LMFDB - Embedded newform 46.4.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [46,4,Mod(1,46)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(46, 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("46.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 46 = 2 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	46.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:	$2.71408786026$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{73}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 18 $ x^2 - x - 18
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-3.77200$ of defining polynomial
Character	$\chi$	$=$	46.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} +5.77200 q^{3} +4.00000 q^{4} -3.54400 q^{5} +11.5440 q^{6} -11.0880 q^{7} +8.00000 q^{8} +6.31601 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} +5.77200 q^{3} +4.00000 q^{4} -3.54400 q^{5} +11.5440 q^{6} -11.0880 q^{7} +8.00000 q^{8} +6.31601 q^{9} -7.08801 q^{10} -6.00000 q^{11} +23.0880 q^{12} +21.4920 q^{13} -22.1760 q^{14} -20.4560 q^{15} +16.0000 q^{16} -7.36799 q^{17} +12.6320 q^{18} -93.4400 q^{19} -14.1760 q^{20} -64.0000 q^{21} -12.0000 q^{22} +23.0000 q^{23} +46.1760 q^{24} -112.440 q^{25} +42.9840 q^{26} -119.388 q^{27} -44.3520 q^{28} +112.476 q^{29} -40.9120 q^{30} +286.268 q^{31} +32.0000 q^{32} -34.6320 q^{33} -14.7360 q^{34} +39.2959 q^{35} +25.2640 q^{36} -59.3361 q^{37} -186.880 q^{38} +124.052 q^{39} -28.3520 q^{40} +62.6119 q^{41} -128.000 q^{42} +507.304 q^{43} -24.0000 q^{44} -22.3839 q^{45} +46.0000 q^{46} +536.300 q^{47} +92.3520 q^{48} -220.056 q^{49} -224.880 q^{50} -42.5280 q^{51} +85.9681 q^{52} +187.336 q^{53} -238.776 q^{54} +21.2640 q^{55} -88.7041 q^{56} -539.336 q^{57} +224.952 q^{58} +49.6799 q^{59} -81.8240 q^{60} -778.776 q^{61} +572.536 q^{62} -70.0319 q^{63} +64.0000 q^{64} -76.1678 q^{65} -69.2640 q^{66} -661.232 q^{67} -29.4720 q^{68} +132.756 q^{69} +78.5919 q^{70} +289.212 q^{71} +50.5280 q^{72} -651.316 q^{73} -118.672 q^{74} -649.004 q^{75} -373.760 q^{76} +66.5280 q^{77} +248.104 q^{78} -50.0720 q^{79} -56.7041 q^{80} -859.640 q^{81} +125.224 q^{82} +807.016 q^{83} -256.000 q^{84} +26.1122 q^{85} +1014.61 q^{86} +649.212 q^{87} -48.0000 q^{88} +946.104 q^{89} -44.7679 q^{90} -238.304 q^{91} +92.0000 q^{92} +1652.34 q^{93} +1072.60 q^{94} +331.152 q^{95} +184.704 q^{96} +715.529 q^{97} -440.112 q^{98} -37.8960 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{2} + 3 q^{3} + 8 q^{4} + 10 q^{5} + 6 q^{6} + 12 q^{7} + 16 q^{8} - 13 q^{9}+O(q^{10}) $ 2 * q + 4 * q^2 + 3 * q^3 + 8 * q^4 + 10 * q^5 + 6 * q^6 + 12 * q^7 + 16 * q^8 - 13 * q^9	\( 2 q + 4 q^{2} + 3 q^{3} + 8 q^{4} + 10 q^{5} + 6 q^{6} + 12 q^{7} + 16 q^{8} - 13 q^{9} + 20 q^{10} - 12 q^{11} + 12 q^{12} - 51 q^{13} + 24 q^{14} - 58 q^{15} + 32 q^{16} - 66 q^{17} - 26 q^{18} - 16 q^{19} + 40 q^{20} - 128 q^{21} - 24 q^{22} + 46 q^{23} + 24 q^{24} - 54 q^{25} - 102 q^{26} + 9 q^{27} + 48 q^{28} - 57 q^{29} - 116 q^{30} - 17 q^{31} + 64 q^{32} - 18 q^{33} - 132 q^{34} + 352 q^{35} - 52 q^{36} + 206 q^{37} - 32 q^{38} + 325 q^{39} + 80 q^{40} + 373 q^{41} - 256 q^{42} + 314 q^{43} - 48 q^{44} - 284 q^{45} + 92 q^{46} + 859 q^{47} + 48 q^{48} - 30 q^{49} - 108 q^{50} + 120 q^{51} - 204 q^{52} + 50 q^{53} + 18 q^{54} - 60 q^{55} + 96 q^{56} - 754 q^{57} - 114 q^{58} + 612 q^{59} - 232 q^{60} - 1062 q^{61} - 34 q^{62} - 516 q^{63} + 128 q^{64} - 1058 q^{65} - 36 q^{66} - 844 q^{67} - 264 q^{68} + 69 q^{69} + 704 q^{70} + 399 q^{71} - 104 q^{72} - 1277 q^{73} + 412 q^{74} - 811 q^{75} - 64 q^{76} - 72 q^{77} + 650 q^{78} + 122 q^{79} + 160 q^{80} - 694 q^{81} + 746 q^{82} + 1802 q^{83} - 512 q^{84} - 768 q^{85} + 628 q^{86} + 1119 q^{87} - 96 q^{88} + 2046 q^{89} - 568 q^{90} - 1912 q^{91} + 184 q^{92} + 2493 q^{93} + 1718 q^{94} + 1380 q^{95} + 96 q^{96} - 910 q^{97} - 60 q^{98} + 78 q^{99}+O(q^{100}) \) 2 * q + 4 * q^2 + 3 * q^3 + 8 * q^4 + 10 * q^5 + 6 * q^6 + 12 * q^7 + 16 * q^8 - 13 * q^9 + 20 * q^10 - 12 * q^11 + 12 * q^12 - 51 * q^13 + 24 * q^14 - 58 * q^15 + 32 * q^16 - 66 * q^17 - 26 * q^18 - 16 * q^19 + 40 * q^20 - 128 * q^21 - 24 * q^22 + 46 * q^23 + 24 * q^24 - 54 * q^25 - 102 * q^26 + 9 * q^27 + 48 * q^28 - 57 * q^29 - 116 * q^30 - 17 * q^31 + 64 * q^32 - 18 * q^33 - 132 * q^34 + 352 * q^35 - 52 * q^36 + 206 * q^37 - 32 * q^38 + 325 * q^39 + 80 * q^40 + 373 * q^41 - 256 * q^42 + 314 * q^43 - 48 * q^44 - 284 * q^45 + 92 * q^46 + 859 * q^47 + 48 * q^48 - 30 * q^49 - 108 * q^50 + 120 * q^51 - 204 * q^52 + 50 * q^53 + 18 * q^54 - 60 * q^55 + 96 * q^56 - 754 * q^57 - 114 * q^58 + 612 * q^59 - 232 * q^60 - 1062 * q^61 - 34 * q^62 - 516 * q^63 + 128 * q^64 - 1058 * q^65 - 36 * q^66 - 844 * q^67 - 264 * q^68 + 69 * q^69 + 704 * q^70 + 399 * q^71 - 104 * q^72 - 1277 * q^73 + 412 * q^74 - 811 * q^75 - 64 * q^76 - 72 * q^77 + 650 * q^78 + 122 * q^79 + 160 * q^80 - 694 * q^81 + 746 * q^82 + 1802 * q^83 - 512 * q^84 - 768 * q^85 + 628 * q^86 + 1119 * q^87 - 96 * q^88 + 2046 * q^89 - 568 * q^90 - 1912 * q^91 + 184 * q^92 + 2493 * q^93 + 1718 * q^94 + 1380 * q^95 + 96 * q^96 - 910 * q^97 - 60 * q^98 + 78 * 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 $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	5.77200	1.11082	0.555411	−	0.831576i	$-0.312561\pi$
$3$	5.77200	1.11082	0.555411	+	0.831576i	$0.312561\pi$
$4$	4.00000	0.500000
$5$	−3.54400	−0.316985	−0.158493	−	0.987360i	$-0.550663\pi$
$5$	−3.54400	−0.316985	−0.158493	+	0.987360i	$0.550663\pi$
$6$	11.5440	0.785470
$7$	−11.0880	−0.598696	−0.299348	−	0.954144i	$-0.596769\pi$
$7$	−11.0880	−0.598696	−0.299348	+	0.954144i	$0.596769\pi$
$8$	8.00000	0.353553
$9$	6.31601	0.233926
$10$	−7.08801	−0.224142
$11$	−6.00000	−0.164461	−0.0822304	−	0.996613i	$-0.526204\pi$
$11$	−6.00000	−0.164461	−0.0822304	+	0.996613i	$0.526204\pi$
$12$	23.0880	0.555411
$13$	21.4920	0.458524	0.229262	−	0.973365i	$-0.426369\pi$
$13$	21.4920	0.458524	0.229262	+	0.973365i	$0.426369\pi$
$14$	−22.1760	−0.423342
$15$	−20.4560	−0.352114
$16$	16.0000	0.250000
$17$	−7.36799	−0.105118	−0.0525588	−	0.998618i	$-0.516738\pi$
$17$	−7.36799	−0.105118	−0.0525588	+	0.998618i	$0.516738\pi$
$18$	12.6320	0.165411
$19$	−93.4400	−1.12824	−0.564121	−	0.825692i	$-0.690785\pi$
$19$	−93.4400	−1.12824	−0.564121	+	0.825692i	$0.690785\pi$
$20$	−14.1760	−0.158493
$21$	−64.0000	−0.665045
$22$	−12.0000	−0.116291
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	46.1760	0.392735
$25$	−112.440	−0.899520
$26$	42.9840	0.324226
$27$	−119.388	−0.850972
$28$	−44.3520	−0.299348
$29$	112.476	0.720217	0.360108	−	0.932911i	$-0.382740\pi$
$29$	112.476	0.720217	0.360108	+	0.932911i	$0.382740\pi$
$30$	−40.9120	−0.248982
$31$	286.268	1.65856	0.829279	−	0.558835i	$-0.188752\pi$
$31$	286.268	1.65856	0.829279	+	0.558835i	$0.188752\pi$
$32$	32.0000	0.176777
$33$	−34.6320	−0.182687
$34$	−14.7360	−0.0743294
$35$	39.2959	0.189778
$36$	25.2640	0.116963
$37$	−59.3361	−0.263643	−0.131821	−	0.991273i	$-0.542083\pi$
$37$	−59.3361	−0.263643	−0.131821	+	0.991273i	$0.542083\pi$
$38$	−186.880	−0.797788
$39$	124.052	0.509339
$40$	−28.3520	−0.112071
$41$	62.6119	0.238496	0.119248	−	0.992864i	$-0.461952\pi$
$41$	62.6119	0.238496	0.119248	+	0.992864i	$0.461952\pi$
$42$	−128.000	−0.470258
$43$	507.304	1.79914	0.899572	−	0.436773i	$-0.143879\pi$
$43$	507.304	1.79914	0.899572	+	0.436773i	$0.143879\pi$
$44$	−24.0000	−0.0822304
$45$	−22.3839	−0.0741512
$46$	46.0000	0.147442
$47$	536.300	1.66441	0.832206	−	0.554466i	$-0.187077\pi$
$47$	536.300	1.66441	0.832206	+	0.554466i	$0.187077\pi$
$48$	92.3520	0.277706
$49$	−220.056	−0.641563
$50$	−224.880	−0.636057
$51$	−42.5280	−0.116767
$52$	85.9681	0.229262
$53$	187.336	0.485521	0.242760	−	0.970086i	$-0.421947\pi$
$53$	187.336	0.485521	0.242760	+	0.970086i	$0.421947\pi$
$54$	−238.776	−0.601728
$55$	21.2640	0.0521316
$56$	−88.7041	−0.211671
$57$	−539.336	−1.25328
$58$	224.952	0.509270
$59$	49.6799	0.109623	0.0548116	−	0.998497i	$-0.482544\pi$
$59$	49.6799	0.109623	0.0548116	+	0.998497i	$0.482544\pi$
$60$	−81.8240	−0.176057
$61$	−778.776	−1.63462	−0.817312	−	0.576195i	$-0.804537\pi$
$61$	−778.776	−1.63462	−0.817312	+	0.576195i	$0.804537\pi$
$62$	572.536	1.17278
$63$	−70.0319	−0.140051
$64$	64.0000	0.125000
$65$	−76.1678	−0.145345
$66$	−69.2640	−0.129179
$67$	−661.232	−1.20571	−0.602853	−	0.797852i	$-0.705970\pi$
$67$	−661.232	−1.20571	−0.602853	+	0.797852i	$0.705970\pi$
$68$	−29.4720	−0.0525588
$69$	132.756	0.231622
$70$	78.5919	0.134193
$71$	289.212	0.483425	0.241712	−	0.970348i	$-0.422291\pi$
$71$	289.212	0.483425	0.241712	+	0.970348i	$0.422291\pi$
$72$	50.5280	0.0827054
$73$	−651.316	−1.04426	−0.522129	−	0.852867i	$-0.674862\pi$
$73$	−651.316	−1.04426	−0.522129	+	0.852867i	$0.674862\pi$
$74$	−118.672	−0.186424
$75$	−649.004	−0.999207
$76$	−373.760	−0.564121
$77$	66.5280	0.0984620
$78$	248.104	0.360157
$79$	−50.0720	−0.0713107	−0.0356554	−	0.999364i	$-0.511352\pi$
$79$	−50.0720	−0.0713107	−0.0356554	+	0.999364i	$0.511352\pi$
$80$	−56.7041	−0.0792463
$81$	−859.640	−1.17920
$82$	125.224	0.168642
$83$	807.016	1.06725	0.533624	−	0.845722i	$-0.320830\pi$
$83$	807.016	1.06725	0.533624	+	0.845722i	$0.320830\pi$
$84$	−256.000	−0.332522
$85$	26.1122	0.0333207
$86$	1014.61	1.27219
$87$	649.212	0.800033
$88$	−48.0000	−0.0581456
$89$	946.104	1.12682	0.563409	−	0.826178i	$-0.309490\pi$
$89$	946.104	1.12682	0.563409	+	0.826178i	$0.309490\pi$
$90$	−44.7679	−0.0524328
$91$	−238.304	−0.274517
$92$	92.0000	0.104257
$93$	1652.34	1.84236
$94$	1072.60	1.17692
$95$	331.152	0.357636
$96$	184.704	0.196367
$97$	715.529	0.748978	0.374489	−	0.927231i	$-0.377818\pi$
$97$	715.529	0.748978	0.374489	+	0.927231i	$0.377818\pi$
$98$	−440.112	−0.453654
$99$	−37.8960	−0.0384717
$100$	−449.760	−0.449760
$101$	−272.544	−0.268507	−0.134253	−	0.990947i	$-0.542864\pi$
$101$	−272.544	−0.268507	−0.134253	+	0.990947i	$0.542864\pi$
$102$	−85.0561	−0.0825667
$103$	−609.904	−0.583453	−0.291726	−	0.956502i	$-0.594230\pi$
$103$	−609.904	−0.583453	−0.291726	+	0.956502i	$0.594230\pi$
$104$	171.936	0.162113
$105$	226.816	0.210810
$106$	374.672	0.343315
$107$	−212.240	−0.191757	−0.0958785	−	0.995393i	$-0.530566\pi$
$107$	−212.240	−0.191757	−0.0958785	+	0.995393i	$0.530566\pi$
$108$	−477.552	−0.425486
$109$	−1287.18	−1.13110	−0.565550	−	0.824714i	$-0.691336\pi$
$109$	−1287.18	−1.13110	−0.565550	+	0.824714i	$0.691336\pi$
$110$	42.5280	0.0368626
$111$	−342.488	−0.292860
$112$	−177.408	−0.149674
$113$	−313.336	−0.260851	−0.130426	−	0.991458i	$-0.541634\pi$
$113$	−313.336	−0.260851	−0.130426	+	0.991458i	$0.541634\pi$
$114$	−1078.67	−0.886201
$115$	−81.5121	−0.0660960
$116$	449.904	0.360108
$117$	135.744	0.107261
$118$	99.3598	0.0775153
$119$	81.6963	0.0629335
$120$	−163.648	−0.124491
$121$	−1295.00	−0.972953
$122$	−1557.55	−1.15585
$123$	361.396	0.264927
$124$	1145.07	0.829279
$125$	841.488	0.602120
$126$	−140.064	−0.0990308
$127$	−1152.43	−0.805208	−0.402604	−	0.915374i	$-0.631895\pi$
$127$	−1152.43	−0.805208	−0.402604	+	0.915374i	$0.631895\pi$
$128$	128.000	0.0883883
$129$	2928.16	1.99853
$130$	−152.336	−0.102775
$131$	−2368.37	−1.57959	−0.789793	−	0.613374i	$-0.789812\pi$
$131$	−2368.37	−1.57959	−0.789793	+	0.613374i	$0.789812\pi$
$132$	−138.528	−0.0913433
$133$	1036.06	0.675475
$134$	−1322.46	−0.852563
$135$	423.112	0.269746
$136$	−58.9439	−0.0371647
$137$	−2872.44	−1.79131	−0.895654	−	0.444752i	$-0.853292\pi$
$137$	−2872.44	−1.79131	−0.895654	+	0.444752i	$0.853292\pi$
$138$	265.512	0.163782
$139$	1637.24	0.999054	0.499527	−	0.866298i	$-0.333507\pi$
$139$	1637.24	0.999054	0.499527	+	0.866298i	$0.333507\pi$
$140$	157.184	0.0948889
$141$	3095.52	1.84887
$142$	578.424	0.341833
$143$	−128.952	−0.0754092
$144$	101.056	0.0584815
$145$	−398.616	−0.228298
$146$	−1302.63	−0.738401
$147$	−1270.16	−0.712662
$148$	−237.344	−0.131821
$149$	3125.40	1.71841	0.859204	−	0.511633i	$-0.170959\pi$
$149$	3125.40	1.71841	0.859204	+	0.511633i	$0.170959\pi$
$150$	−1298.01	−0.706546
$151$	−370.436	−0.199640	−0.0998200	−	0.995006i	$-0.531827\pi$
$151$	−370.436	−0.199640	−0.0998200	+	0.995006i	$0.531827\pi$
$152$	−747.520	−0.398894
$153$	−46.5363	−0.0245898
$154$	133.056	0.0696232
$155$	−1014.54	−0.525738
$156$	496.208	0.254669
$157$	−1993.44	−1.01334	−0.506669	−	0.862141i	$-0.669123\pi$
$157$	−1993.44	−1.01334	−0.506669	+	0.862141i	$0.669123\pi$
$158$	−100.144	−0.0504243
$159$	1081.30	0.539327
$160$	−113.408	−0.0560356
$161$	−255.024	−0.124837
$162$	−1719.28	−0.833824
$163$	1722.10	0.827517	0.413759	−	0.910387i	$-0.364216\pi$
$163$	1722.10	0.827517	0.413759	+	0.910387i	$0.364216\pi$
$164$	250.448	0.119248
$165$	122.736	0.0579090
$166$	1614.03	0.754658
$167$	−1870.88	−0.866904	−0.433452	−	0.901177i	$-0.642705\pi$
$167$	−1870.88	−0.866904	−0.433452	+	0.901177i	$0.642705\pi$
$168$	−512.000	−0.235129
$169$	−1735.09	−0.789756
$170$	52.2244	0.0235613
$171$	−590.168	−0.263925
$172$	2029.22	0.899572
$173$	−700.512	−0.307855	−0.153927	−	0.988082i	$-0.549192\pi$
$173$	−700.512	−0.307855	−0.153927	+	0.988082i	$0.549192\pi$
$174$	1298.42	0.565708
$175$	1246.74	0.538539
$176$	−96.0000	−0.0411152
$177$	286.752	0.121772
$178$	1892.21	0.796781
$179$	3804.58	1.58865	0.794323	−	0.607495i	$-0.207826\pi$
$179$	3804.58	1.58865	0.794323	+	0.607495i	$0.207826\pi$
$180$	−89.5358	−0.0370756
$181$	3660.10	1.50306	0.751529	−	0.659700i	$-0.229317\pi$
$181$	3660.10	1.50306	0.751529	+	0.659700i	$0.229317\pi$
$182$	−476.607	−0.194113
$183$	−4495.10	−1.81578
$184$	184.000	0.0737210
$185$	210.287	0.0835710
$186$	3304.68	1.30275
$187$	44.2079	0.0172877
$188$	2145.20	0.832206
$189$	1323.78	0.509474
$190$	662.304	0.252887
$191$	−1999.46	−0.757467	−0.378733	−	0.925506i	$-0.623640\pi$
$191$	−1999.46	−0.757467	−0.378733	+	0.925506i	$0.623640\pi$
$192$	369.408	0.138853
$193$	879.885	0.328163	0.164082	−	0.986447i	$-0.447534\pi$
$193$	879.885	0.328163	0.164082	+	0.986447i	$0.447534\pi$
$194$	1431.06	0.529608
$195$	−439.641	−0.161453
$196$	−880.224	−0.320781
$197$	−2760.80	−0.998473	−0.499236	−	0.866466i	$-0.666386\pi$
$197$	−2760.80	−0.998473	−0.499236	+	0.866466i	$0.666386\pi$
$198$	−75.7921	−0.0272036
$199$	3377.19	1.20303	0.601515	−	0.798862i	$-0.294564\pi$
$199$	3377.19	1.20303	0.601515	+	0.798862i	$0.294564\pi$
$200$	−899.520	−0.318028
$201$	−3816.63	−1.33933
$202$	−545.089	−0.189863
$203$	−1247.14	−0.431191
$204$	−170.112	−0.0583835
$205$	−221.897	−0.0755998
$206$	−1219.81	−0.412564
$207$	145.268	0.0487770
$208$	343.872	0.114631
$209$	560.640	0.185552
$210$	453.632	0.149065
$211$	−1072.19	−0.349823	−0.174912	−	0.984584i	$-0.555964\pi$
$211$	−1072.19	−0.349823	−0.174912	+	0.984584i	$0.555964\pi$
$212$	749.344	0.242760
$213$	1669.33	0.536999
$214$	−424.480	−0.135593
$215$	−1797.89	−0.570302
$216$	−955.104	−0.300864
$217$	−3174.14	−0.992972
$218$	−2574.37	−0.799809
$219$	−3759.40	−1.15998
$220$	85.0561	0.0260658
$221$	−158.353	−0.0481990
$222$	−684.976	−0.207084
$223$	1494.88	0.448899	0.224450	−	0.974486i	$-0.427942\pi$
$223$	1494.88	0.448899	0.224450	+	0.974486i	$0.427942\pi$
$224$	−354.816	−0.105836
$225$	−710.172	−0.210421
$226$	−626.672	−0.184450
$227$	2714.01	0.793547	0.396773	−	0.917917i	$-0.370130\pi$
$227$	2714.01	0.793547	0.396773	+	0.917917i	$0.370130\pi$
$228$	−2157.34	−0.626639
$229$	2512.00	0.724881	0.362441	−	0.932007i	$-0.381944\pi$
$229$	2512.00	0.724881	0.362441	+	0.932007i	$0.381944\pi$
$230$	−163.024	−0.0467369
$231$	384.000	0.109374
$232$	899.808	0.254635
$233$	−1728.36	−0.485961	−0.242981	−	0.970031i	$-0.578125\pi$
$233$	−1728.36	−0.485961	−0.242981	+	0.970031i	$0.578125\pi$
$234$	271.487	0.0758448
$235$	−1900.65	−0.527594
$236$	198.720	0.0548116
$237$	−289.016	−0.0792135
$238$	163.393	0.0445007
$239$	−1689.48	−0.457252	−0.228626	−	0.973514i	$-0.573423\pi$
$239$	−1689.48	−0.457252	−0.228626	+	0.973514i	$0.573423\pi$
$240$	−327.296	−0.0880286
$241$	3155.01	0.843286	0.421643	−	0.906762i	$-0.361454\pi$
$241$	3155.01	0.843286	0.421643	+	0.906762i	$0.361454\pi$
$242$	−2590.00	−0.687981
$243$	−1738.37	−0.458915
$244$	−3115.10	−0.817312
$245$	779.880	0.203366
$246$	722.793	0.187332
$247$	−2008.22	−0.517327
$248$	2290.15	0.586389
$249$	4658.10	1.18552
$250$	1682.98	0.425763
$251$	6341.93	1.59482	0.797408	−	0.603440i	$-0.206204\pi$
$251$	6341.93	1.59482	0.797408	+	0.603440i	$0.206204\pi$
$252$	−280.128	−0.0700253
$253$	−138.000	−0.0342924
$254$	−2304.86	−0.569368
$255$	150.720	0.0370134
$256$	256.000	0.0625000
$257$	−5956.53	−1.44575	−0.722875	−	0.690979i	$-0.757180\pi$
$257$	−5956.53	−1.44575	−0.722875	+	0.690979i	$0.757180\pi$
$258$	5856.32	1.41317
$259$	657.919	0.157842
$260$	−304.671	−0.0726727
$261$	710.399	0.168477
$262$	−4736.75	−1.11694
$263$	−7147.68	−1.67583	−0.837917	−	0.545797i	$-0.816227\pi$
$263$	−7147.68	−1.67583	−0.837917	+	0.545797i	$0.816227\pi$
$264$	−277.056	−0.0645895
$265$	−663.920	−0.153903
$266$	2072.13	0.477633
$267$	5460.91	1.25169
$268$	−2644.93	−0.602853
$269$	7432.72	1.68469	0.842343	−	0.538941i	$-0.181176\pi$
$269$	7432.72	1.68469	0.842343	+	0.538941i	$0.181176\pi$
$270$	846.223	0.190739
$271$	3236.06	0.725376	0.362688	−	0.931911i	$-0.381859\pi$
$271$	3236.06	0.725376	0.362688	+	0.931911i	$0.381859\pi$
$272$	−117.888	−0.0262794
$273$	−1375.49	−0.304939
$274$	−5744.88	−1.26665
$275$	674.640	0.147936
$276$	531.024	0.115811
$277$	5437.77	1.17951	0.589755	−	0.807582i	$-0.299224\pi$
$277$	5437.77	1.17951	0.589755	+	0.807582i	$0.299224\pi$
$278$	3274.47	0.706438
$279$	1808.07	0.387980
$280$	314.368	0.0670966
$281$	244.617	0.0519312	0.0259656	−	0.999663i	$-0.491734\pi$
$281$	244.617	0.0519312	0.0259656	+	0.999663i	$0.491734\pi$
$282$	6191.05	1.30735
$283$	−1050.75	−0.220710	−0.110355	−	0.993892i	$-0.535199\pi$
$283$	−1050.75	−0.220710	−0.110355	+	0.993892i	$0.535199\pi$
$284$	1156.85	0.241712
$285$	1911.41	0.397271
$286$	−257.904	−0.0533224
$287$	−694.242	−0.142787
$288$	202.112	0.0413527
$289$	−4858.71	−0.988950
$290$	−797.231	−0.161431
$291$	4130.03	0.831982
$292$	−2605.26	−0.522129
$293$	5643.46	1.12524	0.562618	−	0.826717i	$-0.309794\pi$
$293$	5643.46	1.12524	0.562618	+	0.826717i	$0.309794\pi$
$294$	−2540.33	−0.503928
$295$	−176.066	−0.0347490
$296$	−474.689	−0.0932119
$297$	716.328	0.139951
$298$	6250.80	1.21510
$299$	494.316	0.0956089
$300$	−2596.02	−0.499604
$301$	−5624.99	−1.07714
$302$	−740.872	−0.141167
$303$	−1573.13	−0.298263
$304$	−1495.04	−0.282061
$305$	2759.99	0.518152
$306$	−93.0725	−0.0173876
$307$	5876.55	1.09248	0.546241	−	0.837628i	$-0.316058\pi$
$307$	5876.55	1.09248	0.546241	+	0.837628i	$0.316058\pi$
$308$	266.112	0.0492310
$309$	−3520.37	−0.648113
$310$	−2029.07	−0.371753
$311$	8748.00	1.59503	0.797514	−	0.603301i	$-0.206148\pi$
$311$	8748.00	1.59503	0.797514	+	0.603301i	$0.206148\pi$
$312$	992.416	0.180078
$313$	−5029.42	−0.908241	−0.454120	−	0.890940i	$-0.650046\pi$
$313$	−5029.42	−0.908241	−0.454120	+	0.890940i	$0.650046\pi$
$314$	−3986.88	−0.716537
$315$	248.193	0.0443940
$316$	−200.288	−0.0356554
$317$	−7199.63	−1.27562	−0.637810	−	0.770193i	$-0.720160\pi$
$317$	−7199.63	−1.27562	−0.637810	+	0.770193i	$0.720160\pi$
$318$	2162.61	0.381362
$319$	−674.856	−0.118447
$320$	−226.816	−0.0396232
$321$	−1225.05	−0.213008
$322$	−510.048	−0.0882729
$323$	688.465	0.118598
$324$	−3438.56	−0.589602
$325$	−2416.56	−0.412452
$326$	3444.20	0.585143
$327$	−7429.63	−1.25645
$328$	500.896	0.0843211
$329$	−5946.50	−0.996478
$330$	245.472	0.0409478
$331$	−772.092	−0.128212	−0.0641058	−	0.997943i	$-0.520420\pi$
$331$	−772.092	−0.128212	−0.0641058	+	0.997943i	$0.520420\pi$
$332$	3228.06	0.533624
$333$	−374.767	−0.0616730
$334$	−3741.76	−0.612994
$335$	2343.41	0.382191
$336$	−1024.00	−0.166261
$337$	−11069.6	−1.78932	−0.894659	−	0.446750i	$-0.852581\pi$
$337$	−11069.6	−1.78932	−0.894659	+	0.446750i	$0.852581\pi$
$338$	−3470.19	−0.558442
$339$	−1808.58	−0.289759
$340$	104.449	0.0166604
$341$	−1717.61	−0.272768
$342$	−1180.34	−0.186624
$343$	6243.17	0.982797
$344$	4058.43	0.636093
$345$	−470.488	−0.0734209
$346$	−1401.02	−0.217686
$347$	−1202.99	−0.186109	−0.0930547	−	0.995661i	$-0.529663\pi$
$347$	−1202.99	−0.186109	−0.0930547	+	0.995661i	$0.529663\pi$
$348$	2596.85	0.400016
$349$	−4573.69	−0.701501	−0.350750	−	0.936469i	$-0.614073\pi$
$349$	−4573.69	−0.701501	−0.350750	+	0.936469i	$0.614073\pi$
$350$	2493.47	0.380805
$351$	−2565.89	−0.390191
$352$	−192.000	−0.0290728
$353$	−974.740	−0.146969	−0.0734846	−	0.997296i	$-0.523412\pi$
$353$	−974.740	−0.146969	−0.0734846	+	0.997296i	$0.523412\pi$
$354$	573.505	0.0861058
$355$	−1024.97	−0.153239
$356$	3784.42	0.563409
$357$	471.551	0.0699080
$358$	7609.16	1.12334
$359$	−4872.46	−0.716319	−0.358160	−	0.933660i	$-0.616596\pi$
$359$	−4872.46	−0.716319	−0.358160	+	0.933660i	$0.616596\pi$
$360$	−179.072	−0.0262164
$361$	1872.04	0.272932
$362$	7320.21	1.06282
$363$	−7474.74	−1.08078
$364$	−953.215	−0.137258
$365$	2308.27	0.331014
$366$	−8990.19	−1.28395
$367$	11508.8	1.63693	0.818464	−	0.574557i	$-0.194826\pi$
$367$	11508.8	1.63693	0.818464	+	0.574557i	$0.194826\pi$
$368$	368.000	0.0521286
$369$	395.457	0.0557905
$370$	420.575	0.0590936
$371$	−2077.18	−0.290679
$372$	6609.36	0.921181
$373$	−3989.01	−0.553735	−0.276868	−	0.960908i	$-0.589296\pi$
$373$	−3989.01	−0.553735	−0.276868	+	0.960908i	$0.589296\pi$
$374$	88.4159	0.0122243
$375$	4857.07	0.668848
$376$	4290.40	0.588459
$377$	2417.34	0.330237
$378$	2647.55	0.360252
$379$	2191.96	0.297080	0.148540	−	0.988906i	$-0.452543\pi$
$379$	2191.96	0.297080	0.148540	+	0.988906i	$0.452543\pi$
$380$	1324.61	0.178818
$381$	−6651.81	−0.894443
$382$	−3998.93	−0.535610
$383$	10659.4	1.42212	0.711060	−	0.703131i	$-0.248215\pi$
$383$	10659.4	1.42212	0.711060	+	0.703131i	$0.248215\pi$
$384$	738.816	0.0981837
$385$	−235.776	−0.0312110
$386$	1759.77	0.232046
$387$	3204.14	0.420867
$388$	2862.11	0.374489
$389$	8828.21	1.15066	0.575332	−	0.817920i	$-0.304873\pi$
$389$	8828.21	1.15066	0.575332	+	0.817920i	$0.304873\pi$
$390$	−879.281	−0.114164
$391$	−169.464	−0.0219185
$392$	−1760.45	−0.226827
$393$	−13670.3	−1.75464
$394$	−5521.61	−0.706027
$395$	177.456	0.0226044
$396$	−151.584	−0.0192358
$397$	−4309.68	−0.544828	−0.272414	−	0.962180i	$-0.587822\pi$
$397$	−4309.68	−0.544828	−0.272414	+	0.962180i	$0.587822\pi$
$398$	6754.39	0.850670
$399$	5980.16	0.750332
$400$	−1799.04	−0.224880
$401$	10650.5	1.32634	0.663169	−	0.748470i	$-0.269211\pi$
$401$	10650.5	1.32634	0.663169	+	0.748470i	$0.269211\pi$
$402$	−7633.27	−0.947047
$403$	6152.48	0.760489
$404$	−1090.18	−0.134253
$405$	3046.57	0.373791
$406$	−2494.27	−0.304898
$407$	356.016	0.0433589
$408$	−340.224	−0.0412834
$409$	−299.234	−0.0361764	−0.0180882	−	0.999836i	$-0.505758\pi$
$409$	−299.234	−0.0361764	−0.0180882	+	0.999836i	$0.505758\pi$
$410$	−443.794	−0.0534571
$411$	−16579.7	−1.98982
$412$	−2439.62	−0.291726
$413$	−550.851	−0.0656310
$414$	290.536	0.0344905
$415$	−2860.07	−0.338302
$416$	687.745	0.0810564
$417$	9450.13	1.10977
$418$	1121.28	0.131205
$419$	−9596.39	−1.11889	−0.559445	−	0.828868i	$-0.688986\pi$
$419$	−9596.39	−1.11889	−0.559445	+	0.828868i	$0.688986\pi$
$420$	907.265	0.105405
$421$	14049.2	1.62641	0.813203	−	0.581980i	$-0.197722\pi$
$421$	14049.2	1.62641	0.813203	+	0.581980i	$0.197722\pi$
$422$	−2144.38	−0.247362
$423$	3387.27	0.389350
$424$	1498.69	0.171657
$425$	828.457	0.0945554
$426$	3338.66	0.379716
$427$	8635.08	0.978643
$428$	−848.959	−0.0958785
$429$	−744.312	−0.0837662
$430$	−3595.78	−0.403264
$431$	−5348.79	−0.597777	−0.298889	−	0.954288i	$-0.596616\pi$
$431$	−5348.79	−0.597777	−0.298889	+	0.954288i	$0.596616\pi$
$432$	−1910.21	−0.212743
$433$	10727.2	1.19057	0.595284	−	0.803516i	$-0.297040\pi$
$433$	10727.2	1.19057	0.595284	+	0.803516i	$0.297040\pi$
$434$	−6348.29	−0.702137
$435$	−2300.81	−0.253599
$436$	−5148.74	−0.565550
$437$	−2149.12	−0.235255
$438$	−7518.79	−0.820233
$439$	−1425.53	−0.154981	−0.0774907	−	0.996993i	$-0.524691\pi$
$439$	−1425.53	−0.154981	−0.0774907	+	0.996993i	$0.524691\pi$
$440$	170.112	0.0184313
$441$	−1389.88	−0.150078
$442$	−316.706	−0.0340818
$443$	−13585.6	−1.45705	−0.728524	−	0.685020i	$-0.759793\pi$
$443$	−13585.6	−1.45705	−0.728524	+	0.685020i	$0.759793\pi$
$444$	−1369.95	−0.146430
$445$	−3353.00	−0.357185
$446$	2989.76	0.317420
$447$	18039.8	1.90885
$448$	−709.632	−0.0748370
$449$	16471.6	1.73128	0.865638	−	0.500670i	$-0.166913\pi$
$449$	16471.6	1.73128	0.865638	+	0.500670i	$0.166913\pi$
$450$	−1420.34	−0.148790
$451$	−375.672	−0.0392233
$452$	−1253.34	−0.130426
$453$	−2138.16	−0.221765
$454$	5428.02	0.561122
$455$	844.549	0.0870177
$456$	−4314.69	−0.443100
$457$	1032.87	0.105724	0.0528619	−	0.998602i	$-0.483166\pi$
$457$	1032.87	0.105724	0.0528619	+	0.998602i	$0.483166\pi$
$458$	5024.00	0.512568
$459$	879.650	0.0894522
$460$	−326.048	−0.0330480
$461$	239.436	0.0241902	0.0120951	−	0.999927i	$-0.496150\pi$
$461$	239.436	0.0241902	0.0120951	+	0.999927i	$0.496150\pi$
$462$	768.000	0.0773389
$463$	−16596.4	−1.66587	−0.832935	−	0.553370i	$-0.813341\pi$
$463$	−16596.4	−1.66587	−0.832935	+	0.553370i	$0.813341\pi$
$464$	1799.62	0.180054
$465$	−5855.90	−0.584002
$466$	−3456.73	−0.343626
$467$	10251.7	1.01583	0.507917	−	0.861406i	$-0.330416\pi$
$467$	10251.7	1.01583	0.507917	+	0.861406i	$0.330416\pi$
$468$	542.975	0.0536304
$469$	7331.75	0.721852
$470$	−3801.30	−0.373066
$471$	−11506.1	−1.12564
$472$	397.439	0.0387577
$473$	−3043.82	−0.295888
$474$	−578.032	−0.0560124
$475$	10506.4	1.01488
$476$	326.785	0.0314668
$477$	1183.22	0.113576
$478$	−3378.95	−0.323326
$479$	−4030.99	−0.384511	−0.192256	−	0.981345i	$-0.561580\pi$
$479$	−4030.99	−0.384511	−0.192256	+	0.981345i	$0.561580\pi$
$480$	−654.592	−0.0622456
$481$	−1275.25	−0.120887
$482$	6310.02	0.596293
$483$	−1472.00	−0.138671
$484$	−5180.00	−0.486476
$485$	−2535.84	−0.237415
$486$	−3476.74	−0.324502
$487$	6054.93	0.563399	0.281699	−	0.959503i	$-0.409102\pi$
$487$	6054.93	0.563399	0.281699	+	0.959503i	$0.409102\pi$
$488$	−6230.21	−0.577927
$489$	9939.97	0.919225
$490$	1559.76	0.143802
$491$	−19864.4	−1.82580	−0.912902	−	0.408178i	$-0.866164\pi$
$491$	−19864.4	−1.82580	−0.912902	+	0.408178i	$0.866164\pi$
$492$	1445.59	0.132463
$493$	−828.722	−0.0757075
$494$	−4016.43	−0.365805
$495$	134.304	0.0121950
$496$	4580.29	0.414639
$497$	−3206.79	−0.289425
$498$	9316.20	0.838291
$499$	−12128.9	−1.08811	−0.544053	−	0.839051i	$-0.683111\pi$
$499$	−12128.9	−1.08811	−0.544053	+	0.839051i	$0.683111\pi$
$500$	3365.95	0.301060
$501$	−10798.7	−0.962977
$502$	12683.9	1.12771
$503$	−18351.3	−1.62673	−0.813363	−	0.581756i	$-0.802366\pi$
$503$	−18351.3	−1.62673	−0.813363	+	0.581756i	$0.802366\pi$
$504$	−560.255	−0.0495154
$505$	965.899	0.0851127
$506$	−276.000	−0.0242484
$507$	−10015.0	−0.877278
$508$	−4609.71	−0.402604
$509$	−10876.1	−0.947106	−0.473553	−	0.880765i	$-0.657029\pi$
$509$	−10876.1	−0.947106	−0.473553	+	0.880765i	$0.657029\pi$
$510$	301.439	0.0261724
$511$	7221.80	0.625193
$512$	512.000	0.0441942
$513$	11155.6	0.960103
$514$	−11913.1	−1.02230
$515$	2161.50	0.184946
$516$	11712.6	0.999264
$517$	−3217.80	−0.273731
$518$	1315.84	0.111611
$519$	−4043.35	−0.341972
$520$	−609.342	−0.0513874
$521$	4317.61	0.363067	0.181533	−	0.983385i	$-0.441894\pi$
$521$	4317.61	0.363067	0.181533	+	0.983385i	$0.441894\pi$
$522$	1420.80	0.119132
$523$	−11789.9	−0.985733	−0.492866	−	0.870105i	$-0.664051\pi$
$523$	−11789.9	−0.985733	−0.492866	+	0.870105i	$0.664051\pi$
$524$	−9473.49	−0.789793
$525$	7196.16	0.598221
$526$	−14295.4	−1.18499
$527$	−2109.22	−0.174344
$528$	−554.112	−0.0456717
$529$	529.000	0.0434783
$530$	−1327.84	−0.108826
$531$	313.778	0.0256437
$532$	4144.26	0.337737
$533$	1345.66	0.109356
$534$	10921.8	0.885082
$535$	752.179	0.0607842
$536$	−5289.86	−0.426282
$537$	21960.0	1.76470
$538$	14865.4	1.19125
$539$	1320.34	0.105512
$540$	1692.45	0.134873
$541$	8944.99	0.710860	0.355430	−	0.934703i	$-0.384334\pi$
$541$	8944.99	0.710860	0.355430	+	0.934703i	$0.384334\pi$
$542$	6472.13	0.512918
$543$	21126.1	1.66963
$544$	−235.776	−0.0185823
$545$	4561.79	0.358542
$546$	−2750.98	−0.215625
$547$	16376.3	1.28007	0.640036	−	0.768345i	$-0.278919\pi$
$547$	16376.3	1.28007	0.640036	+	0.768345i	$0.278919\pi$
$548$	−11489.8	−0.895654
$549$	−4918.75	−0.382381
$550$	1349.28	0.104606
$551$	−10509.8	−0.812579
$552$	1062.05	0.0818909
$553$	555.199	0.0426934
$554$	10875.5	0.834039
$555$	1213.78	0.0928325
$556$	6548.94	0.499527
$557$	18239.2	1.38747	0.693736	−	0.720230i	$-0.255964\pi$
$557$	18239.2	1.38747	0.693736	+	0.720230i	$0.255964\pi$
$558$	3616.14	0.274343
$559$	10903.0	0.824951
$560$	628.735	0.0474445
$561$	255.168	0.0192036
$562$	489.235	0.0367209
$563$	−286.757	−0.0214660	−0.0107330	−	0.999942i	$-0.503416\pi$
$563$	−286.757	−0.0214660	−0.0107330	+	0.999942i	$0.503416\pi$
$564$	12382.1	0.924433
$565$	1110.46	0.0826860
$566$	−2101.51	−0.156065
$567$	9531.70	0.705985
$568$	2313.70	0.170916
$569$	13951.6	1.02791	0.513955	−	0.857817i	$-0.328180\pi$
$569$	13951.6	1.02791	0.513955	+	0.857817i	$0.328180\pi$
$570$	3822.82	0.280913
$571$	−2020.68	−0.148096	−0.0740481	−	0.997255i	$-0.523592\pi$
$571$	−2020.68	−0.148096	−0.0740481	+	0.997255i	$0.523592\pi$
$572$	−515.808	−0.0377046
$573$	−11540.9	−0.841411
$574$	−1388.48	−0.100965
$575$	−2586.12	−0.187563
$576$	404.224	0.0292408
$577$	−21630.4	−1.56064	−0.780318	−	0.625383i	$-0.784943\pi$
$577$	−21630.4	−1.56064	−0.780318	+	0.625383i	$0.784943\pi$
$578$	−9717.43	−0.699293
$579$	5078.70	0.364531
$580$	−1594.46	−0.114149
$581$	−8948.20	−0.638957
$582$	8260.06	0.588300
$583$	−1124.02	−0.0798491
$584$	−5210.53	−0.369201
$585$	−481.076	−0.0340001
$586$	11286.9	0.795663
$587$	1510.94	0.106240	0.0531202	−	0.998588i	$-0.483083\pi$
$587$	1510.94	0.106240	0.0531202	+	0.998588i	$0.483083\pi$
$588$	−5080.66	−0.356331
$589$	−26748.9	−1.87126
$590$	−352.131	−0.0245712
$591$	−15935.4	−1.10913
$592$	−949.377	−0.0659107
$593$	−19464.5	−1.34791	−0.673957	−	0.738771i	$-0.735407\pi$
$593$	−19464.5	−1.34791	−0.673957	+	0.738771i	$0.735407\pi$
$594$	1432.66	0.0989606
$595$	−289.532	−0.0199490
$596$	12501.6	0.859204
$597$	19493.2	1.33635
$598$	988.633	0.0676057
$599$	−11515.5	−0.785497	−0.392748	−	0.919646i	$-0.628476\pi$
$599$	−11515.5	−0.785497	−0.392748	+	0.919646i	$0.628476\pi$
$600$	−5192.03	−0.353273
$601$	372.589	0.0252882	0.0126441	−	0.999920i	$-0.495975\pi$
$601$	372.589	0.0252882	0.0126441	+	0.999920i	$0.495975\pi$
$602$	−11250.0	−0.761653
$603$	−4176.35	−0.282046
$604$	−1481.74	−0.0998200
$605$	4589.48	0.308412
$606$	−3146.25	−0.210904
$607$	−19564.0	−1.30820	−0.654099	−	0.756409i	$-0.726952\pi$
$607$	−19564.0	−1.30820	−0.654099	+	0.756409i	$0.726952\pi$
$608$	−2990.08	−0.199447
$609$	−7198.47	−0.478976
$610$	5519.97	0.366389
$611$	11526.2	0.763173
$612$	−186.145	−0.0122949
$613$	−14060.7	−0.926435	−0.463217	−	0.886245i	$-0.653305\pi$
$613$	−14060.7	−0.926435	−0.463217	+	0.886245i	$0.653305\pi$
$614$	11753.1	0.772502
$615$	−1280.79	−0.0839779
$616$	532.224	0.0348116
$617$	−282.447	−0.0184293	−0.00921465	−	0.999958i	$-0.502933\pi$
$617$	−282.447	−0.0184293	−0.00921465	+	0.999958i	$0.502933\pi$
$618$	−7040.74	−0.458285
$619$	6071.66	0.394250	0.197125	−	0.980378i	$-0.436840\pi$
$619$	6071.66	0.394250	0.197125	+	0.980378i	$0.436840\pi$
$620$	−4058.14	−0.262869
$621$	−2745.93	−0.177440
$622$	17496.0	1.12785
$623$	−10490.4	−0.674622
$624$	1984.83	0.127335
$625$	11072.8	0.708657
$626$	−10058.8	−0.642223
$627$	3236.02	0.206115
$628$	−7973.76	−0.506669
$629$	437.188	0.0277135
$630$	496.387	0.0313913
$631$	3977.43	0.250933	0.125467	−	0.992098i	$-0.459957\pi$
$631$	3977.43	0.250933	0.125467	+	0.992098i	$0.459957\pi$
$632$	−400.576	−0.0252121
$633$	−6188.69	−0.388591
$634$	−14399.3	−0.902000
$635$	4084.21	0.255239
$636$	4325.22	0.269664
$637$	−4729.45	−0.294172
$638$	−1349.71	−0.0837549
$639$	1826.66	0.113086
$640$	−453.632	−0.0280178
$641$	18024.3	1.11064	0.555318	−	0.831638i	$-0.312597\pi$
$641$	18024.3	1.11064	0.555318	+	0.831638i	$0.312597\pi$
$642$	−2450.10	−0.150619
$643$	9926.77	0.608824	0.304412	−	0.952541i	$-0.401540\pi$
$643$	9926.77	0.608824	0.304412	+	0.952541i	$0.401540\pi$
$644$	−1020.10	−0.0624184
$645$	−10377.4	−0.633504
$646$	1376.93	0.0838616
$647$	2274.51	0.138207	0.0691036	−	0.997609i	$-0.477986\pi$
$647$	2274.51	0.138207	0.0691036	+	0.997609i	$0.477986\pi$
$648$	−6877.12	−0.416912
$649$	−298.079	−0.0180287
$650$	−4833.13	−0.291647
$651$	−18321.2	−1.10302
$652$	6888.40	0.413759
$653$	1794.68	0.107552	0.0537758	−	0.998553i	$-0.482874\pi$
$653$	1794.68	0.107552	0.0537758	+	0.998553i	$0.482874\pi$
$654$	−14859.3	−0.888445
$655$	8393.52	0.500705
$656$	1001.79	0.0596240
$657$	−4113.72	−0.244279
$658$	−11893.0	−0.704616
$659$	4081.99	0.241292	0.120646	−	0.992696i	$-0.461503\pi$
$659$	4081.99	0.241292	0.120646	+	0.992696i	$0.461503\pi$
$660$	490.944	0.0289545
$661$	−15350.1	−0.903253	−0.451626	−	0.892207i	$-0.649156\pi$
$661$	−15350.1	−0.903253	−0.451626	+	0.892207i	$0.649156\pi$
$662$	−1544.18	−0.0906593
$663$	−914.014	−0.0535405
$664$	6456.13	0.377329
$665$	−3671.81	−0.214116
$666$	−749.534	−0.0436094
$667$	2586.95	0.150176
$668$	−7483.52	−0.433452
$669$	8628.45	0.498647
$670$	4686.82	0.270250
$671$	4672.66	0.268831
$672$	−2048.00	−0.117564
$673$	26310.5	1.50698	0.753488	−	0.657461i	$-0.228370\pi$
$673$	26310.5	1.50698	0.753488	+	0.657461i	$0.228370\pi$
$674$	−22139.2	−1.26524
$675$	13424.0	0.765467
$676$	−6940.37	−0.394878
$677$	−22299.1	−1.26591	−0.632957	−	0.774187i	$-0.718159\pi$
$677$	−22299.1	−1.26591	−0.632957	+	0.774187i	$0.718159\pi$
$678$	−3617.15	−0.204891
$679$	−7933.79	−0.448411
$680$	208.897	0.0117807
$681$	15665.3	0.881489
$682$	−3435.22	−0.192876
$683$	24001.7	1.34466	0.672328	−	0.740253i	$-0.265294\pi$
$683$	24001.7	1.34466	0.672328	+	0.740253i	$0.265294\pi$
$684$	−2360.67	−0.131963
$685$	10179.9	0.567818
$686$	12486.3	0.694943
$687$	14499.3	0.805214
$688$	8116.87	0.449786
$689$	4026.23	0.222623
$690$	−940.976	−0.0519164
$691$	9627.58	0.530030	0.265015	−	0.964244i	$-0.414623\pi$
$691$	9627.58	0.530030	0.265015	+	0.964244i	$0.414623\pi$
$692$	−2802.05	−0.153927
$693$	420.192	0.0230328
$694$	−2405.98	−0.131599
$695$	−5802.37	−0.316686
$696$	5193.70	0.282854
$697$	−461.324	−0.0250702
$698$	−9147.37	−0.496036
$699$	−9976.12	−0.539816
$700$	4986.94	0.269270
$701$	11750.7	0.633121	0.316561	−	0.948572i	$-0.397472\pi$
$701$	11750.7	0.633121	0.316561	+	0.948572i	$0.397472\pi$
$702$	−5131.78	−0.275907
$703$	5544.36	0.297453
$704$	−384.000	−0.0205576
$705$	−10970.6	−0.586064
$706$	−1949.48	−0.103923
$707$	3021.98	0.160754
$708$	1147.01	0.0608860
$709$	1045.77	0.0553946	0.0276973	−	0.999616i	$-0.491183\pi$
$709$	1045.77	0.0553946	0.0276973	+	0.999616i	$0.491183\pi$
$710$	−2049.94	−0.108356
$711$	−316.255	−0.0166814
$712$	7568.83	0.398390
$713$	6584.17	0.345833
$714$	943.103	0.0494324
$715$	457.007	0.0239036
$716$	15218.3	0.794323
$717$	−9751.66	−0.507925
$718$	−9744.92	−0.506514
$719$	9367.97	0.485906	0.242953	−	0.970038i	$-0.421884\pi$
$719$	9367.97	0.485906	0.242953	+	0.970038i	$0.421884\pi$
$720$	−358.143	−0.0185378
$721$	6762.62	0.349311
$722$	3744.08	0.192992
$723$	18210.7	0.936741
$724$	14640.4	0.751529
$725$	−12646.8	−0.647849
$726$	−14949.5	−0.764225
$727$	−24447.9	−1.24721	−0.623605	−	0.781740i	$-0.714332\pi$
$727$	−24447.9	−1.24721	−0.623605	+	0.781740i	$0.714332\pi$
$728$	−1906.43	−0.0970563
$729$	13176.4	0.669432
$730$	4616.53	0.234062
$731$	−3737.81	−0.189122
$732$	−17980.4	−0.907888
$733$	24144.2	1.21662	0.608312	−	0.793698i	$-0.291847\pi$
$733$	24144.2	1.21662	0.608312	+	0.793698i	$0.291847\pi$
$734$	23017.5	1.15748
$735$	4501.47	0.225904
$736$	736.000	0.0368605
$737$	3967.39	0.198291
$738$	790.915	0.0394498
$739$	10006.7	0.498108	0.249054	−	0.968490i	$-0.419880\pi$
$739$	10006.7	0.498108	0.249054	+	0.968490i	$0.419880\pi$
$740$	841.149	0.0417855
$741$	−11591.4	−0.574658
$742$	−4154.37	−0.205541
$743$	−7313.96	−0.361135	−0.180567	−	0.983563i	$-0.557793\pi$
$743$	−7313.96	−0.361135	−0.180567	+	0.983563i	$0.557793\pi$
$744$	13218.7	0.651373
$745$	−11076.4	−0.544710
$746$	−7978.03	−0.391550
$747$	5097.12	0.249657
$748$	176.832	0.00864386
$749$	2353.32	0.114804
$750$	9714.15	0.472947
$751$	−3297.61	−0.160228	−0.0801141	−	0.996786i	$-0.525528\pi$
$751$	−3297.61	−0.160228	−0.0801141	+	0.996786i	$0.525528\pi$
$752$	8580.80	0.416103
$753$	36605.6	1.77156
$754$	4834.68	0.233513
$755$	1312.83	0.0632830
$756$	5295.10	0.254737
$757$	−23745.7	−1.14009	−0.570047	−	0.821612i	$-0.693075\pi$
$757$	−23745.7	−1.14009	−0.570047	+	0.821612i	$0.693075\pi$
$758$	4383.92	0.210068
$759$	−796.536	−0.0380928
$760$	2649.21	0.126444
$761$	25723.6	1.22533	0.612666	−	0.790342i	$-0.290097\pi$
$761$	25723.6	1.22533	0.612666	+	0.790342i	$0.290097\pi$
$762$	−13303.6	−0.632467
$763$	14272.3	0.677185
$764$	−7997.85	−0.378733
$765$	164.925	0.00779459
$766$	21318.9	1.00559
$767$	1067.72	0.0502649
$768$	1477.63	0.0694264
$769$	−36423.8	−1.70803	−0.854016	−	0.520246i	$-0.825840\pi$
$769$	−36423.8	−1.70803	−0.854016	+	0.520246i	$0.825840\pi$
$770$	−471.551	−0.0220695
$771$	−34381.1	−1.60597
$772$	3519.54	0.164082
$773$	−20401.3	−0.949265	−0.474633	−	0.880184i	$-0.657419\pi$
$773$	−20401.3	−0.949265	−0.474633	+	0.880184i	$0.657419\pi$
$774$	6408.27	0.297598
$775$	−32188.0	−1.49191
$776$	5724.23	0.264804
$777$	3797.51	0.175334
$778$	17656.4	0.813642
$779$	−5850.46	−0.269082
$780$	−1758.56	−0.0807265
$781$	−1735.27	−0.0795044
$782$	−338.927	−0.0154987
$783$	−13428.3	−0.612884
$784$	−3520.90	−0.160391
$785$	7064.76	0.321213
$786$	−27340.5	−1.24072
$787$	23639.8	1.07073	0.535367	−	0.844620i	$-0.320173\pi$
$787$	23639.8	1.07073	0.535367	+	0.844620i	$0.320173\pi$
$788$	−11043.2	−0.499236
$789$	−41256.4	−1.86155
$790$	354.911	0.0159838
$791$	3474.27	0.156171
$792$	−303.168	−0.0136018
$793$	−16737.5	−0.749515
$794$	−8619.36	−0.385251
$795$	−3832.15	−0.170959
$796$	13508.8	0.601515
$797$	−41015.8	−1.82291	−0.911453	−	0.411405i	$-0.865038\pi$
$797$	−41015.8	−1.82291	−0.911453	+	0.411405i	$0.865038\pi$
$798$	11960.3	0.530565
$799$	−3951.45	−0.174959
$800$	−3598.08	−0.159014
$801$	5975.60	0.263592
$802$	21301.0	0.937862
$803$	3907.90	0.171739
$804$	−15266.5	−0.669663
$805$	903.807	0.0395714
$806$	12305.0	0.537747
$807$	42901.7	1.87139
$808$	−2180.36	−0.0949315
$809$	−30619.8	−1.33070	−0.665349	−	0.746532i	$-0.731717\pi$
$809$	−30619.8	−1.33070	−0.665349	+	0.746532i	$0.731717\pi$
$810$	6093.14	0.264310
$811$	−7000.16	−0.303093	−0.151547	−	0.988450i	$-0.548425\pi$
$811$	−7000.16	−0.303093	−0.151547	+	0.988450i	$0.548425\pi$
$812$	−4988.54	−0.215595
$813$	18678.6	0.805764
$814$	712.033	0.0306594
$815$	−6103.13	−0.262311
$816$	−680.449	−0.0291918
$817$	−47402.5	−2.02987
$818$	−598.468	−0.0255806
$819$	−1505.13	−0.0642166
$820$	−887.588	−0.0377999
$821$	31972.1	1.35912	0.679558	−	0.733621i	$-0.262171\pi$
$821$	31972.1	1.35912	0.679558	+	0.733621i	$0.262171\pi$
$822$	−33159.5	−1.40702
$823$	6616.25	0.280228	0.140114	−	0.990135i	$-0.455253\pi$
$823$	6616.25	0.280228	0.140114	+	0.990135i	$0.455253\pi$
$824$	−4879.23	−0.206282
$825$	3894.02	0.164330
$826$	−1101.70	−0.0464081
$827$	−18261.5	−0.767852	−0.383926	−	0.923364i	$-0.625428\pi$
$827$	−18261.5	−0.767852	−0.383926	+	0.923364i	$0.625428\pi$
$828$	581.073	0.0243885
$829$	16935.3	0.709513	0.354757	−	0.934959i	$-0.384564\pi$
$829$	16935.3	0.709513	0.354757	+	0.934959i	$0.384564\pi$
$830$	−5720.14	−0.239215
$831$	31386.8	1.31023
$832$	1375.49	0.0573155
$833$	1621.37	0.0674396
$834$	18900.3	0.784727
$835$	6630.41	0.274796
$836$	2242.56	0.0927758
$837$	−34177.0	−1.41139
$838$	−19192.8	−0.791174
$839$	11971.2	0.492598	0.246299	−	0.969194i	$-0.420785\pi$
$839$	11971.2	0.492598	0.246299	+	0.969194i	$0.420785\pi$
$840$	1814.53	0.0745324
$841$	−11738.1	−0.481288
$842$	28098.4	1.15004
$843$	1411.93	0.0576863
$844$	−4288.77	−0.174912
$845$	6149.18	0.250341
$846$	6774.55	0.275312
$847$	14359.0	0.582503
$848$	2997.38	0.121380
$849$	−6064.95	−0.245169
$850$	1656.91	0.0668608
$851$	−1364.73	−0.0549734
$852$	6677.33	0.268499
$853$	14844.9	0.595872	0.297936	−	0.954586i	$-0.403702\pi$
$853$	14844.9	0.595872	0.297936	+	0.954586i	$0.403702\pi$
$854$	17270.2	0.692005
$855$	2091.56	0.0836605
$856$	−1697.92	−0.0677963
$857$	45234.9	1.80303	0.901514	−	0.432751i	$-0.142457\pi$
$857$	45234.9	1.80303	0.901514	+	0.432751i	$0.142457\pi$
$858$	−1488.62	−0.0592317
$859$	−43687.6	−1.73528	−0.867639	−	0.497195i	$-0.834363\pi$
$859$	−43687.6	−1.73528	−0.867639	+	0.497195i	$0.834363\pi$
$860$	−7191.55	−0.285151
$861$	−4007.16	−0.158611
$862$	−10697.6	−0.422692
$863$	22267.6	0.878331	0.439165	−	0.898406i	$-0.355274\pi$
$863$	22267.6	0.878331	0.439165	+	0.898406i	$0.355274\pi$
$864$	−3820.42	−0.150432
$865$	2482.62	0.0975855
$866$	21454.4	0.841858
$867$	−28044.5	−1.09855
$868$	−12696.6	−0.496486
$869$	300.432	0.0117278
$870$	−4601.62	−0.179321
$871$	−14211.2	−0.552846
$872$	−10297.5	−0.399904
$873$	4519.28	0.175206
$874$	−4298.24	−0.166350
$875$	−9330.43	−0.360487
$876$	−15037.6	−0.579992
$877$	−17550.1	−0.675743	−0.337871	−	0.941192i	$-0.609707\pi$
$877$	−17550.1	−0.675743	−0.337871	+	0.941192i	$0.609707\pi$
$878$	−2851.06	−0.109588
$879$	32574.1	1.24994
$880$	340.224	0.0130329
$881$	−28114.7	−1.07515	−0.537577	−	0.843215i	$-0.680660\pi$
$881$	−28114.7	−1.07515	−0.537577	+	0.843215i	$0.680660\pi$
$882$	−2779.75	−0.106121
$883$	46811.6	1.78407	0.892036	−	0.451964i	$-0.149277\pi$
$883$	46811.6	1.78407	0.892036	+	0.451964i	$0.149277\pi$
$884$	−633.412	−0.0240995
$885$	−1016.25	−0.0385999
$886$	−27171.2	−1.03029
$887$	1604.14	0.0607234	0.0303617	−	0.999539i	$-0.490334\pi$
$887$	1604.14	0.0607234	0.0303617	+	0.999539i	$0.490334\pi$
$888$	−2739.90	−0.103542
$889$	12778.1	0.482075
$890$	−6705.99	−0.252568
$891$	5157.84	0.193933
$892$	5979.52	0.224450
$893$	−50111.9	−1.87786
$894$	36079.6	1.34976
$895$	−13483.4	−0.503578
$896$	−1419.26	−0.0529178
$897$	2853.20	0.106204
$898$	32943.2	1.22420
$899$	32198.3	1.19452
$900$	−2840.69	−0.105211
$901$	−1380.29	−0.0510368
$902$	−751.343	−0.0277350
$903$	−32467.5	−1.19651
$904$	−2506.69	−0.0922248
$905$	−12971.4	−0.476447
$906$	−4276.31	−0.156811
$907$	−1200.10	−0.0439345	−0.0219672	−	0.999759i	$-0.506993\pi$
$907$	−1200.10	−0.0439345	−0.0219672	+	0.999759i	$0.506993\pi$
$908$	10856.0	0.396773
$909$	−1721.39	−0.0628108
$910$	1689.10	0.0615308
$911$	34847.5	1.26734	0.633672	−	0.773602i	$-0.281547\pi$
$911$	34847.5	1.26734	0.633672	+	0.773602i	$0.281547\pi$
$912$	−8629.38	−0.313319
$913$	−4842.10	−0.175520
$914$	2065.75	0.0747580
$915$	15930.6	0.575575
$916$	10048.0	0.362441
$917$	26260.5	0.945692
$918$	1759.30	0.0632522
$919$	−44895.1	−1.61148	−0.805741	−	0.592268i	$-0.798233\pi$
$919$	−44895.1	−1.61148	−0.805741	+	0.592268i	$0.798233\pi$
$920$	−652.097	−0.0233685
$921$	33919.4	1.21355
$922$	478.873	0.0171050
$923$	6215.75	0.221662
$924$	1536.00	0.0546869
$925$	6671.75	0.237152
$926$	−33192.7	−1.17795
$927$	−3852.16	−0.136485
$928$	3599.23	0.127318
$929$	17783.9	0.628063	0.314032	−	0.949413i	$-0.398320\pi$
$929$	17783.9	0.628063	0.314032	+	0.949413i	$0.398320\pi$
$930$	−11711.8	−0.412952
$931$	20562.0	0.723839
$932$	−6913.46	−0.242981
$933$	50493.5	1.77179
$934$	20503.5	0.718303
$935$	−156.673	−0.00547995
$936$	1085.95	0.0379224
$937$	−25058.9	−0.873682	−0.436841	−	0.899539i	$-0.643903\pi$
$937$	−25058.9	−0.873682	−0.436841	+	0.899539i	$0.643903\pi$
$938$	14663.5	0.510426
$939$	−29029.8	−1.00889
$940$	−7602.60	−0.263797
$941$	29903.4	1.03594	0.517972	−	0.855398i	$-0.326687\pi$
$941$	29903.4	1.03594	0.517972	+	0.855398i	$0.326687\pi$
$942$	−23012.3	−0.795946
$943$	1440.07	0.0497299
$944$	794.878	0.0274058
$945$	−4691.47	−0.161496
$946$	−6087.65	−0.209225
$947$	17921.2	0.614952	0.307476	−	0.951556i	$-0.400516\pi$
$947$	17921.2	0.614952	0.307476	+	0.951556i	$0.400516\pi$
$948$	−1156.06	−0.0396068
$949$	−13998.1	−0.478817
$950$	21012.8	0.717627
$951$	−41556.3	−1.41699
$952$	653.571	0.0222504
$953$	31122.3	1.05787	0.528935	−	0.848662i	$-0.322592\pi$
$953$	31122.3	1.05787	0.528935	+	0.848662i	$0.322592\pi$
$954$	2366.43	0.0803103
$955$	7086.11	0.240106
$956$	−6757.91	−0.228626
$957$	−3895.27	−0.131574
$958$	−8061.99	−0.271890
$959$	31849.6	1.07245
$960$	−1309.18	−0.0440143
$961$	52158.4	1.75081
$962$	−2550.50	−0.0854798
$963$	−1340.51	−0.0448570
$964$	12620.0	0.421643
$965$	−3118.32	−0.104023
$966$	−2944.00	−0.0980555
$967$	6627.78	0.220409	0.110204	−	0.993909i	$-0.464849\pi$
$967$	6627.78	0.220409	0.110204	+	0.993909i	$0.464849\pi$
$968$	−10360.0	−0.343991
$969$	3973.82	0.131742
$970$	−5071.67	−0.167878
$971$	38645.1	1.27722	0.638609	−	0.769531i	$-0.279510\pi$
$971$	38645.1	1.27722	0.638609	+	0.769531i	$0.279510\pi$
$972$	−6953.47	−0.229457
$973$	−18153.7	−0.598130
$974$	12109.9	0.398383
$975$	−13948.4	−0.458161
$976$	−12460.4	−0.408656
$977$	−14137.0	−0.462930	−0.231465	−	0.972843i	$-0.574352\pi$
$977$	−14137.0	−0.462930	−0.231465	+	0.972843i	$0.574352\pi$
$978$	19879.9	0.649990
$979$	−5676.62	−0.185317
$980$	3119.52	0.101683
$981$	−8129.87	−0.264594
$982$	−39728.9	−1.29104
$983$	32966.5	1.06965	0.534825	−	0.844963i	$-0.320377\pi$
$983$	32966.5	1.06965	0.534825	+	0.844963i	$0.320377\pi$
$984$	2891.17	0.0936658
$985$	9784.30	0.316501
$986$	−1657.44	−0.0535333
$987$	−34323.2	−1.10691
$988$	−8032.86	−0.258663
$989$	11668.0	0.375147
$990$	268.607	0.00862313
$991$	47592.2	1.52555	0.762774	−	0.646666i	$-0.223837\pi$
$991$	47592.2	1.52555	0.762774	+	0.646666i	$0.223837\pi$
$992$	9160.58	0.293194
$993$	−4456.52	−0.142420
$994$	−6413.57	−0.204654
$995$	−11968.8	−0.381343
$996$	18632.4	0.592761
$997$	11153.1	0.354285	0.177142	−	0.984185i	$-0.443315\pi$
$997$	11153.1	0.354285	0.177142	+	0.984185i	$0.443315\pi$
$998$	−24257.8	−0.769407
$999$	7084.02	0.224353

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	46.4.a.d.1.2	✓	2
3.2	odd	2		414.4.a.f.1.2		2
4.3	odd	2		368.4.a.f.1.1		2
5.2	odd	4		1150.4.b.j.599.3		4
5.3	odd	4		1150.4.b.j.599.2		4
5.4	even	2		1150.4.a.j.1.1		2
7.6	odd	2		2254.4.a.f.1.1		2
8.3	odd	2		1472.4.a.n.1.2		2
8.5	even	2		1472.4.a.k.1.1		2
23.22	odd	2		1058.4.a.j.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
46.4.a.d.1.2	✓	2	1.1	even	1	trivial
368.4.a.f.1.1		2	4.3	odd	2
414.4.a.f.1.2		2	3.2	odd	2
1058.4.a.j.1.2		2	23.22	odd	2
1150.4.a.j.1.1		2	5.4	even	2
1150.4.b.j.599.2		4	5.3	odd	4
1150.4.b.j.599.3		4	5.2	odd	4
1472.4.a.k.1.1		2	8.5	even	2
1472.4.a.n.1.2		2	8.3	odd	2
2254.4.a.f.1.1		2	7.6	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:	\( N \)	\(=\)	\( 46 = 2 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	46.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +5.77200 q^{3} +4.00000 q^{4} -3.54400 q^{5} +11.5440 q^{6} -11.0880 q^{7} +8.00000 q^{8} +6.31601 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} +5.77200 q^{3} +4.00000 q^{4} -3.54400 q^{5} +11.5440 q^{6} -11.0880 q^{7} +8.00000 q^{8} +6.31601 q^{9} -7.08801 q^{10} -6.00000 q^{11} +23.0880 q^{12} +21.4920 q^{13} -22.1760 q^{14} -20.4560 q^{15} +16.0000 q^{16} -7.36799 q^{17} +12.6320 q^{18} -93.4400 q^{19} -14.1760 q^{20} -64.0000 q^{21} -12.0000 q^{22} +23.0000 q^{23} +46.1760 q^{24} -112.440 q^{25} +42.9840 q^{26} -119.388 q^{27} -44.3520 q^{28} +112.476 q^{29} -40.9120 q^{30} +286.268 q^{31} +32.0000 q^{32} -34.6320 q^{33} -14.7360 q^{34} +39.2959 q^{35} +25.2640 q^{36} -59.3361 q^{37} -186.880 q^{38} +124.052 q^{39} -28.3520 q^{40} +62.6119 q^{41} -128.000 q^{42} +507.304 q^{43} -24.0000 q^{44} -22.3839 q^{45} +46.0000 q^{46} +536.300 q^{47} +92.3520 q^{48} -220.056 q^{49} -224.880 q^{50} -42.5280 q^{51} +85.9681 q^{52} +187.336 q^{53} -238.776 q^{54} +21.2640 q^{55} -88.7041 q^{56} -539.336 q^{57} +224.952 q^{58} +49.6799 q^{59} -81.8240 q^{60} -778.776 q^{61} +572.536 q^{62} -70.0319 q^{63} +64.0000 q^{64} -76.1678 q^{65} -69.2640 q^{66} -661.232 q^{67} -29.4720 q^{68} +132.756 q^{69} +78.5919 q^{70} +289.212 q^{71} +50.5280 q^{72} -651.316 q^{73} -118.672 q^{74} -649.004 q^{75} -373.760 q^{76} +66.5280 q^{77} +248.104 q^{78} -50.0720 q^{79} -56.7041 q^{80} -859.640 q^{81} +125.224 q^{82} +807.016 q^{83} -256.000 q^{84} +26.1122 q^{85} +1014.61 q^{86} +649.212 q^{87} -48.0000 q^{88} +946.104 q^{89} -44.7679 q^{90} -238.304 q^{91} +92.0000 q^{92} +1652.34 q^{93} +1072.60 q^{94} +331.152 q^{95} +184.704 q^{96} +715.529 q^{97} -440.112 q^{98} -37.8960 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{2} + 3 q^{3} + 8 q^{4} + 10 q^{5} + 6 q^{6} + 12 q^{7} + 16 q^{8} - 13 q^{9}+O(q^{10}) \) 2 * q + 4 * q^2 + 3 * q^3 + 8 * q^4 + 10 * q^5 + 6 * q^6 + 12 * q^7 + 16 * q^8 - 13 * q^9	\( 2 q + 4 q^{2} + 3 q^{3} + 8 q^{4} + 10 q^{5} + 6 q^{6} + 12 q^{7} + 16 q^{8} - 13 q^{9} + 20 q^{10} - 12 q^{11} + 12 q^{12} - 51 q^{13} + 24 q^{14} - 58 q^{15} + 32 q^{16} - 66 q^{17} - 26 q^{18} - 16 q^{19} + 40 q^{20} - 128 q^{21} - 24 q^{22} + 46 q^{23} + 24 q^{24} - 54 q^{25} - 102 q^{26} + 9 q^{27} + 48 q^{28} - 57 q^{29} - 116 q^{30} - 17 q^{31} + 64 q^{32} - 18 q^{33} - 132 q^{34} + 352 q^{35} - 52 q^{36} + 206 q^{37} - 32 q^{38} + 325 q^{39} + 80 q^{40} + 373 q^{41} - 256 q^{42} + 314 q^{43} - 48 q^{44} - 284 q^{45} + 92 q^{46} + 859 q^{47} + 48 q^{48} - 30 q^{49} - 108 q^{50} + 120 q^{51} - 204 q^{52} + 50 q^{53} + 18 q^{54} - 60 q^{55} + 96 q^{56} - 754 q^{57} - 114 q^{58} + 612 q^{59} - 232 q^{60} - 1062 q^{61} - 34 q^{62} - 516 q^{63} + 128 q^{64} - 1058 q^{65} - 36 q^{66} - 844 q^{67} - 264 q^{68} + 69 q^{69} + 704 q^{70} + 399 q^{71} - 104 q^{72} - 1277 q^{73} + 412 q^{74} - 811 q^{75} - 64 q^{76} - 72 q^{77} + 650 q^{78} + 122 q^{79} + 160 q^{80} - 694 q^{81} + 746 q^{82} + 1802 q^{83} - 512 q^{84} - 768 q^{85} + 628 q^{86} + 1119 q^{87} - 96 q^{88} + 2046 q^{89} - 568 q^{90} - 1912 q^{91} + 184 q^{92} + 2493 q^{93} + 1718 q^{94} + 1380 q^{95} + 96 q^{96} - 910 q^{97} - 60 q^{98} + 78 q^{99}+O(q^{100}) \) 2 * q + 4 * q^2 + 3 * q^3 + 8 * q^4 + 10 * q^5 + 6 * q^6 + 12 * q^7 + 16 * q^8 - 13 * q^9 + 20 * q^10 - 12 * q^11 + 12 * q^12 - 51 * q^13 + 24 * q^14 - 58 * q^15 + 32 * q^16 - 66 * q^17 - 26 * q^18 - 16 * q^19 + 40 * q^20 - 128 * q^21 - 24 * q^22 + 46 * q^23 + 24 * q^24 - 54 * q^25 - 102 * q^26 + 9 * q^27 + 48 * q^28 - 57 * q^29 - 116 * q^30 - 17 * q^31 + 64 * q^32 - 18 * q^33 - 132 * q^34 + 352 * q^35 - 52 * q^36 + 206 * q^37 - 32 * q^38 + 325 * q^39 + 80 * q^40 + 373 * q^41 - 256 * q^42 + 314 * q^43 - 48 * q^44 - 284 * q^45 + 92 * q^46 + 859 * q^47 + 48 * q^48 - 30 * q^49 - 108 * q^50 + 120 * q^51 - 204 * q^52 + 50 * q^53 + 18 * q^54 - 60 * q^55 + 96 * q^56 - 754 * q^57 - 114 * q^58 + 612 * q^59 - 232 * q^60 - 1062 * q^61 - 34 * q^62 - 516 * q^63 + 128 * q^64 - 1058 * q^65 - 36 * q^66 - 844 * q^67 - 264 * q^68 + 69 * q^69 + 704 * q^70 + 399 * q^71 - 104 * q^72 - 1277 * q^73 + 412 * q^74 - 811 * q^75 - 64 * q^76 - 72 * q^77 + 650 * q^78 + 122 * q^79 + 160 * q^80 - 694 * q^81 + 746 * q^82 + 1802 * q^83 - 512 * q^84 - 768 * q^85 + 628 * q^86 + 1119 * q^87 - 96 * q^88 + 2046 * q^89 - 568 * q^90 - 1912 * q^91 + 184 * q^92 + 2493 * q^93 + 1718 * q^94 + 1380 * q^95 + 96 * q^96 - 910 * q^97 - 60 * q^98 + 78 * q^99

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