LMFDB - Embedded newform 143.4.a.c.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,4,Mod(1,143)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(143, 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("143.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	143.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:	$8.43727313082$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 59x^{7} - 12x^{6} + 1144x^{5} + 345x^{4} - 7888x^{3} - 2245x^{2} + 9710x - 2988 $ x^9 - 59x^7 - 12x^6 + 1144x^5 + 345x^4 - 7888x^3 - 2245x^2 + 9710*x - 2988
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$0.765277$ of defining polynomial
Character	$\chi$	$=$	143.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.765277 q^{2} -9.54214 q^{3} -7.41435 q^{4} -17.1562 q^{5} -7.30238 q^{6} -4.60754 q^{7} -11.7962 q^{8} +64.0525 q^{9} +O(q^{10})$	\(q+0.765277 q^{2} -9.54214 q^{3} -7.41435 q^{4} -17.1562 q^{5} -7.30238 q^{6} -4.60754 q^{7} -11.7962 q^{8} +64.0525 q^{9} -13.1292 q^{10} -11.0000 q^{11} +70.7488 q^{12} -13.0000 q^{13} -3.52604 q^{14} +163.707 q^{15} +50.2874 q^{16} -27.1592 q^{17} +49.0179 q^{18} -120.619 q^{19} +127.202 q^{20} +43.9658 q^{21} -8.41805 q^{22} -6.70134 q^{23} +112.562 q^{24} +169.335 q^{25} -9.94860 q^{26} -353.560 q^{27} +34.1619 q^{28} -257.148 q^{29} +125.281 q^{30} +78.1221 q^{31} +132.854 q^{32} +104.964 q^{33} -20.7843 q^{34} +79.0479 q^{35} -474.908 q^{36} +348.558 q^{37} -92.3069 q^{38} +124.048 q^{39} +202.379 q^{40} -66.6085 q^{41} +33.6460 q^{42} -139.541 q^{43} +81.5579 q^{44} -1098.90 q^{45} -5.12838 q^{46} +56.5721 q^{47} -479.850 q^{48} -321.771 q^{49} +129.588 q^{50} +259.157 q^{51} +96.3866 q^{52} +527.757 q^{53} -270.572 q^{54} +188.718 q^{55} +54.3517 q^{56} +1150.96 q^{57} -196.790 q^{58} -333.407 q^{59} -1213.78 q^{60} +548.859 q^{61} +59.7850 q^{62} -295.124 q^{63} -300.629 q^{64} +223.031 q^{65} +80.3262 q^{66} -211.547 q^{67} +201.368 q^{68} +63.9451 q^{69} +60.4935 q^{70} +846.848 q^{71} -755.579 q^{72} +540.090 q^{73} +266.744 q^{74} -1615.82 q^{75} +894.311 q^{76} +50.6829 q^{77} +94.9310 q^{78} -1294.67 q^{79} -862.741 q^{80} +1644.30 q^{81} -50.9740 q^{82} -1460.55 q^{83} -325.978 q^{84} +465.949 q^{85} -106.787 q^{86} +2453.75 q^{87} +129.759 q^{88} -393.293 q^{89} -840.961 q^{90} +59.8980 q^{91} +49.6861 q^{92} -745.452 q^{93} +43.2933 q^{94} +2069.36 q^{95} -1267.71 q^{96} -51.8927 q^{97} -246.244 q^{98} -704.577 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 8 q^{3} + 46 q^{4} + 30 q^{5} + 34 q^{6} + 25 q^{7} + 36 q^{8} + 91 q^{9}+O(q^{10}) $ 9 * q + 8 * q^3 + 46 * q^4 + 30 * q^5 + 34 * q^6 + 25 * q^7 + 36 * q^8 + 91 * q^9	\( 9 q + 8 q^{3} + 46 q^{4} + 30 q^{5} + 34 q^{6} + 25 q^{7} + 36 q^{8} + 91 q^{9} - 22 q^{10} - 99 q^{11} + 181 q^{12} - 117 q^{13} + 351 q^{15} + 130 q^{16} + 53 q^{17} + 33 q^{18} + 69 q^{19} + 282 q^{20} + 463 q^{21} + 216 q^{23} - 121 q^{24} + 617 q^{25} + 275 q^{27} + 279 q^{28} - 91 q^{29} + 29 q^{30} + 636 q^{31} + 663 q^{32} - 88 q^{33} + 423 q^{34} - 358 q^{35} - 252 q^{36} + 967 q^{37} - 101 q^{38} - 104 q^{39} + 652 q^{40} - 226 q^{41} - 1186 q^{42} + 42 q^{43} - 506 q^{44} + 5 q^{45} - 1127 q^{46} - 269 q^{47} - 1820 q^{48} + 228 q^{49} - 1374 q^{50} - 589 q^{51} - 598 q^{52} + 1227 q^{53} - 2438 q^{54} - 330 q^{55} - 659 q^{56} - 71 q^{57} + 471 q^{58} - 613 q^{59} - 859 q^{60} + 427 q^{61} - 1714 q^{62} + 305 q^{63} - 1194 q^{64} - 390 q^{65} - 374 q^{66} - 271 q^{67} - 2835 q^{68} - 846 q^{69} - 102 q^{70} + 2279 q^{71} - 2400 q^{72} + 3602 q^{73} - 4955 q^{74} - 883 q^{75} + 1126 q^{76} - 275 q^{77} - 442 q^{78} - 1182 q^{79} - 2360 q^{80} + 2697 q^{81} + 1007 q^{82} - 1877 q^{83} + 1618 q^{84} - 441 q^{85} + 830 q^{86} + 1942 q^{87} - 396 q^{88} + 1258 q^{89} - 5669 q^{90} - 325 q^{91} + 1046 q^{92} + 1556 q^{93} + 1439 q^{94} + 2032 q^{95} - 3417 q^{96} + 4002 q^{97} - 1855 q^{98} - 1001 q^{99}+O(q^{100}) \) 9 * q + 8 * q^3 + 46 * q^4 + 30 * q^5 + 34 * q^6 + 25 * q^7 + 36 * q^8 + 91 * q^9 - 22 * q^10 - 99 * q^11 + 181 * q^12 - 117 * q^13 + 351 * q^15 + 130 * q^16 + 53 * q^17 + 33 * q^18 + 69 * q^19 + 282 * q^20 + 463 * q^21 + 216 * q^23 - 121 * q^24 + 617 * q^25 + 275 * q^27 + 279 * q^28 - 91 * q^29 + 29 * q^30 + 636 * q^31 + 663 * q^32 - 88 * q^33 + 423 * q^34 - 358 * q^35 - 252 * q^36 + 967 * q^37 - 101 * q^38 - 104 * q^39 + 652 * q^40 - 226 * q^41 - 1186 * q^42 + 42 * q^43 - 506 * q^44 + 5 * q^45 - 1127 * q^46 - 269 * q^47 - 1820 * q^48 + 228 * q^49 - 1374 * q^50 - 589 * q^51 - 598 * q^52 + 1227 * q^53 - 2438 * q^54 - 330 * q^55 - 659 * q^56 - 71 * q^57 + 471 * q^58 - 613 * q^59 - 859 * q^60 + 427 * q^61 - 1714 * q^62 + 305 * q^63 - 1194 * q^64 - 390 * q^65 - 374 * q^66 - 271 * q^67 - 2835 * q^68 - 846 * q^69 - 102 * q^70 + 2279 * q^71 - 2400 * q^72 + 3602 * q^73 - 4955 * q^74 - 883 * q^75 + 1126 * q^76 - 275 * q^77 - 442 * q^78 - 1182 * q^79 - 2360 * q^80 + 2697 * q^81 + 1007 * q^82 - 1877 * q^83 + 1618 * q^84 - 441 * q^85 + 830 * q^86 + 1942 * q^87 - 396 * q^88 + 1258 * q^89 - 5669 * q^90 - 325 * q^91 + 1046 * q^92 + 1556 * q^93 + 1439 * q^94 + 2032 * q^95 - 3417 * q^96 + 4002 * q^97 - 1855 * q^98 - 1001 * 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 $

$2$	0.765277	0.270566	0.135283	−	0.990807i	$-0.456806\pi$
$2$	0.765277	0.270566	0.135283	+	0.990807i	$0.456806\pi$
$3$	−9.54214	−1.83639	−0.918193	−	0.396133i	$-0.870352\pi$
$3$	−9.54214	−1.83639	−0.918193	+	0.396133i	$0.870352\pi$
$4$	−7.41435	−0.926794
$5$	−17.1562	−1.53450	−0.767249	−	0.641350i	$-0.778375\pi$
$5$	−17.1562	−1.53450	−0.767249	+	0.641350i	$0.778375\pi$
$6$	−7.30238	−0.496864
$7$	−4.60754	−0.248784	−0.124392	−	0.992233i	$-0.539698\pi$
$7$	−4.60754	−0.248784	−0.124392	+	0.992233i	$0.539698\pi$
$8$	−11.7962	−0.521326
$9$	64.0525	2.37231
$10$	−13.1292	−0.415183
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	70.7488	1.70195
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	−3.52604	−0.0673125
$15$	163.707	2.81793
$16$	50.2874	0.785741
$17$	−27.1592	−0.387475	−0.193738	−	0.981053i	$-0.562061\pi$
$17$	−27.1592	−0.387475	−0.193738	+	0.981053i	$0.562061\pi$
$18$	49.0179	0.641868
$19$	−120.619	−1.45641	−0.728207	−	0.685357i	$-0.759646\pi$
$19$	−120.619	−1.45641	−0.728207	+	0.685357i	$0.759646\pi$
$20$	127.202	1.42216
$21$	43.9658	0.456863
$22$	−8.41805	−0.0815788
$23$	−6.70134	−0.0607533	−0.0303766	−	0.999539i	$-0.509671\pi$
$23$	−6.70134	−0.0607533	−0.0303766	+	0.999539i	$0.509671\pi$
$24$	112.562	0.957355
$25$	169.335	1.35468
$26$	−9.94860	−0.0750416
$27$	−353.560	−2.52010
$28$	34.1619	0.230571
$29$	−257.148	−1.64659	−0.823297	−	0.567610i	$-0.807868\pi$
$29$	−257.148	−1.64659	−0.823297	+	0.567610i	$0.807868\pi$
$30$	125.281	0.762437
$31$	78.1221	0.452617	0.226309	−	0.974056i	$-0.427334\pi$
$31$	78.1221	0.452617	0.226309	+	0.974056i	$0.427334\pi$
$32$	132.854	0.733920
$33$	104.964	0.553691
$34$	−20.7843	−0.104838
$35$	79.0479	0.381758
$36$	−474.908	−2.19865
$37$	348.558	1.54872	0.774359	−	0.632746i	$-0.218072\pi$
$37$	348.558	1.54872	0.774359	+	0.632746i	$0.218072\pi$
$38$	−92.3069	−0.394057
$39$	124.048	0.509322
$40$	202.379	0.799973
$41$	−66.6085	−0.253720	−0.126860	−	0.991921i	$-0.540490\pi$
$41$	−66.6085	−0.253720	−0.126860	+	0.991921i	$0.540490\pi$
$42$	33.6460	0.123612
$43$	−139.541	−0.494878	−0.247439	−	0.968903i	$-0.579589\pi$
$43$	−139.541	−0.494878	−0.247439	+	0.968903i	$0.579589\pi$
$44$	81.5579	0.279439
$45$	−1098.90	−3.64031
$46$	−5.12838	−0.0164378
$47$	56.5721	0.175572	0.0877860	−	0.996139i	$-0.472021\pi$
$47$	56.5721	0.175572	0.0877860	+	0.996139i	$0.472021\pi$
$48$	−479.850	−1.44292
$49$	−321.771	−0.938107
$50$	129.588	0.366531
$51$	259.157	0.711554
$52$	96.3866	0.257046
$53$	527.757	1.36779	0.683896	−	0.729580i	$-0.260284\pi$
$53$	527.757	1.36779	0.683896	+	0.729580i	$0.260284\pi$
$54$	−270.572	−0.681854
$55$	188.718	0.462668
$56$	54.3517	0.129697
$57$	1150.96	2.67454
$58$	−196.790	−0.445513
$59$	−333.407	−0.735694	−0.367847	−	0.929886i	$-0.619905\pi$
$59$	−333.407	−0.735694	−0.367847	+	0.929886i	$0.619905\pi$
$60$	−1213.78	−2.61164
$61$	548.859	1.15204	0.576018	−	0.817437i	$-0.304606\pi$
$61$	548.859	1.15204	0.576018	+	0.817437i	$0.304606\pi$
$62$	59.7850	0.122463
$63$	−295.124	−0.590193
$64$	−300.629	−0.587167
$65$	223.031	0.425593
$66$	80.3262	0.149810
$67$	−211.547	−0.385740	−0.192870	−	0.981224i	$-0.561780\pi$
$67$	−211.547	−0.385740	−0.192870	+	0.981224i	$0.561780\pi$
$68$	201.368	0.359110
$69$	63.9451	0.111567
$70$	60.4935	0.103291
$71$	846.848	1.41553	0.707763	−	0.706450i	$-0.249704\pi$
$71$	846.848	1.41553	0.707763	+	0.706450i	$0.249704\pi$
$72$	−755.579	−1.23675
$73$	540.090	0.865928	0.432964	−	0.901411i	$-0.357468\pi$
$73$	540.090	0.865928	0.432964	+	0.901411i	$0.357468\pi$
$74$	266.744	0.419031
$75$	−1615.82	−2.48772
$76$	894.311	1.34980
$77$	50.6829	0.0750111
$78$	94.9310	0.137805
$79$	−1294.67	−1.84382	−0.921909	−	0.387406i	$-0.873371\pi$
$79$	−1294.67	−1.84382	−0.921909	+	0.387406i	$0.873371\pi$
$80$	−862.741	−1.20572
$81$	1644.30	2.25556
$82$	−50.9740	−0.0686480
$83$	−1460.55	−1.93153	−0.965763	−	0.259425i	$-0.916467\pi$
$83$	−1460.55	−1.93153	−0.965763	+	0.259425i	$0.916467\pi$
$84$	−325.978	−0.423418
$85$	465.949	0.594580
$86$	−106.787	−0.133897
$87$	2453.75	3.02378
$88$	129.759	0.157186
$89$	−393.293	−0.468415	−0.234208	−	0.972187i	$-0.575250\pi$
$89$	−393.293	−0.468415	−0.234208	+	0.972187i	$0.575250\pi$
$90$	−840.961	−0.984946
$91$	59.8980	0.0690002
$92$	49.6861	0.0563058
$93$	−745.452	−0.831180
$94$	43.2933	0.0475039
$95$	2069.36	2.23487
$96$	−1267.71	−1.34776
$97$	−51.8927	−0.0543186	−0.0271593	−	0.999631i	$-0.508646\pi$
$97$	−51.8927	−0.0543186	−0.0271593	+	0.999631i	$0.508646\pi$
$98$	−246.244	−0.253820
$99$	−704.577	−0.715280
$100$	−1255.51	−1.25551
$101$	−1608.92	−1.58508	−0.792542	−	0.609817i	$-0.791243\pi$
$101$	−1608.92	−1.58508	−0.792542	+	0.609817i	$0.791243\pi$
$102$	198.327	0.192523
$103$	1279.86	1.22435	0.612176	−	0.790721i	$-0.290294\pi$
$103$	1279.86	1.22435	0.612176	+	0.790721i	$0.290294\pi$
$104$	153.351	0.144590
$105$	−754.286	−0.701055
$106$	403.880	0.370078
$107$	195.933	0.177024	0.0885121	−	0.996075i	$-0.471789\pi$
$107$	195.933	0.177024	0.0885121	+	0.996075i	$0.471789\pi$
$108$	2621.42	2.33561
$109$	1301.97	1.14409	0.572046	−	0.820222i	$-0.306150\pi$
$109$	1301.97	1.14409	0.572046	+	0.820222i	$0.306150\pi$
$110$	144.422	0.125182
$111$	−3325.99	−2.84405
$112$	−231.701	−0.195479
$113$	455.508	0.379209	0.189604	−	0.981861i	$-0.439279\pi$
$113$	455.508	0.379209	0.189604	+	0.981861i	$0.439279\pi$
$114$	880.806	0.723641
$115$	114.970	0.0932258
$116$	1906.59	1.52605
$117$	−832.682	−0.657962
$118$	−255.149	−0.199054
$119$	125.137	0.0963975
$120$	−1931.13	−1.46906
$121$	121.000	0.0909091
$122$	420.029	0.311702
$123$	635.588	0.465927
$124$	−579.224	−0.419483
$125$	−760.626	−0.544260
$126$	−225.852	−0.159686
$127$	−92.1973	−0.0644188	−0.0322094	−	0.999481i	$-0.510254\pi$
$127$	−92.1973	−0.0644188	−0.0322094	+	0.999481i	$0.510254\pi$
$128$	−1292.90	−0.892788
$129$	1331.52	0.908788
$130$	170.680	0.115151
$131$	270.704	0.180546	0.0902731	−	0.995917i	$-0.471226\pi$
$131$	270.704	0.180546	0.0902731	+	0.995917i	$0.471226\pi$
$132$	−778.237	−0.513158
$133$	555.756	0.362332
$134$	−161.892	−0.104368
$135$	6065.75	3.86709
$136$	320.377	0.202001
$137$	2631.89	1.64129	0.820646	−	0.571436i	$-0.193614\pi$
$137$	2631.89	1.64129	0.820646	+	0.571436i	$0.193614\pi$
$138$	48.9357	0.0301861
$139$	1986.23	1.21201	0.606006	−	0.795460i	$-0.292771\pi$
$139$	1986.23	1.21201	0.606006	+	0.795460i	$0.292771\pi$
$140$	−586.089	−0.353811
$141$	−539.819	−0.322418
$142$	648.073	0.382994
$143$	143.000	0.0836242
$144$	3221.03	1.86402
$145$	4411.69	2.52670
$146$	413.318	0.234291
$147$	3070.38	1.72273
$148$	−2584.33	−1.43534
$149$	817.443	0.449446	0.224723	−	0.974423i	$-0.427852\pi$
$149$	817.443	0.449446	0.224723	+	0.974423i	$0.427852\pi$
$150$	−1236.55	−0.673093
$151$	−1584.77	−0.854082	−0.427041	−	0.904232i	$-0.640444\pi$
$151$	−1584.77	−0.854082	−0.427041	+	0.904232i	$0.640444\pi$
$152$	1422.85	0.759266
$153$	−1739.62	−0.919213
$154$	38.7865	0.0202955
$155$	−1340.28	−0.694540
$156$	−919.734	−0.472036
$157$	300.034	0.152518	0.0762589	−	0.997088i	$-0.475702\pi$
$157$	300.034	0.152518	0.0762589	+	0.997088i	$0.475702\pi$
$158$	−990.781	−0.498875
$159$	−5035.93	−2.51179
$160$	−2279.27	−1.12620
$161$	30.8767	0.0151144
$162$	1258.35	0.610279
$163$	1764.24	0.847766	0.423883	−	0.905717i	$-0.360667\pi$
$163$	1764.24	0.847766	0.423883	+	0.905717i	$0.360667\pi$
$164$	493.859	0.235146
$165$	−1800.78	−0.849638
$166$	−1117.73	−0.522606
$167$	−2262.97	−1.04858	−0.524292	−	0.851538i	$-0.675670\pi$
$167$	−2262.97	−1.04858	−0.524292	+	0.851538i	$0.675670\pi$
$168$	−518.631	−0.238174
$169$	169.000	0.0769231
$170$	356.580	0.160873
$171$	−7725.94	−3.45507
$172$	1034.60	0.458650
$173$	−3704.00	−1.62780	−0.813901	−	0.581003i	$-0.802660\pi$
$173$	−3704.00	−1.62780	−0.813901	+	0.581003i	$0.802660\pi$
$174$	1877.80	0.818134
$175$	−780.219	−0.337023
$176$	−553.161	−0.236910
$177$	3181.42	1.35102
$178$	−300.978	−0.126737
$179$	−1024.05	−0.427604	−0.213802	−	0.976877i	$-0.568585\pi$
$179$	−1024.05	−0.427604	−0.213802	+	0.976877i	$0.568585\pi$
$180$	8147.61	3.37382
$181$	3561.20	1.46244	0.731221	−	0.682141i	$-0.238951\pi$
$181$	3561.20	1.46244	0.731221	+	0.682141i	$0.238951\pi$
$182$	45.8386	0.0186691
$183$	−5237.29	−2.11558
$184$	79.0507	0.0316722
$185$	−5979.93	−2.37651
$186$	−570.477	−0.224889
$187$	298.751	0.116828
$188$	−419.445	−0.162719
$189$	1629.04	0.626960
$190$	1583.64	0.604679
$191$	−4947.45	−1.87427	−0.937134	−	0.348971i	$-0.886531\pi$
$191$	−4947.45	−1.87427	−0.937134	+	0.348971i	$0.886531\pi$
$192$	2868.65	1.07826
$193$	4032.80	1.50408	0.752039	−	0.659118i	$-0.229070\pi$
$193$	4032.80	1.50408	0.752039	+	0.659118i	$0.229070\pi$
$194$	−39.7123	−0.0146968
$195$	−2128.19	−0.781553
$196$	2385.72	0.869432
$197$	−3930.21	−1.42140	−0.710700	−	0.703495i	$-0.751622\pi$
$197$	−3930.21	−1.42140	−0.710700	+	0.703495i	$0.751622\pi$
$198$	−539.197	−0.193531
$199$	1404.23	0.500217	0.250109	−	0.968218i	$-0.419534\pi$
$199$	1404.23	0.500217	0.250109	+	0.968218i	$0.419534\pi$
$200$	−1997.52	−0.706231
$201$	2018.61	0.708368
$202$	−1231.27	−0.428870
$203$	1184.82	0.409646
$204$	−1921.48	−0.659464
$205$	1142.75	0.389332
$206$	979.447	0.331268
$207$	−429.238	−0.144126
$208$	−653.736	−0.217925
$209$	1326.81	0.439126
$210$	−577.238	−0.189682
$211$	−5389.48	−1.75842	−0.879211	−	0.476432i	$-0.841930\pi$
$211$	−5389.48	−1.75842	−0.879211	+	0.476432i	$0.841930\pi$
$212$	−3912.97	−1.26766
$213$	−8080.75	−2.59945
$214$	149.943	0.0478968
$215$	2393.99	0.759389
$216$	4170.68	1.31379
$217$	−359.950	−0.112604
$218$	996.367	0.309553
$219$	−5153.61	−1.59018
$220$	−1399.22	−0.428798
$221$	353.070	0.107466
$222$	−2545.31	−0.769503
$223$	−4999.29	−1.50124	−0.750621	−	0.660733i	$-0.770246\pi$
$223$	−4999.29	−1.50124	−0.750621	+	0.660733i	$0.770246\pi$
$224$	−612.129	−0.182587
$225$	10846.4	3.21373
$226$	348.590	0.102601
$227$	1621.30	0.474051	0.237025	−	0.971503i	$-0.423828\pi$
$227$	1621.30	0.474051	0.237025	+	0.971503i	$0.423828\pi$
$228$	−8533.65	−2.47875
$229$	1980.22	0.571426	0.285713	−	0.958315i	$-0.407770\pi$
$229$	1980.22	0.571426	0.285713	+	0.958315i	$0.407770\pi$
$230$	87.9836	0.0252238
$231$	−483.624	−0.137749
$232$	3033.39	0.858412
$233$	696.381	0.195800	0.0979001	−	0.995196i	$-0.468787\pi$
$233$	696.381	0.195800	0.0979001	+	0.995196i	$0.468787\pi$
$234$	−637.233	−0.178022
$235$	−970.562	−0.269415
$236$	2472.00	0.681836
$237$	12353.9	3.38596
$238$	95.7646	0.0260819
$239$	−1909.56	−0.516816	−0.258408	−	0.966036i	$-0.583198\pi$
$239$	−1909.56	−0.516816	−0.258408	+	0.966036i	$0.583198\pi$
$240$	8232.40	2.21416
$241$	4527.84	1.21022	0.605112	−	0.796141i	$-0.293128\pi$
$241$	4527.84	1.21022	0.605112	+	0.796141i	$0.293128\pi$
$242$	92.5985	0.0245969
$243$	−6144.07	−1.62198
$244$	−4069.43	−1.06770
$245$	5520.36	1.43952
$246$	486.401	0.126064
$247$	1568.05	0.403937
$248$	−921.547	−0.235961
$249$	13936.8	3.54703
$250$	−582.090	−0.147258
$251$	−3625.62	−0.911742	−0.455871	−	0.890046i	$-0.650672\pi$
$251$	−3625.62	−0.911742	−0.455871	+	0.890046i	$0.650672\pi$
$252$	2188.16	0.546987
$253$	73.7147	0.0183178
$254$	−70.5565	−0.0174296
$255$	−4446.15	−1.09188
$256$	1415.61	0.345608
$257$	−33.4012	−0.00810703	−0.00405351	−	0.999992i	$-0.501290\pi$
$257$	−33.4012	−0.00810703	−0.00405351	+	0.999992i	$0.501290\pi$
$258$	1018.98	0.245887
$259$	−1605.99	−0.385296
$260$	−1653.63	−0.394437
$261$	−16471.0	−3.90624
$262$	207.164	0.0488497
$263$	885.980	0.207726	0.103863	−	0.994592i	$-0.466880\pi$
$263$	885.980	0.207726	0.103863	+	0.994592i	$0.466880\pi$
$264$	−1238.18	−0.288653
$265$	−9054.30	−2.09887
$266$	425.308	0.0980349
$267$	3752.86	0.860191
$268$	1568.48	0.357501
$269$	−1464.23	−0.331881	−0.165940	−	0.986136i	$-0.553066\pi$
$269$	−1464.23	−0.331881	−0.165940	+	0.986136i	$0.553066\pi$
$270$	4641.98	1.04630
$271$	1010.25	0.226452	0.113226	−	0.993569i	$-0.463882\pi$
$271$	1010.25	0.226452	0.113226	+	0.993569i	$0.463882\pi$
$272$	−1365.77	−0.304455
$273$	−571.555	−0.126711
$274$	2014.12	0.444079
$275$	−1862.69	−0.408452
$276$	−474.112	−0.103399
$277$	5869.48	1.27315	0.636576	−	0.771214i	$-0.280350\pi$
$277$	5869.48	1.27315	0.636576	+	0.771214i	$0.280350\pi$
$278$	1520.01	0.327930
$279$	5003.91	1.07375
$280$	−932.468	−0.199020
$281$	5296.86	1.12450	0.562249	−	0.826968i	$-0.309936\pi$
$281$	5296.86	1.12450	0.562249	+	0.826968i	$0.309936\pi$
$282$	−413.111	−0.0872354
$283$	9032.41	1.89725	0.948624	−	0.316407i	$-0.102476\pi$
$283$	9032.41	1.89725	0.948624	+	0.316407i	$0.102476\pi$
$284$	−6278.83	−1.31190
$285$	−19746.2	−4.10408
$286$	109.435	0.0226259
$287$	306.901	0.0631213
$288$	8509.62	1.74109
$289$	−4175.38	−0.849863
$290$	3376.17	0.683639
$291$	495.168	0.0997500
$292$	−4004.41	−0.802536
$293$	−1016.00	−0.202578	−0.101289	−	0.994857i	$-0.532297\pi$
$293$	−1016.00	−0.202578	−0.101289	+	0.994857i	$0.532297\pi$
$294$	2349.69	0.466112
$295$	5720.00	1.12892
$296$	−4111.68	−0.807387
$297$	3889.16	0.759839
$298$	625.570	0.121605
$299$	87.1174	0.0168499
$300$	11980.3	2.30560
$301$	642.939	0.123118
$302$	−1212.78	−0.231086
$303$	15352.5	2.91083
$304$	−6065.61	−1.14436
$305$	−9416.33	−1.76780
$306$	−1331.29	−0.248708
$307$	5978.71	1.11148	0.555738	−	0.831357i	$-0.312436\pi$
$307$	5978.71	1.11148	0.555738	+	0.831357i	$0.312436\pi$
$308$	−375.781	−0.0695198
$309$	−12212.6	−2.24838
$310$	−1025.68	−0.187919
$311$	−7881.59	−1.43705	−0.718527	−	0.695499i	$-0.755183\pi$
$311$	−7881.59	−1.43705	−0.718527	+	0.695499i	$0.755183\pi$
$312$	−1463.30	−0.265523
$313$	−6214.18	−1.12219	−0.561096	−	0.827751i	$-0.689620\pi$
$313$	−6214.18	−1.12219	−0.561096	+	0.827751i	$0.689620\pi$
$314$	229.609	0.0412662
$315$	5063.21	0.905650
$316$	9599.13	1.70884
$317$	7409.37	1.31278	0.656391	−	0.754421i	$-0.272082\pi$
$317$	7409.37	1.31278	0.656391	+	0.754421i	$0.272082\pi$
$318$	−3853.88	−0.679607
$319$	2828.63	0.496467
$320$	5157.66	0.901006
$321$	−1869.62	−0.325085
$322$	23.6292	0.00408945
$323$	3275.92	0.564325
$324$	−12191.5	−2.09044
$325$	−2201.36	−0.375721
$326$	1350.13	0.229377
$327$	−12423.6	−2.10099
$328$	785.730	0.132270
$329$	−260.658	−0.0436794
$330$	−1378.09	−0.229883
$331$	8130.48	1.35013	0.675063	−	0.737760i	$-0.264117\pi$
$331$	8130.48	1.35013	0.675063	+	0.737760i	$0.264117\pi$
$332$	10829.1	1.79013
$333$	22326.0	3.67405
$334$	−1731.80	−0.283712
$335$	3629.34	0.591917
$336$	2210.93	0.358976
$337$	4741.96	0.766502	0.383251	−	0.923644i	$-0.374805\pi$
$337$	4741.96	0.766502	0.383251	+	0.923644i	$0.374805\pi$
$338$	129.332	0.0208128
$339$	−4346.52	−0.696374
$340$	−3454.71	−0.551053
$341$	−859.343	−0.136469
$342$	−5912.49	−0.934827
$343$	3062.96	0.482169
$344$	1646.06	0.257993
$345$	−1097.06	−0.171199
$346$	−2834.59	−0.440429
$347$	4248.16	0.657214	0.328607	−	0.944467i	$-0.393421\pi$
$347$	4248.16	0.657214	0.328607	+	0.944467i	$0.393421\pi$
$348$	−18192.9	−2.80242
$349$	−3888.51	−0.596411	−0.298205	−	0.954502i	$-0.596388\pi$
$349$	−3888.51	−0.596411	−0.298205	+	0.954502i	$0.596388\pi$
$350$	−597.084	−0.0911870
$351$	4596.28	0.698950
$352$	−1461.39	−0.221285
$353$	286.193	0.0431516	0.0215758	−	0.999767i	$-0.493132\pi$
$353$	286.193	0.0431516	0.0215758	+	0.999767i	$0.493132\pi$
$354$	2434.67	0.365540
$355$	−14528.7	−2.17212
$356$	2916.01	0.434124
$357$	−1194.08	−0.177023
$358$	−783.682	−0.115695
$359$	2797.34	0.411248	0.205624	−	0.978631i	$-0.434078\pi$
$359$	2797.34	0.411248	0.205624	+	0.978631i	$0.434078\pi$
$360$	12962.9	1.89779
$361$	7689.93	1.12114
$362$	2725.31	0.395688
$363$	−1154.60	−0.166944
$364$	−444.105	−0.0639489
$365$	−9265.89	−1.32876
$366$	−4007.98	−0.572405
$367$	9825.39	1.39750	0.698748	−	0.715367i	$-0.253741\pi$
$367$	9825.39	1.39750	0.698748	+	0.715367i	$0.253741\pi$
$368$	−336.993	−0.0477363
$369$	−4266.44	−0.601903
$370$	−4576.31	−0.643002
$371$	−2431.66	−0.340284
$372$	5527.04	0.770333
$373$	−7772.12	−1.07889	−0.539444	−	0.842022i	$-0.681365\pi$
$373$	−7772.12	−1.07889	−0.539444	+	0.842022i	$0.681365\pi$
$374$	228.628	0.0316098
$375$	7258.00	0.999471
$376$	−667.338	−0.0915301
$377$	3342.93	0.456683
$378$	1246.67	0.169634
$379$	−4645.18	−0.629570	−0.314785	−	0.949163i	$-0.601932\pi$
$379$	−4645.18	−0.629570	−0.314785	+	0.949163i	$0.601932\pi$
$380$	−15343.0	−2.07126
$381$	879.760	0.118298
$382$	−3786.17	−0.507114
$383$	5414.13	0.722322	0.361161	−	0.932503i	$-0.382380\pi$
$383$	5414.13	0.722322	0.361161	+	0.932503i	$0.382380\pi$
$384$	12337.0	1.63950
$385$	−869.526	−0.115104
$386$	3086.21	0.406953
$387$	−8937.93	−1.17401
$388$	384.751	0.0503422
$389$	5464.02	0.712176	0.356088	−	0.934452i	$-0.384110\pi$
$389$	5464.02	0.712176	0.356088	+	0.934452i	$0.384110\pi$
$390$	−1628.66	−0.211462
$391$	182.003	0.0235404
$392$	3795.69	0.489059
$393$	−2583.10	−0.331553
$394$	−3007.70	−0.384583
$395$	22211.6	2.82934
$396$	5223.98	0.662917
$397$	761.736	0.0962984	0.0481492	−	0.998840i	$-0.484668\pi$
$397$	761.736	0.0962984	0.0481492	+	0.998840i	$0.484668\pi$
$398$	1074.63	0.135342
$399$	−5303.11	−0.665382
$400$	8515.43	1.06443
$401$	1168.07	0.145463	0.0727313	−	0.997352i	$-0.476828\pi$
$401$	1168.07	0.145463	0.0727313	+	0.997352i	$0.476828\pi$
$402$	1544.80	0.191660
$403$	−1015.59	−0.125533
$404$	11929.1	1.46905
$405$	−28210.0	−3.46115
$406$	906.716	0.110836
$407$	−3834.14	−0.466956
$408$	−3057.08	−0.370951
$409$	−6496.98	−0.785464	−0.392732	−	0.919653i	$-0.628470\pi$
$409$	−6496.98	−0.785464	−0.392732	+	0.919653i	$0.628470\pi$
$410$	874.520	0.105340
$411$	−25113.8	−3.01405
$412$	−9489.33	−1.13472
$413$	1536.19	0.183029
$414$	−328.486	−0.0389956
$415$	25057.6	2.96392
$416$	−1727.10	−0.203553
$417$	−18952.9	−2.22572
$418$	1015.38	0.118813
$419$	−1130.92	−0.131859	−0.0659297	−	0.997824i	$-0.521001\pi$
$419$	−1130.92	−0.131859	−0.0659297	+	0.997824i	$0.521001\pi$
$420$	5592.54	0.649733
$421$	−1999.44	−0.231465	−0.115732	−	0.993280i	$-0.536921\pi$
$421$	−1999.44	−0.231465	−0.115732	+	0.993280i	$0.536921\pi$
$422$	−4124.45	−0.475770
$423$	3623.58	0.416512
$424$	−6225.55	−0.713064
$425$	−4599.02	−0.524906
$426$	−6184.01	−0.703324
$427$	−2528.89	−0.286608
$428$	−1452.72	−0.164065
$429$	−1364.53	−0.153566
$430$	1832.07	0.205465
$431$	−7360.14	−0.822565	−0.411282	−	0.911508i	$-0.634919\pi$
$431$	−7360.14	−0.822565	−0.411282	+	0.911508i	$0.634919\pi$
$432$	−17779.6	−1.98015
$433$	6965.19	0.773038	0.386519	−	0.922281i	$-0.373677\pi$
$433$	6965.19	0.773038	0.386519	+	0.922281i	$0.373677\pi$
$434$	−275.462	−0.0304668
$435$	−42097.0	−4.63999
$436$	−9653.26	−1.06034
$437$	808.308	0.0884820
$438$	−3943.94	−0.430248
$439$	6034.51	0.656063	0.328031	−	0.944667i	$-0.393615\pi$
$439$	6034.51	0.656063	0.328031	+	0.944667i	$0.393615\pi$
$440$	−2226.17	−0.241201
$441$	−20610.2	−2.22548
$442$	270.196	0.0290768
$443$	8249.55	0.884759	0.442379	−	0.896828i	$-0.354134\pi$
$443$	8249.55	0.884759	0.442379	+	0.896828i	$0.354134\pi$
$444$	24660.1	2.63584
$445$	6747.41	0.718782
$446$	−3825.84	−0.406186
$447$	−7800.16	−0.825357
$448$	1385.16	0.146077
$449$	7293.54	0.766600	0.383300	−	0.923624i	$-0.374788\pi$
$449$	7293.54	0.766600	0.383300	+	0.923624i	$0.374788\pi$
$450$	8300.46	0.869528
$451$	732.694	0.0764993
$452$	−3377.30	−0.351448
$453$	15122.1	1.56842
$454$	1240.74	0.128262
$455$	−1027.62	−0.105881
$456$	−13577.0	−1.39431
$457$	−1476.68	−0.151151	−0.0755756	−	0.997140i	$-0.524079\pi$
$457$	−1476.68	−0.151151	−0.0755756	+	0.997140i	$0.524079\pi$
$458$	1515.42	0.154609
$459$	9602.42	0.976476
$460$	−852.425	−0.0864011
$461$	−3162.07	−0.319463	−0.159731	−	0.987161i	$-0.551063\pi$
$461$	−3162.07	−0.319463	−0.159731	+	0.987161i	$0.551063\pi$
$462$	−370.106	−0.0372703
$463$	−6371.33	−0.639527	−0.319763	−	0.947497i	$-0.603603\pi$
$463$	−6371.33	−0.639527	−0.319763	+	0.947497i	$0.603603\pi$
$464$	−12931.3	−1.29380
$465$	12789.1	1.27544
$466$	532.925	0.0529769
$467$	14599.9	1.44668	0.723341	−	0.690491i	$-0.242605\pi$
$467$	14599.9	1.44668	0.723341	+	0.690491i	$0.242605\pi$
$468$	6173.80	0.609795
$469$	974.711	0.0959658
$470$	−742.749	−0.0728945
$471$	−2862.97	−0.280082
$472$	3932.95	0.383536
$473$	1534.95	0.149211
$474$	9454.17	0.916128
$475$	−20425.0	−1.97298
$476$	−927.811	−0.0893406
$477$	33804.1	3.24483
$478$	−1461.34	−0.139833
$479$	1662.93	0.158624	0.0793122	−	0.996850i	$-0.474728\pi$
$479$	1662.93	0.158624	0.0793122	+	0.996850i	$0.474728\pi$
$480$	21749.1	2.06814
$481$	−4531.26	−0.429537
$482$	3465.05	0.327446
$483$	−294.630	−0.0277559
$484$	−897.136	−0.0842540
$485$	890.282	0.0833518
$486$	−4701.91	−0.438854
$487$	−924.268	−0.0860012	−0.0430006	−	0.999075i	$-0.513692\pi$
$487$	−924.268	−0.0860012	−0.0430006	+	0.999075i	$0.513692\pi$
$488$	−6474.48	−0.600586
$489$	−16834.6	−1.55683
$490$	4224.61	0.389486
$491$	5265.07	0.483930	0.241965	−	0.970285i	$-0.422208\pi$
$491$	5265.07	0.483930	0.241965	+	0.970285i	$0.422208\pi$
$492$	−4712.47	−0.431818
$493$	6983.95	0.638015
$494$	1199.99	0.109292
$495$	12087.9	1.09760
$496$	3928.56	0.355640
$497$	−3901.88	−0.352160
$498$	10665.5	0.959707
$499$	12609.2	1.13120	0.565598	−	0.824681i	$-0.308646\pi$
$499$	12609.2	1.13120	0.565598	+	0.824681i	$0.308646\pi$
$500$	5639.55	0.504416
$501$	21593.6	1.92561
$502$	−2774.61	−0.246687
$503$	−491.059	−0.0435293	−0.0217647	−	0.999763i	$-0.506928\pi$
$503$	−491.059	−0.0435293	−0.0217647	+	0.999763i	$0.506928\pi$
$504$	3481.36	0.307683
$505$	27603.0	2.43231
$506$	56.4122	0.00495618
$507$	−1612.62	−0.141260
$508$	683.583	0.0597030
$509$	−9036.02	−0.786866	−0.393433	−	0.919353i	$-0.628713\pi$
$509$	−9036.02	−0.786866	−0.393433	+	0.919353i	$0.628713\pi$
$510$	−3402.54	−0.295425
$511$	−2488.48	−0.215429
$512$	11426.5	0.986298
$513$	42646.1	3.67031
$514$	−25.5611	−0.00219349
$515$	−21957.5	−1.87877
$516$	−9872.34	−0.842259
$517$	−622.293	−0.0529369
$518$	−1229.03	−0.104248
$519$	35344.1	2.98927
$520$	−2630.93	−0.221873
$521$	−6608.36	−0.555696	−0.277848	−	0.960625i	$-0.589621\pi$
$521$	−6608.36	−0.555696	−0.277848	+	0.960625i	$0.589621\pi$
$522$	−12604.9	−1.05690
$523$	−6437.67	−0.538240	−0.269120	−	0.963107i	$-0.586733\pi$
$523$	−6437.67	−0.538240	−0.269120	+	0.963107i	$0.586733\pi$
$524$	−2007.10	−0.167329
$525$	7444.96	0.618904
$526$	678.020	0.0562036
$527$	−2121.73	−0.175378
$528$	5278.35	0.435058
$529$	−12122.1	−0.996309
$530$	−6929.05	−0.567884
$531$	−21355.6	−1.74530
$532$	−4120.57	−0.335807
$533$	865.911	0.0703691
$534$	2871.97	0.232739
$535$	−3361.47	−0.271643
$536$	2495.46	0.201096
$537$	9771.63	0.785246
$538$	−1120.55	−0.0897958
$539$	3539.48	0.282850
$540$	−44973.6	−3.58399
$541$	9122.32	0.724952	0.362476	−	0.931993i	$-0.381931\pi$
$541$	9122.32	0.724952	0.362476	+	0.931993i	$0.381931\pi$
$542$	773.123	0.0612703
$543$	−33981.5	−2.68561
$544$	−3608.21	−0.284376
$545$	−22336.8	−1.75561
$546$	−437.398	−0.0342837
$547$	−12728.6	−0.994944	−0.497472	−	0.867480i	$-0.665738\pi$
$547$	−12728.6	−0.994944	−0.497472	+	0.867480i	$0.665738\pi$
$548$	−19513.7	−1.52114
$549$	35155.8	2.73299
$550$	−1425.47	−0.110513
$551$	31017.0	2.39813
$552$	−754.313	−0.0581625
$553$	5965.24	0.458712
$554$	4491.78	0.344472
$555$	57061.4	4.36418
$556$	−14726.6	−1.12329
$557$	−9499.03	−0.722598	−0.361299	−	0.932450i	$-0.617667\pi$
$557$	−9499.03	−0.722598	−0.361299	+	0.932450i	$0.617667\pi$
$558$	3829.38	0.290521
$559$	1814.03	0.137255
$560$	3975.11	0.299963
$561$	−2850.73	−0.214542
$562$	4053.56	0.304251
$563$	−6227.76	−0.466196	−0.233098	−	0.972453i	$-0.574886\pi$
$563$	−6227.76	−0.466196	−0.233098	+	0.972453i	$0.574886\pi$
$564$	4002.40	0.298815
$565$	−7814.79	−0.581895
$566$	6912.30	0.513331
$567$	−7576.20	−0.561147
$568$	−9989.63	−0.737950
$569$	17393.6	1.28151	0.640754	−	0.767746i	$-0.278622\pi$
$569$	17393.6	1.28151	0.640754	+	0.767746i	$0.278622\pi$
$570$	−15111.3	−1.11042
$571$	−7734.09	−0.566833	−0.283417	−	0.958997i	$-0.591468\pi$
$571$	−7734.09	−0.566833	−0.283417	+	0.958997i	$0.591468\pi$
$572$	−1060.25	−0.0775024
$573$	47209.3	3.44188
$574$	234.864	0.0170785
$575$	−1134.77	−0.0823014
$576$	−19256.1	−1.39294
$577$	−5598.19	−0.403909	−0.201955	−	0.979395i	$-0.564729\pi$
$577$	−5598.19	−0.403909	−0.201955	+	0.979395i	$0.564729\pi$
$578$	−3195.32	−0.229944
$579$	−38481.5	−2.76207
$580$	−32709.8	−2.34173
$581$	6729.56	0.480532
$582$	378.941	0.0269890
$583$	−5805.32	−0.412405
$584$	−6371.03	−0.451430
$585$	14285.7	1.00964
$586$	−777.521	−0.0548108
$587$	375.821	0.0264256	0.0132128	−	0.999913i	$-0.495794\pi$
$587$	375.821	0.0264256	0.0132128	+	0.999913i	$0.495794\pi$
$588$	−22764.9	−1.59661
$589$	−9423.00	−0.659199
$590$	4377.39	0.305448
$591$	37502.6	2.61024
$592$	17528.1	1.21689
$593$	5396.41	0.373700	0.186850	−	0.982388i	$-0.440172\pi$
$593$	5396.41	0.373700	0.186850	+	0.982388i	$0.440172\pi$
$594$	2976.29	0.205587
$595$	−2146.88	−0.147922
$596$	−6060.81	−0.416544
$597$	−13399.4	−0.918592
$598$	66.6690	0.00455902
$599$	26512.5	1.80847	0.904234	−	0.427038i	$-0.140443\pi$
$599$	26512.5	1.80847	0.904234	+	0.427038i	$0.140443\pi$
$600$	19060.6	1.29691
$601$	−12182.2	−0.826827	−0.413413	−	0.910543i	$-0.635664\pi$
$601$	−12182.2	−0.826827	−0.413413	+	0.910543i	$0.635664\pi$
$602$	492.027	0.0333115
$603$	−13550.1	−0.915096
$604$	11750.0	0.791558
$605$	−2075.90	−0.139500
$606$	11749.0	0.787572
$607$	−14074.8	−0.941148	−0.470574	−	0.882360i	$-0.655953\pi$
$607$	−14074.8	−0.941148	−0.470574	+	0.882360i	$0.655953\pi$
$608$	−16024.7	−1.06889
$609$	−11305.7	−0.752268
$610$	−7206.10	−0.478306
$611$	−735.437	−0.0486949
$612$	12898.1	0.851921
$613$	−5247.05	−0.345720	−0.172860	−	0.984946i	$-0.555301\pi$
$613$	−5247.05	−0.345720	−0.172860	+	0.984946i	$0.555301\pi$
$614$	4575.37	0.300728
$615$	−10904.3	−0.714964
$616$	−597.868	−0.0391052
$617$	−13209.6	−0.861912	−0.430956	−	0.902373i	$-0.641824\pi$
$617$	−13209.6	−0.861912	−0.430956	+	0.902373i	$0.641824\pi$
$618$	−9346.02	−0.608337
$619$	−20822.3	−1.35205	−0.676026	−	0.736878i	$-0.736299\pi$
$619$	−20822.3	−1.35205	−0.676026	+	0.736878i	$0.736299\pi$
$620$	9937.29	0.643696
$621$	2369.33	0.153104
$622$	−6031.60	−0.388818
$623$	1812.11	0.116534
$624$	6238.05	0.400195
$625$	−8117.46	−0.519518
$626$	−4755.57	−0.303627
$627$	−12660.6	−0.806404
$628$	−2224.56	−0.141353
$629$	−9466.57	−0.600090
$630$	3874.76	0.245038
$631$	3455.46	0.218003	0.109001	−	0.994042i	$-0.465235\pi$
$631$	3455.46	0.218003	0.109001	+	0.994042i	$0.465235\pi$
$632$	15272.2	0.961230
$633$	51427.2	3.22914
$634$	5670.22	0.355194
$635$	1581.76	0.0988505
$636$	37338.1	2.32791
$637$	4183.02	0.260184
$638$	2164.69	0.134327
$639$	54242.7	3.35807
$640$	22181.2	1.36998
$641$	297.324	0.0183207	0.00916036	−	0.999958i	$-0.497084\pi$
$641$	297.324	0.0183207	0.00916036	+	0.999958i	$0.497084\pi$
$642$	−1430.78	−0.0879570
$643$	−1512.07	−0.0927375	−0.0463687	−	0.998924i	$-0.514765\pi$
$643$	−1512.07	−0.0927375	−0.0463687	+	0.998924i	$0.514765\pi$
$644$	−228.931	−0.0140080
$645$	−22843.8	−1.39453
$646$	2506.98	0.152687
$647$	13459.8	0.817863	0.408932	−	0.912565i	$-0.365901\pi$
$647$	13459.8	0.817863	0.408932	+	0.912565i	$0.365901\pi$
$648$	−19396.6	−1.17588
$649$	3667.48	0.221820
$650$	−1684.65	−0.101658
$651$	3434.70	0.206784
$652$	−13080.7	−0.785705
$653$	−30509.5	−1.82838	−0.914188	−	0.405291i	$-0.867170\pi$
$653$	−30509.5	−1.82838	−0.914188	+	0.405291i	$0.867170\pi$
$654$	−9507.48	−0.568458
$655$	−4644.26	−0.277048
$656$	−3349.57	−0.199358
$657$	34594.1	2.05425
$658$	−199.475	−0.0118182
$659$	5574.58	0.329522	0.164761	−	0.986334i	$-0.447315\pi$
$659$	5574.58	0.329522	0.164761	+	0.986334i	$0.447315\pi$
$660$	13351.6	0.787439
$661$	14283.1	0.840467	0.420233	−	0.907416i	$-0.361948\pi$
$661$	14283.1	0.840467	0.420233	+	0.907416i	$0.361948\pi$
$662$	6222.07	0.365298
$663$	−3369.04	−0.197350
$664$	17229.1	1.00695
$665$	−9534.67	−0.555998
$666$	17085.6	0.994074
$667$	1723.24	0.100036
$668$	16778.4	0.971822
$669$	47703.9	2.75686
$670$	2777.45	0.160153
$671$	−6037.45	−0.347352
$672$	5841.02	0.335301
$673$	−10315.3	−0.590828	−0.295414	−	0.955369i	$-0.595458\pi$
$673$	−10315.3	−0.590828	−0.295414	+	0.955369i	$0.595458\pi$
$674$	3628.91	0.207389
$675$	−59870.2	−3.41394
$676$	−1253.03	−0.0712918
$677$	−21225.7	−1.20498	−0.602488	−	0.798128i	$-0.705824\pi$
$677$	−21225.7	−1.20498	−0.602488	+	0.798128i	$0.705824\pi$
$678$	−3326.29	−0.188415
$679$	239.098	0.0135136
$680$	−5496.45	−0.309970
$681$	−15470.7	−0.870540
$682$	−657.635	−0.0369240
$683$	30133.7	1.68819	0.844095	−	0.536194i	$-0.180138\pi$
$683$	30133.7	1.68819	0.844095	+	0.536194i	$0.180138\pi$
$684$	57282.9	3.20214
$685$	−45153.2	−2.51856
$686$	2344.01	0.130459
$687$	−18895.5	−1.04936
$688$	−7017.14	−0.388846
$689$	−6860.83	−0.379357
$690$	−839.552	−0.0463206
$691$	14928.6	0.821868	0.410934	−	0.911665i	$-0.365203\pi$
$691$	14928.6	0.821868	0.410934	+	0.911665i	$0.365203\pi$
$692$	27462.8	1.50864
$693$	3246.37	0.177950
$694$	3251.02	0.177820
$695$	−34076.1	−1.85983
$696$	−28945.0	−1.57638
$697$	1809.03	0.0983100
$698$	−2975.79	−0.161369
$699$	−6644.97	−0.359565
$700$	5784.82	0.312351
$701$	−21726.6	−1.17061	−0.585307	−	0.810812i	$-0.699026\pi$
$701$	−21726.6	−1.17061	−0.585307	+	0.810812i	$0.699026\pi$
$702$	3517.43	0.189112
$703$	−42042.7	−2.25558
$704$	3306.92	0.177037
$705$	9261.24	0.494750
$706$	219.017	0.0116754
$707$	7413.16	0.394343
$708$	−23588.2	−1.25211
$709$	−23270.5	−1.23264	−0.616320	−	0.787495i	$-0.711377\pi$
$709$	−23270.5	−1.23264	−0.616320	+	0.787495i	$0.711377\pi$
$710$	−11118.5	−0.587703
$711$	−82926.8	−4.37412
$712$	4639.38	0.244197
$713$	−523.523	−0.0274980
$714$	−913.799	−0.0478965
$715$	−2453.34	−0.128321
$716$	7592.67	0.396301
$717$	18221.3	0.949074
$718$	2140.74	0.111270
$719$	−15953.3	−0.827481	−0.413740	−	0.910395i	$-0.635778\pi$
$719$	−15953.3	−0.827481	−0.413740	+	0.910395i	$0.635778\pi$
$720$	−55260.7	−2.86034
$721$	−5897.00	−0.304599
$722$	5884.93	0.303344
$723$	−43205.3	−2.22244
$724$	−26404.0	−1.35538
$725$	−43544.3	−2.23061
$726$	−883.588	−0.0451695
$727$	17892.4	0.912783	0.456392	−	0.889779i	$-0.349142\pi$
$727$	17892.4	0.912783	0.456392	+	0.889779i	$0.349142\pi$
$728$	−706.572	−0.0359715
$729$	14231.3	0.723027
$730$	−7090.97	−0.359519
$731$	3789.82	0.191753
$732$	38831.1	1.96071
$733$	22696.0	1.14365	0.571826	−	0.820375i	$-0.306235\pi$
$733$	22696.0	1.14365	0.571826	+	0.820375i	$0.306235\pi$
$734$	7519.15	0.378116
$735$	−52676.1	−2.64352
$736$	−890.298	−0.0445881
$737$	2327.02	0.116305
$738$	−3265.01	−0.162855
$739$	5274.53	0.262553	0.131276	−	0.991346i	$-0.458092\pi$
$739$	5274.53	0.262553	0.131276	+	0.991346i	$0.458092\pi$
$740$	44337.3	2.20253
$741$	−14962.5	−0.741784
$742$	−1860.89	−0.0920694
$743$	23897.6	1.17997	0.589986	−	0.807413i	$-0.299133\pi$
$743$	23897.6	1.17997	0.589986	+	0.807413i	$0.299133\pi$
$744$	8793.54	0.433316
$745$	−14024.2	−0.689674
$746$	−5947.82	−0.291911
$747$	−93552.2	−4.58219
$748$	−2215.05	−0.108276
$749$	−902.770	−0.0440407
$750$	5554.38	0.270423
$751$	10218.3	0.496502	0.248251	−	0.968696i	$-0.420144\pi$
$751$	10218.3	0.496502	0.248251	+	0.968696i	$0.420144\pi$
$752$	2844.86	0.137954
$753$	34596.2	1.67431
$754$	2558.27	0.123563
$755$	27188.6	1.31059
$756$	−12078.3	−0.581062
$757$	−24621.5	−1.18215	−0.591073	−	0.806618i	$-0.701295\pi$
$757$	−24621.5	−1.18215	−0.591073	+	0.806618i	$0.701295\pi$
$758$	−3554.85	−0.170340
$759$	−703.397	−0.0336386
$760$	−24410.7	−1.16509
$761$	24507.2	1.16739	0.583697	−	0.811971i	$-0.301606\pi$
$761$	24507.2	1.16739	0.583697	+	0.811971i	$0.301606\pi$
$762$	673.260	0.0320074
$763$	−5998.87	−0.284631
$764$	36682.1	1.73706
$765$	29845.2	1.41053
$766$	4143.31	0.195436
$767$	4334.29	0.204045
$768$	−13508.0	−0.634670
$769$	19383.4	0.908949	0.454474	−	0.890760i	$-0.349827\pi$
$769$	19383.4	0.908949	0.454474	+	0.890760i	$0.349827\pi$
$770$	−665.429	−0.0311434
$771$	318.719	0.0148876
$772$	−29900.6	−1.39397
$773$	23126.6	1.07607	0.538037	−	0.842922i	$-0.319166\pi$
$773$	23126.6	1.07607	0.538037	+	0.842922i	$0.319166\pi$
$774$	−6840.00	−0.317647
$775$	13228.8	0.613153
$776$	612.140	0.0283177
$777$	15324.6	0.707552
$778$	4181.49	0.192691
$779$	8034.25	0.369521
$780$	15779.2	0.724339
$781$	−9315.33	−0.426797
$782$	139.283	0.00636924
$783$	90917.4	4.14958
$784$	−16181.0	−0.737109
$785$	−5147.44	−0.234038
$786$	−1976.79	−0.0897070
$787$	21746.1	0.984962	0.492481	−	0.870323i	$-0.336090\pi$
$787$	21746.1	0.984962	0.492481	+	0.870323i	$0.336090\pi$
$788$	29140.0	1.31734
$789$	−8454.15	−0.381465
$790$	16998.0	0.765523
$791$	−2098.77	−0.0943410
$792$	8311.37	0.372894
$793$	−7135.16	−0.319517
$794$	582.939	0.0260551
$795$	86397.4	3.85434
$796$	−10411.5	−0.463598
$797$	−22143.6	−0.984149	−0.492075	−	0.870553i	$-0.663761\pi$
$797$	−22143.6	−0.984149	−0.492075	+	0.870553i	$0.663761\pi$
$798$	−4058.35	−0.180030
$799$	−1536.45	−0.0680298
$800$	22496.8	0.994229
$801$	−25191.4	−1.11123
$802$	893.896	0.0393573
$803$	−5940.99	−0.261087
$804$	−14966.7	−0.656511
$805$	−529.727	−0.0231931
$806$	−777.205	−0.0339651
$807$	13971.9	0.609462
$808$	18979.2	0.826345
$809$	−412.718	−0.0179362	−0.00896811	−	0.999960i	$-0.502855\pi$
$809$	−412.718	−0.0179362	−0.00896811	+	0.999960i	$0.502855\pi$
$810$	−21588.5	−0.936472
$811$	−24786.5	−1.07321	−0.536604	−	0.843834i	$-0.680293\pi$
$811$	−24786.5	−1.07321	−0.536604	+	0.843834i	$0.680293\pi$
$812$	−8784.68	−0.379657
$813$	−9639.97	−0.415853
$814$	−2934.18	−0.126343
$815$	−30267.7	−1.30090
$816$	13032.3	0.559097
$817$	16831.3	0.720748
$818$	−4971.99	−0.212520
$819$	3836.62	0.163690
$820$	−8472.74	−0.360830
$821$	17895.9	0.760745	0.380372	−	0.924833i	$-0.375796\pi$
$821$	17895.9	0.760745	0.380372	+	0.924833i	$0.375796\pi$
$822$	−19219.0	−0.815500
$823$	−29788.0	−1.26166	−0.630830	−	0.775921i	$-0.717285\pi$
$823$	−29788.0	−1.26166	−0.630830	+	0.775921i	$0.717285\pi$
$824$	−15097.5	−0.638286
$825$	17774.0	0.750076
$826$	1175.61	0.0495214
$827$	4785.93	0.201237	0.100619	−	0.994925i	$-0.467918\pi$
$827$	4785.93	0.201237	0.100619	+	0.994925i	$0.467918\pi$
$828$	3182.52	0.133575
$829$	−28518.2	−1.19479	−0.597393	−	0.801948i	$-0.703797\pi$
$829$	−28518.2	−1.19479	−0.597393	+	0.801948i	$0.703797\pi$
$830$	19176.0	0.801938
$831$	−56007.4	−2.33800
$832$	3908.18	0.162851
$833$	8739.04	0.363493
$834$	−14504.2	−0.602205
$835$	38823.9	1.60905
$836$	−9837.42	−0.406979
$837$	−27620.9	−1.14064
$838$	−865.468	−0.0356767
$839$	2539.34	0.104491	0.0522454	−	0.998634i	$-0.483362\pi$
$839$	2539.34	0.104491	0.0522454	+	0.998634i	$0.483362\pi$
$840$	8897.75	0.365478
$841$	41736.3	1.71127
$842$	−1530.12	−0.0626265
$843$	−50543.4	−2.06501
$844$	39959.5	1.62969
$845$	−2899.40	−0.118038
$846$	2773.04	0.112694
$847$	−557.512	−0.0226167
$848$	26539.5	1.07473
$849$	−86188.5	−3.48408
$850$	−3519.52	−0.142022
$851$	−2335.81	−0.0940898
$852$	59913.5	2.40916
$853$	41815.4	1.67847	0.839233	−	0.543772i	$-0.183004\pi$
$853$	41815.4	1.67847	0.839233	+	0.543772i	$0.183004\pi$
$854$	−1935.30	−0.0775464
$855$	132548.	5.30180
$856$	−2311.28	−0.0922873
$857$	27901.8	1.11214	0.556071	−	0.831135i	$-0.312308\pi$
$857$	27901.8	1.11214	0.556071	+	0.831135i	$0.312308\pi$
$858$	−1044.24	−0.0415499
$859$	24207.8	0.961536	0.480768	−	0.876848i	$-0.340358\pi$
$859$	24207.8	0.961536	0.480768	+	0.876848i	$0.340358\pi$
$860$	−17749.9	−0.703797
$861$	−2928.50	−0.115915
$862$	−5632.55	−0.222558
$863$	41886.8	1.65220	0.826098	−	0.563527i	$-0.190556\pi$
$863$	41886.8	1.65220	0.826098	+	0.563527i	$0.190556\pi$
$864$	−46971.8	−1.84955
$865$	63546.6	2.49786
$866$	5330.30	0.209158
$867$	39842.0	1.56068
$868$	2668.80	0.104361
$869$	14241.4	0.555932
$870$	−32215.9	−1.25542
$871$	2750.11	0.106985
$872$	−15358.4	−0.596444
$873$	−3323.86	−0.128861
$874$	618.580	0.0239402
$875$	3504.61	0.135403
$876$	38210.7	1.47377
$877$	−8888.50	−0.342239	−0.171119	−	0.985250i	$-0.554738\pi$
$877$	−8888.50	−0.342239	−0.171119	+	0.985250i	$0.554738\pi$
$878$	4618.07	0.177508
$879$	9694.81	0.372011
$880$	9490.15	0.363537
$881$	−25780.5	−0.985889	−0.492945	−	0.870061i	$-0.664079\pi$
$881$	−25780.5	−0.985889	−0.492945	+	0.870061i	$0.664079\pi$
$882$	−15772.5	−0.602141
$883$	−2605.05	−0.0992830	−0.0496415	−	0.998767i	$-0.515808\pi$
$883$	−2605.05	−0.0992830	−0.0496415	+	0.998767i	$0.515808\pi$
$884$	−2617.78	−0.0995991
$885$	−54581.1	−2.07313
$886$	6313.19	0.239386
$887$	−28810.6	−1.09060	−0.545302	−	0.838240i	$-0.683585\pi$
$887$	−28810.6	−1.09060	−0.545302	+	0.838240i	$0.683585\pi$
$888$	39234.2	1.48267
$889$	424.803	0.0160263
$890$	5163.64	0.194478
$891$	−18087.4	−0.680078
$892$	37066.5	1.39134
$893$	−6823.66	−0.255706
$894$	−5969.28	−0.223314
$895$	17568.8	0.656157
$896$	5957.06	0.222111
$897$	−831.287	−0.0309430
$898$	5581.58	0.207416
$899$	−20089.0	−0.745277
$900$	−80418.7	−2.97847
$901$	−14333.5	−0.529985
$902$	560.714	0.0206981
$903$	−6135.02	−0.226092
$904$	−5373.29	−0.197691
$905$	−61096.7	−2.24411
$906$	11572.6	0.424363
$907$	17259.8	0.631867	0.315934	−	0.948781i	$-0.397682\pi$
$907$	17259.8	0.631867	0.315934	+	0.948781i	$0.397682\pi$
$908$	−12020.9	−0.439347
$909$	−103055.	−3.76032
$910$	−786.416	−0.0286477
$911$	−18624.6	−0.677346	−0.338673	−	0.940904i	$-0.609978\pi$
$911$	−18624.6	−0.677346	−0.338673	+	0.940904i	$0.609978\pi$
$912$	57879.0	2.10150
$913$	16066.1	0.582377
$914$	−1130.07	−0.0408964
$915$	89852.0	3.24636
$916$	−14682.0	−0.529594
$917$	−1247.28	−0.0449170
$918$	7348.51	0.264202
$919$	−37786.7	−1.35633	−0.678166	−	0.734909i	$-0.737225\pi$
$919$	−37786.7	−1.35633	−0.678166	+	0.734909i	$0.737225\pi$
$920$	−1356.21	−0.0486010
$921$	−57049.7	−2.04110
$922$	−2419.86	−0.0864358
$923$	−11009.0	−0.392596
$924$	3585.76	0.127665
$925$	59023.2	2.09802
$926$	−4875.83	−0.173034
$927$	81978.2	2.90455
$928$	−34163.1	−1.20847
$929$	802.716	0.0283490	0.0141745	−	0.999900i	$-0.495488\pi$
$929$	802.716	0.0283490	0.0141745	+	0.999900i	$0.495488\pi$
$930$	9787.23	0.345092
$931$	38811.6	1.36627
$932$	−5163.22	−0.181466
$933$	75207.2	2.63899
$934$	11172.9	0.391423
$935$	−5125.44	−0.179273
$936$	9822.53	0.343012
$937$	−9285.83	−0.323751	−0.161876	−	0.986811i	$-0.551754\pi$
$937$	−9285.83	−0.323751	−0.161876	+	0.986811i	$0.551754\pi$
$938$	745.924	0.0259651
$939$	59296.5	2.06078
$940$	7196.08	0.249692
$941$	15587.1	0.539984	0.269992	−	0.962863i	$-0.412979\pi$
$941$	15587.1	0.539984	0.269992	+	0.962863i	$0.412979\pi$
$942$	−2190.96	−0.0757807
$943$	446.366	0.0154143
$944$	−16766.2	−0.578064
$945$	−27948.2	−0.962068
$946$	1174.66	0.0403716
$947$	36020.9	1.23603	0.618016	−	0.786166i	$-0.287937\pi$
$947$	36020.9	1.23603	0.618016	+	0.786166i	$0.287937\pi$
$948$	−91596.3	−3.13809
$949$	−7021.17	−0.240165
$950$	−15630.8	−0.533822
$951$	−70701.3	−2.41077
$952$	−1476.15	−0.0502545
$953$	−12192.9	−0.414446	−0.207223	−	0.978294i	$-0.566443\pi$
$953$	−12192.9	−0.414446	−0.207223	+	0.978294i	$0.566443\pi$
$954$	25869.5	0.877942
$955$	84879.5	2.87606
$956$	14158.1	0.478982
$957$	−26991.2	−0.911705
$958$	1272.60	0.0429184
$959$	−12126.5	−0.408327
$960$	−49215.1	−1.65459
$961$	−23687.9	−0.795138
$962$	−3467.67	−0.116218
$963$	12550.0	0.419957
$964$	−33571.0	−1.12163
$965$	−69187.5	−2.30801
$966$	−225.473	−0.00750982
$967$	−5307.92	−0.176516	−0.0882581	−	0.996098i	$-0.528130\pi$
$967$	−5307.92	−0.176516	−0.0882581	+	0.996098i	$0.528130\pi$
$968$	−1427.35	−0.0473932
$969$	−31259.3	−1.03632
$970$	681.313	0.0225522
$971$	41414.0	1.36873	0.684366	−	0.729139i	$-0.260079\pi$
$971$	41414.0	1.36873	0.684366	+	0.729139i	$0.260079\pi$
$972$	45554.3	1.50324
$973$	−9151.62	−0.301529
$974$	−707.321	−0.0232690
$975$	21005.7	0.689970
$976$	27600.7	0.905201
$977$	−32318.8	−1.05831	−0.529155	−	0.848525i	$-0.677491\pi$
$977$	−32318.8	−1.05831	−0.529155	+	0.848525i	$0.677491\pi$
$978$	−12883.2	−0.421225
$979$	4326.22	0.141232
$980$	−40929.9	−1.33414
$981$	83394.4	2.71415
$982$	4029.24	0.130935
$983$	−3000.94	−0.0973705	−0.0486852	−	0.998814i	$-0.515503\pi$
$983$	−3000.94	−0.0973705	−0.0486852	+	0.998814i	$0.515503\pi$
$984$	−7497.55	−0.242900
$985$	67427.5	2.18114
$986$	5344.66	0.172625
$987$	2487.23	0.0802123
$988$	−11626.0	−0.374366
$989$	935.110	0.0300655
$990$	9250.57	0.296972
$991$	9742.43	0.312289	0.156144	−	0.987734i	$-0.450093\pi$
$991$	9742.43	0.312289	0.156144	+	0.987734i	$0.450093\pi$
$992$	10378.8	0.332185
$993$	−77582.2	−2.47935
$994$	−2986.02	−0.0952826
$995$	−24091.3	−0.767582
$996$	−103332.	−3.28736
$997$	13288.0	0.422100	0.211050	−	0.977475i	$-0.432312\pi$
$997$	13288.0	0.422100	0.211050	+	0.977475i	$0.432312\pi$
$998$	9649.55	0.306063
$999$	−123236.	−3.90293

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.a.c.1.6	✓	9
3.2	odd	2		1287.4.a.k.1.4		9
4.3	odd	2		2288.4.a.r.1.9		9
11.10	odd	2		1573.4.a.e.1.4		9
13.12	even	2		1859.4.a.d.1.4		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.a.c.1.6	✓	9	1.1	even	1	trivial
1287.4.a.k.1.4		9	3.2	odd	2
1573.4.a.e.1.4		9	11.10	odd	2
1859.4.a.d.1.4		9	13.12	even	2
2288.4.a.r.1.9		9	4.3	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:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.a (trivial)

\(f(q)\)	\(=\)	\(q+0.765277 q^{2} -9.54214 q^{3} -7.41435 q^{4} -17.1562 q^{5} -7.30238 q^{6} -4.60754 q^{7} -11.7962 q^{8} +64.0525 q^{9} +O(q^{10})\)	\(q+0.765277 q^{2} -9.54214 q^{3} -7.41435 q^{4} -17.1562 q^{5} -7.30238 q^{6} -4.60754 q^{7} -11.7962 q^{8} +64.0525 q^{9} -13.1292 q^{10} -11.0000 q^{11} +70.7488 q^{12} -13.0000 q^{13} -3.52604 q^{14} +163.707 q^{15} +50.2874 q^{16} -27.1592 q^{17} +49.0179 q^{18} -120.619 q^{19} +127.202 q^{20} +43.9658 q^{21} -8.41805 q^{22} -6.70134 q^{23} +112.562 q^{24} +169.335 q^{25} -9.94860 q^{26} -353.560 q^{27} +34.1619 q^{28} -257.148 q^{29} +125.281 q^{30} +78.1221 q^{31} +132.854 q^{32} +104.964 q^{33} -20.7843 q^{34} +79.0479 q^{35} -474.908 q^{36} +348.558 q^{37} -92.3069 q^{38} +124.048 q^{39} +202.379 q^{40} -66.6085 q^{41} +33.6460 q^{42} -139.541 q^{43} +81.5579 q^{44} -1098.90 q^{45} -5.12838 q^{46} +56.5721 q^{47} -479.850 q^{48} -321.771 q^{49} +129.588 q^{50} +259.157 q^{51} +96.3866 q^{52} +527.757 q^{53} -270.572 q^{54} +188.718 q^{55} +54.3517 q^{56} +1150.96 q^{57} -196.790 q^{58} -333.407 q^{59} -1213.78 q^{60} +548.859 q^{61} +59.7850 q^{62} -295.124 q^{63} -300.629 q^{64} +223.031 q^{65} +80.3262 q^{66} -211.547 q^{67} +201.368 q^{68} +63.9451 q^{69} +60.4935 q^{70} +846.848 q^{71} -755.579 q^{72} +540.090 q^{73} +266.744 q^{74} -1615.82 q^{75} +894.311 q^{76} +50.6829 q^{77} +94.9310 q^{78} -1294.67 q^{79} -862.741 q^{80} +1644.30 q^{81} -50.9740 q^{82} -1460.55 q^{83} -325.978 q^{84} +465.949 q^{85} -106.787 q^{86} +2453.75 q^{87} +129.759 q^{88} -393.293 q^{89} -840.961 q^{90} +59.8980 q^{91} +49.6861 q^{92} -745.452 q^{93} +43.2933 q^{94} +2069.36 q^{95} -1267.71 q^{96} -51.8927 q^{97} -246.244 q^{98} -704.577 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 8 q^{3} + 46 q^{4} + 30 q^{5} + 34 q^{6} + 25 q^{7} + 36 q^{8} + 91 q^{9}+O(q^{10}) \) 9 * q + 8 * q^3 + 46 * q^4 + 30 * q^5 + 34 * q^6 + 25 * q^7 + 36 * q^8 + 91 * q^9	\( 9 q + 8 q^{3} + 46 q^{4} + 30 q^{5} + 34 q^{6} + 25 q^{7} + 36 q^{8} + 91 q^{9} - 22 q^{10} - 99 q^{11} + 181 q^{12} - 117 q^{13} + 351 q^{15} + 130 q^{16} + 53 q^{17} + 33 q^{18} + 69 q^{19} + 282 q^{20} + 463 q^{21} + 216 q^{23} - 121 q^{24} + 617 q^{25} + 275 q^{27} + 279 q^{28} - 91 q^{29} + 29 q^{30} + 636 q^{31} + 663 q^{32} - 88 q^{33} + 423 q^{34} - 358 q^{35} - 252 q^{36} + 967 q^{37} - 101 q^{38} - 104 q^{39} + 652 q^{40} - 226 q^{41} - 1186 q^{42} + 42 q^{43} - 506 q^{44} + 5 q^{45} - 1127 q^{46} - 269 q^{47} - 1820 q^{48} + 228 q^{49} - 1374 q^{50} - 589 q^{51} - 598 q^{52} + 1227 q^{53} - 2438 q^{54} - 330 q^{55} - 659 q^{56} - 71 q^{57} + 471 q^{58} - 613 q^{59} - 859 q^{60} + 427 q^{61} - 1714 q^{62} + 305 q^{63} - 1194 q^{64} - 390 q^{65} - 374 q^{66} - 271 q^{67} - 2835 q^{68} - 846 q^{69} - 102 q^{70} + 2279 q^{71} - 2400 q^{72} + 3602 q^{73} - 4955 q^{74} - 883 q^{75} + 1126 q^{76} - 275 q^{77} - 442 q^{78} - 1182 q^{79} - 2360 q^{80} + 2697 q^{81} + 1007 q^{82} - 1877 q^{83} + 1618 q^{84} - 441 q^{85} + 830 q^{86} + 1942 q^{87} - 396 q^{88} + 1258 q^{89} - 5669 q^{90} - 325 q^{91} + 1046 q^{92} + 1556 q^{93} + 1439 q^{94} + 2032 q^{95} - 3417 q^{96} + 4002 q^{97} - 1855 q^{98} - 1001 q^{99}+O(q^{100}) \) 9 * q + 8 * q^3 + 46 * q^4 + 30 * q^5 + 34 * q^6 + 25 * q^7 + 36 * q^8 + 91 * q^9 - 22 * q^10 - 99 * q^11 + 181 * q^12 - 117 * q^13 + 351 * q^15 + 130 * q^16 + 53 * q^17 + 33 * q^18 + 69 * q^19 + 282 * q^20 + 463 * q^21 + 216 * q^23 - 121 * q^24 + 617 * q^25 + 275 * q^27 + 279 * q^28 - 91 * q^29 + 29 * q^30 + 636 * q^31 + 663 * q^32 - 88 * q^33 + 423 * q^34 - 358 * q^35 - 252 * q^36 + 967 * q^37 - 101 * q^38 - 104 * q^39 + 652 * q^40 - 226 * q^41 - 1186 * q^42 + 42 * q^43 - 506 * q^44 + 5 * q^45 - 1127 * q^46 - 269 * q^47 - 1820 * q^48 + 228 * q^49 - 1374 * q^50 - 589 * q^51 - 598 * q^52 + 1227 * q^53 - 2438 * q^54 - 330 * q^55 - 659 * q^56 - 71 * q^57 + 471 * q^58 - 613 * q^59 - 859 * q^60 + 427 * q^61 - 1714 * q^62 + 305 * q^63 - 1194 * q^64 - 390 * q^65 - 374 * q^66 - 271 * q^67 - 2835 * q^68 - 846 * q^69 - 102 * q^70 + 2279 * q^71 - 2400 * q^72 + 3602 * q^73 - 4955 * q^74 - 883 * q^75 + 1126 * q^76 - 275 * q^77 - 442 * q^78 - 1182 * q^79 - 2360 * q^80 + 2697 * q^81 + 1007 * q^82 - 1877 * q^83 + 1618 * q^84 - 441 * q^85 + 830 * q^86 + 1942 * q^87 - 396 * q^88 + 1258 * q^89 - 5669 * q^90 - 325 * q^91 + 1046 * q^92 + 1556 * q^93 + 1439 * q^94 + 2032 * q^95 - 3417 * q^96 + 4002 * q^97 - 1855 * q^98 - 1001 * q^99

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