LMFDB - Embedded newform 1849.4.a.i.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1849,4,Mod(1,1849)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1849, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1849 = 43^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1849.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:	$109.094531601$
Analytic rank:	$1$
Dimension:	$50$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.43471 q^{2} -1.13642 q^{3} +3.79726 q^{4} -2.82850 q^{5} +3.90328 q^{6} -33.5669 q^{7} +14.4352 q^{8} -25.7086 q^{9} +O(q^{10})$	\(q-3.43471 q^{2} -1.13642 q^{3} +3.79726 q^{4} -2.82850 q^{5} +3.90328 q^{6} -33.5669 q^{7} +14.4352 q^{8} -25.7086 q^{9} +9.71508 q^{10} -8.65202 q^{11} -4.31528 q^{12} +54.3373 q^{13} +115.293 q^{14} +3.21436 q^{15} -79.9589 q^{16} -76.6586 q^{17} +88.3015 q^{18} +95.8312 q^{19} -10.7405 q^{20} +38.1461 q^{21} +29.7172 q^{22} -162.323 q^{23} -16.4045 q^{24} -117.000 q^{25} -186.633 q^{26} +59.8990 q^{27} -127.462 q^{28} +17.8240 q^{29} -11.0404 q^{30} +135.293 q^{31} +159.154 q^{32} +9.83232 q^{33} +263.300 q^{34} +94.9439 q^{35} -97.6220 q^{36} +204.476 q^{37} -329.153 q^{38} -61.7500 q^{39} -40.8300 q^{40} -302.873 q^{41} -131.021 q^{42} -32.8540 q^{44} +72.7166 q^{45} +557.532 q^{46} -79.5496 q^{47} +90.8669 q^{48} +783.738 q^{49} +401.860 q^{50} +87.1163 q^{51} +206.333 q^{52} +445.730 q^{53} -205.736 q^{54} +24.4722 q^{55} -484.546 q^{56} -108.904 q^{57} -61.2204 q^{58} -219.828 q^{59} +12.2058 q^{60} +116.310 q^{61} -464.693 q^{62} +862.957 q^{63} +93.0220 q^{64} -153.693 q^{65} -33.7712 q^{66} +859.592 q^{67} -291.092 q^{68} +184.467 q^{69} -326.105 q^{70} +1028.88 q^{71} -371.108 q^{72} +136.880 q^{73} -702.318 q^{74} +132.961 q^{75} +363.896 q^{76} +290.422 q^{77} +212.094 q^{78} -584.277 q^{79} +226.164 q^{80} +626.060 q^{81} +1040.28 q^{82} +27.3094 q^{83} +144.851 q^{84} +216.829 q^{85} -20.2556 q^{87} -124.894 q^{88} -1120.94 q^{89} -249.761 q^{90} -1823.94 q^{91} -616.381 q^{92} -153.750 q^{93} +273.230 q^{94} -271.058 q^{95} -180.866 q^{96} +643.857 q^{97} -2691.92 q^{98} +222.431 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - 10 q^{2} - 2 q^{3} + 186 q^{4} + 8 q^{5} - 51 q^{6} - 6 q^{7} - 138 q^{8} + 360 q^{9}+O(q^{10}) $ 50 * q - 10 * q^2 - 2 * q^3 + 186 * q^4 + 8 * q^5 - 51 * q^6 - 6 * q^7 - 138 * q^8 + 360 * q^9	\( 50 q - 10 q^{2} - 2 q^{3} + 186 q^{4} + 8 q^{5} - 51 q^{6} - 6 q^{7} - 138 q^{8} + 360 q^{9} - 137 q^{10} - 252 q^{11} - 48 q^{12} - 192 q^{13} - 272 q^{14} - 314 q^{15} + 542 q^{16} - 236 q^{17} - 386 q^{18} + 12 q^{19} + 108 q^{20} - 408 q^{21} + 1235 q^{22} - 630 q^{23} - 613 q^{24} + 1098 q^{25} + 1493 q^{26} + 10 q^{27} - 242 q^{28} + 208 q^{29} - 48 q^{30} - 932 q^{31} - 1124 q^{32} + 254 q^{33} + 765 q^{34} - 1452 q^{35} + 747 q^{36} - 90 q^{37} - 1213 q^{38} - 1610 q^{39} - 1693 q^{40} - 1354 q^{41} - 16 q^{42} - 2704 q^{44} + 4508 q^{45} + 233 q^{46} - 3484 q^{47} - 376 q^{48} + 1324 q^{49} - 408 q^{50} + 4054 q^{51} - 2176 q^{52} - 726 q^{53} - 6497 q^{54} - 3288 q^{55} - 7097 q^{56} - 870 q^{57} + 275 q^{58} - 4370 q^{59} - 3891 q^{60} + 1172 q^{61} - 1546 q^{62} - 3686 q^{63} + 606 q^{64} + 2610 q^{65} - 4697 q^{66} - 344 q^{67} - 3221 q^{68} + 136 q^{69} - 1310 q^{70} + 162 q^{71} - 5814 q^{72} + 746 q^{73} - 4332 q^{74} + 236 q^{75} + 1338 q^{76} + 2024 q^{77} - 2782 q^{78} - 2656 q^{79} - 5713 q^{80} - 86 q^{81} - 4168 q^{82} - 3514 q^{83} - 4269 q^{84} - 7558 q^{85} - 10278 q^{87} + 11692 q^{88} + 2640 q^{89} - 8286 q^{90} - 5946 q^{91} - 4271 q^{92} - 2 q^{93} + 9062 q^{94} - 12140 q^{95} - 700 q^{96} - 3864 q^{97} - 2826 q^{98} - 8174 q^{99}+O(q^{100}) \) 50 * q - 10 * q^2 - 2 * q^3 + 186 * q^4 + 8 * q^5 - 51 * q^6 - 6 * q^7 - 138 * q^8 + 360 * q^9 - 137 * q^10 - 252 * q^11 - 48 * q^12 - 192 * q^13 - 272 * q^14 - 314 * q^15 + 542 * q^16 - 236 * q^17 - 386 * q^18 + 12 * q^19 + 108 * q^20 - 408 * q^21 + 1235 * q^22 - 630 * q^23 - 613 * q^24 + 1098 * q^25 + 1493 * q^26 + 10 * q^27 - 242 * q^28 + 208 * q^29 - 48 * q^30 - 932 * q^31 - 1124 * q^32 + 254 * q^33 + 765 * q^34 - 1452 * q^35 + 747 * q^36 - 90 * q^37 - 1213 * q^38 - 1610 * q^39 - 1693 * q^40 - 1354 * q^41 - 16 * q^42 - 2704 * q^44 + 4508 * q^45 + 233 * q^46 - 3484 * q^47 - 376 * q^48 + 1324 * q^49 - 408 * q^50 + 4054 * q^51 - 2176 * q^52 - 726 * q^53 - 6497 * q^54 - 3288 * q^55 - 7097 * q^56 - 870 * q^57 + 275 * q^58 - 4370 * q^59 - 3891 * q^60 + 1172 * q^61 - 1546 * q^62 - 3686 * q^63 + 606 * q^64 + 2610 * q^65 - 4697 * q^66 - 344 * q^67 - 3221 * q^68 + 136 * q^69 - 1310 * q^70 + 162 * q^71 - 5814 * q^72 + 746 * q^73 - 4332 * q^74 + 236 * q^75 + 1338 * q^76 + 2024 * q^77 - 2782 * q^78 - 2656 * q^79 - 5713 * q^80 - 86 * q^81 - 4168 * q^82 - 3514 * q^83 - 4269 * q^84 - 7558 * q^85 - 10278 * q^87 + 11692 * q^88 + 2640 * q^89 - 8286 * q^90 - 5946 * q^91 - 4271 * q^92 - 2 * q^93 + 9062 * q^94 - 12140 * q^95 - 700 * q^96 - 3864 * q^97 - 2826 * q^98 - 8174 * 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 $

$2$	−3.43471	−1.21435	−0.607177	−	0.794566i	$-0.707698\pi$
$2$	−3.43471	−1.21435	−0.607177	+	0.794566i	$0.707698\pi$
$3$	−1.13642	−0.218704	−0.109352	−	0.994003i	$-0.534878\pi$
$3$	−1.13642	−0.218704	−0.109352	+	0.994003i	$0.534878\pi$
$4$	3.79726	0.474657
$5$	−2.82850	−0.252989	−0.126494	−	0.991967i	$-0.540373\pi$
$5$	−2.82850	−0.252989	−0.126494	+	0.991967i	$0.540373\pi$
$6$	3.90328	0.265584
$7$	−33.5669	−1.81244	−0.906222	−	0.422803i	$-0.861046\pi$
$7$	−33.5669	−1.81244	−0.906222	+	0.422803i	$0.861046\pi$
$8$	14.4352	0.637952
$9$	−25.7086	−0.952169
$10$	9.71508	0.307218
$11$	−8.65202	−0.237153	−0.118576	−	0.992945i	$-0.537833\pi$
$11$	−8.65202	−0.237153	−0.118576	+	0.992945i	$0.537833\pi$
$12$	−4.31528	−0.103809
$13$	54.3373	1.15927	0.579633	−	0.814878i	$-0.303196\pi$
$13$	54.3373	1.15927	0.579633	+	0.814878i	$0.303196\pi$
$14$	115.293	2.20095
$15$	3.21436	0.0553296
$16$	−79.9589	−1.24936
$17$	−76.6586	−1.09367	−0.546836	−	0.837240i	$-0.684168\pi$
$17$	−76.6586	−1.09367	−0.546836	+	0.837240i	$0.684168\pi$
$18$	88.3015	1.15627
$19$	95.8312	1.15711	0.578557	−	0.815642i	$-0.303616\pi$
$19$	95.8312	1.15711	0.578557	+	0.815642i	$0.303616\pi$
$20$	−10.7405	−0.120083
$21$	38.1461	0.396389
$22$	29.7172	0.287988
$23$	−162.323	−1.47159	−0.735796	−	0.677203i	$-0.763192\pi$
$23$	−162.323	−1.47159	−0.735796	+	0.677203i	$0.763192\pi$
$24$	−16.4045	−0.139523
$25$	−117.000	−0.935997
$26$	−186.633	−1.40776
$27$	59.8990	0.426947
$28$	−127.462	−0.860289
$29$	17.8240	0.114132	0.0570661	−	0.998370i	$-0.481825\pi$
$29$	17.8240	0.114132	0.0570661	+	0.998370i	$0.481825\pi$
$30$	−11.0404	−0.0671898
$31$	135.293	0.783851	0.391925	−	0.919997i	$-0.371809\pi$
$31$	135.293	0.783851	0.391925	+	0.919997i	$0.371809\pi$
$32$	159.154	0.879211
$33$	9.83232	0.0518663
$34$	263.300	1.32811
$35$	94.9439	0.458527
$36$	−97.6220	−0.451954
$37$	204.476	0.908533	0.454267	−	0.890866i	$-0.349901\pi$
$37$	204.476	0.908533	0.454267	+	0.890866i	$0.349901\pi$
$38$	−329.153	−1.40515
$39$	−61.7500	−0.253536
$40$	−40.8300	−0.161395
$41$	−302.873	−1.15368	−0.576840	−	0.816857i	$-0.695714\pi$
$41$	−302.873	−1.15368	−0.576840	+	0.816857i	$0.695714\pi$
$42$	−131.021	−0.481356
$43$	0	0
$43$	0	0
$44$	−32.8540	−0.112566
$45$	72.7166	0.240888
$46$	557.532	1.78704
$47$	−79.5496	−0.246883	−0.123442	−	0.992352i	$-0.539393\pi$
$47$	−79.5496	−0.246883	−0.123442	+	0.992352i	$0.539393\pi$
$48$	90.8669	0.273240
$49$	783.738	2.28495
$50$	401.860	1.13663
$51$	87.1163	0.239191
$52$	206.333	0.550254
$53$	445.730	1.15520	0.577601	−	0.816319i	$-0.303989\pi$
$53$	445.730	1.15520	0.577601	+	0.816319i	$0.303989\pi$
$54$	−205.736	−0.518465
$55$	24.4722	0.0599970
$56$	−484.546	−1.15625
$57$	−108.904	−0.253066
$58$	−61.2204	−0.138597
$59$	−219.828	−0.485070	−0.242535	−	0.970143i	$-0.577979\pi$
$59$	−219.828	−0.485070	−0.242535	+	0.970143i	$0.577979\pi$
$60$	12.2058	0.0262626
$61$	116.310	0.244130	0.122065	−	0.992522i	$-0.461048\pi$
$61$	116.310	0.244130	0.122065	+	0.992522i	$0.461048\pi$
$62$	−464.693	−0.951873
$63$	862.957	1.72575
$64$	93.0220	0.181684
$65$	−153.693	−0.293281
$66$	−33.7712	−0.0629841
$67$	859.592	1.56740	0.783701	−	0.621139i	$-0.213330\pi$
$67$	859.592	1.56740	0.783701	+	0.621139i	$0.213330\pi$
$68$	−291.092	−0.519120
$69$	184.467	0.321843
$70$	−326.105	−0.556815
$71$	1028.88	1.71979	0.859897	−	0.510468i	$-0.170528\pi$
$71$	1028.88	1.71979	0.859897	+	0.510468i	$0.170528\pi$
$72$	−371.108	−0.607438
$73$	136.880	0.219461	0.109730	−	0.993961i	$-0.465001\pi$
$73$	136.880	0.219461	0.109730	+	0.993961i	$0.465001\pi$
$74$	−702.318	−1.10328
$75$	132.961	0.204706
$76$	363.896	0.549233
$77$	290.422	0.429826
$78$	212.094	0.307883
$79$	−584.277	−0.832105	−0.416053	−	0.909341i	$-0.636587\pi$
$79$	−584.277	−0.832105	−0.416053	+	0.909341i	$0.636587\pi$
$80$	226.164	0.316073
$81$	626.060	0.858793
$82$	1040.28	1.40098
$83$	27.3094	0.0361156	0.0180578	−	0.999837i	$-0.494252\pi$
$83$	27.3094	0.0361156	0.0180578	+	0.999837i	$0.494252\pi$
$84$	144.851	0.188149
$85$	216.829	0.276687
$86$	0	0
$87$	−20.2556	−0.0249612
$88$	−124.894	−0.151292
$89$	−1120.94	−1.33506	−0.667528	−	0.744585i	$-0.732647\pi$
$89$	−1120.94	−1.33506	−0.667528	+	0.744585i	$0.732647\pi$
$90$	−249.761	−0.292523
$91$	−1823.94	−2.10110
$92$	−616.381	−0.698502
$93$	−153.750	−0.171431
$94$	273.230	0.299804
$95$	−271.058	−0.292737
$96$	−180.866	−0.192287
$97$	643.857	0.673956	0.336978	−	0.941513i	$-0.390595\pi$
$97$	643.857	0.673956	0.336978	+	0.941513i	$0.390595\pi$
$98$	−2691.92	−2.77474
$99$	222.431	0.225810
$100$	−444.278	−0.444278
$101$	1533.90	1.51118	0.755590	−	0.655045i	$-0.227350\pi$
$101$	1533.90	1.51118	0.755590	+	0.655045i	$0.227350\pi$
$102$	−299.220	−0.290462
$103$	−1838.68	−1.75893	−0.879467	−	0.475961i	$-0.842101\pi$
$103$	−1838.68	−1.75893	−0.879467	+	0.475961i	$0.842101\pi$
$104$	784.371	0.739556
$105$	−107.896	−0.100282
$106$	−1530.96	−1.40283
$107$	596.356	0.538803	0.269402	−	0.963028i	$-0.413174\pi$
$107$	596.356	0.538803	0.269402	+	0.963028i	$0.413174\pi$
$108$	227.452	0.202654
$109$	−1348.07	−1.18460	−0.592300	−	0.805718i	$-0.701780\pi$
$109$	−1348.07	−1.18460	−0.592300	+	0.805718i	$0.701780\pi$
$110$	−84.0550	−0.0728576
$111$	−232.371	−0.198700
$112$	2683.97	2.26439
$113$	1033.37	0.860275	0.430137	−	0.902763i	$-0.358465\pi$
$113$	1033.37	0.860275	0.430137	+	0.902763i	$0.358465\pi$
$114$	374.056	0.307312
$115$	459.129	0.372296
$116$	67.6824	0.0541737
$117$	−1396.93	−1.10382
$118$	755.045	0.589047
$119$	2573.19	1.98222
$120$	46.4000	0.0352977
$121$	−1256.14	−0.943759
$122$	−399.490	−0.296460
$123$	344.191	0.252314
$124$	513.743	0.372060
$125$	684.495	0.489785
$126$	−2964.01	−2.09567
$127$	1189.24	0.830928	0.415464	−	0.909610i	$-0.363619\pi$
$127$	1189.24	0.830928	0.415464	+	0.909610i	$0.363619\pi$
$128$	−1592.74	−1.09984
$129$	0	0
$130$	527.891	0.356147
$131$	1423.04	0.949094	0.474547	−	0.880230i	$-0.342612\pi$
$131$	1423.04	0.949094	0.474547	+	0.880230i	$0.342612\pi$
$132$	37.3359	0.0246187
$133$	−3216.76	−2.09720
$134$	−2952.45	−1.90338
$135$	−169.424	−0.108013
$136$	−1106.58	−0.697711
$137$	−565.231	−0.352488	−0.176244	−	0.984346i	$-0.556395\pi$
$137$	−565.231	−0.352488	−0.176244	+	0.984346i	$0.556395\pi$
$138$	−633.591	−0.390832
$139$	26.2087	0.0159928	0.00799638	−	0.999968i	$-0.497455\pi$
$139$	26.2087	0.0159928	0.00799638	+	0.999968i	$0.497455\pi$
$140$	360.527	0.217643
$141$	90.4018	0.0539943
$142$	−3533.90	−2.08844
$143$	−470.127	−0.274923
$144$	2055.63	1.18960
$145$	−50.4152	−0.0288742
$146$	−470.144	−0.266503
$147$	−890.655	−0.499728
$148$	776.450	0.431242
$149$	1937.30	1.06517	0.532583	−	0.846378i	$-0.321222\pi$
$149$	1937.30	1.06517	0.532583	+	0.846378i	$0.321222\pi$
$150$	−456.682	−0.248586
$151$	−290.926	−0.156790	−0.0783948	−	0.996922i	$-0.524979\pi$
$151$	−290.926	−0.156790	−0.0783948	+	0.996922i	$0.524979\pi$
$152$	1383.34	0.738184
$153$	1970.78	1.04136
$154$	−997.515	−0.521961
$155$	−382.676	−0.198305
$156$	−234.481	−0.120343
$157$	3041.68	1.54619	0.773097	−	0.634288i	$-0.218706\pi$
$157$	3041.68	1.54619	0.773097	+	0.634288i	$0.218706\pi$
$158$	2006.82	1.01047
$159$	−506.537	−0.252648
$160$	−450.167	−0.222430
$161$	5448.67	2.66718
$162$	−2150.34	−1.04288
$163$	1241.97	0.596801	0.298401	−	0.954441i	$-0.403547\pi$
$163$	1241.97	0.596801	0.298401	+	0.954441i	$0.403547\pi$
$164$	−1150.09	−0.547603
$165$	−27.8107	−0.0131216
$166$	−93.7998	−0.0438571
$167$	1158.03	0.536593	0.268296	−	0.963336i	$-0.413539\pi$
$167$	1158.03	0.536593	0.268296	+	0.963336i	$0.413539\pi$
$168$	550.647	0.252877
$169$	755.542	0.343897
$170$	−744.744	−0.335996
$171$	−2463.68	−1.10177
$172$	0	0
$173$	773.746	0.340039	0.170020	−	0.985441i	$-0.445617\pi$
$173$	773.746	0.340039	0.170020	+	0.985441i	$0.445617\pi$
$174$	69.5721	0.0303117
$175$	3927.32	1.69644
$176$	691.806	0.296289
$177$	249.816	0.106087
$178$	3850.12	1.62123
$179$	2989.47	1.24829	0.624143	−	0.781310i	$-0.285448\pi$
$179$	2989.47	1.24829	0.624143	+	0.781310i	$0.285448\pi$
$180$	276.124	0.114339
$181$	3175.06	1.30387	0.651934	−	0.758276i	$-0.273958\pi$
$181$	3175.06	1.30387	0.651934	+	0.758276i	$0.273958\pi$
$182$	6264.70	2.55148
$183$	−132.176	−0.0533922
$184$	−2343.16	−0.938806
$185$	−578.361	−0.229848
$186$	528.087	0.208178
$187$	663.251	0.259368
$188$	−302.071	−0.117185
$189$	−2010.63	−0.773818
$190$	931.008	0.355486
$191$	−3155.65	−1.19547	−0.597735	−	0.801693i	$-0.703933\pi$
$191$	−3155.65	−1.19547	−0.597735	+	0.801693i	$0.703933\pi$
$192$	−105.712	−0.0397350
$193$	−295.876	−0.110350	−0.0551752	−	0.998477i	$-0.517572\pi$
$193$	−295.876	−0.110350	−0.0551752	+	0.998477i	$0.517572\pi$
$194$	−2211.46	−0.818422
$195$	174.660	0.0641417
$196$	2976.06	1.08457
$197$	−4324.76	−1.56409	−0.782047	−	0.623219i	$-0.785825\pi$
$197$	−4324.76	−1.56409	−0.782047	+	0.623219i	$0.785825\pi$
$198$	−763.986	−0.274213
$199$	−5148.55	−1.83402	−0.917012	−	0.398860i	$-0.869406\pi$
$199$	−5148.55	−1.83402	−0.917012	+	0.398860i	$0.869406\pi$
$200$	−1688.91	−0.597121
$201$	−976.857	−0.342797
$202$	−5268.52	−1.83511
$203$	−598.297	−0.206858
$204$	330.803	0.113534
$205$	856.677	0.291868
$206$	6315.33	2.13597
$207$	4173.08	1.40120
$208$	−4344.75	−1.44834
$209$	−829.133	−0.274413
$210$	370.592	0.121778
$211$	3094.70	1.00971	0.504853	−	0.863206i	$-0.331547\pi$
$211$	3094.70	1.00971	0.504853	+	0.863206i	$0.331547\pi$
$212$	1692.55	0.548325
$213$	−1169.24	−0.376126
$214$	−2048.31	−0.654298
$215$	0	0
$216$	864.655	0.272372
$217$	−4541.37	−1.42068
$218$	4630.22	1.43852
$219$	−155.553	−0.0479969
$220$	92.9273	0.0284780
$221$	−4165.42	−1.26786
$222$	798.128	0.241292
$223$	509.504	0.153000	0.0764998	−	0.997070i	$-0.475626\pi$
$223$	509.504	0.153000	0.0764998	+	0.997070i	$0.475626\pi$
$224$	−5342.32	−1.59352
$225$	3007.89	0.891227
$226$	−3549.32	−1.04468
$227$	−3714.74	−1.08615	−0.543075	−	0.839684i	$-0.682740\pi$
$227$	−3714.74	−1.08615	−0.543075	+	0.839684i	$0.682740\pi$
$228$	−413.538	−0.120120
$229$	2358.34	0.680538	0.340269	−	0.940328i	$-0.389482\pi$
$229$	2358.34	0.680538	0.340269	+	0.940328i	$0.389482\pi$
$230$	−1576.98	−0.452099
$231$	−330.041	−0.0940047
$232$	257.293	0.0728110
$233$	−1098.23	−0.308787	−0.154393	−	0.988009i	$-0.549342\pi$
$233$	−1098.23	−0.308787	−0.154393	+	0.988009i	$0.549342\pi$
$234$	4798.07	1.34042
$235$	225.006	0.0624586
$236$	−834.742	−0.230242
$237$	663.984	0.181985
$238$	−8838.18	−2.40712
$239$	1499.69	0.405886	0.202943	−	0.979191i	$-0.434949\pi$
$239$	1499.69	0.405886	0.202943	+	0.979191i	$0.434949\pi$
$240$	−257.017	−0.0691265
$241$	−2578.81	−0.689278	−0.344639	−	0.938735i	$-0.611999\pi$
$241$	−2578.81	−0.689278	−0.344639	+	0.938735i	$0.611999\pi$
$242$	4314.49	1.14606
$243$	−2328.74	−0.614769
$244$	441.657	0.115878
$245$	−2216.80	−0.578066
$246$	−1182.20	−0.306399
$247$	5207.21	1.34140
$248$	1952.99	0.500059
$249$	−31.0349	−0.00789862
$250$	−2351.05	−0.594773
$251$	−3641.51	−0.915738	−0.457869	−	0.889020i	$-0.651387\pi$
$251$	−3641.51	−0.915738	−0.457869	+	0.889020i	$0.651387\pi$
$252$	3276.87	0.819140
$253$	1404.42	0.348992
$254$	−4084.69	−1.00904
$255$	−246.408	−0.0605125
$256$	4726.42	1.15391
$257$	149.473	0.0362796	0.0181398	−	0.999835i	$-0.494226\pi$
$257$	149.473	0.0362796	0.0181398	+	0.999835i	$0.494226\pi$
$258$	0	0
$259$	−6863.64	−1.64666
$260$	−583.612	−0.139208
$261$	−458.230	−0.108673
$262$	−4887.72	−1.15254
$263$	−502.011	−0.117701	−0.0588504	−	0.998267i	$-0.518743\pi$
$263$	−502.011	−0.117701	−0.0588504	+	0.998267i	$0.518743\pi$
$264$	141.932	0.0330882
$265$	−1260.75	−0.292253
$266$	11048.6	2.54675
$267$	1273.86	0.291982
$268$	3264.09	0.743978
$269$	−6223.49	−1.41061	−0.705303	−	0.708906i	$-0.749189\pi$
$269$	−6223.49	−1.41061	−0.705303	+	0.708906i	$0.749189\pi$
$270$	581.924	0.131166
$271$	2572.19	0.576565	0.288283	−	0.957545i	$-0.406916\pi$
$271$	2572.19	0.576565	0.288283	+	0.957545i	$0.406916\pi$
$272$	6129.53	1.36639
$273$	2072.76	0.459520
$274$	1941.41	0.428046
$275$	1012.28	0.221974
$276$	700.468	0.152765
$277$	6947.90	1.50707	0.753536	−	0.657407i	$-0.228347\pi$
$277$	6947.90	1.50707	0.753536	+	0.657407i	$0.228347\pi$
$278$	−90.0194	−0.0194209
$279$	−3478.19	−0.746358
$280$	1370.54	0.292519
$281$	−2013.18	−0.427388	−0.213694	−	0.976901i	$-0.568550\pi$
$281$	−2013.18	−0.427388	−0.213694	+	0.976901i	$0.568550\pi$
$282$	−310.504	−0.0655683
$283$	4743.92	0.996455	0.498227	−	0.867046i	$-0.333984\pi$
$283$	4743.92	0.996455	0.498227	+	0.867046i	$0.333984\pi$
$284$	3906.92	0.816313
$285$	308.036	0.0640227
$286$	1614.75	0.333854
$287$	10166.5	2.09098
$288$	−4091.62	−0.837157
$289$	963.534	0.196119
$290$	173.162	0.0350635
$291$	−731.691	−0.147397
$292$	519.770	0.104169
$293$	−7007.19	−1.39715	−0.698575	−	0.715537i	$-0.746182\pi$
$293$	−7007.19	−1.39715	−0.698575	+	0.715537i	$0.746182\pi$
$294$	3059.15	0.606847
$295$	621.782	0.122717
$296$	2951.66	0.579601
$297$	−518.248	−0.101252
$298$	−6654.06	−1.29349
$299$	−8820.18	−1.70597
$300$	504.886	0.0971654
$301$	0	0
$302$	999.248	0.190398
$303$	−1743.16	−0.330501
$304$	−7662.56	−1.44565
$305$	−328.981	−0.0617620
$306$	−6769.07	−1.26458
$307$	−1306.12	−0.242815	−0.121407	−	0.992603i	$-0.538741\pi$
$307$	−1306.12	−0.242815	−0.121407	+	0.992603i	$0.538741\pi$
$308$	1102.81	0.204020
$309$	2089.51	0.384686
$310$	1314.38	0.240813
$311$	−4743.40	−0.864866	−0.432433	−	0.901666i	$-0.642345\pi$
$311$	−4743.40	−0.864866	−0.432433	+	0.901666i	$0.642345\pi$
$312$	−891.374	−0.161744
$313$	−5460.04	−0.986005	−0.493002	−	0.870028i	$-0.664101\pi$
$313$	−5460.04	−0.986005	−0.493002	+	0.870028i	$0.664101\pi$
$314$	−10447.3	−1.87763
$315$	−2440.87	−0.436595
$316$	−2218.65	−0.394965
$317$	7010.45	1.24210	0.621051	−	0.783770i	$-0.286706\pi$
$317$	7010.45	1.24210	0.621051	+	0.783770i	$0.286706\pi$
$318$	1739.81	0.306804
$319$	−154.214	−0.0270668
$320$	−263.113	−0.0459639
$321$	−677.711	−0.117838
$322$	−18714.6	−3.23890
$323$	−7346.28	−1.26550
$324$	2377.31	0.407633
$325$	−6357.44	−1.08507
$326$	−4265.81	−0.724728
$327$	1531.97	0.259077
$328$	−4372.04	−0.735993
$329$	2670.24	0.447462
$330$	95.5218	0.0159343
$331$	2338.01	0.388244	0.194122	−	0.980977i	$-0.437814\pi$
$331$	2338.01	0.388244	0.194122	+	0.980977i	$0.437814\pi$
$332$	103.701	0.0171425
$333$	−5256.79	−0.865077
$334$	−3977.50	−0.651614
$335$	−2431.35	−0.396535
$336$	−3050.12	−0.495231
$337$	2441.37	0.394628	0.197314	−	0.980340i	$-0.436778\pi$
$337$	2441.37	0.394628	0.197314	+	0.980340i	$0.436778\pi$
$338$	−2595.07	−0.417613
$339$	−1174.34	−0.188146
$340$	823.354	0.131331
$341$	−1170.56	−0.185892
$342$	8462.04	1.33794
$343$	−14794.2	−2.32890
$344$	0	0
$345$	−521.764	−0.0814227
$346$	−2657.59	−0.412928
$347$	−2549.11	−0.394361	−0.197180	−	0.980367i	$-0.563178\pi$
$347$	−2549.11	−0.394361	−0.197180	+	0.980367i	$0.563178\pi$
$348$	−76.9156	−0.0118480
$349$	4610.07	0.707081	0.353541	−	0.935419i	$-0.384978\pi$
$349$	4610.07	0.707081	0.353541	+	0.935419i	$0.384978\pi$
$350$	−13489.2	−2.06008
$351$	3254.75	0.494945
$352$	−1377.01	−0.208507
$353$	−6868.97	−1.03569	−0.517845	−	0.855474i	$-0.673266\pi$
$353$	−6868.97	−1.03569	−0.517845	+	0.855474i	$0.673266\pi$
$354$	−858.048	−0.128827
$355$	−2910.18	−0.435088
$356$	−4256.52	−0.633694
$357$	−2924.23	−0.433519
$358$	−10268.0	−1.51586
$359$	−11827.0	−1.73873	−0.869366	−	0.494168i	$-0.835473\pi$
$359$	−11827.0	−1.73873	−0.869366	+	0.494168i	$0.835473\pi$
$360$	1049.68	0.153675
$361$	2324.62	0.338915
$362$	−10905.4	−1.58336
$363$	1427.51	0.206404
$364$	−6925.96	−0.997304
$365$	−387.165	−0.0555210
$366$	453.988	0.0648370
$367$	10023.2	1.42563	0.712816	−	0.701351i	$-0.247419\pi$
$367$	10023.2	1.42563	0.712816	+	0.701351i	$0.247419\pi$
$368$	12979.1	1.83855
$369$	7786.44	1.09850
$370$	1986.51	0.279118
$371$	−14961.8	−2.09374
$372$	−583.828	−0.0813711
$373$	−12954.9	−1.79833	−0.899166	−	0.437608i	$-0.855826\pi$
$373$	−12954.9	−1.79833	−0.899166	+	0.437608i	$0.855826\pi$
$374$	−2278.08	−0.314964
$375$	−777.874	−0.107118
$376$	−1148.32	−0.157500
$377$	968.509	0.132310
$378$	6905.92	0.939689
$379$	−13013.5	−1.76374	−0.881872	−	0.471488i	$-0.843717\pi$
$379$	−13013.5	−1.76374	−0.881872	+	0.471488i	$0.843717\pi$
$380$	−1029.28	−0.138950
$381$	−1351.47	−0.181727
$382$	10838.8	1.45173
$383$	−5448.90	−0.726960	−0.363480	−	0.931602i	$-0.618412\pi$
$383$	−5448.90	−0.726960	−0.363480	+	0.931602i	$0.618412\pi$
$384$	1810.02	0.240539
$385$	−821.457	−0.108741
$386$	1016.25	0.134005
$387$	0	0
$388$	2444.89	0.319898
$389$	4972.81	0.648153	0.324077	−	0.946031i	$-0.394946\pi$
$389$	4972.81	0.648153	0.324077	+	0.946031i	$0.394946\pi$
$390$	−599.906	−0.0778908
$391$	12443.4	1.60944
$392$	11313.4	1.45769
$393$	−1617.17	−0.207571
$394$	14854.3	1.89937
$395$	1652.63	0.210513
$396$	844.627	0.107182
$397$	10080.8	1.27441	0.637204	−	0.770695i	$-0.280091\pi$
$397$	10080.8	1.27441	0.637204	+	0.770695i	$0.280091\pi$
$398$	17683.8	2.22716
$399$	3655.59	0.458667
$400$	9355.16	1.16939
$401$	−431.785	−0.0537713	−0.0268857	−	0.999639i	$-0.508559\pi$
$401$	−431.785	−0.0537713	−0.0268857	+	0.999639i	$0.508559\pi$
$402$	3355.23	0.416277
$403$	7351.47	0.908691
$404$	5824.63	0.717293
$405$	−1770.81	−0.217265
$406$	2054.98	0.251199
$407$	−1769.13	−0.215461
$408$	1257.54	0.152592
$409$	−15428.6	−1.86526	−0.932632	−	0.360828i	$-0.882494\pi$
$409$	−15428.6	−1.86526	−0.932632	+	0.360828i	$0.882494\pi$
$410$	−2942.44	−0.354431
$411$	642.339	0.0770906
$412$	−6981.93	−0.834891
$413$	7378.93	0.879161
$414$	−14333.3	−1.70156
$415$	−77.2444	−0.00913682
$416$	8648.01	1.01924
$417$	−29.7841	−0.00349768
$418$	2847.84	0.333235
$419$	−8702.42	−1.01466	−0.507328	−	0.861753i	$-0.669367\pi$
$419$	−8702.42	−1.01466	−0.507328	+	0.861753i	$0.669367\pi$
$420$	−409.710	−0.0475995
$421$	−4123.21	−0.477323	−0.238661	−	0.971103i	$-0.576709\pi$
$421$	−4123.21	−0.477323	−0.238661	+	0.971103i	$0.576709\pi$
$422$	−10629.4	−1.22614
$423$	2045.11	0.235074
$424$	6434.21	0.736964
$425$	8969.02	1.02367
$426$	4015.99	0.456750
$427$	−3904.15	−0.442471
$428$	2264.52	0.255747
$429$	534.262	0.0601268
$430$	0	0
$431$	−2310.06	−0.258171	−0.129086	−	0.991633i	$-0.541204\pi$
$431$	−2310.06	−0.258171	−0.129086	+	0.991633i	$0.541204\pi$
$432$	−4789.46	−0.533410
$433$	−9811.69	−1.08896	−0.544480	−	0.838774i	$-0.683273\pi$
$433$	−9811.69	−1.08896	−0.544480	+	0.838774i	$0.683273\pi$
$434$	15598.3	1.72522
$435$	57.2928	0.00631490
$436$	−5118.96	−0.562279
$437$	−15555.6	−1.70280
$438$	534.281	0.0582853
$439$	−8625.01	−0.937698	−0.468849	−	0.883278i	$-0.655331\pi$
$439$	−8625.01	−0.937698	−0.468849	+	0.883278i	$0.655331\pi$
$440$	353.262	0.0382752
$441$	−20148.8	−2.17566
$442$	14307.0	1.53963
$443$	−10509.3	−1.12712	−0.563558	−	0.826076i	$-0.690568\pi$
$443$	−10509.3	−1.12712	−0.563558	+	0.826076i	$0.690568\pi$
$444$	−882.373	−0.0943144
$445$	3170.59	0.337754
$446$	−1750.00	−0.185796
$447$	−2201.58	−0.232956
$448$	−3122.46	−0.329291
$449$	12991.4	1.36549	0.682743	−	0.730658i	$-0.260787\pi$
$449$	12991.4	1.36549	0.682743	+	0.730658i	$0.260787\pi$
$450$	−10331.2	−1.08227
$451$	2620.47	0.273599
$452$	3923.96	0.408336
$453$	330.614	0.0342905
$454$	12759.1	1.31897
$455$	5159.00	0.531555
$456$	−1572.06	−0.161444
$457$	9830.48	1.00624	0.503119	−	0.864217i	$-0.332186\pi$
$457$	9830.48	1.00624	0.503119	+	0.864217i	$0.332186\pi$
$458$	−8100.21	−0.826414
$459$	−4591.77	−0.466940
$460$	1743.43	0.176713
$461$	13731.6	1.38730	0.693651	−	0.720311i	$-0.256001\pi$
$461$	13731.6	1.38730	0.693651	+	0.720311i	$0.256001\pi$
$462$	1133.60	0.114155
$463$	2930.80	0.294181	0.147090	−	0.989123i	$-0.453009\pi$
$463$	2930.80	0.294181	0.147090	+	0.989123i	$0.453009\pi$
$464$	−1425.19	−0.142592
$465$	434.881	0.0433702
$466$	3772.10	0.374977
$467$	−15928.6	−1.57835	−0.789174	−	0.614170i	$-0.789491\pi$
$467$	−15928.6	−1.57835	−0.789174	+	0.614170i	$0.789491\pi$
$468$	−5304.52	−0.523935
$469$	−28853.9	−2.84083
$470$	−772.831	−0.0758469
$471$	−3456.63	−0.338159
$472$	−3173.26	−0.309451
$473$	0	0
$474$	−2280.60	−0.220994
$475$	−11212.2	−1.08306
$476$	9771.07	0.940875
$477$	−11459.1	−1.09995
$478$	−5150.99	−0.492889
$479$	642.583	0.0612952	0.0306476	−	0.999530i	$-0.490243\pi$
$479$	642.583	0.0612952	0.0306476	+	0.999530i	$0.490243\pi$
$480$	511.579	0.0486464
$481$	11110.7	1.05323
$482$	8857.49	0.837028
$483$	−6191.98	−0.583323
$484$	−4769.90	−0.447962
$485$	−1821.15	−0.170503
$486$	7998.56	0.746547
$487$	18634.0	1.73386	0.866928	−	0.498434i	$-0.166091\pi$
$487$	18634.0	1.73386	0.866928	+	0.498434i	$0.166091\pi$
$488$	1678.95	0.155743
$489$	−1411.40	−0.130523
$490$	7614.08	0.701977
$491$	18317.8	1.68365	0.841823	−	0.539754i	$-0.181483\pi$
$491$	18317.8	1.68365	0.841823	+	0.539754i	$0.181483\pi$
$492$	1306.98	0.119763
$493$	−1366.36	−0.124823
$494$	−17885.3	−1.62894
$495$	−629.145	−0.0571272
$496$	−10817.9	−0.979310
$497$	−34536.3	−3.11703
$498$	106.596	0.00959173
$499$	−17631.0	−1.58171	−0.790854	−	0.612005i	$-0.790363\pi$
$499$	−17631.0	−1.58171	−0.790854	+	0.612005i	$0.790363\pi$
$500$	2599.21	0.232480
$501$	−1316.01	−0.117355
$502$	12507.6	1.11203
$503$	−8292.71	−0.735096	−0.367548	−	0.930004i	$-0.619803\pi$
$503$	−8292.71	−0.735096	−0.367548	+	0.930004i	$0.619803\pi$
$504$	12457.0	1.10095
$505$	−4338.65	−0.382311
$506$	−4823.78	−0.423801
$507$	−858.613	−0.0752118
$508$	4515.85	0.394406
$509$	2838.44	0.247174	0.123587	−	0.992334i	$-0.460560\pi$
$509$	2838.44	0.247174	0.123587	+	0.992334i	$0.460560\pi$
$510$	846.342	0.0734836
$511$	−4594.65	−0.397760
$512$	−3492.00	−0.301418
$513$	5740.20	0.494027
$514$	−513.396	−0.0440563
$515$	5200.69	0.444990
$516$	0	0
$517$	688.265	0.0585490
$518$	23574.7	1.99963
$519$	−879.300	−0.0743680
$520$	−2218.59	−0.187099
$521$	10587.5	0.890299	0.445150	−	0.895456i	$-0.353150\pi$
$521$	10587.5	0.890299	0.445150	+	0.895456i	$0.353150\pi$
$522$	1573.89	0.131968
$523$	17462.6	1.46001	0.730007	−	0.683439i	$-0.239517\pi$
$523$	17462.6	1.46001	0.730007	+	0.683439i	$0.239517\pi$
$524$	5403.64	0.450494
$525$	−4463.08	−0.371019
$526$	1724.26	0.142931
$527$	−10371.4	−0.857276
$528$	−786.182	−0.0647996
$529$	14181.7	1.16559
$530$	4330.30	0.354899
$531$	5651.45	0.461868
$532$	−12214.9	−0.995454
$533$	−16457.3	−1.33742
$534$	−4375.36	−0.354570
$535$	−1686.79	−0.136311
$536$	12408.4	0.999927
$537$	−3397.29	−0.273005
$538$	21375.9	1.71298
$539$	−6780.91	−0.541882
$540$	−643.348	−0.0512690
$541$	1614.09	0.128272	0.0641360	−	0.997941i	$-0.479571\pi$
$541$	1614.09	0.128272	0.0641360	+	0.997941i	$0.479571\pi$
$542$	−8834.72	−0.700154
$543$	−3608.20	−0.285161
$544$	−12200.5	−0.961569
$545$	3813.00	0.299690
$546$	−7119.33	−0.558020
$547$	−22672.4	−1.77222	−0.886109	−	0.463477i	$-0.846602\pi$
$547$	−22672.4	−1.77222	−0.886109	+	0.463477i	$0.846602\pi$
$548$	−2146.33	−0.167311
$549$	−2990.15	−0.232453
$550$	−3476.90	−0.269556
$551$	1708.10	0.132064
$552$	2662.82	0.205321
$553$	19612.4	1.50814
$554$	−23864.0	−1.83012
$555$	657.261	0.0502688
$556$	99.5212	0.00759108
$557$	−15228.6	−1.15845	−0.579226	−	0.815167i	$-0.696645\pi$
$557$	−15228.6	−1.15845	−0.579226	+	0.815167i	$0.696645\pi$
$558$	11946.6	0.906343
$559$	0	0
$560$	−7591.61	−0.572865
$561$	−753.732	−0.0567247
$562$	6914.69	0.519001
$563$	−4374.53	−0.327468	−0.163734	−	0.986505i	$-0.552354\pi$
$563$	−4374.53	−0.327468	−0.163734	+	0.986505i	$0.552354\pi$
$564$	343.279	0.0256288
$565$	−2922.88	−0.217640
$566$	−16294.0	−1.21005
$567$	−21014.9	−1.55651
$568$	14852.1	1.09715
$569$	818.728	0.0603214	0.0301607	−	0.999545i	$-0.490398\pi$
$569$	818.728	0.0603214	0.0301607	+	0.999545i	$0.490398\pi$
$570$	−1058.02	−0.0777463
$571$	−1233.69	−0.0904173	−0.0452087	−	0.998978i	$-0.514395\pi$
$571$	−1233.69	−0.0904173	−0.0452087	+	0.998978i	$0.514395\pi$
$572$	−1785.20	−0.130494
$573$	3586.14	0.261454
$574$	−34919.1	−2.53919
$575$	18991.7	1.37741
$576$	−2391.46	−0.172993
$577$	−7097.43	−0.512080	−0.256040	−	0.966666i	$-0.582418\pi$
$577$	−7097.43	−0.512080	−0.256040	+	0.966666i	$0.582418\pi$
$578$	−3309.46	−0.238158
$579$	336.239	0.0241341
$580$	−191.439	−0.0137053
$581$	−916.691	−0.0654574
$582$	2513.15	0.178992
$583$	−3856.47	−0.273960
$584$	1975.90	0.140005
$585$	3951.22	0.279253
$586$	24067.7	1.69663
$587$	−12554.1	−0.882730	−0.441365	−	0.897328i	$-0.645506\pi$
$587$	−12554.1	−0.882730	−0.441365	+	0.897328i	$0.645506\pi$
$588$	−3382.05	−0.237199
$589$	12965.3	0.907005
$590$	−2135.64	−0.149022
$591$	4914.75	0.342074
$592$	−16349.7	−1.13508
$593$	6924.59	0.479526	0.239763	−	0.970831i	$-0.422930\pi$
$593$	6924.59	0.479526	0.239763	+	0.970831i	$0.422930\pi$
$594$	1780.03	0.122956
$595$	−7278.27	−0.501479
$596$	7356.42	0.505589
$597$	5850.91	0.401108
$598$	30294.8	2.07165
$599$	16074.6	1.09648	0.548240	−	0.836321i	$-0.315298\pi$
$599$	16074.6	1.09648	0.548240	+	0.836321i	$0.315298\pi$
$600$	1919.32	0.130593
$601$	126.013	0.00855269	0.00427635	−	0.999991i	$-0.498639\pi$
$601$	126.013	0.00855269	0.00427635	+	0.999991i	$0.498639\pi$
$602$	0	0
$603$	−22098.9	−1.49243
$604$	−1104.72	−0.0744214
$605$	3553.00	0.238760
$606$	5987.25	0.401346
$607$	174.746	0.0116849	0.00584245	−	0.999983i	$-0.498140\pi$
$607$	174.746	0.0116849	0.00584245	+	0.999983i	$0.498140\pi$
$608$	15251.9	1.01735
$609$	679.917	0.0452407
$610$	1129.96	0.0750010
$611$	−4322.51	−0.286203
$612$	7483.56	0.494289
$613$	2579.36	0.169950	0.0849750	−	0.996383i	$-0.472919\pi$
$613$	2579.36	0.169950	0.0849750	+	0.996383i	$0.472919\pi$
$614$	4486.14	0.294863
$615$	−973.544	−0.0638327
$616$	4192.30	0.274209
$617$	3453.87	0.225361	0.112680	−	0.993631i	$-0.464056\pi$
$617$	3453.87	0.225361	0.112680	+	0.993631i	$0.464056\pi$
$618$	−7176.86	−0.467145
$619$	23838.1	1.54787	0.773936	−	0.633264i	$-0.218285\pi$
$619$	23838.1	1.54787	0.773936	+	0.633264i	$0.218285\pi$
$620$	−1453.12	−0.0941270
$621$	−9722.98	−0.628292
$622$	16292.2	1.05025
$623$	37626.7	2.41971
$624$	4937.46	0.316757
$625$	12688.9	0.812087
$626$	18753.7	1.19736
$627$	942.243	0.0600153
$628$	11550.0	0.733913
$629$	−15674.9	−0.993638
$630$	8383.69	0.530181
$631$	−11630.5	−0.733762	−0.366881	−	0.930268i	$-0.619574\pi$
$631$	−11630.5	−0.733762	−0.366881	+	0.930268i	$0.619574\pi$
$632$	−8434.17	−0.530844
$633$	−3516.88	−0.220827
$634$	−24078.9	−1.50835
$635$	−3363.76	−0.210215
$636$	−1923.45	−0.119921
$637$	42586.2	2.64886
$638$	529.680	0.0328687
$639$	−26451.0	−1.63753
$640$	4505.05	0.278247
$641$	16501.9	1.01683	0.508414	−	0.861113i	$-0.330232\pi$
$641$	16501.9	1.01683	0.508414	+	0.861113i	$0.330232\pi$
$642$	2327.74	0.143098
$643$	−7764.80	−0.476227	−0.238113	−	0.971237i	$-0.576529\pi$
$643$	−7764.80	−0.476227	−0.238113	+	0.971237i	$0.576529\pi$
$644$	20690.0	1.26600
$645$	0	0
$646$	25232.4	1.53677
$647$	−23206.2	−1.41009	−0.705046	−	0.709161i	$-0.749074\pi$
$647$	−23206.2	−1.41009	−0.705046	+	0.709161i	$0.749074\pi$
$648$	9037.32	0.547869
$649$	1901.95	0.115036
$650$	21836.0	1.31766
$651$	5160.91	0.310710
$652$	4716.08	0.283276
$653$	−9085.23	−0.544460	−0.272230	−	0.962232i	$-0.587761\pi$
$653$	−9085.23	−0.544460	−0.272230	+	0.962232i	$0.587761\pi$
$654$	−5261.88	−0.314611
$655$	−4025.06	−0.240110
$656$	24217.4	1.44136
$657$	−3518.99	−0.208963
$658$	−9171.50	−0.543377
$659$	−21346.5	−1.26183	−0.630913	−	0.775854i	$-0.717320\pi$
$659$	−21346.5	−1.26183	−0.630913	+	0.775854i	$0.717320\pi$
$660$	−105.604	−0.00622825
$661$	−998.527	−0.0587567	−0.0293784	−	0.999568i	$-0.509353\pi$
$661$	−998.527	−0.0587567	−0.0293784	+	0.999568i	$0.509353\pi$
$662$	−8030.41	−0.471466
$663$	4733.66	0.277286
$664$	394.216	0.0230400
$665$	9098.59	0.530569
$666$	18055.6	1.05051
$667$	−2893.24	−0.167956
$668$	4397.33	0.254698
$669$	−579.010	−0.0334616
$670$	8351.00	0.481534
$671$	−1006.31	−0.0578961
$672$	6071.11	0.348509
$673$	24703.1	1.41491	0.707455	−	0.706758i	$-0.249843\pi$
$673$	24703.1	1.41491	0.707455	+	0.706758i	$0.249843\pi$
$674$	−8385.40	−0.479219
$675$	−7008.16	−0.399621
$676$	2868.99	0.163233
$677$	20119.2	1.14216	0.571082	−	0.820893i	$-0.306524\pi$
$677$	20119.2	1.14216	0.571082	+	0.820893i	$0.306524\pi$
$678$	4033.52	0.228475
$679$	−21612.3	−1.22151
$680$	3129.97	0.176513
$681$	4221.51	0.237545
$682$	4020.54	0.225739
$683$	−9869.00	−0.552894	−0.276447	−	0.961029i	$-0.589157\pi$
$683$	−9869.00	−0.552894	−0.276447	+	0.961029i	$0.589157\pi$
$684$	−9355.23	−0.522962
$685$	1598.75	0.0891755
$686$	50813.9	2.82811
$687$	−2680.06	−0.148836
$688$	0	0
$689$	24219.8	1.33919
$690$	1792.11	0.0988760
$691$	−410.966	−0.0226250	−0.0113125	−	0.999936i	$-0.503601\pi$
$691$	−410.966	−0.0226250	−0.0113125	+	0.999936i	$0.503601\pi$
$692$	2938.11	0.161402
$693$	−7466.32	−0.409267
$694$	8755.45	0.478894
$695$	−74.1312	−0.00404598
$696$	−292.393	−0.0159241
$697$	23217.8	1.26175
$698$	−15834.3	−0.858647
$699$	1248.05	0.0675329
$700$	14913.0	0.805228
$701$	9413.69	0.507204	0.253602	−	0.967309i	$-0.418385\pi$
$701$	9413.69	0.507204	0.253602	+	0.967309i	$0.418385\pi$
$702$	−11179.1	−0.601039
$703$	19595.2	1.05128
$704$	−804.828	−0.0430868
$705$	−255.701	−0.0136599
$706$	23593.0	1.25769
$707$	−51488.5	−2.73893
$708$	948.617	0.0503548
$709$	7139.41	0.378175	0.189087	−	0.981960i	$-0.439447\pi$
$709$	7139.41	0.378175	0.189087	+	0.981960i	$0.439447\pi$
$710$	9995.63	0.528351
$711$	15020.9	0.792304
$712$	−16181.1	−0.851702
$713$	−21961.2	−1.15351
$714$	10043.9	0.526446
$715$	1329.75	0.0695524
$716$	11351.8	0.592508
$717$	−1704.27	−0.0887688
$718$	40622.4	2.11144
$719$	1775.83	0.0921100	0.0460550	−	0.998939i	$-0.485335\pi$
$719$	1775.83	0.0921100	0.0460550	+	0.998939i	$0.485335\pi$
$720$	−5814.34	−0.300955
$721$	61718.7	3.18797
$722$	−7984.39	−0.411563
$723$	2930.61	0.150748
$724$	12056.5	0.618891
$725$	−2085.40	−0.106827
$726$	−4903.07	−0.250647
$727$	12260.4	0.625463	0.312732	−	0.949842i	$-0.398756\pi$
$727$	12260.4	0.625463	0.312732	+	0.949842i	$0.398756\pi$
$728$	−26328.9	−1.34040
$729$	−14257.2	−0.724341
$730$	1329.80	0.0674222
$731$	0	0
$732$	−501.908	−0.0253430
$733$	7176.95	0.361646	0.180823	−	0.983516i	$-0.442124\pi$
$733$	7176.95	0.361646	0.180823	+	0.983516i	$0.442124\pi$
$734$	−34426.8	−1.73122
$735$	2519.22	0.126425
$736$	−25834.3	−1.29384
$737$	−7437.21	−0.371714
$738$	−26744.2	−1.33397
$739$	−14928.3	−0.743092	−0.371546	−	0.928415i	$-0.621172\pi$
$739$	−14928.3	−0.743092	−0.371546	+	0.928415i	$0.621172\pi$
$740$	−2196.19	−0.109099
$741$	−5917.57	−0.293370
$742$	51389.5	2.54254
$743$	10031.8	0.495333	0.247666	−	0.968845i	$-0.420336\pi$
$743$	10031.8	0.495333	0.247666	+	0.968845i	$0.420336\pi$
$744$	−2219.41	−0.109365
$745$	−5479.64	−0.269475
$746$	44496.3	2.18381
$747$	−702.084	−0.0343881
$748$	2518.54	0.123111
$749$	−20017.8	−0.976550
$750$	2671.77	0.130079
$751$	−7723.92	−0.375300	−0.187650	−	0.982236i	$-0.560087\pi$
$751$	−7723.92	−0.375300	−0.187650	+	0.982236i	$0.560087\pi$
$752$	6360.70	0.308445
$753$	4138.29	0.200276
$754$	−3326.55	−0.160671
$755$	822.884	0.0396660
$756$	−7634.87	−0.367298
$757$	−2723.98	−0.130786	−0.0653928	−	0.997860i	$-0.520830\pi$
$757$	−2723.98	−0.130786	−0.0653928	+	0.997860i	$0.520830\pi$
$758$	44697.7	2.14181
$759$	−1596.01	−0.0763261
$760$	−3912.78	−0.186752
$761$	35688.3	1.70000	0.849999	−	0.526784i	$-0.176602\pi$
$761$	35688.3	1.70000	0.849999	+	0.526784i	$0.176602\pi$
$762$	4641.93	0.220681
$763$	45250.4	2.14702
$764$	−11982.8	−0.567439
$765$	−5574.35	−0.263452
$766$	18715.4	0.882788
$767$	−11944.8	−0.562325
$768$	−5371.20	−0.252365
$769$	8833.25	0.414220	0.207110	−	0.978318i	$-0.433594\pi$
$769$	8833.25	0.414220	0.207110	+	0.978318i	$0.433594\pi$
$770$	2821.47	0.132050
$771$	−169.864	−0.00793449
$772$	−1123.52	−0.0523786
$773$	15932.9	0.741356	0.370678	−	0.928761i	$-0.379125\pi$
$773$	15932.9	0.741356	0.370678	+	0.928761i	$0.379125\pi$
$774$	0	0
$775$	−15829.2	−0.733682
$776$	9294.21	0.429952
$777$	7799.98	0.360132
$778$	−17080.2	−0.787088
$779$	−29024.7	−1.33494
$780$	663.228	0.0304453
$781$	−8901.87	−0.407854
$782$	−42739.6	−1.95443
$783$	1067.64	0.0487285
$784$	−62666.8	−2.85472
$785$	−8603.39	−0.391169
$786$	5554.51	0.252064
$787$	28093.0	1.27244	0.636218	−	0.771510i	$-0.280498\pi$
$787$	28093.0	1.27244	0.636218	+	0.771510i	$0.280498\pi$
$788$	−16422.2	−0.742409
$789$	570.495	0.0257416
$790$	−5676.30	−0.255638
$791$	−34687.0	−1.55920
$792$	3210.84	0.144056
$793$	6319.95	0.283011
$794$	−34624.6	−1.54758
$795$	1432.74	0.0639169
$796$	−19550.4	−0.870533
$797$	31595.5	1.40423	0.702115	−	0.712064i	$-0.252239\pi$
$797$	31595.5	1.40423	0.702115	+	0.712064i	$0.252239\pi$
$798$	−12555.9	−0.556985
$799$	6098.16	0.270009
$800$	−18621.0	−0.822939
$801$	28817.9	1.27120
$802$	1483.06	0.0652975
$803$	−1184.29	−0.0520457
$804$	−3709.38	−0.162711
$805$	−15411.6	−0.674765
$806$	−25250.2	−1.10347
$807$	7072.50	0.308505
$808$	22142.2	0.964061
$809$	−8768.27	−0.381058	−0.190529	−	0.981682i	$-0.561020\pi$
$809$	−8768.27	−0.381058	−0.190529	+	0.981682i	$0.561020\pi$
$810$	6082.23	0.263837
$811$	−8266.76	−0.357935	−0.178968	−	0.983855i	$-0.557276\pi$
$811$	−8266.76	−0.357935	−0.178968	+	0.983855i	$0.557276\pi$
$812$	−2271.89	−0.0981868
$813$	−2923.08	−0.126097
$814$	6076.47	0.261646
$815$	−3512.91	−0.150984
$816$	−6965.72	−0.298835
$817$	0	0
$818$	52992.7	2.26509
$819$	46890.7	2.00060
$820$	3253.02	0.138537
$821$	−43950.7	−1.86832	−0.934160	−	0.356855i	$-0.883849\pi$
$821$	−43950.7	−1.86832	−0.934160	+	0.356855i	$0.883849\pi$
$822$	−2206.25	−0.0936154
$823$	46213.0	1.95733	0.978666	−	0.205457i	$-0.0658680\pi$
$823$	46213.0	1.95733	0.978666	+	0.205457i	$0.0658680\pi$
$824$	−26541.7	−1.12212
$825$	−1150.38	−0.0485467
$826$	−25344.5	−1.06761
$827$	802.687	0.0337511	0.0168755	−	0.999858i	$-0.494628\pi$
$827$	802.687	0.0337511	0.0168755	+	0.999858i	$0.494628\pi$
$828$	15846.3	0.665092
$829$	7150.10	0.299558	0.149779	−	0.988720i	$-0.452144\pi$
$829$	7150.10	0.299558	0.149779	+	0.988720i	$0.452144\pi$
$830$	265.313	0.0110953
$831$	−7895.73	−0.329603
$832$	5054.57	0.210620
$833$	−60080.2	−2.49899
$834$	102.300	0.00424742
$835$	−3275.48	−0.135752
$836$	−3148.43	−0.130252
$837$	8103.93	0.334663
$838$	29890.3	1.23215
$839$	588.326	0.0242089	0.0121044	−	0.999927i	$-0.496147\pi$
$839$	588.326	0.0242089	0.0121044	+	0.999927i	$0.496147\pi$
$840$	−1557.50	−0.0639750
$841$	−24071.3	−0.986974
$842$	14162.0	0.579639
$843$	2287.81	0.0934715
$844$	11751.4	0.479264
$845$	−2137.05	−0.0870021
$846$	−7024.35	−0.285464
$847$	42164.8	1.71051
$848$	−35640.1	−1.44326
$849$	−5391.08	−0.217929
$850$	−30806.0	−1.24310
$851$	−33191.2	−1.33699
$852$	−4439.90	−0.178531
$853$	−41492.4	−1.66550	−0.832751	−	0.553648i	$-0.813235\pi$
$853$	−41492.4	−1.66550	−0.832751	+	0.553648i	$0.813235\pi$
$854$	13409.6	0.537317
$855$	6968.52	0.278735
$856$	8608.53	0.343731
$857$	11068.4	0.441176	0.220588	−	0.975367i	$-0.429202\pi$
$857$	11068.4	0.441176	0.220588	+	0.975367i	$0.429202\pi$
$858$	−1835.04	−0.0730153
$859$	8924.67	0.354489	0.177244	−	0.984167i	$-0.443282\pi$
$859$	8924.67	0.354489	0.177244	+	0.984167i	$0.443282\pi$
$860$	0	0
$861$	−11553.4	−0.457306
$862$	7934.40	0.313511
$863$	5135.14	0.202552	0.101276	−	0.994858i	$-0.467708\pi$
$863$	5135.14	0.202552	0.101276	+	0.994858i	$0.467708\pi$
$864$	9533.18	0.375377
$865$	−2188.54	−0.0860260
$866$	33700.3	1.32238
$867$	−1094.98	−0.0428921
$868$	−17244.8	−0.674338
$869$	5055.18	0.197336
$870$	−196.784	−0.00766852
$871$	46707.9	1.81703
$872$	−19459.6	−0.755718
$873$	−16552.6	−0.641720
$874$	53429.0	2.06781
$875$	−22976.4	−0.887707
$876$	−590.676	−0.0227821
$877$	6291.03	0.242227	0.121114	−	0.992639i	$-0.461353\pi$
$877$	6291.03	0.242227	0.121114	+	0.992639i	$0.461353\pi$
$878$	29624.4	1.13870
$879$	7963.11	0.305562
$880$	−1956.77	−0.0749577
$881$	48382.5	1.85022	0.925112	−	0.379695i	$-0.123971\pi$
$881$	48382.5	1.85022	0.925112	+	0.379695i	$0.123971\pi$
$882$	69205.2	2.64202
$883$	−21310.2	−0.812169	−0.406084	−	0.913836i	$-0.633106\pi$
$883$	−21310.2	−0.812169	−0.406084	+	0.913836i	$0.633106\pi$
$884$	−15817.2	−0.601798
$885$	−706.605	−0.0268387
$886$	36096.5	1.36872
$887$	−6283.54	−0.237859	−0.118929	−	0.992903i	$-0.537946\pi$
$887$	−6283.54	−0.237859	−0.118929	+	0.992903i	$0.537946\pi$
$888$	−3354.33	−0.126761
$889$	−39919.1	−1.50601
$890$	−10890.1	−0.410153
$891$	−5416.69	−0.203665
$892$	1934.72	0.0726224
$893$	−7623.34	−0.285672
$894$	7561.81	0.282891
$895$	−8455.70	−0.315802
$896$	53463.3	1.99340
$897$	10023.4	0.373102
$898$	−44621.8	−1.65818
$899$	2411.47	0.0894627
$900$	11421.7	0.423027
$901$	−34169.0	−1.26341
$902$	−9000.55	−0.332246
$903$	0	0
$904$	14916.9	0.548814
$905$	−8980.64	−0.329864
$906$	−1135.57	−0.0416409
$907$	9911.20	0.362840	0.181420	−	0.983406i	$-0.441931\pi$
$907$	9911.20	0.362840	0.181420	+	0.983406i	$0.441931\pi$
$908$	−14105.8	−0.515549
$909$	−39434.5	−1.43890
$910$	−17719.7	−0.645496
$911$	−44778.4	−1.62851	−0.814256	−	0.580505i	$-0.802855\pi$
$911$	−44778.4	−1.62851	−0.814256	+	0.580505i	$0.802855\pi$
$912$	8707.88	0.316170
$913$	−236.281	−0.00856491
$914$	−33764.9	−1.22193
$915$	373.861	0.0135076
$916$	8955.21	0.323022
$917$	−47767.0	−1.72018
$918$	15771.4	0.567031
$919$	−9209.38	−0.330565	−0.165283	−	0.986246i	$-0.552854\pi$
$919$	−9209.38	−0.330565	−0.165283	+	0.986246i	$0.552854\pi$
$920$	6627.63	0.237507
$921$	1484.30	0.0531046
$922$	−47164.3	−1.68468
$923$	55906.4	1.99370
$924$	−1253.25	−0.0446200
$925$	−23923.7	−0.850384
$926$	−10066.5	−0.357240
$927$	47269.7	1.67480
$928$	2836.77	0.100346
$929$	−37773.3	−1.33402	−0.667009	−	0.745049i	$-0.732426\pi$
$929$	−37773.3	−1.33402	−0.667009	+	0.745049i	$0.732426\pi$
$930$	−1493.69	−0.0526668
$931$	75106.5	2.64395
$932$	−4170.25	−0.146568
$933$	5390.49	0.189150
$934$	54710.2	1.91667
$935$	−1876.00	−0.0656170
$936$	−20165.0	−0.704182
$937$	−7402.89	−0.258102	−0.129051	−	0.991638i	$-0.541193\pi$
$937$	−7402.89	−0.258102	−0.129051	+	0.991638i	$0.541193\pi$
$938$	99104.7	3.44977
$939$	6204.89	0.215643
$940$	854.406	0.0296464
$941$	−29080.2	−1.00742	−0.503712	−	0.863872i	$-0.668033\pi$
$941$	−29080.2	−1.00742	−0.503712	+	0.863872i	$0.668033\pi$
$942$	11872.5	0.410645
$943$	49163.2	1.69775
$944$	17577.2	0.606026
$945$	5687.05	0.195767
$946$	0	0
$947$	−26077.7	−0.894837	−0.447419	−	0.894325i	$-0.647657\pi$
$947$	−26077.7	−0.894837	−0.447419	+	0.894325i	$0.647657\pi$
$948$	2521.32	0.0863804
$949$	7437.70	0.254413
$950$	38510.7	1.31521
$951$	−7966.81	−0.271653
$952$	37144.6	1.26456
$953$	31004.8	1.05388	0.526939	−	0.849903i	$-0.323340\pi$
$953$	31004.8	1.05388	0.526939	+	0.849903i	$0.323340\pi$
$954$	39358.7	1.33573
$955$	8925.75	0.302440
$956$	5694.70	0.192657
$957$	175.251	0.00591962
$958$	−2207.09	−0.0744341
$959$	18973.0	0.638865
$960$	299.006	0.0100525
$961$	−11486.8	−0.385578
$962$	−38162.1	−1.27900
$963$	−15331.5	−0.513032
$964$	−9792.42	−0.327171
$965$	836.885	0.0279174
$966$	21267.7	0.708361
$967$	8359.12	0.277985	0.138992	−	0.990293i	$-0.455614\pi$
$967$	8359.12	0.277985	0.138992	+	0.990293i	$0.455614\pi$
$968$	−18132.7	−0.602073
$969$	8348.46	0.276771
$970$	6255.12	0.207051
$971$	23620.0	0.780641	0.390321	−	0.920679i	$-0.372364\pi$
$971$	23620.0	0.780641	0.390321	+	0.920679i	$0.372364\pi$
$972$	−8842.83	−0.291805
$973$	−879.745	−0.0289860
$974$	−64002.5	−2.10552
$975$	7224.72	0.237309
$976$	−9299.98	−0.305005
$977$	20068.3	0.657156	0.328578	−	0.944477i	$-0.393431\pi$
$977$	20068.3	0.657156	0.328578	+	0.944477i	$0.393431\pi$
$978$	4847.75	0.158501
$979$	9698.43	0.316612
$980$	−8417.76	−0.274383
$981$	34656.8	1.12794
$982$	−62916.3	−2.04454
$983$	26290.9	0.853052	0.426526	−	0.904475i	$-0.359737\pi$
$983$	26290.9	0.853052	0.426526	+	0.904475i	$0.359737\pi$
$984$	4968.47	0.160965
$985$	12232.6	0.395698
$986$	4693.07	0.151580
$987$	−3034.51	−0.0978617
$988$	19773.1	0.636707
$989$	0	0
$990$	2160.93	0.0693727
$991$	−21747.2	−0.697097	−0.348549	−	0.937291i	$-0.613325\pi$
$991$	−21747.2	−0.697097	−0.348549	+	0.937291i	$0.613325\pi$
$992$	21532.5	0.689170
$993$	−2656.96	−0.0849106
$994$	118622.	3.78518
$995$	14562.6	0.463987
$996$	−117.847	−0.00374914
$997$	39252.8	1.24689	0.623445	−	0.781868i	$-0.285733\pi$
$997$	39252.8	1.24689	0.623445	+	0.781868i	$0.285733\pi$
$998$	60557.5	1.92075
$999$	12247.9	0.387896

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.i.1.13	✓	50
43.42	odd	2		1849.4.a.j.1.38	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.4.a.i.1.13	✓	50	1.1	even	1	trivial
1849.4.a.j.1.38	yes	50	43.42	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:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q-3.43471 q^{2} -1.13642 q^{3} +3.79726 q^{4} -2.82850 q^{5} +3.90328 q^{6} -33.5669 q^{7} +14.4352 q^{8} -25.7086 q^{9} +O(q^{10})\)	\(q-3.43471 q^{2} -1.13642 q^{3} +3.79726 q^{4} -2.82850 q^{5} +3.90328 q^{6} -33.5669 q^{7} +14.4352 q^{8} -25.7086 q^{9} +9.71508 q^{10} -8.65202 q^{11} -4.31528 q^{12} +54.3373 q^{13} +115.293 q^{14} +3.21436 q^{15} -79.9589 q^{16} -76.6586 q^{17} +88.3015 q^{18} +95.8312 q^{19} -10.7405 q^{20} +38.1461 q^{21} +29.7172 q^{22} -162.323 q^{23} -16.4045 q^{24} -117.000 q^{25} -186.633 q^{26} +59.8990 q^{27} -127.462 q^{28} +17.8240 q^{29} -11.0404 q^{30} +135.293 q^{31} +159.154 q^{32} +9.83232 q^{33} +263.300 q^{34} +94.9439 q^{35} -97.6220 q^{36} +204.476 q^{37} -329.153 q^{38} -61.7500 q^{39} -40.8300 q^{40} -302.873 q^{41} -131.021 q^{42} -32.8540 q^{44} +72.7166 q^{45} +557.532 q^{46} -79.5496 q^{47} +90.8669 q^{48} +783.738 q^{49} +401.860 q^{50} +87.1163 q^{51} +206.333 q^{52} +445.730 q^{53} -205.736 q^{54} +24.4722 q^{55} -484.546 q^{56} -108.904 q^{57} -61.2204 q^{58} -219.828 q^{59} +12.2058 q^{60} +116.310 q^{61} -464.693 q^{62} +862.957 q^{63} +93.0220 q^{64} -153.693 q^{65} -33.7712 q^{66} +859.592 q^{67} -291.092 q^{68} +184.467 q^{69} -326.105 q^{70} +1028.88 q^{71} -371.108 q^{72} +136.880 q^{73} -702.318 q^{74} +132.961 q^{75} +363.896 q^{76} +290.422 q^{77} +212.094 q^{78} -584.277 q^{79} +226.164 q^{80} +626.060 q^{81} +1040.28 q^{82} +27.3094 q^{83} +144.851 q^{84} +216.829 q^{85} -20.2556 q^{87} -124.894 q^{88} -1120.94 q^{89} -249.761 q^{90} -1823.94 q^{91} -616.381 q^{92} -153.750 q^{93} +273.230 q^{94} -271.058 q^{95} -180.866 q^{96} +643.857 q^{97} -2691.92 q^{98} +222.431 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 10 q^{2} - 2 q^{3} + 186 q^{4} + 8 q^{5} - 51 q^{6} - 6 q^{7} - 138 q^{8} + 360 q^{9}+O(q^{10}) \) 50 * q - 10 * q^2 - 2 * q^3 + 186 * q^4 + 8 * q^5 - 51 * q^6 - 6 * q^7 - 138 * q^8 + 360 * q^9	\( 50 q - 10 q^{2} - 2 q^{3} + 186 q^{4} + 8 q^{5} - 51 q^{6} - 6 q^{7} - 138 q^{8} + 360 q^{9} - 137 q^{10} - 252 q^{11} - 48 q^{12} - 192 q^{13} - 272 q^{14} - 314 q^{15} + 542 q^{16} - 236 q^{17} - 386 q^{18} + 12 q^{19} + 108 q^{20} - 408 q^{21} + 1235 q^{22} - 630 q^{23} - 613 q^{24} + 1098 q^{25} + 1493 q^{26} + 10 q^{27} - 242 q^{28} + 208 q^{29} - 48 q^{30} - 932 q^{31} - 1124 q^{32} + 254 q^{33} + 765 q^{34} - 1452 q^{35} + 747 q^{36} - 90 q^{37} - 1213 q^{38} - 1610 q^{39} - 1693 q^{40} - 1354 q^{41} - 16 q^{42} - 2704 q^{44} + 4508 q^{45} + 233 q^{46} - 3484 q^{47} - 376 q^{48} + 1324 q^{49} - 408 q^{50} + 4054 q^{51} - 2176 q^{52} - 726 q^{53} - 6497 q^{54} - 3288 q^{55} - 7097 q^{56} - 870 q^{57} + 275 q^{58} - 4370 q^{59} - 3891 q^{60} + 1172 q^{61} - 1546 q^{62} - 3686 q^{63} + 606 q^{64} + 2610 q^{65} - 4697 q^{66} - 344 q^{67} - 3221 q^{68} + 136 q^{69} - 1310 q^{70} + 162 q^{71} - 5814 q^{72} + 746 q^{73} - 4332 q^{74} + 236 q^{75} + 1338 q^{76} + 2024 q^{77} - 2782 q^{78} - 2656 q^{79} - 5713 q^{80} - 86 q^{81} - 4168 q^{82} - 3514 q^{83} - 4269 q^{84} - 7558 q^{85} - 10278 q^{87} + 11692 q^{88} + 2640 q^{89} - 8286 q^{90} - 5946 q^{91} - 4271 q^{92} - 2 q^{93} + 9062 q^{94} - 12140 q^{95} - 700 q^{96} - 3864 q^{97} - 2826 q^{98} - 8174 q^{99}+O(q^{100}) \) 50 * q - 10 * q^2 - 2 * q^3 + 186 * q^4 + 8 * q^5 - 51 * q^6 - 6 * q^7 - 138 * q^8 + 360 * q^9 - 137 * q^10 - 252 * q^11 - 48 * q^12 - 192 * q^13 - 272 * q^14 - 314 * q^15 + 542 * q^16 - 236 * q^17 - 386 * q^18 + 12 * q^19 + 108 * q^20 - 408 * q^21 + 1235 * q^22 - 630 * q^23 - 613 * q^24 + 1098 * q^25 + 1493 * q^26 + 10 * q^27 - 242 * q^28 + 208 * q^29 - 48 * q^30 - 932 * q^31 - 1124 * q^32 + 254 * q^33 + 765 * q^34 - 1452 * q^35 + 747 * q^36 - 90 * q^37 - 1213 * q^38 - 1610 * q^39 - 1693 * q^40 - 1354 * q^41 - 16 * q^42 - 2704 * q^44 + 4508 * q^45 + 233 * q^46 - 3484 * q^47 - 376 * q^48 + 1324 * q^49 - 408 * q^50 + 4054 * q^51 - 2176 * q^52 - 726 * q^53 - 6497 * q^54 - 3288 * q^55 - 7097 * q^56 - 870 * q^57 + 275 * q^58 - 4370 * q^59 - 3891 * q^60 + 1172 * q^61 - 1546 * q^62 - 3686 * q^63 + 606 * q^64 + 2610 * q^65 - 4697 * q^66 - 344 * q^67 - 3221 * q^68 + 136 * q^69 - 1310 * q^70 + 162 * q^71 - 5814 * q^72 + 746 * q^73 - 4332 * q^74 + 236 * q^75 + 1338 * q^76 + 2024 * q^77 - 2782 * q^78 - 2656 * q^79 - 5713 * q^80 - 86 * q^81 - 4168 * q^82 - 3514 * q^83 - 4269 * q^84 - 7558 * q^85 - 10278 * q^87 + 11692 * q^88 + 2640 * q^89 - 8286 * q^90 - 5946 * q^91 - 4271 * q^92 - 2 * q^93 + 9062 * q^94 - 12140 * q^95 - 700 * q^96 - 3864 * q^97 - 2826 * q^98 - 8174 * q^99

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