LMFDB - Embedded newform 1849.4.a.g.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1849 = 43^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1849.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$109.094531601$
Analytic rank:	$1$
Dimension:	$30$
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.830523 q^{2} -7.00735 q^{3} -7.31023 q^{4} -4.56308 q^{5} -5.81976 q^{6} +20.3840 q^{7} -12.7155 q^{8} +22.1029 q^{9} +O(q^{10})$	\(q+0.830523 q^{2} -7.00735 q^{3} -7.31023 q^{4} -4.56308 q^{5} -5.81976 q^{6} +20.3840 q^{7} -12.7155 q^{8} +22.1029 q^{9} -3.78975 q^{10} -14.9524 q^{11} +51.2253 q^{12} -38.4779 q^{13} +16.9294 q^{14} +31.9751 q^{15} +47.9213 q^{16} -56.2723 q^{17} +18.3570 q^{18} +82.5783 q^{19} +33.3572 q^{20} -142.838 q^{21} -12.4183 q^{22} -84.1335 q^{23} +89.1019 q^{24} -104.178 q^{25} -31.9568 q^{26} +34.3154 q^{27} -149.012 q^{28} -144.523 q^{29} +26.5561 q^{30} +136.963 q^{31} +141.524 q^{32} +104.777 q^{33} -46.7354 q^{34} -93.0141 q^{35} -161.578 q^{36} -250.262 q^{37} +68.5831 q^{38} +269.628 q^{39} +58.0219 q^{40} +447.286 q^{41} -118.630 q^{42} +109.306 q^{44} -100.858 q^{45} -69.8748 q^{46} +338.476 q^{47} -335.802 q^{48} +72.5092 q^{49} -86.5224 q^{50} +394.319 q^{51} +281.282 q^{52} +540.674 q^{53} +28.4997 q^{54} +68.2293 q^{55} -259.193 q^{56} -578.655 q^{57} -120.029 q^{58} +48.6306 q^{59} -233.746 q^{60} +710.497 q^{61} +113.751 q^{62} +450.547 q^{63} -265.832 q^{64} +175.578 q^{65} +87.0197 q^{66} +907.541 q^{67} +411.363 q^{68} +589.553 q^{69} -77.2504 q^{70} +856.353 q^{71} -281.050 q^{72} -785.853 q^{73} -207.848 q^{74} +730.013 q^{75} -603.666 q^{76} -304.791 q^{77} +223.932 q^{78} +385.961 q^{79} -218.669 q^{80} -837.239 q^{81} +371.482 q^{82} +959.796 q^{83} +1044.18 q^{84} +256.775 q^{85} +1012.72 q^{87} +190.128 q^{88} -1204.79 q^{89} -83.7646 q^{90} -784.335 q^{91} +615.035 q^{92} -959.746 q^{93} +281.112 q^{94} -376.812 q^{95} -991.706 q^{96} -500.574 q^{97} +60.2205 q^{98} -330.493 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 6 q^{2} - 2 q^{3} + 114 q^{4} - 27 q^{5} + 8 q^{6} - 48 q^{7} - 90 q^{8} + 216 q^{9}+O(q^{10}) $ 30 * q - 6 * q^2 - 2 * q^3 + 114 * q^4 - 27 * q^5 + 8 * q^6 - 48 * q^7 - 90 * q^8 + 216 * q^9	\( 30 q - 6 q^{2} - 2 q^{3} + 114 q^{4} - 27 q^{5} + 8 q^{6} - 48 q^{7} - 90 q^{8} + 216 q^{9} - 27 q^{10} + 80 q^{11} + 36 q^{12} - 13 q^{13} + 36 q^{14} + 16 q^{15} + 318 q^{16} + 66 q^{17} - 80 q^{18} - 254 q^{19} - 312 q^{20} - 548 q^{21} - 305 q^{22} - 105 q^{23} + 123 q^{24} + 523 q^{25} - 549 q^{26} + 10 q^{27} - 578 q^{28} - 793 q^{29} - 1560 q^{30} - 359 q^{31} - 676 q^{32} - 208 q^{33} - 1007 q^{34} - 514 q^{35} + 776 q^{36} - 510 q^{37} - 2066 q^{38} - 898 q^{39} - 1248 q^{40} - 270 q^{41} + 915 q^{42} + 3256 q^{44} - 807 q^{45} - 1960 q^{46} + 1421 q^{47} + 632 q^{48} + 386 q^{49} + 141 q^{50} - 209 q^{51} + 2825 q^{52} - 21 q^{53} + 2368 q^{54} - 2258 q^{55} + 2521 q^{56} - 1723 q^{57} - 347 q^{58} + 1752 q^{59} + 2711 q^{60} - 1759 q^{61} - 395 q^{62} - 2204 q^{63} + 222 q^{64} - 1151 q^{65} + 160 q^{66} - 3001 q^{67} + 1921 q^{68} - 1660 q^{69} - 1597 q^{70} - 727 q^{71} - 9100 q^{72} - 4623 q^{73} - 2649 q^{74} - 1027 q^{75} - 874 q^{76} - 3556 q^{77} - 4979 q^{78} + 546 q^{79} - 5809 q^{80} - 410 q^{81} + 4397 q^{82} - 492 q^{83} - 10611 q^{84} + 1723 q^{85} + 5937 q^{87} - 3974 q^{88} - 5218 q^{89} + 10492 q^{90} - 1104 q^{91} + 1060 q^{92} - 1997 q^{93} + 2134 q^{94} + 6346 q^{95} - 11984 q^{96} + 2590 q^{97} - 6270 q^{98} - 2693 q^{99}+O(q^{100}) \) 30 * q - 6 * q^2 - 2 * q^3 + 114 * q^4 - 27 * q^5 + 8 * q^6 - 48 * q^7 - 90 * q^8 + 216 * q^9 - 27 * q^10 + 80 * q^11 + 36 * q^12 - 13 * q^13 + 36 * q^14 + 16 * q^15 + 318 * q^16 + 66 * q^17 - 80 * q^18 - 254 * q^19 - 312 * q^20 - 548 * q^21 - 305 * q^22 - 105 * q^23 + 123 * q^24 + 523 * q^25 - 549 * q^26 + 10 * q^27 - 578 * q^28 - 793 * q^29 - 1560 * q^30 - 359 * q^31 - 676 * q^32 - 208 * q^33 - 1007 * q^34 - 514 * q^35 + 776 * q^36 - 510 * q^37 - 2066 * q^38 - 898 * q^39 - 1248 * q^40 - 270 * q^41 + 915 * q^42 + 3256 * q^44 - 807 * q^45 - 1960 * q^46 + 1421 * q^47 + 632 * q^48 + 386 * q^49 + 141 * q^50 - 209 * q^51 + 2825 * q^52 - 21 * q^53 + 2368 * q^54 - 2258 * q^55 + 2521 * q^56 - 1723 * q^57 - 347 * q^58 + 1752 * q^59 + 2711 * q^60 - 1759 * q^61 - 395 * q^62 - 2204 * q^63 + 222 * q^64 - 1151 * q^65 + 160 * q^66 - 3001 * q^67 + 1921 * q^68 - 1660 * q^69 - 1597 * q^70 - 727 * q^71 - 9100 * q^72 - 4623 * q^73 - 2649 * q^74 - 1027 * q^75 - 874 * q^76 - 3556 * q^77 - 4979 * q^78 + 546 * q^79 - 5809 * q^80 - 410 * q^81 + 4397 * q^82 - 492 * q^83 - 10611 * q^84 + 1723 * q^85 + 5937 * q^87 - 3974 * q^88 - 5218 * q^89 + 10492 * q^90 - 1104 * q^91 + 1060 * q^92 - 1997 * q^93 + 2134 * q^94 + 6346 * q^95 - 11984 * q^96 + 2590 * q^97 - 6270 * q^98 - 2693 * 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 $

$2$	0.830523	0.293634	0.146817	−	0.989164i	$-0.453097\pi$
$2$	0.830523	0.293634	0.146817	+	0.989164i	$0.453097\pi$
$3$	−7.00735	−1.34856	−0.674282	−	0.738474i	$-0.735547\pi$
$3$	−7.00735	−1.34856	−0.674282	+	0.738474i	$0.735547\pi$
$4$	−7.31023	−0.913779
$5$	−4.56308	−0.408135	−0.204067	−	0.978957i	$-0.565416\pi$
$5$	−4.56308	−0.408135	−0.204067	+	0.978957i	$0.565416\pi$
$6$	−5.81976	−0.395985
$7$	20.3840	1.10063	0.550317	−	0.834956i	$-0.314507\pi$
$7$	20.3840	1.10063	0.550317	+	0.834956i	$0.314507\pi$
$8$	−12.7155	−0.561951
$9$	22.1029	0.818628
$10$	−3.78975	−0.119842
$11$	−14.9524	−0.409848	−0.204924	−	0.978778i	$-0.565695\pi$
$11$	−14.9524	−0.409848	−0.204924	+	0.978778i	$0.565695\pi$
$12$	51.2253	1.23229
$13$	−38.4779	−0.820912	−0.410456	−	0.911880i	$-0.634630\pi$
$13$	−38.4779	−0.820912	−0.410456	+	0.911880i	$0.634630\pi$
$14$	16.9294	0.323184
$15$	31.9751	0.550396
$16$	47.9213	0.748771
$17$	−56.2723	−0.802825	−0.401413	−	0.915897i	$-0.631481\pi$
$17$	−56.2723	−0.802825	−0.401413	+	0.915897i	$0.631481\pi$
$18$	18.3570	0.240377
$19$	82.5783	0.997092	0.498546	−	0.866863i	$-0.333867\pi$
$19$	82.5783	0.997092	0.498546	+	0.866863i	$0.333867\pi$
$20$	33.3572	0.372945
$21$	−142.838	−1.48428
$22$	−12.4183	−0.120346
$23$	−84.1335	−0.762741	−0.381371	−	0.924422i	$-0.624548\pi$
$23$	−84.1335	−0.762741	−0.381371	+	0.924422i	$0.624548\pi$
$24$	89.1019	0.757827
$25$	−104.178	−0.833426
$26$	−31.9568	−0.241048
$27$	34.3154	0.244593
$28$	−149.012	−1.00574
$29$	−144.523	−0.925420	−0.462710	−	0.886510i	$-0.653123\pi$
$29$	−144.523	−0.925420	−0.462710	+	0.886510i	$0.653123\pi$
$30$	26.5561	0.161615
$31$	136.963	0.793524	0.396762	−	0.917922i	$-0.370134\pi$
$31$	136.963	0.793524	0.396762	+	0.917922i	$0.370134\pi$
$32$	141.524	0.781816
$33$	104.777	0.552707
$34$	−46.7354	−0.235737
$35$	−93.0141	−0.449207
$36$	−161.578	−0.748045
$37$	−250.262	−1.11197	−0.555984	−	0.831193i	$-0.687658\pi$
$37$	−250.262	−1.11197	−0.555984	+	0.831193i	$0.687658\pi$
$38$	68.5831	0.292780
$39$	269.628	1.10705
$40$	58.0219	0.229352
$41$	447.286	1.70377	0.851883	−	0.523732i	$-0.175461\pi$
$41$	447.286	1.70377	0.851883	+	0.523732i	$0.175461\pi$
$42$	−118.630	−0.435835
$43$	0	0
$43$	0	0
$44$	109.306	0.374511
$45$	−100.858	−0.334110
$46$	−69.8748	−0.223967
$47$	338.476	1.05047	0.525233	−	0.850959i	$-0.323978\pi$
$47$	338.476	1.05047	0.525233	+	0.850959i	$0.323978\pi$
$48$	−335.802	−1.00977
$49$	72.5092	0.211397
$50$	−86.5224	−0.244722
$51$	394.319	1.08266
$52$	281.282	0.750132
$53$	540.674	1.40127	0.700634	−	0.713520i	$-0.252900\pi$
$53$	540.674	1.40127	0.700634	+	0.713520i	$0.252900\pi$
$54$	28.4997	0.0718208
$55$	68.2293	0.167273
$56$	−259.193	−0.618503
$57$	−578.655	−1.34464
$58$	−120.029	−0.271735
$59$	48.6306	0.107308	0.0536540	−	0.998560i	$-0.482913\pi$
$59$	48.6306	0.107308	0.0536540	+	0.998560i	$0.482913\pi$
$60$	−233.746	−0.502940
$61$	710.497	1.49131	0.745654	−	0.666333i	$-0.232137\pi$
$61$	710.497	1.49131	0.745654	+	0.666333i	$0.232137\pi$
$62$	113.751	0.233006
$63$	450.547	0.901010
$64$	−265.832	−0.519203
$65$	175.578	0.335043
$66$	87.0197	0.162294
$67$	907.541	1.65483	0.827417	−	0.561588i	$-0.189810\pi$
$67$	907.541	1.65483	0.827417	+	0.561588i	$0.189810\pi$
$68$	411.363	0.733605
$69$	589.553	1.02861
$70$	−77.2504	−0.131903
$71$	856.353	1.43141	0.715707	−	0.698401i	$-0.246105\pi$
$71$	856.353	1.43141	0.715707	+	0.698401i	$0.246105\pi$
$72$	−281.050	−0.460029
$73$	−785.853	−1.25996	−0.629980	−	0.776611i	$-0.716937\pi$
$73$	−785.853	−1.25996	−0.629980	+	0.776611i	$0.716937\pi$
$74$	−207.848	−0.326512
$75$	730.013	1.12393
$76$	−603.666	−0.911122
$77$	−304.791	−0.451093
$78$	223.932	0.325069
$79$	385.961	0.549671	0.274836	−	0.961491i	$-0.411377\pi$
$79$	385.961	0.549671	0.274836	+	0.961491i	$0.411377\pi$
$80$	−218.669	−0.305599
$81$	−837.239	−1.14848
$82$	371.482	0.500284
$83$	959.796	1.26929	0.634646	−	0.772803i	$-0.281146\pi$
$83$	959.796	1.26929	0.634646	+	0.772803i	$0.281146\pi$
$84$	1044.18	1.35630
$85$	256.775	0.327661
$86$	0	0
$87$	1012.72	1.24799
$88$	190.128	0.230315
$89$	−1204.79	−1.43491	−0.717457	−	0.696603i	$-0.754694\pi$
$89$	−1204.79	−1.43491	−0.717457	+	0.696603i	$0.754694\pi$
$90$	−83.7646	−0.0981062
$91$	−784.335	−0.903524
$92$	615.035	0.696977
$93$	−959.746	−1.07012
$94$	281.112	0.308453
$95$	−376.812	−0.406948
$96$	−991.706	−1.05433
$97$	−500.574	−0.523976	−0.261988	−	0.965071i	$-0.584378\pi$
$97$	−500.574	−0.523976	−0.261988	+	0.965071i	$0.584378\pi$
$98$	60.2205	0.0620734
$99$	−330.493	−0.335513
$100$	761.567	0.761567
$101$	−1497.80	−1.47561	−0.737807	−	0.675012i	$-0.764138\pi$
$101$	−1497.80	−1.47561	−0.737807	+	0.675012i	$0.764138\pi$
$102$	327.491	0.317907
$103$	2.90953	0.00278334	0.00139167	−	0.999999i	$-0.499557\pi$
$103$	2.90953	0.00278334	0.00139167	+	0.999999i	$0.499557\pi$
$104$	489.266	0.461312
$105$	651.782	0.605785
$106$	449.042	0.411460
$107$	−1294.15	−1.16926	−0.584629	−	0.811301i	$-0.698760\pi$
$107$	−1294.15	−1.16926	−0.584629	+	0.811301i	$0.698760\pi$
$108$	−250.853	−0.223504
$109$	239.337	0.210315	0.105158	−	0.994456i	$-0.466465\pi$
$109$	239.337	0.210315	0.105158	+	0.994456i	$0.466465\pi$
$110$	56.6660	0.0491172
$111$	1753.67	1.49956
$112$	976.831	0.824123
$113$	18.8930	0.0157283	0.00786416	−	0.999969i	$-0.497497\pi$
$113$	18.8930	0.0157283	0.00786416	+	0.999969i	$0.497497\pi$
$114$	−480.586	−0.394833
$115$	383.908	0.311301
$116$	1056.49	0.845630
$117$	−850.475	−0.672021
$118$	40.3889	0.0315093
$119$	−1147.06	−0.883618
$120$	−406.580	−0.309296
$121$	−1107.42	−0.832024
$122$	590.084	0.437899
$123$	−3134.29	−2.29764
$124$	−1001.23	−0.725105
$125$	1045.76	0.748285
$126$	374.190	0.264567
$127$	1964.13	1.37235	0.686175	−	0.727436i	$-0.259288\pi$
$127$	1964.13	1.37235	0.686175	+	0.727436i	$0.259288\pi$
$128$	−1352.97	−0.934272
$129$	0	0
$130$	145.822	0.0983800
$131$	122.057	0.0814059	0.0407030	−	0.999171i	$-0.487040\pi$
$131$	122.057	0.0814059	0.0407030	+	0.999171i	$0.487040\pi$
$132$	−765.944	−0.505052
$133$	1683.28	1.09743
$134$	753.734	0.485916
$135$	−156.584	−0.0998267
$136$	715.530	0.451149
$137$	−999.830	−0.623513	−0.311756	−	0.950162i	$-0.600917\pi$
$137$	−999.830	−0.623513	−0.311756	+	0.950162i	$0.600917\pi$
$138$	489.637	0.302034
$139$	79.5799	0.0485603	0.0242801	−	0.999705i	$-0.492271\pi$
$139$	79.5799	0.0485603	0.0242801	+	0.999705i	$0.492271\pi$
$140$	679.955	0.410476
$141$	−2371.82	−1.41662
$142$	711.221	0.420312
$143$	575.339	0.336449
$144$	1059.20	0.612964
$145$	659.469	0.377696
$146$	−652.669	−0.369967
$147$	−508.097	−0.285083
$148$	1829.47	1.01609
$149$	235.834	0.129666	0.0648330	−	0.997896i	$-0.479349\pi$
$149$	235.834	0.129666	0.0648330	+	0.997896i	$0.479349\pi$
$150$	606.293	0.330024
$151$	−564.405	−0.304176	−0.152088	−	0.988367i	$-0.548600\pi$
$151$	−564.405	−0.304176	−0.152088	+	0.988367i	$0.548600\pi$
$152$	−1050.02	−0.560317
$153$	−1243.78	−0.657215
$154$	−253.136	−0.132456
$155$	−624.973	−0.323865
$156$	−1971.04	−1.01160
$157$	486.141	0.247123	0.123561	−	0.992337i	$-0.460568\pi$
$157$	486.141	0.247123	0.123561	+	0.992337i	$0.460568\pi$
$158$	320.550	0.161402
$159$	−3788.69	−1.88970
$160$	−645.785	−0.319086
$161$	−1714.98	−0.839500
$162$	−695.347	−0.337232
$163$	−982.776	−0.472251	−0.236126	−	0.971723i	$-0.575878\pi$
$163$	−982.776	−0.472251	−0.236126	+	0.971723i	$0.575878\pi$
$164$	−3269.77	−1.55687
$165$	−478.106	−0.225579
$166$	797.132	0.372708
$167$	2035.17	0.943029	0.471514	−	0.881858i	$-0.343708\pi$
$167$	2035.17	0.943029	0.471514	+	0.881858i	$0.343708\pi$
$168$	1816.26	0.834091
$169$	−716.450	−0.326104
$170$	213.258	0.0962124
$171$	1825.22	0.816247
$172$	0	0
$173$	3600.69	1.58240	0.791201	−	0.611556i	$-0.209456\pi$
$173$	3600.69	1.58240	0.791201	+	0.611556i	$0.209456\pi$
$174$	841.088	0.366452
$175$	−2123.57	−0.917298
$176$	−716.541	−0.306883
$177$	−340.772	−0.144712
$178$	−1000.60	−0.421340
$179$	−1335.29	−0.557564	−0.278782	−	0.960354i	$-0.589931\pi$
$179$	−1335.29	−0.557564	−0.278782	+	0.960354i	$0.589931\pi$
$180$	737.292	0.305303
$181$	1886.27	0.774614	0.387307	−	0.921951i	$-0.373405\pi$
$181$	1886.27	0.774614	0.387307	+	0.921951i	$0.373405\pi$
$182$	−651.409	−0.265306
$183$	−4978.70	−2.01113
$184$	1069.80	0.428623
$185$	1141.97	0.453832
$186$	−797.091	−0.314223
$187$	841.408	0.329037
$188$	−2474.34	−0.959893
$189$	699.486	0.269207
$190$	−312.951	−0.119494
$191$	144.895	0.0548911	0.0274456	−	0.999623i	$-0.491263\pi$
$191$	144.895	0.0548911	0.0274456	+	0.999623i	$0.491263\pi$
$192$	1862.78	0.700179
$193$	3015.69	1.12474	0.562368	−	0.826887i	$-0.309890\pi$
$193$	3015.69	1.12474	0.562368	+	0.826887i	$0.309890\pi$
$194$	−415.739	−0.153857
$195$	−1230.34	−0.451827
$196$	−530.059	−0.193170
$197$	−3923.49	−1.41897	−0.709485	−	0.704720i	$-0.751073\pi$
$197$	−3923.49	−1.41897	−0.709485	+	0.704720i	$0.751073\pi$
$198$	−274.482	−0.0985181
$199$	2882.17	1.02669	0.513346	−	0.858182i	$-0.328406\pi$
$199$	2882.17	1.02669	0.513346	+	0.858182i	$0.328406\pi$
$200$	1324.68	0.468345
$201$	−6359.46	−2.23165
$202$	−1243.96	−0.433290
$203$	−2945.96	−1.01855
$204$	−2882.57	−0.989314
$205$	−2041.01	−0.695366
$206$	2.41643	0.000817285 0
$207$	−1859.60	−0.624401
$208$	−1843.91	−0.614675
$209$	−1234.75	−0.408657
$210$	541.320	0.177879
$211$	−3809.94	−1.24307	−0.621533	−	0.783388i	$-0.713490\pi$
$211$	−3809.94	−1.24307	−0.621533	+	0.783388i	$0.713490\pi$
$212$	−3952.45	−1.28045
$213$	−6000.76	−1.93035
$214$	−1074.83	−0.343334
$215$	0	0
$216$	−436.337	−0.137449
$217$	2791.86	0.873380
$218$	198.775	0.0617557
$219$	5506.74	1.69914
$220$	−498.772	−0.152851
$221$	2165.24	0.659049
$222$	1456.47	0.440322
$223$	2160.95	0.648913	0.324456	−	0.945901i	$-0.394819\pi$
$223$	2160.95	0.648913	0.324456	+	0.945901i	$0.394819\pi$
$224$	2884.83	0.860494
$225$	−2302.65	−0.682266
$226$	15.6910	0.00461837
$227$	−2048.34	−0.598913	−0.299457	−	0.954110i	$-0.596805\pi$
$227$	−2048.34	−0.598913	−0.299457	+	0.954110i	$0.596805\pi$
$228$	4230.10	1.22871
$229$	−246.349	−0.0710882	−0.0355441	−	0.999368i	$-0.511316\pi$
$229$	−246.349	−0.0710882	−0.0355441	+	0.999368i	$0.511316\pi$
$230$	318.845	0.0914087
$231$	2135.78	0.608329
$232$	1837.68	0.520041
$233$	−5331.57	−1.49907	−0.749534	−	0.661965i	$-0.769723\pi$
$233$	−5331.57	−1.49907	−0.749534	+	0.661965i	$0.769723\pi$
$234$	−706.339	−0.197328
$235$	−1544.50	−0.428731
$236$	−355.501	−0.0980558
$237$	−2704.57	−0.741268
$238$	−952.657	−0.259460
$239$	−3285.36	−0.889172	−0.444586	−	0.895736i	$-0.646649\pi$
$239$	−3285.36	−0.889172	−0.444586	+	0.895736i	$0.646649\pi$
$240$	1532.29	0.412121
$241$	−6049.31	−1.61689	−0.808445	−	0.588571i	$-0.799691\pi$
$241$	−6049.31	−1.61689	−0.808445	+	0.588571i	$0.799691\pi$
$242$	−919.741	−0.244311
$243$	4940.31	1.30420
$244$	−5193.90	−1.36273
$245$	−330.865	−0.0862784
$246$	−2603.10	−0.674665
$247$	−3177.44	−0.818525
$248$	−1741.55	−0.445922
$249$	−6725.62	−1.71172
$250$	868.528	0.219722
$251$	−3881.73	−0.976147	−0.488073	−	0.872803i	$-0.662300\pi$
$251$	−3881.73	−0.976147	−0.488073	+	0.872803i	$0.662300\pi$
$252$	−3293.61	−0.823324
$253$	1258.00	0.312608
$254$	1631.26	0.402969
$255$	−1799.31	−0.441872
$256$	1002.98	0.244869
$257$	6016.31	1.46026	0.730131	−	0.683307i	$-0.239459\pi$
$257$	6016.31	1.46026	0.730131	+	0.683307i	$0.239459\pi$
$258$	0	0
$259$	−5101.35	−1.22387
$260$	−1283.52	−0.306155
$261$	−3194.38	−0.757575
$262$	101.371	0.0239036
$263$	−795.657	−0.186549	−0.0932743	−	0.995640i	$-0.529733\pi$
$263$	−795.657	−0.186549	−0.0932743	+	0.995640i	$0.529733\pi$
$264$	−1332.29	−0.310594
$265$	−2467.14	−0.571906
$266$	1398.00	0.322244
$267$	8442.37	1.93507
$268$	−6634.34	−1.51215
$269$	−6264.61	−1.41993	−0.709963	−	0.704239i	$-0.751289\pi$
$269$	−6264.61	−1.41993	−0.709963	+	0.704239i	$0.751289\pi$
$270$	−130.047	−0.0293125
$271$	6986.31	1.56601	0.783004	−	0.622017i	$-0.213686\pi$
$271$	6986.31	1.56601	0.783004	+	0.622017i	$0.213686\pi$
$272$	−2696.64	−0.601132
$273$	5496.11	1.21846
$274$	−830.382	−0.183085
$275$	1557.72	0.341578
$276$	−4309.77	−0.939919
$277$	−78.7787	−0.0170879	−0.00854396	−	0.999963i	$-0.502720\pi$
$277$	−78.7787	−0.0170879	−0.00854396	+	0.999963i	$0.502720\pi$
$278$	66.0930	0.0142590
$279$	3027.28	0.649601
$280$	1182.72	0.252432
$281$	−6663.90	−1.41472	−0.707358	−	0.706856i	$-0.750113\pi$
$281$	−6663.90	−1.41472	−0.707358	+	0.706856i	$0.750113\pi$
$282$	−1969.85	−0.415968
$283$	−1831.66	−0.384738	−0.192369	−	0.981323i	$-0.561617\pi$
$283$	−1831.66	−0.384738	−0.192369	+	0.981323i	$0.561617\pi$
$284$	−6260.14	−1.30800
$285$	2640.45	0.548796
$286$	477.832	0.0987930
$287$	9117.51	1.87522
$288$	3128.09	0.640016
$289$	−1746.43	−0.355471
$290$	547.704	0.110905
$291$	3507.70	0.706615
$292$	5744.77	1.15133
$293$	−1423.07	−0.283742	−0.141871	−	0.989885i	$-0.545312\pi$
$293$	−1423.07	−0.283742	−0.141871	+	0.989885i	$0.545312\pi$
$294$	−421.986	−0.0837100
$295$	−221.906	−0.0437961
$296$	3182.20	0.624871
$297$	−513.099	−0.100246
$298$	195.865	0.0380744
$299$	3237.28	0.626143
$300$	−5336.57	−1.02702
$301$	0	0
$302$	−468.752	−0.0893166
$303$	10495.6	1.98996
$304$	3957.26	0.746594
$305$	−3242.06	−0.608654
$306$	−1032.99	−0.192981
$307$	8324.83	1.54763	0.773816	−	0.633411i	$-0.218346\pi$
$307$	8324.83	1.54763	0.773816	+	0.633411i	$0.218346\pi$
$308$	2228.09	0.412200
$309$	−20.3881	−0.00375352
$310$	−519.054	−0.0950977
$311$	−9795.80	−1.78607	−0.893037	−	0.449984i	$-0.851430\pi$
$311$	−9795.80	−1.78607	−0.893037	+	0.449984i	$0.851430\pi$
$312$	−3428.46	−0.622109
$313$	−9275.95	−1.67511	−0.837553	−	0.546357i	$-0.816014\pi$
$313$	−9275.95	−1.67511	−0.837553	+	0.546357i	$0.816014\pi$
$314$	403.751	0.0725636
$315$	−2055.89	−0.367733
$316$	−2821.47	−0.502278
$317$	7079.71	1.25437	0.627186	−	0.778870i	$-0.284207\pi$
$317$	7079.71	1.25437	0.627186	+	0.778870i	$0.284207\pi$
$318$	−3146.59	−0.554881
$319$	2160.97	0.379282
$320$	1213.01	0.211905
$321$	9068.59	1.57682
$322$	−1424.33	−0.246506
$323$	−4646.87	−0.800491
$324$	6120.41	1.04945
$325$	4008.56	0.684169
$326$	−816.218	−0.138669
$327$	−1677.12	−0.283624
$328$	−5687.47	−0.957433
$329$	6899.52	1.15618
$330$	−397.078	−0.0662377
$331$	−4093.53	−0.679760	−0.339880	−	0.940469i	$-0.610386\pi$
$331$	−4093.53	−0.679760	−0.339880	+	0.940469i	$0.610386\pi$
$332$	−7016.33	−1.15985
$333$	−5531.52	−0.910287
$334$	1690.25	0.276906
$335$	−4141.19	−0.675395
$336$	−6844.99	−1.11138
$337$	−2177.63	−0.351997	−0.175999	−	0.984390i	$-0.556315\pi$
$337$	−2177.63	−0.351997	−0.175999	+	0.984390i	$0.556315\pi$
$338$	−595.028	−0.0957552
$339$	−132.390	−0.0212107
$340$	−1877.09	−0.299410
$341$	−2047.93	−0.325224
$342$	1515.89	0.239678
$343$	−5513.70	−0.867964
$344$	0	0
$345$	−2690.18	−0.419810
$346$	2990.46	0.464647
$347$	−6825.91	−1.05601	−0.528003	−	0.849243i	$-0.677059\pi$
$347$	−6825.91	−1.05601	−0.528003	+	0.849243i	$0.677059\pi$
$348$	−7403.22	−1.14039
$349$	6001.37	0.920475	0.460238	−	0.887796i	$-0.347764\pi$
$349$	6001.37	0.920475	0.460238	+	0.887796i	$0.347764\pi$
$350$	−1763.68	−0.269350
$351$	−1320.38	−0.200789
$352$	−2116.13	−0.320426
$353$	−5847.25	−0.881636	−0.440818	−	0.897596i	$-0.645312\pi$
$353$	−5847.25	−0.881636	−0.440818	+	0.897596i	$0.645312\pi$
$354$	−283.019	−0.0424923
$355$	−3907.61	−0.584210
$356$	8807.28	1.31119
$357$	8037.82	1.19162
$358$	−1108.99	−0.163720
$359$	4930.18	0.724805	0.362403	−	0.932022i	$-0.381957\pi$
$359$	4930.18	0.724805	0.362403	+	0.932022i	$0.381957\pi$
$360$	1282.45	0.187754
$361$	−39.8311	−0.00580713
$362$	1566.59	0.227453
$363$	7760.11	1.12204
$364$	5733.67	0.825621
$365$	3585.91	0.514234
$366$	−4134.92	−0.590535
$367$	−3457.00	−0.491700	−0.245850	−	0.969308i	$-0.579067\pi$
$367$	−3457.00	−0.491700	−0.245850	+	0.969308i	$0.579067\pi$
$368$	−4031.79	−0.571118
$369$	9886.35	1.39475
$370$	948.429	0.133261
$371$	11021.1	1.54229
$372$	7015.97	0.977852
$373$	205.191	0.0284836	0.0142418	−	0.999899i	$-0.495467\pi$
$373$	205.191	0.0284836	0.0142418	+	0.999899i	$0.495467\pi$
$374$	698.809	0.0966164
$375$	−7328.00	−1.00911
$376$	−4303.90	−0.590310
$377$	5560.93	0.759688
$378$	580.939	0.0790484
$379$	11728.4	1.58957	0.794785	−	0.606891i	$-0.207584\pi$
$379$	11728.4	1.58957	0.794785	+	0.606891i	$0.207584\pi$
$380$	2754.58	0.371860
$381$	−13763.4	−1.85070
$382$	120.338	0.0161179
$383$	4805.06	0.641063	0.320531	−	0.947238i	$-0.396139\pi$
$383$	4805.06	0.641063	0.320531	+	0.947238i	$0.396139\pi$
$384$	9480.73	1.25993
$385$	1390.79	0.184107
$386$	2504.60	0.330261
$387$	0	0
$388$	3659.31	0.478798
$389$	−8640.08	−1.12614	−0.563071	−	0.826409i	$-0.690380\pi$
$389$	−8640.08	−1.12614	−0.563071	+	0.826409i	$0.690380\pi$
$390$	−1021.82	−0.132672
$391$	4734.38	0.612348
$392$	−921.990	−0.118795
$393$	−855.297	−0.109781
$394$	−3258.55	−0.416658
$395$	−1761.17	−0.224340
$396$	2415.98	0.306585
$397$	−1045.09	−0.132120	−0.0660599	−	0.997816i	$-0.521043\pi$
$397$	−1045.09	−0.132120	−0.0660599	+	0.997816i	$0.521043\pi$
$398$	2393.71	0.301472
$399$	−11795.3	−1.47996
$400$	−4992.36	−0.624045
$401$	−512.318	−0.0638003	−0.0319002	−	0.999491i	$-0.510156\pi$
$401$	−512.318	−0.0638003	−0.0319002	+	0.999491i	$0.510156\pi$
$402$	−5281.68	−0.655289
$403$	−5270.04	−0.651413
$404$	10949.3	1.34838
$405$	3820.39	0.468733
$406$	−2446.68	−0.299081
$407$	3742.03	0.455738
$408$	−5013.97	−0.608403
$409$	−4472.52	−0.540714	−0.270357	−	0.962760i	$-0.587142\pi$
$409$	−4472.52	−0.540714	−0.270357	+	0.962760i	$0.587142\pi$
$410$	−1695.10	−0.204183
$411$	7006.16	0.840848
$412$	−21.2693	−0.00254336
$413$	991.289	0.118107
$414$	−1544.44	−0.183345
$415$	−4379.63	−0.518042
$416$	−5445.54	−0.641802
$417$	−557.644	−0.0654867
$418$	−1025.49	−0.119996
$419$	1189.05	0.138637	0.0693185	−	0.997595i	$-0.477918\pi$
$419$	1189.05	0.138637	0.0693185	+	0.997595i	$0.477918\pi$
$420$	−4764.68	−0.553554
$421$	−2778.77	−0.321684	−0.160842	−	0.986980i	$-0.551421\pi$
$421$	−2778.77	−0.321684	−0.160842	+	0.986980i	$0.551421\pi$
$422$	−3164.24	−0.365007
$423$	7481.33	0.859940
$424$	−6874.94	−0.787444
$425$	5862.35	0.669096
$426$	−4983.77	−0.566818
$427$	14482.8	1.64139
$428$	9460.57	1.06844
$429$	−4031.60	−0.453724
$430$	0	0
$431$	13056.6	1.45920	0.729599	−	0.683876i	$-0.239707\pi$
$431$	13056.6	1.45920	0.729599	+	0.683876i	$0.239707\pi$
$432$	1644.44	0.183144
$433$	−1122.53	−0.124585	−0.0622927	−	0.998058i	$-0.519841\pi$
$433$	−1122.53	−0.124585	−0.0622927	+	0.998058i	$0.519841\pi$
$434$	2318.70	0.256454
$435$	−4621.13	−0.509348
$436$	−1749.61	−0.192182
$437$	−6947.60	−0.760523
$438$	4573.48	0.498925
$439$	8780.26	0.954576	0.477288	−	0.878747i	$-0.341620\pi$
$439$	8780.26	0.954576	0.477288	+	0.878747i	$0.341620\pi$
$440$	−867.569	−0.0939994
$441$	1602.67	0.173055
$442$	1798.28	0.193519
$443$	−15938.5	−1.70939	−0.854694	−	0.519133i	$-0.826255\pi$
$443$	−15938.5	−1.70939	−0.854694	+	0.519133i	$0.826255\pi$
$444$	−12819.8	−1.37027
$445$	5497.55	0.585638
$446$	1794.71	0.190543
$447$	−1652.57	−0.174863
$448$	−5418.73	−0.571453
$449$	−12696.6	−1.33450	−0.667248	−	0.744835i	$-0.732528\pi$
$449$	−12696.6	−1.33450	−0.667248	+	0.744835i	$0.732528\pi$
$450$	−1912.40	−0.200337
$451$	−6688.03	−0.698286
$452$	−138.112	−0.0143722
$453$	3954.98	0.410202
$454$	−1701.20	−0.175861
$455$	3578.99	0.368760
$456$	7357.88	0.755624
$457$	11229.2	1.14941	0.574704	−	0.818362i	$-0.305117\pi$
$457$	11229.2	1.14941	0.574704	+	0.818362i	$0.305117\pi$
$458$	−204.598	−0.0208739
$459$	−1931.01	−0.196365
$460$	−2806.46	−0.284460
$461$	2948.65	0.297900	0.148950	−	0.988845i	$-0.452411\pi$
$461$	2948.65	0.297900	0.148950	+	0.988845i	$0.452411\pi$
$462$	1773.81	0.178626
$463$	−15736.8	−1.57959	−0.789797	−	0.613368i	$-0.789814\pi$
$463$	−15736.8	−1.57959	−0.789797	+	0.613368i	$0.789814\pi$
$464$	−6925.72	−0.692928
$465$	4379.40	0.436753
$466$	−4427.99	−0.440178
$467$	14900.1	1.47643	0.738215	−	0.674566i	$-0.235669\pi$
$467$	14900.1	1.47643	0.738215	+	0.674566i	$0.235669\pi$
$468$	6217.17	0.614079
$469$	18499.4	1.82137
$470$	−1282.74	−0.125890
$471$	−3406.56	−0.333261
$472$	−618.363	−0.0603018
$473$	0	0
$474$	−2246.20	−0.217662
$475$	−8602.86	−0.831003
$476$	8385.25	0.807431
$477$	11950.5	1.14712
$478$	−2728.56	−0.261091
$479$	6419.60	0.612357	0.306178	−	0.951974i	$-0.400950\pi$
$479$	6419.60	0.612357	0.306178	+	0.951974i	$0.400950\pi$
$480$	4525.24	0.430308
$481$	9629.55	0.912827
$482$	−5024.09	−0.474774
$483$	12017.5	1.13212
$484$	8095.53	0.760286
$485$	2284.16	0.213853
$486$	4103.04	0.382959
$487$	14002.5	1.30290	0.651450	−	0.758691i	$-0.274161\pi$
$487$	14002.5	1.30290	0.651450	+	0.758691i	$0.274161\pi$
$488$	−9034.32	−0.838042
$489$	6886.65	0.636861
$490$	−274.791	−0.0253343
$491$	4910.67	0.451356	0.225678	−	0.974202i	$-0.427540\pi$
$491$	4910.67	0.451356	0.225678	+	0.974202i	$0.427540\pi$
$492$	22912.4	2.09953
$493$	8132.62	0.742951
$494$	−2638.94	−0.240347
$495$	1508.07	0.136935
$496$	6563.44	0.594168
$497$	17455.9	1.57546
$498$	−5585.78	−0.502620
$499$	957.649	0.0859123	0.0429562	−	0.999077i	$-0.486322\pi$
$499$	957.649	0.0859123	0.0429562	+	0.999077i	$0.486322\pi$
$500$	−7644.75	−0.683767
$501$	−14261.1	−1.27174
$502$	−3223.87	−0.286630
$503$	−12247.8	−1.08569	−0.542843	−	0.839834i	$-0.682652\pi$
$503$	−12247.8	−1.08569	−0.542843	+	0.839834i	$0.682652\pi$
$504$	−5728.93	−0.506323
$505$	6834.60	0.602249
$506$	1044.80	0.0917925
$507$	5020.42	0.439772
$508$	−14358.3	−1.25403
$509$	9063.40	0.789250	0.394625	−	0.918842i	$-0.370875\pi$
$509$	9063.40	0.789250	0.394625	+	0.918842i	$0.370875\pi$
$510$	−1494.37	−0.129749
$511$	−16018.9	−1.38676
$512$	11656.8	1.00617
$513$	2833.71	0.243881
$514$	4996.69	0.428783
$515$	−13.2764	−0.00113598
$516$	0	0
$517$	−5061.05	−0.430531
$518$	−4236.79	−0.359370
$519$	−25231.3	−2.13397
$520$	−2232.56	−0.188278
$521$	−14421.2	−1.21267	−0.606336	−	0.795208i	$-0.707362\pi$
$521$	−14421.2	−1.21267	−0.606336	+	0.795208i	$0.707362\pi$
$522$	−2653.00	−0.222450
$523$	−5350.14	−0.447314	−0.223657	−	0.974668i	$-0.571800\pi$
$523$	−5350.14	−0.447314	−0.223657	+	0.974668i	$0.571800\pi$
$524$	−892.266	−0.0743870
$525$	14880.6	1.23704
$526$	−660.811	−0.0547771
$527$	−7707.21	−0.637061
$528$	5021.05	0.413851
$529$	−5088.55	−0.418226
$530$	−2049.02	−0.167931
$531$	1074.88	0.0878453
$532$	−12305.2	−1.00281
$533$	−17210.6	−1.39864
$534$	7011.59	0.568204
$535$	5905.34	0.477215
$536$	−11539.8	−0.929935
$537$	9356.82	0.751912
$538$	−5202.91	−0.416939
$539$	−1084.19	−0.0866407
$540$	1144.67	0.0912196
$541$	−5131.45	−0.407797	−0.203898	−	0.978992i	$-0.565361\pi$
$541$	−5131.45	−0.407797	−0.203898	+	0.978992i	$0.565361\pi$
$542$	5802.29	0.459833
$543$	−13217.7	−1.04462
$544$	−7963.86	−0.627662
$545$	−1092.12	−0.0858369
$546$	4564.65	0.357782
$547$	16592.7	1.29699	0.648494	−	0.761220i	$-0.275399\pi$
$547$	16592.7	1.29699	0.648494	+	0.761220i	$0.275399\pi$
$548$	7308.99	0.569753
$549$	15704.1	1.22083
$550$	1293.72	0.100299
$551$	−11934.4	−0.922729
$552$	−7496.46	−0.578026
$553$	7867.45	0.604987
$554$	−65.4275	−0.00501760
$555$	−8002.15	−0.612023
$556$	−581.748	−0.0443734
$557$	4232.85	0.321996	0.160998	−	0.986955i	$-0.448529\pi$
$557$	4232.85	0.321996	0.160998	+	0.986955i	$0.448529\pi$
$558$	2514.23	0.190745
$559$	0	0
$560$	−4457.36	−0.336353
$561$	−5896.04	−0.443727
$562$	−5534.53	−0.415409
$563$	2958.31	0.221453	0.110726	−	0.993851i	$-0.464682\pi$
$563$	2958.31	0.221453	0.110726	+	0.993851i	$0.464682\pi$
$564$	17338.6	1.29448
$565$	−86.2101	−0.00641927
$566$	−1521.23	−0.112972
$567$	−17066.3	−1.26405
$568$	−10889.0	−0.804384
$569$	5234.91	0.385692	0.192846	−	0.981229i	$-0.438228\pi$
$569$	5234.91	0.385692	0.192846	+	0.981229i	$0.438228\pi$
$570$	2192.95	0.161145
$571$	13989.0	1.02525	0.512627	−	0.858611i	$-0.328672\pi$
$571$	13989.0	1.02525	0.512627	+	0.858611i	$0.328672\pi$
$572$	−4205.86	−0.307440
$573$	−1015.33	−0.0740242
$574$	7572.30	0.550630
$575$	8764.88	0.635688
$576$	−5875.67	−0.425034
$577$	23239.0	1.67670	0.838348	−	0.545135i	$-0.183522\pi$
$577$	23239.0	1.67670	0.838348	+	0.545135i	$0.183522\pi$
$578$	−1450.45	−0.104379
$579$	−21132.0	−1.51678
$580$	−4820.87	−0.345131
$581$	19564.5	1.39703
$582$	2913.22	0.207486
$583$	−8084.39	−0.574308
$584$	9992.51	0.708036
$585$	3880.79	0.274275
$586$	−1181.89	−0.0833165
$587$	−6240.67	−0.438807	−0.219404	−	0.975634i	$-0.570411\pi$
$587$	−6240.67	−0.438807	−0.219404	+	0.975634i	$0.570411\pi$
$588$	3714.31	0.260502
$589$	11310.1	0.791217
$590$	−184.298	−0.0128600
$591$	27493.3	1.91357
$592$	−11992.9	−0.832609
$593$	−11379.5	−0.788029	−0.394014	−	0.919104i	$-0.628914\pi$
$593$	−11379.5	−0.788029	−0.394014	+	0.919104i	$0.628914\pi$
$594$	−426.141	−0.0294356
$595$	5234.12	0.360635
$596$	−1724.00	−0.118486
$597$	−20196.4	−1.38456
$598$	2688.64	0.183857
$599$	−23163.8	−1.58005	−0.790024	−	0.613076i	$-0.789932\pi$
$599$	−23163.8	−1.58005	−0.790024	+	0.613076i	$0.789932\pi$
$600$	−9282.49	−0.631593
$601$	−4928.18	−0.334484	−0.167242	−	0.985916i	$-0.553486\pi$
$601$	−4928.18	−0.334484	−0.167242	+	0.985916i	$0.553486\pi$
$602$	0	0
$603$	20059.3	1.35469
$604$	4125.93	0.277950
$605$	5053.27	0.339578
$606$	8716.86	0.584320
$607$	7495.38	0.501199	0.250600	−	0.968091i	$-0.419372\pi$
$607$	7495.38	0.501199	0.250600	+	0.968091i	$0.419372\pi$
$608$	11686.8	0.779542
$609$	20643.3	1.37358
$610$	−2692.60	−0.178722
$611$	−13023.9	−0.862339
$612$	9092.34	0.600549
$613$	−7140.15	−0.470453	−0.235227	−	0.971941i	$-0.575583\pi$
$613$	−7140.15	−0.470453	−0.235227	+	0.971941i	$0.575583\pi$
$614$	6913.96	0.454438
$615$	14302.0	0.937746
$616$	3875.57	0.253492
$617$	−14180.3	−0.925249	−0.462624	−	0.886554i	$-0.653092\pi$
$617$	−14180.3	−0.925249	−0.462624	+	0.886554i	$0.653092\pi$
$618$	−16.9328	−0.00110216
$619$	10072.1	0.654007	0.327003	−	0.945023i	$-0.393961\pi$
$619$	10072.1	0.654007	0.327003	+	0.945023i	$0.393961\pi$
$620$	4568.70	0.295941
$621$	−2887.07	−0.186561
$622$	−8135.64	−0.524452
$623$	−24558.5	−1.57932
$624$	12920.9	0.828929
$625$	8250.39	0.528025
$626$	−7703.89	−0.491868
$627$	8652.30	0.551100
$628$	−3553.80	−0.225815
$629$	14082.8	0.892716
$630$	−1707.46	−0.107979
$631$	−10425.8	−0.657755	−0.328877	−	0.944373i	$-0.606670\pi$
$631$	−10425.8	−0.657755	−0.328877	+	0.944373i	$0.606670\pi$
$632$	−4907.69	−0.308888
$633$	26697.6	1.67636
$634$	5879.86	0.368327
$635$	−8962.50	−0.560104
$636$	27696.2	1.72677
$637$	−2790.00	−0.173538
$638$	1794.73	0.111370
$639$	18927.9	1.17179
$640$	6173.72	0.381309
$641$	11982.7	0.738359	0.369180	−	0.929358i	$-0.379639\pi$
$641$	11982.7	0.738359	0.369180	+	0.929358i	$0.379639\pi$
$642$	7531.67	0.463009
$643$	3919.88	0.240412	0.120206	−	0.992749i	$-0.461644\pi$
$643$	3919.88	0.240412	0.120206	+	0.992749i	$0.461644\pi$
$644$	12536.9	0.767117
$645$	0	0
$646$	−3859.33	−0.235052
$647$	−179.894	−0.0109310	−0.00546549	−	0.999985i	$-0.501740\pi$
$647$	−179.894	−0.0109310	−0.00546549	+	0.999985i	$0.501740\pi$
$648$	10645.9	0.645388
$649$	−727.147	−0.0439800
$650$	3329.20	0.200896
$651$	−19563.5	−1.17781
$652$	7184.32	0.431533
$653$	24418.3	1.46334	0.731670	−	0.681659i	$-0.238741\pi$
$653$	24418.3	1.46334	0.731670	+	0.681659i	$0.238741\pi$
$654$	−1392.89	−0.0832816
$655$	−556.957	−0.0332246
$656$	21434.6	1.27573
$657$	−17369.7	−1.03144
$658$	5730.21	0.339494
$659$	12541.3	0.741336	0.370668	−	0.928765i	$-0.379129\pi$
$659$	12541.3	0.741336	0.370668	+	0.928765i	$0.379129\pi$
$660$	3495.07	0.206129
$661$	−19977.8	−1.17556	−0.587782	−	0.809019i	$-0.699999\pi$
$661$	−19977.8	−1.17556	−0.587782	+	0.809019i	$0.699999\pi$
$662$	−3399.77	−0.199601
$663$	−15172.6	−0.888770
$664$	−12204.3	−0.713280
$665$	−7680.94	−0.447901
$666$	−4594.06	−0.267291
$667$	12159.2	0.705856
$668$	−14877.5	−0.861720
$669$	−15142.5	−0.875101
$670$	−3439.35	−0.198319
$671$	−10623.7	−0.611210
$672$	−20215.0	−1.16043
$673$	−4879.78	−0.279497	−0.139749	−	0.990187i	$-0.544629\pi$
$673$	−4879.78	−0.279497	−0.139749	+	0.990187i	$0.544629\pi$
$674$	−1808.57	−0.103358
$675$	−3574.92	−0.203850
$676$	5237.42	0.297987
$677$	−25770.9	−1.46301	−0.731505	−	0.681836i	$-0.761182\pi$
$677$	−25770.9	−1.46301	−0.731505	+	0.681836i	$0.761182\pi$
$678$	−109.953	−0.00622817
$679$	−10203.7	−0.576706
$680$	−3265.02	−0.184129
$681$	14353.5	0.807674
$682$	−1700.85	−0.0954970
$683$	−17463.2	−0.978345	−0.489172	−	0.872187i	$-0.662701\pi$
$683$	−17463.2	−0.978345	−0.489172	+	0.872187i	$0.662701\pi$
$684$	−13342.8	−0.745869
$685$	4562.31	0.254477
$686$	−4579.25	−0.254864
$687$	1726.25	0.0958670
$688$	0	0
$689$	−20804.0	−1.15032
$690$	−2234.26	−0.123271
$691$	12899.2	0.710140	0.355070	−	0.934840i	$-0.384457\pi$
$691$	12899.2	0.710140	0.355070	+	0.934840i	$0.384457\pi$
$692$	−26321.9	−1.44597
$693$	−6736.78	−0.369277
$694$	−5669.07	−0.310079
$695$	−363.130	−0.0198191
$696$	−12877.3	−0.701309
$697$	−25169.8	−1.36783
$698$	4984.27	0.270283
$699$	37360.2	2.02159
$700$	15523.8	0.838207
$701$	−27155.9	−1.46314	−0.731572	−	0.681764i	$-0.761213\pi$
$701$	−27155.9	−1.46314	−0.731572	+	0.681764i	$0.761213\pi$
$702$	−1096.61	−0.0589585
$703$	−20666.2	−1.10873
$704$	3974.84	0.212795
$705$	10822.8	0.578172
$706$	−4856.27	−0.258879
$707$	−30531.3	−1.62411
$708$	2491.12	0.132235
$709$	32347.2	1.71343	0.856717	−	0.515787i	$-0.172500\pi$
$709$	32347.2	1.71343	0.856717	+	0.515787i	$0.172500\pi$
$710$	−3245.36	−0.171544
$711$	8530.88	0.449976
$712$	15319.5	0.806351
$713$	−11523.2	−0.605253
$714$	6675.60	0.349899
$715$	−2625.32	−0.137317
$716$	9761.25	0.509490
$717$	23021.6	1.19911
$718$	4094.63	0.212828
$719$	2462.26	0.127715	0.0638574	−	0.997959i	$-0.479660\pi$
$719$	2462.26	0.127715	0.0638574	+	0.997959i	$0.479660\pi$
$720$	−4833.23	−0.250172
$721$	59.3080	0.00306344
$722$	−33.0807	−0.00170517
$723$	42389.7	2.18048
$724$	−13789.0	−0.707826
$725$	15056.1	0.771269
$726$	6444.95	0.329469
$727$	−34210.8	−1.74526	−0.872632	−	0.488379i	$-0.837588\pi$
$727$	−34210.8	−1.74526	−0.872632	+	0.488379i	$0.837588\pi$
$728$	9973.22	0.507736
$729$	−12013.0	−0.610325
$730$	2978.18	0.150997
$731$	0	0
$732$	36395.4	1.83772
$733$	5710.38	0.287746	0.143873	−	0.989596i	$-0.454044\pi$
$733$	5710.38	0.287746	0.143873	+	0.989596i	$0.454044\pi$
$734$	−2871.12	−0.144380
$735$	2318.49	0.116352
$736$	−11906.9	−0.596323
$737$	−13570.0	−0.678231
$738$	8210.84	0.409546
$739$	−27827.8	−1.38520	−0.692601	−	0.721321i	$-0.743535\pi$
$739$	−27827.8	−1.38520	−0.692601	+	0.721321i	$0.743535\pi$
$740$	−8348.04	−0.414703
$741$	22265.4	1.10383
$742$	9153.29	0.452868
$743$	−4999.54	−0.246858	−0.123429	−	0.992353i	$-0.539389\pi$
$743$	−4999.54	−0.246858	−0.123429	+	0.992353i	$0.539389\pi$
$744$	12203.7	0.601354
$745$	−1076.13	−0.0529212
$746$	170.416	0.00836375
$747$	21214.3	1.03908
$748$	−6150.89	−0.300667
$749$	−26380.1	−1.28693
$750$	−6086.08	−0.296309
$751$	−3252.06	−0.158015	−0.0790077	−	0.996874i	$-0.525175\pi$
$751$	−3252.06	−0.158015	−0.0790077	+	0.996874i	$0.525175\pi$
$752$	16220.2	0.786558
$753$	27200.7	1.31640
$754$	4618.48	0.223071
$755$	2575.43	0.124145
$756$	−5113.41	−0.245996
$757$	32449.8	1.55800	0.779000	−	0.627024i	$-0.215727\pi$
$757$	32449.8	1.55800	0.779000	+	0.627024i	$0.215727\pi$
$758$	9740.70	0.466752
$759$	−8815.26	−0.421573
$760$	4791.35	0.228685
$761$	−1370.12	−0.0652650	−0.0326325	−	0.999467i	$-0.510389\pi$
$761$	−1370.12	−0.0652650	−0.0326325	+	0.999467i	$0.510389\pi$
$762$	−11430.8	−0.543430
$763$	4878.66	0.231480
$764$	−1059.21	−0.0501583
$765$	5675.49	0.268232
$766$	3990.71	0.188238
$767$	−1871.21	−0.0880904
$768$	−7028.25	−0.330222
$769$	7651.00	0.358780	0.179390	−	0.983778i	$-0.442588\pi$
$769$	7651.00	0.358780	0.179390	+	0.983778i	$0.442588\pi$
$770$	1155.08	0.0540601
$771$	−42158.4	−1.96926
$772$	−22045.4	−1.02776
$773$	13408.1	0.623873	0.311937	−	0.950103i	$-0.399022\pi$
$773$	13408.1	0.623873	0.311937	+	0.950103i	$0.399022\pi$
$774$	0	0
$775$	−14268.5	−0.661344
$776$	6365.05	0.294449
$777$	35746.9	1.65047
$778$	−7175.78	−0.330674
$779$	36936.1	1.69881
$780$	8994.04	0.412870
$781$	−12804.6	−0.586662
$782$	3932.01	0.179806
$783$	−4959.35	−0.226351
$784$	3474.74	0.158288
$785$	−2218.30	−0.100859
$786$	−710.343	−0.0322355
$787$	−18848.1	−0.853700	−0.426850	−	0.904323i	$-0.640377\pi$
$787$	−18848.1	−0.853700	−0.426850	+	0.904323i	$0.640377\pi$
$788$	28681.6	1.29663
$789$	5575.44	0.251573
$790$	−1462.70	−0.0658739
$791$	385.115	0.0173111
$792$	4202.38	0.188542
$793$	−27338.4	−1.22423
$794$	−867.971	−0.0387949
$795$	17288.1	0.771253
$796$	−21069.3	−0.938169
$797$	32490.5	1.44401	0.722004	−	0.691889i	$-0.243221\pi$
$797$	32490.5	1.44401	0.722004	+	0.691889i	$0.243221\pi$
$798$	−9796.29	−0.434567
$799$	−19046.8	−0.843340
$800$	−14743.7	−0.651586
$801$	−26629.4	−1.17466
$802$	−425.492	−0.0187340
$803$	11750.4	0.516393
$804$	46489.1	2.03924
$805$	7825.60	0.342629
$806$	−4376.89	−0.191277
$807$	43898.3	1.91486
$808$	19045.3	0.829222
$809$	14885.6	0.646908	0.323454	−	0.946244i	$-0.395156\pi$
$809$	14885.6	0.646908	0.323454	+	0.946244i	$0.395156\pi$
$810$	3172.93	0.137636
$811$	23932.3	1.03622	0.518112	−	0.855313i	$-0.326635\pi$
$811$	23932.3	1.03622	0.518112	+	0.855313i	$0.326635\pi$
$812$	21535.6	0.930729
$813$	−48955.5	−2.11186
$814$	3107.84	0.133820
$815$	4484.49	0.192742
$816$	18896.3	0.810666
$817$	0	0
$818$	−3714.53	−0.158772
$819$	−17336.1	−0.739650
$820$	14920.2	0.635411
$821$	−35623.3	−1.51433	−0.757164	−	0.653225i	$-0.773416\pi$
$821$	−35623.3	−1.51433	−0.757164	+	0.653225i	$0.773416\pi$
$822$	5818.78	0.246902
$823$	−409.139	−0.0173289	−0.00866446	−	0.999962i	$-0.502758\pi$
$823$	−409.139	−0.0173289	−0.00866446	+	0.999962i	$0.502758\pi$
$824$	−36.9961	−0.00156410
$825$	−10915.5	−0.460641
$826$	823.288	0.0346802
$827$	21237.5	0.892988	0.446494	−	0.894787i	$-0.352672\pi$
$827$	21237.5	0.892988	0.446494	+	0.894787i	$0.352672\pi$
$828$	13594.1	0.570564
$829$	−1728.67	−0.0724236	−0.0362118	−	0.999344i	$-0.511529\pi$
$829$	−1728.67	−0.0724236	−0.0362118	+	0.999344i	$0.511529\pi$
$830$	−3637.38	−0.152115
$831$	552.030	0.0230442
$832$	10228.7	0.426220
$833$	−4080.26	−0.169715
$834$	−463.136	−0.0192291
$835$	−9286.63	−0.384883
$836$	9026.29	0.373422
$837$	4699.93	0.194090
$838$	987.534	0.0407086
$839$	−41221.3	−1.69621	−0.848104	−	0.529830i	$-0.822256\pi$
$839$	−41221.3	−1.69621	−0.848104	+	0.529830i	$0.822256\pi$
$840$	−8287.74	−0.340422
$841$	−3502.19	−0.143597
$842$	−2307.83	−0.0944575
$843$	46696.3	1.90784
$844$	27851.5	1.13589
$845$	3269.22	0.133094
$846$	6213.41	0.252508
$847$	−22573.8	−0.915755
$848$	25909.8	1.04923
$849$	12835.1	0.518844
$850$	4868.81	0.196469
$851$	21055.4	0.848143
$852$	43867.0	1.76392
$853$	−14786.9	−0.593547	−0.296773	−	0.954948i	$-0.595911\pi$
$853$	−14786.9	−0.593547	−0.296773	+	0.954948i	$0.595911\pi$
$854$	12028.3	0.481967
$855$	−8328.64	−0.333139
$856$	16455.8	0.657066
$857$	−20068.7	−0.799921	−0.399961	−	0.916532i	$-0.630976\pi$
$857$	−20068.7	−0.799921	−0.399961	+	0.916532i	$0.630976\pi$
$858$	−3348.34	−0.133229
$859$	−37526.7	−1.49056	−0.745282	−	0.666750i	$-0.767685\pi$
$859$	−37526.7	−1.49056	−0.745282	+	0.666750i	$0.767685\pi$
$860$	0	0
$861$	−63889.5	−2.52886
$862$	10843.8	0.428470
$863$	28185.4	1.11175	0.555875	−	0.831266i	$-0.312383\pi$
$863$	28185.4	1.11175	0.555875	+	0.831266i	$0.312383\pi$
$864$	4856.44	0.191226
$865$	−16430.3	−0.645833
$866$	−932.290	−0.0365826
$867$	12237.9	0.479376
$868$	−20409.1	−0.798076
$869$	−5771.07	−0.225282
$870$	−3837.96	−0.149562
$871$	−34920.3	−1.35847
$872$	−3043.29	−0.118187
$873$	−11064.2	−0.428941
$874$	−5770.14	−0.223316
$875$	21316.8	0.823588
$876$	−40255.6	−1.55264
$877$	17560.4	0.676136	0.338068	−	0.941122i	$-0.390227\pi$
$877$	17560.4	0.676136	0.338068	+	0.941122i	$0.390227\pi$
$878$	7292.20	0.280296
$879$	9971.94	0.382645
$880$	3269.64	0.125249
$881$	−35647.1	−1.36320	−0.681601	−	0.731724i	$-0.738716\pi$
$881$	−35647.1	−1.36320	−0.681601	+	0.731724i	$0.738716\pi$
$882$	1331.05	0.0508150
$883$	−50715.7	−1.93286	−0.966431	−	0.256925i	$-0.917291\pi$
$883$	−50715.7	−1.93286	−0.966431	+	0.256925i	$0.917291\pi$
$884$	−15828.4	−0.602225
$885$	1554.97	0.0590619
$886$	−13237.3	−0.501935
$887$	−14869.8	−0.562884	−0.281442	−	0.959578i	$-0.590813\pi$
$887$	−14869.8	−0.562884	−0.281442	+	0.959578i	$0.590813\pi$
$888$	−22298.8	−0.842679
$889$	40036.9	1.51046
$890$	4565.84	0.171963
$891$	12518.8	0.470701
$892$	−15797.0	−0.592963
$893$	27950.8	1.04741
$894$	−1372.50	−0.0513458
$895$	6093.02	0.227561
$896$	−27579.0	−1.02829
$897$	−22684.8	−0.844395
$898$	−10544.8	−0.391854
$899$	−19794.2	−0.734343
$900$	16832.9	0.623440
$901$	−30424.9	−1.12497
$902$	−5554.56	−0.205041
$903$	0	0
$904$	−240.233	−0.00883854
$905$	−8607.19	−0.316147
$906$	3284.71	0.120449
$907$	−38314.2	−1.40265	−0.701324	−	0.712843i	$-0.747407\pi$
$907$	−38314.2	−1.40265	−0.701324	+	0.712843i	$0.747407\pi$
$908$	14973.9	0.547274
$909$	−33105.8	−1.20798
$910$	2972.43	0.108280
$911$	41494.7	1.50909	0.754545	−	0.656248i	$-0.227858\pi$
$911$	41494.7	1.50909	0.754545	+	0.656248i	$0.227858\pi$
$912$	−27729.9	−1.00683
$913$	−14351.3	−0.520217
$914$	9326.09	0.337505
$915$	22718.2	0.820810
$916$	1800.87	0.0649589
$917$	2488.02	0.0895982
$918$	−1603.74	−0.0576595
$919$	−22998.3	−0.825511	−0.412756	−	0.910842i	$-0.635434\pi$
$919$	−22998.3	−0.825511	−0.412756	+	0.910842i	$0.635434\pi$
$920$	−4881.59	−0.174936
$921$	−58335.0	−2.08708
$922$	2448.92	0.0874738
$923$	−32950.7	−1.17506
$924$	−15613.0	−0.555878
$925$	26071.8	0.926743
$926$	−13069.8	−0.463823
$927$	64.3091	0.00227852
$928$	−20453.4	−0.723508
$929$	−43145.2	−1.52373	−0.761867	−	0.647733i	$-0.775717\pi$
$929$	−43145.2	−1.52373	−0.761867	+	0.647733i	$0.775717\pi$
$930$	3637.19	0.128245
$931$	5987.68	0.210782
$932$	38975.0	1.36982
$933$	68642.6	2.40864
$934$	12374.8	0.433530
$935$	−3839.42	−0.134291
$936$	10814.2	0.377643
$937$	19389.3	0.676009	0.338005	−	0.941144i	$-0.390248\pi$
$937$	19389.3	0.676009	0.338005	+	0.941144i	$0.390248\pi$
$938$	15364.1	0.534816
$939$	64999.8	2.25899
$940$	11290.6	0.391766
$941$	27492.5	0.952424	0.476212	−	0.879330i	$-0.342009\pi$
$941$	27492.5	0.952424	0.476212	+	0.879330i	$0.342009\pi$
$942$	−2829.22	−0.0978568
$943$	−37631.8	−1.29953
$944$	2330.45	0.0803491
$945$	−3191.82	−0.109873
$946$	0	0
$947$	−36198.3	−1.24212	−0.621059	−	0.783764i	$-0.713297\pi$
$947$	−36198.3	−1.24212	−0.621059	+	0.783764i	$0.713297\pi$
$948$	19771.0	0.677355
$949$	30238.0	1.03432
$950$	−7144.87	−0.244011
$951$	−49610.0	−1.69160
$952$	14585.4	0.496550
$953$	−29531.3	−1.00379	−0.501895	−	0.864929i	$-0.667363\pi$
$953$	−29531.3	−1.00379	−0.501895	+	0.864929i	$0.667363\pi$
$954$	9925.15	0.336833
$955$	−661.166	−0.0224030
$956$	24016.7	0.812507
$957$	−15142.7	−0.511486
$958$	5331.62	0.179809
$959$	−20380.6	−0.686260
$960$	−8500.01	−0.285767
$961$	−11032.2	−0.370320
$962$	7997.57	0.268037
$963$	−28604.6	−0.957187
$964$	44221.9	1.47748
$965$	−13760.9	−0.459044
$966$	9980.78	0.332429
$967$	9561.17	0.317959	0.158980	−	0.987282i	$-0.449180\pi$
$967$	9561.17	0.317959	0.158980	+	0.987282i	$0.449180\pi$
$968$	14081.5	0.467557
$969$	32562.2	1.07951
$970$	1897.05	0.0627944
$971$	4107.09	0.135739	0.0678696	−	0.997694i	$-0.478380\pi$
$971$	4107.09	0.135739	0.0678696	+	0.997694i	$0.478380\pi$
$972$	−36114.8	−1.19175
$973$	1622.16	0.0534472
$974$	11629.4	0.382576
$975$	−28089.4	−0.922647
$976$	34048.0	1.11665
$977$	28818.7	0.943698	0.471849	−	0.881679i	$-0.343587\pi$
$977$	28818.7	0.943698	0.471849	+	0.881679i	$0.343587\pi$
$978$	5719.52	0.187004
$979$	18014.5	0.588097
$980$	2418.70	0.0788394
$981$	5290.06	0.172170
$982$	4078.43	0.132533
$983$	9721.35	0.315425	0.157713	−	0.987485i	$-0.449588\pi$
$983$	9721.35	0.315425	0.157713	+	0.987485i	$0.449588\pi$
$984$	39854.1	1.29116
$985$	17903.2	0.579131
$986$	6754.33	0.218156
$987$	−48347.3	−1.55918
$988$	23227.8	0.747951
$989$	0	0
$990$	1252.48	0.0402087
$991$	−35015.2	−1.12240	−0.561198	−	0.827682i	$-0.689659\pi$
$991$	−35015.2	−1.12240	−0.561198	+	0.827682i	$0.689659\pi$
$992$	19383.5	0.620390
$993$	28684.8	0.916700
$994$	14497.6	0.462610
$995$	−13151.6	−0.419028
$996$	49165.9	1.56414
$997$	−13390.4	−0.425355	−0.212677	−	0.977122i	$-0.568218\pi$
$997$	−13390.4	−0.425355	−0.212677	+	0.977122i	$0.568218\pi$
$998$	795.350	0.0252268
$999$	−8587.83	−0.271979

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.g.1.17		30
43.8	odd	14		43.4.e.a.21.7	✓	60
43.27	odd	14		43.4.e.a.41.7	yes	60
43.42	odd	2		1849.4.a.h.1.14		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.e.a.21.7	✓	60	43.8	odd	14
43.4.e.a.41.7	yes	60	43.27	odd	14
1849.4.a.g.1.17		30	1.1	even	1	trivial
1849.4.a.h.1.14		30	43.42	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q+0.830523 q^{2} -7.00735 q^{3} -7.31023 q^{4} -4.56308 q^{5} -5.81976 q^{6} +20.3840 q^{7} -12.7155 q^{8} +22.1029 q^{9} +O(q^{10})\)	\(q+0.830523 q^{2} -7.00735 q^{3} -7.31023 q^{4} -4.56308 q^{5} -5.81976 q^{6} +20.3840 q^{7} -12.7155 q^{8} +22.1029 q^{9} -3.78975 q^{10} -14.9524 q^{11} +51.2253 q^{12} -38.4779 q^{13} +16.9294 q^{14} +31.9751 q^{15} +47.9213 q^{16} -56.2723 q^{17} +18.3570 q^{18} +82.5783 q^{19} +33.3572 q^{20} -142.838 q^{21} -12.4183 q^{22} -84.1335 q^{23} +89.1019 q^{24} -104.178 q^{25} -31.9568 q^{26} +34.3154 q^{27} -149.012 q^{28} -144.523 q^{29} +26.5561 q^{30} +136.963 q^{31} +141.524 q^{32} +104.777 q^{33} -46.7354 q^{34} -93.0141 q^{35} -161.578 q^{36} -250.262 q^{37} +68.5831 q^{38} +269.628 q^{39} +58.0219 q^{40} +447.286 q^{41} -118.630 q^{42} +109.306 q^{44} -100.858 q^{45} -69.8748 q^{46} +338.476 q^{47} -335.802 q^{48} +72.5092 q^{49} -86.5224 q^{50} +394.319 q^{51} +281.282 q^{52} +540.674 q^{53} +28.4997 q^{54} +68.2293 q^{55} -259.193 q^{56} -578.655 q^{57} -120.029 q^{58} +48.6306 q^{59} -233.746 q^{60} +710.497 q^{61} +113.751 q^{62} +450.547 q^{63} -265.832 q^{64} +175.578 q^{65} +87.0197 q^{66} +907.541 q^{67} +411.363 q^{68} +589.553 q^{69} -77.2504 q^{70} +856.353 q^{71} -281.050 q^{72} -785.853 q^{73} -207.848 q^{74} +730.013 q^{75} -603.666 q^{76} -304.791 q^{77} +223.932 q^{78} +385.961 q^{79} -218.669 q^{80} -837.239 q^{81} +371.482 q^{82} +959.796 q^{83} +1044.18 q^{84} +256.775 q^{85} +1012.72 q^{87} +190.128 q^{88} -1204.79 q^{89} -83.7646 q^{90} -784.335 q^{91} +615.035 q^{92} -959.746 q^{93} +281.112 q^{94} -376.812 q^{95} -991.706 q^{96} -500.574 q^{97} +60.2205 q^{98} -330.493 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 6 q^{2} - 2 q^{3} + 114 q^{4} - 27 q^{5} + 8 q^{6} - 48 q^{7} - 90 q^{8} + 216 q^{9}+O(q^{10}) \) 30 * q - 6 * q^2 - 2 * q^3 + 114 * q^4 - 27 * q^5 + 8 * q^6 - 48 * q^7 - 90 * q^8 + 216 * q^9	\( 30 q - 6 q^{2} - 2 q^{3} + 114 q^{4} - 27 q^{5} + 8 q^{6} - 48 q^{7} - 90 q^{8} + 216 q^{9} - 27 q^{10} + 80 q^{11} + 36 q^{12} - 13 q^{13} + 36 q^{14} + 16 q^{15} + 318 q^{16} + 66 q^{17} - 80 q^{18} - 254 q^{19} - 312 q^{20} - 548 q^{21} - 305 q^{22} - 105 q^{23} + 123 q^{24} + 523 q^{25} - 549 q^{26} + 10 q^{27} - 578 q^{28} - 793 q^{29} - 1560 q^{30} - 359 q^{31} - 676 q^{32} - 208 q^{33} - 1007 q^{34} - 514 q^{35} + 776 q^{36} - 510 q^{37} - 2066 q^{38} - 898 q^{39} - 1248 q^{40} - 270 q^{41} + 915 q^{42} + 3256 q^{44} - 807 q^{45} - 1960 q^{46} + 1421 q^{47} + 632 q^{48} + 386 q^{49} + 141 q^{50} - 209 q^{51} + 2825 q^{52} - 21 q^{53} + 2368 q^{54} - 2258 q^{55} + 2521 q^{56} - 1723 q^{57} - 347 q^{58} + 1752 q^{59} + 2711 q^{60} - 1759 q^{61} - 395 q^{62} - 2204 q^{63} + 222 q^{64} - 1151 q^{65} + 160 q^{66} - 3001 q^{67} + 1921 q^{68} - 1660 q^{69} - 1597 q^{70} - 727 q^{71} - 9100 q^{72} - 4623 q^{73} - 2649 q^{74} - 1027 q^{75} - 874 q^{76} - 3556 q^{77} - 4979 q^{78} + 546 q^{79} - 5809 q^{80} - 410 q^{81} + 4397 q^{82} - 492 q^{83} - 10611 q^{84} + 1723 q^{85} + 5937 q^{87} - 3974 q^{88} - 5218 q^{89} + 10492 q^{90} - 1104 q^{91} + 1060 q^{92} - 1997 q^{93} + 2134 q^{94} + 6346 q^{95} - 11984 q^{96} + 2590 q^{97} - 6270 q^{98} - 2693 q^{99}+O(q^{100}) \) 30 * q - 6 * q^2 - 2 * q^3 + 114 * q^4 - 27 * q^5 + 8 * q^6 - 48 * q^7 - 90 * q^8 + 216 * q^9 - 27 * q^10 + 80 * q^11 + 36 * q^12 - 13 * q^13 + 36 * q^14 + 16 * q^15 + 318 * q^16 + 66 * q^17 - 80 * q^18 - 254 * q^19 - 312 * q^20 - 548 * q^21 - 305 * q^22 - 105 * q^23 + 123 * q^24 + 523 * q^25 - 549 * q^26 + 10 * q^27 - 578 * q^28 - 793 * q^29 - 1560 * q^30 - 359 * q^31 - 676 * q^32 - 208 * q^33 - 1007 * q^34 - 514 * q^35 + 776 * q^36 - 510 * q^37 - 2066 * q^38 - 898 * q^39 - 1248 * q^40 - 270 * q^41 + 915 * q^42 + 3256 * q^44 - 807 * q^45 - 1960 * q^46 + 1421 * q^47 + 632 * q^48 + 386 * q^49 + 141 * q^50 - 209 * q^51 + 2825 * q^52 - 21 * q^53 + 2368 * q^54 - 2258 * q^55 + 2521 * q^56 - 1723 * q^57 - 347 * q^58 + 1752 * q^59 + 2711 * q^60 - 1759 * q^61 - 395 * q^62 - 2204 * q^63 + 222 * q^64 - 1151 * q^65 + 160 * q^66 - 3001 * q^67 + 1921 * q^68 - 1660 * q^69 - 1597 * q^70 - 727 * q^71 - 9100 * q^72 - 4623 * q^73 - 2649 * q^74 - 1027 * q^75 - 874 * q^76 - 3556 * q^77 - 4979 * q^78 + 546 * q^79 - 5809 * q^80 - 410 * q^81 + 4397 * q^82 - 492 * q^83 - 10611 * q^84 + 1723 * q^85 + 5937 * q^87 - 3974 * q^88 - 5218 * q^89 + 10492 * q^90 - 1104 * q^91 + 1060 * q^92 - 1997 * q^93 + 2134 * q^94 + 6346 * q^95 - 11984 * q^96 + 2590 * q^97 - 6270 * q^98 - 2693 * q^99

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