LMFDB - Embedded newform 1849.4.a.j.1.38

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			1.38
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	$-0.292302\pi$
$2$	3.43471	1.21435	0.607177	+	0.794566i	$0.292302\pi$
$3$	1.13642	0.218704	0.109352	−	0.994003i	$-0.465122\pi$
$3$	1.13642	0.218704	0.109352	+	0.994003i	$0.465122\pi$
$4$	3.79726	0.474657
$5$	2.82850	0.252989	0.126494	−	0.991967i	$-0.459627\pi$
$5$	2.82850	0.252989	0.126494	+	0.991967i	$0.459627\pi$
$6$	3.90328	0.265584
$7$	33.5669	1.81244	0.906222	−	0.422803i	$-0.138954\pi$
$7$	33.5669	1.81244	0.906222	+	0.422803i	$0.138954\pi$
$8$	−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	$-0.696384\pi$
$19$	−95.8312	−1.15711	−0.578557	+	0.815642i	$0.696384\pi$
$20$	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	$-0.518175\pi$
$29$	−17.8240	−0.114132	−0.0570661	+	0.998370i	$0.518175\pi$
$30$	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	$-0.650099\pi$
$37$	−204.476	−0.908533	−0.454267	+	0.890866i	$0.650099\pi$
$38$	−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	$-0.538952\pi$
$61$	−116.310	−0.244130	−0.122065	+	0.992522i	$0.538952\pi$
$62$	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	$-0.829472\pi$
$71$	−1028.88	−1.71979	−0.859897	+	0.510468i	$0.829472\pi$
$72$	371.108	0.607438
$73$	−136.880	−0.219461	−0.109730	−	0.993961i	$-0.534999\pi$
$73$	−136.880	−0.219461	−0.109730	+	0.993961i	$0.534999\pi$
$74$	−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	$-0.267353\pi$
$89$	1120.94	1.33506	0.667528	+	0.744585i	$0.267353\pi$
$90$	−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	$-0.641535\pi$
$113$	−1033.37	−0.860275	−0.430137	+	0.902763i	$0.641535\pi$
$114$	−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	$-0.657388\pi$
$131$	−1423.04	−0.949094	−0.474547	+	0.880230i	$0.657388\pi$
$132$	−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	$-0.443605\pi$
$137$	565.231	0.352488	0.176244	+	0.984346i	$0.443605\pi$
$138$	−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	$-0.678778\pi$
$149$	−1937.30	−1.06517	−0.532583	+	0.846378i	$0.678778\pi$
$150$	−456.682	−0.248586
$151$	290.926	0.156790	0.0783948	−	0.996922i	$-0.475021\pi$
$151$	290.926	0.156790	0.0783948	+	0.996922i	$0.475021\pi$
$152$	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	$-0.781294\pi$
$157$	−3041.68	−1.54619	−0.773097	+	0.634288i	$0.781294\pi$
$158$	−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	$-0.596453\pi$
$163$	−1241.97	−0.596801	−0.298401	+	0.954441i	$0.596453\pi$
$164$	−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	$-0.714552\pi$
$179$	−2989.47	−1.24829	−0.624143	+	0.781310i	$0.714552\pi$
$180$	−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	$-0.296067\pi$
$191$	3155.65	1.19547	0.597735	+	0.801693i	$0.296067\pi$
$192$	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	$-0.130594\pi$
$199$	5148.55	1.83402	0.917012	+	0.398860i	$0.130594\pi$
$200$	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	$-0.668453\pi$
$211$	−3094.70	−1.00971	−0.504853	+	0.863206i	$0.668453\pi$
$212$	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	$-0.524374\pi$
$223$	−509.504	−0.153000	−0.0764998	+	0.997070i	$0.524374\pi$
$224$	−5342.32	−1.59352
$225$	3007.89	0.891227
$226$	−3549.32	−1.04468
$227$	3714.74	1.08615	0.543075	−	0.839684i	$-0.317260\pi$
$227$	3714.74	1.08615	0.543075	+	0.839684i	$0.317260\pi$
$228$	−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	$-0.450658\pi$
$233$	1098.23	0.308787	0.154393	+	0.988009i	$0.450658\pi$
$234$	−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	$-0.388001\pi$
$241$	2578.81	0.689278	0.344639	+	0.938735i	$0.388001\pi$
$242$	−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	$-0.505774\pi$
$257$	−149.473	−0.0362796	−0.0181398	+	0.999835i	$0.505774\pi$
$258$	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	$-0.481257\pi$
$263$	502.011	0.117701	0.0588504	+	0.998267i	$0.481257\pi$
$264$	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	$-0.771653\pi$
$277$	−6947.90	−1.50707	−0.753536	+	0.657407i	$0.771653\pi$
$278$	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	$-0.335899\pi$
$313$	5460.04	0.986005	0.493002	+	0.870028i	$0.335899\pi$
$314$	−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	$-0.562186\pi$
$331$	−2338.01	−0.388244	−0.194122	+	0.980977i	$0.562186\pi$
$332$	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	$-0.436822\pi$
$347$	2549.11	0.394361	0.197180	+	0.980367i	$0.436822\pi$
$348$	−76.9156	−0.0118480
$349$	−4610.07	−0.707081	−0.353541	−	0.935419i	$-0.615022\pi$
$349$	−4610.07	−0.707081	−0.353541	+	0.935419i	$0.615022\pi$
$350$	−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	$-0.144174\pi$
$373$	12954.9	1.79833	0.899166	+	0.437608i	$0.144174\pi$
$374$	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	$-0.381588\pi$
$383$	5448.90	0.726960	0.363480	+	0.931602i	$0.381588\pi$
$384$	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	$-0.605054\pi$
$389$	−4972.81	−0.648153	−0.324077	+	0.946031i	$0.605054\pi$
$390$	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	$-0.117506\pi$
$409$	15428.6	1.86526	0.932632	+	0.360828i	$0.117506\pi$
$410$	−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	$-0.330633\pi$
$419$	8702.42	1.01466	0.507328	+	0.861753i	$0.330633\pi$
$420$	409.710	0.0475995
$421$	4123.21	0.477323	0.238661	−	0.971103i	$-0.423291\pi$
$421$	4123.21	0.477323	0.238661	+	0.971103i	$0.423291\pi$
$422$	−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	$-0.316727\pi$
$433$	9811.69	1.08896	0.544480	+	0.838774i	$0.316727\pi$
$434$	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	$-0.739213\pi$
$449$	−12991.4	−1.36549	−0.682743	+	0.730658i	$0.739213\pi$
$450$	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	$-0.667814\pi$
$457$	−9830.48	−1.00624	−0.503119	+	0.864217i	$0.667814\pi$
$458$	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	$-0.546991\pi$
$463$	−2930.80	−0.294181	−0.147090	+	0.989123i	$0.546991\pi$
$464$	1425.19	0.142592
$465$	434.881	0.0433702
$466$	3772.10	0.374977
$467$	15928.6	1.57835	0.789174	−	0.614170i	$-0.210509\pi$
$467$	15928.6	1.57835	0.789174	+	0.614170i	$0.210509\pi$
$468$	−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	$-0.818517\pi$
$491$	−18317.8	−1.68365	−0.841823	+	0.539754i	$0.818517\pi$
$492$	−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	$-0.209637\pi$
$499$	17631.0	1.58171	0.790854	+	0.612005i	$0.209637\pi$
$500$	−2599.21	−0.232480
$501$	1316.01	0.117355
$502$	−12507.6	−1.11203
$503$	8292.71	0.735096	0.367548	−	0.930004i	$-0.380197\pi$
$503$	8292.71	0.735096	0.367548	+	0.930004i	$0.380197\pi$
$504$	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	$-0.646850\pi$
$521$	−10587.5	−0.890299	−0.445150	+	0.895456i	$0.646850\pi$
$522$	1573.89	0.131968
$523$	−17462.6	−1.46001	−0.730007	−	0.683439i	$-0.760483\pi$
$523$	−17462.6	−1.46001	−0.730007	+	0.683439i	$0.760483\pi$
$524$	−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	$-0.485605\pi$
$571$	1233.69	0.0904173	0.0452087	+	0.998978i	$0.485605\pi$
$572$	−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	$-0.417582\pi$
$577$	7097.43	0.512080	0.256040	+	0.966666i	$0.417582\pi$
$578$	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	$-0.354494\pi$
$587$	12554.1	0.882730	0.441365	+	0.897328i	$0.354494\pi$
$588$	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	$-0.577070\pi$
$593$	−6924.59	−0.479526	−0.239763	+	0.970831i	$0.577070\pi$
$594$	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	$-0.501361\pi$
$601$	−126.013	−0.00855269	−0.00427635	+	0.999991i	$0.501361\pi$
$602$	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	$-0.501860\pi$
$607$	−174.746	−0.0116849	−0.00584245	+	0.999983i	$0.501860\pi$
$608$	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	$-0.380426\pi$
$631$	11630.5	0.733762	0.366881	+	0.930268i	$0.380426\pi$
$632$	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	$-0.669768\pi$
$641$	−16501.9	−1.01683	−0.508414	+	0.861113i	$0.669768\pi$
$642$	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	$-0.250926\pi$
$647$	23206.2	1.41009	0.705046	+	0.709161i	$0.250926\pi$
$648$	−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	$-0.412239\pi$
$653$	9085.23	0.544460	0.272230	+	0.962232i	$0.412239\pi$
$654$	−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	$-0.750157\pi$
$673$	−24703.1	−1.41491	−0.707455	+	0.706758i	$0.750157\pi$
$674$	8385.40	0.479219
$675$	7008.16	0.399621
$676$	2868.99	0.163233
$677$	−20119.2	−1.14216	−0.571082	−	0.820893i	$-0.693476\pi$
$677$	−20119.2	−1.14216	−0.571082	+	0.820893i	$0.693476\pi$
$678$	−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	$-0.496399\pi$
$691$	410.966	0.0226250	0.0113125	+	0.999936i	$0.496399\pi$
$692$	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	$-0.601244\pi$
$727$	−12260.4	−0.625463	−0.312732	+	0.949842i	$0.601244\pi$
$728$	−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	$-0.557876\pi$
$733$	−7176.95	−0.361646	−0.180823	+	0.983516i	$0.557876\pi$
$734$	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	$-0.378828\pi$
$739$	14928.3	0.743092	0.371546	+	0.928415i	$0.378828\pi$
$740$	−2196.19	−0.109099
$741$	−5917.57	−0.293370
$742$	51389.5	2.54254
$743$	−10031.8	−0.495333	−0.247666	−	0.968845i	$-0.579664\pi$
$743$	−10031.8	−0.495333	−0.247666	+	0.968845i	$0.579664\pi$
$744$	−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	$-0.439913\pi$
$751$	7723.92	0.375300	0.187650	+	0.982236i	$0.439913\pi$
$752$	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	$-0.479170\pi$
$757$	2723.98	0.130786	0.0653928	+	0.997860i	$0.479170\pi$
$758$	−44697.7	−2.14181
$759$	1596.01	0.0763261
$760$	3912.78	0.186752
$761$	−35688.3	−1.70000	−0.849999	−	0.526784i	$-0.823398\pi$
$761$	−35688.3	−1.70000	−0.849999	+	0.526784i	$0.823398\pi$
$762$	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	$-0.620875\pi$
$773$	−15932.9	−0.741356	−0.370678	+	0.928761i	$0.620875\pi$
$774$	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	$-0.442724\pi$
$811$	8266.76	0.357935	0.178968	+	0.983855i	$0.442724\pi$
$812$	−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	$-0.547856\pi$
$829$	−7150.10	−0.299558	−0.149779	+	0.988720i	$0.547856\pi$
$830$	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	$-0.503853\pi$
$839$	−588.326	−0.0242089	−0.0121044	+	0.999927i	$0.503853\pi$
$840$	−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	$-0.556718\pi$
$859$	−8924.67	−0.354489	−0.177244	+	0.984167i	$0.556718\pi$
$860$	0	0
$861$	−11553.4	−0.457306
$862$	−7934.40	−0.313511
$863$	−5135.14	−0.202552	−0.101276	−	0.994858i	$-0.532292\pi$
$863$	−5135.14	−0.202552	−0.101276	+	0.994858i	$0.532292\pi$
$864$	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	$-0.462054\pi$
$887$	6283.54	0.237859	0.118929	+	0.992903i	$0.462054\pi$
$888$	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	$-0.197145\pi$
$911$	44778.4	1.62851	0.814256	+	0.580505i	$0.197145\pi$
$912$	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	$-0.267574\pi$
$929$	37773.3	1.33402	0.667009	+	0.745049i	$0.267574\pi$
$930$	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	$-0.458807\pi$
$937$	7402.89	0.258102	0.129051	+	0.991638i	$0.458807\pi$
$938$	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	$-0.676660\pi$
$953$	−31004.8	−1.05388	−0.526939	+	0.849903i	$0.676660\pi$
$954$	−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	$-0.640263\pi$
$983$	−26290.9	−0.853052	−0.426526	+	0.904475i	$0.640263\pi$
$984$	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	$-0.386675\pi$
$991$	21747.2	0.697097	0.348549	+	0.937291i	$0.386675\pi$
$992$	−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	$-0.714267\pi$
$997$	−39252.8	−1.24689	−0.623445	+	0.781868i	$0.714267\pi$
$998$	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.j.1.38	yes	50
43.42	odd	2		1849.4.a.i.1.13	✓	50

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more