732928	0.366464	+	0.930432i	$0.380568\pi$
$194$	−3506.65	−1.29775
$195$	3013.84	1.10680
$196$	−5334.10	−1.94391
$197$	−1660.73	−0.600618	−0.300309	−	0.953842i	$-0.597090\pi$
$197$	−1660.73	−0.600618	−0.300309	+	0.953842i	$0.597090\pi$
$198$	1470.82	0.527912
$199$	3059.56	1.08988	0.544941	−	0.838475i	$-0.316552\pi$
$199$	3059.56	1.08988	0.544941	+	0.838475i	$0.316552\pi$
$200$	−2330.37	−0.823911
$201$	1385.15	0.486073
$202$	−4872.73	−1.69725
$203$	−254.520	−0.0879989
$204$	−19685.6	−6.75622
$205$	−177.328	−0.0604153
$206$	−6216.70	−2.10261
$207$	1035.43	0.347668
$208$	−10782.7	−3.59444
$209$	192.342	0.0636583
$210$	5389.75	1.77109
$211$	5113.19	1.66828	0.834138	−	0.551555i	$-0.185965\pi$
$211$	5113.19	1.66828	0.834138	+	0.551555i	$0.185965\pi$
$212$	5137.34	1.66431
$213$	3868.53	1.24445
$214$	7310.95	2.33536
$215$	6093.59	1.93293
$216$	−2097.67	−0.660781
$217$	−1336.73	−0.418171
$218$	−8470.96	−2.63177
$219$	−4887.49	−1.50806
$220$	−3221.85	−0.987352
$221$	−3995.22	−1.21605
$222$	1142.45	0.345388
$223$	−559.360	−0.167971	−0.0839855	−	0.996467i	$-0.526765\pi$
$223$	−559.360	−0.167971	−0.0839855	+	0.996467i	$0.526765\pi$
$224$	−11485.7	−3.42599
$225$	618.534	0.183269
$226$	13430.7	3.95309
$227$	−3376.79	−0.987337	−0.493669	−	0.869650i	$-0.664344\pi$
$227$	−3376.79	−0.987337	−0.493669	+	0.869650i	$0.664344\pi$
$228$	2966.70	0.861730
$229$	1186.22	0.342304	0.171152	−	0.985245i	$-0.445251\pi$
$229$	1186.22	0.342304	0.171152	+	0.985245i	$0.445251\pi$
$230$	−3029.63	−0.868556
$231$	854.927	0.243507
$232$	2082.18	0.589231
$233$	3952.49	1.11132	0.555658	−	0.831411i	$-0.312467\pi$
$233$	3952.49	1.11132	0.555658	+	0.831411i	$0.312467\pi$
$234$	4604.17	1.28626
$235$	−5125.75	−1.42284
$236$	−21173.6	−5.84018
$237$	3039.45	0.833054
$238$	−7144.79	−1.94591
$239$	−2221.78	−0.601318	−0.300659	−	0.953732i	$-0.597207\pi$
$239$	−2221.78	−0.601318	−0.300659	+	0.953732i	$0.597207\pi$
$240$	−27408.1	−7.37160
$241$	−3727.28	−0.996247	−0.498123	−	0.867106i	$-0.665977\pi$
$241$	−3727.28	−0.996247	−0.498123	+	0.867106i	$0.665977\pi$
$242$	−682.636	−0.181328
$243$	5113.31	1.34987
$244$	−12393.7	−3.25175
$245$	−2751.73	−0.717557
$246$	−579.509	−0.150196
$247$	602.096	0.155103
$248$	10935.5	2.80003
$249$	638.948	0.162617
$250$	6858.66	1.73512
$251$	4900.71	1.23239	0.616195	−	0.787594i	$-0.288673\pi$
$251$	4900.71	1.23239	0.616195	+	0.787594i	$0.288673\pi$
$252$	6164.20	1.54091
$253$	−480.562	−0.119418
$254$	−7768.27	−1.91899
$255$	−10155.3	−2.49392
$256$	34270.3	8.36678
$257$	6406.74	1.55503	0.777513	−	0.628867i	$-0.216481\pi$
$257$	6406.74	1.55503	0.777513	+	0.628867i	$0.216481\pi$
$258$	19913.9	4.80536
$259$	310.423	0.0744740
$260$	−10085.5	−2.40568
$261$	−552.657	−0.131068
$262$	−739.052	−0.174270
$263$	−5865.65	−1.37525	−0.687626	−	0.726065i	$-0.741347\pi$
$263$	−5865.65	−1.37525	−0.687626	+	0.726065i	$0.741347\pi$
$264$	−6993.99	−1.63049
$265$	2650.23	0.614347
$266$	1076.75	0.248194
$267$	−2801.18	−0.642059
$268$	−4635.24	−1.05650
$269$	−5909.17	−1.33936	−0.669681	−	0.742649i	$-0.733569\pi$
$269$	−5909.17	−1.33936	−0.669681	+	0.742649i	$0.733569\pi$
$270$	−1629.09	−0.367198
$271$	−124.394	−0.0278834	−0.0139417	−	0.999903i	$-0.504438\pi$
$271$	−124.394	−0.0278834	−0.0139417	+	0.999903i	$0.504438\pi$
$272$	36332.8	8.09927
$273$	2676.21	0.593303
$274$	9674.95	2.13316
$275$	−287.073	−0.0629498
$276$	−7412.23	−1.61654
$277$	1765.97	0.383056	0.191528	−	0.981487i	$-0.438656\pi$
$277$	1765.97	0.383056	0.191528	+	0.981487i	$0.438656\pi$
$278$	9217.22	1.98853
$279$	−2902.54	−0.622833
$280$	−11980.7	−2.55709
$281$	2026.57	0.430232	0.215116	−	0.976588i	$-0.430987\pi$
$281$	2026.57	0.430232	0.215116	+	0.976588i	$0.430987\pi$
$282$	−16751.0	−3.53725
$283$	−9343.58	−1.96261	−0.981304	−	0.192462i	$-0.938353\pi$
$283$	−9343.58	−1.96261	−0.981304	+	0.192462i	$0.938353\pi$
$284$	−12945.6	−2.70486
$285$	1530.45	0.318090
$286$	−2136.88	−0.441806
$287$	−157.463	−0.0323858
$288$	−24939.8	−5.10275
$289$	8549.13	1.74010
$290$	1617.06	0.327437
$291$	−4425.85	−0.891574
$292$	16355.5	3.27784
$293$	4844.74	0.965981	0.482991	−	0.875626i	$-0.339551\pi$
$293$	4844.74	0.965981	0.482991	+	0.875626i	$0.339551\pi$
$294$	−8992.65	−1.78388
$295$	−10922.9	−2.15578
$296$	−2539.51	−0.498669
$297$	−258.408	−0.0504860
$298$	2620.87	0.509473
$299$	−1504.32	−0.290961
$300$	−4427.84	−0.852139
$301$	5410.95	1.03615
$302$	−7339.98	−1.39857
$303$	−6150.02	−1.16604
$304$	−5475.50	−1.03303
$305$	−6393.61	−1.20032
$306$	−15514.0	−2.89829
$307$	8558.20	1.59102	0.795509	−	0.605942i	$-0.207204\pi$
$307$	8558.20	1.59102	0.795509	+	0.605942i	$0.207204\pi$
$308$	−2860.92	−0.529273
$309$	−7846.28	−1.44453
$310$	8492.72	1.55598
$311$	−3250.32	−0.592632	−0.296316	−	0.955090i	$-0.595758\pi$
$311$	−3250.32	−0.592632	−0.296316	+	0.955090i	$0.595758\pi$
$312$	−21893.6	−3.97269
$313$	3172.88	0.572977	0.286488	−	0.958084i	$-0.407512\pi$
$313$	3172.88	0.572977	0.286488	+	0.958084i	$0.407512\pi$
$314$	−5162.15	−0.927760
$315$	3179.95	0.568794
$316$	−10171.2	−1.81068
$317$	7181.77	1.27245	0.636227	−	0.771502i	$-0.280494\pi$
$317$	7181.77	1.27245	0.636227	+	0.771502i	$0.280494\pi$
$318$	8660.94	1.52730
$319$	256.499	0.0450194
$320$	42179.3	7.36841
$321$	9227.36	1.60443
$322$	−2690.23	−0.465592
$323$	−2028.80	−0.349490
$324$	−19233.7	−3.29795
$325$	−898.638	−0.153377
$326$	80.5011	0.0136765
$327$	−10691.5	−1.80807
$328$	1288.17	0.216852
$329$	−4551.53	−0.762718
$330$	−5431.66	−0.906070
$331$	−5676.35	−0.942600	−0.471300	−	0.881973i	$-0.656215\pi$
$331$	−5676.35	−0.942600	−0.471300	+	0.881973i	$0.656215\pi$
$332$	−2138.17	−0.353456
$333$	674.045	0.110923
$334$	10913.1	1.78783
$335$	−2391.20	−0.389986
$336$	−24337.7	−3.95157
$337$	1479.76	0.239191	0.119596	−	0.992823i	$-0.461840\pi$
$337$	1479.76	0.239191	0.119596	+	0.992823i	$0.461840\pi$
$338$	5705.46	0.918154
$339$	16951.3	2.71583
$340$	33983.7	5.42065
$341$	1347.12	0.213932
$342$	2338.02	0.369666
$343$	−6187.35	−0.974010
$344$	−44265.9	−6.93796
$345$	−3823.78	−0.596712
$346$	−19420.2	−3.01745
$347$	6185.52	0.956933	0.478467	−	0.878106i	$-0.341193\pi$
$347$	6185.52	0.956933	0.478467	+	0.878106i	$0.341193\pi$
$348$	3956.26	0.609419
$349$	−9727.39	−1.49196	−0.745981	−	0.665967i	$-0.768019\pi$
$349$	−9727.39	−1.49196	−0.745981	+	0.665967i	$0.768019\pi$
$350$	−1607.06	−0.245432
$351$	−808.905	−0.123009
$352$	11575.0	1.75270
$353$	−9377.44	−1.41391	−0.706956	−	0.707258i	$-0.749932\pi$
$353$	−9377.44	−1.41391	−0.706956	+	0.707258i	$0.749932\pi$
$354$	−35696.1	−5.35939
$355$	−6678.31	−0.998445
$356$	9373.86	1.39554
$357$	−9017.65	−1.33688
$358$	4567.73	0.674336
$359$	−8200.62	−1.20560	−0.602802	−	0.797890i	$-0.705949\pi$
$359$	−8200.62	−1.20560	−0.602802	+	0.797890i	$0.705949\pi$
$360$	−26014.6	−3.80858
$361$	−6553.25	−0.955424
$362$	13093.7	1.90108
$363$	−861.575	−0.124576
$364$	−8955.66	−1.28957
$365$	8437.37	1.20995
$366$	−20894.3	−2.98406
$367$	3054.69	0.434478	0.217239	−	0.976118i	$-0.430295\pi$
$367$	3054.69	0.434478	0.217239	+	0.976118i	$0.430295\pi$
$368$	13680.4	1.93788
$369$	−341.911	−0.0482362
$370$	−1972.23	−0.277112
$371$	2353.33	0.329323
$372$	20778.1	2.89596
$373$	7425.26	1.03074	0.515369	−	0.856968i	$-0.327655\pi$
$373$	7425.26	1.03074	0.515369	+	0.856968i	$0.327655\pi$
$374$	7200.34	0.995510
$375$	8656.52	1.19205
$376$	37235.2	5.10707
$377$	802.929	0.109689
$378$	−1446.59	−0.196837
$379$	−11183.6	−1.51573	−0.757865	−	0.652411i	$-0.773758\pi$
$379$	−11183.6	−1.51573	−0.757865	+	0.652411i	$0.773758\pi$
$380$	−5121.47	−0.691384
$381$	−9804.56	−1.31838
$382$	−3237.83	−0.433670
$383$	−11496.4	−1.53379	−0.766894	−	0.641774i	$-0.778199\pi$
$383$	−11496.4	−1.53379	−0.766894	+	0.641774i	$0.778199\pi$
$384$	77900.5	10.3525
$385$	−1475.88	−0.195371
$386$	−11086.7	−1.46191
$387$	11749.2	1.54327
$388$	14810.6	1.93788
$389$	7490.02	0.976244	0.488122	−	0.872775i	$-0.337682\pi$
$389$	7490.02	0.976244	0.488122	+	0.872775i	$0.337682\pi$
$390$	−17002.9	−2.20763
$391$	5068.90	0.655615
$392$	19989.5	2.57556
$393$	−932.779	−0.119726
$394$	9369.18	1.19800
$395$	−5247.07	−0.668376
$396$	−6212.13	−0.788311
$397$	6749.82	0.853309	0.426655	−	0.904415i	$-0.359692\pi$
$397$	6749.82	0.853309	0.426655	+	0.904415i	$0.359692\pi$
$398$	−17260.9	−2.17389
$399$	1359.00	0.170513
$400$	8172.27	1.02153
$401$	−4405.23	−0.548596	−0.274298	−	0.961645i	$-0.588445\pi$
$401$	−4405.23	−0.548596	−0.274298	+	0.961645i	$0.588445\pi$
$402$	−7814.46	−0.969527
$403$	4216.95	0.521244
$404$	20580.4	2.53444
$405$	−9922.16	−1.21737
$406$	1435.90	0.175524
$407$	−312.837	−0.0381001
$408$	73771.6	8.95157
$409$	5569.62	0.673350	0.336675	−	0.941621i	$-0.390698\pi$
$409$	5569.62	0.673350	0.336675	+	0.941621i	$0.390698\pi$
$410$	1000.42	0.120505
$411$	12211.0	1.46551
$412$	26256.7	3.13975
$413$	−9699.25	−1.15561
$414$	−5841.50	−0.693463
$415$	−1103.03	−0.130471
$416$	36233.8	4.27045
$417$	11633.3	1.36616
$418$	−1085.12	−0.126974
$419$	2762.63	0.322108	0.161054	−	0.986946i	$-0.448511\pi$
$419$	2762.63	0.322108	0.161054	+	0.986946i	$0.448511\pi$
$420$	−22764.1	−2.64470
$421$	−7613.48	−0.881373	−0.440687	−	0.897661i	$-0.645265\pi$
$421$	−7613.48	−0.881373	−0.440687	+	0.897661i	$0.645265\pi$
$422$	−28846.6	−3.32757
$423$	−9883.08	−1.13601
$424$	−19252.1	−2.20511
$425$	3028.01	0.345600
$426$	−21824.7	−2.48219
$427$	−5677.36	−0.643435
$428$	−30878.4	−3.48730
$429$	−2697.02	−0.303528
$430$	−34377.7	−3.85544
$431$	−3176.41	−0.354994	−0.177497	−	0.984121i	$-0.556800\pi$
$431$	−3176.41	−0.354994	−0.177497	+	0.984121i	$0.556800\pi$
$432$	7356.24	0.819276
$433$	−3115.60	−0.345788	−0.172894	−	0.984940i	$-0.555312\pi$
$433$	−3115.60	−0.345788	−0.172894	+	0.984940i	$0.555312\pi$
$434$	7541.31	0.834089
$435$	2040.93	0.224955
$436$	35777.8	3.92992
$437$	−763.904	−0.0836212
$438$	27573.3	3.00800
$439$	1642.03	0.178519	0.0892594	−	0.996008i	$-0.471550\pi$
$439$	1642.03	0.178519	0.0892594	+	0.996008i	$0.471550\pi$
$440$	12073.9	1.30818
$441$	−5305.67	−0.572904
$442$	22539.5	2.42556
$443$	8654.86	0.928227	0.464114	−	0.885776i	$-0.346373\pi$
$443$	8654.86	0.928227	0.464114	+	0.885776i	$0.346373\pi$
$444$	−4825.22	−0.515754
$445$	4835.74	0.515137
$446$	3155.70	0.335037
$447$	3307.88	0.350016
$448$	37454.1	3.94986
$449$	−9716.76	−1.02130	−0.510648	−	0.859790i	$-0.670595\pi$
$449$	−9716.76	−1.02130	−0.510648	+	0.859790i	$0.670595\pi$
$450$	−3489.53	−0.365551
$451$	158.687	0.0165683
$452$	−56725.7	−5.90299
$453$	−9264.01	−0.960841
$454$	19050.6	1.96936
$455$	−4620.00	−0.476020
$456$	−11117.7	−1.14174
$457$	−7019.80	−0.718540	−0.359270	−	0.933234i	$-0.616974\pi$
$457$	−7019.80	−0.718540	−0.359270	+	0.933234i	$0.616974\pi$
$458$	−6692.19	−0.682763
$459$	2725.65	0.277173
$460$	12795.9	1.29698
$461$	7615.64	0.769405	0.384703	−	0.923041i	$-0.374304\pi$
$461$	7615.64	0.769405	0.384703	+	0.923041i	$0.374304\pi$
$462$	−4823.17	−0.485702
$463$	−12458.5	−1.25053	−0.625265	−	0.780413i	$-0.715009\pi$
$463$	−12458.5	−1.25053	−0.625265	+	0.780413i	$0.715009\pi$
$464$	−7301.89	−0.730564
$465$	10718.9	1.06898
$466$	−22298.4	−2.21664
$467$	−15641.3	−1.54988	−0.774939	−	0.632037i	$-0.782219\pi$
$467$	−15641.3	−1.54988	−0.774939	+	0.632037i	$0.782219\pi$
$468$	−19446.1	−1.92072
$469$	−2123.33	−0.209053
$470$	28917.5	2.83801
$471$	−6515.30	−0.637387
$472$	79347.7	7.73787
$473$	−5453.02	−0.530085
$474$	−17147.4	−1.66162
$475$	−456.333	−0.0440800
$476$	30176.6	2.90576
$477$	5109.96	0.490501
$478$	12534.4	1.19940
$479$	18499.3	1.76462	0.882311	−	0.470667i	$-0.155987\pi$
$479$	18499.3	1.76462	0.882311	+	0.470667i	$0.155987\pi$
$480$	92101.3	8.75798
$481$	−979.287	−0.0928308
$482$	21027.9	1.98713
$483$	−3395.42	−0.319869
$484$	2883.17	0.270771
$485$	7640.43	0.715328
$486$	−28847.3	−2.69247
$487$	−17226.8	−1.60292	−0.801458	−	0.598051i	$-0.795942\pi$
$487$	−17226.8	−1.60292	−0.801458	+	0.598051i	$0.795942\pi$
$488$	46445.4	4.30837
$489$	101.603	0.00939599
$490$	15524.2	1.43125
$491$	−8640.03	−0.794133	−0.397066	−	0.917790i	$-0.629972\pi$
$491$	−8640.03	−0.794133	−0.397066	+	0.917790i	$0.629972\pi$
$492$	2447.60	0.224281
$493$	−2705.51	−0.247161
$494$	−3396.80	−0.309371
$495$	−3204.68	−0.290989
$496$	−38349.3	−3.47164
$497$	−5930.17	−0.535220
$498$	−3604.70	−0.324359
$499$	1320.70	0.118482	0.0592411	−	0.998244i	$-0.481132\pi$
$499$	1320.70	0.118482	0.0592411	+	0.998244i	$0.481132\pi$
$500$	−28968.1	−2.59099
$501$	13773.7	1.22827
$502$	−27647.9	−2.45814
$503$	−12384.2	−1.09778	−0.548889	−	0.835895i	$-0.684949\pi$
$503$	−12384.2	−1.09778	−0.548889	+	0.835895i	$0.684949\pi$
$504$	−23100.3	−2.04160
$505$	10616.9	0.935536
$506$	2711.15	0.238192
$507$	7201.03	0.630787
$508$	32809.9	2.86556
$509$	−4840.79	−0.421541	−0.210770	−	0.977536i	$-0.567597\pi$
$509$	−4840.79	−0.421541	−0.210770	+	0.977536i	$0.567597\pi$
$510$	57292.4	4.97441
$511$	7492.16	0.648598
$512$	−105817.	−9.13377
$513$	−410.766	−0.0353524
$514$	−36144.4	−3.10167
$515$	13545.2	1.15898
$516$	−84107.8	−7.17566
$517$	4586.93	0.390199
$518$	−1751.29	−0.148547
$519$	−24510.8	−2.07304
$520$	37795.3	3.18737
$521$	22639.7	1.90377	0.951885	−	0.306456i	$-0.0991433\pi$
$521$	22639.7	1.90377	0.951885	+	0.306456i	$0.0991433\pi$
$522$	3117.88	0.261429
$523$	−14146.9	−1.18280	−0.591398	−	0.806379i	$-0.701424\pi$
$523$	−14146.9	−1.18280	−0.591398	+	0.806379i	$0.701424\pi$
$524$	3121.45	0.260231
$525$	−2028.32	−0.168616
$526$	33091.7	2.74310
$527$	−14209.3	−1.17451
$528$	24526.9	2.02158
$529$	−10258.4	−0.843133
$530$	−14951.6	−1.22538
$531$	−21060.7	−1.72120
$532$	−4547.73	−0.370619
$533$	496.745	0.0403685
$534$	15803.2	1.28066
$535$	−15929.4	−1.28727
$536$	17370.5	1.39980
$537$	5765.07	0.463280
$538$	33337.3	2.67151
$539$	2462.46	0.196782
$540$	6880.60	0.548322
$541$	9917.26	0.788126	0.394063	−	0.919083i	$-0.371069\pi$
$541$	9917.26	0.788126	0.394063	+	0.919083i	$0.371069\pi$
$542$	701.783	0.0556166
$543$	16526.0	1.30607
$544$	−122092.	−9.62250
$545$	18456.9	1.45065
$546$	−15098.2	−1.18341
$547$	1706.06	0.133356	0.0666782	−	0.997775i	$-0.478760\pi$
$547$	1706.06	0.133356	0.0666782	+	0.997775i	$0.478760\pi$
$548$	−40862.9	−3.18536
$549$	−12327.7	−0.958346
$550$	1619.56	0.125560
$551$	407.732	0.0315244
$552$	27777.3	2.14181
$553$	−4659.26	−0.358285
$554$	−9962.90	−0.764049
$555$	−2489.21	−0.190380
$556$	−38929.7	−2.96940
$557$	4195.77	0.319175	0.159587	−	0.987184i	$-0.448984\pi$
$557$	4195.77	0.319175	0.159587	+	0.987184i	$0.448984\pi$
$558$	16375.0	1.24231
$559$	−17069.8	−1.29155
$560$	42014.6	3.17043
$561$	9087.76	0.683932
$562$	−11433.2	−0.858147
$563$	−18833.7	−1.40985	−0.704924	−	0.709283i	$-0.749019\pi$
$563$	−18833.7	−1.40985	−0.704924	+	0.709283i	$0.749019\pi$
$564$	70749.1	5.28205
$565$	−29263.4	−2.17897
$566$	52712.9	3.91464
$567$	−8810.62	−0.652577
$568$	48513.5	3.58377
$569$	−13373.8	−0.985341	−0.492671	−	0.870216i	$-0.663979\pi$
$569$	−13373.8	−0.985341	−0.492671	+	0.870216i	$0.663979\pi$
$570$	−8634.19	−0.634467
$571$	−13532.5	−0.991799	−0.495900	−	0.868380i	$-0.665162\pi$
$571$	−13532.5	−0.991799	−0.495900	+	0.868380i	$0.665162\pi$
$572$	9025.30	0.659732
$573$	−4086.57	−0.297938
$574$	888.344	0.0645972
$575$	1140.14	0.0826905
$576$	81326.8	5.88301
$577$	1636.92	0.118104	0.0590520	−	0.998255i	$-0.481192\pi$
$577$	1636.92	0.118104	0.0590520	+	0.998255i	$0.481192\pi$
$578$	−48230.9	−3.47083
$579$	−13992.8	−1.00435
$580$	−6829.77	−0.488949
$581$	−979.461	−0.0699396
$582$	24969.0	1.77834
$583$	−2371.63	−0.168478
$584$	−61291.9	−4.34294
$585$	−10031.7	−0.708994
$586$	−27332.1	−1.92676
$587$	−8396.30	−0.590379	−0.295190	−	0.955439i	$-0.595383\pi$
$587$	−8396.30	−0.590379	−0.295190	+	0.955439i	$0.595383\pi$
$588$	37981.2	2.66381
$589$	2141.39	0.149804
$590$	61622.8	4.29995
$591$	11825.1	0.823046
$592$	8905.70	0.618280
$593$	−8093.52	−0.560474	−0.280237	−	0.959931i	$-0.590413\pi$
$593$	−8093.52	−0.560474	−0.280237	+	0.959931i	$0.590413\pi$
$594$	1457.84	0.100700
$595$	15567.3	1.07260
$596$	−11069.5	−0.760776
$597$	−21785.4	−1.49350
$598$	8486.82	0.580354
$599$	10289.3	0.701851	0.350925	−	0.936403i	$-0.385867\pi$
$599$	10289.3	0.701851	0.350925	+	0.936403i	$0.385867\pi$
$600$	16593.3	1.12903
$601$	3012.59	0.204470	0.102235	−	0.994760i	$-0.467401\pi$
$601$	3012.59	0.204470	0.102235	+	0.994760i	$0.467401\pi$
$602$	−30526.5	−2.06672
$603$	−4610.54	−0.311369
$604$	31001.0	2.08843
$605$	1487.35	0.0999496
$606$	34696.0	2.32579
$607$	−14078.1	−0.941375	−0.470687	−	0.882300i	$-0.655994\pi$
$607$	−14078.1	−0.941375	−0.470687	+	0.882300i	$0.655994\pi$
$608$	18399.7	1.22731
$609$	1812.30	0.120588
$610$	36070.3	2.39417
$611$	14358.6	0.950717
$612$	65524.7	4.32790
$613$	−21014.9	−1.38464	−0.692319	−	0.721592i	$-0.743411\pi$
$613$	−21014.9	−1.38464	−0.692319	+	0.721592i	$0.743411\pi$
$614$	−48282.1	−3.17346
$615$	1262.66	0.0827890
$616$	10721.3	0.701254
$617$	−17374.4	−1.13365	−0.566827	−	0.823837i	$-0.691829\pi$
$617$	−17374.4	−1.13365	−0.566827	+	0.823837i	$0.691829\pi$
$618$	44265.7	2.88128
$619$	10525.0	0.683418	0.341709	−	0.939806i	$-0.388994\pi$
$619$	10525.0	0.683418	0.341709	+	0.939806i	$0.388994\pi$
$620$	−35869.7	−2.32349
$621$	1026.29	0.0663182
$622$	18337.1	1.18207
$623$	4294.01	0.276141
$624$	76777.6	4.92558
$625$	−18206.1	−1.16519
$626$	−17900.2	−1.14287
$627$	−1369.56	−0.0872329
$628$	21802.7	1.38539
$629$	3299.76	0.209173
$630$	−17940.1	−1.13452
$631$	−2988.22	−0.188525	−0.0942625	−	0.995547i	$-0.530049\pi$
$631$	−2988.22	−0.188525	−0.0942625	+	0.995547i	$0.530049\pi$
$632$	38116.5	2.39904
$633$	−36408.2	−2.28609
$634$	−40516.8	−2.53805
$635$	16925.8	1.05776
$636$	−36580.2	−2.28066
$637$	7708.34	0.479459
$638$	−1447.07	−0.0897962
$639$	−12876.6	−0.797168
$640$	−134481.	−8.30599
$641$	6975.99	0.429852	0.214926	−	0.976630i	$-0.431049\pi$
$641$	6975.99	0.429852	0.214926	+	0.976630i	$0.431049\pi$
$642$	−52057.2	−3.20021
$643$	−12958.0	−0.794732	−0.397366	−	0.917660i	$-0.630076\pi$
$643$	−12958.0	−0.794732	−0.397366	+	0.917660i	$0.630076\pi$
$644$	11362.4	0.695251
$645$	−43389.1	−2.64875
$646$	11445.7	0.697097
$647$	1823.10	0.110778	0.0553890	−	0.998465i	$-0.482360\pi$
$647$	1823.10	0.110778	0.0553890	+	0.998465i	$0.482360\pi$
$648$	72077.9	4.36958
$649$	9774.67	0.591201
$650$	5069.77	0.305927
$651$	9518.11	0.573033
$652$	−340.003	−0.0204226
$653$	1362.54	0.0816543	0.0408271	−	0.999166i	$-0.487001\pi$
$653$	1362.54	0.0816543	0.0408271	+	0.999166i	$0.487001\pi$
$654$	60317.1	3.60640
$655$	1610.28	0.0960590
$656$	−4517.43	−0.268866
$657$	16268.3	0.966036
$658$	25678.0	1.52133
$659$	−26968.4	−1.59414	−0.797070	−	0.603887i	$-0.793618\pi$
$659$	−26968.4	−1.59414	−0.797070	+	0.603887i	$0.793618\pi$
$660$	22941.1	1.35300
$661$	9573.81	0.563355	0.281678	−	0.959509i	$-0.409109\pi$
$661$	9573.81	0.563355	0.281678	+	0.959509i	$0.409109\pi$
$662$	32023.8	1.88012
$663$	28447.8	1.66640
$664$	8012.78	0.468307
$665$	−2346.06	−0.136807
$666$	−3802.70	−0.221249
$667$	−1018.71	−0.0591372
$668$	−46092.2	−2.66970
$669$	3982.90	0.230176
$670$	13490.3	0.777872
$671$	5721.51	0.329175
$672$	81783.5	4.69474
$673$	9284.60	0.531790	0.265895	−	0.964002i	$-0.414332\pi$
$673$	9284.60	0.531790	0.265895	+	0.964002i	$0.414332\pi$
$674$	−8348.22	−0.477094
$675$	613.075	0.0349589
$676$	−24097.5	−1.37105
$677$	−2995.98	−0.170081	−0.0850405	−	0.996377i	$-0.527102\pi$
$677$	−2995.98	−0.170081	−0.0850405	+	0.996377i	$0.527102\pi$
$678$	−95632.7	−5.41704
$679$	6784.50	0.383454
$680$	−127353.	−7.18203
$681$	24044.3	1.35298
$682$	−7599.95	−0.426711
$683$	−23615.5	−1.32302	−0.661510	−	0.749936i	$-0.730084\pi$
$683$	−23615.5	−1.32302	−0.661510	+	0.749936i	$0.730084\pi$
$684$	−9874.83	−0.552008
$685$	−21080.2	−1.17581
$686$	34906.6	1.94277
$687$	−8446.41	−0.469069
$688$	155234.	8.60210
$689$	−7424.01	−0.410497
$690$	21572.3	1.19021
$691$	35071.9	1.93082	0.965410	−	0.260735i	$-0.0839650\pi$
$691$	35071.9	1.93082	0.965410	+	0.260735i	$0.0839650\pi$
$692$	82022.9	4.50584
$693$	−2845.67	−0.155986
$694$	−34896.3	−1.90871
$695$	−20082.9	−1.09610
$696$	−14826.0	−0.807442
$697$	−1673.81	−0.0909613
$698$	54878.2	2.97589
$699$	−28143.5	−1.52287
$700$	6787.56	0.366494
$701$	7131.66	0.384250	0.192125	−	0.981370i	$-0.438462\pi$
$701$	7131.66	0.384250	0.192125	+	0.981370i	$0.438462\pi$
$702$	4563.53	0.245355
$703$	−497.287	−0.0266793
$704$	−37745.3	−2.02071
$705$	36497.7	1.94976
$706$	52903.9	2.82021
$707$	9427.52	0.501497
$708$	150765.	8.00298
$709$	5438.50	0.288078	0.144039	−	0.989572i	$-0.453991\pi$
$709$	5438.50	0.288078	0.144039	+	0.989572i	$0.453991\pi$
$710$	37676.5	1.99151
$711$	−10117.0	−0.533638
$712$	−35128.4	−1.84901
$713$	−5350.22	−0.281020
$714$	50874.1	2.66655
$715$	4655.92	0.243527
$716$	−19292.2	−1.00696
$717$	15820.1	0.824006
$718$	46264.7	2.40471
$719$	−3873.07	−0.200891	−0.100446	−	0.994943i	$-0.532027\pi$
$719$	−3873.07	−0.200891	−0.100446	+	0.994943i	$0.532027\pi$
$720$	91229.4	4.72211
$721$	12027.8	0.621273
$722$	36970.9	1.90570
$723$	26539.9	1.36519
$724$	−55302.4	−2.83881
$725$	−608.545	−0.0311735
$726$	4860.67	0.248480
$727$	6068.42	0.309581	0.154790	−	0.987947i	$-0.450530\pi$
$727$	6068.42	0.309581	0.154790	+	0.987947i	$0.450530\pi$
$728$	33561.2	1.70860
$729$	−14614.8	−0.742510
$730$	−47600.4	−2.41338
$731$	57517.7	2.91022
$732$	88249.0	4.45598
$733$	−30664.6	−1.54519	−0.772595	−	0.634899i	$-0.781042\pi$
$733$	−30664.6	−1.54519	−0.772595	+	0.634899i	$0.781042\pi$
$734$	−17233.4	−0.866615
$735$	19593.5	0.983290
$736$	−45971.3	−2.30234
$737$	2139.84	0.106950
$738$	1928.93	0.0962125
$739$	−7584.66	−0.377545	−0.188773	−	0.982021i	$-0.560451\pi$
$739$	−7584.66	−0.377545	−0.188773	+	0.982021i	$0.560451\pi$
$740$	8329.88	0.413801
$741$	−4287.20	−0.212543
$742$	−13276.6	−0.656872
$743$	20534.0	1.01389	0.506943	−	0.861979i	$-0.330775\pi$
$743$	20534.0	1.01389	0.506943	+	0.861979i	$0.330775\pi$
$744$	−77865.8	−3.83696
$745$	−5710.45	−0.280825
$746$	−41890.4	−2.05592
$747$	−2126.78	−0.104170
$748$	−30411.2	−1.48656
$749$	−14144.9	−0.690043
$750$	−48836.7	−2.37769
$751$	−29893.3	−1.45249	−0.726245	−	0.687436i	$-0.758736\pi$
$751$	−29893.3	−1.45249	−0.726245	+	0.687436i	$0.758736\pi$
$752$	−130578.	−6.33206
$753$	−34895.2	−1.68878
$754$	−4529.82	−0.218788
$755$	15992.6	0.770903
$756$	6109.79	0.293930
$757$	11798.5	0.566480	0.283240	−	0.959049i	$-0.408591\pi$
$757$	11798.5	0.566480	0.283240	+	0.959049i	$0.408591\pi$
$758$	63093.5	3.02330
$759$	3421.82	0.163642
$760$	19192.7	0.916041
$761$	−22656.1	−1.07921	−0.539607	−	0.841917i	$-0.681427\pi$
$761$	−22656.1	−1.07921	−0.539607	+	0.841917i	$0.681427\pi$
$762$	55313.6	2.62966
$763$	16389.2	0.777627
$764$	13675.3	0.647583
$765$	33802.5	1.59756
$766$	64858.5	3.05931
$767$	30598.0	1.44046
$768$	−244020.	−11.4653
$769$	−12616.0	−0.591608	−0.295804	−	0.955249i	$-0.595587\pi$
$769$	−12616.0	−0.591608	−0.295804	+	0.955249i	$0.595587\pi$
$770$	8326.33	0.389689
$771$	−45618.9	−2.13090
$772$	46825.4	2.18301
$773$	−41730.6	−1.94172	−0.970858	−	0.239656i	$-0.922965\pi$
$773$	−41730.6	−1.94172	−0.970858	+	0.239656i	$0.922965\pi$
$774$	−66284.4	−3.07822
$775$	−3196.06	−0.148137
$776$	−55502.7	−2.56757
$777$	−2210.35	−0.102054
$778$	−42255.8	−1.94723
$779$	252.250	0.0116018
$780$	71813.3	3.29658
$781$	5976.28	0.273813
$782$	−28596.8	−1.30770
$783$	−547.780	−0.0250013
$784$	−70100.2	−3.19334
$785$	11247.5	0.511389
$786$	5262.38	0.238808
$787$	−32124.1	−1.45502	−0.727511	−	0.686096i	$-0.759323\pi$
$787$	−32124.1	−1.45502	−0.727511	+	0.686096i	$0.759323\pi$
$788$	−39571.5	−1.78893
$789$	41766.1	1.88455
$790$	29601.9	1.33315
$791$	−25985.1	−1.16804
$792$	23279.9	1.04446
$793$	17910.3	0.802033
$794$	−38079.9	−1.70202
$795$	−18870.8	−0.841860
$796$	72902.6	3.24619
$797$	−11062.7	−0.491669	−0.245834	−	0.969312i	$-0.579062\pi$
$797$	−11062.7	−0.491669	−0.245834	+	0.969312i	$0.579062\pi$
$798$	−7666.93	−0.340108
$799$	−48382.2	−2.14223
$800$	−27461.8	−1.21365
$801$	9323.90	0.411291
$802$	24852.6	1.09424
$803$	−7550.41	−0.331816
$804$	33005.0	1.44776
$805$	5861.58	0.256638
$806$	−23790.4	−1.03968
$807$	42075.9	1.83537
$808$	−77124.7	−3.35797
$809$	16738.0	0.727411	0.363706	−	0.931514i	$-0.381511\pi$
$809$	16738.0	0.727411	0.363706	+	0.931514i	$0.381511\pi$
$810$	55977.0	2.42819
$811$	26909.6	1.16513	0.582566	−	0.812783i	$-0.302049\pi$
$811$	26909.6	1.16513	0.582566	+	0.812783i	$0.302049\pi$
$812$	−6064.65	−0.262103
$813$	885.742	0.0382095
$814$	1764.91	0.0759950
$815$	−175.399	−0.00753860
$816$	−258706.	−11.0987
$817$	−8668.15	−0.371187
$818$	−31421.7	−1.34307
$819$	−8907.92	−0.380059
$820$	−4225.35	−0.179946
$821$	−19470.2	−0.827665	−0.413833	−	0.910353i	$-0.635810\pi$
$821$	−19470.2	−0.827665	−0.413833	+	0.910353i	$0.635810\pi$
$822$	−68890.0	−2.92313
$823$	−30665.5	−1.29883	−0.649413	−	0.760436i	$-0.724985\pi$
$823$	−30665.5	−1.29883	−0.649413	+	0.760436i	$0.724985\pi$
$824$	−98396.9	−4.15997
$825$	2044.09	0.0862620
$826$	54719.4	2.30500
$827$	45680.4	1.92075	0.960376	−	0.278707i	$-0.0899059\pi$
$827$	45680.4	1.92075	0.960376	+	0.278707i	$0.0899059\pi$
$828$	24672.0	1.03552
$829$	16135.6	0.676011	0.338005	−	0.941144i	$-0.390248\pi$
$829$	16135.6	0.676011	0.338005	+	0.941144i	$0.390248\pi$
$830$	6222.87	0.260240
$831$	−12574.5	−0.524914
$832$	−118156.	−4.92345
$833$	−25973.7	−1.08035
$834$	−65630.8	−2.72495
$835$	−23777.8	−0.985467
$836$	4583.09	0.189605
$837$	−2876.92	−0.118806
$838$	−15585.7	−0.642482
$839$	−35902.8	−1.47735	−0.738677	−	0.674059i	$-0.764549\pi$
$839$	−35902.8	−1.47735	−0.738677	+	0.674059i	$0.764549\pi$
$840$	85308.0	3.50406
$841$	−23845.3	−0.977706
$842$	42952.3	1.75800
$843$	−14430.1	−0.589561
$844$	121836.	4.96893
$845$	−12431.3	−0.506094
$846$	55756.6	2.26590
$847$	1320.73	0.0535783
$848$	67514.4	2.73403
$849$	66530.5	2.68942
$850$	−17082.9	−0.689338
$851$	1242.46	0.0500482
$852$	92178.6	3.70656
$853$	35471.8	1.42384	0.711918	−	0.702263i	$-0.247827\pi$
$853$	35471.8	1.42384	0.711918	+	0.702263i	$0.247827\pi$
$854$	32029.5	1.28340
$855$	−5094.17	−0.203763
$856$	115716.	4.62045
$857$	−22360.6	−0.891275	−0.445637	−	0.895214i	$-0.647023\pi$
$857$	−22360.6	−0.891275	−0.445637	+	0.895214i	$0.647023\pi$
$858$	15215.6	0.605420
$859$	−23585.5	−0.936817	−0.468408	−	0.883512i	$-0.655172\pi$
$859$	−23585.5	−0.936817	−0.468408	+	0.883512i	$0.655172\pi$
$860$	145197.	5.75718
$861$	1121.21	0.0443793
$862$	17920.1	0.708075
$863$	−13982.1	−0.551514	−0.275757	−	0.961227i	$-0.588928\pi$
$863$	−13982.1	−0.551514	−0.275757	+	0.961227i	$0.588928\pi$
$864$	−24719.7	−0.973357
$865$	42313.5	1.66324
$866$	17577.0	0.689713
$867$	−60873.7	−2.38452
$868$	−31851.3	−1.24551
$869$	4695.49	0.183295
$870$	−11514.2	−0.448697
$871$	6698.42	0.260582
$872$	−134077.	−5.20690
$873$	14731.7	0.571125
$874$	4309.65	0.166792
$875$	−13269.8	−0.512687
$876$	−116458.	−4.49173
$877$	32352.0	1.24567	0.622833	−	0.782355i	$-0.285982\pi$
$877$	32352.0	1.24567	0.622833	+	0.782355i	$0.285982\pi$
$878$	−9263.69	−0.356076
$879$	−34496.7	−1.32371
$880$	−42341.3	−1.62196
$881$	−9422.40	−0.360328	−0.180164	−	0.983637i	$-0.557663\pi$
$881$	−9422.40	−0.360328	−0.180164	+	0.983637i	$0.557663\pi$
$882$	29932.5	1.14272
$883$	47577.7	1.81327	0.906635	−	0.421917i	$-0.138643\pi$
$883$	47577.7	1.81327	0.906635	+	0.421917i	$0.138643\pi$
$884$	−95197.5	−3.62199
$885$	77776.0	2.95414
$886$	−48827.4	−1.85145
$887$	10532.3	0.398692	0.199346	−	0.979929i	$-0.436118\pi$
$887$	10532.3	0.398692	0.199346	+	0.979929i	$0.436118\pi$
$888$	18082.5	0.683342
$889$	15029.7	0.567018
$890$	−27281.4	−1.02750
$891$	8879.13	0.333852
$892$	−13328.3	−0.500298
$893$	7291.40	0.273233
$894$	−18661.8	−0.698147
$895$	−9952.36	−0.371699
$896$	−119416.	−4.45245
$897$	10711.5	0.398713
$898$	54818.2	2.03709
$899$	2855.66	0.105942
$900$	14738.3	0.545864
$901$	25015.6	0.924962
$902$	−895.252	−0.0330473
$903$	−38528.4	−1.41987
$904$	212579.	7.82110
$905$	−28529.1	−1.04789
$906$	52264.0	1.91651
$907$	41812.7	1.53072	0.765362	−	0.643600i	$-0.222560\pi$
$907$	41812.7	1.53072	0.765362	+	0.643600i	$0.222560\pi$
$908$	−80461.6	−2.94076
$909$	20470.7	0.746941
$910$	26064.3	0.949474
$911$	17118.8	0.622579	0.311290	−	0.950315i	$-0.399239\pi$
$911$	17118.8	0.622579	0.311290	+	0.950315i	$0.399239\pi$
$912$	38988.1	1.41560
$913$	987.077	0.0357804
$914$	39603.0	1.43321
$915$	45525.4	1.64483
$916$	28265.0	1.01954
$917$	1429.88	0.0514927
$918$	−15377.1	−0.552853
$919$	−9482.48	−0.340368	−0.170184	−	0.985412i	$-0.554436\pi$
$919$	−9482.48	−0.340368	−0.170184	+	0.985412i	$0.554436\pi$
$920$	−47952.4	−1.71842
$921$	−60938.3	−2.18022
$922$	−42964.5	−1.53467
$923$	18707.8	0.667144
$924$	20371.1	0.725280
$925$	742.208	0.0263823
$926$	70286.0	2.49432
$927$	26116.8	0.925338
$928$	24537.0	0.867961
$929$	39495.4	1.39484	0.697418	−	0.716665i	$-0.254332\pi$
$929$	39495.4	1.39484	0.697418	+	0.716665i	$0.254332\pi$
$930$	−60472.0	−2.13221
$931$	3914.34	0.137795
$932$	94179.3	3.31003
$933$	23143.7	0.812103
$934$	88242.2	3.09140
$935$	−15688.4	−0.548733
$936$	72874.0	2.54483
$937$	37081.0	1.29283	0.646416	−	0.762985i	$-0.276267\pi$
$937$	37081.0	1.29283	0.646416	+	0.762985i	$0.276267\pi$
$938$	11979.0	0.416981
$939$	−22592.3	−0.785168
$940$	−122136.	−4.23790
$941$	−33455.2	−1.15899	−0.579494	−	0.814977i	$-0.696750\pi$
$941$	−33455.2	−1.15899	−0.579494	+	0.814977i	$0.696750\pi$
$942$	36756.8	1.27134
$943$	−630.240	−0.0217640
$944$	−278261.	−9.59387
$945$	3151.89	0.108498
$946$	30763.9	1.05731
$947$	−52718.4	−1.80899	−0.904497	−	0.426480i	$-0.859753\pi$
$947$	−52718.4	−1.80899	−0.904497	+	0.426480i	$0.859753\pi$
$948$	72423.6	2.48123
$949$	−23635.4	−0.808468
$950$	2574.46	0.0879225
$951$	−51137.4	−1.74368
$952$	−113086.	−3.84995
$953$	23838.2	0.810277	0.405138	−	0.914255i	$-0.367223\pi$
$953$	23838.2	0.810277	0.405138	+	0.914255i	$0.367223\pi$
$954$	−28828.4	−0.978359
$955$	7054.72	0.239042
$956$	−52940.2	−1.79101
$957$	−1826.39	−0.0616914
$958$	−104366.	−3.51974
$959$	−18718.6	−0.630298
$960$	−300335.	−10.0972
$961$	−14793.1	−0.496564
$962$	5524.76	0.185161
$963$	−30713.8	−1.02777
$964$	−88813.1	−2.96730
$965$	24156.1	0.805815
$966$	19155.7	0.638016
$967$	−16761.1	−0.557394	−0.278697	−	0.960379i	$-0.589902\pi$
$967$	−16761.1	−0.557394	−0.278697	+	0.960379i	$0.589902\pi$
$968$	−10804.6	−0.358754
$969$	14445.9	0.478917
$970$	−43104.4	−1.42680
$971$	−1930.06	−0.0637884	−0.0318942	−	0.999491i	$-0.510154\pi$
$971$	−1930.06	−0.0637884	−0.0318942	+	0.999491i	$0.510154\pi$
$972$	121839.	4.02056
$973$	−17833.0	−0.587565
$974$	97186.9	3.19720
$975$	6398.71	0.210177
$976$	−162877.	−5.34177
$977$	21695.1	0.710427	0.355213	−	0.934785i	$-0.384408\pi$
$977$	21695.1	0.710427	0.355213	+	0.934785i	$0.384408\pi$
$978$	−573.204	−0.0187414
$979$	−4327.40	−0.141271
$980$	−65567.7	−2.13723
$981$	35587.1	1.15821
$982$	48743.7	1.58399
$983$	−58946.4	−1.91261	−0.956306	−	0.292369i	$-0.905556\pi$
$983$	−58946.4	−1.91261	−0.956306	+	0.292369i	$0.905556\pi$
$984$	−9172.37	−0.297159
$985$	−20413.9	−0.660347
$986$	15263.5	0.492989
$987$	32409.0	1.04518
$988$	14346.6	0.461971
$989$	21657.2	0.696317
$990$	18079.6	0.580411
$991$	14177.6	0.454458	0.227229	−	0.973841i	$-0.427033\pi$
$991$	14177.6	0.454458	0.227229	+	0.973841i	$0.427033\pi$
$992$	128868.	4.12455
$993$	40418.2	1.29167
$994$	33455.7	1.06756
$995$	37608.6	1.19827
$996$	15224.8	0.484352
$997$	−45727.3	−1.45256	−0.726278	−	0.687401i	$-0.758752\pi$
$997$	−45727.3	−1.45256	−0.726278	+	0.687401i	$0.758752\pi$
$998$	−7450.87	−0.236326
$999$	668.096	0.0211588

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.4.a.a.1.1	✓	77

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.4.a.a.1.1	✓	77	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1441 = 11 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1441.a (trivial)

\(f(q)\)	\(=\)	\(q-5.64162 q^{2} -7.12045 q^{3} +23.8278 q^{4} +12.2922 q^{5} +40.1708 q^{6} +10.9151 q^{7} -89.2945 q^{8} +23.7008 q^{9} +O(q^{10})\)	\(q-5.64162 q^{2} -7.12045 q^{3} +23.8278 q^{4} +12.2922 q^{5} +40.1708 q^{6} +10.9151 q^{7} -89.2945 q^{8} +23.7008 q^{9} -69.3477 q^{10} -11.0000 q^{11} -169.665 q^{12} -34.4337 q^{13} -61.5790 q^{14} -87.5258 q^{15} +313.143 q^{16} +116.026 q^{17} -133.711 q^{18} -17.4856 q^{19} +292.896 q^{20} -77.7206 q^{21} +62.0578 q^{22} +43.6875 q^{23} +635.817 q^{24} +26.0976 q^{25} +194.262 q^{26} +23.4916 q^{27} +260.084 q^{28} -23.3181 q^{29} +493.787 q^{30} -122.466 q^{31} -1052.28 q^{32} +78.3250 q^{33} -654.576 q^{34} +134.171 q^{35} +564.739 q^{36} +28.4397 q^{37} +98.6473 q^{38} +245.184 q^{39} -1097.62 q^{40} -14.4261 q^{41} +438.470 q^{42} +495.729 q^{43} -262.106 q^{44} +291.335 q^{45} -246.468 q^{46} -416.993 q^{47} -2229.72 q^{48} -223.860 q^{49} -147.233 q^{50} -826.160 q^{51} -820.482 q^{52} +215.603 q^{53} -132.531 q^{54} -135.214 q^{55} -974.661 q^{56} +124.506 q^{57} +131.552 q^{58} -888.606 q^{59} -2085.55 q^{60} -520.137 q^{61} +690.905 q^{62} +258.697 q^{63} +3431.39 q^{64} -423.266 q^{65} -441.879 q^{66} -194.531 q^{67} +2764.66 q^{68} -311.075 q^{69} -756.939 q^{70} -543.298 q^{71} -2116.35 q^{72} +686.401 q^{73} -160.446 q^{74} -185.827 q^{75} -416.645 q^{76} -120.066 q^{77} -1383.23 q^{78} -426.863 q^{79} +3849.21 q^{80} -807.193 q^{81} +81.3865 q^{82} -89.7343 q^{83} -1851.91 q^{84} +1426.22 q^{85} -2796.71 q^{86} +166.035 q^{87} +982.240 q^{88} +393.400 q^{89} -1643.60 q^{90} -375.849 q^{91} +1040.98 q^{92} +872.011 q^{93} +2352.52 q^{94} -214.937 q^{95} +7492.67 q^{96} +621.569 q^{97} +1262.93 q^{98} -260.709 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 77 q - 14 q^{2} - 10 q^{3} + 296 q^{4} - 42 q^{5} - 13 q^{6} - 59 q^{7} - 150 q^{8} + 541 q^{9}+O(q^{10}) \) 77 * q - 14 * q^2 - 10 * q^3 + 296 * q^4 - 42 * q^5 - 13 * q^6 - 59 * q^7 - 150 * q^8 + 541 * q^9	\( 77 q - 14 q^{2} - 10 q^{3} + 296 q^{4} - 42 q^{5} - 13 q^{6} - 59 q^{7} - 150 q^{8} + 541 q^{9} + 2 q^{10} - 847 q^{11} - 88 q^{12} - 20 q^{13} - 282 q^{14} - 330 q^{15} + 936 q^{16} - 56 q^{17} - 343 q^{18} - 157 q^{19} - 450 q^{20} - 122 q^{21} + 154 q^{22} - 764 q^{23} - 346 q^{24} + 1413 q^{25} - 408 q^{26} - 358 q^{27} - 228 q^{28} - 557 q^{29} - 267 q^{30} - 780 q^{31} - 1739 q^{32} + 110 q^{33} - 1104 q^{34} - 1254 q^{35} + 375 q^{36} - 541 q^{37} - 2133 q^{38} - 1458 q^{39} - 554 q^{40} - 1723 q^{41} - 5 q^{42} - 688 q^{43} - 3256 q^{44} - 1588 q^{45} + 276 q^{46} - 3086 q^{47} - 4280 q^{48} + 2452 q^{49} - 2234 q^{50} - 1570 q^{51} - 715 q^{52} - 1230 q^{53} - 5166 q^{54} + 462 q^{55} - 3203 q^{56} + 1024 q^{57} - 3016 q^{58} - 5408 q^{59} - 8221 q^{60} + 566 q^{61} - 3642 q^{62} - 3035 q^{63} + 1084 q^{64} - 1794 q^{65} + 143 q^{66} - 1925 q^{67} - 1105 q^{68} - 3710 q^{69} - 5875 q^{70} - 9614 q^{71} - 2198 q^{72} - 384 q^{73} - 2378 q^{74} - 3888 q^{75} - 2809 q^{76} + 649 q^{77} - 1731 q^{78} - 1086 q^{79} - 4357 q^{80} + 2329 q^{81} - 3167 q^{82} - 3045 q^{83} - 5359 q^{84} + 2582 q^{85} - 6468 q^{86} - 4432 q^{87} + 1650 q^{88} - 2831 q^{89} + 512 q^{90} - 6002 q^{91} - 7134 q^{92} - 4428 q^{93} + 1697 q^{94} - 10434 q^{95} + 195 q^{96} - 2506 q^{97} - 3435 q^{98} - 5951 q^{99}+O(q^{100}) \) 77 * q - 14 * q^2 - 10 * q^3 + 296 * q^4 - 42 * q^5 - 13 * q^6 - 59 * q^7 - 150 * q^8 + 541 * q^9 + 2 * q^10 - 847 * q^11 - 88 * q^12 - 20 * q^13 - 282 * q^14 - 330 * q^15 + 936 * q^16 - 56 * q^17 - 343 * q^18 - 157 * q^19 - 450 * q^20 - 122 * q^21 + 154 * q^22 - 764 * q^23 - 346 * q^24 + 1413 * q^25 - 408 * q^26 - 358 * q^27 - 228 * q^28 - 557 * q^29 - 267 * q^30 - 780 * q^31 - 1739 * q^32 + 110 * q^33 - 1104 * q^34 - 1254 * q^35 + 375 * q^36 - 541 * q^37 - 2133 * q^38 - 1458 * q^39 - 554 * q^40 - 1723 * q^41 - 5 * q^42 - 688 * q^43 - 3256 * q^44 - 1588 * q^45 + 276 * q^46 - 3086 * q^47 - 4280 * q^48 + 2452 * q^49 - 2234 * q^50 - 1570 * q^51 - 715 * q^52 - 1230 * q^53 - 5166 * q^54 + 462 * q^55 - 3203 * q^56 + 1024 * q^57 - 3016 * q^58 - 5408 * q^59 - 8221 * q^60 + 566 * q^61 - 3642 * q^62 - 3035 * q^63 + 1084 * q^64 - 1794 * q^65 + 143 * q^66 - 1925 * q^67 - 1105 * q^68 - 3710 * q^69 - 5875 * q^70 - 9614 * q^71 - 2198 * q^72 - 384 * q^73 - 2378 * q^74 - 3888 * q^75 - 2809 * q^76 + 649 * q^77 - 1731 * q^78 - 1086 * q^79 - 4357 * q^80 + 2329 * q^81 - 3167 * q^82 - 3045 * q^83 - 5359 * q^84 + 2582 * q^85 - 6468 * q^86 - 4432 * q^87 + 1650 * q^88 - 2831 * q^89 + 512 * q^90 - 6002 * q^91 - 7134 * q^92 - 4428 * q^93 + 1697 * q^94 - 10434 * q^95 + 195 * q^96 - 2506 * q^97 - 3435 * q^98 - 5951 * q^99

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