LMFDB - Embedded newform 43.4.a.b.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,4,Mod(1,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, 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("43.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	43.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:	$2.53708213025$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 32x^{4} - 16x^{3} + 251x^{2} + 276x + 60 $ x^6 - 32x^4 - 16x^3 + 251x^2 + 276x + 60
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-3.17112$ of defining polynomial
Character	$\chi$	$=$	43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.17112 q^{2} +2.46717 q^{3} +9.39827 q^{4} -7.54340 q^{5} +10.2909 q^{6} +4.58222 q^{7} +5.83236 q^{8} -20.9131 q^{9} +O(q^{10})$	\(q+4.17112 q^{2} +2.46717 q^{3} +9.39827 q^{4} -7.54340 q^{5} +10.2909 q^{6} +4.58222 q^{7} +5.83236 q^{8} -20.9131 q^{9} -31.4645 q^{10} +26.9150 q^{11} +23.1872 q^{12} -15.6529 q^{13} +19.1130 q^{14} -18.6109 q^{15} -50.8587 q^{16} +27.2420 q^{17} -87.2309 q^{18} +38.3104 q^{19} -70.8949 q^{20} +11.3051 q^{21} +112.266 q^{22} +82.5575 q^{23} +14.3894 q^{24} -68.0971 q^{25} -65.2903 q^{26} -118.210 q^{27} +43.0650 q^{28} -34.2852 q^{29} -77.6283 q^{30} +119.055 q^{31} -258.797 q^{32} +66.4040 q^{33} +113.630 q^{34} -34.5655 q^{35} -196.547 q^{36} +378.527 q^{37} +159.797 q^{38} -38.6185 q^{39} -43.9958 q^{40} +385.478 q^{41} +47.1551 q^{42} -43.0000 q^{43} +252.955 q^{44} +157.756 q^{45} +344.358 q^{46} +271.022 q^{47} -125.477 q^{48} -322.003 q^{49} -284.041 q^{50} +67.2108 q^{51} -147.110 q^{52} -329.363 q^{53} -493.068 q^{54} -203.031 q^{55} +26.7252 q^{56} +94.5184 q^{57} -143.008 q^{58} -173.956 q^{59} -174.910 q^{60} +54.5012 q^{61} +496.592 q^{62} -95.8283 q^{63} -672.604 q^{64} +118.076 q^{65} +276.979 q^{66} -906.954 q^{67} +256.028 q^{68} +203.684 q^{69} -144.177 q^{70} -621.376 q^{71} -121.972 q^{72} -1025.87 q^{73} +1578.88 q^{74} -168.007 q^{75} +360.052 q^{76} +123.331 q^{77} -161.082 q^{78} -737.945 q^{79} +383.647 q^{80} +273.009 q^{81} +1607.88 q^{82} +558.465 q^{83} +106.249 q^{84} -205.498 q^{85} -179.358 q^{86} -84.5875 q^{87} +156.978 q^{88} +1631.31 q^{89} +658.018 q^{90} -71.7252 q^{91} +775.898 q^{92} +293.729 q^{93} +1130.47 q^{94} -288.991 q^{95} -638.496 q^{96} -406.607 q^{97} -1343.12 q^{98} -562.875 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 7 q^{3} + 22 q^{4} + 43 q^{5} - 3 q^{6} + 8 q^{7} + 54 q^{8} + 81 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 + 7 * q^3 + 22 * q^4 + 43 * q^5 - 3 * q^6 + 8 * q^7 + 54 * q^8 + 81 * q^9	\( 6 q + 6 q^{2} + 7 q^{3} + 22 q^{4} + 43 q^{5} - 3 q^{6} + 8 q^{7} + 54 q^{8} + 81 q^{9} + 57 q^{10} - 28 q^{11} - 157 q^{12} + 56 q^{13} - 184 q^{14} - 124 q^{15} - 54 q^{16} + 19 q^{17} - 81 q^{18} - 75 q^{19} + 135 q^{20} - 18 q^{21} - 504 q^{22} + 131 q^{23} - 567 q^{24} + 105 q^{25} + 44 q^{26} + 238 q^{27} - 404 q^{28} + 515 q^{29} - 396 q^{30} + 237 q^{31} + 558 q^{32} + 540 q^{33} - 107 q^{34} + 198 q^{35} + 73 q^{36} + 269 q^{37} + 527 q^{38} + 290 q^{39} + 613 q^{40} + 471 q^{41} + 362 q^{42} - 258 q^{43} - 428 q^{44} + 334 q^{45} - 67 q^{46} + 415 q^{47} - 989 q^{48} + 350 q^{49} + 1335 q^{50} - 1241 q^{51} - 8 q^{52} + 450 q^{53} + 402 q^{54} - 1732 q^{55} - 780 q^{56} - 1000 q^{57} - 1055 q^{58} + 356 q^{59} - 2732 q^{60} - 1328 q^{61} + 1603 q^{62} - 2290 q^{63} + 466 q^{64} - 62 q^{65} + 156 q^{66} - 632 q^{67} + 571 q^{68} - 1130 q^{69} - 1902 q^{70} - 144 q^{71} + 567 q^{72} + 864 q^{73} + 1207 q^{74} - 2494 q^{75} + 1005 q^{76} + 2660 q^{77} + 2222 q^{78} - 1613 q^{79} + 2399 q^{80} - 102 q^{81} + 1673 q^{82} - 682 q^{83} + 3758 q^{84} + 84 q^{85} - 258 q^{86} + 449 q^{87} - 608 q^{88} + 3378 q^{89} + 930 q^{90} - 3900 q^{91} + 3491 q^{92} + 1879 q^{93} + 3197 q^{94} - 79 q^{95} - 591 q^{96} - 55 q^{97} + 2398 q^{98} - 1612 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 7 * q^3 + 22 * q^4 + 43 * q^5 - 3 * q^6 + 8 * q^7 + 54 * q^8 + 81 * q^9 + 57 * q^10 - 28 * q^11 - 157 * q^12 + 56 * q^13 - 184 * q^14 - 124 * q^15 - 54 * q^16 + 19 * q^17 - 81 * q^18 - 75 * q^19 + 135 * q^20 - 18 * q^21 - 504 * q^22 + 131 * q^23 - 567 * q^24 + 105 * q^25 + 44 * q^26 + 238 * q^27 - 404 * q^28 + 515 * q^29 - 396 * q^30 + 237 * q^31 + 558 * q^32 + 540 * q^33 - 107 * q^34 + 198 * q^35 + 73 * q^36 + 269 * q^37 + 527 * q^38 + 290 * q^39 + 613 * q^40 + 471 * q^41 + 362 * q^42 - 258 * q^43 - 428 * q^44 + 334 * q^45 - 67 * q^46 + 415 * q^47 - 989 * q^48 + 350 * q^49 + 1335 * q^50 - 1241 * q^51 - 8 * q^52 + 450 * q^53 + 402 * q^54 - 1732 * q^55 - 780 * q^56 - 1000 * q^57 - 1055 * q^58 + 356 * q^59 - 2732 * q^60 - 1328 * q^61 + 1603 * q^62 - 2290 * q^63 + 466 * q^64 - 62 * q^65 + 156 * q^66 - 632 * q^67 + 571 * q^68 - 1130 * q^69 - 1902 * q^70 - 144 * q^71 + 567 * q^72 + 864 * q^73 + 1207 * q^74 - 2494 * q^75 + 1005 * q^76 + 2660 * q^77 + 2222 * q^78 - 1613 * q^79 + 2399 * q^80 - 102 * q^81 + 1673 * q^82 - 682 * q^83 + 3758 * q^84 + 84 * q^85 - 258 * q^86 + 449 * q^87 - 608 * q^88 + 3378 * q^89 + 930 * q^90 - 3900 * q^91 + 3491 * q^92 + 1879 * q^93 + 3197 * q^94 - 79 * q^95 - 591 * q^96 - 55 * q^97 + 2398 * q^98 - 1612 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	4.17112	1.47471	0.737357	−	0.675503i	$-0.236073\pi$
$2$	4.17112	1.47471	0.737357	+	0.675503i	$0.236073\pi$
$3$	2.46717	0.474808	0.237404	−	0.971411i	$-0.423704\pi$
$3$	2.46717	0.474808	0.237404	+	0.971411i	$0.423704\pi$
$4$	9.39827	1.17478
$5$	−7.54340	−0.674702	−0.337351	−	0.941379i	$-0.609531\pi$
$5$	−7.54340	−0.674702	−0.337351	+	0.941379i	$0.609531\pi$
$6$	10.2909	0.700206
$7$	4.58222	0.247417	0.123708	−	0.992319i	$-0.460521\pi$
$7$	4.58222	0.247417	0.123708	+	0.992319i	$0.460521\pi$
$8$	5.83236	0.257756
$9$	−20.9131	−0.774558
$10$	−31.4645	−0.994994
$11$	26.9150	0.737744	0.368872	−	0.929480i	$-0.379744\pi$
$11$	26.9150	0.737744	0.368872	+	0.929480i	$0.379744\pi$
$12$	23.1872	0.557796
$13$	−15.6529	−0.333949	−0.166975	−	0.985961i	$-0.553400\pi$
$13$	−15.6529	−0.333949	−0.166975	+	0.985961i	$0.553400\pi$
$14$	19.1130	0.364869
$15$	−18.6109	−0.320354
$16$	−50.8587	−0.794667
$17$	27.2420	0.388657	0.194328	−	0.980937i	$-0.437747\pi$
$17$	27.2420	0.388657	0.194328	+	0.980937i	$0.437747\pi$
$18$	−87.2309	−1.14225
$19$	38.3104	0.462580	0.231290	−	0.972885i	$-0.425705\pi$
$19$	38.3104	0.462580	0.231290	+	0.972885i	$0.425705\pi$
$20$	−70.8949	−0.792629
$21$	11.3051	0.117475
$22$	112.266	1.08796
$23$	82.5575	0.748453	0.374227	−	0.927337i	$-0.377908\pi$
$23$	82.5575	0.748453	0.374227	+	0.927337i	$0.377908\pi$
$24$	14.3894	0.122385
$25$	−68.0971	−0.544777
$26$	−65.2903	−0.492480
$27$	−118.210	−0.842574
$28$	43.0650	0.290661
$29$	−34.2852	−0.219538	−0.109769	−	0.993957i	$-0.535011\pi$
$29$	−34.2852	−0.219538	−0.109769	+	0.993957i	$0.535011\pi$
$30$	−77.6283	−0.472431
$31$	119.055	0.689770	0.344885	−	0.938645i	$-0.387918\pi$
$31$	119.055	0.689770	0.344885	+	0.938645i	$0.387918\pi$
$32$	−258.797	−1.42966
$33$	66.4040	0.350286
$34$	113.630	0.573158
$35$	−34.5655	−0.166933
$36$	−196.547	−0.909938
$37$	378.527	1.68188	0.840939	−	0.541129i	$-0.182003\pi$
$37$	378.527	1.68188	0.840939	+	0.541129i	$0.182003\pi$
$38$	159.797	0.682173
$39$	−38.6185	−0.158562
$40$	−43.9958	−0.173909
$41$	385.478	1.46833	0.734166	−	0.678970i	$-0.237573\pi$
$41$	385.478	1.46833	0.734166	+	0.678970i	$0.237573\pi$
$42$	47.1551	0.173243
$43$	−43.0000	−0.152499
$43$	−43.0000	−0.152499
$44$	252.955	0.866689
$45$	157.756	0.522596
$46$	344.358	1.10376
$47$	271.022	0.841120	0.420560	−	0.907265i	$-0.361834\pi$
$47$	271.022	0.841120	0.420560	+	0.907265i	$0.361834\pi$
$48$	−125.477	−0.377314
$49$	−322.003	−0.938785
$50$	−284.041	−0.803390
$51$	67.2108	0.184537
$52$	−147.110	−0.392318
$53$	−329.363	−0.853612	−0.426806	−	0.904343i	$-0.640361\pi$
$53$	−329.363	−0.853612	−0.426806	+	0.904343i	$0.640361\pi$
$54$	−493.068	−1.24256
$55$	−203.031	−0.497757
$56$	26.7252	0.0637732
$57$	94.5184	0.219636
$58$	−143.008	−0.323756
$59$	−173.956	−0.383849	−0.191924	−	0.981410i	$-0.561473\pi$
$59$	−173.956	−0.383849	−0.191924	+	0.981410i	$0.561473\pi$
$60$	−174.910	−0.376346
$61$	54.5012	0.114396	0.0571981	−	0.998363i	$-0.481783\pi$
$61$	54.5012	0.114396	0.0571981	+	0.998363i	$0.481783\pi$
$62$	496.592	1.01721
$63$	−95.8283	−0.191639
$64$	−672.604	−1.31368
$65$	118.076	0.225316
$66$	276.979	0.516572
$67$	−906.954	−1.65376	−0.826881	−	0.562377i	$-0.809887\pi$
$67$	−906.954	−1.65376	−0.826881	+	0.562377i	$0.809887\pi$
$68$	256.028	0.456588
$69$	203.684	0.355371
$70$	−144.177	−0.246178
$71$	−621.376	−1.03864	−0.519322	−	0.854579i	$-0.673816\pi$
$71$	−621.376	−1.03864	−0.519322	+	0.854579i	$0.673816\pi$
$72$	−121.972	−0.199647
$73$	−1025.87	−1.64477	−0.822387	−	0.568928i	$-0.807358\pi$
$73$	−1025.87	−1.64477	−0.822387	+	0.568928i	$0.807358\pi$
$74$	1578.88	2.48029
$75$	−168.007	−0.258664
$76$	360.052	0.543431
$77$	123.331	0.182530
$78$	−161.082	−0.233833
$79$	−737.945	−1.05095	−0.525476	−	0.850808i	$-0.676113\pi$
$79$	−737.945	−1.05095	−0.525476	+	0.850808i	$0.676113\pi$
$80$	383.647	0.536164
$81$	273.009	0.374497
$82$	1607.88	2.16537
$83$	558.465	0.738548	0.369274	−	0.929321i	$-0.379606\pi$
$83$	558.465	0.738548	0.369274	+	0.929321i	$0.379606\pi$
$84$	106.249	0.138008
$85$	−205.498	−0.262228
$86$	−179.358	−0.224892
$87$	−84.5875	−0.104238
$88$	156.978	0.190158
$89$	1631.31	1.94291	0.971453	−	0.237231i	$-0.0762398\pi$
$89$	1631.31	1.94291	0.971453	+	0.237231i	$0.0762398\pi$
$90$	658.018	0.770680
$91$	−71.7252	−0.0826247
$92$	775.898	0.879271
$93$	293.729	0.327508
$94$	1130.47	1.24041
$95$	−288.991	−0.312104
$96$	−638.496	−0.678815
$97$	−406.607	−0.425616	−0.212808	−	0.977094i	$-0.568261\pi$
$97$	−406.607	−0.425616	−0.212808	+	0.977094i	$0.568261\pi$
$98$	−1343.12	−1.38444
$99$	−562.875	−0.571425
$100$	−639.995	−0.639995
$101$	1000.43	0.985606	0.492803	−	0.870141i	$-0.335972\pi$
$101$	1000.43	0.985606	0.492803	+	0.870141i	$0.335972\pi$
$102$	280.345	0.272140
$103$	−1659.81	−1.58783	−0.793913	−	0.608031i	$-0.791960\pi$
$103$	−1659.81	−1.58783	−0.793913	+	0.608031i	$0.791960\pi$
$104$	−91.2935	−0.0860775
$105$	−85.2792	−0.0792609
$106$	−1373.81	−1.25883
$107$	−151.590	−0.136961	−0.0684803	−	0.997652i	$-0.521815\pi$
$107$	−151.590	−0.136961	−0.0684803	+	0.997652i	$0.521815\pi$
$108$	−1110.97	−0.989842
$109$	1092.76	0.960254	0.480127	−	0.877199i	$-0.340591\pi$
$109$	1092.76	0.960254	0.480127	+	0.877199i	$0.340591\pi$
$110$	−846.866	−0.734050
$111$	933.892	0.798569
$112$	−233.046	−0.196614
$113$	−970.442	−0.807889	−0.403945	−	0.914783i	$-0.632361\pi$
$113$	−970.442	−0.807889	−0.403945	+	0.914783i	$0.632361\pi$
$114$	394.248	0.323901
$115$	−622.764	−0.504983
$116$	−322.222	−0.257910
$117$	327.351	0.258663
$118$	−725.590	−0.566068
$119$	124.829	0.0961602
$120$	−108.545	−0.0825732
$121$	−606.582	−0.455734
$122$	227.331	0.168702
$123$	951.042	0.697175
$124$	1118.91	0.810331
$125$	1456.61	1.04226
$126$	−399.712	−0.282612
$127$	2115.78	1.47831	0.739155	−	0.673535i	$-0.235225\pi$
$127$	2115.78	1.47831	0.739155	+	0.673535i	$0.235225\pi$
$128$	−735.139	−0.507638
$129$	−106.088	−0.0724075
$130$	492.511	0.332277
$131$	−1695.44	−1.13077	−0.565386	−	0.824826i	$-0.691273\pi$
$131$	−1695.44	−1.13077	−0.565386	+	0.824826i	$0.691273\pi$
$132$	624.083	0.411511
$133$	175.547	0.114450
$134$	−3783.02	−2.43883
$135$	891.704	0.568486
$136$	158.885	0.100179
$137$	1613.51	1.00622	0.503108	−	0.864224i	$-0.332190\pi$
$137$	1613.51	1.00622	0.503108	+	0.864224i	$0.332190\pi$
$138$	849.590	0.524071
$139$	2072.45	1.26463	0.632313	−	0.774713i	$-0.282106\pi$
$139$	2072.45	1.26463	0.632313	+	0.774713i	$0.282106\pi$
$140$	−324.856	−0.196110
$141$	668.658	0.399370
$142$	−2591.84	−1.53170
$143$	−421.299	−0.246369
$144$	1063.61	0.615515
$145$	258.627	0.148123
$146$	−4279.01	−2.42557
$147$	−794.438	−0.445742
$148$	3557.50	1.97584
$149$	−811.396	−0.446122	−0.223061	−	0.974805i	$-0.571605\pi$
$149$	−811.396	−0.446122	−0.223061	+	0.974805i	$0.571605\pi$
$150$	−700.779	−0.381456
$151$	−944.326	−0.508928	−0.254464	−	0.967082i	$-0.581899\pi$
$151$	−944.326	−0.508928	−0.254464	+	0.967082i	$0.581899\pi$
$152$	223.440	0.119233
$153$	−569.714	−0.301037
$154$	514.427	0.269180
$155$	−898.078	−0.465390
$156$	−362.947	−0.186276
$157$	2138.58	1.08712	0.543558	−	0.839372i	$-0.317077\pi$
$157$	2138.58	1.08712	0.543558	+	0.839372i	$0.317077\pi$
$158$	−3078.06	−1.54986
$159$	−812.595	−0.405302
$160$	1952.21	0.964597
$161$	378.297	0.185180
$162$	1138.75	0.552277
$163$	−2184.57	−1.04975	−0.524873	−	0.851180i	$-0.675887\pi$
$163$	−2184.57	−1.04975	−0.524873	+	0.851180i	$0.675887\pi$
$164$	3622.83	1.72497
$165$	−500.912	−0.236339
$166$	2329.43	1.08915
$167$	3334.42	1.54506	0.772531	−	0.634978i	$-0.218991\pi$
$167$	3334.42	1.54506	0.772531	+	0.634978i	$0.218991\pi$
$168$	65.9356	0.0302800
$169$	−1951.99	−0.888478
$170$	−857.156	−0.386711
$171$	−801.188	−0.358295
$172$	−404.126	−0.179153
$173$	1169.82	0.514105	0.257052	−	0.966397i	$-0.417249\pi$
$173$	1169.82	0.514105	0.257052	+	0.966397i	$0.417249\pi$
$174$	−352.825	−0.153722
$175$	−312.036	−0.134787
$176$	−1368.86	−0.586260
$177$	−429.178	−0.182254
$178$	6804.40	2.86523
$179$	206.597	0.0862669	0.0431334	−	0.999069i	$-0.486266\pi$
$179$	206.597	0.0862669	0.0431334	+	0.999069i	$0.486266\pi$
$180$	1482.63	0.613937
$181$	652.242	0.267849	0.133925	−	0.990992i	$-0.457242\pi$
$181$	652.242	0.267849	0.133925	+	0.990992i	$0.457242\pi$
$182$	−299.175	−0.121848
$183$	134.464	0.0543162
$184$	481.505	0.192919
$185$	−2855.38	−1.13477
$186$	1225.18	0.482981
$187$	733.220	0.286729
$188$	2547.14	0.988134
$189$	−541.664	−0.208467
$190$	−1205.42	−0.460264
$191$	−1128.21	−0.427404	−0.213702	−	0.976899i	$-0.568552\pi$
$191$	−1128.21	−0.427404	−0.213702	+	0.976899i	$0.568552\pi$
$192$	−1659.43	−0.623745
$193$	355.606	0.132627	0.0663136	−	0.997799i	$-0.478876\pi$
$193$	355.606	0.132627	0.0663136	+	0.997799i	$0.478876\pi$
$194$	−1696.01	−0.627662
$195$	291.315	0.106982
$196$	−3026.27	−1.10287
$197$	4347.00	1.57214	0.786068	−	0.618140i	$-0.212114\pi$
$197$	4347.00	1.57214	0.786068	+	0.618140i	$0.212114\pi$
$198$	−2347.82	−0.842689
$199$	430.375	0.153309	0.0766545	−	0.997058i	$-0.475576\pi$
$199$	430.375	0.153309	0.0766545	+	0.997058i	$0.475576\pi$
$200$	−397.167	−0.140420
$201$	−2237.61	−0.785219
$202$	4172.91	1.45349
$203$	−157.102	−0.0543174
$204$	631.665	0.216791
$205$	−2907.82	−0.990687
$206$	−6923.28	−2.34159
$207$	−1726.53	−0.579720
$208$	796.087	0.265378
$209$	1031.13	0.341265
$210$	−355.710	−0.116887
$211$	103.702	0.0338347	0.0169174	−	0.999857i	$-0.494615\pi$
$211$	103.702	0.0338347	0.0169174	+	0.999857i	$0.494615\pi$
$212$	−3095.44	−1.00281
$213$	−1533.04	−0.493156
$214$	−632.302	−0.201978
$215$	324.366	0.102891
$216$	−689.442	−0.217179
$217$	545.535	0.170661
$218$	4558.05	1.41610
$219$	−2530.99	−0.780951
$220$	−1908.14	−0.584757
$221$	−426.418	−0.129792
$222$	3895.38	1.17766
$223$	4447.94	1.33568	0.667839	−	0.744306i	$-0.267219\pi$
$223$	4447.94	1.33568	0.667839	+	0.744306i	$0.267219\pi$
$224$	−1185.86	−0.353723
$225$	1424.12	0.421961
$226$	−4047.83	−1.19141
$227$	509.808	0.149062	0.0745311	−	0.997219i	$-0.476254\pi$
$227$	509.808	0.149062	0.0745311	+	0.997219i	$0.476254\pi$
$228$	888.310	0.258025
$229$	−4754.86	−1.37210	−0.686049	−	0.727556i	$-0.740656\pi$
$229$	−4754.86	−1.37210	−0.686049	+	0.727556i	$0.740656\pi$
$230$	−2597.63	−0.744706
$231$	304.278	0.0866667
$232$	−199.964	−0.0565873
$233$	893.223	0.251146	0.125573	−	0.992084i	$-0.459923\pi$
$233$	893.223	0.251146	0.125573	+	0.992084i	$0.459923\pi$
$234$	1365.42	0.381454
$235$	−2044.43	−0.567506
$236$	−1634.88	−0.450939
$237$	−1820.64	−0.499000
$238$	520.677	0.141809
$239$	−3883.75	−1.05112	−0.525562	−	0.850755i	$-0.676145\pi$
$239$	−3883.75	−1.05112	−0.525562	+	0.850755i	$0.676145\pi$
$240$	946.524	0.254575
$241$	−3118.83	−0.833616	−0.416808	−	0.908995i	$-0.636851\pi$
$241$	−3118.83	−0.833616	−0.416808	+	0.908995i	$0.636851\pi$
$242$	−2530.13	−0.672078
$243$	3865.22	1.02039
$244$	512.217	0.134391
$245$	2429.00	0.633400
$246$	3966.91	1.02813
$247$	−599.670	−0.154478
$248$	694.370	0.177793
$249$	1377.83	0.350668
$250$	6075.70	1.53704
$251$	5196.19	1.30669	0.653347	−	0.757058i	$-0.273364\pi$
$251$	5196.19	1.30669	0.653347	+	0.757058i	$0.273364\pi$
$252$	−900.620	−0.225134
$253$	2222.04	0.552167
$254$	8825.19	2.18009
$255$	−506.998	−0.124508
$256$	2314.47	0.565057
$257$	−2441.32	−0.592550	−0.296275	−	0.955103i	$-0.595744\pi$
$257$	−2441.32	−0.592550	−0.296275	+	0.955103i	$0.595744\pi$
$258$	−442.508	−0.106780
$259$	1734.50	0.416125
$260$	1109.71	0.264698
$261$	717.008	0.170045
$262$	−7071.89	−1.66757
$263$	5831.01	1.36713	0.683566	−	0.729889i	$-0.260428\pi$
$263$	5831.01	1.36713	0.683566	+	0.729889i	$0.260428\pi$
$264$	387.292	0.0902885
$265$	2484.52	0.575934
$266$	732.227	0.168781
$267$	4024.73	0.922507
$268$	−8523.80	−1.94281
$269$	−2605.41	−0.590538	−0.295269	−	0.955414i	$-0.595409\pi$
$269$	−2605.41	−0.590538	−0.295269	+	0.955414i	$0.595409\pi$
$270$	3719.41	0.838355
$271$	1793.84	0.402097	0.201049	−	0.979581i	$-0.435565\pi$
$271$	1793.84	0.402097	0.201049	+	0.979581i	$0.435565\pi$
$272$	−1385.49	−0.308853
$273$	−176.958	−0.0392308
$274$	6730.16	1.48388
$275$	−1832.83	−0.401906
$276$	1914.27	0.417485
$277$	−825.071	−0.178967	−0.0894833	−	0.995988i	$-0.528522\pi$
$277$	−825.071	−0.178967	−0.0894833	+	0.995988i	$0.528522\pi$
$278$	8644.45	1.86496
$279$	−2489.80	−0.534267
$280$	−201.599	−0.0430279
$281$	−5114.69	−1.08582	−0.542912	−	0.839789i	$-0.682678\pi$
$281$	−5114.69	−1.08582	−0.542912	+	0.839789i	$0.682678\pi$
$282$	2789.06	0.588957
$283$	−3703.40	−0.777895	−0.388947	−	0.921260i	$-0.627161\pi$
$283$	−3703.40	−0.777895	−0.388947	+	0.921260i	$0.627161\pi$
$284$	−5839.86	−1.22018
$285$	−712.990	−0.148189
$286$	−1757.29	−0.363324
$287$	1766.35	0.363290
$288$	5412.23	1.10736
$289$	−4170.87	−0.848946
$290$	1078.77	0.218439
$291$	−1003.17	−0.202085
$292$	−9641.37	−1.93225
$293$	749.193	0.149380	0.0746899	−	0.997207i	$-0.476203\pi$
$293$	749.193	0.149380	0.0746899	+	0.997207i	$0.476203\pi$
$294$	−3313.70	−0.657343
$295$	1312.22	0.258984
$296$	2207.71	0.433515
$297$	−3181.62	−0.621603
$298$	−3384.43	−0.657902
$299$	−1292.27	−0.249946
$300$	−1578.98	−0.303874
$301$	−197.036	−0.0377307
$302$	−3938.90	−0.750524
$303$	2468.23	0.467973
$304$	−1948.42	−0.367597
$305$	−411.125	−0.0771834
$306$	−2376.35	−0.443944
$307$	−4761.00	−0.885097	−0.442548	−	0.896745i	$-0.645925\pi$
$307$	−4761.00	−0.885097	−0.442548	+	0.896745i	$0.645925\pi$
$308$	1159.09	0.214433
$309$	−4095.04	−0.753912
$310$	−3745.99	−0.686317
$311$	−5995.99	−1.09325	−0.546626	−	0.837377i	$-0.684088\pi$
$311$	−5995.99	−1.09325	−0.546626	+	0.837377i	$0.684088\pi$
$312$	−225.237	−0.0408703
$313$	398.261	0.0719203	0.0359602	−	0.999353i	$-0.488551\pi$
$313$	398.261	0.0719203	0.0359602	+	0.999353i	$0.488551\pi$
$314$	8920.27	1.60318
$315$	722.871	0.129299
$316$	−6935.40	−1.23464
$317$	4657.19	0.825154	0.412577	−	0.910923i	$-0.364629\pi$
$317$	4657.19	0.825154	0.412577	+	0.910923i	$0.364629\pi$
$318$	−3389.43	−0.597704
$319$	−922.786	−0.161963
$320$	5073.72	0.886342
$321$	−374.000	−0.0650300
$322$	1577.92	0.273088
$323$	1043.65	0.179785
$324$	2565.81	0.439954
$325$	1065.92	0.181928
$326$	−9112.11	−1.54808
$327$	2696.03	0.455936
$328$	2248.25	0.378472
$329$	1241.88	0.208107
$330$	−2089.37	−0.348533
$331$	10013.6	1.66282	0.831412	−	0.555656i	$-0.187533\pi$
$331$	10013.6	1.66282	0.831412	+	0.555656i	$0.187533\pi$
$332$	5248.60	0.867634
$333$	−7916.16	−1.30271
$334$	13908.3	2.27852
$335$	6841.52	1.11580
$336$	−574.964	−0.0933538
$337$	−3872.11	−0.625897	−0.312949	−	0.949770i	$-0.601317\pi$
$337$	−3872.11	−0.625897	−0.312949	+	0.949770i	$0.601317\pi$
$338$	−8141.97	−1.31025
$339$	−2394.25	−0.383592
$340$	−1931.32	−0.308061
$341$	3204.36	0.508874
$342$	−3341.85	−0.528382
$343$	−3047.19	−0.479688
$344$	−250.791	−0.0393075
$345$	−1536.47	−0.239770
$346$	4879.48	0.758158
$347$	10290.8	1.59204	0.796022	−	0.605267i	$-0.206934\pi$
$347$	10290.8	1.59204	0.796022	+	0.605267i	$0.206934\pi$
$348$	−794.976	−0.122457
$349$	700.572	0.107452	0.0537260	−	0.998556i	$-0.482890\pi$
$349$	700.572	0.107452	0.0537260	+	0.998556i	$0.482890\pi$
$350$	−1301.54	−0.198772
$351$	1850.33	0.281377
$352$	−6965.52	−1.05473
$353$	3608.33	0.544057	0.272028	−	0.962289i	$-0.412306\pi$
$353$	3608.33	0.544057	0.272028	+	0.962289i	$0.412306\pi$
$354$	−1790.16	−0.268773
$355$	4687.29	0.700776
$356$	15331.5	2.28250
$357$	307.975	0.0456576
$358$	861.741	0.127219
$359$	−12085.9	−1.77680	−0.888399	−	0.459072i	$-0.848182\pi$
$359$	−12085.9	−1.77680	−0.888399	+	0.459072i	$0.848182\pi$
$360$	920.087	0.134702
$361$	−5391.31	−0.786020
$362$	2720.58	0.395001
$363$	−1496.54	−0.216386
$364$	−674.093	−0.0970661
$365$	7738.52	1.10973
$366$	560.866	0.0801009
$367$	968.974	0.137820	0.0689101	−	0.997623i	$-0.478048\pi$
$367$	968.974	0.137820	0.0689101	+	0.997623i	$0.478048\pi$
$368$	−4198.77	−0.594771
$369$	−8061.53	−1.13731
$370$	−11910.2	−1.67346
$371$	−1509.21	−0.211198
$372$	2760.54	0.384751
$373$	13006.0	1.80543	0.902713	−	0.430243i	$-0.141572\pi$
$373$	13006.0	1.80543	0.902713	+	0.430243i	$0.141572\pi$
$374$	3058.35	0.422844
$375$	3593.71	0.494875
$376$	1580.70	0.216804
$377$	536.664	0.0733146
$378$	−2259.35	−0.307429
$379$	1901.08	0.257657	0.128828	−	0.991667i	$-0.458878\pi$
$379$	1901.08	0.257657	0.128828	+	0.991667i	$0.458878\pi$
$380$	−2716.01	−0.366654
$381$	5220.00	0.701913
$382$	−4705.89	−0.630299
$383$	−9501.65	−1.26765	−0.633827	−	0.773475i	$-0.718517\pi$
$383$	−9501.65	−1.26765	−0.633827	+	0.773475i	$0.718517\pi$
$384$	−1813.71	−0.241031
$385$	−930.332	−0.123154
$386$	1483.27	0.195587
$387$	899.262	0.118119
$388$	−3821.40	−0.500006
$389$	4640.26	0.604808	0.302404	−	0.953180i	$-0.402211\pi$
$389$	4640.26	0.604808	0.302404	+	0.953180i	$0.402211\pi$
$390$	1215.11	0.157768
$391$	2249.03	0.290891
$392$	−1878.04	−0.241978
$393$	−4182.94	−0.536899
$394$	18131.9	2.31845
$395$	5566.61	0.709080
$396$	−5290.05	−0.671301
$397$	4633.90	0.585815	0.292908	−	0.956141i	$-0.405377\pi$
$397$	4633.90	0.585815	0.292908	+	0.956141i	$0.405377\pi$
$398$	1795.15	0.226087
$399$	433.104	0.0543417
$400$	3463.33	0.432916
$401$	−11801.3	−1.46965	−0.734823	−	0.678258i	$-0.762735\pi$
$401$	−11801.3	−1.46965	−0.734823	+	0.678258i	$0.762735\pi$
$402$	−9333.35	−1.15797
$403$	−1863.56	−0.230348
$404$	9402.29	1.15787
$405$	−2059.41	−0.252674
$406$	−655.293	−0.0801026
$407$	10188.1	1.24080
$408$	391.998	0.0475656
$409$	5588.72	0.675658	0.337829	−	0.941207i	$-0.390307\pi$
$409$	5588.72	0.675658	0.337829	+	0.941207i	$0.390307\pi$
$410$	−12128.9	−1.46098
$411$	3980.81	0.477759
$412$	−15599.4	−1.86535
$413$	−797.103	−0.0949706
$414$	−7201.57	−0.854922
$415$	−4212.72	−0.498300
$416$	4050.93	0.477435
$417$	5113.09	0.600454
$418$	4300.95	0.503269
$419$	−6908.94	−0.805547	−0.402773	−	0.915300i	$-0.631954\pi$
$419$	−6908.94	−0.805547	−0.402773	+	0.915300i	$0.631954\pi$
$420$	−801.477	−0.0931144
$421$	16499.6	1.91007	0.955036	−	0.296491i	$-0.0958165\pi$
$421$	16499.6	1.91007	0.955036	+	0.296491i	$0.0958165\pi$
$422$	432.553	0.0498966
$423$	−5667.90	−0.651496
$424$	−1920.96	−0.220024
$425$	−1855.10	−0.211731
$426$	−6394.51	−0.727265
$427$	249.737	0.0283035
$428$	−1424.69	−0.160899
$429$	−1039.42	−0.116978
$430$	1352.97	0.151735
$431$	−7101.67	−0.793679	−0.396839	−	0.917888i	$-0.629893\pi$
$431$	−7101.67	−0.793679	−0.396839	+	0.917888i	$0.629893\pi$
$432$	6011.99	0.669565
$433$	−8935.72	−0.991739	−0.495870	−	0.868397i	$-0.665151\pi$
$433$	−8935.72	−0.991739	−0.495870	+	0.868397i	$0.665151\pi$
$434$	2275.50	0.251676
$435$	638.077	0.0703298
$436$	10270.1	1.12809
$437$	3162.81	0.346219
$438$	−10557.1	−1.15168
$439$	17789.3	1.93403	0.967015	−	0.254720i	$-0.0819833\pi$
$439$	17789.3	1.93403	0.967015	+	0.254720i	$0.0819833\pi$
$440$	−1184.15	−0.128300
$441$	6734.07	0.727143
$442$	−1778.64	−0.191406
$443$	2744.62	0.294359	0.147180	−	0.989110i	$-0.452980\pi$
$443$	2744.62	0.294359	0.147180	+	0.989110i	$0.452980\pi$
$444$	8776.97	0.938146
$445$	−12305.6	−1.31088
$446$	18552.9	1.96974
$447$	−2001.85	−0.211822
$448$	−3082.02	−0.325026
$449$	−12051.9	−1.26673	−0.633366	−	0.773853i	$-0.718327\pi$
$449$	−12051.9	−1.26673	−0.633366	+	0.773853i	$0.718327\pi$
$450$	5940.17	0.622272
$451$	10375.2	1.08325
$452$	−9120.47	−0.949095
$453$	−2329.81	−0.241643
$454$	2126.47	0.219824
$455$	541.052	0.0557471
$456$	551.265	0.0566126
$457$	130.425	0.0133502	0.00667509	−	0.999978i	$-0.497875\pi$
$457$	130.425	0.0133502	0.00667509	+	0.999978i	$0.497875\pi$
$458$	−19833.1	−2.02345
$459$	−3220.28	−0.327472
$460$	−5852.91	−0.593246
$461$	−981.122	−0.0991223	−0.0495612	−	0.998771i	$-0.515782\pi$
$461$	−981.122	−0.0991223	−0.0495612	+	0.998771i	$0.515782\pi$
$462$	1269.18	0.127809
$463$	6359.89	0.638378	0.319189	−	0.947691i	$-0.396589\pi$
$463$	6359.89	0.638378	0.319189	+	0.947691i	$0.396589\pi$
$464$	1743.70	0.174460
$465$	−2215.71	−0.220970
$466$	3725.75	0.370369
$467$	−14159.9	−1.40309	−0.701546	−	0.712624i	$-0.747506\pi$
$467$	−14159.9	−1.40309	−0.701546	+	0.712624i	$0.747506\pi$
$468$	3076.53	0.303873
$469$	−4155.86	−0.409168
$470$	−8527.57	−0.836909
$471$	5276.24	0.516170
$472$	−1014.57	−0.0989395
$473$	−1157.35	−0.112505
$474$	−7594.10	−0.735883
$475$	−2608.83	−0.252003
$476$	1173.18	0.112967
$477$	6887.98	0.661172
$478$	−16199.6	−1.55011
$479$	−20583.3	−1.96342	−0.981709	−	0.190390i	$-0.939025\pi$
$479$	−20583.3	−1.96342	−0.981709	+	0.190390i	$0.939025\pi$
$480$	4816.43	0.457998
$481$	−5925.06	−0.561662
$482$	−13009.0	−1.22935
$483$	933.324	0.0879248
$484$	−5700.82	−0.535389
$485$	3067.20	0.287164
$486$	16122.3	1.50478
$487$	−17672.3	−1.64437	−0.822186	−	0.569218i	$-0.807246\pi$
$487$	−17672.3	−1.64437	−0.822186	+	0.569218i	$0.807246\pi$
$488$	317.871	0.0294863
$489$	−5389.71	−0.498428
$490$	10131.7	0.934085
$491$	−3484.50	−0.320271	−0.160136	−	0.987095i	$-0.551193\pi$
$491$	−3484.50	−0.320271	−0.160136	+	0.987095i	$0.551193\pi$
$492$	8938.15	0.819030
$493$	−933.998	−0.0853249
$494$	−2501.30	−0.227811
$495$	4245.99	0.385542
$496$	−6054.97	−0.548137
$497$	−2847.28	−0.256978
$498$	5747.09	0.517135
$499$	1393.45	0.125009	0.0625046	−	0.998045i	$-0.480091\pi$
$499$	1393.45	0.125009	0.0625046	+	0.998045i	$0.480091\pi$
$500$	13689.6	1.22444
$501$	8226.59	0.733607
$502$	21673.9	1.92700
$503$	3191.15	0.282875	0.141438	−	0.989947i	$-0.454828\pi$
$503$	3191.15	0.282875	0.141438	+	0.989947i	$0.454828\pi$
$504$	−558.905	−0.0493960
$505$	−7546.63	−0.664991
$506$	9268.39	0.814289
$507$	−4815.89	−0.421856
$508$	19884.7	1.73670
$509$	10831.8	0.943247	0.471624	−	0.881800i	$-0.343668\pi$
$509$	10831.8	0.943247	0.471624	+	0.881800i	$0.343668\pi$
$510$	−2114.75	−0.183613
$511$	−4700.75	−0.406945
$512$	15535.1	1.34094
$513$	−4528.67	−0.389757
$514$	−10183.0	−0.873842
$515$	12520.6	1.07131
$516$	−997.048	−0.0850631
$517$	7294.56	0.620531
$518$	7234.80	0.613666
$519$	2886.16	0.244101
$520$	688.664	0.0580767
$521$	14277.5	1.20059	0.600296	−	0.799778i	$-0.295049\pi$
$521$	14277.5	1.20059	0.600296	+	0.799778i	$0.295049\pi$
$522$	2990.73	0.250768
$523$	4181.28	0.349588	0.174794	−	0.984605i	$-0.444074\pi$
$523$	4181.28	0.349588	0.174794	+	0.984605i	$0.444074\pi$
$524$	−15934.2	−1.32841
$525$	−769.847	−0.0639978
$526$	24321.9	2.01613
$527$	3243.29	0.268084
$528$	−3377.22	−0.278361
$529$	−5351.26	−0.439817
$530$	10363.2	0.849339
$531$	3637.94	0.297313
$532$	1649.84	0.134454
$533$	−6033.87	−0.490348
$534$	16787.6	1.36043
$535$	1143.51	0.0924077
$536$	−5289.68	−0.426267
$537$	509.710	0.0409602
$538$	−10867.5	−0.870875
$539$	−8666.72	−0.692583
$540$	8380.48	0.667849
$541$	5123.26	0.407146	0.203573	−	0.979060i	$-0.434745\pi$
$541$	5123.26	0.407146	0.203573	+	0.979060i	$0.434745\pi$
$542$	7482.35	0.592979
$543$	1609.19	0.127177
$544$	−7050.15	−0.555648
$545$	−8243.14	−0.647885
$546$	−738.116	−0.0578543
$547$	−15435.6	−1.20654	−0.603271	−	0.797537i	$-0.706136\pi$
$547$	−15435.6	−1.20654	−0.603271	+	0.797537i	$0.706136\pi$
$548$	15164.2	1.18209
$549$	−1139.79	−0.0886064
$550$	−7644.98	−0.592696
$551$	−1313.48	−0.101554
$552$	1187.96	0.0915992
$553$	−3381.43	−0.260023
$554$	−3441.47	−0.263925
$555$	−7044.73	−0.538796
$556$	19477.5	1.48566
$557$	−978.643	−0.0744460	−0.0372230	−	0.999307i	$-0.511851\pi$
$557$	−978.643	−0.0744460	−0.0372230	+	0.999307i	$0.511851\pi$
$558$	−10385.3	−0.787891
$559$	673.076	0.0509268
$560$	1757.96	0.132656
$561$	1808.98	0.136141
$562$	−21334.0	−1.60128
$563$	−24362.4	−1.82371	−0.911857	−	0.410507i	$-0.865352\pi$
$563$	−24362.4	−1.82371	−0.911857	+	0.410507i	$0.865352\pi$
$564$	6284.23	0.469174
$565$	7320.43	0.545085
$566$	−15447.3	−1.14717
$567$	1250.99	0.0926569
$568$	−3624.09	−0.267717
$569$	−12733.1	−0.938135	−0.469067	−	0.883162i	$-0.655410\pi$
$569$	−12733.1	−0.938135	−0.469067	+	0.883162i	$0.655410\pi$
$570$	−2973.97	−0.218537
$571$	−6363.95	−0.466415	−0.233208	−	0.972427i	$-0.574922\pi$
$571$	−6363.95	−0.466415	−0.233208	+	0.972427i	$0.574922\pi$
$572$	−3959.48	−0.289430
$573$	−2783.48	−0.202935
$574$	7367.65	0.535749
$575$	−5621.93	−0.407740
$576$	14066.2	1.01752
$577$	−11981.3	−0.864449	−0.432225	−	0.901766i	$-0.642271\pi$
$577$	−11981.3	−0.864449	−0.432225	+	0.901766i	$0.642271\pi$
$578$	−17397.2	−1.25195
$579$	877.340	0.0629724
$580$	2430.65	0.174012
$581$	2559.01	0.182729
$582$	−4184.35	−0.298018
$583$	−8864.80	−0.629747
$584$	−5983.22	−0.423951
$585$	−2469.34	−0.174521
$586$	3124.97	0.220293
$587$	17927.4	1.26055	0.630276	−	0.776371i	$-0.282942\pi$
$587$	17927.4	1.26055	0.630276	+	0.776371i	$0.282942\pi$
$588$	−7466.34	−0.523651
$589$	4561.04	0.319074
$590$	5473.42	0.381927
$591$	10724.8	0.746462
$592$	−19251.4	−1.33653
$593$	19927.7	1.37999	0.689993	−	0.723816i	$-0.257613\pi$
$593$	19927.7	1.37999	0.689993	+	0.723816i	$0.257613\pi$
$594$	−13270.9	−0.916688
$595$	−941.636	−0.0648795
$596$	−7625.72	−0.524097
$597$	1061.81	0.0727923
$598$	−5390.20	−0.368598
$599$	−4155.72	−0.283469	−0.141735	−	0.989905i	$-0.545268\pi$
$599$	−4155.72	−0.283469	−0.141735	+	0.989905i	$0.545268\pi$
$600$	−979.879	−0.0666723
$601$	−4104.20	−0.278559	−0.139279	−	0.990253i	$-0.544479\pi$
$601$	−4104.20	−0.278559	−0.139279	+	0.990253i	$0.544479\pi$
$602$	−821.860	−0.0556420
$603$	18967.2	1.28093
$604$	−8875.03	−0.597880
$605$	4575.69	0.307485
$606$	10295.3	0.690127
$607$	5870.16	0.392525	0.196262	−	0.980551i	$-0.437120\pi$
$607$	5870.16	0.392525	0.196262	+	0.980551i	$0.437120\pi$
$608$	−9914.61	−0.661333
$609$	−387.599	−0.0257903
$610$	−1714.85	−0.113823
$611$	−4242.29	−0.280891
$612$	−5354.33	−0.353653
$613$	29802.4	1.96363	0.981817	−	0.189830i	$-0.0607936\pi$
$613$	29802.4	1.96363	0.981817	+	0.189830i	$0.0607936\pi$
$614$	−19858.7	−1.30527
$615$	−7174.09	−0.470386
$616$	719.308	0.0470483
$617$	27394.8	1.78748	0.893738	−	0.448588i	$-0.148073\pi$
$617$	27394.8	1.78748	0.893738	+	0.448588i	$0.148073\pi$
$618$	−17080.9	−1.11181
$619$	−25129.8	−1.63174	−0.815872	−	0.578232i	$-0.803743\pi$
$619$	−25129.8	−1.63174	−0.815872	+	0.578232i	$0.803743\pi$
$620$	−8440.38	−0.546732
$621$	−9759.11	−0.630627
$622$	−25010.0	−1.61223
$623$	7475.03	0.480708
$624$	1964.08	0.126004
$625$	−2475.65	−0.158442
$626$	1661.20	0.106062
$627$	2543.96	0.162035
$628$	20098.9	1.27713
$629$	10311.9	0.653673
$630$	3015.19	0.190679
$631$	−1190.63	−0.0751160	−0.0375580	−	0.999294i	$-0.511958\pi$
$631$	−1190.63	−0.0751160	−0.0375580	+	0.999294i	$0.511958\pi$
$632$	−4303.96	−0.270890
$633$	255.850	0.0160650
$634$	19425.7	1.21687
$635$	−15960.2	−0.997420
$636$	−7636.98	−0.476142
$637$	5040.29	0.313507
$638$	−3849.06	−0.238849
$639$	12994.9	0.804490
$640$	5545.45	0.342505
$641$	28828.0	1.77635	0.888174	−	0.459508i	$-0.151974\pi$
$641$	28828.0	1.77635	0.888174	+	0.459508i	$0.151974\pi$
$642$	−1560.00	−0.0959007
$643$	16853.2	1.03363	0.516816	−	0.856096i	$-0.327117\pi$
$643$	16853.2	1.03363	0.516816	+	0.856096i	$0.327117\pi$
$644$	3555.34	0.217546
$645$	800.268	0.0488535
$646$	4353.21	0.265131
$647$	−20234.3	−1.22951	−0.614754	−	0.788719i	$-0.710745\pi$
$647$	−20234.3	−1.22951	−0.614754	+	0.788719i	$0.710745\pi$
$648$	1592.28	0.0965291
$649$	−4682.02	−0.283182
$650$	4446.08	0.268292
$651$	1345.93	0.0810310
$652$	−20531.2	−1.23323
$653$	24965.3	1.49612	0.748062	−	0.663629i	$-0.230985\pi$
$653$	24965.3	1.49612	0.748062	+	0.663629i	$0.230985\pi$
$654$	11245.5	0.672375
$655$	12789.4	0.762935
$656$	−19604.9	−1.16683
$657$	21454.0	1.27397
$658$	5180.05	0.306899
$659$	9033.00	0.533954	0.266977	−	0.963703i	$-0.413975\pi$
$659$	9033.00	0.533954	0.266977	+	0.963703i	$0.413975\pi$
$660$	−4707.71	−0.277647
$661$	−19710.5	−1.15983	−0.579915	−	0.814677i	$-0.696914\pi$
$661$	−19710.5	−1.15983	−0.579915	+	0.814677i	$0.696914\pi$
$662$	41767.8	2.45219
$663$	−1052.05	−0.0616261
$664$	3257.17	0.190365
$665$	−1324.22	−0.0772196
$666$	−33019.3	−1.92113
$667$	−2830.50	−0.164314
$668$	31337.8	1.81511
$669$	10973.8	0.634190
$670$	28536.8	1.64548
$671$	1466.90	0.0843951
$672$	−2925.73	−0.167950
$673$	19293.1	1.10504	0.552521	−	0.833499i	$-0.313666\pi$
$673$	19293.1	1.10504	0.552521	+	0.833499i	$0.313666\pi$
$674$	−16151.1	−0.923020
$675$	8049.74	0.459014
$676$	−18345.3	−1.04377
$677$	−16029.1	−0.909968	−0.454984	−	0.890500i	$-0.650355\pi$
$677$	−16029.1	−0.909968	−0.454984	+	0.890500i	$0.650355\pi$
$678$	−9986.70	−0.565689
$679$	−1863.16	−0.105304
$680$	−1198.54	−0.0675908
$681$	1257.78	0.0707759
$682$	13365.8	0.750443
$683$	−4293.48	−0.240535	−0.120267	−	0.992742i	$-0.538375\pi$
$683$	−4293.48	−0.240535	−0.120267	+	0.992742i	$0.538375\pi$
$684$	−7529.78	−0.420919
$685$	−12171.4	−0.678896
$686$	−12710.2	−0.707403
$687$	−11731.1	−0.651482
$688$	2186.92	0.121186
$689$	5155.49	0.285063
$690$	−6408.80	−0.353592
$691$	−19631.7	−1.08079	−0.540393	−	0.841413i	$-0.681724\pi$
$691$	−19631.7	−1.08079	−0.540393	+	0.841413i	$0.681724\pi$
$692$	10994.3	0.603962
$693$	−2579.22	−0.141380
$694$	42924.2	2.34781
$695$	−15633.3	−0.853246
$696$	−493.345	−0.0268681
$697$	10501.2	0.570677
$698$	2922.17	0.158461
$699$	2203.74	0.119246
$700$	−2932.60	−0.158345
$701$	−13399.7	−0.721967	−0.360983	−	0.932572i	$-0.617559\pi$
$701$	−13399.7	−0.721967	−0.360983	+	0.932572i	$0.617559\pi$
$702$	7717.95	0.414951
$703$	14501.5	0.778003
$704$	−18103.1	−0.969158
$705$	−5043.96	−0.269456
$706$	15050.8	0.802329
$707$	4584.18	0.243855
$708$	−4033.53	−0.214109
$709$	−510.833	−0.0270589	−0.0135294	−	0.999908i	$-0.504307\pi$
$709$	−510.833	−0.0270589	−0.0135294	+	0.999908i	$0.504307\pi$
$710$	19551.3	1.03344
$711$	15432.7	0.814023
$712$	9514.40	0.500796
$713$	9828.87	0.516261
$714$	1284.60	0.0673319
$715$	3178.03	0.166226
$716$	1941.65	0.101345
$717$	−9581.88	−0.499082
$718$	−50411.9	−2.62027
$719$	−29685.4	−1.53975	−0.769875	−	0.638195i	$-0.779681\pi$
$719$	−29685.4	−1.53975	−0.769875	+	0.638195i	$0.779681\pi$
$720$	−8023.24	−0.415290
$721$	−7605.63	−0.392855
$722$	−22487.8	−1.15916
$723$	−7694.69	−0.395807
$724$	6129.94	0.314665
$725$	2334.72	0.119599
$726$	−6242.26	−0.319108
$727$	−10575.9	−0.539529	−0.269765	−	0.962926i	$-0.586946\pi$
$727$	−10575.9	−0.539529	−0.269765	+	0.962926i	$0.586946\pi$
$728$	−418.327	−0.0212970
$729$	2164.94	0.109990
$730$	32278.3	1.63654
$731$	−1171.41	−0.0592696
$732$	1263.73	0.0638098
$733$	−4428.93	−0.223173	−0.111587	−	0.993755i	$-0.535593\pi$
$733$	−4428.93	−0.223173	−0.111587	+	0.993755i	$0.535593\pi$
$734$	4041.71	0.203246
$735$	5992.76	0.300743
$736$	−21365.6	−1.07004
$737$	−24410.7	−1.22005
$738$	−33625.6	−1.67720
$739$	20131.6	1.00210	0.501052	−	0.865417i	$-0.332947\pi$
$739$	20131.6	1.00210	0.501052	+	0.865417i	$0.332947\pi$
$740$	−26835.7	−1.33311
$741$	−1479.49	−0.0733474
$742$	−6295.11	−0.311457
$743$	−7362.63	−0.363538	−0.181769	−	0.983341i	$-0.558182\pi$
$743$	−7362.63	−0.363538	−0.181769	+	0.983341i	$0.558182\pi$
$744$	1713.13	0.0844173
$745$	6120.69	0.300999
$746$	54249.5	2.66249
$747$	−11679.2	−0.572048
$748$	6891.00	0.336845
$749$	−694.621	−0.0338864
$750$	14989.8	0.729800
$751$	−7494.93	−0.364173	−0.182087	−	0.983283i	$-0.558285\pi$
$751$	−7494.93	−0.364173	−0.182087	+	0.983283i	$0.558285\pi$
$752$	−13783.8	−0.668410
$753$	12819.9	0.620429
$754$	2238.49	0.108118
$755$	7123.43	0.343375
$756$	−5090.70	−0.244903
$757$	26060.4	1.25123	0.625615	−	0.780132i	$-0.284848\pi$
$757$	26060.4	1.25123	0.625615	+	0.780132i	$0.284848\pi$
$758$	7929.64	0.379971
$759$	5482.15	0.262173
$760$	−1685.50	−0.0804467
$761$	−23064.0	−1.09865	−0.549323	−	0.835610i	$-0.685114\pi$
$761$	−23064.0	−1.09865	−0.549323	+	0.835610i	$0.685114\pi$
$762$	21773.3	1.03512
$763$	5007.28	0.237583
$764$	−10603.2	−0.502108
$765$	4297.58	0.203110
$766$	−39632.6	−1.86943
$767$	2722.91	0.128186
$768$	5710.21	0.268293
$769$	19455.7	0.912341	0.456171	−	0.889892i	$-0.349221\pi$
$769$	19455.7	0.912341	0.456171	+	0.889892i	$0.349221\pi$
$770$	−3880.53	−0.181616
$771$	−6023.16	−0.281347
$772$	3342.08	0.155808
$773$	−14025.4	−0.652599	−0.326300	−	0.945266i	$-0.605802\pi$
$773$	−14025.4	−0.652599	−0.326300	+	0.945266i	$0.605802\pi$
$774$	3750.93	0.174192
$775$	−8107.28	−0.375771
$776$	−2371.48	−0.109705
$777$	4279.30	0.197579
$778$	19355.1	0.891920
$779$	14767.8	0.679220
$780$	2737.85	0.125681
$781$	−16724.3	−0.766253
$782$	9381.00	0.428982
$783$	4052.85	0.184977
$784$	16376.7	0.746021
$785$	−16132.1	−0.733479
$786$	−17447.6	−0.791774
$787$	−41219.6	−1.86699	−0.933495	−	0.358589i	$-0.883258\pi$
$787$	−41219.6	−1.86699	−0.933495	+	0.358589i	$0.883258\pi$
$788$	40854.3	1.84692
$789$	14386.1	0.649124
$790$	23219.0	1.04569
$791$	−4446.78	−0.199885
$792$	−3282.89	−0.147288
$793$	−853.104	−0.0382025
$794$	19328.6	0.863910
$795$	6129.73	0.273458
$796$	4044.78	0.180105
$797$	10289.5	0.457305	0.228653	−	0.973508i	$-0.426568\pi$
$797$	10289.5	0.457305	0.228653	+	0.973508i	$0.426568\pi$
$798$	1806.53	0.0801385
$799$	7383.19	0.326907
$800$	17623.3	0.778847
$801$	−34115.7	−1.50489
$802$	−49224.6	−2.16731
$803$	−27611.2	−1.21342
$804$	−21029.7	−0.922462
$805$	−2853.65	−0.124941
$806$	−7773.12	−0.339698
$807$	−6428.00	−0.280392
$808$	5834.85	0.254046
$809$	−20063.0	−0.871912	−0.435956	−	0.899968i	$-0.643590\pi$
$809$	−20063.0	−0.871912	−0.435956	+	0.899968i	$0.643590\pi$
$810$	−8590.07	−0.372623
$811$	26523.6	1.14842	0.574210	−	0.818708i	$-0.305309\pi$
$811$	26523.6	1.14842	0.574210	+	0.818708i	$0.305309\pi$
$812$	−1476.49	−0.0638112
$813$	4425.73	0.190919
$814$	42495.7	1.82982
$815$	16479.1	0.708267
$816$	−3418.25	−0.146646
$817$	−1647.35	−0.0705427
$818$	23311.2	0.996403
$819$	1499.99	0.0639976
$820$	−27328.5	−1.16384
$821$	−9204.45	−0.391276	−0.195638	−	0.980676i	$-0.562678\pi$
$821$	−9204.45	−0.391276	−0.195638	+	0.980676i	$0.562678\pi$
$822$	16604.5	0.704558
$823$	15569.2	0.659427	0.329713	−	0.944081i	$-0.393048\pi$
$823$	15569.2	0.659427	0.329713	+	0.944081i	$0.393048\pi$
$824$	−9680.62	−0.409272
$825$	−4521.92	−0.190828
$826$	−3324.82	−0.140055
$827$	−11786.2	−0.495582	−0.247791	−	0.968814i	$-0.579705\pi$
$827$	−11786.2	−0.495582	−0.247791	+	0.968814i	$0.579705\pi$
$828$	−16226.4	−0.681046
$829$	−33661.5	−1.41027	−0.705133	−	0.709075i	$-0.749113\pi$
$829$	−33661.5	−1.41027	−0.705133	+	0.709075i	$0.749113\pi$
$830$	−17571.8	−0.734850
$831$	−2035.59	−0.0849747
$832$	10528.2	0.438702
$833$	−8772.02	−0.364865
$834$	21327.3	0.885498
$835$	−25152.9	−1.04246
$836$	9690.79	0.400913
$837$	−14073.4	−0.581182
$838$	−28818.1	−1.18795
$839$	−2686.31	−0.110538	−0.0552691	−	0.998471i	$-0.517602\pi$
$839$	−2686.31	−0.110538	−0.0552691	+	0.998471i	$0.517602\pi$
$840$	−497.379	−0.0204300
$841$	−23213.5	−0.951803
$842$	68821.8	2.81681
$843$	−12618.8	−0.515558
$844$	974.618	0.0397485
$845$	14724.6	0.599458
$846$	−23641.5	−0.960771
$847$	−2779.49	−0.112756
$848$	16750.9	0.678337
$849$	−9136.93	−0.369350
$850$	−7737.86	−0.312243
$851$	31250.3	1.25881
$852$	−14407.9	−0.579352
$853$	7920.78	0.317940	0.158970	−	0.987283i	$-0.449183\pi$
$853$	7920.78	0.317940	0.158970	+	0.987283i	$0.449183\pi$
$854$	1041.68	0.0417396
$855$	6043.68	0.241742
$856$	−884.129	−0.0353025
$857$	36678.1	1.46196	0.730980	−	0.682398i	$-0.239063\pi$
$857$	36678.1	1.46196	0.730980	+	0.682398i	$0.239063\pi$
$858$	−4335.54	−0.172509
$859$	31205.9	1.23950	0.619750	−	0.784799i	$-0.287234\pi$
$859$	31205.9	1.23950	0.619750	+	0.784799i	$0.287234\pi$
$860$	3048.48	0.120875
$861$	4357.88	0.172493
$862$	−29622.0	−1.17045
$863$	38340.4	1.51231	0.756155	−	0.654392i	$-0.227076\pi$
$863$	38340.4	1.51231	0.756155	+	0.654392i	$0.227076\pi$
$864$	30592.3	1.20460
$865$	−8824.46	−0.346868
$866$	−37272.0	−1.46253
$867$	−10290.3	−0.403086
$868$	5127.09	0.200489
$869$	−19861.8	−0.775334
$870$	2661.50	0.103716
$871$	14196.5	0.552273
$872$	6373.38	0.247511
$873$	8503.40	0.329664
$874$	13192.5	0.510575
$875$	6674.51	0.257874
$876$	−23786.9	−0.917449
$877$	−38409.6	−1.47890	−0.739452	−	0.673210i	$-0.764915\pi$
$877$	−38409.6	−1.47890	−0.739452	+	0.673210i	$0.764915\pi$
$878$	74201.5	2.85214
$879$	1848.39	0.0709267
$880$	10325.9	0.395551
$881$	41203.4	1.57568	0.787842	−	0.615877i	$-0.211198\pi$
$881$	41203.4	1.57568	0.787842	+	0.615877i	$0.211198\pi$
$882$	28088.6	1.07233
$883$	30194.6	1.15077	0.575384	−	0.817883i	$-0.304852\pi$
$883$	30194.6	1.15077	0.575384	+	0.817883i	$0.304852\pi$
$884$	−4007.59	−0.152477
$885$	3237.47	0.122967
$886$	11448.2	0.434096
$887$	−13570.8	−0.513712	−0.256856	−	0.966450i	$-0.582687\pi$
$887$	−13570.8	−0.513712	−0.256856	+	0.966450i	$0.582687\pi$
$888$	5446.80	0.205836
$889$	9694.99	0.365759
$890$	−51328.3	−1.93318
$891$	7348.03	0.276283
$892$	41803.0	1.56913
$893$	10383.0	0.389085
$894$	−8349.98	−0.312377
$895$	−1558.44	−0.0582045
$896$	−3368.57	−0.125598
$897$	−3188.25	−0.118676
$898$	−50269.8	−1.86807
$899$	−4081.82	−0.151431
$900$	13384.2	0.495713
$901$	−8972.51	−0.331762
$902$	43276.1	1.59749
$903$	−486.121	−0.0179148
$904$	−5659.96	−0.208239
$905$	−4920.12	−0.180719
$906$	−9717.94	−0.356354
$907$	21966.6	0.804176	0.402088	−	0.915601i	$-0.368285\pi$
$907$	21966.6	0.804176	0.402088	+	0.915601i	$0.368285\pi$
$908$	4791.31	0.175116
$909$	−20922.0	−0.763409
$910$	2256.79	0.0822110
$911$	27091.0	0.985252	0.492626	−	0.870241i	$-0.336037\pi$
$911$	27091.0	0.985252	0.492626	+	0.870241i	$0.336037\pi$
$912$	−4807.08	−0.174538
$913$	15031.1	0.544859
$914$	544.020	0.0196877
$915$	−1014.32	−0.0366473
$916$	−44687.5	−1.61192
$917$	−7768.88	−0.279772
$918$	−13432.2	−0.482928
$919$	−24533.7	−0.880622	−0.440311	−	0.897845i	$-0.645132\pi$
$919$	−24533.7	−0.880622	−0.440311	+	0.897845i	$0.645132\pi$
$920$	−3632.19	−0.130163
$921$	−11746.2	−0.420251
$922$	−4092.38	−0.146177
$923$	9726.35	0.346855
$924$	2859.69	0.101815
$925$	−25776.6	−0.916248
$926$	26527.9	0.941426
$927$	34711.8	1.22986
$928$	8872.89	0.313865
$929$	9220.40	0.325631	0.162816	−	0.986657i	$-0.447942\pi$
$929$	9220.40	0.325631	0.162816	+	0.986657i	$0.447942\pi$
$930$	−9242.02	−0.325868
$931$	−12336.1	−0.434263
$932$	8394.76	0.295042
$933$	−14793.1	−0.519084
$934$	−59062.9	−2.06916
$935$	−5530.97	−0.193457
$936$	1909.23	0.0666720
$937$	22526.6	0.785392	0.392696	−	0.919668i	$-0.371542\pi$
$937$	22526.6	0.785392	0.392696	+	0.919668i	$0.371542\pi$
$938$	−17334.6	−0.603407
$939$	982.580	0.0341483
$940$	−19214.1	−0.666697
$941$	−776.782	−0.0269100	−0.0134550	−	0.999909i	$-0.504283\pi$
$941$	−776.782	−0.0269100	−0.0134550	+	0.999909i	$0.504283\pi$
$942$	22007.8	0.761204
$943$	31824.1	1.09898
$944$	8847.15	0.305032
$945$	4085.99	0.140653
$946$	−4827.43	−0.165913
$947$	−45677.6	−1.56739	−0.783697	−	0.621143i	$-0.786669\pi$
$947$	−45677.6	−1.56739	−0.783697	+	0.621143i	$0.786669\pi$
$948$	−17110.8	−0.586217
$949$	16057.8	0.549271
$950$	−10881.7	−0.371632
$951$	11490.1	0.391790
$952$	728.048	0.0247859
$953$	−41584.5	−1.41349	−0.706743	−	0.707470i	$-0.749836\pi$
$953$	−41584.5	−1.41349	−0.706743	+	0.707470i	$0.749836\pi$
$954$	28730.6	0.975040
$955$	8510.52	0.288371
$956$	−36500.5	−1.23484
$957$	−2276.67	−0.0769012
$958$	−85855.7	−2.89548
$959$	7393.47	0.248955
$960$	12517.7	0.420842
$961$	−15617.0	−0.524217
$962$	−24714.2	−0.828292
$963$	3170.22	0.106084
$964$	−29311.6	−0.979318
$965$	−2682.48	−0.0894839
$966$	3893.01	0.129664
$967$	5961.61	0.198255	0.0991274	−	0.995075i	$-0.468395\pi$
$967$	5961.61	0.198255	0.0991274	+	0.995075i	$0.468395\pi$
$968$	−3537.80	−0.117468
$969$	2574.87	0.0853631
$970$	12793.7	0.423485
$971$	−25246.9	−0.834410	−0.417205	−	0.908812i	$-0.636990\pi$
$971$	−25246.9	−0.834410	−0.417205	+	0.908812i	$0.636990\pi$
$972$	36326.4	1.19874
$973$	9496.43	0.312890
$974$	−73713.5	−2.42498
$975$	2629.81	0.0863807
$976$	−2771.86	−0.0909068
$977$	44505.1	1.45736	0.728682	−	0.684852i	$-0.240133\pi$
$977$	44505.1	1.45736	0.728682	+	0.684852i	$0.240133\pi$
$978$	−22481.1	−0.735039
$979$	43906.8	1.43337
$980$	22828.4	0.744109
$981$	−22853.0	−0.743772
$982$	−14534.3	−0.472308
$983$	14970.7	0.485750	0.242875	−	0.970058i	$-0.421910\pi$
$983$	14970.7	0.485750	0.242875	+	0.970058i	$0.421910\pi$
$984$	5546.82	0.179701
$985$	−32791.1	−1.06072
$986$	−3895.82	−0.125830
$987$	3063.94	0.0988109
$988$	−5635.86	−0.181478
$989$	−3549.97	−0.114138
$990$	17710.6	0.568564
$991$	−10815.1	−0.346674	−0.173337	−	0.984863i	$-0.555455\pi$
$991$	−10815.1	−0.346674	−0.173337	+	0.984863i	$0.555455\pi$
$992$	−30811.0	−0.986139
$993$	24705.2	0.789522
$994$	−11876.4	−0.378969
$995$	−3246.49	−0.103438
$996$	12949.2	0.411959
$997$	−39556.1	−1.25652	−0.628262	−	0.778002i	$-0.716233\pi$
$997$	−39556.1	−1.25652	−0.628262	+	0.778002i	$0.716233\pi$
$998$	5812.27	0.184353
$999$	−44745.6	−1.41711

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.4.a.b.1.5	✓	6
3.2	odd	2		387.4.a.h.1.2		6
4.3	odd	2		688.4.a.i.1.3		6
5.4	even	2		1075.4.a.b.1.2		6
7.6	odd	2		2107.4.a.c.1.5		6
43.42	odd	2		1849.4.a.c.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.a.b.1.5	✓	6	1.1	even	1	trivial
387.4.a.h.1.2		6	3.2	odd	2
688.4.a.i.1.3		6	4.3	odd	2
1075.4.a.b.1.2		6	5.4	even	2
1849.4.a.c.1.2		6	43.42	odd	2
2107.4.a.c.1.5		6	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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	43.a (trivial)

\(f(q)\)	\(=\)	\(q+4.17112 q^{2} +2.46717 q^{3} +9.39827 q^{4} -7.54340 q^{5} +10.2909 q^{6} +4.58222 q^{7} +5.83236 q^{8} -20.9131 q^{9} +O(q^{10})\)	\(q+4.17112 q^{2} +2.46717 q^{3} +9.39827 q^{4} -7.54340 q^{5} +10.2909 q^{6} +4.58222 q^{7} +5.83236 q^{8} -20.9131 q^{9} -31.4645 q^{10} +26.9150 q^{11} +23.1872 q^{12} -15.6529 q^{13} +19.1130 q^{14} -18.6109 q^{15} -50.8587 q^{16} +27.2420 q^{17} -87.2309 q^{18} +38.3104 q^{19} -70.8949 q^{20} +11.3051 q^{21} +112.266 q^{22} +82.5575 q^{23} +14.3894 q^{24} -68.0971 q^{25} -65.2903 q^{26} -118.210 q^{27} +43.0650 q^{28} -34.2852 q^{29} -77.6283 q^{30} +119.055 q^{31} -258.797 q^{32} +66.4040 q^{33} +113.630 q^{34} -34.5655 q^{35} -196.547 q^{36} +378.527 q^{37} +159.797 q^{38} -38.6185 q^{39} -43.9958 q^{40} +385.478 q^{41} +47.1551 q^{42} -43.0000 q^{43} +252.955 q^{44} +157.756 q^{45} +344.358 q^{46} +271.022 q^{47} -125.477 q^{48} -322.003 q^{49} -284.041 q^{50} +67.2108 q^{51} -147.110 q^{52} -329.363 q^{53} -493.068 q^{54} -203.031 q^{55} +26.7252 q^{56} +94.5184 q^{57} -143.008 q^{58} -173.956 q^{59} -174.910 q^{60} +54.5012 q^{61} +496.592 q^{62} -95.8283 q^{63} -672.604 q^{64} +118.076 q^{65} +276.979 q^{66} -906.954 q^{67} +256.028 q^{68} +203.684 q^{69} -144.177 q^{70} -621.376 q^{71} -121.972 q^{72} -1025.87 q^{73} +1578.88 q^{74} -168.007 q^{75} +360.052 q^{76} +123.331 q^{77} -161.082 q^{78} -737.945 q^{79} +383.647 q^{80} +273.009 q^{81} +1607.88 q^{82} +558.465 q^{83} +106.249 q^{84} -205.498 q^{85} -179.358 q^{86} -84.5875 q^{87} +156.978 q^{88} +1631.31 q^{89} +658.018 q^{90} -71.7252 q^{91} +775.898 q^{92} +293.729 q^{93} +1130.47 q^{94} -288.991 q^{95} -638.496 q^{96} -406.607 q^{97} -1343.12 q^{98} -562.875 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 7 q^{3} + 22 q^{4} + 43 q^{5} - 3 q^{6} + 8 q^{7} + 54 q^{8} + 81 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 + 7 * q^3 + 22 * q^4 + 43 * q^5 - 3 * q^6 + 8 * q^7 + 54 * q^8 + 81 * q^9	\( 6 q + 6 q^{2} + 7 q^{3} + 22 q^{4} + 43 q^{5} - 3 q^{6} + 8 q^{7} + 54 q^{8} + 81 q^{9} + 57 q^{10} - 28 q^{11} - 157 q^{12} + 56 q^{13} - 184 q^{14} - 124 q^{15} - 54 q^{16} + 19 q^{17} - 81 q^{18} - 75 q^{19} + 135 q^{20} - 18 q^{21} - 504 q^{22} + 131 q^{23} - 567 q^{24} + 105 q^{25} + 44 q^{26} + 238 q^{27} - 404 q^{28} + 515 q^{29} - 396 q^{30} + 237 q^{31} + 558 q^{32} + 540 q^{33} - 107 q^{34} + 198 q^{35} + 73 q^{36} + 269 q^{37} + 527 q^{38} + 290 q^{39} + 613 q^{40} + 471 q^{41} + 362 q^{42} - 258 q^{43} - 428 q^{44} + 334 q^{45} - 67 q^{46} + 415 q^{47} - 989 q^{48} + 350 q^{49} + 1335 q^{50} - 1241 q^{51} - 8 q^{52} + 450 q^{53} + 402 q^{54} - 1732 q^{55} - 780 q^{56} - 1000 q^{57} - 1055 q^{58} + 356 q^{59} - 2732 q^{60} - 1328 q^{61} + 1603 q^{62} - 2290 q^{63} + 466 q^{64} - 62 q^{65} + 156 q^{66} - 632 q^{67} + 571 q^{68} - 1130 q^{69} - 1902 q^{70} - 144 q^{71} + 567 q^{72} + 864 q^{73} + 1207 q^{74} - 2494 q^{75} + 1005 q^{76} + 2660 q^{77} + 2222 q^{78} - 1613 q^{79} + 2399 q^{80} - 102 q^{81} + 1673 q^{82} - 682 q^{83} + 3758 q^{84} + 84 q^{85} - 258 q^{86} + 449 q^{87} - 608 q^{88} + 3378 q^{89} + 930 q^{90} - 3900 q^{91} + 3491 q^{92} + 1879 q^{93} + 3197 q^{94} - 79 q^{95} - 591 q^{96} - 55 q^{97} + 2398 q^{98} - 1612 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 7 * q^3 + 22 * q^4 + 43 * q^5 - 3 * q^6 + 8 * q^7 + 54 * q^8 + 81 * q^9 + 57 * q^10 - 28 * q^11 - 157 * q^12 + 56 * q^13 - 184 * q^14 - 124 * q^15 - 54 * q^16 + 19 * q^17 - 81 * q^18 - 75 * q^19 + 135 * q^20 - 18 * q^21 - 504 * q^22 + 131 * q^23 - 567 * q^24 + 105 * q^25 + 44 * q^26 + 238 * q^27 - 404 * q^28 + 515 * q^29 - 396 * q^30 + 237 * q^31 + 558 * q^32 + 540 * q^33 - 107 * q^34 + 198 * q^35 + 73 * q^36 + 269 * q^37 + 527 * q^38 + 290 * q^39 + 613 * q^40 + 471 * q^41 + 362 * q^42 - 258 * q^43 - 428 * q^44 + 334 * q^45 - 67 * q^46 + 415 * q^47 - 989 * q^48 + 350 * q^49 + 1335 * q^50 - 1241 * q^51 - 8 * q^52 + 450 * q^53 + 402 * q^54 - 1732 * q^55 - 780 * q^56 - 1000 * q^57 - 1055 * q^58 + 356 * q^59 - 2732 * q^60 - 1328 * q^61 + 1603 * q^62 - 2290 * q^63 + 466 * q^64 - 62 * q^65 + 156 * q^66 - 632 * q^67 + 571 * q^68 - 1130 * q^69 - 1902 * q^70 - 144 * q^71 + 567 * q^72 + 864 * q^73 + 1207 * q^74 - 2494 * q^75 + 1005 * q^76 + 2660 * q^77 + 2222 * q^78 - 1613 * q^79 + 2399 * q^80 - 102 * q^81 + 1673 * q^82 - 682 * q^83 + 3758 * q^84 + 84 * q^85 - 258 * q^86 + 449 * q^87 - 608 * q^88 + 3378 * q^89 + 930 * q^90 - 3900 * q^91 + 3491 * q^92 + 1879 * q^93 + 3197 * q^94 - 79 * q^95 - 591 * q^96 - 55 * q^97 + 2398 * q^98 - 1612 * q^99

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