LMFDB - Embedded newform 1.40.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,40,Mod(1,1)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1, base_ring=CyclotomicField(1))

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

N = Newforms(chi, 40, names="a")

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

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 40);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 40 $
Character orbit:	$[\chi]$	$=$	1.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:	$9.63395513897$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 175630027x - 142249227846 $ x^3 - 175630027*x - 142249227846
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{10}\cdot 3^{5}\cdot 5\cdot 13 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-812.996$ of defining polynomial
Character	$\chi$	$=$	1.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+241488. q^{2} -3.14962e9 q^{3} -4.91439e11 q^{4} +5.36221e13 q^{5} -7.60595e14 q^{6} +1.82084e16 q^{7} -2.51436e17 q^{8} +5.86757e18 q^{9} +O(q^{10})$	\(q+241488. q^{2} -3.14962e9 q^{3} -4.91439e11 q^{4} +5.36221e13 q^{5} -7.60595e14 q^{6} +1.82084e16 q^{7} -2.51436e17 q^{8} +5.86757e18 q^{9} +1.29491e19 q^{10} +2.56889e20 q^{11} +1.54785e21 q^{12} -2.93238e21 q^{13} +4.39709e21 q^{14} -1.68890e23 q^{15} +2.09453e23 q^{16} -9.89190e22 q^{17} +1.41695e24 q^{18} +1.24548e25 q^{19} -2.63520e25 q^{20} -5.73494e25 q^{21} +6.20355e25 q^{22} -1.86286e26 q^{23} +7.91928e26 q^{24} +1.05635e27 q^{25} -7.08133e26 q^{26} -5.71661e27 q^{27} -8.94830e27 q^{28} +1.31775e28 q^{29} -4.07848e28 q^{30} +1.89026e29 q^{31} +1.88809e29 q^{32} -8.09103e29 q^{33} -2.38877e28 q^{34} +9.76371e29 q^{35} -2.88356e30 q^{36} +3.22957e30 q^{37} +3.00769e30 q^{38} +9.23588e30 q^{39} -1.34825e31 q^{40} -2.27011e31 q^{41} -1.38492e31 q^{42} +5.36582e31 q^{43} -1.26245e32 q^{44} +3.14632e32 q^{45} -4.49858e31 q^{46} +1.87430e32 q^{47} -6.59698e32 q^{48} -5.78000e32 q^{49} +2.55095e32 q^{50} +3.11557e32 q^{51} +1.44109e33 q^{52} -3.22443e32 q^{53} -1.38049e33 q^{54} +1.37749e34 q^{55} -4.57823e33 q^{56} -3.92280e34 q^{57} +3.18220e33 q^{58} +1.01307e34 q^{59} +8.29990e34 q^{60} -8.66378e34 q^{61} +4.56473e34 q^{62} +1.06839e35 q^{63} -6.95530e34 q^{64} -1.57240e35 q^{65} -1.95389e35 q^{66} -5.98696e33 q^{67} +4.86127e34 q^{68} +5.86730e35 q^{69} +2.35782e35 q^{70} +5.02476e35 q^{71} -1.47532e36 q^{72} +1.14062e36 q^{73} +7.79901e35 q^{74} -3.32709e36 q^{75} -6.12079e36 q^{76} +4.67752e36 q^{77} +2.23035e36 q^{78} +7.78268e36 q^{79} +1.12313e37 q^{80} -5.77348e36 q^{81} -5.48205e36 q^{82} -4.09909e37 q^{83} +2.81838e37 q^{84} -5.30425e36 q^{85} +1.29578e37 q^{86} -4.15041e37 q^{87} -6.45911e37 q^{88} +2.04808e38 q^{89} +7.59797e37 q^{90} -5.33937e37 q^{91} +9.15483e37 q^{92} -5.95359e38 q^{93} +4.52621e37 q^{94} +6.67854e38 q^{95} -5.94676e38 q^{96} -2.29267e38 q^{97} -1.39580e38 q^{98} +1.50731e39 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 548856 q^{2} + 1109442852 q^{3} + 272078981184 q^{4} + 17426916500490 q^{5} + 15\!\cdots\!96 q^{6}+ \cdots + 83\!\cdots\!91 q^{9}+O(q^{10}) $ 3 * q + 548856 * q^2 + 1109442852 * q^3 + 272078981184 * q^4 + 17426916500490 * q^5 + 1529727847867296 * q^6 - 17996297718635544 * q^7 + 255044243806133760 * q^8 + 8305879902078677391 * q^9	$ 3 q + 548856 q^{2} + 1109442852 q^{3} + 272078981184 q^{4} + 17426916500490 q^{5} + 15\!\cdots\!96 q^{6}+ \cdots + 10\!\cdots\!72 q^{99}+O(q^{100}) $ 3 * q + 548856 * q^2 + 1109442852 * q^3 + 272078981184 * q^4 + 17426916500490 * q^5 + 1529727847867296 * q^6 - 17996297718635544 * q^7 + 255044243806133760 * q^8 + 8305879902078677391 * q^9 + 90373081165367671440 * q^10 + 667814968265751536076 * q^11 + 3676571280854873162496 * q^12 + 3156080701447967254962 * q^13 - 63063724565889303463872 * q^14 - 171209278264452417200520 * q^15 - 351730940560369057001472 * q^16 + 890025791008793741893206 * q^17 + 8758537968130529168653272 * q^18 + 9227612185007697573518580 * q^19 - 14662452947108747596260480 * q^20 - 190208658572592931471251744 * q^21 - 122745877544387429034313248 * q^22 + 305308591470919570740188472 * q^23 + 1672960268636194560046295040 * q^24 + 1866127065486173095027030725 * q^25 + 283778605804595582169202896 * q^26 - 11508090459893795046427628760 * q^27 - 41794856371466593385827533312 * q^28 - 2492682219258648277296444030 * q^29 + 105977898643957401776506418880 * q^30 + 306107671747822704409554746016 * q^31 - 56572224161556180973554008064 * q^32 - 157376353761155567959844693616 * q^33 - 1683392869529765869103799245712 * q^34 - 1197259217905835166323668756560 * q^35 + 188684323073267404408057366848 * q^36 + 7599073412303579174888591086506 * q^37 + 2479871855304922949496616465440 * q^38 + 22252083518345402015145920059992 * q^39 - 32669995448979982796588503833600 * q^40 + 2391924206237769506232479990286 * q^41 - 195689966839404680756969540713728 * q^42 + 162865923671547339657067136304492 * q^43 - 45577647299113910363374898556672 * q^44 + 588908524142943445153326555470130 * q^45 - 24296541145531030477977021520704 * q^46 + 202683231875405841765643043683056 * q^47 - 1747281225742357435119054532067328 * q^48 + 368237681722499062385273201641179 * q^49 - 2624175085265540082696197615369400 * q^50 + 785651103815434341253216161914376 * q^51 + 3782687188757116950236456253499776 * q^52 + 5869079988764517679853946632443002 * q^53 + 7930814851979058696152103557167680 * q^54 - 4993109836111426485910134681304920 * q^55 - 6272116703248607238900430116679680 * q^56 - 46129102671186186415908500969957520 * q^57 + 2579097256656295554169870267982160 * q^58 - 56082681385621280317109288669637060 * q^59 + 127333179651658235430567238147607040 * q^60 + 39577675682126428331898689976833826 * q^61 + 262011550289381451529348830657714432 * q^62 - 174786720262353444072185876495505528 * q^63 - 169364906963561439583712861665099776 * q^64 - 264857762104053085095614223637519620 * q^65 - 287121760972609093376568794235255168 * q^66 - 140659929656119892877736400727430044 * q^67 - 130643133997460537100958647836349312 * q^68 + 1584175048695702801789842685209503392 * q^69 - 480338235822643784458804278358623360 * q^70 + 3849053210874068146700295241416217896 * q^71 - 1699150852984576616740529956276922880 * q^72 - 180754136492273067100959984036797778 * q^73 - 5070707041697857186532012041702753392 * q^74 - 4308561205008052508725896857031567300 * q^75 - 7362591710990284189025184136271151360 * q^76 + 5690389092595065468343565382905921952 * q^77 + 9330105385756793042468361274821534144 * q^78 + 13807772201216229289895673856694559120 * q^79 + 26839954555034162361105063302056304640 * q^80 - 18798023146176620962298765658838887237 * q^81 + 5068915865662526415092477483885831472 * q^82 - 20899400147905548803677768348186808268 * q^83 - 72152575898640813291791263837177976832 * q^84 - 105991789747453754784809897833488498060 * q^85 + 170012097580285110854272781787916483296 * q^86 - 73247996942640959139716393654519138280 * q^87 + 69412125637007165807333386173055825920 * q^88 + 205050039910109857136561853222076224510 * q^89 + 93221656611667223268126392859978755280 * q^90 - 165525104998331842571199169888366982544 * q^91 + 262356454404517646077951321169615264256 * q^92 - 167325068951627887866919523900021629056 * q^93 - 1127972668535151884588260809571286639232 * q^94 + 724803433705663618674774120451764528600 * q^95 - 1451094524490643350592064137029388468224 * q^96 + 173490888317728793437812209497231327206 * q^97 + 2246791677555180938475077451719860538808 * q^98 + 1057018158118568141770036034713090936572 * 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 $

$2$	241488.	0.325694	0.162847	−	0.986651i	$-0.447932\pi$
$2$	241488.	0.325694	0.162847	+	0.986651i	$0.447932\pi$
$3$	−3.14962e9	−1.56457	−0.782283	−	0.622923i	$-0.785945\pi$
$3$	−3.14962e9	−1.56457	−0.782283	+	0.622923i	$0.785945\pi$
$4$	−4.91439e11	−0.893923
$5$	5.36221e13	1.25727	0.628636	−	0.777700i	$-0.283614\pi$
$5$	5.36221e13	1.25727	0.628636	+	0.777700i	$0.283614\pi$
$6$	−7.60595e14	−0.509571
$7$	1.82084e16	0.603752	0.301876	−	0.953347i	$-0.402387\pi$
$7$	1.82084e16	0.603752	0.301876	+	0.953347i	$0.402387\pi$
$8$	−2.51436e17	−0.616840
$9$	5.86757e18	1.44787
$10$	1.29491e19	0.409486
$11$	2.56889e20	1.26645	0.633225	−	0.773968i	$-0.281731\pi$
$11$	2.56889e20	1.26645	0.633225	+	0.773968i	$0.281731\pi$
$12$	1.54785e21	1.39860
$13$	−2.93238e21	−0.556319	−0.278160	−	0.960535i	$-0.589724\pi$
$13$	−2.93238e21	−0.556319	−0.278160	+	0.960535i	$0.589724\pi$
$14$	4.39709e21	0.196639
$15$	−1.68890e23	−1.96709
$16$	2.09453e23	0.693022
$17$	−9.89190e22	−0.100352	−0.0501759	−	0.998740i	$-0.515978\pi$
$17$	−9.89190e22	−0.100352	−0.0501759	+	0.998740i	$0.515978\pi$
$18$	1.41695e24	0.471563
$19$	1.24548e25	1.44425	0.722125	−	0.691763i	$-0.243166\pi$
$19$	1.24548e25	1.44425	0.722125	+	0.691763i	$0.243166\pi$
$20$	−2.63520e25	−1.12390
$21$	−5.73494e25	−0.944611
$22$	6.20355e25	0.412476
$23$	−1.86286e26	−0.520580	−0.260290	−	0.965531i	$-0.583818\pi$
$23$	−1.86286e26	−0.520580	−0.260290	+	0.965531i	$0.583818\pi$
$24$	7.91928e26	0.965087
$25$	1.05635e27	0.580732
$26$	−7.08133e26	−0.181190
$27$	−5.71661e27	−0.700721
$28$	−8.94830e27	−0.539708
$29$	1.31775e28	0.400932	0.200466	−	0.979701i	$-0.435754\pi$
$29$	1.31775e28	0.400932	0.200466	+	0.979701i	$0.435754\pi$
$30$	−4.07848e28	−0.640669
$31$	1.89026e29	1.56663	0.783317	−	0.621623i	$-0.213526\pi$
$31$	1.89026e29	1.56663	0.783317	+	0.621623i	$0.213526\pi$
$32$	1.88809e29	0.842553
$33$	−8.09103e29	−1.98145
$34$	−2.38877e28	−0.0326840
$35$	9.76371e29	0.759081
$36$	−2.88356e30	−1.29428
$37$	3.22957e30	0.849593	0.424797	−	0.905289i	$-0.360346\pi$
$37$	3.22957e30	0.849593	0.424797	+	0.905289i	$0.360346\pi$
$38$	3.00769e30	0.470384
$39$	9.23588e30	0.870399
$40$	−1.34825e31	−0.775536
$41$	−2.27011e31	−0.806793	−0.403397	−	0.915025i	$-0.632171\pi$
$41$	−2.27011e31	−0.806793	−0.403397	+	0.915025i	$0.632171\pi$
$42$	−1.38492e31	−0.307654
$43$	5.36582e31	0.753357	0.376679	−	0.926344i	$-0.377066\pi$
$43$	5.36582e31	0.753357	0.376679	+	0.926344i	$0.377066\pi$
$44$	−1.26245e32	−1.13211
$45$	3.14632e32	1.82036
$46$	−4.49858e31	−0.169550
$47$	1.87430e32	0.464442	0.232221	−	0.972663i	$-0.425401\pi$
$47$	1.87430e32	0.464442	0.232221	+	0.972663i	$0.425401\pi$
$48$	−6.59698e32	−1.08428
$49$	−5.78000e32	−0.635483
$50$	2.55095e32	0.189141
$51$	3.11557e32	0.157007
$52$	1.44109e33	0.497307
$53$	−3.22443e32	−0.0767490	−0.0383745	−	0.999263i	$-0.512218\pi$
$53$	−3.22443e32	−0.0767490	−0.0383745	+	0.999263i	$0.512218\pi$
$54$	−1.38049e33	−0.228221
$55$	1.37749e34	1.59227
$56$	−4.57823e33	−0.372419
$57$	−3.92280e34	−2.25962
$58$	3.18220e33	0.130581
$59$	1.01307e34	0.297870	0.148935	−	0.988847i	$-0.452415\pi$
$59$	1.01307e34	0.297870	0.148935	+	0.988847i	$0.452415\pi$
$60$	8.29990e34	1.75842
$61$	−8.66378e34	−1.32977	−0.664884	−	0.746947i	$-0.731519\pi$
$61$	−8.66378e34	−1.32977	−0.664884	+	0.746947i	$0.731519\pi$
$62$	4.56473e34	0.510244
$63$	1.06839e35	0.874155
$64$	−6.95530e34	−0.418607
$65$	−1.57240e35	−0.699445
$66$	−1.95389e35	−0.645345
$67$	−5.98696e33	−0.0147485	−0.00737424	−	0.999973i	$-0.502347\pi$
$67$	−5.98696e33	−0.0147485	−0.00737424	+	0.999973i	$0.502347\pi$
$68$	4.86127e34	0.0897069
$69$	5.86730e35	0.814482
$70$	2.35782e35	0.247228
$71$	5.02476e35	0.399556	0.199778	−	0.979841i	$-0.435978\pi$
$71$	5.02476e35	0.399556	0.199778	+	0.979841i	$0.435978\pi$
$72$	−1.47532e36	−0.893104
$73$	1.14062e36	0.527651	0.263826	−	0.964570i	$-0.415016\pi$
$73$	1.14062e36	0.527651	0.263826	+	0.964570i	$0.415016\pi$
$74$	7.79901e35	0.276708
$75$	−3.32709e36	−0.908594
$76$	−6.12079e36	−1.29105
$77$	4.67752e36	0.764622
$78$	2.23035e36	0.283484
$79$	7.78268e36	0.771615	0.385808	−	0.922579i	$-0.373923\pi$
$79$	7.78268e36	0.771615	0.385808	+	0.922579i	$0.373923\pi$
$80$	1.12313e37	0.871317
$81$	−5.77348e36	−0.351544
$82$	−5.48205e36	−0.262768
$83$	−4.09909e37	−1.55119	−0.775594	−	0.631232i	$-0.782550\pi$
$83$	−4.09909e37	−1.55119	−0.775594	+	0.631232i	$0.782550\pi$
$84$	2.81838e37	0.844410
$85$	−5.30425e36	−0.126170
$86$	1.29578e37	0.245364
$87$	−4.15041e37	−0.627286
$88$	−6.45911e37	−0.781197
$89$	2.04808e38	1.98720	0.993600	−	0.112954i	$-0.0360312\pi$
$89$	2.04808e38	1.98720	0.993600	+	0.112954i	$0.0360312\pi$
$90$	7.59797e37	0.592883
$91$	−5.33937e37	−0.335879
$92$	9.15483e37	0.465358
$93$	−5.95359e38	−2.45110
$94$	4.52621e37	0.151266
$95$	6.67854e38	1.81581
$96$	−5.94676e38	−1.31823
$97$	−2.29267e38	−0.415234	−0.207617	−	0.978210i	$-0.566571\pi$
$97$	−2.29267e38	−0.415234	−0.207617	+	0.978210i	$0.566571\pi$
$98$	−1.39580e38	−0.206973
$99$	1.50731e39	1.83365
$100$	−5.19130e38	−0.519130
$101$	1.29569e39	1.06717	0.533587	−	0.845745i	$-0.320844\pi$
$101$	1.29569e39	1.06717	0.533587	+	0.845745i	$0.320844\pi$
$102$	7.52373e37	0.0511364
$103$	−2.69807e39	−1.51610	−0.758049	−	0.652198i	$-0.773847\pi$
$103$	−2.69807e39	−1.51610	−0.758049	+	0.652198i	$0.773847\pi$
$104$	7.37304e38	0.343160
$105$	−3.07520e39	−1.18763
$106$	−7.78659e37	−0.0249967
$107$	1.69252e39	0.452430	0.226215	−	0.974077i	$-0.427365\pi$
$107$	1.69252e39	0.452430	0.226215	+	0.974077i	$0.427365\pi$
$108$	2.80937e39	0.626391
$109$	1.65572e39	0.308439	0.154220	−	0.988037i	$-0.450714\pi$
$109$	1.65572e39	0.308439	0.154220	+	0.988037i	$0.450714\pi$
$110$	3.32648e39	0.518594
$111$	−1.01719e40	−1.32924
$112$	3.81379e39	0.418414
$113$	1.65677e40	1.52839	0.764193	−	0.644988i	$-0.223137\pi$
$113$	1.65677e40	1.52839	0.764193	+	0.644988i	$0.223137\pi$
$114$	−9.47308e39	−0.735947
$115$	−9.98905e39	−0.654510
$116$	−6.47593e39	−0.358403
$117$	−1.72059e40	−0.805478
$118$	2.44645e39	0.0970145
$119$	−1.80115e39	−0.0605877
$120$	4.24649e40	1.21338
$121$	2.48471e40	0.603895
$122$	−2.09220e40	−0.433098
$123$	7.15000e40	1.26228
$124$	−9.28946e40	−1.40045
$125$	−4.08946e40	−0.527134
$126$	2.58003e40	0.284707
$127$	1.00910e41	0.954473	0.477236	−	0.878775i	$-0.341639\pi$
$127$	1.00910e41	0.954473	0.477236	+	0.878775i	$0.341639\pi$
$128$	−1.20595e41	−0.978891
$129$	−1.69003e41	−1.17868
$130$	−3.79716e40	−0.227805
$131$	3.37684e40	0.174470	0.0872348	−	0.996188i	$-0.472197\pi$
$131$	3.37684e40	0.174470	0.0872348	+	0.996188i	$0.472197\pi$
$132$	3.97625e41	1.77126
$133$	2.26782e41	0.871969
$134$	−1.44578e39	−0.00480350
$135$	−3.06537e41	−0.880997
$136$	2.48718e40	0.0619011
$137$	−5.27644e41	−1.13839	−0.569193	−	0.822204i	$-0.692744\pi$
$137$	−5.27644e41	−1.13839	−0.569193	+	0.822204i	$0.692744\pi$
$138$	1.41688e41	0.265272
$139$	6.43985e41	1.04734	0.523669	−	0.851922i	$-0.324563\pi$
$139$	6.43985e41	1.04734	0.523669	+	0.851922i	$0.324563\pi$
$140$	−4.79827e41	−0.678560
$141$	−5.90335e41	−0.726650
$142$	1.21342e41	0.130133
$143$	−7.53295e41	−0.704551
$144$	1.22898e42	1.00341
$145$	7.06604e41	0.504081
$146$	2.75447e41	0.171853
$147$	1.82048e42	0.994256
$148$	−1.58714e42	−0.759471
$149$	1.12323e42	0.471341	0.235671	−	0.971833i	$-0.424271\pi$
$149$	1.12323e42	0.471341	0.235671	+	0.971833i	$0.424271\pi$
$150$	−8.03452e41	−0.295924
$151$	−3.59308e42	−1.16256	−0.581281	−	0.813703i	$-0.697448\pi$
$151$	−3.59308e42	−1.16256	−0.581281	+	0.813703i	$0.697448\pi$
$152$	−3.13159e42	−0.890871
$153$	−5.80414e41	−0.145296
$154$	1.12956e42	0.249033
$155$	1.01360e43	1.96968
$156$	−4.53887e42	−0.778070
$157$	−2.11217e42	−0.319659	−0.159829	−	0.987145i	$-0.551094\pi$
$157$	−2.11217e42	−0.319659	−0.159829	+	0.987145i	$0.551094\pi$
$158$	1.87942e42	0.251311
$159$	1.01557e42	0.120079
$160$	1.01243e43	1.05932
$161$	−3.39196e42	−0.314301
$162$	−1.39422e42	−0.114496
$163$	−5.72434e42	−0.416934	−0.208467	−	0.978029i	$-0.566847\pi$
$163$	−5.72434e42	−0.416934	−0.208467	+	0.978029i	$0.566847\pi$
$164$	1.11562e43	0.721211
$165$	−4.33859e43	−2.49122
$166$	−9.89879e42	−0.505213
$167$	3.34941e43	1.52054	0.760268	−	0.649610i	$-0.225068\pi$
$167$	3.34941e43	1.52054	0.760268	+	0.649610i	$0.225068\pi$
$168$	1.44197e43	0.582674
$169$	−1.91849e43	−0.690509
$170$	−1.28091e42	−0.0410927
$171$	7.30795e43	2.09108
$172$	−2.63697e43	−0.673444
$173$	−3.41377e43	−0.778636	−0.389318	−	0.921103i	$-0.627289\pi$
$173$	−3.41377e43	−0.778636	−0.389318	+	0.921103i	$0.627289\pi$
$174$	−1.00227e43	−0.204303
$175$	1.92343e43	0.350618
$176$	5.38062e43	0.877678
$177$	−3.19080e43	−0.466037
$178$	4.94586e43	0.647220
$179$	−1.44182e44	−1.69151	−0.845757	−	0.533569i	$-0.820851\pi$
$179$	−1.44182e44	−1.69151	−0.845757	+	0.533569i	$0.820851\pi$
$180$	−1.54622e44	−1.62727
$181$	3.88244e43	0.366752	0.183376	−	0.983043i	$-0.441297\pi$
$181$	3.88244e43	0.366752	0.183376	+	0.983043i	$0.441297\pi$
$182$	−1.28939e43	−0.109394
$183$	2.72877e44	2.08051
$184$	4.68390e43	0.321114
$185$	1.73176e44	1.06817
$186$	−1.43772e44	−0.798310
$187$	−2.54112e43	−0.127091
$188$	−9.21106e43	−0.415175
$189$	−1.04090e44	−0.423062
$190$	1.61279e44	0.591400
$191$	−1.72164e44	−0.569889	−0.284945	−	0.958544i	$-0.591975\pi$
$191$	−1.72164e44	−0.569889	−0.284945	+	0.958544i	$0.591975\pi$
$192$	2.19066e44	0.654939
$193$	−6.30991e44	−1.70473	−0.852365	−	0.522947i	$-0.824832\pi$
$193$	−6.30991e44	−1.70473	−0.852365	+	0.522947i	$0.824832\pi$
$194$	−5.53651e43	−0.135239
$195$	4.95248e44	1.09433
$196$	2.84052e44	0.568073
$197$	−1.00595e45	−1.82173	−0.910865	−	0.412705i	$-0.864584\pi$
$197$	−1.00595e45	−1.82173	−0.910865	+	0.412705i	$0.864584\pi$
$198$	3.63998e44	0.597211
$199$	1.18780e45	1.76648	0.883242	−	0.468918i	$-0.155356\pi$
$199$	1.18780e45	1.76648	0.883242	+	0.468918i	$0.155356\pi$
$200$	−2.65603e44	−0.358219
$201$	1.88567e43	0.0230750
$202$	3.12894e44	0.347572
$203$	2.39940e44	0.242064
$204$	−1.53112e44	−0.140352
$205$	−1.21728e45	−1.01436
$206$	−6.51551e44	−0.493784
$207$	−1.09305e45	−0.753731
$208$	−6.14195e44	−0.385542
$209$	3.19950e45	1.82907
$210$	−7.42623e44	−0.386805
$211$	−3.02479e43	−0.0143611	−0.00718054	−	0.999974i	$-0.502286\pi$
$211$	−3.02479e43	−0.0143611	−0.00718054	+	0.999974i	$0.502286\pi$
$212$	1.58461e44	0.0686078
$213$	−1.58261e45	−0.625132
$214$	4.08724e44	0.147354
$215$	2.87727e45	0.947175
$216$	1.43736e45	0.432233
$217$	3.44184e45	0.945859
$218$	3.99836e44	0.100457
$219$	−3.59254e45	−0.825545
$220$	−6.76955e45	−1.42337
$221$	2.90068e44	0.0558277
$222$	−2.45640e45	−0.432928
$223$	−6.62720e45	−1.07000	−0.535002	−	0.844851i	$-0.679689\pi$
$223$	−6.62720e45	−1.07000	−0.535002	+	0.844851i	$0.679689\pi$
$224$	3.43790e45	0.508694
$225$	6.19818e45	0.840824
$226$	4.00090e45	0.497787
$227$	−5.09742e45	−0.581897	−0.290948	−	0.956739i	$-0.593971\pi$
$227$	−5.09742e45	−0.581897	−0.290948	+	0.956739i	$0.593971\pi$
$228$	1.92782e46	2.01993
$229$	−5.09087e45	−0.489778	−0.244889	−	0.969551i	$-0.578752\pi$
$229$	−5.09087e45	−0.489778	−0.244889	+	0.969551i	$0.578752\pi$
$230$	−2.41223e45	−0.213170
$231$	−1.47324e46	−1.19630
$232$	−3.31329e45	−0.247311
$233$	2.36093e46	1.62048	0.810239	−	0.586100i	$-0.199337\pi$
$233$	2.36093e46	1.62048	0.810239	+	0.586100i	$0.199337\pi$
$234$	−4.15502e45	−0.262340
$235$	1.00504e46	0.583930
$236$	−4.97864e45	−0.266273
$237$	−2.45125e46	−1.20724
$238$	−4.34956e44	−0.0197331
$239$	−1.68674e46	−0.705162	−0.352581	−	0.935781i	$-0.614696\pi$
$239$	−1.68674e46	−0.705162	−0.352581	+	0.935781i	$0.614696\pi$
$240$	−3.53744e46	−1.36323
$241$	3.12678e46	1.11113	0.555565	−	0.831473i	$-0.312502\pi$
$241$	3.12678e46	1.11113	0.555565	+	0.831473i	$0.312502\pi$
$242$	6.00028e45	0.196685
$243$	4.13512e46	1.25074
$244$	4.25773e46	1.18871
$245$	−3.09936e46	−0.798975
$246$	1.72664e46	0.411118
$247$	−3.65222e46	−0.803464
$248$	−4.75278e46	−0.966362
$249$	1.29106e47	2.42694
$250$	−9.87555e45	−0.171684
$251$	−6.69718e46	−1.07710	−0.538548	−	0.842595i	$-0.681027\pi$
$251$	−6.69718e46	−1.07710	−0.538548	+	0.842595i	$0.681027\pi$
$252$	−5.25048e46	−0.781427
$253$	−4.78548e46	−0.659288
$254$	2.43686e46	0.310866
$255$	1.67064e46	0.197401
$256$	9.11500e45	0.0997878
$257$	−3.87410e46	−0.393074	−0.196537	−	0.980496i	$-0.562970\pi$
$257$	−3.87410e46	−0.393074	−0.196537	+	0.980496i	$0.562970\pi$
$258$	−4.08122e46	−0.383889
$259$	5.88051e46	0.512944
$260$	7.72741e46	0.625250
$261$	7.73197e46	0.580498
$262$	8.15465e45	0.0568238
$263$	−5.89846e45	−0.0381594	−0.0190797	−	0.999818i	$-0.506074\pi$
$263$	−5.89846e45	−0.0381594	−0.0190797	+	0.999818i	$0.506074\pi$
$264$	2.03438e47	1.22223
$265$	−1.72901e46	−0.0964944
$266$	5.47650e46	0.283995
$267$	−6.45068e47	−3.10911
$268$	2.94223e45	0.0131840
$269$	8.99725e46	0.374921	0.187461	−	0.982272i	$-0.439974\pi$
$269$	8.99725e46	0.374921	0.187461	+	0.982272i	$0.439974\pi$
$270$	−7.40249e46	−0.286936
$271$	1.93454e47	0.697711	0.348855	−	0.937177i	$-0.386570\pi$
$271$	1.93454e47	0.697711	0.348855	+	0.937177i	$0.386570\pi$
$272$	−2.07189e46	−0.0695461
$273$	1.68170e47	0.525505
$274$	−1.27420e47	−0.370766
$275$	2.71363e47	0.735468
$276$	−2.88342e47	−0.728084
$277$	−5.39283e47	−1.26900	−0.634500	−	0.772923i	$-0.718794\pi$
$277$	−5.39283e47	−1.26900	−0.634500	+	0.772923i	$0.718794\pi$
$278$	1.55514e47	0.341112
$279$	1.10912e48	2.26828
$280$	−2.45495e47	−0.468231
$281$	3.42772e47	0.609862	0.304931	−	0.952374i	$-0.401367\pi$
$281$	3.42772e47	0.609862	0.304931	+	0.952374i	$0.401367\pi$
$282$	−1.42559e47	−0.236666
$283$	8.61731e47	1.33517	0.667584	−	0.744534i	$-0.267328\pi$
$283$	8.61731e47	1.33517	0.667584	+	0.744534i	$0.267328\pi$
$284$	−2.46937e47	−0.357172
$285$	−2.10349e48	−2.84096
$286$	−1.81911e47	−0.229468
$287$	−4.13350e47	−0.487104
$288$	1.10785e48	1.21991
$289$	−9.61861e47	−0.989929
$290$	1.70636e47	0.164176
$291$	7.22104e47	0.649661
$292$	−5.60548e47	−0.471679
$293$	1.93492e48	1.52316	0.761578	−	0.648073i	$-0.224425\pi$
$293$	1.93492e48	1.52316	0.761578	+	0.648073i	$0.224425\pi$
$294$	4.39624e47	0.323823
$295$	5.43232e47	0.374503
$296$	−8.12030e47	−0.524063
$297$	−1.46853e48	−0.887428
$298$	2.71246e47	0.153513
$299$	5.46260e47	0.289609
$300$	1.63506e48	0.812213
$301$	9.77027e47	0.454841
$302$	−8.67684e47	−0.378640
$303$	−4.08094e48	−1.66966
$304$	2.60870e48	1.00090
$305$	−4.64571e48	−1.67188
$306$	−1.40163e47	−0.0473222
$307$	−1.51569e48	−0.480188	−0.240094	−	0.970750i	$-0.577178\pi$
$307$	−1.51569e48	−0.480188	−0.240094	+	0.970750i	$0.577178\pi$
$308$	−2.29872e48	−0.683514
$309$	8.49790e48	2.37204
$310$	2.44771e48	0.641515
$311$	1.19146e48	0.293260	0.146630	−	0.989191i	$-0.453157\pi$
$311$	1.19146e48	0.293260	0.146630	+	0.989191i	$0.453157\pi$
$312$	−2.32223e48	−0.536897
$313$	−4.44520e47	−0.0965555	−0.0482778	−	0.998834i	$-0.515373\pi$
$313$	−4.44520e47	−0.0965555	−0.0482778	+	0.998834i	$0.515373\pi$
$314$	−5.10064e47	−0.104111
$315$	5.72893e48	1.09905
$316$	−3.82472e48	−0.689765
$317$	−1.03382e48	−0.175303	−0.0876516	−	0.996151i	$-0.527936\pi$
$317$	−1.03382e48	−0.175303	−0.0876516	+	0.996151i	$0.527936\pi$
$318$	2.45248e47	0.0391091
$319$	3.38515e48	0.507761
$320$	−3.72958e48	−0.526303
$321$	−5.33082e48	−0.707857
$322$	−8.19117e47	−0.102366
$323$	−1.23202e48	−0.144933
$324$	2.83732e48	0.314253
$325$	−3.09760e48	−0.323073
$326$	−1.38236e48	−0.135793
$327$	−5.21489e48	−0.482574
$328$	5.70788e48	0.497663
$329$	3.41280e48	0.280408
$330$	−1.04772e49	−0.811375
$331$	6.53650e48	0.477199	0.238599	−	0.971118i	$-0.423312\pi$
$331$	6.53650e48	0.477199	0.238599	+	0.971118i	$0.423312\pi$
$332$	2.01445e49	1.38664
$333$	1.89497e49	1.23010
$334$	8.08841e48	0.495230
$335$	−3.21033e47	−0.0185429
$336$	−1.20120e49	−0.654636
$337$	−2.75713e49	−1.41799	−0.708996	−	0.705213i	$-0.750852\pi$
$337$	−2.75713e49	−1.41799	−0.708996	+	0.705213i	$0.750852\pi$
$338$	−4.63292e48	−0.224895
$339$	−5.21821e49	−2.39126
$340$	2.60672e48	0.112786
$341$	4.85586e49	1.98406
$342$	1.76478e49	0.681054
$343$	−2.70857e49	−0.987427
$344$	−1.34916e49	−0.464701
$345$	3.14617e49	1.02402
$346$	−8.24383e48	−0.253597
$347$	1.59040e48	0.0462468	0.0231234	−	0.999733i	$-0.492639\pi$
$347$	1.59040e48	0.0462468	0.0231234	+	0.999733i	$0.492639\pi$
$348$	2.03967e49	0.560745
$349$	−4.30840e49	−1.12001	−0.560003	−	0.828491i	$-0.689200\pi$
$349$	−4.30840e49	−1.12001	−0.560003	+	0.828491i	$0.689200\pi$
$350$	4.64485e48	0.114194
$351$	1.67633e49	0.389825
$352$	4.85029e49	1.06705
$353$	4.31576e49	0.898361	0.449181	−	0.893441i	$-0.351716\pi$
$353$	4.31576e49	0.898361	0.449181	+	0.893441i	$0.351716\pi$
$354$	−7.70539e48	−0.151786
$355$	2.69439e49	0.502350
$356$	−1.00651e50	−1.77640
$357$	5.67295e48	0.0947935
$358$	−3.48181e49	−0.550916
$359$	−2.80608e49	−0.420492	−0.210246	−	0.977648i	$-0.567427\pi$
$359$	−2.80608e49	−0.420492	−0.210246	+	0.977648i	$0.567427\pi$
$360$	−7.91097e49	−1.12287
$361$	8.07537e49	1.08586
$362$	9.37562e48	0.119449
$363$	−7.82591e49	−0.944834
$364$	2.62398e49	0.300250
$365$	6.11627e49	0.663401
$366$	6.58963e49	0.677610
$367$	8.06624e49	0.786472	0.393236	−	0.919438i	$-0.371356\pi$
$367$	8.06624e49	0.786472	0.393236	+	0.919438i	$0.371356\pi$
$368$	−3.90181e49	−0.360773
$369$	−1.33200e50	−1.16813
$370$	4.18200e49	0.347897
$371$	−5.87115e48	−0.0463374
$372$	2.92583e50	2.19110
$373$	−2.09254e50	−1.48714	−0.743571	−	0.668657i	$-0.766870\pi$
$373$	−2.09254e50	−1.48714	−0.743571	+	0.668657i	$0.766870\pi$
$374$	−6.13649e48	−0.0413927
$375$	1.28803e50	0.824736
$376$	−4.71267e49	−0.286486
$377$	−3.86413e49	−0.223046
$378$	−2.51365e49	−0.137789
$379$	3.48223e49	0.181298	0.0906489	−	0.995883i	$-0.471106\pi$
$379$	3.48223e49	0.181298	0.0906489	+	0.995883i	$0.471106\pi$
$380$	−3.28210e50	−1.62320
$381$	−3.17830e50	−1.49334
$382$	−4.15754e49	−0.185610
$383$	6.27597e49	0.266259	0.133130	−	0.991099i	$-0.457497\pi$
$383$	6.27597e49	0.266259	0.133130	+	0.991099i	$0.457497\pi$
$384$	3.79828e50	1.53154
$385$	2.50819e50	0.961338
$386$	−1.52377e50	−0.555221
$387$	3.14843e50	1.09076
$388$	1.12671e50	0.371187
$389$	−2.37857e50	−0.745245	−0.372623	−	0.927983i	$-0.621541\pi$
$389$	−2.37857e50	−0.745245	−0.372623	+	0.927983i	$0.621541\pi$
$390$	1.19596e50	0.356416
$391$	1.84272e49	0.0522412
$392$	1.45330e50	0.391991
$393$	−1.06358e50	−0.272969
$394$	−2.42924e50	−0.593327
$395$	4.17324e50	0.970130
$396$	−7.40753e50	−1.63915
$397$	−1.69815e50	−0.357734	−0.178867	−	0.983873i	$-0.557243\pi$
$397$	−1.69815e50	−0.357734	−0.178867	+	0.983873i	$0.557243\pi$
$398$	2.86840e50	0.575334
$399$	−7.14277e50	−1.36425
$400$	2.21255e50	0.402460
$401$	1.06858e51	1.85136	0.925681	−	0.378306i	$-0.123493\pi$
$401$	1.06858e51	1.85136	0.925681	+	0.378306i	$0.123493\pi$
$402$	4.55365e48	0.00751539
$403$	−5.54294e50	−0.871549
$404$	−6.36754e50	−0.953971
$405$	−3.09586e50	−0.441986
$406$	5.79426e49	0.0788388
$407$	8.29640e50	1.07597
$408$	−7.83367e49	−0.0968483
$409$	1.58478e50	0.186794	0.0933972	−	0.995629i	$-0.470227\pi$
$409$	1.58478e50	0.186794	0.0933972	+	0.995629i	$0.470227\pi$
$410$	−2.93959e50	−0.330371
$411$	1.66188e51	1.78108
$412$	1.32594e51	1.35528
$413$	1.84464e50	0.179840
$414$	−2.63957e50	−0.245486
$415$	−2.19802e51	−1.95026
$416$	−5.53658e50	−0.468729
$417$	−2.02831e51	−1.63863
$418$	7.72641e50	0.595717
$419$	−2.13326e50	−0.156989	−0.0784947	−	0.996915i	$-0.525011\pi$
$419$	−2.13326e50	−0.156989	−0.0784947	+	0.996915i	$0.525011\pi$
$420$	1.51128e51	1.06165
$421$	−1.07542e51	−0.721232	−0.360616	−	0.932714i	$-0.617434\pi$
$421$	−1.07542e51	−0.721232	−0.360616	+	0.932714i	$0.617434\pi$
$422$	−7.30450e48	−0.00467732
$423$	1.09976e51	0.672451
$424$	8.10737e49	0.0473419
$425$	−1.04493e50	−0.0582776
$426$	−3.82181e50	−0.203602
$427$	−1.57753e51	−0.802851
$428$	−8.31774e50	−0.404438
$429$	2.37259e51	1.10232
$430$	6.94825e50	0.308489
$431$	3.49435e51	1.48272	0.741360	−	0.671108i	$-0.234181\pi$
$431$	3.49435e51	1.48272	0.741360	+	0.671108i	$0.234181\pi$
$432$	−1.19736e51	−0.485615
$433$	2.34196e51	0.907956	0.453978	−	0.891013i	$-0.350005\pi$
$433$	2.34196e51	0.907956	0.453978	+	0.891013i	$0.350005\pi$
$434$	8.31163e50	0.308061
$435$	−2.22554e51	−0.788668
$436$	−8.13685e50	−0.275721
$437$	−2.32016e51	−0.751847
$438$	−8.67553e50	−0.268875
$439$	1.54147e51	0.456960	0.228480	−	0.973549i	$-0.426624\pi$
$439$	1.54147e51	0.456960	0.228480	+	0.973549i	$0.426624\pi$
$440$	−3.46351e51	−0.982177
$441$	−3.39145e51	−0.920096
$442$	7.00477e49	0.0181828
$443$	−6.02650e51	−1.49690	−0.748449	−	0.663192i	$-0.769201\pi$
$443$	−6.02650e51	−1.49690	−0.748449	+	0.663192i	$0.769201\pi$
$444$	4.99889e51	1.18824
$445$	1.09822e52	2.49845
$446$	−1.60039e51	−0.348494
$447$	−3.53774e51	−0.737445
$448$	−1.26645e51	−0.252735
$449$	8.31046e51	1.58789	0.793947	−	0.607987i	$-0.208023\pi$
$449$	8.31046e51	1.58789	0.793947	+	0.607987i	$0.208023\pi$
$450$	1.49678e51	0.273852
$451$	−5.83167e51	−1.02176
$452$	−8.14203e51	−1.36626
$453$	1.13168e52	1.81891
$454$	−1.23096e51	−0.189520
$455$	−2.86309e51	−0.422291
$456$	9.86332e51	1.39383
$457$	−7.27855e51	−0.985551	−0.492776	−	0.870156i	$-0.664018\pi$
$457$	−7.27855e51	−0.985551	−0.492776	+	0.870156i	$0.664018\pi$
$458$	−1.22938e51	−0.159518
$459$	5.65481e50	0.0703187
$460$	4.90901e51	0.585082
$461$	−1.09767e51	−0.125402	−0.0627008	−	0.998032i	$-0.519971\pi$
$461$	−1.09767e51	−0.125402	−0.0627008	+	0.998032i	$0.519971\pi$
$462$	−3.55770e51	−0.389629
$463$	−8.46883e51	−0.889189	−0.444595	−	0.895732i	$-0.646652\pi$
$463$	−8.46883e51	−0.889189	−0.444595	+	0.895732i	$0.646652\pi$
$464$	2.76006e51	0.277855
$465$	−3.19244e52	−3.08170
$466$	5.70136e51	0.527780
$467$	1.69800e52	1.50751	0.753753	−	0.657158i	$-0.228242\pi$
$467$	1.69800e52	1.50751	0.753753	+	0.657158i	$0.228242\pi$
$468$	8.45567e51	0.720035
$469$	−1.09013e50	−0.00890443
$470$	2.42705e51	0.190183
$471$	6.65255e51	0.500127
$472$	−2.54723e51	−0.183738
$473$	1.37842e52	0.954089
$474$	−5.91947e51	−0.393192
$475$	1.31566e52	0.838722
$476$	8.85157e50	0.0541608
$477$	−1.89195e51	−0.111123
$478$	−4.07327e51	−0.229667
$479$	2.99013e51	0.161863	0.0809314	−	0.996720i	$-0.474211\pi$
$479$	2.99013e51	0.161863	0.0809314	+	0.996720i	$0.474211\pi$
$480$	−3.18878e52	−1.65737
$481$	−9.47031e51	−0.472645
$482$	7.55078e51	0.361889
$483$	1.06834e52	0.491745
$484$	−1.22109e52	−0.539836
$485$	−1.22938e52	−0.522061
$486$	9.98580e51	0.407357
$487$	−1.46011e52	−0.572232	−0.286116	−	0.958195i	$-0.592364\pi$
$487$	−1.46011e52	−0.572232	−0.286116	+	0.958195i	$0.592364\pi$
$488$	2.17839e52	0.820254
$489$	1.80295e52	0.652321
$490$	−7.48457e51	−0.260222
$491$	−1.53063e52	−0.511426	−0.255713	−	0.966753i	$-0.582310\pi$
$491$	−1.53063e52	−0.511426	−0.255713	+	0.966753i	$0.582310\pi$
$492$	−3.51379e52	−1.12838
$493$	−1.30350e51	−0.0402343
$494$	−8.81966e51	−0.261684
$495$	8.08254e52	2.30540
$496$	3.95920e52	1.08571
$497$	9.14926e51	0.241233
$498$	3.11775e52	0.790440
$499$	−4.30786e51	−0.105027	−0.0525135	−	0.998620i	$-0.516723\pi$
$499$	−4.30786e51	−0.105027	−0.0525135	+	0.998620i	$0.516723\pi$
$500$	2.00972e52	0.471217
$501$	−1.05494e53	−2.37898
$502$	−1.61729e52	−0.350804
$503$	−7.62462e52	−1.59090	−0.795449	−	0.606020i	$-0.792765\pi$
$503$	−7.62462e52	−1.59090	−0.795449	+	0.606020i	$0.792765\pi$
$504$	−2.68631e52	−0.539214
$505$	6.94778e52	1.34173
$506$	−1.15563e52	−0.214726
$507$	6.04253e52	1.08035
$508$	−4.95914e52	−0.853225
$509$	4.36698e51	0.0723078	0.0361539	−	0.999346i	$-0.488489\pi$
$509$	4.36698e51	0.0723078	0.0361539	+	0.999346i	$0.488489\pi$
$510$	4.03439e51	0.0642923
$511$	2.07689e52	0.318571
$512$	6.84989e52	1.01139
$513$	−7.11993e52	−1.01202
$514$	−9.35547e51	−0.128022
$515$	−1.44676e53	−1.90615
$516$	8.30548e52	1.05365
$517$	4.81487e52	0.588192
$518$	1.42007e52	0.167063
$519$	1.07521e53	1.21823
$520$	3.95358e52	0.431445
$521$	−2.72686e51	−0.0286634	−0.0143317	−	0.999897i	$-0.504562\pi$
$521$	−2.72686e51	−0.0286634	−0.0143317	+	0.999897i	$0.504562\pi$
$522$	1.86718e52	0.189065
$523$	3.45861e52	0.337379	0.168690	−	0.985669i	$-0.446046\pi$
$523$	3.45861e52	0.337379	0.168690	+	0.985669i	$0.446046\pi$
$524$	−1.65951e52	−0.155962
$525$	−6.05808e52	−0.548566
$526$	−1.42441e51	−0.0124283
$527$	−1.86982e52	−0.157215
$528$	−1.69469e53	−1.37319
$529$	−9.33493e52	−0.728997
$530$	−4.17534e51	−0.0314277
$531$	5.94428e52	0.431277
$532$	−1.11449e53	−0.779473
$533$	6.65682e52	0.448835
$534$	−1.55776e53	−1.01262
$535$	9.07568e52	0.568827
$536$	1.50534e51	0.00909746
$537$	4.54117e53	2.64649
$538$	2.17273e52	0.122110
$539$	−1.48482e53	−0.804807
$540$	1.50644e53	0.787544
$541$	−1.10485e53	−0.557129	−0.278565	−	0.960417i	$-0.589859\pi$
$541$	−1.10485e53	−0.557129	−0.278565	+	0.960417i	$0.589859\pi$
$542$	4.67167e52	0.227240
$543$	−1.22282e53	−0.573809
$544$	−1.86768e52	−0.0845518
$545$	8.87832e52	0.387792
$546$	4.06110e52	0.171154
$547$	−1.77885e52	−0.0723413	−0.0361706	−	0.999346i	$-0.511516\pi$
$547$	−1.77885e52	−0.0723413	−0.0361706	+	0.999346i	$0.511516\pi$
$548$	2.59305e53	1.01763
$549$	−5.08354e53	−1.92533
$550$	6.55310e52	0.239538
$551$	1.64123e53	0.579046
$552$	−1.47525e53	−0.502405
$553$	1.41710e53	0.465865
$554$	−1.30230e53	−0.413306
$555$	−5.45440e53	−1.67122
$556$	−3.16480e53	−0.936240
$557$	3.89141e53	1.11155	0.555777	−	0.831332i	$-0.312421\pi$
$557$	3.89141e53	1.11155	0.555777	+	0.831332i	$0.312421\pi$
$558$	2.67839e53	0.738766
$559$	−1.57346e53	−0.419107
$560$	2.04504e53	0.526060
$561$	8.00356e52	0.198842
$562$	8.27752e52	0.198629
$563$	−4.03186e53	−0.934528	−0.467264	−	0.884118i	$-0.654760\pi$
$563$	−4.03186e53	−0.934528	−0.467264	+	0.884118i	$0.654760\pi$
$564$	2.90114e53	0.649570
$565$	8.88397e53	1.92160
$566$	2.08097e53	0.434857
$567$	−1.05126e53	−0.212246
$568$	−1.26341e53	−0.246462
$569$	−6.36680e52	−0.120014	−0.0600070	−	0.998198i	$-0.519112\pi$
$569$	−6.36680e52	−0.120014	−0.0600070	+	0.998198i	$0.519112\pi$
$570$	−5.07967e53	−0.925285
$571$	−6.36424e53	−1.12032	−0.560160	−	0.828384i	$-0.689260\pi$
$571$	−6.36424e53	−1.12032	−0.560160	+	0.828384i	$0.689260\pi$
$572$	3.70199e53	0.629814
$573$	5.42250e53	0.891630
$574$	−9.98190e52	−0.158647
$575$	−1.96782e53	−0.302317
$576$	−4.08107e53	−0.606088
$577$	−9.29606e53	−1.33466	−0.667330	−	0.744762i	$-0.732563\pi$
$577$	−9.29606e53	−1.33466	−0.667330	+	0.744762i	$0.732563\pi$
$578$	−2.32278e53	−0.322414
$579$	1.98738e54	2.66716
$580$	−3.47253e53	−0.450610
$581$	−7.46376e53	−0.936533
$582$	1.74379e53	0.211591
$583$	−8.28319e52	−0.0971988
$584$	−2.86794e53	−0.325476
$585$	−9.22618e53	−1.01270
$586$	4.67260e53	0.496083
$587$	6.03454e52	0.0619728	0.0309864	−	0.999520i	$-0.490135\pi$
$587$	6.03454e52	0.0619728	0.0309864	+	0.999520i	$0.490135\pi$
$588$	−8.94656e53	−0.888788
$589$	2.35428e54	2.26261
$590$	1.31184e53	0.121974
$591$	3.16835e54	2.85022
$592$	6.76443e53	0.588787
$593$	−1.41264e54	−1.18977	−0.594886	−	0.803810i	$-0.702803\pi$
$593$	−1.41264e54	−1.18977	−0.594886	+	0.803810i	$0.702803\pi$
$594$	−3.54633e53	−0.289030
$595$	−9.65816e52	−0.0761752
$596$	−5.51998e53	−0.421343
$597$	−3.74113e54	−2.76378
$598$	1.31915e53	0.0943239
$599$	−1.17608e54	−0.813979	−0.406990	−	0.913433i	$-0.633421\pi$
$599$	−1.17608e54	−0.813979	−0.406990	+	0.913433i	$0.633421\pi$
$600$	8.36550e53	0.560457
$601$	−1.78335e53	−0.115660	−0.0578300	−	0.998326i	$-0.518418\pi$
$601$	−1.78335e53	−0.115660	−0.0578300	+	0.998326i	$0.518418\pi$
$602$	2.35940e53	0.148139
$603$	−3.51289e52	−0.0213539
$604$	1.76578e54	1.03924
$605$	1.33236e54	0.759260
$606$	−9.85497e53	−0.543800
$607$	−1.82763e54	−0.976582	−0.488291	−	0.872681i	$-0.662380\pi$
$607$	−1.82763e54	−0.976582	−0.488291	+	0.872681i	$0.662380\pi$
$608$	2.35158e54	1.21686
$609$	−7.55721e53	−0.378725
$610$	−1.12188e54	−0.544522
$611$	−5.49616e53	−0.258378
$612$	2.85238e53	0.129884
$613$	1.27061e54	0.560446	0.280223	−	0.959935i	$-0.409592\pi$
$613$	1.27061e54	0.560446	0.280223	+	0.959935i	$0.409592\pi$
$614$	−3.66020e53	−0.156395
$615$	3.83398e54	1.58703
$616$	−1.17610e54	−0.471650
$617$	1.76693e54	0.686530	0.343265	−	0.939239i	$-0.388467\pi$
$617$	1.76693e54	0.686530	0.343265	+	0.939239i	$0.388467\pi$
$618$	2.05214e54	0.772559
$619$	−2.12154e54	−0.773897	−0.386948	−	0.922101i	$-0.626471\pi$
$619$	−2.12154e54	−0.773897	−0.386948	+	0.922101i	$0.626471\pi$
$620$	−4.98121e54	−1.76075
$621$	1.06492e54	0.364781
$622$	2.87723e53	0.0955130
$623$	3.72922e54	1.19978
$624$	1.93448e54	0.603205
$625$	−4.11434e54	−1.24348
$626$	−1.07346e53	−0.0314476
$627$	−1.00772e55	−2.86170
$628$	1.03801e54	0.285750
$629$	−3.19466e53	−0.0852583
$630$	1.38347e54	0.357954
$631$	4.38932e54	1.10109	0.550547	−	0.834804i	$-0.314419\pi$
$631$	4.38932e54	1.10109	0.550547	+	0.834804i	$0.314419\pi$
$632$	−1.95684e54	−0.475963
$633$	9.52695e52	0.0224689
$634$	−2.49655e53	−0.0570953
$635$	5.41103e54	1.20003
$636$	−4.99093e53	−0.107341
$637$	1.69491e54	0.353532
$638$	8.17471e53	0.165375
$639$	2.94831e54	0.578505
$640$	−6.46656e54	−1.23073
$641$	8.28753e54	1.53001	0.765004	−	0.644025i	$-0.222737\pi$
$641$	8.28753e54	1.53001	0.765004	+	0.644025i	$0.222737\pi$
$642$	−1.28733e54	−0.230545
$643$	−1.96493e54	−0.341376	−0.170688	−	0.985325i	$-0.554599\pi$
$643$	−1.96493e54	−0.341376	−0.170688	+	0.985325i	$0.554599\pi$
$644$	1.66694e54	0.280961
$645$	−9.06230e54	−1.48192
$646$	−2.97517e53	−0.0472039
$647$	8.12153e54	1.25027	0.625136	−	0.780516i	$-0.285044\pi$
$647$	8.12153e54	1.25027	0.625136	+	0.780516i	$0.285044\pi$
$648$	1.45166e54	0.216846
$649$	2.60247e54	0.377237
$650$	−7.48033e53	−0.105223
$651$	−1.08405e55	−1.47986
$652$	2.81317e54	0.372707
$653$	−1.31229e55	−1.68741	−0.843707	−	0.536804i	$-0.819632\pi$
$653$	−1.31229e55	−1.68741	−0.843707	+	0.536804i	$0.819632\pi$
$654$	−1.25933e54	−0.157172
$655$	1.81073e54	0.219356
$656$	−4.75482e54	−0.559126
$657$	6.69269e54	0.763970
$658$	8.24148e53	0.0913273
$659$	−1.11571e55	−1.20029	−0.600146	−	0.799890i	$-0.704891\pi$
$659$	−1.11571e55	−1.20029	−0.600146	+	0.799890i	$0.704891\pi$
$660$	2.13215e55	2.22696
$661$	−3.62687e54	−0.367793	−0.183897	−	0.982946i	$-0.558871\pi$
$661$	−3.62687e54	−0.367793	−0.183897	+	0.982946i	$0.558871\pi$
$662$	1.57848e54	0.155421
$663$	−9.13603e53	−0.0873462
$664$	1.03066e55	0.956835
$665$	1.21605e55	1.09630
$666$	4.57613e54	0.400636
$667$	−2.45478e54	−0.208717
$668$	−1.64603e55	−1.35924
$669$	2.08732e55	1.67409
$670$	−7.75256e52	−0.00603930
$671$	−2.22563e55	−1.68408
$672$	−1.08281e55	−0.795885
$673$	−1.86876e54	−0.133432	−0.0667159	−	0.997772i	$-0.521252\pi$
$673$	−1.86876e54	−0.133432	−0.0667159	+	0.997772i	$0.521252\pi$
$674$	−6.65812e54	−0.461832
$675$	−6.03872e54	−0.406931
$676$	9.42823e54	0.617262
$677$	1.48956e55	0.947498	0.473749	−	0.880660i	$-0.342900\pi$
$677$	1.48956e55	0.947498	0.473749	+	0.880660i	$0.342900\pi$
$678$	−1.26013e55	−0.778821
$679$	−4.17457e54	−0.250698
$680$	1.33368e54	0.0778265
$681$	1.60549e55	0.910416
$682$	1.17263e55	0.646198
$683$	9.58075e54	0.513093	0.256546	−	0.966532i	$-0.417415\pi$
$683$	9.58075e54	0.513093	0.256546	+	0.966532i	$0.417415\pi$
$684$	−3.59142e55	−1.86927
$685$	−2.82934e55	−1.43126
$686$	−6.54087e54	−0.321599
$687$	1.60343e55	0.766291
$688$	1.12389e55	0.522093
$689$	9.45523e53	0.0426970
$690$	7.59763e54	0.333519
$691$	1.23084e54	0.0525267	0.0262634	−	0.999655i	$-0.491639\pi$
$691$	1.23084e54	0.0525267	0.0262634	+	0.999655i	$0.491639\pi$
$692$	1.67766e55	0.696041
$693$	2.74457e55	1.10707
$694$	3.84062e53	0.0150623
$695$	3.45319e55	1.31679
$696$	1.04356e55	0.386935
$697$	2.24557e54	0.0809633
$698$	−1.04043e55	−0.364779
$699$	−7.43605e55	−2.53535
$700$	−9.45250e54	−0.313426
$701$	−4.60890e55	−1.48627	−0.743133	−	0.669144i	$-0.766661\pi$
$701$	−4.60890e55	−1.48627	−0.743133	+	0.669144i	$0.766661\pi$
$702$	4.04812e54	0.126964
$703$	4.02237e55	1.22702
$704$	−1.78674e55	−0.530145
$705$	−3.16550e55	−0.913597
$706$	1.04220e55	0.292591
$707$	2.35924e55	0.644308
$708$	1.56808e55	0.416602
$709$	−4.42017e54	−0.114245	−0.0571226	−	0.998367i	$-0.518193\pi$
$709$	−4.42017e54	−0.114245	−0.0571226	+	0.998367i	$0.518193\pi$
$710$	6.50661e54	0.163613
$711$	4.56654e55	1.11720
$712$	−5.14961e55	−1.22578
$713$	−3.52128e55	−0.815558
$714$	1.36995e54	0.0308737
$715$	−4.03933e55	−0.885812
$716$	7.08565e55	1.51208
$717$	5.31259e55	1.10327
$718$	−6.77634e54	−0.136952
$719$	4.79691e55	0.943514	0.471757	−	0.881729i	$-0.343620\pi$
$719$	4.79691e55	0.943514	0.471757	+	0.881729i	$0.343620\pi$
$720$	6.59006e55	1.26155
$721$	−4.91274e55	−0.915348
$722$	1.95010e55	0.353657
$723$	−9.84817e55	−1.73844
$724$	−1.90799e55	−0.327848
$725$	1.39200e55	0.232834
$726$	−1.88986e55	−0.307727
$727$	1.02822e56	1.62991	0.814956	−	0.579523i	$-0.196761\pi$
$727$	1.02822e56	1.62991	0.814956	+	0.579523i	$0.196761\pi$
$728$	1.34251e55	0.207184
$729$	−1.06843e56	−1.60531
$730$	1.47700e55	0.216066
$731$	−5.30781e54	−0.0756008
$732$	−1.34102e56	−1.85982
$733$	−5.77006e55	−0.779207	−0.389603	−	0.920983i	$-0.627388\pi$
$733$	−5.77006e55	−0.779207	−0.389603	+	0.920983i	$0.627388\pi$
$734$	1.94790e55	0.256149
$735$	9.76181e55	1.25005
$736$	−3.51724e55	−0.438616
$737$	−1.53798e54	−0.0186782
$738$	−3.21663e55	−0.380454
$739$	1.40056e56	1.61337	0.806686	−	0.590980i	$-0.201259\pi$
$739$	1.40056e56	1.61337	0.806686	+	0.590980i	$0.201259\pi$
$740$	−8.51057e55	−0.954861
$741$	1.15031e56	1.25707
$742$	−1.41781e54	−0.0150918
$743$	7.96262e54	0.0825609	0.0412804	−	0.999148i	$-0.486856\pi$
$743$	7.96262e54	0.0825609	0.0412804	+	0.999148i	$0.486856\pi$
$744$	1.49695e56	1.51194
$745$	6.02299e55	0.592604
$746$	−5.05324e55	−0.484354
$747$	−2.40517e56	−2.24592
$748$	1.24881e55	0.113609
$749$	3.08181e55	0.273156
$750$	3.11042e55	0.268612
$751$	−8.79022e55	−0.739641	−0.369821	−	0.929103i	$-0.620581\pi$
$751$	−8.79022e55	−0.739641	−0.369821	+	0.929103i	$0.620581\pi$
$752$	3.92578e55	0.321868
$753$	2.10936e56	1.68519
$754$	−9.33140e54	−0.0726450
$755$	−1.92669e56	−1.46166
$756$	5.11540e55	0.378185
$757$	−6.05512e54	−0.0436268	−0.0218134	−	0.999762i	$-0.506944\pi$
$757$	−6.05512e54	−0.0436268	−0.0218134	+	0.999762i	$0.506944\pi$
$758$	8.40915e54	0.0590477
$759$	1.50725e56	1.03150
$760$	−1.67922e56	−1.12007
$761$	−2.67473e56	−1.73892	−0.869458	−	0.494008i	$-0.835532\pi$
$761$	−2.67473e56	−1.73892	−0.869458	+	0.494008i	$0.835532\pi$
$762$	−7.67520e55	−0.486371
$763$	3.01479e55	0.186221
$764$	8.46080e55	0.509437
$765$	−3.11230e55	−0.182677
$766$	1.51557e55	0.0867191
$767$	−2.97071e55	−0.165711
$768$	−2.87088e55	−0.156125
$769$	3.07792e55	0.163190	0.0815951	−	0.996666i	$-0.473999\pi$
$769$	3.07792e55	0.163190	0.0815951	+	0.996666i	$0.473999\pi$
$770$	6.05697e55	0.313102
$771$	1.22019e56	0.614991
$772$	3.10094e56	1.52390
$773$	7.39678e55	0.354440	0.177220	−	0.984171i	$-0.443290\pi$
$773$	7.39678e55	0.354440	0.177220	+	0.984171i	$0.443290\pi$
$774$	7.60307e55	0.355255
$775$	1.99676e56	0.909794
$776$	5.76459e55	0.256133
$777$	−1.85214e56	−0.802535
$778$	−5.74396e55	−0.242722
$779$	−2.82738e56	−1.16521
$780$	−2.43384e56	−0.978245
$781$	1.29081e56	0.506018
$782$	4.44995e54	0.0170146
$783$	−7.53305e55	−0.280942
$784$	−1.21064e56	−0.440404
$785$	−1.13259e56	−0.401898
$786$	−2.56841e55	−0.0889046
$787$	−3.95231e56	−1.33458	−0.667289	−	0.744799i	$-0.732545\pi$
$787$	−3.95231e56	−1.33458	−0.667289	+	0.744799i	$0.732545\pi$
$788$	4.94362e56	1.62849
$789$	1.85779e55	0.0597030
$790$	1.00779e56	0.315966
$791$	3.01671e56	0.922767
$792$	−3.78993e56	−1.13107
$793$	2.54055e56	0.739776
$794$	−4.10082e55	−0.116512
$795$	5.44572e55	0.150972
$796$	−5.83734e56	−1.57910
$797$	−1.36161e56	−0.359432	−0.179716	−	0.983719i	$-0.557518\pi$
$797$	−1.36161e56	−0.359432	−0.179716	+	0.983719i	$0.557518\pi$
$798$	−1.72489e56	−0.444330
$799$	−1.85404e55	−0.0466076
$800$	1.99447e56	0.489298
$801$	1.20172e57	2.87721
$802$	2.58049e56	0.602978
$803$	2.93014e56	0.668244
$804$	−9.26690e54	−0.0206273
$805$	−1.81884e56	−0.395162
$806$	−1.33855e56	−0.283858
$807$	−2.83379e56	−0.586590
$808$	−3.25783e56	−0.658275
$809$	5.42801e56	1.07064	0.535321	−	0.844649i	$-0.320191\pi$
$809$	5.42801e56	1.07064	0.535321	+	0.844649i	$0.320191\pi$
$810$	−7.47613e55	−0.143952
$811$	−8.54286e56	−1.60582	−0.802910	−	0.596100i	$-0.796716\pi$
$811$	−8.54286e56	−1.60582	−0.802910	+	0.596100i	$0.796716\pi$
$812$	−1.17916e56	−0.216387
$813$	−6.09306e56	−1.09162
$814$	2.00348e56	0.350436
$815$	−3.06952e56	−0.524199
$816$	6.52566e55	0.108809
$817$	6.68303e56	1.08804
$818$	3.82704e55	0.0608379
$819$	−3.13291e56	−0.486309
$820$	5.98221e56	0.906759
$821$	−2.83593e56	−0.419763	−0.209882	−	0.977727i	$-0.567308\pi$
$821$	−2.83593e56	−0.419763	−0.209882	+	0.977727i	$0.567308\pi$
$822$	4.01323e56	0.580088
$823$	−7.79009e56	−1.09963	−0.549814	−	0.835287i	$-0.685301\pi$
$823$	−7.79009e56	−1.09963	−0.549814	+	0.835287i	$0.685301\pi$
$824$	6.78392e56	0.935190
$825$	−8.54693e56	−1.15069
$826$	4.45458e55	0.0585728
$827$	2.44580e56	0.314097	0.157049	−	0.987591i	$-0.449802\pi$
$827$	2.44580e56	0.314097	0.157049	+	0.987591i	$0.449802\pi$
$828$	5.37166e56	0.673778
$829$	−1.26495e56	−0.154974	−0.0774871	−	0.996993i	$-0.524690\pi$
$829$	−1.26495e56	−0.154974	−0.0774871	+	0.996993i	$0.524690\pi$
$830$	−5.30795e56	−0.635190
$831$	1.69854e57	1.98543
$832$	2.03956e56	0.232879
$833$	5.71751e55	0.0637719
$834$	−4.89812e56	−0.533693
$835$	1.79602e57	1.91173
$836$	−1.57236e57	−1.63505
$837$	−1.08059e57	−1.09777
$838$	−5.15156e55	−0.0511305
$839$	1.05147e57	1.01962	0.509809	−	0.860287i	$-0.329716\pi$
$839$	1.05147e57	1.01962	0.509809	+	0.860287i	$0.329716\pi$
$840$	7.73216e56	0.732579
$841$	−9.06598e56	−0.839253
$842$	−2.59700e56	−0.234901
$843$	−1.07960e57	−0.954170
$844$	1.48650e55	0.0128377
$845$	−1.02874e57	−0.868157
$846$	2.65579e56	0.219013
$847$	4.52425e56	0.364603
$848$	−6.75366e55	−0.0531888
$849$	−2.71413e57	−2.08896
$850$	−2.52337e55	−0.0189807
$851$	−6.01623e56	−0.442281
$852$	7.77757e56	0.558820
$853$	2.14388e57	1.50555	0.752775	−	0.658278i	$-0.228715\pi$
$853$	2.14388e57	1.50555	0.752775	+	0.658278i	$0.228715\pi$
$854$	−3.80955e56	−0.261484
$855$	3.91868e57	2.62906
$856$	−4.25562e56	−0.279077
$857$	1.76630e57	1.13224	0.566119	−	0.824323i	$-0.308444\pi$
$857$	1.76630e57	1.13224	0.566119	+	0.824323i	$0.308444\pi$
$858$	5.72952e56	0.359018
$859$	−1.41212e57	−0.864978	−0.432489	−	0.901639i	$-0.642365\pi$
$859$	−1.41212e57	−0.864978	−0.432489	+	0.901639i	$0.642365\pi$
$860$	−1.41400e57	−0.846702
$861$	1.30190e57	0.762106
$862$	8.43842e56	0.482913
$863$	−2.76506e57	−1.54702	−0.773508	−	0.633787i	$-0.781500\pi$
$863$	−2.76506e57	−1.54702	−0.773508	+	0.633787i	$0.781500\pi$
$864$	−1.07935e57	−0.590395
$865$	−1.83053e57	−0.978958
$866$	5.65553e56	0.295716
$867$	3.02950e57	1.54881
$868$	−1.69146e57	−0.845525
$869$	1.99928e57	0.977212
$870$	−5.37440e56	−0.256865
$871$	1.75560e55	0.00820487
$872$	−4.16307e56	−0.190258
$873$	−1.34524e57	−0.601204
$874$	−5.60289e56	−0.244872
$875$	−7.44623e56	−0.318258
$876$	1.76551e57	0.737974
$877$	−7.42378e56	−0.303482	−0.151741	−	0.988420i	$-0.548488\pi$
$877$	−7.42378e56	−0.303482	−0.151741	+	0.988420i	$0.548488\pi$
$878$	3.72247e56	0.148829
$879$	−6.09427e57	−2.38308
$880$	2.88520e57	1.10348
$881$	6.13623e56	0.229547	0.114773	−	0.993392i	$-0.463386\pi$
$881$	6.13623e56	0.229547	0.114773	+	0.993392i	$0.463386\pi$
$882$	−8.18994e56	−0.299670
$883$	2.47374e57	0.885361	0.442681	−	0.896679i	$-0.354028\pi$
$883$	2.47374e57	0.885361	0.442681	+	0.896679i	$0.354028\pi$
$884$	−1.42551e56	−0.0499057
$885$	−1.71097e57	−0.585936
$886$	−1.45533e57	−0.487531
$887$	4.04554e57	1.32576	0.662882	−	0.748724i	$-0.269333\pi$
$887$	4.04554e57	1.32576	0.662882	+	0.748724i	$0.269333\pi$
$888$	2.55759e57	0.819932
$889$	1.83741e57	0.576265
$890$	2.65208e57	0.813731
$891$	−1.48314e57	−0.445213
$892$	3.25687e57	0.956501
$893$	2.33441e57	0.670770
$894$	−8.54321e56	−0.240182
$895$	−7.73132e57	−2.12669
$896$	−2.19583e57	−0.591008
$897$	−1.72051e57	−0.453112
$898$	2.00687e57	0.517168
$899$	2.49088e57	0.628114
$900$	−3.04603e57	−0.751632
$901$	3.18957e55	0.00770191
$902$	−1.40828e57	−0.332783
$903$	−3.07727e57	−0.711630
$904$	−4.16572e57	−0.942770
$905$	2.08185e57	0.461107
$906$	2.73288e57	0.592407
$907$	1.91109e57	0.405452	0.202726	−	0.979236i	$-0.435020\pi$
$907$	1.91109e57	0.405452	0.202726	+	0.979236i	$0.435020\pi$
$908$	2.50507e57	0.520171
$909$	7.60256e57	1.54513
$910$	−6.91400e56	−0.137538
$911$	−6.02986e57	−1.17408	−0.587041	−	0.809557i	$-0.699707\pi$
$911$	−6.02986e57	−1.17408	−0.587041	+	0.809557i	$0.699707\pi$
$912$	−8.21642e57	−1.56597
$913$	−1.05301e58	−1.96450
$914$	−1.75768e57	−0.320988
$915$	1.46322e58	2.61577
$916$	2.50185e57	0.437824
$917$	6.14867e56	0.105336
$918$	1.36557e56	0.0229024
$919$	6.23642e57	1.02396	0.511980	−	0.858997i	$-0.328912\pi$
$919$	6.23642e57	1.02396	0.511980	+	0.858997i	$0.328912\pi$
$920$	2.51161e57	0.403728
$921$	4.77384e57	0.751286
$922$	−2.65073e56	−0.0408426
$923$	−1.47345e57	−0.222281
$924$	7.24010e57	1.06940
$925$	3.41154e57	0.493386
$926$	−2.04512e57	−0.289604
$927$	−1.58311e58	−2.19511
$928$	2.48802e57	0.337807
$929$	4.25561e57	0.565790	0.282895	−	0.959151i	$-0.408705\pi$
$929$	4.25561e57	0.565790	0.282895	+	0.959151i	$0.408705\pi$
$930$	−7.70936e57	−1.00369
$931$	−7.19888e57	−0.917796
$932$	−1.16026e58	−1.44858
$933$	−3.75266e57	−0.458825
$934$	4.10047e57	0.490986
$935$	−1.36260e57	−0.159787
$936$	4.32619e57	0.496851
$937$	1.14088e58	1.28327	0.641637	−	0.767008i	$-0.278255\pi$
$937$	1.14088e58	1.28327	0.641637	+	0.767008i	$0.278255\pi$
$938$	−2.63252e55	−0.00290012
$939$	1.40007e57	0.151068
$940$	−4.93917e57	−0.521988
$941$	−2.33700e57	−0.241914	−0.120957	−	0.992658i	$-0.538596\pi$
$941$	−2.33700e57	−0.241914	−0.120957	+	0.992658i	$0.538596\pi$
$942$	1.60651e57	0.162889
$943$	4.22890e57	0.420000
$944$	2.12191e57	0.206430
$945$	−5.58153e57	−0.531904
$946$	3.32871e57	0.310741
$947$	−4.94229e56	−0.0451964	−0.0225982	−	0.999745i	$-0.507194\pi$
$947$	−4.94229e56	−0.0451964	−0.0225982	+	0.999745i	$0.507194\pi$
$948$	1.20464e58	1.07918
$949$	−3.34474e57	−0.293542
$950$	3.17716e57	0.273167
$951$	3.25615e57	0.274274
$952$	4.52874e56	0.0373729
$953$	1.48078e56	0.0119723	0.00598617	−	0.999982i	$-0.498095\pi$
$953$	1.48078e56	0.0119723	0.00598617	+	0.999982i	$0.498095\pi$
$954$	−4.56884e56	−0.0361920
$955$	−9.23178e57	−0.716506
$956$	8.28930e57	0.630361
$957$	−1.06619e58	−0.794426
$958$	7.22079e56	0.0527178
$959$	−9.60753e57	−0.687304
$960$	1.17468e58	0.823436
$961$	2.11725e58	1.45434
$962$	−2.28696e57	−0.153938
$963$	9.93101e57	0.655059
$964$	−1.53662e58	−0.993264
$965$	−3.38351e58	−2.14331
$966$	2.57991e57	0.160159
$967$	−6.58500e57	−0.400627	−0.200313	−	0.979732i	$-0.564196\pi$
$967$	−6.58500e57	−0.400627	−0.200313	+	0.979732i	$0.564196\pi$
$968$	−6.24746e57	−0.372507
$969$	3.88039e57	0.226758
$970$	−2.96880e57	−0.170032
$971$	4.39314e57	0.246604	0.123302	−	0.992369i	$-0.460652\pi$
$971$	4.39314e57	0.246604	0.123302	+	0.992369i	$0.460652\pi$
$972$	−2.03216e58	−1.11806
$973$	1.17259e58	0.632333
$974$	−3.52600e57	−0.186373
$975$	9.75628e57	0.505469
$976$	−1.81466e58	−0.921558
$977$	2.41520e58	1.20229	0.601144	−	0.799141i	$-0.294712\pi$
$977$	2.41520e58	1.20229	0.601144	+	0.799141i	$0.294712\pi$
$978$	4.35391e57	0.212457
$979$	5.26129e58	2.51669
$980$	1.52315e58	0.714222
$981$	9.71504e57	0.446580
$982$	−3.69630e57	−0.166568
$983$	7.73253e57	0.341608	0.170804	−	0.985305i	$-0.445364\pi$
$983$	7.73253e57	0.341608	0.170804	+	0.985305i	$0.445364\pi$
$984$	−1.79777e58	−0.778626
$985$	−5.39411e58	−2.29041
$986$	−3.14780e56	−0.0131041
$987$	−1.07490e58	−0.438717
$988$	1.79485e58	0.718235
$989$	−9.99576e57	−0.392183
$990$	1.95183e58	0.750856
$991$	−2.62440e58	−0.989904	−0.494952	−	0.868920i	$-0.664814\pi$
$991$	−2.62440e58	−0.989904	−0.494952	+	0.868920i	$0.664814\pi$
$992$	3.56897e58	1.31997
$993$	−2.05875e58	−0.746609
$994$	2.20944e57	0.0785682
$995$	6.36926e58	2.22095
$996$	−6.34477e58	−2.16950
$997$	−2.17628e58	−0.729726	−0.364863	−	0.931061i	$-0.618884\pi$
$997$	−2.17628e58	−0.729726	−0.364863	+	0.931061i	$0.618884\pi$
$998$	−1.04029e57	−0.0342067
$999$	−1.84622e58	−0.595328

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.40.a.a.1.2	✓	3
3.2	odd	2		9.40.a.b.1.2		3
4.3	odd	2		16.40.a.c.1.3		3
5.2	odd	4		25.40.b.a.24.4		6
5.3	odd	4		25.40.b.a.24.3		6
5.4	even	2		25.40.a.a.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.40.a.a.1.2	✓	3	1.1	even	1	trivial
9.40.a.b.1.2		3	3.2	odd	2
16.40.a.c.1.3		3	4.3	odd	2
25.40.a.a.1.2		3	5.4	even	2
25.40.b.a.24.3		6	5.3	odd	4
25.40.b.a.24.4		6	5.2	odd	4

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:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 40 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q+241488. q^{2} -3.14962e9 q^{3} -4.91439e11 q^{4} +5.36221e13 q^{5} -7.60595e14 q^{6} +1.82084e16 q^{7} -2.51436e17 q^{8} +5.86757e18 q^{9} +O(q^{10})\)	\(q+241488. q^{2} -3.14962e9 q^{3} -4.91439e11 q^{4} +5.36221e13 q^{5} -7.60595e14 q^{6} +1.82084e16 q^{7} -2.51436e17 q^{8} +5.86757e18 q^{9} +1.29491e19 q^{10} +2.56889e20 q^{11} +1.54785e21 q^{12} -2.93238e21 q^{13} +4.39709e21 q^{14} -1.68890e23 q^{15} +2.09453e23 q^{16} -9.89190e22 q^{17} +1.41695e24 q^{18} +1.24548e25 q^{19} -2.63520e25 q^{20} -5.73494e25 q^{21} +6.20355e25 q^{22} -1.86286e26 q^{23} +7.91928e26 q^{24} +1.05635e27 q^{25} -7.08133e26 q^{26} -5.71661e27 q^{27} -8.94830e27 q^{28} +1.31775e28 q^{29} -4.07848e28 q^{30} +1.89026e29 q^{31} +1.88809e29 q^{32} -8.09103e29 q^{33} -2.38877e28 q^{34} +9.76371e29 q^{35} -2.88356e30 q^{36} +3.22957e30 q^{37} +3.00769e30 q^{38} +9.23588e30 q^{39} -1.34825e31 q^{40} -2.27011e31 q^{41} -1.38492e31 q^{42} +5.36582e31 q^{43} -1.26245e32 q^{44} +3.14632e32 q^{45} -4.49858e31 q^{46} +1.87430e32 q^{47} -6.59698e32 q^{48} -5.78000e32 q^{49} +2.55095e32 q^{50} +3.11557e32 q^{51} +1.44109e33 q^{52} -3.22443e32 q^{53} -1.38049e33 q^{54} +1.37749e34 q^{55} -4.57823e33 q^{56} -3.92280e34 q^{57} +3.18220e33 q^{58} +1.01307e34 q^{59} +8.29990e34 q^{60} -8.66378e34 q^{61} +4.56473e34 q^{62} +1.06839e35 q^{63} -6.95530e34 q^{64} -1.57240e35 q^{65} -1.95389e35 q^{66} -5.98696e33 q^{67} +4.86127e34 q^{68} +5.86730e35 q^{69} +2.35782e35 q^{70} +5.02476e35 q^{71} -1.47532e36 q^{72} +1.14062e36 q^{73} +7.79901e35 q^{74} -3.32709e36 q^{75} -6.12079e36 q^{76} +4.67752e36 q^{77} +2.23035e36 q^{78} +7.78268e36 q^{79} +1.12313e37 q^{80} -5.77348e36 q^{81} -5.48205e36 q^{82} -4.09909e37 q^{83} +2.81838e37 q^{84} -5.30425e36 q^{85} +1.29578e37 q^{86} -4.15041e37 q^{87} -6.45911e37 q^{88} +2.04808e38 q^{89} +7.59797e37 q^{90} -5.33937e37 q^{91} +9.15483e37 q^{92} -5.95359e38 q^{93} +4.52621e37 q^{94} +6.67854e38 q^{95} -5.94676e38 q^{96} -2.29267e38 q^{97} -1.39580e38 q^{98} +1.50731e39 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 548856 q^{2} + 1109442852 q^{3} + 272078981184 q^{4} + 17426916500490 q^{5} + 15\!\cdots\!96 q^{6}+ \cdots + 83\!\cdots\!91 q^{9}+O(q^{10}) \) 3 * q + 548856 * q^2 + 1109442852 * q^3 + 272078981184 * q^4 + 17426916500490 * q^5 + 1529727847867296 * q^6 - 17996297718635544 * q^7 + 255044243806133760 * q^8 + 8305879902078677391 * q^9	\( 3 q + 548856 q^{2} + 1109442852 q^{3} + 272078981184 q^{4} + 17426916500490 q^{5} + 15\!\cdots\!96 q^{6}+ \cdots + 10\!\cdots\!72 q^{99}+O(q^{100}) \) 3 * q + 548856 * q^2 + 1109442852 * q^3 + 272078981184 * q^4 + 17426916500490 * q^5 + 1529727847867296 * q^6 - 17996297718635544 * q^7 + 255044243806133760 * q^8 + 8305879902078677391 * q^9 + 90373081165367671440 * q^10 + 667814968265751536076 * q^11 + 3676571280854873162496 * q^12 + 3156080701447967254962 * q^13 - 63063724565889303463872 * q^14 - 171209278264452417200520 * q^15 - 351730940560369057001472 * q^16 + 890025791008793741893206 * q^17 + 8758537968130529168653272 * q^18 + 9227612185007697573518580 * q^19 - 14662452947108747596260480 * q^20 - 190208658572592931471251744 * q^21 - 122745877544387429034313248 * q^22 + 305308591470919570740188472 * q^23 + 1672960268636194560046295040 * q^24 + 1866127065486173095027030725 * q^25 + 283778605804595582169202896 * q^26 - 11508090459893795046427628760 * q^27 - 41794856371466593385827533312 * q^28 - 2492682219258648277296444030 * q^29 + 105977898643957401776506418880 * q^30 + 306107671747822704409554746016 * q^31 - 56572224161556180973554008064 * q^32 - 157376353761155567959844693616 * q^33 - 1683392869529765869103799245712 * q^34 - 1197259217905835166323668756560 * q^35 + 188684323073267404408057366848 * q^36 + 7599073412303579174888591086506 * q^37 + 2479871855304922949496616465440 * q^38 + 22252083518345402015145920059992 * q^39 - 32669995448979982796588503833600 * q^40 + 2391924206237769506232479990286 * q^41 - 195689966839404680756969540713728 * q^42 + 162865923671547339657067136304492 * q^43 - 45577647299113910363374898556672 * q^44 + 588908524142943445153326555470130 * q^45 - 24296541145531030477977021520704 * q^46 + 202683231875405841765643043683056 * q^47 - 1747281225742357435119054532067328 * q^48 + 368237681722499062385273201641179 * q^49 - 2624175085265540082696197615369400 * q^50 + 785651103815434341253216161914376 * q^51 + 3782687188757116950236456253499776 * q^52 + 5869079988764517679853946632443002 * q^53 + 7930814851979058696152103557167680 * q^54 - 4993109836111426485910134681304920 * q^55 - 6272116703248607238900430116679680 * q^56 - 46129102671186186415908500969957520 * q^57 + 2579097256656295554169870267982160 * q^58 - 56082681385621280317109288669637060 * q^59 + 127333179651658235430567238147607040 * q^60 + 39577675682126428331898689976833826 * q^61 + 262011550289381451529348830657714432 * q^62 - 174786720262353444072185876495505528 * q^63 - 169364906963561439583712861665099776 * q^64 - 264857762104053085095614223637519620 * q^65 - 287121760972609093376568794235255168 * q^66 - 140659929656119892877736400727430044 * q^67 - 130643133997460537100958647836349312 * q^68 + 1584175048695702801789842685209503392 * q^69 - 480338235822643784458804278358623360 * q^70 + 3849053210874068146700295241416217896 * q^71 - 1699150852984576616740529956276922880 * q^72 - 180754136492273067100959984036797778 * q^73 - 5070707041697857186532012041702753392 * q^74 - 4308561205008052508725896857031567300 * q^75 - 7362591710990284189025184136271151360 * q^76 + 5690389092595065468343565382905921952 * q^77 + 9330105385756793042468361274821534144 * q^78 + 13807772201216229289895673856694559120 * q^79 + 26839954555034162361105063302056304640 * q^80 - 18798023146176620962298765658838887237 * q^81 + 5068915865662526415092477483885831472 * q^82 - 20899400147905548803677768348186808268 * q^83 - 72152575898640813291791263837177976832 * q^84 - 105991789747453754784809897833488498060 * q^85 + 170012097580285110854272781787916483296 * q^86 - 73247996942640959139716393654519138280 * q^87 + 69412125637007165807333386173055825920 * q^88 + 205050039910109857136561853222076224510 * q^89 + 93221656611667223268126392859978755280 * q^90 - 165525104998331842571199169888366982544 * q^91 + 262356454404517646077951321169615264256 * q^92 - 167325068951627887866919523900021629056 * q^93 - 1127972668535151884588260809571286639232 * q^94 + 724803433705663618674774120451764528600 * q^95 - 1451094524490643350592064137029388468224 * q^96 + 173490888317728793437812209497231327206 * q^97 + 2246791677555180938475077451719860538808 * q^98 + 1057018158118568141770036034713090936572 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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