LMFDB - Embedded newform 143.4.a.c.1.2

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			1.2
Root			$-4.11495$ 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)

$f(q)$	$=$	$q-4.11495 q^{2} +9.51427 q^{3} +8.93279 q^{4} +14.5196 q^{5} -39.1507 q^{6} +21.0410 q^{7} -3.83839 q^{8} +63.5214 q^{9} +O(q^{10})$	\(q-4.11495 q^{2} +9.51427 q^{3} +8.93279 q^{4} +14.5196 q^{5} -39.1507 q^{6} +21.0410 q^{7} -3.83839 q^{8} +63.5214 q^{9} -59.7475 q^{10} -11.0000 q^{11} +84.9890 q^{12} -13.0000 q^{13} -86.5827 q^{14} +138.144 q^{15} -55.6676 q^{16} -67.8303 q^{17} -261.387 q^{18} -88.0550 q^{19} +129.701 q^{20} +200.190 q^{21} +45.2644 q^{22} -118.762 q^{23} -36.5195 q^{24} +85.8194 q^{25} +53.4943 q^{26} +347.475 q^{27} +187.955 q^{28} -78.5245 q^{29} -568.454 q^{30} +156.975 q^{31} +259.776 q^{32} -104.657 q^{33} +279.118 q^{34} +305.508 q^{35} +567.423 q^{36} +372.598 q^{37} +362.342 q^{38} -123.686 q^{39} -55.7320 q^{40} -124.922 q^{41} -823.771 q^{42} -230.472 q^{43} -98.2607 q^{44} +922.307 q^{45} +488.699 q^{46} -486.240 q^{47} -529.636 q^{48} +99.7243 q^{49} -353.142 q^{50} -645.356 q^{51} -116.126 q^{52} -556.482 q^{53} -1429.84 q^{54} -159.716 q^{55} -80.7637 q^{56} -837.779 q^{57} +323.124 q^{58} +530.324 q^{59} +1234.01 q^{60} +479.488 q^{61} -645.944 q^{62} +1336.55 q^{63} -623.625 q^{64} -188.755 q^{65} +430.658 q^{66} -491.331 q^{67} -605.914 q^{68} -1129.93 q^{69} -1257.15 q^{70} +563.185 q^{71} -243.820 q^{72} +1072.56 q^{73} -1533.22 q^{74} +816.509 q^{75} -786.577 q^{76} -231.451 q^{77} +508.960 q^{78} +431.029 q^{79} -808.272 q^{80} +1590.89 q^{81} +514.046 q^{82} -171.261 q^{83} +1788.26 q^{84} -984.870 q^{85} +948.380 q^{86} -747.104 q^{87} +42.2223 q^{88} -1043.37 q^{89} -3795.24 q^{90} -273.533 q^{91} -1060.88 q^{92} +1493.50 q^{93} +2000.85 q^{94} -1278.52 q^{95} +2471.58 q^{96} -1187.12 q^{97} -410.360 q^{98} -698.735 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−4.11495	−1.45485	−0.727427	−	0.686185i	$-0.759284\pi$
$2$	−4.11495	−1.45485	−0.727427	+	0.686185i	$0.759284\pi$
$3$	9.51427	1.83102	0.915511	−	0.402292i	$-0.131786\pi$
$3$	9.51427	1.83102	0.915511	+	0.402292i	$0.131786\pi$
$4$	8.93279	1.11660
$5$	14.5196	1.29867	0.649337	−	0.760501i	$-0.275046\pi$
$5$	14.5196	1.29867	0.649337	+	0.760501i	$0.275046\pi$
$6$	−39.1507	−2.66387
$7$	21.0410	1.13611	0.568054	−	0.822991i	$-0.307696\pi$
$7$	21.0410	1.13611	0.568054	+	0.822991i	$0.307696\pi$
$8$	−3.83839	−0.169635
$9$	63.5214	2.35264
$10$	−59.7475	−1.88938
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	84.9890	2.04452
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	−86.5827	−1.65287
$15$	138.144	2.37790
$16$	−55.6676	−0.869806
$17$	−67.8303	−0.967721	−0.483861	−	0.875145i	$-0.660766\pi$
$17$	−67.8303	−0.967721	−0.483861	+	0.875145i	$0.660766\pi$
$18$	−261.387	−3.42275
$19$	−88.0550	−1.06322	−0.531611	−	0.846989i	$-0.678413\pi$
$19$	−88.0550	−1.06322	−0.531611	+	0.846989i	$0.678413\pi$
$20$	129.701	1.45010
$21$	200.190	2.08024
$22$	45.2644	0.438655
$23$	−118.762	−1.07668	−0.538338	−	0.842729i	$-0.680948\pi$
$23$	−118.762	−1.07668	−0.538338	+	0.842729i	$0.680948\pi$
$24$	−36.5195	−0.310605
$25$	85.8194	0.686555
$26$	53.4943	0.403504
$27$	347.475	2.47672
$28$	187.955	1.26858
$29$	−78.5245	−0.502815	−0.251408	−	0.967881i	$-0.580893\pi$
$29$	−78.5245	−0.502815	−0.251408	+	0.967881i	$0.580893\pi$
$30$	−568.454	−3.45950
$31$	156.975	0.909469	0.454734	−	0.890627i	$-0.349734\pi$
$31$	156.975	0.909469	0.454734	+	0.890627i	$0.349734\pi$
$32$	259.776	1.43507
$33$	−104.657	−0.552074
$34$	279.118	1.40789
$35$	305.508	1.47543
$36$	567.423	2.62696
$37$	372.598	1.65553	0.827766	−	0.561074i	$-0.189612\pi$
$37$	372.598	1.65553	0.827766	+	0.561074i	$0.189612\pi$
$38$	362.342	1.54683
$39$	−123.686	−0.507834
$40$	−55.7320	−0.220300
$41$	−124.922	−0.475841	−0.237920	−	0.971285i	$-0.576466\pi$
$41$	−124.922	−0.475841	−0.237920	+	0.971285i	$0.576466\pi$
$42$	−823.771	−3.02644
$43$	−230.472	−0.817364	−0.408682	−	0.912677i	$-0.634012\pi$
$43$	−230.472	−0.817364	−0.408682	+	0.912677i	$0.634012\pi$
$44$	−98.2607	−0.336667
$45$	922.307	3.05532
$46$	488.699	1.56641
$47$	−486.240	−1.50905	−0.754525	−	0.656271i	$-0.772133\pi$
$47$	−486.240	−1.50905	−0.754525	+	0.656271i	$0.772133\pi$
$48$	−529.636	−1.59263
$49$	99.7243	0.290741
$50$	−353.142	−0.998837
$51$	−645.356	−1.77192
$52$	−116.126	−0.309689
$53$	−556.482	−1.44224	−0.721120	−	0.692810i	$-0.756372\pi$
$53$	−556.482	−1.44224	−0.721120	+	0.692810i	$0.756372\pi$
$54$	−1429.84	−3.60327
$55$	−159.716	−0.391565
$56$	−80.7637	−0.192723
$57$	−837.779	−1.94678
$58$	323.124	0.731522
$59$	530.324	1.17021	0.585104	−	0.810958i	$-0.301054\pi$
$59$	530.324	1.17021	0.585104	+	0.810958i	$0.301054\pi$
$60$	1234.01	2.65516
$61$	479.488	1.00643	0.503214	−	0.864162i	$-0.332151\pi$
$61$	479.488	1.00643	0.503214	+	0.864162i	$0.332151\pi$
$62$	−645.944	−1.32314
$63$	1336.55	2.67286
$64$	−623.625	−1.21802
$65$	−188.755	−0.360187
$66$	430.658	0.803187
$67$	−491.331	−0.895905	−0.447953	−	0.894057i	$-0.647847\pi$
$67$	−491.331	−0.895905	−0.447953	+	0.894057i	$0.647847\pi$
$68$	−605.914	−1.08056
$69$	−1129.93	−1.97142
$70$	−1257.15	−2.14654
$71$	563.185	0.941377	0.470688	−	0.882299i	$-0.344006\pi$
$71$	563.185	0.941377	0.470688	+	0.882299i	$0.344006\pi$
$72$	−243.820	−0.399090
$73$	1072.56	1.71965	0.859823	−	0.510593i	$-0.170574\pi$
$73$	1072.56	1.71965	0.859823	+	0.510593i	$0.170574\pi$
$74$	−1533.22	−2.40856
$75$	816.509	1.25710
$76$	−786.577	−1.18719
$77$	−231.451	−0.342549
$78$	508.960	0.738825
$79$	431.029	0.613855	0.306927	−	0.951733i	$-0.400699\pi$
$79$	431.029	0.613855	0.306927	+	0.951733i	$0.400699\pi$
$80$	−808.272	−1.12959
$81$	1590.89	2.18229
$82$	514.046	0.692279
$83$	−171.261	−0.226486	−0.113243	−	0.993567i	$-0.536124\pi$
$83$	−171.261	−0.226486	−0.113243	+	0.993567i	$0.536124\pi$
$84$	1788.26	2.32279
$85$	−984.870	−1.25675
$86$	948.380	1.18915
$87$	−747.104	−0.920666
$88$	42.2223	0.0511468
$89$	−1043.37	−1.24266	−0.621331	−	0.783548i	$-0.713408\pi$
$89$	−1043.37	−1.24266	−0.621331	+	0.783548i	$0.713408\pi$
$90$	−3795.24	−4.44504
$91$	−273.533	−0.315100
$92$	−1060.88	−1.20222
$93$	1493.50	1.66526
$94$	2000.85	2.19545
$95$	−1278.52	−1.38078
$96$	2471.58	2.62765
$97$	−1187.12	−1.24262	−0.621308	−	0.783567i	$-0.713398\pi$
$97$	−1187.12	−1.24262	−0.621308	+	0.783567i	$0.713398\pi$
$98$	−410.360	−0.422986
$99$	−698.735	−0.709349
$100$	766.607	0.766607
$101$	−1286.78	−1.26772	−0.633858	−	0.773449i	$-0.718530\pi$
$101$	−1286.78	−1.26772	−0.633858	+	0.773449i	$0.718530\pi$
$102$	2655.61	2.57788
$103$	532.926	0.509813	0.254906	−	0.966966i	$-0.417955\pi$
$103$	532.926	0.509813	0.254906	+	0.966966i	$0.417955\pi$
$104$	49.8991	0.0470482
$105$	2906.68	2.70155
$106$	2289.89	2.09825
$107$	−544.809	−0.492230	−0.246115	−	0.969241i	$-0.579154\pi$
$107$	−544.809	−0.492230	−0.246115	+	0.969241i	$0.579154\pi$
$108$	3103.92	2.76551
$109$	742.684	0.652626	0.326313	−	0.945262i	$-0.394194\pi$
$109$	742.684	0.652626	0.326313	+	0.945262i	$0.394194\pi$
$110$	657.222	0.569670
$111$	3545.00	3.03132
$112$	−1171.30	−0.988193
$113$	1703.87	1.41847	0.709233	−	0.704974i	$-0.249042\pi$
$113$	1703.87	1.41847	0.709233	+	0.704974i	$0.249042\pi$
$114$	3447.42	2.83228
$115$	−1724.38	−1.39825
$116$	−701.443	−0.561443
$117$	−825.778	−0.652506
$118$	−2182.26	−1.70248
$119$	−1427.22	−1.09944
$120$	−530.250	−0.403375
$121$	121.000	0.0909091
$122$	−1973.07	−1.46421
$123$	−1188.54	−0.871275
$124$	1402.22	1.01551
$125$	−568.888	−0.407063
$126$	−5499.85	−3.88862
$127$	1669.13	1.16623	0.583115	−	0.812390i	$-0.301834\pi$
$127$	1669.13	1.16623	0.583115	+	0.812390i	$0.301834\pi$
$128$	487.975	0.336963
$129$	−2192.77	−1.49661
$130$	776.717	0.524020
$131$	1856.95	1.23849	0.619245	−	0.785197i	$-0.287439\pi$
$131$	1856.95	1.23849	0.619245	+	0.785197i	$0.287439\pi$
$132$	−934.879	−0.616445
$133$	−1852.77	−1.20793
$134$	2021.80	1.30341
$135$	5045.20	3.21646
$136$	260.359	0.164159
$137$	−902.691	−0.562935	−0.281468	−	0.959571i	$-0.590821\pi$
$137$	−902.691	−0.562935	−0.281468	+	0.959571i	$0.590821\pi$
$138$	4649.61	2.86813
$139$	−990.918	−0.604666	−0.302333	−	0.953202i	$-0.597765\pi$
$139$	−990.918	−0.604666	−0.302333	+	0.953202i	$0.597765\pi$
$140$	2729.04	1.64747
$141$	−4626.22	−2.76311
$142$	−2317.48	−1.36957
$143$	143.000	0.0836242
$144$	−3536.08	−2.04634
$145$	−1140.15	−0.652993
$146$	−4413.54	−2.50183
$147$	948.804	0.532354
$148$	3328.34	1.84857
$149$	727.657	0.400081	0.200040	−	0.979788i	$-0.435893\pi$
$149$	727.657	0.400081	0.200040	+	0.979788i	$0.435893\pi$
$150$	−3359.89	−1.82889
$151$	2738.43	1.47583	0.737913	−	0.674895i	$-0.235811\pi$
$151$	2738.43	1.47583	0.737913	+	0.674895i	$0.235811\pi$
$152$	337.990	0.180359
$153$	−4308.67	−2.27670
$154$	952.409	0.498359
$155$	2279.22	1.18110
$156$	−1104.86	−0.567047
$157$	1079.78	0.548889	0.274445	−	0.961603i	$-0.411506\pi$
$157$	1079.78	0.548889	0.274445	+	0.961603i	$0.411506\pi$
$158$	−1773.66	−0.893069
$159$	−5294.52	−2.64077
$160$	3771.85	1.86369
$161$	−2498.87	−1.22322
$162$	−6546.43	−3.17491
$163$	2808.51	1.34957	0.674783	−	0.738016i	$-0.264237\pi$
$163$	2808.51	1.34957	0.674783	+	0.738016i	$0.264237\pi$
$164$	−1115.90	−0.531323
$165$	−1519.58	−0.716964
$166$	704.729	0.329503
$167$	476.134	0.220625	0.110313	−	0.993897i	$-0.464815\pi$
$167$	476.134	0.220625	0.110313	+	0.993897i	$0.464815\pi$
$168$	−768.408	−0.352881
$169$	169.000	0.0769231
$170$	4052.69	1.82839
$171$	−5593.38	−2.50138
$172$	−2058.76	−0.912668
$173$	320.976	0.141060	0.0705300	−	0.997510i	$-0.477531\pi$
$173$	320.976	0.141060	0.0705300	+	0.997510i	$0.477531\pi$
$174$	3074.29	1.33943
$175$	1805.73	0.780001
$176$	612.343	0.262256
$177$	5045.65	2.14268
$178$	4293.41	1.80789
$179$	−2430.24	−1.01478	−0.507388	−	0.861718i	$-0.669389\pi$
$179$	−2430.24	−1.01478	−0.507388	+	0.861718i	$0.669389\pi$
$180$	8238.77	3.41157
$181$	−1437.66	−0.590388	−0.295194	−	0.955437i	$-0.595384\pi$
$181$	−1437.66	−0.590388	−0.295194	+	0.955437i	$0.595384\pi$
$182$	1125.57	0.458424
$183$	4561.98	1.84279
$184$	455.855	0.182642
$185$	5409.98	2.15000
$186$	−6145.69	−2.42271
$187$	746.133	0.291779
$188$	−4343.48	−1.68500
$189$	7311.22	2.81382
$190$	5261.06	2.00883
$191$	−2716.04	−1.02893	−0.514465	−	0.857511i	$-0.672010\pi$
$191$	−2716.04	−1.02893	−0.514465	+	0.857511i	$0.672010\pi$
$192$	−5933.34	−2.23022
$193$	853.066	0.318161	0.159080	−	0.987266i	$-0.449147\pi$
$193$	853.066	0.318161	0.159080	+	0.987266i	$0.449147\pi$
$194$	4884.93	1.80782
$195$	−1795.87	−0.659511
$196$	890.816	0.324642
$197$	2396.01	0.866540	0.433270	−	0.901264i	$-0.357360\pi$
$197$	2396.01	0.866540	0.433270	+	0.901264i	$0.357360\pi$
$198$	2875.26	1.03200
$199$	−2272.63	−0.809559	−0.404779	−	0.914414i	$-0.632652\pi$
$199$	−2272.63	−0.809559	−0.404779	+	0.914414i	$0.632652\pi$
$200$	−329.409	−0.116464
$201$	−4674.66	−1.64042
$202$	5295.03	1.84434
$203$	−1652.24	−0.571252
$204$	−5764.83	−1.97852
$205$	−1813.81	−0.617962
$206$	−2192.96	−0.741703
$207$	−7543.92	−2.53304
$208$	723.678	0.241241
$209$	968.605	0.320573
$210$	−11960.8	−3.93037
$211$	−1974.54	−0.644230	−0.322115	−	0.946700i	$-0.604394\pi$
$211$	−1974.54	−0.644230	−0.322115	+	0.946700i	$0.604394\pi$
$212$	−4970.94	−1.61040
$213$	5358.30	1.72368
$214$	2241.86	0.716123
$215$	−3346.37	−1.06149
$216$	−1333.74	−0.420138
$217$	3302.91	1.03325
$218$	−3056.11	−0.949475
$219$	10204.7	3.14871
$220$	−1426.71	−0.437221
$221$	881.794	0.268398
$222$	−14587.5	−4.41012
$223$	−4911.99	−1.47503	−0.737514	−	0.675331i	$-0.764001\pi$
$223$	−4911.99	−1.47503	−0.737514	+	0.675331i	$0.764001\pi$
$224$	5465.96	1.63040
$225$	5451.37	1.61522
$226$	−7011.34	−2.06366
$227$	3810.08	1.11403	0.557013	−	0.830504i	$-0.311947\pi$
$227$	3810.08	1.11403	0.557013	+	0.830504i	$0.311947\pi$
$228$	−7483.71	−2.17377
$229$	−1590.52	−0.458970	−0.229485	−	0.973312i	$-0.573704\pi$
$229$	−1590.52	−0.458970	−0.229485	+	0.973312i	$0.573704\pi$
$230$	7095.72	2.03425
$231$	−2202.09	−0.627216
$232$	301.408	0.0852949
$233$	5712.21	1.60609	0.803046	−	0.595917i	$-0.203211\pi$
$233$	5712.21	1.60609	0.803046	+	0.595917i	$0.203211\pi$
$234$	3398.03	0.949301
$235$	−7060.02	−1.95977
$236$	4737.27	1.30665
$237$	4100.93	1.12398
$238$	5872.93	1.59952
$239$	−4831.85	−1.30773	−0.653863	−	0.756613i	$-0.726853\pi$
$239$	−4831.85	−1.30773	−0.653863	+	0.756613i	$0.726853\pi$
$240$	−7690.12	−2.06831
$241$	689.093	0.184184	0.0920921	−	0.995750i	$-0.470645\pi$
$241$	689.093	0.184184	0.0920921	+	0.995750i	$0.470645\pi$
$242$	−497.909	−0.132259
$243$	5754.35	1.51910
$244$	4283.16	1.12378
$245$	1447.96	0.377578
$246$	4890.77	1.26758
$247$	1144.71	0.294884
$248$	−602.532	−0.154277
$249$	−1629.42	−0.414700
$250$	2340.94	0.592217
$251$	6987.56	1.75718	0.878588	−	0.477581i	$-0.158486\pi$
$251$	6987.56	1.75718	0.878588	+	0.477581i	$0.158486\pi$
$252$	11939.2	2.98451
$253$	1306.38	0.324630
$254$	−6868.37	−1.69669
$255$	−9370.32	−2.30115
$256$	2981.01	0.727786
$257$	4252.37	1.03212	0.516062	−	0.856551i	$-0.327397\pi$
$257$	4252.37	1.03212	0.516062	+	0.856551i	$0.327397\pi$
$258$	9023.15	2.17735
$259$	7839.83	1.88086
$260$	−1686.11	−0.402185
$261$	−4987.99	−1.18294
$262$	−7641.24	−1.80182
$263$	−2408.57	−0.564711	−0.282355	−	0.959310i	$-0.591116\pi$
$263$	−2408.57	−0.564711	−0.282355	+	0.959310i	$0.591116\pi$
$264$	401.715	0.0936509
$265$	−8079.91	−1.87300
$266$	7624.04	1.75737
$267$	−9926.90	−2.27534
$268$	−4388.96	−1.00037
$269$	−3811.22	−0.863845	−0.431922	−	0.901911i	$-0.642165\pi$
$269$	−3811.22	−0.863845	−0.431922	+	0.901911i	$0.642165\pi$
$270$	−20760.7	−4.67947
$271$	−8749.47	−1.96123	−0.980613	−	0.195953i	$-0.937220\pi$
$271$	−8749.47	−1.96123	−0.980613	+	0.195953i	$0.937220\pi$
$272$	3775.95	0.841729
$273$	−2602.47	−0.576955
$274$	3714.53	0.818988
$275$	−944.013	−0.207004
$276$	−10093.5	−2.20128
$277$	−2381.76	−0.516628	−0.258314	−	0.966061i	$-0.583167\pi$
$277$	−2381.76	−0.516628	−0.258314	+	0.966061i	$0.583167\pi$
$278$	4077.57	0.879700
$279$	9971.27	2.13966
$280$	−1172.66	−0.250285
$281$	3303.85	0.701391	0.350696	−	0.936490i	$-0.385945\pi$
$281$	3303.85	0.701391	0.350696	+	0.936490i	$0.385945\pi$
$282$	19036.6	4.01991
$283$	−6580.21	−1.38217	−0.691083	−	0.722776i	$-0.742866\pi$
$283$	−6580.21	−1.38217	−0.691083	+	0.722776i	$0.742866\pi$
$284$	5030.82	1.05114
$285$	−12164.2	−2.52824
$286$	−588.437	−0.121661
$287$	−2628.48	−0.540606
$288$	16501.3	3.37622
$289$	−312.054	−0.0635159
$290$	4691.64	0.950009
$291$	−11294.6	−2.27526
$292$	9580.99	1.92015
$293$	−3617.74	−0.721333	−0.360666	−	0.932695i	$-0.617451\pi$
$293$	−3617.74	−0.721333	−0.360666	+	0.932695i	$0.617451\pi$
$294$	−3904.28	−0.774497
$295$	7700.10	1.51972
$296$	−1430.18	−0.280836
$297$	−3822.22	−0.746760
$298$	−2994.27	−0.582059
$299$	1543.90	0.298616
$300$	7293.71	1.40367
$301$	−4849.37	−0.928614
$302$	−11268.5	−2.14711
$303$	−12242.8	−2.32122
$304$	4901.81	0.924795
$305$	6961.98	1.30702
$306$	17730.0	3.31227
$307$	−6537.44	−1.21535	−0.607673	−	0.794187i	$-0.707897\pi$
$307$	−6537.44	−1.21535	−0.607673	+	0.794187i	$0.707897\pi$
$308$	−2067.51	−0.382490
$309$	5070.40	0.933479
$310$	−9378.86	−1.71833
$311$	3444.79	0.628090	0.314045	−	0.949408i	$-0.398316\pi$
$311$	3444.79	0.628090	0.314045	+	0.949408i	$0.398316\pi$
$312$	474.754	0.0861463
$313$	7067.16	1.27623	0.638114	−	0.769942i	$-0.279715\pi$
$313$	7067.16	1.27623	0.638114	+	0.769942i	$0.279715\pi$
$314$	−4443.23	−0.798554
$315$	19406.3	3.47117
$316$	3850.29	0.685430
$317$	2007.70	0.355722	0.177861	−	0.984056i	$-0.443082\pi$
$317$	2007.70	0.355722	0.177861	+	0.984056i	$0.443082\pi$
$318$	21786.7	3.84194
$319$	863.770	0.151604
$320$	−9054.80	−1.58181
$321$	−5183.46	−0.901285
$322$	10282.7	1.77961
$323$	5972.79	1.02890
$324$	14211.1	2.43674
$325$	−1115.65	−0.190416
$326$	−11556.9	−1.96342
$327$	7066.10	1.19497
$328$	479.498	0.0807191
$329$	−10231.0	−1.71444
$330$	6252.99	1.04308
$331$	829.382	0.137725	0.0688625	−	0.997626i	$-0.478063\pi$
$331$	829.382	0.137725	0.0688625	+	0.997626i	$0.478063\pi$
$332$	−1529.84	−0.252894
$333$	23667.9	3.89488
$334$	−1959.27	−0.320977
$335$	−7133.94	−1.16349
$336$	−11144.1	−1.80940
$337$	3396.73	0.549055	0.274528	−	0.961579i	$-0.411479\pi$
$337$	3396.73	0.549055	0.274528	+	0.961579i	$0.411479\pi$
$338$	−695.426	−0.111912
$339$	16211.1	2.59724
$340$	−8797.64	−1.40329
$341$	−1726.72	−0.274215
$342$	23016.4	3.63914
$343$	−5118.77	−0.805794
$344$	884.643	0.138653
$345$	−16406.2	−2.56023
$346$	−1320.80	−0.205222
$347$	3075.16	0.475744	0.237872	−	0.971296i	$-0.423550\pi$
$347$	3075.16	0.475744	0.237872	+	0.971296i	$0.423550\pi$
$348$	−6673.72	−1.02801
$349$	6969.23	1.06892	0.534462	−	0.845193i	$-0.320514\pi$
$349$	6969.23	1.06892	0.534462	+	0.845193i	$0.320514\pi$
$350$	−7430.47	−1.13479
$351$	−4517.17	−0.686919
$352$	−2857.54	−0.432691
$353$	8257.54	1.24506	0.622528	−	0.782598i	$-0.286106\pi$
$353$	8257.54	1.24506	0.622528	+	0.782598i	$0.286106\pi$
$354$	−20762.6	−3.11728
$355$	8177.23	1.22254
$356$	−9320.20	−1.38755
$357$	−13578.9	−2.01309
$358$	10000.3	1.47635
$359$	−11925.3	−1.75319	−0.876596	−	0.481228i	$-0.840191\pi$
$359$	−11925.3	−1.75319	−0.876596	+	0.481228i	$0.840191\pi$
$360$	−3540.18	−0.518288
$361$	894.680	0.130439
$362$	5915.89	0.858928
$363$	1151.23	0.166457
$364$	−2443.42	−0.351840
$365$	15573.2	2.23326
$366$	−18772.3	−2.68099
$367$	−4357.47	−0.619777	−0.309888	−	0.950773i	$-0.600292\pi$
$367$	−4357.47	−0.619777	−0.309888	+	0.950773i	$0.600292\pi$
$368$	6611.18	0.936499
$369$	−7935.19	−1.11948
$370$	−22261.8	−3.12793
$371$	−11708.9	−1.63854
$372$	13341.2	1.85943
$373$	4455.22	0.618451	0.309226	−	0.950989i	$-0.399930\pi$
$373$	4455.22	0.618451	0.309226	+	0.950989i	$0.399930\pi$
$374$	−3070.30	−0.424496
$375$	−5412.55	−0.745342
$376$	1866.38	0.255987
$377$	1020.82	0.139456
$378$	−30085.3	−4.09370
$379$	1694.86	0.229707	0.114854	−	0.993382i	$-0.463360\pi$
$379$	1694.86	0.229707	0.114854	+	0.993382i	$0.463360\pi$
$380$	−11420.8	−1.54178
$381$	15880.5	2.13539
$382$	11176.4	1.49694
$383$	3687.06	0.491906	0.245953	−	0.969282i	$-0.420899\pi$
$383$	3687.06	0.491906	0.245953	+	0.969282i	$0.420899\pi$
$384$	4642.72	0.616987
$385$	−3360.58	−0.444860
$386$	−3510.32	−0.462877
$387$	−14639.9	−1.92297
$388$	−10604.3	−1.38750
$389$	239.576	0.0312261	0.0156131	−	0.999878i	$-0.495030\pi$
$389$	239.576	0.0312261	0.0156131	+	0.999878i	$0.495030\pi$
$390$	7389.90	0.959493
$391$	8055.65	1.04192
$392$	−382.781	−0.0493198
$393$	17667.5	2.26771
$394$	−9859.44	−1.26069
$395$	6258.37	0.797197
$396$	−6241.66	−0.792058
$397$	2222.95	0.281024	0.140512	−	0.990079i	$-0.455125\pi$
$397$	2222.95	0.281024	0.140512	+	0.990079i	$0.455125\pi$
$398$	9351.74	1.17779
$399$	−17627.7	−2.21175
$400$	−4777.35	−0.597169
$401$	3208.55	0.399570	0.199785	−	0.979840i	$-0.435976\pi$
$401$	3208.55	0.399570	0.199785	+	0.979840i	$0.435976\pi$
$402$	19236.0	2.38658
$403$	−2040.67	−0.252241
$404$	−11494.5	−1.41553
$405$	23099.1	2.83408
$406$	6798.86	0.831088
$407$	−4098.57	−0.499162
$408$	2477.13	0.300579
$409$	−3443.20	−0.416273	−0.208136	−	0.978100i	$-0.566740\pi$
$409$	−3443.20	−0.416273	−0.208136	+	0.978100i	$0.566740\pi$
$410$	7463.75	0.899044
$411$	−8588.45	−1.03075
$412$	4760.51	0.569257
$413$	11158.6	1.32948
$414$	31042.8	3.68520
$415$	−2486.64	−0.294131
$416$	−3377.09	−0.398018
$417$	−9427.86	−1.10716
$418$	−3985.76	−0.466387
$419$	−1359.84	−0.158550	−0.0792751	−	0.996853i	$-0.525261\pi$
$419$	−1359.84	−0.158550	−0.0792751	+	0.996853i	$0.525261\pi$
$420$	25964.8	3.01655
$421$	2701.71	0.312763	0.156382	−	0.987697i	$-0.450017\pi$
$421$	2701.71	0.312763	0.156382	+	0.987697i	$0.450017\pi$
$422$	8125.11	0.937261
$423$	−30886.6	−3.55026
$424$	2136.00	0.244654
$425$	−5821.15	−0.664394
$426$	−22049.1	−2.50771
$427$	10088.9	1.14341
$428$	−4866.66	−0.549624
$429$	1360.54	0.153118
$430$	13770.1	1.54431
$431$	−10397.2	−1.16198	−0.580990	−	0.813911i	$-0.697334\pi$
$431$	−10397.2	−1.16198	−0.580990	+	0.813911i	$0.697334\pi$
$432$	−19343.1	−2.15427
$433$	449.460	0.0498838	0.0249419	−	0.999689i	$-0.492060\pi$
$433$	449.460	0.0498838	0.0249419	+	0.999689i	$0.492060\pi$
$434$	−13591.3	−1.50323
$435$	−10847.7	−1.19564
$436$	6634.24	0.728721
$437$	10457.6	1.14475
$438$	−41991.7	−4.58091
$439$	2563.12	0.278658	0.139329	−	0.990246i	$-0.455505\pi$
$439$	2563.12	0.278658	0.139329	+	0.990246i	$0.455505\pi$
$440$	613.052	0.0664230
$441$	6334.63	0.684011
$442$	−3628.53	−0.390479
$443$	−3315.98	−0.355636	−0.177818	−	0.984063i	$-0.556904\pi$
$443$	−3315.98	−0.355636	−0.177818	+	0.984063i	$0.556904\pi$
$444$	31666.7	3.38476
$445$	−15149.3	−1.61381
$446$	20212.6	2.14595
$447$	6923.13	0.732557
$448$	−13121.7	−1.38380
$449$	−12439.1	−1.30744	−0.653719	−	0.756738i	$-0.726792\pi$
$449$	−12439.1	−1.30744	−0.653719	+	0.756738i	$0.726792\pi$
$450$	−22432.1	−2.34991
$451$	1374.14	0.143471
$452$	15220.3	1.58386
$453$	26054.1	2.70227
$454$	−15678.3	−1.62075
$455$	−3971.60	−0.409212
$456$	3215.73	0.330242
$457$	8282.92	0.847831	0.423915	−	0.905702i	$-0.360655\pi$
$457$	8282.92	0.847831	0.423915	+	0.905702i	$0.360655\pi$
$458$	6544.89	0.667735
$459$	−23569.3	−2.39678
$460$	−15403.5	−1.56129
$461$	18386.4	1.85757	0.928786	−	0.370615i	$-0.120853\pi$
$461$	18386.4	1.85757	0.928786	+	0.370615i	$0.120853\pi$
$462$	9061.48	0.912507
$463$	6708.85	0.673405	0.336703	−	0.941611i	$-0.390688\pi$
$463$	6708.85	0.673405	0.336703	+	0.941611i	$0.390688\pi$
$464$	4371.27	0.437351
$465$	21685.1	2.16263
$466$	−23505.4	−2.33663
$467$	1096.61	0.108662	0.0543311	−	0.998523i	$-0.482697\pi$
$467$	1096.61	0.108662	0.0543311	+	0.998523i	$0.482697\pi$
$468$	−7376.50	−0.728588
$469$	−10338.1	−1.01785
$470$	29051.6	2.85117
$471$	10273.3	1.00503
$472$	−2035.59	−0.198508
$473$	2535.19	0.246445
$474$	−16875.1	−1.63523
$475$	−7556.82	−0.729960
$476$	−12749.0	−1.22763
$477$	−35348.5	−3.39308
$478$	19882.8	1.90255
$479$	−12195.4	−1.16330	−0.581652	−	0.813438i	$-0.697593\pi$
$479$	−12195.4	−1.16330	−0.581652	+	0.813438i	$0.697593\pi$
$480$	35886.4	3.41247
$481$	−4843.77	−0.459162
$482$	−2835.58	−0.267961
$483$	−23774.9	−2.23974
$484$	1080.87	0.101509
$485$	−17236.5	−1.61375
$486$	−23678.8	−2.21007
$487$	6926.66	0.644511	0.322256	−	0.946653i	$-0.395559\pi$
$487$	6926.66	0.644511	0.322256	+	0.946653i	$0.395559\pi$
$488$	−1840.46	−0.170725
$489$	26720.9	2.47109
$490$	−5958.27	−0.549321
$491$	5324.17	0.489361	0.244680	−	0.969604i	$-0.421317\pi$
$491$	5324.17	0.489361	0.244680	+	0.969604i	$0.421317\pi$
$492$	−10617.0	−0.972865
$493$	5326.34	0.486585
$494$	−4710.44	−0.429014
$495$	−10145.4	−0.921213
$496$	−8738.41	−0.791061
$497$	11850.0	1.06951
$498$	6704.98	0.603328
$499$	19641.6	1.76208	0.881042	−	0.473038i	$-0.156843\pi$
$499$	19641.6	1.76208	0.881042	+	0.473038i	$0.156843\pi$
$500$	−5081.76	−0.454526
$501$	4530.07	0.403969
$502$	−28753.5	−2.55643
$503$	13089.5	1.16030	0.580150	−	0.814510i	$-0.302994\pi$
$503$	13089.5	1.16030	0.580150	+	0.814510i	$0.302994\pi$
$504$	−5130.22	−0.453409
$505$	−18683.5	−1.64635
$506$	−5375.69	−0.472289
$507$	1607.91	0.140848
$508$	14910.0	1.30221
$509$	8843.96	0.770141	0.385071	−	0.922887i	$-0.374177\pi$
$509$	8843.96	0.770141	0.385071	+	0.922887i	$0.374177\pi$
$510$	38558.4	3.34783
$511$	22567.8	1.95370
$512$	−16170.5	−1.39578
$513$	−30596.9	−2.63330
$514$	−17498.3	−1.50159
$515$	7737.88	0.662081
$516$	−19587.6	−1.67112
$517$	5348.64	0.454996
$518$	−32260.5	−2.73638
$519$	3053.86	0.258284
$520$	724.516	0.0611003
$521$	−11970.1	−1.00656	−0.503281	−	0.864123i	$-0.667874\pi$
$521$	−11970.1	−1.00656	−0.503281	+	0.864123i	$0.667874\pi$
$522$	20525.3	1.72101
$523$	−3639.07	−0.304255	−0.152127	−	0.988361i	$-0.548612\pi$
$523$	−3639.07	−0.304255	−0.152127	+	0.988361i	$0.548612\pi$
$524$	16587.7	1.38290
$525$	17180.2	1.42820
$526$	9911.15	0.821571
$527$	−10647.7	−0.880112
$528$	5826.00	0.480197
$529$	1937.38	0.159232
$530$	33248.4	2.72494
$531$	33686.9	2.75308
$532$	−16550.4	−1.34878
$533$	1623.98	0.131974
$534$	40848.7	3.31029
$535$	−7910.41	−0.639247
$536$	1885.92	0.151977
$537$	−23122.0	−1.85808
$538$	15683.0	1.25677
$539$	−1096.97	−0.0876618
$540$	45067.7	3.59149
$541$	4955.49	0.393814	0.196907	−	0.980422i	$-0.436910\pi$
$541$	4955.49	0.393814	0.196907	+	0.980422i	$0.436910\pi$
$542$	36003.6	2.85330
$543$	−13678.3	−1.08101
$544$	−17620.7	−1.38875
$545$	10783.5	0.847548
$546$	10709.0	0.839385
$547$	−18748.9	−1.46553	−0.732767	−	0.680480i	$-0.761771\pi$
$547$	−18748.9	−1.46553	−0.732767	+	0.680480i	$0.761771\pi$
$548$	−8063.56	−0.628573
$549$	30457.7	2.36777
$550$	3884.56	0.301161
$551$	6914.47	0.534603
$552$	4337.13	0.334421
$553$	9069.28	0.697405
$554$	9800.81	0.751618
$555$	51472.0	3.93669
$556$	−8851.66	−0.675169
$557$	−12132.0	−0.922890	−0.461445	−	0.887169i	$-0.652669\pi$
$557$	−12132.0	−0.922890	−0.461445	+	0.887169i	$0.652669\pi$
$558$	−41031.2	−3.11289
$559$	2996.14	0.226696
$560$	−17006.9	−1.28334
$561$	7098.91	0.534254
$562$	−13595.2	−1.02042
$563$	−11829.0	−0.885491	−0.442746	−	0.896647i	$-0.645996\pi$
$563$	−11829.0	−0.885491	−0.442746	+	0.896647i	$0.645996\pi$
$564$	−41325.1	−3.08528
$565$	24739.5	1.84212
$566$	27077.2	2.01085
$567$	33473.9	2.47932
$568$	−2161.73	−0.159690
$569$	5710.18	0.420709	0.210354	−	0.977625i	$-0.432538\pi$
$569$	5710.18	0.420709	0.210354	+	0.977625i	$0.432538\pi$
$570$	50055.2	3.67821
$571$	−8148.17	−0.597181	−0.298591	−	0.954381i	$-0.596516\pi$
$571$	−8148.17	−0.597181	−0.298591	+	0.954381i	$0.596516\pi$
$572$	1277.39	0.0933747
$573$	−25841.1	−1.88399
$574$	10816.0	0.786503
$575$	−10192.1	−0.739198
$576$	−39613.5	−2.86556
$577$	22699.9	1.63780	0.818898	−	0.573939i	$-0.194585\pi$
$577$	22699.9	1.63780	0.818898	+	0.573939i	$0.194585\pi$
$578$	1284.08	0.0924063
$579$	8116.30	0.582559
$580$	−10184.7	−0.729131
$581$	−3603.50	−0.257312
$582$	46476.6	3.31017
$583$	6121.30	0.434852
$584$	−4116.92	−0.291711
$585$	−11990.0	−0.847393
$586$	14886.8	1.04943
$587$	5868.36	0.412629	0.206314	−	0.978486i	$-0.433853\pi$
$587$	5868.36	0.412629	0.206314	+	0.978486i	$0.433853\pi$
$588$	8475.47	0.594426
$589$	−13822.4	−0.966966
$590$	−31685.5	−2.21097
$591$	22796.3	1.58665
$592$	−20741.6	−1.43999
$593$	−10450.4	−0.723691	−0.361845	−	0.932238i	$-0.617853\pi$
$593$	−10450.4	−0.723691	−0.361845	+	0.932238i	$0.617853\pi$
$594$	15728.2	1.08643
$595$	−20722.7	−1.42781
$596$	6500.01	0.446730
$597$	−21622.4	−1.48232
$598$	−6353.08	−0.434443
$599$	−16870.1	−1.15074	−0.575371	−	0.817893i	$-0.695142\pi$
$599$	−16870.1	−1.15074	−0.575371	+	0.817893i	$0.695142\pi$
$600$	−3134.08	−0.213247
$601$	4957.07	0.336444	0.168222	−	0.985749i	$-0.446197\pi$
$601$	4957.07	0.336444	0.168222	+	0.985749i	$0.446197\pi$
$602$	19954.9	1.35100
$603$	−31210.0	−2.10775
$604$	24461.8	1.64791
$605$	1756.87	0.118061
$606$	50378.4	3.37703
$607$	9812.30	0.656127	0.328063	−	0.944656i	$-0.393604\pi$
$607$	9812.30	0.656127	0.328063	+	0.944656i	$0.393604\pi$
$608$	−22874.6	−1.52580
$609$	−15719.8	−1.04598
$610$	−28648.2	−1.90153
$611$	6321.12	0.418535
$612$	−38488.5	−2.54216
$613$	14477.3	0.953889	0.476945	−	0.878933i	$-0.341744\pi$
$613$	14477.3	0.953889	0.476945	+	0.878933i	$0.341744\pi$
$614$	26901.2	1.76815
$615$	−17257.1	−1.13150
$616$	888.401	0.0581083
$617$	21417.2	1.39745	0.698724	−	0.715392i	$-0.253752\pi$
$617$	21417.2	1.39745	0.698724	+	0.715392i	$0.253752\pi$
$618$	−20864.4	−1.35808
$619$	18220.4	1.18310	0.591549	−	0.806269i	$-0.298517\pi$
$619$	18220.4	1.18310	0.591549	+	0.806269i	$0.298517\pi$
$620$	20359.8	1.31882
$621$	−41266.7	−2.66663
$622$	−14175.1	−0.913780
$623$	−21953.5	−1.41180
$624$	6885.27	0.441717
$625$	−18987.5	−1.21520
$626$	−29081.0	−1.85673
$627$	9215.57	0.586977
$628$	9645.43	0.612889
$629$	−25273.4	−1.60209
$630$	−79855.8	−5.05005
$631$	−8287.18	−0.522833	−0.261416	−	0.965226i	$-0.584190\pi$
$631$	−8287.18	−0.522833	−0.261416	+	0.965226i	$0.584190\pi$
$632$	−1654.46	−0.104131
$633$	−18786.3	−1.17960
$634$	−8261.58	−0.517523
$635$	24235.1	1.51455
$636$	−47294.9	−2.94868
$637$	−1296.42	−0.0806371
$638$	−3554.37	−0.220562
$639$	35774.3	2.21473
$640$	7085.21	0.437605
$641$	7328.62	0.451581	0.225790	−	0.974176i	$-0.427504\pi$
$641$	7328.62	0.451581	0.225790	+	0.974176i	$0.427504\pi$
$642$	21329.7	1.31124
$643$	11831.5	0.725643	0.362822	−	0.931859i	$-0.381813\pi$
$643$	11831.5	0.725643	0.362822	+	0.931859i	$0.381813\pi$
$644$	−22321.9	−1.36585
$645$	−31838.2	−1.94361
$646$	−24577.7	−1.49690
$647$	−21300.8	−1.29431	−0.647157	−	0.762357i	$-0.724042\pi$
$647$	−21300.8	−1.29431	−0.647157	+	0.762357i	$0.724042\pi$
$648$	−6106.46	−0.370192
$649$	−5833.56	−0.352831
$650$	4590.85	0.277028
$651$	31424.8	1.89191
$652$	25087.8	1.50692
$653$	19036.0	1.14079	0.570396	−	0.821370i	$-0.306790\pi$
$653$	19036.0	1.14079	0.570396	+	0.821370i	$0.306790\pi$
$654$	−29076.6	−1.73851
$655$	26962.2	1.60840
$656$	6954.08	0.413889
$657$	68130.8	4.04571
$658$	42100.0	2.49427
$659$	−14924.4	−0.882204	−0.441102	−	0.897457i	$-0.645412\pi$
$659$	−14924.4	−0.882204	−0.441102	+	0.897457i	$0.645412\pi$
$660$	−13574.1	−0.800562
$661$	−11070.1	−0.651401	−0.325700	−	0.945473i	$-0.605600\pi$
$661$	−11070.1	−0.651401	−0.325700	+	0.945473i	$0.605600\pi$
$662$	−3412.87	−0.200370
$663$	8389.63	0.491442
$664$	657.366	0.0384198
$665$	−26901.5	−1.56871
$666$	−97392.2	−5.66648
$667$	9325.72	0.541369
$668$	4253.21	0.246350
$669$	−46734.0	−2.70081
$670$	29355.8	1.69271
$671$	−5274.36	−0.303449
$672$	52004.6	2.98530
$673$	23637.0	1.35385	0.676923	−	0.736054i	$-0.263313\pi$
$673$	23637.0	1.35385	0.676923	+	0.736054i	$0.263313\pi$
$674$	−13977.4	−0.798795
$675$	29820.0	1.70041
$676$	1509.64	0.0858922
$677$	−1520.44	−0.0863152	−0.0431576	−	0.999068i	$-0.513742\pi$
$677$	−1520.44	−0.0863152	−0.0431576	+	0.999068i	$0.513742\pi$
$678$	−66707.8	−3.77861
$679$	−24978.2	−1.41175
$680$	3780.32	0.213189
$681$	36250.2	2.03981
$682$	7105.38	0.398943
$683$	6652.20	0.372679	0.186339	−	0.982485i	$-0.440338\pi$
$683$	6652.20	0.372679	0.186339	+	0.982485i	$0.440338\pi$
$684$	−49964.5	−2.79304
$685$	−13106.7	−0.731070
$686$	21063.5	1.17231
$687$	−15132.6	−0.840385
$688$	12829.8	0.710948
$689$	7234.27	0.400005
$690$	67510.6	3.72476
$691$	23343.2	1.28512	0.642558	−	0.766237i	$-0.277873\pi$
$691$	23343.2	1.28512	0.642558	+	0.766237i	$0.277873\pi$
$692$	2867.21	0.157507
$693$	−14702.1	−0.805897
$694$	−12654.1	−0.692138
$695$	−14387.8	−0.785264
$696$	2867.68	0.156177
$697$	8473.46	0.460481
$698$	−28678.0	−1.55513
$699$	54347.5	2.94079
$700$	16130.2	0.870948
$701$	7828.97	0.421820	0.210910	−	0.977505i	$-0.432357\pi$
$701$	7828.97	0.421820	0.210910	+	0.977505i	$0.432357\pi$
$702$	18587.9	0.999367
$703$	−32809.1	−1.76020
$704$	6859.88	0.367246
$705$	−67170.9	−3.58837
$706$	−33979.3	−1.81137
$707$	−27075.1	−1.44026
$708$	45071.7	2.39251
$709$	−18640.5	−0.987388	−0.493694	−	0.869636i	$-0.664354\pi$
$709$	−18640.5	−0.987388	−0.493694	+	0.869636i	$0.664354\pi$
$710$	−33648.9	−1.77862
$711$	27379.5	1.44418
$712$	4004.86	0.210798
$713$	−18642.6	−0.979204
$714$	55876.6	2.92875
$715$	2076.31	0.108601
$716$	−21708.9	−1.13310
$717$	−45971.6	−2.39448
$718$	49072.2	2.55064
$719$	−26264.6	−1.36231	−0.681157	−	0.732137i	$-0.738523\pi$
$719$	−26264.6	−1.36231	−0.681157	+	0.732137i	$0.738523\pi$
$720$	−51342.5	−2.65753
$721$	11213.3	0.579202
$722$	−3681.56	−0.189770
$723$	6556.22	0.337245
$724$	−12842.3	−0.659227
$725$	−6738.92	−0.345210
$726$	−4737.24	−0.242170
$727$	7633.32	0.389414	0.194707	−	0.980861i	$-0.437624\pi$
$727$	7633.32	0.389414	0.194707	+	0.980861i	$0.437624\pi$
$728$	1049.93	0.0534518
$729$	11794.4	0.599218
$730$	−64083.0	−3.24907
$731$	15633.0	0.790981
$732$	40751.2	2.05766
$733$	−25771.8	−1.29864	−0.649320	−	0.760515i	$-0.724946\pi$
$733$	−25771.8	−1.29864	−0.649320	+	0.760515i	$0.724946\pi$
$734$	17930.8	0.901684
$735$	13776.3	0.691355
$736$	−30851.5	−1.54511
$737$	5404.64	0.270126
$738$	32652.9	1.62869
$739$	−9792.38	−0.487441	−0.243720	−	0.969846i	$-0.578368\pi$
$739$	−9792.38	−0.487441	−0.243720	+	0.969846i	$0.578368\pi$
$740$	48326.2	2.40068
$741$	10891.1	0.539940
$742$	48181.7	2.38384
$743$	31044.3	1.53284	0.766422	−	0.642337i	$-0.222035\pi$
$743$	31044.3	1.53284	0.766422	+	0.642337i	$0.222035\pi$
$744$	−5732.65	−0.282486
$745$	10565.3	0.519574
$746$	−18333.0	−0.899756
$747$	−10878.7	−0.532840
$748$	6665.05	0.325800
$749$	−11463.3	−0.559227
$750$	22272.4	1.08436
$751$	10058.0	0.488709	0.244354	−	0.969686i	$-0.421424\pi$
$751$	10058.0	0.488709	0.244354	+	0.969686i	$0.421424\pi$
$752$	27067.8	1.31258
$753$	66481.6	3.21743
$754$	−4200.62	−0.202888
$755$	39760.9	1.91662
$756$	65309.6	3.14191
$757$	9356.49	0.449230	0.224615	−	0.974448i	$-0.427888\pi$
$757$	9356.49	0.449230	0.224615	+	0.974448i	$0.427888\pi$
$758$	−6974.26	−0.334191
$759$	12429.3	0.594405
$760$	4907.48	0.234228
$761$	10953.3	0.521757	0.260879	−	0.965372i	$-0.415988\pi$
$761$	10953.3	0.521757	0.260879	+	0.965372i	$0.415988\pi$
$762$	−65347.6	−3.10668
$763$	15626.8	0.741453
$764$	−24261.8	−1.14890
$765$	−62560.3	−2.95670
$766$	−15172.1	−0.715651
$767$	−6894.21	−0.324557
$768$	28362.1	1.33259
$769$	17928.1	0.840709	0.420354	−	0.907360i	$-0.361906\pi$
$769$	17928.1	0.840709	0.420354	+	0.907360i	$0.361906\pi$
$770$	13828.6	0.647206
$771$	40458.2	1.88984
$772$	7620.26	0.355258
$773$	16680.2	0.776126	0.388063	−	0.921633i	$-0.373144\pi$
$773$	16680.2	0.776126	0.388063	+	0.921633i	$0.373144\pi$
$774$	60242.4	2.79764
$775$	13471.5	0.624400
$776$	4556.63	0.210791
$777$	74590.3	3.44390
$778$	−985.841	−0.0454295
$779$	11000.0	0.505924
$780$	−16042.1	−0.736410
$781$	−6195.04	−0.283836
$782$	−33148.6	−1.51584
$783$	−27285.3	−1.24533
$784$	−5551.41	−0.252888
$785$	15678.0	0.712828
$786$	−72700.9	−3.29918
$787$	−16312.0	−0.738829	−0.369415	−	0.929265i	$-0.620442\pi$
$787$	−16312.0	−0.738829	−0.369415	+	0.929265i	$0.620442\pi$
$788$	21403.0	0.967578
$789$	−22915.8	−1.03400
$790$	−25752.9	−1.15981
$791$	35851.2	1.61153
$792$	2682.02	0.120330
$793$	−6233.34	−0.279133
$794$	−9147.32	−0.408849
$795$	−76874.5	−3.42950
$796$	−20300.9	−0.903953
$797$	−30565.9	−1.35847	−0.679234	−	0.733921i	$-0.737688\pi$
$797$	−30565.9	−1.35847	−0.679234	+	0.733921i	$0.737688\pi$
$798$	72537.2	3.21778
$799$	32981.8	1.46034
$800$	22293.8	0.985258
$801$	−66276.2	−2.92354
$802$	−13203.0	−0.581315
$803$	−11798.2	−0.518493
$804$	−41757.8	−1.83169
$805$	−36282.6	−1.58857
$806$	8397.27	0.366974
$807$	−36261.0	−1.58172
$808$	4939.17	0.215049
$809$	3118.56	0.135529	0.0677643	−	0.997701i	$-0.478413\pi$
$809$	3118.56	0.135529	0.0677643	+	0.997701i	$0.478413\pi$
$810$	−95051.6	−4.12318
$811$	5944.09	0.257368	0.128684	−	0.991686i	$-0.458925\pi$
$811$	5944.09	0.257368	0.128684	+	0.991686i	$0.458925\pi$
$812$	−14759.1	−0.637860
$813$	−83244.8	−3.59105
$814$	16865.4	0.726207
$815$	40778.5	1.75265
$816$	35925.4	1.54123
$817$	20294.2	0.869039
$818$	14168.6	0.605616
$819$	−17375.2	−0.741317
$820$	−16202.4	−0.690016
$821$	21983.7	0.934515	0.467257	−	0.884121i	$-0.345242\pi$
$821$	21983.7	0.934515	0.467257	+	0.884121i	$0.345242\pi$
$822$	35341.0	1.49959
$823$	−33099.2	−1.40190	−0.700950	−	0.713210i	$-0.747241\pi$
$823$	−33099.2	−1.40190	−0.700950	+	0.713210i	$0.747241\pi$
$824$	−2045.58	−0.0864819
$825$	−8981.60	−0.379029
$826$	−45916.9	−1.93420
$827$	15901.5	0.668620	0.334310	−	0.942463i	$-0.391497\pi$
$827$	15901.5	0.668620	0.334310	+	0.942463i	$0.391497\pi$
$828$	−67388.3	−2.82839
$829$	−10261.2	−0.429899	−0.214950	−	0.976625i	$-0.568959\pi$
$829$	−10261.2	−0.429899	−0.214950	+	0.976625i	$0.568959\pi$
$830$	10232.4	0.427917
$831$	−22660.7	−0.945958
$832$	8107.13	0.337817
$833$	−6764.33	−0.281357
$834$	38795.2	1.61075
$835$	6913.29	0.286520
$836$	8652.35	0.357952
$837$	54544.8	2.25250
$838$	5595.67	0.230667
$839$	13744.7	0.565577	0.282789	−	0.959182i	$-0.408741\pi$
$839$	13744.7	0.565577	0.282789	+	0.959182i	$0.408741\pi$
$840$	−11157.0	−0.458277
$841$	−18222.9	−0.747177
$842$	−11117.4	−0.455025
$843$	31433.7	1.28426
$844$	−17638.1	−0.719347
$845$	2453.82	0.0998980
$846$	127097.	5.16511
$847$	2545.96	0.103283
$848$	30978.0	1.25447
$849$	−62605.9	−2.53078
$850$	23953.7	0.966596
$851$	−44250.4	−1.78247
$852$	47864.5	1.92466
$853$	10317.2	0.414133	0.207067	−	0.978327i	$-0.433608\pi$
$853$	10317.2	0.414133	0.207067	+	0.978327i	$0.433608\pi$
$854$	−41515.3	−1.66350
$855$	−81213.7	−3.24848
$856$	2091.19	0.0834993
$857$	−15890.5	−0.633384	−0.316692	−	0.948528i	$-0.602572\pi$
$857$	−15890.5	−0.633384	−0.316692	+	0.948528i	$0.602572\pi$
$858$	−5598.56	−0.222764
$859$	30397.7	1.20740	0.603700	−	0.797212i	$-0.293692\pi$
$859$	30397.7	1.20740	0.603700	+	0.797212i	$0.293692\pi$
$860$	−29892.4	−1.18526
$861$	−25008.0	−0.989863
$862$	42783.7	1.69051
$863$	−5790.29	−0.228394	−0.114197	−	0.993458i	$-0.536429\pi$
$863$	−5790.29	−0.228394	−0.114197	+	0.993458i	$0.536429\pi$
$864$	90265.6	3.55428
$865$	4660.45	0.183191
$866$	−1849.51	−0.0725736
$867$	−2968.96	−0.116299
$868$	29504.2	1.15373
$869$	−4741.32	−0.185084
$870$	44637.6	1.73949
$871$	6387.30	0.248479
$872$	−2850.71	−0.110708
$873$	−75407.5	−2.92343
$874$	−43032.4	−1.66544
$875$	−11970.0	−0.462467
$876$	91156.2	3.51585
$877$	−50303.4	−1.93686	−0.968429	−	0.249288i	$-0.919803\pi$
$877$	−50303.4	−1.93686	−0.968429	+	0.249288i	$0.919803\pi$
$878$	−10547.1	−0.405407
$879$	−34420.1	−1.32078
$880$	8890.99	0.340585
$881$	27072.6	1.03530	0.517651	−	0.855592i	$-0.326807\pi$
$881$	27072.6	1.03530	0.517651	+	0.855592i	$0.326807\pi$
$882$	−26066.7	−0.995136
$883$	4541.08	0.173068	0.0865342	−	0.996249i	$-0.472421\pi$
$883$	4541.08	0.173068	0.0865342	+	0.996249i	$0.472421\pi$
$884$	7876.88	0.299692
$885$	73260.9	2.78264
$886$	13645.1	0.517399
$887$	−210.429	−0.00796561	−0.00398281	−	0.999992i	$-0.501268\pi$
$887$	−210.429	−0.00796561	−0.00398281	+	0.999992i	$0.501268\pi$
$888$	−13607.1	−0.514216
$889$	35120.1	1.32496
$890$	62338.7	2.34786
$891$	−17499.8	−0.657985
$892$	−43877.8	−1.64702
$893$	42815.8	1.60445
$894$	−28488.3	−1.06576
$895$	−35286.2	−1.31786
$896$	10267.5	0.382826
$897$	14689.1	0.546773
$898$	51186.4	1.90213
$899$	−12326.4	−0.457295
$900$	48695.9	1.80355
$901$	37746.3	1.39569
$902$	−5654.50	−0.208730
$903$	−46138.2	−1.70031
$904$	−6540.12	−0.240621
$905$	−20874.2	−0.766722
$906$	−107211.	−3.93141
$907$	−25105.7	−0.919099	−0.459549	−	0.888152i	$-0.651989\pi$
$907$	−25105.7	−0.919099	−0.459549	+	0.888152i	$0.651989\pi$
$908$	34034.7	1.24392
$909$	−81738.0	−2.98249
$910$	16342.9	0.595343
$911$	−26997.0	−0.981835	−0.490918	−	0.871206i	$-0.663338\pi$
$911$	−26997.0	−0.981835	−0.490918	+	0.871206i	$0.663338\pi$
$912$	46637.1	1.69332
$913$	1883.87	0.0682880
$914$	−34083.8	−1.23347
$915$	66238.2	2.39319
$916$	−14207.7	−0.512486
$917$	39072.1	1.40706
$918$	96986.4	3.48696
$919$	4305.70	0.154550	0.0772752	−	0.997010i	$-0.475378\pi$
$919$	4305.70	0.154550	0.0772752	+	0.997010i	$0.475378\pi$
$920$	6618.84	0.237192
$921$	−62199.0	−2.22533
$922$	−75659.2	−2.70250
$923$	−7321.41	−0.261091
$924$	−19670.8	−0.700349
$925$	31976.1	1.13661
$926$	−27606.6	−0.979706
$927$	33852.2	1.19941
$928$	−20398.8	−0.721577
$929$	15683.8	0.553895	0.276947	−	0.960885i	$-0.410677\pi$
$929$	15683.8	0.553895	0.276947	+	0.960885i	$0.410677\pi$
$930$	−89233.0	−3.14631
$931$	−8781.22	−0.309122
$932$	51026.0	1.79336
$933$	32774.7	1.15005
$934$	−4512.51	−0.158088
$935$	10833.6	0.378926
$936$	3169.66	0.110688
$937$	−6659.77	−0.232193	−0.116097	−	0.993238i	$-0.537038\pi$
$937$	−6659.77	−0.232193	−0.116097	+	0.993238i	$0.537038\pi$
$938$	42540.8	1.48082
$939$	67238.9	2.33680
$940$	−63065.7	−2.18827
$941$	−3705.85	−0.128382	−0.0641909	−	0.997938i	$-0.520447\pi$
$941$	−3705.85	−0.128382	−0.0641909	+	0.997938i	$0.520447\pi$
$942$	−42274.1	−1.46217
$943$	14835.9	0.512327
$944$	−29521.8	−1.01785
$945$	106156.	3.65424
$946$	−10432.2	−0.358541
$947$	−1026.82	−0.0352347	−0.0176173	−	0.999845i	$-0.505608\pi$
$947$	−1026.82	−0.0352347	−0.0176173	+	0.999845i	$0.505608\pi$
$948$	36632.7	1.25504
$949$	−13943.3	−0.476944
$950$	31095.9	1.06198
$951$	19101.8	0.651334
$952$	5478.22	0.186502
$953$	23338.5	0.793294	0.396647	−	0.917971i	$-0.370174\pi$
$953$	23338.5	0.793294	0.396647	+	0.917971i	$0.370174\pi$
$954$	145457.	4.93643
$955$	−39435.9	−1.33625
$956$	−43161.9	−1.46021
$957$	8218.14	0.277591
$958$	50183.5	1.69244
$959$	−18993.5	−0.639555
$960$	−86149.8	−2.89633
$961$	−5149.86	−0.172866
$962$	19931.9	0.668013
$963$	−34607.0	−1.15804
$964$	6155.52	0.205660
$965$	12386.2	0.413187
$966$	97832.6	3.25850
$967$	−12758.8	−0.424296	−0.212148	−	0.977238i	$-0.568046\pi$
$967$	−12758.8	−0.424296	−0.212148	+	0.977238i	$0.568046\pi$
$968$	−464.446	−0.0154213
$969$	56826.8	1.88394
$970$	70927.4	2.34777
$971$	−57003.9	−1.88398	−0.941988	−	0.335646i	$-0.891045\pi$
$971$	−57003.9	−1.88398	−0.941988	+	0.335646i	$0.891045\pi$
$972$	51402.4	1.69623
$973$	−20849.9	−0.686966
$974$	−28502.8	−0.937669
$975$	−10614.6	−0.348656
$976$	−26691.9	−0.875396
$977$	−52213.2	−1.70977	−0.854887	−	0.518814i	$-0.826374\pi$
$977$	−52213.2	−1.70977	−0.854887	+	0.518814i	$0.826374\pi$
$978$	−109955.	−3.59507
$979$	11477.1	0.374677
$980$	12934.3	0.421604
$981$	47176.3	1.53540
$982$	−21908.7	−0.711949
$983$	35106.2	1.13908	0.569539	−	0.821964i	$-0.307122\pi$
$983$	35106.2	1.13908	0.569539	+	0.821964i	$0.307122\pi$
$984$	4562.08	0.147798
$985$	34789.1	1.12535
$986$	−21917.6	−0.707910
$987$	−97340.3	−3.13919
$988$	10225.5	0.329268
$989$	27371.3	0.880037
$990$	41747.7	1.34023
$991$	−20324.8	−0.651501	−0.325750	−	0.945456i	$-0.605617\pi$
$991$	−20324.8	−0.651501	−0.325750	+	0.945456i	$0.605617\pi$
$992$	40778.4	1.30516
$993$	7890.97	0.252178
$994$	−48762.1	−1.55597
$995$	−32997.7	−1.05135
$996$	−14555.3	−0.463054
$997$	−60406.4	−1.91885	−0.959423	−	0.281971i	$-0.909012\pi$
$997$	−60406.4	−1.91885	−0.959423	+	0.281971i	$0.909012\pi$
$998$	−80824.3	−2.56358
$999$	129468.	4.10029

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.a.c.1.2	✓	9
3.2	odd	2		1287.4.a.k.1.8		9
4.3	odd	2		2288.4.a.r.1.1		9
11.10	odd	2		1573.4.a.e.1.8		9
13.12	even	2		1859.4.a.d.1.8		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.a.c.1.2	✓	9	1.1	even	1	trivial
1287.4.a.k.1.8		9	3.2	odd	2
1573.4.a.e.1.8		9	11.10	odd	2
1859.4.a.d.1.8		9	13.12	even	2
2288.4.a.r.1.1		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)

\(f(q)\)	\(=\)	\(q-4.11495 q^{2} +9.51427 q^{3} +8.93279 q^{4} +14.5196 q^{5} -39.1507 q^{6} +21.0410 q^{7} -3.83839 q^{8} +63.5214 q^{9} +O(q^{10})\)	\(q-4.11495 q^{2} +9.51427 q^{3} +8.93279 q^{4} +14.5196 q^{5} -39.1507 q^{6} +21.0410 q^{7} -3.83839 q^{8} +63.5214 q^{9} -59.7475 q^{10} -11.0000 q^{11} +84.9890 q^{12} -13.0000 q^{13} -86.5827 q^{14} +138.144 q^{15} -55.6676 q^{16} -67.8303 q^{17} -261.387 q^{18} -88.0550 q^{19} +129.701 q^{20} +200.190 q^{21} +45.2644 q^{22} -118.762 q^{23} -36.5195 q^{24} +85.8194 q^{25} +53.4943 q^{26} +347.475 q^{27} +187.955 q^{28} -78.5245 q^{29} -568.454 q^{30} +156.975 q^{31} +259.776 q^{32} -104.657 q^{33} +279.118 q^{34} +305.508 q^{35} +567.423 q^{36} +372.598 q^{37} +362.342 q^{38} -123.686 q^{39} -55.7320 q^{40} -124.922 q^{41} -823.771 q^{42} -230.472 q^{43} -98.2607 q^{44} +922.307 q^{45} +488.699 q^{46} -486.240 q^{47} -529.636 q^{48} +99.7243 q^{49} -353.142 q^{50} -645.356 q^{51} -116.126 q^{52} -556.482 q^{53} -1429.84 q^{54} -159.716 q^{55} -80.7637 q^{56} -837.779 q^{57} +323.124 q^{58} +530.324 q^{59} +1234.01 q^{60} +479.488 q^{61} -645.944 q^{62} +1336.55 q^{63} -623.625 q^{64} -188.755 q^{65} +430.658 q^{66} -491.331 q^{67} -605.914 q^{68} -1129.93 q^{69} -1257.15 q^{70} +563.185 q^{71} -243.820 q^{72} +1072.56 q^{73} -1533.22 q^{74} +816.509 q^{75} -786.577 q^{76} -231.451 q^{77} +508.960 q^{78} +431.029 q^{79} -808.272 q^{80} +1590.89 q^{81} +514.046 q^{82} -171.261 q^{83} +1788.26 q^{84} -984.870 q^{85} +948.380 q^{86} -747.104 q^{87} +42.2223 q^{88} -1043.37 q^{89} -3795.24 q^{90} -273.533 q^{91} -1060.88 q^{92} +1493.50 q^{93} +2000.85 q^{94} -1278.52 q^{95} +2471.58 q^{96} -1187.12 q^{97} -410.360 q^{98} -698.735 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 8 q^{3} + 46 q^{4} + 30 q^{5} + 34 q^{6} + 25 q^{7} + 36 q^{8} + 91 q^{9}+O(q^{10}) \) 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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