LMFDB - Embedded newform 201.4.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,4,Mod(1,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, 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("201.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	201.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:	$11.8593839112$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 28x^{4} + 22x^{3} + 202x^{2} - 96x - 384 $ x^6 - x^5 - 28x^4 + 22x^3 + 202x^2 - 96x - 384
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-4.17870$ of defining polynomial
Character	$\chi$	$=$	201.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.17870 q^{2} +3.00000 q^{3} +18.8190 q^{4} +17.1025 q^{5} -15.5361 q^{6} -19.8930 q^{7} -56.0282 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-5.17870 q^{2} +3.00000 q^{3} +18.8190 q^{4} +17.1025 q^{5} -15.5361 q^{6} -19.8930 q^{7} -56.0282 q^{8} +9.00000 q^{9} -88.5686 q^{10} -47.5262 q^{11} +56.4569 q^{12} -63.9393 q^{13} +103.020 q^{14} +51.3074 q^{15} +139.602 q^{16} +10.7343 q^{17} -46.6083 q^{18} -133.613 q^{19} +321.851 q^{20} -59.6790 q^{21} +246.124 q^{22} +122.631 q^{23} -168.084 q^{24} +167.494 q^{25} +331.123 q^{26} +27.0000 q^{27} -374.365 q^{28} -161.568 q^{29} -265.706 q^{30} -228.530 q^{31} -274.729 q^{32} -142.579 q^{33} -55.5896 q^{34} -340.219 q^{35} +169.371 q^{36} -273.765 q^{37} +691.942 q^{38} -191.818 q^{39} -958.220 q^{40} +156.472 q^{41} +309.060 q^{42} +414.336 q^{43} -894.394 q^{44} +153.922 q^{45} -635.069 q^{46} -215.040 q^{47} +418.805 q^{48} +52.7308 q^{49} -867.404 q^{50} +32.2028 q^{51} -1203.27 q^{52} +674.981 q^{53} -139.825 q^{54} -812.815 q^{55} +1114.57 q^{56} -400.839 q^{57} +836.714 q^{58} -577.322 q^{59} +965.552 q^{60} +245.936 q^{61} +1183.49 q^{62} -179.037 q^{63} +305.930 q^{64} -1093.52 q^{65} +738.372 q^{66} -67.0000 q^{67} +202.008 q^{68} +367.893 q^{69} +1761.89 q^{70} -325.388 q^{71} -504.253 q^{72} +285.617 q^{73} +1417.75 q^{74} +502.483 q^{75} -2514.46 q^{76} +945.438 q^{77} +993.368 q^{78} -298.664 q^{79} +2387.53 q^{80} +81.0000 q^{81} -810.321 q^{82} +92.1606 q^{83} -1123.10 q^{84} +183.583 q^{85} -2145.72 q^{86} -484.705 q^{87} +2662.81 q^{88} -871.095 q^{89} -797.117 q^{90} +1271.94 q^{91} +2307.79 q^{92} -685.589 q^{93} +1113.63 q^{94} -2285.11 q^{95} -824.188 q^{96} +1304.42 q^{97} -273.077 q^{98} -427.736 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 5 q^{2} + 18 q^{3} + 13 q^{4} - 12 q^{5} - 15 q^{6} - 62 q^{7} - 75 q^{8} + 54 q^{9}+O(q^{10}) $ 6 * q - 5 * q^2 + 18 * q^3 + 13 * q^4 - 12 * q^5 - 15 * q^6 - 62 * q^7 - 75 * q^8 + 54 * q^9	\( 6 q - 5 q^{2} + 18 q^{3} + 13 q^{4} - 12 q^{5} - 15 q^{6} - 62 q^{7} - 75 q^{8} + 54 q^{9} - 111 q^{10} - 72 q^{11} + 39 q^{12} - 192 q^{13} + 3 q^{14} - 36 q^{15} - 27 q^{16} - 100 q^{17} - 45 q^{18} - 266 q^{19} + 255 q^{20} - 186 q^{21} + 44 q^{22} + 50 q^{23} - 225 q^{24} - 6 q^{25} + 472 q^{26} + 162 q^{27} - 333 q^{28} - 242 q^{29} - 333 q^{30} - 438 q^{31} + 35 q^{32} - 216 q^{33} - 150 q^{34} - 258 q^{35} + 117 q^{36} - 596 q^{37} + 664 q^{38} - 576 q^{39} - 831 q^{40} + 54 q^{41} + 9 q^{42} - 360 q^{43} - 714 q^{44} - 108 q^{45} - 871 q^{46} - 720 q^{47} - 81 q^{48} - 302 q^{49} + 4 q^{50} - 300 q^{51} - 1118 q^{52} + 694 q^{53} - 135 q^{54} - 990 q^{55} + 1917 q^{56} - 798 q^{57} + 1354 q^{58} - 378 q^{59} + 765 q^{60} - 1396 q^{61} + 1475 q^{62} - 558 q^{63} + 1225 q^{64} - 348 q^{65} + 132 q^{66} - 402 q^{67} + 2032 q^{68} + 150 q^{69} + 2415 q^{70} - 964 q^{71} - 675 q^{72} - 192 q^{73} + 2751 q^{74} - 18 q^{75} - 2306 q^{76} + 2724 q^{77} + 1416 q^{78} - 802 q^{79} + 4221 q^{80} + 486 q^{81} + 1735 q^{82} + 2126 q^{83} - 999 q^{84} - 1206 q^{85} - 609 q^{86} - 726 q^{87} + 3656 q^{88} + 432 q^{89} - 999 q^{90} + 1258 q^{91} + 3163 q^{92} - 1314 q^{93} + 1742 q^{94} + 936 q^{95} + 105 q^{96} + 1290 q^{97} + 2492 q^{98} - 648 q^{99}+O(q^{100}) \) 6 * q - 5 * q^2 + 18 * q^3 + 13 * q^4 - 12 * q^5 - 15 * q^6 - 62 * q^7 - 75 * q^8 + 54 * q^9 - 111 * q^10 - 72 * q^11 + 39 * q^12 - 192 * q^13 + 3 * q^14 - 36 * q^15 - 27 * q^16 - 100 * q^17 - 45 * q^18 - 266 * q^19 + 255 * q^20 - 186 * q^21 + 44 * q^22 + 50 * q^23 - 225 * q^24 - 6 * q^25 + 472 * q^26 + 162 * q^27 - 333 * q^28 - 242 * q^29 - 333 * q^30 - 438 * q^31 + 35 * q^32 - 216 * q^33 - 150 * q^34 - 258 * q^35 + 117 * q^36 - 596 * q^37 + 664 * q^38 - 576 * q^39 - 831 * q^40 + 54 * q^41 + 9 * q^42 - 360 * q^43 - 714 * q^44 - 108 * q^45 - 871 * q^46 - 720 * q^47 - 81 * q^48 - 302 * q^49 + 4 * q^50 - 300 * q^51 - 1118 * q^52 + 694 * q^53 - 135 * q^54 - 990 * q^55 + 1917 * q^56 - 798 * q^57 + 1354 * q^58 - 378 * q^59 + 765 * q^60 - 1396 * q^61 + 1475 * q^62 - 558 * q^63 + 1225 * q^64 - 348 * q^65 + 132 * q^66 - 402 * q^67 + 2032 * q^68 + 150 * q^69 + 2415 * q^70 - 964 * q^71 - 675 * q^72 - 192 * q^73 + 2751 * q^74 - 18 * q^75 - 2306 * q^76 + 2724 * q^77 + 1416 * q^78 - 802 * q^79 + 4221 * q^80 + 486 * q^81 + 1735 * q^82 + 2126 * q^83 - 999 * q^84 - 1206 * q^85 - 609 * q^86 - 726 * q^87 + 3656 * q^88 + 432 * q^89 - 999 * q^90 + 1258 * q^91 + 3163 * q^92 - 1314 * q^93 + 1742 * q^94 + 936 * q^95 + 105 * q^96 + 1290 * q^97 + 2492 * q^98 - 648 * 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 $

$2$	−5.17870	−1.83095	−0.915474	−	0.402377i	$-0.868184\pi$
$2$	−5.17870	−1.83095	−0.915474	+	0.402377i	$0.868184\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	18.8190	2.35237
$5$	17.1025	1.52969	0.764846	−	0.644214i	$-0.222815\pi$
$5$	17.1025	1.52969	0.764846	+	0.644214i	$0.222815\pi$
$6$	−15.5361	−1.05710
$7$	−19.8930	−1.07412	−0.537060	−	0.843544i	$-0.680465\pi$
$7$	−19.8930	−1.07412	−0.537060	+	0.843544i	$0.680465\pi$
$8$	−56.0282	−2.47612
$9$	9.00000	0.333333
$10$	−88.5686	−2.80078
$11$	−47.5262	−1.30270	−0.651350	−	0.758778i	$-0.725797\pi$
$11$	−47.5262	−1.30270	−0.651350	+	0.758778i	$0.725797\pi$
$12$	56.4569	1.35814
$13$	−63.9393	−1.36412	−0.682061	−	0.731295i	$-0.738916\pi$
$13$	−63.9393	−1.36412	−0.682061	+	0.731295i	$0.738916\pi$
$14$	103.020	1.96666
$15$	51.3074	0.883168
$16$	139.602	2.18127
$17$	10.7343	0.153144	0.0765719	−	0.997064i	$-0.475603\pi$
$17$	10.7343	0.153144	0.0765719	+	0.997064i	$0.475603\pi$
$18$	−46.6083	−0.610316
$19$	−133.613	−1.61331	−0.806655	−	0.591022i	$-0.798725\pi$
$19$	−133.613	−1.61331	−0.806655	+	0.591022i	$0.798725\pi$
$20$	321.851	3.59840
$21$	−59.6790	−0.620144
$22$	246.124	2.38517
$23$	122.631	1.11175	0.555877	−	0.831265i	$-0.312383\pi$
$23$	122.631	1.11175	0.555877	+	0.831265i	$0.312383\pi$
$24$	−168.084	−1.42959
$25$	167.494	1.33996
$26$	331.123	2.49764
$27$	27.0000	0.192450
$28$	−374.365	−2.52673
$29$	−161.568	−1.03457	−0.517284	−	0.855814i	$-0.673057\pi$
$29$	−161.568	−1.03457	−0.517284	+	0.855814i	$0.673057\pi$
$30$	−265.706	−1.61703
$31$	−228.530	−1.32404	−0.662018	−	0.749488i	$-0.730300\pi$
$31$	−228.530	−1.32404	−0.662018	+	0.749488i	$0.730300\pi$
$32$	−274.729	−1.51768
$33$	−142.579	−0.752114
$34$	−55.5896	−0.280398
$35$	−340.219	−1.64307
$36$	169.371	0.784123
$37$	−273.765	−1.21640	−0.608198	−	0.793785i	$-0.708107\pi$
$37$	−273.765	−1.21640	−0.608198	+	0.793785i	$0.708107\pi$
$38$	691.942	2.95389
$39$	−191.818	−0.787576
$40$	−958.220	−3.78770
$41$	156.472	0.596019	0.298010	−	0.954563i	$-0.403677\pi$
$41$	156.472	0.596019	0.298010	+	0.954563i	$0.403677\pi$
$42$	309.060	1.13545
$43$	414.336	1.46943	0.734716	−	0.678374i	$-0.237315\pi$
$43$	414.336	1.46943	0.734716	+	0.678374i	$0.237315\pi$
$44$	−894.394	−3.06443
$45$	153.922	0.509897
$46$	−635.069	−2.03556
$47$	−215.040	−0.667379	−0.333689	−	0.942683i	$-0.608294\pi$
$47$	−215.040	−0.667379	−0.333689	+	0.942683i	$0.608294\pi$
$48$	418.805	1.25936
$49$	52.7308	0.153734
$50$	−867.404	−2.45339
$51$	32.2028	0.0884176
$52$	−1203.27	−3.20892
$53$	674.981	1.74936	0.874678	−	0.484705i	$-0.161073\pi$
$53$	674.981	1.74936	0.874678	+	0.484705i	$0.161073\pi$
$54$	−139.825	−0.352366
$55$	−812.815	−1.99273
$56$	1114.57	2.65965
$57$	−400.839	−0.931445
$58$	836.714	1.89424
$59$	−577.322	−1.27391	−0.636957	−	0.770900i	$-0.719807\pi$
$59$	−577.322	−1.27391	−0.636957	+	0.770900i	$0.719807\pi$
$60$	965.552	2.07754
$61$	245.936	0.516212	0.258106	−	0.966117i	$-0.416902\pi$
$61$	245.936	0.516212	0.258106	+	0.966117i	$0.416902\pi$
$62$	1183.49	2.42424
$63$	−179.037	−0.358040
$64$	305.930	0.597519
$65$	−1093.52	−2.08668
$66$	738.372	1.37708
$67$	−67.0000	−0.122169
$67$	−67.0000	−0.122169
$68$	202.008	0.360251
$69$	367.893	0.641871
$70$	1761.89	3.00838
$71$	−325.388	−0.543894	−0.271947	−	0.962312i	$-0.587668\pi$
$71$	−325.388	−0.543894	−0.271947	+	0.962312i	$0.587668\pi$
$72$	−504.253	−0.825373
$73$	285.617	0.457930	0.228965	−	0.973435i	$-0.426466\pi$
$73$	285.617	0.457930	0.228965	+	0.973435i	$0.426466\pi$
$74$	1417.75	2.22716
$75$	502.483	0.773624
$76$	−2514.46	−3.79510
$77$	945.438	1.39926
$78$	993.368	1.44201
$79$	−298.664	−0.425346	−0.212673	−	0.977123i	$-0.568217\pi$
$79$	−298.664	−0.425346	−0.212673	+	0.977123i	$0.568217\pi$
$80$	2387.53	3.33668
$81$	81.0000	0.111111
$82$	−810.321	−1.09128
$83$	92.1606	0.121879	0.0609394	−	0.998141i	$-0.480590\pi$
$83$	92.1606	0.121879	0.0609394	+	0.998141i	$0.480590\pi$
$84$	−1123.10	−1.45881
$85$	183.583	0.234263
$86$	−2145.72	−2.69045
$87$	−484.705	−0.597308
$88$	2662.81	3.22564
$89$	−871.095	−1.03748	−0.518741	−	0.854931i	$-0.673599\pi$
$89$	−871.095	−1.03748	−0.518741	+	0.854931i	$0.673599\pi$
$90$	−797.117	−0.933595
$91$	1271.94	1.46523
$92$	2307.79	2.61526
$93$	−685.589	−0.764433
$94$	1113.63	1.22194
$95$	−2285.11	−2.46787
$96$	−824.188	−0.876233
$97$	1304.42	1.36540	0.682701	−	0.730698i	$-0.260805\pi$
$97$	1304.42	1.36540	0.682701	+	0.730698i	$0.260805\pi$
$98$	−273.077	−0.281479
$99$	−427.736	−0.434233
$100$	3152.07	3.15207
$101$	510.823	0.503256	0.251628	−	0.967824i	$-0.419034\pi$
$101$	510.823	0.503256	0.251628	+	0.967824i	$0.419034\pi$
$102$	−166.769	−0.161888
$103$	−231.951	−0.221891	−0.110945	−	0.993826i	$-0.535388\pi$
$103$	−231.951	−0.221891	−0.110945	+	0.993826i	$0.535388\pi$
$104$	3582.40	3.37773
$105$	−1020.66	−0.948628
$106$	−3495.53	−3.20298
$107$	−1478.37	−1.33570	−0.667849	−	0.744297i	$-0.732785\pi$
$107$	−1478.37	−1.33570	−0.667849	+	0.744297i	$0.732785\pi$
$108$	508.112	0.452714
$109$	658.718	0.578841	0.289421	−	0.957202i	$-0.406537\pi$
$109$	658.718	0.578841	0.289421	+	0.957202i	$0.406537\pi$
$110$	4209.33	3.64858
$111$	−821.294	−0.702286
$112$	−2777.09	−2.34295
$113$	−1789.89	−1.49008	−0.745040	−	0.667020i	$-0.767570\pi$
$113$	−1789.89	−1.49008	−0.745040	+	0.667020i	$0.767570\pi$
$114$	2075.82	1.70543
$115$	2097.29	1.70064
$116$	−3040.55	−2.43369
$117$	−575.454	−0.454707
$118$	2989.78	2.33247
$119$	−213.537	−0.164495
$120$	−2874.66	−2.18683
$121$	927.740	0.697025
$122$	−1273.63	−0.945157
$123$	469.415	0.344112
$124$	−4300.69	−3.11462
$125$	726.760	0.520027
$126$	927.179	0.655553
$127$	−2031.17	−1.41919	−0.709595	−	0.704610i	$-0.751122\pi$
$127$	−2031.17	−1.41919	−0.709595	+	0.704610i	$0.751122\pi$
$128$	613.517	0.423654
$129$	1243.01	0.848377
$130$	5663.02	3.82061
$131$	1391.38	0.927982	0.463991	−	0.885840i	$-0.346417\pi$
$131$	1391.38	0.927982	0.463991	+	0.885840i	$0.346417\pi$
$132$	−2683.18	−1.76925
$133$	2657.96	1.73289
$134$	346.973	0.223686
$135$	461.767	0.294389
$136$	−601.422	−0.379202
$137$	952.632	0.594079	0.297040	−	0.954865i	$-0.404001\pi$
$137$	952.632	0.594079	0.297040	+	0.954865i	$0.404001\pi$
$138$	−1905.21	−1.17523
$139$	−2608.20	−1.59154	−0.795771	−	0.605598i	$-0.792934\pi$
$139$	−2608.20	−1.59154	−0.795771	+	0.605598i	$0.792934\pi$
$140$	−6402.57	−3.86511
$141$	−645.120	−0.385311
$142$	1685.09	0.995842
$143$	3038.79	1.77704
$144$	1256.41	0.727091
$145$	−2763.22	−1.58257
$146$	−1479.12	−0.838446
$147$	158.192	0.0887584
$148$	−5151.97	−2.86141
$149$	740.605	0.407200	0.203600	−	0.979054i	$-0.434736\pi$
$149$	740.605	0.407200	0.203600	+	0.979054i	$0.434736\pi$
$150$	−2602.21	−1.41646
$151$	187.011	0.100786	0.0503930	−	0.998729i	$-0.483953\pi$
$151$	187.011	0.100786	0.0503930	+	0.998729i	$0.483953\pi$
$152$	7486.09	3.99475
$153$	96.6085	0.0510479
$154$	−4896.14	−2.56196
$155$	−3908.42	−2.02537
$156$	−3609.81	−1.85267
$157$	−1404.43	−0.713920	−0.356960	−	0.934120i	$-0.616187\pi$
$157$	−1404.43	−0.713920	−0.356960	+	0.934120i	$0.616187\pi$
$158$	1546.69	0.778786
$159$	2024.94	1.00999
$160$	−4698.55	−2.32158
$161$	−2439.50	−1.19416
$162$	−419.475	−0.203439
$163$	772.758	0.371332	0.185666	−	0.982613i	$-0.440556\pi$
$163$	772.758	0.371332	0.185666	+	0.982613i	$0.440556\pi$
$164$	2944.64	1.40206
$165$	−2438.45	−1.15050
$166$	−477.272	−0.223154
$167$	3961.74	1.83574	0.917870	−	0.396882i	$-0.129908\pi$
$167$	3961.74	1.83574	0.917870	+	0.396882i	$0.129908\pi$
$168$	3343.70	1.53555
$169$	1891.24	0.860828
$170$	−950.720	−0.428923
$171$	−1202.52	−0.537770
$172$	7797.37	3.45665
$173$	1554.69	0.683244	0.341622	−	0.939837i	$-0.389024\pi$
$173$	1554.69	0.683244	0.341622	+	0.939837i	$0.389024\pi$
$174$	2510.14	1.09364
$175$	−3331.96	−1.43927
$176$	−6634.73	−2.84154
$177$	−1731.96	−0.735494
$178$	4511.14	1.89958
$179$	3149.93	1.31529	0.657644	−	0.753329i	$-0.271553\pi$
$179$	3149.93	1.31529	0.657644	+	0.753329i	$0.271553\pi$
$180$	2896.66	1.19947
$181$	2663.53	1.09381	0.546903	−	0.837196i	$-0.315807\pi$
$181$	2663.53	1.09381	0.546903	+	0.837196i	$0.315807\pi$
$182$	−6587.02	−2.68276
$183$	737.809	0.298035
$184$	−6870.79	−2.75283
$185$	−4682.05	−1.86071
$186$	3550.46	1.39964
$187$	−510.159	−0.199500
$188$	−4046.83	−1.56992
$189$	−537.111	−0.206715
$190$	11833.9	4.51854
$191$	931.037	0.352709	0.176355	−	0.984327i	$-0.443569\pi$
$191$	931.037	0.352709	0.176355	+	0.984327i	$0.443569\pi$
$192$	917.789	0.344978
$193$	−2387.28	−0.890365	−0.445183	−	0.895440i	$-0.646861\pi$
$193$	−2387.28	−0.890365	−0.445183	+	0.895440i	$0.646861\pi$
$194$	−6755.22	−2.49998
$195$	−3280.56	−1.20475
$196$	992.339	0.361640
$197$	−4052.34	−1.46557	−0.732785	−	0.680460i	$-0.761780\pi$
$197$	−4052.34	−1.46557	−0.732785	+	0.680460i	$0.761780\pi$
$198$	2215.12	0.795058
$199$	−1137.87	−0.405334	−0.202667	−	0.979248i	$-0.564961\pi$
$199$	−1137.87	−0.405334	−0.202667	+	0.979248i	$0.564961\pi$
$200$	−9384.41	−3.31789
$201$	−201.000	−0.0705346
$202$	−2645.40	−0.921435
$203$	3214.07	1.11125
$204$	606.024	0.207991
$205$	2676.05	0.911726
$206$	1201.20	0.406271
$207$	1103.68	0.370584
$208$	−8926.03	−2.97552
$209$	6350.12	2.10166
$210$	5285.68	1.73689
$211$	−58.7371	−0.0191641	−0.00958207	−	0.999954i	$-0.503050\pi$
$211$	−58.7371	−0.0191641	−0.00958207	+	0.999954i	$0.503050\pi$
$212$	12702.4	4.11513
$213$	−976.165	−0.314017
$214$	7656.05	2.44559
$215$	7086.16	2.24778
$216$	−1512.76	−0.476529
$217$	4546.14	1.42217
$218$	−3411.30	−1.05983
$219$	856.850	0.264386
$220$	−15296.3	−4.68763
$221$	−686.342	−0.208907
$222$	4253.24	1.28585
$223$	−922.207	−0.276931	−0.138465	−	0.990367i	$-0.544217\pi$
$223$	−922.207	−0.276931	−0.138465	+	0.990367i	$0.544217\pi$
$224$	5465.19	1.63017
$225$	1507.45	0.446652
$226$	9269.33	2.72826
$227$	−263.908	−0.0771639	−0.0385820	−	0.999255i	$-0.512284\pi$
$227$	−263.908	−0.0771639	−0.0385820	+	0.999255i	$0.512284\pi$
$228$	−7543.37	−2.19110
$229$	3880.60	1.11981	0.559906	−	0.828556i	$-0.310837\pi$
$229$	3880.60	1.11981	0.559906	+	0.828556i	$0.310837\pi$
$230$	−10861.3	−3.11378
$231$	2836.31	0.807860
$232$	9052.37	2.56171
$233$	2188.81	0.615422	0.307711	−	0.951480i	$-0.400437\pi$
$233$	2188.81	0.615422	0.307711	+	0.951480i	$0.400437\pi$
$234$	2980.10	0.832545
$235$	−3677.71	−1.02088
$236$	−10864.6	−2.99671
$237$	−895.992	−0.245573
$238$	1105.84	0.301181
$239$	3498.75	0.946926	0.473463	−	0.880814i	$-0.343004\pi$
$239$	3498.75	0.946926	0.473463	+	0.880814i	$0.343004\pi$
$240$	7162.59	1.92643
$241$	152.096	0.0406529	0.0203265	−	0.999793i	$-0.493529\pi$
$241$	152.096	0.0406529	0.0203265	+	0.999793i	$0.493529\pi$
$242$	−4804.49	−1.27622
$243$	243.000	0.0641500
$244$	4628.26	1.21432
$245$	901.827	0.235166
$246$	−2430.96	−0.630051
$247$	8543.12	2.20075
$248$	12804.1	3.27847
$249$	276.482	0.0703667
$250$	−3763.67	−0.952142
$251$	2288.41	0.575471	0.287736	−	0.957710i	$-0.407098\pi$
$251$	2288.41	0.575471	0.287736	+	0.957710i	$0.407098\pi$
$252$	−3369.29	−0.842243
$253$	−5828.19	−1.44828
$254$	10518.8	2.59846
$255$	550.748	0.135252
$256$	−5624.66	−1.37321
$257$	−596.791	−0.144851	−0.0724257	−	0.997374i	$-0.523074\pi$
$257$	−596.791	−0.144851	−0.0724257	+	0.997374i	$0.523074\pi$
$258$	−6437.16	−1.55333
$259$	5446.00	1.30656
$260$	−20578.9	−4.90865
$261$	−1454.11	−0.344856
$262$	−7205.55	−1.69909
$263$	−2727.66	−0.639524	−0.319762	−	0.947498i	$-0.603603\pi$
$263$	−2727.66	−0.639524	−0.319762	+	0.947498i	$0.603603\pi$
$264$	7988.42	1.86232
$265$	11543.8	2.67597
$266$	−13764.8	−3.17283
$267$	−2613.29	−0.598990
$268$	−1260.87	−0.287388
$269$	−6932.23	−1.57125	−0.785623	−	0.618705i	$-0.787657\pi$
$269$	−6932.23	−1.57125	−0.785623	+	0.618705i	$0.787657\pi$
$270$	−2391.35	−0.539011
$271$	−5422.56	−1.21549	−0.607744	−	0.794133i	$-0.707925\pi$
$271$	−5422.56	−1.21549	−0.607744	+	0.794133i	$0.707925\pi$
$272$	1498.52	0.334048
$273$	3815.83	0.845951
$274$	−4933.40	−1.08773
$275$	−7960.38	−1.74556
$276$	6923.36	1.50992
$277$	−6630.36	−1.43819	−0.719097	−	0.694910i	$-0.755444\pi$
$277$	−6630.36	−1.43819	−0.719097	+	0.694910i	$0.755444\pi$
$278$	13507.1	2.91403
$279$	−2056.77	−0.441345
$280$	19061.9	4.06844
$281$	2024.87	0.429871	0.214935	−	0.976628i	$-0.431046\pi$
$281$	2024.87	0.429871	0.214935	+	0.976628i	$0.431046\pi$
$282$	3340.88	0.705485
$283$	4523.07	0.950066	0.475033	−	0.879968i	$-0.342436\pi$
$283$	4523.07	0.950066	0.475033	+	0.879968i	$0.342436\pi$
$284$	−6123.47	−1.27944
$285$	−6855.33	−1.42482
$286$	−15737.0	−3.25367
$287$	−3112.69	−0.640196
$288$	−2472.56	−0.505893
$289$	−4797.78	−0.976547
$290$	14309.9	2.89760
$291$	3913.27	0.788315
$292$	5375.01	1.07722
$293$	6283.51	1.25286	0.626428	−	0.779480i	$-0.284516\pi$
$293$	6283.51	1.25286	0.626428	+	0.779480i	$0.284516\pi$
$294$	−819.231	−0.162512
$295$	−9873.63	−1.94869
$296$	15338.5	3.01194
$297$	−1283.21	−0.250705
$298$	−3835.37	−0.745561
$299$	−7840.94	−1.51657
$300$	9456.21	1.81985
$301$	−8242.37	−1.57835
$302$	−968.472	−0.184534
$303$	1532.47	0.290555
$304$	−18652.6	−3.51907
$305$	4206.12	0.789644
$306$	−500.307	−0.0934661
$307$	−967.760	−0.179912	−0.0899560	−	0.995946i	$-0.528673\pi$
$307$	−967.760	−0.179912	−0.0899560	+	0.995946i	$0.528673\pi$
$308$	17792.2	3.29157
$309$	−695.852	−0.128109
$310$	20240.5	3.70834
$311$	−8781.30	−1.60110	−0.800550	−	0.599266i	$-0.795459\pi$
$311$	−8781.30	−1.60110	−0.800550	+	0.599266i	$0.795459\pi$
$312$	10747.2	1.95013
$313$	−5968.74	−1.07787	−0.538935	−	0.842347i	$-0.681173\pi$
$313$	−5968.74	−1.07787	−0.538935	+	0.842347i	$0.681173\pi$
$314$	7273.10	1.30715
$315$	−3061.97	−0.547691
$316$	−5620.54	−1.00057
$317$	5644.82	1.00014	0.500071	−	0.865985i	$-0.333307\pi$
$317$	5644.82	1.00014	0.500071	+	0.865985i	$0.333307\pi$
$318$	−10486.6	−1.84924
$319$	7678.73	1.34773
$320$	5232.15	0.914019
$321$	−4435.12	−0.771165
$322$	12633.4	2.18644
$323$	−1434.24	−0.247069
$324$	1524.34	0.261374
$325$	−10709.5	−1.82786
$326$	−4001.89	−0.679889
$327$	1976.15	0.334194
$328$	−8766.83	−1.47581
$329$	4277.78	0.716845
$330$	12628.0	2.10651
$331$	−6758.38	−1.12228	−0.561139	−	0.827721i	$-0.689637\pi$
$331$	−6758.38	−1.12228	−0.561139	+	0.827721i	$0.689637\pi$
$332$	1734.37	0.286704
$333$	−2463.88	−0.405465
$334$	−20516.7	−3.36114
$335$	−1145.87	−0.186882
$336$	−8331.27	−1.35270
$337$	−5580.49	−0.902043	−0.451022	−	0.892513i	$-0.648940\pi$
$337$	−5580.49	−0.902043	−0.451022	+	0.892513i	$0.648940\pi$
$338$	−9794.16	−1.57613
$339$	−5369.68	−0.860298
$340$	3454.83	0.551072
$341$	10861.1	1.72482
$342$	6227.47	0.984629
$343$	5774.32	0.908991
$344$	−23214.5	−3.63849
$345$	6291.88	0.981865
$346$	−8051.30	−1.25098
$347$	11435.5	1.76914	0.884569	−	0.466408i	$-0.154452\pi$
$347$	11435.5	1.76914	0.884569	+	0.466408i	$0.154452\pi$
$348$	−9121.64	−1.40509
$349$	12826.2	1.96725	0.983625	−	0.180227i	$-0.0576833\pi$
$349$	12826.2	1.96725	0.983625	+	0.180227i	$0.0576833\pi$
$350$	17255.3	2.63523
$351$	−1726.36	−0.262525
$352$	13056.8	1.97708
$353$	984.504	0.148442	0.0742208	−	0.997242i	$-0.476353\pi$
$353$	984.504	0.148442	0.0742208	+	0.997242i	$0.476353\pi$
$354$	8969.33	1.34665
$355$	−5564.94	−0.831990
$356$	−16393.1	−2.44054
$357$	−640.610	−0.0949711
$358$	−16312.5	−2.40822
$359$	−12071.1	−1.77461	−0.887307	−	0.461179i	$-0.847427\pi$
$359$	−12071.1	−1.77461	−0.887307	+	0.461179i	$0.847427\pi$
$360$	−8623.98	−1.26257
$361$	10993.4	1.60277
$362$	−13793.6	−2.00270
$363$	2783.22	0.402427
$364$	23936.7	3.44676
$365$	4884.75	0.700492
$366$	−3820.89	−0.545686
$367$	−1821.14	−0.259027	−0.129513	−	0.991578i	$-0.541342\pi$
$367$	−1821.14	−0.259027	−0.129513	+	0.991578i	$0.541342\pi$
$368$	17119.5	2.42504
$369$	1408.25	0.198673
$370$	24247.0	3.40686
$371$	−13427.4	−1.87902
$372$	−12902.1	−1.79823
$373$	3732.78	0.518166	0.259083	−	0.965855i	$-0.416580\pi$
$373$	3732.78	0.518166	0.259083	+	0.965855i	$0.416580\pi$
$374$	2641.96	0.365275
$375$	2180.28	0.300238
$376$	12048.3	1.65251
$377$	10330.6	1.41128
$378$	2781.54	0.378483
$379$	−8364.65	−1.13368	−0.566838	−	0.823829i	$-0.691833\pi$
$379$	−8364.65	−1.13368	−0.566838	+	0.823829i	$0.691833\pi$
$380$	−43003.4	−5.80534
$381$	−6093.51	−0.819369
$382$	−4821.57	−0.645793
$383$	−5225.76	−0.697190	−0.348595	−	0.937273i	$-0.613341\pi$
$383$	−5225.76	−0.697190	−0.348595	+	0.937273i	$0.613341\pi$
$384$	1840.55	0.244597
$385$	16169.3	2.14043
$386$	12363.0	1.63021
$387$	3729.02	0.489811
$388$	24547.9	3.21193
$389$	−7561.82	−0.985602	−0.492801	−	0.870142i	$-0.664027\pi$
$389$	−7561.82	−0.985602	−0.492801	+	0.870142i	$0.664027\pi$
$390$	16989.1	2.20583
$391$	1316.35	0.170258
$392$	−2954.41	−0.380664
$393$	4174.15	0.535771
$394$	20985.9	2.68338
$395$	−5107.89	−0.650648
$396$	−8049.54	−1.02148
$397$	5426.24	0.685983	0.342992	−	0.939338i	$-0.388560\pi$
$397$	5426.24	0.685983	0.342992	+	0.939338i	$0.388560\pi$
$398$	5892.69	0.742145
$399$	7973.88	1.00048
$400$	23382.5	2.92281
$401$	5393.63	0.671683	0.335842	−	0.941918i	$-0.390979\pi$
$401$	5393.63	0.671683	0.335842	+	0.941918i	$0.390979\pi$
$402$	1040.92	0.129145
$403$	14612.0	1.80615
$404$	9613.16	1.18384
$405$	1385.30	0.169966
$406$	−16644.7	−2.03464
$407$	13011.0	1.58460
$408$	−1804.27	−0.218932
$409$	10202.0	1.23339	0.616697	−	0.787201i	$-0.288471\pi$
$409$	10202.0	1.23339	0.616697	+	0.787201i	$0.288471\pi$
$410$	−13858.5	−1.66932
$411$	2857.90	0.342992
$412$	−4365.07	−0.521970
$413$	11484.6	1.36834
$414$	−5715.62	−0.678521
$415$	1576.17	0.186437
$416$	17566.0	2.07030
$417$	−7824.59	−0.918877
$418$	−32885.4	−3.84803
$419$	−9113.93	−1.06264	−0.531318	−	0.847172i	$-0.678303\pi$
$419$	−9113.93	−1.06264	−0.531318	+	0.847172i	$0.678303\pi$
$420$	−19207.7	−2.23152
$421$	−15183.0	−1.75765	−0.878827	−	0.477141i	$-0.841673\pi$
$421$	−15183.0	−1.75765	−0.878827	+	0.477141i	$0.841673\pi$
$422$	304.182	0.0350885
$423$	−1935.36	−0.222460
$424$	−37818.0	−4.33161
$425$	1797.93	0.205206
$426$	5055.27	0.574949
$427$	−4892.41	−0.554473
$428$	−27821.4	−3.14205
$429$	9116.38	1.02597
$430$	−36697.1	−4.11557
$431$	−7276.89	−0.813261	−0.406631	−	0.913593i	$-0.633296\pi$
$431$	−7276.89	−0.813261	−0.406631	+	0.913593i	$0.633296\pi$
$432$	3769.24	0.419786
$433$	−6042.93	−0.670680	−0.335340	−	0.942097i	$-0.608851\pi$
$433$	−6042.93	−0.670680	−0.335340	+	0.942097i	$0.608851\pi$
$434$	−23543.1	−2.60393
$435$	−8289.65	−0.913697
$436$	12396.4	1.36165
$437$	−16385.1	−1.79360
$438$	−4437.37	−0.484077
$439$	6774.05	0.736465	0.368232	−	0.929734i	$-0.379963\pi$
$439$	6774.05	0.736465	0.368232	+	0.929734i	$0.379963\pi$
$440$	45540.6	4.93423
$441$	474.577	0.0512447
$442$	3554.36	0.382497
$443$	9178.85	0.984425	0.492212	−	0.870475i	$-0.336188\pi$
$443$	9178.85	0.984425	0.492212	+	0.870475i	$0.336188\pi$
$444$	−15455.9	−1.65204
$445$	−14897.9	−1.58703
$446$	4775.84	0.507046
$447$	2221.82	0.235097
$448$	−6085.85	−0.641807
$449$	7219.71	0.758840	0.379420	−	0.925224i	$-0.376124\pi$
$449$	7219.71	0.758840	0.379420	+	0.925224i	$0.376124\pi$
$450$	−7806.63	−0.817796
$451$	−7436.51	−0.776434
$452$	−33683.9	−3.50522
$453$	561.032	0.0581889
$454$	1366.70	0.141283
$455$	21753.4	2.24135
$456$	22458.3	2.30637
$457$	473.710	0.0484885	0.0242442	−	0.999706i	$-0.492282\pi$
$457$	473.710	0.0484885	0.0242442	+	0.999706i	$0.492282\pi$
$458$	−20096.4	−2.05032
$459$	289.825	0.0294725
$460$	39468.9	4.00053
$461$	7642.27	0.772095	0.386048	−	0.922479i	$-0.373840\pi$
$461$	7642.27	0.772095	0.386048	+	0.922479i	$0.373840\pi$
$462$	−14688.4	−1.47915
$463$	12532.9	1.25800	0.628998	−	0.777407i	$-0.283465\pi$
$463$	12532.9	1.25800	0.628998	+	0.777407i	$0.283465\pi$
$464$	−22555.2	−2.25668
$465$	−11725.3	−1.16935
$466$	−11335.2	−1.12681
$467$	130.326	0.0129139	0.00645695	−	0.999979i	$-0.497945\pi$
$467$	130.326	0.0129139	0.00645695	+	0.999979i	$0.497945\pi$
$468$	−10829.4	−1.06964
$469$	1332.83	0.131225
$470$	19045.8	1.86918
$471$	−4213.28	−0.412182
$472$	32346.3	3.15436
$473$	−19691.8	−1.91423
$474$	4640.07	0.449632
$475$	−22379.4	−2.16176
$476$	−4018.54	−0.386953
$477$	6074.83	0.583118
$478$	−18119.0	−1.73377
$479$	−8321.30	−0.793758	−0.396879	−	0.917871i	$-0.629907\pi$
$479$	−8321.30	−0.793758	−0.396879	+	0.917871i	$0.629907\pi$
$480$	−14095.7	−1.34037
$481$	17504.3	1.65931
$482$	−787.659	−0.0744334
$483$	−7318.49	−0.689447
$484$	17459.1	1.63966
$485$	22308.8	2.08864
$486$	−1258.42	−0.117455
$487$	−5361.18	−0.498847	−0.249423	−	0.968395i	$-0.580241\pi$
$487$	−5361.18	−0.498847	−0.249423	+	0.968395i	$0.580241\pi$
$488$	−13779.4	−1.27820
$489$	2318.27	0.214389
$490$	−4670.29	−0.430576
$491$	9471.75	0.870579	0.435290	−	0.900291i	$-0.356646\pi$
$491$	9471.75	0.870579	0.435290	+	0.900291i	$0.356646\pi$
$492$	8833.91	0.809479
$493$	−1734.32	−0.158438
$494$	−44242.3	−4.02946
$495$	−7315.34	−0.664242
$496$	−31903.1	−2.88809
$497$	6472.94	0.584208
$498$	−1431.82	−0.128838
$499$	3118.68	0.279783	0.139891	−	0.990167i	$-0.455325\pi$
$499$	3118.68	0.279783	0.139891	+	0.990167i	$0.455325\pi$
$500$	13676.9	1.22330
$501$	11885.2	1.05986
$502$	−11851.0	−1.05366
$503$	276.578	0.0245169	0.0122584	−	0.999925i	$-0.496098\pi$
$503$	276.578	0.0245169	0.0122584	+	0.999925i	$0.496098\pi$
$504$	10031.1	0.886550
$505$	8736.34	0.769826
$506$	30182.4	2.65173
$507$	5673.72	0.496999
$508$	−38224.5	−3.33846
$509$	12105.2	1.05413	0.527065	−	0.849825i	$-0.323293\pi$
$509$	12105.2	1.05413	0.527065	+	0.849825i	$0.323293\pi$
$510$	−2852.16	−0.247639
$511$	−5681.77	−0.491872
$512$	24220.3	2.09062
$513$	−3607.55	−0.310482
$514$	3090.61	0.265215
$515$	−3966.93	−0.339425
$516$	23392.1	1.99570
$517$	10220.0	0.869393
$518$	−28203.2	−2.39223
$519$	4664.08	0.394471
$520$	61267.9	5.16688
$521$	−5275.07	−0.443580	−0.221790	−	0.975095i	$-0.571190\pi$
$521$	−5275.07	−0.443580	−0.221790	+	0.975095i	$0.571190\pi$
$522$	7530.42	0.631413
$523$	−9834.97	−0.822281	−0.411141	−	0.911572i	$-0.634869\pi$
$523$	−9834.97	−0.822281	−0.411141	+	0.911572i	$0.634869\pi$
$524$	26184.4	2.18296
$525$	−9995.89	−0.830965
$526$	14125.8	1.17094
$527$	−2453.10	−0.202768
$528$	−19904.2	−1.64057
$529$	2871.36	0.235996
$530$	−59782.2	−4.89957
$531$	−5195.89	−0.424638
$532$	50020.0	4.07640
$533$	−10004.7	−0.813043
$534$	13533.4	1.09672
$535$	−25283.8	−2.04320
$536$	3753.89	0.302506
$537$	9449.78	0.759382
$538$	35899.9	2.87687
$539$	−2506.10	−0.200269
$540$	8689.97	0.692512
$541$	−12840.0	−1.02040	−0.510198	−	0.860057i	$-0.670428\pi$
$541$	−12840.0	−1.02040	−0.510198	+	0.860057i	$0.670428\pi$
$542$	28081.8	2.22550
$543$	7990.59	0.631509
$544$	−2949.02	−0.232423
$545$	11265.7	0.885449
$546$	−19761.1	−1.54889
$547$	3681.13	0.287740	0.143870	−	0.989597i	$-0.454045\pi$
$547$	3681.13	0.287740	0.143870	+	0.989597i	$0.454045\pi$
$548$	17927.5	1.39749
$549$	2213.43	0.172071
$550$	41224.4	3.19603
$551$	21587.6	1.66908
$552$	−20612.4	−1.58935
$553$	5941.32	0.456872
$554$	34336.7	2.63326
$555$	−14046.2	−1.07428
$556$	−49083.5	−3.74389
$557$	−804.641	−0.0612096	−0.0306048	−	0.999532i	$-0.509743\pi$
$557$	−804.641	−0.0612096	−0.0306048	+	0.999532i	$0.509743\pi$
$558$	10651.4	0.808080
$559$	−26492.4	−2.00449
$560$	−47495.1	−3.58399
$561$	−1530.48	−0.115182
$562$	−10486.2	−0.787071
$563$	12520.4	0.937247	0.468624	−	0.883398i	$-0.344750\pi$
$563$	12520.4	0.937247	0.468624	+	0.883398i	$0.344750\pi$
$564$	−12140.5	−0.906394
$565$	−30611.6	−2.27936
$566$	−23423.6	−1.73952
$567$	−1611.33	−0.119347
$568$	18230.9	1.34675
$569$	−13185.7	−0.971483	−0.485741	−	0.874103i	$-0.661450\pi$
$569$	−13185.7	−0.971483	−0.485741	+	0.874103i	$0.661450\pi$
$570$	35501.7	2.60878
$571$	22261.3	1.63154	0.815768	−	0.578379i	$-0.196315\pi$
$571$	22261.3	1.63154	0.815768	+	0.578379i	$0.196315\pi$
$572$	57186.9	4.18025
$573$	2793.11	0.203637
$574$	16119.7	1.17217
$575$	20540.0	1.48970
$576$	2753.37	0.199173
$577$	7227.34	0.521452	0.260726	−	0.965413i	$-0.416038\pi$
$577$	7227.34	0.521452	0.260726	+	0.965413i	$0.416038\pi$
$578$	24846.3	1.78801
$579$	−7161.85	−0.514053
$580$	−52000.8	−3.72279
$581$	−1833.35	−0.130912
$582$	−20265.6	−1.44336
$583$	−32079.3	−2.27888
$584$	−16002.6	−1.13389
$585$	−9841.68	−0.695562
$586$	−32540.4	−2.29391
$587$	−9912.69	−0.697002	−0.348501	−	0.937308i	$-0.613309\pi$
$587$	−9912.69	−0.697002	−0.348501	+	0.937308i	$0.613309\pi$
$588$	2977.02	0.208793
$589$	30534.5	2.13608
$590$	51132.6	3.56796
$591$	−12157.0	−0.846147
$592$	−38218.0	−2.65329
$593$	20892.8	1.44682	0.723409	−	0.690419i	$-0.242574\pi$
$593$	20892.8	1.44682	0.723409	+	0.690419i	$0.242574\pi$
$594$	6645.35	0.459027
$595$	−3652.01	−0.251626
$596$	13937.4	0.957884
$597$	−3413.61	−0.234020
$598$	40605.9	2.77675
$599$	−3408.81	−0.232521	−0.116261	−	0.993219i	$-0.537091\pi$
$599$	−3408.81	−0.232521	−0.116261	+	0.993219i	$0.537091\pi$
$600$	−28153.2	−1.91558
$601$	−486.918	−0.0330479	−0.0165240	−	0.999863i	$-0.505260\pi$
$601$	−486.918	−0.0330479	−0.0165240	+	0.999863i	$0.505260\pi$
$602$	42684.8	2.88987
$603$	−603.000	−0.0407231
$604$	3519.34	0.237086
$605$	15866.6	1.06623
$606$	−7936.21	−0.531991
$607$	12510.5	0.836551	0.418275	−	0.908320i	$-0.362635\pi$
$607$	12510.5	0.836551	0.418275	+	0.908320i	$0.362635\pi$
$608$	36707.4	2.44849
$609$	9642.22	0.641581
$610$	−21782.2	−1.44580
$611$	13749.5	0.910385
$612$	1818.07	0.120084
$613$	−17380.6	−1.14518	−0.572591	−	0.819841i	$-0.694062\pi$
$613$	−17380.6	−1.14518	−0.572591	+	0.819841i	$0.694062\pi$
$614$	5011.74	0.329409
$615$	8028.16	0.526385
$616$	−52971.2	−3.46472
$617$	25618.2	1.67155	0.835776	−	0.549070i	$-0.185018\pi$
$617$	25618.2	1.67155	0.835776	+	0.549070i	$0.185018\pi$
$618$	3603.61	0.234561
$619$	−10914.4	−0.708700	−0.354350	−	0.935113i	$-0.615298\pi$
$619$	−10914.4	−0.708700	−0.354350	+	0.935113i	$0.615298\pi$
$620$	−73552.4	−4.76441
$621$	3311.04	0.213957
$622$	45475.8	2.93153
$623$	17328.7	1.11438
$624$	−26778.1	−1.71792
$625$	−8507.42	−0.544475
$626$	30910.3	1.97352
$627$	19050.3	1.21339
$628$	−26429.8	−1.67940
$629$	−2938.67	−0.186283
$630$	15857.0	1.00279
$631$	−9358.65	−0.590431	−0.295216	−	0.955431i	$-0.595391\pi$
$631$	−9358.65	−0.590431	−0.295216	+	0.955431i	$0.595391\pi$
$632$	16733.6	1.05321
$633$	−176.211	−0.0110644
$634$	−29232.9	−1.83121
$635$	−34738.0	−2.17092
$636$	38107.3	2.37587
$637$	−3371.57	−0.209712
$638$	−39765.8	−2.46762
$639$	−2928.49	−0.181298
$640$	10492.7	0.648060
$641$	−16314.5	−1.00528	−0.502639	−	0.864496i	$-0.667638\pi$
$641$	−16314.5	−1.00528	−0.502639	+	0.864496i	$0.667638\pi$
$642$	22968.1	1.41196
$643$	−31509.9	−1.93255	−0.966274	−	0.257517i	$-0.917096\pi$
$643$	−31509.9	−1.93255	−0.966274	+	0.257517i	$0.917096\pi$
$644$	−45908.8	−2.80910
$645$	21258.5	1.29776
$646$	7427.49	0.452370
$647$	−27339.2	−1.66123	−0.830614	−	0.556848i	$-0.812011\pi$
$647$	−27339.2	−1.66123	−0.830614	+	0.556848i	$0.812011\pi$
$648$	−4538.28	−0.275124
$649$	27437.9	1.65953
$650$	55461.2	3.34672
$651$	13638.4	0.821093
$652$	14542.5	0.873510
$653$	8494.51	0.509060	0.254530	−	0.967065i	$-0.418079\pi$
$653$	8494.51	0.509060	0.254530	+	0.967065i	$0.418079\pi$
$654$	−10233.9	−0.611892
$655$	23796.1	1.41953
$656$	21843.7	1.30008
$657$	2570.55	0.152643
$658$	−22153.4	−1.31251
$659$	−9356.77	−0.553092	−0.276546	−	0.961001i	$-0.589190\pi$
$659$	−9356.77	−0.553092	−0.276546	+	0.961001i	$0.589190\pi$
$660$	−45889.0	−2.70641
$661$	−4071.72	−0.239594	−0.119797	−	0.992798i	$-0.538224\pi$
$661$	−4071.72	−0.239594	−0.119797	+	0.992798i	$0.538224\pi$
$662$	34999.7	2.05483
$663$	−2059.03	−0.120612
$664$	−5163.59	−0.301786
$665$	45457.7	2.65079
$666$	12759.7	0.742386
$667$	−19813.3	−1.15018
$668$	74555.8	4.31834
$669$	−2766.62	−0.159886
$670$	5934.10	0.342170
$671$	−11688.4	−0.672468
$672$	16395.6	0.941179
$673$	−25173.5	−1.44185	−0.720927	−	0.693011i	$-0.756284\pi$
$673$	−25173.5	−1.44185	−0.720927	+	0.693011i	$0.756284\pi$
$674$	28899.7	1.65159
$675$	4522.35	0.257875
$676$	35591.1	2.02498
$677$	7502.47	0.425913	0.212957	−	0.977062i	$-0.431691\pi$
$677$	7502.47	0.425913	0.212957	+	0.977062i	$0.431691\pi$
$678$	27808.0	1.57516
$679$	−25948.9	−1.46661
$680$	−10285.8	−0.580062
$681$	−791.725	−0.0445506
$682$	−56246.6	−3.15806
$683$	−8794.77	−0.492712	−0.246356	−	0.969179i	$-0.579233\pi$
$683$	−8794.77	−0.492712	−0.246356	+	0.969179i	$0.579233\pi$
$684$	−22630.1	−1.26503
$685$	16292.4	0.908758
$686$	−29903.5	−1.66432
$687$	11641.8	0.646524
$688$	57841.9	3.20524
$689$	−43157.9	−2.38633
$690$	−32583.8	−1.79774
$691$	20329.3	1.11919	0.559597	−	0.828765i	$-0.310956\pi$
$691$	20329.3	1.11919	0.559597	+	0.828765i	$0.310956\pi$
$692$	29257.7	1.60724
$693$	8508.94	0.466418
$694$	−59221.2	−3.23920
$695$	−44606.6	−2.43457
$696$	27157.1	1.47901
$697$	1679.61	0.0912767
$698$	−66423.0	−3.60193
$699$	6566.42	0.355314
$700$	−62704.1	−3.38570
$701$	−13862.7	−0.746917	−0.373458	−	0.927647i	$-0.621828\pi$
$701$	−13862.7	−0.746917	−0.373458	+	0.927647i	$0.621828\pi$
$702$	8940.31	0.480670
$703$	36578.5	1.96242
$704$	−14539.7	−0.778387
$705$	−11033.1	−0.589407
$706$	−5098.45	−0.271789
$707$	−10161.8	−0.540557
$708$	−32593.8	−1.73015
$709$	29954.8	1.58671	0.793354	−	0.608761i	$-0.208333\pi$
$709$	29954.8	1.58671	0.793354	+	0.608761i	$0.208333\pi$
$710$	28819.2	1.52333
$711$	−2687.98	−0.141782
$712$	48805.9	2.56893
$713$	−28024.8	−1.47200
$714$	3317.53	0.173887
$715$	51970.9	2.71832
$716$	59278.3	3.09404
$717$	10496.2	0.546708
$718$	62512.5	3.24923
$719$	−3499.61	−0.181521	−0.0907604	−	0.995873i	$-0.528930\pi$
$719$	−3499.61	−0.181521	−0.0907604	+	0.995873i	$0.528930\pi$
$720$	21487.8	1.11223
$721$	4614.19	0.238338
$722$	−56931.6	−2.93459
$723$	456.288	0.0234710
$724$	50124.9	2.57303
$725$	−27061.8	−1.38627
$726$	−14413.5	−0.736824
$727$	−34516.1	−1.76084	−0.880420	−	0.474195i	$-0.842739\pi$
$727$	−34516.1	−1.76084	−0.880420	+	0.474195i	$0.842739\pi$
$728$	−71264.7	−3.62808
$729$	729.000	0.0370370
$730$	−25296.7	−1.28256
$731$	4447.59	0.225034
$732$	13884.8	0.701088
$733$	−7096.80	−0.357607	−0.178804	−	0.983885i	$-0.557223\pi$
$733$	−7096.80	−0.357607	−0.178804	+	0.983885i	$0.557223\pi$
$734$	9431.16	0.474265
$735$	2705.48	0.135773
$736$	−33690.3	−1.68729
$737$	3184.26	0.159150
$738$	−7292.89	−0.363760
$739$	−11644.9	−0.579652	−0.289826	−	0.957079i	$-0.593597\pi$
$739$	−11644.9	−0.579652	−0.289826	+	0.957079i	$0.593597\pi$
$740$	−88111.3	−4.37708
$741$	25629.4	1.27060
$742$	69536.5	3.44038
$743$	−14355.1	−0.708798	−0.354399	−	0.935094i	$-0.615315\pi$
$743$	−14355.1	−0.708798	−0.354399	+	0.935094i	$0.615315\pi$
$744$	38412.3	1.89283
$745$	12666.2	0.622890
$746$	−19331.0	−0.948735
$747$	829.445	0.0406262
$748$	−9600.67	−0.469298
$749$	29409.2	1.43470
$750$	−11291.0	−0.549720
$751$	10672.7	0.518576	0.259288	−	0.965800i	$-0.416512\pi$
$751$	10672.7	0.518576	0.259288	+	0.965800i	$0.416512\pi$
$752$	−30019.9	−1.45574
$753$	6865.24	0.332248
$754$	−53498.9	−2.58397
$755$	3198.34	0.154172
$756$	−10107.9	−0.486269
$757$	−19660.8	−0.943966	−0.471983	−	0.881608i	$-0.656462\pi$
$757$	−19660.8	−0.943966	−0.471983	+	0.881608i	$0.656462\pi$
$758$	43318.0	2.07570
$759$	−17484.6	−0.836165
$760$	128031.	6.11073
$761$	−12154.8	−0.578990	−0.289495	−	0.957179i	$-0.593487\pi$
$761$	−12154.8	−0.578990	−0.289495	+	0.957179i	$0.593487\pi$
$762$	31556.5	1.50022
$763$	−13103.9	−0.621745
$764$	17521.2	0.829703
$765$	1652.24	0.0780876
$766$	27062.6	1.27652
$767$	36913.6	1.73777
$768$	−16874.0	−0.792822
$769$	−18117.5	−0.849588	−0.424794	−	0.905290i	$-0.639653\pi$
$769$	−18117.5	−0.849588	−0.424794	+	0.905290i	$0.639653\pi$
$770$	−83736.1	−3.91901
$771$	−1790.37	−0.0836300
$772$	−44926.2	−2.09447
$773$	17653.7	0.821420	0.410710	−	0.911766i	$-0.365281\pi$
$773$	17653.7	0.821420	0.410710	+	0.911766i	$0.365281\pi$
$774$	−19311.5	−0.896818
$775$	−38277.4	−1.77415
$776$	−73084.4	−3.38090
$777$	16338.0	0.754340
$778$	39160.4	1.80459
$779$	−20906.7	−0.961565
$780$	−61736.7	−2.83401
$781$	15464.5	0.708530
$782$	−6817.01	−0.311734
$783$	−4362.34	−0.199103
$784$	7361.30	0.335336
$785$	−24019.2	−1.09208
$786$	−21616.7	−0.980968
$787$	−26746.4	−1.21144	−0.605722	−	0.795677i	$-0.707115\pi$
$787$	−26746.4	−1.21144	−0.605722	+	0.795677i	$0.707115\pi$
$788$	−76260.8	−3.44756
$789$	−8182.99	−0.369230
$790$	26452.2	1.19130
$791$	35606.3	1.60052
$792$	23965.3	1.07521
$793$	−15725.0	−0.704175
$794$	−28100.9	−1.25600
$795$	34631.5	1.54497
$796$	−21413.5	−0.953495
$797$	−13401.5	−0.595614	−0.297807	−	0.954626i	$-0.596255\pi$
$797$	−13401.5	−0.595614	−0.297807	+	0.954626i	$0.596255\pi$
$798$	−41294.3	−1.83183
$799$	−2308.30	−0.102205
$800$	−46015.6	−2.03362
$801$	−7839.86	−0.345827
$802$	−27932.0	−1.22982
$803$	−13574.3	−0.596545
$804$	−3782.61	−0.165923
$805$	−41721.4	−1.82669
$806$	−75671.4	−3.30696
$807$	−20796.7	−0.907159
$808$	−28620.5	−1.24612
$809$	−27040.3	−1.17514	−0.587569	−	0.809174i	$-0.699915\pi$
$809$	−27040.3	−1.17514	−0.587569	+	0.809174i	$0.699915\pi$
$810$	−7174.06	−0.311198
$811$	31869.6	1.37989	0.689947	−	0.723860i	$-0.257634\pi$
$811$	31869.6	1.37989	0.689947	+	0.723860i	$0.257634\pi$
$812$	60485.5	2.61407
$813$	−16267.7	−0.701762
$814$	−67380.1	−2.90132
$815$	13216.1	0.568023
$816$	4495.56	0.192863
$817$	−55360.6	−2.37065
$818$	−52833.3	−2.25828
$819$	11447.5	0.488410
$820$	50360.6	2.14472
$821$	−7917.76	−0.336579	−0.168290	−	0.985738i	$-0.553824\pi$
$821$	−7917.76	−0.336579	−0.168290	+	0.985738i	$0.553824\pi$
$822$	−14800.2	−0.628000
$823$	22398.1	0.948663	0.474331	−	0.880346i	$-0.342690\pi$
$823$	22398.1	0.948663	0.474331	+	0.880346i	$0.342690\pi$
$824$	12995.8	0.549428
$825$	−23881.1	−1.00780
$826$	−59475.6	−2.50535
$827$	−29166.0	−1.22636	−0.613181	−	0.789942i	$-0.710110\pi$
$827$	−29166.0	−1.22636	−0.613181	+	0.789942i	$0.710110\pi$
$828$	20770.1	0.871752
$829$	6606.26	0.276773	0.138387	−	0.990378i	$-0.455808\pi$
$829$	6606.26	0.276773	0.138387	+	0.990378i	$0.455808\pi$
$830$	−8162.53	−0.341356
$831$	−19891.1	−0.830342
$832$	−19560.9	−0.815088
$833$	566.027	0.0235434
$834$	40521.2	1.68242
$835$	67755.5	2.80811
$836$	119503.	4.94388
$837$	−6170.30	−0.254811
$838$	47198.4	1.94563
$839$	13210.9	0.543612	0.271806	−	0.962352i	$-0.412379\pi$
$839$	13210.9	0.543612	0.271806	+	0.962352i	$0.412379\pi$
$840$	57185.6	2.34892
$841$	1715.30	0.0703307
$842$	78628.0	3.21817
$843$	6074.61	0.248186
$844$	−1105.37	−0.0450811
$845$	32344.8	1.31680
$846$	10022.6	0.407312
$847$	−18455.5	−0.748688
$848$	94228.4	3.81582
$849$	13569.2	0.548521
$850$	−9310.95	−0.375721
$851$	−33572.0	−1.35233
$852$	−18370.4	−0.738685
$853$	−33279.5	−1.33584	−0.667918	−	0.744235i	$-0.732814\pi$
$853$	−33279.5	−1.33584	−0.667918	+	0.744235i	$0.732814\pi$
$854$	25336.3	1.01521
$855$	−20566.0	−0.822623
$856$	82830.5	3.30734
$857$	7964.68	0.317466	0.158733	−	0.987322i	$-0.449259\pi$
$857$	7964.68	0.317466	0.158733	+	0.987322i	$0.449259\pi$
$858$	−47211.0	−1.87851
$859$	19688.4	0.782025	0.391013	−	0.920385i	$-0.372125\pi$
$859$	19688.4	0.782025	0.391013	+	0.920385i	$0.372125\pi$
$860$	133354.	5.28761
$861$	−9338.07	−0.369618
$862$	37684.9	1.48904
$863$	40716.5	1.60603	0.803017	−	0.595956i	$-0.203227\pi$
$863$	40716.5	1.60603	0.803017	+	0.595956i	$0.203227\pi$
$864$	−7417.69	−0.292078
$865$	26589.1	1.04515
$866$	31294.5	1.22798
$867$	−14393.3	−0.563810
$868$	85553.5	3.34548
$869$	14194.4	0.554098
$870$	42929.6	1.67293
$871$	4283.94	0.166654
$872$	−36906.7	−1.43328
$873$	11739.8	0.455134
$874$	84853.5	3.28400
$875$	−14457.4	−0.558572
$876$	16125.0	0.621934
$877$	−49953.6	−1.92339	−0.961695	−	0.274123i	$-0.911612\pi$
$877$	−49953.6	−1.92339	−0.961695	+	0.274123i	$0.911612\pi$
$878$	−35080.8	−1.34843
$879$	18850.5	0.723336
$880$	−113470.	−4.34668
$881$	−22769.5	−0.870742	−0.435371	−	0.900251i	$-0.643383\pi$
$881$	−22769.5	−0.870742	−0.435371	+	0.900251i	$0.643383\pi$
$882$	−2457.69	−0.0938264
$883$	50231.1	1.91439	0.957197	−	0.289436i	$-0.0934678\pi$
$883$	50231.1	1.91439	0.957197	+	0.289436i	$0.0934678\pi$
$884$	−12916.2	−0.491426
$885$	−29620.9	−1.12508
$886$	−47534.5	−1.80243
$887$	−42303.0	−1.60135	−0.800674	−	0.599100i	$-0.795525\pi$
$887$	−42303.0	−1.60135	−0.800674	+	0.599100i	$0.795525\pi$
$888$	46015.6	1.73894
$889$	40406.0	1.52438
$890$	77151.7	2.90576
$891$	−3849.62	−0.144744
$892$	−17355.0	−0.651444
$893$	28732.1	1.07669
$894$	−11506.1	−0.430450
$895$	53871.5	2.01198
$896$	−12204.7	−0.455056
$897$	−23522.8	−0.875590
$898$	−37388.7	−1.38940
$899$	36923.1	1.36981
$900$	28368.6	1.05069
$901$	7245.44	0.267903
$902$	38511.5	1.42161
$903$	−24727.1	−0.911259
$904$	100284.	3.68961
$905$	45553.0	1.67318
$906$	−2905.42	−0.106541
$907$	22846.6	0.836392	0.418196	−	0.908357i	$-0.362662\pi$
$907$	22846.6	0.836392	0.418196	+	0.908357i	$0.362662\pi$
$908$	−4966.48	−0.181518
$909$	4597.41	0.167752
$910$	−112654.	−4.10380
$911$	4572.33	0.166287	0.0831437	−	0.996538i	$-0.473504\pi$
$911$	4572.33	0.166287	0.0831437	+	0.996538i	$0.473504\pi$
$912$	−55957.7	−2.03174
$913$	−4380.04	−0.158771
$914$	−2453.21	−0.0887799
$915$	12618.4	0.455901
$916$	73028.8	2.63421
$917$	−27678.7	−0.996764
$918$	−1500.92	−0.0539627
$919$	−10989.0	−0.394443	−0.197221	−	0.980359i	$-0.563192\pi$
$919$	−10989.0	−0.394443	−0.197221	+	0.980359i	$0.563192\pi$
$920$	−117507.	−4.21098
$921$	−2903.28	−0.103872
$922$	−39577.0	−1.41367
$923$	20805.1	0.741938
$924$	53376.5	1.90039
$925$	−45854.1	−1.62992
$926$	−64904.0	−2.30332
$927$	−2087.56	−0.0739637
$928$	44387.5	1.57014
$929$	−6117.50	−0.216048	−0.108024	−	0.994148i	$-0.534452\pi$
$929$	−6117.50	−0.216048	−0.108024	+	0.994148i	$0.534452\pi$
$930$	60721.6	2.14101
$931$	−7045.52	−0.248021
$932$	41191.0	1.44770
$933$	−26343.9	−0.924395
$934$	−674.922	−0.0236447
$935$	−8724.98	−0.305174
$936$	32241.6	1.12591
$937$	−7620.10	−0.265675	−0.132838	−	0.991138i	$-0.542409\pi$
$937$	−7620.10	−0.265675	−0.132838	+	0.991138i	$0.542409\pi$
$938$	−6902.33	−0.240266
$939$	−17906.2	−0.622308
$940$	−69210.7	−2.40149
$941$	−26936.3	−0.933156	−0.466578	−	0.884480i	$-0.654513\pi$
$941$	−26936.3	−0.933156	−0.466578	+	0.884480i	$0.654513\pi$
$942$	21819.3	0.754683
$943$	19188.3	0.662627
$944$	−80595.0	−2.77875
$945$	−9185.92	−0.316209
$946$	101978.	3.50485
$947$	46617.1	1.59963	0.799816	−	0.600245i	$-0.204930\pi$
$947$	46617.1	1.59963	0.799816	+	0.600245i	$0.204930\pi$
$948$	−16861.6	−0.577680
$949$	−18262.1	−0.624672
$950$	115896.	3.95808
$951$	16934.5	0.577432
$952$	11964.1	0.407309
$953$	−24370.8	−0.828381	−0.414191	−	0.910190i	$-0.635935\pi$
$953$	−24370.8	−0.828381	−0.414191	+	0.910190i	$0.635935\pi$
$954$	−31459.7	−1.06766
$955$	15923.0	0.539537
$956$	65842.8	2.22752
$957$	23036.2	0.778113
$958$	43093.6	1.45333
$959$	−18950.7	−0.638112
$960$	15696.5	0.527709
$961$	22434.8	0.753072
$962$	−90649.7	−3.03811
$963$	−13305.3	−0.445232
$964$	2862.29	0.0956307
$965$	−40828.5	−1.36198
$966$	37900.3	1.26234
$967$	−39552.5	−1.31533	−0.657665	−	0.753311i	$-0.728456\pi$
$967$	−39552.5	−1.31533	−0.657665	+	0.753311i	$0.728456\pi$
$968$	−51979.6	−1.72592
$969$	−4302.71	−0.142645
$970$	−115531.	−3.82420
$971$	37842.9	1.25071	0.625353	−	0.780342i	$-0.284955\pi$
$971$	37842.9	1.25071	0.625353	+	0.780342i	$0.284955\pi$
$972$	4573.01	0.150905
$973$	51884.8	1.70951
$974$	27764.0	0.913362
$975$	−32128.4	−1.05532
$976$	34333.1	1.12600
$977$	7623.59	0.249642	0.124821	−	0.992179i	$-0.460164\pi$
$977$	7623.59	0.249642	0.124821	+	0.992179i	$0.460164\pi$
$978$	−12005.7	−0.392534
$979$	41399.8	1.35153
$980$	16971.4	0.553197
$981$	5928.46	0.192947
$982$	−49051.4	−1.59398
$983$	−51716.5	−1.67803	−0.839013	−	0.544112i	$-0.816867\pi$
$983$	−51716.5	−1.67803	−0.839013	+	0.544112i	$0.816867\pi$
$984$	−26300.5	−0.852062
$985$	−69305.0	−2.24187
$986$	8981.52	0.290091
$987$	12833.4	0.413870
$988$	160773.	5.17698
$989$	50810.4	1.63365
$990$	37884.0	1.21619
$991$	−39963.6	−1.28101	−0.640507	−	0.767953i	$-0.721276\pi$
$991$	−39963.6	−1.28101	−0.640507	+	0.767953i	$0.721276\pi$
$992$	62783.8	2.00946
$993$	−20275.1	−0.647948
$994$	−33521.4	−1.06965
$995$	−19460.4	−0.620036
$996$	5203.10	0.165529
$997$	−36192.9	−1.14969	−0.574846	−	0.818262i	$-0.694938\pi$
$997$	−36192.9	−1.14969	−0.574846	+	0.818262i	$0.694938\pi$
$998$	−16150.7	−0.512267
$999$	−7391.65	−0.234095

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.4.a.b.1.1	✓	6
3.2	odd	2		603.4.a.b.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.4.a.b.1.1	✓	6	1.1	even	1	trivial
603.4.a.b.1.6		6	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:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	201.a (trivial)

\(f(q)\)	\(=\)	\(q-5.17870 q^{2} +3.00000 q^{3} +18.8190 q^{4} +17.1025 q^{5} -15.5361 q^{6} -19.8930 q^{7} -56.0282 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-5.17870 q^{2} +3.00000 q^{3} +18.8190 q^{4} +17.1025 q^{5} -15.5361 q^{6} -19.8930 q^{7} -56.0282 q^{8} +9.00000 q^{9} -88.5686 q^{10} -47.5262 q^{11} +56.4569 q^{12} -63.9393 q^{13} +103.020 q^{14} +51.3074 q^{15} +139.602 q^{16} +10.7343 q^{17} -46.6083 q^{18} -133.613 q^{19} +321.851 q^{20} -59.6790 q^{21} +246.124 q^{22} +122.631 q^{23} -168.084 q^{24} +167.494 q^{25} +331.123 q^{26} +27.0000 q^{27} -374.365 q^{28} -161.568 q^{29} -265.706 q^{30} -228.530 q^{31} -274.729 q^{32} -142.579 q^{33} -55.5896 q^{34} -340.219 q^{35} +169.371 q^{36} -273.765 q^{37} +691.942 q^{38} -191.818 q^{39} -958.220 q^{40} +156.472 q^{41} +309.060 q^{42} +414.336 q^{43} -894.394 q^{44} +153.922 q^{45} -635.069 q^{46} -215.040 q^{47} +418.805 q^{48} +52.7308 q^{49} -867.404 q^{50} +32.2028 q^{51} -1203.27 q^{52} +674.981 q^{53} -139.825 q^{54} -812.815 q^{55} +1114.57 q^{56} -400.839 q^{57} +836.714 q^{58} -577.322 q^{59} +965.552 q^{60} +245.936 q^{61} +1183.49 q^{62} -179.037 q^{63} +305.930 q^{64} -1093.52 q^{65} +738.372 q^{66} -67.0000 q^{67} +202.008 q^{68} +367.893 q^{69} +1761.89 q^{70} -325.388 q^{71} -504.253 q^{72} +285.617 q^{73} +1417.75 q^{74} +502.483 q^{75} -2514.46 q^{76} +945.438 q^{77} +993.368 q^{78} -298.664 q^{79} +2387.53 q^{80} +81.0000 q^{81} -810.321 q^{82} +92.1606 q^{83} -1123.10 q^{84} +183.583 q^{85} -2145.72 q^{86} -484.705 q^{87} +2662.81 q^{88} -871.095 q^{89} -797.117 q^{90} +1271.94 q^{91} +2307.79 q^{92} -685.589 q^{93} +1113.63 q^{94} -2285.11 q^{95} -824.188 q^{96} +1304.42 q^{97} -273.077 q^{98} -427.736 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 5 q^{2} + 18 q^{3} + 13 q^{4} - 12 q^{5} - 15 q^{6} - 62 q^{7} - 75 q^{8} + 54 q^{9}+O(q^{10}) \) 6 * q - 5 * q^2 + 18 * q^3 + 13 * q^4 - 12 * q^5 - 15 * q^6 - 62 * q^7 - 75 * q^8 + 54 * q^9	\( 6 q - 5 q^{2} + 18 q^{3} + 13 q^{4} - 12 q^{5} - 15 q^{6} - 62 q^{7} - 75 q^{8} + 54 q^{9} - 111 q^{10} - 72 q^{11} + 39 q^{12} - 192 q^{13} + 3 q^{14} - 36 q^{15} - 27 q^{16} - 100 q^{17} - 45 q^{18} - 266 q^{19} + 255 q^{20} - 186 q^{21} + 44 q^{22} + 50 q^{23} - 225 q^{24} - 6 q^{25} + 472 q^{26} + 162 q^{27} - 333 q^{28} - 242 q^{29} - 333 q^{30} - 438 q^{31} + 35 q^{32} - 216 q^{33} - 150 q^{34} - 258 q^{35} + 117 q^{36} - 596 q^{37} + 664 q^{38} - 576 q^{39} - 831 q^{40} + 54 q^{41} + 9 q^{42} - 360 q^{43} - 714 q^{44} - 108 q^{45} - 871 q^{46} - 720 q^{47} - 81 q^{48} - 302 q^{49} + 4 q^{50} - 300 q^{51} - 1118 q^{52} + 694 q^{53} - 135 q^{54} - 990 q^{55} + 1917 q^{56} - 798 q^{57} + 1354 q^{58} - 378 q^{59} + 765 q^{60} - 1396 q^{61} + 1475 q^{62} - 558 q^{63} + 1225 q^{64} - 348 q^{65} + 132 q^{66} - 402 q^{67} + 2032 q^{68} + 150 q^{69} + 2415 q^{70} - 964 q^{71} - 675 q^{72} - 192 q^{73} + 2751 q^{74} - 18 q^{75} - 2306 q^{76} + 2724 q^{77} + 1416 q^{78} - 802 q^{79} + 4221 q^{80} + 486 q^{81} + 1735 q^{82} + 2126 q^{83} - 999 q^{84} - 1206 q^{85} - 609 q^{86} - 726 q^{87} + 3656 q^{88} + 432 q^{89} - 999 q^{90} + 1258 q^{91} + 3163 q^{92} - 1314 q^{93} + 1742 q^{94} + 936 q^{95} + 105 q^{96} + 1290 q^{97} + 2492 q^{98} - 648 q^{99}+O(q^{100}) \) 6 * q - 5 * q^2 + 18 * q^3 + 13 * q^4 - 12 * q^5 - 15 * q^6 - 62 * q^7 - 75 * q^8 + 54 * q^9 - 111 * q^10 - 72 * q^11 + 39 * q^12 - 192 * q^13 + 3 * q^14 - 36 * q^15 - 27 * q^16 - 100 * q^17 - 45 * q^18 - 266 * q^19 + 255 * q^20 - 186 * q^21 + 44 * q^22 + 50 * q^23 - 225 * q^24 - 6 * q^25 + 472 * q^26 + 162 * q^27 - 333 * q^28 - 242 * q^29 - 333 * q^30 - 438 * q^31 + 35 * q^32 - 216 * q^33 - 150 * q^34 - 258 * q^35 + 117 * q^36 - 596 * q^37 + 664 * q^38 - 576 * q^39 - 831 * q^40 + 54 * q^41 + 9 * q^42 - 360 * q^43 - 714 * q^44 - 108 * q^45 - 871 * q^46 - 720 * q^47 - 81 * q^48 - 302 * q^49 + 4 * q^50 - 300 * q^51 - 1118 * q^52 + 694 * q^53 - 135 * q^54 - 990 * q^55 + 1917 * q^56 - 798 * q^57 + 1354 * q^58 - 378 * q^59 + 765 * q^60 - 1396 * q^61 + 1475 * q^62 - 558 * q^63 + 1225 * q^64 - 348 * q^65 + 132 * q^66 - 402 * q^67 + 2032 * q^68 + 150 * q^69 + 2415 * q^70 - 964 * q^71 - 675 * q^72 - 192 * q^73 + 2751 * q^74 - 18 * q^75 - 2306 * q^76 + 2724 * q^77 + 1416 * q^78 - 802 * q^79 + 4221 * q^80 + 486 * q^81 + 1735 * q^82 + 2126 * q^83 - 999 * q^84 - 1206 * q^85 - 609 * q^86 - 726 * q^87 + 3656 * q^88 + 432 * q^89 - 999 * q^90 + 1258 * q^91 + 3163 * q^92 - 1314 * q^93 + 1742 * q^94 + 936 * q^95 + 105 * q^96 + 1290 * q^97 + 2492 * q^98 - 648 * q^99

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